id	sid	tid	token	lemma	pos
ejpam-4607	1	1	european	european	PROPN
ejpam-4607	1	2	journal	journal	PROPN
ejpam-4607	1	3	of	of	ADP
ejpam-4607	1	4	pure	pure	ADJ
ejpam-4607	1	5	and	and	CCONJ
ejpam-4607	1	6	applied	apply	VERB
ejpam-4607	1	7	mathematics	mathematic	NOUN
ejpam-4607	1	8	vol	vol	NOUN
ejpam-4607	1	9	.	.	PUNCT
ejpam-4607	2	1	16	16	NUM
ejpam-4607	2	2	,	,	PUNCT
ejpam-4607	2	3	no	no	INTJ
ejpam-4607	2	4	.	.	NOUN
ejpam-4607	2	5	1	1	NUM
ejpam-4607	2	6	,	,	PUNCT
ejpam-4607	2	7	2023	2023	NUM
ejpam-4607	2	8	,	,	PUNCT
ejpam-4607	2	9	62	62	NUM
ejpam-4607	2	10	-	-	SYM
ejpam-4607	2	11	70	70	NUM
ejpam-4607	2	12	issn	issn	PROPN
ejpam-4607	2	13	1307	1307	NUM
ejpam-4607	2	14	-	-	SYM
ejpam-4607	2	15	5543	5543	NUM
ejpam-4607	2	16	–	–	PUNCT
ejpam-4607	3	1	ejpam.com	ejpam.com	X
ejpam-4607	3	2	published	publish	VERB
ejpam-4607	3	3	by	by	ADP
ejpam-4607	3	4	new	new	PROPN
ejpam-4607	3	5	york	york	PROPN
ejpam-4607	3	6	business	business	PROPN
ejpam-4607	3	7	global	global	ADJ
ejpam-4607	3	8	results	result	NOUN
ejpam-4607	3	9	about	about	ADP
ejpam-4607	3	10	c	c	NOUN
ejpam-4607	3	11	-	-	PUNCT
ejpam-4607	3	12	κ	κ	NOUN
ejpam-4607	3	13	-	-	PUNCT
ejpam-4607	3	14	normality	normality	NOUN
ejpam-4607	3	15	and	and	CCONJ
ejpam-4607	3	16	c	c	NOUN
ejpam-4607	3	17	-	-	PUNCT
ejpam-4607	3	18	mild	mild	ADJ
ejpam-4607	3	19	normality	normality	NOUN
ejpam-4607	3	20	lutfi	lutfi	PROPN
ejpam-4607	3	21	kalantan1	kalantan1	PROPN
ejpam-4607	3	22	,	,	PUNCT
ejpam-4607	3	23	alya’a	alya’a	PROPN
ejpam-4607	3	24	al	al	PROPN
ejpam-4607	3	25	-	-	PUNCT
ejpam-4607	3	26	awadi1,2,∗	awadi1,2,∗	ADV
ejpam-4607	3	27	,	,	PUNCT
ejpam-4607	3	28	sadeq	sadeq	ADJ
ejpam-4607	3	29	thabit3	thabit3	NOUN
ejpam-4607	3	30	1	1	NUM
ejpam-4607	3	31	king	king	PROPN
ejpam-4607	3	32	abdulaziz	abdulaziz	PROPN
ejpam-4607	3	33	university	university	PROPN
ejpam-4607	3	34	,	,	PUNCT
ejpam-4607	3	35	department	department	NOUN
ejpam-4607	3	36	of	of	ADP
ejpam-4607	3	37	mathematics	mathematic	NOUN
ejpam-4607	3	38	,	,	PUNCT
ejpam-4607	3	39	p.o.box	p.o.box	PROPN
ejpam-4607	3	40	80203	80203	NUM
ejpam-4607	3	41	,	,	PUNCT
ejpam-4607	3	42	jeddah	jeddah	PROPN
ejpam-4607	3	43	21589	21589	NUM
ejpam-4607	3	44	,	,	PUNCT
ejpam-4607	3	45	saudi	saudi	PROPN
ejpam-4607	3	46	arabia	arabia	PROPN
ejpam-4607	3	47	.	.	PUNCT
ejpam-4607	4	1	2	2	NUM
ejpam-4607	4	2	department	department	NOUN
ejpam-4607	4	3	of	of	ADP
ejpam-4607	4	4	mathematics	mathematic	NOUN
ejpam-4607	4	5	,	,	PUNCT
ejpam-4607	4	6	faculty	faculty	NOUN
ejpam-4607	4	7	of	of	ADP
ejpam-4607	4	8	science	science	NOUN
ejpam-4607	4	9	,	,	PUNCT
ejpam-4607	4	10	university	university	NOUN
ejpam-4607	4	11	of	of	ADP
ejpam-4607	4	12	jeddah	jeddah	PROPN
ejpam-4607	4	13	,	,	PUNCT
ejpam-4607	4	14	p.o	p.o	PROPN
ejpam-4607	4	15	.	.	PROPN
ejpam-4607	4	16	box	box	PROPN
ejpam-4607	4	17	80327	80327	NUM
ejpam-4607	4	18	,	,	PUNCT
ejpam-4607	4	19	jeddah	jeddah	PROPN
ejpam-4607	4	20	,	,	PUNCT
ejpam-4607	4	21	21589	21589	NUM
ejpam-4607	4	22	,	,	PUNCT
ejpam-4607	4	23	saudi	saudi	PROPN
ejpam-4607	4	24	arabia	arabia	PROPN
ejpam-4607	4	25	3	3	NUM
ejpam-4607	4	26	hadhramout	hadhramout	PROPN
ejpam-4607	4	27	university	university	NOUN
ejpam-4607	4	28	,	,	PUNCT
ejpam-4607	4	29	department	department	NOUN
ejpam-4607	4	30	of	of	ADP
ejpam-4607	4	31	mathematics	mathematics	PROPN
ejpam-4607	4	32	,	,	PUNCT
ejpam-4607	4	33	yemen	yemen	PROPN
ejpam-4607	4	34	abstract	abstract	NOUN
ejpam-4607	4	35	.	.	PUNCT
ejpam-4607	5	1	a	a	DET
ejpam-4607	5	2	topological	topological	ADJ
ejpam-4607	5	3	space	space	NOUN
ejpam-4607	5	4	x	x	PUNCT
ejpam-4607	5	5	is	be	AUX
ejpam-4607	5	6	c	c	NOUN
ejpam-4607	5	7	-	-	PUNCT
ejpam-4607	5	8	κ	κ	NOUN
ejpam-4607	5	9	-	-	ADJ
ejpam-4607	5	10	normal	normal	ADJ
ejpam-4607	5	11	(	(	PUNCT
ejpam-4607	5	12	c	c	NOUN
ejpam-4607	5	13	-	-	PUNCT
ejpam-4607	5	14	mildly	mildly	ADV
ejpam-4607	5	15	normal	normal	ADJ
ejpam-4607	5	16	)	)	PUNCT
ejpam-4607	5	17	if	if	SCONJ
ejpam-4607	5	18	there	there	PRON
ejpam-4607	5	19	exist	exist	VERB
ejpam-4607	5	20	a	a	DET
ejpam-4607	5	21	κ	κ	NOUN
ejpam-4607	5	22	-	-	ADJ
ejpam-4607	5	23	normal	normal	ADJ
ejpam-4607	5	24	(	(	PUNCT
ejpam-4607	5	25	mildly	mildly	ADV
ejpam-4607	5	26	normal	normal	ADJ
ejpam-4607	5	27	)	)	PUNCT
ejpam-4607	5	28	space	space	NOUN
ejpam-4607	5	29	y	y	PROPN
ejpam-4607	5	30	and	and	CCONJ
ejpam-4607	5	31	a	a	DET
ejpam-4607	5	32	bijective	bijective	ADJ
ejpam-4607	5	33	function	function	NOUN
ejpam-4607	6	1	f	f	NOUN
ejpam-4607	6	2	:	:	PUNCT
ejpam-4607	6	3	x	x	PUNCT
ejpam-4607	6	4	−→	−→	NOUN
ejpam-4607	6	5	y	y	PROPN
ejpam-4607	6	6	such	such	ADJ
ejpam-4607	6	7	that	that	SCONJ
ejpam-4607	6	8	the	the	DET
ejpam-4607	6	9	restriction	restriction	NOUN
ejpam-4607	6	10	f|a	f|a	PUNCT
ejpam-4607	6	11	:	:	PUNCT
ejpam-4607	6	12	a	a	DET
ejpam-4607	6	13	−→	−→	NOUN
ejpam-4607	6	14	f(a	f(a	NOUN
ejpam-4607	6	15	)	)	PUNCT
ejpam-4607	6	16	is	be	AUX
ejpam-4607	6	17	a	a	DET
ejpam-4607	6	18	homeomorphism	homeomorphism	NOUN
ejpam-4607	6	19	for	for	ADP
ejpam-4607	6	20	each	each	DET
ejpam-4607	6	21	compact	compact	ADJ
ejpam-4607	6	22	subspace	subspace	NOUN
ejpam-4607	6	23	a	a	DET
ejpam-4607	6	24	⊆	⊆	NUM
ejpam-4607	6	25	x.	x.	NOUN
ejpam-4607	6	26	we	we	PRON
ejpam-4607	6	27	present	present	VERB
ejpam-4607	6	28	new	new	ADJ
ejpam-4607	6	29	results	result	NOUN
ejpam-4607	6	30	about	about	ADP
ejpam-4607	6	31	those	those	DET
ejpam-4607	6	32	two	two	NUM
ejpam-4607	6	33	topological	topological	ADJ
ejpam-4607	6	34	properties	property	NOUN
ejpam-4607	6	35	and	and	CCONJ
ejpam-4607	6	36	use	use	VERB
ejpam-4607	6	37	a	a	DET
ejpam-4607	6	38	discrete	discrete	ADJ
ejpam-4607	6	39	extension	extension	NOUN
ejpam-4607	6	40	space	space	NOUN
ejpam-4607	6	41	to	to	PART
ejpam-4607	6	42	solve	solve	VERB
ejpam-4607	6	43	open	open	ADJ
ejpam-4607	6	44	problems	problem	NOUN
ejpam-4607	6	45	regarding	regard	VERB
ejpam-4607	6	46	c2	c2	PROPN
ejpam-4607	6	47	-	-	PUNCT
ejpam-4607	6	48	paracompactness	paracompactness	PROPN
ejpam-4607	6	49	and	and	CCONJ
ejpam-4607	6	50	α	α	NOUN
ejpam-4607	6	51	-	-	NOUN
ejpam-4607	6	52	normality	normality	NOUN
ejpam-4607	6	53	.	.	PUNCT
ejpam-4607	7	1	2020	2020	NUM
ejpam-4607	7	2	mathematics	mathematic	NOUN
ejpam-4607	7	3	subject	subject	NOUN
ejpam-4607	7	4	classifications	classification	NOUN
ejpam-4607	7	5	:	:	PUNCT
ejpam-4607	7	6	54d15	54d15	NUM
ejpam-4607	7	7	,	,	PUNCT
ejpam-4607	7	8	54c10	54c10	NUM
ejpam-4607	7	9	key	key	ADJ
ejpam-4607	7	10	words	word	NOUN
ejpam-4607	7	11	and	and	CCONJ
ejpam-4607	7	12	phrases	phrase	NOUN
ejpam-4607	7	13	:	:	PUNCT
ejpam-4607	7	14	κ	κ	NOUN
ejpam-4607	7	15	-	-	ADJ
ejpam-4607	7	16	normal	normal	ADJ
ejpam-4607	7	17	,	,	PUNCT
ejpam-4607	7	18	normal	normal	ADJ
ejpam-4607	7	19	,	,	PUNCT
ejpam-4607	7	20	mildly	mildly	ADV
ejpam-4607	7	21	normal	normal	ADJ
ejpam-4607	7	22	,	,	PUNCT
ejpam-4607	7	23	compact	compact	ADJ
ejpam-4607	7	24	,	,	PUNCT
ejpam-4607	7	25	c	c	NOUN
ejpam-4607	7	26	-	-	ADJ
ejpam-4607	7	27	normal	normal	ADJ
ejpam-4607	7	28	,	,	PUNCT
ejpam-4607	7	29	c−κ	c−κ	ADJ
ejpam-4607	7	30	-	-	ADJ
ejpam-4607	7	31	normal	normal	ADJ
ejpam-4607	7	32	,	,	PUNCT
ejpam-4607	7	33	c	c	NOUN
ejpam-4607	7	34	-	-	PUNCT
ejpam-4607	7	35	mildly	mildly	ADV
ejpam-4607	7	36	normal	normal	ADJ
ejpam-4607	7	37	,	,	PUNCT
ejpam-4607	7	38	minimal	minimal	ADJ
ejpam-4607	7	39	hausdorff	hausdorff	NOUN
ejpam-4607	7	40	,	,	PUNCT
ejpam-4607	7	41	discrete	discrete	ADJ
ejpam-4607	7	42	extension	extension	NOUN
ejpam-4607	7	43	,	,	PUNCT
ejpam-4607	7	44	epinormal	epinormal	NOUN
ejpam-4607	7	45	,	,	PUNCT
ejpam-4607	7	46	epi	epi	ADJ
ejpam-4607	7	47	-	-	ADJ
ejpam-4607	7	48	mildly	mildly	ADV
ejpam-4607	7	49	normal	normal	ADJ
ejpam-4607	7	50	,	,	PUNCT
ejpam-4607	7	51	α	α	NOUN
ejpam-4607	7	52	-	-	ADJ
ejpam-4607	7	53	normal	normal	ADJ
ejpam-4607	7	54	,	,	PUNCT
ejpam-4607	7	55	c2	c2	PROPN
ejpam-4607	7	56	-	-	PUNCT
ejpam-4607	7	57	paracompact	paracompact	PROPN
ejpam-4607	7	58	1	1	NUM
ejpam-4607	7	59	.	.	PUNCT
ejpam-4607	7	60	preliminaries	preliminary	NOUN
ejpam-4607	7	61	in	in	ADP
ejpam-4607	7	62	the	the	DET
ejpam-4607	7	63	present	present	ADJ
ejpam-4607	7	64	work	work	NOUN
ejpam-4607	7	65	,	,	PUNCT
ejpam-4607	7	66	we	we	PRON
ejpam-4607	7	67	give	give	VERB
ejpam-4607	7	68	some	some	DET
ejpam-4607	7	69	new	new	ADJ
ejpam-4607	7	70	results	result	NOUN
ejpam-4607	7	71	about	about	ADP
ejpam-4607	7	72	c	c	NOUN
ejpam-4607	7	73	-	-	PUNCT
ejpam-4607	7	74	κ	κ	NOUN
ejpam-4607	7	75	-	-	PUNCT
ejpam-4607	7	76	normality	normality	NOUN
ejpam-4607	7	77	and	and	CCONJ
ejpam-4607	7	78	c	c	NOUN
ejpam-4607	7	79	-	-	PUNCT
ejpam-4607	7	80	mild	mild	ADJ
ejpam-4607	7	81	normality	normality	NOUN
ejpam-4607	7	82	[	[	X
ejpam-4607	7	83	2	2	NUM
ejpam-4607	7	84	]	]	PUNCT
ejpam-4607	7	85	and	and	CCONJ
ejpam-4607	7	86	use	use	VERB
ejpam-4607	7	87	the	the	DET
ejpam-4607	7	88	discrete	discrete	ADJ
ejpam-4607	7	89	extension	extension	NOUN
ejpam-4607	7	90	space	space	NOUN
ejpam-4607	7	91	to	to	PART
ejpam-4607	7	92	answer	answer	VERB
ejpam-4607	7	93	the	the	DET
ejpam-4607	7	94	open	open	ADJ
ejpam-4607	7	95	problems	problem	NOUN
ejpam-4607	7	96	“	"	PUNCT
ejpam-4607	7	97	is	be	AUX
ejpam-4607	7	98	c2paracompactness	c2paracompactness	ADV
ejpam-4607	7	99	hereditary	hereditary	ADJ
ejpam-4607	7	100	with	with	ADP
ejpam-4607	7	101	respect	respect	NOUN
ejpam-4607	7	102	to	to	ADP
ejpam-4607	7	103	closed	closed	ADJ
ejpam-4607	7	104	subspaces	subspace	NOUN
ejpam-4607	7	105	?	?	PUNCT
ejpam-4607	7	106	”	"	PUNCT
ejpam-4607	8	1	[	[	X
ejpam-4607	8	2	5	5	NUM
ejpam-4607	8	3	]	]	PUNCT
ejpam-4607	8	4	and	and	CCONJ
ejpam-4607	8	5	“	"	PUNCT
ejpam-4607	8	6	is	be	AUX
ejpam-4607	8	7	α	α	DET
ejpam-4607	8	8	-	-	PUNCT
ejpam-4607	8	9	normality	normality	NOUN
ejpam-4607	8	10	preserved	preserve	VERB
ejpam-4607	8	11	by	by	ADP
ejpam-4607	8	12	the	the	DET
ejpam-4607	8	13	discrete	discrete	ADJ
ejpam-4607	8	14	extension	extension	NOUN
ejpam-4607	8	15	?	?	PUNCT
ejpam-4607	8	16	”	"	PUNCT
ejpam-4607	9	1	[	[	X
ejpam-4607	9	2	3	3	NUM
ejpam-4607	9	3	]	]	PUNCT
ejpam-4607	9	4	.	.	PUNCT
ejpam-4607	10	1	throughout	throughout	ADP
ejpam-4607	10	2	this	this	DET
ejpam-4607	10	3	paper	paper	NOUN
ejpam-4607	10	4	,	,	PUNCT
ejpam-4607	10	5	we	we	PRON
ejpam-4607	10	6	denote	denote	VERB
ejpam-4607	10	7	the	the	DET
ejpam-4607	10	8	set	set	NOUN
ejpam-4607	10	9	of	of	ADP
ejpam-4607	10	10	positive	positive	ADJ
ejpam-4607	10	11	integers	integer	NOUN
ejpam-4607	10	12	by	by	ADP
ejpam-4607	10	13	n	n	CCONJ
ejpam-4607	10	14	,	,	PUNCT
ejpam-4607	10	15	the	the	DET
ejpam-4607	10	16	rationals	rational	NOUN
ejpam-4607	10	17	by	by	ADP
ejpam-4607	10	18	q	q	NOUN
ejpam-4607	10	19	,	,	PUNCT
ejpam-4607	10	20	the	the	DET
ejpam-4607	10	21	irrationals	irrational	NOUN
ejpam-4607	10	22	by	by	ADP
ejpam-4607	10	23	p	p	NOUN
ejpam-4607	10	24	,	,	PUNCT
ejpam-4607	10	25	and	and	CCONJ
ejpam-4607	10	26	the	the	DET
ejpam-4607	10	27	set	set	NOUN
ejpam-4607	10	28	of	of	ADP
ejpam-4607	10	29	real	real	ADJ
ejpam-4607	10	30	numbers	number	NOUN
ejpam-4607	10	31	by	by	ADP
ejpam-4607	10	32	r.	r.	PROPN
ejpam-4607	10	33	two	two	NUM
ejpam-4607	10	34	subsets	subset	NOUN
ejpam-4607	10	35	a	a	PRON
ejpam-4607	10	36	and	and	CCONJ
ejpam-4607	10	37	b	b	NOUN
ejpam-4607	10	38	of	of	ADP
ejpam-4607	10	39	a	a	DET
ejpam-4607	10	40	space	space	NOUN
ejpam-4607	10	41	x	x	PRON
ejpam-4607	10	42	are	be	AUX
ejpam-4607	10	43	called	call	VERB
ejpam-4607	10	44	separated	separate	VERB
ejpam-4607	10	45	if	if	SCONJ
ejpam-4607	10	46	there	there	PRON
ejpam-4607	10	47	are	be	VERB
ejpam-4607	10	48	two	two	NUM
ejpam-4607	10	49	disjoint	disjoint	ADJ
ejpam-4607	10	50	open	open	ADJ
ejpam-4607	10	51	subsets	subset	NOUN
ejpam-4607	10	52	u	u	NOUN
ejpam-4607	10	53	and	and	CCONJ
ejpam-4607	10	54	v	v	ADP
ejpam-4607	10	55	such	such	ADJ
ejpam-4607	10	56	that	that	SCONJ
ejpam-4607	10	57	a	a	DET
ejpam-4607	10	58	⊆	⊆	NUM
ejpam-4607	10	59	u	u	NOUN
ejpam-4607	10	60	and	and	CCONJ
ejpam-4607	10	61	b	b	NOUN
ejpam-4607	10	62	⊆	⊆	NUM
ejpam-4607	10	63	v	v	NOUN
ejpam-4607	10	64	.	.	PUNCT
ejpam-4607	11	1	a	a	DET
ejpam-4607	11	2	space	space	NOUN
ejpam-4607	11	3	x	x	PUNCT
ejpam-4607	11	4	is	be	AUX
ejpam-4607	11	5	regular	regular	ADJ
ejpam-4607	11	6	if	if	SCONJ
ejpam-4607	11	7	for	for	ADP
ejpam-4607	11	8	any	any	DET
ejpam-4607	11	9	closed	closed	ADJ
ejpam-4607	11	10	subset	subset	NOUN
ejpam-4607	11	11	e	e	NOUN
ejpam-4607	11	12	of	of	ADP
ejpam-4607	11	13	x	x	PROPN
ejpam-4607	11	14	and	and	CCONJ
ejpam-4607	11	15	for	for	ADP
ejpam-4607	11	16	any	any	DET
ejpam-4607	11	17	element	element	NOUN
ejpam-4607	11	18	x	x	SYM
ejpam-4607	11	19	∈	∈	PROPN
ejpam-4607	11	20	x	x	X
ejpam-4607	12	1	\e	\e	PROPN
ejpam-4607	12	2	we	we	PRON
ejpam-4607	12	3	have	have	VERB
ejpam-4607	12	4	{	{	PUNCT
ejpam-4607	12	5	x	x	NOUN
ejpam-4607	12	6	}	}	PUNCT
ejpam-4607	12	7	and	and	CCONJ
ejpam-4607	12	8	e	e	NOUN
ejpam-4607	12	9	can	can	AUX
ejpam-4607	12	10	be	be	AUX
ejpam-4607	12	11	separated	separate	VERB
ejpam-4607	12	12	.	.	PUNCT
ejpam-4607	13	1	a	a	DET
ejpam-4607	13	2	t3	t3	PROPN
ejpam-4607	13	3	space	space	NOUN
ejpam-4607	13	4	is	be	AUX
ejpam-4607	13	5	a	a	DET
ejpam-4607	13	6	t1	t1	NOUN
ejpam-4607	13	7	regular	regular	ADJ
ejpam-4607	13	8	space	space	NOUN
ejpam-4607	13	9	,	,	PUNCT
ejpam-4607	13	10	a	a	DET
ejpam-4607	13	11	normal	normal	ADJ
ejpam-4607	13	12	space	space	NOUN
ejpam-4607	13	13	is	be	AUX
ejpam-4607	13	14	a	a	DET
ejpam-4607	13	15	space	space	NOUN
ejpam-4607	13	16	where	where	SCONJ
ejpam-4607	13	17	any	any	DET
ejpam-4607	13	18	two	two	NUM
ejpam-4607	13	19	disjoint	disjoint	ADJ
ejpam-4607	13	20	closed	closed	ADJ
ejpam-4607	13	21	subsets	subset	NOUN
ejpam-4607	13	22	can	can	AUX
ejpam-4607	13	23	be	be	AUX
ejpam-4607	13	24	separated	separate	VERB
ejpam-4607	13	25	,	,	PUNCT
ejpam-4607	13	26	a	a	DET
ejpam-4607	13	27	t4	t4	PROPN
ejpam-4607	13	28	space	space	NOUN
ejpam-4607	13	29	is	be	AUX
ejpam-4607	13	30	a	a	DET
ejpam-4607	13	31	t1	t1	NOUN
ejpam-4607	13	32	normal	normal	ADJ
ejpam-4607	13	33	space	space	NOUN
ejpam-4607	13	34	,	,	PUNCT
ejpam-4607	13	35	and	and	CCONJ
ejpam-4607	13	36	a	a	DET
ejpam-4607	13	37	tychonoff	tychonoff	NOUN
ejpam-4607	13	38	space	space	NOUN
ejpam-4607	13	39	(	(	PUNCT
ejpam-4607	13	40	t3	t3	NOUN
ejpam-4607	13	41	1	1	NUM
ejpam-4607	13	42	2	2	NUM
ejpam-4607	13	43	)	)	PUNCT
ejpam-4607	13	44	is	be	AUX
ejpam-4607	13	45	a	a	DET
ejpam-4607	13	46	t1	t1	NOUN
ejpam-4607	13	47	completely	completely	ADV
ejpam-4607	13	48	regular	regular	ADJ
ejpam-4607	13	49	space	space	NOUN
ejpam-4607	13	50	.	.	PUNCT
ejpam-4607	14	1	we	we	PRON
ejpam-4607	14	2	do	do	AUX
ejpam-4607	14	3	not	not	PART
ejpam-4607	14	4	∗corresponding	∗corresponde	VERB
ejpam-4607	14	5	author	author	NOUN
ejpam-4607	14	6	.	.	PUNCT
ejpam-4607	15	1	doi	doi	NOUN
ejpam-4607	15	2	:	:	PUNCT
ejpam-4607	15	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4607	https://doi.org/10.29020/nybg.ejpam.v16i1.4607	ADJ
ejpam-4607	15	4	email	email	NOUN
ejpam-4607	15	5	addresses	address	NOUN
ejpam-4607	15	6	:	:	PUNCT
ejpam-4607	16	1	lkalantan@kau.edu.sa	lkalantan@kau.edu.sa	NOUN
ejpam-4607	16	2	,	,	PUNCT
ejpam-4607	16	3	lnkalantan@hotmail.com	lnkalantan@hotmail.com	PROPN
ejpam-4607	16	4	(	(	PUNCT
ejpam-4607	16	5	l.	l.	PROPN
ejpam-4607	16	6	kalantan	kalantan	PROPN
ejpam-4607	16	7	)	)	PUNCT
ejpam-4607	16	8	,	,	PUNCT
ejpam-4607	16	9	amohammedalawadi@stu.kau.edu.sa	amohammedalawadi@stu.kau.edu.sa	NOUN
ejpam-4607	16	10	,	,	PUNCT
ejpam-4607	16	11	aaalawadi@uj.edu.sa	aaalawadi@uj.edu.sa	PROPN
ejpam-4607	16	12	(	(	PUNCT
ejpam-4607	16	13	a.	a.	NOUN
ejpam-4607	16	14	alawadi	alawadi	NOUN
ejpam-4607	16	15	)	)	PUNCT
ejpam-4607	16	16	,	,	PUNCT
ejpam-4607	16	17	sthabit@hu.edu.ye,sthabit1975@gmail.com	sthabit@hu.edu.ye,sthabit1975@gmail.com	PROPN
ejpam-4607	16	18	.	.	PROPN
ejpam-4607	16	19	(	(	PUNCT
ejpam-4607	16	20	s.	s.	PROPN
ejpam-4607	16	21	thabit	thabit	PROPN
ejpam-4607	16	22	)	)	PUNCT
ejpam-4607	16	23	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4607	17	1	62	62	NUM
ejpam-4607	18	1	©	©	PROPN
ejpam-4607	18	2	2023	2023	NUM
ejpam-4607	18	3	ejpam	ejpam	NOUN
ejpam-4607	18	4	all	all	DET
ejpam-4607	18	5	rights	right	NOUN
ejpam-4607	18	6	reserved	reserve	VERB
ejpam-4607	18	7	.	.	PUNCT
ejpam-4607	19	1	l.	l.	PROPN
ejpam-4607	19	2	kalantan	kalantan	PROPN
ejpam-4607	19	3	,	,	PUNCT
ejpam-4607	19	4	a.alawadi	a.alawadi	NOUN
ejpam-4607	19	5	,	,	PUNCT
ejpam-4607	19	6	s.thabit	s.thabit	NOUN
ejpam-4607	19	7	/	/	SYM
ejpam-4607	19	8	eur	eur	PROPN
ejpam-4607	19	9	.	.	PUNCT
ejpam-4607	20	1	j.	j.	PROPN
ejpam-4607	20	2	pure	pure	PROPN
ejpam-4607	20	3	appl	appl	PROPN
ejpam-4607	20	4	.	.	PROPN
ejpam-4607	20	5	math	math	PROPN
ejpam-4607	20	6	,	,	PUNCT
ejpam-4607	20	7	16	16	NUM
ejpam-4607	20	8	(	(	PUNCT
ejpam-4607	20	9	1	1	NUM
ejpam-4607	20	10	)	)	PUNCT
ejpam-4607	20	11	(	(	PUNCT
ejpam-4607	20	12	2023	2023	NUM
ejpam-4607	20	13	)	)	PUNCT
ejpam-4607	20	14	,	,	PUNCT
ejpam-4607	20	15	62	62	NUM
ejpam-4607	20	16	-	-	SYM
ejpam-4607	20	17	70	70	NUM
ejpam-4607	20	18	63	63	NUM
ejpam-4607	20	19	assume	assume	VERB
ejpam-4607	20	20	t2	t2	PROPN
ejpam-4607	20	21	in	in	ADP
ejpam-4607	20	22	the	the	DET
ejpam-4607	20	23	definition	definition	NOUN
ejpam-4607	20	24	of	of	ADP
ejpam-4607	20	25	compactness	compactness	NOUN
ejpam-4607	20	26	,	,	PUNCT
ejpam-4607	20	27	countable	countable	ADJ
ejpam-4607	20	28	compactness	compactness	NOUN
ejpam-4607	20	29	,	,	PUNCT
ejpam-4607	20	30	local	local	ADJ
ejpam-4607	20	31	compactness	compactness	NOUN
ejpam-4607	20	32	,	,	PUNCT
ejpam-4607	20	33	and	and	CCONJ
ejpam-4607	20	34	paracompactness	paracompactness	NOUN
ejpam-4607	20	35	.	.	PUNCT
ejpam-4607	21	1	we	we	PRON
ejpam-4607	21	2	do	do	AUX
ejpam-4607	21	3	not	not	PART
ejpam-4607	21	4	assume	assume	VERB
ejpam-4607	21	5	regularity	regularity	NOUN
ejpam-4607	21	6	in	in	ADP
ejpam-4607	21	7	the	the	DET
ejpam-4607	21	8	definition	definition	NOUN
ejpam-4607	21	9	of	of	ADP
ejpam-4607	21	10	lindelöfness	lindelöfness	PROPN
ejpam-4607	21	11	.	.	PUNCT
ejpam-4607	22	1	for	for	ADP
ejpam-4607	22	2	a	a	DET
ejpam-4607	22	3	subset	subset	NOUN
ejpam-4607	22	4	a	a	PRON
ejpam-4607	22	5	of	of	ADP
ejpam-4607	22	6	a	a	DET
ejpam-4607	22	7	space	space	NOUN
ejpam-4607	22	8	x	x	NOUN
ejpam-4607	22	9	,	,	PUNCT
ejpam-4607	22	10	inta	inta	PROPN
ejpam-4607	22	11	and	and	CCONJ
ejpam-4607	22	12	a	a	DET
ejpam-4607	22	13	denote	denote	NOUN
ejpam-4607	22	14	the	the	DET
ejpam-4607	22	15	interior	interior	NOUN
ejpam-4607	22	16	and	and	CCONJ
ejpam-4607	22	17	the	the	DET
ejpam-4607	22	18	closure	closure	NOUN
ejpam-4607	22	19	of	of	ADP
ejpam-4607	22	20	a	a	PRON
ejpam-4607	22	21	,	,	PUNCT
ejpam-4607	22	22	respectively	respectively	ADV
ejpam-4607	22	23	.	.	PUNCT
ejpam-4607	23	1	an	an	DET
ejpam-4607	23	2	ordinal	ordinal	ADJ
ejpam-4607	23	3	γ	γ	X
ejpam-4607	23	4	is	be	AUX
ejpam-4607	23	5	the	the	DET
ejpam-4607	23	6	set	set	NOUN
ejpam-4607	23	7	of	of	ADP
ejpam-4607	23	8	all	all	DET
ejpam-4607	23	9	ordinal	ordinal	ADJ
ejpam-4607	23	10	α	α	PRON
ejpam-4607	23	11	such	such	ADJ
ejpam-4607	23	12	that	that	SCONJ
ejpam-4607	23	13	α	α	NOUN
ejpam-4607	23	14	<	<	X
ejpam-4607	23	15	γ	γ	X
ejpam-4607	23	16	.	.	PUNCT
ejpam-4607	24	1	the	the	DET
ejpam-4607	24	2	first	first	ADJ
ejpam-4607	24	3	infinite	infinite	ADJ
ejpam-4607	24	4	ordinal	ordinal	ADJ
ejpam-4607	24	5	is	be	AUX
ejpam-4607	24	6	ω0	ω0	NUM
ejpam-4607	24	7	and	and	CCONJ
ejpam-4607	24	8	the	the	DET
ejpam-4607	24	9	first	first	ADJ
ejpam-4607	24	10	uncountable	uncountable	ADJ
ejpam-4607	24	11	ordinal	ordinal	NOUN
ejpam-4607	24	12	is	be	AUX
ejpam-4607	24	13	ω1	ω1	PROPN
ejpam-4607	24	14	.	.	PUNCT
ejpam-4607	25	1	a	a	DET
ejpam-4607	25	2	subset	subset	NOUN
ejpam-4607	25	3	a	a	PRON
ejpam-4607	25	4	of	of	ADP
ejpam-4607	25	5	a	a	DET
ejpam-4607	25	6	space	space	NOUN
ejpam-4607	25	7	x	x	PUNCT
ejpam-4607	25	8	is	be	AUX
ejpam-4607	25	9	called	call	VERB
ejpam-4607	25	10	a	a	DET
ejpam-4607	25	11	closed	closed	ADJ
ejpam-4607	25	12	domain	domain	NOUN
ejpam-4607	25	13	[	[	X
ejpam-4607	25	14	12	12	NUM
ejpam-4607	25	15	]	]	PUNCT
ejpam-4607	25	16	,	,	PUNCT
ejpam-4607	25	17	called	call	VERB
ejpam-4607	25	18	also	also	ADV
ejpam-4607	25	19	regularly	regularly	ADV
ejpam-4607	25	20	closed	close	VERB
ejpam-4607	25	21	[	[	X
ejpam-4607	25	22	23	23	NUM
ejpam-4607	25	23	]	]	PUNCT
ejpam-4607	25	24	,	,	PUNCT
ejpam-4607	25	25	κ	κ	NOUN
ejpam-4607	25	26	-	-	PUNCT
ejpam-4607	25	27	closed	closed	ADJ
ejpam-4607	25	28	[	[	X
ejpam-4607	25	29	14	14	NUM
ejpam-4607	25	30	]	]	X
ejpam-4607	25	31	,	,	PUNCT
ejpam-4607	25	32	if	if	SCONJ
ejpam-4607	25	33	a	a	DET
ejpam-4607	25	34	=	=	X
ejpam-4607	25	35	inta	inta	PROPN
ejpam-4607	25	36	.	.	PUNCT
ejpam-4607	26	1	on	on	ADP
ejpam-4607	26	2	1972	1972	NUM
ejpam-4607	26	3	,	,	PUNCT
ejpam-4607	26	4	s̆c̆epin	s̆c̆epin	CCONJ
ejpam-4607	26	5	introduced	introduce	VERB
ejpam-4607	26	6	the	the	DET
ejpam-4607	26	7	notion	notion	NOUN
ejpam-4607	26	8	of	of	ADP
ejpam-4607	26	9	κ	κ	NOUN
ejpam-4607	26	10	-	-	NOUN
ejpam-4607	26	11	normality	normality	NOUN
ejpam-4607	26	12	[	[	X
ejpam-4607	26	13	22	22	NUM
ejpam-4607	26	14	]	]	PUNCT
ejpam-4607	26	15	.	.	PUNCT
ejpam-4607	27	1	a	a	DET
ejpam-4607	27	2	space	space	NOUN
ejpam-4607	27	3	x	x	PUNCT
ejpam-4607	27	4	is	be	AUX
ejpam-4607	27	5	κ	κ	NOUN
ejpam-4607	27	6	-	-	ADJ
ejpam-4607	27	7	normal	normal	ADJ
ejpam-4607	27	8	if	if	SCONJ
ejpam-4607	27	9	x	x	PRON
ejpam-4607	27	10	is	be	AUX
ejpam-4607	27	11	regular	regular	ADJ
ejpam-4607	27	12	and	and	CCONJ
ejpam-4607	27	13	any	any	DET
ejpam-4607	27	14	two	two	NUM
ejpam-4607	27	15	disjoint	disjoint	ADJ
ejpam-4607	27	16	closed	close	VERB
ejpam-4607	27	17	domains	domain	NOUN
ejpam-4607	27	18	can	can	AUX
ejpam-4607	27	19	be	be	AUX
ejpam-4607	27	20	separated	separate	VERB
ejpam-4607	27	21	.	.	PUNCT
ejpam-4607	28	1	about	about	ADP
ejpam-4607	28	2	the	the	DET
ejpam-4607	28	3	same	same	ADJ
ejpam-4607	28	4	time	time	NOUN
ejpam-4607	28	5	,	,	PUNCT
ejpam-4607	28	6	singal	singal	PROPN
ejpam-4607	28	7	defined	define	VERB
ejpam-4607	28	8	the	the	DET
ejpam-4607	28	9	notion	notion	NOUN
ejpam-4607	28	10	of	of	ADP
ejpam-4607	28	11	mild	mild	ADJ
ejpam-4607	28	12	normality	normality	NOUN
ejpam-4607	28	13	[	[	X
ejpam-4607	28	14	23	23	NUM
ejpam-4607	28	15	]	]	PUNCT
ejpam-4607	28	16	.	.	PUNCT
ejpam-4607	29	1	a	a	DET
ejpam-4607	29	2	space	space	NOUN
ejpam-4607	29	3	x	x	PUNCT
ejpam-4607	29	4	is	be	AUX
ejpam-4607	29	5	mildly	mildly	ADV
ejpam-4607	29	6	normal	normal	ADJ
ejpam-4607	29	7	if	if	SCONJ
ejpam-4607	29	8	any	any	DET
ejpam-4607	29	9	two	two	NUM
ejpam-4607	29	10	disjoint	disjoint	ADJ
ejpam-4607	29	11	closed	close	VERB
ejpam-4607	29	12	domains	domain	NOUN
ejpam-4607	29	13	can	can	AUX
ejpam-4607	29	14	be	be	AUX
ejpam-4607	29	15	separated	separate	VERB
ejpam-4607	29	16	.	.	PUNCT
ejpam-4607	30	1	we	we	PRON
ejpam-4607	30	2	begin	begin	VERB
ejpam-4607	30	3	by	by	ADP
ejpam-4607	30	4	recalling	recall	VERB
ejpam-4607	30	5	the	the	DET
ejpam-4607	30	6	following	follow	VERB
ejpam-4607	30	7	definitions	definition	NOUN
ejpam-4607	30	8	.	.	PUNCT
ejpam-4607	31	1	definition	definition	NOUN
ejpam-4607	31	2	1	1	NUM
ejpam-4607	31	3	.	.	PUNCT
ejpam-4607	32	1	[	[	X
ejpam-4607	32	2	15	15	NUM
ejpam-4607	32	3	]	]	X
ejpam-4607	32	4	a	a	DET
ejpam-4607	32	5	space	space	NOUN
ejpam-4607	32	6	(	(	PUNCT
ejpam-4607	32	7	x	x	X
ejpam-4607	32	8	,	,	PUNCT
ejpam-4607	32	9	τ	τ	PROPN
ejpam-4607	32	10	)	)	PUNCT
ejpam-4607	32	11	is	be	AUX
ejpam-4607	32	12	called	call	VERB
ejpam-4607	32	13	epi	epi	ADJ
ejpam-4607	32	14	-	-	ADJ
ejpam-4607	32	15	mildly	mildly	ADV
ejpam-4607	32	16	normal	normal	ADJ
ejpam-4607	32	17	if	if	SCONJ
ejpam-4607	32	18	there	there	PRON
ejpam-4607	32	19	exists	exist	VERB
ejpam-4607	32	20	a	a	DET
ejpam-4607	32	21	coarser	coarse	ADJ
ejpam-4607	32	22	topology	topology	NOUN
ejpam-4607	32	23	τ	τ	NOUN
ejpam-4607	32	24	′	′	NOUN
ejpam-4607	32	25	on	on	ADP
ejpam-4607	32	26	x	x	INTJ
ejpam-4607	32	27	such	such	ADJ
ejpam-4607	32	28	that	that	SCONJ
ejpam-4607	32	29	(	(	PUNCT
ejpam-4607	32	30	x	x	X
ejpam-4607	32	31	,	,	PUNCT
ejpam-4607	32	32	τ	τ	PROPN
ejpam-4607	32	33	′	′	NUM
ejpam-4607	32	34	)	)	PUNCT
ejpam-4607	32	35	is	be	AUX
ejpam-4607	32	36	hausdorff	hausdorff	NOUN
ejpam-4607	32	37	(	(	PUNCT
ejpam-4607	32	38	t2	t2	NOUN
ejpam-4607	32	39	)	)	PUNCT
ejpam-4607	32	40	mildly	mildly	ADV
ejpam-4607	32	41	normal	normal	ADJ
ejpam-4607	32	42	.	.	PUNCT
ejpam-4607	33	1	definition	definition	NOUN
ejpam-4607	33	2	2	2	NUM
ejpam-4607	33	3	.	.	PUNCT
ejpam-4607	34	1	[	[	X
ejpam-4607	34	2	4	4	X
ejpam-4607	34	3	]	]	PUNCT
ejpam-4607	34	4	a	a	DET
ejpam-4607	34	5	topological	topological	ADJ
ejpam-4607	34	6	space	space	NOUN
ejpam-4607	34	7	(	(	PUNCT
ejpam-4607	34	8	x	x	X
ejpam-4607	34	9	,	,	PUNCT
ejpam-4607	34	10	τ	τ	PROPN
ejpam-4607	34	11	)	)	PUNCT
ejpam-4607	34	12	is	be	AUX
ejpam-4607	34	13	called	call	VERB
ejpam-4607	34	14	epi	epi	NOUN
ejpam-4607	34	15	-	-	NOUN
ejpam-4607	34	16	normal	normal	ADJ
ejpam-4607	34	17	if	if	SCONJ
ejpam-4607	34	18	there	there	PRON
ejpam-4607	34	19	is	be	VERB
ejpam-4607	34	20	a	a	DET
ejpam-4607	34	21	topology	topology	NOUN
ejpam-4607	34	22	τ	τ	NOUN
ejpam-4607	34	23	′	′	NOUN
ejpam-4607	34	24	on	on	ADP
ejpam-4607	34	25	x	x	SYM
ejpam-4607	34	26	coarser	coarse	ADJ
ejpam-4607	34	27	than	than	ADP
ejpam-4607	34	28	τ	τ	PROPN
ejpam-4607	34	29	such	such	ADJ
ejpam-4607	34	30	that	that	SCONJ
ejpam-4607	34	31	(	(	PUNCT
ejpam-4607	34	32	x	x	X
ejpam-4607	34	33	,	,	PUNCT
ejpam-4607	34	34	τ	τ	PROPN
ejpam-4607	34	35	′	′	NUM
ejpam-4607	34	36	)	)	PUNCT
ejpam-4607	34	37	is	be	AUX
ejpam-4607	34	38	t4	t4	PROPN
ejpam-4607	34	39	.	.	PUNCT
ejpam-4607	35	1	in	in	ADP
ejpam-4607	35	2	a	a	DET
ejpam-4607	35	3	personal	personal	ADJ
ejpam-4607	35	4	contact	contact	NOUN
ejpam-4607	35	5	,	,	PUNCT
ejpam-4607	35	6	arhangel’skii	arhangel’skii	PROPN
ejpam-4607	35	7	intoduced	intoduce	VERB
ejpam-4607	35	8	in	in	ADP
ejpam-4607	35	9	2012	2012	NUM
ejpam-4607	35	10	to	to	PART
ejpam-4607	35	11	kalantan	kalantan	VERB
ejpam-4607	35	12	the	the	DET
ejpam-4607	35	13	following	follow	VERB
ejpam-4607	35	14	definition	definition	NOUN
ejpam-4607	35	15	:	:	PUNCT
ejpam-4607	35	16	definition	definition	NOUN
ejpam-4607	35	17	3	3	NUM
ejpam-4607	35	18	.	.	PUNCT
ejpam-4607	36	1	(	(	PUNCT
ejpam-4607	36	2	arhangel’skii	arhangel’skii	NOUN
ejpam-4607	36	3	)	)	PUNCT
ejpam-4607	36	4	a	a	DET
ejpam-4607	36	5	topological	topological	ADJ
ejpam-4607	36	6	space	space	NOUN
ejpam-4607	36	7	x	x	PUNCT
ejpam-4607	36	8	is	be	AUX
ejpam-4607	36	9	called	call	VERB
ejpam-4607	36	10	c	c	NOUN
ejpam-4607	36	11	-	-	PUNCT
ejpam-4607	36	12	κ	κ	NOUN
ejpam-4607	36	13	-	-	ADJ
ejpam-4607	36	14	normal	normal	ADJ
ejpam-4607	36	15	if	if	SCONJ
ejpam-4607	36	16	there	there	PRON
ejpam-4607	36	17	exist	exist	VERB
ejpam-4607	36	18	a	a	DET
ejpam-4607	36	19	κ	κ	NOUN
ejpam-4607	36	20	-	-	ADJ
ejpam-4607	36	21	normal	normal	ADJ
ejpam-4607	36	22	space	space	NOUN
ejpam-4607	36	23	y	y	PROPN
ejpam-4607	36	24	and	and	CCONJ
ejpam-4607	36	25	a	a	DET
ejpam-4607	36	26	bijective	bijective	ADJ
ejpam-4607	36	27	function	function	NOUN
ejpam-4607	37	1	f	f	NOUN
ejpam-4607	37	2	:	:	PUNCT
ejpam-4607	37	3	x	x	PUNCT
ejpam-4607	37	4	−→	−→	NOUN
ejpam-4607	37	5	y	y	PROPN
ejpam-4607	37	6	such	such	ADJ
ejpam-4607	37	7	that	that	SCONJ
ejpam-4607	37	8	the	the	DET
ejpam-4607	37	9	restriction	restriction	NOUN
ejpam-4607	37	10	f|a	f|a	PUNCT
ejpam-4607	37	11	:	:	PUNCT
ejpam-4607	37	12	a	a	DET
ejpam-4607	37	13	−→	−→	NOUN
ejpam-4607	37	14	f(a	f(a	NOUN
ejpam-4607	37	15	)	)	PUNCT
ejpam-4607	37	16	is	be	AUX
ejpam-4607	37	17	a	a	DET
ejpam-4607	37	18	homeomorphism	homeomorphism	NOUN
ejpam-4607	37	19	for	for	ADP
ejpam-4607	37	20	each	each	DET
ejpam-4607	37	21	compact	compact	ADJ
ejpam-4607	37	22	subspace	subspace	NOUN
ejpam-4607	37	23	a	a	DET
ejpam-4607	37	24	⊆	⊆	NUM
ejpam-4607	37	25	x.	x.	NOUN
ejpam-4607	37	26	definition	definition	NOUN
ejpam-4607	37	27	4	4	NUM
ejpam-4607	37	28	.	.	PUNCT
ejpam-4607	38	1	[	[	X
ejpam-4607	38	2	2	2	X
ejpam-4607	38	3	]	]	PUNCT
ejpam-4607	38	4	a	a	DET
ejpam-4607	38	5	topological	topological	ADJ
ejpam-4607	38	6	space	space	NOUN
ejpam-4607	38	7	x	x	PUNCT
ejpam-4607	38	8	is	be	AUX
ejpam-4607	38	9	called	call	VERB
ejpam-4607	38	10	c	c	NOUN
ejpam-4607	38	11	-	-	PUNCT
ejpam-4607	38	12	mildly	mildly	ADV
ejpam-4607	38	13	normal	normal	ADJ
ejpam-4607	38	14	if	if	SCONJ
ejpam-4607	38	15	there	there	PRON
ejpam-4607	38	16	exist	exist	VERB
ejpam-4607	38	17	a	a	DET
ejpam-4607	38	18	mildly	mildly	ADV
ejpam-4607	38	19	normal	normal	ADJ
ejpam-4607	38	20	space	space	NOUN
ejpam-4607	38	21	y	y	PROPN
ejpam-4607	38	22	and	and	CCONJ
ejpam-4607	38	23	a	a	DET
ejpam-4607	38	24	bijective	bijective	ADJ
ejpam-4607	38	25	function	function	NOUN
ejpam-4607	39	1	f	f	NOUN
ejpam-4607	39	2	:	:	PUNCT
ejpam-4607	39	3	x	x	PUNCT
ejpam-4607	39	4	−→	−→	NOUN
ejpam-4607	39	5	y	y	PROPN
ejpam-4607	39	6	such	such	ADJ
ejpam-4607	39	7	that	that	SCONJ
ejpam-4607	39	8	the	the	DET
ejpam-4607	39	9	restriction	restriction	NOUN
ejpam-4607	39	10	f|a	f|a	PUNCT
ejpam-4607	39	11	:	:	PUNCT
ejpam-4607	39	12	a	a	DET
ejpam-4607	39	13	−→	−→	NOUN
ejpam-4607	39	14	f(a	f(a	NOUN
ejpam-4607	39	15	)	)	PUNCT
ejpam-4607	39	16	is	be	AUX
ejpam-4607	39	17	a	a	DET
ejpam-4607	39	18	homeomorphism	homeomorphism	NOUN
ejpam-4607	39	19	for	for	ADP
ejpam-4607	39	20	each	each	DET
ejpam-4607	39	21	compact	compact	ADJ
ejpam-4607	39	22	subspace	subspace	NOUN
ejpam-4607	39	23	a	a	DET
ejpam-4607	39	24	⊆	⊆	NUM
ejpam-4607	39	25	x	x	X
ejpam-4607	39	26	.	.	PUNCT
ejpam-4607	40	1	in	in	ADP
ejpam-4607	40	2	[	[	X
ejpam-4607	40	3	2	2	NUM
ejpam-4607	40	4	]	]	PUNCT
ejpam-4607	40	5	,	,	PUNCT
ejpam-4607	40	6	the	the	DET
ejpam-4607	40	7	following	follow	VERB
ejpam-4607	40	8	theorem	theorem	NOUN
ejpam-4607	40	9	was	be	AUX
ejpam-4607	40	10	proved	prove	VERB
ejpam-4607	40	11	.	.	PUNCT
ejpam-4607	41	1	theorem	theorem	NOUN
ejpam-4607	41	2	1	1	NUM
ejpam-4607	41	3	.	.	PUNCT
ejpam-4607	42	1	if	if	SCONJ
ejpam-4607	42	2	x	x	PRON
ejpam-4607	42	3	is	be	AUX
ejpam-4607	42	4	c	c	NOUN
ejpam-4607	42	5	-	-	PUNCT
ejpam-4607	42	6	mildly	mildly	ADV
ejpam-4607	42	7	normal	normal	ADJ
ejpam-4607	42	8	(	(	PUNCT
ejpam-4607	42	9	c	c	NOUN
ejpam-4607	42	10	-	-	PUNCT
ejpam-4607	42	11	κ	κ	NOUN
ejpam-4607	42	12	-	-	ADJ
ejpam-4607	42	13	normal	normal	ADJ
ejpam-4607	42	14	)	)	PUNCT
ejpam-4607	42	15	fréchet	fréchet	NOUN
ejpam-4607	42	16	space	space	NOUN
ejpam-4607	42	17	and	and	CCONJ
ejpam-4607	42	18	f	f	NOUN
ejpam-4607	42	19	:	:	PUNCT
ejpam-4607	42	20	x	x	PUNCT
ejpam-4607	42	21	−→	−→	NOUN
ejpam-4607	42	22	y	y	PROPN
ejpam-4607	42	23	is	be	AUX
ejpam-4607	42	24	a	a	DET
ejpam-4607	42	25	witness	witness	NOUN
ejpam-4607	42	26	of	of	ADP
ejpam-4607	42	27	the	the	DET
ejpam-4607	42	28	c	c	NOUN
ejpam-4607	42	29	-	-	PUNCT
ejpam-4607	42	30	mild	mild	ADJ
ejpam-4607	42	31	normality	normality	NOUN
ejpam-4607	42	32	(	(	PUNCT
ejpam-4607	42	33	c	c	NOUN
ejpam-4607	42	34	-	-	PUNCT
ejpam-4607	42	35	κ	κ	NOUN
ejpam-4607	42	36	-	-	PUNCT
ejpam-4607	42	37	normality	normality	NOUN
ejpam-4607	42	38	)	)	PUNCT
ejpam-4607	42	39	of	of	ADP
ejpam-4607	42	40	x	x	PRON
ejpam-4607	42	41	,	,	PUNCT
ejpam-4607	42	42	then	then	ADV
ejpam-4607	42	43	f	f	PROPN
ejpam-4607	42	44	is	be	AUX
ejpam-4607	42	45	continuous	continuous	ADJ
ejpam-4607	42	46	.	.	PUNCT
ejpam-4607	43	1	2	2	X
ejpam-4607	43	2	.	.	X
ejpam-4607	43	3	main	main	ADJ
ejpam-4607	43	4	results	result	NOUN
ejpam-4607	43	5	and	and	CCONJ
ejpam-4607	43	6	examples	example	NOUN
ejpam-4607	43	7	recall	recall	VERB
ejpam-4607	43	8	that	that	SCONJ
ejpam-4607	43	9	a	a	DET
ejpam-4607	43	10	topological	topological	ADJ
ejpam-4607	43	11	space	space	NOUN
ejpam-4607	43	12	x	x	PUNCT
ejpam-4607	43	13	is	be	AUX
ejpam-4607	43	14	called	call	VERB
ejpam-4607	43	15	almost	almost	ADV
ejpam-4607	43	16	compact	compact	ADJ
ejpam-4607	43	17	[	[	X
ejpam-4607	43	18	19	19	NUM
ejpam-4607	43	19	]	]	X
ejpam-4607	43	20	if	if	SCONJ
ejpam-4607	43	21	each	each	DET
ejpam-4607	43	22	open	open	ADJ
ejpam-4607	43	23	cover	cover	NOUN
ejpam-4607	43	24	of	of	ADP
ejpam-4607	43	25	x	x	PUNCT
ejpam-4607	43	26	has	have	VERB
ejpam-4607	43	27	a	a	DET
ejpam-4607	43	28	finite	finite	NOUN
ejpam-4607	43	29	subfamily	subfamily	ADV
ejpam-4607	43	30	such	such	ADJ
ejpam-4607	43	31	that	that	SCONJ
ejpam-4607	43	32	the	the	DET
ejpam-4607	43	33	closures	closure	NOUN
ejpam-4607	43	34	of	of	ADP
ejpam-4607	43	35	whose	whose	DET
ejpam-4607	43	36	members	member	NOUN
ejpam-4607	43	37	covers	cover	VERB
ejpam-4607	43	38	x.	x.	NOUN
ejpam-4607	43	39	a	a	DET
ejpam-4607	43	40	space	space	NOUN
ejpam-4607	43	41	x	x	PUNCT
ejpam-4607	43	42	is	be	AUX
ejpam-4607	43	43	said	say	VERB
ejpam-4607	43	44	to	to	PART
ejpam-4607	43	45	be	be	AUX
ejpam-4607	43	46	almost	almost	ADV
ejpam-4607	43	47	regular	regular	ADJ
ejpam-4607	43	48	[	[	X
ejpam-4607	43	49	23	23	NUM
ejpam-4607	43	50	]	]	X
ejpam-4607	43	51	if	if	SCONJ
ejpam-4607	43	52	for	for	ADP
ejpam-4607	43	53	any	any	DET
ejpam-4607	43	54	closed	closed	ADJ
ejpam-4607	43	55	domain	domain	NOUN
ejpam-4607	43	56	subset	subset	VERB
ejpam-4607	43	57	a	a	PRON
ejpam-4607	43	58	and	and	CCONJ
ejpam-4607	43	59	any	any	DET
ejpam-4607	43	60	x	x	X
ejpam-4607	43	61	̸∈	̸∈	PROPN
ejpam-4607	43	62	a	a	PROPN
ejpam-4607	43	63	,	,	PUNCT
ejpam-4607	43	64	there	there	PRON
ejpam-4607	43	65	exist	exist	VERB
ejpam-4607	43	66	two	two	NUM
ejpam-4607	43	67	disjoint	disjoint	ADJ
ejpam-4607	43	68	open	open	ADJ
ejpam-4607	43	69	sets	set	NOUN
ejpam-4607	43	70	u	u	NOUN
ejpam-4607	43	71	and	and	CCONJ
ejpam-4607	43	72	v	v	ADP
ejpam-4607	43	73	such	such	ADJ
ejpam-4607	43	74	that	that	SCONJ
ejpam-4607	43	75	x	x	SYM
ejpam-4607	43	76	∈	∈	PROPN
ejpam-4607	43	77	u	u	NOUN
ejpam-4607	43	78	and	and	CCONJ
ejpam-4607	43	79	a	a	DET
ejpam-4607	43	80	⊆	⊆	NUM
ejpam-4607	43	81	v	v	NOUN
ejpam-4607	43	82	.	.	PUNCT
ejpam-4607	44	1	a	a	DET
ejpam-4607	44	2	technique	technique	NOUN
ejpam-4607	44	3	which	which	PRON
ejpam-4607	44	4	is	be	AUX
ejpam-4607	44	5	useful	useful	ADJ
ejpam-4607	44	6	in	in	ADP
ejpam-4607	44	7	the	the	DET
ejpam-4607	44	8	theory	theory	NOUN
ejpam-4607	44	9	of	of	ADP
ejpam-4607	44	10	coarser	coarse	ADJ
ejpam-4607	44	11	topologies	topology	NOUN
ejpam-4607	44	12	is	be	AUX
ejpam-4607	44	13	the	the	DET
ejpam-4607	44	14	semiregularization	semiregularization	NOUN
ejpam-4607	44	15	.	.	PUNCT
ejpam-4607	45	1	the	the	DET
ejpam-4607	45	2	topology	topology	NOUN
ejpam-4607	45	3	on	on	ADP
ejpam-4607	45	4	x	x	PUNCT
ejpam-4607	45	5	generated	generate	VERB
ejpam-4607	45	6	by	by	ADP
ejpam-4607	45	7	the	the	DET
ejpam-4607	45	8	family	family	NOUN
ejpam-4607	45	9	of	of	ADP
ejpam-4607	45	10	all	all	DET
ejpam-4607	45	11	open	open	ADJ
ejpam-4607	45	12	domains	domain	NOUN
ejpam-4607	45	13	is	be	AUX
ejpam-4607	45	14	denoted	denote	VERB
ejpam-4607	45	15	by	by	ADP
ejpam-4607	45	16	τ	τ	PROPN
ejpam-4607	45	17	s.	s.	PROPN
ejpam-4607	45	18	the	the	DET
ejpam-4607	45	19	space	space	NOUN
ejpam-4607	45	20	(	(	PUNCT
ejpam-4607	45	21	x	x	X
ejpam-4607	45	22	,	,	PUNCT
ejpam-4607	45	23	τ	τ	PROPN
ejpam-4607	45	24	s	s	PART
ejpam-4607	45	25	)	)	PUNCT
ejpam-4607	45	26	is	be	AUX
ejpam-4607	45	27	called	call	VERB
ejpam-4607	45	28	the	the	DET
ejpam-4607	45	29	semiregularization	semiregularization	NOUN
ejpam-4607	45	30	of	of	ADP
ejpam-4607	45	31	x.	x.	PROPN
ejpam-4607	45	32	a	a	DET
ejpam-4607	45	33	space	space	NOUN
ejpam-4607	45	34	(	(	PUNCT
ejpam-4607	45	35	x	x	X
ejpam-4607	45	36	,	,	PUNCT
ejpam-4607	45	37	τ	τ	PROPN
ejpam-4607	45	38	)	)	PUNCT
ejpam-4607	45	39	is	be	AUX
ejpam-4607	45	40	semi	semi	ADJ
ejpam-4607	45	41	-	-	ADJ
ejpam-4607	45	42	regular	regular	ADJ
ejpam-4607	45	43	if	if	SCONJ
ejpam-4607	45	44	τ	τ	PROPN
ejpam-4607	45	45	=	=	PROPN
ejpam-4607	45	46	τ	τ	PROPN
ejpam-4607	45	47	s.	s.	PROPN
ejpam-4607	45	48	l.	l.	PROPN
ejpam-4607	45	49	kalantan	kalantan	PROPN
ejpam-4607	45	50	,	,	PUNCT
ejpam-4607	45	51	a.alawadi	a.alawadi	NOUN
ejpam-4607	45	52	,	,	PUNCT
ejpam-4607	45	53	s.thabit	s.thabit	NOUN
ejpam-4607	45	54	/	/	SYM
ejpam-4607	45	55	eur	eur	PROPN
ejpam-4607	45	56	.	.	PUNCT
ejpam-4607	46	1	j.	j.	PROPN
ejpam-4607	46	2	pure	pure	PROPN
ejpam-4607	46	3	appl	appl	PROPN
ejpam-4607	46	4	.	.	PROPN
ejpam-4607	46	5	math	math	PROPN
ejpam-4607	46	6	,	,	PUNCT
ejpam-4607	46	7	16	16	NUM
ejpam-4607	46	8	(	(	PUNCT
ejpam-4607	46	9	1	1	NUM
ejpam-4607	46	10	)	)	PUNCT
ejpam-4607	46	11	(	(	PUNCT
ejpam-4607	46	12	2023	2023	NUM
ejpam-4607	46	13	)	)	PUNCT
ejpam-4607	46	14	,	,	PUNCT
ejpam-4607	46	15	62	62	NUM
ejpam-4607	46	16	-	-	SYM
ejpam-4607	46	17	70	70	NUM
ejpam-4607	46	18	64	64	NUM
ejpam-4607	46	19	theorem	theorem	NOUN
ejpam-4607	46	20	2	2	NUM
ejpam-4607	46	21	.	.	PUNCT
ejpam-4607	47	1	let	let	VERB
ejpam-4607	47	2	x	x	PRON
ejpam-4607	47	3	be	be	AUX
ejpam-4607	47	4	an	an	DET
ejpam-4607	47	5	almost	almost	ADV
ejpam-4607	47	6	regular	regular	ADJ
ejpam-4607	47	7	hausdorff	hausdorff	NOUN
ejpam-4607	47	8	space	space	NOUN
ejpam-4607	47	9	.	.	PUNCT
ejpam-4607	48	1	if	if	SCONJ
ejpam-4607	48	2	x	x	PRON
ejpam-4607	48	3	is	be	AUX
ejpam-4607	48	4	mildly	mildly	ADV
ejpam-4607	48	5	normal	normal	ADJ
ejpam-4607	48	6	then	then	ADV
ejpam-4607	48	7	x	x	PUNCT
ejpam-4607	48	8	is	be	AUX
ejpam-4607	48	9	c	c	NOUN
ejpam-4607	48	10	-	-	PUNCT
ejpam-4607	48	11	κ	κ	NOUN
ejpam-4607	48	12	-	-	ADJ
ejpam-4607	48	13	normal	normal	ADJ
ejpam-4607	48	14	.	.	PUNCT
ejpam-4607	49	1	proof	proof	NOUN
ejpam-4607	49	2	.	.	PUNCT
ejpam-4607	50	1	since	since	SCONJ
ejpam-4607	50	2	(	(	PUNCT
ejpam-4607	50	3	x	x	X
ejpam-4607	50	4	,	,	PUNCT
ejpam-4607	50	5	τ	τ	PROPN
ejpam-4607	50	6	)	)	PUNCT
ejpam-4607	50	7	is	be	AUX
ejpam-4607	50	8	an	an	DET
ejpam-4607	50	9	almost	almost	ADV
ejpam-4607	50	10	regular	regular	ADJ
ejpam-4607	50	11	hausdorff	hausdorff	NOUN
ejpam-4607	50	12	space	space	NOUN
ejpam-4607	50	13	,	,	PUNCT
ejpam-4607	50	14	then	then	ADV
ejpam-4607	50	15	(	(	PUNCT
ejpam-4607	50	16	x	x	X
ejpam-4607	50	17	,	,	PUNCT
ejpam-4607	50	18	τ	τ	PROPN
ejpam-4607	50	19	s	s	PART
ejpam-4607	50	20	)	)	PUNCT
ejpam-4607	50	21	is	be	AUX
ejpam-4607	50	22	a	a	DET
ejpam-4607	50	23	hausdorff	hausdorff	NOUN
ejpam-4607	50	24	regular	regular	ADJ
ejpam-4607	50	25	space	space	NOUN
ejpam-4607	50	26	[	[	X
ejpam-4607	50	27	20	20	NUM
ejpam-4607	50	28	]	]	PUNCT
ejpam-4607	50	29	.	.	PUNCT
ejpam-4607	51	1	since	since	SCONJ
ejpam-4607	51	2	x	x	PRON
ejpam-4607	51	3	is	be	AUX
ejpam-4607	51	4	mildly	mildly	ADV
ejpam-4607	51	5	normal	normal	ADJ
ejpam-4607	51	6	space	space	NOUN
ejpam-4607	51	7	we	we	PRON
ejpam-4607	51	8	get	get	VERB
ejpam-4607	51	9	(	(	PUNCT
ejpam-4607	51	10	x	x	X
ejpam-4607	51	11	,	,	PUNCT
ejpam-4607	51	12	τ	τ	PROPN
ejpam-4607	51	13	s	s	PART
ejpam-4607	51	14	)	)	PUNCT
ejpam-4607	51	15	is	be	AUX
ejpam-4607	51	16	mildly	mildly	ADV
ejpam-4607	51	17	normal	normal	ADJ
ejpam-4607	51	18	[	[	X
ejpam-4607	51	19	15	15	NUM
ejpam-4607	51	20	]	]	PUNCT
ejpam-4607	51	21	.	.	PUNCT
ejpam-4607	52	1	then	then	ADV
ejpam-4607	52	2	the	the	DET
ejpam-4607	52	3	identity	identity	NOUN
ejpam-4607	52	4	function	function	NOUN
ejpam-4607	52	5	idx	idx	NOUN
ejpam-4607	52	6	:	:	PUNCT
ejpam-4607	52	7	(	(	PUNCT
ejpam-4607	52	8	x	x	X
ejpam-4607	52	9	,	,	PUNCT
ejpam-4607	52	10	τ	τ	PROPN
ejpam-4607	52	11	)	)	PUNCT
ejpam-4607	52	12	−→	−→	NOUN
ejpam-4607	52	13	(	(	PUNCT
ejpam-4607	52	14	x	x	X
ejpam-4607	52	15	,	,	PUNCT
ejpam-4607	52	16	τ	τ	PROPN
ejpam-4607	52	17	s	s	PART
ejpam-4607	52	18	)	)	PUNCT
ejpam-4607	52	19	is	be	AUX
ejpam-4607	52	20	a	a	DET
ejpam-4607	52	21	continuous	continuous	ADJ
ejpam-4607	52	22	bijective	bijective	ADJ
ejpam-4607	52	23	function	function	NOUN
ejpam-4607	52	24	.	.	PUNCT
ejpam-4607	53	1	if	if	SCONJ
ejpam-4607	53	2	c	c	PROPN
ejpam-4607	53	3	is	be	AUX
ejpam-4607	53	4	any	any	DET
ejpam-4607	53	5	compact	compact	ADJ
ejpam-4607	53	6	subspace	subspace	NOUN
ejpam-4607	53	7	of	of	ADP
ejpam-4607	53	8	(	(	PUNCT
ejpam-4607	53	9	x	x	PROPN
ejpam-4607	53	10	,	,	PUNCT
ejpam-4607	53	11	τ	τ	PROPN
ejpam-4607	53	12	)	)	PUNCT
ejpam-4607	53	13	,	,	PUNCT
ejpam-4607	53	14	then	then	ADV
ejpam-4607	53	15	the	the	DET
ejpam-4607	53	16	restriction	restriction	NOUN
ejpam-4607	53	17	of	of	ADP
ejpam-4607	53	18	the	the	DET
ejpam-4607	53	19	identity	identity	NOUN
ejpam-4607	53	20	function	function	NOUN
ejpam-4607	53	21	from	from	ADP
ejpam-4607	53	22	c	c	PROPN
ejpam-4607	53	23	onto	onto	ADP
ejpam-4607	53	24	idx(c	idx(c	PROPN
ejpam-4607	53	25	)	)	PUNCT
ejpam-4607	53	26	is	be	AUX
ejpam-4607	53	27	continuous	continuous	ADJ
ejpam-4607	53	28	and	and	CCONJ
ejpam-4607	53	29	“	"	PUNCT
ejpam-4607	53	30	every	every	DET
ejpam-4607	53	31	continuous	continuous	ADJ
ejpam-4607	53	32	one	one	NUM
ejpam-4607	53	33	-	-	PUNCT
ejpam-4607	53	34	to	to	ADP
ejpam-4607	53	35	-	-	PUNCT
ejpam-4607	53	36	one	one	NUM
ejpam-4607	53	37	mapping	mapping	NOUN
ejpam-4607	53	38	of	of	ADP
ejpam-4607	53	39	a	a	DET
ejpam-4607	53	40	compact	compact	ADJ
ejpam-4607	53	41	space	space	NOUN
ejpam-4607	53	42	onto	onto	ADP
ejpam-4607	53	43	a	a	DET
ejpam-4607	53	44	hausdorff	hausdorff	NOUN
ejpam-4607	53	45	space	space	NOUN
ejpam-4607	53	46	is	be	AUX
ejpam-4607	53	47	a	a	DET
ejpam-4607	53	48	homeomorphism	homeomorphism	NOUN
ejpam-4607	53	49	.	.	PUNCT
ejpam-4607	53	50	”	"	PUNCT
ejpam-4607	54	1	[	[	X
ejpam-4607	54	2	12	12	NUM
ejpam-4607	54	3	,	,	PUNCT
ejpam-4607	54	4	theorem	theorem	VERB
ejpam-4607	54	5	3.1.13	3.1.13	NUM
ejpam-4607	54	6	]	]	PUNCT
ejpam-4607	54	7	.	.	PUNCT
ejpam-4607	55	1	so	so	ADV
ejpam-4607	55	2	x	x	PUNCT
ejpam-4607	55	3	is	be	AUX
ejpam-4607	55	4	c	c	NOUN
ejpam-4607	55	5	-	-	PUNCT
ejpam-4607	55	6	κ	κ	PRON
ejpam-4607	55	7	-	-	ADJ
ejpam-4607	55	8	normal	normal	ADJ
ejpam-4607	55	9	space	space	NOUN
ejpam-4607	55	10	.	.	PUNCT
ejpam-4607	56	1	theorem	theorem	NOUN
ejpam-4607	56	2	3	3	NUM
ejpam-4607	56	3	.	.	PUNCT
ejpam-4607	57	1	if	if	SCONJ
ejpam-4607	57	2	(	(	PUNCT
ejpam-4607	57	3	x	x	X
ejpam-4607	57	4	,	,	PUNCT
ejpam-4607	57	5	τ	τ	PROPN
ejpam-4607	57	6	)	)	PUNCT
ejpam-4607	57	7	is	be	AUX
ejpam-4607	57	8	almost	almost	ADV
ejpam-4607	57	9	regular	regular	ADJ
ejpam-4607	57	10	almost	almost	ADV
ejpam-4607	57	11	compact	compact	ADJ
ejpam-4607	57	12	space	space	NOUN
ejpam-4607	57	13	and	and	CCONJ
ejpam-4607	57	14	τ	τ	PRON
ejpam-4607	57	15	s	s	NOUN
ejpam-4607	57	16	is	be	AUX
ejpam-4607	57	17	t1	t1	NOUN
ejpam-4607	57	18	,	,	PUNCT
ejpam-4607	57	19	then	then	ADV
ejpam-4607	57	20	(	(	PUNCT
ejpam-4607	57	21	x	x	X
ejpam-4607	57	22	,	,	PUNCT
ejpam-4607	57	23	τ	τ	PROPN
ejpam-4607	57	24	)	)	PUNCT
ejpam-4607	57	25	is	be	AUX
ejpam-4607	57	26	c	c	NOUN
ejpam-4607	57	27	-	-	PUNCT
ejpam-4607	57	28	κ	κ	NOUN
ejpam-4607	57	29	-	-	ADJ
ejpam-4607	57	30	normal	normal	ADJ
ejpam-4607	57	31	(	(	PUNCT
ejpam-4607	57	32	c	c	NOUN
ejpam-4607	57	33	-	-	PUNCT
ejpam-4607	57	34	mildly	mildly	ADV
ejpam-4607	57	35	normal	normal	ADJ
ejpam-4607	57	36	)	)	PUNCT
ejpam-4607	57	37	.	.	PUNCT
ejpam-4607	58	1	proof	proof	NOUN
ejpam-4607	58	2	.	.	PUNCT
ejpam-4607	59	1	since	since	SCONJ
ejpam-4607	59	2	(	(	PUNCT
ejpam-4607	59	3	x	x	X
ejpam-4607	59	4	,	,	PUNCT
ejpam-4607	59	5	τ	τ	PROPN
ejpam-4607	59	6	)	)	PUNCT
ejpam-4607	59	7	is	be	AUX
ejpam-4607	59	8	an	an	DET
ejpam-4607	59	9	almost	almost	ADV
ejpam-4607	59	10	regular	regular	ADJ
ejpam-4607	59	11	space	space	NOUN
ejpam-4607	59	12	,	,	PUNCT
ejpam-4607	59	13	(	(	PUNCT
ejpam-4607	59	14	x	x	X
ejpam-4607	59	15	,	,	PUNCT
ejpam-4607	59	16	τ	τ	PROPN
ejpam-4607	59	17	s	s	PART
ejpam-4607	59	18	)	)	PUNCT
ejpam-4607	59	19	is	be	AUX
ejpam-4607	59	20	regular	regular	ADJ
ejpam-4607	59	21	space	space	NOUN
ejpam-4607	59	22	[	[	X
ejpam-4607	59	23	20	20	NUM
ejpam-4607	59	24	]	]	PUNCT
ejpam-4607	59	25	.	.	PUNCT
ejpam-4607	60	1	hence	hence	ADV
ejpam-4607	60	2	(	(	PUNCT
ejpam-4607	60	3	x	x	X
ejpam-4607	60	4	,	,	PUNCT
ejpam-4607	60	5	τ	τ	PROPN
ejpam-4607	60	6	s	s	PART
ejpam-4607	60	7	)	)	PUNCT
ejpam-4607	60	8	is	be	AUX
ejpam-4607	60	9	t3	t3	PROPN
ejpam-4607	60	10	.	.	PUNCT
ejpam-4607	61	1	moreover	moreover	ADV
ejpam-4607	61	2	,	,	PUNCT
ejpam-4607	61	3	the	the	DET
ejpam-4607	61	4	coarser	coarse	ADJ
ejpam-4607	61	5	topology	topology	NOUN
ejpam-4607	61	6	of	of	ADP
ejpam-4607	61	7	an	an	DET
ejpam-4607	61	8	almost	almost	ADV
ejpam-4607	61	9	compact	compact	ADJ
ejpam-4607	61	10	space	space	NOUN
ejpam-4607	61	11	is	be	AUX
ejpam-4607	61	12	an	an	DET
ejpam-4607	61	13	almost	almost	ADV
ejpam-4607	61	14	compact	compact	ADJ
ejpam-4607	61	15	space	space	NOUN
ejpam-4607	61	16	.	.	PUNCT
ejpam-4607	62	1	so	so	ADV
ejpam-4607	62	2	τ	τ	PROPN
ejpam-4607	62	3	s	s	PART
ejpam-4607	62	4	is	be	AUX
ejpam-4607	62	5	almost	almost	ADV
ejpam-4607	62	6	compact	compact	ADJ
ejpam-4607	62	7	.	.	PUNCT
ejpam-4607	63	1	but	but	CCONJ
ejpam-4607	63	2	every	every	DET
ejpam-4607	63	3	almost	almost	ADV
ejpam-4607	63	4	regular	regular	ADJ
ejpam-4607	63	5	almost	almost	ADV
ejpam-4607	63	6	compact	compact	ADJ
ejpam-4607	63	7	space	space	NOUN
ejpam-4607	63	8	is	be	AUX
ejpam-4607	63	9	mildly	mildly	ADV
ejpam-4607	63	10	normal	normal	ADJ
ejpam-4607	63	11	[	[	X
ejpam-4607	63	12	23	23	NUM
ejpam-4607	63	13	]	]	PUNCT
ejpam-4607	63	14	.	.	PUNCT
ejpam-4607	64	1	thus	thus	ADV
ejpam-4607	64	2	τ	τ	X
ejpam-4607	64	3	s	s	PART
ejpam-4607	64	4	is	be	AUX
ejpam-4607	64	5	regular	regular	ADJ
ejpam-4607	64	6	mildly	mildly	ADV
ejpam-4607	64	7	normal	normal	ADJ
ejpam-4607	64	8	.	.	PUNCT
ejpam-4607	65	1	therefore	therefore	ADV
ejpam-4607	65	2	by	by	ADP
ejpam-4607	65	3	using	use	VERB
ejpam-4607	65	4	the	the	DET
ejpam-4607	65	5	same	same	ADJ
ejpam-4607	65	6	argument	argument	NOUN
ejpam-4607	65	7	of	of	ADP
ejpam-4607	65	8	the	the	DET
ejpam-4607	65	9	proof	proof	NOUN
ejpam-4607	65	10	of	of	ADP
ejpam-4607	65	11	theorem	theorem	NOUN
ejpam-4607	65	12	2	2	NUM
ejpam-4607	65	13	we	we	PRON
ejpam-4607	65	14	conclude	conclude	VERB
ejpam-4607	65	15	that	that	PRON
ejpam-4607	65	16	(	(	PUNCT
ejpam-4607	65	17	x	x	X
ejpam-4607	65	18	,	,	PUNCT
ejpam-4607	65	19	τ	τ	PROPN
ejpam-4607	65	20	)	)	PUNCT
ejpam-4607	65	21	is	be	AUX
ejpam-4607	65	22	c	c	NOUN
ejpam-4607	65	23	-	-	PUNCT
ejpam-4607	65	24	κ	κ	NOUN
ejpam-4607	65	25	-	-	ADJ
ejpam-4607	65	26	normal	normal	ADJ
ejpam-4607	65	27	(	(	PUNCT
ejpam-4607	65	28	c	c	NOUN
ejpam-4607	65	29	-	-	PUNCT
ejpam-4607	65	30	mildly	mildly	ADV
ejpam-4607	65	31	normal	normal	ADJ
ejpam-4607	65	32	)	)	PUNCT
ejpam-4607	65	33	.	.	PUNCT
ejpam-4607	66	1	theorem	theorem	VERB
ejpam-4607	66	2	4	4	NUM
ejpam-4607	66	3	.	.	PUNCT
ejpam-4607	67	1	c	c	X
ejpam-4607	67	2	-	-	PUNCT
ejpam-4607	67	3	κ	κ	NOUN
ejpam-4607	67	4	-	-	PUNCT
ejpam-4607	67	5	normality	normality	NOUN
ejpam-4607	67	6	(	(	PUNCT
ejpam-4607	67	7	c	c	NOUN
ejpam-4607	67	8	-	-	PUNCT
ejpam-4607	67	9	mild	mild	ADJ
ejpam-4607	67	10	normality	normality	NOUN
ejpam-4607	67	11	)	)	PUNCT
ejpam-4607	67	12	is	be	AUX
ejpam-4607	67	13	an	an	DET
ejpam-4607	67	14	additive	additive	ADJ
ejpam-4607	67	15	property	property	NOUN
ejpam-4607	67	16	.	.	PUNCT
ejpam-4607	68	1	proof	proof	NOUN
ejpam-4607	68	2	.	.	PUNCT
ejpam-4607	69	1	let	let	VERB
ejpam-4607	69	2	xα	xα	INTJ
ejpam-4607	69	3	be	be	AUX
ejpam-4607	69	4	a	a	DET
ejpam-4607	69	5	c	c	NOUN
ejpam-4607	69	6	-	-	PUNCT
ejpam-4607	69	7	κ	κ	NOUN
ejpam-4607	69	8	-	-	ADJ
ejpam-4607	69	9	normal	normal	ADJ
ejpam-4607	69	10	(	(	PUNCT
ejpam-4607	69	11	c	c	NOUN
ejpam-4607	69	12	-	-	PUNCT
ejpam-4607	69	13	mildly	mildly	ADV
ejpam-4607	69	14	normal	normal	ADJ
ejpam-4607	69	15	)	)	PUNCT
ejpam-4607	69	16	space	space	NOUN
ejpam-4607	69	17	for	for	ADP
ejpam-4607	69	18	each	each	DET
ejpam-4607	69	19	α	α	NOUN
ejpam-4607	69	20	∈	∈	PROPN
ejpam-4607	69	21	λ	λ	PROPN
ejpam-4607	69	22	.	.	PUNCT
ejpam-4607	70	1	we	we	PRON
ejpam-4607	70	2	show	show	VERB
ejpam-4607	70	3	that	that	SCONJ
ejpam-4607	70	4	their	their	PRON
ejpam-4607	70	5	sum	sum	NOUN
ejpam-4607	70	6	⊕α∈λxα	⊕α∈λxα	NOUN
ejpam-4607	70	7	is	be	AUX
ejpam-4607	70	8	c	c	NOUN
ejpam-4607	70	9	-	-	PUNCT
ejpam-4607	70	10	κ	κ	NOUN
ejpam-4607	70	11	-	-	ADJ
ejpam-4607	70	12	normal	normal	ADJ
ejpam-4607	70	13	(	(	PUNCT
ejpam-4607	70	14	c	c	NOUN
ejpam-4607	70	15	-	-	PUNCT
ejpam-4607	70	16	mildly	mildly	ADV
ejpam-4607	70	17	normal	normal	ADJ
ejpam-4607	70	18	)	)	PUNCT
ejpam-4607	70	19	.	.	PUNCT
ejpam-4607	71	1	for	for	ADP
ejpam-4607	71	2	each	each	DET
ejpam-4607	71	3	α	α	PROPN
ejpam-4607	71	4	∈	∈	PROPN
ejpam-4607	71	5	λ	λ	PROPN
ejpam-4607	71	6	,	,	PUNCT
ejpam-4607	71	7	pick	pick	VERB
ejpam-4607	71	8	a	a	DET
ejpam-4607	71	9	κnormal	κnormal	NOUN
ejpam-4607	71	10	(	(	PUNCT
ejpam-4607	71	11	mildly	mildly	ADV
ejpam-4607	71	12	normal	normal	ADJ
ejpam-4607	71	13	)	)	PUNCT
ejpam-4607	71	14	space	space	NOUN
ejpam-4607	71	15	yα	yα	NOUN
ejpam-4607	71	16	and	and	CCONJ
ejpam-4607	71	17	a	a	DET
ejpam-4607	71	18	bijective	bijective	ADJ
ejpam-4607	71	19	function	function	NOUN
ejpam-4607	71	20	fα	fα	ADP
ejpam-4607	71	21	:	:	PUNCT
ejpam-4607	71	22	xα	xα	INTJ
ejpam-4607	72	1	−→	−→	NOUN
ejpam-4607	72	2	yα	yα	VERB
ejpam-4607	72	3	such	such	ADJ
ejpam-4607	72	4	that	that	PRON
ejpam-4607	72	5	fα|cα	fα|cα	PUNCT
ejpam-4607	72	6	:	:	PUNCT
ejpam-4607	72	7	cα	cα	AUX
ejpam-4607	72	8	−→	−→	NOUN
ejpam-4607	72	9	fα(cα	fα(cα	NOUN
ejpam-4607	72	10	)	)	PUNCT
ejpam-4607	72	11	is	be	AUX
ejpam-4607	72	12	a	a	DET
ejpam-4607	72	13	homeomorphism	homeomorphism	NOUN
ejpam-4607	72	14	for	for	ADP
ejpam-4607	72	15	each	each	DET
ejpam-4607	72	16	compact	compact	ADJ
ejpam-4607	72	17	subspace	subspace	NOUN
ejpam-4607	72	18	cα	cα	ADP
ejpam-4607	72	19	of	of	ADP
ejpam-4607	72	20	xα	xα	PROPN
ejpam-4607	72	21	.	.	PUNCT
ejpam-4607	73	1	since	since	SCONJ
ejpam-4607	73	2	regularity	regularity	NOUN
ejpam-4607	73	3	is	be	AUX
ejpam-4607	73	4	additive	additive	ADJ
ejpam-4607	73	5	[	[	X
ejpam-4607	73	6	12	12	NUM
ejpam-4607	73	7	,	,	PUNCT
ejpam-4607	73	8	theorem	theorem	VERB
ejpam-4607	73	9	2.2.7	2.2.7	PRON
ejpam-4607	73	10	]	]	PUNCT
ejpam-4607	73	11	,	,	PUNCT
ejpam-4607	73	12	then	then	ADV
ejpam-4607	73	13	(	(	PUNCT
ejpam-4607	73	14	yα,⊕α∈λτ	yα,⊕α∈λτ	PROPN
ejpam-4607	73	15	′	′	NUM
ejpam-4607	73	16	α	α	X
ejpam-4607	73	17	)	)	PUNCT
ejpam-4607	73	18	is	be	AUX
ejpam-4607	73	19	a	a	DET
ejpam-4607	73	20	regular	regular	ADJ
ejpam-4607	73	21	space	space	NOUN
ejpam-4607	73	22	.	.	PUNCT
ejpam-4607	74	1	on	on	ADP
ejpam-4607	74	2	the	the	DET
ejpam-4607	74	3	other	other	ADJ
ejpam-4607	74	4	hand	hand	NOUN
ejpam-4607	74	5	,	,	PUNCT
ejpam-4607	74	6	mild	mild	ADJ
ejpam-4607	74	7	normality	normality	NOUN
ejpam-4607	74	8	is	be	AUX
ejpam-4607	74	9	an	an	DET
ejpam-4607	74	10	additive	additive	ADJ
ejpam-4607	74	11	property	property	NOUN
ejpam-4607	74	12	because	because	SCONJ
ejpam-4607	74	13	each	each	DET
ejpam-4607	74	14	factor	factor	NOUN
ejpam-4607	74	15	is	be	AUX
ejpam-4607	74	16	open	open	ADJ
ejpam-4607	74	17	-	-	PUNCT
ejpam-4607	74	18	and	and	CCONJ
ejpam-4607	74	19	-	-	PUNCT
ejpam-4607	74	20	closed	close	VERB
ejpam-4607	74	21	in	in	ADP
ejpam-4607	74	22	⊕α∈λxα	⊕α∈λxα	NOUN
ejpam-4607	74	23	and	and	CCONJ
ejpam-4607	74	24	the	the	DET
ejpam-4607	74	25	intersection	intersection	NOUN
ejpam-4607	74	26	of	of	ADP
ejpam-4607	74	27	any	any	DET
ejpam-4607	74	28	closed	closed	ADJ
ejpam-4607	74	29	domain	domain	NOUN
ejpam-4607	74	30	in	in	ADP
ejpam-4607	74	31	⊕α∈λxα	⊕α∈λxα	NOUN
ejpam-4607	74	32	with	with	ADP
ejpam-4607	74	33	each	each	DET
ejpam-4607	74	34	factor	factor	NOUN
ejpam-4607	74	35	xα	xα	INTJ
ejpam-4607	74	36	will	will	AUX
ejpam-4607	74	37	be	be	AUX
ejpam-4607	74	38	a	a	DET
ejpam-4607	74	39	closed	closed	ADJ
ejpam-4607	74	40	domain	domain	NOUN
ejpam-4607	74	41	in	in	ADP
ejpam-4607	74	42	xα	xα	PROPN
ejpam-4607	74	43	.	.	PUNCT
ejpam-4607	75	1	then	then	ADV
ejpam-4607	75	2	the	the	DET
ejpam-4607	75	3	sum	sum	NOUN
ejpam-4607	75	4	⊕α∈λyα	⊕α∈λyα	PROPN
ejpam-4607	75	5	is	be	AUX
ejpam-4607	75	6	κ	κ	NOUN
ejpam-4607	75	7	-	-	ADJ
ejpam-4607	75	8	normal	normal	ADJ
ejpam-4607	75	9	(	(	PUNCT
ejpam-4607	75	10	mildly	mildly	ADV
ejpam-4607	75	11	normal	normal	ADJ
ejpam-4607	75	12	)	)	PUNCT
ejpam-4607	75	13	.	.	PUNCT
ejpam-4607	76	1	consider	consider	VERB
ejpam-4607	76	2	the	the	DET
ejpam-4607	76	3	function	function	NOUN
ejpam-4607	76	4	sum	sum	NOUN
ejpam-4607	77	1	[	[	X
ejpam-4607	77	2	12	12	NUM
ejpam-4607	77	3	,	,	PUNCT
ejpam-4607	77	4	exercises	exercise	VERB
ejpam-4607	77	5	2.2.e	2.2.e	NUM
ejpam-4607	77	6	]	]	PUNCT
ejpam-4607	77	7	,	,	PUNCT
ejpam-4607	77	8	⊕α∈λfα	⊕α∈λfα	NOUN
ejpam-4607	77	9	:	:	PUNCT
ejpam-4607	77	10	⊕α∈λxα	⊕α∈λxα	NOUN
ejpam-4607	77	11	−→	−→	NOUN
ejpam-4607	77	12	⊕α∈λyα	⊕α∈λyα	NOUN
ejpam-4607	77	13	defined	define	VERB
ejpam-4607	77	14	by	by	ADP
ejpam-4607	77	15	⊕α∈λfα(x	⊕α∈λfα(x	ADJ
ejpam-4607	77	16	)	)	PUNCT
ejpam-4607	77	17	=	=	SYM
ejpam-4607	78	1	fβ(x	fβ(x	NOUN
ejpam-4607	78	2	)	)	PUNCT
ejpam-4607	78	3	if	if	SCONJ
ejpam-4607	78	4	x	x	PROPN
ejpam-4607	78	5	∈	∈	PROPN
ejpam-4607	78	6	xβ	xβ	PROPN
ejpam-4607	78	7	,	,	PUNCT
ejpam-4607	78	8	β	β	X
ejpam-4607	78	9	∈	∈	PROPN
ejpam-4607	78	10	λ	λ	PROPN
ejpam-4607	78	11	.	.	PUNCT
ejpam-4607	79	1	now	now	ADV
ejpam-4607	79	2	,	,	PUNCT
ejpam-4607	79	3	a	a	DET
ejpam-4607	79	4	subspace	subspace	NOUN
ejpam-4607	79	5	c	c	NOUN
ejpam-4607	79	6	⊆	⊆	NUM
ejpam-4607	79	7	⊕α∈λxα	⊕α∈λxα	NOUN
ejpam-4607	79	8	is	be	AUX
ejpam-4607	79	9	compact	compact	ADJ
ejpam-4607	79	10	if	if	SCONJ
ejpam-4607	80	1	and	and	CCONJ
ejpam-4607	80	2	only	only	ADV
ejpam-4607	80	3	if	if	SCONJ
ejpam-4607	80	4	the	the	DET
ejpam-4607	80	5	set	set	NOUN
ejpam-4607	80	6	λ0	λ0	NOUN
ejpam-4607	80	7	=	=	SYM
ejpam-4607	80	8	{	{	PUNCT
ejpam-4607	80	9	α	α	NOUN
ejpam-4607	80	10	∈	∈	PROPN
ejpam-4607	80	11	λ	λ	X
ejpam-4607	80	12	:	:	PUNCT
ejpam-4607	80	13	c	c	PROPN
ejpam-4607	80	14	∩xα	∩xα	NOUN
ejpam-4607	80	15	̸=	̸=	PROPN
ejpam-4607	80	16	∅	∅	NOUN
ejpam-4607	80	17	}	}	PUNCT
ejpam-4607	80	18	is	be	AUX
ejpam-4607	80	19	finite	finite	ADJ
ejpam-4607	80	20	and	and	CCONJ
ejpam-4607	80	21	c	c	PROPN
ejpam-4607	80	22	∩xα	∩xα	NOUN
ejpam-4607	80	23	is	be	AUX
ejpam-4607	80	24	compact	compact	ADJ
ejpam-4607	80	25	in	in	ADP
ejpam-4607	80	26	xα	xα	INTJ
ejpam-4607	80	27	for	for	ADP
ejpam-4607	80	28	each	each	DET
ejpam-4607	80	29	α	α	NOUN
ejpam-4607	80	30	∈	∈	PROPN
ejpam-4607	80	31	λ0	λ0	NOUN
ejpam-4607	80	32	.	.	PUNCT
ejpam-4607	81	1	if	if	SCONJ
ejpam-4607	81	2	c	c	PROPN
ejpam-4607	81	3	⊆	⊆	NUM
ejpam-4607	81	4	⊕α∈λxα	⊕α∈λxα	NOUN
ejpam-4607	81	5	is	be	AUX
ejpam-4607	81	6	compact	compact	ADJ
ejpam-4607	81	7	,	,	PUNCT
ejpam-4607	81	8	then	then	ADV
ejpam-4607	81	9	(	(	PUNCT
ejpam-4607	81	10	⊕α∈λfα)|c	⊕α∈λfα)|c	PROPN
ejpam-4607	81	11	is	be	AUX
ejpam-4607	81	12	a	a	DET
ejpam-4607	81	13	homeomorphism	homeomorphism	NOUN
ejpam-4607	81	14	because	because	SCONJ
ejpam-4607	81	15	fα|c∩xα	fα|c∩xα	NOUN
ejpam-4607	81	16	is	be	AUX
ejpam-4607	81	17	a	a	DET
ejpam-4607	81	18	homeomorphism	homeomorphism	NOUN
ejpam-4607	81	19	for	for	ADP
ejpam-4607	81	20	each	each	DET
ejpam-4607	81	21	α	α	NOUN
ejpam-4607	81	22	∈	∈	PROPN
ejpam-4607	81	23	λ0	λ0	NOUN
ejpam-4607	81	24	.	.	PUNCT
ejpam-4607	82	1	recall	recall	VERB
ejpam-4607	82	2	that	that	SCONJ
ejpam-4607	82	3	a	a	DET
ejpam-4607	82	4	topology	topology	NOUN
ejpam-4607	82	5	τ	τ	X
ejpam-4607	82	6	on	on	ADP
ejpam-4607	82	7	a	a	DET
ejpam-4607	82	8	non	non	ADJ
ejpam-4607	82	9	-	-	ADJ
ejpam-4607	82	10	empty	empty	ADJ
ejpam-4607	82	11	set	set	NOUN
ejpam-4607	82	12	x	x	PUNCT
ejpam-4607	82	13	is	be	AUX
ejpam-4607	82	14	said	say	VERB
ejpam-4607	82	15	to	to	PART
ejpam-4607	82	16	be	be	AUX
ejpam-4607	82	17	minimal	minimal	ADJ
ejpam-4607	82	18	hausdorff	hausdorff	NOUN
ejpam-4607	82	19	if	if	SCONJ
ejpam-4607	82	20	(	(	PUNCT
ejpam-4607	82	21	x	x	X
ejpam-4607	82	22	,	,	PUNCT
ejpam-4607	82	23	τ	τ	PROPN
ejpam-4607	82	24	)	)	PUNCT
ejpam-4607	82	25	is	be	AUX
ejpam-4607	82	26	hausdorff	hausdorff	NOUN
ejpam-4607	82	27	and	and	CCONJ
ejpam-4607	82	28	there	there	PRON
ejpam-4607	82	29	is	be	VERB
ejpam-4607	82	30	no	no	DET
ejpam-4607	82	31	hausdorff	hausdorff	NOUN
ejpam-4607	82	32	topology	topology	NOUN
ejpam-4607	82	33	on	on	ADP
ejpam-4607	82	34	x	x	PUNCT
ejpam-4607	82	35	strictly	strictly	ADV
ejpam-4607	82	36	coarser	coarse	ADJ
ejpam-4607	82	37	than	than	ADP
ejpam-4607	82	38	τ	τ	PROPN
ejpam-4607	82	39	,	,	PUNCT
ejpam-4607	82	40	see	see	VERB
ejpam-4607	82	41	[	[	X
ejpam-4607	82	42	7	7	NUM
ejpam-4607	82	43	,	,	PUNCT
ejpam-4607	82	44	8	8	NUM
ejpam-4607	82	45	]	]	PUNCT
ejpam-4607	82	46	.	.	PUNCT
ejpam-4607	83	1	it	it	PRON
ejpam-4607	83	2	was	be	AUX
ejpam-4607	83	3	proved	prove	VERB
ejpam-4607	83	4	that	that	SCONJ
ejpam-4607	83	5	“	"	PUNCT
ejpam-4607	83	6	if	if	SCONJ
ejpam-4607	83	7	the	the	DET
ejpam-4607	83	8	product	product	NOUN
ejpam-4607	83	9	space	space	NOUN
ejpam-4607	83	10	is	be	AUX
ejpam-4607	83	11	minimal	minimal	ADJ
ejpam-4607	83	12	hausdorff	hausdorff	NOUN
ejpam-4607	83	13	,	,	PUNCT
ejpam-4607	83	14	then	then	ADV
ejpam-4607	83	15	each	each	DET
ejpam-4607	83	16	factor	factor	NOUN
ejpam-4607	83	17	is	be	AUX
ejpam-4607	83	18	minimal	minimal	ADJ
ejpam-4607	83	19	hausdorff	hausdorff	NOUN
ejpam-4607	83	20	”	"	PUNCT
ejpam-4607	84	1	[	[	X
ejpam-4607	84	2	7	7	NUM
ejpam-4607	84	3	]	]	PUNCT
ejpam-4607	84	4	,	,	PUNCT
ejpam-4607	84	5	in	in	ADP
ejpam-4607	84	6	[	[	X
ejpam-4607	84	7	13	13	NUM
ejpam-4607	84	8	]	]	PUNCT
ejpam-4607	84	9	the	the	DET
ejpam-4607	84	10	converse	converse	NOUN
ejpam-4607	84	11	of	of	ADP
ejpam-4607	84	12	the	the	DET
ejpam-4607	84	13	previous	previous	ADJ
ejpam-4607	84	14	statement	statement	NOUN
ejpam-4607	84	15	was	be	AUX
ejpam-4607	84	16	proved	prove	VERB
ejpam-4607	84	17	.	.	PUNCT
ejpam-4607	85	1	namely	namely	ADV
ejpam-4607	85	2	,	,	PUNCT
ejpam-4607	85	3	“	"	PUNCT
ejpam-4607	85	4	the	the	DET
ejpam-4607	85	5	product	product	NOUN
ejpam-4607	85	6	of	of	ADP
ejpam-4607	85	7	minimal	minimal	ADJ
ejpam-4607	85	8	hausdorff	hausdorff	NOUN
ejpam-4607	85	9	spaces	space	NOUN
ejpam-4607	85	10	is	be	AUX
ejpam-4607	85	11	minimal	minimal	ADJ
ejpam-4607	85	12	hausdorff	hausdorff	NOUN
ejpam-4607	85	13	”	"	PUNCT
ejpam-4607	85	14	.	.	PUNCT
ejpam-4607	86	1	in	in	ADP
ejpam-4607	86	2	the	the	DET
ejpam-4607	86	3	next	next	ADJ
ejpam-4607	86	4	theorem	theorem	NOUN
ejpam-4607	86	5	we	we	PRON
ejpam-4607	86	6	will	will	AUX
ejpam-4607	86	7	use	use	VERB
ejpam-4607	86	8	the	the	DET
ejpam-4607	86	9	following	following	NOUN
ejpam-4607	86	10	theorem	theorem	NOUN
ejpam-4607	86	11	:	:	PUNCT
ejpam-4607	86	12	“	"	PUNCT
ejpam-4607	86	13	a	a	DET
ejpam-4607	86	14	minimal	minimal	ADJ
ejpam-4607	86	15	hausdorff	hausdorff	NOUN
ejpam-4607	86	16	space	space	NOUN
ejpam-4607	86	17	is	be	AUX
ejpam-4607	86	18	compact	compact	ADJ
ejpam-4607	86	19	if	if	SCONJ
ejpam-4607	87	1	and	and	CCONJ
ejpam-4607	87	2	only	only	ADV
ejpam-4607	87	3	if	if	SCONJ
ejpam-4607	87	4	it	it	PRON
ejpam-4607	87	5	is	be	AUX
ejpam-4607	87	6	completely	completely	ADV
ejpam-4607	87	7	hausdorff	hausdorff	NOUN
ejpam-4607	87	8	(	(	PUNCT
ejpam-4607	87	9	t2	t2	NOUN
ejpam-4607	87	10	1	1	NUM
ejpam-4607	87	11	2	2	NUM
ejpam-4607	87	12	)	)	PUNCT
ejpam-4607	87	13	”	"	PUNCT
ejpam-4607	88	1	[	[	X
ejpam-4607	88	2	21	21	NUM
ejpam-4607	88	3	,	,	PUNCT
ejpam-4607	88	4	theorem	theorem	VERB
ejpam-4607	88	5	1.4	1.4	NUM
ejpam-4607	88	6	]	]	PUNCT
ejpam-4607	88	7	.	.	PUNCT
ejpam-4607	89	1	we	we	PRON
ejpam-4607	89	2	conclude	conclude	VERB
ejpam-4607	89	3	the	the	DET
ejpam-4607	89	4	following	follow	VERB
ejpam-4607	89	5	theorems	theorems	PROPN
ejpam-4607	89	6	.	.	PUNCT
ejpam-4607	89	7	l.	l.	PROPN
ejpam-4607	89	8	kalantan	kalantan	PROPN
ejpam-4607	89	9	,	,	PUNCT
ejpam-4607	89	10	a.alawadi	a.alawadi	NOUN
ejpam-4607	89	11	,	,	PUNCT
ejpam-4607	89	12	s.thabit	s.thabit	NOUN
ejpam-4607	89	13	/	/	SYM
ejpam-4607	89	14	eur	eur	PROPN
ejpam-4607	89	15	.	.	PUNCT
ejpam-4607	90	1	j.	j.	PROPN
ejpam-4607	90	2	pure	pure	PROPN
ejpam-4607	90	3	appl	appl	PROPN
ejpam-4607	90	4	.	.	PROPN
ejpam-4607	90	5	math	math	PROPN
ejpam-4607	90	6	,	,	PUNCT
ejpam-4607	90	7	16	16	NUM
ejpam-4607	90	8	(	(	PUNCT
ejpam-4607	90	9	1	1	NUM
ejpam-4607	90	10	)	)	PUNCT
ejpam-4607	90	11	(	(	PUNCT
ejpam-4607	90	12	2023	2023	NUM
ejpam-4607	90	13	)	)	PUNCT
ejpam-4607	90	14	,	,	PUNCT
ejpam-4607	90	15	62	62	NUM
ejpam-4607	90	16	-	-	SYM
ejpam-4607	90	17	70	70	NUM
ejpam-4607	90	18	65	65	NUM
ejpam-4607	90	19	theorem	theorem	NOUN
ejpam-4607	90	20	5	5	NUM
ejpam-4607	90	21	.	.	PUNCT
ejpam-4607	91	1	let	let	VERB
ejpam-4607	91	2	x	x	PRON
ejpam-4607	91	3	and	and	CCONJ
ejpam-4607	91	4	y	y	PROPN
ejpam-4607	91	5	be	be	AUX
ejpam-4607	91	6	minimal	minimal	ADJ
ejpam-4607	91	7	hausdorff	hausdorff	NOUN
ejpam-4607	91	8	spaces	space	NOUN
ejpam-4607	91	9	,	,	PUNCT
ejpam-4607	91	10	if	if	SCONJ
ejpam-4607	91	11	x	x	PRON
ejpam-4607	91	12	and	and	CCONJ
ejpam-4607	91	13	y	y	PROPN
ejpam-4607	91	14	are	be	AUX
ejpam-4607	91	15	κ	κ	NOUN
ejpam-4607	91	16	-	-	ADJ
ejpam-4607	91	17	normal	normal	ADJ
ejpam-4607	91	18	spaces	space	NOUN
ejpam-4607	91	19	then	then	ADV
ejpam-4607	91	20	x	x	SYM
ejpam-4607	91	21	×	×	PROPN
ejpam-4607	91	22	y	y	PROPN
ejpam-4607	91	23	is	be	AUX
ejpam-4607	91	24	κ	κ	NOUN
ejpam-4607	91	25	-	-	ADJ
ejpam-4607	91	26	normal	normal	ADJ
ejpam-4607	91	27	.	.	PUNCT
ejpam-4607	92	1	proof	proof	NOUN
ejpam-4607	92	2	.	.	PUNCT
ejpam-4607	93	1	since	since	SCONJ
ejpam-4607	93	2	x	x	PROPN
ejpam-4607	93	3	and	and	CCONJ
ejpam-4607	93	4	y	y	PROPN
ejpam-4607	93	5	are	be	AUX
ejpam-4607	93	6	κ	κ	NOUN
ejpam-4607	93	7	-	-	ADJ
ejpam-4607	93	8	normal	normal	ADJ
ejpam-4607	93	9	,	,	PUNCT
ejpam-4607	93	10	they	they	PRON
ejpam-4607	93	11	are	be	AUX
ejpam-4607	93	12	regular	regular	ADJ
ejpam-4607	93	13	hausdorff	hausdorff	NOUN
ejpam-4607	93	14	spaces	space	NOUN
ejpam-4607	93	15	,	,	PUNCT
ejpam-4607	93	16	which	which	PRON
ejpam-4607	93	17	implies	imply	VERB
ejpam-4607	93	18	t3	t3	NOUN
ejpam-4607	93	19	,	,	PUNCT
ejpam-4607	93	20	hence	hence	ADV
ejpam-4607	93	21	t2	t2	NOUN
ejpam-4607	93	22	1	1	NUM
ejpam-4607	93	23	2	2	NUM
ejpam-4607	93	24	.	.	PUNCT
ejpam-4607	94	1	since	since	SCONJ
ejpam-4607	94	2	the	the	DET
ejpam-4607	94	3	t2	t2	NOUN
ejpam-4607	94	4	1	1	NUM
ejpam-4607	94	5	2	2	NUM
ejpam-4607	94	6	is	be	AUX
ejpam-4607	94	7	multiplicative	multiplicative	ADJ
ejpam-4607	94	8	,	,	PUNCT
ejpam-4607	94	9	the	the	DET
ejpam-4607	94	10	product	product	NOUN
ejpam-4607	94	11	space	space	NOUN
ejpam-4607	94	12	is	be	AUX
ejpam-4607	94	13	t2	t2	NOUN
ejpam-4607	94	14	1	1	NUM
ejpam-4607	94	15	2	2	NUM
ejpam-4607	94	16	.	.	PUNCT
ejpam-4607	95	1	so	so	ADV
ejpam-4607	95	2	x	x	SYM
ejpam-4607	95	3	×	×	NOUN
ejpam-4607	95	4	y	y	PROPN
ejpam-4607	95	5	is	be	AUX
ejpam-4607	95	6	t2	t2	NOUN
ejpam-4607	95	7	1	1	NUM
ejpam-4607	95	8	2	2	NUM
ejpam-4607	95	9	minimal	minimal	ADJ
ejpam-4607	95	10	hausdorff	hausdorff	NOUN
ejpam-4607	95	11	space	space	NOUN
ejpam-4607	95	12	which	which	PRON
ejpam-4607	95	13	implies	imply	VERB
ejpam-4607	95	14	that	that	SCONJ
ejpam-4607	95	15	x	x	SYM
ejpam-4607	95	16	×	×	NOUN
ejpam-4607	95	17	y	y	PROPN
ejpam-4607	95	18	is	be	AUX
ejpam-4607	95	19	t2	t2	NOUN
ejpam-4607	95	20	compact	compact	ADJ
ejpam-4607	95	21	,	,	PUNCT
ejpam-4607	95	22	hence	hence	ADV
ejpam-4607	95	23	t4	t4	PROPN
ejpam-4607	95	24	and	and	CCONJ
ejpam-4607	95	25	thus	thus	ADV
ejpam-4607	95	26	κ	κ	NOUN
ejpam-4607	95	27	-	-	ADJ
ejpam-4607	95	28	normal	normal	ADJ
ejpam-4607	95	29	.	.	PUNCT
ejpam-4607	96	1	now	now	ADV
ejpam-4607	96	2	,	,	PUNCT
ejpam-4607	96	3	we	we	PRON
ejpam-4607	96	4	give	give	VERB
ejpam-4607	96	5	the	the	DET
ejpam-4607	96	6	following	follow	VERB
ejpam-4607	96	7	characterization	characterization	NOUN
ejpam-4607	96	8	in	in	ADP
ejpam-4607	96	9	the	the	DET
ejpam-4607	96	10	class	class	NOUN
ejpam-4607	96	11	of	of	ADP
ejpam-4607	96	12	minimal	minimal	ADJ
ejpam-4607	96	13	hausdorff	hausdorff	NOUN
ejpam-4607	96	14	spaces	space	NOUN
ejpam-4607	96	15	.	.	PUNCT
ejpam-4607	97	1	theorem	theorem	ADJ
ejpam-4607	97	2	6	6	NUM
ejpam-4607	97	3	.	.	PUNCT
ejpam-4607	98	1	let	let	VERB
ejpam-4607	98	2	x	x	PRON
ejpam-4607	98	3	be	be	AUX
ejpam-4607	98	4	a	a	DET
ejpam-4607	98	5	minimal	minimal	ADJ
ejpam-4607	98	6	hausdorff	hausdorff	NOUN
ejpam-4607	98	7	fréchet	fréchet	NOUN
ejpam-4607	98	8	space	space	NOUN
ejpam-4607	98	9	.	.	PUNCT
ejpam-4607	99	1	the	the	DET
ejpam-4607	99	2	following	follow	VERB
ejpam-4607	99	3	are	be	AUX
ejpam-4607	99	4	equivalent	equivalent	ADJ
ejpam-4607	99	5	.	.	PUNCT
ejpam-4607	100	1	(	(	PUNCT
ejpam-4607	100	2	i	i	NOUN
ejpam-4607	100	3	)	)	PUNCT
ejpam-4607	100	4	x	x	X
ejpam-4607	100	5	is	be	AUX
ejpam-4607	100	6	c	c	NOUN
ejpam-4607	100	7	-	-	PUNCT
ejpam-4607	100	8	κ	κ	NOUN
ejpam-4607	100	9	-	-	ADJ
ejpam-4607	100	10	normal	normal	ADJ
ejpam-4607	100	11	.	.	PUNCT
ejpam-4607	101	1	(	(	PUNCT
ejpam-4607	101	2	ii	ii	NOUN
ejpam-4607	101	3	)	)	PUNCT
ejpam-4607	101	4	x	x	PRON
ejpam-4607	101	5	is	be	AUX
ejpam-4607	101	6	locally	locally	ADV
ejpam-4607	101	7	compact	compact	ADJ
ejpam-4607	101	8	.	.	PUNCT
ejpam-4607	102	1	(	(	PUNCT
ejpam-4607	102	2	iii	iii	X
ejpam-4607	102	3	)	)	PUNCT
ejpam-4607	102	4	x	x	PRON
ejpam-4607	102	5	is	be	AUX
ejpam-4607	102	6	compact	compact	ADJ
ejpam-4607	102	7	(	(	PUNCT
ejpam-4607	102	8	iv	iv	X
ejpam-4607	102	9	)	)	PUNCT
ejpam-4607	102	10	x	x	X
ejpam-4607	102	11	is	be	AUX
ejpam-4607	102	12	t4	t4	PROPN
ejpam-4607	102	13	.	.	PUNCT
ejpam-4607	103	1	(	(	PUNCT
ejpam-4607	103	2	v	v	NOUN
ejpam-4607	103	3	)	)	PUNCT
ejpam-4607	103	4	x	x	PRON
ejpam-4607	103	5	is	be	AUX
ejpam-4607	103	6	epinormal	epinormal	ADJ
ejpam-4607	103	7	,	,	PUNCT
ejpam-4607	103	8	hence	hence	ADV
ejpam-4607	103	9	epi	epi	ADJ
ejpam-4607	103	10	-	-	ADJ
ejpam-4607	103	11	mildly	mildly	ADV
ejpam-4607	103	12	normal	normal	ADJ
ejpam-4607	103	13	.	.	PUNCT
ejpam-4607	104	1	proof	proof	NOUN
ejpam-4607	104	2	.	.	PUNCT
ejpam-4607	105	1	(	(	PUNCT
ejpam-4607	105	2	1	1	X
ejpam-4607	105	3	)	)	PUNCT
ejpam-4607	105	4	⇒	⇒	NOUN
ejpam-4607	105	5	(	(	PUNCT
ejpam-4607	105	6	2	2	NUM
ejpam-4607	105	7	)	)	PUNCT
ejpam-4607	105	8	since	since	SCONJ
ejpam-4607	105	9	x	x	PRON
ejpam-4607	105	10	is	be	AUX
ejpam-4607	105	11	c	c	NOUN
ejpam-4607	105	12	-	-	PUNCT
ejpam-4607	105	13	κ	κ	NOUN
ejpam-4607	105	14	-	-	ADJ
ejpam-4607	105	15	normal	normal	ADJ
ejpam-4607	105	16	fréchet	fréchet	NOUN
ejpam-4607	105	17	space	space	NOUN
ejpam-4607	105	18	,	,	PUNCT
ejpam-4607	105	19	x	x	X
ejpam-4607	105	20	is	be	AUX
ejpam-4607	105	21	t2	t2	NOUN
ejpam-4607	105	22	1	1	NUM
ejpam-4607	105	23	2	2	NUM
ejpam-4607	105	24	see	see	VERB
ejpam-4607	105	25	[	[	X
ejpam-4607	105	26	2	2	NUM
ejpam-4607	105	27	]	]	PUNCT
ejpam-4607	105	28	,	,	PUNCT
ejpam-4607	105	29	by	by	ADP
ejpam-4607	105	30	theorem	theorem	NOUN
ejpam-4607	105	31	“	"	PUNCT
ejpam-4607	105	32	a	a	DET
ejpam-4607	105	33	minimal	minimal	ADJ
ejpam-4607	105	34	hausdorff	hausdorff	NOUN
ejpam-4607	105	35	space	space	NOUN
ejpam-4607	105	36	is	be	AUX
ejpam-4607	105	37	compact	compact	ADJ
ejpam-4607	105	38	if	if	SCONJ
ejpam-4607	105	39	and	and	CCONJ
ejpam-4607	105	40	only	only	ADV
ejpam-4607	105	41	if	if	SCONJ
ejpam-4607	105	42	it	it	PRON
ejpam-4607	105	43	is	be	AUX
ejpam-4607	105	44	completely	completely	ADV
ejpam-4607	105	45	hausdorff	hausdorff	NOUN
ejpam-4607	105	46	(	(	PUNCT
ejpam-4607	105	47	t2	t2	NOUN
ejpam-4607	105	48	1	1	NUM
ejpam-4607	105	49	2	2	NUM
ejpam-4607	105	50	)	)	PUNCT
ejpam-4607	105	51	”	"	PUNCT
ejpam-4607	106	1	[	[	X
ejpam-4607	106	2	21	21	NUM
ejpam-4607	106	3	,	,	PUNCT
ejpam-4607	106	4	theorem	theorem	VERB
ejpam-4607	106	5	1.4	1.4	NUM
ejpam-4607	106	6	]	]	PUNCT
ejpam-4607	106	7	,	,	PUNCT
ejpam-4607	106	8	gives	give	VERB
ejpam-4607	106	9	that	that	PRON
ejpam-4607	106	10	x	x	PRON
ejpam-4607	106	11	is	be	AUX
ejpam-4607	106	12	t2	t2	NOUN
ejpam-4607	106	13	compact	compact	ADJ
ejpam-4607	106	14	,	,	PUNCT
ejpam-4607	106	15	hence	hence	ADV
ejpam-4607	106	16	locally	locally	ADV
ejpam-4607	106	17	compact	compact	ADJ
ejpam-4607	106	18	.	.	PUNCT
ejpam-4607	107	1	(	(	PUNCT
ejpam-4607	107	2	2	2	X
ejpam-4607	107	3	)	)	PUNCT
ejpam-4607	107	4	⇒	⇒	NOUN
ejpam-4607	107	5	(	(	PUNCT
ejpam-4607	107	6	3	3	NUM
ejpam-4607	107	7	)	)	PUNCT
ejpam-4607	107	8	since	since	SCONJ
ejpam-4607	107	9	any	any	DET
ejpam-4607	107	10	t2	t2	NOUN
ejpam-4607	107	11	locally	locally	ADV
ejpam-4607	107	12	compact	compact	ADJ
ejpam-4607	107	13	space	space	NOUN
ejpam-4607	107	14	is	be	AUX
ejpam-4607	107	15	tychonoff	tychonoff	NOUN
ejpam-4607	107	16	and	and	CCONJ
ejpam-4607	107	17	hence	hence	ADV
ejpam-4607	107	18	t2	t2	NOUN
ejpam-4607	107	19	1	1	NUM
ejpam-4607	107	20	2	2	NUM
ejpam-4607	107	21	,	,	PUNCT
ejpam-4607	107	22	we	we	PRON
ejpam-4607	107	23	obtain	obtain	VERB
ejpam-4607	107	24	x	x	VERB
ejpam-4607	107	25	is	be	AUX
ejpam-4607	107	26	compact	compact	ADJ
ejpam-4607	107	27	.	.	PUNCT
ejpam-4607	108	1	(	(	PUNCT
ejpam-4607	108	2	3	3	X
ejpam-4607	108	3	)	)	PUNCT
ejpam-4607	108	4	⇒	⇒	NOUN
ejpam-4607	108	5	(	(	PUNCT
ejpam-4607	108	6	4	4	X
ejpam-4607	108	7	)	)	PUNCT
ejpam-4607	108	8	any	any	DET
ejpam-4607	108	9	t2	t2	NOUN
ejpam-4607	108	10	compact	compact	ADJ
ejpam-4607	108	11	space	space	NOUN
ejpam-4607	108	12	is	be	AUX
ejpam-4607	108	13	t4	t4	PROPN
ejpam-4607	108	14	.	.	PUNCT
ejpam-4607	109	1	(	(	PUNCT
ejpam-4607	109	2	4	4	X
ejpam-4607	109	3	)	)	PUNCT
ejpam-4607	109	4	⇒	⇒	NOUN
ejpam-4607	109	5	(	(	PUNCT
ejpam-4607	109	6	5	5	NUM
ejpam-4607	109	7	)	)	PUNCT
ejpam-4607	109	8	any	any	DET
ejpam-4607	109	9	t4	t4	PROPN
ejpam-4607	109	10	is	be	AUX
ejpam-4607	109	11	epinormal	epinormal	ADJ
ejpam-4607	109	12	,	,	PUNCT
ejpam-4607	109	13	hence	hence	ADV
ejpam-4607	109	14	epi	epi	ADJ
ejpam-4607	109	15	-	-	ADJ
ejpam-4607	109	16	mildly	mildly	ADV
ejpam-4607	109	17	normal	normal	ADJ
ejpam-4607	109	18	.	.	PUNCT
ejpam-4607	110	1	(	(	PUNCT
ejpam-4607	110	2	5	5	X
ejpam-4607	110	3	)	)	PUNCT
ejpam-4607	110	4	⇒	⇒	NOUN
ejpam-4607	110	5	(	(	PUNCT
ejpam-4607	110	6	1	1	X
ejpam-4607	110	7	)	)	PUNCT
ejpam-4607	110	8	any	any	DET
ejpam-4607	110	9	epinormal	epinormal	NOUN
ejpam-4607	110	10	space	space	NOUN
ejpam-4607	110	11	is	be	AUX
ejpam-4607	110	12	c	c	NOUN
ejpam-4607	110	13	-	-	PUNCT
ejpam-4607	110	14	κ	κ	NOUN
ejpam-4607	110	15	-	-	ADJ
ejpam-4607	110	16	normal	normal	ADJ
ejpam-4607	110	17	[	[	X
ejpam-4607	110	18	2	2	NUM
ejpam-4607	110	19	]	]	PUNCT
ejpam-4607	110	20	.	.	PUNCT
ejpam-4607	111	1	from	from	ADP
ejpam-4607	111	2	the	the	DET
ejpam-4607	111	3	above	above	ADJ
ejpam-4607	111	4	theorem	theorem	NOUN
ejpam-4607	111	5	,	,	PUNCT
ejpam-4607	111	6	we	we	PRON
ejpam-4607	111	7	conclude	conclude	VERB
ejpam-4607	111	8	the	the	DET
ejpam-4607	111	9	following	follow	VERB
ejpam-4607	111	10	corollary	corollary	ADJ
ejpam-4607	111	11	corollary	corollary	ADJ
ejpam-4607	111	12	1	1	NUM
ejpam-4607	111	13	.	.	PUNCT
ejpam-4607	112	1	in	in	ADP
ejpam-4607	112	2	class	class	NOUN
ejpam-4607	112	3	of	of	ADP
ejpam-4607	112	4	minimal	minimal	ADJ
ejpam-4607	112	5	hausdorff	hausdorff	NOUN
ejpam-4607	112	6	,	,	PUNCT
ejpam-4607	112	7	any	any	DET
ejpam-4607	112	8	frėchet	frėchet	ADJ
ejpam-4607	112	9	c	c	NOUN
ejpam-4607	112	10	-	-	PUNCT
ejpam-4607	112	11	κ	κ	PRON
ejpam-4607	112	12	-	-	ADJ
ejpam-4607	112	13	normal	normal	ADJ
ejpam-4607	112	14	space	space	NOUN
ejpam-4607	112	15	is	be	AUX
ejpam-4607	112	16	κ	κ	NOUN
ejpam-4607	112	17	-	-	ADJ
ejpam-4607	112	18	normal	normal	ADJ
ejpam-4607	112	19	.	.	PUNCT
ejpam-4607	113	1	since	since	SCONJ
ejpam-4607	113	2	κ	κ	NOUN
ejpam-4607	113	3	-	-	PUNCT
ejpam-4607	113	4	normality	normality	NOUN
ejpam-4607	113	5	is	be	AUX
ejpam-4607	113	6	not	not	PART
ejpam-4607	113	7	hereditary	hereditary	ADJ
ejpam-4607	113	8	[	[	X
ejpam-4607	113	9	16	16	NUM
ejpam-4607	113	10	]	]	PUNCT
ejpam-4607	113	11	,	,	PUNCT
ejpam-4607	113	12	it	it	PRON
ejpam-4607	113	13	seems	seem	VERB
ejpam-4607	113	14	to	to	ADP
ejpam-4607	113	15	us	we	PRON
ejpam-4607	113	16	that	that	SCONJ
ejpam-4607	113	17	both	both	DET
ejpam-4607	113	18	c	c	NOUN
ejpam-4607	113	19	-	-	PUNCT
ejpam-4607	113	20	mild	mild	ADJ
ejpam-4607	113	21	normality	normality	NOUN
ejpam-4607	113	22	and	and	CCONJ
ejpam-4607	113	23	c	c	NOUN
ejpam-4607	113	24	-	-	PUNCT
ejpam-4607	113	25	κ	κ	NOUN
ejpam-4607	113	26	-	-	PUNCT
ejpam-4607	113	27	normality	normality	NOUN
ejpam-4607	113	28	are	be	AUX
ejpam-4607	113	29	not	not	PART
ejpam-4607	113	30	hereditary	hereditary	ADJ
ejpam-4607	113	31	,	,	PUNCT
ejpam-4607	113	32	but	but	CCONJ
ejpam-4607	113	33	we	we	PRON
ejpam-4607	113	34	still	still	ADV
ejpam-4607	113	35	could	could	AUX
ejpam-4607	113	36	not	not	PART
ejpam-4607	113	37	find	find	VERB
ejpam-4607	113	38	a	a	DET
ejpam-4607	113	39	counterexample	counterexample	NOUN
ejpam-4607	113	40	.	.	PUNCT
ejpam-4607	114	1	the	the	DET
ejpam-4607	114	2	question	question	NOUN
ejpam-4607	114	3	“	"	PUNCT
ejpam-4607	114	4	is	be	AUX
ejpam-4607	114	5	there	there	PRON
ejpam-4607	114	6	a	a	DET
ejpam-4607	114	7	tychonoff	tychonoff	NOUN
ejpam-4607	114	8	space	space	NOUN
ejpam-4607	114	9	which	which	PRON
ejpam-4607	114	10	is	be	AUX
ejpam-4607	114	11	not	not	PART
ejpam-4607	114	12	c	c	NOUN
ejpam-4607	114	13	-	-	PUNCT
ejpam-4607	114	14	κ	κ	NOUN
ejpam-4607	114	15	-	-	ADJ
ejpam-4607	114	16	normal	normal	ADJ
ejpam-4607	114	17	(	(	PUNCT
ejpam-4607	114	18	c	c	NOUN
ejpam-4607	114	19	-	-	PUNCT
ejpam-4607	114	20	mildly	mildly	ADV
ejpam-4607	114	21	normal	normal	ADJ
ejpam-4607	114	22	)	)	PUNCT
ejpam-4607	114	23	?	?	PUNCT
ejpam-4607	115	1	¨	¨	NOUN
ejpam-4607	115	2	we	we	PRON
ejpam-4607	115	3	answer	answer	VERB
ejpam-4607	115	4	this	this	PRON
ejpam-4607	115	5	in	in	ADP
ejpam-4607	115	6	the	the	DET
ejpam-4607	115	7	class	class	NOUN
ejpam-4607	115	8	of	of	ADP
ejpam-4607	115	9	minimal	minimal	ADJ
ejpam-4607	115	10	tychonoff	tychonoff	NOUN
ejpam-4607	115	11	spaces	space	NOUN
ejpam-4607	115	12	by	by	ADP
ejpam-4607	115	13	using	use	VERB
ejpam-4607	115	14	theorem	theorem	NOUN
ejpam-4607	115	15	“	"	PUNCT
ejpam-4607	115	16	all	all	DET
ejpam-4607	115	17	minimal	minimal	ADJ
ejpam-4607	115	18	completely	completely	ADV
ejpam-4607	115	19	regular	regular	ADJ
ejpam-4607	115	20	spaces	space	NOUN
ejpam-4607	115	21	are	be	AUX
ejpam-4607	115	22	compact	compact	ADJ
ejpam-4607	115	23	”	"	PUNCT
ejpam-4607	115	24	,	,	PUNCT
ejpam-4607	115	25	[	[	X
ejpam-4607	115	26	7	7	NUM
ejpam-4607	115	27	]	]	PUNCT
ejpam-4607	115	28	,	,	PUNCT
ejpam-4607	115	29	hence	hence	ADV
ejpam-4607	115	30	t4	t4	PROPN
ejpam-4607	115	31	.	.	PUNCT
ejpam-4607	116	1	so	so	ADV
ejpam-4607	116	2	we	we	PRON
ejpam-4607	116	3	get	get	VERB
ejpam-4607	116	4	the	the	DET
ejpam-4607	116	5	following	follow	VERB
ejpam-4607	116	6	corollary	corollary	NOUN
ejpam-4607	116	7	.	.	PUNCT
ejpam-4607	117	1	corollary	corollary	ADJ
ejpam-4607	117	2	2	2	NUM
ejpam-4607	117	3	.	.	PUNCT
ejpam-4607	118	1	any	any	DET
ejpam-4607	118	2	minimal	minimal	ADJ
ejpam-4607	118	3	tychonoff	tychonoff	NOUN
ejpam-4607	118	4	space	space	NOUN
ejpam-4607	118	5	is	be	AUX
ejpam-4607	118	6	c	c	NOUN
ejpam-4607	118	7	-	-	PUNCT
ejpam-4607	118	8	κ	κ	NOUN
ejpam-4607	118	9	-	-	ADJ
ejpam-4607	118	10	normal	normal	ADJ
ejpam-4607	118	11	.	.	PUNCT
ejpam-4607	119	1	we	we	PRON
ejpam-4607	119	2	know	know	VERB
ejpam-4607	119	3	tychonoff	tychonoff	NOUN
ejpam-4607	119	4	spaces	space	NOUN
ejpam-4607	119	5	which	which	PRON
ejpam-4607	119	6	are	be	AUX
ejpam-4607	119	7	not	not	PART
ejpam-4607	119	8	κ	κ	NOUN
ejpam-4607	119	9	-	-	ADJ
ejpam-4607	119	10	normal	normal	ADJ
ejpam-4607	119	11	(	(	PUNCT
ejpam-4607	119	12	mildly	mildly	ADV
ejpam-4607	119	13	normal	normal	ADJ
ejpam-4607	119	14	)	)	PUNCT
ejpam-4607	119	15	.	.	PUNCT
ejpam-4607	120	1	this	this	DET
ejpam-4607	120	2	spaces	space	NOUN
ejpam-4607	120	3	turn	turn	VERB
ejpam-4607	120	4	out	out	ADP
ejpam-4607	120	5	to	to	PART
ejpam-4607	120	6	be	be	AUX
ejpam-4607	120	7	c	c	NOUN
ejpam-4607	120	8	-	-	PUNCT
ejpam-4607	120	9	κ	κ	NOUN
ejpam-4607	120	10	-	-	ADJ
ejpam-4607	120	11	normal	normal	ADJ
ejpam-4607	120	12	(	(	PUNCT
ejpam-4607	120	13	c	c	NOUN
ejpam-4607	120	14	-	-	PUNCT
ejpam-4607	120	15	mildly	mildly	ADV
ejpam-4607	120	16	normal	normal	ADJ
ejpam-4607	120	17	)	)	PUNCT
ejpam-4607	120	18	see	see	VERB
ejpam-4607	121	1	[	[	X
ejpam-4607	121	2	2	2	NUM
ejpam-4607	121	3	,	,	PUNCT
ejpam-4607	121	4	example	example	NOUN
ejpam-4607	121	5	3	3	NUM
ejpam-4607	121	6	]	]	PUNCT
ejpam-4607	121	7	,	,	PUNCT
ejpam-4607	121	8	and	and	CCONJ
ejpam-4607	121	9	also	also	ADV
ejpam-4607	121	10	see	see	VERB
ejpam-4607	121	11	example	example	NOUN
ejpam-4607	121	12	5	5	NUM
ejpam-4607	121	13	below	below	ADV
ejpam-4607	121	14	.	.	PUNCT
ejpam-4607	122	1	let	let	VERB
ejpam-4607	122	2	m	m	PRON
ejpam-4607	122	3	be	be	AUX
ejpam-4607	122	4	a	a	DET
ejpam-4607	122	5	non	non	ADJ
ejpam-4607	122	6	-	-	ADJ
ejpam-4607	122	7	empty	empty	ADJ
ejpam-4607	122	8	proper	proper	ADJ
ejpam-4607	122	9	subset	subset	NOUN
ejpam-4607	122	10	of	of	ADP
ejpam-4607	122	11	a	a	DET
ejpam-4607	122	12	topological	topological	ADJ
ejpam-4607	122	13	space	space	NOUN
ejpam-4607	122	14	(	(	PUNCT
ejpam-4607	122	15	x	x	X
ejpam-4607	122	16	,	,	PUNCT
ejpam-4607	122	17	τ	τ	PROPN
ejpam-4607	122	18	)	)	PUNCT
ejpam-4607	122	19	.	.	PUNCT
ejpam-4607	123	1	define	define	VERB
ejpam-4607	123	2	a	a	DET
ejpam-4607	123	3	new	new	ADJ
ejpam-4607	123	4	topology	topology	NOUN
ejpam-4607	123	5	τ	τ	X
ejpam-4607	123	6	(	(	PUNCT
ejpam-4607	123	7	m	m	NOUN
ejpam-4607	123	8	)	)	PUNCT
ejpam-4607	123	9	on	on	ADP
ejpam-4607	123	10	x	x	PUNCT
ejpam-4607	123	11	as	as	SCONJ
ejpam-4607	123	12	follows	follow	VERB
ejpam-4607	123	13	:	:	PUNCT
ejpam-4607	123	14	τ	τ	PROPN
ejpam-4607	123	15	(	(	PUNCT
ejpam-4607	123	16	m	m	NOUN
ejpam-4607	123	17	)	)	PUNCT
ejpam-4607	123	18	=	=	PRON
ejpam-4607	123	19	{	{	PUNCT
ejpam-4607	123	20	u	u	NOUN
ejpam-4607	123	21	∪k	∪k	PROPN
ejpam-4607	123	22	:	:	PUNCT
ejpam-4607	123	23	u	u	PROPN
ejpam-4607	123	24	∈	∈	PROPN
ejpam-4607	123	25	τ	τ	X
ejpam-4607	123	26	and	and	CCONJ
ejpam-4607	123	27	k	k	PROPN
ejpam-4607	123	28	⊆	⊆	NUM
ejpam-4607	123	29	x	x	X
ejpam-4607	123	30	\m	\m	NOUN
ejpam-4607	123	31	}	}	PUNCT
ejpam-4607	123	32	.	.	PUNCT
ejpam-4607	124	1	(	(	PUNCT
ejpam-4607	124	2	x	x	X
ejpam-4607	124	3	,	,	PUNCT
ejpam-4607	124	4	τ	τ	PROPN
ejpam-4607	124	5	(	(	PUNCT
ejpam-4607	124	6	m	m	NOUN
ejpam-4607	124	7	)	)	PUNCT
ejpam-4607	124	8	)	)	PUNCT
ejpam-4607	124	9	is	be	AUX
ejpam-4607	124	10	called	call	VERB
ejpam-4607	124	11	a	a	DET
ejpam-4607	124	12	discrete	discrete	ADJ
ejpam-4607	124	13	extension	extension	NOUN
ejpam-4607	124	14	of	of	ADP
ejpam-4607	124	15	(	(	PUNCT
ejpam-4607	124	16	x	x	INTJ
ejpam-4607	124	17	,	,	PUNCT
ejpam-4607	124	18	τ	τ	PROPN
ejpam-4607	124	19	)	)	PUNCT
ejpam-4607	124	20	and	and	CCONJ
ejpam-4607	124	21	we	we	PRON
ejpam-4607	124	22	denote	denote	VERB
ejpam-4607	124	23	it	it	PRON
ejpam-4607	124	24	by	by	ADP
ejpam-4607	124	25	xm	xm	PROPN
ejpam-4607	124	26	see	see	VERB
ejpam-4607	124	27	[	[	X
ejpam-4607	124	28	12	12	NUM
ejpam-4607	124	29	,	,	PUNCT
ejpam-4607	124	30	example	example	NOUN
ejpam-4607	124	31	5.1.22	5.1.22	NUM
ejpam-4607	124	32	]	]	PUNCT
ejpam-4607	124	33	.	.	PUNCT
ejpam-4607	125	1	in	in	ADP
ejpam-4607	125	2	general	general	ADJ
ejpam-4607	125	3	,	,	PUNCT
ejpam-4607	125	4	c	c	NOUN
ejpam-4607	125	5	-	-	PUNCT
ejpam-4607	125	6	κ	κ	NOUN
ejpam-4607	125	7	-	-	PUNCT
ejpam-4607	125	8	normality	normality	NOUN
ejpam-4607	125	9	is	be	AUX
ejpam-4607	125	10	not	not	PART
ejpam-4607	125	11	preserved	preserve	VERB
ejpam-4607	125	12	by	by	ADP
ejpam-4607	125	13	a	a	DET
ejpam-4607	125	14	discrete	discrete	ADJ
ejpam-4607	125	15	extension	extension	NOUN
ejpam-4607	125	16	space	space	NOUN
ejpam-4607	125	17	.	.	PUNCT
ejpam-4607	126	1	here	here	ADV
ejpam-4607	126	2	is	be	AUX
ejpam-4607	126	3	an	an	DET
ejpam-4607	126	4	example	example	NOUN
ejpam-4607	126	5	of	of	ADP
ejpam-4607	126	6	c	c	NOUN
ejpam-4607	126	7	-	-	PUNCT
ejpam-4607	126	8	κ	κ	PRON
ejpam-4607	126	9	-	-	ADJ
ejpam-4607	126	10	normal	normal	ADJ
ejpam-4607	126	11	space	space	NOUN
ejpam-4607	126	12	whose	whose	DET
ejpam-4607	126	13	a	a	DET
ejpam-4607	126	14	discrete	discrete	ADJ
ejpam-4607	126	15	extension	extension	NOUN
ejpam-4607	126	16	space	space	NOUN
ejpam-4607	126	17	is	be	AUX
ejpam-4607	126	18	not	not	PART
ejpam-4607	126	19	c	c	NOUN
ejpam-4607	126	20	-	-	PUNCT
ejpam-4607	126	21	κ	κ	NOUN
ejpam-4607	126	22	-	-	ADJ
ejpam-4607	126	23	normal	normal	ADJ
ejpam-4607	126	24	.	.	PUNCT
ejpam-4607	127	1	l.	l.	PROPN
ejpam-4607	127	2	kalantan	kalantan	PROPN
ejpam-4607	127	3	,	,	PUNCT
ejpam-4607	127	4	a.alawadi	a.alawadi	NOUN
ejpam-4607	127	5	,	,	PUNCT
ejpam-4607	127	6	s.thabit	s.thabit	NOUN
ejpam-4607	127	7	/	/	SYM
ejpam-4607	127	8	eur	eur	PROPN
ejpam-4607	127	9	.	.	PUNCT
ejpam-4607	128	1	j.	j.	PROPN
ejpam-4607	128	2	pure	pure	PROPN
ejpam-4607	128	3	appl	appl	PROPN
ejpam-4607	128	4	.	.	PROPN
ejpam-4607	128	5	math	math	PROPN
ejpam-4607	128	6	,	,	PUNCT
ejpam-4607	128	7	16	16	NUM
ejpam-4607	128	8	(	(	PUNCT
ejpam-4607	128	9	1	1	NUM
ejpam-4607	128	10	)	)	PUNCT
ejpam-4607	128	11	(	(	PUNCT
ejpam-4607	128	12	2023	2023	NUM
ejpam-4607	128	13	)	)	PUNCT
ejpam-4607	128	14	,	,	PUNCT
ejpam-4607	128	15	62	62	NUM
ejpam-4607	128	16	-	-	SYM
ejpam-4607	128	17	70	70	NUM
ejpam-4607	128	18	66	66	NUM
ejpam-4607	128	19	example	example	NOUN
ejpam-4607	128	20	1	1	NUM
ejpam-4607	128	21	.	.	X
ejpam-4607	129	1	consider	consider	VERB
ejpam-4607	129	2	(	(	PUNCT
ejpam-4607	129	3	r	r	NOUN
ejpam-4607	129	4	,	,	PUNCT
ejpam-4607	129	5	i	i	PROPN
ejpam-4607	129	6	)	)	PUNCT
ejpam-4607	129	7	where	where	SCONJ
ejpam-4607	129	8	i	i	PRON
ejpam-4607	129	9	is	be	AUX
ejpam-4607	129	10	the	the	DET
ejpam-4607	129	11	indiscrete	indiscrete	ADJ
ejpam-4607	129	12	topology	topology	NOUN
ejpam-4607	129	13	.	.	PUNCT
ejpam-4607	130	1	let	let	VERB
ejpam-4607	130	2	m	m	NOUN
ejpam-4607	130	3	=	=	VERB
ejpam-4607	130	4	r	r	NOUN
ejpam-4607	130	5	\	\	NOUN
ejpam-4607	130	6	{	{	PUNCT
ejpam-4607	130	7	1	1	NUM
ejpam-4607	130	8	,	,	PUNCT
ejpam-4607	130	9	2	2	NUM
ejpam-4607	130	10	,	,	PUNCT
ejpam-4607	130	11	3	3	NUM
ejpam-4607	130	12	}	}	PUNCT
ejpam-4607	130	13	.	.	PUNCT
ejpam-4607	131	1	we	we	PRON
ejpam-4607	131	2	have	have	VERB
ejpam-4607	131	3	1	1	NUM
ejpam-4607	131	4	/∈	/∈	NOUN
ejpam-4607	132	1	m	m	VERB
ejpam-4607	132	2	and	and	CCONJ
ejpam-4607	132	3	m	m	VERB
ejpam-4607	132	4	is	be	AUX
ejpam-4607	132	5	closed	close	VERB
ejpam-4607	132	6	in	in	ADP
ejpam-4607	132	7	rm	rm	PROPN
ejpam-4607	132	8	.	.	PUNCT
ejpam-4607	133	1	the	the	DET
ejpam-4607	133	2	only	only	ADJ
ejpam-4607	133	3	open	open	ADJ
ejpam-4607	133	4	set	set	VERB
ejpam-4607	133	5	in	in	ADP
ejpam-4607	133	6	rm	rm	NOUN
ejpam-4607	133	7	containing	contain	VERB
ejpam-4607	133	8	m	m	PROPN
ejpam-4607	133	9	is	be	AUX
ejpam-4607	133	10	r.	r.	PROPN
ejpam-4607	133	11	but	but	CCONJ
ejpam-4607	133	12	r	r	PROPN
ejpam-4607	133	13	∩	∩	X
ejpam-4607	133	14	{	{	PUNCT
ejpam-4607	133	15	1	1	NUM
ejpam-4607	133	16	}	}	PUNCT
ejpam-4607	133	17	=	=	NOUN
ejpam-4607	133	18	̸	̸	X
ejpam-4607	133	19	∅.	∅.	ADV
ejpam-4607	133	20	thus	thus	ADV
ejpam-4607	133	21	rm	rm	NOUN
ejpam-4607	133	22	is	be	AUX
ejpam-4607	133	23	not	not	PART
ejpam-4607	133	24	regular	regular	ADJ
ejpam-4607	133	25	.	.	PUNCT
ejpam-4607	134	1	so	so	ADV
ejpam-4607	134	2	,	,	PUNCT
ejpam-4607	134	3	rm	rm	PROPN
ejpam-4607	134	4	is	be	AUX
ejpam-4607	134	5	not	not	PART
ejpam-4607	134	6	c	c	NOUN
ejpam-4607	134	7	-	-	PUNCT
ejpam-4607	134	8	κ	κ	NOUN
ejpam-4607	134	9	-	-	NOUN
ejpam-4607	134	10	normal	normal	ADJ
ejpam-4607	134	11	because	because	SCONJ
ejpam-4607	134	12	it	it	PRON
ejpam-4607	134	13	is	be	AUX
ejpam-4607	134	14	a	a	DET
ejpam-4607	134	15	compact	compact	ADJ
ejpam-4607	134	16	non	non	ADJ
ejpam-4607	134	17	-	-	ADJ
ejpam-4607	134	18	regular	regular	ADJ
ejpam-4607	134	19	space	space	NOUN
ejpam-4607	135	1	[	[	X
ejpam-4607	135	2	2	2	NUM
ejpam-4607	135	3	]	]	PUNCT
ejpam-4607	135	4	.	.	PUNCT
ejpam-4607	136	1	recall	recall	VERB
ejpam-4607	136	2	that	that	SCONJ
ejpam-4607	136	3	a	a	DET
ejpam-4607	136	4	topological	topological	ADJ
ejpam-4607	136	5	space	space	NOUN
ejpam-4607	136	6	x	x	PUNCT
ejpam-4607	136	7	is	be	AUX
ejpam-4607	136	8	called	call	VERB
ejpam-4607	136	9	c2	c2	PROPN
ejpam-4607	136	10	-	-	PUNCT
ejpam-4607	136	11	paracompact	paracompact	NOUN
ejpam-4607	136	12	if	if	SCONJ
ejpam-4607	136	13	there	there	PRON
ejpam-4607	136	14	exist	exist	VERB
ejpam-4607	136	15	a	a	DET
ejpam-4607	136	16	hausdorff	hausdorff	NOUN
ejpam-4607	136	17	paracompact	paracompact	NOUN
ejpam-4607	136	18	space	space	NOUN
ejpam-4607	136	19	y	y	PROPN
ejpam-4607	136	20	and	and	CCONJ
ejpam-4607	136	21	a	a	DET
ejpam-4607	136	22	bijective	bijective	ADJ
ejpam-4607	136	23	function	function	NOUN
ejpam-4607	137	1	f	f	NOUN
ejpam-4607	137	2	:	:	PUNCT
ejpam-4607	137	3	x	x	PUNCT
ejpam-4607	137	4	−→	−→	NOUN
ejpam-4607	137	5	y	y	PROPN
ejpam-4607	137	6	such	such	ADJ
ejpam-4607	137	7	that	that	SCONJ
ejpam-4607	137	8	the	the	DET
ejpam-4607	137	9	restriction	restriction	NOUN
ejpam-4607	137	10	f|a	f|a	PUNCT
ejpam-4607	137	11	:	:	PUNCT
ejpam-4607	137	12	a	a	DET
ejpam-4607	137	13	−→	−→	NOUN
ejpam-4607	137	14	f(a	f(a	NOUN
ejpam-4607	137	15	)	)	PUNCT
ejpam-4607	137	16	is	be	AUX
ejpam-4607	137	17	a	a	DET
ejpam-4607	137	18	homeomorphism	homeomorphism	NOUN
ejpam-4607	137	19	for	for	ADP
ejpam-4607	137	20	each	each	DET
ejpam-4607	137	21	compact	compact	ADJ
ejpam-4607	137	22	subspace	subspace	NOUN
ejpam-4607	137	23	a	a	PRON
ejpam-4607	137	24	⊆	⊆	NUM
ejpam-4607	137	25	x	x	SYM
ejpam-4607	138	1	[	[	X
ejpam-4607	138	2	17	17	NUM
ejpam-4607	138	3	]	]	PUNCT
ejpam-4607	138	4	.	.	PUNCT
ejpam-4607	139	1	from	from	ADP
ejpam-4607	139	2	definition	definition	NOUN
ejpam-4607	139	3	since	since	SCONJ
ejpam-4607	139	4	any	any	DET
ejpam-4607	139	5	t2	t2	NOUN
ejpam-4607	139	6	paracompact	paracompact	NOUN
ejpam-4607	139	7	space	space	NOUN
ejpam-4607	139	8	is	be	AUX
ejpam-4607	139	9	t4	t4	PROPN
ejpam-4607	139	10	,	,	PUNCT
ejpam-4607	139	11	any	any	DET
ejpam-4607	139	12	c2	c2	PROPN
ejpam-4607	139	13	-	-	PUNCT
ejpam-4607	139	14	paracompact	paracompact	NOUN
ejpam-4607	139	15	space	space	NOUN
ejpam-4607	139	16	is	be	AUX
ejpam-4607	139	17	c	c	NOUN
ejpam-4607	139	18	-	-	PUNCT
ejpam-4607	139	19	κ	κ	NOUN
ejpam-4607	139	20	-	-	ADJ
ejpam-4607	139	21	normal	normal	ADJ
ejpam-4607	139	22	.	.	PUNCT
ejpam-4607	140	1	the	the	DET
ejpam-4607	140	2	converse	converse	NOUN
ejpam-4607	140	3	is	be	AUX
ejpam-4607	140	4	not	not	PART
ejpam-4607	140	5	true	true	ADJ
ejpam-4607	140	6	,	,	PUNCT
ejpam-4607	140	7	we	we	PRON
ejpam-4607	140	8	did	do	AUX
ejpam-4607	140	9	show	show	VERB
ejpam-4607	140	10	in	in	ADP
ejpam-4607	140	11	[	[	X
ejpam-4607	140	12	2	2	X
ejpam-4607	140	13	]	]	PUNCT
ejpam-4607	140	14	that	that	DET
ejpam-4607	140	15	example	example	NOUN
ejpam-4607	140	16	2	2	NUM
ejpam-4607	140	17	below	below	ADV
ejpam-4607	140	18	is	be	AUX
ejpam-4607	140	19	a	a	DET
ejpam-4607	140	20	c	c	NOUN
ejpam-4607	140	21	-	-	PUNCT
ejpam-4607	140	22	κ	κ	NOUN
ejpam-4607	140	23	-	-	ADJ
ejpam-4607	140	24	normal	normal	ADJ
ejpam-4607	140	25	and	and	CCONJ
ejpam-4607	140	26	it	it	PRON
ejpam-4607	140	27	was	be	AUX
ejpam-4607	140	28	shown	show	VERB
ejpam-4607	140	29	in	in	ADP
ejpam-4607	140	30	[	[	X
ejpam-4607	140	31	5	5	NUM
ejpam-4607	140	32	,	,	PUNCT
ejpam-4607	140	33	example	example	NOUN
ejpam-4607	140	34	4	4	NUM
ejpam-4607	140	35	]	]	X
ejpam-4607	140	36	it	it	PRON
ejpam-4607	140	37	is	be	AUX
ejpam-4607	140	38	not	not	PART
ejpam-4607	140	39	c2	c2	NOUN
ejpam-4607	140	40	-	-	PUNCT
ejpam-4607	140	41	paracompact	paracompact	NOUN
ejpam-4607	140	42	.	.	PUNCT
ejpam-4607	141	1	by	by	ADP
ejpam-4607	141	2	using	use	VERB
ejpam-4607	141	3	the	the	DET
ejpam-4607	141	4	discrete	discrete	ADJ
ejpam-4607	141	5	extension	extension	NOUN
ejpam-4607	141	6	space	space	NOUN
ejpam-4607	141	7	,	,	PUNCT
ejpam-4607	141	8	we	we	PRON
ejpam-4607	141	9	answer	answer	VERB
ejpam-4607	141	10	the	the	DET
ejpam-4607	141	11	following	follow	VERB
ejpam-4607	141	12	open	open	ADJ
ejpam-4607	141	13	problem	problem	NOUN
ejpam-4607	141	14	:	:	PUNCT
ejpam-4607	141	15	“	"	PUNCT
ejpam-4607	141	16	is	be	AUX
ejpam-4607	141	17	c2paracompactness	c2paracompactness	ADV
ejpam-4607	141	18	hereditary	hereditary	ADJ
ejpam-4607	141	19	with	with	ADP
ejpam-4607	141	20	respect	respect	NOUN
ejpam-4607	141	21	to	to	ADP
ejpam-4607	141	22	closed	closed	ADJ
ejpam-4607	141	23	subspaces	subspace	NOUN
ejpam-4607	141	24	?	?	PUNCT
ejpam-4607	141	25	”	"	PUNCT
ejpam-4607	142	1	[	[	X
ejpam-4607	142	2	5	5	NUM
ejpam-4607	142	3	]	]	PUNCT
ejpam-4607	142	4	.	.	PUNCT
ejpam-4607	143	1	the	the	DET
ejpam-4607	143	2	answer	answer	NOUN
ejpam-4607	143	3	is	be	AUX
ejpam-4607	143	4	negative	negative	ADJ
ejpam-4607	143	5	even	even	ADV
ejpam-4607	143	6	for	for	ADP
ejpam-4607	143	7	open	open	ADJ
ejpam-4607	143	8	subspaces	subspace	NOUN
ejpam-4607	143	9	and	and	CCONJ
ejpam-4607	143	10	here	here	ADV
ejpam-4607	143	11	is	be	AUX
ejpam-4607	143	12	a	a	DET
ejpam-4607	143	13	counterexample	counterexample	NOUN
ejpam-4607	143	14	.	.	PUNCT
ejpam-4607	143	15	example	example	NOUN
ejpam-4607	144	1	2	2	NUM
ejpam-4607	144	2	.	.	X
ejpam-4607	144	3	consider	consider	VERB
ejpam-4607	144	4	the	the	DET
ejpam-4607	144	5	infinite	infinite	ADJ
ejpam-4607	144	6	tychonoff	tychonoff	NOUN
ejpam-4607	144	7	product	product	NOUN
ejpam-4607	144	8	space	space	NOUN
ejpam-4607	144	9	g	g	NOUN
ejpam-4607	144	10	=	=	PUNCT
ejpam-4607	144	11	dω1	dω1	PROPN
ejpam-4607	144	12	=	=	SYM
ejpam-4607	144	13	∏	∏	PROPN
ejpam-4607	144	14	α∈ω1	α∈ω1	NOUN
ejpam-4607	144	15	d	d	NOUN
ejpam-4607	144	16	,	,	PUNCT
ejpam-4607	144	17	where	where	SCONJ
ejpam-4607	144	18	d	d	NOUN
ejpam-4607	144	19	=	=	SYM
ejpam-4607	144	20	{	{	PUNCT
ejpam-4607	144	21	0	0	NUM
ejpam-4607	144	22	,	,	PUNCT
ejpam-4607	144	23	1	1	NUM
ejpam-4607	144	24	}	}	PUNCT
ejpam-4607	144	25	considered	consider	VERB
ejpam-4607	144	26	with	with	ADP
ejpam-4607	144	27	the	the	DET
ejpam-4607	144	28	discrete	discrete	ADJ
ejpam-4607	144	29	topology	topology	NOUN
ejpam-4607	144	30	.	.	PUNCT
ejpam-4607	145	1	let	let	VERB
ejpam-4607	145	2	h	h	NOUN
ejpam-4607	145	3	be	be	AUX
ejpam-4607	145	4	the	the	DET
ejpam-4607	145	5	subspace	subspace	NOUN
ejpam-4607	145	6	of	of	ADP
ejpam-4607	145	7	g	g	PROPN
ejpam-4607	145	8	consisting	consist	VERB
ejpam-4607	145	9	of	of	ADP
ejpam-4607	145	10	all	all	DET
ejpam-4607	145	11	points	point	NOUN
ejpam-4607	145	12	of	of	ADP
ejpam-4607	145	13	g	g	NOUN
ejpam-4607	145	14	with	with	ADP
ejpam-4607	145	15	at	at	ADP
ejpam-4607	145	16	most	most	ADV
ejpam-4607	145	17	countably	countably	ADV
ejpam-4607	145	18	many	many	ADJ
ejpam-4607	145	19	non	non	ADJ
ejpam-4607	145	20	-	-	ADJ
ejpam-4607	145	21	zero	zero	NUM
ejpam-4607	145	22	coordinates	coordinate	NOUN
ejpam-4607	145	23	.	.	PUNCT
ejpam-4607	146	1	put	put	VERB
ejpam-4607	146	2	m	m	NOUN
ejpam-4607	146	3	=	=	NOUN
ejpam-4607	146	4	g	g	PROPN
ejpam-4607	146	5	×	×	PROPN
ejpam-4607	146	6	h.	h.	PROPN
ejpam-4607	146	7	raushan	raushan	PROPN
ejpam-4607	146	8	buzyakova	buzyakova	PROPN
ejpam-4607	146	9	proved	prove	VERB
ejpam-4607	146	10	that	that	SCONJ
ejpam-4607	146	11	m	m	NOUN
ejpam-4607	146	12	can	can	AUX
ejpam-4607	146	13	not	not	PART
ejpam-4607	146	14	be	be	AUX
ejpam-4607	146	15	mapped	map	VERB
ejpam-4607	146	16	onto	onto	ADP
ejpam-4607	146	17	a	a	DET
ejpam-4607	146	18	normal	normal	ADJ
ejpam-4607	146	19	space	space	NOUN
ejpam-4607	146	20	z	z	NOUN
ejpam-4607	146	21	by	by	ADP
ejpam-4607	146	22	a	a	DET
ejpam-4607	146	23	bijective	bijective	ADJ
ejpam-4607	146	24	continuous	continuous	ADJ
ejpam-4607	146	25	function	function	NOUN
ejpam-4607	147	1	[	[	X
ejpam-4607	147	2	9	9	NUM
ejpam-4607	147	3	,	,	PUNCT
ejpam-4607	147	4	example	example	NOUN
ejpam-4607	147	5	4	4	NUM
ejpam-4607	147	6	]	]	PUNCT
ejpam-4607	147	7	result	result	NOUN
ejpam-4607	147	8	and	and	CCONJ
ejpam-4607	147	9	the	the	DET
ejpam-4607	147	10	fact	fact	NOUN
ejpam-4607	147	11	that	that	SCONJ
ejpam-4607	147	12	m	m	NOUN
ejpam-4607	147	13	is	be	AUX
ejpam-4607	147	14	a	a	DET
ejpam-4607	147	15	k	k	NOUN
ejpam-4607	147	16	-	-	NOUN
ejpam-4607	147	17	space	space	NOUN
ejpam-4607	147	18	,	,	PUNCT
ejpam-4607	147	19	we	we	PRON
ejpam-4607	147	20	conclude	conclude	VERB
ejpam-4607	147	21	that	that	SCONJ
ejpam-4607	147	22	m	m	VERB
ejpam-4607	147	23	is	be	AUX
ejpam-4607	147	24	a	a	DET
ejpam-4607	147	25	tychonoff	tychonoff	NOUN
ejpam-4607	147	26	space	space	NOUN
ejpam-4607	147	27	which	which	PRON
ejpam-4607	147	28	is	be	AUX
ejpam-4607	147	29	not	not	PART
ejpam-4607	147	30	c2	c2	NOUN
ejpam-4607	147	31	-	-	PUNCT
ejpam-4607	147	32	paracompact	paracompact	NOUN
ejpam-4607	148	1	[	[	X
ejpam-4607	148	2	5	5	NUM
ejpam-4607	148	3	,	,	PUNCT
ejpam-4607	148	4	example	example	NOUN
ejpam-4607	148	5	4	4	NUM
ejpam-4607	148	6	]	]	PUNCT
ejpam-4607	148	7	.	.	PUNCT
ejpam-4607	149	1	let	let	VERB
ejpam-4607	149	2	x	x	PRON
ejpam-4607	149	3	be	be	AUX
ejpam-4607	149	4	any	any	DET
ejpam-4607	149	5	compactification	compactification	NOUN
ejpam-4607	149	6	of	of	ADP
ejpam-4607	149	7	m	m	PRON
ejpam-4607	149	8	and	and	CCONJ
ejpam-4607	149	9	consider	consider	VERB
ejpam-4607	149	10	the	the	DET
ejpam-4607	149	11	discrete	discrete	ADJ
ejpam-4607	149	12	extension	extension	NOUN
ejpam-4607	149	13	space	space	NOUN
ejpam-4607	149	14	xm	xm	PROPN
ejpam-4607	149	15	of	of	ADP
ejpam-4607	149	16	x.	x.	NOUN
ejpam-4607	149	17	by	by	ADP
ejpam-4607	149	18	theorem	theorem	NOUN
ejpam-4607	149	19	“	"	PUNCT
ejpam-4607	149	20	every	every	DET
ejpam-4607	149	21	lower	low	ADJ
ejpam-4607	149	22	compact	compact	ADJ
ejpam-4607	149	23	space	space	NOUN
ejpam-4607	149	24	is	be	AUX
ejpam-4607	149	25	c2	c2	NOUN
ejpam-4607	149	26	-	-	PUNCT
ejpam-4607	149	27	paracompact	paracompact	NOUN
ejpam-4607	149	28	”	"	PUNCT
ejpam-4607	150	1	[	[	X
ejpam-4607	150	2	17	17	NUM
ejpam-4607	150	3	,	,	PUNCT
ejpam-4607	150	4	theorem	theorem	VERB
ejpam-4607	150	5	2.20	2.20	NUM
ejpam-4607	150	6	]	]	PUNCT
ejpam-4607	150	7	,	,	PUNCT
ejpam-4607	150	8	xm	xm	PROPN
ejpam-4607	150	9	is	be	AUX
ejpam-4607	150	10	c2paracompact	c2paracompact	ADJ
ejpam-4607	150	11	.	.	PUNCT
ejpam-4607	151	1	since	since	SCONJ
ejpam-4607	151	2	m	m	PRON
ejpam-4607	151	3	as	as	ADP
ejpam-4607	151	4	a	a	DET
ejpam-4607	151	5	subspace	subspace	NOUN
ejpam-4607	151	6	of	of	ADP
ejpam-4607	151	7	xm	xm	PROPN
ejpam-4607	151	8	is	be	AUX
ejpam-4607	151	9	the	the	DET
ejpam-4607	151	10	same	same	ADJ
ejpam-4607	151	11	as	as	ADP
ejpam-4607	151	12	a	a	DET
ejpam-4607	151	13	subspace	subspace	NOUN
ejpam-4607	151	14	of	of	ADP
ejpam-4607	151	15	x	x	PUNCT
ejpam-4607	151	16	and	and	CCONJ
ejpam-4607	151	17	m	m	PROPN
ejpam-4607	151	18	is	be	AUX
ejpam-4607	151	19	closed	closed	ADJ
ejpam-4607	151	20	-	-	PUNCT
ejpam-4607	151	21	and	and	CCONJ
ejpam-4607	151	22	-	-	PUNCT
ejpam-4607	151	23	open	open	ADJ
ejpam-4607	151	24	in	in	ADP
ejpam-4607	151	25	xm	xm	PROPN
ejpam-4607	151	26	,	,	PUNCT
ejpam-4607	151	27	we	we	PRON
ejpam-4607	151	28	get	get	VERB
ejpam-4607	151	29	that	that	PRON
ejpam-4607	151	30	c2	c2	PROPN
ejpam-4607	151	31	-	-	PUNCT
ejpam-4607	151	32	paracompactness	paracompactness	PROPN
ejpam-4607	151	33	is	be	AUX
ejpam-4607	151	34	not	not	PART
ejpam-4607	151	35	hereditary	hereditary	ADJ
ejpam-4607	151	36	with	with	ADP
ejpam-4607	151	37	respect	respect	NOUN
ejpam-4607	151	38	to	to	ADP
ejpam-4607	151	39	both	both	PRON
ejpam-4607	151	40	closed	closed	ADJ
ejpam-4607	151	41	and	and	CCONJ
ejpam-4607	151	42	open	open	ADJ
ejpam-4607	151	43	subspaces	subspace	NOUN
ejpam-4607	151	44	.	.	PUNCT
ejpam-4607	152	1	recall	recall	VERB
ejpam-4607	152	2	that	that	SCONJ
ejpam-4607	152	3	a	a	DET
ejpam-4607	152	4	space	space	NOUN
ejpam-4607	152	5	x	x	PUNCT
ejpam-4607	152	6	is	be	AUX
ejpam-4607	152	7	called	call	VERB
ejpam-4607	152	8	α	α	PRON
ejpam-4607	152	9	-	-	ADJ
ejpam-4607	152	10	normal	normal	ADJ
ejpam-4607	152	11	if	if	SCONJ
ejpam-4607	152	12	for	for	ADP
ejpam-4607	152	13	any	any	DET
ejpam-4607	152	14	two	two	NUM
ejpam-4607	152	15	disjoint	disjoint	NOUN
ejpam-4607	152	16	closed	closed	ADJ
ejpam-4607	152	17	subsets	subset	NOUN
ejpam-4607	152	18	a	a	PRON
ejpam-4607	152	19	and	and	CCONJ
ejpam-4607	152	20	b	b	NOUN
ejpam-4607	152	21	of	of	ADP
ejpam-4607	152	22	x	x	PRON
ejpam-4607	152	23	there	there	PRON
ejpam-4607	152	24	exist	exist	VERB
ejpam-4607	152	25	disjoint	disjoint	ADJ
ejpam-4607	152	26	open	open	ADJ
ejpam-4607	152	27	subsets	subset	NOUN
ejpam-4607	152	28	u	u	NOUN
ejpam-4607	152	29	and	and	CCONJ
ejpam-4607	152	30	v	v	NOUN
ejpam-4607	152	31	of	of	ADP
ejpam-4607	152	32	x	x	PUNCT
ejpam-4607	152	33	such	such	ADJ
ejpam-4607	152	34	that	that	DET
ejpam-4607	152	35	a∩u	a∩u	PROPN
ejpam-4607	152	36	is	be	AUX
ejpam-4607	152	37	dense	dense	ADJ
ejpam-4607	152	38	in	in	ADP
ejpam-4607	152	39	a	a	DET
ejpam-4607	152	40	and	and	CCONJ
ejpam-4607	152	41	b	b	NOUN
ejpam-4607	152	42	∩	∩	NOUN
ejpam-4607	152	43	v	v	NOUN
ejpam-4607	152	44	is	be	AUX
ejpam-4607	152	45	dense	dense	ADJ
ejpam-4607	152	46	in	in	ADP
ejpam-4607	152	47	b	b	PROPN
ejpam-4607	152	48	[	[	X
ejpam-4607	152	49	6	6	NUM
ejpam-4607	152	50	]	]	PUNCT
ejpam-4607	152	51	.	.	PUNCT
ejpam-4607	153	1	we	we	PRON
ejpam-4607	153	2	answer	answer	VERB
ejpam-4607	153	3	the	the	DET
ejpam-4607	153	4	following	follow	VERB
ejpam-4607	153	5	open	open	ADJ
ejpam-4607	153	6	problem	problem	NOUN
ejpam-4607	153	7	:	:	PUNCT
ejpam-4607	153	8	“	"	PUNCT
ejpam-4607	153	9	is	be	AUX
ejpam-4607	153	10	α	α	DET
ejpam-4607	153	11	-	-	PUNCT
ejpam-4607	153	12	normality	normality	NOUN
ejpam-4607	153	13	preserved	preserve	VERB
ejpam-4607	153	14	by	by	ADP
ejpam-4607	153	15	the	the	DET
ejpam-4607	153	16	discrete	discrete	ADJ
ejpam-4607	153	17	extension	extension	NOUN
ejpam-4607	153	18	?	?	PUNCT
ejpam-4607	153	19	”	"	PUNCT
ejpam-4607	154	1	[	[	X
ejpam-4607	154	2	3	3	NUM
ejpam-4607	154	3	]	]	PUNCT
ejpam-4607	154	4	.	.	PUNCT
ejpam-4607	155	1	the	the	DET
ejpam-4607	155	2	answer	answer	NOUN
ejpam-4607	155	3	is	be	AUX
ejpam-4607	155	4	no	no	PRON
ejpam-4607	156	1	and	and	CCONJ
ejpam-4607	156	2	here	here	ADV
ejpam-4607	156	3	is	be	AUX
ejpam-4607	156	4	an	an	DET
ejpam-4607	156	5	example	example	NOUN
ejpam-4607	156	6	of	of	ADP
ejpam-4607	156	7	an	an	DET
ejpam-4607	156	8	α	α	NOUN
ejpam-4607	156	9	-	-	ADJ
ejpam-4607	156	10	normal	normal	ADJ
ejpam-4607	156	11	space	space	NOUN
ejpam-4607	156	12	whose	whose	DET
ejpam-4607	156	13	a	a	DET
ejpam-4607	156	14	discrete	discrete	ADJ
ejpam-4607	156	15	extension	extension	NOUN
ejpam-4607	156	16	space	space	NOUN
ejpam-4607	156	17	is	be	AUX
ejpam-4607	156	18	not	not	PART
ejpam-4607	156	19	α	α	NOUN
ejpam-4607	156	20	-	-	ADJ
ejpam-4607	156	21	normal	normal	ADJ
ejpam-4607	156	22	.	.	PUNCT
ejpam-4607	157	1	example	example	NOUN
ejpam-4607	158	1	3	3	X
ejpam-4607	158	2	.	.	PUNCT
ejpam-4607	158	3	let	let	VERB
ejpam-4607	158	4	m=((ω1	m=((ω1	NOUN
ejpam-4607	158	5	+	+	CCONJ
ejpam-4607	158	6	1	1	X
ejpam-4607	158	7	)	)	PUNCT
ejpam-4607	158	8	×	×	NOUN
ejpam-4607	158	9	(	(	PUNCT
ejpam-4607	158	10	ω0	ω0	ADV
ejpam-4607	158	11	+	+	NOUN
ejpam-4607	158	12	1	1	NUM
ejpam-4607	158	13	)	)	PUNCT
ejpam-4607	158	14	)	)	PUNCT
ejpam-4607	158	15	\	\	NOUN
ejpam-4607	159	1	{	{	PUNCT
ejpam-4607	159	2	⟨ω1	⟨ω1	NOUN
ejpam-4607	159	3	,	,	PUNCT
ejpam-4607	159	4	ω0⟩	ω0⟩	NUM
ejpam-4607	159	5	}	}	PUNCT
ejpam-4607	159	6	is	be	AUX
ejpam-4607	159	7	a	a	DET
ejpam-4607	159	8	tychonoff	tychonoff	NOUN
ejpam-4607	159	9	plank	plank	NOUN
ejpam-4607	159	10	space	space	NOUN
ejpam-4607	159	11	see	see	VERB
ejpam-4607	159	12	[	[	X
ejpam-4607	159	13	24	24	NUM
ejpam-4607	159	14	,	,	PUNCT
ejpam-4607	159	15	example	example	NOUN
ejpam-4607	159	16	87	87	NUM
ejpam-4607	159	17	]	]	PUNCT
ejpam-4607	159	18	we	we	PRON
ejpam-4607	159	19	know	know	VERB
ejpam-4607	159	20	that	that	SCONJ
ejpam-4607	159	21	m	m	PROPN
ejpam-4607	159	22	is	be	AUX
ejpam-4607	159	23	a	a	DET
ejpam-4607	159	24	tychonoff	tychonoff	NOUN
ejpam-4607	159	25	non	non	ADJ
ejpam-4607	159	26	α	α	ADJ
ejpam-4607	159	27	-	-	ADJ
ejpam-4607	159	28	normal	normal	ADJ
ejpam-4607	159	29	space	space	NOUN
ejpam-4607	160	1	[	[	X
ejpam-4607	160	2	6	6	NUM
ejpam-4607	160	3	]	]	PUNCT
ejpam-4607	160	4	,	,	PUNCT
ejpam-4607	160	5	take	take	VERB
ejpam-4607	160	6	the	the	DET
ejpam-4607	160	7	compactification	compactification	NOUN
ejpam-4607	160	8	x	x	PUNCT
ejpam-4607	160	9	of	of	ADP
ejpam-4607	160	10	m	m	PRON
ejpam-4607	160	11	then	then	ADV
ejpam-4607	160	12	it	it	PRON
ejpam-4607	160	13	is	be	AUX
ejpam-4607	160	14	α	α	PRON
ejpam-4607	160	15	-	-	ADJ
ejpam-4607	160	16	normal	normal	ADJ
ejpam-4607	160	17	being	be	AUX
ejpam-4607	160	18	t2	t2	NOUN
ejpam-4607	160	19	compact	compact	ADJ
ejpam-4607	160	20	space	space	NOUN
ejpam-4607	160	21	.	.	PUNCT
ejpam-4607	161	1	consider	consider	VERB
ejpam-4607	161	2	the	the	DET
ejpam-4607	161	3	discrete	discrete	ADJ
ejpam-4607	161	4	extension	extension	NOUN
ejpam-4607	161	5	xm	xm	PROPN
ejpam-4607	161	6	.	.	PUNCT
ejpam-4607	162	1	observe	observe	VERB
ejpam-4607	162	2	that	that	SCONJ
ejpam-4607	162	3	m	m	NOUN
ejpam-4607	162	4	is	be	AUX
ejpam-4607	162	5	closed	close	VERB
ejpam-4607	162	6	in	in	ADP
ejpam-4607	162	7	xm	xm	PROPN
ejpam-4607	162	8	.	.	PUNCT
ejpam-4607	163	1	since	since	SCONJ
ejpam-4607	163	2	α	α	NOUN
ejpam-4607	163	3	-	-	NOUN
ejpam-4607	163	4	normality	normality	NOUN
ejpam-4607	163	5	is	be	AUX
ejpam-4607	163	6	hereditary	hereditary	ADJ
ejpam-4607	163	7	with	with	ADP
ejpam-4607	163	8	respect	respect	NOUN
ejpam-4607	163	9	to	to	ADP
ejpam-4607	163	10	closed	closed	ADJ
ejpam-4607	163	11	subspaces	subspace	NOUN
ejpam-4607	163	12	[	[	X
ejpam-4607	163	13	6	6	NUM
ejpam-4607	163	14	]	]	PUNCT
ejpam-4607	163	15	,	,	PUNCT
ejpam-4607	163	16	we	we	PRON
ejpam-4607	163	17	conclude	conclude	VERB
ejpam-4607	163	18	that	that	SCONJ
ejpam-4607	163	19	xm	xm	PROPN
ejpam-4607	163	20	can	can	AUX
ejpam-4607	163	21	not	not	PART
ejpam-4607	163	22	be	be	AUX
ejpam-4607	163	23	α	α	NOUN
ejpam-4607	163	24	-	-	ADJ
ejpam-4607	163	25	normal	normal	ADJ
ejpam-4607	163	26	.	.	PUNCT
ejpam-4607	163	27	.	.	PUNCT
ejpam-4607	164	1	the	the	DET
ejpam-4607	164	2	following	follow	VERB
ejpam-4607	164	3	example	example	NOUN
ejpam-4607	164	4	answers	answer	VERB
ejpam-4607	164	5	three	three	NUM
ejpam-4607	164	6	kinds	kind	NOUN
ejpam-4607	164	7	of	of	ADP
ejpam-4607	164	8	invariants	invariant	NOUN
ejpam-4607	164	9	.	.	PUNCT
ejpam-4607	165	1	we	we	PRON
ejpam-4607	165	2	used	use	VERB
ejpam-4607	165	3	two	two	NUM
ejpam-4607	165	4	well	well	ADV
ejpam-4607	165	5	-	-	PUNCT
ejpam-4607	165	6	known	know	VERB
ejpam-4607	165	7	spaces	space	NOUN
ejpam-4607	165	8	,	,	PUNCT
ejpam-4607	165	9	the	the	DET
ejpam-4607	165	10	alexandroff	alexandroff	ADJ
ejpam-4607	165	11	duplicate	duplicate	NOUN
ejpam-4607	165	12	space	space	NOUN
ejpam-4607	165	13	and	and	CCONJ
ejpam-4607	165	14	the	the	DET
ejpam-4607	165	15	closed	closed	ADJ
ejpam-4607	165	16	extension	extension	NOUN
ejpam-4607	165	17	space	space	NOUN
ejpam-4607	165	18	.	.	PUNCT
ejpam-4607	166	1	let	let	VERB
ejpam-4607	166	2	x	x	PRON
ejpam-4607	166	3	be	be	AUX
ejpam-4607	166	4	any	any	DET
ejpam-4607	166	5	t1	t1	NOUN
ejpam-4607	166	6	topological	topological	ADJ
ejpam-4607	166	7	space	space	NOUN
ejpam-4607	166	8	.	.	PUNCT
ejpam-4607	167	1	let	let	VERB
ejpam-4607	167	2	x	x	X
ejpam-4607	167	3	′	′	NUM
ejpam-4607	168	1	=	=	PUNCT
ejpam-4607	168	2	x	x	SYM
ejpam-4607	168	3	×	×	NOUN
ejpam-4607	168	4	{	{	PUNCT
ejpam-4607	168	5	1	1	NUM
ejpam-4607	168	6	}	}	PUNCT
ejpam-4607	168	7	.	.	PUNCT
ejpam-4607	169	1	note	note	VERB
ejpam-4607	169	2	that	that	SCONJ
ejpam-4607	169	3	x	x	NOUN
ejpam-4607	169	4	∩	∩	NOUN
ejpam-4607	169	5	x	x	SYM
ejpam-4607	169	6	′	′	NUM
ejpam-4607	169	7	=	=	PUNCT
ejpam-4607	169	8	∅.	∅.	AUX
ejpam-4607	169	9	let	let	VERB
ejpam-4607	169	10	a(x	a(x	NOUN
ejpam-4607	169	11	)	)	PUNCT
ejpam-4607	169	12	=	=	PUNCT
ejpam-4607	169	13	x	x	SYM
ejpam-4607	169	14	∪x	∪x	X
ejpam-4607	169	15	′.	′.	NOUN
ejpam-4607	169	16	for	for	ADP
ejpam-4607	169	17	simplicity	simplicity	NOUN
ejpam-4607	169	18	,	,	PUNCT
ejpam-4607	169	19	for	for	ADP
ejpam-4607	169	20	an	an	DET
ejpam-4607	169	21	element	element	NOUN
ejpam-4607	169	22	x	x	SYM
ejpam-4607	169	23	∈	∈	PROPN
ejpam-4607	169	24	x	x	NOUN
ejpam-4607	169	25	,	,	PUNCT
ejpam-4607	169	26	we	we	PRON
ejpam-4607	169	27	will	will	AUX
ejpam-4607	169	28	denote	denote	VERB
ejpam-4607	169	29	the	the	DET
ejpam-4607	169	30	element	element	NOUN
ejpam-4607	169	31	⟨x	⟨x	VERB
ejpam-4607	169	32	,	,	PUNCT
ejpam-4607	169	33	1⟩	1⟩	NUM
ejpam-4607	169	34	l.	l.	PROPN
ejpam-4607	169	35	kalantan	kalantan	PROPN
ejpam-4607	169	36	,	,	PUNCT
ejpam-4607	169	37	a.alawadi	a.alawadi	NOUN
ejpam-4607	169	38	,	,	PUNCT
ejpam-4607	169	39	s.thabit	s.thabit	NOUN
ejpam-4607	169	40	/	/	SYM
ejpam-4607	169	41	eur	eur	PROPN
ejpam-4607	169	42	.	.	PUNCT
ejpam-4607	170	1	j.	j.	PROPN
ejpam-4607	170	2	pure	pure	PROPN
ejpam-4607	170	3	appl	appl	PROPN
ejpam-4607	170	4	.	.	PROPN
ejpam-4607	170	5	math	math	PROPN
ejpam-4607	170	6	,	,	PUNCT
ejpam-4607	170	7	16	16	NUM
ejpam-4607	170	8	(	(	PUNCT
ejpam-4607	170	9	1	1	NUM
ejpam-4607	170	10	)	)	PUNCT
ejpam-4607	170	11	(	(	PUNCT
ejpam-4607	170	12	2023	2023	NUM
ejpam-4607	170	13	)	)	PUNCT
ejpam-4607	170	14	,	,	PUNCT
ejpam-4607	170	15	62	62	NUM
ejpam-4607	170	16	-	-	SYM
ejpam-4607	170	17	70	70	NUM
ejpam-4607	170	18	67	67	NUM
ejpam-4607	170	19	in	in	ADP
ejpam-4607	170	20	x	x	X
ejpam-4607	170	21	′	′	NUM
ejpam-4607	170	22	by	by	ADP
ejpam-4607	170	23	x′	x′	PROPN
ejpam-4607	170	24	and	and	CCONJ
ejpam-4607	170	25	for	for	ADP
ejpam-4607	170	26	a	a	DET
ejpam-4607	170	27	subset	subset	NOUN
ejpam-4607	170	28	b	b	NOUN
ejpam-4607	170	29	⊆	⊆	NUM
ejpam-4607	170	30	x	x	PRON
ejpam-4607	170	31	let	let	VERB
ejpam-4607	170	32	b′	b′	NOUN
ejpam-4607	170	33	=	=	PUNCT
ejpam-4607	170	34	{	{	PUNCT
ejpam-4607	170	35	x′	x′	PROPN
ejpam-4607	170	36	:	:	PUNCT
ejpam-4607	171	1	x	x	SYM
ejpam-4607	171	2	∈	∈	PROPN
ejpam-4607	171	3	b	b	AUX
ejpam-4607	171	4	}	}	PUNCT
ejpam-4607	171	5	=	=	SYM
ejpam-4607	171	6	b	b	SYM
ejpam-4607	171	7	×	×	NOUN
ejpam-4607	171	8	{	{	PUNCT
ejpam-4607	171	9	1	1	NUM
ejpam-4607	171	10	}	}	SYM
ejpam-4607	171	11	⊆	⊆	NUM
ejpam-4607	171	12	x	x	SYM
ejpam-4607	171	13	′.	′.	NOUN
ejpam-4607	171	14	for	for	ADP
ejpam-4607	171	15	each	each	DET
ejpam-4607	171	16	x′	x′	PROPN
ejpam-4607	171	17	∈	∈	PROPN
ejpam-4607	171	18	x	x	SYM
ejpam-4607	171	19	′	′	NOUN
ejpam-4607	171	20	,	,	PUNCT
ejpam-4607	171	21	let	let	VERB
ejpam-4607	171	22	b(x′	b(x′	NUM
ejpam-4607	171	23	)	)	PUNCT
ejpam-4607	171	24	=	=	PRON
ejpam-4607	171	25	{	{	PUNCT
ejpam-4607	171	26	{	{	PUNCT
ejpam-4607	171	27	x′	x′	NUM
ejpam-4607	171	28	}	}	PUNCT
ejpam-4607	171	29	}	}	PUNCT
ejpam-4607	171	30	.	.	PUNCT
ejpam-4607	172	1	for	for	ADP
ejpam-4607	172	2	each	each	DET
ejpam-4607	172	3	x	x	SYM
ejpam-4607	172	4	∈	∈	PROPN
ejpam-4607	172	5	x	x	NOUN
ejpam-4607	172	6	,	,	PUNCT
ejpam-4607	172	7	let	let	VERB
ejpam-4607	172	8	b(x	b(x	NOUN
ejpam-4607	172	9	)	)	PUNCT
ejpam-4607	173	1	=	=	PRON
ejpam-4607	173	2	{	{	PUNCT
ejpam-4607	173	3	u	u	NOUN
ejpam-4607	173	4	∪	∪	X
ejpam-4607	173	5	(	(	PUNCT
ejpam-4607	173	6	u	u	NOUN
ejpam-4607	173	7	′	′	NOUN
ejpam-4607	173	8	\	\	NOUN
ejpam-4607	173	9	{	{	PUNCT
ejpam-4607	173	10	x′	x′	NUM
ejpam-4607	173	11	}	}	PUNCT
ejpam-4607	173	12	)	)	PUNCT
ejpam-4607	173	13	:	:	PUNCT
ejpam-4607	173	14	u	u	NOUN
ejpam-4607	173	15	is	be	AUX
ejpam-4607	173	16	open	open	ADJ
ejpam-4607	173	17	in	in	ADP
ejpam-4607	173	18	x	x	PUNCT
ejpam-4607	173	19	with	with	ADP
ejpam-4607	173	20	x	x	PROPN
ejpam-4607	173	21	∈	∈	PROPN
ejpam-4607	173	22	u	u	NOUN
ejpam-4607	173	23	}	}	PUNCT
ejpam-4607	173	24	.	.	PUNCT
ejpam-4607	174	1	let	let	VERB
ejpam-4607	174	2	τ	τ	PROPN
ejpam-4607	174	3	denote	denote	VERB
ejpam-4607	174	4	the	the	DET
ejpam-4607	174	5	unique	unique	ADJ
ejpam-4607	174	6	topology	topology	NOUN
ejpam-4607	174	7	on	on	ADP
ejpam-4607	174	8	a(x	a(x	NOUN
ejpam-4607	174	9	)	)	PUNCT
ejpam-4607	174	10	which	which	PRON
ejpam-4607	174	11	has	have	AUX
ejpam-4607	174	12	{	{	PUNCT
ejpam-4607	174	13	b(x	b(x	NOUN
ejpam-4607	174	14	)	)	PUNCT
ejpam-4607	174	15	:	:	PUNCT
ejpam-4607	175	1	x	x	X
ejpam-4607	175	2	∈	∈	NOUN
ejpam-4607	175	3	x	x	SYM
ejpam-4607	175	4	}	}	PUNCT
ejpam-4607	175	5	∪	∪	ADJ
ejpam-4607	175	6	{	{	PUNCT
ejpam-4607	175	7	b(x′	b(x′	NUM
ejpam-4607	175	8	)	)	PUNCT
ejpam-4607	175	9	:	:	PUNCT
ejpam-4607	175	10	x′	x′	X
ejpam-4607	175	11	∈	∈	NOUN
ejpam-4607	175	12	x	x	NOUN
ejpam-4607	175	13	′	′	NOUN
ejpam-4607	175	14	}	}	PUNCT
ejpam-4607	175	15	as	as	ADP
ejpam-4607	175	16	its	its	PRON
ejpam-4607	175	17	neighborhood	neighborhood	NOUN
ejpam-4607	175	18	system	system	NOUN
ejpam-4607	175	19	.	.	PUNCT
ejpam-4607	176	1	a(x	a(x	NOUN
ejpam-4607	176	2	)	)	PUNCT
ejpam-4607	176	3	with	with	ADP
ejpam-4607	176	4	this	this	DET
ejpam-4607	176	5	topology	topology	NOUN
ejpam-4607	176	6	is	be	AUX
ejpam-4607	176	7	called	call	VERB
ejpam-4607	176	8	the	the	DET
ejpam-4607	176	9	alexandroff	alexandroff	ADJ
ejpam-4607	176	10	duplicate	duplicate	NOUN
ejpam-4607	176	11	of	of	ADP
ejpam-4607	176	12	x	x	PUNCT
ejpam-4607	177	1	[	[	X
ejpam-4607	177	2	11	11	NUM
ejpam-4607	177	3	]	]	PUNCT
ejpam-4607	177	4	.	.	PUNCT
ejpam-4607	177	5	example	example	NOUN
ejpam-4607	178	1	4	4	X
ejpam-4607	178	2	.	.	PUNCT
ejpam-4607	178	3	consider	consider	VERB
ejpam-4607	178	4	the	the	DET
ejpam-4607	178	5	alexandroff	alexandroff	NOUN
ejpam-4607	178	6	duplicate	duplicate	ADJ
ejpam-4607	178	7	space	space	NOUN
ejpam-4607	178	8	a(r	a(r	NOUN
ejpam-4607	178	9	)	)	PUNCT
ejpam-4607	178	10	of	of	ADP
ejpam-4607	178	11	r	r	NOUN
ejpam-4607	178	12	with	with	ADP
ejpam-4607	178	13	its	its	PRON
ejpam-4607	178	14	usual	usual	ADJ
ejpam-4607	178	15	metric	metric	ADJ
ejpam-4607	178	16	topology	topology	NOUN
ejpam-4607	178	17	.	.	PUNCT
ejpam-4607	179	1	it	it	PRON
ejpam-4607	179	2	is	be	AUX
ejpam-4607	179	3	c2	c2	NOUN
ejpam-4607	179	4	-	-	PUNCT
ejpam-4607	179	5	paracompact	paracompact	NOUN
ejpam-4607	180	1	[	[	X
ejpam-4607	180	2	5	5	NUM
ejpam-4607	180	3	]	]	PUNCT
ejpam-4607	180	4	,	,	PUNCT
ejpam-4607	180	5	hence	hence	ADV
ejpam-4607	180	6	c	c	NOUN
ejpam-4607	180	7	-	-	PUNCT
ejpam-4607	180	8	κ	κ	NOUN
ejpam-4607	180	9	-	-	ADJ
ejpam-4607	180	10	normal	normal	ADJ
ejpam-4607	180	11	.	.	PUNCT
ejpam-4607	181	1	now	now	ADV
ejpam-4607	181	2	,	,	PUNCT
ejpam-4607	181	3	let	let	VERB
ejpam-4607	181	4	i	i	PRON
ejpam-4607	181	5	=	=	PUNCT
ejpam-4607	181	6	√	√	NUM
ejpam-4607	181	7	−1	−1	NOUN
ejpam-4607	181	8	̸∈	̸∈	PROPN
ejpam-4607	181	9	r	r	NOUN
ejpam-4607	181	10	and	and	CCONJ
ejpam-4607	181	11	put	put	VERB
ejpam-4607	181	12	x	x	PUNCT
ejpam-4607	181	13	=	=	PUNCT
ejpam-4607	181	14	r∪{i	r∪{i	ADV
ejpam-4607	181	15	}	}	PUNCT
ejpam-4607	181	16	.	.	PUNCT
ejpam-4607	182	1	let	let	VERB
ejpam-4607	182	2	τ	τ	PRON
ejpam-4607	182	3	be	be	AUX
ejpam-4607	182	4	the	the	DET
ejpam-4607	182	5	closed	closed	ADJ
ejpam-4607	182	6	extension	extension	NOUN
ejpam-4607	182	7	topology	topology	NOUN
ejpam-4607	182	8	on	on	ADP
ejpam-4607	182	9	x	x	PUNCT
ejpam-4607	182	10	generated	generate	VERB
ejpam-4607	182	11	from	from	ADP
ejpam-4607	182	12	r	r	NOUN
ejpam-4607	182	13	with	with	ADP
ejpam-4607	182	14	its	its	PRON
ejpam-4607	182	15	usual	usual	ADJ
ejpam-4607	182	16	metric	metric	ADJ
ejpam-4607	182	17	topology	topology	NOUN
ejpam-4607	182	18	and	and	CCONJ
ejpam-4607	182	19	i.	i.	NOUN
ejpam-4607	183	1	so	so	ADV
ejpam-4607	183	2	,	,	PUNCT
ejpam-4607	183	3	τ=	τ=	X
ejpam-4607	183	4	{	{	PUNCT
ejpam-4607	183	5	∅	∅	NOUN
ejpam-4607	183	6	}	}	PUNCT
ejpam-4607	183	7	∪	∪	NOUN
ejpam-4607	183	8	{	{	PUNCT
ejpam-4607	183	9	w	w	NOUN
ejpam-4607	183	10	∪	∪	X
ejpam-4607	183	11	{	{	PUNCT
ejpam-4607	183	12	i	i	NOUN
ejpam-4607	183	13	}	}	PUNCT
ejpam-4607	183	14	:	:	PUNCT
ejpam-4607	183	15	w	w	ADP
ejpam-4607	183	16	⊆	⊆	NUM
ejpam-4607	183	17	r;w	r;w	NOUN
ejpam-4607	183	18	is	be	AUX
ejpam-4607	183	19	open	open	ADJ
ejpam-4607	183	20	in	in	ADP
ejpam-4607	183	21	the	the	DET
ejpam-4607	183	22	usual	usual	ADJ
ejpam-4607	183	23	metric	metric	ADJ
ejpam-4607	183	24	topology	topology	NOUN
ejpam-4607	183	25	}	}	PUNCT
ejpam-4607	183	26	.	.	PUNCT
ejpam-4607	184	1	(	(	PUNCT
ejpam-4607	184	2	x	x	X
ejpam-4607	184	3	,	,	PUNCT
ejpam-4607	184	4	τ	τ	PROPN
ejpam-4607	184	5	)	)	PUNCT
ejpam-4607	184	6	is	be	AUX
ejpam-4607	184	7	not	not	PART
ejpam-4607	184	8	c	c	NOUN
ejpam-4607	184	9	-	-	ADJ
ejpam-4607	184	10	normal	normal	ADJ
ejpam-4607	184	11	see	see	VERB
ejpam-4607	184	12	[	[	X
ejpam-4607	184	13	1	1	NUM
ejpam-4607	184	14	]	]	PUNCT
ejpam-4607	184	15	.	.	PUNCT
ejpam-4607	185	1	so	so	ADV
ejpam-4607	185	2	it	it	PRON
ejpam-4607	185	3	is	be	AUX
ejpam-4607	185	4	not	not	PART
ejpam-4607	185	5	not	not	PART
ejpam-4607	185	6	c	c	NOUN
ejpam-4607	185	7	-	-	PUNCT
ejpam-4607	185	8	κ	κ	NOUN
ejpam-4607	185	9	-	-	NOUN
ejpam-4607	185	10	normal	normal	ADJ
ejpam-4607	185	11	because	because	SCONJ
ejpam-4607	185	12	it	it	PRON
ejpam-4607	185	13	is	be	AUX
ejpam-4607	185	14	fréchet	fréchet	VERB
ejpam-4607	185	15	being	be	AUX
ejpam-4607	185	16	first	first	ADV
ejpam-4607	185	17	countable	countable	ADJ
ejpam-4607	185	18	,	,	PUNCT
ejpam-4607	185	19	lindelöf	lindelöf	NOUN
ejpam-4607	185	20	space	space	NOUN
ejpam-4607	185	21	,	,	PUNCT
ejpam-4607	185	22	which	which	PRON
ejpam-4607	185	23	is	be	AUX
ejpam-4607	185	24	not	not	PART
ejpam-4607	185	25	c	c	NOUN
ejpam-4607	185	26	-	-	ADJ
ejpam-4607	185	27	normal	normal	ADJ
ejpam-4607	185	28	[	[	X
ejpam-4607	185	29	2	2	NUM
ejpam-4607	185	30	,	,	PUNCT
ejpam-4607	185	31	theorem0.10	theorem0.10	ADP
ejpam-4607	185	32	]	]	PUNCT
ejpam-4607	185	33	.	.	PUNCT
ejpam-4607	186	1	define	define	VERB
ejpam-4607	186	2	g	g	NOUN
ejpam-4607	186	3	:	:	PUNCT
ejpam-4607	186	4	a(r	a(r	NOUN
ejpam-4607	186	5	)	)	PUNCT
ejpam-4607	186	6	−→	−→	NOUN
ejpam-4607	186	7	x	x	SYM
ejpam-4607	186	8	by	by	ADP
ejpam-4607	186	9	g(x	g(x	NOUN
ejpam-4607	186	10	)	)	PUNCT
ejpam-4607	187	1	=	=	PRON
ejpam-4607	187	2	{	{	PUNCT
ejpam-4607	187	3	i	i	INTJ
ejpam-4607	187	4	;	;	PUNCT
ejpam-4607	187	5	if	if	SCONJ
ejpam-4607	187	6	x	x	PUNCT
ejpam-4607	187	7	∈	∈	PROPN
ejpam-4607	187	8	r′	r′	PROPN
ejpam-4607	187	9	x	x	X
ejpam-4607	187	10	;	;	PUNCT
ejpam-4607	187	11	if	if	SCONJ
ejpam-4607	187	12	x	x	SYM
ejpam-4607	187	13	∈	∈	NOUN
ejpam-4607	187	14	r	r	NOUN
ejpam-4607	187	15	g	g	NOUN
ejpam-4607	187	16	is	be	AUX
ejpam-4607	187	17	an	an	DET
ejpam-4607	187	18	open	open	ADJ
ejpam-4607	187	19	onto	onto	ADP
ejpam-4607	187	20	function	function	NOUN
ejpam-4607	187	21	.	.	PUNCT
ejpam-4607	188	1	thus	thus	ADV
ejpam-4607	188	2	c	c	X
ejpam-4607	188	3	-	-	PUNCT
ejpam-4607	188	4	κ	κ	NOUN
ejpam-4607	188	5	-	-	PUNCT
ejpam-4607	188	6	normality	normality	NOUN
ejpam-4607	188	7	is	be	AUX
ejpam-4607	188	8	neither	neither	CCONJ
ejpam-4607	188	9	invariant	invariant	ADJ
ejpam-4607	188	10	,	,	PUNCT
ejpam-4607	188	11	open	open	ADJ
ejpam-4607	188	12	invariant	invariant	ADJ
ejpam-4607	188	13	,	,	PUNCT
ejpam-4607	188	14	nor	nor	CCONJ
ejpam-4607	188	15	quotient	quotient	NOUN
ejpam-4607	188	16	invariant	invariant	ADJ
ejpam-4607	188	17	.	.	PUNCT
ejpam-4607	188	18	.	.	PUNCT
ejpam-4607	189	1	since	since	SCONJ
ejpam-4607	189	2	κ	κ	NOUN
ejpam-4607	189	3	-	-	PUNCT
ejpam-4607	189	4	normality	normality	NOUN
ejpam-4607	189	5	is	be	AUX
ejpam-4607	189	6	not	not	PART
ejpam-4607	189	7	multiplicative	multiplicative	ADJ
ejpam-4607	189	8	,	,	PUNCT
ejpam-4607	189	9	it	it	PRON
ejpam-4607	189	10	seems	seem	VERB
ejpam-4607	189	11	to	to	ADP
ejpam-4607	189	12	us	we	PRON
ejpam-4607	189	13	that	that	SCONJ
ejpam-4607	189	14	both	both	DET
ejpam-4607	189	15	c	c	NOUN
ejpam-4607	189	16	-	-	PUNCT
ejpam-4607	189	17	mild	mild	ADJ
ejpam-4607	189	18	normality	normality	NOUN
ejpam-4607	189	19	and	and	CCONJ
ejpam-4607	189	20	c	c	NOUN
ejpam-4607	189	21	-	-	PUNCT
ejpam-4607	189	22	κ	κ	NOUN
ejpam-4607	189	23	-	-	PUNCT
ejpam-4607	189	24	normality	normality	NOUN
ejpam-4607	189	25	are	be	AUX
ejpam-4607	189	26	not	not	PART
ejpam-4607	189	27	multiplicative	multiplicative	ADJ
ejpam-4607	189	28	,	,	PUNCT
ejpam-4607	189	29	but	but	CCONJ
ejpam-4607	189	30	we	we	PRON
ejpam-4607	189	31	still	still	ADV
ejpam-4607	189	32	could	could	AUX
ejpam-4607	189	33	not	not	PART
ejpam-4607	189	34	find	find	VERB
ejpam-4607	189	35	a	a	DET
ejpam-4607	189	36	counterexample	counterexample	NOUN
ejpam-4607	189	37	.	.	PUNCT
ejpam-4607	190	1	we	we	PRON
ejpam-4607	190	2	know	know	VERB
ejpam-4607	190	3	the	the	DET
ejpam-4607	190	4	example	example	NOUN
ejpam-4607	190	5	of	of	ADP
ejpam-4607	190	6	two	two	NUM
ejpam-4607	190	7	linearly	linearly	ADV
ejpam-4607	190	8	ordered	order	VERB
ejpam-4607	190	9	topological	topological	ADJ
ejpam-4607	190	10	spaces	space	NOUN
ejpam-4607	190	11	whose	whose	DET
ejpam-4607	190	12	product	product	NOUN
ejpam-4607	190	13	is	be	AUX
ejpam-4607	190	14	not	not	PART
ejpam-4607	190	15	κ	κ	NOUN
ejpam-4607	190	16	-	-	ADJ
ejpam-4607	190	17	normal	normal	ADJ
ejpam-4607	190	18	(	(	PUNCT
ejpam-4607	190	19	mildly	mildly	ADV
ejpam-4607	190	20	normal	normal	ADJ
ejpam-4607	190	21	)	)	PUNCT
ejpam-4607	190	22	was	be	AUX
ejpam-4607	190	23	given	give	VERB
ejpam-4607	190	24	in	in	ADP
ejpam-4607	190	25	[	[	X
ejpam-4607	190	26	14	14	NUM
ejpam-4607	190	27	]	]	PUNCT
ejpam-4607	190	28	.	.	PUNCT
ejpam-4607	191	1	this	this	DET
ejpam-4607	191	2	space	space	NOUN
ejpam-4607	191	3	turns	turn	VERB
ejpam-4607	191	4	out	out	ADP
ejpam-4607	191	5	to	to	PART
ejpam-4607	191	6	be	be	AUX
ejpam-4607	191	7	c	c	NOUN
ejpam-4607	191	8	-	-	PUNCT
ejpam-4607	191	9	κ	κ	NOUN
ejpam-4607	191	10	-	-	NOUN
ejpam-4607	191	11	normal	normal	ADJ
ejpam-4607	191	12	.	.	PUNCT
ejpam-4607	192	1	here	here	ADV
ejpam-4607	192	2	is	be	AUX
ejpam-4607	192	3	an	an	DET
ejpam-4607	192	4	example	example	NOUN
ejpam-4607	192	5	.	.	PUNCT
ejpam-4607	193	1	example	example	NOUN
ejpam-4607	194	1	5	5	NUM
ejpam-4607	194	2	.	.	PUNCT
ejpam-4607	195	1	we	we	PRON
ejpam-4607	195	2	will	will	AUX
ejpam-4607	195	3	define	define	VERB
ejpam-4607	195	4	a	a	DET
ejpam-4607	195	5	hausdorff	hausdorff	NOUN
ejpam-4607	195	6	compact	compact	ADJ
ejpam-4607	195	7	linearly	linearly	ADV
ejpam-4607	195	8	ordered	order	VERB
ejpam-4607	195	9	space	space	NOUN
ejpam-4607	195	10	y	y	PROPN
ejpam-4607	195	11	such	such	ADJ
ejpam-4607	195	12	that	that	PRON
ejpam-4607	195	13	ω1×y	ω1×y	VERB
ejpam-4607	195	14	is	be	AUX
ejpam-4607	195	15	c	c	NOUN
ejpam-4607	195	16	-	-	PUNCT
ejpam-4607	195	17	κ	κ	NOUN
ejpam-4607	195	18	-	-	ADJ
ejpam-4607	195	19	normal	normal	ADJ
ejpam-4607	195	20	.	.	PUNCT
ejpam-4607	196	1	let	let	AUX
ejpam-4607	196	2	{	{	PUNCT
ejpam-4607	196	3	yn	yn	X
ejpam-4607	196	4	:	:	PUNCT
ejpam-4607	196	5	n	n	CCONJ
ejpam-4607	196	6	<	<	X
ejpam-4607	196	7	ω0	ω0	PROPN
ejpam-4607	196	8	}	}	PUNCT
ejpam-4607	196	9	be	be	AUX
ejpam-4607	196	10	a	a	DET
ejpam-4607	196	11	countably	countably	ADV
ejpam-4607	196	12	infinite	infinite	ADJ
ejpam-4607	196	13	set	set	NOUN
ejpam-4607	196	14	such	such	ADJ
ejpam-4607	196	15	that	that	SCONJ
ejpam-4607	196	16	{	{	PUNCT
ejpam-4607	196	17	yn	yn	X
ejpam-4607	196	18	:	:	PUNCT
ejpam-4607	196	19	n	n	CCONJ
ejpam-4607	196	20	<	<	X
ejpam-4607	196	21	ω0	ω0	PROPN
ejpam-4607	196	22	}	}	PUNCT
ejpam-4607	196	23	∩	∩	NOUN
ejpam-4607	196	24	(	(	PUNCT
ejpam-4607	196	25	ω1	ω1	PROPN
ejpam-4607	196	26	+	+	CCONJ
ejpam-4607	196	27	1	1	NUM
ejpam-4607	196	28	)	)	PUNCT
ejpam-4607	196	29	=	=	VERB
ejpam-4607	196	30	∅.	∅.	AUX
ejpam-4607	196	31	let	let	VERB
ejpam-4607	196	32	y	y	PROPN
ejpam-4607	196	33	=	=	PRON
ejpam-4607	196	34	{	{	PUNCT
ejpam-4607	196	35	yn	yn	X
ejpam-4607	196	36	:	:	PUNCT
ejpam-4607	196	37	n	n	PROPN
ejpam-4607	196	38	<	<	X
ejpam-4607	196	39	ω0	ω0	PROPN
ejpam-4607	196	40	}	}	PUNCT
ejpam-4607	196	41	∪	∪	X
ejpam-4607	196	42	(	(	PUNCT
ejpam-4607	196	43	ω1	ω1	PROPN
ejpam-4607	196	44	+	+	CCONJ
ejpam-4607	196	45	1	1	NUM
ejpam-4607	196	46	)	)	PUNCT
ejpam-4607	196	47	.	.	PUNCT
ejpam-4607	197	1	let	let	VERB
ejpam-4607	197	2	τ	τ	PRON
ejpam-4607	197	3	be	be	AUX
ejpam-4607	197	4	the	the	DET
ejpam-4607	197	5	topology	topology	NOUN
ejpam-4607	197	6	on	on	ADP
ejpam-4607	197	7	y	y	PROPN
ejpam-4607	197	8	generated	generate	VERB
ejpam-4607	197	9	by	by	ADP
ejpam-4607	197	10	the	the	DET
ejpam-4607	197	11	following	follow	VERB
ejpam-4607	197	12	neighborhood	neighborhood	NOUN
ejpam-4607	197	13	system	system	NOUN
ejpam-4607	197	14	:	:	PUNCT
ejpam-4607	197	15	for	for	ADP
ejpam-4607	197	16	an	an	DET
ejpam-4607	197	17	α	α	PROPN
ejpam-4607	197	18	∈	∈	PROPN
ejpam-4607	197	19	ω1	ω1	PROPN
ejpam-4607	197	20	,	,	PUNCT
ejpam-4607	197	21	a	a	DET
ejpam-4607	197	22	basic	basic	ADJ
ejpam-4607	197	23	open	open	ADJ
ejpam-4607	197	24	neighborhood	neighborhood	NOUN
ejpam-4607	197	25	of	of	ADP
ejpam-4607	197	26	α	α	PROPN
ejpam-4607	197	27	is	be	AUX
ejpam-4607	197	28	the	the	DET
ejpam-4607	197	29	same	same	ADJ
ejpam-4607	197	30	as	as	ADP
ejpam-4607	197	31	in	in	ADP
ejpam-4607	197	32	ω1	ω1	PROPN
ejpam-4607	197	33	with	with	ADP
ejpam-4607	197	34	its	its	PRON
ejpam-4607	197	35	usual	usual	ADJ
ejpam-4607	197	36	order	order	NOUN
ejpam-4607	197	37	topology	topology	NOUN
ejpam-4607	197	38	.	.	PUNCT
ejpam-4607	198	1	for	for	ADP
ejpam-4607	198	2	n	n	PRON
ejpam-4607	198	3	∈	∈	PROPN
ejpam-4607	198	4	ω0	ω0	NOUN
ejpam-4607	198	5	,	,	PUNCT
ejpam-4607	198	6	a	a	DET
ejpam-4607	198	7	basic	basic	ADJ
ejpam-4607	198	8	open	open	ADJ
ejpam-4607	198	9	neighborhood	neighborhood	NOUN
ejpam-4607	198	10	of	of	ADP
ejpam-4607	198	11	yn	yn	PRON
ejpam-4607	198	12	is	be	AUX
ejpam-4607	198	13	{	{	PUNCT
ejpam-4607	198	14	yn	yn	NOUN
ejpam-4607	198	15	}	}	PUNCT
ejpam-4607	198	16	.	.	PUNCT
ejpam-4607	199	1	a	a	DET
ejpam-4607	199	2	basic	basic	ADJ
ejpam-4607	199	3	open	open	ADJ
ejpam-4607	199	4	neighborhood	neighborhood	NOUN
ejpam-4607	199	5	of	of	ADP
ejpam-4607	199	6	ω1	ω1	PROPN
ejpam-4607	199	7	is	be	AUX
ejpam-4607	199	8	of	of	ADP
ejpam-4607	199	9	the	the	DET
ejpam-4607	199	10	form	form	NOUN
ejpam-4607	199	11	(	(	PUNCT
ejpam-4607	199	12	α	α	NOUN
ejpam-4607	199	13	,	,	PUNCT
ejpam-4607	199	14	ω1	ω1	PROPN
ejpam-4607	199	15	]	]	PUNCT
ejpam-4607	199	16	∪	∪	X
ejpam-4607	199	17	{	{	PUNCT
ejpam-4607	199	18	yn	yn	NOUN
ejpam-4607	199	19	:	:	PUNCT
ejpam-4607	199	20	n	n	PRON
ejpam-4607	199	21	≥	≥	X
ejpam-4607	199	22	k	k	X
ejpam-4607	199	23	}	}	PUNCT
ejpam-4607	199	24	where	where	SCONJ
ejpam-4607	199	25	α	α	PRON
ejpam-4607	199	26	<	<	X
ejpam-4607	199	27	ω1	ω1	PROPN
ejpam-4607	199	28	and	and	CCONJ
ejpam-4607	199	29	k	k	PROPN
ejpam-4607	199	30	∈	∈	PROPN
ejpam-4607	199	31	ω0	ω0	NOUN
ejpam-4607	199	32	.	.	PUNCT
ejpam-4607	200	1	in	in	ADP
ejpam-4607	200	2	other	other	ADJ
ejpam-4607	200	3	words	word	NOUN
ejpam-4607	200	4	,	,	PUNCT
ejpam-4607	200	5	{	{	PUNCT
ejpam-4607	200	6	yn	yn	X
ejpam-4607	200	7	:	:	PUNCT
ejpam-4607	200	8	n	n	PROPN
ejpam-4607	200	9	<	<	X
ejpam-4607	200	10	ω0	ω0	PROPN
ejpam-4607	200	11	}	}	PUNCT
ejpam-4607	200	12	is	be	AUX
ejpam-4607	200	13	a	a	DET
ejpam-4607	200	14	sequence	sequence	NOUN
ejpam-4607	200	15	of	of	ADP
ejpam-4607	200	16	isolated	isolated	ADJ
ejpam-4607	200	17	points	point	NOUN
ejpam-4607	200	18	which	which	PRON
ejpam-4607	200	19	converges	converge	VERB
ejpam-4607	200	20	to	to	ADP
ejpam-4607	200	21	ω1	ω1	PROPN
ejpam-4607	200	22	.	.	PUNCT
ejpam-4607	201	1	note	note	VERB
ejpam-4607	201	2	that	that	SCONJ
ejpam-4607	201	3	if	if	SCONJ
ejpam-4607	201	4	we	we	PRON
ejpam-4607	201	5	define	define	VERB
ejpam-4607	201	6	an	an	DET
ejpam-4607	201	7	order	order	NOUN
ejpam-4607	201	8	<	<	X
ejpam-4607	201	9	on	on	ADP
ejpam-4607	201	10	y	y	PROPN
ejpam-4607	201	11	as	as	SCONJ
ejpam-4607	201	12	follows	follow	VERB
ejpam-4607	201	13	:	:	PUNCT
ejpam-4607	201	14	for	for	ADP
ejpam-4607	201	15	each	each	DET
ejpam-4607	201	16	n	n	PRON
ejpam-4607	201	17	∈	∈	PROPN
ejpam-4607	201	18	ω0	ω0	NOUN
ejpam-4607	201	19	,	,	PUNCT
ejpam-4607	201	20	ω1	ω1	PROPN
ejpam-4607	201	21	<	<	X
ejpam-4607	201	22	yn+1	yn+1	PROPN
ejpam-4607	201	23	<	<	X
ejpam-4607	201	24	yn	yn	PROPN
ejpam-4607	201	25	,	,	PUNCT
ejpam-4607	201	26	and	and	CCONJ
ejpam-4607	201	27	<	<	X
ejpam-4607	201	28	on	on	ADP
ejpam-4607	201	29	ω1	ω1	PROPN
ejpam-4607	201	30	+	+	CCONJ
ejpam-4607	201	31	1	1	NUM
ejpam-4607	201	32	is	be	AUX
ejpam-4607	201	33	the	the	DET
ejpam-4607	201	34	same	same	ADJ
ejpam-4607	201	35	as	as	ADP
ejpam-4607	201	36	the	the	DET
ejpam-4607	201	37	usual	usual	ADJ
ejpam-4607	201	38	order	order	NOUN
ejpam-4607	201	39	on	on	ADP
ejpam-4607	201	40	ω1	ω1	PROPN
ejpam-4607	201	41	+	+	CCONJ
ejpam-4607	201	42	1	1	NUM
ejpam-4607	201	43	,	,	PUNCT
ejpam-4607	201	44	then	then	ADV
ejpam-4607	201	45	(	(	PUNCT
ejpam-4607	201	46	y	y	PROPN
ejpam-4607	201	47	,	,	PUNCT
ejpam-4607	201	48	τ	τ	PROPN
ejpam-4607	201	49	)	)	PUNCT
ejpam-4607	201	50	is	be	AUX
ejpam-4607	201	51	a	a	DET
ejpam-4607	201	52	linearly	linearly	ADV
ejpam-4607	201	53	ordered	order	VERB
ejpam-4607	201	54	topological	topological	ADJ
ejpam-4607	201	55	space	space	NOUN
ejpam-4607	201	56	.	.	PUNCT
ejpam-4607	202	1	it	it	PRON
ejpam-4607	202	2	was	be	AUX
ejpam-4607	202	3	shown	show	VERB
ejpam-4607	202	4	in	in	ADP
ejpam-4607	202	5	[	[	X
ejpam-4607	202	6	14	14	NUM
ejpam-4607	202	7	]	]	PUNCT
ejpam-4607	202	8	that	that	SCONJ
ejpam-4607	202	9	(	(	PUNCT
ejpam-4607	202	10	y	y	PROPN
ejpam-4607	202	11	,	,	PUNCT
ejpam-4607	202	12	τ	τ	PROPN
ejpam-4607	202	13	)	)	PUNCT
ejpam-4607	202	14	is	be	AUX
ejpam-4607	202	15	a	a	DET
ejpam-4607	202	16	hausdorff	hausdorff	ADJ
ejpam-4607	202	17	compact	compact	ADJ
ejpam-4607	202	18	space	space	NOUN
ejpam-4607	202	19	,	,	PUNCT
ejpam-4607	202	20	hence	hence	ADV
ejpam-4607	202	21	it	it	PRON
ejpam-4607	202	22	is	be	AUX
ejpam-4607	202	23	mildly	mildly	ADV
ejpam-4607	202	24	normal	normal	ADJ
ejpam-4607	202	25	.	.	PUNCT
ejpam-4607	203	1	also	also	ADV
ejpam-4607	203	2	,	,	PUNCT
ejpam-4607	203	3	it	it	PRON
ejpam-4607	203	4	is	be	AUX
ejpam-4607	203	5	well	well	ADV
ejpam-4607	203	6	known	know	VERB
ejpam-4607	203	7	that	that	SCONJ
ejpam-4607	203	8	ω1	ω1	PROPN
ejpam-4607	203	9	is	be	AUX
ejpam-4607	203	10	a	a	DET
ejpam-4607	203	11	hausdorff	hausdorff	NOUN
ejpam-4607	203	12	normal	normal	ADJ
ejpam-4607	203	13	space	space	NOUN
ejpam-4607	203	14	and	and	CCONJ
ejpam-4607	203	15	hence	hence	ADV
ejpam-4607	203	16	mildly	mildly	ADV
ejpam-4607	203	17	normal	normal	ADJ
ejpam-4607	203	18	.	.	PUNCT
ejpam-4607	204	1	but	but	CCONJ
ejpam-4607	204	2	ω1	ω1	PROPN
ejpam-4607	204	3	×	×	PROPN
ejpam-4607	204	4	y	y	PROPN
ejpam-4607	204	5	is	be	AUX
ejpam-4607	204	6	not	not	PART
ejpam-4607	204	7	mildly	mildly	ADV
ejpam-4607	204	8	normal	normal	ADJ
ejpam-4607	204	9	[	[	X
ejpam-4607	204	10	14	14	NUM
ejpam-4607	204	11	]	]	PUNCT
ejpam-4607	204	12	.	.	PUNCT
ejpam-4607	205	1	a	a	DET
ejpam-4607	205	2	similar	similar	ADJ
ejpam-4607	205	3	proof	proof	NOUN
ejpam-4607	205	4	as	as	ADP
ejpam-4607	205	5	in	in	ADP
ejpam-4607	205	6	[	[	X
ejpam-4607	205	7	15	15	NUM
ejpam-4607	205	8	]	]	PUNCT
ejpam-4607	205	9	shows	show	VERB
ejpam-4607	205	10	that	that	SCONJ
ejpam-4607	205	11	ω1	ω1	PROPN
ejpam-4607	205	12	×	×	PROPN
ejpam-4607	205	13	y	y	PROPN
ejpam-4607	205	14	is	be	AUX
ejpam-4607	205	15	c	c	NOUN
ejpam-4607	205	16	-	-	PUNCT
ejpam-4607	205	17	κ	κ	NOUN
ejpam-4607	205	18	-	-	NOUN
ejpam-4607	205	19	normal	normal	ADJ
ejpam-4607	205	20	.	.	PUNCT
ejpam-4607	206	1	here	here	ADV
ejpam-4607	206	2	are	be	AUX
ejpam-4607	206	3	cases	case	NOUN
ejpam-4607	206	4	when	when	SCONJ
ejpam-4607	206	5	the	the	DET
ejpam-4607	206	6	product	product	NOUN
ejpam-4607	206	7	of	of	ADP
ejpam-4607	206	8	two	two	NUM
ejpam-4607	206	9	c	c	NOUN
ejpam-4607	206	10	-	-	PUNCT
ejpam-4607	206	11	κ	κ	NOUN
ejpam-4607	206	12	-	-	ADJ
ejpam-4607	206	13	normal	normal	ADJ
ejpam-4607	206	14	spaces	space	NOUN
ejpam-4607	206	15	will	will	AUX
ejpam-4607	206	16	be	be	AUX
ejpam-4607	206	17	c	c	NOUN
ejpam-4607	206	18	-	-	PUNCT
ejpam-4607	206	19	κ	κ	NOUN
ejpam-4607	206	20	-	-	ADJ
ejpam-4607	206	21	normal	normal	ADJ
ejpam-4607	206	22	.	.	PUNCT
ejpam-4607	207	1	since	since	SCONJ
ejpam-4607	207	2	the	the	DET
ejpam-4607	207	3	product	product	NOUN
ejpam-4607	207	4	of	of	ADP
ejpam-4607	207	5	ordinals	ordinal	NOUN
ejpam-4607	207	6	is	be	AUX
ejpam-4607	207	7	always	always	ADV
ejpam-4607	207	8	κ	κ	NOUN
ejpam-4607	207	9	-	-	ADJ
ejpam-4607	207	10	normal	normal	ADJ
ejpam-4607	207	11	(	(	PUNCT
ejpam-4607	207	12	mildly	mildly	ADV
ejpam-4607	207	13	normal	normal	ADJ
ejpam-4607	207	14	)	)	PUNCT
ejpam-4607	208	1	[	[	X
ejpam-4607	208	2	18	18	NUM
ejpam-4607	208	3	]	]	PUNCT
ejpam-4607	208	4	,	,	PUNCT
ejpam-4607	208	5	we	we	PRON
ejpam-4607	208	6	conclude	conclude	VERB
ejpam-4607	208	7	the	the	DET
ejpam-4607	208	8	following	follow	VERB
ejpam-4607	208	9	theorem	theorem	PROPN
ejpam-4607	208	10	.	.	PUNCT
ejpam-4607	208	11	theorem	theorem	PROPN
ejpam-4607	208	12	7	7	NUM
ejpam-4607	208	13	.	.	PUNCT
ejpam-4607	209	1	the	the	DET
ejpam-4607	209	2	product	product	NOUN
ejpam-4607	209	3	of	of	ADP
ejpam-4607	209	4	ordinals	ordinal	NOUN
ejpam-4607	209	5	is	be	AUX
ejpam-4607	209	6	c	c	NOUN
ejpam-4607	209	7	-	-	PUNCT
ejpam-4607	209	8	κ	κ	NOUN
ejpam-4607	209	9	-	-	ADJ
ejpam-4607	209	10	normal	normal	ADJ
ejpam-4607	209	11	(	(	PUNCT
ejpam-4607	209	12	c	c	NOUN
ejpam-4607	209	13	-	-	PUNCT
ejpam-4607	209	14	mildly	mildly	ADV
ejpam-4607	209	15	normal	normal	ADJ
ejpam-4607	209	16	)	)	PUNCT
ejpam-4607	209	17	.	.	PUNCT
ejpam-4607	210	1	l.	l.	PROPN
ejpam-4607	210	2	kalantan	kalantan	PROPN
ejpam-4607	210	3	,	,	PUNCT
ejpam-4607	210	4	a.alawadi	a.alawadi	NOUN
ejpam-4607	210	5	,	,	PUNCT
ejpam-4607	210	6	s.thabit	s.thabit	NOUN
ejpam-4607	210	7	/	/	SYM
ejpam-4607	210	8	eur	eur	PROPN
ejpam-4607	210	9	.	.	PUNCT
ejpam-4607	211	1	j.	j.	PROPN
ejpam-4607	211	2	pure	pure	PROPN
ejpam-4607	211	3	appl	appl	PROPN
ejpam-4607	211	4	.	.	PROPN
ejpam-4607	211	5	math	math	PROPN
ejpam-4607	211	6	,	,	PUNCT
ejpam-4607	211	7	16	16	NUM
ejpam-4607	211	8	(	(	PUNCT
ejpam-4607	211	9	1	1	NUM
ejpam-4607	211	10	)	)	PUNCT
ejpam-4607	211	11	(	(	PUNCT
ejpam-4607	211	12	2023	2023	NUM
ejpam-4607	211	13	)	)	PUNCT
ejpam-4607	211	14	,	,	PUNCT
ejpam-4607	211	15	62	62	NUM
ejpam-4607	211	16	-	-	SYM
ejpam-4607	211	17	70	70	NUM
ejpam-4607	211	18	68	68	NUM
ejpam-4607	211	19	theorem	theorem	NOUN
ejpam-4607	211	20	8	8	NUM
ejpam-4607	211	21	.	.	PUNCT
ejpam-4607	212	1	if	if	SCONJ
ejpam-4607	212	2	x	x	PRON
ejpam-4607	212	3	and	and	CCONJ
ejpam-4607	212	4	y	y	PROPN
ejpam-4607	212	5	are	be	AUX
ejpam-4607	212	6	minimal	minimal	ADJ
ejpam-4607	212	7	hausdorff	hausdorff	NOUN
ejpam-4607	212	8	fréchet	fréchet	NOUN
ejpam-4607	212	9	c	c	NOUN
ejpam-4607	212	10	-	-	PUNCT
ejpam-4607	212	11	κ	κ	NOUN
ejpam-4607	212	12	-	-	ADJ
ejpam-4607	212	13	normal	normal	ADJ
ejpam-4607	212	14	,	,	PUNCT
ejpam-4607	212	15	then	then	ADV
ejpam-4607	212	16	x	x	SYM
ejpam-4607	212	17	×	×	PROPN
ejpam-4607	212	18	y	y	PROPN
ejpam-4607	212	19	is	be	AUX
ejpam-4607	212	20	c	c	NOUN
ejpam-4607	212	21	-	-	PUNCT
ejpam-4607	212	22	κ	κ	NOUN
ejpam-4607	212	23	-	-	ADJ
ejpam-4607	212	24	normal	normal	ADJ
ejpam-4607	212	25	.	.	PUNCT
ejpam-4607	213	1	proof	proof	NOUN
ejpam-4607	213	2	.	.	PUNCT
ejpam-4607	214	1	since	since	SCONJ
ejpam-4607	214	2	x	x	PROPN
ejpam-4607	214	3	and	and	CCONJ
ejpam-4607	214	4	y	y	PROPN
ejpam-4607	214	5	are	be	AUX
ejpam-4607	214	6	minimal	minimal	ADJ
ejpam-4607	214	7	hausdorff	hausdorff	NOUN
ejpam-4607	214	8	fréchet	fréchet	NOUN
ejpam-4607	214	9	c	c	NOUN
ejpam-4607	214	10	-	-	PUNCT
ejpam-4607	214	11	κ	κ	NOUN
ejpam-4607	214	12	-	-	ADJ
ejpam-4607	214	13	normal	normal	ADJ
ejpam-4607	214	14	,	,	PUNCT
ejpam-4607	214	15	x	x	PUNCT
ejpam-4607	214	16	and	and	CCONJ
ejpam-4607	214	17	y	y	PROPN
ejpam-4607	214	18	are	be	AUX
ejpam-4607	214	19	t2	t2	NOUN
ejpam-4607	214	20	1	1	NUM
ejpam-4607	214	21	2	2	NUM
ejpam-4607	214	22	[	[	X
ejpam-4607	214	23	2	2	NUM
ejpam-4607	214	24	]	]	PUNCT
ejpam-4607	214	25	.	.	PUNCT
ejpam-4607	215	1	since	since	SCONJ
ejpam-4607	215	2	the	the	DET
ejpam-4607	215	3	t2	t2	NOUN
ejpam-4607	215	4	1	1	NUM
ejpam-4607	215	5	2	2	NUM
ejpam-4607	215	6	is	be	AUX
ejpam-4607	215	7	multiplicative	multiplicative	ADJ
ejpam-4607	215	8	,	,	PUNCT
ejpam-4607	215	9	the	the	DET
ejpam-4607	215	10	product	product	NOUN
ejpam-4607	215	11	space	space	NOUN
ejpam-4607	215	12	is	be	AUX
ejpam-4607	215	13	t2	t2	NOUN
ejpam-4607	215	14	1	1	NUM
ejpam-4607	215	15	2	2	NUM
ejpam-4607	215	16	.	.	PUNCT
ejpam-4607	216	1	so	so	ADV
ejpam-4607	216	2	x×y	x×y	PROPN
ejpam-4607	216	3	is	be	AUX
ejpam-4607	216	4	t2	t2	NOUN
ejpam-4607	216	5	1	1	NUM
ejpam-4607	216	6	2	2	NUM
ejpam-4607	216	7	minimal	minimal	ADJ
ejpam-4607	216	8	hausdorff	hausdorff	NOUN
ejpam-4607	216	9	space	space	NOUN
ejpam-4607	216	10	implies	imply	VERB
ejpam-4607	216	11	that	that	SCONJ
ejpam-4607	216	12	x	x	SYM
ejpam-4607	216	13	×	×	NOUN
ejpam-4607	216	14	y	y	PROPN
ejpam-4607	216	15	is	be	AUX
ejpam-4607	216	16	t2	t2	NOUN
ejpam-4607	216	17	compact	compact	ADJ
ejpam-4607	216	18	,	,	PUNCT
ejpam-4607	216	19	hence	hence	ADV
ejpam-4607	216	20	c	c	NOUN
ejpam-4607	216	21	-	-	PUNCT
ejpam-4607	216	22	κ	κ	NOUN
ejpam-4607	216	23	-	-	ADJ
ejpam-4607	216	24	normal	normal	ADJ
ejpam-4607	216	25	.	.	PUNCT
ejpam-4607	217	1	theorem	theorem	VERB
ejpam-4607	217	2	9	9	NUM
ejpam-4607	217	3	.	.	PUNCT
ejpam-4607	218	1	if	if	SCONJ
ejpam-4607	218	2	x	x	PRON
ejpam-4607	218	3	is	be	AUX
ejpam-4607	218	4	fréchet	fréchet	ADJ
ejpam-4607	218	5	and	and	CCONJ
ejpam-4607	218	6	countably	countably	ADV
ejpam-4607	218	7	compact	compact	ADJ
ejpam-4607	218	8	c	c	NOUN
ejpam-4607	218	9	-	-	PUNCT
ejpam-4607	218	10	κ	κ	PRON
ejpam-4607	218	11	-	-	ADJ
ejpam-4607	218	12	normal	normal	ADJ
ejpam-4607	218	13	space	space	NOUN
ejpam-4607	218	14	,	,	PUNCT
ejpam-4607	218	15	and	and	CCONJ
ejpam-4607	218	16	z	z	NOUN
ejpam-4607	218	17	is	be	AUX
ejpam-4607	218	18	t2	t2	NOUN
ejpam-4607	218	19	paracompact	paracompact	NOUN
ejpam-4607	218	20	first	first	ADJ
ejpam-4607	218	21	countable	countable	ADJ
ejpam-4607	218	22	space	space	NOUN
ejpam-4607	218	23	then	then	ADV
ejpam-4607	218	24	x	x	SYM
ejpam-4607	218	25	×	×	PROPN
ejpam-4607	218	26	z	z	NOUN
ejpam-4607	218	27	is	be	AUX
ejpam-4607	218	28	c	c	NOUN
ejpam-4607	218	29	-	-	PUNCT
ejpam-4607	218	30	κ	κ	NOUN
ejpam-4607	218	31	-	-	ADJ
ejpam-4607	218	32	normal	normal	ADJ
ejpam-4607	218	33	.	.	PUNCT
ejpam-4607	219	1	proof	proof	NOUN
ejpam-4607	219	2	.	.	PUNCT
ejpam-4607	220	1	let	let	VERB
ejpam-4607	220	2	y	y	PRON
ejpam-4607	220	3	be	be	AUX
ejpam-4607	220	4	a	a	DET
ejpam-4607	220	5	κ	κ	NOUN
ejpam-4607	220	6	-	-	ADJ
ejpam-4607	220	7	normal	normal	ADJ
ejpam-4607	220	8	space	space	NOUN
ejpam-4607	220	9	,	,	PUNCT
ejpam-4607	220	10	f	f	X
ejpam-4607	220	11	:	:	PUNCT
ejpam-4607	220	12	x	x	PUNCT
ejpam-4607	220	13	−→	−→	NOUN
ejpam-4607	220	14	y	y	NOUN
ejpam-4607	220	15	be	be	AUX
ejpam-4607	220	16	a	a	DET
ejpam-4607	220	17	bijective	bijective	ADJ
ejpam-4607	220	18	function	function	NOUN
ejpam-4607	220	19	such	such	ADJ
ejpam-4607	220	20	that	that	SCONJ
ejpam-4607	220	21	the	the	DET
ejpam-4607	220	22	restriction	restriction	NOUN
ejpam-4607	220	23	on	on	ADP
ejpam-4607	220	24	any	any	DET
ejpam-4607	220	25	compact	compact	ADJ
ejpam-4607	220	26	subspace	subspace	NOUN
ejpam-4607	220	27	is	be	AUX
ejpam-4607	220	28	a	a	DET
ejpam-4607	220	29	homeomorphism	homeomorphism	NOUN
ejpam-4607	220	30	.	.	PUNCT
ejpam-4607	221	1	now	now	ADV
ejpam-4607	221	2	,	,	PUNCT
ejpam-4607	221	3	x	x	PRON
ejpam-4607	221	4	is	be	AUX
ejpam-4607	221	5	fréchet	fréchet	VERB
ejpam-4607	221	6	gives	give	VERB
ejpam-4607	221	7	that	that	SCONJ
ejpam-4607	221	8	f	f	PROPN
ejpam-4607	221	9	is	be	AUX
ejpam-4607	221	10	continuous	continuous	ADJ
ejpam-4607	221	11	,	,	PUNCT
ejpam-4607	221	12	see	see	ADJ
ejpam-4607	221	13	theorem	theorem	NOUN
ejpam-4607	221	14	1	1	NUM
ejpam-4607	221	15	.	.	PUNCT
ejpam-4607	222	1	since	since	SCONJ
ejpam-4607	222	2	x	x	PRON
ejpam-4607	222	3	is	be	AUX
ejpam-4607	222	4	countably	countably	ADV
ejpam-4607	222	5	compact	compact	ADJ
ejpam-4607	222	6	and	and	CCONJ
ejpam-4607	222	7	f	f	PROPN
ejpam-4607	222	8	continuous	continuous	ADJ
ejpam-4607	222	9	surjective	surjective	NOUN
ejpam-4607	222	10	,	,	PUNCT
ejpam-4607	222	11	we	we	PRON
ejpam-4607	222	12	have	have	VERB
ejpam-4607	222	13	y	y	PROPN
ejpam-4607	222	14	is	be	AUX
ejpam-4607	222	15	countably	countably	ADV
ejpam-4607	222	16	compact	compact	ADJ
ejpam-4607	222	17	κ	κ	NOUN
ejpam-4607	222	18	-	-	ADJ
ejpam-4607	222	19	normal	normal	ADJ
ejpam-4607	222	20	.	.	PUNCT
ejpam-4607	223	1	since	since	SCONJ
ejpam-4607	223	2	a	a	DET
ejpam-4607	223	3	product	product	NOUN
ejpam-4607	223	4	of	of	ADP
ejpam-4607	223	5	a	a	DET
ejpam-4607	223	6	countably	countably	ADV
ejpam-4607	223	7	compact	compact	ADJ
ejpam-4607	223	8	κ	κ	NOUN
ejpam-4607	223	9	-	-	ADJ
ejpam-4607	223	10	normal	normal	ADJ
ejpam-4607	223	11	space	space	NOUN
ejpam-4607	223	12	with	with	ADP
ejpam-4607	223	13	a	a	DET
ejpam-4607	223	14	paracompact	paracompact	ADJ
ejpam-4607	223	15	first	first	ADJ
ejpam-4607	223	16	countable	countable	ADJ
ejpam-4607	223	17	space	space	NOUN
ejpam-4607	223	18	is	be	AUX
ejpam-4607	223	19	κ	κ	NOUN
ejpam-4607	223	20	-	-	ADJ
ejpam-4607	223	21	normal	normal	ADJ
ejpam-4607	223	22	,	,	PUNCT
ejpam-4607	223	23	y	y	PROPN
ejpam-4607	223	24	×	×	PROPN
ejpam-4607	223	25	z	z	PROPN
ejpam-4607	223	26	is	be	AUX
ejpam-4607	223	27	κ	κ	NOUN
ejpam-4607	223	28	-	-	ADJ
ejpam-4607	223	29	normal	normal	ADJ
ejpam-4607	223	30	[	[	X
ejpam-4607	223	31	14	14	NUM
ejpam-4607	223	32	]	]	PUNCT
ejpam-4607	223	33	.	.	PUNCT
ejpam-4607	224	1	now	now	ADV
ejpam-4607	224	2	,	,	PUNCT
ejpam-4607	224	3	define	define	VERB
ejpam-4607	224	4	g	g	NOUN
ejpam-4607	224	5	:	:	PUNCT
ejpam-4607	224	6	x	x	SYM
ejpam-4607	224	7	×	×	NOUN
ejpam-4607	224	8	z	z	NOUN
ejpam-4607	224	9	−→	−→	NOUN
ejpam-4607	224	10	y	y	PROPN
ejpam-4607	224	11	×	×	PROPN
ejpam-4607	224	12	z	z	PROPN
ejpam-4607	224	13	by	by	ADP
ejpam-4607	224	14	g(⟨x	g(⟨x	NOUN
ejpam-4607	224	15	,	,	PUNCT
ejpam-4607	224	16	i⟩	i⟩	PUNCT
ejpam-4607	224	17	)	)	PUNCT
ejpam-4607	225	1	=	=	SYM
ejpam-4607	225	2	⟨f(x	⟨f(x	NOUN
ejpam-4607	225	3	)	)	PUNCT
ejpam-4607	225	4	,	,	PUNCT
ejpam-4607	225	5	i⟩.	i⟩.	NOUN
ejpam-4607	225	6	then	then	ADV
ejpam-4607	225	7	g	g	PROPN
ejpam-4607	225	8	is	be	AUX
ejpam-4607	225	9	a	a	DET
ejpam-4607	225	10	bijective	bijective	ADJ
ejpam-4607	225	11	function	function	NOUN
ejpam-4607	225	12	and	and	CCONJ
ejpam-4607	226	1	g	g	NOUN
ejpam-4607	226	2	=	=	SYM
ejpam-4607	226	3	f	f	PROPN
ejpam-4607	226	4	×	×	PROPN
ejpam-4607	226	5	idz	idz	PROPN
ejpam-4607	226	6	,	,	PUNCT
ejpam-4607	226	7	where	where	SCONJ
ejpam-4607	226	8	idz	idz	NOUN
ejpam-4607	226	9	is	be	AUX
ejpam-4607	226	10	the	the	DET
ejpam-4607	226	11	identity	identity	NOUN
ejpam-4607	226	12	function	function	NOUN
ejpam-4607	226	13	on	on	ADP
ejpam-4607	226	14	z.	z.	PROPN
ejpam-4607	226	15	let	let	VERB
ejpam-4607	226	16	c	c	PRON
ejpam-4607	226	17	be	be	AUX
ejpam-4607	226	18	any	any	DET
ejpam-4607	226	19	compact	compact	ADJ
ejpam-4607	226	20	subspace	subspace	NOUN
ejpam-4607	226	21	of	of	ADP
ejpam-4607	226	22	x	x	SYM
ejpam-4607	226	23	×	×	PROPN
ejpam-4607	226	24	z.	z.	PROPN
ejpam-4607	226	25	then	then	ADV
ejpam-4607	226	26	c	c	PROPN
ejpam-4607	226	27	⊆	⊆	NUM
ejpam-4607	226	28	p1(c	p1(c	SYM
ejpam-4607	226	29	)	)	PUNCT
ejpam-4607	226	30	×	×	NOUN
ejpam-4607	226	31	p2(c	p2(c	PROPN
ejpam-4607	226	32	)	)	PUNCT
ejpam-4607	226	33	,	,	PUNCT
ejpam-4607	226	34	where	where	SCONJ
ejpam-4607	226	35	p1	p1	NOUN
ejpam-4607	226	36	and	and	CCONJ
ejpam-4607	226	37	p2	p2	PROPN
ejpam-4607	226	38	are	be	AUX
ejpam-4607	226	39	the	the	DET
ejpam-4607	226	40	usual	usual	ADJ
ejpam-4607	226	41	projection	projection	NOUN
ejpam-4607	226	42	functions	function	NOUN
ejpam-4607	226	43	.	.	PUNCT
ejpam-4607	227	1	p1(c	p1(c	X
ejpam-4607	227	2	)	)	PUNCT
ejpam-4607	227	3	is	be	AUX
ejpam-4607	227	4	a	a	DET
ejpam-4607	227	5	compact	compact	ADJ
ejpam-4607	227	6	subspace	subspace	NOUN
ejpam-4607	227	7	of	of	ADP
ejpam-4607	227	8	x	x	X
ejpam-4607	227	9	and	and	CCONJ
ejpam-4607	227	10	p2(c	p2(c	NUM
ejpam-4607	227	11	)	)	PUNCT
ejpam-4607	227	12	is	be	AUX
ejpam-4607	227	13	a	a	DET
ejpam-4607	227	14	compact	compact	ADJ
ejpam-4607	227	15	subspace	subspace	NOUN
ejpam-4607	227	16	of	of	ADP
ejpam-4607	227	17	z	z	PROPN
ejpam-4607	227	18	,	,	PUNCT
ejpam-4607	227	19	thus	thus	ADV
ejpam-4607	227	20	p1(c	p1(c	X
ejpam-4607	227	21	)	)	PUNCT
ejpam-4607	227	22	×	×	NOUN
ejpam-4607	227	23	p2(c	p2(c	PROPN
ejpam-4607	227	24	)	)	PUNCT
ejpam-4607	227	25	is	be	AUX
ejpam-4607	227	26	a	a	DET
ejpam-4607	227	27	compact	compact	ADJ
ejpam-4607	227	28	subspace	subspace	NOUN
ejpam-4607	227	29	of	of	ADP
ejpam-4607	227	30	x	x	X
ejpam-4607	227	31	×	×	PROPN
ejpam-4607	227	32	z.	z.	PROPN
ejpam-4607	228	1	now	now	ADV
ejpam-4607	228	2	,	,	PUNCT
ejpam-4607	228	3	f|p1(c	f|p1(c	PROPN
ejpam-4607	228	4	)	)	PUNCT
ejpam-4607	228	5	:	:	PUNCT
ejpam-4607	229	1	p1(c	p1(c	X
ejpam-4607	229	2	)	)	PUNCT
ejpam-4607	229	3	−→	−→	NOUN
ejpam-4607	229	4	f(p1(c	f(p1(c	PROPN
ejpam-4607	229	5	)	)	PUNCT
ejpam-4607	229	6	)	)	PUNCT
ejpam-4607	229	7	is	be	AUX
ejpam-4607	229	8	a	a	DET
ejpam-4607	229	9	homeomorphism	homeomorphism	NOUN
ejpam-4607	229	10	and	and	CCONJ
ejpam-4607	229	11	idz|p2(c	idz|p2(c	NOUN
ejpam-4607	229	12	)	)	PUNCT
ejpam-4607	229	13	:	:	PUNCT
ejpam-4607	230	1	p2(c	p2(c	X
ejpam-4607	230	2	)	)	PUNCT
ejpam-4607	230	3	−→	−→	NOUN
ejpam-4607	230	4	p2(c	p2(c	PROPN
ejpam-4607	230	5	)	)	PUNCT
ejpam-4607	230	6	is	be	AUX
ejpam-4607	230	7	a	a	DET
ejpam-4607	230	8	homeomorphism	homeomorphism	NOUN
ejpam-4607	230	9	.	.	PUNCT
ejpam-4607	231	1	thus	thus	ADV
ejpam-4607	231	2	(	(	PUNCT
ejpam-4607	231	3	f	f	PROPN
ejpam-4607	231	4	×	×	PROPN
ejpam-4607	231	5	idz)|(p1(c)×p2(c	idz)|(p1(c)×p2(c	PROPN
ejpam-4607	231	6	)	)	PUNCT
ejpam-4607	231	7	)	)	PUNCT
ejpam-4607	231	8	:	:	PUNCT
ejpam-4607	232	1	p1(c	p1(c	X
ejpam-4607	232	2	)	)	PUNCT
ejpam-4607	232	3	×	×	NOUN
ejpam-4607	232	4	p2(c	p2(c	NOUN
ejpam-4607	232	5	)	)	PUNCT
ejpam-4607	232	6	−→	−→	NOUN
ejpam-4607	232	7	fp1(c)×	fp1(c)×	NOUN
ejpam-4607	232	8	p2(c	p2(c	X
ejpam-4607	232	9	)	)	PUNCT
ejpam-4607	232	10	is	be	AUX
ejpam-4607	232	11	a	a	DET
ejpam-4607	232	12	homeomorphism	homeomorphism	NOUN
ejpam-4607	232	13	.	.	PUNCT
ejpam-4607	233	1	we	we	PRON
ejpam-4607	233	2	conclude	conclude	VERB
ejpam-4607	233	3	that	that	PRON
ejpam-4607	233	4	g|c	g|c	PROPN
ejpam-4607	233	5	:	:	PUNCT
ejpam-4607	234	1	c	c	X
ejpam-4607	234	2	−→	−→	NOUN
ejpam-4607	234	3	g(c	g(c	NOUN
ejpam-4607	234	4	)	)	PUNCT
ejpam-4607	234	5	is	be	AUX
ejpam-4607	234	6	a	a	DET
ejpam-4607	234	7	homeomorphism	homeomorphism	NOUN
ejpam-4607	234	8	because	because	SCONJ
ejpam-4607	234	9	g|c	g|c	PROPN
ejpam-4607	234	10	=	=	PRON
ejpam-4607	234	11	(	(	PUNCT
ejpam-4607	234	12	(	(	PUNCT
ejpam-4607	234	13	f	f	X
ejpam-4607	234	14	×	×	PROPN
ejpam-4607	234	15	idz)|p1(c)×p2(c	idz)|p1(c)×p2(c	PROPN
ejpam-4607	234	16	)	)	PUNCT
ejpam-4607	234	17	)	)	PUNCT
ejpam-4607	235	1	|c	|c	X
ejpam-4607	235	2	.	.	PUNCT
ejpam-4607	236	1	recall	recall	VERB
ejpam-4607	236	2	that	that	SCONJ
ejpam-4607	236	3	a	a	DET
ejpam-4607	236	4	space	space	NOUN
ejpam-4607	236	5	x	x	PUNCT
ejpam-4607	236	6	is	be	AUX
ejpam-4607	236	7	dowker	dowker	NOUN
ejpam-4607	236	8	if	if	SCONJ
ejpam-4607	236	9	x	x	PRON
ejpam-4607	236	10	is	be	AUX
ejpam-4607	236	11	t4	t4	PROPN
ejpam-4607	236	12	and	and	CCONJ
ejpam-4607	236	13	x	x	SYM
ejpam-4607	236	14	×	×	NOUN
ejpam-4607	236	15	i	i	PRON
ejpam-4607	236	16	is	be	AUX
ejpam-4607	236	17	not	not	PART
ejpam-4607	236	18	normal	normal	ADJ
ejpam-4607	236	19	,	,	PUNCT
ejpam-4607	236	20	where	where	SCONJ
ejpam-4607	236	21	i	i	PRON
ejpam-4607	236	22	is	be	AUX
ejpam-4607	236	23	the	the	DET
ejpam-4607	236	24	closed	closed	ADJ
ejpam-4607	236	25	unit	unit	NOUN
ejpam-4607	236	26	interval	interval	NOUN
ejpam-4607	236	27	considered	consider	VERB
ejpam-4607	236	28	with	with	ADP
ejpam-4607	236	29	its	its	PRON
ejpam-4607	236	30	usual	usual	ADJ
ejpam-4607	236	31	metric	metric	ADJ
ejpam-4607	236	32	topology	topology	NOUN
ejpam-4607	236	33	,	,	PUNCT
ejpam-4607	236	34	[	[	X
ejpam-4607	236	35	12	12	NUM
ejpam-4607	236	36	]	]	PUNCT
ejpam-4607	236	37	.	.	PUNCT
ejpam-4607	237	1	dowker	dowker	PROPN
ejpam-4607	237	2	,	,	PUNCT
ejpam-4607	237	3	in	in	ADP
ejpam-4607	237	4	[	[	X
ejpam-4607	237	5	10	10	NUM
ejpam-4607	237	6	]	]	PUNCT
ejpam-4607	237	7	,	,	PUNCT
ejpam-4607	237	8	stated	state	VERB
ejpam-4607	237	9	the	the	DET
ejpam-4607	237	10	following	following	NOUN
ejpam-4607	237	11	theorem	theorem	NOUN
ejpam-4607	237	12	:	:	PUNCT
ejpam-4607	237	13	“	"	PUNCT
ejpam-4607	237	14	a	a	DET
ejpam-4607	237	15	space	space	NOUN
ejpam-4607	237	16	x	x	PUNCT
ejpam-4607	237	17	is	be	AUX
ejpam-4607	237	18	normal	normal	ADJ
ejpam-4607	237	19	and	and	CCONJ
ejpam-4607	237	20	countably	countably	ADV
ejpam-4607	237	21	paracompact	paracompact	ADJ
ejpam-4607	238	1	if	if	SCONJ
ejpam-4607	238	2	and	and	CCONJ
ejpam-4607	238	3	only	only	ADV
ejpam-4607	238	4	if	if	SCONJ
ejpam-4607	238	5	x×	x×	PROPN
ejpam-4607	238	6	i	i	PRON
ejpam-4607	238	7	is	be	AUX
ejpam-4607	238	8	normal	normal	ADJ
ejpam-4607	238	9	”	"	PUNCT
ejpam-4607	238	10	.	.	PUNCT
ejpam-4607	239	1	here	here	ADV
ejpam-4607	239	2	is	be	AUX
ejpam-4607	239	3	a	a	DET
ejpam-4607	239	4	c	c	NOUN
ejpam-4607	239	5	-	-	PUNCT
ejpam-4607	239	6	κ	κ	NOUN
ejpam-4607	239	7	-	-	ADJ
ejpam-4607	239	8	normal	normal	ADJ
ejpam-4607	239	9	version	version	NOUN
ejpam-4607	239	10	,	,	PUNCT
ejpam-4607	239	11	one	one	NUM
ejpam-4607	239	12	direction	direction	NOUN
ejpam-4607	239	13	of	of	ADP
ejpam-4607	239	14	the	the	DET
ejpam-4607	239	15	dowker	dowker	NOUN
ejpam-4607	239	16	’s	’s	PART
ejpam-4607	239	17	theorem	theorem	NOUN
ejpam-4607	239	18	.	.	PUNCT
ejpam-4607	240	1	if	if	SCONJ
ejpam-4607	240	2	c	c	NOUN
ejpam-4607	240	3	-	-	PUNCT
ejpam-4607	240	4	κ	κ	NOUN
ejpam-4607	240	5	-	-	PUNCT
ejpam-4607	240	6	normality	normality	NOUN
ejpam-4607	240	7	is	be	AUX
ejpam-4607	240	8	hereditary	hereditary	ADJ
ejpam-4607	240	9	with	with	ADP
ejpam-4607	240	10	respect	respect	NOUN
ejpam-4607	240	11	to	to	ADP
ejpam-4607	240	12	closed	closed	ADJ
ejpam-4607	240	13	spaces	space	NOUN
ejpam-4607	240	14	,	,	PUNCT
ejpam-4607	240	15	then	then	ADV
ejpam-4607	240	16	the	the	DET
ejpam-4607	240	17	converse	converse	NOUN
ejpam-4607	240	18	will	will	AUX
ejpam-4607	240	19	be	be	AUX
ejpam-4607	240	20	true	true	ADJ
ejpam-4607	240	21	.	.	PUNCT
ejpam-4607	241	1	theorem	theorem	ADJ
ejpam-4607	241	2	10	10	NUM
ejpam-4607	241	3	.	.	PUNCT
ejpam-4607	242	1	if	if	SCONJ
ejpam-4607	242	2	x	x	PRON
ejpam-4607	242	3	is	be	AUX
ejpam-4607	242	4	t1	t1	NUM
ejpam-4607	242	5	fréchet	fréchet	NOUN
ejpam-4607	242	6	c	c	NOUN
ejpam-4607	242	7	-	-	PUNCT
ejpam-4607	242	8	κ	κ	NOUN
ejpam-4607	242	9	-	-	ADJ
ejpam-4607	242	10	normal	normal	ADJ
ejpam-4607	242	11	lindelöf	lindelöf	NOUN
ejpam-4607	242	12	space	space	NOUN
ejpam-4607	242	13	,	,	PUNCT
ejpam-4607	242	14	then	then	ADV
ejpam-4607	242	15	x	x	SYM
ejpam-4607	242	16	×	×	NOUN
ejpam-4607	242	17	i	i	PRON
ejpam-4607	242	18	is	be	AUX
ejpam-4607	242	19	c	c	NOUN
ejpam-4607	242	20	-	-	PUNCT
ejpam-4607	242	21	κ	κ	PRON
ejpam-4607	242	22	-	-	ADJ
ejpam-4607	242	23	normal	normal	ADJ
ejpam-4607	242	24	space	space	NOUN
ejpam-4607	242	25	.	.	PUNCT
ejpam-4607	243	1	proof	proof	NOUN
ejpam-4607	243	2	.	.	PUNCT
ejpam-4607	244	1	let	let	VERB
ejpam-4607	244	2	x	x	PRON
ejpam-4607	244	3	be	be	AUX
ejpam-4607	244	4	a	a	DET
ejpam-4607	244	5	t1	t1	NOUN
ejpam-4607	244	6	fréchet	fréchet	NOUN
ejpam-4607	244	7	c	c	NOUN
ejpam-4607	244	8	-	-	PUNCT
ejpam-4607	244	9	κ	κ	NOUN
ejpam-4607	244	10	-	-	ADJ
ejpam-4607	244	11	normal	normal	ADJ
ejpam-4607	244	12	lindelöf	lindelöf	NOUN
ejpam-4607	244	13	space	space	NOUN
ejpam-4607	244	14	.	.	PUNCT
ejpam-4607	245	1	pick	pick	VERB
ejpam-4607	245	2	a	a	DET
ejpam-4607	245	3	witness	witness	NOUN
ejpam-4607	245	4	function	function	NOUN
ejpam-4607	245	5	f	f	PROPN
ejpam-4607	245	6	and	and	CCONJ
ejpam-4607	245	7	a	a	DET
ejpam-4607	245	8	κ	κ	NOUN
ejpam-4607	245	9	-	-	ADJ
ejpam-4607	245	10	normal	normal	ADJ
ejpam-4607	245	11	space	space	NOUN
ejpam-4607	245	12	y	y	PROPN
ejpam-4607	245	13	.	.	PUNCT
ejpam-4607	246	1	then	then	ADV
ejpam-4607	246	2	by	by	ADP
ejpam-4607	246	3	theorem	theorem	NOUN
ejpam-4607	246	4	1	1	NUM
ejpam-4607	246	5	the	the	DET
ejpam-4607	246	6	witness	witness	NOUN
ejpam-4607	246	7	function	function	NOUN
ejpam-4607	246	8	f	f	NOUN
ejpam-4607	246	9	:	:	PUNCT
ejpam-4607	246	10	x	x	PUNCT
ejpam-4607	246	11	−→	−→	NOUN
ejpam-4607	246	12	y	y	PROPN
ejpam-4607	246	13	is	be	AUX
ejpam-4607	246	14	continuous	continuous	ADJ
ejpam-4607	246	15	and	and	CCONJ
ejpam-4607	246	16	the	the	DET
ejpam-4607	246	17	witness	witness	NOUN
ejpam-4607	246	18	space	space	NOUN
ejpam-4607	246	19	y	y	PROPN
ejpam-4607	246	20	is	be	AUX
ejpam-4607	246	21	t3	t3	PROPN
ejpam-4607	246	22	,	,	PUNCT
ejpam-4607	246	23	[	[	X
ejpam-4607	246	24	2	2	NUM
ejpam-4607	246	25	]	]	PUNCT
ejpam-4607	246	26	.	.	PUNCT
ejpam-4607	247	1	since	since	SCONJ
ejpam-4607	247	2	x	x	PROPN
ejpam-4607	247	3	is	be	AUX
ejpam-4607	247	4	lindelöf	lindelöf	NOUN
ejpam-4607	247	5	and	and	CCONJ
ejpam-4607	247	6	t3	t3	PROPN
ejpam-4607	247	7	,	,	PUNCT
ejpam-4607	247	8	we	we	PRON
ejpam-4607	247	9	get	get	VERB
ejpam-4607	247	10	y	y	PROPN
ejpam-4607	247	11	is	be	AUX
ejpam-4607	247	12	paracompact	paracompact	ADJ
ejpam-4607	247	13	,	,	PUNCT
ejpam-4607	247	14	and	and	CCONJ
ejpam-4607	247	15	hence	hence	ADV
ejpam-4607	247	16	t4	t4	PROPN
ejpam-4607	247	17	.	.	PUNCT
ejpam-4607	248	1	so	so	ADV
ejpam-4607	248	2	,	,	PUNCT
ejpam-4607	248	3	by	by	ADP
ejpam-4607	248	4	dowker	dowker	NOUN
ejpam-4607	248	5	’s	’s	PART
ejpam-4607	248	6	theorem	theorem	NOUN
ejpam-4607	248	7	y	y	PROPN
ejpam-4607	248	8	×	×	PROPN
ejpam-4607	248	9	i	i	PRON
ejpam-4607	248	10	is	be	AUX
ejpam-4607	248	11	t4	t4	PROPN
ejpam-4607	248	12	.	.	PUNCT
ejpam-4607	249	1	by	by	ADP
ejpam-4607	249	2	a	a	DET
ejpam-4607	249	3	similar	similar	ADJ
ejpam-4607	249	4	argument	argument	NOUN
ejpam-4607	249	5	as	as	ADP
ejpam-4607	249	6	in	in	ADP
ejpam-4607	249	7	the	the	DET
ejpam-4607	249	8	proof	proof	NOUN
ejpam-4607	249	9	of	of	ADP
ejpam-4607	249	10	theorem9	theorem9	PROPN
ejpam-4607	249	11	,	,	PUNCT
ejpam-4607	249	12	we	we	PRON
ejpam-4607	249	13	can	can	AUX
ejpam-4607	249	14	prove	prove	VERB
ejpam-4607	249	15	that	that	SCONJ
ejpam-4607	249	16	x	x	PRON
ejpam-4607	249	17	×	×	NOUN
ejpam-4607	249	18	i	i	PRON
ejpam-4607	249	19	is	be	AUX
ejpam-4607	249	20	a	a	DET
ejpam-4607	249	21	c	c	NOUN
ejpam-4607	249	22	-	-	PUNCT
ejpam-4607	249	23	κ	κ	NOUN
ejpam-4607	249	24	-	-	ADJ
ejpam-4607	249	25	normal	normal	ADJ
ejpam-4607	249	26	space	space	NOUN
ejpam-4607	249	27	.	.	PUNCT
ejpam-4607	250	1	recall	recall	VERB
ejpam-4607	250	2	that	that	SCONJ
ejpam-4607	250	3	a	a	DET
ejpam-4607	250	4	space	space	NOUN
ejpam-4607	250	5	x	x	PUNCT
ejpam-4607	250	6	is	be	AUX
ejpam-4607	250	7	called	call	VERB
ejpam-4607	250	8	nearly	nearly	ADV
ejpam-4607	250	9	compact	compact	ADJ
ejpam-4607	250	10	[	[	X
ejpam-4607	250	11	24	24	NUM
ejpam-4607	250	12	]	]	X
ejpam-4607	250	13	if	if	SCONJ
ejpam-4607	250	14	each	each	DET
ejpam-4607	250	15	open	open	ADJ
ejpam-4607	250	16	cover	cover	NOUN
ejpam-4607	250	17	of	of	ADP
ejpam-4607	250	18	x	x	PUNCT
ejpam-4607	250	19	has	have	VERB
ejpam-4607	250	20	a	a	DET
ejpam-4607	250	21	finite	finite	NOUN
ejpam-4607	250	22	subfamily	subfamily	ADV
ejpam-4607	250	23	the	the	DET
ejpam-4607	250	24	interiors	interior	NOUN
ejpam-4607	250	25	of	of	ADP
ejpam-4607	250	26	the	the	DET
ejpam-4607	250	27	closures	closure	NOUN
ejpam-4607	250	28	of	of	ADP
ejpam-4607	250	29	whose	whose	DET
ejpam-4607	250	30	members	member	NOUN
ejpam-4607	250	31	covers	cover	VERB
ejpam-4607	250	32	x.	x.	NOUN
ejpam-4607	250	33	references	reference	VERB
ejpam-4607	250	34	69	69	NUM
ejpam-4607	250	35	theorem	theorem	NOUN
ejpam-4607	250	36	11	11	NUM
ejpam-4607	250	37	.	.	PUNCT
ejpam-4607	251	1	let	let	VERB
ejpam-4607	251	2	x	x	PRON
ejpam-4607	251	3	,	,	PUNCT
ejpam-4607	251	4	y	y	PROPN
ejpam-4607	251	5	are	be	AUX
ejpam-4607	251	6	hausdorff	hausdorff	NOUN
ejpam-4607	251	7	nearly	nearly	ADV
ejpam-4607	251	8	compact	compact	ADJ
ejpam-4607	251	9	c	c	NOUN
ejpam-4607	251	10	-	-	PUNCT
ejpam-4607	251	11	κ	κ	PRON
ejpam-4607	251	12	-	-	ADJ
ejpam-4607	251	13	normal	normal	ADJ
ejpam-4607	251	14	space	space	NOUN
ejpam-4607	251	15	,	,	PUNCT
ejpam-4607	251	16	then	then	ADV
ejpam-4607	251	17	x	x	SYM
ejpam-4607	251	18	×	×	PROPN
ejpam-4607	251	19	y	y	PROPN
ejpam-4607	251	20	is	be	AUX
ejpam-4607	251	21	a	a	DET
ejpam-4607	251	22	c	c	NOUN
ejpam-4607	251	23	-	-	PUNCT
ejpam-4607	251	24	κ	κ	NOUN
ejpam-4607	251	25	-	-	ADJ
ejpam-4607	251	26	normal	normal	ADJ
ejpam-4607	251	27	space	space	NOUN
ejpam-4607	251	28	.	.	PUNCT
ejpam-4607	252	1	proof	proof	NOUN
ejpam-4607	252	2	.	.	PUNCT
ejpam-4607	253	1	since	since	SCONJ
ejpam-4607	253	2	(	(	PUNCT
ejpam-4607	253	3	x	x	X
ejpam-4607	253	4	,	,	PUNCT
ejpam-4607	253	5	τ	τ	PROPN
ejpam-4607	253	6	)	)	PUNCT
ejpam-4607	253	7	and	and	CCONJ
ejpam-4607	253	8	(	(	PUNCT
ejpam-4607	253	9	y	y	PROPN
ejpam-4607	253	10	,	,	PUNCT
ejpam-4607	253	11	τ	τ	PROPN
ejpam-4607	253	12	′	′	NUM
ejpam-4607	253	13	)	)	PUNCT
ejpam-4607	253	14	are	be	AUX
ejpam-4607	253	15	nearly	nearly	ADV
ejpam-4607	253	16	compact	compact	ADJ
ejpam-4607	253	17	hausdorff	hausdorff	NOUN
ejpam-4607	253	18	spaces	space	NOUN
ejpam-4607	253	19	,	,	PUNCT
ejpam-4607	253	20	we	we	PRON
ejpam-4607	253	21	get	get	VERB
ejpam-4607	253	22	(	(	PUNCT
ejpam-4607	253	23	x	x	X
ejpam-4607	253	24	,	,	PUNCT
ejpam-4607	253	25	τ	τ	PROPN
ejpam-4607	253	26	s	s	PART
ejpam-4607	253	27	)	)	PUNCT
ejpam-4607	253	28	and	and	CCONJ
ejpam-4607	253	29	(	(	PUNCT
ejpam-4607	253	30	y	y	PROPN
ejpam-4607	253	31	,	,	PUNCT
ejpam-4607	253	32	τ	τ	PROPN
ejpam-4607	253	33	′s	′s	PROPN
ejpam-4607	253	34	)	)	PUNCT
ejpam-4607	253	35	are	be	AUX
ejpam-4607	253	36	hausdorff	hausdorff	ADJ
ejpam-4607	253	37	compact	compact	ADJ
ejpam-4607	253	38	spaces	space	NOUN
ejpam-4607	253	39	[	[	X
ejpam-4607	253	40	20	20	NUM
ejpam-4607	253	41	]	]	PUNCT
ejpam-4607	253	42	,	,	PUNCT
ejpam-4607	253	43	and	and	CCONJ
ejpam-4607	253	44	(	(	PUNCT
ejpam-4607	253	45	x	x	X
ejpam-4607	253	46	,	,	PUNCT
ejpam-4607	253	47	τ	τ	PROPN
ejpam-4607	253	48	s	s	PART
ejpam-4607	253	49	)	)	PUNCT
ejpam-4607	253	50	×	×	NOUN
ejpam-4607	253	51	(	(	PUNCT
ejpam-4607	253	52	y	y	PROPN
ejpam-4607	253	53	,	,	PUNCT
ejpam-4607	253	54	τ	τ	PROPN
ejpam-4607	253	55	′s	′s	PROPN
ejpam-4607	253	56	)	)	PUNCT
ejpam-4607	253	57	is	be	AUX
ejpam-4607	253	58	a	a	DET
ejpam-4607	253	59	t2	t2	NOUN
ejpam-4607	253	60	compact	compact	ADJ
ejpam-4607	253	61	topological	topological	ADJ
ejpam-4607	253	62	space	space	NOUN
ejpam-4607	253	63	which	which	PRON
ejpam-4607	253	64	is	be	AUX
ejpam-4607	253	65	coarser	coarse	ADJ
ejpam-4607	253	66	than	than	ADP
ejpam-4607	253	67	the	the	DET
ejpam-4607	253	68	topology	topology	NOUN
ejpam-4607	253	69	on	on	ADP
ejpam-4607	253	70	x	x	PUNCT
ejpam-4607	253	71	×y	×y	PRON
ejpam-4607	253	72	.	.	PUNCT
ejpam-4607	254	1	thus	thus	ADV
ejpam-4607	254	2	,	,	PUNCT
ejpam-4607	254	3	x	x	X
ejpam-4607	254	4	×y	×y	ADV
ejpam-4607	254	5	is	be	AUX
ejpam-4607	254	6	epinormal	epinormal	ADJ
ejpam-4607	254	7	and	and	CCONJ
ejpam-4607	254	8	hence	hence	ADV
ejpam-4607	254	9	it	it	PRON
ejpam-4607	254	10	is	be	AUX
ejpam-4607	254	11	c	c	NOUN
ejpam-4607	254	12	-	-	PUNCT
ejpam-4607	254	13	κ	κ	NOUN
ejpam-4607	254	14	-	-	ADJ
ejpam-4607	254	15	normal	normal	ADJ
ejpam-4607	254	16	[	[	X
ejpam-4607	254	17	2	2	NUM
ejpam-4607	254	18	]	]	PUNCT
ejpam-4607	254	19	.	.	PUNCT
ejpam-4607	255	1	the	the	DET
ejpam-4607	255	2	following	follow	VERB
ejpam-4607	255	3	problems	problem	NOUN
ejpam-4607	255	4	are	be	AUX
ejpam-4607	255	5	still	still	ADV
ejpam-4607	255	6	open	open	ADJ
ejpam-4607	255	7	:	:	PUNCT
ejpam-4607	255	8	(	(	PUNCT
ejpam-4607	255	9	i	i	NOUN
ejpam-4607	255	10	)	)	PUNCT
ejpam-4607	255	11	does	do	AUX
ejpam-4607	255	12	there	there	PRON
ejpam-4607	255	13	exist	exist	VERB
ejpam-4607	255	14	a	a	DET
ejpam-4607	255	15	tychonoff	tychonoff	NOUN
ejpam-4607	255	16	space	space	NOUN
ejpam-4607	255	17	which	which	PRON
ejpam-4607	255	18	is	be	AUX
ejpam-4607	255	19	not	not	PART
ejpam-4607	255	20	c	c	NOUN
ejpam-4607	255	21	-	-	PUNCT
ejpam-4607	255	22	κ	κ	NOUN
ejpam-4607	255	23	-	-	ADJ
ejpam-4607	255	24	normal	normal	ADJ
ejpam-4607	255	25	?	?	PUNCT
ejpam-4607	256	1	observe	observe	VERB
ejpam-4607	256	2	that	that	SCONJ
ejpam-4607	256	3	such	such	DET
ejpam-4607	256	4	a	a	DET
ejpam-4607	256	5	space	space	NOUN
ejpam-4607	256	6	is	be	AUX
ejpam-4607	256	7	not	not	PART
ejpam-4607	256	8	in	in	ADP
ejpam-4607	256	9	the	the	DET
ejpam-4607	256	10	class	class	NOUN
ejpam-4607	256	11	of	of	ADP
ejpam-4607	256	12	minimal	minimal	ADJ
ejpam-4607	256	13	hausdorff	hausdorff	NOUN
ejpam-4607	256	14	space	space	NOUN
ejpam-4607	256	15	,	,	PUNCT
ejpam-4607	256	16	not	not	PART
ejpam-4607	256	17	in	in	ADP
ejpam-4607	256	18	the	the	DET
ejpam-4607	256	19	class	class	NOUN
ejpam-4607	256	20	of	of	ADP
ejpam-4607	256	21	minimal	minimal	ADJ
ejpam-4607	256	22	t3	t3	PROPN
ejpam-4607	256	23	spaces	space	NOUN
ejpam-4607	256	24	,	,	PUNCT
ejpam-4607	256	25	not	not	PART
ejpam-4607	256	26	locally	locally	ADV
ejpam-4607	256	27	compact	compact	ADJ
ejpam-4607	256	28	,	,	PUNCT
ejpam-4607	256	29	not	not	PART
ejpam-4607	256	30	submetrizable	submetrizable	ADJ
ejpam-4607	256	31	,	,	PUNCT
ejpam-4607	256	32	not	not	PART
ejpam-4607	256	33	c	c	NOUN
ejpam-4607	256	34	-	-	ADJ
ejpam-4607	256	35	normal	normal	ADJ
ejpam-4607	256	36	,	,	PUNCT
ejpam-4607	256	37	a	a	DET
ejpam-4607	256	38	space	space	NOUN
ejpam-4607	256	39	can	can	AUX
ejpam-4607	256	40	not	not	PART
ejpam-4607	256	41	be	be	AUX
ejpam-4607	256	42	ordinal	ordinal	ADJ
ejpam-4607	256	43	,	,	PUNCT
ejpam-4607	256	44	can	can	AUX
ejpam-4607	256	45	not	not	PART
ejpam-4607	256	46	epinormal	epinormal	VERB
ejpam-4607	256	47	,	,	PUNCT
ejpam-4607	256	48	not	not	PART
ejpam-4607	256	49	lindelöf	lindelöf	PROPN
ejpam-4607	256	50	.	.	PUNCT
ejpam-4607	257	1	observe	observe	VERB
ejpam-4607	257	2	also	also	ADV
ejpam-4607	257	3	that	that	SCONJ
ejpam-4607	257	4	the	the	DET
ejpam-4607	257	5	existence	existence	NOUN
ejpam-4607	257	6	of	of	ADP
ejpam-4607	257	7	such	such	DET
ejpam-4607	257	8	a	a	DET
ejpam-4607	257	9	space	space	NOUN
ejpam-4607	257	10	,	,	PUNCT
ejpam-4607	257	11	will	will	AUX
ejpam-4607	257	12	show	show	VERB
ejpam-4607	257	13	that	that	SCONJ
ejpam-4607	257	14	c	c	NOUN
ejpam-4607	257	15	-	-	PUNCT
ejpam-4607	257	16	κ	κ	NOUN
ejpam-4607	257	17	-	-	ADJ
ejpam-4607	257	18	normal	normal	ADJ
ejpam-4607	257	19	is	be	AUX
ejpam-4607	257	20	not	not	PART
ejpam-4607	257	21	hereditary	hereditary	ADJ
ejpam-4607	257	22	just	just	ADV
ejpam-4607	257	23	by	by	ADP
ejpam-4607	257	24	taking	take	VERB
ejpam-4607	257	25	a	a	DET
ejpam-4607	257	26	compactification	compactification	NOUN
ejpam-4607	257	27	of	of	ADP
ejpam-4607	257	28	it	it	PRON
ejpam-4607	257	29	.	.	PUNCT
ejpam-4607	258	1	(	(	PUNCT
ejpam-4607	258	2	ii	ii	NOUN
ejpam-4607	258	3	)	)	PUNCT
ejpam-4607	258	4	is	be	AUX
ejpam-4607	258	5	c	c	NOUN
ejpam-4607	258	6	-	-	PUNCT
ejpam-4607	258	7	κ	κ	NOUN
ejpam-4607	258	8	-	-	PUNCT
ejpam-4607	258	9	normality	normality	NOUN
ejpam-4607	258	10	(	(	PUNCT
ejpam-4607	258	11	c	c	NOUN
ejpam-4607	258	12	-	-	PUNCT
ejpam-4607	258	13	mild	mild	ADJ
ejpam-4607	258	14	normality	normality	NOUN
ejpam-4607	258	15	)	)	PUNCT
ejpam-4607	258	16	multiplicative	multiplicative	PROPN
ejpam-4607	258	17	?	?	PUNCT
ejpam-4607	259	1	references	reference	NOUN
ejpam-4607	259	2	[	[	X
ejpam-4607	259	3	1	1	NUM
ejpam-4607	259	4	]	]	X
ejpam-4607	259	5	d	d	X
ejpam-4607	259	6	abuzaid	abuzaid	PROPN
ejpam-4607	259	7	,	,	PUNCT
ejpam-4607	259	8	s	s	PART
ejpam-4607	259	9	al	al	PROPN
ejpam-4607	259	10	-	-	PUNCT
ejpam-4607	259	11	qarhi	qarhi	NOUN
ejpam-4607	259	12	,	,	PUNCT
ejpam-4607	259	13	and	and	CCONJ
ejpam-4607	259	14	l	l	NOUN
ejpam-4607	259	15	kalantani	kalantani	NOUN
ejpam-4607	259	16	.	.	PUNCT
ejpam-4607	260	1	closed	close	VERB
ejpam-4607	260	2	extension	extension	NOUN
ejpam-4607	260	3	topological	topological	ADJ
ejpam-4607	260	4	spaces	space	NOUN
ejpam-4607	260	5	.	.	PUNCT
ejpam-4607	261	1	european	european	ADJ
ejpam-4607	261	2	journal	journal	PROPN
ejpam-4607	261	3	of	of	ADP
ejpam-4607	261	4	pure	pure	ADJ
ejpam-4607	261	5	and	and	CCONJ
ejpam-4607	261	6	applied	applied	ADJ
ejpam-4607	261	7	mathematics	mathematic	NOUN
ejpam-4607	261	8	(	(	PUNCT
ejpam-4607	261	9	ejpam	ejpam	PROPN
ejpam-4607	261	10	)	)	PUNCT
ejpam-4607	261	11	,	,	PUNCT
ejpam-4607	261	12	15(2):672–680	15(2):672–680	NUM
ejpam-4607	261	13	,	,	PUNCT
ejpam-4607	261	14	2022	2022	NUM
ejpam-4607	261	15	.	.	PUNCT
ejpam-4607	262	1	[	[	X
ejpam-4607	262	2	2	2	NUM
ejpam-4607	262	3	]	]	PUNCT
ejpam-4607	262	4	a	a	DET
ejpam-4607	262	5	al	al	PROPN
ejpam-4607	262	6	-	-	PUNCT
ejpam-4607	262	7	awadi	awadi	NOUN
ejpam-4607	262	8	,	,	PUNCT
ejpam-4607	262	9	l	l	PROPN
ejpam-4607	262	10	kalantan	kalantan	PROPN
ejpam-4607	262	11	,	,	PUNCT
ejpam-4607	262	12	and	and	CCONJ
ejpam-4607	262	13	s	s	VERB
ejpam-4607	262	14	thabit	thabit	NOUN
ejpam-4607	262	15	.	.	PUNCT
ejpam-4607	263	1	c	c	X
ejpam-4607	263	2	-	-	PUNCT
ejpam-4607	263	3	κ	κ	NOUN
ejpam-4607	263	4	-	-	ADJ
ejpam-4607	263	5	normal	normal	ADJ
ejpam-4607	263	6	and	and	CCONJ
ejpam-4607	263	7	c	c	NOUN
ejpam-4607	263	8	-	-	PUNCT
ejpam-4607	263	9	mildly	mildly	ADV
ejpam-4607	263	10	normal	normal	ADJ
ejpam-4607	263	11	topological	topological	ADJ
ejpam-4607	263	12	properties	property	NOUN
ejpam-4607	263	13	.	.	PUNCT
ejpam-4607	264	1	to	to	PART
ejpam-4607	264	2	appear	appear	VERB
ejpam-4607	264	3	.	.	PUNCT
ejpam-4607	265	1	[	[	X
ejpam-4607	265	2	3	3	X
ejpam-4607	265	3	]	]	PUNCT
ejpam-4607	265	4	a	a	DET
ejpam-4607	265	5	alawadi	alawadi	NOUN
ejpam-4607	265	6	,	,	PUNCT
ejpam-4607	265	7	l	l	PROPN
ejpam-4607	265	8	kalantan	kalantan	PROPN
ejpam-4607	265	9	,	,	PUNCT
ejpam-4607	265	10	and	and	CCONJ
ejpam-4607	265	11	m	m	PROPN
ejpam-4607	265	12	saeed	saeed	PROPN
ejpam-4607	265	13	.	.	PUNCT
ejpam-4607	266	1	on	on	ADP
ejpam-4607	266	2	the	the	DET
ejpam-4607	266	3	discrete	discrete	ADJ
ejpam-4607	266	4	extension	extension	NOUN
ejpam-4607	266	5	spaces	space	NOUN
ejpam-4607	266	6	.	.	PUNCT
ejpam-4607	267	1	journal	journal	PROPN
ejpam-4607	267	2	of	of	ADP
ejpam-4607	267	3	mathematical	mathematical	ADJ
ejpam-4607	267	4	analysis	analysis	NOUN
ejpam-4607	267	5	,	,	PUNCT
ejpam-4607	267	6	9(2):150–157	9(2):150–157	NOUN
ejpam-4607	267	7	,	,	PUNCT
ejpam-4607	267	8	2018	2018	NUM
ejpam-4607	267	9	.	.	PUNCT
ejpam-4607	268	1	[	[	X
ejpam-4607	268	2	4	4	NUM
ejpam-4607	268	3	]	]	SYM
ejpam-4607	268	4	s	s	PART
ejpam-4607	268	5	alzahrani	alzahrani	NOUN
ejpam-4607	268	6	and	and	CCONJ
ejpam-4607	268	7	l	l	PROPN
ejpam-4607	268	8	kalantan	kalantan	PROPN
ejpam-4607	268	9	.	.	PUNCT
ejpam-4607	269	1	epinormality	epinormality	NOUN
ejpam-4607	269	2	.	.	PUNCT
ejpam-4607	270	1	journal	journal	PROPN
ejpam-4607	270	2	of	of	ADP
ejpam-4607	270	3	nonlinear	nonlinear	PROPN
ejpam-4607	270	4	sciences	sciences	PROPN
ejpam-4607	270	5	&	&	CCONJ
ejpam-4607	270	6	applications	application	NOUN
ejpam-4607	270	7	,	,	PUNCT
ejpam-4607	270	8	9(9):5398–5402	9(9):5398–5402	PROPN
ejpam-4607	270	9	,	,	PUNCT
ejpam-4607	270	10	2016	2016	NUM
ejpam-4607	270	11	.	.	PUNCT
ejpam-4607	271	1	[	[	X
ejpam-4607	271	2	5	5	NUM
ejpam-4607	271	3	]	]	PUNCT
ejpam-4607	271	4	h	h	NOUN
ejpam-4607	271	5	alzumi	alzumi	PROPN
ejpam-4607	271	6	,	,	PUNCT
ejpam-4607	271	7	l	l	PROPN
ejpam-4607	271	8	kalantan	kalantan	PROPN
ejpam-4607	271	9	,	,	PUNCT
ejpam-4607	271	10	and	and	CCONJ
ejpam-4607	271	11	m	m	PROPN
ejpam-4607	271	12	m	m	PROPN
ejpam-4607	271	13	saeed	saeed	PROPN
ejpam-4607	271	14	.	.	PUNCT
ejpam-4607	272	1	results	result	NOUN
ejpam-4607	272	2	on	on	ADP
ejpam-4607	272	3	c2	c2	PROPN
ejpam-4607	272	4	-	-	PUNCT
ejpam-4607	272	5	paracompactness	paracompactness	NOUN
ejpam-4607	272	6	.	.	PUNCT
ejpam-4607	273	1	european	european	PROPN
ejpam-4607	273	2	journal	journal	PROPN
ejpam-4607	273	3	of	of	ADP
ejpam-4607	273	4	pure	pure	ADJ
ejpam-4607	273	5	and	and	CCONJ
ejpam-4607	273	6	applied	applied	ADJ
ejpam-4607	273	7	mathematics	mathematic	NOUN
ejpam-4607	273	8	.	.	PUNCT
ejpam-4607	273	9	,	,	PUNCT
ejpam-4607	273	10	14(2):351–357	14(2):351–357	PROPN
ejpam-4607	273	11	,	,	PUNCT
ejpam-4607	273	12	2021	2021	NUM
ejpam-4607	273	13	.	.	PUNCT
ejpam-4607	274	1	[	[	X
ejpam-4607	274	2	6	6	NUM
ejpam-4607	274	3	]	]	PUNCT
ejpam-4607	274	4	a	a	DET
ejpam-4607	274	5	v	v	NOUN
ejpam-4607	274	6	arhangel’skii	arhangel’skii	NOUN
ejpam-4607	274	7	and	and	CCONJ
ejpam-4607	274	8	l	l	NOUN
ejpam-4607	274	9	d	d	X
ejpam-4607	274	10	ludwig	ludwig	PROPN
ejpam-4607	274	11	.	.	PUNCT
ejpam-4607	275	1	on	on	ADP
ejpam-4607	275	2	α	α	NOUN
ejpam-4607	275	3	-	-	ADJ
ejpam-4607	275	4	normal	normal	ADJ
ejpam-4607	275	5	and	and	CCONJ
ejpam-4607	275	6	β	β	NOUN
ejpam-4607	275	7	-	-	ADJ
ejpam-4607	275	8	normal	normal	ADJ
ejpam-4607	275	9	spaces	space	NOUN
ejpam-4607	275	10	.	.	PUNCT
ejpam-4607	276	1	commentationes	commentatione	NOUN
ejpam-4607	276	2	mathematicae	mathematicae	VERB
ejpam-4607	276	3	universitatis	universitatis	PROPN
ejpam-4607	276	4	carolinae	carolinae	PROPN
ejpam-4607	276	5	.	.	PUNCT
ejpam-4607	277	1	,	,	PUNCT
ejpam-4607	277	2	42(3):507–519	42(3):507–519	NUM
ejpam-4607	277	3	,	,	PUNCT
ejpam-4607	277	4	2001	2001	NUM
ejpam-4607	277	5	.	.	PUNCT
ejpam-4607	278	1	[	[	X
ejpam-4607	278	2	7	7	X
ejpam-4607	278	3	]	]	X
ejpam-4607	278	4	m	m	VERB
ejpam-4607	278	5	p	p	NOUN
ejpam-4607	278	6	berri	berri	PROPN
ejpam-4607	278	7	.	.	PUNCT
ejpam-4607	279	1	minimal	minimal	ADJ
ejpam-4607	279	2	topological	topological	ADJ
ejpam-4607	279	3	spaces	space	NOUN
ejpam-4607	279	4	.	.	PUNCT
ejpam-4607	280	1	transactions	transaction	NOUN
ejpam-4607	280	2	of	of	ADP
ejpam-4607	280	3	the	the	DET
ejpam-4607	280	4	american	american	PROPN
ejpam-4607	280	5	mathematical	mathematical	PROPN
ejpam-4607	280	6	society	society	NOUN
ejpam-4607	280	7	.	.	PUNCT
ejpam-4607	280	8	,	,	PUNCT
ejpam-4607	280	9	108(1):97–105	108(1):97–105	NUM
ejpam-4607	280	10	,	,	PUNCT
ejpam-4607	280	11	1963	1963	NUM
ejpam-4607	280	12	.	.	PUNCT
ejpam-4607	281	1	[	[	X
ejpam-4607	281	2	8	8	NUM
ejpam-4607	281	3	]	]	PUNCT
ejpam-4607	281	4	n	n	X
ejpam-4607	281	5	bourbaki	bourbaki	VERB
ejpam-4607	281	6	.	.	PUNCT
ejpam-4607	282	1	general	general	ADJ
ejpam-4607	282	2	topology	topology	PROPN
ejpam-4607	282	3	.	.	PUNCT
ejpam-4607	283	1	springer	springer	NOUN
ejpam-4607	283	2	-	-	PUNCT
ejpam-4607	283	3	verlag	verlag	PROPN
ejpam-4607	283	4	,	,	PUNCT
ejpam-4607	283	5	1995	1995	NUM
ejpam-4607	283	6	.	.	PUNCT
ejpam-4607	284	1	[	[	X
ejpam-4607	284	2	9	9	NUM
ejpam-4607	284	3	]	]	X
ejpam-4607	284	4	r	r	NOUN
ejpam-4607	284	5	z	z	NOUN
ejpam-4607	284	6	buzyakova	buzyakova	NOUN
ejpam-4607	284	7	.	.	PUNCT
ejpam-4607	285	1	an	an	DET
ejpam-4607	285	2	example	example	NOUN
ejpam-4607	285	3	of	of	ADP
ejpam-4607	285	4	a	a	DET
ejpam-4607	285	5	product	product	NOUN
ejpam-4607	285	6	of	of	ADP
ejpam-4607	285	7	two	two	NUM
ejpam-4607	285	8	normal	normal	ADJ
ejpam-4607	285	9	groups	group	NOUN
ejpam-4607	285	10	that	that	PRON
ejpam-4607	285	11	can	can	AUX
ejpam-4607	285	12	not	not	PART
ejpam-4607	285	13	be	be	AUX
ejpam-4607	285	14	condensed	condense	VERB
ejpam-4607	285	15	onto	onto	ADP
ejpam-4607	285	16	a	a	DET
ejpam-4607	285	17	normal	normal	ADJ
ejpam-4607	285	18	space	space	NOUN
ejpam-4607	285	19	.	.	PUNCT
ejpam-4607	286	1	vestnik	vestnik	PROPN
ejpam-4607	286	2	moskovskogo	moskovskogo	PROPN
ejpam-4607	286	3	universiteta	universiteta	PROPN
ejpam-4607	286	4	.	.	PUNCT
ejpam-4607	287	1	seriya	seriya	PROPN
ejpam-4607	287	2	1	1	NUM
ejpam-4607	287	3	.	.	PUNCT
ejpam-4607	287	4	matematika	matematika	PROPN
ejpam-4607	287	5	.	.	PUNCT
ejpam-4607	287	6	mekhanika	mekhanika	PROPN
ejpam-4607	287	7	.	.	PROPN
ejpam-4607	287	8	,	,	PUNCT
ejpam-4607	287	9	3:59–59	3:59–59	NUM
ejpam-4607	287	10	,	,	PUNCT
ejpam-4607	287	11	1997	1997	NUM
ejpam-4607	287	12	.	.	PUNCT
ejpam-4607	288	1	references	reference	NOUN
ejpam-4607	288	2	70	70	NUM
ejpam-4607	289	1	[	[	X
ejpam-4607	289	2	10	10	NUM
ejpam-4607	289	3	]	]	X
ejpam-4607	289	4	c	c	NOUN
ejpam-4607	289	5	h	h	NOUN
ejpam-4607	289	6	dowker	dowker	PROPN
ejpam-4607	289	7	.	.	PUNCT
ejpam-4607	290	1	on	on	ADP
ejpam-4607	290	2	countably	countably	ADV
ejpam-4607	290	3	paracompact	paracompact	ADJ
ejpam-4607	290	4	spaces	space	NOUN
ejpam-4607	290	5	.	.	PUNCT
ejpam-4607	291	1	canadian	canadian	ADJ
ejpam-4607	291	2	journal	journal	PROPN
ejpam-4607	291	3	of	of	ADP
ejpam-4607	291	4	mathematics	mathematics	PROPN
ejpam-4607	291	5	.	.	PUNCT
ejpam-4607	291	6	,	,	PUNCT
ejpam-4607	291	7	3:219–224	3:219–224	NUM
ejpam-4607	291	8	,	,	PUNCT
ejpam-4607	291	9	1951	1951	NUM
ejpam-4607	291	10	.	.	PUNCT
ejpam-4607	292	1	[	[	X
ejpam-4607	292	2	11	11	NUM
ejpam-4607	292	3	]	]	X
ejpam-4607	292	4	r	r	NOUN
ejpam-4607	292	5	engelking	engelking	NOUN
ejpam-4607	292	6	.	.	PUNCT
ejpam-4607	293	1	on	on	ADP
ejpam-4607	293	2	the	the	DET
ejpam-4607	293	3	double	double	ADJ
ejpam-4607	293	4	circumference	circumference	NOUN
ejpam-4607	293	5	of	of	ADP
ejpam-4607	293	6	alexandroff	alexandroff	NOUN
ejpam-4607	293	7	.	.	PUNCT
ejpam-4607	294	1	bull	bull	NOUN
ejpam-4607	294	2	.	.	PUNCT
ejpam-4607	295	1	acad	acad	PROPN
ejpam-4607	295	2	.	.	PUNCT
ejpam-4607	296	1	pol	pol	PROPN
ejpam-4607	296	2	.	.	PUNCT
ejpam-4607	297	1	sci	sci	PROPN
ejpam-4607	297	2	.	.	PUNCT
ejpam-4607	297	3	ser	ser	PROPN
ejpam-4607	297	4	.	.	PUNCT
ejpam-4607	298	1	astron	astron	PROPN
ejpam-4607	298	2	.	.	PUNCT
ejpam-4607	298	3	math	math	NOUN
ejpam-4607	298	4	.	.	PUNCT
ejpam-4607	299	1	phys	phy	NOUN
ejpam-4607	299	2	.	.	PUNCT
ejpam-4607	299	3	,	,	PUNCT
ejpam-4607	299	4	16(8):629–634	16(8):629–634	PROPN
ejpam-4607	299	5	,	,	PUNCT
ejpam-4607	299	6	1968	1968	NUM
ejpam-4607	299	7	.	.	PUNCT
ejpam-4607	300	1	[	[	X
ejpam-4607	300	2	12	12	NUM
ejpam-4607	300	3	]	]	X
ejpam-4607	300	4	r	r	NOUN
ejpam-4607	300	5	engelking	engelking	NOUN
ejpam-4607	300	6	.	.	PUNCT
ejpam-4607	301	1	general	general	ADJ
ejpam-4607	301	2	topology	topology	PROPN
ejpam-4607	301	3	.	.	PUNCT
ejpam-4607	302	1	pwn	pwn	PROPN
ejpam-4607	302	2	,	,	PUNCT
ejpam-4607	302	3	warszawa	warszawa	PROPN
ejpam-4607	302	4	,	,	PUNCT
ejpam-4607	302	5	1977	1977	NUM
ejpam-4607	302	6	.	.	PUNCT
ejpam-4607	303	1	[	[	X
ejpam-4607	303	2	13	13	NUM
ejpam-4607	303	3	]	]	SYM
ejpam-4607	303	4	s	s	VERB
ejpam-4607	303	5	ikenage	ikenage	NOUN
ejpam-4607	303	6	.	.	PUNCT
ejpam-4607	304	1	product	product	NOUN
ejpam-4607	304	2	of	of	ADP
ejpam-4607	304	3	minimal	minimal	ADJ
ejpam-4607	304	4	topological	topological	ADJ
ejpam-4607	304	5	spaces	space	NOUN
ejpam-4607	304	6	.	.	PUNCT
ejpam-4607	305	1	proceedings	proceeding	NOUN
ejpam-4607	305	2	of	of	ADP
ejpam-4607	305	3	the	the	DET
ejpam-4607	305	4	japan	japan	PROPN
ejpam-4607	305	5	academy	academy	PROPN
ejpam-4607	305	6	.	.	PUNCT
ejpam-4607	305	7	,	,	PUNCT
ejpam-4607	305	8	40(5):329–331	40(5):329–331	PROPN
ejpam-4607	305	9	,	,	PUNCT
ejpam-4607	305	10	1964	1964	NUM
ejpam-4607	305	11	.	.	PUNCT
ejpam-4607	306	1	[	[	X
ejpam-4607	306	2	14	14	NUM
ejpam-4607	306	3	]	]	PUNCT
ejpam-4607	306	4	l	l	PROPN
ejpam-4607	306	5	kalantan	kalantan	PROPN
ejpam-4607	306	6	.	.	PUNCT
ejpam-4607	307	1	results	result	VERB
ejpam-4607	307	2	about	about	ADP
ejpam-4607	307	3	κ	κ	NOUN
ejpam-4607	307	4	-	-	NOUN
ejpam-4607	307	5	normality	normality	NOUN
ejpam-4607	307	6	.	.	PUNCT
ejpam-4607	308	1	topology	topology	NOUN
ejpam-4607	308	2	and	and	CCONJ
ejpam-4607	308	3	its	its	PRON
ejpam-4607	308	4	applications	application	NOUN
ejpam-4607	308	5	,	,	PUNCT
ejpam-4607	308	6	125(1):47–62	125(1):47–62	NUM
ejpam-4607	308	7	,	,	PUNCT
ejpam-4607	308	8	2002	2002	NUM
ejpam-4607	308	9	.	.	PUNCT
ejpam-4607	309	1	[	[	X
ejpam-4607	309	2	15	15	NUM
ejpam-4607	309	3	]	]	X
ejpam-4607	309	4	l	l	NOUN
ejpam-4607	309	5	kalantan	kalantan	PROPN
ejpam-4607	309	6	and	and	CCONJ
ejpam-4607	309	7	i	i	PROPN
ejpam-4607	309	8	alshammari	alshammari	PROPN
ejpam-4607	309	9	.	.	PUNCT
ejpam-4607	310	1	epi	epi	ADJ
ejpam-4607	310	2	-	-	ADJ
ejpam-4607	310	3	mild	mild	ADJ
ejpam-4607	310	4	normality	normality	NOUN
ejpam-4607	310	5	.	.	PUNCT
ejpam-4607	311	1	open	open	ADJ
ejpam-4607	311	2	mathematics	mathematic	NOUN
ejpam-4607	311	3	.	.	PUNCT
ejpam-4607	311	4	,	,	PUNCT
ejpam-4607	311	5	16(1):1170	16(1):1170	NUM
ejpam-4607	311	6	–	–	PUNCT
ejpam-4607	311	7	1175	1175	NUM
ejpam-4607	311	8	,	,	PUNCT
ejpam-4607	311	9	2018	2018	NUM
ejpam-4607	311	10	.	.	PUNCT
ejpam-4607	312	1	[	[	X
ejpam-4607	312	2	16	16	NUM
ejpam-4607	312	3	]	]	PUNCT
ejpam-4607	312	4	l	l	NOUN
ejpam-4607	312	5	kalantan	kalantan	PROPN
ejpam-4607	312	6	and	and	CCONJ
ejpam-4607	312	7	n	n	PRON
ejpam-4607	312	8	kemoto	kemoto	NOUN
ejpam-4607	312	9	.	.	PUNCT
ejpam-4607	313	1	mild	mild	ADJ
ejpam-4607	313	2	normality	normality	NOUN
ejpam-4607	313	3	in	in	ADP
ejpam-4607	313	4	products	product	NOUN
ejpam-4607	313	5	of	of	ADP
ejpam-4607	313	6	ordinals	ordinal	NOUN
ejpam-4607	313	7	.	.	PUNCT
ejpam-4607	314	1	houston	houston	PROPN
ejpam-4607	314	2	journal	journal	PROPN
ejpam-4607	314	3	of	of	ADP
ejpam-4607	314	4	mathematics	mathematics	PROPN
ejpam-4607	314	5	.	.	PUNCT
ejpam-4607	314	6	,	,	PUNCT
ejpam-4607	314	7	29(4):937–947	29(4):937–947	PROPN
ejpam-4607	314	8	,	,	PUNCT
ejpam-4607	314	9	2003	2003	NUM
ejpam-4607	314	10	.	.	PUNCT
ejpam-4607	315	1	[	[	X
ejpam-4607	315	2	17	17	NUM
ejpam-4607	315	3	]	]	X
ejpam-4607	315	4	l	l	NOUN
ejpam-4607	315	5	kalantan	kalantan	PROPN
ejpam-4607	315	6	,	,	PUNCT
ejpam-4607	315	7	m	m	PROPN
ejpam-4607	315	8	m	m	VERB
ejpam-4607	315	9	saeed	saeed	NOUN
ejpam-4607	315	10	,	,	PUNCT
ejpam-4607	315	11	and	and	CCONJ
ejpam-4607	315	12	h	h	PROPN
ejpam-4607	315	13	alzumi	alzumi	PROPN
ejpam-4607	315	14	.	.	PUNCT
ejpam-4607	316	1	c	c	X
ejpam-4607	316	2	-	-	PUNCT
ejpam-4607	316	3	paracompactness	paracompactness	PROPN
ejpam-4607	316	4	and	and	CCONJ
ejpam-4607	316	5	c2	c2	PROPN
ejpam-4607	316	6	-	-	PUNCT
ejpam-4607	316	7	paracompactness	paracompactness	NOUN
ejpam-4607	316	8	.	.	PUNCT
ejpam-4607	317	1	turkish	turkish	ADJ
ejpam-4607	317	2	journal	journal	NOUN
ejpam-4607	317	3	of	of	ADP
ejpam-4607	317	4	mathematics	mathematic	NOUN
ejpam-4607	317	5	.	.	PUNCT
ejpam-4607	317	6	,	,	PUNCT
ejpam-4607	317	7	43(1):9–20	43(1):9–20	NOUN
ejpam-4607	317	8	,	,	PUNCT
ejpam-4607	317	9	2019	2019	NUM
ejpam-4607	317	10	.	.	PUNCT
ejpam-4607	318	1	[	[	X
ejpam-4607	318	2	18	18	NUM
ejpam-4607	318	3	]	]	PUNCT
ejpam-4607	318	4	l	l	NOUN
ejpam-4607	318	5	kalantan	kalantan	PROPN
ejpam-4607	318	6	and	and	CCONJ
ejpam-4607	318	7	p	p	PROPN
ejpam-4607	318	8	szeptycki	szeptycki	PROPN
ejpam-4607	318	9	.	.	PUNCT
ejpam-4607	319	1	κ	κ	NOUN
ejpam-4607	319	2	-	-	PUNCT
ejpam-4607	319	3	normality	normality	NOUN
ejpam-4607	319	4	and	and	CCONJ
ejpam-4607	319	5	products	product	NOUN
ejpam-4607	319	6	of	of	ADP
ejpam-4607	319	7	ordinals	ordinal	NOUN
ejpam-4607	319	8	.	.	PUNCT
ejpam-4607	320	1	topology	topology	NOUN
ejpam-4607	320	2	and	and	CCONJ
ejpam-4607	320	3	its	its	PRON
ejpam-4607	320	4	applications	application	NOUN
ejpam-4607	320	5	,	,	PUNCT
ejpam-4607	320	6	123(3):537–545	123(3):537–545	NUM
ejpam-4607	320	7	,	,	PUNCT
ejpam-4607	320	8	2002	2002	NUM
ejpam-4607	320	9	.	.	PUNCT
ejpam-4607	321	1	[	[	X
ejpam-4607	321	2	19	19	NUM
ejpam-4607	321	3	]	]	X
ejpam-4607	321	4	p	p	X
ejpam-4607	321	5	t	t	PROPN
ejpam-4607	321	6	lambrinos	lambrino	NOUN
ejpam-4607	321	7	.	.	PUNCT
ejpam-4607	322	1	on	on	ADP
ejpam-4607	322	2	almost	almost	ADV
ejpam-4607	322	3	compact	compact	ADJ
ejpam-4607	322	4	and	and	CCONJ
ejpam-4607	322	5	nearly	nearly	ADV
ejpam-4607	322	6	compact	compact	ADJ
ejpam-4607	322	7	spaces	space	NOUN
ejpam-4607	322	8	.	.	PUNCT
ejpam-4607	323	1	rendiconti	rendiconti	ADJ
ejpam-4607	323	2	del	del	PROPN
ejpam-4607	323	3	circolo	circolo	PROPN
ejpam-4607	323	4	matematico	matematico	NOUN
ejpam-4607	323	5	di	di	NOUN
ejpam-4607	323	6	palermo	palermo	NOUN
ejpam-4607	323	7	,	,	PUNCT
ejpam-4607	323	8	24(1):14–18	24(1):14–18	NUM
ejpam-4607	323	9	,	,	PUNCT
ejpam-4607	323	10	1975	1975	NUM
ejpam-4607	323	11	.	.	PUNCT
ejpam-4607	324	1	[	[	X
ejpam-4607	324	2	20	20	NUM
ejpam-4607	324	3	]	]	X
ejpam-4607	324	4	m	m	VERB
ejpam-4607	324	5	mršević	mršević	ADJ
ejpam-4607	324	6	,	,	PUNCT
ejpam-4607	324	7	i	i	PRON
ejpam-4607	324	8	l	l	VERB
ejpam-4607	324	9	reilly	reilly	ADV
ejpam-4607	324	10	,	,	PUNCT
ejpam-4607	324	11	and	and	CCONJ
ejpam-4607	324	12	m	m	PROPN
ejpam-4607	324	13	k	k	NOUN
ejpam-4607	324	14	vamanamurthy	vamanamurthy	NOUN
ejpam-4607	324	15	.	.	PUNCT
ejpam-4607	325	1	on	on	ADP
ejpam-4607	325	2	semi	semi	ADJ
ejpam-4607	325	3	-	-	ADJ
ejpam-4607	325	4	regularization	regularization	ADJ
ejpam-4607	325	5	topologies	topology	NOUN
ejpam-4607	325	6	.	.	PUNCT
ejpam-4607	326	1	journal	journal	NOUN
ejpam-4607	326	2	of	of	ADP
ejpam-4607	326	3	the	the	DET
ejpam-4607	326	4	australian	australian	ADJ
ejpam-4607	326	5	mathematical	mathematical	ADJ
ejpam-4607	326	6	society	society	NOUN
ejpam-4607	326	7	,	,	PUNCT
ejpam-4607	326	8	38(1):40–54	38(1):40–54	NUM
ejpam-4607	326	9	,	,	PUNCT
ejpam-4607	326	10	1985	1985	NUM
ejpam-4607	326	11	.	.	PUNCT
ejpam-4607	327	1	[	[	X
ejpam-4607	327	2	21	21	NUM
ejpam-4607	327	3	]	]	X
ejpam-4607	327	4	j	j	PROPN
ejpam-4607	327	5	r	r	NOUN
ejpam-4607	327	6	porter	porter	NOUN
ejpam-4607	327	7	and	and	CCONJ
ejpam-4607	327	8	r	r	NOUN
ejpam-4607	327	9	m	m	PROPN
ejpam-4607	327	10	stephenson	stephenson	NOUN
ejpam-4607	327	11	.	.	PUNCT
ejpam-4607	328	1	minimal	minimal	ADJ
ejpam-4607	328	2	hausdorff	hausdorff	NOUN
ejpam-4607	328	3	spaces	space	NOUN
ejpam-4607	328	4	—	—	PUNCT
ejpam-4607	328	5	then	then	ADV
ejpam-4607	328	6	and	and	CCONJ
ejpam-4607	328	7	now	now	ADV
ejpam-4607	328	8	.	.	PUNCT
ejpam-4607	329	1	in	in	ADP
ejpam-4607	329	2	handbook	handbook	NOUN
ejpam-4607	329	3	of	of	ADP
ejpam-4607	329	4	the	the	DET
ejpam-4607	329	5	history	history	NOUN
ejpam-4607	329	6	of	of	ADP
ejpam-4607	329	7	general	general	ADJ
ejpam-4607	329	8	topology	topology	NOUN
ejpam-4607	329	9	,	,	PUNCT
ejpam-4607	329	10	pages	page	NOUN
ejpam-4607	329	11	669–687	669–687	NUM
ejpam-4607	329	12	,	,	PUNCT
ejpam-4607	329	13	1998	1998	NUM
ejpam-4607	329	14	.	.	PUNCT
ejpam-4607	330	1	[	[	X
ejpam-4607	330	2	22	22	NUM
ejpam-4607	330	3	]	]	X
ejpam-4607	330	4	e	e	X
ejpam-4607	330	5	v	v	NUM
ejpam-4607	330	6	shchepin	shchepin	NOUN
ejpam-4607	330	7	.	.	PUNCT
ejpam-4607	331	1	real	real	ADJ
ejpam-4607	331	2	functions	function	NOUN
ejpam-4607	331	3	and	and	CCONJ
ejpam-4607	331	4	spaces	space	NOUN
ejpam-4607	331	5	that	that	PRON
ejpam-4607	331	6	are	be	AUX
ejpam-4607	331	7	nearly	nearly	ADV
ejpam-4607	331	8	normal	normal	ADJ
ejpam-4607	331	9	.	.	PUNCT
ejpam-4607	332	1	sibirskii	sibirskii	VERB
ejpam-4607	332	2	matematicheskii	matematicheskii	PROPN
ejpam-4607	332	3	zhurnal	zhurnal	PROPN
ejpam-4607	332	4	,	,	PUNCT
ejpam-4607	332	5	13(5):1182–1196	13(5):1182–1196	NUM
ejpam-4607	332	6	,	,	PUNCT
ejpam-4607	332	7	1972	1972	NUM
ejpam-4607	332	8	.	.	PUNCT
ejpam-4607	333	1	[	[	X
ejpam-4607	333	2	23	23	NUM
ejpam-4607	333	3	]	]	X
ejpam-4607	333	4	m	m	VERB
ejpam-4607	333	5	k	k	NOUN
ejpam-4607	333	6	singal	singal	NOUN
ejpam-4607	333	7	and	and	CCONJ
ejpam-4607	333	8	a	a	DET
ejpam-4607	333	9	r	r	NOUN
ejpam-4607	333	10	singal	singal	NOUN
ejpam-4607	333	11	.	.	PUNCT
ejpam-4607	334	1	mildly	mildly	ADV
ejpam-4607	334	2	normal	normal	ADJ
ejpam-4607	334	3	spaces	space	NOUN
ejpam-4607	334	4	.	.	PUNCT
ejpam-4607	335	1	kyungpook	kyungpook	PROPN
ejpam-4607	335	2	mathematical	mathematical	PROPN
ejpam-4607	335	3	journal	journal	NOUN
ejpam-4607	335	4	,	,	PUNCT
ejpam-4607	335	5	13(1):29–31	13(1):29–31	NUM
ejpam-4607	335	6	,	,	PUNCT
ejpam-4607	335	7	1973	1973	NUM
ejpam-4607	335	8	.	.	PUNCT
ejpam-4607	336	1	[	[	X
ejpam-4607	336	2	24	24	NUM
ejpam-4607	336	3	]	]	PUNCT
ejpam-4607	336	4	l	l	NOUN
ejpam-4607	336	5	steen	steen	PROPN
ejpam-4607	336	6	and	and	CCONJ
ejpam-4607	336	7	j	j	PROPN
ejpam-4607	336	8	a	a	DET
ejpam-4607	336	9	seebach	seebach	NOUN
ejpam-4607	336	10	.	.	PUNCT
ejpam-4607	337	1	counterexamples	counterexample	NOUN
ejpam-4607	337	2	in	in	ADP
ejpam-4607	337	3	topology	topology	NOUN
ejpam-4607	337	4	.	.	PUNCT
ejpam-4607	338	1	dover	dover	PROPN
ejpam-4607	338	2	publications	publications	PROPN
ejpam-4607	338	3	inc	inc	PROPN
ejpam-4607	338	4	,	,	PUNCT
ejpam-4607	338	5	usa	usa	PROPN
ejpam-4607	338	6	,	,	PUNCT
ejpam-4607	338	7	1995	1995	NUM
ejpam-4607	338	8	.	.	PUNCT