id	sid	tid	token	lemma	pos
ejpam-3253	1	1	european	european	PROPN
ejpam-3253	1	2	journal	journal	PROPN
ejpam-3253	1	3	of	of	ADP
ejpam-3253	1	4	pure	pure	ADJ
ejpam-3253	1	5	and	and	CCONJ
ejpam-3253	1	6	applied	apply	VERB
ejpam-3253	1	7	mathematics	mathematic	NOUN
ejpam-3253	1	8	vol	vol	NOUN
ejpam-3253	1	9	.	.	PUNCT
ejpam-3253	2	1	11	11	NUM
ejpam-3253	2	2	,	,	PUNCT
ejpam-3253	2	3	no	no	INTJ
ejpam-3253	2	4	.	.	NOUN
ejpam-3253	2	5	3	3	NUM
ejpam-3253	2	6	,	,	PUNCT
ejpam-3253	2	7	2018	2018	NUM
ejpam-3253	2	8	,	,	PUNCT
ejpam-3253	2	9	882	882	NUM
ejpam-3253	2	10	-	-	SYM
ejpam-3253	2	11	892	892	NUM
ejpam-3253	2	12	issn	issn	PROPN
ejpam-3253	2	13	1307	1307	NUM
ejpam-3253	2	14	-	-	SYM
ejpam-3253	2	15	5543	5543	NUM
ejpam-3253	2	16	–	–	PUNCT
ejpam-3253	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3253	2	18	published	publish	VERB
ejpam-3253	2	19	by	by	ADP
ejpam-3253	2	20	new	new	PROPN
ejpam-3253	2	21	york	york	PROPN
ejpam-3253	2	22	business	business	PROPN
ejpam-3253	2	23	global	global	PROPN
ejpam-3253	2	24	c	c	NOUN
ejpam-3253	2	25	-	-	PUNCT
ejpam-3253	2	26	tychonoff	tychonoff	NOUN
ejpam-3253	2	27	and	and	CCONJ
ejpam-3253	2	28	l	l	NOUN
ejpam-3253	2	29	-	-	NOUN
ejpam-3253	2	30	tychonoff	tychonoff	NOUN
ejpam-3253	2	31	topological	topological	ADJ
ejpam-3253	2	32	spaces	space	NOUN
ejpam-3253	2	33	samirah	samirah	PROPN
ejpam-3253	2	34	alzahrani	alzahrani	PROPN
ejpam-3253	2	35	department	department	PROPN
ejpam-3253	2	36	of	of	ADP
ejpam-3253	2	37	mathematics	mathematics	PROPN
ejpam-3253	2	38	and	and	CCONJ
ejpam-3253	2	39	statistics	statistic	NOUN
ejpam-3253	2	40	,	,	PUNCT
ejpam-3253	2	41	faculty	faculty	NOUN
ejpam-3253	2	42	of	of	ADP
ejpam-3253	2	43	science	science	NOUN
ejpam-3253	2	44	,	,	PUNCT
ejpam-3253	2	45	taif	taif	PROPN
ejpam-3253	2	46	university	university	PROPN
ejpam-3253	2	47	,	,	PUNCT
ejpam-3253	2	48	p.o.box	p.o.box	PROPN
ejpam-3253	2	49	888	888	NUM
ejpam-3253	2	50	,	,	PUNCT
ejpam-3253	2	51	taif	taif	PROPN
ejpam-3253	2	52	21974	21974	NUM
ejpam-3253	3	1	,	,	PUNCT
ejpam-3253	3	2	saudi	saudi	PROPN
ejpam-3253	3	3	arabia	arabia	PROPN
ejpam-3253	3	4	abstract	abstract	NOUN
ejpam-3253	3	5	.	.	PUNCT
ejpam-3253	4	1	a	a	DET
ejpam-3253	4	2	topological	topological	ADJ
ejpam-3253	4	3	space	space	NOUN
ejpam-3253	4	4	x	x	PUNCT
ejpam-3253	4	5	is	be	AUX
ejpam-3253	4	6	called	call	VERB
ejpam-3253	4	7	c	c	NOUN
ejpam-3253	4	8	-	-	PUNCT
ejpam-3253	4	9	tychonoff	tychonoff	NOUN
ejpam-3253	4	10	if	if	SCONJ
ejpam-3253	4	11	there	there	PRON
ejpam-3253	4	12	exist	exist	VERB
ejpam-3253	4	13	a	a	DET
ejpam-3253	4	14	one	one	NUM
ejpam-3253	4	15	-	-	PUNCT
ejpam-3253	4	16	to	to	ADP
ejpam-3253	4	17	-	-	PUNCT
ejpam-3253	4	18	one	one	NUM
ejpam-3253	4	19	function	function	NOUN
ejpam-3253	4	20	f	f	NOUN
ejpam-3253	4	21	from	from	ADP
ejpam-3253	4	22	x	x	PRON
ejpam-3253	4	23	onto	onto	ADP
ejpam-3253	4	24	a	a	DET
ejpam-3253	4	25	tychonoff	tychonoff	NOUN
ejpam-3253	4	26	space	space	NOUN
ejpam-3253	4	27	y	y	PRON
ejpam-3253	4	28	such	such	ADJ
ejpam-3253	4	29	that	that	SCONJ
ejpam-3253	4	30	the	the	DET
ejpam-3253	4	31	restriction	restriction	NOUN
ejpam-3253	4	32	f|k	f|k	PUNCT
ejpam-3253	5	1	:	:	PUNCT
ejpam-3253	5	2	k	k	X
ejpam-3253	5	3	−→	−→	NOUN
ejpam-3253	5	4	f(k	f(k	VERB
ejpam-3253	5	5	)	)	PUNCT
ejpam-3253	5	6	is	be	AUX
ejpam-3253	5	7	a	a	DET
ejpam-3253	5	8	homeomorphism	homeomorphism	NOUN
ejpam-3253	5	9	for	for	ADP
ejpam-3253	5	10	each	each	DET
ejpam-3253	5	11	compact	compact	ADJ
ejpam-3253	5	12	subspace	subspace	NOUN
ejpam-3253	5	13	k	k	PROPN
ejpam-3253	5	14	⊆	⊆	NUM
ejpam-3253	5	15	x.	x.	NOUN
ejpam-3253	5	16	we	we	PRON
ejpam-3253	5	17	discuss	discuss	VERB
ejpam-3253	5	18	this	this	DET
ejpam-3253	5	19	property	property	NOUN
ejpam-3253	5	20	and	and	CCONJ
ejpam-3253	5	21	illustrate	illustrate	VERB
ejpam-3253	5	22	the	the	DET
ejpam-3253	5	23	relationships	relationship	NOUN
ejpam-3253	5	24	between	between	ADP
ejpam-3253	5	25	c	c	NOUN
ejpam-3253	5	26	-	-	PUNCT
ejpam-3253	5	27	tychonoffness	tychonoffness	NOUN
ejpam-3253	5	28	and	and	CCONJ
ejpam-3253	5	29	some	some	DET
ejpam-3253	5	30	other	other	ADJ
ejpam-3253	5	31	properties	property	NOUN
ejpam-3253	5	32	like	like	ADP
ejpam-3253	5	33	submetrizability	submetrizability	NOUN
ejpam-3253	5	34	,	,	PUNCT
ejpam-3253	5	35	local	local	ADJ
ejpam-3253	5	36	compactness	compactness	NOUN
ejpam-3253	5	37	,	,	PUNCT
ejpam-3253	5	38	ltychonoffness	ltychonoffness	NOUN
ejpam-3253	5	39	,	,	PUNCT
ejpam-3253	5	40	c	c	NOUN
ejpam-3253	5	41	-	-	NOUN
ejpam-3253	5	42	normality	normality	NOUN
ejpam-3253	5	43	,	,	PUNCT
ejpam-3253	5	44	c	c	NOUN
ejpam-3253	5	45	-	-	PUNCT
ejpam-3253	5	46	regularity	regularity	NOUN
ejpam-3253	5	47	,	,	PUNCT
ejpam-3253	5	48	epinormality	epinormality	NOUN
ejpam-3253	5	49	,	,	PUNCT
ejpam-3253	5	50	σ	σ	NOUN
ejpam-3253	5	51	-	-	PUNCT
ejpam-3253	5	52	compactness	compactness	NOUN
ejpam-3253	5	53	,	,	PUNCT
ejpam-3253	5	54	pseudocompactness	pseudocompactness	NOUN
ejpam-3253	5	55	and	and	CCONJ
ejpam-3253	5	56	zero	zero	NUM
ejpam-3253	5	57	-	-	PUNCT
ejpam-3253	5	58	dimensional	dimensional	ADJ
ejpam-3253	5	59	.	.	PUNCT
ejpam-3253	6	1	2010	2010	NUM
ejpam-3253	6	2	mathematics	mathematic	NOUN
ejpam-3253	6	3	subject	subject	NOUN
ejpam-3253	6	4	classifications	classification	NOUN
ejpam-3253	6	5	:	:	PUNCT
ejpam-3253	6	6	54d10	54d10	NUM
ejpam-3253	6	7	,	,	PUNCT
ejpam-3253	6	8	54d15	54d15	NUM
ejpam-3253	6	9	,	,	PUNCT
ejpam-3253	6	10	54c10	54c10	NUM
ejpam-3253	6	11	key	key	ADJ
ejpam-3253	6	12	words	word	NOUN
ejpam-3253	6	13	and	and	CCONJ
ejpam-3253	6	14	phrases	phrase	NOUN
ejpam-3253	6	15	:	:	PUNCT
ejpam-3253	6	16	tychonoff	tychonoff	NOUN
ejpam-3253	6	17	,	,	PUNCT
ejpam-3253	6	18	c	c	NOUN
ejpam-3253	6	19	-	-	PUNCT
ejpam-3253	6	20	tychonoff	tychonoff	NOUN
ejpam-3253	6	21	,	,	PUNCT
ejpam-3253	6	22	c	c	NOUN
ejpam-3253	6	23	-	-	ADJ
ejpam-3253	6	24	normal	normal	ADJ
ejpam-3253	6	25	,	,	PUNCT
ejpam-3253	6	26	c	c	NOUN
ejpam-3253	6	27	-	-	ADJ
ejpam-3253	6	28	regular	regular	ADJ
ejpam-3253	6	29	,	,	PUNCT
ejpam-3253	6	30	epinormal	epinormal	ADJ
ejpam-3253	6	31	,	,	PUNCT
ejpam-3253	6	32	submetrizable	submetrizable	ADJ
ejpam-3253	6	33	,	,	PUNCT
ejpam-3253	6	34	l	l	NOUN
ejpam-3253	6	35	-	-	NOUN
ejpam-3253	6	36	tychonoff	tychonoff	NOUN
ejpam-3253	6	37	1	1	NUM
ejpam-3253	6	38	.	.	PUNCT
ejpam-3253	6	39	introduction	introduction	NOUN
ejpam-3253	6	40	we	we	PRON
ejpam-3253	6	41	define	define	VERB
ejpam-3253	6	42	a	a	DET
ejpam-3253	6	43	new	new	ADJ
ejpam-3253	6	44	topological	topological	ADJ
ejpam-3253	6	45	property	property	NOUN
ejpam-3253	6	46	called	call	VERB
ejpam-3253	6	47	c	c	NOUN
ejpam-3253	6	48	-	-	PUNCT
ejpam-3253	6	49	tychonoff	tychonoff	NOUN
ejpam-3253	6	50	.	.	PUNCT
ejpam-3253	7	1	unlike	unlike	ADP
ejpam-3253	7	2	c	c	X
ejpam-3253	7	3	-	-	PUNCT
ejpam-3253	7	4	normality[2	normality[2	PROPN
ejpam-3253	7	5	]	]	PUNCT
ejpam-3253	7	6	,	,	PUNCT
ejpam-3253	7	7	we	we	PRON
ejpam-3253	7	8	prove	prove	VERB
ejpam-3253	7	9	that	that	SCONJ
ejpam-3253	7	10	c	c	NOUN
ejpam-3253	7	11	-	-	PUNCT
ejpam-3253	7	12	tychonoffness	tychonoffness	NOUN
ejpam-3253	7	13	is	be	AUX
ejpam-3253	7	14	a	a	DET
ejpam-3253	7	15	topological	topological	ADJ
ejpam-3253	7	16	property	property	NOUN
ejpam-3253	7	17	which	which	PRON
ejpam-3253	7	18	is	be	AUX
ejpam-3253	7	19	multiplicative	multiplicative	ADJ
ejpam-3253	7	20	and	and	CCONJ
ejpam-3253	7	21	hereditary	hereditary	ADJ
ejpam-3253	7	22	.	.	PUNCT
ejpam-3253	8	1	we	we	PRON
ejpam-3253	8	2	show	show	VERB
ejpam-3253	8	3	that	that	SCONJ
ejpam-3253	8	4	c	c	NOUN
ejpam-3253	8	5	-	-	PUNCT
ejpam-3253	8	6	tychonoff	tychonoff	NOUN
ejpam-3253	8	7	and	and	CCONJ
ejpam-3253	8	8	c	c	NOUN
ejpam-3253	8	9	-	-	ADJ
ejpam-3253	8	10	normal	normal	ADJ
ejpam-3253	8	11	are	be	AUX
ejpam-3253	8	12	independent	independent	ADJ
ejpam-3253	8	13	.	.	PUNCT
ejpam-3253	9	1	also	also	ADV
ejpam-3253	9	2	we	we	PRON
ejpam-3253	9	3	investigate	investigate	VERB
ejpam-3253	9	4	the	the	DET
ejpam-3253	9	5	function	function	NOUN
ejpam-3253	9	6	witnesses	witness	NOUN
ejpam-3253	9	7	the	the	DET
ejpam-3253	9	8	c	c	NOUN
ejpam-3253	9	9	-	-	PUNCT
ejpam-3253	9	10	tychonoffness	tychonoffness	NOUN
ejpam-3253	9	11	when	when	SCONJ
ejpam-3253	9	12	it	it	PRON
ejpam-3253	9	13	is	be	AUX
ejpam-3253	9	14	continuous	continuous	ADJ
ejpam-3253	9	15	and	and	CCONJ
ejpam-3253	9	16	when	when	SCONJ
ejpam-3253	9	17	it	it	PRON
ejpam-3253	9	18	is	be	AUX
ejpam-3253	9	19	not	not	PART
ejpam-3253	9	20	.	.	PUNCT
ejpam-3253	10	1	we	we	PRON
ejpam-3253	10	2	introduce	introduce	VERB
ejpam-3253	10	3	the	the	DET
ejpam-3253	10	4	notion	notion	NOUN
ejpam-3253	10	5	of	of	ADP
ejpam-3253	10	6	l	l	NOUN
ejpam-3253	10	7	-	-	NOUN
ejpam-3253	10	8	tychonoffness	tychonoffness	NOUN
ejpam-3253	10	9	.	.	PUNCT
ejpam-3253	11	1	throughout	throughout	ADP
ejpam-3253	11	2	this	this	DET
ejpam-3253	11	3	paper	paper	NOUN
ejpam-3253	11	4	,	,	PUNCT
ejpam-3253	11	5	we	we	PRON
ejpam-3253	11	6	denoted	denote	VERB
ejpam-3253	11	7	of	of	ADP
ejpam-3253	11	8	the	the	DET
ejpam-3253	11	9	set	set	NOUN
ejpam-3253	11	10	of	of	ADP
ejpam-3253	11	11	positive	positive	ADJ
ejpam-3253	11	12	integers	integer	NOUN
ejpam-3253	11	13	by	by	ADP
ejpam-3253	11	14	n	n	CCONJ
ejpam-3253	11	15	,	,	PUNCT
ejpam-3253	11	16	and	and	CCONJ
ejpam-3253	11	17	an	an	DET
ejpam-3253	11	18	order	order	NOUN
ejpam-3253	11	19	pair	pair	NOUN
ejpam-3253	11	20	by	by	ADP
ejpam-3253	11	21	〈	〈	PROPN
ejpam-3253	11	22	x	x	PROPN
ejpam-3253	11	23	,	,	PUNCT
ejpam-3253	11	24	y	y	PROPN
ejpam-3253	11	25	〉	〉	PROPN
ejpam-3253	11	26	.	.	PUNCT
ejpam-3253	12	1	an	an	DET
ejpam-3253	12	2	ordinal	ordinal	ADJ
ejpam-3253	12	3	γ	γ	X
ejpam-3253	12	4	is	be	AUX
ejpam-3253	12	5	the	the	DET
ejpam-3253	12	6	set	set	NOUN
ejpam-3253	12	7	of	of	ADP
ejpam-3253	12	8	all	all	DET
ejpam-3253	12	9	ordinal	ordinal	ADJ
ejpam-3253	12	10	α	α	NOUN
ejpam-3253	12	11	,	,	PUNCT
ejpam-3253	12	12	with	with	ADP
ejpam-3253	12	13	α	α	PROPN
ejpam-3253	12	14	<	<	X
ejpam-3253	12	15	γ	γ	X
ejpam-3253	12	16	,	,	PUNCT
ejpam-3253	12	17	we	we	PRON
ejpam-3253	12	18	denoted	denote	VERB
ejpam-3253	12	19	the	the	DET
ejpam-3253	12	20	first	first	ADJ
ejpam-3253	12	21	infinite	infinite	ADJ
ejpam-3253	12	22	ordinal	ordinal	NOUN
ejpam-3253	12	23	by	by	ADP
ejpam-3253	12	24	ω0	ω0	PROPN
ejpam-3253	12	25	and	and	CCONJ
ejpam-3253	12	26	the	the	DET
ejpam-3253	12	27	first	first	ADJ
ejpam-3253	12	28	uncountable	uncountable	ADJ
ejpam-3253	12	29	ordinal	ordinal	NOUN
ejpam-3253	12	30	by	by	ADP
ejpam-3253	12	31	ω1	ω1	PROPN
ejpam-3253	12	32	.	.	PUNCT
ejpam-3253	13	1	a	a	DET
ejpam-3253	13	2	t3	t3	PROPN
ejpam-3253	13	3	space	space	NOUN
ejpam-3253	13	4	is	be	AUX
ejpam-3253	13	5	a	a	DET
ejpam-3253	13	6	t1	t1	NOUN
ejpam-3253	13	7	regular	regular	ADJ
ejpam-3253	13	8	space	space	NOUN
ejpam-3253	13	9	,	,	PUNCT
ejpam-3253	13	10	a	a	DET
ejpam-3253	13	11	tychonoff	tychonoff	NOUN
ejpam-3253	13	12	(	(	PUNCT
ejpam-3253	13	13	t3	t3	NOUN
ejpam-3253	13	14	1	1	NUM
ejpam-3253	13	15	2	2	NUM
ejpam-3253	13	16	)	)	PUNCT
ejpam-3253	13	17	space	space	NOUN
ejpam-3253	13	18	is	be	AUX
ejpam-3253	13	19	a	a	DET
ejpam-3253	13	20	t1	t1	NOUN
ejpam-3253	13	21	completely	completely	ADV
ejpam-3253	13	22	regular	regular	ADJ
ejpam-3253	13	23	space	space	NOUN
ejpam-3253	13	24	,	,	PUNCT
ejpam-3253	13	25	and	and	CCONJ
ejpam-3253	13	26	a	a	DET
ejpam-3253	13	27	t4	t4	PROPN
ejpam-3253	13	28	space	space	NOUN
ejpam-3253	13	29	is	be	AUX
ejpam-3253	13	30	a	a	DET
ejpam-3253	13	31	t1	t1	NOUN
ejpam-3253	13	32	normal	normal	ADJ
ejpam-3253	13	33	space	space	NOUN
ejpam-3253	13	34	.	.	PUNCT
ejpam-3253	14	1	for	for	ADP
ejpam-3253	14	2	a	a	DET
ejpam-3253	14	3	subset	subset	NOUN
ejpam-3253	14	4	b	b	NOUN
ejpam-3253	14	5	of	of	ADP
ejpam-3253	14	6	a	a	DET
ejpam-3253	14	7	space	space	NOUN
ejpam-3253	14	8	x	x	NOUN
ejpam-3253	14	9	,	,	PUNCT
ejpam-3253	14	10	intb	intb	AUX
ejpam-3253	14	11	denote	denote	VERB
ejpam-3253	14	12	the	the	DET
ejpam-3253	14	13	interior	interior	NOUN
ejpam-3253	14	14	of	of	ADP
ejpam-3253	14	15	b	b	PROPN
ejpam-3253	14	16	and	and	CCONJ
ejpam-3253	14	17	b	b	NOUN
ejpam-3253	14	18	denote	denote	VERB
ejpam-3253	14	19	the	the	DET
ejpam-3253	14	20	closure	closure	NOUN
ejpam-3253	14	21	of	of	ADP
ejpam-3253	14	22	b.	b.	PROPN
ejpam-3253	14	23	a	a	DET
ejpam-3253	14	24	space	space	NOUN
ejpam-3253	15	1	x	x	PUNCT
ejpam-3253	15	2	is	be	AUX
ejpam-3253	15	3	locally	locally	ADV
ejpam-3253	15	4	compact	compact	ADJ
ejpam-3253	15	5	if	if	SCONJ
ejpam-3253	15	6	for	for	ADP
ejpam-3253	15	7	each	each	DET
ejpam-3253	15	8	y	y	PROPN
ejpam-3253	15	9	∈	∈	PROPN
ejpam-3253	15	10	x	x	X
ejpam-3253	15	11	and	and	CCONJ
ejpam-3253	15	12	each	each	DET
ejpam-3253	15	13	open	open	ADJ
ejpam-3253	15	14	neighborhood	neighborhood	NOUN
ejpam-3253	15	15	u	u	NOUN
ejpam-3253	15	16	of	of	ADP
ejpam-3253	15	17	y	y	PRON
ejpam-3253	15	18	there	there	PRON
ejpam-3253	15	19	exists	exist	VERB
ejpam-3253	15	20	an	an	DET
ejpam-3253	15	21	open	open	ADJ
ejpam-3253	15	22	neighborhood	neighborhood	NOUN
ejpam-3253	15	23	v	v	NOUN
ejpam-3253	15	24	of	of	ADP
ejpam-3253	15	25	y	y	PRON
ejpam-3253	15	26	such	such	ADJ
ejpam-3253	15	27	that	that	SCONJ
ejpam-3253	15	28	y	y	PROPN
ejpam-3253	15	29	∈	∈	PROPN
ejpam-3253	15	30	v	v	ADP
ejpam-3253	15	31	⊆	⊆	NUM
ejpam-3253	15	32	v	v	ADP
ejpam-3253	15	33	⊆	⊆	NUM
ejpam-3253	15	34	u	u	NOUN
ejpam-3253	15	35	and	and	CCONJ
ejpam-3253	15	36	v	v	NOUN
ejpam-3253	15	37	is	be	AUX
ejpam-3253	15	38	compact	compact	ADJ
ejpam-3253	15	39	,	,	PUNCT
ejpam-3253	15	40	we	we	PRON
ejpam-3253	15	41	do	do	AUX
ejpam-3253	15	42	not	not	PART
ejpam-3253	15	43	assume	assume	VERB
ejpam-3253	15	44	t2	t2	NOUN
ejpam-3253	15	45	in	in	ADP
ejpam-3253	15	46	the	the	DET
ejpam-3253	15	47	definition	definition	NOUN
ejpam-3253	15	48	of	of	ADP
ejpam-3253	15	49	local	local	ADJ
ejpam-3253	15	50	compactness	compactness	NOUN
ejpam-3253	15	51	.	.	PUNCT
ejpam-3253	16	1	doi	doi	NOUN
ejpam-3253	16	2	:	:	PUNCT
ejpam-3253	16	3	https://doi.org/10.29020/nybg.ejpam.v11i3.3253	https://doi.org/10.29020/nybg.ejpam.v11i3.3253	NOUN
ejpam-3253	16	4	email	email	NOUN
ejpam-3253	16	5	address	address	NOUN
ejpam-3253	16	6	:	:	PUNCT
ejpam-3253	16	7	mam	mam	NOUN
ejpam-3253	16	8	1420@hotmail.com	1420@hotmail.com	X
ejpam-3253	16	9	samar.alz@tu.edu.sa	samar.alz@tu.edu.sa	PROPN
ejpam-3253	16	10	(	(	PUNCT
ejpam-3253	16	11	s.	s.	PROPN
ejpam-3253	16	12	alzahrani	alzahrani	PROPN
ejpam-3253	16	13	)	)	PUNCT
ejpam-3253	16	14	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3253	17	1	882	882	NUM
ejpam-3253	17	2	c	c	NOUN
ejpam-3253	17	3	©	©	PROPN
ejpam-3253	17	4	2018	2018	NUM
ejpam-3253	17	5	ejpam	ejpam	VERB
ejpam-3253	17	6	all	all	DET
ejpam-3253	17	7	rights	right	NOUN
ejpam-3253	17	8	reserved	reserve	VERB
ejpam-3253	17	9	.	.	PUNCT
ejpam-3253	18	1	s.	s.	PROPN
ejpam-3253	18	2	alzahrani	alzahrani	PROPN
ejpam-3253	18	3	/	/	SYM
ejpam-3253	18	4	eur	eur	PROPN
ejpam-3253	18	5	.	.	PUNCT
ejpam-3253	19	1	j.	j.	PROPN
ejpam-3253	19	2	pure	pure	PROPN
ejpam-3253	19	3	appl	appl	PROPN
ejpam-3253	19	4	.	.	PROPN
ejpam-3253	19	5	math	math	PROPN
ejpam-3253	19	6	,	,	PUNCT
ejpam-3253	19	7	11	11	NUM
ejpam-3253	19	8	(	(	PUNCT
ejpam-3253	19	9	3	3	NUM
ejpam-3253	19	10	)	)	PUNCT
ejpam-3253	19	11	(	(	PUNCT
ejpam-3253	19	12	2018	2018	NUM
ejpam-3253	19	13	)	)	PUNCT
ejpam-3253	19	14	,	,	PUNCT
ejpam-3253	19	15	882	882	NUM
ejpam-3253	19	16	-	-	SYM
ejpam-3253	19	17	892	892	NUM
ejpam-3253	19	18	883	883	NUM
ejpam-3253	19	19	2	2	NUM
ejpam-3253	19	20	.	.	PUNCT
ejpam-3253	20	1	c	c	X
ejpam-3253	20	2	-	-	PUNCT
ejpam-3253	20	3	tychonoffness	tychonoffness	NOUN
ejpam-3253	20	4	definition	definition	NOUN
ejpam-3253	20	5	1	1	NUM
ejpam-3253	20	6	.	.	PUNCT
ejpam-3253	21	1	a	a	DET
ejpam-3253	21	2	topological	topological	ADJ
ejpam-3253	21	3	space	space	NOUN
ejpam-3253	21	4	x	x	PUNCT
ejpam-3253	21	5	is	be	AUX
ejpam-3253	21	6	called	call	VERB
ejpam-3253	21	7	c	c	NOUN
ejpam-3253	21	8	-	-	PUNCT
ejpam-3253	21	9	tychonoff	tychonoff	NOUN
ejpam-3253	21	10	if	if	SCONJ
ejpam-3253	21	11	there	there	PRON
ejpam-3253	21	12	exist	exist	VERB
ejpam-3253	21	13	a	a	DET
ejpam-3253	21	14	one	one	NUM
ejpam-3253	21	15	-	-	PUNCT
ejpam-3253	21	16	to	to	ADP
ejpam-3253	21	17	-	-	PUNCT
ejpam-3253	21	18	one	one	NUM
ejpam-3253	21	19	function	function	NOUN
ejpam-3253	21	20	f	f	NOUN
ejpam-3253	21	21	from	from	ADP
ejpam-3253	21	22	x	x	PRON
ejpam-3253	21	23	onto	onto	ADP
ejpam-3253	21	24	a	a	DET
ejpam-3253	21	25	tychonoff	tychonoff	NOUN
ejpam-3253	21	26	space	space	NOUN
ejpam-3253	21	27	y	y	PRON
ejpam-3253	21	28	such	such	ADJ
ejpam-3253	21	29	that	that	SCONJ
ejpam-3253	21	30	the	the	DET
ejpam-3253	21	31	restriction	restriction	NOUN
ejpam-3253	21	32	f|k	f|k	PUNCT
ejpam-3253	22	1	:	:	PUNCT
ejpam-3253	22	2	k	k	X
ejpam-3253	22	3	−→	−→	NOUN
ejpam-3253	22	4	f(k	f(k	VERB
ejpam-3253	22	5	)	)	PUNCT
ejpam-3253	22	6	is	be	AUX
ejpam-3253	22	7	a	a	DET
ejpam-3253	22	8	homeomorphism	homeomorphism	NOUN
ejpam-3253	22	9	for	for	ADP
ejpam-3253	22	10	each	each	DET
ejpam-3253	22	11	compact	compact	ADJ
ejpam-3253	22	12	subspace	subspace	NOUN
ejpam-3253	22	13	k	k	PROPN
ejpam-3253	22	14	⊆	⊆	NUM
ejpam-3253	22	15	x.	x.	NOUN
ejpam-3253	22	16	recall	recall	VERB
ejpam-3253	22	17	that	that	SCONJ
ejpam-3253	22	18	a	a	DET
ejpam-3253	22	19	topological	topological	ADJ
ejpam-3253	22	20	space	space	NOUN
ejpam-3253	22	21	(	(	PUNCT
ejpam-3253	22	22	x	x	X
ejpam-3253	22	23	,	,	PUNCT
ejpam-3253	22	24	τ	τ	PROPN
ejpam-3253	22	25	)	)	PUNCT
ejpam-3253	22	26	is	be	AUX
ejpam-3253	22	27	called	call	VERB
ejpam-3253	22	28	submetrizable	submetrizable	ADJ
ejpam-3253	22	29	if	if	SCONJ
ejpam-3253	22	30	there	there	PRON
ejpam-3253	22	31	exists	exist	VERB
ejpam-3253	22	32	a	a	DET
ejpam-3253	22	33	metric	metric	ADJ
ejpam-3253	22	34	d	d	NOUN
ejpam-3253	22	35	on	on	ADP
ejpam-3253	22	36	x	x	SYM
ejpam-3253	22	37	such	such	ADJ
ejpam-3253	22	38	that	that	SCONJ
ejpam-3253	22	39	the	the	DET
ejpam-3253	22	40	topology	topology	NOUN
ejpam-3253	23	1	τ	τ	X
ejpam-3253	23	2	d	d	NOUN
ejpam-3253	23	3	on	on	ADP
ejpam-3253	23	4	x	x	PUNCT
ejpam-3253	23	5	generated	generate	VERB
ejpam-3253	23	6	by	by	ADP
ejpam-3253	23	7	d	d	PROPN
ejpam-3253	23	8	is	be	AUX
ejpam-3253	23	9	coarser	coarse	ADJ
ejpam-3253	23	10	than	than	ADP
ejpam-3253	23	11	τ	τ	PROPN
ejpam-3253	23	12	,	,	PUNCT
ejpam-3253	23	13	i.e.	i.e.	X
ejpam-3253	23	14	,	,	PUNCT
ejpam-3253	23	15	τ	τ	PROPN
ejpam-3253	23	16	d	d	PROPN
ejpam-3253	23	17	⊆	⊆	NUM
ejpam-3253	23	18	τ	τ	X
ejpam-3253	23	19	,	,	PUNCT
ejpam-3253	23	20	see	see	VERB
ejpam-3253	23	21	[	[	X
ejpam-3253	23	22	10	10	NUM
ejpam-3253	23	23	]	]	PUNCT
ejpam-3253	23	24	.	.	PUNCT
ejpam-3253	24	1	theorem	theorem	NOUN
ejpam-3253	24	2	1	1	NUM
ejpam-3253	24	3	.	.	PUNCT
ejpam-3253	25	1	every	every	DET
ejpam-3253	25	2	submetrizable	submetrizable	ADJ
ejpam-3253	25	3	space	space	NOUN
ejpam-3253	25	4	is	be	AUX
ejpam-3253	25	5	c	c	NOUN
ejpam-3253	25	6	-	-	PUNCT
ejpam-3253	25	7	tychonoff	tychonoff	NOUN
ejpam-3253	25	8	.	.	PUNCT
ejpam-3253	26	1	proof	proof	NOUN
ejpam-3253	26	2	.	.	PUNCT
ejpam-3253	27	1	let	let	VERB
ejpam-3253	27	2	τ	τ	PROPN
ejpam-3253	27	3	′	′	AUX
ejpam-3253	27	4	be	be	AUX
ejpam-3253	27	5	a	a	DET
ejpam-3253	27	6	metrizable	metrizable	ADJ
ejpam-3253	27	7	topology	topology	NOUN
ejpam-3253	27	8	on	on	ADP
ejpam-3253	27	9	x	x	SYM
ejpam-3253	27	10	such	such	ADJ
ejpam-3253	27	11	that	that	SCONJ
ejpam-3253	27	12	τ	τ	PROPN
ejpam-3253	27	13	′	′	NUM
ejpam-3253	27	14	⊆τ	⊆τ	NOUN
ejpam-3253	27	15	.	.	PUNCT
ejpam-3253	28	1	then	then	ADV
ejpam-3253	28	2	(	(	PUNCT
ejpam-3253	28	3	x	x	X
ejpam-3253	28	4	,	,	PUNCT
ejpam-3253	28	5	τ	τ	PROPN
ejpam-3253	28	6	′	′	NUM
ejpam-3253	28	7	)	)	PUNCT
ejpam-3253	28	8	is	be	AUX
ejpam-3253	28	9	tychonoff	tychonoff	NOUN
ejpam-3253	28	10	and	and	CCONJ
ejpam-3253	28	11	the	the	DET
ejpam-3253	28	12	identity	identity	NOUN
ejpam-3253	28	13	function	function	NOUN
ejpam-3253	28	14	idx	idx	NOUN
ejpam-3253	28	15	:	:	PUNCT
ejpam-3253	28	16	(	(	PUNCT
ejpam-3253	28	17	x	x	X
ejpam-3253	28	18	,	,	PUNCT
ejpam-3253	28	19	τ	τ	PROPN
ejpam-3253	28	20	)	)	PUNCT
ejpam-3253	29	1	−→	−→	NOUN
ejpam-3253	29	2	(	(	PUNCT
ejpam-3253	29	3	x	x	X
ejpam-3253	29	4	,	,	PUNCT
ejpam-3253	29	5	τ	τ	PROPN
ejpam-3253	29	6	′	′	NUM
ejpam-3253	29	7	)	)	PUNCT
ejpam-3253	29	8	is	be	AUX
ejpam-3253	29	9	a	a	DET
ejpam-3253	29	10	bijective	bijective	ADJ
ejpam-3253	29	11	and	and	CCONJ
ejpam-3253	29	12	continuous	continuous	ADJ
ejpam-3253	29	13	.	.	PUNCT
ejpam-3253	30	1	if	if	SCONJ
ejpam-3253	30	2	k	k	PROPN
ejpam-3253	30	3	is	be	AUX
ejpam-3253	30	4	any	any	DET
ejpam-3253	30	5	compact	compact	ADJ
ejpam-3253	30	6	subspace	subspace	NOUN
ejpam-3253	30	7	of	of	ADP
ejpam-3253	30	8	(	(	PUNCT
ejpam-3253	30	9	x	x	PROPN
ejpam-3253	30	10	,	,	PUNCT
ejpam-3253	30	11	τ	τ	PROPN
ejpam-3253	30	12	)	)	PUNCT
ejpam-3253	30	13	,	,	PUNCT
ejpam-3253	30	14	then	then	ADV
ejpam-3253	30	15	idx(k	idx(k	NOUN
ejpam-3253	30	16	)	)	PUNCT
ejpam-3253	30	17	is	be	AUX
ejpam-3253	30	18	hausdorff	hausdorff	NOUN
ejpam-3253	30	19	being	be	AUX
ejpam-3253	30	20	a	a	DET
ejpam-3253	30	21	subspace	subspace	NOUN
ejpam-3253	30	22	of	of	ADP
ejpam-3253	30	23	the	the	DET
ejpam-3253	30	24	metrizable	metrizable	ADJ
ejpam-3253	30	25	space	space	NOUN
ejpam-3253	30	26	(	(	PUNCT
ejpam-3253	30	27	x	x	X
ejpam-3253	30	28	,	,	PUNCT
ejpam-3253	30	29	τ	τ	PROPN
ejpam-3253	30	30	′	′	NUM
ejpam-3253	30	31	)	)	PUNCT
ejpam-3253	30	32	,	,	PUNCT
ejpam-3253	30	33	and	and	CCONJ
ejpam-3253	30	34	the	the	DET
ejpam-3253	30	35	restriction	restriction	NOUN
ejpam-3253	30	36	of	of	ADP
ejpam-3253	30	37	the	the	DET
ejpam-3253	30	38	identity	identity	NOUN
ejpam-3253	30	39	function	function	NOUN
ejpam-3253	30	40	on	on	ADP
ejpam-3253	30	41	k	k	PROPN
ejpam-3253	30	42	onto	onto	ADP
ejpam-3253	30	43	idx(k	idx(k	NOUN
ejpam-3253	30	44	)	)	PUNCT
ejpam-3253	30	45	is	be	AUX
ejpam-3253	30	46	a	a	DET
ejpam-3253	30	47	homeomorphism	homeomorphism	NOUN
ejpam-3253	30	48	by	by	ADP
ejpam-3253	30	49	[	[	X
ejpam-3253	30	50	8	8	NUM
ejpam-3253	30	51	,	,	PUNCT
ejpam-3253	30	52	3.1.13	3.1.13	NUM
ejpam-3253	30	53	]	]	PUNCT
ejpam-3253	30	54	.	.	PUNCT
ejpam-3253	31	1	since	since	SCONJ
ejpam-3253	31	2	any	any	DET
ejpam-3253	31	3	hausdorff	hausdorff	NOUN
ejpam-3253	31	4	locally	locally	ADV
ejpam-3253	31	5	compact	compact	ADJ
ejpam-3253	31	6	space	space	NOUN
ejpam-3253	31	7	is	be	AUX
ejpam-3253	31	8	tychonoff	tychonoff	NOUN
ejpam-3253	31	9	,	,	PUNCT
ejpam-3253	31	10	then	then	ADV
ejpam-3253	31	11	we	we	PRON
ejpam-3253	31	12	have	have	VERB
ejpam-3253	31	13	the	the	DET
ejpam-3253	31	14	following	follow	VERB
ejpam-3253	31	15	theorem	theorem	VERB
ejpam-3253	31	16	.	.	PUNCT
ejpam-3253	31	17	theorem	theorem	NOUN
ejpam-3253	31	18	2	2	NUM
ejpam-3253	31	19	.	.	PUNCT
ejpam-3253	32	1	every	every	DET
ejpam-3253	32	2	hausdorff	hausdorff	NOUN
ejpam-3253	32	3	locally	locally	ADV
ejpam-3253	32	4	compact	compact	ADJ
ejpam-3253	32	5	space	space	NOUN
ejpam-3253	32	6	is	be	AUX
ejpam-3253	32	7	c	c	NOUN
ejpam-3253	32	8	-	-	PUNCT
ejpam-3253	32	9	tychonoff	tychonoff	NOUN
ejpam-3253	32	10	.	.	PUNCT
ejpam-3253	33	1	the	the	DET
ejpam-3253	33	2	converse	converse	NOUN
ejpam-3253	33	3	of	of	ADP
ejpam-3253	33	4	theorem	theorem	NOUN
ejpam-3253	33	5	1	1	NUM
ejpam-3253	33	6	is	be	AUX
ejpam-3253	33	7	not	not	PART
ejpam-3253	33	8	true	true	ADJ
ejpam-3253	33	9	in	in	ADP
ejpam-3253	33	10	general	general	ADJ
ejpam-3253	33	11	.	.	PUNCT
ejpam-3253	34	1	for	for	ADP
ejpam-3253	34	2	example	example	NOUN
ejpam-3253	34	3	,	,	PUNCT
ejpam-3253	34	4	the	the	DET
ejpam-3253	34	5	tychonoff	tychonoff	NOUN
ejpam-3253	34	6	plank	plank	NOUN
ejpam-3253	34	7	(	(	PUNCT
ejpam-3253	34	8	(	(	PUNCT
ejpam-3253	34	9	ω1	ω1	PROPN
ejpam-3253	34	10	+	+	PROPN
ejpam-3253	34	11	1)×	1)×	NUM
ejpam-3253	34	12	(	(	PUNCT
ejpam-3253	34	13	ω0	ω0	ADV
ejpam-3253	34	14	+	+	NOUN
ejpam-3253	34	15	1	1	NUM
ejpam-3253	34	16	)	)	PUNCT
ejpam-3253	34	17	)	)	PUNCT
ejpam-3253	34	18	\	\	NOUN
ejpam-3253	34	19	{	{	PUNCT
ejpam-3253	34	20	〈	〈	PROPN
ejpam-3253	34	21	ω1	ω1	PROPN
ejpam-3253	34	22	,	,	PUNCT
ejpam-3253	34	23	ω0	ω0	PROPN
ejpam-3253	34	24	〉	〉	NOUN
ejpam-3253	34	25	}	}	PUNCT
ejpam-3253	34	26	is	be	AUX
ejpam-3253	34	27	c	c	NOUN
ejpam-3253	34	28	-	-	PUNCT
ejpam-3253	34	29	tychonoff	tychonoff	NOUN
ejpam-3253	34	30	being	being	NOUN
ejpam-3253	34	31	hausdorff	hausdorff	NOUN
ejpam-3253	34	32	locally	locally	ADV
ejpam-3253	34	33	compact	compact	ADJ
ejpam-3253	34	34	,	,	PUNCT
ejpam-3253	34	35	but	but	CCONJ
ejpam-3253	34	36	it	it	PRON
ejpam-3253	34	37	is	be	AUX
ejpam-3253	34	38	not	not	PART
ejpam-3253	34	39	submetrizabl	submetrizabl	ADJ
ejpam-3253	34	40	,	,	PUNCT
ejpam-3253	34	41	because	because	SCONJ
ejpam-3253	34	42	if	if	SCONJ
ejpam-3253	34	43	it	it	PRON
ejpam-3253	34	44	was	be	AUX
ejpam-3253	34	45	,	,	PUNCT
ejpam-3253	34	46	then	then	ADV
ejpam-3253	34	47	(	(	PUNCT
ejpam-3253	34	48	ω1	ω1	PROPN
ejpam-3253	34	49	+	+	CCONJ
ejpam-3253	34	50	1)×{0	1)×{0	NUM
ejpam-3253	34	51	}	}	SYM
ejpam-3253	34	52	⊆	⊆	NUM
ejpam-3253	34	53	(	(	PUNCT
ejpam-3253	34	54	(	(	PUNCT
ejpam-3253	34	55	ω1	ω1	PROPN
ejpam-3253	34	56	+	+	PROPN
ejpam-3253	34	57	1)×	1)×	NUM
ejpam-3253	34	58	(	(	PUNCT
ejpam-3253	34	59	ω0	ω0	ADV
ejpam-3253	34	60	+	+	CCONJ
ejpam-3253	34	61	1))\{〈ω1	1))\{〈ω1	NUM
ejpam-3253	34	62	,	,	PUNCT
ejpam-3253	34	63	ω0	ω0	PROPN
ejpam-3253	34	64	〉	〉	NOUN
ejpam-3253	34	65	}	}	PUNCT
ejpam-3253	34	66	is	be	AUX
ejpam-3253	34	67	submetrizabl	submetrizabl	ADJ
ejpam-3253	34	68	,	,	PUNCT
ejpam-3253	34	69	because	because	SCONJ
ejpam-3253	34	70	submetrizablity	submetrizablity	NOUN
ejpam-3253	34	71	is	be	AUX
ejpam-3253	34	72	hereditary	hereditary	ADJ
ejpam-3253	34	73	,	,	PUNCT
ejpam-3253	34	74	but	but	CCONJ
ejpam-3253	34	75	(	(	PUNCT
ejpam-3253	34	76	(	(	PUNCT
ejpam-3253	34	77	ω1	ω1	PROPN
ejpam-3253	34	78	+	+	CCONJ
ejpam-3253	34	79	1	1	NUM
ejpam-3253	34	80	)	)	PUNCT
ejpam-3253	34	81	×	×	NOUN
ejpam-3253	34	82	{	{	PUNCT
ejpam-3253	34	83	0	0	NUM
ejpam-3253	34	84	}	}	PUNCT
ejpam-3253	34	85	∼=	∼=	NOUN
ejpam-3253	34	86	ω1	ω1	NOUN
ejpam-3253	34	87	+	+	CCONJ
ejpam-3253	34	88	1	1	NUM
ejpam-3253	34	89	and	and	CCONJ
ejpam-3253	34	90	ω1	ω1	PROPN
ejpam-3253	34	91	+	+	CCONJ
ejpam-3253	34	92	1	1	NUM
ejpam-3253	34	93	is	be	AUX
ejpam-3253	34	94	not	not	PART
ejpam-3253	34	95	submetrizabl	submetrizabl	ADJ
ejpam-3253	34	96	.	.	PUNCT
ejpam-3253	35	1	the	the	DET
ejpam-3253	35	2	converse	converse	NOUN
ejpam-3253	35	3	of	of	ADP
ejpam-3253	35	4	theorem	theorem	ADJ
ejpam-3253	35	5	2	2	NUM
ejpam-3253	35	6	is	be	AUX
ejpam-3253	35	7	not	not	PART
ejpam-3253	35	8	true	true	ADJ
ejpam-3253	35	9	in	in	ADP
ejpam-3253	35	10	general	general	ADJ
ejpam-3253	35	11	as	as	ADP
ejpam-3253	35	12	the	the	DET
ejpam-3253	35	13	dieudonné	dieudonné	NOUN
ejpam-3253	35	14	plank	plank	NOUN
ejpam-3253	35	15	[	[	X
ejpam-3253	35	16	16	16	NUM
ejpam-3253	35	17	]	]	PUNCT
ejpam-3253	35	18	is	be	AUX
ejpam-3253	35	19	tychonoff	tychonoff	NOUN
ejpam-3253	35	20	,	,	PUNCT
ejpam-3253	35	21	hence	hence	ADV
ejpam-3253	35	22	c	c	NOUN
ejpam-3253	35	23	-	-	PUNCT
ejpam-3253	35	24	tychonoff	tychonoff	NOUN
ejpam-3253	35	25	but	but	CCONJ
ejpam-3253	35	26	not	not	PART
ejpam-3253	35	27	locally	locally	ADV
ejpam-3253	35	28	compact	compact	ADJ
ejpam-3253	35	29	.	.	PUNCT
ejpam-3253	36	1	hausdorffness	hausdorffness	PROPN
ejpam-3253	36	2	is	be	AUX
ejpam-3253	36	3	essential	essential	ADJ
ejpam-3253	36	4	in	in	ADP
ejpam-3253	36	5	theorem	theorem	NOUN
ejpam-3253	36	6	2	2	NUM
ejpam-3253	36	7	.	.	PUNCT
ejpam-3253	37	1	here	here	ADV
ejpam-3253	37	2	is	be	AUX
ejpam-3253	37	3	an	an	DET
ejpam-3253	37	4	example	example	NOUN
ejpam-3253	37	5	of	of	ADP
ejpam-3253	37	6	a	a	DET
ejpam-3253	37	7	locally	locally	ADV
ejpam-3253	37	8	compact	compact	ADJ
ejpam-3253	37	9	space	space	NOUN
ejpam-3253	37	10	which	which	PRON
ejpam-3253	37	11	is	be	AUX
ejpam-3253	37	12	neither	neither	PRON
ejpam-3253	37	13	c	c	NOUN
ejpam-3253	37	14	-	-	PUNCT
ejpam-3253	37	15	tychonoff	tychonoff	NOUN
ejpam-3253	37	16	nor	nor	CCONJ
ejpam-3253	37	17	hausdorff	hausdorff	NOUN
ejpam-3253	37	18	.	.	PUNCT
ejpam-3253	37	19	example	example	NOUN
ejpam-3253	38	1	1	1	NUM
ejpam-3253	38	2	.	.	PUNCT
ejpam-3253	39	1	the	the	DET
ejpam-3253	39	2	particular	particular	ADJ
ejpam-3253	39	3	point	point	NOUN
ejpam-3253	39	4	topology	topology	NOUN
ejpam-3253	39	5	τ√2	τ√2	VERB
ejpam-3253	39	6	on	on	ADP
ejpam-3253	39	7	r	r	NOUN
ejpam-3253	39	8	,	,	PUNCT
ejpam-3253	39	9	see	see	VERB
ejpam-3253	39	10	[	[	X
ejpam-3253	39	11	16	16	NUM
ejpam-3253	39	12	]	]	PUNCT
ejpam-3253	39	13	,	,	PUNCT
ejpam-3253	39	14	is	be	AUX
ejpam-3253	39	15	not	not	PART
ejpam-3253	39	16	c	c	NOUN
ejpam-3253	39	17	-	-	PUNCT
ejpam-3253	39	18	tychonoff	tychonoff	NOUN
ejpam-3253	39	19	.	.	PUNCT
ejpam-3253	40	1	it	it	PRON
ejpam-3253	40	2	is	be	AUX
ejpam-3253	40	3	well	well	ADV
ejpam-3253	40	4	-	-	PUNCT
ejpam-3253	40	5	known	know	VERB
ejpam-3253	40	6	that	that	SCONJ
ejpam-3253	40	7	(	(	PUNCT
ejpam-3253	40	8	r	r	NOUN
ejpam-3253	40	9	,	,	PUNCT
ejpam-3253	40	10	τ√2	τ√2	PRON
ejpam-3253	40	11	)	)	PUNCT
ejpam-3253	40	12	is	be	AUX
ejpam-3253	40	13	neither	neither	CCONJ
ejpam-3253	40	14	t1	t1	NOUN
ejpam-3253	40	15	nor	nor	CCONJ
ejpam-3253	40	16	tychonoff	tychonoff	NOUN
ejpam-3253	40	17	.	.	PUNCT
ejpam-3253	41	1	if	if	SCONJ
ejpam-3253	41	2	b	b	PROPN
ejpam-3253	41	3	⊆	⊆	NUM
ejpam-3253	41	4	r	r	NOUN
ejpam-3253	41	5	,	,	PUNCT
ejpam-3253	41	6	then	then	ADV
ejpam-3253	41	7	{	{	PUNCT
ejpam-3253	41	8	{	{	PUNCT
ejpam-3253	41	9	x	x	NOUN
ejpam-3253	41	10	,	,	PUNCT
ejpam-3253	41	11	√	√	ADV
ejpam-3253	41	12	2	2	NUM
ejpam-3253	41	13	}	}	PUNCT
ejpam-3253	41	14	:	:	PUNCT
ejpam-3253	41	15	x	x	X
ejpam-3253	41	16	∈	∈	PROPN
ejpam-3253	41	17	b	b	AUX
ejpam-3253	41	18	}	}	PUNCT
ejpam-3253	41	19	is	be	AUX
ejpam-3253	41	20	an	an	DET
ejpam-3253	41	21	open	open	ADJ
ejpam-3253	41	22	cover	cover	NOUN
ejpam-3253	41	23	for	for	ADP
ejpam-3253	41	24	b	b	NOUN
ejpam-3253	41	25	,	,	PUNCT
ejpam-3253	41	26	thus	thus	ADV
ejpam-3253	41	27	a	a	DET
ejpam-3253	41	28	subset	subset	NOUN
ejpam-3253	41	29	b	b	NOUN
ejpam-3253	41	30	of	of	ADP
ejpam-3253	41	31	r	r	NOUN
ejpam-3253	41	32	is	be	AUX
ejpam-3253	41	33	compact	compact	ADJ
ejpam-3253	41	34	if	if	SCONJ
ejpam-3253	41	35	and	and	CCONJ
ejpam-3253	41	36	only	only	ADV
ejpam-3253	41	37	if	if	SCONJ
ejpam-3253	41	38	it	it	PRON
ejpam-3253	41	39	is	be	AUX
ejpam-3253	41	40	finite	finite	ADJ
ejpam-3253	41	41	.	.	PUNCT
ejpam-3253	41	42	to	to	PART
ejpam-3253	41	43	show	show	VERB
ejpam-3253	41	44	that	that	SCONJ
ejpam-3253	41	45	(	(	PUNCT
ejpam-3253	41	46	r	r	NOUN
ejpam-3253	41	47	,	,	PUNCT
ejpam-3253	41	48	τ√2	τ√2	PRON
ejpam-3253	41	49	)	)	PUNCT
ejpam-3253	41	50	is	be	AUX
ejpam-3253	41	51	not	not	PART
ejpam-3253	41	52	c	c	NOUN
ejpam-3253	41	53	-	-	PUNCT
ejpam-3253	41	54	tychonoff	tychonoff	NOUN
ejpam-3253	41	55	,	,	PUNCT
ejpam-3253	41	56	suppose	suppose	VERB
ejpam-3253	41	57	that	that	SCONJ
ejpam-3253	41	58	(	(	PUNCT
ejpam-3253	41	59	r	r	NOUN
ejpam-3253	41	60	,	,	PUNCT
ejpam-3253	41	61	τ√2	τ√2	PRON
ejpam-3253	41	62	)	)	PUNCT
ejpam-3253	41	63	is	be	AUX
ejpam-3253	41	64	c	c	NOUN
ejpam-3253	41	65	-	-	PUNCT
ejpam-3253	41	66	tychonoff	tychonoff	NOUN
ejpam-3253	41	67	.	.	PUNCT
ejpam-3253	42	1	let	let	VERB
ejpam-3253	42	2	z	z	PRON
ejpam-3253	42	3	be	be	AUX
ejpam-3253	42	4	a	a	DET
ejpam-3253	42	5	tychonoff	tychonoff	NOUN
ejpam-3253	42	6	space	space	NOUN
ejpam-3253	42	7	and	and	CCONJ
ejpam-3253	42	8	f	f	NOUN
ejpam-3253	42	9	:	:	PUNCT
ejpam-3253	42	10	r	r	NOUN
ejpam-3253	42	11	−→	−→	NOUN
ejpam-3253	42	12	z	z	NOUN
ejpam-3253	42	13	be	be	AUX
ejpam-3253	42	14	a	a	DET
ejpam-3253	42	15	bijective	bijective	ADJ
ejpam-3253	42	16	function	function	NOUN
ejpam-3253	42	17	such	such	ADJ
ejpam-3253	42	18	that	that	SCONJ
ejpam-3253	42	19	the	the	DET
ejpam-3253	42	20	restriction	restriction	NOUN
ejpam-3253	42	21	f|k	f|k	PUNCT
ejpam-3253	43	1	:	:	PUNCT
ejpam-3253	43	2	k	k	X
ejpam-3253	43	3	−→	−→	NOUN
ejpam-3253	43	4	f(k	f(k	VERB
ejpam-3253	43	5	)	)	PUNCT
ejpam-3253	43	6	is	be	AUX
ejpam-3253	43	7	a	a	DET
ejpam-3253	43	8	homeomorphism	homeomorphism	NOUN
ejpam-3253	43	9	for	for	ADP
ejpam-3253	43	10	each	each	DET
ejpam-3253	43	11	compact	compact	ADJ
ejpam-3253	43	12	subspace	subspace	NOUN
ejpam-3253	43	13	k	k	PROPN
ejpam-3253	43	14	of	of	ADP
ejpam-3253	43	15	(	(	PUNCT
ejpam-3253	43	16	r	r	NOUN
ejpam-3253	43	17	,	,	PUNCT
ejpam-3253	43	18	τ√2	τ√2	NOUN
ejpam-3253	43	19	)	)	PUNCT
ejpam-3253	43	20	.	.	PUNCT
ejpam-3253	44	1	take	take	VERB
ejpam-3253	44	2	k	k	NOUN
ejpam-3253	44	3	=	=	PRON
ejpam-3253	44	4	{	{	PUNCT
ejpam-3253	44	5	x	x	NOUN
ejpam-3253	44	6	,	,	PUNCT
ejpam-3253	44	7	√	√	ADV
ejpam-3253	44	8	2	2	NUM
ejpam-3253	44	9	}	}	PUNCT
ejpam-3253	44	10	,	,	PUNCT
ejpam-3253	44	11	such	such	ADJ
ejpam-3253	44	12	that	that	SCONJ
ejpam-3253	44	13	x	x	PROPN
ejpam-3253	44	14	6=	6=	NUM
ejpam-3253	44	15	√	√	ADP
ejpam-3253	44	16	2	2	NUM
ejpam-3253	44	17	,	,	PUNCT
ejpam-3253	44	18	hence	hence	ADV
ejpam-3253	44	19	k	k	PROPN
ejpam-3253	44	20	is	be	AUX
ejpam-3253	44	21	a	a	DET
ejpam-3253	44	22	compact	compact	ADJ
ejpam-3253	44	23	subspace	subspace	NOUN
ejpam-3253	44	24	of	of	ADP
ejpam-3253	44	25	(	(	PUNCT
ejpam-3253	44	26	r	r	NOUN
ejpam-3253	44	27	,	,	PUNCT
ejpam-3253	44	28	τ√2	τ√2	NOUN
ejpam-3253	44	29	)	)	PUNCT
ejpam-3253	44	30	.	.	PUNCT
ejpam-3253	45	1	by	by	ADP
ejpam-3253	45	2	assumption	assumption	NOUN
ejpam-3253	45	3	f|k	f|k	X
ejpam-3253	45	4	:	:	PUNCT
ejpam-3253	46	1	k	k	X
ejpam-3253	46	2	−→	−→	NOUN
ejpam-3253	46	3	f(k	f(k	VERB
ejpam-3253	46	4	)	)	PUNCT
ejpam-3253	46	5	=	=	SYM
ejpam-3253	46	6	{	{	PUNCT
ejpam-3253	46	7	f(x	f(x	PROPN
ejpam-3253	46	8	)	)	PUNCT
ejpam-3253	46	9	,	,	PUNCT
ejpam-3253	46	10	f	f	X
ejpam-3253	46	11	(	(	PUNCT
ejpam-3253	46	12	√	√	ADP
ejpam-3253	46	13	2	2	NUM
ejpam-3253	46	14	)	)	PUNCT
ejpam-3253	46	15	}	}	PUNCT
ejpam-3253	46	16	is	be	AUX
ejpam-3253	46	17	a	a	DET
ejpam-3253	46	18	homeomorphism	homeomorphism	NOUN
ejpam-3253	46	19	.	.	PUNCT
ejpam-3253	47	1	because	because	SCONJ
ejpam-3253	47	2	f(k	f(k	VERB
ejpam-3253	47	3	)	)	PUNCT
ejpam-3253	47	4	is	be	AUX
ejpam-3253	47	5	a	a	DET
ejpam-3253	47	6	finite	finite	ADJ
ejpam-3253	47	7	subspace	subspace	NOUN
ejpam-3253	47	8	of	of	ADP
ejpam-3253	47	9	z	z	PROPN
ejpam-3253	47	10	and	and	CCONJ
ejpam-3253	47	11	z	z	PROPN
ejpam-3253	47	12	is	be	AUX
ejpam-3253	47	13	t1	t1	NOUN
ejpam-3253	47	14	,	,	PUNCT
ejpam-3253	47	15	then	then	ADV
ejpam-3253	47	16	f(k	f(k	VERB
ejpam-3253	47	17	)	)	PUNCT
ejpam-3253	47	18	is	be	AUX
ejpam-3253	47	19	discrete	discrete	ADJ
ejpam-3253	47	20	subspace	subspace	NOUN
ejpam-3253	47	21	of	of	ADP
ejpam-3253	47	22	z.	z.	PROPN
ejpam-3253	47	23	therefore	therefore	ADV
ejpam-3253	47	24	,	,	PUNCT
ejpam-3253	47	25	we	we	PRON
ejpam-3253	47	26	obtain	obtain	VERB
ejpam-3253	47	27	that	that	SCONJ
ejpam-3253	47	28	f|k	f|k	PRON
ejpam-3253	47	29	is	be	AUX
ejpam-3253	47	30	not	not	PART
ejpam-3253	47	31	continuous	continuous	ADJ
ejpam-3253	47	32	and	and	CCONJ
ejpam-3253	47	33	this	this	DET
ejpam-3253	47	34	a	a	DET
ejpam-3253	47	35	contradiction	contradiction	NOUN
ejpam-3253	47	36	as	as	SCONJ
ejpam-3253	47	37	f|k	f|k	PRON
ejpam-3253	47	38	is	be	AUX
ejpam-3253	47	39	a	a	DET
ejpam-3253	47	40	homeomorphism	homeomorphism	NOUN
ejpam-3253	47	41	.	.	PUNCT
ejpam-3253	48	1	thus	thus	ADV
ejpam-3253	48	2	(	(	PUNCT
ejpam-3253	48	3	r	r	NOUN
ejpam-3253	48	4	,	,	PUNCT
ejpam-3253	48	5	τ√2	τ√2	PRON
ejpam-3253	48	6	)	)	PUNCT
ejpam-3253	48	7	is	be	AUX
ejpam-3253	48	8	not	not	PART
ejpam-3253	48	9	c	c	NOUN
ejpam-3253	48	10	-	-	PUNCT
ejpam-3253	48	11	tychonoff	tychonoff	NOUN
ejpam-3253	48	12	.	.	PUNCT
ejpam-3253	49	1	s.	s.	PROPN
ejpam-3253	49	2	alzahrani	alzahrani	PROPN
ejpam-3253	49	3	/	/	SYM
ejpam-3253	49	4	eur	eur	PROPN
ejpam-3253	49	5	.	.	PUNCT
ejpam-3253	50	1	j.	j.	PROPN
ejpam-3253	50	2	pure	pure	PROPN
ejpam-3253	50	3	appl	appl	PROPN
ejpam-3253	50	4	.	.	PROPN
ejpam-3253	50	5	math	math	PROPN
ejpam-3253	50	6	,	,	PUNCT
ejpam-3253	50	7	11	11	NUM
ejpam-3253	50	8	(	(	PUNCT
ejpam-3253	50	9	3	3	NUM
ejpam-3253	50	10	)	)	PUNCT
ejpam-3253	50	11	(	(	PUNCT
ejpam-3253	50	12	2018	2018	NUM
ejpam-3253	50	13	)	)	PUNCT
ejpam-3253	50	14	,	,	PUNCT
ejpam-3253	50	15	882	882	NUM
ejpam-3253	50	16	-	-	SYM
ejpam-3253	50	17	892	892	NUM
ejpam-3253	50	18	884	884	NUM
ejpam-3253	50	19	by	by	ADP
ejpam-3253	50	20	the	the	DET
ejpam-3253	50	21	definition	definition	NOUN
ejpam-3253	50	22	,	,	PUNCT
ejpam-3253	50	23	it	it	PRON
ejpam-3253	50	24	is	be	AUX
ejpam-3253	50	25	clear	clear	ADJ
ejpam-3253	50	26	that	that	SCONJ
ejpam-3253	50	27	a	a	DET
ejpam-3253	50	28	compact	compact	ADJ
ejpam-3253	50	29	c	c	NOUN
ejpam-3253	50	30	-	-	PUNCT
ejpam-3253	50	31	tychonoff	tychonoff	NOUN
ejpam-3253	50	32	space	space	NOUN
ejpam-3253	50	33	must	must	AUX
ejpam-3253	50	34	be	be	AUX
ejpam-3253	50	35	tychonoff	tychonoff	NOUN
ejpam-3253	50	36	see	see	NOUN
ejpam-3253	50	37	theorem	theorem	VERB
ejpam-3253	50	38	3	3	NUM
ejpam-3253	50	39	below	below	ADV
ejpam-3253	50	40	.	.	PUNCT
ejpam-3253	51	1	obviously	obviously	ADV
ejpam-3253	51	2	,	,	PUNCT
ejpam-3253	51	3	any	any	DET
ejpam-3253	51	4	tychonoff	tychonoff	NOUN
ejpam-3253	51	5	space	space	NOUN
ejpam-3253	51	6	is	be	AUX
ejpam-3253	51	7	c	c	NOUN
ejpam-3253	51	8	-	-	PUNCT
ejpam-3253	51	9	tychonoff	tychonoff	NOUN
ejpam-3253	51	10	,	,	PUNCT
ejpam-3253	51	11	just	just	ADV
ejpam-3253	51	12	by	by	ADP
ejpam-3253	51	13	taking	take	VERB
ejpam-3253	51	14	y	y	PROPN
ejpam-3253	51	15	=	=	PUNCT
ejpam-3253	52	1	x	x	PROPN
ejpam-3253	52	2	and	and	CCONJ
ejpam-3253	52	3	f	f	X
ejpam-3253	52	4	to	to	PART
ejpam-3253	52	5	be	be	AUX
ejpam-3253	52	6	the	the	DET
ejpam-3253	52	7	identity	identity	NOUN
ejpam-3253	52	8	function	function	NOUN
ejpam-3253	52	9	,	,	PUNCT
ejpam-3253	52	10	but	but	CCONJ
ejpam-3253	52	11	the	the	DET
ejpam-3253	52	12	converse	converse	NOUN
ejpam-3253	52	13	is	be	AUX
ejpam-3253	52	14	not	not	PART
ejpam-3253	52	15	true	true	ADJ
ejpam-3253	52	16	in	in	ADP
ejpam-3253	52	17	general	general	ADJ
ejpam-3253	52	18	.	.	PUNCT
ejpam-3253	53	1	for	for	ADP
ejpam-3253	53	2	example	example	NOUN
ejpam-3253	53	3	,	,	PUNCT
ejpam-3253	53	4	the	the	DET
ejpam-3253	53	5	half	half	ADJ
ejpam-3253	53	6	-	-	PUNCT
ejpam-3253	53	7	disc	disc	NOUN
ejpam-3253	53	8	space	space	NOUN
ejpam-3253	53	9	[	[	X
ejpam-3253	53	10	16	16	NUM
ejpam-3253	53	11	]	]	PUNCT
ejpam-3253	53	12	is	be	AUX
ejpam-3253	53	13	c	c	NOUN
ejpam-3253	53	14	-	-	PUNCT
ejpam-3253	53	15	tychonoff	tychonoff	NOUN
ejpam-3253	53	16	which	which	PRON
ejpam-3253	53	17	is	be	AUX
ejpam-3253	53	18	not	not	PART
ejpam-3253	53	19	tychonoff	tychonoff	NOUN
ejpam-3253	53	20	.	.	PUNCT
ejpam-3253	54	1	it	it	PRON
ejpam-3253	54	2	is	be	AUX
ejpam-3253	54	3	c	c	NOUN
ejpam-3253	54	4	-	-	PUNCT
ejpam-3253	54	5	tychonoff	tychonoff	NOUN
ejpam-3253	54	6	because	because	SCONJ
ejpam-3253	54	7	it	it	PRON
ejpam-3253	54	8	is	be	AUX
ejpam-3253	54	9	submetrizable	submetrizable	ADJ
ejpam-3253	54	10	.	.	PUNCT
ejpam-3253	55	1	c	c	X
ejpam-3253	55	2	-	-	PUNCT
ejpam-3253	55	3	tychonoffness	tychonoffness	NOUN
ejpam-3253	55	4	does	do	AUX
ejpam-3253	55	5	not	not	PART
ejpam-3253	55	6	imply	imply	VERB
ejpam-3253	55	7	tychonoffness	tychonoffness	NOUN
ejpam-3253	55	8	even	even	ADV
ejpam-3253	55	9	with	with	ADP
ejpam-3253	55	10	first	first	ADJ
ejpam-3253	55	11	countability	countability	NOUN
ejpam-3253	55	12	.	.	PUNCT
ejpam-3253	56	1	for	for	ADP
ejpam-3253	56	2	example	example	NOUN
ejpam-3253	56	3	,	,	PUNCT
ejpam-3253	56	4	smirnov	smirnov	PROPN
ejpam-3253	56	5	’s	’s	PART
ejpam-3253	56	6	deleted	delete	VERB
ejpam-3253	56	7	sequence	sequence	NOUN
ejpam-3253	56	8	topology	topology	NOUN
ejpam-3253	57	1	[	[	X
ejpam-3253	57	2	16	16	NUM
ejpam-3253	57	3	]	]	PUNCT
ejpam-3253	57	4	is	be	AUX
ejpam-3253	57	5	first	first	ADV
ejpam-3253	57	6	countable	countable	ADJ
ejpam-3253	57	7	and	and	CCONJ
ejpam-3253	57	8	c	c	NOUN
ejpam-3253	57	9	-	-	PUNCT
ejpam-3253	57	10	tychonoff	tychonoff	NOUN
ejpam-3253	57	11	being	be	AUX
ejpam-3253	57	12	submetrizabl	submetrizabl	NOUN
ejpam-3253	57	13	but	but	CCONJ
ejpam-3253	57	14	not	not	PART
ejpam-3253	57	15	tychonoff	tychonoff	NOUN
ejpam-3253	57	16	.	.	PUNCT
ejpam-3253	58	1	theorem	theorem	NOUN
ejpam-3253	58	2	3	3	NUM
ejpam-3253	58	3	.	.	PUNCT
ejpam-3253	59	1	if	if	SCONJ
ejpam-3253	59	2	x	x	PRON
ejpam-3253	59	3	is	be	AUX
ejpam-3253	59	4	a	a	DET
ejpam-3253	59	5	compact	compact	ADJ
ejpam-3253	59	6	non	non	ADJ
ejpam-3253	59	7	-	-	ADJ
ejpam-3253	59	8	tychonoff	tychonoff	ADJ
ejpam-3253	59	9	space	space	NOUN
ejpam-3253	59	10	,	,	PUNCT
ejpam-3253	59	11	then	then	ADV
ejpam-3253	59	12	x	x	PUNCT
ejpam-3253	59	13	cennot	cennot	ADV
ejpam-3253	59	14	be	be	AUX
ejpam-3253	59	15	c	c	NOUN
ejpam-3253	59	16	-	-	PUNCT
ejpam-3253	59	17	tychonoff	tychonoff	NOUN
ejpam-3253	59	18	.	.	PUNCT
ejpam-3253	60	1	we	we	PRON
ejpam-3253	60	2	conclude	conclude	VERB
ejpam-3253	60	3	that	that	SCONJ
ejpam-3253	60	4	from	from	ADP
ejpam-3253	60	5	the	the	DET
ejpam-3253	60	6	above	above	ADJ
ejpam-3253	60	7	theorem	theorem	NOUN
ejpam-3253	60	8	,	,	PUNCT
ejpam-3253	60	9	r	r	NOUN
ejpam-3253	60	10	with	with	ADP
ejpam-3253	60	11	the	the	DET
ejpam-3253	60	12	finite	finite	PROPN
ejpam-3253	60	13	complement	complement	NOUN
ejpam-3253	60	14	topology	topology	NOUN
ejpam-3253	60	15	is	be	AUX
ejpam-3253	60	16	not	not	PART
ejpam-3253	60	17	c	c	NOUN
ejpam-3253	60	18	-	-	PUNCT
ejpam-3253	60	19	tychonoff	tychonoff	NOUN
ejpam-3253	60	20	.	.	PUNCT
ejpam-3253	61	1	theorem	theorem	VERB
ejpam-3253	61	2	4	4	NUM
ejpam-3253	61	3	.	.	PUNCT
ejpam-3253	62	1	if	if	SCONJ
ejpam-3253	62	2	x	x	PRON
ejpam-3253	62	3	is	be	AUX
ejpam-3253	62	4	a	a	DET
ejpam-3253	62	5	t1	t1	NOUN
ejpam-3253	62	6	-	-	PUNCT
ejpam-3253	62	7	space	space	NOUN
ejpam-3253	62	8	such	such	ADJ
ejpam-3253	62	9	that	that	SCONJ
ejpam-3253	62	10	the	the	DET
ejpam-3253	62	11	only	only	ADJ
ejpam-3253	62	12	compact	compact	ADJ
ejpam-3253	62	13	subspace	subspace	NOUN
ejpam-3253	62	14	are	be	AUX
ejpam-3253	62	15	the	the	DET
ejpam-3253	62	16	finite	finite	ADJ
ejpam-3253	62	17	subspace	subspace	NOUN
ejpam-3253	62	18	,	,	PUNCT
ejpam-3253	62	19	then	then	ADV
ejpam-3253	62	20	x	x	PUNCT
ejpam-3253	62	21	is	be	AUX
ejpam-3253	62	22	c	c	NOUN
ejpam-3253	62	23	-	-	PUNCT
ejpam-3253	62	24	tychonoff	tychonoff	NOUN
ejpam-3253	62	25	.	.	PUNCT
ejpam-3253	63	1	proof	proof	NOUN
ejpam-3253	63	2	.	.	PUNCT
ejpam-3253	64	1	let	let	VERB
ejpam-3253	64	2	y	y	NOUN
ejpam-3253	64	3	=	=	PUNCT
ejpam-3253	64	4	x	x	PUNCT
ejpam-3253	64	5	and	and	CCONJ
ejpam-3253	64	6	consider	consider	VERB
ejpam-3253	64	7	y	y	NOUN
ejpam-3253	64	8	with	with	ADP
ejpam-3253	64	9	the	the	DET
ejpam-3253	64	10	discrete	discrete	ADJ
ejpam-3253	64	11	topology	topology	NOUN
ejpam-3253	64	12	.	.	PUNCT
ejpam-3253	65	1	then	then	ADV
ejpam-3253	65	2	the	the	DET
ejpam-3253	65	3	identity	identity	NOUN
ejpam-3253	65	4	function	function	NOUN
ejpam-3253	65	5	from	from	ADP
ejpam-3253	65	6	x	x	PUNCT
ejpam-3253	65	7	onto	onto	ADP
ejpam-3253	65	8	y	y	PROPN
ejpam-3253	65	9	is	be	AUX
ejpam-3253	65	10	a	a	DET
ejpam-3253	65	11	bijective	bijective	ADJ
ejpam-3253	65	12	function	function	NOUN
ejpam-3253	65	13	.	.	PUNCT
ejpam-3253	66	1	if	if	SCONJ
ejpam-3253	66	2	k	k	PROPN
ejpam-3253	66	3	is	be	AUX
ejpam-3253	66	4	any	any	DET
ejpam-3253	66	5	compact	compact	ADJ
ejpam-3253	66	6	subspace	subspace	NOUN
ejpam-3253	66	7	of	of	ADP
ejpam-3253	66	8	(	(	PUNCT
ejpam-3253	66	9	x	x	PROPN
ejpam-3253	66	10	,	,	PUNCT
ejpam-3253	66	11	τ	τ	PROPN
ejpam-3253	66	12	)	)	PUNCT
ejpam-3253	66	13	,	,	PUNCT
ejpam-3253	66	14	then	then	ADV
ejpam-3253	66	15	by	by	ADP
ejpam-3253	66	16	assumption	assumption	NOUN
ejpam-3253	66	17	k	k	PROPN
ejpam-3253	66	18	is	be	AUX
ejpam-3253	66	19	a	a	DET
ejpam-3253	66	20	finite	finite	ADJ
ejpam-3253	66	21	subspace	subspace	NOUN
ejpam-3253	66	22	.	.	PUNCT
ejpam-3253	67	1	because	because	SCONJ
ejpam-3253	67	2	any	any	DET
ejpam-3253	67	3	finite	finite	NOUN
ejpam-3253	67	4	set	set	VERB
ejpam-3253	67	5	in	in	ADP
ejpam-3253	67	6	a	a	DET
ejpam-3253	67	7	t1	t1	NOUN
ejpam-3253	67	8	-	-	PUNCT
ejpam-3253	67	9	space	space	NOUN
ejpam-3253	67	10	is	be	AUX
ejpam-3253	67	11	discrete	discrete	ADJ
ejpam-3253	67	12	,	,	PUNCT
ejpam-3253	67	13	hence	hence	ADV
ejpam-3253	67	14	the	the	DET
ejpam-3253	67	15	restriction	restriction	NOUN
ejpam-3253	67	16	of	of	ADP
ejpam-3253	67	17	the	the	DET
ejpam-3253	67	18	identity	identity	NOUN
ejpam-3253	67	19	function	function	NOUN
ejpam-3253	67	20	on	on	ADP
ejpam-3253	67	21	k	k	PROPN
ejpam-3253	67	22	onto	onto	ADP
ejpam-3253	67	23	k	k	PROPN
ejpam-3253	67	24	is	be	AUX
ejpam-3253	67	25	a	a	DET
ejpam-3253	67	26	homeomorphism	homeomorphism	NOUN
ejpam-3253	67	27	since	since	SCONJ
ejpam-3253	67	28	both	both	PRON
ejpam-3253	67	29	of	of	ADP
ejpam-3253	67	30	the	the	DET
ejpam-3253	67	31	domain	domain	NOUN
ejpam-3253	67	32	and	and	CCONJ
ejpam-3253	67	33	the	the	DET
ejpam-3253	67	34	codomain	codomain	NOUN
ejpam-3253	67	35	are	be	AUX
ejpam-3253	67	36	discrete	discrete	ADJ
ejpam-3253	67	37	and	and	CCONJ
ejpam-3253	67	38	have	have	VERB
ejpam-3253	67	39	the	the	DET
ejpam-3253	67	40	same	same	ADJ
ejpam-3253	67	41	cardinality	cardinality	NOUN
ejpam-3253	67	42	.	.	PUNCT
ejpam-3253	68	1	if	if	SCONJ
ejpam-3253	68	2	x	x	PRON
ejpam-3253	68	3	is	be	AUX
ejpam-3253	68	4	c	c	NOUN
ejpam-3253	68	5	-	-	PUNCT
ejpam-3253	68	6	tychonoff	tychonoff	NOUN
ejpam-3253	68	7	and	and	CCONJ
ejpam-3253	68	8	f	f	NOUN
ejpam-3253	68	9	:	:	PUNCT
ejpam-3253	69	1	x	x	PUNCT
ejpam-3253	69	2	−→	−→	NOUN
ejpam-3253	69	3	y	y	PROPN
ejpam-3253	69	4	is	be	AUX
ejpam-3253	69	5	a	a	DET
ejpam-3253	69	6	witness	witness	NOUN
ejpam-3253	69	7	of	of	ADP
ejpam-3253	69	8	the	the	DET
ejpam-3253	69	9	c	c	NOUN
ejpam-3253	69	10	-	-	PUNCT
ejpam-3253	69	11	tychonoffness	tychonoffness	NOUN
ejpam-3253	69	12	of	of	ADP
ejpam-3253	69	13	x	x	PRON
ejpam-3253	69	14	,	,	PUNCT
ejpam-3253	69	15	then	then	ADV
ejpam-3253	69	16	f	f	PROPN
ejpam-3253	69	17	may	may	AUX
ejpam-3253	69	18	not	not	PART
ejpam-3253	69	19	be	be	AUX
ejpam-3253	69	20	continuous	continuous	ADJ
ejpam-3253	69	21	.	.	PUNCT
ejpam-3253	70	1	here	here	ADV
ejpam-3253	70	2	is	be	AUX
ejpam-3253	70	3	an	an	DET
ejpam-3253	70	4	example	example	NOUN
ejpam-3253	70	5	.	.	PUNCT
ejpam-3253	71	1	example	example	NOUN
ejpam-3253	72	1	2	2	NUM
ejpam-3253	72	2	.	.	X
ejpam-3253	72	3	consider	consider	VERB
ejpam-3253	72	4	r	r	NOUN
ejpam-3253	72	5	with	with	ADP
ejpam-3253	72	6	the	the	DET
ejpam-3253	72	7	countable	countable	ADJ
ejpam-3253	72	8	complement	complement	NOUN
ejpam-3253	72	9	topology	topology	NOUN
ejpam-3253	72	10	cc	cc	ADP
ejpam-3253	73	1	[	[	X
ejpam-3253	73	2	16	16	NUM
ejpam-3253	73	3	]	]	PUNCT
ejpam-3253	73	4	.	.	PUNCT
ejpam-3253	74	1	since	since	SCONJ
ejpam-3253	74	2	the	the	DET
ejpam-3253	74	3	only	only	ADJ
ejpam-3253	74	4	compact	compact	ADJ
ejpam-3253	74	5	subspace	subspace	NOUN
ejpam-3253	74	6	are	be	AUX
ejpam-3253	74	7	the	the	DET
ejpam-3253	74	8	finite	finite	ADJ
ejpam-3253	74	9	subspaces	subspace	NOUN
ejpam-3253	74	10	and	and	CCONJ
ejpam-3253	74	11	(	(	PUNCT
ejpam-3253	74	12	r	r	NOUN
ejpam-3253	74	13	,	,	PUNCT
ejpam-3253	74	14	cc	cc	NOUN
ejpam-3253	74	15	)	)	PUNCT
ejpam-3253	74	16	is	be	AUX
ejpam-3253	74	17	t1	t1	NOUN
ejpam-3253	74	18	,	,	PUNCT
ejpam-3253	74	19	then	then	ADV
ejpam-3253	74	20	the	the	DET
ejpam-3253	74	21	compact	compact	ADJ
ejpam-3253	74	22	subspace	subspace	NOUN
ejpam-3253	74	23	are	be	AUX
ejpam-3253	74	24	discrete	discrete	ADJ
ejpam-3253	74	25	.	.	PUNCT
ejpam-3253	75	1	hence	hence	ADV
ejpam-3253	75	2	r	r	NOUN
ejpam-3253	75	3	with	with	ADP
ejpam-3253	75	4	the	the	DET
ejpam-3253	75	5	discrete	discrete	ADJ
ejpam-3253	75	6	topology	topology	NOUN
ejpam-3253	75	7	and	and	CCONJ
ejpam-3253	75	8	the	the	DET
ejpam-3253	75	9	identity	identity	NOUN
ejpam-3253	75	10	function	function	NOUN
ejpam-3253	75	11	will	will	AUX
ejpam-3253	75	12	give	give	VERB
ejpam-3253	75	13	the	the	DET
ejpam-3253	75	14	c	c	NOUN
ejpam-3253	75	15	-	-	PUNCT
ejpam-3253	75	16	tychonoffness	tychonoffness	NOUN
ejpam-3253	75	17	,	,	PUNCT
ejpam-3253	75	18	see	see	VERB
ejpam-3253	75	19	theorem	theorem	ADJ
ejpam-3253	75	20	4	4	NUM
ejpam-3253	75	21	.	.	X
ejpam-3253	75	22	observe	observe	VERB
ejpam-3253	75	23	that	that	SCONJ
ejpam-3253	75	24	the	the	DET
ejpam-3253	75	25	identity	identity	NOUN
ejpam-3253	75	26	function	function	NOUN
ejpam-3253	75	27	in	in	ADP
ejpam-3253	75	28	this	this	DET
ejpam-3253	75	29	case	case	NOUN
ejpam-3253	75	30	is	be	AUX
ejpam-3253	75	31	not	not	PART
ejpam-3253	75	32	continuous	continuous	ADJ
ejpam-3253	75	33	.	.	PUNCT
ejpam-3253	76	1	recall	recall	VERB
ejpam-3253	76	2	that	that	SCONJ
ejpam-3253	76	3	a	a	DET
ejpam-3253	76	4	space	space	NOUN
ejpam-3253	76	5	x	x	PUNCT
ejpam-3253	76	6	is	be	AUX
ejpam-3253	76	7	fréchet	fréchet	VERB
ejpam-3253	76	8	if	if	SCONJ
ejpam-3253	76	9	for	for	ADP
ejpam-3253	76	10	any	any	DET
ejpam-3253	76	11	subset	subset	NOUN
ejpam-3253	76	12	b	b	PROPN
ejpam-3253	76	13	of	of	ADP
ejpam-3253	76	14	x	x	X
ejpam-3253	76	15	and	and	CCONJ
ejpam-3253	76	16	any	any	DET
ejpam-3253	76	17	x	x	SYM
ejpam-3253	76	18	∈	∈	PROPN
ejpam-3253	76	19	b	b	NOUN
ejpam-3253	76	20	there	there	PRON
ejpam-3253	76	21	exist	exist	VERB
ejpam-3253	76	22	a	a	DET
ejpam-3253	76	23	sequence	sequence	NOUN
ejpam-3253	76	24	(	(	PUNCT
ejpam-3253	76	25	bn)n∈n	bn)n∈n	NOUN
ejpam-3253	76	26	of	of	ADP
ejpam-3253	76	27	points	point	NOUN
ejpam-3253	76	28	of	of	ADP
ejpam-3253	76	29	b	b	NOUN
ejpam-3253	76	30	such	such	ADJ
ejpam-3253	77	1	that	that	PRON
ejpam-3253	77	2	bn	bn	ADP
ejpam-3253	77	3	−→	−→	NOUN
ejpam-3253	77	4	x	x	NOUN
ejpam-3253	77	5	,	,	PUNCT
ejpam-3253	77	6	see	see	VERB
ejpam-3253	77	7	[	[	X
ejpam-3253	77	8	8	8	NUM
ejpam-3253	77	9	]	]	PUNCT
ejpam-3253	77	10	.	.	PUNCT
ejpam-3253	78	1	theorem	theorem	NOUN
ejpam-3253	78	2	5	5	NUM
ejpam-3253	78	3	.	.	PUNCT
ejpam-3253	79	1	ifx	ifx	PROPN
ejpam-3253	79	2	is	be	AUX
ejpam-3253	79	3	c	c	NOUN
ejpam-3253	79	4	-	-	PUNCT
ejpam-3253	79	5	tychonoff	tychonoff	NOUN
ejpam-3253	79	6	and	and	CCONJ
ejpam-3253	79	7	fréchet	fréchet	NOUN
ejpam-3253	79	8	,	,	PUNCT
ejpam-3253	79	9	then	then	ADV
ejpam-3253	79	10	any	any	DET
ejpam-3253	79	11	function	function	NOUN
ejpam-3253	79	12	witnesses	witness	VERB
ejpam-3253	79	13	its	its	PRON
ejpam-3253	79	14	c	c	NOUN
ejpam-3253	79	15	-	-	PUNCT
ejpam-3253	79	16	tychonoffness	tychonoffness	NOUN
ejpam-3253	79	17	is	be	AUX
ejpam-3253	79	18	continuous	continuous	ADJ
ejpam-3253	79	19	.	.	PUNCT
ejpam-3253	80	1	proof	proof	NOUN
ejpam-3253	80	2	.	.	PUNCT
ejpam-3253	81	1	let	let	VERB
ejpam-3253	81	2	x	x	PRON
ejpam-3253	81	3	be	be	AUX
ejpam-3253	81	4	c	c	NOUN
ejpam-3253	81	5	-	-	PUNCT
ejpam-3253	81	6	tychonoff	tychonoff	NOUN
ejpam-3253	81	7	and	and	CCONJ
ejpam-3253	81	8	fréchet	fréchet	NOUN
ejpam-3253	81	9	.	.	PUNCT
ejpam-3253	82	1	let	let	VERB
ejpam-3253	82	2	f	f	NOUN
ejpam-3253	82	3	:	:	PUNCT
ejpam-3253	82	4	x	x	PUNCT
ejpam-3253	82	5	−→	−→	NOUN
ejpam-3253	82	6	y	y	NOUN
ejpam-3253	82	7	be	be	AUX
ejpam-3253	82	8	a	a	DET
ejpam-3253	82	9	witness	witness	NOUN
ejpam-3253	82	10	of	of	ADP
ejpam-3253	82	11	the	the	DET
ejpam-3253	82	12	c	c	NOUN
ejpam-3253	82	13	-	-	PUNCT
ejpam-3253	82	14	tychonoffness	tychonoffness	NOUN
ejpam-3253	82	15	of	of	ADP
ejpam-3253	82	16	x.	x.	PROPN
ejpam-3253	82	17	take	take	VERB
ejpam-3253	82	18	b	b	NOUN
ejpam-3253	82	19	⊆	⊆	NUM
ejpam-3253	82	20	x	x	PUNCT
ejpam-3253	82	21	and	and	CCONJ
ejpam-3253	82	22	pick	pick	VERB
ejpam-3253	82	23	y	y	PROPN
ejpam-3253	82	24	∈	∈	PROPN
ejpam-3253	82	25	f(b	f(b	PROPN
ejpam-3253	82	26	)	)	PUNCT
ejpam-3253	82	27	.	.	PUNCT
ejpam-3253	83	1	there	there	PRON
ejpam-3253	83	2	is	be	VERB
ejpam-3253	83	3	a	a	DET
ejpam-3253	83	4	unique	unique	ADJ
ejpam-3253	83	5	x	x	SYM
ejpam-3253	83	6	∈	∈	NOUN
ejpam-3253	83	7	x	x	PUNCT
ejpam-3253	83	8	such	such	ADJ
ejpam-3253	83	9	that	that	SCONJ
ejpam-3253	83	10	f(x	f(x	NOUN
ejpam-3253	83	11	)	)	PUNCT
ejpam-3253	84	1	=	=	SYM
ejpam-3253	84	2	y	y	PROPN
ejpam-3253	84	3	,	,	PUNCT
ejpam-3253	84	4	thus	thus	ADV
ejpam-3253	84	5	x	x	SYM
ejpam-3253	84	6	∈	∈	PROPN
ejpam-3253	84	7	b.	b.	PROPN
ejpam-3253	84	8	since	since	SCONJ
ejpam-3253	84	9	x	x	PROPN
ejpam-3253	84	10	is	be	AUX
ejpam-3253	84	11	fréchet	fréchet	ADJ
ejpam-3253	84	12	,	,	PUNCT
ejpam-3253	84	13	then	then	ADV
ejpam-3253	84	14	there	there	PRON
ejpam-3253	84	15	exists	exist	VERB
ejpam-3253	84	16	a	a	DET
ejpam-3253	84	17	sequence	sequence	NOUN
ejpam-3253	84	18	(	(	PUNCT
ejpam-3253	84	19	bn	bn	NOUN
ejpam-3253	84	20	)	)	PUNCT
ejpam-3253	84	21	⊆	⊆	NUM
ejpam-3253	84	22	b	b	NOUN
ejpam-3253	84	23	such	such	ADJ
ejpam-3253	84	24	that	that	PRON
ejpam-3253	85	1	bn	bn	NUM
ejpam-3253	85	2	−→	−→	NOUN
ejpam-3253	85	3	x.	x.	NOUN
ejpam-3253	86	1	the	the	DET
ejpam-3253	86	2	sequence	sequence	NOUN
ejpam-3253	86	3	k	k	PROPN
ejpam-3253	87	1	=	=	PUNCT
ejpam-3253	87	2	{	{	PUNCT
ejpam-3253	87	3	x	x	NOUN
ejpam-3253	87	4	}	}	PUNCT
ejpam-3253	87	5	∪	∪	ADJ
ejpam-3253	87	6	{	{	PUNCT
ejpam-3253	87	7	bn	bn	NOUN
ejpam-3253	87	8	:	:	PUNCT
ejpam-3253	87	9	n	n	CCONJ
ejpam-3253	87	10	∈	∈	PROPN
ejpam-3253	87	11	n	n	CCONJ
ejpam-3253	87	12	}	}	PUNCT
ejpam-3253	87	13	of	of	ADP
ejpam-3253	87	14	x	x	SYM
ejpam-3253	87	15	is	be	AUX
ejpam-3253	87	16	compact	compact	ADJ
ejpam-3253	87	17	since	since	SCONJ
ejpam-3253	87	18	it	it	PRON
ejpam-3253	87	19	is	be	AUX
ejpam-3253	87	20	a	a	DET
ejpam-3253	87	21	convergent	convergent	ADJ
ejpam-3253	87	22	sequence	sequence	NOUN
ejpam-3253	87	23	with	with	ADP
ejpam-3253	87	24	its	its	PRON
ejpam-3253	87	25	limit	limit	NOUN
ejpam-3253	87	26	,	,	PUNCT
ejpam-3253	87	27	thus	thus	ADV
ejpam-3253	87	28	f|k	f|k	X
ejpam-3253	88	1	:	:	PUNCT
ejpam-3253	88	2	k	k	X
ejpam-3253	88	3	−→	−→	NOUN
ejpam-3253	88	4	f(k	f(k	VERB
ejpam-3253	88	5	)	)	PUNCT
ejpam-3253	88	6	is	be	AUX
ejpam-3253	88	7	a	a	DET
ejpam-3253	88	8	homeomorphism	homeomorphism	NOUN
ejpam-3253	88	9	.	.	PUNCT
ejpam-3253	89	1	let	let	VERB
ejpam-3253	89	2	s.	s.	PROPN
ejpam-3253	89	3	alzahrani	alzahrani	PROPN
ejpam-3253	89	4	/	/	SYM
ejpam-3253	89	5	eur	eur	PROPN
ejpam-3253	89	6	.	.	PUNCT
ejpam-3253	90	1	j.	j.	PROPN
ejpam-3253	90	2	pure	pure	PROPN
ejpam-3253	90	3	appl	appl	PROPN
ejpam-3253	90	4	.	.	PROPN
ejpam-3253	90	5	math	math	PROPN
ejpam-3253	90	6	,	,	PUNCT
ejpam-3253	90	7	11	11	NUM
ejpam-3253	90	8	(	(	PUNCT
ejpam-3253	90	9	3	3	NUM
ejpam-3253	90	10	)	)	PUNCT
ejpam-3253	90	11	(	(	PUNCT
ejpam-3253	90	12	2018	2018	NUM
ejpam-3253	90	13	)	)	PUNCT
ejpam-3253	90	14	,	,	PUNCT
ejpam-3253	90	15	882	882	NUM
ejpam-3253	90	16	-	-	SYM
ejpam-3253	90	17	892	892	NUM
ejpam-3253	90	18	885	885	NUM
ejpam-3253	90	19	w	w	NOUN
ejpam-3253	90	20	⊆	⊆	NUM
ejpam-3253	90	21	y	y	NOUN
ejpam-3253	90	22	be	be	AUX
ejpam-3253	90	23	any	any	DET
ejpam-3253	90	24	open	open	ADJ
ejpam-3253	90	25	neighborhood	neighborhood	NOUN
ejpam-3253	90	26	of	of	ADP
ejpam-3253	90	27	y.	y.	PROPN
ejpam-3253	90	28	then	then	ADV
ejpam-3253	90	29	w	w	PROPN
ejpam-3253	90	30	∩	∩	NOUN
ejpam-3253	90	31	f(k	f(k	VERB
ejpam-3253	90	32	)	)	PUNCT
ejpam-3253	90	33	is	be	AUX
ejpam-3253	90	34	open	open	ADJ
ejpam-3253	90	35	in	in	ADP
ejpam-3253	90	36	the	the	DET
ejpam-3253	90	37	subspace	subspace	NOUN
ejpam-3253	90	38	f(k	f(k	VERB
ejpam-3253	90	39	)	)	PUNCT
ejpam-3253	90	40	containing	contain	VERB
ejpam-3253	90	41	y.	y.	NOUN
ejpam-3253	90	42	since	since	SCONJ
ejpam-3253	90	43	f({bn	f({bn	NUM
ejpam-3253	90	44	:	:	PUNCT
ejpam-3253	90	45	n	n	CCONJ
ejpam-3253	90	46	∈	∈	PROPN
ejpam-3253	90	47	n	n	CCONJ
ejpam-3253	90	48	}	}	PUNCT
ejpam-3253	90	49	)	)	PUNCT
ejpam-3253	90	50	⊆	⊆	NUM
ejpam-3253	90	51	f(k	f(k	ADJ
ejpam-3253	90	52	)	)	PUNCT
ejpam-3253	90	53	∩	∩	NOUN
ejpam-3253	90	54	f(b	f(b	PROPN
ejpam-3253	90	55	)	)	PUNCT
ejpam-3253	90	56	and	and	CCONJ
ejpam-3253	90	57	w	w	NOUN
ejpam-3253	90	58	∩	∩	NOUN
ejpam-3253	90	59	f(k	f(k	VERB
ejpam-3253	90	60	)	)	PUNCT
ejpam-3253	90	61	6=	6=	ADP
ejpam-3253	90	62	∅	∅	NOUN
ejpam-3253	90	63	,	,	PUNCT
ejpam-3253	90	64	then	then	ADV
ejpam-3253	90	65	we	we	PRON
ejpam-3253	90	66	have	have	VERB
ejpam-3253	90	67	w	w	NOUN
ejpam-3253	90	68	∩	∩	NOUN
ejpam-3253	90	69	f(b	f(b	PROPN
ejpam-3253	90	70	)	)	PUNCT
ejpam-3253	90	71	6=	6=	ADP
ejpam-3253	90	72	∅.	∅.	VERB
ejpam-3253	90	73	hence	hence	ADV
ejpam-3253	90	74	y	y	PROPN
ejpam-3253	90	75	∈	∈	PROPN
ejpam-3253	90	76	f(b	f(b	PROPN
ejpam-3253	90	77	)	)	PUNCT
ejpam-3253	90	78	and	and	CCONJ
ejpam-3253	90	79	f(b	f(b	PROPN
ejpam-3253	90	80	)	)	PUNCT
ejpam-3253	90	81	⊆	⊆	NUM
ejpam-3253	90	82	f(b	f(b	NOUN
ejpam-3253	90	83	)	)	PUNCT
ejpam-3253	90	84	.	.	PUNCT
ejpam-3253	91	1	thus	thus	ADV
ejpam-3253	91	2	f	f	PROPN
ejpam-3253	91	3	is	be	AUX
ejpam-3253	91	4	continuous	continuous	ADJ
ejpam-3253	91	5	.	.	PUNCT
ejpam-3253	92	1	since	since	SCONJ
ejpam-3253	92	2	any	any	DET
ejpam-3253	92	3	first	first	ADJ
ejpam-3253	92	4	countable	countable	ADJ
ejpam-3253	92	5	space	space	NOUN
ejpam-3253	92	6	is	be	AUX
ejpam-3253	92	7	fréchet	fréchet	VERB
ejpam-3253	92	8	[	[	X
ejpam-3253	92	9	8	8	NUM
ejpam-3253	92	10	]	]	PUNCT
ejpam-3253	92	11	,	,	PUNCT
ejpam-3253	92	12	we	we	PRON
ejpam-3253	92	13	conclude	conclude	VERB
ejpam-3253	92	14	the	the	DET
ejpam-3253	92	15	following	follow	VERB
ejpam-3253	92	16	corollary	corollary	ADJ
ejpam-3253	92	17	:	:	PUNCT
ejpam-3253	92	18	corollary	corollary	ADJ
ejpam-3253	92	19	1	1	NUM
ejpam-3253	92	20	.	.	PUNCT
ejpam-3253	93	1	if	if	SCONJ
ejpam-3253	93	2	x	x	PRON
ejpam-3253	93	3	is	be	AUX
ejpam-3253	93	4	c	c	NOUN
ejpam-3253	93	5	-	-	PUNCT
ejpam-3253	93	6	tychonoff	tychonoff	NOUN
ejpam-3253	93	7	first	first	ADV
ejpam-3253	93	8	countable	countable	ADJ
ejpam-3253	93	9	and	and	CCONJ
ejpam-3253	93	10	f	f	NOUN
ejpam-3253	93	11	:	:	PUNCT
ejpam-3253	93	12	x	x	PUNCT
ejpam-3253	93	13	−→	−→	NOUN
ejpam-3253	93	14	y	y	NOUN
ejpam-3253	93	15	witnessing	witness	VERB
ejpam-3253	93	16	the	the	DET
ejpam-3253	93	17	ctychonoffness	ctychonoffness	NOUN
ejpam-3253	93	18	of	of	ADP
ejpam-3253	93	19	x	x	NOUN
ejpam-3253	93	20	,	,	PUNCT
ejpam-3253	93	21	then	then	ADV
ejpam-3253	93	22	f	f	PROPN
ejpam-3253	93	23	is	be	AUX
ejpam-3253	93	24	continuous	continuous	ADJ
ejpam-3253	93	25	.	.	PUNCT
ejpam-3253	93	26	corollary	corollary	ADJ
ejpam-3253	93	27	2	2	NUM
ejpam-3253	93	28	.	.	PUNCT
ejpam-3253	94	1	any	any	DET
ejpam-3253	94	2	c	c	NOUN
ejpam-3253	94	3	-	-	PUNCT
ejpam-3253	94	4	tychonoff	tychonoff	NOUN
ejpam-3253	94	5	fréchet	fréchet	NOUN
ejpam-3253	94	6	space	space	NOUN
ejpam-3253	94	7	is	be	AUX
ejpam-3253	94	8	urysohn	urysohn	ADJ
ejpam-3253	94	9	.	.	PUNCT
ejpam-3253	95	1	proof	proof	NOUN
ejpam-3253	95	2	.	.	PUNCT
ejpam-3253	96	1	let	let	VERB
ejpam-3253	96	2	(	(	PUNCT
ejpam-3253	96	3	x	x	X
ejpam-3253	96	4	,	,	PUNCT
ejpam-3253	96	5	τ	τ	PROPN
ejpam-3253	96	6	)	)	PUNCT
ejpam-3253	96	7	be	be	AUX
ejpam-3253	96	8	any	any	DET
ejpam-3253	96	9	c	c	NOUN
ejpam-3253	96	10	-	-	PUNCT
ejpam-3253	96	11	tychonoff	tychonoff	NOUN
ejpam-3253	96	12	fréchet	fréchet	NOUN
ejpam-3253	96	13	space	space	NOUN
ejpam-3253	96	14	.	.	PUNCT
ejpam-3253	97	1	we	we	PRON
ejpam-3253	97	2	may	may	AUX
ejpam-3253	97	3	assume	assume	VERB
ejpam-3253	97	4	that	that	SCONJ
ejpam-3253	97	5	x	x	PRON
ejpam-3253	97	6	has	have	VERB
ejpam-3253	97	7	more	more	ADJ
ejpam-3253	97	8	than	than	ADP
ejpam-3253	97	9	one	one	NUM
ejpam-3253	97	10	element	element	NOUN
ejpam-3253	97	11	.	.	PUNCT
ejpam-3253	98	1	pick	pick	VERB
ejpam-3253	98	2	a	a	DET
ejpam-3253	98	3	tychonoff	tychonoff	NOUN
ejpam-3253	98	4	space	space	NOUN
ejpam-3253	98	5	(	(	PUNCT
ejpam-3253	98	6	y	y	PROPN
ejpam-3253	98	7	,	,	PUNCT
ejpam-3253	98	8	τ	τ	PROPN
ejpam-3253	98	9	′	′	NUM
ejpam-3253	98	10	)	)	PUNCT
ejpam-3253	98	11	and	and	CCONJ
ejpam-3253	98	12	a	a	DET
ejpam-3253	98	13	bijection	bijection	NOUN
ejpam-3253	98	14	function	function	NOUN
ejpam-3253	98	15	f	f	NOUN
ejpam-3253	98	16	:	:	PUNCT
ejpam-3253	98	17	(	(	PUNCT
ejpam-3253	98	18	x	x	X
ejpam-3253	98	19	,	,	PUNCT
ejpam-3253	98	20	τ	τ	PROPN
ejpam-3253	98	21	)	)	PUNCT
ejpam-3253	98	22	−→	−→	NOUN
ejpam-3253	98	23	(	(	PUNCT
ejpam-3253	98	24	y	y	PROPN
ejpam-3253	98	25	,	,	PUNCT
ejpam-3253	98	26	τ	τ	PROPN
ejpam-3253	98	27	′	′	NUM
ejpam-3253	98	28	)	)	PUNCT
ejpam-3253	98	29	such	such	ADJ
ejpam-3253	98	30	that	that	DET
ejpam-3253	98	31	f|a	f|a	NOUN
ejpam-3253	98	32	:	:	PUNCT
ejpam-3253	98	33	a	a	DET
ejpam-3253	98	34	−→	−→	NOUN
ejpam-3253	98	35	f(a	f(a	NOUN
ejpam-3253	98	36	)	)	PUNCT
ejpam-3253	98	37	is	be	AUX
ejpam-3253	98	38	a	a	DET
ejpam-3253	98	39	homeomorphism	homeomorphism	NOUN
ejpam-3253	98	40	for	for	ADP
ejpam-3253	98	41	each	each	DET
ejpam-3253	98	42	compact	compact	ADJ
ejpam-3253	98	43	subspace	subspace	NOUN
ejpam-3253	98	44	a	a	PRON
ejpam-3253	98	45	of	of	ADP
ejpam-3253	98	46	x.	x.	NOUN
ejpam-3253	98	47	since	since	SCONJ
ejpam-3253	98	48	x	x	PROPN
ejpam-3253	98	49	is	be	AUX
ejpam-3253	98	50	fréchet	fréchet	ADJ
ejpam-3253	98	51	,	,	PUNCT
ejpam-3253	98	52	then	then	ADV
ejpam-3253	98	53	f	f	PROPN
ejpam-3253	98	54	is	be	AUX
ejpam-3253	98	55	continuous	continuous	ADJ
ejpam-3253	98	56	.	.	PUNCT
ejpam-3253	99	1	define	define	VERB
ejpam-3253	99	2	a	a	DET
ejpam-3253	99	3	topology	topology	NOUN
ejpam-3253	99	4	τ	τ	NOUN
ejpam-3253	99	5	?	?	PUNCT
ejpam-3253	100	1	on	on	ADP
ejpam-3253	100	2	x	x	X
ejpam-3253	100	3	as	as	SCONJ
ejpam-3253	100	4	follows	follow	VERB
ejpam-3253	100	5	:	:	PUNCT
ejpam-3253	100	6	τ	τ	X
ejpam-3253	100	7	?	?	PUNCT
ejpam-3253	101	1	=	=	PRON
ejpam-3253	101	2	{	{	PUNCT
ejpam-3253	101	3	f−1(u	f−1(u	PROPN
ejpam-3253	101	4	)	)	PUNCT
ejpam-3253	101	5	:	:	PUNCT
ejpam-3253	102	1	u	u	PROPN
ejpam-3253	102	2	∈	∈	PROPN
ejpam-3253	102	3	τ	τ	X
ejpam-3253	102	4	′	′	NUM
ejpam-3253	102	5	}	}	PUNCT
ejpam-3253	102	6	.	.	PUNCT
ejpam-3253	103	1	it	it	PRON
ejpam-3253	103	2	clear	clear	ADJ
ejpam-3253	103	3	that	that	SCONJ
ejpam-3253	103	4	τ	τ	PROPN
ejpam-3253	103	5	?	?	PUNCT
ejpam-3253	103	6	is	be	AUX
ejpam-3253	103	7	a	a	DET
ejpam-3253	103	8	topology	topology	NOUN
ejpam-3253	103	9	on	on	ADP
ejpam-3253	103	10	x	x	SYM
ejpam-3253	103	11	coarser	coarse	ADJ
ejpam-3253	103	12	that	that	SCONJ
ejpam-3253	103	13	τ	τ	PROPN
ejpam-3253	103	14	such	such	ADJ
ejpam-3253	103	15	that	that	SCONJ
ejpam-3253	103	16	f	f	X
ejpam-3253	103	17	:	:	PUNCT
ejpam-3253	103	18	(	(	PUNCT
ejpam-3253	103	19	x	x	X
ejpam-3253	103	20	,	,	PUNCT
ejpam-3253	103	21	τ	τ	PROPN
ejpam-3253	103	22	?	?	PUNCT
ejpam-3253	103	23	)	)	PUNCT
ejpam-3253	104	1	−→	−→	NOUN
ejpam-3253	104	2	(	(	PUNCT
ejpam-3253	104	3	y	y	PROPN
ejpam-3253	104	4	,	,	PUNCT
ejpam-3253	104	5	τ	τ	PROPN
ejpam-3253	104	6	′	′	NUM
ejpam-3253	104	7	)	)	PUNCT
ejpam-3253	104	8	is	be	AUX
ejpam-3253	104	9	continuous	continuous	ADJ
ejpam-3253	104	10	.	.	PUNCT
ejpam-3253	105	1	if	if	SCONJ
ejpam-3253	105	2	w	w	PROPN
ejpam-3253	105	3	∈	∈	PROPN
ejpam-3253	105	4	τ	τ	X
ejpam-3253	105	5	?	?	PUNCT
ejpam-3253	105	6	,	,	PUNCT
ejpam-3253	105	7	then	then	ADV
ejpam-3253	105	8	w	w	NOUN
ejpam-3253	105	9	is	be	AUX
ejpam-3253	105	10	of	of	ADP
ejpam-3253	105	11	the	the	DET
ejpam-3253	105	12	form	form	NOUN
ejpam-3253	105	13	w	w	PROPN
ejpam-3253	105	14	=	=	SYM
ejpam-3253	105	15	f−1(u	f−1(u	PROPN
ejpam-3253	105	16	)	)	PUNCT
ejpam-3253	105	17	where	where	SCONJ
ejpam-3253	105	18	u	u	PROPN
ejpam-3253	105	19	∈	∈	PROPN
ejpam-3253	105	20	τ	τ	X
ejpam-3253	105	21	′.	′.	NOUN
ejpam-3253	105	22	so	so	ADV
ejpam-3253	105	23	,	,	PUNCT
ejpam-3253	105	24	f(w	f(w	PROPN
ejpam-3253	105	25	)	)	PUNCT
ejpam-3253	106	1	=	=	PUNCT
ejpam-3253	106	2	f(f−1(u	f(f−1(u	PROPN
ejpam-3253	106	3	)	)	PUNCT
ejpam-3253	106	4	)	)	PUNCT
ejpam-3253	107	1	=	=	SYM
ejpam-3253	107	2	u	u	NOUN
ejpam-3253	107	3	which	which	PRON
ejpam-3253	107	4	gives	give	VERB
ejpam-3253	107	5	that	that	SCONJ
ejpam-3253	107	6	f	f	PROPN
ejpam-3253	107	7	is	be	AUX
ejpam-3253	107	8	open	open	ADJ
ejpam-3253	107	9	,	,	PUNCT
ejpam-3253	107	10	hence	hence	ADV
ejpam-3253	107	11	homeomorphism	homeomorphism	X
ejpam-3253	107	12	.	.	PUNCT
ejpam-3253	108	1	thus	thus	ADV
ejpam-3253	108	2	(	(	PUNCT
ejpam-3253	108	3	x	x	X
ejpam-3253	108	4	,	,	PUNCT
ejpam-3253	108	5	τ	τ	PROPN
ejpam-3253	108	6	?	?	PUNCT
ejpam-3253	108	7	)	)	PUNCT
ejpam-3253	108	8	is	be	AUX
ejpam-3253	108	9	tychonoff	tychonoff	NOUN
ejpam-3253	108	10	.	.	PUNCT
ejpam-3253	109	1	pick	pick	VERB
ejpam-3253	109	2	distinct	distinct	ADJ
ejpam-3253	109	3	a	a	DET
ejpam-3253	109	4	,	,	PUNCT
ejpam-3253	109	5	b	b	X
ejpam-3253	109	6	∈	∈	PROPN
ejpam-3253	109	7	x.	x.	NOUN
ejpam-3253	109	8	using	use	VERB
ejpam-3253	109	9	t2	t2	PROPN
ejpam-3253	109	10	of	of	ADP
ejpam-3253	109	11	(	(	PUNCT
ejpam-3253	109	12	x	x	INTJ
ejpam-3253	109	13	,	,	PUNCT
ejpam-3253	109	14	τ	τ	PROPN
ejpam-3253	109	15	?	?	PUNCT
ejpam-3253	109	16	)	)	PUNCT
ejpam-3253	109	17	,	,	PUNCT
ejpam-3253	109	18	choose	choose	VERB
ejpam-3253	109	19	g	g	PROPN
ejpam-3253	109	20	,	,	PUNCT
ejpam-3253	109	21	h	h	NOUN
ejpam-3253	109	22	∈	∈	PROPN
ejpam-3253	109	23	τ	τ	X
ejpam-3253	109	24	?	?	PUNCT
ejpam-3253	110	1	such	such	ADJ
ejpam-3253	110	2	that	that	SCONJ
ejpam-3253	110	3	a	a	DET
ejpam-3253	110	4	∈	∈	PROPN
ejpam-3253	110	5	g	g	NOUN
ejpam-3253	110	6	,	,	PUNCT
ejpam-3253	110	7	b	b	PROPN
ejpam-3253	110	8	∈	∈	PROPN
ejpam-3253	110	9	h	h	NOUN
ejpam-3253	110	10	,	,	PUNCT
ejpam-3253	110	11	and	and	CCONJ
ejpam-3253	110	12	g	g	ADP
ejpam-3253	110	13	∩h	∩h	NOUN
ejpam-3253	110	14	=	=	PUNCT
ejpam-3253	110	15	∅.	∅.	VERB
ejpam-3253	110	16	using	use	VERB
ejpam-3253	110	17	regularity	regularity	NOUN
ejpam-3253	110	18	of	of	ADP
ejpam-3253	110	19	(	(	PUNCT
ejpam-3253	110	20	x	x	INTJ
ejpam-3253	110	21	,	,	PUNCT
ejpam-3253	110	22	τ	τ	PROPN
ejpam-3253	110	23	?	?	PUNCT
ejpam-3253	110	24	)	)	PUNCT
ejpam-3253	110	25	,	,	PUNCT
ejpam-3253	110	26	choose	choose	VERB
ejpam-3253	110	27	u	u	NOUN
ejpam-3253	110	28	,	,	PUNCT
ejpam-3253	110	29	v	v	PROPN
ejpam-3253	110	30	∈	∈	PROPN
ejpam-3253	110	31	τ	τ	X
ejpam-3253	110	32	?	?	PUNCT
ejpam-3253	111	1	such	such	ADJ
ejpam-3253	111	2	that	that	SCONJ
ejpam-3253	111	3	a	a	DET
ejpam-3253	111	4	∈	∈	PROPN
ejpam-3253	111	5	u	u	NOUN
ejpam-3253	111	6	⊆	⊆	NUM
ejpam-3253	111	7	u	u	NOUN
ejpam-3253	111	8	τ	τ	X
ejpam-3253	111	9	?	?	PUNCT
ejpam-3253	112	1	⊆	⊆	NUM
ejpam-3253	112	2	g	g	NOUN
ejpam-3253	112	3	and	and	CCONJ
ejpam-3253	112	4	b	b	PROPN
ejpam-3253	112	5	∈	∈	NOUN
ejpam-3253	112	6	v	v	ADP
ejpam-3253	112	7	⊆	⊆	NUM
ejpam-3253	112	8	v	v	ADP
ejpam-3253	112	9	τ	τ	X
ejpam-3253	112	10	?	?	PUNCT
ejpam-3253	113	1	⊆	⊆	NUM
ejpam-3253	113	2	h.	h.	NOUN
ejpam-3253	113	3	we	we	PRON
ejpam-3253	113	4	have	have	VERB
ejpam-3253	113	5	that	that	DET
ejpam-3253	113	6	u	u	NOUN
ejpam-3253	113	7	,	,	PUNCT
ejpam-3253	113	8	v	v	PROPN
ejpam-3253	113	9	∈	∈	NOUN
ejpam-3253	113	10	τ	τ	X
ejpam-3253	114	1	and	and	CCONJ
ejpam-3253	114	2	since	since	SCONJ
ejpam-3253	114	3	b	b	PROPN
ejpam-3253	114	4	τ	τ	X
ejpam-3253	114	5	⊆	⊆	NUM
ejpam-3253	114	6	b	b	SYM
ejpam-3253	114	7	τ	τ	PROPN
ejpam-3253	114	8	?	?	PUNCT
ejpam-3253	114	9	for	for	ADP
ejpam-3253	114	10	any	any	DET
ejpam-3253	114	11	b	b	NOUN
ejpam-3253	114	12	⊆	⊆	NUM
ejpam-3253	114	13	x	x	SYM
ejpam-3253	114	14	,	,	PUNCT
ejpam-3253	114	15	we	we	PRON
ejpam-3253	114	16	get	get	VERB
ejpam-3253	114	17	u	u	PRON
ejpam-3253	114	18	τ	τ	PROPN
ejpam-3253	114	19	∩	∩	NOUN
ejpam-3253	114	20	v	v	ADP
ejpam-3253	114	21	τ	τ	X
ejpam-3253	114	22	=	=	PUNCT
ejpam-3253	114	23	∅.	∅.	NOUN
ejpam-3253	114	24	therefore	therefore	ADV
ejpam-3253	114	25	,	,	PUNCT
ejpam-3253	114	26	(	(	PUNCT
ejpam-3253	114	27	x	x	X
ejpam-3253	114	28	,	,	PUNCT
ejpam-3253	114	29	τ	τ	PROPN
ejpam-3253	114	30	)	)	PUNCT
ejpam-3253	114	31	is	be	AUX
ejpam-3253	114	32	urysohn	urysohn	ADJ
ejpam-3253	114	33	.	.	PUNCT
ejpam-3253	115	1	so	so	ADV
ejpam-3253	115	2	,	,	PUNCT
ejpam-3253	115	3	we	we	PRON
ejpam-3253	115	4	conclude	conclude	VERB
ejpam-3253	115	5	that	that	SCONJ
ejpam-3253	115	6	any	any	DET
ejpam-3253	115	7	first	first	ADJ
ejpam-3253	115	8	countable	countable	ADJ
ejpam-3253	115	9	c	c	NOUN
ejpam-3253	115	10	-	-	PUNCT
ejpam-3253	115	11	tychonoff	tychonoff	NOUN
ejpam-3253	115	12	space	space	NOUN
ejpam-3253	115	13	is	be	AUX
ejpam-3253	115	14	hausdorff	hausdorff	NOUN
ejpam-3253	115	15	.	.	PUNCT
ejpam-3253	116	1	recall	recall	VERB
ejpam-3253	116	2	that	that	SCONJ
ejpam-3253	116	3	a	a	DET
ejpam-3253	116	4	space	space	NOUN
ejpam-3253	116	5	x	x	PUNCT
ejpam-3253	116	6	is	be	AUX
ejpam-3253	116	7	a	a	DET
ejpam-3253	116	8	k	k	NOUN
ejpam-3253	116	9	-	-	NOUN
ejpam-3253	116	10	space	space	NOUN
ejpam-3253	116	11	if	if	SCONJ
ejpam-3253	116	12	x	x	PRON
ejpam-3253	116	13	is	be	AUX
ejpam-3253	116	14	t2	t2	NOUN
ejpam-3253	116	15	and	and	CCONJ
ejpam-3253	116	16	it	it	PRON
ejpam-3253	116	17	is	be	AUX
ejpam-3253	116	18	a	a	DET
ejpam-3253	116	19	quotient	quotient	NOUN
ejpam-3253	116	20	image	image	NOUN
ejpam-3253	116	21	of	of	ADP
ejpam-3253	116	22	a	a	DET
ejpam-3253	116	23	locally	locally	ADV
ejpam-3253	116	24	compact	compact	ADJ
ejpam-3253	116	25	space	space	NOUN
ejpam-3253	117	1	[	[	X
ejpam-3253	117	2	8	8	NUM
ejpam-3253	117	3	]	]	PUNCT
ejpam-3253	117	4	.	.	PUNCT
ejpam-3253	118	1	by	by	ADP
ejpam-3253	118	2	the	the	DET
ejpam-3253	118	3	theorem	theorem	NOUN
ejpam-3253	118	4	:	:	PUNCT
ejpam-3253	118	5	“	"	PUNCT
ejpam-3253	118	6	a	a	DET
ejpam-3253	118	7	function	function	NOUN
ejpam-3253	118	8	f	f	NOUN
ejpam-3253	118	9	from	from	ADP
ejpam-3253	118	10	a	a	DET
ejpam-3253	118	11	k	k	NOUN
ejpam-3253	118	12	-	-	NOUN
ejpam-3253	118	13	space	space	NOUN
ejpam-3253	118	14	x	x	PUNCT
ejpam-3253	118	15	into	into	ADP
ejpam-3253	118	16	a	a	DET
ejpam-3253	118	17	space	space	NOUN
ejpam-3253	118	18	y	y	NOUN
ejpam-3253	118	19	is	be	AUX
ejpam-3253	118	20	continuous	continuous	ADJ
ejpam-3253	118	21	if	if	SCONJ
ejpam-3253	118	22	and	and	CCONJ
ejpam-3253	118	23	only	only	ADV
ejpam-3253	118	24	if	if	SCONJ
ejpam-3253	118	25	f|z	f|z	ADV
ejpam-3253	118	26	:	:	PUNCT
ejpam-3253	118	27	z	z	X
ejpam-3253	118	28	−→	−→	NOUN
ejpam-3253	118	29	y	y	PROPN
ejpam-3253	118	30	is	be	AUX
ejpam-3253	118	31	continuous	continuous	ADJ
ejpam-3253	118	32	for	for	ADP
ejpam-3253	118	33	each	each	DET
ejpam-3253	118	34	compact	compact	ADJ
ejpam-3253	118	35	subspace	subspace	NOUN
ejpam-3253	118	36	z	z	PROPN
ejpam-3253	118	37	of	of	ADP
ejpam-3253	118	38	x	x	NOUN
ejpam-3253	118	39	”	"	PUNCT
ejpam-3253	118	40	,	,	PUNCT
ejpam-3253	118	41	[	[	X
ejpam-3253	118	42	8	8	NUM
ejpam-3253	118	43	,	,	PUNCT
ejpam-3253	118	44	3.3.21	3.3.21	PROPN
ejpam-3253	118	45	]	]	PUNCT
ejpam-3253	118	46	.	.	PUNCT
ejpam-3253	119	1	we	we	PRON
ejpam-3253	119	2	conclude	conclude	VERB
ejpam-3253	119	3	the	the	DET
ejpam-3253	119	4	following	follow	VERB
ejpam-3253	119	5	:	:	PUNCT
ejpam-3253	119	6	corollary	corollary	ADJ
ejpam-3253	119	7	3	3	X
ejpam-3253	119	8	.	.	PUNCT
ejpam-3253	120	1	if	if	SCONJ
ejpam-3253	120	2	x	x	PRON
ejpam-3253	120	3	is	be	AUX
ejpam-3253	120	4	a	a	DET
ejpam-3253	120	5	c	c	NOUN
ejpam-3253	120	6	-	-	PUNCT
ejpam-3253	120	7	tychonoff	tychonoff	NOUN
ejpam-3253	120	8	k	k	NOUN
ejpam-3253	120	9	-	-	NOUN
ejpam-3253	120	10	space	space	NOUN
ejpam-3253	120	11	and	and	CCONJ
ejpam-3253	120	12	f	f	NOUN
ejpam-3253	120	13	:	:	PUNCT
ejpam-3253	120	14	x	x	PUNCT
ejpam-3253	120	15	−→	−→	NOUN
ejpam-3253	120	16	y	y	NOUN
ejpam-3253	120	17	witnessing	witness	VERB
ejpam-3253	120	18	the	the	DET
ejpam-3253	120	19	ctychonoffness	ctychonoffness	NOUN
ejpam-3253	120	20	of	of	ADP
ejpam-3253	120	21	x	x	NOUN
ejpam-3253	120	22	,	,	PUNCT
ejpam-3253	120	23	then	then	ADV
ejpam-3253	120	24	f	f	PROPN
ejpam-3253	120	25	is	be	AUX
ejpam-3253	120	26	continuous	continuous	ADJ
ejpam-3253	120	27	.	.	PUNCT
ejpam-3253	121	1	recall	recall	VERB
ejpam-3253	121	2	that	that	SCONJ
ejpam-3253	121	3	a	a	DET
ejpam-3253	121	4	topological	topological	ADJ
ejpam-3253	121	5	space	space	NOUN
ejpam-3253	121	6	x	x	PUNCT
ejpam-3253	121	7	is	be	AUX
ejpam-3253	121	8	called	call	VERB
ejpam-3253	121	9	c	c	NOUN
ejpam-3253	121	10	-	-	NOUN
ejpam-3253	121	11	normal	normal	ADJ
ejpam-3253	121	12	if	if	SCONJ
ejpam-3253	121	13	there	there	PRON
ejpam-3253	121	14	exist	exist	VERB
ejpam-3253	121	15	a	a	DET
ejpam-3253	121	16	one	one	NUM
ejpam-3253	121	17	-	-	PUNCT
ejpam-3253	121	18	to	to	ADP
ejpam-3253	121	19	-	-	PUNCT
ejpam-3253	121	20	one	one	NUM
ejpam-3253	121	21	function	function	NOUN
ejpam-3253	121	22	f	f	NOUN
ejpam-3253	121	23	from	from	ADP
ejpam-3253	121	24	x	x	PRON
ejpam-3253	121	25	onto	onto	ADP
ejpam-3253	121	26	a	a	DET
ejpam-3253	121	27	normal	normal	ADJ
ejpam-3253	121	28	space	space	NOUN
ejpam-3253	121	29	y	y	PRON
ejpam-3253	121	30	such	such	ADJ
ejpam-3253	121	31	that	that	SCONJ
ejpam-3253	121	32	the	the	DET
ejpam-3253	121	33	restriction	restriction	NOUN
ejpam-3253	121	34	f|k	f|k	PUNCT
ejpam-3253	122	1	:	:	PUNCT
ejpam-3253	122	2	k	k	X
ejpam-3253	122	3	−→	−→	NOUN
ejpam-3253	122	4	f(k	f(k	VERB
ejpam-3253	122	5	)	)	PUNCT
ejpam-3253	122	6	is	be	AUX
ejpam-3253	122	7	a	a	DET
ejpam-3253	122	8	homeomorphism	homeomorphism	NOUN
ejpam-3253	122	9	for	for	ADP
ejpam-3253	122	10	each	each	DET
ejpam-3253	122	11	compact	compact	ADJ
ejpam-3253	122	12	subspace	subspace	NOUN
ejpam-3253	122	13	k	k	PROPN
ejpam-3253	122	14	⊆	⊆	NUM
ejpam-3253	122	15	x[2	x[2	NOUN
ejpam-3253	122	16	]	]	PUNCT
ejpam-3253	122	17	.	.	PUNCT
ejpam-3253	123	1	theorem	theorem	ADJ
ejpam-3253	123	2	6	6	NUM
ejpam-3253	123	3	.	.	PUNCT
ejpam-3253	124	1	every	every	DET
ejpam-3253	124	2	c	c	NOUN
ejpam-3253	124	3	-	-	PUNCT
ejpam-3253	124	4	tychonoff	tychonoff	NOUN
ejpam-3253	124	5	fréchet	fréchet	NOUN
ejpam-3253	124	6	lindelöf	lindelöf	NOUN
ejpam-3253	124	7	space	space	NOUN
ejpam-3253	124	8	is	be	AUX
ejpam-3253	124	9	c	c	NOUN
ejpam-3253	124	10	-	-	ADJ
ejpam-3253	124	11	normal	normal	ADJ
ejpam-3253	124	12	.	.	PUNCT
ejpam-3253	125	1	s.	s.	PROPN
ejpam-3253	125	2	alzahrani	alzahrani	PROPN
ejpam-3253	125	3	/	/	SYM
ejpam-3253	125	4	eur	eur	PROPN
ejpam-3253	125	5	.	.	PUNCT
ejpam-3253	126	1	j.	j.	PROPN
ejpam-3253	126	2	pure	pure	PROPN
ejpam-3253	126	3	appl	appl	PROPN
ejpam-3253	126	4	.	.	PROPN
ejpam-3253	126	5	math	math	PROPN
ejpam-3253	126	6	,	,	PUNCT
ejpam-3253	126	7	11	11	NUM
ejpam-3253	126	8	(	(	PUNCT
ejpam-3253	126	9	3	3	NUM
ejpam-3253	126	10	)	)	PUNCT
ejpam-3253	126	11	(	(	PUNCT
ejpam-3253	126	12	2018	2018	NUM
ejpam-3253	126	13	)	)	PUNCT
ejpam-3253	126	14	,	,	PUNCT
ejpam-3253	126	15	882	882	NUM
ejpam-3253	126	16	-	-	SYM
ejpam-3253	126	17	892	892	NUM
ejpam-3253	126	18	886	886	NUM
ejpam-3253	126	19	proof	proof	NOUN
ejpam-3253	126	20	.	.	PUNCT
ejpam-3253	127	1	let	let	VERB
ejpam-3253	127	2	x	x	PRON
ejpam-3253	127	3	be	be	AUX
ejpam-3253	127	4	any	any	DET
ejpam-3253	127	5	c	c	NOUN
ejpam-3253	127	6	-	-	PUNCT
ejpam-3253	127	7	tychonoff	tychonoff	NOUN
ejpam-3253	127	8	fréchet	fréchet	NOUN
ejpam-3253	127	9	lindelöf	lindelöf	NOUN
ejpam-3253	127	10	space	space	NOUN
ejpam-3253	127	11	.	.	PUNCT
ejpam-3253	128	1	pick	pick	VERB
ejpam-3253	128	2	a	a	DET
ejpam-3253	128	3	tychonoff	tychonoff	NOUN
ejpam-3253	128	4	space	space	NOUN
ejpam-3253	128	5	y	y	PROPN
ejpam-3253	128	6	and	and	CCONJ
ejpam-3253	128	7	a	a	DET
ejpam-3253	128	8	bijective	bijective	ADJ
ejpam-3253	128	9	function	function	NOUN
ejpam-3253	129	1	f	f	NOUN
ejpam-3253	129	2	:	:	PUNCT
ejpam-3253	129	3	x	x	PUNCT
ejpam-3253	129	4	−→	−→	NOUN
ejpam-3253	129	5	y	y	PROPN
ejpam-3253	129	6	such	such	ADJ
ejpam-3253	129	7	that	that	SCONJ
ejpam-3253	129	8	the	the	DET
ejpam-3253	129	9	restriction	restriction	NOUN
ejpam-3253	129	10	f|k	f|k	PUNCT
ejpam-3253	129	11	:	:	PUNCT
ejpam-3253	129	12	k	k	X
ejpam-3253	129	13	−→	−→	NOUN
ejpam-3253	129	14	f(k	f(k	VERB
ejpam-3253	129	15	)	)	PUNCT
ejpam-3253	129	16	is	be	AUX
ejpam-3253	129	17	a	a	DET
ejpam-3253	129	18	homeomorphism	homeomorphism	NOUN
ejpam-3253	129	19	for	for	ADP
ejpam-3253	129	20	each	each	DET
ejpam-3253	129	21	compact	compact	ADJ
ejpam-3253	129	22	subspace	subspace	NOUN
ejpam-3253	129	23	k	k	PROPN
ejpam-3253	129	24	⊆	⊆	NUM
ejpam-3253	129	25	x.	x.	NOUN
ejpam-3253	129	26	by	by	ADP
ejpam-3253	129	27	theorem	theorem	NOUN
ejpam-3253	129	28	5	5	NUM
ejpam-3253	129	29	,	,	PUNCT
ejpam-3253	129	30	f	f	PROPN
ejpam-3253	129	31	is	be	AUX
ejpam-3253	129	32	continuous	continuous	ADJ
ejpam-3253	129	33	.	.	PUNCT
ejpam-3253	130	1	since	since	SCONJ
ejpam-3253	130	2	the	the	DET
ejpam-3253	130	3	continuous	continuous	ADJ
ejpam-3253	130	4	image	image	NOUN
ejpam-3253	130	5	of	of	ADP
ejpam-3253	130	6	a	a	DET
ejpam-3253	130	7	lindelöf	lindelöf	NOUN
ejpam-3253	130	8	space	space	NOUN
ejpam-3253	130	9	is	be	AUX
ejpam-3253	130	10	lindelöf	lindelöf	NOUN
ejpam-3253	130	11	[	[	X
ejpam-3253	130	12	8	8	NUM
ejpam-3253	130	13	,	,	PUNCT
ejpam-3253	130	14	3.8.7	3.8.7	NUM
ejpam-3253	130	15	]	]	PUNCT
ejpam-3253	130	16	,	,	PUNCT
ejpam-3253	130	17	we	we	PRON
ejpam-3253	130	18	conclude	conclude	VERB
ejpam-3253	130	19	that	that	SCONJ
ejpam-3253	130	20	y	y	PROPN
ejpam-3253	130	21	is	be	AUX
ejpam-3253	130	22	lindelöf	lindelöf	NOUN
ejpam-3253	130	23	,	,	PUNCT
ejpam-3253	130	24	hence	hence	ADV
ejpam-3253	130	25	normal	normal	ADJ
ejpam-3253	130	26	as	as	ADP
ejpam-3253	130	27	any	any	DET
ejpam-3253	130	28	regular	regular	ADJ
ejpam-3253	130	29	lindelöf	lindelöf	NOUN
ejpam-3253	130	30	space	space	NOUN
ejpam-3253	130	31	is	be	AUX
ejpam-3253	130	32	normal	normal	ADJ
ejpam-3253	130	33	[	[	X
ejpam-3253	130	34	8	8	NUM
ejpam-3253	130	35	,	,	PUNCT
ejpam-3253	130	36	3.8.2	3.8.2	NUM
ejpam-3253	130	37	]	]	PUNCT
ejpam-3253	130	38	.	.	PUNCT
ejpam-3253	131	1	therefore	therefore	ADV
ejpam-3253	131	2	,	,	PUNCT
ejpam-3253	131	3	x	x	X
ejpam-3253	131	4	is	be	AUX
ejpam-3253	131	5	c	c	NOUN
ejpam-3253	131	6	-	-	NOUN
ejpam-3253	131	7	normal	normal	ADJ
ejpam-3253	131	8	.	.	PUNCT
ejpam-3253	132	1	c	c	X
ejpam-3253	132	2	-	-	PUNCT
ejpam-3253	132	3	normality	normality	NOUN
ejpam-3253	132	4	and	and	CCONJ
ejpam-3253	132	5	c	c	NOUN
ejpam-3253	132	6	-	-	PUNCT
ejpam-3253	132	7	tychonoffness	tychonoffness	NOUN
ejpam-3253	132	8	are	be	AUX
ejpam-3253	132	9	independent	independent	ADJ
ejpam-3253	132	10	from	from	ADP
ejpam-3253	132	11	each	each	DET
ejpam-3253	132	12	other	other	ADJ
ejpam-3253	132	13	.	.	PUNCT
ejpam-3253	133	1	here	here	ADV
ejpam-3253	133	2	is	be	AUX
ejpam-3253	133	3	an	an	DET
ejpam-3253	133	4	example	example	NOUN
ejpam-3253	133	5	of	of	ADP
ejpam-3253	133	6	a	a	DET
ejpam-3253	133	7	c	c	NOUN
ejpam-3253	133	8	-	-	NOUN
ejpam-3253	133	9	normal	normal	ADJ
ejpam-3253	133	10	which	which	PRON
ejpam-3253	133	11	is	be	AUX
ejpam-3253	133	12	not	not	PART
ejpam-3253	133	13	c	c	NOUN
ejpam-3253	133	14	-	-	PUNCT
ejpam-3253	133	15	tychonoff	tychonoff	NOUN
ejpam-3253	133	16	.	.	PUNCT
ejpam-3253	134	1	example	example	NOUN
ejpam-3253	135	1	3	3	X
ejpam-3253	135	2	.	.	X
ejpam-3253	135	3	consider	consider	VERB
ejpam-3253	135	4	r	r	NOUN
ejpam-3253	135	5	with	with	ADP
ejpam-3253	135	6	its	its	PRON
ejpam-3253	135	7	right	right	ADJ
ejpam-3253	135	8	ray	ray	NOUN
ejpam-3253	135	9	topology	topology	NOUN
ejpam-3253	135	10	r	r	NOUN
ejpam-3253	136	1	[	[	X
ejpam-3253	136	2	16	16	NUM
ejpam-3253	136	3	]	]	PUNCT
ejpam-3253	136	4	.	.	PUNCT
ejpam-3253	137	1	so	so	ADV
ejpam-3253	137	2	,	,	PUNCT
ejpam-3253	137	3	r	r	AUX
ejpam-3253	137	4	=	=	SYM
ejpam-3253	137	5	{	{	PUNCT
ejpam-3253	137	6	∅,r	∅,r	ADV
ejpam-3253	137	7	}	}	PUNCT
ejpam-3253	137	8	∪	∪	X
ejpam-3253	137	9	{	{	PUNCT
ejpam-3253	137	10	(	(	PUNCT
ejpam-3253	137	11	x,∞	x,∞	PROPN
ejpam-3253	137	12	)	)	PUNCT
ejpam-3253	137	13	:	:	PUNCT
ejpam-3253	138	1	x	x	X
ejpam-3253	138	2	∈	∈	NOUN
ejpam-3253	138	3	r	r	NOUN
ejpam-3253	138	4	}	}	PUNCT
ejpam-3253	138	5	.	.	PUNCT
ejpam-3253	139	1	since	since	SCONJ
ejpam-3253	139	2	any	any	DET
ejpam-3253	139	3	two	two	NUM
ejpam-3253	139	4	non	non	ADJ
ejpam-3253	139	5	-	-	ADJ
ejpam-3253	139	6	empty	empty	ADJ
ejpam-3253	139	7	closed	closed	ADJ
ejpam-3253	139	8	sets	set	NOUN
ejpam-3253	139	9	must	must	AUX
ejpam-3253	139	10	intersect	intersect	VERB
ejpam-3253	139	11	,	,	PUNCT
ejpam-3253	139	12	then	then	ADV
ejpam-3253	139	13	(	(	PUNCT
ejpam-3253	139	14	r	r	NOUN
ejpam-3253	139	15	,	,	PUNCT
ejpam-3253	139	16	r	r	NOUN
ejpam-3253	139	17	)	)	PUNCT
ejpam-3253	139	18	is	be	AUX
ejpam-3253	139	19	normal	normal	ADJ
ejpam-3253	139	20	,	,	PUNCT
ejpam-3253	139	21	hence	hence	ADV
ejpam-3253	139	22	c	c	NOUN
ejpam-3253	139	23	-	-	ADJ
ejpam-3253	139	24	normal	normal	ADJ
ejpam-3253	139	25	[	[	X
ejpam-3253	139	26	2	2	NUM
ejpam-3253	139	27	]	]	PUNCT
ejpam-3253	139	28	.	.	PUNCT
ejpam-3253	140	1	now	now	ADV
ejpam-3253	140	2	,	,	PUNCT
ejpam-3253	140	3	suppose	suppose	VERB
ejpam-3253	140	4	that	that	SCONJ
ejpam-3253	140	5	(	(	PUNCT
ejpam-3253	140	6	r	r	NOUN
ejpam-3253	140	7	,	,	PUNCT
ejpam-3253	140	8	r	r	NOUN
ejpam-3253	140	9	)	)	PUNCT
ejpam-3253	140	10	is	be	AUX
ejpam-3253	140	11	c	c	NOUN
ejpam-3253	140	12	-	-	PUNCT
ejpam-3253	140	13	tychonoff	tychonoff	NOUN
ejpam-3253	140	14	.	.	PUNCT
ejpam-3253	141	1	pick	pick	VERB
ejpam-3253	141	2	a	a	DET
ejpam-3253	141	3	tychonoff	tychonoff	NOUN
ejpam-3253	141	4	space	space	NOUN
ejpam-3253	141	5	y	y	PROPN
ejpam-3253	141	6	and	and	CCONJ
ejpam-3253	141	7	a	a	DET
ejpam-3253	141	8	bijective	bijective	ADJ
ejpam-3253	141	9	function	function	NOUN
ejpam-3253	142	1	f	f	NOUN
ejpam-3253	142	2	:	:	PUNCT
ejpam-3253	142	3	r	r	VERB
ejpam-3253	142	4	−→	−→	ADJ
ejpam-3253	142	5	y	y	PROPN
ejpam-3253	142	6	such	such	ADJ
ejpam-3253	142	7	that	that	SCONJ
ejpam-3253	142	8	the	the	DET
ejpam-3253	142	9	restriction	restriction	NOUN
ejpam-3253	142	10	f|k	f|k	PUNCT
ejpam-3253	143	1	:	:	PUNCT
ejpam-3253	144	1	k	k	X
ejpam-3253	144	2	−→	−→	NOUN
ejpam-3253	144	3	f(k	f(k	VERB
ejpam-3253	144	4	)	)	PUNCT
ejpam-3253	144	5	is	be	AUX
ejpam-3253	144	6	a	a	DET
ejpam-3253	144	7	homeomorphism	homeomorphism	NOUN
ejpam-3253	144	8	for	for	ADP
ejpam-3253	144	9	each	each	DET
ejpam-3253	144	10	compact	compact	ADJ
ejpam-3253	144	11	subspace	subspace	NOUN
ejpam-3253	144	12	k	k	PROPN
ejpam-3253	144	13	⊆	⊆	NUM
ejpam-3253	144	14	r.	r.	NOUN
ejpam-3253	144	15	it	it	PRON
ejpam-3253	144	16	is	be	AUX
ejpam-3253	144	17	well	well	ADV
ejpam-3253	144	18	-	-	PUNCT
ejpam-3253	144	19	known	know	VERB
ejpam-3253	144	20	that	that	SCONJ
ejpam-3253	144	21	a	a	DET
ejpam-3253	144	22	subspace	subspace	NOUN
ejpam-3253	144	23	k	k	PROPN
ejpam-3253	144	24	of	of	ADP
ejpam-3253	144	25	(	(	PUNCT
ejpam-3253	144	26	r	r	NOUN
ejpam-3253	144	27	,	,	PUNCT
ejpam-3253	144	28	r	r	NOUN
ejpam-3253	144	29	)	)	PUNCT
ejpam-3253	144	30	is	be	AUX
ejpam-3253	144	31	compact	compact	ADJ
ejpam-3253	144	32	if	if	SCONJ
ejpam-3253	145	1	and	and	CCONJ
ejpam-3253	145	2	only	only	ADV
ejpam-3253	145	3	if	if	SCONJ
ejpam-3253	145	4	k	k	PROPN
ejpam-3253	145	5	has	have	VERB
ejpam-3253	145	6	a	a	DET
ejpam-3253	145	7	minimal	minimal	ADJ
ejpam-3253	145	8	element	element	NOUN
ejpam-3253	145	9	.	.	PUNCT
ejpam-3253	146	1	thus	thus	ADV
ejpam-3253	146	2	[	[	X
ejpam-3253	146	3	2,∞	2,∞	NUM
ejpam-3253	146	4	)	)	PUNCT
ejpam-3253	146	5	is	be	AUX
ejpam-3253	146	6	compact	compact	ADJ
ejpam-3253	146	7	,	,	PUNCT
ejpam-3253	146	8	hence	hence	ADV
ejpam-3253	146	9	f|[2,∞	f|[2,∞	ADJ
ejpam-3253	146	10	)	)	PUNCT
ejpam-3253	146	11	:	:	PUNCT
ejpam-3253	147	1	[	[	X
ejpam-3253	147	2	2,∞	2,∞	NUM
ejpam-3253	147	3	)	)	PUNCT
ejpam-3253	147	4	−→	−→	NOUN
ejpam-3253	147	5	f([2,∞	f([2,∞	PROPN
ejpam-3253	147	6	)	)	PUNCT
ejpam-3253	147	7	)	)	PUNCT
ejpam-3253	148	1	⊂	⊂	PROPN
ejpam-3253	149	1	y	y	PROPN
ejpam-3253	149	2	is	be	AUX
ejpam-3253	149	3	a	a	DET
ejpam-3253	149	4	homeomorphism	homeomorphism	NOUN
ejpam-3253	149	5	.	.	PUNCT
ejpam-3253	150	1	i.e.	i.e.	X
ejpam-3253	150	2	f([2,∞	f([2,∞	NOUN
ejpam-3253	150	3	)	)	PUNCT
ejpam-3253	150	4	)	)	PUNCT
ejpam-3253	151	1	as	as	ADP
ejpam-3253	151	2	a	a	DET
ejpam-3253	151	3	subspace	subspace	NOUN
ejpam-3253	151	4	of	of	ADP
ejpam-3253	151	5	(	(	PUNCT
ejpam-3253	151	6	r	r	NOUN
ejpam-3253	151	7	,	,	PUNCT
ejpam-3253	151	8	r	r	NOUN
ejpam-3253	151	9	)	)	PUNCT
ejpam-3253	151	10	is	be	AUX
ejpam-3253	151	11	regular	regular	ADJ
ejpam-3253	151	12	which	which	PRON
ejpam-3253	151	13	is	be	AUX
ejpam-3253	151	14	a	a	DET
ejpam-3253	151	15	contradiction	contradiction	NOUN
ejpam-3253	151	16	as	as	ADP
ejpam-3253	151	17	[	[	X
ejpam-3253	151	18	2	2	NUM
ejpam-3253	151	19	,	,	PUNCT
ejpam-3253	151	20	3	3	NUM
ejpam-3253	151	21	]	]	PUNCT
ejpam-3253	151	22	is	be	AUX
ejpam-3253	151	23	closed	close	VERB
ejpam-3253	151	24	in	in	ADP
ejpam-3253	151	25	[	[	NOUN
ejpam-3253	151	26	2,∞	2,∞	NUM
ejpam-3253	151	27	)	)	PUNCT
ejpam-3253	151	28	and	and	CCONJ
ejpam-3253	151	29	5	5	NUM
ejpam-3253	151	30	6∈	6∈	NOUN
ejpam-3253	152	1	[	[	X
ejpam-3253	152	2	2	2	NUM
ejpam-3253	152	3	,	,	PUNCT
ejpam-3253	152	4	3	3	NUM
ejpam-3253	152	5	]	]	PUNCT
ejpam-3253	152	6	and	and	CCONJ
ejpam-3253	152	7	any	any	DET
ejpam-3253	152	8	non	non	ADJ
ejpam-3253	152	9	-	-	ADJ
ejpam-3253	152	10	empty	empty	ADJ
ejpam-3253	152	11	open	open	ADJ
ejpam-3253	152	12	sets	set	NOUN
ejpam-3253	152	13	in	in	ADP
ejpam-3253	152	14	[	[	X
ejpam-3253	152	15	2,∞	2,∞	NUM
ejpam-3253	152	16	)	)	PUNCT
ejpam-3253	152	17	must	must	AUX
ejpam-3253	152	18	intersect	intersect	VERB
ejpam-3253	152	19	.	.	PUNCT
ejpam-3253	153	1	therefore	therefore	ADV
ejpam-3253	153	2	,	,	PUNCT
ejpam-3253	153	3	(	(	PUNCT
ejpam-3253	153	4	r	r	NOUN
ejpam-3253	153	5	,	,	PUNCT
ejpam-3253	153	6	r	r	NOUN
ejpam-3253	153	7	)	)	PUNCT
ejpam-3253	153	8	can	can	AUX
ejpam-3253	153	9	not	not	PART
ejpam-3253	153	10	be	be	AUX
ejpam-3253	153	11	c	c	NOUN
ejpam-3253	153	12	-	-	PUNCT
ejpam-3253	153	13	tychonoff	tychonoff	NOUN
ejpam-3253	153	14	.	.	PUNCT
ejpam-3253	154	1	here	here	ADV
ejpam-3253	154	2	is	be	AUX
ejpam-3253	154	3	an	an	DET
ejpam-3253	154	4	example	example	NOUN
ejpam-3253	154	5	of	of	ADP
ejpam-3253	154	6	a	a	DET
ejpam-3253	154	7	c	c	NOUN
ejpam-3253	154	8	-	-	PUNCT
ejpam-3253	154	9	tychonoff	tychonoff	NOUN
ejpam-3253	154	10	space	space	NOUN
ejpam-3253	154	11	which	which	PRON
ejpam-3253	154	12	is	be	AUX
ejpam-3253	154	13	not	not	PART
ejpam-3253	154	14	c	c	NOUN
ejpam-3253	154	15	-	-	NOUN
ejpam-3253	154	16	normal	normal	ADJ
ejpam-3253	154	17	.	.	PUNCT
ejpam-3253	154	18	example	example	NOUN
ejpam-3253	155	1	4	4	NUM
ejpam-3253	155	2	.	.	X
ejpam-3253	155	3	consider	consider	VERB
ejpam-3253	155	4	the	the	DET
ejpam-3253	155	5	infinite	infinite	ADJ
ejpam-3253	155	6	tychonoff	tychonoff	NOUN
ejpam-3253	155	7	product	product	NOUN
ejpam-3253	155	8	space	space	NOUN
ejpam-3253	155	9	g	g	NOUN
ejpam-3253	155	10	=	=	PUNCT
ejpam-3253	155	11	dω1	dω1	PROPN
ejpam-3253	155	12	=	=	SYM
ejpam-3253	155	13	∏	∏	PROPN
ejpam-3253	155	14	α∈ω1	α∈ω1	NOUN
ejpam-3253	155	15	d	d	NOUN
ejpam-3253	155	16	,	,	PUNCT
ejpam-3253	155	17	where	where	SCONJ
ejpam-3253	155	18	d	d	NOUN
ejpam-3253	155	19	=	=	SYM
ejpam-3253	155	20	{	{	PUNCT
ejpam-3253	155	21	0	0	NUM
ejpam-3253	155	22	,	,	PUNCT
ejpam-3253	155	23	1	1	NUM
ejpam-3253	155	24	}	}	PUNCT
ejpam-3253	155	25	considered	consider	VERB
ejpam-3253	155	26	with	with	ADP
ejpam-3253	155	27	the	the	DET
ejpam-3253	155	28	discrete	discrete	ADJ
ejpam-3253	155	29	topology	topology	NOUN
ejpam-3253	155	30	.	.	PUNCT
ejpam-3253	156	1	let	let	VERB
ejpam-3253	156	2	h	h	NOUN
ejpam-3253	156	3	be	be	AUX
ejpam-3253	156	4	the	the	DET
ejpam-3253	156	5	subspace	subspace	NOUN
ejpam-3253	156	6	of	of	ADP
ejpam-3253	156	7	g	g	PROPN
ejpam-3253	156	8	consisting	consist	VERB
ejpam-3253	156	9	of	of	ADP
ejpam-3253	156	10	all	all	DET
ejpam-3253	156	11	points	point	NOUN
ejpam-3253	156	12	of	of	ADP
ejpam-3253	156	13	g	g	NOUN
ejpam-3253	156	14	with	with	ADP
ejpam-3253	156	15	at	at	ADP
ejpam-3253	156	16	most	most	ADV
ejpam-3253	156	17	countably	countably	ADV
ejpam-3253	156	18	many	many	ADJ
ejpam-3253	156	19	non	non	ADJ
ejpam-3253	156	20	-	-	ADJ
ejpam-3253	156	21	zero	zero	NUM
ejpam-3253	156	22	coordinates	coordinate	NOUN
ejpam-3253	156	23	.	.	PUNCT
ejpam-3253	157	1	put	put	VERB
ejpam-3253	157	2	m	m	PROPN
ejpam-3253	157	3	=	=	NOUN
ejpam-3253	157	4	g	g	PROPN
ejpam-3253	157	5	×h	×h	PROPN
ejpam-3253	157	6	.	.	PUNCT
ejpam-3253	158	1	raushan	raushan	PROPN
ejpam-3253	158	2	buzyakova	buzyakova	PROPN
ejpam-3253	158	3	proved	prove	VERB
ejpam-3253	158	4	thatm	thatm	NOUN
ejpam-3253	158	5	can	can	AUX
ejpam-3253	158	6	not	not	PART
ejpam-3253	158	7	be	be	AUX
ejpam-3253	158	8	mapped	map	VERB
ejpam-3253	158	9	onto	onto	ADP
ejpam-3253	158	10	a	a	DET
ejpam-3253	158	11	normal	normal	ADJ
ejpam-3253	158	12	space	space	NOUN
ejpam-3253	158	13	z	z	NOUN
ejpam-3253	158	14	by	by	ADP
ejpam-3253	158	15	a	a	DET
ejpam-3253	158	16	bijective	bijective	ADJ
ejpam-3253	158	17	continuous	continuous	ADJ
ejpam-3253	158	18	function	function	NOUN
ejpam-3253	159	1	[	[	X
ejpam-3253	159	2	7	7	NUM
ejpam-3253	159	3	]	]	PUNCT
ejpam-3253	159	4	.	.	PUNCT
ejpam-3253	160	1	using	use	VERB
ejpam-3253	160	2	buzyakova	buzyakova	PROPN
ejpam-3253	160	3	’s	’s	PART
ejpam-3253	160	4	result	result	NOUN
ejpam-3253	160	5	and	and	CCONJ
ejpam-3253	160	6	the	the	DET
ejpam-3253	160	7	fact	fact	NOUN
ejpam-3253	160	8	that	that	SCONJ
ejpam-3253	160	9	m	m	NOUN
ejpam-3253	160	10	is	be	AUX
ejpam-3253	160	11	a	a	DET
ejpam-3253	160	12	k	k	NOUN
ejpam-3253	160	13	-	-	NOUN
ejpam-3253	160	14	space	space	NOUN
ejpam-3253	160	15	,	,	PUNCT
ejpam-3253	160	16	we	we	PRON
ejpam-3253	160	17	conclude	conclude	VERB
ejpam-3253	160	18	that	that	SCONJ
ejpam-3253	160	19	m	m	VERB
ejpam-3253	160	20	is	be	AUX
ejpam-3253	160	21	a	a	DET
ejpam-3253	160	22	tychonoff	tychonoff	NOUN
ejpam-3253	160	23	space	space	NOUN
ejpam-3253	160	24	which	which	PRON
ejpam-3253	160	25	is	be	AUX
ejpam-3253	160	26	not	not	PART
ejpam-3253	160	27	c	c	NOUN
ejpam-3253	160	28	-	-	ADJ
ejpam-3253	160	29	normal	normal	ADJ
ejpam-3253	160	30	[	[	X
ejpam-3253	160	31	13	13	NUM
ejpam-3253	160	32	]	]	PUNCT
ejpam-3253	160	33	.	.	PUNCT
ejpam-3253	161	1	since	since	SCONJ
ejpam-3253	161	2	m	m	PROPN
ejpam-3253	161	3	is	be	AUX
ejpam-3253	161	4	tychonoff	tychonoff	NOUN
ejpam-3253	161	5	,	,	PUNCT
ejpam-3253	161	6	then	then	ADV
ejpam-3253	161	7	it	it	PRON
ejpam-3253	161	8	is	be	AUX
ejpam-3253	161	9	c	c	NOUN
ejpam-3253	161	10	-	-	PUNCT
ejpam-3253	161	11	tychonoff	tychonoff	NOUN
ejpam-3253	161	12	.	.	PUNCT
ejpam-3253	162	1	theorem	theorem	VERB
ejpam-3253	162	2	7	7	NUM
ejpam-3253	162	3	.	.	PUNCT
ejpam-3253	163	1	c	c	X
ejpam-3253	163	2	-	-	PUNCT
ejpam-3253	163	3	tychonoffness	tychonoffness	NOUN
ejpam-3253	163	4	is	be	AUX
ejpam-3253	163	5	a	a	DET
ejpam-3253	163	6	topological	topological	ADJ
ejpam-3253	163	7	property	property	NOUN
ejpam-3253	163	8	.	.	PUNCT
ejpam-3253	164	1	proof	proof	NOUN
ejpam-3253	164	2	.	.	PUNCT
ejpam-3253	165	1	let	let	VERB
ejpam-3253	165	2	x	x	PRON
ejpam-3253	165	3	be	be	AUX
ejpam-3253	165	4	a	a	DET
ejpam-3253	165	5	c	c	NOUN
ejpam-3253	165	6	-	-	PUNCT
ejpam-3253	165	7	tychonoff	tychonoff	NOUN
ejpam-3253	165	8	space	space	NOUN
ejpam-3253	165	9	and	and	CCONJ
ejpam-3253	165	10	x	x	PUNCT
ejpam-3253	165	11	∼=	∼=	NOUN
ejpam-3253	165	12	y	y	NOUN
ejpam-3253	165	13	.	.	PUNCT
ejpam-3253	166	1	let	let	VERB
ejpam-3253	166	2	z	z	PRON
ejpam-3253	166	3	be	be	AUX
ejpam-3253	166	4	a	a	DET
ejpam-3253	166	5	tychonoff	tychonoff	NOUN
ejpam-3253	166	6	space	space	NOUN
ejpam-3253	166	7	and	and	CCONJ
ejpam-3253	166	8	let	let	VERB
ejpam-3253	166	9	f	f	NOUN
ejpam-3253	166	10	:	:	PUNCT
ejpam-3253	166	11	x	x	PUNCT
ejpam-3253	166	12	−→	−→	NOUN
ejpam-3253	166	13	z	z	NOUN
ejpam-3253	166	14	be	be	AUX
ejpam-3253	166	15	a	a	DET
ejpam-3253	166	16	bijective	bijective	ADJ
ejpam-3253	166	17	function	function	NOUN
ejpam-3253	166	18	such	such	ADJ
ejpam-3253	166	19	that	that	SCONJ
ejpam-3253	166	20	the	the	DET
ejpam-3253	166	21	restriction	restriction	NOUN
ejpam-3253	166	22	f|k	f|k	PUNCT
ejpam-3253	167	1	:	:	PUNCT
ejpam-3253	167	2	k	k	X
ejpam-3253	167	3	−→	−→	NOUN
ejpam-3253	167	4	f(k	f(k	VERB
ejpam-3253	167	5	)	)	PUNCT
ejpam-3253	167	6	is	be	AUX
ejpam-3253	167	7	a	a	DET
ejpam-3253	167	8	homeomorphism	homeomorphism	NOUN
ejpam-3253	167	9	for	for	ADP
ejpam-3253	167	10	each	each	DET
ejpam-3253	167	11	compact	compact	ADJ
ejpam-3253	167	12	subspace	subspace	NOUN
ejpam-3253	167	13	k	k	PROPN
ejpam-3253	167	14	⊆	⊆	NUM
ejpam-3253	167	15	x.	x.	NOUN
ejpam-3253	167	16	let	let	VERB
ejpam-3253	167	17	h	h	NOUN
ejpam-3253	167	18	:	:	PUNCT
ejpam-3253	167	19	y	y	PROPN
ejpam-3253	167	20	−→	−→	NOUN
ejpam-3253	167	21	x	x	VERB
ejpam-3253	167	22	be	be	AUX
ejpam-3253	167	23	a	a	DET
ejpam-3253	167	24	homeomorphism	homeomorphism	NOUN
ejpam-3253	167	25	.	.	PUNCT
ejpam-3253	168	1	then	then	ADV
ejpam-3253	168	2	z	z	PROPN
ejpam-3253	168	3	and	and	CCONJ
ejpam-3253	168	4	f	f	PROPN
ejpam-3253	168	5	◦	◦	NOUN
ejpam-3253	168	6	h	h	NOUN
ejpam-3253	168	7	:	:	PUNCT
ejpam-3253	168	8	y	y	PROPN
ejpam-3253	168	9	−→	−→	NOUN
ejpam-3253	168	10	z	z	NOUN
ejpam-3253	168	11	satisfies	satisfy	VERB
ejpam-3253	168	12	the	the	DET
ejpam-3253	168	13	requirement	requirement	NOUN
ejpam-3253	168	14	.	.	PUNCT
ejpam-3253	169	1	theorem	theorem	ADJ
ejpam-3253	169	2	8	8	NUM
ejpam-3253	169	3	.	.	PUNCT
ejpam-3253	170	1	c	c	X
ejpam-3253	170	2	-	-	PUNCT
ejpam-3253	170	3	tychonoffness	tychonoffness	NOUN
ejpam-3253	170	4	is	be	AUX
ejpam-3253	170	5	an	an	DET
ejpam-3253	170	6	additive	additive	ADJ
ejpam-3253	170	7	property	property	NOUN
ejpam-3253	170	8	.	.	PUNCT
ejpam-3253	171	1	s.	s.	PROPN
ejpam-3253	171	2	alzahrani	alzahrani	PROPN
ejpam-3253	171	3	/	/	SYM
ejpam-3253	171	4	eur	eur	PROPN
ejpam-3253	171	5	.	.	PUNCT
ejpam-3253	172	1	j.	j.	PROPN
ejpam-3253	172	2	pure	pure	PROPN
ejpam-3253	172	3	appl	appl	PROPN
ejpam-3253	172	4	.	.	PROPN
ejpam-3253	172	5	math	math	PROPN
ejpam-3253	172	6	,	,	PUNCT
ejpam-3253	172	7	11	11	NUM
ejpam-3253	172	8	(	(	PUNCT
ejpam-3253	172	9	3	3	NUM
ejpam-3253	172	10	)	)	PUNCT
ejpam-3253	172	11	(	(	PUNCT
ejpam-3253	172	12	2018	2018	NUM
ejpam-3253	172	13	)	)	PUNCT
ejpam-3253	172	14	,	,	PUNCT
ejpam-3253	172	15	882	882	NUM
ejpam-3253	172	16	-	-	SYM
ejpam-3253	172	17	892	892	NUM
ejpam-3253	172	18	887	887	NUM
ejpam-3253	172	19	proof	proof	NOUN
ejpam-3253	172	20	.	.	PUNCT
ejpam-3253	173	1	let	let	VERB
ejpam-3253	173	2	xs	xs	PROPN
ejpam-3253	173	3	be	be	AUX
ejpam-3253	173	4	a	a	DET
ejpam-3253	173	5	c	c	NOUN
ejpam-3253	173	6	-	-	PUNCT
ejpam-3253	173	7	tychonoff	tychonoff	NOUN
ejpam-3253	173	8	space	space	NOUN
ejpam-3253	173	9	for	for	ADP
ejpam-3253	173	10	each	each	DET
ejpam-3253	173	11	s	s	PART
ejpam-3253	173	12	∈	∈	PROPN
ejpam-3253	173	13	s.	s.	PROPN
ejpam-3253	173	14	we	we	PRON
ejpam-3253	173	15	prove	prove	VERB
ejpam-3253	173	16	that	that	SCONJ
ejpam-3253	173	17	their	their	PRON
ejpam-3253	173	18	sum	sum	NOUN
ejpam-3253	173	19	⊕s∈sxs	⊕s∈sxs	PROPN
ejpam-3253	173	20	is	be	AUX
ejpam-3253	173	21	c	c	NOUN
ejpam-3253	173	22	-	-	PUNCT
ejpam-3253	173	23	tychonoff	tychonoff	NOUN
ejpam-3253	173	24	.	.	PUNCT
ejpam-3253	174	1	for	for	ADP
ejpam-3253	174	2	each	each	DET
ejpam-3253	174	3	s	s	X
ejpam-3253	174	4	∈	∈	PROPN
ejpam-3253	174	5	s	s	NOUN
ejpam-3253	174	6	,	,	PUNCT
ejpam-3253	174	7	pick	pick	VERB
ejpam-3253	174	8	a	a	DET
ejpam-3253	174	9	tychonoff	tychonoff	NOUN
ejpam-3253	174	10	space	space	NOUN
ejpam-3253	174	11	ys	ys	NOUN
ejpam-3253	174	12	and	and	CCONJ
ejpam-3253	174	13	a	a	DET
ejpam-3253	174	14	bijective	bijective	ADJ
ejpam-3253	174	15	function	function	NOUN
ejpam-3253	174	16	fs	fs	INTJ
ejpam-3253	174	17	:	:	PUNCT
ejpam-3253	174	18	xs	xs	PROPN
ejpam-3253	174	19	−→	−→	PROPN
ejpam-3253	174	20	ys	ys	INTJ
ejpam-3253	174	21	such	such	ADJ
ejpam-3253	174	22	that	that	PRON
ejpam-3253	175	1	fs|ks	fs|ks	PROPN
ejpam-3253	175	2	:	:	PUNCT
ejpam-3253	175	3	ks	ks	PROPN
ejpam-3253	175	4	−→	−→	PROPN
ejpam-3253	175	5	fs(ks	fs(ks	PROPN
ejpam-3253	175	6	)	)	PUNCT
ejpam-3253	175	7	is	be	AUX
ejpam-3253	175	8	a	a	DET
ejpam-3253	175	9	homeomorphism	homeomorphism	NOUN
ejpam-3253	175	10	for	for	ADP
ejpam-3253	175	11	each	each	DET
ejpam-3253	175	12	compact	compact	ADJ
ejpam-3253	175	13	subspace	subspace	NOUN
ejpam-3253	175	14	ks	ks	PROPN
ejpam-3253	175	15	of	of	ADP
ejpam-3253	175	16	xs	xs	PROPN
ejpam-3253	175	17	.	.	PUNCT
ejpam-3253	176	1	because	because	SCONJ
ejpam-3253	176	2	ys	ys	PROPN
ejpam-3253	176	3	is	be	AUX
ejpam-3253	176	4	tychonoff	tychonoff	NOUN
ejpam-3253	176	5	for	for	ADP
ejpam-3253	176	6	each	each	DET
ejpam-3253	176	7	s	s	X
ejpam-3253	176	8	∈	∈	PROPN
ejpam-3253	176	9	s	s	NOUN
ejpam-3253	176	10	,	,	PUNCT
ejpam-3253	176	11	then	then	ADV
ejpam-3253	176	12	the	the	DET
ejpam-3253	176	13	sum	sum	NOUN
ejpam-3253	176	14	⊕s∈sys	⊕s∈sys	PROPN
ejpam-3253	176	15	is	be	AUX
ejpam-3253	176	16	tychonoff	tychonoff	NOUN
ejpam-3253	176	17	,	,	PUNCT
ejpam-3253	176	18	[	[	X
ejpam-3253	176	19	8	8	NUM
ejpam-3253	176	20	,	,	PUNCT
ejpam-3253	176	21	2.2.7	2.2.7	NUM
ejpam-3253	176	22	]	]	PUNCT
ejpam-3253	176	23	.	.	PUNCT
ejpam-3253	177	1	consider	consider	VERB
ejpam-3253	177	2	the	the	DET
ejpam-3253	177	3	function	function	NOUN
ejpam-3253	177	4	sum	sum	NOUN
ejpam-3253	178	1	[	[	X
ejpam-3253	178	2	8	8	NUM
ejpam-3253	178	3	,	,	PUNCT
ejpam-3253	178	4	2.2.e	2.2.e	NUM
ejpam-3253	178	5	]	]	X
ejpam-3253	178	6	f	f	X
ejpam-3253	178	7	=	=	PUNCT
ejpam-3253	178	8	⊕s∈sfs	⊕s∈sfs	PROPN
ejpam-3253	178	9	:	:	PUNCT
ejpam-3253	178	10	⊕s∈sxs	⊕s∈sxs	VERB
ejpam-3253	178	11	−→	−→	ADJ
ejpam-3253	178	12	⊕s∈sys	⊕s∈sy	NOUN
ejpam-3253	178	13	defined	define	VERB
ejpam-3253	178	14	by	by	ADP
ejpam-3253	178	15	f(x	f(x	PROPN
ejpam-3253	178	16	)	)	PUNCT
ejpam-3253	178	17	=	=	SYM
ejpam-3253	178	18	fs(x	fs(x	NOUN
ejpam-3253	178	19	)	)	PUNCT
ejpam-3253	178	20	if	if	SCONJ
ejpam-3253	178	21	x	x	PROPN
ejpam-3253	178	22	∈	∈	PROPN
ejpam-3253	178	23	xs	xs	PROPN
ejpam-3253	178	24	,	,	PUNCT
ejpam-3253	178	25	s	s	PROPN
ejpam-3253	178	26	∈	∈	PROPN
ejpam-3253	178	27	s.	s.	PROPN
ejpam-3253	178	28	a	a	DET
ejpam-3253	178	29	subspace	subspace	NOUN
ejpam-3253	178	30	k	k	PROPN
ejpam-3253	178	31	⊆	⊆	NUM
ejpam-3253	178	32	⊕α∈λxα	⊕α∈λxα	NOUN
ejpam-3253	178	33	is	be	AUX
ejpam-3253	178	34	compact	compact	ADJ
ejpam-3253	178	35	if	if	SCONJ
ejpam-3253	179	1	and	and	CCONJ
ejpam-3253	179	2	only	only	ADV
ejpam-3253	179	3	if	if	SCONJ
ejpam-3253	179	4	the	the	DET
ejpam-3253	179	5	set	set	NOUN
ejpam-3253	179	6	s0	s0	NOUN
ejpam-3253	179	7	=	=	PUNCT
ejpam-3253	179	8	{	{	PUNCT
ejpam-3253	179	9	s	s	NOUN
ejpam-3253	179	10	∈	∈	NOUN
ejpam-3253	179	11	s	s	PART
ejpam-3253	179	12	:	:	PUNCT
ejpam-3253	179	13	k	k	PROPN
ejpam-3253	179	14	∩	∩	PROPN
ejpam-3253	179	15	xs	xs	PROPN
ejpam-3253	179	16	6=	6=	PROPN
ejpam-3253	179	17	∅	∅	NOUN
ejpam-3253	179	18	}	}	PUNCT
ejpam-3253	179	19	is	be	AUX
ejpam-3253	179	20	finite	finite	ADJ
ejpam-3253	179	21	and	and	CCONJ
ejpam-3253	179	22	k	k	PROPN
ejpam-3253	179	23	∩	∩	PROPN
ejpam-3253	179	24	xs	xs	PROPN
ejpam-3253	179	25	is	be	AUX
ejpam-3253	179	26	compact	compact	ADJ
ejpam-3253	179	27	in	in	ADP
ejpam-3253	179	28	xs	xs	PROPN
ejpam-3253	179	29	for	for	ADP
ejpam-3253	179	30	each	each	DET
ejpam-3253	179	31	s	s	PROPN
ejpam-3253	179	32	∈	∈	PROPN
ejpam-3253	179	33	s0	s0	NOUN
ejpam-3253	179	34	.	.	PUNCT
ejpam-3253	180	1	if	if	SCONJ
ejpam-3253	180	2	k	k	PROPN
ejpam-3253	180	3	⊆	⊆	NUM
ejpam-3253	180	4	⊕s∈sxs	⊕s∈sxs	PROPN
ejpam-3253	180	5	is	be	AUX
ejpam-3253	180	6	compact	compact	ADJ
ejpam-3253	180	7	.	.	PUNCT
ejpam-3253	181	1	then	then	ADV
ejpam-3253	181	2	(	(	PUNCT
ejpam-3253	181	3	⊕s∈sfs)|k	⊕s∈sfs)|k	NOUN
ejpam-3253	181	4	is	be	AUX
ejpam-3253	181	5	a	a	DET
ejpam-3253	181	6	homeomorphism	homeomorphism	NOUN
ejpam-3253	181	7	since	since	SCONJ
ejpam-3253	181	8	fs|k∩xs	fs|k∩xs	NOUN
ejpam-3253	181	9	is	be	AUX
ejpam-3253	181	10	a	a	DET
ejpam-3253	181	11	homeomorphism	homeomorphism	NOUN
ejpam-3253	181	12	for	for	ADP
ejpam-3253	181	13	each	each	DET
ejpam-3253	181	14	s	s	PROPN
ejpam-3253	181	15	∈	∈	PROPN
ejpam-3253	181	16	s0	s0	PROPN
ejpam-3253	181	17	.	.	PUNCT
ejpam-3253	182	1	theorem	theorem	VERB
ejpam-3253	182	2	9	9	NUM
ejpam-3253	182	3	.	.	X
ejpam-3253	183	1	c	c	X
ejpam-3253	183	2	-	-	PUNCT
ejpam-3253	183	3	tychonoffness	tychonoffness	NOUN
ejpam-3253	183	4	is	be	AUX
ejpam-3253	183	5	a	a	DET
ejpam-3253	183	6	multiplicative	multiplicative	ADJ
ejpam-3253	183	7	property	property	NOUN
ejpam-3253	183	8	.	.	PUNCT
ejpam-3253	184	1	proof	proof	NOUN
ejpam-3253	184	2	.	.	PUNCT
ejpam-3253	185	1	let	let	VERB
ejpam-3253	185	2	xs	xs	PROPN
ejpam-3253	185	3	be	be	AUX
ejpam-3253	185	4	a	a	DET
ejpam-3253	185	5	c	c	NOUN
ejpam-3253	185	6	-	-	PUNCT
ejpam-3253	185	7	tychonoff	tychonoff	NOUN
ejpam-3253	185	8	space	space	NOUN
ejpam-3253	185	9	for	for	ADP
ejpam-3253	185	10	each	each	DET
ejpam-3253	185	11	s	s	PROPN
ejpam-3253	186	1	∈	∈	PROPN
ejpam-3253	186	2	s.	s.	PROPN
ejpam-3253	186	3	pick	pick	VERB
ejpam-3253	186	4	a	a	DET
ejpam-3253	186	5	tychonoff	tychonoff	NOUN
ejpam-3253	186	6	space	space	NOUN
ejpam-3253	186	7	ys	ys	NOUN
ejpam-3253	186	8	and	and	CCONJ
ejpam-3253	186	9	a	a	DET
ejpam-3253	186	10	bijective	bijective	ADJ
ejpam-3253	186	11	function	function	NOUN
ejpam-3253	186	12	fs	fs	INTJ
ejpam-3253	186	13	:	:	PUNCT
ejpam-3253	186	14	xs	xs	PROPN
ejpam-3253	186	15	−→	−→	PROPN
ejpam-3253	186	16	ys	ys	INTJ
ejpam-3253	186	17	such	such	ADJ
ejpam-3253	186	18	that	that	PRON
ejpam-3253	186	19	fs|ks	fs|ks	PROPN
ejpam-3253	186	20	:	:	PUNCT
ejpam-3253	186	21	ks	ks	PROPN
ejpam-3253	186	22	−→	−→	PROPN
ejpam-3253	186	23	fs(ks	fs(ks	PROPN
ejpam-3253	186	24	)	)	PUNCT
ejpam-3253	186	25	is	be	AUX
ejpam-3253	186	26	a	a	DET
ejpam-3253	186	27	homeomorphism	homeomorphism	NOUN
ejpam-3253	186	28	for	for	ADP
ejpam-3253	186	29	each	each	DET
ejpam-3253	186	30	compact	compact	ADJ
ejpam-3253	186	31	subspace	subspace	NOUN
ejpam-3253	186	32	ks	ks	PROPN
ejpam-3253	186	33	of	of	ADP
ejpam-3253	186	34	xs	xs	PROPN
ejpam-3253	186	35	.	.	PUNCT
ejpam-3253	187	1	since	since	SCONJ
ejpam-3253	187	2	ys	ys	PROPN
ejpam-3253	187	3	is	be	AUX
ejpam-3253	187	4	tychonoff	tychonoff	NOUN
ejpam-3253	187	5	for	for	ADP
ejpam-3253	187	6	each	each	DET
ejpam-3253	187	7	s	s	X
ejpam-3253	187	8	∈	∈	PROPN
ejpam-3253	187	9	s	s	NOUN
ejpam-3253	187	10	,	,	PUNCT
ejpam-3253	187	11	then	then	ADV
ejpam-3253	187	12	the	the	DET
ejpam-3253	187	13	cartesian	cartesian	ADJ
ejpam-3253	187	14	product	product	NOUN
ejpam-3253	187	15	∏	∏	PROPN
ejpam-3253	187	16	s∈s	s∈s	NOUN
ejpam-3253	187	17	ys	ys	NOUN
ejpam-3253	187	18	is	be	AUX
ejpam-3253	187	19	tychonoff	tychonoff	NOUN
ejpam-3253	187	20	[	[	X
ejpam-3253	187	21	8	8	NUM
ejpam-3253	187	22	,	,	PUNCT
ejpam-3253	187	23	2.3.11	2.3.11	NUM
ejpam-3253	187	24	]	]	PUNCT
ejpam-3253	187	25	.	.	PUNCT
ejpam-3253	188	1	define	define	VERB
ejpam-3253	188	2	f	f	PROPN
ejpam-3253	188	3	:	:	PUNCT
ejpam-3253	188	4	∏	∏	NUM
ejpam-3253	188	5	s∈s	s∈s	NOUN
ejpam-3253	189	1	xs	xs	PROPN
ejpam-3253	190	1	−→	−→	PROPN
ejpam-3253	190	2	∏	∏	PROPN
ejpam-3253	190	3	s∈s	s∈s	NOUN
ejpam-3253	190	4	ys	ys	NOUN
ejpam-3253	190	5	by	by	ADP
ejpam-3253	190	6	f((xs	f((xs	PROPN
ejpam-3253	190	7	:	:	PUNCT
ejpam-3253	190	8	s	s	VERB
ejpam-3253	190	9	∈	∈	PROPN
ejpam-3253	190	10	s	s	NOUN
ejpam-3253	190	11	)	)	PUNCT
ejpam-3253	190	12	)	)	PUNCT
ejpam-3253	191	1	=	=	SYM
ejpam-3253	191	2	(	(	PUNCT
ejpam-3253	191	3	fs(xs	fs(x	NOUN
ejpam-3253	191	4	)	)	PUNCT
ejpam-3253	191	5	:	:	PUNCT
ejpam-3253	191	6	s	s	VERB
ejpam-3253	191	7	∈	∈	PROPN
ejpam-3253	191	8	s	s	PART
ejpam-3253	191	9	)	)	PUNCT
ejpam-3253	191	10	for	for	ADP
ejpam-3253	191	11	each	each	DET
ejpam-3253	191	12	s	s	X
ejpam-3253	191	13	∈	∈	PROPN
ejpam-3253	191	14	s	s	NOUN
ejpam-3253	191	15	,	,	PUNCT
ejpam-3253	191	16	then	then	ADV
ejpam-3253	191	17	f	f	PROPN
ejpam-3253	191	18	is	be	AUX
ejpam-3253	191	19	bijective	bijective	ADJ
ejpam-3253	191	20	.	.	PUNCT
ejpam-3253	192	1	let	let	VERB
ejpam-3253	192	2	k	k	PROPN
ejpam-3253	192	3	⊆∏	⊆∏	PROPN
ejpam-3253	192	4	s∈s	s∈s	NOUN
ejpam-3253	192	5	xs	xs	PROPN
ejpam-3253	192	6	be	be	AUX
ejpam-3253	192	7	any	any	DET
ejpam-3253	192	8	compact	compact	ADJ
ejpam-3253	192	9	subspace	subspace	NOUN
ejpam-3253	192	10	and	and	CCONJ
ejpam-3253	192	11	let	let	VERB
ejpam-3253	192	12	ps	ps	PART
ejpam-3253	192	13	be	be	AUX
ejpam-3253	192	14	the	the	DET
ejpam-3253	192	15	usual	usual	ADJ
ejpam-3253	192	16	projection	projection	NOUN
ejpam-3253	192	17	,	,	PUNCT
ejpam-3253	192	18	then	then	ADV
ejpam-3253	192	19	ps(k	ps(k	PUNCT
ejpam-3253	192	20	)	)	PUNCT
ejpam-3253	192	21	⊆	⊆	NUM
ejpam-3253	192	22	xs	xs	NOUN
ejpam-3253	192	23	is	be	AUX
ejpam-3253	192	24	compact	compact	ADJ
ejpam-3253	192	25	.	.	PUNCT
ejpam-3253	193	1	now	now	ADV
ejpam-3253	193	2	,	,	PUNCT
ejpam-3253	193	3	k	k	PROPN
ejpam-3253	193	4	⊆	⊆	NUM
ejpam-3253	193	5	∏	∏	PROPN
ejpam-3253	193	6	s∈s	s∈s	NOUN
ejpam-3253	193	7	ps(k	ps(k	PUNCT
ejpam-3253	193	8	)	)	PUNCT
ejpam-3253	193	9	=	=	SYM
ejpam-3253	194	1	k	k	X
ejpam-3253	194	2	?	?	PROPN
ejpam-3253	194	3	is	be	AUX
ejpam-3253	194	4	compact	compact	ADJ
ejpam-3253	194	5	,	,	PUNCT
ejpam-3253	194	6	by	by	ADP
ejpam-3253	194	7	the	the	DET
ejpam-3253	194	8	tychonoff	tychonoff	NOUN
ejpam-3253	194	9	theorem	theorem	VERB
ejpam-3253	194	10	.	.	PUNCT
ejpam-3253	195	1	hence	hence	ADV
ejpam-3253	195	2	f|k	f|k	PUNCT
ejpam-3253	195	3	?	?	PUNCT
ejpam-3253	196	1	=	=	SYM
ejpam-3253	196	2	∏	∏	PROPN
ejpam-3253	196	3	s∈s	s∈s	NOUN
ejpam-3253	196	4	fs	fs	X
ejpam-3253	196	5	|ps(k	|ps(k	NOUN
ejpam-3253	196	6	)	)	PUNCT
ejpam-3253	196	7	is	be	AUX
ejpam-3253	196	8	a	a	DET
ejpam-3253	196	9	homeomorphism	homeomorphism	NOUN
ejpam-3253	196	10	.	.	PUNCT
ejpam-3253	197	1	thus	thus	ADV
ejpam-3253	197	2	f|k	f|k	PRON
ejpam-3253	197	3	is	be	AUX
ejpam-3253	197	4	a	a	DET
ejpam-3253	197	5	homeomorphism	homeomorphism	NOUN
ejpam-3253	197	6	,	,	PUNCT
ejpam-3253	197	7	because	because	SCONJ
ejpam-3253	197	8	the	the	DET
ejpam-3253	197	9	restriction	restriction	NOUN
ejpam-3253	197	10	of	of	ADP
ejpam-3253	197	11	a	a	DET
ejpam-3253	197	12	homeomorphism	homeomorphism	NOUN
ejpam-3253	197	13	is	be	AUX
ejpam-3253	197	14	a	a	DET
ejpam-3253	197	15	homeomorphism	homeomorphism	NOUN
ejpam-3253	197	16	.	.	PUNCT
ejpam-3253	198	1	theorem	theorem	ADJ
ejpam-3253	198	2	10	10	NUM
ejpam-3253	198	3	.	.	PUNCT
ejpam-3253	199	1	c	c	X
ejpam-3253	199	2	-	-	PUNCT
ejpam-3253	199	3	tychonoffness	tychonoffness	NOUN
ejpam-3253	199	4	is	be	AUX
ejpam-3253	199	5	a	a	DET
ejpam-3253	199	6	hereditary	hereditary	ADJ
ejpam-3253	199	7	property	property	NOUN
ejpam-3253	199	8	.	.	PUNCT
ejpam-3253	200	1	proof	proof	NOUN
ejpam-3253	200	2	.	.	PUNCT
ejpam-3253	201	1	let	let	VERB
ejpam-3253	201	2	a	a	DET
ejpam-3253	201	3	be	be	AUX
ejpam-3253	201	4	any	any	DET
ejpam-3253	201	5	non	non	ADJ
ejpam-3253	201	6	empty	empty	ADJ
ejpam-3253	201	7	subspace	subspace	NOUN
ejpam-3253	201	8	of	of	ADP
ejpam-3253	201	9	c	c	NOUN
ejpam-3253	201	10	-	-	PUNCT
ejpam-3253	201	11	tychonoff	tychonoff	NOUN
ejpam-3253	201	12	space	space	NOUN
ejpam-3253	201	13	x.	x.	NOUN
ejpam-3253	201	14	pick	pick	VERB
ejpam-3253	201	15	a	a	DET
ejpam-3253	201	16	bijective	bijective	ADJ
ejpam-3253	201	17	function	function	NOUN
ejpam-3253	201	18	f	f	NOUN
ejpam-3253	201	19	from	from	ADP
ejpam-3253	201	20	x	x	PRON
ejpam-3253	201	21	onto	onto	ADP
ejpam-3253	201	22	a	a	DET
ejpam-3253	201	23	tychonoff	tychonoff	NOUN
ejpam-3253	201	24	space	space	NOUN
ejpam-3253	201	25	y	y	PRON
ejpam-3253	201	26	such	such	ADJ
ejpam-3253	201	27	that	that	SCONJ
ejpam-3253	202	1	f|k	f|k	PRON
ejpam-3253	202	2	:	:	PUNCT
ejpam-3253	202	3	k	k	X
ejpam-3253	202	4	−→	−→	NOUN
ejpam-3253	202	5	f(k	f(k	VERB
ejpam-3253	202	6	)	)	PUNCT
ejpam-3253	202	7	is	be	AUX
ejpam-3253	202	8	a	a	DET
ejpam-3253	202	9	homeomorphism	homeomorphism	NOUN
ejpam-3253	202	10	for	for	ADP
ejpam-3253	202	11	each	each	DET
ejpam-3253	202	12	compact	compact	ADJ
ejpam-3253	202	13	subspace	subspace	NOUN
ejpam-3253	202	14	k	k	PROPN
ejpam-3253	202	15	⊆	⊆	NUM
ejpam-3253	202	16	x.	x.	NOUN
ejpam-3253	202	17	let	let	VERB
ejpam-3253	202	18	b	b	NOUN
ejpam-3253	202	19	=	=	SYM
ejpam-3253	202	20	f(a	f(a	PROPN
ejpam-3253	202	21	)	)	PUNCT
ejpam-3253	202	22	⊆	⊆	NUM
ejpam-3253	202	23	y	y	NOUN
ejpam-3253	202	24	.	.	PUNCT
ejpam-3253	203	1	then	then	ADV
ejpam-3253	203	2	b	b	PROPN
ejpam-3253	203	3	is	be	AUX
ejpam-3253	203	4	tychonoff	tychonoff	NOUN
ejpam-3253	203	5	being	be	AUX
ejpam-3253	203	6	a	a	DET
ejpam-3253	203	7	subspace	subspace	NOUN
ejpam-3253	203	8	of	of	ADP
ejpam-3253	203	9	a	a	DET
ejpam-3253	203	10	tychonoff	tychonoff	NOUN
ejpam-3253	203	11	space	space	NOUN
ejpam-3253	203	12	y	y	PROPN
ejpam-3253	203	13	.	.	PUNCT
ejpam-3253	204	1	now	now	ADV
ejpam-3253	204	2	,	,	PUNCT
ejpam-3253	204	3	we	we	PRON
ejpam-3253	204	4	have	have	VERB
ejpam-3253	204	5	f|a	f|a	NOUN
ejpam-3253	204	6	:	:	PUNCT
ejpam-3253	204	7	a	a	DET
ejpam-3253	204	8	−→	−→	NOUN
ejpam-3253	204	9	b	b	NOUN
ejpam-3253	204	10	is	be	AUX
ejpam-3253	204	11	a	a	DET
ejpam-3253	204	12	bijective	bijective	ADJ
ejpam-3253	204	13	function	function	NOUN
ejpam-3253	204	14	.	.	PUNCT
ejpam-3253	205	1	since	since	SCONJ
ejpam-3253	205	2	any	any	DET
ejpam-3253	205	3	compact	compact	ADJ
ejpam-3253	205	4	subspace	subspace	NOUN
ejpam-3253	205	5	of	of	ADP
ejpam-3253	205	6	a	a	PRON
ejpam-3253	205	7	is	be	AUX
ejpam-3253	205	8	compact	compact	ADJ
ejpam-3253	205	9	in	in	ADP
ejpam-3253	205	10	x	x	PUNCT
ejpam-3253	205	11	and	and	CCONJ
ejpam-3253	205	12	f|a	f|a	X
ejpam-3253	205	13	|k	|k	X
ejpam-3253	206	1	=	=	PUNCT
ejpam-3253	206	2	f|k	f|k	NOUN
ejpam-3253	206	3	,	,	PUNCT
ejpam-3253	206	4	we	we	PRON
ejpam-3253	206	5	conclude	conclude	VERB
ejpam-3253	206	6	that	that	SCONJ
ejpam-3253	206	7	a	a	PRON
ejpam-3253	206	8	is	be	AUX
ejpam-3253	206	9	c	c	NOUN
ejpam-3253	206	10	-	-	PUNCT
ejpam-3253	206	11	tychonoff	tychonoff	NOUN
ejpam-3253	206	12	.	.	PUNCT
ejpam-3253	207	1	frome	frome	PROPN
ejpam-3253	207	2	theorem	theorem	VERB
ejpam-3253	207	3	9	9	NUM
ejpam-3253	207	4	and	and	CCONJ
ejpam-3253	207	5	theorem	theorem	VERB
ejpam-3253	207	6	10	10	NUM
ejpam-3253	207	7	,	,	PUNCT
ejpam-3253	207	8	we	we	PRON
ejpam-3253	207	9	conclude	conclude	VERB
ejpam-3253	207	10	the	the	DET
ejpam-3253	207	11	following	follow	VERB
ejpam-3253	207	12	corollary	corollary	NOUN
ejpam-3253	207	13	.	.	PUNCT
ejpam-3253	208	1	corollary	corollary	ADJ
ejpam-3253	208	2	4	4	NUM
ejpam-3253	208	3	.	.	X
ejpam-3253	209	1	∏	∏	PROPN
ejpam-3253	209	2	s∈s	s∈s	NOUN
ejpam-3253	209	3	xs	xs	PROPN
ejpam-3253	209	4	is	be	AUX
ejpam-3253	209	5	c	c	NOUN
ejpam-3253	209	6	-	-	PUNCT
ejpam-3253	209	7	tychonoff	tychonoff	NOUN
ejpam-3253	209	8	if	if	SCONJ
ejpam-3253	210	1	and	and	CCONJ
ejpam-3253	210	2	only	only	ADV
ejpam-3253	210	3	if	if	SCONJ
ejpam-3253	210	4	xs	xs	PROPN
ejpam-3253	210	5	is	be	AUX
ejpam-3253	210	6	c	c	NOUN
ejpam-3253	210	7	-	-	PUNCT
ejpam-3253	210	8	tychonoff	tychonoff	NOUN
ejpam-3253	210	9	∀s	∀s	PROPN
ejpam-3253	210	10	∈	∈	PROPN
ejpam-3253	210	11	s.	s.	PROPN
ejpam-3253	210	12	3	3	NUM
ejpam-3253	210	13	.	.	PUNCT
ejpam-3253	211	1	l	l	NOUN
ejpam-3253	211	2	-	-	NOUN
ejpam-3253	211	3	tychonoffness	tychonoffness	NOUN
ejpam-3253	211	4	and	and	CCONJ
ejpam-3253	211	5	other	other	ADJ
ejpam-3253	211	6	properties	property	NOUN
ejpam-3253	211	7	we	we	PRON
ejpam-3253	211	8	introduce	introduce	VERB
ejpam-3253	211	9	another	another	DET
ejpam-3253	211	10	new	new	ADJ
ejpam-3253	211	11	topological	topological	ADJ
ejpam-3253	211	12	property	property	NOUN
ejpam-3253	211	13	called	call	VERB
ejpam-3253	211	14	l	l	NOUN
ejpam-3253	211	15	-	-	NOUN
ejpam-3253	211	16	tychonoff	tychonoff	NOUN
ejpam-3253	211	17	.	.	PUNCT
ejpam-3253	212	1	s.	s.	PROPN
ejpam-3253	212	2	alzahrani	alzahrani	PROPN
ejpam-3253	212	3	/	/	SYM
ejpam-3253	212	4	eur	eur	PROPN
ejpam-3253	212	5	.	.	PUNCT
ejpam-3253	213	1	j.	j.	PROPN
ejpam-3253	213	2	pure	pure	PROPN
ejpam-3253	213	3	appl	appl	PROPN
ejpam-3253	213	4	.	.	PROPN
ejpam-3253	213	5	math	math	PROPN
ejpam-3253	213	6	,	,	PUNCT
ejpam-3253	213	7	11	11	NUM
ejpam-3253	213	8	(	(	PUNCT
ejpam-3253	213	9	3	3	NUM
ejpam-3253	213	10	)	)	PUNCT
ejpam-3253	213	11	(	(	PUNCT
ejpam-3253	213	12	2018	2018	NUM
ejpam-3253	213	13	)	)	PUNCT
ejpam-3253	213	14	,	,	PUNCT
ejpam-3253	213	15	882	882	NUM
ejpam-3253	213	16	-	-	SYM
ejpam-3253	213	17	892	892	NUM
ejpam-3253	213	18	888	888	NUM
ejpam-3253	213	19	definition	definition	NOUN
ejpam-3253	213	20	2	2	NUM
ejpam-3253	213	21	.	.	PUNCT
ejpam-3253	214	1	a	a	DET
ejpam-3253	214	2	topological	topological	ADJ
ejpam-3253	214	3	space	space	NOUN
ejpam-3253	214	4	x	x	PUNCT
ejpam-3253	214	5	is	be	AUX
ejpam-3253	214	6	called	call	VERB
ejpam-3253	214	7	l	l	NOUN
ejpam-3253	214	8	-	-	NOUN
ejpam-3253	214	9	tychonoff	tychonoff	NOUN
ejpam-3253	214	10	if	if	SCONJ
ejpam-3253	214	11	there	there	PRON
ejpam-3253	214	12	exist	exist	VERB
ejpam-3253	214	13	a	a	DET
ejpam-3253	214	14	one	one	NUM
ejpam-3253	214	15	-	-	PUNCT
ejpam-3253	214	16	to	to	ADP
ejpam-3253	214	17	-	-	PUNCT
ejpam-3253	214	18	one	one	NUM
ejpam-3253	214	19	function	function	NOUN
ejpam-3253	214	20	f	f	NOUN
ejpam-3253	214	21	from	from	ADP
ejpam-3253	214	22	x	x	PRON
ejpam-3253	214	23	onto	onto	ADP
ejpam-3253	214	24	a	a	DET
ejpam-3253	214	25	tychonoff	tychonoff	NOUN
ejpam-3253	214	26	space	space	NOUN
ejpam-3253	214	27	y	y	PRON
ejpam-3253	214	28	such	such	ADJ
ejpam-3253	214	29	that	that	SCONJ
ejpam-3253	214	30	the	the	DET
ejpam-3253	214	31	restriction	restriction	NOUN
ejpam-3253	214	32	f|l	f|l	NOUN
ejpam-3253	215	1	:	:	PUNCT
ejpam-3253	215	2	l	l	PUNCT
ejpam-3253	215	3	−→	−→	NOUN
ejpam-3253	215	4	f(l	f(l	PROPN
ejpam-3253	215	5	)	)	PUNCT
ejpam-3253	215	6	is	be	AUX
ejpam-3253	215	7	a	a	DET
ejpam-3253	215	8	homeomorphism	homeomorphism	NOUN
ejpam-3253	215	9	for	for	ADP
ejpam-3253	215	10	each	each	DET
ejpam-3253	215	11	lindelöf	lindelöf	NOUN
ejpam-3253	215	12	subspace	subspace	NOUN
ejpam-3253	215	13	l	l	PROPN
ejpam-3253	215	14	⊆	⊆	NUM
ejpam-3253	215	15	x.	x.	NOUN
ejpam-3253	215	16	by	by	ADP
ejpam-3253	215	17	the	the	DET
ejpam-3253	215	18	definition	definition	NOUN
ejpam-3253	215	19	it	it	PRON
ejpam-3253	215	20	is	be	AUX
ejpam-3253	215	21	clear	clear	ADJ
ejpam-3253	215	22	that	that	SCONJ
ejpam-3253	215	23	a	a	DET
ejpam-3253	215	24	lindelöf	lindelöf	NOUN
ejpam-3253	215	25	l	l	NOUN
ejpam-3253	215	26	-	-	NOUN
ejpam-3253	215	27	tychonoff	tychonoff	NOUN
ejpam-3253	215	28	space	space	NOUN
ejpam-3253	215	29	must	must	AUX
ejpam-3253	215	30	be	be	AUX
ejpam-3253	215	31	tychonoff	tychonoff	NOUN
ejpam-3253	215	32	.	.	PUNCT
ejpam-3253	216	1	since	since	SCONJ
ejpam-3253	216	2	any	any	DET
ejpam-3253	216	3	compact	compact	ADJ
ejpam-3253	216	4	space	space	NOUN
ejpam-3253	216	5	is	be	AUX
ejpam-3253	216	6	lindelöf	lindelöf	NOUN
ejpam-3253	216	7	,	,	PUNCT
ejpam-3253	216	8	then	then	ADV
ejpam-3253	216	9	any	any	DET
ejpam-3253	216	10	l	l	NOUN
ejpam-3253	216	11	-	-	PUNCT
ejpam-3253	216	12	tychonoff	tychonoff	NOUN
ejpam-3253	216	13	space	space	NOUN
ejpam-3253	216	14	is	be	AUX
ejpam-3253	216	15	c	c	NOUN
ejpam-3253	216	16	-	-	PUNCT
ejpam-3253	216	17	tychonoff	tychonoff	NOUN
ejpam-3253	216	18	.	.	PUNCT
ejpam-3253	217	1	the	the	DET
ejpam-3253	217	2	converse	converse	NOUN
ejpam-3253	217	3	is	be	AUX
ejpam-3253	217	4	not	not	PART
ejpam-3253	217	5	true	true	ADJ
ejpam-3253	217	6	in	in	ADP
ejpam-3253	217	7	general	general	ADJ
ejpam-3253	217	8	.	.	PUNCT
ejpam-3253	218	1	obviously	obviously	ADV
ejpam-3253	218	2	,	,	PUNCT
ejpam-3253	218	3	no	no	DET
ejpam-3253	218	4	lindelöf	lindelöf	NOUN
ejpam-3253	218	5	non	non	ADJ
ejpam-3253	218	6	-	-	ADJ
ejpam-3253	218	7	tychonoff	tychonoff	ADJ
ejpam-3253	218	8	space	space	NOUN
ejpam-3253	218	9	is	be	AUX
ejpam-3253	218	10	l	l	NOUN
ejpam-3253	218	11	-	-	NOUN
ejpam-3253	218	12	tychonoff	tychonoff	NOUN
ejpam-3253	218	13	.	.	PUNCT
ejpam-3253	219	1	so	so	ADV
ejpam-3253	219	2	,	,	PUNCT
ejpam-3253	219	3	no	no	DET
ejpam-3253	219	4	countable	countable	ADJ
ejpam-3253	219	5	complement	complement	NOUN
ejpam-3253	219	6	topology	topology	NOUN
ejpam-3253	219	7	on	on	ADP
ejpam-3253	219	8	uncountable	uncountable	ADJ
ejpam-3253	219	9	set	set	NOUN
ejpam-3253	219	10	x	x	PUNCT
ejpam-3253	219	11	is	be	AUX
ejpam-3253	219	12	l	l	NOUN
ejpam-3253	219	13	-	-	NOUN
ejpam-3253	219	14	tychonoff	tychonoff	NOUN
ejpam-3253	219	15	,	,	PUNCT
ejpam-3253	219	16	but	but	CCONJ
ejpam-3253	219	17	it	it	PRON
ejpam-3253	219	18	is	be	AUX
ejpam-3253	219	19	ctychonoff	ctychonoff	NOUN
ejpam-3253	219	20	,	,	PUNCT
ejpam-3253	219	21	see	see	VERB
ejpam-3253	219	22	example	example	NOUN
ejpam-3253	220	1	2	2	X
ejpam-3253	220	2	.	.	PUNCT
ejpam-3253	220	3	an	an	DET
ejpam-3253	220	4	example	example	NOUN
ejpam-3253	220	5	of	of	ADP
ejpam-3253	220	6	an	an	DET
ejpam-3253	220	7	l	l	NOUN
ejpam-3253	220	8	-	-	PUNCT
ejpam-3253	220	9	tychonoff	tychonoff	NOUN
ejpam-3253	220	10	space	space	NOUN
ejpam-3253	220	11	which	which	PRON
ejpam-3253	220	12	is	be	AUX
ejpam-3253	220	13	not	not	PART
ejpam-3253	220	14	tychonoff	tychonoff	NOUN
ejpam-3253	220	15	.	.	PUNCT
ejpam-3253	221	1	example	example	NOUN
ejpam-3253	221	2	5	5	NUM
ejpam-3253	221	3	.	.	X
ejpam-3253	221	4	consider	consider	VERB
ejpam-3253	221	5	ω2	ω2	ADJ
ejpam-3253	221	6	,	,	PUNCT
ejpam-3253	221	7	the	the	DET
ejpam-3253	221	8	successor	successor	NOUN
ejpam-3253	221	9	cardinal	cardinal	ADJ
ejpam-3253	221	10	number	number	NOUN
ejpam-3253	221	11	of	of	ADP
ejpam-3253	221	12	the	the	DET
ejpam-3253	221	13	cardinal	cardinal	ADJ
ejpam-3253	221	14	number	number	NOUN
ejpam-3253	221	15	ω1	ω1	PROPN
ejpam-3253	221	16	.	.	PUNCT
ejpam-3253	222	1	let	let	VERB
ejpam-3253	222	2	x	x	PUNCT
ejpam-3253	223	1	=	=	SYM
ejpam-3253	223	2	ω2	ω2	ADJ
ejpam-3253	223	3	∪	∪	X
ejpam-3253	223	4	{	{	PUNCT
ejpam-3253	223	5	i	i	PROPN
ejpam-3253	223	6	,	,	PUNCT
ejpam-3253	223	7	j	j	PROPN
ejpam-3253	223	8	}	}	PUNCT
ejpam-3253	223	9	where	where	SCONJ
ejpam-3253	223	10	{	{	PUNCT
ejpam-3253	223	11	i	i	NOUN
ejpam-3253	223	12	,	,	PUNCT
ejpam-3253	223	13	j	j	NOUN
ejpam-3253	223	14	}	}	PUNCT
ejpam-3253	223	15	∩	∩	ADJ
ejpam-3253	223	16	ω2	ω2	NOUN
ejpam-3253	223	17	=	=	SYM
ejpam-3253	223	18	∅	∅	NOUN
ejpam-3253	223	19	,	,	PUNCT
ejpam-3253	223	20	so	so	SCONJ
ejpam-3253	223	21	i	i	PRON
ejpam-3253	223	22	6∈	6∈	PROPN
ejpam-3253	224	1	ω2	ω2	ADJ
ejpam-3253	224	2	and	and	CCONJ
ejpam-3253	224	3	j	j	PROPN
ejpam-3253	224	4	6∈	6∈	PROPN
ejpam-3253	224	5	ω2	ω2	PROPN
ejpam-3253	224	6	.	.	PUNCT
ejpam-3253	225	1	generate	generate	VERB
ejpam-3253	225	2	a	a	DET
ejpam-3253	225	3	topology	topology	NOUN
ejpam-3253	225	4	on	on	ADP
ejpam-3253	225	5	x	x	PUNCT
ejpam-3253	225	6	as	as	SCONJ
ejpam-3253	225	7	follows	follow	VERB
ejpam-3253	225	8	:	:	PUNCT
ejpam-3253	225	9	each	each	DET
ejpam-3253	225	10	α	α	PROPN
ejpam-3253	225	11	∈	∈	PROPN
ejpam-3253	225	12	ω2	ω2	NOUN
ejpam-3253	225	13	is	be	AUX
ejpam-3253	225	14	isolated	isolate	VERB
ejpam-3253	225	15	.	.	PUNCT
ejpam-3253	226	1	a	a	DET
ejpam-3253	226	2	basic	basic	ADJ
ejpam-3253	226	3	open	open	ADJ
ejpam-3253	226	4	neighborhood	neighborhood	NOUN
ejpam-3253	226	5	of	of	ADP
ejpam-3253	226	6	i	i	PRON
ejpam-3253	226	7	is	be	AUX
ejpam-3253	226	8	of	of	ADP
ejpam-3253	226	9	the	the	DET
ejpam-3253	226	10	form	form	NOUN
ejpam-3253	226	11	u	u	NOUN
ejpam-3253	226	12	=	=	X
ejpam-3253	226	13	{	{	PUNCT
ejpam-3253	226	14	i	i	NOUN
ejpam-3253	226	15	}	}	PUNCT
ejpam-3253	226	16	∪	∪	ADJ
ejpam-3253	226	17	(	(	PUNCT
ejpam-3253	226	18	ω2	ω2	ADJ
ejpam-3253	226	19	\	\	PROPN
ejpam-3253	226	20	e	e	X
ejpam-3253	226	21	)	)	PUNCT
ejpam-3253	226	22	where	where	SCONJ
ejpam-3253	226	23	e	e	PROPN
ejpam-3253	226	24	⊂	⊂	PROPN
ejpam-3253	226	25	ω2	ω2	ADJ
ejpam-3253	226	26	with	with	ADP
ejpam-3253	226	27	|e|	|e|	PROPN
ejpam-3253	226	28	=	=	SYM
ejpam-3253	226	29	ω1	ω1	PROPN
ejpam-3253	226	30	.	.	PROPN
ejpam-3253	226	31	similarly	similarly	ADV
ejpam-3253	226	32	,	,	PUNCT
ejpam-3253	226	33	a	a	DET
ejpam-3253	226	34	basic	basic	ADJ
ejpam-3253	226	35	open	open	ADJ
ejpam-3253	226	36	neighborhood	neighborhood	NOUN
ejpam-3253	226	37	of	of	ADP
ejpam-3253	226	38	j	j	PROPN
ejpam-3253	226	39	is	be	AUX
ejpam-3253	226	40	of	of	ADP
ejpam-3253	226	41	the	the	DET
ejpam-3253	226	42	form	form	NOUN
ejpam-3253	226	43	v	v	NOUN
ejpam-3253	226	44	=	=	SYM
ejpam-3253	226	45	{	{	PUNCT
ejpam-3253	226	46	j	j	NOUN
ejpam-3253	226	47	}	}	PUNCT
ejpam-3253	226	48	∪	∪	NOUN
ejpam-3253	226	49	(	(	PUNCT
ejpam-3253	226	50	ω2	ω2	ADJ
ejpam-3253	226	51	\	\	PROPN
ejpam-3253	226	52	f	f	PROPN
ejpam-3253	226	53	)	)	PUNCT
ejpam-3253	227	1	where	where	SCONJ
ejpam-3253	227	2	f	f	PROPN
ejpam-3253	227	3	⊂	⊂	PROPN
ejpam-3253	227	4	ω2	ω2	ADJ
ejpam-3253	227	5	with	with	ADP
ejpam-3253	227	6	|f	|f	PROPN
ejpam-3253	227	7	|	|	PROPN
ejpam-3253	227	8	=	=	SYM
ejpam-3253	227	9	ω1	ω1	PROPN
ejpam-3253	227	10	.	.	PUNCT
ejpam-3253	228	1	then	then	ADV
ejpam-3253	228	2	x	x	PRON
ejpam-3253	228	3	is	be	AUX
ejpam-3253	228	4	not	not	PART
ejpam-3253	228	5	t2	t2	NOUN
ejpam-3253	228	6	as	as	SCONJ
ejpam-3253	228	7	i	i	PRON
ejpam-3253	228	8	and	and	CCONJ
ejpam-3253	228	9	j	j	PROPN
ejpam-3253	228	10	can	can	AUX
ejpam-3253	228	11	not	not	PART
ejpam-3253	228	12	be	be	AUX
ejpam-3253	228	13	separated	separate	VERB
ejpam-3253	228	14	by	by	ADP
ejpam-3253	228	15	disjoint	disjoint	ADJ
ejpam-3253	228	16	open	open	ADJ
ejpam-3253	228	17	sets	set	NOUN
ejpam-3253	228	18	.	.	PUNCT
ejpam-3253	229	1	x	x	PRON
ejpam-3253	229	2	is	be	AUX
ejpam-3253	229	3	not	not	PART
ejpam-3253	229	4	lindelöf	lindelöf	NOUN
ejpam-3253	229	5	as	as	SCONJ
ejpam-3253	229	6	the	the	DET
ejpam-3253	229	7	open	open	ADJ
ejpam-3253	229	8	cover	cover	NOUN
ejpam-3253	229	9	{	{	PUNCT
ejpam-3253	229	10	{	{	PUNCT
ejpam-3253	229	11	i	i	NOUN
ejpam-3253	229	12	}	}	PUNCT
ejpam-3253	229	13	∪	∪	ADJ
ejpam-3253	229	14	(	(	PUNCT
ejpam-3253	229	15	ω2	ω2	ADJ
ejpam-3253	229	16	\	\	PROPN
ejpam-3253	229	17	ω1	ω1	PROPN
ejpam-3253	229	18	)	)	PUNCT
ejpam-3253	229	19	,	,	PUNCT
ejpam-3253	229	20	{	{	PUNCT
ejpam-3253	229	21	j	j	NOUN
ejpam-3253	229	22	}	}	PUNCT
ejpam-3253	229	23	∪	∪	NOUN
ejpam-3253	229	24	(	(	PUNCT
ejpam-3253	229	25	ω2	ω2	ADJ
ejpam-3253	229	26	\	\	PROPN
ejpam-3253	229	27	ω1	ω1	PROPN
ejpam-3253	229	28	)	)	PUNCT
ejpam-3253	229	29	,	,	PUNCT
ejpam-3253	229	30	{	{	PUNCT
ejpam-3253	229	31	α	α	NOUN
ejpam-3253	229	32	}	}	PUNCT
ejpam-3253	229	33	:	:	PUNCT
ejpam-3253	229	34	α	α	PROPN
ejpam-3253	229	35	∈	∈	PROPN
ejpam-3253	229	36	ω1	ω1	PROPN
ejpam-3253	229	37	}	}	PUNCT
ejpam-3253	229	38	of	of	ADP
ejpam-3253	229	39	x	x	PUNCT
ejpam-3253	229	40	has	have	VERB
ejpam-3253	229	41	no	no	DET
ejpam-3253	229	42	countable	countable	ADJ
ejpam-3253	229	43	subcover	subcover	NOUN
ejpam-3253	229	44	.	.	PUNCT
ejpam-3253	230	1	also	also	ADV
ejpam-3253	230	2	,	,	PUNCT
ejpam-3253	230	3	if	if	SCONJ
ejpam-3253	230	4	c	c	PROPN
ejpam-3253	230	5	is	be	AUX
ejpam-3253	230	6	any	any	DET
ejpam-3253	230	7	countable	countable	ADJ
ejpam-3253	230	8	subspace	subspace	NOUN
ejpam-3253	230	9	of	of	ADP
ejpam-3253	230	10	x	x	PRON
ejpam-3253	230	11	,	,	PUNCT
ejpam-3253	230	12	then	then	ADV
ejpam-3253	230	13	c	c	PROPN
ejpam-3253	230	14	is	be	AUX
ejpam-3253	230	15	discrete	discrete	ADJ
ejpam-3253	230	16	as	as	ADP
ejpam-3253	230	17	a	a	DET
ejpam-3253	230	18	subspace	subspace	NOUN
ejpam-3253	230	19	because	because	SCONJ
ejpam-3253	230	20	if	if	SCONJ
ejpam-3253	230	21	i	i	PRON
ejpam-3253	230	22	∈	∈	VERB
ejpam-3253	230	23	c	c	X
ejpam-3253	230	24	,	,	PUNCT
ejpam-3253	230	25	then	then	ADV
ejpam-3253	230	26	u	u	NOUN
ejpam-3253	230	27	=	=	PUNCT
ejpam-3253	230	28	{	{	PUNCT
ejpam-3253	230	29	i}∪	i}∪	X
ejpam-3253	230	30	(	(	PUNCT
ejpam-3253	230	31	ω2	ω2	ADJ
ejpam-3253	230	32	\	\	PROPN
ejpam-3253	230	33	(	(	PUNCT
ejpam-3253	230	34	ω1	ω1	PROPN
ejpam-3253	230	35	∪	∪	X
ejpam-3253	230	36	(	(	PUNCT
ejpam-3253	230	37	c	c	NOUN
ejpam-3253	230	38	\	\	PROPN
ejpam-3253	230	39	{	{	PUNCT
ejpam-3253	230	40	j	j	NOUN
ejpam-3253	230	41	}	}	PUNCT
ejpam-3253	230	42	)	)	PUNCT
ejpam-3253	230	43	)	)	PUNCT
ejpam-3253	230	44	)	)	PUNCT
ejpam-3253	230	45	is	be	AUX
ejpam-3253	230	46	an	an	DET
ejpam-3253	230	47	open	open	ADJ
ejpam-3253	230	48	neighborhood	neighborhood	NOUN
ejpam-3253	230	49	of	of	ADP
ejpam-3253	230	50	i	i	PRON
ejpam-3253	230	51	in	in	ADP
ejpam-3253	230	52	x	x	PUNCT
ejpam-3253	231	1	such	such	ADJ
ejpam-3253	231	2	that	that	SCONJ
ejpam-3253	231	3	u	u	NOUN
ejpam-3253	231	4	∩c	∩c	NOUN
ejpam-3253	231	5	=	=	PUNCT
ejpam-3253	231	6	{	{	PUNCT
ejpam-3253	231	7	i	i	NOUN
ejpam-3253	231	8	}	}	PUNCT
ejpam-3253	231	9	.	.	PUNCT
ejpam-3253	232	1	similarly	similarly	ADV
ejpam-3253	232	2	,	,	PUNCT
ejpam-3253	232	3	if	if	SCONJ
ejpam-3253	232	4	j	j	PROPN
ejpam-3253	232	5	∈	∈	PROPN
ejpam-3253	232	6	c.	c.	PROPN
ejpam-3253	232	7	it	it	PRON
ejpam-3253	232	8	is	be	AUX
ejpam-3253	232	9	clear	clear	ADJ
ejpam-3253	232	10	that	that	SCONJ
ejpam-3253	232	11	if	if	SCONJ
ejpam-3253	232	12	c	c	PROPN
ejpam-3253	232	13	is	be	AUX
ejpam-3253	232	14	countable	countable	ADJ
ejpam-3253	232	15	,	,	PUNCT
ejpam-3253	232	16	then	then	ADV
ejpam-3253	232	17	c	c	PROPN
ejpam-3253	232	18	is	be	AUX
ejpam-3253	232	19	lindelöf	lindelöf	PROPN
ejpam-3253	232	20	.	.	PUNCT
ejpam-3253	233	1	assume	assume	VERB
ejpam-3253	233	2	that	that	SCONJ
ejpam-3253	233	3	c	c	PROPN
ejpam-3253	233	4	is	be	AUX
ejpam-3253	233	5	uncountable	uncountable	ADJ
ejpam-3253	233	6	.	.	PUNCT
ejpam-3253	234	1	then	then	ADV
ejpam-3253	234	2	|c|	|c|	PROPN
ejpam-3253	234	3	≥	≥	PROPN
ejpam-3253	234	4	ω1	ω1	PROPN
ejpam-3253	234	5	.	.	PROPN
ejpam-3253	234	6	suppose	suppose	VERB
ejpam-3253	234	7	that	that	SCONJ
ejpam-3253	234	8	{	{	PUNCT
ejpam-3253	234	9	i	i	PRON
ejpam-3253	234	10	,	,	PUNCT
ejpam-3253	234	11	j	j	PROPN
ejpam-3253	234	12	}	}	PUNCT
ejpam-3253	234	13	⊂	⊂	PROPN
ejpam-3253	234	14	c.	c.	PROPN
ejpam-3253	234	15	partition	partition	PROPN
ejpam-3253	234	16	c	c	PROPN
ejpam-3253	234	17	into	into	ADP
ejpam-3253	234	18	three	three	NUM
ejpam-3253	234	19	partitions	partition	NOUN
ejpam-3253	234	20	c1	c1	PROPN
ejpam-3253	234	21	,	,	PUNCT
ejpam-3253	234	22	c2	c2	PROPN
ejpam-3253	234	23	,	,	PUNCT
ejpam-3253	234	24	and	and	CCONJ
ejpam-3253	234	25	c3	c3	X
ejpam-3253	234	26	such	such	ADJ
ejpam-3253	234	27	that	that	SCONJ
ejpam-3253	234	28	i	i	PROPN
ejpam-3253	234	29	∈	∈	PROPN
ejpam-3253	234	30	c1	c1	NOUN
ejpam-3253	234	31	with	with	ADP
ejpam-3253	234	32	|c1|	|c1|	PROPN
ejpam-3253	234	33	=	=	SYM
ejpam-3253	234	34	ω1	ω1	PROPN
ejpam-3253	234	35	,	,	PUNCT
ejpam-3253	234	36	j	j	PROPN
ejpam-3253	234	37	∈	∈	PROPN
ejpam-3253	234	38	c2	c2	PROPN
ejpam-3253	234	39	with	with	ADP
ejpam-3253	234	40	|c2|	|c2|	PROPN
ejpam-3253	234	41	=	=	SYM
ejpam-3253	234	42	ω1	ω1	PROPN
ejpam-3253	234	43	,	,	PUNCT
ejpam-3253	234	44	and	and	CCONJ
ejpam-3253	234	45	|c3|	|c3|	ADJ
ejpam-3253	234	46	≥	≥	NUM
ejpam-3253	234	47	ω1	ω1	PROPN
ejpam-3253	234	48	.	.	PUNCT
ejpam-3253	235	1	the	the	DET
ejpam-3253	235	2	open	open	ADJ
ejpam-3253	235	3	cover	cover	NOUN
ejpam-3253	235	4	{	{	PUNCT
ejpam-3253	235	5	{	{	PUNCT
ejpam-3253	235	6	i}∪(ω2\((c1∪c2)\{i	i}∪(ω2\((c1∪c2)\{i	PROPN
ejpam-3253	235	7	,	,	PUNCT
ejpam-3253	235	8	j	j	NOUN
ejpam-3253	235	9	}	}	PUNCT
ejpam-3253	235	10	)	)	PUNCT
ejpam-3253	235	11	)	)	PUNCT
ejpam-3253	235	12	,	,	PUNCT
ejpam-3253	235	13	{	{	PUNCT
ejpam-3253	235	14	j}∪(ω2\((c1∪c2)\{i	j}∪(ω2\((c1∪c2)\{i	NOUN
ejpam-3253	235	15	,	,	PUNCT
ejpam-3253	235	16	j	j	NOUN
ejpam-3253	235	17	}	}	PUNCT
ejpam-3253	235	18	)	)	PUNCT
ejpam-3253	235	19	)	)	PUNCT
ejpam-3253	235	20	)	)	PUNCT
ejpam-3253	235	21	,	,	PUNCT
ejpam-3253	235	22	{	{	PUNCT
ejpam-3253	235	23	α	α	NOUN
ejpam-3253	235	24	}	}	PUNCT
ejpam-3253	235	25	:	:	PUNCT
ejpam-3253	235	26	α	α	PROPN
ejpam-3253	235	27	∈	∈	PROPN
ejpam-3253	235	28	c1∪c2	c1∪c2	NOUN
ejpam-3253	235	29	}	}	PUNCT
ejpam-3253	235	30	of	of	ADP
ejpam-3253	235	31	c	c	NOUN
ejpam-3253	235	32	has	have	VERB
ejpam-3253	235	33	no	no	DET
ejpam-3253	235	34	countable	countable	ADJ
ejpam-3253	235	35	subcover	subcover	NOUN
ejpam-3253	235	36	.	.	PUNCT
ejpam-3253	236	1	if	if	SCONJ
ejpam-3253	236	2	c	c	PROPN
ejpam-3253	236	3	contains	contain	VERB
ejpam-3253	236	4	either	either	CCONJ
ejpam-3253	236	5	i	i	PRON
ejpam-3253	236	6	or	or	CCONJ
ejpam-3253	236	7	j	j	PROPN
ejpam-3253	236	8	,	,	PUNCT
ejpam-3253	236	9	we	we	PRON
ejpam-3253	236	10	do	do	VERB
ejpam-3253	236	11	the	the	DET
ejpam-3253	236	12	same	same	ADJ
ejpam-3253	236	13	idea	idea	NOUN
ejpam-3253	236	14	but	but	CCONJ
ejpam-3253	236	15	for	for	ADP
ejpam-3253	236	16	just	just	ADV
ejpam-3253	236	17	two	two	NUM
ejpam-3253	236	18	partitions	partition	NOUN
ejpam-3253	236	19	.	.	PUNCT
ejpam-3253	237	1	thus	thus	ADV
ejpam-3253	237	2	a	a	DET
ejpam-3253	237	3	subspace	subspace	NOUN
ejpam-3253	237	4	c	c	PROPN
ejpam-3253	237	5	of	of	ADP
ejpam-3253	237	6	x	x	PROPN
ejpam-3253	237	7	is	be	AUX
ejpam-3253	237	8	lindelöf	lindelöf	NOUN
ejpam-3253	237	9	if	if	SCONJ
ejpam-3253	237	10	and	and	CCONJ
ejpam-3253	237	11	only	only	ADV
ejpam-3253	237	12	if	if	SCONJ
ejpam-3253	237	13	c	c	PROPN
ejpam-3253	237	14	is	be	AUX
ejpam-3253	237	15	countable	countable	ADJ
ejpam-3253	237	16	.	.	PUNCT
ejpam-3253	238	1	thus	thus	ADV
ejpam-3253	238	2	x	x	X
ejpam-3253	238	3	is	be	AUX
ejpam-3253	238	4	l	l	NOUN
ejpam-3253	238	5	-	-	NOUN
ejpam-3253	238	6	tychonoff	tychonoff	NOUN
ejpam-3253	238	7	which	which	PRON
ejpam-3253	238	8	is	be	AUX
ejpam-3253	238	9	not	not	PART
ejpam-3253	238	10	tychonoff	tychonoff	NOUN
ejpam-3253	238	11	.	.	PUNCT
ejpam-3253	239	1	a	a	DET
ejpam-3253	239	2	function	function	NOUN
ejpam-3253	239	3	f	f	NOUN
ejpam-3253	239	4	:	:	PUNCT
ejpam-3253	239	5	x	x	PUNCT
ejpam-3253	239	6	−→	−→	NOUN
ejpam-3253	239	7	y	y	NOUN
ejpam-3253	239	8	witnessing	witness	VERB
ejpam-3253	239	9	the	the	DET
ejpam-3253	239	10	l	l	NOUN
ejpam-3253	239	11	-	-	NOUN
ejpam-3253	239	12	tychonoffness	tychonoffness	NOUN
ejpam-3253	239	13	of	of	ADP
ejpam-3253	239	14	x	x	PUNCT
ejpam-3253	239	15	need	need	AUX
ejpam-3253	239	16	not	not	PART
ejpam-3253	239	17	be	be	AUX
ejpam-3253	239	18	continuous	continuous	ADJ
ejpam-3253	239	19	.	.	PUNCT
ejpam-3253	240	1	but	but	CCONJ
ejpam-3253	240	2	it	it	PRON
ejpam-3253	240	3	will	will	AUX
ejpam-3253	240	4	be	be	AUX
ejpam-3253	240	5	if	if	SCONJ
ejpam-3253	240	6	x	x	PRON
ejpam-3253	240	7	is	be	AUX
ejpam-3253	240	8	of	of	ADP
ejpam-3253	240	9	countable	countable	ADJ
ejpam-3253	240	10	tightness	tightness	NOUN
ejpam-3253	240	11	.	.	PUNCT
ejpam-3253	241	1	recall	recall	VERB
ejpam-3253	241	2	that	that	SCONJ
ejpam-3253	241	3	a	a	DET
ejpam-3253	241	4	space	space	NOUN
ejpam-3253	241	5	x	x	VERB
ejpam-3253	241	6	is	be	AUX
ejpam-3253	241	7	of	of	ADP
ejpam-3253	241	8	countable	countable	ADJ
ejpam-3253	241	9	tightness	tightness	NOUN
ejpam-3253	241	10	if	if	SCONJ
ejpam-3253	241	11	for	for	ADP
ejpam-3253	241	12	each	each	DET
ejpam-3253	241	13	subset	subset	NOUN
ejpam-3253	241	14	b	b	PROPN
ejpam-3253	241	15	of	of	ADP
ejpam-3253	241	16	x	x	PUNCT
ejpam-3253	241	17	and	and	CCONJ
ejpam-3253	241	18	each	each	DET
ejpam-3253	241	19	x	x	SYM
ejpam-3253	241	20	∈	∈	PROPN
ejpam-3253	241	21	b	b	NOUN
ejpam-3253	241	22	,	,	PUNCT
ejpam-3253	241	23	there	there	PRON
ejpam-3253	241	24	exists	exist	VERB
ejpam-3253	241	25	a	a	DET
ejpam-3253	241	26	countable	countable	ADJ
ejpam-3253	241	27	subset	subset	NOUN
ejpam-3253	241	28	b0	b0	NOUN
ejpam-3253	241	29	of	of	ADP
ejpam-3253	241	30	b	b	NOUN
ejpam-3253	241	31	such	such	ADJ
ejpam-3253	241	32	that	that	SCONJ
ejpam-3253	241	33	x	x	SYM
ejpam-3253	241	34	∈	∈	PROPN
ejpam-3253	241	35	b0	b0	NOUN
ejpam-3253	241	36	[	[	X
ejpam-3253	241	37	8	8	NUM
ejpam-3253	241	38	]	]	PUNCT
ejpam-3253	241	39	.	.	PUNCT
ejpam-3253	242	1	theorem	theorem	VERB
ejpam-3253	242	2	11	11	NUM
ejpam-3253	242	3	.	.	PUNCT
ejpam-3253	243	1	if	if	SCONJ
ejpam-3253	243	2	x	x	PRON
ejpam-3253	243	3	is	be	AUX
ejpam-3253	243	4	l	l	NOUN
ejpam-3253	243	5	-	-	NOUN
ejpam-3253	243	6	tychonoff	tychonoff	NOUN
ejpam-3253	243	7	and	and	CCONJ
ejpam-3253	243	8	of	of	ADP
ejpam-3253	243	9	countable	countable	ADJ
ejpam-3253	243	10	tightness	tightness	NOUN
ejpam-3253	243	11	and	and	CCONJ
ejpam-3253	243	12	f	f	NOUN
ejpam-3253	243	13	:	:	PUNCT
ejpam-3253	243	14	x	x	PUNCT
ejpam-3253	243	15	−→	−→	NOUN
ejpam-3253	243	16	y	y	PROPN
ejpam-3253	243	17	is	be	AUX
ejpam-3253	243	18	a	a	DET
ejpam-3253	243	19	witness	witness	NOUN
ejpam-3253	243	20	of	of	ADP
ejpam-3253	243	21	the	the	DET
ejpam-3253	243	22	l	l	NOUN
ejpam-3253	243	23	-	-	NOUN
ejpam-3253	243	24	tychonoffness	tychonoffness	NOUN
ejpam-3253	243	25	of	of	ADP
ejpam-3253	243	26	x	x	PRON
ejpam-3253	243	27	,	,	PUNCT
ejpam-3253	243	28	then	then	ADV
ejpam-3253	243	29	f	f	PROPN
ejpam-3253	243	30	is	be	AUX
ejpam-3253	243	31	continuous	continuous	ADJ
ejpam-3253	243	32	.	.	PUNCT
ejpam-3253	244	1	proof	proof	NOUN
ejpam-3253	244	2	.	.	PUNCT
ejpam-3253	245	1	let	let	VERB
ejpam-3253	245	2	a	a	DET
ejpam-3253	245	3	be	be	AUX
ejpam-3253	245	4	any	any	DET
ejpam-3253	245	5	non	non	ADJ
ejpam-3253	245	6	-	-	ADJ
ejpam-3253	245	7	empty	empty	ADJ
ejpam-3253	245	8	subset	subset	NOUN
ejpam-3253	245	9	of	of	ADP
ejpam-3253	245	10	x.	x.	NOUN
ejpam-3253	245	11	let	let	VERB
ejpam-3253	245	12	y	y	PROPN
ejpam-3253	245	13	∈	∈	PROPN
ejpam-3253	245	14	f(a	f(a	PROPN
ejpam-3253	245	15	)	)	PUNCT
ejpam-3253	245	16	be	be	AUX
ejpam-3253	245	17	arbitrary	arbitrary	ADJ
ejpam-3253	245	18	.	.	PUNCT
ejpam-3253	246	1	let	let	VERB
ejpam-3253	246	2	x	x	PUNCT
ejpam-3253	246	3	∈	∈	PROPN
ejpam-3253	246	4	x	x	PUNCT
ejpam-3253	246	5	be	be	AUX
ejpam-3253	246	6	the	the	DET
ejpam-3253	246	7	unique	unique	ADJ
ejpam-3253	246	8	element	element	NOUN
ejpam-3253	246	9	such	such	ADJ
ejpam-3253	246	10	thatf(x	thatf(x	NOUN
ejpam-3253	246	11	)	)	PUNCT
ejpam-3253	246	12	=	=	VERB
ejpam-3253	247	1	y.	y.	NOUN
ejpam-3253	247	2	then	then	ADV
ejpam-3253	247	3	x	x	SYM
ejpam-3253	247	4	∈	∈	PROPN
ejpam-3253	247	5	a.	a.	NOUN
ejpam-3253	247	6	pick	pick	VERB
ejpam-3253	247	7	a	a	DET
ejpam-3253	247	8	countable	countable	ADJ
ejpam-3253	247	9	subset	subset	NOUN
ejpam-3253	247	10	a0	a0	NOUN
ejpam-3253	247	11	⊆	⊆	NUM
ejpam-3253	247	12	a	a	DET
ejpam-3253	247	13	such	such	ADJ
ejpam-3253	247	14	that	that	SCONJ
ejpam-3253	247	15	x	x	SYM
ejpam-3253	247	16	∈	∈	PROPN
ejpam-3253	247	17	a0	a0	PROPN
ejpam-3253	247	18	.	.	PUNCT
ejpam-3253	248	1	let	let	VERB
ejpam-3253	248	2	b	b	NOUN
ejpam-3253	248	3	=	=	PRON
ejpam-3253	248	4	{	{	PUNCT
ejpam-3253	248	5	x	x	NOUN
ejpam-3253	248	6	}	}	PUNCT
ejpam-3253	248	7	∪	∪	ADJ
ejpam-3253	248	8	a0	a0	NOUN
ejpam-3253	248	9	;	;	PUNCT
ejpam-3253	248	10	then	then	ADV
ejpam-3253	248	11	b	b	X
ejpam-3253	248	12	is	be	AUX
ejpam-3253	248	13	a	a	DET
ejpam-3253	248	14	lindelöf	lindelöf	NOUN
ejpam-3253	248	15	subspace	subspace	NOUN
ejpam-3253	248	16	of	of	ADP
ejpam-3253	248	17	x	x	PUNCT
ejpam-3253	248	18	and	and	CCONJ
ejpam-3253	248	19	hence	hence	ADV
ejpam-3253	248	20	f|b	f|b	PROPN
ejpam-3253	248	21	:	:	PUNCT
ejpam-3253	248	22	b	b	X
ejpam-3253	248	23	−→	−→	ADJ
ejpam-3253	248	24	f(b	f(b	PROPN
ejpam-3253	248	25	)	)	PUNCT
ejpam-3253	248	26	is	be	AUX
ejpam-3253	248	27	a	a	DET
ejpam-3253	248	28	homeomorphism	homeomorphism	NOUN
ejpam-3253	248	29	.	.	PUNCT
ejpam-3253	249	1	now	now	ADV
ejpam-3253	249	2	,	,	PUNCT
ejpam-3253	249	3	let	let	VERB
ejpam-3253	249	4	v	v	PRON
ejpam-3253	249	5	⊆	⊆	NUM
ejpam-3253	249	6	y	y	NOUN
ejpam-3253	249	7	be	be	AUX
ejpam-3253	249	8	any	any	DET
ejpam-3253	249	9	open	open	ADJ
ejpam-3253	249	10	neighborhood	neighborhood	NOUN
ejpam-3253	249	11	of	of	ADP
ejpam-3253	249	12	y	y	PROPN
ejpam-3253	249	13	;	;	PUNCT
ejpam-3253	249	14	then	then	ADV
ejpam-3253	249	15	v	v	ADP
ejpam-3253	249	16	∩	∩	ADJ
ejpam-3253	249	17	f(b	f(b	NOUN
ejpam-3253	249	18	)	)	PUNCT
ejpam-3253	249	19	is	be	AUX
ejpam-3253	249	20	open	open	ADJ
ejpam-3253	249	21	in	in	ADP
ejpam-3253	249	22	the	the	DET
ejpam-3253	249	23	subspace	subspace	NOUN
ejpam-3253	249	24	f(b	f(b	PROPN
ejpam-3253	249	25	)	)	PUNCT
ejpam-3253	249	26	containing	contain	VERB
ejpam-3253	249	27	y.	y.	NOUN
ejpam-3253	249	28	thus	thus	ADV
ejpam-3253	249	29	f−1(v	f−1(v	NOUN
ejpam-3253	249	30	)	)	PUNCT
ejpam-3253	250	1	∩b	∩b	NOUN
ejpam-3253	250	2	is	be	AUX
ejpam-3253	250	3	open	open	ADJ
ejpam-3253	250	4	in	in	ADP
ejpam-3253	250	5	the	the	DET
ejpam-3253	250	6	subspace	subspace	NOUN
ejpam-3253	250	7	b	b	PROPN
ejpam-3253	250	8	containing	contain	VERB
ejpam-3253	250	9	x.	x.	NOUN
ejpam-3253	250	10	thus	thus	ADV
ejpam-3253	250	11	(	(	PUNCT
ejpam-3253	250	12	f−1(v	f−1(v	PROPN
ejpam-3253	250	13	)	)	PUNCT
ejpam-3253	250	14	∩b	∩b	PROPN
ejpam-3253	250	15	)	)	PUNCT
ejpam-3253	250	16	∩a0	∩a0	VERB
ejpam-3253	251	1	6=	6=	X
ejpam-3253	251	2	∅.	∅.	VERB
ejpam-3253	251	3	so	so	ADV
ejpam-3253	251	4	(	(	PUNCT
ejpam-3253	251	5	f−1(v	f−1(v	PROPN
ejpam-3253	251	6	)	)	PUNCT
ejpam-3253	251	7	∩b	∩b	NOUN
ejpam-3253	251	8	)	)	PUNCT
ejpam-3253	252	1	∩a	∩a	PROPN
ejpam-3253	252	2	6=	6=	ADP
ejpam-3253	252	3	∅.	∅.	VERB
ejpam-3253	252	4	hence	hence	ADV
ejpam-3253	252	5	∅	∅	NOUN
ejpam-3253	252	6	6=	6=	ADP
ejpam-3253	252	7	f((f−1(v	f((f−1(v	NOUN
ejpam-3253	252	8	)	)	PUNCT
ejpam-3253	252	9	∩	∩	PROPN
ejpam-3253	252	10	b	b	X
ejpam-3253	252	11	)	)	PUNCT
ejpam-3253	252	12	∩	∩	NOUN
ejpam-3253	252	13	a	a	X
ejpam-3253	252	14	)	)	PUNCT
ejpam-3253	252	15	⊆	⊆	NUM
ejpam-3253	252	16	f(f−1(v	f(f−1(v	PROPN
ejpam-3253	252	17	)	)	PUNCT
ejpam-3253	252	18	∩	∩	PROPN
ejpam-3253	252	19	a	a	X
ejpam-3253	252	20	)	)	PUNCT
ejpam-3253	252	21	=	=	SYM
ejpam-3253	252	22	v	v	NUM
ejpam-3253	252	23	∩	∩	ADJ
ejpam-3253	252	24	f(a	f(a	NOUN
ejpam-3253	252	25	)	)	PUNCT
ejpam-3253	252	26	.	.	PUNCT
ejpam-3253	253	1	thus	thus	ADV
ejpam-3253	253	2	y	y	PROPN
ejpam-3253	253	3	∈	∈	PROPN
ejpam-3253	253	4	f(a	f(a	PROPN
ejpam-3253	253	5	)	)	PUNCT
ejpam-3253	253	6	.	.	PUNCT
ejpam-3253	254	1	therefore	therefore	ADV
ejpam-3253	254	2	,	,	PUNCT
ejpam-3253	254	3	f	f	PROPN
ejpam-3253	254	4	is	be	AUX
ejpam-3253	254	5	continuous	continuous	ADJ
ejpam-3253	254	6	.	.	PUNCT
ejpam-3253	255	1	s.	s.	PROPN
ejpam-3253	255	2	alzahrani	alzahrani	PROPN
ejpam-3253	255	3	/	/	SYM
ejpam-3253	255	4	eur	eur	PROPN
ejpam-3253	255	5	.	.	PUNCT
ejpam-3253	256	1	j.	j.	PROPN
ejpam-3253	256	2	pure	pure	PROPN
ejpam-3253	256	3	appl	appl	PROPN
ejpam-3253	256	4	.	.	PROPN
ejpam-3253	256	5	math	math	PROPN
ejpam-3253	256	6	,	,	PUNCT
ejpam-3253	256	7	11	11	NUM
ejpam-3253	256	8	(	(	PUNCT
ejpam-3253	256	9	3	3	NUM
ejpam-3253	256	10	)	)	PUNCT
ejpam-3253	256	11	(	(	PUNCT
ejpam-3253	256	12	2018	2018	NUM
ejpam-3253	256	13	)	)	PUNCT
ejpam-3253	256	14	,	,	PUNCT
ejpam-3253	256	15	882	882	NUM
ejpam-3253	256	16	-	-	SYM
ejpam-3253	256	17	892	892	NUM
ejpam-3253	256	18	889	889	NUM
ejpam-3253	256	19	recall	recall	NOUN
ejpam-3253	256	20	that	that	SCONJ
ejpam-3253	256	21	if	if	SCONJ
ejpam-3253	256	22	(	(	PUNCT
ejpam-3253	256	23	xn)n∈n	xn)n∈n	PROPN
ejpam-3253	256	24	is	be	AUX
ejpam-3253	256	25	a	a	DET
ejpam-3253	256	26	sequence	sequence	NOUN
ejpam-3253	256	27	in	in	ADP
ejpam-3253	256	28	a	a	DET
ejpam-3253	256	29	topological	topological	ADJ
ejpam-3253	256	30	space	space	NOUN
ejpam-3253	256	31	x	x	NOUN
ejpam-3253	256	32	,	,	PUNCT
ejpam-3253	256	33	then	then	ADV
ejpam-3253	256	34	the	the	DET
ejpam-3253	256	35	convergency	convergency	NOUN
ejpam-3253	256	36	set	set	NOUN
ejpam-3253	256	37	of	of	ADP
ejpam-3253	256	38	(	(	PUNCT
ejpam-3253	256	39	xn	xn	X
ejpam-3253	256	40	)	)	PUNCT
ejpam-3253	256	41	is	be	AUX
ejpam-3253	256	42	defined	define	VERB
ejpam-3253	256	43	by	by	ADP
ejpam-3253	256	44	c(xn	c(xn	NOUN
ejpam-3253	256	45	)	)	PUNCT
ejpam-3253	256	46	=	=	PRON
ejpam-3253	256	47	{	{	PUNCT
ejpam-3253	256	48	x	x	PUNCT
ejpam-3253	256	49	∈	∈	PROPN
ejpam-3253	256	50	x	x	X
ejpam-3253	256	51	:	:	PUNCT
ejpam-3253	256	52	xn	xn	PUNCT
ejpam-3253	257	1	−→	−→	ADJ
ejpam-3253	257	2	x	x	SYM
ejpam-3253	257	3	}	}	PUNCT
ejpam-3253	257	4	and	and	CCONJ
ejpam-3253	257	5	a	a	DET
ejpam-3253	257	6	topological	topological	ADJ
ejpam-3253	257	7	space	space	NOUN
ejpam-3253	257	8	x	x	PUNCT
ejpam-3253	257	9	is	be	AUX
ejpam-3253	257	10	sequential	sequential	ADJ
ejpam-3253	257	11	if	if	SCONJ
ejpam-3253	257	12	for	for	ADP
ejpam-3253	257	13	any	any	DET
ejpam-3253	257	14	a	a	DET
ejpam-3253	257	15	⊆	⊆	NUM
ejpam-3253	257	16	x	x	SYM
ejpam-3253	257	17	we	we	PRON
ejpam-3253	257	18	have	have	VERB
ejpam-3253	257	19	that	that	SCONJ
ejpam-3253	257	20	a	a	PRON
ejpam-3253	257	21	is	be	AUX
ejpam-3253	257	22	closed	close	VERB
ejpam-3253	257	23	if	if	SCONJ
ejpam-3253	257	24	and	and	CCONJ
ejpam-3253	257	25	only	only	ADV
ejpam-3253	257	26	if	if	SCONJ
ejpam-3253	257	27	c(xn	c(xn	NOUN
ejpam-3253	257	28	)	)	PUNCT
ejpam-3253	257	29	⊆	⊆	NUM
ejpam-3253	257	30	a	a	PRON
ejpam-3253	257	31	for	for	ADP
ejpam-3253	257	32	any	any	DET
ejpam-3253	257	33	sequence	sequence	NOUN
ejpam-3253	257	34	(	(	PUNCT
ejpam-3253	257	35	xn	xn	PROPN
ejpam-3253	257	36	)	)	PUNCT
ejpam-3253	257	37	⊆	⊆	NUM
ejpam-3253	257	38	a	a	PRON
ejpam-3253	257	39	,	,	PUNCT
ejpam-3253	257	40	see	see	VERB
ejpam-3253	257	41	[	[	X
ejpam-3253	257	42	8	8	NUM
ejpam-3253	257	43	]	]	PUNCT
ejpam-3253	257	44	.	.	PUNCT
ejpam-3253	258	1	we	we	PRON
ejpam-3253	258	2	have	have	VERB
ejpam-3253	258	3	the	the	DET
ejpam-3253	258	4	following	following	ADJ
ejpam-3253	258	5	implications	implication	NOUN
ejpam-3253	258	6	,	,	PUNCT
ejpam-3253	258	7	see	see	VERB
ejpam-3253	258	8	[	[	X
ejpam-3253	258	9	8	8	NUM
ejpam-3253	258	10	,	,	PUNCT
ejpam-3253	258	11	1.6.14	1.6.14	NUM
ejpam-3253	258	12	,	,	PUNCT
ejpam-3253	258	13	1.7.13	1.7.13	NUM
ejpam-3253	258	14	]	]	PUNCT
ejpam-3253	258	15	.	.	PUNCT
ejpam-3253	259	1	first	first	ADJ
ejpam-3253	259	2	countability	countability	NOUN
ejpam-3253	259	3	⇒	⇒	NOUN
ejpam-3253	259	4	fréchet	fréchet	PROPN
ejpam-3253	259	5	⇒	⇒	PROPN
ejpam-3253	259	6	sequential	sequential	ADJ
ejpam-3253	259	7	⇒	⇒	NOUN
ejpam-3253	259	8	countable	countable	ADJ
ejpam-3253	259	9	tightness	tightness	NOUN
ejpam-3253	259	10	.	.	PUNCT
ejpam-3253	260	1	corollary	corollary	ADJ
ejpam-3253	260	2	5	5	NUM
ejpam-3253	260	3	.	.	PUNCT
ejpam-3253	261	1	if	if	SCONJ
ejpam-3253	261	2	x	x	PRON
ejpam-3253	261	3	is	be	AUX
ejpam-3253	261	4	l	l	NOUN
ejpam-3253	261	5	-	-	NOUN
ejpam-3253	261	6	tychonoff	tychonoff	NOUN
ejpam-3253	261	7	and	and	CCONJ
ejpam-3253	261	8	first	first	ADJ
ejpam-3253	261	9	countable	countable	ADJ
ejpam-3253	261	10	(	(	PUNCT
ejpam-3253	261	11	fréchet	fréchet	NOUN
ejpam-3253	261	12	,	,	PUNCT
ejpam-3253	261	13	sequential	sequential	ADJ
ejpam-3253	261	14	)	)	PUNCT
ejpam-3253	261	15	and	and	CCONJ
ejpam-3253	261	16	f	f	X
ejpam-3253	261	17	:	:	PUNCT
ejpam-3253	262	1	x	x	PUNCT
ejpam-3253	262	2	−→	−→	NOUN
ejpam-3253	262	3	y	y	PROPN
ejpam-3253	262	4	is	be	AUX
ejpam-3253	262	5	a	a	DET
ejpam-3253	262	6	witness	witness	NOUN
ejpam-3253	262	7	of	of	ADP
ejpam-3253	262	8	the	the	DET
ejpam-3253	262	9	l	l	NOUN
ejpam-3253	262	10	-	-	NOUN
ejpam-3253	262	11	tychonoffness	tychonoffness	NOUN
ejpam-3253	262	12	of	of	ADP
ejpam-3253	262	13	x	x	PRON
ejpam-3253	262	14	,	,	PUNCT
ejpam-3253	262	15	then	then	ADV
ejpam-3253	262	16	f	f	PROPN
ejpam-3253	262	17	is	be	AUX
ejpam-3253	262	18	continuous	continuous	ADJ
ejpam-3253	262	19	.	.	PUNCT
ejpam-3253	263	1	theorem	theorem	NOUN
ejpam-3253	263	2	12	12	NUM
ejpam-3253	263	3	.	.	PUNCT
ejpam-3253	264	1	l	l	NOUN
ejpam-3253	264	2	-	-	NOUN
ejpam-3253	264	3	tychonoffness	tychonoffness	NOUN
ejpam-3253	264	4	is	be	AUX
ejpam-3253	264	5	a	a	DET
ejpam-3253	264	6	topological	topological	ADJ
ejpam-3253	264	7	property	property	NOUN
ejpam-3253	264	8	.	.	PUNCT
ejpam-3253	265	1	theorem	theorem	VERB
ejpam-3253	265	2	13	13	NUM
ejpam-3253	265	3	.	.	PUNCT
ejpam-3253	266	1	l	l	NOUN
ejpam-3253	266	2	-	-	NOUN
ejpam-3253	266	3	tychonoffness	tychonoffness	NOUN
ejpam-3253	266	4	is	be	AUX
ejpam-3253	266	5	an	an	DET
ejpam-3253	266	6	additive	additive	ADJ
ejpam-3253	266	7	property	property	NOUN
ejpam-3253	266	8	.	.	PUNCT
ejpam-3253	267	1	theorem	theorem	VERB
ejpam-3253	267	2	14	14	NUM
ejpam-3253	267	3	.	.	PUNCT
ejpam-3253	268	1	l	l	NOUN
ejpam-3253	268	2	-	-	NOUN
ejpam-3253	268	3	tychonoffness	tychonoffness	NOUN
ejpam-3253	268	4	is	be	AUX
ejpam-3253	268	5	a	a	DET
ejpam-3253	268	6	multiplicative	multiplicative	ADJ
ejpam-3253	268	7	property	property	NOUN
ejpam-3253	268	8	.	.	PUNCT
ejpam-3253	269	1	theorem	theorem	VERB
ejpam-3253	269	2	15	15	NUM
ejpam-3253	269	3	.	.	PUNCT
ejpam-3253	270	1	l	l	NOUN
ejpam-3253	270	2	-	-	NOUN
ejpam-3253	270	3	tychonoffness	tychonoffness	NOUN
ejpam-3253	270	4	is	be	AUX
ejpam-3253	270	5	a	a	DET
ejpam-3253	270	6	hereditary	hereditary	ADJ
ejpam-3253	270	7	property	property	NOUN
ejpam-3253	270	8	.	.	PUNCT
ejpam-3253	271	1	theorem	theorem	VERB
ejpam-3253	271	2	16	16	NUM
ejpam-3253	271	3	.	.	PUNCT
ejpam-3253	272	1	if	if	SCONJ
ejpam-3253	272	2	any	any	DET
ejpam-3253	272	3	countable	countable	ADJ
ejpam-3253	272	4	subspace	subspace	NOUN
ejpam-3253	272	5	of	of	ADP
ejpam-3253	272	6	a	a	DET
ejpam-3253	272	7	space	space	NOUN
ejpam-3253	272	8	x	x	PUNCT
ejpam-3253	272	9	is	be	AUX
ejpam-3253	272	10	discrete	discrete	ADJ
ejpam-3253	272	11	and	and	CCONJ
ejpam-3253	272	12	the	the	DET
ejpam-3253	272	13	only	only	ADJ
ejpam-3253	272	14	lindelöf	lindelöf	NOUN
ejpam-3253	272	15	subspaces	subspace	NOUN
ejpam-3253	272	16	are	be	AUX
ejpam-3253	272	17	the	the	DET
ejpam-3253	272	18	countable	countable	ADJ
ejpam-3253	272	19	subspaces	subspace	NOUN
ejpam-3253	272	20	,	,	PUNCT
ejpam-3253	272	21	then	then	ADV
ejpam-3253	272	22	x	x	PUNCT
ejpam-3253	272	23	is	be	AUX
ejpam-3253	272	24	l	l	NOUN
ejpam-3253	272	25	-	-	NOUN
ejpam-3253	272	26	tychonoff	tychonoff	NOUN
ejpam-3253	272	27	.	.	PUNCT
ejpam-3253	273	1	proof	proof	NOUN
ejpam-3253	273	2	.	.	PUNCT
ejpam-3253	274	1	let	let	VERB
ejpam-3253	274	2	y	y	NOUN
ejpam-3253	274	3	=	=	PUNCT
ejpam-3253	274	4	x	x	PUNCT
ejpam-3253	274	5	and	and	CCONJ
ejpam-3253	274	6	consider	consider	VERB
ejpam-3253	274	7	y	y	NOUN
ejpam-3253	274	8	with	with	ADP
ejpam-3253	274	9	the	the	DET
ejpam-3253	274	10	discrete	discrete	ADJ
ejpam-3253	274	11	topology	topology	NOUN
ejpam-3253	274	12	.	.	PUNCT
ejpam-3253	275	1	then	then	ADV
ejpam-3253	275	2	the	the	DET
ejpam-3253	275	3	identity	identity	NOUN
ejpam-3253	275	4	function	function	NOUN
ejpam-3253	275	5	from	from	ADP
ejpam-3253	275	6	x	x	PUNCT
ejpam-3253	275	7	onto	onto	ADP
ejpam-3253	275	8	y	y	PROPN
ejpam-3253	275	9	is	be	AUX
ejpam-3253	275	10	a	a	DET
ejpam-3253	275	11	bijective	bijective	ADJ
ejpam-3253	275	12	function	function	NOUN
ejpam-3253	275	13	.	.	PUNCT
ejpam-3253	276	1	if	if	SCONJ
ejpam-3253	276	2	k	k	PROPN
ejpam-3253	276	3	is	be	AUX
ejpam-3253	276	4	any	any	DET
ejpam-3253	276	5	lindelöf	lindelöf	NOUN
ejpam-3253	276	6	subspace	subspace	NOUN
ejpam-3253	276	7	of	of	ADP
ejpam-3253	276	8	x	x	PRON
ejpam-3253	276	9	,	,	PUNCT
ejpam-3253	276	10	then	then	ADV
ejpam-3253	276	11	,	,	PUNCT
ejpam-3253	276	12	by	by	ADP
ejpam-3253	276	13	assumption	assumption	NOUN
ejpam-3253	276	14	,	,	PUNCT
ejpam-3253	276	15	k	k	PROPN
ejpam-3253	276	16	is	be	AUX
ejpam-3253	276	17	countable	countable	ADJ
ejpam-3253	276	18	and	and	CCONJ
ejpam-3253	276	19	discrete	discrete	ADJ
ejpam-3253	276	20	,	,	PUNCT
ejpam-3253	276	21	hence	hence	ADV
ejpam-3253	276	22	the	the	DET
ejpam-3253	276	23	restriction	restriction	NOUN
ejpam-3253	276	24	of	of	ADP
ejpam-3253	276	25	the	the	DET
ejpam-3253	276	26	identity	identity	NOUN
ejpam-3253	276	27	function	function	NOUN
ejpam-3253	276	28	on	on	ADP
ejpam-3253	276	29	k	k	PROPN
ejpam-3253	276	30	onto	onto	ADP
ejpam-3253	276	31	k	k	PROPN
ejpam-3253	276	32	is	be	AUX
ejpam-3253	276	33	a	a	DET
ejpam-3253	276	34	homeomorphism	homeomorphism	NOUN
ejpam-3253	276	35	.	.	PUNCT
ejpam-3253	277	1	theorem	theorem	NOUN
ejpam-3253	277	2	17	17	NUM
ejpam-3253	277	3	.	.	PUNCT
ejpam-3253	278	1	if	if	SCONJ
ejpam-3253	278	2	x	x	PRON
ejpam-3253	278	3	is	be	AUX
ejpam-3253	278	4	c	c	NOUN
ejpam-3253	278	5	-	-	PUNCT
ejpam-3253	278	6	tychonoff	tychonoff	NOUN
ejpam-3253	278	7	space	space	NOUN
ejpam-3253	278	8	such	such	ADJ
ejpam-3253	278	9	that	that	SCONJ
ejpam-3253	278	10	each	each	DET
ejpam-3253	278	11	lindelöf	lindelöf	NOUN
ejpam-3253	278	12	subspace	subspace	NOUN
ejpam-3253	278	13	is	be	AUX
ejpam-3253	278	14	contained	contain	VERB
ejpam-3253	278	15	in	in	ADP
ejpam-3253	278	16	a	a	DET
ejpam-3253	278	17	compact	compact	ADJ
ejpam-3253	278	18	subspace	subspace	NOUN
ejpam-3253	278	19	,	,	PUNCT
ejpam-3253	278	20	then	then	ADV
ejpam-3253	278	21	x	x	PUNCT
ejpam-3253	278	22	is	be	AUX
ejpam-3253	278	23	l	l	NOUN
ejpam-3253	278	24	-	-	NOUN
ejpam-3253	278	25	tychonoff	tychonoff	NOUN
ejpam-3253	278	26	.	.	PUNCT
ejpam-3253	279	1	proof	proof	NOUN
ejpam-3253	279	2	.	.	PUNCT
ejpam-3253	280	1	assume	assume	VERB
ejpam-3253	280	2	that	that	SCONJ
ejpam-3253	280	3	x	x	PRON
ejpam-3253	280	4	is	be	AUX
ejpam-3253	280	5	c	c	NOUN
ejpam-3253	280	6	-	-	PUNCT
ejpam-3253	280	7	tychonoff	tychonoff	NOUN
ejpam-3253	280	8	and	and	CCONJ
ejpam-3253	280	9	if	if	SCONJ
ejpam-3253	280	10	l	l	NOUN
ejpam-3253	280	11	is	be	AUX
ejpam-3253	280	12	any	any	DET
ejpam-3253	280	13	lindelöf	lindelöf	NOUN
ejpam-3253	280	14	subspace	subspace	NOUN
ejpam-3253	280	15	of	of	ADP
ejpam-3253	280	16	x	x	PRON
ejpam-3253	280	17	,	,	PUNCT
ejpam-3253	280	18	then	then	ADV
ejpam-3253	280	19	there	there	PRON
ejpam-3253	280	20	exists	exist	VERB
ejpam-3253	280	21	a	a	DET
ejpam-3253	280	22	compact	compact	ADJ
ejpam-3253	280	23	subspace	subspace	NOUN
ejpam-3253	280	24	k	k	PROPN
ejpam-3253	280	25	with	with	ADP
ejpam-3253	280	26	l	l	PROPN
ejpam-3253	280	27	⊆	⊆	NUM
ejpam-3253	280	28	k.	k.	NOUN
ejpam-3253	280	29	let	let	VERB
ejpam-3253	280	30	f	f	PRON
ejpam-3253	280	31	be	be	AUX
ejpam-3253	280	32	a	a	DET
ejpam-3253	280	33	bijective	bijective	ADJ
ejpam-3253	280	34	function	function	NOUN
ejpam-3253	280	35	from	from	ADP
ejpam-3253	280	36	x	x	PRON
ejpam-3253	280	37	onto	onto	ADP
ejpam-3253	280	38	a	a	DET
ejpam-3253	280	39	tychonoff	tychonoff	NOUN
ejpam-3253	280	40	space	space	NOUN
ejpam-3253	280	41	y	y	PRON
ejpam-3253	280	42	such	such	ADJ
ejpam-3253	280	43	that	that	SCONJ
ejpam-3253	280	44	the	the	DET
ejpam-3253	280	45	restriction	restriction	NOUN
ejpam-3253	280	46	f|c	f|c	NOUN
ejpam-3253	280	47	:	:	PUNCT
ejpam-3253	281	1	c	c	AUX
ejpam-3253	281	2	−→	−→	NOUN
ejpam-3253	281	3	f(c	f(c	PROPN
ejpam-3253	281	4	)	)	PUNCT
ejpam-3253	281	5	is	be	AUX
ejpam-3253	281	6	a	a	DET
ejpam-3253	281	7	homeomorphism	homeomorphism	NOUN
ejpam-3253	281	8	for	for	ADP
ejpam-3253	281	9	each	each	DET
ejpam-3253	281	10	compact	compact	ADJ
ejpam-3253	281	11	subspace	subspace	NOUN
ejpam-3253	281	12	c	c	PROPN
ejpam-3253	281	13	of	of	ADP
ejpam-3253	281	14	x.	x.	NOUN
ejpam-3253	281	15	now	now	ADV
ejpam-3253	281	16	,	,	PUNCT
ejpam-3253	281	17	let	let	VERB
ejpam-3253	281	18	l	l	NOUN
ejpam-3253	281	19	be	be	AUX
ejpam-3253	281	20	any	any	DET
ejpam-3253	281	21	lindelöf	lindelöf	NOUN
ejpam-3253	281	22	subspace	subspace	NOUN
ejpam-3253	281	23	of	of	ADP
ejpam-3253	281	24	x.	x.	PROPN
ejpam-3253	281	25	pick	pick	VERB
ejpam-3253	281	26	a	a	DET
ejpam-3253	281	27	compact	compact	ADJ
ejpam-3253	281	28	subspace	subspace	NOUN
ejpam-3253	281	29	k	k	PROPN
ejpam-3253	281	30	of	of	ADP
ejpam-3253	281	31	x	x	SYM
ejpam-3253	281	32	where	where	SCONJ
ejpam-3253	281	33	l	l	NOUN
ejpam-3253	281	34	⊆	⊆	NUM
ejpam-3253	281	35	k	k	NOUN
ejpam-3253	281	36	,	,	PUNCT
ejpam-3253	281	37	then	then	ADV
ejpam-3253	281	38	f|k	f|k	PUNCT
ejpam-3253	281	39	:	:	PUNCT
ejpam-3253	281	40	k	k	X
ejpam-3253	281	41	−→	−→	NOUN
ejpam-3253	281	42	f(k	f(k	VERB
ejpam-3253	281	43	)	)	PUNCT
ejpam-3253	281	44	is	be	AUX
ejpam-3253	281	45	a	a	DET
ejpam-3253	281	46	homeomorphism	homeomorphism	NOUN
ejpam-3253	281	47	,	,	PUNCT
ejpam-3253	281	48	thus	thus	ADV
ejpam-3253	281	49	f|l	f|l	NOUN
ejpam-3253	281	50	:	:	PUNCT
ejpam-3253	282	1	l	l	PUNCT
ejpam-3253	282	2	−→	−→	NOUN
ejpam-3253	282	3	f(l	f(l	PROPN
ejpam-3253	282	4	)	)	PUNCT
ejpam-3253	282	5	is	be	AUX
ejpam-3253	282	6	a	a	DET
ejpam-3253	282	7	homeomorphism	homeomorphism	NOUN
ejpam-3253	282	8	as	as	ADP
ejpam-3253	282	9	(	(	PUNCT
ejpam-3253	282	10	f|k)|l	f|k)|l	PROPN
ejpam-3253	282	11	=	=	PUNCT
ejpam-3253	282	12	f|l	f|l	PROPN
ejpam-3253	282	13	.	.	PUNCT
ejpam-3253	283	1	now	now	ADV
ejpam-3253	283	2	,	,	PUNCT
ejpam-3253	283	3	we	we	PRON
ejpam-3253	283	4	study	study	VERB
ejpam-3253	283	5	some	some	DET
ejpam-3253	283	6	relationships	relationship	NOUN
ejpam-3253	283	7	between	between	ADP
ejpam-3253	283	8	c	c	NOUN
ejpam-3253	283	9	-	-	PUNCT
ejpam-3253	283	10	tychonoffness	tychonoffness	NOUN
ejpam-3253	283	11	and	and	CCONJ
ejpam-3253	283	12	some	some	DET
ejpam-3253	283	13	other	other	ADJ
ejpam-3253	283	14	properties	property	NOUN
ejpam-3253	283	15	.	.	PUNCT
ejpam-3253	284	1	s.	s.	PROPN
ejpam-3253	284	2	alzahrani	alzahrani	PROPN
ejpam-3253	284	3	/	/	SYM
ejpam-3253	284	4	eur	eur	PROPN
ejpam-3253	284	5	.	.	PUNCT
ejpam-3253	285	1	j.	j.	PROPN
ejpam-3253	285	2	pure	pure	PROPN
ejpam-3253	285	3	appl	appl	PROPN
ejpam-3253	285	4	.	.	PROPN
ejpam-3253	285	5	math	math	PROPN
ejpam-3253	285	6	,	,	PUNCT
ejpam-3253	285	7	11	11	NUM
ejpam-3253	285	8	(	(	PUNCT
ejpam-3253	285	9	3	3	NUM
ejpam-3253	285	10	)	)	PUNCT
ejpam-3253	285	11	(	(	PUNCT
ejpam-3253	285	12	2018	2018	NUM
ejpam-3253	285	13	)	)	PUNCT
ejpam-3253	285	14	,	,	PUNCT
ejpam-3253	285	15	882	882	NUM
ejpam-3253	285	16	-	-	SYM
ejpam-3253	285	17	892	892	NUM
ejpam-3253	285	18	890	890	NUM
ejpam-3253	285	19	recall	recall	NOUN
ejpam-3253	285	20	that	that	SCONJ
ejpam-3253	285	21	a	a	DET
ejpam-3253	285	22	topological	topological	ADJ
ejpam-3253	285	23	space	space	NOUN
ejpam-3253	285	24	x	x	PUNCT
ejpam-3253	285	25	is	be	AUX
ejpam-3253	285	26	called	call	VERB
ejpam-3253	285	27	c	c	NOUN
ejpam-3253	285	28	-	-	PUNCT
ejpam-3253	285	29	regular	regular	ADJ
ejpam-3253	285	30	if	if	SCONJ
ejpam-3253	285	31	there	there	PRON
ejpam-3253	285	32	exist	exist	VERB
ejpam-3253	285	33	a	a	DET
ejpam-3253	285	34	one	one	NUM
ejpam-3253	285	35	-	-	PUNCT
ejpam-3253	285	36	to	to	ADP
ejpam-3253	285	37	-	-	PUNCT
ejpam-3253	285	38	one	one	NUM
ejpam-3253	285	39	function	function	NOUN
ejpam-3253	285	40	f	f	NOUN
ejpam-3253	285	41	from	from	ADP
ejpam-3253	285	42	x	x	PRON
ejpam-3253	285	43	onto	onto	ADP
ejpam-3253	285	44	a	a	DET
ejpam-3253	285	45	regular	regular	ADJ
ejpam-3253	285	46	space	space	NOUN
ejpam-3253	285	47	y	y	NOUN
ejpam-3253	285	48	such	such	ADJ
ejpam-3253	285	49	that	that	SCONJ
ejpam-3253	285	50	the	the	DET
ejpam-3253	285	51	restriction	restriction	NOUN
ejpam-3253	285	52	f|k	f|k	PUNCT
ejpam-3253	285	53	:	:	PUNCT
ejpam-3253	286	1	k	k	X
ejpam-3253	286	2	−→	−→	NOUN
ejpam-3253	286	3	f(k	f(k	VERB
ejpam-3253	286	4	)	)	PUNCT
ejpam-3253	286	5	is	be	AUX
ejpam-3253	286	6	a	a	DET
ejpam-3253	286	7	homeomorphism	homeomorphism	NOUN
ejpam-3253	286	8	for	for	ADP
ejpam-3253	286	9	each	each	DET
ejpam-3253	286	10	compact	compact	ADJ
ejpam-3253	286	11	subspace	subspace	NOUN
ejpam-3253	286	12	k	k	PROPN
ejpam-3253	287	1	⊆	⊆	NUM
ejpam-3253	287	2	x	x	PUNCT
ejpam-3253	288	1	[	[	X
ejpam-3253	288	2	5	5	NUM
ejpam-3253	288	3	]	]	PUNCT
ejpam-3253	288	4	.	.	PUNCT
ejpam-3253	289	1	any	any	DET
ejpam-3253	289	2	c	c	NOUN
ejpam-3253	289	3	-	-	PUNCT
ejpam-3253	289	4	tychonoff	tychonoff	NOUN
ejpam-3253	289	5	space	space	NOUN
ejpam-3253	289	6	is	be	AUX
ejpam-3253	289	7	c	c	NOUN
ejpam-3253	289	8	-	-	ADJ
ejpam-3253	289	9	regular	regular	ADJ
ejpam-3253	289	10	space	space	NOUN
ejpam-3253	289	11	,	,	PUNCT
ejpam-3253	289	12	but	but	CCONJ
ejpam-3253	289	13	the	the	DET
ejpam-3253	289	14	converse	converse	NOUN
ejpam-3253	289	15	is	be	AUX
ejpam-3253	289	16	not	not	PART
ejpam-3253	289	17	true	true	ADJ
ejpam-3253	289	18	in	in	ADP
ejpam-3253	289	19	general	general	ADJ
ejpam-3253	289	20	.	.	PUNCT
ejpam-3253	290	1	for	for	ADP
ejpam-3253	290	2	example	example	NOUN
ejpam-3253	290	3	,	,	PUNCT
ejpam-3253	290	4	any	any	DET
ejpam-3253	290	5	indiscrete	indiscrete	ADJ
ejpam-3253	290	6	space	space	NOUN
ejpam-3253	290	7	which	which	PRON
ejpam-3253	290	8	has	have	VERB
ejpam-3253	290	9	more	more	ADJ
ejpam-3253	290	10	than	than	ADP
ejpam-3253	290	11	one	one	NUM
ejpam-3253	290	12	element	element	NOUN
ejpam-3253	290	13	is	be	AUX
ejpam-3253	290	14	an	an	DET
ejpam-3253	290	15	example	example	NOUN
ejpam-3253	290	16	of	of	ADP
ejpam-3253	290	17	c	c	NOUN
ejpam-3253	290	18	-	-	PUNCT
ejpam-3253	290	19	regular	regular	ADJ
ejpam-3253	290	20	space	space	NOUN
ejpam-3253	290	21	which	which	PRON
ejpam-3253	290	22	is	be	AUX
ejpam-3253	290	23	not	not	PART
ejpam-3253	290	24	c	c	NOUN
ejpam-3253	290	25	-	-	PUNCT
ejpam-3253	290	26	tychonoff	tychonoff	NOUN
ejpam-3253	290	27	by	by	ADP
ejpam-3253	290	28	theorem	theorem	NOUN
ejpam-3253	290	29	3	3	PROPN
ejpam-3253	290	30	.	.	NOUN
ejpam-3253	290	31	recall	recall	VERB
ejpam-3253	290	32	that	that	SCONJ
ejpam-3253	290	33	a	a	DET
ejpam-3253	290	34	topological	topological	ADJ
ejpam-3253	290	35	space	space	NOUN
ejpam-3253	290	36	(	(	PUNCT
ejpam-3253	290	37	x	x	X
ejpam-3253	290	38	,	,	PUNCT
ejpam-3253	290	39	τ	τ	PROPN
ejpam-3253	290	40	)	)	PUNCT
ejpam-3253	290	41	is	be	AUX
ejpam-3253	290	42	called	call	VERB
ejpam-3253	290	43	epinormal	epinormal	NOUN
ejpam-3253	290	44	if	if	SCONJ
ejpam-3253	290	45	there	there	PRON
ejpam-3253	290	46	is	be	VERB
ejpam-3253	290	47	a	a	DET
ejpam-3253	290	48	coarser	coarse	ADJ
ejpam-3253	290	49	topology	topology	NOUN
ejpam-3253	290	50	τ	τ	NOUN
ejpam-3253	290	51	′	′	NOUN
ejpam-3253	290	52	on	on	ADP
ejpam-3253	290	53	x	x	INTJ
ejpam-3253	290	54	such	such	ADJ
ejpam-3253	290	55	that	that	SCONJ
ejpam-3253	290	56	(	(	PUNCT
ejpam-3253	290	57	x	x	X
ejpam-3253	290	58	,	,	PUNCT
ejpam-3253	290	59	τ	τ	PROPN
ejpam-3253	290	60	′	′	NUM
ejpam-3253	290	61	)	)	PUNCT
ejpam-3253	290	62	is	be	AUX
ejpam-3253	290	63	t4	t4	PROPN
ejpam-3253	290	64	[	[	X
ejpam-3253	290	65	3	3	NUM
ejpam-3253	290	66	]	]	PUNCT
ejpam-3253	290	67	.	.	PUNCT
ejpam-3253	291	1	by	by	ADP
ejpam-3253	291	2	a	a	DET
ejpam-3253	291	3	similar	similar	ADJ
ejpam-3253	291	4	proof	proof	NOUN
ejpam-3253	291	5	as	as	ADP
ejpam-3253	291	6	that	that	PRON
ejpam-3253	291	7	of	of	ADP
ejpam-3253	291	8	theorem	theorem	NOUN
ejpam-3253	291	9	1	1	NUM
ejpam-3253	291	10	above	above	ADV
ejpam-3253	291	11	,	,	PUNCT
ejpam-3253	291	12	we	we	PRON
ejpam-3253	291	13	can	can	AUX
ejpam-3253	291	14	prove	prove	VERB
ejpam-3253	291	15	the	the	DET
ejpam-3253	291	16	following	follow	VERB
ejpam-3253	291	17	corollary	corollary	ADJ
ejpam-3253	291	18	:	:	PUNCT
ejpam-3253	291	19	corollary	corollary	ADJ
ejpam-3253	291	20	6	6	NUM
ejpam-3253	291	21	.	.	PUNCT
ejpam-3253	292	1	any	any	DET
ejpam-3253	292	2	epinormal	epinormal	NOUN
ejpam-3253	292	3	space	space	NOUN
ejpam-3253	292	4	is	be	AUX
ejpam-3253	292	5	c	c	NOUN
ejpam-3253	292	6	-	-	PUNCT
ejpam-3253	292	7	tychonoff	tychonoff	NOUN
ejpam-3253	292	8	.	.	PUNCT
ejpam-3253	293	1	r	r	NOUN
ejpam-3253	293	2	with	with	ADP
ejpam-3253	293	3	the	the	DET
ejpam-3253	293	4	countable	countable	ADJ
ejpam-3253	293	5	complement	complement	NOUN
ejpam-3253	293	6	topology	topology	NOUN
ejpam-3253	293	7	cc	cc	ADP
ejpam-3253	294	1	[	[	X
ejpam-3253	294	2	16	16	NUM
ejpam-3253	294	3	]	]	PUNCT
ejpam-3253	294	4	,	,	PUNCT
ejpam-3253	294	5	is	be	AUX
ejpam-3253	294	6	an	an	DET
ejpam-3253	294	7	example	example	NOUN
ejpam-3253	294	8	of	of	ADP
ejpam-3253	294	9	c	c	NOUN
ejpam-3253	294	10	-	-	PUNCT
ejpam-3253	294	11	tychonoff	tychonoff	NOUN
ejpam-3253	294	12	space	space	NOUN
ejpam-3253	294	13	which	which	PRON
ejpam-3253	294	14	is	be	AUX
ejpam-3253	294	15	not	not	PART
ejpam-3253	294	16	epinormal	epinormal	ADJ
ejpam-3253	294	17	because	because	SCONJ
ejpam-3253	294	18	(	(	PUNCT
ejpam-3253	294	19	r	r	NOUN
ejpam-3253	294	20	,	,	PUNCT
ejpam-3253	294	21	cc	cc	NOUN
ejpam-3253	294	22	)	)	PUNCT
ejpam-3253	294	23	is	be	AUX
ejpam-3253	294	24	not	not	PART
ejpam-3253	294	25	t2	t2	NOUN
ejpam-3253	294	26	and	and	CCONJ
ejpam-3253	294	27	any	any	DET
ejpam-3253	294	28	epinormal	epinormal	NOUN
ejpam-3253	294	29	space	space	NOUN
ejpam-3253	294	30	is	be	AUX
ejpam-3253	294	31	t2	t2	NOUN
ejpam-3253	294	32	[	[	X
ejpam-3253	294	33	3	3	NUM
ejpam-3253	294	34	]	]	PUNCT
ejpam-3253	294	35	.	.	PUNCT
ejpam-3253	295	1	let	let	VERB
ejpam-3253	295	2	x	x	PRON
ejpam-3253	295	3	be	be	AUX
ejpam-3253	295	4	any	any	DET
ejpam-3253	295	5	hausdorff	hausdorff	NOUN
ejpam-3253	295	6	non	non	ADJ
ejpam-3253	295	7	-	-	ADJ
ejpam-3253	295	8	k	k	ADJ
ejpam-3253	295	9	-	-	NOUN
ejpam-3253	295	10	space	space	NOUN
ejpam-3253	295	11	.	.	PUNCT
ejpam-3253	296	1	let	let	VERB
ejpam-3253	296	2	kx	kx	PROPN
ejpam-3253	296	3	=	=	PUNCT
ejpam-3253	296	4	x.	x.	NOUN
ejpam-3253	296	5	define	define	VERB
ejpam-3253	296	6	a	a	DET
ejpam-3253	296	7	topology	topology	NOUN
ejpam-3253	296	8	on	on	ADP
ejpam-3253	296	9	kx	kx	PROPN
ejpam-3253	296	10	as	as	SCONJ
ejpam-3253	296	11	follows	follow	VERB
ejpam-3253	296	12	:	:	PUNCT
ejpam-3253	296	13	a	a	DET
ejpam-3253	296	14	subset	subset	NOUN
ejpam-3253	296	15	of	of	ADP
ejpam-3253	296	16	kx	kx	PROPN
ejpam-3253	296	17	is	be	AUX
ejpam-3253	296	18	open	open	ADJ
ejpam-3253	296	19	if	if	SCONJ
ejpam-3253	297	1	and	and	CCONJ
ejpam-3253	297	2	only	only	ADV
ejpam-3253	297	3	if	if	SCONJ
ejpam-3253	297	4	its	its	PRON
ejpam-3253	297	5	intersection	intersection	NOUN
ejpam-3253	297	6	with	with	ADP
ejpam-3253	297	7	any	any	DET
ejpam-3253	297	8	compact	compact	ADJ
ejpam-3253	297	9	subspace	subspace	NOUN
ejpam-3253	297	10	c	c	PROPN
ejpam-3253	297	11	of	of	ADP
ejpam-3253	297	12	the	the	DET
ejpam-3253	297	13	space	space	NOUN
ejpam-3253	297	14	x	x	PUNCT
ejpam-3253	297	15	is	be	AUX
ejpam-3253	297	16	open	open	ADJ
ejpam-3253	297	17	in	in	ADP
ejpam-3253	297	18	c.	c.	PROPN
ejpam-3253	297	19	kx	kx	PROPN
ejpam-3253	297	20	with	with	ADP
ejpam-3253	297	21	this	this	DET
ejpam-3253	297	22	topology	topology	NOUN
ejpam-3253	297	23	is	be	AUX
ejpam-3253	297	24	hausdorff	hausdorff	NOUN
ejpam-3253	297	25	and	and	CCONJ
ejpam-3253	297	26	k	k	NOUN
ejpam-3253	297	27	-	-	NOUN
ejpam-3253	297	28	space	space	NOUN
ejpam-3253	297	29	such	such	ADJ
ejpam-3253	297	30	that	that	SCONJ
ejpam-3253	297	31	x	x	PROPN
ejpam-3253	297	32	and	and	CCONJ
ejpam-3253	297	33	kx	kx	PROPN
ejpam-3253	297	34	have	have	VERB
ejpam-3253	297	35	the	the	DET
ejpam-3253	297	36	same	same	ADJ
ejpam-3253	297	37	compact	compact	ADJ
ejpam-3253	297	38	subspace	subspace	NOUN
ejpam-3253	297	39	and	and	CCONJ
ejpam-3253	297	40	the	the	DET
ejpam-3253	297	41	same	same	ADJ
ejpam-3253	297	42	topology	topology	NOUN
ejpam-3253	297	43	on	on	ADP
ejpam-3253	297	44	these	these	DET
ejpam-3253	297	45	subspace	subspace	NOUN
ejpam-3253	298	1	[	[	X
ejpam-3253	298	2	6	6	NUM
ejpam-3253	298	3	]	]	PUNCT
ejpam-3253	298	4	,	,	PUNCT
ejpam-3253	298	5	we	we	PRON
ejpam-3253	298	6	conclude	conclude	VERB
ejpam-3253	298	7	the	the	DET
ejpam-3253	298	8	following	following	NOUN
ejpam-3253	298	9	:	:	PUNCT
ejpam-3253	298	10	theorem	theorem	NOUN
ejpam-3253	298	11	18	18	NUM
ejpam-3253	298	12	.	.	PUNCT
ejpam-3253	299	1	if	if	SCONJ
ejpam-3253	299	2	x	x	PRON
ejpam-3253	299	3	is	be	AUX
ejpam-3253	299	4	hausdorff	hausdorff	NOUN
ejpam-3253	299	5	but	but	CCONJ
ejpam-3253	299	6	not	not	PART
ejpam-3253	299	7	k	k	NOUN
ejpam-3253	299	8	-	-	NOUN
ejpam-3253	299	9	space	space	NOUN
ejpam-3253	299	10	,	,	PUNCT
ejpam-3253	299	11	then	then	ADV
ejpam-3253	299	12	x	x	PUNCT
ejpam-3253	299	13	is	be	AUX
ejpam-3253	299	14	c	c	NOUN
ejpam-3253	299	15	-	-	PUNCT
ejpam-3253	299	16	tychonoff	tychonoff	NOUN
ejpam-3253	299	17	if	if	SCONJ
ejpam-3253	300	1	and	and	CCONJ
ejpam-3253	300	2	only	only	ADV
ejpam-3253	300	3	if	if	SCONJ
ejpam-3253	300	4	kx	kx	PROPN
ejpam-3253	300	5	is	be	AUX
ejpam-3253	300	6	c	c	NOUN
ejpam-3253	300	7	-	-	PUNCT
ejpam-3253	300	8	tychonoff	tychonoff	NOUN
ejpam-3253	300	9	.	.	PUNCT
ejpam-3253	301	1	c	c	X
ejpam-3253	301	2	-	-	PUNCT
ejpam-3253	301	3	tychonoffness	tychonoffness	NOUN
ejpam-3253	301	4	and	and	CCONJ
ejpam-3253	301	5	σ	σ	PROPN
ejpam-3253	301	6	-	-	PUNCT
ejpam-3253	301	7	compactness	compactness	NOUN
ejpam-3253	301	8	are	be	AUX
ejpam-3253	301	9	independent	independent	ADJ
ejpam-3253	301	10	from	from	ADP
ejpam-3253	301	11	each	each	DET
ejpam-3253	301	12	other	other	ADJ
ejpam-3253	301	13	.	.	PUNCT
ejpam-3253	302	1	for	for	ADP
ejpam-3253	302	2	example	example	NOUN
ejpam-3253	302	3	the	the	DET
ejpam-3253	302	4	rational	rational	ADJ
ejpam-3253	302	5	sequence	sequence	NOUN
ejpam-3253	302	6	space	space	NOUN
ejpam-3253	302	7	[	[	X
ejpam-3253	302	8	16	16	NUM
ejpam-3253	302	9	]	]	PUNCT
ejpam-3253	302	10	is	be	AUX
ejpam-3253	302	11	c	c	NOUN
ejpam-3253	302	12	-	-	PUNCT
ejpam-3253	302	13	tychonoff	tychonoff	NOUN
ejpam-3253	302	14	being	being	NOUN
ejpam-3253	302	15	tychonoff	tychonoff	NOUN
ejpam-3253	302	16	,	,	PUNCT
ejpam-3253	302	17	but	but	CCONJ
ejpam-3253	302	18	not	not	PART
ejpam-3253	302	19	σ	σ	NOUN
ejpam-3253	302	20	-	-	NOUN
ejpam-3253	302	21	compact	compact	ADJ
ejpam-3253	302	22	.	.	PUNCT
ejpam-3253	303	1	r	r	NOUN
ejpam-3253	303	2	with	with	ADP
ejpam-3253	303	3	the	the	DET
ejpam-3253	303	4	finite	finite	PROPN
ejpam-3253	303	5	complement	complement	NOUN
ejpam-3253	303	6	topology	topology	NOUN
ejpam-3253	303	7	is	be	AUX
ejpam-3253	303	8	not	not	PART
ejpam-3253	303	9	c	c	NOUN
ejpam-3253	303	10	-	-	PUNCT
ejpam-3253	303	11	tychonoff	tychonoff	NOUN
ejpam-3253	303	12	by	by	ADP
ejpam-3253	303	13	theorem	theorem	NOUN
ejpam-3253	303	14	3	3	NUM
ejpam-3253	303	15	,	,	PUNCT
ejpam-3253	303	16	but	but	CCONJ
ejpam-3253	303	17	it	it	PRON
ejpam-3253	303	18	is	be	AUX
ejpam-3253	303	19	σ	σ	ADJ
ejpam-3253	303	20	-	-	ADJ
ejpam-3253	303	21	compact	compact	ADJ
ejpam-3253	303	22	being	being	NOUN
ejpam-3253	303	23	compact	compact	ADJ
ejpam-3253	303	24	.	.	PUNCT
ejpam-3253	304	1	any	any	DET
ejpam-3253	304	2	pseudocompact	pseudocompact	NOUN
ejpam-3253	304	3	is	be	AUX
ejpam-3253	304	4	c	c	NOUN
ejpam-3253	304	5	-	-	PUNCT
ejpam-3253	304	6	tychonoff	tychonoff	NOUN
ejpam-3253	304	7	being	being	NOUN
ejpam-3253	304	8	tychonoff	tychonoff	NOUN
ejpam-3253	304	9	,	,	PUNCT
ejpam-3253	304	10	but	but	CCONJ
ejpam-3253	304	11	the	the	DET
ejpam-3253	304	12	converse	converse	NOUN
ejpam-3253	304	13	is	be	AUX
ejpam-3253	304	14	not	not	PART
ejpam-3253	304	15	true	true	ADJ
ejpam-3253	304	16	,	,	PUNCT
ejpam-3253	304	17	for	for	ADP
ejpam-3253	304	18	example	example	NOUN
ejpam-3253	304	19	sorgenfrey	sorgenfrey	PROPN
ejpam-3253	304	20	line	line	PROPN
ejpam-3253	304	21	square	square	PROPN
ejpam-3253	304	22	topology	topology	NOUN
ejpam-3253	305	1	[	[	X
ejpam-3253	305	2	16	16	NUM
ejpam-3253	305	3	]	]	PUNCT
ejpam-3253	305	4	,	,	PUNCT
ejpam-3253	305	5	it	it	PRON
ejpam-3253	305	6	is	be	AUX
ejpam-3253	305	7	c	c	NOUN
ejpam-3253	305	8	-	-	PUNCT
ejpam-3253	305	9	tychonoff	tychonoff	NOUN
ejpam-3253	305	10	being	being	NOUN
ejpam-3253	305	11	tychonoff	tychonoff	NOUN
ejpam-3253	305	12	but	but	CCONJ
ejpam-3253	305	13	not	not	PART
ejpam-3253	305	14	pseudocompact	pseudocompact	NOUN
ejpam-3253	305	15	.	.	PUNCT
ejpam-3253	306	1	also	also	ADV
ejpam-3253	306	2	any	any	DET
ejpam-3253	306	3	zero	zero	NUM
ejpam-3253	306	4	-	-	PUNCT
ejpam-3253	306	5	dimensional	dimensional	ADJ
ejpam-3253	306	6	space	space	NOUN
ejpam-3253	306	7	is	be	AUX
ejpam-3253	306	8	c	c	NOUN
ejpam-3253	306	9	-	-	PUNCT
ejpam-3253	306	10	tychonoff	tychonoff	NOUN
ejpam-3253	306	11	,	,	PUNCT
ejpam-3253	306	12	but	but	CCONJ
ejpam-3253	306	13	the	the	DET
ejpam-3253	306	14	converse	converse	NOUN
ejpam-3253	306	15	is	be	AUX
ejpam-3253	306	16	not	not	PART
ejpam-3253	306	17	true	true	ADJ
ejpam-3253	306	18	,	,	PUNCT
ejpam-3253	306	19	for	for	ADP
ejpam-3253	306	20	example	example	NOUN
ejpam-3253	306	21	niemytzki	niemytzki	PROPN
ejpam-3253	306	22	’s	’s	PART
ejpam-3253	306	23	tangent	tangent	NOUN
ejpam-3253	306	24	disc	disc	NOUN
ejpam-3253	306	25	topology	topology	NOUN
ejpam-3253	307	1	[	[	X
ejpam-3253	307	2	16	16	NUM
ejpam-3253	307	3	]	]	PUNCT
ejpam-3253	307	4	,	,	PUNCT
ejpam-3253	307	5	it	it	PRON
ejpam-3253	307	6	is	be	AUX
ejpam-3253	307	7	c	c	NOUN
ejpam-3253	307	8	-	-	PUNCT
ejpam-3253	307	9	tychonoff	tychonoff	NOUN
ejpam-3253	307	10	being	being	NOUN
ejpam-3253	307	11	tychonoff	tychonoff	NOUN
ejpam-3253	307	12	but	but	CCONJ
ejpam-3253	307	13	not	not	PART
ejpam-3253	307	14	zero	zero	NUM
ejpam-3253	307	15	-	-	PUNCT
ejpam-3253	307	16	dimensional	dimensional	ADJ
ejpam-3253	307	17	because	because	SCONJ
ejpam-3253	307	18	it	it	PRON
ejpam-3253	307	19	is	be	AUX
ejpam-3253	307	20	connected	connect	VERB
ejpam-3253	307	21	.	.	PUNCT
ejpam-3253	308	1	let	let	VERB
ejpam-3253	308	2	x	x	PRON
ejpam-3253	308	3	be	be	AUX
ejpam-3253	308	4	any	any	DET
ejpam-3253	308	5	topological	topological	ADJ
ejpam-3253	308	6	space	space	NOUN
ejpam-3253	308	7	.	.	PUNCT
ejpam-3253	309	1	let	let	VERB
ejpam-3253	309	2	x	x	X
ejpam-3253	309	3	′	′	NUM
ejpam-3253	310	1	=	=	PUNCT
ejpam-3253	310	2	x	x	SYM
ejpam-3253	310	3	×	×	NOUN
ejpam-3253	310	4	{	{	PUNCT
ejpam-3253	310	5	a	a	NOUN
ejpam-3253	310	6	}	}	PUNCT
ejpam-3253	310	7	.	.	PUNCT
ejpam-3253	311	1	note	note	VERB
ejpam-3253	311	2	that	that	SCONJ
ejpam-3253	311	3	x	x	NOUN
ejpam-3253	311	4	∩	∩	NOUN
ejpam-3253	311	5	x	x	SYM
ejpam-3253	311	6	′	′	NUM
ejpam-3253	311	7	=	=	PUNCT
ejpam-3253	311	8	∅.	∅.	AUX
ejpam-3253	311	9	let	let	VERB
ejpam-3253	311	10	a(x	a(x	NOUN
ejpam-3253	311	11	)	)	PUNCT
ejpam-3253	311	12	=	=	PUNCT
ejpam-3253	311	13	x	x	SYM
ejpam-3253	311	14	∪x	∪x	X
ejpam-3253	311	15	′.	′.	NOUN
ejpam-3253	311	16	for	for	ADP
ejpam-3253	311	17	simplicity	simplicity	NOUN
ejpam-3253	311	18	,	,	PUNCT
ejpam-3253	311	19	for	for	ADP
ejpam-3253	311	20	an	an	DET
ejpam-3253	311	21	element	element	NOUN
ejpam-3253	311	22	x	x	SYM
ejpam-3253	311	23	∈	∈	PROPN
ejpam-3253	311	24	x	x	NOUN
ejpam-3253	311	25	,	,	PUNCT
ejpam-3253	311	26	we	we	PRON
ejpam-3253	311	27	will	will	AUX
ejpam-3253	311	28	denote	denote	VERB
ejpam-3253	311	29	the	the	DET
ejpam-3253	311	30	element	element	NOUN
ejpam-3253	311	31	〈	〈	PROPN
ejpam-3253	311	32	x	x	PROPN
ejpam-3253	311	33	,	,	PUNCT
ejpam-3253	311	34	a	a	DET
ejpam-3253	311	35	〉	〉	NOUN
ejpam-3253	311	36	in	in	ADP
ejpam-3253	311	37	x	x	X
ejpam-3253	311	38	′	′	NUM
ejpam-3253	311	39	by	by	ADP
ejpam-3253	311	40	x′	x′	PROPN
ejpam-3253	311	41	and	and	CCONJ
ejpam-3253	311	42	for	for	ADP
ejpam-3253	311	43	a	a	DET
ejpam-3253	311	44	subset	subset	NOUN
ejpam-3253	311	45	e	e	NOUN
ejpam-3253	311	46	⊆	⊆	NUM
ejpam-3253	311	47	x	x	PART
ejpam-3253	311	48	let	let	VERB
ejpam-3253	311	49	e′	e′	X
ejpam-3253	311	50	=	=	SYM
ejpam-3253	311	51	{	{	PUNCT
ejpam-3253	311	52	x′	x′	PROPN
ejpam-3253	311	53	:	:	PUNCT
ejpam-3253	312	1	x	x	SYM
ejpam-3253	312	2	∈	∈	NOUN
ejpam-3253	312	3	e	e	NOUN
ejpam-3253	312	4	}	}	PUNCT
ejpam-3253	312	5	=	=	SYM
ejpam-3253	312	6	e	e	X
ejpam-3253	312	7	×	×	NOUN
ejpam-3253	312	8	{	{	PUNCT
ejpam-3253	312	9	a	a	NOUN
ejpam-3253	312	10	}	}	PUNCT
ejpam-3253	312	11	⊆	⊆	NUM
ejpam-3253	312	12	x	x	NOUN
ejpam-3253	312	13	′.	′.	NOUN
ejpam-3253	312	14	for	for	ADP
ejpam-3253	312	15	each	each	DET
ejpam-3253	312	16	x′	x′	PROPN
ejpam-3253	312	17	∈	∈	PROPN
ejpam-3253	312	18	x	x	SYM
ejpam-3253	312	19	′	′	NOUN
ejpam-3253	312	20	,	,	PUNCT
ejpam-3253	312	21	let	let	VERB
ejpam-3253	312	22	b(x′	b(x′	NUM
ejpam-3253	312	23	)	)	PUNCT
ejpam-3253	312	24	=	=	PRON
ejpam-3253	312	25	{	{	PUNCT
ejpam-3253	312	26	{	{	PUNCT
ejpam-3253	312	27	x′	x′	NUM
ejpam-3253	312	28	}	}	PUNCT
ejpam-3253	312	29	}	}	PUNCT
ejpam-3253	312	30	.	.	PUNCT
ejpam-3253	313	1	for	for	ADP
ejpam-3253	313	2	each	each	DET
ejpam-3253	313	3	x	x	SYM
ejpam-3253	313	4	∈	∈	PROPN
ejpam-3253	313	5	x	x	NOUN
ejpam-3253	313	6	,	,	PUNCT
ejpam-3253	313	7	let	let	VERB
ejpam-3253	313	8	b(x	b(x	NOUN
ejpam-3253	313	9	)	)	PUNCT
ejpam-3253	314	1	=	=	PRON
ejpam-3253	314	2	{	{	PUNCT
ejpam-3253	314	3	u	u	NOUN
ejpam-3253	314	4	∪	∪	X
ejpam-3253	314	5	(	(	PUNCT
ejpam-3253	314	6	u	u	NOUN
ejpam-3253	314	7	′	′	NOUN
ejpam-3253	314	8	\	\	NOUN
ejpam-3253	314	9	{	{	PUNCT
ejpam-3253	314	10	x′	x′	NUM
ejpam-3253	314	11	}	}	PUNCT
ejpam-3253	314	12	)	)	PUNCT
ejpam-3253	314	13	:	:	PUNCT
ejpam-3253	314	14	u	u	NOUN
ejpam-3253	314	15	is	be	AUX
ejpam-3253	314	16	open	open	ADJ
ejpam-3253	314	17	in	in	ADP
ejpam-3253	314	18	x	x	PUNCT
ejpam-3253	314	19	with	with	ADP
ejpam-3253	314	20	x	x	PROPN
ejpam-3253	314	21	∈	∈	PROPN
ejpam-3253	314	22	u	u	NOUN
ejpam-3253	314	23	}	}	PUNCT
ejpam-3253	314	24	.	.	PUNCT
ejpam-3253	315	1	let	let	VERB
ejpam-3253	315	2	τ	τ	PROPN
ejpam-3253	315	3	denote	denote	VERB
ejpam-3253	315	4	the	the	DET
ejpam-3253	315	5	unique	unique	ADJ
ejpam-3253	315	6	topology	topology	NOUN
ejpam-3253	315	7	on	on	ADP
ejpam-3253	315	8	a(x	a(x	NOUN
ejpam-3253	315	9	)	)	PUNCT
ejpam-3253	315	10	which	which	PRON
ejpam-3253	315	11	has	have	AUX
ejpam-3253	315	12	{	{	PUNCT
ejpam-3253	315	13	b(x	b(x	NOUN
ejpam-3253	315	14	)	)	PUNCT
ejpam-3253	315	15	:	:	PUNCT
ejpam-3253	316	1	x	x	X
ejpam-3253	316	2	∈	∈	NOUN
ejpam-3253	316	3	x	x	SYM
ejpam-3253	316	4	}	}	PUNCT
ejpam-3253	316	5	∪	∪	ADJ
ejpam-3253	316	6	{	{	PUNCT
ejpam-3253	316	7	b(x′	b(x′	NUM
ejpam-3253	316	8	)	)	PUNCT
ejpam-3253	316	9	:	:	PUNCT
ejpam-3253	316	10	x′	x′	X
ejpam-3253	316	11	∈	∈	NOUN
ejpam-3253	316	12	x	x	NOUN
ejpam-3253	316	13	′	′	NOUN
ejpam-3253	316	14	}	}	PUNCT
ejpam-3253	316	15	as	as	ADP
ejpam-3253	316	16	its	its	PRON
ejpam-3253	316	17	neighborhood	neighborhood	NOUN
ejpam-3253	316	18	system	system	NOUN
ejpam-3253	316	19	.	.	PUNCT
ejpam-3253	317	1	a(x	a(x	NOUN
ejpam-3253	317	2	)	)	PUNCT
ejpam-3253	317	3	with	with	ADP
ejpam-3253	317	4	this	this	DET
ejpam-3253	317	5	topology	topology	NOUN
ejpam-3253	317	6	is	be	AUX
ejpam-3253	317	7	called	call	VERB
ejpam-3253	317	8	the	the	DET
ejpam-3253	317	9	alexandroff	alexandroff	ADJ
ejpam-3253	317	10	duplicate	duplicate	NOUN
ejpam-3253	317	11	of	of	ADP
ejpam-3253	317	12	x.	x.	NOUN
ejpam-3253	317	13	similar	similar	ADJ
ejpam-3253	317	14	proof	proof	NOUN
ejpam-3253	317	15	as	as	ADP
ejpam-3253	317	16	in	in	ADP
ejpam-3253	317	17	[	[	X
ejpam-3253	317	18	2	2	NUM
ejpam-3253	317	19	]	]	PUNCT
ejpam-3253	317	20	,	,	PUNCT
ejpam-3253	317	21	we	we	PRON
ejpam-3253	317	22	get	get	VERB
ejpam-3253	317	23	the	the	DET
ejpam-3253	317	24	following	follow	VERB
ejpam-3253	317	25	theorem	theorem	VERB
ejpam-3253	317	26	.	.	PROPN
ejpam-3253	318	1	references	reference	NOUN
ejpam-3253	318	2	891	891	NUM
ejpam-3253	318	3	theorem	theorem	NOUN
ejpam-3253	318	4	19	19	NUM
ejpam-3253	318	5	.	.	PUNCT
ejpam-3253	319	1	if	if	SCONJ
ejpam-3253	319	2	x	x	PRON
ejpam-3253	319	3	is	be	AUX
ejpam-3253	319	4	c	c	NOUN
ejpam-3253	319	5	-	-	PUNCT
ejpam-3253	319	6	tychonoff	tychonoff	NOUN
ejpam-3253	319	7	,	,	PUNCT
ejpam-3253	319	8	then	then	ADV
ejpam-3253	319	9	its	its	PRON
ejpam-3253	319	10	alexandroff	alexandroff	NOUN
ejpam-3253	319	11	duplicate	duplicate	VERB
ejpam-3253	319	12	a(x	a(x	NOUN
ejpam-3253	319	13	)	)	PUNCT
ejpam-3253	319	14	is	be	AUX
ejpam-3253	319	15	also	also	ADV
ejpam-3253	319	16	ctychonoff	ctychonoff	NOUN
ejpam-3253	319	17	.	.	PUNCT
ejpam-3253	320	1	also	also	ADV
ejpam-3253	320	2	a	a	DET
ejpam-3253	320	3	similar	similar	ADJ
ejpam-3253	320	4	proof	proof	NOUN
ejpam-3253	320	5	as	as	ADP
ejpam-3253	320	6	in	in	ADP
ejpam-3253	320	7	[	[	X
ejpam-3253	320	8	15	15	NUM
ejpam-3253	320	9	]	]	PUNCT
ejpam-3253	320	10	,	,	PUNCT
ejpam-3253	320	11	we	we	PRON
ejpam-3253	320	12	get	get	VERB
ejpam-3253	320	13	the	the	DET
ejpam-3253	320	14	following	follow	VERB
ejpam-3253	320	15	theorem	theorem	VERB
ejpam-3253	320	16	.	.	PUNCT
ejpam-3253	320	17	theorem	theorem	NOUN
ejpam-3253	320	18	20	20	NUM
ejpam-3253	320	19	.	.	PUNCT
ejpam-3253	321	1	if	if	SCONJ
ejpam-3253	321	2	x	x	PRON
ejpam-3253	321	3	is	be	AUX
ejpam-3253	321	4	l	l	NOUN
ejpam-3253	321	5	-	-	NOUN
ejpam-3253	321	6	tychonoff	tychonoff	NOUN
ejpam-3253	321	7	,	,	PUNCT
ejpam-3253	321	8	then	then	ADV
ejpam-3253	321	9	its	its	PRON
ejpam-3253	321	10	alexandroff	alexandroff	NOUN
ejpam-3253	321	11	duplicate	duplicate	VERB
ejpam-3253	321	12	a(x	a(x	NOUN
ejpam-3253	321	13	)	)	PUNCT
ejpam-3253	321	14	is	be	AUX
ejpam-3253	321	15	also	also	ADV
ejpam-3253	321	16	ltychonoff	ltychonoff	ADJ
ejpam-3253	321	17	.	.	PUNCT
ejpam-3253	322	1	acknowledgements	acknowledgement	NOUN
ejpam-3253	322	2	the	the	DET
ejpam-3253	322	3	authors	author	NOUN
ejpam-3253	322	4	wish	wish	VERB
ejpam-3253	322	5	to	to	PART
ejpam-3253	322	6	express	express	VERB
ejpam-3253	322	7	their	their	PRON
ejpam-3253	322	8	sincere	sincere	ADJ
ejpam-3253	322	9	thanks	thank	NOUN
ejpam-3253	322	10	to	to	ADP
ejpam-3253	322	11	the	the	DET
ejpam-3253	322	12	referee	referee	NOUN
ejpam-3253	322	13	for	for	ADP
ejpam-3253	322	14	his	his	PRON
ejpam-3253	322	15	/	/	SYM
ejpam-3253	322	16	her	her	PRON
ejpam-3253	322	17	helpful	helpful	ADJ
ejpam-3253	322	18	comments	comment	NOUN
ejpam-3253	322	19	and	and	CCONJ
ejpam-3253	322	20	valuable	valuable	ADJ
ejpam-3253	322	21	suggestions	suggestion	NOUN
ejpam-3253	322	22	.	.	PUNCT
ejpam-3253	323	1	references	reference	NOUN
ejpam-3253	323	2	[	[	X
ejpam-3253	323	3	1	1	NUM
ejpam-3253	323	4	]	]	PUNCT
ejpam-3253	323	5	p.	p.	NOUN
ejpam-3253	323	6	s.	s.	PROPN
ejpam-3253	323	7	alexandroff	alexandroff	PROPN
ejpam-3253	323	8	and	and	CCONJ
ejpam-3253	323	9	p.	p.	PROPN
ejpam-3253	323	10	s.	s.	PROPN
ejpam-3253	323	11	urysohn	urysohn	PROPN
ejpam-3253	323	12	,	,	PUNCT
ejpam-3253	323	13	memoire	memoire	PROPN
ejpam-3253	323	14	sur	sur	PROPN
ejpam-3253	323	15	les	les	X
ejpam-3253	323	16	espaces	espace	VERB
ejpam-3253	323	17	topologigues	topologigue	NOUN
ejpam-3253	323	18	compact	compact	ADJ
ejpam-3253	323	19	,	,	PUNCT
ejpam-3253	323	20	verh	verh	ADJ
ejpam-3253	323	21	.	.	PUNCT
ejpam-3253	323	22	akad	akad	PROPN
ejpam-3253	323	23	.	.	PUNCT
ejpam-3253	324	1	wetensch	wetensch	PROPN
ejpam-3253	324	2	.	.	PUNCT
ejpam-3253	325	1	amsterdam	amsterdam	PROPN
ejpam-3253	325	2	,	,	PUNCT
ejpam-3253	325	3	14	14	NUM
ejpam-3253	325	4	(	(	PUNCT
ejpam-3253	325	5	1929	1929	NUM
ejpam-3253	325	6	)	)	PUNCT
ejpam-3253	325	7	.	.	PUNCT
ejpam-3253	326	1	[	[	X
ejpam-3253	326	2	2	2	X
ejpam-3253	326	3	]	]	PUNCT
ejpam-3253	326	4	s.	s.	PROPN
ejpam-3253	326	5	alzahrani	alzahrani	PROPN
ejpam-3253	326	6	and	and	CCONJ
ejpam-3253	326	7	l.	l.	PROPN
ejpam-3253	326	8	kalantan	kalantan	PROPN
ejpam-3253	326	9	,	,	PUNCT
ejpam-3253	326	10	c	c	NOUN
ejpam-3253	326	11	-	-	ADJ
ejpam-3253	326	12	normal	normal	ADJ
ejpam-3253	326	13	topological	topological	ADJ
ejpam-3253	326	14	property	property	NOUN
ejpam-3253	326	15	,	,	PUNCT
ejpam-3253	326	16	filomat	filomat	NOUN
ejpam-3253	326	17	31:2	31:2	NUM
ejpam-3253	326	18	(	(	PUNCT
ejpam-3253	326	19	2017	2017	NUM
ejpam-3253	326	20	)	)	PUNCT
ejpam-3253	326	21	,	,	PUNCT
ejpam-3253	326	22	407	407	NUM
ejpam-3253	326	23	-	-	SYM
ejpam-3253	326	24	411	411	NUM
ejpam-3253	326	25	.	.	PUNCT
ejpam-3253	327	1	[	[	X
ejpam-3253	327	2	3	3	X
ejpam-3253	327	3	]	]	PUNCT
ejpam-3253	327	4	s.	s.	PROPN
ejpam-3253	327	5	alzahrani	alzahrani	PROPN
ejpam-3253	327	6	and	and	CCONJ
ejpam-3253	327	7	l.	l.	PROPN
ejpam-3253	327	8	kalantan	kalantan	PROPN
ejpam-3253	327	9	,	,	PUNCT
ejpam-3253	327	10	epinormality	epinormality	PROPN
ejpam-3253	327	11	,	,	PUNCT
ejpam-3253	327	12	j.	j.	PROPN
ejpam-3253	327	13	nonlinear	nonlinear	PROPN
ejpam-3253	327	14	sci	sci	PROPN
ejpam-3253	327	15	.	.	PUNCT
ejpam-3253	327	16	appl	appl	PROPN
ejpam-3253	327	17	.	.	PROPN
ejpam-3253	328	1	9	9	NUM
ejpam-3253	328	2	(	(	PUNCT
ejpam-3253	328	3	2016	2016	NUM
ejpam-3253	328	4	)	)	PUNCT
ejpam-3253	328	5	,	,	PUNCT
ejpam-3253	328	6	53985402	53985402	NUM
ejpam-3253	328	7	.	.	PUNCT
ejpam-3253	329	1	[	[	X
ejpam-3253	329	2	4	4	X
ejpam-3253	329	3	]	]	PUNCT
ejpam-3253	329	4	s.	s.	PROPN
ejpam-3253	329	5	alzahrani	alzahrani	PROPN
ejpam-3253	329	6	,	,	PUNCT
ejpam-3253	329	7	epiregular	epiregular	ADJ
ejpam-3253	329	8	topological	topological	ADJ
ejpam-3253	329	9	spaces	space	NOUN
ejpam-3253	329	10	,	,	PUNCT
ejpam-3253	329	11	to	to	PART
ejpam-3253	329	12	appear	appear	VERB
ejpam-3253	329	13	in	in	ADP
ejpam-3253	329	14	afrika	afrika	ADJ
ejpam-3253	329	15	matematika	matematika	NOUN
ejpam-3253	329	16	.	.	PUNCT
ejpam-3253	330	1	[	[	X
ejpam-3253	330	2	5	5	X
ejpam-3253	330	3	]	]	PUNCT
ejpam-3253	330	4	s.	s.	PROPN
ejpam-3253	330	5	alzahrani	alzahrani	PROPN
ejpam-3253	330	6	,	,	PUNCT
ejpam-3253	330	7	c	c	X
ejpam-3253	330	8	-	-	PUNCT
ejpam-3253	330	9	regular	regular	ADJ
ejpam-3253	330	10	topological	topological	ADJ
ejpam-3253	330	11	spaces	space	NOUN
ejpam-3253	330	12	,	,	PUNCT
ejpam-3253	330	13	to	to	PART
ejpam-3253	330	14	appear	appear	VERB
ejpam-3253	330	15	.	.	PUNCT
ejpam-3253	331	1	[	[	X
ejpam-3253	331	2	6	6	NUM
ejpam-3253	331	3	]	]	PUNCT
ejpam-3253	331	4	a.	a.	NOUN
ejpam-3253	331	5	arhangel’skii	arhangel’skii	PROPN
ejpam-3253	331	6	,	,	PUNCT
ejpam-3253	331	7	bicompact	bicompact	ADJ
ejpam-3253	331	8	sets	set	NOUN
ejpam-3253	331	9	and	and	CCONJ
ejpam-3253	331	10	the	the	DET
ejpam-3253	331	11	topology	topology	NOUN
ejpam-3253	331	12	of	of	ADP
ejpam-3253	331	13	spaces	space	NOUN
ejpam-3253	331	14	,	,	PUNCT
ejpam-3253	331	15	trudy	trudy	PROPN
ejpam-3253	331	16	moskove	moskove	PROPN
ejpam-3253	331	17	.	.	PUNCT
ejpam-3253	332	1	mat	mat	NOUN
ejpam-3253	332	2	.	.	PROPN
ejpam-3253	332	3	obsc	obsc	PROPN
ejpam-3253	332	4	.	.	PUNCT
ejpam-3253	333	1	13	13	NUM
ejpam-3253	333	2	(	(	PUNCT
ejpam-3253	333	3	1965	1965	NUM
ejpam-3253	333	4	)	)	PUNCT
ejpam-3253	333	5	,	,	PUNCT
ejpam-3253	333	6	3	3	NUM
ejpam-3253	333	7	-	-	SYM
ejpam-3253	333	8	55	55	NUM
ejpam-3253	333	9	.	.	PUNCT
ejpam-3253	334	1	[	[	X
ejpam-3253	334	2	7	7	X
ejpam-3253	334	3	]	]	PUNCT
ejpam-3253	334	4	r.	r.	PROPN
ejpam-3253	334	5	z.	z.	PROPN
ejpam-3253	334	6	buzyakova	buzyakova	PROPN
ejpam-3253	334	7	,	,	PUNCT
ejpam-3253	334	8	an	an	DET
ejpam-3253	334	9	example	example	NOUN
ejpam-3253	334	10	of	of	ADP
ejpam-3253	334	11	two	two	NUM
ejpam-3253	334	12	normal	normal	ADJ
ejpam-3253	334	13	groups	group	NOUN
ejpam-3253	334	14	that	that	PRON
ejpam-3253	334	15	can	can	AUX
ejpam-3253	334	16	not	not	PART
ejpam-3253	334	17	be	be	AUX
ejpam-3253	334	18	condensed	condense	VERB
ejpam-3253	334	19	onto	onto	ADP
ejpam-3253	334	20	a	a	DET
ejpam-3253	334	21	normal	normal	ADJ
ejpam-3253	334	22	space	space	NOUN
ejpam-3253	334	23	,	,	PUNCT
ejpam-3253	334	24	moscow	moscow	PROPN
ejpam-3253	334	25	univ	univ	PROPN
ejpam-3253	334	26	.	.	PUNCT
ejpam-3253	335	1	math	math	NOUN
ejpam-3253	335	2	.	.	PUNCT
ejpam-3253	336	1	bull	bull	NOUN
ejpam-3253	336	2	.	.	PUNCT
ejpam-3253	337	1	52:3	52:3	NUM
ejpam-3253	337	2	:	:	PUNCT
ejpam-3253	337	3	page	page	NOUN
ejpam-3253	337	4	42	42	NUM
ejpam-3253	337	5	.	.	PUNCT
ejpam-3253	338	1	russian	russian	ADJ
ejpam-3253	338	2	original	original	ADJ
ejpam-3253	338	3	in	in	ADP
ejpam-3253	338	4	:	:	PUNCT
ejpam-3253	338	5	vestnik	vestnik	PROPN
ejpam-3253	338	6	moskov	moskov	PROPN
ejpam-3253	338	7	.	.	PUNCT
ejpam-3253	339	1	univ	univ	PROPN
ejpam-3253	339	2	.	.	PUNCT
ejpam-3253	339	3	ser	ser	PROPN
ejpam-3253	339	4	.	.	PUNCT
ejpam-3253	340	1	i	i	PRON
ejpam-3253	340	2	mat	mat	PROPN
ejpam-3253	340	3	.	.	PUNCT
ejpam-3253	340	4	mekh	mekh	PROPN
ejpam-3253	340	5	.	.	PUNCT
ejpam-3253	341	1	3	3	NUM
ejpam-3253	341	2	:	:	PUNCT
ejpam-3253	341	3	page	page	NOUN
ejpam-3253	341	4	59	59	NUM
ejpam-3253	341	5	.	.	PUNCT
ejpam-3253	342	1	[	[	X
ejpam-3253	342	2	8	8	NUM
ejpam-3253	342	3	]	]	X
ejpam-3253	342	4	r.	r.	PROPN
ejpam-3253	342	5	engelking	engelking	NOUN
ejpam-3253	342	6	,	,	PUNCT
ejpam-3253	342	7	general	general	ADJ
ejpam-3253	342	8	topology	topology	NOUN
ejpam-3253	342	9	,	,	PUNCT
ejpam-3253	342	10	(	(	PUNCT
ejpam-3253	342	11	pwn	pwn	PROPN
ejpam-3253	342	12	,	,	PUNCT
ejpam-3253	342	13	warszawa	warszawa	X
ejpam-3253	342	14	,	,	PUNCT
ejpam-3253	342	15	1977	1977	NUM
ejpam-3253	342	16	)	)	PUNCT
ejpam-3253	342	17	.	.	PUNCT
ejpam-3253	343	1	[	[	X
ejpam-3253	343	2	9	9	NUM
ejpam-3253	343	3	]	]	X
ejpam-3253	343	4	engelking	engelking	NOUN
ejpam-3253	343	5	,	,	PUNCT
ejpam-3253	343	6	r.	r.	PROPN
ejpam-3253	343	7	,	,	PUNCT
ejpam-3253	343	8	on	on	ADP
ejpam-3253	343	9	the	the	DET
ejpam-3253	343	10	double	double	ADJ
ejpam-3253	343	11	circumference	circumference	NOUN
ejpam-3253	343	12	of	of	ADP
ejpam-3253	343	13	alexandroff	alexandroff	NOUN
ejpam-3253	343	14	,	,	PUNCT
ejpam-3253	343	15	bull	bull	NOUN
ejpam-3253	343	16	.	.	PUNCT
ejpam-3253	344	1	acad	acad	PROPN
ejpam-3253	344	2	.	.	PUNCT
ejpam-3253	345	1	pol	pol	PROPN
ejpam-3253	345	2	.	.	PUNCT
ejpam-3253	346	1	sci	sci	PROPN
ejpam-3253	346	2	.	.	PUNCT
ejpam-3253	346	3	ser	ser	PROPN
ejpam-3253	346	4	.	.	PUNCT
ejpam-3253	347	1	astron	astron	PROPN
ejpam-3253	347	2	.	.	PUNCT
ejpam-3253	347	3	math	math	NOUN
ejpam-3253	347	4	.	.	PUNCT
ejpam-3253	348	1	phys	phy	NOUN
ejpam-3253	348	2	.	.	PUNCT
ejpam-3253	348	3	,	,	PUNCT
ejpam-3253	348	4	vol	vol	NOUN
ejpam-3253	348	5	16	16	NUM
ejpam-3253	348	6	,	,	PUNCT
ejpam-3253	348	7	no	no	DET
ejpam-3253	348	8	8	8	NUM
ejpam-3253	348	9	,	,	PUNCT
ejpam-3253	348	10	1968	1968	NUM
ejpam-3253	348	11	,	,	PUNCT
ejpam-3253	348	12	629	629	NUM
ejpam-3253	348	13	-	-	SYM
ejpam-3253	348	14	634	634	NUM
ejpam-3253	348	15	.	.	PUNCT
ejpam-3253	349	1	[	[	X
ejpam-3253	349	2	10	10	NUM
ejpam-3253	349	3	]	]	X
ejpam-3253	349	4	g.	g.	PROPN
ejpam-3253	349	5	gruenhage	gruenhage	PROPN
ejpam-3253	349	6	,	,	PUNCT
ejpam-3253	349	7	generalized	generalize	VERB
ejpam-3253	349	8	metric	metric	ADJ
ejpam-3253	349	9	spaces	space	NOUN
ejpam-3253	349	10	,	,	PUNCT
ejpam-3253	349	11	in	in	ADP
ejpam-3253	349	12	:	:	PUNCT
ejpam-3253	349	13	handbook	handbook	NOUN
ejpam-3253	349	14	of	of	ADP
ejpam-3253	349	15	set	set	ADJ
ejpam-3253	349	16	theoretic	theoretic	NOUN
ejpam-3253	349	17	topology	topology	NOUN
ejpam-3253	349	18	,	,	PUNCT
ejpam-3253	349	19	north	north	NOUN
ejpam-3253	349	20	holland	holland	PROPN
ejpam-3253	349	21	,	,	PUNCT
ejpam-3253	349	22	1984	1984	NUM
ejpam-3253	349	23	,	,	PUNCT
ejpam-3253	349	24	423	423	NUM
ejpam-3253	349	25	-	-	SYM
ejpam-3253	349	26	501	501	NUM
ejpam-3253	349	27	.	.	PUNCT
ejpam-3253	350	1	[	[	X
ejpam-3253	350	2	11	11	NUM
ejpam-3253	350	3	]	]	PUNCT
ejpam-3253	350	4	m.	m.	NOUN
ejpam-3253	350	5	mrsevic	mrsevic	PROPN
ejpam-3253	350	6	,	,	PUNCT
ejpam-3253	350	7	i.l	i.l	PROPN
ejpam-3253	350	8	.	.	PROPN
ejpam-3253	350	9	reilly	reilly	PROPN
ejpam-3253	350	10	and	and	CCONJ
ejpam-3253	350	11	m.k	m.k	PROPN
ejpam-3253	350	12	.	.	PROPN
ejpam-3253	350	13	vamanamurthy	vamanamurthy	PROPN
ejpam-3253	350	14	,	,	PUNCT
ejpam-3253	350	15	on	on	ADP
ejpam-3253	350	16	semi	semi	ADJ
ejpam-3253	350	17	-	-	ADJ
ejpam-3253	350	18	regularization	regularization	ADJ
ejpam-3253	350	19	topologies	topology	NOUN
ejpam-3253	350	20	,	,	PUNCT
ejpam-3253	350	21	j.	j.	PROPN
ejpam-3253	350	22	austral	austral	PROPN
ejpam-3253	350	23	.	.	PUNCT
ejpam-3253	351	1	math	math	NOUN
ejpam-3253	351	2	.	.	PUNCT
ejpam-3253	352	1	soc	soc	PROPN
ejpam-3253	352	2	.	.	PUNCT
ejpam-3253	353	1	(	(	PUNCT
ejpam-3253	353	2	series	series	PROPN
ejpam-3253	353	3	)	)	PUNCT
ejpam-3253	353	4	38	38	NUM
ejpam-3253	353	5	(	(	PUNCT
ejpam-3253	353	6	1985	1985	NUM
ejpam-3253	353	7	)	)	PUNCT
ejpam-3253	353	8	,	,	PUNCT
ejpam-3253	353	9	40	40	NUM
ejpam-3253	353	10	-	-	SYM
ejpam-3253	353	11	54	54	NUM
ejpam-3253	353	12	.	.	PUNCT
ejpam-3253	354	1	references	reference	NOUN
ejpam-3253	354	2	892	892	NUM
ejpam-3253	355	1	[	[	X
ejpam-3253	355	2	12	12	NUM
ejpam-3253	355	3	]	]	PUNCT
ejpam-3253	355	4	a.	a.	PROPN
ejpam-3253	355	5	s.	s.	PROPN
ejpam-3253	355	6	parhomenko	parhomenko	PROPN
ejpam-3253	355	7	,	,	PUNCT
ejpam-3253	355	8	on	on	ADP
ejpam-3253	355	9	condensations	condensation	NOUN
ejpam-3253	355	10	into	into	ADP
ejpam-3253	355	11	compact	compact	ADJ
ejpam-3253	355	12	spaces	space	NOUN
ejpam-3253	355	13	,	,	PUNCT
ejpam-3253	355	14	izv	izv	PROPN
ejpam-3253	355	15	.	.	PROPN
ejpam-3253	355	16	akad	akad	PROPN
ejpam-3253	355	17	.	.	PUNCT
ejpam-3253	356	1	nauk	nauk	PROPN
ejpam-3253	356	2	sssr	sssr	PROPN
ejpam-3253	356	3	.	.	PUNCT
ejpam-3253	357	1	ser	ser	PROPN
ejpam-3253	357	2	.	.	PROPN
ejpam-3253	358	1	mat	mat	NOUN
ejpam-3253	358	2	.	.	PUNCT
ejpam-3253	359	1	5(1941	5(1941	NUM
ejpam-3253	359	2	)	)	PUNCT
ejpam-3253	359	3	,	,	PUNCT
ejpam-3253	359	4	225	225	NUM
ejpam-3253	359	5	-	-	SYM
ejpam-3253	359	6	232	232	NUM
ejpam-3253	359	7	.	.	PUNCT
ejpam-3253	360	1	[	[	X
ejpam-3253	360	2	13	13	NUM
ejpam-3253	360	3	]	]	PUNCT
ejpam-3253	360	4	m.	m.	NOUN
ejpam-3253	360	5	saeed	saeed	PROPN
ejpam-3253	360	6	,	,	PUNCT
ejpam-3253	360	7	countable	countable	ADJ
ejpam-3253	360	8	normality	normality	NOUN
ejpam-3253	360	9	,	,	PUNCT
ejpam-3253	360	10	to	to	PART
ejpam-3253	360	11	appear	appear	VERB
ejpam-3253	360	12	.	.	PUNCT
ejpam-3253	361	1	[	[	X
ejpam-3253	361	2	14	14	NUM
ejpam-3253	361	3	]	]	X
ejpam-3253	361	4	e.	e.	PROPN
ejpam-3253	361	5	v.	v.	PROPN
ejpam-3253	361	6	shchepin	shchepin	PROPN
ejpam-3253	361	7	,	,	PUNCT
ejpam-3253	361	8	real	real	ADV
ejpam-3253	361	9	valued	value	VERB
ejpam-3253	361	10	functions	function	NOUN
ejpam-3253	361	11	and	and	CCONJ
ejpam-3253	361	12	spaces	space	NOUN
ejpam-3253	361	13	close	close	ADV
ejpam-3253	361	14	to	to	ADP
ejpam-3253	361	15	normal	normal	ADJ
ejpam-3253	361	16	,	,	PUNCT
ejpam-3253	361	17	sib	sib	PROPN
ejpam-3253	361	18	.	.	PUNCT
ejpam-3253	362	1	j.	j.	PROPN
ejpam-3253	362	2	math	math	PROPN
ejpam-3253	362	3	.	.	PUNCT
ejpam-3253	363	1	13:5	13:5	NUM
ejpam-3253	363	2	(	(	PUNCT
ejpam-3253	363	3	1972	1972	NUM
ejpam-3253	363	4	)	)	PUNCT
ejpam-3253	363	5	1182	1182	NUM
ejpam-3253	363	6	-	-	SYM
ejpam-3253	363	7	1196	1196	NUM
ejpam-3253	363	8	.	.	PUNCT
ejpam-3253	364	1	[	[	X
ejpam-3253	364	2	15	15	NUM
ejpam-3253	364	3	]	]	X
ejpam-3253	364	4	l.	l.	PROPN
ejpam-3253	364	5	kalantan	kalantan	PROPN
ejpam-3253	364	6	and	and	CCONJ
ejpam-3253	364	7	m.	m.	PROPN
ejpam-3253	364	8	saeed	saeed	PROPN
ejpam-3253	364	9	,	,	PUNCT
ejpam-3253	364	10	l	l	NOUN
ejpam-3253	364	11	-	-	NOUN
ejpam-3253	364	12	normality	normality	NOUN
ejpam-3253	364	13	,	,	PUNCT
ejpam-3253	364	14	topology	topology	NOUN
ejpam-3253	364	15	proceedings	proceeding	NOUN
ejpam-3253	364	16	,	,	PUNCT
ejpam-3253	364	17	vol	vol	NOUN
ejpam-3253	364	18	50(2017	50(2017	NUM
ejpam-3253	364	19	)	)	PUNCT
ejpam-3253	364	20	,	,	PUNCT
ejpam-3253	364	21	141	141	NUM
ejpam-3253	364	22	-	-	SYM
ejpam-3253	364	23	149	149	NUM
ejpam-3253	364	24	.	.	PUNCT
ejpam-3253	365	1	[	[	X
ejpam-3253	365	2	16	16	NUM
ejpam-3253	365	3	]	]	X
ejpam-3253	365	4	l.	l.	PROPN
ejpam-3253	365	5	steen	steen	PROPN
ejpam-3253	365	6	and	and	CCONJ
ejpam-3253	365	7	j.	j.	PROPN
ejpam-3253	365	8	a.	a.	PROPN
ejpam-3253	365	9	seebach	seebach	PROPN
ejpam-3253	365	10	,	,	PUNCT
ejpam-3253	365	11	counterexamples	counterexample	NOUN
ejpam-3253	365	12	in	in	ADP
ejpam-3253	365	13	topology	topology	NOUN
ejpam-3253	365	14	,	,	PUNCT
ejpam-3253	365	15	dover	dover	PROPN
ejpam-3253	365	16	publications	publications	PROPN
ejpam-3253	365	17	,	,	PUNCT
ejpam-3253	365	18	inc	inc	PROPN
ejpam-3253	365	19	.	.	PROPN
ejpam-3253	365	20	1995	1995	NUM
ejpam-3253	365	21	.	.	PUNCT