id	sid	tid	token	lemma	pos
ejpam-4598	1	1	european	european	PROPN
ejpam-4598	1	2	journal	journal	PROPN
ejpam-4598	1	3	of	of	ADP
ejpam-4598	1	4	pure	pure	ADJ
ejpam-4598	1	5	and	and	CCONJ
ejpam-4598	1	6	applied	apply	VERB
ejpam-4598	1	7	mathematics	mathematic	NOUN
ejpam-4598	1	8	vol	vol	NOUN
ejpam-4598	1	9	.	.	PROPN
ejpam-4598	2	1	15	15	NUM
ejpam-4598	2	2	,	,	PUNCT
ejpam-4598	2	3	no	no	INTJ
ejpam-4598	2	4	.	.	NOUN
ejpam-4598	2	5	4	4	NUM
ejpam-4598	2	6	,	,	PUNCT
ejpam-4598	2	7	2022	2022	NUM
ejpam-4598	2	8	,	,	PUNCT
ejpam-4598	2	9	1808	1808	NUM
ejpam-4598	2	10	-	-	SYM
ejpam-4598	2	11	1821	1821	NUM
ejpam-4598	2	12	issn	issn	PROPN
ejpam-4598	2	13	1307	1307	NUM
ejpam-4598	2	14	-	-	SYM
ejpam-4598	2	15	5543	5543	NUM
ejpam-4598	2	16	–	–	PUNCT
ejpam-4598	2	17	ejpam.com	ejpam.com	X
ejpam-4598	2	18	published	publish	VERB
ejpam-4598	2	19	by	by	ADP
ejpam-4598	2	20	new	new	PROPN
ejpam-4598	2	21	york	york	PROPN
ejpam-4598	2	22	business	business	PROPN
ejpam-4598	2	23	global	global	PROPN
ejpam-4598	2	24	epi	epi	NOUN
ejpam-4598	2	25	-	-	ADJ
ejpam-4598	2	26	completely	completely	ADV
ejpam-4598	2	27	regular	regular	ADJ
ejpam-4598	2	28	topological	topological	ADJ
ejpam-4598	2	29	spaces	space	NOUN
ejpam-4598	2	30	ibtesam	ibtesam	VERB
ejpam-4598	2	31	alshammari1,∗	alshammari1,∗	ADP
ejpam-4598	2	32	1	1	NUM
ejpam-4598	2	33	department	department	NOUN
ejpam-4598	2	34	of	of	ADP
ejpam-4598	2	35	mathematics	mathematic	NOUN
ejpam-4598	2	36	,	,	PUNCT
ejpam-4598	2	37	faculty	faculty	NOUN
ejpam-4598	2	38	of	of	ADP
ejpam-4598	2	39	science	science	NOUN
ejpam-4598	2	40	,	,	PUNCT
ejpam-4598	2	41	university	university	NOUN
ejpam-4598	2	42	of	of	ADP
ejpam-4598	2	43	hafr	hafr	PROPN
ejpam-4598	2	44	al	al	PROPN
ejpam-4598	2	45	batin	batin	PROPN
ejpam-4598	2	46	,	,	PUNCT
ejpam-4598	2	47	saudi	saudi	PROPN
ejpam-4598	2	48	arabia	arabia	PROPN
ejpam-4598	2	49	abstract	abstract	NOUN
ejpam-4598	2	50	.	.	PUNCT
ejpam-4598	3	1	the	the	DET
ejpam-4598	3	2	purpose	purpose	NOUN
ejpam-4598	3	3	of	of	ADP
ejpam-4598	3	4	this	this	DET
ejpam-4598	3	5	work	work	NOUN
ejpam-4598	3	6	is	be	AUX
ejpam-4598	3	7	to	to	PART
ejpam-4598	3	8	introduce	introduce	VERB
ejpam-4598	3	9	and	and	CCONJ
ejpam-4598	3	10	study	study	VERB
ejpam-4598	3	11	a	a	DET
ejpam-4598	3	12	new	new	ADJ
ejpam-4598	3	13	topological	topological	ADJ
ejpam-4598	3	14	property	property	NOUN
ejpam-4598	3	15	called	call	VERB
ejpam-4598	3	16	epi	epi	NOUN
ejpam-4598	3	17	-	-	ADJ
ejpam-4598	3	18	complete	complete	ADJ
ejpam-4598	3	19	-	-	PUNCT
ejpam-4598	3	20	regularity	regularity	NOUN
ejpam-4598	3	21	.	.	PUNCT
ejpam-4598	4	1	a	a	DET
ejpam-4598	4	2	space	space	NOUN
ejpam-4598	4	3	(	(	PUNCT
ejpam-4598	4	4	x	x	X
ejpam-4598	4	5	,	,	PUNCT
ejpam-4598	4	6	t	t	PROPN
ejpam-4598	4	7	)	)	PUNCT
ejpam-4598	4	8	is	be	AUX
ejpam-4598	4	9	called	call	VERB
ejpam-4598	4	10	an	an	DET
ejpam-4598	4	11	epi	epi	NOUN
ejpam-4598	4	12	-	-	PUNCT
ejpam-4598	4	13	completely	completely	ADV
ejpam-4598	4	14	-	-	PUNCT
ejpam-4598	4	15	regular	regular	ADJ
ejpam-4598	4	16	space	space	NOUN
ejpam-4598	4	17	if	if	SCONJ
ejpam-4598	4	18	there	there	PRON
ejpam-4598	4	19	exists	exist	VERB
ejpam-4598	4	20	a	a	DET
ejpam-4598	4	21	topology	topology	NOUN
ejpam-4598	4	22	t	t	NOUN
ejpam-4598	4	23	′	′	NUM
ejpam-4598	4	24	on	on	ADP
ejpam-4598	4	25	x	x	PUNCT
ejpam-4598	4	26	which	which	PRON
ejpam-4598	4	27	is	be	AUX
ejpam-4598	4	28	coarser	coarse	ADJ
ejpam-4598	4	29	than	than	ADP
ejpam-4598	4	30	t	t	NOUN
ejpam-4598	4	31	such	such	ADJ
ejpam-4598	4	32	that	that	SCONJ
ejpam-4598	4	33	(	(	PUNCT
ejpam-4598	4	34	x	x	X
ejpam-4598	4	35	,	,	PUNCT
ejpam-4598	4	36	t	t	PROPN
ejpam-4598	4	37	′	′	NUM
ejpam-4598	4	38	)	)	PUNCT
ejpam-4598	4	39	is	be	AUX
ejpam-4598	4	40	tychonoff	tychonoff	NOUN
ejpam-4598	4	41	.	.	PUNCT
ejpam-4598	5	1	this	this	DET
ejpam-4598	5	2	new	new	ADJ
ejpam-4598	5	3	property	property	NOUN
ejpam-4598	5	4	is	be	AUX
ejpam-4598	5	5	investigated	investigate	VERB
ejpam-4598	5	6	and	and	CCONJ
ejpam-4598	5	7	some	some	DET
ejpam-4598	5	8	examples	example	NOUN
ejpam-4598	5	9	are	be	AUX
ejpam-4598	5	10	presented	present	VERB
ejpam-4598	5	11	in	in	ADP
ejpam-4598	5	12	this	this	DET
ejpam-4598	5	13	work	work	NOUN
ejpam-4598	5	14	to	to	PART
ejpam-4598	5	15	illustrate	illustrate	VERB
ejpam-4598	5	16	its	its	PRON
ejpam-4598	5	17	relationships	relationship	NOUN
ejpam-4598	5	18	with	with	ADP
ejpam-4598	5	19	other	other	ADJ
ejpam-4598	5	20	kinds	kind	NOUN
ejpam-4598	5	21	of	of	ADP
ejpam-4598	5	22	normality	normality	NOUN
ejpam-4598	5	23	and	and	CCONJ
ejpam-4598	5	24	complete	complete	ADJ
ejpam-4598	5	25	-	-	PUNCT
ejpam-4598	5	26	regularity	regularity	NOUN
ejpam-4598	5	27	.	.	PUNCT
ejpam-4598	6	1	2020	2020	NUM
ejpam-4598	6	2	mathematics	mathematic	NOUN
ejpam-4598	6	3	subject	subject	NOUN
ejpam-4598	6	4	classifications	classification	NOUN
ejpam-4598	6	5	:	:	PUNCT
ejpam-4598	6	6	54a10	54a10	NUM
ejpam-4598	6	7	,	,	PUNCT
ejpam-4598	6	8	54b10	54b10	NUM
ejpam-4598	6	9	,	,	PUNCT
ejpam-4598	6	10	54c10	54c10	NUM
ejpam-4598	6	11	,	,	PUNCT
ejpam-4598	6	12	54d10	54d10	NUM
ejpam-4598	6	13	,	,	PUNCT
ejpam-4598	6	14	54d20	54d20	NUM
ejpam-4598	6	15	,	,	PUNCT
ejpam-4598	6	16	54d15	54d15	NUM
ejpam-4598	6	17	,	,	PUNCT
ejpam-4598	6	18	54d70	54d70	NUM
ejpam-4598	6	19	key	key	ADJ
ejpam-4598	6	20	words	word	NOUN
ejpam-4598	6	21	and	and	CCONJ
ejpam-4598	6	22	phrases	phrase	NOUN
ejpam-4598	6	23	:	:	PUNCT
ejpam-4598	6	24	epi	epi	NOUN
ejpam-4598	6	25	-	-	ADJ
ejpam-4598	6	26	normal	normal	ADJ
ejpam-4598	6	27	,	,	PUNCT
ejpam-4598	6	28	epi	epi	NOUN
ejpam-4598	6	29	-	-	NOUN
ejpam-4598	6	30	regular	regular	ADJ
ejpam-4598	6	31	,	,	PUNCT
ejpam-4598	6	32	epi	epi	NOUN
ejpam-4598	6	33	-	-	PUNCT
ejpam-4598	6	34	almost	almost	ADV
ejpam-4598	6	35	normal	normal	ADJ
ejpam-4598	6	36	,	,	PUNCT
ejpam-4598	6	37	epi	epi	NOUN
ejpam-4598	6	38	-	-	ADJ
ejpam-4598	6	39	quasi	quasi	ADJ
ejpam-4598	6	40	normal	normal	ADJ
ejpam-4598	6	41	,	,	PUNCT
ejpam-4598	6	42	epipartially	epipartially	ADV
ejpam-4598	6	43	normal	normal	ADJ
ejpam-4598	6	44	,	,	PUNCT
ejpam-4598	6	45	completely	completely	ADV
ejpam-4598	6	46	regular	regular	ADJ
ejpam-4598	6	47	and	and	CCONJ
ejpam-4598	6	48	epi	epi	NOUN
ejpam-4598	6	49	-	-	ADJ
ejpam-4598	6	50	mildly	mildly	ADV
ejpam-4598	6	51	normal	normal	ADJ
ejpam-4598	6	52	1	1	NUM
ejpam-4598	6	53	.	.	PUNCT
ejpam-4598	7	1	introduction	introduction	NOUN
ejpam-4598	7	2	the	the	DET
ejpam-4598	7	3	notion	notion	NOUN
ejpam-4598	7	4	of	of	ADP
ejpam-4598	7	5	epi	epi	NOUN
ejpam-4598	7	6	-	-	NOUN
ejpam-4598	7	7	normality	normality	NOUN
ejpam-4598	7	8	was	be	AUX
ejpam-4598	7	9	introduced	introduce	VERB
ejpam-4598	7	10	by	by	ADP
ejpam-4598	7	11	arhangel’skii	arhangel’skii	PROPN
ejpam-4598	7	12	during	during	ADP
ejpam-4598	7	13	his	his	PRON
ejpam-4598	7	14	visiting	visit	VERB
ejpam-4598	7	15	to	to	ADP
ejpam-4598	7	16	department	department	NOUN
ejpam-4598	7	17	of	of	ADP
ejpam-4598	7	18	mathematics	mathematics	PROPN
ejpam-4598	7	19	in	in	ADP
ejpam-4598	7	20	king	king	PROPN
ejpam-4598	7	21	abdulaziz	abdulaziz	PROPN
ejpam-4598	7	22	university	university	PROPN
ejpam-4598	7	23	,	,	PUNCT
ejpam-4598	7	24	saudi	saudi	PROPN
ejpam-4598	7	25	arabia	arabia	PROPN
ejpam-4598	7	26	on	on	ADP
ejpam-4598	7	27	2012	2012	NUM
ejpam-4598	7	28	.	.	PUNCT
ejpam-4598	8	1	the	the	DET
ejpam-4598	8	2	notion	notion	NOUN
ejpam-4598	8	3	of	of	ADP
ejpam-4598	8	4	epi	epi	NOUN
ejpam-4598	8	5	-	-	NOUN
ejpam-4598	8	6	normality	normality	NOUN
ejpam-4598	8	7	has	have	AUX
ejpam-4598	8	8	been	be	AUX
ejpam-4598	8	9	studied	study	VERB
ejpam-4598	8	10	by	by	ADP
ejpam-4598	8	11	kalantan	kalantan	PROPN
ejpam-4598	8	12	and	and	CCONJ
ejpam-4598	8	13	alzahrani	alzahrani	NOUN
ejpam-4598	8	14	in	in	ADP
ejpam-4598	8	15	2016	2016	NUM
ejpam-4598	8	16	[	[	X
ejpam-4598	8	17	15	15	NUM
ejpam-4598	8	18	]	]	PUNCT
ejpam-4598	8	19	.	.	PUNCT
ejpam-4598	9	1	then	then	ADV
ejpam-4598	9	2	,	,	PUNCT
ejpam-4598	9	3	alzahrani	alzahrani	NOUN
ejpam-4598	9	4	studied	study	VERB
ejpam-4598	9	5	the	the	DET
ejpam-4598	9	6	notion	notion	NOUN
ejpam-4598	9	7	of	of	ADP
ejpam-4598	9	8	epi	epi	NOUN
ejpam-4598	9	9	-	-	NOUN
ejpam-4598	9	10	regularity	regularity	NOUN
ejpam-4598	9	11	in	in	ADP
ejpam-4598	9	12	2018	2018	NUM
ejpam-4598	9	13	[	[	X
ejpam-4598	9	14	5	5	NUM
ejpam-4598	9	15	]	]	PUNCT
ejpam-4598	9	16	.	.	PUNCT
ejpam-4598	10	1	kalantan	kalantan	PROPN
ejpam-4598	10	2	and	and	CCONJ
ejpam-4598	10	3	alshammari	alshammari	PROPN
ejpam-4598	10	4	studied	study	VERB
ejpam-4598	10	5	the	the	DET
ejpam-4598	10	6	notion	notion	NOUN
ejpam-4598	10	7	of	of	ADP
ejpam-4598	10	8	epi	epi	ADJ
ejpam-4598	10	9	-	-	ADJ
ejpam-4598	10	10	mild	mild	ADJ
ejpam-4598	10	11	normality	normality	NOUN
ejpam-4598	10	12	in	in	ADP
ejpam-4598	10	13	2018	2018	NUM
ejpam-4598	10	14	[	[	X
ejpam-4598	10	15	18	18	NUM
ejpam-4598	10	16	]	]	PUNCT
ejpam-4598	10	17	.	.	PUNCT
ejpam-4598	11	1	at	at	ADP
ejpam-4598	11	2	the	the	DET
ejpam-4598	11	3	beginning	beginning	NOUN
ejpam-4598	11	4	of	of	ADP
ejpam-4598	11	5	2020	2020	NUM
ejpam-4598	11	6	,	,	PUNCT
ejpam-4598	11	7	alshammari	alshammari	PROPN
ejpam-4598	11	8	studied	study	VERB
ejpam-4598	11	9	the	the	DET
ejpam-4598	11	10	notion	notion	NOUN
ejpam-4598	11	11	of	of	ADP
ejpam-4598	11	12	epi	epi	NOUN
ejpam-4598	11	13	-	-	ADJ
ejpam-4598	11	14	almost	almost	ADV
ejpam-4598	11	15	normality	normality	NOUN
ejpam-4598	11	16	[	[	X
ejpam-4598	11	17	3	3	NUM
ejpam-4598	11	18	]	]	PUNCT
ejpam-4598	11	19	.	.	PUNCT
ejpam-4598	12	1	thabit	thabit	PROPN
ejpam-4598	12	2	studied	study	VERB
ejpam-4598	12	3	the	the	DET
ejpam-4598	12	4	notion	notion	NOUN
ejpam-4598	12	5	of	of	ADP
ejpam-4598	12	6	epi	epi	ADJ
ejpam-4598	12	7	-	-	ADJ
ejpam-4598	12	8	partial	partial	ADJ
ejpam-4598	12	9	normality	normality	NOUN
ejpam-4598	12	10	in	in	ADP
ejpam-4598	12	11	2021	2021	NUM
ejpam-4598	12	12	[	[	X
ejpam-4598	12	13	32	32	NUM
ejpam-4598	12	14	]	]	PUNCT
ejpam-4598	12	15	.	.	PUNCT
ejpam-4598	13	1	at	at	ADP
ejpam-4598	13	2	the	the	DET
ejpam-4598	13	3	end	end	NOUN
ejpam-4598	13	4	of	of	ADP
ejpam-4598	13	5	2021	2021	NUM
ejpam-4598	13	6	,	,	PUNCT
ejpam-4598	13	7	thabit	thabit	NOUN
ejpam-4598	13	8	and	and	CCONJ
ejpam-4598	13	9	others	other	NOUN
ejpam-4598	13	10	studied	study	VERB
ejpam-4598	13	11	the	the	DET
ejpam-4598	13	12	notion	notion	NOUN
ejpam-4598	13	13	of	of	ADP
ejpam-4598	13	14	epiquasi	epiquasi	NOUN
ejpam-4598	13	15	normality	normality	NOUN
ejpam-4598	13	16	[	[	X
ejpam-4598	13	17	31	31	NUM
ejpam-4598	13	18	]	]	PUNCT
ejpam-4598	13	19	.	.	PUNCT
ejpam-4598	14	1	the	the	DET
ejpam-4598	14	2	space	space	NOUN
ejpam-4598	14	3	x	x	PRON
ejpam-4598	14	4	means	mean	VERB
ejpam-4598	14	5	a	a	DET
ejpam-4598	14	6	topological	topological	ADJ
ejpam-4598	14	7	space	space	NOUN
ejpam-4598	14	8	in	in	ADP
ejpam-4598	14	9	whole	whole	ADJ
ejpam-4598	14	10	paper	paper	NOUN
ejpam-4598	14	11	.	.	PUNCT
ejpam-4598	15	1	we	we	PRON
ejpam-4598	15	2	need	need	VERB
ejpam-4598	15	3	to	to	PART
ejpam-4598	15	4	recall	recall	VERB
ejpam-4598	15	5	that	that	PRON
ejpam-4598	15	6	:	:	PUNCT
ejpam-4598	15	7	a	a	DET
ejpam-4598	15	8	subset	subset	NOUN
ejpam-4598	15	9	a	a	PRON
ejpam-4598	15	10	of	of	ADP
ejpam-4598	15	11	a	a	DET
ejpam-4598	15	12	space	space	NOUN
ejpam-4598	15	13	x	x	PUNCT
ejpam-4598	15	14	is	be	AUX
ejpam-4598	15	15	said	say	VERB
ejpam-4598	15	16	to	to	PART
ejpam-4598	15	17	be	be	AUX
ejpam-4598	15	18	a	a	DET
ejpam-4598	15	19	closed	closed	ADJ
ejpam-4598	15	20	domain	domain	NOUN
ejpam-4598	15	21	subset	subset	NOUN
ejpam-4598	15	22	if	if	SCONJ
ejpam-4598	15	23	it	it	PRON
ejpam-4598	15	24	is	be	AUX
ejpam-4598	15	25	the	the	DET
ejpam-4598	15	26	closure	closure	NOUN
ejpam-4598	15	27	of	of	ADP
ejpam-4598	15	28	its	its	PRON
ejpam-4598	15	29	own	own	ADJ
ejpam-4598	15	30	interior	interior	NOUN
ejpam-4598	15	31	[	[	X
ejpam-4598	15	32	20	20	NUM
ejpam-4598	15	33	]	]	PUNCT
ejpam-4598	15	34	.	.	PUNCT
ejpam-4598	16	1	the	the	DET
ejpam-4598	16	2	complement	complement	NOUN
ejpam-4598	16	3	of	of	ADP
ejpam-4598	16	4	a	a	DET
ejpam-4598	16	5	closed	closed	ADJ
ejpam-4598	16	6	domain	domain	NOUN
ejpam-4598	16	7	subset	subset	NOUN
ejpam-4598	16	8	is	be	AUX
ejpam-4598	16	9	called	call	VERB
ejpam-4598	16	10	open	open	ADJ
ejpam-4598	16	11	domain	domain	NOUN
ejpam-4598	16	12	.	.	PUNCT
ejpam-4598	17	1	a	a	DET
ejpam-4598	17	2	subset	subset	NOUN
ejpam-4598	17	3	a	a	PRON
ejpam-4598	17	4	of	of	ADP
ejpam-4598	17	5	a	a	DET
ejpam-4598	17	6	space	space	NOUN
ejpam-4598	17	7	x	x	PUNCT
ejpam-4598	17	8	is	be	AUX
ejpam-4598	17	9	called	call	VERB
ejpam-4598	17	10	π	π	PROPN
ejpam-4598	17	11	-	-	VERB
ejpam-4598	17	12	closed	closed	ADJ
ejpam-4598	17	13	if	if	SCONJ
ejpam-4598	17	14	it	it	PRON
ejpam-4598	17	15	is	be	AUX
ejpam-4598	17	16	a	a	DET
ejpam-4598	17	17	finite	finite	ADJ
ejpam-4598	17	18	intersection	intersection	NOUN
ejpam-4598	17	19	of	of	ADP
ejpam-4598	17	20	closed	closed	ADJ
ejpam-4598	17	21	domain	domain	NOUN
ejpam-4598	17	22	subsets	subset	NOUN
ejpam-4598	17	23	[	[	X
ejpam-4598	17	24	33	33	NUM
ejpam-4598	17	25	]	]	PUNCT
ejpam-4598	17	26	.	.	PUNCT
ejpam-4598	18	1	the	the	DET
ejpam-4598	18	2	complement	complement	NOUN
ejpam-4598	18	3	of	of	ADP
ejpam-4598	18	4	a	a	DET
ejpam-4598	18	5	π	π	PROPN
ejpam-4598	18	6	-	-	ADJ
ejpam-4598	18	7	closed	closed	ADJ
ejpam-4598	18	8	subset	subset	NOUN
ejpam-4598	18	9	is	be	AUX
ejpam-4598	18	10	called	call	VERB
ejpam-4598	18	11	π	π	PROPN
ejpam-4598	18	12	-	-	NOUN
ejpam-4598	18	13	open	open	ADJ
ejpam-4598	18	14	.	.	PUNCT
ejpam-4598	19	1	two	two	NUM
ejpam-4598	19	2	subsets	subset	NOUN
ejpam-4598	19	3	a	a	PRON
ejpam-4598	19	4	and	and	CCONJ
ejpam-4598	19	5	b	b	NOUN
ejpam-4598	19	6	of	of	ADP
ejpam-4598	19	7	a	a	DET
ejpam-4598	19	8	space	space	NOUN
ejpam-4598	19	9	x	x	PRON
ejpam-4598	19	10	are	be	AUX
ejpam-4598	19	11	said	say	VERB
ejpam-4598	19	12	to	to	PART
ejpam-4598	19	13	be	be	AUX
ejpam-4598	19	14	separated	separate	VERB
ejpam-4598	19	15	if	if	SCONJ
ejpam-4598	19	16	there	there	PRON
ejpam-4598	19	17	exist	exist	VERB
ejpam-4598	19	18	two	two	NUM
ejpam-4598	19	19	disjoint	disjoint	ADJ
ejpam-4598	19	20	open	open	ADJ
ejpam-4598	19	21	subsets	subset	NOUN
ejpam-4598	19	22	u	u	NOUN
ejpam-4598	19	23	and	and	CCONJ
ejpam-4598	19	24	v	v	NOUN
ejpam-4598	19	25	of	of	ADP
ejpam-4598	19	26	x	x	PUNCT
ejpam-4598	19	27	such	such	ADJ
ejpam-4598	19	28	that	that	SCONJ
ejpam-4598	19	29	a	a	DET
ejpam-4598	19	30	⊆	⊆	NUM
ejpam-4598	19	31	u	u	NOUN
ejpam-4598	19	32	and	and	CCONJ
ejpam-4598	19	33	b	b	NOUN
ejpam-4598	19	34	⊆	⊆	NUM
ejpam-4598	19	35	v	v	ADP
ejpam-4598	19	36	[	[	PUNCT
ejpam-4598	19	37	11	11	NUM
ejpam-4598	19	38	,	,	PUNCT
ejpam-4598	19	39	12	12	NUM
ejpam-4598	19	40	,	,	PUNCT
ejpam-4598	19	41	23	23	NUM
ejpam-4598	19	42	]	]	PUNCT
ejpam-4598	19	43	.	.	PUNCT
ejpam-4598	20	1	if	if	SCONJ
ejpam-4598	20	2	t	t	PROPN
ejpam-4598	20	3	and	and	CCONJ
ejpam-4598	20	4	t	t	PROPN
ejpam-4598	20	5	′	′	NOUN
ejpam-4598	20	6	are	be	AUX
ejpam-4598	20	7	two	two	NUM
ejpam-4598	20	8	topologies	topology	NOUN
ejpam-4598	20	9	on	on	ADP
ejpam-4598	20	10	x	x	SYM
ejpam-4598	20	11	such	such	ADJ
ejpam-4598	20	12	that	that	SCONJ
ejpam-4598	20	13	t	t	PROPN
ejpam-4598	20	14	′	′	NUM
ejpam-4598	20	15	⊆	⊆	NUM
ejpam-4598	20	16	t	t	NOUN
ejpam-4598	20	17	,	,	PUNCT
ejpam-4598	20	18	then	then	ADV
ejpam-4598	20	19	t	t	PROPN
ejpam-4598	20	20	′	′	NUM
ejpam-4598	20	21	is	be	AUX
ejpam-4598	20	22	called	call	VERB
ejpam-4598	20	23	a	a	DET
ejpam-4598	20	24	topology	topology	NOUN
ejpam-4598	20	25	coarser	coarse	ADJ
ejpam-4598	20	26	than	than	ADP
ejpam-4598	20	27	t	t	PROPN
ejpam-4598	20	28	,	,	PUNCT
ejpam-4598	20	29	and	and	CCONJ
ejpam-4598	20	30	t	t	PROPN
ejpam-4598	20	31	is	be	AUX
ejpam-4598	20	32	called	call	VERB
ejpam-4598	20	33	finer	fine	ADJ
ejpam-4598	20	34	[	[	X
ejpam-4598	20	35	12	12	NUM
ejpam-4598	20	36	]	]	PUNCT
ejpam-4598	20	37	.	.	PUNCT
ejpam-4598	21	1	a	a	DET
ejpam-4598	21	2	t4	t4	PROPN
ejpam-4598	21	3	-	-	PUNCT
ejpam-4598	21	4	space	space	NOUN
ejpam-4598	21	5	is	be	AUX
ejpam-4598	21	6	a	a	DET
ejpam-4598	21	7	t1	t1	NOUN
ejpam-4598	21	8	normal	normal	ADJ
ejpam-4598	21	9	space	space	NOUN
ejpam-4598	21	10	,	,	PUNCT
ejpam-4598	21	11	a	a	DET
ejpam-4598	21	12	t3	t3	NOUN
ejpam-4598	21	13	-	-	PUNCT
ejpam-4598	21	14	space	space	NOUN
ejpam-4598	21	15	is	be	AUX
ejpam-4598	21	16	a	a	DET
ejpam-4598	21	17	t1	t1	NOUN
ejpam-4598	21	18	regular	regular	ADJ
ejpam-4598	21	19	space	space	NOUN
ejpam-4598	21	20	and	and	CCONJ
ejpam-4598	21	21	a	a	DET
ejpam-4598	21	22	tychonoff	tychonoff	NOUN
ejpam-4598	21	23	space	space	NOUN
ejpam-4598	21	24	is	be	AUX
ejpam-4598	21	25	a	a	DET
ejpam-4598	21	26	∗corresponding	∗corresponde	VERB
ejpam-4598	21	27	author	author	NOUN
ejpam-4598	21	28	.	.	PUNCT
ejpam-4598	22	1	doi	doi	NOUN
ejpam-4598	22	2	:	:	PUNCT
ejpam-4598	22	3	https://doi.org/10.29020/nybg.ejpam.v15i4.4598	https://doi.org/10.29020/nybg.ejpam.v15i4.4598	PROPN
ejpam-4598	22	4	email	email	NOUN
ejpam-4598	22	5	addresses	address	NOUN
ejpam-4598	22	6	:	:	PUNCT
ejpam-4598	23	1	iealshamri@hotmail.com	iealshamri@hotmail.com	PROPN
ejpam-4598	23	2	,	,	PUNCT
ejpam-4598	23	3	iealshamri@uhb.edu.sa	iealshamri@uhb.edu.sa	PROPN
ejpam-4598	23	4	(	(	PUNCT
ejpam-4598	23	5	i.	i.	PROPN
ejpam-4598	23	6	alshammari	alshammari	PROPN
ejpam-4598	23	7	)	)	PUNCT
ejpam-4598	23	8	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4598	23	9	1808	1808	NUM
ejpam-4598	24	1	©	©	ADP
ejpam-4598	24	2	2022	2022	NUM
ejpam-4598	24	3	ejpam	ejpam	VERB
ejpam-4598	24	4	all	all	DET
ejpam-4598	24	5	rights	right	NOUN
ejpam-4598	24	6	reserved	reserve	VERB
ejpam-4598	24	7	.	.	PUNCT
ejpam-4598	25	1	i.	i.	PROPN
ejpam-4598	25	2	alshammari	alshammari	PROPN
ejpam-4598	25	3	/	/	SYM
ejpam-4598	25	4	eur	eur	PROPN
ejpam-4598	25	5	.	.	PUNCT
ejpam-4598	26	1	j.	j.	PROPN
ejpam-4598	26	2	pure	pure	PROPN
ejpam-4598	26	3	appl	appl	PROPN
ejpam-4598	26	4	.	.	PROPN
ejpam-4598	26	5	math	math	PROPN
ejpam-4598	26	6	,	,	PUNCT
ejpam-4598	26	7	15	15	NUM
ejpam-4598	26	8	(	(	PUNCT
ejpam-4598	26	9	4	4	NUM
ejpam-4598	26	10	)	)	PUNCT
ejpam-4598	26	11	(	(	PUNCT
ejpam-4598	26	12	2022	2022	NUM
ejpam-4598	26	13	)	)	PUNCT
ejpam-4598	26	14	,	,	PUNCT
ejpam-4598	26	15	1808	1808	NUM
ejpam-4598	26	16	-	-	SYM
ejpam-4598	26	17	1821	1821	NUM
ejpam-4598	26	18	1809	1809	NUM
ejpam-4598	26	19	t1	t1	NOUN
ejpam-4598	26	20	completely	completely	ADV
ejpam-4598	26	21	regular	regular	ADJ
ejpam-4598	26	22	space	space	NOUN
ejpam-4598	26	23	.	.	PUNCT
ejpam-4598	27	1	a	a	DET
ejpam-4598	27	2	space	space	NOUN
ejpam-4598	27	3	x	x	PUNCT
ejpam-4598	27	4	is	be	AUX
ejpam-4598	27	5	said	say	VERB
ejpam-4598	27	6	to	to	PART
ejpam-4598	27	7	be	be	AUX
ejpam-4598	27	8	π	π	NOUN
ejpam-4598	27	9	-	-	ADJ
ejpam-4598	27	10	normal	normal	ADJ
ejpam-4598	27	11	[	[	X
ejpam-4598	27	12	14	14	NUM
ejpam-4598	27	13	]	]	X
ejpam-4598	27	14	,	,	PUNCT
ejpam-4598	27	15	if	if	SCONJ
ejpam-4598	27	16	any	any	DET
ejpam-4598	27	17	pair	pair	NOUN
ejpam-4598	27	18	of	of	ADP
ejpam-4598	27	19	disjoint	disjoint	NOUN
ejpam-4598	27	20	closed	closed	ADJ
ejpam-4598	27	21	subsets	subset	NOUN
ejpam-4598	27	22	a	a	PRON
ejpam-4598	27	23	and	and	CCONJ
ejpam-4598	27	24	b	b	NOUN
ejpam-4598	27	25	of	of	ADP
ejpam-4598	27	26	x	x	PRON
ejpam-4598	27	27	,	,	PUNCT
ejpam-4598	27	28	one	one	NUM
ejpam-4598	27	29	of	of	ADP
ejpam-4598	27	30	which	which	PRON
ejpam-4598	27	31	is	be	AUX
ejpam-4598	27	32	π	π	PROPN
ejpam-4598	27	33	-	-	VERB
ejpam-4598	27	34	closed	closed	ADJ
ejpam-4598	27	35	,	,	PUNCT
ejpam-4598	27	36	can	can	AUX
ejpam-4598	27	37	be	be	AUX
ejpam-4598	27	38	separated	separate	VERB
ejpam-4598	27	39	.	.	PUNCT
ejpam-4598	28	1	a	a	DET
ejpam-4598	28	2	space	space	NOUN
ejpam-4598	28	3	x	x	PUNCT
ejpam-4598	28	4	is	be	AUX
ejpam-4598	28	5	said	say	VERB
ejpam-4598	28	6	to	to	PART
ejpam-4598	28	7	be	be	AUX
ejpam-4598	28	8	almost	almost	ADV
ejpam-4598	28	9	-	-	PUNCT
ejpam-4598	28	10	normal	normal	ADJ
ejpam-4598	28	11	[	[	X
ejpam-4598	28	12	14	14	NUM
ejpam-4598	28	13	,	,	PUNCT
ejpam-4598	28	14	28	28	NUM
ejpam-4598	28	15	]	]	PUNCT
ejpam-4598	28	16	,	,	PUNCT
ejpam-4598	28	17	if	if	SCONJ
ejpam-4598	28	18	any	any	DET
ejpam-4598	28	19	pair	pair	NOUN
ejpam-4598	28	20	of	of	ADP
ejpam-4598	28	21	disjoint	disjoint	NOUN
ejpam-4598	28	22	closed	closed	ADJ
ejpam-4598	28	23	subsets	subset	NOUN
ejpam-4598	28	24	a	a	PRON
ejpam-4598	28	25	and	and	CCONJ
ejpam-4598	28	26	b	b	NOUN
ejpam-4598	28	27	of	of	ADP
ejpam-4598	28	28	x	x	PRON
ejpam-4598	28	29	,	,	PUNCT
ejpam-4598	28	30	one	one	NUM
ejpam-4598	28	31	of	of	ADP
ejpam-4598	28	32	which	which	PRON
ejpam-4598	28	33	is	be	AUX
ejpam-4598	28	34	closed	closed	ADJ
ejpam-4598	28	35	domain	domain	NOUN
ejpam-4598	28	36	,	,	PUNCT
ejpam-4598	28	37	can	can	AUX
ejpam-4598	28	38	be	be	AUX
ejpam-4598	28	39	separated	separate	VERB
ejpam-4598	28	40	.	.	PUNCT
ejpam-4598	29	1	a	a	DET
ejpam-4598	29	2	space	space	NOUN
ejpam-4598	29	3	x	x	PUNCT
ejpam-4598	29	4	is	be	AUX
ejpam-4598	29	5	said	say	VERB
ejpam-4598	29	6	to	to	PART
ejpam-4598	29	7	be	be	AUX
ejpam-4598	29	8	mildly	mildly	ADV
ejpam-4598	29	9	normal	normal	ADJ
ejpam-4598	29	10	[	[	X
ejpam-4598	29	11	29	29	NUM
ejpam-4598	29	12	]	]	PUNCT
ejpam-4598	29	13	,	,	PUNCT
ejpam-4598	29	14	if	if	SCONJ
ejpam-4598	29	15	any	any	DET
ejpam-4598	29	16	pair	pair	NOUN
ejpam-4598	29	17	of	of	ADP
ejpam-4598	29	18	disjoint	disjoint	NOUN
ejpam-4598	29	19	closed	closed	ADJ
ejpam-4598	29	20	domain	domain	NOUN
ejpam-4598	29	21	subsets	subset	NOUN
ejpam-4598	29	22	a	a	PRON
ejpam-4598	29	23	and	and	CCONJ
ejpam-4598	29	24	b	b	NOUN
ejpam-4598	29	25	of	of	ADP
ejpam-4598	29	26	x	x	PRON
ejpam-4598	29	27	can	can	AUX
ejpam-4598	29	28	be	be	AUX
ejpam-4598	29	29	separated	separate	VERB
ejpam-4598	29	30	.	.	PUNCT
ejpam-4598	30	1	a	a	DET
ejpam-4598	30	2	space	space	NOUN
ejpam-4598	30	3	x	x	PUNCT
ejpam-4598	30	4	is	be	AUX
ejpam-4598	30	5	said	say	VERB
ejpam-4598	30	6	to	to	PART
ejpam-4598	30	7	be	be	AUX
ejpam-4598	30	8	partially	partially	ADV
ejpam-4598	30	9	normal	normal	ADJ
ejpam-4598	30	10	[	[	X
ejpam-4598	30	11	4	4	NUM
ejpam-4598	30	12	]	]	PUNCT
ejpam-4598	30	13	,	,	PUNCT
ejpam-4598	30	14	if	if	SCONJ
ejpam-4598	30	15	any	any	DET
ejpam-4598	30	16	pair	pair	NOUN
ejpam-4598	30	17	of	of	ADP
ejpam-4598	30	18	disjoint	disjoint	NOUN
ejpam-4598	30	19	closed	closed	ADJ
ejpam-4598	30	20	subsets	subset	NOUN
ejpam-4598	30	21	a	a	PRON
ejpam-4598	30	22	and	and	CCONJ
ejpam-4598	30	23	b	b	NOUN
ejpam-4598	30	24	of	of	ADP
ejpam-4598	30	25	x	x	PRON
ejpam-4598	30	26	,	,	PUNCT
ejpam-4598	30	27	one	one	NUM
ejpam-4598	30	28	of	of	ADP
ejpam-4598	30	29	which	which	PRON
ejpam-4598	30	30	is	be	AUX
ejpam-4598	30	31	closed	closed	ADJ
ejpam-4598	30	32	domain	domain	NOUN
ejpam-4598	30	33	and	and	CCONJ
ejpam-4598	30	34	the	the	DET
ejpam-4598	30	35	other	other	ADJ
ejpam-4598	30	36	is	be	AUX
ejpam-4598	30	37	π	π	PROPN
ejpam-4598	30	38	-	-	VERB
ejpam-4598	30	39	closed	closed	ADJ
ejpam-4598	30	40	,	,	PUNCT
ejpam-4598	30	41	can	can	AUX
ejpam-4598	30	42	be	be	AUX
ejpam-4598	30	43	separated	separate	VERB
ejpam-4598	30	44	.	.	PUNCT
ejpam-4598	31	1	a	a	DET
ejpam-4598	31	2	space	space	NOUN
ejpam-4598	31	3	(	(	PUNCT
ejpam-4598	31	4	x	x	X
ejpam-4598	31	5	,	,	PUNCT
ejpam-4598	31	6	t	t	PROPN
ejpam-4598	31	7	)	)	PUNCT
ejpam-4598	31	8	is	be	AUX
ejpam-4598	31	9	said	say	VERB
ejpam-4598	31	10	to	to	PART
ejpam-4598	31	11	be	be	AUX
ejpam-4598	31	12	epi	epi	NOUN
ejpam-4598	31	13	-	-	ADJ
ejpam-4598	31	14	normal	normal	ADJ
ejpam-4598	31	15	[	[	X
ejpam-4598	31	16	15	15	NUM
ejpam-4598	31	17	]	]	X
ejpam-4598	31	18	(	(	PUNCT
ejpam-4598	31	19	resp	resp	NOUN
ejpam-4598	31	20	.	.	PUNCT
ejpam-4598	32	1	epi	epi	X
ejpam-4598	32	2	-	-	ADJ
ejpam-4598	32	3	mildly	mildly	ADV
ejpam-4598	32	4	normal	normal	ADJ
ejpam-4598	32	5	[	[	X
ejpam-4598	32	6	18	18	NUM
ejpam-4598	32	7	]	]	PUNCT
ejpam-4598	32	8	,	,	PUNCT
ejpam-4598	32	9	epi	epi	NOUN
ejpam-4598	32	10	-	-	PUNCT
ejpam-4598	32	11	almost	almost	ADV
ejpam-4598	32	12	normal	normal	ADJ
ejpam-4598	32	13	[	[	X
ejpam-4598	32	14	3	3	NUM
ejpam-4598	32	15	]	]	PUNCT
ejpam-4598	32	16	,	,	PUNCT
ejpam-4598	32	17	epi	epi	X
ejpam-4598	32	18	-	-	NOUN
ejpam-4598	32	19	regular	regular	ADJ
ejpam-4598	32	20	[	[	X
ejpam-4598	32	21	5	5	NUM
ejpam-4598	32	22	]	]	PUNCT
ejpam-4598	32	23	,	,	PUNCT
ejpam-4598	32	24	epi	epi	X
ejpam-4598	32	25	-	-	ADJ
ejpam-4598	32	26	quasi	quasi	ADJ
ejpam-4598	32	27	normal	normal	ADJ
ejpam-4598	33	1	[	[	X
ejpam-4598	33	2	31	31	NUM
ejpam-4598	33	3	]	]	PUNCT
ejpam-4598	33	4	,	,	PUNCT
ejpam-4598	33	5	epi	epi	X
ejpam-4598	33	6	-	-	ADJ
ejpam-4598	33	7	partially	partially	ADV
ejpam-4598	33	8	normal	normal	ADJ
ejpam-4598	33	9	[	[	X
ejpam-4598	33	10	32	32	NUM
ejpam-4598	33	11	]	]	PUNCT
ejpam-4598	33	12	)	)	PUNCT
ejpam-4598	33	13	,	,	PUNCT
ejpam-4598	33	14	if	if	SCONJ
ejpam-4598	33	15	there	there	PRON
ejpam-4598	33	16	exists	exist	VERB
ejpam-4598	33	17	a	a	DET
ejpam-4598	33	18	topology	topology	NOUN
ejpam-4598	33	19	t	t	NOUN
ejpam-4598	33	20	′	′	NUM
ejpam-4598	33	21	on	on	ADP
ejpam-4598	33	22	x	x	SYM
ejpam-4598	33	23	coarser	coarse	ADJ
ejpam-4598	33	24	than	than	ADP
ejpam-4598	33	25	t	t	NOUN
ejpam-4598	33	26	such	such	ADJ
ejpam-4598	33	27	that	that	SCONJ
ejpam-4598	33	28	(	(	PUNCT
ejpam-4598	33	29	x	x	X
ejpam-4598	33	30	,	,	PUNCT
ejpam-4598	33	31	t	t	PROPN
ejpam-4598	33	32	′	′	NUM
ejpam-4598	33	33	)	)	PUNCT
ejpam-4598	33	34	is	be	AUX
ejpam-4598	33	35	a	a	DET
ejpam-4598	33	36	t4	t4	PROPN
ejpam-4598	33	37	(	(	PUNCT
ejpam-4598	33	38	resp	resp	PROPN
ejpam-4598	33	39	.	.	PUNCT
ejpam-4598	34	1	hausdorff	hausdorff	PROPN
ejpam-4598	34	2	mildly	mildly	ADV
ejpam-4598	34	3	-	-	PUNCT
ejpam-4598	34	4	normal	normal	ADJ
ejpam-4598	34	5	,	,	PUNCT
ejpam-4598	34	6	hausdorff	hausdorff	NOUN
ejpam-4598	34	7	almost	almost	ADV
ejpam-4598	34	8	-	-	PUNCT
ejpam-4598	34	9	normal	normal	ADJ
ejpam-4598	34	10	,	,	PUNCT
ejpam-4598	34	11	t3	t3	NOUN
ejpam-4598	34	12	,	,	PUNCT
ejpam-4598	34	13	hausdorff	hausdorff	NOUN
ejpam-4598	34	14	-	-	PUNCT
ejpam-4598	34	15	quasi	quasi	NOUN
ejpam-4598	34	16	-	-	ADJ
ejpam-4598	34	17	normal	normal	ADJ
ejpam-4598	34	18	,	,	PUNCT
ejpam-4598	34	19	hausdorff	hausdorff	NOUN
ejpam-4598	34	20	partially	partially	ADV
ejpam-4598	34	21	-	-	PUNCT
ejpam-4598	34	22	normal	normal	ADJ
ejpam-4598	34	23	)	)	PUNCT
ejpam-4598	34	24	space	space	NOUN
ejpam-4598	34	25	.	.	PUNCT
ejpam-4598	35	1	a	a	DET
ejpam-4598	35	2	space	space	NOUN
ejpam-4598	35	3	x	x	PUNCT
ejpam-4598	35	4	is	be	AUX
ejpam-4598	35	5	said	say	VERB
ejpam-4598	35	6	to	to	PART
ejpam-4598	35	7	be	be	AUX
ejpam-4598	35	8	hausdorff	hausdorff	NOUN
ejpam-4598	35	9	or	or	CCONJ
ejpam-4598	35	10	a	a	DET
ejpam-4598	35	11	t2	t2	NOUN
ejpam-4598	35	12	-	-	PUNCT
ejpam-4598	35	13	space	space	NOUN
ejpam-4598	35	14	,	,	PUNCT
ejpam-4598	35	15	if	if	SCONJ
ejpam-4598	35	16	for	for	ADP
ejpam-4598	35	17	each	each	PRON
ejpam-4598	35	18	distinct	distinct	ADJ
ejpam-4598	35	19	two	two	NUM
ejpam-4598	35	20	points	point	NOUN
ejpam-4598	35	21	x	x	X
ejpam-4598	35	22	,	,	PUNCT
ejpam-4598	35	23	y	y	PROPN
ejpam-4598	35	24	∈	∈	PROPN
ejpam-4598	35	25	x	x	PUNCT
ejpam-4598	35	26	there	there	PRON
ejpam-4598	35	27	exist	exist	VERB
ejpam-4598	35	28	two	two	NUM
ejpam-4598	35	29	open	open	ADJ
ejpam-4598	35	30	subsets	subset	NOUN
ejpam-4598	35	31	u	u	NOUN
ejpam-4598	35	32	and	and	CCONJ
ejpam-4598	35	33	v	v	NOUN
ejpam-4598	35	34	of	of	ADP
ejpam-4598	35	35	x	x	PUNCT
ejpam-4598	36	1	such	such	ADJ
ejpam-4598	36	2	that	that	SCONJ
ejpam-4598	36	3	x	x	SYM
ejpam-4598	36	4	∈	∈	PROPN
ejpam-4598	36	5	u	u	NOUN
ejpam-4598	36	6	,	,	PUNCT
ejpam-4598	36	7	y	y	PROPN
ejpam-4598	36	8	∈	∈	PROPN
ejpam-4598	36	9	v	v	NOUN
ejpam-4598	36	10	are	be	AUX
ejpam-4598	36	11	u	u	NOUN
ejpam-4598	36	12	∩v	∩v	NOUN
ejpam-4598	36	13	=	=	PUNCT
ejpam-4598	36	14	∅	∅	NOUN
ejpam-4598	37	1	[	[	X
ejpam-4598	37	2	12	12	NUM
ejpam-4598	37	3	]	]	PUNCT
ejpam-4598	37	4	.	.	PUNCT
ejpam-4598	38	1	a	a	DET
ejpam-4598	38	2	space	space	NOUN
ejpam-4598	38	3	x	x	PUNCT
ejpam-4598	38	4	is	be	AUX
ejpam-4598	38	5	said	say	VERB
ejpam-4598	38	6	to	to	PART
ejpam-4598	38	7	be	be	AUX
ejpam-4598	38	8	completely	completely	ADV
ejpam-4598	38	9	hausdorff	hausdorff	ADJ
ejpam-4598	38	10	or	or	CCONJ
ejpam-4598	38	11	urysohn	urysohn	NOUN
ejpam-4598	39	1	[	[	X
ejpam-4598	39	2	12	12	NUM
ejpam-4598	39	3	,	,	PUNCT
ejpam-4598	39	4	30	30	NUM
ejpam-4598	39	5	]	]	PUNCT
ejpam-4598	39	6	,	,	PUNCT
ejpam-4598	39	7	if	if	SCONJ
ejpam-4598	39	8	for	for	ADP
ejpam-4598	39	9	each	each	DET
ejpam-4598	39	10	distinct	distinct	ADJ
ejpam-4598	39	11	two	two	NUM
ejpam-4598	39	12	points	point	NOUN
ejpam-4598	39	13	x	x	X
ejpam-4598	39	14	,	,	PUNCT
ejpam-4598	39	15	y	y	PROPN
ejpam-4598	39	16	∈	∈	PROPN
ejpam-4598	39	17	x	x	PUNCT
ejpam-4598	39	18	there	there	PRON
ejpam-4598	39	19	exist	exist	VERB
ejpam-4598	39	20	two	two	NUM
ejpam-4598	39	21	open	open	ADJ
ejpam-4598	39	22	subsets	subset	NOUN
ejpam-4598	39	23	u	u	NOUN
ejpam-4598	39	24	and	and	CCONJ
ejpam-4598	39	25	v	v	NOUN
ejpam-4598	39	26	of	of	ADP
ejpam-4598	39	27	x	x	PUNCT
ejpam-4598	39	28	such	such	ADJ
ejpam-4598	39	29	that	that	SCONJ
ejpam-4598	39	30	x	x	SYM
ejpam-4598	39	31	∈	∈	PROPN
ejpam-4598	39	32	u	u	NOUN
ejpam-4598	39	33	,	,	PUNCT
ejpam-4598	39	34	y	y	PROPN
ejpam-4598	39	35	∈	∈	PROPN
ejpam-4598	39	36	v	v	NOUN
ejpam-4598	39	37	and	and	CCONJ
ejpam-4598	39	38	u	u	NOUN
ejpam-4598	39	39	∩	∩	NOUN
ejpam-4598	39	40	v	v	NOUN
ejpam-4598	39	41	=	=	PUNCT
ejpam-4598	39	42	∅.	∅.	ADP
ejpam-4598	39	43	a	a	DET
ejpam-4598	39	44	space	space	NOUN
ejpam-4598	39	45	x	x	PUNCT
ejpam-4598	39	46	is	be	AUX
ejpam-4598	39	47	said	say	VERB
ejpam-4598	39	48	to	to	PART
ejpam-4598	39	49	be	be	AUX
ejpam-4598	39	50	almost	almost	ADV
ejpam-4598	39	51	completely	completely	ADV
ejpam-4598	39	52	-	-	PUNCT
ejpam-4598	39	53	regular	regular	ADJ
ejpam-4598	39	54	if	if	SCONJ
ejpam-4598	39	55	for	for	SCONJ
ejpam-4598	39	56	each	each	DET
ejpam-4598	39	57	x	x	SYM
ejpam-4598	39	58	∈	∈	PROPN
ejpam-4598	39	59	x	x	X
ejpam-4598	39	60	and	and	CCONJ
ejpam-4598	39	61	each	each	DET
ejpam-4598	39	62	closed	closed	ADJ
ejpam-4598	39	63	domain	domain	NOUN
ejpam-4598	39	64	subset	subset	NOUN
ejpam-4598	39	65	f	f	PROPN
ejpam-4598	39	66	of	of	ADP
ejpam-4598	39	67	x	x	INTJ
ejpam-4598	39	68	such	such	ADJ
ejpam-4598	39	69	that	that	SCONJ
ejpam-4598	39	70	x	x	SYM
ejpam-4598	39	71	̸∈	̸∈	PROPN
ejpam-4598	39	72	f	f	PROPN
ejpam-4598	39	73	,	,	PUNCT
ejpam-4598	39	74	there	there	PRON
ejpam-4598	39	75	exists	exist	VERB
ejpam-4598	39	76	a	a	DET
ejpam-4598	39	77	continuous	continuous	ADJ
ejpam-4598	39	78	function	function	NOUN
ejpam-4598	39	79	f	f	NOUN
ejpam-4598	39	80	:	:	PUNCT
ejpam-4598	39	81	x	x	X
ejpam-4598	39	82	→	→	PUNCT
ejpam-4598	40	1	[	[	X
ejpam-4598	40	2	0	0	NUM
ejpam-4598	40	3	,	,	PUNCT
ejpam-4598	40	4	1	1	NUM
ejpam-4598	40	5	]	]	PUNCT
ejpam-4598	40	6	such	such	ADJ
ejpam-4598	40	7	that	that	SCONJ
ejpam-4598	40	8	f(x	f(x	NOUN
ejpam-4598	40	9	)	)	PUNCT
ejpam-4598	40	10	=	=	SYM
ejpam-4598	40	11	0	0	NUM
ejpam-4598	40	12	and	and	CCONJ
ejpam-4598	40	13	f(f	f(f	PROPN
ejpam-4598	40	14	)	)	PUNCT
ejpam-4598	41	1	=	=	PUNCT
ejpam-4598	41	2	{	{	PUNCT
ejpam-4598	41	3	1	1	NUM
ejpam-4598	41	4	}	}	PUNCT
ejpam-4598	41	5	[	[	X
ejpam-4598	41	6	28	28	NUM
ejpam-4598	41	7	]	]	PUNCT
ejpam-4598	41	8	.	.	PUNCT
ejpam-4598	42	1	a	a	DET
ejpam-4598	42	2	space	space	NOUN
ejpam-4598	42	3	x	x	PUNCT
ejpam-4598	42	4	is	be	AUX
ejpam-4598	42	5	said	say	VERB
ejpam-4598	42	6	to	to	PART
ejpam-4598	42	7	be	be	AUX
ejpam-4598	42	8	almost	almost	ADV
ejpam-4598	42	9	-	-	PUNCT
ejpam-4598	42	10	regular	regular	ADJ
ejpam-4598	42	11	if	if	SCONJ
ejpam-4598	42	12	for	for	SCONJ
ejpam-4598	42	13	each	each	DET
ejpam-4598	42	14	x	x	SYM
ejpam-4598	42	15	∈	∈	PROPN
ejpam-4598	42	16	x	x	X
ejpam-4598	42	17	and	and	CCONJ
ejpam-4598	42	18	each	each	DET
ejpam-4598	42	19	closed	closed	ADJ
ejpam-4598	42	20	domain	domain	NOUN
ejpam-4598	42	21	subset	subset	NOUN
ejpam-4598	42	22	f	f	PROPN
ejpam-4598	42	23	of	of	ADP
ejpam-4598	42	24	x	x	INTJ
ejpam-4598	42	25	such	such	ADJ
ejpam-4598	42	26	that	that	SCONJ
ejpam-4598	42	27	x	x	SYM
ejpam-4598	42	28	̸∈	̸∈	PROPN
ejpam-4598	42	29	f	f	PROPN
ejpam-4598	42	30	,	,	PUNCT
ejpam-4598	42	31	there	there	PRON
ejpam-4598	42	32	exist	exist	VERB
ejpam-4598	42	33	two	two	NUM
ejpam-4598	42	34	disjoint	disjoint	ADJ
ejpam-4598	42	35	open	open	ADJ
ejpam-4598	42	36	subsets	subset	NOUN
ejpam-4598	42	37	u	u	NOUN
ejpam-4598	42	38	and	and	CCONJ
ejpam-4598	42	39	v	v	ADP
ejpam-4598	42	40	such	such	ADJ
ejpam-4598	42	41	that	that	SCONJ
ejpam-4598	42	42	x	x	SYM
ejpam-4598	42	43	∈	∈	PROPN
ejpam-4598	42	44	u	u	NOUN
ejpam-4598	42	45	and	and	CCONJ
ejpam-4598	42	46	f	f	PROPN
ejpam-4598	43	1	⊆	⊆	NUM
ejpam-4598	43	2	v	v	ADP
ejpam-4598	43	3	[	[	X
ejpam-4598	43	4	27	27	NUM
ejpam-4598	43	5	]	]	PUNCT
ejpam-4598	43	6	.	.	PUNCT
ejpam-4598	44	1	a	a	DET
ejpam-4598	44	2	space	space	NOUN
ejpam-4598	44	3	x	x	PUNCT
ejpam-4598	44	4	is	be	AUX
ejpam-4598	44	5	said	say	VERB
ejpam-4598	44	6	to	to	PART
ejpam-4598	44	7	be	be	AUX
ejpam-4598	44	8	sub	sub	ADJ
ejpam-4598	44	9	-	-	ADJ
ejpam-4598	44	10	metrizable	metrizable	ADJ
ejpam-4598	44	11	[	[	X
ejpam-4598	44	12	13	13	NUM
ejpam-4598	44	13	]	]	PUNCT
ejpam-4598	44	14	,	,	PUNCT
ejpam-4598	44	15	if	if	SCONJ
ejpam-4598	44	16	there	there	PRON
ejpam-4598	44	17	exists	exist	VERB
ejpam-4598	44	18	a	a	DET
ejpam-4598	44	19	metric	metric	ADJ
ejpam-4598	44	20	d	d	NOUN
ejpam-4598	44	21	on	on	ADP
ejpam-4598	44	22	x	x	SYM
ejpam-4598	44	23	such	such	ADJ
ejpam-4598	44	24	that	that	SCONJ
ejpam-4598	44	25	the	the	DET
ejpam-4598	44	26	topology	topology	NOUN
ejpam-4598	44	27	td	td	NOUN
ejpam-4598	44	28	on	on	ADP
ejpam-4598	44	29	x	x	PUNCT
ejpam-4598	44	30	generated	generate	VERB
ejpam-4598	44	31	by	by	ADP
ejpam-4598	44	32	d	d	PROPN
ejpam-4598	44	33	is	be	AUX
ejpam-4598	44	34	coarser	coarse	ADJ
ejpam-4598	44	35	than	than	ADP
ejpam-4598	44	36	t	t	PROPN
ejpam-4598	44	37	.	.	PUNCT
ejpam-4598	45	1	the	the	DET
ejpam-4598	45	2	topology	topology	NOUN
ejpam-4598	45	3	on	on	ADP
ejpam-4598	45	4	x	x	PUNCT
ejpam-4598	45	5	generated	generate	VERB
ejpam-4598	45	6	by	by	ADP
ejpam-4598	45	7	the	the	DET
ejpam-4598	45	8	family	family	NOUN
ejpam-4598	45	9	of	of	ADP
ejpam-4598	45	10	all	all	DET
ejpam-4598	45	11	open	open	ADJ
ejpam-4598	45	12	domain	domain	NOUN
ejpam-4598	45	13	subsets	subset	NOUN
ejpam-4598	45	14	of	of	ADP
ejpam-4598	45	15	x	x	PRON
ejpam-4598	45	16	,	,	PUNCT
ejpam-4598	45	17	denoted	denote	VERB
ejpam-4598	45	18	by	by	ADP
ejpam-4598	45	19	ts	ts	PROPN
ejpam-4598	45	20	,	,	PUNCT
ejpam-4598	45	21	is	be	AUX
ejpam-4598	45	22	coarser	coarse	ADJ
ejpam-4598	45	23	than	than	ADP
ejpam-4598	45	24	t	t	PROPN
ejpam-4598	45	25	,	,	PUNCT
ejpam-4598	45	26	and	and	CCONJ
ejpam-4598	45	27	(	(	PUNCT
ejpam-4598	45	28	x	x	NOUN
ejpam-4598	45	29	,	,	PUNCT
ejpam-4598	45	30	ts	ts	NOUN
ejpam-4598	45	31	)	)	PUNCT
ejpam-4598	45	32	is	be	AUX
ejpam-4598	45	33	called	call	VERB
ejpam-4598	45	34	the	the	DET
ejpam-4598	45	35	semi	semi	NOUN
ejpam-4598	45	36	-	-	NOUN
ejpam-4598	45	37	regularization	regularization	NOUN
ejpam-4598	45	38	of	of	ADP
ejpam-4598	45	39	x.	x.	NOUN
ejpam-4598	45	40	a	a	DET
ejpam-4598	45	41	space	space	NOUN
ejpam-4598	45	42	(	(	PUNCT
ejpam-4598	45	43	x	x	X
ejpam-4598	45	44	,	,	PUNCT
ejpam-4598	45	45	t	t	PROPN
ejpam-4598	45	46	)	)	PUNCT
ejpam-4598	45	47	is	be	AUX
ejpam-4598	45	48	called	call	VERB
ejpam-4598	45	49	semi	semi	ADJ
ejpam-4598	45	50	-	-	ADJ
ejpam-4598	45	51	regular	regular	ADJ
ejpam-4598	45	52	if	if	SCONJ
ejpam-4598	45	53	t	t	NOUN
ejpam-4598	45	54	=	=	SYM
ejpam-4598	45	55	ts	ts	X
ejpam-4598	46	1	[	[	X
ejpam-4598	46	2	22	22	NUM
ejpam-4598	46	3	]	]	PUNCT
ejpam-4598	46	4	.	.	PUNCT
ejpam-4598	47	1	a	a	DET
ejpam-4598	47	2	space	space	NOUN
ejpam-4598	47	3	x	x	PUNCT
ejpam-4598	47	4	is	be	AUX
ejpam-4598	47	5	called	call	VERB
ejpam-4598	47	6	h	h	NOUN
ejpam-4598	47	7	-	-	PUNCT
ejpam-4598	47	8	closed	closed	ADJ
ejpam-4598	47	9	[	[	X
ejpam-4598	47	10	12	12	NUM
ejpam-4598	47	11	]	]	PUNCT
ejpam-4598	47	12	,	,	PUNCT
ejpam-4598	47	13	if	if	SCONJ
ejpam-4598	47	14	x	x	PRON
ejpam-4598	47	15	hausdorff	hausdorff	VERB
ejpam-4598	47	16	almost	almost	ADV
ejpam-4598	47	17	-	-	PUNCT
ejpam-4598	47	18	compact	compact	ADJ
ejpam-4598	47	19	[	[	X
ejpam-4598	47	20	19	19	NUM
ejpam-4598	47	21	,	,	PUNCT
ejpam-4598	47	22	24	24	NUM
ejpam-4598	47	23	]	]	PUNCT
ejpam-4598	47	24	.	.	PUNCT
ejpam-4598	48	1	a	a	DET
ejpam-4598	48	2	space	space	NOUN
ejpam-4598	48	3	x	x	PUNCT
ejpam-4598	48	4	is	be	AUX
ejpam-4598	48	5	called	call	VERB
ejpam-4598	48	6	c	c	NOUN
ejpam-4598	48	7	-	-	ADJ
ejpam-4598	48	8	normal	normal	ADJ
ejpam-4598	48	9	[	[	X
ejpam-4598	48	10	8	8	NUM
ejpam-4598	48	11	]	]	PUNCT
ejpam-4598	48	12	(	(	PUNCT
ejpam-4598	48	13	resp	resp	NOUN
ejpam-4598	48	14	.	.	PUNCT
ejpam-4598	49	1	c	c	X
ejpam-4598	49	2	-	-	PUNCT
ejpam-4598	49	3	regular	regular	ADJ
ejpam-4598	49	4	[	[	X
ejpam-4598	49	5	6	6	NUM
ejpam-4598	49	6	]	]	PUNCT
ejpam-4598	49	7	,	,	PUNCT
ejpam-4598	49	8	c	c	NOUN
ejpam-4598	49	9	-	-	PUNCT
ejpam-4598	49	10	tychonoff	tychonoff	NOUN
ejpam-4598	49	11	[	[	X
ejpam-4598	49	12	7	7	NUM
ejpam-4598	49	13	]	]	PUNCT
ejpam-4598	49	14	)	)	PUNCT
ejpam-4598	49	15	if	if	SCONJ
ejpam-4598	49	16	there	there	PRON
ejpam-4598	49	17	exist	exist	VERB
ejpam-4598	49	18	a	a	DET
ejpam-4598	49	19	normal	normal	ADJ
ejpam-4598	49	20	(	(	PUNCT
ejpam-4598	49	21	resp	resp	NOUN
ejpam-4598	49	22	.	.	PUNCT
ejpam-4598	50	1	regular	regular	ADJ
ejpam-4598	50	2	,	,	PUNCT
ejpam-4598	50	3	tychonoff	tychonoff	NOUN
ejpam-4598	50	4	)	)	PUNCT
ejpam-4598	50	5	space	space	NOUN
ejpam-4598	50	6	y	y	PROPN
ejpam-4598	50	7	and	and	CCONJ
ejpam-4598	50	8	a	a	DET
ejpam-4598	50	9	bijective	bijective	ADJ
ejpam-4598	50	10	function	function	NOUN
ejpam-4598	50	11	f	f	NOUN
ejpam-4598	50	12	:	:	PUNCT
ejpam-4598	50	13	x	x	X
ejpam-4598	50	14	→	→	SYM
ejpam-4598	50	15	y	y	PROPN
ejpam-4598	50	16	such	such	ADJ
ejpam-4598	50	17	that	that	SCONJ
ejpam-4598	50	18	the	the	DET
ejpam-4598	50	19	restriction	restriction	NOUN
ejpam-4598	50	20	function	function	NOUN
ejpam-4598	50	21	f	f	PROPN
ejpam-4598	50	22	|a	|a	VERB
ejpam-4598	50	23	:	:	PUNCT
ejpam-4598	50	24	a	a	DET
ejpam-4598	50	25	→	→	SYM
ejpam-4598	50	26	f(a	f(a	NOUN
ejpam-4598	50	27	)	)	PUNCT
ejpam-4598	50	28	is	be	AUX
ejpam-4598	50	29	a	a	DET
ejpam-4598	50	30	homeomorphism	homeomorphism	NOUN
ejpam-4598	50	31	for	for	ADP
ejpam-4598	50	32	each	each	DET
ejpam-4598	50	33	compact	compact	ADJ
ejpam-4598	50	34	subspace	subspace	NOUN
ejpam-4598	50	35	a	a	DET
ejpam-4598	50	36	⊆	⊆	NUM
ejpam-4598	50	37	x.	x.	NOUN
ejpam-4598	50	38	a	a	DET
ejpam-4598	50	39	space	space	NOUN
ejpam-4598	50	40	x	x	PUNCT
ejpam-4598	50	41	is	be	AUX
ejpam-4598	50	42	called	call	VERB
ejpam-4598	50	43	l	l	NOUN
ejpam-4598	50	44	-	-	ADJ
ejpam-4598	50	45	normal	normal	ADJ
ejpam-4598	50	46	[	[	X
ejpam-4598	50	47	16	16	NUM
ejpam-4598	50	48	]	]	X
ejpam-4598	50	49	(	(	PUNCT
ejpam-4598	50	50	resp	resp	NOUN
ejpam-4598	50	51	.	.	PUNCT
ejpam-4598	51	1	cc	cc	NOUN
ejpam-4598	51	2	-	-	ADJ
ejpam-4598	51	3	normal	normal	ADJ
ejpam-4598	51	4	[	[	X
ejpam-4598	51	5	17	17	NUM
ejpam-4598	51	6	]	]	SYM
ejpam-4598	51	7	)	)	PUNCT
ejpam-4598	51	8	if	if	SCONJ
ejpam-4598	51	9	there	there	PRON
ejpam-4598	51	10	exist	exist	VERB
ejpam-4598	51	11	a	a	DET
ejpam-4598	51	12	normal	normal	ADJ
ejpam-4598	51	13	space	space	NOUN
ejpam-4598	51	14	y	y	PROPN
ejpam-4598	51	15	and	and	CCONJ
ejpam-4598	51	16	a	a	DET
ejpam-4598	51	17	bijective	bijective	ADJ
ejpam-4598	51	18	function	function	NOUN
ejpam-4598	52	1	f	f	NOUN
ejpam-4598	52	2	:	:	PUNCT
ejpam-4598	52	3	x	x	X
ejpam-4598	52	4	→	→	SYM
ejpam-4598	52	5	y	y	PROPN
ejpam-4598	52	6	such	such	ADJ
ejpam-4598	52	7	that	that	SCONJ
ejpam-4598	52	8	the	the	DET
ejpam-4598	52	9	restriction	restriction	NOUN
ejpam-4598	52	10	function	function	NOUN
ejpam-4598	52	11	f	f	PROPN
ejpam-4598	52	12	|a	|a	VERB
ejpam-4598	52	13	:	:	PUNCT
ejpam-4598	52	14	a	a	DET
ejpam-4598	52	15	→	→	SYM
ejpam-4598	52	16	f(a	f(a	NOUN
ejpam-4598	52	17	)	)	PUNCT
ejpam-4598	52	18	is	be	AUX
ejpam-4598	52	19	a	a	DET
ejpam-4598	52	20	homeomorphism	homeomorphism	NOUN
ejpam-4598	52	21	for	for	ADP
ejpam-4598	52	22	each	each	DET
ejpam-4598	52	23	lindelöf	lindelöf	NOUN
ejpam-4598	52	24	(	(	PUNCT
ejpam-4598	52	25	resp	resp	NOUN
ejpam-4598	52	26	.	.	PUNCT
ejpam-4598	53	1	countably	countably	ADV
ejpam-4598	53	2	compact	compact	ADJ
ejpam-4598	53	3	)	)	PUNCT
ejpam-4598	53	4	subspace	subspace	NOUN
ejpam-4598	53	5	a	a	DET
ejpam-4598	53	6	⊆	⊆	NUM
ejpam-4598	53	7	x.	x.	NOUN
ejpam-4598	53	8	a	a	DET
ejpam-4598	53	9	space	space	NOUN
ejpam-4598	53	10	x	x	PUNCT
ejpam-4598	53	11	is	be	AUX
ejpam-4598	53	12	called	call	VERB
ejpam-4598	53	13	l	l	NOUN
ejpam-4598	53	14	-	-	NOUN
ejpam-4598	53	15	regular	regular	ADJ
ejpam-4598	53	16	[	[	X
ejpam-4598	53	17	6	6	NUM
ejpam-4598	53	18	]	]	PUNCT
ejpam-4598	53	19	(	(	PUNCT
ejpam-4598	53	20	resp	resp	NOUN
ejpam-4598	53	21	.	.	PUNCT
ejpam-4598	54	1	l	l	NOUN
ejpam-4598	54	2	-	-	NOUN
ejpam-4598	54	3	tychonoff	tychonoff	NOUN
ejpam-4598	54	4	[	[	X
ejpam-4598	54	5	7	7	NUM
ejpam-4598	54	6	]	]	PUNCT
ejpam-4598	54	7	)	)	PUNCT
ejpam-4598	54	8	if	if	SCONJ
ejpam-4598	54	9	there	there	PRON
ejpam-4598	54	10	exist	exist	VERB
ejpam-4598	54	11	a	a	DET
ejpam-4598	54	12	regular	regular	ADJ
ejpam-4598	54	13	(	(	PUNCT
ejpam-4598	54	14	resp	resp	NOUN
ejpam-4598	54	15	.	.	PUNCT
ejpam-4598	54	16	tychonoff	tychonoff	NOUN
ejpam-4598	54	17	)	)	PUNCT
ejpam-4598	54	18	space	space	NOUN
ejpam-4598	54	19	y	y	PROPN
ejpam-4598	54	20	and	and	CCONJ
ejpam-4598	54	21	a	a	DET
ejpam-4598	54	22	bijective	bijective	ADJ
ejpam-4598	54	23	function	function	NOUN
ejpam-4598	55	1	f	f	NOUN
ejpam-4598	55	2	:	:	PUNCT
ejpam-4598	55	3	x	x	X
ejpam-4598	55	4	→	→	SYM
ejpam-4598	55	5	y	y	PROPN
ejpam-4598	55	6	such	such	ADJ
ejpam-4598	55	7	that	that	SCONJ
ejpam-4598	55	8	the	the	DET
ejpam-4598	55	9	restriction	restriction	NOUN
ejpam-4598	55	10	function	function	NOUN
ejpam-4598	55	11	f	f	PROPN
ejpam-4598	55	12	|a	|a	VERB
ejpam-4598	55	13	:	:	PUNCT
ejpam-4598	55	14	a	a	DET
ejpam-4598	55	15	→	→	SYM
ejpam-4598	55	16	f(a	f(a	NOUN
ejpam-4598	55	17	)	)	PUNCT
ejpam-4598	55	18	is	be	AUX
ejpam-4598	55	19	a	a	DET
ejpam-4598	55	20	homeomorphism	homeomorphism	NOUN
ejpam-4598	55	21	for	for	SCONJ
ejpam-4598	55	22	each	each	DET
ejpam-4598	55	23	lindelöf	lindelöf	NOUN
ejpam-4598	55	24	subspace	subspace	VERB
ejpam-4598	55	25	a	a	DET
ejpam-4598	55	26	⊆	⊆	NUM
ejpam-4598	55	27	x.	x.	NOUN
ejpam-4598	55	28	the	the	DET
ejpam-4598	55	29	basic	basic	ADJ
ejpam-4598	55	30	definitions	definition	NOUN
ejpam-4598	55	31	and	and	CCONJ
ejpam-4598	55	32	any	any	DET
ejpam-4598	55	33	undefined	undefined	ADJ
ejpam-4598	55	34	terms	term	NOUN
ejpam-4598	55	35	in	in	ADP
ejpam-4598	55	36	this	this	DET
ejpam-4598	55	37	article	article	NOUN
ejpam-4598	55	38	can	can	AUX
ejpam-4598	55	39	be	be	AUX
ejpam-4598	55	40	found	find	VERB
ejpam-4598	55	41	in	in	ADP
ejpam-4598	55	42	[	[	X
ejpam-4598	55	43	31	31	NUM
ejpam-4598	55	44	]	]	PUNCT
ejpam-4598	55	45	and	and	CCONJ
ejpam-4598	56	1	[	[	X
ejpam-4598	56	2	32	32	NUM
ejpam-4598	56	3	]	]	PUNCT
ejpam-4598	56	4	.	.	PUNCT
ejpam-4598	57	1	in	in	ADP
ejpam-4598	57	2	this	this	DET
ejpam-4598	57	3	paper	paper	NOUN
ejpam-4598	57	4	,	,	PUNCT
ejpam-4598	57	5	i	i	PRON
ejpam-4598	57	6	introduce	introduce	VERB
ejpam-4598	57	7	and	and	CCONJ
ejpam-4598	57	8	study	study	VERB
ejpam-4598	57	9	a	a	DET
ejpam-4598	57	10	new	new	ADJ
ejpam-4598	57	11	topological	topological	ADJ
ejpam-4598	57	12	property	property	NOUN
ejpam-4598	57	13	called	call	VERB
ejpam-4598	57	14	epi	epi	NOUN
ejpam-4598	57	15	-	-	ADJ
ejpam-4598	57	16	complete	complete	ADJ
ejpam-4598	57	17	regularity	regularity	NOUN
ejpam-4598	57	18	.	.	PUNCT
ejpam-4598	58	1	i	i	PRON
ejpam-4598	58	2	show	show	VERB
ejpam-4598	58	3	that	that	SCONJ
ejpam-4598	58	4	this	this	DET
ejpam-4598	58	5	new	new	ADJ
ejpam-4598	58	6	property	property	NOUN
ejpam-4598	58	7	is	be	AUX
ejpam-4598	58	8	different	different	ADJ
ejpam-4598	58	9	from	from	ADP
ejpam-4598	58	10	epi	epi	NOUN
ejpam-4598	58	11	-	-	NOUN
ejpam-4598	58	12	normality	normality	ADJ
ejpam-4598	58	13	,	,	PUNCT
ejpam-4598	58	14	epi	epi	NOUN
ejpam-4598	58	15	-	-	NOUN
ejpam-4598	58	16	regularity	regularity	NOUN
ejpam-4598	58	17	,	,	PUNCT
ejpam-4598	58	18	epi	epi	ADJ
ejpam-4598	58	19	-	-	ADJ
ejpam-4598	58	20	mild	mild	ADJ
ejpam-4598	58	21	normality	normality	NOUN
ejpam-4598	58	22	,	,	PUNCT
ejpam-4598	58	23	epi	epi	NOUN
ejpam-4598	58	24	-	-	ADJ
ejpam-4598	58	25	quasi	quasi	ADJ
ejpam-4598	58	26	normality	normality	NOUN
ejpam-4598	58	27	,	,	PUNCT
ejpam-4598	58	28	epi	epi	ADJ
ejpam-4598	58	29	-	-	ADJ
ejpam-4598	58	30	partial	partial	ADJ
ejpam-4598	58	31	normality	normality	NOUN
ejpam-4598	58	32	and	and	CCONJ
ejpam-4598	58	33	epi	epi	NOUN
ejpam-4598	58	34	-	-	ADJ
ejpam-4598	58	35	almost	almost	ADV
ejpam-4598	58	36	normality	normality	NOUN
ejpam-4598	58	37	.	.	PUNCT
ejpam-4598	59	1	some	some	DET
ejpam-4598	59	2	properties	property	NOUN
ejpam-4598	59	3	,	,	PUNCT
ejpam-4598	59	4	counterexample	counterexample	NOUN
ejpam-4598	59	5	and	and	CCONJ
ejpam-4598	59	6	relationships	relationship	NOUN
ejpam-4598	59	7	of	of	ADP
ejpam-4598	59	8	this	this	DET
ejpam-4598	59	9	property	property	NOUN
ejpam-4598	59	10	are	be	AUX
ejpam-4598	59	11	investigated	investigate	VERB
ejpam-4598	59	12	.	.	PUNCT
ejpam-4598	60	1	this	this	DET
ejpam-4598	60	2	paper	paper	NOUN
ejpam-4598	60	3	contains	contain	VERB
ejpam-4598	60	4	three	three	NUM
ejpam-4598	60	5	main	main	ADJ
ejpam-4598	60	6	sections	section	NOUN
ejpam-4598	60	7	starting	start	VERB
ejpam-4598	60	8	from	from	ADP
ejpam-4598	60	9	section	section	NOUN
ejpam-4598	60	10	2	2	NUM
ejpam-4598	60	11	.	.	PUNCT
ejpam-4598	61	1	in	in	ADP
ejpam-4598	61	2	section	section	NOUN
ejpam-4598	61	3	2	2	NUM
ejpam-4598	61	4	,	,	PUNCT
ejpam-4598	61	5	the	the	DET
ejpam-4598	61	6	definition	definition	NOUN
ejpam-4598	61	7	of	of	ADP
ejpam-4598	61	8	epi	epi	NOUN
ejpam-4598	61	9	-	-	ADJ
ejpam-4598	61	10	complete	complete	ADJ
ejpam-4598	61	11	regularity	regularity	NOUN
ejpam-4598	61	12	is	be	AUX
ejpam-4598	61	13	introduced	introduce	VERB
ejpam-4598	61	14	and	and	CCONJ
ejpam-4598	61	15	some	some	DET
ejpam-4598	61	16	examples	example	NOUN
ejpam-4598	61	17	are	be	AUX
ejpam-4598	61	18	presented	present	VERB
ejpam-4598	61	19	.	.	PUNCT
ejpam-4598	62	1	some	some	DET
ejpam-4598	62	2	properties	property	NOUN
ejpam-4598	62	3	of	of	ADP
ejpam-4598	62	4	epi	epi	NOUN
ejpam-4598	62	5	-	-	ADJ
ejpam-4598	62	6	complete	complete	ADJ
ejpam-4598	62	7	regularity	regularity	NOUN
ejpam-4598	62	8	are	be	AUX
ejpam-4598	62	9	studied	study	VERB
ejpam-4598	62	10	and	and	CCONJ
ejpam-4598	62	11	given	give	VERB
ejpam-4598	62	12	in	in	ADP
ejpam-4598	62	13	section	section	NOUN
ejpam-4598	62	14	3	3	NUM
ejpam-4598	62	15	.	.	PUNCT
ejpam-4598	62	16	i.	i.	PROPN
ejpam-4598	62	17	alshammari	alshammari	PROPN
ejpam-4598	62	18	/	/	SYM
ejpam-4598	62	19	eur	eur	PROPN
ejpam-4598	62	20	.	.	PUNCT
ejpam-4598	63	1	j.	j.	PROPN
ejpam-4598	63	2	pure	pure	PROPN
ejpam-4598	63	3	appl	appl	PROPN
ejpam-4598	63	4	.	.	PROPN
ejpam-4598	63	5	math	math	PROPN
ejpam-4598	63	6	,	,	PUNCT
ejpam-4598	63	7	15	15	NUM
ejpam-4598	63	8	(	(	PUNCT
ejpam-4598	63	9	4	4	NUM
ejpam-4598	63	10	)	)	PUNCT
ejpam-4598	63	11	(	(	PUNCT
ejpam-4598	63	12	2022	2022	NUM
ejpam-4598	63	13	)	)	PUNCT
ejpam-4598	63	14	,	,	PUNCT
ejpam-4598	63	15	1808	1808	NUM
ejpam-4598	63	16	-	-	SYM
ejpam-4598	63	17	1821	1821	NUM
ejpam-4598	63	18	1810	1810	NUM
ejpam-4598	63	19	2	2	NUM
ejpam-4598	63	20	.	.	PUNCT
ejpam-4598	63	21	preliminaries	preliminary	NOUN
ejpam-4598	63	22	first	first	ADV
ejpam-4598	63	23	,	,	PUNCT
ejpam-4598	63	24	i	i	PRON
ejpam-4598	63	25	present	present	VERB
ejpam-4598	63	26	the	the	DET
ejpam-4598	63	27	main	main	ADJ
ejpam-4598	63	28	definition	definition	NOUN
ejpam-4598	63	29	of	of	ADP
ejpam-4598	63	30	this	this	DET
ejpam-4598	63	31	study	study	NOUN
ejpam-4598	63	32	:	:	PUNCT
ejpam-4598	63	33	definition	definition	NOUN
ejpam-4598	63	34	1	1	NUM
ejpam-4598	63	35	.	.	PUNCT
ejpam-4598	64	1	a	a	DET
ejpam-4598	64	2	space	space	NOUN
ejpam-4598	64	3	(	(	PUNCT
ejpam-4598	64	4	x	x	X
ejpam-4598	64	5	,	,	PUNCT
ejpam-4598	64	6	t	t	PROPN
ejpam-4598	64	7	)	)	PUNCT
ejpam-4598	64	8	is	be	AUX
ejpam-4598	64	9	called	call	VERB
ejpam-4598	64	10	an	an	DET
ejpam-4598	64	11	epi	epi	NOUN
ejpam-4598	64	12	-	-	PUNCT
ejpam-4598	64	13	completely	completely	ADV
ejpam-4598	64	14	-	-	PUNCT
ejpam-4598	64	15	regular	regular	ADJ
ejpam-4598	64	16	space	space	NOUN
ejpam-4598	64	17	if	if	SCONJ
ejpam-4598	64	18	there	there	PRON
ejpam-4598	64	19	exists	exist	VERB
ejpam-4598	64	20	a	a	DET
ejpam-4598	64	21	topology	topology	NOUN
ejpam-4598	64	22	t	t	NOUN
ejpam-4598	64	23	′	′	NUM
ejpam-4598	64	24	on	on	ADP
ejpam-4598	64	25	x	x	PUNCT
ejpam-4598	64	26	which	which	PRON
ejpam-4598	64	27	is	be	AUX
ejpam-4598	64	28	coarser	coarse	ADJ
ejpam-4598	64	29	than	than	ADP
ejpam-4598	64	30	t	t	NOUN
ejpam-4598	64	31	such	such	ADJ
ejpam-4598	64	32	that	that	SCONJ
ejpam-4598	64	33	(	(	PUNCT
ejpam-4598	64	34	x	x	X
ejpam-4598	64	35	,	,	PUNCT
ejpam-4598	64	36	t	t	PROPN
ejpam-4598	64	37	′	′	NUM
ejpam-4598	64	38	)	)	PUNCT
ejpam-4598	64	39	is	be	AUX
ejpam-4598	64	40	tychonoff	tychonoff	NOUN
ejpam-4598	64	41	.	.	PUNCT
ejpam-4598	65	1	from	from	ADP
ejpam-4598	65	2	definition	definition	NOUN
ejpam-4598	65	3	1	1	NUM
ejpam-4598	65	4	,	,	PUNCT
ejpam-4598	65	5	note	note	VERB
ejpam-4598	65	6	that	that	SCONJ
ejpam-4598	65	7	:	:	PUNCT
ejpam-4598	65	8	every	every	DET
ejpam-4598	65	9	epi	epi	NOUN
ejpam-4598	65	10	-	-	ADJ
ejpam-4598	65	11	completely	completely	ADV
ejpam-4598	65	12	regular	regular	ADJ
ejpam-4598	65	13	space	space	NOUN
ejpam-4598	65	14	is	be	AUX
ejpam-4598	65	15	hausdorff	hausdorff	NOUN
ejpam-4598	65	16	and	and	CCONJ
ejpam-4598	65	17	any	any	DET
ejpam-4598	65	18	tychonoff	tychonoff	NOUN
ejpam-4598	65	19	space	space	NOUN
ejpam-4598	65	20	is	be	AUX
ejpam-4598	65	21	epi	epi	NOUN
ejpam-4598	65	22	-	-	ADJ
ejpam-4598	65	23	completely	completely	ADV
ejpam-4598	65	24	-	-	PUNCT
ejpam-4598	65	25	regular	regular	ADJ
ejpam-4598	65	26	,	,	PUNCT
ejpam-4598	65	27	but	but	CCONJ
ejpam-4598	65	28	the	the	DET
ejpam-4598	65	29	converses	converse	NOUN
ejpam-4598	65	30	are	be	AUX
ejpam-4598	65	31	not	not	PART
ejpam-4598	65	32	true	true	ADJ
ejpam-4598	65	33	in	in	ADP
ejpam-4598	65	34	general	general	ADJ
ejpam-4598	65	35	,	,	PUNCT
ejpam-4598	65	36	for	for	ADP
ejpam-4598	65	37	example	example	NOUN
ejpam-4598	65	38	:	:	PUNCT
ejpam-4598	65	39	the	the	DET
ejpam-4598	65	40	irregular	irregular	ADJ
ejpam-4598	65	41	lattice	lattice	NOUN
ejpam-4598	65	42	topology	topology	NOUN
ejpam-4598	65	43	,	,	PUNCT
ejpam-4598	65	44	example	example	NOUN
ejpam-4598	65	45	6	6	NUM
ejpam-4598	65	46	is	be	AUX
ejpam-4598	65	47	a	a	DET
ejpam-4598	65	48	hausdorff	hausdorff	NOUN
ejpam-4598	65	49	space	space	NOUN
ejpam-4598	65	50	which	which	PRON
ejpam-4598	65	51	is	be	AUX
ejpam-4598	65	52	not	not	PART
ejpam-4598	65	53	epi	epi	NOUN
ejpam-4598	65	54	-	-	ADJ
ejpam-4598	65	55	completely	completely	ADV
ejpam-4598	65	56	regular	regular	ADJ
ejpam-4598	65	57	.	.	PUNCT
ejpam-4598	66	1	the	the	DET
ejpam-4598	66	2	smirnov	smirnov	PROPN
ejpam-4598	66	3	’s	’s	PART
ejpam-4598	66	4	deleted	delete	VERB
ejpam-4598	66	5	sequence	sequence	NOUN
ejpam-4598	66	6	topology	topology	NOUN
ejpam-4598	66	7	,	,	PUNCT
ejpam-4598	66	8	example	example	NOUN
ejpam-4598	66	9	10	10	NUM
ejpam-4598	66	10	,	,	PUNCT
ejpam-4598	66	11	and	and	CCONJ
ejpam-4598	66	12	the	the	DET
ejpam-4598	66	13	half	half	ADJ
ejpam-4598	66	14	disc	disc	NOUN
ejpam-4598	66	15	topology	topology	NOUN
ejpam-4598	66	16	,	,	PUNCT
ejpam-4598	66	17	example	example	NOUN
ejpam-4598	66	18	5	5	NUM
ejpam-4598	66	19	,	,	PUNCT
ejpam-4598	66	20	are	be	AUX
ejpam-4598	66	21	epi	epi	NOUN
ejpam-4598	66	22	-	-	ADJ
ejpam-4598	66	23	completely	completely	ADV
ejpam-4598	66	24	regular	regular	ADJ
ejpam-4598	66	25	spaces	space	NOUN
ejpam-4598	66	26	which	which	PRON
ejpam-4598	66	27	are	be	AUX
ejpam-4598	66	28	not	not	PART
ejpam-4598	66	29	tychonoff	tychonoff	NOUN
ejpam-4598	66	30	.	.	PUNCT
ejpam-4598	67	1	now	now	ADV
ejpam-4598	67	2	,	,	PUNCT
ejpam-4598	67	3	i	i	PRON
ejpam-4598	67	4	present	present	VERB
ejpam-4598	67	5	the	the	DET
ejpam-4598	67	6	next	next	ADJ
ejpam-4598	67	7	results	result	NOUN
ejpam-4598	67	8	:	:	PUNCT
ejpam-4598	67	9	theorem	theorem	NOUN
ejpam-4598	67	10	1	1	NUM
ejpam-4598	67	11	.	.	PUNCT
ejpam-4598	68	1	every	every	DET
ejpam-4598	68	2	epi	epi	NOUN
ejpam-4598	68	3	-	-	ADJ
ejpam-4598	68	4	completely	completely	ADV
ejpam-4598	68	5	-	-	PUNCT
ejpam-4598	68	6	regular	regular	ADJ
ejpam-4598	68	7	space	space	NOUN
ejpam-4598	68	8	is	be	AUX
ejpam-4598	68	9	urysohn	urysohn	ADJ
ejpam-4598	68	10	.	.	PUNCT
ejpam-4598	69	1	proof	proof	NOUN
ejpam-4598	69	2	.	.	PUNCT
ejpam-4598	70	1	let	let	AUX
ejpam-4598	70	2	(	(	PUNCT
ejpam-4598	70	3	x	x	X
ejpam-4598	70	4	,	,	PUNCT
ejpam-4598	70	5	t	t	PROPN
ejpam-4598	70	6	)	)	PUNCT
ejpam-4598	70	7	be	be	AUX
ejpam-4598	70	8	an	an	DET
ejpam-4598	70	9	epi	epi	NOUN
ejpam-4598	70	10	-	-	PUNCT
ejpam-4598	70	11	completely	completely	ADV
ejpam-4598	70	12	-	-	PUNCT
ejpam-4598	70	13	regular	regular	ADJ
ejpam-4598	70	14	space	space	NOUN
ejpam-4598	70	15	.	.	PUNCT
ejpam-4598	71	1	then	then	ADV
ejpam-4598	71	2	,	,	PUNCT
ejpam-4598	71	3	there	there	PRON
ejpam-4598	71	4	exists	exist	VERB
ejpam-4598	71	5	a	a	DET
ejpam-4598	71	6	topology	topology	NOUN
ejpam-4598	71	7	t	t	NOUN
ejpam-4598	71	8	′	′	NUM
ejpam-4598	71	9	on	on	ADP
ejpam-4598	71	10	x	x	PUNCT
ejpam-4598	71	11	that	that	PRON
ejpam-4598	71	12	is	be	AUX
ejpam-4598	71	13	coarser	coarse	ADJ
ejpam-4598	71	14	than	than	ADP
ejpam-4598	71	15	t	t	NOUN
ejpam-4598	71	16	such	such	ADJ
ejpam-4598	71	17	that	that	SCONJ
ejpam-4598	71	18	(	(	PUNCT
ejpam-4598	71	19	x	x	X
ejpam-4598	71	20	,	,	PUNCT
ejpam-4598	71	21	t	t	PROPN
ejpam-4598	71	22	′	′	NUM
ejpam-4598	71	23	)	)	PUNCT
ejpam-4598	71	24	is	be	AUX
ejpam-4598	71	25	t1	t1	NOUN
ejpam-4598	71	26	-	-	PUNCT
ejpam-4598	71	27	completely	completely	ADV
ejpam-4598	71	28	-	-	PUNCT
ejpam-4598	71	29	regular	regular	ADJ
ejpam-4598	71	30	.	.	PUNCT
ejpam-4598	72	1	thus	thus	ADV
ejpam-4598	72	2	,	,	PUNCT
ejpam-4598	72	3	(	(	PUNCT
ejpam-4598	72	4	x	x	X
ejpam-4598	72	5	,	,	PUNCT
ejpam-4598	72	6	t	t	PROPN
ejpam-4598	72	7	′	′	NUM
ejpam-4598	72	8	)	)	PUNCT
ejpam-4598	72	9	is	be	AUX
ejpam-4598	72	10	tychonoff	tychonoff	NOUN
ejpam-4598	72	11	.	.	PUNCT
ejpam-4598	73	1	hence	hence	ADV
ejpam-4598	73	2	,	,	PUNCT
ejpam-4598	73	3	(	(	PUNCT
ejpam-4598	73	4	x	x	X
ejpam-4598	73	5	,	,	PUNCT
ejpam-4598	73	6	t	t	PROPN
ejpam-4598	73	7	′	′	NUM
ejpam-4598	73	8	)	)	PUNCT
ejpam-4598	73	9	is	be	AUX
ejpam-4598	73	10	uryshon	uryshon	ADJ
ejpam-4598	73	11	(	(	PUNCT
ejpam-4598	73	12	completely	completely	ADV
ejpam-4598	73	13	hausdorff	hausdorff	NOUN
ejpam-4598	73	14	)	)	PUNCT
ejpam-4598	73	15	.	.	PUNCT
ejpam-4598	74	1	since	since	SCONJ
ejpam-4598	74	2	t	t	PROPN
ejpam-4598	74	3	′	′	NUM
ejpam-4598	74	4	⊆	⊆	NUM
ejpam-4598	74	5	t	t	NOUN
ejpam-4598	74	6	,	,	PUNCT
ejpam-4598	74	7	we	we	PRON
ejpam-4598	74	8	conclude	conclude	VERB
ejpam-4598	74	9	:	:	PUNCT
ejpam-4598	74	10	(	(	PUNCT
ejpam-4598	74	11	x	x	X
ejpam-4598	74	12	,	,	PUNCT
ejpam-4598	74	13	t	t	PROPN
ejpam-4598	74	14	)	)	PUNCT
ejpam-4598	74	15	is	be	AUX
ejpam-4598	74	16	urysohn	urysohn	PROPN
ejpam-4598	74	17	.	.	PUNCT
ejpam-4598	75	1	observe	observe	VERB
ejpam-4598	75	2	that	that	SCONJ
ejpam-4598	75	3	:	:	PUNCT
ejpam-4598	75	4	any	any	DET
ejpam-4598	75	5	urysohn	urysohn	NOUN
ejpam-4598	75	6	space	space	NOUN
ejpam-4598	75	7	is	be	AUX
ejpam-4598	75	8	not	not	PART
ejpam-4598	75	9	necessary	necessary	ADJ
ejpam-4598	75	10	to	to	PART
ejpam-4598	75	11	be	be	AUX
ejpam-4598	75	12	epi	epi	NOUN
ejpam-4598	75	13	-	-	ADJ
ejpam-4598	75	14	completely	completely	ADV
ejpam-4598	75	15	regular	regular	ADJ
ejpam-4598	75	16	.	.	PUNCT
ejpam-4598	76	1	for	for	ADP
ejpam-4598	76	2	example	example	NOUN
ejpam-4598	76	3	,	,	PUNCT
ejpam-4598	76	4	the	the	DET
ejpam-4598	76	5	tychonoff	tychonoff	NOUN
ejpam-4598	76	6	corkscrew	corkscrew	NOUN
ejpam-4598	76	7	topology	topology	NOUN
ejpam-4598	76	8	,	,	PUNCT
ejpam-4598	76	9	example	example	NOUN
ejpam-4598	76	10	9	9	NUM
ejpam-4598	76	11	,	,	PUNCT
ejpam-4598	76	12	and	and	CCONJ
ejpam-4598	76	13	the	the	DET
ejpam-4598	76	14	irregular	irregular	ADJ
ejpam-4598	76	15	lattice	lattice	NOUN
ejpam-4598	76	16	topology	topology	NOUN
ejpam-4598	76	17	,	,	PUNCT
ejpam-4598	76	18	example	example	NOUN
ejpam-4598	76	19	6	6	NUM
ejpam-4598	76	20	,	,	PUNCT
ejpam-4598	76	21	are	be	AUX
ejpam-4598	76	22	urysohn	urysohn	PROPN
ejpam-4598	76	23	spaces	space	NOUN
ejpam-4598	76	24	which	which	PRON
ejpam-4598	76	25	are	be	AUX
ejpam-4598	76	26	not	not	PART
ejpam-4598	76	27	epi	epi	NOUN
ejpam-4598	76	28	-	-	ADJ
ejpam-4598	76	29	completely	completely	ADV
ejpam-4598	76	30	-	-	PUNCT
ejpam-4598	76	31	regular	regular	ADJ
ejpam-4598	76	32	.	.	PUNCT
ejpam-4598	77	1	thus	thus	ADV
ejpam-4598	77	2	,	,	PUNCT
ejpam-4598	77	3	the	the	DET
ejpam-4598	77	4	converse	converse	NOUN
ejpam-4598	77	5	of	of	ADP
ejpam-4598	77	6	theorem	theorem	NOUN
ejpam-4598	77	7	1	1	NUM
ejpam-4598	77	8	is	be	AUX
ejpam-4598	77	9	not	not	PART
ejpam-4598	77	10	true	true	ADJ
ejpam-4598	77	11	in	in	ADP
ejpam-4598	77	12	general	general	ADJ
ejpam-4598	77	13	.	.	PUNCT
ejpam-4598	78	1	theorem	theorem	NOUN
ejpam-4598	78	2	2	2	NUM
ejpam-4598	78	3	.	.	PUNCT
ejpam-4598	79	1	every	every	DET
ejpam-4598	79	2	epi	epi	NOUN
ejpam-4598	79	3	-	-	ADJ
ejpam-4598	79	4	completely	completely	ADV
ejpam-4598	79	5	-	-	PUNCT
ejpam-4598	79	6	regular	regular	ADJ
ejpam-4598	79	7	space	space	NOUN
ejpam-4598	79	8	is	be	AUX
ejpam-4598	79	9	epi	epi	NOUN
ejpam-4598	79	10	-	-	ADJ
ejpam-4598	79	11	regular	regular	ADJ
ejpam-4598	79	12	.	.	PUNCT
ejpam-4598	80	1	proof	proof	NOUN
ejpam-4598	80	2	.	.	PUNCT
ejpam-4598	81	1	let	let	AUX
ejpam-4598	81	2	(	(	PUNCT
ejpam-4598	81	3	x	x	X
ejpam-4598	81	4	,	,	PUNCT
ejpam-4598	81	5	t	t	PROPN
ejpam-4598	81	6	)	)	PUNCT
ejpam-4598	81	7	be	be	AUX
ejpam-4598	81	8	an	an	DET
ejpam-4598	81	9	epi	epi	NOUN
ejpam-4598	81	10	-	-	PUNCT
ejpam-4598	81	11	completely	completely	ADV
ejpam-4598	81	12	-	-	PUNCT
ejpam-4598	81	13	regular	regular	ADJ
ejpam-4598	81	14	space	space	NOUN
ejpam-4598	81	15	.	.	PUNCT
ejpam-4598	82	1	then	then	ADV
ejpam-4598	82	2	,	,	PUNCT
ejpam-4598	82	3	there	there	PRON
ejpam-4598	82	4	exists	exist	VERB
ejpam-4598	82	5	a	a	DET
ejpam-4598	82	6	topology	topology	NOUN
ejpam-4598	82	7	t	t	NOUN
ejpam-4598	82	8	′	′	NUM
ejpam-4598	82	9	on	on	ADP
ejpam-4598	82	10	x	x	SYM
ejpam-4598	82	11	coarser	coarse	ADJ
ejpam-4598	82	12	than	than	ADP
ejpam-4598	82	13	t	t	NOUN
ejpam-4598	82	14	such	such	ADJ
ejpam-4598	82	15	that	that	SCONJ
ejpam-4598	82	16	(	(	PUNCT
ejpam-4598	82	17	x	x	X
ejpam-4598	82	18	,	,	PUNCT
ejpam-4598	82	19	t	t	PROPN
ejpam-4598	82	20	′	′	NUM
ejpam-4598	82	21	)	)	PUNCT
ejpam-4598	82	22	is	be	AUX
ejpam-4598	82	23	t1	t1	NOUN
ejpam-4598	82	24	-	-	PUNCT
ejpam-4598	82	25	completely	completely	ADV
ejpam-4598	82	26	-	-	PUNCT
ejpam-4598	82	27	regular	regular	ADJ
ejpam-4598	82	28	.	.	PUNCT
ejpam-4598	83	1	since	since	SCONJ
ejpam-4598	83	2	every	every	DET
ejpam-4598	83	3	completelyregular	completelyregular	ADJ
ejpam-4598	83	4	space	space	NOUN
ejpam-4598	83	5	is	be	AUX
ejpam-4598	83	6	regular	regular	ADJ
ejpam-4598	83	7	[	[	X
ejpam-4598	83	8	12	12	NUM
ejpam-4598	83	9	]	]	PUNCT
ejpam-4598	83	10	,	,	PUNCT
ejpam-4598	83	11	we	we	PRON
ejpam-4598	83	12	get	get	VERB
ejpam-4598	83	13	:	:	PUNCT
ejpam-4598	83	14	(	(	PUNCT
ejpam-4598	83	15	x	x	X
ejpam-4598	83	16	,	,	PUNCT
ejpam-4598	83	17	t	t	PROPN
ejpam-4598	83	18	′	′	NUM
ejpam-4598	83	19	)	)	PUNCT
ejpam-4598	83	20	is	be	AUX
ejpam-4598	83	21	a	a	DET
ejpam-4598	83	22	t1	t1	NOUN
ejpam-4598	83	23	-	-	PUNCT
ejpam-4598	83	24	regular	regular	ADJ
ejpam-4598	83	25	space	space	NOUN
ejpam-4598	83	26	.	.	PUNCT
ejpam-4598	84	1	hence	hence	ADV
ejpam-4598	84	2	,	,	PUNCT
ejpam-4598	84	3	(	(	PUNCT
ejpam-4598	84	4	x	x	X
ejpam-4598	84	5	,	,	PUNCT
ejpam-4598	84	6	t	t	PROPN
ejpam-4598	84	7	′	′	NUM
ejpam-4598	84	8	)	)	PUNCT
ejpam-4598	84	9	is	be	AUX
ejpam-4598	84	10	t3	t3	NOUN
ejpam-4598	84	11	-	-	PUNCT
ejpam-4598	84	12	space	space	NOUN
ejpam-4598	84	13	.	.	PUNCT
ejpam-4598	85	1	therefore	therefore	ADV
ejpam-4598	85	2	,	,	PUNCT
ejpam-4598	85	3	(	(	PUNCT
ejpam-4598	85	4	x	x	X
ejpam-4598	85	5	,	,	PUNCT
ejpam-4598	85	6	t	t	PROPN
ejpam-4598	85	7	)	)	PUNCT
ejpam-4598	85	8	is	be	AUX
ejpam-4598	85	9	epi	epi	NOUN
ejpam-4598	85	10	-	-	ADJ
ejpam-4598	85	11	regular	regular	ADJ
ejpam-4598	85	12	.	.	PUNCT
ejpam-4598	86	1	note	note	VERB
ejpam-4598	86	2	that	that	SCONJ
ejpam-4598	86	3	:	:	PUNCT
ejpam-4598	86	4	the	the	DET
ejpam-4598	86	5	converse	converse	NOUN
ejpam-4598	86	6	of	of	ADP
ejpam-4598	86	7	theorem	theorem	ADJ
ejpam-4598	86	8	2	2	NUM
ejpam-4598	86	9	is	be	AUX
ejpam-4598	86	10	not	not	PART
ejpam-4598	86	11	necessarily	necessarily	ADV
ejpam-4598	86	12	true	true	ADJ
ejpam-4598	86	13	in	in	ADP
ejpam-4598	86	14	general	general	ADJ
ejpam-4598	86	15	.	.	PUNCT
ejpam-4598	87	1	for	for	ADP
ejpam-4598	87	2	example	example	NOUN
ejpam-4598	87	3	,	,	PUNCT
ejpam-4598	87	4	the	the	DET
ejpam-4598	87	5	tychonoff	tychonoff	NOUN
ejpam-4598	87	6	corkscrew	corkscrew	NOUN
ejpam-4598	87	7	topology	topology	NOUN
ejpam-4598	87	8	,	,	PUNCT
ejpam-4598	87	9	example	example	NOUN
ejpam-4598	87	10	9	9	NUM
ejpam-4598	87	11	,	,	PUNCT
ejpam-4598	87	12	is	be	AUX
ejpam-4598	87	13	an	an	DET
ejpam-4598	87	14	epi	epi	ADJ
ejpam-4598	87	15	-	-	ADJ
ejpam-4598	87	16	regular	regular	ADJ
ejpam-4598	87	17	space	space	NOUN
ejpam-4598	87	18	which	which	PRON
ejpam-4598	87	19	is	be	AUX
ejpam-4598	87	20	not	not	PART
ejpam-4598	87	21	epicompletely	epicompletely	ADV
ejpam-4598	87	22	-	-	PUNCT
ejpam-4598	87	23	regular	regular	ADJ
ejpam-4598	87	24	.	.	PUNCT
ejpam-4598	88	1	also	also	ADV
ejpam-4598	88	2	,	,	PUNCT
ejpam-4598	88	3	complete	complete	ADJ
ejpam-4598	88	4	regularity	regularity	NOUN
ejpam-4598	88	5	and	and	CCONJ
ejpam-4598	88	6	epi	epi	NOUN
ejpam-4598	88	7	-	-	ADJ
ejpam-4598	88	8	complete	complete	ADJ
ejpam-4598	88	9	regularity	regularity	NOUN
ejpam-4598	88	10	are	be	AUX
ejpam-4598	88	11	different	different	ADJ
ejpam-4598	88	12	from	from	ADP
ejpam-4598	88	13	each	each	DET
ejpam-4598	88	14	other	other	ADJ
ejpam-4598	88	15	,	,	PUNCT
ejpam-4598	88	16	for	for	ADP
ejpam-4598	88	17	example	example	NOUN
ejpam-4598	88	18	,	,	PUNCT
ejpam-4598	88	19	the	the	DET
ejpam-4598	88	20	half	half	ADJ
ejpam-4598	88	21	disc	disc	NOUN
ejpam-4598	88	22	topology	topology	NOUN
ejpam-4598	88	23	,	,	PUNCT
ejpam-4598	88	24	example	example	NOUN
ejpam-4598	88	25	5	5	NUM
ejpam-4598	88	26	,	,	PUNCT
ejpam-4598	88	27	is	be	AUX
ejpam-4598	88	28	an	an	DET
ejpam-4598	88	29	epi	epi	ADJ
ejpam-4598	88	30	-	-	ADJ
ejpam-4598	88	31	completelyregular	completelyregular	ADJ
ejpam-4598	88	32	space	space	NOUN
ejpam-4598	88	33	,	,	PUNCT
ejpam-4598	88	34	which	which	PRON
ejpam-4598	88	35	is	be	AUX
ejpam-4598	88	36	not	not	PART
ejpam-4598	88	37	completely	completely	ADV
ejpam-4598	88	38	-	-	PUNCT
ejpam-4598	88	39	regular	regular	ADJ
ejpam-4598	88	40	and	and	CCONJ
ejpam-4598	88	41	any	any	DET
ejpam-4598	88	42	uncountable	uncountable	ADJ
ejpam-4598	88	43	indiscrete	indiscrete	ADJ
ejpam-4598	88	44	space	space	NOUN
ejpam-4598	88	45	is	be	AUX
ejpam-4598	88	46	a	a	DET
ejpam-4598	88	47	completely	completely	ADV
ejpam-4598	88	48	-	-	PUNCT
ejpam-4598	88	49	regular	regular	ADJ
ejpam-4598	88	50	space	space	NOUN
ejpam-4598	88	51	which	which	PRON
ejpam-4598	88	52	is	be	AUX
ejpam-4598	88	53	not	not	PART
ejpam-4598	88	54	epi	epi	NOUN
ejpam-4598	88	55	-	-	ADJ
ejpam-4598	88	56	completely	completely	ADV
ejpam-4598	88	57	-	-	PUNCT
ejpam-4598	88	58	regular	regular	ADJ
ejpam-4598	88	59	.	.	PUNCT
ejpam-4598	89	1	theorem	theorem	NOUN
ejpam-4598	89	2	3	3	NUM
ejpam-4598	89	3	.	.	PUNCT
ejpam-4598	90	1	every	every	DET
ejpam-4598	90	2	epi	epi	NOUN
ejpam-4598	90	3	-	-	PUNCT
ejpam-4598	90	4	almost	almost	ADV
ejpam-4598	90	5	-	-	PUNCT
ejpam-4598	90	6	normal	normal	ADJ
ejpam-4598	90	7	space	space	NOUN
ejpam-4598	90	8	is	be	AUX
ejpam-4598	90	9	epi	epi	NOUN
ejpam-4598	90	10	-	-	ADJ
ejpam-4598	90	11	completely	completely	ADV
ejpam-4598	90	12	-	-	PUNCT
ejpam-4598	90	13	regular	regular	ADJ
ejpam-4598	90	14	.	.	PUNCT
ejpam-4598	91	1	proof	proof	NOUN
ejpam-4598	91	2	.	.	PUNCT
ejpam-4598	92	1	let	let	AUX
ejpam-4598	92	2	(	(	PUNCT
ejpam-4598	92	3	x	x	X
ejpam-4598	92	4	,	,	PUNCT
ejpam-4598	92	5	t	t	PROPN
ejpam-4598	92	6	)	)	PUNCT
ejpam-4598	92	7	be	be	AUX
ejpam-4598	92	8	an	an	DET
ejpam-4598	92	9	epi	epi	NOUN
ejpam-4598	92	10	-	-	PUNCT
ejpam-4598	92	11	almost	almost	ADV
ejpam-4598	92	12	-	-	PUNCT
ejpam-4598	92	13	normal	normal	ADJ
ejpam-4598	92	14	space	space	NOUN
ejpam-4598	92	15	.	.	PUNCT
ejpam-4598	93	1	then	then	ADV
ejpam-4598	93	2	,	,	PUNCT
ejpam-4598	93	3	there	there	PRON
ejpam-4598	93	4	exists	exist	VERB
ejpam-4598	93	5	a	a	DET
ejpam-4598	93	6	topology	topology	NOUN
ejpam-4598	93	7	t	t	NOUN
ejpam-4598	93	8	′	′	NUM
ejpam-4598	93	9	on	on	ADP
ejpam-4598	93	10	x	x	PUNCT
ejpam-4598	93	11	which	which	PRON
ejpam-4598	93	12	is	be	AUX
ejpam-4598	93	13	coarser	coarse	ADJ
ejpam-4598	93	14	than	than	ADP
ejpam-4598	93	15	t	t	NOUN
ejpam-4598	93	16	such	such	ADJ
ejpam-4598	93	17	that	that	SCONJ
ejpam-4598	93	18	(	(	PUNCT
ejpam-4598	93	19	x	x	X
ejpam-4598	93	20	,	,	PUNCT
ejpam-4598	93	21	t	t	PROPN
ejpam-4598	93	22	′	′	NUM
ejpam-4598	93	23	)	)	PUNCT
ejpam-4598	93	24	is	be	AUX
ejpam-4598	93	25	a	a	DET
ejpam-4598	93	26	hausdorff	hausdorff	NOUN
ejpam-4598	93	27	almost	almost	ADV
ejpam-4598	93	28	-	-	PUNCT
ejpam-4598	93	29	normal	normal	ADJ
ejpam-4598	93	30	space	space	NOUN
ejpam-4598	93	31	.	.	PUNCT
ejpam-4598	94	1	since	since	SCONJ
ejpam-4598	94	2	every	every	DET
ejpam-4598	94	3	almost	almost	ADV
ejpam-4598	94	4	-	-	PUNCT
ejpam-4598	94	5	normal	normal	ADJ
ejpam-4598	94	6	t1	t1	NOUN
ejpam-4598	94	7	-	-	PUNCT
ejpam-4598	94	8	space	space	NOUN
ejpam-4598	94	9	is	be	AUX
ejpam-4598	94	10	almost	almost	ADV
ejpam-4598	94	11	-	-	PUNCT
ejpam-4598	94	12	regular	regular	ADJ
ejpam-4598	94	13	[	[	X
ejpam-4598	94	14	27	27	NUM
ejpam-4598	94	15	]	]	PUNCT
ejpam-4598	94	16	,	,	PUNCT
ejpam-4598	94	17	we	we	PRON
ejpam-4598	94	18	have	have	VERB
ejpam-4598	94	19	:	:	PUNCT
ejpam-4598	94	20	(	(	PUNCT
ejpam-4598	94	21	x	x	X
ejpam-4598	94	22	,	,	PUNCT
ejpam-4598	94	23	t	t	PROPN
ejpam-4598	94	24	′	′	NUM
ejpam-4598	94	25	)	)	PUNCT
ejpam-4598	94	26	is	be	AUX
ejpam-4598	94	27	hausdorff	hausdorff	NOUN
ejpam-4598	94	28	almost	almost	ADV
ejpam-4598	94	29	-	-	PUNCT
ejpam-4598	94	30	normal	normal	ADJ
ejpam-4598	94	31	almost	almost	ADV
ejpam-4598	94	32	-	-	PUNCT
ejpam-4598	94	33	regular	regular	ADJ
ejpam-4598	94	34	.	.	PUNCT
ejpam-4598	95	1	since	since	SCONJ
ejpam-4598	95	2	every	every	DET
ejpam-4598	95	3	almost	almost	ADV
ejpam-4598	95	4	-	-	PUNCT
ejpam-4598	95	5	normal	normal	ADJ
ejpam-4598	95	6	almost	almost	ADV
ejpam-4598	95	7	-	-	PUNCT
ejpam-4598	95	8	regular	regular	ADJ
ejpam-4598	95	9	space	space	NOUN
ejpam-4598	95	10	is	be	AUX
ejpam-4598	95	11	almostcompletely	almostcompletely	ADV
ejpam-4598	95	12	regular	regular	ADJ
ejpam-4598	95	13	[	[	X
ejpam-4598	95	14	28	28	NUM
ejpam-4598	95	15	]	]	PUNCT
ejpam-4598	95	16	,	,	PUNCT
ejpam-4598	95	17	we	we	PRON
ejpam-4598	95	18	get	get	VERB
ejpam-4598	95	19	:	:	PUNCT
ejpam-4598	95	20	(	(	PUNCT
ejpam-4598	95	21	x	x	X
ejpam-4598	95	22	,	,	PUNCT
ejpam-4598	95	23	t	t	PROPN
ejpam-4598	95	24	′	′	NUM
ejpam-4598	95	25	)	)	PUNCT
ejpam-4598	95	26	is	be	AUX
ejpam-4598	95	27	hausdorff	hausdorff	NOUN
ejpam-4598	95	28	almost	almost	ADV
ejpam-4598	95	29	-	-	PUNCT
ejpam-4598	95	30	completely	completely	ADV
ejpam-4598	95	31	regular	regular	ADJ
ejpam-4598	95	32	.	.	PUNCT
ejpam-4598	96	1	let	let	VERB
ejpam-4598	96	2	the	the	DET
ejpam-4598	96	3	i.	i.	PROPN
ejpam-4598	96	4	alshammari	alshammari	PROPN
ejpam-4598	96	5	/	/	SYM
ejpam-4598	96	6	eur	eur	PROPN
ejpam-4598	96	7	.	.	PUNCT
ejpam-4598	97	1	j.	j.	PROPN
ejpam-4598	97	2	pure	pure	PROPN
ejpam-4598	97	3	appl	appl	PROPN
ejpam-4598	97	4	.	.	PROPN
ejpam-4598	97	5	math	math	PROPN
ejpam-4598	97	6	,	,	PUNCT
ejpam-4598	97	7	15	15	NUM
ejpam-4598	97	8	(	(	PUNCT
ejpam-4598	97	9	4	4	NUM
ejpam-4598	97	10	)	)	PUNCT
ejpam-4598	97	11	(	(	PUNCT
ejpam-4598	97	12	2022	2022	NUM
ejpam-4598	97	13	)	)	PUNCT
ejpam-4598	97	14	,	,	PUNCT
ejpam-4598	97	15	1808	1808	NUM
ejpam-4598	97	16	-	-	SYM
ejpam-4598	97	17	1821	1821	NUM
ejpam-4598	97	18	1811	1811	NUM
ejpam-4598	97	19	semi	semi	ADJ
ejpam-4598	97	20	regularization	regularization	NOUN
ejpam-4598	97	21	of	of	ADP
ejpam-4598	97	22	(	(	PUNCT
ejpam-4598	97	23	x	x	PROPN
ejpam-4598	97	24	,	,	PUNCT
ejpam-4598	97	25	t	t	PROPN
ejpam-4598	97	26	′	′	NUM
ejpam-4598	97	27	)	)	PUNCT
ejpam-4598	97	28	be	be	AUX
ejpam-4598	97	29	(	(	PUNCT
ejpam-4598	97	30	x	x	NOUN
ejpam-4598	97	31	,	,	PUNCT
ejpam-4598	97	32	t	t	PROPN
ejpam-4598	97	33	′	′	NUM
ejpam-4598	97	34	s	s	PART
ejpam-4598	97	35	)	)	PUNCT
ejpam-4598	97	36	.	.	PUNCT
ejpam-4598	98	1	then	then	ADV
ejpam-4598	98	2	,	,	PUNCT
ejpam-4598	98	3	(	(	PUNCT
ejpam-4598	98	4	x	x	X
ejpam-4598	98	5	,	,	PUNCT
ejpam-4598	98	6	t	t	PROPN
ejpam-4598	98	7	′	′	NOUN
ejpam-4598	98	8	s	s	PART
ejpam-4598	98	9	)	)	PUNCT
ejpam-4598	98	10	is	be	AUX
ejpam-4598	98	11	a	a	DET
ejpam-4598	98	12	hausdorff	hausdorff	NOUN
ejpam-4598	98	13	completely	completely	ADV
ejpam-4598	98	14	-	-	PUNCT
ejpam-4598	98	15	regular	regular	ADJ
ejpam-4598	98	16	space	space	NOUN
ejpam-4598	98	17	because	because	SCONJ
ejpam-4598	98	18	the	the	DET
ejpam-4598	98	19	semi	semi	ADJ
ejpam-4598	98	20	regularization	regularization	NOUN
ejpam-4598	98	21	of	of	ADP
ejpam-4598	98	22	a	a	DET
ejpam-4598	98	23	hausdorff	hausdorff	NOUN
ejpam-4598	98	24	almost	almost	ADV
ejpam-4598	98	25	completely	completely	ADV
ejpam-4598	98	26	regular	regular	ADJ
ejpam-4598	98	27	space	space	NOUN
ejpam-4598	98	28	is	be	AUX
ejpam-4598	98	29	hausdorff	hausdorff	NOUN
ejpam-4598	98	30	completely	completely	ADV
ejpam-4598	98	31	regular	regular	ADJ
ejpam-4598	98	32	[	[	X
ejpam-4598	98	33	22	22	NUM
ejpam-4598	98	34	]	]	PUNCT
ejpam-4598	98	35	.	.	PUNCT
ejpam-4598	99	1	since	since	SCONJ
ejpam-4598	99	2	t	t	PROPN
ejpam-4598	99	3	′	′	NUM
ejpam-4598	99	4	s	s	NOUN
ejpam-4598	99	5	⊆	⊆	NUM
ejpam-4598	99	6	t	t	NOUN
ejpam-4598	99	7	′	′	NUM
ejpam-4598	99	8	⊆	⊆	NUM
ejpam-4598	99	9	t	t	NOUN
ejpam-4598	99	10	,	,	PUNCT
ejpam-4598	99	11	we	we	PRON
ejpam-4598	99	12	conclude	conclude	VERB
ejpam-4598	99	13	:	:	PUNCT
ejpam-4598	99	14	t	t	NOUN
ejpam-4598	99	15	′	′	NOUN
ejpam-4598	99	16	s	s	VERB
ejpam-4598	99	17	is	be	AUX
ejpam-4598	99	18	a	a	DET
ejpam-4598	99	19	topology	topology	NOUN
ejpam-4598	99	20	on	on	ADP
ejpam-4598	99	21	x	x	PUNCT
ejpam-4598	99	22	that	that	PRON
ejpam-4598	99	23	is	be	AUX
ejpam-4598	99	24	coarser	coarse	ADJ
ejpam-4598	99	25	than	than	ADP
ejpam-4598	99	26	t	t	NOUN
ejpam-4598	99	27	such	such	ADJ
ejpam-4598	99	28	that	that	SCONJ
ejpam-4598	99	29	(	(	PUNCT
ejpam-4598	99	30	x	x	X
ejpam-4598	99	31	,	,	PUNCT
ejpam-4598	99	32	t	t	PROPN
ejpam-4598	99	33	′	′	NOUN
ejpam-4598	99	34	s	s	PART
ejpam-4598	99	35	)	)	PUNCT
ejpam-4598	99	36	is	be	AUX
ejpam-4598	99	37	hausdorff	hausdorff	NOUN
ejpam-4598	99	38	completely	completely	ADV
ejpam-4598	99	39	-	-	PUNCT
ejpam-4598	99	40	regular	regular	ADJ
ejpam-4598	99	41	and	and	CCONJ
ejpam-4598	99	42	hence	hence	ADV
ejpam-4598	99	43	tychonoff	tychonoff	NOUN
ejpam-4598	99	44	.	.	PUNCT
ejpam-4598	100	1	therefore	therefore	ADV
ejpam-4598	100	2	,	,	PUNCT
ejpam-4598	100	3	(	(	PUNCT
ejpam-4598	100	4	x	x	X
ejpam-4598	100	5	,	,	PUNCT
ejpam-4598	100	6	t	t	PROPN
ejpam-4598	100	7	)	)	PUNCT
ejpam-4598	100	8	is	be	AUX
ejpam-4598	100	9	epi	epi	NOUN
ejpam-4598	100	10	-	-	ADJ
ejpam-4598	100	11	completely	completely	ADV
ejpam-4598	100	12	-	-	PUNCT
ejpam-4598	100	13	regular	regular	ADJ
ejpam-4598	100	14	.	.	PUNCT
ejpam-4598	101	1	since	since	SCONJ
ejpam-4598	101	2	every	every	DET
ejpam-4598	101	3	epi	epi	NOUN
ejpam-4598	101	4	-	-	ADJ
ejpam-4598	101	5	completely	completely	ADV
ejpam-4598	101	6	-	-	PUNCT
ejpam-4598	101	7	regular	regular	ADJ
ejpam-4598	101	8	space	space	NOUN
ejpam-4598	101	9	is	be	AUX
ejpam-4598	101	10	epi	epi	NOUN
ejpam-4598	101	11	-	-	ADJ
ejpam-4598	101	12	regular	regular	ADJ
ejpam-4598	101	13	(	(	PUNCT
ejpam-4598	101	14	theorem	theorem	NOUN
ejpam-4598	101	15	2	2	NUM
ejpam-4598	101	16	)	)	PUNCT
ejpam-4598	101	17	,	,	PUNCT
ejpam-4598	101	18	every	every	DET
ejpam-4598	101	19	sub	sub	ADJ
ejpam-4598	101	20	-	-	ADJ
ejpam-4598	101	21	metrizable	metrizable	ADJ
ejpam-4598	101	22	space	space	NOUN
ejpam-4598	101	23	is	be	AUX
ejpam-4598	101	24	epi	epi	NOUN
ejpam-4598	101	25	-	-	ADJ
ejpam-4598	101	26	normal	normal	ADJ
ejpam-4598	101	27	and	and	CCONJ
ejpam-4598	101	28	every	every	DET
ejpam-4598	101	29	epi	epi	ADJ
ejpam-4598	101	30	-	-	ADJ
ejpam-4598	101	31	normal	normal	ADJ
ejpam-4598	101	32	space	space	NOUN
ejpam-4598	101	33	is	be	AUX
ejpam-4598	101	34	epi	epi	ADJ
ejpam-4598	101	35	-	-	ADJ
ejpam-4598	101	36	almost	almost	ADV
ejpam-4598	101	37	-	-	PUNCT
ejpam-4598	101	38	normal	normal	ADJ
ejpam-4598	101	39	[	[	X
ejpam-4598	101	40	3	3	NUM
ejpam-4598	101	41	,	,	PUNCT
ejpam-4598	101	42	15	15	NUM
ejpam-4598	101	43	]	]	PUNCT
ejpam-4598	101	44	,	,	PUNCT
ejpam-4598	101	45	we	we	PRON
ejpam-4598	101	46	obtain	obtain	VERB
ejpam-4598	101	47	:	:	PUNCT
ejpam-4598	101	48	corollary	corollary	ADJ
ejpam-4598	101	49	1	1	NUM
ejpam-4598	101	50	.	.	PUNCT
ejpam-4598	102	1	(	(	PUNCT
ejpam-4598	102	2	1	1	X
ejpam-4598	102	3	)	)	PUNCT
ejpam-4598	102	4	every	every	DET
ejpam-4598	102	5	sub	sub	ADJ
ejpam-4598	102	6	-	-	ADJ
ejpam-4598	102	7	metrizable	metrizable	ADJ
ejpam-4598	102	8	space	space	NOUN
ejpam-4598	102	9	is	be	AUX
ejpam-4598	102	10	epi	epi	NOUN
ejpam-4598	102	11	-	-	ADJ
ejpam-4598	102	12	completely	completely	ADV
ejpam-4598	102	13	-	-	PUNCT
ejpam-4598	102	14	regular	regular	ADJ
ejpam-4598	102	15	.	.	PUNCT
ejpam-4598	103	1	(	(	PUNCT
ejpam-4598	103	2	2	2	X
ejpam-4598	103	3	)	)	PUNCT
ejpam-4598	103	4	every	every	DET
ejpam-4598	103	5	epi	epi	ADJ
ejpam-4598	103	6	-	-	ADJ
ejpam-4598	103	7	normal	normal	ADJ
ejpam-4598	103	8	space	space	NOUN
ejpam-4598	103	9	is	be	AUX
ejpam-4598	103	10	epi	epi	NOUN
ejpam-4598	103	11	-	-	ADJ
ejpam-4598	103	12	completely	completely	ADV
ejpam-4598	103	13	-	-	PUNCT
ejpam-4598	103	14	regular	regular	ADJ
ejpam-4598	103	15	.	.	PUNCT
ejpam-4598	104	1	thus	thus	ADV
ejpam-4598	104	2	,	,	PUNCT
ejpam-4598	104	3	we	we	PRON
ejpam-4598	104	4	conclude	conclude	VERB
ejpam-4598	104	5	the	the	DET
ejpam-4598	104	6	following	follow	VERB
ejpam-4598	104	7	implications	implication	NOUN
ejpam-4598	104	8	:	:	PUNCT
ejpam-4598	104	9	epi	epi	NOUN
ejpam-4598	104	10	-	-	ADJ
ejpam-4598	104	11	normal	normal	ADJ
ejpam-4598	104	12	=	=	NOUN
ejpam-4598	104	13	⇒	⇒	NOUN
ejpam-4598	104	14	epi	epi	NOUN
ejpam-4598	104	15	-	-	PUNCT
ejpam-4598	104	16	almost	almost	ADV
ejpam-4598	104	17	-	-	PUNCT
ejpam-4598	104	18	normal	normal	ADJ
ejpam-4598	104	19	=	=	NOUN
ejpam-4598	104	20	⇒	⇒	X
ejpam-4598	104	21	epi	epi	NOUN
ejpam-4598	104	22	-	-	PUNCT
ejpam-4598	104	23	completely	completely	ADV
ejpam-4598	104	24	-	-	PUNCT
ejpam-4598	104	25	regular	regular	ADJ
ejpam-4598	104	26	=	=	NOUN
ejpam-4598	104	27	⇒	⇒	NOUN
ejpam-4598	104	28	epi	epi	NOUN
ejpam-4598	104	29	-	-	NOUN
ejpam-4598	104	30	regular	regular	ADJ
ejpam-4598	104	31	the	the	DET
ejpam-4598	104	32	next	next	ADJ
ejpam-4598	104	33	example	example	NOUN
ejpam-4598	104	34	is	be	AUX
ejpam-4598	104	35	an	an	DET
ejpam-4598	104	36	epi	epi	NOUN
ejpam-4598	104	37	-	-	ADJ
ejpam-4598	104	38	completely	completely	ADV
ejpam-4598	104	39	regular	regular	ADJ
ejpam-4598	104	40	space	space	NOUN
ejpam-4598	104	41	which	which	PRON
ejpam-4598	104	42	is	be	AUX
ejpam-4598	104	43	not	not	PART
ejpam-4598	104	44	epi	epi	NOUN
ejpam-4598	104	45	-	-	ADJ
ejpam-4598	104	46	normal	normal	ADJ
ejpam-4598	104	47	.	.	PUNCT
ejpam-4598	104	48	example	example	NOUN
ejpam-4598	105	1	1	1	NUM
ejpam-4598	105	2	.	.	X
ejpam-4598	105	3	consider	consider	VERB
ejpam-4598	105	4	the	the	DET
ejpam-4598	105	5	example	example	NOUN
ejpam-4598	105	6	10	10	NUM
ejpam-4598	105	7	in	in	ADP
ejpam-4598	105	8	[	[	X
ejpam-4598	105	9	26	26	NUM
ejpam-4598	105	10	]	]	PUNCT
ejpam-4598	105	11	,	,	PUNCT
ejpam-4598	105	12	let	let	VERB
ejpam-4598	105	13	g	g	NOUN
ejpam-4598	105	14	=	=	PUNCT
ejpam-4598	105	15	dω1	dω1	NOUN
ejpam-4598	105	16	,	,	PUNCT
ejpam-4598	105	17	where	where	SCONJ
ejpam-4598	105	18	d	d	NOUN
ejpam-4598	105	19	=	=	SYM
ejpam-4598	105	20	{	{	PUNCT
ejpam-4598	105	21	0	0	NUM
ejpam-4598	105	22	,	,	PUNCT
ejpam-4598	105	23	1	1	NUM
ejpam-4598	105	24	}	}	PUNCT
ejpam-4598	105	25	with	with	ADP
ejpam-4598	105	26	the	the	DET
ejpam-4598	105	27	discrete	discrete	ADJ
ejpam-4598	105	28	topology	topology	NOUN
ejpam-4598	105	29	.	.	PUNCT
ejpam-4598	106	1	let	let	VERB
ejpam-4598	106	2	h	h	PRON
ejpam-4598	106	3	be	be	AUX
ejpam-4598	106	4	a	a	DET
ejpam-4598	106	5	subspace	subspace	NOUN
ejpam-4598	106	6	of	of	ADP
ejpam-4598	106	7	g	g	NOUN
ejpam-4598	106	8	consisting	consist	VERB
ejpam-4598	106	9	of	of	ADP
ejpam-4598	106	10	all	all	DET
ejpam-4598	106	11	points	point	NOUN
ejpam-4598	106	12	of	of	ADP
ejpam-4598	106	13	g	g	NOUN
ejpam-4598	106	14	with	with	ADP
ejpam-4598	106	15	at	at	ADP
ejpam-4598	106	16	most	most	ADV
ejpam-4598	106	17	countably	countably	ADV
ejpam-4598	106	18	many	many	ADJ
ejpam-4598	106	19	non	non	ADJ
ejpam-4598	106	20	zero	zero	NUM
ejpam-4598	106	21	coordinates	coordinate	NOUN
ejpam-4598	106	22	.	.	PUNCT
ejpam-4598	107	1	put	put	VERB
ejpam-4598	107	2	x	x	PUNCT
ejpam-4598	107	3	=	=	PRON
ejpam-4598	107	4	g	g	PROPN
ejpam-4598	107	5	×	×	PROPN
ejpam-4598	107	6	h.	h.	PROPN
ejpam-4598	107	7	raushan	raushan	PROPN
ejpam-4598	107	8	buzyakova	buzyakova	PROPN
ejpam-4598	107	9	proved	prove	VERB
ejpam-4598	107	10	that	that	SCONJ
ejpam-4598	107	11	x	x	PRON
ejpam-4598	107	12	can	can	AUX
ejpam-4598	107	13	not	not	PART
ejpam-4598	107	14	be	be	AUX
ejpam-4598	107	15	mapped	map	VERB
ejpam-4598	107	16	onto	onto	ADP
ejpam-4598	107	17	a	a	DET
ejpam-4598	107	18	normal	normal	ADJ
ejpam-4598	107	19	space	space	NOUN
ejpam-4598	107	20	y	y	NOUN
ejpam-4598	107	21	by	by	ADP
ejpam-4598	107	22	a	a	DET
ejpam-4598	107	23	bijective	bijective	ADJ
ejpam-4598	107	24	continuous	continuous	ADJ
ejpam-4598	107	25	function	function	NOUN
ejpam-4598	108	1	[	[	X
ejpam-4598	108	2	9	9	NUM
ejpam-4598	108	3	]	]	PUNCT
ejpam-4598	108	4	.	.	PUNCT
ejpam-4598	109	1	it	it	PRON
ejpam-4598	109	2	can	can	AUX
ejpam-4598	109	3	be	be	AUX
ejpam-4598	109	4	observed	observe	VERB
ejpam-4598	109	5	that	that	SCONJ
ejpam-4598	109	6	:	:	PUNCT
ejpam-4598	109	7	h	h	NOUN
ejpam-4598	109	8	is	be	AUX
ejpam-4598	109	9	a	a	DET
ejpam-4598	109	10	t2	t2	NOUN
ejpam-4598	109	11	-	-	PUNCT
ejpam-4598	109	12	fréchet	fréchet	NOUN
ejpam-4598	109	13	space	space	NOUN
ejpam-4598	109	14	and	and	CCONJ
ejpam-4598	109	15	hence	hence	ADV
ejpam-4598	109	16	it	it	PRON
ejpam-4598	109	17	is	be	AUX
ejpam-4598	109	18	a	a	DET
ejpam-4598	109	19	k	k	NOUN
ejpam-4598	109	20	-	-	NOUN
ejpam-4598	109	21	space	space	NOUN
ejpam-4598	109	22	.	.	PUNCT
ejpam-4598	110	1	g	g	NOUN
ejpam-4598	110	2	is	be	AUX
ejpam-4598	110	3	also	also	ADV
ejpam-4598	110	4	a	a	DET
ejpam-4598	110	5	t2	t2	NOUN
ejpam-4598	110	6	-	-	PUNCT
ejpam-4598	110	7	compact	compact	ADJ
ejpam-4598	110	8	space	space	NOUN
ejpam-4598	110	9	.	.	PUNCT
ejpam-4598	111	1	hence	hence	ADV
ejpam-4598	111	2	,	,	PUNCT
ejpam-4598	111	3	x	x	PUNCT
ejpam-4598	112	1	=	=	SYM
ejpam-4598	112	2	h	h	NOUN
ejpam-4598	112	3	×	×	NOUN
ejpam-4598	112	4	g	g	PROPN
ejpam-4598	112	5	is	be	AUX
ejpam-4598	112	6	a	a	DET
ejpam-4598	112	7	k	k	NOUN
ejpam-4598	112	8	-	-	NOUN
ejpam-4598	112	9	space	space	NOUN
ejpam-4598	112	10	[	[	X
ejpam-4598	112	11	26	26	NUM
ejpam-4598	112	12	]	]	PUNCT
ejpam-4598	112	13	.	.	PUNCT
ejpam-4598	113	1	since	since	SCONJ
ejpam-4598	113	2	x	x	PRON
ejpam-4598	113	3	is	be	AUX
ejpam-4598	113	4	tychonoff	tychonoff	NOUN
ejpam-4598	113	5	,	,	PUNCT
ejpam-4598	113	6	we	we	PRON
ejpam-4598	113	7	get	get	VERB
ejpam-4598	113	8	x	x	PUNCT
ejpam-4598	113	9	is	be	AUX
ejpam-4598	113	10	epi	epi	NOUN
ejpam-4598	113	11	-	-	ADJ
ejpam-4598	113	12	completely	completely	ADV
ejpam-4598	113	13	regular	regular	ADJ
ejpam-4598	113	14	.	.	PUNCT
ejpam-4598	114	1	the	the	DET
ejpam-4598	114	2	space	space	NOUN
ejpam-4598	114	3	x	x	PUNCT
ejpam-4598	114	4	is	be	AUX
ejpam-4598	114	5	not	not	PART
ejpam-4598	114	6	c	c	NOUN
ejpam-4598	114	7	-	-	ADJ
ejpam-4598	114	8	normal	normal	ADJ
ejpam-4598	114	9	[	[	X
ejpam-4598	114	10	26	26	NUM
ejpam-4598	114	11	]	]	PUNCT
ejpam-4598	114	12	.	.	PUNCT
ejpam-4598	115	1	since	since	SCONJ
ejpam-4598	115	2	every	every	DET
ejpam-4598	115	3	c	c	NOUN
ejpam-4598	115	4	-	-	PUNCT
ejpam-4598	115	5	tychonoff	tychonoff	NOUN
ejpam-4598	115	6	fréchet	fréchet	NOUN
ejpam-4598	115	7	lindelöf	lindelöf	NOUN
ejpam-4598	115	8	space	space	NOUN
ejpam-4598	115	9	is	be	AUX
ejpam-4598	115	10	c	c	NOUN
ejpam-4598	115	11	-	-	ADJ
ejpam-4598	115	12	normal	normal	ADJ
ejpam-4598	115	13	,	,	PUNCT
ejpam-4598	115	14	we	we	PRON
ejpam-4598	115	15	conclude	conclude	VERB
ejpam-4598	115	16	:	:	PUNCT
ejpam-4598	115	17	x	x	X
ejpam-4598	115	18	is	be	AUX
ejpam-4598	115	19	not	not	PART
ejpam-4598	115	20	lindelöf	lindelöf	NOUN
ejpam-4598	115	21	.	.	PUNCT
ejpam-4598	116	1	since	since	SCONJ
ejpam-4598	116	2	x	x	PRON
ejpam-4598	116	3	is	be	AUX
ejpam-4598	116	4	not	not	PART
ejpam-4598	116	5	cnormal	cnormal	ADJ
ejpam-4598	116	6	,	,	PUNCT
ejpam-4598	116	7	we	we	PRON
ejpam-4598	116	8	obtainx	obtainx	VERB
ejpam-4598	116	9	is	be	AUX
ejpam-4598	116	10	neither	neither	DET
ejpam-4598	116	11	cc	cc	NOUN
ejpam-4598	116	12	-	-	ADJ
ejpam-4598	116	13	normal	normal	ADJ
ejpam-4598	116	14	,	,	PUNCT
ejpam-4598	116	15	sub	sub	ADJ
ejpam-4598	116	16	-	-	ADJ
ejpam-4598	116	17	metrizable	metrizable	ADJ
ejpam-4598	116	18	nor	nor	CCONJ
ejpam-4598	116	19	epi	epi	NOUN
ejpam-4598	116	20	-	-	NOUN
ejpam-4598	116	21	normal	normal	ADJ
ejpam-4598	116	22	.	.	PUNCT
ejpam-4598	117	1	the	the	DET
ejpam-4598	117	2	spacex	spacex	NOUN
ejpam-4598	117	3	is	be	AUX
ejpam-4598	117	4	not	not	PART
ejpam-4598	117	5	a	a	DET
ejpam-4598	117	6	locally	locally	ADV
ejpam-4598	117	7	compact	compact	ADJ
ejpam-4598	117	8	space	space	NOUN
ejpam-4598	117	9	as	as	ADV
ejpam-4598	117	10	well	well	ADV
ejpam-4598	117	11	.	.	PUNCT
ejpam-4598	118	1	thus	thus	ADV
ejpam-4598	118	2	,	,	PUNCT
ejpam-4598	118	3	the	the	DET
ejpam-4598	118	4	space	space	NOUN
ejpam-4598	118	5	x	x	PUNCT
ejpam-4598	118	6	is	be	AUX
ejpam-4598	118	7	an	an	DET
ejpam-4598	118	8	epi	epi	NOUN
ejpam-4598	118	9	-	-	ADJ
ejpam-4598	118	10	completely	completely	ADV
ejpam-4598	118	11	regular	regular	ADJ
ejpam-4598	118	12	space	space	NOUN
ejpam-4598	118	13	which	which	PRON
ejpam-4598	118	14	is	be	AUX
ejpam-4598	118	15	neither	neither	CCONJ
ejpam-4598	118	16	c	c	NOUN
ejpam-4598	118	17	-	-	ADJ
ejpam-4598	118	18	normal	normal	ADJ
ejpam-4598	118	19	,	,	PUNCT
ejpam-4598	118	20	cc	cc	NOUN
ejpam-4598	118	21	-	-	ADJ
ejpam-4598	118	22	normal	normal	ADJ
ejpam-4598	118	23	,	,	PUNCT
ejpam-4598	118	24	epi	epi	NOUN
ejpam-4598	118	25	-	-	ADJ
ejpam-4598	118	26	normal	normal	ADJ
ejpam-4598	118	27	,	,	PUNCT
ejpam-4598	118	28	sub	sub	ADJ
ejpam-4598	118	29	-	-	ADJ
ejpam-4598	118	30	metrizable	metrizable	ADJ
ejpam-4598	118	31	nor	nor	CCONJ
ejpam-4598	118	32	locally	locally	ADV
ejpam-4598	118	33	compact	compact	ADJ
ejpam-4598	118	34	.	.	PUNCT
ejpam-4598	119	1	observe	observe	VERB
ejpam-4598	119	2	that	that	SCONJ
ejpam-4598	119	3	:	:	PUNCT
ejpam-4598	119	4	any	any	DET
ejpam-4598	119	5	c	c	NOUN
ejpam-4598	119	6	-	-	PUNCT
ejpam-4598	119	7	tychonoff	tychonoff	NOUN
ejpam-4598	119	8	(	(	PUNCT
ejpam-4598	119	9	resp	resp	NOUN
ejpam-4598	119	10	.	.	PUNCT
ejpam-4598	120	1	c	c	X
ejpam-4598	120	2	-	-	PUNCT
ejpam-4598	120	3	normal	normal	ADJ
ejpam-4598	120	4	)	)	PUNCT
ejpam-4598	120	5	space	space	NOUN
ejpam-4598	120	6	is	be	AUX
ejpam-4598	120	7	not	not	PART
ejpam-4598	120	8	necessary	necessary	ADJ
ejpam-4598	120	9	to	to	PART
ejpam-4598	120	10	be	be	AUX
ejpam-4598	120	11	epicompletely	epicompletely	ADV
ejpam-4598	120	12	regular	regular	ADJ
ejpam-4598	120	13	.	.	PUNCT
ejpam-4598	121	1	here	here	ADV
ejpam-4598	121	2	is	be	AUX
ejpam-4598	121	3	a	a	DET
ejpam-4598	121	4	counterexample	counterexample	NOUN
ejpam-4598	121	5	:	:	PUNCT
ejpam-4598	121	6	example	example	NOUN
ejpam-4598	121	7	2	2	NUM
ejpam-4598	121	8	.	.	PUNCT
ejpam-4598	122	1	the	the	DET
ejpam-4598	122	2	countable	countable	ADJ
ejpam-4598	122	3	complement	complement	NOUN
ejpam-4598	122	4	topology	topology	NOUN
ejpam-4598	122	5	(	(	PUNCT
ejpam-4598	122	6	r	r	NOUN
ejpam-4598	122	7	,	,	PUNCT
ejpam-4598	122	8	cc	cc	NOUN
ejpam-4598	122	9	)	)	PUNCT
ejpam-4598	122	10	is	be	AUX
ejpam-4598	122	11	both	both	PRON
ejpam-4598	122	12	c	c	NOUN
ejpam-4598	122	13	-	-	PUNCT
ejpam-4598	122	14	tychonoff	tychonoff	NOUN
ejpam-4598	122	15	and	and	CCONJ
ejpam-4598	122	16	cregular	cregular	ADJ
ejpam-4598	122	17	space	space	NOUN
ejpam-4598	122	18	[	[	X
ejpam-4598	122	19	6	6	NUM
ejpam-4598	122	20	,	,	PUNCT
ejpam-4598	122	21	7	7	NUM
ejpam-4598	122	22	]	]	PUNCT
ejpam-4598	122	23	,	,	PUNCT
ejpam-4598	122	24	which	which	PRON
ejpam-4598	122	25	is	be	AUX
ejpam-4598	122	26	neither	neither	DET
ejpam-4598	122	27	epi	epi	NOUN
ejpam-4598	122	28	-	-	ADJ
ejpam-4598	122	29	completely	completely	ADV
ejpam-4598	122	30	-	-	PUNCT
ejpam-4598	122	31	regular	regular	ADJ
ejpam-4598	122	32	,	,	PUNCT
ejpam-4598	122	33	epi	epi	NOUN
ejpam-4598	122	34	-	-	NOUN
ejpam-4598	122	35	regular	regular	ADJ
ejpam-4598	122	36	nor	nor	CCONJ
ejpam-4598	122	37	epi	epi	NOUN
ejpam-4598	122	38	-	-	ADJ
ejpam-4598	122	39	mildly	mildly	ADV
ejpam-4598	122	40	normal	normal	ADJ
ejpam-4598	122	41	because	because	SCONJ
ejpam-4598	122	42	it	it	PRON
ejpam-4598	122	43	is	be	AUX
ejpam-4598	122	44	not	not	PART
ejpam-4598	122	45	hausdorff	hausdorff	NOUN
ejpam-4598	122	46	.	.	PUNCT
ejpam-4598	123	1	the	the	DET
ejpam-4598	123	2	following	following	ADJ
ejpam-4598	123	3	example	example	NOUN
ejpam-4598	123	4	is	be	AUX
ejpam-4598	123	5	a	a	DET
ejpam-4598	123	6	normal	normal	ADJ
ejpam-4598	123	7	space	space	NOUN
ejpam-4598	123	8	,	,	PUNCT
ejpam-4598	123	9	which	which	PRON
ejpam-4598	123	10	is	be	AUX
ejpam-4598	123	11	not	not	PART
ejpam-4598	123	12	epi	epi	NOUN
ejpam-4598	123	13	-	-	ADJ
ejpam-4598	123	14	completely	completely	ADV
ejpam-4598	123	15	regular	regular	ADJ
ejpam-4598	123	16	.	.	PUNCT
ejpam-4598	124	1	example	example	NOUN
ejpam-4598	125	1	3	3	NUM
ejpam-4598	125	2	.	.	PUNCT
ejpam-4598	126	1	the	the	DET
ejpam-4598	126	2	left	left	ADJ
ejpam-4598	126	3	ray	ray	NOUN
ejpam-4598	126	4	topology	topology	NOUN
ejpam-4598	126	5	(	(	PUNCT
ejpam-4598	126	6	r	r	NOUN
ejpam-4598	126	7	,	,	PUNCT
ejpam-4598	126	8	l	l	NOUN
ejpam-4598	126	9	)	)	PUNCT
ejpam-4598	126	10	,	,	PUNCT
ejpam-4598	126	11	the	the	DET
ejpam-4598	126	12	right	right	ADJ
ejpam-4598	126	13	ray	ray	NOUN
ejpam-4598	126	14	topology	topology	NOUN
ejpam-4598	126	15	(	(	PUNCT
ejpam-4598	126	16	r	r	NOUN
ejpam-4598	126	17	,	,	PUNCT
ejpam-4598	126	18	r	r	NOUN
ejpam-4598	126	19	)	)	PUNCT
ejpam-4598	127	1	[	[	X
ejpam-4598	127	2	30	30	NUM
ejpam-4598	127	3	]	]	PUNCT
ejpam-4598	127	4	are	be	AUX
ejpam-4598	127	5	normal	normal	ADJ
ejpam-4598	127	6	spaces	space	NOUN
ejpam-4598	127	7	,	,	PUNCT
ejpam-4598	127	8	which	which	PRON
ejpam-4598	127	9	are	be	AUX
ejpam-4598	127	10	not	not	PART
ejpam-4598	127	11	epi	epi	NOUN
ejpam-4598	127	12	-	-	ADJ
ejpam-4598	127	13	completely	completely	ADV
ejpam-4598	127	14	regular	regular	ADJ
ejpam-4598	127	15	because	because	SCONJ
ejpam-4598	127	16	they	they	PRON
ejpam-4598	127	17	are	be	AUX
ejpam-4598	127	18	not	not	PART
ejpam-4598	127	19	hausdorff	hausdorff	ADJ
ejpam-4598	127	20	.	.	PUNCT
ejpam-4598	128	1	note	note	VERB
ejpam-4598	128	2	that	that	SCONJ
ejpam-4598	128	3	:	:	PUNCT
ejpam-4598	128	4	complete	complete	ADJ
ejpam-4598	128	5	regularity	regularity	NOUN
ejpam-4598	128	6	(	(	PUNCT
ejpam-4598	128	7	resp	resp	NOUN
ejpam-4598	128	8	.	.	PUNCT
ejpam-4598	129	1	l	l	NOUN
ejpam-4598	129	2	-	-	NOUN
ejpam-4598	129	3	regularity	regularity	NOUN
ejpam-4598	129	4	)	)	PUNCT
ejpam-4598	129	5	does	do	AUX
ejpam-4598	129	6	not	not	PART
ejpam-4598	129	7	imply	imply	VERB
ejpam-4598	129	8	to	to	ADP
ejpam-4598	129	9	epi	epi	NOUN
ejpam-4598	129	10	-	-	NOUN
ejpam-4598	129	11	completeregularity	completeregularity	NOUN
ejpam-4598	129	12	in	in	ADP
ejpam-4598	129	13	general	general	ADJ
ejpam-4598	129	14	as	as	SCONJ
ejpam-4598	129	15	shown	show	VERB
ejpam-4598	129	16	by	by	ADP
ejpam-4598	129	17	the	the	DET
ejpam-4598	129	18	next	next	ADJ
ejpam-4598	129	19	example	example	NOUN
ejpam-4598	129	20	.	.	PUNCT
ejpam-4598	130	1	i.	i.	PROPN
ejpam-4598	130	2	alshammari	alshammari	PROPN
ejpam-4598	130	3	/	/	SYM
ejpam-4598	130	4	eur	eur	PROPN
ejpam-4598	130	5	.	.	PUNCT
ejpam-4598	131	1	j.	j.	PROPN
ejpam-4598	131	2	pure	pure	PROPN
ejpam-4598	131	3	appl	appl	PROPN
ejpam-4598	131	4	.	.	PROPN
ejpam-4598	131	5	math	math	PROPN
ejpam-4598	131	6	,	,	PUNCT
ejpam-4598	131	7	15	15	NUM
ejpam-4598	131	8	(	(	PUNCT
ejpam-4598	131	9	4	4	NUM
ejpam-4598	131	10	)	)	PUNCT
ejpam-4598	131	11	(	(	PUNCT
ejpam-4598	131	12	2022	2022	NUM
ejpam-4598	131	13	)	)	PUNCT
ejpam-4598	131	14	,	,	PUNCT
ejpam-4598	131	15	1808	1808	NUM
ejpam-4598	131	16	-	-	SYM
ejpam-4598	131	17	1821	1821	NUM
ejpam-4598	131	18	1812	1812	NUM
ejpam-4598	131	19	example	example	NOUN
ejpam-4598	131	20	4	4	NUM
ejpam-4598	131	21	.	.	PUNCT
ejpam-4598	132	1	the	the	DET
ejpam-4598	132	2	double	double	ADJ
ejpam-4598	132	3	pointed	point	VERB
ejpam-4598	132	4	reals	real	NOUN
ejpam-4598	132	5	topology	topology	NOUN
ejpam-4598	132	6	[	[	X
ejpam-4598	132	7	30	30	NUM
ejpam-4598	132	8	,	,	PUNCT
ejpam-4598	132	9	example	example	NOUN
ejpam-4598	132	10	62	62	NUM
ejpam-4598	132	11	]	]	PUNCT
ejpam-4598	132	12	,	,	PUNCT
ejpam-4598	132	13	is	be	AUX
ejpam-4598	132	14	both	both	CCONJ
ejpam-4598	132	15	a	a	DET
ejpam-4598	132	16	regular	regular	ADJ
ejpam-4598	132	17	and	and	CCONJ
ejpam-4598	132	18	completely	completely	ADV
ejpam-4598	132	19	regular	regular	ADJ
ejpam-4598	132	20	space	space	NOUN
ejpam-4598	132	21	[	[	X
ejpam-4598	132	22	30	30	NUM
ejpam-4598	132	23	]	]	PUNCT
ejpam-4598	132	24	,	,	PUNCT
ejpam-4598	132	25	which	which	PRON
ejpam-4598	132	26	is	be	AUX
ejpam-4598	132	27	not	not	PART
ejpam-4598	132	28	epi	epi	NOUN
ejpam-4598	132	29	-	-	ADJ
ejpam-4598	132	30	completely	completely	ADV
ejpam-4598	132	31	regular	regular	ADJ
ejpam-4598	132	32	because	because	SCONJ
ejpam-4598	132	33	it	it	PRON
ejpam-4598	132	34	is	be	AUX
ejpam-4598	132	35	not	not	PART
ejpam-4598	132	36	hausdorff	hausdorff	NOUN
ejpam-4598	132	37	.	.	PUNCT
ejpam-4598	133	1	the	the	DET
ejpam-4598	133	2	next	next	ADJ
ejpam-4598	133	3	example	example	NOUN
ejpam-4598	133	4	is	be	AUX
ejpam-4598	133	5	an	an	DET
ejpam-4598	133	6	epi	epi	NOUN
ejpam-4598	133	7	-	-	PUNCT
ejpam-4598	133	8	completely	completely	ADV
ejpam-4598	133	9	-	-	PUNCT
ejpam-4598	133	10	regular	regular	ADJ
ejpam-4598	133	11	space	space	NOUN
ejpam-4598	133	12	which	which	PRON
ejpam-4598	133	13	is	be	AUX
ejpam-4598	133	14	neither	neither	CCONJ
ejpam-4598	133	15	tychonoff	tychonoff	NOUN
ejpam-4598	133	16	nor	nor	CCONJ
ejpam-4598	133	17	completely	completely	ADV
ejpam-4598	133	18	-	-	PUNCT
ejpam-4598	133	19	regular	regular	ADJ
ejpam-4598	133	20	.	.	PUNCT
ejpam-4598	133	21	example	example	NOUN
ejpam-4598	134	1	5	5	NUM
ejpam-4598	134	2	.	.	PUNCT
ejpam-4598	134	3	the	the	DET
ejpam-4598	134	4	half	half	ADJ
ejpam-4598	134	5	disc	disc	NOUN
ejpam-4598	134	6	topology	topology	NOUN
ejpam-4598	134	7	[	[	X
ejpam-4598	134	8	30	30	NUM
ejpam-4598	134	9	,	,	PUNCT
ejpam-4598	134	10	example	example	NOUN
ejpam-4598	134	11	78	78	NUM
ejpam-4598	134	12	]	]	PUNCT
ejpam-4598	134	13	is	be	AUX
ejpam-4598	134	14	not	not	PART
ejpam-4598	134	15	tychonoff	tychonoff	NOUN
ejpam-4598	134	16	.	.	PUNCT
ejpam-4598	135	1	the	the	DET
ejpam-4598	135	2	semi	semi	ADJ
ejpam-4598	135	3	regularization	regularization	NOUN
ejpam-4598	135	4	of	of	ADP
ejpam-4598	135	5	x	x	SYM
ejpam-4598	135	6	is	be	AUX
ejpam-4598	135	7	the	the	DET
ejpam-4598	135	8	closed	close	VERB
ejpam-4598	135	9	upper	upper	ADJ
ejpam-4598	135	10	half	half	ADJ
ejpam-4598	135	11	plane	plane	NOUN
ejpam-4598	135	12	with	with	ADP
ejpam-4598	135	13	the	the	DET
ejpam-4598	135	14	euclidean	euclidean	ADJ
ejpam-4598	135	15	topology	topology	NOUN
ejpam-4598	135	16	u	u	NOUN
ejpam-4598	135	17	on	on	ADP
ejpam-4598	135	18	r	r	NOUN
ejpam-4598	135	19	that	that	PRON
ejpam-4598	135	20	is	be	AUX
ejpam-4598	135	21	a	a	DET
ejpam-4598	135	22	topology	topology	NOUN
ejpam-4598	135	23	coarser	coarse	ADJ
ejpam-4598	135	24	than	than	ADP
ejpam-4598	135	25	t	t	PROPN
ejpam-4598	135	26	and	and	CCONJ
ejpam-4598	135	27	(	(	PUNCT
ejpam-4598	135	28	x	x	NOUN
ejpam-4598	135	29	,	,	PUNCT
ejpam-4598	135	30	u	u	NOUN
ejpam-4598	135	31	)	)	PUNCT
ejpam-4598	135	32	is	be	AUX
ejpam-4598	135	33	a	a	DET
ejpam-4598	135	34	t4	t4	PROPN
ejpam-4598	135	35	-	-	PUNCT
ejpam-4598	135	36	space	space	NOUN
ejpam-4598	135	37	.	.	PUNCT
ejpam-4598	136	1	thus	thus	ADV
ejpam-4598	136	2	,	,	PUNCT
ejpam-4598	136	3	x	x	X
ejpam-4598	136	4	is	be	AUX
ejpam-4598	136	5	epi	epi	NOUN
ejpam-4598	136	6	-	-	ADJ
ejpam-4598	136	7	normal	normal	ADJ
ejpam-4598	136	8	.	.	PUNCT
ejpam-4598	137	1	hence	hence	ADV
ejpam-4598	137	2	,	,	PUNCT
ejpam-4598	137	3	x	x	X
ejpam-4598	137	4	is	be	AUX
ejpam-4598	137	5	epi	epi	VERB
ejpam-4598	137	6	-	-	ADJ
ejpam-4598	137	7	completely	completely	ADV
ejpam-4598	137	8	-	-	PUNCT
ejpam-4598	137	9	regular	regular	ADJ
ejpam-4598	137	10	.	.	PUNCT
ejpam-4598	138	1	since	since	SCONJ
ejpam-4598	138	2	(	(	PUNCT
ejpam-4598	138	3	x	x	X
ejpam-4598	138	4	,	,	PUNCT
ejpam-4598	138	5	t	t	PROPN
ejpam-4598	138	6	)	)	PUNCT
ejpam-4598	138	7	is	be	AUX
ejpam-4598	138	8	an	an	DET
ejpam-4598	138	9	almost	almost	ADV
ejpam-4598	138	10	-	-	PUNCT
ejpam-4598	138	11	completely	completely	ADV
ejpam-4598	138	12	regular	regular	ADJ
ejpam-4598	138	13	space	space	NOUN
ejpam-4598	138	14	if	if	SCONJ
ejpam-4598	138	15	and	and	CCONJ
ejpam-4598	138	16	only	only	ADV
ejpam-4598	138	17	if	if	SCONJ
ejpam-4598	138	18	(	(	PUNCT
ejpam-4598	138	19	x	x	NOUN
ejpam-4598	138	20	,	,	PUNCT
ejpam-4598	138	21	ts	ts	NOUN
ejpam-4598	138	22	)	)	PUNCT
ejpam-4598	138	23	is	be	AUX
ejpam-4598	138	24	completely	completely	ADV
ejpam-4598	138	25	-	-	PUNCT
ejpam-4598	138	26	regular	regular	ADJ
ejpam-4598	138	27	[	[	X
ejpam-4598	138	28	22	22	NUM
ejpam-4598	138	29	]	]	PUNCT
ejpam-4598	138	30	,	,	PUNCT
ejpam-4598	138	31	we	we	PRON
ejpam-4598	138	32	get	get	VERB
ejpam-4598	138	33	:	:	PUNCT
ejpam-4598	138	34	the	the	DET
ejpam-4598	138	35	half	half	ADJ
ejpam-4598	138	36	disc	disc	NOUN
ejpam-4598	138	37	topology	topology	NOUN
ejpam-4598	138	38	is	be	AUX
ejpam-4598	138	39	almost	almost	ADV
ejpam-4598	138	40	-	-	PUNCT
ejpam-4598	138	41	completely	completely	ADV
ejpam-4598	138	42	regular	regular	ADJ
ejpam-4598	138	43	.	.	PUNCT
ejpam-4598	139	1	therefore	therefore	ADV
ejpam-4598	139	2	,	,	PUNCT
ejpam-4598	139	3	the	the	DET
ejpam-4598	139	4	half	half	ADJ
ejpam-4598	139	5	disc	disc	NOUN
ejpam-4598	139	6	topology	topology	NOUN
ejpam-4598	139	7	is	be	AUX
ejpam-4598	139	8	an	an	DET
ejpam-4598	139	9	epi	epi	NOUN
ejpam-4598	139	10	-	-	PUNCT
ejpam-4598	139	11	completely	completely	ADV
ejpam-4598	139	12	-	-	PUNCT
ejpam-4598	139	13	regular	regular	ADJ
ejpam-4598	139	14	space	space	NOUN
ejpam-4598	139	15	,	,	PUNCT
ejpam-4598	139	16	which	which	PRON
ejpam-4598	139	17	is	be	AUX
ejpam-4598	139	18	neither	neither	CCONJ
ejpam-4598	139	19	completely	completely	ADV
ejpam-4598	139	20	-	-	PUNCT
ejpam-4598	139	21	regular	regular	ADJ
ejpam-4598	139	22	,	,	PUNCT
ejpam-4598	139	23	tychonoff	tychonoff	NOUN
ejpam-4598	139	24	nor	nor	CCONJ
ejpam-4598	139	25	almost	almost	ADV
ejpam-4598	139	26	-	-	PUNCT
ejpam-4598	139	27	normal	normal	ADJ
ejpam-4598	139	28	.	.	PUNCT
ejpam-4598	140	1	a	a	DET
ejpam-4598	140	2	urysohn	urysohn	PROPN
ejpam-4598	140	3	epi	epi	NOUN
ejpam-4598	140	4	-	-	ADJ
ejpam-4598	140	5	mildly	mildly	ADV
ejpam-4598	140	6	normal	normal	ADJ
ejpam-4598	140	7	lindelöf	lindelöf	NOUN
ejpam-4598	140	8	space	space	NOUN
ejpam-4598	140	9	is	be	AUX
ejpam-4598	140	10	not	not	PART
ejpam-4598	140	11	necessary	necessary	ADJ
ejpam-4598	140	12	to	to	PART
ejpam-4598	140	13	be	be	AUX
ejpam-4598	140	14	epi	epi	NOUN
ejpam-4598	140	15	-	-	NOUN
ejpam-4598	140	16	completelyregular	completelyregular	ADJ
ejpam-4598	140	17	,	,	PUNCT
ejpam-4598	140	18	for	for	ADP
ejpam-4598	140	19	example	example	NOUN
ejpam-4598	140	20	:	:	PUNCT
ejpam-4598	140	21	example	example	NOUN
ejpam-4598	141	1	6	6	NUM
ejpam-4598	141	2	.	.	PUNCT
ejpam-4598	142	1	the	the	DET
ejpam-4598	142	2	irregular	irregular	ADJ
ejpam-4598	142	3	lattice	lattice	NOUN
ejpam-4598	142	4	topology	topology	NOUN
ejpam-4598	142	5	[	[	X
ejpam-4598	142	6	30	30	NUM
ejpam-4598	142	7	,	,	PUNCT
ejpam-4598	142	8	example	example	NOUN
ejpam-4598	142	9	79	79	NUM
ejpam-4598	142	10	]	]	PUNCT
ejpam-4598	142	11	,	,	PUNCT
ejpam-4598	142	12	is	be	AUX
ejpam-4598	142	13	a	a	DET
ejpam-4598	142	14	urysohn	urysohn	PROPN
ejpam-4598	142	15	lindelöf	lindelöf	NOUN
ejpam-4598	142	16	space	space	NOUN
ejpam-4598	142	17	,	,	PUNCT
ejpam-4598	142	18	which	which	PRON
ejpam-4598	142	19	is	be	AUX
ejpam-4598	142	20	neither	neither	CCONJ
ejpam-4598	142	21	normal	normal	ADJ
ejpam-4598	142	22	,	,	PUNCT
ejpam-4598	142	23	completely	completely	ADV
ejpam-4598	142	24	regular	regular	ADJ
ejpam-4598	142	25	nor	nor	CCONJ
ejpam-4598	142	26	semi	semi	ADJ
ejpam-4598	142	27	-	-	ADJ
ejpam-4598	142	28	regular	regular	ADJ
ejpam-4598	142	29	[	[	X
ejpam-4598	142	30	30	30	NUM
ejpam-4598	142	31	]	]	PUNCT
ejpam-4598	142	32	.	.	PUNCT
ejpam-4598	143	1	it	it	PRON
ejpam-4598	143	2	is	be	AUX
ejpam-4598	143	3	also	also	ADV
ejpam-4598	143	4	a	a	DET
ejpam-4598	143	5	mildly	mildly	ADV
ejpam-4598	143	6	-	-	PUNCT
ejpam-4598	143	7	normal	normal	ADJ
ejpam-4598	143	8	space	space	NOUN
ejpam-4598	143	9	,	,	PUNCT
ejpam-4598	143	10	which	which	PRON
ejpam-4598	143	11	is	be	AUX
ejpam-4598	143	12	not	not	PART
ejpam-4598	143	13	partially	partially	ADV
ejpam-4598	143	14	-	-	PUNCT
ejpam-4598	143	15	normal	normal	ADJ
ejpam-4598	143	16	[	[	X
ejpam-4598	143	17	4	4	NUM
ejpam-4598	143	18	]	]	PUNCT
ejpam-4598	143	19	.	.	PUNCT
ejpam-4598	144	1	hence	hence	ADV
ejpam-4598	144	2	,	,	PUNCT
ejpam-4598	144	3	it	it	PRON
ejpam-4598	144	4	is	be	AUX
ejpam-4598	144	5	neither	neither	CCONJ
ejpam-4598	144	6	quasi	quasi	ADJ
ejpam-4598	144	7	-	-	ADJ
ejpam-4598	144	8	normal	normal	ADJ
ejpam-4598	144	9	,	,	PUNCT
ejpam-4598	144	10	almost	almost	ADV
ejpam-4598	144	11	-	-	PUNCT
ejpam-4598	144	12	normal	normal	ADJ
ejpam-4598	144	13	nor	nor	CCONJ
ejpam-4598	144	14	semi	semi	ADJ
ejpam-4598	144	15	-	-	ADJ
ejpam-4598	144	16	normal	normal	ADJ
ejpam-4598	144	17	.	.	PUNCT
ejpam-4598	145	1	since	since	SCONJ
ejpam-4598	145	2	every	every	DET
ejpam-4598	145	3	almost	almost	ADV
ejpam-4598	145	4	-	-	PUNCT
ejpam-4598	145	5	regular	regular	ADJ
ejpam-4598	145	6	lindelöf	lindelöf	NOUN
ejpam-4598	145	7	space	space	NOUN
ejpam-4598	145	8	is	be	AUX
ejpam-4598	145	9	quasi	quasi	ADJ
ejpam-4598	145	10	-	-	ADJ
ejpam-4598	145	11	normal	normal	ADJ
ejpam-4598	145	12	[	[	X
ejpam-4598	145	13	21	21	NUM
ejpam-4598	145	14	]	]	PUNCT
ejpam-4598	145	15	,	,	PUNCT
ejpam-4598	145	16	and	and	CCONJ
ejpam-4598	145	17	x	x	X
ejpam-4598	145	18	is	be	AUX
ejpam-4598	145	19	a	a	DET
ejpam-4598	145	20	lindelöf	lindelöf	NOUN
ejpam-4598	145	21	non	non	X
ejpam-4598	145	22	quasi	quasi	ADJ
ejpam-4598	145	23	-	-	ADJ
ejpam-4598	145	24	normal	normal	ADJ
ejpam-4598	145	25	space	space	NOUN
ejpam-4598	145	26	,	,	PUNCT
ejpam-4598	145	27	it	it	PRON
ejpam-4598	145	28	is	be	AUX
ejpam-4598	145	29	not	not	PART
ejpam-4598	145	30	almost	almost	ADV
ejpam-4598	145	31	-	-	PUNCT
ejpam-4598	145	32	regular	regular	ADJ
ejpam-4598	145	33	.	.	PUNCT
ejpam-4598	146	1	since	since	SCONJ
ejpam-4598	146	2	(	(	PUNCT
ejpam-4598	146	3	x	x	X
ejpam-4598	146	4	,	,	PUNCT
ejpam-4598	146	5	t	t	PROPN
ejpam-4598	146	6	)	)	PUNCT
ejpam-4598	146	7	is	be	AUX
ejpam-4598	146	8	a	a	DET
ejpam-4598	146	9	hausdorff	hausdorff	NOUN
ejpam-4598	146	10	mildly	mildly	ADV
ejpam-4598	146	11	-	-	PUNCT
ejpam-4598	146	12	normal	normal	ADJ
ejpam-4598	146	13	space	space	NOUN
ejpam-4598	146	14	,	,	PUNCT
ejpam-4598	146	15	it	it	PRON
ejpam-4598	146	16	is	be	AUX
ejpam-4598	146	17	epi	epi	NOUN
ejpam-4598	146	18	-	-	ADJ
ejpam-4598	146	19	mildly	mildly	ADV
ejpam-4598	146	20	normal	normal	ADJ
ejpam-4598	146	21	.	.	PUNCT
ejpam-4598	147	1	hence	hence	ADV
ejpam-4598	147	2	,	,	PUNCT
ejpam-4598	147	3	the	the	DET
ejpam-4598	147	4	irregular	irregular	ADJ
ejpam-4598	147	5	lattice	lattice	NOUN
ejpam-4598	147	6	topology	topology	NOUN
ejpam-4598	147	7	is	be	AUX
ejpam-4598	147	8	a	a	DET
ejpam-4598	147	9	urysohn	urysohn	PROPN
ejpam-4598	147	10	epi	epi	NOUN
ejpam-4598	147	11	-	-	PUNCT
ejpam-4598	147	12	mildly	mildly	ADV
ejpam-4598	147	13	-	-	PUNCT
ejpam-4598	147	14	normal	normal	ADJ
ejpam-4598	147	15	space	space	NOUN
ejpam-4598	147	16	,	,	PUNCT
ejpam-4598	147	17	which	which	PRON
ejpam-4598	147	18	is	be	AUX
ejpam-4598	147	19	neither	neither	DET
ejpam-4598	147	20	epi	epi	NOUN
ejpam-4598	147	21	-	-	ADJ
ejpam-4598	147	22	almost	almost	ADV
ejpam-4598	147	23	-	-	PUNCT
ejpam-4598	147	24	normal	normal	ADJ
ejpam-4598	147	25	,	,	PUNCT
ejpam-4598	147	26	epi	epi	NOUN
ejpam-4598	147	27	-	-	NOUN
ejpam-4598	147	28	regular	regular	ADJ
ejpam-4598	147	29	nor	nor	CCONJ
ejpam-4598	147	30	epicompletely	epicompletely	ADV
ejpam-4598	147	31	-	-	PUNCT
ejpam-4598	147	32	regular	regular	ADJ
ejpam-4598	147	33	.	.	PUNCT
ejpam-4598	148	1	an	an	DET
ejpam-4598	148	2	almost	almost	ADV
ejpam-4598	148	3	-	-	PUNCT
ejpam-4598	148	4	completely	completely	ADV
ejpam-4598	148	5	regular	regular	ADJ
ejpam-4598	148	6	space	space	NOUN
ejpam-4598	148	7	is	be	AUX
ejpam-4598	148	8	not	not	PART
ejpam-4598	148	9	necessarily	necessarily	ADV
ejpam-4598	148	10	epi	epi	NOUN
ejpam-4598	148	11	-	-	ADJ
ejpam-4598	148	12	completely	completely	ADV
ejpam-4598	148	13	-	-	PUNCT
ejpam-4598	148	14	regular	regular	ADJ
ejpam-4598	148	15	.	.	PUNCT
ejpam-4598	149	1	for	for	ADP
ejpam-4598	149	2	example	example	NOUN
ejpam-4598	149	3	:	:	PUNCT
ejpam-4598	149	4	example	example	NOUN
ejpam-4598	149	5	7	7	NUM
ejpam-4598	149	6	.	.	PUNCT
ejpam-4598	150	1	the	the	DET
ejpam-4598	150	2	telophase	telophase	NOUN
ejpam-4598	150	3	topology	topology	NOUN
ejpam-4598	150	4	[	[	X
ejpam-4598	150	5	30	30	NUM
ejpam-4598	150	6	,	,	PUNCT
ejpam-4598	150	7	example	example	NOUN
ejpam-4598	150	8	73	73	NUM
ejpam-4598	150	9	]	]	PUNCT
ejpam-4598	150	10	,	,	PUNCT
ejpam-4598	150	11	is	be	AUX
ejpam-4598	150	12	a	a	DET
ejpam-4598	150	13	t1	t1	NOUN
ejpam-4598	150	14	-	-	ADJ
ejpam-4598	150	15	compact	compact	ADJ
ejpam-4598	150	16	,	,	PUNCT
ejpam-4598	150	17	paracompact	paracompact	ADJ
ejpam-4598	150	18	space	space	NOUN
ejpam-4598	150	19	,	,	PUNCT
ejpam-4598	150	20	which	which	PRON
ejpam-4598	150	21	is	be	AUX
ejpam-4598	150	22	neither	neither	DET
ejpam-4598	150	23	hausdorff	hausdorff	NOUN
ejpam-4598	150	24	,	,	PUNCT
ejpam-4598	150	25	normal	normal	ADJ
ejpam-4598	150	26	nor	nor	CCONJ
ejpam-4598	150	27	semi	semi	ADJ
ejpam-4598	150	28	-	-	ADJ
ejpam-4598	150	29	regular	regular	ADJ
ejpam-4598	150	30	[	[	X
ejpam-4598	150	31	30	30	NUM
ejpam-4598	150	32	]	]	PUNCT
ejpam-4598	150	33	.	.	PUNCT
ejpam-4598	151	1	clearly	clearly	ADV
ejpam-4598	151	2	that	that	PRON
ejpam-4598	151	3	:	:	PUNCT
ejpam-4598	151	4	x	x	X
ejpam-4598	151	5	is	be	AUX
ejpam-4598	151	6	an	an	DET
ejpam-4598	151	7	almost	almost	ADV
ejpam-4598	151	8	-	-	PUNCT
ejpam-4598	151	9	regular	regular	ADJ
ejpam-4598	151	10	space	space	NOUN
ejpam-4598	151	11	.	.	PUNCT
ejpam-4598	152	1	since	since	SCONJ
ejpam-4598	152	2	it	it	PRON
ejpam-4598	152	3	is	be	AUX
ejpam-4598	152	4	an	an	DET
ejpam-4598	152	5	almost	almost	ADV
ejpam-4598	152	6	-	-	PUNCT
ejpam-4598	152	7	regular	regular	ADJ
ejpam-4598	152	8	paracompact	paracompact	ADJ
ejpam-4598	152	9	space	space	NOUN
ejpam-4598	152	10	,	,	PUNCT
ejpam-4598	152	11	it	it	PRON
ejpam-4598	152	12	is	be	AUX
ejpam-4598	152	13	almost	almost	ADV
ejpam-4598	152	14	-	-	PUNCT
ejpam-4598	152	15	normal	normal	ADJ
ejpam-4598	152	16	.	.	PUNCT
ejpam-4598	153	1	since	since	SCONJ
ejpam-4598	153	2	every	every	DET
ejpam-4598	153	3	almost	almost	ADV
ejpam-4598	153	4	-	-	PUNCT
ejpam-4598	153	5	normal	normal	ADJ
ejpam-4598	153	6	t1	t1	NOUN
ejpam-4598	153	7	space	space	NOUN
ejpam-4598	153	8	is	be	AUX
ejpam-4598	153	9	almost	almost	ADV
ejpam-4598	153	10	-	-	PUNCT
ejpam-4598	153	11	completely	completely	ADV
ejpam-4598	153	12	regular	regular	ADJ
ejpam-4598	153	13	,	,	PUNCT
ejpam-4598	153	14	we	we	PRON
ejpam-4598	153	15	have	have	VERB
ejpam-4598	153	16	:	:	PUNCT
ejpam-4598	153	17	the	the	DET
ejpam-4598	153	18	telophase	telophase	NOUN
ejpam-4598	153	19	topology	topology	NOUN
ejpam-4598	153	20	is	be	AUX
ejpam-4598	153	21	t1	t1	NOUN
ejpam-4598	153	22	-	-	PUNCT
ejpam-4598	153	23	almost	almost	ADV
ejpam-4598	153	24	-	-	PUNCT
ejpam-4598	153	25	completely	completely	ADV
ejpam-4598	153	26	regular	regular	ADJ
ejpam-4598	153	27	.	.	PUNCT
ejpam-4598	154	1	since	since	SCONJ
ejpam-4598	154	2	the	the	DET
ejpam-4598	154	3	telophase	telophase	NOUN
ejpam-4598	154	4	topology	topology	NOUN
ejpam-4598	154	5	is	be	AUX
ejpam-4598	154	6	not	not	PART
ejpam-4598	154	7	hausdorff	hausdorff	NOUN
ejpam-4598	154	8	,	,	PUNCT
ejpam-4598	154	9	it	it	PRON
ejpam-4598	154	10	is	be	AUX
ejpam-4598	154	11	neither	neither	CCONJ
ejpam-4598	154	12	epi	epi	NOUN
ejpam-4598	154	13	-	-	ADJ
ejpam-4598	154	14	completely	completely	ADV
ejpam-4598	154	15	-	-	PUNCT
ejpam-4598	154	16	regular	regular	ADJ
ejpam-4598	154	17	,	,	PUNCT
ejpam-4598	154	18	epi	epi	NOUN
ejpam-4598	154	19	-	-	ADJ
ejpam-4598	154	20	mildly	mildly	ADV
ejpam-4598	154	21	normal	normal	ADJ
ejpam-4598	154	22	nor	nor	CCONJ
ejpam-4598	154	23	epi	epi	NOUN
ejpam-4598	154	24	-	-	NOUN
ejpam-4598	154	25	regular	regular	ADJ
ejpam-4598	154	26	.	.	PUNCT
ejpam-4598	155	1	therefore	therefore	ADV
ejpam-4598	155	2	,	,	PUNCT
ejpam-4598	155	3	the	the	DET
ejpam-4598	155	4	telophase	telophase	NOUN
ejpam-4598	155	5	topology	topology	NOUN
ejpam-4598	155	6	is	be	AUX
ejpam-4598	155	7	an	an	DET
ejpam-4598	155	8	almost	almost	ADV
ejpam-4598	155	9	-	-	PUNCT
ejpam-4598	155	10	completely	completely	ADV
ejpam-4598	155	11	regular	regular	ADJ
ejpam-4598	155	12	space	space	NOUN
ejpam-4598	155	13	,	,	PUNCT
ejpam-4598	155	14	which	which	PRON
ejpam-4598	155	15	is	be	AUX
ejpam-4598	155	16	neither	neither	DET
ejpam-4598	155	17	epi	epi	NOUN
ejpam-4598	155	18	-	-	NOUN
ejpam-4598	155	19	completelyregular	completelyregular	ADJ
ejpam-4598	155	20	,	,	PUNCT
ejpam-4598	155	21	epi	epi	ADJ
ejpam-4598	155	22	-	-	PUNCT
ejpam-4598	155	23	mildly	mildly	ADV
ejpam-4598	155	24	-	-	PUNCT
ejpam-4598	155	25	normal	normal	ADJ
ejpam-4598	155	26	nor	nor	CCONJ
ejpam-4598	155	27	epi	epi	NOUN
ejpam-4598	155	28	-	-	NOUN
ejpam-4598	155	29	regular	regular	ADJ
ejpam-4598	155	30	.	.	PUNCT
ejpam-4598	156	1	an	an	DET
ejpam-4598	156	2	epi	epi	NOUN
ejpam-4598	156	3	-	-	PUNCT
ejpam-4598	156	4	completely	completely	ADV
ejpam-4598	156	5	-	-	PUNCT
ejpam-4598	156	6	regular	regular	ADJ
ejpam-4598	156	7	space	space	NOUN
ejpam-4598	156	8	need	need	AUX
ejpam-4598	156	9	not	not	PART
ejpam-4598	156	10	be	be	AUX
ejpam-4598	156	11	almost	almost	ADV
ejpam-4598	156	12	-	-	PUNCT
ejpam-4598	156	13	normal	normal	ADJ
ejpam-4598	156	14	nor	nor	CCONJ
ejpam-4598	156	15	quasi	quasi	ADJ
ejpam-4598	156	16	-	-	ADJ
ejpam-4598	156	17	normal	normal	ADJ
ejpam-4598	156	18	.	.	PUNCT
ejpam-4598	157	1	here	here	ADV
ejpam-4598	157	2	is	be	AUX
ejpam-4598	157	3	an	an	DET
ejpam-4598	157	4	example	example	NOUN
ejpam-4598	157	5	:	:	PUNCT
ejpam-4598	157	6	example	example	NOUN
ejpam-4598	157	7	8	8	NUM
ejpam-4598	157	8	.	.	PUNCT
ejpam-4598	158	1	the	the	DET
ejpam-4598	158	2	thomas	thomas	PROPN
ejpam-4598	158	3	’	'	PUNCT
ejpam-4598	158	4	plank	plank	NOUN
ejpam-4598	158	5	topology	topology	NOUN
ejpam-4598	158	6	[	[	X
ejpam-4598	158	7	30	30	NUM
ejpam-4598	158	8	,	,	PUNCT
ejpam-4598	158	9	example	example	NOUN
ejpam-4598	158	10	93	93	NUM
ejpam-4598	158	11	]	]	PUNCT
ejpam-4598	158	12	,	,	PUNCT
ejpam-4598	158	13	let	let	VERB
ejpam-4598	158	14	x	x	SYM
ejpam-4598	158	15	=	=	SYM
ejpam-4598	158	16	∞⋃	∞⋃	PROPN
ejpam-4598	158	17	i=0	i=0	PROPN
ejpam-4598	158	18	li	li	PROPN
ejpam-4598	158	19	,	,	PUNCT
ejpam-4598	158	20	where	where	SCONJ
ejpam-4598	158	21	l0	l0	PROPN
ejpam-4598	158	22	=	=	SYM
ejpam-4598	158	23	(	(	PUNCT
ejpam-4598	158	24	0	0	NUM
ejpam-4598	158	25	,	,	PUNCT
ejpam-4598	158	26	1)×{0	1)×{0	NUM
ejpam-4598	158	27	}	}	PUNCT
ejpam-4598	158	28	and	and	CCONJ
ejpam-4598	158	29	li	li	PROPN
ejpam-4598	158	30	=	=	PUNCT
ejpam-4598	159	1	[	[	X
ejpam-4598	159	2	0	0	NUM
ejpam-4598	159	3	,	,	PUNCT
ejpam-4598	159	4	1)×{1	1)×{1	NUM
ejpam-4598	159	5	i	i	NOUN
ejpam-4598	159	6	}	}	PUNCT
ejpam-4598	159	7	for	for	ADP
ejpam-4598	159	8	each	each	DET
ejpam-4598	159	9	i	i	PRON
ejpam-4598	159	10	≥	≥	NOUN
ejpam-4598	159	11	1	1	NUM
ejpam-4598	159	12	.	.	PUNCT
ejpam-4598	160	1	for	for	ADP
ejpam-4598	160	2	each	each	DET
ejpam-4598	160	3	i	i	PRON
ejpam-4598	160	4	≥	≥	NOUN
ejpam-4598	160	5	1	1	NUM
ejpam-4598	160	6	,	,	PUNCT
ejpam-4598	160	7	each	each	DET
ejpam-4598	160	8	point	point	NOUN
ejpam-4598	160	9	(	(	PUNCT
ejpam-4598	160	10	x	x	NOUN
ejpam-4598	160	11	,	,	PUNCT
ejpam-4598	160	12	1i	1i	NOUN
ejpam-4598	160	13	)	)	PUNCT
ejpam-4598	160	14	∈	∈	PROPN
ejpam-4598	160	15	li	li	PROPN
ejpam-4598	160	16	,	,	PUNCT
ejpam-4598	160	17	x	x	SYM
ejpam-4598	160	18	̸=	̸=	PROPN
ejpam-4598	160	19	0	0	NUM
ejpam-4598	160	20	,	,	PUNCT
ejpam-4598	160	21	we	we	PRON
ejpam-4598	160	22	have	have	AUX
ejpam-4598	160	23	{	{	PUNCT
ejpam-4598	160	24	(	(	PUNCT
ejpam-4598	160	25	x	x	X
ejpam-4598	160	26	,	,	PUNCT
ejpam-4598	160	27	1i	1i	NOUN
ejpam-4598	160	28	)	)	PUNCT
ejpam-4598	160	29	}	}	PUNCT
ejpam-4598	160	30	is	be	AUX
ejpam-4598	160	31	an	an	DET
ejpam-4598	160	32	open	open	ADJ
ejpam-4598	160	33	subset	subset	NOUN
ejpam-4598	160	34	of	of	ADP
ejpam-4598	160	35	x.	x.	NOUN
ejpam-4598	160	36	for	for	ADP
ejpam-4598	160	37	each	each	DET
ejpam-4598	160	38	i	i	PRON
ejpam-4598	160	39	≥	≥	NOUN
ejpam-4598	160	40	1	1	NUM
ejpam-4598	160	41	,	,	PUNCT
ejpam-4598	160	42	the	the	DET
ejpam-4598	160	43	basic	basic	ADJ
ejpam-4598	160	44	open	open	ADJ
ejpam-4598	160	45	subset	subset	NOUN
ejpam-4598	160	46	of	of	ADP
ejpam-4598	160	47	the	the	DET
ejpam-4598	160	48	i.	i.	PROPN
ejpam-4598	160	49	alshammari	alshammari	PROPN
ejpam-4598	160	50	/	/	SYM
ejpam-4598	160	51	eur	eur	PROPN
ejpam-4598	160	52	.	.	PUNCT
ejpam-4598	161	1	j.	j.	PROPN
ejpam-4598	161	2	pure	pure	PROPN
ejpam-4598	161	3	appl	appl	PROPN
ejpam-4598	161	4	.	.	PROPN
ejpam-4598	161	5	math	math	PROPN
ejpam-4598	161	6	,	,	PUNCT
ejpam-4598	161	7	15	15	NUM
ejpam-4598	161	8	(	(	PUNCT
ejpam-4598	161	9	4	4	NUM
ejpam-4598	161	10	)	)	PUNCT
ejpam-4598	161	11	(	(	PUNCT
ejpam-4598	161	12	2022	2022	NUM
ejpam-4598	161	13	)	)	PUNCT
ejpam-4598	161	14	,	,	PUNCT
ejpam-4598	161	15	1808	1808	NUM
ejpam-4598	161	16	-	-	SYM
ejpam-4598	161	17	1821	1821	NUM
ejpam-4598	161	18	1813	1813	NUM
ejpam-4598	161	19	points	point	NOUN
ejpam-4598	161	20	(	(	PUNCT
ejpam-4598	161	21	0	0	NUM
ejpam-4598	161	22	,	,	PUNCT
ejpam-4598	161	23	1i	1i	NOUN
ejpam-4598	161	24	)	)	PUNCT
ejpam-4598	162	1	∈	∈	PROPN
ejpam-4598	162	2	li	li	PROPN
ejpam-4598	162	3	is	be	AUX
ejpam-4598	162	4	a	a	DET
ejpam-4598	162	5	subset	subset	NOUN
ejpam-4598	162	6	wi	wi	PROPN
ejpam-4598	162	7	of	of	ADP
ejpam-4598	162	8	li	li	PROPN
ejpam-4598	162	9	such	such	ADJ
ejpam-4598	162	10	that	that	SCONJ
ejpam-4598	162	11	li	li	PROPN
ejpam-4598	162	12	−wi	−wi	PROPN
ejpam-4598	162	13	is	be	AUX
ejpam-4598	162	14	finite	finite	ADJ
ejpam-4598	162	15	.	.	PUNCT
ejpam-4598	163	1	the	the	DET
ejpam-4598	163	2	basic	basic	ADJ
ejpam-4598	163	3	open	open	ADJ
ejpam-4598	163	4	subset	subset	NOUN
ejpam-4598	163	5	of	of	ADP
ejpam-4598	163	6	any	any	DET
ejpam-4598	163	7	point	point	NOUN
ejpam-4598	163	8	(	(	PUNCT
ejpam-4598	163	9	x	x	X
ejpam-4598	163	10	,	,	PUNCT
ejpam-4598	163	11	0	0	NUM
ejpam-4598	163	12	)	)	PUNCT
ejpam-4598	163	13	∈	∈	PROPN
ejpam-4598	163	14	l0	l0	PROPN
ejpam-4598	163	15	is	be	AUX
ejpam-4598	163	16	of	of	ADP
ejpam-4598	163	17	the	the	DET
ejpam-4598	163	18	form	form	NOUN
ejpam-4598	163	19	ui(x	ui(x	ADJ
ejpam-4598	163	20	,	,	PUNCT
ejpam-4598	163	21	0	0	NUM
ejpam-4598	163	22	)	)	PUNCT
ejpam-4598	164	1	=	=	PRON
ejpam-4598	164	2	{	{	PUNCT
ejpam-4598	164	3	(	(	PUNCT
ejpam-4598	164	4	x	x	NOUN
ejpam-4598	164	5	,	,	PUNCT
ejpam-4598	164	6	0	0	NUM
ejpam-4598	164	7	)	)	PUNCT
ejpam-4598	164	8	}	}	PUNCT
ejpam-4598	164	9	∪	∪	X
ejpam-4598	164	10	{	{	PUNCT
ejpam-4598	164	11	(	(	PUNCT
ejpam-4598	164	12	x	x	NOUN
ejpam-4598	164	13	,	,	PUNCT
ejpam-4598	164	14	1	1	NUM
ejpam-4598	164	15	n	n	CCONJ
ejpam-4598	164	16	)	)	PUNCT
ejpam-4598	164	17	:	:	PUNCT
ejpam-4598	165	1	n	n	CCONJ
ejpam-4598	165	2	>	>	X
ejpam-4598	165	3	i	i	PROPN
ejpam-4598	165	4	}	}	PUNCT
ejpam-4598	165	5	.	.	PUNCT
ejpam-4598	166	1	it	it	PRON
ejpam-4598	166	2	can	can	AUX
ejpam-4598	166	3	be	be	AUX
ejpam-4598	166	4	observed	observe	VERB
ejpam-4598	166	5	that	that	SCONJ
ejpam-4598	166	6	:	:	PUNCT
ejpam-4598	166	7	each	each	DET
ejpam-4598	166	8	basic	basic	ADJ
ejpam-4598	166	9	open	open	ADJ
ejpam-4598	166	10	subsets	subset	NOUN
ejpam-4598	166	11	of	of	ADP
ejpam-4598	166	12	x	x	PUNCT
ejpam-4598	166	13	is	be	AUX
ejpam-4598	166	14	clopen	clopen	ADJ
ejpam-4598	166	15	(	(	PUNCT
ejpam-4598	166	16	closed	closed	ADJ
ejpam-4598	166	17	-	-	PUNCT
ejpam-4598	166	18	and	and	CCONJ
ejpam-4598	166	19	-	-	PUNCT
ejpam-4598	166	20	open	open	ADJ
ejpam-4598	166	21	)	)	PUNCT
ejpam-4598	166	22	.	.	PUNCT
ejpam-4598	167	1	hence	hence	ADV
ejpam-4598	167	2	,	,	PUNCT
ejpam-4598	167	3	(	(	PUNCT
ejpam-4598	167	4	x	x	X
ejpam-4598	167	5	,	,	PUNCT
ejpam-4598	167	6	t	t	PROPN
ejpam-4598	167	7	)	)	PUNCT
ejpam-4598	167	8	is	be	AUX
ejpam-4598	167	9	a	a	DET
ejpam-4598	167	10	zero	zero	NUM
ejpam-4598	167	11	-	-	PUNCT
ejpam-4598	167	12	dimensional	dimensional	ADJ
ejpam-4598	167	13	,	,	PUNCT
ejpam-4598	167	14	hausdorff	hausdorff	NOUN
ejpam-4598	167	15	,	,	PUNCT
ejpam-4598	167	16	regular	regular	ADJ
ejpam-4598	167	17	,	,	PUNCT
ejpam-4598	167	18	completely	completely	ADV
ejpam-4598	167	19	-	-	PUNCT
ejpam-4598	167	20	regular	regular	ADJ
ejpam-4598	167	21	,	,	PUNCT
ejpam-4598	167	22	semi	semi	ADJ
ejpam-4598	167	23	-	-	ADJ
ejpam-4598	167	24	regular	regular	ADJ
ejpam-4598	167	25	,	,	PUNCT
ejpam-4598	167	26	urysohn	urysohn	NOUN
ejpam-4598	167	27	,	,	PUNCT
ejpam-4598	167	28	locallycompact	locallycompact	NOUN
ejpam-4598	167	29	and	and	CCONJ
ejpam-4598	167	30	tychonoff	tychonoff	NOUN
ejpam-4598	167	31	space	space	NOUN
ejpam-4598	167	32	,	,	PUNCT
ejpam-4598	167	33	and	and	CCONJ
ejpam-4598	167	34	it	it	PRON
ejpam-4598	167	35	is	be	AUX
ejpam-4598	167	36	neither	neither	CCONJ
ejpam-4598	167	37	normal	normal	ADJ
ejpam-4598	167	38	nor	nor	CCONJ
ejpam-4598	167	39	paracompact	paracompact	ADJ
ejpam-4598	167	40	[	[	X
ejpam-4598	167	41	30	30	NUM
ejpam-4598	167	42	]	]	PUNCT
ejpam-4598	167	43	.	.	PUNCT
ejpam-4598	168	1	hence	hence	ADV
ejpam-4598	168	2	,	,	PUNCT
ejpam-4598	168	3	the	the	DET
ejpam-4598	168	4	thomas	thomas	PROPN
ejpam-4598	168	5	’	'	PUNCT
ejpam-4598	168	6	plank	plank	NOUN
ejpam-4598	168	7	topology	topology	NOUN
ejpam-4598	168	8	is	be	AUX
ejpam-4598	168	9	an	an	DET
ejpam-4598	168	10	almost	almost	ADV
ejpam-4598	168	11	-	-	PUNCT
ejpam-4598	168	12	regular	regular	ADJ
ejpam-4598	168	13	and	and	CCONJ
ejpam-4598	168	14	almost	almost	ADV
ejpam-4598	168	15	-	-	PUNCT
ejpam-4598	168	16	completely	completely	ADV
ejpam-4598	168	17	regular	regular	ADJ
ejpam-4598	168	18	space	space	NOUN
ejpam-4598	168	19	.	.	PUNCT
ejpam-4598	169	1	since	since	SCONJ
ejpam-4598	169	2	it	it	PRON
ejpam-4598	169	3	is	be	AUX
ejpam-4598	169	4	hausdorff	hausdorff	NOUN
ejpam-4598	169	5	,	,	PUNCT
ejpam-4598	169	6	we	we	PRON
ejpam-4598	169	7	have	have	VERB
ejpam-4598	169	8	:	:	PUNCT
ejpam-4598	169	9	the	the	DET
ejpam-4598	169	10	thomas	thomas	PROPN
ejpam-4598	169	11	’	'	PUNCT
ejpam-4598	169	12	plank	plank	NOUN
ejpam-4598	169	13	topology	topology	NOUN
ejpam-4598	169	14	is	be	AUX
ejpam-4598	169	15	epi	epi	NOUN
ejpam-4598	169	16	-	-	ADJ
ejpam-4598	169	17	completely	completely	ADV
ejpam-4598	169	18	-	-	PUNCT
ejpam-4598	169	19	regular	regular	ADJ
ejpam-4598	169	20	and	and	CCONJ
ejpam-4598	169	21	epiregular	epiregular	ADJ
ejpam-4598	169	22	space	space	NOUN
ejpam-4598	169	23	.	.	PUNCT
ejpam-4598	170	1	since	since	SCONJ
ejpam-4598	170	2	x	x	PRON
ejpam-4598	170	3	is	be	AUX
ejpam-4598	170	4	hausdorff	hausdorff	NOUN
ejpam-4598	170	5	locally	locally	ADV
ejpam-4598	170	6	-	-	PUNCT
ejpam-4598	170	7	compact	compact	ADJ
ejpam-4598	170	8	,	,	PUNCT
ejpam-4598	170	9	we	we	PRON
ejpam-4598	170	10	obtain	obtain	VERB
ejpam-4598	170	11	:	:	PUNCT
ejpam-4598	170	12	x	x	X
ejpam-4598	170	13	is	be	AUX
ejpam-4598	170	14	a	a	DET
ejpam-4598	170	15	k	k	NOUN
ejpam-4598	170	16	-	-	NOUN
ejpam-4598	170	17	space	space	NOUN
ejpam-4598	170	18	.	.	PUNCT
ejpam-4598	171	1	thus	thus	ADV
ejpam-4598	171	2	,	,	PUNCT
ejpam-4598	171	3	x	x	X
ejpam-4598	171	4	is	be	AUX
ejpam-4598	171	5	c	c	NOUN
ejpam-4598	171	6	-	-	NOUN
ejpam-4598	171	7	normal	normal	ADJ
ejpam-4598	171	8	.	.	PUNCT
ejpam-4598	172	1	it	it	PRON
ejpam-4598	172	2	can	can	AUX
ejpam-4598	172	3	be	be	AUX
ejpam-4598	172	4	observed	observe	VERB
ejpam-4598	172	5	that	that	SCONJ
ejpam-4598	172	6	:	:	PUNCT
ejpam-4598	172	7	each	each	DET
ejpam-4598	172	8	li	li	PROPN
ejpam-4598	172	9	,	,	PUNCT
ejpam-4598	172	10	i	i	PRON
ejpam-4598	172	11	≥	≥	VERB
ejpam-4598	172	12	1	1	NUM
ejpam-4598	172	13	is	be	AUX
ejpam-4598	172	14	open	open	ADJ
ejpam-4598	172	15	because	because	SCONJ
ejpam-4598	172	16	l0	l0	PROPN
ejpam-4598	172	17	is	be	AUX
ejpam-4598	172	18	closed	close	VERB
ejpam-4598	172	19	[	[	X
ejpam-4598	172	20	30	30	NUM
ejpam-4598	172	21	]	]	PUNCT
ejpam-4598	172	22	.	.	PUNCT
ejpam-4598	173	1	also	also	ADV
ejpam-4598	173	2	,	,	PUNCT
ejpam-4598	173	3	a	a	PRON
ejpam-4598	173	4	=	=	X
ejpam-4598	173	5	{	{	PUNCT
ejpam-4598	173	6	(	(	PUNCT
ejpam-4598	173	7	0	0	NUM
ejpam-4598	173	8	,	,	PUNCT
ejpam-4598	173	9	1	1	NUM
ejpam-4598	173	10	n	n	CCONJ
ejpam-4598	173	11	)	)	PUNCT
ejpam-4598	173	12	:	:	PUNCT
ejpam-4598	173	13	n	n	PRON
ejpam-4598	173	14	≥	≥	NOUN
ejpam-4598	173	15	1	1	NUM
ejpam-4598	173	16	}	}	PUNCT
ejpam-4598	173	17	is	be	AUX
ejpam-4598	173	18	a	a	DET
ejpam-4598	173	19	closed	closed	ADJ
ejpam-4598	173	20	subset	subset	NOUN
ejpam-4598	173	21	of	of	ADP
ejpam-4598	173	22	x	x	PUNCT
ejpam-4598	174	1	[	[	X
ejpam-4598	174	2	30	30	NUM
ejpam-4598	174	3	]	]	PUNCT
ejpam-4598	174	4	.	.	PUNCT
ejpam-4598	175	1	since	since	SCONJ
ejpam-4598	175	2	a	a	DET
ejpam-4598	175	3	∩	∩	ADJ
ejpam-4598	175	4	l0	l0	NOUN
ejpam-4598	175	5	=	=	NOUN
ejpam-4598	175	6	∅	∅	NOUN
ejpam-4598	175	7	,	,	PUNCT
ejpam-4598	175	8	we	we	PRON
ejpam-4598	175	9	get	get	VERB
ejpam-4598	175	10	:	:	PUNCT
ejpam-4598	175	11	a	a	PRON
ejpam-4598	175	12	and	and	CCONJ
ejpam-4598	175	13	l0	l0	PROPN
ejpam-4598	175	14	are	be	AUX
ejpam-4598	175	15	disjoint	disjoint	NOUN
ejpam-4598	175	16	closed	closed	ADJ
ejpam-4598	175	17	subsets	subset	NOUN
ejpam-4598	175	18	of	of	ADP
ejpam-4598	175	19	x	x	PRON
ejpam-4598	175	20	,	,	PUNCT
ejpam-4598	175	21	which	which	PRON
ejpam-4598	175	22	can	can	AUX
ejpam-4598	175	23	not	not	PART
ejpam-4598	175	24	be	be	AUX
ejpam-4598	175	25	separated	separate	VERB
ejpam-4598	175	26	[	[	PUNCT
ejpam-4598	175	27	30	30	NUM
ejpam-4598	175	28	]	]	PUNCT
ejpam-4598	175	29	.	.	PUNCT
ejpam-4598	176	1	let	let	VERB
ejpam-4598	176	2	u	u	NOUN
ejpam-4598	176	3	=	=	PUNCT
ejpam-4598	176	4	⋃	⋃	NOUN
ejpam-4598	176	5	n∈n	n∈n	NOUN
ejpam-4598	176	6	l2n	l2n	NOUN
ejpam-4598	176	7	and	and	CCONJ
ejpam-4598	176	8	v	v	NOUN
ejpam-4598	176	9	=	=	SYM
ejpam-4598	176	10	⋃	⋃	NOUN
ejpam-4598	176	11	n∈n	n∈n	NOUN
ejpam-4598	176	12	l2n+1	l2n+1	NOUN
ejpam-4598	176	13	.	.	PUNCT
ejpam-4598	177	1	then	then	ADV
ejpam-4598	177	2	,	,	PUNCT
ejpam-4598	177	3	u	u	NOUN
ejpam-4598	177	4	and	and	CCONJ
ejpam-4598	177	5	v	v	NOUN
ejpam-4598	177	6	are	be	AUX
ejpam-4598	177	7	disjoint	disjoint	ADJ
ejpam-4598	177	8	open	open	ADJ
ejpam-4598	177	9	subsets	subset	NOUN
ejpam-4598	177	10	of	of	ADP
ejpam-4598	177	11	x.	x.	NOUN
ejpam-4598	177	12	thus	thus	ADV
ejpam-4598	177	13	,	,	PUNCT
ejpam-4598	177	14	u	u	PROPN
ejpam-4598	177	15	=	=	PROPN
ejpam-4598	177	16	u	u	PROPN
ejpam-4598	177	17	∪	∪	VERB
ejpam-4598	177	18	l0	l0	PROPN
ejpam-4598	177	19	and	and	CCONJ
ejpam-4598	177	20	v	v	NOUN
ejpam-4598	177	21	=	=	NOUN
ejpam-4598	177	22	v	v	NOUN
ejpam-4598	177	23	∪	∪	X
ejpam-4598	177	24	l0	l0	PROPN
ejpam-4598	177	25	.	.	PUNCT
ejpam-4598	178	1	hence	hence	ADV
ejpam-4598	178	2	,	,	PUNCT
ejpam-4598	178	3	u	u	NOUN
ejpam-4598	178	4	and	and	CCONJ
ejpam-4598	178	5	v	v	NOUN
ejpam-4598	178	6	are	be	AUX
ejpam-4598	178	7	closed	closed	ADJ
ejpam-4598	178	8	-	-	PUNCT
ejpam-4598	178	9	domains	domain	NOUN
ejpam-4598	178	10	in	in	ADP
ejpam-4598	178	11	x	x	SYM
ejpam-4598	178	12	such	such	ADJ
ejpam-4598	178	13	that	that	SCONJ
ejpam-4598	178	14	u	u	PROPN
ejpam-4598	178	15	∩	∩	NOUN
ejpam-4598	178	16	v	v	ADP
ejpam-4598	178	17	=	=	SYM
ejpam-4598	178	18	l0	l0	PROPN
ejpam-4598	178	19	.	.	PUNCT
ejpam-4598	179	1	therefore	therefore	ADV
ejpam-4598	179	2	,	,	PUNCT
ejpam-4598	179	3	l0	l0	PROPN
ejpam-4598	179	4	is	be	AUX
ejpam-4598	179	5	a	a	DET
ejpam-4598	179	6	π	π	PROPN
ejpam-4598	179	7	-	-	ADJ
ejpam-4598	179	8	closed	closed	ADJ
ejpam-4598	179	9	subset	subset	NOUN
ejpam-4598	179	10	of	of	ADP
ejpam-4598	179	11	x.	x.	NOUN
ejpam-4598	179	12	since	since	SCONJ
ejpam-4598	179	13	a	a	PRON
ejpam-4598	179	14	and	and	CCONJ
ejpam-4598	179	15	l0	l0	PROPN
ejpam-4598	179	16	can	can	AUX
ejpam-4598	179	17	not	not	PART
ejpam-4598	179	18	be	be	AUX
ejpam-4598	179	19	separated	separate	VERB
ejpam-4598	179	20	,	,	PUNCT
ejpam-4598	179	21	we	we	PRON
ejpam-4598	179	22	obtain	obtain	VERB
ejpam-4598	179	23	:	:	PUNCT
ejpam-4598	179	24	x	x	X
ejpam-4598	179	25	is	be	AUX
ejpam-4598	179	26	not	not	PART
ejpam-4598	179	27	π	π	NOUN
ejpam-4598	179	28	-	-	NOUN
ejpam-4598	179	29	normal	normal	ADJ
ejpam-4598	179	30	.	.	PUNCT
ejpam-4598	180	1	claim	claim	VERB
ejpam-4598	180	2	1	1	NUM
ejpam-4598	180	3	:	:	PUNCT
ejpam-4598	180	4	any	any	DET
ejpam-4598	180	5	singleton	singleton	NOUN
ejpam-4598	180	6	{	{	PUNCT
ejpam-4598	180	7	(	(	PUNCT
ejpam-4598	180	8	x	x	X
ejpam-4598	180	9	,	,	PUNCT
ejpam-4598	180	10	0	0	NUM
ejpam-4598	180	11	)	)	PUNCT
ejpam-4598	180	12	}	}	PUNCT
ejpam-4598	180	13	is	be	AUX
ejpam-4598	180	14	π	π	PROPN
ejpam-4598	180	15	-	-	VERB
ejpam-4598	180	16	closed	closed	ADJ
ejpam-4598	180	17	and	and	CCONJ
ejpam-4598	180	18	any	any	DET
ejpam-4598	180	19	singleton	singleton	NOUN
ejpam-4598	180	20	{	{	PUNCT
ejpam-4598	180	21	(	(	PUNCT
ejpam-4598	180	22	0	0	NUM
ejpam-4598	180	23	,	,	PUNCT
ejpam-4598	180	24	1i	1i	NOUN
ejpam-4598	180	25	)	)	PUNCT
ejpam-4598	180	26	}	}	PUNCT
ejpam-4598	180	27	,	,	PUNCT
ejpam-4598	180	28	i	i	PRON
ejpam-4598	180	29	≥	≥	VERB
ejpam-4598	180	30	1	1	NUM
ejpam-4598	180	31	is	be	AUX
ejpam-4598	180	32	also	also	ADV
ejpam-4598	180	33	π	π	PROPN
ejpam-4598	180	34	-	-	VERB
ejpam-4598	180	35	closed	closed	ADJ
ejpam-4598	180	36	in	in	ADP
ejpam-4598	180	37	x.	x.	NOUN
ejpam-4598	180	38	proof	proof	NOUN
ejpam-4598	180	39	of	of	ADP
ejpam-4598	180	40	the	the	DET
ejpam-4598	180	41	claim	claim	NOUN
ejpam-4598	180	42	1	1	NUM
ejpam-4598	180	43	:	:	PUNCT
ejpam-4598	180	44	let	let	VERB
ejpam-4598	180	45	ux	ux	INTJ
ejpam-4598	180	46	=	=	PRON
ejpam-4598	180	47	{	{	PUNCT
ejpam-4598	180	48	(	(	PUNCT
ejpam-4598	180	49	x	x	NOUN
ejpam-4598	180	50	,	,	PUNCT
ejpam-4598	180	51	1	1	NUM
ejpam-4598	180	52	2n	2n	NUM
ejpam-4598	180	53	)	)	PUNCT
ejpam-4598	180	54	:	:	PUNCT
ejpam-4598	180	55	n	n	X
ejpam-4598	180	56	∈	∈	PROPN
ejpam-4598	180	57	n	n	CCONJ
ejpam-4598	180	58	}	}	PUNCT
ejpam-4598	180	59	and	and	CCONJ
ejpam-4598	180	60	vx	vx	PROPN
ejpam-4598	180	61	=	=	PUNCT
ejpam-4598	180	62	{	{	PUNCT
ejpam-4598	180	63	(	(	PUNCT
ejpam-4598	180	64	x	x	NOUN
ejpam-4598	180	65	,	,	PUNCT
ejpam-4598	180	66	1	1	NUM
ejpam-4598	180	67	2n+1	2n+1	NUM
ejpam-4598	180	68	)	)	PUNCT
ejpam-4598	180	69	:	:	PUNCT
ejpam-4598	180	70	n	n	X
ejpam-4598	180	71	∈	∈	PROPN
ejpam-4598	180	72	n	n	CCONJ
ejpam-4598	180	73	}	}	PUNCT
ejpam-4598	180	74	.	.	PUNCT
ejpam-4598	181	1	then	then	ADV
ejpam-4598	181	2	,	,	PUNCT
ejpam-4598	181	3	ux	ux	PROPN
ejpam-4598	181	4	and	and	CCONJ
ejpam-4598	181	5	vx	vx	PROPN
ejpam-4598	181	6	are	be	AUX
ejpam-4598	181	7	disjoint	disjoint	VERB
ejpam-4598	181	8	open	open	ADJ
ejpam-4598	181	9	subsets	subset	NOUN
ejpam-4598	181	10	of	of	ADP
ejpam-4598	181	11	x	x	SYM
ejpam-4598	181	12	such	such	ADJ
ejpam-4598	181	13	that	that	PRON
ejpam-4598	181	14	ux	ux	NOUN
ejpam-4598	181	15	=	=	SYM
ejpam-4598	181	16	ux∪{(x	ux∪{(x	NOUN
ejpam-4598	181	17	,	,	PUNCT
ejpam-4598	181	18	0	0	NUM
ejpam-4598	181	19	)	)	PUNCT
ejpam-4598	181	20	}	}	PUNCT
ejpam-4598	181	21	and	and	CCONJ
ejpam-4598	181	22	vx	vx	X
ejpam-4598	181	23	=	=	PUNCT
ejpam-4598	181	24	vx∪{(x	vx∪{(x	NOUN
ejpam-4598	181	25	,	,	PUNCT
ejpam-4598	181	26	0	0	NUM
ejpam-4598	181	27	)	)	PUNCT
ejpam-4598	181	28	}	}	PUNCT
ejpam-4598	181	29	.	.	PUNCT
ejpam-4598	182	1	therefore	therefore	ADV
ejpam-4598	182	2	,	,	PUNCT
ejpam-4598	182	3	ux	ux	PROPN
ejpam-4598	182	4	and	and	CCONJ
ejpam-4598	182	5	vx	vx	PROPN
ejpam-4598	182	6	are	be	AUX
ejpam-4598	182	7	closed	closed	ADJ
ejpam-4598	182	8	domain	domain	NOUN
ejpam-4598	182	9	subsets	subset	NOUN
ejpam-4598	182	10	ofx	ofx	NOUN
ejpam-4598	182	11	and	and	CCONJ
ejpam-4598	182	12	ux∩vx	ux∩vx	PROPN
ejpam-4598	182	13	=	=	SYM
ejpam-4598	182	14	{	{	PUNCT
ejpam-4598	182	15	(	(	PUNCT
ejpam-4598	182	16	x	x	NOUN
ejpam-4598	182	17	,	,	PUNCT
ejpam-4598	182	18	0	0	NUM
ejpam-4598	182	19	)	)	PUNCT
ejpam-4598	182	20	}	}	PUNCT
ejpam-4598	182	21	.	.	PUNCT
ejpam-4598	183	1	thus	thus	ADV
ejpam-4598	183	2	,	,	PUNCT
ejpam-4598	183	3	{	{	PUNCT
ejpam-4598	183	4	(	(	PUNCT
ejpam-4598	183	5	x	x	X
ejpam-4598	183	6	,	,	PUNCT
ejpam-4598	183	7	0	0	NUM
ejpam-4598	183	8	)	)	PUNCT
ejpam-4598	183	9	}	}	PUNCT
ejpam-4598	183	10	is	be	AUX
ejpam-4598	183	11	π	π	PROPN
ejpam-4598	183	12	-	-	VERB
ejpam-4598	183	13	closed	closed	ADJ
ejpam-4598	183	14	in	in	ADP
ejpam-4598	183	15	x	x	PUNCT
ejpam-4598	183	16	for	for	ADP
ejpam-4598	183	17	each	each	DET
ejpam-4598	183	18	x	x	SYM
ejpam-4598	183	19	∈	∈	PROPN
ejpam-4598	183	20	(	(	PUNCT
ejpam-4598	183	21	0	0	NUM
ejpam-4598	183	22	,	,	PUNCT
ejpam-4598	183	23	1	1	NUM
ejpam-4598	183	24	)	)	PUNCT
ejpam-4598	183	25	.	.	PUNCT
ejpam-4598	184	1	now	now	ADV
ejpam-4598	184	2	,	,	PUNCT
ejpam-4598	184	3	fix	fix	VERB
ejpam-4598	184	4	a	a	DET
ejpam-4598	184	5	sequence	sequence	NOUN
ejpam-4598	184	6	⟨(xik	⟨(xik	PROPN
ejpam-4598	184	7	,	,	PUNCT
ejpam-4598	184	8	1	1	NUM
ejpam-4598	184	9	i	i	NOUN
ejpam-4598	184	10	)	)	PUNCT
ejpam-4598	184	11	⟩	⟩	NOUN
ejpam-4598	184	12	of	of	ADP
ejpam-4598	184	13	distinct	distinct	ADJ
ejpam-4598	184	14	points	point	NOUN
ejpam-4598	184	15	of	of	ADP
ejpam-4598	184	16	li	li	PROPN
ejpam-4598	184	17	.	.	PROPN
ejpam-4598	184	18	consider	consider	VERB
ejpam-4598	184	19	the	the	DET
ejpam-4598	184	20	two	two	NUM
ejpam-4598	184	21	subsequences	subsequence	NOUN
ejpam-4598	184	22	ui	ui	NOUN
ejpam-4598	184	23	=	=	PUNCT
ejpam-4598	184	24	{	{	PUNCT
ejpam-4598	184	25	(	(	PUNCT
ejpam-4598	184	26	xi2k	xi2k	PROPN
ejpam-4598	184	27	,	,	PUNCT
ejpam-4598	184	28	1	1	NUM
ejpam-4598	184	29	i	i	NOUN
ejpam-4598	184	30	)	)	PUNCT
ejpam-4598	184	31	:	:	PUNCT
ejpam-4598	185	1	k	k	PROPN
ejpam-4598	185	2	∈	∈	PROPN
ejpam-4598	185	3	n	n	CCONJ
ejpam-4598	185	4	}	}	PUNCT
ejpam-4598	185	5	and	and	CCONJ
ejpam-4598	185	6	vi	vi	NOUN
ejpam-4598	185	7	=	=	SYM
ejpam-4598	185	8	{	{	PUNCT
ejpam-4598	185	9	(	(	PUNCT
ejpam-4598	185	10	xi2k+1	xi2k+1	PROPN
ejpam-4598	185	11	,	,	PUNCT
ejpam-4598	185	12	1	1	NUM
ejpam-4598	185	13	i	i	NOUN
ejpam-4598	185	14	)	)	PUNCT
ejpam-4598	185	15	:	:	PUNCT
ejpam-4598	185	16	k	k	PROPN
ejpam-4598	185	17	∈	∈	PROPN
ejpam-4598	185	18	n	n	CCONJ
ejpam-4598	185	19	}	}	PUNCT
ejpam-4598	185	20	.	.	PUNCT
ejpam-4598	186	1	then	then	ADV
ejpam-4598	186	2	,	,	PUNCT
ejpam-4598	186	3	ui	ui	PROPN
ejpam-4598	186	4	and	and	CCONJ
ejpam-4598	186	5	vi	vi	PROPN
ejpam-4598	186	6	are	be	AUX
ejpam-4598	186	7	disjoint	disjoint	ADJ
ejpam-4598	186	8	open	open	ADJ
ejpam-4598	186	9	subsets	subset	NOUN
ejpam-4598	186	10	ofx	ofx	PROPN
ejpam-4598	186	11	,	,	PUNCT
ejpam-4598	186	12	ui	ui	PROPN
ejpam-4598	186	13	,	,	PUNCT
ejpam-4598	186	14	vi	vi	PROPN
ejpam-4598	186	15	⊂	⊂	PROPN
ejpam-4598	186	16	li	li	PROPN
ejpam-4598	186	17	for	for	ADP
ejpam-4598	186	18	each	each	DET
ejpam-4598	186	19	i	i	PRON
ejpam-4598	186	20	≥	≥	NOUN
ejpam-4598	186	21	1	1	NUM
ejpam-4598	186	22	,	,	PUNCT
ejpam-4598	186	23	ui	ui	NOUN
ejpam-4598	186	24	=	=	PUNCT
ejpam-4598	186	25	ui∪{(0	ui∪{(0	PROPN
ejpam-4598	186	26	,	,	PUNCT
ejpam-4598	186	27	1i	1i	NOUN
ejpam-4598	186	28	)	)	PUNCT
ejpam-4598	186	29	}	}	PUNCT
ejpam-4598	186	30	and	and	CCONJ
ejpam-4598	186	31	vi	vi	NOUN
ejpam-4598	186	32	=	=	SYM
ejpam-4598	186	33	vi∪{(0	vi∪{(0	ADJ
ejpam-4598	186	34	,	,	PUNCT
ejpam-4598	186	35	1i	1i	NOUN
ejpam-4598	186	36	)	)	PUNCT
ejpam-4598	186	37	}	}	PUNCT
ejpam-4598	186	38	.	.	PUNCT
ejpam-4598	187	1	since	since	SCONJ
ejpam-4598	187	2	ui	ui	PROPN
ejpam-4598	187	3	and	and	CCONJ
ejpam-4598	187	4	vi	vi	PROPN
ejpam-4598	187	5	are	be	AUX
ejpam-4598	187	6	closed	closed	ADJ
ejpam-4598	187	7	-	-	PUNCT
ejpam-4598	187	8	domains	domain	NOUN
ejpam-4598	187	9	of	of	ADP
ejpam-4598	187	10	x	x	PRON
ejpam-4598	187	11	,	,	PUNCT
ejpam-4598	187	12	we	we	PRON
ejpam-4598	187	13	get	get	VERB
ejpam-4598	187	14	:	:	PUNCT
ejpam-4598	187	15	{	{	PUNCT
ejpam-4598	187	16	(	(	PUNCT
ejpam-4598	187	17	0	0	NUM
ejpam-4598	187	18	,	,	PUNCT
ejpam-4598	187	19	1i	1i	NOUN
ejpam-4598	187	20	)	)	PUNCT
ejpam-4598	187	21	}	}	PUNCT
ejpam-4598	187	22	is	be	AUX
ejpam-4598	187	23	π	π	PROPN
ejpam-4598	187	24	-	-	VERB
ejpam-4598	187	25	closed	closed	ADJ
ejpam-4598	187	26	for	for	SCONJ
ejpam-4598	187	27	each	each	DET
ejpam-4598	187	28	i	i	PRON
ejpam-4598	187	29	≥	≥	NOUN
ejpam-4598	187	30	1	1	NUM
ejpam-4598	187	31	.	.	PUNCT
ejpam-4598	188	1	now	now	ADV
ejpam-4598	188	2	,	,	PUNCT
ejpam-4598	188	3	let	let	VERB
ejpam-4598	188	4	g	g	NOUN
ejpam-4598	188	5	=	=	SYM
ejpam-4598	188	6	⋃	⋃	ADP
ejpam-4598	188	7	i≥1	i≥1	ADJ
ejpam-4598	188	8	ui	ui	NOUN
ejpam-4598	188	9	and	and	CCONJ
ejpam-4598	188	10	h	h	NOUN
ejpam-4598	188	11	=	=	SYM
ejpam-4598	189	1	⋃	⋃	PROPN
ejpam-4598	189	2	i≥1	i≥1	PROPN
ejpam-4598	189	3	vi	vi	PROPN
ejpam-4598	189	4	.	.	PUNCT
ejpam-4598	190	1	then	then	ADV
ejpam-4598	190	2	,	,	PUNCT
ejpam-4598	190	3	g	g	PROPN
ejpam-4598	190	4	and	and	CCONJ
ejpam-4598	190	5	h	h	NOUN
ejpam-4598	190	6	are	be	AUX
ejpam-4598	190	7	disjoint	disjoint	VERB
ejpam-4598	190	8	open	open	ADJ
ejpam-4598	190	9	subsets	subset	NOUN
ejpam-4598	190	10	ofx	ofx	PROPN
ejpam-4598	190	11	such	such	ADJ
ejpam-4598	190	12	thatg	thatg	PROPN
ejpam-4598	190	13	=	=	SYM
ejpam-4598	190	14	g∪a∪{(x2k	g∪a∪{(x2k	NOUN
ejpam-4598	190	15	,	,	PUNCT
ejpam-4598	190	16	0	0	NUM
ejpam-4598	190	17	)	)	PUNCT
ejpam-4598	190	18	:	:	PUNCT
ejpam-4598	191	1	k	k	PROPN
ejpam-4598	191	2	∈	∈	PROPN
ejpam-4598	191	3	n	n	CCONJ
ejpam-4598	191	4	}	}	PUNCT
ejpam-4598	191	5	andh	andh	NOUN
ejpam-4598	191	6	=	=	SYM
ejpam-4598	191	7	h∪a∪{(x2k+1	h∪a∪{(x2k+1	NOUN
ejpam-4598	191	8	,	,	PUNCT
ejpam-4598	191	9	0	0	NUM
ejpam-4598	191	10	)	)	PUNCT
ejpam-4598	191	11	:	:	PUNCT
ejpam-4598	192	1	k	k	PROPN
ejpam-4598	192	2	∈	∈	PROPN
ejpam-4598	192	3	n	n	CCONJ
ejpam-4598	192	4	}	}	PUNCT
ejpam-4598	192	5	,	,	PUNCT
ejpam-4598	192	6	where	where	SCONJ
ejpam-4598	192	7	a	a	PRON
ejpam-4598	192	8	=	=	X
ejpam-4598	192	9	{	{	PUNCT
ejpam-4598	192	10	(	(	PUNCT
ejpam-4598	192	11	0	0	NUM
ejpam-4598	192	12	,	,	PUNCT
ejpam-4598	192	13	1	1	NUM
ejpam-4598	192	14	n	n	CCONJ
ejpam-4598	192	15	)	)	PUNCT
ejpam-4598	192	16	:	:	PUNCT
ejpam-4598	192	17	n	n	X
ejpam-4598	192	18	∈	∈	PROPN
ejpam-4598	192	19	n	n	CCONJ
ejpam-4598	192	20	}	}	PUNCT
ejpam-4598	192	21	.	.	PUNCT
ejpam-4598	193	1	then	then	ADV
ejpam-4598	193	2	,	,	PUNCT
ejpam-4598	193	3	g	g	PROPN
ejpam-4598	193	4	andh	andh	NOUN
ejpam-4598	193	5	are	be	AUX
ejpam-4598	193	6	closed	closed	ADJ
ejpam-4598	193	7	-	-	PUNCT
ejpam-4598	193	8	domains	domain	NOUN
ejpam-4598	193	9	inx	inx	VERB
ejpam-4598	193	10	such	such	ADJ
ejpam-4598	193	11	thatg∩h	thatg∩h	NOUN
ejpam-4598	193	12	=	=	NOUN
ejpam-4598	193	13	a.	a.	NOUN
ejpam-4598	193	14	hence	hence	ADV
ejpam-4598	193	15	,	,	PUNCT
ejpam-4598	193	16	a	a	PRON
ejpam-4598	193	17	is	be	AUX
ejpam-4598	193	18	π	π	NOUN
ejpam-4598	193	19	-	-	VERB
ejpam-4598	193	20	closed	closed	ADJ
ejpam-4598	193	21	.	.	PUNCT
ejpam-4598	194	1	since	since	SCONJ
ejpam-4598	194	2	a∩l0	a∩l0	NOUN
ejpam-4598	194	3	=	=	PUNCT
ejpam-4598	194	4	∅	∅	NOUN
ejpam-4598	194	5	and	and	CCONJ
ejpam-4598	194	6	they	they	PRON
ejpam-4598	194	7	can	can	AUX
ejpam-4598	194	8	not	not	PART
ejpam-4598	194	9	be	be	AUX
ejpam-4598	194	10	separated	separate	VERB
ejpam-4598	194	11	[	[	PUNCT
ejpam-4598	194	12	30	30	NUM
ejpam-4598	194	13	]	]	PUNCT
ejpam-4598	194	14	,	,	PUNCT
ejpam-4598	194	15	we	we	PRON
ejpam-4598	194	16	obtain	obtain	VERB
ejpam-4598	194	17	that	that	PRON
ejpam-4598	194	18	:	:	PUNCT
ejpam-4598	194	19	x	x	X
ejpam-4598	194	20	is	be	AUX
ejpam-4598	194	21	not	not	PART
ejpam-4598	194	22	quasi	quasi	ADJ
ejpam-4598	194	23	-	-	ADJ
ejpam-4598	194	24	normal	normal	ADJ
ejpam-4598	194	25	.	.	PUNCT
ejpam-4598	195	1	it	it	PRON
ejpam-4598	195	2	is	be	AUX
ejpam-4598	195	3	easy	easy	ADJ
ejpam-4598	195	4	to	to	PART
ejpam-4598	195	5	show	show	VERB
ejpam-4598	195	6	that	that	SCONJ
ejpam-4598	195	7	x	x	PRON
ejpam-4598	195	8	can	can	AUX
ejpam-4598	195	9	not	not	PART
ejpam-4598	195	10	be	be	AUX
ejpam-4598	195	11	semi	semi	ADJ
ejpam-4598	195	12	-	-	ADJ
ejpam-4598	195	13	normal	normal	ADJ
ejpam-4598	195	14	.	.	PUNCT
ejpam-4598	196	1	claim	claim	NOUN
ejpam-4598	196	2	2	2	NUM
ejpam-4598	196	3	:	:	PUNCT
ejpam-4598	196	4	the	the	DET
ejpam-4598	196	5	thomas	thomas	PROPN
ejpam-4598	196	6	’	'	PUNCT
ejpam-4598	196	7	plank	plank	NOUN
ejpam-4598	196	8	topology	topology	NOUN
ejpam-4598	196	9	is	be	AUX
ejpam-4598	196	10	not	not	PART
ejpam-4598	196	11	almost	almost	ADV
ejpam-4598	196	12	-	-	PUNCT
ejpam-4598	196	13	normal	normal	ADJ
ejpam-4598	196	14	.	.	PUNCT
ejpam-4598	197	1	proof	proof	NOUN
ejpam-4598	197	2	of	of	ADP
ejpam-4598	197	3	the	the	DET
ejpam-4598	197	4	claim	claim	NOUN
ejpam-4598	197	5	2	2	NUM
ejpam-4598	197	6	:	:	PUNCT
ejpam-4598	197	7	it	it	PRON
ejpam-4598	197	8	can	can	AUX
ejpam-4598	197	9	be	be	AUX
ejpam-4598	197	10	observed	observe	VERB
ejpam-4598	197	11	that	that	SCONJ
ejpam-4598	197	12	,	,	PUNCT
ejpam-4598	197	13	a1	a1	NOUN
ejpam-4598	197	14	=	=	SYM
ejpam-4598	197	15	{	{	PUNCT
ejpam-4598	197	16	(	(	PUNCT
ejpam-4598	197	17	0	0	NUM
ejpam-4598	197	18	,	,	PUNCT
ejpam-4598	197	19	1	1	NUM
ejpam-4598	197	20	2n	2n	NUM
ejpam-4598	197	21	)	)	PUNCT
ejpam-4598	197	22	:	:	PUNCT
ejpam-4598	197	23	n	n	X
ejpam-4598	197	24	∈	∈	PROPN
ejpam-4598	197	25	n	n	CCONJ
ejpam-4598	197	26	}	}	PUNCT
ejpam-4598	197	27	is	be	AUX
ejpam-4598	197	28	a	a	DET
ejpam-4598	197	29	closed	closed	ADJ
ejpam-4598	197	30	subset	subset	NOUN
ejpam-4598	197	31	of	of	ADP
ejpam-4598	197	32	x	x	PUNCT
ejpam-4598	197	33	and	and	CCONJ
ejpam-4598	197	34	u	u	X
ejpam-4598	197	35	=	=	PUNCT
ejpam-4598	197	36	⋃	⋃	NOUN
ejpam-4598	197	37	n∈n	n∈n	NOUN
ejpam-4598	197	38	l2n	l2n	ADP
ejpam-4598	197	39	is	be	AUX
ejpam-4598	197	40	an	an	DET
ejpam-4598	197	41	open	open	ADJ
ejpam-4598	197	42	-	-	PUNCT
ejpam-4598	197	43	domain	domain	NOUN
ejpam-4598	197	44	subset	subset	NOUN
ejpam-4598	197	45	of	of	ADP
ejpam-4598	197	46	x	x	SYM
ejpam-4598	197	47	such	such	ADJ
ejpam-4598	197	48	that	that	DET
ejpam-4598	197	49	a1	a1	NOUN
ejpam-4598	197	50	⊆	⊆	NUM
ejpam-4598	197	51	u	u	NOUN
ejpam-4598	197	52	.	.	PUNCT
ejpam-4598	198	1	then	then	ADV
ejpam-4598	198	2	,	,	PUNCT
ejpam-4598	198	3	for	for	ADP
ejpam-4598	198	4	each	each	DET
ejpam-4598	198	5	open	open	ADJ
ejpam-4598	198	6	subset	subset	NOUN
ejpam-4598	198	7	w	w	NOUN
ejpam-4598	198	8	of	of	ADP
ejpam-4598	198	9	x	x	SYM
ejpam-4598	198	10	such	such	ADJ
ejpam-4598	198	11	that	that	DET
ejpam-4598	198	12	a1	a1	NOUN
ejpam-4598	198	13	⊂	⊂	PROPN
ejpam-4598	198	14	w	w	PROPN
ejpam-4598	198	15	,	,	PUNCT
ejpam-4598	198	16	we	we	PRON
ejpam-4598	198	17	have	have	AUX
ejpam-4598	198	18	:	:	PUNCT
ejpam-4598	198	19	a1	a1	VERB
ejpam-4598	198	20	⊆	⊆	NUM
ejpam-4598	198	21	w	w	ADP
ejpam-4598	198	22	⊆	⊆	NUM
ejpam-4598	198	23	w	w	NOUN
ejpam-4598	198	24	̸⊆	̸⊆	NOUN
ejpam-4598	198	25	u	u	NOUN
ejpam-4598	198	26	because	because	SCONJ
ejpam-4598	198	27	there	there	PRON
ejpam-4598	198	28	are	be	VERB
ejpam-4598	198	29	some	some	DET
ejpam-4598	198	30	points	point	NOUN
ejpam-4598	198	31	(	(	PUNCT
ejpam-4598	198	32	x	x	X
ejpam-4598	198	33	,	,	PUNCT
ejpam-4598	198	34	0	0	NUM
ejpam-4598	198	35	)	)	PUNCT
ejpam-4598	198	36	∈	∈	PROPN
ejpam-4598	198	37	w	w	NOUN
ejpam-4598	198	38	,	,	PUNCT
ejpam-4598	198	39	and	and	CCONJ
ejpam-4598	198	40	(	(	PUNCT
ejpam-4598	198	41	x	x	NOUN
ejpam-4598	198	42	,	,	PUNCT
ejpam-4598	198	43	0	0	NUM
ejpam-4598	198	44	)	)	PUNCT
ejpam-4598	198	45	̸∈	̸∈	PROPN
ejpam-4598	198	46	u	u	PROPN
ejpam-4598	198	47	for	for	ADP
ejpam-4598	198	48	each	each	DET
ejpam-4598	198	49	(	(	PUNCT
ejpam-4598	198	50	x	x	NOUN
ejpam-4598	198	51	,	,	PUNCT
ejpam-4598	198	52	0	0	NUM
ejpam-4598	198	53	)	)	PUNCT
ejpam-4598	198	54	∈	∈	PROPN
ejpam-4598	198	55	l0	l0	PROPN
ejpam-4598	198	56	.	.	PUNCT
ejpam-4598	199	1	hence	hence	ADV
ejpam-4598	199	2	,	,	PUNCT
ejpam-4598	199	3	x	x	PRON
ejpam-4598	199	4	is	be	AUX
ejpam-4598	199	5	not	not	PART
ejpam-4598	199	6	almost	almost	ADV
ejpam-4598	199	7	-	-	PUNCT
ejpam-4598	199	8	normal	normal	ADJ
ejpam-4598	199	9	.	.	PUNCT
ejpam-4598	200	1	note	note	VERB
ejpam-4598	200	2	that	that	SCONJ
ejpam-4598	200	3	:	:	PUNCT
ejpam-4598	200	4	a	a	X
ejpam-4598	200	5	=	=	X
ejpam-4598	200	6	{	{	PUNCT
ejpam-4598	200	7	(	(	PUNCT
ejpam-4598	200	8	0	0	NUM
ejpam-4598	200	9	,	,	PUNCT
ejpam-4598	200	10	1	1	NUM
ejpam-4598	200	11	n	n	CCONJ
ejpam-4598	200	12	)	)	PUNCT
ejpam-4598	200	13	;	;	PUNCT
ejpam-4598	200	14	n	n	X
ejpam-4598	200	15	∈	∈	PROPN
ejpam-4598	200	16	n	n	CCONJ
ejpam-4598	200	17	}	}	PUNCT
ejpam-4598	200	18	and	and	CCONJ
ejpam-4598	200	19	l0	l0	PROPN
ejpam-4598	200	20	are	be	AUX
ejpam-4598	200	21	disjoint	disjoint	NOUN
ejpam-4598	200	22	π	π	PROPN
ejpam-4598	200	23	-	-	ADJ
ejpam-4598	200	24	closed	closed	ADJ
ejpam-4598	200	25	subsets	subset	NOUN
ejpam-4598	200	26	that	that	PRON
ejpam-4598	200	27	can	can	AUX
ejpam-4598	200	28	not	not	PART
ejpam-4598	200	29	be	be	AUX
ejpam-4598	200	30	separated	separate	VERB
ejpam-4598	200	31	.	.	PUNCT
ejpam-4598	201	1	if	if	SCONJ
ejpam-4598	201	2	u	u	PROPN
ejpam-4598	201	3	=	=	PUNCT
ejpam-4598	201	4	⋃	⋃	NOUN
ejpam-4598	201	5	n∈n	n∈n	NOUN
ejpam-4598	201	6	ln	ln	ADV
ejpam-4598	201	7	is	be	AUX
ejpam-4598	201	8	π	π	ADJ
ejpam-4598	201	9	-	-	ADJ
ejpam-4598	201	10	open	open	ADJ
ejpam-4598	201	11	subset	subset	NOUN
ejpam-4598	201	12	of	of	ADP
ejpam-4598	201	13	x	x	SYM
ejpam-4598	201	14	such	such	ADJ
ejpam-4598	201	15	that	that	SCONJ
ejpam-4598	201	16	a	a	DET
ejpam-4598	201	17	⊆	⊆	NUM
ejpam-4598	201	18	u	u	NOUN
ejpam-4598	201	19	.	.	PUNCT
ejpam-4598	202	1	for	for	ADP
ejpam-4598	202	2	each	each	DET
ejpam-4598	202	3	open	open	ADJ
ejpam-4598	202	4	set	set	NOUN
ejpam-4598	202	5	w	w	PROPN
ejpam-4598	202	6	of	of	ADP
ejpam-4598	202	7	x	x	SYM
ejpam-4598	202	8	,	,	PUNCT
ejpam-4598	202	9	we	we	PRON
ejpam-4598	202	10	have	have	VERB
ejpam-4598	202	11	:	:	PUNCT
ejpam-4598	202	12	a	a	DET
ejpam-4598	202	13	⊆	⊆	NUM
ejpam-4598	202	14	w	w	ADP
ejpam-4598	202	15	⊆	⊆	NUM
ejpam-4598	202	16	w	w	NOUN
ejpam-4598	202	17	̸⊆	̸⊆	NOUN
ejpam-4598	202	18	u	u	NOUN
ejpam-4598	202	19	and	and	CCONJ
ejpam-4598	202	20	a	a	DET
ejpam-4598	202	21	⊆	⊆	NUM
ejpam-4598	202	22	w	w	ADP
ejpam-4598	202	23	⊆	⊆	NUM
ejpam-4598	202	24	int(w	int(w	NOUN
ejpam-4598	202	25	)	)	PUNCT
ejpam-4598	202	26	̸⊆	̸⊆	NOUN
ejpam-4598	202	27	u	u	NOUN
ejpam-4598	202	28	.	.	PUNCT
ejpam-4598	203	1	thus	thus	ADV
ejpam-4598	203	2	,	,	PUNCT
ejpam-4598	203	3	x	x	PRON
ejpam-4598	203	4	is	be	AUX
ejpam-4598	203	5	neither	neither	CCONJ
ejpam-4598	203	6	quasi	quasi	ADJ
ejpam-4598	203	7	-	-	ADJ
ejpam-4598	203	8	normal	normal	ADJ
ejpam-4598	203	9	nor	nor	CCONJ
ejpam-4598	203	10	semi	semi	ADJ
ejpam-4598	203	11	-	-	ADJ
ejpam-4598	203	12	normal	normal	ADJ
ejpam-4598	203	13	.	.	PUNCT
ejpam-4598	204	1	therefore	therefore	ADV
ejpam-4598	204	2	,	,	PUNCT
ejpam-4598	204	3	the	the	DET
ejpam-4598	204	4	thomas	thomas	PROPN
ejpam-4598	204	5	’	'	PUNCT
ejpam-4598	204	6	plank	plank	NOUN
ejpam-4598	204	7	topology	topology	NOUN
ejpam-4598	204	8	is	be	AUX
ejpam-4598	204	9	an	an	DET
ejpam-4598	204	10	epicompletely	epicompletely	ADV
ejpam-4598	204	11	-	-	PUNCT
ejpam-4598	204	12	regular	regular	ADJ
ejpam-4598	204	13	space	space	NOUN
ejpam-4598	204	14	,	,	PUNCT
ejpam-4598	204	15	which	which	PRON
ejpam-4598	204	16	is	be	AUX
ejpam-4598	204	17	neither	neither	CCONJ
ejpam-4598	204	18	almost	almost	ADV
ejpam-4598	204	19	-	-	PUNCT
ejpam-4598	204	20	normal	normal	ADJ
ejpam-4598	204	21	,	,	PUNCT
ejpam-4598	204	22	semi	semi	ADJ
ejpam-4598	204	23	-	-	ADJ
ejpam-4598	204	24	normal	normal	ADJ
ejpam-4598	204	25	nor	nor	CCONJ
ejpam-4598	204	26	quasi	quasi	ADJ
ejpam-4598	204	27	-	-	ADJ
ejpam-4598	204	28	normal	normal	ADJ
ejpam-4598	204	29	.	.	PUNCT
ejpam-4598	205	1	i.	i.	PROPN
ejpam-4598	205	2	alshammari	alshammari	PROPN
ejpam-4598	205	3	/	/	SYM
ejpam-4598	205	4	eur	eur	PROPN
ejpam-4598	205	5	.	.	PUNCT
ejpam-4598	206	1	j.	j.	PROPN
ejpam-4598	206	2	pure	pure	PROPN
ejpam-4598	206	3	appl	appl	PROPN
ejpam-4598	206	4	.	.	PROPN
ejpam-4598	206	5	math	math	PROPN
ejpam-4598	206	6	,	,	PUNCT
ejpam-4598	206	7	15	15	NUM
ejpam-4598	206	8	(	(	PUNCT
ejpam-4598	206	9	4	4	NUM
ejpam-4598	206	10	)	)	PUNCT
ejpam-4598	206	11	(	(	PUNCT
ejpam-4598	206	12	2022	2022	NUM
ejpam-4598	206	13	)	)	PUNCT
ejpam-4598	206	14	,	,	PUNCT
ejpam-4598	206	15	1808	1808	NUM
ejpam-4598	206	16	-	-	SYM
ejpam-4598	206	17	1821	1821	NUM
ejpam-4598	206	18	1814	1814	NUM
ejpam-4598	206	19	note	note	VERB
ejpam-4598	206	20	that	that	SCONJ
ejpam-4598	206	21	:	:	PUNCT
ejpam-4598	206	22	an	an	DET
ejpam-4598	206	23	epi	epi	NOUN
ejpam-4598	206	24	-	-	NOUN
ejpam-4598	206	25	regularity	regularity	NOUN
ejpam-4598	206	26	does	do	AUX
ejpam-4598	206	27	not	not	PART
ejpam-4598	206	28	imply	imply	VERB
ejpam-4598	206	29	to	to	ADP
ejpam-4598	206	30	epi	epi	VERB
ejpam-4598	206	31	-	-	ADJ
ejpam-4598	206	32	complete	complete	ADJ
ejpam-4598	206	33	-	-	PUNCT
ejpam-4598	206	34	regularity	regularity	NOUN
ejpam-4598	206	35	as	as	SCONJ
ejpam-4598	206	36	shown	show	VERB
ejpam-4598	206	37	by	by	ADP
ejpam-4598	206	38	the	the	DET
ejpam-4598	206	39	next	next	ADJ
ejpam-4598	206	40	example	example	NOUN
ejpam-4598	206	41	:	:	PUNCT
ejpam-4598	206	42	example	example	NOUN
ejpam-4598	206	43	9	9	NUM
ejpam-4598	206	44	.	.	PUNCT
ejpam-4598	207	1	the	the	DET
ejpam-4598	207	2	tychonoff	tychonoff	NOUN
ejpam-4598	207	3	corkscrew	corkscrew	NOUN
ejpam-4598	207	4	topology	topology	NOUN
ejpam-4598	207	5	:	:	PUNCT
ejpam-4598	207	6	[	[	X
ejpam-4598	207	7	30	30	NUM
ejpam-4598	207	8	,	,	PUNCT
ejpam-4598	207	9	example	example	NOUN
ejpam-4598	207	10	90	90	NUM
ejpam-4598	207	11	]	]	PUNCT
ejpam-4598	207	12	,	,	PUNCT
ejpam-4598	207	13	let	let	VERB
ejpam-4598	207	14	x	x	PUNCT
ejpam-4598	207	15	=	=	PRON
ejpam-4598	207	16	s	s	PROPN
ejpam-4598	207	17	∪{a+	∪{a+	PROPN
ejpam-4598	207	18	,	,	PUNCT
ejpam-4598	207	19	a−	a−	PROPN
ejpam-4598	207	20	}	}	PUNCT
ejpam-4598	207	21	,	,	PUNCT
ejpam-4598	207	22	where	where	SCONJ
ejpam-4598	207	23	(	(	PUNCT
ejpam-4598	207	24	s	s	X
ejpam-4598	207	25	,	,	PUNCT
ejpam-4598	207	26	t	t	PROPN
ejpam-4598	207	27	)	)	PUNCT
ejpam-4598	207	28	is	be	AUX
ejpam-4598	207	29	homeomorphic	homeomorphic	ADJ
ejpam-4598	207	30	to	to	ADP
ejpam-4598	207	31	the	the	DET
ejpam-4598	207	32	deleted	delete	VERB
ejpam-4598	207	33	tychonoff	tychonoff	NOUN
ejpam-4598	207	34	plank	plank	NOUN
ejpam-4598	207	35	topology	topology	NOUN
ejpam-4598	207	36	[	[	X
ejpam-4598	207	37	30	30	NUM
ejpam-4598	207	38	]	]	PUNCT
ejpam-4598	207	39	.	.	PUNCT
ejpam-4598	208	1	the	the	DET
ejpam-4598	208	2	basic	basic	ADJ
ejpam-4598	208	3	open	open	ADJ
ejpam-4598	208	4	subset	subset	NOUN
ejpam-4598	208	5	u	u	NOUN
ejpam-4598	208	6	of	of	ADP
ejpam-4598	208	7	a+	a+	PUNCT
ejpam-4598	208	8	contains	contain	VERB
ejpam-4598	208	9	all	all	DET
ejpam-4598	208	10	points	point	NOUN
ejpam-4598	208	11	ofx	ofx	NOUN
ejpam-4598	208	12	which	which	PRON
ejpam-4598	208	13	lies	lie	VERB
ejpam-4598	208	14	above	above	ADP
ejpam-4598	208	15	a	a	DET
ejpam-4598	208	16	certain	certain	ADJ
ejpam-4598	208	17	level	level	NOUN
ejpam-4598	208	18	k.	k.	PROPN
ejpam-4598	209	1	that	that	PRON
ejpam-4598	209	2	means	mean	VERB
ejpam-4598	209	3	:	:	PUNCT
ejpam-4598	209	4	u	u	NOUN
ejpam-4598	209	5	=	=	PUNCT
ejpam-4598	209	6	{	{	PUNCT
ejpam-4598	209	7	x	x	SYM
ejpam-4598	209	8	∈	∈	PROPN
ejpam-4598	209	9	x	x	X
ejpam-4598	209	10	:	:	PUNCT
ejpam-4598	209	11	l(x	l(x	PROPN
ejpam-4598	209	12	)	)	PUNCT
ejpam-4598	209	13	>	>	X
ejpam-4598	209	14	k+1	k+1	X
ejpam-4598	209	15	}	}	PUNCT
ejpam-4598	209	16	.	.	PUNCT
ejpam-4598	210	1	the	the	DET
ejpam-4598	210	2	basic	basic	ADJ
ejpam-4598	210	3	open	open	NOUN
ejpam-4598	210	4	subset	subset	ADJ
ejpam-4598	210	5	v	v	NOUN
ejpam-4598	210	6	of	of	ADP
ejpam-4598	210	7	a−	a−	PROPN
ejpam-4598	210	8	contains	contain	VERB
ejpam-4598	210	9	all	all	DET
ejpam-4598	210	10	points	point	NOUN
ejpam-4598	210	11	of	of	ADP
ejpam-4598	210	12	x	x	PUNCT
ejpam-4598	210	13	which	which	PRON
ejpam-4598	210	14	lies	lie	VERB
ejpam-4598	210	15	below	below	ADP
ejpam-4598	210	16	a	a	DET
ejpam-4598	210	17	certain	certain	ADJ
ejpam-4598	210	18	level	level	NOUN
ejpam-4598	210	19	k.	k.	PROPN
ejpam-4598	211	1	that	that	PRON
ejpam-4598	211	2	means	mean	VERB
ejpam-4598	211	3	:	:	PUNCT
ejpam-4598	211	4	v	v	X
ejpam-4598	211	5	=	=	SYM
ejpam-4598	211	6	{	{	PUNCT
ejpam-4598	211	7	x	x	SYM
ejpam-4598	211	8	∈	∈	NOUN
ejpam-4598	211	9	x	x	X
ejpam-4598	211	10	:	:	PUNCT
ejpam-4598	211	11	l(x	l(x	PROPN
ejpam-4598	211	12	)	)	PUNCT
ejpam-4598	211	13	<	<	X
ejpam-4598	211	14	k+1	k+1	X
ejpam-4598	211	15	}	}	PUNCT
ejpam-4598	211	16	.	.	PUNCT
ejpam-4598	212	1	the	the	DET
ejpam-4598	212	2	space	space	NOUN
ejpam-4598	212	3	(	(	PUNCT
ejpam-4598	212	4	x	x	X
ejpam-4598	212	5	,	,	PUNCT
ejpam-4598	212	6	t	t	PROPN
ejpam-4598	212	7	)	)	PUNCT
ejpam-4598	212	8	is	be	AUX
ejpam-4598	212	9	a	a	DET
ejpam-4598	212	10	hausdorff	hausdorff	NOUN
ejpam-4598	212	11	,	,	PUNCT
ejpam-4598	212	12	regular	regular	ADJ
ejpam-4598	212	13	and	and	CCONJ
ejpam-4598	212	14	semi	semi	ADJ
ejpam-4598	212	15	-	-	ADJ
ejpam-4598	212	16	regular	regular	ADJ
ejpam-4598	212	17	space	space	NOUN
ejpam-4598	212	18	,	,	PUNCT
ejpam-4598	212	19	which	which	PRON
ejpam-4598	212	20	is	be	AUX
ejpam-4598	212	21	neither	neither	DET
ejpam-4598	212	22	tychonoff	tychonoff	NOUN
ejpam-4598	212	23	,	,	PUNCT
ejpam-4598	212	24	urysohn	urysohn	NOUN
ejpam-4598	212	25	,	,	PUNCT
ejpam-4598	212	26	locallycompact	locallycompact	NOUN
ejpam-4598	212	27	,	,	PUNCT
ejpam-4598	212	28	lindelöf	lindelöf	PROPN
ejpam-4598	212	29	,	,	PUNCT
ejpam-4598	212	30	first	first	ADJ
ejpam-4598	212	31	-	-	PUNCT
ejpam-4598	212	32	countable	countable	ADJ
ejpam-4598	212	33	,	,	PUNCT
ejpam-4598	212	34	normal	normal	ADJ
ejpam-4598	212	35	nor	nor	CCONJ
ejpam-4598	212	36	completely	completely	ADV
ejpam-4598	212	37	-	-	PUNCT
ejpam-4598	212	38	regular	regular	ADJ
ejpam-4598	212	39	[	[	X
ejpam-4598	212	40	30	30	NUM
ejpam-4598	212	41	]	]	PUNCT
ejpam-4598	212	42	.	.	PUNCT
ejpam-4598	213	1	since	since	SCONJ
ejpam-4598	213	2	(	(	PUNCT
ejpam-4598	213	3	x	x	X
ejpam-4598	213	4	,	,	PUNCT
ejpam-4598	213	5	t	t	PROPN
ejpam-4598	213	6	)	)	PUNCT
ejpam-4598	213	7	is	be	AUX
ejpam-4598	213	8	a	a	DET
ejpam-4598	213	9	hausdorff	hausdorff	NOUN
ejpam-4598	213	10	regular	regular	ADJ
ejpam-4598	213	11	space	space	NOUN
ejpam-4598	213	12	,	,	PUNCT
ejpam-4598	213	13	it	it	PRON
ejpam-4598	213	14	is	be	AUX
ejpam-4598	213	15	epi	epi	NOUN
ejpam-4598	213	16	-	-	NOUN
ejpam-4598	213	17	regular	regular	ADJ
ejpam-4598	213	18	.	.	PUNCT
ejpam-4598	214	1	since	since	SCONJ
ejpam-4598	214	2	every	every	DET
ejpam-4598	214	3	regular	regular	ADJ
ejpam-4598	214	4	almost	almost	ADV
ejpam-4598	214	5	-	-	PUNCT
ejpam-4598	214	6	normal	normal	ADJ
ejpam-4598	214	7	space	space	NOUN
ejpam-4598	214	8	is	be	AUX
ejpam-4598	214	9	completely	completely	ADV
ejpam-4598	214	10	-	-	PUNCT
ejpam-4598	214	11	regular	regular	ADJ
ejpam-4598	214	12	[	[	X
ejpam-4598	214	13	28	28	NUM
ejpam-4598	214	14	]	]	PUNCT
ejpam-4598	214	15	,	,	PUNCT
ejpam-4598	214	16	and	and	CCONJ
ejpam-4598	214	17	x	x	X
ejpam-4598	214	18	is	be	AUX
ejpam-4598	214	19	regular	regular	ADJ
ejpam-4598	214	20	non	non	ADJ
ejpam-4598	214	21	completely	completely	ADV
ejpam-4598	214	22	-	-	PUNCT
ejpam-4598	214	23	regular	regular	ADJ
ejpam-4598	214	24	,	,	PUNCT
ejpam-4598	214	25	we	we	PRON
ejpam-4598	214	26	obtain	obtain	VERB
ejpam-4598	214	27	:	:	PUNCT
ejpam-4598	214	28	(	(	PUNCT
ejpam-4598	214	29	x	x	X
ejpam-4598	214	30	,	,	PUNCT
ejpam-4598	214	31	t	t	PROPN
ejpam-4598	214	32	)	)	PUNCT
ejpam-4598	214	33	is	be	AUX
ejpam-4598	214	34	not	not	PART
ejpam-4598	214	35	almost	almost	ADV
ejpam-4598	214	36	-	-	PUNCT
ejpam-4598	214	37	normal	normal	ADJ
ejpam-4598	214	38	.	.	PUNCT
ejpam-4598	215	1	claim	claim	VERB
ejpam-4598	215	2	1	1	NUM
ejpam-4598	215	3	:	:	PUNCT
ejpam-4598	215	4	any	any	DET
ejpam-4598	215	5	hausdorff	hausdorff	NOUN
ejpam-4598	215	6	topology	topology	NOUN
ejpam-4598	215	7	t	t	PROPN
ejpam-4598	215	8	′	′	NUM
ejpam-4598	215	9	onx	onx	PROPN
ejpam-4598	215	10	,	,	PUNCT
ejpam-4598	215	11	which	which	PRON
ejpam-4598	215	12	is	be	AUX
ejpam-4598	215	13	coarser	coarse	ADJ
ejpam-4598	215	14	than	than	ADP
ejpam-4598	215	15	t	t	PROPN
ejpam-4598	215	16	,	,	PUNCT
ejpam-4598	215	17	can	can	AUX
ejpam-4598	215	18	not	not	PART
ejpam-4598	215	19	be	be	AUX
ejpam-4598	215	20	completelyregular	completelyregular	ADJ
ejpam-4598	215	21	.	.	PUNCT
ejpam-4598	216	1	proof	proof	NOUN
ejpam-4598	216	2	of	of	ADP
ejpam-4598	216	3	the	the	DET
ejpam-4598	216	4	claim	claim	NOUN
ejpam-4598	216	5	1	1	NUM
ejpam-4598	216	6	:	:	PUNCT
ejpam-4598	216	7	let	let	VERB
ejpam-4598	216	8	t	t	PROPN
ejpam-4598	216	9	′	′	NOUN
ejpam-4598	216	10	be	be	AUX
ejpam-4598	216	11	any	any	DET
ejpam-4598	216	12	hausdorff	hausdorff	NOUN
ejpam-4598	216	13	topology	topology	NOUN
ejpam-4598	216	14	on	on	ADP
ejpam-4598	216	15	x	x	PUNCT
ejpam-4598	216	16	which	which	PRON
ejpam-4598	216	17	is	be	AUX
ejpam-4598	216	18	coarser	coarse	ADJ
ejpam-4598	216	19	than	than	ADP
ejpam-4598	216	20	t	t	PROPN
ejpam-4598	216	21	.	.	PUNCT
ejpam-4598	217	1	i	i	PRON
ejpam-4598	217	2	show	show	VERB
ejpam-4598	217	3	(	(	PUNCT
ejpam-4598	217	4	x	x	X
ejpam-4598	217	5	,	,	PUNCT
ejpam-4598	217	6	t	t	PROPN
ejpam-4598	217	7	′	′	NUM
ejpam-4598	217	8	)	)	PUNCT
ejpam-4598	217	9	is	be	AUX
ejpam-4598	217	10	not	not	PART
ejpam-4598	217	11	a	a	DET
ejpam-4598	217	12	completely	completely	ADV
ejpam-4598	217	13	-	-	PUNCT
ejpam-4598	217	14	regular	regular	ADJ
ejpam-4598	217	15	space	space	NOUN
ejpam-4598	217	16	.	.	PUNCT
ejpam-4598	218	1	let	let	VERB
ejpam-4598	218	2	a	a	DET
ejpam-4598	218	3	be	be	AUX
ejpam-4598	218	4	any	any	DET
ejpam-4598	218	5	closed	closed	ADJ
ejpam-4598	218	6	subset	subset	NOUN
ejpam-4598	218	7	of	of	ADP
ejpam-4598	218	8	(	(	PUNCT
ejpam-4598	218	9	x	x	PROPN
ejpam-4598	218	10	,	,	PUNCT
ejpam-4598	218	11	t	t	PROPN
ejpam-4598	218	12	′	′	NUM
ejpam-4598	218	13	)	)	PUNCT
ejpam-4598	218	14	and	and	CCONJ
ejpam-4598	218	15	a+	a+	PUNCT
ejpam-4598	218	16	̸∈	̸∈	PROPN
ejpam-4598	218	17	a.	a.	PROPN
ejpam-4598	218	18	then	then	ADV
ejpam-4598	218	19	,	,	PUNCT
ejpam-4598	218	20	a	a	PRON
ejpam-4598	218	21	is	be	AUX
ejpam-4598	218	22	a	a	DET
ejpam-4598	218	23	closed	closed	ADJ
ejpam-4598	218	24	subset	subset	NOUN
ejpam-4598	218	25	of	of	ADP
ejpam-4598	218	26	(	(	PUNCT
ejpam-4598	218	27	x	x	PROPN
ejpam-4598	218	28	,	,	PUNCT
ejpam-4598	218	29	t	t	PROPN
ejpam-4598	218	30	)	)	PUNCT
ejpam-4598	218	31	and	and	CCONJ
ejpam-4598	218	32	a+	a+	PUNCT
ejpam-4598	218	33	̸∈	̸∈	PROPN
ejpam-4598	218	34	a.	a.	PROPN
ejpam-4598	218	35	thus	thus	ADV
ejpam-4598	218	36	,	,	PUNCT
ejpam-4598	218	37	x	x	SYM
ejpam-4598	218	38	\	\	PROPN
ejpam-4598	219	1	a	a	PRON
ejpam-4598	219	2	is	be	AUX
ejpam-4598	219	3	an	an	DET
ejpam-4598	219	4	open	open	ADJ
ejpam-4598	219	5	subset	subset	NOUN
ejpam-4598	219	6	of	of	ADP
ejpam-4598	219	7	(	(	PUNCT
ejpam-4598	219	8	x	x	PROPN
ejpam-4598	219	9	,	,	PUNCT
ejpam-4598	219	10	t	t	PROPN
ejpam-4598	219	11	)	)	PUNCT
ejpam-4598	219	12	containing	contain	VERB
ejpam-4598	219	13	a+	a+	PROPN
ejpam-4598	219	14	.	.	PUNCT
ejpam-4598	219	15	but	but	CCONJ
ejpam-4598	219	16	a+	a+	PUNCT
ejpam-4598	219	17	can	can	AUX
ejpam-4598	219	18	not	not	PART
ejpam-4598	219	19	be	be	AUX
ejpam-4598	219	20	separated	separate	VERB
ejpam-4598	219	21	by	by	ADP
ejpam-4598	219	22	a	a	DET
ejpam-4598	219	23	continuous	continuous	ADJ
ejpam-4598	219	24	function	function	NOUN
ejpam-4598	219	25	from	from	ADP
ejpam-4598	219	26	a	a	DET
ejpam-4598	219	27	closed	closed	ADJ
ejpam-4598	219	28	subset	subset	NOUN
ejpam-4598	219	29	a	a	PRON
ejpam-4598	219	30	of	of	ADP
ejpam-4598	219	31	x	x	PUNCT
ejpam-4598	219	32	consisting	consist	VERB
ejpam-4598	219	33	the	the	DET
ejpam-4598	219	34	complement	complement	NOUN
ejpam-4598	219	35	of	of	ADP
ejpam-4598	219	36	the	the	DET
ejpam-4598	219	37	basis	basis	NOUN
ejpam-4598	219	38	neighborhood	neighborhood	NOUN
ejpam-4598	219	39	of	of	ADP
ejpam-4598	219	40	a+	a+	PUNCT
ejpam-4598	219	41	[	[	X
ejpam-4598	219	42	30	30	NUM
ejpam-4598	219	43	]	]	PUNCT
ejpam-4598	219	44	.	.	PUNCT
ejpam-4598	220	1	thus	thus	ADV
ejpam-4598	220	2	,	,	PUNCT
ejpam-4598	220	3	(	(	PUNCT
ejpam-4598	220	4	x	x	X
ejpam-4598	220	5	,	,	PUNCT
ejpam-4598	220	6	t	t	PROPN
ejpam-4598	220	7	′	′	NUM
ejpam-4598	220	8	)	)	PUNCT
ejpam-4598	220	9	is	be	AUX
ejpam-4598	220	10	not	not	PART
ejpam-4598	220	11	a	a	DET
ejpam-4598	220	12	completely	completely	ADV
ejpam-4598	220	13	-	-	PUNCT
ejpam-4598	220	14	regular	regular	ADJ
ejpam-4598	220	15	space	space	NOUN
ejpam-4598	220	16	.	.	PUNCT
ejpam-4598	221	1	therefore	therefore	ADV
ejpam-4598	221	2	,	,	PUNCT
ejpam-4598	221	3	any	any	DET
ejpam-4598	221	4	hausdorff	hausdorff	NOUN
ejpam-4598	221	5	topology	topology	NOUN
ejpam-4598	221	6	t	t	NOUN
ejpam-4598	221	7	′	′	NUM
ejpam-4598	221	8	on	on	ADP
ejpam-4598	221	9	x	x	X
ejpam-4598	221	10	,	,	PUNCT
ejpam-4598	221	11	which	which	PRON
ejpam-4598	221	12	is	be	AUX
ejpam-4598	221	13	coarser	coarse	ADJ
ejpam-4598	221	14	than	than	SCONJ
ejpam-4598	221	15	t	t	PROPN
ejpam-4598	221	16	can	can	AUX
ejpam-4598	221	17	not	not	PART
ejpam-4598	221	18	be	be	AUX
ejpam-4598	221	19	completely	completely	ADV
ejpam-4598	221	20	-	-	PUNCT
ejpam-4598	221	21	regular	regular	ADJ
ejpam-4598	221	22	.	.	PUNCT
ejpam-4598	222	1	hence	hence	ADV
ejpam-4598	222	2	,	,	PUNCT
ejpam-4598	222	3	(	(	PUNCT
ejpam-4598	222	4	x	x	X
ejpam-4598	222	5	,	,	PUNCT
ejpam-4598	222	6	t	t	PROPN
ejpam-4598	222	7	)	)	PUNCT
ejpam-4598	222	8	is	be	AUX
ejpam-4598	222	9	not	not	PART
ejpam-4598	222	10	epi	epi	NOUN
ejpam-4598	222	11	-	-	ADJ
ejpam-4598	222	12	completely	completely	ADV
ejpam-4598	222	13	-	-	PUNCT
ejpam-4598	222	14	regular	regular	ADJ
ejpam-4598	222	15	.	.	PUNCT
ejpam-4598	223	1	hence	hence	ADV
ejpam-4598	223	2	,	,	PUNCT
ejpam-4598	223	3	x	x	PRON
ejpam-4598	223	4	is	be	AUX
ejpam-4598	223	5	not	not	PART
ejpam-4598	223	6	epi	epi	NOUN
ejpam-4598	223	7	-	-	ADJ
ejpam-4598	223	8	almost	almost	ADV
ejpam-4598	223	9	-	-	PUNCT
ejpam-4598	223	10	normal	normal	ADJ
ejpam-4598	223	11	.	.	PUNCT
ejpam-4598	224	1	since	since	SCONJ
ejpam-4598	224	2	every	every	DET
ejpam-4598	224	3	t1	t1	NOUN
ejpam-4598	224	4	-	-	PUNCT
ejpam-4598	224	5	semi	semi	ADV
ejpam-4598	224	6	-	-	ADJ
ejpam-4598	224	7	regular	regular	ADJ
ejpam-4598	224	8	almost	almost	ADV
ejpam-4598	224	9	-	-	PUNCT
ejpam-4598	224	10	completely	completely	ADV
ejpam-4598	224	11	regular	regular	ADJ
ejpam-4598	224	12	space	space	NOUN
ejpam-4598	224	13	is	be	AUX
ejpam-4598	224	14	epi	epi	NOUN
ejpam-4598	224	15	-	-	ADJ
ejpam-4598	224	16	completely	completely	ADV
ejpam-4598	224	17	-	-	PUNCT
ejpam-4598	224	18	regular	regular	ADJ
ejpam-4598	224	19	(	(	PUNCT
ejpam-4598	224	20	corollary	corollary	ADJ
ejpam-4598	224	21	7	7	NUM
ejpam-4598	224	22	)	)	PUNCT
ejpam-4598	224	23	,	,	PUNCT
ejpam-4598	224	24	and	and	CCONJ
ejpam-4598	224	25	x	x	X
ejpam-4598	224	26	is	be	AUX
ejpam-4598	224	27	t1	t1	NOUN
ejpam-4598	224	28	-	-	PUNCT
ejpam-4598	224	29	semiregular	semiregular	ADJ
ejpam-4598	224	30	non	non	ADJ
ejpam-4598	224	31	epi	epi	NOUN
ejpam-4598	224	32	-	-	ADJ
ejpam-4598	224	33	completely	completely	ADV
ejpam-4598	224	34	-	-	PUNCT
ejpam-4598	224	35	regular	regular	ADJ
ejpam-4598	224	36	,	,	PUNCT
ejpam-4598	224	37	we	we	PRON
ejpam-4598	224	38	obtain	obtain	VERB
ejpam-4598	224	39	that	that	PRON
ejpam-4598	224	40	:	:	PUNCT
ejpam-4598	224	41	x	x	X
ejpam-4598	224	42	is	be	AUX
ejpam-4598	224	43	not	not	PART
ejpam-4598	224	44	almost	almost	ADV
ejpam-4598	224	45	-	-	PUNCT
ejpam-4598	224	46	completely	completely	ADV
ejpam-4598	224	47	regular	regular	ADJ
ejpam-4598	224	48	.	.	PUNCT
ejpam-4598	225	1	therefore	therefore	ADV
ejpam-4598	225	2	,	,	PUNCT
ejpam-4598	225	3	the	the	DET
ejpam-4598	225	4	tychonoff	tychonoff	NOUN
ejpam-4598	225	5	corkscrew	corkscrew	NOUN
ejpam-4598	225	6	topology	topology	NOUN
ejpam-4598	225	7	is	be	AUX
ejpam-4598	225	8	an	an	DET
ejpam-4598	225	9	epi	epi	ADJ
ejpam-4598	225	10	-	-	ADJ
ejpam-4598	225	11	regular	regular	ADJ
ejpam-4598	225	12	space	space	NOUN
ejpam-4598	225	13	,	,	PUNCT
ejpam-4598	225	14	which	which	PRON
ejpam-4598	225	15	is	be	AUX
ejpam-4598	225	16	neither	neither	CCONJ
ejpam-4598	225	17	epicompletely	epicompletely	ADV
ejpam-4598	225	18	-	-	PUNCT
ejpam-4598	225	19	regular	regular	ADJ
ejpam-4598	225	20	,	,	PUNCT
ejpam-4598	225	21	almost	almost	ADV
ejpam-4598	225	22	-	-	PUNCT
ejpam-4598	225	23	completely	completely	ADV
ejpam-4598	225	24	regular	regular	ADJ
ejpam-4598	225	25	nor	nor	CCONJ
ejpam-4598	225	26	epi	epi	NOUN
ejpam-4598	225	27	-	-	PUNCT
ejpam-4598	225	28	almost	almost	ADV
ejpam-4598	225	29	-	-	PUNCT
ejpam-4598	225	30	normal	normal	ADJ
ejpam-4598	225	31	.	.	PUNCT
ejpam-4598	226	1	note	note	VERB
ejpam-4598	226	2	that	that	SCONJ
ejpam-4598	226	3	:	:	PUNCT
ejpam-4598	226	4	the	the	DET
ejpam-4598	226	5	mrówka	mrówka	NOUN
ejpam-4598	226	6	space	space	NOUN
ejpam-4598	226	7	ψ(a	ψ(a	PROPN
ejpam-4598	226	8	)	)	PUNCT
ejpam-4598	227	1	[	[	X
ejpam-4598	227	2	15	15	NUM
ejpam-4598	227	3	,	,	PUNCT
ejpam-4598	227	4	example	example	NOUN
ejpam-4598	227	5	2.10	2.10	NUM
ejpam-4598	227	6	]	]	PUNCT
ejpam-4598	227	7	,	,	PUNCT
ejpam-4598	227	8	is	be	AUX
ejpam-4598	227	9	a	a	DET
ejpam-4598	227	10	tychonoff	tychonoff	NOUN
ejpam-4598	227	11	,	,	PUNCT
ejpam-4598	227	12	first	first	ADJ
ejpam-4598	227	13	-	-	PUNCT
ejpam-4598	227	14	countable	countable	ADJ
ejpam-4598	227	15	and	and	CCONJ
ejpam-4598	227	16	locally	locally	ADV
ejpam-4598	227	17	compact	compact	ADJ
ejpam-4598	227	18	space	space	NOUN
ejpam-4598	227	19	,	,	PUNCT
ejpam-4598	227	20	which	which	PRON
ejpam-4598	227	21	is	be	AUX
ejpam-4598	227	22	neither	neither	CCONJ
ejpam-4598	227	23	normal	normal	ADJ
ejpam-4598	227	24	,	,	PUNCT
ejpam-4598	227	25	countably	countably	ADV
ejpam-4598	227	26	-	-	ADJ
ejpam-4598	227	27	compact	compact	ADJ
ejpam-4598	227	28	nor	nor	CCONJ
ejpam-4598	227	29	epi	epi	NOUN
ejpam-4598	227	30	-	-	ADJ
ejpam-4598	227	31	normal	normal	ADJ
ejpam-4598	227	32	.	.	PUNCT
ejpam-4598	228	1	hence	hence	ADV
ejpam-4598	228	2	,	,	PUNCT
ejpam-4598	228	3	it	it	PRON
ejpam-4598	228	4	is	be	AUX
ejpam-4598	228	5	an	an	DET
ejpam-4598	228	6	epi	epi	NOUN
ejpam-4598	228	7	-	-	PUNCT
ejpam-4598	228	8	completely	completely	ADV
ejpam-4598	228	9	-	-	PUNCT
ejpam-4598	228	10	regular	regular	ADJ
ejpam-4598	228	11	space	space	NOUN
ejpam-4598	228	12	,	,	PUNCT
ejpam-4598	228	13	which	which	PRON
ejpam-4598	228	14	is	be	AUX
ejpam-4598	228	15	not	not	PART
ejpam-4598	228	16	epi	epi	NOUN
ejpam-4598	228	17	-	-	ADJ
ejpam-4598	228	18	normal	normal	ADJ
ejpam-4598	228	19	.	.	PUNCT
ejpam-4598	229	1	the	the	DET
ejpam-4598	229	2	space	space	NOUN
ejpam-4598	229	3	presented	present	VERB
ejpam-4598	229	4	in	in	ADP
ejpam-4598	229	5	[	[	X
ejpam-4598	229	6	15	15	NUM
ejpam-4598	229	7	,	,	PUNCT
ejpam-4598	229	8	example	example	NOUN
ejpam-4598	229	9	3.1	3.1	NUM
ejpam-4598	229	10	]	]	PUNCT
ejpam-4598	229	11	,	,	PUNCT
ejpam-4598	229	12	is	be	AUX
ejpam-4598	229	13	a	a	DET
ejpam-4598	229	14	sub	sub	ADJ
ejpam-4598	229	15	-	-	ADJ
ejpam-4598	229	16	metrizable	metrizable	ADJ
ejpam-4598	229	17	,	,	PUNCT
ejpam-4598	229	18	epi	epi	NOUN
ejpam-4598	229	19	-	-	ADJ
ejpam-4598	229	20	normal	normal	ADJ
ejpam-4598	229	21	,	,	PUNCT
ejpam-4598	229	22	tychonoff	tychonoff	NOUN
ejpam-4598	229	23	and	and	CCONJ
ejpam-4598	229	24	c	c	NOUN
ejpam-4598	229	25	-	-	PUNCT
ejpam-4598	229	26	normal	normal	ADJ
ejpam-4598	229	27	space	space	NOUN
ejpam-4598	229	28	,	,	PUNCT
ejpam-4598	229	29	which	which	PRON
ejpam-4598	229	30	is	be	AUX
ejpam-4598	229	31	not	not	PART
ejpam-4598	229	32	mildly	mildly	ADV
ejpam-4598	229	33	-	-	PUNCT
ejpam-4598	229	34	normal	normal	ADJ
ejpam-4598	229	35	.	.	PUNCT
ejpam-4598	230	1	the	the	DET
ejpam-4598	230	2	space	space	NOUN
ejpam-4598	230	3	presented	present	VERB
ejpam-4598	230	4	in	in	ADP
ejpam-4598	230	5	[	[	X
ejpam-4598	230	6	6	6	NUM
ejpam-4598	230	7	,	,	PUNCT
ejpam-4598	230	8	example	example	NOUN
ejpam-4598	230	9	2.8	2.8	NUM
ejpam-4598	230	10	]	]	PUNCT
ejpam-4598	230	11	,	,	PUNCT
ejpam-4598	230	12	is	be	AUX
ejpam-4598	230	13	an	an	DET
ejpam-4598	230	14	epi	epi	ADJ
ejpam-4598	230	15	-	-	ADJ
ejpam-4598	230	16	completelyregular	completelyregular	ADJ
ejpam-4598	230	17	space	space	NOUN
ejpam-4598	230	18	,	,	PUNCT
ejpam-4598	230	19	which	which	PRON
ejpam-4598	230	20	is	be	AUX
ejpam-4598	230	21	neither	neither	CCONJ
ejpam-4598	230	22	c	c	NOUN
ejpam-4598	230	23	-	-	ADJ
ejpam-4598	230	24	normal	normal	ADJ
ejpam-4598	230	25	nor	nor	CCONJ
ejpam-4598	230	26	epi	epi	NOUN
ejpam-4598	230	27	-	-	ADJ
ejpam-4598	230	28	normal	normal	ADJ
ejpam-4598	230	29	.	.	PUNCT
ejpam-4598	231	1	now	now	ADV
ejpam-4598	231	2	,	,	PUNCT
ejpam-4598	231	3	since	since	SCONJ
ejpam-4598	231	4	every	every	DET
ejpam-4598	231	5	hausdorff	hausdorff	NOUN
ejpam-4598	231	6	locally	locally	ADV
ejpam-4598	231	7	compact	compact	ADJ
ejpam-4598	231	8	space	space	NOUN
ejpam-4598	231	9	is	be	AUX
ejpam-4598	231	10	tychonoff	tychonoff	NOUN
ejpam-4598	231	11	[	[	X
ejpam-4598	231	12	12	12	NUM
ejpam-4598	231	13	]	]	PUNCT
ejpam-4598	231	14	,	,	PUNCT
ejpam-4598	231	15	we	we	PRON
ejpam-4598	231	16	get	get	VERB
ejpam-4598	231	17	:	:	PUNCT
ejpam-4598	231	18	corollary	corollary	ADJ
ejpam-4598	231	19	2	2	NUM
ejpam-4598	231	20	.	.	PUNCT
ejpam-4598	232	1	every	every	DET
ejpam-4598	232	2	hausdorff	hausdorff	NOUN
ejpam-4598	232	3	locally	locally	ADV
ejpam-4598	232	4	-	-	PUNCT
ejpam-4598	232	5	compact	compact	ADJ
ejpam-4598	232	6	space	space	NOUN
ejpam-4598	232	7	is	be	AUX
ejpam-4598	232	8	epi	epi	NOUN
ejpam-4598	232	9	-	-	ADJ
ejpam-4598	232	10	completely	completely	ADV
ejpam-4598	232	11	-	-	PUNCT
ejpam-4598	232	12	regular	regular	ADJ
ejpam-4598	232	13	.	.	PUNCT
ejpam-4598	233	1	the	the	DET
ejpam-4598	233	2	converse	converse	NOUN
ejpam-4598	233	3	of	of	ADP
ejpam-4598	233	4	corollary	corollary	ADJ
ejpam-4598	233	5	2	2	NUM
ejpam-4598	233	6	can	can	AUX
ejpam-4598	233	7	not	not	PART
ejpam-4598	233	8	be	be	AUX
ejpam-4598	233	9	true	true	ADJ
ejpam-4598	233	10	in	in	ADP
ejpam-4598	233	11	general	general	ADJ
ejpam-4598	233	12	.	.	PUNCT
ejpam-4598	234	1	here	here	ADV
ejpam-4598	234	2	is	be	AUX
ejpam-4598	234	3	a	a	DET
ejpam-4598	234	4	counterexample	counterexample	NOUN
ejpam-4598	234	5	:	:	PUNCT
ejpam-4598	234	6	example	example	NOUN
ejpam-4598	234	7	10	10	NUM
ejpam-4598	234	8	.	.	PUNCT
ejpam-4598	235	1	the	the	DET
ejpam-4598	235	2	smirnov	smirnov	PROPN
ejpam-4598	235	3	’s	’s	PART
ejpam-4598	235	4	deleted	delete	VERB
ejpam-4598	235	5	sequence	sequence	NOUN
ejpam-4598	235	6	topology	topology	NOUN
ejpam-4598	235	7	[	[	X
ejpam-4598	235	8	30	30	NUM
ejpam-4598	235	9	,	,	PUNCT
ejpam-4598	235	10	example	example	NOUN
ejpam-4598	235	11	64	64	NUM
ejpam-4598	235	12	]	]	PUNCT
ejpam-4598	235	13	,	,	PUNCT
ejpam-4598	235	14	is	be	AUX
ejpam-4598	235	15	a	a	DET
ejpam-4598	235	16	urysohn	urysohn	PROPN
ejpam-4598	235	17	space	space	NOUN
ejpam-4598	235	18	,	,	PUNCT
ejpam-4598	235	19	which	which	PRON
ejpam-4598	235	20	is	be	AUX
ejpam-4598	235	21	neither	neither	PRON
ejpam-4598	235	22	semi	semi	ADJ
ejpam-4598	235	23	-	-	ADJ
ejpam-4598	235	24	regular	regular	ADJ
ejpam-4598	235	25	,	,	PUNCT
ejpam-4598	235	26	completely	completely	ADV
ejpam-4598	235	27	-	-	PUNCT
ejpam-4598	235	28	regular	regular	ADJ
ejpam-4598	235	29	,	,	PUNCT
ejpam-4598	235	30	locally	locally	ADV
ejpam-4598	235	31	-	-	PUNCT
ejpam-4598	235	32	compact	compact	ADJ
ejpam-4598	235	33	nor	nor	CCONJ
ejpam-4598	235	34	almost	almost	ADV
ejpam-4598	235	35	-	-	PUNCT
ejpam-4598	235	36	normal	normal	ADJ
ejpam-4598	235	37	.	.	PUNCT
ejpam-4598	236	1	since	since	SCONJ
ejpam-4598	236	2	any	any	DET
ejpam-4598	236	3	closed	closed	ADJ
ejpam-4598	236	4	domain	domain	NOUN
ejpam-4598	236	5	subset	subset	NOUN
ejpam-4598	236	6	of	of	ADP
ejpam-4598	236	7	x	x	PRON
ejpam-4598	236	8	is	be	AUX
ejpam-4598	236	9	just	just	ADV
ejpam-4598	236	10	the	the	DET
ejpam-4598	236	11	closed	closed	ADJ
ejpam-4598	236	12	domain	domain	NOUN
ejpam-4598	236	13	in	in	ADP
ejpam-4598	236	14	the	the	DET
ejpam-4598	236	15	euclidean	euclidean	ADJ
ejpam-4598	236	16	topology	topology	NOUN
ejpam-4598	236	17	and	and	CCONJ
ejpam-4598	236	18	u	u	NOUN
ejpam-4598	236	19	⊆	⊆	NUM
ejpam-4598	236	20	t	t	NOUN
ejpam-4598	236	21	[	[	X
ejpam-4598	236	22	30	30	NUM
ejpam-4598	236	23	]	]	PUNCT
ejpam-4598	236	24	,	,	PUNCT
ejpam-4598	236	25	we	we	PRON
ejpam-4598	236	26	obtain	obtain	VERB
ejpam-4598	236	27	:	:	PUNCT
ejpam-4598	236	28	x	x	X
ejpam-4598	236	29	is	be	AUX
ejpam-4598	236	30	both	both	PRON
ejpam-4598	236	31	almost	almost	ADV
ejpam-4598	236	32	-	-	PUNCT
ejpam-4598	236	33	regular	regular	ADJ
ejpam-4598	236	34	and	and	CCONJ
ejpam-4598	236	35	almost	almost	ADV
ejpam-4598	236	36	-	-	PUNCT
ejpam-4598	236	37	completely	completely	ADV
ejpam-4598	236	38	regular	regular	ADJ
ejpam-4598	236	39	.	.	PUNCT
ejpam-4598	237	1	the	the	DET
ejpam-4598	237	2	smirnov	smirnov	PROPN
ejpam-4598	237	3	’s	’s	PART
ejpam-4598	237	4	deleted	delete	VERB
ejpam-4598	237	5	sequence	sequence	NOUN
ejpam-4598	237	6	topology	topology	NOUN
ejpam-4598	237	7	is	be	AUX
ejpam-4598	237	8	not	not	PART
ejpam-4598	237	9	almost	almost	ADV
ejpam-4598	237	10	-	-	PUNCT
ejpam-4598	237	11	normal	normal	ADJ
ejpam-4598	237	12	because	because	SCONJ
ejpam-4598	237	13	the	the	DET
ejpam-4598	237	14	closed	closed	ADJ
ejpam-4598	237	15	domain	domain	NOUN
ejpam-4598	237	16	subset	subset	VERB
ejpam-4598	237	17	b	b	NOUN
ejpam-4598	238	1	=	=	PUNCT
ejpam-4598	239	1	[	[	X
ejpam-4598	239	2	−1	−1	NOUN
ejpam-4598	239	3	,	,	PUNCT
ejpam-4598	239	4	0	0	NUM
ejpam-4598	239	5	]	]	PUNCT
ejpam-4598	239	6	is	be	AUX
ejpam-4598	239	7	disjoint	disjoint	ADJ
ejpam-4598	239	8	from	from	ADP
ejpam-4598	239	9	the	the	DET
ejpam-4598	239	10	closed	closed	NOUN
ejpam-4598	239	11	subset	subset	VERB
ejpam-4598	239	12	a	a	DET
ejpam-4598	239	13	=	=	X
ejpam-4598	239	14	{	{	PUNCT
ejpam-4598	239	15	1	1	NUM
ejpam-4598	239	16	n	n	NOUN
ejpam-4598	239	17	:	:	PUNCT
ejpam-4598	239	18	n	n	CCONJ
ejpam-4598	239	19	∈	∈	PROPN
ejpam-4598	239	20	n	n	CCONJ
ejpam-4598	239	21	}	}	PUNCT
ejpam-4598	239	22	,	,	PUNCT
ejpam-4598	239	23	and	and	CCONJ
ejpam-4598	239	24	they	they	PRON
ejpam-4598	239	25	can	can	AUX
ejpam-4598	239	26	not	not	PART
ejpam-4598	239	27	be	be	AUX
ejpam-4598	239	28	i.	i.	PROPN
ejpam-4598	239	29	alshammari	alshammari	PROPN
ejpam-4598	239	30	/	/	SYM
ejpam-4598	239	31	eur	eur	PROPN
ejpam-4598	239	32	.	.	PUNCT
ejpam-4598	240	1	j.	j.	PROPN
ejpam-4598	240	2	pure	pure	PROPN
ejpam-4598	240	3	appl	appl	PROPN
ejpam-4598	240	4	.	.	PROPN
ejpam-4598	240	5	math	math	PROPN
ejpam-4598	240	6	,	,	PUNCT
ejpam-4598	240	7	15	15	NUM
ejpam-4598	240	8	(	(	PUNCT
ejpam-4598	240	9	4	4	NUM
ejpam-4598	240	10	)	)	PUNCT
ejpam-4598	240	11	(	(	PUNCT
ejpam-4598	240	12	2022	2022	NUM
ejpam-4598	240	13	)	)	PUNCT
ejpam-4598	240	14	,	,	PUNCT
ejpam-4598	240	15	1808	1808	NUM
ejpam-4598	240	16	-	-	SYM
ejpam-4598	240	17	1821	1821	NUM
ejpam-4598	240	18	1815	1815	NUM
ejpam-4598	240	19	separated	separate	VERB
ejpam-4598	240	20	.	.	PUNCT
ejpam-4598	241	1	since	since	SCONJ
ejpam-4598	241	2	u	u	PROPN
ejpam-4598	241	3	⊆	⊆	NUM
ejpam-4598	241	4	t	t	NOUN
ejpam-4598	241	5	,	,	PUNCT
ejpam-4598	241	6	u	u	NOUN
ejpam-4598	241	7	is	be	AUX
ejpam-4598	241	8	the	the	DET
ejpam-4598	241	9	euclidian	euclidian	ADJ
ejpam-4598	241	10	topology	topology	NOUN
ejpam-4598	241	11	on	on	ADP
ejpam-4598	241	12	r	r	NOUN
ejpam-4598	241	13	,	,	PUNCT
ejpam-4598	241	14	which	which	PRON
ejpam-4598	241	15	is	be	AUX
ejpam-4598	241	16	coarser	coarse	ADJ
ejpam-4598	241	17	than	than	ADP
ejpam-4598	241	18	t	t	PROPN
ejpam-4598	241	19	,	,	PUNCT
ejpam-4598	241	20	and	and	CCONJ
ejpam-4598	241	21	(	(	PUNCT
ejpam-4598	241	22	r	r	NOUN
ejpam-4598	241	23	,	,	PUNCT
ejpam-4598	241	24	u	u	NOUN
ejpam-4598	241	25	)	)	PUNCT
ejpam-4598	241	26	is	be	AUX
ejpam-4598	241	27	a	a	DET
ejpam-4598	241	28	t4	t4	PROPN
ejpam-4598	241	29	-	-	PUNCT
ejpam-4598	241	30	space	space	NOUN
ejpam-4598	241	31	,	,	PUNCT
ejpam-4598	241	32	we	we	PRON
ejpam-4598	241	33	obtain	obtain	VERB
ejpam-4598	241	34	:	:	PUNCT
ejpam-4598	241	35	x	x	X
ejpam-4598	241	36	is	be	AUX
ejpam-4598	241	37	epi	epi	NOUN
ejpam-4598	241	38	-	-	ADJ
ejpam-4598	241	39	normal	normal	ADJ
ejpam-4598	241	40	(	(	PUNCT
ejpam-4598	241	41	in	in	ADP
ejpam-4598	241	42	fact	fact	NOUN
ejpam-4598	241	43	it	it	PRON
ejpam-4598	241	44	is	be	AUX
ejpam-4598	241	45	sub	sub	ADJ
ejpam-4598	241	46	-	-	ADJ
ejpam-4598	241	47	metrizable	metrizable	ADJ
ejpam-4598	241	48	[	[	X
ejpam-4598	241	49	5	5	NUM
ejpam-4598	241	50	]	]	PUNCT
ejpam-4598	241	51	)	)	PUNCT
ejpam-4598	241	52	.	.	PUNCT
ejpam-4598	242	1	since	since	SCONJ
ejpam-4598	242	2	the	the	DET
ejpam-4598	242	3	smirnov	smirnov	PROPN
ejpam-4598	242	4	’s	’s	PART
ejpam-4598	242	5	deleted	delete	VERB
ejpam-4598	242	6	sequence	sequence	NOUN
ejpam-4598	242	7	topology	topology	NOUN
ejpam-4598	242	8	is	be	AUX
ejpam-4598	242	9	a	a	DET
ejpam-4598	242	10	lindelöf	lindelöf	NOUN
ejpam-4598	242	11	non	non	PRON
ejpam-4598	242	12	regular	regular	ADJ
ejpam-4598	242	13	space	space	NOUN
ejpam-4598	242	14	,	,	PUNCT
ejpam-4598	242	15	it	it	PRON
ejpam-4598	242	16	is	be	AUX
ejpam-4598	242	17	not	not	PART
ejpam-4598	242	18	l	l	NOUN
ejpam-4598	242	19	-	-	ADJ
ejpam-4598	242	20	regular	regular	ADJ
ejpam-4598	242	21	[	[	X
ejpam-4598	242	22	6	6	NUM
ejpam-4598	242	23	]	]	PUNCT
ejpam-4598	242	24	.	.	PUNCT
ejpam-4598	243	1	therefore	therefore	ADV
ejpam-4598	243	2	,	,	PUNCT
ejpam-4598	243	3	the	the	DET
ejpam-4598	243	4	smirnov	smirnov	PROPN
ejpam-4598	243	5	’s	’s	PART
ejpam-4598	243	6	deleted	delete	VERB
ejpam-4598	243	7	sequence	sequence	NOUN
ejpam-4598	243	8	is	be	AUX
ejpam-4598	243	9	an	an	DET
ejpam-4598	243	10	epi	epi	NOUN
ejpam-4598	243	11	-	-	PUNCT
ejpam-4598	243	12	completely	completely	ADV
ejpam-4598	243	13	-	-	PUNCT
ejpam-4598	243	14	regular	regular	ADJ
ejpam-4598	243	15	space	space	NOUN
ejpam-4598	243	16	,	,	PUNCT
ejpam-4598	243	17	which	which	PRON
ejpam-4598	243	18	is	be	AUX
ejpam-4598	243	19	neither	neither	CCONJ
ejpam-4598	243	20	completely	completely	ADV
ejpam-4598	243	21	-	-	PUNCT
ejpam-4598	243	22	regular	regular	ADJ
ejpam-4598	243	23	,	,	PUNCT
ejpam-4598	243	24	almost	almost	ADV
ejpam-4598	243	25	-	-	PUNCT
ejpam-4598	243	26	normal	normal	ADJ
ejpam-4598	243	27	,	,	PUNCT
ejpam-4598	243	28	l	l	NOUN
ejpam-4598	243	29	-	-	ADJ
ejpam-4598	243	30	regular	regular	ADJ
ejpam-4598	243	31	nor	nor	CCONJ
ejpam-4598	243	32	locally	locally	ADV
ejpam-4598	243	33	-	-	PUNCT
ejpam-4598	243	34	compact	compact	ADJ
ejpam-4598	243	35	.	.	PUNCT
ejpam-4598	244	1	the	the	DET
ejpam-4598	244	2	niemytzki	niemytzki	PROPN
ejpam-4598	244	3	plane	plane	NOUN
ejpam-4598	244	4	topology	topology	NOUN
ejpam-4598	244	5	,	,	PUNCT
ejpam-4598	244	6	the	the	DET
ejpam-4598	244	7	sorgenfrey	sorgenfrey	PROPN
ejpam-4598	244	8	line	line	NOUN
ejpam-4598	244	9	square	square	PROPN
ejpam-4598	244	10	and	and	CCONJ
ejpam-4598	244	11	the	the	DET
ejpam-4598	244	12	michael	michael	PROPN
ejpam-4598	244	13	line	line	NOUN
ejpam-4598	244	14	are	be	AUX
ejpam-4598	244	15	tychonoff	tychonoff	NOUN
ejpam-4598	244	16	and	and	CCONJ
ejpam-4598	244	17	hence	hence	ADV
ejpam-4598	244	18	epi	epi	NOUN
ejpam-4598	244	19	-	-	PUNCT
ejpam-4598	244	20	completely	completely	ADV
ejpam-4598	244	21	-	-	PUNCT
ejpam-4598	244	22	regular	regular	ADJ
ejpam-4598	244	23	spaces	space	NOUN
ejpam-4598	244	24	[	[	X
ejpam-4598	244	25	30	30	NUM
ejpam-4598	244	26	]	]	PUNCT
ejpam-4598	244	27	,	,	PUNCT
ejpam-4598	244	28	which	which	PRON
ejpam-4598	244	29	are	be	AUX
ejpam-4598	244	30	not	not	PART
ejpam-4598	244	31	locally	locally	ADV
ejpam-4598	244	32	-	-	PUNCT
ejpam-4598	244	33	compact	compact	ADJ
ejpam-4598	244	34	.	.	PUNCT
ejpam-4598	244	35	example	example	NOUN
ejpam-4598	245	1	11	11	NUM
ejpam-4598	245	2	.	.	PUNCT
ejpam-4598	246	1	the	the	DET
ejpam-4598	246	2	deleted	delete	VERB
ejpam-4598	246	3	tychonoff	tychonoff	NOUN
ejpam-4598	246	4	plank	plank	NOUN
ejpam-4598	246	5	[	[	X
ejpam-4598	246	6	30	30	NUM
ejpam-4598	246	7	,	,	PUNCT
ejpam-4598	246	8	example	example	NOUN
ejpam-4598	246	9	87	87	NUM
ejpam-4598	246	10	]	]	PUNCT
ejpam-4598	246	11	,	,	PUNCT
ejpam-4598	246	12	is	be	AUX
ejpam-4598	246	13	a	a	DET
ejpam-4598	246	14	tychonoff	tychonoff	NOUN
ejpam-4598	246	15	locallycompact	locallycompact	NOUN
ejpam-4598	246	16	space	space	NOUN
ejpam-4598	246	17	.	.	PUNCT
ejpam-4598	247	1	hence	hence	ADV
ejpam-4598	247	2	,	,	PUNCT
ejpam-4598	247	3	it	it	PRON
ejpam-4598	247	4	is	be	AUX
ejpam-4598	247	5	an	an	DET
ejpam-4598	247	6	epi	epi	NOUN
ejpam-4598	247	7	-	-	PUNCT
ejpam-4598	247	8	completely	completely	ADV
ejpam-4598	247	9	-	-	PUNCT
ejpam-4598	247	10	regular	regular	ADJ
ejpam-4598	247	11	space	space	NOUN
ejpam-4598	247	12	.	.	PUNCT
ejpam-4598	248	1	the	the	DET
ejpam-4598	248	2	deleted	delete	VERB
ejpam-4598	248	3	tychonoff	tychonoff	NOUN
ejpam-4598	248	4	plank	plank	NOUN
ejpam-4598	248	5	is	be	AUX
ejpam-4598	248	6	neither	neither	CCONJ
ejpam-4598	248	7	almost	almost	ADV
ejpam-4598	248	8	-	-	PUNCT
ejpam-4598	248	9	normal	normal	ADJ
ejpam-4598	248	10	nor	nor	CCONJ
ejpam-4598	248	11	sub	sub	ADJ
ejpam-4598	248	12	-	-	ADJ
ejpam-4598	248	13	metrizable	metrizable	ADJ
ejpam-4598	248	14	[	[	X
ejpam-4598	248	15	6	6	NUM
ejpam-4598	248	16	,	,	PUNCT
ejpam-4598	248	17	8	8	NUM
ejpam-4598	248	18	]	]	PUNCT
ejpam-4598	248	19	.	.	PUNCT
ejpam-4598	249	1	therefore	therefore	ADV
ejpam-4598	249	2	,	,	PUNCT
ejpam-4598	249	3	the	the	DET
ejpam-4598	249	4	deleted	delete	VERB
ejpam-4598	249	5	tychonoff	tychonoff	NOUN
ejpam-4598	249	6	plank	plank	NOUN
ejpam-4598	249	7	topology	topology	NOUN
ejpam-4598	249	8	is	be	AUX
ejpam-4598	249	9	an	an	DET
ejpam-4598	249	10	epi	epi	NOUN
ejpam-4598	249	11	-	-	PUNCT
ejpam-4598	249	12	completely	completely	ADV
ejpam-4598	249	13	-	-	PUNCT
ejpam-4598	249	14	regular	regular	ADJ
ejpam-4598	249	15	space	space	NOUN
ejpam-4598	249	16	,	,	PUNCT
ejpam-4598	249	17	which	which	PRON
ejpam-4598	249	18	is	be	AUX
ejpam-4598	249	19	not	not	PART
ejpam-4598	249	20	sub	sub	ADJ
ejpam-4598	249	21	-	-	ADJ
ejpam-4598	249	22	metrizable	metrizable	ADJ
ejpam-4598	249	23	.	.	PUNCT
ejpam-4598	249	24	example	example	NOUN
ejpam-4598	250	1	12	12	NUM
ejpam-4598	250	2	.	.	PUNCT
ejpam-4598	251	1	the	the	DET
ejpam-4598	251	2	odd	odd	ADV
ejpam-4598	251	3	-	-	PUNCT
ejpam-4598	251	4	even	even	ADV
ejpam-4598	251	5	topology	topology	NOUN
ejpam-4598	251	6	[	[	X
ejpam-4598	251	7	30	30	NUM
ejpam-4598	251	8	,	,	PUNCT
ejpam-4598	251	9	example	example	NOUN
ejpam-4598	251	10	6	6	NUM
ejpam-4598	251	11	]	]	PUNCT
ejpam-4598	251	12	,	,	PUNCT
ejpam-4598	251	13	is	be	AUX
ejpam-4598	251	14	a	a	DET
ejpam-4598	251	15	completely	completely	ADV
ejpam-4598	251	16	regular	regular	ADJ
ejpam-4598	251	17	and	and	CCONJ
ejpam-4598	251	18	normal	normal	ADJ
ejpam-4598	251	19	space	space	NOUN
ejpam-4598	251	20	,	,	PUNCT
ejpam-4598	251	21	which	which	PRON
ejpam-4598	251	22	is	be	AUX
ejpam-4598	251	23	not	not	PART
ejpam-4598	251	24	epi	epi	NOUN
ejpam-4598	251	25	-	-	ADJ
ejpam-4598	251	26	completely	completely	ADV
ejpam-4598	251	27	regular	regular	ADJ
ejpam-4598	251	28	being	be	AUX
ejpam-4598	251	29	not	not	PART
ejpam-4598	251	30	hausdorff	hausdorff	NOUN
ejpam-4598	251	31	.	.	PUNCT
ejpam-4598	252	1	every	every	DET
ejpam-4598	252	2	hausdorff	hausdorff	NOUN
ejpam-4598	252	3	semi	semi	ADJ
ejpam-4598	252	4	-	-	ADJ
ejpam-4598	252	5	regular	regular	ADJ
ejpam-4598	252	6	almost	almost	ADV
ejpam-4598	252	7	-	-	PUNCT
ejpam-4598	252	8	compact	compact	ADJ
ejpam-4598	252	9	(	(	PUNCT
ejpam-4598	252	10	resp	resp	NOUN
ejpam-4598	252	11	.	.	PUNCT
ejpam-4598	253	1	h	h	NOUN
ejpam-4598	253	2	-	-	PUNCT
ejpam-4598	253	3	closed	closed	ADJ
ejpam-4598	253	4	)	)	PUNCT
ejpam-4598	253	5	space	space	NOUN
ejpam-4598	253	6	is	be	AUX
ejpam-4598	253	7	not	not	PART
ejpam-4598	253	8	necessary	necessary	ADJ
ejpam-4598	253	9	to	to	PART
ejpam-4598	253	10	be	be	AUX
ejpam-4598	253	11	epi	epi	NOUN
ejpam-4598	253	12	-	-	ADJ
ejpam-4598	253	13	completely	completely	ADV
ejpam-4598	253	14	regular	regular	ADJ
ejpam-4598	253	15	.	.	PUNCT
ejpam-4598	254	1	here	here	ADV
ejpam-4598	254	2	is	be	AUX
ejpam-4598	254	3	a	a	DET
ejpam-4598	254	4	counterexample	counterexample	NOUN
ejpam-4598	254	5	:	:	PUNCT
ejpam-4598	254	6	example	example	NOUN
ejpam-4598	254	7	13	13	NUM
ejpam-4598	254	8	.	.	PUNCT
ejpam-4598	255	1	the	the	DET
ejpam-4598	255	2	minimal	minimal	ADJ
ejpam-4598	255	3	hausdorff	hausdorff	NOUN
ejpam-4598	255	4	topology	topology	NOUN
ejpam-4598	255	5	[	[	X
ejpam-4598	255	6	30	30	NUM
ejpam-4598	255	7	,	,	PUNCT
ejpam-4598	255	8	example	example	NOUN
ejpam-4598	255	9	100	100	NUM
ejpam-4598	255	10	]	]	PUNCT
ejpam-4598	255	11	,	,	PUNCT
ejpam-4598	255	12	is	be	AUX
ejpam-4598	255	13	a	a	DET
ejpam-4598	255	14	hausdorff	hausdorff	NOUN
ejpam-4598	255	15	,	,	PUNCT
ejpam-4598	255	16	semiregular	semiregular	PROPN
ejpam-4598	255	17	,	,	PUNCT
ejpam-4598	255	18	second	second	ADV
ejpam-4598	255	19	-	-	PUNCT
ejpam-4598	255	20	countable	countable	ADJ
ejpam-4598	255	21	and	and	CCONJ
ejpam-4598	255	22	almost	almost	ADV
ejpam-4598	255	23	-	-	PUNCT
ejpam-4598	255	24	compact	compact	ADJ
ejpam-4598	255	25	space	space	NOUN
ejpam-4598	255	26	,	,	PUNCT
ejpam-4598	255	27	which	which	PRON
ejpam-4598	255	28	is	be	AUX
ejpam-4598	255	29	neither	neither	CCONJ
ejpam-4598	255	30	urysohn	urysohn	NOUN
ejpam-4598	255	31	,	,	PUNCT
ejpam-4598	255	32	regular	regular	ADJ
ejpam-4598	255	33	,	,	PUNCT
ejpam-4598	255	34	normal	normal	ADJ
ejpam-4598	255	35	nor	nor	CCONJ
ejpam-4598	255	36	compact	compact	ADJ
ejpam-4598	255	37	[	[	X
ejpam-4598	255	38	30	30	NUM
ejpam-4598	255	39	]	]	PUNCT
ejpam-4598	255	40	.	.	PUNCT
ejpam-4598	256	1	since	since	SCONJ
ejpam-4598	256	2	x	x	PRON
ejpam-4598	256	3	is	be	AUX
ejpam-4598	256	4	a	a	DET
ejpam-4598	256	5	semi	semi	ADJ
ejpam-4598	256	6	-	-	ADJ
ejpam-4598	256	7	regular	regular	ADJ
ejpam-4598	256	8	non	non	ADJ
ejpam-4598	256	9	regular	regular	ADJ
ejpam-4598	256	10	space	space	NOUN
ejpam-4598	256	11	,	,	PUNCT
ejpam-4598	256	12	we	we	PRON
ejpam-4598	256	13	have	have	VERB
ejpam-4598	256	14	:	:	PUNCT
ejpam-4598	256	15	x	x	X
ejpam-4598	256	16	is	be	AUX
ejpam-4598	256	17	not	not	PART
ejpam-4598	256	18	almost	almost	ADV
ejpam-4598	256	19	-	-	PUNCT
ejpam-4598	256	20	regular	regular	ADJ
ejpam-4598	256	21	.	.	PUNCT
ejpam-4598	257	1	since	since	SCONJ
ejpam-4598	257	2	x	x	PRON
ejpam-4598	257	3	is	be	AUX
ejpam-4598	257	4	a	a	DET
ejpam-4598	257	5	t1	t1	NOUN
ejpam-4598	257	6	non	non	ADJ
ejpam-4598	257	7	almost	almost	ADV
ejpam-4598	257	8	-	-	PUNCT
ejpam-4598	257	9	regular	regular	ADJ
ejpam-4598	257	10	space	space	NOUN
ejpam-4598	257	11	,	,	PUNCT
ejpam-4598	257	12	it	it	PRON
ejpam-4598	257	13	is	be	AUX
ejpam-4598	257	14	not	not	PART
ejpam-4598	257	15	almost	almost	ADV
ejpam-4598	257	16	-	-	PUNCT
ejpam-4598	257	17	normal	normal	ADJ
ejpam-4598	257	18	.	.	PUNCT
ejpam-4598	258	1	hence	hence	ADV
ejpam-4598	258	2	,	,	PUNCT
ejpam-4598	258	3	x	x	X
ejpam-4598	258	4	is	be	AUX
ejpam-4598	258	5	a	a	DET
ejpam-4598	258	6	quasi	quasi	ADJ
ejpam-4598	258	7	-	-	ADJ
ejpam-4598	258	8	normal	normal	ADJ
ejpam-4598	258	9	space	space	NOUN
ejpam-4598	258	10	,	,	PUNCT
ejpam-4598	258	11	which	which	PRON
ejpam-4598	258	12	is	be	AUX
ejpam-4598	258	13	not	not	PART
ejpam-4598	258	14	semi	semi	ADJ
ejpam-4598	258	15	-	-	ADJ
ejpam-4598	258	16	normal	normal	ADJ
ejpam-4598	258	17	[	[	X
ejpam-4598	258	18	31	31	NUM
ejpam-4598	258	19	]	]	PUNCT
ejpam-4598	258	20	.	.	PUNCT
ejpam-4598	259	1	since	since	SCONJ
ejpam-4598	259	2	x	x	PRON
ejpam-4598	259	3	is	be	AUX
ejpam-4598	259	4	not	not	PART
ejpam-4598	259	5	urysohn	urysohn	ADJ
ejpam-4598	259	6	,	,	PUNCT
ejpam-4598	259	7	it	it	PRON
ejpam-4598	259	8	is	be	AUX
ejpam-4598	259	9	neither	neither	CCONJ
ejpam-4598	259	10	epi	epi	NOUN
ejpam-4598	259	11	-	-	ADJ
ejpam-4598	259	12	almost	almost	ADV
ejpam-4598	259	13	-	-	PUNCT
ejpam-4598	259	14	normal	normal	ADJ
ejpam-4598	259	15	,	,	PUNCT
ejpam-4598	259	16	epi	epi	NOUN
ejpam-4598	259	17	-	-	NOUN
ejpam-4598	259	18	regular	regular	ADJ
ejpam-4598	259	19	,	,	PUNCT
ejpam-4598	259	20	epi	epi	NOUN
ejpam-4598	259	21	-	-	ADJ
ejpam-4598	259	22	completely	completely	ADV
ejpam-4598	259	23	-	-	PUNCT
ejpam-4598	259	24	regular	regular	ADJ
ejpam-4598	259	25	nor	nor	CCONJ
ejpam-4598	259	26	epi	epi	NOUN
ejpam-4598	259	27	-	-	ADJ
ejpam-4598	259	28	normal	normal	ADJ
ejpam-4598	259	29	.	.	PUNCT
ejpam-4598	260	1	therefore	therefore	ADV
ejpam-4598	260	2	,	,	PUNCT
ejpam-4598	260	3	the	the	DET
ejpam-4598	260	4	minimal	minimal	ADJ
ejpam-4598	260	5	hausdorff	hausdorff	NOUN
ejpam-4598	260	6	topology	topology	NOUN
ejpam-4598	260	7	is	be	AUX
ejpam-4598	260	8	a	a	DET
ejpam-4598	260	9	semi	semi	ADJ
ejpam-4598	260	10	-	-	ADJ
ejpam-4598	260	11	regular	regular	ADJ
ejpam-4598	260	12	,	,	PUNCT
ejpam-4598	260	13	hausdorff	hausdorff	NOUN
ejpam-4598	260	14	and	and	CCONJ
ejpam-4598	260	15	epi	epi	NOUN
ejpam-4598	260	16	-	-	NOUN
ejpam-4598	260	17	quasi	quasi	ADJ
ejpam-4598	260	18	-	-	ADJ
ejpam-4598	260	19	normal	normal	ADJ
ejpam-4598	260	20	almostcompact	almostcompact	NOUN
ejpam-4598	260	21	h	h	NOUN
ejpam-4598	260	22	-	-	PUNCT
ejpam-4598	260	23	closed	close	VERB
ejpam-4598	260	24	space	space	NOUN
ejpam-4598	260	25	[	[	X
ejpam-4598	260	26	31	31	NUM
ejpam-4598	260	27	]	]	PUNCT
ejpam-4598	260	28	,	,	PUNCT
ejpam-4598	260	29	which	which	PRON
ejpam-4598	260	30	is	be	AUX
ejpam-4598	260	31	neither	neither	CCONJ
ejpam-4598	260	32	almost	almost	ADV
ejpam-4598	260	33	-	-	PUNCT
ejpam-4598	260	34	regular	regular	ADJ
ejpam-4598	260	35	,	,	PUNCT
ejpam-4598	260	36	epi	epi	NOUN
ejpam-4598	260	37	-	-	NOUN
ejpam-4598	260	38	regular	regular	ADJ
ejpam-4598	260	39	,	,	PUNCT
ejpam-4598	260	40	epi	epi	NOUN
ejpam-4598	260	41	-	-	NOUN
ejpam-4598	260	42	completelyregular	completelyregular	ADJ
ejpam-4598	260	43	nor	nor	CCONJ
ejpam-4598	260	44	urysohn	urysohn	NOUN
ejpam-4598	260	45	.	.	PUNCT
ejpam-4598	261	1	observe	observe	VERB
ejpam-4598	261	2	that	that	SCONJ
ejpam-4598	261	3	:	:	PUNCT
ejpam-4598	261	4	a	a	DET
ejpam-4598	261	5	normal	normal	ADJ
ejpam-4598	261	6	compact	compact	ADJ
ejpam-4598	261	7	space	space	NOUN
ejpam-4598	261	8	need	need	AUX
ejpam-4598	261	9	not	not	PART
ejpam-4598	261	10	be	be	AUX
ejpam-4598	261	11	epi	epi	NOUN
ejpam-4598	261	12	-	-	ADJ
ejpam-4598	261	13	completely	completely	ADV
ejpam-4598	261	14	regular	regular	ADJ
ejpam-4598	261	15	.	.	PUNCT
ejpam-4598	262	1	for	for	ADP
ejpam-4598	262	2	example	example	NOUN
ejpam-4598	262	3	:	:	PUNCT
ejpam-4598	262	4	the	the	DET
ejpam-4598	262	5	excluded	exclude	VERB
ejpam-4598	262	6	point	point	NOUN
ejpam-4598	262	7	topology	topology	NOUN
ejpam-4598	262	8	[	[	X
ejpam-4598	262	9	30	30	NUM
ejpam-4598	262	10	,	,	PUNCT
ejpam-4598	262	11	example	example	NOUN
ejpam-4598	262	12	15	15	NUM
ejpam-4598	262	13	]	]	PUNCT
ejpam-4598	262	14	,	,	PUNCT
ejpam-4598	262	15	and	and	CCONJ
ejpam-4598	262	16	the	the	DET
ejpam-4598	262	17	either	either	ADV
ejpam-4598	262	18	-	-	PUNCT
ejpam-4598	262	19	or	or	CCONJ
ejpam-4598	262	20	-	-	PUNCT
ejpam-4598	262	21	topology	topology	NOUN
ejpam-4598	262	22	[	[	X
ejpam-4598	262	23	30	30	NUM
ejpam-4598	262	24	,	,	PUNCT
ejpam-4598	262	25	example	example	NOUN
ejpam-4598	262	26	17	17	NUM
ejpam-4598	262	27	]	]	PUNCT
ejpam-4598	262	28	,	,	PUNCT
ejpam-4598	262	29	are	be	AUX
ejpam-4598	262	30	normal	normal	ADJ
ejpam-4598	262	31	compact	compact	ADJ
ejpam-4598	262	32	spaces	space	NOUN
ejpam-4598	262	33	,	,	PUNCT
ejpam-4598	262	34	which	which	PRON
ejpam-4598	262	35	are	be	AUX
ejpam-4598	262	36	neither	neither	CCONJ
ejpam-4598	262	37	epi	epi	NOUN
ejpam-4598	262	38	-	-	ADJ
ejpam-4598	262	39	completely	completely	ADV
ejpam-4598	262	40	-	-	PUNCT
ejpam-4598	262	41	regular	regular	ADJ
ejpam-4598	262	42	,	,	PUNCT
ejpam-4598	262	43	epi	epi	NOUN
ejpam-4598	262	44	-	-	NOUN
ejpam-4598	262	45	regular	regular	ADJ
ejpam-4598	262	46	nor	nor	CCONJ
ejpam-4598	262	47	epi	epi	NOUN
ejpam-4598	262	48	-	-	ADJ
ejpam-4598	262	49	normal	normal	ADJ
ejpam-4598	262	50	.	.	PUNCT
ejpam-4598	263	1	3	3	X
ejpam-4598	263	2	.	.	X
ejpam-4598	264	1	some	some	DET
ejpam-4598	264	2	properties	property	NOUN
ejpam-4598	264	3	of	of	ADP
ejpam-4598	264	4	epi	epi	NOUN
ejpam-4598	264	5	-	-	NOUN
ejpam-4598	264	6	complete	complete	ADJ
ejpam-4598	264	7	regularity	regularity	NOUN
ejpam-4598	264	8	in	in	ADP
ejpam-4598	264	9	this	this	DET
ejpam-4598	264	10	section	section	NOUN
ejpam-4598	264	11	,	,	PUNCT
ejpam-4598	264	12	i	i	PRON
ejpam-4598	264	13	present	present	VERB
ejpam-4598	264	14	the	the	DET
ejpam-4598	264	15	following	follow	VERB
ejpam-4598	264	16	results	result	NOUN
ejpam-4598	264	17	:	:	PUNCT
ejpam-4598	264	18	theorem	theorem	VERB
ejpam-4598	264	19	4	4	NUM
ejpam-4598	264	20	.	.	PUNCT
ejpam-4598	265	1	epi	epi	X
ejpam-4598	265	2	-	-	ADJ
ejpam-4598	265	3	complete	complete	ADJ
ejpam-4598	265	4	regularity	regularity	NOUN
ejpam-4598	265	5	is	be	AUX
ejpam-4598	265	6	a	a	DET
ejpam-4598	265	7	topological	topological	ADJ
ejpam-4598	265	8	property	property	NOUN
ejpam-4598	265	9	.	.	PUNCT
ejpam-4598	266	1	proof	proof	NOUN
ejpam-4598	266	2	.	.	PUNCT
ejpam-4598	267	1	let	let	AUX
ejpam-4598	267	2	(	(	PUNCT
ejpam-4598	267	3	x	x	X
ejpam-4598	267	4	,	,	PUNCT
ejpam-4598	267	5	t	t	NOUN
ejpam-4598	267	6	)	)	PUNCT
ejpam-4598	267	7	∼=	∼=	PROPN
ejpam-4598	267	8	(	(	PUNCT
ejpam-4598	267	9	y	y	PROPN
ejpam-4598	267	10	,	,	PUNCT
ejpam-4598	267	11	s	s	PART
ejpam-4598	267	12	)	)	PUNCT
ejpam-4598	267	13	and	and	CCONJ
ejpam-4598	267	14	(	(	PUNCT
ejpam-4598	267	15	x	x	X
ejpam-4598	267	16	,	,	PUNCT
ejpam-4598	267	17	t	t	PROPN
ejpam-4598	267	18	)	)	PUNCT
ejpam-4598	267	19	be	be	AUX
ejpam-4598	267	20	an	an	DET
ejpam-4598	267	21	epi	epi	NOUN
ejpam-4598	267	22	-	-	PUNCT
ejpam-4598	267	23	completely	completely	ADV
ejpam-4598	267	24	-	-	PUNCT
ejpam-4598	267	25	regular	regular	ADJ
ejpam-4598	267	26	space	space	NOUN
ejpam-4598	267	27	.	.	PUNCT
ejpam-4598	268	1	there	there	PRON
ejpam-4598	268	2	are	be	VERB
ejpam-4598	268	3	a	a	DET
ejpam-4598	268	4	homeomorphism	homeomorphism	ADJ
ejpam-4598	268	5	f	f	NOUN
ejpam-4598	268	6	:	:	PUNCT
ejpam-4598	268	7	x	x	X
ejpam-4598	268	8	→	→	SYM
ejpam-4598	268	9	y	y	PROPN
ejpam-4598	268	10	and	and	CCONJ
ejpam-4598	268	11	a	a	DET
ejpam-4598	268	12	topology	topology	NOUN
ejpam-4598	268	13	t	t	NOUN
ejpam-4598	268	14	′	′	NUM
ejpam-4598	268	15	on	on	ADP
ejpam-4598	268	16	x	x	PUNCT
ejpam-4598	268	17	that	that	PRON
ejpam-4598	268	18	is	be	AUX
ejpam-4598	268	19	coarser	coarse	ADJ
ejpam-4598	268	20	than	than	ADP
ejpam-4598	268	21	t	t	NOUN
ejpam-4598	268	22	such	such	ADJ
ejpam-4598	268	23	that	that	SCONJ
ejpam-4598	268	24	(	(	PUNCT
ejpam-4598	268	25	x	x	X
ejpam-4598	268	26	,	,	PUNCT
ejpam-4598	268	27	t	t	PROPN
ejpam-4598	268	28	′	′	NUM
ejpam-4598	268	29	)	)	PUNCT
ejpam-4598	268	30	is	be	AUX
ejpam-4598	268	31	tychonoff	tychonoff	NOUN
ejpam-4598	268	32	.	.	PUNCT
ejpam-4598	269	1	define	define	VERB
ejpam-4598	269	2	s	s	PRON
ejpam-4598	269	3	′	′	NOUN
ejpam-4598	269	4	on	on	ADP
ejpam-4598	269	5	y	y	PROPN
ejpam-4598	269	6	by	by	ADP
ejpam-4598	269	7	s	s	PRON
ejpam-4598	269	8	′	′	NOUN
ejpam-4598	269	9	=	=	SYM
ejpam-4598	269	10	{	{	PUNCT
ejpam-4598	269	11	f(u	f(u	PROPN
ejpam-4598	269	12	)	)	PUNCT
ejpam-4598	269	13	:	:	PUNCT
ejpam-4598	270	1	u	u	PROPN
ejpam-4598	270	2	∈	∈	PROPN
ejpam-4598	270	3	t	t	NOUN
ejpam-4598	270	4	′	′	NUM
ejpam-4598	270	5	}	}	PUNCT
ejpam-4598	270	6	.	.	PUNCT
ejpam-4598	271	1	then	then	ADV
ejpam-4598	271	2	,	,	PUNCT
ejpam-4598	271	3	s	s	VERB
ejpam-4598	271	4	′	′	NOUN
ejpam-4598	271	5	is	be	AUX
ejpam-4598	271	6	a	a	DET
ejpam-4598	271	7	topology	topology	NOUN
ejpam-4598	271	8	on	on	ADP
ejpam-4598	271	9	y	y	PROPN
ejpam-4598	271	10	,	,	PUNCT
ejpam-4598	271	11	which	which	PRON
ejpam-4598	271	12	is	be	AUX
ejpam-4598	271	13	coarser	coarse	ADJ
ejpam-4598	271	14	than	than	ADP
ejpam-4598	271	15	s	s	PROPN
ejpam-4598	271	16	,	,	PUNCT
ejpam-4598	271	17	and	and	CCONJ
ejpam-4598	271	18	(	(	PUNCT
ejpam-4598	271	19	y	y	NOUN
ejpam-4598	271	20	,	,	PUNCT
ejpam-4598	271	21	s	s	PART
ejpam-4598	271	22	′	′	NOUN
ejpam-4598	271	23	)	)	PUNCT
ejpam-4598	271	24	is	be	AUX
ejpam-4598	271	25	tychonoff	tychonoff	NOUN
ejpam-4598	271	26	.	.	PUNCT
ejpam-4598	272	1	thus	thus	ADV
ejpam-4598	272	2	,	,	PUNCT
ejpam-4598	272	3	(	(	PUNCT
ejpam-4598	272	4	y	y	NOUN
ejpam-4598	272	5	,	,	PUNCT
ejpam-4598	272	6	s	s	PART
ejpam-4598	272	7	)	)	PUNCT
ejpam-4598	272	8	is	be	AUX
ejpam-4598	272	9	epi	epi	NOUN
ejpam-4598	272	10	-	-	ADJ
ejpam-4598	272	11	completely	completely	ADV
ejpam-4598	272	12	-	-	PUNCT
ejpam-4598	272	13	regular	regular	ADJ
ejpam-4598	272	14	.	.	PUNCT
ejpam-4598	273	1	theorem	theorem	NOUN
ejpam-4598	273	2	5	5	NUM
ejpam-4598	273	3	.	.	PUNCT
ejpam-4598	274	1	epi	epi	NOUN
ejpam-4598	274	2	-	-	ADJ
ejpam-4598	274	3	complete	complete	ADJ
ejpam-4598	274	4	regularity	regularity	NOUN
ejpam-4598	274	5	is	be	AUX
ejpam-4598	274	6	an	an	DET
ejpam-4598	274	7	additive	additive	ADJ
ejpam-4598	274	8	property	property	NOUN
ejpam-4598	274	9	.	.	PUNCT
ejpam-4598	275	1	i.	i.	PROPN
ejpam-4598	275	2	alshammari	alshammari	PROPN
ejpam-4598	275	3	/	/	SYM
ejpam-4598	275	4	eur	eur	PROPN
ejpam-4598	275	5	.	.	PUNCT
ejpam-4598	276	1	j.	j.	PROPN
ejpam-4598	276	2	pure	pure	PROPN
ejpam-4598	276	3	appl	appl	PROPN
ejpam-4598	276	4	.	.	PROPN
ejpam-4598	276	5	math	math	PROPN
ejpam-4598	276	6	,	,	PUNCT
ejpam-4598	276	7	15	15	NUM
ejpam-4598	276	8	(	(	PUNCT
ejpam-4598	276	9	4	4	NUM
ejpam-4598	276	10	)	)	PUNCT
ejpam-4598	276	11	(	(	PUNCT
ejpam-4598	276	12	2022	2022	NUM
ejpam-4598	276	13	)	)	PUNCT
ejpam-4598	276	14	,	,	PUNCT
ejpam-4598	276	15	1808	1808	NUM
ejpam-4598	276	16	-	-	SYM
ejpam-4598	276	17	1821	1821	NUM
ejpam-4598	276	18	1816	1816	NUM
ejpam-4598	276	19	proof	proof	NOUN
ejpam-4598	276	20	.	.	PUNCT
ejpam-4598	277	1	let	let	VERB
ejpam-4598	277	2	xs	xs	PROPN
ejpam-4598	277	3	be	be	AUX
ejpam-4598	277	4	an	an	DET
ejpam-4598	277	5	epi	epi	NOUN
ejpam-4598	277	6	-	-	PUNCT
ejpam-4598	277	7	completely	completely	ADV
ejpam-4598	277	8	-	-	PUNCT
ejpam-4598	277	9	regular	regular	ADJ
ejpam-4598	277	10	space	space	NOUN
ejpam-4598	277	11	for	for	ADP
ejpam-4598	277	12	each	each	DET
ejpam-4598	277	13	s	s	PROPN
ejpam-4598	277	14	∈	∈	PROPN
ejpam-4598	277	15	s.	s.	PROPN
ejpam-4598	277	16	then	then	ADV
ejpam-4598	277	17	,	,	PUNCT
ejpam-4598	277	18	there	there	PRON
ejpam-4598	277	19	exists	exist	VERB
ejpam-4598	277	20	a	a	DET
ejpam-4598	277	21	topology	topology	NOUN
ejpam-4598	277	22	ts′	ts′	ADJ
ejpam-4598	277	23	on	on	ADP
ejpam-4598	277	24	xs	xs	PROPN
ejpam-4598	277	25	,	,	PUNCT
ejpam-4598	277	26	which	which	PRON
ejpam-4598	277	27	is	be	AUX
ejpam-4598	277	28	coarser	coarse	ADJ
ejpam-4598	277	29	than	than	ADP
ejpam-4598	277	30	ts	ts	ADV
ejpam-4598	277	31	,	,	PUNCT
ejpam-4598	277	32	such	such	ADJ
ejpam-4598	277	33	that	that	SCONJ
ejpam-4598	277	34	(	(	PUNCT
ejpam-4598	277	35	xs	xs	PROPN
ejpam-4598	277	36	,	,	PUNCT
ejpam-4598	277	37	ts′	ts′	NUM
ejpam-4598	277	38	)	)	PUNCT
ejpam-4598	277	39	is	be	AUX
ejpam-4598	277	40	a	a	DET
ejpam-4598	277	41	t1	t1	ADJ
ejpam-4598	277	42	-	-	PUNCT
ejpam-4598	277	43	completelyregular	completelyregular	ADJ
ejpam-4598	277	44	space	space	NOUN
ejpam-4598	277	45	.	.	PUNCT
ejpam-4598	278	1	since	since	SCONJ
ejpam-4598	278	2	both	both	CCONJ
ejpam-4598	278	3	t1	t1	NOUN
ejpam-4598	278	4	and	and	CCONJ
ejpam-4598	278	5	complete	complete	ADJ
ejpam-4598	278	6	-	-	PUNCT
ejpam-4598	278	7	regularity	regularity	NOUN
ejpam-4598	278	8	are	be	AUX
ejpam-4598	278	9	additive	additive	ADJ
ejpam-4598	278	10	properties	property	NOUN
ejpam-4598	278	11	,	,	PUNCT
ejpam-4598	278	12	we	we	PRON
ejpam-4598	278	13	obtain	obtain	VERB
ejpam-4598	278	14	:	:	PUNCT
ejpam-4598	278	15	(	(	PUNCT
ejpam-4598	278	16	x	x	X
ejpam-4598	278	17	,	,	PUNCT
ejpam-4598	278	18	⊕	⊕	PROPN
ejpam-4598	278	19	s∈s	s∈s	NOUN
ejpam-4598	278	20	ts′	ts′	NOUN
ejpam-4598	278	21	)	)	PUNCT
ejpam-4598	278	22	is	be	AUX
ejpam-4598	278	23	t1	t1	NOUN
ejpam-4598	278	24	-	-	PUNCT
ejpam-4598	278	25	completely	completely	ADV
ejpam-4598	278	26	regular	regular	ADJ
ejpam-4598	278	27	(	(	PUNCT
ejpam-4598	278	28	tychonoff	tychonoff	NOUN
ejpam-4598	278	29	)	)	PUNCT
ejpam-4598	278	30	.	.	PUNCT
ejpam-4598	279	1	since	since	SCONJ
ejpam-4598	279	2	⊕	⊕	PROPN
ejpam-4598	279	3	s∈s	s∈s	NOUN
ejpam-4598	279	4	ts′	ts′	NUM
ejpam-4598	279	5	is	be	AUX
ejpam-4598	279	6	a	a	DET
ejpam-4598	279	7	topology	topology	NOUN
ejpam-4598	279	8	coarser	coarse	ADJ
ejpam-4598	279	9	than	than	ADP
ejpam-4598	279	10	⊕	⊕	PROPN
ejpam-4598	279	11	s∈s	s∈s	NOUN
ejpam-4598	279	12	ts	ts	ADP
ejpam-4598	279	13	,	,	PUNCT
ejpam-4598	279	14	we	we	PRON
ejpam-4598	279	15	get	get	VERB
ejpam-4598	279	16	:	:	PUNCT
ejpam-4598	279	17	(	(	PUNCT
ejpam-4598	279	18	x	x	X
ejpam-4598	279	19	,	,	PUNCT
ejpam-4598	279	20	⊕	⊕	PROPN
ejpam-4598	279	21	s∈s	s∈s	NOUN
ejpam-4598	279	22	ts	ts	NOUN
ejpam-4598	279	23	)	)	PUNCT
ejpam-4598	279	24	is	be	AUX
ejpam-4598	279	25	epi	epi	NOUN
ejpam-4598	279	26	-	-	ADJ
ejpam-4598	279	27	completely	completely	ADV
ejpam-4598	279	28	-	-	PUNCT
ejpam-4598	279	29	regular	regular	ADJ
ejpam-4598	279	30	.	.	PUNCT
ejpam-4598	280	1	theorem	theorem	VERB
ejpam-4598	280	2	6	6	NUM
ejpam-4598	280	3	.	.	PUNCT
ejpam-4598	281	1	epi	epi	NOUN
ejpam-4598	281	2	-	-	ADJ
ejpam-4598	281	3	complete	complete	ADJ
ejpam-4598	281	4	regularity	regularity	NOUN
ejpam-4598	281	5	is	be	AUX
ejpam-4598	281	6	a	a	DET
ejpam-4598	281	7	hereditary	hereditary	ADJ
ejpam-4598	281	8	property	property	NOUN
ejpam-4598	281	9	.	.	PUNCT
ejpam-4598	282	1	proof	proof	NOUN
ejpam-4598	282	2	.	.	PUNCT
ejpam-4598	283	1	let	let	AUX
ejpam-4598	283	2	(	(	PUNCT
ejpam-4598	283	3	x	x	X
ejpam-4598	283	4	,	,	PUNCT
ejpam-4598	283	5	t	t	PROPN
ejpam-4598	283	6	)	)	PUNCT
ejpam-4598	283	7	be	be	AUX
ejpam-4598	283	8	an	an	DET
ejpam-4598	283	9	epi	epi	NOUN
ejpam-4598	283	10	-	-	PUNCT
ejpam-4598	283	11	completely	completely	ADV
ejpam-4598	283	12	-	-	PUNCT
ejpam-4598	283	13	regular	regular	ADJ
ejpam-4598	283	14	space	space	NOUN
ejpam-4598	283	15	,	,	PUNCT
ejpam-4598	283	16	and	and	CCONJ
ejpam-4598	283	17	(	(	PUNCT
ejpam-4598	283	18	m	m	PROPN
ejpam-4598	283	19	,	,	PUNCT
ejpam-4598	283	20	tm	tm	NOUN
ejpam-4598	283	21	)	)	PUNCT
ejpam-4598	283	22	be	be	AUX
ejpam-4598	283	23	a	a	DET
ejpam-4598	283	24	subspace	subspace	NOUN
ejpam-4598	283	25	of	of	ADP
ejpam-4598	283	26	x.	x.	NOUN
ejpam-4598	283	27	then	then	ADV
ejpam-4598	283	28	,	,	PUNCT
ejpam-4598	283	29	there	there	PRON
ejpam-4598	283	30	exists	exist	VERB
ejpam-4598	283	31	a	a	DET
ejpam-4598	283	32	topology	topology	NOUN
ejpam-4598	283	33	t	t	NOUN
ejpam-4598	283	34	′	′	NUM
ejpam-4598	283	35	on	on	ADP
ejpam-4598	283	36	x	x	PUNCT
ejpam-4598	283	37	that	that	PRON
ejpam-4598	283	38	is	be	AUX
ejpam-4598	283	39	coarser	coarse	ADJ
ejpam-4598	283	40	than	than	ADP
ejpam-4598	283	41	t	t	NOUN
ejpam-4598	283	42	such	such	ADJ
ejpam-4598	283	43	that	that	SCONJ
ejpam-4598	283	44	(	(	PUNCT
ejpam-4598	283	45	x	x	X
ejpam-4598	283	46	,	,	PUNCT
ejpam-4598	283	47	t	t	PROPN
ejpam-4598	283	48	′	′	NUM
ejpam-4598	283	49	)	)	PUNCT
ejpam-4598	283	50	is	be	AUX
ejpam-4598	283	51	t1	t1	NOUN
ejpam-4598	283	52	-	-	PUNCT
ejpam-4598	283	53	completely	completely	ADV
ejpam-4598	283	54	-	-	PUNCT
ejpam-4598	283	55	regular	regular	ADJ
ejpam-4598	283	56	.	.	PUNCT
ejpam-4598	284	1	to	to	PART
ejpam-4598	284	2	show	show	VERB
ejpam-4598	284	3	(	(	PUNCT
ejpam-4598	284	4	m	m	PROPN
ejpam-4598	284	5	,	,	PUNCT
ejpam-4598	284	6	tm	tm	NOUN
ejpam-4598	284	7	)	)	PUNCT
ejpam-4598	284	8	is	be	AUX
ejpam-4598	284	9	epi	epi	NOUN
ejpam-4598	284	10	-	-	ADJ
ejpam-4598	284	11	completely	completely	ADV
ejpam-4598	284	12	-	-	PUNCT
ejpam-4598	284	13	regular	regular	ADJ
ejpam-4598	284	14	,	,	PUNCT
ejpam-4598	284	15	define	define	VERB
ejpam-4598	284	16	tm	tm	PRON
ejpam-4598	284	17	′	′	NUM
ejpam-4598	284	18	on	on	ADP
ejpam-4598	284	19	m	m	VERB
ejpam-4598	284	20	by	by	ADP
ejpam-4598	284	21	:	:	PUNCT
ejpam-4598	284	22	tm	tm	NOUN
ejpam-4598	284	23	′	′	NOUN
ejpam-4598	285	1	=	=	PUNCT
ejpam-4598	285	2	{	{	PUNCT
ejpam-4598	285	3	u	u	NOUN
ejpam-4598	285	4	∩	∩	NOUN
ejpam-4598	285	5	m	m	VERB
ejpam-4598	285	6	:	:	PUNCT
ejpam-4598	285	7	u	u	PROPN
ejpam-4598	285	8	∈	∈	PROPN
ejpam-4598	285	9	t	t	NOUN
ejpam-4598	285	10	′	′	NUM
ejpam-4598	285	11	}	}	PUNCT
ejpam-4598	285	12	.	.	PUNCT
ejpam-4598	286	1	then	then	ADV
ejpam-4598	286	2	,	,	PUNCT
ejpam-4598	286	3	tm	tm	DET
ejpam-4598	286	4	′	′	NUM
ejpam-4598	286	5	⊆	⊆	NUM
ejpam-4598	286	6	tm	tm	NOUN
ejpam-4598	286	7	.	.	PUNCT
ejpam-4598	287	1	hence	hence	ADV
ejpam-4598	287	2	,	,	PUNCT
ejpam-4598	287	3	tm	tm	DET
ejpam-4598	287	4	′	′	NUM
ejpam-4598	287	5	is	be	AUX
ejpam-4598	287	6	a	a	DET
ejpam-4598	287	7	topology	topology	NOUN
ejpam-4598	287	8	on	on	ADP
ejpam-4598	287	9	m	m	PROPN
ejpam-4598	287	10	which	which	PRON
ejpam-4598	287	11	is	be	AUX
ejpam-4598	287	12	coarser	coarse	ADJ
ejpam-4598	287	13	than	than	ADP
ejpam-4598	287	14	tm	tm	PROPN
ejpam-4598	287	15	.	.	PUNCT
ejpam-4598	288	1	since	since	SCONJ
ejpam-4598	288	2	(	(	PUNCT
ejpam-4598	288	3	x	x	X
ejpam-4598	288	4	,	,	PUNCT
ejpam-4598	288	5	t	t	PROPN
ejpam-4598	288	6	′	′	NUM
ejpam-4598	288	7	)	)	PUNCT
ejpam-4598	288	8	is	be	AUX
ejpam-4598	288	9	a	a	DET
ejpam-4598	288	10	t1	t1	VERB
ejpam-4598	288	11	-	-	PUNCT
ejpam-4598	288	12	completely	completely	ADV
ejpam-4598	288	13	-	-	PUNCT
ejpam-4598	288	14	regular	regular	ADJ
ejpam-4598	288	15	space	space	NOUN
ejpam-4598	288	16	and	and	CCONJ
ejpam-4598	288	17	(	(	PUNCT
ejpam-4598	288	18	m	m	PROPN
ejpam-4598	288	19	,	,	PUNCT
ejpam-4598	288	20	tm	tm	PROPN
ejpam-4598	288	21	′	′	NOUN
ejpam-4598	288	22	)	)	PUNCT
ejpam-4598	288	23	is	be	AUX
ejpam-4598	288	24	a	a	DET
ejpam-4598	288	25	subspace	subspace	NOUN
ejpam-4598	288	26	of	of	ADP
ejpam-4598	288	27	x	x	PRON
ejpam-4598	288	28	,	,	PUNCT
ejpam-4598	288	29	we	we	PRON
ejpam-4598	288	30	obtain	obtain	VERB
ejpam-4598	288	31	:	:	PUNCT
ejpam-4598	288	32	(	(	PUNCT
ejpam-4598	288	33	m	m	PROPN
ejpam-4598	288	34	,	,	PUNCT
ejpam-4598	288	35	tm	tm	PROPN
ejpam-4598	288	36	′	′	NOUN
ejpam-4598	288	37	)	)	PUNCT
ejpam-4598	288	38	is	be	AUX
ejpam-4598	288	39	a	a	DET
ejpam-4598	288	40	t1	t1	VERB
ejpam-4598	288	41	-	-	PUNCT
ejpam-4598	288	42	completely	completely	ADV
ejpam-4598	288	43	-	-	PUNCT
ejpam-4598	288	44	regular	regular	ADJ
ejpam-4598	288	45	subspace	subspace	NOUN
ejpam-4598	288	46	.	.	PUNCT
ejpam-4598	289	1	therefore	therefore	ADV
ejpam-4598	289	2	,	,	PUNCT
ejpam-4598	289	3	(	(	PUNCT
ejpam-4598	289	4	m	m	PROPN
ejpam-4598	289	5	,	,	PUNCT
ejpam-4598	289	6	tm	tm	NOUN
ejpam-4598	289	7	)	)	PUNCT
ejpam-4598	289	8	is	be	AUX
ejpam-4598	289	9	epi	epi	NOUN
ejpam-4598	289	10	-	-	ADJ
ejpam-4598	289	11	completely	completely	ADV
ejpam-4598	289	12	-	-	PUNCT
ejpam-4598	289	13	regular	regular	ADJ
ejpam-4598	289	14	.	.	PUNCT
ejpam-4598	290	1	theorem	theorem	VERB
ejpam-4598	290	2	7	7	NUM
ejpam-4598	290	3	.	.	PUNCT
ejpam-4598	291	1	a	a	DET
ejpam-4598	291	2	product	product	NOUN
ejpam-4598	291	3	space	space	NOUN
ejpam-4598	291	4	x	x	PUNCT
ejpam-4598	292	1	=	=	SYM
ejpam-4598	292	2	π	π	X
ejpam-4598	292	3	α∈λ	α∈λ	NOUN
ejpam-4598	292	4	xα	xα	INTJ
ejpam-4598	292	5	,	,	PUNCT
ejpam-4598	292	6	xα	xα	ADP
ejpam-4598	292	7	̸=	̸=	NOUN
ejpam-4598	292	8	∅	∅	NOUN
ejpam-4598	292	9	for	for	ADP
ejpam-4598	292	10	each	each	DET
ejpam-4598	292	11	α	α	NOUN
ejpam-4598	292	12	∈	∈	PROPN
ejpam-4598	292	13	λ	λ	NOUN
ejpam-4598	292	14	,	,	PUNCT
ejpam-4598	292	15	is	be	AUX
ejpam-4598	292	16	an	an	DET
ejpam-4598	292	17	epi	epi	ADJ
ejpam-4598	292	18	-	-	ADJ
ejpam-4598	292	19	completelyregular	completelyregular	ADJ
ejpam-4598	292	20	space	space	NOUN
ejpam-4598	292	21	if	if	SCONJ
ejpam-4598	292	22	and	and	CCONJ
ejpam-4598	292	23	only	only	ADV
ejpam-4598	292	24	if	if	SCONJ
ejpam-4598	292	25	each	each	DET
ejpam-4598	292	26	factor	factor	NOUN
ejpam-4598	292	27	xα	xα	VERB
ejpam-4598	292	28	is	be	AUX
ejpam-4598	292	29	epi	epi	NOUN
ejpam-4598	292	30	-	-	ADJ
ejpam-4598	292	31	completely	completely	ADV
ejpam-4598	292	32	-	-	PUNCT
ejpam-4598	292	33	regular	regular	ADJ
ejpam-4598	292	34	for	for	ADP
ejpam-4598	292	35	each	each	DET
ejpam-4598	292	36	α	α	PRON
ejpam-4598	292	37	∈	∈	PROPN
ejpam-4598	292	38	λ	λ	PROPN
ejpam-4598	292	39	.	.	PUNCT
ejpam-4598	292	40	proof	proof	NOUN
ejpam-4598	292	41	.	.	PUNCT
ejpam-4598	293	1	let	let	VERB
ejpam-4598	293	2	(	(	PUNCT
ejpam-4598	293	3	π	π	PROPN
ejpam-4598	293	4	α∈λ	α∈λ	NOUN
ejpam-4598	293	5	xα	xα	PROPN
ejpam-4598	293	6	,	,	PUNCT
ejpam-4598	293	7	t	t	PROPN
ejpam-4598	293	8	)	)	PUNCT
ejpam-4598	293	9	be	be	AUX
ejpam-4598	293	10	an	an	DET
ejpam-4598	293	11	epi	epi	NOUN
ejpam-4598	293	12	-	-	PUNCT
ejpam-4598	293	13	completely	completely	ADV
ejpam-4598	293	14	-	-	PUNCT
ejpam-4598	293	15	regular	regular	ADJ
ejpam-4598	293	16	space	space	NOUN
ejpam-4598	293	17	,	,	PUNCT
ejpam-4598	293	18	xα	xα	CCONJ
ejpam-4598	293	19	̸=	̸=	NOUN
ejpam-4598	293	20	∅	∅	NOUN
ejpam-4598	293	21	for	for	ADP
ejpam-4598	293	22	each	each	DET
ejpam-4598	293	23	α	α	NOUN
ejpam-4598	293	24	∈	∈	PROPN
ejpam-4598	293	25	λ	λ	PROPN
ejpam-4598	293	26	.	.	PUNCT
ejpam-4598	294	1	there	there	PRON
ejpam-4598	294	2	exists	exist	VERB
ejpam-4598	294	3	a	a	DET
ejpam-4598	294	4	topology	topology	NOUN
ejpam-4598	294	5	t	t	NOUN
ejpam-4598	294	6	′	′	NUM
ejpam-4598	294	7	which	which	PRON
ejpam-4598	294	8	is	be	AUX
ejpam-4598	294	9	coarser	coarse	ADJ
ejpam-4598	294	10	than	than	ADP
ejpam-4598	294	11	t	t	PRON
ejpam-4598	294	12	such	such	ADJ
ejpam-4598	294	13	that	that	SCONJ
ejpam-4598	294	14	(	(	PUNCT
ejpam-4598	294	15	π	π	PROPN
ejpam-4598	294	16	α∈λ	α∈λ	NOUN
ejpam-4598	294	17	xα	xα	PROPN
ejpam-4598	294	18	,	,	PUNCT
ejpam-4598	294	19	t	t	PROPN
ejpam-4598	294	20	′	′	NUM
ejpam-4598	294	21	)	)	PUNCT
ejpam-4598	294	22	is	be	AUX
ejpam-4598	294	23	t1	t1	NOUN
ejpam-4598	294	24	-	-	PUNCT
ejpam-4598	294	25	completelyregular	completelyregular	NOUN
ejpam-4598	294	26	.	.	PUNCT
ejpam-4598	295	1	thus	thus	ADV
ejpam-4598	295	2	,	,	PUNCT
ejpam-4598	295	3	we	we	PRON
ejpam-4598	295	4	have	have	VERB
ejpam-4598	295	5	each	each	DET
ejpam-4598	295	6	factor	factor	NOUN
ejpam-4598	295	7	(	(	PUNCT
ejpam-4598	295	8	xα	xα	PROPN
ejpam-4598	295	9	,	,	PUNCT
ejpam-4598	295	10	t	t	PROPN
ejpam-4598	295	11	′	′	NUM
ejpam-4598	295	12	α	α	X
ejpam-4598	295	13	)	)	PUNCT
ejpam-4598	295	14	is	be	AUX
ejpam-4598	295	15	a	a	DET
ejpam-4598	295	16	t1	t1	VERB
ejpam-4598	295	17	-	-	PUNCT
ejpam-4598	295	18	completely	completely	ADV
ejpam-4598	295	19	-	-	PUNCT
ejpam-4598	295	20	regular	regular	ADJ
ejpam-4598	295	21	space	space	NOUN
ejpam-4598	296	1	[	[	X
ejpam-4598	296	2	12	12	NUM
ejpam-4598	296	3	]	]	PUNCT
ejpam-4598	296	4	,	,	PUNCT
ejpam-4598	296	5	where	where	SCONJ
ejpam-4598	296	6	tα′	tα′	NOUN
ejpam-4598	296	7	is	be	AUX
ejpam-4598	296	8	a	a	DET
ejpam-4598	296	9	topology	topology	NOUN
ejpam-4598	296	10	coarser	coarse	ADJ
ejpam-4598	296	11	than	than	ADP
ejpam-4598	296	12	tα	tα	PROPN
ejpam-4598	296	13	for	for	ADP
ejpam-4598	296	14	each	each	DET
ejpam-4598	296	15	α	α	PRON
ejpam-4598	296	16	∈	∈	PROPN
ejpam-4598	296	17	λ	λ	PROPN
ejpam-4598	296	18	.	.	PUNCT
ejpam-4598	296	19	thus	thus	ADV
ejpam-4598	296	20	,	,	PUNCT
ejpam-4598	296	21	(	(	PUNCT
ejpam-4598	296	22	xα	xα	INTJ
ejpam-4598	296	23	,	,	PUNCT
ejpam-4598	296	24	tα	tα	PROPN
ejpam-4598	296	25	)	)	PUNCT
ejpam-4598	296	26	is	be	AUX
ejpam-4598	296	27	an	an	DET
ejpam-4598	296	28	epi	epi	NOUN
ejpam-4598	296	29	-	-	ADJ
ejpam-4598	296	30	completely	completely	ADV
ejpam-4598	296	31	regular	regular	ADJ
ejpam-4598	296	32	space	space	NOUN
ejpam-4598	296	33	for	for	ADP
ejpam-4598	296	34	each	each	DET
ejpam-4598	296	35	α	α	PRON
ejpam-4598	296	36	∈	∈	PROPN
ejpam-4598	296	37	λ	λ	NOUN
ejpam-4598	296	38	.	.	PUNCT
ejpam-4598	297	1	conversely	conversely	ADV
ejpam-4598	297	2	,	,	PUNCT
ejpam-4598	297	3	suppose	suppose	VERB
ejpam-4598	297	4	that	that	SCONJ
ejpam-4598	297	5	(	(	PUNCT
ejpam-4598	297	6	xα	xα	INTJ
ejpam-4598	297	7	,	,	PUNCT
ejpam-4598	297	8	tα	tα	PROPN
ejpam-4598	297	9	)	)	PUNCT
ejpam-4598	297	10	is	be	AUX
ejpam-4598	297	11	an	an	DET
ejpam-4598	297	12	epi	epi	NOUN
ejpam-4598	297	13	-	-	PUNCT
ejpam-4598	297	14	completely	completely	ADV
ejpam-4598	297	15	-	-	PUNCT
ejpam-4598	297	16	regular	regular	ADJ
ejpam-4598	297	17	space	space	NOUN
ejpam-4598	297	18	for	for	ADP
ejpam-4598	297	19	each	each	DET
ejpam-4598	297	20	α	α	NOUN
ejpam-4598	297	21	∈	∈	PROPN
ejpam-4598	297	22	λ	λ	PROPN
ejpam-4598	297	23	.	.	PUNCT
ejpam-4598	298	1	then	then	ADV
ejpam-4598	298	2	,	,	PUNCT
ejpam-4598	298	3	for	for	ADP
ejpam-4598	298	4	each	each	DET
ejpam-4598	298	5	α	α	PROPN
ejpam-4598	298	6	∈	∈	PROPN
ejpam-4598	298	7	λ	λ	NOUN
ejpam-4598	298	8	,	,	PUNCT
ejpam-4598	298	9	there	there	PRON
ejpam-4598	298	10	exists	exist	VERB
ejpam-4598	298	11	a	a	DET
ejpam-4598	298	12	topology	topology	NOUN
ejpam-4598	298	13	tα′	tα′	NOUN
ejpam-4598	298	14	that	that	PRON
ejpam-4598	298	15	is	be	AUX
ejpam-4598	298	16	coarser	coarse	ADJ
ejpam-4598	298	17	than	than	ADP
ejpam-4598	298	18	tα	tα	ADP
ejpam-4598	298	19	such	such	ADJ
ejpam-4598	298	20	that	that	PRON
ejpam-4598	298	21	(	(	PUNCT
ejpam-4598	298	22	xα	xα	ADJ
ejpam-4598	298	23	,	,	PUNCT
ejpam-4598	298	24	tα′	tα′	NOUN
ejpam-4598	298	25	)	)	PUNCT
ejpam-4598	298	26	is	be	AUX
ejpam-4598	298	27	a	a	DET
ejpam-4598	298	28	t1	t1	VERB
ejpam-4598	298	29	-	-	PUNCT
ejpam-4598	298	30	completely	completely	ADV
ejpam-4598	298	31	-	-	PUNCT
ejpam-4598	298	32	regular	regular	ADJ
ejpam-4598	298	33	space	space	NOUN
ejpam-4598	298	34	.	.	PUNCT
ejpam-4598	299	1	thus	thus	ADV
ejpam-4598	299	2	,	,	PUNCT
ejpam-4598	299	3	the	the	DET
ejpam-4598	299	4	product	product	NOUN
ejpam-4598	299	5	space	space	NOUN
ejpam-4598	299	6	(	(	PUNCT
ejpam-4598	299	7	π	π	PROPN
ejpam-4598	299	8	α∈λ	α∈λ	NOUN
ejpam-4598	299	9	xα	xα	PROPN
ejpam-4598	299	10	,	,	PUNCT
ejpam-4598	299	11	t	t	PROPN
ejpam-4598	299	12	′	′	NUM
ejpam-4598	299	13	)	)	PUNCT
ejpam-4598	299	14	is	be	AUX
ejpam-4598	299	15	t1	t1	NOUN
ejpam-4598	299	16	-	-	PUNCT
ejpam-4598	299	17	completely	completely	ADV
ejpam-4598	299	18	-	-	PUNCT
ejpam-4598	299	19	regular	regular	ADJ
ejpam-4598	299	20	,	,	PUNCT
ejpam-4598	299	21	where	where	SCONJ
ejpam-4598	299	22	t	t	PROPN
ejpam-4598	299	23	′	′	NOUN
ejpam-4598	299	24	is	be	AUX
ejpam-4598	299	25	coarser	coarse	ADJ
ejpam-4598	299	26	than	than	ADP
ejpam-4598	299	27	t	t	PROPN
ejpam-4598	299	28	.	.	PUNCT
ejpam-4598	300	1	therefore	therefore	ADV
ejpam-4598	300	2	,	,	PUNCT
ejpam-4598	300	3	(	(	PUNCT
ejpam-4598	300	4	π	π	PROPN
ejpam-4598	300	5	α∈λ	α∈λ	NOUN
ejpam-4598	300	6	xα	xα	PROPN
ejpam-4598	300	7	,	,	PUNCT
ejpam-4598	300	8	t	t	PROPN
ejpam-4598	300	9	)	)	PUNCT
ejpam-4598	300	10	is	be	AUX
ejpam-4598	300	11	epi	epi	NOUN
ejpam-4598	300	12	-	-	ADJ
ejpam-4598	300	13	completely	completely	ADV
ejpam-4598	300	14	-	-	PUNCT
ejpam-4598	300	15	regular	regular	ADJ
ejpam-4598	300	16	.	.	PUNCT
ejpam-4598	301	1	corollary	corollary	ADJ
ejpam-4598	301	2	3	3	NUM
ejpam-4598	301	3	.	.	PUNCT
ejpam-4598	302	1	epi	epi	X
ejpam-4598	302	2	-	-	ADJ
ejpam-4598	302	3	complete	complete	ADJ
ejpam-4598	302	4	regularity	regularity	NOUN
ejpam-4598	302	5	is	be	AUX
ejpam-4598	302	6	a	a	DET
ejpam-4598	302	7	multiplicative	multiplicative	ADJ
ejpam-4598	302	8	property	property	NOUN
ejpam-4598	302	9	.	.	PUNCT
ejpam-4598	303	1	theorem	theorem	VERB
ejpam-4598	303	2	8	8	NUM
ejpam-4598	303	3	.	.	PUNCT
ejpam-4598	304	1	every	every	DET
ejpam-4598	304	2	epi	epi	NOUN
ejpam-4598	304	3	-	-	ADJ
ejpam-4598	304	4	completely	completely	ADV
ejpam-4598	304	5	regular	regular	ADJ
ejpam-4598	304	6	nearly	nearly	ADV
ejpam-4598	304	7	-	-	PUNCT
ejpam-4598	304	8	compact	compact	ADJ
ejpam-4598	304	9	(	(	PUNCT
ejpam-4598	304	10	resp	resp	NOUN
ejpam-4598	304	11	.	.	PUNCT
ejpam-4598	305	1	nearly	nearly	ADV
ejpam-4598	305	2	-	-	PUNCT
ejpam-4598	305	3	paracompact	paracompact	ADJ
ejpam-4598	305	4	)	)	PUNCT
ejpam-4598	305	5	space	space	NOUN
ejpam-4598	305	6	is	be	AUX
ejpam-4598	305	7	epi	epi	NOUN
ejpam-4598	305	8	-	-	ADJ
ejpam-4598	305	9	normal	normal	ADJ
ejpam-4598	305	10	.	.	PUNCT
ejpam-4598	306	1	proof	proof	NOUN
ejpam-4598	306	2	.	.	PUNCT
ejpam-4598	307	1	let	let	AUX
ejpam-4598	307	2	(	(	PUNCT
ejpam-4598	307	3	x	x	X
ejpam-4598	307	4	,	,	PUNCT
ejpam-4598	307	5	t	t	PROPN
ejpam-4598	307	6	)	)	PUNCT
ejpam-4598	307	7	be	be	AUX
ejpam-4598	307	8	an	an	DET
ejpam-4598	307	9	epi	epi	NOUN
ejpam-4598	307	10	-	-	PUNCT
ejpam-4598	307	11	completely	completely	ADV
ejpam-4598	307	12	-	-	PUNCT
ejpam-4598	307	13	regular	regular	ADJ
ejpam-4598	307	14	nearly	nearly	ADV
ejpam-4598	307	15	-	-	PUNCT
ejpam-4598	307	16	compact	compact	ADJ
ejpam-4598	307	17	(	(	PUNCT
ejpam-4598	307	18	resp	resp	NOUN
ejpam-4598	307	19	.	.	PUNCT
ejpam-4598	308	1	nearly	nearly	ADV
ejpam-4598	308	2	-	-	PUNCT
ejpam-4598	308	3	paracompact	paracompact	ADJ
ejpam-4598	308	4	)	)	PUNCT
ejpam-4598	308	5	space	space	NOUN
ejpam-4598	308	6	.	.	PUNCT
ejpam-4598	309	1	then	then	ADV
ejpam-4598	309	2	,	,	PUNCT
ejpam-4598	309	3	there	there	PRON
ejpam-4598	309	4	exists	exist	VERB
ejpam-4598	309	5	a	a	DET
ejpam-4598	309	6	topology	topology	NOUN
ejpam-4598	309	7	t	t	NOUN
ejpam-4598	309	8	′	′	NUM
ejpam-4598	309	9	on	on	ADP
ejpam-4598	309	10	x	x	PUNCT
ejpam-4598	309	11	which	which	PRON
ejpam-4598	309	12	is	be	AUX
ejpam-4598	309	13	coarser	coarse	ADJ
ejpam-4598	309	14	than	than	ADP
ejpam-4598	309	15	t	t	NOUN
ejpam-4598	309	16	such	such	ADJ
ejpam-4598	309	17	that	that	SCONJ
ejpam-4598	309	18	(	(	PUNCT
ejpam-4598	309	19	x	x	X
ejpam-4598	309	20	,	,	PUNCT
ejpam-4598	309	21	t	t	PROPN
ejpam-4598	309	22	′	′	NUM
ejpam-4598	309	23	)	)	PUNCT
ejpam-4598	309	24	is	be	AUX
ejpam-4598	309	25	a	a	DET
ejpam-4598	309	26	tychonoff	tychonoff	NOUN
ejpam-4598	309	27	compact	compact	ADJ
ejpam-4598	309	28	(	(	PUNCT
ejpam-4598	309	29	resp	resp	NOUN
ejpam-4598	309	30	.	.	PUNCT
ejpam-4598	309	31	paracompact	paracompact	ADJ
ejpam-4598	309	32	)	)	PUNCT
ejpam-4598	309	33	space	space	NOUN
ejpam-4598	309	34	.	.	PUNCT
ejpam-4598	310	1	thus	thus	ADV
ejpam-4598	310	2	,	,	PUNCT
ejpam-4598	310	3	(	(	PUNCT
ejpam-4598	310	4	x	x	X
ejpam-4598	310	5	,	,	PUNCT
ejpam-4598	310	6	t	t	PROPN
ejpam-4598	310	7	′	′	NUM
ejpam-4598	310	8	)	)	PUNCT
ejpam-4598	310	9	is	be	AUX
ejpam-4598	310	10	a	a	DET
ejpam-4598	310	11	t1	t1	ADJ
ejpam-4598	310	12	-	-	PUNCT
ejpam-4598	310	13	normal	normal	ADJ
ejpam-4598	310	14	space	space	NOUN
ejpam-4598	310	15	.	.	PUNCT
ejpam-4598	311	1	hence	hence	ADV
ejpam-4598	311	2	,	,	PUNCT
ejpam-4598	311	3	(	(	PUNCT
ejpam-4598	311	4	x	x	X
ejpam-4598	311	5	,	,	PUNCT
ejpam-4598	311	6	t	t	PROPN
ejpam-4598	311	7	′	′	NUM
ejpam-4598	311	8	)	)	PUNCT
ejpam-4598	311	9	is	be	AUX
ejpam-4598	311	10	a	a	DET
ejpam-4598	311	11	t4	t4	PROPN
ejpam-4598	311	12	-	-	PUNCT
ejpam-4598	311	13	space	space	NOUN
ejpam-4598	311	14	.	.	PUNCT
ejpam-4598	312	1	therefore	therefore	ADV
ejpam-4598	312	2	,	,	PUNCT
ejpam-4598	312	3	(	(	PUNCT
ejpam-4598	312	4	x	x	X
ejpam-4598	312	5	,	,	PUNCT
ejpam-4598	312	6	t	t	PROPN
ejpam-4598	312	7	)	)	PUNCT
ejpam-4598	312	8	is	be	AUX
ejpam-4598	312	9	epi	epi	NOUN
ejpam-4598	312	10	-	-	ADJ
ejpam-4598	312	11	normal	normal	ADJ
ejpam-4598	312	12	.	.	PUNCT
ejpam-4598	313	1	now	now	ADV
ejpam-4598	313	2	,	,	PUNCT
ejpam-4598	313	3	we	we	PRON
ejpam-4598	313	4	recall	recall	VERB
ejpam-4598	313	5	the	the	DET
ejpam-4598	313	6	definition	definition	NOUN
ejpam-4598	313	7	of	of	ADP
ejpam-4598	313	8	the	the	DET
ejpam-4598	313	9	alexandroff	alexandroff	NOUN
ejpam-4598	313	10	duplicate	duplicate	ADJ
ejpam-4598	313	11	space	space	NOUN
ejpam-4598	313	12	.	.	PUNCT
ejpam-4598	314	1	for	for	ADP
ejpam-4598	314	2	any	any	DET
ejpam-4598	314	3	space	space	NOUN
ejpam-4598	314	4	x	x	NOUN
ejpam-4598	314	5	,	,	PUNCT
ejpam-4598	314	6	let	let	VERB
ejpam-4598	314	7	x	x	X
ejpam-4598	314	8	′	′	NUM
ejpam-4598	315	1	=	=	PUNCT
ejpam-4598	315	2	x	x	SYM
ejpam-4598	315	3	×	×	NOUN
ejpam-4598	315	4	{	{	PUNCT
ejpam-4598	315	5	1	1	NUM
ejpam-4598	315	6	}	}	PUNCT
ejpam-4598	315	7	.	.	PUNCT
ejpam-4598	316	1	clearly	clearly	ADV
ejpam-4598	316	2	that	that	SCONJ
ejpam-4598	316	3	x	x	X
ejpam-4598	316	4	∩x	∩x	NOUN
ejpam-4598	316	5	′	′	NUM
ejpam-4598	316	6	=	=	PUNCT
ejpam-4598	316	7	∅.	∅.	AUX
ejpam-4598	316	8	let	let	VERB
ejpam-4598	316	9	a(x	a(x	NOUN
ejpam-4598	316	10	)	)	PUNCT
ejpam-4598	316	11	=	=	PUNCT
ejpam-4598	316	12	x	x	SYM
ejpam-4598	316	13	∪x	∪x	X
ejpam-4598	316	14	′.	′.	NOUN
ejpam-4598	316	15	for	for	ADP
ejpam-4598	316	16	an	an	DET
ejpam-4598	316	17	element	element	NOUN
ejpam-4598	316	18	x	x	SYM
ejpam-4598	316	19	∈	∈	PROPN
ejpam-4598	316	20	x	x	NOUN
ejpam-4598	316	21	,	,	PUNCT
ejpam-4598	316	22	the	the	DET
ejpam-4598	316	23	element	element	NOUN
ejpam-4598	316	24	(	(	PUNCT
ejpam-4598	316	25	x	x	X
ejpam-4598	316	26	,	,	PUNCT
ejpam-4598	316	27	1	1	NUM
ejpam-4598	316	28	)	)	PUNCT
ejpam-4598	316	29	∈	∈	NOUN
ejpam-4598	316	30	x	x	PUNCT
ejpam-4598	317	1	′	′	NOUN
ejpam-4598	318	1	and	and	CCONJ
ejpam-4598	318	2	for	for	ADP
ejpam-4598	318	3	a	a	DET
ejpam-4598	318	4	subset	subset	NOUN
ejpam-4598	318	5	b	b	NOUN
ejpam-4598	318	6	⊆	⊆	NUM
ejpam-4598	318	7	x	x	NUM
ejpam-4598	318	8	,	,	PUNCT
ejpam-4598	318	9	let	let	VERB
ejpam-4598	318	10	b×{1	b×{1	NOUN
ejpam-4598	318	11	}	}	PUNCT
ejpam-4598	318	12	=	=	SYM
ejpam-4598	318	13	{	{	PUNCT
ejpam-4598	318	14	(	(	PUNCT
ejpam-4598	318	15	x	x	NOUN
ejpam-4598	318	16	,	,	PUNCT
ejpam-4598	318	17	1	1	NUM
ejpam-4598	318	18	)	)	PUNCT
ejpam-4598	318	19	:	:	PUNCT
ejpam-4598	319	1	x	x	X
ejpam-4598	319	2	∈	∈	PROPN
ejpam-4598	319	3	b	b	X
ejpam-4598	319	4	}	}	PUNCT
ejpam-4598	319	5	⊆	⊆	NUM
ejpam-4598	319	6	x	x	SYM
ejpam-4598	319	7	′.	′.	NOUN
ejpam-4598	319	8	for	for	ADP
ejpam-4598	319	9	each	each	DET
ejpam-4598	319	10	(	(	PUNCT
ejpam-4598	319	11	x	x	NOUN
ejpam-4598	319	12	,	,	PUNCT
ejpam-4598	319	13	1	1	NUM
ejpam-4598	319	14	)	)	PUNCT
ejpam-4598	319	15	∈	∈	NOUN
ejpam-4598	319	16	x	x	SYM
ejpam-4598	319	17	′	′	NOUN
ejpam-4598	319	18	,	,	PUNCT
ejpam-4598	319	19	let	let	VERB
ejpam-4598	319	20	b((x	b((x	NOUN
ejpam-4598	319	21	,	,	PUNCT
ejpam-4598	319	22	1	1	NUM
ejpam-4598	319	23	)	)	PUNCT
ejpam-4598	319	24	)	)	PUNCT
ejpam-4598	320	1	=	=	PRON
ejpam-4598	320	2	{	{	PUNCT
ejpam-4598	320	3	{	{	PUNCT
ejpam-4598	320	4	(	(	PUNCT
ejpam-4598	320	5	x	x	NOUN
ejpam-4598	320	6	,	,	PUNCT
ejpam-4598	320	7	1	1	NUM
ejpam-4598	320	8	)	)	PUNCT
ejpam-4598	320	9	}	}	PUNCT
ejpam-4598	320	10	}	}	PUNCT
ejpam-4598	320	11	.	.	PUNCT
ejpam-4598	321	1	for	for	ADP
ejpam-4598	321	2	each	each	DET
ejpam-4598	321	3	x	x	SYM
ejpam-4598	321	4	∈	∈	PROPN
ejpam-4598	321	5	x	x	NOUN
ejpam-4598	321	6	,	,	PUNCT
ejpam-4598	321	7	let	let	VERB
ejpam-4598	321	8	b(x	b(x	NOUN
ejpam-4598	321	9	)	)	PUNCT
ejpam-4598	321	10	=	=	SYM
ejpam-4598	321	11	{	{	PUNCT
ejpam-4598	321	12	u∪(u×{1}\{(x	u∪(u×{1}\{(x	PROPN
ejpam-4598	321	13	,	,	PUNCT
ejpam-4598	321	14	1	1	NUM
ejpam-4598	321	15	)	)	PUNCT
ejpam-4598	321	16	}	}	PUNCT
ejpam-4598	321	17	)	)	PUNCT
ejpam-4598	321	18	:	:	PUNCT
ejpam-4598	321	19	i.	i.	PROPN
ejpam-4598	321	20	alshammari	alshammari	PROPN
ejpam-4598	321	21	/	/	SYM
ejpam-4598	321	22	eur	eur	PROPN
ejpam-4598	321	23	.	.	PUNCT
ejpam-4598	322	1	j.	j.	PROPN
ejpam-4598	322	2	pure	pure	PROPN
ejpam-4598	322	3	appl	appl	PROPN
ejpam-4598	322	4	.	.	PROPN
ejpam-4598	322	5	math	math	PROPN
ejpam-4598	322	6	,	,	PUNCT
ejpam-4598	322	7	15	15	NUM
ejpam-4598	322	8	(	(	PUNCT
ejpam-4598	322	9	4	4	NUM
ejpam-4598	322	10	)	)	PUNCT
ejpam-4598	322	11	(	(	PUNCT
ejpam-4598	322	12	2022	2022	NUM
ejpam-4598	322	13	)	)	PUNCT
ejpam-4598	322	14	,	,	PUNCT
ejpam-4598	322	15	1808	1808	NUM
ejpam-4598	322	16	-	-	SYM
ejpam-4598	322	17	1821	1821	NUM
ejpam-4598	322	18	1817	1817	NUM
ejpam-4598	322	19	u	u	NOUN
ejpam-4598	322	20	is	be	AUX
ejpam-4598	322	21	open	open	ADJ
ejpam-4598	322	22	in	in	ADP
ejpam-4598	322	23	x	x	PUNCT
ejpam-4598	322	24	with	with	ADP
ejpam-4598	322	25	x	x	PROPN
ejpam-4598	322	26	∈	∈	PROPN
ejpam-4598	322	27	u	u	NOUN
ejpam-4598	322	28	}	}	PUNCT
ejpam-4598	322	29	.	.	PUNCT
ejpam-4598	323	1	let	let	VERB
ejpam-4598	323	2	t	t	PROPN
ejpam-4598	323	3	denote	denote	VERB
ejpam-4598	323	4	the	the	DET
ejpam-4598	323	5	unique	unique	ADJ
ejpam-4598	323	6	topology	topology	NOUN
ejpam-4598	323	7	on	on	ADP
ejpam-4598	323	8	a(x	a(x	NOUN
ejpam-4598	323	9	)	)	PUNCT
ejpam-4598	323	10	which	which	PRON
ejpam-4598	323	11	has	have	AUX
ejpam-4598	323	12	{	{	PUNCT
ejpam-4598	323	13	b(x	b(x	NOUN
ejpam-4598	323	14	)	)	PUNCT
ejpam-4598	323	15	:	:	PUNCT
ejpam-4598	324	1	x	x	X
ejpam-4598	324	2	∈	∈	NOUN
ejpam-4598	324	3	x	x	SYM
ejpam-4598	324	4	}	}	PUNCT
ejpam-4598	324	5	∪	∪	ADJ
ejpam-4598	324	6	{	{	PUNCT
ejpam-4598	324	7	b((x	b((x	NOUN
ejpam-4598	324	8	,	,	PUNCT
ejpam-4598	324	9	1	1	NUM
ejpam-4598	324	10	)	)	PUNCT
ejpam-4598	324	11	)	)	PUNCT
ejpam-4598	324	12	:	:	PUNCT
ejpam-4598	324	13	(	(	PUNCT
ejpam-4598	324	14	x	x	X
ejpam-4598	324	15	,	,	PUNCT
ejpam-4598	324	16	1	1	NUM
ejpam-4598	324	17	)	)	PUNCT
ejpam-4598	324	18	∈	∈	NOUN
ejpam-4598	324	19	x	x	NOUN
ejpam-4598	324	20	′	′	NOUN
ejpam-4598	324	21	}	}	PUNCT
ejpam-4598	324	22	as	as	ADP
ejpam-4598	324	23	its	its	PRON
ejpam-4598	324	24	neighborhood	neighborhood	NOUN
ejpam-4598	324	25	system	system	NOUN
ejpam-4598	324	26	.	.	PUNCT
ejpam-4598	325	1	the	the	DET
ejpam-4598	325	2	space	space	NOUN
ejpam-4598	325	3	a(x	a(x	NOUN
ejpam-4598	325	4	)	)	PUNCT
ejpam-4598	325	5	with	with	ADP
ejpam-4598	325	6	this	this	DET
ejpam-4598	325	7	topology	topology	NOUN
ejpam-4598	325	8	is	be	AUX
ejpam-4598	325	9	called	call	VERB
ejpam-4598	325	10	the	the	DET
ejpam-4598	325	11	alexandroff	alexandroff	ADJ
ejpam-4598	325	12	duplicate	duplicate	NOUN
ejpam-4598	325	13	of	of	ADP
ejpam-4598	325	14	x	x	PUNCT
ejpam-4598	326	1	[	[	X
ejpam-4598	326	2	2	2	NUM
ejpam-4598	326	3	]	]	PUNCT
ejpam-4598	326	4	.	.	PUNCT
ejpam-4598	327	1	theorem	theorem	VERB
ejpam-4598	327	2	9	9	NUM
ejpam-4598	327	3	.	.	PUNCT
ejpam-4598	328	1	the	the	DET
ejpam-4598	328	2	alexandroff	alexandroff	NOUN
ejpam-4598	328	3	duplicate	duplicate	VERB
ejpam-4598	328	4	a(x	a(x	NOUN
ejpam-4598	328	5	)	)	PUNCT
ejpam-4598	328	6	of	of	ADP
ejpam-4598	328	7	an	an	DET
ejpam-4598	328	8	epi	epi	NOUN
ejpam-4598	328	9	-	-	PUNCT
ejpam-4598	328	10	completely	completely	ADV
ejpam-4598	328	11	-	-	PUNCT
ejpam-4598	328	12	regular	regular	ADJ
ejpam-4598	328	13	space	space	NOUN
ejpam-4598	328	14	x	x	PUNCT
ejpam-4598	328	15	is	be	AUX
ejpam-4598	328	16	epi	epi	VERB
ejpam-4598	328	17	-	-	ADJ
ejpam-4598	328	18	completely	completely	ADV
ejpam-4598	328	19	-	-	PUNCT
ejpam-4598	328	20	regular	regular	ADJ
ejpam-4598	328	21	.	.	PUNCT
ejpam-4598	329	1	proof	proof	NOUN
ejpam-4598	329	2	.	.	PUNCT
ejpam-4598	330	1	let	let	AUX
ejpam-4598	330	2	(	(	PUNCT
ejpam-4598	330	3	x	x	X
ejpam-4598	330	4	,	,	PUNCT
ejpam-4598	330	5	t	t	PROPN
ejpam-4598	330	6	)	)	PUNCT
ejpam-4598	330	7	be	be	AUX
ejpam-4598	330	8	an	an	DET
ejpam-4598	330	9	epi	epi	NOUN
ejpam-4598	330	10	-	-	PUNCT
ejpam-4598	330	11	completely	completely	ADV
ejpam-4598	330	12	-	-	PUNCT
ejpam-4598	330	13	regular	regular	ADJ
ejpam-4598	330	14	space	space	NOUN
ejpam-4598	330	15	.	.	PUNCT
ejpam-4598	331	1	then	then	ADV
ejpam-4598	331	2	,	,	PUNCT
ejpam-4598	331	3	there	there	PRON
ejpam-4598	331	4	exists	exist	VERB
ejpam-4598	331	5	a	a	DET
ejpam-4598	331	6	topology	topology	NOUN
ejpam-4598	331	7	t	t	NOUN
ejpam-4598	331	8	′	′	NUM
ejpam-4598	331	9	on	on	ADP
ejpam-4598	331	10	x	x	PUNCT
ejpam-4598	331	11	that	that	PRON
ejpam-4598	331	12	is	be	AUX
ejpam-4598	331	13	coarser	coarse	ADJ
ejpam-4598	331	14	than	than	ADP
ejpam-4598	331	15	t	t	NOUN
ejpam-4598	331	16	such	such	ADJ
ejpam-4598	331	17	that	that	SCONJ
ejpam-4598	331	18	(	(	PUNCT
ejpam-4598	331	19	x	x	X
ejpam-4598	331	20	,	,	PUNCT
ejpam-4598	331	21	t	t	PROPN
ejpam-4598	331	22	′	′	NUM
ejpam-4598	331	23	)	)	PUNCT
ejpam-4598	331	24	is	be	AUX
ejpam-4598	331	25	t1	t1	NOUN
ejpam-4598	331	26	-	-	PUNCT
ejpam-4598	331	27	completely	completely	ADV
ejpam-4598	331	28	-	-	PUNCT
ejpam-4598	331	29	regular	regular	ADJ
ejpam-4598	331	30	.	.	PUNCT
ejpam-4598	332	1	since	since	SCONJ
ejpam-4598	332	2	t1	t1	NOUN
ejpam-4598	332	3	and	and	CCONJ
ejpam-4598	332	4	complete	complete	ADJ
ejpam-4598	332	5	-	-	PUNCT
ejpam-4598	332	6	regularity	regularity	NOUN
ejpam-4598	332	7	are	be	AUX
ejpam-4598	332	8	preserved	preserve	VERB
ejpam-4598	332	9	by	by	ADP
ejpam-4598	332	10	the	the	DET
ejpam-4598	332	11	alexandroff	alexandroff	NOUN
ejpam-4598	332	12	duplicate	duplicate	NOUN
ejpam-4598	332	13	space	space	NOUN
ejpam-4598	332	14	[	[	X
ejpam-4598	332	15	2	2	NUM
ejpam-4598	332	16	]	]	PUNCT
ejpam-4598	332	17	,	,	PUNCT
ejpam-4598	332	18	we	we	PRON
ejpam-4598	332	19	obtain	obtain	VERB
ejpam-4598	332	20	:	:	PUNCT
ejpam-4598	332	21	a(x	a(x	NOUN
ejpam-4598	332	22	,	,	PUNCT
ejpam-4598	332	23	t	t	NOUN
ejpam-4598	332	24	′	′	NUM
ejpam-4598	332	25	)	)	PUNCT
ejpam-4598	332	26	is	be	AUX
ejpam-4598	332	27	also	also	ADV
ejpam-4598	332	28	a	a	DET
ejpam-4598	332	29	t1	t1	VERB
ejpam-4598	332	30	-	-	PUNCT
ejpam-4598	332	31	completely	completely	ADV
ejpam-4598	332	32	-	-	PUNCT
ejpam-4598	332	33	regular	regular	ADJ
ejpam-4598	332	34	space	space	NOUN
ejpam-4598	332	35	,	,	PUNCT
ejpam-4598	332	36	which	which	PRON
ejpam-4598	332	37	is	be	AUX
ejpam-4598	332	38	coarser	coarse	ADJ
ejpam-4598	332	39	than	than	ADP
ejpam-4598	332	40	a(x	a(x	NOUN
ejpam-4598	332	41	,	,	PUNCT
ejpam-4598	332	42	t	t	NOUN
ejpam-4598	332	43	)	)	PUNCT
ejpam-4598	332	44	by	by	ADP
ejpam-4598	332	45	the	the	DET
ejpam-4598	332	46	topology	topology	NOUN
ejpam-4598	332	47	of	of	ADP
ejpam-4598	332	48	the	the	DET
ejpam-4598	332	49	alexandroff	alexandroff	NOUN
ejpam-4598	332	50	duplicate	duplicate	NOUN
ejpam-4598	332	51	.	.	PUNCT
ejpam-4598	333	1	hence	hence	ADV
ejpam-4598	333	2	,	,	PUNCT
ejpam-4598	333	3	a(x	a(x	PROPN
ejpam-4598	333	4	)	)	PUNCT
ejpam-4598	333	5	is	be	AUX
ejpam-4598	333	6	epi	epi	NOUN
ejpam-4598	333	7	-	-	ADJ
ejpam-4598	333	8	completely	completely	ADV
ejpam-4598	333	9	-	-	PUNCT
ejpam-4598	333	10	regular	regular	ADJ
ejpam-4598	333	11	.	.	PUNCT
ejpam-4598	334	1	since	since	SCONJ
ejpam-4598	334	2	every	every	DET
ejpam-4598	334	3	subspace	subspace	NOUN
ejpam-4598	334	4	of	of	ADP
ejpam-4598	334	5	a	a	DET
ejpam-4598	334	6	cube	cube	NOUN
ejpam-4598	334	7	is	be	AUX
ejpam-4598	334	8	completely	completely	ADV
ejpam-4598	334	9	-	-	PUNCT
ejpam-4598	334	10	regular	regular	ADJ
ejpam-4598	334	11	[	[	X
ejpam-4598	334	12	12	12	NUM
ejpam-4598	334	13	]	]	PUNCT
ejpam-4598	334	14	,	,	PUNCT
ejpam-4598	334	15	we	we	PRON
ejpam-4598	334	16	get	get	VERB
ejpam-4598	334	17	:	:	PUNCT
ejpam-4598	334	18	corollary	corollary	ADJ
ejpam-4598	334	19	4	4	NUM
ejpam-4598	334	20	.	.	PUNCT
ejpam-4598	335	1	every	every	DET
ejpam-4598	335	2	t1	t1	NOUN
ejpam-4598	335	3	-	-	PUNCT
ejpam-4598	335	4	subspace	subspace	NOUN
ejpam-4598	335	5	of	of	ADP
ejpam-4598	335	6	a	a	DET
ejpam-4598	335	7	cube	cube	NOUN
ejpam-4598	335	8	is	be	AUX
ejpam-4598	335	9	epi	epi	NOUN
ejpam-4598	335	10	-	-	ADJ
ejpam-4598	335	11	completely	completely	ADV
ejpam-4598	335	12	-	-	PUNCT
ejpam-4598	335	13	regular	regular	ADJ
ejpam-4598	335	14	.	.	PUNCT
ejpam-4598	336	1	since	since	SCONJ
ejpam-4598	336	2	every	every	DET
ejpam-4598	336	3	c2	c2	PROPN
ejpam-4598	336	4	-	-	PUNCT
ejpam-4598	336	5	paracompact	paracompact	NOUN
ejpam-4598	336	6	fréchet	fréchet	NOUN
ejpam-4598	336	7	space	space	NOUN
ejpam-4598	336	8	is	be	AUX
ejpam-4598	336	9	epi	epi	NOUN
ejpam-4598	336	10	-	-	ADJ
ejpam-4598	336	11	normal	normal	ADJ
ejpam-4598	336	12	,	,	PUNCT
ejpam-4598	336	13	and	and	CCONJ
ejpam-4598	336	14	any	any	DET
ejpam-4598	336	15	mrôwka	mrôwka	ADJ
ejpam-4598	336	16	space	space	NOUN
ejpam-4598	336	17	ψ(a	ψ(a	PROPN
ejpam-4598	336	18	)	)	PUNCT
ejpam-4598	336	19	is	be	AUX
ejpam-4598	336	20	tychonoff	tychonoff	NOUN
ejpam-4598	337	1	[	[	X
ejpam-4598	337	2	18	18	NUM
ejpam-4598	337	3	]	]	PUNCT
ejpam-4598	337	4	,	,	PUNCT
ejpam-4598	337	5	we	we	PRON
ejpam-4598	337	6	obtain	obtain	VERB
ejpam-4598	337	7	:	:	PUNCT
ejpam-4598	337	8	corollary	corollary	ADJ
ejpam-4598	337	9	5	5	NUM
ejpam-4598	337	10	.	.	PUNCT
ejpam-4598	338	1	(	(	PUNCT
ejpam-4598	338	2	1	1	X
ejpam-4598	338	3	)	)	PUNCT
ejpam-4598	338	4	every	every	DET
ejpam-4598	338	5	c2	c2	PROPN
ejpam-4598	338	6	-	-	PUNCT
ejpam-4598	338	7	paracompact	paracompact	ADJ
ejpam-4598	338	8	first	first	ADJ
ejpam-4598	338	9	-	-	PUNCT
ejpam-4598	338	10	countable	countable	ADJ
ejpam-4598	338	11	space	space	NOUN
ejpam-4598	338	12	is	be	AUX
ejpam-4598	338	13	epi	epi	NOUN
ejpam-4598	338	14	-	-	ADJ
ejpam-4598	338	15	completely	completely	ADV
ejpam-4598	338	16	-	-	PUNCT
ejpam-4598	338	17	regular	regular	ADJ
ejpam-4598	338	18	.	.	PUNCT
ejpam-4598	339	1	(	(	PUNCT
ejpam-4598	339	2	2	2	X
ejpam-4598	339	3	)	)	PUNCT
ejpam-4598	339	4	any	any	DET
ejpam-4598	339	5	mrôwka	mrôwka	ADJ
ejpam-4598	339	6	space	space	NOUN
ejpam-4598	339	7	ψ(a	ψ(a	PROPN
ejpam-4598	339	8	)	)	PUNCT
ejpam-4598	339	9	is	be	AUX
ejpam-4598	339	10	epi	epi	NOUN
ejpam-4598	339	11	-	-	ADJ
ejpam-4598	339	12	completely	completely	ADV
ejpam-4598	339	13	-	-	PUNCT
ejpam-4598	339	14	regular	regular	ADJ
ejpam-4598	339	15	.	.	PUNCT
ejpam-4598	340	1	note	note	VERB
ejpam-4598	340	2	that	that	SCONJ
ejpam-4598	340	3	:	:	PUNCT
ejpam-4598	340	4	a	a	DET
ejpam-4598	340	5	space	space	NOUN
ejpam-4598	340	6	(	(	PUNCT
ejpam-4598	340	7	x	x	X
ejpam-4598	340	8	,	,	PUNCT
ejpam-4598	340	9	t	t	PROPN
ejpam-4598	340	10	)	)	PUNCT
ejpam-4598	340	11	is	be	AUX
ejpam-4598	340	12	an	an	DET
ejpam-4598	340	13	almost	almost	ADV
ejpam-4598	340	14	-	-	PUNCT
ejpam-4598	340	15	completely	completely	ADV
ejpam-4598	340	16	regular	regular	ADJ
ejpam-4598	340	17	space	space	NOUN
ejpam-4598	340	18	if	if	SCONJ
ejpam-4598	340	19	and	and	CCONJ
ejpam-4598	340	20	only	only	ADV
ejpam-4598	340	21	if	if	SCONJ
ejpam-4598	340	22	the	the	DET
ejpam-4598	340	23	semi	semi	ADJ
ejpam-4598	340	24	-	-	NOUN
ejpam-4598	340	25	regularization	regularization	ADJ
ejpam-4598	340	26	(	(	PUNCT
ejpam-4598	340	27	x	x	NOUN
ejpam-4598	340	28	,	,	PUNCT
ejpam-4598	340	29	ts	ts	NOUN
ejpam-4598	340	30	)	)	PUNCT
ejpam-4598	340	31	of	of	ADP
ejpam-4598	340	32	(	(	PUNCT
ejpam-4598	340	33	x	x	X
ejpam-4598	340	34	,	,	PUNCT
ejpam-4598	340	35	t	t	PROPN
ejpam-4598	340	36	)	)	PUNCT
ejpam-4598	340	37	is	be	AUX
ejpam-4598	340	38	completely	completely	ADV
ejpam-4598	340	39	-	-	PUNCT
ejpam-4598	340	40	regular	regular	ADJ
ejpam-4598	340	41	[	[	X
ejpam-4598	340	42	22	22	NUM
ejpam-4598	340	43	]	]	PUNCT
ejpam-4598	340	44	.	.	PUNCT
ejpam-4598	341	1	also	also	ADV
ejpam-4598	341	2	,	,	PUNCT
ejpam-4598	341	3	complete	complete	ADJ
ejpam-4598	341	4	-	-	PUNCT
ejpam-4598	341	5	regularity	regularity	NOUN
ejpam-4598	341	6	is	be	AUX
ejpam-4598	341	7	not	not	PART
ejpam-4598	341	8	a	a	DET
ejpam-4598	341	9	semi	semi	ADJ
ejpam-4598	341	10	-	-	ADJ
ejpam-4598	341	11	regularization	regularization	ADJ
ejpam-4598	341	12	property	property	NOUN
ejpam-4598	341	13	,	,	PUNCT
ejpam-4598	341	14	but	but	CCONJ
ejpam-4598	341	15	almost	almost	ADV
ejpam-4598	341	16	-	-	PUNCT
ejpam-4598	341	17	complete	complete	ADJ
ejpam-4598	341	18	regularity	regularity	NOUN
ejpam-4598	341	19	is	be	AUX
ejpam-4598	341	20	[	[	X
ejpam-4598	341	21	22	22	NUM
ejpam-4598	341	22	]	]	PUNCT
ejpam-4598	341	23	.	.	PUNCT
ejpam-4598	342	1	for	for	ADP
ejpam-4598	342	2	example	example	NOUN
ejpam-4598	342	3	,	,	PUNCT
ejpam-4598	342	4	the	the	DET
ejpam-4598	342	5	half	half	ADJ
ejpam-4598	342	6	disc	disc	NOUN
ejpam-4598	342	7	topology	topology	NOUN
ejpam-4598	342	8	(	(	PUNCT
ejpam-4598	342	9	x	x	X
ejpam-4598	342	10	,	,	PUNCT
ejpam-4598	342	11	t	t	PROPN
ejpam-4598	342	12	)	)	PUNCT
ejpam-4598	342	13	is	be	AUX
ejpam-4598	342	14	not	not	PART
ejpam-4598	342	15	completely	completely	ADV
ejpam-4598	342	16	-	-	PUNCT
ejpam-4598	342	17	regular	regular	ADJ
ejpam-4598	342	18	[	[	X
ejpam-4598	342	19	30	30	NUM
ejpam-4598	342	20	]	]	PUNCT
ejpam-4598	342	21	,	,	PUNCT
ejpam-4598	342	22	and	and	CCONJ
ejpam-4598	342	23	its	its	PRON
ejpam-4598	342	24	semi	semi	ADJ
ejpam-4598	342	25	-	-	NOUN
ejpam-4598	342	26	regularization	regularization	ADJ
ejpam-4598	342	27	(	(	PUNCT
ejpam-4598	342	28	x	x	NOUN
ejpam-4598	342	29	,	,	PUNCT
ejpam-4598	342	30	ts	ts	NOUN
ejpam-4598	342	31	)	)	PUNCT
ejpam-4598	342	32	is	be	AUX
ejpam-4598	342	33	the	the	DET
ejpam-4598	342	34	usual	usual	ADJ
ejpam-4598	342	35	topology	topology	NOUN
ejpam-4598	342	36	on	on	ADP
ejpam-4598	342	37	the	the	DET
ejpam-4598	342	38	closed	closed	ADJ
ejpam-4598	342	39	upper	upper	ADJ
ejpam-4598	342	40	half	half	ADJ
ejpam-4598	342	41	plane	plane	NOUN
ejpam-4598	342	42	,	,	PUNCT
ejpam-4598	342	43	which	which	PRON
ejpam-4598	342	44	is	be	AUX
ejpam-4598	342	45	completely	completely	ADV
ejpam-4598	342	46	-	-	PUNCT
ejpam-4598	342	47	regular	regular	ADJ
ejpam-4598	342	48	.	.	PUNCT
ejpam-4598	343	1	theorem	theorem	NOUN
ejpam-4598	343	2	10	10	NUM
ejpam-4598	343	3	.	.	PUNCT
ejpam-4598	344	1	if	if	SCONJ
ejpam-4598	344	2	(	(	PUNCT
ejpam-4598	344	3	x	x	X
ejpam-4598	344	4	,	,	PUNCT
ejpam-4598	344	5	t	t	PROPN
ejpam-4598	344	6	)	)	PUNCT
ejpam-4598	344	7	is	be	AUX
ejpam-4598	344	8	an	an	DET
ejpam-4598	344	9	almost	almost	ADV
ejpam-4598	344	10	-	-	PUNCT
ejpam-4598	344	11	completely	completely	ADV
ejpam-4598	344	12	regular	regular	ADJ
ejpam-4598	344	13	space	space	NOUN
ejpam-4598	344	14	such	such	ADJ
ejpam-4598	344	15	that	that	SCONJ
ejpam-4598	344	16	the	the	DET
ejpam-4598	344	17	semi	semi	NOUN
ejpam-4598	344	18	-	-	NOUN
ejpam-4598	344	19	regularization	regularization	ADJ
ejpam-4598	344	20	(	(	PUNCT
ejpam-4598	344	21	x	x	NOUN
ejpam-4598	344	22	,	,	PUNCT
ejpam-4598	344	23	ts	ts	NOUN
ejpam-4598	344	24	)	)	PUNCT
ejpam-4598	344	25	of	of	ADP
ejpam-4598	344	26	(	(	PUNCT
ejpam-4598	344	27	x	x	X
ejpam-4598	344	28	,	,	PUNCT
ejpam-4598	344	29	t	t	PROPN
ejpam-4598	344	30	)	)	PUNCT
ejpam-4598	344	31	is	be	AUX
ejpam-4598	344	32	t1	t1	NOUN
ejpam-4598	344	33	,	,	PUNCT
ejpam-4598	344	34	then	then	ADV
ejpam-4598	344	35	(	(	PUNCT
ejpam-4598	344	36	x	x	X
ejpam-4598	344	37	,	,	PUNCT
ejpam-4598	344	38	t	t	PROPN
ejpam-4598	344	39	)	)	PUNCT
ejpam-4598	344	40	is	be	AUX
ejpam-4598	344	41	epi	epi	NOUN
ejpam-4598	344	42	-	-	ADJ
ejpam-4598	344	43	completely	completely	ADV
ejpam-4598	344	44	-	-	PUNCT
ejpam-4598	344	45	regular	regular	ADJ
ejpam-4598	344	46	.	.	PUNCT
ejpam-4598	345	1	proof	proof	NOUN
ejpam-4598	345	2	.	.	PUNCT
ejpam-4598	346	1	let	let	AUX
ejpam-4598	346	2	(	(	PUNCT
ejpam-4598	346	3	x	x	X
ejpam-4598	346	4	,	,	PUNCT
ejpam-4598	346	5	t	t	PROPN
ejpam-4598	346	6	)	)	PUNCT
ejpam-4598	346	7	be	be	AUX
ejpam-4598	346	8	an	an	DET
ejpam-4598	346	9	almost	almost	ADV
ejpam-4598	346	10	-	-	PUNCT
ejpam-4598	346	11	completely	completely	ADV
ejpam-4598	346	12	regular	regular	ADJ
ejpam-4598	346	13	space	space	NOUN
ejpam-4598	346	14	and	and	CCONJ
ejpam-4598	346	15	the	the	DET
ejpam-4598	346	16	semi	semi	ADJ
ejpam-4598	346	17	-	-	NOUN
ejpam-4598	346	18	regularization	regularization	ADJ
ejpam-4598	346	19	(	(	PUNCT
ejpam-4598	346	20	x	x	NOUN
ejpam-4598	346	21	,	,	PUNCT
ejpam-4598	346	22	ts	ts	NOUN
ejpam-4598	346	23	)	)	PUNCT
ejpam-4598	346	24	of	of	ADP
ejpam-4598	346	25	(	(	PUNCT
ejpam-4598	346	26	x	x	X
ejpam-4598	346	27	,	,	PUNCT
ejpam-4598	346	28	t	t	PROPN
ejpam-4598	346	29	)	)	PUNCT
ejpam-4598	346	30	be	be	AUX
ejpam-4598	346	31	t1	t1	ADJ
ejpam-4598	346	32	.	.	PUNCT
ejpam-4598	347	1	since	since	SCONJ
ejpam-4598	347	2	the	the	DET
ejpam-4598	347	3	semi	semi	NOUN
ejpam-4598	347	4	-	-	NOUN
ejpam-4598	347	5	regularization	regularization	NOUN
ejpam-4598	347	6	of	of	ADP
ejpam-4598	347	7	an	an	DET
ejpam-4598	347	8	almost	almost	ADV
ejpam-4598	347	9	-	-	PUNCT
ejpam-4598	347	10	completely	completely	ADV
ejpam-4598	347	11	regular	regular	ADJ
ejpam-4598	347	12	space	space	NOUN
ejpam-4598	347	13	is	be	AUX
ejpam-4598	347	14	completely	completely	ADV
ejpam-4598	347	15	-	-	PUNCT
ejpam-4598	347	16	regular	regular	ADJ
ejpam-4598	347	17	[	[	X
ejpam-4598	347	18	22	22	NUM
ejpam-4598	347	19	]	]	PUNCT
ejpam-4598	347	20	,	,	PUNCT
ejpam-4598	347	21	we	we	PRON
ejpam-4598	347	22	get	get	VERB
ejpam-4598	347	23	:	:	PUNCT
ejpam-4598	347	24	(	(	PUNCT
ejpam-4598	347	25	x	x	NOUN
ejpam-4598	347	26	,	,	PUNCT
ejpam-4598	347	27	ts	ts	NOUN
ejpam-4598	347	28	)	)	PUNCT
ejpam-4598	347	29	is	be	AUX
ejpam-4598	347	30	t1	t1	NOUN
ejpam-4598	347	31	-	-	PUNCT
ejpam-4598	347	32	completely	completely	ADV
ejpam-4598	347	33	-	-	PUNCT
ejpam-4598	347	34	regular	regular	ADJ
ejpam-4598	347	35	.	.	PUNCT
ejpam-4598	348	1	thus	thus	ADV
ejpam-4598	348	2	,	,	PUNCT
ejpam-4598	348	3	(	(	PUNCT
ejpam-4598	348	4	x	x	X
ejpam-4598	348	5	,	,	PUNCT
ejpam-4598	348	6	ts	ts	NOUN
ejpam-4598	348	7	)	)	PUNCT
ejpam-4598	348	8	is	be	AUX
ejpam-4598	348	9	tychonoff	tychonoff	NOUN
ejpam-4598	348	10	.	.	PUNCT
ejpam-4598	349	1	since	since	SCONJ
ejpam-4598	349	2	ts	ts	PROPN
ejpam-4598	349	3	is	be	AUX
ejpam-4598	349	4	a	a	DET
ejpam-4598	349	5	topology	topology	NOUN
ejpam-4598	349	6	on	on	ADP
ejpam-4598	349	7	x	x	PUNCT
ejpam-4598	349	8	which	which	PRON
ejpam-4598	349	9	is	be	AUX
ejpam-4598	349	10	coarser	coarse	ADJ
ejpam-4598	349	11	than	than	ADP
ejpam-4598	349	12	t	t	PROPN
ejpam-4598	349	13	,	,	PUNCT
ejpam-4598	349	14	we	we	PRON
ejpam-4598	349	15	obtain	obtain	VERB
ejpam-4598	349	16	:	:	PUNCT
ejpam-4598	349	17	(	(	PUNCT
ejpam-4598	349	18	x	x	X
ejpam-4598	349	19	,	,	PUNCT
ejpam-4598	349	20	t	t	PROPN
ejpam-4598	349	21	)	)	PUNCT
ejpam-4598	349	22	is	be	AUX
ejpam-4598	349	23	epi	epi	NOUN
ejpam-4598	349	24	-	-	ADJ
ejpam-4598	349	25	completely	completely	ADV
ejpam-4598	349	26	-	-	PUNCT
ejpam-4598	349	27	regular	regular	ADJ
ejpam-4598	349	28	.	.	PUNCT
ejpam-4598	350	1	since	since	SCONJ
ejpam-4598	350	2	every	every	DET
ejpam-4598	350	3	extremally	extremally	ADV
ejpam-4598	350	4	-	-	PUNCT
ejpam-4598	350	5	disconnected	disconnect	VERB
ejpam-4598	350	6	space	space	NOUN
ejpam-4598	350	7	is	be	AUX
ejpam-4598	350	8	t1	t1	NOUN
ejpam-4598	350	9	-	-	PUNCT
ejpam-4598	350	10	π	π	NOUN
ejpam-4598	350	11	-	-	ADJ
ejpam-4598	350	12	normal	normal	ADJ
ejpam-4598	350	13	[	[	X
ejpam-4598	350	14	14	14	NUM
ejpam-4598	350	15	]	]	PUNCT
ejpam-4598	350	16	,	,	PUNCT
ejpam-4598	350	17	we	we	PRON
ejpam-4598	350	18	get	get	VERB
ejpam-4598	350	19	:	:	PUNCT
ejpam-4598	350	20	every	every	DET
ejpam-4598	350	21	extremallydisconnected	extremallydisconnected	ADJ
ejpam-4598	350	22	space	space	NOUN
ejpam-4598	350	23	is	be	AUX
ejpam-4598	350	24	t1	t1	NOUN
ejpam-4598	350	25	-	-	PUNCT
ejpam-4598	350	26	almost	almost	ADV
ejpam-4598	350	27	-	-	PUNCT
ejpam-4598	350	28	completely	completely	ADV
ejpam-4598	350	29	regular	regular	ADJ
ejpam-4598	350	30	.	.	PUNCT
ejpam-4598	351	1	since	since	SCONJ
ejpam-4598	351	2	every	every	DET
ejpam-4598	351	3	extremally	extremally	ADV
ejpam-4598	351	4	-	-	PUNCT
ejpam-4598	351	5	disconnected	disconnected	ADJ
ejpam-4598	351	6	semi	semi	ADJ
ejpam-4598	351	7	-	-	ADJ
ejpam-4598	351	8	regular	regular	ADJ
ejpam-4598	351	9	space	space	NOUN
ejpam-4598	351	10	is	be	AUX
ejpam-4598	351	11	tychonoff	tychonoff	NOUN
ejpam-4598	351	12	[	[	X
ejpam-4598	351	13	3	3	NUM
ejpam-4598	351	14	]	]	PUNCT
ejpam-4598	351	15	,	,	PUNCT
ejpam-4598	351	16	we	we	PRON
ejpam-4598	351	17	conclude	conclude	VERB
ejpam-4598	351	18	:	:	PUNCT
ejpam-4598	351	19	corollary	corollary	ADJ
ejpam-4598	351	20	6	6	NUM
ejpam-4598	351	21	.	.	PUNCT
ejpam-4598	352	1	(	(	PUNCT
ejpam-4598	352	2	a	a	X
ejpam-4598	352	3	)	)	PUNCT
ejpam-4598	352	4	every	every	DET
ejpam-4598	352	5	hausdorff	hausdorff	NOUN
ejpam-4598	352	6	extremally	extremally	ADV
ejpam-4598	352	7	-	-	PUNCT
ejpam-4598	352	8	disconnected	disconnect	VERB
ejpam-4598	352	9	space	space	NOUN
ejpam-4598	352	10	is	be	AUX
ejpam-4598	352	11	epi	epi	NOUN
ejpam-4598	352	12	-	-	ADJ
ejpam-4598	352	13	completely	completely	ADV
ejpam-4598	352	14	-	-	PUNCT
ejpam-4598	352	15	regular	regular	ADJ
ejpam-4598	352	16	.	.	PUNCT
ejpam-4598	353	1	i.	i.	PROPN
ejpam-4598	353	2	alshammari	alshammari	PROPN
ejpam-4598	353	3	/	/	SYM
ejpam-4598	353	4	eur	eur	PROPN
ejpam-4598	353	5	.	.	PUNCT
ejpam-4598	354	1	j.	j.	PROPN
ejpam-4598	354	2	pure	pure	PROPN
ejpam-4598	354	3	appl	appl	PROPN
ejpam-4598	354	4	.	.	PROPN
ejpam-4598	354	5	math	math	PROPN
ejpam-4598	354	6	,	,	PUNCT
ejpam-4598	354	7	15	15	NUM
ejpam-4598	354	8	(	(	PUNCT
ejpam-4598	354	9	4	4	NUM
ejpam-4598	354	10	)	)	PUNCT
ejpam-4598	354	11	(	(	PUNCT
ejpam-4598	354	12	2022	2022	NUM
ejpam-4598	354	13	)	)	PUNCT
ejpam-4598	354	14	,	,	PUNCT
ejpam-4598	354	15	1808	1808	NUM
ejpam-4598	354	16	-	-	SYM
ejpam-4598	354	17	1821	1821	NUM
ejpam-4598	354	18	1818	1818	NUM
ejpam-4598	354	19	(	(	PUNCT
ejpam-4598	354	20	b	b	X
ejpam-4598	354	21	)	)	PUNCT
ejpam-4598	354	22	every	every	DET
ejpam-4598	354	23	extremally	extremally	ADV
ejpam-4598	354	24	-	-	PUNCT
ejpam-4598	354	25	disconnected	disconnected	ADJ
ejpam-4598	354	26	semi	semi	ADJ
ejpam-4598	354	27	-	-	ADJ
ejpam-4598	354	28	regular	regular	ADJ
ejpam-4598	354	29	space	space	NOUN
ejpam-4598	354	30	is	be	AUX
ejpam-4598	354	31	epi	epi	NOUN
ejpam-4598	354	32	-	-	ADJ
ejpam-4598	354	33	completely	completely	ADV
ejpam-4598	354	34	-	-	PUNCT
ejpam-4598	354	35	regular	regular	ADJ
ejpam-4598	354	36	.	.	PUNCT
ejpam-4598	355	1	in	in	ADP
ejpam-4598	355	2	fact	fact	NOUN
ejpam-4598	355	3	,	,	PUNCT
ejpam-4598	355	4	an	an	DET
ejpam-4598	355	5	epi	epi	NOUN
ejpam-4598	355	6	-	-	ADJ
ejpam-4598	355	7	completely	completely	ADV
ejpam-4598	355	8	-	-	PUNCT
ejpam-4598	355	9	regular	regular	ADJ
ejpam-4598	355	10	space	space	NOUN
ejpam-4598	355	11	is	be	AUX
ejpam-4598	355	12	not	not	PART
ejpam-4598	355	13	necessary	necessary	ADJ
ejpam-4598	355	14	to	to	PART
ejpam-4598	355	15	be	be	AUX
ejpam-4598	355	16	extremally	extremally	ADV
ejpam-4598	355	17	-	-	PUNCT
ejpam-4598	355	18	disconnected	disconnected	ADJ
ejpam-4598	355	19	.	.	PUNCT
ejpam-4598	356	1	for	for	ADP
ejpam-4598	356	2	example	example	NOUN
ejpam-4598	356	3	:	:	PUNCT
ejpam-4598	356	4	the	the	DET
ejpam-4598	356	5	rational	rational	ADJ
ejpam-4598	356	6	sequence	sequence	NOUN
ejpam-4598	356	7	topology	topology	NOUN
ejpam-4598	356	8	[	[	X
ejpam-4598	356	9	30	30	NUM
ejpam-4598	356	10	,	,	PUNCT
ejpam-4598	356	11	example	example	NOUN
ejpam-4598	356	12	65	65	NUM
ejpam-4598	356	13	]	]	PUNCT
ejpam-4598	356	14	,	,	PUNCT
ejpam-4598	356	15	is	be	AUX
ejpam-4598	356	16	a	a	DET
ejpam-4598	356	17	semi	semi	ADJ
ejpam-4598	356	18	-	-	ADJ
ejpam-4598	356	19	regular	regular	ADJ
ejpam-4598	356	20	epicompletely	epicompletely	ADV
ejpam-4598	356	21	-	-	PUNCT
ejpam-4598	356	22	regular	regular	ADJ
ejpam-4598	356	23	space	space	NOUN
ejpam-4598	356	24	being	being	NOUN
ejpam-4598	356	25	tychonoff	tychonoff	NOUN
ejpam-4598	356	26	,	,	PUNCT
ejpam-4598	356	27	which	which	PRON
ejpam-4598	356	28	is	be	AUX
ejpam-4598	356	29	not	not	PART
ejpam-4598	356	30	extremally	extremally	ADV
ejpam-4598	356	31	disconnected	disconnect	VERB
ejpam-4598	356	32	.	.	PUNCT
ejpam-4598	357	1	the	the	DET
ejpam-4598	357	2	next	next	ADJ
ejpam-4598	357	3	result	result	NOUN
ejpam-4598	357	4	is	be	AUX
ejpam-4598	357	5	obvious	obvious	ADJ
ejpam-4598	357	6	:	:	PUNCT
ejpam-4598	357	7	theorem	theorem	NOUN
ejpam-4598	357	8	11	11	NUM
ejpam-4598	357	9	.	.	PUNCT
ejpam-4598	358	1	if	if	SCONJ
ejpam-4598	358	2	the	the	DET
ejpam-4598	358	3	semi	semi	ADJ
ejpam-4598	358	4	-	-	ADJ
ejpam-4598	358	5	regularization	regularization	ADJ
ejpam-4598	358	6	space	space	NOUN
ejpam-4598	358	7	(	(	PUNCT
ejpam-4598	358	8	x	x	NOUN
ejpam-4598	358	9	,	,	PUNCT
ejpam-4598	358	10	ts	ts	NOUN
ejpam-4598	358	11	)	)	PUNCT
ejpam-4598	358	12	of	of	ADP
ejpam-4598	358	13	a	a	DET
ejpam-4598	358	14	space	space	NOUN
ejpam-4598	358	15	(	(	PUNCT
ejpam-4598	358	16	x	x	X
ejpam-4598	358	17	,	,	PUNCT
ejpam-4598	358	18	t	t	PROPN
ejpam-4598	358	19	)	)	PUNCT
ejpam-4598	358	20	is	be	AUX
ejpam-4598	358	21	an	an	DET
ejpam-4598	358	22	epi	epi	ADJ
ejpam-4598	358	23	-	-	ADJ
ejpam-4598	358	24	completelyregular	completelyregular	ADJ
ejpam-4598	358	25	space	space	NOUN
ejpam-4598	358	26	,	,	PUNCT
ejpam-4598	358	27	then	then	ADV
ejpam-4598	358	28	(	(	PUNCT
ejpam-4598	358	29	x	x	X
ejpam-4598	358	30	,	,	PUNCT
ejpam-4598	358	31	t	t	PROPN
ejpam-4598	358	32	)	)	PUNCT
ejpam-4598	358	33	is	be	AUX
ejpam-4598	358	34	epi	epi	NOUN
ejpam-4598	358	35	-	-	ADJ
ejpam-4598	358	36	completely	completely	ADV
ejpam-4598	358	37	-	-	PUNCT
ejpam-4598	358	38	regular	regular	ADJ
ejpam-4598	358	39	.	.	PUNCT
ejpam-4598	359	1	theorem	theorem	NOUN
ejpam-4598	359	2	12	12	NUM
ejpam-4598	359	3	.	.	PUNCT
ejpam-4598	360	1	every	every	DET
ejpam-4598	360	2	hausdorff	hausdorff	NOUN
ejpam-4598	360	3	almost	almost	ADV
ejpam-4598	360	4	-	-	PUNCT
ejpam-4598	360	5	completely	completely	ADV
ejpam-4598	360	6	regular	regular	ADJ
ejpam-4598	360	7	space	space	NOUN
ejpam-4598	360	8	is	be	AUX
ejpam-4598	360	9	epi	epi	NOUN
ejpam-4598	360	10	-	-	ADJ
ejpam-4598	360	11	completely	completely	ADV
ejpam-4598	360	12	-	-	PUNCT
ejpam-4598	360	13	regular	regular	ADJ
ejpam-4598	360	14	.	.	PUNCT
ejpam-4598	361	1	proof	proof	NOUN
ejpam-4598	361	2	.	.	PUNCT
ejpam-4598	362	1	let	let	AUX
ejpam-4598	362	2	(	(	PUNCT
ejpam-4598	362	3	x	x	X
ejpam-4598	362	4	,	,	PUNCT
ejpam-4598	362	5	t	t	PROPN
ejpam-4598	362	6	)	)	PUNCT
ejpam-4598	362	7	be	be	AUX
ejpam-4598	362	8	a	a	DET
ejpam-4598	362	9	hausdorff	hausdorff	NOUN
ejpam-4598	362	10	almost	almost	ADV
ejpam-4598	362	11	-	-	PUNCT
ejpam-4598	362	12	completely	completely	ADV
ejpam-4598	362	13	regular	regular	ADJ
ejpam-4598	362	14	space	space	NOUN
ejpam-4598	362	15	.	.	PUNCT
ejpam-4598	363	1	let	let	VERB
ejpam-4598	363	2	(	(	PUNCT
ejpam-4598	363	3	x	x	NOUN
ejpam-4598	363	4	,	,	PUNCT
ejpam-4598	363	5	ts	ts	NOUN
ejpam-4598	363	6	)	)	PUNCT
ejpam-4598	363	7	be	be	AUX
ejpam-4598	363	8	the	the	DET
ejpam-4598	363	9	semi	semi	NOUN
ejpam-4598	363	10	-	-	NOUN
ejpam-4598	363	11	regularization	regularization	NOUN
ejpam-4598	363	12	of	of	ADP
ejpam-4598	363	13	(	(	PUNCT
ejpam-4598	363	14	x	x	PROPN
ejpam-4598	363	15	,	,	PUNCT
ejpam-4598	363	16	t	t	PROPN
ejpam-4598	363	17	)	)	PUNCT
ejpam-4598	363	18	.	.	PUNCT
ejpam-4598	364	1	then	then	ADV
ejpam-4598	364	2	,	,	PUNCT
ejpam-4598	364	3	(	(	PUNCT
ejpam-4598	364	4	x	x	X
ejpam-4598	364	5	,	,	PUNCT
ejpam-4598	364	6	ts	ts	NOUN
ejpam-4598	364	7	)	)	PUNCT
ejpam-4598	364	8	is	be	AUX
ejpam-4598	364	9	a	a	DET
ejpam-4598	364	10	hausdorff	hausdorff	NOUN
ejpam-4598	364	11	completely	completely	ADV
ejpam-4598	364	12	regular	regular	ADJ
ejpam-4598	364	13	space	space	NOUN
ejpam-4598	364	14	because	because	SCONJ
ejpam-4598	364	15	the	the	DET
ejpam-4598	364	16	semi	semi	NOUN
ejpam-4598	364	17	-	-	NOUN
ejpam-4598	364	18	regularization	regularization	NOUN
ejpam-4598	364	19	of	of	ADP
ejpam-4598	364	20	a	a	DET
ejpam-4598	364	21	hausdorff	hausdorff	NOUN
ejpam-4598	364	22	almost	almost	ADV
ejpam-4598	364	23	-	-	PUNCT
ejpam-4598	364	24	completely	completely	ADV
ejpam-4598	364	25	regular	regular	ADJ
ejpam-4598	364	26	space	space	NOUN
ejpam-4598	364	27	is	be	AUX
ejpam-4598	364	28	hausdorff	hausdorff	NOUN
ejpam-4598	364	29	completely	completely	ADV
ejpam-4598	364	30	regular	regular	ADJ
ejpam-4598	364	31	[	[	X
ejpam-4598	364	32	22	22	NUM
ejpam-4598	364	33	]	]	PUNCT
ejpam-4598	364	34	.	.	PUNCT
ejpam-4598	365	1	thus	thus	ADV
ejpam-4598	365	2	,	,	PUNCT
ejpam-4598	365	3	(	(	PUNCT
ejpam-4598	365	4	x	x	X
ejpam-4598	365	5	,	,	PUNCT
ejpam-4598	365	6	ts	ts	NOUN
ejpam-4598	365	7	)	)	PUNCT
ejpam-4598	365	8	is	be	AUX
ejpam-4598	365	9	tychonoff	tychonoff	NOUN
ejpam-4598	365	10	.	.	PUNCT
ejpam-4598	366	1	since	since	SCONJ
ejpam-4598	366	2	ts	ts	ADP
ejpam-4598	366	3	⊆	⊆	NUM
ejpam-4598	366	4	t	t	NOUN
ejpam-4598	366	5	,	,	PUNCT
ejpam-4598	366	6	we	we	PRON
ejpam-4598	366	7	conclude	conclude	VERB
ejpam-4598	366	8	:	:	PUNCT
ejpam-4598	366	9	(	(	PUNCT
ejpam-4598	366	10	x	x	X
ejpam-4598	366	11	,	,	PUNCT
ejpam-4598	366	12	t	t	PROPN
ejpam-4598	366	13	)	)	PUNCT
ejpam-4598	366	14	is	be	AUX
ejpam-4598	366	15	epi	epi	NOUN
ejpam-4598	366	16	-	-	ADJ
ejpam-4598	366	17	completely	completely	ADV
ejpam-4598	366	18	regular	regular	ADJ
ejpam-4598	366	19	.	.	PUNCT
ejpam-4598	367	1	the	the	DET
ejpam-4598	367	2	next	next	ADJ
ejpam-4598	367	3	results	result	NOUN
ejpam-4598	367	4	are	be	AUX
ejpam-4598	367	5	obvious	obvious	ADJ
ejpam-4598	367	6	:	:	PUNCT
ejpam-4598	367	7	corollary	corollary	ADJ
ejpam-4598	367	8	7	7	NUM
ejpam-4598	367	9	.	.	PUNCT
ejpam-4598	368	1	(	(	PUNCT
ejpam-4598	368	2	1	1	X
ejpam-4598	368	3	)	)	PUNCT
ejpam-4598	368	4	every	every	DET
ejpam-4598	368	5	t1	t1	NOUN
ejpam-4598	368	6	-	-	PUNCT
ejpam-4598	368	7	semi	semi	ADV
ejpam-4598	368	8	-	-	ADJ
ejpam-4598	368	9	regular	regular	ADJ
ejpam-4598	368	10	(	(	PUNCT
ejpam-4598	368	11	resp	resp	NOUN
ejpam-4598	368	12	.	.	PUNCT
ejpam-4598	369	1	semi	semi	ADJ
ejpam-4598	369	2	-	-	ADJ
ejpam-4598	369	3	normal	normal	ADJ
ejpam-4598	369	4	)	)	PUNCT
ejpam-4598	369	5	almost	almost	ADV
ejpam-4598	369	6	-	-	PUNCT
ejpam-4598	369	7	completely	completely	ADV
ejpam-4598	369	8	regular	regular	ADJ
ejpam-4598	369	9	space	space	NOUN
ejpam-4598	369	10	is	be	AUX
ejpam-4598	369	11	epicompletely	epicompletely	ADV
ejpam-4598	369	12	-	-	PUNCT
ejpam-4598	369	13	regular	regular	ADJ
ejpam-4598	369	14	.	.	PUNCT
ejpam-4598	370	1	(	(	PUNCT
ejpam-4598	370	2	2	2	X
ejpam-4598	370	3	)	)	PUNCT
ejpam-4598	370	4	any	any	DET
ejpam-4598	370	5	nearly	nearly	ADV
ejpam-4598	370	6	-	-	PUNCT
ejpam-4598	370	7	paracompact	paracompact	ADJ
ejpam-4598	370	8	hausdorff	hausdorff	NOUN
ejpam-4598	370	9	space	space	NOUN
ejpam-4598	370	10	is	be	AUX
ejpam-4598	370	11	epi	epi	NOUN
ejpam-4598	370	12	-	-	ADJ
ejpam-4598	370	13	normal	normal	ADJ
ejpam-4598	370	14	.	.	PUNCT
ejpam-4598	371	1	(	(	PUNCT
ejpam-4598	371	2	3	3	X
ejpam-4598	371	3	)	)	PUNCT
ejpam-4598	371	4	every	every	DET
ejpam-4598	371	5	almost	almost	ADV
ejpam-4598	371	6	-	-	PUNCT
ejpam-4598	371	7	regular	regular	ADJ
ejpam-4598	371	8	hausdorff	hausdorff	NOUN
ejpam-4598	371	9	lindelöf	lindelöf	NOUN
ejpam-4598	371	10	space	space	NOUN
ejpam-4598	371	11	is	be	AUX
ejpam-4598	371	12	epi	epi	ADJ
ejpam-4598	371	13	-	-	ADJ
ejpam-4598	371	14	quasi	quasi	ADJ
ejpam-4598	371	15	-	-	ADJ
ejpam-4598	371	16	normal	normal	ADJ
ejpam-4598	371	17	.	.	PUNCT
ejpam-4598	372	1	since	since	SCONJ
ejpam-4598	372	2	every	every	DET
ejpam-4598	372	3	epi	epi	NOUN
ejpam-4598	372	4	-	-	ADJ
ejpam-4598	372	5	completely	completely	ADV
ejpam-4598	372	6	-	-	PUNCT
ejpam-4598	372	7	regular	regular	ADJ
ejpam-4598	372	8	space	space	NOUN
ejpam-4598	372	9	is	be	AUX
ejpam-4598	372	10	epi	epi	NOUN
ejpam-4598	372	11	-	-	ADJ
ejpam-4598	372	12	regular	regular	ADJ
ejpam-4598	372	13	,	,	PUNCT
ejpam-4598	372	14	and	and	CCONJ
ejpam-4598	372	15	every	every	DET
ejpam-4598	372	16	epi	epi	ADJ
ejpam-4598	372	17	-	-	ADJ
ejpam-4598	372	18	regular	regular	ADJ
ejpam-4598	372	19	space	space	NOUN
ejpam-4598	372	20	is	be	AUX
ejpam-4598	372	21	c	c	NOUN
ejpam-4598	372	22	-	-	ADJ
ejpam-4598	372	23	regular	regular	ADJ
ejpam-4598	372	24	,	,	PUNCT
ejpam-4598	372	25	we	we	PRON
ejpam-4598	372	26	get	get	VERB
ejpam-4598	372	27	:	:	PUNCT
ejpam-4598	372	28	every	every	DET
ejpam-4598	372	29	epi	epi	NOUN
ejpam-4598	372	30	-	-	ADJ
ejpam-4598	372	31	completely	completely	ADV
ejpam-4598	372	32	-	-	PUNCT
ejpam-4598	372	33	regular	regular	ADJ
ejpam-4598	372	34	space	space	NOUN
ejpam-4598	372	35	is	be	AUX
ejpam-4598	372	36	c	c	NOUN
ejpam-4598	372	37	-	-	ADJ
ejpam-4598	372	38	regular	regular	ADJ
ejpam-4598	372	39	,	,	PUNCT
ejpam-4598	372	40	but	but	CCONJ
ejpam-4598	372	41	the	the	DET
ejpam-4598	372	42	converse	converse	NOUN
ejpam-4598	372	43	is	be	AUX
ejpam-4598	372	44	not	not	PART
ejpam-4598	372	45	true	true	ADJ
ejpam-4598	372	46	in	in	ADP
ejpam-4598	372	47	general	general	ADJ
ejpam-4598	372	48	.	.	PUNCT
ejpam-4598	373	1	for	for	ADP
ejpam-4598	373	2	example	example	NOUN
ejpam-4598	373	3	:	:	PUNCT
ejpam-4598	373	4	the	the	DET
ejpam-4598	373	5	odd	odd	ADV
ejpam-4598	373	6	-	-	PUNCT
ejpam-4598	373	7	even	even	ADV
ejpam-4598	373	8	topology	topology	NOUN
ejpam-4598	373	9	,	,	PUNCT
ejpam-4598	373	10	example	example	NOUN
ejpam-4598	373	11	12	12	NUM
ejpam-4598	373	12	,	,	PUNCT
ejpam-4598	373	13	is	be	AUX
ejpam-4598	373	14	a	a	DET
ejpam-4598	373	15	normal	normal	ADJ
ejpam-4598	373	16	and	and	CCONJ
ejpam-4598	373	17	completely	completely	ADV
ejpam-4598	373	18	-	-	PUNCT
ejpam-4598	373	19	regular	regular	ADJ
ejpam-4598	373	20	space	space	NOUN
ejpam-4598	373	21	[	[	X
ejpam-4598	373	22	30	30	NUM
ejpam-4598	373	23	]	]	PUNCT
ejpam-4598	373	24	,	,	PUNCT
ejpam-4598	373	25	which	which	PRON
ejpam-4598	373	26	is	be	AUX
ejpam-4598	373	27	not	not	PART
ejpam-4598	373	28	t1	t1	NOUN
ejpam-4598	373	29	.	.	PUNCT
ejpam-4598	374	1	thus	thus	ADV
ejpam-4598	374	2	,	,	PUNCT
ejpam-4598	374	3	the	the	DET
ejpam-4598	374	4	odd	odd	ADV
ejpam-4598	374	5	-	-	PUNCT
ejpam-4598	374	6	even	even	ADJ
ejpam-4598	374	7	topology	topology	NOUN
ejpam-4598	374	8	is	be	AUX
ejpam-4598	374	9	a	a	DET
ejpam-4598	374	10	c	c	NOUN
ejpam-4598	374	11	-	-	PUNCT
ejpam-4598	374	12	regular	regular	ADJ
ejpam-4598	374	13	space	space	NOUN
ejpam-4598	374	14	,	,	PUNCT
ejpam-4598	374	15	which	which	PRON
ejpam-4598	374	16	is	be	AUX
ejpam-4598	374	17	not	not	PART
ejpam-4598	374	18	epi	epi	NOUN
ejpam-4598	374	19	-	-	ADJ
ejpam-4598	374	20	completely	completely	ADV
ejpam-4598	374	21	regular	regular	ADJ
ejpam-4598	374	22	.	.	PUNCT
ejpam-4598	375	1	theorem	theorem	VERB
ejpam-4598	375	2	13	13	NUM
ejpam-4598	375	3	.	.	PUNCT
ejpam-4598	376	1	every	every	DET
ejpam-4598	376	2	semi	semi	ADJ
ejpam-4598	376	3	-	-	ADJ
ejpam-4598	376	4	regular	regular	ADJ
ejpam-4598	376	5	almost	almost	ADV
ejpam-4598	376	6	-	-	PUNCT
ejpam-4598	376	7	normal	normal	ADJ
ejpam-4598	376	8	t1	t1	NOUN
ejpam-4598	376	9	-	-	PUNCT
ejpam-4598	376	10	space	space	NOUN
ejpam-4598	376	11	is	be	AUX
ejpam-4598	376	12	tychonoff	tychonoff	NOUN
ejpam-4598	376	13	.	.	PUNCT
ejpam-4598	377	1	proof	proof	NOUN
ejpam-4598	377	2	.	.	PUNCT
ejpam-4598	378	1	let	let	VERB
ejpam-4598	378	2	x	x	PRON
ejpam-4598	378	3	be	be	AUX
ejpam-4598	378	4	a	a	DET
ejpam-4598	378	5	semi	semi	ADJ
ejpam-4598	378	6	-	-	ADJ
ejpam-4598	378	7	regular	regular	ADJ
ejpam-4598	378	8	t1	t1	NOUN
ejpam-4598	378	9	-	-	PUNCT
ejpam-4598	378	10	almost	almost	ADV
ejpam-4598	378	11	-	-	PUNCT
ejpam-4598	378	12	normal	normal	ADJ
ejpam-4598	378	13	space	space	NOUN
ejpam-4598	378	14	.	.	PUNCT
ejpam-4598	379	1	then	then	ADV
ejpam-4598	379	2	,	,	PUNCT
ejpam-4598	379	3	x	x	PRON
ejpam-4598	379	4	is	be	AUX
ejpam-4598	379	5	almost	almost	ADV
ejpam-4598	379	6	-	-	PUNCT
ejpam-4598	379	7	regular	regular	ADJ
ejpam-4598	379	8	.	.	PUNCT
ejpam-4598	380	1	since	since	SCONJ
ejpam-4598	380	2	every	every	DET
ejpam-4598	380	3	semi	semi	ADJ
ejpam-4598	380	4	-	-	ADJ
ejpam-4598	380	5	regular	regular	ADJ
ejpam-4598	380	6	almost	almost	ADV
ejpam-4598	380	7	-	-	PUNCT
ejpam-4598	380	8	regular	regular	ADJ
ejpam-4598	380	9	is	be	AUX
ejpam-4598	380	10	regular	regular	ADJ
ejpam-4598	380	11	,	,	PUNCT
ejpam-4598	380	12	we	we	PRON
ejpam-4598	380	13	obtain	obtain	VERB
ejpam-4598	380	14	:	:	PUNCT
ejpam-4598	380	15	x	x	X
ejpam-4598	380	16	is	be	AUX
ejpam-4598	380	17	a	a	DET
ejpam-4598	380	18	t1	t1	NOUN
ejpam-4598	380	19	-	-	PUNCT
ejpam-4598	380	20	regular	regular	ADJ
ejpam-4598	380	21	almostnormal	almostnormal	ADJ
ejpam-4598	380	22	space	space	NOUN
ejpam-4598	380	23	.	.	PUNCT
ejpam-4598	381	1	hence	hence	ADV
ejpam-4598	381	2	,	,	PUNCT
ejpam-4598	381	3	x	x	X
ejpam-4598	381	4	is	be	AUX
ejpam-4598	381	5	a	a	DET
ejpam-4598	381	6	t1	t1	VERB
ejpam-4598	381	7	-	-	PUNCT
ejpam-4598	381	8	completely	completely	ADV
ejpam-4598	381	9	-	-	PUNCT
ejpam-4598	381	10	regular	regular	ADJ
ejpam-4598	381	11	space	space	NOUN
ejpam-4598	381	12	because	because	SCONJ
ejpam-4598	381	13	every	every	DET
ejpam-4598	381	14	regular	regular	ADJ
ejpam-4598	381	15	almostnormal	almostnormal	ADJ
ejpam-4598	381	16	space	space	NOUN
ejpam-4598	381	17	is	be	AUX
ejpam-4598	381	18	completely	completely	ADV
ejpam-4598	381	19	-	-	PUNCT
ejpam-4598	381	20	regular	regular	ADJ
ejpam-4598	381	21	[	[	X
ejpam-4598	381	22	10	10	NUM
ejpam-4598	381	23	]	]	PUNCT
ejpam-4598	381	24	.	.	PUNCT
ejpam-4598	382	1	therefore	therefore	ADV
ejpam-4598	382	2	,	,	PUNCT
ejpam-4598	382	3	x	x	X
ejpam-4598	382	4	is	be	AUX
ejpam-4598	382	5	tychonoff	tychonoff	NOUN
ejpam-4598	382	6	.	.	PUNCT
ejpam-4598	383	1	from	from	ADP
ejpam-4598	383	2	theorem	theorem	ADJ
ejpam-4598	383	3	13	13	NUM
ejpam-4598	383	4	,	,	PUNCT
ejpam-4598	383	5	we	we	PRON
ejpam-4598	383	6	conclude	conclude	VERB
ejpam-4598	383	7	the	the	DET
ejpam-4598	383	8	next	next	ADJ
ejpam-4598	383	9	corollary	corollary	NOUN
ejpam-4598	383	10	:	:	PUNCT
ejpam-4598	383	11	corollary	corollary	ADJ
ejpam-4598	383	12	8	8	NUM
ejpam-4598	383	13	.	.	PUNCT
ejpam-4598	384	1	every	every	DET
ejpam-4598	384	2	semi	semi	ADJ
ejpam-4598	384	3	-	-	ADJ
ejpam-4598	384	4	regular	regular	ADJ
ejpam-4598	384	5	almost	almost	ADV
ejpam-4598	384	6	-	-	PUNCT
ejpam-4598	384	7	normal	normal	ADJ
ejpam-4598	384	8	t1	t1	NOUN
ejpam-4598	384	9	-	-	PUNCT
ejpam-4598	384	10	space	space	NOUN
ejpam-4598	384	11	is	be	AUX
ejpam-4598	384	12	epi	epi	NOUN
ejpam-4598	384	13	-	-	ADJ
ejpam-4598	384	14	completely	completely	ADV
ejpam-4598	384	15	regular	regular	ADJ
ejpam-4598	384	16	.	.	PUNCT
ejpam-4598	385	1	the	the	DET
ejpam-4598	385	2	next	next	ADJ
ejpam-4598	385	3	theorem	theorem	NOUN
ejpam-4598	385	4	has	have	AUX
ejpam-4598	385	5	been	be	AUX
ejpam-4598	385	6	presented	present	VERB
ejpam-4598	385	7	in	in	ADP
ejpam-4598	385	8	[	[	X
ejpam-4598	385	9	25	25	NUM
ejpam-4598	385	10	,	,	PUNCT
ejpam-4598	385	11	theorem	theorem	VERB
ejpam-4598	385	12	9	9	NUM
ejpam-4598	385	13	1.17	1.17	NUM
ejpam-4598	385	14	,	,	PUNCT
ejpam-4598	385	15	page	page	NOUN
ejpam-4598	385	16	306	306	NUM
ejpam-4598	385	17	]	]	PUNCT
ejpam-4598	385	18	:	:	PUNCT
ejpam-4598	385	19	theorem	theorem	VERB
ejpam-4598	385	20	14	14	NUM
ejpam-4598	385	21	.	.	PUNCT
ejpam-4598	386	1	[	[	X
ejpam-4598	386	2	25	25	NUM
ejpam-4598	386	3	]	]	PUNCT
ejpam-4598	386	4	,	,	PUNCT
ejpam-4598	386	5	a	a	DET
ejpam-4598	386	6	space	space	NOUN
ejpam-4598	386	7	(	(	PUNCT
ejpam-4598	386	8	x	x	X
ejpam-4598	386	9	,	,	PUNCT
ejpam-4598	386	10	t	t	PROPN
ejpam-4598	386	11	)	)	PUNCT
ejpam-4598	386	12	is	be	AUX
ejpam-4598	386	13	a	a	DET
ejpam-4598	386	14	t1	t1	NOUN
ejpam-4598	386	15	-	-	PUNCT
ejpam-4598	386	16	space	space	NOUN
ejpam-4598	386	17	if	if	SCONJ
ejpam-4598	386	18	and	and	CCONJ
ejpam-4598	386	19	only	only	ADV
ejpam-4598	386	20	if	if	SCONJ
ejpam-4598	386	21	t	t	PROPN
ejpam-4598	386	22	contains	contain	VERB
ejpam-4598	386	23	the	the	DET
ejpam-4598	386	24	finite	finite	ADJ
ejpam-4598	386	25	complement	complement	NOUN
ejpam-4598	386	26	topology	topology	NOUN
ejpam-4598	386	27	on	on	ADP
ejpam-4598	386	28	x.	x.	NOUN
ejpam-4598	386	29	i.e.	i.e.	X
ejpam-4598	386	30	cf	cf	PROPN
ejpam-4598	386	31	⊆	⊆	NUM
ejpam-4598	386	32	t	t	NOUN
ejpam-4598	386	33	and	and	CCONJ
ejpam-4598	386	34	(	(	PUNCT
ejpam-4598	386	35	x	x	NOUN
ejpam-4598	386	36	,	,	PUNCT
ejpam-4598	386	37	cf	cf	NOUN
ejpam-4598	386	38	)	)	PUNCT
ejpam-4598	386	39	is	be	AUX
ejpam-4598	386	40	the	the	DET
ejpam-4598	386	41	finite	finite	ADJ
ejpam-4598	386	42	complement	complement	NOUN
ejpam-4598	386	43	topology	topology	NOUN
ejpam-4598	386	44	on	on	ADP
ejpam-4598	386	45	x.	x.	NOUN
ejpam-4598	386	46	references	reference	NOUN
ejpam-4598	386	47	1819	1819	NUM
ejpam-4598	386	48	from	from	ADP
ejpam-4598	386	49	theorem	theorem	ADJ
ejpam-4598	386	50	14	14	NUM
ejpam-4598	386	51	,	,	PUNCT
ejpam-4598	386	52	we	we	PRON
ejpam-4598	386	53	conclude	conclude	VERB
ejpam-4598	386	54	:	:	PUNCT
ejpam-4598	386	55	corollary	corollary	ADJ
ejpam-4598	386	56	9	9	NUM
ejpam-4598	386	57	.	.	PUNCT
ejpam-4598	387	1	if	if	SCONJ
ejpam-4598	387	2	(	(	PUNCT
ejpam-4598	387	3	x	x	X
ejpam-4598	387	4	,	,	PUNCT
ejpam-4598	387	5	t	t	PROPN
ejpam-4598	387	6	)	)	PUNCT
ejpam-4598	387	7	is	be	AUX
ejpam-4598	387	8	a	a	DET
ejpam-4598	387	9	t1	t1	NOUN
ejpam-4598	387	10	-	-	PUNCT
ejpam-4598	387	11	space	space	NOUN
ejpam-4598	387	12	,	,	PUNCT
ejpam-4598	387	13	then	then	ADV
ejpam-4598	387	14	there	there	PRON
ejpam-4598	387	15	exists	exist	VERB
ejpam-4598	387	16	a	a	DET
ejpam-4598	387	17	topology	topology	NOUN
ejpam-4598	387	18	t	t	NOUN
ejpam-4598	387	19	′	′	NOUN
ejpam-4598	387	20	coarser	coarse	ADJ
ejpam-4598	387	21	than	than	ADP
ejpam-4598	387	22	t	t	PRON
ejpam-4598	387	23	such	such	ADJ
ejpam-4598	387	24	that	that	SCONJ
ejpam-4598	387	25	(	(	PUNCT
ejpam-4598	387	26	x	x	X
ejpam-4598	387	27	,	,	PUNCT
ejpam-4598	387	28	t	t	PROPN
ejpam-4598	387	29	′	′	NUM
ejpam-4598	387	30	)	)	PUNCT
ejpam-4598	387	31	is	be	AUX
ejpam-4598	387	32	t1	t1	NOUN
ejpam-4598	387	33	almost	almost	ADV
ejpam-4598	387	34	completely	completely	ADV
ejpam-4598	387	35	regular	regular	ADJ
ejpam-4598	387	36	(	(	PUNCT
ejpam-4598	387	37	resp	resp	NOUN
ejpam-4598	387	38	.	.	PUNCT
ejpam-4598	388	1	almost	almost	ADV
ejpam-4598	388	2	regular	regular	ADV
ejpam-4598	388	3	)	)	PUNCT
ejpam-4598	388	4	.	.	PUNCT
ejpam-4598	389	1	we	we	PRON
ejpam-4598	389	2	can	can	AUX
ejpam-4598	389	3	say	say	VERB
ejpam-4598	389	4	that	that	SCONJ
ejpam-4598	389	5	(	(	PUNCT
ejpam-4598	389	6	x	x	X
ejpam-4598	389	7	,	,	PUNCT
ejpam-4598	389	8	t	t	PROPN
ejpam-4598	389	9	)	)	PUNCT
ejpam-4598	389	10	is	be	AUX
ejpam-4598	389	11	epi	epi	NOUN
ejpam-4598	389	12	-	-	PUNCT
ejpam-4598	389	13	almost	almost	ADV
ejpam-4598	389	14	completely	completely	ADV
ejpam-4598	389	15	regular	regular	ADJ
ejpam-4598	389	16	(	(	PUNCT
ejpam-4598	389	17	resp	resp	NOUN
ejpam-4598	389	18	.	.	PUNCT
ejpam-4598	390	1	epi	epi	X
ejpam-4598	390	2	-	-	PUNCT
ejpam-4598	390	3	almost	almost	ADV
ejpam-4598	390	4	regular	regular	ADJ
ejpam-4598	390	5	)	)	PUNCT
ejpam-4598	390	6	.	.	PUNCT
ejpam-4598	391	1	recall	recall	VERB
ejpam-4598	391	2	that	that	PRON
ejpam-4598	391	3	:	:	PUNCT
ejpam-4598	391	4	any	any	DET
ejpam-4598	391	5	closed	closed	ADJ
ejpam-4598	391	6	extension	extension	NOUN
ejpam-4598	391	7	space	space	NOUN
ejpam-4598	391	8	(	(	PUNCT
ejpam-4598	391	9	xp	xp	INTJ
ejpam-4598	391	10	,	,	PUNCT
ejpam-4598	391	11	t	t	PROPN
ejpam-4598	391	12	∗	∗	NOUN
ejpam-4598	391	13	)	)	PUNCT
ejpam-4598	391	14	of	of	ADP
ejpam-4598	391	15	a	a	DET
ejpam-4598	391	16	given	give	VERB
ejpam-4598	391	17	space	space	NOUN
ejpam-4598	391	18	(	(	PUNCT
ejpam-4598	391	19	x	x	X
ejpam-4598	391	20	,	,	PUNCT
ejpam-4598	391	21	t	t	PROPN
ejpam-4598	391	22	)	)	PUNCT
ejpam-4598	391	23	is	be	AUX
ejpam-4598	391	24	always	always	ADV
ejpam-4598	391	25	connected	connect	VERB
ejpam-4598	391	26	,	,	PUNCT
ejpam-4598	391	27	π	π	PROPN
ejpam-4598	391	28	-	-	ADJ
ejpam-4598	391	29	normal	normal	ADJ
ejpam-4598	391	30	,	,	PUNCT
ejpam-4598	391	31	almost	almost	ADV
ejpam-4598	391	32	normal	normal	ADJ
ejpam-4598	391	33	,	,	PUNCT
ejpam-4598	391	34	separable	separable	ADJ
ejpam-4598	391	35	and	and	CCONJ
ejpam-4598	391	36	it	it	PRON
ejpam-4598	391	37	can	can	AUX
ejpam-4598	391	38	not	not	PART
ejpam-4598	391	39	be	be	AUX
ejpam-4598	391	40	t1	t1	NOUN
ejpam-4598	392	1	[	[	X
ejpam-4598	392	2	1	1	NUM
ejpam-4598	392	3	]	]	PUNCT
ejpam-4598	392	4	.	.	PUNCT
ejpam-4598	393	1	thus	thus	ADV
ejpam-4598	393	2	,	,	PUNCT
ejpam-4598	393	3	we	we	PRON
ejpam-4598	393	4	conclude	conclude	VERB
ejpam-4598	393	5	:	:	PUNCT
ejpam-4598	393	6	corollary	corollary	ADJ
ejpam-4598	393	7	10	10	NUM
ejpam-4598	393	8	.	.	PUNCT
ejpam-4598	394	1	every	every	DET
ejpam-4598	394	2	closed	close	VERB
ejpam-4598	394	3	extension	extension	NOUN
ejpam-4598	394	4	space	space	NOUN
ejpam-4598	394	5	(	(	PUNCT
ejpam-4598	394	6	xp	xp	INTJ
ejpam-4598	394	7	,	,	PUNCT
ejpam-4598	394	8	t	t	PROPN
ejpam-4598	394	9	∗	∗	NOUN
ejpam-4598	394	10	)	)	PUNCT
ejpam-4598	394	11	of	of	ADP
ejpam-4598	394	12	a	a	DET
ejpam-4598	394	13	given	give	VERB
ejpam-4598	394	14	space	space	NOUN
ejpam-4598	394	15	(	(	PUNCT
ejpam-4598	394	16	x	x	X
ejpam-4598	394	17	,	,	PUNCT
ejpam-4598	394	18	t	t	PROPN
ejpam-4598	394	19	)	)	PUNCT
ejpam-4598	394	20	can	can	AUX
ejpam-4598	394	21	not	not	PART
ejpam-4598	394	22	be	be	AUX
ejpam-4598	394	23	epi	epi	NOUN
ejpam-4598	394	24	-	-	ADJ
ejpam-4598	394	25	completely	completely	ADV
ejpam-4598	394	26	regular	regular	ADJ
ejpam-4598	394	27	.	.	PUNCT
ejpam-4598	395	1	the	the	DET
ejpam-4598	395	2	next	next	ADJ
ejpam-4598	395	3	problem	problem	NOUN
ejpam-4598	395	4	is	be	AUX
ejpam-4598	395	5	still	still	ADV
ejpam-4598	395	6	open	open	ADJ
ejpam-4598	395	7	in	in	ADP
ejpam-4598	395	8	this	this	DET
ejpam-4598	395	9	work	work	NOUN
ejpam-4598	395	10	:	:	PUNCT
ejpam-4598	395	11	problem	problem	NOUN
ejpam-4598	395	12	:	:	PUNCT
ejpam-4598	395	13	•	•	NUM
ejpam-4598	395	14	is	be	AUX
ejpam-4598	395	15	there	there	PRON
ejpam-4598	395	16	an	an	DET
ejpam-4598	395	17	example	example	NOUN
ejpam-4598	395	18	of	of	ADP
ejpam-4598	395	19	an	an	DET
ejpam-4598	395	20	epi	epi	NOUN
ejpam-4598	395	21	-	-	PUNCT
ejpam-4598	395	22	completely	completely	ADV
ejpam-4598	395	23	-	-	PUNCT
ejpam-4598	395	24	regular	regular	ADJ
ejpam-4598	395	25	space	space	NOUN
ejpam-4598	395	26	,	,	PUNCT
ejpam-4598	395	27	which	which	PRON
ejpam-4598	395	28	is	be	AUX
ejpam-4598	395	29	not	not	PART
ejpam-4598	395	30	epi	epi	NOUN
ejpam-4598	395	31	-	-	NOUN
ejpam-4598	395	32	mildlynormal	mildlynormal	ADJ
ejpam-4598	395	33	?	?	PUNCT
ejpam-4598	395	34	.	.	PUNCT
ejpam-4598	396	1	4	4	X
ejpam-4598	396	2	.	.	X
ejpam-4598	396	3	conclusion	conclusion	NOUN
ejpam-4598	396	4	a	a	DET
ejpam-4598	396	5	new	new	ADJ
ejpam-4598	396	6	version	version	NOUN
ejpam-4598	396	7	of	of	ADP
ejpam-4598	396	8	complete	complete	ADJ
ejpam-4598	396	9	regularity	regularity	NOUN
ejpam-4598	396	10	called	call	VERB
ejpam-4598	396	11	epi	epi	NOUN
ejpam-4598	396	12	-	-	ADJ
ejpam-4598	396	13	complete	complete	ADJ
ejpam-4598	396	14	regularity	regularity	NOUN
ejpam-4598	396	15	has	have	AUX
ejpam-4598	396	16	been	be	AUX
ejpam-4598	396	17	studied	study	VERB
ejpam-4598	396	18	in	in	ADP
ejpam-4598	396	19	this	this	DET
ejpam-4598	396	20	work	work	NOUN
ejpam-4598	396	21	.	.	PUNCT
ejpam-4598	397	1	i	i	PRON
ejpam-4598	397	2	have	have	AUX
ejpam-4598	397	3	shown	show	VERB
ejpam-4598	397	4	that	that	SCONJ
ejpam-4598	397	5	epi	epi	NOUN
ejpam-4598	397	6	-	-	ADJ
ejpam-4598	397	7	complete	complete	ADJ
ejpam-4598	397	8	regularity	regularity	NOUN
ejpam-4598	397	9	is	be	AUX
ejpam-4598	397	10	different	different	ADJ
ejpam-4598	397	11	from	from	ADP
ejpam-4598	397	12	both	both	DET
ejpam-4598	397	13	epi	epi	NOUN
ejpam-4598	397	14	-	-	NOUN
ejpam-4598	397	15	regularity	regularity	NOUN
ejpam-4598	397	16	and	and	CCONJ
ejpam-4598	397	17	epi	epi	NOUN
ejpam-4598	397	18	-	-	NOUN
ejpam-4598	397	19	normality	normality	NOUN
ejpam-4598	397	20	.	.	PUNCT
ejpam-4598	398	1	i	i	PRON
ejpam-4598	398	2	have	have	AUX
ejpam-4598	398	3	proved	prove	VERB
ejpam-4598	398	4	that	that	SCONJ
ejpam-4598	398	5	epi	epi	NOUN
ejpam-4598	398	6	-	-	ADJ
ejpam-4598	398	7	complete	complete	ADJ
ejpam-4598	398	8	regularity	regularity	NOUN
ejpam-4598	398	9	is	be	AUX
ejpam-4598	398	10	a	a	DET
ejpam-4598	398	11	topological	topological	ADJ
ejpam-4598	398	12	,	,	PUNCT
ejpam-4598	398	13	productive	productive	ADJ
ejpam-4598	398	14	,	,	PUNCT
ejpam-4598	398	15	hereditary	hereditary	ADJ
ejpam-4598	398	16	and	and	CCONJ
ejpam-4598	398	17	additive	additive	ADJ
ejpam-4598	398	18	property	property	NOUN
ejpam-4598	398	19	.	.	PUNCT
ejpam-4598	399	1	some	some	DET
ejpam-4598	399	2	properties	property	NOUN
ejpam-4598	399	3	,	,	PUNCT
ejpam-4598	399	4	counterexamples	counterexample	NOUN
ejpam-4598	399	5	and	and	CCONJ
ejpam-4598	399	6	relationships	relationship	NOUN
ejpam-4598	399	7	with	with	ADP
ejpam-4598	399	8	some	some	DET
ejpam-4598	399	9	other	other	ADJ
ejpam-4598	399	10	forms	form	NOUN
ejpam-4598	399	11	of	of	ADP
ejpam-4598	399	12	topological	topological	ADJ
ejpam-4598	399	13	properties	property	NOUN
ejpam-4598	399	14	have	have	AUX
ejpam-4598	399	15	been	be	AUX
ejpam-4598	399	16	presented	present	VERB
ejpam-4598	399	17	and	and	CCONJ
ejpam-4598	399	18	proved	prove	VERB
ejpam-4598	399	19	.	.	PUNCT
ejpam-4598	400	1	references	reference	NOUN
ejpam-4598	400	2	[	[	X
ejpam-4598	400	3	1	1	X
ejpam-4598	400	4	]	]	X
ejpam-4598	400	5	dina	dina	PROPN
ejpam-4598	400	6	abuzaid	abuzaid	PROPN
ejpam-4598	400	7	,	,	PUNCT
ejpam-4598	400	8	suad	suad	PROPN
ejpam-4598	400	9	al	al	PROPN
ejpam-4598	400	10	-	-	PUNCT
ejpam-4598	400	11	qarhi	qarhi	PROPN
ejpam-4598	400	12	,	,	PUNCT
ejpam-4598	400	13	and	and	CCONJ
ejpam-4598	400	14	lutfi	lutfi	PROPN
ejpam-4598	400	15	kalantan	kalantan	PROPN
ejpam-4598	400	16	.	.	PUNCT
ejpam-4598	401	1	closed	close	VERB
ejpam-4598	401	2	extension	extension	NOUN
ejpam-4598	401	3	topological	topological	ADJ
ejpam-4598	401	4	spaces	space	NOUN
ejpam-4598	401	5	.	.	PUNCT
ejpam-4598	402	1	european	european	ADJ
ejpam-4598	402	2	journal	journal	PROPN
ejpam-4598	402	3	of	of	ADP
ejpam-4598	402	4	pure	pure	ADJ
ejpam-4598	402	5	and	and	CCONJ
ejpam-4598	402	6	applied	applied	ADJ
ejpam-4598	402	7	mathematics	mathematic	NOUN
ejpam-4598	402	8	(	(	PUNCT
ejpam-4598	402	9	ujpam	ujpam	PROPN
ejpam-4598	402	10	)	)	PUNCT
ejpam-4598	402	11	.	.	PUNCT
ejpam-4598	402	12	,	,	PUNCT
ejpam-4598	402	13	15(2):672	15(2):672	NUM
ejpam-4598	402	14	–	–	PUNCT
ejpam-4598	402	15	680	680	NUM
ejpam-4598	402	16	,	,	PUNCT
ejpam-4598	402	17	2022	2022	NUM
ejpam-4598	402	18	.	.	PUNCT
ejpam-4598	403	1	[	[	X
ejpam-4598	403	2	2	2	NUM
ejpam-4598	403	3	]	]	PUNCT
ejpam-4598	403	4	khulod	khulod	NOUN
ejpam-4598	403	5	almontashery	almontashery	NOUN
ejpam-4598	403	6	and	and	CCONJ
ejpam-4598	403	7	lutfi	lutfi	PROPN
ejpam-4598	403	8	kalantan	kalantan	PROPN
ejpam-4598	403	9	.	.	PUNCT
ejpam-4598	404	1	results	result	VERB
ejpam-4598	404	2	about	about	ADP
ejpam-4598	404	3	the	the	DET
ejpam-4598	404	4	alexandroff	alexandroff	ADJ
ejpam-4598	404	5	duplicate	duplicate	ADJ
ejpam-4598	404	6	space	space	NOUN
ejpam-4598	404	7	.	.	PUNCT
ejpam-4598	405	1	appl	appl	PROPN
ejpam-4598	405	2	.	.	PUNCT
ejpam-4598	406	1	gen	gen	PROPN
ejpam-4598	406	2	.	.	PROPN
ejpam-4598	406	3	topol	topol	PROPN
ejpam-4598	406	4	.	.	PUNCT
ejpam-4598	406	5	,	,	PUNCT
ejpam-4598	406	6	17(2):117–122	17(2):117–122	PROPN
ejpam-4598	406	7	,	,	PUNCT
ejpam-4598	406	8	2016	2016	NUM
ejpam-4598	406	9	.	.	PUNCT
ejpam-4598	407	1	[	[	X
ejpam-4598	407	2	3	3	NUM
ejpam-4598	407	3	]	]	X
ejpam-4598	407	4	ibtesam	ibtesam	PROPN
ejpam-4598	407	5	alshammari	alshammari	PROPN
ejpam-4598	407	6	.	.	PUNCT
ejpam-4598	408	1	epi	epi	X
ejpam-4598	408	2	-	-	PUNCT
ejpam-4598	408	3	almost	almost	ADV
ejpam-4598	408	4	normality	normality	NOUN
ejpam-4598	408	5	.	.	PUNCT
ejpam-4598	409	1	journal	journal	NOUN
ejpam-4598	409	2	of	of	ADP
ejpam-4598	409	3	mathematical	mathematical	ADJ
ejpam-4598	409	4	analysis	analysis	NOUN
ejpam-4598	409	5	,	,	PUNCT
ejpam-4598	409	6	,	,	PUNCT
ejpam-4598	409	7	11:52–57	11:52–57	NUM
ejpam-4598	409	8	,	,	PUNCT
ejpam-4598	409	9	2020	2020	NUM
ejpam-4598	409	10	.	.	PUNCT
ejpam-4598	410	1	[	[	X
ejpam-4598	410	2	4	4	NUM
ejpam-4598	410	3	]	]	X
ejpam-4598	410	4	ibtesam	ibtesam	PROPN
ejpam-4598	410	5	alshammari	alshammari	PROPN
ejpam-4598	410	6	,	,	PUNCT
ejpam-4598	410	7	lutfi	lutfi	PROPN
ejpam-4598	410	8	kalantan	kalantan	PROPN
ejpam-4598	410	9	,	,	PUNCT
ejpam-4598	410	10	and	and	CCONJ
ejpam-4598	410	11	sadeq	sadeq	VERB
ejpam-4598	410	12	ali	ali	PROPN
ejpam-4598	410	13	thabit	thabit	PROPN
ejpam-4598	410	14	.	.	PUNCT
ejpam-4598	411	1	partial	partial	ADJ
ejpam-4598	411	2	normality	normality	NOUN
ejpam-4598	411	3	.	.	PUNCT
ejpam-4598	412	1	journal	journal	NOUN
ejpam-4598	412	2	of	of	ADP
ejpam-4598	412	3	mathematical	mathematical	ADJ
ejpam-4598	412	4	analysis	analysis	NOUN
ejpam-4598	412	5	,	,	PUNCT
ejpam-4598	412	6	10:1–8	10:1–8	NUM
ejpam-4598	412	7	,	,	PUNCT
ejpam-4598	412	8	2019	2019	NUM
ejpam-4598	412	9	.	.	PUNCT
ejpam-4598	413	1	[	[	X
ejpam-4598	413	2	5	5	X
ejpam-4598	413	3	]	]	PUNCT
ejpam-4598	413	4	s.	s.	PROPN
ejpam-4598	413	5	alzahrani	alzahrani	PROPN
ejpam-4598	413	6	.	.	PUNCT
ejpam-4598	414	1	epiregular	epiregular	ADJ
ejpam-4598	414	2	topological	topological	ADJ
ejpam-4598	414	3	spaces	space	NOUN
ejpam-4598	414	4	.	.	PUNCT
ejpam-4598	415	1	afr	afr	PROPN
ejpam-4598	415	2	.	.	PUNCT
ejpam-4598	416	1	mat	mat	PROPN
ejpam-4598	416	2	.	.	PROPN
ejpam-4598	416	3	,	,	PUNCT
ejpam-4598	416	4	29:803–808	29:803–808	NOUN
ejpam-4598	416	5	,	,	PUNCT
ejpam-4598	416	6	2018	2018	NUM
ejpam-4598	416	7	.	.	PUNCT
ejpam-4598	417	1	[	[	X
ejpam-4598	417	2	6	6	NUM
ejpam-4598	417	3	]	]	PUNCT
ejpam-4598	417	4	samirah	samirah	PROPN
ejpam-4598	417	5	alzahrani	alzahrani	PROPN
ejpam-4598	417	6	.	.	PUNCT
ejpam-4598	418	1	c	c	X
ejpam-4598	418	2	-	-	PUNCT
ejpam-4598	418	3	regular	regular	ADJ
ejpam-4598	418	4	topological	topological	ADJ
ejpam-4598	418	5	spaces	space	NOUN
ejpam-4598	418	6	.	.	PUNCT
ejpam-4598	419	1	journal	journal	NOUN
ejpam-4598	419	2	of	of	ADP
ejpam-4598	419	3	mathematical	mathematical	ADJ
ejpam-4598	419	4	analysis	analysis	NOUN
ejpam-4598	419	5	jma	jma	PROPN
ejpam-4598	419	6	,	,	PUNCT
ejpam-4598	419	7	9:141–149	9:141–149	NUM
ejpam-4598	419	8	,	,	PUNCT
ejpam-4598	419	9	2018	2018	NUM
ejpam-4598	419	10	.	.	PUNCT
ejpam-4598	420	1	references	reference	NOUN
ejpam-4598	420	2	1820	1820	NUM
ejpam-4598	421	1	[	[	X
ejpam-4598	421	2	7	7	NUM
ejpam-4598	421	3	]	]	PUNCT
ejpam-4598	421	4	samirah	samirah	PROPN
ejpam-4598	421	5	alzahrani	alzahrani	PROPN
ejpam-4598	421	6	.	.	PUNCT
ejpam-4598	422	1	c	c	X
ejpam-4598	422	2	-	-	PUNCT
ejpam-4598	422	3	tychonoff	tychonoff	NOUN
ejpam-4598	422	4	and	and	CCONJ
ejpam-4598	422	5	l	l	NOUN
ejpam-4598	422	6	-	-	NOUN
ejpam-4598	422	7	tychonoff	tychonoff	NOUN
ejpam-4598	422	8	topological	topological	ADJ
ejpam-4598	422	9	spaces	space	NOUN
ejpam-4598	422	10	.	.	PUNCT
ejpam-4598	423	1	european	european	ADJ
ejpam-4598	423	2	journal	journal	PROPN
ejpam-4598	423	3	of	of	ADP
ejpam-4598	423	4	pure	pure	ADJ
ejpam-4598	423	5	and	and	CCONJ
ejpam-4598	423	6	applied	applied	ADJ
ejpam-4598	423	7	mathematics	mathematic	NOUN
ejpam-4598	423	8	,	,	PUNCT
ejpam-4598	423	9	11(3):882–892	11(3):882–892	NUM
ejpam-4598	423	10	,	,	PUNCT
ejpam-4598	423	11	2018	2018	NUM
ejpam-4598	423	12	.	.	PUNCT
ejpam-4598	424	1	[	[	X
ejpam-4598	424	2	8	8	NUM
ejpam-4598	424	3	]	]	PUNCT
ejpam-4598	424	4	samirah	samirah	PROPN
ejpam-4598	424	5	alzahrani	alzahrani	PROPN
ejpam-4598	424	6	and	and	CCONJ
ejpam-4598	424	7	lutfi	lutfi	PROPN
ejpam-4598	424	8	kalantan	kalantan	PROPN
ejpam-4598	424	9	.	.	PUNCT
ejpam-4598	425	1	c	c	X
ejpam-4598	425	2	-	-	PUNCT
ejpam-4598	425	3	normal	normal	ADJ
ejpam-4598	425	4	topological	topological	ADJ
ejpam-4598	425	5	property	property	NOUN
ejpam-4598	425	6	.	.	PUNCT
ejpam-4598	426	1	filomat	filomat	NOUN
ejpam-4598	426	2	,	,	PUNCT
ejpam-4598	426	3	31:2:407–411	31:2:407–411	NUM
ejpam-4598	426	4	,	,	PUNCT
ejpam-4598	426	5	2017	2017	NUM
ejpam-4598	426	6	.	.	PUNCT
ejpam-4598	427	1	[	[	X
ejpam-4598	427	2	9	9	NUM
ejpam-4598	427	3	]	]	PUNCT
ejpam-4598	427	4	r.	r.	PROPN
ejpam-4598	427	5	z.	z.	PROPN
ejpam-4598	427	6	buzyakova	buzyakova	PROPN
ejpam-4598	427	7	.	.	PUNCT
ejpam-4598	428	1	an	an	DET
ejpam-4598	428	2	exampe	exampe	NOUN
ejpam-4598	428	3	of	of	ADP
ejpam-4598	428	4	a	a	DET
ejpam-4598	428	5	product	product	NOUN
ejpam-4598	428	6	of	of	ADP
ejpam-4598	428	7	two	two	NUM
ejpam-4598	428	8	normal	normal	ADJ
ejpam-4598	428	9	groups	group	NOUN
ejpam-4598	428	10	that	that	PRON
ejpam-4598	428	11	can	can	AUX
ejpam-4598	428	12	not	not	PART
ejpam-4598	428	13	be	be	AUX
ejpam-4598	428	14	condensed	condense	VERB
ejpam-4598	428	15	onto	onto	ADP
ejpam-4598	428	16	a	a	DET
ejpam-4598	428	17	normal	normal	ADJ
ejpam-4598	428	18	space	space	NOUN
ejpam-4598	428	19	.	.	PUNCT
ejpam-4598	429	1	moscow	moscow	PROPN
ejpam-4598	429	2	univ	univ	PROPN
ejpam-4598	429	3	.	.	PUNCT
ejpam-4598	429	4	math	math	NOUN
ejpam-4598	429	5	.	.	PUNCT
ejpam-4598	430	1	bull	bull	PROPN
ejpam-4598	430	2	.	.	PUNCT
ejpam-4598	430	3	,	,	PUNCT
ejpam-4598	431	1	52(3):page	52(3):page	NUM
ejpam-4598	431	2	42	42	NUM
ejpam-4598	431	3	,	,	PUNCT
ejpam-4598	431	4	1961	1961	NUM
ejpam-4598	431	5	.	.	PUNCT
ejpam-4598	432	1	[	[	X
ejpam-4598	432	2	10	10	NUM
ejpam-4598	432	3	]	]	PUNCT
ejpam-4598	432	4	a.	a.	NOUN
ejpam-4598	432	5	k.	k.	PROPN
ejpam-4598	432	6	das	das	PROPN
ejpam-4598	432	7	.	.	PUNCT
ejpam-4598	433	1	simultaneous	simultaneous	ADJ
ejpam-4598	433	2	generalizations	generalization	NOUN
ejpam-4598	433	3	of	of	ADP
ejpam-4598	433	4	regularity	regularity	NOUN
ejpam-4598	433	5	and	and	CCONJ
ejpam-4598	433	6	normality	normality	NOUN
ejpam-4598	433	7	.	.	PUNCT
ejpam-4598	434	1	european	european	ADJ
ejpam-4598	434	2	journal	journal	PROPN
ejpam-4598	434	3	of	of	ADP
ejpam-4598	434	4	pure	pure	ADJ
ejpam-4598	434	5	and	and	CCONJ
ejpam-4598	434	6	applied	applied	ADJ
ejpam-4598	434	7	mathematics	mathematic	NOUN
ejpam-4598	434	8	,	,	PUNCT
ejpam-4598	434	9	4(1):34–41	4(1):34–41	NUM
ejpam-4598	434	10	,	,	PUNCT
ejpam-4598	434	11	2011	2011	NUM
ejpam-4598	434	12	.	.	PUNCT
ejpam-4598	435	1	[	[	X
ejpam-4598	435	2	11	11	NUM
ejpam-4598	435	3	]	]	PUNCT
ejpam-4598	435	4	j.	j.	PROPN
ejpam-4598	435	5	dugundji	dugundji	PROPN
ejpam-4598	435	6	.	.	PUNCT
ejpam-4598	435	7	topology	topology	PROPN
ejpam-4598	435	8	.	.	PUNCT
ejpam-4598	436	1	allyn	allyn	PROPN
ejpam-4598	436	2	and	and	CCONJ
ejpam-4598	436	3	bacon	bacon	PROPN
ejpam-4598	436	4	,	,	PUNCT
ejpam-4598	436	5	inc	inc	PROPN
ejpam-4598	436	6	.	.	PROPN
ejpam-4598	436	7	,	,	PUNCT
ejpam-4598	436	8	470	470	NUM
ejpam-4598	436	9	atlantic	atlantic	PROPN
ejpam-4598	436	10	avenue	avenue	PROPN
ejpam-4598	436	11	,	,	PUNCT
ejpam-4598	436	12	boston	boston	PROPN
ejpam-4598	436	13	,	,	PUNCT
ejpam-4598	436	14	1966	1966	NUM
ejpam-4598	436	15	.	.	PUNCT
ejpam-4598	437	1	[	[	X
ejpam-4598	437	2	12	12	NUM
ejpam-4598	437	3	]	]	X
ejpam-4598	437	4	r.	r.	PROPN
ejpam-4598	437	5	engelking	engelke	VERB
ejpam-4598	437	6	.	.	PUNCT
ejpam-4598	438	1	general	general	ADJ
ejpam-4598	438	2	topology	topology	NOUN
ejpam-4598	438	3	,	,	PUNCT
ejpam-4598	438	4	volume	volume	NOUN
ejpam-4598	438	5	6	6	NUM
ejpam-4598	438	6	.	.	PUNCT
ejpam-4598	439	1	berlin	berlin	PROPN
ejpam-4598	439	2	:	:	PUNCT
ejpam-4598	439	3	heldermann	heldermann	PROPN
ejpam-4598	439	4	(	(	PUNCT
ejpam-4598	439	5	sigma	sigma	PROPN
ejpam-4598	439	6	series	series	PROPN
ejpam-4598	439	7	in	in	ADP
ejpam-4598	439	8	pure	pure	ADJ
ejpam-4598	439	9	mathematics	mathematic	NOUN
ejpam-4598	439	10	)	)	PUNCT
ejpam-4598	439	11	,	,	PUNCT
ejpam-4598	439	12	poland	poland	PROPN
ejpam-4598	439	13	,	,	PUNCT
ejpam-4598	439	14	1989	1989	NUM
ejpam-4598	439	15	.	.	PUNCT
ejpam-4598	440	1	[	[	X
ejpam-4598	440	2	13	13	NUM
ejpam-4598	440	3	]	]	X
ejpam-4598	440	4	g.	g.	PROPN
ejpam-4598	440	5	gruenhage	gruenhage	PROPN
ejpam-4598	440	6	.	.	PUNCT
ejpam-4598	441	1	generalized	generalize	VERB
ejpam-4598	441	2	metric	metric	ADJ
ejpam-4598	441	3	spaces	space	NOUN
ejpam-4598	441	4	.	.	PUNCT
ejpam-4598	442	1	in	in	ADP
ejpam-4598	442	2	:	:	PUNCT
ejpam-4598	442	3	handbook	handbook	NOUN
ejpam-4598	442	4	of	of	ADP
ejpam-4598	442	5	set	set	NOUN
ejpam-4598	442	6	-	-	PUNCT
ejpam-4598	442	7	theoretic	theoretic	NOUN
ejpam-4598	442	8	topology	topology	NOUN
ejpam-4598	442	9	,	,	PUNCT
ejpam-4598	442	10	k.	k.	PROPN
ejpam-4598	442	11	kunen	kunen	PROPN
ejpam-4598	442	12	and	and	CCONJ
ejpam-4598	442	13	j.	j.	PROPN
ejpam-4598	442	14	vaughan	vaughan	PROPN
ejpam-4598	442	15	,	,	PUNCT
ejpam-4598	442	16	eds	eds	PROPN
ejpam-4598	442	17	.	.	PROPN
ejpam-4598	442	18	,	,	PUNCT
ejpam-4598	442	19	north	north	NOUN
ejpam-4598	442	20	-	-	PUNCT
ejpam-4598	442	21	holland	holland	PROPN
ejpam-4598	442	22	,	,	PUNCT
ejpam-4598	442	23	amsterdam	amsterdam	PROPN
ejpam-4598	442	24	,	,	PUNCT
ejpam-4598	442	25	pages	page	NOUN
ejpam-4598	442	26	423–501	423–501	NUM
ejpam-4598	442	27	,	,	PUNCT
ejpam-4598	442	28	1984	1984	NUM
ejpam-4598	442	29	.	.	PUNCT
ejpam-4598	443	1	[	[	X
ejpam-4598	443	2	14	14	NUM
ejpam-4598	443	3	]	]	X
ejpam-4598	443	4	l.	l.	PROPN
ejpam-4598	443	5	kalantan	kalantan	PROPN
ejpam-4598	443	6	.	.	PUNCT
ejpam-4598	444	1	π	π	X
ejpam-4598	444	2	-	-	ADJ
ejpam-4598	444	3	normal	normal	ADJ
ejpam-4598	444	4	topological	topological	ADJ
ejpam-4598	444	5	spaces	space	NOUN
ejpam-4598	444	6	.	.	PUNCT
ejpam-4598	445	1	filomat	filomat	NOUN
ejpam-4598	445	2	,	,	PUNCT
ejpam-4598	445	3	22	22	NUM
ejpam-4598	445	4	-	-	SYM
ejpam-4598	445	5	1:173–181	1:173–181	NUM
ejpam-4598	445	6	,	,	PUNCT
ejpam-4598	445	7	2008	2008	NUM
ejpam-4598	445	8	.	.	PUNCT
ejpam-4598	446	1	[	[	X
ejpam-4598	446	2	15	15	NUM
ejpam-4598	446	3	]	]	X
ejpam-4598	446	4	l.	l.	PROPN
ejpam-4598	446	5	kalantan	kalantan	PROPN
ejpam-4598	446	6	and	and	CCONJ
ejpam-4598	446	7	s.	s.	PROPN
ejpam-4598	446	8	alzahrani	alzahrani	PROPN
ejpam-4598	446	9	.	.	PUNCT
ejpam-4598	447	1	epinormality	epinormality	PROPN
ejpam-4598	447	2	.	.	PUNCT
ejpam-4598	448	1	j.	j.	PROPN
ejpam-4598	448	2	nonlinear	nonlinear	PROPN
ejpam-4598	448	3	sci	sci	PROPN
ejpam-4598	448	4	.	.	PUNCT
ejpam-4598	448	5	appl	appl	PROPN
ejpam-4598	448	6	.	.	PROPN
ejpam-4598	448	7	,	,	PUNCT
ejpam-4598	448	8	(	(	PUNCT
ejpam-4598	448	9	9):5398–5402	9):5398–5402	NOUN
ejpam-4598	448	10	,	,	PUNCT
ejpam-4598	448	11	2016	2016	NUM
ejpam-4598	448	12	.	.	PUNCT
ejpam-4598	449	1	[	[	X
ejpam-4598	449	2	16	16	NUM
ejpam-4598	449	3	]	]	X
ejpam-4598	449	4	l.	l.	PROPN
ejpam-4598	449	5	kalantan	kalantan	PROPN
ejpam-4598	449	6	and	and	CCONJ
ejpam-4598	449	7	m.	m.	PROPN
ejpam-4598	449	8	saeed	saeed	PROPN
ejpam-4598	449	9	.	.	PUNCT
ejpam-4598	450	1	l	l	NOUN
ejpam-4598	450	2	-	-	NOUN
ejpam-4598	450	3	normality	normality	NOUN
ejpam-4598	450	4	.	.	PUNCT
ejpam-4598	451	1	topology	topology	NOUN
ejpam-4598	451	2	proceedings	proceeding	NOUN
ejpam-4598	451	3	,	,	PUNCT
ejpam-4598	451	4	50:141–149	50:141–149	NUM
ejpam-4598	451	5	,	,	PUNCT
ejpam-4598	451	6	2017	2017	NUM
ejpam-4598	451	7	.	.	PUNCT
ejpam-4598	452	1	[	[	X
ejpam-4598	452	2	17	17	NUM
ejpam-4598	452	3	]	]	X
ejpam-4598	452	4	lutfi	lutfi	PROPN
ejpam-4598	452	5	kalantan	kalantan	PROPN
ejpam-4598	452	6	and	and	CCONJ
ejpam-4598	452	7	manal	manal	ADJ
ejpam-4598	452	8	alhomieyed	alhomieye	VERB
ejpam-4598	452	9	.	.	PUNCT
ejpam-4598	453	1	cc	cc	NOUN
ejpam-4598	453	2	-	-	ADJ
ejpam-4598	453	3	normal	normal	ADJ
ejpam-4598	453	4	topological	topological	ADJ
ejpam-4598	453	5	spaces	space	NOUN
ejpam-4598	453	6	.	.	PUNCT
ejpam-4598	454	1	turk	turk	PROPN
ejpam-4598	454	2	.	.	PUNCT
ejpam-4598	455	1	j.	j.	PROPN
ejpam-4598	455	2	math	math	PROPN
ejpam-4598	455	3	.	.	PUNCT
ejpam-4598	455	4	,	,	PUNCT
ejpam-4598	455	5	41:749–755	41:749–755	NUM
ejpam-4598	455	6	,	,	PUNCT
ejpam-4598	455	7	2017	2017	NUM
ejpam-4598	455	8	.	.	PUNCT
ejpam-4598	456	1	[	[	X
ejpam-4598	456	2	18	18	NUM
ejpam-4598	456	3	]	]	X
ejpam-4598	456	4	lutfi	lutfi	PROPN
ejpam-4598	456	5	kalantan	kalantan	PROPN
ejpam-4598	456	6	and	and	CCONJ
ejpam-4598	456	7	ibtesam	ibtesam	PROPN
ejpam-4598	456	8	alshammari	alshammari	PROPN
ejpam-4598	456	9	.	.	PUNCT
ejpam-4598	457	1	epi	epi	ADJ
ejpam-4598	457	2	-	-	ADJ
ejpam-4598	457	3	mild	mild	ADJ
ejpam-4598	457	4	normality	normality	NOUN
ejpam-4598	457	5	.	.	PUNCT
ejpam-4598	458	1	open	open	ADJ
ejpam-4598	459	1	mat.j	mat.j	PROPN
ejpam-4598	459	2	.	.	PROPN
ejpam-4598	459	3	,	,	PUNCT
ejpam-4598	459	4	16:1170	16:1170	NUM
ejpam-4598	459	5	–	–	PUNCT
ejpam-4598	459	6	1175	1175	NUM
ejpam-4598	459	7	,	,	PUNCT
ejpam-4598	459	8	2018	2018	NUM
ejpam-4598	459	9	.	.	PUNCT
ejpam-4598	460	1	[	[	X
ejpam-4598	460	2	19	19	NUM
ejpam-4598	460	3	]	]	PUNCT
ejpam-4598	460	4	j.	j.	PROPN
ejpam-4598	460	5	k.	k.	PROPN
ejpam-4598	460	6	kohli	kohli	PROPN
ejpam-4598	460	7	and	and	CCONJ
ejpam-4598	460	8	a.	a.	PROPN
ejpam-4598	460	9	k.	k.	PROPN
ejpam-4598	460	10	das	das	PROPN
ejpam-4598	460	11	.	.	PUNCT
ejpam-4598	461	1	a	a	DET
ejpam-4598	461	2	class	class	NOUN
ejpam-4598	461	3	of	of	ADP
ejpam-4598	461	4	spaces	space	NOUN
ejpam-4598	461	5	containing	contain	VERB
ejpam-4598	461	6	all	all	PRON
ejpam-4598	461	7	generalized	generalize	VERB
ejpam-4598	461	8	absolutely	absolutely	ADV
ejpam-4598	461	9	closed	closed	ADJ
ejpam-4598	461	10	(	(	PUNCT
ejpam-4598	461	11	almost	almost	ADV
ejpam-4598	461	12	compact	compact	ADJ
ejpam-4598	461	13	)	)	PUNCT
ejpam-4598	461	14	spaces	space	NOUN
ejpam-4598	461	15	.	.	PUNCT
ejpam-4598	462	1	applied	apply	VERB
ejpam-4598	462	2	general	general	ADJ
ejpam-4598	462	3	topology	topology	NOUN
ejpam-4598	462	4	,	,	PUNCT
ejpam-4598	462	5	7(2):233–244	7(2):233–244	NUM
ejpam-4598	462	6	,	,	PUNCT
ejpam-4598	462	7	2006	2006	NUM
ejpam-4598	462	8	.	.	PUNCT
ejpam-4598	463	1	[	[	X
ejpam-4598	463	2	20	20	NUM
ejpam-4598	463	3	]	]	X
ejpam-4598	463	4	c.	c.	PROPN
ejpam-4598	463	5	kuratowski	kuratowski	PROPN
ejpam-4598	463	6	.	.	PUNCT
ejpam-4598	464	1	topology	topology	PROPN
ejpam-4598	465	1	i	i	PRON
ejpam-4598	465	2	,	,	PUNCT
ejpam-4598	465	3	volume	volume	VERB
ejpam-4598	465	4	4th	4th	ADJ
ejpam-4598	465	5	ed	ed	NOUN
ejpam-4598	465	6	.	.	PUNCT
ejpam-4598	466	1	in	in	ADP
ejpam-4598	466	2	france	france	PROPN
ejpam-4598	466	3	.	.	PUNCT
ejpam-4598	467	1	hafner	hafner	PROPN
ejpam-4598	467	2	,	,	PUNCT
ejpam-4598	467	3	new	new	PROPN
ejpam-4598	467	4	york	york	PROPN
ejpam-4598	467	5	,	,	PUNCT
ejpam-4598	467	6	1958	1958	NUM
ejpam-4598	467	7	.	.	PUNCT
ejpam-4598	468	1	[	[	X
ejpam-4598	468	2	21	21	NUM
ejpam-4598	468	3	]	]	X
ejpam-4598	468	4	s.	s.	PROPN
ejpam-4598	468	5	lal	lal	PROPN
ejpam-4598	468	6	and	and	CCONJ
ejpam-4598	468	7	m.	m.	PROPN
ejpam-4598	468	8	s.	s.	PROPN
ejpam-4598	468	9	rahman	rahman	PROPN
ejpam-4598	468	10	.	.	PUNCT
ejpam-4598	469	1	a	a	DET
ejpam-4598	469	2	note	note	NOUN
ejpam-4598	469	3	of	of	ADP
ejpam-4598	469	4	quasi	quasi	ADJ
ejpam-4598	469	5	-	-	ADJ
ejpam-4598	469	6	normal	normal	ADJ
ejpam-4598	469	7	spaces	space	NOUN
ejpam-4598	469	8	.	.	PUNCT
ejpam-4598	470	1	indian	indian	ADJ
ejpam-4598	470	2	journal	journal	PROPN
ejpam-4598	470	3	of	of	ADP
ejpam-4598	470	4	mathematics	mathematic	NOUN
ejpam-4598	470	5	,	,	PUNCT
ejpam-4598	470	6	32(1):87–94	32(1):87–94	NUM
ejpam-4598	470	7	,	,	PUNCT
ejpam-4598	470	8	1990	1990	NUM
ejpam-4598	470	9	.	.	PUNCT
ejpam-4598	471	1	[	[	X
ejpam-4598	471	2	22	22	NUM
ejpam-4598	471	3	]	]	PUNCT
ejpam-4598	471	4	m.	m.	NOUN
ejpam-4598	471	5	mršević	mršević	PROPN
ejpam-4598	471	6	,	,	PUNCT
ejpam-4598	471	7	i.	i.	PROPN
ejpam-4598	471	8	l.	l.	PROPN
ejpam-4598	471	9	reilly	reilly	PROPN
ejpam-4598	471	10	,	,	PUNCT
ejpam-4598	471	11	and	and	CCONJ
ejpam-4598	471	12	m.k	m.k	PROPN
ejpam-4598	471	13	.	.	PROPN
ejpam-4598	471	14	vamanamurthy	vamanamurthy	NOUN
ejpam-4598	471	15	.	.	PUNCT
ejpam-4598	472	1	on	on	ADP
ejpam-4598	472	2	semi	semi	ADJ
ejpam-4598	472	3	regularization	regularization	NOUN
ejpam-4598	472	4	topologies	topology	NOUN
ejpam-4598	472	5	.	.	PUNCT
ejpam-4598	473	1	j.	j.	PROPN
ejpam-4598	473	2	austral	austral	PROPN
ejpam-4598	473	3	.	.	PUNCT
ejpam-4598	474	1	math	math	NOUN
ejpam-4598	474	2	.	.	PUNCT
ejpam-4598	475	1	soc	soc	PROPN
ejpam-4598	475	2	.	.	PUNCT
ejpam-4598	475	3	,	,	PUNCT
ejpam-4598	475	4	(	(	PUNCT
ejpam-4598	475	5	series	series	NOUN
ejpam-4598	475	6	a	a	PROPN
ejpam-4598	475	7	)	)	PUNCT
ejpam-4598	475	8	,	,	PUNCT
ejpam-4598	475	9	38:40–54	38:40–54	NUM
ejpam-4598	475	10	,	,	PUNCT
ejpam-4598	475	11	1985	1985	NUM
ejpam-4598	475	12	.	.	PUNCT
ejpam-4598	476	1	[	[	X
ejpam-4598	476	2	23	23	NUM
ejpam-4598	476	3	]	]	X
ejpam-4598	476	4	c.	c.	PROPN
ejpam-4598	476	5	patty	patty	PROPN
ejpam-4598	476	6	.	.	PUNCT
ejpam-4598	477	1	foundation	foundation	PROPN
ejpam-4598	477	2	of	of	ADP
ejpam-4598	477	3	topology	topology	NOUN
ejpam-4598	477	4	.	.	PUNCT
ejpam-4598	478	1	pws	pws	PROPN
ejpam-4598	478	2	-	-	PUNCT
ejpam-4598	478	3	kent	kent	PROPN
ejpam-4598	478	4	publishing	publishing	PROPN
ejpam-4598	478	5	company	company	NOUN
ejpam-4598	478	6	,	,	PUNCT
ejpam-4598	478	7	boston	boston	PROPN
ejpam-4598	478	8	,	,	PUNCT
ejpam-4598	478	9	1993	1993	NUM
ejpam-4598	478	10	.	.	PUNCT
ejpam-4598	479	1	[	[	X
ejpam-4598	479	2	24	24	NUM
ejpam-4598	479	3	]	]	PUNCT
ejpam-4598	479	4	j.	j.	PROPN
ejpam-4598	479	5	r.	r.	PROPN
ejpam-4598	479	6	porter	porter	PROPN
ejpam-4598	479	7	and	and	CCONJ
ejpam-4598	479	8	j.	j.	PROPN
ejpam-4598	479	9	d.	d.	PROPN
ejpam-4598	479	10	thomas	thomas	PROPN
ejpam-4598	479	11	.	.	PUNCT
ejpam-4598	480	1	on	on	ADP
ejpam-4598	480	2	h	h	NOUN
ejpam-4598	480	3	-	-	PUNCT
ejpam-4598	480	4	closed	closed	ADJ
ejpam-4598	480	5	and	and	CCONJ
ejpam-4598	480	6	minimal	minimal	ADJ
ejpam-4598	480	7	hausdorff	hausdorff	NOUN
ejpam-4598	480	8	spaces	space	NOUN
ejpam-4598	480	9	.	.	PUNCT
ejpam-4598	481	1	trans	trans	PROPN
ejpam-4598	481	2	.	.	PUNCT
ejpam-4598	482	1	amer	amer	PROPN
ejpam-4598	482	2	.	.	PUNCT
ejpam-4598	482	3	math	math	PROPN
ejpam-4598	482	4	.	.	PUNCT
ejpam-4598	483	1	soc	soc	PROPN
ejpam-4598	483	2	.	.	PUNCT
ejpam-4598	483	3	,	,	PUNCT
ejpam-4598	483	4	138:159–170	138:159–170	NUM
ejpam-4598	483	5	,	,	PUNCT
ejpam-4598	483	6	1996	1996	NUM
ejpam-4598	483	7	.	.	PUNCT
ejpam-4598	484	1	references	reference	NOUN
ejpam-4598	484	2	1821	1821	NUM
ejpam-4598	485	1	[	[	X
ejpam-4598	485	2	25	25	NUM
ejpam-4598	485	3	]	]	PUNCT
ejpam-4598	485	4	m.	m.	PROPN
ejpam-4598	485	5	d.	d.	PROPN
ejpam-4598	485	6	raisinghania	raisinghania	PROPN
ejpam-4598	485	7	and	and	CCONJ
ejpam-4598	485	8	r.	r.	PROPN
ejpam-4598	485	9	s.	s.	PROPN
ejpam-4598	485	10	aggarwal	aggarwal	PROPN
ejpam-4598	485	11	.	.	PUNCT
ejpam-4598	486	1	topology	topology	NOUN
ejpam-4598	486	2	for	for	ADP
ejpam-4598	486	3	post	post	ADJ
ejpam-4598	486	4	-	-	ADJ
ejpam-4598	486	5	graduate	graduate	ADJ
ejpam-4598	486	6	students	student	NOUN
ejpam-4598	486	7	in	in	ADP
ejpam-4598	486	8	indian	indian	ADJ
ejpam-4598	486	9	universities	university	NOUN
ejpam-4598	486	10	.	.	PUNCT
ejpam-4598	487	1	s.	s.	PROPN
ejpam-4598	487	2	chand	chand	PROPN
ejpam-4598	487	3	and	and	CCONJ
ejpam-4598	487	4	company	company	PROPN
ejpam-4598	487	5	ltd	ltd	PROPN
ejpam-4598	487	6	,	,	PUNCT
ejpam-4598	487	7	ram	ram	NOUN
ejpam-4598	487	8	nagar	nagar	NOUN
ejpam-4598	487	9	,	,	PUNCT
ejpam-4598	487	10	new	new	ADJ
ejpam-4598	487	11	delhi-110055	delhi-110055	NOUN
ejpam-4598	487	12	,	,	PUNCT
ejpam-4598	487	13	india	india	PROPN
ejpam-4598	487	14	,	,	PUNCT
ejpam-4598	487	15	1973	1973	NUM
ejpam-4598	487	16	.	.	PUNCT
ejpam-4598	488	1	[	[	X
ejpam-4598	488	2	26	26	NUM
ejpam-4598	488	3	]	]	PUNCT
ejpam-4598	488	4	maha	maha	PROPN
ejpam-4598	488	5	mohammed	mohammed	PROPN
ejpam-4598	488	6	saeed	saeed	PROPN
ejpam-4598	488	7	.	.	PUNCT
ejpam-4598	489	1	countable	countable	ADJ
ejpam-4598	489	2	normality	normality	NOUN
ejpam-4598	489	3	.	.	PUNCT
ejpam-4598	490	1	journal	journal	NOUN
ejpam-4598	490	2	of	of	ADP
ejpam-4598	490	3	mathematical	mathematical	ADJ
ejpam-4598	490	4	analysis	analysis	NOUN
ejpam-4598	490	5	,	,	PUNCT
ejpam-4598	490	6	9:116–123	9:116–123	NOUN
ejpam-4598	490	7	,	,	PUNCT
ejpam-4598	490	8	2018	2018	NUM
ejpam-4598	490	9	.	.	PUNCT
ejpam-4598	491	1	[	[	X
ejpam-4598	491	2	27	27	NUM
ejpam-4598	491	3	]	]	PUNCT
ejpam-4598	491	4	m.	m.	NOUN
ejpam-4598	491	5	k.	k.	PROPN
ejpam-4598	491	6	singal	singal	PROPN
ejpam-4598	491	7	and	and	CCONJ
ejpam-4598	491	8	s.	s.	PROPN
ejpam-4598	491	9	arya	arya	PROPN
ejpam-4598	491	10	.	.	PUNCT
ejpam-4598	492	1	on	on	ADP
ejpam-4598	492	2	almost	almost	ADV
ejpam-4598	492	3	regular	regular	ADJ
ejpam-4598	492	4	spaces	space	NOUN
ejpam-4598	492	5	.	.	PUNCT
ejpam-4598	493	1	glasnik	glasnik	PROPN
ejpam-4598	493	2	matematicki	matematicki	PROPN
ejpam-4598	493	3	,	,	PUNCT
ejpam-4598	493	4	4(24):89	4(24):89	NUM
ejpam-4598	493	5	–	–	PUNCT
ejpam-4598	493	6	99	99	NUM
ejpam-4598	493	7	,	,	PUNCT
ejpam-4598	493	8	1969	1969	NUM
ejpam-4598	493	9	.	.	PUNCT
ejpam-4598	494	1	[	[	X
ejpam-4598	494	2	28	28	NUM
ejpam-4598	494	3	]	]	X
ejpam-4598	494	4	m.	m.	NOUN
ejpam-4598	494	5	k.	k.	PROPN
ejpam-4598	494	6	singal	singal	PROPN
ejpam-4598	494	7	and	and	CCONJ
ejpam-4598	494	8	s.	s.	PROPN
ejpam-4598	494	9	p.	p.	PROPN
ejpam-4598	494	10	arya	arya	PROPN
ejpam-4598	494	11	.	.	PUNCT
ejpam-4598	495	1	on	on	ADP
ejpam-4598	495	2	almost	almost	ADV
ejpam-4598	495	3	normal	normal	ADJ
ejpam-4598	495	4	and	and	CCONJ
ejpam-4598	495	5	almost	almost	ADV
ejpam-4598	495	6	completely	completely	ADV
ejpam-4598	495	7	regular	regular	ADJ
ejpam-4598	495	8	spaces	space	NOUN
ejpam-4598	495	9	.	.	PUNCT
ejpam-4598	496	1	glasnik	glasnik	PROPN
ejpam-4598	496	2	matematicki	matematicki	PROPN
ejpam-4598	496	3	,	,	PUNCT
ejpam-4598	496	4	5(5):141–152	5(5):141–152	NUM
ejpam-4598	496	5	,	,	PUNCT
ejpam-4598	496	6	1970	1970	NUM
ejpam-4598	496	7	.	.	PUNCT
ejpam-4598	497	1	[	[	X
ejpam-4598	497	2	29	29	NUM
ejpam-4598	497	3	]	]	PUNCT
ejpam-4598	497	4	m.	m.	NOUN
ejpam-4598	497	5	k.	k.	PROPN
ejpam-4598	497	6	singal	singal	PROPN
ejpam-4598	497	7	and	and	CCONJ
ejpam-4598	497	8	a.	a.	PROPN
ejpam-4598	497	9	r.	r.	PROPN
ejpam-4598	497	10	singal	singal	PROPN
ejpam-4598	497	11	.	.	PUNCT
ejpam-4598	498	1	mildly	mildly	ADV
ejpam-4598	498	2	normal	normal	ADJ
ejpam-4598	498	3	spaces	space	NOUN
ejpam-4598	498	4	.	.	PUNCT
ejpam-4598	499	1	kyungpook	kyungpook	PROPN
ejpam-4598	499	2	mathematical	mathematical	PROPN
ejpam-4598	499	3	journal	journal	NOUN
ejpam-4598	499	4	,	,	PUNCT
ejpam-4598	499	5	13	13	NUM
ejpam-4598	499	6	-	-	SYM
ejpam-4598	499	7	1:27–31	1:27–31	NUM
ejpam-4598	499	8	,	,	PUNCT
ejpam-4598	499	9	1973	1973	NUM
ejpam-4598	499	10	.	.	PUNCT
ejpam-4598	500	1	[	[	X
ejpam-4598	500	2	30	30	NUM
ejpam-4598	500	3	]	]	X
ejpam-4598	500	4	a.	a.	PROPN
ejpam-4598	500	5	l.	l.	PROPN
ejpam-4598	500	6	steen	steen	PROPN
ejpam-4598	500	7	and	and	CCONJ
ejpam-4598	500	8	j.	j.	PROPN
ejpam-4598	500	9	a.	a.	PROPN
ejpam-4598	500	10	seebach	seebach	PROPN
ejpam-4598	500	11	.	.	PUNCT
ejpam-4598	501	1	counterexamples	counterexample	NOUN
ejpam-4598	501	2	in	in	ADP
ejpam-4598	501	3	topology	topology	NOUN
ejpam-4598	501	4	.	.	PUNCT
ejpam-4598	502	1	dover	dover	PROPN
ejpam-4598	502	2	publications	publications	PROPN
ejpam-4598	502	3	,	,	PUNCT
ejpam-4598	502	4	inc	inc	PROPN
ejpam-4598	502	5	.	.	PROPN
ejpam-4598	502	6	,	,	PUNCT
ejpam-4598	502	7	new	new	PROPN
ejpam-4598	502	8	york	york	PROPN
ejpam-4598	502	9	,	,	PUNCT
ejpam-4598	502	10	1995	1995	NUM
ejpam-4598	502	11	.	.	PUNCT
ejpam-4598	503	1	[	[	X
ejpam-4598	503	2	31	31	NUM
ejpam-4598	503	3	]	]	PUNCT
ejpam-4598	503	4	sadeq	sadeq	PROPN
ejpam-4598	503	5	ali	ali	PROPN
ejpam-4598	503	6	thabit	thabit	PROPN
ejpam-4598	503	7	,	,	PUNCT
ejpam-4598	503	8	ibtesam	ibtesam	PROPN
ejpam-4598	503	9	alshammari	alshammari	NOUN
ejpam-4598	503	10	,	,	PUNCT
ejpam-4598	503	11	and	and	CCONJ
ejpam-4598	503	12	wafa	wafa	PROPN
ejpam-4598	503	13	alqurashi	alqurashi	PROPN
ejpam-4598	503	14	.	.	PUNCT
ejpam-4598	504	1	epi	epi	NOUN
ejpam-4598	504	2	-	-	ADJ
ejpam-4598	504	3	quasi	quasi	ADJ
ejpam-4598	504	4	normality	normality	NOUN
ejpam-4598	504	5	.	.	PUNCT
ejpam-4598	505	1	open	open	ADJ
ejpam-4598	505	2	mathematics	mathematic	NOUN
ejpam-4598	505	3	(	(	PUNCT
ejpam-4598	505	4	de	de	X
ejpam-4598	505	5	gruyter	gruyter	NOUN
ejpam-4598	505	6	open	open	ADJ
ejpam-4598	505	7	access	access	NOUN
ejpam-4598	505	8	)	)	PUNCT
ejpam-4598	505	9	,	,	PUNCT
ejpam-4598	505	10	19:1755–1770	19:1755–1770	NUM
ejpam-4598	505	11	,	,	PUNCT
ejpam-4598	505	12	2021	2021	NUM
ejpam-4598	505	13	.	.	PUNCT
ejpam-4598	506	1	[	[	X
ejpam-4598	506	2	32	32	NUM
ejpam-4598	506	3	]	]	PUNCT
ejpam-4598	506	4	sadeq	sadeq	PROPN
ejpam-4598	506	5	ali	ali	PROPN
ejpam-4598	506	6	saad	saad	PROPN
ejpam-4598	506	7	thabit	thabit	PROPN
ejpam-4598	506	8	.	.	PUNCT
ejpam-4598	507	1	epi	epi	ADJ
ejpam-4598	507	2	-	-	ADJ
ejpam-4598	507	3	partial	partial	ADJ
ejpam-4598	507	4	normality	normality	NOUN
ejpam-4598	507	5	.	.	PUNCT
ejpam-4598	508	1	journal	journal	PROPN
ejpam-4598	508	2	of	of	ADP
ejpam-4598	508	3	physics	physics	PROPN
ejpam-4598	508	4	:	:	PUNCT
ejpam-4598	508	5	conference	conference	NOUN
ejpam-4598	508	6	series	series	NOUN
ejpam-4598	508	7	,	,	PUNCT
ejpam-4598	508	8	iop	iop	PROPN
ejpam-4598	508	9	publishing	publishing	PROPN
ejpam-4598	508	10	ltd	ltd	PROPN
ejpam-4598	508	11	(	(	PUNCT
ejpam-4598	508	12	j.	j.	PROPN
ejpam-4598	508	13	phys	phys	PROPN
ejpam-4598	508	14	.	.	PUNCT
ejpam-4598	508	15	:	:	PUNCT
ejpam-4598	509	1	conf	conf	PROPN
ejpam-4598	509	2	.	.	PUNCT
ejpam-4598	509	3	ser	ser	PROPN
ejpam-4598	509	4	)	)	PUNCT
ejpam-4598	509	5	,	,	PUNCT
ejpam-4598	509	6	1900(012013):1–11	1900(012013):1–11	NUM
ejpam-4598	509	7	,	,	PUNCT
ejpam-4598	509	8	2021	2021	NUM
ejpam-4598	509	9	.	.	PUNCT
ejpam-4598	510	1	[	[	X
ejpam-4598	510	2	33	33	NUM
ejpam-4598	510	3	]	]	X
ejpam-4598	510	4	v.	v.	NOUN
ejpam-4598	510	5	zaitsev	zaitsev	NOUN
ejpam-4598	510	6	.	.	PUNCT
ejpam-4598	511	1	on	on	ADP
ejpam-4598	511	2	certain	certain	ADJ
ejpam-4598	511	3	classes	class	NOUN
ejpam-4598	511	4	of	of	ADP
ejpam-4598	511	5	topological	topological	ADJ
ejpam-4598	511	6	spaces	space	NOUN
ejpam-4598	511	7	and	and	CCONJ
ejpam-4598	511	8	their	their	PRON
ejpam-4598	511	9	bicompactifications	bicompactification	NOUN
ejpam-4598	511	10	.	.	PUNCT
ejpam-4598	512	1	doklady	doklady	PROPN
ejpam-4598	512	2	akademii	akademii	NOUN
ejpam-4598	512	3	nauk	nauk	NOUN
ejpam-4598	512	4	sssr	sssr	NOUN
ejpam-4598	512	5	,	,	PUNCT
ejpam-4598	512	6	178:778–779	178:778–779	NUM
ejpam-4598	512	7	,	,	PUNCT
ejpam-4598	512	8	1968	1968	NUM
ejpam-4598	512	9	.	.	PUNCT