id	sid	tid	token	lemma	pos
ejpam-4061	1	1	european	european	PROPN
ejpam-4061	1	2	journal	journal	PROPN
ejpam-4061	1	3	of	of	ADP
ejpam-4061	1	4	pure	pure	ADJ
ejpam-4061	1	5	and	and	CCONJ
ejpam-4061	1	6	applied	apply	VERB
ejpam-4061	1	7	mathematics	mathematic	NOUN
ejpam-4061	1	8	vol	vol	NOUN
ejpam-4061	1	9	.	.	PUNCT
ejpam-4061	2	1	14	14	NUM
ejpam-4061	2	2	,	,	PUNCT
ejpam-4061	2	3	no	no	INTJ
ejpam-4061	2	4	.	.	NOUN
ejpam-4061	2	5	4	4	NUM
ejpam-4061	2	6	,	,	PUNCT
ejpam-4061	2	7	2021	2021	NUM
ejpam-4061	2	8	,	,	PUNCT
ejpam-4061	2	9	1161	1161	NUM
ejpam-4061	2	10	-	-	SYM
ejpam-4061	2	11	1168	1168	NUM
ejpam-4061	2	12	issn	issn	PROPN
ejpam-4061	2	13	1307	1307	NUM
ejpam-4061	2	14	-	-	SYM
ejpam-4061	2	15	5543	5543	NUM
ejpam-4061	2	16	–	–	PUNCT
ejpam-4061	3	1	ejpam.com	ejpam.com	X
ejpam-4061	3	2	published	publish	VERB
ejpam-4061	3	3	by	by	ADP
ejpam-4061	3	4	new	new	PROPN
ejpam-4061	3	5	york	york	PROPN
ejpam-4061	3	6	business	business	PROPN
ejpam-4061	3	7	global	global	ADJ
ejpam-4061	3	8	new	new	ADJ
ejpam-4061	3	9	topologies	topology	NOUN
ejpam-4061	3	10	between	between	ADP
ejpam-4061	3	11	the	the	DET
ejpam-4061	3	12	usual	usual	ADJ
ejpam-4061	3	13	topology	topology	NOUN
ejpam-4061	3	14	and	and	CCONJ
ejpam-4061	3	15	the	the	DET
ejpam-4061	3	16	half	half	ADJ
ejpam-4061	3	17	-	-	PUNCT
ejpam-4061	3	18	disc	disc	NOUN
ejpam-4061	3	19	nadiah	nadiah	PROPN
ejpam-4061	3	20	alghamdi1,2	alghamdi1,2	PROPN
ejpam-4061	3	21	,	,	PUNCT
ejpam-4061	3	22	lutfi	lutfi	PROPN
ejpam-4061	3	23	kalantan1,∗	kalantan1,∗	PROPN
ejpam-4061	3	24	1	1	NUM
ejpam-4061	3	25	king	king	PROPN
ejpam-4061	3	26	abdulaziz	abdulaziz	PROPN
ejpam-4061	3	27	university	university	PROPN
ejpam-4061	3	28	,	,	PUNCT
ejpam-4061	3	29	department	department	NOUN
ejpam-4061	3	30	of	of	ADP
ejpam-4061	3	31	mathematics	mathematic	NOUN
ejpam-4061	3	32	,	,	PUNCT
ejpam-4061	3	33	p.o.box	p.o.box	PROPN
ejpam-4061	3	34	80203	80203	NUM
ejpam-4061	3	35	,	,	PUNCT
ejpam-4061	3	36	jeddah	jeddah	PROPN
ejpam-4061	3	37	21589	21589	NUM
ejpam-4061	3	38	,	,	PUNCT
ejpam-4061	3	39	saudi	saudi	PROPN
ejpam-4061	3	40	arabia	arabia	PROPN
ejpam-4061	3	41	2	2	NUM
ejpam-4061	3	42	umm	umm	INTJ
ejpam-4061	3	43	al	al	PROPN
ejpam-4061	3	44	-	-	PUNCT
ejpam-4061	3	45	qura	qura	PROPN
ejpam-4061	3	46	university	university	PROPN
ejpam-4061	3	47	.	.	PUNCT
ejpam-4061	4	1	department	department	PROPN
ejpam-4061	4	2	of	of	ADP
ejpam-4061	4	3	mathematics	mathematics	PROPN
ejpam-4061	4	4	,	,	PUNCT
ejpam-4061	4	5	saudi	saudi	PROPN
ejpam-4061	4	6	arabia	arabia	PROPN
ejpam-4061	4	7	abstract	abstract	NOUN
ejpam-4061	4	8	.	.	PUNCT
ejpam-4061	5	1	we	we	PRON
ejpam-4061	5	2	generate	generate	VERB
ejpam-4061	5	3	new	new	ADJ
ejpam-4061	5	4	topologies	topology	NOUN
ejpam-4061	5	5	on	on	ADP
ejpam-4061	5	6	the	the	DET
ejpam-4061	5	7	closed	closed	ADJ
ejpam-4061	5	8	upper	upper	ADJ
ejpam-4061	5	9	half	half	ADJ
ejpam-4061	5	10	plane	plane	NOUN
ejpam-4061	5	11	which	which	PRON
ejpam-4061	5	12	lie	lie	VERB
ejpam-4061	5	13	between	between	ADP
ejpam-4061	5	14	the	the	DET
ejpam-4061	5	15	usual	usual	ADJ
ejpam-4061	5	16	topology	topology	NOUN
ejpam-4061	5	17	and	and	CCONJ
ejpam-4061	5	18	the	the	DET
ejpam-4061	5	19	half	half	ADJ
ejpam-4061	5	20	-	-	PUNCT
ejpam-4061	5	21	disc	disc	NOUN
ejpam-4061	5	22	topology	topology	NOUN
ejpam-4061	5	23	.	.	PUNCT
ejpam-4061	6	1	we	we	PRON
ejpam-4061	6	2	study	study	VERB
ejpam-4061	6	3	some	some	PRON
ejpam-4061	6	4	of	of	ADP
ejpam-4061	6	5	their	their	PRON
ejpam-4061	6	6	fundamental	fundamental	ADJ
ejpam-4061	6	7	properties	property	NOUN
ejpam-4061	6	8	and	and	CCONJ
ejpam-4061	6	9	weaker	weak	ADJ
ejpam-4061	6	10	versions	version	NOUN
ejpam-4061	6	11	of	of	ADP
ejpam-4061	6	12	normality	normality	NOUN
ejpam-4061	6	13	.	.	PUNCT
ejpam-4061	7	1	2020	2020	NUM
ejpam-4061	7	2	mathematics	mathematic	NOUN
ejpam-4061	7	3	subject	subject	NOUN
ejpam-4061	7	4	classifications	classification	NOUN
ejpam-4061	7	5	:	:	PUNCT
ejpam-4061	7	6	54a10	54a10	NUM
ejpam-4061	7	7	,	,	PUNCT
ejpam-4061	7	8	54g20	54g20	NUM
ejpam-4061	7	9	key	key	ADJ
ejpam-4061	7	10	words	word	NOUN
ejpam-4061	7	11	and	and	CCONJ
ejpam-4061	7	12	phrases	phrase	NOUN
ejpam-4061	7	13	:	:	PUNCT
ejpam-4061	7	14	h	h	NOUN
ejpam-4061	7	15	-	-	PUNCT
ejpam-4061	7	16	space	space	NOUN
ejpam-4061	7	17	,	,	PUNCT
ejpam-4061	7	18	half	half	ADJ
ejpam-4061	7	19	-	-	PUNCT
ejpam-4061	7	20	disc	disc	NOUN
ejpam-4061	7	21	,	,	PUNCT
ejpam-4061	7	22	usual	usual	ADJ
ejpam-4061	7	23	metric	metric	ADJ
ejpam-4061	7	24	topology	topology	NOUN
ejpam-4061	7	25	,	,	PUNCT
ejpam-4061	7	26	mildly	mildly	ADV
ejpam-4061	7	27	normal	normal	ADJ
ejpam-4061	7	28	,	,	PUNCT
ejpam-4061	7	29	κ	κ	NOUN
ejpam-4061	7	30	-	-	ADJ
ejpam-4061	7	31	normal	normal	ADJ
ejpam-4061	7	32	,	,	PUNCT
ejpam-4061	7	33	κ	κ	NOUN
ejpam-4061	7	34	-	-	ADJ
ejpam-4061	7	35	metrizable	metrizable	ADJ
ejpam-4061	7	36	,	,	PUNCT
ejpam-4061	7	37	submetrizable	submetrizable	ADJ
ejpam-4061	7	38	.	.	PUNCT
ejpam-4061	8	1	we	we	PRON
ejpam-4061	8	2	generate	generate	VERB
ejpam-4061	8	3	new	new	ADJ
ejpam-4061	8	4	topologies	topology	NOUN
ejpam-4061	8	5	on	on	ADP
ejpam-4061	8	6	the	the	DET
ejpam-4061	8	7	closed	closed	ADJ
ejpam-4061	8	8	upper	upper	ADJ
ejpam-4061	8	9	half	half	ADJ
ejpam-4061	8	10	plane	plane	NOUN
ejpam-4061	8	11	which	which	PRON
ejpam-4061	8	12	lie	lie	VERB
ejpam-4061	8	13	between	between	ADP
ejpam-4061	8	14	the	the	DET
ejpam-4061	8	15	usual	usual	ADJ
ejpam-4061	8	16	metric	metric	ADJ
ejpam-4061	8	17	topology	topology	NOUN
ejpam-4061	8	18	and	and	CCONJ
ejpam-4061	8	19	the	the	DET
ejpam-4061	8	20	half	half	ADJ
ejpam-4061	8	21	-	-	PUNCT
ejpam-4061	8	22	disc	disc	NOUN
ejpam-4061	8	23	topology	topology	NOUN
ejpam-4061	8	24	.	.	PUNCT
ejpam-4061	9	1	these	these	DET
ejpam-4061	9	2	new	new	ADJ
ejpam-4061	9	3	spaces	space	NOUN
ejpam-4061	9	4	may	may	AUX
ejpam-4061	9	5	work	work	VERB
ejpam-4061	9	6	as	as	ADP
ejpam-4061	9	7	counterexamples	counterexample	NOUN
ejpam-4061	9	8	in	in	ADP
ejpam-4061	9	9	topology	topology	NOUN
ejpam-4061	9	10	and	and	CCONJ
ejpam-4061	9	11	help	help	VERB
ejpam-4061	9	12	in	in	ADP
ejpam-4061	9	13	study	study	NOUN
ejpam-4061	9	14	of	of	ADP
ejpam-4061	9	15	some	some	DET
ejpam-4061	9	16	advances	advance	NOUN
ejpam-4061	9	17	topological	topological	ADJ
ejpam-4061	9	18	properties	property	NOUN
ejpam-4061	9	19	.	.	PUNCT
ejpam-4061	10	1	we	we	PRON
ejpam-4061	10	2	study	study	VERB
ejpam-4061	10	3	some	some	PRON
ejpam-4061	10	4	of	of	ADP
ejpam-4061	10	5	their	their	PRON
ejpam-4061	10	6	fundamental	fundamental	ADJ
ejpam-4061	10	7	properties	property	NOUN
ejpam-4061	10	8	and	and	CCONJ
ejpam-4061	10	9	weaker	weak	ADJ
ejpam-4061	10	10	versions	version	NOUN
ejpam-4061	10	11	of	of	ADP
ejpam-4061	10	12	normality	normality	NOUN
ejpam-4061	10	13	.	.	PUNCT
ejpam-4061	11	1	throughout	throughout	ADP
ejpam-4061	11	2	this	this	DET
ejpam-4061	11	3	paper	paper	NOUN
ejpam-4061	11	4	,	,	PUNCT
ejpam-4061	11	5	we	we	PRON
ejpam-4061	11	6	denote	denote	VERB
ejpam-4061	11	7	an	an	DET
ejpam-4061	11	8	ordered	order	VERB
ejpam-4061	11	9	pair	pair	NOUN
ejpam-4061	11	10	by	by	ADP
ejpam-4061	11	11	⟨x	⟨x	NUM
ejpam-4061	11	12	,	,	PUNCT
ejpam-4061	11	13	y⟩	y⟩	NOUN
ejpam-4061	11	14	,	,	PUNCT
ejpam-4061	11	15	the	the	DET
ejpam-4061	11	16	set	set	NOUN
ejpam-4061	11	17	of	of	ADP
ejpam-4061	11	18	positive	positive	ADJ
ejpam-4061	11	19	integers	integer	NOUN
ejpam-4061	11	20	by	by	ADP
ejpam-4061	11	21	n	n	CCONJ
ejpam-4061	11	22	,	,	PUNCT
ejpam-4061	11	23	the	the	DET
ejpam-4061	11	24	rationals	rational	NOUN
ejpam-4061	11	25	by	by	ADP
ejpam-4061	11	26	q	q	NOUN
ejpam-4061	11	27	,	,	PUNCT
ejpam-4061	11	28	the	the	DET
ejpam-4061	11	29	irrationals	irrational	NOUN
ejpam-4061	11	30	by	by	ADP
ejpam-4061	11	31	p	p	NOUN
ejpam-4061	11	32	,	,	PUNCT
ejpam-4061	11	33	and	and	CCONJ
ejpam-4061	11	34	the	the	DET
ejpam-4061	11	35	set	set	NOUN
ejpam-4061	11	36	of	of	ADP
ejpam-4061	11	37	real	real	ADJ
ejpam-4061	11	38	numbers	number	NOUN
ejpam-4061	11	39	by	by	ADP
ejpam-4061	11	40	r.	r.	PROPN
ejpam-4061	11	41	a	a	DET
ejpam-4061	11	42	t4	t4	PROPN
ejpam-4061	11	43	space	space	NOUN
ejpam-4061	11	44	is	be	AUX
ejpam-4061	11	45	a	a	DET
ejpam-4061	11	46	t1	t1	NOUN
ejpam-4061	11	47	normal	normal	ADJ
ejpam-4061	11	48	space	space	NOUN
ejpam-4061	11	49	and	and	CCONJ
ejpam-4061	11	50	a	a	DET
ejpam-4061	11	51	tychonoff	tychonoff	NOUN
ejpam-4061	11	52	space	space	NOUN
ejpam-4061	11	53	(	(	PUNCT
ejpam-4061	11	54	t3	t3	NOUN
ejpam-4061	11	55	1	1	NUM
ejpam-4061	11	56	2	2	NUM
ejpam-4061	11	57	)	)	PUNCT
ejpam-4061	11	58	is	be	AUX
ejpam-4061	11	59	a	a	DET
ejpam-4061	11	60	t1	t1	NOUN
ejpam-4061	11	61	completely	completely	ADV
ejpam-4061	11	62	regular	regular	ADJ
ejpam-4061	11	63	space	space	NOUN
ejpam-4061	11	64	.	.	PUNCT
ejpam-4061	12	1	we	we	PRON
ejpam-4061	12	2	do	do	AUX
ejpam-4061	12	3	not	not	PART
ejpam-4061	12	4	assume	assume	VERB
ejpam-4061	12	5	t2	t2	NOUN
ejpam-4061	12	6	in	in	ADP
ejpam-4061	12	7	the	the	DET
ejpam-4061	12	8	definition	definition	NOUN
ejpam-4061	12	9	of	of	ADP
ejpam-4061	12	10	compactness	compactness	NOUN
ejpam-4061	12	11	and	and	CCONJ
ejpam-4061	12	12	countable	countable	ADJ
ejpam-4061	12	13	compactness	compactness	NOUN
ejpam-4061	12	14	.	.	PUNCT
ejpam-4061	13	1	we	we	PRON
ejpam-4061	13	2	do	do	AUX
ejpam-4061	13	3	not	not	PART
ejpam-4061	13	4	assume	assume	VERB
ejpam-4061	13	5	regularity	regularity	NOUN
ejpam-4061	13	6	in	in	ADP
ejpam-4061	13	7	the	the	DET
ejpam-4061	13	8	definition	definition	NOUN
ejpam-4061	13	9	of	of	ADP
ejpam-4061	13	10	lindelöfness	lindelöfness	PROPN
ejpam-4061	13	11	.	.	PUNCT
ejpam-4061	14	1	for	for	ADP
ejpam-4061	14	2	a	a	DET
ejpam-4061	14	3	subset	subset	NOUN
ejpam-4061	14	4	a	a	PRON
ejpam-4061	14	5	of	of	ADP
ejpam-4061	14	6	a	a	DET
ejpam-4061	14	7	space	space	NOUN
ejpam-4061	14	8	x	x	NOUN
ejpam-4061	14	9	,	,	PUNCT
ejpam-4061	14	10	inta	inta	PROPN
ejpam-4061	14	11	and	and	CCONJ
ejpam-4061	14	12	a	a	DET
ejpam-4061	14	13	denote	denote	NOUN
ejpam-4061	14	14	the	the	DET
ejpam-4061	14	15	interior	interior	NOUN
ejpam-4061	14	16	and	and	CCONJ
ejpam-4061	14	17	the	the	DET
ejpam-4061	14	18	closure	closure	NOUN
ejpam-4061	14	19	of	of	ADP
ejpam-4061	14	20	a	a	PRON
ejpam-4061	14	21	,	,	PUNCT
ejpam-4061	14	22	respectively	respectively	ADV
ejpam-4061	14	23	.	.	PUNCT
ejpam-4061	15	1	if	if	SCONJ
ejpam-4061	15	2	two	two	NUM
ejpam-4061	15	3	topologies	topology	NOUN
ejpam-4061	15	4	τ	τ	X
ejpam-4061	15	5	and	and	CCONJ
ejpam-4061	15	6	τ	τ	PROPN
ejpam-4061	15	7	′	′	NOUN
ejpam-4061	15	8	on	on	ADP
ejpam-4061	15	9	a	a	DET
ejpam-4061	15	10	set	set	NOUN
ejpam-4061	15	11	x	x	SYM
ejpam-4061	15	12	are	be	AUX
ejpam-4061	15	13	considered	consider	VERB
ejpam-4061	15	14	,	,	PUNCT
ejpam-4061	15	15	we	we	PRON
ejpam-4061	15	16	denote	denote	VERB
ejpam-4061	15	17	the	the	DET
ejpam-4061	15	18	interior	interior	NOUN
ejpam-4061	15	19	of	of	ADP
ejpam-4061	15	20	a	a	DET
ejpam-4061	15	21	in	in	ADP
ejpam-4061	15	22	(	(	PUNCT
ejpam-4061	15	23	x	x	INTJ
ejpam-4061	15	24	,	,	PUNCT
ejpam-4061	15	25	τ	τ	PROPN
ejpam-4061	15	26	)	)	PUNCT
ejpam-4061	15	27	by	by	ADP
ejpam-4061	15	28	int	int	NOUN
ejpam-4061	15	29	τa	τa	NOUN
ejpam-4061	15	30	and	and	CCONJ
ejpam-4061	15	31	the	the	DET
ejpam-4061	15	32	closure	closure	NOUN
ejpam-4061	15	33	of	of	ADP
ejpam-4061	15	34	a	a	DET
ejpam-4061	15	35	in	in	ADP
ejpam-4061	15	36	(	(	PUNCT
ejpam-4061	15	37	x	x	INTJ
ejpam-4061	15	38	,	,	PUNCT
ejpam-4061	15	39	τ	τ	PROPN
ejpam-4061	15	40	′	′	NUM
ejpam-4061	15	41	)	)	PUNCT
ejpam-4061	15	42	by	by	ADP
ejpam-4061	15	43	a	a	DET
ejpam-4061	15	44	τ	τ	NOUN
ejpam-4061	15	45	′	′	NUM
ejpam-4061	15	46	.	.	PUNCT
ejpam-4061	16	1	we	we	PRON
ejpam-4061	16	2	start	start	VERB
ejpam-4061	16	3	by	by	ADP
ejpam-4061	16	4	state	state	NOUN
ejpam-4061	16	5	some	some	DET
ejpam-4061	16	6	definitions	definition	NOUN
ejpam-4061	16	7	and	and	CCONJ
ejpam-4061	16	8	fix	fix	VERB
ejpam-4061	16	9	some	some	DET
ejpam-4061	16	10	notations	notation	NOUN
ejpam-4061	16	11	.	.	PUNCT
ejpam-4061	17	1	let	let	VERB
ejpam-4061	17	2	x	x	SYM
ejpam-4061	17	3	=	=	NOUN
ejpam-4061	17	4	{	{	PUNCT
ejpam-4061	17	5	⟨x	⟨x	NUM
ejpam-4061	17	6	,	,	PUNCT
ejpam-4061	17	7	y⟩	y⟩	NOUN
ejpam-4061	17	8	∈	∈	PROPN
ejpam-4061	17	9	r2	r2	PROPN
ejpam-4061	17	10	:	:	PUNCT
ejpam-4061	17	11	y	y	NOUN
ejpam-4061	17	12	≥	≥	NOUN
ejpam-4061	17	13	0	0	NUM
ejpam-4061	17	14	}	}	PUNCT
ejpam-4061	17	15	be	be	AUX
ejpam-4061	17	16	the	the	DET
ejpam-4061	17	17	closed	closed	ADJ
ejpam-4061	17	18	upper	upper	ADJ
ejpam-4061	17	19	half	half	ADJ
ejpam-4061	17	20	plane	plane	NOUN
ejpam-4061	17	21	.	.	PUNCT
ejpam-4061	18	1	k	k	X
ejpam-4061	19	1	=	=	X
ejpam-4061	19	2	{	{	PUNCT
ejpam-4061	19	3	⟨x	⟨x	NUM
ejpam-4061	19	4	,	,	PUNCT
ejpam-4061	19	5	y⟩	y⟩	NOUN
ejpam-4061	19	6	∈	∈	PROPN
ejpam-4061	19	7	r2	r2	PROPN
ejpam-4061	19	8	:	:	PUNCT
ejpam-4061	19	9	y	y	PROPN
ejpam-4061	19	10	>	>	X
ejpam-4061	19	11	0	0	NUM
ejpam-4061	19	12	}	}	PUNCT
ejpam-4061	19	13	,	,	PUNCT
ejpam-4061	19	14	so	so	CCONJ
ejpam-4061	19	15	the	the	DET
ejpam-4061	19	16	x	x	X
ejpam-4061	19	17	-	-	ADJ
ejpam-4061	19	18	axis	axis	NOUN
ejpam-4061	19	19	is	be	AUX
ejpam-4061	19	20	l	l	NOUN
ejpam-4061	19	21	=	=	PUNCT
ejpam-4061	19	22	x	x	SYM
ejpam-4061	19	23	\k	\k	NOUN
ejpam-4061	19	24	.	.	PUNCT
ejpam-4061	20	1	denote	denote	VERB
ejpam-4061	20	2	the	the	DET
ejpam-4061	20	3	usual	usual	ADJ
ejpam-4061	20	4	metric	metric	ADJ
ejpam-4061	20	5	topology	topology	NOUN
ejpam-4061	20	6	on	on	ADP
ejpam-4061	20	7	x	x	PUNCT
ejpam-4061	20	8	by	by	ADP
ejpam-4061	20	9	u	u	NOUN
ejpam-4061	20	10	and	and	CCONJ
ejpam-4061	20	11	the	the	DET
ejpam-4061	20	12	half	half	ADJ
ejpam-4061	20	13	-	-	PUNCT
ejpam-4061	20	14	disc	disc	NOUN
ejpam-4061	20	15	topology	topology	NOUN
ejpam-4061	20	16	on	on	ADP
ejpam-4061	20	17	x	x	PART
ejpam-4061	20	18	be	be	AUX
ejpam-4061	20	19	h.	h.	NOUN
ejpam-4061	20	20	for	for	ADP
ejpam-4061	20	21	every	every	DET
ejpam-4061	20	22	⟨a	⟨a	NOUN
ejpam-4061	20	23	,	,	PUNCT
ejpam-4061	20	24	b⟩	b⟩	PUNCT
ejpam-4061	20	25	∈	∈	PROPN
ejpam-4061	20	26	x	x	X
ejpam-4061	20	27	and	and	CCONJ
ejpam-4061	20	28	r	r	X
ejpam-4061	20	29	>	>	X
ejpam-4061	20	30	0	0	NUM
ejpam-4061	20	31	where	where	SCONJ
ejpam-4061	20	32	r	r	NOUN
ejpam-4061	20	33	∈	∈	PROPN
ejpam-4061	20	34	r	r	NOUN
ejpam-4061	20	35	,	,	PUNCT
ejpam-4061	20	36	let	let	VERB
ejpam-4061	20	37	ur(⟨a	ur(⟨a	PRON
ejpam-4061	20	38	,	,	PUNCT
ejpam-4061	20	39	b⟩	b⟩	PRON
ejpam-4061	20	40	)	)	PUNCT
ejpam-4061	20	41	be	be	AUX
ejpam-4061	20	42	the	the	DET
ejpam-4061	20	43	set	set	NOUN
ejpam-4061	20	44	of	of	ADP
ejpam-4061	20	45	all	all	DET
ejpam-4061	20	46	points	point	NOUN
ejpam-4061	20	47	in	in	ADP
ejpam-4061	20	48	x	x	PUNCT
ejpam-4061	20	49	inside	inside	ADP
ejpam-4061	20	50	the	the	DET
ejpam-4061	20	51	circle	circle	NOUN
ejpam-4061	20	52	of	of	ADP
ejpam-4061	20	53	radius	radius	NOUN
ejpam-4061	20	54	r	r	NOUN
ejpam-4061	20	55	centered	center	VERB
ejpam-4061	20	56	at	at	ADP
ejpam-4061	20	57	⟨a	⟨a	PROPN
ejpam-4061	20	58	,	,	PUNCT
ejpam-4061	20	59	b⟩.	b⟩.	NOUN
ejpam-4061	21	1	so	so	ADV
ejpam-4061	21	2	,	,	PUNCT
ejpam-4061	21	3	ur(⟨a	ur(⟨a	NOUN
ejpam-4061	21	4	,	,	PUNCT
ejpam-4061	21	5	b⟩	b⟩	PUNCT
ejpam-4061	21	6	)	)	PUNCT
ejpam-4061	22	1	=	=	PRON
ejpam-4061	22	2	{	{	PUNCT
ejpam-4061	22	3	⟨x	⟨x	NUM
ejpam-4061	22	4	,	,	PUNCT
ejpam-4061	22	5	y⟩	y⟩	NOUN
ejpam-4061	22	6	∈	∈	PROPN
ejpam-4061	22	7	x	x	X
ejpam-4061	22	8	:	:	PUNCT
ejpam-4061	22	9	∗corresponding	∗corresponde	VERB
ejpam-4061	22	10	author	author	NOUN
ejpam-4061	22	11	.	.	PUNCT
ejpam-4061	23	1	doi	doi	NOUN
ejpam-4061	23	2	:	:	PUNCT
ejpam-4061	23	3	https://doi.org/10.29020/nybg.ejpam.v14i4.4061	https://doi.org/10.29020/nybg.ejpam.v14i4.4061	NOUN
ejpam-4061	23	4	email	email	NOUN
ejpam-4061	23	5	addresses	address	NOUN
ejpam-4061	23	6	:	:	PUNCT
ejpam-4061	23	7	nalghamdi0454@stu.kau.edu.sa	nalghamdi0454@stu.kau.edu.sa	NOUN
ejpam-4061	23	8	,	,	PUNCT
ejpam-4061	23	9	namghamdi@uqu.edu.sa	namghamdi@uqu.edu.sa	PROPN
ejpam-4061	23	10	(	(	PUNCT
ejpam-4061	23	11	n.	n.	NOUN
ejpam-4061	23	12	alghamdi	alghamdi	PROPN
ejpam-4061	23	13	)	)	PUNCT
ejpam-4061	23	14	,	,	PUNCT
ejpam-4061	23	15	lnkalantan@hotmail.com	lnkalantan@hotmail.com	PROPN
ejpam-4061	23	16	,	,	PUNCT
ejpam-4061	23	17	lkalantan@kau.edu.sa	lkalantan@kau.edu.sa	PROPN
ejpam-4061	23	18	(	(	PUNCT
ejpam-4061	23	19	l.	l.	PROPN
ejpam-4061	23	20	kalantan	kalantan	PROPN
ejpam-4061	23	21	)	)	PUNCT
ejpam-4061	23	22	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4061	24	1	1161	1161	NUM
ejpam-4061	24	2	©	©	PROPN
ejpam-4061	24	3	2021	2021	NUM
ejpam-4061	24	4	ejpam	ejpam	VERB
ejpam-4061	24	5	all	all	DET
ejpam-4061	24	6	rights	right	NOUN
ejpam-4061	24	7	reserved	reserve	VERB
ejpam-4061	24	8	.	.	PUNCT
ejpam-4061	25	1	n.	n.	PROPN
ejpam-4061	25	2	alghamdi	alghamdi	PROPN
ejpam-4061	25	3	,	,	PUNCT
ejpam-4061	25	4	l.	l.	PROPN
ejpam-4061	25	5	kalantan	kalantan	PROPN
ejpam-4061	25	6	/	/	SYM
ejpam-4061	25	7	eur	eur	PROPN
ejpam-4061	25	8	.	.	PUNCT
ejpam-4061	26	1	j.	j.	PROPN
ejpam-4061	26	2	pure	pure	PROPN
ejpam-4061	26	3	appl	appl	PROPN
ejpam-4061	26	4	.	.	PROPN
ejpam-4061	26	5	math	math	PROPN
ejpam-4061	26	6	,	,	PUNCT
ejpam-4061	26	7	14	14	NUM
ejpam-4061	26	8	(	(	PUNCT
ejpam-4061	26	9	4	4	NUM
ejpam-4061	26	10	)	)	PUNCT
ejpam-4061	26	11	(	(	PUNCT
ejpam-4061	26	12	2021	2021	NUM
ejpam-4061	26	13	)	)	PUNCT
ejpam-4061	26	14	,	,	PUNCT
ejpam-4061	26	15	1161	1161	NUM
ejpam-4061	26	16	-	-	SYM
ejpam-4061	26	17	1168	1168	NUM
ejpam-4061	26	18	1162√	1162√	NUM
ejpam-4061	26	19	(	(	PUNCT
ejpam-4061	26	20	x−	x−	PROPN
ejpam-4061	26	21	a)2	a)2	PROPN
ejpam-4061	26	22	+	+	CCONJ
ejpam-4061	26	23	(	(	PUNCT
ejpam-4061	26	24	y	y	PROPN
ejpam-4061	26	25	−	−	PROPN
ejpam-4061	27	1	b)2	b)2	PROPN
ejpam-4061	27	2	<	<	X
ejpam-4061	27	3	r	r	NOUN
ejpam-4061	27	4	}	}	PUNCT
ejpam-4061	27	5	.	.	PUNCT
ejpam-4061	28	1	for	for	ADP
ejpam-4061	28	2	every	every	DET
ejpam-4061	28	3	⟨a	⟨a	NOUN
ejpam-4061	28	4	,	,	PUNCT
ejpam-4061	28	5	0⟩	0⟩	PROPN
ejpam-4061	28	6	∈	∈	PROPN
ejpam-4061	28	7	l	l	NOUN
ejpam-4061	28	8	,	,	PUNCT
ejpam-4061	28	9	let	let	VERB
ejpam-4061	28	10	c(⟨a	c(⟨a	ADJ
ejpam-4061	28	11	,	,	PUNCT
ejpam-4061	28	12	0⟩	0⟩	PROPN
ejpam-4061	28	13	,	,	PUNCT
ejpam-4061	28	14	r	r	NOUN
ejpam-4061	28	15	)	)	PUNCT
ejpam-4061	28	16	be	be	VERB
ejpam-4061	28	17	the	the	DET
ejpam-4061	28	18	set	set	NOUN
ejpam-4061	28	19	of	of	ADP
ejpam-4061	28	20	all	all	DET
ejpam-4061	28	21	points	point	NOUN
ejpam-4061	28	22	of	of	ADP
ejpam-4061	28	23	k	k	PROPN
ejpam-4061	28	24	inside	inside	ADP
ejpam-4061	28	25	the	the	DET
ejpam-4061	28	26	circle	circle	NOUN
ejpam-4061	28	27	of	of	ADP
ejpam-4061	28	28	radius	radius	NOUN
ejpam-4061	28	29	r	r	NOUN
ejpam-4061	28	30	centered	center	VERB
ejpam-4061	28	31	at	at	ADP
ejpam-4061	28	32	⟨a	⟨a	PROPN
ejpam-4061	28	33	,	,	PUNCT
ejpam-4061	28	34	0⟩.	0⟩.	PROPN
ejpam-4061	29	1	so	so	ADV
ejpam-4061	29	2	,	,	PUNCT
ejpam-4061	29	3	c(⟨a	c(⟨a	NOUN
ejpam-4061	29	4	,	,	PUNCT
ejpam-4061	29	5	0⟩	0⟩	PROPN
ejpam-4061	29	6	,	,	PUNCT
ejpam-4061	29	7	r	r	NOUN
ejpam-4061	29	8	)	)	PUNCT
ejpam-4061	29	9	=	=	SYM
ejpam-4061	29	10	ur(⟨a	ur(⟨a	NOUN
ejpam-4061	29	11	,	,	PUNCT
ejpam-4061	29	12	0⟩	0⟩	ADJ
ejpam-4061	29	13	)	)	PUNCT
ejpam-4061	29	14	∩	∩	NOUN
ejpam-4061	29	15	k.	k.	PROPN
ejpam-4061	29	16	let	let	VERB
ejpam-4061	29	17	cr(⟨a	cr(⟨a	NUM
ejpam-4061	29	18	,	,	PUNCT
ejpam-4061	29	19	0⟩	0⟩	PROPN
ejpam-4061	29	20	)	)	PUNCT
ejpam-4061	30	1	=	=	SYM
ejpam-4061	30	2	c(⟨a	c(⟨a	PROPN
ejpam-4061	30	3	,	,	PUNCT
ejpam-4061	30	4	0⟩	0⟩	PROPN
ejpam-4061	30	5	,	,	PUNCT
ejpam-4061	30	6	r	r	NOUN
ejpam-4061	30	7	)	)	PUNCT
ejpam-4061	30	8	∪	∪	NOUN
ejpam-4061	30	9	{	{	PUNCT
ejpam-4061	30	10	⟨a	⟨a	NOUN
ejpam-4061	30	11	,	,	PUNCT
ejpam-4061	30	12	0⟩	0⟩	PROPN
ejpam-4061	30	13	}	}	PUNCT
ejpam-4061	30	14	.	.	PUNCT
ejpam-4061	31	1	recall	recall	VERB
ejpam-4061	31	2	that	that	SCONJ
ejpam-4061	31	3	the	the	DET
ejpam-4061	31	4	half	half	ADJ
ejpam-4061	31	5	-	-	PUNCT
ejpam-4061	31	6	disc	disc	NOUN
ejpam-4061	31	7	topology	topology	NOUN
ejpam-4061	31	8	h	h	NOUN
ejpam-4061	31	9	on	on	ADP
ejpam-4061	31	10	x	x	PUNCT
ejpam-4061	32	1	[	[	X
ejpam-4061	32	2	8	8	NUM
ejpam-4061	32	3	,	,	PUNCT
ejpam-4061	32	4	example	example	NOUN
ejpam-4061	32	5	78	78	NUM
ejpam-4061	32	6	]	]	PUNCT
ejpam-4061	32	7	is	be	AUX
ejpam-4061	32	8	generated	generate	VERB
ejpam-4061	32	9	by	by	ADP
ejpam-4061	32	10	the	the	DET
ejpam-4061	32	11	following	follow	VERB
ejpam-4061	32	12	neighborhood	neighborhood	NOUN
ejpam-4061	32	13	system	system	NOUN
ejpam-4061	32	14	:	:	PUNCT
ejpam-4061	32	15	for	for	ADP
ejpam-4061	32	16	every	every	DET
ejpam-4061	32	17	⟨a	⟨a	NOUN
ejpam-4061	32	18	,	,	PUNCT
ejpam-4061	32	19	0⟩	0⟩	PROPN
ejpam-4061	32	20	∈	∈	PROPN
ejpam-4061	32	21	l	l	NOUN
ejpam-4061	32	22	,	,	PUNCT
ejpam-4061	32	23	let	let	VERB
ejpam-4061	32	24	b(⟨a	b(⟨a	NOUN
ejpam-4061	32	25	,	,	PUNCT
ejpam-4061	32	26	0⟩	0⟩	PROPN
ejpam-4061	32	27	)	)	PUNCT
ejpam-4061	33	1	=	=	PRON
ejpam-4061	33	2	{	{	PUNCT
ejpam-4061	33	3	cr(⟨a	cr(⟨a	NOUN
ejpam-4061	33	4	,	,	PUNCT
ejpam-4061	33	5	0⟩	0⟩	PROPN
ejpam-4061	33	6	)	)	PUNCT
ejpam-4061	33	7	:	:	PUNCT
ejpam-4061	34	1	r	r	X
ejpam-4061	34	2	>	>	X
ejpam-4061	34	3	0	0	NUM
ejpam-4061	34	4	}	}	PUNCT
ejpam-4061	34	5	and	and	CCONJ
ejpam-4061	34	6	for	for	ADP
ejpam-4061	34	7	every	every	DET
ejpam-4061	34	8	⟨a	⟨a	NOUN
ejpam-4061	34	9	,	,	PUNCT
ejpam-4061	34	10	b⟩	b⟩	PUNCT
ejpam-4061	34	11	∈	∈	PROPN
ejpam-4061	34	12	k	k	NOUN
ejpam-4061	34	13	,	,	PUNCT
ejpam-4061	34	14	let	let	VERB
ejpam-4061	34	15	b(⟨a	b(⟨a	NOUN
ejpam-4061	34	16	,	,	PUNCT
ejpam-4061	34	17	b⟩	b⟩	PUNCT
ejpam-4061	34	18	)	)	PUNCT
ejpam-4061	34	19	=	=	PRON
ejpam-4061	34	20	{	{	PUNCT
ejpam-4061	34	21	ur(⟨a	ur(⟨a	NOUN
ejpam-4061	34	22	,	,	PUNCT
ejpam-4061	34	23	b⟩	b⟩	PRON
ejpam-4061	34	24	)	)	PUNCT
ejpam-4061	34	25	:	:	PUNCT
ejpam-4061	35	1	r	r	X
ejpam-4061	35	2	>	>	X
ejpam-4061	35	3	0	0	NUM
ejpam-4061	35	4	}	}	PUNCT
ejpam-4061	35	5	.	.	PUNCT
ejpam-4061	36	1	observe	observe	VERB
ejpam-4061	36	2	that	that	SCONJ
ejpam-4061	36	3	k	k	PROPN
ejpam-4061	36	4	as	as	ADP
ejpam-4061	36	5	a	a	DET
ejpam-4061	36	6	subspace	subspace	NOUN
ejpam-4061	36	7	of	of	ADP
ejpam-4061	36	8	x	x	PUNCT
ejpam-4061	36	9	with	with	ADP
ejpam-4061	36	10	the	the	DET
ejpam-4061	36	11	usual	usual	ADJ
ejpam-4061	36	12	metric	metric	ADJ
ejpam-4061	36	13	topology	topology	NOUN
ejpam-4061	36	14	coincides	coincide	VERB
ejpam-4061	36	15	with	with	ADP
ejpam-4061	36	16	k	k	PROPN
ejpam-4061	36	17	as	as	ADP
ejpam-4061	36	18	a	a	DET
ejpam-4061	36	19	subspace	subspace	NOUN
ejpam-4061	36	20	of	of	ADP
ejpam-4061	36	21	x	x	PUNCT
ejpam-4061	36	22	with	with	ADP
ejpam-4061	36	23	the	the	DET
ejpam-4061	36	24	half	half	ADJ
ejpam-4061	36	25	-	-	PUNCT
ejpam-4061	36	26	disc	disc	NOUN
ejpam-4061	36	27	topology	topology	NOUN
ejpam-4061	36	28	.	.	PUNCT
ejpam-4061	37	1	⟨a	⟨a	X
ejpam-4061	37	2	,	,	PUNCT
ejpam-4061	37	3	b⟩•	b⟩•	PROPN
ejpam-4061	37	4	⟨a	⟨a	PROPN
ejpam-4061	37	5	,	,	PUNCT
ejpam-4061	37	6	b⟩	b⟩	PUNCT
ejpam-4061	37	7	∈	∈	PROPN
ejpam-4061	37	8	k	k	PROPN
ejpam-4061	37	9	,	,	PUNCT
ejpam-4061	37	10	ur(⟨a	ur(⟨a	NOUN
ejpam-4061	37	11	,	,	PUNCT
ejpam-4061	37	12	b⟩	b⟩	PRON
ejpam-4061	37	13	)	)	PUNCT
ejpam-4061	37	14	⟨a	⟨a	PROPN
ejpam-4061	37	15	,	,	PUNCT
ejpam-4061	37	16	0⟩	0⟩	PROPN
ejpam-4061	37	17	•	•	NUM
ejpam-4061	37	18	◦	◦	PROPN
ejpam-4061	37	19	◦	◦	NOUN
ejpam-4061	37	20	⟨a	⟨a	NOUN
ejpam-4061	37	21	,	,	PUNCT
ejpam-4061	37	22	0⟩	0⟩	PROPN
ejpam-4061	37	23	∈	∈	PROPN
ejpam-4061	37	24	l	l	NOUN
ejpam-4061	37	25	,	,	PUNCT
ejpam-4061	37	26	ur(⟨a	ur(⟨a	ADV
ejpam-4061	37	27	,	,	PUNCT
ejpam-4061	37	28	0⟩	0⟩	PROPN
ejpam-4061	37	29	)	)	PUNCT
ejpam-4061	37	30	⟨a	⟨a	PROPN
ejpam-4061	37	31	,	,	PUNCT
ejpam-4061	37	32	0⟩	0⟩	PROPN
ejpam-4061	37	33	•	•	NUM
ejpam-4061	37	34	◦	◦	PROPN
ejpam-4061	37	35	◦	◦	NOUN
ejpam-4061	37	36	⟨a	⟨a	NOUN
ejpam-4061	37	37	,	,	PUNCT
ejpam-4061	37	38	0⟩	0⟩	PROPN
ejpam-4061	37	39	∈	∈	PROPN
ejpam-4061	37	40	l	l	NOUN
ejpam-4061	37	41	,	,	PUNCT
ejpam-4061	37	42	cr(⟨a	cr(⟨a	NUM
ejpam-4061	37	43	,	,	PUNCT
ejpam-4061	37	44	0⟩	0⟩	PROPN
ejpam-4061	37	45	)	)	PUNCT
ejpam-4061	37	46	1	1	NUM
ejpam-4061	37	47	.	.	X
ejpam-4061	37	48	h	h	NOUN
ejpam-4061	37	49	-	-	PUNCT
ejpam-4061	37	50	generated	generate	VERB
ejpam-4061	37	51	topology	topology	NOUN
ejpam-4061	37	52	.	.	PUNCT
ejpam-4061	38	1	definition	definition	NOUN
ejpam-4061	38	2	1	1	NUM
ejpam-4061	38	3	.	.	PUNCT
ejpam-4061	39	1	let	let	VERB
ejpam-4061	39	2	a	a	PRON
ejpam-4061	39	3	be	be	AUX
ejpam-4061	39	4	a	a	DET
ejpam-4061	39	5	non	non	ADJ
ejpam-4061	39	6	-	-	ADJ
ejpam-4061	39	7	empty	empty	ADJ
ejpam-4061	39	8	proper	proper	ADJ
ejpam-4061	39	9	subset	subset	NOUN
ejpam-4061	39	10	of	of	ADP
ejpam-4061	39	11	the	the	DET
ejpam-4061	39	12	x	x	ADJ
ejpam-4061	39	13	-	-	ADJ
ejpam-4061	39	14	axis	axis	ADJ
ejpam-4061	39	15	l.	l.	NOUN
ejpam-4061	39	16	for	for	ADP
ejpam-4061	39	17	each	each	DET
ejpam-4061	39	18	⟨a	⟨a	NOUN
ejpam-4061	39	19	,	,	PUNCT
ejpam-4061	39	20	b⟩	b⟩	PUNCT
ejpam-4061	39	21	∈	∈	NOUN
ejpam-4061	39	22	k∪a	k∪a	NOUN
ejpam-4061	39	23	,	,	PUNCT
ejpam-4061	39	24	let	let	VERB
ejpam-4061	39	25	b(⟨a	b(⟨a	NOUN
ejpam-4061	39	26	,	,	PUNCT
ejpam-4061	39	27	b⟩	b⟩	PUNCT
ejpam-4061	39	28	)	)	PUNCT
ejpam-4061	39	29	=	=	PRON
ejpam-4061	40	1	{	{	PUNCT
ejpam-4061	40	2	ur(⟨a	ur(⟨a	NOUN
ejpam-4061	40	3	,	,	PUNCT
ejpam-4061	40	4	b⟩	b⟩	PRON
ejpam-4061	40	5	)	)	PUNCT
ejpam-4061	40	6	:	:	PUNCT
ejpam-4061	40	7	r	r	X
ejpam-4061	40	8	>	>	X
ejpam-4061	40	9	0	0	NUM
ejpam-4061	40	10	}	}	PUNCT
ejpam-4061	40	11	.	.	PUNCT
ejpam-4061	41	1	for	for	ADP
ejpam-4061	41	2	each	each	DET
ejpam-4061	41	3	⟨a	⟨a	PROPN
ejpam-4061	41	4	,	,	PUNCT
ejpam-4061	41	5	0⟩	0⟩	PROPN
ejpam-4061	41	6	∈	∈	PROPN
ejpam-4061	41	7	l	l	NOUN
ejpam-4061	41	8	\	\	PROPN
ejpam-4061	42	1	a	a	PRON
ejpam-4061	42	2	,	,	PUNCT
ejpam-4061	42	3	let	let	VERB
ejpam-4061	42	4	b(⟨a	b(⟨a	NOUN
ejpam-4061	42	5	,	,	PUNCT
ejpam-4061	42	6	0⟩	0⟩	PROPN
ejpam-4061	42	7	)	)	PUNCT
ejpam-4061	43	1	=	=	PRON
ejpam-4061	43	2	{	{	PUNCT
ejpam-4061	43	3	cr(⟨a	cr(⟨a	NOUN
ejpam-4061	43	4	,	,	PUNCT
ejpam-4061	43	5	0⟩	0⟩	PROPN
ejpam-4061	43	6	)	)	PUNCT
ejpam-4061	43	7	:	:	PUNCT
ejpam-4061	44	1	r	r	X
ejpam-4061	44	2	>	>	X
ejpam-4061	44	3	0	0	NUM
ejpam-4061	44	4	}	}	PUNCT
ejpam-4061	44	5	.	.	PUNCT
ejpam-4061	45	1	so	so	ADV
ejpam-4061	45	2	,	,	PUNCT
ejpam-4061	45	3	the	the	DET
ejpam-4061	45	4	points	point	NOUN
ejpam-4061	45	5	in	in	ADP
ejpam-4061	45	6	k	k	PROPN
ejpam-4061	45	7	∪	∪	NOUN
ejpam-4061	45	8	a	a	PRON
ejpam-4061	45	9	will	will	AUX
ejpam-4061	45	10	have	have	VERB
ejpam-4061	45	11	the	the	DET
ejpam-4061	45	12	same	same	ADJ
ejpam-4061	45	13	local	local	ADJ
ejpam-4061	45	14	base	base	NOUN
ejpam-4061	45	15	as	as	ADP
ejpam-4061	45	16	in	in	ADP
ejpam-4061	45	17	(	(	PUNCT
ejpam-4061	45	18	x	x	INTJ
ejpam-4061	45	19	,	,	PUNCT
ejpam-4061	45	20	u	u	NOUN
ejpam-4061	45	21	)	)	PUNCT
ejpam-4061	45	22	.	.	PUNCT
ejpam-4061	46	1	the	the	DET
ejpam-4061	46	2	points	point	NOUN
ejpam-4061	46	3	in	in	ADP
ejpam-4061	46	4	l	l	NOUN
ejpam-4061	46	5	\a	\a	ADJ
ejpam-4061	46	6	will	will	AUX
ejpam-4061	46	7	have	have	VERB
ejpam-4061	46	8	the	the	DET
ejpam-4061	46	9	same	same	ADJ
ejpam-4061	46	10	local	local	ADJ
ejpam-4061	46	11	base	base	NOUN
ejpam-4061	46	12	as	as	ADP
ejpam-4061	46	13	in	in	ADP
ejpam-4061	46	14	(	(	PUNCT
ejpam-4061	46	15	x	x	NOUN
ejpam-4061	46	16	,	,	PUNCT
ejpam-4061	46	17	h	h	NOUN
ejpam-4061	46	18	)	)	PUNCT
ejpam-4061	46	19	.	.	PUNCT
ejpam-4061	47	1	we	we	PRON
ejpam-4061	47	2	call	call	VERB
ejpam-4061	47	3	the	the	DET
ejpam-4061	47	4	topology	topology	NOUN
ejpam-4061	47	5	on	on	ADP
ejpam-4061	47	6	x	x	PUNCT
ejpam-4061	47	7	generated	generate	VERB
ejpam-4061	47	8	by	by	ADP
ejpam-4061	47	9	the	the	DET
ejpam-4061	47	10	neighborhood	neighborhood	NOUN
ejpam-4061	47	11	system	system	NOUN
ejpam-4061	47	12	{	{	PUNCT
ejpam-4061	47	13	b(⟨a	b(⟨a	NOUN
ejpam-4061	47	14	,	,	PUNCT
ejpam-4061	47	15	b⟩	b⟩	PRON
ejpam-4061	47	16	)	)	PUNCT
ejpam-4061	47	17	:	:	PUNCT
ejpam-4061	48	1	⟨a	⟨a	NOUN
ejpam-4061	48	2	,	,	PUNCT
ejpam-4061	48	3	b⟩	b⟩	PUNCT
ejpam-4061	48	4	∈	∈	PROPN
ejpam-4061	48	5	x	x	SYM
ejpam-4061	48	6	}	}	PUNCT
ejpam-4061	48	7	the	the	DET
ejpam-4061	48	8	h	h	NOUN
ejpam-4061	48	9	-	-	PUNCT
ejpam-4061	48	10	generated	generate	VERB
ejpam-4061	48	11	topology	topology	NOUN
ejpam-4061	48	12	on	on	ADP
ejpam-4061	48	13	x	x	PUNCT
ejpam-4061	48	14	from	from	ADP
ejpam-4061	48	15	u	u	NOUN
ejpam-4061	48	16	and	and	CCONJ
ejpam-4061	48	17	h	h	NOUN
ejpam-4061	48	18	,	,	PUNCT
ejpam-4061	48	19	shortly	shortly	ADV
ejpam-4061	48	20	h	h	NOUN
ejpam-4061	48	21	-	-	PUNCT
ejpam-4061	48	22	topology	topology	NOUN
ejpam-4061	48	23	,	,	PUNCT
ejpam-4061	48	24	and	and	CCONJ
ejpam-4061	48	25	denote	denote	VERB
ejpam-4061	48	26	it	it	PRON
ejpam-4061	48	27	by	by	ADP
ejpam-4061	48	28	uah	uah	PROPN
ejpam-4061	48	29	.	.	PUNCT
ejpam-4061	49	1	we	we	PRON
ejpam-4061	49	2	call	call	VERB
ejpam-4061	49	3	x	x	PUNCT
ejpam-4061	49	4	with	with	ADP
ejpam-4061	49	5	this	this	DET
ejpam-4061	49	6	h	h	NOUN
ejpam-4061	49	7	-	-	PUNCT
ejpam-4061	49	8	generated	generate	VERB
ejpam-4061	49	9	topology	topology	NOUN
ejpam-4061	49	10	an	an	DET
ejpam-4061	49	11	h	h	NOUN
ejpam-4061	49	12	-	-	PUNCT
ejpam-4061	49	13	space	space	NOUN
ejpam-4061	49	14	and	and	CCONJ
ejpam-4061	49	15	denote	denote	VERB
ejpam-4061	49	16	it	it	PRON
ejpam-4061	49	17	by	by	ADP
ejpam-4061	49	18	(	(	PUNCT
ejpam-4061	49	19	x	x	INTJ
ejpam-4061	49	20	,	,	PUNCT
ejpam-4061	49	21	uah	uah	PROPN
ejpam-4061	49	22	)	)	PUNCT
ejpam-4061	49	23	.	.	PUNCT
ejpam-4061	50	1	observe	observe	VERB
ejpam-4061	50	2	that	that	SCONJ
ejpam-4061	50	3	if	if	SCONJ
ejpam-4061	50	4	a	a	DET
ejpam-4061	50	5	=	=	NOUN
ejpam-4061	50	6	∅	∅	NOUN
ejpam-4061	50	7	,	,	PUNCT
ejpam-4061	50	8	then	then	ADV
ejpam-4061	50	9	the	the	DET
ejpam-4061	50	10	h	h	NOUN
ejpam-4061	50	11	-	-	PUNCT
ejpam-4061	50	12	generated	generate	VERB
ejpam-4061	50	13	topology	topology	NOUN
ejpam-4061	50	14	on	on	ADP
ejpam-4061	50	15	x	x	X
ejpam-4061	50	16	,	,	PUNCT
ejpam-4061	50	17	uah	uah	PROPN
ejpam-4061	50	18	is	be	AUX
ejpam-4061	50	19	just	just	ADV
ejpam-4061	50	20	the	the	DET
ejpam-4061	50	21	half	half	ADJ
ejpam-4061	50	22	-	-	PUNCT
ejpam-4061	50	23	disc	disc	NOUN
ejpam-4061	50	24	topology	topology	NOUN
ejpam-4061	50	25	h	h	NOUN
ejpam-4061	50	26	and	and	CCONJ
ejpam-4061	50	27	if	if	SCONJ
ejpam-4061	50	28	a	a	DET
ejpam-4061	50	29	=	=	SYM
ejpam-4061	50	30	l	l	NOUN
ejpam-4061	50	31	,	,	PUNCT
ejpam-4061	50	32	then	then	ADV
ejpam-4061	50	33	the	the	DET
ejpam-4061	50	34	h	h	NOUN
ejpam-4061	50	35	-	-	PUNCT
ejpam-4061	50	36	generated	generate	VERB
ejpam-4061	50	37	topology	topology	NOUN
ejpam-4061	50	38	on	on	ADP
ejpam-4061	50	39	x	x	X
ejpam-4061	50	40	,	,	PUNCT
ejpam-4061	50	41	uah	uah	PROPN
ejpam-4061	50	42	is	be	AUX
ejpam-4061	50	43	just	just	ADV
ejpam-4061	50	44	the	the	DET
ejpam-4061	50	45	usual	usual	ADJ
ejpam-4061	50	46	metric	metric	ADJ
ejpam-4061	50	47	topology	topology	NOUN
ejpam-4061	50	48	u	u	NOUN
ejpam-4061	50	49	.	.	PUNCT
ejpam-4061	51	1	so	so	ADV
ejpam-4061	51	2	,	,	PUNCT
ejpam-4061	51	3	from	from	ADP
ejpam-4061	51	4	now	now	ADV
ejpam-4061	51	5	on	on	ADV
ejpam-4061	51	6	,	,	PUNCT
ejpam-4061	51	7	when	when	SCONJ
ejpam-4061	51	8	we	we	PRON
ejpam-4061	51	9	consider	consider	VERB
ejpam-4061	51	10	an	an	DET
ejpam-4061	51	11	h	h	NOUN
ejpam-4061	51	12	-	-	PUNCT
ejpam-4061	51	13	space	space	NOUN
ejpam-4061	51	14	(	(	PUNCT
ejpam-4061	51	15	x	x	NOUN
ejpam-4061	51	16	,	,	PUNCT
ejpam-4061	51	17	uah	uah	PROPN
ejpam-4061	51	18	)	)	PUNCT
ejpam-4061	51	19	,	,	PUNCT
ejpam-4061	51	20	we	we	PRON
ejpam-4061	51	21	are	be	AUX
ejpam-4061	51	22	assuming	assume	VERB
ejpam-4061	51	23	that	that	SCONJ
ejpam-4061	51	24	a	a	PRON
ejpam-4061	51	25	is	be	AUX
ejpam-4061	51	26	a	a	DET
ejpam-4061	51	27	non	non	ADJ
ejpam-4061	51	28	-	-	ADJ
ejpam-4061	51	29	empty	empty	ADJ
ejpam-4061	51	30	proper	proper	ADJ
ejpam-4061	51	31	subset	subset	NOUN
ejpam-4061	51	32	of	of	ADP
ejpam-4061	51	33	the	the	DET
ejpam-4061	51	34	x	x	ADJ
ejpam-4061	51	35	-	-	ADJ
ejpam-4061	51	36	axis	axis	ADJ
ejpam-4061	51	37	l.	l.	NOUN
ejpam-4061	51	38	in	in	ADP
ejpam-4061	51	39	definition	definition	NOUN
ejpam-4061	51	40	1	1	NUM
ejpam-4061	51	41	,	,	PUNCT
ejpam-4061	51	42	if	if	SCONJ
ejpam-4061	51	43	we	we	PRON
ejpam-4061	51	44	interchange	interchange	VERB
ejpam-4061	51	45	the	the	DET
ejpam-4061	51	46	local	local	ADJ
ejpam-4061	51	47	bases	basis	NOUN
ejpam-4061	51	48	as	as	SCONJ
ejpam-4061	51	49	follows	follow	VERB
ejpam-4061	51	50	:	:	PUNCT
ejpam-4061	51	51	the	the	DET
ejpam-4061	51	52	points	point	NOUN
ejpam-4061	51	53	in	in	ADP
ejpam-4061	51	54	k	k	PROPN
ejpam-4061	51	55	∪	∪	X
ejpam-4061	51	56	(	(	PUNCT
ejpam-4061	51	57	l	l	NOUN
ejpam-4061	51	58	\a	\a	NUM
ejpam-4061	51	59	)	)	PUNCT
ejpam-4061	51	60	will	will	AUX
ejpam-4061	51	61	have	have	VERB
ejpam-4061	51	62	the	the	DET
ejpam-4061	51	63	same	same	ADJ
ejpam-4061	51	64	local	local	ADJ
ejpam-4061	51	65	base	base	NOUN
ejpam-4061	51	66	as	as	ADP
ejpam-4061	51	67	in	in	ADP
ejpam-4061	51	68	(	(	PUNCT
ejpam-4061	51	69	x	x	INTJ
ejpam-4061	51	70	,	,	PUNCT
ejpam-4061	51	71	u	u	NOUN
ejpam-4061	51	72	)	)	PUNCT
ejpam-4061	51	73	.	.	PUNCT
ejpam-4061	52	1	the	the	DET
ejpam-4061	52	2	points	point	NOUN
ejpam-4061	52	3	in	in	ADP
ejpam-4061	52	4	a	a	PRON
ejpam-4061	52	5	will	will	AUX
ejpam-4061	52	6	have	have	VERB
ejpam-4061	52	7	the	the	DET
ejpam-4061	52	8	same	same	ADJ
ejpam-4061	52	9	local	local	ADJ
ejpam-4061	52	10	base	base	NOUN
ejpam-4061	52	11	as	as	ADP
ejpam-4061	52	12	in	in	ADP
ejpam-4061	52	13	(	(	PUNCT
ejpam-4061	52	14	x	x	NOUN
ejpam-4061	52	15	,	,	PUNCT
ejpam-4061	52	16	h	h	NOUN
ejpam-4061	52	17	)	)	PUNCT
ejpam-4061	52	18	.	.	PUNCT
ejpam-4061	53	1	then	then	ADV
ejpam-4061	53	2	we	we	PRON
ejpam-4061	53	3	get	get	VERB
ejpam-4061	53	4	the	the	DET
ejpam-4061	53	5	h	h	NOUN
ejpam-4061	53	6	-	-	PUNCT
ejpam-4061	53	7	space	space	NOUN
ejpam-4061	53	8	(	(	PUNCT
ejpam-4061	53	9	x	x	X
ejpam-4061	53	10	,	,	PUNCT
ejpam-4061	53	11	hau	hau	PROPN
ejpam-4061	53	12	)	)	PUNCT
ejpam-4061	53	13	and	and	CCONJ
ejpam-4061	53	14	it	it	PRON
ejpam-4061	53	15	is	be	AUX
ejpam-4061	53	16	easy	easy	ADJ
ejpam-4061	53	17	to	to	PART
ejpam-4061	53	18	see	see	VERB
ejpam-4061	53	19	that	that	PRON
ejpam-4061	53	20	(	(	PUNCT
ejpam-4061	53	21	x	x	X
ejpam-4061	53	22	,	,	PUNCT
ejpam-4061	53	23	hau	hau	NOUN
ejpam-4061	53	24	)	)	PUNCT
ejpam-4061	53	25	∼=	∼=	PROPN
ejpam-4061	53	26	(	(	PUNCT
ejpam-4061	53	27	x	x	NOUN
ejpam-4061	53	28	,	,	PUNCT
ejpam-4061	53	29	ul\ah	ul\ah	PROPN
ejpam-4061	53	30	)	)	PUNCT
ejpam-4061	53	31	.	.	PUNCT
ejpam-4061	54	1	so	so	ADV
ejpam-4061	54	2	,	,	PUNCT
ejpam-4061	54	3	in	in	ADP
ejpam-4061	54	4	this	this	DET
ejpam-4061	54	5	paper	paper	NOUN
ejpam-4061	54	6	,	,	PUNCT
ejpam-4061	54	7	we	we	PRON
ejpam-4061	54	8	will	will	AUX
ejpam-4061	54	9	study	study	VERB
ejpam-4061	54	10	the	the	DET
ejpam-4061	54	11	h	h	NOUN
ejpam-4061	54	12	-	-	PUNCT
ejpam-4061	54	13	spaces	space	NOUN
ejpam-4061	54	14	of	of	ADP
ejpam-4061	54	15	definition	definition	NOUN
ejpam-4061	54	16	1	1	NUM
ejpam-4061	54	17	,	,	PUNCT
ejpam-4061	54	18	(	(	PUNCT
ejpam-4061	54	19	x	x	X
ejpam-4061	54	20	,	,	PUNCT
ejpam-4061	54	21	uah	uah	PROPN
ejpam-4061	54	22	)	)	PUNCT
ejpam-4061	54	23	.	.	PUNCT
ejpam-4061	55	1	observe	observe	VERB
ejpam-4061	55	2	that	that	SCONJ
ejpam-4061	55	3	k	k	PROPN
ejpam-4061	55	4	as	as	ADP
ejpam-4061	55	5	a	a	DET
ejpam-4061	55	6	subspace	subspace	NOUN
ejpam-4061	55	7	of	of	ADP
ejpam-4061	55	8	x	x	PUNCT
ejpam-4061	55	9	with	with	ADP
ejpam-4061	55	10	the	the	DET
ejpam-4061	55	11	usual	usual	ADJ
ejpam-4061	55	12	metric	metric	ADJ
ejpam-4061	55	13	topology	topology	NOUN
ejpam-4061	55	14	coincides	coincide	VERB
ejpam-4061	55	15	with	with	ADP
ejpam-4061	55	16	k	k	PROPN
ejpam-4061	55	17	as	as	ADP
ejpam-4061	55	18	a	a	DET
ejpam-4061	55	19	subspace	subspace	NOUN
ejpam-4061	55	20	of	of	ADP
ejpam-4061	55	21	x	x	PUNCT
ejpam-4061	55	22	with	with	ADP
ejpam-4061	55	23	the	the	DET
ejpam-4061	55	24	h	h	NOUN
ejpam-4061	55	25	-	-	PUNCT
ejpam-4061	55	26	topology	topology	NOUN
ejpam-4061	55	27	.	.	PUNCT
ejpam-4061	56	1	2	2	X
ejpam-4061	56	2	.	.	X
ejpam-4061	56	3	basic	basic	ADJ
ejpam-4061	56	4	properties	property	NOUN
ejpam-4061	56	5	of	of	ADP
ejpam-4061	56	6	an	an	DET
ejpam-4061	56	7	h	h	NOUN
ejpam-4061	56	8	-	-	PUNCT
ejpam-4061	56	9	space	space	NOUN
ejpam-4061	56	10	.	.	PUNCT
ejpam-4061	57	1	since	since	SCONJ
ejpam-4061	57	2	any	any	DET
ejpam-4061	57	3	basic	basic	ADJ
ejpam-4061	57	4	open	open	ADJ
ejpam-4061	57	5	set	set	NOUN
ejpam-4061	57	6	in	in	ADP
ejpam-4061	57	7	(	(	PUNCT
ejpam-4061	57	8	x	x	INTJ
ejpam-4061	57	9	,	,	PUNCT
ejpam-4061	57	10	u	u	NOUN
ejpam-4061	57	11	)	)	PUNCT
ejpam-4061	57	12	is	be	AUX
ejpam-4061	57	13	also	also	ADV
ejpam-4061	57	14	open	open	ADJ
ejpam-4061	57	15	in	in	ADP
ejpam-4061	57	16	(	(	PUNCT
ejpam-4061	57	17	x	x	INTJ
ejpam-4061	57	18	,	,	PUNCT
ejpam-4061	57	19	uah	uah	PROPN
ejpam-4061	57	20	)	)	PUNCT
ejpam-4061	57	21	,	,	PUNCT
ejpam-4061	57	22	we	we	PRON
ejpam-4061	57	23	get	get	VERB
ejpam-4061	57	24	the	the	DET
ejpam-4061	57	25	following	follow	VERB
ejpam-4061	57	26	fact	fact	NOUN
ejpam-4061	57	27	.	.	PUNCT
ejpam-4061	58	1	n.	n.	PROPN
ejpam-4061	58	2	alghamdi	alghamdi	PROPN
ejpam-4061	58	3	,	,	PUNCT
ejpam-4061	58	4	l.	l.	PROPN
ejpam-4061	58	5	kalantan	kalantan	PROPN
ejpam-4061	58	6	/	/	SYM
ejpam-4061	58	7	eur	eur	PROPN
ejpam-4061	58	8	.	.	PUNCT
ejpam-4061	59	1	j.	j.	PROPN
ejpam-4061	59	2	pure	pure	PROPN
ejpam-4061	59	3	appl	appl	PROPN
ejpam-4061	59	4	.	.	PROPN
ejpam-4061	59	5	math	math	PROPN
ejpam-4061	59	6	,	,	PUNCT
ejpam-4061	59	7	14	14	NUM
ejpam-4061	59	8	(	(	PUNCT
ejpam-4061	59	9	4	4	NUM
ejpam-4061	59	10	)	)	PUNCT
ejpam-4061	59	11	(	(	PUNCT
ejpam-4061	59	12	2021	2021	NUM
ejpam-4061	59	13	)	)	PUNCT
ejpam-4061	59	14	,	,	PUNCT
ejpam-4061	59	15	1161	1161	NUM
ejpam-4061	59	16	-	-	SYM
ejpam-4061	59	17	1168	1168	NUM
ejpam-4061	59	18	1163	1163	NUM
ejpam-4061	59	19	theorem	theorem	NOUN
ejpam-4061	59	20	1	1	NUM
ejpam-4061	59	21	.	.	PUNCT
ejpam-4061	60	1	the	the	DET
ejpam-4061	60	2	usual	usual	ADJ
ejpam-4061	60	3	topology	topology	NOUN
ejpam-4061	60	4	u	u	NOUN
ejpam-4061	60	5	on	on	ADP
ejpam-4061	60	6	x	x	SYM
ejpam-4061	60	7	is	be	AUX
ejpam-4061	60	8	coarser	coarse	ADJ
ejpam-4061	60	9	than	than	ADP
ejpam-4061	60	10	the	the	DET
ejpam-4061	60	11	h	h	NOUN
ejpam-4061	60	12	-	-	PUNCT
ejpam-4061	60	13	topology	topology	NOUN
ejpam-4061	60	14	uah	uah	NOUN
ejpam-4061	60	15	and	and	CCONJ
ejpam-4061	60	16	the	the	DET
ejpam-4061	60	17	h	h	NOUN
ejpam-4061	60	18	-	-	PUNCT
ejpam-4061	60	19	topology	topology	NOUN
ejpam-4061	60	20	uah	uah	NOUN
ejpam-4061	60	21	is	be	AUX
ejpam-4061	60	22	coarser	coarse	ADJ
ejpam-4061	60	23	than	than	ADP
ejpam-4061	60	24	the	the	DET
ejpam-4061	60	25	half	half	ADJ
ejpam-4061	60	26	-	-	PUNCT
ejpam-4061	60	27	disc	disc	NOUN
ejpam-4061	60	28	topology	topology	NOUN
ejpam-4061	60	29	h.	h.	PROPN
ejpam-4061	60	30	that	that	PRON
ejpam-4061	60	31	is	be	AUX
ejpam-4061	60	32	,	,	PUNCT
ejpam-4061	60	33	u	u	PROPN
ejpam-4061	60	34	⊂	⊂	PROPN
ejpam-4061	60	35	uah	uah	PROPN
ejpam-4061	60	36	⊂	⊂	PROPN
ejpam-4061	60	37	h.	h.	PROPN
ejpam-4061	60	38	by	by	ADP
ejpam-4061	60	39	theorem	theorem	NOUN
ejpam-4061	60	40	1	1	NUM
ejpam-4061	60	41	,	,	PUNCT
ejpam-4061	60	42	we	we	PRON
ejpam-4061	60	43	conclude	conclude	VERB
ejpam-4061	60	44	that	that	SCONJ
ejpam-4061	60	45	any	any	DET
ejpam-4061	60	46	h	h	NOUN
ejpam-4061	60	47	-	-	PUNCT
ejpam-4061	60	48	space	space	NOUN
ejpam-4061	60	49	(	(	PUNCT
ejpam-4061	60	50	x	x	NOUN
ejpam-4061	60	51	,	,	PUNCT
ejpam-4061	60	52	uah	uah	PROPN
ejpam-4061	60	53	)	)	PUNCT
ejpam-4061	60	54	is	be	AUX
ejpam-4061	60	55	t0	t0	NOUN
ejpam-4061	60	56	,	,	PUNCT
ejpam-4061	60	57	t1	t1	PROPN
ejpam-4061	60	58	,	,	PUNCT
ejpam-4061	60	59	t2	t2	NOUN
ejpam-4061	60	60	hausdorff	hausdorff	NOUN
ejpam-4061	60	61	,	,	PUNCT
ejpam-4061	60	62	and	and	CCONJ
ejpam-4061	60	63	t2	t2	NOUN
ejpam-4061	60	64	1	1	NUM
ejpam-4061	60	65	2	2	NUM
ejpam-4061	60	66	urysohn	urysohn	NOUN
ejpam-4061	60	67	(	(	PUNCT
ejpam-4061	60	68	completely	completely	ADV
ejpam-4061	60	69	hausdorff	hausdorff	NOUN
ejpam-4061	60	70	)	)	PUNCT
ejpam-4061	61	1	[	[	X
ejpam-4061	61	2	1	1	NUM
ejpam-4061	61	3	]	]	PUNCT
ejpam-4061	61	4	.	.	PUNCT
ejpam-4061	62	1	now	now	ADV
ejpam-4061	62	2	,	,	PUNCT
ejpam-4061	62	3	take	take	VERB
ejpam-4061	62	4	any	any	DET
ejpam-4061	62	5	⟨x	⟨x	VERB
ejpam-4061	62	6	,	,	PUNCT
ejpam-4061	62	7	0⟩	0⟩	PROPN
ejpam-4061	62	8	∈	∈	PROPN
ejpam-4061	62	9	l	l	NOUN
ejpam-4061	62	10	\a	\a	ADJ
ejpam-4061	62	11	.	.	PUNCT
ejpam-4061	63	1	for	for	ADP
ejpam-4061	63	2	any	any	DET
ejpam-4061	63	3	0	0	NUM
ejpam-4061	63	4	<	<	X
ejpam-4061	63	5	ϵ	ϵ	X
ejpam-4061	63	6	<	<	X
ejpam-4061	63	7	r	r	NOUN
ejpam-4061	63	8	,	,	PUNCT
ejpam-4061	63	9	we	we	PRON
ejpam-4061	63	10	have	have	VERB
ejpam-4061	63	11	that	that	DET
ejpam-4061	63	12	cϵ(⟨x	cϵ(⟨x	NOUN
ejpam-4061	63	13	,	,	PUNCT
ejpam-4061	63	14	0⟩	0⟩	PROPN
ejpam-4061	63	15	)	)	PUNCT
ejpam-4061	63	16	̸⊂	̸⊂	ADV
ejpam-4061	63	17	cr(⟨x	cr(⟨x	NOUN
ejpam-4061	63	18	,	,	PUNCT
ejpam-4061	63	19	0⟩	0⟩	PROPN
ejpam-4061	63	20	)	)	PUNCT
ejpam-4061	63	21	,	,	PUNCT
ejpam-4061	63	22	thus	thus	ADV
ejpam-4061	63	23	any	any	DET
ejpam-4061	63	24	h	h	NOUN
ejpam-4061	63	25	-	-	PUNCT
ejpam-4061	63	26	space	space	NOUN
ejpam-4061	63	27	(	(	PUNCT
ejpam-4061	63	28	x	x	NOUN
ejpam-4061	63	29	,	,	PUNCT
ejpam-4061	63	30	uah	uah	PROPN
ejpam-4061	63	31	)	)	PUNCT
ejpam-4061	63	32	is	be	AUX
ejpam-4061	63	33	not	not	PART
ejpam-4061	63	34	regular	regular	ADJ
ejpam-4061	63	35	nor	nor	CCONJ
ejpam-4061	63	36	zero	zero	NUM
ejpam-4061	63	37	-	-	PUNCT
ejpam-4061	63	38	dimensional	dimensional	ADJ
ejpam-4061	63	39	,	,	PUNCT
ejpam-4061	63	40	hence	hence	ADV
ejpam-4061	63	41	neither	neither	CCONJ
ejpam-4061	63	42	normal	normal	ADJ
ejpam-4061	63	43	,	,	PUNCT
ejpam-4061	63	44	t4	t4	PROPN
ejpam-4061	63	45	,	,	PUNCT
ejpam-4061	63	46	nor	nor	CCONJ
ejpam-4061	63	47	metrizable	metrizable	ADJ
ejpam-4061	63	48	.	.	PUNCT
ejpam-4061	64	1	we	we	PRON
ejpam-4061	64	2	conclude	conclude	VERB
ejpam-4061	64	3	also	also	ADV
ejpam-4061	64	4	that	that	SCONJ
ejpam-4061	64	5	any	any	DET
ejpam-4061	64	6	h	h	NOUN
ejpam-4061	64	7	-	-	PUNCT
ejpam-4061	64	8	space	space	NOUN
ejpam-4061	64	9	(	(	PUNCT
ejpam-4061	64	10	x	x	NOUN
ejpam-4061	64	11	,	,	PUNCT
ejpam-4061	64	12	uah	uah	PROPN
ejpam-4061	64	13	)	)	PUNCT
ejpam-4061	64	14	can	can	AUX
ejpam-4061	64	15	not	not	PART
ejpam-4061	64	16	be	be	AUX
ejpam-4061	64	17	tychonoff	tychonoff	NOUN
ejpam-4061	64	18	t3	t3	PROPN
ejpam-4061	64	19	1	1	NUM
ejpam-4061	64	20	2	2	NUM
ejpam-4061	64	21	hence	hence	ADV
ejpam-4061	64	22	has	have	VERB
ejpam-4061	64	23	no	no	DET
ejpam-4061	64	24	compactification	compactification	NOUN
ejpam-4061	64	25	and	and	CCONJ
ejpam-4061	64	26	is	be	AUX
ejpam-4061	64	27	neither	neither	CCONJ
ejpam-4061	64	28	paracompact	paracompact	ADJ
ejpam-4061	64	29	,	,	PUNCT
ejpam-4061	64	30	as	as	SCONJ
ejpam-4061	64	31	any	any	DET
ejpam-4061	64	32	t2	t2	NOUN
ejpam-4061	64	33	paracompact	paracompact	NOUN
ejpam-4061	64	34	space	space	NOUN
ejpam-4061	64	35	is	be	AUX
ejpam-4061	64	36	t4	t4	PROPN
ejpam-4061	64	37	,	,	PUNCT
ejpam-4061	64	38	nor	nor	CCONJ
ejpam-4061	64	39	locally	locally	ADV
ejpam-4061	64	40	compact	compact	ADJ
ejpam-4061	64	41	,	,	PUNCT
ejpam-4061	64	42	as	as	ADP
ejpam-4061	64	43	any	any	DET
ejpam-4061	64	44	t2	t2	NOUN
ejpam-4061	64	45	locally	locally	ADV
ejpam-4061	64	46	compact	compact	ADJ
ejpam-4061	64	47	space	space	NOUN
ejpam-4061	64	48	is	be	AUX
ejpam-4061	64	49	tychonoff	tychonoff	NOUN
ejpam-4061	64	50	.	.	PUNCT
ejpam-4061	65	1	the	the	DET
ejpam-4061	65	2	subset	subset	NOUN
ejpam-4061	65	3	d	d	X
ejpam-4061	65	4	=	=	X
ejpam-4061	65	5	{	{	PUNCT
ejpam-4061	65	6	⟨x	⟨x	NUM
ejpam-4061	65	7	,	,	PUNCT
ejpam-4061	65	8	y⟩	y⟩	NOUN
ejpam-4061	65	9	∈	∈	PROPN
ejpam-4061	66	1	x	x	X
ejpam-4061	66	2	:	:	PUNCT
ejpam-4061	66	3	x	x	X
ejpam-4061	66	4	,	,	PUNCT
ejpam-4061	66	5	y	y	PROPN
ejpam-4061	66	6	∈	∈	PROPN
ejpam-4061	66	7	q	q	PROPN
ejpam-4061	66	8	}	}	PUNCT
ejpam-4061	66	9	is	be	AUX
ejpam-4061	66	10	a	a	DET
ejpam-4061	66	11	countable	countable	ADJ
ejpam-4061	66	12	dense	dense	ADJ
ejpam-4061	66	13	subset	subset	NOUN
ejpam-4061	66	14	,	,	PUNCT
ejpam-4061	66	15	thus	thus	ADV
ejpam-4061	66	16	any	any	DET
ejpam-4061	66	17	h	h	NOUN
ejpam-4061	66	18	-	-	PUNCT
ejpam-4061	66	19	space	space	NOUN
ejpam-4061	66	20	(	(	PUNCT
ejpam-4061	66	21	x	x	NOUN
ejpam-4061	66	22	,	,	PUNCT
ejpam-4061	66	23	uah	uah	PROPN
ejpam-4061	66	24	)	)	PUNCT
ejpam-4061	66	25	is	be	AUX
ejpam-4061	66	26	separable	separable	ADJ
ejpam-4061	66	27	.	.	PUNCT
ejpam-4061	67	1	for	for	ADP
ejpam-4061	67	2	⟨x	⟨x	NUM
ejpam-4061	67	3	,	,	PUNCT
ejpam-4061	67	4	y⟩	y⟩	NOUN
ejpam-4061	67	5	∈	∈	PROPN
ejpam-4061	67	6	k	k	PROPN
ejpam-4061	67	7	∪	∪	ADP
ejpam-4061	67	8	a	a	PRON
ejpam-4061	67	9	,	,	PUNCT
ejpam-4061	67	10	the	the	DET
ejpam-4061	67	11	family	family	NOUN
ejpam-4061	67	12	b(⟨x	b(⟨x	NOUN
ejpam-4061	67	13	,	,	PUNCT
ejpam-4061	67	14	y⟩	y⟩	NOUN
ejpam-4061	67	15	)	)	PUNCT
ejpam-4061	67	16	=	=	PUNCT
ejpam-4061	68	1	{	{	PUNCT
ejpam-4061	68	2	u	u	NOUN
ejpam-4061	68	3	1	1	NUM
ejpam-4061	68	4	n	n	PROPN
ejpam-4061	68	5	(	(	PUNCT
ejpam-4061	68	6	⟨x	⟨x	NUM
ejpam-4061	68	7	,	,	PUNCT
ejpam-4061	68	8	y⟩	y⟩	NOUN
ejpam-4061	68	9	)	)	PUNCT
ejpam-4061	68	10	:	:	PUNCT
ejpam-4061	69	1	n	n	X
ejpam-4061	69	2	∈	∈	PROPN
ejpam-4061	69	3	n	n	CCONJ
ejpam-4061	69	4	}	}	PUNCT
ejpam-4061	69	5	is	be	AUX
ejpam-4061	69	6	a	a	DET
ejpam-4061	69	7	countable	countable	ADJ
ejpam-4061	69	8	local	local	ADJ
ejpam-4061	69	9	base	base	NOUN
ejpam-4061	69	10	for	for	ADP
ejpam-4061	69	11	(	(	PUNCT
ejpam-4061	69	12	x	x	INTJ
ejpam-4061	69	13	,	,	PUNCT
ejpam-4061	69	14	uah	uah	PROPN
ejpam-4061	69	15	)	)	PUNCT
ejpam-4061	69	16	at	at	ADP
ejpam-4061	69	17	⟨x	⟨x	VERB
ejpam-4061	69	18	,	,	PUNCT
ejpam-4061	69	19	y⟩.	y⟩.	NUM
ejpam-4061	69	20	for	for	ADP
ejpam-4061	69	21	⟨x	⟨x	NUM
ejpam-4061	69	22	,	,	PUNCT
ejpam-4061	69	23	0⟩	0⟩	PROPN
ejpam-4061	69	24	∈	∈	PROPN
ejpam-4061	69	25	l	l	NOUN
ejpam-4061	69	26	\	\	PROPN
ejpam-4061	69	27	a	a	PRON
ejpam-4061	69	28	,	,	PUNCT
ejpam-4061	69	29	the	the	DET
ejpam-4061	69	30	family	family	NOUN
ejpam-4061	69	31	b(⟨x	b(⟨x	NOUN
ejpam-4061	69	32	,	,	PUNCT
ejpam-4061	69	33	0⟩	0⟩	PROPN
ejpam-4061	69	34	)	)	PUNCT
ejpam-4061	70	1	=	=	PRON
ejpam-4061	70	2	{	{	PUNCT
ejpam-4061	70	3	c	c	NOUN
ejpam-4061	70	4	1	1	NUM
ejpam-4061	70	5	n	n	PROPN
ejpam-4061	70	6	(	(	PUNCT
ejpam-4061	70	7	⟨x	⟨x	NUM
ejpam-4061	70	8	,	,	PUNCT
ejpam-4061	70	9	0⟩	0⟩	PROPN
ejpam-4061	70	10	)	)	PUNCT
ejpam-4061	70	11	:	:	PUNCT
ejpam-4061	70	12	n	n	X
ejpam-4061	70	13	∈	∈	PROPN
ejpam-4061	70	14	n	n	CCONJ
ejpam-4061	70	15	}	}	PUNCT
ejpam-4061	70	16	is	be	AUX
ejpam-4061	70	17	a	a	DET
ejpam-4061	70	18	countable	countable	ADJ
ejpam-4061	70	19	local	local	ADJ
ejpam-4061	70	20	base	base	NOUN
ejpam-4061	70	21	for	for	ADP
ejpam-4061	70	22	(	(	PUNCT
ejpam-4061	70	23	x	x	INTJ
ejpam-4061	70	24	,	,	PUNCT
ejpam-4061	70	25	uah	uah	PROPN
ejpam-4061	70	26	)	)	PUNCT
ejpam-4061	70	27	at	at	ADP
ejpam-4061	70	28	⟨x	⟨x	VERB
ejpam-4061	70	29	,	,	PUNCT
ejpam-4061	70	30	0⟩.	0⟩.	PROPN
ejpam-4061	70	31	therefore	therefore	ADV
ejpam-4061	70	32	,	,	PUNCT
ejpam-4061	70	33	any	any	DET
ejpam-4061	70	34	h	h	NOUN
ejpam-4061	70	35	-	-	PUNCT
ejpam-4061	70	36	space	space	NOUN
ejpam-4061	70	37	(	(	PUNCT
ejpam-4061	70	38	x	x	NOUN
ejpam-4061	70	39	,	,	PUNCT
ejpam-4061	70	40	uah	uah	PROPN
ejpam-4061	70	41	)	)	PUNCT
ejpam-4061	70	42	is	be	AUX
ejpam-4061	70	43	first	first	ADV
ejpam-4061	70	44	countable	countable	ADJ
ejpam-4061	70	45	.	.	PUNCT
ejpam-4061	71	1	theorem	theorem	NOUN
ejpam-4061	71	2	2	2	NUM
ejpam-4061	71	3	.	.	PUNCT
ejpam-4061	72	1	an	an	DET
ejpam-4061	72	2	h	h	NOUN
ejpam-4061	72	3	-	-	PUNCT
ejpam-4061	72	4	space	space	NOUN
ejpam-4061	72	5	(	(	PUNCT
ejpam-4061	72	6	x	x	NOUN
ejpam-4061	72	7	,	,	PUNCT
ejpam-4061	72	8	uah	uah	PROPN
ejpam-4061	72	9	)	)	PUNCT
ejpam-4061	72	10	is	be	AUX
ejpam-4061	72	11	second	second	ADV
ejpam-4061	72	12	countable	countable	ADJ
ejpam-4061	72	13	if	if	SCONJ
ejpam-4061	72	14	and	and	CCONJ
ejpam-4061	72	15	only	only	ADV
ejpam-4061	72	16	if	if	SCONJ
ejpam-4061	72	17	l\a	l\a	PROPN
ejpam-4061	72	18	is	be	AUX
ejpam-4061	72	19	countable	countable	ADJ
ejpam-4061	72	20	.	.	PUNCT
ejpam-4061	73	1	proof	proof	NOUN
ejpam-4061	73	2	.	.	PUNCT
ejpam-4061	74	1	if	if	SCONJ
ejpam-4061	74	2	l	l	NOUN
ejpam-4061	74	3	\	\	PROPN
ejpam-4061	75	1	a	a	PRON
ejpam-4061	75	2	is	be	AUX
ejpam-4061	75	3	uncountable	uncountable	ADJ
ejpam-4061	75	4	,	,	PUNCT
ejpam-4061	75	5	then	then	ADV
ejpam-4061	75	6	l	l	NOUN
ejpam-4061	75	7	\	\	PROPN
ejpam-4061	76	1	a	a	PRON
ejpam-4061	76	2	is	be	AUX
ejpam-4061	76	3	an	an	DET
ejpam-4061	76	4	uncountable	uncountable	ADJ
ejpam-4061	76	5	discrete	discrete	ADJ
ejpam-4061	76	6	subspace	subspace	NOUN
ejpam-4061	76	7	of	of	ADP
ejpam-4061	76	8	the	the	DET
ejpam-4061	76	9	h	h	NOUN
ejpam-4061	76	10	-	-	PUNCT
ejpam-4061	76	11	space	space	NOUN
ejpam-4061	76	12	(	(	PUNCT
ejpam-4061	76	13	x	x	NOUN
ejpam-4061	76	14	,	,	PUNCT
ejpam-4061	76	15	uah	uah	PROPN
ejpam-4061	76	16	)	)	PUNCT
ejpam-4061	76	17	,	,	PUNCT
ejpam-4061	76	18	thus	thus	ADV
ejpam-4061	76	19	can	can	AUX
ejpam-4061	76	20	not	not	PART
ejpam-4061	76	21	be	be	AUX
ejpam-4061	76	22	second	second	ADV
ejpam-4061	76	23	countable	countable	ADJ
ejpam-4061	76	24	.	.	PUNCT
ejpam-4061	77	1	assume	assume	VERB
ejpam-4061	77	2	that	that	SCONJ
ejpam-4061	77	3	l	l	NOUN
ejpam-4061	77	4	\	\	PROPN
ejpam-4061	78	1	a	a	PRON
ejpam-4061	78	2	is	be	AUX
ejpam-4061	78	3	countable	countable	ADJ
ejpam-4061	78	4	.	.	PUNCT
ejpam-4061	79	1	since	since	SCONJ
ejpam-4061	79	2	x	x	PROPN
ejpam-4061	79	3	=	=	SYM
ejpam-4061	79	4	k	k	PROPN
ejpam-4061	79	5	∪	∪	VERB
ejpam-4061	79	6	a	a	DET
ejpam-4061	79	7	∪	∪	NOUN
ejpam-4061	79	8	(	(	PUNCT
ejpam-4061	79	9	l	l	NOUN
ejpam-4061	79	10	\	\	PROPN
ejpam-4061	79	11	a	a	PRON
ejpam-4061	79	12	)	)	PUNCT
ejpam-4061	79	13	and	and	CCONJ
ejpam-4061	79	14	k	k	PROPN
ejpam-4061	79	15	∪	∪	NOUN
ejpam-4061	79	16	a	a	PRON
ejpam-4061	79	17	is	be	AUX
ejpam-4061	79	18	a	a	DET
ejpam-4061	79	19	separable	separable	ADJ
ejpam-4061	79	20	metrizable	metrizable	ADJ
ejpam-4061	79	21	subspace	subspace	NOUN
ejpam-4061	79	22	from	from	ADP
ejpam-4061	79	23	(	(	PUNCT
ejpam-4061	79	24	x	x	INTJ
ejpam-4061	79	25	,	,	PUNCT
ejpam-4061	79	26	u	u	NOUN
ejpam-4061	79	27	)	)	PUNCT
ejpam-4061	79	28	,	,	PUNCT
ejpam-4061	79	29	then	then	ADV
ejpam-4061	79	30	k	k	PROPN
ejpam-4061	79	31	∪a	∪a	NUM
ejpam-4061	79	32	is	be	AUX
ejpam-4061	79	33	second	second	ADV
ejpam-4061	79	34	countable	countable	ADJ
ejpam-4061	79	35	.	.	PUNCT
ejpam-4061	80	1	let	let	VERB
ejpam-4061	80	2	b′	b′	NOUN
ejpam-4061	80	3	be	be	AUX
ejpam-4061	80	4	a	a	DET
ejpam-4061	80	5	countable	countable	ADJ
ejpam-4061	80	6	base	base	NOUN
ejpam-4061	80	7	for	for	ADP
ejpam-4061	80	8	k	k	PROPN
ejpam-4061	80	9	∪	∪	PROPN
ejpam-4061	80	10	a.	a.	NOUN
ejpam-4061	80	11	let	let	VERB
ejpam-4061	80	12	b⋆	b⋆	X
ejpam-4061	80	13	=	=	PRON
ejpam-4061	80	14	{	{	PUNCT
ejpam-4061	80	15	b(⟨x	b(⟨x	NOUN
ejpam-4061	80	16	,	,	PUNCT
ejpam-4061	80	17	0⟩	0⟩	PROPN
ejpam-4061	80	18	)	)	PUNCT
ejpam-4061	81	1	=	=	PRON
ejpam-4061	81	2	{	{	PUNCT
ejpam-4061	81	3	c	c	NOUN
ejpam-4061	81	4	1	1	NUM
ejpam-4061	81	5	n	n	PROPN
ejpam-4061	81	6	(	(	PUNCT
ejpam-4061	81	7	⟨x	⟨x	NUM
ejpam-4061	81	8	,	,	PUNCT
ejpam-4061	81	9	0⟩	0⟩	PROPN
ejpam-4061	81	10	)	)	PUNCT
ejpam-4061	81	11	:	:	PUNCT
ejpam-4061	82	1	n	n	X
ejpam-4061	82	2	∈	∈	PROPN
ejpam-4061	82	3	n	n	CCONJ
ejpam-4061	82	4	}	}	PUNCT
ejpam-4061	82	5	:	:	PUNCT
ejpam-4061	82	6	⟨x	⟨x	NUM
ejpam-4061	82	7	,	,	PUNCT
ejpam-4061	82	8	0⟩	0⟩	PROPN
ejpam-4061	82	9	∈	∈	PROPN
ejpam-4061	82	10	l	l	X
ejpam-4061	82	11	\	\	PROPN
ejpam-4061	83	1	a	a	PRON
ejpam-4061	83	2	}	}	PUNCT
ejpam-4061	83	3	.	.	PUNCT
ejpam-4061	84	1	we	we	PRON
ejpam-4061	84	2	show	show	VERB
ejpam-4061	84	3	that	that	PRON
ejpam-4061	84	4	b	b	X
ejpam-4061	84	5	=	=	PUNCT
ejpam-4061	84	6	b′⋃b⋆	b′⋃b⋆	NOUN
ejpam-4061	84	7	is	be	AUX
ejpam-4061	84	8	a	a	DET
ejpam-4061	84	9	countable	countable	ADJ
ejpam-4061	84	10	base	base	NOUN
ejpam-4061	84	11	for	for	ADP
ejpam-4061	84	12	the	the	DET
ejpam-4061	84	13	hspace	hspace	NOUN
ejpam-4061	84	14	(	(	PUNCT
ejpam-4061	84	15	x	x	NOUN
ejpam-4061	84	16	,	,	PUNCT
ejpam-4061	84	17	uah	uah	PROPN
ejpam-4061	84	18	)	)	PUNCT
ejpam-4061	84	19	.	.	PUNCT
ejpam-4061	85	1	let	let	VERB
ejpam-4061	85	2	w	w	NOUN
ejpam-4061	85	3	be	be	AUX
ejpam-4061	85	4	an	an	DET
ejpam-4061	85	5	arbitrary	arbitrary	ADJ
ejpam-4061	85	6	non	non	ADJ
ejpam-4061	85	7	-	-	ADJ
ejpam-4061	85	8	empty	empty	ADJ
ejpam-4061	85	9	open	open	ADJ
ejpam-4061	85	10	set	set	NOUN
ejpam-4061	85	11	in	in	ADP
ejpam-4061	85	12	(	(	PUNCT
ejpam-4061	85	13	x	x	INTJ
ejpam-4061	85	14	,	,	PUNCT
ejpam-4061	85	15	uah	uah	PROPN
ejpam-4061	85	16	)	)	PUNCT
ejpam-4061	85	17	and	and	CCONJ
ejpam-4061	85	18	pick	pick	VERB
ejpam-4061	85	19	an	an	DET
ejpam-4061	85	20	arbitrary	arbitrary	ADJ
ejpam-4061	85	21	⟨x	⟨x	NUM
ejpam-4061	85	22	,	,	PUNCT
ejpam-4061	85	23	y⟩	y⟩	NOUN
ejpam-4061	85	24	∈	∈	PROPN
ejpam-4061	85	25	w	w	PROPN
ejpam-4061	85	26	.	.	PUNCT
ejpam-4061	86	1	case	case	NOUN
ejpam-4061	86	2	1	1	NUM
ejpam-4061	86	3	:	:	PUNCT
ejpam-4061	86	4	if	if	SCONJ
ejpam-4061	86	5	⟨x	⟨x	VERB
ejpam-4061	86	6	,	,	PUNCT
ejpam-4061	86	7	y⟩	y⟩	NOUN
ejpam-4061	86	8	∈	∈	PROPN
ejpam-4061	86	9	k	k	PROPN
ejpam-4061	87	1	∪a	∪a	PROPN
ejpam-4061	87	2	,	,	PUNCT
ejpam-4061	87	3	then	then	ADV
ejpam-4061	87	4	there	there	PRON
ejpam-4061	87	5	exists	exist	VERB
ejpam-4061	87	6	r	r	NOUN
ejpam-4061	87	7	>	>	X
ejpam-4061	87	8	0	0	NUM
ejpam-4061	87	9	such	such	ADJ
ejpam-4061	87	10	that	that	SCONJ
ejpam-4061	87	11	ur(⟨x	ur(⟨x	NOUN
ejpam-4061	87	12	,	,	PUNCT
ejpam-4061	87	13	y⟩	y⟩	NOUN
ejpam-4061	87	14	)	)	PUNCT
ejpam-4061	87	15	⊆	⊆	NUM
ejpam-4061	87	16	w	w	NOUN
ejpam-4061	87	17	.	.	PUNCT
ejpam-4061	88	1	since	since	SCONJ
ejpam-4061	88	2	ur(⟨x	ur(⟨x	NOUN
ejpam-4061	88	3	,	,	PUNCT
ejpam-4061	88	4	y⟩	y⟩	NOUN
ejpam-4061	88	5	)	)	PUNCT
ejpam-4061	88	6	is	be	AUX
ejpam-4061	88	7	open	open	ADJ
ejpam-4061	88	8	in	in	ADP
ejpam-4061	88	9	k	k	PROPN
ejpam-4061	88	10	∪a	∪a	X
ejpam-4061	88	11	containing	contain	VERB
ejpam-4061	88	12	⟨x	⟨x	VERB
ejpam-4061	88	13	,	,	PUNCT
ejpam-4061	88	14	y⟩	y⟩	NOUN
ejpam-4061	88	15	,	,	PUNCT
ejpam-4061	88	16	then	then	ADV
ejpam-4061	88	17	there	there	PRON
ejpam-4061	88	18	exists	exist	VERB
ejpam-4061	88	19	b	b	PROPN
ejpam-4061	88	20	∈	∈	PROPN
ejpam-4061	88	21	b′	b′	NOUN
ejpam-4061	89	1	⊂	⊂	PROPN
ejpam-4061	89	2	b	b	X
ejpam-4061	89	3	such	such	ADJ
ejpam-4061	89	4	that	that	PRON
ejpam-4061	89	5	⟨x	⟨x	VERB
ejpam-4061	89	6	,	,	PUNCT
ejpam-4061	89	7	y⟩	y⟩	NOUN
ejpam-4061	89	8	∈	∈	PROPN
ejpam-4061	89	9	b	b	PROPN
ejpam-4061	89	10	⊆	⊆	NUM
ejpam-4061	89	11	ur(⟨x	ur(⟨x	NOUN
ejpam-4061	89	12	,	,	PUNCT
ejpam-4061	89	13	y⟩	y⟩	NOUN
ejpam-4061	89	14	)	)	PUNCT
ejpam-4061	90	1	⊆	⊆	NUM
ejpam-4061	90	2	w	w	NOUN
ejpam-4061	90	3	.	.	PUNCT
ejpam-4061	90	4	case	case	NOUN
ejpam-4061	90	5	2	2	NUM
ejpam-4061	90	6	:	:	PUNCT
ejpam-4061	90	7	if	if	SCONJ
ejpam-4061	90	8	⟨x	⟨x	VERB
ejpam-4061	90	9	,	,	PUNCT
ejpam-4061	90	10	y⟩	y⟩	NOUN
ejpam-4061	90	11	∈	∈	PROPN
ejpam-4061	90	12	l\a	l\a	PROPN
ejpam-4061	90	13	,	,	PUNCT
ejpam-4061	90	14	so	so	SCONJ
ejpam-4061	90	15	y	y	PROPN
ejpam-4061	90	16	=	=	SYM
ejpam-4061	90	17	0	0	PROPN
ejpam-4061	90	18	,	,	PUNCT
ejpam-4061	90	19	then	then	ADV
ejpam-4061	90	20	there	there	PRON
ejpam-4061	90	21	exists	exist	VERB
ejpam-4061	90	22	r	r	NOUN
ejpam-4061	90	23	>	>	X
ejpam-4061	90	24	0	0	NUM
ejpam-4061	90	25	such	such	ADJ
ejpam-4061	90	26	that	that	SCONJ
ejpam-4061	90	27	cr(⟨x	cr(⟨x	NOUN
ejpam-4061	90	28	,	,	PUNCT
ejpam-4061	90	29	0⟩	0⟩	PROPN
ejpam-4061	90	30	)	)	PUNCT
ejpam-4061	90	31	⊆	⊆	NUM
ejpam-4061	90	32	w	w	NOUN
ejpam-4061	90	33	,	,	PUNCT
ejpam-4061	90	34	thus	thus	ADV
ejpam-4061	90	35	there	there	PRON
ejpam-4061	90	36	exists	exist	VERB
ejpam-4061	90	37	an	an	DET
ejpam-4061	90	38	n	n	NOUN
ejpam-4061	90	39	∈	∈	NOUN
ejpam-4061	90	40	n	n	PRON
ejpam-4061	90	41	such	such	ADJ
ejpam-4061	90	42	that	that	SCONJ
ejpam-4061	90	43	0	0	NUM
ejpam-4061	90	44	<	<	X
ejpam-4061	90	45	1	1	NUM
ejpam-4061	90	46	n	n	NOUN
ejpam-4061	90	47	<	<	X
ejpam-4061	90	48	r	r	NOUN
ejpam-4061	90	49	,	,	PUNCT
ejpam-4061	90	50	thus	thus	ADV
ejpam-4061	90	51	⟨x	⟨x	VERB
ejpam-4061	90	52	,	,	PUNCT
ejpam-4061	90	53	0⟩	0⟩	PROPN
ejpam-4061	90	54	∈	∈	PROPN
ejpam-4061	90	55	c	c	NOUN
ejpam-4061	90	56	1	1	NUM
ejpam-4061	90	57	n	n	PROPN
ejpam-4061	90	58	(	(	PUNCT
ejpam-4061	90	59	⟨x	⟨x	NUM
ejpam-4061	90	60	,	,	PUNCT
ejpam-4061	90	61	0⟩	0⟩	PROPN
ejpam-4061	90	62	)	)	PUNCT
ejpam-4061	90	63	⊆	⊆	NUM
ejpam-4061	90	64	cr(⟨x	cr(⟨x	NOUN
ejpam-4061	90	65	,	,	PUNCT
ejpam-4061	90	66	0⟩	0⟩	PROPN
ejpam-4061	90	67	)	)	PUNCT
ejpam-4061	90	68	⊆	⊆	NUM
ejpam-4061	90	69	w	w	NOUN
ejpam-4061	90	70	,	,	PUNCT
ejpam-4061	90	71	where	where	SCONJ
ejpam-4061	90	72	c	c	PROPN
ejpam-4061	90	73	1	1	NUM
ejpam-4061	90	74	n	n	NOUN
ejpam-4061	90	75	(	(	PUNCT
ejpam-4061	90	76	⟨x	⟨x	NUM
ejpam-4061	90	77	,	,	PUNCT
ejpam-4061	90	78	0⟩	0⟩	ADJ
ejpam-4061	90	79	)	)	PUNCT
ejpam-4061	90	80	∈	∈	PROPN
ejpam-4061	90	81	b⋆.	b⋆.	NOUN
ejpam-4061	90	82	therefore	therefore	ADV
ejpam-4061	90	83	,	,	PUNCT
ejpam-4061	90	84	b	b	PROPN
ejpam-4061	90	85	is	be	AUX
ejpam-4061	90	86	a	a	DET
ejpam-4061	90	87	base	base	NOUN
ejpam-4061	90	88	for	for	ADP
ejpam-4061	90	89	the	the	DET
ejpam-4061	90	90	h	h	NOUN
ejpam-4061	90	91	-	-	PUNCT
ejpam-4061	90	92	space	space	NOUN
ejpam-4061	90	93	(	(	PUNCT
ejpam-4061	90	94	x	x	NOUN
ejpam-4061	90	95	,	,	PUNCT
ejpam-4061	90	96	uah	uah	PROPN
ejpam-4061	90	97	)	)	PUNCT
ejpam-4061	90	98	.	.	PUNCT
ejpam-4061	91	1	for	for	ADP
ejpam-4061	91	2	each	each	DET
ejpam-4061	91	3	n	n	PRON
ejpam-4061	91	4	∈	∈	PROPN
ejpam-4061	91	5	n	n	CCONJ
ejpam-4061	91	6	,	,	PUNCT
ejpam-4061	91	7	let	let	VERB
ejpam-4061	91	8	gn	gn	INTJ
ejpam-4061	91	9	=	=	PUNCT
ejpam-4061	92	1	r	r	NOUN
ejpam-4061	92	2	×	×	NOUN
ejpam-4061	93	1	[	[	X
ejpam-4061	93	2	0	0	NUM
ejpam-4061	93	3	,	,	PUNCT
ejpam-4061	93	4	n	n	CCONJ
ejpam-4061	93	5	)	)	PUNCT
ejpam-4061	93	6	,	,	PUNCT
ejpam-4061	93	7	then	then	ADV
ejpam-4061	93	8	the	the	DET
ejpam-4061	93	9	family	family	NOUN
ejpam-4061	93	10	{	{	PUNCT
ejpam-4061	93	11	gn	gn	X
ejpam-4061	93	12	:	:	PUNCT
ejpam-4061	93	13	n	n	CCONJ
ejpam-4061	93	14	∈	∈	PROPN
ejpam-4061	93	15	n	n	CCONJ
ejpam-4061	93	16	}	}	PUNCT
ejpam-4061	93	17	is	be	AUX
ejpam-4061	93	18	a	a	DET
ejpam-4061	93	19	countable	countable	ADJ
ejpam-4061	93	20	open	open	ADJ
ejpam-4061	93	21	cover	cover	NOUN
ejpam-4061	93	22	for	for	ADP
ejpam-4061	93	23	x	x	SYM
ejpam-4061	93	24	which	which	PRON
ejpam-4061	93	25	has	have	VERB
ejpam-4061	93	26	no	no	DET
ejpam-4061	93	27	finite	finite	PROPN
ejpam-4061	93	28	subcover	subcover	PROPN
ejpam-4061	93	29	.	.	PUNCT
ejpam-4061	94	1	thus	thus	ADV
ejpam-4061	94	2	any	any	DET
ejpam-4061	94	3	h	h	NOUN
ejpam-4061	94	4	-	-	PUNCT
ejpam-4061	94	5	space	space	NOUN
ejpam-4061	94	6	(	(	PUNCT
ejpam-4061	94	7	x	x	NOUN
ejpam-4061	94	8	,	,	PUNCT
ejpam-4061	94	9	uah	uah	PROPN
ejpam-4061	94	10	)	)	PUNCT
ejpam-4061	94	11	is	be	AUX
ejpam-4061	94	12	neither	neither	CCONJ
ejpam-4061	94	13	compact	compact	ADJ
ejpam-4061	94	14	nor	nor	CCONJ
ejpam-4061	94	15	countably	countably	ADV
ejpam-4061	94	16	compact	compact	ADJ
ejpam-4061	94	17	.	.	PUNCT
ejpam-4061	95	1	since	since	SCONJ
ejpam-4061	95	2	any	any	DET
ejpam-4061	95	3	second	second	ADJ
ejpam-4061	95	4	countable	countable	NOUN
ejpam-4061	95	5	is	be	AUX
ejpam-4061	95	6	lindelöf	lindelöf	NOUN
ejpam-4061	95	7	,	,	PUNCT
ejpam-4061	95	8	by	by	ADP
ejpam-4061	95	9	theorem	theorem	NOUN
ejpam-4061	95	10	2	2	NUM
ejpam-4061	95	11	,	,	PUNCT
ejpam-4061	95	12	we	we	PRON
ejpam-4061	95	13	conclude	conclude	VERB
ejpam-4061	95	14	the	the	DET
ejpam-4061	95	15	following	following	NOUN
ejpam-4061	95	16	.	.	PUNCT
ejpam-4061	96	1	theorem	theorem	NOUN
ejpam-4061	96	2	3	3	NUM
ejpam-4061	96	3	.	.	PUNCT
ejpam-4061	97	1	the	the	DET
ejpam-4061	97	2	h	h	NOUN
ejpam-4061	97	3	-	-	PUNCT
ejpam-4061	97	4	spaces	space	NOUN
ejpam-4061	97	5	(	(	PUNCT
ejpam-4061	97	6	x	x	INTJ
ejpam-4061	97	7	,	,	PUNCT
ejpam-4061	97	8	uah	uah	PROPN
ejpam-4061	97	9	)	)	PUNCT
ejpam-4061	97	10	is	be	AUX
ejpam-4061	97	11	lindelöf	lindelöf	NOUN
ejpam-4061	97	12	if	if	SCONJ
ejpam-4061	97	13	l	l	NOUN
ejpam-4061	97	14	\a	\a	ADJ
ejpam-4061	97	15	is	be	AUX
ejpam-4061	97	16	countable	countable	ADJ
ejpam-4061	97	17	.	.	PUNCT
ejpam-4061	98	1	n.	n.	PROPN
ejpam-4061	98	2	alghamdi	alghamdi	PROPN
ejpam-4061	98	3	,	,	PUNCT
ejpam-4061	98	4	l.	l.	PROPN
ejpam-4061	98	5	kalantan	kalantan	PROPN
ejpam-4061	98	6	/	/	SYM
ejpam-4061	98	7	eur	eur	PROPN
ejpam-4061	98	8	.	.	PUNCT
ejpam-4061	99	1	j.	j.	PROPN
ejpam-4061	99	2	pure	pure	PROPN
ejpam-4061	99	3	appl	appl	PROPN
ejpam-4061	99	4	.	.	PROPN
ejpam-4061	99	5	math	math	PROPN
ejpam-4061	99	6	,	,	PUNCT
ejpam-4061	99	7	14	14	NUM
ejpam-4061	99	8	(	(	PUNCT
ejpam-4061	99	9	4	4	NUM
ejpam-4061	99	10	)	)	PUNCT
ejpam-4061	99	11	(	(	PUNCT
ejpam-4061	99	12	2021	2021	NUM
ejpam-4061	99	13	)	)	PUNCT
ejpam-4061	99	14	,	,	PUNCT
ejpam-4061	99	15	1161	1161	NUM
ejpam-4061	99	16	-	-	SYM
ejpam-4061	99	17	1168	1168	NUM
ejpam-4061	99	18	1164	1164	NUM
ejpam-4061	99	19	3	3	NUM
ejpam-4061	99	20	.	.	PUNCT
ejpam-4061	99	21	other	other	ADJ
ejpam-4061	99	22	properties	property	NOUN
ejpam-4061	99	23	of	of	ADP
ejpam-4061	99	24	an	an	DET
ejpam-4061	99	25	h	h	NOUN
ejpam-4061	99	26	-	-	PUNCT
ejpam-4061	99	27	space	space	NOUN
ejpam-4061	99	28	.	.	PUNCT
ejpam-4061	100	1	definition	definition	NOUN
ejpam-4061	100	2	2	2	NUM
ejpam-4061	100	3	.	.	PUNCT
ejpam-4061	101	1	a	a	DET
ejpam-4061	101	2	subset	subset	NOUN
ejpam-4061	101	3	a	a	PRON
ejpam-4061	101	4	of	of	ADP
ejpam-4061	101	5	a	a	DET
ejpam-4061	101	6	space	space	NOUN
ejpam-4061	101	7	x	x	PUNCT
ejpam-4061	101	8	is	be	AUX
ejpam-4061	101	9	called	call	VERB
ejpam-4061	101	10	a	a	DET
ejpam-4061	101	11	closed	closed	ADJ
ejpam-4061	101	12	domain	domain	NOUN
ejpam-4061	101	13	of	of	ADP
ejpam-4061	101	14	x	x	PUNCT
ejpam-4061	102	1	[	[	X
ejpam-4061	102	2	1	1	NUM
ejpam-4061	102	3	,	,	PUNCT
ejpam-4061	102	4	1.1.c	1.1.c	NUM
ejpam-4061	102	5	]	]	X
ejpam-4061	102	6	(	(	PUNCT
ejpam-4061	102	7	also	also	ADV
ejpam-4061	102	8	called	call	VERB
ejpam-4061	102	9	regularly	regularly	ADV
ejpam-4061	102	10	closed	closed	ADJ
ejpam-4061	102	11	,	,	PUNCT
ejpam-4061	102	12	κ	κ	NOUN
ejpam-4061	102	13	-	-	PUNCT
ejpam-4061	102	14	closed	closed	ADJ
ejpam-4061	102	15	)	)	PUNCT
ejpam-4061	102	16	if	if	SCONJ
ejpam-4061	102	17	a	a	DET
ejpam-4061	102	18	=	=	X
ejpam-4061	102	19	inta	inta	PROPN
ejpam-4061	102	20	.	.	PUNCT
ejpam-4061	103	1	a	a	DET
ejpam-4061	103	2	space	space	NOUN
ejpam-4061	103	3	x	x	PUNCT
ejpam-4061	103	4	is	be	AUX
ejpam-4061	103	5	called	call	VERB
ejpam-4061	103	6	mildly	mildly	ADV
ejpam-4061	103	7	normal	normal	ADJ
ejpam-4061	103	8	[	[	X
ejpam-4061	103	9	7	7	NUM
ejpam-4061	103	10	]	]	X
ejpam-4061	103	11	(	(	PUNCT
ejpam-4061	103	12	also	also	ADV
ejpam-4061	103	13	called	call	VERB
ejpam-4061	103	14	κ	κ	NOUN
ejpam-4061	103	15	-	-	ADJ
ejpam-4061	103	16	normal	normal	ADJ
ejpam-4061	103	17	[	[	X
ejpam-4061	103	18	10	10	NUM
ejpam-4061	103	19	]	]	SYM
ejpam-4061	103	20	)	)	PUNCT
ejpam-4061	103	21	if	if	SCONJ
ejpam-4061	103	22	for	for	ADP
ejpam-4061	103	23	any	any	DET
ejpam-4061	103	24	two	two	NUM
ejpam-4061	103	25	disjoint	disjoint	NOUN
ejpam-4061	103	26	closed	close	VERB
ejpam-4061	103	27	domains	domain	NOUN
ejpam-4061	103	28	a	a	PRON
ejpam-4061	103	29	and	and	CCONJ
ejpam-4061	103	30	b	b	NOUN
ejpam-4061	103	31	of	of	ADP
ejpam-4061	103	32	x	x	PRON
ejpam-4061	103	33	there	there	PRON
ejpam-4061	103	34	exist	exist	VERB
ejpam-4061	103	35	two	two	NUM
ejpam-4061	103	36	disjoint	disjoint	ADJ
ejpam-4061	103	37	open	open	ADJ
ejpam-4061	103	38	subsets	subset	NOUN
ejpam-4061	103	39	u	u	NOUN
ejpam-4061	103	40	and	and	CCONJ
ejpam-4061	103	41	v	v	NOUN
ejpam-4061	103	42	of	of	ADP
ejpam-4061	103	43	x	x	PUNCT
ejpam-4061	103	44	such	such	ADJ
ejpam-4061	103	45	that	that	SCONJ
ejpam-4061	103	46	a	a	DET
ejpam-4061	103	47	⊆	⊆	NUM
ejpam-4061	103	48	u	u	NOUN
ejpam-4061	103	49	and	and	CCONJ
ejpam-4061	103	50	b	b	NOUN
ejpam-4061	103	51	⊆	⊆	NUM
ejpam-4061	103	52	v	v	NOUN
ejpam-4061	103	53	,	,	PUNCT
ejpam-4061	103	54	see	see	VERB
ejpam-4061	103	55	also	also	ADV
ejpam-4061	103	56	[	[	X
ejpam-4061	103	57	2	2	NUM
ejpam-4061	103	58	,	,	PUNCT
ejpam-4061	103	59	5	5	NUM
ejpam-4061	103	60	]	]	PUNCT
ejpam-4061	103	61	.	.	PUNCT
ejpam-4061	104	1	a	a	DET
ejpam-4061	104	2	space	space	NOUN
ejpam-4061	104	3	x	x	PUNCT
ejpam-4061	104	4	is	be	AUX
ejpam-4061	104	5	called	call	VERB
ejpam-4061	104	6	almost	almost	ADV
ejpam-4061	104	7	normal	normal	ADJ
ejpam-4061	104	8	[	[	X
ejpam-4061	104	9	6	6	NUM
ejpam-4061	104	10	]	]	X
ejpam-4061	104	11	if	if	SCONJ
ejpam-4061	104	12	for	for	ADP
ejpam-4061	104	13	any	any	DET
ejpam-4061	104	14	two	two	NUM
ejpam-4061	104	15	disjoint	disjoint	NOUN
ejpam-4061	104	16	closed	closed	ADJ
ejpam-4061	104	17	subsets	subset	NOUN
ejpam-4061	104	18	a	a	PRON
ejpam-4061	104	19	and	and	CCONJ
ejpam-4061	104	20	b	b	NOUN
ejpam-4061	104	21	of	of	ADP
ejpam-4061	104	22	x	x	PRON
ejpam-4061	104	23	one	one	NUM
ejpam-4061	104	24	of	of	ADP
ejpam-4061	104	25	which	which	PRON
ejpam-4061	104	26	is	be	AUX
ejpam-4061	104	27	closed	closed	ADJ
ejpam-4061	104	28	domain	domain	NOUN
ejpam-4061	104	29	,	,	PUNCT
ejpam-4061	104	30	there	there	PRON
ejpam-4061	104	31	exist	exist	VERB
ejpam-4061	104	32	two	two	NUM
ejpam-4061	104	33	disjoint	disjoint	ADJ
ejpam-4061	104	34	open	open	ADJ
ejpam-4061	104	35	subsets	subset	NOUN
ejpam-4061	104	36	u	u	NOUN
ejpam-4061	104	37	and	and	CCONJ
ejpam-4061	104	38	v	v	NOUN
ejpam-4061	104	39	of	of	ADP
ejpam-4061	104	40	x	x	PUNCT
ejpam-4061	104	41	such	such	ADJ
ejpam-4061	104	42	that	that	SCONJ
ejpam-4061	104	43	a	a	DET
ejpam-4061	104	44	⊆	⊆	NUM
ejpam-4061	104	45	u	u	NOUN
ejpam-4061	104	46	and	and	CCONJ
ejpam-4061	104	47	b	b	NOUN
ejpam-4061	104	48	⊆	⊆	NUM
ejpam-4061	104	49	v	v	NOUN
ejpam-4061	104	50	,	,	PUNCT
ejpam-4061	104	51	see	see	VERB
ejpam-4061	104	52	also	also	ADV
ejpam-4061	104	53	[	[	X
ejpam-4061	104	54	4	4	NUM
ejpam-4061	104	55	]	]	PUNCT
ejpam-4061	104	56	.	.	PUNCT
ejpam-4061	105	1	it	it	PRON
ejpam-4061	105	2	is	be	AUX
ejpam-4061	105	3	clear	clear	ADJ
ejpam-4061	105	4	from	from	ADP
ejpam-4061	105	5	the	the	DET
ejpam-4061	105	6	definitions	definition	NOUN
ejpam-4061	105	7	that	that	SCONJ
ejpam-4061	105	8	normal	normal	ADJ
ejpam-4061	105	9	⇒	⇒	NOUN
ejpam-4061	105	10	almost	almost	ADV
ejpam-4061	105	11	normal	normal	ADJ
ejpam-4061	105	12	⇒	⇒	NOUN
ejpam-4061	105	13	mildly	mildly	ADV
ejpam-4061	105	14	normal	normal	ADJ
ejpam-4061	105	15	.	.	PUNCT
ejpam-4061	106	1	each	each	DET
ejpam-4061	106	2	implication	implication	NOUN
ejpam-4061	106	3	above	above	ADV
ejpam-4061	106	4	is	be	AUX
ejpam-4061	106	5	not	not	PART
ejpam-4061	106	6	reversible	reversible	ADJ
ejpam-4061	106	7	,	,	PUNCT
ejpam-4061	106	8	see	see	VERB
ejpam-4061	106	9	[	[	X
ejpam-4061	106	10	2	2	NUM
ejpam-4061	106	11	,	,	PUNCT
ejpam-4061	106	12	4	4	NUM
ejpam-4061	106	13	]	]	PUNCT
ejpam-4061	106	14	.	.	PUNCT
ejpam-4061	107	1	lemma	lemma	PROPN
ejpam-4061	107	2	1	1	X
ejpam-4061	107	3	.	.	PUNCT
ejpam-4061	108	1	let	let	VERB
ejpam-4061	108	2	d	d	PRON
ejpam-4061	108	3	be	be	AUX
ejpam-4061	108	4	any	any	DET
ejpam-4061	108	5	non	non	ADJ
ejpam-4061	108	6	-	-	ADJ
ejpam-4061	108	7	empty	empty	ADJ
ejpam-4061	108	8	closed	closed	ADJ
ejpam-4061	108	9	domain	domain	NOUN
ejpam-4061	108	10	in	in	ADP
ejpam-4061	108	11	(	(	PUNCT
ejpam-4061	108	12	x	x	INTJ
ejpam-4061	108	13	,	,	PUNCT
ejpam-4061	108	14	uah	uah	PROPN
ejpam-4061	108	15	)	)	PUNCT
ejpam-4061	108	16	,	,	PUNCT
ejpam-4061	108	17	then	then	ADV
ejpam-4061	108	18	d	d	PROPN
ejpam-4061	108	19	is	be	AUX
ejpam-4061	108	20	a	a	DET
ejpam-4061	108	21	closed	closed	ADJ
ejpam-4061	108	22	set	set	NOUN
ejpam-4061	108	23	in	in	ADP
ejpam-4061	108	24	(	(	PUNCT
ejpam-4061	108	25	x	x	INTJ
ejpam-4061	108	26	,	,	PUNCT
ejpam-4061	108	27	u	u	NOUN
ejpam-4061	108	28	)	)	PUNCT
ejpam-4061	108	29	.	.	PUNCT
ejpam-4061	109	1	proof	proof	NOUN
ejpam-4061	109	2	.	.	PUNCT
ejpam-4061	110	1	if	if	SCONJ
ejpam-4061	110	2	d	d	NOUN
ejpam-4061	110	3	=	=	SYM
ejpam-4061	110	4	x	x	NOUN
ejpam-4061	110	5	,	,	PUNCT
ejpam-4061	110	6	we	we	PRON
ejpam-4061	110	7	are	be	AUX
ejpam-4061	110	8	done	do	VERB
ejpam-4061	110	9	.	.	PUNCT
ejpam-4061	111	1	assume	assume	VERB
ejpam-4061	111	2	x	x	X
ejpam-4061	111	3	\d	\d	PROPN
ejpam-4061	111	4	̸=	̸=	PROPN
ejpam-4061	111	5	∅.	∅.	ADV
ejpam-4061	111	6	let	let	VERB
ejpam-4061	111	7	⟨x	⟨x	VERB
ejpam-4061	111	8	,	,	PUNCT
ejpam-4061	111	9	y⟩	y⟩	NOUN
ejpam-4061	111	10	∈	∈	PROPN
ejpam-4061	111	11	x	x	PROPN
ejpam-4061	111	12	\d	\d	NOUN
ejpam-4061	111	13	be	be	AUX
ejpam-4061	111	14	arbitrary	arbitrary	ADJ
ejpam-4061	111	15	.	.	PUNCT
ejpam-4061	112	1	case	case	NOUN
ejpam-4061	112	2	1	1	NUM
ejpam-4061	112	3	:	:	PUNCT
ejpam-4061	112	4	⟨x	⟨x	NUM
ejpam-4061	112	5	,	,	PUNCT
ejpam-4061	112	6	y⟩	y⟩	NOUN
ejpam-4061	112	7	∈	∈	PROPN
ejpam-4061	113	1	k	k	PROPN
ejpam-4061	113	2	∪a	∪a	PROPN
ejpam-4061	113	3	.	.	PUNCT
ejpam-4061	114	1	since	since	SCONJ
ejpam-4061	114	2	d	d	PROPN
ejpam-4061	114	3	is	be	AUX
ejpam-4061	114	4	closed	close	VERB
ejpam-4061	114	5	in	in	ADP
ejpam-4061	114	6	(	(	PUNCT
ejpam-4061	114	7	x	x	INTJ
ejpam-4061	114	8	,	,	PUNCT
ejpam-4061	114	9	uah	uah	PROPN
ejpam-4061	114	10	)	)	PUNCT
ejpam-4061	114	11	,	,	PUNCT
ejpam-4061	114	12	then	then	ADV
ejpam-4061	114	13	x	x	PUNCT
ejpam-4061	114	14	\d	\d	NOUN
ejpam-4061	114	15	is	be	AUX
ejpam-4061	114	16	open	open	ADJ
ejpam-4061	114	17	in	in	ADP
ejpam-4061	114	18	(	(	PUNCT
ejpam-4061	114	19	x	x	INTJ
ejpam-4061	114	20	,	,	PUNCT
ejpam-4061	114	21	uah	uah	PROPN
ejpam-4061	114	22	)	)	PUNCT
ejpam-4061	114	23	,	,	PUNCT
ejpam-4061	114	24	thus	thus	ADV
ejpam-4061	114	25	there	there	PRON
ejpam-4061	114	26	exists	exist	VERB
ejpam-4061	114	27	r	r	NOUN
ejpam-4061	114	28	>	>	X
ejpam-4061	114	29	0	0	NUM
ejpam-4061	114	30	such	such	ADJ
ejpam-4061	114	31	that	that	SCONJ
ejpam-4061	114	32	ur(⟨x	ur(⟨x	NOUN
ejpam-4061	114	33	,	,	PUNCT
ejpam-4061	114	34	y⟩	y⟩	NOUN
ejpam-4061	114	35	)	)	PUNCT
ejpam-4061	114	36	⊆	⊆	NUM
ejpam-4061	114	37	x	x	PUNCT
ejpam-4061	114	38	\d	\d	NOUN
ejpam-4061	114	39	.	.	PUNCT
ejpam-4061	115	1	but	but	CCONJ
ejpam-4061	115	2	ur(⟨x	ur(⟨x	NOUN
ejpam-4061	115	3	,	,	PUNCT
ejpam-4061	115	4	y⟩	y⟩	NOUN
ejpam-4061	115	5	)	)	PUNCT
ejpam-4061	115	6	is	be	AUX
ejpam-4061	115	7	also	also	ADV
ejpam-4061	115	8	a	a	DET
ejpam-4061	115	9	basic	basic	ADJ
ejpam-4061	115	10	open	open	ADJ
ejpam-4061	115	11	set	set	NOUN
ejpam-4061	115	12	in	in	ADP
ejpam-4061	115	13	(	(	PUNCT
ejpam-4061	115	14	x	x	INTJ
ejpam-4061	115	15	,	,	PUNCT
ejpam-4061	115	16	u	u	NOUN
ejpam-4061	115	17	)	)	PUNCT
ejpam-4061	115	18	.	.	PUNCT
ejpam-4061	116	1	case	case	NOUN
ejpam-4061	116	2	2	2	NUM
ejpam-4061	116	3	:	:	PUNCT
ejpam-4061	116	4	y	y	PROPN
ejpam-4061	116	5	=	=	PUNCT
ejpam-4061	116	6	0	0	NUM
ejpam-4061	116	7	and	and	CCONJ
ejpam-4061	116	8	⟨x	⟨x	NUM
ejpam-4061	116	9	,	,	PUNCT
ejpam-4061	116	10	0⟩	0⟩	PROPN
ejpam-4061	116	11	∈	∈	PROPN
ejpam-4061	116	12	l	l	NOUN
ejpam-4061	116	13	\a	\a	ADJ
ejpam-4061	116	14	.	.	PUNCT
ejpam-4061	117	1	there	there	PRON
ejpam-4061	117	2	exists	exist	VERB
ejpam-4061	117	3	r	r	NOUN
ejpam-4061	117	4	>	>	X
ejpam-4061	117	5	0	0	NUM
ejpam-4061	117	6	such	such	ADJ
ejpam-4061	117	7	that	that	SCONJ
ejpam-4061	117	8	cr(⟨x	cr(⟨x	NOUN
ejpam-4061	117	9	,	,	PUNCT
ejpam-4061	117	10	0⟩	0⟩	PROPN
ejpam-4061	117	11	)	)	PUNCT
ejpam-4061	117	12	⊆	⊆	NUM
ejpam-4061	117	13	x	x	SYM
ejpam-4061	117	14	\d	\d	NOUN
ejpam-4061	117	15	.	.	PUNCT
ejpam-4061	117	16	.	.	PUNCT
ejpam-4061	117	17	.	.	PUNCT
ejpam-4061	118	1	(	(	PUNCT
ejpam-4061	118	2	⋆	⋆	NOUN
ejpam-4061	118	3	)	)	PUNCT
ejpam-4061	118	4	suppose	suppose	VERB
ejpam-4061	118	5	that	that	SCONJ
ejpam-4061	118	6	for	for	ADP
ejpam-4061	118	7	all	all	PRON
ejpam-4061	118	8	0	0	NUM
ejpam-4061	118	9	<	<	X
ejpam-4061	118	10	ε	ε	PROPN
ejpam-4061	118	11	≤	≤	ADJ
ejpam-4061	118	12	r	r	NOUN
ejpam-4061	118	13	we	we	PRON
ejpam-4061	118	14	have	have	VERB
ejpam-4061	118	15	uε(⟨x	uε(⟨x	NOUN
ejpam-4061	118	16	,	,	PUNCT
ejpam-4061	118	17	0⟩	0⟩	PROPN
ejpam-4061	118	18	)	)	PUNCT
ejpam-4061	118	19	̸⊆	̸⊆	NOUN
ejpam-4061	118	20	x	x	SYM
ejpam-4061	118	21	\	\	PROPN
ejpam-4061	118	22	d.	d.	PROPN
ejpam-4061	118	23	that	that	PRON
ejpam-4061	118	24	is	be	AUX
ejpam-4061	118	25	,	,	PUNCT
ejpam-4061	118	26	uε(⟨x	uε(⟨x	ADP
ejpam-4061	118	27	,	,	PUNCT
ejpam-4061	118	28	0⟩	0⟩	ADJ
ejpam-4061	118	29	)	)	PUNCT
ejpam-4061	118	30	∩	∩	NOUN
ejpam-4061	118	31	d	d	X
ejpam-4061	118	32	̸=	̸=	PROPN
ejpam-4061	118	33	∅.	∅.	AUX
ejpam-4061	118	34	fix	fix	VERB
ejpam-4061	118	35	such	such	DET
ejpam-4061	118	36	an	an	DET
ejpam-4061	118	37	ε	ε	PROPN
ejpam-4061	118	38	,	,	PUNCT
ejpam-4061	118	39	then	then	ADV
ejpam-4061	118	40	there	there	PRON
ejpam-4061	118	41	exists	exist	VERB
ejpam-4061	118	42	z	z	PROPN
ejpam-4061	118	43	∈	∈	PROPN
ejpam-4061	118	44	(	(	PUNCT
ejpam-4061	118	45	x	x	NOUN
ejpam-4061	118	46	−	−	PROPN
ejpam-4061	118	47	ε	ε	PROPN
ejpam-4061	118	48	,	,	PUNCT
ejpam-4061	118	49	x	x	PROPN
ejpam-4061	118	50	+	+	NUM
ejpam-4061	118	51	ε	ε	PROPN
ejpam-4061	118	52	)	)	PUNCT
ejpam-4061	118	53	;	;	PUNCT
ejpam-4061	118	54	z	z	PROPN
ejpam-4061	118	55	̸=	̸=	PROPN
ejpam-4061	118	56	x	x	PUNCT
ejpam-4061	118	57	such	such	ADJ
ejpam-4061	118	58	that	that	SCONJ
ejpam-4061	118	59	⟨z	⟨z	PROPN
ejpam-4061	118	60	,	,	PUNCT
ejpam-4061	118	61	0⟩	0⟩	PROPN
ejpam-4061	118	62	∈	∈	PROPN
ejpam-4061	119	1	d	d	X
ejpam-4061	119	2	=	=	SYM
ejpam-4061	119	3	intuahd	intuahd	ADJ
ejpam-4061	119	4	uah	uah	NOUN
ejpam-4061	119	5	.	.	PUNCT
ejpam-4061	120	1	for	for	ADP
ejpam-4061	120	2	all	all	PRON
ejpam-4061	120	3	0	0	NUM
ejpam-4061	120	4	<	<	X
ejpam-4061	120	5	δ	δ	X
ejpam-4061	120	6	<	<	X
ejpam-4061	120	7	ε	ε	PROPN
ejpam-4061	120	8	,	,	PUNCT
ejpam-4061	120	9	we	we	PRON
ejpam-4061	120	10	have	have	VERB
ejpam-4061	120	11	cδ(⟨z	cδ(⟨z	NOUN
ejpam-4061	120	12	,	,	PUNCT
ejpam-4061	120	13	0⟩	0⟩	PROPN
ejpam-4061	120	14	)	)	PUNCT
ejpam-4061	120	15	∩	∩	ADJ
ejpam-4061	120	16	intuahd	intuahd	PROPN
ejpam-4061	120	17	̸=	̸=	PROPN
ejpam-4061	120	18	∅	∅	NOUN
ejpam-4061	120	19	if	if	SCONJ
ejpam-4061	120	20	⟨z	⟨z	PROPN
ejpam-4061	120	21	,	,	PUNCT
ejpam-4061	120	22	0⟩	0⟩	PROPN
ejpam-4061	120	23	∈	∈	PROPN
ejpam-4061	120	24	l	l	NOUN
ejpam-4061	120	25	\	\	PROPN
ejpam-4061	120	26	a	a	PRON
ejpam-4061	120	27	or	or	CCONJ
ejpam-4061	120	28	uδ(⟨z	uδ(⟨z	NOUN
ejpam-4061	120	29	,	,	PUNCT
ejpam-4061	120	30	0⟩	0⟩	ADJ
ejpam-4061	120	31	)	)	PUNCT
ejpam-4061	120	32	∩	∩	ADJ
ejpam-4061	120	33	intuahd	intuahd	PROPN
ejpam-4061	120	34	̸=	̸=	PROPN
ejpam-4061	120	35	∅	∅	NOUN
ejpam-4061	120	36	if	if	SCONJ
ejpam-4061	120	37	⟨z	⟨z	PROPN
ejpam-4061	120	38	,	,	PUNCT
ejpam-4061	120	39	0⟩	0⟩	PROPN
ejpam-4061	120	40	∈	∈	PROPN
ejpam-4061	120	41	a.	a.	NOUN
ejpam-4061	120	42	if	if	SCONJ
ejpam-4061	120	43	⟨z	⟨z	PROPN
ejpam-4061	120	44	,	,	PUNCT
ejpam-4061	120	45	0⟩	0⟩	PROPN
ejpam-4061	120	46	∈	∈	PROPN
ejpam-4061	120	47	l	l	NOUN
ejpam-4061	120	48	\	\	PROPN
ejpam-4061	121	1	a	a	DET
ejpam-4061	121	2	,	,	PUNCT
ejpam-4061	121	3	then⟨z	then⟨z	PROPN
ejpam-4061	121	4	,	,	PUNCT
ejpam-4061	121	5	0⟩	0⟩	PROPN
ejpam-4061	121	6	∈	∈	PROPN
ejpam-4061	121	7	intuahd	intuahd	NOUN
ejpam-4061	121	8	,	,	PUNCT
ejpam-4061	121	9	because	because	SCONJ
ejpam-4061	121	10	cδ(⟨z	cδ(⟨z	NOUN
ejpam-4061	121	11	,	,	PUNCT
ejpam-4061	121	12	0⟩)∩l	0⟩)∩l	X
ejpam-4061	121	13	=	=	SYM
ejpam-4061	121	14	{	{	PUNCT
ejpam-4061	121	15	⟨z	⟨z	PROPN
ejpam-4061	121	16	,	,	PUNCT
ejpam-4061	121	17	0⟩	0⟩	PROPN
ejpam-4061	121	18	}	}	PUNCT
ejpam-4061	121	19	and	and	CCONJ
ejpam-4061	121	20	cδ(⟨z	cδ(⟨z	NOUN
ejpam-4061	121	21	,	,	PUNCT
ejpam-4061	121	22	0⟩)∩k	0⟩)∩k	NUM
ejpam-4061	122	1	⊆	⊆	NUM
ejpam-4061	122	2	x	x	PUNCT
ejpam-4061	122	3	\d	\d	NOUN
ejpam-4061	122	4	.	.	PUNCT
ejpam-4061	123	1	now	now	ADV
ejpam-4061	123	2	,	,	PUNCT
ejpam-4061	123	3	⟨z	⟨z	PROPN
ejpam-4061	123	4	,	,	PUNCT
ejpam-4061	123	5	0⟩	0⟩	PROPN
ejpam-4061	123	6	∈	∈	PROPN
ejpam-4061	123	7	intuahd	intuahd	NOUN
ejpam-4061	123	8	means	mean	VERB
ejpam-4061	123	9	that	that	SCONJ
ejpam-4061	123	10	there	there	PRON
ejpam-4061	123	11	exists	exist	VERB
ejpam-4061	123	12	δ′	δ′	PROPN
ejpam-4061	123	13	<	<	X
ejpam-4061	123	14	δ	δ	PROPN
ejpam-4061	123	15	such	such	ADJ
ejpam-4061	123	16	that	that	DET
ejpam-4061	123	17	cδ′(⟨z	cδ′(⟨z	NOUN
ejpam-4061	123	18	,	,	PUNCT
ejpam-4061	123	19	0⟩	0⟩	PROPN
ejpam-4061	123	20	)	)	PUNCT
ejpam-4061	124	1	⊆	⊆	NUM
ejpam-4061	124	2	d	d	NOUN
ejpam-4061	124	3	which	which	PRON
ejpam-4061	124	4	contradicts	contradict	VERB
ejpam-4061	124	5	(	(	PUNCT
ejpam-4061	124	6	⋆	⋆	NOUN
ejpam-4061	124	7	)	)	PUNCT
ejpam-4061	124	8	,	,	PUNCT
ejpam-4061	124	9	because	because	SCONJ
ejpam-4061	124	10	cδ′(⟨z	cδ′(⟨z	ADJ
ejpam-4061	124	11	,	,	PUNCT
ejpam-4061	124	12	0⟩	0⟩	ADJ
ejpam-4061	124	13	)	)	PUNCT
ejpam-4061	124	14	∩	∩	NOUN
ejpam-4061	124	15	k	k	PROPN
ejpam-4061	124	16	⊆	⊆	NUM
ejpam-4061	124	17	cr(⟨x	cr(⟨x	NOUN
ejpam-4061	124	18	,	,	PUNCT
ejpam-4061	124	19	0⟩	0⟩	PROPN
ejpam-4061	124	20	)	)	PUNCT
ejpam-4061	124	21	⊆	⊆	NUM
ejpam-4061	124	22	x	x	SYM
ejpam-4061	124	23	\	\	PROPN
ejpam-4061	124	24	d.	d.	PROPN
ejpam-4061	124	25	if	if	SCONJ
ejpam-4061	124	26	⟨z	⟨z	PROPN
ejpam-4061	124	27	,	,	PUNCT
ejpam-4061	124	28	0⟩	0⟩	PROPN
ejpam-4061	124	29	∈	∈	PROPN
ejpam-4061	124	30	a	a	PRON
ejpam-4061	124	31	,	,	PUNCT
ejpam-4061	124	32	and	and	CCONJ
ejpam-4061	124	33	uδ(⟨z	uδ(⟨z	NOUN
ejpam-4061	124	34	,	,	PUNCT
ejpam-4061	124	35	0⟩	0⟩	ADJ
ejpam-4061	124	36	)	)	PUNCT
ejpam-4061	124	37	∩	∩	ADJ
ejpam-4061	124	38	intuahd	intuahd	PROPN
ejpam-4061	124	39	̸=	̸=	PROPN
ejpam-4061	124	40	∅	∅	NOUN
ejpam-4061	124	41	,	,	PUNCT
ejpam-4061	124	42	then	then	ADV
ejpam-4061	124	43	pick	pick	VERB
ejpam-4061	124	44	⟨u	⟨u	NOUN
ejpam-4061	124	45	,	,	PUNCT
ejpam-4061	124	46	0⟩	0⟩	PROPN
ejpam-4061	124	47	∈	∈	PROPN
ejpam-4061	124	48	uδ(⟨z	uδ(⟨z	NOUN
ejpam-4061	124	49	,	,	PUNCT
ejpam-4061	124	50	0⟩	0⟩	ADJ
ejpam-4061	124	51	)	)	PUNCT
ejpam-4061	124	52	∩	∩	ADJ
ejpam-4061	124	53	intuahd	intuahd	NOUN
ejpam-4061	124	54	,	,	PUNCT
ejpam-4061	124	55	thus	thus	ADV
ejpam-4061	124	56	⟨u	⟨u	NOUN
ejpam-4061	124	57	,	,	PUNCT
ejpam-4061	124	58	0⟩	0⟩	PROPN
ejpam-4061	124	59	∈	∈	PROPN
ejpam-4061	124	60	intuahd	intuahd	NOUN
ejpam-4061	124	61	.	.	PUNCT
ejpam-4061	125	1	then	then	ADV
ejpam-4061	125	2	there	there	PRON
ejpam-4061	125	3	exists	exist	VERB
ejpam-4061	125	4	δ′	δ′	PROPN
ejpam-4061	125	5	<	<	X
ejpam-4061	125	6	δ	δ	PROPN
ejpam-4061	125	7	such	such	ADJ
ejpam-4061	125	8	that	that	SCONJ
ejpam-4061	125	9	uδ′(⟨u	uδ′(⟨u	PROPN
ejpam-4061	125	10	,	,	PUNCT
ejpam-4061	125	11	0⟩	0⟩	PROPN
ejpam-4061	125	12	)	)	PUNCT
ejpam-4061	126	1	⊆	⊆	NUM
ejpam-4061	126	2	d	d	NOUN
ejpam-4061	126	3	if	if	SCONJ
ejpam-4061	126	4	⟨u	⟨u	NOUN
ejpam-4061	126	5	,	,	PUNCT
ejpam-4061	126	6	0⟩	0⟩	PROPN
ejpam-4061	126	7	∈	∈	PROPN
ejpam-4061	126	8	a	a	PRON
ejpam-4061	126	9	or	or	CCONJ
ejpam-4061	126	10	cδ′(⟨u	cδ′(⟨u	NOUN
ejpam-4061	126	11	,	,	PUNCT
ejpam-4061	126	12	0⟩	0⟩	PROPN
ejpam-4061	126	13	)	)	PUNCT
ejpam-4061	127	1	⊆	⊆	NUM
ejpam-4061	127	2	d	d	NOUN
ejpam-4061	127	3	,	,	PUNCT
ejpam-4061	127	4	if	if	SCONJ
ejpam-4061	127	5	⟨u	⟨u	NOUN
ejpam-4061	127	6	,	,	PUNCT
ejpam-4061	127	7	0⟩	0⟩	PROPN
ejpam-4061	127	8	∈	∈	PROPN
ejpam-4061	127	9	l	l	NOUN
ejpam-4061	127	10	\	\	PROPN
ejpam-4061	127	11	a.	a.	NOUN
ejpam-4061	127	12	in	in	ADP
ejpam-4061	127	13	both	both	DET
ejpam-4061	127	14	cases	case	NOUN
ejpam-4061	127	15	,	,	PUNCT
ejpam-4061	127	16	we	we	PRON
ejpam-4061	127	17	get	get	VERB
ejpam-4061	127	18	a	a	DET
ejpam-4061	127	19	contradiction	contradiction	NOUN
ejpam-4061	127	20	to	to	ADP
ejpam-4061	127	21	(	(	PUNCT
ejpam-4061	127	22	⋆	⋆	NOUN
ejpam-4061	127	23	)	)	PUNCT
ejpam-4061	127	24	,	,	PUNCT
ejpam-4061	127	25	because	because	SCONJ
ejpam-4061	127	26	uδ′(⟨u	uδ′(⟨u	PROPN
ejpam-4061	127	27	,	,	PUNCT
ejpam-4061	127	28	0⟩)∩k	0⟩)∩k	NUM
ejpam-4061	127	29	⊆	⊆	NUM
ejpam-4061	127	30	cr(⟨x	cr(⟨x	NOUN
ejpam-4061	127	31	,	,	PUNCT
ejpam-4061	127	32	0⟩	0⟩	PROPN
ejpam-4061	127	33	)	)	PUNCT
ejpam-4061	127	34	⊆	⊆	NUM
ejpam-4061	127	35	x\d	x\d	PROPN
ejpam-4061	127	36	and	and	CCONJ
ejpam-4061	127	37	cδ′(⟨u	cδ′(⟨u	NOUN
ejpam-4061	127	38	,	,	PUNCT
ejpam-4061	127	39	0⟩)∩k	0⟩)∩k	NUM
ejpam-4061	127	40	⊆	⊆	NUM
ejpam-4061	127	41	cr(⟨x	cr(⟨x	NOUN
ejpam-4061	127	42	,	,	PUNCT
ejpam-4061	127	43	0⟩	0⟩	PROPN
ejpam-4061	127	44	)	)	PUNCT
ejpam-4061	127	45	⊆	⊆	NUM
ejpam-4061	127	46	x\d	x\d	NOUN
ejpam-4061	127	47	.	.	PUNCT
ejpam-4061	128	1	thus	thus	ADV
ejpam-4061	128	2	x	x	PUNCT
ejpam-4061	128	3	\d	\d	NOUN
ejpam-4061	128	4	is	be	AUX
ejpam-4061	128	5	open	open	ADJ
ejpam-4061	128	6	in	in	ADP
ejpam-4061	128	7	the	the	DET
ejpam-4061	128	8	usual	usual	ADJ
ejpam-4061	128	9	metric	metric	ADJ
ejpam-4061	128	10	topology	topology	NOUN
ejpam-4061	128	11	.	.	PUNCT
ejpam-4061	129	1	therefore	therefore	ADV
ejpam-4061	129	2	,	,	PUNCT
ejpam-4061	129	3	d	d	X
ejpam-4061	129	4	is	be	AUX
ejpam-4061	129	5	a	a	DET
ejpam-4061	129	6	closed	closed	ADJ
ejpam-4061	129	7	set	set	NOUN
ejpam-4061	129	8	in	in	ADP
ejpam-4061	129	9	(	(	PUNCT
ejpam-4061	129	10	x	x	INTJ
ejpam-4061	129	11	,	,	PUNCT
ejpam-4061	129	12	u	u	NOUN
ejpam-4061	129	13	)	)	PUNCT
ejpam-4061	129	14	.	.	PUNCT
ejpam-4061	130	1	lemma	lemma	PROPN
ejpam-4061	130	2	2	2	X
ejpam-4061	130	3	.	.	PUNCT
ejpam-4061	131	1	let	let	VERB
ejpam-4061	131	2	d	d	PRON
ejpam-4061	131	3	be	be	AUX
ejpam-4061	131	4	any	any	DET
ejpam-4061	131	5	non	non	ADJ
ejpam-4061	131	6	-	-	ADJ
ejpam-4061	131	7	empty	empty	ADJ
ejpam-4061	131	8	closed	closed	ADJ
ejpam-4061	131	9	domain	domain	NOUN
ejpam-4061	131	10	in	in	ADP
ejpam-4061	131	11	(	(	PUNCT
ejpam-4061	131	12	x	x	INTJ
ejpam-4061	131	13	,	,	PUNCT
ejpam-4061	131	14	uah	uah	PROPN
ejpam-4061	131	15	)	)	PUNCT
ejpam-4061	131	16	,	,	PUNCT
ejpam-4061	131	17	then	then	ADV
ejpam-4061	131	18	(	(	PUNCT
ejpam-4061	131	19	intuahd	intuahd	PROPN
ejpam-4061	131	20	)	)	PUNCT
ejpam-4061	131	21	∩(k∪	∩(k∪	PROPN
ejpam-4061	131	22	a	a	X
ejpam-4061	131	23	)	)	PUNCT
ejpam-4061	131	24	=	=	SYM
ejpam-4061	131	25	(	(	PUNCT
ejpam-4061	131	26	intud	intud	NOUN
ejpam-4061	131	27	)	)	PUNCT
ejpam-4061	132	1	∩	∩	NOUN
ejpam-4061	132	2	(	(	PUNCT
ejpam-4061	132	3	k	k	X
ejpam-4061	132	4	∪a	∪a	NUM
ejpam-4061	132	5	)	)	PUNCT
ejpam-4061	132	6	.	.	PUNCT
ejpam-4061	133	1	proof	proof	NOUN
ejpam-4061	133	2	.	.	PUNCT
ejpam-4061	134	1	let	let	VERB
ejpam-4061	134	2	⟨u	⟨u	NOUN
ejpam-4061	134	3	,	,	PUNCT
ejpam-4061	134	4	v⟩	v⟩	NOUN
ejpam-4061	134	5	∈	∈	PROPN
ejpam-4061	134	6	k	k	X
ejpam-4061	134	7	∪a	∪a	PROPN
ejpam-4061	134	8	.	.	PUNCT
ejpam-4061	134	9	⟨u	⟨u	NOUN
ejpam-4061	134	10	,	,	PUNCT
ejpam-4061	134	11	v⟩	v⟩	NOUN
ejpam-4061	134	12	∈	∈	PROPN
ejpam-4061	134	13	intuahd	intuahd	NOUN
ejpam-4061	134	14	if	if	SCONJ
ejpam-4061	134	15	and	and	CCONJ
ejpam-4061	134	16	only	only	ADV
ejpam-4061	134	17	if	if	SCONJ
ejpam-4061	134	18	there	there	PRON
ejpam-4061	134	19	exists	exist	VERB
ejpam-4061	134	20	r	r	NOUN
ejpam-4061	134	21	>	>	X
ejpam-4061	134	22	0	0	NUM
ejpam-4061	134	23	such	such	ADJ
ejpam-4061	134	24	that	that	DET
ejpam-4061	134	25	ur(⟨u	ur(⟨u	NOUN
ejpam-4061	134	26	,	,	PUNCT
ejpam-4061	134	27	v⟩	v⟩	NOUN
ejpam-4061	134	28	)	)	PUNCT
ejpam-4061	135	1	⊆	⊆	NUM
ejpam-4061	135	2	d	d	NOUN
ejpam-4061	135	3	if	if	SCONJ
ejpam-4061	135	4	and	and	CCONJ
ejpam-4061	135	5	only	only	ADV
ejpam-4061	135	6	if	if	SCONJ
ejpam-4061	135	7	⟨u	⟨u	NOUN
ejpam-4061	135	8	,	,	PUNCT
ejpam-4061	135	9	v⟩	v⟩	NOUN
ejpam-4061	135	10	∈	∈	PROPN
ejpam-4061	135	11	intud	intud	VERB
ejpam-4061	135	12	n.	n.	PROPN
ejpam-4061	135	13	alghamdi	alghamdi	PROPN
ejpam-4061	135	14	,	,	PUNCT
ejpam-4061	135	15	l.	l.	PROPN
ejpam-4061	135	16	kalantan	kalantan	PROPN
ejpam-4061	135	17	/	/	SYM
ejpam-4061	135	18	eur	eur	PROPN
ejpam-4061	135	19	.	.	PUNCT
ejpam-4061	136	1	j.	j.	PROPN
ejpam-4061	136	2	pure	pure	PROPN
ejpam-4061	136	3	appl	appl	PROPN
ejpam-4061	136	4	.	.	PROPN
ejpam-4061	136	5	math	math	PROPN
ejpam-4061	136	6	,	,	PUNCT
ejpam-4061	136	7	14	14	NUM
ejpam-4061	136	8	(	(	PUNCT
ejpam-4061	136	9	4	4	NUM
ejpam-4061	136	10	)	)	PUNCT
ejpam-4061	136	11	(	(	PUNCT
ejpam-4061	136	12	2021	2021	NUM
ejpam-4061	136	13	)	)	PUNCT
ejpam-4061	136	14	,	,	PUNCT
ejpam-4061	136	15	1161	1161	NUM
ejpam-4061	136	16	-	-	SYM
ejpam-4061	136	17	1168	1168	NUM
ejpam-4061	136	18	1165	1165	NUM
ejpam-4061	136	19	lemma	lemma	PROPN
ejpam-4061	136	20	3	3	X
ejpam-4061	136	21	.	.	PUNCT
ejpam-4061	137	1	let	let	VERB
ejpam-4061	137	2	d	d	PRON
ejpam-4061	137	3	be	be	AUX
ejpam-4061	137	4	any	any	DET
ejpam-4061	137	5	non	non	ADJ
ejpam-4061	137	6	-	-	ADJ
ejpam-4061	137	7	empty	empty	ADJ
ejpam-4061	137	8	closed	closed	ADJ
ejpam-4061	137	9	domain	domain	NOUN
ejpam-4061	137	10	in	in	ADP
ejpam-4061	137	11	(	(	PUNCT
ejpam-4061	137	12	x	x	INTJ
ejpam-4061	137	13	,	,	PUNCT
ejpam-4061	137	14	uah	uah	PROPN
ejpam-4061	137	15	)	)	PUNCT
ejpam-4061	137	16	,	,	PUNCT
ejpam-4061	137	17	and	and	CCONJ
ejpam-4061	137	18	⟨x	⟨x	NUM
ejpam-4061	137	19	,	,	PUNCT
ejpam-4061	137	20	0⟩	0⟩	PROPN
ejpam-4061	137	21	∈	∈	PROPN
ejpam-4061	137	22	(	(	PUNCT
ejpam-4061	137	23	l	l	NOUN
ejpam-4061	137	24	\a)∩	\a)∩	PROPN
ejpam-4061	137	25	(	(	PUNCT
ejpam-4061	137	26	intuahd	intuahd	PROPN
ejpam-4061	137	27	)	)	PUNCT
ejpam-4061	137	28	,	,	PUNCT
ejpam-4061	137	29	then	then	ADV
ejpam-4061	137	30	there	there	PRON
ejpam-4061	137	31	exists	exist	VERB
ejpam-4061	137	32	r	r	NOUN
ejpam-4061	137	33	>	>	X
ejpam-4061	137	34	0	0	NUM
ejpam-4061	138	1	such	such	ADJ
ejpam-4061	138	2	that	that	SCONJ
ejpam-4061	138	3	ur(⟨x	ur(⟨x	NOUN
ejpam-4061	138	4	,	,	PUNCT
ejpam-4061	138	5	0⟩	0⟩	PROPN
ejpam-4061	138	6	)	)	PUNCT
ejpam-4061	138	7	⊆	⊆	NUM
ejpam-4061	138	8	d.	d.	PROPN
ejpam-4061	138	9	proof	proof	NOUN
ejpam-4061	138	10	.	.	PUNCT
ejpam-4061	139	1	since	since	SCONJ
ejpam-4061	139	2	⟨x	⟨x	VERB
ejpam-4061	139	3	,	,	PUNCT
ejpam-4061	139	4	0⟩	0⟩	PROPN
ejpam-4061	139	5	∈	∈	PROPN
ejpam-4061	139	6	l	l	NOUN
ejpam-4061	139	7	\	\	PROPN
ejpam-4061	139	8	a	a	DET
ejpam-4061	139	9	and	and	CCONJ
ejpam-4061	139	10	⟨x	⟨x	VERB
ejpam-4061	139	11	,	,	PUNCT
ejpam-4061	139	12	0⟩	0⟩	PROPN
ejpam-4061	139	13	∈	∈	PROPN
ejpam-4061	139	14	intuahd	intuahd	NOUN
ejpam-4061	139	15	,	,	PUNCT
ejpam-4061	139	16	then	then	ADV
ejpam-4061	139	17	there	there	PRON
ejpam-4061	139	18	exists	exist	VERB
ejpam-4061	139	19	r	r	NOUN
ejpam-4061	139	20	>	>	X
ejpam-4061	139	21	0	0	NUM
ejpam-4061	139	22	such	such	ADJ
ejpam-4061	139	23	that	that	SCONJ
ejpam-4061	139	24	cr(⟨x	cr(⟨x	NOUN
ejpam-4061	139	25	,	,	PUNCT
ejpam-4061	139	26	0⟩	0⟩	PROPN
ejpam-4061	139	27	)	)	PUNCT
ejpam-4061	140	1	⊆	⊆	NUM
ejpam-4061	140	2	d	d	SYM
ejpam-4061	140	3	⊆	⊆	NUM
ejpam-4061	140	4	d	d	NOUN
ejpam-4061	140	5	⟨x	⟨x	NUM
ejpam-4061	140	6	,	,	PUNCT
ejpam-4061	140	7	0⟩	0⟩	NUM
ejpam-4061	140	8	•	•	NUM
ejpam-4061	140	9	◦	◦	NOUN
ejpam-4061	140	10	◦	◦	NOUN
ejpam-4061	140	11	now	now	ADV
ejpam-4061	140	12	cr(⟨x	cr(⟨x	NOUN
ejpam-4061	140	13	,	,	PUNCT
ejpam-4061	140	14	0⟩	0⟩	ADJ
ejpam-4061	140	15	)	)	PUNCT
ejpam-4061	141	1	uah	uah	NOUN
ejpam-4061	141	2	⊆	⊆	NUM
ejpam-4061	141	3	d	d	NOUN
ejpam-4061	141	4	uah	uah	NOUN
ejpam-4061	141	5	=	=	NOUN
ejpam-4061	141	6	d	d	PROPN
ejpam-4061	141	7	as	as	SCONJ
ejpam-4061	141	8	d	d	PROPN
ejpam-4061	141	9	is	be	AUX
ejpam-4061	141	10	closed	closed	ADJ
ejpam-4061	141	11	.	.	PUNCT
ejpam-4061	142	1	⊆	⊆	NUM
ejpam-4061	142	2	d	d	NOUN
ejpam-4061	142	3	⟨x	⟨x	NUM
ejpam-4061	142	4	,	,	PUNCT
ejpam-4061	142	5	0⟩	0⟩	PROPN
ejpam-4061	142	6	•	•	NUM
ejpam-4061	142	7	◦	◦	NOUN
ejpam-4061	142	8	◦	◦	NOUN
ejpam-4061	142	9	but	but	CCONJ
ejpam-4061	142	10	ur(⟨x	ur(⟨x	NOUN
ejpam-4061	142	11	,	,	PUNCT
ejpam-4061	142	12	0⟩	0⟩	PROPN
ejpam-4061	142	13	)	)	PUNCT
ejpam-4061	142	14	⊆	⊆	NUM
ejpam-4061	142	15	cr(⟨x	cr(⟨x	NOUN
ejpam-4061	142	16	,	,	PUNCT
ejpam-4061	142	17	0⟩	0⟩	ADJ
ejpam-4061	142	18	)	)	PUNCT
ejpam-4061	142	19	uah	uah	NOUN
ejpam-4061	142	20	⊆	⊆	NUM
ejpam-4061	142	21	d.	d.	NOUN
ejpam-4061	142	22	theorem	theorem	VERB
ejpam-4061	142	23	4	4	NUM
ejpam-4061	142	24	.	.	PUNCT
ejpam-4061	143	1	let	let	VERB
ejpam-4061	143	2	d	d	PRON
ejpam-4061	143	3	be	be	AUX
ejpam-4061	143	4	any	any	DET
ejpam-4061	143	5	non	non	ADJ
ejpam-4061	143	6	-	-	ADJ
ejpam-4061	143	7	empty	empty	ADJ
ejpam-4061	143	8	closed	closed	ADJ
ejpam-4061	143	9	domain	domain	NOUN
ejpam-4061	143	10	in	in	ADP
ejpam-4061	143	11	(	(	PUNCT
ejpam-4061	143	12	x	x	INTJ
ejpam-4061	143	13	,	,	PUNCT
ejpam-4061	143	14	uah	uah	PROPN
ejpam-4061	143	15	)	)	PUNCT
ejpam-4061	143	16	,	,	PUNCT
ejpam-4061	143	17	then	then	ADV
ejpam-4061	143	18	d	d	PROPN
ejpam-4061	143	19	is	be	AUX
ejpam-4061	143	20	a	a	DET
ejpam-4061	143	21	closed	closed	ADJ
ejpam-4061	143	22	domain	domain	NOUN
ejpam-4061	143	23	in	in	ADP
ejpam-4061	143	24	(	(	PUNCT
ejpam-4061	143	25	x	x	INTJ
ejpam-4061	143	26	,	,	PUNCT
ejpam-4061	143	27	u	u	NOUN
ejpam-4061	143	28	)	)	PUNCT
ejpam-4061	143	29	.	.	PUNCT
ejpam-4061	144	1	proof	proof	NOUN
ejpam-4061	144	2	.	.	PUNCT
ejpam-4061	145	1	assume	assume	VERB
ejpam-4061	145	2	d	d	X
ejpam-4061	145	3	=	=	SYM
ejpam-4061	145	4	intuahd	intuahd	ADJ
ejpam-4061	145	5	uah	uah	ADJ
ejpam-4061	145	6	̸=	̸=	PROPN
ejpam-4061	145	7	∅	∅	NOUN
ejpam-4061	145	8	,	,	PUNCT
ejpam-4061	145	9	we	we	PRON
ejpam-4061	145	10	show	show	VERB
ejpam-4061	145	11	d	d	NOUN
ejpam-4061	145	12	=	=	PRON
ejpam-4061	145	13	intud	intud	VERB
ejpam-4061	145	14	u	u	NOUN
ejpam-4061	145	15	.since	.since	NOUN
ejpam-4061	145	16	intud	intud	VERB
ejpam-4061	145	17	⊆	⊆	NUM
ejpam-4061	145	18	d	d	NOUN
ejpam-4061	145	19	,	,	PUNCT
ejpam-4061	145	20	then	then	ADV
ejpam-4061	145	21	intud	intud	VERB
ejpam-4061	145	22	u	u	NOUN
ejpam-4061	145	23	⊆	⊆	PROPN
ejpam-4061	145	24	d	d	SYM
ejpam-4061	145	25	u	u	NOUN
ejpam-4061	145	26	=	=	SYM
ejpam-4061	145	27	d	d	PROPN
ejpam-4061	145	28	,	,	PUNCT
ejpam-4061	145	29	by	by	ADP
ejpam-4061	145	30	lemma	lemma	PROPN
ejpam-4061	145	31	1	1	NUM
ejpam-4061	145	32	.	.	PUNCT
ejpam-4061	146	1	now	now	ADV
ejpam-4061	146	2	,	,	PUNCT
ejpam-4061	146	3	we	we	PRON
ejpam-4061	146	4	show	show	VERB
ejpam-4061	146	5	d	d	PROPN
ejpam-4061	146	6	⊆	⊆	NUM
ejpam-4061	146	7	intud	intud	VERB
ejpam-4061	146	8	u	u	NOUN
ejpam-4061	146	9	.	.	PUNCT
ejpam-4061	147	1	let	let	VERB
ejpam-4061	147	2	⟨x	⟨x	VERB
ejpam-4061	147	3	,	,	PUNCT
ejpam-4061	147	4	y⟩	y⟩	NOUN
ejpam-4061	147	5	∈	∈	PROPN
ejpam-4061	148	1	d	d	X
ejpam-4061	148	2	arbitrary	arbitrary	ADJ
ejpam-4061	148	3	.	.	PUNCT
ejpam-4061	149	1	if	if	SCONJ
ejpam-4061	149	2	⟨x	⟨x	VERB
ejpam-4061	149	3	,	,	PUNCT
ejpam-4061	149	4	y⟩	y⟩	NOUN
ejpam-4061	149	5	∈	∈	PROPN
ejpam-4061	149	6	intud	intud	NOUN
ejpam-4061	149	7	,	,	PUNCT
ejpam-4061	149	8	then	then	ADV
ejpam-4061	149	9	clearly	clearly	ADV
ejpam-4061	149	10	⟨x	⟨x	VERB
ejpam-4061	149	11	,	,	PUNCT
ejpam-4061	149	12	y⟩	y⟩	NOUN
ejpam-4061	149	13	∈	∈	PROPN
ejpam-4061	149	14	intud	intud	VERB
ejpam-4061	149	15	u	u	NOUN
ejpam-4061	149	16	.	.	PUNCT
ejpam-4061	150	1	so	so	ADV
ejpam-4061	150	2	,	,	PUNCT
ejpam-4061	150	3	assume	assume	VERB
ejpam-4061	150	4	that	that	SCONJ
ejpam-4061	150	5	⟨x	⟨x	VERB
ejpam-4061	150	6	,	,	PUNCT
ejpam-4061	150	7	y⟩	y⟩	NOUN
ejpam-4061	150	8	∈	∈	PROPN
ejpam-4061	151	1	d	d	X
ejpam-4061	151	2	\	\	PROPN
ejpam-4061	151	3	intud	intud	NOUN
ejpam-4061	151	4	.	.	PUNCT
ejpam-4061	152	1	to	to	PART
ejpam-4061	152	2	show	show	VERB
ejpam-4061	152	3	⟨x	⟨x	VERB
ejpam-4061	152	4	,	,	PUNCT
ejpam-4061	152	5	y⟩	y⟩	NOUN
ejpam-4061	152	6	∈	∈	PROPN
ejpam-4061	152	7	intud	intud	VERB
ejpam-4061	152	8	u	u	NOUN
ejpam-4061	152	9	we	we	PRON
ejpam-4061	152	10	have	have	VERB
ejpam-4061	152	11	to	to	PART
ejpam-4061	152	12	show	show	VERB
ejpam-4061	152	13	that	that	SCONJ
ejpam-4061	152	14	for	for	ADP
ejpam-4061	152	15	all	all	DET
ejpam-4061	152	16	r	r	NOUN
ejpam-4061	152	17	>	>	X
ejpam-4061	152	18	0	0	NUM
ejpam-4061	152	19	,	,	PUNCT
ejpam-4061	152	20	we	we	PRON
ejpam-4061	152	21	have	have	VERB
ejpam-4061	152	22	ur(⟨x	ur(⟨x	NOUN
ejpam-4061	152	23	,	,	PUNCT
ejpam-4061	152	24	y⟩	y⟩	NOUN
ejpam-4061	152	25	)	)	PUNCT
ejpam-4061	152	26	∩	∩	NOUN
ejpam-4061	152	27	intud	intud	VERB
ejpam-4061	152	28	̸=	̸=	PROPN
ejpam-4061	152	29	∅	∅	NOUN
ejpam-4061	152	30	case	case	NOUN
ejpam-4061	152	31	1	1	NUM
ejpam-4061	152	32	:	:	PUNCT
ejpam-4061	152	33	⟨x	⟨x	NUM
ejpam-4061	152	34	,	,	PUNCT
ejpam-4061	152	35	y⟩	y⟩	NOUN
ejpam-4061	152	36	∈	∈	PROPN
ejpam-4061	152	37	k	k	PROPN
ejpam-4061	152	38	∪a	∪a	PROPN
ejpam-4061	152	39	.	.	PUNCT
ejpam-4061	153	1	let	let	VERB
ejpam-4061	153	2	r	r	PRON
ejpam-4061	153	3	>	>	X
ejpam-4061	153	4	0	0	NUM
ejpam-4061	153	5	be	be	AUX
ejpam-4061	153	6	arbitrary	arbitrary	ADJ
ejpam-4061	153	7	,	,	PUNCT
ejpam-4061	153	8	we	we	PRON
ejpam-4061	153	9	have	have	VERB
ejpam-4061	153	10	ur(⟨x	ur(⟨x	NOUN
ejpam-4061	153	11	,	,	PUNCT
ejpam-4061	153	12	y⟩	y⟩	NOUN
ejpam-4061	153	13	)	)	PUNCT
ejpam-4061	153	14	∩	∩	NOUN
ejpam-4061	153	15	intuahd	intuahd	PROPN
ejpam-4061	153	16	̸=	̸=	PROPN
ejpam-4061	153	17	∅.	∅.	NOUN
ejpam-4061	153	18	by	by	ADP
ejpam-4061	153	19	lemma	lemma	PROPN
ejpam-4061	153	20	2	2	NUM
ejpam-4061	153	21	,	,	PUNCT
ejpam-4061	153	22	we	we	PRON
ejpam-4061	153	23	have	have	VERB
ejpam-4061	153	24	(	(	PUNCT
ejpam-4061	154	1	intuahd	intuahd	ADJ
ejpam-4061	154	2	)	)	PUNCT
ejpam-4061	154	3	∩	∩	NOUN
ejpam-4061	154	4	(	(	PUNCT
ejpam-4061	154	5	k	k	X
ejpam-4061	154	6	∪	∪	X
ejpam-4061	154	7	a	a	X
ejpam-4061	154	8	)	)	PUNCT
ejpam-4061	154	9	=	=	SYM
ejpam-4061	154	10	(	(	PUNCT
ejpam-4061	154	11	intud	intud	NOUN
ejpam-4061	154	12	)	)	PUNCT
ejpam-4061	154	13	∩	∩	NOUN
ejpam-4061	154	14	(	(	PUNCT
ejpam-4061	154	15	k	k	X
ejpam-4061	154	16	∪	∪	ADP
ejpam-4061	154	17	a	a	PRON
ejpam-4061	154	18	)	)	PUNCT
ejpam-4061	154	19	,	,	PUNCT
ejpam-4061	154	20	since	since	SCONJ
ejpam-4061	154	21	⟨x	⟨x	VERB
ejpam-4061	154	22	,	,	PUNCT
ejpam-4061	154	23	y⟩	y⟩	NOUN
ejpam-4061	154	24	∈	∈	PROPN
ejpam-4061	155	1	k	k	PROPN
ejpam-4061	155	2	∪	∪	ADP
ejpam-4061	155	3	a	a	PRON
ejpam-4061	155	4	,	,	PUNCT
ejpam-4061	155	5	then	then	ADV
ejpam-4061	155	6	ur(⟨x	ur(⟨x	NOUN
ejpam-4061	155	7	,	,	PUNCT
ejpam-4061	155	8	y⟩	y⟩	NOUN
ejpam-4061	155	9	)	)	PUNCT
ejpam-4061	155	10	∩	∩	NOUN
ejpam-4061	155	11	intud	intud	VERB
ejpam-4061	155	12	̸=	̸=	PROPN
ejpam-4061	155	13	∅.	∅.	PRON
ejpam-4061	155	14	case	case	NOUN
ejpam-4061	155	15	2	2	NUM
ejpam-4061	155	16	:	:	PUNCT
ejpam-4061	155	17	⟨x	⟨x	NUM
ejpam-4061	155	18	,	,	PUNCT
ejpam-4061	155	19	y⟩	y⟩	NOUN
ejpam-4061	155	20	∈	∈	PROPN
ejpam-4061	155	21	l	l	NOUN
ejpam-4061	155	22	\a	\a	PROPN
ejpam-4061	155	23	,	,	PUNCT
ejpam-4061	155	24	then	then	ADV
ejpam-4061	155	25	y	y	PROPN
ejpam-4061	155	26	=	=	SYM
ejpam-4061	155	27	0	0	X
ejpam-4061	155	28	.	.	PUNCT
ejpam-4061	156	1	we	we	PRON
ejpam-4061	156	2	want	want	VERB
ejpam-4061	156	3	to	to	PART
ejpam-4061	156	4	show	show	VERB
ejpam-4061	156	5	that	that	SCONJ
ejpam-4061	156	6	for	for	ADP
ejpam-4061	156	7	any	any	DET
ejpam-4061	156	8	r	r	NOUN
ejpam-4061	156	9	>	>	X
ejpam-4061	156	10	0	0	NUM
ejpam-4061	156	11	we	we	PRON
ejpam-4061	156	12	have	have	VERB
ejpam-4061	156	13	ur(⟨x	ur(⟨x	NOUN
ejpam-4061	156	14	,	,	PUNCT
ejpam-4061	156	15	0⟩)∩	0⟩)∩	PRON
ejpam-4061	156	16	intud	intud	VERB
ejpam-4061	156	17	̸=	̸=	PROPN
ejpam-4061	156	18	∅.	∅.	ADV
ejpam-4061	156	19	suppose	suppose	VERB
ejpam-4061	156	20	that	that	SCONJ
ejpam-4061	156	21	there	there	PRON
ejpam-4061	156	22	exists	exist	VERB
ejpam-4061	156	23	r	r	NOUN
ejpam-4061	156	24	>	>	X
ejpam-4061	156	25	0	0	NUM
ejpam-4061	156	26	such	such	ADJ
ejpam-4061	156	27	that	that	SCONJ
ejpam-4061	156	28	ur(⟨x	ur(⟨x	NOUN
ejpam-4061	156	29	,	,	PUNCT
ejpam-4061	156	30	0⟩	0⟩	PROPN
ejpam-4061	156	31	)	)	PUNCT
ejpam-4061	156	32	∩	∩	NOUN
ejpam-4061	156	33	intud	intud	VERB
ejpam-4061	156	34	=	=	VERB
ejpam-4061	156	35	∅	∅	NOUN
ejpam-4061	156	36	.	.	PUNCT
ejpam-4061	156	37	.	.	PUNCT
ejpam-4061	156	38	.	.	PUNCT
ejpam-4061	157	1	(	(	PUNCT
ejpam-4061	157	2	⋆	⋆	NOUN
ejpam-4061	157	3	)	)	PUNCT
ejpam-4061	157	4	.	.	PUNCT
ejpam-4061	158	1	since	since	SCONJ
ejpam-4061	158	2	cr(⟨x	cr(⟨x	NOUN
ejpam-4061	158	3	,	,	PUNCT
ejpam-4061	158	4	0⟩	0⟩	PROPN
ejpam-4061	158	5	)	)	PUNCT
ejpam-4061	158	6	⊆	⊆	NUM
ejpam-4061	158	7	ur(⟨x	ur(⟨x	NOUN
ejpam-4061	158	8	,	,	PUNCT
ejpam-4061	158	9	0⟩	0⟩	PROPN
ejpam-4061	158	10	)	)	PUNCT
ejpam-4061	158	11	,	,	PUNCT
ejpam-4061	158	12	then	then	ADV
ejpam-4061	158	13	cr(⟨x	cr(⟨x	NOUN
ejpam-4061	158	14	,	,	PUNCT
ejpam-4061	158	15	0⟩	0⟩	ADJ
ejpam-4061	158	16	)	)	PUNCT
ejpam-4061	158	17	∩	∩	NOUN
ejpam-4061	158	18	intud	intud	VERB
ejpam-4061	158	19	=	=	PUNCT
ejpam-4061	158	20	∅.	∅.	NOUN
ejpam-4061	158	21	claim	claim	NOUN
ejpam-4061	158	22	:	:	PUNCT
ejpam-4061	158	23	cr(⟨x	cr(⟨x	NOUN
ejpam-4061	158	24	,	,	PUNCT
ejpam-4061	158	25	0⟩	0⟩	ADJ
ejpam-4061	158	26	)	)	PUNCT
ejpam-4061	158	27	∩	∩	ADJ
ejpam-4061	158	28	intuahd	intuahd	NOUN
ejpam-4061	158	29	=	=	PUNCT
ejpam-4061	158	30	∅.	∅.	NOUN
ejpam-4061	158	31	if	if	SCONJ
ejpam-4061	158	32	we	we	PRON
ejpam-4061	158	33	prove	prove	VERB
ejpam-4061	158	34	the	the	DET
ejpam-4061	158	35	claim	claim	NOUN
ejpam-4061	158	36	,	,	PUNCT
ejpam-4061	158	37	we	we	PRON
ejpam-4061	158	38	get	get	AUX
ejpam-4061	158	39	⟨x	⟨x	VERB
ejpam-4061	158	40	,	,	PUNCT
ejpam-4061	158	41	0⟩	0⟩	PROPN
ejpam-4061	158	42	∈	∈	PROPN
ejpam-4061	158	43	d	d	PRON
ejpam-4061	158	44	\	\	PROPN
ejpam-4061	158	45	intuahd	intuahd	NOUN
ejpam-4061	158	46	,	,	PUNCT
ejpam-4061	158	47	but	but	CCONJ
ejpam-4061	158	48	⟨x	⟨x	NUM
ejpam-4061	158	49	,	,	PUNCT
ejpam-4061	158	50	0⟩	0⟩	PROPN
ejpam-4061	158	51	̸∈	̸∈	PROPN
ejpam-4061	158	52	intuahd	intuahd	ADJ
ejpam-4061	158	53	uah	uah	PROPN
ejpam-4061	158	54	,	,	PUNCT
ejpam-4061	158	55	thus	thus	ADV
ejpam-4061	158	56	d	d	PRON
ejpam-4061	158	57	is	be	AUX
ejpam-4061	158	58	not	not	PART
ejpam-4061	158	59	a	a	DET
ejpam-4061	158	60	closed	closed	ADJ
ejpam-4061	158	61	domain	domain	NOUN
ejpam-4061	158	62	in	in	ADP
ejpam-4061	158	63	(	(	PUNCT
ejpam-4061	158	64	x	x	INTJ
ejpam-4061	158	65	,	,	PUNCT
ejpam-4061	158	66	uah	uah	PROPN
ejpam-4061	158	67	)	)	PUNCT
ejpam-4061	158	68	,	,	PUNCT
ejpam-4061	158	69	which	which	PRON
ejpam-4061	158	70	is	be	AUX
ejpam-4061	158	71	a	a	DET
ejpam-4061	158	72	contradiction	contradiction	NOUN
ejpam-4061	158	73	.	.	PUNCT
ejpam-4061	159	1	n.	n.	PROPN
ejpam-4061	159	2	alghamdi	alghamdi	PROPN
ejpam-4061	159	3	,	,	PUNCT
ejpam-4061	159	4	l.	l.	PROPN
ejpam-4061	159	5	kalantan	kalantan	PROPN
ejpam-4061	159	6	/	/	SYM
ejpam-4061	159	7	eur	eur	PROPN
ejpam-4061	159	8	.	.	PUNCT
ejpam-4061	160	1	j.	j.	PROPN
ejpam-4061	160	2	pure	pure	PROPN
ejpam-4061	160	3	appl	appl	PROPN
ejpam-4061	160	4	.	.	PROPN
ejpam-4061	160	5	math	math	PROPN
ejpam-4061	160	6	,	,	PUNCT
ejpam-4061	160	7	14	14	NUM
ejpam-4061	160	8	(	(	PUNCT
ejpam-4061	160	9	4	4	NUM
ejpam-4061	160	10	)	)	PUNCT
ejpam-4061	160	11	(	(	PUNCT
ejpam-4061	160	12	2021	2021	NUM
ejpam-4061	160	13	)	)	PUNCT
ejpam-4061	160	14	,	,	PUNCT
ejpam-4061	160	15	1161	1161	NUM
ejpam-4061	160	16	-	-	SYM
ejpam-4061	160	17	1168	1168	NUM
ejpam-4061	160	18	1166	1166	NUM
ejpam-4061	160	19	proof	proof	NOUN
ejpam-4061	160	20	of	of	ADP
ejpam-4061	160	21	claim	claim	NOUN
ejpam-4061	160	22	:	:	PUNCT
ejpam-4061	160	23	suppose	suppose	VERB
ejpam-4061	160	24	cr(⟨x	cr(⟨x	NOUN
ejpam-4061	160	25	,	,	PUNCT
ejpam-4061	160	26	0⟩)∩	0⟩)∩	NUM
ejpam-4061	161	1	intuahd	intuahd	PROPN
ejpam-4061	161	2	̸=	̸=	PROPN
ejpam-4061	161	3	∅.	∅.	ADP
ejpam-4061	161	4	pick	pick	PROPN
ejpam-4061	161	5	⟨u	⟨u	NOUN
ejpam-4061	161	6	,	,	PUNCT
ejpam-4061	161	7	v⟩	v⟩	NOUN
ejpam-4061	161	8	∈	∈	NOUN
ejpam-4061	161	9	cr(⟨x	cr(⟨x	NOUN
ejpam-4061	161	10	,	,	PUNCT
ejpam-4061	161	11	0⟩)∩	0⟩)∩	PUNCT
ejpam-4061	161	12	intuahd	intuahd	ADJ
ejpam-4061	161	13	.	.	PUNCT
ejpam-4061	162	1	if	if	SCONJ
ejpam-4061	162	2	v	v	NOUN
ejpam-4061	162	3	>	>	X
ejpam-4061	162	4	0	0	NUM
ejpam-4061	162	5	,	,	PUNCT
ejpam-4061	162	6	then	then	ADV
ejpam-4061	162	7	⟨u	⟨u	NOUN
ejpam-4061	162	8	,	,	PUNCT
ejpam-4061	162	9	v⟩	v⟩	NOUN
ejpam-4061	162	10	∈	∈	PROPN
ejpam-4061	163	1	k	k	NOUN
ejpam-4061	163	2	,	,	PUNCT
ejpam-4061	163	3	since	since	SCONJ
ejpam-4061	163	4	cr(⟨x	cr(⟨x	NOUN
ejpam-4061	163	5	,	,	PUNCT
ejpam-4061	163	6	0⟩	0⟩	PROPN
ejpam-4061	163	7	)	)	PUNCT
ejpam-4061	163	8	⊆	⊆	NUM
ejpam-4061	163	9	ur(⟨x	ur(⟨x	NOUN
ejpam-4061	163	10	,	,	PUNCT
ejpam-4061	163	11	0⟩	0⟩	PROPN
ejpam-4061	163	12	)	)	PUNCT
ejpam-4061	163	13	,	,	PUNCT
ejpam-4061	163	14	and	and	CCONJ
ejpam-4061	163	15	(	(	PUNCT
ejpam-4061	163	16	intuahd	intuahd	ADJ
ejpam-4061	163	17	)	)	PUNCT
ejpam-4061	163	18	∩k	∩k	NOUN
ejpam-4061	163	19	=	=	SYM
ejpam-4061	163	20	(	(	PUNCT
ejpam-4061	163	21	intud	intud	NOUN
ejpam-4061	163	22	)	)	PUNCT
ejpam-4061	163	23	∩k	∩k	PROPN
ejpam-4061	163	24	,	,	PUNCT
ejpam-4061	163	25	then	then	ADV
ejpam-4061	163	26	⟨u	⟨u	NOUN
ejpam-4061	163	27	,	,	PUNCT
ejpam-4061	163	28	v⟩	v⟩	NOUN
ejpam-4061	163	29	∈	∈	PROPN
ejpam-4061	163	30	ur(⟨x	ur(⟨x	NOUN
ejpam-4061	163	31	,	,	PUNCT
ejpam-4061	163	32	0⟩	0⟩	PROPN
ejpam-4061	163	33	)	)	PUNCT
ejpam-4061	163	34	∩	∩	NOUN
ejpam-4061	163	35	intud	intud	NOUN
ejpam-4061	163	36	,	,	PUNCT
ejpam-4061	163	37	which	which	PRON
ejpam-4061	163	38	is	be	AUX
ejpam-4061	163	39	a	a	DET
ejpam-4061	163	40	contradicts	contradict	NOUN
ejpam-4061	163	41	(	(	PUNCT
ejpam-4061	163	42	⋆	⋆	NOUN
ejpam-4061	163	43	)	)	PUNCT
ejpam-4061	163	44	.	.	PUNCT
ejpam-4061	164	1	then	then	ADV
ejpam-4061	164	2	v	v	X
ejpam-4061	164	3	=	=	SYM
ejpam-4061	164	4	0	0	NUM
ejpam-4061	164	5	,	,	PUNCT
ejpam-4061	164	6	so	so	SCONJ
ejpam-4061	164	7	⟨u	⟨u	NOUN
ejpam-4061	164	8	,	,	PUNCT
ejpam-4061	164	9	v⟩	v⟩	NOUN
ejpam-4061	164	10	=	=	PUNCT
ejpam-4061	164	11	⟨x	⟨x	NUM
ejpam-4061	164	12	,	,	PUNCT
ejpam-4061	164	13	0⟩	0⟩	PROPN
ejpam-4061	164	14	,	,	PUNCT
ejpam-4061	164	15	hence	hence	ADV
ejpam-4061	164	16	⟨x	⟨x	VERB
ejpam-4061	164	17	,	,	PUNCT
ejpam-4061	164	18	0⟩	0⟩	PROPN
ejpam-4061	164	19	∈	∈	PROPN
ejpam-4061	164	20	intuahd	intuahd	NOUN
ejpam-4061	164	21	,	,	PUNCT
ejpam-4061	164	22	therefore	therefore	ADV
ejpam-4061	164	23	there	there	PRON
ejpam-4061	164	24	exists	exist	VERB
ejpam-4061	164	25	0	0	PUNCT
ejpam-4061	164	26	<	<	X
ejpam-4061	164	27	s	s	X
ejpam-4061	164	28	<	<	X
ejpam-4061	164	29	r	r	NOUN
ejpam-4061	164	30	such	such	ADJ
ejpam-4061	164	31	that	that	SCONJ
ejpam-4061	164	32	cs(⟨x	cs(⟨x	NOUN
ejpam-4061	164	33	,	,	PUNCT
ejpam-4061	164	34	0⟩	0⟩	PROPN
ejpam-4061	164	35	)	)	PUNCT
ejpam-4061	165	1	⊆	⊆	NUM
ejpam-4061	165	2	intuahd	intuahd	NOUN
ejpam-4061	165	3	⊂	⊂	PROPN
ejpam-4061	165	4	d	d	X
ejpam-4061	165	5	.	.	PUNCT
ejpam-4061	166	1	by	by	ADP
ejpam-4061	166	2	lemma	lemma	PROPN
ejpam-4061	166	3	3	3	NUM
ejpam-4061	166	4	us(⟨x	us(⟨x	NOUN
ejpam-4061	166	5	,	,	PUNCT
ejpam-4061	166	6	0⟩	0⟩	PROPN
ejpam-4061	166	7	)	)	PUNCT
ejpam-4061	166	8	⊆	⊆	NUM
ejpam-4061	166	9	intuahd	intuahd	NOUN
ejpam-4061	166	10	,	,	PUNCT
ejpam-4061	166	11	then	then	ADV
ejpam-4061	166	12	⟨x	⟨x	VERB
ejpam-4061	166	13	,	,	PUNCT
ejpam-4061	166	14	0⟩	0⟩	PROPN
ejpam-4061	166	15	∈	∈	PROPN
ejpam-4061	166	16	intud	intud	NOUN
ejpam-4061	166	17	,	,	PUNCT
ejpam-4061	166	18	but	but	CCONJ
ejpam-4061	166	19	⟨x	⟨x	NUM
ejpam-4061	166	20	,	,	PUNCT
ejpam-4061	166	21	0⟩	0⟩	PROPN
ejpam-4061	166	22	∈	∈	PROPN
ejpam-4061	166	23	d	d	X
ejpam-4061	166	24	\	\	PROPN
ejpam-4061	166	25	intud	intud	NOUN
ejpam-4061	166	26	,	,	PUNCT
ejpam-4061	166	27	which	which	PRON
ejpam-4061	166	28	is	be	AUX
ejpam-4061	166	29	a	a	DET
ejpam-4061	166	30	contradiction	contradiction	NOUN
ejpam-4061	166	31	.	.	PUNCT
ejpam-4061	167	1	so	so	ADV
ejpam-4061	167	2	,	,	PUNCT
ejpam-4061	167	3	claim	claim	NOUN
ejpam-4061	167	4	is	be	AUX
ejpam-4061	167	5	proved	prove	VERB
ejpam-4061	167	6	.	.	PUNCT
ejpam-4061	168	1	theorem	theorem	ADJ
ejpam-4061	168	2	5	5	NUM
ejpam-4061	168	3	.	.	PUNCT
ejpam-4061	169	1	any	any	DET
ejpam-4061	169	2	h	h	NOUN
ejpam-4061	169	3	-	-	PUNCT
ejpam-4061	169	4	spaces	space	NOUN
ejpam-4061	169	5	(	(	PUNCT
ejpam-4061	169	6	x	x	INTJ
ejpam-4061	169	7	,	,	PUNCT
ejpam-4061	169	8	uah	uah	PROPN
ejpam-4061	169	9	)	)	PUNCT
ejpam-4061	169	10	is	be	AUX
ejpam-4061	169	11	mildly	mildly	ADV
ejpam-4061	169	12	normal	normal	ADJ
ejpam-4061	169	13	.	.	PUNCT
ejpam-4061	170	1	proof	proof	NOUN
ejpam-4061	170	2	.	.	PUNCT
ejpam-4061	171	1	let	let	VERB
ejpam-4061	171	2	e	e	NOUN
ejpam-4061	171	3	and	and	CCONJ
ejpam-4061	171	4	f	f	PROPN
ejpam-4061	171	5	be	be	VERB
ejpam-4061	171	6	any	any	DET
ejpam-4061	171	7	tow	tow	NOUN
ejpam-4061	171	8	disjoint	disjoint	NOUN
ejpam-4061	171	9	closed	close	VERB
ejpam-4061	171	10	domains	domain	NOUN
ejpam-4061	171	11	in	in	ADP
ejpam-4061	171	12	(	(	PUNCT
ejpam-4061	171	13	x	x	INTJ
ejpam-4061	171	14	,	,	PUNCT
ejpam-4061	171	15	uah	uah	PROPN
ejpam-4061	171	16	)	)	PUNCT
ejpam-4061	171	17	,	,	PUNCT
ejpam-4061	171	18	by	by	ADP
ejpam-4061	171	19	theorem	theorem	NOUN
ejpam-4061	171	20	4	4	NUM
ejpam-4061	171	21	,	,	PUNCT
ejpam-4061	171	22	e	e	PROPN
ejpam-4061	171	23	and	and	CCONJ
ejpam-4061	171	24	f	f	PROPN
ejpam-4061	171	25	are	be	AUX
ejpam-4061	171	26	closed	close	VERB
ejpam-4061	171	27	domains	domain	NOUN
ejpam-4061	171	28	in	in	ADP
ejpam-4061	171	29	(	(	PUNCT
ejpam-4061	171	30	x	x	NOUN
ejpam-4061	171	31	,	,	PUNCT
ejpam-4061	171	32	u	u	NOUN
ejpam-4061	171	33	)	)	PUNCT
ejpam-4061	171	34	,	,	PUNCT
ejpam-4061	171	35	and	and	CCONJ
ejpam-4061	171	36	(	(	PUNCT
ejpam-4061	171	37	x	x	NOUN
ejpam-4061	171	38	,	,	PUNCT
ejpam-4061	171	39	u	u	NOUN
ejpam-4061	171	40	)	)	PUNCT
ejpam-4061	171	41	is	be	AUX
ejpam-4061	171	42	mildly	mildly	ADV
ejpam-4061	171	43	normal	normal	ADJ
ejpam-4061	171	44	,	,	PUNCT
ejpam-4061	171	45	then	then	ADV
ejpam-4061	171	46	there	there	PRON
ejpam-4061	171	47	exists	exist	VERB
ejpam-4061	171	48	u	u	NOUN
ejpam-4061	171	49	and	and	CCONJ
ejpam-4061	171	50	v	v	NOUN
ejpam-4061	171	51	in	in	ADP
ejpam-4061	171	52	u	u	PRON
ejpam-4061	171	53	such	such	ADJ
ejpam-4061	171	54	that	that	SCONJ
ejpam-4061	171	55	e	e	PROPN
ejpam-4061	171	56	⊂	⊂	PROPN
ejpam-4061	171	57	u	u	PROPN
ejpam-4061	171	58	,	,	PUNCT
ejpam-4061	171	59	f	f	PROPN
ejpam-4061	171	60	⊂	⊂	PROPN
ejpam-4061	171	61	v	v	PROPN
ejpam-4061	171	62	and	and	CCONJ
ejpam-4061	171	63	u	u	NOUN
ejpam-4061	171	64	∩	∩	NOUN
ejpam-4061	171	65	v	v	NOUN
ejpam-4061	171	66	=	=	PUNCT
ejpam-4061	171	67	∅.	∅.	NOUN
ejpam-4061	171	68	since	since	SCONJ
ejpam-4061	171	69	u	u	NOUN
ejpam-4061	171	70	⊆	⊆	NUM
ejpam-4061	171	71	uah	uah	NOUN
ejpam-4061	171	72	,	,	PUNCT
ejpam-4061	171	73	then	then	ADV
ejpam-4061	171	74	u	u	NOUN
ejpam-4061	171	75	and	and	CCONJ
ejpam-4061	171	76	v	v	NOUN
ejpam-4061	171	77	are	be	AUX
ejpam-4061	171	78	both	both	ADV
ejpam-4061	171	79	open	open	ADJ
ejpam-4061	171	80	in	in	ADP
ejpam-4061	171	81	h	h	NOUN
ejpam-4061	171	82	-	-	PUNCT
ejpam-4061	171	83	space	space	NOUN
ejpam-4061	171	84	,	,	PUNCT
ejpam-4061	171	85	thus	thus	ADV
ejpam-4061	171	86	(	(	PUNCT
ejpam-4061	171	87	x	x	X
ejpam-4061	171	88	,	,	PUNCT
ejpam-4061	171	89	uah	uah	PROPN
ejpam-4061	171	90	)	)	PUNCT
ejpam-4061	171	91	is	be	AUX
ejpam-4061	171	92	mildly	mildly	ADV
ejpam-4061	171	93	normal	normal	ADJ
ejpam-4061	171	94	.	.	PUNCT
ejpam-4061	172	1	theorem	theorem	VERB
ejpam-4061	172	2	6	6	NUM
ejpam-4061	172	3	.	.	PUNCT
ejpam-4061	173	1	any	any	DET
ejpam-4061	173	2	closed	closed	ADJ
ejpam-4061	173	3	domain	domain	NOUN
ejpam-4061	173	4	in	in	ADP
ejpam-4061	173	5	usual	usual	ADJ
ejpam-4061	173	6	metric	metric	ADJ
ejpam-4061	173	7	space	space	NOUN
ejpam-4061	173	8	(	(	PUNCT
ejpam-4061	173	9	x	x	X
ejpam-4061	173	10	,	,	PUNCT
ejpam-4061	173	11	u	u	NOUN
ejpam-4061	173	12	)	)	PUNCT
ejpam-4061	173	13	is	be	AUX
ejpam-4061	173	14	closed	close	VERB
ejpam-4061	173	15	domain	domain	NOUN
ejpam-4061	173	16	in	in	ADP
ejpam-4061	173	17	hspaces	hspace	NOUN
ejpam-4061	173	18	(	(	PUNCT
ejpam-4061	173	19	x	x	X
ejpam-4061	173	20	,	,	PUNCT
ejpam-4061	173	21	uah	uah	PROPN
ejpam-4061	173	22	)	)	PUNCT
ejpam-4061	173	23	.	.	PUNCT
ejpam-4061	174	1	proof	proof	NOUN
ejpam-4061	174	2	.	.	PUNCT
ejpam-4061	175	1	let	let	VERB
ejpam-4061	175	2	d	d	PRON
ejpam-4061	175	3	be	be	AUX
ejpam-4061	175	4	a	a	DET
ejpam-4061	175	5	closed	closed	ADJ
ejpam-4061	175	6	domain	domain	NOUN
ejpam-4061	175	7	in	in	ADP
ejpam-4061	175	8	usual	usual	ADJ
ejpam-4061	175	9	metric	metric	ADJ
ejpam-4061	175	10	space	space	NOUN
ejpam-4061	175	11	,	,	PUNCT
ejpam-4061	175	12	we	we	PRON
ejpam-4061	175	13	want	want	VERB
ejpam-4061	175	14	to	to	PART
ejpam-4061	175	15	show	show	VERB
ejpam-4061	175	16	that	that	PRON
ejpam-4061	175	17	intuahd	intuahd	ADJ
ejpam-4061	175	18	uah	uah	NOUN
ejpam-4061	175	19	=	=	NOUN
ejpam-4061	175	20	intud	intud	VERB
ejpam-4061	175	21	u	u	NOUN
ejpam-4061	175	22	.	.	PUNCT
ejpam-4061	176	1	we	we	PRON
ejpam-4061	176	2	have	have	AUX
ejpam-4061	176	3	intuahd	intuahd	VERB
ejpam-4061	176	4	uah	uah	ADJ
ejpam-4061	176	5	⊆	⊆	ADJ
ejpam-4061	176	6	intud	intud	NOUN
ejpam-4061	176	7	u	u	NOUN
ejpam-4061	176	8	.	.	PUNCT
ejpam-4061	177	1	claim	claim	NOUN
ejpam-4061	177	2	:	:	PUNCT
ejpam-4061	177	3	intud	intud	VERB
ejpam-4061	177	4	u	u	NOUN
ejpam-4061	177	5	⊆	⊆	NUM
ejpam-4061	177	6	intuahd	intuahd	ADJ
ejpam-4061	177	7	uah	uah	NOUN
ejpam-4061	177	8	.	.	PUNCT
ejpam-4061	178	1	proof	proof	NOUN
ejpam-4061	178	2	of	of	ADP
ejpam-4061	178	3	claim	claim	NOUN
ejpam-4061	178	4	:	:	PUNCT
ejpam-4061	178	5	let	let	VERB
ejpam-4061	178	6	⟨x	⟨x	VERB
ejpam-4061	178	7	,	,	PUNCT
ejpam-4061	178	8	y⟩	y⟩	NOUN
ejpam-4061	178	9	∈	∈	PROPN
ejpam-4061	178	10	intud	intud	VERB
ejpam-4061	178	11	u	u	NOUN
ejpam-4061	178	12	be	be	VERB
ejpam-4061	178	13	arbitrary	arbitrary	ADJ
ejpam-4061	178	14	,	,	PUNCT
ejpam-4061	178	15	then	then	ADV
ejpam-4061	178	16	for	for	ADP
ejpam-4061	178	17	all	all	DET
ejpam-4061	178	18	r	r	NOUN
ejpam-4061	178	19	>	>	X
ejpam-4061	178	20	0	0	NUM
ejpam-4061	178	21	we	we	PRON
ejpam-4061	178	22	have	have	VERB
ejpam-4061	178	23	ur(⟨x	ur(⟨x	NOUN
ejpam-4061	178	24	,	,	PUNCT
ejpam-4061	178	25	y⟩	y⟩	NOUN
ejpam-4061	178	26	)	)	PUNCT
ejpam-4061	178	27	∩	∩	NOUN
ejpam-4061	178	28	intud	intud	VERB
ejpam-4061	178	29	̸=	̸=	PROPN
ejpam-4061	178	30	∅	∅	NOUN
ejpam-4061	178	31	,	,	PUNCT
ejpam-4061	178	32	by	by	ADP
ejpam-4061	178	33	lemma	lemma	PROPN
ejpam-4061	178	34	2	2	NUM
ejpam-4061	178	35	we	we	PRON
ejpam-4061	178	36	have	have	VERB
ejpam-4061	178	37	ur(⟨x	ur(⟨x	NOUN
ejpam-4061	178	38	,	,	PUNCT
ejpam-4061	178	39	y⟩)∩intuahd	y⟩)∩intuahd	ADP
ejpam-4061	178	40	̸=	̸=	PROPN
ejpam-4061	178	41	∅	∅	NOUN
ejpam-4061	178	42	,	,	PUNCT
ejpam-4061	178	43	therefore	therefore	ADV
ejpam-4061	178	44	⟨x	⟨x	VERB
ejpam-4061	178	45	,	,	PUNCT
ejpam-4061	178	46	y⟩	y⟩	NOUN
ejpam-4061	178	47	∈	∈	PROPN
ejpam-4061	178	48	intuahd	intuahd	PROPN
ejpam-4061	178	49	uah	uah	PROPN
ejpam-4061	178	50	.	.	PUNCT
ejpam-4061	179	1	recall	recall	VERB
ejpam-4061	179	2	that	that	SCONJ
ejpam-4061	179	3	a	a	DET
ejpam-4061	179	4	space	space	NOUN
ejpam-4061	179	5	x	x	PUNCT
ejpam-4061	179	6	is	be	AUX
ejpam-4061	179	7	semiregular	semiregular	ADJ
ejpam-4061	179	8	if	if	SCONJ
ejpam-4061	179	9	it	it	PRON
ejpam-4061	179	10	has	have	VERB
ejpam-4061	179	11	a	a	DET
ejpam-4061	179	12	base	base	NOUN
ejpam-4061	179	13	consisting	consist	VERB
ejpam-4061	179	14	of	of	ADP
ejpam-4061	179	15	open	open	ADJ
ejpam-4061	179	16	domains	domain	NOUN
ejpam-4061	179	17	,	,	PUNCT
ejpam-4061	179	18	[	[	X
ejpam-4061	179	19	1	1	NUM
ejpam-4061	179	20	,	,	PUNCT
ejpam-4061	179	21	1.7.8	1.7.8	NUM
ejpam-4061	179	22	(	(	PUNCT
ejpam-4061	179	23	a	a	NOUN
ejpam-4061	179	24	)	)	PUNCT
ejpam-4061	179	25	]	]	PUNCT
ejpam-4061	179	26	,	,	PUNCT
ejpam-4061	179	27	see	see	VERB
ejpam-4061	179	28	also	also	ADV
ejpam-4061	179	29	[	[	X
ejpam-4061	179	30	9	9	NUM
ejpam-4061	179	31	]	]	PUNCT
ejpam-4061	179	32	.	.	PUNCT
ejpam-4061	180	1	now	now	ADV
ejpam-4061	180	2	,	,	PUNCT
ejpam-4061	180	3	let	let	VERB
ejpam-4061	180	4	(	(	PUNCT
ejpam-4061	180	5	x	x	X
ejpam-4061	180	6	,	,	PUNCT
ejpam-4061	180	7	τ	τ	PROPN
ejpam-4061	180	8	)	)	PUNCT
ejpam-4061	180	9	be	be	AUX
ejpam-4061	180	10	a	a	DET
ejpam-4061	180	11	t2	t2	NOUN
ejpam-4061	180	12	space	space	NOUN
ejpam-4061	180	13	.	.	PUNCT
ejpam-4061	181	1	generate	generate	VERB
ejpam-4061	181	2	a	a	DET
ejpam-4061	181	3	coarser	coarse	ADJ
ejpam-4061	181	4	topology	topology	NOUN
ejpam-4061	181	5	τ	τ	PROPN
ejpam-4061	181	6	′	′	NOUN
ejpam-4061	181	7	⊆	⊆	NUM
ejpam-4061	181	8	τ	τ	X
ejpam-4061	181	9	on	on	ADP
ejpam-4061	181	10	x	x	PUNCT
ejpam-4061	181	11	by	by	ADP
ejpam-4061	181	12	the	the	DET
ejpam-4061	181	13	base	base	NOUN
ejpam-4061	181	14	of	of	ADP
ejpam-4061	181	15	all	all	DET
ejpam-4061	181	16	open	open	ADJ
ejpam-4061	181	17	domains	domain	NOUN
ejpam-4061	181	18	in	in	ADP
ejpam-4061	181	19	(	(	PUNCT
ejpam-4061	181	20	x	x	INTJ
ejpam-4061	181	21	,	,	PUNCT
ejpam-4061	181	22	τ	τ	PROPN
ejpam-4061	181	23	)	)	PUNCT
ejpam-4061	181	24	.	.	PUNCT
ejpam-4061	182	1	then	then	ADV
ejpam-4061	182	2	(	(	PUNCT
ejpam-4061	182	3	x	x	X
ejpam-4061	182	4	,	,	PUNCT
ejpam-4061	182	5	τ	τ	PROPN
ejpam-4061	182	6	′	′	NUM
ejpam-4061	182	7	)	)	PUNCT
ejpam-4061	182	8	is	be	AUX
ejpam-4061	182	9	semiregular	semiregular	ADJ
ejpam-4061	182	10	and	and	CCONJ
ejpam-4061	182	11	the	the	DET
ejpam-4061	182	12	two	two	NUM
ejpam-4061	182	13	spaces	space	NOUN
ejpam-4061	182	14	(	(	PUNCT
ejpam-4061	182	15	x	x	X
ejpam-4061	182	16	,	,	PUNCT
ejpam-4061	182	17	τ	τ	PROPN
ejpam-4061	182	18	)	)	PUNCT
ejpam-4061	182	19	and	and	CCONJ
ejpam-4061	182	20	(	(	PUNCT
ejpam-4061	182	21	x	x	X
ejpam-4061	182	22	,	,	PUNCT
ejpam-4061	182	23	τ	τ	PROPN
ejpam-4061	182	24	′	′	NUM
ejpam-4061	182	25	)	)	PUNCT
ejpam-4061	182	26	have	have	AUX
ejpam-4061	182	27	the	the	DET
ejpam-4061	182	28	same	same	ADJ
ejpam-4061	182	29	open	open	ADJ
ejpam-4061	182	30	domains	domain	NOUN
ejpam-4061	182	31	.	.	PUNCT
ejpam-4061	183	1	(	(	PUNCT
ejpam-4061	183	2	x	x	X
ejpam-4061	183	3	,	,	PUNCT
ejpam-4061	183	4	τ	τ	PROPN
ejpam-4061	183	5	′	′	NUM
ejpam-4061	183	6	)	)	PUNCT
ejpam-4061	183	7	is	be	AUX
ejpam-4061	183	8	called	call	VERB
ejpam-4061	183	9	the	the	DET
ejpam-4061	183	10	semiregularization	semiregularization	NOUN
ejpam-4061	183	11	of	of	ADP
ejpam-4061	183	12	(	(	PUNCT
ejpam-4061	183	13	x	x	INTJ
ejpam-4061	183	14	,	,	PUNCT
ejpam-4061	183	15	τ	τ	PROPN
ejpam-4061	183	16	)	)	PUNCT
ejpam-4061	184	1	[	[	X
ejpam-4061	184	2	1	1	NUM
ejpam-4061	184	3	,	,	PUNCT
ejpam-4061	184	4	1.7.8	1.7.8	NUM
ejpam-4061	184	5	(	(	PUNCT
ejpam-4061	184	6	b	b	NOUN
ejpam-4061	184	7	)	)	PUNCT
ejpam-4061	184	8	]	]	PUNCT
ejpam-4061	184	9	,	,	PUNCT
ejpam-4061	184	10	see	see	VERB
ejpam-4061	184	11	also	also	ADV
ejpam-4061	184	12	[	[	X
ejpam-4061	184	13	9	9	NUM
ejpam-4061	184	14	]	]	PUNCT
ejpam-4061	184	15	.	.	PUNCT
ejpam-4061	185	1	since	since	SCONJ
ejpam-4061	185	2	any	any	DET
ejpam-4061	185	3	closed	closed	ADJ
ejpam-4061	185	4	domain	domain	NOUN
ejpam-4061	185	5	in	in	ADP
ejpam-4061	185	6	an	an	DET
ejpam-4061	185	7	h	h	NOUN
ejpam-4061	185	8	-	-	PUNCT
ejpam-4061	185	9	space	space	NOUN
ejpam-4061	185	10	(	(	PUNCT
ejpam-4061	185	11	x	x	NOUN
ejpam-4061	185	12	,	,	PUNCT
ejpam-4061	185	13	uah	uah	PROPN
ejpam-4061	185	14	)	)	PUNCT
ejpam-4061	185	15	is	be	AUX
ejpam-4061	185	16	a	a	DET
ejpam-4061	185	17	closed	closed	ADJ
ejpam-4061	185	18	domain	domain	NOUN
ejpam-4061	185	19	in	in	ADP
ejpam-4061	185	20	the	the	DET
ejpam-4061	185	21	usual	usual	ADJ
ejpam-4061	185	22	metric	metric	ADJ
ejpam-4061	185	23	space	space	NOUN
ejpam-4061	185	24	(	(	PUNCT
ejpam-4061	185	25	x	x	X
ejpam-4061	185	26	,	,	PUNCT
ejpam-4061	185	27	u	u	NOUN
ejpam-4061	185	28	)	)	PUNCT
ejpam-4061	185	29	,	,	PUNCT
ejpam-4061	185	30	see	see	VERB
ejpam-4061	185	31	theorem	theorem	ADJ
ejpam-4061	185	32	4	4	NUM
ejpam-4061	185	33	and	and	CCONJ
ejpam-4061	185	34	theorem	theorem	VERB
ejpam-4061	185	35	6	6	NUM
ejpam-4061	185	36	,	,	PUNCT
ejpam-4061	185	37	we	we	PRON
ejpam-4061	185	38	conclude	conclude	VERB
ejpam-4061	185	39	that	that	SCONJ
ejpam-4061	185	40	any	any	DET
ejpam-4061	185	41	open	open	ADJ
ejpam-4061	185	42	domain	domain	NOUN
ejpam-4061	185	43	in	in	ADP
ejpam-4061	185	44	an	an	DET
ejpam-4061	185	45	h	h	NOUN
ejpam-4061	185	46	-	-	PUNCT
ejpam-4061	185	47	space	space	NOUN
ejpam-4061	185	48	(	(	PUNCT
ejpam-4061	185	49	x	x	NOUN
ejpam-4061	185	50	,	,	PUNCT
ejpam-4061	185	51	uah	uah	PROPN
ejpam-4061	185	52	)	)	PUNCT
ejpam-4061	185	53	is	be	AUX
ejpam-4061	185	54	an	an	DET
ejpam-4061	185	55	open	open	ADJ
ejpam-4061	185	56	domain	domain	NOUN
ejpam-4061	185	57	in	in	ADP
ejpam-4061	185	58	the	the	DET
ejpam-4061	185	59	usual	usual	ADJ
ejpam-4061	185	60	metric	metric	ADJ
ejpam-4061	185	61	space	space	NOUN
ejpam-4061	185	62	(	(	PUNCT
ejpam-4061	185	63	x	x	X
ejpam-4061	185	64	,	,	PUNCT
ejpam-4061	185	65	u	u	NOUN
ejpam-4061	185	66	)	)	PUNCT
ejpam-4061	185	67	.	.	PUNCT
ejpam-4061	186	1	thus	thus	ADV
ejpam-4061	186	2	the	the	DET
ejpam-4061	186	3	semiregularization	semiregularization	NOUN
ejpam-4061	186	4	of	of	ADP
ejpam-4061	186	5	an	an	DET
ejpam-4061	186	6	h	h	NOUN
ejpam-4061	186	7	-	-	PUNCT
ejpam-4061	186	8	space	space	NOUN
ejpam-4061	186	9	(	(	PUNCT
ejpam-4061	186	10	x	x	NOUN
ejpam-4061	186	11	,	,	PUNCT
ejpam-4061	186	12	uah	uah	PROPN
ejpam-4061	186	13	)	)	PUNCT
ejpam-4061	186	14	is	be	AUX
ejpam-4061	186	15	(	(	PUNCT
ejpam-4061	186	16	x	x	INTJ
ejpam-4061	186	17	,	,	PUNCT
ejpam-4061	186	18	u	u	NOUN
ejpam-4061	186	19	)	)	PUNCT
ejpam-4061	186	20	.	.	PUNCT
ejpam-4061	187	1	we	we	PRON
ejpam-4061	187	2	can	can	AUX
ejpam-4061	187	3	conclude	conclude	VERB
ejpam-4061	187	4	more	more	ADV
ejpam-4061	187	5	interesting	interesting	ADJ
ejpam-4061	187	6	result	result	NOUN
ejpam-4061	187	7	from	from	ADP
ejpam-4061	187	8	theorem	theorem	ADJ
ejpam-4061	187	9	4	4	NUM
ejpam-4061	187	10	.	.	PUNCT
ejpam-4061	187	11	since	since	SCONJ
ejpam-4061	187	12	anh	anh	NOUN
ejpam-4061	187	13	-	-	PUNCT
ejpam-4061	187	14	space	space	NOUN
ejpam-4061	187	15	(	(	PUNCT
ejpam-4061	187	16	x	x	NOUN
ejpam-4061	187	17	,	,	PUNCT
ejpam-4061	187	18	uah	uah	PROPN
ejpam-4061	187	19	)	)	PUNCT
ejpam-4061	187	20	and	and	CCONJ
ejpam-4061	187	21	the	the	DET
ejpam-4061	187	22	usual	usual	ADJ
ejpam-4061	187	23	metric	metric	ADJ
ejpam-4061	187	24	space	space	NOUN
ejpam-4061	187	25	(	(	PUNCT
ejpam-4061	187	26	x	x	X
ejpam-4061	187	27	,	,	PUNCT
ejpam-4061	187	28	u	u	NOUN
ejpam-4061	187	29	)	)	PUNCT
ejpam-4061	187	30	are	be	AUX
ejpam-4061	187	31	having	have	VERB
ejpam-4061	187	32	the	the	DET
ejpam-4061	187	33	same	same	ADJ
ejpam-4061	187	34	closed	closed	ADJ
ejpam-4061	187	35	domain	domain	NOUN
ejpam-4061	187	36	,	,	PUNCT
ejpam-4061	187	37	then	then	ADV
ejpam-4061	187	38	any	any	DET
ejpam-4061	187	39	h	h	NOUN
ejpam-4061	187	40	-	-	PUNCT
ejpam-4061	187	41	space	space	NOUN
ejpam-4061	187	42	(	(	PUNCT
ejpam-4061	187	43	x	x	NOUN
ejpam-4061	187	44	,	,	PUNCT
ejpam-4061	187	45	uah	uah	PROPN
ejpam-4061	187	46	)	)	PUNCT
ejpam-4061	187	47	is	be	AUX
ejpam-4061	187	48	κ	κ	NOUN
ejpam-4061	187	49	-	-	ADV
ejpam-4061	187	50	metrizable	metrizable	ADJ
ejpam-4061	187	51	.	.	PUNCT
ejpam-4061	188	1	let	let	VERB
ejpam-4061	188	2	us	we	PRON
ejpam-4061	188	3	recall	recall	VERB
ejpam-4061	188	4	the	the	DET
ejpam-4061	188	5	definitions	definition	NOUN
ejpam-4061	188	6	.	.	PUNCT
ejpam-4061	189	1	denote	denote	VERB
ejpam-4061	189	2	the	the	DET
ejpam-4061	189	3	family	family	NOUN
ejpam-4061	189	4	of	of	ADP
ejpam-4061	189	5	all	all	DET
ejpam-4061	189	6	closed	closed	ADJ
ejpam-4061	189	7	domains	domain	NOUN
ejpam-4061	189	8	in	in	ADP
ejpam-4061	189	9	x	x	PUNCT
ejpam-4061	189	10	by	by	ADP
ejpam-4061	189	11	r[x	r[x	NOUN
ejpam-4061	189	12	]	]	PUNCT
ejpam-4061	189	13	.	.	PUNCT
ejpam-4061	190	1	a	a	DET
ejpam-4061	190	2	κ	κ	NOUN
ejpam-4061	190	3	-	-	NOUN
ejpam-4061	190	4	metric	metric	ADJ
ejpam-4061	190	5	on	on	ADP
ejpam-4061	190	6	a	a	DET
ejpam-4061	190	7	t3	t3	NOUN
ejpam-4061	190	8	space	space	NOUN
ejpam-4061	190	9	is	be	AUX
ejpam-4061	190	10	a	a	DET
ejpam-4061	190	11	non	non	ADJ
ejpam-4061	190	12	-	-	ADJ
ejpam-4061	190	13	negative	negative	ADJ
ejpam-4061	190	14	real	real	ADV
ejpam-4061	190	15	-	-	PUNCT
ejpam-4061	190	16	valued	value	VERB
ejpam-4061	190	17	function	function	NOUN
ejpam-4061	190	18	ϕ(x	ϕ(x	PROPN
ejpam-4061	190	19	,	,	PUNCT
ejpam-4061	190	20	c	c	NOUN
ejpam-4061	190	21	)	)	PUNCT
ejpam-4061	190	22	of	of	ADP
ejpam-4061	190	23	two	two	NUM
ejpam-4061	190	24	variables	variable	NOUN
ejpam-4061	190	25	,	,	PUNCT
ejpam-4061	190	26	x	x	X
ejpam-4061	190	27	∈	∈	NOUN
ejpam-4061	190	28	x	x	X
ejpam-4061	190	29	and	and	CCONJ
ejpam-4061	190	30	c	c	PROPN
ejpam-4061	190	31	∈	∈	PROPN
ejpam-4061	190	32	r[x	r[x	NOUN
ejpam-4061	190	33	]	]	X
ejpam-4061	190	34	,	,	PUNCT
ejpam-4061	190	35	with	with	ADP
ejpam-4061	190	36	the	the	DET
ejpam-4061	190	37	requirements	requirement	NOUN
ejpam-4061	190	38	:	:	PUNCT
ejpam-4061	190	39	(	(	PUNCT
ejpam-4061	190	40	i	i	NOUN
ejpam-4061	190	41	)	)	PUNCT
ejpam-4061	190	42	(	(	PUNCT
ejpam-4061	190	43	k1	k1	NOUN
ejpam-4061	190	44	)	)	PUNCT
ejpam-4061	190	45	(	(	PUNCT
ejpam-4061	190	46	membership	membership	NOUN
ejpam-4061	190	47	axiom	axiom	NOUN
ejpam-4061	190	48	)	)	PUNCT
ejpam-4061	190	49	for	for	ADP
ejpam-4061	190	50	every	every	DET
ejpam-4061	190	51	x	x	SYM
ejpam-4061	190	52	∈	∈	PROPN
ejpam-4061	190	53	x	x	X
ejpam-4061	190	54	and	and	CCONJ
ejpam-4061	190	55	c	c	PROPN
ejpam-4061	190	56	∈	∈	PROPN
ejpam-4061	190	57	r[x	r[x	NOUN
ejpam-4061	190	58	]	]	X
ejpam-4061	190	59	,	,	PUNCT
ejpam-4061	190	60	ϕ(x	ϕ(x	PROPN
ejpam-4061	190	61	,	,	PUNCT
ejpam-4061	190	62	c	c	NOUN
ejpam-4061	190	63	)	)	PUNCT
ejpam-4061	190	64	=	=	SYM
ejpam-4061	191	1	0	0	NUM
ejpam-4061	191	2	⇔	⇔	X
ejpam-4061	191	3	x	x	SYM
ejpam-4061	191	4	∈	∈	PROPN
ejpam-4061	191	5	c.	c.	PROPN
ejpam-4061	191	6	(	(	PUNCT
ejpam-4061	191	7	ii	ii	PROPN
ejpam-4061	191	8	)	)	PUNCT
ejpam-4061	191	9	(	(	PUNCT
ejpam-4061	191	10	k2	k2	NOUN
ejpam-4061	191	11	)	)	PUNCT
ejpam-4061	191	12	(	(	PUNCT
ejpam-4061	191	13	monotonicity	monotonicity	NOUN
ejpam-4061	191	14	)	)	PUNCT
ejpam-4061	191	15	if	if	SCONJ
ejpam-4061	191	16	c	c	X
ejpam-4061	191	17	,	,	PUNCT
ejpam-4061	191	18	c	c	NOUN
ejpam-4061	191	19	′	′	NOUN
ejpam-4061	191	20	∈	∈	PROPN
ejpam-4061	191	21	r[x	r[x	NOUN
ejpam-4061	191	22	]	]	PUNCT
ejpam-4061	191	23	and	and	CCONJ
ejpam-4061	191	24	c	c	X
ejpam-4061	191	25	⊂	⊂	PROPN
ejpam-4061	191	26	c	c	PROPN
ejpam-4061	191	27	′	′	PROPN
ejpam-4061	191	28	,	,	PUNCT
ejpam-4061	191	29	then	then	ADV
ejpam-4061	191	30	ϕ(x	ϕ(x	PROPN
ejpam-4061	191	31	,	,	PUNCT
ejpam-4061	191	32	c	c	NOUN
ejpam-4061	191	33	)	)	PUNCT
ejpam-4061	191	34	≥	≥	NOUN
ejpam-4061	191	35	ϕ(x	ϕ(x	NOUN
ejpam-4061	191	36	,	,	PUNCT
ejpam-4061	191	37	c	c	NOUN
ejpam-4061	191	38	′	′	NOUN
ejpam-4061	191	39	)	)	PUNCT
ejpam-4061	191	40	,	,	PUNCT
ejpam-4061	191	41	for	for	ADP
ejpam-4061	191	42	all	all	PRON
ejpam-4061	191	43	x	x	SYM
ejpam-4061	191	44	∈	∈	NOUN
ejpam-4061	191	45	x.	x.	NOUN
ejpam-4061	191	46	(	(	PUNCT
ejpam-4061	191	47	iii	iii	NOUN
ejpam-4061	191	48	)	)	PUNCT
ejpam-4061	191	49	(	(	PUNCT
ejpam-4061	191	50	k3	k3	PROPN
ejpam-4061	191	51	)	)	PUNCT
ejpam-4061	191	52	(	(	PUNCT
ejpam-4061	191	53	continuity	continuity	NOUN
ejpam-4061	191	54	)	)	PUNCT
ejpam-4061	191	55	for	for	ADP
ejpam-4061	191	56	every	every	DET
ejpam-4061	191	57	c	c	PROPN
ejpam-4061	191	58	∈	∈	PROPN
ejpam-4061	191	59	r[x	r[x	NOUN
ejpam-4061	191	60	]	]	X
ejpam-4061	191	61	,	,	PUNCT
ejpam-4061	191	62	ϕ(x	ϕ(x	PROPN
ejpam-4061	191	63	,	,	PUNCT
ejpam-4061	191	64	c	c	NOUN
ejpam-4061	191	65	)	)	PUNCT
ejpam-4061	191	66	is	be	AUX
ejpam-4061	191	67	continuous	continuous	ADJ
ejpam-4061	191	68	in	in	ADP
ejpam-4061	191	69	x.	x.	NOUN
ejpam-4061	191	70	references	reference	NOUN
ejpam-4061	191	71	1167	1167	NUM
ejpam-4061	191	72	(	(	PUNCT
ejpam-4061	191	73	iv	iv	X
ejpam-4061	191	74	)	)	PUNCT
ejpam-4061	191	75	(	(	PUNCT
ejpam-4061	191	76	k4	k4	PROPN
ejpam-4061	191	77	)	)	PUNCT
ejpam-4061	191	78	(	(	PUNCT
ejpam-4061	191	79	union	union	NOUN
ejpam-4061	191	80	axiom	axiom	PROPN
ejpam-4061	191	81	)	)	PUNCT
ejpam-4061	191	82	ϕ	ϕ	PROPN
ejpam-4061	191	83	(	(	PUNCT
ejpam-4061	191	84	x	x	X
ejpam-4061	191	85	,	,	PUNCT
ejpam-4061	191	86	⋃	⋃	NOUN
ejpam-4061	191	87	α∈λ	α∈λ	NOUN
ejpam-4061	191	88	cα	cα	NOUN
ejpam-4061	191	89	)	)	PUNCT
ejpam-4061	192	1	=	=	SYM
ejpam-4061	192	2	inf{ϕ(x	inf{ϕ(x	PROPN
ejpam-4061	192	3	,	,	PUNCT
ejpam-4061	192	4	cα	cα	NOUN
ejpam-4061	192	5	)	)	PUNCT
ejpam-4061	192	6	:	:	PUNCT
ejpam-4061	192	7	α	α	PROPN
ejpam-4061	192	8	∈	∈	PROPN
ejpam-4061	192	9	λ	λ	PROPN
ejpam-4061	192	10	}	}	PUNCT
ejpam-4061	192	11	for	for	ADP
ejpam-4061	192	12	every	every	DET
ejpam-4061	192	13	increasing	increase	VERB
ejpam-4061	192	14	transfinite	transfinite	ADJ
ejpam-4061	192	15	sequence	sequence	NOUN
ejpam-4061	192	16	{	{	PUNCT
ejpam-4061	192	17	cα	cα	PROPN
ejpam-4061	192	18	∈	∈	PROPN
ejpam-4061	192	19	r[x	r[x	NOUN
ejpam-4061	192	20	]	]	X
ejpam-4061	192	21	:	:	PUNCT
ejpam-4061	192	22	α	α	X
ejpam-4061	192	23	∈	∈	PROPN
ejpam-4061	192	24	λ	λ	X
ejpam-4061	192	25	}	}	PUNCT
ejpam-4061	192	26	.	.	PUNCT
ejpam-4061	193	1	a	a	DET
ejpam-4061	193	2	space	space	NOUN
ejpam-4061	193	3	on	on	ADP
ejpam-4061	193	4	which	which	PRON
ejpam-4061	193	5	there	there	PRON
ejpam-4061	193	6	exists	exist	VERB
ejpam-4061	193	7	a	a	DET
ejpam-4061	193	8	κ	κ	NOUN
ejpam-4061	193	9	-	-	ADJ
ejpam-4061	193	10	metric	metric	ADJ
ejpam-4061	193	11	on	on	ADP
ejpam-4061	193	12	it	it	PRON
ejpam-4061	193	13	is	be	AUX
ejpam-4061	193	14	said	say	VERB
ejpam-4061	193	15	to	to	PART
ejpam-4061	193	16	be	be	AUX
ejpam-4061	193	17	κ	κ	NOUN
ejpam-4061	193	18	-	-	ADJ
ejpam-4061	193	19	metrizable	metrizable	ADJ
ejpam-4061	194	1	[	[	X
ejpam-4061	194	2	11	11	NUM
ejpam-4061	194	3	]	]	PUNCT
ejpam-4061	194	4	.	.	PUNCT
ejpam-4061	195	1	the	the	DET
ejpam-4061	195	2	concept	concept	NOUN
ejpam-4061	195	3	of	of	ADP
ejpam-4061	195	4	κ	κ	NOUN
ejpam-4061	195	5	-	-	NOUN
ejpam-4061	195	6	metrizability	metrizability	NOUN
ejpam-4061	195	7	is	be	AUX
ejpam-4061	195	8	a	a	DET
ejpam-4061	195	9	generalization	generalization	NOUN
ejpam-4061	195	10	of	of	ADP
ejpam-4061	195	11	metrizability	metrizability	NOUN
ejpam-4061	195	12	,	,	PUNCT
ejpam-4061	195	13	in	in	ADP
ejpam-4061	195	14	the	the	DET
ejpam-4061	195	15	sense	sense	NOUN
ejpam-4061	195	16	that	that	SCONJ
ejpam-4061	195	17	every	every	DET
ejpam-4061	195	18	metric	metric	NOUN
ejpam-4061	195	19	is	be	AUX
ejpam-4061	195	20	a	a	DET
ejpam-4061	195	21	κ	κ	NOUN
ejpam-4061	195	22	-	-	NOUN
ejpam-4061	195	23	metric	metric	ADJ
ejpam-4061	195	24	,	,	PUNCT
ejpam-4061	195	25	and	and	CCONJ
ejpam-4061	195	26	every	every	DET
ejpam-4061	195	27	metrizable	metrizable	ADJ
ejpam-4061	195	28	space	space	NOUN
ejpam-4061	195	29	is	be	AUX
ejpam-4061	195	30	κ	κ	NOUN
ejpam-4061	195	31	-	-	ADJ
ejpam-4061	195	32	metrizable	metrizable	ADJ
ejpam-4061	195	33	.	.	PUNCT
ejpam-4061	196	1	in	in	ADP
ejpam-4061	196	2	[	[	X
ejpam-4061	196	3	11	11	NUM
ejpam-4061	196	4	]	]	PUNCT
ejpam-4061	196	5	,	,	PUNCT
ejpam-4061	196	6	ščepin	ščepin	PROPN
ejpam-4061	196	7	proved	prove	VERB
ejpam-4061	196	8	that	that	SCONJ
ejpam-4061	196	9	“	"	PUNCT
ejpam-4061	196	10	any	any	DET
ejpam-4061	196	11	κ	κ	NOUN
ejpam-4061	196	12	-	-	ADJ
ejpam-4061	196	13	metrizable	metrizable	ADJ
ejpam-4061	196	14	space	space	NOUN
ejpam-4061	196	15	is	be	AUX
ejpam-4061	196	16	mildly	mildly	ADV
ejpam-4061	196	17	normal	normal	ADJ
ejpam-4061	196	18	”	"	PUNCT
ejpam-4061	196	19	,	,	PUNCT
ejpam-4061	196	20	which	which	PRON
ejpam-4061	196	21	gives	give	VERB
ejpam-4061	196	22	another	another	DET
ejpam-4061	196	23	proof	proof	NOUN
ejpam-4061	196	24	that	that	SCONJ
ejpam-4061	196	25	any	any	DET
ejpam-4061	196	26	hspaces	hspace	NOUN
ejpam-4061	196	27	(	(	PUNCT
ejpam-4061	196	28	x	x	X
ejpam-4061	196	29	,	,	PUNCT
ejpam-4061	196	30	uah	uah	PROPN
ejpam-4061	196	31	)	)	PUNCT
ejpam-4061	196	32	is	be	AUX
ejpam-4061	196	33	mildly	mildly	ADV
ejpam-4061	196	34	normal	normal	ADJ
ejpam-4061	196	35	.	.	PUNCT
ejpam-4061	197	1	also	also	ADV
ejpam-4061	197	2	,	,	PUNCT
ejpam-4061	197	3	in	in	ADP
ejpam-4061	197	4	[	[	PUNCT
ejpam-4061	197	5	11	11	NUM
ejpam-4061	197	6	]	]	PUNCT
ejpam-4061	197	7	,	,	PUNCT
ejpam-4061	197	8	ščepin	ščepin	PROPN
ejpam-4061	197	9	proved	prove	VERB
ejpam-4061	197	10	that	that	SCONJ
ejpam-4061	197	11	“	"	PUNCT
ejpam-4061	197	12	κ	κ	NOUN
ejpam-4061	197	13	-	-	NOUN
ejpam-4061	197	14	metrizability	metrizability	NOUN
ejpam-4061	197	15	is	be	AUX
ejpam-4061	197	16	countable	countable	ADJ
ejpam-4061	197	17	multiplicative	multiplicative	ADJ
ejpam-4061	197	18	”	"	PUNCT
ejpam-4061	197	19	,	,	PUNCT
ejpam-4061	197	20	we	we	PRON
ejpam-4061	197	21	get	get	VERB
ejpam-4061	197	22	the	the	DET
ejpam-4061	197	23	following	follow	VERB
ejpam-4061	197	24	corollary	corollary	NOUN
ejpam-4061	197	25	.	.	PUNCT
ejpam-4061	198	1	corollary	corollary	ADJ
ejpam-4061	198	2	1	1	NUM
ejpam-4061	198	3	.	.	PUNCT
ejpam-4061	199	1	if	if	SCONJ
ejpam-4061	199	2	λ	λ	PROPN
ejpam-4061	199	3	is	be	AUX
ejpam-4061	199	4	countable	countable	ADJ
ejpam-4061	199	5	and	and	CCONJ
ejpam-4061	199	6	for	for	ADP
ejpam-4061	199	7	each	each	DET
ejpam-4061	199	8	α	α	PROPN
ejpam-4061	199	9	∈	∈	PROPN
ejpam-4061	199	10	λ	λ	PROPN
ejpam-4061	199	11	,	,	PUNCT
ejpam-4061	199	12	aα	aα	PROPN
ejpam-4061	199	13	is	be	AUX
ejpam-4061	199	14	a	a	DET
ejpam-4061	199	15	non	non	ADJ
ejpam-4061	199	16	-	-	ADJ
ejpam-4061	199	17	empty	empty	ADJ
ejpam-4061	199	18	proper	proper	ADJ
ejpam-4061	199	19	subset	subset	NOUN
ejpam-4061	199	20	of	of	ADP
ejpam-4061	199	21	the	the	DET
ejpam-4061	199	22	x	x	ADJ
ejpam-4061	199	23	-	-	ADJ
ejpam-4061	199	24	axis	axis	ADJ
ejpam-4061	199	25	l	l	NOUN
ejpam-4061	199	26	,	,	PUNCT
ejpam-4061	199	27	then	then	ADV
ejpam-4061	199	28	∏	∏	PROPN
ejpam-4061	199	29	α∈λ(x	α∈λ(x	PROPN
ejpam-4061	199	30	,	,	PUNCT
ejpam-4061	199	31	uaαh	uaαh	NOUN
ejpam-4061	199	32	)	)	PUNCT
ejpam-4061	199	33	is	be	AUX
ejpam-4061	199	34	κ	κ	NOUN
ejpam-4061	199	35	-	-	ADJ
ejpam-4061	199	36	metrizable	metrizable	ADJ
ejpam-4061	199	37	,	,	PUNCT
ejpam-4061	199	38	hence	hence	ADV
ejpam-4061	199	39	mildly	mildly	ADV
ejpam-4061	199	40	normal	normal	ADJ
ejpam-4061	199	41	.	.	PUNCT
ejpam-4061	200	1	here	here	ADV
ejpam-4061	200	2	are	be	AUX
ejpam-4061	200	3	some	some	DET
ejpam-4061	200	4	open	open	ADJ
ejpam-4061	200	5	problems	problem	NOUN
ejpam-4061	200	6	about	about	ADP
ejpam-4061	200	7	this	this	DET
ejpam-4061	200	8	h	h	NOUN
ejpam-4061	200	9	-	-	NOUN
ejpam-4061	200	10	space	space	NOUN
ejpam-4061	200	11	.	.	PUNCT
ejpam-4061	201	1	(	(	PUNCT
ejpam-4061	201	2	i	i	NOUN
ejpam-4061	201	3	)	)	PUNCT
ejpam-4061	201	4	is	be	AUX
ejpam-4061	201	5	any	any	DET
ejpam-4061	201	6	h	h	NOUN
ejpam-4061	201	7	-	-	PUNCT
ejpam-4061	201	8	space	space	NOUN
ejpam-4061	201	9	(	(	PUNCT
ejpam-4061	201	10	x	x	NOUN
ejpam-4061	201	11	,	,	PUNCT
ejpam-4061	201	12	uah	uah	ADJ
ejpam-4061	201	13	)	)	PUNCT
ejpam-4061	201	14	almost	almost	ADV
ejpam-4061	201	15	normal	normal	ADJ
ejpam-4061	201	16	,	,	PUNCT
ejpam-4061	201	17	[	[	X
ejpam-4061	201	18	6	6	NUM
ejpam-4061	201	19	]	]	PUNCT
ejpam-4061	201	20	?	?	PUNCT
ejpam-4061	202	1	(	(	PUNCT
ejpam-4061	202	2	ii	ii	NOUN
ejpam-4061	202	3	)	)	PUNCT
ejpam-4061	202	4	is	be	AUX
ejpam-4061	202	5	any	any	DET
ejpam-4061	202	6	h	h	NOUN
ejpam-4061	202	7	-	-	PUNCT
ejpam-4061	202	8	space	space	NOUN
ejpam-4061	202	9	(	(	PUNCT
ejpam-4061	202	10	x	x	NOUN
ejpam-4061	202	11	,	,	PUNCT
ejpam-4061	202	12	uah	uah	PROPN
ejpam-4061	202	13	)	)	PUNCT
ejpam-4061	202	14	cc	cc	NOUN
ejpam-4061	202	15	-	-	NOUN
ejpam-4061	202	16	normal	normal	ADJ
ejpam-4061	202	17	,	,	PUNCT
ejpam-4061	202	18	[	[	X
ejpam-4061	202	19	3	3	NUM
ejpam-4061	202	20	]	]	PUNCT
ejpam-4061	202	21	?	?	PUNCT
ejpam-4061	203	1	references	reference	NOUN
ejpam-4061	203	2	[	[	X
ejpam-4061	203	3	1	1	NUM
ejpam-4061	203	4	]	]	X
ejpam-4061	203	5	r	r	NOUN
ejpam-4061	203	6	engelking	engelking	NOUN
ejpam-4061	203	7	.	.	PUNCT
ejpam-4061	204	1	general	general	ADJ
ejpam-4061	204	2	topology	topology	PROPN
ejpam-4061	204	3	.	.	PUNCT
ejpam-4061	205	1	pwn	pwn	PROPN
ejpam-4061	205	2	,	,	PUNCT
ejpam-4061	205	3	warszawa	warszawa	PROPN
ejpam-4061	205	4	,	,	PUNCT
ejpam-4061	205	5	1977	1977	NUM
ejpam-4061	205	6	.	.	PUNCT
ejpam-4061	206	1	[	[	X
ejpam-4061	206	2	2	2	NUM
ejpam-4061	206	3	]	]	PUNCT
ejpam-4061	206	4	l	l	NOUN
ejpam-4061	206	5	kalantan	kalantan	PROPN
ejpam-4061	206	6	.	.	PUNCT
ejpam-4061	207	1	results	result	VERB
ejpam-4061	207	2	about	about	ADP
ejpam-4061	207	3	κ	κ	NOUN
ejpam-4061	207	4	-	-	NOUN
ejpam-4061	207	5	normality	normality	NOUN
ejpam-4061	207	6	.	.	PUNCT
ejpam-4061	208	1	topology	topology	NOUN
ejpam-4061	208	2	and	and	CCONJ
ejpam-4061	208	3	its	its	PRON
ejpam-4061	208	4	applications	application	NOUN
ejpam-4061	208	5	,	,	PUNCT
ejpam-4061	208	6	125(1):47–62	125(1):47–62	NUM
ejpam-4061	208	7	,	,	PUNCT
ejpam-4061	208	8	2002	2002	NUM
ejpam-4061	208	9	.	.	PUNCT
ejpam-4061	209	1	[	[	X
ejpam-4061	209	2	3	3	NUM
ejpam-4061	209	3	]	]	X
ejpam-4061	209	4	l	l	NOUN
ejpam-4061	209	5	kalantan	kalantan	PROPN
ejpam-4061	209	6	and	and	CCONJ
ejpam-4061	209	7	m	m	AUX
ejpam-4061	209	8	alhomieyed	alhomieye	VERB
ejpam-4061	209	9	.	.	PUNCT
ejpam-4061	210	1	cc	cc	NOUN
ejpam-4061	210	2	-	-	ADJ
ejpam-4061	210	3	normal	normal	ADJ
ejpam-4061	210	4	topological	topological	ADJ
ejpam-4061	210	5	spaces	space	NOUN
ejpam-4061	210	6	.	.	PUNCT
ejpam-4061	211	1	turkish	turkish	ADJ
ejpam-4061	211	2	journal	journal	NOUN
ejpam-4061	211	3	of	of	ADP
ejpam-4061	211	4	mathematics	mathematic	NOUN
ejpam-4061	211	5	,	,	PUNCT
ejpam-4061	211	6	41(3):749–755	41(3):749–755	PROPN
ejpam-4061	211	7	,	,	PUNCT
ejpam-4061	211	8	2017	2017	NUM
ejpam-4061	211	9	.	.	PUNCT
ejpam-4061	212	1	[	[	X
ejpam-4061	212	2	4	4	NUM
ejpam-4061	212	3	]	]	X
ejpam-4061	212	4	l	l	NOUN
ejpam-4061	212	5	kalantan	kalantan	PROPN
ejpam-4061	212	6	and	and	CCONJ
ejpam-4061	212	7	f	f	PROPN
ejpam-4061	212	8	allahabi	allahabi	NOUN
ejpam-4061	212	9	.	.	PUNCT
ejpam-4061	213	1	on	on	ADP
ejpam-4061	213	2	almost	almost	ADV
ejpam-4061	213	3	normality	normality	NOUN
ejpam-4061	213	4	.	.	PUNCT
ejpam-4061	214	1	demonstratio	demonstratio	PROPN
ejpam-4061	214	2	mathematica	mathematica	PROPN
ejpam-4061	214	3	,	,	PUNCT
ejpam-4061	214	4	41(4):961–968	41(4):961–968	PROPN
ejpam-4061	214	5	,	,	PUNCT
ejpam-4061	214	6	2008	2008	NUM
ejpam-4061	214	7	.	.	PUNCT
ejpam-4061	215	1	[	[	X
ejpam-4061	215	2	5	5	NUM
ejpam-4061	215	3	]	]	PUNCT
ejpam-4061	215	4	l	l	NOUN
ejpam-4061	215	5	kalantan	kalantan	PROPN
ejpam-4061	215	6	and	and	CCONJ
ejpam-4061	215	7	p	p	PROPN
ejpam-4061	215	8	szeptycki	szeptycki	PROPN
ejpam-4061	215	9	.	.	PUNCT
ejpam-4061	216	1	κ	κ	NOUN
ejpam-4061	216	2	-	-	PUNCT
ejpam-4061	216	3	normality	normality	NOUN
ejpam-4061	216	4	and	and	CCONJ
ejpam-4061	216	5	products	product	NOUN
ejpam-4061	216	6	of	of	ADP
ejpam-4061	216	7	ordinals	ordinal	NOUN
ejpam-4061	216	8	.	.	PUNCT
ejpam-4061	217	1	topology	topology	NOUN
ejpam-4061	217	2	and	and	CCONJ
ejpam-4061	217	3	its	its	PRON
ejpam-4061	217	4	applications	application	NOUN
ejpam-4061	217	5	,	,	PUNCT
ejpam-4061	217	6	123(3):537–545	123(3):537–545	NUM
ejpam-4061	217	7	,	,	PUNCT
ejpam-4061	217	8	2002	2002	NUM
ejpam-4061	217	9	.	.	PUNCT
ejpam-4061	218	1	[	[	X
ejpam-4061	218	2	6	6	NUM
ejpam-4061	218	3	]	]	PUNCT
ejpam-4061	218	4	m	m	NOUN
ejpam-4061	218	5	singal	singal	ADJ
ejpam-4061	218	6	and	and	CCONJ
ejpam-4061	218	7	s	s	VERB
ejpam-4061	218	8	arya	arya	NOUN
ejpam-4061	218	9	.	.	PUNCT
ejpam-4061	219	1	almost	almost	ADV
ejpam-4061	219	2	normal	normal	ADJ
ejpam-4061	219	3	and	and	CCONJ
ejpam-4061	219	4	almost	almost	ADV
ejpam-4061	219	5	completely	completely	ADV
ejpam-4061	219	6	regular	regular	ADJ
ejpam-4061	219	7	spaces	space	NOUN
ejpam-4061	219	8	.	.	PUNCT
ejpam-4061	220	1	kyungpook	kyungpook	PROPN
ejpam-4061	220	2	mathematical	mathematical	PROPN
ejpam-4061	220	3	journal	journal	NOUN
ejpam-4061	220	4	,	,	PUNCT
ejpam-4061	220	5	25(1):141–152	25(1):141–152	NUM
ejpam-4061	220	6	,	,	PUNCT
ejpam-4061	220	7	1970	1970	NUM
ejpam-4061	220	8	.	.	PUNCT
ejpam-4061	221	1	[	[	X
ejpam-4061	221	2	7	7	X
ejpam-4061	221	3	]	]	X
ejpam-4061	221	4	m	m	VERB
ejpam-4061	221	5	k	k	NOUN
ejpam-4061	221	6	singal	singal	NOUN
ejpam-4061	221	7	and	and	CCONJ
ejpam-4061	221	8	a	a	DET
ejpam-4061	221	9	r	r	NOUN
ejpam-4061	221	10	singal	singal	NOUN
ejpam-4061	221	11	.	.	PUNCT
ejpam-4061	222	1	mildly	mildly	ADV
ejpam-4061	222	2	normal	normal	ADJ
ejpam-4061	222	3	spaces	space	NOUN
ejpam-4061	222	4	.	.	PUNCT
ejpam-4061	223	1	kyungpook	kyungpook	PROPN
ejpam-4061	223	2	mathematical	mathematical	PROPN
ejpam-4061	223	3	journal	journal	NOUN
ejpam-4061	223	4	,	,	PUNCT
ejpam-4061	223	5	13(1):29–31	13(1):29–31	NUM
ejpam-4061	223	6	,	,	PUNCT
ejpam-4061	223	7	1973	1973	NUM
ejpam-4061	223	8	.	.	PUNCT
ejpam-4061	224	1	references	reference	NOUN
ejpam-4061	224	2	1168	1168	NUM
ejpam-4061	224	3	[	[	X
ejpam-4061	224	4	8	8	NUM
ejpam-4061	224	5	]	]	PUNCT
ejpam-4061	224	6	l	l	NOUN
ejpam-4061	224	7	steen	steen	PROPN
ejpam-4061	224	8	and	and	CCONJ
ejpam-4061	224	9	j	j	PROPN
ejpam-4061	224	10	a	a	DET
ejpam-4061	224	11	seebach	seebach	NOUN
ejpam-4061	224	12	.	.	PUNCT
ejpam-4061	225	1	counterexamples	counterexample	NOUN
ejpam-4061	225	2	in	in	ADP
ejpam-4061	225	3	topology	topology	NOUN
ejpam-4061	225	4	.	.	PUNCT
ejpam-4061	226	1	dover	dover	PROPN
ejpam-4061	226	2	publications	publications	PROPN
ejpam-4061	226	3	inc	inc	PROPN
ejpam-4061	226	4	,	,	PUNCT
ejpam-4061	226	5	usa	usa	PROPN
ejpam-4061	226	6	,	,	PUNCT
ejpam-4061	226	7	1995	1995	NUM
ejpam-4061	226	8	.	.	PUNCT
ejpam-4061	227	1	[	[	X
ejpam-4061	227	2	9	9	NUM
ejpam-4061	227	3	]	]	SYM
ejpam-4061	227	4	m	m	VERB
ejpam-4061	227	5	h	h	NOUN
ejpam-4061	227	6	stone	stone	NOUN
ejpam-4061	227	7	.	.	PUNCT
ejpam-4061	228	1	applications	application	NOUN
ejpam-4061	228	2	of	of	ADP
ejpam-4061	228	3	the	the	DET
ejpam-4061	228	4	theory	theory	NOUN
ejpam-4061	228	5	of	of	ADP
ejpam-4061	228	6	boolean	boolean	ADJ
ejpam-4061	228	7	rings	ring	NOUN
ejpam-4061	228	8	to	to	ADP
ejpam-4061	228	9	general	general	ADJ
ejpam-4061	228	10	topology	topology	NOUN
ejpam-4061	228	11	.	.	PUNCT
ejpam-4061	229	1	transactions	transaction	NOUN
ejpam-4061	229	2	of	of	ADP
ejpam-4061	229	3	the	the	DET
ejpam-4061	229	4	american	american	PROPN
ejpam-4061	229	5	mathematical	mathematical	PROPN
ejpam-4061	229	6	society	society	NOUN
ejpam-4061	229	7	,	,	PUNCT
ejpam-4061	229	8	41(3):375–481	41(3):375–481	PRON
ejpam-4061	229	9	,	,	PUNCT
ejpam-4061	229	10	1937	1937	NUM
ejpam-4061	229	11	.	.	PUNCT
ejpam-4061	230	1	[	[	X
ejpam-4061	230	2	10	10	NUM
ejpam-4061	230	3	]	]	X
ejpam-4061	230	4	e	e	X
ejpam-4061	230	5	v	v	X
ejpam-4061	230	6	ščepin	ščepin	NOUN
ejpam-4061	230	7	.	.	PUNCT
ejpam-4061	231	1	real	real	ADJ
ejpam-4061	231	2	valued	value	VERB
ejpam-4061	231	3	functions	function	NOUN
ejpam-4061	231	4	and	and	CCONJ
ejpam-4061	231	5	spaces	space	NOUN
ejpam-4061	231	6	close	close	ADV
ejpam-4061	231	7	to	to	ADP
ejpam-4061	231	8	normal	normal	ADJ
ejpam-4061	231	9	.	.	PUNCT
ejpam-4061	232	1	sib	sib	NOUN
ejpam-4061	232	2	.	.	PUNCT
ejpam-4061	232	3	matem	matem	PROPN
ejpam-4061	232	4	.	.	PUNCT
ejpam-4061	233	1	journ	journ	PROPN
ejpam-4061	233	2	.	.	PUNCT
ejpam-4061	233	3	,	,	PUNCT
ejpam-4061	234	1	13(5):1182–1196	13(5):1182–1196	NUM
ejpam-4061	234	2	,	,	PUNCT
ejpam-4061	234	3	1972	1972	NUM
ejpam-4061	234	4	.	.	PUNCT
ejpam-4061	235	1	[	[	X
ejpam-4061	235	2	11	11	NUM
ejpam-4061	235	3	]	]	X
ejpam-4061	235	4	e	e	X
ejpam-4061	235	5	v	v	X
ejpam-4061	235	6	ščepin	ščepin	NOUN
ejpam-4061	235	7	.	.	PUNCT
ejpam-4061	236	1	on	on	ADP
ejpam-4061	236	2	κ	κ	NOUN
ejpam-4061	236	3	-	-	ADJ
ejpam-4061	236	4	metrizable	metrizable	ADJ
ejpam-4061	236	5	spaces	space	NOUN
ejpam-4061	236	6	.	.	PUNCT
ejpam-4061	237	1	mathematics	mathematic	NOUN
ejpam-4061	237	2	of	of	ADP
ejpam-4061	237	3	the	the	DET
ejpam-4061	237	4	ussr	ussr	PROPN
ejpam-4061	237	5	-	-	PUNCT
ejpam-4061	237	6	izvestiya	izvestiya	PROPN
ejpam-4061	237	7	,	,	PUNCT
ejpam-4061	237	8	14(2):407	14(2):407	NUM
ejpam-4061	237	9	,	,	PUNCT
ejpam-4061	237	10	1980	1980	NUM
ejpam-4061	237	11	.	.	PUNCT