id	sid	tid	token	lemma	pos
ejpam-4570	1	1	european	european	PROPN
ejpam-4570	1	2	journal	journal	PROPN
ejpam-4570	1	3	of	of	ADP
ejpam-4570	1	4	pure	pure	ADJ
ejpam-4570	1	5	and	and	CCONJ
ejpam-4570	1	6	applied	apply	VERB
ejpam-4570	1	7	mathematics	mathematic	NOUN
ejpam-4570	1	8	vol	vol	NOUN
ejpam-4570	1	9	.	.	PROPN
ejpam-4570	2	1	15	15	NUM
ejpam-4570	2	2	,	,	PUNCT
ejpam-4570	2	3	no	no	INTJ
ejpam-4570	2	4	.	.	NOUN
ejpam-4570	2	5	4	4	NUM
ejpam-4570	2	6	,	,	PUNCT
ejpam-4570	2	7	2022	2022	NUM
ejpam-4570	2	8	,	,	PUNCT
ejpam-4570	2	9	1760	1760	NUM
ejpam-4570	2	10	-	-	SYM
ejpam-4570	2	11	1782	1782	NUM
ejpam-4570	2	12	issn	issn	PROPN
ejpam-4570	2	13	1307	1307	NUM
ejpam-4570	2	14	-	-	SYM
ejpam-4570	2	15	5543	5543	NUM
ejpam-4570	2	16	–	–	PUNCT
ejpam-4570	2	17	ejpam.com	ejpam.com	X
ejpam-4570	2	18	published	publish	VERB
ejpam-4570	2	19	by	by	ADP
ejpam-4570	2	20	new	new	PROPN
ejpam-4570	2	21	york	york	PROPN
ejpam-4570	2	22	business	business	PROPN
ejpam-4570	2	23	global	global	PROPN
ejpam-4570	2	24	c	c	NOUN
ejpam-4570	2	25	-	-	PUNCT
ejpam-4570	2	26	almost	almost	ADV
ejpam-4570	2	27	normality	normality	NOUN
ejpam-4570	2	28	and	and	CCONJ
ejpam-4570	2	29	l	l	NOUN
ejpam-4570	2	30	-	-	ADJ
ejpam-4570	2	31	almost	almost	ADV
ejpam-4570	2	32	normality	normality	NOUN
ejpam-4570	2	33	wafa	wafa	PROPN
ejpam-4570	2	34	khalaf	khalaf	PROPN
ejpam-4570	2	35	alqurashi1,∗	alqurashi1,∗	PROPN
ejpam-4570	2	36	,	,	PUNCT
ejpam-4570	2	37	sadeq	sadeq	VERB
ejpam-4570	2	38	ali	ali	PROPN
ejpam-4570	2	39	thabit2	thabit2	PROPN
ejpam-4570	2	40	1	1	NUM
ejpam-4570	2	41	department	department	NOUN
ejpam-4570	2	42	of	of	ADP
ejpam-4570	2	43	mathematical	mathematical	ADJ
ejpam-4570	2	44	sciences	science	NOUN
ejpam-4570	2	45	,	,	PUNCT
ejpam-4570	2	46	faculty	faculty	NOUN
ejpam-4570	2	47	of	of	ADP
ejpam-4570	2	48	applied	apply	VERB
ejpam-4570	2	49	sciences	science	NOUN
ejpam-4570	2	50	,	,	PUNCT
ejpam-4570	2	51	umm	umm	INTJ
ejpam-4570	2	52	al	al	PROPN
ejpam-4570	2	53	-	-	PUNCT
ejpam-4570	2	54	qura	qura	PROPN
ejpam-4570	2	55	university	university	NOUN
ejpam-4570	2	56	,	,	PUNCT
ejpam-4570	2	57	saudi	saudi	PROPN
ejpam-4570	2	58	arabia	arabia	PROPN
ejpam-4570	2	59	2	2	NUM
ejpam-4570	2	60	department	department	NOUN
ejpam-4570	2	61	of	of	ADP
ejpam-4570	2	62	mathematics	mathematic	NOUN
ejpam-4570	2	63	,	,	PUNCT
ejpam-4570	2	64	faculty	faculty	NOUN
ejpam-4570	2	65	of	of	ADP
ejpam-4570	2	66	education	education	NOUN
ejpam-4570	2	67	-al	-al	NOUN
ejpam-4570	2	68	-	-	PUNCT
ejpam-4570	2	69	mahra	mahra	NOUN
ejpam-4570	2	70	,	,	PUNCT
ejpam-4570	2	71	hadhramout	hadhramout	NOUN
ejpam-4570	2	72	university	university	NOUN
ejpam-4570	2	73	,	,	PUNCT
ejpam-4570	2	74	yemen	yemen	PROPN
ejpam-4570	2	75	abstract	abstract	NOUN
ejpam-4570	2	76	.	.	PUNCT
ejpam-4570	3	1	the	the	DET
ejpam-4570	3	2	main	main	ADJ
ejpam-4570	3	3	purpose	purpose	NOUN
ejpam-4570	3	4	of	of	ADP
ejpam-4570	3	5	this	this	DET
ejpam-4570	3	6	paper	paper	NOUN
ejpam-4570	3	7	is	be	AUX
ejpam-4570	3	8	to	to	PART
ejpam-4570	3	9	introduce	introduce	VERB
ejpam-4570	3	10	and	and	CCONJ
ejpam-4570	3	11	study	study	VERB
ejpam-4570	3	12	new	new	ADJ
ejpam-4570	3	13	topological	topological	ADJ
ejpam-4570	3	14	properties	property	NOUN
ejpam-4570	3	15	called	call	VERB
ejpam-4570	3	16	c	c	NOUN
ejpam-4570	3	17	-	-	PUNCT
ejpam-4570	3	18	almost	almost	ADV
ejpam-4570	3	19	normality	normality	NOUN
ejpam-4570	3	20	and	and	CCONJ
ejpam-4570	3	21	l	l	NOUN
ejpam-4570	3	22	-	-	ADJ
ejpam-4570	3	23	almost	almost	ADV
ejpam-4570	3	24	normality	normality	NOUN
ejpam-4570	3	25	.	.	PUNCT
ejpam-4570	4	1	a	a	DET
ejpam-4570	4	2	space	space	NOUN
ejpam-4570	4	3	x	x	PUNCT
ejpam-4570	4	4	is	be	AUX
ejpam-4570	4	5	called	call	VERB
ejpam-4570	4	6	a	a	DET
ejpam-4570	4	7	c	c	NOUN
ejpam-4570	4	8	-	-	PUNCT
ejpam-4570	4	9	almost	almost	ADV
ejpam-4570	4	10	normal	normal	ADJ
ejpam-4570	4	11	(	(	PUNCT
ejpam-4570	4	12	resp	resp	NOUN
ejpam-4570	4	13	.	.	PUNCT
ejpam-4570	5	1	l	l	NOUN
ejpam-4570	5	2	-	-	PUNCT
ejpam-4570	5	3	almost	almost	ADV
ejpam-4570	5	4	normal	normal	ADJ
ejpam-4570	5	5	)	)	PUNCT
ejpam-4570	5	6	space	space	NOUN
ejpam-4570	5	7	if	if	SCONJ
ejpam-4570	5	8	there	there	PRON
ejpam-4570	5	9	exist	exist	VERB
ejpam-4570	5	10	an	an	DET
ejpam-4570	5	11	almost	almost	ADV
ejpam-4570	5	12	normal	normal	ADJ
ejpam-4570	5	13	space	space	NOUN
ejpam-4570	5	14	y	y	PROPN
ejpam-4570	5	15	and	and	CCONJ
ejpam-4570	5	16	a	a	DET
ejpam-4570	5	17	bijective	bijective	ADJ
ejpam-4570	5	18	function	function	NOUN
ejpam-4570	6	1	f	f	NOUN
ejpam-4570	6	2	:	:	PUNCT
ejpam-4570	6	3	x	x	X
ejpam-4570	6	4	→	→	SYM
ejpam-4570	6	5	y	y	PROPN
ejpam-4570	6	6	such	such	ADJ
ejpam-4570	6	7	that	that	SCONJ
ejpam-4570	6	8	the	the	DET
ejpam-4570	6	9	restriction	restriction	NOUN
ejpam-4570	6	10	function	function	NOUN
ejpam-4570	6	11	f	f	PROPN
ejpam-4570	6	12	|a	|a	VERB
ejpam-4570	6	13	:	:	PUNCT
ejpam-4570	6	14	a	a	DET
ejpam-4570	6	15	→	→	SYM
ejpam-4570	6	16	f(a	f(a	NOUN
ejpam-4570	6	17	)	)	PUNCT
ejpam-4570	6	18	is	be	AUX
ejpam-4570	6	19	a	a	DET
ejpam-4570	6	20	homeomorphism	homeomorphism	NOUN
ejpam-4570	6	21	for	for	ADP
ejpam-4570	6	22	each	each	DET
ejpam-4570	6	23	compact	compact	ADJ
ejpam-4570	6	24	(	(	PUNCT
ejpam-4570	6	25	resp	resp	NOUN
ejpam-4570	6	26	.	.	PUNCT
ejpam-4570	7	1	lindelöf	lindelöf	PROPN
ejpam-4570	7	2	)	)	PUNCT
ejpam-4570	7	3	subspace	subspace	NOUN
ejpam-4570	7	4	a	a	DET
ejpam-4570	7	5	⊆	⊆	NUM
ejpam-4570	7	6	x.	x.	NOUN
ejpam-4570	7	7	we	we	PRON
ejpam-4570	7	8	investigate	investigate	VERB
ejpam-4570	7	9	these	these	DET
ejpam-4570	7	10	properties	property	NOUN
ejpam-4570	7	11	and	and	CCONJ
ejpam-4570	7	12	present	present	VERB
ejpam-4570	7	13	some	some	DET
ejpam-4570	7	14	examples	example	NOUN
ejpam-4570	7	15	to	to	PART
ejpam-4570	7	16	illustrate	illustrate	VERB
ejpam-4570	7	17	the	the	DET
ejpam-4570	7	18	relationships	relationship	NOUN
ejpam-4570	7	19	among	among	ADP
ejpam-4570	7	20	them	they	PRON
ejpam-4570	7	21	with	with	ADP
ejpam-4570	7	22	other	other	ADJ
ejpam-4570	7	23	kinds	kind	NOUN
ejpam-4570	7	24	of	of	ADP
ejpam-4570	7	25	topological	topological	ADJ
ejpam-4570	7	26	properties	property	NOUN
ejpam-4570	7	27	.	.	PUNCT
ejpam-4570	8	1	2020	2020	NUM
ejpam-4570	8	2	mathematics	mathematic	NOUN
ejpam-4570	8	3	subject	subject	NOUN
ejpam-4570	8	4	classifications	classification	NOUN
ejpam-4570	8	5	:	:	PUNCT
ejpam-4570	8	6	54c10	54c10	NUM
ejpam-4570	8	7	,	,	PUNCT
ejpam-4570	8	8	54d10	54d10	NUM
ejpam-4570	8	9	,	,	PUNCT
ejpam-4570	8	10	54d20	54d20	NUM
ejpam-4570	8	11	,	,	PUNCT
ejpam-4570	8	12	54d15	54d15	NUM
ejpam-4570	8	13	,	,	PUNCT
ejpam-4570	8	14	54d70	54d70	NUM
ejpam-4570	8	15	key	key	ADJ
ejpam-4570	8	16	words	word	NOUN
ejpam-4570	8	17	and	and	CCONJ
ejpam-4570	8	18	phrases	phrase	NOUN
ejpam-4570	8	19	:	:	PUNCT
ejpam-4570	8	20	epi	epi	NOUN
ejpam-4570	8	21	-	-	ADJ
ejpam-4570	8	22	normal	normal	ADJ
ejpam-4570	8	23	,	,	PUNCT
ejpam-4570	8	24	epi	epi	NOUN
ejpam-4570	8	25	-	-	PUNCT
ejpam-4570	8	26	almost	almost	ADV
ejpam-4570	8	27	normal	normal	ADJ
ejpam-4570	8	28	,	,	PUNCT
ejpam-4570	8	29	c	c	NOUN
ejpam-4570	8	30	-	-	ADJ
ejpam-4570	8	31	normal	normal	ADJ
ejpam-4570	8	32	,	,	PUNCT
ejpam-4570	8	33	epi	epi	NOUN
ejpam-4570	8	34	-	-	NOUN
ejpam-4570	8	35	regular	regular	ADJ
ejpam-4570	8	36	,	,	PUNCT
ejpam-4570	8	37	c	c	NOUN
ejpam-4570	8	38	-	-	ADJ
ejpam-4570	8	39	regular	regular	ADJ
ejpam-4570	8	40	,	,	PUNCT
ejpam-4570	8	41	l	l	NOUN
ejpam-4570	8	42	-	-	ADJ
ejpam-4570	8	43	normal	normal	ADJ
ejpam-4570	8	44	,	,	PUNCT
ejpam-4570	8	45	l	l	NOUN
ejpam-4570	8	46	-	-	ADJ
ejpam-4570	8	47	regular	regular	ADJ
ejpam-4570	8	48	1	1	NUM
ejpam-4570	8	49	.	.	PUNCT
ejpam-4570	8	50	introduction	introduction	NOUN
ejpam-4570	8	51	the	the	DET
ejpam-4570	8	52	notions	notion	NOUN
ejpam-4570	8	53	of	of	ADP
ejpam-4570	8	54	epi	epi	NOUN
ejpam-4570	8	55	-	-	NOUN
ejpam-4570	8	56	normality	normality	ADJ
ejpam-4570	8	57	,	,	PUNCT
ejpam-4570	8	58	c	c	NOUN
ejpam-4570	8	59	-	-	PUNCT
ejpam-4570	8	60	normality	normality	NOUN
ejpam-4570	8	61	and	and	CCONJ
ejpam-4570	8	62	l	l	NOUN
ejpam-4570	8	63	-	-	NOUN
ejpam-4570	8	64	normality	normality	NOUN
ejpam-4570	8	65	were	be	AUX
ejpam-4570	8	66	introduced	introduce	VERB
ejpam-4570	8	67	by	by	ADP
ejpam-4570	8	68	arhangel’skii	arhangel’skii	PROPN
ejpam-4570	8	69	during	during	ADP
ejpam-4570	8	70	his	his	PRON
ejpam-4570	8	71	visiting	visit	VERB
ejpam-4570	8	72	to	to	ADP
ejpam-4570	8	73	department	department	NOUN
ejpam-4570	8	74	of	of	ADP
ejpam-4570	8	75	mathematics	mathematics	PROPN
ejpam-4570	8	76	in	in	ADP
ejpam-4570	8	77	king	king	PROPN
ejpam-4570	8	78	abdulaziz	abdulaziz	PROPN
ejpam-4570	8	79	university	university	PROPN
ejpam-4570	8	80	,	,	PUNCT
ejpam-4570	8	81	saudi	saudi	PROPN
ejpam-4570	8	82	arabia	arabia	PROPN
ejpam-4570	8	83	on	on	ADP
ejpam-4570	8	84	2012	2012	NUM
ejpam-4570	8	85	.	.	PUNCT
ejpam-4570	9	1	c	c	X
ejpam-4570	9	2	-	-	PUNCT
ejpam-4570	9	3	normality	normality	NOUN
ejpam-4570	9	4	has	have	AUX
ejpam-4570	9	5	been	be	AUX
ejpam-4570	9	6	studied	study	VERB
ejpam-4570	9	7	by	by	ADP
ejpam-4570	9	8	alzahrani	alzahrani	NOUN
ejpam-4570	9	9	and	and	CCONJ
ejpam-4570	9	10	kalantan	kalantan	PROPN
ejpam-4570	9	11	in	in	ADP
ejpam-4570	9	12	2017	2017	NUM
ejpam-4570	9	13	,	,	PUNCT
ejpam-4570	9	14	see	see	VERB
ejpam-4570	9	15	[	[	X
ejpam-4570	9	16	10	10	NUM
ejpam-4570	9	17	]	]	PUNCT
ejpam-4570	9	18	.	.	PUNCT
ejpam-4570	10	1	l	l	NOUN
ejpam-4570	10	2	-	-	NOUN
ejpam-4570	10	3	normality	normality	NOUN
ejpam-4570	10	4	has	have	AUX
ejpam-4570	10	5	been	be	AUX
ejpam-4570	10	6	studied	study	VERB
ejpam-4570	10	7	by	by	ADP
ejpam-4570	10	8	kalantan	kalantan	PROPN
ejpam-4570	10	9	and	and	CCONJ
ejpam-4570	10	10	saeed	saeed	PROPN
ejpam-4570	10	11	in	in	ADP
ejpam-4570	10	12	2017	2017	NUM
ejpam-4570	10	13	,	,	PUNCT
ejpam-4570	10	14	see	see	VERB
ejpam-4570	10	15	[	[	X
ejpam-4570	10	16	16	16	NUM
ejpam-4570	10	17	]	]	PUNCT
ejpam-4570	10	18	.	.	PUNCT
ejpam-4570	11	1	then	then	ADV
ejpam-4570	11	2	,	,	PUNCT
ejpam-4570	11	3	alzahrani	alzahrani	NOUN
ejpam-4570	11	4	studied	study	VERB
ejpam-4570	11	5	the	the	DET
ejpam-4570	11	6	notions	notion	NOUN
ejpam-4570	11	7	of	of	ADP
ejpam-4570	11	8	c	c	NOUN
ejpam-4570	11	9	-	-	PUNCT
ejpam-4570	11	10	regularity	regularity	NOUN
ejpam-4570	11	11	,	,	PUNCT
ejpam-4570	11	12	l	l	NOUN
ejpam-4570	11	13	-	-	NOUN
ejpam-4570	11	14	regularity	regularity	NOUN
ejpam-4570	11	15	,	,	PUNCT
ejpam-4570	11	16	c	c	NOUN
ejpam-4570	11	17	-	-	PUNCT
ejpam-4570	11	18	tychonoff	tychonoff	NOUN
ejpam-4570	11	19	and	and	CCONJ
ejpam-4570	11	20	l	l	NOUN
ejpam-4570	11	21	-	-	NOUN
ejpam-4570	11	22	tychonoff	tychonoff	NOUN
ejpam-4570	11	23	in	in	ADP
ejpam-4570	11	24	2018	2018	NUM
ejpam-4570	11	25	,	,	PUNCT
ejpam-4570	11	26	see	see	VERB
ejpam-4570	11	27	[	[	X
ejpam-4570	11	28	8	8	NUM
ejpam-4570	11	29	,	,	PUNCT
ejpam-4570	11	30	9	9	NUM
ejpam-4570	11	31	]	]	PUNCT
ejpam-4570	11	32	.	.	PUNCT
ejpam-4570	12	1	thabit	thabit	PROPN
ejpam-4570	12	2	studied	study	VERB
ejpam-4570	12	3	the	the	DET
ejpam-4570	12	4	notion	notion	NOUN
ejpam-4570	12	5	of	of	ADP
ejpam-4570	12	6	epi	epi	ADJ
ejpam-4570	12	7	-	-	ADJ
ejpam-4570	12	8	partial	partial	ADJ
ejpam-4570	12	9	normality	normality	NOUN
ejpam-4570	12	10	in	in	ADP
ejpam-4570	12	11	2021	2021	NUM
ejpam-4570	12	12	,	,	PUNCT
ejpam-4570	12	13	see	see	VERB
ejpam-4570	12	14	[	[	X
ejpam-4570	12	15	34	34	NUM
ejpam-4570	12	16	]	]	PUNCT
ejpam-4570	12	17	.	.	PUNCT
ejpam-4570	13	1	at	at	ADP
ejpam-4570	13	2	the	the	DET
ejpam-4570	13	3	end	end	NOUN
ejpam-4570	13	4	of	of	ADP
ejpam-4570	13	5	2021	2021	NUM
ejpam-4570	13	6	,	,	PUNCT
ejpam-4570	13	7	thabit	thabit	NOUN
ejpam-4570	13	8	and	and	CCONJ
ejpam-4570	13	9	others	other	NOUN
ejpam-4570	13	10	studied	study	VERB
ejpam-4570	13	11	the	the	DET
ejpam-4570	13	12	notion	notion	NOUN
ejpam-4570	13	13	of	of	ADP
ejpam-4570	13	14	epi	epi	NOUN
ejpam-4570	13	15	-	-	ADJ
ejpam-4570	13	16	quasi	quasi	ADJ
ejpam-4570	13	17	normality	normality	NOUN
ejpam-4570	13	18	[	[	X
ejpam-4570	13	19	33	33	NUM
ejpam-4570	13	20	]	]	PUNCT
ejpam-4570	13	21	.	.	PUNCT
ejpam-4570	14	1	recently	recently	ADV
ejpam-4570	14	2	,	,	PUNCT
ejpam-4570	14	3	thabit	thabit	NOUN
ejpam-4570	14	4	and	and	CCONJ
ejpam-4570	14	5	alqurashi	alqurashi	PROPN
ejpam-4570	14	6	studied	study	VERB
ejpam-4570	14	7	the	the	DET
ejpam-4570	14	8	notion	notion	NOUN
ejpam-4570	14	9	of	of	ADP
ejpam-4570	14	10	c	c	NOUN
ejpam-4570	14	11	-	-	PUNCT
ejpam-4570	14	12	quasi	quasi	ADJ
ejpam-4570	14	13	normality	normality	NOUN
ejpam-4570	14	14	and	and	CCONJ
ejpam-4570	14	15	l	l	ADJ
ejpam-4570	14	16	-	-	ADJ
ejpam-4570	14	17	quasi	quasi	ADJ
ejpam-4570	14	18	normality	normality	NOUN
ejpam-4570	14	19	in	in	ADP
ejpam-4570	14	20	[	[	X
ejpam-4570	14	21	32	32	NUM
ejpam-4570	14	22	]	]	PUNCT
ejpam-4570	14	23	.	.	PUNCT
ejpam-4570	15	1	in	in	ADP
ejpam-4570	15	2	this	this	DET
ejpam-4570	15	3	paper	paper	NOUN
ejpam-4570	15	4	,	,	PUNCT
ejpam-4570	15	5	we	we	PRON
ejpam-4570	15	6	study	study	VERB
ejpam-4570	15	7	two	two	NUM
ejpam-4570	15	8	new	new	ADJ
ejpam-4570	15	9	properties	property	NOUN
ejpam-4570	15	10	which	which	PRON
ejpam-4570	15	11	are	be	AUX
ejpam-4570	15	12	c	c	NOUN
ejpam-4570	15	13	-	-	PUNCT
ejpam-4570	15	14	almost	almost	ADV
ejpam-4570	15	15	normality	normality	NOUN
ejpam-4570	15	16	and	and	CCONJ
ejpam-4570	15	17	l	l	NOUN
ejpam-4570	15	18	-	-	ADJ
ejpam-4570	15	19	almost	almost	ADV
ejpam-4570	15	20	normality	normality	NOUN
ejpam-4570	15	21	.	.	PUNCT
ejpam-4570	16	1	we	we	PRON
ejpam-4570	16	2	show	show	VERB
ejpam-4570	16	3	that	that	SCONJ
ejpam-4570	16	4	these	these	DET
ejpam-4570	16	5	new	new	ADJ
ejpam-4570	16	6	properties	property	NOUN
ejpam-4570	16	7	are	be	AUX
ejpam-4570	16	8	different	different	ADJ
ejpam-4570	16	9	from	from	ADP
ejpam-4570	16	10	each	each	DET
ejpam-4570	16	11	other	other	ADJ
ejpam-4570	16	12	,	,	PUNCT
ejpam-4570	16	13	and	and	CCONJ
ejpam-4570	16	14	they	they	PRON
ejpam-4570	16	15	are	be	AUX
ejpam-4570	16	16	different	different	ADJ
ejpam-4570	16	17	from	from	ADP
ejpam-4570	16	18	c	c	NOUN
ejpam-4570	16	19	-	-	PUNCT
ejpam-4570	16	20	normality	normality	ADJ
ejpam-4570	16	21	,	,	PUNCT
ejpam-4570	16	22	l	l	NOUN
ejpam-4570	16	23	-	-	NOUN
ejpam-4570	16	24	normality	normality	ADJ
ejpam-4570	16	25	,	,	PUNCT
ejpam-4570	16	26	c	c	NOUN
ejpam-4570	16	27	-	-	PUNCT
ejpam-4570	16	28	regularity	regularity	NOUN
ejpam-4570	16	29	,	,	PUNCT
ejpam-4570	16	30	l	l	NOUN
ejpam-4570	16	31	-	-	NOUN
ejpam-4570	16	32	regularity	regularity	NOUN
ejpam-4570	16	33	,	,	PUNCT
ejpam-4570	16	34	epi	epi	NOUN
ejpam-4570	16	35	-	-	ADJ
ejpam-4570	16	36	almost	almost	ADV
ejpam-4570	16	37	normality	normality	NOUN
ejpam-4570	16	38	,	,	PUNCT
ejpam-4570	16	39	c	c	NOUN
ejpam-4570	16	40	-	-	PUNCT
ejpam-4570	16	41	quasi	quasi	ADJ
ejpam-4570	16	42	normality	normality	NOUN
ejpam-4570	16	43	,	,	PUNCT
ejpam-4570	16	44	l	l	ADJ
ejpam-4570	16	45	-	-	ADJ
ejpam-4570	16	46	quasi	quasi	ADJ
ejpam-4570	16	47	normality	normality	NOUN
ejpam-4570	16	48	and	and	CCONJ
ejpam-4570	16	49	so	so	ADV
ejpam-4570	16	50	on	on	ADV
ejpam-4570	16	51	.	.	PUNCT
ejpam-4570	17	1	some	some	DET
ejpam-4570	17	2	properties	property	NOUN
ejpam-4570	17	3	,	,	PUNCT
ejpam-4570	17	4	counterexample	counterexample	NOUN
ejpam-4570	17	5	and	and	CCONJ
ejpam-4570	17	6	relationships	relationship	NOUN
ejpam-4570	17	7	of	of	ADP
ejpam-4570	17	8	these	these	DET
ejpam-4570	17	9	properties	property	NOUN
ejpam-4570	17	10	are	be	AUX
ejpam-4570	17	11	∗corresponding	∗corresponde	VERB
ejpam-4570	17	12	author	author	NOUN
ejpam-4570	17	13	.	.	PUNCT
ejpam-4570	18	1	doi	doi	NOUN
ejpam-4570	18	2	:	:	PUNCT
ejpam-4570	18	3	https://doi.org/10.29020/nybg.ejpam.v15i4.4570	https://doi.org/10.29020/nybg.ejpam.v15i4.4570	PROPN
ejpam-4570	18	4	email	email	NOUN
ejpam-4570	18	5	addresses	address	NOUN
ejpam-4570	18	6	:	:	PUNCT
ejpam-4570	18	7	wafa-math@hotmail.com	wafa-math@hotmail.com	PROPN
ejpam-4570	18	8	,	,	PUNCT
ejpam-4570	18	9	wkqurashi@uqu.edu.sa	wkqurashi@uqu.edu.sa	PROPN
ejpam-4570	18	10	(	(	PUNCT
ejpam-4570	18	11	wafa	wafa	PROPN
ejpam-4570	18	12	khalaf	khalaf	PROPN
ejpam-4570	18	13	alqurashi	alqurashi	PROPN
ejpam-4570	18	14	)	)	PUNCT
ejpam-4570	18	15	,	,	PUNCT
ejpam-4570	18	16	sthabit1975@gmail.com	sthabit1975@gmail.com	X
ejpam-4570	18	17	,	,	PUNCT
ejpam-4570	18	18	s.thabit@hu.edu.ye	s.thabit@hu.edu.ye	PROPN
ejpam-4570	18	19	(	(	PUNCT
ejpam-4570	18	20	sadeq	sadeq	PROPN
ejpam-4570	18	21	ali	ali	PROPN
ejpam-4570	18	22	thabit	thabit	PROPN
ejpam-4570	18	23	)	)	PUNCT
ejpam-4570	18	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4570	18	25	1760	1760	NUM
ejpam-4570	19	1	©	©	ADP
ejpam-4570	19	2	2022	2022	NUM
ejpam-4570	19	3	ejpam	ejpam	VERB
ejpam-4570	19	4	all	all	DET
ejpam-4570	19	5	rights	right	NOUN
ejpam-4570	19	6	reserved	reserve	VERB
ejpam-4570	19	7	.	.	PUNCT
ejpam-4570	20	1	wafa	wafa	PROPN
ejpam-4570	20	2	khalaf	khalaf	PROPN
ejpam-4570	20	3	alqurashi	alqurashi	PROPN
ejpam-4570	20	4	,	,	PUNCT
ejpam-4570	20	5	sadeq	sadeq	PROPN
ejpam-4570	20	6	ali	ali	PROPN
ejpam-4570	20	7	thabit	thabit	PROPN
ejpam-4570	20	8	/	/	SYM
ejpam-4570	20	9	eur	eur	PROPN
ejpam-4570	20	10	.	.	PUNCT
ejpam-4570	21	1	j.	j.	PROPN
ejpam-4570	21	2	pure	pure	PROPN
ejpam-4570	21	3	appl	appl	PROPN
ejpam-4570	21	4	.	.	PROPN
ejpam-4570	21	5	math	math	PROPN
ejpam-4570	21	6	,	,	PUNCT
ejpam-4570	21	7	15	15	NUM
ejpam-4570	21	8	(	(	PUNCT
ejpam-4570	21	9	4	4	NUM
ejpam-4570	21	10	)	)	PUNCT
ejpam-4570	21	11	(	(	PUNCT
ejpam-4570	21	12	2022	2022	NUM
ejpam-4570	21	13	)	)	PUNCT
ejpam-4570	21	14	,	,	PUNCT
ejpam-4570	21	15	1760	1760	NUM
ejpam-4570	21	16	-	-	SYM
ejpam-4570	21	17	1782	1782	NUM
ejpam-4570	21	18	1761	1761	NUM
ejpam-4570	21	19	investigated	investigate	VERB
ejpam-4570	21	20	.	.	PUNCT
ejpam-4570	22	1	throughout	throughout	ADP
ejpam-4570	22	2	this	this	DET
ejpam-4570	22	3	paper	paper	NOUN
ejpam-4570	22	4	,	,	PUNCT
ejpam-4570	22	5	a	a	DET
ejpam-4570	22	6	space	space	NOUN
ejpam-4570	22	7	x	x	NOUN
ejpam-4570	22	8	means	mean	VERB
ejpam-4570	22	9	a	a	DET
ejpam-4570	22	10	topological	topological	ADJ
ejpam-4570	22	11	space	space	NOUN
ejpam-4570	22	12	.	.	PUNCT
ejpam-4570	23	1	the	the	DET
ejpam-4570	23	2	set	set	NOUN
ejpam-4570	23	3	of	of	ADP
ejpam-4570	23	4	all	all	DET
ejpam-4570	23	5	real	real	ADJ
ejpam-4570	23	6	numbers	number	NOUN
ejpam-4570	23	7	is	be	AUX
ejpam-4570	23	8	denoted	denote	VERB
ejpam-4570	23	9	by	by	ADP
ejpam-4570	23	10	r	r	NOUN
ejpam-4570	23	11	,	,	PUNCT
ejpam-4570	23	12	the	the	DET
ejpam-4570	23	13	set	set	NOUN
ejpam-4570	23	14	of	of	ADP
ejpam-4570	23	15	all	all	DET
ejpam-4570	23	16	rational	rational	ADJ
ejpam-4570	23	17	numbers	number	NOUN
ejpam-4570	23	18	is	be	AUX
ejpam-4570	23	19	denoted	denote	VERB
ejpam-4570	23	20	by	by	ADP
ejpam-4570	23	21	q	q	PROPN
ejpam-4570	23	22	and	and	CCONJ
ejpam-4570	23	23	the	the	DET
ejpam-4570	23	24	set	set	NOUN
ejpam-4570	23	25	of	of	ADP
ejpam-4570	23	26	all	all	DET
ejpam-4570	23	27	irrational	irrational	ADJ
ejpam-4570	23	28	numbers	number	NOUN
ejpam-4570	23	29	is	be	AUX
ejpam-4570	23	30	denoted	denote	VERB
ejpam-4570	23	31	by	by	ADP
ejpam-4570	23	32	p.	p.	NOUN
ejpam-4570	23	33	for	for	ADP
ejpam-4570	23	34	a	a	DET
ejpam-4570	23	35	subset	subset	NOUN
ejpam-4570	24	1	a	a	PRON
ejpam-4570	24	2	of	of	ADP
ejpam-4570	24	3	a	a	DET
ejpam-4570	24	4	space	space	NOUN
ejpam-4570	24	5	x	x	NOUN
ejpam-4570	24	6	,	,	PUNCT
ejpam-4570	24	7	a	a	PRON
ejpam-4570	24	8	and	and	CCONJ
ejpam-4570	24	9	int(a	int(a	PROPN
ejpam-4570	24	10	)	)	PUNCT
ejpam-4570	24	11	denote	denote	NOUN
ejpam-4570	24	12	to	to	ADP
ejpam-4570	24	13	the	the	DET
ejpam-4570	24	14	closure	closure	NOUN
ejpam-4570	24	15	and	and	CCONJ
ejpam-4570	24	16	the	the	DET
ejpam-4570	24	17	interior	interior	NOUN
ejpam-4570	24	18	of	of	ADP
ejpam-4570	24	19	a	a	PRON
ejpam-4570	24	20	in	in	ADP
ejpam-4570	24	21	x	x	NOUN
ejpam-4570	24	22	,	,	PUNCT
ejpam-4570	24	23	respectively	respectively	ADV
ejpam-4570	24	24	.	.	PUNCT
ejpam-4570	25	1	we	we	PRON
ejpam-4570	25	2	need	need	VERB
ejpam-4570	25	3	to	to	PART
ejpam-4570	25	4	recall	recall	VERB
ejpam-4570	25	5	the	the	DET
ejpam-4570	25	6	following	follow	VERB
ejpam-4570	25	7	definitions	definition	NOUN
ejpam-4570	25	8	:	:	PUNCT
ejpam-4570	25	9	a	a	DET
ejpam-4570	25	10	subset	subset	NOUN
ejpam-4570	25	11	a	a	PRON
ejpam-4570	25	12	of	of	ADP
ejpam-4570	25	13	a	a	DET
ejpam-4570	25	14	space	space	NOUN
ejpam-4570	25	15	x	x	PUNCT
ejpam-4570	25	16	is	be	AUX
ejpam-4570	25	17	said	say	VERB
ejpam-4570	25	18	to	to	PART
ejpam-4570	25	19	be	be	AUX
ejpam-4570	25	20	a	a	DET
ejpam-4570	25	21	regularly	regularly	ADV
ejpam-4570	25	22	-	-	PUNCT
ejpam-4570	25	23	open	open	NOUN
ejpam-4570	25	24	set	set	NOUN
ejpam-4570	25	25	or	or	CCONJ
ejpam-4570	25	26	an	an	DET
ejpam-4570	25	27	open	open	ADJ
ejpam-4570	25	28	domain	domain	NOUN
ejpam-4570	25	29	set	set	VERB
ejpam-4570	25	30	if	if	SCONJ
ejpam-4570	25	31	it	it	PRON
ejpam-4570	25	32	is	be	AUX
ejpam-4570	25	33	the	the	DET
ejpam-4570	25	34	interior	interior	NOUN
ejpam-4570	25	35	of	of	ADP
ejpam-4570	25	36	its	its	PRON
ejpam-4570	25	37	own	own	ADJ
ejpam-4570	25	38	closure	closure	NOUN
ejpam-4570	25	39	,	,	PUNCT
ejpam-4570	25	40	or	or	CCONJ
ejpam-4570	25	41	equivalently	equivalently	ADV
ejpam-4570	25	42	if	if	SCONJ
ejpam-4570	25	43	it	it	PRON
ejpam-4570	25	44	is	be	AUX
ejpam-4570	25	45	the	the	DET
ejpam-4570	25	46	interior	interior	NOUN
ejpam-4570	25	47	of	of	ADP
ejpam-4570	25	48	some	some	DET
ejpam-4570	25	49	closed	close	VERB
ejpam-4570	25	50	set	set	NOUN
ejpam-4570	25	51	[	[	X
ejpam-4570	25	52	19	19	NUM
ejpam-4570	25	53	]	]	PUNCT
ejpam-4570	25	54	.	.	PUNCT
ejpam-4570	26	1	a	a	DET
ejpam-4570	26	2	complement	complement	NOUN
ejpam-4570	26	3	of	of	ADP
ejpam-4570	26	4	an	an	DET
ejpam-4570	26	5	open	open	ADJ
ejpam-4570	26	6	domain	domain	NOUN
ejpam-4570	26	7	subset	subset	NOUN
ejpam-4570	26	8	is	be	AUX
ejpam-4570	26	9	called	call	VERB
ejpam-4570	26	10	a	a	DET
ejpam-4570	26	11	closed	closed	ADJ
ejpam-4570	26	12	domain	domain	NOUN
ejpam-4570	26	13	subset	subset	NOUN
ejpam-4570	26	14	.	.	PUNCT
ejpam-4570	27	1	a	a	DET
ejpam-4570	27	2	subset	subset	NOUN
ejpam-4570	27	3	a	a	PRON
ejpam-4570	27	4	of	of	ADP
ejpam-4570	27	5	a	a	DET
ejpam-4570	27	6	space	space	NOUN
ejpam-4570	27	7	x	x	PUNCT
ejpam-4570	27	8	is	be	AUX
ejpam-4570	27	9	called	call	VERB
ejpam-4570	27	10	a	a	DET
ejpam-4570	27	11	π	π	PROPN
ejpam-4570	27	12	-	-	ADJ
ejpam-4570	27	13	closed	closed	ADJ
ejpam-4570	27	14	set	set	NOUN
ejpam-4570	27	15	if	if	SCONJ
ejpam-4570	27	16	it	it	PRON
ejpam-4570	27	17	is	be	AUX
ejpam-4570	27	18	a	a	DET
ejpam-4570	27	19	finite	finite	ADJ
ejpam-4570	27	20	intersection	intersection	NOUN
ejpam-4570	27	21	of	of	ADP
ejpam-4570	27	22	closed	closed	ADJ
ejpam-4570	27	23	domain	domain	NOUN
ejpam-4570	27	24	sets	set	NOUN
ejpam-4570	27	25	[	[	X
ejpam-4570	27	26	36	36	NUM
ejpam-4570	27	27	]	]	PUNCT
ejpam-4570	27	28	.	.	PUNCT
ejpam-4570	28	1	two	two	NUM
ejpam-4570	28	2	sets	set	VERB
ejpam-4570	28	3	a	a	PRON
ejpam-4570	28	4	and	and	CCONJ
ejpam-4570	28	5	b	b	NOUN
ejpam-4570	28	6	of	of	ADP
ejpam-4570	28	7	a	a	DET
ejpam-4570	28	8	space	space	NOUN
ejpam-4570	28	9	x	x	PRON
ejpam-4570	28	10	are	be	AUX
ejpam-4570	28	11	said	say	VERB
ejpam-4570	28	12	to	to	PART
ejpam-4570	28	13	be	be	AUX
ejpam-4570	28	14	separated	separate	VERB
ejpam-4570	28	15	if	if	SCONJ
ejpam-4570	28	16	there	there	PRON
ejpam-4570	28	17	exist	exist	VERB
ejpam-4570	28	18	two	two	NUM
ejpam-4570	28	19	disjoint	disjoint	ADJ
ejpam-4570	28	20	open	open	ADJ
ejpam-4570	28	21	sets	set	NOUN
ejpam-4570	28	22	u	u	NOUN
ejpam-4570	28	23	and	and	CCONJ
ejpam-4570	28	24	v	v	NOUN
ejpam-4570	28	25	in	in	ADP
ejpam-4570	28	26	x	x	PUNCT
ejpam-4570	28	27	such	such	ADJ
ejpam-4570	28	28	that	that	SCONJ
ejpam-4570	28	29	a	a	DET
ejpam-4570	28	30	⊆	⊆	NUM
ejpam-4570	28	31	u	u	NOUN
ejpam-4570	28	32	and	and	CCONJ
ejpam-4570	28	33	b	b	NOUN
ejpam-4570	28	34	⊆	⊆	NUM
ejpam-4570	28	35	v	v	ADP
ejpam-4570	28	36	[	[	PUNCT
ejpam-4570	28	37	11	11	NUM
ejpam-4570	28	38	,	,	PUNCT
ejpam-4570	28	39	12	12	NUM
ejpam-4570	28	40	,	,	PUNCT
ejpam-4570	28	41	22	22	NUM
ejpam-4570	28	42	]	]	PUNCT
ejpam-4570	28	43	.	.	PUNCT
ejpam-4570	29	1	if	if	SCONJ
ejpam-4570	29	2	t	t	PROPN
ejpam-4570	29	3	and	and	CCONJ
ejpam-4570	29	4	t	t	PROPN
ejpam-4570	29	5	′	′	NOUN
ejpam-4570	29	6	are	be	AUX
ejpam-4570	29	7	two	two	NUM
ejpam-4570	29	8	topologies	topology	NOUN
ejpam-4570	29	9	on	on	ADP
ejpam-4570	29	10	x	x	SYM
ejpam-4570	29	11	such	such	ADJ
ejpam-4570	29	12	that	that	SCONJ
ejpam-4570	29	13	t	t	PROPN
ejpam-4570	29	14	′	′	NUM
ejpam-4570	29	15	⊆	⊆	NUM
ejpam-4570	29	16	t	t	NOUN
ejpam-4570	29	17	,	,	PUNCT
ejpam-4570	29	18	then	then	ADV
ejpam-4570	29	19	t	t	PROPN
ejpam-4570	29	20	′	′	NUM
ejpam-4570	29	21	is	be	AUX
ejpam-4570	29	22	called	call	VERB
ejpam-4570	29	23	a	a	DET
ejpam-4570	29	24	topology	topology	NOUN
ejpam-4570	29	25	that	that	PRON
ejpam-4570	29	26	is	be	AUX
ejpam-4570	29	27	coarser	coarse	ADJ
ejpam-4570	29	28	than	than	ADP
ejpam-4570	29	29	t	t	PROPN
ejpam-4570	29	30	and	and	CCONJ
ejpam-4570	29	31	t	t	PROPN
ejpam-4570	29	32	is	be	AUX
ejpam-4570	29	33	called	call	VERB
ejpam-4570	29	34	finer	fine	ADJ
ejpam-4570	29	35	[	[	X
ejpam-4570	29	36	12	12	NUM
ejpam-4570	29	37	]	]	PUNCT
ejpam-4570	29	38	.	.	PUNCT
ejpam-4570	30	1	a	a	DET
ejpam-4570	30	2	space	space	NOUN
ejpam-4570	30	3	x	x	PUNCT
ejpam-4570	30	4	is	be	AUX
ejpam-4570	30	5	said	say	VERB
ejpam-4570	30	6	to	to	PART
ejpam-4570	30	7	be	be	AUX
ejpam-4570	30	8	a	a	DET
ejpam-4570	30	9	normal	normal	ADJ
ejpam-4570	30	10	space	space	NOUN
ejpam-4570	30	11	[	[	X
ejpam-4570	30	12	12	12	NUM
ejpam-4570	30	13	]	]	X
ejpam-4570	30	14	,	,	PUNCT
ejpam-4570	30	15	if	if	SCONJ
ejpam-4570	30	16	any	any	DET
ejpam-4570	30	17	pair	pair	NOUN
ejpam-4570	30	18	of	of	ADP
ejpam-4570	30	19	disjoint	disjoint	NOUN
ejpam-4570	30	20	closed	closed	ADJ
ejpam-4570	30	21	subsets	subset	NOUN
ejpam-4570	30	22	a	a	PRON
ejpam-4570	30	23	and	and	CCONJ
ejpam-4570	30	24	b	b	NOUN
ejpam-4570	30	25	of	of	ADP
ejpam-4570	30	26	x	x	PRON
ejpam-4570	30	27	can	can	AUX
ejpam-4570	30	28	be	be	AUX
ejpam-4570	30	29	separated	separate	VERB
ejpam-4570	30	30	by	by	ADP
ejpam-4570	30	31	two	two	NUM
ejpam-4570	30	32	disjoint	disjoint	ADJ
ejpam-4570	30	33	open	open	ADJ
ejpam-4570	30	34	subsets	subset	NOUN
ejpam-4570	30	35	.	.	PUNCT
ejpam-4570	31	1	a	a	DET
ejpam-4570	31	2	space	space	NOUN
ejpam-4570	31	3	x	x	PUNCT
ejpam-4570	31	4	is	be	AUX
ejpam-4570	31	5	said	say	VERB
ejpam-4570	31	6	to	to	PART
ejpam-4570	31	7	be	be	AUX
ejpam-4570	31	8	a	a	DET
ejpam-4570	31	9	π	π	ADJ
ejpam-4570	31	10	-	-	ADJ
ejpam-4570	31	11	normal	normal	ADJ
ejpam-4570	31	12	space	space	NOUN
ejpam-4570	31	13	[	[	X
ejpam-4570	31	14	14	14	NUM
ejpam-4570	31	15	]	]	X
ejpam-4570	31	16	,	,	PUNCT
ejpam-4570	31	17	if	if	SCONJ
ejpam-4570	31	18	any	any	DET
ejpam-4570	31	19	pair	pair	NOUN
ejpam-4570	31	20	of	of	ADP
ejpam-4570	31	21	disjoint	disjoint	NOUN
ejpam-4570	31	22	closed	closed	ADJ
ejpam-4570	31	23	subsets	subset	NOUN
ejpam-4570	31	24	a	a	PRON
ejpam-4570	31	25	and	and	CCONJ
ejpam-4570	31	26	b	b	NOUN
ejpam-4570	31	27	of	of	ADP
ejpam-4570	31	28	x	x	PRON
ejpam-4570	31	29	,	,	PUNCT
ejpam-4570	31	30	one	one	NUM
ejpam-4570	31	31	of	of	ADP
ejpam-4570	31	32	which	which	PRON
ejpam-4570	31	33	is	be	AUX
ejpam-4570	31	34	π	π	PROPN
ejpam-4570	31	35	-	-	VERB
ejpam-4570	31	36	closed	closed	ADJ
ejpam-4570	31	37	,	,	PUNCT
ejpam-4570	31	38	can	can	AUX
ejpam-4570	31	39	be	be	AUX
ejpam-4570	31	40	separated	separate	VERB
ejpam-4570	31	41	by	by	ADP
ejpam-4570	31	42	two	two	NUM
ejpam-4570	31	43	disjoint	disjoint	ADJ
ejpam-4570	31	44	open	open	ADJ
ejpam-4570	31	45	subsets	subset	NOUN
ejpam-4570	31	46	.	.	PUNCT
ejpam-4570	32	1	a	a	DET
ejpam-4570	32	2	space	space	NOUN
ejpam-4570	32	3	x	x	PUNCT
ejpam-4570	32	4	is	be	AUX
ejpam-4570	32	5	said	say	VERB
ejpam-4570	32	6	to	to	PART
ejpam-4570	32	7	be	be	AUX
ejpam-4570	32	8	an	an	DET
ejpam-4570	32	9	almost	almost	ADV
ejpam-4570	32	10	-	-	PUNCT
ejpam-4570	32	11	normal	normal	ADJ
ejpam-4570	32	12	space	space	NOUN
ejpam-4570	33	1	[	[	X
ejpam-4570	33	2	14	14	NUM
ejpam-4570	33	3	,	,	PUNCT
ejpam-4570	33	4	26	26	NUM
ejpam-4570	33	5	]	]	PUNCT
ejpam-4570	33	6	,	,	PUNCT
ejpam-4570	33	7	if	if	SCONJ
ejpam-4570	33	8	any	any	DET
ejpam-4570	33	9	pair	pair	NOUN
ejpam-4570	33	10	of	of	ADP
ejpam-4570	33	11	disjoint	disjoint	NOUN
ejpam-4570	33	12	closed	closed	ADJ
ejpam-4570	33	13	subsets	subset	NOUN
ejpam-4570	33	14	a	a	PRON
ejpam-4570	33	15	and	and	CCONJ
ejpam-4570	33	16	b	b	NOUN
ejpam-4570	33	17	of	of	ADP
ejpam-4570	33	18	x	x	PRON
ejpam-4570	33	19	,	,	PUNCT
ejpam-4570	33	20	one	one	NUM
ejpam-4570	33	21	of	of	ADP
ejpam-4570	33	22	which	which	PRON
ejpam-4570	33	23	is	be	AUX
ejpam-4570	33	24	closed	closed	ADJ
ejpam-4570	33	25	domain	domain	NOUN
ejpam-4570	33	26	,	,	PUNCT
ejpam-4570	33	27	can	can	AUX
ejpam-4570	33	28	be	be	AUX
ejpam-4570	33	29	separated	separate	VERB
ejpam-4570	33	30	by	by	ADP
ejpam-4570	33	31	two	two	NUM
ejpam-4570	33	32	disjoint	disjoint	ADJ
ejpam-4570	33	33	open	open	ADJ
ejpam-4570	33	34	subsets	subset	NOUN
ejpam-4570	33	35	.	.	PUNCT
ejpam-4570	34	1	a	a	DET
ejpam-4570	34	2	space	space	NOUN
ejpam-4570	34	3	x	x	PUNCT
ejpam-4570	34	4	is	be	AUX
ejpam-4570	34	5	said	say	VERB
ejpam-4570	34	6	to	to	PART
ejpam-4570	34	7	be	be	AUX
ejpam-4570	34	8	a	a	DET
ejpam-4570	34	9	mildly	mildly	ADV
ejpam-4570	34	10	normal	normal	ADJ
ejpam-4570	34	11	space	space	NOUN
ejpam-4570	34	12	[	[	X
ejpam-4570	34	13	27	27	NUM
ejpam-4570	34	14	]	]	PUNCT
ejpam-4570	34	15	,	,	PUNCT
ejpam-4570	34	16	if	if	SCONJ
ejpam-4570	34	17	any	any	DET
ejpam-4570	34	18	pair	pair	NOUN
ejpam-4570	34	19	of	of	ADP
ejpam-4570	34	20	disjoint	disjoint	NOUN
ejpam-4570	34	21	closed	closed	ADJ
ejpam-4570	34	22	domain	domain	NOUN
ejpam-4570	34	23	subsets	subset	NOUN
ejpam-4570	34	24	a	a	PRON
ejpam-4570	34	25	and	and	CCONJ
ejpam-4570	34	26	b	b	NOUN
ejpam-4570	34	27	of	of	ADP
ejpam-4570	34	28	x	x	PRON
ejpam-4570	34	29	can	can	AUX
ejpam-4570	34	30	be	be	AUX
ejpam-4570	34	31	separated	separate	VERB
ejpam-4570	34	32	by	by	ADP
ejpam-4570	34	33	two	two	NUM
ejpam-4570	34	34	disjoint	disjoint	ADJ
ejpam-4570	34	35	open	open	ADJ
ejpam-4570	34	36	subsets	subset	NOUN
ejpam-4570	34	37	.	.	PUNCT
ejpam-4570	35	1	a	a	DET
ejpam-4570	35	2	space	space	NOUN
ejpam-4570	35	3	x	x	PUNCT
ejpam-4570	35	4	is	be	AUX
ejpam-4570	35	5	said	say	VERB
ejpam-4570	35	6	to	to	PART
ejpam-4570	35	7	be	be	AUX
ejpam-4570	35	8	a	a	DET
ejpam-4570	35	9	partially	partially	ADV
ejpam-4570	35	10	normal	normal	ADJ
ejpam-4570	35	11	space	space	NOUN
ejpam-4570	35	12	[	[	X
ejpam-4570	35	13	6	6	NUM
ejpam-4570	35	14	]	]	PUNCT
ejpam-4570	35	15	,	,	PUNCT
ejpam-4570	35	16	if	if	SCONJ
ejpam-4570	35	17	any	any	DET
ejpam-4570	35	18	pair	pair	NOUN
ejpam-4570	35	19	of	of	ADP
ejpam-4570	35	20	disjoint	disjoint	NOUN
ejpam-4570	35	21	closed	closed	ADJ
ejpam-4570	35	22	subsets	subset	NOUN
ejpam-4570	35	23	a	a	PRON
ejpam-4570	35	24	and	and	CCONJ
ejpam-4570	35	25	b	b	NOUN
ejpam-4570	35	26	of	of	ADP
ejpam-4570	35	27	x	x	PRON
ejpam-4570	35	28	,	,	PUNCT
ejpam-4570	35	29	one	one	NUM
ejpam-4570	35	30	of	of	ADP
ejpam-4570	35	31	which	which	PRON
ejpam-4570	35	32	is	be	AUX
ejpam-4570	35	33	closed	closed	ADJ
ejpam-4570	35	34	domain	domain	NOUN
ejpam-4570	35	35	and	and	CCONJ
ejpam-4570	35	36	the	the	DET
ejpam-4570	35	37	other	other	ADJ
ejpam-4570	35	38	is	be	AUX
ejpam-4570	35	39	π	π	PROPN
ejpam-4570	35	40	-	-	VERB
ejpam-4570	35	41	closed	closed	ADJ
ejpam-4570	35	42	,	,	PUNCT
ejpam-4570	35	43	can	can	AUX
ejpam-4570	35	44	be	be	AUX
ejpam-4570	35	45	separated	separate	VERB
ejpam-4570	35	46	by	by	ADP
ejpam-4570	35	47	two	two	NUM
ejpam-4570	35	48	disjoint	disjoint	ADJ
ejpam-4570	35	49	open	open	ADJ
ejpam-4570	35	50	subsets	subset	NOUN
ejpam-4570	35	51	.	.	PUNCT
ejpam-4570	36	1	a	a	DET
ejpam-4570	36	2	space	space	NOUN
ejpam-4570	36	3	x	x	PUNCT
ejpam-4570	36	4	is	be	AUX
ejpam-4570	36	5	said	say	VERB
ejpam-4570	36	6	to	to	PART
ejpam-4570	36	7	be	be	AUX
ejpam-4570	36	8	a	a	DET
ejpam-4570	36	9	completely	completely	ADV
ejpam-4570	36	10	regular	regular	ADJ
ejpam-4570	36	11	(	(	PUNCT
ejpam-4570	36	12	resp	resp	NOUN
ejpam-4570	36	13	.	.	PUNCT
ejpam-4570	37	1	an	an	DET
ejpam-4570	37	2	almost	almost	ADV
ejpam-4570	37	3	completely	completely	ADV
ejpam-4570	37	4	regular	regular	ADJ
ejpam-4570	37	5	)	)	PUNCT
ejpam-4570	37	6	space	space	NOUN
ejpam-4570	37	7	if	if	SCONJ
ejpam-4570	37	8	for	for	ADP
ejpam-4570	37	9	each	each	DET
ejpam-4570	37	10	x	x	SYM
ejpam-4570	37	11	∈	∈	PROPN
ejpam-4570	37	12	x	x	X
ejpam-4570	37	13	and	and	CCONJ
ejpam-4570	37	14	each	each	PRON
ejpam-4570	37	15	closed	close	VERB
ejpam-4570	37	16	(	(	PUNCT
ejpam-4570	37	17	resp	resp	NOUN
ejpam-4570	37	18	.	.	PUNCT
ejpam-4570	38	1	closed	closed	ADJ
ejpam-4570	38	2	domain	domain	NOUN
ejpam-4570	38	3	)	)	PUNCT
ejpam-4570	38	4	set	set	VERB
ejpam-4570	38	5	f	f	PROPN
ejpam-4570	38	6	in	in	ADP
ejpam-4570	38	7	x	x	PUNCT
ejpam-4570	38	8	such	such	ADJ
ejpam-4570	38	9	that	that	SCONJ
ejpam-4570	38	10	x	x	SYM
ejpam-4570	38	11	̸∈	̸∈	PROPN
ejpam-4570	38	12	f	f	PROPN
ejpam-4570	38	13	,	,	PUNCT
ejpam-4570	38	14	there	there	PRON
ejpam-4570	38	15	exists	exist	VERB
ejpam-4570	38	16	a	a	DET
ejpam-4570	38	17	continuous	continuous	ADJ
ejpam-4570	38	18	function	function	NOUN
ejpam-4570	38	19	f	f	NOUN
ejpam-4570	38	20	:	:	PUNCT
ejpam-4570	38	21	x	x	X
ejpam-4570	38	22	→	→	PUNCT
ejpam-4570	39	1	[	[	X
ejpam-4570	39	2	0	0	NUM
ejpam-4570	39	3	,	,	PUNCT
ejpam-4570	39	4	1	1	NUM
ejpam-4570	39	5	]	]	PUNCT
ejpam-4570	39	6	such	such	ADJ
ejpam-4570	39	7	that	that	SCONJ
ejpam-4570	39	8	f(x	f(x	NOUN
ejpam-4570	39	9	)	)	PUNCT
ejpam-4570	39	10	=	=	SYM
ejpam-4570	39	11	0	0	NUM
ejpam-4570	39	12	and	and	CCONJ
ejpam-4570	39	13	f(f	f(f	PROPN
ejpam-4570	39	14	)	)	PUNCT
ejpam-4570	40	1	=	=	PUNCT
ejpam-4570	40	2	{	{	PUNCT
ejpam-4570	40	3	1	1	NUM
ejpam-4570	40	4	}	}	PUNCT
ejpam-4570	41	1	[	[	X
ejpam-4570	41	2	12	12	NUM
ejpam-4570	41	3	,	,	PUNCT
ejpam-4570	41	4	26	26	NUM
ejpam-4570	41	5	]	]	PUNCT
ejpam-4570	41	6	.	.	PUNCT
ejpam-4570	42	1	a	a	DET
ejpam-4570	42	2	space	space	NOUN
ejpam-4570	42	3	x	x	PUNCT
ejpam-4570	42	4	is	be	AUX
ejpam-4570	42	5	said	say	VERB
ejpam-4570	42	6	to	to	PART
ejpam-4570	42	7	be	be	AUX
ejpam-4570	42	8	a	a	DET
ejpam-4570	42	9	regular	regular	ADJ
ejpam-4570	42	10	(	(	PUNCT
ejpam-4570	42	11	resp	resp	NOUN
ejpam-4570	42	12	.	.	PUNCT
ejpam-4570	43	1	an	an	DET
ejpam-4570	43	2	almost	almost	ADV
ejpam-4570	43	3	regular	regular	ADJ
ejpam-4570	43	4	)	)	PUNCT
ejpam-4570	43	5	space	space	NOUN
ejpam-4570	43	6	if	if	SCONJ
ejpam-4570	43	7	for	for	ADP
ejpam-4570	43	8	each	each	DET
ejpam-4570	43	9	x	x	SYM
ejpam-4570	43	10	∈	∈	PROPN
ejpam-4570	43	11	x	x	X
ejpam-4570	43	12	and	and	CCONJ
ejpam-4570	43	13	each	each	PRON
ejpam-4570	43	14	closed	close	VERB
ejpam-4570	43	15	(	(	PUNCT
ejpam-4570	43	16	resp	resp	NOUN
ejpam-4570	43	17	.	.	PUNCT
ejpam-4570	44	1	closed	closed	ADJ
ejpam-4570	44	2	domain	domain	NOUN
ejpam-4570	44	3	)	)	PUNCT
ejpam-4570	44	4	set	set	VERB
ejpam-4570	44	5	f	f	PROPN
ejpam-4570	44	6	in	in	ADP
ejpam-4570	44	7	x	x	PUNCT
ejpam-4570	44	8	such	such	ADJ
ejpam-4570	44	9	that	that	SCONJ
ejpam-4570	44	10	x	x	SYM
ejpam-4570	44	11	̸∈	̸∈	PROPN
ejpam-4570	44	12	f	f	PROPN
ejpam-4570	44	13	,	,	PUNCT
ejpam-4570	44	14	there	there	PRON
ejpam-4570	44	15	exist	exist	VERB
ejpam-4570	44	16	two	two	NUM
ejpam-4570	44	17	disjoint	disjoint	ADJ
ejpam-4570	44	18	open	open	ADJ
ejpam-4570	44	19	subsets	subset	NOUN
ejpam-4570	44	20	u	u	NOUN
ejpam-4570	44	21	and	and	CCONJ
ejpam-4570	44	22	v	v	ADP
ejpam-4570	44	23	such	such	ADJ
ejpam-4570	44	24	that	that	SCONJ
ejpam-4570	44	25	x	x	SYM
ejpam-4570	44	26	∈	∈	PROPN
ejpam-4570	44	27	u	u	NOUN
ejpam-4570	44	28	and	and	CCONJ
ejpam-4570	44	29	f	f	PROPN
ejpam-4570	44	30	⊆	⊆	NUM
ejpam-4570	44	31	v	v	ADP
ejpam-4570	44	32	[	[	X
ejpam-4570	44	33	25	25	NUM
ejpam-4570	44	34	]	]	PUNCT
ejpam-4570	44	35	.	.	PUNCT
ejpam-4570	45	1	a	a	DET
ejpam-4570	45	2	space	space	NOUN
ejpam-4570	45	3	(	(	PUNCT
ejpam-4570	45	4	x	x	X
ejpam-4570	45	5	,	,	PUNCT
ejpam-4570	45	6	t	t	PROPN
ejpam-4570	45	7	)	)	PUNCT
ejpam-4570	45	8	is	be	AUX
ejpam-4570	45	9	said	say	VERB
ejpam-4570	45	10	to	to	PART
ejpam-4570	45	11	be	be	AUX
ejpam-4570	45	12	an	an	DET
ejpam-4570	45	13	epi	epi	ADJ
ejpam-4570	45	14	-	-	ADJ
ejpam-4570	45	15	normal	normal	ADJ
ejpam-4570	45	16	space	space	NOUN
ejpam-4570	46	1	[	[	X
ejpam-4570	46	2	15	15	NUM
ejpam-4570	46	3	]	]	PUNCT
ejpam-4570	46	4	,	,	PUNCT
ejpam-4570	46	5	if	if	SCONJ
ejpam-4570	46	6	there	there	PRON
ejpam-4570	46	7	exists	exist	VERB
ejpam-4570	46	8	a	a	DET
ejpam-4570	46	9	topology	topology	NOUN
ejpam-4570	46	10	t	t	NOUN
ejpam-4570	46	11	′	′	NUM
ejpam-4570	46	12	on	on	ADP
ejpam-4570	46	13	x	x	SYM
ejpam-4570	46	14	coarser	coarse	ADJ
ejpam-4570	46	15	than	than	ADP
ejpam-4570	46	16	t	t	NOUN
ejpam-4570	46	17	such	such	ADJ
ejpam-4570	46	18	that	that	SCONJ
ejpam-4570	46	19	(	(	PUNCT
ejpam-4570	46	20	x	x	X
ejpam-4570	46	21	,	,	PUNCT
ejpam-4570	46	22	t	t	PROPN
ejpam-4570	46	23	′	′	NUM
ejpam-4570	46	24	)	)	PUNCT
ejpam-4570	46	25	is	be	AUX
ejpam-4570	46	26	t4	t4	PROPN
ejpam-4570	46	27	(	(	PUNCT
ejpam-4570	46	28	t1	t1	NOUN
ejpam-4570	46	29	-	-	PUNCT
ejpam-4570	46	30	normal	normal	ADJ
ejpam-4570	46	31	)	)	PUNCT
ejpam-4570	46	32	.	.	PUNCT
ejpam-4570	47	1	a	a	DET
ejpam-4570	47	2	space	space	NOUN
ejpam-4570	47	3	(	(	PUNCT
ejpam-4570	47	4	x	x	X
ejpam-4570	47	5	,	,	PUNCT
ejpam-4570	47	6	t	t	PROPN
ejpam-4570	47	7	)	)	PUNCT
ejpam-4570	47	8	is	be	AUX
ejpam-4570	47	9	said	say	VERB
ejpam-4570	47	10	to	to	PART
ejpam-4570	47	11	be	be	AUX
ejpam-4570	47	12	an	an	DET
ejpam-4570	47	13	epi	epi	NOUN
ejpam-4570	47	14	-	-	ADJ
ejpam-4570	47	15	mildly	mildly	ADV
ejpam-4570	47	16	normal	normal	ADJ
ejpam-4570	47	17	space	space	NOUN
ejpam-4570	47	18	[	[	X
ejpam-4570	47	19	17	17	NUM
ejpam-4570	47	20	]	]	PUNCT
ejpam-4570	47	21	,	,	PUNCT
ejpam-4570	47	22	if	if	SCONJ
ejpam-4570	47	23	there	there	PRON
ejpam-4570	47	24	exists	exist	VERB
ejpam-4570	47	25	a	a	DET
ejpam-4570	47	26	topology	topology	NOUN
ejpam-4570	47	27	t	t	NOUN
ejpam-4570	47	28	′	′	NUM
ejpam-4570	47	29	on	on	ADP
ejpam-4570	47	30	x	x	SYM
ejpam-4570	47	31	coarser	coarse	ADJ
ejpam-4570	47	32	than	than	ADP
ejpam-4570	47	33	t	t	NOUN
ejpam-4570	47	34	such	such	ADJ
ejpam-4570	47	35	that	that	SCONJ
ejpam-4570	47	36	(	(	PUNCT
ejpam-4570	47	37	x	x	X
ejpam-4570	47	38	,	,	PUNCT
ejpam-4570	47	39	t	t	PROPN
ejpam-4570	47	40	′	′	NUM
ejpam-4570	47	41	)	)	PUNCT
ejpam-4570	47	42	is	be	AUX
ejpam-4570	47	43	hausdorff	hausdorff	NOUN
ejpam-4570	47	44	mildly	mildly	ADV
ejpam-4570	47	45	normal	normal	ADJ
ejpam-4570	47	46	.	.	PUNCT
ejpam-4570	48	1	a	a	DET
ejpam-4570	48	2	space	space	NOUN
ejpam-4570	48	3	(	(	PUNCT
ejpam-4570	48	4	x	x	X
ejpam-4570	48	5	,	,	PUNCT
ejpam-4570	48	6	t	t	PROPN
ejpam-4570	48	7	)	)	PUNCT
ejpam-4570	48	8	is	be	AUX
ejpam-4570	48	9	said	say	VERB
ejpam-4570	48	10	to	to	PART
ejpam-4570	48	11	be	be	AUX
ejpam-4570	48	12	an	an	DET
ejpam-4570	48	13	epi	epi	NOUN
ejpam-4570	48	14	-	-	ADJ
ejpam-4570	48	15	almost	almost	ADV
ejpam-4570	48	16	normal	normal	ADJ
ejpam-4570	48	17	space	space	NOUN
ejpam-4570	48	18	[	[	X
ejpam-4570	48	19	4	4	NUM
ejpam-4570	48	20	]	]	PUNCT
ejpam-4570	48	21	,	,	PUNCT
ejpam-4570	48	22	if	if	SCONJ
ejpam-4570	48	23	there	there	PRON
ejpam-4570	48	24	exists	exist	VERB
ejpam-4570	48	25	a	a	DET
ejpam-4570	48	26	topology	topology	NOUN
ejpam-4570	48	27	t	t	NOUN
ejpam-4570	48	28	′	′	NUM
ejpam-4570	48	29	on	on	ADP
ejpam-4570	48	30	x	x	SYM
ejpam-4570	48	31	coarser	coarse	ADJ
ejpam-4570	48	32	than	than	ADP
ejpam-4570	48	33	t	t	NOUN
ejpam-4570	48	34	such	such	ADJ
ejpam-4570	48	35	that	that	SCONJ
ejpam-4570	48	36	(	(	PUNCT
ejpam-4570	48	37	x	x	X
ejpam-4570	48	38	,	,	PUNCT
ejpam-4570	48	39	t	t	PROPN
ejpam-4570	48	40	′	′	NUM
ejpam-4570	48	41	)	)	PUNCT
ejpam-4570	48	42	is	be	AUX
ejpam-4570	48	43	hausdorff	hausdorff	NOUN
ejpam-4570	48	44	almost	almost	ADV
ejpam-4570	48	45	normal	normal	ADJ
ejpam-4570	48	46	.	.	PUNCT
ejpam-4570	49	1	a	a	DET
ejpam-4570	49	2	space	space	NOUN
ejpam-4570	49	3	(	(	PUNCT
ejpam-4570	49	4	x	x	X
ejpam-4570	49	5	,	,	PUNCT
ejpam-4570	49	6	t	t	PROPN
ejpam-4570	49	7	)	)	PUNCT
ejpam-4570	49	8	is	be	AUX
ejpam-4570	49	9	said	say	VERB
ejpam-4570	49	10	to	to	PART
ejpam-4570	49	11	be	be	AUX
ejpam-4570	49	12	an	an	DET
ejpam-4570	49	13	epi	epi	ADJ
ejpam-4570	49	14	-	-	ADJ
ejpam-4570	49	15	regular	regular	ADJ
ejpam-4570	49	16	space	space	NOUN
ejpam-4570	49	17	[	[	X
ejpam-4570	49	18	7	7	NUM
ejpam-4570	49	19	]	]	PUNCT
ejpam-4570	49	20	,	,	PUNCT
ejpam-4570	49	21	if	if	SCONJ
ejpam-4570	49	22	there	there	PRON
ejpam-4570	49	23	exists	exist	VERB
ejpam-4570	49	24	a	a	DET
ejpam-4570	49	25	topology	topology	NOUN
ejpam-4570	49	26	t	t	NOUN
ejpam-4570	49	27	′	′	NUM
ejpam-4570	49	28	on	on	ADP
ejpam-4570	49	29	x	x	SYM
ejpam-4570	49	30	coarser	coarse	ADJ
ejpam-4570	49	31	than	than	ADP
ejpam-4570	49	32	t	t	NOUN
ejpam-4570	49	33	such	such	ADJ
ejpam-4570	49	34	that	that	SCONJ
ejpam-4570	49	35	(	(	PUNCT
ejpam-4570	49	36	x	x	X
ejpam-4570	49	37	,	,	PUNCT
ejpam-4570	49	38	t	t	PROPN
ejpam-4570	49	39	′	′	NUM
ejpam-4570	49	40	)	)	PUNCT
ejpam-4570	49	41	is	be	AUX
ejpam-4570	49	42	t3	t3	PROPN
ejpam-4570	49	43	(	(	PUNCT
ejpam-4570	49	44	regular	regular	ADJ
ejpam-4570	49	45	and	and	CCONJ
ejpam-4570	49	46	t1	t1	NOUN
ejpam-4570	49	47	)	)	PUNCT
ejpam-4570	49	48	.	.	PUNCT
ejpam-4570	50	1	a	a	DET
ejpam-4570	50	2	space	space	NOUN
ejpam-4570	50	3	(	(	PUNCT
ejpam-4570	50	4	x	x	X
ejpam-4570	50	5	,	,	PUNCT
ejpam-4570	50	6	t	t	PROPN
ejpam-4570	50	7	)	)	PUNCT
ejpam-4570	50	8	is	be	AUX
ejpam-4570	50	9	said	say	VERB
ejpam-4570	50	10	to	to	PART
ejpam-4570	50	11	be	be	AUX
ejpam-4570	50	12	an	an	DET
ejpam-4570	50	13	epi	epi	NOUN
ejpam-4570	50	14	-	-	ADJ
ejpam-4570	50	15	partially	partially	ADV
ejpam-4570	50	16	normal	normal	ADJ
ejpam-4570	50	17	space	space	NOUN
ejpam-4570	50	18	[	[	X
ejpam-4570	50	19	34	34	NUM
ejpam-4570	50	20	]	]	PUNCT
ejpam-4570	50	21	,	,	PUNCT
ejpam-4570	50	22	if	if	SCONJ
ejpam-4570	50	23	there	there	PRON
ejpam-4570	50	24	exists	exist	VERB
ejpam-4570	50	25	a	a	DET
ejpam-4570	50	26	topology	topology	NOUN
ejpam-4570	50	27	t	t	NOUN
ejpam-4570	50	28	′	′	NUM
ejpam-4570	50	29	on	on	ADP
ejpam-4570	50	30	x	x	SYM
ejpam-4570	50	31	coarser	coarse	ADJ
ejpam-4570	50	32	than	than	ADP
ejpam-4570	50	33	t	t	NOUN
ejpam-4570	50	34	such	such	ADJ
ejpam-4570	50	35	that	that	SCONJ
ejpam-4570	50	36	(	(	PUNCT
ejpam-4570	50	37	x	x	X
ejpam-4570	50	38	,	,	PUNCT
ejpam-4570	50	39	t	t	PROPN
ejpam-4570	50	40	′	′	NUM
ejpam-4570	50	41	)	)	PUNCT
ejpam-4570	50	42	is	be	AUX
ejpam-4570	50	43	hausdorff	hausdorff	NOUN
ejpam-4570	50	44	partially	partially	ADV
ejpam-4570	50	45	normal	normal	ADJ
ejpam-4570	50	46	.	.	PUNCT
ejpam-4570	51	1	a	a	DET
ejpam-4570	51	2	space	space	NOUN
ejpam-4570	51	3	(	(	PUNCT
ejpam-4570	51	4	x	x	X
ejpam-4570	51	5	,	,	PUNCT
ejpam-4570	51	6	t	t	PROPN
ejpam-4570	51	7	)	)	PUNCT
ejpam-4570	51	8	is	be	AUX
ejpam-4570	51	9	said	say	VERB
ejpam-4570	51	10	to	to	PART
ejpam-4570	51	11	be	be	AUX
ejpam-4570	51	12	an	an	DET
ejpam-4570	51	13	epi	epi	NOUN
ejpam-4570	51	14	-	-	ADJ
ejpam-4570	51	15	quasi	quasi	ADJ
ejpam-4570	51	16	normal	normal	ADJ
ejpam-4570	51	17	space	space	NOUN
ejpam-4570	51	18	[	[	X
ejpam-4570	51	19	33	33	NUM
ejpam-4570	51	20	]	]	PUNCT
ejpam-4570	51	21	,	,	PUNCT
ejpam-4570	51	22	if	if	SCONJ
ejpam-4570	51	23	there	there	PRON
ejpam-4570	51	24	exists	exist	VERB
ejpam-4570	51	25	a	a	DET
ejpam-4570	51	26	topology	topology	NOUN
ejpam-4570	51	27	t	t	NOUN
ejpam-4570	51	28	′	′	NUM
ejpam-4570	51	29	on	on	ADP
ejpam-4570	51	30	x	x	SYM
ejpam-4570	51	31	coarser	coarse	ADJ
ejpam-4570	51	32	than	than	ADP
ejpam-4570	51	33	t	t	NOUN
ejpam-4570	51	34	such	such	ADJ
ejpam-4570	51	35	that	that	SCONJ
ejpam-4570	51	36	(	(	PUNCT
ejpam-4570	51	37	x	x	X
ejpam-4570	51	38	,	,	PUNCT
ejpam-4570	51	39	t	t	PROPN
ejpam-4570	51	40	′	′	NUM
ejpam-4570	51	41	)	)	PUNCT
ejpam-4570	51	42	is	be	AUX
ejpam-4570	51	43	hausdorff	hausdorff	NOUN
ejpam-4570	51	44	quasi	quasi	X
ejpam-4570	51	45	normal	normal	ADJ
ejpam-4570	51	46	.	.	PUNCT
ejpam-4570	52	1	a	a	DET
ejpam-4570	52	2	space	space	NOUN
ejpam-4570	52	3	x	x	PUNCT
ejpam-4570	52	4	is	be	AUX
ejpam-4570	52	5	said	say	VERB
ejpam-4570	52	6	to	to	PART
ejpam-4570	52	7	be	be	AUX
ejpam-4570	52	8	hausdorff	hausdorff	NOUN
ejpam-4570	52	9	or	or	CCONJ
ejpam-4570	52	10	a	a	DET
ejpam-4570	52	11	t2	t2	NOUN
ejpam-4570	52	12	-	-	PUNCT
ejpam-4570	52	13	space	space	NOUN
ejpam-4570	52	14	,	,	PUNCT
ejpam-4570	52	15	if	if	SCONJ
ejpam-4570	52	16	for	for	ADP
ejpam-4570	52	17	each	each	PRON
ejpam-4570	52	18	distinct	distinct	ADJ
ejpam-4570	52	19	two	two	NUM
ejpam-4570	52	20	points	point	NOUN
ejpam-4570	52	21	x	x	X
ejpam-4570	52	22	,	,	PUNCT
ejpam-4570	52	23	y	y	PROPN
ejpam-4570	52	24	∈	∈	PROPN
ejpam-4570	52	25	x	x	PUNCT
ejpam-4570	52	26	there	there	PRON
ejpam-4570	52	27	exist	exist	VERB
ejpam-4570	52	28	two	two	NUM
ejpam-4570	52	29	open	open	ADJ
ejpam-4570	52	30	subsets	subset	NOUN
ejpam-4570	52	31	u	u	NOUN
ejpam-4570	52	32	and	and	CCONJ
ejpam-4570	52	33	v	v	NOUN
ejpam-4570	52	34	of	of	ADP
ejpam-4570	52	35	x	x	PUNCT
ejpam-4570	53	1	such	such	ADJ
ejpam-4570	53	2	that	that	SCONJ
ejpam-4570	53	3	x	x	SYM
ejpam-4570	53	4	∈	∈	PROPN
ejpam-4570	53	5	u	u	NOUN
ejpam-4570	53	6	,	,	PUNCT
ejpam-4570	53	7	y	y	PROPN
ejpam-4570	53	8	∈	∈	PROPN
ejpam-4570	53	9	v	v	NOUN
ejpam-4570	53	10	are	be	AUX
ejpam-4570	53	11	u	u	NOUN
ejpam-4570	53	12	∩	∩	ADJ
ejpam-4570	53	13	v	v	NOUN
ejpam-4570	53	14	=	=	NOUN
ejpam-4570	53	15	∅	∅	NOUN
ejpam-4570	53	16	[	[	X
ejpam-4570	53	17	12	12	NUM
ejpam-4570	53	18	]	]	PUNCT
ejpam-4570	53	19	.	.	PUNCT
ejpam-4570	54	1	a	a	DET
ejpam-4570	54	2	space	space	NOUN
ejpam-4570	54	3	x	x	PUNCT
ejpam-4570	54	4	is	be	AUX
ejpam-4570	54	5	said	say	VERB
ejpam-4570	54	6	to	to	PART
ejpam-4570	54	7	be	be	AUX
ejpam-4570	54	8	completely	completely	ADV
ejpam-4570	54	9	hausdorff	hausdorff	ADJ
ejpam-4570	54	10	or	or	CCONJ
ejpam-4570	54	11	urysohn	urysohn	NOUN
ejpam-4570	54	12	[	[	X
ejpam-4570	54	13	12	12	NUM
ejpam-4570	54	14	,	,	PUNCT
ejpam-4570	54	15	29	29	NUM
ejpam-4570	54	16	]	]	PUNCT
ejpam-4570	54	17	,	,	PUNCT
ejpam-4570	54	18	if	if	SCONJ
ejpam-4570	54	19	for	for	ADP
ejpam-4570	54	20	each	each	DET
ejpam-4570	54	21	distinct	distinct	ADJ
ejpam-4570	54	22	two	two	NUM
ejpam-4570	54	23	points	point	NOUN
ejpam-4570	54	24	x	x	X
ejpam-4570	54	25	,	,	PUNCT
ejpam-4570	54	26	y	y	PROPN
ejpam-4570	54	27	∈	∈	PROPN
ejpam-4570	54	28	x	x	PUNCT
ejpam-4570	54	29	there	there	PRON
ejpam-4570	54	30	exist	exist	VERB
ejpam-4570	54	31	two	two	NUM
ejpam-4570	54	32	open	open	ADJ
ejpam-4570	54	33	subsets	subset	NOUN
ejpam-4570	54	34	u	u	NOUN
ejpam-4570	54	35	and	and	CCONJ
ejpam-4570	54	36	v	v	NOUN
ejpam-4570	54	37	of	of	ADP
ejpam-4570	54	38	x	x	PUNCT
ejpam-4570	54	39	such	such	ADJ
ejpam-4570	54	40	that	that	SCONJ
ejpam-4570	54	41	x	x	SYM
ejpam-4570	54	42	∈	∈	PROPN
ejpam-4570	54	43	u	u	NOUN
ejpam-4570	54	44	,	,	PUNCT
ejpam-4570	54	45	y	y	PROPN
ejpam-4570	54	46	∈	∈	PROPN
ejpam-4570	54	47	v	v	NOUN
ejpam-4570	54	48	and	and	CCONJ
ejpam-4570	54	49	u	u	NOUN
ejpam-4570	54	50	∩	∩	NOUN
ejpam-4570	54	51	v	v	NOUN
ejpam-4570	54	52	=	=	PUNCT
ejpam-4570	54	53	∅.	∅.	ADP
ejpam-4570	54	54	a	a	DET
ejpam-4570	54	55	space	space	NOUN
ejpam-4570	54	56	x	x	PUNCT
ejpam-4570	54	57	is	be	AUX
ejpam-4570	54	58	said	say	VERB
ejpam-4570	54	59	to	to	PART
ejpam-4570	54	60	be	be	AUX
ejpam-4570	54	61	a	a	DET
ejpam-4570	54	62	sub	sub	ADJ
ejpam-4570	54	63	-	-	ADJ
ejpam-4570	54	64	metrizable	metrizable	ADJ
ejpam-4570	54	65	space	space	NOUN
ejpam-4570	55	1	[	[	X
ejpam-4570	55	2	13	13	NUM
ejpam-4570	55	3	]	]	PUNCT
ejpam-4570	55	4	,	,	PUNCT
ejpam-4570	55	5	if	if	SCONJ
ejpam-4570	55	6	there	there	PRON
ejpam-4570	55	7	exists	exist	VERB
ejpam-4570	55	8	a	a	DET
ejpam-4570	55	9	metric	metric	ADJ
ejpam-4570	55	10	d	d	NOUN
ejpam-4570	55	11	on	on	ADP
ejpam-4570	55	12	x	x	SYM
ejpam-4570	55	13	such	such	ADJ
ejpam-4570	55	14	that	that	SCONJ
ejpam-4570	55	15	the	the	DET
ejpam-4570	55	16	topology	topology	NOUN
ejpam-4570	55	17	td	td	NOUN
ejpam-4570	55	18	on	on	ADP
ejpam-4570	55	19	wafa	wafa	PROPN
ejpam-4570	55	20	khalaf	khalaf	PROPN
ejpam-4570	55	21	alqurashi	alqurashi	PROPN
ejpam-4570	55	22	,	,	PUNCT
ejpam-4570	55	23	sadeq	sadeq	PROPN
ejpam-4570	55	24	ali	ali	PROPN
ejpam-4570	55	25	thabit	thabit	PROPN
ejpam-4570	55	26	/	/	SYM
ejpam-4570	55	27	eur	eur	PROPN
ejpam-4570	55	28	.	.	PUNCT
ejpam-4570	56	1	j.	j.	PROPN
ejpam-4570	56	2	pure	pure	PROPN
ejpam-4570	56	3	appl	appl	PROPN
ejpam-4570	56	4	.	.	PROPN
ejpam-4570	56	5	math	math	PROPN
ejpam-4570	56	6	,	,	PUNCT
ejpam-4570	56	7	15	15	NUM
ejpam-4570	56	8	(	(	PUNCT
ejpam-4570	56	9	4	4	NUM
ejpam-4570	56	10	)	)	PUNCT
ejpam-4570	56	11	(	(	PUNCT
ejpam-4570	56	12	2022	2022	NUM
ejpam-4570	56	13	)	)	PUNCT
ejpam-4570	56	14	,	,	PUNCT
ejpam-4570	56	15	1760	1760	NUM
ejpam-4570	56	16	-	-	SYM
ejpam-4570	56	17	1782	1782	NUM
ejpam-4570	56	18	1762	1762	NUM
ejpam-4570	56	19	x	x	PUNCT
ejpam-4570	56	20	generated	generate	VERB
ejpam-4570	56	21	by	by	ADP
ejpam-4570	56	22	d	d	PROPN
ejpam-4570	56	23	is	be	AUX
ejpam-4570	56	24	coarser	coarse	ADJ
ejpam-4570	56	25	than	than	ADP
ejpam-4570	56	26	t	t	PROPN
ejpam-4570	56	27	.	.	PUNCT
ejpam-4570	57	1	a	a	DET
ejpam-4570	57	2	space	space	NOUN
ejpam-4570	57	3	x	x	PUNCT
ejpam-4570	57	4	is	be	AUX
ejpam-4570	57	5	called	call	VERB
ejpam-4570	57	6	a	a	DET
ejpam-4570	57	7	c	c	NOUN
ejpam-4570	57	8	-	-	ADJ
ejpam-4570	57	9	normal	normal	ADJ
ejpam-4570	57	10	[	[	X
ejpam-4570	57	11	10	10	NUM
ejpam-4570	57	12	]	]	PUNCT
ejpam-4570	57	13	,	,	PUNCT
ejpam-4570	57	14	(	(	PUNCT
ejpam-4570	57	15	resp	resp	NOUN
ejpam-4570	57	16	.	.	PUNCT
ejpam-4570	58	1	c	c	X
ejpam-4570	58	2	-	-	PUNCT
ejpam-4570	58	3	regular	regular	ADJ
ejpam-4570	58	4	[	[	X
ejpam-4570	58	5	8	8	NUM
ejpam-4570	58	6	]	]	PUNCT
ejpam-4570	58	7	;	;	PUNCT
ejpam-4570	58	8	c	c	X
ejpam-4570	58	9	-	-	PUNCT
ejpam-4570	58	10	tychonoff	tychonoff	NOUN
ejpam-4570	58	11	[	[	X
ejpam-4570	58	12	9	9	NUM
ejpam-4570	58	13	]	]	SYM
ejpam-4570	58	14	)	)	PUNCT
ejpam-4570	58	15	space	space	NOUN
ejpam-4570	58	16	if	if	SCONJ
ejpam-4570	58	17	there	there	PRON
ejpam-4570	58	18	exist	exist	VERB
ejpam-4570	58	19	a	a	DET
ejpam-4570	58	20	normal	normal	ADJ
ejpam-4570	58	21	(	(	PUNCT
ejpam-4570	58	22	resp	resp	NOUN
ejpam-4570	58	23	.	.	PUNCT
ejpam-4570	59	1	regular	regular	ADJ
ejpam-4570	59	2	,	,	PUNCT
ejpam-4570	59	3	tychonoff	tychonoff	NOUN
ejpam-4570	59	4	)	)	PUNCT
ejpam-4570	59	5	space	space	NOUN
ejpam-4570	59	6	y	y	PROPN
ejpam-4570	59	7	and	and	CCONJ
ejpam-4570	59	8	a	a	DET
ejpam-4570	59	9	bijective	bijective	ADJ
ejpam-4570	59	10	function	function	NOUN
ejpam-4570	59	11	f	f	NOUN
ejpam-4570	59	12	:	:	PUNCT
ejpam-4570	59	13	x	x	X
ejpam-4570	59	14	→	→	SYM
ejpam-4570	59	15	y	y	PROPN
ejpam-4570	59	16	such	such	ADJ
ejpam-4570	59	17	that	that	SCONJ
ejpam-4570	59	18	the	the	DET
ejpam-4570	59	19	restriction	restriction	NOUN
ejpam-4570	59	20	function	function	NOUN
ejpam-4570	59	21	f	f	PROPN
ejpam-4570	59	22	|a	|a	VERB
ejpam-4570	59	23	:	:	PUNCT
ejpam-4570	59	24	a	a	DET
ejpam-4570	59	25	→	→	SYM
ejpam-4570	59	26	f(a	f(a	NOUN
ejpam-4570	59	27	)	)	PUNCT
ejpam-4570	59	28	is	be	AUX
ejpam-4570	59	29	a	a	DET
ejpam-4570	59	30	homeomorphism	homeomorphism	NOUN
ejpam-4570	59	31	for	for	ADP
ejpam-4570	59	32	each	each	DET
ejpam-4570	59	33	compact	compact	ADJ
ejpam-4570	59	34	subspace	subspace	NOUN
ejpam-4570	59	35	a	a	DET
ejpam-4570	59	36	⊆	⊆	NUM
ejpam-4570	59	37	x.	x.	NOUN
ejpam-4570	59	38	a	a	DET
ejpam-4570	59	39	space	space	NOUN
ejpam-4570	59	40	x	x	PUNCT
ejpam-4570	59	41	is	be	AUX
ejpam-4570	59	42	called	call	VERB
ejpam-4570	59	43	an	an	DET
ejpam-4570	59	44	l	l	NOUN
ejpam-4570	59	45	-	-	ADJ
ejpam-4570	59	46	normal	normal	ADJ
ejpam-4570	59	47	[	[	X
ejpam-4570	59	48	16	16	NUM
ejpam-4570	59	49	]	]	PUNCT
ejpam-4570	59	50	(	(	PUNCT
ejpam-4570	59	51	resp	resp	NOUN
ejpam-4570	59	52	.	.	PUNCT
ejpam-4570	60	1	l	l	NOUN
ejpam-4570	60	2	-	-	NOUN
ejpam-4570	60	3	regular	regular	ADJ
ejpam-4570	60	4	[	[	X
ejpam-4570	60	5	8	8	NUM
ejpam-4570	60	6	]	]	PUNCT
ejpam-4570	60	7	,	,	PUNCT
ejpam-4570	60	8	l	l	NOUN
ejpam-4570	60	9	-	-	NOUN
ejpam-4570	60	10	tychonoff	tychonoff	NOUN
ejpam-4570	60	11	[	[	X
ejpam-4570	60	12	9	9	NUM
ejpam-4570	60	13	]	]	SYM
ejpam-4570	60	14	)	)	PUNCT
ejpam-4570	60	15	space	space	NOUN
ejpam-4570	60	16	if	if	SCONJ
ejpam-4570	60	17	there	there	PRON
ejpam-4570	60	18	exist	exist	VERB
ejpam-4570	60	19	a	a	DET
ejpam-4570	60	20	normal	normal	ADJ
ejpam-4570	60	21	(	(	PUNCT
ejpam-4570	60	22	resp	resp	NOUN
ejpam-4570	60	23	.	.	PUNCT
ejpam-4570	61	1	regular	regular	ADJ
ejpam-4570	61	2	,	,	PUNCT
ejpam-4570	61	3	tychonoff	tychonoff	NOUN
ejpam-4570	61	4	)	)	PUNCT
ejpam-4570	61	5	space	space	NOUN
ejpam-4570	61	6	y	y	PROPN
ejpam-4570	61	7	and	and	CCONJ
ejpam-4570	61	8	a	a	DET
ejpam-4570	61	9	bijective	bijective	ADJ
ejpam-4570	61	10	function	function	NOUN
ejpam-4570	61	11	f	f	NOUN
ejpam-4570	61	12	:	:	PUNCT
ejpam-4570	61	13	x	x	X
ejpam-4570	61	14	→	→	SYM
ejpam-4570	61	15	y	y	PROPN
ejpam-4570	61	16	such	such	ADJ
ejpam-4570	61	17	that	that	SCONJ
ejpam-4570	61	18	the	the	DET
ejpam-4570	61	19	restriction	restriction	NOUN
ejpam-4570	61	20	function	function	NOUN
ejpam-4570	61	21	f	f	PROPN
ejpam-4570	61	22	|a	|a	VERB
ejpam-4570	61	23	:	:	PUNCT
ejpam-4570	61	24	a	a	DET
ejpam-4570	61	25	→	→	SYM
ejpam-4570	61	26	f(a	f(a	NOUN
ejpam-4570	61	27	)	)	PUNCT
ejpam-4570	61	28	is	be	AUX
ejpam-4570	61	29	a	a	DET
ejpam-4570	61	30	homeomorphism	homeomorphism	NOUN
ejpam-4570	61	31	for	for	SCONJ
ejpam-4570	61	32	each	each	DET
ejpam-4570	61	33	lindelöf	lindelöf	NOUN
ejpam-4570	61	34	subspace	subspace	VERB
ejpam-4570	61	35	a	a	DET
ejpam-4570	61	36	⊆	⊆	NUM
ejpam-4570	61	37	x.	x.	NOUN
ejpam-4570	61	38	a	a	DET
ejpam-4570	61	39	space	space	NOUN
ejpam-4570	61	40	x	x	PUNCT
ejpam-4570	61	41	is	be	AUX
ejpam-4570	61	42	called	call	VERB
ejpam-4570	61	43	a	a	DET
ejpam-4570	61	44	c	c	NOUN
ejpam-4570	61	45	-	-	PUNCT
ejpam-4570	61	46	almost	almost	ADV
ejpam-4570	61	47	regular	regular	ADJ
ejpam-4570	61	48	(	(	PUNCT
ejpam-4570	61	49	resp	resp	NOUN
ejpam-4570	61	50	.	.	PUNCT
ejpam-4570	62	1	c	c	X
ejpam-4570	62	2	-	-	PUNCT
ejpam-4570	62	3	completely	completely	ADV
ejpam-4570	62	4	regular	regular	ADJ
ejpam-4570	62	5	,	,	PUNCT
ejpam-4570	62	6	c	c	NOUN
ejpam-4570	62	7	-	-	PUNCT
ejpam-4570	62	8	almost	almost	ADV
ejpam-4570	62	9	completely	completely	ADV
ejpam-4570	62	10	regular	regular	ADJ
ejpam-4570	62	11	,	,	PUNCT
ejpam-4570	62	12	c2	c2	PROPN
ejpam-4570	62	13	-	-	PUNCT
ejpam-4570	62	14	almost	almost	ADV
ejpam-4570	62	15	regular	regular	ADJ
ejpam-4570	62	16	,	,	PUNCT
ejpam-4570	62	17	c2	c2	PROPN
ejpam-4570	62	18	-	-	PUNCT
ejpam-4570	62	19	almost	almost	ADV
ejpam-4570	62	20	completely	completely	ADV
ejpam-4570	62	21	regular	regular	ADJ
ejpam-4570	62	22	)	)	PUNCT
ejpam-4570	62	23	space	space	NOUN
ejpam-4570	62	24	[	[	X
ejpam-4570	62	25	31	31	NUM
ejpam-4570	62	26	]	]	PUNCT
ejpam-4570	62	27	,	,	PUNCT
ejpam-4570	62	28	if	if	SCONJ
ejpam-4570	62	29	there	there	PRON
ejpam-4570	62	30	exist	exist	VERB
ejpam-4570	62	31	an	an	DET
ejpam-4570	62	32	almost	almost	ADV
ejpam-4570	62	33	regular	regular	ADJ
ejpam-4570	62	34	(	(	PUNCT
ejpam-4570	62	35	resp	resp	NOUN
ejpam-4570	62	36	.	.	PUNCT
ejpam-4570	63	1	completely	completely	ADV
ejpam-4570	63	2	regular	regular	ADJ
ejpam-4570	63	3	,	,	PUNCT
ejpam-4570	63	4	almost	almost	ADV
ejpam-4570	63	5	completely	completely	ADV
ejpam-4570	63	6	regular	regular	ADJ
ejpam-4570	63	7	,	,	PUNCT
ejpam-4570	63	8	hausdorff	hausdorff	NOUN
ejpam-4570	63	9	almost	almost	ADV
ejpam-4570	63	10	regular	regular	ADJ
ejpam-4570	63	11	,	,	PUNCT
ejpam-4570	63	12	hausdorff	hausdorff	NOUN
ejpam-4570	63	13	almost	almost	ADV
ejpam-4570	63	14	completely	completely	ADV
ejpam-4570	63	15	regular	regular	ADJ
ejpam-4570	63	16	)	)	PUNCT
ejpam-4570	63	17	space	space	NOUN
ejpam-4570	63	18	y	y	PROPN
ejpam-4570	63	19	and	and	CCONJ
ejpam-4570	63	20	a	a	DET
ejpam-4570	63	21	bijective	bijective	ADJ
ejpam-4570	63	22	function	function	NOUN
ejpam-4570	63	23	f	f	NOUN
ejpam-4570	64	1	:	:	PUNCT
ejpam-4570	64	2	x	x	X
ejpam-4570	64	3	→	→	SYM
ejpam-4570	64	4	y	y	PROPN
ejpam-4570	64	5	such	such	ADJ
ejpam-4570	64	6	that	that	SCONJ
ejpam-4570	64	7	the	the	DET
ejpam-4570	64	8	restriction	restriction	NOUN
ejpam-4570	64	9	function	function	NOUN
ejpam-4570	64	10	f	f	PROPN
ejpam-4570	64	11	|a	|a	VERB
ejpam-4570	64	12	:	:	PUNCT
ejpam-4570	64	13	a	a	DET
ejpam-4570	64	14	→	→	SYM
ejpam-4570	64	15	f(a	f(a	NOUN
ejpam-4570	64	16	)	)	PUNCT
ejpam-4570	64	17	is	be	AUX
ejpam-4570	64	18	a	a	DET
ejpam-4570	64	19	homeomorphism	homeomorphism	NOUN
ejpam-4570	64	20	for	for	ADP
ejpam-4570	64	21	each	each	DET
ejpam-4570	64	22	compact	compact	ADJ
ejpam-4570	64	23	subspace	subspace	NOUN
ejpam-4570	64	24	a	a	DET
ejpam-4570	64	25	⊆	⊆	NUM
ejpam-4570	64	26	x.	x.	NOUN
ejpam-4570	64	27	a	a	DET
ejpam-4570	64	28	space	space	NOUN
ejpam-4570	64	29	x	x	PUNCT
ejpam-4570	64	30	is	be	AUX
ejpam-4570	64	31	called	call	VERB
ejpam-4570	64	32	an	an	DET
ejpam-4570	64	33	l	l	NOUN
ejpam-4570	64	34	-	-	ADJ
ejpam-4570	64	35	almost	almost	ADV
ejpam-4570	64	36	regular	regular	ADJ
ejpam-4570	64	37	(	(	PUNCT
ejpam-4570	64	38	resp	resp	NOUN
ejpam-4570	64	39	.	.	PUNCT
ejpam-4570	65	1	l	l	NOUN
ejpam-4570	65	2	-	-	PUNCT
ejpam-4570	65	3	completely	completely	ADV
ejpam-4570	65	4	regular	regular	ADJ
ejpam-4570	65	5	,	,	PUNCT
ejpam-4570	65	6	l	l	NOUN
ejpam-4570	65	7	-	-	PUNCT
ejpam-4570	65	8	almost	almost	ADV
ejpam-4570	65	9	completely	completely	ADV
ejpam-4570	65	10	regular	regular	ADJ
ejpam-4570	65	11	,	,	PUNCT
ejpam-4570	65	12	l2	l2	NOUN
ejpam-4570	65	13	-	-	PUNCT
ejpam-4570	65	14	almost	almost	ADV
ejpam-4570	65	15	regular	regular	ADJ
ejpam-4570	65	16	,	,	PUNCT
ejpam-4570	65	17	l2	l2	NOUN
ejpam-4570	65	18	-	-	PUNCT
ejpam-4570	65	19	almost	almost	ADV
ejpam-4570	65	20	completely	completely	ADV
ejpam-4570	65	21	regular	regular	ADJ
ejpam-4570	65	22	)	)	PUNCT
ejpam-4570	65	23	space	space	NOUN
ejpam-4570	66	1	[	[	X
ejpam-4570	66	2	3	3	NUM
ejpam-4570	66	3	]	]	PUNCT
ejpam-4570	66	4	,	,	PUNCT
ejpam-4570	66	5	if	if	SCONJ
ejpam-4570	66	6	there	there	PRON
ejpam-4570	66	7	exist	exist	VERB
ejpam-4570	66	8	an	an	DET
ejpam-4570	66	9	almost	almost	ADV
ejpam-4570	66	10	regular	regular	ADJ
ejpam-4570	66	11	(	(	PUNCT
ejpam-4570	66	12	resp	resp	NOUN
ejpam-4570	66	13	.	.	PUNCT
ejpam-4570	67	1	completely	completely	ADV
ejpam-4570	67	2	regular	regular	ADJ
ejpam-4570	67	3	,	,	PUNCT
ejpam-4570	67	4	almost	almost	ADV
ejpam-4570	67	5	completely	completely	ADV
ejpam-4570	67	6	regular	regular	ADJ
ejpam-4570	67	7	,	,	PUNCT
ejpam-4570	67	8	hausdorff	hausdorff	NOUN
ejpam-4570	67	9	almost	almost	ADV
ejpam-4570	67	10	regular	regular	ADJ
ejpam-4570	67	11	,	,	PUNCT
ejpam-4570	67	12	hausdorff	hausdorff	NOUN
ejpam-4570	67	13	almost	almost	ADV
ejpam-4570	67	14	completely	completely	ADV
ejpam-4570	67	15	regular	regular	ADJ
ejpam-4570	67	16	)	)	PUNCT
ejpam-4570	67	17	space	space	NOUN
ejpam-4570	67	18	y	y	PROPN
ejpam-4570	67	19	and	and	CCONJ
ejpam-4570	67	20	a	a	DET
ejpam-4570	67	21	bijective	bijective	ADJ
ejpam-4570	67	22	function	function	NOUN
ejpam-4570	67	23	f	f	NOUN
ejpam-4570	68	1	:	:	PUNCT
ejpam-4570	68	2	x	x	X
ejpam-4570	68	3	→	→	SYM
ejpam-4570	68	4	y	y	PROPN
ejpam-4570	68	5	such	such	ADJ
ejpam-4570	68	6	that	that	SCONJ
ejpam-4570	68	7	the	the	DET
ejpam-4570	68	8	restriction	restriction	NOUN
ejpam-4570	68	9	function	function	NOUN
ejpam-4570	68	10	f	f	PROPN
ejpam-4570	68	11	|a	|a	VERB
ejpam-4570	68	12	:	:	PUNCT
ejpam-4570	68	13	a	a	DET
ejpam-4570	68	14	→	→	SYM
ejpam-4570	68	15	f(a	f(a	NOUN
ejpam-4570	68	16	)	)	PUNCT
ejpam-4570	68	17	is	be	AUX
ejpam-4570	68	18	a	a	DET
ejpam-4570	68	19	homeomorphism	homeomorphism	NOUN
ejpam-4570	68	20	for	for	SCONJ
ejpam-4570	68	21	each	each	DET
ejpam-4570	68	22	lindelöf	lindelöf	NOUN
ejpam-4570	68	23	subspace	subspace	VERB
ejpam-4570	68	24	a	a	DET
ejpam-4570	68	25	⊆	⊆	NUM
ejpam-4570	68	26	x.	x.	NOUN
ejpam-4570	68	27	a	a	DET
ejpam-4570	68	28	space	space	NOUN
ejpam-4570	68	29	x	x	PUNCT
ejpam-4570	68	30	is	be	AUX
ejpam-4570	68	31	called	call	VERB
ejpam-4570	68	32	a	a	DET
ejpam-4570	68	33	c	c	NOUN
ejpam-4570	68	34	-	-	PUNCT
ejpam-4570	68	35	quasi	quasi	ADJ
ejpam-4570	68	36	normal	normal	ADJ
ejpam-4570	68	37	(	(	PUNCT
ejpam-4570	68	38	resp	resp	NOUN
ejpam-4570	68	39	.	.	PUNCT
ejpam-4570	69	1	l	l	ADJ
ejpam-4570	69	2	-	-	ADJ
ejpam-4570	69	3	quasi	quasi	ADJ
ejpam-4570	69	4	normal	normal	ADJ
ejpam-4570	69	5	)	)	PUNCT
ejpam-4570	69	6	space	space	NOUN
ejpam-4570	69	7	[	[	X
ejpam-4570	69	8	32	32	NUM
ejpam-4570	69	9	]	]	PUNCT
ejpam-4570	69	10	,	,	PUNCT
ejpam-4570	69	11	if	if	SCONJ
ejpam-4570	69	12	there	there	PRON
ejpam-4570	69	13	exist	exist	VERB
ejpam-4570	69	14	a	a	DET
ejpam-4570	69	15	quasi	quasi	ADJ
ejpam-4570	69	16	normal	normal	ADJ
ejpam-4570	69	17	space	space	NOUN
ejpam-4570	69	18	y	y	PROPN
ejpam-4570	69	19	and	and	CCONJ
ejpam-4570	69	20	a	a	DET
ejpam-4570	69	21	bijective	bijective	ADJ
ejpam-4570	69	22	function	function	NOUN
ejpam-4570	70	1	f	f	NOUN
ejpam-4570	70	2	:	:	PUNCT
ejpam-4570	70	3	x	x	X
ejpam-4570	70	4	→	→	SYM
ejpam-4570	70	5	y	y	PROPN
ejpam-4570	70	6	such	such	ADJ
ejpam-4570	70	7	that	that	SCONJ
ejpam-4570	70	8	the	the	DET
ejpam-4570	70	9	restriction	restriction	NOUN
ejpam-4570	70	10	function	function	NOUN
ejpam-4570	70	11	f	f	PROPN
ejpam-4570	70	12	|a	|a	VERB
ejpam-4570	70	13	:	:	PUNCT
ejpam-4570	70	14	a	a	DET
ejpam-4570	70	15	→	→	SYM
ejpam-4570	70	16	f(a	f(a	NOUN
ejpam-4570	70	17	)	)	PUNCT
ejpam-4570	70	18	is	be	AUX
ejpam-4570	70	19	a	a	DET
ejpam-4570	70	20	homeomorphism	homeomorphism	NOUN
ejpam-4570	70	21	for	for	ADP
ejpam-4570	70	22	each	each	DET
ejpam-4570	70	23	compact	compact	ADJ
ejpam-4570	70	24	(	(	PUNCT
ejpam-4570	70	25	resp	resp	NOUN
ejpam-4570	70	26	.	.	PUNCT
ejpam-4570	71	1	lindelöf	lindelöf	PROPN
ejpam-4570	71	2	)	)	PUNCT
ejpam-4570	71	3	subspace	subspace	NOUN
ejpam-4570	71	4	a	a	DET
ejpam-4570	71	5	⊆	⊆	NUM
ejpam-4570	71	6	x.	x.	NOUN
ejpam-4570	71	7	the	the	DET
ejpam-4570	71	8	topology	topology	NOUN
ejpam-4570	71	9	on	on	ADP
ejpam-4570	71	10	x	x	PUNCT
ejpam-4570	71	11	generated	generate	VERB
ejpam-4570	71	12	by	by	ADP
ejpam-4570	71	13	the	the	DET
ejpam-4570	71	14	family	family	NOUN
ejpam-4570	71	15	of	of	ADP
ejpam-4570	71	16	all	all	DET
ejpam-4570	71	17	open	open	ADJ
ejpam-4570	71	18	domain	domain	NOUN
ejpam-4570	71	19	subsets	subset	NOUN
ejpam-4570	71	20	denoted	denote	VERB
ejpam-4570	71	21	by	by	ADP
ejpam-4570	71	22	ts	ts	X
ejpam-4570	71	23	is	be	AUX
ejpam-4570	71	24	coarser	coarse	ADJ
ejpam-4570	71	25	than	than	ADP
ejpam-4570	71	26	t	t	PROPN
ejpam-4570	71	27	and	and	CCONJ
ejpam-4570	71	28	(	(	PUNCT
ejpam-4570	71	29	x	x	NOUN
ejpam-4570	71	30	,	,	PUNCT
ejpam-4570	71	31	ts	ts	NOUN
ejpam-4570	71	32	)	)	PUNCT
ejpam-4570	71	33	is	be	AUX
ejpam-4570	71	34	called	call	VERB
ejpam-4570	71	35	the	the	DET
ejpam-4570	71	36	semi	semi	ADJ
ejpam-4570	71	37	regularization	regularization	NOUN
ejpam-4570	71	38	of	of	ADP
ejpam-4570	71	39	x.	x.	NOUN
ejpam-4570	71	40	a	a	DET
ejpam-4570	71	41	space	space	NOUN
ejpam-4570	71	42	(	(	PUNCT
ejpam-4570	71	43	x	x	X
ejpam-4570	71	44	,	,	PUNCT
ejpam-4570	71	45	t	t	PROPN
ejpam-4570	71	46	)	)	PUNCT
ejpam-4570	71	47	is	be	AUX
ejpam-4570	71	48	called	call	VERB
ejpam-4570	71	49	semi	semi	ADJ
ejpam-4570	71	50	-	-	ADJ
ejpam-4570	71	51	regular	regular	ADJ
ejpam-4570	71	52	if	if	SCONJ
ejpam-4570	71	53	t	t	NOUN
ejpam-4570	71	54	=	=	SYM
ejpam-4570	71	55	ts	ts	X
ejpam-4570	72	1	[	[	X
ejpam-4570	72	2	21	21	NUM
ejpam-4570	72	3	]	]	PUNCT
ejpam-4570	72	4	.	.	PUNCT
ejpam-4570	73	1	a	a	DET
ejpam-4570	73	2	space	space	NOUN
ejpam-4570	73	3	x	x	PUNCT
ejpam-4570	73	4	is	be	AUX
ejpam-4570	73	5	called	call	VERB
ejpam-4570	73	6	an	an	DET
ejpam-4570	73	7	h	h	NOUN
ejpam-4570	73	8	-	-	PUNCT
ejpam-4570	73	9	closed	close	VERB
ejpam-4570	73	10	space	space	NOUN
ejpam-4570	73	11	[	[	X
ejpam-4570	73	12	12	12	NUM
ejpam-4570	73	13	]	]	PUNCT
ejpam-4570	73	14	,	,	PUNCT
ejpam-4570	73	15	if	if	SCONJ
ejpam-4570	73	16	x	x	PRON
ejpam-4570	73	17	is	be	AUX
ejpam-4570	73	18	closed	close	VERB
ejpam-4570	73	19	in	in	ADP
ejpam-4570	73	20	every	every	DET
ejpam-4570	73	21	hausdorff	hausdorff	NOUN
ejpam-4570	73	22	space	space	NOUN
ejpam-4570	73	23	in	in	ADP
ejpam-4570	73	24	which	which	PRON
ejpam-4570	73	25	x	x	PRON
ejpam-4570	73	26	can	can	AUX
ejpam-4570	73	27	be	be	AUX
ejpam-4570	73	28	embedded	embed	VERB
ejpam-4570	73	29	or	or	CCONJ
ejpam-4570	73	30	x	x	ADJ
ejpam-4570	73	31	is	be	AUX
ejpam-4570	73	32	hausdorff	hausdorff	NOUN
ejpam-4570	73	33	almost	almost	ADV
ejpam-4570	73	34	compact	compact	ADJ
ejpam-4570	74	1	[	[	X
ejpam-4570	74	2	18	18	NUM
ejpam-4570	74	3	,	,	PUNCT
ejpam-4570	74	4	23	23	NUM
ejpam-4570	74	5	]	]	PUNCT
ejpam-4570	74	6	.	.	PUNCT
ejpam-4570	75	1	let	let	VERB
ejpam-4570	75	2	m	m	PRON
ejpam-4570	75	3	be	be	AUX
ejpam-4570	75	4	a	a	DET
ejpam-4570	75	5	non	non	ADJ
ejpam-4570	75	6	-	-	ADJ
ejpam-4570	75	7	empty	empty	ADJ
ejpam-4570	75	8	subset	subset	NOUN
ejpam-4570	75	9	of	of	ADP
ejpam-4570	75	10	a	a	DET
ejpam-4570	75	11	space	space	NOUN
ejpam-4570	75	12	(	(	PUNCT
ejpam-4570	75	13	x	x	X
ejpam-4570	75	14	,	,	PUNCT
ejpam-4570	75	15	t	t	PROPN
ejpam-4570	75	16	)	)	PUNCT
ejpam-4570	75	17	.	.	PUNCT
ejpam-4570	76	1	define	define	VERB
ejpam-4570	76	2	a	a	DET
ejpam-4570	76	3	topology	topology	NOUN
ejpam-4570	76	4	t(m	t(m	PROPN
ejpam-4570	76	5	)	)	PUNCT
ejpam-4570	76	6	on	on	ADP
ejpam-4570	76	7	x	x	PUNCT
ejpam-4570	76	8	as	as	SCONJ
ejpam-4570	76	9	follows	follow	VERB
ejpam-4570	76	10	:	:	PUNCT
ejpam-4570	76	11	t(m	t(m	PROPN
ejpam-4570	76	12	)	)	PUNCT
ejpam-4570	77	1	=	=	PRON
ejpam-4570	77	2	{	{	PUNCT
ejpam-4570	77	3	u	u	NOUN
ejpam-4570	77	4	∪k	∪k	PROPN
ejpam-4570	77	5	:	:	PUNCT
ejpam-4570	77	6	u	u	PROPN
ejpam-4570	77	7	∈	∈	PROPN
ejpam-4570	77	8	t	t	PROPN
ejpam-4570	77	9	and	and	CCONJ
ejpam-4570	77	10	k	k	PROPN
ejpam-4570	77	11	⊆	⊆	NUM
ejpam-4570	77	12	x	x	X
ejpam-4570	77	13	\m	\m	NOUN
ejpam-4570	77	14	}	}	PUNCT
ejpam-4570	77	15	.	.	PUNCT
ejpam-4570	78	1	then	then	ADV
ejpam-4570	78	2	,	,	PUNCT
ejpam-4570	78	3	(	(	PUNCT
ejpam-4570	78	4	x	x	NOUN
ejpam-4570	78	5	,	,	PUNCT
ejpam-4570	78	6	t(m	t(m	PROPN
ejpam-4570	78	7	)	)	PUNCT
ejpam-4570	78	8	)	)	PUNCT
ejpam-4570	78	9	is	be	AUX
ejpam-4570	78	10	called	call	VERB
ejpam-4570	78	11	a	a	DET
ejpam-4570	78	12	discrete	discrete	ADJ
ejpam-4570	78	13	extension	extension	NOUN
ejpam-4570	78	14	of	of	ADP
ejpam-4570	78	15	(	(	PUNCT
ejpam-4570	78	16	x	x	PROPN
ejpam-4570	78	17	,	,	PUNCT
ejpam-4570	78	18	t	t	PROPN
ejpam-4570	78	19	)	)	PUNCT
ejpam-4570	78	20	denoted	denote	VERB
ejpam-4570	78	21	by	by	ADP
ejpam-4570	78	22	xm	xm	PROPN
ejpam-4570	78	23	,	,	PUNCT
ejpam-4570	78	24	where	where	SCONJ
ejpam-4570	78	25	td	td	NOUN
ejpam-4570	78	26	⊆	⊆	NUM
ejpam-4570	78	27	t	t	NOUN
ejpam-4570	78	28	⊆	⊆	NUM
ejpam-4570	78	29	t(m	t(m	PROPN
ejpam-4570	78	30	)	)	PUNCT
ejpam-4570	78	31	,	,	PUNCT
ejpam-4570	78	32	see	see	VERB
ejpam-4570	78	33	[	[	X
ejpam-4570	78	34	2	2	NUM
ejpam-4570	78	35	]	]	PUNCT
ejpam-4570	78	36	.	.	PUNCT
ejpam-4570	79	1	let	let	AUX
ejpam-4570	79	2	(	(	PUNCT
ejpam-4570	79	3	x	x	X
ejpam-4570	79	4	,	,	PUNCT
ejpam-4570	79	5	t	t	PROPN
ejpam-4570	79	6	)	)	PUNCT
ejpam-4570	79	7	be	be	AUX
ejpam-4570	79	8	a	a	DET
ejpam-4570	79	9	space	space	NOUN
ejpam-4570	79	10	and	and	CCONJ
ejpam-4570	79	11	p	p	PROPN
ejpam-4570	79	12	̸∈	̸∈	PROPN
ejpam-4570	79	13	x.	x.	PROPN
ejpam-4570	79	14	put	put	VERB
ejpam-4570	79	15	xp	xp	NOUN
ejpam-4570	80	1	=	=	NOUN
ejpam-4570	80	2	x	x	SYM
ejpam-4570	80	3	∪	∪	X
ejpam-4570	80	4	{	{	PUNCT
ejpam-4570	80	5	p	p	NOUN
ejpam-4570	80	6	}	}	PUNCT
ejpam-4570	80	7	.	.	PUNCT
ejpam-4570	81	1	define	define	VERB
ejpam-4570	81	2	a	a	DET
ejpam-4570	81	3	topology	topology	NOUN
ejpam-4570	81	4	t	t	NOUN
ejpam-4570	81	5	∗	∗	NOUN
ejpam-4570	81	6	on	on	ADP
ejpam-4570	81	7	xp	xp	INTJ
ejpam-4570	81	8	by	by	ADP
ejpam-4570	81	9	:	:	PUNCT
ejpam-4570	81	10	t	t	NOUN
ejpam-4570	81	11	∗	∗	NOUN
ejpam-4570	81	12	=	=	PUNCT
ejpam-4570	81	13	{	{	PUNCT
ejpam-4570	81	14	u	u	NOUN
ejpam-4570	81	15	∪	∪	X
ejpam-4570	81	16	{	{	PUNCT
ejpam-4570	81	17	p	p	NOUN
ejpam-4570	81	18	}	}	PUNCT
ejpam-4570	81	19	:	:	PUNCT
ejpam-4570	81	20	u	u	PROPN
ejpam-4570	81	21	∈	∈	PROPN
ejpam-4570	81	22	t	t	PROPN
ejpam-4570	81	23	}	}	PUNCT
ejpam-4570	81	24	∪	∪	VERB
ejpam-4570	81	25	{	{	PUNCT
ejpam-4570	81	26	∅	∅	NOUN
ejpam-4570	81	27	}	}	PUNCT
ejpam-4570	81	28	.	.	PUNCT
ejpam-4570	82	1	the	the	DET
ejpam-4570	82	2	space	space	NOUN
ejpam-4570	82	3	(	(	PUNCT
ejpam-4570	82	4	xp	xp	INTJ
ejpam-4570	82	5	,	,	PUNCT
ejpam-4570	82	6	t	t	PROPN
ejpam-4570	82	7	∗	∗	NOUN
ejpam-4570	82	8	)	)	PUNCT
ejpam-4570	82	9	is	be	AUX
ejpam-4570	82	10	called	call	VERB
ejpam-4570	82	11	the	the	DET
ejpam-4570	82	12	closed	closed	ADJ
ejpam-4570	82	13	extension	extension	NOUN
ejpam-4570	82	14	of	of	ADP
ejpam-4570	82	15	(	(	PUNCT
ejpam-4570	82	16	x	x	PROPN
ejpam-4570	82	17	,	,	PUNCT
ejpam-4570	82	18	t	t	PROPN
ejpam-4570	82	19	)	)	PUNCT
ejpam-4570	82	20	,	,	PUNCT
ejpam-4570	82	21	[	[	X
ejpam-4570	82	22	29	29	NUM
ejpam-4570	82	23	,	,	PUNCT
ejpam-4570	82	24	example	example	NOUN
ejpam-4570	82	25	12	12	NUM
ejpam-4570	82	26	]	]	PUNCT
ejpam-4570	82	27	,	,	PUNCT
ejpam-4570	82	28	see	see	VERB
ejpam-4570	82	29	[	[	X
ejpam-4570	82	30	1	1	NUM
ejpam-4570	82	31	]	]	PUNCT
ejpam-4570	82	32	.	.	PUNCT
ejpam-4570	83	1	2	2	X
ejpam-4570	83	2	.	.	X
ejpam-4570	83	3	preliminaries	preliminary	NOUN
ejpam-4570	83	4	first	first	ADV
ejpam-4570	83	5	,	,	PUNCT
ejpam-4570	83	6	we	we	PRON
ejpam-4570	83	7	give	give	VERB
ejpam-4570	83	8	the	the	DET
ejpam-4570	83	9	main	main	ADJ
ejpam-4570	83	10	definitions	definition	NOUN
ejpam-4570	83	11	of	of	ADP
ejpam-4570	83	12	this	this	DET
ejpam-4570	83	13	work	work	NOUN
ejpam-4570	83	14	:	:	PUNCT
ejpam-4570	83	15	definition	definition	NOUN
ejpam-4570	83	16	1	1	NUM
ejpam-4570	83	17	.	.	PUNCT
ejpam-4570	84	1	let	let	VERB
ejpam-4570	84	2	x	x	PRON
ejpam-4570	84	3	be	be	AUX
ejpam-4570	84	4	a	a	DET
ejpam-4570	84	5	space	space	NOUN
ejpam-4570	84	6	.	.	PUNCT
ejpam-4570	85	1	(	(	PUNCT
ejpam-4570	85	2	1	1	X
ejpam-4570	85	3	)	)	PUNCT
ejpam-4570	85	4	a	a	DET
ejpam-4570	85	5	space	space	NOUN
ejpam-4570	85	6	x	x	PUNCT
ejpam-4570	85	7	is	be	AUX
ejpam-4570	85	8	called	call	VERB
ejpam-4570	85	9	a	a	DET
ejpam-4570	85	10	c	c	NOUN
ejpam-4570	85	11	-	-	PUNCT
ejpam-4570	85	12	almost	almost	ADV
ejpam-4570	85	13	normal	normal	ADJ
ejpam-4570	85	14	space	space	NOUN
ejpam-4570	85	15	if	if	SCONJ
ejpam-4570	85	16	there	there	PRON
ejpam-4570	85	17	exist	exist	VERB
ejpam-4570	85	18	an	an	DET
ejpam-4570	85	19	almost	almost	ADV
ejpam-4570	85	20	normal	normal	ADJ
ejpam-4570	85	21	space	space	NOUN
ejpam-4570	85	22	y	y	PROPN
ejpam-4570	85	23	and	and	CCONJ
ejpam-4570	85	24	a	a	DET
ejpam-4570	85	25	bijective	bijective	ADJ
ejpam-4570	85	26	function	function	NOUN
ejpam-4570	86	1	f	f	NOUN
ejpam-4570	86	2	:	:	PUNCT
ejpam-4570	86	3	x	x	X
ejpam-4570	86	4	→	→	SYM
ejpam-4570	86	5	y	y	PROPN
ejpam-4570	86	6	such	such	ADJ
ejpam-4570	86	7	that	that	SCONJ
ejpam-4570	86	8	the	the	DET
ejpam-4570	86	9	restriction	restriction	NOUN
ejpam-4570	86	10	function	function	NOUN
ejpam-4570	86	11	f	f	PROPN
ejpam-4570	86	12	|a	|a	VERB
ejpam-4570	86	13	:	:	PUNCT
ejpam-4570	86	14	a	a	DET
ejpam-4570	86	15	→	→	SYM
ejpam-4570	86	16	f(a	f(a	NOUN
ejpam-4570	86	17	)	)	PUNCT
ejpam-4570	86	18	is	be	AUX
ejpam-4570	86	19	a	a	DET
ejpam-4570	86	20	homeomorphism	homeomorphism	NOUN
ejpam-4570	86	21	for	for	ADP
ejpam-4570	86	22	each	each	DET
ejpam-4570	86	23	compact	compact	ADJ
ejpam-4570	86	24	subspace	subspace	NOUN
ejpam-4570	86	25	a	a	DET
ejpam-4570	86	26	⊆	⊆	NUM
ejpam-4570	86	27	x.	x.	NOUN
ejpam-4570	86	28	(	(	PUNCT
ejpam-4570	86	29	2	2	NUM
ejpam-4570	86	30	)	)	PUNCT
ejpam-4570	86	31	a	a	DET
ejpam-4570	86	32	space	space	NOUN
ejpam-4570	86	33	x	x	PUNCT
ejpam-4570	86	34	is	be	AUX
ejpam-4570	86	35	called	call	VERB
ejpam-4570	86	36	an	an	DET
ejpam-4570	86	37	l	l	NOUN
ejpam-4570	86	38	-	-	ADJ
ejpam-4570	86	39	almost	almost	ADV
ejpam-4570	86	40	normal	normal	ADJ
ejpam-4570	86	41	space	space	NOUN
ejpam-4570	86	42	if	if	SCONJ
ejpam-4570	86	43	there	there	PRON
ejpam-4570	86	44	exist	exist	VERB
ejpam-4570	86	45	an	an	DET
ejpam-4570	86	46	almost	almost	ADV
ejpam-4570	86	47	normal	normal	ADJ
ejpam-4570	86	48	space	space	NOUN
ejpam-4570	86	49	y	y	PROPN
ejpam-4570	86	50	and	and	CCONJ
ejpam-4570	86	51	a	a	DET
ejpam-4570	86	52	bijective	bijective	ADJ
ejpam-4570	86	53	function	function	NOUN
ejpam-4570	87	1	f	f	NOUN
ejpam-4570	87	2	:	:	PUNCT
ejpam-4570	87	3	x	x	X
ejpam-4570	87	4	→	→	SYM
ejpam-4570	87	5	y	y	PROPN
ejpam-4570	87	6	such	such	ADJ
ejpam-4570	87	7	that	that	SCONJ
ejpam-4570	87	8	the	the	DET
ejpam-4570	87	9	restriction	restriction	NOUN
ejpam-4570	87	10	function	function	NOUN
ejpam-4570	87	11	f	f	PROPN
ejpam-4570	87	12	|a	|a	VERB
ejpam-4570	87	13	:	:	PUNCT
ejpam-4570	87	14	a	a	DET
ejpam-4570	87	15	→	→	SYM
ejpam-4570	87	16	f(a	f(a	NOUN
ejpam-4570	87	17	)	)	PUNCT
ejpam-4570	87	18	is	be	AUX
ejpam-4570	87	19	a	a	DET
ejpam-4570	87	20	homeomorphism	homeomorphism	NOUN
ejpam-4570	87	21	for	for	SCONJ
ejpam-4570	87	22	each	each	DET
ejpam-4570	87	23	lindelöf	lindelöf	NOUN
ejpam-4570	87	24	subspace	subspace	VERB
ejpam-4570	87	25	a	a	DET
ejpam-4570	87	26	⊆	⊆	NUM
ejpam-4570	87	27	x.	x.	NOUN
ejpam-4570	87	28	wafa	wafa	PROPN
ejpam-4570	87	29	khalaf	khalaf	PROPN
ejpam-4570	87	30	alqurashi	alqurashi	PROPN
ejpam-4570	87	31	,	,	PUNCT
ejpam-4570	87	32	sadeq	sadeq	PROPN
ejpam-4570	87	33	ali	ali	PROPN
ejpam-4570	87	34	thabit	thabit	PROPN
ejpam-4570	87	35	/	/	SYM
ejpam-4570	87	36	eur	eur	PROPN
ejpam-4570	87	37	.	.	PUNCT
ejpam-4570	88	1	j.	j.	PROPN
ejpam-4570	88	2	pure	pure	PROPN
ejpam-4570	88	3	appl	appl	PROPN
ejpam-4570	88	4	.	.	PROPN
ejpam-4570	88	5	math	math	PROPN
ejpam-4570	88	6	,	,	PUNCT
ejpam-4570	88	7	15	15	NUM
ejpam-4570	88	8	(	(	PUNCT
ejpam-4570	88	9	4	4	NUM
ejpam-4570	88	10	)	)	PUNCT
ejpam-4570	88	11	(	(	PUNCT
ejpam-4570	88	12	2022	2022	NUM
ejpam-4570	88	13	)	)	PUNCT
ejpam-4570	88	14	,	,	PUNCT
ejpam-4570	88	15	1760	1760	NUM
ejpam-4570	88	16	-	-	SYM
ejpam-4570	88	17	1782	1782	NUM
ejpam-4570	88	18	1763	1763	NUM
ejpam-4570	88	19	from	from	ADP
ejpam-4570	88	20	definition	definition	NOUN
ejpam-4570	88	21	1	1	NUM
ejpam-4570	88	22	,	,	PUNCT
ejpam-4570	88	23	it	it	PRON
ejpam-4570	88	24	is	be	AUX
ejpam-4570	88	25	clear	clear	ADJ
ejpam-4570	88	26	that	that	SCONJ
ejpam-4570	88	27	every	every	DET
ejpam-4570	88	28	almost	almost	ADV
ejpam-4570	88	29	normal	normal	ADJ
ejpam-4570	88	30	space	space	NOUN
ejpam-4570	88	31	is	be	AUX
ejpam-4570	88	32	both	both	PRON
ejpam-4570	88	33	c	c	NOUN
ejpam-4570	88	34	-	-	PUNCT
ejpam-4570	88	35	almost	almost	ADV
ejpam-4570	88	36	normal	normal	ADJ
ejpam-4570	88	37	and	and	CCONJ
ejpam-4570	88	38	l	l	NOUN
ejpam-4570	88	39	-	-	PUNCT
ejpam-4570	88	40	almost	almost	ADV
ejpam-4570	88	41	normal	normal	ADJ
ejpam-4570	88	42	,	,	PUNCT
ejpam-4570	88	43	because	because	SCONJ
ejpam-4570	88	44	y	y	PROPN
ejpam-4570	88	45	=	=	PUNCT
ejpam-4570	88	46	x	x	X
ejpam-4570	88	47	and	and	CCONJ
ejpam-4570	88	48	the	the	DET
ejpam-4570	88	49	identity	identity	NOUN
ejpam-4570	88	50	function	function	NOUN
ejpam-4570	88	51	f	f	NOUN
ejpam-4570	88	52	:	:	PUNCT
ejpam-4570	88	53	x	x	X
ejpam-4570	88	54	→	→	PUNCT
ejpam-4570	88	55	x	x	AUX
ejpam-4570	88	56	satisfy	satisfy	VERB
ejpam-4570	88	57	the	the	DET
ejpam-4570	88	58	requirements	requirement	NOUN
ejpam-4570	88	59	.	.	PUNCT
ejpam-4570	89	1	next	next	ADV
ejpam-4570	89	2	,	,	PUNCT
ejpam-4570	89	3	we	we	PRON
ejpam-4570	89	4	present	present	VERB
ejpam-4570	89	5	the	the	DET
ejpam-4570	89	6	following	following	ADJ
ejpam-4570	89	7	basic	basic	ADJ
ejpam-4570	89	8	results	result	NOUN
ejpam-4570	89	9	:	:	PUNCT
ejpam-4570	89	10	theorem	theorem	NOUN
ejpam-4570	89	11	1	1	NUM
ejpam-4570	89	12	.	.	PUNCT
ejpam-4570	90	1	every	every	DET
ejpam-4570	90	2	c	c	NOUN
ejpam-4570	90	3	-	-	ADJ
ejpam-4570	90	4	normal	normal	ADJ
ejpam-4570	90	5	space	space	NOUN
ejpam-4570	90	6	is	be	AUX
ejpam-4570	90	7	c	c	NOUN
ejpam-4570	90	8	-	-	PUNCT
ejpam-4570	90	9	almost	almost	ADV
ejpam-4570	90	10	normal	normal	ADJ
ejpam-4570	90	11	.	.	PUNCT
ejpam-4570	91	1	proof	proof	NOUN
ejpam-4570	91	2	.	.	PUNCT
ejpam-4570	92	1	let	let	VERB
ejpam-4570	92	2	x	x	PRON
ejpam-4570	92	3	be	be	AUX
ejpam-4570	92	4	a	a	DET
ejpam-4570	92	5	c	c	NOUN
ejpam-4570	92	6	-	-	ADJ
ejpam-4570	92	7	normal	normal	ADJ
ejpam-4570	92	8	space	space	NOUN
ejpam-4570	92	9	.	.	PUNCT
ejpam-4570	93	1	then	then	ADV
ejpam-4570	93	2	,	,	PUNCT
ejpam-4570	93	3	there	there	PRON
ejpam-4570	93	4	exist	exist	VERB
ejpam-4570	93	5	a	a	DET
ejpam-4570	93	6	normal	normal	ADJ
ejpam-4570	93	7	space	space	NOUN
ejpam-4570	93	8	y	y	PROPN
ejpam-4570	93	9	and	and	CCONJ
ejpam-4570	93	10	a	a	DET
ejpam-4570	93	11	bijective	bijective	ADJ
ejpam-4570	93	12	function	function	NOUN
ejpam-4570	93	13	f	f	NOUN
ejpam-4570	94	1	:	:	PUNCT
ejpam-4570	94	2	x	x	X
ejpam-4570	94	3	→	→	SYM
ejpam-4570	94	4	y	y	PROPN
ejpam-4570	94	5	such	such	ADJ
ejpam-4570	94	6	that	that	SCONJ
ejpam-4570	94	7	the	the	DET
ejpam-4570	94	8	restriction	restriction	NOUN
ejpam-4570	94	9	function	function	NOUN
ejpam-4570	94	10	f	f	PROPN
ejpam-4570	94	11	|c	|c	VERB
ejpam-4570	94	12	:	:	PUNCT
ejpam-4570	94	13	c	c	PROPN
ejpam-4570	94	14	→	→	SYM
ejpam-4570	94	15	f(c	f(c	PROPN
ejpam-4570	94	16	)	)	PUNCT
ejpam-4570	94	17	is	be	AUX
ejpam-4570	94	18	a	a	DET
ejpam-4570	94	19	homeomorphism	homeomorphism	NOUN
ejpam-4570	94	20	for	for	ADP
ejpam-4570	94	21	each	each	DET
ejpam-4570	94	22	compact	compact	ADJ
ejpam-4570	94	23	subspace	subspace	NOUN
ejpam-4570	94	24	c	c	PROPN
ejpam-4570	94	25	⊆	⊆	NUM
ejpam-4570	94	26	x.	x.	NOUN
ejpam-4570	94	27	since	since	SCONJ
ejpam-4570	94	28	y	y	PROPN
ejpam-4570	94	29	is	be	AUX
ejpam-4570	94	30	a	a	DET
ejpam-4570	94	31	normal	normal	ADJ
ejpam-4570	94	32	space	space	NOUN
ejpam-4570	94	33	,	,	PUNCT
ejpam-4570	94	34	we	we	PRON
ejpam-4570	94	35	have	have	VERB
ejpam-4570	94	36	y	y	PROPN
ejpam-4570	94	37	is	be	AUX
ejpam-4570	94	38	almost	almost	ADV
ejpam-4570	94	39	normal	normal	ADJ
ejpam-4570	94	40	.	.	PUNCT
ejpam-4570	95	1	therefore	therefore	ADV
ejpam-4570	95	2	,	,	PUNCT
ejpam-4570	95	3	x	x	X
ejpam-4570	95	4	is	be	AUX
ejpam-4570	95	5	c	c	NOUN
ejpam-4570	95	6	-	-	PUNCT
ejpam-4570	95	7	almost	almost	ADV
ejpam-4570	95	8	normal	normal	ADJ
ejpam-4570	95	9	.	.	PUNCT
ejpam-4570	96	1	the	the	DET
ejpam-4570	96	2	converse	converse	NOUN
ejpam-4570	96	3	of	of	ADP
ejpam-4570	96	4	theorem	theorem	NOUN
ejpam-4570	96	5	1	1	NUM
ejpam-4570	96	6	is	be	AUX
ejpam-4570	96	7	not	not	PART
ejpam-4570	96	8	necessary	necessary	ADJ
ejpam-4570	96	9	to	to	PART
ejpam-4570	96	10	be	be	AUX
ejpam-4570	96	11	true	true	ADJ
ejpam-4570	96	12	in	in	ADP
ejpam-4570	96	13	general	general	ADJ
ejpam-4570	96	14	.	.	PUNCT
ejpam-4570	97	1	for	for	ADP
ejpam-4570	97	2	example	example	NOUN
ejpam-4570	97	3	,	,	PUNCT
ejpam-4570	97	4	the	the	DET
ejpam-4570	97	5	finite	finite	ADJ
ejpam-4570	97	6	complement	complement	NOUN
ejpam-4570	97	7	topology	topology	NOUN
ejpam-4570	97	8	(	(	PUNCT
ejpam-4570	97	9	r	r	NOUN
ejpam-4570	97	10	,	,	PUNCT
ejpam-4570	97	11	cf	cf	NOUN
ejpam-4570	97	12	)	)	PUNCT
ejpam-4570	97	13	,	,	PUNCT
ejpam-4570	97	14	example	example	NOUN
ejpam-4570	97	15	3	3	NUM
ejpam-4570	97	16	,	,	PUNCT
ejpam-4570	97	17	is	be	AUX
ejpam-4570	97	18	a	a	DET
ejpam-4570	97	19	c	c	NOUN
ejpam-4570	97	20	-	-	PUNCT
ejpam-4570	97	21	almost	almost	ADV
ejpam-4570	97	22	normal	normal	ADJ
ejpam-4570	97	23	space	space	NOUN
ejpam-4570	97	24	,	,	PUNCT
ejpam-4570	97	25	which	which	PRON
ejpam-4570	97	26	is	be	AUX
ejpam-4570	97	27	not	not	PART
ejpam-4570	97	28	c	c	NOUN
ejpam-4570	97	29	-	-	NOUN
ejpam-4570	97	30	normal	normal	ADJ
ejpam-4570	97	31	.	.	PUNCT
ejpam-4570	98	1	the	the	DET
ejpam-4570	98	2	deleted	delete	VERB
ejpam-4570	98	3	tychonoff	tychonoff	NOUN
ejpam-4570	98	4	plank	plank	NOUN
ejpam-4570	98	5	topology	topology	NOUN
ejpam-4570	98	6	,	,	PUNCT
ejpam-4570	98	7	example	example	NOUN
ejpam-4570	98	8	6	6	NUM
ejpam-4570	98	9	,	,	PUNCT
ejpam-4570	98	10	is	be	AUX
ejpam-4570	98	11	an	an	DET
ejpam-4570	98	12	example	example	NOUN
ejpam-4570	98	13	of	of	ADP
ejpam-4570	98	14	a	a	DET
ejpam-4570	98	15	c	c	NOUN
ejpam-4570	98	16	-	-	PUNCT
ejpam-4570	98	17	almost	almost	ADV
ejpam-4570	98	18	normal	normal	ADJ
ejpam-4570	98	19	space	space	NOUN
ejpam-4570	98	20	,	,	PUNCT
ejpam-4570	98	21	which	which	PRON
ejpam-4570	98	22	is	be	AUX
ejpam-4570	98	23	not	not	PART
ejpam-4570	98	24	almost	almost	ADV
ejpam-4570	98	25	normal	normal	ADJ
ejpam-4570	98	26	.	.	PUNCT
ejpam-4570	99	1	the	the	DET
ejpam-4570	99	2	modified	modify	VERB
ejpam-4570	99	3	dieudonné	dieudonné	NOUN
ejpam-4570	99	4	plank	plank	NOUN
ejpam-4570	99	5	,	,	PUNCT
ejpam-4570	99	6	example	example	NOUN
ejpam-4570	99	7	8	8	NUM
ejpam-4570	99	8	,	,	PUNCT
ejpam-4570	99	9	is	be	AUX
ejpam-4570	99	10	an	an	DET
ejpam-4570	99	11	l	l	NOUN
ejpam-4570	99	12	-	-	ADJ
ejpam-4570	99	13	almost	almost	ADV
ejpam-4570	99	14	normal	normal	ADJ
ejpam-4570	99	15	space	space	NOUN
ejpam-4570	99	16	,	,	PUNCT
ejpam-4570	99	17	which	which	PRON
ejpam-4570	99	18	is	be	AUX
ejpam-4570	99	19	not	not	PART
ejpam-4570	99	20	almost	almost	ADV
ejpam-4570	99	21	normal	normal	ADJ
ejpam-4570	99	22	.	.	PUNCT
ejpam-4570	100	1	since	since	SCONJ
ejpam-4570	100	2	every	every	DET
ejpam-4570	100	3	sub	sub	ADJ
ejpam-4570	100	4	-	-	ADJ
ejpam-4570	100	5	metrizable	metrizable	ADJ
ejpam-4570	100	6	space	space	NOUN
ejpam-4570	100	7	is	be	AUX
ejpam-4570	100	8	epi	epi	NOUN
ejpam-4570	100	9	-	-	ADJ
ejpam-4570	100	10	normal	normal	ADJ
ejpam-4570	100	11	and	and	CCONJ
ejpam-4570	100	12	every	every	DET
ejpam-4570	100	13	epi	epi	ADJ
ejpam-4570	100	14	-	-	ADJ
ejpam-4570	100	15	normal	normal	ADJ
ejpam-4570	100	16	space	space	NOUN
ejpam-4570	100	17	is	be	AUX
ejpam-4570	100	18	c	c	NOUN
ejpam-4570	100	19	-	-	ADJ
ejpam-4570	100	20	normal	normal	ADJ
ejpam-4570	100	21	[	[	X
ejpam-4570	100	22	10	10	NUM
ejpam-4570	100	23	]	]	PUNCT
ejpam-4570	100	24	,	,	PUNCT
ejpam-4570	100	25	we	we	PRON
ejpam-4570	100	26	get	get	VERB
ejpam-4570	100	27	the	the	DET
ejpam-4570	100	28	following	follow	VERB
ejpam-4570	100	29	corollary	corollary	ADJ
ejpam-4570	100	30	:	:	PUNCT
ejpam-4570	100	31	corollary	corollary	ADJ
ejpam-4570	100	32	1	1	NUM
ejpam-4570	100	33	.	.	PUNCT
ejpam-4570	101	1	(	(	PUNCT
ejpam-4570	101	2	1	1	X
ejpam-4570	101	3	)	)	PUNCT
ejpam-4570	101	4	every	every	DET
ejpam-4570	101	5	sub	sub	ADJ
ejpam-4570	101	6	-	-	ADJ
ejpam-4570	101	7	metrizable	metrizable	ADJ
ejpam-4570	101	8	space	space	NOUN
ejpam-4570	101	9	is	be	AUX
ejpam-4570	101	10	c	c	NOUN
ejpam-4570	101	11	-	-	PUNCT
ejpam-4570	101	12	almost	almost	ADV
ejpam-4570	101	13	normal	normal	ADJ
ejpam-4570	101	14	.	.	PUNCT
ejpam-4570	102	1	(	(	PUNCT
ejpam-4570	102	2	2	2	X
ejpam-4570	102	3	)	)	PUNCT
ejpam-4570	102	4	every	every	DET
ejpam-4570	102	5	epi	epi	ADJ
ejpam-4570	102	6	-	-	ADJ
ejpam-4570	102	7	normal	normal	ADJ
ejpam-4570	102	8	space	space	NOUN
ejpam-4570	102	9	is	be	AUX
ejpam-4570	102	10	c	c	NOUN
ejpam-4570	102	11	-	-	PUNCT
ejpam-4570	102	12	almost	almost	ADV
ejpam-4570	102	13	normal	normal	ADJ
ejpam-4570	102	14	.	.	PUNCT
ejpam-4570	103	1	now	now	ADV
ejpam-4570	103	2	,	,	PUNCT
ejpam-4570	103	3	we	we	PRON
ejpam-4570	103	4	improve	improve	VERB
ejpam-4570	103	5	corollary	corollary	ADJ
ejpam-4570	103	6	1	1	NUM
ejpam-4570	103	7	by	by	ADP
ejpam-4570	103	8	the	the	DET
ejpam-4570	103	9	following	follow	VERB
ejpam-4570	103	10	theorem	theorem	NOUN
ejpam-4570	103	11	:	:	PUNCT
ejpam-4570	103	12	theorem	theorem	NOUN
ejpam-4570	103	13	2	2	NUM
ejpam-4570	103	14	.	.	PUNCT
ejpam-4570	104	1	every	every	DET
ejpam-4570	104	2	epi	epi	NOUN
ejpam-4570	104	3	-	-	ADJ
ejpam-4570	104	4	almost	almost	ADV
ejpam-4570	104	5	normal	normal	ADJ
ejpam-4570	104	6	space	space	NOUN
ejpam-4570	104	7	is	be	AUX
ejpam-4570	104	8	c	c	NOUN
ejpam-4570	104	9	-	-	PUNCT
ejpam-4570	104	10	almost	almost	ADV
ejpam-4570	104	11	normal	normal	ADJ
ejpam-4570	104	12	.	.	PUNCT
ejpam-4570	105	1	proof	proof	NOUN
ejpam-4570	105	2	.	.	PUNCT
ejpam-4570	106	1	let	let	VERB
ejpam-4570	106	2	x	x	PRON
ejpam-4570	106	3	be	be	AUX
ejpam-4570	106	4	an	an	DET
ejpam-4570	106	5	epi	epi	NOUN
ejpam-4570	106	6	-	-	ADJ
ejpam-4570	106	7	almost	almost	ADV
ejpam-4570	106	8	normal	normal	ADJ
ejpam-4570	106	9	space	space	NOUN
ejpam-4570	106	10	.	.	PUNCT
ejpam-4570	107	1	then	then	ADV
ejpam-4570	107	2	,	,	PUNCT
ejpam-4570	107	3	there	there	PRON
ejpam-4570	107	4	exist	exist	VERB
ejpam-4570	107	5	a	a	DET
ejpam-4570	107	6	topology	topology	NOUN
ejpam-4570	107	7	t	t	NOUN
ejpam-4570	107	8	′	′	NUM
ejpam-4570	107	9	on	on	ADP
ejpam-4570	107	10	x	x	X
ejpam-4570	107	11	,	,	PUNCT
ejpam-4570	107	12	which	which	PRON
ejpam-4570	107	13	is	be	AUX
ejpam-4570	107	14	coarser	coarse	ADJ
ejpam-4570	107	15	than	than	ADP
ejpam-4570	107	16	t	t	PROPN
ejpam-4570	107	17	,	,	PUNCT
ejpam-4570	107	18	such	such	ADJ
ejpam-4570	107	19	that	that	SCONJ
ejpam-4570	107	20	(	(	PUNCT
ejpam-4570	107	21	x	x	X
ejpam-4570	107	22	,	,	PUNCT
ejpam-4570	107	23	t	t	PROPN
ejpam-4570	107	24	′	′	NUM
ejpam-4570	107	25	)	)	PUNCT
ejpam-4570	107	26	is	be	AUX
ejpam-4570	107	27	hausdorff	hausdorff	NOUN
ejpam-4570	107	28	almost	almost	ADV
ejpam-4570	107	29	normal	normal	ADJ
ejpam-4570	107	30	.	.	PUNCT
ejpam-4570	108	1	thus	thus	ADV
ejpam-4570	108	2	,	,	PUNCT
ejpam-4570	108	3	the	the	DET
ejpam-4570	108	4	identity	identity	NOUN
ejpam-4570	108	5	mapping	mapping	NOUN
ejpam-4570	108	6	ix	ix	X
ejpam-4570	108	7	:	:	PUNCT
ejpam-4570	108	8	(	(	PUNCT
ejpam-4570	108	9	x	x	X
ejpam-4570	108	10	,	,	PUNCT
ejpam-4570	108	11	t	t	PROPN
ejpam-4570	108	12	)	)	PUNCT
ejpam-4570	108	13	→	→	SYM
ejpam-4570	108	14	(	(	PUNCT
ejpam-4570	108	15	x	x	X
ejpam-4570	108	16	,	,	PUNCT
ejpam-4570	108	17	t	t	PROPN
ejpam-4570	108	18	′	′	NUM
ejpam-4570	108	19	)	)	PUNCT
ejpam-4570	108	20	is	be	AUX
ejpam-4570	108	21	a	a	DET
ejpam-4570	108	22	bijective	bijective	ADJ
ejpam-4570	108	23	continuous	continuous	ADJ
ejpam-4570	108	24	function	function	NOUN
ejpam-4570	108	25	.	.	PUNCT
ejpam-4570	109	1	let	let	VERB
ejpam-4570	109	2	d	d	PRON
ejpam-4570	109	3	be	be	AUX
ejpam-4570	109	4	any	any	DET
ejpam-4570	109	5	compact	compact	ADJ
ejpam-4570	109	6	subspace	subspace	NOUN
ejpam-4570	109	7	of	of	ADP
ejpam-4570	109	8	(	(	PUNCT
ejpam-4570	109	9	x	x	PROPN
ejpam-4570	109	10	,	,	PUNCT
ejpam-4570	109	11	t	t	PROPN
ejpam-4570	109	12	)	)	PUNCT
ejpam-4570	109	13	.	.	PUNCT
ejpam-4570	110	1	then	then	ADV
ejpam-4570	110	2	,	,	PUNCT
ejpam-4570	110	3	ix(d	ix(d	PUNCT
ejpam-4570	110	4	)	)	PUNCT
ejpam-4570	110	5	is	be	AUX
ejpam-4570	110	6	a	a	DET
ejpam-4570	110	7	compact	compact	ADJ
ejpam-4570	110	8	hausdorff	hausdorff	NOUN
ejpam-4570	110	9	subspace	subspace	NOUN
ejpam-4570	110	10	of	of	ADP
ejpam-4570	110	11	(	(	PUNCT
ejpam-4570	110	12	x	x	PROPN
ejpam-4570	110	13	,	,	PUNCT
ejpam-4570	110	14	t	t	PROPN
ejpam-4570	110	15	′	′	NUM
ejpam-4570	110	16	)	)	PUNCT
ejpam-4570	110	17	as	as	ADP
ejpam-4570	110	18	ix(d	ix(d	NOUN
ejpam-4570	110	19	)	)	PUNCT
ejpam-4570	111	1	=	=	PUNCT
ejpam-4570	111	2	d	d	NOUN
ejpam-4570	111	3	is	be	AUX
ejpam-4570	111	4	a	a	DET
ejpam-4570	111	5	compact	compact	ADJ
ejpam-4570	111	6	hausdorff	hausdorff	NOUN
ejpam-4570	111	7	subspace	subspace	NOUN
ejpam-4570	111	8	in	in	ADP
ejpam-4570	111	9	both	both	DET
ejpam-4570	111	10	(	(	PUNCT
ejpam-4570	111	11	x	x	X
ejpam-4570	111	12	,	,	PUNCT
ejpam-4570	111	13	t	t	PROPN
ejpam-4570	111	14	)	)	PUNCT
ejpam-4570	111	15	and	and	CCONJ
ejpam-4570	111	16	(	(	PUNCT
ejpam-4570	111	17	x	x	X
ejpam-4570	111	18	,	,	PUNCT
ejpam-4570	111	19	t	t	PROPN
ejpam-4570	111	20	′	′	NUM
ejpam-4570	111	21	)	)	PUNCT
ejpam-4570	111	22	.	.	PUNCT
ejpam-4570	112	1	therefore	therefore	ADV
ejpam-4570	112	2	,	,	PUNCT
ejpam-4570	112	3	the	the	DET
ejpam-4570	112	4	restriction	restriction	NOUN
ejpam-4570	112	5	of	of	ADP
ejpam-4570	112	6	the	the	DET
ejpam-4570	112	7	identity	identity	NOUN
ejpam-4570	112	8	function	function	NOUN
ejpam-4570	112	9	on	on	ADP
ejpam-4570	112	10	d	d	PROPN
ejpam-4570	112	11	onto	onto	ADP
ejpam-4570	112	12	ix(d	ix(d	PUNCT
ejpam-4570	112	13	)	)	PUNCT
ejpam-4570	112	14	is	be	AUX
ejpam-4570	112	15	a	a	DET
ejpam-4570	112	16	homeomorphism	homeomorphism	NOUN
ejpam-4570	112	17	,	,	PUNCT
ejpam-4570	112	18	as	as	SCONJ
ejpam-4570	112	19	every	every	DET
ejpam-4570	112	20	continuous	continuous	ADJ
ejpam-4570	112	21	1	1	NUM
ejpam-4570	112	22	-	-	SYM
ejpam-4570	112	23	1	1	NUM
ejpam-4570	112	24	function	function	NOUN
ejpam-4570	112	25	of	of	ADP
ejpam-4570	112	26	a	a	DET
ejpam-4570	112	27	compact	compact	ADJ
ejpam-4570	112	28	space	space	NOUN
ejpam-4570	112	29	onto	onto	ADP
ejpam-4570	112	30	a	a	DET
ejpam-4570	112	31	hausdorff	hausdorff	NOUN
ejpam-4570	112	32	space	space	NOUN
ejpam-4570	112	33	is	be	AUX
ejpam-4570	112	34	a	a	DET
ejpam-4570	112	35	homeomorphism	homeomorphism	NOUN
ejpam-4570	112	36	[	[	X
ejpam-4570	112	37	12	12	NUM
ejpam-4570	112	38	]	]	PUNCT
ejpam-4570	112	39	.	.	PUNCT
ejpam-4570	113	1	hence	hence	ADV
ejpam-4570	113	2	,	,	PUNCT
ejpam-4570	113	3	x	x	X
ejpam-4570	113	4	is	be	AUX
ejpam-4570	113	5	c	c	NOUN
ejpam-4570	113	6	-	-	PUNCT
ejpam-4570	113	7	almost	almost	ADV
ejpam-4570	113	8	normal	normal	ADJ
ejpam-4570	113	9	.	.	PUNCT
ejpam-4570	114	1	the	the	DET
ejpam-4570	114	2	converse	converse	NOUN
ejpam-4570	114	3	of	of	ADP
ejpam-4570	114	4	theorem	theorem	ADJ
ejpam-4570	114	5	2	2	NUM
ejpam-4570	114	6	is	be	AUX
ejpam-4570	114	7	not	not	PART
ejpam-4570	114	8	necessarily	necessarily	ADV
ejpam-4570	114	9	true	true	ADJ
ejpam-4570	114	10	in	in	ADP
ejpam-4570	114	11	general	general	ADJ
ejpam-4570	114	12	.	.	PUNCT
ejpam-4570	115	1	for	for	ADP
ejpam-4570	115	2	example	example	NOUN
ejpam-4570	115	3	,	,	PUNCT
ejpam-4570	115	4	the	the	DET
ejpam-4570	115	5	particular	particular	ADJ
ejpam-4570	115	6	point	point	NOUN
ejpam-4570	115	7	topology	topology	NOUN
ejpam-4570	115	8	(	(	PUNCT
ejpam-4570	115	9	r	r	NOUN
ejpam-4570	115	10	,	,	PUNCT
ejpam-4570	115	11	tp	tp	NOUN
ejpam-4570	115	12	)	)	PUNCT
ejpam-4570	115	13	,	,	PUNCT
ejpam-4570	115	14	example	example	NOUN
ejpam-4570	115	15	1	1	NUM
ejpam-4570	115	16	,	,	PUNCT
ejpam-4570	115	17	is	be	AUX
ejpam-4570	115	18	a	a	DET
ejpam-4570	115	19	c	c	NOUN
ejpam-4570	115	20	-	-	PUNCT
ejpam-4570	115	21	almost	almost	ADV
ejpam-4570	115	22	normal	normal	ADJ
ejpam-4570	115	23	space	space	NOUN
ejpam-4570	115	24	,	,	PUNCT
ejpam-4570	115	25	which	which	PRON
ejpam-4570	115	26	is	be	AUX
ejpam-4570	115	27	neither	neither	DET
ejpam-4570	115	28	epi	epi	NOUN
ejpam-4570	115	29	-	-	ADJ
ejpam-4570	115	30	almost	almost	ADV
ejpam-4570	115	31	normal	normal	ADJ
ejpam-4570	115	32	,	,	PUNCT
ejpam-4570	115	33	epi	epi	NOUN
ejpam-4570	115	34	-	-	ADJ
ejpam-4570	115	35	normal	normal	ADJ
ejpam-4570	115	36	nor	nor	CCONJ
ejpam-4570	115	37	sub	sub	ADJ
ejpam-4570	115	38	-	-	ADJ
ejpam-4570	115	39	metrizable	metrizable	ADJ
ejpam-4570	115	40	being	be	AUX
ejpam-4570	115	41	not	not	PART
ejpam-4570	115	42	hausdorff	hausdorff	NOUN
ejpam-4570	115	43	.	.	PUNCT
ejpam-4570	116	1	the	the	DET
ejpam-4570	116	2	countable	countable	ADJ
ejpam-4570	116	3	complement	complement	NOUN
ejpam-4570	116	4	topology	topology	NOUN
ejpam-4570	116	5	,	,	PUNCT
ejpam-4570	116	6	example	example	NOUN
ejpam-4570	116	7	4	4	NUM
ejpam-4570	116	8	,	,	PUNCT
ejpam-4570	116	9	is	be	AUX
ejpam-4570	116	10	a	a	DET
ejpam-4570	116	11	c	c	NOUN
ejpam-4570	116	12	-	-	PUNCT
ejpam-4570	116	13	almost	almost	ADV
ejpam-4570	116	14	normal	normal	ADJ
ejpam-4570	116	15	space	space	NOUN
ejpam-4570	116	16	,	,	PUNCT
ejpam-4570	116	17	which	which	PRON
ejpam-4570	116	18	is	be	AUX
ejpam-4570	116	19	neither	neither	DET
ejpam-4570	116	20	epi	epi	NOUN
ejpam-4570	116	21	-	-	ADJ
ejpam-4570	116	22	normal	normal	ADJ
ejpam-4570	116	23	,	,	PUNCT
ejpam-4570	116	24	epi	epi	NOUN
ejpam-4570	116	25	-	-	PUNCT
ejpam-4570	116	26	almost	almost	ADV
ejpam-4570	116	27	normal	normal	ADJ
ejpam-4570	116	28	nor	nor	CCONJ
ejpam-4570	116	29	sub	sub	ADJ
ejpam-4570	116	30	-	-	ADJ
ejpam-4570	116	31	metrizable	metrizable	ADJ
ejpam-4570	116	32	.	.	PUNCT
ejpam-4570	117	1	some	some	DET
ejpam-4570	117	2	other	other	ADJ
ejpam-4570	117	3	counterexamples	counterexample	NOUN
ejpam-4570	117	4	are	be	AUX
ejpam-4570	117	5	given	give	VERB
ejpam-4570	117	6	in	in	ADP
ejpam-4570	117	7	section	section	NOUN
ejpam-4570	117	8	4	4	NUM
ejpam-4570	117	9	.	.	PUNCT
ejpam-4570	118	1	in	in	ADP
ejpam-4570	118	2	view	view	NOUN
ejpam-4570	118	3	of	of	ADP
ejpam-4570	118	4	the	the	DET
ejpam-4570	118	5	fact	fact	NOUN
ejpam-4570	118	6	:	:	PUNCT
ejpam-4570	118	7	“	"	PUNCT
ejpam-4570	118	8	if	if	SCONJ
ejpam-4570	118	9	x	x	PRON
ejpam-4570	118	10	is	be	AUX
ejpam-4570	118	11	a	a	DET
ejpam-4570	118	12	t1	t1	NOUN
ejpam-4570	118	13	-	-	PUNCT
ejpam-4570	118	14	space	space	NOUN
ejpam-4570	118	15	such	such	ADJ
ejpam-4570	118	16	that	that	SCONJ
ejpam-4570	118	17	the	the	DET
ejpam-4570	118	18	only	only	ADJ
ejpam-4570	118	19	compact	compact	ADJ
ejpam-4570	118	20	subsets	subset	NOUN
ejpam-4570	118	21	of	of	ADP
ejpam-4570	118	22	x	x	SYM
ejpam-4570	118	23	are	be	AUX
ejpam-4570	118	24	the	the	DET
ejpam-4570	118	25	finite	finite	ADJ
ejpam-4570	118	26	subsets	subset	NOUN
ejpam-4570	118	27	,	,	PUNCT
ejpam-4570	118	28	then	then	ADV
ejpam-4570	118	29	x	x	PUNCT
ejpam-4570	118	30	is	be	AUX
ejpam-4570	118	31	c	c	NOUN
ejpam-4570	118	32	-	-	PUNCT
ejpam-4570	118	33	normal”[10	normal”[10	X
ejpam-4570	118	34	]	]	PUNCT
ejpam-4570	118	35	,	,	PUNCT
ejpam-4570	118	36	we	we	PRON
ejpam-4570	118	37	conclude	conclude	VERB
ejpam-4570	118	38	.	.	PUNCT
ejpam-4570	119	1	corollary	corollary	ADJ
ejpam-4570	119	2	2	2	NUM
ejpam-4570	119	3	.	.	PUNCT
ejpam-4570	120	1	if	if	SCONJ
ejpam-4570	120	2	x	x	PRON
ejpam-4570	120	3	is	be	AUX
ejpam-4570	120	4	a	a	DET
ejpam-4570	120	5	t1	t1	NOUN
ejpam-4570	120	6	-	-	PUNCT
ejpam-4570	120	7	space	space	NOUN
ejpam-4570	120	8	such	such	ADJ
ejpam-4570	120	9	that	that	SCONJ
ejpam-4570	120	10	the	the	DET
ejpam-4570	120	11	only	only	ADJ
ejpam-4570	120	12	compact	compact	ADJ
ejpam-4570	120	13	subsets	subset	NOUN
ejpam-4570	120	14	of	of	ADP
ejpam-4570	120	15	x	x	SYM
ejpam-4570	120	16	are	be	AUX
ejpam-4570	120	17	the	the	DET
ejpam-4570	120	18	finite	finite	ADJ
ejpam-4570	120	19	subsets	subset	NOUN
ejpam-4570	120	20	,	,	PUNCT
ejpam-4570	120	21	then	then	ADV
ejpam-4570	120	22	x	x	PUNCT
ejpam-4570	120	23	is	be	AUX
ejpam-4570	120	24	c	c	NOUN
ejpam-4570	120	25	-	-	PUNCT
ejpam-4570	120	26	almost	almost	ADV
ejpam-4570	120	27	normal	normal	ADJ
ejpam-4570	120	28	.	.	PUNCT
ejpam-4570	121	1	wafa	wafa	PROPN
ejpam-4570	121	2	khalaf	khalaf	PROPN
ejpam-4570	121	3	alqurashi	alqurashi	PROPN
ejpam-4570	121	4	,	,	PUNCT
ejpam-4570	121	5	sadeq	sadeq	PROPN
ejpam-4570	121	6	ali	ali	PROPN
ejpam-4570	121	7	thabit	thabit	PROPN
ejpam-4570	121	8	/	/	SYM
ejpam-4570	121	9	eur	eur	PROPN
ejpam-4570	121	10	.	.	PUNCT
ejpam-4570	122	1	j.	j.	PROPN
ejpam-4570	122	2	pure	pure	PROPN
ejpam-4570	122	3	appl	appl	PROPN
ejpam-4570	122	4	.	.	PROPN
ejpam-4570	122	5	math	math	PROPN
ejpam-4570	122	6	,	,	PUNCT
ejpam-4570	122	7	15	15	NUM
ejpam-4570	122	8	(	(	PUNCT
ejpam-4570	122	9	4	4	NUM
ejpam-4570	122	10	)	)	PUNCT
ejpam-4570	122	11	(	(	PUNCT
ejpam-4570	122	12	2022	2022	NUM
ejpam-4570	122	13	)	)	PUNCT
ejpam-4570	122	14	,	,	PUNCT
ejpam-4570	122	15	1760	1760	NUM
ejpam-4570	122	16	-	-	SYM
ejpam-4570	122	17	1782	1782	NUM
ejpam-4570	122	18	1764	1764	NUM
ejpam-4570	122	19	theorem	theorem	NOUN
ejpam-4570	122	20	3	3	NUM
ejpam-4570	122	21	.	.	PUNCT
ejpam-4570	123	1	every	every	DET
ejpam-4570	123	2	compact	compact	ADJ
ejpam-4570	123	3	c	c	NOUN
ejpam-4570	123	4	-	-	PUNCT
ejpam-4570	123	5	almost	almost	ADV
ejpam-4570	123	6	normal	normal	ADJ
ejpam-4570	123	7	space	space	NOUN
ejpam-4570	123	8	is	be	AUX
ejpam-4570	123	9	almost	almost	ADV
ejpam-4570	123	10	normal	normal	ADJ
ejpam-4570	123	11	.	.	PUNCT
ejpam-4570	124	1	proof	proof	NOUN
ejpam-4570	124	2	.	.	PUNCT
ejpam-4570	125	1	let	let	VERB
ejpam-4570	125	2	x	x	PRON
ejpam-4570	125	3	be	be	AUX
ejpam-4570	125	4	a	a	DET
ejpam-4570	125	5	compact	compact	ADJ
ejpam-4570	125	6	c	c	NOUN
ejpam-4570	125	7	-	-	PUNCT
ejpam-4570	125	8	almost	almost	ADV
ejpam-4570	125	9	normal	normal	ADJ
ejpam-4570	125	10	space	space	NOUN
ejpam-4570	125	11	.	.	PUNCT
ejpam-4570	126	1	then	then	ADV
ejpam-4570	126	2	,	,	PUNCT
ejpam-4570	126	3	there	there	PRON
ejpam-4570	126	4	exist	exist	VERB
ejpam-4570	126	5	an	an	DET
ejpam-4570	126	6	almost	almost	ADV
ejpam-4570	126	7	normal	normal	ADJ
ejpam-4570	126	8	space	space	NOUN
ejpam-4570	126	9	y	y	PROPN
ejpam-4570	126	10	and	and	CCONJ
ejpam-4570	126	11	a	a	DET
ejpam-4570	126	12	bijective	bijective	ADJ
ejpam-4570	126	13	function	function	NOUN
ejpam-4570	126	14	f	f	NOUN
ejpam-4570	127	1	:	:	PUNCT
ejpam-4570	127	2	x	x	X
ejpam-4570	127	3	→	→	SYM
ejpam-4570	127	4	y	y	PROPN
ejpam-4570	127	5	such	such	ADJ
ejpam-4570	127	6	that	that	SCONJ
ejpam-4570	127	7	the	the	DET
ejpam-4570	127	8	restriction	restriction	NOUN
ejpam-4570	127	9	function	function	NOUN
ejpam-4570	127	10	f	f	PROPN
ejpam-4570	127	11	|c	|c	VERB
ejpam-4570	127	12	:	:	PUNCT
ejpam-4570	127	13	c	c	PROPN
ejpam-4570	127	14	→	→	SYM
ejpam-4570	127	15	f(c	f(c	PROPN
ejpam-4570	127	16	)	)	PUNCT
ejpam-4570	127	17	is	be	AUX
ejpam-4570	127	18	a	a	DET
ejpam-4570	127	19	homeomorphism	homeomorphism	NOUN
ejpam-4570	127	20	for	for	ADP
ejpam-4570	127	21	each	each	DET
ejpam-4570	127	22	compact	compact	ADJ
ejpam-4570	127	23	subspace	subspace	NOUN
ejpam-4570	127	24	c	c	PROPN
ejpam-4570	127	25	of	of	ADP
ejpam-4570	127	26	x.	x.	NOUN
ejpam-4570	127	27	since	since	SCONJ
ejpam-4570	127	28	x	x	PRON
ejpam-4570	127	29	is	be	AUX
ejpam-4570	127	30	compact	compact	ADJ
ejpam-4570	127	31	,	,	PUNCT
ejpam-4570	127	32	take	take	VERB
ejpam-4570	127	33	c	c	NOUN
ejpam-4570	127	34	=	=	PUNCT
ejpam-4570	127	35	x.	x.	NOUN
ejpam-4570	127	36	since	since	SCONJ
ejpam-4570	127	37	f	f	PROPN
ejpam-4570	127	38	is	be	AUX
ejpam-4570	127	39	bijective	bijective	ADJ
ejpam-4570	127	40	,	,	PUNCT
ejpam-4570	127	41	we	we	PRON
ejpam-4570	127	42	get	get	VERB
ejpam-4570	127	43	f	f	NOUN
ejpam-4570	127	44	:	:	PUNCT
ejpam-4570	127	45	x	x	X
ejpam-4570	127	46	→	→	SYM
ejpam-4570	127	47	y	y	PROPN
ejpam-4570	127	48	is	be	AUX
ejpam-4570	127	49	a	a	DET
ejpam-4570	127	50	homeomorphism	homeomorphism	NOUN
ejpam-4570	127	51	.	.	PUNCT
ejpam-4570	128	1	since	since	SCONJ
ejpam-4570	128	2	y	y	PROPN
ejpam-4570	128	3	is	be	AUX
ejpam-4570	128	4	an	an	DET
ejpam-4570	128	5	almost	almost	ADV
ejpam-4570	128	6	normal	normal	ADJ
ejpam-4570	128	7	space	space	NOUN
ejpam-4570	128	8	,	,	PUNCT
ejpam-4570	128	9	we	we	PRON
ejpam-4570	128	10	get	get	VERB
ejpam-4570	128	11	x	x	SYM
ejpam-4570	128	12	is	be	AUX
ejpam-4570	128	13	almost	almost	ADV
ejpam-4570	128	14	normal	normal	ADJ
ejpam-4570	128	15	.	.	PUNCT
ejpam-4570	129	1	corollary	corollary	ADJ
ejpam-4570	129	2	3	3	X
ejpam-4570	129	3	.	.	PUNCT
ejpam-4570	130	1	if	if	SCONJ
ejpam-4570	130	2	x	x	PRON
ejpam-4570	130	3	is	be	AUX
ejpam-4570	130	4	a	a	DET
ejpam-4570	130	5	compact	compact	ADJ
ejpam-4570	130	6	non	non	NOUN
ejpam-4570	130	7	almost	almost	ADV
ejpam-4570	130	8	normal	normal	ADJ
ejpam-4570	130	9	space	space	NOUN
ejpam-4570	130	10	,	,	PUNCT
ejpam-4570	130	11	then	then	ADV
ejpam-4570	130	12	x	x	PUNCT
ejpam-4570	130	13	can	can	AUX
ejpam-4570	130	14	not	not	PART
ejpam-4570	130	15	be	be	AUX
ejpam-4570	130	16	c	c	NOUN
ejpam-4570	130	17	-	-	PUNCT
ejpam-4570	130	18	almost	almost	ADV
ejpam-4570	130	19	normal	normal	ADJ
ejpam-4570	130	20	.	.	PUNCT
ejpam-4570	131	1	a	a	DET
ejpam-4570	131	2	space	space	NOUN
ejpam-4570	131	3	x	x	PUNCT
ejpam-4570	131	4	is	be	AUX
ejpam-4570	131	5	called	call	VERB
ejpam-4570	131	6	a	a	DET
ejpam-4570	131	7	locally	locally	ADV
ejpam-4570	131	8	compact	compact	ADJ
ejpam-4570	131	9	space	space	NOUN
ejpam-4570	131	10	if	if	SCONJ
ejpam-4570	131	11	for	for	ADP
ejpam-4570	131	12	each	each	DET
ejpam-4570	131	13	x	x	SYM
ejpam-4570	131	14	∈	∈	PROPN
ejpam-4570	131	15	x	x	X
ejpam-4570	131	16	and	and	CCONJ
ejpam-4570	131	17	each	each	DET
ejpam-4570	131	18	open	open	ADJ
ejpam-4570	131	19	neighborhood	neighborhood	NOUN
ejpam-4570	131	20	v	v	NOUN
ejpam-4570	131	21	of	of	ADP
ejpam-4570	131	22	x	x	PUNCT
ejpam-4570	131	23	there	there	PRON
ejpam-4570	131	24	exists	exist	VERB
ejpam-4570	131	25	an	an	DET
ejpam-4570	131	26	open	open	ADJ
ejpam-4570	131	27	neighborhood	neighborhood	NOUN
ejpam-4570	131	28	u	u	NOUN
ejpam-4570	131	29	of	of	ADP
ejpam-4570	131	30	x	x	SYM
ejpam-4570	131	31	such	such	ADJ
ejpam-4570	131	32	that	that	SCONJ
ejpam-4570	131	33	x	x	SYM
ejpam-4570	131	34	∈	∈	NOUN
ejpam-4570	131	35	u	u	NOUN
ejpam-4570	131	36	⊆	⊆	NUM
ejpam-4570	131	37	u	u	NOUN
ejpam-4570	131	38	⊆	⊆	NUM
ejpam-4570	131	39	v	v	NOUN
ejpam-4570	131	40	and	and	CCONJ
ejpam-4570	131	41	u	u	NOUN
ejpam-4570	131	42	is	be	AUX
ejpam-4570	131	43	compact	compact	ADJ
ejpam-4570	131	44	[	[	X
ejpam-4570	131	45	12	12	NUM
ejpam-4570	131	46	]	]	PUNCT
ejpam-4570	131	47	.	.	PUNCT
ejpam-4570	132	1	in	in	ADP
ejpam-4570	132	2	view	view	NOUN
ejpam-4570	132	3	of	of	ADP
ejpam-4570	132	4	the	the	DET
ejpam-4570	132	5	fact	fact	NOUN
ejpam-4570	132	6	:	:	PUNCT
ejpam-4570	132	7	“	"	PUNCT
ejpam-4570	132	8	every	every	DET
ejpam-4570	132	9	hausdorff	hausdorff	NOUN
ejpam-4570	132	10	locally	locally	ADV
ejpam-4570	132	11	compact	compact	ADJ
ejpam-4570	132	12	space	space	NOUN
ejpam-4570	132	13	is	be	AUX
ejpam-4570	132	14	a	a	DET
ejpam-4570	132	15	c	c	NOUN
ejpam-4570	132	16	-	-	ADJ
ejpam-4570	132	17	normal	normal	ADJ
ejpam-4570	132	18	space”[10	space”[10	NOUN
ejpam-4570	132	19	]	]	PUNCT
ejpam-4570	132	20	,	,	PUNCT
ejpam-4570	132	21	we	we	PRON
ejpam-4570	132	22	get	get	VERB
ejpam-4570	132	23	:	:	PUNCT
ejpam-4570	132	24	corollary	corollary	ADJ
ejpam-4570	132	25	4	4	NUM
ejpam-4570	132	26	.	.	PUNCT
ejpam-4570	133	1	every	every	DET
ejpam-4570	133	2	hausdorff	hausdorff	NOUN
ejpam-4570	133	3	locally	locally	ADV
ejpam-4570	133	4	compact	compact	ADJ
ejpam-4570	133	5	space	space	NOUN
ejpam-4570	133	6	is	be	AUX
ejpam-4570	133	7	c	c	NOUN
ejpam-4570	133	8	-	-	PUNCT
ejpam-4570	133	9	almost	almost	ADV
ejpam-4570	133	10	normal	normal	ADJ
ejpam-4570	133	11	.	.	PUNCT
ejpam-4570	134	1	the	the	DET
ejpam-4570	134	2	converse	converse	NOUN
ejpam-4570	134	3	of	of	ADP
ejpam-4570	134	4	corollary	corollary	ADJ
ejpam-4570	134	5	4	4	NUM
ejpam-4570	134	6	is	be	AUX
ejpam-4570	134	7	not	not	PART
ejpam-4570	134	8	necessarily	necessarily	ADV
ejpam-4570	134	9	true	true	ADJ
ejpam-4570	134	10	in	in	ADP
ejpam-4570	134	11	general	general	ADJ
ejpam-4570	134	12	.	.	PUNCT
ejpam-4570	135	1	for	for	ADP
ejpam-4570	135	2	example	example	NOUN
ejpam-4570	135	3	,	,	PUNCT
ejpam-4570	135	4	the	the	DET
ejpam-4570	135	5	dieudonné	dieudonné	NOUN
ejpam-4570	135	6	plank	plank	NOUN
ejpam-4570	135	7	topology	topology	NOUN
ejpam-4570	135	8	,	,	PUNCT
ejpam-4570	135	9	example	example	NOUN
ejpam-4570	135	10	5	5	NUM
ejpam-4570	135	11	,	,	PUNCT
ejpam-4570	135	12	is	be	AUX
ejpam-4570	135	13	a	a	DET
ejpam-4570	135	14	c	c	NOUN
ejpam-4570	135	15	-	-	PUNCT
ejpam-4570	135	16	almost	almost	ADV
ejpam-4570	135	17	normal	normal	ADJ
ejpam-4570	135	18	space	space	NOUN
ejpam-4570	135	19	,	,	PUNCT
ejpam-4570	135	20	which	which	PRON
ejpam-4570	135	21	is	be	AUX
ejpam-4570	135	22	not	not	PART
ejpam-4570	135	23	locally	locally	ADV
ejpam-4570	135	24	compact	compact	ADJ
ejpam-4570	135	25	.	.	PUNCT
ejpam-4570	136	1	theorem	theorem	ADJ
ejpam-4570	136	2	4	4	NUM
ejpam-4570	136	3	.	.	PUNCT
ejpam-4570	137	1	c	c	X
ejpam-4570	137	2	-	-	PUNCT
ejpam-4570	137	3	almost	almost	ADV
ejpam-4570	137	4	normality	normality	NOUN
ejpam-4570	137	5	is	be	AUX
ejpam-4570	137	6	a	a	DET
ejpam-4570	137	7	topological	topological	ADJ
ejpam-4570	137	8	property	property	NOUN
ejpam-4570	137	9	.	.	PUNCT
ejpam-4570	138	1	proof	proof	NOUN
ejpam-4570	138	2	.	.	PUNCT
ejpam-4570	139	1	let	let	VERB
ejpam-4570	139	2	x	x	PRON
ejpam-4570	139	3	be	be	AUX
ejpam-4570	139	4	a	a	DET
ejpam-4570	139	5	c	c	NOUN
ejpam-4570	139	6	-	-	PUNCT
ejpam-4570	139	7	almost	almost	ADV
ejpam-4570	139	8	normal	normal	ADJ
ejpam-4570	139	9	space	space	NOUN
ejpam-4570	139	10	and	and	CCONJ
ejpam-4570	139	11	x	x	PUNCT
ejpam-4570	139	12	∼=	∼=	NOUN
ejpam-4570	139	13	z.	z.	NOUN
ejpam-4570	139	14	let	let	VERB
ejpam-4570	139	15	y	y	PRON
ejpam-4570	139	16	be	be	AUX
ejpam-4570	139	17	an	an	DET
ejpam-4570	139	18	almost	almost	ADV
ejpam-4570	139	19	normal	normal	ADJ
ejpam-4570	139	20	space	space	NOUN
ejpam-4570	139	21	and	and	CCONJ
ejpam-4570	139	22	f	f	NOUN
ejpam-4570	139	23	:	:	PUNCT
ejpam-4570	139	24	x	x	X
ejpam-4570	139	25	→	→	SYM
ejpam-4570	139	26	y	y	X
ejpam-4570	139	27	be	be	AUX
ejpam-4570	139	28	a	a	DET
ejpam-4570	139	29	bijective	bijective	ADJ
ejpam-4570	139	30	function	function	NOUN
ejpam-4570	139	31	such	such	ADJ
ejpam-4570	139	32	that	that	SCONJ
ejpam-4570	139	33	the	the	DET
ejpam-4570	139	34	restriction	restriction	NOUN
ejpam-4570	139	35	function	function	NOUN
ejpam-4570	139	36	f	f	PROPN
ejpam-4570	139	37	|c	|c	VERB
ejpam-4570	139	38	:	:	PUNCT
ejpam-4570	139	39	c	c	PROPN
ejpam-4570	139	40	→	→	SYM
ejpam-4570	139	41	f(c	f(c	PROPN
ejpam-4570	139	42	)	)	PUNCT
ejpam-4570	139	43	is	be	AUX
ejpam-4570	139	44	a	a	DET
ejpam-4570	139	45	homeomorphism	homeomorphism	NOUN
ejpam-4570	139	46	for	for	ADP
ejpam-4570	139	47	each	each	DET
ejpam-4570	139	48	compact	compact	ADJ
ejpam-4570	139	49	subspace	subspace	NOUN
ejpam-4570	139	50	c	c	PROPN
ejpam-4570	139	51	⊆	⊆	PROPN
ejpam-4570	139	52	x.	x.	NOUN
ejpam-4570	139	53	let	let	VERB
ejpam-4570	139	54	g	g	NOUN
ejpam-4570	139	55	:	:	PUNCT
ejpam-4570	139	56	z	z	X
ejpam-4570	139	57	→	→	PUNCT
ejpam-4570	139	58	x	x	X
ejpam-4570	139	59	be	be	AUX
ejpam-4570	139	60	a	a	DET
ejpam-4570	139	61	homeomorphism	homeomorphism	NOUN
ejpam-4570	139	62	.	.	PUNCT
ejpam-4570	140	1	then	then	ADV
ejpam-4570	140	2	,	,	PUNCT
ejpam-4570	140	3	y	y	PROPN
ejpam-4570	140	4	and	and	CCONJ
ejpam-4570	140	5	f	f	PROPN
ejpam-4570	140	6	◦	◦	NOUN
ejpam-4570	140	7	g	g	NOUN
ejpam-4570	140	8	:	:	PUNCT
ejpam-4570	140	9	z	z	PROPN
ejpam-4570	140	10	→	→	SYM
ejpam-4570	140	11	y	y	PROPN
ejpam-4570	140	12	satisfy	satisfy	VERB
ejpam-4570	140	13	the	the	DET
ejpam-4570	140	14	requirements	requirement	NOUN
ejpam-4570	140	15	.	.	PUNCT
ejpam-4570	141	1	theorem	theorem	NOUN
ejpam-4570	141	2	5	5	NUM
ejpam-4570	141	3	.	.	PUNCT
ejpam-4570	141	4	c	c	X
ejpam-4570	141	5	-	-	PUNCT
ejpam-4570	141	6	almost	almost	ADV
ejpam-4570	141	7	normality	normality	NOUN
ejpam-4570	141	8	is	be	AUX
ejpam-4570	141	9	an	an	DET
ejpam-4570	141	10	additive	additive	ADJ
ejpam-4570	141	11	property	property	NOUN
ejpam-4570	141	12	.	.	PUNCT
ejpam-4570	142	1	proof	proof	NOUN
ejpam-4570	142	2	.	.	PUNCT
ejpam-4570	143	1	let	let	VERB
ejpam-4570	143	2	xs	xs	PROPN
ejpam-4570	143	3	be	be	AUX
ejpam-4570	143	4	a	a	DET
ejpam-4570	143	5	c	c	NOUN
ejpam-4570	143	6	-	-	PUNCT
ejpam-4570	143	7	almost	almost	ADV
ejpam-4570	143	8	normal	normal	ADJ
ejpam-4570	143	9	space	space	NOUN
ejpam-4570	143	10	for	for	ADP
ejpam-4570	143	11	each	each	DET
ejpam-4570	143	12	s	s	PROPN
ejpam-4570	143	13	∈	∈	PROPN
ejpam-4570	143	14	s.	s.	PROPN
ejpam-4570	143	15	then	then	ADV
ejpam-4570	143	16	,	,	PUNCT
ejpam-4570	143	17	there	there	PRON
ejpam-4570	143	18	exist	exist	VERB
ejpam-4570	143	19	an	an	DET
ejpam-4570	143	20	almost	almost	ADV
ejpam-4570	143	21	normal	normal	ADJ
ejpam-4570	143	22	space	space	NOUN
ejpam-4570	143	23	ys	ys	NOUN
ejpam-4570	143	24	and	and	CCONJ
ejpam-4570	143	25	a	a	DET
ejpam-4570	143	26	bijective	bijective	ADJ
ejpam-4570	143	27	function	function	NOUN
ejpam-4570	143	28	fs	fs	ADP
ejpam-4570	143	29	:	:	PUNCT
ejpam-4570	143	30	xs	xs	PROPN
ejpam-4570	143	31	→	→	PUNCT
ejpam-4570	143	32	ys	ys	NOUN
ejpam-4570	143	33	such	such	ADJ
ejpam-4570	143	34	that	that	SCONJ
ejpam-4570	143	35	the	the	DET
ejpam-4570	143	36	restriction	restriction	NOUN
ejpam-4570	143	37	function	function	NOUN
ejpam-4570	143	38	fs|cs	fs|cs	NOUN
ejpam-4570	143	39	:	:	PUNCT
ejpam-4570	143	40	cs	cs	PROPN
ejpam-4570	143	41	→	→	SYM
ejpam-4570	143	42	fs(cs	fs(cs	PROPN
ejpam-4570	143	43	)	)	PUNCT
ejpam-4570	143	44	is	be	AUX
ejpam-4570	143	45	a	a	DET
ejpam-4570	143	46	homeomorphism	homeomorphism	NOUN
ejpam-4570	143	47	for	for	ADP
ejpam-4570	143	48	each	each	DET
ejpam-4570	143	49	compact	compact	ADJ
ejpam-4570	143	50	subspace	subspace	NOUN
ejpam-4570	143	51	cs	cs	PROPN
ejpam-4570	143	52	⊆	⊆	NUM
ejpam-4570	143	53	xs	xs	NOUN
ejpam-4570	143	54	.	.	PUNCT
ejpam-4570	144	1	since	since	SCONJ
ejpam-4570	144	2	ys	ys	PROPN
ejpam-4570	144	3	is	be	AUX
ejpam-4570	144	4	an	an	DET
ejpam-4570	144	5	almost	almost	ADV
ejpam-4570	144	6	normal	normal	ADJ
ejpam-4570	144	7	space	space	NOUN
ejpam-4570	144	8	for	for	ADP
ejpam-4570	144	9	each	each	DET
ejpam-4570	144	10	s	s	X
ejpam-4570	144	11	∈	∈	PROPN
ejpam-4570	144	12	s	s	NOUN
ejpam-4570	144	13	,	,	PUNCT
ejpam-4570	144	14	the	the	DET
ejpam-4570	144	15	sum	sum	NOUN
ejpam-4570	144	16	⊕	⊕	PROPN
ejpam-4570	144	17	s∈s	s∈s	NOUN
ejpam-4570	144	18	ys	ys	NOUN
ejpam-4570	144	19	is	be	AUX
ejpam-4570	144	20	almost	almost	ADV
ejpam-4570	144	21	normal	normal	ADJ
ejpam-4570	144	22	.	.	PUNCT
ejpam-4570	145	1	consider	consider	VERB
ejpam-4570	145	2	the	the	DET
ejpam-4570	145	3	function	function	NOUN
ejpam-4570	145	4	sum	sum	NOUN
ejpam-4570	146	1	[	[	X
ejpam-4570	146	2	12	12	NUM
ejpam-4570	146	3	]	]	PUNCT
ejpam-4570	146	4	,	,	PUNCT
ejpam-4570	146	5	⊕	⊕	PROPN
ejpam-4570	146	6	s∈s	s∈s	VERB
ejpam-4570	146	7	fs	fs	ADP
ejpam-4570	146	8	:	:	PUNCT
ejpam-4570	146	9	⊕	⊕	PROPN
ejpam-4570	146	10	s∈s	s∈s	NOUN
ejpam-4570	146	11	xs	xs	PROPN
ejpam-4570	146	12	→	→	SYM
ejpam-4570	146	13	⊕	⊕	PROPN
ejpam-4570	146	14	s∈s	s∈s	NOUN
ejpam-4570	146	15	ys	ys	NOUN
ejpam-4570	146	16	defined	define	VERB
ejpam-4570	146	17	by	by	ADP
ejpam-4570	146	18	⊕	⊕	PROPN
ejpam-4570	146	19	s∈s	s∈s	NOUN
ejpam-4570	146	20	fs(x	fs(x	NOUN
ejpam-4570	146	21	)	)	PUNCT
ejpam-4570	146	22	=	=	SYM
ejpam-4570	146	23	ft(x	ft(x	X
ejpam-4570	146	24	)	)	PUNCT
ejpam-4570	146	25	if	if	SCONJ
ejpam-4570	146	26	x	x	SYM
ejpam-4570	146	27	∈	∈	PROPN
ejpam-4570	146	28	xt	xt	PROPN
ejpam-4570	146	29	and	and	CCONJ
ejpam-4570	146	30	t	t	PROPN
ejpam-4570	146	31	∈	∈	PROPN
ejpam-4570	146	32	s.	s.	PROPN
ejpam-4570	146	33	now	now	ADV
ejpam-4570	146	34	,	,	PUNCT
ejpam-4570	146	35	the	the	DET
ejpam-4570	146	36	subspace	subspace	NOUN
ejpam-4570	146	37	c	c	PROPN
ejpam-4570	146	38	⊆	⊆	NUM
ejpam-4570	146	39	⊕	⊕	PROPN
ejpam-4570	146	40	s∈s	s∈s	NOUN
ejpam-4570	146	41	xs	xs	PROPN
ejpam-4570	146	42	is	be	AUX
ejpam-4570	146	43	compact	compact	ADJ
ejpam-4570	146	44	if	if	SCONJ
ejpam-4570	147	1	and	and	CCONJ
ejpam-4570	147	2	only	only	ADV
ejpam-4570	147	3	if	if	SCONJ
ejpam-4570	147	4	the	the	DET
ejpam-4570	147	5	set	set	NOUN
ejpam-4570	147	6	s0	s0	NOUN
ejpam-4570	147	7	=	=	PUNCT
ejpam-4570	147	8	{	{	PUNCT
ejpam-4570	147	9	s	s	NOUN
ejpam-4570	147	10	∈	∈	NOUN
ejpam-4570	147	11	s	s	PART
ejpam-4570	147	12	:	:	PUNCT
ejpam-4570	147	13	c	c	PROPN
ejpam-4570	147	14	∩	∩	PROPN
ejpam-4570	147	15	xs	xs	PROPN
ejpam-4570	147	16	̸=	̸=	PROPN
ejpam-4570	147	17	∅	∅	NOUN
ejpam-4570	147	18	}	}	PUNCT
ejpam-4570	147	19	is	be	AUX
ejpam-4570	147	20	finite	finite	ADJ
ejpam-4570	147	21	and	and	CCONJ
ejpam-4570	147	22	c	c	PROPN
ejpam-4570	147	23	∩	∩	PROPN
ejpam-4570	147	24	xs	xs	PROPN
ejpam-4570	147	25	is	be	AUX
ejpam-4570	147	26	compact	compact	ADJ
ejpam-4570	147	27	in	in	ADP
ejpam-4570	147	28	xs	xs	PROPN
ejpam-4570	147	29	for	for	ADP
ejpam-4570	147	30	each	each	DET
ejpam-4570	147	31	s	s	PROPN
ejpam-4570	147	32	∈	∈	PROPN
ejpam-4570	147	33	s0	s0	NOUN
ejpam-4570	147	34	.	.	PUNCT
ejpam-4570	148	1	if	if	SCONJ
ejpam-4570	148	2	c	c	PROPN
ejpam-4570	148	3	⊆	⊆	NUM
ejpam-4570	148	4	⊕	⊕	PROPN
ejpam-4570	148	5	s∈s	s∈s	NOUN
ejpam-4570	148	6	xs	xs	PROPN
ejpam-4570	148	7	is	be	AUX
ejpam-4570	148	8	compact	compact	ADJ
ejpam-4570	148	9	,	,	PUNCT
ejpam-4570	148	10	then	then	ADV
ejpam-4570	148	11	(	(	PUNCT
ejpam-4570	148	12	⊕	⊕	PROPN
ejpam-4570	148	13	s∈s	s∈s	NOUN
ejpam-4570	148	14	fs)|c	fs)|c	ADJ
ejpam-4570	148	15	is	be	AUX
ejpam-4570	148	16	a	a	DET
ejpam-4570	148	17	homeomorphism	homeomorphism	NOUN
ejpam-4570	148	18	because	because	SCONJ
ejpam-4570	148	19	fs|(c∩xs	fs|(c∩xs	PROPN
ejpam-4570	148	20	)	)	PUNCT
ejpam-4570	148	21	is	be	AUX
ejpam-4570	148	22	a	a	DET
ejpam-4570	148	23	homeomorphism	homeomorphism	NOUN
ejpam-4570	148	24	for	for	ADP
ejpam-4570	148	25	each	each	DET
ejpam-4570	148	26	s	s	PROPN
ejpam-4570	148	27	∈	∈	PROPN
ejpam-4570	148	28	s0	s0	NOUN
ejpam-4570	148	29	.	.	PUNCT
ejpam-4570	149	1	hence	hence	ADV
ejpam-4570	149	2	,	,	PUNCT
ejpam-4570	149	3	⊕	⊕	PROPN
ejpam-4570	149	4	s∈s	s∈s	NOUN
ejpam-4570	149	5	xs	xs	PROPN
ejpam-4570	149	6	is	be	AUX
ejpam-4570	149	7	c	c	NOUN
ejpam-4570	149	8	-	-	PUNCT
ejpam-4570	149	9	almost	almost	ADV
ejpam-4570	149	10	normal	normal	ADJ
ejpam-4570	149	11	.	.	PUNCT
ejpam-4570	150	1	note	note	VERB
ejpam-4570	150	2	that	that	SCONJ
ejpam-4570	150	3	:	:	PUNCT
ejpam-4570	150	4	if	if	SCONJ
ejpam-4570	150	5	x	x	PRON
ejpam-4570	150	6	is	be	AUX
ejpam-4570	150	7	a	a	DET
ejpam-4570	150	8	c	c	NOUN
ejpam-4570	150	9	-	-	PUNCT
ejpam-4570	150	10	almost	almost	ADV
ejpam-4570	150	11	normal	normal	ADJ
ejpam-4570	150	12	space	space	NOUN
ejpam-4570	150	13	and	and	CCONJ
ejpam-4570	150	14	f	f	NOUN
ejpam-4570	150	15	:	:	PUNCT
ejpam-4570	150	16	x	x	X
ejpam-4570	150	17	→	→	SYM
ejpam-4570	150	18	y	y	PROPN
ejpam-4570	150	19	is	be	AUX
ejpam-4570	150	20	a	a	DET
ejpam-4570	150	21	witness	witness	NOUN
ejpam-4570	150	22	of	of	ADP
ejpam-4570	150	23	the	the	DET
ejpam-4570	150	24	c	c	NOUN
ejpam-4570	150	25	-	-	PUNCT
ejpam-4570	150	26	almost	almost	ADV
ejpam-4570	150	27	normality	normality	NOUN
ejpam-4570	150	28	of	of	ADP
ejpam-4570	150	29	x	x	PRON
ejpam-4570	150	30	,	,	PUNCT
ejpam-4570	150	31	then	then	ADV
ejpam-4570	150	32	f	f	PROPN
ejpam-4570	150	33	may	may	AUX
ejpam-4570	150	34	not	not	PART
ejpam-4570	150	35	be	be	AUX
ejpam-4570	150	36	continuous	continuous	ADJ
ejpam-4570	150	37	.	.	PUNCT
ejpam-4570	151	1	for	for	ADP
ejpam-4570	151	2	example	example	NOUN
ejpam-4570	151	3	,	,	PUNCT
ejpam-4570	151	4	the	the	DET
ejpam-4570	151	5	countable	countable	ADJ
ejpam-4570	151	6	complement	complement	NOUN
ejpam-4570	151	7	topology	topology	NOUN
ejpam-4570	151	8	,	,	PUNCT
ejpam-4570	151	9	example	example	NOUN
ejpam-4570	151	10	4	4	NUM
ejpam-4570	151	11	,	,	PUNCT
ejpam-4570	151	12	is	be	AUX
ejpam-4570	151	13	a	a	DET
ejpam-4570	151	14	c	c	NOUN
ejpam-4570	151	15	-	-	PUNCT
ejpam-4570	151	16	almost	almost	ADV
ejpam-4570	151	17	normal	normal	ADJ
ejpam-4570	151	18	space	space	NOUN
ejpam-4570	151	19	and	and	CCONJ
ejpam-4570	151	20	the	the	DET
ejpam-4570	151	21	witness	witness	NOUN
ejpam-4570	151	22	of	of	ADP
ejpam-4570	151	23	the	the	DET
ejpam-4570	151	24	c	c	NOUN
ejpam-4570	151	25	-	-	PUNCT
ejpam-4570	151	26	almost	almost	ADV
ejpam-4570	151	27	normality	normality	NOUN
ejpam-4570	151	28	of	of	ADP
ejpam-4570	151	29	x	x	PUNCT
ejpam-4570	151	30	is	be	AUX
ejpam-4570	151	31	not	not	PART
ejpam-4570	151	32	continuous	continuous	ADJ
ejpam-4570	151	33	.	.	PUNCT
ejpam-4570	152	1	but	but	CCONJ
ejpam-4570	152	2	it	it	PRON
ejpam-4570	152	3	will	will	AUX
ejpam-4570	152	4	be	be	AUX
ejpam-4570	152	5	if	if	SCONJ
ejpam-4570	152	6	x	x	PRON
ejpam-4570	152	7	is	be	AUX
ejpam-4570	152	8	fréchet	fréchet	ADJ
ejpam-4570	152	9	.	.	PUNCT
ejpam-4570	153	1	a	a	DET
ejpam-4570	153	2	space	space	NOUN
ejpam-4570	153	3	x	x	PUNCT
ejpam-4570	153	4	is	be	AUX
ejpam-4570	153	5	called	call	VERB
ejpam-4570	153	6	a	a	DET
ejpam-4570	153	7	fréchet	fréchet	NOUN
ejpam-4570	153	8	space	space	NOUN
ejpam-4570	153	9	if	if	SCONJ
ejpam-4570	153	10	for	for	ADP
ejpam-4570	153	11	any	any	DET
ejpam-4570	153	12	subset	subset	NOUN
ejpam-4570	153	13	b	b	PROPN
ejpam-4570	153	14	of	of	ADP
ejpam-4570	153	15	x	x	X
ejpam-4570	153	16	and	and	CCONJ
ejpam-4570	153	17	any	any	DET
ejpam-4570	153	18	x	x	SYM
ejpam-4570	153	19	∈	∈	PROPN
ejpam-4570	153	20	b	b	NOUN
ejpam-4570	153	21	,	,	PUNCT
ejpam-4570	153	22	there	there	PRON
ejpam-4570	153	23	exists	exist	VERB
ejpam-4570	153	24	a	a	DET
ejpam-4570	153	25	sequence	sequence	NOUN
ejpam-4570	153	26	(	(	PUNCT
ejpam-4570	153	27	an)n∈n	an)n∈n	NUM
ejpam-4570	153	28	of	of	ADP
ejpam-4570	153	29	points	point	NOUN
ejpam-4570	153	30	of	of	ADP
ejpam-4570	153	31	b	b	NOUN
ejpam-4570	153	32	such	such	ADJ
ejpam-4570	153	33	that	that	SCONJ
ejpam-4570	153	34	an	an	DET
ejpam-4570	153	35	−→	−→	NOUN
ejpam-4570	153	36	x	x	SYM
ejpam-4570	154	1	[	[	X
ejpam-4570	154	2	12	12	NUM
ejpam-4570	154	3	]	]	PUNCT
ejpam-4570	154	4	.	.	PUNCT
ejpam-4570	155	1	wafa	wafa	PROPN
ejpam-4570	155	2	khalaf	khalaf	PROPN
ejpam-4570	155	3	alqurashi	alqurashi	PROPN
ejpam-4570	155	4	,	,	PUNCT
ejpam-4570	155	5	sadeq	sadeq	PROPN
ejpam-4570	155	6	ali	ali	PROPN
ejpam-4570	155	7	thabit	thabit	PROPN
ejpam-4570	155	8	/	/	SYM
ejpam-4570	155	9	eur	eur	PROPN
ejpam-4570	155	10	.	.	PUNCT
ejpam-4570	156	1	j.	j.	PROPN
ejpam-4570	156	2	pure	pure	PROPN
ejpam-4570	156	3	appl	appl	PROPN
ejpam-4570	156	4	.	.	PROPN
ejpam-4570	156	5	math	math	PROPN
ejpam-4570	156	6	,	,	PUNCT
ejpam-4570	156	7	15	15	NUM
ejpam-4570	156	8	(	(	PUNCT
ejpam-4570	156	9	4	4	NUM
ejpam-4570	156	10	)	)	PUNCT
ejpam-4570	156	11	(	(	PUNCT
ejpam-4570	156	12	2022	2022	NUM
ejpam-4570	156	13	)	)	PUNCT
ejpam-4570	156	14	,	,	PUNCT
ejpam-4570	156	15	1760	1760	NUM
ejpam-4570	156	16	-	-	SYM
ejpam-4570	156	17	1782	1782	NUM
ejpam-4570	156	18	1765	1765	NUM
ejpam-4570	156	19	theorem	theorem	VERB
ejpam-4570	156	20	6	6	NUM
ejpam-4570	156	21	.	.	PUNCT
ejpam-4570	157	1	if	if	SCONJ
ejpam-4570	157	2	x	x	PRON
ejpam-4570	157	3	is	be	AUX
ejpam-4570	157	4	a	a	DET
ejpam-4570	157	5	c	c	NOUN
ejpam-4570	157	6	-	-	PUNCT
ejpam-4570	157	7	almost	almost	ADV
ejpam-4570	157	8	normal	normal	ADJ
ejpam-4570	157	9	fréchet	fréchet	NOUN
ejpam-4570	157	10	space	space	NOUN
ejpam-4570	157	11	and	and	CCONJ
ejpam-4570	157	12	f	f	NOUN
ejpam-4570	157	13	:	:	PUNCT
ejpam-4570	157	14	x	x	X
ejpam-4570	157	15	→	→	SYM
ejpam-4570	157	16	y	y	PROPN
ejpam-4570	157	17	is	be	AUX
ejpam-4570	157	18	a	a	DET
ejpam-4570	157	19	witness	witness	NOUN
ejpam-4570	157	20	of	of	ADP
ejpam-4570	157	21	the	the	DET
ejpam-4570	157	22	c	c	NOUN
ejpam-4570	157	23	-	-	PUNCT
ejpam-4570	157	24	almost	almost	ADV
ejpam-4570	157	25	normality	normality	NOUN
ejpam-4570	157	26	of	of	ADP
ejpam-4570	157	27	x	x	PRON
ejpam-4570	157	28	,	,	PUNCT
ejpam-4570	157	29	then	then	ADV
ejpam-4570	157	30	f	f	PROPN
ejpam-4570	157	31	is	be	AUX
ejpam-4570	157	32	continuous	continuous	ADJ
ejpam-4570	157	33	.	.	PUNCT
ejpam-4570	158	1	proof	proof	NOUN
ejpam-4570	158	2	.	.	PUNCT
ejpam-4570	159	1	let	let	VERB
ejpam-4570	159	2	x	x	PRON
ejpam-4570	159	3	be	be	AUX
ejpam-4570	159	4	a	a	DET
ejpam-4570	159	5	c	c	NOUN
ejpam-4570	159	6	-	-	PUNCT
ejpam-4570	159	7	almost	almost	ADV
ejpam-4570	159	8	normal	normal	ADJ
ejpam-4570	159	9	fréchet	fréchet	NOUN
ejpam-4570	159	10	space	space	NOUN
ejpam-4570	159	11	and	and	CCONJ
ejpam-4570	159	12	f	f	NOUN
ejpam-4570	159	13	:	:	PUNCT
ejpam-4570	159	14	x	x	X
ejpam-4570	159	15	→	→	SYM
ejpam-4570	159	16	y	y	X
ejpam-4570	159	17	be	be	AUX
ejpam-4570	159	18	a	a	DET
ejpam-4570	159	19	witness	witness	NOUN
ejpam-4570	159	20	of	of	ADP
ejpam-4570	159	21	the	the	DET
ejpam-4570	159	22	c	c	NOUN
ejpam-4570	159	23	-	-	PUNCT
ejpam-4570	159	24	almost	almost	ADV
ejpam-4570	159	25	normality	normality	NOUN
ejpam-4570	159	26	of	of	ADP
ejpam-4570	159	27	x.	x.	NOUN
ejpam-4570	159	28	take	take	VERB
ejpam-4570	159	29	b	b	NOUN
ejpam-4570	159	30	⊆	⊆	NUM
ejpam-4570	159	31	x	x	PUNCT
ejpam-4570	159	32	and	and	CCONJ
ejpam-4570	159	33	pick	pick	VERB
ejpam-4570	159	34	y	y	PROPN
ejpam-4570	159	35	∈	∈	PROPN
ejpam-4570	159	36	f(b	f(b	PROPN
ejpam-4570	159	37	)	)	PUNCT
ejpam-4570	159	38	.	.	PUNCT
ejpam-4570	160	1	since	since	SCONJ
ejpam-4570	160	2	f	f	PROPN
ejpam-4570	160	3	is	be	AUX
ejpam-4570	160	4	bijective	bijective	ADJ
ejpam-4570	160	5	,	,	PUNCT
ejpam-4570	160	6	there	there	PRON
ejpam-4570	160	7	exists	exist	VERB
ejpam-4570	160	8	a	a	DET
ejpam-4570	160	9	unique	unique	ADJ
ejpam-4570	160	10	element	element	NOUN
ejpam-4570	160	11	x	x	SYM
ejpam-4570	160	12	∈	∈	NOUN
ejpam-4570	160	13	x	x	PUNCT
ejpam-4570	160	14	such	such	ADJ
ejpam-4570	160	15	that	that	SCONJ
ejpam-4570	160	16	y	y	PROPN
ejpam-4570	160	17	=	=	SYM
ejpam-4570	160	18	f(x	f(x	PROPN
ejpam-4570	160	19	)	)	PUNCT
ejpam-4570	160	20	∈	∈	PROPN
ejpam-4570	160	21	f(b	f(b	PROPN
ejpam-4570	160	22	)	)	PUNCT
ejpam-4570	160	23	.	.	PUNCT
ejpam-4570	161	1	thus	thus	ADV
ejpam-4570	161	2	,	,	PUNCT
ejpam-4570	161	3	x	x	PROPN
ejpam-4570	161	4	∈	∈	PROPN
ejpam-4570	161	5	b.	b.	PROPN
ejpam-4570	161	6	since	since	SCONJ
ejpam-4570	161	7	x	x	PROPN
ejpam-4570	161	8	is	be	AUX
ejpam-4570	161	9	fréchet	fréchet	VERB
ejpam-4570	161	10	,	,	PUNCT
ejpam-4570	161	11	there	there	PRON
ejpam-4570	161	12	exists	exist	VERB
ejpam-4570	161	13	a	a	DET
ejpam-4570	161	14	sequence	sequence	NOUN
ejpam-4570	161	15	(	(	PUNCT
ejpam-4570	161	16	an	an	NOUN
ejpam-4570	161	17	)	)	PUNCT
ejpam-4570	161	18	⊆	⊆	NUM
ejpam-4570	161	19	b	b	NOUN
ejpam-4570	161	20	such	such	ADJ
ejpam-4570	161	21	that	that	SCONJ
ejpam-4570	161	22	an	an	DET
ejpam-4570	161	23	−→	−→	NOUN
ejpam-4570	161	24	x.	x.	NOUN
ejpam-4570	161	25	since	since	SCONJ
ejpam-4570	161	26	the	the	DET
ejpam-4570	161	27	subspace	subspace	NOUN
ejpam-4570	161	28	k	k	PROPN
ejpam-4570	161	29	=	=	PUNCT
ejpam-4570	161	30	{	{	PUNCT
ejpam-4570	161	31	x	x	NOUN
ejpam-4570	161	32	}	}	PUNCT
ejpam-4570	161	33	∪	∪	ADJ
ejpam-4570	161	34	{	{	PUNCT
ejpam-4570	161	35	an	an	DET
ejpam-4570	161	36	:	:	PUNCT
ejpam-4570	161	37	n	n	CCONJ
ejpam-4570	161	38	∈	∈	PROPN
ejpam-4570	161	39	n	n	CCONJ
ejpam-4570	161	40	}	}	PUNCT
ejpam-4570	161	41	of	of	ADP
ejpam-4570	161	42	x	x	SYM
ejpam-4570	161	43	is	be	AUX
ejpam-4570	161	44	compact	compact	ADJ
ejpam-4570	161	45	,	,	PUNCT
ejpam-4570	161	46	the	the	DET
ejpam-4570	161	47	induced	induce	VERB
ejpam-4570	161	48	mapping	mapping	NOUN
ejpam-4570	161	49	f	f	NOUN
ejpam-4570	161	50	|k	|k	NOUN
ejpam-4570	161	51	:	:	PUNCT
ejpam-4570	161	52	k	k	X
ejpam-4570	161	53	→	→	SYM
ejpam-4570	161	54	f(k	f(k	VERB
ejpam-4570	161	55	)	)	PUNCT
ejpam-4570	161	56	is	be	AUX
ejpam-4570	161	57	a	a	DET
ejpam-4570	161	58	homeomorphism	homeomorphism	NOUN
ejpam-4570	161	59	.	.	PUNCT
ejpam-4570	162	1	let	let	VERB
ejpam-4570	162	2	w	w	PRON
ejpam-4570	162	3	⊆	⊆	NUM
ejpam-4570	162	4	y	y	NOUN
ejpam-4570	162	5	be	be	AUX
ejpam-4570	162	6	any	any	DET
ejpam-4570	162	7	open	open	ADJ
ejpam-4570	162	8	neighborhood	neighborhood	NOUN
ejpam-4570	162	9	of	of	ADP
ejpam-4570	162	10	y.	y.	PROPN
ejpam-4570	162	11	then	then	ADV
ejpam-4570	162	12	,	,	PUNCT
ejpam-4570	162	13	w	w	PROPN
ejpam-4570	162	14	∩	∩	NOUN
ejpam-4570	162	15	f(k	f(k	VERB
ejpam-4570	162	16	)	)	PUNCT
ejpam-4570	162	17	is	be	AUX
ejpam-4570	162	18	an	an	DET
ejpam-4570	162	19	open	open	ADJ
ejpam-4570	162	20	neighborhood	neighborhood	NOUN
ejpam-4570	162	21	of	of	ADP
ejpam-4570	162	22	y	y	PROPN
ejpam-4570	162	23	in	in	ADP
ejpam-4570	162	24	the	the	DET
ejpam-4570	162	25	subspace	subspace	NOUN
ejpam-4570	162	26	f(k	f(k	VERB
ejpam-4570	162	27	)	)	PUNCT
ejpam-4570	162	28	.	.	PUNCT
ejpam-4570	163	1	since	since	SCONJ
ejpam-4570	163	2	f	f	PROPN
ejpam-4570	163	3	|k	|k	PROPN
ejpam-4570	163	4	is	be	AUX
ejpam-4570	163	5	a	a	DET
ejpam-4570	163	6	homeomorphism	homeomorphism	NOUN
ejpam-4570	163	7	,	,	PUNCT
ejpam-4570	163	8	we	we	PRON
ejpam-4570	163	9	have	have	VERB
ejpam-4570	163	10	f−1(w	f−1(w	ADJ
ejpam-4570	163	11	∩	∩	NOUN
ejpam-4570	163	12	f(k	f(k	VERB
ejpam-4570	163	13	)	)	PUNCT
ejpam-4570	163	14	)	)	PUNCT
ejpam-4570	164	1	=	=	SYM
ejpam-4570	164	2	f−1(w	f−1(w	ADJ
ejpam-4570	164	3	)	)	PUNCT
ejpam-4570	164	4	∩	∩	NOUN
ejpam-4570	164	5	k	k	PROPN
ejpam-4570	164	6	is	be	AUX
ejpam-4570	164	7	an	an	DET
ejpam-4570	164	8	open	open	ADJ
ejpam-4570	164	9	neighborhood	neighborhood	NOUN
ejpam-4570	164	10	of	of	ADP
ejpam-4570	164	11	x	x	PUNCT
ejpam-4570	164	12	in	in	ADP
ejpam-4570	164	13	a	a	DET
ejpam-4570	164	14	subspace	subspace	NOUN
ejpam-4570	164	15	k	k	PROPN
ejpam-4570	164	16	of	of	ADP
ejpam-4570	164	17	x.	x.	NOUN
ejpam-4570	164	18	then	then	ADV
ejpam-4570	164	19	,	,	PUNCT
ejpam-4570	164	20	there	there	PRON
ejpam-4570	164	21	exists	exist	VERB
ejpam-4570	164	22	an	an	DET
ejpam-4570	164	23	m	m	NOUN
ejpam-4570	164	24	∈	∈	NOUN
ejpam-4570	164	25	n	n	PRON
ejpam-4570	164	26	such	such	ADJ
ejpam-4570	164	27	that	that	SCONJ
ejpam-4570	164	28	an	an	DET
ejpam-4570	164	29	∈	∈	PROPN
ejpam-4570	164	30	f−1(w	f−1(w	NOUN
ejpam-4570	164	31	∩	∩	NOUN
ejpam-4570	164	32	f(k	f(k	VERB
ejpam-4570	164	33	)	)	PUNCT
ejpam-4570	164	34	)	)	PUNCT
ejpam-4570	164	35	for	for	ADP
ejpam-4570	164	36	each	each	DET
ejpam-4570	164	37	n	n	PRON
ejpam-4570	164	38	≥	≥	NOUN
ejpam-4570	164	39	m.	m.	NOUN
ejpam-4570	164	40	hence	hence	ADV
ejpam-4570	164	41	,	,	PUNCT
ejpam-4570	164	42	f(an	f(an	PROPN
ejpam-4570	164	43	)	)	PUNCT
ejpam-4570	164	44	∈	∈	PROPN
ejpam-4570	164	45	w	w	NOUN
ejpam-4570	164	46	∩	∩	NOUN
ejpam-4570	164	47	f(k	f(k	VERB
ejpam-4570	164	48	)	)	PUNCT
ejpam-4570	164	49	for	for	ADP
ejpam-4570	164	50	each	each	DET
ejpam-4570	164	51	n	n	DET
ejpam-4570	164	52	≥	≥	NOUN
ejpam-4570	164	53	m	m	PROPN
ejpam-4570	164	54	and	and	CCONJ
ejpam-4570	164	55	thus	thus	ADV
ejpam-4570	164	56	w	w	ADP
ejpam-4570	164	57	∩	∩	ADJ
ejpam-4570	164	58	f(b	f(b	X
ejpam-4570	164	59	)	)	PUNCT
ejpam-4570	164	60	̸=	̸=	PROPN
ejpam-4570	164	61	∅.	∅.	PRON
ejpam-4570	164	62	so	so	ADV
ejpam-4570	164	63	,	,	PUNCT
ejpam-4570	164	64	we	we	PRON
ejpam-4570	164	65	get	get	VERB
ejpam-4570	164	66	y	y	PROPN
ejpam-4570	164	67	∈	∈	PROPN
ejpam-4570	164	68	f(b	f(b	PROPN
ejpam-4570	164	69	)	)	PUNCT
ejpam-4570	164	70	.	.	PUNCT
ejpam-4570	165	1	therefore	therefore	ADV
ejpam-4570	165	2	,	,	PUNCT
ejpam-4570	165	3	we	we	PRON
ejpam-4570	165	4	obtain	obtain	VERB
ejpam-4570	165	5	f(b	f(b	PROPN
ejpam-4570	165	6	)	)	PUNCT
ejpam-4570	165	7	⊆	⊆	NUM
ejpam-4570	165	8	f(b	f(b	NOUN
ejpam-4570	165	9	)	)	PUNCT
ejpam-4570	165	10	.	.	PUNCT
ejpam-4570	166	1	thus	thus	ADV
ejpam-4570	166	2	,	,	PUNCT
ejpam-4570	166	3	f	f	PROPN
ejpam-4570	166	4	is	be	AUX
ejpam-4570	166	5	continuous	continuous	ADJ
ejpam-4570	166	6	.	.	PUNCT
ejpam-4570	167	1	recall	recall	VERB
ejpam-4570	167	2	that	that	PRON
ejpam-4570	167	3	:	:	PUNCT
ejpam-4570	167	4	a	a	DET
ejpam-4570	167	5	space	space	NOUN
ejpam-4570	167	6	x	x	PUNCT
ejpam-4570	167	7	is	be	AUX
ejpam-4570	167	8	called	call	VERB
ejpam-4570	167	9	a	a	DET
ejpam-4570	167	10	k	k	NOUN
ejpam-4570	167	11	-	-	NOUN
ejpam-4570	167	12	space	space	NOUN
ejpam-4570	167	13	if	if	SCONJ
ejpam-4570	167	14	x	x	PRON
ejpam-4570	167	15	is	be	AUX
ejpam-4570	167	16	hausdorff	hausdorff	NOUN
ejpam-4570	167	17	and	and	CCONJ
ejpam-4570	167	18	it	it	PRON
ejpam-4570	167	19	is	be	AUX
ejpam-4570	167	20	a	a	DET
ejpam-4570	167	21	quotient	quotient	NOUN
ejpam-4570	167	22	image	image	NOUN
ejpam-4570	167	23	of	of	ADP
ejpam-4570	167	24	a	a	DET
ejpam-4570	167	25	locally	locally	ADV
ejpam-4570	167	26	compact	compact	ADJ
ejpam-4570	167	27	space	space	NOUN
ejpam-4570	168	1	[	[	X
ejpam-4570	168	2	12	12	NUM
ejpam-4570	168	3	]	]	PUNCT
ejpam-4570	168	4	.	.	PUNCT
ejpam-4570	169	1	in	in	ADP
ejpam-4570	169	2	view	view	NOUN
ejpam-4570	169	3	of	of	ADP
ejpam-4570	169	4	the	the	DET
ejpam-4570	169	5	facts	fact	NOUN
ejpam-4570	169	6	that	that	SCONJ
ejpam-4570	169	7	:	:	PUNCT
ejpam-4570	169	8	“	"	PUNCT
ejpam-4570	169	9	a	a	DET
ejpam-4570	169	10	function	function	NOUN
ejpam-4570	169	11	f	f	NOUN
ejpam-4570	169	12	from	from	ADP
ejpam-4570	169	13	a	a	DET
ejpam-4570	169	14	k	k	NOUN
ejpam-4570	169	15	-	-	NOUN
ejpam-4570	169	16	space	space	NOUN
ejpam-4570	169	17	x	x	PUNCT
ejpam-4570	169	18	into	into	ADP
ejpam-4570	169	19	a	a	DET
ejpam-4570	169	20	space	space	NOUN
ejpam-4570	169	21	y	y	NOUN
ejpam-4570	169	22	is	be	AUX
ejpam-4570	169	23	continuous	continuous	ADJ
ejpam-4570	169	24	if	if	SCONJ
ejpam-4570	169	25	and	and	CCONJ
ejpam-4570	169	26	only	only	ADV
ejpam-4570	169	27	if	if	SCONJ
ejpam-4570	169	28	f	f	PROPN
ejpam-4570	169	29	|z	|z	PROPN
ejpam-4570	169	30	:	:	PUNCT
ejpam-4570	169	31	z	z	PROPN
ejpam-4570	169	32	→	→	SYM
ejpam-4570	169	33	y	y	PROPN
ejpam-4570	169	34	is	be	AUX
ejpam-4570	169	35	continuous	continuous	ADJ
ejpam-4570	169	36	for	for	ADP
ejpam-4570	169	37	each	each	DET
ejpam-4570	169	38	compact	compact	ADJ
ejpam-4570	169	39	subspace	subspace	NOUN
ejpam-4570	169	40	z	z	PROPN
ejpam-4570	169	41	of	of	ADP
ejpam-4570	169	42	x	x	NOUN
ejpam-4570	169	43	”	"	PUNCT
ejpam-4570	169	44	,	,	PUNCT
ejpam-4570	169	45	every	every	DET
ejpam-4570	169	46	first	first	ADJ
ejpam-4570	169	47	countable	countable	ADJ
ejpam-4570	169	48	space	space	NOUN
ejpam-4570	169	49	is	be	AUX
ejpam-4570	169	50	fréchet	fréchet	VERB
ejpam-4570	169	51	and	and	CCONJ
ejpam-4570	169	52	every	every	DET
ejpam-4570	169	53	hausdorff	hausdorff	NOUN
ejpam-4570	169	54	locally	locally	ADV
ejpam-4570	169	55	compact	compact	ADJ
ejpam-4570	169	56	is	be	AUX
ejpam-4570	169	57	a	a	DET
ejpam-4570	169	58	k	k	NOUN
ejpam-4570	169	59	-	-	NOUN
ejpam-4570	169	60	space	space	NOUN
ejpam-4570	170	1	[	[	X
ejpam-4570	170	2	12	12	NUM
ejpam-4570	170	3	]	]	PUNCT
ejpam-4570	170	4	,	,	PUNCT
ejpam-4570	170	5	we	we	PRON
ejpam-4570	170	6	obtain	obtain	VERB
ejpam-4570	170	7	:	:	PUNCT
ejpam-4570	170	8	corollary	corollary	ADJ
ejpam-4570	170	9	5	5	NUM
ejpam-4570	170	10	.	.	PUNCT
ejpam-4570	171	1	if	if	SCONJ
ejpam-4570	171	2	x	x	PRON
ejpam-4570	171	3	is	be	AUX
ejpam-4570	171	4	a	a	DET
ejpam-4570	171	5	c	c	NOUN
ejpam-4570	171	6	-	-	PUNCT
ejpam-4570	171	7	almost	almost	ADV
ejpam-4570	171	8	normal	normal	ADJ
ejpam-4570	171	9	first	first	ADJ
ejpam-4570	171	10	countable	countable	ADJ
ejpam-4570	171	11	(	(	PUNCT
ejpam-4570	171	12	resp	resp	NOUN
ejpam-4570	171	13	.	.	PUNCT
ejpam-4570	172	1	k	k	X
ejpam-4570	172	2	-	-	NOUN
ejpam-4570	172	3	space	space	NOUN
ejpam-4570	172	4	,	,	PUNCT
ejpam-4570	172	5	hausdorff	hausdorff	X
ejpam-4570	172	6	locally	locally	ADV
ejpam-4570	172	7	compact	compact	ADJ
ejpam-4570	172	8	)	)	PUNCT
ejpam-4570	172	9	space	space	NOUN
ejpam-4570	172	10	and	and	CCONJ
ejpam-4570	172	11	f	f	NOUN
ejpam-4570	172	12	:	:	PUNCT
ejpam-4570	172	13	x	x	X
ejpam-4570	172	14	→	→	SYM
ejpam-4570	172	15	y	y	PROPN
ejpam-4570	172	16	is	be	AUX
ejpam-4570	172	17	a	a	DET
ejpam-4570	172	18	witness	witness	NOUN
ejpam-4570	172	19	of	of	ADP
ejpam-4570	172	20	the	the	DET
ejpam-4570	172	21	c	c	NOUN
ejpam-4570	172	22	-	-	PUNCT
ejpam-4570	172	23	almost	almost	ADV
ejpam-4570	172	24	normality	normality	NOUN
ejpam-4570	172	25	of	of	ADP
ejpam-4570	172	26	x	x	PRON
ejpam-4570	172	27	,	,	PUNCT
ejpam-4570	172	28	then	then	ADV
ejpam-4570	172	29	f	f	PROPN
ejpam-4570	172	30	is	be	AUX
ejpam-4570	172	31	continuous	continuous	ADJ
ejpam-4570	172	32	.	.	PUNCT
ejpam-4570	173	1	next	next	ADV
ejpam-4570	173	2	,	,	PUNCT
ejpam-4570	173	3	we	we	PRON
ejpam-4570	173	4	give	give	VERB
ejpam-4570	173	5	the	the	DET
ejpam-4570	173	6	following	follow	VERB
ejpam-4570	173	7	results	result	NOUN
ejpam-4570	173	8	:	:	PUNCT
ejpam-4570	173	9	proposition	proposition	NOUN
ejpam-4570	173	10	1	1	NUM
ejpam-4570	173	11	.	.	PUNCT
ejpam-4570	174	1	if	if	SCONJ
ejpam-4570	174	2	x	x	PRON
ejpam-4570	174	3	is	be	AUX
ejpam-4570	174	4	a	a	DET
ejpam-4570	174	5	t1	t1	NOUN
ejpam-4570	174	6	c	c	NOUN
ejpam-4570	174	7	-	-	PUNCT
ejpam-4570	174	8	almost	almost	ADV
ejpam-4570	174	9	normal	normal	ADJ
ejpam-4570	174	10	space	space	NOUN
ejpam-4570	174	11	,	,	PUNCT
ejpam-4570	174	12	then	then	ADV
ejpam-4570	174	13	a	a	DET
ejpam-4570	174	14	witness	witness	NOUN
ejpam-4570	174	15	y	y	PROPN
ejpam-4570	174	16	is	be	AUX
ejpam-4570	174	17	a	a	DET
ejpam-4570	174	18	t1	t1	NOUN
ejpam-4570	174	19	-	-	PUNCT
ejpam-4570	174	20	space	space	NOUN
ejpam-4570	174	21	.	.	PUNCT
ejpam-4570	175	1	proof	proof	NOUN
ejpam-4570	175	2	.	.	PUNCT
ejpam-4570	176	1	let	let	VERB
ejpam-4570	176	2	x	x	PRON
ejpam-4570	176	3	be	be	AUX
ejpam-4570	176	4	a	a	DET
ejpam-4570	176	5	t1	t1	NOUN
ejpam-4570	176	6	c	c	NOUN
ejpam-4570	176	7	-	-	PUNCT
ejpam-4570	176	8	almost	almost	ADV
ejpam-4570	176	9	normal	normal	ADJ
ejpam-4570	176	10	space	space	NOUN
ejpam-4570	176	11	.	.	PUNCT
ejpam-4570	177	1	since	since	SCONJ
ejpam-4570	177	2	x	x	PRON
ejpam-4570	177	3	is	be	AUX
ejpam-4570	177	4	a	a	DET
ejpam-4570	177	5	c	c	NOUN
ejpam-4570	177	6	-	-	PUNCT
ejpam-4570	177	7	almost	almost	ADV
ejpam-4570	177	8	normal	normal	ADJ
ejpam-4570	177	9	space	space	NOUN
ejpam-4570	177	10	,	,	PUNCT
ejpam-4570	177	11	there	there	PRON
ejpam-4570	177	12	exist	exist	VERB
ejpam-4570	177	13	an	an	DET
ejpam-4570	177	14	almost	almost	ADV
ejpam-4570	177	15	normal	normal	ADJ
ejpam-4570	177	16	space	space	NOUN
ejpam-4570	177	17	y	y	PROPN
ejpam-4570	177	18	and	and	CCONJ
ejpam-4570	177	19	a	a	DET
ejpam-4570	177	20	bijective	bijective	ADJ
ejpam-4570	177	21	function	function	NOUN
ejpam-4570	177	22	f	f	NOUN
ejpam-4570	177	23	:	:	PUNCT
ejpam-4570	177	24	(	(	PUNCT
ejpam-4570	177	25	x	x	X
ejpam-4570	177	26	,	,	PUNCT
ejpam-4570	177	27	t	t	PROPN
ejpam-4570	177	28	)	)	PUNCT
ejpam-4570	177	29	→	→	SYM
ejpam-4570	177	30	(	(	PUNCT
ejpam-4570	177	31	y	y	PROPN
ejpam-4570	177	32	,	,	PUNCT
ejpam-4570	177	33	t	t	PROPN
ejpam-4570	177	34	′	′	NUM
ejpam-4570	177	35	)	)	PUNCT
ejpam-4570	177	36	such	such	ADJ
ejpam-4570	177	37	that	that	SCONJ
ejpam-4570	177	38	f	f	PROPN
ejpam-4570	177	39	|c	|c	VERB
ejpam-4570	177	40	:	:	PUNCT
ejpam-4570	177	41	c	c	PROPN
ejpam-4570	177	42	→	→	SYM
ejpam-4570	177	43	f(c	f(c	PROPN
ejpam-4570	177	44	)	)	PUNCT
ejpam-4570	177	45	is	be	AUX
ejpam-4570	177	46	a	a	DET
ejpam-4570	177	47	homeomorphism	homeomorphism	NOUN
ejpam-4570	177	48	for	for	ADP
ejpam-4570	177	49	each	each	DET
ejpam-4570	177	50	compact	compact	ADJ
ejpam-4570	177	51	subset	subset	NOUN
ejpam-4570	177	52	c	c	NOUN
ejpam-4570	177	53	⊆	⊆	PROPN
ejpam-4570	177	54	x.	x.	NOUN
ejpam-4570	177	55	suppose	suppose	VERB
ejpam-4570	177	56	y	y	PROPN
ejpam-4570	177	57	is	be	AUX
ejpam-4570	177	58	not	not	PART
ejpam-4570	177	59	t1	t1	NOUN
ejpam-4570	177	60	.	.	PUNCT
ejpam-4570	178	1	then	then	ADV
ejpam-4570	178	2	,	,	PUNCT
ejpam-4570	178	3	there	there	PRON
ejpam-4570	178	4	exist	exist	VERB
ejpam-4570	178	5	two	two	NUM
ejpam-4570	178	6	distinct	distinct	ADJ
ejpam-4570	178	7	elements	element	NOUN
ejpam-4570	178	8	x	x	PUNCT
ejpam-4570	178	9	and	and	CCONJ
ejpam-4570	178	10	y	y	PROPN
ejpam-4570	178	11	in	in	ADP
ejpam-4570	178	12	y	y	PRON
ejpam-4570	178	13	such	such	ADJ
ejpam-4570	178	14	that	that	SCONJ
ejpam-4570	178	15	if	if	SCONJ
ejpam-4570	178	16	u	u	NOUN
ejpam-4570	178	17	is	be	AUX
ejpam-4570	178	18	an	an	DET
ejpam-4570	178	19	open	open	ADJ
ejpam-4570	178	20	neighborhood	neighborhood	NOUN
ejpam-4570	178	21	of	of	ADP
ejpam-4570	178	22	x	x	NOUN
ejpam-4570	178	23	,	,	PUNCT
ejpam-4570	178	24	then	then	ADV
ejpam-4570	178	25	y	y	PROPN
ejpam-4570	178	26	∈	∈	PROPN
ejpam-4570	178	27	u	u	NOUN
ejpam-4570	178	28	or	or	CCONJ
ejpam-4570	178	29	if	if	SCONJ
ejpam-4570	178	30	v	v	NOUN
ejpam-4570	178	31	is	be	AUX
ejpam-4570	178	32	an	an	DET
ejpam-4570	178	33	open	open	ADJ
ejpam-4570	178	34	neighborhood	neighborhood	NOUN
ejpam-4570	178	35	of	of	ADP
ejpam-4570	178	36	y	y	PROPN
ejpam-4570	178	37	,	,	PUNCT
ejpam-4570	178	38	then	then	ADV
ejpam-4570	178	39	x	x	PART
ejpam-4570	178	40	∈	∈	PROPN
ejpam-4570	178	41	v	v	NOUN
ejpam-4570	178	42	.	.	PUNCT
ejpam-4570	179	1	thus	thus	ADV
ejpam-4570	179	2	,	,	PUNCT
ejpam-4570	179	3	the	the	DET
ejpam-4570	179	4	set	set	NOUN
ejpam-4570	179	5	m	m	NOUN
ejpam-4570	179	6	=	=	SYM
ejpam-4570	179	7	{	{	PUNCT
ejpam-4570	179	8	f−1(x	f−1(x	NOUN
ejpam-4570	179	9	)	)	PUNCT
ejpam-4570	179	10	,	,	PUNCT
ejpam-4570	179	11	f−1(y	f−1(y	PROPN
ejpam-4570	179	12	)	)	PUNCT
ejpam-4570	179	13	}	}	PUNCT
ejpam-4570	179	14	is	be	AUX
ejpam-4570	179	15	a	a	DET
ejpam-4570	179	16	t1	t1	ADJ
ejpam-4570	179	17	-	-	ADJ
ejpam-4570	179	18	compact	compact	ADJ
ejpam-4570	179	19	subspace	subspace	NOUN
ejpam-4570	179	20	of	of	ADP
ejpam-4570	179	21	x.	x.	NOUN
ejpam-4570	179	22	then	then	ADV
ejpam-4570	179	23	,	,	PUNCT
ejpam-4570	179	24	f	f	PROPN
ejpam-4570	179	25	|m	|m	NOUN
ejpam-4570	179	26	:	:	PUNCT
ejpam-4570	179	27	m	m	PROPN
ejpam-4570	179	28	→	→	SYM
ejpam-4570	179	29	f(m	f(m	PROPN
ejpam-4570	179	30	)	)	PUNCT
ejpam-4570	179	31	is	be	AUX
ejpam-4570	179	32	a	a	DET
ejpam-4570	179	33	homeomorphism	homeomorphism	NOUN
ejpam-4570	179	34	.	.	PUNCT
ejpam-4570	180	1	but	but	CCONJ
ejpam-4570	180	2	f(m	f(m	PROPN
ejpam-4570	180	3	)	)	PUNCT
ejpam-4570	180	4	=	=	PRON
ejpam-4570	180	5	{	{	PUNCT
ejpam-4570	180	6	x	x	NOUN
ejpam-4570	180	7	,	,	PUNCT
ejpam-4570	180	8	y	y	NOUN
ejpam-4570	180	9	}	}	PUNCT
ejpam-4570	180	10	can	can	AUX
ejpam-4570	180	11	not	not	PART
ejpam-4570	180	12	be	be	AUX
ejpam-4570	180	13	t1	t1	NOUN
ejpam-4570	180	14	,	,	PUNCT
ejpam-4570	180	15	which	which	PRON
ejpam-4570	180	16	is	be	AUX
ejpam-4570	180	17	a	a	DET
ejpam-4570	180	18	contradiction	contradiction	NOUN
ejpam-4570	180	19	.	.	PUNCT
ejpam-4570	181	1	therefore	therefore	ADV
ejpam-4570	181	2	,	,	PUNCT
ejpam-4570	181	3	y	y	PROPN
ejpam-4570	181	4	must	must	AUX
ejpam-4570	181	5	be	be	AUX
ejpam-4570	181	6	t1	t1	NOUN
ejpam-4570	181	7	.	.	PUNCT
ejpam-4570	182	1	proposition	proposition	NOUN
ejpam-4570	182	2	2	2	NUM
ejpam-4570	182	3	.	.	PUNCT
ejpam-4570	183	1	if	if	SCONJ
ejpam-4570	183	2	x	x	PRON
ejpam-4570	183	3	is	be	AUX
ejpam-4570	183	4	a	a	DET
ejpam-4570	183	5	t1	t1	NOUN
ejpam-4570	183	6	l	l	NOUN
ejpam-4570	183	7	-	-	PUNCT
ejpam-4570	183	8	almost	almost	ADV
ejpam-4570	183	9	normal	normal	ADJ
ejpam-4570	183	10	space	space	NOUN
ejpam-4570	183	11	,	,	PUNCT
ejpam-4570	183	12	then	then	ADV
ejpam-4570	183	13	a	a	DET
ejpam-4570	183	14	witness	witness	NOUN
ejpam-4570	183	15	y	y	PROPN
ejpam-4570	183	16	is	be	AUX
ejpam-4570	183	17	a	a	DET
ejpam-4570	183	18	t1	t1	NOUN
ejpam-4570	183	19	-	-	PUNCT
ejpam-4570	183	20	space	space	NOUN
ejpam-4570	183	21	.	.	PUNCT
ejpam-4570	184	1	proof	proof	NOUN
ejpam-4570	184	2	.	.	PUNCT
ejpam-4570	185	1	similar	similar	ADJ
ejpam-4570	185	2	to	to	ADP
ejpam-4570	185	3	the	the	DET
ejpam-4570	185	4	proof	proof	NOUN
ejpam-4570	185	5	of	of	ADP
ejpam-4570	185	6	proposition	proposition	NOUN
ejpam-4570	185	7	1	1	NUM
ejpam-4570	185	8	.	.	PUNCT
ejpam-4570	185	9	theorem	theorem	VERB
ejpam-4570	185	10	7	7	NUM
ejpam-4570	185	11	.	.	PUNCT
ejpam-4570	186	1	if	if	SCONJ
ejpam-4570	186	2	(	(	PUNCT
ejpam-4570	186	3	x	x	X
ejpam-4570	186	4	,	,	PUNCT
ejpam-4570	186	5	t	t	PROPN
ejpam-4570	186	6	)	)	PUNCT
ejpam-4570	186	7	is	be	AUX
ejpam-4570	186	8	a	a	DET
ejpam-4570	186	9	c	c	NOUN
ejpam-4570	186	10	-	-	PUNCT
ejpam-4570	186	11	almost	almost	ADV
ejpam-4570	186	12	normal	normal	ADJ
ejpam-4570	186	13	fréchet	fréchet	NOUN
ejpam-4570	186	14	(	(	PUNCT
ejpam-4570	186	15	resp	resp	NOUN
ejpam-4570	186	16	.	.	PUNCT
ejpam-4570	187	1	first	first	ADV
ejpam-4570	187	2	countable	countable	ADJ
ejpam-4570	187	3	,	,	PUNCT
ejpam-4570	187	4	k	k	NOUN
ejpam-4570	187	5	-	-	NOUN
ejpam-4570	187	6	space	space	NOUN
ejpam-4570	187	7	)	)	PUNCT
ejpam-4570	187	8	such	such	ADJ
ejpam-4570	187	9	that	that	SCONJ
ejpam-4570	187	10	the	the	DET
ejpam-4570	187	11	witness	witness	NOUN
ejpam-4570	187	12	(	(	PUNCT
ejpam-4570	187	13	y	y	PROPN
ejpam-4570	187	14	,	,	PUNCT
ejpam-4570	187	15	t	t	PROPN
ejpam-4570	187	16	′	′	NUM
ejpam-4570	187	17	)	)	PUNCT
ejpam-4570	187	18	of	of	ADP
ejpam-4570	187	19	the	the	DET
ejpam-4570	187	20	c	c	NOUN
ejpam-4570	187	21	-	-	PUNCT
ejpam-4570	187	22	almost	almost	ADV
ejpam-4570	187	23	normality	normality	NOUN
ejpam-4570	187	24	of	of	ADP
ejpam-4570	187	25	x	x	SYM
ejpam-4570	187	26	is	be	AUX
ejpam-4570	187	27	hausdorff	hausdorff	NOUN
ejpam-4570	187	28	,	,	PUNCT
ejpam-4570	187	29	then	then	ADV
ejpam-4570	187	30	(	(	PUNCT
ejpam-4570	187	31	x	x	X
ejpam-4570	187	32	,	,	PUNCT
ejpam-4570	187	33	t	t	PROPN
ejpam-4570	187	34	)	)	PUNCT
ejpam-4570	187	35	is	be	AUX
ejpam-4570	187	36	epi	epi	NOUN
ejpam-4570	187	37	-	-	ADJ
ejpam-4570	187	38	almost	almost	ADV
ejpam-4570	187	39	normal	normal	ADJ
ejpam-4570	187	40	.	.	PUNCT
ejpam-4570	188	1	wafa	wafa	PROPN
ejpam-4570	188	2	khalaf	khalaf	PROPN
ejpam-4570	188	3	alqurashi	alqurashi	PROPN
ejpam-4570	188	4	,	,	PUNCT
ejpam-4570	188	5	sadeq	sadeq	PROPN
ejpam-4570	188	6	ali	ali	PROPN
ejpam-4570	188	7	thabit	thabit	PROPN
ejpam-4570	188	8	/	/	SYM
ejpam-4570	188	9	eur	eur	PROPN
ejpam-4570	188	10	.	.	PUNCT
ejpam-4570	189	1	j.	j.	PROPN
ejpam-4570	189	2	pure	pure	PROPN
ejpam-4570	189	3	appl	appl	PROPN
ejpam-4570	189	4	.	.	PROPN
ejpam-4570	189	5	math	math	PROPN
ejpam-4570	189	6	,	,	PUNCT
ejpam-4570	189	7	15	15	NUM
ejpam-4570	189	8	(	(	PUNCT
ejpam-4570	189	9	4	4	NUM
ejpam-4570	189	10	)	)	PUNCT
ejpam-4570	189	11	(	(	PUNCT
ejpam-4570	189	12	2022	2022	NUM
ejpam-4570	189	13	)	)	PUNCT
ejpam-4570	189	14	,	,	PUNCT
ejpam-4570	189	15	1760	1760	NUM
ejpam-4570	189	16	-	-	SYM
ejpam-4570	189	17	1782	1782	NUM
ejpam-4570	189	18	1766	1766	NUM
ejpam-4570	189	19	proof	proof	NOUN
ejpam-4570	189	20	.	.	PUNCT
ejpam-4570	190	1	let	let	VERB
ejpam-4570	190	2	x	x	PRON
ejpam-4570	190	3	be	be	AUX
ejpam-4570	190	4	a	a	DET
ejpam-4570	190	5	c	c	NOUN
ejpam-4570	190	6	-	-	PUNCT
ejpam-4570	190	7	almost	almost	ADV
ejpam-4570	190	8	normal	normal	ADJ
ejpam-4570	190	9	fréchet	fréchet	NOUN
ejpam-4570	190	10	space	space	NOUN
ejpam-4570	190	11	(	(	PUNCT
ejpam-4570	190	12	resp	resp	NOUN
ejpam-4570	190	13	.	.	PUNCT
ejpam-4570	191	1	first	first	ADV
ejpam-4570	191	2	countable	countable	ADJ
ejpam-4570	191	3	,	,	PUNCT
ejpam-4570	191	4	k	k	NOUN
ejpam-4570	191	5	-	-	NOUN
ejpam-4570	191	6	space	space	NOUN
ejpam-4570	191	7	)	)	PUNCT
ejpam-4570	191	8	and	and	CCONJ
ejpam-4570	191	9	the	the	DET
ejpam-4570	191	10	witness	witness	NOUN
ejpam-4570	191	11	y	y	PROPN
ejpam-4570	191	12	of	of	ADP
ejpam-4570	191	13	the	the	DET
ejpam-4570	191	14	c	c	NOUN
ejpam-4570	191	15	-	-	PUNCT
ejpam-4570	191	16	almost	almost	ADV
ejpam-4570	191	17	normality	normality	NOUN
ejpam-4570	191	18	of	of	ADP
ejpam-4570	191	19	x	x	PART
ejpam-4570	191	20	be	be	AUX
ejpam-4570	191	21	hausdorff	hausdorff	NOUN
ejpam-4570	191	22	.	.	PUNCT
ejpam-4570	192	1	then	then	ADV
ejpam-4570	192	2	,	,	PUNCT
ejpam-4570	192	3	there	there	PRON
ejpam-4570	192	4	exist	exist	VERB
ejpam-4570	192	5	a	a	DET
ejpam-4570	192	6	hausdorff	hausdorff	NOUN
ejpam-4570	192	7	almost	almost	ADV
ejpam-4570	192	8	normal	normal	ADJ
ejpam-4570	192	9	space	space	NOUN
ejpam-4570	192	10	y	y	PROPN
ejpam-4570	192	11	and	and	CCONJ
ejpam-4570	192	12	a	a	DET
ejpam-4570	192	13	bijective	bijective	ADJ
ejpam-4570	192	14	function	function	NOUN
ejpam-4570	192	15	f	f	NOUN
ejpam-4570	192	16	:	:	PUNCT
ejpam-4570	192	17	(	(	PUNCT
ejpam-4570	192	18	x	x	X
ejpam-4570	192	19	,	,	PUNCT
ejpam-4570	192	20	t	t	PROPN
ejpam-4570	192	21	)	)	PUNCT
ejpam-4570	192	22	→	→	SYM
ejpam-4570	192	23	(	(	PUNCT
ejpam-4570	192	24	y	y	PROPN
ejpam-4570	192	25	,	,	PUNCT
ejpam-4570	192	26	t	t	PROPN
ejpam-4570	192	27	′	′	NUM
ejpam-4570	192	28	)	)	PUNCT
ejpam-4570	192	29	such	such	ADJ
ejpam-4570	192	30	that	that	SCONJ
ejpam-4570	192	31	f	f	PROPN
ejpam-4570	192	32	|c	|c	VERB
ejpam-4570	192	33	:	:	PUNCT
ejpam-4570	192	34	c	c	PROPN
ejpam-4570	192	35	→	→	SYM
ejpam-4570	192	36	f(c	f(c	PROPN
ejpam-4570	192	37	)	)	PUNCT
ejpam-4570	192	38	is	be	AUX
ejpam-4570	192	39	a	a	DET
ejpam-4570	192	40	homeomorphism	homeomorphism	NOUN
ejpam-4570	192	41	for	for	ADP
ejpam-4570	192	42	each	each	DET
ejpam-4570	192	43	compact	compact	ADJ
ejpam-4570	192	44	subset	subset	NOUN
ejpam-4570	192	45	c	c	NOUN
ejpam-4570	192	46	⊆	⊆	NUM
ejpam-4570	192	47	x.	x.	NOUN
ejpam-4570	192	48	since	since	SCONJ
ejpam-4570	192	49	x	x	PROPN
ejpam-4570	192	50	is	be	AUX
ejpam-4570	192	51	fréchet	fréchet	VERB
ejpam-4570	192	52	(	(	PUNCT
ejpam-4570	192	53	resp	resp	NOUN
ejpam-4570	192	54	.	.	PUNCT
ejpam-4570	193	1	first	first	ADV
ejpam-4570	193	2	countable	countable	ADJ
ejpam-4570	193	3	,	,	PUNCT
ejpam-4570	193	4	k	k	NOUN
ejpam-4570	193	5	-	-	NOUN
ejpam-4570	193	6	space	space	NOUN
ejpam-4570	193	7	)	)	PUNCT
ejpam-4570	193	8	,	,	PUNCT
ejpam-4570	193	9	we	we	PRON
ejpam-4570	193	10	have	have	VERB
ejpam-4570	193	11	f	f	PROPN
ejpam-4570	193	12	is	be	AUX
ejpam-4570	193	13	continuous	continuous	ADJ
ejpam-4570	193	14	.	.	PUNCT
ejpam-4570	194	1	define	define	VERB
ejpam-4570	194	2	a	a	DET
ejpam-4570	194	3	topology	topology	NOUN
ejpam-4570	194	4	t	t	NOUN
ejpam-4570	194	5	⋆	⋆	VERB
ejpam-4570	194	6	on	on	ADP
ejpam-4570	194	7	x	x	PUNCT
ejpam-4570	194	8	as	as	SCONJ
ejpam-4570	194	9	follows	follow	VERB
ejpam-4570	194	10	:	:	PUNCT
ejpam-4570	195	1	t	t	NOUN
ejpam-4570	195	2	⋆	⋆	X
ejpam-4570	195	3	=	=	SYM
ejpam-4570	195	4	{	{	PUNCT
ejpam-4570	195	5	f−1(u	f−1(u	PROPN
ejpam-4570	195	6	)	)	PUNCT
ejpam-4570	195	7	:	:	PUNCT
ejpam-4570	196	1	u	u	PROPN
ejpam-4570	196	2	∈	∈	PROPN
ejpam-4570	196	3	t	t	NOUN
ejpam-4570	196	4	′	′	NOUN
ejpam-4570	196	5	}	}	PUNCT
ejpam-4570	196	6	.	.	PUNCT
ejpam-4570	197	1	clearly	clearly	ADV
ejpam-4570	197	2	,	,	PUNCT
ejpam-4570	197	3	t	t	PROPN
ejpam-4570	197	4	⋆	⋆	NOUN
ejpam-4570	197	5	is	be	AUX
ejpam-4570	197	6	a	a	DET
ejpam-4570	197	7	topology	topology	NOUN
ejpam-4570	197	8	on	on	ADP
ejpam-4570	197	9	x	x	NOUN
ejpam-4570	197	10	,	,	PUNCT
ejpam-4570	197	11	which	which	PRON
ejpam-4570	197	12	is	be	AUX
ejpam-4570	197	13	coarser	coarse	ADJ
ejpam-4570	197	14	than	than	ADP
ejpam-4570	197	15	t	t	PROPN
ejpam-4570	197	16	,	,	PUNCT
ejpam-4570	197	17	such	such	ADJ
ejpam-4570	197	18	that	that	SCONJ
ejpam-4570	197	19	f	f	X
ejpam-4570	197	20	:	:	PUNCT
ejpam-4570	197	21	(	(	PUNCT
ejpam-4570	197	22	x	x	X
ejpam-4570	197	23	,	,	PUNCT
ejpam-4570	197	24	t	t	PROPN
ejpam-4570	197	25	⋆	⋆	NOUN
ejpam-4570	197	26	)	)	PUNCT
ejpam-4570	197	27	→	→	SYM
ejpam-4570	197	28	(	(	PUNCT
ejpam-4570	197	29	y	y	PROPN
ejpam-4570	197	30	,	,	PUNCT
ejpam-4570	197	31	t	t	PROPN
ejpam-4570	197	32	′	′	NUM
ejpam-4570	197	33	)	)	PUNCT
ejpam-4570	197	34	is	be	AUX
ejpam-4570	197	35	continuous	continuous	ADJ
ejpam-4570	197	36	.	.	PUNCT
ejpam-4570	198	1	if	if	SCONJ
ejpam-4570	198	2	w	w	PROPN
ejpam-4570	198	3	∈	∈	PROPN
ejpam-4570	198	4	t	t	PROPN
ejpam-4570	198	5	⋆	⋆	NOUN
ejpam-4570	198	6	,	,	PUNCT
ejpam-4570	198	7	then	then	ADV
ejpam-4570	198	8	w	w	PROPN
ejpam-4570	198	9	=	=	PUNCT
ejpam-4570	198	10	f−1(u	f−1(u	PROPN
ejpam-4570	198	11	)	)	PUNCT
ejpam-4570	198	12	for	for	ADP
ejpam-4570	198	13	some	some	DET
ejpam-4570	198	14	open	open	ADJ
ejpam-4570	198	15	set	set	NOUN
ejpam-4570	198	16	u	u	NOUN
ejpam-4570	198	17	in	in	ADP
ejpam-4570	198	18	t	t	PROPN
ejpam-4570	198	19	′.	′.	NOUN
ejpam-4570	198	20	so	so	ADV
ejpam-4570	198	21	,	,	PUNCT
ejpam-4570	198	22	f(w	f(w	PROPN
ejpam-4570	198	23	)	)	PUNCT
ejpam-4570	198	24	=	=	PUNCT
ejpam-4570	198	25	f(f−1(u	f(f−1(u	PROPN
ejpam-4570	198	26	)	)	PUNCT
ejpam-4570	198	27	)	)	PUNCT
ejpam-4570	199	1	=	=	SYM
ejpam-4570	199	2	u	u	PROPN
ejpam-4570	199	3	,	,	PUNCT
ejpam-4570	199	4	which	which	PRON
ejpam-4570	199	5	is	be	AUX
ejpam-4570	199	6	an	an	DET
ejpam-4570	199	7	open	open	ADJ
ejpam-4570	199	8	set	set	NOUN
ejpam-4570	199	9	in	in	ADP
ejpam-4570	199	10	(	(	PUNCT
ejpam-4570	199	11	y	y	PROPN
ejpam-4570	199	12	,	,	PUNCT
ejpam-4570	199	13	t	t	PROPN
ejpam-4570	199	14	′	′	NUM
ejpam-4570	199	15	)	)	PUNCT
ejpam-4570	199	16	.	.	PUNCT
ejpam-4570	200	1	thus	thus	ADV
ejpam-4570	200	2	,	,	PUNCT
ejpam-4570	200	3	f	f	X
ejpam-4570	200	4	:	:	PUNCT
ejpam-4570	200	5	(	(	PUNCT
ejpam-4570	200	6	x	x	X
ejpam-4570	200	7	,	,	PUNCT
ejpam-4570	200	8	t	t	PROPN
ejpam-4570	200	9	⋆	⋆	NOUN
ejpam-4570	200	10	)	)	PUNCT
ejpam-4570	200	11	→	→	SYM
ejpam-4570	200	12	(	(	PUNCT
ejpam-4570	200	13	y	y	PROPN
ejpam-4570	200	14	,	,	PUNCT
ejpam-4570	200	15	t	t	PROPN
ejpam-4570	200	16	′	′	NUM
ejpam-4570	200	17	)	)	PUNCT
ejpam-4570	200	18	is	be	AUX
ejpam-4570	200	19	open	open	ADJ
ejpam-4570	200	20	and	and	CCONJ
ejpam-4570	200	21	hence	hence	ADV
ejpam-4570	200	22	a	a	DET
ejpam-4570	200	23	homoeomorphism	homoeomorphism	NOUN
ejpam-4570	200	24	.	.	PUNCT
ejpam-4570	201	1	since	since	SCONJ
ejpam-4570	201	2	(	(	PUNCT
ejpam-4570	201	3	y	y	PROPN
ejpam-4570	201	4	,	,	PUNCT
ejpam-4570	201	5	t	t	PROPN
ejpam-4570	201	6	′	′	NUM
ejpam-4570	201	7	)	)	PUNCT
ejpam-4570	201	8	is	be	AUX
ejpam-4570	201	9	hausdorff	hausdorff	NOUN
ejpam-4570	201	10	almost	almost	ADV
ejpam-4570	201	11	normal	normal	ADJ
ejpam-4570	201	12	and	and	CCONJ
ejpam-4570	201	13	(	(	PUNCT
ejpam-4570	201	14	x	x	X
ejpam-4570	201	15	,	,	PUNCT
ejpam-4570	201	16	t	t	PROPN
ejpam-4570	201	17	⋆	⋆	NOUN
ejpam-4570	201	18	)	)	PUNCT
ejpam-4570	201	19	∼=	∼=	PROPN
ejpam-4570	201	20	(	(	PUNCT
ejpam-4570	201	21	y	y	PROPN
ejpam-4570	201	22	,	,	PUNCT
ejpam-4570	201	23	t	t	PROPN
ejpam-4570	201	24	′	′	NUM
ejpam-4570	201	25	)	)	PUNCT
ejpam-4570	201	26	,	,	PUNCT
ejpam-4570	201	27	we	we	PRON
ejpam-4570	201	28	obtain	obtain	VERB
ejpam-4570	201	29	(	(	PUNCT
ejpam-4570	201	30	x	x	X
ejpam-4570	201	31	,	,	PUNCT
ejpam-4570	201	32	t	t	PROPN
ejpam-4570	201	33	⋆	⋆	PROPN
ejpam-4570	201	34	)	)	PUNCT
ejpam-4570	201	35	is	be	AUX
ejpam-4570	201	36	hausdorff	hausdorff	NOUN
ejpam-4570	201	37	almost	almost	ADV
ejpam-4570	201	38	normal	normal	ADJ
ejpam-4570	201	39	.	.	PUNCT
ejpam-4570	202	1	since	since	SCONJ
ejpam-4570	202	2	t	t	PROPN
ejpam-4570	202	3	⋆	⋆	VERB
ejpam-4570	202	4	⊆	⊆	NUM
ejpam-4570	202	5	t	t	NOUN
ejpam-4570	202	6	,	,	PUNCT
ejpam-4570	202	7	we	we	PRON
ejpam-4570	202	8	conclude	conclude	VERB
ejpam-4570	202	9	:	:	PUNCT
ejpam-4570	202	10	(	(	PUNCT
ejpam-4570	202	11	x	x	X
ejpam-4570	202	12	,	,	PUNCT
ejpam-4570	202	13	t	t	PROPN
ejpam-4570	202	14	)	)	PUNCT
ejpam-4570	202	15	is	be	AUX
ejpam-4570	202	16	epi	epi	NOUN
ejpam-4570	202	17	-	-	ADJ
ejpam-4570	202	18	almost	almost	ADV
ejpam-4570	202	19	normal	normal	ADJ
ejpam-4570	202	20	since	since	SCONJ
ejpam-4570	202	21	every	every	DET
ejpam-4570	202	22	hausdorff	hausdorff	NOUN
ejpam-4570	202	23	nearly	nearly	ADV
ejpam-4570	202	24	compact	compact	ADJ
ejpam-4570	202	25	space	space	NOUN
ejpam-4570	202	26	is	be	AUX
ejpam-4570	202	27	epi	epi	NOUN
ejpam-4570	202	28	-	-	ADJ
ejpam-4570	202	29	normal	normal	ADJ
ejpam-4570	202	30	[	[	X
ejpam-4570	202	31	17	17	NUM
ejpam-4570	202	32	,	,	PUNCT
ejpam-4570	202	33	theorem	theorem	VERB
ejpam-4570	202	34	17	17	NUM
ejpam-4570	202	35	]	]	PUNCT
ejpam-4570	202	36	,	,	PUNCT
ejpam-4570	202	37	every	every	DET
ejpam-4570	202	38	epi	epi	ADJ
ejpam-4570	202	39	-	-	ADJ
ejpam-4570	202	40	normal	normal	ADJ
ejpam-4570	202	41	space	space	NOUN
ejpam-4570	202	42	is	be	AUX
ejpam-4570	202	43	epi	epi	NOUN
ejpam-4570	202	44	-	-	ADJ
ejpam-4570	202	45	almost	almost	ADV
ejpam-4570	202	46	normal	normal	ADJ
ejpam-4570	202	47	and	and	CCONJ
ejpam-4570	202	48	every	every	DET
ejpam-4570	202	49	epi	epi	NOUN
ejpam-4570	202	50	-	-	ADJ
ejpam-4570	202	51	almost	almost	ADV
ejpam-4570	202	52	normal	normal	ADJ
ejpam-4570	202	53	space	space	NOUN
ejpam-4570	202	54	is	be	AUX
ejpam-4570	202	55	c	c	NOUN
ejpam-4570	202	56	-	-	PUNCT
ejpam-4570	202	57	almost	almost	ADV
ejpam-4570	202	58	normal	normal	ADJ
ejpam-4570	202	59	(	(	PUNCT
ejpam-4570	202	60	theorem	theorem	NOUN
ejpam-4570	202	61	2	2	NUM
ejpam-4570	202	62	)	)	PUNCT
ejpam-4570	202	63	,	,	PUNCT
ejpam-4570	202	64	we	we	PRON
ejpam-4570	202	65	conclude	conclude	VERB
ejpam-4570	202	66	:	:	PUNCT
ejpam-4570	202	67	corollary	corollary	ADJ
ejpam-4570	202	68	6	6	NUM
ejpam-4570	202	69	.	.	PUNCT
ejpam-4570	203	1	(	(	PUNCT
ejpam-4570	203	2	1	1	X
ejpam-4570	203	3	)	)	PUNCT
ejpam-4570	203	4	every	every	DET
ejpam-4570	203	5	hausdorff	hausdorff	NOUN
ejpam-4570	203	6	nearly	nearly	ADV
ejpam-4570	203	7	compact	compact	ADJ
ejpam-4570	203	8	space	space	NOUN
ejpam-4570	203	9	is	be	AUX
ejpam-4570	203	10	c	c	NOUN
ejpam-4570	203	11	-	-	PUNCT
ejpam-4570	203	12	almost	almost	ADV
ejpam-4570	203	13	normal	normal	ADJ
ejpam-4570	203	14	.	.	PUNCT
ejpam-4570	204	1	(	(	PUNCT
ejpam-4570	204	2	2	2	X
ejpam-4570	204	3	)	)	PUNCT
ejpam-4570	204	4	every	every	DET
ejpam-4570	204	5	hausdorff	hausdorff	NOUN
ejpam-4570	204	6	nearly	nearly	ADV
ejpam-4570	204	7	paracompact	paracompact	ADJ
ejpam-4570	204	8	space	space	NOUN
ejpam-4570	204	9	is	be	AUX
ejpam-4570	204	10	c	c	NOUN
ejpam-4570	204	11	-	-	PUNCT
ejpam-4570	204	12	almost	almost	ADV
ejpam-4570	204	13	normal	normal	ADJ
ejpam-4570	204	14	.	.	PUNCT
ejpam-4570	205	1	theorem	theorem	VERB
ejpam-4570	205	2	8	8	NUM
ejpam-4570	205	3	.	.	PUNCT
ejpam-4570	206	1	every	every	DET
ejpam-4570	206	2	l	l	NOUN
ejpam-4570	206	3	-	-	ADJ
ejpam-4570	206	4	almost	almost	ADV
ejpam-4570	206	5	normal	normal	ADJ
ejpam-4570	206	6	space	space	NOUN
ejpam-4570	206	7	is	be	AUX
ejpam-4570	206	8	c	c	NOUN
ejpam-4570	206	9	-	-	PUNCT
ejpam-4570	206	10	almost	almost	ADV
ejpam-4570	206	11	normal	normal	ADJ
ejpam-4570	206	12	.	.	PUNCT
ejpam-4570	207	1	proof	proof	NOUN
ejpam-4570	207	2	.	.	PUNCT
ejpam-4570	208	1	let	let	VERB
ejpam-4570	208	2	x	x	PRON
ejpam-4570	208	3	be	be	AUX
ejpam-4570	208	4	an	an	DET
ejpam-4570	208	5	l	l	NOUN
ejpam-4570	208	6	-	-	ADJ
ejpam-4570	208	7	almost	almost	ADV
ejpam-4570	208	8	normal	normal	ADJ
ejpam-4570	208	9	space	space	NOUN
ejpam-4570	208	10	.	.	PUNCT
ejpam-4570	209	1	then	then	ADV
ejpam-4570	209	2	,	,	PUNCT
ejpam-4570	209	3	there	there	PRON
ejpam-4570	209	4	exist	exist	VERB
ejpam-4570	209	5	an	an	DET
ejpam-4570	209	6	almost	almost	ADV
ejpam-4570	209	7	normal	normal	ADJ
ejpam-4570	209	8	space	space	NOUN
ejpam-4570	209	9	y	y	PROPN
ejpam-4570	209	10	and	and	CCONJ
ejpam-4570	209	11	a	a	DET
ejpam-4570	209	12	bijective	bijective	ADJ
ejpam-4570	209	13	function	function	NOUN
ejpam-4570	209	14	f	f	NOUN
ejpam-4570	210	1	:	:	PUNCT
ejpam-4570	210	2	x	x	X
ejpam-4570	210	3	→	→	SYM
ejpam-4570	210	4	y	y	PROPN
ejpam-4570	210	5	such	such	ADJ
ejpam-4570	210	6	that	that	SCONJ
ejpam-4570	210	7	the	the	DET
ejpam-4570	210	8	restriction	restriction	NOUN
ejpam-4570	210	9	function	function	NOUN
ejpam-4570	210	10	f	f	PROPN
ejpam-4570	210	11	|a	|a	VERB
ejpam-4570	210	12	:	:	PUNCT
ejpam-4570	210	13	a	a	DET
ejpam-4570	210	14	→	→	SYM
ejpam-4570	210	15	f(a	f(a	NOUN
ejpam-4570	210	16	)	)	PUNCT
ejpam-4570	210	17	is	be	AUX
ejpam-4570	210	18	a	a	DET
ejpam-4570	210	19	homeomorphism	homeomorphism	NOUN
ejpam-4570	210	20	for	for	SCONJ
ejpam-4570	210	21	each	each	DET
ejpam-4570	210	22	lindelöf	lindelöf	NOUN
ejpam-4570	210	23	subspace	subspace	NOUN
ejpam-4570	210	24	a	a	PRON
ejpam-4570	210	25	of	of	ADP
ejpam-4570	210	26	x.	x.	NOUN
ejpam-4570	210	27	since	since	SCONJ
ejpam-4570	210	28	every	every	DET
ejpam-4570	210	29	compact	compact	ADJ
ejpam-4570	210	30	subset	subset	NOUN
ejpam-4570	210	31	is	be	AUX
ejpam-4570	210	32	lindelöf	lindelöf	NOUN
ejpam-4570	210	33	,	,	PUNCT
ejpam-4570	210	34	we	we	PRON
ejpam-4570	210	35	have	have	VERB
ejpam-4570	210	36	each	each	DET
ejpam-4570	210	37	compact	compact	ADJ
ejpam-4570	210	38	subspace	subspace	NOUN
ejpam-4570	210	39	c	c	PROPN
ejpam-4570	210	40	of	of	ADP
ejpam-4570	210	41	x	x	PROPN
ejpam-4570	210	42	is	be	AUX
ejpam-4570	210	43	a	a	DET
ejpam-4570	210	44	lindelöf	lindelöf	NOUN
ejpam-4570	210	45	subspace	subspace	NOUN
ejpam-4570	210	46	of	of	ADP
ejpam-4570	210	47	x.	x.	NOUN
ejpam-4570	210	48	thus	thus	ADV
ejpam-4570	210	49	,	,	PUNCT
ejpam-4570	210	50	the	the	DET
ejpam-4570	210	51	restriction	restriction	NOUN
ejpam-4570	210	52	function	function	NOUN
ejpam-4570	210	53	f	f	PROPN
ejpam-4570	210	54	|c	|c	VERB
ejpam-4570	210	55	:	:	PUNCT
ejpam-4570	210	56	c	c	PROPN
ejpam-4570	210	57	→	→	SYM
ejpam-4570	210	58	f(c	f(c	PROPN
ejpam-4570	210	59	)	)	PUNCT
ejpam-4570	210	60	is	be	AUX
ejpam-4570	210	61	a	a	DET
ejpam-4570	210	62	homeomorphism	homeomorphism	NOUN
ejpam-4570	210	63	for	for	ADP
ejpam-4570	210	64	each	each	DET
ejpam-4570	210	65	compact	compact	ADJ
ejpam-4570	210	66	subspace	subspace	NOUN
ejpam-4570	210	67	c	c	PROPN
ejpam-4570	210	68	of	of	ADP
ejpam-4570	210	69	x.	x.	NOUN
ejpam-4570	210	70	therefore	therefore	ADV
ejpam-4570	210	71	,	,	PUNCT
ejpam-4570	210	72	x	x	X
ejpam-4570	210	73	is	be	AUX
ejpam-4570	210	74	c	c	NOUN
ejpam-4570	210	75	-	-	PUNCT
ejpam-4570	210	76	almost	almost	ADV
ejpam-4570	210	77	normal	normal	ADJ
ejpam-4570	210	78	.	.	PUNCT
ejpam-4570	211	1	the	the	DET
ejpam-4570	211	2	converse	converse	NOUN
ejpam-4570	211	3	of	of	ADP
ejpam-4570	211	4	theorem	theorem	NOUN
ejpam-4570	211	5	8	8	NUM
ejpam-4570	211	6	is	be	AUX
ejpam-4570	211	7	not	not	PART
ejpam-4570	211	8	necessarily	necessarily	ADV
ejpam-4570	211	9	true	true	ADJ
ejpam-4570	211	10	in	in	ADP
ejpam-4570	211	11	general	general	ADJ
ejpam-4570	211	12	.	.	PUNCT
ejpam-4570	212	1	for	for	ADP
ejpam-4570	212	2	example	example	NOUN
ejpam-4570	212	3	,	,	PUNCT
ejpam-4570	212	4	the	the	DET
ejpam-4570	212	5	countable	countable	ADJ
ejpam-4570	212	6	complement	complement	NOUN
ejpam-4570	212	7	extension	extension	NOUN
ejpam-4570	212	8	topology	topology	NOUN
ejpam-4570	212	9	,	,	PUNCT
ejpam-4570	212	10	example	example	NOUN
ejpam-4570	212	11	10	10	NUM
ejpam-4570	212	12	,	,	PUNCT
ejpam-4570	212	13	and	and	CCONJ
ejpam-4570	212	14	the	the	DET
ejpam-4570	212	15	smirnov	smirnov	PROPN
ejpam-4570	212	16	’s	’s	PART
ejpam-4570	212	17	deleted	delete	VERB
ejpam-4570	212	18	sequence	sequence	NOUN
ejpam-4570	212	19	topology	topology	NOUN
ejpam-4570	212	20	,	,	PUNCT
ejpam-4570	212	21	example	example	NOUN
ejpam-4570	212	22	9	9	NUM
ejpam-4570	212	23	,	,	PUNCT
ejpam-4570	212	24	are	be	AUX
ejpam-4570	212	25	c	c	NOUN
ejpam-4570	212	26	-	-	PUNCT
ejpam-4570	212	27	almost	almost	ADV
ejpam-4570	212	28	normal	normal	ADJ
ejpam-4570	212	29	space	space	NOUN
ejpam-4570	212	30	,	,	PUNCT
ejpam-4570	212	31	which	which	PRON
ejpam-4570	212	32	are	be	AUX
ejpam-4570	212	33	not	not	PART
ejpam-4570	212	34	l	l	NOUN
ejpam-4570	212	35	-	-	ADJ
ejpam-4570	212	36	almost	almost	ADV
ejpam-4570	212	37	normal	normal	ADJ
ejpam-4570	212	38	.	.	PUNCT
ejpam-4570	213	1	theorem	theorem	VERB
ejpam-4570	213	2	9	9	NUM
ejpam-4570	213	3	.	.	PUNCT
ejpam-4570	214	1	every	every	DET
ejpam-4570	214	2	l	l	ADJ
ejpam-4570	214	3	-	-	ADJ
ejpam-4570	214	4	normal	normal	ADJ
ejpam-4570	214	5	space	space	NOUN
ejpam-4570	214	6	is	be	AUX
ejpam-4570	214	7	l	l	NOUN
ejpam-4570	214	8	-	-	ADJ
ejpam-4570	214	9	almost	almost	ADV
ejpam-4570	214	10	normal	normal	ADJ
ejpam-4570	214	11	.	.	PUNCT
ejpam-4570	215	1	proof	proof	NOUN
ejpam-4570	215	2	.	.	PUNCT
ejpam-4570	216	1	it	it	PRON
ejpam-4570	216	2	is	be	AUX
ejpam-4570	216	3	similar	similar	ADJ
ejpam-4570	216	4	to	to	ADP
ejpam-4570	216	5	that	that	PRON
ejpam-4570	216	6	of	of	ADP
ejpam-4570	216	7	theorem	theorem	NOUN
ejpam-4570	216	8	1	1	NUM
ejpam-4570	216	9	.	.	PUNCT
ejpam-4570	217	1	the	the	DET
ejpam-4570	217	2	converse	converse	NOUN
ejpam-4570	217	3	of	of	ADP
ejpam-4570	217	4	theorem	theorem	NOUN
ejpam-4570	217	5	9	9	NUM
ejpam-4570	217	6	is	be	AUX
ejpam-4570	217	7	not	not	PART
ejpam-4570	217	8	necessary	necessary	ADJ
ejpam-4570	217	9	to	to	PART
ejpam-4570	217	10	be	be	AUX
ejpam-4570	217	11	true	true	ADJ
ejpam-4570	217	12	.	.	PUNCT
ejpam-4570	218	1	for	for	ADP
ejpam-4570	218	2	example	example	NOUN
ejpam-4570	218	3	,	,	PUNCT
ejpam-4570	218	4	the	the	DET
ejpam-4570	218	5	finite	finite	PROPN
ejpam-4570	218	6	complement	complement	NOUN
ejpam-4570	218	7	topology	topology	NOUN
ejpam-4570	218	8	,	,	PUNCT
ejpam-4570	218	9	example	example	NOUN
ejpam-4570	218	10	3	3	NUM
ejpam-4570	218	11	,	,	PUNCT
ejpam-4570	218	12	is	be	AUX
ejpam-4570	218	13	an	an	DET
ejpam-4570	218	14	l	l	NOUN
ejpam-4570	218	15	-	-	ADJ
ejpam-4570	218	16	almost	almost	ADV
ejpam-4570	218	17	normal	normal	ADJ
ejpam-4570	218	18	space	space	NOUN
ejpam-4570	218	19	,	,	PUNCT
ejpam-4570	218	20	which	which	PRON
ejpam-4570	218	21	is	be	AUX
ejpam-4570	218	22	not	not	PART
ejpam-4570	218	23	l	l	NOUN
ejpam-4570	218	24	-	-	ADJ
ejpam-4570	218	25	normal	normal	ADJ
ejpam-4570	218	26	.	.	PUNCT
ejpam-4570	219	1	the	the	DET
ejpam-4570	219	2	rational	rational	ADJ
ejpam-4570	219	3	sequence	sequence	NOUN
ejpam-4570	219	4	topology	topology	NOUN
ejpam-4570	219	5	,	,	PUNCT
ejpam-4570	219	6	example	example	NOUN
ejpam-4570	219	7	19	19	NUM
ejpam-4570	219	8	,	,	PUNCT
ejpam-4570	219	9	is	be	AUX
ejpam-4570	219	10	an	an	DET
ejpam-4570	219	11	l	l	NOUN
ejpam-4570	219	12	-	-	ADJ
ejpam-4570	219	13	almost	almost	ADV
ejpam-4570	219	14	normal	normal	ADJ
ejpam-4570	219	15	space	space	NOUN
ejpam-4570	219	16	,	,	PUNCT
ejpam-4570	219	17	which	which	PRON
ejpam-4570	219	18	is	be	AUX
ejpam-4570	219	19	not	not	PART
ejpam-4570	219	20	l	l	NOUN
ejpam-4570	219	21	-	-	ADJ
ejpam-4570	219	22	normal	normal	ADJ
ejpam-4570	219	23	.	.	PUNCT
ejpam-4570	220	1	theorem	theorem	VERB
ejpam-4570	220	2	10	10	NUM
ejpam-4570	220	3	.	.	PUNCT
ejpam-4570	221	1	every	every	DET
ejpam-4570	221	2	lindelöf	lindelöf	NOUN
ejpam-4570	221	3	l	l	NOUN
ejpam-4570	221	4	-	-	PUNCT
ejpam-4570	221	5	almost	almost	ADV
ejpam-4570	221	6	normal	normal	ADJ
ejpam-4570	221	7	space	space	NOUN
ejpam-4570	221	8	is	be	AUX
ejpam-4570	221	9	almost	almost	ADV
ejpam-4570	221	10	normal	normal	ADJ
ejpam-4570	221	11	.	.	PUNCT
ejpam-4570	222	1	proof	proof	NOUN
ejpam-4570	222	2	.	.	PUNCT
ejpam-4570	223	1	it	it	PRON
ejpam-4570	223	2	is	be	AUX
ejpam-4570	223	3	similar	similar	ADJ
ejpam-4570	223	4	to	to	ADP
ejpam-4570	223	5	that	that	PRON
ejpam-4570	223	6	of	of	ADP
ejpam-4570	223	7	theorem	theorem	NOUN
ejpam-4570	223	8	3	3	NUM
ejpam-4570	223	9	.	.	PUNCT
ejpam-4570	223	10	wafa	wafa	PROPN
ejpam-4570	223	11	khalaf	khalaf	PROPN
ejpam-4570	223	12	alqurashi	alqurashi	PROPN
ejpam-4570	223	13	,	,	PUNCT
ejpam-4570	223	14	sadeq	sadeq	PROPN
ejpam-4570	223	15	ali	ali	PROPN
ejpam-4570	223	16	thabit	thabit	PROPN
ejpam-4570	223	17	/	/	SYM
ejpam-4570	223	18	eur	eur	PROPN
ejpam-4570	223	19	.	.	PUNCT
ejpam-4570	224	1	j.	j.	PROPN
ejpam-4570	224	2	pure	pure	PROPN
ejpam-4570	224	3	appl	appl	PROPN
ejpam-4570	224	4	.	.	PROPN
ejpam-4570	224	5	math	math	PROPN
ejpam-4570	224	6	,	,	PUNCT
ejpam-4570	224	7	15	15	NUM
ejpam-4570	224	8	(	(	PUNCT
ejpam-4570	224	9	4	4	NUM
ejpam-4570	224	10	)	)	PUNCT
ejpam-4570	224	11	(	(	PUNCT
ejpam-4570	224	12	2022	2022	NUM
ejpam-4570	224	13	)	)	PUNCT
ejpam-4570	224	14	,	,	PUNCT
ejpam-4570	224	15	1760	1760	NUM
ejpam-4570	224	16	-	-	SYM
ejpam-4570	224	17	1782	1782	NUM
ejpam-4570	224	18	1767	1767	NUM
ejpam-4570	224	19	corollary	corollary	NOUN
ejpam-4570	224	20	7	7	NUM
ejpam-4570	224	21	.	.	PUNCT
ejpam-4570	225	1	every	every	DET
ejpam-4570	225	2	lindelöf	lindelöf	NOUN
ejpam-4570	225	3	non	non	VERB
ejpam-4570	225	4	almost	almost	ADV
ejpam-4570	225	5	normal	normal	ADJ
ejpam-4570	225	6	space	space	NOUN
ejpam-4570	225	7	can	can	AUX
ejpam-4570	225	8	not	not	PART
ejpam-4570	225	9	be	be	AUX
ejpam-4570	225	10	l	l	NOUN
ejpam-4570	225	11	-	-	ADJ
ejpam-4570	225	12	almost	almost	ADV
ejpam-4570	225	13	normal	normal	ADJ
ejpam-4570	225	14	.	.	PUNCT
ejpam-4570	226	1	some	some	DET
ejpam-4570	226	2	counterexamples	counterexample	NOUN
ejpam-4570	226	3	are	be	AUX
ejpam-4570	226	4	given	give	VERB
ejpam-4570	226	5	in	in	ADP
ejpam-4570	226	6	section	section	NOUN
ejpam-4570	226	7	4	4	NUM
ejpam-4570	226	8	.	.	PUNCT
ejpam-4570	227	1	note	note	VERB
ejpam-4570	227	2	that	that	SCONJ
ejpam-4570	227	3	:	:	PUNCT
ejpam-4570	227	4	if	if	SCONJ
ejpam-4570	227	5	x	x	PRON
ejpam-4570	227	6	is	be	AUX
ejpam-4570	227	7	l	l	NOUN
ejpam-4570	227	8	-	-	ADJ
ejpam-4570	227	9	almost	almost	ADV
ejpam-4570	227	10	normal	normal	ADJ
ejpam-4570	227	11	and	and	CCONJ
ejpam-4570	227	12	f	f	X
ejpam-4570	227	13	:	:	PUNCT
ejpam-4570	227	14	x	x	X
ejpam-4570	227	15	→	→	SYM
ejpam-4570	227	16	y	y	PROPN
ejpam-4570	227	17	is	be	AUX
ejpam-4570	227	18	a	a	DET
ejpam-4570	227	19	witness	witness	NOUN
ejpam-4570	227	20	of	of	ADP
ejpam-4570	227	21	the	the	DET
ejpam-4570	227	22	l	l	NOUN
ejpam-4570	227	23	-	-	ADJ
ejpam-4570	227	24	almost	almost	ADV
ejpam-4570	227	25	normality	normality	NOUN
ejpam-4570	227	26	of	of	ADP
ejpam-4570	227	27	x	x	PRON
ejpam-4570	227	28	,	,	PUNCT
ejpam-4570	227	29	then	then	ADV
ejpam-4570	227	30	f	f	PROPN
ejpam-4570	227	31	may	may	AUX
ejpam-4570	227	32	not	not	PART
ejpam-4570	227	33	be	be	AUX
ejpam-4570	227	34	continuous	continuous	ADJ
ejpam-4570	227	35	,	,	PUNCT
ejpam-4570	227	36	see	see	VERB
ejpam-4570	227	37	example	example	NOUN
ejpam-4570	227	38	4	4	NUM
ejpam-4570	227	39	.	.	PUNCT
ejpam-4570	228	1	but	but	CCONJ
ejpam-4570	228	2	it	it	PRON
ejpam-4570	228	3	will	will	AUX
ejpam-4570	228	4	be	be	AUX
ejpam-4570	228	5	if	if	SCONJ
ejpam-4570	228	6	x	x	PRON
ejpam-4570	228	7	is	be	AUX
ejpam-4570	228	8	of	of	ADP
ejpam-4570	228	9	a	a	DET
ejpam-4570	228	10	countable	countable	ADJ
ejpam-4570	228	11	tightness	tightness	NOUN
ejpam-4570	228	12	.	.	PUNCT
ejpam-4570	229	1	a	a	DET
ejpam-4570	229	2	space	space	NOUN
ejpam-4570	229	3	x	x	NOUN
ejpam-4570	229	4	is	be	AUX
ejpam-4570	229	5	of	of	ADP
ejpam-4570	229	6	a	a	DET
ejpam-4570	229	7	countable	countable	ADJ
ejpam-4570	229	8	tightness	tightness	NOUN
ejpam-4570	229	9	if	if	SCONJ
ejpam-4570	229	10	for	for	ADP
ejpam-4570	229	11	each	each	DET
ejpam-4570	229	12	subset	subset	NOUN
ejpam-4570	229	13	b	b	PROPN
ejpam-4570	229	14	of	of	ADP
ejpam-4570	229	15	x	x	PUNCT
ejpam-4570	229	16	and	and	CCONJ
ejpam-4570	230	1	each	each	DET
ejpam-4570	230	2	x	x	SYM
ejpam-4570	230	3	∈	∈	PROPN
ejpam-4570	230	4	b	b	NOUN
ejpam-4570	230	5	,	,	PUNCT
ejpam-4570	230	6	there	there	PRON
ejpam-4570	230	7	exists	exist	VERB
ejpam-4570	230	8	a	a	DET
ejpam-4570	230	9	countable	countable	ADJ
ejpam-4570	230	10	subset	subset	NOUN
ejpam-4570	230	11	b0	b0	NOUN
ejpam-4570	230	12	of	of	ADP
ejpam-4570	230	13	b	b	NOUN
ejpam-4570	230	14	such	such	ADJ
ejpam-4570	230	15	that	that	SCONJ
ejpam-4570	230	16	x	x	SYM
ejpam-4570	230	17	∈	∈	PROPN
ejpam-4570	230	18	b0	b0	NOUN
ejpam-4570	230	19	[	[	X
ejpam-4570	230	20	12	12	NUM
ejpam-4570	230	21	]	]	PUNCT
ejpam-4570	230	22	.	.	PUNCT
ejpam-4570	231	1	note	note	VERB
ejpam-4570	231	2	that	that	SCONJ
ejpam-4570	231	3	:	:	PUNCT
ejpam-4570	231	4	first	first	ADJ
ejpam-4570	231	5	countable	countable	ADJ
ejpam-4570	231	6	=	=	NOUN
ejpam-4570	231	7	⇒	⇒	NOUN
ejpam-4570	231	8	fréchet	fréchet	NOUN
ejpam-4570	232	1	=	=	NOUN
ejpam-4570	232	2	⇒	⇒	VERB
ejpam-4570	232	3	sequential	sequential	ADJ
ejpam-4570	232	4	=	=	NOUN
ejpam-4570	232	5	⇒	⇒	NOUN
ejpam-4570	232	6	countable	countable	ADJ
ejpam-4570	232	7	tightness	tightness	NOUN
ejpam-4570	232	8	theorem	theorem	VERB
ejpam-4570	232	9	11	11	NUM
ejpam-4570	232	10	.	.	PUNCT
ejpam-4570	233	1	if	if	SCONJ
ejpam-4570	233	2	x	x	PRON
ejpam-4570	233	3	is	be	AUX
ejpam-4570	233	4	an	an	DET
ejpam-4570	233	5	l	l	NOUN
ejpam-4570	233	6	-	-	ADJ
ejpam-4570	233	7	almost	almost	ADV
ejpam-4570	233	8	normal	normal	ADJ
ejpam-4570	233	9	space	space	NOUN
ejpam-4570	233	10	of	of	ADP
ejpam-4570	233	11	a	a	DET
ejpam-4570	233	12	countable	countable	ADJ
ejpam-4570	233	13	tightness	tightness	NOUN
ejpam-4570	233	14	and	and	CCONJ
ejpam-4570	233	15	f	f	NOUN
ejpam-4570	233	16	:	:	PUNCT
ejpam-4570	233	17	x	x	X
ejpam-4570	233	18	→	→	SYM
ejpam-4570	233	19	y	y	PROPN
ejpam-4570	233	20	is	be	AUX
ejpam-4570	233	21	a	a	DET
ejpam-4570	233	22	witness	witness	NOUN
ejpam-4570	233	23	of	of	ADP
ejpam-4570	233	24	the	the	DET
ejpam-4570	233	25	l	l	NOUN
ejpam-4570	233	26	-	-	ADJ
ejpam-4570	233	27	almost	almost	ADV
ejpam-4570	233	28	normality	normality	NOUN
ejpam-4570	233	29	of	of	ADP
ejpam-4570	233	30	x	x	PRON
ejpam-4570	233	31	,	,	PUNCT
ejpam-4570	233	32	then	then	ADV
ejpam-4570	233	33	f	f	PROPN
ejpam-4570	233	34	is	be	AUX
ejpam-4570	233	35	continuous	continuous	ADJ
ejpam-4570	233	36	.	.	PUNCT
ejpam-4570	234	1	proof	proof	NOUN
ejpam-4570	234	2	.	.	PUNCT
ejpam-4570	235	1	let	let	VERB
ejpam-4570	235	2	a	a	DET
ejpam-4570	235	3	be	be	AUX
ejpam-4570	235	4	any	any	DET
ejpam-4570	235	5	non	non	ADJ
ejpam-4570	235	6	-	-	ADJ
ejpam-4570	235	7	empty	empty	ADJ
ejpam-4570	235	8	subset	subset	NOUN
ejpam-4570	235	9	of	of	ADP
ejpam-4570	235	10	x.	x.	NOUN
ejpam-4570	235	11	let	let	VERB
ejpam-4570	235	12	y	y	PROPN
ejpam-4570	235	13	∈	∈	PROPN
ejpam-4570	235	14	f(a	f(a	PROPN
ejpam-4570	235	15	)	)	PUNCT
ejpam-4570	235	16	be	be	AUX
ejpam-4570	235	17	arbitrary	arbitrary	ADJ
ejpam-4570	235	18	.	.	PUNCT
ejpam-4570	236	1	let	let	VERB
ejpam-4570	236	2	x	x	PUNCT
ejpam-4570	236	3	∈	∈	PROPN
ejpam-4570	236	4	x	x	PUNCT
ejpam-4570	236	5	be	be	AUX
ejpam-4570	236	6	the	the	DET
ejpam-4570	236	7	unique	unique	ADJ
ejpam-4570	236	8	element	element	NOUN
ejpam-4570	236	9	such	such	ADJ
ejpam-4570	236	10	that	that	PRON
ejpam-4570	236	11	y	y	PROPN
ejpam-4570	236	12	=	=	SYM
ejpam-4570	236	13	f(x	f(x	PROPN
ejpam-4570	236	14	)	)	PUNCT
ejpam-4570	236	15	.	.	PUNCT
ejpam-4570	237	1	then	then	ADV
ejpam-4570	237	2	,	,	PUNCT
ejpam-4570	237	3	x	x	PUNCT
ejpam-4570	237	4	∈	∈	NOUN
ejpam-4570	237	5	a.	a.	NOUN
ejpam-4570	237	6	pick	pick	VERB
ejpam-4570	237	7	a	a	DET
ejpam-4570	237	8	countable	countable	ADJ
ejpam-4570	237	9	subset	subset	NOUN
ejpam-4570	237	10	a0	a0	NOUN
ejpam-4570	237	11	⊆	⊆	NUM
ejpam-4570	237	12	a	a	DET
ejpam-4570	237	13	such	such	ADJ
ejpam-4570	237	14	that	that	SCONJ
ejpam-4570	237	15	x	x	SYM
ejpam-4570	237	16	∈	∈	PROPN
ejpam-4570	237	17	a0	a0	PROPN
ejpam-4570	237	18	.	.	PUNCT
ejpam-4570	238	1	let	let	VERB
ejpam-4570	238	2	b	b	NOUN
ejpam-4570	238	3	=	=	PRON
ejpam-4570	238	4	{	{	PUNCT
ejpam-4570	238	5	x	x	NOUN
ejpam-4570	238	6	}	}	PUNCT
ejpam-4570	238	7	∪	∪	ADJ
ejpam-4570	238	8	a0	a0	PROPN
ejpam-4570	238	9	.	.	PUNCT
ejpam-4570	239	1	then	then	ADV
ejpam-4570	239	2	,	,	PUNCT
ejpam-4570	239	3	b	b	PROPN
ejpam-4570	239	4	is	be	AUX
ejpam-4570	239	5	a	a	DET
ejpam-4570	239	6	lindelöf	lindelöf	NOUN
ejpam-4570	239	7	subspace	subspace	NOUN
ejpam-4570	239	8	of	of	ADP
ejpam-4570	239	9	x	x	X
ejpam-4570	239	10	and	and	CCONJ
ejpam-4570	239	11	hence	hence	ADV
ejpam-4570	239	12	f	f	PROPN
ejpam-4570	239	13	|b	|b	NOUN
ejpam-4570	239	14	:	:	PUNCT
ejpam-4570	239	15	b	b	X
ejpam-4570	239	16	→	→	SYM
ejpam-4570	239	17	f(b	f(b	PROPN
ejpam-4570	239	18	)	)	PUNCT
ejpam-4570	239	19	is	be	AUX
ejpam-4570	239	20	a	a	DET
ejpam-4570	239	21	homoeomorphism	homoeomorphism	NOUN
ejpam-4570	239	22	.	.	PUNCT
ejpam-4570	240	1	now	now	ADV
ejpam-4570	240	2	,	,	PUNCT
ejpam-4570	240	3	let	let	VERB
ejpam-4570	240	4	v	v	PRON
ejpam-4570	240	5	⊆	⊆	NUM
ejpam-4570	240	6	y	y	NOUN
ejpam-4570	240	7	be	be	AUX
ejpam-4570	240	8	any	any	DET
ejpam-4570	240	9	open	open	ADJ
ejpam-4570	240	10	neighborhood	neighborhood	NOUN
ejpam-4570	240	11	of	of	ADP
ejpam-4570	240	12	y.	y.	PROPN
ejpam-4570	240	13	then	then	ADV
ejpam-4570	240	14	,	,	PUNCT
ejpam-4570	240	15	v	v	PROPN
ejpam-4570	240	16	∩f(b	∩f(b	NOUN
ejpam-4570	240	17	)	)	PUNCT
ejpam-4570	240	18	is	be	AUX
ejpam-4570	240	19	open	open	ADJ
ejpam-4570	240	20	in	in	ADP
ejpam-4570	240	21	the	the	DET
ejpam-4570	240	22	subspace	subspace	NOUN
ejpam-4570	240	23	f(b	f(b	PROPN
ejpam-4570	240	24	)	)	PUNCT
ejpam-4570	240	25	containing	contain	VERB
ejpam-4570	240	26	y.	y.	PROPN
ejpam-4570	240	27	thus	thus	ADV
ejpam-4570	240	28	,	,	PUNCT
ejpam-4570	240	29	f−1(v	f−1(v	NOUN
ejpam-4570	240	30	)	)	PUNCT
ejpam-4570	241	1	∩b	∩b	NOUN
ejpam-4570	241	2	is	be	AUX
ejpam-4570	241	3	an	an	DET
ejpam-4570	241	4	open	open	ADJ
ejpam-4570	241	5	set	set	NOUN
ejpam-4570	241	6	in	in	ADP
ejpam-4570	241	7	the	the	DET
ejpam-4570	241	8	subspace	subspace	NOUN
ejpam-4570	241	9	b	b	PROPN
ejpam-4570	241	10	containing	contain	VERB
ejpam-4570	241	11	x.	x.	NOUN
ejpam-4570	241	12	thus	thus	ADV
ejpam-4570	241	13	,	,	PUNCT
ejpam-4570	241	14	(	(	PUNCT
ejpam-4570	241	15	f−1(v	f−1(v	PROPN
ejpam-4570	241	16	)	)	PUNCT
ejpam-4570	241	17	∩b)∩a0	∩b)∩a0	PROPN
ejpam-4570	241	18	̸=	̸=	PROPN
ejpam-4570	241	19	∅.	∅.	ADV
ejpam-4570	241	20	so	so	ADV
ejpam-4570	241	21	,	,	PUNCT
ejpam-4570	241	22	(	(	PUNCT
ejpam-4570	241	23	f−1(v	f−1(v	NOUN
ejpam-4570	241	24	)	)	PUNCT
ejpam-4570	241	25	∩b)∩a	∩b)∩a	VERB
ejpam-4570	242	1	̸=	̸=	PROPN
ejpam-4570	242	2	∅.	∅.	PRON
ejpam-4570	242	3	hence	hence	ADV
ejpam-4570	242	4	,	,	PUNCT
ejpam-4570	242	5	∅	∅	NOUN
ejpam-4570	242	6	̸=	̸=	PROPN
ejpam-4570	242	7	f((f−1(v	f((f−1(v	PROPN
ejpam-4570	242	8	)	)	PUNCT
ejpam-4570	242	9	∩	∩	PROPN
ejpam-4570	242	10	b	b	X
ejpam-4570	242	11	)	)	PUNCT
ejpam-4570	242	12	∩	∩	NOUN
ejpam-4570	242	13	a	a	X
ejpam-4570	242	14	)	)	PUNCT
ejpam-4570	242	15	⊆	⊆	NUM
ejpam-4570	242	16	f(f−1(v	f(f−1(v	PROPN
ejpam-4570	242	17	)	)	PUNCT
ejpam-4570	242	18	∩	∩	PROPN
ejpam-4570	242	19	a	a	X
ejpam-4570	242	20	)	)	PUNCT
ejpam-4570	242	21	=	=	SYM
ejpam-4570	242	22	v	v	NUM
ejpam-4570	242	23	∩	∩	ADJ
ejpam-4570	242	24	f(a	f(a	NOUN
ejpam-4570	242	25	)	)	PUNCT
ejpam-4570	242	26	.	.	PUNCT
ejpam-4570	243	1	hence	hence	ADV
ejpam-4570	243	2	,	,	PUNCT
ejpam-4570	243	3	y	y	PROPN
ejpam-4570	243	4	∈	∈	PROPN
ejpam-4570	243	5	f(a	f(a	PROPN
ejpam-4570	243	6	)	)	PUNCT
ejpam-4570	243	7	.	.	PUNCT
ejpam-4570	244	1	thus	thus	ADV
ejpam-4570	244	2	,	,	PUNCT
ejpam-4570	244	3	we	we	PRON
ejpam-4570	244	4	obtain	obtain	VERB
ejpam-4570	244	5	f(a	f(a	NOUN
ejpam-4570	244	6	)	)	PUNCT
ejpam-4570	244	7	⊆	⊆	NUM
ejpam-4570	244	8	f(a	f(a	NOUN
ejpam-4570	244	9	)	)	PUNCT
ejpam-4570	244	10	.	.	PUNCT
ejpam-4570	245	1	therefore	therefore	ADV
ejpam-4570	245	2	,	,	PUNCT
ejpam-4570	245	3	f	f	PROPN
ejpam-4570	245	4	is	be	AUX
ejpam-4570	245	5	continuous	continuous	ADJ
ejpam-4570	245	6	.	.	PUNCT
ejpam-4570	246	1	corollary	corollary	ADJ
ejpam-4570	246	2	8	8	NUM
ejpam-4570	246	3	.	.	PUNCT
ejpam-4570	247	1	if	if	SCONJ
ejpam-4570	247	2	x	x	PRON
ejpam-4570	247	3	is	be	AUX
ejpam-4570	247	4	an	an	DET
ejpam-4570	247	5	l	l	NOUN
ejpam-4570	247	6	-	-	ADJ
ejpam-4570	247	7	almost	almost	ADV
ejpam-4570	247	8	normal	normal	ADJ
ejpam-4570	247	9	fréchet	fréchet	NOUN
ejpam-4570	247	10	(	(	PUNCT
ejpam-4570	247	11	resp	resp	NOUN
ejpam-4570	247	12	.	.	PUNCT
ejpam-4570	248	1	first	first	ADJ
ejpam-4570	248	2	countable	countable	ADJ
ejpam-4570	248	3	,	,	PUNCT
ejpam-4570	248	4	sequential	sequential	ADJ
ejpam-4570	248	5	)	)	PUNCT
ejpam-4570	248	6	space	space	NOUN
ejpam-4570	248	7	and	and	CCONJ
ejpam-4570	248	8	f	f	NOUN
ejpam-4570	248	9	:	:	PUNCT
ejpam-4570	248	10	x	x	X
ejpam-4570	248	11	→	→	SYM
ejpam-4570	248	12	y	y	PROPN
ejpam-4570	248	13	is	be	AUX
ejpam-4570	248	14	a	a	DET
ejpam-4570	248	15	witness	witness	NOUN
ejpam-4570	248	16	of	of	ADP
ejpam-4570	248	17	the	the	DET
ejpam-4570	248	18	l	l	NOUN
ejpam-4570	248	19	-	-	ADJ
ejpam-4570	248	20	almost	almost	ADV
ejpam-4570	248	21	normality	normality	NOUN
ejpam-4570	248	22	of	of	ADP
ejpam-4570	248	23	x	x	PRON
ejpam-4570	248	24	,	,	PUNCT
ejpam-4570	248	25	then	then	ADV
ejpam-4570	248	26	f	f	PROPN
ejpam-4570	248	27	is	be	AUX
ejpam-4570	248	28	continuous	continuous	ADJ
ejpam-4570	248	29	.	.	PUNCT
ejpam-4570	249	1	theorem	theorem	NOUN
ejpam-4570	249	2	12	12	NUM
ejpam-4570	249	3	.	.	PUNCT
ejpam-4570	250	1	if	if	SCONJ
ejpam-4570	250	2	x	x	PRON
ejpam-4570	250	3	is	be	AUX
ejpam-4570	250	4	a	a	DET
ejpam-4570	250	5	t3	t3	PROPN
ejpam-4570	250	6	separable	separable	NOUN
ejpam-4570	250	7	,	,	PUNCT
ejpam-4570	250	8	l	l	NOUN
ejpam-4570	250	9	-	-	PUNCT
ejpam-4570	250	10	almost	almost	ADV
ejpam-4570	250	11	normal	normal	ADJ
ejpam-4570	250	12	space	space	NOUN
ejpam-4570	250	13	and	and	CCONJ
ejpam-4570	250	14	of	of	ADP
ejpam-4570	250	15	a	a	DET
ejpam-4570	250	16	countable	countable	ADJ
ejpam-4570	250	17	tightness	tightness	NOUN
ejpam-4570	250	18	,	,	PUNCT
ejpam-4570	250	19	then	then	ADV
ejpam-4570	250	20	x	x	PUNCT
ejpam-4570	250	21	is	be	AUX
ejpam-4570	250	22	almost	almost	ADV
ejpam-4570	250	23	normal	normal	ADJ
ejpam-4570	250	24	and	and	CCONJ
ejpam-4570	250	25	epi	epi	NOUN
ejpam-4570	250	26	-	-	ADJ
ejpam-4570	250	27	almost	almost	ADV
ejpam-4570	250	28	normal	normal	ADJ
ejpam-4570	250	29	.	.	PUNCT
ejpam-4570	251	1	proof	proof	NOUN
ejpam-4570	251	2	.	.	PUNCT
ejpam-4570	252	1	let	let	VERB
ejpam-4570	252	2	x	x	PRON
ejpam-4570	252	3	be	be	AUX
ejpam-4570	252	4	a	a	DET
ejpam-4570	252	5	t3	t3	PROPN
ejpam-4570	252	6	separable	separable	NOUN
ejpam-4570	252	7	,	,	PUNCT
ejpam-4570	252	8	l	l	NOUN
ejpam-4570	252	9	-	-	PUNCT
ejpam-4570	252	10	almost	almost	ADV
ejpam-4570	252	11	normal	normal	ADJ
ejpam-4570	252	12	space	space	NOUN
ejpam-4570	252	13	and	and	CCONJ
ejpam-4570	252	14	of	of	ADP
ejpam-4570	252	15	a	a	DET
ejpam-4570	252	16	countable	countable	ADJ
ejpam-4570	252	17	tightness	tightness	NOUN
ejpam-4570	252	18	.	.	PUNCT
ejpam-4570	253	1	let	let	VERB
ejpam-4570	253	2	y	y	PRON
ejpam-4570	253	3	be	be	AUX
ejpam-4570	253	4	an	an	DET
ejpam-4570	253	5	almost	almost	ADV
ejpam-4570	253	6	normal	normal	ADJ
ejpam-4570	253	7	space	space	NOUN
ejpam-4570	253	8	and	and	CCONJ
ejpam-4570	253	9	f	f	NOUN
ejpam-4570	253	10	:	:	PUNCT
ejpam-4570	253	11	x	x	X
ejpam-4570	253	12	→	→	SYM
ejpam-4570	253	13	y	y	X
ejpam-4570	253	14	be	be	AUX
ejpam-4570	253	15	a	a	DET
ejpam-4570	253	16	bijective	bijective	ADJ
ejpam-4570	253	17	witness	witness	NOUN
ejpam-4570	253	18	of	of	ADP
ejpam-4570	253	19	the	the	DET
ejpam-4570	253	20	l	l	NOUN
ejpam-4570	253	21	-	-	ADJ
ejpam-4570	253	22	almost	almost	ADV
ejpam-4570	253	23	normality	normality	NOUN
ejpam-4570	253	24	of	of	ADP
ejpam-4570	253	25	x.	x.	NOUN
ejpam-4570	253	26	since	since	SCONJ
ejpam-4570	253	27	x	x	PROPN
ejpam-4570	253	28	is	be	AUX
ejpam-4570	253	29	of	of	ADP
ejpam-4570	253	30	a	a	DET
ejpam-4570	253	31	countable	countable	ADJ
ejpam-4570	253	32	tightness	tightness	NOUN
ejpam-4570	253	33	,	,	PUNCT
ejpam-4570	253	34	we	we	PRON
ejpam-4570	253	35	have	have	VERB
ejpam-4570	253	36	f	f	PROPN
ejpam-4570	253	37	is	be	AUX
ejpam-4570	253	38	continuous	continuous	ADJ
ejpam-4570	253	39	.	.	PUNCT
ejpam-4570	254	1	let	let	VERB
ejpam-4570	254	2	d	d	PRON
ejpam-4570	254	3	be	be	AUX
ejpam-4570	254	4	a	a	DET
ejpam-4570	254	5	countable	countable	ADJ
ejpam-4570	254	6	dense	dense	ADJ
ejpam-4570	254	7	subset	subset	NOUN
ejpam-4570	254	8	of	of	ADP
ejpam-4570	254	9	x.	x.	NOUN
ejpam-4570	254	10	we	we	PRON
ejpam-4570	254	11	show	show	VERB
ejpam-4570	254	12	that	that	SCONJ
ejpam-4570	254	13	f	f	PROPN
ejpam-4570	254	14	is	be	AUX
ejpam-4570	254	15	closed	closed	ADJ
ejpam-4570	254	16	.	.	PUNCT
ejpam-4570	255	1	let	let	VERB
ejpam-4570	255	2	h	h	NOUN
ejpam-4570	255	3	be	be	AUX
ejpam-4570	255	4	any	any	DET
ejpam-4570	255	5	proper	proper	ADJ
ejpam-4570	255	6	closed	closed	ADJ
ejpam-4570	255	7	subset	subset	NOUN
ejpam-4570	255	8	of	of	ADP
ejpam-4570	255	9	x.	x.	PROPN
ejpam-4570	255	10	suppose	suppose	VERB
ejpam-4570	255	11	f(p	f(p	NOUN
ejpam-4570	255	12	)	)	PUNCT
ejpam-4570	256	1	=	=	PUNCT
ejpam-4570	256	2	q	q	PUNCT
ejpam-4570	256	3	∈	∈	PROPN
ejpam-4570	256	4	y	y	PROPN
ejpam-4570	256	5	\f(h	\f(h	PROPN
ejpam-4570	256	6	)	)	PUNCT
ejpam-4570	256	7	,	,	PUNCT
ejpam-4570	256	8	then	then	ADV
ejpam-4570	256	9	p	p	PROPN
ejpam-4570	256	10	̸∈	̸∈	PROPN
ejpam-4570	256	11	h.	h.	PROPN
ejpam-4570	256	12	by	by	ADP
ejpam-4570	256	13	regularity	regularity	NOUN
ejpam-4570	256	14	of	of	ADP
ejpam-4570	256	15	x	x	PRON
ejpam-4570	256	16	,	,	PUNCT
ejpam-4570	256	17	there	there	PRON
ejpam-4570	256	18	are	be	VERB
ejpam-4570	256	19	two	two	NUM
ejpam-4570	256	20	disjoint	disjoint	ADJ
ejpam-4570	256	21	open	open	ADJ
ejpam-4570	256	22	sets	set	NOUN
ejpam-4570	256	23	u	u	NOUN
ejpam-4570	256	24	and	and	CCONJ
ejpam-4570	256	25	v	v	NOUN
ejpam-4570	256	26	in	in	ADP
ejpam-4570	256	27	x	x	PUNCT
ejpam-4570	256	28	such	such	ADJ
ejpam-4570	256	29	that	that	SCONJ
ejpam-4570	256	30	p	p	PROPN
ejpam-4570	256	31	∈	∈	PROPN
ejpam-4570	256	32	u	u	NOUN
ejpam-4570	256	33	and	and	CCONJ
ejpam-4570	256	34	h	h	NOUN
ejpam-4570	256	35	⊆	⊆	NUM
ejpam-4570	256	36	v	v	NOUN
ejpam-4570	256	37	.	.	PUNCT
ejpam-4570	257	1	then	then	ADV
ejpam-4570	257	2	,	,	PUNCT
ejpam-4570	257	3	u	u	NOUN
ejpam-4570	257	4	∩	∩	NOUN
ejpam-4570	257	5	(	(	PUNCT
ejpam-4570	257	6	d	d	X
ejpam-4570	257	7	∪	∪	X
ejpam-4570	257	8	{	{	PUNCT
ejpam-4570	257	9	p	p	NOUN
ejpam-4570	257	10	}	}	PUNCT
ejpam-4570	257	11	)	)	PUNCT
ejpam-4570	257	12	is	be	AUX
ejpam-4570	257	13	open	open	ADJ
ejpam-4570	257	14	in	in	ADP
ejpam-4570	257	15	the	the	DET
ejpam-4570	257	16	lindelöf	lindelöf	NOUN
ejpam-4570	257	17	subspace	subspace	NOUN
ejpam-4570	257	18	d	d	X
ejpam-4570	257	19	∪	∪	X
ejpam-4570	257	20	{	{	PUNCT
ejpam-4570	257	21	p	p	NOUN
ejpam-4570	257	22	}	}	PUNCT
ejpam-4570	257	23	.	.	PUNCT
ejpam-4570	258	1	so	so	ADV
ejpam-4570	258	2	,	,	PUNCT
ejpam-4570	258	3	f(u	f(u	ADJ
ejpam-4570	258	4	∩	∩	NOUN
ejpam-4570	258	5	(	(	PUNCT
ejpam-4570	258	6	d	d	X
ejpam-4570	258	7	∪	∪	X
ejpam-4570	258	8	{	{	PUNCT
ejpam-4570	258	9	p	p	NOUN
ejpam-4570	258	10	}	}	PUNCT
ejpam-4570	258	11	)	)	PUNCT
ejpam-4570	258	12	)	)	PUNCT
ejpam-4570	258	13	is	be	AUX
ejpam-4570	258	14	open	open	ADJ
ejpam-4570	258	15	in	in	ADP
ejpam-4570	258	16	the	the	DET
ejpam-4570	258	17	subspace	subspace	NOUN
ejpam-4570	258	18	f(d	f(d	PROPN
ejpam-4570	258	19	∪	∪	X
ejpam-4570	258	20	{	{	PUNCT
ejpam-4570	258	21	p	p	NOUN
ejpam-4570	258	22	}	}	PUNCT
ejpam-4570	258	23	)	)	PUNCT
ejpam-4570	258	24	of	of	ADP
ejpam-4570	258	25	y	y	PROPN
ejpam-4570	258	26	containing	contain	VERB
ejpam-4570	258	27	q.	q.	PROPN
ejpam-4570	258	28	then	then	ADV
ejpam-4570	258	29	,	,	PUNCT
ejpam-4570	258	30	f(u	f(u	PROPN
ejpam-4570	258	31	∩(d∪{p	∩(d∪{p	NOUN
ejpam-4570	258	32	}	}	PUNCT
ejpam-4570	258	33	)	)	PUNCT
ejpam-4570	258	34	)	)	PUNCT
ejpam-4570	259	1	=	=	PUNCT
ejpam-4570	259	2	f(u)∩f(d∪{p	f(u)∩f(d∪{p	NOUN
ejpam-4570	259	3	}	}	PUNCT
ejpam-4570	259	4	)	)	PUNCT
ejpam-4570	259	5	=	=	PUNCT
ejpam-4570	259	6	w	w	PROPN
ejpam-4570	259	7	∩f(d∪{p	∩f(d∪{p	PROPN
ejpam-4570	259	8	}	}	PUNCT
ejpam-4570	259	9	)	)	PUNCT
ejpam-4570	259	10	for	for	ADP
ejpam-4570	259	11	some	some	DET
ejpam-4570	259	12	open	open	ADJ
ejpam-4570	259	13	subset	subset	NOUN
ejpam-4570	259	14	w	w	NOUN
ejpam-4570	259	15	in	in	ADP
ejpam-4570	259	16	y	y	PROPN
ejpam-4570	259	17	with	with	ADP
ejpam-4570	259	18	q	q	PROPN
ejpam-4570	259	19	∈	∈	PROPN
ejpam-4570	259	20	w	w	NOUN
ejpam-4570	259	21	.	.	PUNCT
ejpam-4570	260	1	we	we	PRON
ejpam-4570	260	2	claim	claim	VERB
ejpam-4570	260	3	w	w	ADP
ejpam-4570	260	4	∩f(h	∩f(h	NOUN
ejpam-4570	260	5	)	)	PUNCT
ejpam-4570	261	1	=	=	VERB
ejpam-4570	261	2	∅.	∅.	AUX
ejpam-4570	261	3	suppose	suppose	VERB
ejpam-4570	261	4	w	w	ADP
ejpam-4570	261	5	∩f(h	∩f(h	NOUN
ejpam-4570	261	6	)	)	PUNCT
ejpam-4570	262	1	̸=	̸=	PROPN
ejpam-4570	262	2	∅.	∅.	NOUN
ejpam-4570	262	3	then	then	ADV
ejpam-4570	262	4	,	,	PUNCT
ejpam-4570	262	5	there	there	PRON
ejpam-4570	262	6	exists	exist	VERB
ejpam-4570	262	7	an	an	DET
ejpam-4570	262	8	y	y	PROPN
ejpam-4570	262	9	∈	∈	PROPN
ejpam-4570	262	10	w	w	ADP
ejpam-4570	262	11	∩f(h	∩f(h	NOUN
ejpam-4570	262	12	)	)	PUNCT
ejpam-4570	262	13	.	.	PUNCT
ejpam-4570	263	1	let	let	VERB
ejpam-4570	263	2	x	x	PUNCT
ejpam-4570	263	3	∈	∈	NOUN
ejpam-4570	263	4	h	h	NOUN
ejpam-4570	263	5	such	such	ADJ
ejpam-4570	263	6	that	that	SCONJ
ejpam-4570	263	7	f(x	f(x	NOUN
ejpam-4570	263	8	)	)	PUNCT
ejpam-4570	264	1	=	=	PUNCT
ejpam-4570	264	2	y.	y.	NOUN
ejpam-4570	264	3	note	note	VERB
ejpam-4570	264	4	that	that	SCONJ
ejpam-4570	264	5	x	x	PUNCT
ejpam-4570	264	6	∈	∈	NOUN
ejpam-4570	264	7	v	v	NOUN
ejpam-4570	264	8	.	.	PUNCT
ejpam-4570	265	1	since	since	SCONJ
ejpam-4570	265	2	d	d	PROPN
ejpam-4570	265	3	is	be	AUX
ejpam-4570	265	4	dense	dense	ADJ
ejpam-4570	265	5	in	in	ADP
ejpam-4570	265	6	x	x	PUNCT
ejpam-4570	265	7	and	and	CCONJ
ejpam-4570	265	8	also	also	ADV
ejpam-4570	265	9	dense	dense	ADJ
ejpam-4570	265	10	in	in	ADP
ejpam-4570	265	11	the	the	DET
ejpam-4570	265	12	open	open	ADJ
ejpam-4570	265	13	set	set	NOUN
ejpam-4570	265	14	v	v	NOUN
ejpam-4570	265	15	,	,	PUNCT
ejpam-4570	265	16	we	we	PRON
ejpam-4570	265	17	get	get	VERB
ejpam-4570	265	18	x	x	X
ejpam-4570	265	19	∈	∈	NOUN
ejpam-4570	265	20	v	v	ADP
ejpam-4570	265	21	∩d	∩d	NOUN
ejpam-4570	265	22	.	.	PUNCT
ejpam-4570	266	1	since	since	SCONJ
ejpam-4570	266	2	w	w	NOUN
ejpam-4570	266	3	is	be	AUX
ejpam-4570	266	4	open	open	ADJ
ejpam-4570	266	5	in	in	ADP
ejpam-4570	266	6	y	y	PROPN
ejpam-4570	266	7	and	and	CCONJ
ejpam-4570	266	8	f	f	PROPN
ejpam-4570	266	9	is	be	AUX
ejpam-4570	266	10	continuous	continuous	ADJ
ejpam-4570	266	11	,	,	PUNCT
ejpam-4570	266	12	we	we	PRON
ejpam-4570	266	13	have	have	AUX
ejpam-4570	266	14	f−1(w	f−1(w	ADV
ejpam-4570	266	15	)	)	PUNCT
ejpam-4570	266	16	is	be	AUX
ejpam-4570	266	17	open	open	ADJ
ejpam-4570	266	18	in	in	ADP
ejpam-4570	266	19	x	x	PUNCT
ejpam-4570	266	20	containing	contain	VERB
ejpam-4570	266	21	x	x	X
ejpam-4570	266	22	and	and	CCONJ
ejpam-4570	266	23	f−1(w	f−1(w	ADJ
ejpam-4570	266	24	)	)	PUNCT
ejpam-4570	266	25	∩(v	∩(v	NOUN
ejpam-4570	266	26	∩d	∩d	NOUN
ejpam-4570	266	27	)	)	PUNCT
ejpam-4570	267	1	̸=	̸=	PROPN
ejpam-4570	267	2	∅.	∅.	ADV
ejpam-4570	267	3	choose	choose	VERB
ejpam-4570	267	4	d	d	PROPN
ejpam-4570	267	5	∈	∈	PROPN
ejpam-4570	267	6	f−1(w	f−1(w	PROPN
ejpam-4570	267	7	)	)	PUNCT
ejpam-4570	267	8	∩	∩	NOUN
ejpam-4570	267	9	(	(	PUNCT
ejpam-4570	267	10	v	v	NOUN
ejpam-4570	267	11	∩d	∩d	NOUN
ejpam-4570	267	12	)	)	PUNCT
ejpam-4570	267	13	.	.	PUNCT
ejpam-4570	268	1	then	then	ADV
ejpam-4570	268	2	,	,	PUNCT
ejpam-4570	268	3	f(d	f(d	PROPN
ejpam-4570	268	4	)	)	PUNCT
ejpam-4570	268	5	∈	∈	PROPN
ejpam-4570	268	6	w	w	PROPN
ejpam-4570	268	7	∩f(v	∩f(v	PROPN
ejpam-4570	268	8	∩d	∩d	NOUN
ejpam-4570	268	9	)	)	PUNCT
ejpam-4570	269	1	⊆	⊆	NUM
ejpam-4570	269	2	w	w	PROPN
ejpam-4570	269	3	∩f(d∪{p	∩f(d∪{p	PROPN
ejpam-4570	269	4	}	}	PUNCT
ejpam-4570	269	5	)	)	PUNCT
ejpam-4570	270	1	=	=	SYM
ejpam-4570	270	2	f(u	f(u	ADJ
ejpam-4570	270	3	∩	∩	NOUN
ejpam-4570	270	4	(	(	PUNCT
ejpam-4570	270	5	d∪{p	d∪{p	NOUN
ejpam-4570	270	6	}	}	PUNCT
ejpam-4570	270	7	)	)	PUNCT
ejpam-4570	270	8	)	)	PUNCT
ejpam-4570	270	9	.	.	PUNCT
ejpam-4570	271	1	so	so	ADV
ejpam-4570	271	2	,	,	PUNCT
ejpam-4570	271	3	f(d	f(d	PROPN
ejpam-4570	271	4	)	)	PUNCT
ejpam-4570	271	5	∈	∈	PROPN
ejpam-4570	271	6	f(u	f(u	PROPN
ejpam-4570	271	7	)	)	PUNCT
ejpam-4570	271	8	∩	∩	NOUN
ejpam-4570	271	9	f(v	f(v	PROPN
ejpam-4570	271	10	)	)	PUNCT
ejpam-4570	271	11	,	,	PUNCT
ejpam-4570	271	12	which	which	PRON
ejpam-4570	271	13	is	be	AUX
ejpam-4570	271	14	a	a	DET
ejpam-4570	271	15	contradiction	contradiction	NOUN
ejpam-4570	271	16	.	.	PUNCT
ejpam-4570	272	1	hence	hence	ADV
ejpam-4570	272	2	,	,	PUNCT
ejpam-4570	272	3	it	it	PRON
ejpam-4570	272	4	must	must	AUX
ejpam-4570	272	5	be	be	AUX
ejpam-4570	272	6	w	w	ADP
ejpam-4570	272	7	∩	∩	ADJ
ejpam-4570	272	8	f(h	f(h	NOUN
ejpam-4570	272	9	)	)	PUNCT
ejpam-4570	273	1	=	=	PUNCT
ejpam-4570	273	2	∅.	∅.	NOUN
ejpam-4570	273	3	it	it	PRON
ejpam-4570	273	4	can	can	AUX
ejpam-4570	273	5	be	be	AUX
ejpam-4570	273	6	observed	observe	VERB
ejpam-4570	273	7	that	that	SCONJ
ejpam-4570	273	8	q	q	PUNCT
ejpam-4570	273	9	∈	∈	PROPN
ejpam-4570	273	10	w	w	NOUN
ejpam-4570	273	11	as	as	ADP
ejpam-4570	273	12	q	q	PROPN
ejpam-4570	273	13	∈	∈	PROPN
ejpam-4570	273	14	y	y	PROPN
ejpam-4570	273	15	\	\	PROPN
ejpam-4570	273	16	f(h	f(h	PROPN
ejpam-4570	273	17	)	)	PUNCT
ejpam-4570	273	18	was	be	AUX
ejpam-4570	273	19	arbitrary	arbitrary	ADJ
ejpam-4570	273	20	,	,	PUNCT
ejpam-4570	273	21	then	then	ADV
ejpam-4570	273	22	f(h	f(h	PROPN
ejpam-4570	273	23	)	)	PUNCT
ejpam-4570	273	24	is	be	AUX
ejpam-4570	273	25	closed	closed	ADJ
ejpam-4570	273	26	.	.	PUNCT
ejpam-4570	274	1	so	so	ADV
ejpam-4570	274	2	,	,	PUNCT
ejpam-4570	274	3	f	f	PROPN
ejpam-4570	274	4	is	be	AUX
ejpam-4570	274	5	a	a	DET
ejpam-4570	274	6	homeomorphism	homeomorphism	NOUN
ejpam-4570	274	7	.	.	PUNCT
ejpam-4570	275	1	since	since	SCONJ
ejpam-4570	275	2	y	y	PROPN
ejpam-4570	275	3	is	be	AUX
ejpam-4570	275	4	an	an	DET
ejpam-4570	275	5	almost	almost	ADV
ejpam-4570	275	6	normal	normal	ADJ
ejpam-4570	275	7	space	space	NOUN
ejpam-4570	275	8	,	,	PUNCT
ejpam-4570	275	9	we	we	PRON
ejpam-4570	275	10	have	have	VERB
ejpam-4570	275	11	x	x	INTJ
ejpam-4570	275	12	is	be	AUX
ejpam-4570	275	13	almost	almost	ADV
ejpam-4570	275	14	normal	normal	ADJ
ejpam-4570	275	15	.	.	PUNCT
ejpam-4570	276	1	since	since	SCONJ
ejpam-4570	276	2	x	x	PRON
ejpam-4570	276	3	is	be	AUX
ejpam-4570	276	4	hausdorff	hausdorff	NOUN
ejpam-4570	276	5	almost	almost	ADV
ejpam-4570	276	6	normal	normal	ADJ
ejpam-4570	276	7	,	,	PUNCT
ejpam-4570	276	8	we	we	PRON
ejpam-4570	276	9	get	get	VERB
ejpam-4570	276	10	x	x	PUNCT
ejpam-4570	276	11	is	be	AUX
ejpam-4570	276	12	epi	epi	NOUN
ejpam-4570	276	13	-	-	ADJ
ejpam-4570	276	14	almost	almost	ADV
ejpam-4570	276	15	normal	normal	ADJ
ejpam-4570	276	16	.	.	PUNCT
ejpam-4570	277	1	wafa	wafa	PROPN
ejpam-4570	277	2	khalaf	khalaf	PROPN
ejpam-4570	277	3	alqurashi	alqurashi	PROPN
ejpam-4570	277	4	,	,	PUNCT
ejpam-4570	277	5	sadeq	sadeq	PROPN
ejpam-4570	277	6	ali	ali	PROPN
ejpam-4570	277	7	thabit	thabit	PROPN
ejpam-4570	277	8	/	/	SYM
ejpam-4570	277	9	eur	eur	PROPN
ejpam-4570	277	10	.	.	PUNCT
ejpam-4570	278	1	j.	j.	PROPN
ejpam-4570	278	2	pure	pure	PROPN
ejpam-4570	278	3	appl	appl	PROPN
ejpam-4570	278	4	.	.	PROPN
ejpam-4570	278	5	math	math	PROPN
ejpam-4570	278	6	,	,	PUNCT
ejpam-4570	278	7	15	15	NUM
ejpam-4570	278	8	(	(	PUNCT
ejpam-4570	278	9	4	4	NUM
ejpam-4570	278	10	)	)	PUNCT
ejpam-4570	278	11	(	(	PUNCT
ejpam-4570	278	12	2022	2022	NUM
ejpam-4570	278	13	)	)	PUNCT
ejpam-4570	278	14	,	,	PUNCT
ejpam-4570	278	15	1760	1760	NUM
ejpam-4570	278	16	-	-	SYM
ejpam-4570	278	17	1782	1782	NUM
ejpam-4570	278	18	1768	1768	NUM
ejpam-4570	278	19	since	since	SCONJ
ejpam-4570	278	20	every	every	DET
ejpam-4570	278	21	second	second	ADJ
ejpam-4570	278	22	countable	countable	ADJ
ejpam-4570	278	23	space	space	NOUN
ejpam-4570	278	24	is	be	AUX
ejpam-4570	278	25	a	a	DET
ejpam-4570	278	26	lindelöf	lindelöf	NOUN
ejpam-4570	278	27	separable	separable	ADJ
ejpam-4570	278	28	space	space	NOUN
ejpam-4570	279	1	[	[	X
ejpam-4570	279	2	12	12	NUM
ejpam-4570	279	3	]	]	PUNCT
ejpam-4570	279	4	,	,	PUNCT
ejpam-4570	279	5	and	and	CCONJ
ejpam-4570	279	6	every	every	DET
ejpam-4570	279	7	lindelöf	lindelöf	NOUN
ejpam-4570	279	8	l	l	NOUN
ejpam-4570	279	9	-	-	PUNCT
ejpam-4570	279	10	almost	almost	ADV
ejpam-4570	279	11	normal	normal	ADJ
ejpam-4570	279	12	space	space	NOUN
ejpam-4570	279	13	is	be	AUX
ejpam-4570	279	14	almost	almost	ADV
ejpam-4570	279	15	normal	normal	ADJ
ejpam-4570	279	16	(	(	PUNCT
ejpam-4570	279	17	theorem	theorem	NOUN
ejpam-4570	279	18	10	10	NUM
ejpam-4570	279	19	)	)	PUNCT
ejpam-4570	279	20	,	,	PUNCT
ejpam-4570	279	21	we	we	PRON
ejpam-4570	279	22	get	get	VERB
ejpam-4570	279	23	:	:	PUNCT
ejpam-4570	279	24	corollary	corollary	ADJ
ejpam-4570	279	25	9	9	NUM
ejpam-4570	279	26	.	.	PUNCT
ejpam-4570	280	1	(	(	PUNCT
ejpam-4570	280	2	1	1	X
ejpam-4570	280	3	)	)	PUNCT
ejpam-4570	280	4	every	every	DET
ejpam-4570	280	5	hausdorff	hausdorff	NOUN
ejpam-4570	280	6	second	second	ADJ
ejpam-4570	280	7	countable	countable	ADJ
ejpam-4570	280	8	l	l	NOUN
ejpam-4570	280	9	-	-	ADJ
ejpam-4570	280	10	almost	almost	ADV
ejpam-4570	280	11	normal	normal	ADJ
ejpam-4570	280	12	space	space	NOUN
ejpam-4570	280	13	is	be	AUX
ejpam-4570	280	14	epi	epi	NOUN
ejpam-4570	280	15	-	-	ADJ
ejpam-4570	280	16	almost	almost	ADV
ejpam-4570	280	17	normal	normal	ADJ
ejpam-4570	280	18	.	.	PUNCT
ejpam-4570	281	1	(	(	PUNCT
ejpam-4570	281	2	2	2	X
ejpam-4570	281	3	)	)	PUNCT
ejpam-4570	281	4	every	every	DET
ejpam-4570	281	5	second	second	ADJ
ejpam-4570	281	6	countable	countable	ADJ
ejpam-4570	281	7	l	l	NOUN
ejpam-4570	281	8	-	-	ADJ
ejpam-4570	281	9	almost	almost	ADV
ejpam-4570	281	10	normal	normal	ADJ
ejpam-4570	281	11	space	space	NOUN
ejpam-4570	281	12	is	be	AUX
ejpam-4570	281	13	almost	almost	ADV
ejpam-4570	281	14	normal	normal	ADJ
ejpam-4570	281	15	.	.	PUNCT
ejpam-4570	282	1	observed	observe	VERB
ejpam-4570	282	2	that	that	SCONJ
ejpam-4570	282	3	:	:	PUNCT
ejpam-4570	282	4	epi	epi	ADJ
ejpam-4570	282	5	-	-	PUNCT
ejpam-4570	282	6	almost	almost	ADV
ejpam-4570	282	7	normality	normality	NOUN
ejpam-4570	282	8	and	and	CCONJ
ejpam-4570	282	9	l	l	NOUN
ejpam-4570	282	10	-	-	ADJ
ejpam-4570	282	11	almost	almost	ADV
ejpam-4570	282	12	normality	normality	NOUN
ejpam-4570	282	13	are	be	AUX
ejpam-4570	282	14	different	different	ADJ
ejpam-4570	282	15	from	from	ADP
ejpam-4570	282	16	each	each	DET
ejpam-4570	282	17	other	other	ADJ
ejpam-4570	282	18	.	.	PUNCT
ejpam-4570	283	1	the	the	DET
ejpam-4570	283	2	countable	countable	ADJ
ejpam-4570	283	3	complement	complement	NOUN
ejpam-4570	283	4	topology	topology	NOUN
ejpam-4570	283	5	,	,	PUNCT
ejpam-4570	283	6	example	example	NOUN
ejpam-4570	283	7	4	4	NUM
ejpam-4570	283	8	,	,	PUNCT
ejpam-4570	283	9	and	and	CCONJ
ejpam-4570	283	10	the	the	DET
ejpam-4570	283	11	finite	finite	PROPN
ejpam-4570	283	12	complement	complement	NOUN
ejpam-4570	283	13	topology	topology	NOUN
ejpam-4570	283	14	,	,	PUNCT
ejpam-4570	283	15	example	example	NOUN
ejpam-4570	283	16	3	3	NUM
ejpam-4570	283	17	,	,	PUNCT
ejpam-4570	283	18	are	be	AUX
ejpam-4570	283	19	l	l	ADJ
ejpam-4570	283	20	-	-	ADJ
ejpam-4570	283	21	almost	almost	ADV
ejpam-4570	283	22	normal	normal	ADJ
ejpam-4570	283	23	spaces	space	NOUN
ejpam-4570	283	24	,	,	PUNCT
ejpam-4570	283	25	which	which	PRON
ejpam-4570	283	26	are	be	AUX
ejpam-4570	283	27	not	not	PART
ejpam-4570	283	28	epi	epi	NOUN
ejpam-4570	283	29	-	-	ADJ
ejpam-4570	283	30	almost	almost	ADV
ejpam-4570	283	31	normal	normal	ADJ
ejpam-4570	283	32	because	because	SCONJ
ejpam-4570	283	33	they	they	PRON
ejpam-4570	283	34	are	be	AUX
ejpam-4570	283	35	not	not	PART
ejpam-4570	283	36	hausdorff	hausdorff	ADJ
ejpam-4570	283	37	.	.	PUNCT
ejpam-4570	284	1	the	the	DET
ejpam-4570	284	2	smirnov	smirnov	PROPN
ejpam-4570	284	3	’s	’s	PART
ejpam-4570	284	4	deleted	delete	VERB
ejpam-4570	284	5	sequence	sequence	NOUN
ejpam-4570	284	6	topology	topology	NOUN
ejpam-4570	284	7	,	,	PUNCT
ejpam-4570	284	8	example	example	NOUN
ejpam-4570	284	9	9	9	NUM
ejpam-4570	284	10	,	,	PUNCT
ejpam-4570	284	11	and	and	CCONJ
ejpam-4570	284	12	the	the	DET
ejpam-4570	284	13	countable	countable	ADJ
ejpam-4570	284	14	complement	complement	NOUN
ejpam-4570	284	15	extension	extension	NOUN
ejpam-4570	284	16	topology	topology	NOUN
ejpam-4570	284	17	,	,	PUNCT
ejpam-4570	284	18	example	example	NOUN
ejpam-4570	284	19	10	10	NUM
ejpam-4570	284	20	,	,	PUNCT
ejpam-4570	284	21	are	be	AUX
ejpam-4570	284	22	epi	epi	NOUN
ejpam-4570	284	23	-	-	ADJ
ejpam-4570	284	24	almost	almost	ADV
ejpam-4570	284	25	normal	normal	ADJ
ejpam-4570	284	26	spaces	space	NOUN
ejpam-4570	284	27	,	,	PUNCT
ejpam-4570	284	28	which	which	PRON
ejpam-4570	284	29	are	be	AUX
ejpam-4570	284	30	not	not	PART
ejpam-4570	284	31	l	l	NOUN
ejpam-4570	284	32	-	-	ADJ
ejpam-4570	284	33	almost	almost	ADV
ejpam-4570	284	34	normal	normal	ADJ
ejpam-4570	284	35	.	.	PUNCT
ejpam-4570	285	1	theorem	theorem	VERB
ejpam-4570	285	2	13	13	NUM
ejpam-4570	285	3	.	.	PUNCT
ejpam-4570	286	1	l	l	NOUN
ejpam-4570	286	2	-	-	PUNCT
ejpam-4570	286	3	almost	almost	ADV
ejpam-4570	286	4	normality	normality	NOUN
ejpam-4570	286	5	is	be	AUX
ejpam-4570	286	6	a	a	DET
ejpam-4570	286	7	topological	topological	ADJ
ejpam-4570	286	8	property	property	NOUN
ejpam-4570	286	9	.	.	PUNCT
ejpam-4570	287	1	proof	proof	NOUN
ejpam-4570	287	2	.	.	PUNCT
ejpam-4570	288	1	it	it	PRON
ejpam-4570	288	2	is	be	AUX
ejpam-4570	288	3	similar	similar	ADJ
ejpam-4570	288	4	to	to	ADP
ejpam-4570	288	5	that	that	PRON
ejpam-4570	288	6	of	of	ADP
ejpam-4570	288	7	theorem	theorem	ADJ
ejpam-4570	288	8	4	4	NUM
ejpam-4570	288	9	.	.	PUNCT
ejpam-4570	288	10	theorem	theorem	VERB
ejpam-4570	288	11	14	14	NUM
ejpam-4570	288	12	.	.	PUNCT
ejpam-4570	289	1	l	l	NOUN
ejpam-4570	289	2	-	-	PUNCT
ejpam-4570	289	3	almost	almost	ADV
ejpam-4570	289	4	normality	normality	NOUN
ejpam-4570	289	5	is	be	AUX
ejpam-4570	289	6	an	an	DET
ejpam-4570	289	7	additive	additive	ADJ
ejpam-4570	289	8	property	property	NOUN
ejpam-4570	289	9	.	.	PUNCT
ejpam-4570	290	1	proof	proof	NOUN
ejpam-4570	290	2	.	.	PUNCT
ejpam-4570	291	1	the	the	DET
ejpam-4570	291	2	proof	proof	NOUN
ejpam-4570	291	3	is	be	AUX
ejpam-4570	291	4	similar	similar	ADJ
ejpam-4570	291	5	to	to	ADP
ejpam-4570	291	6	that	that	PRON
ejpam-4570	291	7	of	of	ADP
ejpam-4570	291	8	theorem	theorem	ADJ
ejpam-4570	291	9	5	5	NUM
ejpam-4570	291	10	.	.	PUNCT
ejpam-4570	291	11	theorem	theorem	VERB
ejpam-4570	291	12	15	15	NUM
ejpam-4570	291	13	.	.	PUNCT
ejpam-4570	292	1	if	if	SCONJ
ejpam-4570	292	2	x	x	PRON
ejpam-4570	292	3	is	be	AUX
ejpam-4570	292	4	a	a	DET
ejpam-4570	292	5	c	c	NOUN
ejpam-4570	292	6	-	-	PUNCT
ejpam-4570	292	7	almost	almost	ADV
ejpam-4570	292	8	normal	normal	ADJ
ejpam-4570	292	9	space	space	NOUN
ejpam-4570	292	10	such	such	ADJ
ejpam-4570	292	11	that	that	SCONJ
ejpam-4570	292	12	every	every	DET
ejpam-4570	292	13	lindelöf	lindelöf	NOUN
ejpam-4570	292	14	subspace	subspace	NOUN
ejpam-4570	292	15	of	of	ADP
ejpam-4570	292	16	x	x	PRON
ejpam-4570	292	17	is	be	AUX
ejpam-4570	292	18	contained	contain	VERB
ejpam-4570	292	19	in	in	ADP
ejpam-4570	292	20	a	a	DET
ejpam-4570	292	21	compact	compact	ADJ
ejpam-4570	292	22	subspace	subspace	NOUN
ejpam-4570	292	23	of	of	ADP
ejpam-4570	292	24	x	x	PRON
ejpam-4570	292	25	,	,	PUNCT
ejpam-4570	292	26	then	then	ADV
ejpam-4570	292	27	x	x	PUNCT
ejpam-4570	292	28	is	be	AUX
ejpam-4570	292	29	l	l	NOUN
ejpam-4570	292	30	-	-	ADJ
ejpam-4570	292	31	almost	almost	ADV
ejpam-4570	292	32	normal	normal	ADJ
ejpam-4570	292	33	.	.	PUNCT
ejpam-4570	293	1	proof	proof	NOUN
ejpam-4570	293	2	.	.	PUNCT
ejpam-4570	294	1	let	let	VERB
ejpam-4570	294	2	x	x	PRON
ejpam-4570	294	3	be	be	AUX
ejpam-4570	294	4	a	a	DET
ejpam-4570	294	5	c	c	NOUN
ejpam-4570	294	6	-	-	PUNCT
ejpam-4570	294	7	almost	almost	ADV
ejpam-4570	294	8	normal	normal	ADJ
ejpam-4570	294	9	space	space	NOUN
ejpam-4570	294	10	such	such	ADJ
ejpam-4570	294	11	that	that	SCONJ
ejpam-4570	294	12	if	if	SCONJ
ejpam-4570	294	13	a	a	PRON
ejpam-4570	294	14	is	be	AUX
ejpam-4570	294	15	a	a	DET
ejpam-4570	294	16	lindelöf	lindelöf	NOUN
ejpam-4570	294	17	subspace	subspace	NOUN
ejpam-4570	294	18	of	of	ADP
ejpam-4570	294	19	x	x	PRON
ejpam-4570	294	20	,	,	PUNCT
ejpam-4570	294	21	there	there	PRON
ejpam-4570	294	22	exists	exist	VERB
ejpam-4570	294	23	a	a	DET
ejpam-4570	294	24	compact	compact	ADJ
ejpam-4570	294	25	subspace	subspace	NOUN
ejpam-4570	294	26	b	b	PROPN
ejpam-4570	294	27	of	of	ADP
ejpam-4570	294	28	x	x	SYM
ejpam-4570	294	29	such	such	ADJ
ejpam-4570	294	30	that	that	SCONJ
ejpam-4570	294	31	a	a	DET
ejpam-4570	294	32	⊆	⊆	NUM
ejpam-4570	294	33	b.	b.	NOUN
ejpam-4570	294	34	let	let	VERB
ejpam-4570	294	35	y	y	PRON
ejpam-4570	294	36	be	be	AUX
ejpam-4570	294	37	any	any	DET
ejpam-4570	294	38	almost	almost	ADV
ejpam-4570	294	39	normal	normal	ADJ
ejpam-4570	294	40	space	space	NOUN
ejpam-4570	294	41	and	and	CCONJ
ejpam-4570	294	42	f	f	NOUN
ejpam-4570	294	43	:	:	PUNCT
ejpam-4570	294	44	x	x	X
ejpam-4570	294	45	→	→	SYM
ejpam-4570	294	46	y	y	X
ejpam-4570	294	47	be	be	AUX
ejpam-4570	294	48	a	a	DET
ejpam-4570	294	49	bijective	bijective	ADJ
ejpam-4570	294	50	function	function	NOUN
ejpam-4570	294	51	such	such	ADJ
ejpam-4570	294	52	that	that	SCONJ
ejpam-4570	294	53	f	f	PROPN
ejpam-4570	294	54	|c	|c	VERB
ejpam-4570	294	55	:	:	PUNCT
ejpam-4570	294	56	c	c	PROPN
ejpam-4570	294	57	→	→	SYM
ejpam-4570	294	58	f(c	f(c	PROPN
ejpam-4570	294	59	)	)	PUNCT
ejpam-4570	294	60	is	be	AUX
ejpam-4570	294	61	a	a	DET
ejpam-4570	294	62	homeomorphism	homeomorphism	NOUN
ejpam-4570	294	63	for	for	ADP
ejpam-4570	294	64	each	each	DET
ejpam-4570	294	65	compact	compact	ADJ
ejpam-4570	294	66	subspace	subspace	NOUN
ejpam-4570	294	67	c	c	PROPN
ejpam-4570	294	68	of	of	ADP
ejpam-4570	294	69	x.	x.	NOUN
ejpam-4570	294	70	now	now	ADV
ejpam-4570	294	71	,	,	PUNCT
ejpam-4570	294	72	let	let	VERB
ejpam-4570	294	73	a	a	PRON
ejpam-4570	294	74	be	be	AUX
ejpam-4570	294	75	any	any	DET
ejpam-4570	294	76	lindelöf	lindelöf	NOUN
ejpam-4570	294	77	subspace	subspace	NOUN
ejpam-4570	294	78	of	of	ADP
ejpam-4570	294	79	x.	x.	PROPN
ejpam-4570	294	80	pick	pick	VERB
ejpam-4570	294	81	a	a	DET
ejpam-4570	294	82	compact	compact	ADJ
ejpam-4570	294	83	subspace	subspace	NOUN
ejpam-4570	294	84	b	b	PROPN
ejpam-4570	294	85	of	of	ADP
ejpam-4570	294	86	x	x	SYM
ejpam-4570	294	87	such	such	ADJ
ejpam-4570	294	88	that	that	SCONJ
ejpam-4570	294	89	a	a	DET
ejpam-4570	294	90	⊆	⊆	NUM
ejpam-4570	294	91	b.	b.	NOUN
ejpam-4570	294	92	then	then	ADV
ejpam-4570	294	93	,	,	PUNCT
ejpam-4570	294	94	f	f	PROPN
ejpam-4570	294	95	|b	|b	NOUN
ejpam-4570	294	96	:	:	PUNCT
ejpam-4570	294	97	b	b	X
ejpam-4570	294	98	→	→	SYM
ejpam-4570	294	99	f(b	f(b	PROPN
ejpam-4570	294	100	)	)	PUNCT
ejpam-4570	294	101	is	be	AUX
ejpam-4570	294	102	a	a	DET
ejpam-4570	294	103	homeomorphism	homeomorphism	NOUN
ejpam-4570	294	104	.	.	PUNCT
ejpam-4570	295	1	thus	thus	ADV
ejpam-4570	295	2	,	,	PUNCT
ejpam-4570	295	3	f	f	PROPN
ejpam-4570	295	4	|a	|a	VERB
ejpam-4570	295	5	:	:	PUNCT
ejpam-4570	295	6	a	a	DET
ejpam-4570	295	7	→	→	SYM
ejpam-4570	295	8	f(a	f(a	NOUN
ejpam-4570	295	9	)	)	PUNCT
ejpam-4570	295	10	is	be	AUX
ejpam-4570	295	11	a	a	DET
ejpam-4570	295	12	homeomorphism	homeomorphism	NOUN
ejpam-4570	295	13	as	as	ADP
ejpam-4570	295	14	(	(	PUNCT
ejpam-4570	295	15	f	f	PROPN
ejpam-4570	295	16	|b)|a	|b)|a	PROPN
ejpam-4570	295	17	=	=	SYM
ejpam-4570	295	18	f	f	PROPN
ejpam-4570	295	19	|a	|a	NOUN
ejpam-4570	295	20	.	.	PUNCT
ejpam-4570	296	1	therefore	therefore	ADV
ejpam-4570	296	2	,	,	PUNCT
ejpam-4570	296	3	x	x	X
ejpam-4570	296	4	is	be	AUX
ejpam-4570	296	5	l	l	NOUN
ejpam-4570	296	6	-	-	ADJ
ejpam-4570	296	7	almost	almost	ADV
ejpam-4570	296	8	normal	normal	ADJ
ejpam-4570	296	9	.	.	PUNCT
ejpam-4570	297	1	since	since	SCONJ
ejpam-4570	297	2	every	every	DET
ejpam-4570	297	3	almost	almost	ADV
ejpam-4570	297	4	compact	compact	ADJ
ejpam-4570	297	5	urysohn	urysohn	NOUN
ejpam-4570	297	6	space	space	NOUN
ejpam-4570	297	7	is	be	AUX
ejpam-4570	297	8	almost	almost	ADV
ejpam-4570	297	9	regular	regular	ADJ
ejpam-4570	297	10	,	,	PUNCT
ejpam-4570	297	11	every	every	DET
ejpam-4570	297	12	hausdorff	hausdorff	NOUN
ejpam-4570	297	13	almost	almost	ADV
ejpam-4570	297	14	regular	regular	ADJ
ejpam-4570	297	15	nearly	nearly	ADV
ejpam-4570	297	16	compact	compact	ADJ
ejpam-4570	297	17	(	(	PUNCT
ejpam-4570	297	18	nearly	nearly	ADV
ejpam-4570	297	19	paracompact	paracompact	ADJ
ejpam-4570	297	20	)	)	PUNCT
ejpam-4570	297	21	space	space	NOUN
ejpam-4570	297	22	is	be	AUX
ejpam-4570	297	23	almost	almost	ADV
ejpam-4570	297	24	normal	normal	ADJ
ejpam-4570	297	25	,	,	PUNCT
ejpam-4570	297	26	every	every	DET
ejpam-4570	297	27	hausdorff	hausdorff	NOUN
ejpam-4570	297	28	almost	almost	ADV
ejpam-4570	297	29	compact	compact	ADJ
ejpam-4570	297	30	almost	almost	ADV
ejpam-4570	297	31	regular	regular	ADJ
ejpam-4570	297	32	space	space	NOUN
ejpam-4570	297	33	is	be	AUX
ejpam-4570	297	34	almost	almost	ADV
ejpam-4570	297	35	normal	normal	ADJ
ejpam-4570	297	36	[	[	X
ejpam-4570	297	37	20	20	NUM
ejpam-4570	297	38	,	,	PUNCT
ejpam-4570	297	39	21	21	NUM
ejpam-4570	297	40	]	]	PUNCT
ejpam-4570	297	41	,	,	PUNCT
ejpam-4570	297	42	and	and	CCONJ
ejpam-4570	297	43	every	every	DET
ejpam-4570	297	44	hausdorff	hausdorff	NOUN
ejpam-4570	297	45	paracompact	paracompact	NOUN
ejpam-4570	297	46	space	space	NOUN
ejpam-4570	297	47	is	be	AUX
ejpam-4570	297	48	almost	almost	ADV
ejpam-4570	297	49	normal	normal	ADJ
ejpam-4570	297	50	[	[	X
ejpam-4570	297	51	26	26	NUM
ejpam-4570	297	52	]	]	PUNCT
ejpam-4570	297	53	,	,	PUNCT
ejpam-4570	297	54	we	we	PRON
ejpam-4570	297	55	get	get	VERB
ejpam-4570	297	56	:	:	PUNCT
ejpam-4570	297	57	corollary	corollary	ADJ
ejpam-4570	297	58	10	10	NUM
ejpam-4570	297	59	.	.	PUNCT
ejpam-4570	298	1	(	(	PUNCT
ejpam-4570	298	2	1	1	X
ejpam-4570	298	3	)	)	PUNCT
ejpam-4570	298	4	every	every	DET
ejpam-4570	298	5	hausdorff	hausdorff	NOUN
ejpam-4570	298	6	almost	almost	ADV
ejpam-4570	298	7	compact	compact	ADJ
ejpam-4570	298	8	almost	almost	ADV
ejpam-4570	298	9	regular	regular	ADJ
ejpam-4570	298	10	(	(	PUNCT
ejpam-4570	298	11	almost	almost	ADV
ejpam-4570	298	12	completely	completely	ADV
ejpam-4570	298	13	regular	regular	ADJ
ejpam-4570	298	14	)	)	PUNCT
ejpam-4570	298	15	space	space	NOUN
ejpam-4570	298	16	is	be	AUX
ejpam-4570	298	17	l	l	NOUN
ejpam-4570	298	18	-	-	ADJ
ejpam-4570	298	19	almost	almost	ADV
ejpam-4570	298	20	normal	normal	ADJ
ejpam-4570	298	21	.	.	PUNCT
ejpam-4570	299	1	(	(	PUNCT
ejpam-4570	299	2	2	2	X
ejpam-4570	299	3	)	)	PUNCT
ejpam-4570	299	4	every	every	DET
ejpam-4570	299	5	urysohn	urysohn	NOUN
ejpam-4570	299	6	almost	almost	ADV
ejpam-4570	299	7	compact	compact	ADJ
ejpam-4570	299	8	space	space	NOUN
ejpam-4570	299	9	is	be	AUX
ejpam-4570	299	10	l	l	NOUN
ejpam-4570	299	11	-	-	ADJ
ejpam-4570	299	12	almost	almost	ADV
ejpam-4570	299	13	normal	normal	ADJ
ejpam-4570	299	14	.	.	PUNCT
ejpam-4570	300	1	(	(	PUNCT
ejpam-4570	300	2	3	3	X
ejpam-4570	300	3	)	)	PUNCT
ejpam-4570	300	4	every	every	DET
ejpam-4570	300	5	hausdorff	hausdorff	NOUN
ejpam-4570	300	6	nearly	nearly	ADV
ejpam-4570	300	7	compact	compact	ADJ
ejpam-4570	300	8	almost	almost	ADV
ejpam-4570	300	9	regular	regular	ADJ
ejpam-4570	300	10	(	(	PUNCT
ejpam-4570	300	11	almost	almost	ADV
ejpam-4570	300	12	completely	completely	ADV
ejpam-4570	300	13	regular	regular	ADJ
ejpam-4570	300	14	)	)	PUNCT
ejpam-4570	300	15	space	space	NOUN
ejpam-4570	300	16	is	be	AUX
ejpam-4570	300	17	l	l	NOUN
ejpam-4570	300	18	-	-	ADJ
ejpam-4570	300	19	almost	almost	ADV
ejpam-4570	300	20	normal	normal	ADJ
ejpam-4570	300	21	.	.	PUNCT
ejpam-4570	301	1	(	(	PUNCT
ejpam-4570	301	2	4	4	X
ejpam-4570	301	3	)	)	PUNCT
ejpam-4570	301	4	every	every	DET
ejpam-4570	301	5	hausdorff	hausdorff	NOUN
ejpam-4570	301	6	nearly	nearly	ADV
ejpam-4570	301	7	paracompact	paracompact	ADJ
ejpam-4570	301	8	almost	almost	ADV
ejpam-4570	301	9	regular	regular	ADJ
ejpam-4570	301	10	(	(	PUNCT
ejpam-4570	301	11	almost	almost	ADV
ejpam-4570	301	12	completely	completely	ADV
ejpam-4570	301	13	regular	regular	ADJ
ejpam-4570	301	14	)	)	PUNCT
ejpam-4570	301	15	space	space	NOUN
ejpam-4570	301	16	is	be	AUX
ejpam-4570	301	17	l	l	NOUN
ejpam-4570	301	18	-	-	ADJ
ejpam-4570	301	19	almost	almost	ADV
ejpam-4570	301	20	normal	normal	ADJ
ejpam-4570	301	21	.	.	PUNCT
ejpam-4570	302	1	wafa	wafa	PROPN
ejpam-4570	302	2	khalaf	khalaf	PROPN
ejpam-4570	302	3	alqurashi	alqurashi	PROPN
ejpam-4570	302	4	,	,	PUNCT
ejpam-4570	302	5	sadeq	sadeq	PROPN
ejpam-4570	302	6	ali	ali	PROPN
ejpam-4570	302	7	thabit	thabit	PROPN
ejpam-4570	302	8	/	/	SYM
ejpam-4570	302	9	eur	eur	PROPN
ejpam-4570	302	10	.	.	PUNCT
ejpam-4570	303	1	j.	j.	PROPN
ejpam-4570	303	2	pure	pure	PROPN
ejpam-4570	303	3	appl	appl	PROPN
ejpam-4570	303	4	.	.	PROPN
ejpam-4570	303	5	math	math	PROPN
ejpam-4570	303	6	,	,	PUNCT
ejpam-4570	303	7	15	15	NUM
ejpam-4570	303	8	(	(	PUNCT
ejpam-4570	303	9	4	4	NUM
ejpam-4570	303	10	)	)	PUNCT
ejpam-4570	303	11	(	(	PUNCT
ejpam-4570	303	12	2022	2022	NUM
ejpam-4570	303	13	)	)	PUNCT
ejpam-4570	303	14	,	,	PUNCT
ejpam-4570	303	15	1760	1760	NUM
ejpam-4570	303	16	-	-	SYM
ejpam-4570	303	17	1782	1782	NUM
ejpam-4570	303	18	1769	1769	NUM
ejpam-4570	303	19	3	3	NUM
ejpam-4570	303	20	.	.	PUNCT
ejpam-4570	303	21	properties	property	NOUN
ejpam-4570	303	22	and	and	CCONJ
ejpam-4570	303	23	relationships	relationship	NOUN
ejpam-4570	303	24	of	of	ADP
ejpam-4570	303	25	both	both	PRON
ejpam-4570	303	26	c	c	NOUN
ejpam-4570	303	27	-	-	PUNCT
ejpam-4570	303	28	almost	almost	ADV
ejpam-4570	303	29	normality	normality	NOUN
ejpam-4570	303	30	and	and	CCONJ
ejpam-4570	303	31	l	l	NOUN
ejpam-4570	303	32	-	-	ADJ
ejpam-4570	303	33	almost	almost	ADV
ejpam-4570	303	34	normality	normality	NOUN
ejpam-4570	303	35	in	in	ADP
ejpam-4570	303	36	this	this	DET
ejpam-4570	303	37	section	section	NOUN
ejpam-4570	304	1	,	,	PUNCT
ejpam-4570	304	2	we	we	PRON
ejpam-4570	304	3	present	present	VERB
ejpam-4570	304	4	some	some	DET
ejpam-4570	304	5	properties	property	NOUN
ejpam-4570	304	6	and	and	CCONJ
ejpam-4570	304	7	relationships	relationship	NOUN
ejpam-4570	304	8	of	of	ADP
ejpam-4570	304	9	c	c	NOUN
ejpam-4570	304	10	-	-	PUNCT
ejpam-4570	304	11	almost	almost	ADV
ejpam-4570	304	12	normality	normality	NOUN
ejpam-4570	304	13	and	and	CCONJ
ejpam-4570	304	14	l	l	NOUN
ejpam-4570	304	15	-	-	ADJ
ejpam-4570	304	16	almost	almost	ADV
ejpam-4570	304	17	normality	normality	NOUN
ejpam-4570	304	18	:	:	PUNCT
ejpam-4570	304	19	theorem	theorem	VERB
ejpam-4570	304	20	16	16	NUM
ejpam-4570	304	21	.	.	PUNCT
ejpam-4570	305	1	every	every	DET
ejpam-4570	305	2	c	c	NOUN
ejpam-4570	305	3	-	-	PUNCT
ejpam-4570	305	4	completely	completely	ADV
ejpam-4570	305	5	regular	regular	ADJ
ejpam-4570	305	6	fréchet	fréchet	NOUN
ejpam-4570	305	7	(	(	PUNCT
ejpam-4570	305	8	resp	resp	NOUN
ejpam-4570	305	9	.	.	PUNCT
ejpam-4570	306	1	first	first	ADV
ejpam-4570	306	2	countable	countable	ADJ
ejpam-4570	306	3	,	,	PUNCT
ejpam-4570	306	4	k	k	NOUN
ejpam-4570	306	5	-	-	NOUN
ejpam-4570	306	6	space	space	NOUN
ejpam-4570	306	7	)	)	PUNCT
ejpam-4570	306	8	lindelöf	lindelöf	NOUN
ejpam-4570	306	9	space	space	NOUN
ejpam-4570	306	10	is	be	AUX
ejpam-4570	306	11	c	c	NOUN
ejpam-4570	306	12	-	-	PUNCT
ejpam-4570	306	13	almost	almost	ADV
ejpam-4570	306	14	normal	normal	ADJ
ejpam-4570	306	15	.	.	PUNCT
ejpam-4570	307	1	proof	proof	NOUN
ejpam-4570	307	2	.	.	PUNCT
ejpam-4570	308	1	let	let	VERB
ejpam-4570	308	2	x	x	PRON
ejpam-4570	308	3	be	be	AUX
ejpam-4570	308	4	a	a	DET
ejpam-4570	308	5	c	c	NOUN
ejpam-4570	308	6	-	-	PUNCT
ejpam-4570	308	7	completely	completely	ADV
ejpam-4570	308	8	regular	regular	ADJ
ejpam-4570	308	9	fréchet	fréchet	NOUN
ejpam-4570	308	10	(	(	PUNCT
ejpam-4570	308	11	resp	resp	NOUN
ejpam-4570	308	12	.	.	PUNCT
ejpam-4570	309	1	first	first	ADV
ejpam-4570	309	2	countable	countable	ADJ
ejpam-4570	309	3	,	,	PUNCT
ejpam-4570	309	4	k	k	NOUN
ejpam-4570	309	5	-	-	NOUN
ejpam-4570	309	6	space	space	NOUN
ejpam-4570	309	7	)	)	PUNCT
ejpam-4570	309	8	lindelöf	lindelöf	NOUN
ejpam-4570	309	9	space	space	NOUN
ejpam-4570	309	10	.	.	PUNCT
ejpam-4570	310	1	then	then	ADV
ejpam-4570	310	2	,	,	PUNCT
ejpam-4570	310	3	there	there	PRON
ejpam-4570	310	4	exist	exist	VERB
ejpam-4570	310	5	a	a	DET
ejpam-4570	310	6	completely	completely	ADV
ejpam-4570	310	7	regular	regular	ADJ
ejpam-4570	310	8	space	space	NOUN
ejpam-4570	310	9	y	y	PROPN
ejpam-4570	310	10	and	and	CCONJ
ejpam-4570	310	11	a	a	DET
ejpam-4570	310	12	bijective	bijective	ADJ
ejpam-4570	310	13	function	function	NOUN
ejpam-4570	311	1	f	f	NOUN
ejpam-4570	311	2	:	:	PUNCT
ejpam-4570	311	3	x	x	X
ejpam-4570	311	4	→	→	PUNCT
ejpam-4570	311	5	y	y	NUM
ejpam-4570	311	6	such	such	ADJ
ejpam-4570	311	7	that	that	SCONJ
ejpam-4570	311	8	f	f	PROPN
ejpam-4570	311	9	|a	|a	VERB
ejpam-4570	311	10	:	:	PUNCT
ejpam-4570	311	11	a	a	DET
ejpam-4570	311	12	→	→	SYM
ejpam-4570	311	13	f(a	f(a	NOUN
ejpam-4570	311	14	)	)	PUNCT
ejpam-4570	311	15	is	be	AUX
ejpam-4570	311	16	a	a	DET
ejpam-4570	311	17	homeomorphism	homeomorphism	NOUN
ejpam-4570	311	18	for	for	ADP
ejpam-4570	311	19	each	each	DET
ejpam-4570	311	20	compact	compact	NOUN
ejpam-4570	311	21	subset	subset	VERB
ejpam-4570	311	22	a	a	DET
ejpam-4570	311	23	⊆	⊆	NUM
ejpam-4570	311	24	x.	x.	NOUN
ejpam-4570	311	25	since	since	SCONJ
ejpam-4570	311	26	x	x	PROPN
ejpam-4570	311	27	is	be	AUX
ejpam-4570	311	28	fréchet	fréchet	VERB
ejpam-4570	311	29	(	(	PUNCT
ejpam-4570	311	30	resp	resp	NOUN
ejpam-4570	311	31	.	.	PUNCT
ejpam-4570	312	1	first	first	ADV
ejpam-4570	312	2	countable	countable	ADJ
ejpam-4570	312	3	,	,	PUNCT
ejpam-4570	312	4	k	k	NOUN
ejpam-4570	312	5	-	-	NOUN
ejpam-4570	312	6	space	space	NOUN
ejpam-4570	312	7	)	)	PUNCT
ejpam-4570	312	8	,	,	PUNCT
ejpam-4570	312	9	we	we	PRON
ejpam-4570	312	10	have	have	VERB
ejpam-4570	312	11	f	f	PROPN
ejpam-4570	312	12	is	be	AUX
ejpam-4570	312	13	continuous	continuous	ADJ
ejpam-4570	312	14	.	.	PUNCT
ejpam-4570	313	1	since	since	SCONJ
ejpam-4570	313	2	a	a	DET
ejpam-4570	313	3	continuous	continuous	ADJ
ejpam-4570	313	4	image	image	NOUN
ejpam-4570	313	5	of	of	ADP
ejpam-4570	313	6	a	a	DET
ejpam-4570	313	7	lindelöf	lindelöf	NOUN
ejpam-4570	313	8	space	space	NOUN
ejpam-4570	313	9	is	be	AUX
ejpam-4570	313	10	lindelöf	lindelöf	PUNCT
ejpam-4570	313	11	[	[	X
ejpam-4570	313	12	12	12	NUM
ejpam-4570	313	13	]	]	PUNCT
ejpam-4570	313	14	,	,	PUNCT
ejpam-4570	313	15	we	we	PRON
ejpam-4570	313	16	conclude	conclude	VERB
ejpam-4570	313	17	:	:	PUNCT
ejpam-4570	313	18	y	y	PROPN
ejpam-4570	313	19	is	be	AUX
ejpam-4570	313	20	a	a	DET
ejpam-4570	313	21	lindelöf	lindelöf	NOUN
ejpam-4570	313	22	space	space	NOUN
ejpam-4570	313	23	.	.	PUNCT
ejpam-4570	314	1	hence	hence	ADV
ejpam-4570	314	2	,	,	PUNCT
ejpam-4570	314	3	y	y	PROPN
ejpam-4570	314	4	is	be	AUX
ejpam-4570	314	5	normal	normal	ADJ
ejpam-4570	314	6	because	because	SCONJ
ejpam-4570	314	7	any	any	DET
ejpam-4570	314	8	completely	completely	ADV
ejpam-4570	314	9	regular	regular	ADJ
ejpam-4570	314	10	lindelöf	lindelöf	NOUN
ejpam-4570	314	11	space	space	NOUN
ejpam-4570	314	12	is	be	AUX
ejpam-4570	314	13	normal	normal	ADJ
ejpam-4570	314	14	[	[	X
ejpam-4570	314	15	12	12	NUM
ejpam-4570	314	16	]	]	PUNCT
ejpam-4570	314	17	.	.	PUNCT
ejpam-4570	315	1	thus	thus	ADV
ejpam-4570	315	2	,	,	PUNCT
ejpam-4570	315	3	x	x	PRON
ejpam-4570	315	4	is	be	AUX
ejpam-4570	315	5	a	a	DET
ejpam-4570	315	6	c	c	NOUN
ejpam-4570	315	7	-	-	ADJ
ejpam-4570	315	8	normal	normal	ADJ
ejpam-4570	315	9	space	space	NOUN
ejpam-4570	315	10	.	.	PUNCT
ejpam-4570	316	1	hence	hence	ADV
ejpam-4570	316	2	,	,	PUNCT
ejpam-4570	316	3	x	x	X
ejpam-4570	316	4	is	be	AUX
ejpam-4570	316	5	c	c	NOUN
ejpam-4570	316	6	-	-	PUNCT
ejpam-4570	316	7	almost	almost	ADV
ejpam-4570	316	8	normal	normal	ADJ
ejpam-4570	316	9	.	.	PUNCT
ejpam-4570	317	1	theorem	theorem	VERB
ejpam-4570	317	2	17	17	NUM
ejpam-4570	317	3	.	.	PUNCT
ejpam-4570	318	1	every	every	DET
ejpam-4570	318	2	c	c	NOUN
ejpam-4570	318	3	-	-	PUNCT
ejpam-4570	318	4	regular	regular	ADJ
ejpam-4570	318	5	fréchet	fréchet	NOUN
ejpam-4570	318	6	(	(	PUNCT
ejpam-4570	318	7	resp	resp	NOUN
ejpam-4570	318	8	.	.	PUNCT
ejpam-4570	319	1	first	first	ADV
ejpam-4570	319	2	countable	countable	ADJ
ejpam-4570	319	3	,	,	PUNCT
ejpam-4570	319	4	k	k	NOUN
ejpam-4570	319	5	-	-	NOUN
ejpam-4570	319	6	space	space	NOUN
ejpam-4570	319	7	)	)	PUNCT
ejpam-4570	319	8	lindelöf	lindelöf	NOUN
ejpam-4570	319	9	space	space	NOUN
ejpam-4570	319	10	is	be	AUX
ejpam-4570	319	11	c	c	NOUN
ejpam-4570	319	12	-	-	PUNCT
ejpam-4570	319	13	almost	almost	ADV
ejpam-4570	319	14	normal	normal	ADJ
ejpam-4570	319	15	.	.	PUNCT
ejpam-4570	320	1	proof	proof	NOUN
ejpam-4570	320	2	.	.	PUNCT
ejpam-4570	321	1	similar	similar	ADJ
ejpam-4570	321	2	to	to	ADP
ejpam-4570	321	3	the	the	DET
ejpam-4570	321	4	proof	proof	NOUN
ejpam-4570	321	5	of	of	ADP
ejpam-4570	321	6	theorem	theorem	NOUN
ejpam-4570	321	7	16	16	NUM
ejpam-4570	321	8	.	.	PUNCT
ejpam-4570	322	1	since	since	SCONJ
ejpam-4570	322	2	every	every	DET
ejpam-4570	322	3	t1	t1	NOUN
ejpam-4570	322	4	c	c	NOUN
ejpam-4570	322	5	-	-	PUNCT
ejpam-4570	322	6	completely	completely	ADV
ejpam-4570	322	7	regular	regular	ADJ
ejpam-4570	322	8	fréchet	fréchet	NOUN
ejpam-4570	322	9	(	(	PUNCT
ejpam-4570	322	10	resp	resp	NOUN
ejpam-4570	322	11	.	.	PUNCT
ejpam-4570	323	1	first	first	ADV
ejpam-4570	323	2	countable	countable	ADJ
ejpam-4570	323	3	,	,	PUNCT
ejpam-4570	323	4	k	k	NOUN
ejpam-4570	323	5	-	-	NOUN
ejpam-4570	323	6	space	space	NOUN
ejpam-4570	323	7	)	)	PUNCT
ejpam-4570	323	8	lindelöf	lindelöf	NOUN
ejpam-4570	323	9	space	space	NOUN
ejpam-4570	323	10	is	be	AUX
ejpam-4570	323	11	epi	epi	NOUN
ejpam-4570	323	12	-	-	ADJ
ejpam-4570	323	13	normal	normal	ADJ
ejpam-4570	323	14	,	,	PUNCT
ejpam-4570	323	15	see	see	VERB
ejpam-4570	323	16	theorem	theorem	VERB
ejpam-4570	323	17	2.26	2.26	NUM
ejpam-4570	323	18	in	in	ADP
ejpam-4570	323	19	[	[	X
ejpam-4570	323	20	31	31	NUM
ejpam-4570	323	21	]	]	PUNCT
ejpam-4570	323	22	,	,	PUNCT
ejpam-4570	323	23	we	we	PRON
ejpam-4570	323	24	conclude	conclude	VERB
ejpam-4570	323	25	:	:	PUNCT
ejpam-4570	323	26	corollary	corollary	ADJ
ejpam-4570	323	27	11	11	NUM
ejpam-4570	323	28	.	.	PUNCT
ejpam-4570	324	1	(	(	PUNCT
ejpam-4570	324	2	1	1	X
ejpam-4570	324	3	)	)	PUNCT
ejpam-4570	324	4	every	every	DET
ejpam-4570	324	5	t1	t1	NOUN
ejpam-4570	324	6	c	c	NOUN
ejpam-4570	324	7	-	-	PUNCT
ejpam-4570	324	8	completely	completely	ADV
ejpam-4570	324	9	regular	regular	ADJ
ejpam-4570	324	10	fréchet	fréchet	NOUN
ejpam-4570	324	11	(	(	PUNCT
ejpam-4570	324	12	resp	resp	NOUN
ejpam-4570	324	13	.	.	PUNCT
ejpam-4570	325	1	first	first	ADV
ejpam-4570	325	2	countable	countable	ADJ
ejpam-4570	325	3	,	,	PUNCT
ejpam-4570	325	4	k	k	NOUN
ejpam-4570	325	5	-	-	NOUN
ejpam-4570	325	6	space	space	NOUN
ejpam-4570	325	7	)	)	PUNCT
ejpam-4570	325	8	lindelöf	lindelöf	NOUN
ejpam-4570	325	9	space	space	NOUN
ejpam-4570	325	10	is	be	AUX
ejpam-4570	325	11	epi	epi	NOUN
ejpam-4570	325	12	-	-	ADJ
ejpam-4570	325	13	almost	almost	ADV
ejpam-4570	325	14	normal	normal	ADJ
ejpam-4570	325	15	.	.	PUNCT
ejpam-4570	326	1	(	(	PUNCT
ejpam-4570	326	2	2	2	X
ejpam-4570	326	3	)	)	PUNCT
ejpam-4570	326	4	every	every	DET
ejpam-4570	326	5	t1	t1	NOUN
ejpam-4570	326	6	c	c	NOUN
ejpam-4570	326	7	-	-	PUNCT
ejpam-4570	326	8	regular	regular	ADJ
ejpam-4570	326	9	fréchet	fréchet	NOUN
ejpam-4570	326	10	(	(	PUNCT
ejpam-4570	326	11	resp	resp	NOUN
ejpam-4570	326	12	.	.	PUNCT
ejpam-4570	327	1	first	first	ADV
ejpam-4570	327	2	countable	countable	ADJ
ejpam-4570	327	3	,	,	PUNCT
ejpam-4570	327	4	k	k	NOUN
ejpam-4570	327	5	-	-	NOUN
ejpam-4570	327	6	space	space	NOUN
ejpam-4570	327	7	)	)	PUNCT
ejpam-4570	327	8	lindelöf	lindelöf	NOUN
ejpam-4570	327	9	space	space	NOUN
ejpam-4570	327	10	is	be	AUX
ejpam-4570	327	11	epi	epi	NOUN
ejpam-4570	327	12	-	-	ADJ
ejpam-4570	327	13	almost	almost	ADV
ejpam-4570	327	14	normal	normal	ADJ
ejpam-4570	327	15	.	.	PUNCT
ejpam-4570	328	1	since	since	SCONJ
ejpam-4570	328	2	every	every	DET
ejpam-4570	328	3	c	c	NOUN
ejpam-4570	328	4	-	-	PUNCT
ejpam-4570	328	5	regular	regular	ADJ
ejpam-4570	328	6	fréchet	fréchet	NOUN
ejpam-4570	328	7	lindelöf	lindelöf	NOUN
ejpam-4570	328	8	space	space	NOUN
ejpam-4570	328	9	is	be	AUX
ejpam-4570	328	10	c	c	NOUN
ejpam-4570	328	11	-	-	ADJ
ejpam-4570	328	12	normal	normal	ADJ
ejpam-4570	328	13	[	[	X
ejpam-4570	328	14	8	8	NUM
ejpam-4570	328	15	]	]	PUNCT
ejpam-4570	328	16	,	,	PUNCT
ejpam-4570	328	17	and	and	CCONJ
ejpam-4570	328	18	every	every	DET
ejpam-4570	328	19	σ	σ	NOUN
ejpam-4570	328	20	-	-	ADJ
ejpam-4570	328	21	compact	compact	ADJ
ejpam-4570	328	22	(	(	PUNCT
ejpam-4570	328	23	resp	resp	NOUN
ejpam-4570	328	24	.	.	PUNCT
ejpam-4570	329	1	second	second	ADJ
ejpam-4570	329	2	countable	countable	ADJ
ejpam-4570	329	3	)	)	PUNCT
ejpam-4570	329	4	space	space	NOUN
ejpam-4570	329	5	is	be	AUX
ejpam-4570	329	6	lindelöf	lindelöf	PUNCT
ejpam-4570	329	7	[	[	X
ejpam-4570	329	8	12	12	NUM
ejpam-4570	329	9	]	]	PUNCT
ejpam-4570	329	10	,	,	PUNCT
ejpam-4570	329	11	we	we	PRON
ejpam-4570	329	12	conclude	conclude	VERB
ejpam-4570	329	13	:	:	PUNCT
ejpam-4570	329	14	corollary	corollary	ADJ
ejpam-4570	329	15	12	12	NUM
ejpam-4570	329	16	.	.	PUNCT
ejpam-4570	330	1	(	(	PUNCT
ejpam-4570	330	2	1	1	X
ejpam-4570	330	3	)	)	PUNCT
ejpam-4570	330	4	every	every	DET
ejpam-4570	330	5	c	c	NOUN
ejpam-4570	330	6	-	-	PUNCT
ejpam-4570	330	7	regular	regular	ADJ
ejpam-4570	330	8	fréchet	fréchet	NOUN
ejpam-4570	330	9	(	(	PUNCT
ejpam-4570	330	10	resp	resp	NOUN
ejpam-4570	330	11	.	.	PUNCT
ejpam-4570	331	1	first	first	ADV
ejpam-4570	331	2	countable	countable	ADJ
ejpam-4570	331	3	,	,	PUNCT
ejpam-4570	331	4	k	k	NOUN
ejpam-4570	331	5	-	-	NOUN
ejpam-4570	331	6	space	space	NOUN
ejpam-4570	331	7	)	)	PUNCT
ejpam-4570	331	8	σ	σ	VERB
ejpam-4570	331	9	-	-	ADJ
ejpam-4570	331	10	compact	compact	ADJ
ejpam-4570	331	11	space	space	NOUN
ejpam-4570	331	12	is	be	AUX
ejpam-4570	331	13	c	c	NOUN
ejpam-4570	331	14	-	-	PUNCT
ejpam-4570	331	15	almost	almost	ADV
ejpam-4570	331	16	normal	normal	ADJ
ejpam-4570	331	17	.	.	PUNCT
ejpam-4570	332	1	(	(	PUNCT
ejpam-4570	332	2	2	2	X
ejpam-4570	332	3	)	)	PUNCT
ejpam-4570	332	4	every	every	DET
ejpam-4570	332	5	c	c	NOUN
ejpam-4570	332	6	-	-	PUNCT
ejpam-4570	332	7	completely	completely	ADV
ejpam-4570	332	8	regular	regular	ADJ
ejpam-4570	332	9	fréchet	fréchet	NOUN
ejpam-4570	332	10	(	(	PUNCT
ejpam-4570	332	11	resp	resp	NOUN
ejpam-4570	332	12	.	.	PUNCT
ejpam-4570	333	1	first	first	ADV
ejpam-4570	333	2	countable	countable	ADJ
ejpam-4570	333	3	,	,	PUNCT
ejpam-4570	333	4	k	k	NOUN
ejpam-4570	333	5	-	-	NOUN
ejpam-4570	333	6	space	space	NOUN
ejpam-4570	333	7	)	)	PUNCT
ejpam-4570	333	8	σ	σ	VERB
ejpam-4570	333	9	-	-	ADJ
ejpam-4570	333	10	compact	compact	ADJ
ejpam-4570	333	11	space	space	NOUN
ejpam-4570	333	12	is	be	AUX
ejpam-4570	333	13	c	c	NOUN
ejpam-4570	333	14	-	-	PUNCT
ejpam-4570	333	15	almost	almost	ADV
ejpam-4570	333	16	normal	normal	ADJ
ejpam-4570	333	17	.	.	PUNCT
ejpam-4570	334	1	(	(	PUNCT
ejpam-4570	334	2	3	3	X
ejpam-4570	334	3	)	)	PUNCT
ejpam-4570	334	4	every	every	DET
ejpam-4570	334	5	c	c	NOUN
ejpam-4570	334	6	-	-	PUNCT
ejpam-4570	334	7	regular	regular	ADJ
ejpam-4570	334	8	fréchet	fréchet	NOUN
ejpam-4570	334	9	lindelöf	lindelöf	NOUN
ejpam-4570	334	10	space	space	NOUN
ejpam-4570	334	11	is	be	AUX
ejpam-4570	334	12	c	c	NOUN
ejpam-4570	334	13	-	-	PUNCT
ejpam-4570	334	14	almost	almost	ADV
ejpam-4570	334	15	normal	normal	ADJ
ejpam-4570	334	16	.	.	PUNCT
ejpam-4570	335	1	(	(	PUNCT
ejpam-4570	335	2	4	4	X
ejpam-4570	335	3	)	)	PUNCT
ejpam-4570	335	4	every	every	DET
ejpam-4570	335	5	c	c	NOUN
ejpam-4570	335	6	-	-	PUNCT
ejpam-4570	335	7	completely	completely	ADV
ejpam-4570	335	8	regular	regular	ADJ
ejpam-4570	335	9	fréchet	fréchet	NOUN
ejpam-4570	335	10	lindelöf	lindelöf	NOUN
ejpam-4570	335	11	space	space	NOUN
ejpam-4570	335	12	is	be	AUX
ejpam-4570	335	13	c	c	NOUN
ejpam-4570	335	14	-	-	PUNCT
ejpam-4570	335	15	almost	almost	ADV
ejpam-4570	335	16	normal	normal	ADJ
ejpam-4570	335	17	.	.	PUNCT
ejpam-4570	336	1	the	the	DET
ejpam-4570	336	2	next	next	ADJ
ejpam-4570	336	3	result	result	NOUN
ejpam-4570	336	4	is	be	AUX
ejpam-4570	336	5	obvious	obvious	ADJ
ejpam-4570	336	6	:	:	PUNCT
ejpam-4570	336	7	wafa	wafa	PROPN
ejpam-4570	336	8	khalaf	khalaf	PROPN
ejpam-4570	336	9	alqurashi	alqurashi	PROPN
ejpam-4570	336	10	,	,	PUNCT
ejpam-4570	336	11	sadeq	sadeq	PROPN
ejpam-4570	336	12	ali	ali	PROPN
ejpam-4570	336	13	thabit	thabit	PROPN
ejpam-4570	336	14	/	/	SYM
ejpam-4570	336	15	eur	eur	PROPN
ejpam-4570	336	16	.	.	PUNCT
ejpam-4570	337	1	j.	j.	PROPN
ejpam-4570	337	2	pure	pure	PROPN
ejpam-4570	337	3	appl	appl	PROPN
ejpam-4570	337	4	.	.	PROPN
ejpam-4570	337	5	math	math	PROPN
ejpam-4570	337	6	,	,	PUNCT
ejpam-4570	337	7	15	15	NUM
ejpam-4570	337	8	(	(	PUNCT
ejpam-4570	337	9	4	4	NUM
ejpam-4570	337	10	)	)	PUNCT
ejpam-4570	337	11	(	(	PUNCT
ejpam-4570	337	12	2022	2022	NUM
ejpam-4570	337	13	)	)	PUNCT
ejpam-4570	337	14	,	,	PUNCT
ejpam-4570	337	15	1760	1760	NUM
ejpam-4570	337	16	-	-	SYM
ejpam-4570	337	17	1782	1782	NUM
ejpam-4570	337	18	1770	1770	NUM
ejpam-4570	337	19	theorem	theorem	NOUN
ejpam-4570	337	20	18	18	NUM
ejpam-4570	337	21	.	.	PUNCT
ejpam-4570	338	1	(	(	PUNCT
ejpam-4570	338	2	1	1	X
ejpam-4570	338	3	)	)	PUNCT
ejpam-4570	338	4	every	every	DET
ejpam-4570	338	5	c	c	NOUN
ejpam-4570	338	6	-	-	PUNCT
ejpam-4570	338	7	almost	almost	ADV
ejpam-4570	338	8	regular	regular	ADJ
ejpam-4570	338	9	(	(	PUNCT
ejpam-4570	338	10	resp	resp	NOUN
ejpam-4570	338	11	.	.	PUNCT
ejpam-4570	339	1	c	c	X
ejpam-4570	339	2	-	-	PUNCT
ejpam-4570	339	3	almost	almost	ADV
ejpam-4570	339	4	completely	completely	ADV
ejpam-4570	339	5	regular	regular	ADJ
ejpam-4570	339	6	)	)	PUNCT
ejpam-4570	339	7	compact	compact	ADJ
ejpam-4570	339	8	space	space	NOUN
ejpam-4570	339	9	is	be	AUX
ejpam-4570	339	10	c	c	NOUN
ejpam-4570	339	11	-	-	PUNCT
ejpam-4570	339	12	almost	almost	ADV
ejpam-4570	339	13	normal	normal	ADJ
ejpam-4570	339	14	.	.	PUNCT
ejpam-4570	340	1	(	(	PUNCT
ejpam-4570	340	2	2	2	X
ejpam-4570	340	3	)	)	PUNCT
ejpam-4570	340	4	every	every	DET
ejpam-4570	340	5	l	l	NOUN
ejpam-4570	340	6	-	-	PUNCT
ejpam-4570	340	7	almost	almost	ADV
ejpam-4570	340	8	regular	regular	ADJ
ejpam-4570	340	9	(	(	PUNCT
ejpam-4570	340	10	resp	resp	NOUN
ejpam-4570	340	11	.	.	PUNCT
ejpam-4570	341	1	l	l	VERB
ejpam-4570	341	2	-	-	PUNCT
ejpam-4570	341	3	almost	almost	ADV
ejpam-4570	341	4	completely	completely	ADV
ejpam-4570	341	5	regular	regular	ADJ
ejpam-4570	341	6	)	)	PUNCT
ejpam-4570	341	7	lindelöf	lindelöf	NOUN
ejpam-4570	341	8	paracompact	paracompact	NOUN
ejpam-4570	341	9	space	space	NOUN
ejpam-4570	341	10	is	be	AUX
ejpam-4570	341	11	l	l	NOUN
ejpam-4570	341	12	-	-	ADJ
ejpam-4570	341	13	almost	almost	ADV
ejpam-4570	341	14	normal	normal	ADJ
ejpam-4570	341	15	.	.	PUNCT
ejpam-4570	342	1	the	the	DET
ejpam-4570	342	2	next	next	ADJ
ejpam-4570	342	3	lemma	lemma	PROPN
ejpam-4570	342	4	can	can	AUX
ejpam-4570	342	5	be	be	AUX
ejpam-4570	342	6	proved	prove	VERB
ejpam-4570	342	7	easily	easily	ADV
ejpam-4570	342	8	:	:	PUNCT
ejpam-4570	342	9	lemma	lemma	PROPN
ejpam-4570	342	10	1	1	X
ejpam-4570	342	11	.	.	PUNCT
ejpam-4570	343	1	every	every	DET
ejpam-4570	343	2	t1	t1	NOUN
ejpam-4570	343	3	-	-	PUNCT
ejpam-4570	343	4	almost	almost	ADV
ejpam-4570	343	5	normal	normal	ADJ
ejpam-4570	343	6	space	space	NOUN
ejpam-4570	343	7	is	be	AUX
ejpam-4570	343	8	almost	almost	ADV
ejpam-4570	343	9	regular	regular	ADJ
ejpam-4570	343	10	[	[	X
ejpam-4570	343	11	27	27	NUM
ejpam-4570	343	12	]	]	PUNCT
ejpam-4570	343	13	.	.	PUNCT
ejpam-4570	344	1	theorem	theorem	NOUN
ejpam-4570	344	2	19	19	NUM
ejpam-4570	344	3	.	.	PUNCT
ejpam-4570	345	1	if	if	SCONJ
ejpam-4570	345	2	x	x	PRON
ejpam-4570	345	3	is	be	AUX
ejpam-4570	345	4	a	a	DET
ejpam-4570	345	5	t1	t1	NOUN
ejpam-4570	345	6	c	c	NOUN
ejpam-4570	345	7	-	-	PUNCT
ejpam-4570	345	8	almost	almost	ADV
ejpam-4570	345	9	normal	normal	ADJ
ejpam-4570	345	10	space	space	NOUN
ejpam-4570	345	11	,	,	PUNCT
ejpam-4570	345	12	then	then	ADV
ejpam-4570	345	13	x	x	PUNCT
ejpam-4570	345	14	is	be	AUX
ejpam-4570	345	15	c	c	NOUN
ejpam-4570	345	16	-	-	PUNCT
ejpam-4570	345	17	almost	almost	ADV
ejpam-4570	345	18	regular	regular	ADJ
ejpam-4570	345	19	.	.	PUNCT
ejpam-4570	346	1	proof	proof	NOUN
ejpam-4570	346	2	.	.	PUNCT
ejpam-4570	347	1	let	let	VERB
ejpam-4570	347	2	x	x	PRON
ejpam-4570	347	3	be	be	AUX
ejpam-4570	347	4	a	a	DET
ejpam-4570	347	5	t1	t1	NOUN
ejpam-4570	347	6	c	c	NOUN
ejpam-4570	347	7	-	-	PUNCT
ejpam-4570	347	8	almost	almost	ADV
ejpam-4570	347	9	normal	normal	ADJ
ejpam-4570	347	10	space	space	NOUN
ejpam-4570	347	11	.	.	PUNCT
ejpam-4570	348	1	then	then	ADV
ejpam-4570	348	2	,	,	PUNCT
ejpam-4570	348	3	there	there	PRON
ejpam-4570	348	4	exist	exist	VERB
ejpam-4570	348	5	an	an	DET
ejpam-4570	348	6	almost	almost	ADV
ejpam-4570	348	7	normal	normal	ADJ
ejpam-4570	348	8	space	space	NOUN
ejpam-4570	348	9	y	y	PROPN
ejpam-4570	348	10	and	and	CCONJ
ejpam-4570	348	11	a	a	DET
ejpam-4570	348	12	bijective	bijective	ADJ
ejpam-4570	348	13	function	function	NOUN
ejpam-4570	348	14	f	f	NOUN
ejpam-4570	348	15	:	:	PUNCT
ejpam-4570	348	16	(	(	PUNCT
ejpam-4570	348	17	x	x	X
ejpam-4570	348	18	,	,	PUNCT
ejpam-4570	348	19	t	t	PROPN
ejpam-4570	348	20	)	)	PUNCT
ejpam-4570	348	21	→	→	SYM
ejpam-4570	348	22	(	(	PUNCT
ejpam-4570	348	23	y	y	PROPN
ejpam-4570	348	24	,	,	PUNCT
ejpam-4570	348	25	t	t	PROPN
ejpam-4570	348	26	′	′	NUM
ejpam-4570	348	27	)	)	PUNCT
ejpam-4570	348	28	such	such	ADJ
ejpam-4570	348	29	that	that	SCONJ
ejpam-4570	348	30	f	f	PROPN
ejpam-4570	348	31	|a	|a	VERB
ejpam-4570	348	32	:	:	PUNCT
ejpam-4570	348	33	a	a	DET
ejpam-4570	348	34	→	→	SYM
ejpam-4570	348	35	f(a	f(a	NOUN
ejpam-4570	348	36	)	)	PUNCT
ejpam-4570	348	37	is	be	AUX
ejpam-4570	348	38	a	a	DET
ejpam-4570	348	39	homeomorphism	homeomorphism	NOUN
ejpam-4570	348	40	for	for	ADP
ejpam-4570	348	41	each	each	DET
ejpam-4570	348	42	compact	compact	NOUN
ejpam-4570	348	43	subset	subset	VERB
ejpam-4570	348	44	a	a	DET
ejpam-4570	348	45	⊆	⊆	NUM
ejpam-4570	348	46	x.	x.	NOUN
ejpam-4570	348	47	by	by	ADP
ejpam-4570	348	48	proposition	proposition	NOUN
ejpam-4570	348	49	1	1	NUM
ejpam-4570	348	50	,	,	PUNCT
ejpam-4570	348	51	y	y	PROPN
ejpam-4570	348	52	is	be	AUX
ejpam-4570	348	53	a	a	DET
ejpam-4570	348	54	t1	t1	NOUN
ejpam-4570	348	55	almost	almost	ADV
ejpam-4570	348	56	normal	normal	ADJ
ejpam-4570	348	57	space	space	NOUN
ejpam-4570	348	58	.	.	PUNCT
ejpam-4570	349	1	by	by	ADP
ejpam-4570	349	2	lemma	lemma	PROPN
ejpam-4570	349	3	1	1	NUM
ejpam-4570	349	4	we	we	PRON
ejpam-4570	349	5	get	get	VERB
ejpam-4570	349	6	:	:	PUNCT
ejpam-4570	349	7	the	the	DET
ejpam-4570	349	8	space	space	NOUN
ejpam-4570	349	9	y	y	PROPN
ejpam-4570	349	10	is	be	AUX
ejpam-4570	349	11	almost	almost	ADV
ejpam-4570	349	12	regular	regular	ADJ
ejpam-4570	349	13	.	.	PUNCT
ejpam-4570	350	1	therefore	therefore	ADV
ejpam-4570	350	2	,	,	PUNCT
ejpam-4570	350	3	x	x	X
ejpam-4570	350	4	is	be	AUX
ejpam-4570	350	5	c	c	NOUN
ejpam-4570	350	6	-	-	PUNCT
ejpam-4570	350	7	almost	almost	ADV
ejpam-4570	350	8	regular	regular	ADJ
ejpam-4570	350	9	.	.	PUNCT
ejpam-4570	351	1	theorem	theorem	NOUN
ejpam-4570	351	2	20	20	NUM
ejpam-4570	351	3	.	.	PUNCT
ejpam-4570	352	1	if	if	SCONJ
ejpam-4570	352	2	x	x	PRON
ejpam-4570	352	3	is	be	AUX
ejpam-4570	352	4	a	a	DET
ejpam-4570	352	5	t1	t1	NOUN
ejpam-4570	352	6	l	l	NOUN
ejpam-4570	352	7	-	-	PUNCT
ejpam-4570	352	8	almost	almost	ADV
ejpam-4570	352	9	normal	normal	ADJ
ejpam-4570	352	10	space	space	NOUN
ejpam-4570	352	11	,	,	PUNCT
ejpam-4570	352	12	then	then	ADV
ejpam-4570	352	13	x	x	PUNCT
ejpam-4570	352	14	is	be	AUX
ejpam-4570	352	15	l	l	NOUN
ejpam-4570	352	16	-	-	ADJ
ejpam-4570	352	17	almost	almost	ADV
ejpam-4570	352	18	regular	regular	ADJ
ejpam-4570	352	19	.	.	PUNCT
ejpam-4570	353	1	proof	proof	NOUN
ejpam-4570	353	2	.	.	PUNCT
ejpam-4570	354	1	similar	similar	ADJ
ejpam-4570	354	2	to	to	ADP
ejpam-4570	354	3	the	the	DET
ejpam-4570	354	4	proof	proof	NOUN
ejpam-4570	354	5	of	of	ADP
ejpam-4570	354	6	theorem	theorem	ADJ
ejpam-4570	354	7	19	19	NUM
ejpam-4570	354	8	.	.	PUNCT
ejpam-4570	354	9	theorem	theorem	NOUN
ejpam-4570	354	10	21	21	NUM
ejpam-4570	354	11	.	.	PUNCT
ejpam-4570	355	1	every	every	DET
ejpam-4570	355	2	c2	c2	PROPN
ejpam-4570	355	3	-	-	PUNCT
ejpam-4570	355	4	almost	almost	ADV
ejpam-4570	355	5	regular	regular	ADJ
ejpam-4570	355	6	fréchet	fréchet	NOUN
ejpam-4570	355	7	(	(	PUNCT
ejpam-4570	355	8	resp	resp	NOUN
ejpam-4570	355	9	.	.	PUNCT
ejpam-4570	356	1	sequential	sequential	ADJ
ejpam-4570	356	2	,	,	PUNCT
ejpam-4570	356	3	first	first	ADV
ejpam-4570	356	4	countable	countable	ADJ
ejpam-4570	356	5	)	)	PUNCT
ejpam-4570	356	6	paracompact	paracompact	ADJ
ejpam-4570	356	7	space	space	NOUN
ejpam-4570	356	8	is	be	AUX
ejpam-4570	356	9	epi	epi	NOUN
ejpam-4570	356	10	-	-	ADJ
ejpam-4570	356	11	almost	almost	ADV
ejpam-4570	356	12	normal	normal	ADJ
ejpam-4570	356	13	and	and	CCONJ
ejpam-4570	356	14	hence	hence	ADV
ejpam-4570	356	15	c	c	NOUN
ejpam-4570	356	16	-	-	PUNCT
ejpam-4570	356	17	almost	almost	ADV
ejpam-4570	356	18	normal	normal	ADJ
ejpam-4570	356	19	.	.	PUNCT
ejpam-4570	357	1	proof	proof	NOUN
ejpam-4570	357	2	.	.	PUNCT
ejpam-4570	358	1	let	let	VERB
ejpam-4570	358	2	x	x	PRON
ejpam-4570	358	3	be	be	AUX
ejpam-4570	358	4	a	a	DET
ejpam-4570	358	5	c2	c2	PROPN
ejpam-4570	358	6	-	-	PUNCT
ejpam-4570	358	7	almost	almost	ADV
ejpam-4570	358	8	regular	regular	ADJ
ejpam-4570	358	9	fréchet	fréchet	NOUN
ejpam-4570	358	10	(	(	PUNCT
ejpam-4570	358	11	resp	resp	NOUN
ejpam-4570	358	12	.	.	PUNCT
ejpam-4570	359	1	sequential	sequential	ADJ
ejpam-4570	359	2	,	,	PUNCT
ejpam-4570	359	3	first	first	ADV
ejpam-4570	359	4	countable	countable	ADJ
ejpam-4570	359	5	)	)	PUNCT
ejpam-4570	359	6	paracompact	paracompact	NOUN
ejpam-4570	359	7	.	.	PUNCT
ejpam-4570	360	1	then	then	ADV
ejpam-4570	360	2	,	,	PUNCT
ejpam-4570	360	3	there	there	PRON
ejpam-4570	360	4	exist	exist	VERB
ejpam-4570	360	5	a	a	DET
ejpam-4570	360	6	hausdorff	hausdorff	NOUN
ejpam-4570	360	7	almost	almost	ADV
ejpam-4570	360	8	regular	regular	ADJ
ejpam-4570	360	9	space	space	NOUN
ejpam-4570	360	10	y	y	PROPN
ejpam-4570	360	11	and	and	CCONJ
ejpam-4570	360	12	a	a	DET
ejpam-4570	360	13	bijective	bijective	ADJ
ejpam-4570	360	14	function	function	NOUN
ejpam-4570	360	15	f	f	NOUN
ejpam-4570	360	16	:	:	PUNCT
ejpam-4570	360	17	(	(	PUNCT
ejpam-4570	360	18	x	x	X
ejpam-4570	360	19	,	,	PUNCT
ejpam-4570	360	20	t	t	PROPN
ejpam-4570	360	21	)	)	PUNCT
ejpam-4570	360	22	→	→	SYM
ejpam-4570	360	23	(	(	PUNCT
ejpam-4570	360	24	y	y	PROPN
ejpam-4570	360	25	,	,	PUNCT
ejpam-4570	360	26	t	t	PROPN
ejpam-4570	360	27	′	′	NUM
ejpam-4570	360	28	)	)	PUNCT
ejpam-4570	360	29	such	such	ADJ
ejpam-4570	360	30	that	that	SCONJ
ejpam-4570	360	31	f	f	PROPN
ejpam-4570	360	32	|a	|a	VERB
ejpam-4570	360	33	:	:	PUNCT
ejpam-4570	360	34	a	a	DET
ejpam-4570	360	35	→	→	SYM
ejpam-4570	360	36	f(a	f(a	NOUN
ejpam-4570	360	37	)	)	PUNCT
ejpam-4570	360	38	is	be	AUX
ejpam-4570	360	39	a	a	DET
ejpam-4570	360	40	homeomorphism	homeomorphism	NOUN
ejpam-4570	360	41	for	for	ADP
ejpam-4570	360	42	each	each	DET
ejpam-4570	360	43	compact	compact	NOUN
ejpam-4570	360	44	subset	subset	VERB
ejpam-4570	360	45	a	a	DET
ejpam-4570	360	46	⊆	⊆	NUM
ejpam-4570	360	47	x.	x.	NOUN
ejpam-4570	360	48	since	since	SCONJ
ejpam-4570	360	49	x	x	PROPN
ejpam-4570	360	50	is	be	AUX
ejpam-4570	360	51	fréchet	fréchet	VERB
ejpam-4570	360	52	(	(	PUNCT
ejpam-4570	360	53	resp	resp	NOUN
ejpam-4570	360	54	.	.	PUNCT
ejpam-4570	361	1	sequential	sequential	ADJ
ejpam-4570	361	2	,	,	PUNCT
ejpam-4570	361	3	first	first	ADV
ejpam-4570	361	4	countable	countable	ADJ
ejpam-4570	361	5	)	)	PUNCT
ejpam-4570	361	6	,	,	PUNCT
ejpam-4570	361	7	we	we	PRON
ejpam-4570	361	8	get	get	VERB
ejpam-4570	361	9	f	f	PROPN
ejpam-4570	361	10	is	be	AUX
ejpam-4570	361	11	continuous	continuous	ADJ
ejpam-4570	361	12	.	.	PUNCT
ejpam-4570	362	1	by	by	ADP
ejpam-4570	362	2	using	use	VERB
ejpam-4570	362	3	similar	similar	ADJ
ejpam-4570	362	4	arguments	argument	NOUN
ejpam-4570	362	5	to	to	ADP
ejpam-4570	362	6	the	the	DET
ejpam-4570	362	7	proof	proof	NOUN
ejpam-4570	362	8	of	of	ADP
ejpam-4570	362	9	theorem	theorem	NOUN
ejpam-4570	362	10	7	7	NUM
ejpam-4570	362	11	,	,	PUNCT
ejpam-4570	362	12	we	we	PRON
ejpam-4570	362	13	conclude	conclude	VERB
ejpam-4570	362	14	:	:	PUNCT
ejpam-4570	362	15	x	x	X
ejpam-4570	362	16	is	be	AUX
ejpam-4570	362	17	hausdorff	hausdorff	NOUN
ejpam-4570	362	18	paracompact	paracompact	NOUN
ejpam-4570	362	19	.	.	PUNCT
ejpam-4570	363	1	since	since	SCONJ
ejpam-4570	363	2	every	every	DET
ejpam-4570	363	3	hausdorff	hausdorff	NOUN
ejpam-4570	363	4	paracompact	paracompact	NOUN
ejpam-4570	363	5	space	space	NOUN
ejpam-4570	363	6	is	be	AUX
ejpam-4570	363	7	t4	t4	PROPN
ejpam-4570	363	8	,	,	PUNCT
ejpam-4570	363	9	we	we	PRON
ejpam-4570	363	10	get	get	VERB
ejpam-4570	363	11	x	x	PROPN
ejpam-4570	363	12	is	be	AUX
ejpam-4570	363	13	hausdorff	hausdorff	NOUN
ejpam-4570	363	14	almost	almost	ADV
ejpam-4570	363	15	normal	normal	ADJ
ejpam-4570	363	16	.	.	PUNCT
ejpam-4570	364	1	therefore	therefore	ADV
ejpam-4570	364	2	,	,	PUNCT
ejpam-4570	364	3	(	(	PUNCT
ejpam-4570	364	4	x	x	X
ejpam-4570	364	5	,	,	PUNCT
ejpam-4570	364	6	t	t	PROPN
ejpam-4570	364	7	)	)	PUNCT
ejpam-4570	364	8	is	be	AUX
ejpam-4570	364	9	epi	epi	NOUN
ejpam-4570	364	10	-	-	ADJ
ejpam-4570	364	11	almost	almost	ADV
ejpam-4570	364	12	normal	normal	ADJ
ejpam-4570	364	13	and	and	CCONJ
ejpam-4570	364	14	hence	hence	ADV
ejpam-4570	364	15	c	c	NOUN
ejpam-4570	364	16	-	-	PUNCT
ejpam-4570	364	17	almost	almost	ADV
ejpam-4570	364	18	normal	normal	ADJ
ejpam-4570	364	19	.	.	PUNCT
ejpam-4570	365	1	the	the	DET
ejpam-4570	365	2	proof	proof	NOUN
ejpam-4570	365	3	of	of	ADP
ejpam-4570	365	4	the	the	DET
ejpam-4570	365	5	next	next	ADJ
ejpam-4570	365	6	results	result	NOUN
ejpam-4570	365	7	is	be	AUX
ejpam-4570	365	8	similar	similar	ADJ
ejpam-4570	365	9	to	to	ADP
ejpam-4570	365	10	that	that	PRON
ejpam-4570	365	11	of	of	ADP
ejpam-4570	365	12	theorem	theorem	ADJ
ejpam-4570	365	13	21	21	NUM
ejpam-4570	365	14	:	:	PUNCT
ejpam-4570	365	15	theorem	theorem	NOUN
ejpam-4570	365	16	22	22	NUM
ejpam-4570	365	17	.	.	PUNCT
ejpam-4570	366	1	(	(	PUNCT
ejpam-4570	366	2	1	1	X
ejpam-4570	366	3	)	)	PUNCT
ejpam-4570	366	4	every	every	DET
ejpam-4570	366	5	c2	c2	PROPN
ejpam-4570	366	6	-	-	PUNCT
ejpam-4570	366	7	almost	almost	ADV
ejpam-4570	366	8	completely	completely	ADV
ejpam-4570	366	9	regular	regular	ADJ
ejpam-4570	366	10	fréchet	fréchet	NOUN
ejpam-4570	366	11	(	(	PUNCT
ejpam-4570	366	12	resp	resp	NOUN
ejpam-4570	366	13	.	.	PUNCT
ejpam-4570	367	1	sequential	sequential	ADJ
ejpam-4570	367	2	,	,	PUNCT
ejpam-4570	367	3	first	first	ADV
ejpam-4570	367	4	countable	countable	ADJ
ejpam-4570	367	5	)	)	PUNCT
ejpam-4570	367	6	paracompact	paracompact	ADJ
ejpam-4570	367	7	space	space	NOUN
ejpam-4570	367	8	is	be	AUX
ejpam-4570	367	9	epi	epi	NOUN
ejpam-4570	367	10	-	-	ADJ
ejpam-4570	367	11	almost	almost	ADV
ejpam-4570	367	12	normal	normal	ADJ
ejpam-4570	367	13	and	and	CCONJ
ejpam-4570	367	14	hence	hence	ADV
ejpam-4570	367	15	c	c	NOUN
ejpam-4570	367	16	-	-	PUNCT
ejpam-4570	367	17	almost	almost	ADV
ejpam-4570	367	18	normal	normal	ADJ
ejpam-4570	367	19	.	.	PUNCT
ejpam-4570	368	1	(	(	PUNCT
ejpam-4570	368	2	2	2	X
ejpam-4570	368	3	)	)	PUNCT
ejpam-4570	368	4	every	every	DET
ejpam-4570	368	5	l2	l2	NOUN
ejpam-4570	368	6	-	-	PUNCT
ejpam-4570	368	7	almost	almost	ADV
ejpam-4570	368	8	regular	regular	ADJ
ejpam-4570	368	9	first	first	ADJ
ejpam-4570	368	10	countable	countable	ADJ
ejpam-4570	368	11	paracompact	paracompact	ADJ
ejpam-4570	368	12	space	space	NOUN
ejpam-4570	368	13	is	be	AUX
ejpam-4570	368	14	epi	epi	NOUN
ejpam-4570	368	15	-	-	ADJ
ejpam-4570	368	16	almost	almost	ADV
ejpam-4570	368	17	normal	normal	ADJ
ejpam-4570	368	18	.	.	PUNCT
ejpam-4570	369	1	(	(	PUNCT
ejpam-4570	369	2	3	3	X
ejpam-4570	369	3	)	)	PUNCT
ejpam-4570	369	4	every	every	DET
ejpam-4570	369	5	l2	l2	NOUN
ejpam-4570	369	6	-	-	PUNCT
ejpam-4570	369	7	almost	almost	ADV
ejpam-4570	369	8	completely	completely	ADV
ejpam-4570	369	9	regular	regular	ADJ
ejpam-4570	369	10	first	first	ADJ
ejpam-4570	369	11	countable	countable	ADJ
ejpam-4570	369	12	paracompact	paracompact	ADJ
ejpam-4570	369	13	space	space	NOUN
ejpam-4570	369	14	is	be	AUX
ejpam-4570	369	15	epi	epi	NOUN
ejpam-4570	369	16	-	-	ADJ
ejpam-4570	369	17	almost	almost	ADV
ejpam-4570	369	18	normal	normal	ADJ
ejpam-4570	369	19	.	.	PUNCT
ejpam-4570	370	1	wafa	wafa	PROPN
ejpam-4570	370	2	khalaf	khalaf	PROPN
ejpam-4570	370	3	alqurashi	alqurashi	PROPN
ejpam-4570	370	4	,	,	PUNCT
ejpam-4570	370	5	sadeq	sadeq	PROPN
ejpam-4570	370	6	ali	ali	PROPN
ejpam-4570	370	7	thabit	thabit	PROPN
ejpam-4570	370	8	/	/	SYM
ejpam-4570	370	9	eur	eur	PROPN
ejpam-4570	370	10	.	.	PUNCT
ejpam-4570	371	1	j.	j.	PROPN
ejpam-4570	371	2	pure	pure	PROPN
ejpam-4570	371	3	appl	appl	PROPN
ejpam-4570	371	4	.	.	PROPN
ejpam-4570	371	5	math	math	PROPN
ejpam-4570	371	6	,	,	PUNCT
ejpam-4570	371	7	15	15	NUM
ejpam-4570	371	8	(	(	PUNCT
ejpam-4570	371	9	4	4	NUM
ejpam-4570	371	10	)	)	PUNCT
ejpam-4570	371	11	(	(	PUNCT
ejpam-4570	371	12	2022	2022	NUM
ejpam-4570	371	13	)	)	PUNCT
ejpam-4570	371	14	,	,	PUNCT
ejpam-4570	371	15	1760	1760	NUM
ejpam-4570	371	16	-	-	SYM
ejpam-4570	371	17	1782	1782	NUM
ejpam-4570	371	18	1771	1771	NUM
ejpam-4570	371	19	theorem	theorem	VERB
ejpam-4570	371	20	23	23	NUM
ejpam-4570	371	21	.	.	PUNCT
ejpam-4570	372	1	every	every	DET
ejpam-4570	372	2	c2	c2	PROPN
ejpam-4570	372	3	-	-	PUNCT
ejpam-4570	372	4	almost	almost	ADV
ejpam-4570	372	5	regular	regular	ADJ
ejpam-4570	372	6	fréchet	fréchet	NOUN
ejpam-4570	372	7	(	(	PUNCT
ejpam-4570	372	8	resp	resp	NOUN
ejpam-4570	372	9	.	.	PUNCT
ejpam-4570	373	1	sequential	sequential	ADJ
ejpam-4570	373	2	,	,	PUNCT
ejpam-4570	373	3	first	first	ADV
ejpam-4570	373	4	countable	countable	ADJ
ejpam-4570	373	5	)	)	PUNCT
ejpam-4570	373	6	lindelöf	lindelöf	NOUN
ejpam-4570	373	7	space	space	NOUN
ejpam-4570	373	8	is	be	AUX
ejpam-4570	373	9	epi	epi	NOUN
ejpam-4570	373	10	-	-	ADJ
ejpam-4570	373	11	almost	almost	ADV
ejpam-4570	373	12	normal	normal	ADJ
ejpam-4570	373	13	.	.	PUNCT
ejpam-4570	374	1	proof	proof	NOUN
ejpam-4570	374	2	.	.	PUNCT
ejpam-4570	375	1	letx	letx	PROPN
ejpam-4570	375	2	be	be	AUX
ejpam-4570	375	3	a	a	DET
ejpam-4570	375	4	c2	c2	PROPN
ejpam-4570	375	5	-	-	PUNCT
ejpam-4570	375	6	almost	almost	ADV
ejpam-4570	375	7	regular	regular	ADJ
ejpam-4570	375	8	fréchet	fréchet	NOUN
ejpam-4570	375	9	(	(	PUNCT
ejpam-4570	375	10	resp	resp	NOUN
ejpam-4570	375	11	.	.	PUNCT
ejpam-4570	376	1	sequential	sequential	ADJ
ejpam-4570	376	2	,	,	PUNCT
ejpam-4570	376	3	first	first	ADV
ejpam-4570	376	4	countable	countable	ADJ
ejpam-4570	376	5	)	)	PUNCT
ejpam-4570	376	6	lindelöf	lindelöf	NOUN
ejpam-4570	376	7	space	space	NOUN
ejpam-4570	376	8	.	.	PUNCT
ejpam-4570	377	1	then	then	ADV
ejpam-4570	377	2	,	,	PUNCT
ejpam-4570	377	3	there	there	PRON
ejpam-4570	377	4	exist	exist	VERB
ejpam-4570	377	5	a	a	DET
ejpam-4570	377	6	hausdorff	hausdorff	NOUN
ejpam-4570	377	7	almost	almost	ADV
ejpam-4570	377	8	regular	regular	ADJ
ejpam-4570	377	9	space	space	NOUN
ejpam-4570	377	10	y	y	PROPN
ejpam-4570	377	11	and	and	CCONJ
ejpam-4570	377	12	a	a	DET
ejpam-4570	377	13	bijective	bijective	ADJ
ejpam-4570	377	14	function	function	NOUN
ejpam-4570	377	15	f	f	NOUN
ejpam-4570	377	16	:	:	PUNCT
ejpam-4570	377	17	(	(	PUNCT
ejpam-4570	377	18	x	x	X
ejpam-4570	377	19	,	,	PUNCT
ejpam-4570	377	20	t	t	PROPN
ejpam-4570	377	21	)	)	PUNCT
ejpam-4570	377	22	→	→	SYM
ejpam-4570	377	23	(	(	PUNCT
ejpam-4570	377	24	y	y	PROPN
ejpam-4570	377	25	,	,	PUNCT
ejpam-4570	377	26	t	t	PROPN
ejpam-4570	377	27	′	′	NUM
ejpam-4570	377	28	)	)	PUNCT
ejpam-4570	377	29	such	such	ADJ
ejpam-4570	377	30	that	that	SCONJ
ejpam-4570	377	31	f	f	PROPN
ejpam-4570	377	32	|a	|a	VERB
ejpam-4570	377	33	:	:	PUNCT
ejpam-4570	377	34	a	a	DET
ejpam-4570	377	35	→	→	SYM
ejpam-4570	377	36	f(a	f(a	NOUN
ejpam-4570	377	37	)	)	PUNCT
ejpam-4570	377	38	is	be	AUX
ejpam-4570	377	39	a	a	DET
ejpam-4570	377	40	homeomorphism	homeomorphism	NOUN
ejpam-4570	377	41	for	for	ADP
ejpam-4570	377	42	each	each	DET
ejpam-4570	377	43	compact	compact	ADJ
ejpam-4570	377	44	subseta	subseta	NOUN
ejpam-4570	377	45	⊆	⊆	NUM
ejpam-4570	377	46	x.	x.	NOUN
ejpam-4570	377	47	sincex	sincex	PROPN
ejpam-4570	377	48	is	be	AUX
ejpam-4570	377	49	fréchet	fréchet	VERB
ejpam-4570	377	50	(	(	PUNCT
ejpam-4570	377	51	resp	resp	NOUN
ejpam-4570	377	52	.	.	PUNCT
ejpam-4570	378	1	sequential	sequential	ADJ
ejpam-4570	378	2	,	,	PUNCT
ejpam-4570	378	3	first	first	ADV
ejpam-4570	378	4	countable	countable	ADJ
ejpam-4570	378	5	)	)	PUNCT
ejpam-4570	378	6	,	,	PUNCT
ejpam-4570	378	7	we	we	PRON
ejpam-4570	378	8	get	get	VERB
ejpam-4570	378	9	f	f	PROPN
ejpam-4570	378	10	is	be	AUX
ejpam-4570	378	11	continuous	continuous	ADJ
ejpam-4570	378	12	.	.	PUNCT
ejpam-4570	379	1	thus	thus	ADV
ejpam-4570	379	2	,	,	PUNCT
ejpam-4570	379	3	f	f	X
ejpam-4570	379	4	:	:	PUNCT
ejpam-4570	379	5	(	(	PUNCT
ejpam-4570	379	6	x	x	X
ejpam-4570	379	7	,	,	PUNCT
ejpam-4570	379	8	t	t	PROPN
ejpam-4570	379	9	)	)	PUNCT
ejpam-4570	379	10	→	→	SYM
ejpam-4570	379	11	(	(	PUNCT
ejpam-4570	379	12	y	y	NOUN
ejpam-4570	379	13	,	,	PUNCT
ejpam-4570	379	14	ts′	ts′	NUM
ejpam-4570	379	15	)	)	PUNCT
ejpam-4570	379	16	is	be	AUX
ejpam-4570	379	17	1	1	NUM
ejpam-4570	379	18	-	-	SYM
ejpam-4570	379	19	1	1	NUM
ejpam-4570	379	20	,	,	PUNCT
ejpam-4570	379	21	onto	onto	ADP
ejpam-4570	379	22	and	and	CCONJ
ejpam-4570	379	23	continuous	continuous	ADJ
ejpam-4570	379	24	function	function	NOUN
ejpam-4570	379	25	such	such	ADJ
ejpam-4570	379	26	that	that	SCONJ
ejpam-4570	379	27	(	(	PUNCT
ejpam-4570	379	28	y	y	NOUN
ejpam-4570	379	29	,	,	PUNCT
ejpam-4570	379	30	ts′	ts′	NUM
ejpam-4570	379	31	)	)	PUNCT
ejpam-4570	379	32	is	be	AUX
ejpam-4570	379	33	a	a	DET
ejpam-4570	379	34	t3	t3	NOUN
ejpam-4570	379	35	-	-	PUNCT
ejpam-4570	379	36	space	space	NOUN
ejpam-4570	379	37	,	,	PUNCT
ejpam-4570	379	38	where	where	SCONJ
ejpam-4570	379	39	(	(	PUNCT
ejpam-4570	379	40	y	y	NOUN
ejpam-4570	379	41	,	,	PUNCT
ejpam-4570	379	42	ts′	ts′	NUM
ejpam-4570	379	43	)	)	PUNCT
ejpam-4570	379	44	is	be	AUX
ejpam-4570	379	45	a	a	DET
ejpam-4570	379	46	semi	semi	ADJ
ejpam-4570	379	47	-	-	NOUN
ejpam-4570	379	48	regularization	regularization	NOUN
ejpam-4570	379	49	of	of	ADP
ejpam-4570	379	50	(	(	PUNCT
ejpam-4570	379	51	y	y	PROPN
ejpam-4570	379	52	,	,	PUNCT
ejpam-4570	379	53	t	t	PROPN
ejpam-4570	379	54	′	′	NUM
ejpam-4570	379	55	)	)	PUNCT
ejpam-4570	379	56	.	.	PUNCT
ejpam-4570	380	1	since	since	SCONJ
ejpam-4570	380	2	a	a	DET
ejpam-4570	380	3	continuous	continuous	ADJ
ejpam-4570	380	4	image	image	NOUN
ejpam-4570	380	5	of	of	ADP
ejpam-4570	380	6	a	a	DET
ejpam-4570	380	7	lindelöf	lindelöf	NOUN
ejpam-4570	380	8	space	space	NOUN
ejpam-4570	380	9	is	be	AUX
ejpam-4570	380	10	lindelöf	lindelöf	PUNCT
ejpam-4570	380	11	[	[	X
ejpam-4570	380	12	12	12	NUM
ejpam-4570	380	13	]	]	PUNCT
ejpam-4570	380	14	,	,	PUNCT
ejpam-4570	380	15	and	and	CCONJ
ejpam-4570	380	16	x	x	X
ejpam-4570	380	17	is	be	AUX
ejpam-4570	380	18	a	a	DET
ejpam-4570	380	19	lindelöf	lindelöf	NOUN
ejpam-4570	380	20	space	space	NOUN
ejpam-4570	380	21	,	,	PUNCT
ejpam-4570	380	22	we	we	PRON
ejpam-4570	380	23	get	get	VERB
ejpam-4570	380	24	:	:	PUNCT
ejpam-4570	380	25	(	(	PUNCT
ejpam-4570	380	26	y	y	NOUN
ejpam-4570	380	27	,	,	PUNCT
ejpam-4570	380	28	ts′	ts′	NUM
ejpam-4570	380	29	)	)	PUNCT
ejpam-4570	380	30	is	be	AUX
ejpam-4570	380	31	t3	t3	PROPN
ejpam-4570	380	32	-	-	PUNCT
ejpam-4570	380	33	lindelöf	lindelöf	PROPN
ejpam-4570	380	34	.	.	PUNCT
ejpam-4570	381	1	since	since	SCONJ
ejpam-4570	381	2	every	every	DET
ejpam-4570	381	3	regular	regular	ADJ
ejpam-4570	381	4	lindelöf	lindelöf	NOUN
ejpam-4570	381	5	space	space	NOUN
ejpam-4570	381	6	is	be	AUX
ejpam-4570	381	7	paracompact	paracompact	ADJ
ejpam-4570	381	8	and	and	CCONJ
ejpam-4570	381	9	hence	hence	ADV
ejpam-4570	381	10	almost	almost	ADV
ejpam-4570	381	11	normal	normal	ADJ
ejpam-4570	381	12	[	[	X
ejpam-4570	381	13	12	12	NUM
ejpam-4570	381	14	,	,	PUNCT
ejpam-4570	381	15	26	26	NUM
ejpam-4570	381	16	]	]	PUNCT
ejpam-4570	381	17	,	,	PUNCT
ejpam-4570	381	18	we	we	PRON
ejpam-4570	381	19	get	get	VERB
ejpam-4570	381	20	:	:	PUNCT
ejpam-4570	381	21	(	(	PUNCT
ejpam-4570	381	22	y	y	NOUN
ejpam-4570	381	23	,	,	PUNCT
ejpam-4570	381	24	ts′	ts′	NUM
ejpam-4570	381	25	)	)	PUNCT
ejpam-4570	381	26	is	be	AUX
ejpam-4570	381	27	a	a	DET
ejpam-4570	381	28	t3	t3	NOUN
ejpam-4570	381	29	-	-	PUNCT
ejpam-4570	381	30	almost	almost	ADV
ejpam-4570	381	31	normal	normal	ADJ
ejpam-4570	381	32	space	space	NOUN
ejpam-4570	381	33	.	.	PUNCT
ejpam-4570	382	1	now	now	ADV
ejpam-4570	382	2	,	,	PUNCT
ejpam-4570	382	3	define	define	VERB
ejpam-4570	382	4	t	t	NOUN
ejpam-4570	382	5	∗	∗	NOUN
ejpam-4570	382	6	=	=	SYM
ejpam-4570	382	7	{	{	PUNCT
ejpam-4570	382	8	f−1(u	f−1(u	PROPN
ejpam-4570	382	9	)	)	PUNCT
ejpam-4570	382	10	:	:	PUNCT
ejpam-4570	383	1	u	u	NOUN
ejpam-4570	383	2	∈	∈	NOUN
ejpam-4570	383	3	ts′	ts′	NUM
ejpam-4570	383	4	}	}	PUNCT
ejpam-4570	383	5	.	.	PUNCT
ejpam-4570	384	1	by	by	ADP
ejpam-4570	384	2	using	use	VERB
ejpam-4570	384	3	similar	similar	ADJ
ejpam-4570	384	4	arguments	argument	NOUN
ejpam-4570	384	5	to	to	ADP
ejpam-4570	384	6	the	the	DET
ejpam-4570	384	7	proof	proof	NOUN
ejpam-4570	384	8	of	of	ADP
ejpam-4570	384	9	theorem	theorem	NOUN
ejpam-4570	384	10	7	7	NUM
ejpam-4570	384	11	,	,	PUNCT
ejpam-4570	384	12	we	we	PRON
ejpam-4570	384	13	conclude	conclude	VERB
ejpam-4570	384	14	:	:	PUNCT
ejpam-4570	384	15	t	t	PROPN
ejpam-4570	384	16	∗	∗	NOUN
ejpam-4570	384	17	is	be	AUX
ejpam-4570	384	18	a	a	DET
ejpam-4570	384	19	topology	topology	NOUN
ejpam-4570	384	20	coarser	coarse	ADJ
ejpam-4570	384	21	than	than	ADP
ejpam-4570	384	22	t	t	PROPN
ejpam-4570	384	23	and	and	CCONJ
ejpam-4570	384	24	(	(	PUNCT
ejpam-4570	384	25	x	x	X
ejpam-4570	384	26	,	,	PUNCT
ejpam-4570	384	27	t	t	PROPN
ejpam-4570	384	28	∗	∗	NOUN
ejpam-4570	384	29	)	)	PUNCT
ejpam-4570	384	30	∼=	∼=	PROPN
ejpam-4570	384	31	(	(	PUNCT
ejpam-4570	384	32	y	y	PROPN
ejpam-4570	384	33	,	,	PUNCT
ejpam-4570	384	34	ts′	ts′	NUM
ejpam-4570	384	35	)	)	PUNCT
ejpam-4570	384	36	.	.	PUNCT
ejpam-4570	385	1	since	since	SCONJ
ejpam-4570	385	2	(	(	PUNCT
ejpam-4570	385	3	y	y	PROPN
ejpam-4570	385	4	,	,	PUNCT
ejpam-4570	385	5	ts′	ts′	NUM
ejpam-4570	385	6	)	)	PUNCT
ejpam-4570	385	7	is	be	AUX
ejpam-4570	385	8	a	a	DET
ejpam-4570	385	9	t3	t3	NOUN
ejpam-4570	385	10	-	-	PUNCT
ejpam-4570	385	11	almost	almost	ADV
ejpam-4570	385	12	normal	normal	ADJ
ejpam-4570	385	13	space	space	NOUN
ejpam-4570	385	14	,	,	PUNCT
ejpam-4570	385	15	we	we	PRON
ejpam-4570	385	16	have	have	VERB
ejpam-4570	385	17	:	:	PUNCT
ejpam-4570	385	18	(	(	PUNCT
ejpam-4570	385	19	x	x	X
ejpam-4570	385	20	,	,	PUNCT
ejpam-4570	385	21	t	t	PROPN
ejpam-4570	385	22	∗	∗	NOUN
ejpam-4570	385	23	)	)	PUNCT
ejpam-4570	385	24	is	be	AUX
ejpam-4570	385	25	t3	t3	NOUN
ejpam-4570	385	26	-	-	PUNCT
ejpam-4570	385	27	almost	almost	ADV
ejpam-4570	385	28	normal	normal	ADJ
ejpam-4570	385	29	.	.	PUNCT
ejpam-4570	386	1	since	since	SCONJ
ejpam-4570	386	2	t	t	PROPN
ejpam-4570	386	3	∗	∗	NOUN
ejpam-4570	386	4	⊆	⊆	NUM
ejpam-4570	386	5	t	t	NOUN
ejpam-4570	386	6	,	,	PUNCT
ejpam-4570	386	7	we	we	PRON
ejpam-4570	386	8	obtain	obtain	VERB
ejpam-4570	386	9	:	:	PUNCT
ejpam-4570	386	10	(	(	PUNCT
ejpam-4570	386	11	x	x	X
ejpam-4570	386	12	,	,	PUNCT
ejpam-4570	386	13	t	t	PROPN
ejpam-4570	386	14	)	)	PUNCT
ejpam-4570	386	15	is	be	AUX
ejpam-4570	386	16	epi	epi	NOUN
ejpam-4570	386	17	-	-	ADJ
ejpam-4570	386	18	almost	almost	ADV
ejpam-4570	386	19	normal	normal	ADJ
ejpam-4570	386	20	.	.	PUNCT
ejpam-4570	387	1	the	the	DET
ejpam-4570	387	2	proof	proof	NOUN
ejpam-4570	387	3	of	of	ADP
ejpam-4570	387	4	the	the	DET
ejpam-4570	387	5	next	next	ADJ
ejpam-4570	387	6	result	result	NOUN
ejpam-4570	387	7	is	be	AUX
ejpam-4570	387	8	similar	similar	ADJ
ejpam-4570	387	9	to	to	ADP
ejpam-4570	387	10	that	that	PRON
ejpam-4570	387	11	of	of	ADP
ejpam-4570	387	12	theorem	theorem	ADJ
ejpam-4570	387	13	23	23	NUM
ejpam-4570	387	14	:	:	PUNCT
ejpam-4570	387	15	theorem	theorem	NOUN
ejpam-4570	387	16	24	24	NUM
ejpam-4570	387	17	.	.	PUNCT
ejpam-4570	388	1	(	(	PUNCT
ejpam-4570	388	2	1	1	X
ejpam-4570	388	3	)	)	PUNCT
ejpam-4570	388	4	every	every	DET
ejpam-4570	388	5	c2	c2	PROPN
ejpam-4570	388	6	-	-	PUNCT
ejpam-4570	388	7	almost	almost	ADV
ejpam-4570	388	8	completely	completely	ADV
ejpam-4570	388	9	regular	regular	ADJ
ejpam-4570	388	10	fréchet	fréchet	NOUN
ejpam-4570	388	11	(	(	PUNCT
ejpam-4570	388	12	resp	resp	NOUN
ejpam-4570	388	13	.	.	PUNCT
ejpam-4570	389	1	sequential	sequential	ADJ
ejpam-4570	389	2	,	,	PUNCT
ejpam-4570	389	3	first	first	ADV
ejpam-4570	389	4	countable	countable	ADJ
ejpam-4570	389	5	)	)	PUNCT
ejpam-4570	389	6	lindelöf	lindelöf	NOUN
ejpam-4570	389	7	space	space	NOUN
ejpam-4570	389	8	is	be	AUX
ejpam-4570	389	9	epi	epi	NOUN
ejpam-4570	389	10	-	-	ADJ
ejpam-4570	389	11	almost	almost	ADV
ejpam-4570	389	12	normal	normal	ADJ
ejpam-4570	389	13	.	.	PUNCT
ejpam-4570	390	1	(	(	PUNCT
ejpam-4570	390	2	2	2	X
ejpam-4570	390	3	)	)	PUNCT
ejpam-4570	390	4	every	every	DET
ejpam-4570	390	5	l2	l2	NOUN
ejpam-4570	390	6	-	-	PUNCT
ejpam-4570	390	7	almost	almost	ADV
ejpam-4570	390	8	regular	regular	ADJ
ejpam-4570	390	9	fréchet	fréchet	NOUN
ejpam-4570	390	10	(	(	PUNCT
ejpam-4570	390	11	resp	resp	NOUN
ejpam-4570	390	12	.	.	PUNCT
ejpam-4570	391	1	sequential	sequential	ADJ
ejpam-4570	391	2	,	,	PUNCT
ejpam-4570	391	3	first	first	ADV
ejpam-4570	391	4	countable	countable	ADJ
ejpam-4570	391	5	)	)	PUNCT
ejpam-4570	391	6	lindelöf	lindelöf	NOUN
ejpam-4570	391	7	space	space	NOUN
ejpam-4570	391	8	is	be	AUX
ejpam-4570	391	9	epi	epi	NOUN
ejpam-4570	391	10	-	-	ADJ
ejpam-4570	391	11	almost	almost	ADV
ejpam-4570	391	12	normal	normal	ADJ
ejpam-4570	391	13	.	.	PUNCT
ejpam-4570	392	1	(	(	PUNCT
ejpam-4570	392	2	3	3	X
ejpam-4570	392	3	)	)	PUNCT
ejpam-4570	392	4	every	every	DET
ejpam-4570	392	5	l2	l2	NOUN
ejpam-4570	392	6	-	-	PUNCT
ejpam-4570	392	7	almost	almost	ADV
ejpam-4570	392	8	completely	completely	ADV
ejpam-4570	392	9	regular	regular	ADJ
ejpam-4570	392	10	fréchet	fréchet	NOUN
ejpam-4570	392	11	(	(	PUNCT
ejpam-4570	392	12	resp	resp	NOUN
ejpam-4570	392	13	.	.	PUNCT
ejpam-4570	393	1	sequential	sequential	ADJ
ejpam-4570	393	2	,	,	PUNCT
ejpam-4570	393	3	first	first	ADV
ejpam-4570	393	4	countable	countable	ADJ
ejpam-4570	393	5	)	)	PUNCT
ejpam-4570	393	6	lindelöf	lindelöf	NOUN
ejpam-4570	393	7	space	space	NOUN
ejpam-4570	393	8	is	be	AUX
ejpam-4570	393	9	epi	epi	NOUN
ejpam-4570	393	10	-	-	ADJ
ejpam-4570	393	11	almost	almost	ADV
ejpam-4570	393	12	normal	normal	ADJ
ejpam-4570	393	13	.	.	PUNCT
ejpam-4570	394	1	since	since	SCONJ
ejpam-4570	394	2	every	every	DET
ejpam-4570	394	3	epi	epi	NOUN
ejpam-4570	394	4	-	-	ADJ
ejpam-4570	394	5	almost	almost	ADV
ejpam-4570	394	6	normal	normal	ADJ
ejpam-4570	394	7	space	space	NOUN
ejpam-4570	394	8	is	be	AUX
ejpam-4570	394	9	c	c	NOUN
ejpam-4570	394	10	-	-	PUNCT
ejpam-4570	394	11	almost	almost	ADV
ejpam-4570	394	12	normal	normal	ADJ
ejpam-4570	394	13	(	(	PUNCT
ejpam-4570	394	14	theorem	theorem	NOUN
ejpam-4570	394	15	2	2	NUM
ejpam-4570	394	16	)	)	PUNCT
ejpam-4570	394	17	,	,	PUNCT
ejpam-4570	394	18	every	every	DET
ejpam-4570	394	19	epi	epi	NOUN
ejpam-4570	394	20	-	-	ADJ
ejpam-4570	394	21	almost	almost	ADV
ejpam-4570	394	22	normal	normal	ADJ
ejpam-4570	394	23	space	space	NOUN
ejpam-4570	394	24	is	be	AUX
ejpam-4570	394	25	epi	epi	NOUN
ejpam-4570	394	26	-	-	ADJ
ejpam-4570	394	27	completely	completely	ADV
ejpam-4570	394	28	regular	regular	ADJ
ejpam-4570	394	29	[	[	X
ejpam-4570	394	30	5	5	NUM
ejpam-4570	394	31	]	]	PUNCT
ejpam-4570	394	32	,	,	PUNCT
ejpam-4570	394	33	and	and	CCONJ
ejpam-4570	394	34	every	every	DET
ejpam-4570	394	35	c2	c2	PROPN
ejpam-4570	394	36	-	-	PUNCT
ejpam-4570	394	37	paracompact	paracompact	NOUN
ejpam-4570	394	38	space	space	NOUN
ejpam-4570	394	39	is	be	AUX
ejpam-4570	394	40	c	c	NOUN
ejpam-4570	394	41	-	-	ADJ
ejpam-4570	394	42	normal	normal	ADJ
ejpam-4570	394	43	[	[	X
ejpam-4570	394	44	24	24	NUM
ejpam-4570	394	45	]	]	PUNCT
ejpam-4570	394	46	,	,	PUNCT
ejpam-4570	394	47	we	we	PRON
ejpam-4570	394	48	conclude	conclude	VERB
ejpam-4570	394	49	:	:	PUNCT
ejpam-4570	394	50	corollary	corollary	ADJ
ejpam-4570	394	51	13	13	NUM
ejpam-4570	394	52	.	.	PUNCT
ejpam-4570	395	1	(	(	PUNCT
ejpam-4570	395	2	1	1	X
ejpam-4570	395	3	)	)	PUNCT
ejpam-4570	395	4	every	every	DET
ejpam-4570	395	5	c2	c2	PROPN
ejpam-4570	395	6	-	-	PUNCT
ejpam-4570	395	7	almost	almost	ADV
ejpam-4570	395	8	regular	regular	ADJ
ejpam-4570	395	9	first	first	ADJ
ejpam-4570	395	10	countable	countable	ADJ
ejpam-4570	395	11	lindelöf	lindelöf	NOUN
ejpam-4570	395	12	space	space	NOUN
ejpam-4570	395	13	is	be	AUX
ejpam-4570	395	14	c	c	NOUN
ejpam-4570	395	15	-	-	PUNCT
ejpam-4570	395	16	almost	almost	ADV
ejpam-4570	395	17	normal	normal	ADJ
ejpam-4570	395	18	.	.	PUNCT
ejpam-4570	396	1	(	(	PUNCT
ejpam-4570	396	2	2	2	X
ejpam-4570	396	3	)	)	PUNCT
ejpam-4570	396	4	every	every	DET
ejpam-4570	396	5	c2	c2	PROPN
ejpam-4570	396	6	-	-	PUNCT
ejpam-4570	396	7	almost	almost	ADV
ejpam-4570	396	8	completely	completely	ADV
ejpam-4570	396	9	regular	regular	ADJ
ejpam-4570	396	10	first	first	ADJ
ejpam-4570	396	11	countable	countable	ADJ
ejpam-4570	396	12	lindelöf	lindelöf	NOUN
ejpam-4570	396	13	space	space	NOUN
ejpam-4570	396	14	is	be	AUX
ejpam-4570	396	15	c	c	NOUN
ejpam-4570	396	16	-	-	PUNCT
ejpam-4570	396	17	almost	almost	ADV
ejpam-4570	396	18	normal	normal	ADJ
ejpam-4570	396	19	.	.	PUNCT
ejpam-4570	397	1	(	(	PUNCT
ejpam-4570	397	2	3	3	X
ejpam-4570	397	3	)	)	PUNCT
ejpam-4570	397	4	every	every	DET
ejpam-4570	397	5	l2	l2	NOUN
ejpam-4570	397	6	-	-	PUNCT
ejpam-4570	397	7	almost	almost	ADV
ejpam-4570	397	8	regular	regular	ADJ
ejpam-4570	397	9	first	first	ADJ
ejpam-4570	397	10	countable	countable	ADJ
ejpam-4570	397	11	lindelöf	lindelöf	NOUN
ejpam-4570	397	12	space	space	NOUN
ejpam-4570	397	13	is	be	AUX
ejpam-4570	397	14	l	l	NOUN
ejpam-4570	397	15	-	-	ADJ
ejpam-4570	397	16	almost	almost	ADV
ejpam-4570	397	17	normal	normal	ADJ
ejpam-4570	397	18	.	.	PUNCT
ejpam-4570	398	1	(	(	PUNCT
ejpam-4570	398	2	4	4	X
ejpam-4570	398	3	)	)	PUNCT
ejpam-4570	398	4	every	every	DET
ejpam-4570	398	5	l2	l2	NOUN
ejpam-4570	398	6	-	-	PUNCT
ejpam-4570	398	7	almost	almost	ADV
ejpam-4570	398	8	completely	completely	ADV
ejpam-4570	398	9	regular	regular	ADJ
ejpam-4570	398	10	first	first	ADJ
ejpam-4570	398	11	countable	countable	ADJ
ejpam-4570	398	12	lindelöf	lindelöf	NOUN
ejpam-4570	398	13	space	space	NOUN
ejpam-4570	398	14	is	be	AUX
ejpam-4570	398	15	l	l	NOUN
ejpam-4570	398	16	-	-	ADJ
ejpam-4570	398	17	almost	almost	ADV
ejpam-4570	398	18	normal	normal	ADJ
ejpam-4570	398	19	.	.	PUNCT
ejpam-4570	399	1	(	(	PUNCT
ejpam-4570	399	2	5	5	X
ejpam-4570	399	3	)	)	PUNCT
ejpam-4570	399	4	every	every	DET
ejpam-4570	399	5	epi	epi	NOUN
ejpam-4570	399	6	-	-	ADJ
ejpam-4570	399	7	almost	almost	ADV
ejpam-4570	399	8	normal	normal	ADJ
ejpam-4570	399	9	space	space	NOUN
ejpam-4570	399	10	is	be	AUX
ejpam-4570	399	11	c	c	NOUN
ejpam-4570	399	12	-	-	PUNCT
ejpam-4570	399	13	completely	completely	ADV
ejpam-4570	399	14	regular	regular	ADJ
ejpam-4570	399	15	.	.	PUNCT
ejpam-4570	400	1	(	(	PUNCT
ejpam-4570	400	2	6	6	NUM
ejpam-4570	400	3	)	)	PUNCT
ejpam-4570	400	4	every	every	DET
ejpam-4570	400	5	c2	c2	PROPN
ejpam-4570	400	6	-	-	PUNCT
ejpam-4570	400	7	paracompact	paracompact	NOUN
ejpam-4570	400	8	space	space	NOUN
ejpam-4570	400	9	is	be	AUX
ejpam-4570	400	10	c	c	NOUN
ejpam-4570	400	11	-	-	PUNCT
ejpam-4570	400	12	almost	almost	ADV
ejpam-4570	400	13	normal	normal	ADJ
ejpam-4570	400	14	.	.	PUNCT
ejpam-4570	401	1	since	since	SCONJ
ejpam-4570	401	2	any	any	DET
ejpam-4570	401	3	closed	closed	ADJ
ejpam-4570	401	4	extension	extension	NOUN
ejpam-4570	401	5	space	space	NOUN
ejpam-4570	401	6	(	(	PUNCT
ejpam-4570	401	7	xp	xp	INTJ
ejpam-4570	401	8	,	,	PUNCT
ejpam-4570	401	9	t	t	PROPN
ejpam-4570	401	10	∗	∗	NOUN
ejpam-4570	401	11	)	)	PUNCT
ejpam-4570	401	12	of	of	ADP
ejpam-4570	401	13	a	a	DET
ejpam-4570	401	14	given	give	VERB
ejpam-4570	401	15	space	space	NOUN
ejpam-4570	401	16	(	(	PUNCT
ejpam-4570	401	17	x	x	X
ejpam-4570	401	18	,	,	PUNCT
ejpam-4570	401	19	t	t	PROPN
ejpam-4570	401	20	)	)	PUNCT
ejpam-4570	401	21	is	be	AUX
ejpam-4570	401	22	π	π	NOUN
ejpam-4570	401	23	-	-	ADJ
ejpam-4570	401	24	normal	normal	ADJ
ejpam-4570	401	25	[	[	X
ejpam-4570	401	26	1	1	NUM
ejpam-4570	401	27	,	,	PUNCT
ejpam-4570	401	28	theorem	theorem	VERB
ejpam-4570	401	29	9	9	NUM
ejpam-4570	401	30	]	]	PUNCT
ejpam-4570	401	31	,	,	PUNCT
ejpam-4570	401	32	we	we	PRON
ejpam-4570	401	33	obtain	obtain	VERB
ejpam-4570	401	34	:	:	PUNCT
ejpam-4570	401	35	wafa	wafa	PROPN
ejpam-4570	401	36	khalaf	khalaf	PROPN
ejpam-4570	401	37	alqurashi	alqurashi	PROPN
ejpam-4570	401	38	,	,	PUNCT
ejpam-4570	401	39	sadeq	sadeq	PROPN
ejpam-4570	401	40	ali	ali	PROPN
ejpam-4570	401	41	thabit	thabit	PROPN
ejpam-4570	401	42	/	/	SYM
ejpam-4570	401	43	eur	eur	PROPN
ejpam-4570	401	44	.	.	PUNCT
ejpam-4570	402	1	j.	j.	PROPN
ejpam-4570	402	2	pure	pure	PROPN
ejpam-4570	402	3	appl	appl	PROPN
ejpam-4570	402	4	.	.	PROPN
ejpam-4570	402	5	math	math	PROPN
ejpam-4570	402	6	,	,	PUNCT
ejpam-4570	402	7	15	15	NUM
ejpam-4570	402	8	(	(	PUNCT
ejpam-4570	402	9	4	4	NUM
ejpam-4570	402	10	)	)	PUNCT
ejpam-4570	402	11	(	(	PUNCT
ejpam-4570	402	12	2022	2022	NUM
ejpam-4570	402	13	)	)	PUNCT
ejpam-4570	402	14	,	,	PUNCT
ejpam-4570	402	15	1760	1760	NUM
ejpam-4570	402	16	-	-	SYM
ejpam-4570	402	17	1782	1782	NUM
ejpam-4570	402	18	1772	1772	NUM
ejpam-4570	402	19	corollary	corollary	NOUN
ejpam-4570	402	20	14	14	NUM
ejpam-4570	402	21	.	.	PUNCT
ejpam-4570	403	1	every	every	DET
ejpam-4570	403	2	closed	close	VERB
ejpam-4570	403	3	extension	extension	NOUN
ejpam-4570	403	4	space	space	NOUN
ejpam-4570	403	5	(	(	PUNCT
ejpam-4570	403	6	xp	xp	INTJ
ejpam-4570	403	7	,	,	PUNCT
ejpam-4570	403	8	t	t	PROPN
ejpam-4570	403	9	∗	∗	NOUN
ejpam-4570	403	10	)	)	PUNCT
ejpam-4570	403	11	of	of	ADP
ejpam-4570	403	12	a	a	DET
ejpam-4570	403	13	given	give	VERB
ejpam-4570	403	14	space	space	NOUN
ejpam-4570	403	15	(	(	PUNCT
ejpam-4570	403	16	x	x	X
ejpam-4570	403	17	,	,	PUNCT
ejpam-4570	403	18	t	t	PROPN
ejpam-4570	403	19	)	)	PUNCT
ejpam-4570	403	20	is	be	AUX
ejpam-4570	403	21	both	both	PRON
ejpam-4570	403	22	c	c	NOUN
ejpam-4570	403	23	-	-	PUNCT
ejpam-4570	403	24	almost	almost	ADV
ejpam-4570	403	25	normal	normal	ADJ
ejpam-4570	403	26	and	and	CCONJ
ejpam-4570	403	27	l	l	NOUN
ejpam-4570	403	28	-	-	PUNCT
ejpam-4570	403	29	almost	almost	ADV
ejpam-4570	403	30	normal	normal	ADJ
ejpam-4570	403	31	.	.	PUNCT
ejpam-4570	404	1	since	since	SCONJ
ejpam-4570	404	2	every	every	DET
ejpam-4570	404	3	quotient	quotient	NOUN
ejpam-4570	404	4	space	space	NOUN
ejpam-4570	404	5	of	of	ADP
ejpam-4570	404	6	an	an	DET
ejpam-4570	404	7	almost	almost	ADV
ejpam-4570	404	8	normal	normal	ADJ
ejpam-4570	404	9	space	space	NOUN
ejpam-4570	404	10	is	be	AUX
ejpam-4570	404	11	almost	almost	ADV
ejpam-4570	404	12	normal	normal	ADJ
ejpam-4570	404	13	[	[	X
ejpam-4570	404	14	26	26	NUM
ejpam-4570	404	15	]	]	PUNCT
ejpam-4570	404	16	,	,	PUNCT
ejpam-4570	404	17	the	the	DET
ejpam-4570	404	18	next	next	ADJ
ejpam-4570	404	19	result	result	NOUN
ejpam-4570	404	20	is	be	AUX
ejpam-4570	404	21	obvious	obvious	ADJ
ejpam-4570	404	22	:	:	PUNCT
ejpam-4570	404	23	theorem	theorem	NOUN
ejpam-4570	404	24	25	25	NUM
ejpam-4570	404	25	.	.	PUNCT
ejpam-4570	405	1	if	if	SCONJ
ejpam-4570	405	2	(	(	PUNCT
ejpam-4570	405	3	x	x	X
ejpam-4570	405	4	,	,	PUNCT
ejpam-4570	405	5	t	t	PROPN
ejpam-4570	405	6	)	)	PUNCT
ejpam-4570	405	7	is	be	AUX
ejpam-4570	405	8	a	a	DET
ejpam-4570	405	9	c	c	NOUN
ejpam-4570	405	10	-	-	PUNCT
ejpam-4570	405	11	almost	almost	ADV
ejpam-4570	405	12	normal	normal	ADJ
ejpam-4570	405	13	(	(	PUNCT
ejpam-4570	405	14	resp	resp	NOUN
ejpam-4570	405	15	.	.	PUNCT
ejpam-4570	406	1	an	an	DET
ejpam-4570	406	2	l	l	NOUN
ejpam-4570	406	3	-	-	ADJ
ejpam-4570	406	4	almost	almost	ADV
ejpam-4570	406	5	normal	normal	ADJ
ejpam-4570	406	6	)	)	PUNCT
ejpam-4570	406	7	first	first	ADJ
ejpam-4570	406	8	countable	countable	ADJ
ejpam-4570	406	9	space	space	NOUN
ejpam-4570	406	10	,	,	PUNCT
ejpam-4570	406	11	then	then	ADV
ejpam-4570	406	12	there	there	PRON
ejpam-4570	406	13	exists	exist	VERB
ejpam-4570	406	14	a	a	DET
ejpam-4570	406	15	topology	topology	NOUN
ejpam-4570	406	16	t	t	NOUN
ejpam-4570	406	17	∗	∗	NOUN
ejpam-4570	406	18	coarser	coarse	ADJ
ejpam-4570	406	19	than	than	ADP
ejpam-4570	406	20	t	t	NOUN
ejpam-4570	406	21	such	such	ADJ
ejpam-4570	406	22	that	that	SCONJ
ejpam-4570	406	23	(	(	PUNCT
ejpam-4570	406	24	x	x	X
ejpam-4570	406	25	,	,	PUNCT
ejpam-4570	406	26	t	t	PROPN
ejpam-4570	406	27	∗	∗	NOUN
ejpam-4570	406	28	)	)	PUNCT
ejpam-4570	406	29	is	be	AUX
ejpam-4570	406	30	almost	almost	ADV
ejpam-4570	406	31	normal	normal	ADJ
ejpam-4570	406	32	.	.	PUNCT
ejpam-4570	407	1	note	note	VERB
ejpam-4570	407	2	that	that	SCONJ
ejpam-4570	407	3	:	:	PUNCT
ejpam-4570	407	4	any	any	DET
ejpam-4570	407	5	tychonoff	tychonoff	NOUN
ejpam-4570	407	6	space	space	NOUN
ejpam-4570	407	7	y	y	PROPN
ejpam-4570	407	8	has	have	VERB
ejpam-4570	407	9	a	a	DET
ejpam-4570	407	10	one	one	NUM
ejpam-4570	407	11	-	-	PUNCT
ejpam-4570	407	12	point	point	NOUN
ejpam-4570	407	13	compactification	compactification	NOUN
ejpam-4570	407	14	x	x	NOUN
ejpam-4570	407	15	,	,	PUNCT
ejpam-4570	407	16	x	x	PUNCT
ejpam-4570	407	17	=	=	SYM
ejpam-4570	407	18	y	y	PROPN
ejpam-4570	407	19	∪	∪	VERB
ejpam-4570	407	20	{	{	PUNCT
ejpam-4570	407	21	p	p	NOUN
ejpam-4570	407	22	}	}	PUNCT
ejpam-4570	407	23	,	,	PUNCT
ejpam-4570	407	24	p	p	PROPN
ejpam-4570	407	25	̸∈	̸∈	PROPN
ejpam-4570	407	26	y	y	PROPN
ejpam-4570	407	27	,	,	PUNCT
ejpam-4570	407	28	x	x	X
ejpam-4570	407	29	is	be	AUX
ejpam-4570	407	30	a	a	DET
ejpam-4570	407	31	hausdorff	hausdorff	ADJ
ejpam-4570	407	32	compact	compact	ADJ
ejpam-4570	407	33	space	space	NOUN
ejpam-4570	407	34	and	and	CCONJ
ejpam-4570	407	35	{	{	PUNCT
ejpam-4570	407	36	p	p	X
ejpam-4570	407	37	}	}	PUNCT
ejpam-4570	407	38	is	be	AUX
ejpam-4570	407	39	closed	closed	ADJ
ejpam-4570	407	40	and	and	CCONJ
ejpam-4570	407	41	open	open	ADJ
ejpam-4570	407	42	subset	subset	NOUN
ejpam-4570	407	43	of	of	ADP
ejpam-4570	407	44	x	x	PUNCT
ejpam-4570	408	1	[	[	X
ejpam-4570	408	2	2	2	NUM
ejpam-4570	408	3	]	]	PUNCT
ejpam-4570	408	4	.	.	PUNCT
ejpam-4570	409	1	now	now	ADV
ejpam-4570	409	2	,	,	PUNCT
ejpam-4570	409	3	we	we	PRON
ejpam-4570	409	4	get	get	VERB
ejpam-4570	409	5	the	the	DET
ejpam-4570	409	6	following	follow	VERB
ejpam-4570	409	7	result	result	NOUN
ejpam-4570	409	8	:	:	PUNCT
ejpam-4570	409	9	theorem	theorem	VERB
ejpam-4570	409	10	26	26	NUM
ejpam-4570	409	11	.	.	PUNCT
ejpam-4570	410	1	if	if	SCONJ
ejpam-4570	410	2	y	y	PROPN
ejpam-4570	410	3	is	be	AUX
ejpam-4570	410	4	a	a	DET
ejpam-4570	410	5	tychonoff	tychonoff	NOUN
ejpam-4570	410	6	space	space	NOUN
ejpam-4570	410	7	,	,	PUNCT
ejpam-4570	410	8	then	then	ADV
ejpam-4570	410	9	any	any	DET
ejpam-4570	410	10	discrete	discrete	ADJ
ejpam-4570	410	11	extension	extension	NOUN
ejpam-4570	410	12	space	space	NOUN
ejpam-4570	410	13	xm	xm	PROPN
ejpam-4570	410	14	of	of	ADP
ejpam-4570	410	15	any	any	DET
ejpam-4570	410	16	compactification	compactification	NOUN
ejpam-4570	410	17	x	x	PUNCT
ejpam-4570	410	18	of	of	ADP
ejpam-4570	410	19	y	y	PROPN
ejpam-4570	410	20	is	be	AUX
ejpam-4570	410	21	c	c	NOUN
ejpam-4570	410	22	-	-	PUNCT
ejpam-4570	410	23	almost	almost	ADV
ejpam-4570	410	24	normal	normal	ADJ
ejpam-4570	410	25	.	.	PUNCT
ejpam-4570	411	1	proof	proof	NOUN
ejpam-4570	411	2	.	.	PUNCT
ejpam-4570	412	1	let	let	VERB
ejpam-4570	412	2	y	y	PRON
ejpam-4570	412	3	be	be	AUX
ejpam-4570	412	4	a	a	DET
ejpam-4570	412	5	tychonoff	tychonoff	NOUN
ejpam-4570	412	6	space	space	NOUN
ejpam-4570	412	7	.	.	PUNCT
ejpam-4570	413	1	then	then	ADV
ejpam-4570	413	2	,	,	PUNCT
ejpam-4570	413	3	any	any	DET
ejpam-4570	413	4	compactification	compactification	NOUN
ejpam-4570	413	5	x	x	PUNCT
ejpam-4570	413	6	of	of	ADP
ejpam-4570	413	7	a	a	DET
ejpam-4570	413	8	tychonoff	tychonoff	NOUN
ejpam-4570	413	9	space	space	NOUN
ejpam-4570	413	10	y	y	PROPN
ejpam-4570	413	11	is	be	AUX
ejpam-4570	413	12	a	a	DET
ejpam-4570	413	13	hausdorff	hausdorff	ADJ
ejpam-4570	413	14	compact	compact	ADJ
ejpam-4570	413	15	space	space	NOUN
ejpam-4570	413	16	and	and	CCONJ
ejpam-4570	413	17	hence	hence	ADV
ejpam-4570	413	18	it	it	PRON
ejpam-4570	413	19	is	be	AUX
ejpam-4570	413	20	a	a	DET
ejpam-4570	413	21	t4	t4	PROPN
ejpam-4570	413	22	-	-	PUNCT
ejpam-4570	413	23	space	space	NOUN
ejpam-4570	413	24	.	.	PUNCT
ejpam-4570	414	1	now	now	ADV
ejpam-4570	414	2	,	,	PUNCT
ejpam-4570	414	3	if	if	SCONJ
ejpam-4570	414	4	xm	xm	PROPN
ejpam-4570	414	5	is	be	AUX
ejpam-4570	414	6	a	a	DET
ejpam-4570	414	7	discrete	discrete	ADJ
ejpam-4570	414	8	extension	extension	NOUN
ejpam-4570	414	9	space	space	NOUN
ejpam-4570	414	10	of	of	ADP
ejpam-4570	414	11	x	x	X
ejpam-4570	414	12	,	,	PUNCT
ejpam-4570	414	13	then	then	ADV
ejpam-4570	414	14	the	the	DET
ejpam-4570	414	15	topology	topology	NOUN
ejpam-4570	414	16	on	on	ADP
ejpam-4570	414	17	x	x	SYM
ejpam-4570	414	18	is	be	AUX
ejpam-4570	414	19	coarser	coarse	ADJ
ejpam-4570	414	20	than	than	ADP
ejpam-4570	414	21	the	the	DET
ejpam-4570	414	22	topology	topology	NOUN
ejpam-4570	414	23	on	on	ADP
ejpam-4570	414	24	xm	xm	PROPN
ejpam-4570	414	25	.	.	PUNCT
ejpam-4570	415	1	then	then	ADV
ejpam-4570	415	2	,	,	PUNCT
ejpam-4570	415	3	xm	xm	PROPN
ejpam-4570	415	4	is	be	AUX
ejpam-4570	415	5	an	an	DET
ejpam-4570	415	6	epi	epi	ADJ
ejpam-4570	415	7	-	-	ADJ
ejpam-4570	415	8	normal	normal	ADJ
ejpam-4570	415	9	space	space	NOUN
ejpam-4570	415	10	.	.	PUNCT
ejpam-4570	416	1	hence	hence	ADV
ejpam-4570	416	2	,	,	PUNCT
ejpam-4570	416	3	xm	xm	PROPN
ejpam-4570	416	4	is	be	AUX
ejpam-4570	416	5	epi	epi	NOUN
ejpam-4570	416	6	-	-	ADJ
ejpam-4570	416	7	almost	almost	ADV
ejpam-4570	416	8	normal	normal	ADJ
ejpam-4570	416	9	.	.	PUNCT
ejpam-4570	417	1	by	by	ADP
ejpam-4570	417	2	theorem	theorem	NOUN
ejpam-4570	417	3	2	2	NUM
ejpam-4570	417	4	,	,	PUNCT
ejpam-4570	417	5	xm	xm	PROPN
ejpam-4570	417	6	is	be	AUX
ejpam-4570	417	7	c	c	NOUN
ejpam-4570	417	8	-	-	PUNCT
ejpam-4570	417	9	almost	almost	ADV
ejpam-4570	417	10	normal	normal	ADJ
ejpam-4570	417	11	.	.	PUNCT
ejpam-4570	418	1	theorem	theorem	VERB
ejpam-4570	418	2	27	27	NUM
ejpam-4570	418	3	.	.	PUNCT
ejpam-4570	419	1	every	every	DET
ejpam-4570	419	2	c	c	NOUN
ejpam-4570	419	3	-	-	PUNCT
ejpam-4570	419	4	almost	almost	ADV
ejpam-4570	419	5	regular	regular	ADJ
ejpam-4570	419	6	first	first	ADJ
ejpam-4570	419	7	countable	countable	ADJ
ejpam-4570	419	8	lindelöf	lindelöf	NOUN
ejpam-4570	419	9	space	space	NOUN
ejpam-4570	419	10	is	be	AUX
ejpam-4570	419	11	c	c	NOUN
ejpam-4570	419	12	-	-	PUNCT
ejpam-4570	419	13	almost	almost	ADV
ejpam-4570	419	14	normal	normal	ADJ
ejpam-4570	419	15	.	.	PUNCT
ejpam-4570	420	1	proof	proof	NOUN
ejpam-4570	420	2	.	.	PUNCT
ejpam-4570	421	1	let	let	VERB
ejpam-4570	421	2	x	x	PRON
ejpam-4570	421	3	be	be	AUX
ejpam-4570	421	4	a	a	DET
ejpam-4570	421	5	c	c	NOUN
ejpam-4570	421	6	-	-	PUNCT
ejpam-4570	421	7	almost	almost	ADV
ejpam-4570	421	8	regular	regular	ADJ
ejpam-4570	421	9	first	first	ADJ
ejpam-4570	421	10	countable	countable	ADJ
ejpam-4570	421	11	lindelöf	lindelöf	NOUN
ejpam-4570	421	12	space	space	NOUN
ejpam-4570	421	13	.	.	PUNCT
ejpam-4570	422	1	then	then	ADV
ejpam-4570	422	2	,	,	PUNCT
ejpam-4570	422	3	there	there	PRON
ejpam-4570	422	4	exist	exist	VERB
ejpam-4570	422	5	an	an	DET
ejpam-4570	422	6	almost	almost	ADV
ejpam-4570	422	7	regular	regular	ADJ
ejpam-4570	422	8	space	space	NOUN
ejpam-4570	422	9	y	y	PROPN
ejpam-4570	422	10	and	and	CCONJ
ejpam-4570	422	11	a	a	DET
ejpam-4570	422	12	bijective	bijective	ADJ
ejpam-4570	422	13	function	function	NOUN
ejpam-4570	422	14	f	f	NOUN
ejpam-4570	422	15	:	:	PUNCT
ejpam-4570	422	16	(	(	PUNCT
ejpam-4570	422	17	x	x	X
ejpam-4570	422	18	,	,	PUNCT
ejpam-4570	422	19	t	t	PROPN
ejpam-4570	422	20	)	)	PUNCT
ejpam-4570	422	21	→	→	SYM
ejpam-4570	422	22	(	(	PUNCT
ejpam-4570	422	23	y	y	PROPN
ejpam-4570	422	24	,	,	PUNCT
ejpam-4570	422	25	t	t	PROPN
ejpam-4570	422	26	′	′	NUM
ejpam-4570	422	27	)	)	PUNCT
ejpam-4570	422	28	such	such	ADJ
ejpam-4570	422	29	that	that	SCONJ
ejpam-4570	422	30	f	f	PROPN
ejpam-4570	422	31	|a	|a	VERB
ejpam-4570	422	32	:	:	PUNCT
ejpam-4570	422	33	a	a	DET
ejpam-4570	422	34	→	→	SYM
ejpam-4570	422	35	f(a	f(a	NOUN
ejpam-4570	422	36	)	)	PUNCT
ejpam-4570	422	37	is	be	AUX
ejpam-4570	422	38	a	a	DET
ejpam-4570	422	39	homeomorphism	homeomorphism	NOUN
ejpam-4570	422	40	for	for	ADP
ejpam-4570	422	41	each	each	DET
ejpam-4570	422	42	compact	compact	NOUN
ejpam-4570	422	43	subset	subset	VERB
ejpam-4570	422	44	a	a	DET
ejpam-4570	422	45	⊆	⊆	NUM
ejpam-4570	422	46	x.	x.	NOUN
ejpam-4570	422	47	since	since	SCONJ
ejpam-4570	422	48	x	x	PRON
ejpam-4570	422	49	is	be	AUX
ejpam-4570	422	50	first	first	ADV
ejpam-4570	422	51	countable	countable	ADJ
ejpam-4570	422	52	,	,	PUNCT
ejpam-4570	422	53	we	we	PRON
ejpam-4570	422	54	get	get	VERB
ejpam-4570	422	55	f	f	PROPN
ejpam-4570	422	56	is	be	AUX
ejpam-4570	422	57	continuous	continuous	ADJ
ejpam-4570	422	58	.	.	PUNCT
ejpam-4570	423	1	thus	thus	ADV
ejpam-4570	423	2	,	,	PUNCT
ejpam-4570	423	3	f	f	X
ejpam-4570	423	4	:	:	PUNCT
ejpam-4570	423	5	(	(	PUNCT
ejpam-4570	423	6	x	x	X
ejpam-4570	423	7	,	,	PUNCT
ejpam-4570	423	8	t	t	PROPN
ejpam-4570	423	9	)	)	PUNCT
ejpam-4570	423	10	→	→	SYM
ejpam-4570	423	11	(	(	PUNCT
ejpam-4570	423	12	y	y	NOUN
ejpam-4570	423	13	,	,	PUNCT
ejpam-4570	423	14	ts′	ts′	NUM
ejpam-4570	423	15	)	)	PUNCT
ejpam-4570	423	16	is	be	AUX
ejpam-4570	423	17	1	1	NUM
ejpam-4570	423	18	-	-	SYM
ejpam-4570	423	19	1	1	NUM
ejpam-4570	423	20	,	,	PUNCT
ejpam-4570	423	21	onto	onto	ADP
ejpam-4570	423	22	and	and	CCONJ
ejpam-4570	423	23	continuous	continuous	ADJ
ejpam-4570	423	24	function	function	NOUN
ejpam-4570	423	25	such	such	ADJ
ejpam-4570	423	26	that	that	SCONJ
ejpam-4570	423	27	(	(	PUNCT
ejpam-4570	423	28	y	y	NOUN
ejpam-4570	423	29	,	,	PUNCT
ejpam-4570	423	30	ts′	ts′	NUM
ejpam-4570	423	31	)	)	PUNCT
ejpam-4570	423	32	is	be	AUX
ejpam-4570	423	33	a	a	DET
ejpam-4570	423	34	regular	regular	ADJ
ejpam-4570	423	35	space	space	NOUN
ejpam-4570	423	36	.	.	PUNCT
ejpam-4570	424	1	since	since	SCONJ
ejpam-4570	424	2	a	a	DET
ejpam-4570	424	3	continuous	continuous	ADJ
ejpam-4570	424	4	image	image	NOUN
ejpam-4570	424	5	of	of	ADP
ejpam-4570	424	6	a	a	DET
ejpam-4570	424	7	lindelöf	lindelöf	NOUN
ejpam-4570	424	8	space	space	NOUN
ejpam-4570	424	9	is	be	AUX
ejpam-4570	424	10	lindelöf	lindelöf	PUNCT
ejpam-4570	424	11	[	[	X
ejpam-4570	424	12	12	12	NUM
ejpam-4570	424	13	]	]	PUNCT
ejpam-4570	424	14	,	,	PUNCT
ejpam-4570	424	15	and	and	CCONJ
ejpam-4570	424	16	x	x	X
ejpam-4570	424	17	is	be	AUX
ejpam-4570	424	18	lindelöf	lindelöf	PROPN
ejpam-4570	424	19	,	,	PUNCT
ejpam-4570	424	20	we	we	PRON
ejpam-4570	424	21	get	get	VERB
ejpam-4570	424	22	:	:	PUNCT
ejpam-4570	424	23	(	(	PUNCT
ejpam-4570	424	24	y	y	NOUN
ejpam-4570	424	25	,	,	PUNCT
ejpam-4570	424	26	ts′	ts′	NUM
ejpam-4570	424	27	)	)	PUNCT
ejpam-4570	424	28	is	be	AUX
ejpam-4570	424	29	a	a	DET
ejpam-4570	424	30	regular	regular	ADJ
ejpam-4570	424	31	lindelöf	lindelöf	NOUN
ejpam-4570	424	32	space	space	NOUN
ejpam-4570	424	33	.	.	PUNCT
ejpam-4570	425	1	since	since	SCONJ
ejpam-4570	425	2	every	every	DET
ejpam-4570	425	3	regular	regular	ADJ
ejpam-4570	425	4	lindelöf	lindelöf	NOUN
ejpam-4570	425	5	space	space	NOUN
ejpam-4570	425	6	is	be	AUX
ejpam-4570	425	7	paracompact	paracompact	ADJ
ejpam-4570	425	8	and	and	CCONJ
ejpam-4570	425	9	hence	hence	ADV
ejpam-4570	425	10	almost	almost	ADV
ejpam-4570	425	11	normal	normal	ADJ
ejpam-4570	425	12	[	[	X
ejpam-4570	425	13	12	12	NUM
ejpam-4570	425	14	,	,	PUNCT
ejpam-4570	425	15	26	26	NUM
ejpam-4570	425	16	]	]	PUNCT
ejpam-4570	425	17	,	,	PUNCT
ejpam-4570	425	18	we	we	PRON
ejpam-4570	425	19	get	get	VERB
ejpam-4570	425	20	:	:	PUNCT
ejpam-4570	425	21	(	(	PUNCT
ejpam-4570	425	22	y	y	NOUN
ejpam-4570	425	23	,	,	PUNCT
ejpam-4570	425	24	ts′	ts′	NUM
ejpam-4570	425	25	)	)	PUNCT
ejpam-4570	425	26	is	be	AUX
ejpam-4570	425	27	an	an	DET
ejpam-4570	425	28	almost	almost	ADV
ejpam-4570	425	29	normal	normal	ADJ
ejpam-4570	425	30	space	space	NOUN
ejpam-4570	425	31	such	such	ADJ
ejpam-4570	425	32	that	that	SCONJ
ejpam-4570	425	33	f	f	PROPN
ejpam-4570	425	34	|a	|a	VERB
ejpam-4570	425	35	:	:	PUNCT
ejpam-4570	425	36	a	a	DET
ejpam-4570	425	37	→	→	SYM
ejpam-4570	425	38	f(a	f(a	NOUN
ejpam-4570	425	39	)	)	PUNCT
ejpam-4570	425	40	is	be	AUX
ejpam-4570	425	41	a	a	DET
ejpam-4570	425	42	homeomorphism	homeomorphism	NOUN
ejpam-4570	425	43	for	for	ADP
ejpam-4570	425	44	each	each	DET
ejpam-4570	425	45	compact	compact	NOUN
ejpam-4570	425	46	subset	subset	VERB
ejpam-4570	425	47	a	a	DET
ejpam-4570	425	48	⊆	⊆	NUM
ejpam-4570	425	49	x.	x.	NOUN
ejpam-4570	425	50	therefore	therefore	ADV
ejpam-4570	425	51	,	,	PUNCT
ejpam-4570	425	52	x	x	X
ejpam-4570	425	53	is	be	AUX
ejpam-4570	425	54	c	c	NOUN
ejpam-4570	425	55	-	-	PUNCT
ejpam-4570	425	56	almost	almost	ADV
ejpam-4570	425	57	normal	normal	ADJ
ejpam-4570	425	58	.	.	PUNCT
ejpam-4570	426	1	corollary	corollary	ADJ
ejpam-4570	426	2	15	15	NUM
ejpam-4570	426	3	.	.	PUNCT
ejpam-4570	427	1	every	every	DET
ejpam-4570	427	2	c	c	NOUN
ejpam-4570	427	3	-	-	PUNCT
ejpam-4570	427	4	almost	almost	ADV
ejpam-4570	427	5	completely	completely	ADV
ejpam-4570	427	6	regular	regular	ADJ
ejpam-4570	427	7	first	first	ADJ
ejpam-4570	427	8	countable	countable	ADJ
ejpam-4570	427	9	lindelöf	lindelöf	NOUN
ejpam-4570	427	10	space	space	NOUN
ejpam-4570	427	11	is	be	AUX
ejpam-4570	427	12	c	c	NOUN
ejpam-4570	427	13	-	-	PUNCT
ejpam-4570	427	14	almost	almost	ADV
ejpam-4570	427	15	normal	normal	ADJ
ejpam-4570	427	16	.	.	PUNCT
ejpam-4570	428	1	from	from	ADP
ejpam-4570	428	2	theorem	theorem	ADJ
ejpam-4570	428	3	27	27	NUM
ejpam-4570	428	4	and	and	CCONJ
ejpam-4570	428	5	every	every	DET
ejpam-4570	428	6	hausdorff	hausdorff	NOUN
ejpam-4570	428	7	first	first	ADV
ejpam-4570	428	8	countable	countable	ADJ
ejpam-4570	428	9	space	space	NOUN
ejpam-4570	428	10	is	be	AUX
ejpam-4570	428	11	c	c	NOUN
ejpam-4570	428	12	-	-	PUNCT
ejpam-4570	428	13	almost	almost	ADV
ejpam-4570	428	14	completely	completely	ADV
ejpam-4570	428	15	regular	regular	ADJ
ejpam-4570	429	1	[	[	X
ejpam-4570	429	2	31	31	NUM
ejpam-4570	429	3	]	]	PUNCT
ejpam-4570	429	4	,	,	PUNCT
ejpam-4570	429	5	we	we	PRON
ejpam-4570	429	6	conclude	conclude	VERB
ejpam-4570	429	7	the	the	DET
ejpam-4570	429	8	next	next	ADJ
ejpam-4570	429	9	corollary	corollary	NOUN
ejpam-4570	429	10	:	:	PUNCT
ejpam-4570	429	11	corollary	corollary	ADJ
ejpam-4570	429	12	16	16	NUM
ejpam-4570	429	13	.	.	PUNCT
ejpam-4570	430	1	(	(	PUNCT
ejpam-4570	430	2	1	1	X
ejpam-4570	430	3	)	)	PUNCT
ejpam-4570	430	4	every	every	DET
ejpam-4570	430	5	hausdorff	hausdorff	NOUN
ejpam-4570	430	6	first	first	ADV
ejpam-4570	430	7	countable	countable	ADJ
ejpam-4570	430	8	lindelöf	lindelöf	NOUN
ejpam-4570	430	9	space	space	NOUN
ejpam-4570	430	10	is	be	AUX
ejpam-4570	430	11	c	c	NOUN
ejpam-4570	430	12	-	-	PUNCT
ejpam-4570	430	13	almost	almost	ADV
ejpam-4570	430	14	normal	normal	ADJ
ejpam-4570	430	15	.	.	PUNCT
ejpam-4570	431	1	(	(	PUNCT
ejpam-4570	431	2	2	2	X
ejpam-4570	431	3	)	)	PUNCT
ejpam-4570	431	4	every	every	DET
ejpam-4570	431	5	hausdorff	hausdorff	NOUN
ejpam-4570	431	6	first	first	ADV
ejpam-4570	431	7	countable	countable	ADJ
ejpam-4570	431	8	lindelöf	lindelöf	NOUN
ejpam-4570	431	9	space	space	NOUN
ejpam-4570	431	10	is	be	AUX
ejpam-4570	431	11	c	c	NOUN
ejpam-4570	431	12	-	-	PUNCT
ejpam-4570	431	13	almost	almost	ADV
ejpam-4570	431	14	normal	normal	ADJ
ejpam-4570	431	15	.	.	PUNCT
ejpam-4570	432	1	wafa	wafa	PROPN
ejpam-4570	432	2	khalaf	khalaf	PROPN
ejpam-4570	432	3	alqurashi	alqurashi	PROPN
ejpam-4570	432	4	,	,	PUNCT
ejpam-4570	432	5	sadeq	sadeq	PROPN
ejpam-4570	432	6	ali	ali	PROPN
ejpam-4570	432	7	thabit	thabit	PROPN
ejpam-4570	432	8	/	/	SYM
ejpam-4570	432	9	eur	eur	PROPN
ejpam-4570	432	10	.	.	PUNCT
ejpam-4570	433	1	j.	j.	PROPN
ejpam-4570	433	2	pure	pure	PROPN
ejpam-4570	433	3	appl	appl	PROPN
ejpam-4570	433	4	.	.	PROPN
ejpam-4570	433	5	math	math	PROPN
ejpam-4570	433	6	,	,	PUNCT
ejpam-4570	433	7	15	15	NUM
ejpam-4570	433	8	(	(	PUNCT
ejpam-4570	433	9	4	4	NUM
ejpam-4570	433	10	)	)	PUNCT
ejpam-4570	433	11	(	(	PUNCT
ejpam-4570	433	12	2022	2022	NUM
ejpam-4570	433	13	)	)	PUNCT
ejpam-4570	433	14	,	,	PUNCT
ejpam-4570	433	15	1760	1760	NUM
ejpam-4570	433	16	-	-	SYM
ejpam-4570	433	17	1782	1782	NUM
ejpam-4570	433	18	1773	1773	NUM
ejpam-4570	433	19	4	4	NUM
ejpam-4570	433	20	.	.	PUNCT
ejpam-4570	434	1	some	some	DET
ejpam-4570	434	2	counterexamples	counterexample	NOUN
ejpam-4570	434	3	it	it	PRON
ejpam-4570	434	4	can	can	AUX
ejpam-4570	434	5	be	be	AUX
ejpam-4570	434	6	observed	observe	VERB
ejpam-4570	434	7	that	that	SCONJ
ejpam-4570	434	8	:	:	PUNCT
ejpam-4570	434	9	any	any	DET
ejpam-4570	434	10	uncountable	uncountable	ADJ
ejpam-4570	434	11	indiscrete	indiscrete	ADJ
ejpam-4570	434	12	space	space	NOUN
ejpam-4570	434	13	is	be	AUX
ejpam-4570	434	14	an	an	DET
ejpam-4570	434	15	example	example	NOUN
ejpam-4570	434	16	of	of	ADP
ejpam-4570	434	17	an	an	DET
ejpam-4570	434	18	l	l	NOUN
ejpam-4570	434	19	-	-	ADJ
ejpam-4570	434	20	almost	almost	ADV
ejpam-4570	434	21	normal	normal	ADJ
ejpam-4570	434	22	space	space	NOUN
ejpam-4570	434	23	,	,	PUNCT
ejpam-4570	434	24	which	which	PRON
ejpam-4570	434	25	is	be	AUX
ejpam-4570	434	26	neither	neither	PRON
ejpam-4570	434	27	c	c	NOUN
ejpam-4570	434	28	-	-	PUNCT
ejpam-4570	434	29	tychonoff	tychonoff	NOUN
ejpam-4570	434	30	nor	nor	CCONJ
ejpam-4570	434	31	epi	epi	NOUN
ejpam-4570	434	32	-	-	ADJ
ejpam-4570	434	33	almost	almost	ADV
ejpam-4570	434	34	normal	normal	ADJ
ejpam-4570	434	35	being	be	AUX
ejpam-4570	434	36	not	not	PART
ejpam-4570	434	37	hausdorff	hausdorff	NOUN
ejpam-4570	434	38	.	.	PUNCT
ejpam-4570	435	1	the	the	DET
ejpam-4570	435	2	following	following	ADJ
ejpam-4570	435	3	example	example	NOUN
ejpam-4570	435	4	is	be	AUX
ejpam-4570	435	5	an	an	DET
ejpam-4570	435	6	l	l	NOUN
ejpam-4570	435	7	-	-	ADJ
ejpam-4570	435	8	almost	almost	ADV
ejpam-4570	435	9	normal	normal	ADJ
ejpam-4570	435	10	space	space	NOUN
ejpam-4570	435	11	,	,	PUNCT
ejpam-4570	435	12	which	which	PRON
ejpam-4570	435	13	is	be	AUX
ejpam-4570	435	14	not	not	PART
ejpam-4570	435	15	c	c	NOUN
ejpam-4570	435	16	-	-	NOUN
ejpam-4570	435	17	regular	regular	ADJ
ejpam-4570	435	18	.	.	PUNCT
ejpam-4570	435	19	example	example	NOUN
ejpam-4570	436	1	1	1	NUM
ejpam-4570	436	2	.	.	PUNCT
ejpam-4570	437	1	the	the	DET
ejpam-4570	437	2	particular	particular	ADJ
ejpam-4570	437	3	point	point	NOUN
ejpam-4570	437	4	topology	topology	NOUN
ejpam-4570	437	5	[	[	X
ejpam-4570	437	6	29	29	NUM
ejpam-4570	437	7	,	,	PUNCT
ejpam-4570	437	8	example	example	NOUN
ejpam-4570	437	9	10	10	NUM
ejpam-4570	437	10	]	]	PUNCT
ejpam-4570	437	11	,	,	PUNCT
ejpam-4570	437	12	(	(	PUNCT
ejpam-4570	437	13	r	r	NOUN
ejpam-4570	437	14	,	,	PUNCT
ejpam-4570	437	15	tp	tp	NOUN
ejpam-4570	437	16	)	)	PUNCT
ejpam-4570	437	17	is	be	AUX
ejpam-4570	437	18	neither	neither	CCONJ
ejpam-4570	437	19	a	a	DET
ejpam-4570	437	20	c	c	NOUN
ejpam-4570	437	21	-	-	ADJ
ejpam-4570	437	22	regular	regular	ADJ
ejpam-4570	437	23	nor	nor	CCONJ
ejpam-4570	437	24	c	c	NOUN
ejpam-4570	437	25	-	-	PUNCT
ejpam-4570	437	26	normal	normal	ADJ
ejpam-4570	437	27	space	space	NOUN
ejpam-4570	437	28	[	[	X
ejpam-4570	437	29	8	8	NUM
ejpam-4570	437	30	,	,	PUNCT
ejpam-4570	437	31	10	10	NUM
ejpam-4570	437	32	]	]	PUNCT
ejpam-4570	437	33	.	.	PUNCT
ejpam-4570	438	1	since	since	SCONJ
ejpam-4570	438	2	the	the	DET
ejpam-4570	438	3	particular	particular	ADJ
ejpam-4570	438	4	point	point	NOUN
ejpam-4570	438	5	topology	topology	NOUN
ejpam-4570	438	6	(	(	PUNCT
ejpam-4570	438	7	r	r	NOUN
ejpam-4570	438	8	,	,	PUNCT
ejpam-4570	438	9	tp	tp	NOUN
ejpam-4570	438	10	)	)	PUNCT
ejpam-4570	438	11	is	be	AUX
ejpam-4570	438	12	almost	almost	ADV
ejpam-4570	438	13	normal	normal	ADJ
ejpam-4570	438	14	,	,	PUNCT
ejpam-4570	438	15	we	we	PRON
ejpam-4570	438	16	get	get	VERB
ejpam-4570	438	17	(	(	PUNCT
ejpam-4570	438	18	r	r	NOUN
ejpam-4570	438	19	,	,	PUNCT
ejpam-4570	438	20	tp	tp	NOUN
ejpam-4570	438	21	)	)	PUNCT
ejpam-4570	438	22	is	be	AUX
ejpam-4570	438	23	c	c	NOUN
ejpam-4570	438	24	-	-	PUNCT
ejpam-4570	438	25	almost	almost	ADV
ejpam-4570	438	26	normal	normal	ADJ
ejpam-4570	438	27	and	and	CCONJ
ejpam-4570	438	28	l	l	NOUN
ejpam-4570	438	29	-	-	PUNCT
ejpam-4570	438	30	almost	almost	ADV
ejpam-4570	438	31	normal	normal	ADJ
ejpam-4570	438	32	.	.	PUNCT
ejpam-4570	439	1	therefore	therefore	ADV
ejpam-4570	439	2	,	,	PUNCT
ejpam-4570	439	3	(	(	PUNCT
ejpam-4570	439	4	r	r	NOUN
ejpam-4570	439	5	,	,	PUNCT
ejpam-4570	439	6	tp	tp	NOUN
ejpam-4570	439	7	)	)	PUNCT
ejpam-4570	439	8	is	be	AUX
ejpam-4570	439	9	an	an	DET
ejpam-4570	439	10	example	example	NOUN
ejpam-4570	439	11	of	of	ADP
ejpam-4570	439	12	a	a	DET
ejpam-4570	439	13	c	c	NOUN
ejpam-4570	439	14	-	-	PUNCT
ejpam-4570	439	15	almost	almost	ADV
ejpam-4570	439	16	normal	normal	ADJ
ejpam-4570	439	17	and	and	CCONJ
ejpam-4570	439	18	l	l	NOUN
ejpam-4570	439	19	-	-	ADJ
ejpam-4570	439	20	almost	almost	ADV
ejpam-4570	439	21	normal	normal	ADJ
ejpam-4570	439	22	space	space	NOUN
ejpam-4570	439	23	,	,	PUNCT
ejpam-4570	439	24	which	which	PRON
ejpam-4570	439	25	is	be	AUX
ejpam-4570	439	26	neither	neither	PRON
ejpam-4570	439	27	c	c	NOUN
ejpam-4570	439	28	-	-	ADJ
ejpam-4570	439	29	regular	regular	ADJ
ejpam-4570	439	30	nor	nor	CCONJ
ejpam-4570	439	31	c	c	NOUN
ejpam-4570	439	32	-	-	ADJ
ejpam-4570	439	33	normal	normal	ADJ
ejpam-4570	439	34	.	.	PUNCT
ejpam-4570	440	1	note	note	VERB
ejpam-4570	440	2	that	that	SCONJ
ejpam-4570	440	3	:	:	PUNCT
ejpam-4570	440	4	c	c	X
ejpam-4570	440	5	-	-	PUNCT
ejpam-4570	440	6	almost	almost	ADV
ejpam-4570	440	7	normality	normality	NOUN
ejpam-4570	440	8	(	(	PUNCT
ejpam-4570	440	9	resp	resp	NOUN
ejpam-4570	440	10	.	.	PUNCT
ejpam-4570	441	1	l	l	NOUN
ejpam-4570	441	2	-	-	PUNCT
ejpam-4570	441	3	almost	almost	ADV
ejpam-4570	441	4	normality	normality	NOUN
ejpam-4570	441	5	)	)	PUNCT
ejpam-4570	441	6	does	do	AUX
ejpam-4570	441	7	not	not	PART
ejpam-4570	441	8	imply	imply	VERB
ejpam-4570	441	9	to	to	ADP
ejpam-4570	441	10	c	c	VERB
ejpam-4570	441	11	-	-	PUNCT
ejpam-4570	441	12	almost	almost	ADV
ejpam-4570	441	13	regularity	regularity	NOUN
ejpam-4570	441	14	.	.	PUNCT
ejpam-4570	442	1	here	here	ADV
ejpam-4570	442	2	is	be	AUX
ejpam-4570	442	3	a	a	DET
ejpam-4570	442	4	counterexample	counterexample	NOUN
ejpam-4570	442	5	.	.	PUNCT
ejpam-4570	442	6	example	example	NOUN
ejpam-4570	443	1	2	2	NUM
ejpam-4570	443	2	.	.	PUNCT
ejpam-4570	444	1	the	the	DET
ejpam-4570	444	2	excluded	exclude	VERB
ejpam-4570	444	3	point	point	NOUN
ejpam-4570	444	4	topology	topology	NOUN
ejpam-4570	444	5	[	[	X
ejpam-4570	444	6	29	29	NUM
ejpam-4570	444	7	,	,	PUNCT
ejpam-4570	444	8	example	example	NOUN
ejpam-4570	444	9	15	15	NUM
ejpam-4570	444	10	]	]	PUNCT
ejpam-4570	444	11	,	,	PUNCT
ejpam-4570	444	12	let	let	VERB
ejpam-4570	444	13	x	x	PRON
ejpam-4570	444	14	be	be	AUX
ejpam-4570	444	15	an	an	DET
ejpam-4570	444	16	uncountable	uncountable	ADJ
ejpam-4570	444	17	set	set	NOUN
ejpam-4570	444	18	and	and	CCONJ
ejpam-4570	444	19	p	p	NOUN
ejpam-4570	444	20	∈	∈	PROPN
ejpam-4570	444	21	x	x	PART
ejpam-4570	444	22	be	be	AUX
ejpam-4570	444	23	fixed	fix	VERB
ejpam-4570	444	24	.	.	PUNCT
ejpam-4570	445	1	the	the	DET
ejpam-4570	445	2	excluded	exclude	VERB
ejpam-4570	445	3	point	point	NOUN
ejpam-4570	445	4	topology	topology	NOUN
ejpam-4570	445	5	on	on	ADP
ejpam-4570	445	6	x	x	PUNCT
ejpam-4570	445	7	is	be	AUX
ejpam-4570	445	8	denoted	denote	VERB
ejpam-4570	445	9	by	by	ADP
ejpam-4570	445	10	ep	ep	PROPN
ejpam-4570	445	11	and	and	CCONJ
ejpam-4570	445	12	defined	define	VERB
ejpam-4570	445	13	as	as	ADP
ejpam-4570	445	14	:	:	PUNCT
ejpam-4570	445	15	u	u	PROPN
ejpam-4570	445	16	∈	∈	PROPN
ejpam-4570	445	17	ep	ep	PROPN
ejpam-4570	445	18	⇐	⇐	PROPN
ejpam-4570	445	19	⇒	⇒	PROPN
ejpam-4570	445	20	u	u	NOUN
ejpam-4570	445	21	=	=	PUNCT
ejpam-4570	445	22	x	x	SYM
ejpam-4570	445	23	∨	∨	PROPN
ejpam-4570	445	24	p	p	X
ejpam-4570	445	25	̸∈	̸∈	PROPN
ejpam-4570	445	26	u	u	PROPN
ejpam-4570	445	27	.	.	PUNCT
ejpam-4570	446	1	then	then	ADV
ejpam-4570	446	2	,	,	PUNCT
ejpam-4570	446	3	(	(	PUNCT
ejpam-4570	446	4	x	x	X
ejpam-4570	446	5	,	,	PUNCT
ejpam-4570	446	6	ep	ep	PROPN
ejpam-4570	446	7	)	)	PUNCT
ejpam-4570	446	8	is	be	AUX
ejpam-4570	446	9	a	a	DET
ejpam-4570	446	10	topological	topological	ADJ
ejpam-4570	446	11	space	space	NOUN
ejpam-4570	446	12	,	,	PUNCT
ejpam-4570	446	13	which	which	PRON
ejpam-4570	446	14	is	be	AUX
ejpam-4570	446	15	a	a	DET
ejpam-4570	446	16	t0	t0	NOUN
ejpam-4570	446	17	,	,	PUNCT
ejpam-4570	446	18	compact	compact	ADJ
ejpam-4570	446	19	,	,	PUNCT
ejpam-4570	446	20	first	first	ADV
ejpam-4570	446	21	countable	countable	ADJ
ejpam-4570	446	22	,	,	PUNCT
ejpam-4570	446	23	paracompact	paracompact	ADJ
ejpam-4570	446	24	and	and	CCONJ
ejpam-4570	446	25	normal	normal	ADJ
ejpam-4570	446	26	space	space	NOUN
ejpam-4570	446	27	,	,	PUNCT
ejpam-4570	446	28	and	and	CCONJ
ejpam-4570	446	29	it	it	PRON
ejpam-4570	446	30	is	be	AUX
ejpam-4570	446	31	neither	neither	CCONJ
ejpam-4570	446	32	t1	t1	NOUN
ejpam-4570	446	33	,	,	PUNCT
ejpam-4570	446	34	regular	regular	ADJ
ejpam-4570	446	35	nor	nor	CCONJ
ejpam-4570	446	36	semi	semi	ADV
ejpam-4570	446	37	regular	regular	ADJ
ejpam-4570	446	38	[	[	X
ejpam-4570	446	39	29	29	NUM
ejpam-4570	446	40	]	]	PUNCT
ejpam-4570	446	41	.	.	PUNCT
ejpam-4570	447	1	since	since	SCONJ
ejpam-4570	447	2	the	the	DET
ejpam-4570	447	3	only	only	ADJ
ejpam-4570	447	4	open	open	ADJ
ejpam-4570	447	5	set	set	NOUN
ejpam-4570	447	6	containing	contain	VERB
ejpam-4570	447	7	p	p	NOUN
ejpam-4570	447	8	is	be	AUX
ejpam-4570	447	9	x	x	X
ejpam-4570	447	10	itself	itself	PRON
ejpam-4570	447	11	,	,	PUNCT
ejpam-4570	447	12	any	any	DET
ejpam-4570	447	13	closed	closed	ADJ
ejpam-4570	447	14	domain	domain	NOUN
ejpam-4570	447	15	set	set	VERB
ejpam-4570	447	16	in	in	ADP
ejpam-4570	447	17	x	x	PART
ejpam-4570	447	18	contains	contain	VERB
ejpam-4570	447	19	p	p	NOUN
ejpam-4570	447	20	and	and	CCONJ
ejpam-4570	447	21	any	any	DET
ejpam-4570	447	22	singleton	singleton	NOUN
ejpam-4570	447	23	{	{	PUNCT
ejpam-4570	447	24	x	x	NOUN
ejpam-4570	447	25	}	}	PUNCT
ejpam-4570	447	26	,	,	PUNCT
ejpam-4570	447	27	where	where	SCONJ
ejpam-4570	447	28	x	x	X
ejpam-4570	447	29	̸=	̸=	PROPN
ejpam-4570	447	30	p	p	NOUN
ejpam-4570	447	31	,	,	PUNCT
ejpam-4570	447	32	is	be	AUX
ejpam-4570	447	33	open	open	ADJ
ejpam-4570	447	34	.	.	PUNCT
ejpam-4570	448	1	thus	thus	ADV
ejpam-4570	448	2	,	,	PUNCT
ejpam-4570	448	3	any	any	DET
ejpam-4570	448	4	closed	closed	ADJ
ejpam-4570	448	5	domain	domain	NOUN
ejpam-4570	448	6	set	set	VERB
ejpam-4570	448	7	f	f	PROPN
ejpam-4570	448	8	in	in	ADP
ejpam-4570	448	9	x	x	PUNCT
ejpam-4570	448	10	such	such	ADJ
ejpam-4570	448	11	that	that	SCONJ
ejpam-4570	448	12	x	x	SYM
ejpam-4570	448	13	̸∈	̸∈	PROPN
ejpam-4570	448	14	f	f	PROPN
ejpam-4570	448	15	,	,	PUNCT
ejpam-4570	448	16	we	we	PRON
ejpam-4570	448	17	obtain	obtain	VERB
ejpam-4570	448	18	:	:	PUNCT
ejpam-4570	448	19	x	x	X
ejpam-4570	448	20	and	and	CCONJ
ejpam-4570	448	21	f	f	PROPN
ejpam-4570	448	22	can	can	AUX
ejpam-4570	448	23	not	not	PART
ejpam-4570	448	24	be	be	AUX
ejpam-4570	448	25	separated	separate	VERB
ejpam-4570	448	26	.	.	PUNCT
ejpam-4570	449	1	hence	hence	ADV
ejpam-4570	449	2	,	,	PUNCT
ejpam-4570	449	3	x	x	PRON
ejpam-4570	449	4	is	be	AUX
ejpam-4570	449	5	neither	neither	CCONJ
ejpam-4570	449	6	almost	almost	ADV
ejpam-4570	449	7	regular	regular	ADJ
ejpam-4570	449	8	nor	nor	CCONJ
ejpam-4570	449	9	almost	almost	ADV
ejpam-4570	449	10	completely	completely	ADV
ejpam-4570	449	11	regular	regular	ADJ
ejpam-4570	449	12	.	.	PUNCT
ejpam-4570	450	1	since	since	SCONJ
ejpam-4570	450	2	x	x	PRON
ejpam-4570	450	3	is	be	AUX
ejpam-4570	450	4	compact	compact	ADJ
ejpam-4570	450	5	lindelöf	lindelöf	NOUN
ejpam-4570	450	6	normal	normal	ADJ
ejpam-4570	450	7	space	space	NOUN
ejpam-4570	450	8	,	,	PUNCT
ejpam-4570	450	9	which	which	PRON
ejpam-4570	450	10	is	be	AUX
ejpam-4570	450	11	neither	neither	CCONJ
ejpam-4570	450	12	almost	almost	ADV
ejpam-4570	450	13	regular	regular	ADJ
ejpam-4570	450	14	nor	nor	CCONJ
ejpam-4570	450	15	almost	almost	ADV
ejpam-4570	450	16	completely	completely	ADV
ejpam-4570	450	17	regular	regular	ADJ
ejpam-4570	450	18	,	,	PUNCT
ejpam-4570	450	19	the	the	DET
ejpam-4570	450	20	space	space	NOUN
ejpam-4570	450	21	x	x	PUNCT
ejpam-4570	450	22	is	be	AUX
ejpam-4570	450	23	c	c	NOUN
ejpam-4570	450	24	-	-	PUNCT
ejpam-4570	450	25	almost	almost	ADV
ejpam-4570	450	26	normal	normal	ADJ
ejpam-4570	450	27	and	and	CCONJ
ejpam-4570	450	28	l	l	NOUN
ejpam-4570	450	29	-	-	ADJ
ejpam-4570	450	30	almost	almost	ADV
ejpam-4570	450	31	normal	normal	ADJ
ejpam-4570	450	32	space	space	NOUN
ejpam-4570	450	33	,	,	PUNCT
ejpam-4570	450	34	which	which	PRON
ejpam-4570	450	35	is	be	AUX
ejpam-4570	450	36	neither	neither	CCONJ
ejpam-4570	450	37	c	c	NOUN
ejpam-4570	450	38	-	-	PUNCT
ejpam-4570	450	39	almost	almost	ADV
ejpam-4570	450	40	regular	regular	ADJ
ejpam-4570	450	41	,	,	PUNCT
ejpam-4570	450	42	l	l	NOUN
ejpam-4570	450	43	-	-	PUNCT
ejpam-4570	450	44	almost	almost	ADV
ejpam-4570	450	45	regular	regular	ADJ
ejpam-4570	450	46	,	,	PUNCT
ejpam-4570	450	47	c	c	X
ejpam-4570	450	48	-	-	PUNCT
ejpam-4570	450	49	almost	almost	ADV
ejpam-4570	450	50	completely	completely	ADV
ejpam-4570	450	51	regular	regular	ADJ
ejpam-4570	450	52	nor	nor	CCONJ
ejpam-4570	450	53	l	l	NOUN
ejpam-4570	450	54	-	-	PUNCT
ejpam-4570	450	55	almost	almost	ADV
ejpam-4570	450	56	completely	completely	ADV
ejpam-4570	450	57	regular	regular	ADJ
ejpam-4570	450	58	[	[	X
ejpam-4570	450	59	3	3	NUM
ejpam-4570	450	60	]	]	PUNCT
ejpam-4570	450	61	.	.	PUNCT
ejpam-4570	451	1	since	since	SCONJ
ejpam-4570	451	2	x	x	PRON
ejpam-4570	451	3	is	be	AUX
ejpam-4570	451	4	not	not	PART
ejpam-4570	451	5	t1	t1	ADJ
ejpam-4570	451	6	,	,	PUNCT
ejpam-4570	451	7	we	we	PRON
ejpam-4570	451	8	obtain	obtain	VERB
ejpam-4570	451	9	:	:	PUNCT
ejpam-4570	451	10	x	x	X
ejpam-4570	451	11	is	be	AUX
ejpam-4570	451	12	neither	neither	CCONJ
ejpam-4570	451	13	epi	epi	NOUN
ejpam-4570	451	14	-	-	ADJ
ejpam-4570	451	15	almost	almost	ADV
ejpam-4570	451	16	regular	regular	ADJ
ejpam-4570	451	17	nor	nor	CCONJ
ejpam-4570	451	18	epi	epi	NOUN
ejpam-4570	451	19	-	-	ADJ
ejpam-4570	451	20	almost	almost	ADV
ejpam-4570	451	21	normal	normal	ADJ
ejpam-4570	451	22	.	.	PUNCT
ejpam-4570	452	1	therefore	therefore	ADV
ejpam-4570	452	2	,	,	PUNCT
ejpam-4570	452	3	the	the	DET
ejpam-4570	452	4	space	space	NOUN
ejpam-4570	452	5	(	(	PUNCT
ejpam-4570	452	6	x	x	X
ejpam-4570	452	7	,	,	PUNCT
ejpam-4570	452	8	ep	ep	PROPN
ejpam-4570	452	9	)	)	PUNCT
ejpam-4570	452	10	is	be	AUX
ejpam-4570	452	11	an	an	DET
ejpam-4570	452	12	example	example	NOUN
ejpam-4570	452	13	of	of	ADP
ejpam-4570	452	14	a	a	DET
ejpam-4570	452	15	lindelöf	lindelöf	NOUN
ejpam-4570	452	16	c	c	NOUN
ejpam-4570	452	17	-	-	PUNCT
ejpam-4570	452	18	almost	almost	ADV
ejpam-4570	452	19	normal	normal	ADJ
ejpam-4570	452	20	and	and	CCONJ
ejpam-4570	452	21	l	l	NOUN
ejpam-4570	452	22	-	-	ADJ
ejpam-4570	452	23	almost	almost	ADV
ejpam-4570	452	24	normal	normal	ADJ
ejpam-4570	452	25	space	space	NOUN
ejpam-4570	452	26	,	,	PUNCT
ejpam-4570	452	27	which	which	PRON
ejpam-4570	452	28	is	be	AUX
ejpam-4570	452	29	neither	neither	CCONJ
ejpam-4570	452	30	c	c	NOUN
ejpam-4570	452	31	-	-	PUNCT
ejpam-4570	452	32	almost	almost	ADV
ejpam-4570	452	33	regular	regular	ADJ
ejpam-4570	452	34	,	,	PUNCT
ejpam-4570	452	35	c	c	NOUN
ejpam-4570	452	36	-	-	ADJ
ejpam-4570	452	37	regular	regular	ADJ
ejpam-4570	452	38	,	,	PUNCT
ejpam-4570	452	39	c	c	NOUN
ejpam-4570	452	40	-	-	PUNCT
ejpam-4570	452	41	completely	completely	ADV
ejpam-4570	452	42	regular	regular	ADJ
ejpam-4570	452	43	,	,	PUNCT
ejpam-4570	452	44	epi	epi	NOUN
ejpam-4570	452	45	-	-	PUNCT
ejpam-4570	452	46	almost	almost	ADV
ejpam-4570	452	47	regular	regular	ADJ
ejpam-4570	452	48	nor	nor	CCONJ
ejpam-4570	452	49	epi	epi	NOUN
ejpam-4570	452	50	-	-	ADJ
ejpam-4570	452	51	almost	almost	ADV
ejpam-4570	452	52	normal	normal	ADJ
ejpam-4570	452	53	.	.	PUNCT
ejpam-4570	453	1	example	example	NOUN
ejpam-4570	454	1	3	3	NUM
ejpam-4570	454	2	.	.	PUNCT
ejpam-4570	455	1	the	the	DET
ejpam-4570	455	2	finite	finite	PROPN
ejpam-4570	455	3	complement	complement	NOUN
ejpam-4570	455	4	topology	topology	NOUN
ejpam-4570	455	5	[	[	X
ejpam-4570	455	6	29	29	NUM
ejpam-4570	455	7	,	,	PUNCT
ejpam-4570	455	8	example	example	NOUN
ejpam-4570	455	9	19	19	NUM
ejpam-4570	455	10	]	]	PUNCT
ejpam-4570	455	11	,	,	PUNCT
ejpam-4570	455	12	(	(	PUNCT
ejpam-4570	455	13	r	r	NOUN
ejpam-4570	455	14	,	,	PUNCT
ejpam-4570	455	15	cf	cf	NOUN
ejpam-4570	455	16	)	)	PUNCT
ejpam-4570	455	17	is	be	AUX
ejpam-4570	455	18	a	a	DET
ejpam-4570	455	19	t1	t1	ADJ
ejpam-4570	455	20	-	-	ADJ
ejpam-4570	455	21	compact	compact	ADJ
ejpam-4570	455	22	space	space	NOUN
ejpam-4570	455	23	and	and	CCONJ
ejpam-4570	455	24	every	every	DET
ejpam-4570	455	25	subspace	subspace	NOUN
ejpam-4570	455	26	of	of	ADP
ejpam-4570	455	27	(	(	PUNCT
ejpam-4570	455	28	r	r	NOUN
ejpam-4570	455	29	,	,	PUNCT
ejpam-4570	455	30	cf	cf	NOUN
ejpam-4570	455	31	)	)	PUNCT
ejpam-4570	455	32	is	be	AUX
ejpam-4570	455	33	compact	compact	ADJ
ejpam-4570	455	34	[	[	X
ejpam-4570	455	35	29	29	NUM
ejpam-4570	455	36	]	]	PUNCT
ejpam-4570	455	37	.	.	PUNCT
ejpam-4570	456	1	note	note	VERB
ejpam-4570	456	2	that	that	SCONJ
ejpam-4570	456	3	:	:	PUNCT
ejpam-4570	456	4	(	(	PUNCT
ejpam-4570	456	5	r	r	NOUN
ejpam-4570	456	6	,	,	PUNCT
ejpam-4570	456	7	cf	cf	NOUN
ejpam-4570	456	8	)	)	PUNCT
ejpam-4570	456	9	is	be	AUX
ejpam-4570	456	10	not	not	PART
ejpam-4570	456	11	a	a	DET
ejpam-4570	456	12	c	c	NOUN
ejpam-4570	456	13	-	-	PUNCT
ejpam-4570	456	14	regular	regular	ADJ
ejpam-4570	456	15	space	space	NOUN
ejpam-4570	456	16	[	[	X
ejpam-4570	456	17	8	8	NUM
ejpam-4570	456	18	]	]	PUNCT
ejpam-4570	456	19	.	.	PUNCT
ejpam-4570	457	1	hence	hence	ADV
ejpam-4570	457	2	,	,	PUNCT
ejpam-4570	457	3	it	it	PRON
ejpam-4570	457	4	is	be	AUX
ejpam-4570	457	5	not	not	PART
ejpam-4570	457	6	c	c	NOUN
ejpam-4570	457	7	-	-	PUNCT
ejpam-4570	457	8	tychonoff	tychonoff	NOUN
ejpam-4570	457	9	.	.	PUNCT
ejpam-4570	458	1	since	since	SCONJ
ejpam-4570	458	2	(	(	PUNCT
ejpam-4570	458	3	r	r	NOUN
ejpam-4570	458	4	,	,	PUNCT
ejpam-4570	458	5	cf	cf	NOUN
ejpam-4570	458	6	)	)	PUNCT
ejpam-4570	458	7	is	be	AUX
ejpam-4570	458	8	an	an	DET
ejpam-4570	458	9	almost	almost	ADV
ejpam-4570	458	10	normal	normal	ADJ
ejpam-4570	458	11	space	space	NOUN
ejpam-4570	458	12	,	,	PUNCT
ejpam-4570	458	13	we	we	PRON
ejpam-4570	458	14	get	get	VERB
ejpam-4570	458	15	(	(	PUNCT
ejpam-4570	458	16	r	r	NOUN
ejpam-4570	458	17	,	,	PUNCT
ejpam-4570	458	18	cf	cf	NOUN
ejpam-4570	458	19	)	)	PUNCT
ejpam-4570	458	20	is	be	AUX
ejpam-4570	458	21	both	both	PRON
ejpam-4570	458	22	c	c	NOUN
ejpam-4570	458	23	-	-	PUNCT
ejpam-4570	458	24	almost	almost	ADV
ejpam-4570	458	25	normal	normal	ADJ
ejpam-4570	458	26	and	and	CCONJ
ejpam-4570	458	27	l	l	NOUN
ejpam-4570	458	28	-	-	PUNCT
ejpam-4570	458	29	almost	almost	ADV
ejpam-4570	458	30	normal	normal	ADJ
ejpam-4570	458	31	.	.	PUNCT
ejpam-4570	459	1	therefore	therefore	ADV
ejpam-4570	459	2	,	,	PUNCT
ejpam-4570	459	3	(	(	PUNCT
ejpam-4570	459	4	r	r	NOUN
ejpam-4570	459	5	,	,	PUNCT
ejpam-4570	459	6	cf	cf	NOUN
ejpam-4570	459	7	)	)	PUNCT
ejpam-4570	459	8	is	be	AUX
ejpam-4570	459	9	an	an	DET
ejpam-4570	459	10	example	example	NOUN
ejpam-4570	459	11	of	of	ADP
ejpam-4570	459	12	a	a	DET
ejpam-4570	459	13	c	c	NOUN
ejpam-4570	459	14	-	-	PUNCT
ejpam-4570	459	15	almost	almost	ADV
ejpam-4570	459	16	normal	normal	ADJ
ejpam-4570	459	17	and	and	CCONJ
ejpam-4570	459	18	l	l	NOUN
ejpam-4570	459	19	-	-	ADJ
ejpam-4570	459	20	almost	almost	ADV
ejpam-4570	459	21	normal	normal	ADJ
ejpam-4570	459	22	space	space	NOUN
ejpam-4570	459	23	,	,	PUNCT
ejpam-4570	459	24	which	which	PRON
ejpam-4570	459	25	is	be	AUX
ejpam-4570	459	26	neither	neither	CCONJ
ejpam-4570	459	27	c	c	NOUN
ejpam-4570	459	28	-	-	ADJ
ejpam-4570	459	29	normal	normal	ADJ
ejpam-4570	459	30	,	,	PUNCT
ejpam-4570	459	31	c	c	NOUN
ejpam-4570	459	32	-	-	PUNCT
ejpam-4570	459	33	regular	regular	ADJ
ejpam-4570	459	34	nor	nor	CCONJ
ejpam-4570	459	35	epi	epi	NOUN
ejpam-4570	459	36	-	-	ADJ
ejpam-4570	459	37	almost	almost	ADV
ejpam-4570	459	38	normal	normal	ADJ
ejpam-4570	459	39	.	.	PUNCT
ejpam-4570	460	1	example	example	NOUN
ejpam-4570	460	2	4	4	NUM
ejpam-4570	460	3	.	.	PUNCT
ejpam-4570	461	1	the	the	DET
ejpam-4570	461	2	countable	countable	ADJ
ejpam-4570	461	3	complement	complement	NOUN
ejpam-4570	461	4	topology	topology	NOUN
ejpam-4570	461	5	[	[	X
ejpam-4570	461	6	29	29	NUM
ejpam-4570	461	7	,	,	PUNCT
ejpam-4570	461	8	example	example	NOUN
ejpam-4570	461	9	20	20	NUM
ejpam-4570	461	10	]	]	PUNCT
ejpam-4570	461	11	,	,	PUNCT
ejpam-4570	461	12	(	(	PUNCT
ejpam-4570	461	13	r	r	NOUN
ejpam-4570	461	14	,	,	PUNCT
ejpam-4570	461	15	cc	cc	NOUN
ejpam-4570	461	16	)	)	PUNCT
ejpam-4570	461	17	is	be	AUX
ejpam-4570	461	18	a	a	DET
ejpam-4570	461	19	c	c	NOUN
ejpam-4570	461	20	-	-	PUNCT
ejpam-4570	461	21	regular	regular	ADJ
ejpam-4570	461	22	space	space	NOUN
ejpam-4570	461	23	that	that	PRON
ejpam-4570	461	24	is	be	AUX
ejpam-4570	461	25	not	not	PART
ejpam-4570	461	26	l	l	NOUN
ejpam-4570	461	27	-	-	ADJ
ejpam-4570	461	28	regular	regular	ADJ
ejpam-4570	461	29	[	[	X
ejpam-4570	461	30	8	8	NUM
ejpam-4570	461	31	]	]	PUNCT
ejpam-4570	461	32	.	.	PUNCT
ejpam-4570	462	1	since	since	SCONJ
ejpam-4570	462	2	(	(	PUNCT
ejpam-4570	462	3	r	r	NOUN
ejpam-4570	462	4	,	,	PUNCT
ejpam-4570	462	5	cc	cc	NOUN
ejpam-4570	462	6	)	)	PUNCT
ejpam-4570	462	7	is	be	AUX
ejpam-4570	462	8	an	an	DET
ejpam-4570	462	9	almost	almost	ADV
ejpam-4570	462	10	normal	normal	ADJ
ejpam-4570	462	11	space	space	NOUN
ejpam-4570	462	12	,	,	PUNCT
ejpam-4570	462	13	we	we	PRON
ejpam-4570	462	14	have	have	AUX
ejpam-4570	462	15	(	(	PUNCT
ejpam-4570	462	16	r	r	NOUN
ejpam-4570	462	17	,	,	PUNCT
ejpam-4570	462	18	cc	cc	NOUN
ejpam-4570	462	19	)	)	PUNCT
ejpam-4570	462	20	is	be	AUX
ejpam-4570	462	21	both	both	PRON
ejpam-4570	462	22	c	c	NOUN
ejpam-4570	462	23	-	-	PUNCT
ejpam-4570	462	24	almost	almost	ADV
ejpam-4570	462	25	normal	normal	ADJ
ejpam-4570	462	26	and	and	CCONJ
ejpam-4570	462	27	l	l	NOUN
ejpam-4570	462	28	-	-	PUNCT
ejpam-4570	462	29	almost	almost	ADV
ejpam-4570	462	30	normal	normal	ADJ
ejpam-4570	462	31	.	.	PUNCT
ejpam-4570	463	1	therefore	therefore	ADV
ejpam-4570	463	2	,	,	PUNCT
ejpam-4570	463	3	(	(	PUNCT
ejpam-4570	463	4	r	r	NOUN
ejpam-4570	463	5	,	,	PUNCT
ejpam-4570	463	6	cc	cc	NOUN
ejpam-4570	463	7	)	)	PUNCT
ejpam-4570	463	8	is	be	AUX
ejpam-4570	463	9	an	an	DET
ejpam-4570	463	10	example	example	NOUN
ejpam-4570	463	11	of	of	ADP
ejpam-4570	463	12	a	a	DET
ejpam-4570	463	13	c	c	NOUN
ejpam-4570	463	14	-	-	PUNCT
ejpam-4570	463	15	almost	almost	ADV
ejpam-4570	463	16	normal	normal	ADJ
ejpam-4570	463	17	and	and	CCONJ
ejpam-4570	463	18	l	l	NOUN
ejpam-4570	463	19	-	-	ADJ
ejpam-4570	463	20	almost	almost	ADV
ejpam-4570	463	21	normal	normal	ADJ
ejpam-4570	463	22	space	space	NOUN
ejpam-4570	463	23	,	,	PUNCT
ejpam-4570	463	24	which	which	PRON
ejpam-4570	463	25	is	be	AUX
ejpam-4570	463	26	neither	neither	CCONJ
ejpam-4570	463	27	l	l	NOUN
ejpam-4570	463	28	-	-	ADJ
ejpam-4570	463	29	regular	regular	ADJ
ejpam-4570	463	30	,	,	PUNCT
ejpam-4570	463	31	l	l	NOUN
ejpam-4570	463	32	-	-	NOUN
ejpam-4570	463	33	tychonoff	tychonoff	NOUN
ejpam-4570	463	34	,	,	PUNCT
ejpam-4570	463	35	l	l	NOUN
ejpam-4570	463	36	-	-	ADJ
ejpam-4570	463	37	normal	normal	ADJ
ejpam-4570	463	38	,	,	PUNCT
ejpam-4570	463	39	normal	normal	ADJ
ejpam-4570	463	40	,	,	PUNCT
ejpam-4570	463	41	regular	regular	ADJ
ejpam-4570	463	42	,	,	PUNCT
ejpam-4570	463	43	epi	epi	NOUN
ejpam-4570	463	44	-	-	NOUN
ejpam-4570	463	45	regular	regular	ADJ
ejpam-4570	463	46	nor	nor	CCONJ
ejpam-4570	463	47	epi	epi	NOUN
ejpam-4570	463	48	-	-	ADJ
ejpam-4570	463	49	almost	almost	ADV
ejpam-4570	463	50	normal	normal	ADJ
ejpam-4570	463	51	.	.	PUNCT
ejpam-4570	464	1	the	the	DET
ejpam-4570	464	2	following	following	ADJ
ejpam-4570	464	3	example	example	NOUN
ejpam-4570	464	4	is	be	AUX
ejpam-4570	464	5	a	a	DET
ejpam-4570	464	6	tychonoff	tychonoff	NOUN
ejpam-4570	464	7	c	c	NOUN
ejpam-4570	464	8	-	-	PUNCT
ejpam-4570	464	9	almost	almost	ADV
ejpam-4570	464	10	normal	normal	ADJ
ejpam-4570	464	11	space	space	NOUN
ejpam-4570	464	12	,	,	PUNCT
ejpam-4570	464	13	which	which	PRON
ejpam-4570	464	14	is	be	AUX
ejpam-4570	464	15	not	not	PART
ejpam-4570	464	16	locally	locally	ADV
ejpam-4570	464	17	compact	compact	ADJ
ejpam-4570	464	18	:	:	PUNCT
ejpam-4570	464	19	wafa	wafa	PROPN
ejpam-4570	464	20	khalaf	khalaf	PROPN
ejpam-4570	464	21	alqurashi	alqurashi	PROPN
ejpam-4570	464	22	,	,	PUNCT
ejpam-4570	464	23	sadeq	sadeq	PROPN
ejpam-4570	464	24	ali	ali	PROPN
ejpam-4570	464	25	thabit	thabit	PROPN
ejpam-4570	464	26	/	/	SYM
ejpam-4570	464	27	eur	eur	PROPN
ejpam-4570	464	28	.	.	PUNCT
ejpam-4570	465	1	j.	j.	PROPN
ejpam-4570	465	2	pure	pure	PROPN
ejpam-4570	465	3	appl	appl	PROPN
ejpam-4570	465	4	.	.	PROPN
ejpam-4570	465	5	math	math	PROPN
ejpam-4570	465	6	,	,	PUNCT
ejpam-4570	465	7	15	15	NUM
ejpam-4570	465	8	(	(	PUNCT
ejpam-4570	465	9	4	4	NUM
ejpam-4570	465	10	)	)	PUNCT
ejpam-4570	465	11	(	(	PUNCT
ejpam-4570	465	12	2022	2022	NUM
ejpam-4570	465	13	)	)	PUNCT
ejpam-4570	465	14	,	,	PUNCT
ejpam-4570	465	15	1760	1760	NUM
ejpam-4570	465	16	-	-	SYM
ejpam-4570	465	17	1782	1782	NUM
ejpam-4570	465	18	1774	1774	NUM
ejpam-4570	465	19	example	example	NOUN
ejpam-4570	465	20	5	5	NUM
ejpam-4570	465	21	.	.	PUNCT
ejpam-4570	466	1	the	the	DET
ejpam-4570	466	2	dieudonné	dieudonné	NOUN
ejpam-4570	466	3	plank	plank	NOUN
ejpam-4570	466	4	topology	topology	NOUN
ejpam-4570	466	5	[	[	X
ejpam-4570	466	6	29	29	NUM
ejpam-4570	466	7	,	,	PUNCT
ejpam-4570	466	8	example	example	NOUN
ejpam-4570	466	9	89	89	NUM
ejpam-4570	466	10	]	]	PUNCT
ejpam-4570	466	11	,	,	PUNCT
ejpam-4570	466	12	is	be	AUX
ejpam-4570	466	13	a	a	DET
ejpam-4570	466	14	c	c	NOUN
ejpam-4570	466	15	-	-	ADJ
ejpam-4570	466	16	normal	normal	ADJ
ejpam-4570	466	17	space	space	NOUN
ejpam-4570	466	18	[	[	X
ejpam-4570	466	19	10	10	NUM
ejpam-4570	466	20	]	]	PUNCT
ejpam-4570	466	21	.	.	PUNCT
ejpam-4570	467	1	hence	hence	ADV
ejpam-4570	467	2	,	,	PUNCT
ejpam-4570	467	3	it	it	PRON
ejpam-4570	467	4	is	be	AUX
ejpam-4570	467	5	c	c	NOUN
ejpam-4570	467	6	-	-	PUNCT
ejpam-4570	467	7	almost	almost	ADV
ejpam-4570	467	8	normal	normal	ADJ
ejpam-4570	467	9	.	.	PUNCT
ejpam-4570	468	1	it	it	PRON
ejpam-4570	468	2	is	be	AUX
ejpam-4570	468	3	well	well	ADV
ejpam-4570	468	4	-	-	PUNCT
ejpam-4570	468	5	known	know	VERB
ejpam-4570	468	6	that	that	SCONJ
ejpam-4570	468	7	the	the	DET
ejpam-4570	468	8	dieudonné	dieudonné	NOUN
ejpam-4570	468	9	plank	plank	NOUN
ejpam-4570	468	10	is	be	AUX
ejpam-4570	468	11	a	a	DET
ejpam-4570	468	12	tychonoff	tychonoff	NOUN
ejpam-4570	468	13	non	non	ADJ
ejpam-4570	468	14	-	-	ADJ
ejpam-4570	468	15	normal	normal	ADJ
ejpam-4570	468	16	space	space	NOUN
ejpam-4570	468	17	,	,	PUNCT
ejpam-4570	468	18	which	which	PRON
ejpam-4570	468	19	is	be	AUX
ejpam-4570	468	20	not	not	PART
ejpam-4570	468	21	locally	locally	ADV
ejpam-4570	468	22	compact	compact	ADJ
ejpam-4570	468	23	[	[	X
ejpam-4570	468	24	29	29	NUM
ejpam-4570	468	25	]	]	PUNCT
ejpam-4570	468	26	.	.	PUNCT
ejpam-4570	469	1	therefore	therefore	ADV
ejpam-4570	469	2	,	,	PUNCT
ejpam-4570	469	3	the	the	DET
ejpam-4570	469	4	dieudonné	dieudonné	NOUN
ejpam-4570	469	5	plank	plank	NOUN
ejpam-4570	469	6	topology	topology	NOUN
ejpam-4570	469	7	is	be	AUX
ejpam-4570	469	8	an	an	DET
ejpam-4570	469	9	example	example	NOUN
ejpam-4570	469	10	of	of	ADP
ejpam-4570	469	11	a	a	DET
ejpam-4570	469	12	c	c	NOUN
ejpam-4570	469	13	-	-	PUNCT
ejpam-4570	469	14	almost	almost	ADV
ejpam-4570	469	15	normal	normal	ADJ
ejpam-4570	469	16	tychonoff	tychonoff	NOUN
ejpam-4570	469	17	space	space	NOUN
ejpam-4570	469	18	,	,	PUNCT
ejpam-4570	469	19	which	which	PRON
ejpam-4570	469	20	is	be	AUX
ejpam-4570	469	21	neither	neither	CCONJ
ejpam-4570	469	22	locally	locally	ADV
ejpam-4570	469	23	compact	compact	ADJ
ejpam-4570	469	24	nor	nor	CCONJ
ejpam-4570	469	25	normal	normal	ADJ
ejpam-4570	469	26	.	.	PUNCT
ejpam-4570	469	27	example	example	NOUN
ejpam-4570	470	1	6	6	NUM
ejpam-4570	470	2	.	.	PUNCT
ejpam-4570	471	1	the	the	DET
ejpam-4570	471	2	deleted	delete	VERB
ejpam-4570	471	3	tychonoff	tychonoff	NOUN
ejpam-4570	471	4	plank	plank	NOUN
ejpam-4570	471	5	[	[	X
ejpam-4570	471	6	29	29	NUM
ejpam-4570	471	7	,	,	PUNCT
ejpam-4570	471	8	example	example	NOUN
ejpam-4570	471	9	87	87	NUM
ejpam-4570	471	10	]	]	PUNCT
ejpam-4570	471	11	,	,	PUNCT
ejpam-4570	471	12	is	be	AUX
ejpam-4570	471	13	a	a	DET
ejpam-4570	471	14	hausdorff	hausdorff	NOUN
ejpam-4570	471	15	locally	locally	ADV
ejpam-4570	471	16	compact	compact	ADJ
ejpam-4570	471	17	space	space	NOUN
ejpam-4570	471	18	.	.	PUNCT
ejpam-4570	472	1	by	by	ADP
ejpam-4570	472	2	corollary	corollary	ADJ
ejpam-4570	472	3	4	4	NUM
ejpam-4570	472	4	,	,	PUNCT
ejpam-4570	472	5	the	the	DET
ejpam-4570	472	6	deleted	delete	VERB
ejpam-4570	472	7	tychonoff	tychonoff	NOUN
ejpam-4570	472	8	plank	plank	NOUN
ejpam-4570	472	9	is	be	AUX
ejpam-4570	472	10	c	c	NOUN
ejpam-4570	472	11	-	-	PUNCT
ejpam-4570	472	12	almost	almost	ADV
ejpam-4570	472	13	normal	normal	ADJ
ejpam-4570	472	14	.	.	PUNCT
ejpam-4570	473	1	it	it	PRON
ejpam-4570	473	2	is	be	AUX
ejpam-4570	473	3	well	well	ADV
ejpam-4570	473	4	-	-	PUNCT
ejpam-4570	473	5	known	know	VERB
ejpam-4570	473	6	that	that	SCONJ
ejpam-4570	473	7	the	the	DET
ejpam-4570	473	8	deleted	delete	VERB
ejpam-4570	473	9	tychonoff	tychonoff	NOUN
ejpam-4570	473	10	plank	plank	NOUN
ejpam-4570	473	11	is	be	AUX
ejpam-4570	473	12	neither	neither	CCONJ
ejpam-4570	473	13	almost	almost	ADV
ejpam-4570	473	14	-	-	PUNCT
ejpam-4570	473	15	normal	normal	ADJ
ejpam-4570	473	16	nor	nor	CCONJ
ejpam-4570	473	17	sub	sub	ADJ
ejpam-4570	473	18	-	-	ADJ
ejpam-4570	473	19	metrizable	metrizable	ADJ
ejpam-4570	473	20	[	[	X
ejpam-4570	473	21	8	8	NUM
ejpam-4570	473	22	,	,	PUNCT
ejpam-4570	473	23	10	10	NUM
ejpam-4570	473	24	]	]	PUNCT
ejpam-4570	473	25	.	.	PUNCT
ejpam-4570	474	1	therefore	therefore	ADV
ejpam-4570	474	2	,	,	PUNCT
ejpam-4570	474	3	the	the	DET
ejpam-4570	474	4	deleted	delete	VERB
ejpam-4570	474	5	tychonoff	tychonoff	NOUN
ejpam-4570	474	6	plank	plank	NOUN
ejpam-4570	474	7	topology	topology	NOUN
ejpam-4570	474	8	is	be	AUX
ejpam-4570	474	9	an	an	DET
ejpam-4570	474	10	example	example	NOUN
ejpam-4570	474	11	of	of	ADP
ejpam-4570	474	12	a	a	DET
ejpam-4570	474	13	c	c	NOUN
ejpam-4570	474	14	-	-	PUNCT
ejpam-4570	474	15	almost	almost	ADV
ejpam-4570	474	16	normal	normal	ADJ
ejpam-4570	474	17	tychonoff	tychonoff	NOUN
ejpam-4570	474	18	space	space	NOUN
ejpam-4570	474	19	,	,	PUNCT
ejpam-4570	474	20	which	which	PRON
ejpam-4570	474	21	is	be	AUX
ejpam-4570	474	22	neither	neither	DET
ejpam-4570	474	23	sub	sub	NOUN
ejpam-4570	474	24	-	-	ADJ
ejpam-4570	474	25	metrizable	metrizable	ADJ
ejpam-4570	474	26	nor	nor	CCONJ
ejpam-4570	474	27	almost	almost	ADV
ejpam-4570	474	28	normal	normal	ADJ
ejpam-4570	474	29	.	.	PUNCT
ejpam-4570	474	30	example	example	NOUN
ejpam-4570	475	1	7	7	NUM
ejpam-4570	475	2	.	.	PUNCT
ejpam-4570	476	1	the	the	DET
ejpam-4570	476	2	left	left	ADJ
ejpam-4570	476	3	ray	ray	NOUN
ejpam-4570	476	4	topology	topology	NOUN
ejpam-4570	476	5	(	(	PUNCT
ejpam-4570	476	6	r	r	NOUN
ejpam-4570	476	7	,	,	PUNCT
ejpam-4570	476	8	l	l	NOUN
ejpam-4570	476	9	)	)	PUNCT
ejpam-4570	476	10	and	and	CCONJ
ejpam-4570	476	11	the	the	DET
ejpam-4570	476	12	right	right	ADJ
ejpam-4570	476	13	ray	ray	NOUN
ejpam-4570	476	14	topology	topology	NOUN
ejpam-4570	476	15	(	(	PUNCT
ejpam-4570	476	16	r	r	NOUN
ejpam-4570	476	17	,	,	PUNCT
ejpam-4570	476	18	r	r	NOUN
ejpam-4570	476	19	)	)	PUNCT
ejpam-4570	476	20	are	be	AUX
ejpam-4570	476	21	almost	almost	ADV
ejpam-4570	476	22	normal	normal	ADJ
ejpam-4570	476	23	spaces	space	NOUN
ejpam-4570	476	24	because	because	SCONJ
ejpam-4570	476	25	they	they	PRON
ejpam-4570	476	26	are	be	AUX
ejpam-4570	476	27	normal	normal	ADJ
ejpam-4570	476	28	.	.	PUNCT
ejpam-4570	477	1	thus	thus	ADV
ejpam-4570	477	2	,	,	PUNCT
ejpam-4570	477	3	(	(	PUNCT
ejpam-4570	477	4	r	r	NOUN
ejpam-4570	477	5	,	,	PUNCT
ejpam-4570	477	6	l	l	NOUN
ejpam-4570	477	7	)	)	PUNCT
ejpam-4570	477	8	and	and	CCONJ
ejpam-4570	477	9	(	(	PUNCT
ejpam-4570	477	10	r	r	NOUN
ejpam-4570	477	11	,	,	PUNCT
ejpam-4570	477	12	r	r	NOUN
ejpam-4570	477	13	)	)	PUNCT
ejpam-4570	477	14	are	be	AUX
ejpam-4570	477	15	c	c	NOUN
ejpam-4570	477	16	-	-	PUNCT
ejpam-4570	477	17	almost	almost	ADV
ejpam-4570	477	18	normal	normal	ADJ
ejpam-4570	477	19	and	and	CCONJ
ejpam-4570	477	20	l	l	NOUN
ejpam-4570	477	21	-	-	ADJ
ejpam-4570	477	22	almost	almost	ADV
ejpam-4570	477	23	normal	normal	ADJ
ejpam-4570	477	24	spaces	space	NOUN
ejpam-4570	477	25	,	,	PUNCT
ejpam-4570	477	26	which	which	PRON
ejpam-4570	477	27	are	be	AUX
ejpam-4570	477	28	neither	neither	CCONJ
ejpam-4570	477	29	c	c	NOUN
ejpam-4570	477	30	-	-	ADJ
ejpam-4570	477	31	regular	regular	ADJ
ejpam-4570	477	32	nor	nor	CCONJ
ejpam-4570	477	33	epi	epi	NOUN
ejpam-4570	477	34	-	-	ADJ
ejpam-4570	477	35	almost	almost	ADV
ejpam-4570	477	36	normal	normal	ADJ
ejpam-4570	477	37	[	[	X
ejpam-4570	477	38	7	7	NUM
ejpam-4570	477	39	]	]	PUNCT
ejpam-4570	477	40	.	.	PUNCT
ejpam-4570	478	1	example	example	NOUN
ejpam-4570	478	2	8	8	NUM
ejpam-4570	478	3	.	.	PUNCT
ejpam-4570	479	1	the	the	DET
ejpam-4570	479	2	modified	modified	ADJ
ejpam-4570	479	3	dieudonné	dieudonné	NOUN
ejpam-4570	479	4	plank	plank	NOUN
ejpam-4570	479	5	[	[	X
ejpam-4570	479	6	16	16	NUM
ejpam-4570	479	7	,	,	PUNCT
ejpam-4570	479	8	example	example	NOUN
ejpam-4570	479	9	2.2	2.2	NUM
ejpam-4570	479	10	]	]	PUNCT
ejpam-4570	479	11	,	,	PUNCT
ejpam-4570	479	12	is	be	AUX
ejpam-4570	479	13	an	an	DET
ejpam-4570	479	14	l	l	ADJ
ejpam-4570	479	15	-	-	ADJ
ejpam-4570	479	16	normal	normal	ADJ
ejpam-4570	479	17	space	space	NOUN
ejpam-4570	479	18	which	which	PRON
ejpam-4570	479	19	is	be	AUX
ejpam-4570	479	20	not	not	PART
ejpam-4570	479	21	mildly	mildly	ADV
ejpam-4570	479	22	normal	normal	ADJ
ejpam-4570	479	23	.	.	PUNCT
ejpam-4570	480	1	hence	hence	ADV
ejpam-4570	480	2	,	,	PUNCT
ejpam-4570	480	3	the	the	DET
ejpam-4570	480	4	modified	modify	VERB
ejpam-4570	480	5	dieudonné	dieudonné	NOUN
ejpam-4570	480	6	plank	plank	NOUN
ejpam-4570	480	7	is	be	AUX
ejpam-4570	480	8	an	an	DET
ejpam-4570	480	9	l	l	NOUN
ejpam-4570	480	10	-	-	ADJ
ejpam-4570	480	11	almost	almost	ADV
ejpam-4570	480	12	normal	normal	ADJ
ejpam-4570	480	13	and	and	CCONJ
ejpam-4570	480	14	c	c	NOUN
ejpam-4570	480	15	-	-	PUNCT
ejpam-4570	480	16	almost	almost	ADV
ejpam-4570	480	17	normal	normal	ADJ
ejpam-4570	480	18	space	space	NOUN
ejpam-4570	480	19	,	,	PUNCT
ejpam-4570	480	20	which	which	PRON
ejpam-4570	480	21	is	be	AUX
ejpam-4570	480	22	not	not	PART
ejpam-4570	480	23	almost	almost	ADV
ejpam-4570	480	24	normal	normal	ADJ
ejpam-4570	480	25	.	.	PUNCT
ejpam-4570	481	1	the	the	DET
ejpam-4570	481	2	following	following	ADJ
ejpam-4570	481	3	example	example	NOUN
ejpam-4570	481	4	is	be	AUX
ejpam-4570	481	5	an	an	DET
ejpam-4570	481	6	l	l	NOUN
ejpam-4570	481	7	-	-	ADJ
ejpam-4570	481	8	quasi	quasi	ADJ
ejpam-4570	481	9	normal	normal	ADJ
ejpam-4570	481	10	space	space	NOUN
ejpam-4570	481	11	,	,	PUNCT
ejpam-4570	481	12	which	which	PRON
ejpam-4570	481	13	is	be	AUX
ejpam-4570	481	14	neither	neither	CCONJ
ejpam-4570	481	15	l	l	NOUN
ejpam-4570	481	16	-	-	ADJ
ejpam-4570	481	17	almost	almost	ADV
ejpam-4570	481	18	normal	normal	ADJ
ejpam-4570	481	19	,	,	PUNCT
ejpam-4570	481	20	almost	almost	ADV
ejpam-4570	481	21	normal	normal	ADJ
ejpam-4570	481	22	nor	nor	CCONJ
ejpam-4570	481	23	l	l	NOUN
ejpam-4570	481	24	-	-	NOUN
ejpam-4570	481	25	tychonoff	tychonoff	NOUN
ejpam-4570	481	26	.	.	PUNCT
ejpam-4570	481	27	example	example	NOUN
ejpam-4570	482	1	9	9	NUM
ejpam-4570	482	2	.	.	PUNCT
ejpam-4570	483	1	the	the	DET
ejpam-4570	483	2	smirnov	smirnov	PROPN
ejpam-4570	483	3	’s	’s	PART
ejpam-4570	483	4	deleted	delete	VERB
ejpam-4570	483	5	sequence	sequence	NOUN
ejpam-4570	483	6	topology	topology	NOUN
ejpam-4570	483	7	[	[	X
ejpam-4570	483	8	29	29	NUM
ejpam-4570	483	9	,	,	PUNCT
ejpam-4570	483	10	example	example	NOUN
ejpam-4570	483	11	64	64	NUM
ejpam-4570	483	12	]	]	PUNCT
ejpam-4570	483	13	,	,	PUNCT
ejpam-4570	483	14	is	be	AUX
ejpam-4570	483	15	a	a	DET
ejpam-4570	483	16	urysohn	urysohn	NOUN
ejpam-4570	483	17	,	,	PUNCT
ejpam-4570	483	18	lindelöf	lindelöf	NOUN
ejpam-4570	483	19	and	and	CCONJ
ejpam-4570	483	20	second	second	ADJ
ejpam-4570	483	21	countable	countable	ADJ
ejpam-4570	483	22	space	space	NOUN
ejpam-4570	483	23	,	,	PUNCT
ejpam-4570	483	24	which	which	PRON
ejpam-4570	483	25	is	be	AUX
ejpam-4570	483	26	neither	neither	CCONJ
ejpam-4570	483	27	regular	regular	ADJ
ejpam-4570	483	28	,	,	PUNCT
ejpam-4570	483	29	normal	normal	ADJ
ejpam-4570	483	30	,	,	PUNCT
ejpam-4570	483	31	semi	semi	ADV
ejpam-4570	483	32	regular	regular	ADJ
ejpam-4570	483	33	nor	nor	CCONJ
ejpam-4570	483	34	compact	compact	ADJ
ejpam-4570	483	35	[	[	X
ejpam-4570	483	36	29	29	NUM
ejpam-4570	483	37	]	]	PUNCT
ejpam-4570	483	38	.	.	PUNCT
ejpam-4570	484	1	since	since	SCONJ
ejpam-4570	484	2	u	u	PROPN
ejpam-4570	484	3	⊆	⊆	NUM
ejpam-4570	484	4	t	t	NOUN
ejpam-4570	484	5	,	,	PUNCT
ejpam-4570	484	6	we	we	PRON
ejpam-4570	484	7	get	get	VERB
ejpam-4570	484	8	:	:	PUNCT
ejpam-4570	484	9	the	the	DET
ejpam-4570	484	10	space	space	NOUN
ejpam-4570	484	11	x	x	PUNCT
ejpam-4570	484	12	is	be	AUX
ejpam-4570	484	13	sub	sub	ADJ
ejpam-4570	484	14	-	-	ADJ
ejpam-4570	484	15	metrizable	metrizable	ADJ
ejpam-4570	484	16	.	.	PUNCT
ejpam-4570	485	1	thus	thus	ADV
ejpam-4570	485	2	,	,	PUNCT
ejpam-4570	485	3	it	it	PRON
ejpam-4570	485	4	is	be	AUX
ejpam-4570	485	5	an	an	DET
ejpam-4570	485	6	epi	epi	NOUN
ejpam-4570	485	7	-	-	ADJ
ejpam-4570	485	8	almost	almost	ADV
ejpam-4570	485	9	normal	normal	ADJ
ejpam-4570	485	10	space	space	NOUN
ejpam-4570	485	11	.	.	PUNCT
ejpam-4570	486	1	hence	hence	ADV
ejpam-4570	486	2	,	,	PUNCT
ejpam-4570	486	3	it	it	PRON
ejpam-4570	486	4	is	be	AUX
ejpam-4570	486	5	a	a	DET
ejpam-4570	486	6	c	c	NOUN
ejpam-4570	486	7	-	-	PUNCT
ejpam-4570	486	8	almost	almost	ADV
ejpam-4570	486	9	normal	normal	ADJ
ejpam-4570	486	10	space	space	NOUN
ejpam-4570	486	11	.	.	PUNCT
ejpam-4570	487	1	since	since	SCONJ
ejpam-4570	487	2	the	the	DET
ejpam-4570	487	3	smirnov	smirnov	PROPN
ejpam-4570	487	4	’s	’s	PART
ejpam-4570	487	5	deleted	delete	VERB
ejpam-4570	487	6	sequence	sequence	NOUN
ejpam-4570	487	7	topology	topology	NOUN
ejpam-4570	487	8	is	be	AUX
ejpam-4570	487	9	a	a	DET
ejpam-4570	487	10	quasi	quasi	NOUN
ejpam-4570	487	11	normal	normal	ADJ
ejpam-4570	487	12	and	and	CCONJ
ejpam-4570	487	13	c	c	NOUN
ejpam-4570	487	14	-	-	PUNCT
ejpam-4570	487	15	regular	regular	ADJ
ejpam-4570	487	16	space	space	NOUN
ejpam-4570	487	17	[	[	X
ejpam-4570	487	18	8	8	NUM
ejpam-4570	487	19	,	,	PUNCT
ejpam-4570	487	20	33	33	NUM
ejpam-4570	487	21	]	]	PUNCT
ejpam-4570	487	22	,	,	PUNCT
ejpam-4570	487	23	which	which	PRON
ejpam-4570	487	24	is	be	AUX
ejpam-4570	487	25	neither	neither	CCONJ
ejpam-4570	487	26	normal	normal	ADJ
ejpam-4570	487	27	nor	nor	CCONJ
ejpam-4570	487	28	almost	almost	ADV
ejpam-4570	487	29	normal	normal	ADJ
ejpam-4570	487	30	,	,	PUNCT
ejpam-4570	487	31	we	we	PRON
ejpam-4570	487	32	obtain	obtain	VERB
ejpam-4570	487	33	that	that	SCONJ
ejpam-4570	487	34	:	:	PUNCT
ejpam-4570	487	35	the	the	DET
ejpam-4570	487	36	smirnov	smirnov	PROPN
ejpam-4570	487	37	’s	’s	PART
ejpam-4570	487	38	deleted	delete	VERB
ejpam-4570	487	39	sequence	sequence	NOUN
ejpam-4570	487	40	topology	topology	NOUN
ejpam-4570	487	41	is	be	AUX
ejpam-4570	487	42	an	an	DET
ejpam-4570	487	43	l	l	NOUN
ejpam-4570	487	44	-	-	ADJ
ejpam-4570	487	45	quasi	quasi	ADJ
ejpam-4570	487	46	normal	normal	ADJ
ejpam-4570	487	47	space	space	NOUN
ejpam-4570	487	48	,	,	PUNCT
ejpam-4570	487	49	but	but	CCONJ
ejpam-4570	487	50	it	it	PRON
ejpam-4570	487	51	is	be	AUX
ejpam-4570	487	52	neither	neither	CCONJ
ejpam-4570	487	53	l	l	NOUN
ejpam-4570	487	54	-	-	ADJ
ejpam-4570	487	55	almost	almost	ADV
ejpam-4570	487	56	normal	normal	ADJ
ejpam-4570	487	57	nor	nor	CCONJ
ejpam-4570	487	58	l	l	NOUN
ejpam-4570	487	59	-	-	NOUN
ejpam-4570	487	60	regular	regular	ADJ
ejpam-4570	487	61	.	.	PUNCT
ejpam-4570	488	1	thus	thus	ADV
ejpam-4570	488	2	,	,	PUNCT
ejpam-4570	488	3	the	the	DET
ejpam-4570	488	4	smirnov	smirnov	PROPN
ejpam-4570	488	5	’s	’s	PART
ejpam-4570	488	6	deleted	delete	VERB
ejpam-4570	488	7	sequence	sequence	NOUN
ejpam-4570	488	8	topology	topology	NOUN
ejpam-4570	488	9	is	be	AUX
ejpam-4570	488	10	an	an	DET
ejpam-4570	488	11	example	example	NOUN
ejpam-4570	488	12	of	of	ADP
ejpam-4570	488	13	an	an	DET
ejpam-4570	488	14	epi	epi	NOUN
ejpam-4570	488	15	-	-	ADJ
ejpam-4570	488	16	almost	almost	ADV
ejpam-4570	488	17	normal	normal	ADJ
ejpam-4570	488	18	,	,	PUNCT
ejpam-4570	488	19	c	c	NOUN
ejpam-4570	488	20	-	-	PUNCT
ejpam-4570	488	21	almost	almost	ADV
ejpam-4570	488	22	normal	normal	ADJ
ejpam-4570	488	23	,	,	PUNCT
ejpam-4570	488	24	c	c	NOUN
ejpam-4570	488	25	-	-	PUNCT
ejpam-4570	488	26	quasi	quasi	ADJ
ejpam-4570	488	27	normal	normal	ADJ
ejpam-4570	488	28	and	and	CCONJ
ejpam-4570	488	29	l	l	ADJ
ejpam-4570	488	30	-	-	ADJ
ejpam-4570	488	31	quasi	quasi	ADJ
ejpam-4570	488	32	normal	normal	ADJ
ejpam-4570	488	33	space	space	NOUN
ejpam-4570	488	34	,	,	PUNCT
ejpam-4570	488	35	which	which	PRON
ejpam-4570	488	36	is	be	AUX
ejpam-4570	488	37	neither	neither	CCONJ
ejpam-4570	488	38	almost	almost	ADV
ejpam-4570	488	39	normal	normal	ADJ
ejpam-4570	488	40	,	,	PUNCT
ejpam-4570	488	41	l	l	NOUN
ejpam-4570	488	42	-	-	NOUN
ejpam-4570	488	43	tychonoff	tychonoff	NOUN
ejpam-4570	488	44	nor	nor	CCONJ
ejpam-4570	488	45	l	l	NOUN
ejpam-4570	488	46	-	-	PUNCT
ejpam-4570	488	47	almost	almost	ADV
ejpam-4570	488	48	normal	normal	ADJ
ejpam-4570	488	49	.	.	PUNCT
ejpam-4570	489	1	the	the	DET
ejpam-4570	489	2	next	next	ADJ
ejpam-4570	489	3	example	example	NOUN
ejpam-4570	489	4	is	be	AUX
ejpam-4570	489	5	an	an	DET
ejpam-4570	489	6	epi	epi	NOUN
ejpam-4570	489	7	-	-	ADJ
ejpam-4570	489	8	almost	almost	ADV
ejpam-4570	489	9	normal	normal	ADJ
ejpam-4570	489	10	space	space	NOUN
ejpam-4570	489	11	,	,	PUNCT
ejpam-4570	489	12	which	which	PRON
ejpam-4570	489	13	is	be	AUX
ejpam-4570	489	14	not	not	PART
ejpam-4570	489	15	l	l	NOUN
ejpam-4570	489	16	-	-	ADJ
ejpam-4570	489	17	almost	almost	ADV
ejpam-4570	489	18	normal	normal	ADJ
ejpam-4570	489	19	.	.	PUNCT
ejpam-4570	490	1	example	example	NOUN
ejpam-4570	490	2	10	10	NUM
ejpam-4570	490	3	.	.	PUNCT
ejpam-4570	491	1	the	the	DET
ejpam-4570	491	2	countable	countable	ADJ
ejpam-4570	491	3	complement	complement	NOUN
ejpam-4570	491	4	extension	extension	NOUN
ejpam-4570	491	5	topology	topology	NOUN
ejpam-4570	491	6	[	[	X
ejpam-4570	491	7	29	29	NUM
ejpam-4570	491	8	,	,	PUNCT
ejpam-4570	491	9	example	example	NOUN
ejpam-4570	491	10	63	63	NUM
ejpam-4570	491	11	]	]	PUNCT
ejpam-4570	491	12	,	,	PUNCT
ejpam-4570	491	13	is	be	AUX
ejpam-4570	491	14	a	a	DET
ejpam-4570	491	15	hausdorff	hausdorff	NOUN
ejpam-4570	491	16	,	,	PUNCT
ejpam-4570	491	17	urysohn	urysohn	PROPN
ejpam-4570	491	18	and	and	CCONJ
ejpam-4570	491	19	lindelöf	lindelöf	NOUN
ejpam-4570	491	20	space	space	NOUN
ejpam-4570	491	21	,	,	PUNCT
ejpam-4570	491	22	which	which	PRON
ejpam-4570	491	23	is	be	AUX
ejpam-4570	491	24	neither	neither	CCONJ
ejpam-4570	491	25	regular	regular	ADJ
ejpam-4570	491	26	,	,	PUNCT
ejpam-4570	491	27	completely	completely	ADV
ejpam-4570	491	28	regular	regular	ADJ
ejpam-4570	491	29	,	,	PUNCT
ejpam-4570	491	30	normal	normal	ADJ
ejpam-4570	491	31	,	,	PUNCT
ejpam-4570	491	32	semi	semi	ADV
ejpam-4570	491	33	regular	regular	ADJ
ejpam-4570	491	34	,	,	PUNCT
ejpam-4570	491	35	compact	compact	ADJ
ejpam-4570	491	36	nor	nor	CCONJ
ejpam-4570	491	37	first	first	ADV
ejpam-4570	491	38	countable	countable	ADJ
ejpam-4570	491	39	[	[	X
ejpam-4570	491	40	29	29	NUM
ejpam-4570	491	41	]	]	PUNCT
ejpam-4570	491	42	.	.	PUNCT
ejpam-4570	492	1	since	since	SCONJ
ejpam-4570	492	2	a	a	DET
ejpam-4570	492	3	subset	subset	NOUN
ejpam-4570	492	4	a	a	PRON
ejpam-4570	492	5	of	of	ADP
ejpam-4570	492	6	x	x	NOUN
ejpam-4570	492	7	is	be	AUX
ejpam-4570	492	8	compact	compact	ADJ
ejpam-4570	492	9	if	if	SCONJ
ejpam-4570	492	10	and	and	CCONJ
ejpam-4570	492	11	only	only	ADV
ejpam-4570	492	12	if	if	SCONJ
ejpam-4570	492	13	it	it	PRON
ejpam-4570	492	14	is	be	AUX
ejpam-4570	492	15	finite	finite	ADJ
ejpam-4570	492	16	[	[	X
ejpam-4570	492	17	29	29	NUM
ejpam-4570	492	18	]	]	PUNCT
ejpam-4570	492	19	,	,	PUNCT
ejpam-4570	492	20	we	we	PRON
ejpam-4570	492	21	get	get	VERB
ejpam-4570	492	22	x	x	PUNCT
ejpam-4570	492	23	is	be	AUX
ejpam-4570	492	24	c	c	NOUN
ejpam-4570	492	25	-	-	PUNCT
ejpam-4570	492	26	almost	almost	ADV
ejpam-4570	492	27	normal	normal	ADJ
ejpam-4570	492	28	.	.	PUNCT
ejpam-4570	493	1	since	since	SCONJ
ejpam-4570	493	2	x	x	PROPN
ejpam-4570	493	3	is	be	AUX
ejpam-4570	493	4	sub	sub	ADJ
ejpam-4570	493	5	-	-	ADJ
ejpam-4570	493	6	metrizable	metrizable	ADJ
ejpam-4570	493	7	,	,	PUNCT
ejpam-4570	493	8	we	we	PRON
ejpam-4570	493	9	have	have	VERB
ejpam-4570	493	10	x	x	PROPN
ejpam-4570	493	11	is	be	AUX
ejpam-4570	493	12	epi	epi	NOUN
ejpam-4570	493	13	-	-	ADJ
ejpam-4570	493	14	almost	almost	ADV
ejpam-4570	493	15	normal	normal	ADJ
ejpam-4570	493	16	.	.	PUNCT
ejpam-4570	494	1	it	it	PRON
ejpam-4570	494	2	can	can	AUX
ejpam-4570	494	3	be	be	AUX
ejpam-4570	494	4	observed	observe	VERB
ejpam-4570	494	5	that	that	SCONJ
ejpam-4570	494	6	:	:	PUNCT
ejpam-4570	494	7	the	the	DET
ejpam-4570	494	8	space	space	NOUN
ejpam-4570	494	9	x	x	PUNCT
ejpam-4570	494	10	is	be	AUX
ejpam-4570	494	11	a	a	DET
ejpam-4570	494	12	quasi	quasi	NOUN
ejpam-4570	494	13	normal	normal	ADJ
ejpam-4570	494	14	and	and	CCONJ
ejpam-4570	494	15	almost	almost	ADV
ejpam-4570	494	16	completely	completely	ADV
ejpam-4570	494	17	regular	regular	ADJ
ejpam-4570	494	18	space	space	NOUN
ejpam-4570	494	19	,	,	PUNCT
ejpam-4570	494	20	which	which	PRON
ejpam-4570	494	21	is	be	AUX
ejpam-4570	494	22	neither	neither	CCONJ
ejpam-4570	494	23	normal	normal	ADJ
ejpam-4570	494	24	nor	nor	CCONJ
ejpam-4570	494	25	almost	almost	ADV
ejpam-4570	494	26	normal	normal	ADJ
ejpam-4570	494	27	[	[	X
ejpam-4570	494	28	30	30	NUM
ejpam-4570	494	29	]	]	PUNCT
ejpam-4570	494	30	.	.	PUNCT
ejpam-4570	495	1	thus	thus	ADV
ejpam-4570	495	2	,	,	PUNCT
ejpam-4570	495	3	x	x	PRON
ejpam-4570	495	4	is	be	AUX
ejpam-4570	495	5	an	an	DET
ejpam-4570	495	6	l	l	NOUN
ejpam-4570	495	7	-	-	PUNCT
ejpam-4570	495	8	almost	almost	ADV
ejpam-4570	495	9	completely	completely	ADV
ejpam-4570	495	10	regular	regular	ADJ
ejpam-4570	495	11	and	and	CCONJ
ejpam-4570	495	12	l	l	ADJ
ejpam-4570	495	13	-	-	ADJ
ejpam-4570	495	14	quasi	quasi	ADJ
ejpam-4570	495	15	normal	normal	ADJ
ejpam-4570	495	16	space	space	NOUN
ejpam-4570	495	17	,	,	PUNCT
ejpam-4570	495	18	but	but	CCONJ
ejpam-4570	495	19	it	it	PRON
ejpam-4570	495	20	is	be	AUX
ejpam-4570	495	21	neither	neither	CCONJ
ejpam-4570	495	22	l	l	NOUN
ejpam-4570	495	23	-	-	ADJ
ejpam-4570	495	24	almost	almost	ADV
ejpam-4570	495	25	normal	normal	ADJ
ejpam-4570	495	26	nor	nor	CCONJ
ejpam-4570	495	27	l	l	NOUN
ejpam-4570	495	28	-	-	NOUN
ejpam-4570	495	29	regular	regular	ADJ
ejpam-4570	495	30	.	.	PUNCT
ejpam-4570	496	1	so	so	ADV
ejpam-4570	496	2	,	,	PUNCT
ejpam-4570	496	3	the	the	DET
ejpam-4570	496	4	countable	countable	ADJ
ejpam-4570	496	5	complement	complement	NOUN
ejpam-4570	496	6	extension	extension	NOUN
ejpam-4570	496	7	topology	topology	NOUN
ejpam-4570	496	8	is	be	AUX
ejpam-4570	496	9	an	an	DET
ejpam-4570	496	10	example	example	NOUN
ejpam-4570	496	11	of	of	ADP
ejpam-4570	496	12	an	an	DET
ejpam-4570	496	13	epi	epi	NOUN
ejpam-4570	496	14	-	-	ADJ
ejpam-4570	496	15	almost	almost	ADV
ejpam-4570	496	16	normal	normal	ADJ
ejpam-4570	496	17	,	,	PUNCT
ejpam-4570	496	18	epi	epi	NOUN
ejpam-4570	496	19	-	-	NOUN
ejpam-4570	496	20	regular	regular	ADJ
ejpam-4570	496	21	,	,	PUNCT
ejpam-4570	496	22	l	l	NOUN
ejpam-4570	496	23	-	-	ADJ
ejpam-4570	496	24	quasi	quasi	ADJ
ejpam-4570	496	25	normal	normal	ADJ
ejpam-4570	496	26	and	and	CCONJ
ejpam-4570	496	27	epi	epi	NOUN
ejpam-4570	496	28	-	-	ADJ
ejpam-4570	496	29	completely	completely	ADV
ejpam-4570	496	30	regular	regular	ADJ
ejpam-4570	496	31	space	space	NOUN
ejpam-4570	496	32	,	,	PUNCT
ejpam-4570	496	33	which	which	PRON
ejpam-4570	496	34	is	be	AUX
ejpam-4570	496	35	neither	neither	CCONJ
ejpam-4570	496	36	l	l	NOUN
ejpam-4570	496	37	-	-	ADJ
ejpam-4570	496	38	almost	almost	ADV
ejpam-4570	496	39	normal	normal	ADJ
ejpam-4570	496	40	nor	nor	CCONJ
ejpam-4570	496	41	l	l	NOUN
ejpam-4570	496	42	-	-	ADJ
ejpam-4570	496	43	regular	regular	ADJ
ejpam-4570	496	44	.	.	PUNCT
ejpam-4570	497	1	wafa	wafa	PROPN
ejpam-4570	497	2	khalaf	khalaf	PROPN
ejpam-4570	497	3	alqurashi	alqurashi	PROPN
ejpam-4570	497	4	,	,	PUNCT
ejpam-4570	497	5	sadeq	sadeq	PROPN
ejpam-4570	497	6	ali	ali	PROPN
ejpam-4570	497	7	thabit	thabit	PROPN
ejpam-4570	497	8	/	/	SYM
ejpam-4570	497	9	eur	eur	PROPN
ejpam-4570	497	10	.	.	PUNCT
ejpam-4570	498	1	j.	j.	PROPN
ejpam-4570	498	2	pure	pure	PROPN
ejpam-4570	498	3	appl	appl	PROPN
ejpam-4570	498	4	.	.	PROPN
ejpam-4570	498	5	math	math	PROPN
ejpam-4570	498	6	,	,	PUNCT
ejpam-4570	498	7	15	15	NUM
ejpam-4570	498	8	(	(	PUNCT
ejpam-4570	498	9	4	4	NUM
ejpam-4570	498	10	)	)	PUNCT
ejpam-4570	498	11	(	(	PUNCT
ejpam-4570	498	12	2022	2022	NUM
ejpam-4570	498	13	)	)	PUNCT
ejpam-4570	498	14	,	,	PUNCT
ejpam-4570	498	15	1760	1760	NUM
ejpam-4570	498	16	-	-	SYM
ejpam-4570	498	17	1782	1782	NUM
ejpam-4570	498	18	1775	1775	NUM
ejpam-4570	498	19	the	the	DET
ejpam-4570	498	20	next	next	ADJ
ejpam-4570	498	21	example	example	NOUN
ejpam-4570	498	22	is	be	AUX
ejpam-4570	498	23	an	an	DET
ejpam-4570	498	24	epi	epi	NOUN
ejpam-4570	498	25	-	-	ADJ
ejpam-4570	498	26	quasi	quasi	ADJ
ejpam-4570	498	27	normal	normal	ADJ
ejpam-4570	498	28	and	and	CCONJ
ejpam-4570	498	29	l	l	ADJ
ejpam-4570	498	30	-	-	ADJ
ejpam-4570	498	31	quasi	quasi	ADJ
ejpam-4570	498	32	normal	normal	ADJ
ejpam-4570	498	33	space	space	NOUN
ejpam-4570	498	34	,	,	PUNCT
ejpam-4570	498	35	which	which	PRON
ejpam-4570	498	36	is	be	AUX
ejpam-4570	498	37	neither	neither	DET
ejpam-4570	498	38	epi	epi	NOUN
ejpam-4570	498	39	-	-	ADJ
ejpam-4570	498	40	almost	almost	ADV
ejpam-4570	498	41	normal	normal	ADJ
ejpam-4570	498	42	,	,	PUNCT
ejpam-4570	498	43	l	l	NOUN
ejpam-4570	498	44	-	-	PUNCT
ejpam-4570	498	45	almost	almost	ADV
ejpam-4570	498	46	normal	normal	ADJ
ejpam-4570	498	47	,	,	PUNCT
ejpam-4570	498	48	almost	almost	ADV
ejpam-4570	498	49	normal	normal	ADJ
ejpam-4570	498	50	nor	nor	CCONJ
ejpam-4570	498	51	c	c	NOUN
ejpam-4570	498	52	-	-	PUNCT
ejpam-4570	498	53	regular	regular	ADJ
ejpam-4570	498	54	.	.	PUNCT
ejpam-4570	498	55	example	example	NOUN
ejpam-4570	499	1	11	11	NUM
ejpam-4570	499	2	.	.	PUNCT
ejpam-4570	500	1	the	the	DET
ejpam-4570	500	2	simplified	simplified	ADJ
ejpam-4570	500	3	arens	arens	PROPN
ejpam-4570	500	4	square	square	ADJ
ejpam-4570	500	5	topology	topology	NOUN
ejpam-4570	500	6	[	[	X
ejpam-4570	500	7	29	29	NUM
ejpam-4570	500	8	,	,	PUNCT
ejpam-4570	500	9	example	example	NOUN
ejpam-4570	500	10	81	81	NUM
ejpam-4570	500	11	]	]	PUNCT
ejpam-4570	500	12	,	,	PUNCT
ejpam-4570	500	13	is	be	AUX
ejpam-4570	500	14	a	a	DET
ejpam-4570	500	15	hausdorff	hausdorff	NOUN
ejpam-4570	500	16	,	,	PUNCT
ejpam-4570	500	17	semi	semi	ADV
ejpam-4570	500	18	regular	regular	ADJ
ejpam-4570	500	19	,	,	PUNCT
ejpam-4570	500	20	lindelöf	lindelöf	PROPN
ejpam-4570	500	21	,	,	PUNCT
ejpam-4570	500	22	σ	σ	NOUN
ejpam-4570	500	23	-	-	ADJ
ejpam-4570	500	24	compact	compact	ADJ
ejpam-4570	500	25	,	,	PUNCT
ejpam-4570	500	26	separable	separable	ADJ
ejpam-4570	500	27	,	,	PUNCT
ejpam-4570	500	28	second	second	ADV
ejpam-4570	500	29	countable	countable	ADJ
ejpam-4570	500	30	and	and	CCONJ
ejpam-4570	500	31	first	first	ADJ
ejpam-4570	500	32	countable	countable	ADJ
ejpam-4570	500	33	space	space	NOUN
ejpam-4570	500	34	,	,	PUNCT
ejpam-4570	500	35	which	which	PRON
ejpam-4570	500	36	is	be	AUX
ejpam-4570	500	37	neither	neither	CCONJ
ejpam-4570	500	38	regular	regular	ADJ
ejpam-4570	500	39	,	,	PUNCT
ejpam-4570	500	40	completely	completely	ADV
ejpam-4570	500	41	hausdorff	hausdorff	NOUN
ejpam-4570	500	42	,	,	PUNCT
ejpam-4570	500	43	urysohn	urysohn	ADJ
ejpam-4570	500	44	,	,	PUNCT
ejpam-4570	500	45	normal	normal	ADJ
ejpam-4570	500	46	,	,	PUNCT
ejpam-4570	500	47	compact	compact	ADJ
ejpam-4570	500	48	,	,	PUNCT
ejpam-4570	500	49	paracompact	paracompact	ADJ
ejpam-4570	500	50	nor	nor	CCONJ
ejpam-4570	500	51	countably	countably	ADV
ejpam-4570	500	52	compact	compact	ADJ
ejpam-4570	500	53	[	[	X
ejpam-4570	500	54	29	29	NUM
ejpam-4570	500	55	]	]	PUNCT
ejpam-4570	500	56	.	.	PUNCT
ejpam-4570	501	1	since	since	SCONJ
ejpam-4570	501	2	x	x	PRON
ejpam-4570	501	3	is	be	AUX
ejpam-4570	501	4	a	a	DET
ejpam-4570	501	5	semi	semi	ADJ
ejpam-4570	501	6	regular	regular	ADJ
ejpam-4570	501	7	non	non	ADJ
ejpam-4570	501	8	regular	regular	ADJ
ejpam-4570	501	9	space	space	NOUN
ejpam-4570	501	10	,	,	PUNCT
ejpam-4570	501	11	we	we	PRON
ejpam-4570	501	12	get	get	VERB
ejpam-4570	501	13	:	:	PUNCT
ejpam-4570	501	14	x	x	X
ejpam-4570	501	15	is	be	AUX
ejpam-4570	501	16	not	not	PART
ejpam-4570	501	17	almost	almost	ADV
ejpam-4570	501	18	regular	regular	ADJ
ejpam-4570	501	19	.	.	PUNCT
ejpam-4570	502	1	since	since	SCONJ
ejpam-4570	502	2	x	x	PRON
ejpam-4570	502	3	is	be	AUX
ejpam-4570	502	4	a	a	DET
ejpam-4570	502	5	t1	t1	NOUN
ejpam-4570	502	6	non	non	ADJ
ejpam-4570	502	7	almost	almost	ADV
ejpam-4570	502	8	regular	regular	ADJ
ejpam-4570	502	9	space	space	NOUN
ejpam-4570	502	10	,	,	PUNCT
ejpam-4570	502	11	we	we	PRON
ejpam-4570	502	12	obtain	obtain	VERB
ejpam-4570	502	13	:	:	PUNCT
ejpam-4570	502	14	x	x	X
ejpam-4570	502	15	is	be	AUX
ejpam-4570	502	16	not	not	PART
ejpam-4570	502	17	almost	almost	ADV
ejpam-4570	502	18	normal	normal	ADJ
ejpam-4570	502	19	.	.	PUNCT
ejpam-4570	503	1	the	the	DET
ejpam-4570	503	2	simplified	simplified	ADJ
ejpam-4570	503	3	arens	arens	PROPN
ejpam-4570	503	4	square	square	ADJ
ejpam-4570	503	5	topology	topology	NOUN
ejpam-4570	503	6	is	be	AUX
ejpam-4570	503	7	an	an	DET
ejpam-4570	503	8	epi	epi	NOUN
ejpam-4570	503	9	-	-	ADJ
ejpam-4570	503	10	quasi	quasi	ADJ
ejpam-4570	503	11	normal	normal	ADJ
ejpam-4570	503	12	and	and	CCONJ
ejpam-4570	503	13	quasi	quasi	ADJ
ejpam-4570	503	14	normal	normal	ADJ
ejpam-4570	503	15	space	space	NOUN
ejpam-4570	503	16	,	,	PUNCT
ejpam-4570	503	17	which	which	PRON
ejpam-4570	503	18	is	be	AUX
ejpam-4570	503	19	not	not	PART
ejpam-4570	503	20	semi	semi	ADV
ejpam-4570	503	21	normal	normal	ADJ
ejpam-4570	503	22	[	[	X
ejpam-4570	503	23	33	33	NUM
ejpam-4570	503	24	]	]	PUNCT
ejpam-4570	503	25	.	.	PUNCT
ejpam-4570	504	1	hence	hence	ADV
ejpam-4570	504	2	,	,	PUNCT
ejpam-4570	504	3	it	it	PRON
ejpam-4570	504	4	is	be	AUX
ejpam-4570	504	5	c	c	NOUN
ejpam-4570	504	6	-	-	PUNCT
ejpam-4570	504	7	quasi	quasi	ADJ
ejpam-4570	504	8	normal	normal	ADJ
ejpam-4570	504	9	and	and	CCONJ
ejpam-4570	504	10	l	l	ADJ
ejpam-4570	504	11	-	-	ADJ
ejpam-4570	504	12	quasi	quasi	ADJ
ejpam-4570	504	13	normal	normal	ADJ
ejpam-4570	504	14	.	.	PUNCT
ejpam-4570	505	1	since	since	SCONJ
ejpam-4570	505	2	x	x	PRON
ejpam-4570	505	3	is	be	AUX
ejpam-4570	505	4	not	not	PART
ejpam-4570	505	5	urysohn	urysohn	ADJ
ejpam-4570	505	6	,	,	PUNCT
ejpam-4570	505	7	it	it	PRON
ejpam-4570	505	8	is	be	AUX
ejpam-4570	505	9	neither	neither	CCONJ
ejpam-4570	505	10	epi	epi	NOUN
ejpam-4570	505	11	-	-	ADJ
ejpam-4570	505	12	almost	almost	ADV
ejpam-4570	505	13	normal	normal	ADJ
ejpam-4570	505	14	,	,	PUNCT
ejpam-4570	505	15	epi	epi	NOUN
ejpam-4570	505	16	-	-	ADJ
ejpam-4570	505	17	regular	regular	ADJ
ejpam-4570	505	18	nor	nor	CCONJ
ejpam-4570	505	19	epi	epi	NOUN
ejpam-4570	505	20	-	-	ADJ
ejpam-4570	505	21	completely	completely	ADV
ejpam-4570	505	22	regular	regular	ADJ
ejpam-4570	505	23	.	.	PUNCT
ejpam-4570	506	1	sincex	sincex	PROPN
ejpam-4570	506	2	is	be	AUX
ejpam-4570	506	3	a	a	DET
ejpam-4570	506	4	hausdorff	hausdorff	NOUN
ejpam-4570	506	5	lindelöf	lindelöf	NOUN
ejpam-4570	506	6	first	first	ADV
ejpam-4570	506	7	countable	countable	ADJ
ejpam-4570	506	8	space	space	NOUN
ejpam-4570	506	9	that	that	PRON
ejpam-4570	506	10	is	be	AUX
ejpam-4570	506	11	not	not	PART
ejpam-4570	506	12	epi	epi	NOUN
ejpam-4570	506	13	-	-	ADJ
ejpam-4570	506	14	almost	almost	ADV
ejpam-4570	506	15	normal	normal	ADJ
ejpam-4570	506	16	,	,	PUNCT
ejpam-4570	506	17	by	by	ADP
ejpam-4570	506	18	corollary	corollary	ADJ
ejpam-4570	506	19	11	11	NUM
ejpam-4570	506	20	the	the	DET
ejpam-4570	506	21	space	space	NOUN
ejpam-4570	506	22	x	x	PUNCT
ejpam-4570	506	23	is	be	AUX
ejpam-4570	506	24	neither	neither	PRON
ejpam-4570	506	25	c	c	NOUN
ejpam-4570	506	26	-	-	ADJ
ejpam-4570	506	27	regular	regular	ADJ
ejpam-4570	506	28	,	,	PUNCT
ejpam-4570	506	29	c	c	NOUN
ejpam-4570	506	30	-	-	PUNCT
ejpam-4570	506	31	completely	completely	ADV
ejpam-4570	506	32	regular	regular	ADJ
ejpam-4570	506	33	nor	nor	CCONJ
ejpam-4570	506	34	c	c	NOUN
ejpam-4570	506	35	-	-	PUNCT
ejpam-4570	506	36	tychonoff	tychonoff	NOUN
ejpam-4570	506	37	.	.	PUNCT
ejpam-4570	507	1	since	since	SCONJ
ejpam-4570	507	2	x	x	PRON
ejpam-4570	507	3	is	be	AUX
ejpam-4570	507	4	a	a	DET
ejpam-4570	507	5	lindelöf	lindelöf	NOUN
ejpam-4570	507	6	space	space	NOUN
ejpam-4570	507	7	that	that	PRON
ejpam-4570	507	8	is	be	AUX
ejpam-4570	507	9	neither	neither	CCONJ
ejpam-4570	507	10	almost	almost	ADV
ejpam-4570	507	11	normal	normal	ADJ
ejpam-4570	507	12	nor	nor	CCONJ
ejpam-4570	507	13	almost	almost	ADV
ejpam-4570	507	14	regular	regular	ADJ
ejpam-4570	507	15	,	,	PUNCT
ejpam-4570	507	16	we	we	PRON
ejpam-4570	507	17	conclude	conclude	VERB
ejpam-4570	507	18	that	that	SCONJ
ejpam-4570	507	19	:	:	PUNCT
ejpam-4570	507	20	the	the	DET
ejpam-4570	507	21	space	space	NOUN
ejpam-4570	507	22	x	x	PUNCT
ejpam-4570	507	23	is	be	AUX
ejpam-4570	507	24	neither	neither	CCONJ
ejpam-4570	507	25	l	l	NOUN
ejpam-4570	507	26	-	-	ADJ
ejpam-4570	507	27	almost	almost	ADV
ejpam-4570	507	28	normal	normal	ADJ
ejpam-4570	507	29	,	,	PUNCT
ejpam-4570	507	30	l	l	NOUN
ejpam-4570	507	31	-	-	PUNCT
ejpam-4570	507	32	almost	almost	ADV
ejpam-4570	507	33	regular	regular	ADJ
ejpam-4570	507	34	nor	nor	CCONJ
ejpam-4570	507	35	l	l	NOUN
ejpam-4570	507	36	-	-	ADJ
ejpam-4570	507	37	completely	completely	ADV
ejpam-4570	507	38	regular	regular	ADJ
ejpam-4570	507	39	.	.	PUNCT
ejpam-4570	508	1	note	note	VERB
ejpam-4570	508	2	that	that	SCONJ
ejpam-4570	508	3	:	:	PUNCT
ejpam-4570	508	4	the	the	DET
ejpam-4570	508	5	simplified	simplify	VERB
ejpam-4570	508	6	arens	arens	PROPN
ejpam-4570	508	7	square	square	ADJ
ejpam-4570	508	8	topology	topology	NOUN
ejpam-4570	508	9	is	be	AUX
ejpam-4570	508	10	c	c	NOUN
ejpam-4570	508	11	-	-	PUNCT
ejpam-4570	508	12	almost	almost	ADV
ejpam-4570	508	13	completely	completely	ADV
ejpam-4570	508	14	regular	regular	ADJ
ejpam-4570	508	15	,	,	PUNCT
ejpam-4570	508	16	c	c	NOUN
ejpam-4570	508	17	-	-	PUNCT
ejpam-4570	508	18	almost	almost	ADV
ejpam-4570	508	19	regular	regular	ADJ
ejpam-4570	508	20	and	and	CCONJ
ejpam-4570	508	21	c	c	NOUN
ejpam-4570	508	22	-	-	PUNCT
ejpam-4570	508	23	almost	almost	ADV
ejpam-4570	508	24	normal	normal	ADJ
ejpam-4570	508	25	(	(	PUNCT
ejpam-4570	508	26	see	see	VERB
ejpam-4570	508	27	theorem	theorem	VERB
ejpam-4570	508	28	27	27	NUM
ejpam-4570	508	29	)	)	PUNCT
ejpam-4570	508	30	.	.	PUNCT
ejpam-4570	509	1	therefore	therefore	ADV
ejpam-4570	509	2	,	,	PUNCT
ejpam-4570	509	3	the	the	DET
ejpam-4570	509	4	simplified	simplified	ADJ
ejpam-4570	509	5	arens	arens	PROPN
ejpam-4570	509	6	square	square	ADJ
ejpam-4570	509	7	topology	topology	NOUN
ejpam-4570	509	8	is	be	AUX
ejpam-4570	509	9	an	an	DET
ejpam-4570	509	10	example	example	NOUN
ejpam-4570	509	11	of	of	ADP
ejpam-4570	509	12	an	an	DET
ejpam-4570	509	13	epi	epi	NOUN
ejpam-4570	509	14	-	-	ADJ
ejpam-4570	509	15	quasi	quasi	ADJ
ejpam-4570	509	16	normal	normal	ADJ
ejpam-4570	509	17	,	,	PUNCT
ejpam-4570	509	18	quasi	quasi	X
ejpam-4570	509	19	normal	normal	ADJ
ejpam-4570	509	20	,	,	PUNCT
ejpam-4570	509	21	l	l	ADJ
ejpam-4570	509	22	-	-	ADJ
ejpam-4570	509	23	quasi	quasi	ADJ
ejpam-4570	509	24	normal	normal	ADJ
ejpam-4570	509	25	,	,	PUNCT
ejpam-4570	509	26	semi	semi	ADV
ejpam-4570	509	27	regular	regular	ADJ
ejpam-4570	509	28	,	,	PUNCT
ejpam-4570	509	29	c	c	NOUN
ejpam-4570	509	30	-	-	PUNCT
ejpam-4570	509	31	quasi	quasi	ADJ
ejpam-4570	509	32	normal	normal	ADJ
ejpam-4570	509	33	,	,	PUNCT
ejpam-4570	509	34	c	c	NOUN
ejpam-4570	509	35	-	-	PUNCT
ejpam-4570	509	36	almost	almost	ADV
ejpam-4570	509	37	completely	completely	ADV
ejpam-4570	509	38	regular	regular	ADJ
ejpam-4570	509	39	and	and	CCONJ
ejpam-4570	509	40	c	c	NOUN
ejpam-4570	509	41	-	-	PUNCT
ejpam-4570	509	42	almost	almost	ADV
ejpam-4570	509	43	normal	normal	ADJ
ejpam-4570	509	44	space	space	NOUN
ejpam-4570	509	45	,	,	PUNCT
ejpam-4570	509	46	which	which	PRON
ejpam-4570	509	47	is	be	AUX
ejpam-4570	509	48	neither	neither	DET
ejpam-4570	509	49	epi	epi	NOUN
ejpam-4570	509	50	-	-	ADJ
ejpam-4570	509	51	almost	almost	ADV
ejpam-4570	509	52	normal	normal	ADJ
ejpam-4570	509	53	,	,	PUNCT
ejpam-4570	509	54	epi	epi	NOUN
ejpam-4570	509	55	-	-	NOUN
ejpam-4570	509	56	regular	regular	ADJ
ejpam-4570	509	57	,	,	PUNCT
ejpam-4570	509	58	c	c	NOUN
ejpam-4570	509	59	-	-	ADJ
ejpam-4570	509	60	regular	regular	ADJ
ejpam-4570	509	61	,	,	PUNCT
ejpam-4570	509	62	l	l	NOUN
ejpam-4570	509	63	-	-	PUNCT
ejpam-4570	509	64	almost	almost	ADV
ejpam-4570	509	65	regular	regular	ADJ
ejpam-4570	509	66	,	,	PUNCT
ejpam-4570	509	67	urysohn	urysohn	ADJ
ejpam-4570	509	68	nor	nor	CCONJ
ejpam-4570	509	69	c	c	NOUN
ejpam-4570	509	70	-	-	ADJ
ejpam-4570	509	71	normal	normal	ADJ
ejpam-4570	509	72	.	.	PUNCT
ejpam-4570	510	1	the	the	DET
ejpam-4570	510	2	following	following	ADJ
ejpam-4570	510	3	example	example	NOUN
ejpam-4570	510	4	is	be	AUX
ejpam-4570	510	5	a	a	DET
ejpam-4570	510	6	c	c	NOUN
ejpam-4570	510	7	-	-	PUNCT
ejpam-4570	510	8	almost	almost	ADV
ejpam-4570	510	9	normal	normal	ADJ
ejpam-4570	510	10	space	space	NOUN
ejpam-4570	510	11	,	,	PUNCT
ejpam-4570	510	12	which	which	PRON
ejpam-4570	510	13	is	be	AUX
ejpam-4570	510	14	neither	neither	CCONJ
ejpam-4570	510	15	l	l	NOUN
ejpam-4570	510	16	-	-	ADJ
ejpam-4570	510	17	almost	almost	ADV
ejpam-4570	510	18	normal	normal	ADJ
ejpam-4570	510	19	nor	nor	CCONJ
ejpam-4570	510	20	almost	almost	ADV
ejpam-4570	510	21	normal	normal	ADJ
ejpam-4570	510	22	.	.	PUNCT
ejpam-4570	511	1	example	example	NOUN
ejpam-4570	511	2	12	12	NUM
ejpam-4570	511	3	.	.	PUNCT
ejpam-4570	512	1	the	the	DET
ejpam-4570	512	2	irregular	irregular	ADJ
ejpam-4570	512	3	lattice	lattice	NOUN
ejpam-4570	512	4	topology	topology	NOUN
ejpam-4570	512	5	[	[	X
ejpam-4570	512	6	29	29	NUM
ejpam-4570	512	7	,	,	PUNCT
ejpam-4570	512	8	example	example	NOUN
ejpam-4570	512	9	79	79	NUM
ejpam-4570	512	10	]	]	PUNCT
ejpam-4570	512	11	,	,	PUNCT
ejpam-4570	512	12	is	be	AUX
ejpam-4570	512	13	a	a	DET
ejpam-4570	512	14	hausdorff	hausdorff	NOUN
ejpam-4570	512	15	,	,	PUNCT
ejpam-4570	512	16	urysohn	urysohn	NOUN
ejpam-4570	512	17	,	,	PUNCT
ejpam-4570	512	18	countable	countable	ADJ
ejpam-4570	512	19	,	,	PUNCT
ejpam-4570	512	20	σ	σ	NOUN
ejpam-4570	512	21	-	-	NOUN
ejpam-4570	512	22	compact	compact	ADJ
ejpam-4570	512	23	,	,	PUNCT
ejpam-4570	512	24	lindelöf	lindelöf	NOUN
ejpam-4570	512	25	and	and	CCONJ
ejpam-4570	512	26	second	second	ADJ
ejpam-4570	512	27	countable	countable	ADJ
ejpam-4570	512	28	space	space	NOUN
ejpam-4570	512	29	,	,	PUNCT
ejpam-4570	512	30	which	which	PRON
ejpam-4570	512	31	is	be	AUX
ejpam-4570	512	32	neither	neither	CCONJ
ejpam-4570	512	33	regular	regular	ADJ
ejpam-4570	512	34	,	,	PUNCT
ejpam-4570	512	35	normal	normal	ADJ
ejpam-4570	512	36	,	,	PUNCT
ejpam-4570	512	37	semi	semi	ADV
ejpam-4570	512	38	regular	regular	ADJ
ejpam-4570	512	39	,	,	PUNCT
ejpam-4570	512	40	completely	completely	ADV
ejpam-4570	512	41	regular	regular	ADJ
ejpam-4570	512	42	,	,	PUNCT
ejpam-4570	512	43	tychonoff	tychonoff	NOUN
ejpam-4570	512	44	,	,	PUNCT
ejpam-4570	512	45	compact	compact	ADJ
ejpam-4570	512	46	nor	nor	CCONJ
ejpam-4570	512	47	paracompact	paracompact	ADJ
ejpam-4570	512	48	[	[	X
ejpam-4570	512	49	29	29	NUM
ejpam-4570	512	50	]	]	PUNCT
ejpam-4570	512	51	.	.	PUNCT
ejpam-4570	513	1	since	since	SCONJ
ejpam-4570	513	2	the	the	DET
ejpam-4570	513	3	irregular	irregular	ADJ
ejpam-4570	513	4	lattice	lattice	NOUN
ejpam-4570	513	5	topology	topology	NOUN
ejpam-4570	513	6	is	be	AUX
ejpam-4570	513	7	mildly	mildly	ADV
ejpam-4570	513	8	normal	normal	ADJ
ejpam-4570	513	9	space	space	NOUN
ejpam-4570	513	10	,	,	PUNCT
ejpam-4570	513	11	which	which	PRON
ejpam-4570	513	12	is	be	AUX
ejpam-4570	513	13	not	not	PART
ejpam-4570	513	14	partially	partially	ADV
ejpam-4570	513	15	normal	normal	ADJ
ejpam-4570	513	16	[	[	X
ejpam-4570	513	17	6	6	NUM
ejpam-4570	513	18	]	]	PUNCT
ejpam-4570	513	19	,	,	PUNCT
ejpam-4570	513	20	we	we	PRON
ejpam-4570	513	21	obtain	obtain	VERB
ejpam-4570	513	22	:	:	PUNCT
ejpam-4570	513	23	it	it	PRON
ejpam-4570	513	24	is	be	AUX
ejpam-4570	513	25	an	an	DET
ejpam-4570	513	26	epi	epi	NOUN
ejpam-4570	513	27	-	-	ADJ
ejpam-4570	513	28	mildly	mildly	ADV
ejpam-4570	513	29	normal	normal	ADJ
ejpam-4570	513	30	space	space	NOUN
ejpam-4570	513	31	,	,	PUNCT
ejpam-4570	513	32	which	which	PRON
ejpam-4570	513	33	is	be	AUX
ejpam-4570	513	34	neither	neither	CCONJ
ejpam-4570	513	35	almost	almost	ADV
ejpam-4570	513	36	normal	normal	ADJ
ejpam-4570	513	37	,	,	PUNCT
ejpam-4570	513	38	epi	epi	NOUN
ejpam-4570	513	39	-	-	ADJ
ejpam-4570	513	40	almost	almost	ADV
ejpam-4570	513	41	normal	normal	ADJ
ejpam-4570	513	42	,	,	PUNCT
ejpam-4570	513	43	epi	epi	NOUN
ejpam-4570	513	44	-	-	ADJ
ejpam-4570	513	45	quasi	quasi	ADJ
ejpam-4570	513	46	normal	normal	ADJ
ejpam-4570	513	47	,	,	PUNCT
ejpam-4570	513	48	almost	almost	ADV
ejpam-4570	513	49	regular	regular	ADJ
ejpam-4570	513	50	,	,	PUNCT
ejpam-4570	513	51	almost	almost	ADV
ejpam-4570	513	52	completely	completely	ADV
ejpam-4570	513	53	regular	regular	ADJ
ejpam-4570	513	54	,	,	PUNCT
ejpam-4570	513	55	almost	almost	ADV
ejpam-4570	513	56	compact	compact	ADJ
ejpam-4570	513	57	,	,	PUNCT
ejpam-4570	513	58	nearly	nearly	ADV
ejpam-4570	513	59	paracompact	paracompact	ADJ
ejpam-4570	513	60	,	,	PUNCT
ejpam-4570	513	61	epi	epi	NOUN
ejpam-4570	513	62	-	-	NOUN
ejpam-4570	513	63	regular	regular	ADJ
ejpam-4570	513	64	nor	nor	CCONJ
ejpam-4570	513	65	h	h	NOUN
ejpam-4570	513	66	-	-	PUNCT
ejpam-4570	513	67	closed	closed	ADJ
ejpam-4570	513	68	[	[	X
ejpam-4570	513	69	33	33	NUM
ejpam-4570	513	70	]	]	PUNCT
ejpam-4570	513	71	.	.	PUNCT
ejpam-4570	514	1	since	since	SCONJ
ejpam-4570	514	2	x	x	PRON
ejpam-4570	514	3	is	be	AUX
ejpam-4570	514	4	a	a	DET
ejpam-4570	514	5	lindelöf	lindelöf	NOUN
ejpam-4570	514	6	space	space	NOUN
ejpam-4570	514	7	which	which	PRON
ejpam-4570	514	8	is	be	AUX
ejpam-4570	514	9	neither	neither	CCONJ
ejpam-4570	514	10	almost	almost	ADV
ejpam-4570	514	11	normal	normal	ADJ
ejpam-4570	514	12	nor	nor	CCONJ
ejpam-4570	514	13	almost	almost	ADV
ejpam-4570	514	14	regular	regular	ADJ
ejpam-4570	514	15	,	,	PUNCT
ejpam-4570	514	16	by	by	ADP
ejpam-4570	514	17	corollary	corollary	ADJ
ejpam-4570	514	18	7	7	NUM
ejpam-4570	514	19	we	we	PRON
ejpam-4570	514	20	get	get	VERB
ejpam-4570	514	21	x	x	PUNCT
ejpam-4570	514	22	is	be	AUX
ejpam-4570	514	23	neither	neither	CCONJ
ejpam-4570	514	24	l	l	NOUN
ejpam-4570	514	25	-	-	ADJ
ejpam-4570	514	26	almost	almost	ADV
ejpam-4570	514	27	normal	normal	ADJ
ejpam-4570	514	28	nor	nor	CCONJ
ejpam-4570	514	29	l	l	NOUN
ejpam-4570	514	30	-	-	PUNCT
ejpam-4570	514	31	almost	almost	ADV
ejpam-4570	514	32	regular	regular	ADJ
ejpam-4570	514	33	.	.	PUNCT
ejpam-4570	515	1	since	since	SCONJ
ejpam-4570	515	2	x	x	PROPN
ejpam-4570	515	3	is	be	AUX
ejpam-4570	515	4	hausdorff	hausdorff	NOUN
ejpam-4570	515	5	second	second	ADJ
ejpam-4570	515	6	countable	countable	ADJ
ejpam-4570	515	7	non	non	ADJ
ejpam-4570	515	8	epi	epi	ADJ
ejpam-4570	515	9	-	-	ADJ
ejpam-4570	515	10	regular	regular	ADJ
ejpam-4570	515	11	space	space	NOUN
ejpam-4570	515	12	,	,	PUNCT
ejpam-4570	515	13	we	we	PRON
ejpam-4570	515	14	conclude	conclude	VERB
ejpam-4570	515	15	x	x	VERB
ejpam-4570	515	16	is	be	AUX
ejpam-4570	515	17	neither	neither	CCONJ
ejpam-4570	515	18	c	c	NOUN
ejpam-4570	515	19	-	-	ADJ
ejpam-4570	515	20	regular	regular	ADJ
ejpam-4570	515	21	,	,	PUNCT
ejpam-4570	515	22	c	c	NOUN
ejpam-4570	515	23	-	-	PUNCT
ejpam-4570	515	24	completely	completely	ADV
ejpam-4570	515	25	regular	regular	ADJ
ejpam-4570	515	26	,	,	PUNCT
ejpam-4570	515	27	c	c	NOUN
ejpam-4570	515	28	-	-	ADJ
ejpam-4570	515	29	normal	normal	ADJ
ejpam-4570	515	30	nor	nor	CCONJ
ejpam-4570	515	31	c	c	NOUN
ejpam-4570	515	32	-	-	PUNCT
ejpam-4570	515	33	tychonoff	tychonoff	NOUN
ejpam-4570	515	34	[	[	X
ejpam-4570	515	35	31	31	NUM
ejpam-4570	515	36	]	]	PUNCT
ejpam-4570	515	37	.	.	PUNCT
ejpam-4570	516	1	by	by	ADP
ejpam-4570	516	2	theorem	theorem	NOUN
ejpam-4570	516	3	27	27	NUM
ejpam-4570	516	4	,	,	PUNCT
ejpam-4570	516	5	we	we	PRON
ejpam-4570	516	6	conclude	conclude	VERB
ejpam-4570	516	7	that	that	SCONJ
ejpam-4570	516	8	:	:	PUNCT
ejpam-4570	516	9	the	the	DET
ejpam-4570	516	10	irregular	irregular	ADJ
ejpam-4570	516	11	lattice	lattice	NOUN
ejpam-4570	516	12	topology	topology	NOUN
ejpam-4570	516	13	is	be	AUX
ejpam-4570	516	14	c	c	NOUN
ejpam-4570	516	15	-	-	PUNCT
ejpam-4570	516	16	almost	almost	ADV
ejpam-4570	516	17	normal	normal	ADJ
ejpam-4570	516	18	.	.	PUNCT
ejpam-4570	517	1	therefore	therefore	ADV
ejpam-4570	517	2	,	,	PUNCT
ejpam-4570	517	3	the	the	DET
ejpam-4570	517	4	irregular	irregular	ADJ
ejpam-4570	517	5	lattice	lattice	NOUN
ejpam-4570	517	6	topology	topology	NOUN
ejpam-4570	517	7	is	be	AUX
ejpam-4570	517	8	epi	epi	NOUN
ejpam-4570	517	9	-	-	ADJ
ejpam-4570	517	10	mildly	mildly	ADV
ejpam-4570	517	11	normal	normal	ADJ
ejpam-4570	517	12	,	,	PUNCT
ejpam-4570	517	13	c	c	NOUN
ejpam-4570	517	14	-	-	PUNCT
ejpam-4570	517	15	almost	almost	ADV
ejpam-4570	517	16	regular	regular	ADJ
ejpam-4570	517	17	,	,	PUNCT
ejpam-4570	517	18	c	c	X
ejpam-4570	517	19	-	-	PUNCT
ejpam-4570	517	20	almost	almost	ADV
ejpam-4570	517	21	completely	completely	ADV
ejpam-4570	517	22	regular	regular	ADJ
ejpam-4570	517	23	and	and	CCONJ
ejpam-4570	517	24	c	c	NOUN
ejpam-4570	517	25	-	-	PUNCT
ejpam-4570	517	26	almost	almost	ADV
ejpam-4570	517	27	normal	normal	ADJ
ejpam-4570	517	28	space	space	NOUN
ejpam-4570	517	29	which	which	PRON
ejpam-4570	517	30	is	be	AUX
ejpam-4570	517	31	neither	neither	CCONJ
ejpam-4570	517	32	almost	almost	ADV
ejpam-4570	517	33	normal	normal	ADJ
ejpam-4570	517	34	,	,	PUNCT
ejpam-4570	517	35	almost	almost	ADV
ejpam-4570	517	36	regular	regular	ADJ
ejpam-4570	517	37	,	,	PUNCT
ejpam-4570	517	38	c	c	NOUN
ejpam-4570	517	39	-	-	ADJ
ejpam-4570	517	40	regular	regular	ADJ
ejpam-4570	517	41	,	,	PUNCT
ejpam-4570	517	42	epi	epi	NOUN
ejpam-4570	517	43	-	-	NOUN
ejpam-4570	517	44	regular	regular	ADJ
ejpam-4570	517	45	,	,	PUNCT
ejpam-4570	517	46	epi	epi	NOUN
ejpam-4570	517	47	-	-	PUNCT
ejpam-4570	517	48	almost	almost	ADV
ejpam-4570	517	49	normal	normal	ADJ
ejpam-4570	517	50	,	,	PUNCT
ejpam-4570	517	51	c	c	NOUN
ejpam-4570	517	52	-	-	ADJ
ejpam-4570	517	53	normal	normal	ADJ
ejpam-4570	517	54	nor	nor	CCONJ
ejpam-4570	517	55	l	l	NOUN
ejpam-4570	517	56	-	-	ADJ
ejpam-4570	517	57	almost	almost	ADV
ejpam-4570	517	58	normal	normal	ADJ
ejpam-4570	517	59	.	.	PUNCT
ejpam-4570	518	1	here	here	ADV
ejpam-4570	518	2	is	be	AUX
ejpam-4570	518	3	an	an	DET
ejpam-4570	518	4	example	example	NOUN
ejpam-4570	518	5	of	of	ADP
ejpam-4570	518	6	an	an	DET
ejpam-4570	518	7	l	l	NOUN
ejpam-4570	518	8	-	-	ADJ
ejpam-4570	518	9	almost	almost	ADV
ejpam-4570	518	10	normal	normal	ADJ
ejpam-4570	518	11	space	space	NOUN
ejpam-4570	518	12	that	that	PRON
ejpam-4570	518	13	is	be	AUX
ejpam-4570	518	14	neither	neither	CCONJ
ejpam-4570	518	15	c	c	NOUN
ejpam-4570	518	16	-	-	PUNCT
ejpam-4570	518	17	almost	almost	ADV
ejpam-4570	518	18	regular	regular	ADJ
ejpam-4570	518	19	nor	nor	CCONJ
ejpam-4570	518	20	epi	epi	NOUN
ejpam-4570	518	21	-	-	ADJ
ejpam-4570	518	22	almost	almost	ADV
ejpam-4570	518	23	normal	normal	ADJ
ejpam-4570	518	24	.	.	PUNCT
ejpam-4570	519	1	example	example	NOUN
ejpam-4570	519	2	13	13	NUM
ejpam-4570	519	3	.	.	PUNCT
ejpam-4570	520	1	the	the	DET
ejpam-4570	520	2	integer	integer	NOUN
ejpam-4570	520	3	broom	broom	NOUN
ejpam-4570	520	4	topology	topology	NOUN
ejpam-4570	520	5	[	[	X
ejpam-4570	520	6	29	29	NUM
ejpam-4570	520	7	,	,	PUNCT
ejpam-4570	520	8	example	example	NOUN
ejpam-4570	520	9	121	121	NUM
ejpam-4570	520	10	]	]	PUNCT
ejpam-4570	520	11	,	,	PUNCT
ejpam-4570	520	12	is	be	AUX
ejpam-4570	520	13	a	a	DET
ejpam-4570	520	14	t0	t0	NOUN
ejpam-4570	520	15	,	,	PUNCT
ejpam-4570	520	16	normal	normal	ADJ
ejpam-4570	520	17	,	,	PUNCT
ejpam-4570	520	18	semi	semi	ADV
ejpam-4570	520	19	normal	normal	ADJ
ejpam-4570	520	20	,	,	PUNCT
ejpam-4570	520	21	compact	compact	ADJ
ejpam-4570	520	22	,	,	PUNCT
ejpam-4570	520	23	lindelöf	lindelöf	PROPN
ejpam-4570	520	24	,	,	PUNCT
ejpam-4570	520	25	separable	separable	ADJ
ejpam-4570	520	26	,	,	PUNCT
ejpam-4570	520	27	countable	countable	ADJ
ejpam-4570	520	28	and	and	CCONJ
ejpam-4570	520	29	paracompact	paracompact	ADJ
ejpam-4570	520	30	space	space	NOUN
ejpam-4570	520	31	,	,	PUNCT
ejpam-4570	520	32	which	which	PRON
ejpam-4570	520	33	is	be	AUX
ejpam-4570	520	34	neither	neither	CCONJ
ejpam-4570	520	35	t1	t1	NOUN
ejpam-4570	520	36	,	,	PUNCT
ejpam-4570	520	37	regular	regular	ADJ
ejpam-4570	520	38	,	,	PUNCT
ejpam-4570	520	39	completely	completely	ADV
ejpam-4570	520	40	regular	regular	ADJ
ejpam-4570	520	41	nor	nor	CCONJ
ejpam-4570	520	42	semi	semi	ADV
ejpam-4570	520	43	regular	regular	ADJ
ejpam-4570	520	44	[	[	X
ejpam-4570	520	45	29	29	NUM
ejpam-4570	520	46	]	]	PUNCT
ejpam-4570	520	47	.	.	PUNCT
ejpam-4570	521	1	thus	thus	ADV
ejpam-4570	521	2	,	,	PUNCT
ejpam-4570	521	3	x	x	PRON
ejpam-4570	521	4	is	be	AUX
ejpam-4570	521	5	an	an	DET
ejpam-4570	521	6	l	l	NOUN
ejpam-4570	521	7	-	-	ADJ
ejpam-4570	521	8	almost	almost	ADV
ejpam-4570	521	9	normal	normal	ADJ
ejpam-4570	521	10	space	space	NOUN
ejpam-4570	521	11	.	.	PUNCT
ejpam-4570	522	1	wafa	wafa	PROPN
ejpam-4570	522	2	khalaf	khalaf	PROPN
ejpam-4570	522	3	alqurashi	alqurashi	PROPN
ejpam-4570	522	4	,	,	PUNCT
ejpam-4570	522	5	sadeq	sadeq	PROPN
ejpam-4570	522	6	ali	ali	PROPN
ejpam-4570	522	7	thabit	thabit	PROPN
ejpam-4570	522	8	/	/	SYM
ejpam-4570	522	9	eur	eur	PROPN
ejpam-4570	522	10	.	.	PUNCT
ejpam-4570	523	1	j.	j.	PROPN
ejpam-4570	523	2	pure	pure	PROPN
ejpam-4570	523	3	appl	appl	PROPN
ejpam-4570	523	4	.	.	PROPN
ejpam-4570	523	5	math	math	PROPN
ejpam-4570	523	6	,	,	PUNCT
ejpam-4570	523	7	15	15	NUM
ejpam-4570	523	8	(	(	PUNCT
ejpam-4570	523	9	4	4	NUM
ejpam-4570	523	10	)	)	PUNCT
ejpam-4570	523	11	(	(	PUNCT
ejpam-4570	523	12	2022	2022	NUM
ejpam-4570	523	13	)	)	PUNCT
ejpam-4570	523	14	,	,	PUNCT
ejpam-4570	523	15	1760	1760	NUM
ejpam-4570	523	16	-	-	SYM
ejpam-4570	523	17	1782	1782	NUM
ejpam-4570	523	18	1776	1776	NUM
ejpam-4570	523	19	since	since	SCONJ
ejpam-4570	523	20	x	x	PRON
ejpam-4570	523	21	is	be	AUX
ejpam-4570	523	22	not	not	PART
ejpam-4570	523	23	t1	t1	ADJ
ejpam-4570	523	24	,	,	PUNCT
ejpam-4570	523	25	it	it	PRON
ejpam-4570	523	26	is	be	AUX
ejpam-4570	523	27	neither	neither	CCONJ
ejpam-4570	523	28	epi	epi	NOUN
ejpam-4570	523	29	-	-	ADJ
ejpam-4570	523	30	almost	almost	ADV
ejpam-4570	523	31	regular	regular	ADJ
ejpam-4570	523	32	nor	nor	CCONJ
ejpam-4570	523	33	epi	epi	NOUN
ejpam-4570	523	34	-	-	ADJ
ejpam-4570	523	35	almost	almost	ADV
ejpam-4570	523	36	normal	normal	ADJ
ejpam-4570	523	37	.	.	PUNCT
ejpam-4570	524	1	since	since	SCONJ
ejpam-4570	524	2	the	the	DET
ejpam-4570	524	3	only	only	ADJ
ejpam-4570	524	4	open	open	ADJ
ejpam-4570	524	5	neighborhood	neighborhood	NOUN
ejpam-4570	524	6	of	of	ADP
ejpam-4570	524	7	the	the	DET
ejpam-4570	524	8	origin	origin	NOUN
ejpam-4570	524	9	is	be	AUX
ejpam-4570	524	10	x	x	X
ejpam-4570	524	11	itself	itself	PRON
ejpam-4570	524	12	[	[	X
ejpam-4570	524	13	29	29	NUM
ejpam-4570	524	14	]	]	PUNCT
ejpam-4570	524	15	,	,	PUNCT
ejpam-4570	524	16	we	we	PRON
ejpam-4570	524	17	conclude	conclude	VERB
ejpam-4570	524	18	:	:	PUNCT
ejpam-4570	524	19	any	any	DET
ejpam-4570	524	20	non	non	ADJ
ejpam-4570	524	21	-	-	ADJ
ejpam-4570	524	22	empty	empty	ADJ
ejpam-4570	524	23	closed	closed	ADJ
ejpam-4570	524	24	domain	domain	NOUN
ejpam-4570	524	25	subset	subset	NOUN
ejpam-4570	524	26	of	of	ADP
ejpam-4570	524	27	x	x	PUNCT
ejpam-4570	524	28	contains	contain	VERB
ejpam-4570	524	29	the	the	DET
ejpam-4570	524	30	origin	origin	NOUN
ejpam-4570	524	31	.	.	PUNCT
ejpam-4570	525	1	so	so	ADV
ejpam-4570	525	2	,	,	PUNCT
ejpam-4570	525	3	if	if	SCONJ
ejpam-4570	525	4	a	a	PRON
ejpam-4570	525	5	is	be	AUX
ejpam-4570	525	6	a	a	DET
ejpam-4570	525	7	closed	closed	ADJ
ejpam-4570	525	8	domain	domain	NOUN
ejpam-4570	525	9	and	and	CCONJ
ejpam-4570	525	10	x	x	PART
ejpam-4570	525	11	̸∈	̸∈	PROPN
ejpam-4570	525	12	a	a	PROPN
ejpam-4570	525	13	,	,	PUNCT
ejpam-4570	525	14	we	we	PRON
ejpam-4570	525	15	get	get	VERB
ejpam-4570	525	16	:	:	PUNCT
ejpam-4570	525	17	x	x	X
ejpam-4570	525	18	and	and	CCONJ
ejpam-4570	525	19	a	a	PRON
ejpam-4570	525	20	can	can	AUX
ejpam-4570	525	21	not	not	PART
ejpam-4570	525	22	be	be	AUX
ejpam-4570	525	23	separated	separate	VERB
ejpam-4570	525	24	.	.	PUNCT
ejpam-4570	526	1	hence	hence	ADV
ejpam-4570	526	2	,	,	PUNCT
ejpam-4570	526	3	x	x	PRON
ejpam-4570	526	4	is	be	AUX
ejpam-4570	526	5	neither	neither	CCONJ
ejpam-4570	526	6	almost	almost	ADV
ejpam-4570	526	7	regular	regular	ADJ
ejpam-4570	526	8	nor	nor	CCONJ
ejpam-4570	526	9	almost	almost	ADV
ejpam-4570	526	10	completely	completely	ADV
ejpam-4570	526	11	regular	regular	ADJ
ejpam-4570	526	12	.	.	PUNCT
ejpam-4570	527	1	since	since	SCONJ
ejpam-4570	527	2	x	x	PRON
ejpam-4570	527	3	is	be	AUX
ejpam-4570	527	4	a	a	DET
ejpam-4570	527	5	lindelöf	lindelöf	NOUN
ejpam-4570	527	6	normal	normal	ADJ
ejpam-4570	527	7	non	non	ADJ
ejpam-4570	527	8	hausdorff	hausdorff	PROPN
ejpam-4570	527	9	space	space	NOUN
ejpam-4570	527	10	,	,	PUNCT
ejpam-4570	527	11	the	the	DET
ejpam-4570	527	12	integer	integer	NOUN
ejpam-4570	527	13	broom	broom	NOUN
ejpam-4570	527	14	topology	topology	NOUN
ejpam-4570	527	15	is	be	AUX
ejpam-4570	527	16	an	an	DET
ejpam-4570	527	17	l	l	ADJ
ejpam-4570	527	18	-	-	ADJ
ejpam-4570	527	19	normal	normal	ADJ
ejpam-4570	527	20	space	space	NOUN
ejpam-4570	527	21	,	,	PUNCT
ejpam-4570	527	22	which	which	PRON
ejpam-4570	527	23	is	be	AUX
ejpam-4570	527	24	not	not	PART
ejpam-4570	527	25	c	c	NOUN
ejpam-4570	527	26	-	-	PUNCT
ejpam-4570	527	27	almost	almost	ADV
ejpam-4570	527	28	regular	regular	ADJ
ejpam-4570	527	29	.	.	PUNCT
ejpam-4570	528	1	therefore	therefore	ADV
ejpam-4570	528	2	,	,	PUNCT
ejpam-4570	528	3	the	the	DET
ejpam-4570	528	4	integer	integer	NOUN
ejpam-4570	528	5	broom	broom	NOUN
ejpam-4570	528	6	topology	topology	NOUN
ejpam-4570	528	7	is	be	AUX
ejpam-4570	528	8	an	an	DET
ejpam-4570	528	9	example	example	NOUN
ejpam-4570	528	10	of	of	ADP
ejpam-4570	528	11	an	an	DET
ejpam-4570	528	12	l	l	NOUN
ejpam-4570	528	13	-	-	ADJ
ejpam-4570	528	14	almost	almost	ADV
ejpam-4570	528	15	normal	normal	ADJ
ejpam-4570	528	16	compact	compact	ADJ
ejpam-4570	528	17	(	(	PUNCT
ejpam-4570	528	18	lindelöf	lindelöf	PROPN
ejpam-4570	528	19	,	,	PUNCT
ejpam-4570	528	20	paracompact	paracompact	ADJ
ejpam-4570	528	21	)	)	PUNCT
ejpam-4570	528	22	space	space	NOUN
ejpam-4570	528	23	,	,	PUNCT
ejpam-4570	528	24	which	which	PRON
ejpam-4570	528	25	is	be	AUX
ejpam-4570	528	26	neither	neither	DET
ejpam-4570	528	27	epi	epi	NOUN
ejpam-4570	528	28	-	-	ADJ
ejpam-4570	528	29	almost	almost	ADV
ejpam-4570	528	30	normal	normal	ADJ
ejpam-4570	528	31	,	,	PUNCT
ejpam-4570	528	32	epi	epi	NOUN
ejpam-4570	528	33	-	-	PUNCT
ejpam-4570	528	34	almost	almost	ADV
ejpam-4570	528	35	regular	regular	ADJ
ejpam-4570	528	36	nor	nor	CCONJ
ejpam-4570	528	37	c	c	NOUN
ejpam-4570	528	38	-	-	PUNCT
ejpam-4570	528	39	almost	almost	ADV
ejpam-4570	528	40	regular	regular	ADJ
ejpam-4570	528	41	.	.	PUNCT
ejpam-4570	529	1	here	here	ADV
ejpam-4570	529	2	is	be	AUX
ejpam-4570	529	3	an	an	DET
ejpam-4570	529	4	example	example	NOUN
ejpam-4570	529	5	of	of	ADP
ejpam-4570	529	6	an	an	DET
ejpam-4570	529	7	epi	epi	NOUN
ejpam-4570	529	8	-	-	NOUN
ejpam-4570	529	9	almost	almost	ADV
ejpam-4570	529	10	completely	completely	ADV
ejpam-4570	529	11	regular	regular	ADJ
ejpam-4570	529	12	,	,	PUNCT
ejpam-4570	529	13	paracompact	paracompact	NOUN
ejpam-4570	529	14	,	,	PUNCT
ejpam-4570	529	15	lindelöf	lindelöf	NOUN
ejpam-4570	529	16	space	space	NOUN
ejpam-4570	529	17	,	,	PUNCT
ejpam-4570	529	18	which	which	PRON
ejpam-4570	529	19	is	be	AUX
ejpam-4570	529	20	neither	neither	CCONJ
ejpam-4570	529	21	c	c	NOUN
ejpam-4570	529	22	-	-	PUNCT
ejpam-4570	529	23	almost	almost	ADV
ejpam-4570	529	24	normal	normal	ADJ
ejpam-4570	529	25	nor	nor	CCONJ
ejpam-4570	529	26	c	c	NOUN
ejpam-4570	529	27	-	-	PUNCT
ejpam-4570	529	28	regular	regular	ADJ
ejpam-4570	529	29	.	.	PUNCT
ejpam-4570	529	30	example	example	NOUN
ejpam-4570	530	1	14	14	NUM
ejpam-4570	530	2	.	.	PUNCT
ejpam-4570	531	1	the	the	DET
ejpam-4570	531	2	maximal	maximal	ADJ
ejpam-4570	531	3	compact	compact	ADJ
ejpam-4570	531	4	topology	topology	NOUN
ejpam-4570	531	5	:	:	PUNCT
ejpam-4570	531	6	[	[	X
ejpam-4570	531	7	29	29	NUM
ejpam-4570	531	8	,	,	PUNCT
ejpam-4570	531	9	example	example	NOUN
ejpam-4570	531	10	99	99	NUM
ejpam-4570	531	11	]	]	PUNCT
ejpam-4570	531	12	,	,	PUNCT
ejpam-4570	531	13	is	be	AUX
ejpam-4570	531	14	a	a	DET
ejpam-4570	531	15	compact	compact	ADJ
ejpam-4570	531	16	,	,	PUNCT
ejpam-4570	531	17	t1	t1	NOUN
ejpam-4570	531	18	,	,	PUNCT
ejpam-4570	531	19	separable	separable	ADJ
ejpam-4570	531	20	,	,	PUNCT
ejpam-4570	531	21	paracompact	paracompact	ADJ
ejpam-4570	531	22	,	,	PUNCT
ejpam-4570	531	23	locally	locally	ADV
ejpam-4570	531	24	compact	compact	ADJ
ejpam-4570	531	25	and	and	CCONJ
ejpam-4570	531	26	lindelöf	lindelöf	NOUN
ejpam-4570	531	27	space	space	NOUN
ejpam-4570	531	28	,	,	PUNCT
ejpam-4570	531	29	which	which	PRON
ejpam-4570	531	30	is	be	AUX
ejpam-4570	531	31	neither	neither	DET
ejpam-4570	531	32	hausdorff	hausdorff	NOUN
ejpam-4570	531	33	,	,	PUNCT
ejpam-4570	531	34	regular	regular	ADJ
ejpam-4570	531	35	,	,	PUNCT
ejpam-4570	531	36	completely	completely	ADV
ejpam-4570	531	37	regular	regular	ADJ
ejpam-4570	531	38	,	,	PUNCT
ejpam-4570	531	39	normal	normal	ADJ
ejpam-4570	531	40	,	,	PUNCT
ejpam-4570	531	41	first	first	ADV
ejpam-4570	531	42	countable	countable	ADJ
ejpam-4570	531	43	nor	nor	CCONJ
ejpam-4570	531	44	second	second	ADJ
ejpam-4570	531	45	countable	countable	ADJ
ejpam-4570	531	46	[	[	X
ejpam-4570	531	47	29	29	NUM
ejpam-4570	531	48	]	]	PUNCT
ejpam-4570	531	49	.	.	PUNCT
ejpam-4570	532	1	x	x	PUNCT
ejpam-4570	532	2	is	be	AUX
ejpam-4570	532	3	a	a	DET
ejpam-4570	532	4	semi	semi	ADJ
ejpam-4570	532	5	normal	normal	ADJ
ejpam-4570	532	6	space	space	NOUN
ejpam-4570	532	7	,	,	PUNCT
ejpam-4570	532	8	which	which	PRON
ejpam-4570	532	9	is	be	AUX
ejpam-4570	532	10	not	not	PART
ejpam-4570	532	11	normal	normal	ADJ
ejpam-4570	532	12	[	[	X
ejpam-4570	532	13	26	26	NUM
ejpam-4570	532	14	,	,	PUNCT
ejpam-4570	532	15	example	example	NOUN
ejpam-4570	532	16	2.3	2.3	NUM
ejpam-4570	532	17	]	]	PUNCT
ejpam-4570	532	18	.	.	PUNCT
ejpam-4570	533	1	since	since	SCONJ
ejpam-4570	533	2	every	every	DET
ejpam-4570	533	3	semi	semi	ADJ
ejpam-4570	533	4	normal	normal	ADJ
ejpam-4570	533	5	mildly	mildly	ADV
ejpam-4570	533	6	normal	normal	ADJ
ejpam-4570	533	7	space	space	NOUN
ejpam-4570	533	8	is	be	AUX
ejpam-4570	533	9	normal	normal	ADJ
ejpam-4570	533	10	[	[	X
ejpam-4570	533	11	28	28	NUM
ejpam-4570	533	12	]	]	PUNCT
ejpam-4570	533	13	,	,	PUNCT
ejpam-4570	533	14	and	and	CCONJ
ejpam-4570	533	15	x	x	X
ejpam-4570	533	16	is	be	AUX
ejpam-4570	533	17	a	a	DET
ejpam-4570	533	18	semi	semi	ADJ
ejpam-4570	533	19	normal	normal	ADJ
ejpam-4570	533	20	non	non	PRON
ejpam-4570	533	21	normal	normal	ADJ
ejpam-4570	533	22	space	space	NOUN
ejpam-4570	533	23	,	,	PUNCT
ejpam-4570	533	24	we	we	PRON
ejpam-4570	533	25	obtain	obtain	VERB
ejpam-4570	533	26	:	:	PUNCT
ejpam-4570	533	27	x	x	X
ejpam-4570	533	28	is	be	AUX
ejpam-4570	533	29	not	not	PART
ejpam-4570	533	30	mildly	mildly	ADV
ejpam-4570	533	31	normal	normal	ADJ
ejpam-4570	533	32	.	.	PUNCT
ejpam-4570	534	1	hence	hence	ADV
ejpam-4570	534	2	,	,	PUNCT
ejpam-4570	534	3	x	x	PRON
ejpam-4570	534	4	is	be	AUX
ejpam-4570	534	5	not	not	PART
ejpam-4570	534	6	almost	almost	ADV
ejpam-4570	534	7	normal	normal	ADJ
ejpam-4570	534	8	.	.	PUNCT
ejpam-4570	535	1	since	since	SCONJ
ejpam-4570	535	2	x	x	PRON
ejpam-4570	535	3	is	be	AUX
ejpam-4570	535	4	a	a	DET
ejpam-4570	535	5	t1	t1	NOUN
ejpam-4570	535	6	-	-	PUNCT
ejpam-4570	535	7	semi	semi	ADJ
ejpam-4570	535	8	normal	normal	ADJ
ejpam-4570	535	9	space	space	NOUN
ejpam-4570	535	10	,	,	PUNCT
ejpam-4570	535	11	we	we	PRON
ejpam-4570	535	12	get	get	VERB
ejpam-4570	535	13	:	:	PUNCT
ejpam-4570	535	14	x	x	X
ejpam-4570	535	15	is	be	AUX
ejpam-4570	535	16	semi	semi	ADV
ejpam-4570	535	17	regular	regular	ADJ
ejpam-4570	535	18	because	because	SCONJ
ejpam-4570	535	19	every	every	DET
ejpam-4570	535	20	t1	t1	NOUN
ejpam-4570	535	21	-	-	PUNCT
ejpam-4570	535	22	semi	semi	ADJ
ejpam-4570	535	23	normal	normal	ADJ
ejpam-4570	535	24	space	space	NOUN
ejpam-4570	535	25	is	be	AUX
ejpam-4570	535	26	semi	semi	ADV
ejpam-4570	535	27	regular	regular	ADV
ejpam-4570	535	28	[	[	X
ejpam-4570	535	29	26	26	NUM
ejpam-4570	535	30	]	]	PUNCT
ejpam-4570	535	31	.	.	PUNCT
ejpam-4570	536	1	since	since	SCONJ
ejpam-4570	536	2	every	every	DET
ejpam-4570	536	3	semi	semi	ADJ
ejpam-4570	536	4	regular	regular	ADJ
ejpam-4570	536	5	almost	almost	ADV
ejpam-4570	536	6	regular	regular	ADJ
ejpam-4570	536	7	space	space	NOUN
ejpam-4570	536	8	is	be	AUX
ejpam-4570	536	9	regular	regular	ADJ
ejpam-4570	536	10	[	[	X
ejpam-4570	536	11	25	25	NUM
ejpam-4570	536	12	]	]	PUNCT
ejpam-4570	536	13	,	,	PUNCT
ejpam-4570	536	14	and	and	CCONJ
ejpam-4570	536	15	x	x	X
ejpam-4570	536	16	is	be	AUX
ejpam-4570	536	17	a	a	DET
ejpam-4570	536	18	semi	semi	ADJ
ejpam-4570	536	19	regular	regular	ADJ
ejpam-4570	536	20	non	non	ADJ
ejpam-4570	536	21	regular	regular	ADJ
ejpam-4570	536	22	space	space	NOUN
ejpam-4570	536	23	,	,	PUNCT
ejpam-4570	536	24	we	we	PRON
ejpam-4570	536	25	obtain	obtain	VERB
ejpam-4570	536	26	:	:	PUNCT
ejpam-4570	536	27	x	x	X
ejpam-4570	536	28	is	be	AUX
ejpam-4570	536	29	not	not	PART
ejpam-4570	536	30	almost	almost	ADV
ejpam-4570	536	31	regular	regular	ADJ
ejpam-4570	536	32	.	.	PUNCT
ejpam-4570	537	1	since	since	SCONJ
ejpam-4570	537	2	x	x	PRON
ejpam-4570	537	3	is	be	AUX
ejpam-4570	537	4	compact	compact	ADJ
ejpam-4570	537	5	space	space	NOUN
ejpam-4570	537	6	which	which	PRON
ejpam-4570	537	7	is	be	AUX
ejpam-4570	537	8	neither	neither	CCONJ
ejpam-4570	537	9	almost	almost	ADV
ejpam-4570	537	10	regular	regular	ADJ
ejpam-4570	537	11	,	,	PUNCT
ejpam-4570	537	12	almost	almost	ADV
ejpam-4570	537	13	normal	normal	ADJ
ejpam-4570	537	14	nor	nor	CCONJ
ejpam-4570	537	15	hausdorff	hausdorff	NOUN
ejpam-4570	537	16	,	,	PUNCT
ejpam-4570	537	17	we	we	PRON
ejpam-4570	537	18	conclude	conclude	VERB
ejpam-4570	537	19	:	:	PUNCT
ejpam-4570	537	20	x	x	X
ejpam-4570	537	21	is	be	AUX
ejpam-4570	537	22	neither	neither	CCONJ
ejpam-4570	537	23	c	c	NOUN
ejpam-4570	537	24	-	-	PUNCT
ejpam-4570	537	25	almost	almost	ADV
ejpam-4570	537	26	regular	regular	ADJ
ejpam-4570	537	27	,	,	PUNCT
ejpam-4570	537	28	c	c	NOUN
ejpam-4570	537	29	-	-	PUNCT
ejpam-4570	537	30	almost	almost	ADV
ejpam-4570	537	31	normal	normal	ADJ
ejpam-4570	537	32	,	,	PUNCT
ejpam-4570	537	33	epi	epi	NOUN
ejpam-4570	537	34	-	-	ADJ
ejpam-4570	537	35	regular	regular	ADJ
ejpam-4570	537	36	nor	nor	CCONJ
ejpam-4570	537	37	epi	epi	NOUN
ejpam-4570	537	38	-	-	ADJ
ejpam-4570	537	39	almost	almost	ADV
ejpam-4570	537	40	normal	normal	ADJ
ejpam-4570	537	41	.	.	PUNCT
ejpam-4570	538	1	therefore	therefore	ADV
ejpam-4570	538	2	,	,	PUNCT
ejpam-4570	538	3	the	the	DET
ejpam-4570	538	4	maximal	maximal	ADJ
ejpam-4570	538	5	compact	compact	ADJ
ejpam-4570	538	6	topology	topology	NOUN
ejpam-4570	538	7	is	be	AUX
ejpam-4570	538	8	an	an	DET
ejpam-4570	538	9	example	example	NOUN
ejpam-4570	538	10	of	of	ADP
ejpam-4570	538	11	an	an	DET
ejpam-4570	538	12	epi	epi	NOUN
ejpam-4570	538	13	-	-	NOUN
ejpam-4570	538	14	almost	almost	ADV
ejpam-4570	538	15	completely	completely	ADV
ejpam-4570	538	16	regular	regular	ADJ
ejpam-4570	538	17	,	,	PUNCT
ejpam-4570	538	18	paracompact	paracompact	NOUN
ejpam-4570	538	19	,	,	PUNCT
ejpam-4570	538	20	lindelöf	lindelöf	NOUN
ejpam-4570	538	21	space	space	NOUN
ejpam-4570	538	22	,	,	PUNCT
ejpam-4570	538	23	which	which	PRON
ejpam-4570	538	24	is	be	AUX
ejpam-4570	538	25	neither	neither	CCONJ
ejpam-4570	538	26	c	c	NOUN
ejpam-4570	538	27	-	-	PUNCT
ejpam-4570	538	28	almost	almost	ADV
ejpam-4570	538	29	regular	regular	ADJ
ejpam-4570	538	30	,	,	PUNCT
ejpam-4570	538	31	epi	epi	NOUN
ejpam-4570	538	32	-	-	PUNCT
ejpam-4570	538	33	almost	almost	ADV
ejpam-4570	538	34	normal	normal	ADJ
ejpam-4570	538	35	nor	nor	CCONJ
ejpam-4570	538	36	c	c	NOUN
ejpam-4570	538	37	-	-	PUNCT
ejpam-4570	538	38	almost	almost	ADV
ejpam-4570	538	39	normal	normal	ADJ
ejpam-4570	538	40	.	.	PUNCT
ejpam-4570	539	1	example	example	NOUN
ejpam-4570	540	1	15	15	NUM
ejpam-4570	540	2	.	.	PUNCT
ejpam-4570	541	1	the	the	DET
ejpam-4570	541	2	modified	modify	VERB
ejpam-4570	541	3	fort	fort	NOUN
ejpam-4570	541	4	space	space	NOUN
ejpam-4570	541	5	[	[	X
ejpam-4570	541	6	29	29	NUM
ejpam-4570	541	7	,	,	PUNCT
ejpam-4570	541	8	example	example	NOUN
ejpam-4570	541	9	27	27	NUM
ejpam-4570	541	10	]	]	PUNCT
ejpam-4570	541	11	:	:	PUNCT
ejpam-4570	541	12	let	let	VERB
ejpam-4570	541	13	x	x	SYM
ejpam-4570	541	14	=	=	SYM
ejpam-4570	541	15	n∪{x1	n∪{x1	X
ejpam-4570	541	16	,	,	PUNCT
ejpam-4570	541	17	x2	x2	PROPN
ejpam-4570	541	18	}	}	PUNCT
ejpam-4570	541	19	.	.	PUNCT
ejpam-4570	542	1	any	any	DET
ejpam-4570	542	2	subset	subset	NOUN
ejpam-4570	542	3	a	a	DET
ejpam-4570	542	4	⊆	⊆	NUM
ejpam-4570	542	5	n	n	NOUN
ejpam-4570	542	6	is	be	AUX
ejpam-4570	542	7	open	open	ADJ
ejpam-4570	542	8	.	.	PUNCT
ejpam-4570	543	1	any	any	DET
ejpam-4570	543	2	set	set	NOUN
ejpam-4570	543	3	u	u	NOUN
ejpam-4570	543	4	such	such	ADJ
ejpam-4570	543	5	that	that	SCONJ
ejpam-4570	543	6	x1	x1	PROPN
ejpam-4570	543	7	∈	∈	PROPN
ejpam-4570	543	8	u	u	NOUN
ejpam-4570	543	9	or	or	CCONJ
ejpam-4570	543	10	x2	x2	PROPN
ejpam-4570	543	11	∈	∈	PROPN
ejpam-4570	543	12	u	u	NOUN
ejpam-4570	543	13	is	be	AUX
ejpam-4570	543	14	open	open	ADJ
ejpam-4570	543	15	if	if	SCONJ
ejpam-4570	543	16	and	and	CCONJ
ejpam-4570	543	17	only	only	ADV
ejpam-4570	543	18	if	if	SCONJ
ejpam-4570	543	19	n−u	n−u	PROPN
ejpam-4570	543	20	is	be	AUX
ejpam-4570	543	21	finite	finite	ADJ
ejpam-4570	543	22	.	.	PUNCT
ejpam-4570	544	1	then	then	ADV
ejpam-4570	544	2	,	,	PUNCT
ejpam-4570	544	3	x	x	PRON
ejpam-4570	544	4	is	be	AUX
ejpam-4570	544	5	a	a	DET
ejpam-4570	544	6	t1	t1	NOUN
ejpam-4570	544	7	,	,	PUNCT
ejpam-4570	544	8	compact	compact	ADJ
ejpam-4570	544	9	and	and	CCONJ
ejpam-4570	544	10	paracompact	paracompact	ADJ
ejpam-4570	544	11	space	space	NOUN
ejpam-4570	544	12	,	,	PUNCT
ejpam-4570	544	13	which	which	PRON
ejpam-4570	544	14	is	be	AUX
ejpam-4570	544	15	neither	neither	DET
ejpam-4570	544	16	hausdorff	hausdorff	NOUN
ejpam-4570	544	17	,	,	PUNCT
ejpam-4570	544	18	regular	regular	ADJ
ejpam-4570	544	19	,	,	PUNCT
ejpam-4570	544	20	semi	semi	ADV
ejpam-4570	544	21	regular	regular	ADJ
ejpam-4570	544	22	,	,	PUNCT
ejpam-4570	544	23	normal	normal	ADJ
ejpam-4570	544	24	,	,	PUNCT
ejpam-4570	544	25	completely	completely	ADV
ejpam-4570	544	26	regular	regular	ADJ
ejpam-4570	544	27	,	,	PUNCT
ejpam-4570	544	28	separable	separable	ADJ
ejpam-4570	544	29	nor	nor	CCONJ
ejpam-4570	544	30	first	first	ADJ
ejpam-4570	544	31	countable	countable	ADJ
ejpam-4570	544	32	.	.	PUNCT
ejpam-4570	545	1	the	the	DET
ejpam-4570	545	2	closure	closure	NOUN
ejpam-4570	545	3	of	of	ADP
ejpam-4570	545	4	any	any	DET
ejpam-4570	545	5	open	open	ADJ
ejpam-4570	545	6	set	set	NOUN
ejpam-4570	545	7	u	u	NOUN
ejpam-4570	545	8	containing	contain	VERB
ejpam-4570	545	9	x1	x1	PROPN
ejpam-4570	545	10	contains	contain	VERB
ejpam-4570	545	11	x2	x2	PROPN
ejpam-4570	546	1	[	[	X
ejpam-4570	546	2	29	29	NUM
ejpam-4570	546	3	]	]	PUNCT
ejpam-4570	546	4	.	.	PUNCT
ejpam-4570	547	1	thus	thus	ADV
ejpam-4570	547	2	,	,	PUNCT
ejpam-4570	547	3	if	if	SCONJ
ejpam-4570	547	4	a	a	PRON
ejpam-4570	547	5	is	be	AUX
ejpam-4570	547	6	a	a	DET
ejpam-4570	547	7	non	non	ADJ
ejpam-4570	547	8	-	-	ADJ
ejpam-4570	547	9	empty	empty	ADJ
ejpam-4570	547	10	closed	closed	ADJ
ejpam-4570	547	11	domain	domain	NOUN
ejpam-4570	547	12	subset	subset	NOUN
ejpam-4570	547	13	of	of	ADP
ejpam-4570	547	14	x	x	SYM
ejpam-4570	547	15	such	such	ADJ
ejpam-4570	547	16	that	that	SCONJ
ejpam-4570	547	17	x1	x1	PROPN
ejpam-4570	547	18	∈	∈	PROPN
ejpam-4570	547	19	a	a	PRON
ejpam-4570	547	20	,	,	PUNCT
ejpam-4570	547	21	then	then	ADV
ejpam-4570	547	22	x2	x2	PROPN
ejpam-4570	547	23	∈	∈	PROPN
ejpam-4570	547	24	a.	a.	NOUN
ejpam-4570	548	1	so	so	ADV
ejpam-4570	548	2	,	,	PUNCT
ejpam-4570	548	3	if	if	SCONJ
ejpam-4570	548	4	a	a	PRON
ejpam-4570	548	5	is	be	AUX
ejpam-4570	548	6	a	a	DET
ejpam-4570	548	7	closed	closed	ADJ
ejpam-4570	548	8	domain	domain	NOUN
ejpam-4570	548	9	containing	contain	VERB
ejpam-4570	548	10	x1	x1	PROPN
ejpam-4570	548	11	such	such	ADJ
ejpam-4570	548	12	that	that	SCONJ
ejpam-4570	548	13	y	y	PROPN
ejpam-4570	548	14	̸∈	̸∈	PROPN
ejpam-4570	548	15	a	a	PROPN
ejpam-4570	548	16	,	,	PUNCT
ejpam-4570	548	17	where	where	SCONJ
ejpam-4570	548	18	x1	x1	ADJ
ejpam-4570	548	19	̸=	̸=	PROPN
ejpam-4570	548	20	y	y	PROPN
ejpam-4570	548	21	̸=	̸=	PROPN
ejpam-4570	548	22	x2	x2	PROPN
ejpam-4570	548	23	,	,	PUNCT
ejpam-4570	548	24	then	then	ADV
ejpam-4570	548	25	y	y	PROPN
ejpam-4570	548	26	and	and	CCONJ
ejpam-4570	548	27	a	a	PRON
ejpam-4570	548	28	can	can	AUX
ejpam-4570	548	29	be	be	AUX
ejpam-4570	548	30	separated	separate	VERB
ejpam-4570	548	31	.	.	PUNCT
ejpam-4570	549	1	hence	hence	ADV
ejpam-4570	549	2	,	,	PUNCT
ejpam-4570	549	3	the	the	DET
ejpam-4570	549	4	space	space	NOUN
ejpam-4570	549	5	x	x	PUNCT
ejpam-4570	549	6	is	be	AUX
ejpam-4570	549	7	almost	almost	ADV
ejpam-4570	549	8	regular	regular	ADJ
ejpam-4570	549	9	and	and	CCONJ
ejpam-4570	549	10	almost	almost	ADV
ejpam-4570	549	11	completely	completely	ADV
ejpam-4570	549	12	regular	regular	ADJ
ejpam-4570	549	13	.	.	PUNCT
ejpam-4570	550	1	since	since	SCONJ
ejpam-4570	550	2	x	x	PRON
ejpam-4570	550	3	is	be	AUX
ejpam-4570	550	4	not	not	PART
ejpam-4570	550	5	hausdorff	hausdorff	NOUN
ejpam-4570	550	6	,	,	PUNCT
ejpam-4570	550	7	the	the	DET
ejpam-4570	550	8	space	space	NOUN
ejpam-4570	550	9	x	x	PUNCT
ejpam-4570	550	10	is	be	AUX
ejpam-4570	550	11	not	not	PART
ejpam-4570	550	12	epi	epi	NOUN
ejpam-4570	550	13	-	-	ADJ
ejpam-4570	550	14	almost	almost	ADV
ejpam-4570	550	15	normal	normal	ADJ
ejpam-4570	550	16	.	.	PUNCT
ejpam-4570	551	1	since	since	SCONJ
ejpam-4570	551	2	x	x	PRON
ejpam-4570	551	3	is	be	AUX
ejpam-4570	551	4	compact	compact	ADJ
ejpam-4570	551	5	almost	almost	ADV
ejpam-4570	551	6	regular	regular	ADJ
ejpam-4570	551	7	,	,	PUNCT
ejpam-4570	551	8	we	we	PRON
ejpam-4570	551	9	have	have	VERB
ejpam-4570	551	10	x	x	NOUN
ejpam-4570	551	11	is	be	AUX
ejpam-4570	551	12	an	an	DET
ejpam-4570	551	13	almost	almost	ADV
ejpam-4570	551	14	normal	normal	ADJ
ejpam-4570	551	15	space	space	NOUN
ejpam-4570	551	16	which	which	PRON
ejpam-4570	551	17	is	be	AUX
ejpam-4570	551	18	not	not	PART
ejpam-4570	551	19	semi	semi	ADV
ejpam-4570	551	20	normal	normal	ADJ
ejpam-4570	551	21	.	.	PUNCT
ejpam-4570	552	1	therefore	therefore	ADV
ejpam-4570	552	2	,	,	PUNCT
ejpam-4570	552	3	the	the	DET
ejpam-4570	552	4	modified	modify	VERB
ejpam-4570	552	5	fort	fort	NOUN
ejpam-4570	552	6	space	space	NOUN
ejpam-4570	552	7	is	be	AUX
ejpam-4570	552	8	an	an	DET
ejpam-4570	552	9	l	l	NOUN
ejpam-4570	552	10	-	-	ADJ
ejpam-4570	552	11	almost	almost	ADV
ejpam-4570	552	12	normal	normal	ADJ
ejpam-4570	552	13	and	and	CCONJ
ejpam-4570	552	14	l	l	NOUN
ejpam-4570	552	15	-	-	PUNCT
ejpam-4570	552	16	almost	almost	ADV
ejpam-4570	552	17	completely	completely	ADV
ejpam-4570	552	18	regular	regular	ADJ
ejpam-4570	552	19	space	space	NOUN
ejpam-4570	552	20	.	.	PUNCT
ejpam-4570	553	1	since	since	SCONJ
ejpam-4570	553	2	x	x	PRON
ejpam-4570	553	3	is	be	AUX
ejpam-4570	553	4	a	a	DET
ejpam-4570	553	5	lindelöf	lindelöf	NOUN
ejpam-4570	553	6	space	space	NOUN
ejpam-4570	553	7	that	that	PRON
ejpam-4570	553	8	is	be	AUX
ejpam-4570	553	9	neither	neither	CCONJ
ejpam-4570	553	10	regular	regular	ADJ
ejpam-4570	553	11	,	,	PUNCT
ejpam-4570	553	12	normal	normal	ADJ
ejpam-4570	553	13	nor	nor	CCONJ
ejpam-4570	553	14	hausdorff	hausdorff	NOUN
ejpam-4570	553	15	,	,	PUNCT
ejpam-4570	553	16	the	the	DET
ejpam-4570	553	17	modified	modified	ADJ
ejpam-4570	553	18	fort	fort	NOUN
ejpam-4570	553	19	space	space	NOUN
ejpam-4570	553	20	is	be	AUX
ejpam-4570	553	21	neither	neither	PRON
ejpam-4570	553	22	c	c	NOUN
ejpam-4570	553	23	-	-	ADJ
ejpam-4570	553	24	regular	regular	ADJ
ejpam-4570	553	25	,	,	PUNCT
ejpam-4570	553	26	c	c	NOUN
ejpam-4570	553	27	-	-	PUNCT
ejpam-4570	553	28	completely	completely	ADV
ejpam-4570	553	29	regular	regular	ADJ
ejpam-4570	553	30	,	,	PUNCT
ejpam-4570	553	31	c	c	NOUN
ejpam-4570	553	32	-	-	ADJ
ejpam-4570	553	33	normal	normal	ADJ
ejpam-4570	553	34	,	,	PUNCT
ejpam-4570	553	35	c2	c2	PROPN
ejpam-4570	553	36	-	-	PUNCT
ejpam-4570	553	37	almost	almost	ADV
ejpam-4570	553	38	regular	regular	ADJ
ejpam-4570	553	39	nor	nor	CCONJ
ejpam-4570	553	40	c2	c2	PROPN
ejpam-4570	553	41	-	-	PUNCT
ejpam-4570	553	42	almost	almost	ADV
ejpam-4570	553	43	completely	completely	ADV
ejpam-4570	553	44	regular	regular	ADJ
ejpam-4570	553	45	[	[	X
ejpam-4570	553	46	31	31	NUM
ejpam-4570	553	47	]	]	PUNCT
ejpam-4570	553	48	.	.	PUNCT
ejpam-4570	554	1	hence	hence	ADV
ejpam-4570	554	2	,	,	PUNCT
ejpam-4570	554	3	it	it	PRON
ejpam-4570	554	4	is	be	AUX
ejpam-4570	554	5	an	an	DET
ejpam-4570	554	6	l	l	NOUN
ejpam-4570	554	7	-	-	ADJ
ejpam-4570	554	8	almost	almost	ADV
ejpam-4570	554	9	normal	normal	ADJ
ejpam-4570	554	10	space	space	NOUN
ejpam-4570	554	11	,	,	PUNCT
ejpam-4570	554	12	which	which	PRON
ejpam-4570	554	13	is	be	AUX
ejpam-4570	554	14	neither	neither	PRON
ejpam-4570	554	15	c	c	NOUN
ejpam-4570	554	16	-	-	ADJ
ejpam-4570	554	17	regular	regular	ADJ
ejpam-4570	554	18	,	,	PUNCT
ejpam-4570	554	19	c	c	NOUN
ejpam-4570	554	20	-	-	ADJ
ejpam-4570	554	21	normal	normal	ADJ
ejpam-4570	554	22	,	,	PUNCT
ejpam-4570	554	23	epi	epi	NOUN
ejpam-4570	554	24	-	-	PUNCT
ejpam-4570	554	25	almost	almost	ADV
ejpam-4570	554	26	normal	normal	ADJ
ejpam-4570	554	27	nor	nor	CCONJ
ejpam-4570	554	28	c2	c2	PROPN
ejpam-4570	554	29	-	-	PUNCT
ejpam-4570	554	30	almost	almost	ADV
ejpam-4570	554	31	regular	regular	ADJ
ejpam-4570	554	32	.	.	PUNCT
ejpam-4570	554	33	example	example	NOUN
ejpam-4570	555	1	16	16	NUM
ejpam-4570	555	2	.	.	PUNCT
ejpam-4570	556	1	the	the	DET
ejpam-4570	556	2	odd	odd	ADV
ejpam-4570	556	3	-	-	PUNCT
ejpam-4570	556	4	even	even	ADV
ejpam-4570	556	5	topology	topology	NOUN
ejpam-4570	556	6	[	[	X
ejpam-4570	556	7	29	29	NUM
ejpam-4570	556	8	,	,	PUNCT
ejpam-4570	556	9	example	example	NOUN
ejpam-4570	556	10	6	6	NUM
ejpam-4570	556	11	]	]	PUNCT
ejpam-4570	556	12	,	,	PUNCT
ejpam-4570	556	13	is	be	AUX
ejpam-4570	556	14	a	a	DET
ejpam-4570	556	15	regular	regular	ADJ
ejpam-4570	556	16	,	,	PUNCT
ejpam-4570	556	17	completely	completely	ADV
ejpam-4570	556	18	regular	regular	ADJ
ejpam-4570	556	19	,	,	PUNCT
ejpam-4570	556	20	normal	normal	ADJ
ejpam-4570	556	21	,	,	PUNCT
ejpam-4570	556	22	lindelöf	lindelöf	NOUN
ejpam-4570	556	23	and	and	CCONJ
ejpam-4570	556	24	locally	locally	ADV
ejpam-4570	556	25	compact	compact	ADJ
ejpam-4570	556	26	,	,	PUNCT
ejpam-4570	556	27	but	but	CCONJ
ejpam-4570	556	28	it	it	PRON
ejpam-4570	556	29	is	be	AUX
ejpam-4570	556	30	neither	neither	DET
ejpam-4570	556	31	t0	t0	NOUN
ejpam-4570	556	32	,	,	PUNCT
ejpam-4570	556	33	compact	compact	ADJ
ejpam-4570	556	34	nor	nor	CCONJ
ejpam-4570	556	35	semi	semi	ADV
ejpam-4570	556	36	regular	regular	ADJ
ejpam-4570	556	37	[	[	X
ejpam-4570	556	38	29	29	NUM
ejpam-4570	556	39	]	]	PUNCT
ejpam-4570	556	40	.	.	PUNCT
ejpam-4570	557	1	thus	thus	ADV
ejpam-4570	557	2	,	,	PUNCT
ejpam-4570	557	3	the	the	DET
ejpam-4570	557	4	odd	odd	ADV
ejpam-4570	557	5	-	-	PUNCT
ejpam-4570	557	6	even	even	ADJ
ejpam-4570	557	7	topology	topology	NOUN
ejpam-4570	557	8	is	be	AUX
ejpam-4570	557	9	a	a	DET
ejpam-4570	557	10	c	c	NOUN
ejpam-4570	557	11	-	-	PUNCT
ejpam-4570	557	12	regular	regular	ADJ
ejpam-4570	557	13	,	,	PUNCT
ejpam-4570	557	14	c	c	NOUN
ejpam-4570	557	15	-	-	PUNCT
ejpam-4570	557	16	completely	completely	ADV
ejpam-4570	557	17	regular	regular	ADJ
ejpam-4570	557	18	,	,	PUNCT
ejpam-4570	557	19	c	c	NOUN
ejpam-4570	557	20	-	-	ADJ
ejpam-4570	557	21	normal	normal	ADJ
ejpam-4570	557	22	and	and	CCONJ
ejpam-4570	557	23	c	c	NOUN
ejpam-4570	557	24	-	-	PUNCT
ejpam-4570	557	25	almost	almost	ADV
ejpam-4570	557	26	wafa	wafa	PROPN
ejpam-4570	557	27	khalaf	khalaf	PROPN
ejpam-4570	557	28	alqurashi	alqurashi	PROPN
ejpam-4570	557	29	,	,	PUNCT
ejpam-4570	557	30	sadeq	sadeq	PROPN
ejpam-4570	557	31	ali	ali	PROPN
ejpam-4570	557	32	thabit	thabit	PROPN
ejpam-4570	557	33	/	/	SYM
ejpam-4570	557	34	eur	eur	PROPN
ejpam-4570	557	35	.	.	PUNCT
ejpam-4570	558	1	j.	j.	PROPN
ejpam-4570	558	2	pure	pure	PROPN
ejpam-4570	558	3	appl	appl	PROPN
ejpam-4570	558	4	.	.	PROPN
ejpam-4570	558	5	math	math	PROPN
ejpam-4570	558	6	,	,	PUNCT
ejpam-4570	558	7	15	15	NUM
ejpam-4570	558	8	(	(	PUNCT
ejpam-4570	558	9	4	4	NUM
ejpam-4570	558	10	)	)	PUNCT
ejpam-4570	558	11	(	(	PUNCT
ejpam-4570	558	12	2022	2022	NUM
ejpam-4570	558	13	)	)	PUNCT
ejpam-4570	558	14	,	,	PUNCT
ejpam-4570	558	15	1760	1760	NUM
ejpam-4570	558	16	-	-	SYM
ejpam-4570	558	17	1782	1782	NUM
ejpam-4570	558	18	1777	1777	NUM
ejpam-4570	558	19	normal	normal	ADJ
ejpam-4570	558	20	space	space	NOUN
ejpam-4570	558	21	,	,	PUNCT
ejpam-4570	558	22	which	which	PRON
ejpam-4570	558	23	is	be	AUX
ejpam-4570	558	24	neither	neither	DET
ejpam-4570	558	25	epi	epi	NOUN
ejpam-4570	558	26	-	-	ADJ
ejpam-4570	558	27	almost	almost	ADV
ejpam-4570	558	28	regular	regular	ADJ
ejpam-4570	558	29	nor	nor	CCONJ
ejpam-4570	558	30	epi	epi	NOUN
ejpam-4570	558	31	-	-	ADJ
ejpam-4570	558	32	almost	almost	ADV
ejpam-4570	558	33	normal	normal	ADJ
ejpam-4570	558	34	because	because	SCONJ
ejpam-4570	558	35	it	it	PRON
ejpam-4570	558	36	is	be	AUX
ejpam-4570	558	37	not	not	PART
ejpam-4570	558	38	t1	t1	NOUN
ejpam-4570	558	39	.	.	PUNCT
ejpam-4570	559	1	the	the	DET
ejpam-4570	559	2	odd	odd	ADV
ejpam-4570	559	3	-	-	PUNCT
ejpam-4570	559	4	even	even	ADV
ejpam-4570	559	5	topology	topology	NOUN
ejpam-4570	559	6	is	be	AUX
ejpam-4570	559	7	also	also	ADV
ejpam-4570	559	8	an	an	DET
ejpam-4570	559	9	l	l	NOUN
ejpam-4570	559	10	-	-	ADJ
ejpam-4570	559	11	normal	normal	ADJ
ejpam-4570	559	12	,	,	PUNCT
ejpam-4570	559	13	l	l	NOUN
ejpam-4570	559	14	-	-	ADJ
ejpam-4570	559	15	regular	regular	ADJ
ejpam-4570	559	16	and	and	CCONJ
ejpam-4570	559	17	l	l	NOUN
ejpam-4570	559	18	-	-	ADJ
ejpam-4570	559	19	almost	almost	ADV
ejpam-4570	559	20	normal	normal	ADJ
ejpam-4570	559	21	space	space	NOUN
ejpam-4570	559	22	.	.	PUNCT
ejpam-4570	560	1	since	since	SCONJ
ejpam-4570	560	2	every	every	DET
ejpam-4570	560	3	c	c	NOUN
ejpam-4570	560	4	-	-	PUNCT
ejpam-4570	560	5	tychonoff	tychonoff	NOUN
ejpam-4570	560	6	first	first	ADJ
ejpam-4570	560	7	countable	countable	ADJ
ejpam-4570	560	8	space	space	NOUN
ejpam-4570	560	9	is	be	AUX
ejpam-4570	560	10	hausdorff	hausdorff	NOUN
ejpam-4570	560	11	(	(	PUNCT
ejpam-4570	560	12	hence	hence	ADV
ejpam-4570	560	13	urysohn	urysohn	ADJ
ejpam-4570	560	14	)	)	PUNCT
ejpam-4570	560	15	,	,	PUNCT
ejpam-4570	560	16	and	and	CCONJ
ejpam-4570	560	17	x	x	X
ejpam-4570	560	18	is	be	AUX
ejpam-4570	560	19	a	a	DET
ejpam-4570	560	20	first	first	ADJ
ejpam-4570	560	21	countable	countable	ADJ
ejpam-4570	560	22	non	non	ADJ
ejpam-4570	560	23	hausdorff	hausdorff	NOUN
ejpam-4570	560	24	space	space	NOUN
ejpam-4570	560	25	,	,	PUNCT
ejpam-4570	560	26	by	by	ADP
ejpam-4570	560	27	corollary	corollary	ADJ
ejpam-4570	560	28	2	2	NUM
ejpam-4570	560	29	in	in	ADP
ejpam-4570	560	30	[	[	PUNCT
ejpam-4570	560	31	9	9	NUM
ejpam-4570	560	32	]	]	PUNCT
ejpam-4570	560	33	,	,	PUNCT
ejpam-4570	560	34	we	we	PRON
ejpam-4570	560	35	obtain	obtain	VERB
ejpam-4570	560	36	:	:	PUNCT
ejpam-4570	560	37	x	x	X
ejpam-4570	560	38	is	be	AUX
ejpam-4570	560	39	not	not	PART
ejpam-4570	560	40	c	c	NOUN
ejpam-4570	560	41	-	-	PUNCT
ejpam-4570	560	42	tychonoff	tychonoff	NOUN
ejpam-4570	560	43	.	.	PUNCT
ejpam-4570	561	1	therefore	therefore	ADV
ejpam-4570	561	2	,	,	PUNCT
ejpam-4570	561	3	the	the	DET
ejpam-4570	561	4	odd	odd	ADV
ejpam-4570	561	5	-	-	PUNCT
ejpam-4570	561	6	even	even	ADJ
ejpam-4570	561	7	topology	topology	NOUN
ejpam-4570	561	8	is	be	AUX
ejpam-4570	561	9	an	an	DET
ejpam-4570	561	10	example	example	NOUN
ejpam-4570	561	11	of	of	ADP
ejpam-4570	561	12	a	a	DET
ejpam-4570	561	13	c	c	NOUN
ejpam-4570	561	14	-	-	PUNCT
ejpam-4570	561	15	completely	completely	ADV
ejpam-4570	561	16	regular	regular	ADJ
ejpam-4570	561	17	,	,	PUNCT
ejpam-4570	561	18	c	c	NOUN
ejpam-4570	561	19	-	-	PUNCT
ejpam-4570	561	20	almost	almost	ADV
ejpam-4570	561	21	normal	normal	ADJ
ejpam-4570	561	22	and	and	CCONJ
ejpam-4570	561	23	l	l	NOUN
ejpam-4570	561	24	-	-	ADJ
ejpam-4570	561	25	almost	almost	ADV
ejpam-4570	561	26	normal	normal	ADJ
ejpam-4570	561	27	space	space	NOUN
ejpam-4570	561	28	,	,	PUNCT
ejpam-4570	561	29	which	which	PRON
ejpam-4570	561	30	is	be	AUX
ejpam-4570	561	31	neither	neither	PRON
ejpam-4570	561	32	c	c	NOUN
ejpam-4570	561	33	-	-	PUNCT
ejpam-4570	561	34	tychonoff	tychonoff	NOUN
ejpam-4570	561	35	nor	nor	CCONJ
ejpam-4570	561	36	l	l	NOUN
ejpam-4570	561	37	-	-	NOUN
ejpam-4570	561	38	tychonoff	tychonoff	NOUN
ejpam-4570	561	39	.	.	PUNCT
ejpam-4570	561	40	example	example	NOUN
ejpam-4570	562	1	17	17	NUM
ejpam-4570	562	2	.	.	PUNCT
ejpam-4570	563	1	the	the	DET
ejpam-4570	563	2	relatively	relatively	ADV
ejpam-4570	563	3	prime	prime	ADJ
ejpam-4570	563	4	integer	integer	NOUN
ejpam-4570	563	5	topology	topology	NOUN
ejpam-4570	563	6	and	and	CCONJ
ejpam-4570	563	7	the	the	DET
ejpam-4570	563	8	prime	prime	ADJ
ejpam-4570	563	9	integer	integer	NOUN
ejpam-4570	563	10	topology	topology	NOUN
ejpam-4570	563	11	[	[	X
ejpam-4570	563	12	29	29	NUM
ejpam-4570	563	13	,	,	PUNCT
ejpam-4570	563	14	example	example	NOUN
ejpam-4570	563	15	60	60	NUM
ejpam-4570	563	16	,	,	PUNCT
ejpam-4570	563	17	61	61	NUM
ejpam-4570	563	18	]	]	PUNCT
ejpam-4570	563	19	,	,	PUNCT
ejpam-4570	563	20	are	be	AUX
ejpam-4570	563	21	hausdorff	hausdorff	NOUN
ejpam-4570	563	22	,	,	PUNCT
ejpam-4570	563	23	semi	semi	ADV
ejpam-4570	563	24	regular	regular	ADJ
ejpam-4570	563	25	,	,	PUNCT
ejpam-4570	563	26	lindelöf	lindelöf	NOUN
ejpam-4570	563	27	,	,	PUNCT
ejpam-4570	563	28	first	first	ADV
ejpam-4570	563	29	countable	countable	ADJ
ejpam-4570	563	30	spaces	space	NOUN
ejpam-4570	563	31	that	that	PRON
ejpam-4570	563	32	are	be	AUX
ejpam-4570	563	33	neither	neither	CCONJ
ejpam-4570	563	34	urysohn	urysohn	NOUN
ejpam-4570	563	35	,	,	PUNCT
ejpam-4570	563	36	paracompact	paracompact	ADJ
ejpam-4570	563	37	,	,	PUNCT
ejpam-4570	563	38	almost	almost	ADV
ejpam-4570	563	39	normal	normal	ADJ
ejpam-4570	563	40	,	,	PUNCT
ejpam-4570	563	41	quasi	quasi	X
ejpam-4570	563	42	normal	normal	ADJ
ejpam-4570	563	43	,	,	PUNCT
ejpam-4570	563	44	almost	almost	ADV
ejpam-4570	563	45	regular	regular	ADJ
ejpam-4570	563	46	nor	nor	CCONJ
ejpam-4570	563	47	regular	regular	ADJ
ejpam-4570	563	48	[	[	X
ejpam-4570	563	49	33	33	NUM
ejpam-4570	563	50	,	,	PUNCT
ejpam-4570	563	51	example	example	NOUN
ejpam-4570	563	52	2.9	2.9	NUM
ejpam-4570	563	53	]	]	PUNCT
ejpam-4570	563	54	.	.	PUNCT
ejpam-4570	564	1	the	the	DET
ejpam-4570	564	2	two	two	NUM
ejpam-4570	564	3	spaces	space	NOUN
ejpam-4570	564	4	are	be	AUX
ejpam-4570	564	5	epi	epi	ADJ
ejpam-4570	564	6	-	-	ADJ
ejpam-4570	564	7	mildly	mildly	ADV
ejpam-4570	564	8	normal	normal	ADJ
ejpam-4570	564	9	spaces	space	NOUN
ejpam-4570	564	10	which	which	PRON
ejpam-4570	564	11	are	be	AUX
ejpam-4570	564	12	neither	neither	CCONJ
ejpam-4570	564	13	almost	almost	ADV
ejpam-4570	564	14	completely	completely	ADV
ejpam-4570	564	15	regular	regular	ADJ
ejpam-4570	564	16	,	,	PUNCT
ejpam-4570	564	17	almost	almost	ADV
ejpam-4570	564	18	regular	regular	ADJ
ejpam-4570	564	19	,	,	PUNCT
ejpam-4570	564	20	epi	epi	NOUN
ejpam-4570	564	21	-	-	PUNCT
ejpam-4570	564	22	almost	almost	ADV
ejpam-4570	564	23	normal	normal	ADJ
ejpam-4570	564	24	,	,	PUNCT
ejpam-4570	564	25	epi	epi	NOUN
ejpam-4570	564	26	-	-	ADJ
ejpam-4570	564	27	regular	regular	ADJ
ejpam-4570	564	28	nor	nor	CCONJ
ejpam-4570	564	29	epi	epi	NOUN
ejpam-4570	564	30	-	-	ADJ
ejpam-4570	564	31	completely	completely	ADV
ejpam-4570	564	32	regular	regular	ADJ
ejpam-4570	564	33	.	.	PUNCT
ejpam-4570	565	1	since	since	SCONJ
ejpam-4570	565	2	the	the	DET
ejpam-4570	565	3	two	two	NUM
ejpam-4570	565	4	spaces	space	NOUN
ejpam-4570	565	5	are	be	AUX
ejpam-4570	565	6	hausdorff	hausdorff	NOUN
ejpam-4570	565	7	lindelöf	lindelöf	NOUN
ejpam-4570	565	8	first	first	ADV
ejpam-4570	565	9	countable	countable	ADJ
ejpam-4570	565	10	space	space	NOUN
ejpam-4570	565	11	which	which	PRON
ejpam-4570	565	12	are	be	AUX
ejpam-4570	565	13	not	not	PART
ejpam-4570	565	14	epi	epi	NOUN
ejpam-4570	565	15	-	-	ADJ
ejpam-4570	565	16	almost	almost	ADV
ejpam-4570	565	17	normal	normal	ADJ
ejpam-4570	565	18	,	,	PUNCT
ejpam-4570	565	19	by	by	ADP
ejpam-4570	565	20	corollary	corollary	ADJ
ejpam-4570	565	21	11	11	NUM
ejpam-4570	565	22	we	we	PRON
ejpam-4570	565	23	get	get	VERB
ejpam-4570	565	24	:	:	PUNCT
ejpam-4570	565	25	the	the	DET
ejpam-4570	565	26	two	two	NUM
ejpam-4570	565	27	spaces	space	NOUN
ejpam-4570	565	28	are	be	AUX
ejpam-4570	565	29	neither	neither	CCONJ
ejpam-4570	565	30	c	c	NOUN
ejpam-4570	565	31	-	-	ADJ
ejpam-4570	565	32	regular	regular	ADJ
ejpam-4570	565	33	nor	nor	CCONJ
ejpam-4570	565	34	c	c	NOUN
ejpam-4570	565	35	-	-	PUNCT
ejpam-4570	565	36	completely	completely	ADV
ejpam-4570	565	37	regular	regular	ADJ
ejpam-4570	565	38	.	.	PUNCT
ejpam-4570	566	1	hence	hence	ADV
ejpam-4570	566	2	,	,	PUNCT
ejpam-4570	566	3	they	they	PRON
ejpam-4570	566	4	are	be	AUX
ejpam-4570	566	5	neither	neither	CCONJ
ejpam-4570	566	6	l	l	NOUN
ejpam-4570	566	7	-	-	ADJ
ejpam-4570	566	8	regular	regular	ADJ
ejpam-4570	566	9	,	,	PUNCT
ejpam-4570	566	10	l	l	NOUN
ejpam-4570	566	11	-	-	PUNCT
ejpam-4570	566	12	completely	completely	ADV
ejpam-4570	566	13	regular	regular	ADJ
ejpam-4570	566	14	nor	nor	CCONJ
ejpam-4570	566	15	l	l	NOUN
ejpam-4570	566	16	-	-	NOUN
ejpam-4570	566	17	tychonoff	tychonoff	NOUN
ejpam-4570	566	18	.	.	PUNCT
ejpam-4570	567	1	since	since	SCONJ
ejpam-4570	567	2	the	the	DET
ejpam-4570	567	3	two	two	NUM
ejpam-4570	567	4	spaces	space	NOUN
ejpam-4570	567	5	are	be	AUX
ejpam-4570	567	6	lindelöf	lindelöf	NOUN
ejpam-4570	567	7	spaces	space	NOUN
ejpam-4570	567	8	which	which	PRON
ejpam-4570	567	9	are	be	AUX
ejpam-4570	567	10	neither	neither	CCONJ
ejpam-4570	567	11	almost	almost	ADV
ejpam-4570	567	12	normal	normal	ADJ
ejpam-4570	567	13	nor	nor	CCONJ
ejpam-4570	567	14	almost	almost	ADV
ejpam-4570	567	15	regular	regular	ADJ
ejpam-4570	567	16	,	,	PUNCT
ejpam-4570	567	17	we	we	PRON
ejpam-4570	567	18	conclude	conclude	VERB
ejpam-4570	567	19	that	that	SCONJ
ejpam-4570	567	20	they	they	PRON
ejpam-4570	567	21	are	be	AUX
ejpam-4570	567	22	neither	neither	CCONJ
ejpam-4570	567	23	l	l	NOUN
ejpam-4570	567	24	-	-	ADJ
ejpam-4570	567	25	almost	almost	ADV
ejpam-4570	567	26	normal	normal	ADJ
ejpam-4570	567	27	nor	nor	CCONJ
ejpam-4570	567	28	l	l	NOUN
ejpam-4570	567	29	-	-	PUNCT
ejpam-4570	567	30	almost	almost	ADV
ejpam-4570	567	31	regular	regular	ADJ
ejpam-4570	567	32	.	.	PUNCT
ejpam-4570	568	1	since	since	SCONJ
ejpam-4570	568	2	the	the	DET
ejpam-4570	568	3	two	two	NUM
ejpam-4570	568	4	spaces	space	NOUN
ejpam-4570	568	5	are	be	AUX
ejpam-4570	568	6	c	c	NOUN
ejpam-4570	568	7	-	-	PUNCT
ejpam-4570	568	8	almost	almost	ADV
ejpam-4570	568	9	regular	regular	ADJ
ejpam-4570	568	10	first	first	ADJ
ejpam-4570	568	11	countable	countable	ADJ
ejpam-4570	568	12	lindelöf	lindelöf	NOUN
ejpam-4570	568	13	spaces	space	NOUN
ejpam-4570	568	14	,	,	PUNCT
ejpam-4570	568	15	by	by	ADP
ejpam-4570	568	16	theorem	theorem	NOUN
ejpam-4570	568	17	27	27	NUM
ejpam-4570	568	18	we	we	PRON
ejpam-4570	568	19	get	get	VERB
ejpam-4570	568	20	:	:	PUNCT
ejpam-4570	568	21	the	the	DET
ejpam-4570	568	22	two	two	NUM
ejpam-4570	568	23	spaces	space	NOUN
ejpam-4570	568	24	are	be	AUX
ejpam-4570	568	25	c	c	NOUN
ejpam-4570	568	26	-	-	PUNCT
ejpam-4570	568	27	almost	almost	ADV
ejpam-4570	568	28	normal	normal	ADJ
ejpam-4570	568	29	.	.	PUNCT
ejpam-4570	569	1	therefore	therefore	ADV
ejpam-4570	569	2	,	,	PUNCT
ejpam-4570	569	3	the	the	DET
ejpam-4570	569	4	relatively	relatively	ADV
ejpam-4570	569	5	prime	prime	ADJ
ejpam-4570	569	6	integer	integer	NOUN
ejpam-4570	569	7	topology	topology	NOUN
ejpam-4570	569	8	and	and	CCONJ
ejpam-4570	569	9	the	the	DET
ejpam-4570	569	10	prime	prime	ADJ
ejpam-4570	569	11	integer	integer	NOUN
ejpam-4570	569	12	topology	topology	NOUN
ejpam-4570	569	13	are	be	AUX
ejpam-4570	569	14	c	c	NOUN
ejpam-4570	569	15	-	-	PUNCT
ejpam-4570	569	16	almost	almost	ADV
ejpam-4570	569	17	completely	completely	ADV
ejpam-4570	569	18	regular	regular	ADJ
ejpam-4570	569	19	and	and	CCONJ
ejpam-4570	569	20	c	c	NOUN
ejpam-4570	569	21	-	-	PUNCT
ejpam-4570	569	22	almost	almost	ADV
ejpam-4570	569	23	normal	normal	ADJ
ejpam-4570	569	24	spaces	space	NOUN
ejpam-4570	569	25	which	which	PRON
ejpam-4570	569	26	are	be	AUX
ejpam-4570	569	27	neither	neither	CCONJ
ejpam-4570	569	28	l	l	NOUN
ejpam-4570	569	29	-	-	ADJ
ejpam-4570	569	30	almost	almost	ADV
ejpam-4570	569	31	normal	normal	ADJ
ejpam-4570	569	32	,	,	PUNCT
ejpam-4570	569	33	almost	almost	ADV
ejpam-4570	569	34	normal	normal	ADJ
ejpam-4570	569	35	nor	nor	CCONJ
ejpam-4570	569	36	epi	epi	NOUN
ejpam-4570	569	37	-	-	ADJ
ejpam-4570	569	38	almost	almost	ADV
ejpam-4570	569	39	normal	normal	ADJ
ejpam-4570	569	40	.	.	PUNCT
ejpam-4570	570	1	example	example	NOUN
ejpam-4570	571	1	18	18	NUM
ejpam-4570	571	2	.	.	PUNCT
ejpam-4570	572	1	let	let	VERB
ejpam-4570	572	2	x	x	PUNCT
ejpam-4570	572	3	=	=	PRON
ejpam-4570	572	4	{	{	PUNCT
ejpam-4570	572	5	aij	aij	PROPN
ejpam-4570	572	6	,	,	PUNCT
ejpam-4570	572	7	bij	bij	NOUN
ejpam-4570	572	8	,	,	PUNCT
ejpam-4570	572	9	ci	ci	PROPN
ejpam-4570	572	10	,	,	PUNCT
ejpam-4570	572	11	a	a	PRON
ejpam-4570	572	12	,	,	PUNCT
ejpam-4570	572	13	b	b	NOUN
ejpam-4570	572	14	:	:	PUNCT
ejpam-4570	572	15	i	i	PROPN
ejpam-4570	572	16	,	,	PUNCT
ejpam-4570	572	17	j	j	PROPN
ejpam-4570	572	18	∈	∈	PROPN
ejpam-4570	572	19	n	n	CCONJ
ejpam-4570	572	20	}	}	PUNCT
ejpam-4570	572	21	.	.	PUNCT
ejpam-4570	573	1	for	for	ADP
ejpam-4570	573	2	each	each	DET
ejpam-4570	573	3	i	i	PROPN
ejpam-4570	573	4	∈	∈	PROPN
ejpam-4570	573	5	n	n	CCONJ
ejpam-4570	573	6	,	,	PUNCT
ejpam-4570	573	7	and	and	CCONJ
ejpam-4570	573	8	each	each	DET
ejpam-4570	573	9	n	n	PRON
ejpam-4570	573	10	∈	∈	PROPN
ejpam-4570	573	11	n	n	CCONJ
ejpam-4570	573	12	,	,	PUNCT
ejpam-4570	573	13	define	define	VERB
ejpam-4570	573	14	un(ci	un(ci	ADJ
ejpam-4570	573	15	)	)	PUNCT
ejpam-4570	573	16	=	=	SYM
ejpam-4570	573	17	{	{	PUNCT
ejpam-4570	573	18	ci	ci	PROPN
ejpam-4570	573	19	,	,	PUNCT
ejpam-4570	573	20	aij	aij	PROPN
ejpam-4570	573	21	,	,	PUNCT
ejpam-4570	573	22	bij	bij	NOUN
ejpam-4570	573	23	:	:	PUNCT
ejpam-4570	573	24	j	j	PROPN
ejpam-4570	573	25	≥	≥	NOUN
ejpam-4570	573	26	n	n	CCONJ
ejpam-4570	573	27	}	}	PUNCT
ejpam-4570	573	28	.	.	PUNCT
ejpam-4570	574	1	for	for	ADP
ejpam-4570	574	2	each	each	DET
ejpam-4570	574	3	n	n	PRON
ejpam-4570	574	4	∈	∈	PROPN
ejpam-4570	574	5	n	n	CCONJ
ejpam-4570	574	6	,	,	PUNCT
ejpam-4570	574	7	define	define	VERB
ejpam-4570	574	8	un(a	un(a	PUNCT
ejpam-4570	574	9	)	)	PUNCT
ejpam-4570	575	1	=	=	PRON
ejpam-4570	575	2	{	{	PUNCT
ejpam-4570	575	3	a	a	NOUN
ejpam-4570	575	4	,	,	PUNCT
ejpam-4570	575	5	aij	aij	PROPN
ejpam-4570	575	6	:	:	PUNCT
ejpam-4570	575	7	i	i	PRON
ejpam-4570	575	8	≥	≥	VERB
ejpam-4570	575	9	n	n	CCONJ
ejpam-4570	575	10	,	,	PUNCT
ejpam-4570	575	11	j	j	PROPN
ejpam-4570	575	12	=	=	SYM
ejpam-4570	575	13	1	1	NUM
ejpam-4570	575	14	,	,	PUNCT
ejpam-4570	575	15	2	2	NUM
ejpam-4570	575	16	,	,	PUNCT
ejpam-4570	575	17	3	3	NUM
ejpam-4570	575	18	,	,	PUNCT
ejpam-4570	575	19	.	.	PUNCT
ejpam-4570	575	20	.	.	PUNCT
ejpam-4570	575	21	.	.	PUNCT
ejpam-4570	576	1	}	}	PUNCT
ejpam-4570	576	2	.	.	PUNCT
ejpam-4570	577	1	and	and	CCONJ
ejpam-4570	577	2	for	for	ADP
ejpam-4570	577	3	each	each	DET
ejpam-4570	577	4	n	n	PRON
ejpam-4570	577	5	∈	∈	PROPN
ejpam-4570	577	6	n	n	CCONJ
ejpam-4570	577	7	,	,	PUNCT
ejpam-4570	577	8	define	define	VERB
ejpam-4570	577	9	un(b	un(b	NOUN
ejpam-4570	577	10	)	)	PUNCT
ejpam-4570	578	1	=	=	PRON
ejpam-4570	578	2	{	{	PUNCT
ejpam-4570	578	3	b	b	NOUN
ejpam-4570	578	4	,	,	PUNCT
ejpam-4570	578	5	bij	bij	NOUN
ejpam-4570	578	6	:	:	PUNCT
ejpam-4570	578	7	i	i	PRON
ejpam-4570	578	8	≥	≥	VERB
ejpam-4570	578	9	n	n	CCONJ
ejpam-4570	578	10	,	,	PUNCT
ejpam-4570	578	11	j	j	PROPN
ejpam-4570	579	1	=	=	SYM
ejpam-4570	579	2	1	1	NUM
ejpam-4570	579	3	,	,	PUNCT
ejpam-4570	579	4	2	2	NUM
ejpam-4570	579	5	,	,	PUNCT
ejpam-4570	579	6	3	3	NUM
ejpam-4570	579	7	,	,	PUNCT
ejpam-4570	579	8	.	.	PUNCT
ejpam-4570	579	9	.	.	PUNCT
ejpam-4570	579	10	.	.	PUNCT
ejpam-4570	580	1	}	}	PUNCT
ejpam-4570	580	2	.	.	PUNCT
ejpam-4570	581	1	now	now	ADV
ejpam-4570	581	2	,	,	PUNCT
ejpam-4570	581	3	for	for	ADP
ejpam-4570	581	4	each	each	DET
ejpam-4570	581	5	i	i	PROPN
ejpam-4570	581	6	,	,	PUNCT
ejpam-4570	581	7	j	j	PROPN
ejpam-4570	581	8	∈	∈	PROPN
ejpam-4570	581	9	n	n	CCONJ
ejpam-4570	581	10	,	,	PUNCT
ejpam-4570	581	11	we	we	PRON
ejpam-4570	581	12	declare	declare	VERB
ejpam-4570	581	13	that	that	SCONJ
ejpam-4570	581	14	the	the	DET
ejpam-4570	581	15	singletons	singleton	NOUN
ejpam-4570	581	16	{	{	PUNCT
ejpam-4570	581	17	aij	aij	NOUN
ejpam-4570	581	18	}	}	PUNCT
ejpam-4570	581	19	and	and	CCONJ
ejpam-4570	581	20	{	{	PUNCT
ejpam-4570	581	21	bij	bij	NOUN
ejpam-4570	581	22	}	}	PUNCT
ejpam-4570	581	23	are	be	AUX
ejpam-4570	581	24	open	open	ADJ
ejpam-4570	581	25	,	,	PUNCT
ejpam-4570	581	26	i.e.	i.e.	X
ejpam-4570	581	27	,	,	PUNCT
ejpam-4570	581	28	each	each	DET
ejpam-4570	581	29	aij	aij	PROPN
ejpam-4570	581	30	and	and	CCONJ
ejpam-4570	581	31	bij	bij	NOUN
ejpam-4570	581	32	are	be	AUX
ejpam-4570	581	33	isolated	isolate	VERB
ejpam-4570	581	34	points	point	NOUN
ejpam-4570	581	35	.	.	PUNCT
ejpam-4570	582	1	a	a	DET
ejpam-4570	582	2	basic	basic	ADJ
ejpam-4570	582	3	open	open	ADJ
ejpam-4570	582	4	neighborhood	neighborhood	NOUN
ejpam-4570	582	5	of	of	ADP
ejpam-4570	582	6	a	a	DET
ejpam-4570	582	7	point	point	NOUN
ejpam-4570	582	8	ci	ci	NOUN
ejpam-4570	582	9	,	,	PUNCT
ejpam-4570	582	10	where	where	SCONJ
ejpam-4570	582	11	i	i	PRON
ejpam-4570	582	12	∈	∈	PROPN
ejpam-4570	582	13	n	n	CCONJ
ejpam-4570	582	14	,	,	PUNCT
ejpam-4570	582	15	is	be	AUX
ejpam-4570	582	16	of	of	ADP
ejpam-4570	582	17	the	the	DET
ejpam-4570	582	18	form	form	NOUN
ejpam-4570	582	19	un(ci	un(ci	ADJ
ejpam-4570	582	20	)	)	PUNCT
ejpam-4570	582	21	,	,	PUNCT
ejpam-4570	582	22	where	where	SCONJ
ejpam-4570	582	23	n	n	DET
ejpam-4570	582	24	∈	∈	PROPN
ejpam-4570	582	25	n.	n.	NOUN
ejpam-4570	582	26	a	a	DET
ejpam-4570	582	27	basic	basic	ADJ
ejpam-4570	582	28	open	open	ADJ
ejpam-4570	582	29	neighborhood	neighborhood	NOUN
ejpam-4570	582	30	of	of	ADP
ejpam-4570	582	31	the	the	DET
ejpam-4570	582	32	point	point	NOUN
ejpam-4570	582	33	a	a	PRON
ejpam-4570	582	34	is	be	AUX
ejpam-4570	582	35	of	of	ADP
ejpam-4570	582	36	the	the	DET
ejpam-4570	582	37	form	form	NOUN
ejpam-4570	582	38	un(a	un(a	ADV
ejpam-4570	582	39	)	)	PUNCT
ejpam-4570	582	40	,	,	PUNCT
ejpam-4570	582	41	where	where	SCONJ
ejpam-4570	582	42	n	n	X
ejpam-4570	582	43	∈	∈	PROPN
ejpam-4570	582	44	n	n	CCONJ
ejpam-4570	582	45	,	,	PUNCT
ejpam-4570	582	46	and	and	CCONJ
ejpam-4570	582	47	a	a	DET
ejpam-4570	582	48	basic	basic	ADJ
ejpam-4570	582	49	open	open	ADJ
ejpam-4570	582	50	neighborhood	neighborhood	NOUN
ejpam-4570	582	51	of	of	ADP
ejpam-4570	582	52	the	the	DET
ejpam-4570	582	53	point	point	NOUN
ejpam-4570	582	54	b	b	NOUN
ejpam-4570	582	55	is	be	AUX
ejpam-4570	582	56	of	of	ADP
ejpam-4570	582	57	the	the	DET
ejpam-4570	582	58	form	form	NOUN
ejpam-4570	582	59	un(b	un(b	NOUN
ejpam-4570	582	60	)	)	PUNCT
ejpam-4570	582	61	,	,	PUNCT
ejpam-4570	582	62	where	where	SCONJ
ejpam-4570	582	63	n	n	X
ejpam-4570	582	64	∈	∈	PROPN
ejpam-4570	582	65	n.	n.	NOUN
ejpam-4570	582	66	then	then	ADV
ejpam-4570	582	67	,	,	PUNCT
ejpam-4570	582	68	x	x	X
ejpam-4570	582	69	is	be	AUX
ejpam-4570	582	70	a	a	DET
ejpam-4570	582	71	semi	semi	ADJ
ejpam-4570	582	72	regular	regular	ADJ
ejpam-4570	582	73	space	space	NOUN
ejpam-4570	582	74	,	,	PUNCT
ejpam-4570	582	75	which	which	PRON
ejpam-4570	582	76	is	be	AUX
ejpam-4570	582	77	not	not	PART
ejpam-4570	582	78	semi	semi	ADV
ejpam-4570	582	79	normal	normal	ADJ
ejpam-4570	582	80	[	[	X
ejpam-4570	582	81	26	26	NUM
ejpam-4570	582	82	,	,	PUNCT
ejpam-4570	582	83	example	example	NOUN
ejpam-4570	582	84	2.4	2.4	NUM
ejpam-4570	582	85	]	]	PUNCT
ejpam-4570	582	86	.	.	PUNCT
ejpam-4570	583	1	x	x	X
ejpam-4570	583	2	is	be	AUX
ejpam-4570	583	3	also	also	ADV
ejpam-4570	583	4	hausdorff	hausdorff	ADJ
ejpam-4570	583	5	space	space	NOUN
ejpam-4570	583	6	,	,	PUNCT
ejpam-4570	583	7	which	which	PRON
ejpam-4570	583	8	is	be	AUX
ejpam-4570	583	9	neither	neither	CCONJ
ejpam-4570	583	10	urysohn	urysohn	NOUN
ejpam-4570	583	11	,	,	PUNCT
ejpam-4570	583	12	regular	regular	ADJ
ejpam-4570	583	13	,	,	PUNCT
ejpam-4570	583	14	mildly	mildly	ADV
ejpam-4570	583	15	normal	normal	ADJ
ejpam-4570	583	16	,	,	PUNCT
ejpam-4570	583	17	compact	compact	ADJ
ejpam-4570	583	18	,	,	PUNCT
ejpam-4570	583	19	paracompact	paracompact	ADJ
ejpam-4570	583	20	nor	nor	CCONJ
ejpam-4570	583	21	epi	epi	NOUN
ejpam-4570	583	22	-	-	ADJ
ejpam-4570	583	23	mildly	mildly	ADV
ejpam-4570	583	24	normal	normal	ADJ
ejpam-4570	583	25	[	[	X
ejpam-4570	583	26	17	17	NUM
ejpam-4570	583	27	,	,	PUNCT
ejpam-4570	583	28	example	example	NOUN
ejpam-4570	583	29	16	16	NUM
ejpam-4570	583	30	]	]	PUNCT
ejpam-4570	583	31	.	.	PUNCT
ejpam-4570	584	1	hence	hence	ADV
ejpam-4570	584	2	,	,	PUNCT
ejpam-4570	584	3	x	x	PRON
ejpam-4570	584	4	is	be	AUX
ejpam-4570	584	5	neither	neither	CCONJ
ejpam-4570	584	6	almost	almost	ADV
ejpam-4570	584	7	normal	normal	ADJ
ejpam-4570	584	8	,	,	PUNCT
ejpam-4570	584	9	epi	epi	NOUN
ejpam-4570	584	10	-	-	ADJ
ejpam-4570	584	11	almost	almost	ADV
ejpam-4570	584	12	normal	normal	ADJ
ejpam-4570	584	13	,	,	PUNCT
ejpam-4570	584	14	epi	epi	NOUN
ejpam-4570	584	15	-	-	ADJ
ejpam-4570	584	16	normal	normal	ADJ
ejpam-4570	584	17	,	,	PUNCT
ejpam-4570	584	18	epi	epi	NOUN
ejpam-4570	584	19	-	-	NOUN
ejpam-4570	584	20	regular	regular	ADJ
ejpam-4570	584	21	nor	nor	CCONJ
ejpam-4570	584	22	epi	epi	NOUN
ejpam-4570	584	23	-	-	ADJ
ejpam-4570	584	24	completely	completely	ADV
ejpam-4570	584	25	regular	regular	ADJ
ejpam-4570	584	26	.	.	PUNCT
ejpam-4570	585	1	since	since	SCONJ
ejpam-4570	585	2	x	x	PRON
ejpam-4570	585	3	is	be	AUX
ejpam-4570	585	4	a	a	DET
ejpam-4570	585	5	countable	countable	ADJ
ejpam-4570	585	6	space	space	NOUN
ejpam-4570	585	7	,	,	PUNCT
ejpam-4570	585	8	it	it	PRON
ejpam-4570	585	9	is	be	AUX
ejpam-4570	585	10	a	a	DET
ejpam-4570	585	11	lindelöf	lindelöf	NOUN
ejpam-4570	585	12	second	second	ADJ
ejpam-4570	585	13	countable	countable	ADJ
ejpam-4570	585	14	space	space	NOUN
ejpam-4570	585	15	.	.	PUNCT
ejpam-4570	586	1	so	so	ADV
ejpam-4570	586	2	,	,	PUNCT
ejpam-4570	586	3	x	x	PRON
ejpam-4570	586	4	is	be	AUX
ejpam-4570	586	5	a	a	DET
ejpam-4570	586	6	hausdorff	hausdorff	NOUN
ejpam-4570	586	7	lindelöf	lindelöf	NOUN
ejpam-4570	586	8	second	second	ADV
ejpam-4570	586	9	countable	countable	ADJ
ejpam-4570	586	10	c	c	NOUN
ejpam-4570	586	11	-	-	PUNCT
ejpam-4570	586	12	paracompact	paracompact	ADJ
ejpam-4570	586	13	space	space	NOUN
ejpam-4570	586	14	,	,	PUNCT
ejpam-4570	586	15	which	which	PRON
ejpam-4570	586	16	is	be	AUX
ejpam-4570	586	17	not	not	PART
ejpam-4570	586	18	c2	c2	NOUN
ejpam-4570	586	19	-	-	PUNCT
ejpam-4570	586	20	paracompact	paracompact	NOUN
ejpam-4570	586	21	[	[	X
ejpam-4570	586	22	24	24	NUM
ejpam-4570	586	23	,	,	PUNCT
ejpam-4570	586	24	example	example	NOUN
ejpam-4570	586	25	2.25	2.25	NUM
ejpam-4570	586	26	]	]	PUNCT
ejpam-4570	586	27	.	.	PUNCT
ejpam-4570	587	1	since	since	SCONJ
ejpam-4570	587	2	x	x	PRON
ejpam-4570	587	3	is	be	AUX
ejpam-4570	587	4	a	a	DET
ejpam-4570	587	5	lindelöf	lindelöf	NOUN
ejpam-4570	587	6	non	non	ADV
ejpam-4570	587	7	almost	almost	ADV
ejpam-4570	587	8	normal	normal	ADJ
ejpam-4570	587	9	space	space	NOUN
ejpam-4570	587	10	,	,	PUNCT
ejpam-4570	587	11	it	it	PRON
ejpam-4570	587	12	is	be	AUX
ejpam-4570	587	13	not	not	PART
ejpam-4570	587	14	l	l	NOUN
ejpam-4570	587	15	-	-	PUNCT
ejpam-4570	587	16	almost	almost	ADV
ejpam-4570	587	17	normal	normal	ADJ
ejpam-4570	587	18	.	.	PUNCT
ejpam-4570	588	1	since	since	SCONJ
ejpam-4570	588	2	x	x	PROPN
ejpam-4570	588	3	is	be	AUX
ejpam-4570	588	4	t1	t1	NOUN
ejpam-4570	588	5	-	-	PUNCT
ejpam-4570	588	6	space	space	NOUN
ejpam-4570	588	7	,	,	PUNCT
ejpam-4570	588	8	it	it	PRON
ejpam-4570	588	9	is	be	AUX
ejpam-4570	588	10	epi	epi	NOUN
ejpam-4570	588	11	-	-	ADJ
ejpam-4570	588	12	almost	almost	ADV
ejpam-4570	588	13	completely	completely	ADV
ejpam-4570	588	14	regular	regular	ADJ
ejpam-4570	588	15	.	.	PUNCT
ejpam-4570	589	1	by	by	ADP
ejpam-4570	589	2	theorem	theorem	NOUN
ejpam-4570	589	3	2.44	2.44	NUM
ejpam-4570	589	4	in	in	ADP
ejpam-4570	589	5	[	[	X
ejpam-4570	589	6	31	31	NUM
ejpam-4570	589	7	]	]	PUNCT
ejpam-4570	589	8	,	,	PUNCT
ejpam-4570	589	9	we	we	PRON
ejpam-4570	589	10	obtain	obtain	VERB
ejpam-4570	589	11	:	:	PUNCT
ejpam-4570	589	12	x	x	X
ejpam-4570	589	13	is	be	AUX
ejpam-4570	589	14	c	c	NOUN
ejpam-4570	589	15	-	-	PUNCT
ejpam-4570	589	16	almost	almost	ADV
ejpam-4570	589	17	completely	completely	ADV
ejpam-4570	589	18	regular	regular	ADJ
ejpam-4570	589	19	.	.	PUNCT
ejpam-4570	590	1	since	since	SCONJ
ejpam-4570	590	2	x	x	PROPN
ejpam-4570	590	3	is	be	AUX
ejpam-4570	590	4	lindelöf	lindelöf	NOUN
ejpam-4570	590	5	space	space	NOUN
ejpam-4570	590	6	,	,	PUNCT
ejpam-4570	590	7	which	which	PRON
ejpam-4570	590	8	is	be	AUX
ejpam-4570	590	9	neither	neither	CCONJ
ejpam-4570	590	10	almost	almost	ADV
ejpam-4570	590	11	regular	regular	ADJ
ejpam-4570	590	12	,	,	PUNCT
ejpam-4570	590	13	almost	almost	ADV
ejpam-4570	590	14	completely	completely	ADV
ejpam-4570	590	15	regular	regular	ADJ
ejpam-4570	590	16	nor	nor	CCONJ
ejpam-4570	590	17	almost	almost	ADV
ejpam-4570	590	18	normal	normal	ADJ
ejpam-4570	590	19	,	,	PUNCT
ejpam-4570	590	20	we	we	PRON
ejpam-4570	590	21	get	get	VERB
ejpam-4570	590	22	:	:	PUNCT
ejpam-4570	590	23	x	x	X
ejpam-4570	590	24	is	be	AUX
ejpam-4570	590	25	neither	neither	CCONJ
ejpam-4570	590	26	l	l	NOUN
ejpam-4570	590	27	-	-	ADJ
ejpam-4570	590	28	almost	almost	ADV
ejpam-4570	590	29	regular	regular	ADJ
ejpam-4570	590	30	,	,	PUNCT
ejpam-4570	590	31	l	l	NOUN
ejpam-4570	590	32	-	-	ADJ
ejpam-4570	590	33	regular	regular	ADJ
ejpam-4570	590	34	,	,	PUNCT
ejpam-4570	590	35	l	l	NOUN
ejpam-4570	590	36	-	-	PUNCT
ejpam-4570	590	37	completely	completely	ADV
ejpam-4570	590	38	regular	regular	ADJ
ejpam-4570	590	39	nor	nor	CCONJ
ejpam-4570	590	40	l	l	NOUN
ejpam-4570	590	41	-	-	ADJ
ejpam-4570	590	42	almost	almost	ADV
ejpam-4570	590	43	normal	normal	ADJ
ejpam-4570	590	44	.	.	PUNCT
ejpam-4570	591	1	since	since	SCONJ
ejpam-4570	591	2	x	x	PRON
ejpam-4570	591	3	is	be	AUX
ejpam-4570	591	4	c	c	NOUN
ejpam-4570	591	5	-	-	PUNCT
ejpam-4570	591	6	almost	almost	ADV
ejpam-4570	591	7	regular	regular	ADJ
ejpam-4570	591	8	first	first	ADJ
ejpam-4570	591	9	countable	countable	ADJ
ejpam-4570	591	10	lindelöf	lindelöf	NOUN
ejpam-4570	591	11	space	space	NOUN
ejpam-4570	591	12	,	,	PUNCT
ejpam-4570	591	13	by	by	ADP
ejpam-4570	591	14	theorem	theorem	VERB
ejpam-4570	591	15	27	27	NUM
ejpam-4570	591	16	we	we	PRON
ejpam-4570	591	17	conclude	conclude	VERB
ejpam-4570	591	18	that	that	SCONJ
ejpam-4570	591	19	:	:	PUNCT
ejpam-4570	591	20	the	the	DET
ejpam-4570	591	21	space	space	NOUN
ejpam-4570	591	22	x	x	PUNCT
ejpam-4570	591	23	is	be	AUX
ejpam-4570	591	24	c	c	NOUN
ejpam-4570	591	25	-	-	PUNCT
ejpam-4570	591	26	almost	almost	ADV
ejpam-4570	591	27	normal	normal	ADJ
ejpam-4570	591	28	.	.	PUNCT
ejpam-4570	592	1	therefore	therefore	ADV
ejpam-4570	592	2	,	,	PUNCT
ejpam-4570	592	3	the	the	DET
ejpam-4570	592	4	space	space	NOUN
ejpam-4570	592	5	x	x	PUNCT
ejpam-4570	592	6	is	be	AUX
ejpam-4570	592	7	an	an	DET
ejpam-4570	592	8	example	example	NOUN
ejpam-4570	592	9	of	of	ADP
ejpam-4570	592	10	a	a	DET
ejpam-4570	592	11	hausdorff	hausdorff	NOUN
ejpam-4570	592	12	countable	countable	ADJ
ejpam-4570	592	13	c	c	NOUN
ejpam-4570	592	14	-	-	PUNCT
ejpam-4570	592	15	almost	almost	ADV
ejpam-4570	592	16	normal	normal	ADJ
ejpam-4570	592	17	space	space	NOUN
ejpam-4570	592	18	,	,	PUNCT
ejpam-4570	592	19	which	which	PRON
ejpam-4570	592	20	is	be	AUX
ejpam-4570	592	21	neither	neither	CCONJ
ejpam-4570	592	22	almost	almost	ADV
ejpam-4570	592	23	normal	normal	ADJ
ejpam-4570	592	24	,	,	PUNCT
ejpam-4570	592	25	l	l	NOUN
ejpam-4570	592	26	-	-	PUNCT
ejpam-4570	592	27	almost	almost	ADV
ejpam-4570	592	28	normal	normal	ADJ
ejpam-4570	592	29	nor	nor	CCONJ
ejpam-4570	592	30	epi	epi	NOUN
ejpam-4570	592	31	-	-	ADJ
ejpam-4570	592	32	almost	almost	ADV
ejpam-4570	592	33	normal	normal	ADJ
ejpam-4570	592	34	.	.	PUNCT
ejpam-4570	593	1	the	the	DET
ejpam-4570	593	2	next	next	ADJ
ejpam-4570	593	3	example	example	NOUN
ejpam-4570	593	4	is	be	AUX
ejpam-4570	593	5	an	an	DET
ejpam-4570	593	6	l	l	NOUN
ejpam-4570	593	7	-	-	ADJ
ejpam-4570	593	8	almost	almost	ADV
ejpam-4570	593	9	normal	normal	ADJ
ejpam-4570	593	10	space	space	NOUN
ejpam-4570	593	11	which	which	PRON
ejpam-4570	593	12	is	be	AUX
ejpam-4570	593	13	neither	neither	CCONJ
ejpam-4570	593	14	l	l	NOUN
ejpam-4570	593	15	-	-	ADJ
ejpam-4570	593	16	normal	normal	ADJ
ejpam-4570	593	17	.	.	PUNCT
ejpam-4570	594	1	wafa	wafa	PROPN
ejpam-4570	594	2	khalaf	khalaf	PROPN
ejpam-4570	594	3	alqurashi	alqurashi	PROPN
ejpam-4570	594	4	,	,	PUNCT
ejpam-4570	594	5	sadeq	sadeq	PROPN
ejpam-4570	594	6	ali	ali	PROPN
ejpam-4570	594	7	thabit	thabit	PROPN
ejpam-4570	594	8	/	/	SYM
ejpam-4570	594	9	eur	eur	PROPN
ejpam-4570	594	10	.	.	PUNCT
ejpam-4570	595	1	j.	j.	PROPN
ejpam-4570	595	2	pure	pure	PROPN
ejpam-4570	595	3	appl	appl	PROPN
ejpam-4570	595	4	.	.	PROPN
ejpam-4570	595	5	math	math	PROPN
ejpam-4570	595	6	,	,	PUNCT
ejpam-4570	595	7	15	15	NUM
ejpam-4570	595	8	(	(	PUNCT
ejpam-4570	595	9	4	4	NUM
ejpam-4570	595	10	)	)	PUNCT
ejpam-4570	595	11	(	(	PUNCT
ejpam-4570	595	12	2022	2022	NUM
ejpam-4570	595	13	)	)	PUNCT
ejpam-4570	595	14	,	,	PUNCT
ejpam-4570	595	15	1760	1760	NUM
ejpam-4570	595	16	-	-	SYM
ejpam-4570	595	17	1782	1782	NUM
ejpam-4570	595	18	1778	1778	NUM
ejpam-4570	595	19	example	example	NOUN
ejpam-4570	595	20	19	19	NUM
ejpam-4570	595	21	.	.	PUNCT
ejpam-4570	596	1	the	the	DET
ejpam-4570	596	2	rational	rational	ADJ
ejpam-4570	596	3	sequence	sequence	NOUN
ejpam-4570	596	4	topology	topology	NOUN
ejpam-4570	596	5	[	[	X
ejpam-4570	596	6	29	29	NUM
ejpam-4570	596	7	,	,	PUNCT
ejpam-4570	596	8	example	example	NOUN
ejpam-4570	596	9	65	65	NUM
ejpam-4570	596	10	]	]	PUNCT
ejpam-4570	596	11	,	,	PUNCT
ejpam-4570	596	12	is	be	AUX
ejpam-4570	596	13	a	a	DET
ejpam-4570	596	14	first	first	ADJ
ejpam-4570	596	15	countable	countable	ADJ
ejpam-4570	596	16	,	,	PUNCT
ejpam-4570	596	17	zero	zero	NUM
ejpam-4570	596	18	-	-	PUNCT
ejpam-4570	596	19	dimensional	dimensional	ADJ
ejpam-4570	596	20	,	,	PUNCT
ejpam-4570	596	21	tychonoff	tychonoff	NOUN
ejpam-4570	596	22	,	,	PUNCT
ejpam-4570	596	23	locally	locally	ADV
ejpam-4570	596	24	compact	compact	ADJ
ejpam-4570	596	25	,	,	PUNCT
ejpam-4570	596	26	separable	separable	ADJ
ejpam-4570	596	27	space	space	NOUN
ejpam-4570	596	28	which	which	PRON
ejpam-4570	596	29	is	be	AUX
ejpam-4570	596	30	neither	neither	CCONJ
ejpam-4570	596	31	paracompact	paracompact	ADJ
ejpam-4570	596	32	,	,	PUNCT
ejpam-4570	596	33	normal	normal	ADJ
ejpam-4570	596	34	nor	nor	CCONJ
ejpam-4570	596	35	lindelöf	lindelöf	NOUN
ejpam-4570	596	36	[	[	X
ejpam-4570	596	37	29	29	NUM
ejpam-4570	596	38	]	]	PUNCT
ejpam-4570	596	39	.	.	PUNCT
ejpam-4570	597	1	also	also	ADV
ejpam-4570	597	2	,	,	PUNCT
ejpam-4570	597	3	(	(	PUNCT
ejpam-4570	597	4	r	r	NOUN
ejpam-4570	597	5	,	,	PUNCT
ejpam-4570	597	6	rs	rs	NOUN
ejpam-4570	597	7	)	)	PUNCT
ejpam-4570	597	8	is	be	AUX
ejpam-4570	597	9	a	a	DET
ejpam-4570	597	10	regular	regular	ADJ
ejpam-4570	597	11	,	,	PUNCT
ejpam-4570	597	12	semi	semi	ADV
ejpam-4570	597	13	regular	regular	ADJ
ejpam-4570	597	14	and	and	CCONJ
ejpam-4570	597	15	almost	almost	ADV
ejpam-4570	597	16	normal	normal	ADJ
ejpam-4570	597	17	space	space	NOUN
ejpam-4570	597	18	,	,	PUNCT
ejpam-4570	597	19	which	which	PRON
ejpam-4570	597	20	is	be	AUX
ejpam-4570	597	21	not	not	PART
ejpam-4570	597	22	normal	normal	ADJ
ejpam-4570	597	23	[	[	X
ejpam-4570	597	24	35	35	NUM
ejpam-4570	597	25	]	]	PUNCT
ejpam-4570	597	26	.	.	PUNCT
ejpam-4570	598	1	observed	observe	VERB
ejpam-4570	598	2	that	that	SCONJ
ejpam-4570	598	3	:	:	PUNCT
ejpam-4570	598	4	in	in	ADP
ejpam-4570	598	5	the	the	DET
ejpam-4570	598	6	rational	rational	ADJ
ejpam-4570	598	7	sequence	sequence	NOUN
ejpam-4570	598	8	topology	topology	NOUN
ejpam-4570	598	9	,	,	PUNCT
ejpam-4570	598	10	we	we	PRON
ejpam-4570	598	11	have	have	VERB
ejpam-4570	598	12	the	the	DET
ejpam-4570	598	13	usual	usual	ADJ
ejpam-4570	598	14	topology	topology	NOUN
ejpam-4570	598	15	u	u	NOUN
ejpam-4570	598	16	on	on	ADP
ejpam-4570	598	17	r	r	NOUN
ejpam-4570	598	18	is	be	AUX
ejpam-4570	598	19	a	a	DET
ejpam-4570	598	20	topology	topology	NOUN
ejpam-4570	598	21	coarser	coarse	ADJ
ejpam-4570	598	22	than	than	ADP
ejpam-4570	598	23	rs	rs	ADJ
ejpam-4570	598	24	,	,	PUNCT
ejpam-4570	598	25	i.e.	i.e.	X
ejpam-4570	598	26	u	u	NOUN
ejpam-4570	598	27	⊆	⊆	NUM
ejpam-4570	598	28	rs	rs	NOUN
ejpam-4570	598	29	.	.	PUNCT
ejpam-4570	599	1	since	since	SCONJ
ejpam-4570	599	2	(	(	PUNCT
ejpam-4570	599	3	r	r	NOUN
ejpam-4570	599	4	,	,	PUNCT
ejpam-4570	599	5	u	u	NOUN
ejpam-4570	599	6	)	)	PUNCT
ejpam-4570	599	7	is	be	AUX
ejpam-4570	599	8	a	a	DET
ejpam-4570	599	9	hausdorff	hausdorff	NOUN
ejpam-4570	599	10	normal	normal	ADJ
ejpam-4570	599	11	space	space	NOUN
ejpam-4570	599	12	,	,	PUNCT
ejpam-4570	599	13	we	we	PRON
ejpam-4570	599	14	get	get	VERB
ejpam-4570	599	15	:	:	PUNCT
ejpam-4570	599	16	the	the	DET
ejpam-4570	599	17	rational	rational	ADJ
ejpam-4570	599	18	sequence	sequence	NOUN
ejpam-4570	599	19	topology	topology	NOUN
ejpam-4570	599	20	is	be	AUX
ejpam-4570	599	21	epi	epi	ADJ
ejpam-4570	599	22	-	-	ADJ
ejpam-4570	599	23	normal	normal	ADJ
ejpam-4570	599	24	sub	sub	ADJ
ejpam-4570	599	25	-	-	ADJ
ejpam-4570	599	26	metrizable	metrizable	ADJ
ejpam-4570	599	27	space	space	NOUN
ejpam-4570	599	28	.	.	PUNCT
ejpam-4570	600	1	hence	hence	ADV
ejpam-4570	600	2	,	,	PUNCT
ejpam-4570	600	3	it	it	PRON
ejpam-4570	600	4	is	be	AUX
ejpam-4570	600	5	an	an	DET
ejpam-4570	600	6	epi	epi	NOUN
ejpam-4570	600	7	-	-	ADJ
ejpam-4570	600	8	almost	almost	ADV
ejpam-4570	600	9	normal	normal	ADJ
ejpam-4570	600	10	space	space	NOUN
ejpam-4570	600	11	.	.	PUNCT
ejpam-4570	601	1	sincex	sincex	PROPN
ejpam-4570	601	2	is	be	AUX
ejpam-4570	601	3	hausdorff	hausdorff	NOUN
ejpam-4570	601	4	almost	almost	ADV
ejpam-4570	601	5	normal	normal	ADJ
ejpam-4570	601	6	space	space	NOUN
ejpam-4570	601	7	,	,	PUNCT
ejpam-4570	601	8	we	we	PRON
ejpam-4570	601	9	get	get	VERB
ejpam-4570	601	10	:	:	PUNCT
ejpam-4570	601	11	it	it	PRON
ejpam-4570	601	12	is	be	AUX
ejpam-4570	601	13	both	both	PRON
ejpam-4570	601	14	c	c	NOUN
ejpam-4570	601	15	-	-	PUNCT
ejpam-4570	601	16	almost	almost	ADV
ejpam-4570	601	17	normal	normal	ADJ
ejpam-4570	601	18	and	and	CCONJ
ejpam-4570	601	19	l	l	NOUN
ejpam-4570	601	20	-	-	PUNCT
ejpam-4570	601	21	almost	almost	ADV
ejpam-4570	601	22	normal	normal	ADJ
ejpam-4570	601	23	.	.	PUNCT
ejpam-4570	602	1	since	since	SCONJ
ejpam-4570	602	2	every	every	DET
ejpam-4570	602	3	tychonoff	tychonoff	NOUN
ejpam-4570	602	4	first	first	ADV
ejpam-4570	602	5	countable	countable	ADJ
ejpam-4570	602	6	separable	separable	ADJ
ejpam-4570	602	7	l	l	ADJ
ejpam-4570	602	8	-	-	ADJ
ejpam-4570	602	9	normal	normal	ADJ
ejpam-4570	602	10	space	space	NOUN
ejpam-4570	602	11	is	be	AUX
ejpam-4570	602	12	normal	normal	ADJ
ejpam-4570	602	13	[	[	X
ejpam-4570	602	14	16	16	NUM
ejpam-4570	602	15	]	]	PUNCT
ejpam-4570	602	16	,	,	PUNCT
ejpam-4570	602	17	x	x	X
ejpam-4570	602	18	is	be	AUX
ejpam-4570	602	19	tychonoff	tychonoff	NOUN
ejpam-4570	602	20	first	first	ADV
ejpam-4570	602	21	countable	countable	ADJ
ejpam-4570	602	22	separable	separable	NOUN
ejpam-4570	602	23	and	and	CCONJ
ejpam-4570	602	24	not	not	PART
ejpam-4570	602	25	normal	normal	ADJ
ejpam-4570	602	26	,	,	PUNCT
ejpam-4570	602	27	we	we	PRON
ejpam-4570	602	28	get	get	VERB
ejpam-4570	602	29	:	:	PUNCT
ejpam-4570	602	30	x	x	X
ejpam-4570	602	31	is	be	AUX
ejpam-4570	602	32	not	not	PART
ejpam-4570	602	33	l	l	NOUN
ejpam-4570	602	34	-	-	ADJ
ejpam-4570	602	35	normal	normal	ADJ
ejpam-4570	602	36	.	.	PUNCT
ejpam-4570	603	1	since	since	SCONJ
ejpam-4570	603	2	every	every	DET
ejpam-4570	603	3	hausdorff	hausdorff	NOUN
ejpam-4570	603	4	locally	locally	ADV
ejpam-4570	603	5	compact	compact	ADJ
ejpam-4570	603	6	space	space	NOUN
ejpam-4570	603	7	is	be	AUX
ejpam-4570	603	8	c	c	NOUN
ejpam-4570	603	9	-	-	ADJ
ejpam-4570	603	10	normal	normal	ADJ
ejpam-4570	603	11	,	,	PUNCT
ejpam-4570	603	12	we	we	PRON
ejpam-4570	603	13	get	get	VERB
ejpam-4570	603	14	the	the	DET
ejpam-4570	603	15	rational	rational	ADJ
ejpam-4570	603	16	sequence	sequence	NOUN
ejpam-4570	603	17	topology	topology	NOUN
ejpam-4570	603	18	is	be	AUX
ejpam-4570	603	19	c	c	NOUN
ejpam-4570	603	20	-	-	ADJ
ejpam-4570	603	21	normal	normal	ADJ
ejpam-4570	603	22	.	.	PUNCT
ejpam-4570	604	1	therefore	therefore	ADV
ejpam-4570	604	2	,	,	PUNCT
ejpam-4570	604	3	the	the	DET
ejpam-4570	604	4	rational	rational	ADJ
ejpam-4570	604	5	sequence	sequence	NOUN
ejpam-4570	604	6	topology	topology	NOUN
ejpam-4570	604	7	is	be	AUX
ejpam-4570	604	8	an	an	DET
ejpam-4570	604	9	example	example	NOUN
ejpam-4570	604	10	of	of	ADP
ejpam-4570	604	11	an	an	DET
ejpam-4570	604	12	epi	epi	NOUN
ejpam-4570	604	13	-	-	ADJ
ejpam-4570	604	14	normal	normal	ADJ
ejpam-4570	604	15	,	,	PUNCT
ejpam-4570	604	16	epi	epi	NOUN
ejpam-4570	604	17	-	-	PUNCT
ejpam-4570	604	18	almost	almost	ADV
ejpam-4570	604	19	normal	normal	ADJ
ejpam-4570	604	20	,	,	PUNCT
ejpam-4570	604	21	c	c	NOUN
ejpam-4570	604	22	-	-	PUNCT
ejpam-4570	604	23	almost	almost	ADV
ejpam-4570	604	24	normal	normal	ADJ
ejpam-4570	604	25	,	,	PUNCT
ejpam-4570	604	26	l	l	NOUN
ejpam-4570	604	27	-	-	PUNCT
ejpam-4570	604	28	almost	almost	ADV
ejpam-4570	604	29	normal	normal	ADJ
ejpam-4570	604	30	,	,	PUNCT
ejpam-4570	604	31	c	c	NOUN
ejpam-4570	604	32	-	-	ADJ
ejpam-4570	604	33	normal	normal	ADJ
ejpam-4570	604	34	,	,	PUNCT
ejpam-4570	604	35	l	l	ADJ
ejpam-4570	604	36	-	-	NOUN
ejpam-4570	604	37	tychonoff	tychonoff	NOUN
ejpam-4570	604	38	space	space	NOUN
ejpam-4570	604	39	which	which	PRON
ejpam-4570	604	40	is	be	AUX
ejpam-4570	604	41	not	not	PART
ejpam-4570	604	42	l	l	NOUN
ejpam-4570	604	43	-	-	ADJ
ejpam-4570	604	44	normal	normal	ADJ
ejpam-4570	604	45	.	.	PUNCT
ejpam-4570	605	1	at	at	ADP
ejpam-4570	605	2	the	the	DET
ejpam-4570	605	3	end	end	NOUN
ejpam-4570	605	4	of	of	ADP
ejpam-4570	605	5	this	this	DET
ejpam-4570	605	6	research	research	NOUN
ejpam-4570	605	7	,	,	PUNCT
ejpam-4570	605	8	we	we	PRON
ejpam-4570	605	9	present	present	VERB
ejpam-4570	605	10	the	the	DET
ejpam-4570	605	11	next	next	ADJ
ejpam-4570	605	12	remarks	remark	NOUN
ejpam-4570	605	13	:	:	PUNCT
ejpam-4570	605	14	remark	remark	NOUN
ejpam-4570	605	15	1	1	NUM
ejpam-4570	605	16	.	.	PUNCT
ejpam-4570	606	1	it	it	PRON
ejpam-4570	606	2	can	can	AUX
ejpam-4570	606	3	be	be	AUX
ejpam-4570	606	4	observed	observe	VERB
ejpam-4570	606	5	that	that	SCONJ
ejpam-4570	606	6	:	:	PUNCT
ejpam-4570	606	7	(	(	PUNCT
ejpam-4570	606	8	1	1	X
ejpam-4570	606	9	)	)	PUNCT
ejpam-4570	606	10	c	c	NOUN
ejpam-4570	606	11	-	-	PUNCT
ejpam-4570	606	12	almost	almost	ADV
ejpam-4570	606	13	normality	normality	NOUN
ejpam-4570	606	14	(	(	PUNCT
ejpam-4570	606	15	resp	resp	NOUN
ejpam-4570	606	16	.	.	PUNCT
ejpam-4570	607	1	l	l	ADJ
ejpam-4570	607	2	-	-	ADJ
ejpam-4570	607	3	quasi	quasi	ADJ
ejpam-4570	607	4	normality	normality	NOUN
ejpam-4570	607	5	)	)	PUNCT
ejpam-4570	607	6	does	do	AUX
ejpam-4570	607	7	not	not	PART
ejpam-4570	607	8	imply	imply	VERB
ejpam-4570	607	9	to	to	ADP
ejpam-4570	607	10	l	l	VERB
ejpam-4570	607	11	-	-	PUNCT
ejpam-4570	607	12	almost	almost	ADV
ejpam-4570	607	13	normality	normality	NOUN
ejpam-4570	607	14	,	,	PUNCT
ejpam-4570	607	15	and	and	CCONJ
ejpam-4570	607	16	any	any	DET
ejpam-4570	607	17	epi	epi	NOUN
ejpam-4570	607	18	-	-	ADJ
ejpam-4570	607	19	almost	almost	ADV
ejpam-4570	607	20	normal	normal	ADJ
ejpam-4570	607	21	space	space	NOUN
ejpam-4570	607	22	is	be	AUX
ejpam-4570	607	23	not	not	PART
ejpam-4570	607	24	necessary	necessary	ADJ
ejpam-4570	607	25	to	to	PART
ejpam-4570	607	26	be	be	AUX
ejpam-4570	607	27	l	l	NOUN
ejpam-4570	607	28	-	-	ADJ
ejpam-4570	607	29	almost	almost	ADV
ejpam-4570	607	30	normal	normal	ADJ
ejpam-4570	607	31	.	.	PUNCT
ejpam-4570	608	1	for	for	ADP
ejpam-4570	608	2	example	example	NOUN
ejpam-4570	608	3	:	:	PUNCT
ejpam-4570	608	4	the	the	DET
ejpam-4570	608	5	smirnov	smirnov	PROPN
ejpam-4570	608	6	’s	’s	PART
ejpam-4570	608	7	deleted	delete	VERB
ejpam-4570	608	8	sequence	sequence	NOUN
ejpam-4570	608	9	topology	topology	NOUN
ejpam-4570	608	10	,	,	PUNCT
ejpam-4570	608	11	example	example	NOUN
ejpam-4570	608	12	9	9	NUM
ejpam-4570	608	13	,	,	PUNCT
ejpam-4570	608	14	and	and	CCONJ
ejpam-4570	608	15	the	the	DET
ejpam-4570	608	16	countable	countable	ADJ
ejpam-4570	608	17	complement	complement	NOUN
ejpam-4570	608	18	extension	extension	NOUN
ejpam-4570	608	19	topology	topology	NOUN
ejpam-4570	608	20	,	,	PUNCT
ejpam-4570	608	21	example	example	NOUN
ejpam-4570	608	22	10	10	NUM
ejpam-4570	608	23	,	,	PUNCT
ejpam-4570	608	24	are	be	AUX
ejpam-4570	608	25	l	l	ADJ
ejpam-4570	608	26	-	-	ADJ
ejpam-4570	608	27	quasi	quasi	ADJ
ejpam-4570	608	28	normal	normal	ADJ
ejpam-4570	608	29	,	,	PUNCT
ejpam-4570	608	30	epi	epi	NOUN
ejpam-4570	608	31	-	-	PUNCT
ejpam-4570	608	32	almost	almost	ADV
ejpam-4570	608	33	normal	normal	ADJ
ejpam-4570	608	34	and	and	CCONJ
ejpam-4570	608	35	c	c	NOUN
ejpam-4570	608	36	-	-	PUNCT
ejpam-4570	608	37	almost	almost	ADV
ejpam-4570	608	38	normal	normal	ADJ
ejpam-4570	608	39	spaces	space	NOUN
ejpam-4570	608	40	,	,	PUNCT
ejpam-4570	608	41	which	which	PRON
ejpam-4570	608	42	are	be	AUX
ejpam-4570	608	43	neither	neither	CCONJ
ejpam-4570	608	44	almost	almost	ADV
ejpam-4570	608	45	normal	normal	ADJ
ejpam-4570	608	46	nor	nor	CCONJ
ejpam-4570	608	47	l	l	NOUN
ejpam-4570	608	48	-	-	ADJ
ejpam-4570	608	49	almost	almost	ADV
ejpam-4570	608	50	normal	normal	ADJ
ejpam-4570	608	51	.	.	PUNCT
ejpam-4570	609	1	(	(	PUNCT
ejpam-4570	609	2	2	2	X
ejpam-4570	609	3	)	)	PUNCT
ejpam-4570	609	4	l	l	NOUN
ejpam-4570	609	5	-	-	PUNCT
ejpam-4570	609	6	almost	almost	ADV
ejpam-4570	609	7	normality	normality	NOUN
ejpam-4570	609	8	and	and	CCONJ
ejpam-4570	609	9	c	c	NOUN
ejpam-4570	609	10	-	-	PUNCT
ejpam-4570	609	11	almost	almost	ADV
ejpam-4570	609	12	normality	normality	NOUN
ejpam-4570	609	13	do	do	AUX
ejpam-4570	609	14	not	not	PART
ejpam-4570	609	15	imply	imply	VERB
ejpam-4570	609	16	to	to	ADP
ejpam-4570	609	17	epi	epi	VERB
ejpam-4570	609	18	-	-	PUNCT
ejpam-4570	609	19	almost	almost	ADV
ejpam-4570	609	20	normality	normality	NOUN
ejpam-4570	609	21	.	.	PUNCT
ejpam-4570	610	1	for	for	ADP
ejpam-4570	610	2	example	example	NOUN
ejpam-4570	610	3	:	:	PUNCT
ejpam-4570	610	4	the	the	DET
ejpam-4570	610	5	integer	integer	NOUN
ejpam-4570	610	6	broom	broom	NOUN
ejpam-4570	610	7	topology	topology	NOUN
ejpam-4570	610	8	,	,	PUNCT
ejpam-4570	610	9	example	example	NOUN
ejpam-4570	610	10	13	13	NUM
ejpam-4570	610	11	,	,	PUNCT
ejpam-4570	610	12	is	be	AUX
ejpam-4570	610	13	both	both	PRON
ejpam-4570	610	14	a	a	DET
ejpam-4570	610	15	c	c	NOUN
ejpam-4570	610	16	-	-	PUNCT
ejpam-4570	610	17	almost	almost	ADV
ejpam-4570	610	18	normal	normal	ADJ
ejpam-4570	610	19	and	and	CCONJ
ejpam-4570	610	20	l	l	NOUN
ejpam-4570	610	21	-	-	ADJ
ejpam-4570	610	22	almost	almost	ADV
ejpam-4570	610	23	normal	normal	ADJ
ejpam-4570	610	24	space	space	NOUN
ejpam-4570	610	25	which	which	PRON
ejpam-4570	610	26	is	be	AUX
ejpam-4570	610	27	not	not	PART
ejpam-4570	610	28	epi	epi	NOUN
ejpam-4570	610	29	-	-	ADJ
ejpam-4570	610	30	almost	almost	ADV
ejpam-4570	610	31	normal	normal	ADJ
ejpam-4570	610	32	.	.	PUNCT
ejpam-4570	611	1	the	the	DET
ejpam-4570	611	2	finite	finite	PROPN
ejpam-4570	611	3	complement	complement	NOUN
ejpam-4570	611	4	topology	topology	NOUN
ejpam-4570	611	5	,	,	PUNCT
ejpam-4570	611	6	example	example	NOUN
ejpam-4570	611	7	3	3	NUM
ejpam-4570	611	8	,	,	PUNCT
ejpam-4570	611	9	and	and	CCONJ
ejpam-4570	611	10	the	the	DET
ejpam-4570	611	11	countable	countable	ADJ
ejpam-4570	611	12	complement	complement	NOUN
ejpam-4570	611	13	topology	topology	NOUN
ejpam-4570	611	14	,	,	PUNCT
ejpam-4570	611	15	example	example	NOUN
ejpam-4570	611	16	4	4	NUM
ejpam-4570	611	17	,	,	PUNCT
ejpam-4570	611	18	are	be	AUX
ejpam-4570	611	19	both	both	PRON
ejpam-4570	611	20	c	c	NOUN
ejpam-4570	611	21	-	-	PUNCT
ejpam-4570	611	22	almost	almost	ADV
ejpam-4570	611	23	normal	normal	ADJ
ejpam-4570	611	24	and	and	CCONJ
ejpam-4570	611	25	l	l	NOUN
ejpam-4570	611	26	-	-	ADJ
ejpam-4570	611	27	almost	almost	ADV
ejpam-4570	611	28	normal	normal	ADJ
ejpam-4570	611	29	spaces	space	NOUN
ejpam-4570	611	30	,	,	PUNCT
ejpam-4570	611	31	which	which	PRON
ejpam-4570	611	32	are	be	AUX
ejpam-4570	611	33	not	not	PART
ejpam-4570	611	34	epi	epi	NOUN
ejpam-4570	611	35	-	-	ADJ
ejpam-4570	611	36	almost	almost	ADV
ejpam-4570	611	37	normal	normal	ADJ
ejpam-4570	611	38	.	.	PUNCT
ejpam-4570	612	1	(	(	PUNCT
ejpam-4570	612	2	3	3	X
ejpam-4570	612	3	)	)	PUNCT
ejpam-4570	612	4	l	l	NOUN
ejpam-4570	612	5	-	-	PUNCT
ejpam-4570	612	6	almost	almost	ADV
ejpam-4570	612	7	normality	normality	NOUN
ejpam-4570	612	8	and	and	CCONJ
ejpam-4570	612	9	c	c	NOUN
ejpam-4570	612	10	-	-	PUNCT
ejpam-4570	612	11	almost	almost	ADV
ejpam-4570	612	12	normality	normality	NOUN
ejpam-4570	612	13	do	do	AUX
ejpam-4570	612	14	not	not	PART
ejpam-4570	612	15	imply	imply	VERB
ejpam-4570	612	16	to	to	ADP
ejpam-4570	612	17	almost	almost	ADV
ejpam-4570	612	18	normality	normality	ADJ
ejpam-4570	612	19	.	.	PUNCT
ejpam-4570	613	1	for	for	ADP
ejpam-4570	613	2	example	example	NOUN
ejpam-4570	613	3	:	:	PUNCT
ejpam-4570	613	4	the	the	DET
ejpam-4570	613	5	modified	modify	VERB
ejpam-4570	613	6	dieudonné	dieudonné	NOUN
ejpam-4570	613	7	plank	plank	NOUN
ejpam-4570	613	8	topology	topology	NOUN
ejpam-4570	613	9	,	,	PUNCT
ejpam-4570	613	10	example	example	NOUN
ejpam-4570	613	11	8	8	NUM
ejpam-4570	613	12	,	,	PUNCT
ejpam-4570	613	13	is	be	AUX
ejpam-4570	613	14	an	an	DET
ejpam-4570	613	15	l	l	NOUN
ejpam-4570	613	16	-	-	ADJ
ejpam-4570	613	17	almost	almost	ADV
ejpam-4570	613	18	normal	normal	ADJ
ejpam-4570	613	19	and	and	CCONJ
ejpam-4570	613	20	c	c	NOUN
ejpam-4570	613	21	-	-	PUNCT
ejpam-4570	613	22	almost	almost	ADV
ejpam-4570	613	23	normal	normal	ADJ
ejpam-4570	613	24	space	space	NOUN
ejpam-4570	613	25	,	,	PUNCT
ejpam-4570	613	26	which	which	PRON
ejpam-4570	613	27	is	be	AUX
ejpam-4570	613	28	not	not	PART
ejpam-4570	613	29	almost	almost	ADV
ejpam-4570	613	30	normal	normal	ADJ
ejpam-4570	613	31	.	.	PUNCT
ejpam-4570	614	1	(	(	PUNCT
ejpam-4570	614	2	4	4	X
ejpam-4570	614	3	)	)	PUNCT
ejpam-4570	614	4	epi	epi	NOUN
ejpam-4570	614	5	-	-	ADJ
ejpam-4570	614	6	quasi	quasi	ADJ
ejpam-4570	614	7	normality	normality	NOUN
ejpam-4570	614	8	and	and	CCONJ
ejpam-4570	614	9	quasi	quasi	ADJ
ejpam-4570	614	10	normality	normality	NOUN
ejpam-4570	614	11	do	do	AUX
ejpam-4570	614	12	not	not	PART
ejpam-4570	614	13	imply	imply	VERB
ejpam-4570	614	14	to	to	ADP
ejpam-4570	614	15	l	l	VERB
ejpam-4570	614	16	-	-	PUNCT
ejpam-4570	614	17	almost	almost	ADV
ejpam-4570	614	18	normality	normality	NOUN
ejpam-4570	614	19	.	.	PUNCT
ejpam-4570	615	1	for	for	ADP
ejpam-4570	615	2	example	example	NOUN
ejpam-4570	615	3	,	,	PUNCT
ejpam-4570	615	4	the	the	DET
ejpam-4570	615	5	simplified	simplified	ADJ
ejpam-4570	615	6	arens	arens	PROPN
ejpam-4570	615	7	square	square	NOUN
ejpam-4570	615	8	topology	topology	NOUN
ejpam-4570	615	9	,	,	PUNCT
ejpam-4570	615	10	example	example	NOUN
ejpam-4570	615	11	11	11	NUM
ejpam-4570	615	12	,	,	PUNCT
ejpam-4570	615	13	is	be	AUX
ejpam-4570	615	14	an	an	DET
ejpam-4570	615	15	epi	epi	NOUN
ejpam-4570	615	16	-	-	ADJ
ejpam-4570	615	17	quasi	quasi	ADJ
ejpam-4570	615	18	normal	normal	ADJ
ejpam-4570	615	19	,	,	PUNCT
ejpam-4570	615	20	quasi	quasi	X
ejpam-4570	615	21	normal	normal	ADJ
ejpam-4570	615	22	,	,	PUNCT
ejpam-4570	615	23	c	c	NOUN
ejpam-4570	615	24	-	-	PUNCT
ejpam-4570	615	25	quasi	quasi	ADJ
ejpam-4570	615	26	normal	normal	ADJ
ejpam-4570	615	27	and	and	CCONJ
ejpam-4570	615	28	l	l	ADJ
ejpam-4570	615	29	-	-	ADJ
ejpam-4570	615	30	quasi	quasi	ADJ
ejpam-4570	615	31	normal	normal	ADJ
ejpam-4570	615	32	space	space	NOUN
ejpam-4570	615	33	which	which	PRON
ejpam-4570	615	34	is	be	AUX
ejpam-4570	615	35	neither	neither	CCONJ
ejpam-4570	615	36	l	l	NOUN
ejpam-4570	615	37	-	-	ADJ
ejpam-4570	615	38	almost	almost	ADV
ejpam-4570	615	39	normal	normal	ADJ
ejpam-4570	615	40	nor	nor	CCONJ
ejpam-4570	615	41	almost	almost	ADV
ejpam-4570	615	42	normal	normal	ADJ
ejpam-4570	615	43	.	.	PUNCT
ejpam-4570	616	1	(	(	PUNCT
ejpam-4570	616	2	5	5	X
ejpam-4570	616	3	)	)	PUNCT
ejpam-4570	616	4	c	c	NOUN
ejpam-4570	616	5	-	-	PUNCT
ejpam-4570	616	6	almost	almost	ADV
ejpam-4570	616	7	normality	normality	NOUN
ejpam-4570	616	8	does	do	AUX
ejpam-4570	616	9	not	not	PART
ejpam-4570	616	10	imply	imply	VERB
ejpam-4570	616	11	almost	almost	ADV
ejpam-4570	616	12	normality	normality	NOUN
ejpam-4570	616	13	or	or	CCONJ
ejpam-4570	616	14	sub	sub	NOUN
ejpam-4570	616	15	-	-	NOUN
ejpam-4570	616	16	metrizability	metrizability	NOUN
ejpam-4570	616	17	.	.	PUNCT
ejpam-4570	617	1	for	for	ADP
ejpam-4570	617	2	example	example	NOUN
ejpam-4570	617	3	,	,	PUNCT
ejpam-4570	617	4	the	the	DET
ejpam-4570	617	5	deleted	delete	VERB
ejpam-4570	617	6	tychonoff	tychonoff	NOUN
ejpam-4570	617	7	plank	plank	NOUN
ejpam-4570	617	8	,	,	PUNCT
ejpam-4570	617	9	example	example	NOUN
ejpam-4570	617	10	6	6	NUM
ejpam-4570	617	11	,	,	PUNCT
ejpam-4570	617	12	is	be	AUX
ejpam-4570	617	13	a	a	DET
ejpam-4570	617	14	c	c	NOUN
ejpam-4570	617	15	-	-	PUNCT
ejpam-4570	617	16	almost	almost	ADV
ejpam-4570	617	17	normal	normal	ADJ
ejpam-4570	617	18	space	space	NOUN
ejpam-4570	617	19	,	,	PUNCT
ejpam-4570	617	20	which	which	PRON
ejpam-4570	617	21	is	be	AUX
ejpam-4570	617	22	neither	neither	DET
ejpam-4570	617	23	sub	sub	NOUN
ejpam-4570	617	24	-	-	ADJ
ejpam-4570	617	25	metrizable	metrizable	ADJ
ejpam-4570	617	26	nor	nor	CCONJ
ejpam-4570	617	27	almost	almost	ADV
ejpam-4570	617	28	normal	normal	ADJ
ejpam-4570	617	29	.	.	PUNCT
ejpam-4570	618	1	(	(	PUNCT
ejpam-4570	618	2	6	6	NUM
ejpam-4570	618	3	)	)	PUNCT
ejpam-4570	618	4	l	l	NOUN
ejpam-4570	618	5	-	-	PUNCT
ejpam-4570	618	6	almost	almost	ADV
ejpam-4570	618	7	normality	normality	NOUN
ejpam-4570	618	8	does	do	AUX
ejpam-4570	618	9	not	not	PART
ejpam-4570	618	10	imply	imply	VERB
ejpam-4570	618	11	to	to	ADP
ejpam-4570	618	12	epi	epi	VERB
ejpam-4570	618	13	-	-	PUNCT
ejpam-4570	618	14	almost	almost	ADV
ejpam-4570	618	15	normality	normality	NOUN
ejpam-4570	618	16	nor	nor	CCONJ
ejpam-4570	618	17	c	c	NOUN
ejpam-4570	618	18	-	-	PUNCT
ejpam-4570	618	19	almost	almost	ADV
ejpam-4570	618	20	regularity	regularity	NOUN
ejpam-4570	618	21	.	.	PUNCT
ejpam-4570	619	1	for	for	ADP
ejpam-4570	619	2	example	example	NOUN
ejpam-4570	619	3	:	:	PUNCT
ejpam-4570	619	4	the	the	DET
ejpam-4570	619	5	excluded	exclude	VERB
ejpam-4570	619	6	point	point	NOUN
ejpam-4570	619	7	topology	topology	NOUN
ejpam-4570	619	8	,	,	PUNCT
ejpam-4570	619	9	example	example	NOUN
ejpam-4570	619	10	2	2	NUM
ejpam-4570	619	11	,	,	PUNCT
ejpam-4570	619	12	is	be	AUX
ejpam-4570	619	13	an	an	DET
ejpam-4570	619	14	l	l	NOUN
ejpam-4570	619	15	-	-	ADJ
ejpam-4570	619	16	almost	almost	ADV
ejpam-4570	619	17	normal	normal	ADJ
ejpam-4570	619	18	and	and	CCONJ
ejpam-4570	619	19	c	c	NOUN
ejpam-4570	619	20	-	-	PUNCT
ejpam-4570	619	21	almost	almost	ADV
ejpam-4570	619	22	normal	normal	ADJ
ejpam-4570	619	23	space	space	NOUN
ejpam-4570	619	24	,	,	PUNCT
ejpam-4570	619	25	which	which	PRON
ejpam-4570	619	26	is	be	AUX
ejpam-4570	619	27	neither	neither	DET
ejpam-4570	619	28	epi	epi	NOUN
ejpam-4570	619	29	-	-	ADJ
ejpam-4570	619	30	almost	almost	ADV
ejpam-4570	619	31	normal	normal	ADJ
ejpam-4570	619	32	nor	nor	CCONJ
ejpam-4570	619	33	c	c	NOUN
ejpam-4570	619	34	-	-	PUNCT
ejpam-4570	619	35	almost	almost	ADV
ejpam-4570	619	36	regular	regular	ADJ
ejpam-4570	619	37	.	.	PUNCT
ejpam-4570	620	1	wafa	wafa	PROPN
ejpam-4570	620	2	khalaf	khalaf	PROPN
ejpam-4570	620	3	alqurashi	alqurashi	PROPN
ejpam-4570	620	4	,	,	PUNCT
ejpam-4570	620	5	sadeq	sadeq	PROPN
ejpam-4570	620	6	ali	ali	PROPN
ejpam-4570	620	7	thabit	thabit	PROPN
ejpam-4570	620	8	/	/	SYM
ejpam-4570	620	9	eur	eur	PROPN
ejpam-4570	620	10	.	.	PUNCT
ejpam-4570	621	1	j.	j.	PROPN
ejpam-4570	621	2	pure	pure	PROPN
ejpam-4570	621	3	appl	appl	PROPN
ejpam-4570	621	4	.	.	PROPN
ejpam-4570	621	5	math	math	PROPN
ejpam-4570	621	6	,	,	PUNCT
ejpam-4570	621	7	15	15	NUM
ejpam-4570	621	8	(	(	PUNCT
ejpam-4570	621	9	4	4	NUM
ejpam-4570	621	10	)	)	PUNCT
ejpam-4570	621	11	(	(	PUNCT
ejpam-4570	621	12	2022	2022	NUM
ejpam-4570	621	13	)	)	PUNCT
ejpam-4570	621	14	,	,	PUNCT
ejpam-4570	621	15	1760	1760	NUM
ejpam-4570	621	16	-	-	SYM
ejpam-4570	621	17	1782	1782	NUM
ejpam-4570	621	18	1779	1779	NUM
ejpam-4570	621	19	(	(	PUNCT
ejpam-4570	621	20	7	7	X
ejpam-4570	621	21	)	)	PUNCT
ejpam-4570	621	22	the	the	DET
ejpam-4570	621	23	space	space	NOUN
ejpam-4570	621	24	ω1	ω1	PROPN
ejpam-4570	621	25	×	×	PROPN
ejpam-4570	621	26	(	(	PUNCT
ejpam-4570	621	27	ω1	ω1	PROPN
ejpam-4570	621	28	+	+	CCONJ
ejpam-4570	621	29	1	1	NUM
ejpam-4570	621	30	)	)	PUNCT
ejpam-4570	621	31	is	be	AUX
ejpam-4570	621	32	both	both	PRON
ejpam-4570	621	33	c	c	NOUN
ejpam-4570	621	34	-	-	ADJ
ejpam-4570	621	35	normal	normal	ADJ
ejpam-4570	621	36	and	and	CCONJ
ejpam-4570	621	37	l	l	ADJ
ejpam-4570	621	38	-	-	ADJ
ejpam-4570	621	39	normal	normal	ADJ
ejpam-4570	621	40	space	space	NOUN
ejpam-4570	621	41	,	,	PUNCT
ejpam-4570	621	42	which	which	PRON
ejpam-4570	621	43	is	be	AUX
ejpam-4570	621	44	not	not	PART
ejpam-4570	621	45	almost	almost	ADV
ejpam-4570	621	46	normal	normal	ADJ
ejpam-4570	621	47	[	[	X
ejpam-4570	621	48	16	16	NUM
ejpam-4570	621	49	,	,	PUNCT
ejpam-4570	621	50	example	example	NOUN
ejpam-4570	621	51	2.4	2.4	NUM
ejpam-4570	621	52	]	]	PUNCT
ejpam-4570	621	53	.	.	PUNCT
ejpam-4570	622	1	thus	thus	ADV
ejpam-4570	622	2	,	,	PUNCT
ejpam-4570	622	3	the	the	DET
ejpam-4570	622	4	space	space	NOUN
ejpam-4570	622	5	ω1×	ω1×	ADV
ejpam-4570	622	6	(	(	PUNCT
ejpam-4570	622	7	ω1	ω1	PROPN
ejpam-4570	622	8	+	+	PROPN
ejpam-4570	622	9	1	1	NUM
ejpam-4570	622	10	)	)	PUNCT
ejpam-4570	622	11	is	be	AUX
ejpam-4570	622	12	both	both	PRON
ejpam-4570	622	13	c	c	NOUN
ejpam-4570	622	14	-	-	PUNCT
ejpam-4570	622	15	almost	almost	ADV
ejpam-4570	622	16	normal	normal	ADJ
ejpam-4570	622	17	and	and	CCONJ
ejpam-4570	622	18	l	l	NOUN
ejpam-4570	622	19	-	-	ADJ
ejpam-4570	622	20	almost	almost	ADV
ejpam-4570	622	21	normal	normal	ADJ
ejpam-4570	622	22	space	space	NOUN
ejpam-4570	622	23	,	,	PUNCT
ejpam-4570	622	24	which	which	PRON
ejpam-4570	622	25	is	be	AUX
ejpam-4570	622	26	not	not	PART
ejpam-4570	622	27	almost	almost	ADV
ejpam-4570	622	28	normal	normal	ADJ
ejpam-4570	622	29	.	.	PUNCT
ejpam-4570	623	1	(	(	PUNCT
ejpam-4570	623	2	8)	8)	NUM
ejpam-4570	623	3	every	every	DET
ejpam-4570	623	4	hausdorff	hausdorff	NOUN
ejpam-4570	623	5	c	c	NOUN
ejpam-4570	623	6	-	-	PUNCT
ejpam-4570	623	7	paracompact	paracompact	ADJ
ejpam-4570	623	8	first	first	ADJ
ejpam-4570	623	9	countable	countable	ADJ
ejpam-4570	623	10	lindelöf	lindelöf	NOUN
ejpam-4570	623	11	space	space	NOUN
ejpam-4570	623	12	is	be	AUX
ejpam-4570	623	13	not	not	PART
ejpam-4570	623	14	necessarily	necessarily	ADV
ejpam-4570	623	15	epi	epi	NOUN
ejpam-4570	623	16	-	-	ADJ
ejpam-4570	623	17	almost	almost	ADV
ejpam-4570	623	18	normal	normal	ADJ
ejpam-4570	623	19	.	.	PUNCT
ejpam-4570	624	1	for	for	ADP
ejpam-4570	624	2	example	example	NOUN
ejpam-4570	624	3	,	,	PUNCT
ejpam-4570	624	4	the	the	DET
ejpam-4570	624	5	space	space	NOUN
ejpam-4570	624	6	presented	present	VERB
ejpam-4570	624	7	in	in	ADP
ejpam-4570	624	8	example	example	NOUN
ejpam-4570	624	9	18	18	NUM
ejpam-4570	624	10	is	be	AUX
ejpam-4570	624	11	a	a	DET
ejpam-4570	624	12	hausdorff	hausdorff	NOUN
ejpam-4570	624	13	c	c	NOUN
ejpam-4570	624	14	-	-	PUNCT
ejpam-4570	624	15	paracompact	paracompact	ADJ
ejpam-4570	624	16	first	first	ADJ
ejpam-4570	624	17	countable	countable	ADJ
ejpam-4570	624	18	lindelöf	lindelöf	NOUN
ejpam-4570	624	19	space	space	NOUN
ejpam-4570	624	20	,	,	PUNCT
ejpam-4570	624	21	which	which	PRON
ejpam-4570	624	22	is	be	AUX
ejpam-4570	624	23	not	not	PART
ejpam-4570	624	24	epi	epi	NOUN
ejpam-4570	624	25	-	-	ADJ
ejpam-4570	624	26	almost	almost	ADV
ejpam-4570	624	27	normal	normal	ADJ
ejpam-4570	624	28	being	be	AUX
ejpam-4570	624	29	not	not	PART
ejpam-4570	624	30	urysohn	urysohn	ADJ
ejpam-4570	624	31	.	.	PUNCT
ejpam-4570	625	1	(	(	PUNCT
ejpam-4570	625	2	9	9	X
ejpam-4570	625	3	)	)	PUNCT
ejpam-4570	625	4	almost	almost	ADV
ejpam-4570	625	5	normality	normality	NOUN
ejpam-4570	625	6	is	be	AUX
ejpam-4570	625	7	not	not	PART
ejpam-4570	625	8	preserved	preserve	VERB
ejpam-4570	625	9	by	by	ADP
ejpam-4570	625	10	a	a	DET
ejpam-4570	625	11	discrete	discrete	ADJ
ejpam-4570	625	12	extension	extension	NOUN
ejpam-4570	625	13	space	space	NOUN
ejpam-4570	625	14	.	.	PUNCT
ejpam-4570	626	1	for	for	ADP
ejpam-4570	626	2	example	example	NOUN
ejpam-4570	626	3	,	,	PUNCT
ejpam-4570	626	4	the	the	DET
ejpam-4570	626	5	space	space	NOUN
ejpam-4570	626	6	presented	present	VERB
ejpam-4570	626	7	in	in	ADP
ejpam-4570	626	8	[	[	X
ejpam-4570	626	9	2	2	NUM
ejpam-4570	626	10	,	,	PUNCT
ejpam-4570	626	11	example	example	NOUN
ejpam-4570	626	12	15	15	NUM
ejpam-4570	626	13	]	]	PUNCT
ejpam-4570	626	14	,	,	PUNCT
ejpam-4570	626	15	x	x	SYM
ejpam-4570	626	16	=	=	SYM
ejpam-4570	626	17	(	(	PUNCT
ejpam-4570	626	18	ω1	ω1	PROPN
ejpam-4570	626	19	×	×	PROPN
ejpam-4570	626	20	y	y	PROPN
ejpam-4570	626	21	)	)	PUNCT
ejpam-4570	626	22	∪	∪	VERB
ejpam-4570	626	23	{	{	PUNCT
ejpam-4570	626	24	p	p	NOUN
ejpam-4570	626	25	}	}	PUNCT
ejpam-4570	626	26	,	,	PUNCT
ejpam-4570	626	27	p	p	PROPN
ejpam-4570	626	28	̸∈	̸∈	PROPN
ejpam-4570	626	29	ω1	ω1	PROPN
ejpam-4570	626	30	×	×	PROPN
ejpam-4570	626	31	y	y	PROPN
ejpam-4570	626	32	,	,	PUNCT
ejpam-4570	626	33	be	be	AUX
ejpam-4570	626	34	a	a	DET
ejpam-4570	626	35	one	one	NUM
ejpam-4570	626	36	-	-	PUNCT
ejpam-4570	626	37	point	point	NOUN
ejpam-4570	626	38	compactification	compactification	NOUN
ejpam-4570	626	39	of	of	ADP
ejpam-4570	626	40	ω1	ω1	PROPN
ejpam-4570	626	41	×	×	PROPN
ejpam-4570	626	42	y	y	PROPN
ejpam-4570	626	43	.	.	PUNCT
ejpam-4570	627	1	then	then	ADV
ejpam-4570	627	2	,	,	PUNCT
ejpam-4570	627	3	x	x	X
ejpam-4570	627	4	is	be	AUX
ejpam-4570	627	5	an	an	DET
ejpam-4570	627	6	almost	almost	ADV
ejpam-4570	627	7	normal	normal	ADJ
ejpam-4570	627	8	space	space	NOUN
ejpam-4570	627	9	being	be	AUX
ejpam-4570	627	10	hausdorff	hausdorff	ADJ
ejpam-4570	627	11	compact	compact	ADJ
ejpam-4570	627	12	space	space	NOUN
ejpam-4570	627	13	.	.	PUNCT
ejpam-4570	628	1	but	but	CCONJ
ejpam-4570	628	2	the	the	DET
ejpam-4570	628	3	discrete	discrete	ADJ
ejpam-4570	628	4	extension	extension	NOUN
ejpam-4570	628	5	x(ω1×y	x(ω1×y	PROPN
ejpam-4570	628	6	)	)	PUNCT
ejpam-4570	629	1	=	=	PUNCT
ejpam-4570	629	2	(	(	PUNCT
ejpam-4570	629	3	ω1	ω1	PROPN
ejpam-4570	629	4	×	×	PROPN
ejpam-4570	629	5	y	y	PROPN
ejpam-4570	629	6	)	)	PUNCT
ejpam-4570	629	7	∪	∪	VERB
ejpam-4570	629	8	{	{	PUNCT
ejpam-4570	629	9	p	p	NOUN
ejpam-4570	629	10	}	}	PUNCT
ejpam-4570	629	11	,	,	PUNCT
ejpam-4570	629	12	{	{	PUNCT
ejpam-4570	629	13	p	p	X
ejpam-4570	629	14	}	}	PUNCT
ejpam-4570	629	15	is	be	AUX
ejpam-4570	629	16	closed	closed	ADJ
ejpam-4570	629	17	and	and	CCONJ
ejpam-4570	629	18	open	open	ADJ
ejpam-4570	629	19	subset	subset	NOUN
ejpam-4570	629	20	of	of	ADP
ejpam-4570	629	21	x(ω1×y	x(ω1×y	PROPN
ejpam-4570	629	22	)	)	PUNCT
ejpam-4570	629	23	,	,	PUNCT
ejpam-4570	629	24	is	be	AUX
ejpam-4570	629	25	not	not	PART
ejpam-4570	629	26	almost	almost	ADV
ejpam-4570	629	27	normal	normal	ADJ
ejpam-4570	629	28	being	be	AUX
ejpam-4570	629	29	not	not	PART
ejpam-4570	629	30	mildly	mildly	ADV
ejpam-4570	629	31	normal	normal	ADJ
ejpam-4570	629	32	.	.	PUNCT
ejpam-4570	630	1	(	(	PUNCT
ejpam-4570	630	2	10	10	NUM
ejpam-4570	630	3	)	)	PUNCT
ejpam-4570	630	4	any	any	DET
ejpam-4570	630	5	t1	t1	ADJ
ejpam-4570	630	6	-	-	ADJ
ejpam-4570	630	7	compact	compact	ADJ
ejpam-4570	630	8	space	space	NOUN
ejpam-4570	630	9	is	be	AUX
ejpam-4570	630	10	not	not	PART
ejpam-4570	630	11	necessary	necessary	ADJ
ejpam-4570	630	12	to	to	PART
ejpam-4570	630	13	be	be	AUX
ejpam-4570	630	14	c	c	NOUN
ejpam-4570	630	15	-	-	PUNCT
ejpam-4570	630	16	almost	almost	ADV
ejpam-4570	630	17	normal	normal	ADJ
ejpam-4570	630	18	.	.	PUNCT
ejpam-4570	631	1	for	for	ADP
ejpam-4570	631	2	example	example	NOUN
ejpam-4570	631	3	,	,	PUNCT
ejpam-4570	631	4	the	the	DET
ejpam-4570	631	5	maximal	maximal	ADJ
ejpam-4570	631	6	compact	compact	ADJ
ejpam-4570	631	7	topology	topology	NOUN
ejpam-4570	631	8	,	,	PUNCT
ejpam-4570	631	9	example	example	NOUN
ejpam-4570	631	10	14	14	NUM
ejpam-4570	631	11	,	,	PUNCT
ejpam-4570	631	12	is	be	AUX
ejpam-4570	631	13	a	a	DET
ejpam-4570	631	14	t1	t1	ADJ
ejpam-4570	631	15	-	-	ADJ
ejpam-4570	631	16	compact	compact	ADJ
ejpam-4570	631	17	space	space	NOUN
ejpam-4570	631	18	which	which	PRON
ejpam-4570	631	19	is	be	AUX
ejpam-4570	631	20	not	not	PART
ejpam-4570	631	21	c	c	NOUN
ejpam-4570	631	22	-	-	PUNCT
ejpam-4570	631	23	almost	almost	ADV
ejpam-4570	631	24	normal	normal	ADJ
ejpam-4570	631	25	.	.	PUNCT
ejpam-4570	632	1	(	(	PUNCT
ejpam-4570	632	2	11	11	NUM
ejpam-4570	632	3	)	)	PUNCT
ejpam-4570	632	4	l	l	NOUN
ejpam-4570	632	5	-	-	PUNCT
ejpam-4570	632	6	almost	almost	ADV
ejpam-4570	632	7	normality	normality	NOUN
ejpam-4570	632	8	and	and	CCONJ
ejpam-4570	632	9	c	c	NOUN
ejpam-4570	632	10	-	-	PUNCT
ejpam-4570	632	11	almost	almost	ADV
ejpam-4570	632	12	normality	normality	NOUN
ejpam-4570	632	13	are	be	AUX
ejpam-4570	632	14	different	different	ADJ
ejpam-4570	632	15	from	from	ADP
ejpam-4570	632	16	l	l	NOUN
ejpam-4570	632	17	-	-	NOUN
ejpam-4570	632	18	normality	normality	NOUN
ejpam-4570	632	19	and	and	CCONJ
ejpam-4570	632	20	c	c	NOUN
ejpam-4570	632	21	-	-	PUNCT
ejpam-4570	632	22	normality	normality	NOUN
ejpam-4570	632	23	respectively	respectively	ADV
ejpam-4570	632	24	.	.	PUNCT
ejpam-4570	633	1	for	for	ADP
ejpam-4570	633	2	example	example	NOUN
ejpam-4570	633	3	,	,	PUNCT
ejpam-4570	633	4	the	the	DET
ejpam-4570	633	5	rational	rational	ADJ
ejpam-4570	633	6	sequence	sequence	NOUN
ejpam-4570	633	7	topology	topology	NOUN
ejpam-4570	633	8	,	,	PUNCT
ejpam-4570	633	9	example	example	NOUN
ejpam-4570	633	10	19	19	NUM
ejpam-4570	633	11	,	,	PUNCT
ejpam-4570	633	12	is	be	AUX
ejpam-4570	633	13	an	an	DET
ejpam-4570	633	14	l	l	NOUN
ejpam-4570	633	15	-	-	ADJ
ejpam-4570	633	16	almost	almost	ADV
ejpam-4570	633	17	normal	normal	ADJ
ejpam-4570	633	18	space	space	NOUN
ejpam-4570	633	19	,	,	PUNCT
ejpam-4570	633	20	which	which	PRON
ejpam-4570	633	21	is	be	AUX
ejpam-4570	633	22	not	not	PART
ejpam-4570	633	23	l	l	NOUN
ejpam-4570	633	24	-	-	ADJ
ejpam-4570	633	25	normal	normal	ADJ
ejpam-4570	633	26	.	.	PUNCT
ejpam-4570	634	1	the	the	DET
ejpam-4570	634	2	finite	finite	PROPN
ejpam-4570	634	3	complement	complement	NOUN
ejpam-4570	634	4	topology	topology	NOUN
ejpam-4570	634	5	,	,	PUNCT
ejpam-4570	634	6	example	example	NOUN
ejpam-4570	634	7	3	3	NUM
ejpam-4570	634	8	,	,	PUNCT
ejpam-4570	634	9	is	be	AUX
ejpam-4570	634	10	both	both	PRON
ejpam-4570	634	11	l	l	NOUN
ejpam-4570	634	12	-	-	ADJ
ejpam-4570	634	13	almost	almost	ADV
ejpam-4570	634	14	normal	normal	ADJ
ejpam-4570	634	15	and	and	CCONJ
ejpam-4570	634	16	c	c	NOUN
ejpam-4570	634	17	-	-	PUNCT
ejpam-4570	634	18	almost	almost	ADV
ejpam-4570	634	19	normal	normal	ADJ
ejpam-4570	634	20	space	space	NOUN
ejpam-4570	634	21	which	which	PRON
ejpam-4570	634	22	is	be	AUX
ejpam-4570	634	23	neither	neither	CCONJ
ejpam-4570	634	24	c	c	NOUN
ejpam-4570	634	25	-	-	ADJ
ejpam-4570	634	26	normal	normal	ADJ
ejpam-4570	634	27	nor	nor	CCONJ
ejpam-4570	634	28	l	l	NOUN
ejpam-4570	634	29	-	-	ADJ
ejpam-4570	634	30	normal	normal	ADJ
ejpam-4570	634	31	.	.	PUNCT
ejpam-4570	635	1	(	(	PUNCT
ejpam-4570	635	2	12	12	NUM
ejpam-4570	635	3	)	)	PUNCT
ejpam-4570	635	4	every	every	DET
ejpam-4570	635	5	c	c	NOUN
ejpam-4570	635	6	-	-	PUNCT
ejpam-4570	635	7	almost	almost	ADV
ejpam-4570	635	8	normal	normal	ADJ
ejpam-4570	635	9	t1	t1	NOUN
ejpam-4570	635	10	compact	compact	ADJ
ejpam-4570	635	11	space	space	NOUN
ejpam-4570	635	12	is	be	AUX
ejpam-4570	635	13	not	not	PART
ejpam-4570	635	14	necessarily	necessarily	ADV
ejpam-4570	635	15	epi	epi	NOUN
ejpam-4570	635	16	-	-	ADJ
ejpam-4570	635	17	almost	almost	ADV
ejpam-4570	635	18	normal	normal	ADJ
ejpam-4570	635	19	or	or	CCONJ
ejpam-4570	635	20	urysohn	urysohn	NOUN
ejpam-4570	635	21	.	.	PUNCT
ejpam-4570	636	1	for	for	ADP
ejpam-4570	636	2	example	example	NOUN
ejpam-4570	636	3	:	:	PUNCT
ejpam-4570	636	4	the	the	DET
ejpam-4570	636	5	modified	modified	ADJ
ejpam-4570	636	6	fort	fort	NOUN
ejpam-4570	636	7	space	space	NOUN
ejpam-4570	636	8	,	,	PUNCT
ejpam-4570	636	9	example	example	NOUN
ejpam-4570	636	10	15	15	NUM
ejpam-4570	636	11	,	,	PUNCT
ejpam-4570	636	12	is	be	AUX
ejpam-4570	636	13	a	a	DET
ejpam-4570	636	14	c	c	NOUN
ejpam-4570	636	15	-	-	PUNCT
ejpam-4570	636	16	almost	almost	ADV
ejpam-4570	636	17	normal	normal	ADJ
ejpam-4570	636	18	t1	t1	ADJ
ejpam-4570	636	19	-	-	ADJ
ejpam-4570	636	20	compact	compact	ADJ
ejpam-4570	636	21	space	space	NOUN
ejpam-4570	636	22	,	,	PUNCT
ejpam-4570	636	23	which	which	PRON
ejpam-4570	636	24	is	be	AUX
ejpam-4570	636	25	neither	neither	DET
ejpam-4570	636	26	epi	epi	NOUN
ejpam-4570	636	27	-	-	ADJ
ejpam-4570	636	28	almost	almost	ADV
ejpam-4570	636	29	normal	normal	ADJ
ejpam-4570	636	30	nor	nor	CCONJ
ejpam-4570	636	31	urysohn	urysohn	ADJ
ejpam-4570	636	32	.	.	PUNCT
ejpam-4570	637	1	(	(	PUNCT
ejpam-4570	637	2	13	13	NUM
ejpam-4570	637	3	)	)	PUNCT
ejpam-4570	637	4	if	if	SCONJ
ejpam-4570	637	5	x	x	PRON
ejpam-4570	637	6	is	be	AUX
ejpam-4570	637	7	c	c	NOUN
ejpam-4570	637	8	-	-	PUNCT
ejpam-4570	637	9	almost	almost	ADV
ejpam-4570	637	10	completely	completely	ADV
ejpam-4570	637	11	regular	regular	ADJ
ejpam-4570	637	12	first	first	ADJ
ejpam-4570	637	13	countable	countable	ADJ
ejpam-4570	637	14	lindelöf	lindelöf	NOUN
ejpam-4570	637	15	space	space	NOUN
ejpam-4570	637	16	is	be	AUX
ejpam-4570	637	17	not	not	PART
ejpam-4570	637	18	necessary	necessary	ADJ
ejpam-4570	637	19	to	to	PART
ejpam-4570	637	20	be	be	AUX
ejpam-4570	637	21	epi	epi	NOUN
ejpam-4570	637	22	-	-	ADJ
ejpam-4570	637	23	almost	almost	ADV
ejpam-4570	637	24	normal	normal	ADJ
ejpam-4570	637	25	,	,	PUNCT
ejpam-4570	637	26	almost	almost	ADV
ejpam-4570	637	27	normal	normal	ADJ
ejpam-4570	637	28	nor	nor	CCONJ
ejpam-4570	637	29	l	l	NOUN
ejpam-4570	637	30	-	-	ADJ
ejpam-4570	637	31	almost	almost	ADV
ejpam-4570	637	32	normal	normal	ADJ
ejpam-4570	637	33	.	.	PUNCT
ejpam-4570	638	1	for	for	ADP
ejpam-4570	638	2	example	example	NOUN
ejpam-4570	638	3	:	:	PUNCT
ejpam-4570	638	4	the	the	DET
ejpam-4570	638	5	irregular	irregular	ADJ
ejpam-4570	638	6	lattice	lattice	NOUN
ejpam-4570	638	7	topology	topology	NOUN
ejpam-4570	638	8	,	,	PUNCT
ejpam-4570	638	9	example	example	NOUN
ejpam-4570	638	10	12	12	NUM
ejpam-4570	638	11	,	,	PUNCT
ejpam-4570	638	12	and	and	CCONJ
ejpam-4570	638	13	the	the	DET
ejpam-4570	638	14	relatively	relatively	ADV
ejpam-4570	638	15	prime	prime	ADJ
ejpam-4570	638	16	integer	integer	NOUN
ejpam-4570	638	17	topology	topology	NOUN
ejpam-4570	638	18	and	and	CCONJ
ejpam-4570	638	19	the	the	DET
ejpam-4570	638	20	prime	prime	ADJ
ejpam-4570	638	21	integer	integer	NOUN
ejpam-4570	638	22	topology	topology	NOUN
ejpam-4570	638	23	,	,	PUNCT
ejpam-4570	638	24	example	example	NOUN
ejpam-4570	638	25	17	17	NUM
ejpam-4570	638	26	,	,	PUNCT
ejpam-4570	638	27	are	be	AUX
ejpam-4570	638	28	c	c	NOUN
ejpam-4570	638	29	-	-	PUNCT
ejpam-4570	638	30	almost	almost	ADV
ejpam-4570	638	31	completely	completely	ADV
ejpam-4570	638	32	regular	regular	ADJ
ejpam-4570	638	33	(	(	PUNCT
ejpam-4570	638	34	c	c	NOUN
ejpam-4570	638	35	-	-	PUNCT
ejpam-4570	638	36	almost	almost	ADV
ejpam-4570	638	37	regular	regular	ADJ
ejpam-4570	638	38	)	)	PUNCT
ejpam-4570	638	39	first	first	ADJ
ejpam-4570	638	40	countable	countable	ADJ
ejpam-4570	638	41	lindelöf	lindelöf	NOUN
ejpam-4570	638	42	spaces	space	NOUN
ejpam-4570	638	43	,	,	PUNCT
ejpam-4570	638	44	which	which	PRON
ejpam-4570	638	45	are	be	AUX
ejpam-4570	638	46	neither	neither	CCONJ
ejpam-4570	638	47	epi	epi	NOUN
ejpam-4570	638	48	-	-	ADJ
ejpam-4570	638	49	almost	almost	ADV
ejpam-4570	638	50	normal	normal	ADJ
ejpam-4570	638	51	,	,	PUNCT
ejpam-4570	638	52	almost	almost	ADV
ejpam-4570	638	53	normal	normal	ADJ
ejpam-4570	638	54	nor	nor	CCONJ
ejpam-4570	638	55	l	l	NOUN
ejpam-4570	638	56	-	-	ADJ
ejpam-4570	638	57	almost	almost	ADV
ejpam-4570	638	58	normal	normal	ADJ
ejpam-4570	638	59	.	.	PUNCT
ejpam-4570	639	1	(	(	PUNCT
ejpam-4570	639	2	14	14	NUM
ejpam-4570	639	3	)	)	PUNCT
ejpam-4570	639	4	a	a	DET
ejpam-4570	639	5	c	c	NOUN
ejpam-4570	639	6	-	-	PUNCT
ejpam-4570	639	7	almost	almost	ADV
ejpam-4570	639	8	normal	normal	ADJ
ejpam-4570	639	9	first	first	ADJ
ejpam-4570	639	10	countable	countable	ADJ
ejpam-4570	639	11	lindelöf	lindelöf	NOUN
ejpam-4570	639	12	k	k	NOUN
ejpam-4570	639	13	-	-	NOUN
ejpam-4570	639	14	space	space	NOUN
ejpam-4570	639	15	is	be	AUX
ejpam-4570	639	16	not	not	PART
ejpam-4570	639	17	necessary	necessary	ADJ
ejpam-4570	639	18	to	to	PART
ejpam-4570	639	19	be	be	AUX
ejpam-4570	639	20	epi	epi	NOUN
ejpam-4570	639	21	-	-	ADJ
ejpam-4570	639	22	almost	almost	ADV
ejpam-4570	639	23	normal	normal	ADJ
ejpam-4570	639	24	.	.	PUNCT
ejpam-4570	640	1	for	for	ADP
ejpam-4570	640	2	example	example	NOUN
ejpam-4570	640	3	,	,	PUNCT
ejpam-4570	640	4	the	the	DET
ejpam-4570	640	5	odd	odd	ADV
ejpam-4570	640	6	-	-	PUNCT
ejpam-4570	640	7	even	even	ADV
ejpam-4570	640	8	-	-	PUNCT
ejpam-4570	640	9	topology	topology	NOUN
ejpam-4570	640	10	,	,	PUNCT
ejpam-4570	640	11	example	example	NOUN
ejpam-4570	640	12	16	16	NUM
ejpam-4570	640	13	,	,	PUNCT
ejpam-4570	640	14	is	be	AUX
ejpam-4570	640	15	a	a	DET
ejpam-4570	640	16	c	c	NOUN
ejpam-4570	640	17	-	-	PUNCT
ejpam-4570	640	18	almost	almost	ADV
ejpam-4570	640	19	normal	normal	ADJ
ejpam-4570	640	20	first	first	ADJ
ejpam-4570	640	21	countable	countable	ADJ
ejpam-4570	640	22	lindelöf	lindelöf	NOUN
ejpam-4570	640	23	k	k	NOUN
ejpam-4570	640	24	-	-	NOUN
ejpam-4570	640	25	space	space	NOUN
ejpam-4570	640	26	,	,	PUNCT
ejpam-4570	640	27	which	which	PRON
ejpam-4570	640	28	is	be	AUX
ejpam-4570	640	29	not	not	PART
ejpam-4570	640	30	epi	epi	NOUN
ejpam-4570	640	31	-	-	ADJ
ejpam-4570	640	32	almost	almost	ADV
ejpam-4570	640	33	normal	normal	ADJ
ejpam-4570	640	34	.	.	PUNCT
ejpam-4570	641	1	(	(	PUNCT
ejpam-4570	641	2	15	15	NUM
ejpam-4570	641	3	)	)	PUNCT
ejpam-4570	641	4	every	every	DET
ejpam-4570	641	5	hausdorff	hausdorff	NOUN
ejpam-4570	641	6	epi	epi	NOUN
ejpam-4570	641	7	-	-	PUNCT
ejpam-4570	641	8	almost	almost	ADV
ejpam-4570	641	9	completely	completely	ADV
ejpam-4570	641	10	regular	regular	ADJ
ejpam-4570	641	11	first	first	ADJ
ejpam-4570	641	12	countable	countable	ADJ
ejpam-4570	641	13	lindelöf	lindelöf	NOUN
ejpam-4570	641	14	k	k	NOUN
ejpam-4570	641	15	-	-	NOUN
ejpam-4570	641	16	space	space	NOUN
ejpam-4570	641	17	is	be	AUX
ejpam-4570	641	18	not	not	PART
ejpam-4570	641	19	necessary	necessary	ADJ
ejpam-4570	641	20	to	to	PART
ejpam-4570	641	21	be	be	AUX
ejpam-4570	641	22	epi	epi	NOUN
ejpam-4570	641	23	-	-	ADJ
ejpam-4570	641	24	almost	almost	ADV
ejpam-4570	641	25	normal	normal	ADJ
ejpam-4570	641	26	,	,	PUNCT
ejpam-4570	641	27	almost	almost	ADV
ejpam-4570	641	28	normal	normal	ADJ
ejpam-4570	641	29	nor	nor	CCONJ
ejpam-4570	641	30	l	l	NOUN
ejpam-4570	641	31	-	-	ADJ
ejpam-4570	641	32	almost	almost	ADV
ejpam-4570	641	33	normal	normal	ADJ
ejpam-4570	641	34	.	.	PUNCT
ejpam-4570	642	1	for	for	ADP
ejpam-4570	642	2	example	example	NOUN
ejpam-4570	642	3	:	:	PUNCT
ejpam-4570	642	4	the	the	DET
ejpam-4570	642	5	space	space	NOUN
ejpam-4570	642	6	presented	present	VERB
ejpam-4570	642	7	in	in	ADP
ejpam-4570	642	8	example	example	NOUN
ejpam-4570	642	9	18	18	NUM
ejpam-4570	642	10	,	,	PUNCT
ejpam-4570	642	11	is	be	AUX
ejpam-4570	642	12	a	a	DET
ejpam-4570	642	13	hausdorff	hausdorff	NOUN
ejpam-4570	642	14	epi	epi	NOUN
ejpam-4570	642	15	-	-	PUNCT
ejpam-4570	642	16	almost	almost	ADV
ejpam-4570	642	17	completely	completely	ADV
ejpam-4570	642	18	regular	regular	ADJ
ejpam-4570	642	19	first	first	ADJ
ejpam-4570	642	20	countable	countable	ADJ
ejpam-4570	642	21	lindelöf	lindelöf	NOUN
ejpam-4570	642	22	k	k	NOUN
ejpam-4570	642	23	-	-	NOUN
ejpam-4570	642	24	space	space	NOUN
ejpam-4570	642	25	,	,	PUNCT
ejpam-4570	642	26	which	which	PRON
ejpam-4570	642	27	is	be	AUX
ejpam-4570	642	28	neither	neither	DET
ejpam-4570	642	29	epi	epi	NOUN
ejpam-4570	642	30	-	-	ADJ
ejpam-4570	642	31	almost	almost	ADV
ejpam-4570	642	32	normal	normal	ADJ
ejpam-4570	642	33	nor	nor	CCONJ
ejpam-4570	642	34	l	l	NOUN
ejpam-4570	642	35	-	-	ADJ
ejpam-4570	642	36	almost	almost	ADV
ejpam-4570	642	37	normal	normal	ADJ
ejpam-4570	642	38	.	.	PUNCT
ejpam-4570	643	1	references	reference	NOUN
ejpam-4570	643	2	1780	1780	NUM
ejpam-4570	643	3	(	(	PUNCT
ejpam-4570	643	4	16	16	NUM
ejpam-4570	643	5	)	)	PUNCT
ejpam-4570	643	6	if	if	SCONJ
ejpam-4570	643	7	x	x	PRON
ejpam-4570	643	8	is	be	AUX
ejpam-4570	643	9	a	a	DET
ejpam-4570	643	10	hausdorff	hausdorff	NOUN
ejpam-4570	643	11	c	c	NOUN
ejpam-4570	643	12	-	-	PUNCT
ejpam-4570	643	13	almost	almost	ADV
ejpam-4570	643	14	normal	normal	ADJ
ejpam-4570	643	15	space	space	NOUN
ejpam-4570	643	16	,	,	PUNCT
ejpam-4570	643	17	then	then	ADV
ejpam-4570	643	18	a	a	DET
ejpam-4570	643	19	witness	witness	NOUN
ejpam-4570	643	20	y	y	NOUN
ejpam-4570	643	21	is	be	AUX
ejpam-4570	643	22	not	not	PART
ejpam-4570	643	23	necessary	necessary	ADJ
ejpam-4570	643	24	to	to	PART
ejpam-4570	643	25	be	be	AUX
ejpam-4570	643	26	hausdorff	hausdorff	NOUN
ejpam-4570	643	27	.	.	PUNCT
ejpam-4570	644	1	for	for	ADP
ejpam-4570	644	2	example	example	NOUN
ejpam-4570	644	3	:	:	PUNCT
ejpam-4570	644	4	the	the	DET
ejpam-4570	644	5	relatively	relatively	ADV
ejpam-4570	644	6	prime	prime	ADJ
ejpam-4570	644	7	integer	integer	NOUN
ejpam-4570	644	8	topology	topology	NOUN
ejpam-4570	644	9	and	and	CCONJ
ejpam-4570	644	10	the	the	DET
ejpam-4570	644	11	prime	prime	ADJ
ejpam-4570	644	12	integer	integer	NOUN
ejpam-4570	644	13	topology	topology	NOUN
ejpam-4570	644	14	,	,	PUNCT
ejpam-4570	644	15	example	example	NOUN
ejpam-4570	644	16	17	17	NUM
ejpam-4570	644	17	,	,	PUNCT
ejpam-4570	644	18	is	be	AUX
ejpam-4570	644	19	a	a	DET
ejpam-4570	644	20	c	c	NOUN
ejpam-4570	644	21	-	-	PUNCT
ejpam-4570	644	22	almost	almost	ADV
ejpam-4570	644	23	normal	normal	ADJ
ejpam-4570	644	24	hausdorff	hausdorff	NOUN
ejpam-4570	644	25	first	first	ADJ
ejpam-4570	644	26	countable	countable	ADJ
ejpam-4570	644	27	space	space	NOUN
ejpam-4570	644	28	,	,	PUNCT
ejpam-4570	644	29	and	and	CCONJ
ejpam-4570	644	30	the	the	DET
ejpam-4570	644	31	witness	witness	NOUN
ejpam-4570	644	32	y	y	PROPN
ejpam-4570	644	33	of	of	ADP
ejpam-4570	644	34	the	the	DET
ejpam-4570	644	35	c	c	NOUN
ejpam-4570	644	36	-	-	PUNCT
ejpam-4570	644	37	almost	almost	ADV
ejpam-4570	644	38	normality	normality	NOUN
ejpam-4570	644	39	of	of	ADP
ejpam-4570	644	40	x	x	PUNCT
ejpam-4570	644	41	can	can	AUX
ejpam-4570	644	42	not	not	PART
ejpam-4570	644	43	be	be	AUX
ejpam-4570	644	44	hausdorff	hausdorff	ADJ
ejpam-4570	644	45	because	because	SCONJ
ejpam-4570	644	46	if	if	SCONJ
ejpam-4570	644	47	y	y	PROPN
ejpam-4570	644	48	is	be	AUX
ejpam-4570	644	49	hausdorff	hausdorff	NOUN
ejpam-4570	644	50	then	then	ADV
ejpam-4570	644	51	x	x	PUNCT
ejpam-4570	644	52	will	will	AUX
ejpam-4570	644	53	be	be	AUX
ejpam-4570	644	54	epi	epi	ADJ
ejpam-4570	644	55	-	-	ADJ
ejpam-4570	644	56	almost	almost	ADV
ejpam-4570	644	57	normal	normal	ADJ
ejpam-4570	644	58	which	which	PRON
ejpam-4570	644	59	is	be	AUX
ejpam-4570	644	60	a	a	DET
ejpam-4570	644	61	contradiction	contradiction	NOUN
ejpam-4570	644	62	.	.	PUNCT
ejpam-4570	645	1	the	the	DET
ejpam-4570	645	2	following	follow	VERB
ejpam-4570	645	3	problems	problem	NOUN
ejpam-4570	645	4	are	be	AUX
ejpam-4570	645	5	still	still	ADV
ejpam-4570	645	6	open	open	ADJ
ejpam-4570	645	7	until	until	ADP
ejpam-4570	645	8	now	now	ADV
ejpam-4570	645	9	in	in	ADP
ejpam-4570	645	10	this	this	DET
ejpam-4570	645	11	work	work	NOUN
ejpam-4570	645	12	:	:	PUNCT
ejpam-4570	645	13	problems	problem	NOUN
ejpam-4570	645	14	:	:	PUNCT
ejpam-4570	645	15	(	(	PUNCT
ejpam-4570	645	16	1	1	X
ejpam-4570	645	17	)	)	PUNCT
ejpam-4570	645	18	is	be	AUX
ejpam-4570	645	19	there	there	PRON
ejpam-4570	645	20	an	an	DET
ejpam-4570	645	21	example	example	NOUN
ejpam-4570	645	22	of	of	ADP
ejpam-4570	645	23	a	a	DET
ejpam-4570	645	24	hausdorff	hausdorff	NOUN
ejpam-4570	645	25	locally	locally	ADV
ejpam-4570	645	26	compact	compact	ADJ
ejpam-4570	645	27	space	space	NOUN
ejpam-4570	645	28	,	,	PUNCT
ejpam-4570	645	29	which	which	PRON
ejpam-4570	645	30	is	be	AUX
ejpam-4570	645	31	not	not	PART
ejpam-4570	645	32	l	l	NOUN
ejpam-4570	645	33	-	-	PUNCT
ejpam-4570	645	34	almost	almost	ADV
ejpam-4570	645	35	normal	normal	ADJ
ejpam-4570	645	36	?	?	PUNCT
ejpam-4570	645	37	.	.	PUNCT
ejpam-4570	646	1	(	(	PUNCT
ejpam-4570	646	2	2	2	X
ejpam-4570	646	3	)	)	PUNCT
ejpam-4570	646	4	is	be	AUX
ejpam-4570	646	5	every	every	DET
ejpam-4570	646	6	c	c	NOUN
ejpam-4570	646	7	-	-	PUNCT
ejpam-4570	646	8	almost	almost	ADV
ejpam-4570	646	9	normal	normal	ADJ
ejpam-4570	646	10	t1	t1	NOUN
ejpam-4570	646	11	first	first	ADJ
ejpam-4570	646	12	countable	countable	ADJ
ejpam-4570	646	13	space	space	NOUN
ejpam-4570	646	14	,	,	PUNCT
ejpam-4570	646	15	hausdorff	hausdorff	NOUN
ejpam-4570	646	16	?	?	PUNCT
ejpam-4570	646	17	.	.	PUNCT
ejpam-4570	647	1	(	(	PUNCT
ejpam-4570	647	2	3	3	X
ejpam-4570	647	3	)	)	PUNCT
ejpam-4570	647	4	is	be	AUX
ejpam-4570	647	5	there	there	PRON
ejpam-4570	647	6	an	an	DET
ejpam-4570	647	7	example	example	NOUN
ejpam-4570	647	8	of	of	ADP
ejpam-4570	647	9	a	a	DET
ejpam-4570	647	10	hausdorff	hausdorff	NOUN
ejpam-4570	647	11	space	space	NOUN
ejpam-4570	647	12	,	,	PUNCT
ejpam-4570	647	13	which	which	PRON
ejpam-4570	647	14	is	be	AUX
ejpam-4570	647	15	not	not	PART
ejpam-4570	647	16	c	c	NOUN
ejpam-4570	647	17	-	-	PUNCT
ejpam-4570	647	18	almost	almost	ADV
ejpam-4570	647	19	normal	normal	ADJ
ejpam-4570	647	20	?	?	PUNCT
ejpam-4570	647	21	.	.	PUNCT
ejpam-4570	648	1	(	(	PUNCT
ejpam-4570	648	2	4	4	X
ejpam-4570	648	3	)	)	PUNCT
ejpam-4570	648	4	are	be	AUX
ejpam-4570	648	5	c	c	NOUN
ejpam-4570	648	6	-	-	PUNCT
ejpam-4570	648	7	almost	almost	ADV
ejpam-4570	648	8	normality	normality	NOUN
ejpam-4570	648	9	and	and	CCONJ
ejpam-4570	648	10	l	l	NOUN
ejpam-4570	648	11	-	-	ADJ
ejpam-4570	648	12	almost	almost	ADV
ejpam-4570	648	13	normality	normality	NOUN
ejpam-4570	648	14	preserved	preserve	VERB
ejpam-4570	648	15	by	by	ADP
ejpam-4570	648	16	discrete	discrete	ADJ
ejpam-4570	648	17	extension	extension	NOUN
ejpam-4570	648	18	spaces	space	NOUN
ejpam-4570	648	19	?	?	PUNCT
ejpam-4570	648	20	.	.	PUNCT
ejpam-4570	649	1	5	5	X
ejpam-4570	649	2	.	.	X
ejpam-4570	649	3	conclusion	conclusion	VERB
ejpam-4570	649	4	new	new	ADJ
ejpam-4570	649	5	versions	version	NOUN
ejpam-4570	649	6	of	of	ADP
ejpam-4570	649	7	normality	normality	NOUN
ejpam-4570	649	8	,	,	PUNCT
ejpam-4570	649	9	called	call	VERB
ejpam-4570	649	10	c	c	NOUN
ejpam-4570	649	11	-	-	PUNCT
ejpam-4570	649	12	almost	almost	ADV
ejpam-4570	649	13	normality	normality	NOUN
ejpam-4570	649	14	and	and	CCONJ
ejpam-4570	649	15	l	l	NOUN
ejpam-4570	649	16	-	-	ADJ
ejpam-4570	649	17	almost	almost	ADV
ejpam-4570	649	18	normality	normality	NOUN
ejpam-4570	649	19	,	,	PUNCT
ejpam-4570	649	20	have	have	AUX
ejpam-4570	649	21	been	be	AUX
ejpam-4570	649	22	studied	study	VERB
ejpam-4570	649	23	.	.	PUNCT
ejpam-4570	650	1	some	some	DET
ejpam-4570	650	2	results	result	NOUN
ejpam-4570	650	3	,	,	PUNCT
ejpam-4570	650	4	properties	property	NOUN
ejpam-4570	650	5	,	,	PUNCT
ejpam-4570	650	6	relationships	relationship	NOUN
ejpam-4570	650	7	and	and	CCONJ
ejpam-4570	650	8	counterexamples	counterexample	NOUN
ejpam-4570	650	9	have	have	AUX
ejpam-4570	650	10	been	be	AUX
ejpam-4570	650	11	presented	present	VERB
ejpam-4570	650	12	and	and	CCONJ
ejpam-4570	650	13	given	give	VERB
ejpam-4570	650	14	.	.	PUNCT
ejpam-4570	651	1	acknowledgements	acknowledgement	NOUN
ejpam-4570	651	2	the	the	DET
ejpam-4570	651	3	authors	author	NOUN
ejpam-4570	651	4	would	would	AUX
ejpam-4570	651	5	like	like	VERB
ejpam-4570	651	6	to	to	PART
ejpam-4570	651	7	thank	thank	VERB
ejpam-4570	651	8	the	the	DET
ejpam-4570	651	9	anonymous	anonymous	ADJ
ejpam-4570	651	10	referee	referee	NOUN
ejpam-4570	651	11	for	for	ADP
ejpam-4570	651	12	his	his	PRON
ejpam-4570	651	13	/	/	SYM
ejpam-4570	651	14	her	her	PRON
ejpam-4570	651	15	comments	comment	NOUN
ejpam-4570	651	16	that	that	PRON
ejpam-4570	651	17	helped	help	VERB
ejpam-4570	651	18	us	we	PRON
ejpam-4570	651	19	improve	improve	VERB
ejpam-4570	651	20	this	this	DET
ejpam-4570	651	21	article	article	NOUN
ejpam-4570	651	22	.	.	PUNCT
ejpam-4570	652	1	references	reference	NOUN
ejpam-4570	652	2	[	[	X
ejpam-4570	652	3	1	1	X
ejpam-4570	652	4	]	]	X
ejpam-4570	652	5	dina	dina	PROPN
ejpam-4570	652	6	abuzaid	abuzaid	PROPN
ejpam-4570	652	7	,	,	PUNCT
ejpam-4570	652	8	suad	suad	PROPN
ejpam-4570	652	9	al	al	PROPN
ejpam-4570	652	10	-	-	PUNCT
ejpam-4570	652	11	qarhi	qarhi	PROPN
ejpam-4570	652	12	,	,	PUNCT
ejpam-4570	652	13	and	and	CCONJ
ejpam-4570	652	14	lutfi	lutfi	PROPN
ejpam-4570	652	15	kalantan	kalantan	PROPN
ejpam-4570	652	16	.	.	PUNCT
ejpam-4570	653	1	closed	close	VERB
ejpam-4570	653	2	extension	extension	NOUN
ejpam-4570	653	3	topological	topological	ADJ
ejpam-4570	653	4	spaces	space	NOUN
ejpam-4570	653	5	.	.	PUNCT
ejpam-4570	654	1	european	european	ADJ
ejpam-4570	654	2	journal	journal	PROPN
ejpam-4570	654	3	of	of	ADP
ejpam-4570	654	4	pure	pure	ADJ
ejpam-4570	654	5	and	and	CCONJ
ejpam-4570	654	6	applied	applied	ADJ
ejpam-4570	654	7	mathematics	mathematic	NOUN
ejpam-4570	654	8	(	(	PUNCT
ejpam-4570	654	9	ujpam	ujpam	PROPN
ejpam-4570	654	10	)	)	PUNCT
ejpam-4570	654	11	.	.	PUNCT
ejpam-4570	654	12	,	,	PUNCT
ejpam-4570	654	13	15(2):672–680	15(2):672–680	NUM
ejpam-4570	654	14	,	,	PUNCT
ejpam-4570	654	15	2022	2022	NUM
ejpam-4570	654	16	.	.	PUNCT
ejpam-4570	655	1	[	[	X
ejpam-4570	655	2	2	2	NUM
ejpam-4570	655	3	]	]	PUNCT
ejpam-4570	655	4	alyaa	alyaa	NOUN
ejpam-4570	655	5	alawadi	alawadi	NOUN
ejpam-4570	655	6	,	,	PUNCT
ejpam-4570	655	7	lutfi	lutfi	PROPN
ejpam-4570	655	8	kalantan	kalantan	PROPN
ejpam-4570	655	9	,	,	PUNCT
ejpam-4570	655	10	and	and	CCONJ
ejpam-4570	655	11	maha	maha	PROPN
ejpam-4570	655	12	mohammed	mohammed	PROPN
ejpam-4570	655	13	saeed	saeed	PROPN
ejpam-4570	655	14	.	.	PUNCT
ejpam-4570	656	1	on	on	ADP
ejpam-4570	656	2	the	the	DET
ejpam-4570	656	3	discrete	discrete	ADJ
ejpam-4570	656	4	extension	extension	NOUN
ejpam-4570	656	5	spaces	space	NOUN
ejpam-4570	656	6	.	.	PUNCT
ejpam-4570	657	1	journal	journal	NOUN
ejpam-4570	657	2	of	of	ADP
ejpam-4570	657	3	mathematical	mathematical	ADJ
ejpam-4570	657	4	analysis	analysis	NOUN
ejpam-4570	657	5	(	(	PUNCT
ejpam-4570	657	6	i	i	NOUN
ejpam-4570	657	7	m	m	VERB
ejpam-4570	657	8	a	a	PROPN
ejpam-4570	657	9	)	)	PUNCT
ejpam-4570	657	10	.	.	PUNCT
ejpam-4570	657	11	,	,	PUNCT
ejpam-4570	657	12	9(2):150–157	9(2):150–157	NOUN
ejpam-4570	657	13	,	,	PUNCT
ejpam-4570	657	14	2018	2018	NUM
ejpam-4570	657	15	.	.	PUNCT
ejpam-4570	658	1	[	[	X
ejpam-4570	658	2	3	3	X
ejpam-4570	658	3	]	]	PUNCT
ejpam-4570	658	4	ohud	ohud	ADJ
ejpam-4570	658	5	alghamdi	alghamdi	NOUN
ejpam-4570	658	6	,	,	PUNCT
ejpam-4570	658	7	sadeq	sadeq	PROPN
ejpam-4570	658	8	ali	ali	PROPN
ejpam-4570	658	9	thabit	thabit	NOUN
ejpam-4570	658	10	,	,	PUNCT
ejpam-4570	658	11	and	and	CCONJ
ejpam-4570	658	12	lutfi	lutfi	PROPN
ejpam-4570	658	13	kalantan	kalantan	PROPN
ejpam-4570	658	14	.	.	PUNCT
ejpam-4570	659	1	l	l	ADJ
ejpam-4570	659	2	-	-	PUNCT
ejpam-4570	659	3	completely	completely	ADV
ejpam-4570	659	4	regula	regula	NOUN
ejpam-4570	659	5	,	,	PUNCT
ejpam-4570	659	6	l	l	NOUN
ejpam-4570	659	7	-	-	PUNCT
ejpam-4570	659	8	almost	almost	ADV
ejpam-4570	659	9	regular	regular	ADJ
ejpam-4570	659	10	and	and	CCONJ
ejpam-4570	659	11	l2	l2	NOUN
ejpam-4570	659	12	-	-	PUNCT
ejpam-4570	659	13	almost	almost	ADV
ejpam-4570	659	14	regular	regular	ADJ
ejpam-4570	659	15	spaces	space	NOUN
ejpam-4570	659	16	.	.	PUNCT
ejpam-4570	660	1	preprint	preprint	NOUN
ejpam-4570	660	2	,	,	PUNCT
ejpam-4570	660	3	2022	2022	NUM
ejpam-4570	660	4	.	.	PUNCT
ejpam-4570	661	1	[	[	X
ejpam-4570	661	2	4	4	NUM
ejpam-4570	661	3	]	]	X
ejpam-4570	661	4	ibtesam	ibtesam	PROPN
ejpam-4570	661	5	alshammari	alshammari	PROPN
ejpam-4570	661	6	.	.	PUNCT
ejpam-4570	662	1	epi	epi	X
ejpam-4570	662	2	-	-	PUNCT
ejpam-4570	662	3	almost	almost	ADV
ejpam-4570	662	4	normality	normality	NOUN
ejpam-4570	662	5	.	.	PUNCT
ejpam-4570	663	1	journal	journal	NOUN
ejpam-4570	663	2	of	of	ADP
ejpam-4570	663	3	mathematical	mathematical	ADJ
ejpam-4570	663	4	analysis	analysis	NOUN
ejpam-4570	663	5	,	,	PUNCT
ejpam-4570	663	6	,	,	PUNCT
ejpam-4570	663	7	11:52–57	11:52–57	NUM
ejpam-4570	663	8	,	,	PUNCT
ejpam-4570	663	9	2020	2020	NUM
ejpam-4570	663	10	.	.	PUNCT
ejpam-4570	664	1	references	reference	NOUN
ejpam-4570	664	2	1781	1781	NUM
ejpam-4570	664	3	[	[	X
ejpam-4570	664	4	5	5	NUM
ejpam-4570	664	5	]	]	X
ejpam-4570	664	6	ibtesam	ibtesam	PROPN
ejpam-4570	664	7	alshammari	alshammari	PROPN
ejpam-4570	664	8	.	.	PUNCT
ejpam-4570	665	1	epi	epi	NOUN
ejpam-4570	665	2	-	-	PUNCT
ejpam-4570	665	3	completely	completely	ADV
ejpam-4570	665	4	regular	regular	ADJ
ejpam-4570	665	5	topological	topological	ADJ
ejpam-4570	665	6	spaces	space	NOUN
ejpam-4570	665	7	.	.	PUNCT
ejpam-4570	666	1	preprint	preprint	NOUN
ejpam-4570	666	2	,	,	PUNCT
ejpam-4570	666	3	2022	2022	NUM
ejpam-4570	666	4	.	.	PUNCT
ejpam-4570	667	1	[	[	X
ejpam-4570	667	2	6	6	NUM
ejpam-4570	667	3	]	]	X
ejpam-4570	667	4	ibtesam	ibtesam	PROPN
ejpam-4570	667	5	alshammari	alshammari	PROPN
ejpam-4570	667	6	,	,	PUNCT
ejpam-4570	667	7	lutfi	lutfi	PROPN
ejpam-4570	667	8	kalantan	kalantan	PROPN
ejpam-4570	667	9	,	,	PUNCT
ejpam-4570	667	10	and	and	CCONJ
ejpam-4570	667	11	sadeq	sadeq	VERB
ejpam-4570	667	12	ali	ali	PROPN
ejpam-4570	667	13	thabit	thabit	PROPN
ejpam-4570	667	14	.	.	PUNCT
ejpam-4570	668	1	partial	partial	ADJ
ejpam-4570	668	2	normality	normality	NOUN
ejpam-4570	668	3	.	.	PUNCT
ejpam-4570	669	1	journal	journal	NOUN
ejpam-4570	669	2	of	of	ADP
ejpam-4570	669	3	mathematical	mathematical	ADJ
ejpam-4570	669	4	analysis	analysis	NOUN
ejpam-4570	669	5	,	,	PUNCT
ejpam-4570	669	6	10:1–8	10:1–8	NUM
ejpam-4570	669	7	,	,	PUNCT
ejpam-4570	669	8	2019	2019	NUM
ejpam-4570	669	9	.	.	PUNCT
ejpam-4570	670	1	[	[	X
ejpam-4570	670	2	7	7	X
ejpam-4570	670	3	]	]	PUNCT
ejpam-4570	670	4	s.	s.	PROPN
ejpam-4570	670	5	alzahrani	alzahrani	PROPN
ejpam-4570	670	6	.	.	PUNCT
ejpam-4570	671	1	epiregular	epiregular	ADJ
ejpam-4570	671	2	topological	topological	ADJ
ejpam-4570	671	3	spaces	space	NOUN
ejpam-4570	671	4	.	.	PUNCT
ejpam-4570	672	1	afr	afr	PROPN
ejpam-4570	672	2	.	.	PUNCT
ejpam-4570	673	1	mat	mat	PROPN
ejpam-4570	673	2	.	.	PROPN
ejpam-4570	673	3	,	,	PUNCT
ejpam-4570	673	4	29:803–808	29:803–808	NOUN
ejpam-4570	673	5	,	,	PUNCT
ejpam-4570	673	6	2018	2018	NUM
ejpam-4570	673	7	.	.	PUNCT
ejpam-4570	674	1	[	[	X
ejpam-4570	674	2	8	8	NUM
ejpam-4570	674	3	]	]	PUNCT
ejpam-4570	674	4	samirah	samirah	PROPN
ejpam-4570	674	5	alzahrani	alzahrani	PROPN
ejpam-4570	674	6	.	.	PUNCT
ejpam-4570	675	1	c	c	X
ejpam-4570	675	2	-	-	PUNCT
ejpam-4570	675	3	regular	regular	ADJ
ejpam-4570	675	4	topological	topological	ADJ
ejpam-4570	675	5	spaces	space	NOUN
ejpam-4570	675	6	.	.	PUNCT
ejpam-4570	676	1	journal	journal	NOUN
ejpam-4570	676	2	of	of	ADP
ejpam-4570	676	3	mathematical	mathematical	ADJ
ejpam-4570	676	4	analysis	analysis	NOUN
ejpam-4570	676	5	jma	jma	PROPN
ejpam-4570	676	6	,	,	PUNCT
ejpam-4570	676	7	9:141–149	9:141–149	NUM
ejpam-4570	676	8	,	,	PUNCT
ejpam-4570	676	9	2018	2018	NUM
ejpam-4570	676	10	.	.	PUNCT
ejpam-4570	677	1	[	[	X
ejpam-4570	677	2	9	9	NUM
ejpam-4570	677	3	]	]	PUNCT
ejpam-4570	677	4	samirah	samirah	PROPN
ejpam-4570	677	5	alzahrani	alzahrani	PROPN
ejpam-4570	677	6	.	.	PUNCT
ejpam-4570	678	1	c	c	X
ejpam-4570	678	2	-	-	PUNCT
ejpam-4570	678	3	tychonoff	tychonoff	NOUN
ejpam-4570	678	4	and	and	CCONJ
ejpam-4570	678	5	l	l	NOUN
ejpam-4570	678	6	-	-	NOUN
ejpam-4570	678	7	tychonoff	tychonoff	NOUN
ejpam-4570	678	8	topological	topological	ADJ
ejpam-4570	678	9	spaces	space	NOUN
ejpam-4570	678	10	.	.	PUNCT
ejpam-4570	679	1	european	european	ADJ
ejpam-4570	679	2	journal	journal	PROPN
ejpam-4570	679	3	of	of	ADP
ejpam-4570	679	4	pure	pure	ADJ
ejpam-4570	679	5	and	and	CCONJ
ejpam-4570	679	6	applied	applied	ADJ
ejpam-4570	679	7	mathematics	mathematic	NOUN
ejpam-4570	679	8	,	,	PUNCT
ejpam-4570	679	9	11(3):882–892	11(3):882–892	NUM
ejpam-4570	679	10	,	,	PUNCT
ejpam-4570	679	11	2018	2018	NUM
ejpam-4570	679	12	.	.	PUNCT
ejpam-4570	680	1	[	[	X
ejpam-4570	680	2	10	10	NUM
ejpam-4570	680	3	]	]	PUNCT
ejpam-4570	680	4	samirah	samirah	PROPN
ejpam-4570	680	5	alzahrani	alzahrani	PROPN
ejpam-4570	680	6	and	and	CCONJ
ejpam-4570	680	7	lutfi	lutfi	PROPN
ejpam-4570	680	8	kalantan	kalantan	PROPN
ejpam-4570	680	9	.	.	PUNCT
ejpam-4570	681	1	c	c	X
ejpam-4570	681	2	-	-	PUNCT
ejpam-4570	681	3	normal	normal	ADJ
ejpam-4570	681	4	topological	topological	ADJ
ejpam-4570	681	5	property	property	NOUN
ejpam-4570	681	6	.	.	PUNCT
ejpam-4570	682	1	filomat	filomat	NOUN
ejpam-4570	682	2	,	,	PUNCT
ejpam-4570	682	3	31:2:407–411	31:2:407–411	NUM
ejpam-4570	682	4	,	,	PUNCT
ejpam-4570	682	5	2017	2017	NUM
ejpam-4570	682	6	.	.	PUNCT
ejpam-4570	683	1	[	[	X
ejpam-4570	683	2	11	11	NUM
ejpam-4570	683	3	]	]	PUNCT
ejpam-4570	683	4	j.	j.	PROPN
ejpam-4570	683	5	dugundji	dugundji	PROPN
ejpam-4570	683	6	.	.	PUNCT
ejpam-4570	683	7	topology	topology	PROPN
ejpam-4570	683	8	.	.	PUNCT
ejpam-4570	684	1	allyn	allyn	PROPN
ejpam-4570	684	2	and	and	CCONJ
ejpam-4570	684	3	bacon	bacon	PROPN
ejpam-4570	684	4	,	,	PUNCT
ejpam-4570	684	5	inc	inc	PROPN
ejpam-4570	684	6	.	.	PROPN
ejpam-4570	684	7	,	,	PUNCT
ejpam-4570	684	8	470	470	NUM
ejpam-4570	684	9	atlantic	atlantic	PROPN
ejpam-4570	684	10	avenue	avenue	PROPN
ejpam-4570	684	11	,	,	PUNCT
ejpam-4570	684	12	boston	boston	PROPN
ejpam-4570	684	13	,	,	PUNCT
ejpam-4570	684	14	1966	1966	NUM
ejpam-4570	684	15	.	.	PUNCT
ejpam-4570	685	1	[	[	X
ejpam-4570	685	2	12	12	NUM
ejpam-4570	685	3	]	]	X
ejpam-4570	685	4	r.	r.	PROPN
ejpam-4570	685	5	engelking	engelke	VERB
ejpam-4570	685	6	.	.	PUNCT
ejpam-4570	686	1	general	general	ADJ
ejpam-4570	686	2	topology	topology	NOUN
ejpam-4570	686	3	,	,	PUNCT
ejpam-4570	686	4	volume	volume	NOUN
ejpam-4570	686	5	6	6	NUM
ejpam-4570	686	6	.	.	PUNCT
ejpam-4570	687	1	berlin	berlin	PROPN
ejpam-4570	687	2	:	:	PUNCT
ejpam-4570	687	3	heldermann	heldermann	PROPN
ejpam-4570	687	4	(	(	PUNCT
ejpam-4570	687	5	sigma	sigma	PROPN
ejpam-4570	687	6	series	series	PROPN
ejpam-4570	687	7	in	in	ADP
ejpam-4570	687	8	pure	pure	ADJ
ejpam-4570	687	9	mathematics	mathematic	NOUN
ejpam-4570	687	10	)	)	PUNCT
ejpam-4570	687	11	,	,	PUNCT
ejpam-4570	687	12	poland	poland	PROPN
ejpam-4570	687	13	,	,	PUNCT
ejpam-4570	687	14	1989	1989	NUM
ejpam-4570	687	15	.	.	PUNCT
ejpam-4570	688	1	[	[	X
ejpam-4570	688	2	13	13	NUM
ejpam-4570	688	3	]	]	X
ejpam-4570	688	4	g.	g.	PROPN
ejpam-4570	688	5	gruenhage	gruenhage	PROPN
ejpam-4570	688	6	.	.	PUNCT
ejpam-4570	689	1	generalized	generalize	VERB
ejpam-4570	689	2	metric	metric	ADJ
ejpam-4570	689	3	spaces	space	NOUN
ejpam-4570	689	4	.	.	PUNCT
ejpam-4570	690	1	in	in	ADP
ejpam-4570	690	2	:	:	PUNCT
ejpam-4570	690	3	handbook	handbook	NOUN
ejpam-4570	690	4	of	of	ADP
ejpam-4570	690	5	set	set	NOUN
ejpam-4570	690	6	-	-	PUNCT
ejpam-4570	690	7	theoretic	theoretic	NOUN
ejpam-4570	690	8	topology	topology	NOUN
ejpam-4570	690	9	,	,	PUNCT
ejpam-4570	690	10	k.	k.	PROPN
ejpam-4570	690	11	kunen	kunen	PROPN
ejpam-4570	690	12	and	and	CCONJ
ejpam-4570	690	13	j.	j.	PROPN
ejpam-4570	690	14	vaughan	vaughan	PROPN
ejpam-4570	690	15	,	,	PUNCT
ejpam-4570	690	16	eds	eds	PROPN
ejpam-4570	690	17	.	.	PROPN
ejpam-4570	690	18	,	,	PUNCT
ejpam-4570	690	19	north	north	NOUN
ejpam-4570	690	20	-	-	PUNCT
ejpam-4570	690	21	holland	holland	PROPN
ejpam-4570	690	22	,	,	PUNCT
ejpam-4570	690	23	amsterdam	amsterdam	PROPN
ejpam-4570	690	24	,	,	PUNCT
ejpam-4570	690	25	pages	page	NOUN
ejpam-4570	690	26	423–501	423–501	NUM
ejpam-4570	690	27	,	,	PUNCT
ejpam-4570	690	28	1984	1984	NUM
ejpam-4570	690	29	.	.	PUNCT
ejpam-4570	691	1	[	[	X
ejpam-4570	691	2	14	14	NUM
ejpam-4570	691	3	]	]	X
ejpam-4570	691	4	l.	l.	PROPN
ejpam-4570	691	5	kalantan	kalantan	PROPN
ejpam-4570	691	6	.	.	PUNCT
ejpam-4570	692	1	π	π	X
ejpam-4570	692	2	-	-	ADJ
ejpam-4570	692	3	normal	normal	ADJ
ejpam-4570	692	4	topological	topological	ADJ
ejpam-4570	692	5	spaces	space	NOUN
ejpam-4570	692	6	.	.	PUNCT
ejpam-4570	693	1	filomat	filomat	NOUN
ejpam-4570	693	2	,	,	PUNCT
ejpam-4570	693	3	22	22	NUM
ejpam-4570	693	4	-	-	SYM
ejpam-4570	693	5	1:173–181	1:173–181	NUM
ejpam-4570	693	6	,	,	PUNCT
ejpam-4570	693	7	2008	2008	NUM
ejpam-4570	693	8	.	.	PUNCT
ejpam-4570	694	1	[	[	X
ejpam-4570	694	2	15	15	NUM
ejpam-4570	694	3	]	]	X
ejpam-4570	694	4	l.	l.	PROPN
ejpam-4570	694	5	kalantan	kalantan	PROPN
ejpam-4570	694	6	and	and	CCONJ
ejpam-4570	694	7	s.	s.	PROPN
ejpam-4570	694	8	alzahrani	alzahrani	PROPN
ejpam-4570	694	9	.	.	PUNCT
ejpam-4570	695	1	epinormality	epinormality	PROPN
ejpam-4570	695	2	.	.	PUNCT
ejpam-4570	696	1	j.	j.	PROPN
ejpam-4570	696	2	nonlinear	nonlinear	PROPN
ejpam-4570	696	3	sci	sci	PROPN
ejpam-4570	696	4	.	.	PUNCT
ejpam-4570	696	5	appl	appl	PROPN
ejpam-4570	696	6	.	.	PROPN
ejpam-4570	696	7	,	,	PUNCT
ejpam-4570	696	8	(	(	PUNCT
ejpam-4570	696	9	9):5398–5402	9):5398–5402	NOUN
ejpam-4570	696	10	,	,	PUNCT
ejpam-4570	696	11	2016	2016	NUM
ejpam-4570	696	12	.	.	PUNCT
ejpam-4570	697	1	[	[	X
ejpam-4570	697	2	16	16	NUM
ejpam-4570	697	3	]	]	X
ejpam-4570	697	4	l.	l.	PROPN
ejpam-4570	697	5	kalantan	kalantan	PROPN
ejpam-4570	697	6	and	and	CCONJ
ejpam-4570	697	7	m.	m.	PROPN
ejpam-4570	697	8	saeed	saeed	PROPN
ejpam-4570	697	9	.	.	PUNCT
ejpam-4570	698	1	l	l	NOUN
ejpam-4570	698	2	-	-	NOUN
ejpam-4570	698	3	normality	normality	NOUN
ejpam-4570	698	4	.	.	PUNCT
ejpam-4570	699	1	topology	topology	NOUN
ejpam-4570	699	2	proceedings	proceeding	NOUN
ejpam-4570	699	3	,	,	PUNCT
ejpam-4570	699	4	50:141–149	50:141–149	NUM
ejpam-4570	699	5	,	,	PUNCT
ejpam-4570	699	6	2017	2017	NUM
ejpam-4570	699	7	.	.	PUNCT
ejpam-4570	700	1	[	[	X
ejpam-4570	700	2	17	17	NUM
ejpam-4570	700	3	]	]	X
ejpam-4570	700	4	lutfi	lutfi	PROPN
ejpam-4570	700	5	kalantan	kalantan	PROPN
ejpam-4570	700	6	and	and	CCONJ
ejpam-4570	700	7	ibtesam	ibtesam	PROPN
ejpam-4570	700	8	alshammari	alshammari	PROPN
ejpam-4570	700	9	.	.	PUNCT
ejpam-4570	701	1	epi	epi	ADJ
ejpam-4570	701	2	-	-	ADJ
ejpam-4570	701	3	mild	mild	ADJ
ejpam-4570	701	4	normality	normality	NOUN
ejpam-4570	701	5	.	.	PUNCT
ejpam-4570	702	1	open	open	ADJ
ejpam-4570	703	1	mat.j	mat.j	PROPN
ejpam-4570	703	2	.	.	PROPN
ejpam-4570	703	3	,	,	PUNCT
ejpam-4570	703	4	16:1170–1175	16:1170–1175	PROPN
ejpam-4570	703	5	,	,	PUNCT
ejpam-4570	703	6	2018	2018	NUM
ejpam-4570	703	7	.	.	PUNCT
ejpam-4570	704	1	[	[	X
ejpam-4570	704	2	18	18	NUM
ejpam-4570	704	3	]	]	PUNCT
ejpam-4570	704	4	j.	j.	PROPN
ejpam-4570	704	5	k.	k.	PROPN
ejpam-4570	704	6	kohli	kohli	PROPN
ejpam-4570	704	7	and	and	CCONJ
ejpam-4570	704	8	a.	a.	PROPN
ejpam-4570	704	9	k.	k.	PROPN
ejpam-4570	704	10	das	das	PROPN
ejpam-4570	704	11	.	.	PUNCT
ejpam-4570	705	1	a	a	DET
ejpam-4570	705	2	class	class	NOUN
ejpam-4570	705	3	of	of	ADP
ejpam-4570	705	4	spaces	space	NOUN
ejpam-4570	705	5	containing	contain	VERB
ejpam-4570	705	6	all	all	PRON
ejpam-4570	705	7	generalized	generalize	VERB
ejpam-4570	705	8	absolutely	absolutely	ADV
ejpam-4570	705	9	closed	closed	ADJ
ejpam-4570	705	10	(	(	PUNCT
ejpam-4570	705	11	almost	almost	ADV
ejpam-4570	705	12	compact	compact	ADJ
ejpam-4570	705	13	)	)	PUNCT
ejpam-4570	705	14	spaces	space	NOUN
ejpam-4570	705	15	.	.	PUNCT
ejpam-4570	706	1	applied	apply	VERB
ejpam-4570	706	2	general	general	ADJ
ejpam-4570	706	3	topology	topology	NOUN
ejpam-4570	706	4	,	,	PUNCT
ejpam-4570	706	5	7(2):233–244	7(2):233–244	NUM
ejpam-4570	706	6	,	,	PUNCT
ejpam-4570	706	7	2006	2006	NUM
ejpam-4570	706	8	.	.	PUNCT
ejpam-4570	707	1	[	[	X
ejpam-4570	707	2	19	19	NUM
ejpam-4570	707	3	]	]	X
ejpam-4570	707	4	c.	c.	PROPN
ejpam-4570	707	5	kuratowski	kuratowski	PROPN
ejpam-4570	707	6	.	.	PUNCT
ejpam-4570	708	1	topology	topology	PROPN
ejpam-4570	709	1	i	i	PRON
ejpam-4570	709	2	,	,	PUNCT
ejpam-4570	709	3	volume	volume	VERB
ejpam-4570	709	4	4th	4th	ADJ
ejpam-4570	709	5	ed	ed	NOUN
ejpam-4570	709	6	.	.	PUNCT
ejpam-4570	710	1	in	in	ADP
ejpam-4570	710	2	france	france	PROPN
ejpam-4570	710	3	.	.	PUNCT
ejpam-4570	711	1	hafner	hafner	PROPN
ejpam-4570	711	2	,	,	PUNCT
ejpam-4570	711	3	new	new	PROPN
ejpam-4570	711	4	york	york	PROPN
ejpam-4570	711	5	,	,	PUNCT
ejpam-4570	711	6	1958	1958	NUM
ejpam-4570	711	7	.	.	PUNCT
ejpam-4570	712	1	[	[	X
ejpam-4570	712	2	20	20	NUM
ejpam-4570	712	3	]	]	PUNCT
ejpam-4570	712	4	p.	p.	NOUN
ejpam-4570	712	5	lambrinos	lambrinos	PROPN
ejpam-4570	712	6	.	.	PUNCT
ejpam-4570	713	1	on	on	ADP
ejpam-4570	713	2	almost	almost	ADV
ejpam-4570	713	3	compact	compact	ADJ
ejpam-4570	713	4	and	and	CCONJ
ejpam-4570	713	5	nearly	nearly	ADV
ejpam-4570	713	6	compact	compact	ADJ
ejpam-4570	713	7	spaces	space	NOUN
ejpam-4570	713	8	.	.	PUNCT
ejpam-4570	714	1	rendiconti	rendiconti	ADJ
ejpam-4570	714	2	del	del	PROPN
ejpam-4570	714	3	circolo	circolo	PROPN
ejpam-4570	714	4	matematico	matematico	NOUN
ejpam-4570	714	5	di	di	NOUN
ejpam-4570	714	6	palermo	palermo	NOUN
ejpam-4570	714	7	,	,	PUNCT
ejpam-4570	714	8	24:14–18	24:14–18	NUM
ejpam-4570	714	9	,	,	PUNCT
ejpam-4570	714	10	1975	1975	NUM
ejpam-4570	714	11	.	.	PUNCT
ejpam-4570	715	1	[	[	X
ejpam-4570	715	2	21	21	NUM
ejpam-4570	715	3	]	]	X
ejpam-4570	715	4	m.	m.	NOUN
ejpam-4570	715	5	mršević	mršević	PROPN
ejpam-4570	715	6	,	,	PUNCT
ejpam-4570	715	7	i.	i.	PROPN
ejpam-4570	715	8	l.	l.	PROPN
ejpam-4570	715	9	reilly	reilly	PROPN
ejpam-4570	715	10	,	,	PUNCT
ejpam-4570	715	11	and	and	CCONJ
ejpam-4570	715	12	m.k	m.k	PROPN
ejpam-4570	715	13	.	.	PROPN
ejpam-4570	715	14	vamanamurthy	vamanamurthy	NOUN
ejpam-4570	715	15	.	.	PUNCT
ejpam-4570	716	1	on	on	ADP
ejpam-4570	716	2	semi	semi	ADJ
ejpam-4570	716	3	regularization	regularization	NOUN
ejpam-4570	716	4	topologies	topology	NOUN
ejpam-4570	716	5	.	.	PUNCT
ejpam-4570	717	1	j.	j.	PROPN
ejpam-4570	717	2	austral	austral	PROPN
ejpam-4570	717	3	.	.	PUNCT
ejpam-4570	718	1	math	math	NOUN
ejpam-4570	718	2	.	.	PUNCT
ejpam-4570	719	1	soc	soc	PROPN
ejpam-4570	719	2	.	.	PUNCT
ejpam-4570	719	3	,	,	PUNCT
ejpam-4570	719	4	(	(	PUNCT
ejpam-4570	719	5	series	series	NOUN
ejpam-4570	719	6	a	a	PROPN
ejpam-4570	719	7	)	)	PUNCT
ejpam-4570	719	8	,	,	PUNCT
ejpam-4570	719	9	38:40–54	38:40–54	NUM
ejpam-4570	719	10	,	,	PUNCT
ejpam-4570	719	11	1985	1985	NUM
ejpam-4570	719	12	.	.	PUNCT
ejpam-4570	720	1	[	[	X
ejpam-4570	720	2	22	22	NUM
ejpam-4570	720	3	]	]	X
ejpam-4570	720	4	c.	c.	PROPN
ejpam-4570	720	5	patty	patty	PROPN
ejpam-4570	720	6	.	.	PUNCT
ejpam-4570	721	1	foundation	foundation	PROPN
ejpam-4570	721	2	of	of	ADP
ejpam-4570	721	3	topology	topology	NOUN
ejpam-4570	721	4	.	.	PUNCT
ejpam-4570	722	1	pws	pws	PROPN
ejpam-4570	722	2	-	-	PUNCT
ejpam-4570	722	3	kent	kent	PROPN
ejpam-4570	722	4	publishing	publishing	PROPN
ejpam-4570	722	5	company	company	NOUN
ejpam-4570	722	6	,	,	PUNCT
ejpam-4570	722	7	boston	boston	PROPN
ejpam-4570	722	8	,	,	PUNCT
ejpam-4570	722	9	1993	1993	NUM
ejpam-4570	722	10	.	.	PUNCT
ejpam-4570	723	1	[	[	X
ejpam-4570	723	2	23	23	NUM
ejpam-4570	723	3	]	]	PUNCT
ejpam-4570	723	4	j.	j.	PROPN
ejpam-4570	723	5	r.	r.	PROPN
ejpam-4570	723	6	porter	porter	PROPN
ejpam-4570	723	7	and	and	CCONJ
ejpam-4570	723	8	j.	j.	PROPN
ejpam-4570	723	9	d.	d.	PROPN
ejpam-4570	723	10	thomas	thomas	PROPN
ejpam-4570	723	11	.	.	PUNCT
ejpam-4570	724	1	on	on	ADP
ejpam-4570	724	2	h	h	NOUN
ejpam-4570	724	3	-	-	PUNCT
ejpam-4570	724	4	closed	closed	ADJ
ejpam-4570	724	5	and	and	CCONJ
ejpam-4570	724	6	minimal	minimal	ADJ
ejpam-4570	724	7	hausdorff	hausdorff	NOUN
ejpam-4570	724	8	spaces	space	NOUN
ejpam-4570	724	9	.	.	PUNCT
ejpam-4570	725	1	trans	trans	PROPN
ejpam-4570	725	2	.	.	PUNCT
ejpam-4570	726	1	amer	amer	PROPN
ejpam-4570	726	2	.	.	PUNCT
ejpam-4570	726	3	math	math	PROPN
ejpam-4570	726	4	.	.	PUNCT
ejpam-4570	727	1	soc	soc	PROPN
ejpam-4570	727	2	.	.	PUNCT
ejpam-4570	727	3	,	,	PUNCT
ejpam-4570	727	4	138:159–170	138:159–170	NUM
ejpam-4570	727	5	,	,	PUNCT
ejpam-4570	727	6	1996	1996	NUM
ejpam-4570	727	7	.	.	PUNCT
ejpam-4570	728	1	references	reference	NOUN
ejpam-4570	728	2	1782	1782	NUM
ejpam-4570	729	1	[	[	X
ejpam-4570	729	2	24	24	NUM
ejpam-4570	729	3	]	]	PUNCT
ejpam-4570	729	4	maha	maha	PROPN
ejpam-4570	729	5	mohammed	mohammed	PROPN
ejpam-4570	729	6	saeed	saeed	PROPN
ejpam-4570	729	7	,	,	PUNCT
ejpam-4570	729	8	lutfi	lutfi	PROPN
ejpam-4570	729	9	kalantan	kalantan	PROPN
ejpam-4570	729	10	,	,	PUNCT
ejpam-4570	729	11	and	and	CCONJ
ejpam-4570	729	12	hala	hala	PROPN
ejpam-4570	729	13	alzumi	alzumi	PROPN
ejpam-4570	729	14	.	.	PUNCT
ejpam-4570	730	1	c	c	X
ejpam-4570	730	2	-	-	PUNCT
ejpam-4570	730	3	paracompactness	paracompactness	NOUN
ejpam-4570	730	4	and	and	CCONJ
ejpam-4570	730	5	c2	c2	PROPN
ejpam-4570	730	6	-paracompactness	-paracompactness	PROPN
ejpam-4570	730	7	.	.	PUNCT
ejpam-4570	731	1	turk	turk	PROPN
ejpam-4570	731	2	.	.	PUNCT
ejpam-4570	732	1	j.	j.	PROPN
ejpam-4570	732	2	math	math	PROPN
ejpam-4570	732	3	.	.	PUNCT
ejpam-4570	732	4	,	,	PUNCT
ejpam-4570	732	5	43:9–20	43:9–20	NUM
ejpam-4570	732	6	,	,	PUNCT
ejpam-4570	732	7	2019	2019	NUM
ejpam-4570	732	8	.	.	PUNCT
ejpam-4570	733	1	[	[	X
ejpam-4570	733	2	25	25	NUM
ejpam-4570	733	3	]	]	PUNCT
ejpam-4570	733	4	m.	m.	NOUN
ejpam-4570	733	5	k.	k.	PROPN
ejpam-4570	733	6	singal	singal	PROPN
ejpam-4570	733	7	and	and	CCONJ
ejpam-4570	733	8	s.	s.	PROPN
ejpam-4570	733	9	arya	arya	PROPN
ejpam-4570	733	10	.	.	PUNCT
ejpam-4570	734	1	on	on	ADP
ejpam-4570	734	2	almost	almost	ADV
ejpam-4570	734	3	regular	regular	ADJ
ejpam-4570	734	4	spaces	space	NOUN
ejpam-4570	734	5	.	.	PUNCT
ejpam-4570	735	1	glasnik	glasnik	PROPN
ejpam-4570	735	2	matematicki	matematicki	PROPN
ejpam-4570	735	3	,	,	PUNCT
ejpam-4570	735	4	4(24):89–99	4(24):89–99	NUM
ejpam-4570	735	5	,	,	PUNCT
ejpam-4570	735	6	1969	1969	NUM
ejpam-4570	735	7	.	.	PUNCT
ejpam-4570	736	1	[	[	X
ejpam-4570	736	2	26	26	NUM
ejpam-4570	736	3	]	]	PUNCT
ejpam-4570	736	4	m.	m.	NOUN
ejpam-4570	736	5	k.	k.	PROPN
ejpam-4570	736	6	singal	singal	PROPN
ejpam-4570	736	7	and	and	CCONJ
ejpam-4570	736	8	s.	s.	PROPN
ejpam-4570	736	9	p.	p.	PROPN
ejpam-4570	736	10	arya	arya	PROPN
ejpam-4570	736	11	.	.	PUNCT
ejpam-4570	737	1	on	on	ADP
ejpam-4570	737	2	almost	almost	ADV
ejpam-4570	737	3	normal	normal	ADJ
ejpam-4570	737	4	and	and	CCONJ
ejpam-4570	737	5	almost	almost	ADV
ejpam-4570	737	6	completely	completely	ADV
ejpam-4570	737	7	regular	regular	ADJ
ejpam-4570	737	8	spaces	space	NOUN
ejpam-4570	737	9	.	.	PUNCT
ejpam-4570	738	1	glasnik	glasnik	PROPN
ejpam-4570	738	2	matematicki	matematicki	PROPN
ejpam-4570	738	3	,	,	PUNCT
ejpam-4570	738	4	5(5):141–152	5(5):141–152	NUM
ejpam-4570	738	5	,	,	PUNCT
ejpam-4570	738	6	1970	1970	NUM
ejpam-4570	738	7	.	.	PUNCT
ejpam-4570	739	1	[	[	X
ejpam-4570	739	2	27	27	NUM
ejpam-4570	739	3	]	]	PUNCT
ejpam-4570	739	4	m.	m.	NOUN
ejpam-4570	739	5	k.	k.	PROPN
ejpam-4570	739	6	singal	singal	PROPN
ejpam-4570	739	7	and	and	CCONJ
ejpam-4570	739	8	a.	a.	PROPN
ejpam-4570	739	9	r.	r.	PROPN
ejpam-4570	739	10	singal	singal	PROPN
ejpam-4570	739	11	.	.	PUNCT
ejpam-4570	740	1	almost	almost	ADV
ejpam-4570	740	2	-	-	PUNCT
ejpam-4570	740	3	continuous	continuous	ADJ
ejpam-4570	740	4	mappings	mapping	NOUN
ejpam-4570	740	5	.	.	PUNCT
ejpam-4570	741	1	yokohama	yokohama	PROPN
ejpam-4570	741	2	mathematical	mathematical	PROPN
ejpam-4570	741	3	journal	journal	PROPN
ejpam-4570	741	4	,	,	PUNCT
ejpam-4570	741	5	16:63–73	16:63–73	PROPN
ejpam-4570	741	6	,	,	PUNCT
ejpam-4570	741	7	1968	1968	NUM
ejpam-4570	741	8	.	.	PUNCT
ejpam-4570	742	1	[	[	X
ejpam-4570	742	2	28	28	NUM
ejpam-4570	742	3	]	]	X
ejpam-4570	742	4	m.	m.	NOUN
ejpam-4570	742	5	k.	k.	PROPN
ejpam-4570	742	6	singal	singal	PROPN
ejpam-4570	742	7	and	and	CCONJ
ejpam-4570	742	8	a.	a.	PROPN
ejpam-4570	742	9	r.	r.	PROPN
ejpam-4570	742	10	singal	singal	PROPN
ejpam-4570	742	11	.	.	PUNCT
ejpam-4570	743	1	mildly	mildly	ADV
ejpam-4570	743	2	normal	normal	ADJ
ejpam-4570	743	3	spaces	space	NOUN
ejpam-4570	743	4	.	.	PUNCT
ejpam-4570	744	1	kyungpook	kyungpook	PROPN
ejpam-4570	744	2	mathematical	mathematical	PROPN
ejpam-4570	744	3	journal	journal	NOUN
ejpam-4570	744	4	,	,	PUNCT
ejpam-4570	744	5	13	13	NUM
ejpam-4570	744	6	-	-	SYM
ejpam-4570	744	7	1:27–31	1:27–31	NUM
ejpam-4570	744	8	,	,	PUNCT
ejpam-4570	744	9	1973	1973	NUM
ejpam-4570	744	10	.	.	PUNCT
ejpam-4570	745	1	[	[	X
ejpam-4570	745	2	29	29	NUM
ejpam-4570	745	3	]	]	PUNCT
ejpam-4570	745	4	a.	a.	PROPN
ejpam-4570	745	5	l.	l.	PROPN
ejpam-4570	745	6	steen	steen	PROPN
ejpam-4570	745	7	and	and	CCONJ
ejpam-4570	745	8	j.	j.	PROPN
ejpam-4570	745	9	a.	a.	PROPN
ejpam-4570	745	10	seebach	seebach	PROPN
ejpam-4570	745	11	.	.	PUNCT
ejpam-4570	746	1	counterexamples	counterexample	NOUN
ejpam-4570	746	2	in	in	ADP
ejpam-4570	746	3	topology	topology	NOUN
ejpam-4570	746	4	.	.	PUNCT
ejpam-4570	747	1	dover	dover	PROPN
ejpam-4570	747	2	publications	publications	PROPN
ejpam-4570	747	3	,	,	PUNCT
ejpam-4570	747	4	inc	inc	PROPN
ejpam-4570	747	5	.	.	PROPN
ejpam-4570	747	6	,	,	PUNCT
ejpam-4570	747	7	new	new	PROPN
ejpam-4570	747	8	york	york	PROPN
ejpam-4570	747	9	,	,	PUNCT
ejpam-4570	747	10	1995	1995	NUM
ejpam-4570	747	11	.	.	PUNCT
ejpam-4570	748	1	[	[	X
ejpam-4570	748	2	30	30	NUM
ejpam-4570	748	3	]	]	PUNCT
ejpam-4570	748	4	s.	s.	PROPN
ejpam-4570	748	5	a.	a.	PROPN
ejpam-4570	748	6	s.	s.	PROPN
ejpam-4570	748	7	thabit	thabit	PROPN
ejpam-4570	748	8	.	.	PUNCT
ejpam-4570	749	1	π	π	X
ejpam-4570	749	2	-	-	NOUN
ejpam-4570	749	3	normality	normality	NOUN
ejpam-4570	749	4	in	in	ADP
ejpam-4570	749	5	topological	topological	ADJ
ejpam-4570	749	6	spaces	space	NOUN
ejpam-4570	749	7	and	and	CCONJ
ejpam-4570	749	8	its	its	PRON
ejpam-4570	749	9	generalization	generalization	NOUN
ejpam-4570	749	10	.	.	PUNCT
ejpam-4570	750	1	ph.d	ph.d	PROPN
ejpam-4570	750	2	thesis	thesis	NOUN
ejpam-4570	750	3	,	,	PUNCT
ejpam-4570	750	4	school	school	NOUN
ejpam-4570	750	5	of	of	ADP
ejpam-4570	750	6	mathematical	mathematical	ADJ
ejpam-4570	750	7	sciences	sciences	PROPN
ejpam-4570	750	8	,	,	PUNCT
ejpam-4570	750	9	universiti	universiti	PROPN
ejpam-4570	750	10	sains	sain	VERB
ejpam-4570	750	11	malaysia	malaysia	PROPN
ejpam-4570	750	12	,	,	PUNCT
ejpam-4570	750	13	usm	usm	PROPN
ejpam-4570	750	14	,	,	PUNCT
ejpam-4570	750	15	malaysia	malaysia	PROPN
ejpam-4570	750	16	,	,	PUNCT
ejpam-4570	750	17	2013	2013	NUM
ejpam-4570	750	18	.	.	PUNCT
ejpam-4570	751	1	[	[	X
ejpam-4570	751	2	31	31	NUM
ejpam-4570	751	3	]	]	PUNCT
ejpam-4570	751	4	sadeq	sadeq	PROPN
ejpam-4570	751	5	ali	ali	PROPN
ejpam-4570	751	6	thabit	thabit	PROPN
ejpam-4570	751	7	,	,	PUNCT
ejpam-4570	751	8	ohud	ohud	ADJ
ejpam-4570	751	9	alghamdi	alghamdi	NOUN
ejpam-4570	751	10	,	,	PUNCT
ejpam-4570	751	11	and	and	CCONJ
ejpam-4570	751	12	lutfi	lutfi	PROPN
ejpam-4570	751	13	kalantan	kalantan	PROPN
ejpam-4570	751	14	.	.	PUNCT
ejpam-4570	752	1	c	c	X
ejpam-4570	752	2	-	-	PUNCT
ejpam-4570	752	3	complete	complete	ADJ
ejpam-4570	752	4	regularity	regularity	NOUN
ejpam-4570	752	5	,	,	PUNCT
ejpam-4570	752	6	c	c	NOUN
ejpam-4570	752	7	-	-	PUNCT
ejpam-4570	752	8	almost	almost	ADV
ejpam-4570	752	9	regularity	regularity	NOUN
ejpam-4570	752	10	and	and	CCONJ
ejpam-4570	752	11	c2	c2	PROPN
ejpam-4570	752	12	-	-	PUNCT
ejpam-4570	752	13	almost	almost	ADV
ejpam-4570	752	14	regularity	regularity	NOUN
ejpam-4570	752	15	.	.	PUNCT
ejpam-4570	753	1	preprint	preprint	NOUN
ejpam-4570	753	2	,	,	PUNCT
ejpam-4570	753	3	2022	2022	NUM
ejpam-4570	753	4	.	.	PUNCT
ejpam-4570	754	1	[	[	X
ejpam-4570	754	2	32	32	NUM
ejpam-4570	754	3	]	]	PUNCT
ejpam-4570	754	4	sadeq	sadeq	PROPN
ejpam-4570	754	5	ali	ali	PROPN
ejpam-4570	754	6	thabit	thabit	PROPN
ejpam-4570	754	7	and	and	CCONJ
ejpam-4570	754	8	wafa	wafa	PROPN
ejpam-4570	754	9	alqurashi	alqurashi	PROPN
ejpam-4570	754	10	.	.	PUNCT
ejpam-4570	755	1	c	c	X
ejpam-4570	755	2	-	-	PUNCT
ejpam-4570	755	3	quasi	quasi	ADJ
ejpam-4570	755	4	normality	normality	NOUN
ejpam-4570	755	5	and	and	CCONJ
ejpam-4570	755	6	l	l	ADJ
ejpam-4570	755	7	-	-	ADJ
ejpam-4570	755	8	quasi	quasi	ADJ
ejpam-4570	755	9	normality	normality	NOUN
ejpam-4570	755	10	.	.	PUNCT
ejpam-4570	756	1	(	(	PUNCT
ejpam-4570	756	2	preprint	preprint	NOUN
ejpam-4570	756	3	)	)	PUNCT
ejpam-4570	756	4	,	,	PUNCT
ejpam-4570	756	5	2022	2022	NUM
ejpam-4570	756	6	.	.	PUNCT
ejpam-4570	757	1	[	[	X
ejpam-4570	757	2	33	33	NUM
ejpam-4570	757	3	]	]	PUNCT
ejpam-4570	757	4	sadeq	sadeq	PROPN
ejpam-4570	757	5	ali	ali	PROPN
ejpam-4570	757	6	thabit	thabit	PROPN
ejpam-4570	757	7	,	,	PUNCT
ejpam-4570	757	8	ibtesam	ibtesam	PROPN
ejpam-4570	757	9	alshammari	alshammari	NOUN
ejpam-4570	757	10	,	,	PUNCT
ejpam-4570	757	11	and	and	CCONJ
ejpam-4570	757	12	wafa	wafa	PROPN
ejpam-4570	757	13	alqurashi	alqurashi	PROPN
ejpam-4570	757	14	.	.	PUNCT
ejpam-4570	758	1	epi	epi	NOUN
ejpam-4570	758	2	-	-	ADJ
ejpam-4570	758	3	quasi	quasi	ADJ
ejpam-4570	758	4	normality	normality	NOUN
ejpam-4570	758	5	.	.	PUNCT
ejpam-4570	759	1	open	open	ADJ
ejpam-4570	759	2	mathematics	mathematic	NOUN
ejpam-4570	759	3	(	(	PUNCT
ejpam-4570	759	4	de	de	X
ejpam-4570	759	5	gruyter	gruyter	NOUN
ejpam-4570	759	6	open	open	ADJ
ejpam-4570	759	7	access	access	NOUN
ejpam-4570	759	8	)	)	PUNCT
ejpam-4570	759	9	,	,	PUNCT
ejpam-4570	759	10	19:1755–1770	19:1755–1770	NUM
ejpam-4570	759	11	,	,	PUNCT
ejpam-4570	759	12	2021	2021	NUM
ejpam-4570	759	13	.	.	PUNCT
ejpam-4570	760	1	[	[	X
ejpam-4570	760	2	34	34	NUM
ejpam-4570	760	3	]	]	PUNCT
ejpam-4570	760	4	sadeq	sadeq	PROPN
ejpam-4570	760	5	ali	ali	PROPN
ejpam-4570	760	6	saad	saad	PROPN
ejpam-4570	760	7	thabit	thabit	PROPN
ejpam-4570	760	8	.	.	PUNCT
ejpam-4570	761	1	epi	epi	ADJ
ejpam-4570	761	2	-	-	ADJ
ejpam-4570	761	3	partial	partial	ADJ
ejpam-4570	761	4	normality	normality	NOUN
ejpam-4570	761	5	.	.	PUNCT
ejpam-4570	762	1	journal	journal	PROPN
ejpam-4570	762	2	of	of	ADP
ejpam-4570	762	3	physics	physics	PROPN
ejpam-4570	762	4	:	:	PUNCT
ejpam-4570	762	5	conference	conference	NOUN
ejpam-4570	762	6	series	series	NOUN
ejpam-4570	762	7	,	,	PUNCT
ejpam-4570	762	8	iop	iop	PROPN
ejpam-4570	762	9	publishing	publishing	PROPN
ejpam-4570	762	10	ltd	ltd	PROPN
ejpam-4570	762	11	(	(	PUNCT
ejpam-4570	762	12	j.	j.	PROPN
ejpam-4570	762	13	phys	phys	PROPN
ejpam-4570	762	14	.	.	PUNCT
ejpam-4570	762	15	:	:	PUNCT
ejpam-4570	763	1	conf	conf	PROPN
ejpam-4570	763	2	.	.	PUNCT
ejpam-4570	763	3	ser	ser	PROPN
ejpam-4570	763	4	)	)	PUNCT
ejpam-4570	763	5	,	,	PUNCT
ejpam-4570	763	6	1900(012013):1–11	1900(012013):1–11	NUM
ejpam-4570	763	7	,	,	PUNCT
ejpam-4570	763	8	2021	2021	NUM
ejpam-4570	763	9	.	.	PUNCT
ejpam-4570	764	1	[	[	X
ejpam-4570	764	2	35	35	NUM
ejpam-4570	764	3	]	]	PUNCT
ejpam-4570	764	4	sadeq	sadeq	PROPN
ejpam-4570	764	5	ali	ali	PROPN
ejpam-4570	764	6	saad	saad	PROPN
ejpam-4570	764	7	thabit	thabit	PROPN
ejpam-4570	764	8	and	and	CCONJ
ejpam-4570	764	9	hailiza	hailiza	PROPN
ejpam-4570	764	10	kamarulhaili	kamarulhaili	NOUN
ejpam-4570	764	11	.	.	PUNCT
ejpam-4570	765	1	on	on	ADP
ejpam-4570	765	2	almost	almost	ADV
ejpam-4570	765	3	regularity	regularity	NOUN
ejpam-4570	765	4	and	and	CCONJ
ejpam-4570	765	5	π	π	NOUN
ejpam-4570	765	6	-	-	NOUN
ejpam-4570	765	7	normality	normality	NOUN
ejpam-4570	765	8	of	of	ADP
ejpam-4570	765	9	topological	topological	ADJ
ejpam-4570	765	10	spaces	space	NOUN
ejpam-4570	765	11	.	.	PUNCT
ejpam-4570	766	1	american	american	PROPN
ejpam-4570	766	2	institute	institute	PROPN
ejpam-4570	766	3	of	of	ADP
ejpam-4570	766	4	physics	physics	PROPN
ejpam-4570	766	5	(	(	PUNCT
ejpam-4570	766	6	aip	aip	PROPN
ejpam-4570	766	7	)	)	PUNCT
ejpam-4570	766	8	,	,	PUNCT
ejpam-4570	766	9	conference	conference	NOUN
ejpam-4570	766	10	proceedings	proceeding	NOUN
ejpam-4570	766	11	series	series	NOUN
ejpam-4570	766	12	,	,	PUNCT
ejpam-4570	766	13	1450:313–318	1450:313–318	NOUN
ejpam-4570	766	14	,	,	PUNCT
ejpam-4570	766	15	2012	2012	NUM
ejpam-4570	766	16	.	.	PUNCT
ejpam-4570	767	1	[	[	X
ejpam-4570	767	2	36	36	NUM
ejpam-4570	767	3	]	]	X
ejpam-4570	767	4	v.	v.	CCONJ
ejpam-4570	767	5	zaitsev	zaitsev	NOUN
ejpam-4570	767	6	.	.	PUNCT
ejpam-4570	768	1	on	on	ADP
ejpam-4570	768	2	certain	certain	ADJ
ejpam-4570	768	3	classes	class	NOUN
ejpam-4570	768	4	of	of	ADP
ejpam-4570	768	5	topological	topological	ADJ
ejpam-4570	768	6	spaces	space	NOUN
ejpam-4570	768	7	and	and	CCONJ
ejpam-4570	768	8	their	their	PRON
ejpam-4570	768	9	bicompactifications	bicompactification	NOUN
ejpam-4570	768	10	.	.	PUNCT
ejpam-4570	769	1	doklady	doklady	PROPN
ejpam-4570	769	2	akademii	akademii	NOUN
ejpam-4570	769	3	nauk	nauk	NOUN
ejpam-4570	769	4	sssr	sssr	NOUN
ejpam-4570	769	5	,	,	PUNCT
ejpam-4570	769	6	178:778–779	178:778–779	NUM
ejpam-4570	769	7	,	,	PUNCT
ejpam-4570	769	8	1968	1968	NUM
ejpam-4570	769	9	.	.	PUNCT