id	sid	tid	token	lemma	pos
ejpam-5223	1	1	european	european	PROPN
ejpam-5223	1	2	journal	journal	PROPN
ejpam-5223	1	3	of	of	ADP
ejpam-5223	1	4	pure	pure	ADJ
ejpam-5223	1	5	and	and	CCONJ
ejpam-5223	1	6	applied	apply	VERB
ejpam-5223	1	7	mathematics	mathematic	NOUN
ejpam-5223	1	8	vol	vol	NOUN
ejpam-5223	1	9	.	.	PROPN
ejpam-5223	2	1	17	17	NUM
ejpam-5223	2	2	,	,	PUNCT
ejpam-5223	2	3	no	no	INTJ
ejpam-5223	2	4	.	.	NOUN
ejpam-5223	2	5	3	3	NUM
ejpam-5223	2	6	,	,	PUNCT
ejpam-5223	2	7	2024	2024	NUM
ejpam-5223	2	8	,	,	PUNCT
ejpam-5223	2	9	1463	1463	NUM
ejpam-5223	2	10	-	-	SYM
ejpam-5223	2	11	1470	1470	NUM
ejpam-5223	2	12	issn	issn	PROPN
ejpam-5223	2	13	1307	1307	NUM
ejpam-5223	2	14	-	-	SYM
ejpam-5223	2	15	5543	5543	NUM
ejpam-5223	2	16	–	–	PUNCT
ejpam-5223	3	1	ejpam.com	ejpam.com	X
ejpam-5223	3	2	published	publish	VERB
ejpam-5223	3	3	by	by	ADP
ejpam-5223	3	4	new	new	PROPN
ejpam-5223	3	5	york	york	PROPN
ejpam-5223	3	6	business	business	PROPN
ejpam-5223	3	7	global	global	ADJ
ejpam-5223	3	8	separation	separation	NOUN
ejpam-5223	3	9	axioms	axiom	VERB
ejpam-5223	3	10	via	via	ADP
ejpam-5223	3	11	f	f	PROPN
ejpam-5223	3	12	-open	-open	PROPN
ejpam-5223	3	13	sets	set	NOUN
ejpam-5223	3	14	m.	m.	NOUN
ejpam-5223	3	15	baloush1,∗	baloush1,∗	NOUN
ejpam-5223	3	16	,	,	PUNCT
ejpam-5223	3	17	t.	t.	NOUN
ejpam-5223	3	18	noiri2	noiri2	PROPN
ejpam-5223	3	19	,	,	PUNCT
ejpam-5223	3	20	m.	m.	NOUN
ejpam-5223	3	21	talafha3	talafha3	PROPN
ejpam-5223	3	22	,	,	PUNCT
ejpam-5223	3	23	s.	s.	PROPN
ejpam-5223	3	24	che	che	PROPN
ejpam-5223	3	25	dzul	dzul	PROPN
ejpam-5223	3	26	-	-	PUNCT
ejpam-5223	3	27	kifli3	kifli3	PROPN
ejpam-5223	3	28	1	1	NUM
ejpam-5223	3	29	department	department	NOUN
ejpam-5223	3	30	of	of	ADP
ejpam-5223	3	31	basic	basic	ADJ
ejpam-5223	3	32	sciences	science	NOUN
ejpam-5223	3	33	,	,	PUNCT
ejpam-5223	3	34	national	national	PROPN
ejpam-5223	3	35	university	university	PROPN
ejpam-5223	3	36	college	college	PROPN
ejpam-5223	3	37	of	of	ADP
ejpam-5223	3	38	technology	technology	NOUN
ejpam-5223	3	39	,	,	PUNCT
ejpam-5223	3	40	amman	amman	PROPN
ejpam-5223	3	41	,	,	PUNCT
ejpam-5223	3	42	jordan	jordan	PROPN
ejpam-5223	3	43	2	2	NUM
ejpam-5223	3	44	2949	2949	NUM
ejpam-5223	3	45	-	-	SYM
ejpam-5223	3	46	1	1	NUM
ejpam-5223	3	47	shiokita	shiokita	NOUN
ejpam-5223	3	48	-	-	PUNCT
ejpam-5223	3	49	cho	cho	ADJ
ejpam-5223	3	50	,	,	PUNCT
ejpam-5223	3	51	hinagu	hinagu	ADJ
ejpam-5223	3	52	,	,	PUNCT
ejpam-5223	3	53	yatsushiro	yatsushiro	PROPN
ejpam-5223	3	54	-	-	PUNCT
ejpam-5223	3	55	shi	shi	PROPN
ejpam-5223	3	56	,	,	PUNCT
ejpam-5223	3	57	kumamoto	kumamoto	PROPN
ejpam-5223	3	58	-	-	PUNCT
ejpam-5223	3	59	ken	ken	PROPN
ejpam-5223	3	60	,	,	PUNCT
ejpam-5223	3	61	869	869	NUM
ejpam-5223	3	62	-	-	SYM
ejpam-5223	3	63	5142	5142	NUM
ejpam-5223	3	64	,	,	PUNCT
ejpam-5223	3	65	japan	japan	PROPN
ejpam-5223	3	66	3	3	NUM
ejpam-5223	3	67	school	school	NOUN
ejpam-5223	3	68	of	of	ADP
ejpam-5223	3	69	mathematical	mathematical	ADJ
ejpam-5223	3	70	sciences	sciences	PROPN
ejpam-5223	3	71	,	,	PUNCT
ejpam-5223	3	72	national	national	ADJ
ejpam-5223	3	73	university	university	PROPN
ejpam-5223	3	74	of	of	ADP
ejpam-5223	3	75	malaysia	malaysia	PROPN
ejpam-5223	3	76	,	,	PUNCT
ejpam-5223	3	77	kuala	kuala	PROPN
ejpam-5223	3	78	lumpur	lumpur	PROPN
ejpam-5223	3	79	,	,	PUNCT
ejpam-5223	3	80	malaysia	malaysia	PROPN
ejpam-5223	3	81	abstract	abstract	NOUN
ejpam-5223	3	82	.	.	PUNCT
ejpam-5223	4	1	in	in	ADP
ejpam-5223	4	2	this	this	DET
ejpam-5223	4	3	paper	paper	NOUN
ejpam-5223	4	4	,	,	PUNCT
ejpam-5223	4	5	we	we	PRON
ejpam-5223	4	6	introduce	introduce	VERB
ejpam-5223	4	7	some	some	DET
ejpam-5223	4	8	types	type	NOUN
ejpam-5223	4	9	of	of	ADP
ejpam-5223	4	10	separation	separation	NOUN
ejpam-5223	4	11	axioms	axiom	NOUN
ejpam-5223	4	12	via	via	ADP
ejpam-5223	4	13	f	f	PROPN
ejpam-5223	4	14	-open	-open	PROPN
ejpam-5223	4	15	sets	set	NOUN
ejpam-5223	4	16	,	,	PUNCT
ejpam-5223	4	17	namely	namely	ADV
ejpam-5223	4	18	fti	fti	PROPN
ejpam-5223	4	19	(	(	PUNCT
ejpam-5223	4	20	i	i	NOUN
ejpam-5223	4	21	=	=	NOUN
ejpam-5223	4	22	0	0	NUM
ejpam-5223	4	23	,	,	PUNCT
ejpam-5223	4	24	1	1	NUM
ejpam-5223	4	25	,	,	PUNCT
ejpam-5223	4	26	2	2	NUM
ejpam-5223	4	27	,	,	PUNCT
ejpam-5223	4	28	3	3	NUM
ejpam-5223	4	29	,	,	PUNCT
ejpam-5223	4	30	4	4	NUM
ejpam-5223	4	31	)	)	PUNCT
ejpam-5223	4	32	,	,	PUNCT
ejpam-5223	4	33	f	f	PROPN
ejpam-5223	4	34	-regular	-regular	ADJ
ejpam-5223	4	35	and	and	CCONJ
ejpam-5223	4	36	f	f	NOUN
ejpam-5223	4	37	-normal	-normal	ADJ
ejpam-5223	4	38	spaces	space	NOUN
ejpam-5223	4	39	,	,	PUNCT
ejpam-5223	4	40	and	and	CCONJ
ejpam-5223	4	41	investigate	investigate	VERB
ejpam-5223	4	42	their	their	PRON
ejpam-5223	4	43	properties	property	NOUN
ejpam-5223	4	44	,	,	PUNCT
ejpam-5223	4	45	relationships	relationship	NOUN
ejpam-5223	4	46	and	and	CCONJ
ejpam-5223	4	47	characterizations	characterization	NOUN
ejpam-5223	4	48	.	.	PUNCT
ejpam-5223	5	1	we	we	PRON
ejpam-5223	5	2	show	show	VERB
ejpam-5223	5	3	that	that	SCONJ
ejpam-5223	5	4	every	every	DET
ejpam-5223	5	5	fti	fti	PROPN
ejpam-5223	5	6	space	space	NOUN
ejpam-5223	5	7	is	be	AUX
ejpam-5223	5	8	a	a	DET
ejpam-5223	5	9	ti	ti	NOUN
ejpam-5223	5	10	space	space	NOUN
ejpam-5223	5	11	for	for	ADP
ejpam-5223	5	12	i	i	PROPN
ejpam-5223	5	13	=	=	SYM
ejpam-5223	5	14	0	0	NUM
ejpam-5223	5	15	,	,	PUNCT
ejpam-5223	5	16	1	1	NUM
ejpam-5223	5	17	,	,	PUNCT
ejpam-5223	5	18	2	2	NUM
ejpam-5223	5	19	,	,	PUNCT
ejpam-5223	5	20	3	3	NUM
ejpam-5223	5	21	,	,	PUNCT
ejpam-5223	5	22	4	4	NUM
ejpam-5223	5	23	.	.	PUNCT
ejpam-5223	6	1	however	however	ADV
ejpam-5223	6	2	,	,	PUNCT
ejpam-5223	6	3	the	the	DET
ejpam-5223	6	4	converse	converse	NOUN
ejpam-5223	6	5	is	be	AUX
ejpam-5223	6	6	true	true	ADJ
ejpam-5223	6	7	whenever	whenever	SCONJ
ejpam-5223	6	8	x	x	PRON
ejpam-5223	6	9	is	be	AUX
ejpam-5223	6	10	finite	finite	ADJ
ejpam-5223	6	11	.	.	PUNCT
ejpam-5223	7	1	2020	2020	NUM
ejpam-5223	7	2	mathematics	mathematic	NOUN
ejpam-5223	7	3	subject	subject	NOUN
ejpam-5223	7	4	classifications	classification	NOUN
ejpam-5223	7	5	:	:	PUNCT
ejpam-5223	7	6	54d40	54d40	NUM
ejpam-5223	7	7	key	key	ADJ
ejpam-5223	7	8	words	word	NOUN
ejpam-5223	7	9	and	and	CCONJ
ejpam-5223	7	10	phrases	phrase	NOUN
ejpam-5223	7	11	:	:	PUNCT
ejpam-5223	7	12	f	f	X
ejpam-5223	7	13	-open	-open	PROPN
ejpam-5223	7	14	,	,	PUNCT
ejpam-5223	7	15	fti	fti	PROPN
ejpam-5223	7	16	(	(	PUNCT
ejpam-5223	7	17	i	i	NOUN
ejpam-5223	7	18	=	=	NOUN
ejpam-5223	7	19	0	0	NUM
ejpam-5223	7	20	,	,	PUNCT
ejpam-5223	7	21	1	1	NUM
ejpam-5223	7	22	,	,	PUNCT
ejpam-5223	7	23	2	2	NUM
ejpam-5223	7	24	,	,	PUNCT
ejpam-5223	7	25	3	3	NUM
ejpam-5223	7	26	,	,	PUNCT
ejpam-5223	7	27	4	4	NUM
ejpam-5223	7	28	)	)	PUNCT
ejpam-5223	7	29	,	,	PUNCT
ejpam-5223	7	30	f	f	PROPN
ejpam-5223	7	31	-regular	-regular	PROPN
ejpam-5223	7	32	,	,	PUNCT
ejpam-5223	7	33	f	f	X
ejpam-5223	7	34	-normal	-normal	ADJ
ejpam-5223	7	35	1	1	NUM
ejpam-5223	7	36	.	.	PUNCT
ejpam-5223	7	37	introduction	introduction	NOUN
ejpam-5223	7	38	in	in	ADP
ejpam-5223	7	39	2012	2012	NUM
ejpam-5223	7	40	,	,	PUNCT
ejpam-5223	7	41	alias	alia	NOUN
ejpam-5223	7	42	et	et	PROPN
ejpam-5223	7	43	al.[3	al.[3	PROPN
ejpam-5223	7	44	]	]	PUNCT
ejpam-5223	7	45	introduced	introduce	VERB
ejpam-5223	7	46	some	some	DET
ejpam-5223	7	47	types	type	NOUN
ejpam-5223	7	48	of	of	ADP
ejpam-5223	7	49	separation	separation	NOUN
ejpam-5223	7	50	axioms	axiom	NOUN
ejpam-5223	7	51	via	via	ADP
ejpam-5223	7	52	ω−open	ω−open	PROPN
ejpam-5223	7	53	sets	set	NOUN
ejpam-5223	7	54	,	,	PUNCT
ejpam-5223	7	55	namely	namely	ADV
ejpam-5223	7	56	ω−regular	ω−regular	NUM
ejpam-5223	7	57	,	,	PUNCT
ejpam-5223	7	58	completely	completely	ADV
ejpam-5223	7	59	ω−regular	ω−regular	NUM
ejpam-5223	7	60	and	and	CCONJ
ejpam-5223	7	61	ω−normal	ω−normal	NUM
ejpam-5223	7	62	space	space	NOUN
ejpam-5223	7	63	and	and	CCONJ
ejpam-5223	7	64	investigated	investigate	VERB
ejpam-5223	7	65	their	their	PRON
ejpam-5223	7	66	fundamental	fundamental	ADJ
ejpam-5223	7	67	properties	property	NOUN
ejpam-5223	7	68	.	.	PUNCT
ejpam-5223	8	1	after	after	ADP
ejpam-5223	8	2	that	that	PRON
ejpam-5223	8	3	,	,	PUNCT
ejpam-5223	8	4	in	in	ADP
ejpam-5223	8	5	2024	2024	NUM
ejpam-5223	8	6	,	,	PUNCT
ejpam-5223	8	7	alqahtani	alqahtani	PROPN
ejpam-5223	8	8	and	and	CCONJ
ejpam-5223	8	9	abd	abd	PROPN
ejpam-5223	8	10	el	el	PROPN
ejpam-5223	8	11	-	-	PROPN
ejpam-5223	8	12	latif	latif	PROPN
ejpam-5223	9	1	[	[	X
ejpam-5223	9	2	1	1	X
ejpam-5223	9	3	]	]	X
ejpam-5223	9	4	interduced	interduce	VERB
ejpam-5223	9	5	some	some	DET
ejpam-5223	9	6	kinds	kind	NOUN
ejpam-5223	9	7	of	of	ADP
ejpam-5223	9	8	separation	separation	NOUN
ejpam-5223	9	9	axioms	axiom	NOUN
ejpam-5223	9	10	via	via	ADP
ejpam-5223	9	11	ℵ−poen	ℵ−poen	PUNCT
ejpam-5223	9	12	sets	set	NOUN
ejpam-5223	9	13	,	,	PUNCT
ejpam-5223	9	14	namley	namley	NOUN
ejpam-5223	9	15	ℵ	ℵ	ADP
ejpam-5223	9	16	−	−	PROPN
ejpam-5223	9	17	t0−space	t0−space	NOUN
ejpam-5223	9	18	,	,	PUNCT
ejpam-5223	9	19	ℵ	ℵ	ADP
ejpam-5223	9	20	−	−	PROPN
ejpam-5223	9	21	t1−space	t1−space	NOUN
ejpam-5223	9	22	and	and	CCONJ
ejpam-5223	9	23	ℵ	ℵ	ADP
ejpam-5223	9	24	−	−	PROPN
ejpam-5223	9	25	t2	t2	NOUN
ejpam-5223	9	26	-	-	PUNCT
ejpam-5223	9	27	space	space	NOUN
ejpam-5223	9	28	.	.	PUNCT
ejpam-5223	10	1	quite	quite	ADV
ejpam-5223	10	2	recently	recently	ADV
ejpam-5223	10	3	,	,	PUNCT
ejpam-5223	10	4	alqahtani	alqahtani	PROPN
ejpam-5223	11	1	[	[	X
ejpam-5223	11	2	2	2	NUM
ejpam-5223	11	3	]	]	PUNCT
ejpam-5223	11	4	has	have	AUX
ejpam-5223	11	5	introduced	introduce	VERB
ejpam-5223	11	6	the	the	DET
ejpam-5223	11	7	notion	notion	NOUN
ejpam-5223	11	8	of	of	ADP
ejpam-5223	11	9	f	f	PROPN
ejpam-5223	11	10	-open	-open	PROPN
ejpam-5223	11	11	sets	set	NOUN
ejpam-5223	11	12	in	in	ADP
ejpam-5223	11	13	a	a	DET
ejpam-5223	11	14	topological	topological	ADJ
ejpam-5223	11	15	space	space	NOUN
ejpam-5223	11	16	and	and	CCONJ
ejpam-5223	11	17	obtained	obtain	VERB
ejpam-5223	11	18	the	the	DET
ejpam-5223	11	19	fundamental	fundamental	ADJ
ejpam-5223	11	20	properties	property	NOUN
ejpam-5223	11	21	of	of	ADP
ejpam-5223	11	22	f	f	PROPN
ejpam-5223	11	23	-open	-open	NOUN
ejpam-5223	11	24	sets	set	NOUN
ejpam-5223	11	25	.	.	PUNCT
ejpam-5223	12	1	furthermore	furthermore	ADV
ejpam-5223	12	2	,	,	PUNCT
ejpam-5223	12	3	several	several	ADJ
ejpam-5223	12	4	notions	notion	NOUN
ejpam-5223	12	5	such	such	ADJ
ejpam-5223	12	6	as	as	ADP
ejpam-5223	12	7	f	f	PROPN
ejpam-5223	12	8	-continuous	-continuous	ADJ
ejpam-5223	12	9	functions	function	NOUN
ejpam-5223	12	10	,	,	PUNCT
ejpam-5223	12	11	f	f	PROPN
ejpam-5223	12	12	-compact	-compact	PROPN
ejpam-5223	12	13	spaces	space	NOUN
ejpam-5223	12	14	and	and	CCONJ
ejpam-5223	12	15	related	related	ADJ
ejpam-5223	12	16	properties	property	NOUN
ejpam-5223	12	17	are	be	AUX
ejpam-5223	12	18	defined	define	VERB
ejpam-5223	12	19	and	and	CCONJ
ejpam-5223	12	20	investigated	investigate	VERB
ejpam-5223	12	21	.	.	PUNCT
ejpam-5223	13	1	motivated	motivate	VERB
ejpam-5223	13	2	by	by	ADP
ejpam-5223	13	3	these	these	DET
ejpam-5223	13	4	works	work	NOUN
ejpam-5223	13	5	,	,	PUNCT
ejpam-5223	13	6	and	and	CCONJ
ejpam-5223	13	7	to	to	PART
ejpam-5223	13	8	simplify	simplify	VERB
ejpam-5223	13	9	the	the	DET
ejpam-5223	13	10	path	path	NOUN
ejpam-5223	13	11	for	for	ADP
ejpam-5223	13	12	many	many	ADJ
ejpam-5223	13	13	future	future	ADJ
ejpam-5223	13	14	articles	article	NOUN
ejpam-5223	13	15	on	on	ADP
ejpam-5223	13	16	this	this	DET
ejpam-5223	13	17	topic	topic	NOUN
ejpam-5223	13	18	,	,	PUNCT
ejpam-5223	13	19	in	in	ADP
ejpam-5223	13	20	this	this	DET
ejpam-5223	13	21	paper	paper	NOUN
ejpam-5223	13	22	,	,	PUNCT
ejpam-5223	13	23	we	we	PRON
ejpam-5223	13	24	introduce	introduce	VERB
ejpam-5223	13	25	some	some	DET
ejpam-5223	13	26	types	type	NOUN
ejpam-5223	13	27	of	of	ADP
ejpam-5223	13	28	separation	separation	NOUN
ejpam-5223	13	29	axioms	axiom	NOUN
ejpam-5223	13	30	via	via	ADP
ejpam-5223	13	31	f	f	PROPN
ejpam-5223	13	32	-open	-open	PROPN
ejpam-5223	13	33	sets	set	NOUN
ejpam-5223	13	34	,	,	PUNCT
ejpam-5223	13	35	namely	namely	ADV
ejpam-5223	13	36	,	,	PUNCT
ejpam-5223	13	37	fti	fti	PROPN
ejpam-5223	13	38	(	(	PUNCT
ejpam-5223	13	39	i	i	NOUN
ejpam-5223	13	40	=	=	NOUN
ejpam-5223	13	41	0	0	NUM
ejpam-5223	13	42	,	,	PUNCT
ejpam-5223	13	43	1	1	NUM
ejpam-5223	13	44	,	,	PUNCT
ejpam-5223	13	45	2	2	NUM
ejpam-5223	13	46	,	,	PUNCT
ejpam-5223	13	47	3	3	NUM
ejpam-5223	13	48	,	,	PUNCT
ejpam-5223	13	49	4	4	NUM
ejpam-5223	13	50	)	)	PUNCT
ejpam-5223	13	51	,	,	PUNCT
ejpam-5223	13	52	f	f	PROPN
ejpam-5223	13	53	-regular	-regular	ADJ
ejpam-5223	13	54	and	and	CCONJ
ejpam-5223	13	55	f	f	NOUN
ejpam-5223	13	56	-normal	-normal	ADJ
ejpam-5223	13	57	spaces	space	NOUN
ejpam-5223	13	58	,	,	PUNCT
ejpam-5223	13	59	and	and	CCONJ
ejpam-5223	13	60	their	their	PRON
ejpam-5223	13	61	relationships	relationship	NOUN
ejpam-5223	13	62	and	and	CCONJ
ejpam-5223	13	63	characterizations	characterization	NOUN
ejpam-5223	13	64	are	be	AUX
ejpam-5223	13	65	obtained	obtain	VERB
ejpam-5223	13	66	.	.	PUNCT
ejpam-5223	14	1	moreover	moreover	ADV
ejpam-5223	14	2	,	,	PUNCT
ejpam-5223	14	3	it	it	PRON
ejpam-5223	14	4	is	be	AUX
ejpam-5223	14	5	shown	show	VERB
ejpam-5223	14	6	that	that	SCONJ
ejpam-5223	14	7	1	1	X
ejpam-5223	14	8	)	)	PUNCT
ejpam-5223	14	9	an	an	DET
ejpam-5223	14	10	f	f	PROPN
ejpam-5223	14	11	-compact	-compact	PROPN
ejpam-5223	14	12	ft2	ft2	NOUN
ejpam-5223	14	13	space	space	NOUN
ejpam-5223	14	14	is	be	AUX
ejpam-5223	14	15	ft4	ft4	NOUN
ejpam-5223	14	16	,	,	PUNCT
ejpam-5223	14	17	2	2	NUM
ejpam-5223	14	18	)	)	PUNCT
ejpam-5223	14	19	f	f	NOUN
ejpam-5223	14	20	-normal	-normal	ADJ
ejpam-5223	14	21	spaces	space	NOUN
ejpam-5223	14	22	are	be	AUX
ejpam-5223	14	23	preserved	preserve	VERB
ejpam-5223	14	24	under	under	ADP
ejpam-5223	14	25	f	f	PROPN
ejpam-5223	14	26	-closed	-close	VERB
ejpam-5223	14	27	preserving	preserving	ADJ
ejpam-5223	14	28	and	and	CCONJ
ejpam-5223	14	29	continuous	continuous	ADJ
ejpam-5223	14	30	surjections	surjection	NOUN
ejpam-5223	14	31	.	.	PUNCT
ejpam-5223	15	1	first	first	ADV
ejpam-5223	15	2	,	,	PUNCT
ejpam-5223	15	3	we	we	PRON
ejpam-5223	15	4	recall	recall	VERB
ejpam-5223	15	5	some	some	DET
ejpam-5223	15	6	notions	notion	NOUN
ejpam-5223	15	7	defind	defind	NOUN
ejpam-5223	15	8	by	by	ADP
ejpam-5223	15	9	alqahtani[2	alqahtani[2	NOUN
ejpam-5223	15	10	]	]	PUNCT
ejpam-5223	15	11	.	.	PUNCT
ejpam-5223	16	1	let	let	VERB
ejpam-5223	16	2	(	(	PUNCT
ejpam-5223	16	3	x	x	NOUN
ejpam-5223	16	4	,	,	PUNCT
ejpam-5223	16	5	τ	τ	X
ejpam-5223	16	6	)	)	PUNCT
ejpam-5223	16	7	be	be	VERB
ejpam-5223	16	8	a	a	DET
ejpam-5223	16	9	topological	topological	ADJ
ejpam-5223	16	10	space	space	NOUN
ejpam-5223	16	11	and	and	CCONJ
ejpam-5223	16	12	a	a	DET
ejpam-5223	16	13	be	be	AUX
ejpam-5223	16	14	a	a	DET
ejpam-5223	16	15	subset	subset	NOUN
ejpam-5223	16	16	of	of	ADP
ejpam-5223	16	17	x.	x.	NOUN
ejpam-5223	16	18	the	the	DET
ejpam-5223	16	19	closure	closure	NOUN
ejpam-5223	16	20	of	of	ADP
ejpam-5223	16	21	a	a	PRON
ejpam-5223	16	22	and	and	CCONJ
ejpam-5223	16	23	interior	interior	ADJ
ejpam-5223	16	24	of	of	ADP
ejpam-5223	16	25	a	a	PRON
ejpam-5223	16	26	are	be	AUX
ejpam-5223	16	27	denoted	denote	VERB
ejpam-5223	16	28	by	by	ADP
ejpam-5223	16	29	cl(a	cl(a	NOUN
ejpam-5223	16	30	)	)	PUNCT
ejpam-5223	16	31	and	and	CCONJ
ejpam-5223	16	32	∗corresponding	∗corresponde	VERB
ejpam-5223	16	33	author	author	NOUN
ejpam-5223	16	34	.	.	PUNCT
ejpam-5223	17	1	doi	doi	NOUN
ejpam-5223	17	2	:	:	PUNCT
ejpam-5223	17	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5223	https://doi.org/10.29020/nybg.ejpam.v17i3.5223	ADJ
ejpam-5223	17	4	email	email	NOUN
ejpam-5223	17	5	addresses	address	NOUN
ejpam-5223	17	6	:	:	PUNCT
ejpam-5223	17	7	malohblosh@yahoo.com	malohblosh@yahoo.com	X
ejpam-5223	18	1	[	[	X
ejpam-5223	18	2	m.	m.	NOUN
ejpam-5223	18	3	baloush	baloush	PROPN
ejpam-5223	18	4	)	)	PUNCT
ejpam-5223	18	5	,	,	PUNCT
ejpam-5223	18	6	t.noiri@nifty.com	t.noiri@nifty.com	X
ejpam-5223	18	7	(	(	PUNCT
ejpam-5223	18	8	t.	t.	PROPN
ejpam-5223	18	9	noiri	noiri	PROPN
ejpam-5223	18	10	)	)	PUNCT
ejpam-5223	18	11	,	,	PUNCT
ejpam-5223	18	12	mitalafha@gmail.com	mitalafha@gmail.com	X
ejpam-5223	18	13	(	(	PUNCT
ejpam-5223	18	14	m.talafha	m.talafha	NOUN
ejpam-5223	18	15	)	)	PUNCT
ejpam-5223	18	16	,	,	PUNCT
ejpam-5223	18	17	syahida@ukm.edu.my	syahida@ukm.edu.my	PROPN
ejpam-5223	18	18	(	(	PUNCT
ejpam-5223	18	19	s.	s.	PROPN
ejpam-5223	18	20	che	che	PROPN
ejpam-5223	18	21	dzul	dzul	PROPN
ejpam-5223	18	22	-	-	PUNCT
ejpam-5223	18	23	kifli	kifli	PROPN
ejpam-5223	18	24	)	)	PUNCT
ejpam-5223	18	25	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5223	18	26	1463	1463	NUM
ejpam-5223	18	27	©	©	ADP
ejpam-5223	18	28	2024	2024	NUM
ejpam-5223	18	29	ejpam	ejpam	NOUN
ejpam-5223	18	30	all	all	DET
ejpam-5223	18	31	rights	right	NOUN
ejpam-5223	18	32	reserved	reserve	VERB
ejpam-5223	18	33	.	.	PUNCT
ejpam-5223	19	1	m.	m.	NOUN
ejpam-5223	19	2	baloush	baloush	PROPN
ejpam-5223	19	3	et	et	PROPN
ejpam-5223	19	4	al	al	PROPN
ejpam-5223	19	5	.	.	PUNCT
ejpam-5223	19	6	/	/	SYM
ejpam-5223	19	7	eur	eur	PROPN
ejpam-5223	19	8	.	.	PUNCT
ejpam-5223	20	1	j.	j.	PROPN
ejpam-5223	20	2	pure	pure	PROPN
ejpam-5223	20	3	appl	appl	PROPN
ejpam-5223	20	4	.	.	PROPN
ejpam-5223	20	5	math	math	PROPN
ejpam-5223	20	6	,	,	PUNCT
ejpam-5223	20	7	17	17	NUM
ejpam-5223	20	8	(	(	PUNCT
ejpam-5223	20	9	3	3	NUM
ejpam-5223	20	10	)	)	PUNCT
ejpam-5223	20	11	(	(	PUNCT
ejpam-5223	20	12	2024	2024	NUM
ejpam-5223	20	13	)	)	PUNCT
ejpam-5223	20	14	,	,	PUNCT
ejpam-5223	20	15	1463	1463	NUM
ejpam-5223	20	16	-	-	SYM
ejpam-5223	20	17	1470	1470	NUM
ejpam-5223	20	18	1464	1464	NUM
ejpam-5223	20	19	int(a	int(a	NOUN
ejpam-5223	20	20	)	)	PUNCT
ejpam-5223	20	21	,	,	PUNCT
ejpam-5223	20	22	respectively	respectively	ADV
ejpam-5223	20	23	.	.	PUNCT
ejpam-5223	21	1	definition	definition	NOUN
ejpam-5223	21	2	1	1	NUM
ejpam-5223	21	3	.	.	PUNCT
ejpam-5223	22	1	[	[	X
ejpam-5223	22	2	2	2	X
ejpam-5223	22	3	]	]	PUNCT
ejpam-5223	22	4	an	an	DET
ejpam-5223	22	5	open	open	NOUN
ejpam-5223	22	6	subset	subset	VERB
ejpam-5223	22	7	a	a	PRON
ejpam-5223	22	8	of	of	ADP
ejpam-5223	22	9	a	a	DET
ejpam-5223	22	10	topological	topological	ADJ
ejpam-5223	22	11	space	space	NOUN
ejpam-5223	22	12	(	(	PUNCT
ejpam-5223	22	13	x	x	X
ejpam-5223	22	14	,	,	PUNCT
ejpam-5223	22	15	τ	τ	X
ejpam-5223	22	16	)	)	PUNCT
ejpam-5223	22	17	is	be	AUX
ejpam-5223	22	18	called	call	VERB
ejpam-5223	22	19	an	an	DET
ejpam-5223	22	20	f−open	f−open	NOUN
ejpam-5223	22	21	set	set	NOUN
ejpam-5223	22	22	if	if	SCONJ
ejpam-5223	22	23	cl(a)\	cl(a)\	NOUN
ejpam-5223	22	24	a	a	PRON
ejpam-5223	22	25	is	be	AUX
ejpam-5223	22	26	a	a	DET
ejpam-5223	22	27	finite	finite	ADJ
ejpam-5223	22	28	set	set	NOUN
ejpam-5223	22	29	.	.	PUNCT
ejpam-5223	23	1	definition	definition	NOUN
ejpam-5223	23	2	2	2	NUM
ejpam-5223	23	3	.	.	PUNCT
ejpam-5223	24	1	[	[	X
ejpam-5223	24	2	2	2	X
ejpam-5223	24	3	]	]	PUNCT
ejpam-5223	24	4	a	a	DET
ejpam-5223	24	5	closed	closed	NOUN
ejpam-5223	24	6	subset	subset	VERB
ejpam-5223	24	7	a	a	PRON
ejpam-5223	24	8	of	of	ADP
ejpam-5223	24	9	a	a	DET
ejpam-5223	24	10	topological	topological	ADJ
ejpam-5223	24	11	space	space	NOUN
ejpam-5223	24	12	(	(	PUNCT
ejpam-5223	24	13	x	x	X
ejpam-5223	24	14	,	,	PUNCT
ejpam-5223	24	15	τ	τ	X
ejpam-5223	24	16	)	)	PUNCT
ejpam-5223	24	17	is	be	AUX
ejpam-5223	24	18	called	call	VERB
ejpam-5223	24	19	an	an	DET
ejpam-5223	24	20	f−closed	f−close	VERB
ejpam-5223	24	21	set	set	NOUN
ejpam-5223	24	22	if	if	SCONJ
ejpam-5223	24	23	a\int(a	a\int(a	NOUN
ejpam-5223	24	24	)	)	PUNCT
ejpam-5223	24	25	is	be	AUX
ejpam-5223	24	26	a	a	DET
ejpam-5223	24	27	finite	finite	ADJ
ejpam-5223	24	28	set	set	NOUN
ejpam-5223	24	29	.	.	PUNCT
ejpam-5223	25	1	definition	definition	NOUN
ejpam-5223	25	2	3	3	NUM
ejpam-5223	25	3	.	.	PUNCT
ejpam-5223	26	1	[	[	X
ejpam-5223	26	2	2	2	X
ejpam-5223	26	3	]	]	PUNCT
ejpam-5223	26	4	let	let	VERB
ejpam-5223	26	5	a	a	PRON
ejpam-5223	26	6	be	be	AUX
ejpam-5223	26	7	a	a	DET
ejpam-5223	26	8	subset	subset	NOUN
ejpam-5223	26	9	of	of	ADP
ejpam-5223	26	10	a	a	DET
ejpam-5223	26	11	topological	topological	ADJ
ejpam-5223	26	12	space	space	NOUN
ejpam-5223	26	13	(	(	PUNCT
ejpam-5223	26	14	x	x	X
ejpam-5223	26	15	,	,	PUNCT
ejpam-5223	26	16	τ	τ	PROPN
ejpam-5223	26	17	)	)	PUNCT
ejpam-5223	26	18	.	.	PUNCT
ejpam-5223	27	1	the	the	DET
ejpam-5223	27	2	f−closure	f−closure	NOUN
ejpam-5223	27	3	of	of	ADP
ejpam-5223	27	4	a	a	PRON
ejpam-5223	27	5	is	be	AUX
ejpam-5223	27	6	defined	define	VERB
ejpam-5223	27	7	as	as	ADP
ejpam-5223	27	8	the	the	DET
ejpam-5223	27	9	intersection	intersection	NOUN
ejpam-5223	27	10	of	of	ADP
ejpam-5223	27	11	all	all	DET
ejpam-5223	27	12	f−closed	f−close	VERB
ejpam-5223	27	13	sets	set	NOUN
ejpam-5223	27	14	containing	contain	VERB
ejpam-5223	27	15	a	a	PRON
ejpam-5223	27	16	,	,	PUNCT
ejpam-5223	27	17	and	and	CCONJ
ejpam-5223	27	18	is	be	AUX
ejpam-5223	27	19	denoted	denote	VERB
ejpam-5223	27	20	by	by	ADP
ejpam-5223	27	21	clf	clf	PROPN
ejpam-5223	27	22	(	(	PUNCT
ejpam-5223	27	23	a	a	NOUN
ejpam-5223	27	24	)	)	PUNCT
ejpam-5223	27	25	.	.	PUNCT
ejpam-5223	28	1	definition	definition	NOUN
ejpam-5223	28	2	4	4	NUM
ejpam-5223	28	3	.	.	PUNCT
ejpam-5223	29	1	[	[	X
ejpam-5223	29	2	2	2	NUM
ejpam-5223	29	3	]	]	X
ejpam-5223	29	4	let	let	VERB
ejpam-5223	29	5	(	(	PUNCT
ejpam-5223	29	6	x	x	NOUN
ejpam-5223	29	7	,	,	PUNCT
ejpam-5223	29	8	τ	τ	X
ejpam-5223	29	9	)	)	PUNCT
ejpam-5223	29	10	be	be	VERB
ejpam-5223	29	11	a	a	DET
ejpam-5223	29	12	topological	topological	ADJ
ejpam-5223	29	13	space	space	NOUN
ejpam-5223	29	14	.	.	PUNCT
ejpam-5223	30	1	then	then	ADV
ejpam-5223	30	2	(	(	PUNCT
ejpam-5223	30	3	x	x	X
ejpam-5223	30	4	,	,	PUNCT
ejpam-5223	30	5	τ	τ	X
ejpam-5223	30	6	)	)	PUNCT
ejpam-5223	30	7	is	be	AUX
ejpam-5223	30	8	called	call	VERB
ejpam-5223	30	9	an	an	DET
ejpam-5223	30	10	f−compact	f−compact	ADJ
ejpam-5223	30	11	space	space	NOUN
ejpam-5223	30	12	if	if	SCONJ
ejpam-5223	30	13	any	any	DET
ejpam-5223	30	14	open	open	ADJ
ejpam-5223	30	15	cover	cover	NOUN
ejpam-5223	30	16	of	of	ADP
ejpam-5223	30	17	x	x	PUNCT
ejpam-5223	30	18	has	have	VERB
ejpam-5223	30	19	a	a	DET
ejpam-5223	30	20	finite	finite	ADJ
ejpam-5223	30	21	subcover	subcover	PROPN
ejpam-5223	30	22	of	of	ADP
ejpam-5223	30	23	f−open	f−open	PROPN
ejpam-5223	30	24	sets	set	NOUN
ejpam-5223	30	25	.	.	PUNCT
ejpam-5223	31	1	2	2	X
ejpam-5223	31	2	.	.	X
ejpam-5223	31	3	separation	separation	NOUN
ejpam-5223	31	4	axioms	axiom	NOUN
ejpam-5223	31	5	via	via	ADP
ejpam-5223	31	6	f	f	PROPN
ejpam-5223	31	7	-open	-open	PROPN
ejpam-5223	31	8	sets	set	NOUN
ejpam-5223	31	9	for	for	ADP
ejpam-5223	31	10	any	any	DET
ejpam-5223	31	11	topological	topological	ADJ
ejpam-5223	31	12	space	space	NOUN
ejpam-5223	31	13	(	(	PUNCT
ejpam-5223	31	14	x	x	X
ejpam-5223	31	15	,	,	PUNCT
ejpam-5223	31	16	τ	τ	PROPN
ejpam-5223	31	17	)	)	PUNCT
ejpam-5223	31	18	,	,	PUNCT
ejpam-5223	31	19	by	by	ADP
ejpam-5223	31	20	τf	τf	ADP
ejpam-5223	31	21	we	we	PRON
ejpam-5223	31	22	denote	denote	VERB
ejpam-5223	31	23	the	the	DET
ejpam-5223	31	24	collection	collection	NOUN
ejpam-5223	31	25	of	of	ADP
ejpam-5223	31	26	all	all	DET
ejpam-5223	31	27	f−	f−	PROPN
ejpam-5223	31	28	open	open	ADJ
ejpam-5223	31	29	subsets	subset	NOUN
ejpam-5223	31	30	of	of	ADP
ejpam-5223	31	31	x.	x.	NOUN
ejpam-5223	31	32	example	example	NOUN
ejpam-5223	31	33	1	1	NUM
ejpam-5223	31	34	.	.	NOUN
ejpam-5223	31	35	1	1	NUM
ejpam-5223	31	36	)	)	PUNCT
ejpam-5223	31	37	for	for	ADP
ejpam-5223	31	38	any	any	DET
ejpam-5223	31	39	discrete	discrete	ADJ
ejpam-5223	31	40	topology	topology	NOUN
ejpam-5223	31	41	τ	τ	X
ejpam-5223	31	42	on	on	ADP
ejpam-5223	31	43	x	x	PRON
ejpam-5223	31	44	,	,	PUNCT
ejpam-5223	31	45	τf	τf	PROPN
ejpam-5223	32	1	=	=	SYM
ejpam-5223	32	2	τ	τ	PROPN
ejpam-5223	32	3	since	since	SCONJ
ejpam-5223	32	4	every	every	DET
ejpam-5223	32	5	a	a	DET
ejpam-5223	32	6	⊆	⊆	NUM
ejpam-5223	32	7	x	x	NOUN
ejpam-5223	32	8	is	be	AUX
ejpam-5223	32	9	clopen	clopen	ADJ
ejpam-5223	32	10	,	,	PUNCT
ejpam-5223	32	11	and	and	CCONJ
ejpam-5223	32	12	therefore	therefore	ADV
ejpam-5223	32	13	cl(a)\a	cl(a)\a	VERB
ejpam-5223	32	14	=	=	NOUN
ejpam-5223	32	15	∅	∅	NOUN
ejpam-5223	32	16	is	be	AUX
ejpam-5223	32	17	finite	finite	ADJ
ejpam-5223	32	18	.	.	X
ejpam-5223	32	19	2	2	NUM
ejpam-5223	32	20	)	)	PUNCT
ejpam-5223	32	21	for	for	ADP
ejpam-5223	32	22	any	any	DET
ejpam-5223	32	23	indiscrete	indiscrete	ADJ
ejpam-5223	32	24	topology	topology	NOUN
ejpam-5223	32	25	τ	τ	PROPN
ejpam-5223	32	26	on	on	ADP
ejpam-5223	32	27	x	x	SYM
ejpam-5223	32	28	,	,	PUNCT
ejpam-5223	32	29	we	we	PRON
ejpam-5223	32	30	have	have	VERB
ejpam-5223	32	31	τf	τf	NUM
ejpam-5223	33	1	=	=	SYM
ejpam-5223	33	2	τ	τ	PROPN
ejpam-5223	33	3	.	.	PUNCT
ejpam-5223	34	1	the	the	DET
ejpam-5223	34	2	only	only	ADJ
ejpam-5223	34	3	open	open	ADJ
ejpam-5223	34	4	sets	set	NOUN
ejpam-5223	34	5	in	in	ADP
ejpam-5223	34	6	x	x	SYM
ejpam-5223	34	7	are	be	AUX
ejpam-5223	34	8	x	x	X
ejpam-5223	34	9	and	and	CCONJ
ejpam-5223	34	10	∅.	∅.	VERB
ejpam-5223	34	11	since	since	SCONJ
ejpam-5223	34	12	both	both	PRON
ejpam-5223	34	13	are	be	AUX
ejpam-5223	34	14	clopen	clopen	ADJ
ejpam-5223	34	15	,	,	PUNCT
ejpam-5223	34	16	so	so	CCONJ
ejpam-5223	34	17	cl(x)\x	cl(x)\x	NOUN
ejpam-5223	34	18	=	=	SYM
ejpam-5223	34	19	∅	∅	NOUN
ejpam-5223	34	20	and	and	CCONJ
ejpam-5223	34	21	cl(∅)\∅	cl(∅)\∅	NOUN
ejpam-5223	34	22	=	=	PUNCT
ejpam-5223	34	23	∅.	∅.	PRON
ejpam-5223	34	24	3	3	NUM
ejpam-5223	34	25	)	)	PUNCT
ejpam-5223	34	26	the	the	DET
ejpam-5223	34	27	odd	odd	ADV
ejpam-5223	34	28	-	-	PUNCT
ejpam-5223	34	29	even	even	ADV
ejpam-5223	34	30	topology	topology	NOUN
ejpam-5223	34	31	on	on	ADP
ejpam-5223	34	32	n	n	CCONJ
ejpam-5223	34	33	induced	induce	VERB
ejpam-5223	34	34	by	by	ADP
ejpam-5223	34	35	its	its	PRON
ejpam-5223	34	36	bases	basis	NOUN
ejpam-5223	34	37	p	p	X
ejpam-5223	34	38	=	=	PUNCT
ejpam-5223	34	39	{	{	PUNCT
ejpam-5223	34	40	{	{	PUNCT
ejpam-5223	34	41	2k	2k	NOUN
ejpam-5223	34	42	−	−	PROPN
ejpam-5223	34	43	1	1	NUM
ejpam-5223	34	44	,	,	PUNCT
ejpam-5223	34	45	2k	2k	NUM
ejpam-5223	34	46	}	}	PUNCT
ejpam-5223	34	47	,	,	PUNCT
ejpam-5223	34	48	k∈	k∈	PROPN
ejpam-5223	34	49	n	n	CCONJ
ejpam-5223	34	50	}	}	PUNCT
ejpam-5223	34	51	=	=	PRON
ejpam-5223	34	52	{	{	PUNCT
ejpam-5223	34	53	{	{	PUNCT
ejpam-5223	34	54	1	1	NUM
ejpam-5223	34	55	,	,	PUNCT
ejpam-5223	34	56	2	2	NUM
ejpam-5223	34	57	}	}	PUNCT
ejpam-5223	34	58	,	,	PUNCT
ejpam-5223	34	59	{	{	PUNCT
ejpam-5223	34	60	3	3	NUM
ejpam-5223	34	61	,	,	PUNCT
ejpam-5223	34	62	4	4	NUM
ejpam-5223	34	63	}	}	PUNCT
ejpam-5223	34	64	,	,	PUNCT
ejpam-5223	34	65	{	{	PUNCT
ejpam-5223	34	66	5	5	NUM
ejpam-5223	34	67	,	,	PUNCT
ejpam-5223	34	68	6	6	NUM
ejpam-5223	34	69	}	}	PUNCT
ejpam-5223	34	70	,	,	PUNCT
ejpam-5223	34	71	·	·	PUNCT
ejpam-5223	34	72	·	·	PUNCT
ejpam-5223	34	73	·	·	PUNCT
ejpam-5223	34	74	}	}	PUNCT
ejpam-5223	34	75	satisfies	satisfy	VERB
ejpam-5223	34	76	τ	τ	X
ejpam-5223	34	77	=	=	PUNCT
ejpam-5223	34	78	τf	τf	PROPN
ejpam-5223	34	79	.	.	PUNCT
ejpam-5223	35	1	4	4	X
ejpam-5223	35	2	)	)	PUNCT
ejpam-5223	35	3	also	also	ADV
ejpam-5223	35	4	,	,	PUNCT
ejpam-5223	35	5	the	the	DET
ejpam-5223	35	6	deleted	delete	VERB
ejpam-5223	35	7	integer	integer	NOUN
ejpam-5223	35	8	topology	topology	NOUN
ejpam-5223	35	9	defined	define	VERB
ejpam-5223	35	10	by	by	ADP
ejpam-5223	35	11	letting	let	VERB
ejpam-5223	35	12	x	x	X
ejpam-5223	35	13	=	=	PUNCT
ejpam-5223	35	14	⋃	⋃	NOUN
ejpam-5223	35	15	n∈n	n∈n	NOUN
ejpam-5223	35	16	(	(	PUNCT
ejpam-5223	35	17	n−	n−	NOUN
ejpam-5223	35	18	1	1	NUM
ejpam-5223	35	19	,	,	PUNCT
ejpam-5223	35	20	n)⊂	n)⊂	NOUN
ejpam-5223	35	21	r	r	NOUN
ejpam-5223	35	22	and	and	CCONJ
ejpam-5223	35	23	p	p	NOUN
ejpam-5223	35	24	=	=	PUNCT
ejpam-5223	35	25	{	{	PUNCT
ejpam-5223	35	26	(	(	PUNCT
ejpam-5223	35	27	0	0	NUM
ejpam-5223	35	28	,	,	PUNCT
ejpam-5223	35	29	1	1	NUM
ejpam-5223	35	30	)	)	PUNCT
ejpam-5223	35	31	,	,	PUNCT
ejpam-5223	35	32	(	(	PUNCT
ejpam-5223	35	33	1	1	NUM
ejpam-5223	35	34	,	,	PUNCT
ejpam-5223	35	35	2	2	NUM
ejpam-5223	35	36	)	)	PUNCT
ejpam-5223	35	37	,	,	PUNCT
ejpam-5223	35	38	(	(	PUNCT
ejpam-5223	35	39	2	2	NUM
ejpam-5223	35	40	,	,	PUNCT
ejpam-5223	35	41	3	3	NUM
ejpam-5223	35	42	)	)	PUNCT
ejpam-5223	35	43	,	,	PUNCT
ejpam-5223	35	44	.	.	PUNCT
ejpam-5223	35	45	.	.	PUNCT
ejpam-5223	36	1	.	.	PUNCT
ejpam-5223	36	2	}	}	PUNCT
ejpam-5223	36	3	satisfies	satisfy	VERB
ejpam-5223	36	4	τ	τ	X
ejpam-5223	36	5	=	=	PUNCT
ejpam-5223	36	6	τf	τf	SCONJ
ejpam-5223	36	7	since	since	SCONJ
ejpam-5223	36	8	every	every	DET
ejpam-5223	36	9	open	open	ADJ
ejpam-5223	36	10	set	set	NOUN
ejpam-5223	36	11	is	be	AUX
ejpam-5223	36	12	clopen	clopen	ADJ
ejpam-5223	36	13	.	.	PUNCT
ejpam-5223	37	1	5	5	NUM
ejpam-5223	37	2	)	)	PUNCT
ejpam-5223	37	3	for	for	ADP
ejpam-5223	37	4	any	any	DET
ejpam-5223	37	5	metrizable	metrizable	ADJ
ejpam-5223	37	6	space	space	NOUN
ejpam-5223	37	7	,	,	PUNCT
ejpam-5223	37	8	the	the	DET
ejpam-5223	37	9	topology	topology	NOUN
ejpam-5223	37	10	τ	τ	PROPN
ejpam-5223	37	11	induced	induce	VERB
ejpam-5223	37	12	by	by	ADP
ejpam-5223	37	13	the	the	DET
ejpam-5223	37	14	metric	metric	NOUN
ejpam-5223	37	15	also	also	ADV
ejpam-5223	37	16	satisfies	satisfy	VERB
ejpam-5223	37	17	τ	τ	X
ejpam-5223	37	18	=	=	SYM
ejpam-5223	37	19	τf	τf	PROPN
ejpam-5223	37	20	.	.	PUNCT
ejpam-5223	38	1	this	this	PRON
ejpam-5223	38	2	is	be	AUX
ejpam-5223	38	3	because	because	SCONJ
ejpam-5223	38	4	every	every	DET
ejpam-5223	38	5	singleton	singleton	NOUN
ejpam-5223	38	6	is	be	AUX
ejpam-5223	38	7	closed	close	VERB
ejpam-5223	38	8	and	and	CCONJ
ejpam-5223	38	9	therefore	therefore	ADV
ejpam-5223	38	10	every	every	DET
ejpam-5223	38	11	open	open	ADJ
ejpam-5223	38	12	set	set	NOUN
ejpam-5223	38	13	is	be	AUX
ejpam-5223	38	14	clopen	clopen	ADJ
ejpam-5223	38	15	.	.	PUNCT
ejpam-5223	39	1	remark	remark	NOUN
ejpam-5223	39	2	1	1	NUM
ejpam-5223	39	3	.	.	PUNCT
ejpam-5223	40	1	the	the	DET
ejpam-5223	40	2	converse	converse	NOUN
ejpam-5223	40	3	of	of	ADP
ejpam-5223	40	4	5	5	NUM
ejpam-5223	40	5	of	of	ADP
ejpam-5223	40	6	example	example	NOUN
ejpam-5223	40	7	1	1	NUM
ejpam-5223	40	8	is	be	AUX
ejpam-5223	40	9	not	not	PART
ejpam-5223	40	10	true	true	ADJ
ejpam-5223	40	11	by	by	ADP
ejpam-5223	40	12	the	the	DET
ejpam-5223	40	13	following	follow	VERB
ejpam-5223	40	14	counter	counter	ADJ
ejpam-5223	40	15	examples	example	NOUN
ejpam-5223	40	16	.	.	PUNCT
ejpam-5223	41	1	example	example	NOUN
ejpam-5223	42	1	2	2	NUM
ejpam-5223	42	2	.	.	PUNCT
ejpam-5223	42	3	the	the	DET
ejpam-5223	42	4	indiscrete	indiscrete	ADJ
ejpam-5223	42	5	topology	topology	NOUN
ejpam-5223	42	6	is	be	AUX
ejpam-5223	42	7	not	not	PART
ejpam-5223	42	8	metrizable	metrizable	ADJ
ejpam-5223	42	9	but	but	CCONJ
ejpam-5223	42	10	yet	yet	ADV
ejpam-5223	42	11	satisfies	satisfy	VERB
ejpam-5223	42	12	τ	τ	PROPN
ejpam-5223	42	13	=	=	SYM
ejpam-5223	42	14	τf	τf	PROPN
ejpam-5223	42	15	.	.	PUNCT
ejpam-5223	43	1	example	example	NOUN
ejpam-5223	44	1	3	3	NUM
ejpam-5223	44	2	.	.	PUNCT
ejpam-5223	45	1	the	the	DET
ejpam-5223	45	2	cofinite	cofinite	NOUN
ejpam-5223	45	3	topology	topology	NOUN
ejpam-5223	45	4	on	on	ADP
ejpam-5223	45	5	r	r	NOUN
ejpam-5223	45	6	which	which	PRON
ejpam-5223	45	7	is	be	AUX
ejpam-5223	45	8	defined	define	VERB
ejpam-5223	45	9	for	for	ADP
ejpam-5223	45	10	a	a	DET
ejpam-5223	45	11	nonempty	nonempty	ADV
ejpam-5223	45	12	set	set	VERB
ejpam-5223	45	13	x	x	PUNCT
ejpam-5223	45	14	by	by	ADP
ejpam-5223	45	15	τcof	τcof	NOUN
ejpam-5223	45	16	=	=	SYM
ejpam-5223	45	17	{	{	PUNCT
ejpam-5223	45	18	u	u	NOUN
ejpam-5223	45	19	⊆	⊆	NUM
ejpam-5223	45	20	x	x	SYM
ejpam-5223	45	21	:	:	PUNCT
ejpam-5223	45	22	x\u	x\u	PROPN
ejpam-5223	45	23	isfinite	isfinite	PROPN
ejpam-5223	45	24	}	}	PUNCT
ejpam-5223	45	25	∪	∪	VERB
ejpam-5223	45	26	{	{	PUNCT
ejpam-5223	45	27	∅	∅	NOUN
ejpam-5223	45	28	}	}	PUNCT
ejpam-5223	45	29	i.e.	i.e.	X
ejpam-5223	45	30	,	,	PUNCT
ejpam-5223	45	31	u⊂	u⊂	ADJ
ejpam-5223	45	32	r	r	NOUN
ejpam-5223	45	33	is	be	AUX
ejpam-5223	45	34	open	open	ADJ
ejpam-5223	45	35	whenever	whenever	SCONJ
ejpam-5223	45	36	r	r	NOUN
ejpam-5223	45	37	\u	\u	PRON
ejpam-5223	45	38	is	be	AUX
ejpam-5223	45	39	finite	finite	NOUN
ejpam-5223	45	40	is	be	AUX
ejpam-5223	45	41	not	not	PART
ejpam-5223	45	42	metrizable	metrizable	ADJ
ejpam-5223	45	43	since	since	SCONJ
ejpam-5223	45	44	r	r	NOUN
ejpam-5223	45	45	is	be	AUX
ejpam-5223	45	46	infinite	infinite	ADJ
ejpam-5223	45	47	.	.	PUNCT
ejpam-5223	46	1	m.	m.	NOUN
ejpam-5223	46	2	baloush	baloush	PROPN
ejpam-5223	46	3	et	et	PROPN
ejpam-5223	46	4	al	al	PROPN
ejpam-5223	46	5	.	.	PUNCT
ejpam-5223	46	6	/	/	SYM
ejpam-5223	46	7	eur	eur	PROPN
ejpam-5223	46	8	.	.	PUNCT
ejpam-5223	47	1	j.	j.	PROPN
ejpam-5223	47	2	pure	pure	PROPN
ejpam-5223	47	3	appl	appl	PROPN
ejpam-5223	47	4	.	.	PROPN
ejpam-5223	47	5	math	math	PROPN
ejpam-5223	47	6	,	,	PUNCT
ejpam-5223	47	7	17	17	NUM
ejpam-5223	47	8	(	(	PUNCT
ejpam-5223	47	9	3	3	NUM
ejpam-5223	47	10	)	)	PUNCT
ejpam-5223	47	11	(	(	PUNCT
ejpam-5223	47	12	2024	2024	NUM
ejpam-5223	47	13	)	)	PUNCT
ejpam-5223	47	14	,	,	PUNCT
ejpam-5223	47	15	1463	1463	NUM
ejpam-5223	47	16	-	-	SYM
ejpam-5223	47	17	1470	1470	NUM
ejpam-5223	47	18	1465	1465	NUM
ejpam-5223	47	19	however	however	ADV
ejpam-5223	47	20	,	,	PUNCT
ejpam-5223	47	21	for	for	ADP
ejpam-5223	47	22	any	any	DET
ejpam-5223	47	23	open	open	ADJ
ejpam-5223	47	24	set	set	NOUN
ejpam-5223	47	25	,	,	PUNCT
ejpam-5223	47	26	cl(u)\u⊆	cl(u)\u⊆	PRON
ejpam-5223	47	27	r\u	r\u	PROPN
ejpam-5223	47	28	,	,	PUNCT
ejpam-5223	47	29	so	so	ADV
ejpam-5223	47	30	it	it	PRON
ejpam-5223	47	31	is	be	AUX
ejpam-5223	47	32	finite	finite	ADJ
ejpam-5223	47	33	and	and	CCONJ
ejpam-5223	47	34	therefore	therefore	ADV
ejpam-5223	47	35	u	u	NOUN
ejpam-5223	47	36	is	be	AUX
ejpam-5223	47	37	f−open	f−open	PROPN
ejpam-5223	47	38	.	.	PUNCT
ejpam-5223	48	1	therefore	therefore	ADV
ejpam-5223	48	2	,	,	PUNCT
ejpam-5223	48	3	τf	τf	PROPN
ejpam-5223	48	4	=	=	SYM
ejpam-5223	48	5	τ	τ	PROPN
ejpam-5223	48	6	.	.	PUNCT
ejpam-5223	49	1	in	in	ADP
ejpam-5223	49	2	general	general	ADJ
ejpam-5223	49	3	,	,	PUNCT
ejpam-5223	49	4	if	if	SCONJ
ejpam-5223	49	5	every	every	DET
ejpam-5223	49	6	open	open	ADJ
ejpam-5223	49	7	set	set	NOUN
ejpam-5223	49	8	is	be	AUX
ejpam-5223	49	9	clopen	clopen	ADJ
ejpam-5223	49	10	,	,	PUNCT
ejpam-5223	49	11	then	then	ADV
ejpam-5223	49	12	τf	τf	ADP
ejpam-5223	50	1	=	=	SYM
ejpam-5223	50	2	τ	τ	PROPN
ejpam-5223	50	3	.	.	PUNCT
ejpam-5223	51	1	we	we	PRON
ejpam-5223	51	2	can	can	AUX
ejpam-5223	51	3	also	also	ADV
ejpam-5223	51	4	see	see	VERB
ejpam-5223	51	5	that	that	SCONJ
ejpam-5223	51	6	if	if	SCONJ
ejpam-5223	51	7	x	x	PRON
ejpam-5223	51	8	is	be	AUX
ejpam-5223	51	9	finite	finite	ADJ
ejpam-5223	51	10	,	,	PUNCT
ejpam-5223	51	11	then	then	ADV
ejpam-5223	51	12	τf	τf	ADP
ejpam-5223	51	13	=	=	SYM
ejpam-5223	51	14	τ	τ	PROPN
ejpam-5223	51	15	.	.	PUNCT
ejpam-5223	51	16	note	note	VERB
ejpam-5223	51	17	that	that	SCONJ
ejpam-5223	51	18	τf	τf	PROPN
ejpam-5223	51	19	is	be	AUX
ejpam-5223	51	20	not	not	PART
ejpam-5223	51	21	necessarily	necessarily	ADV
ejpam-5223	51	22	another	another	DET
ejpam-5223	51	23	topology	topology	NOUN
ejpam-5223	51	24	on	on	ADP
ejpam-5223	51	25	x	x	SYM
ejpam-5223	51	26	,	,	PUNCT
ejpam-5223	51	27	since	since	SCONJ
ejpam-5223	51	28	countable	countable	ADJ
ejpam-5223	51	29	union	union	NOUN
ejpam-5223	51	30	of	of	ADP
ejpam-5223	51	31	f−open	f−open	PROPN
ejpam-5223	51	32	set	set	NOUN
ejpam-5223	51	33	is	be	AUX
ejpam-5223	51	34	not	not	PART
ejpam-5223	51	35	necessarily	necessarily	ADV
ejpam-5223	51	36	an	an	DET
ejpam-5223	51	37	f−open	f−open	ADV
ejpam-5223	51	38	set	set	VERB
ejpam-5223	51	39	as	as	SCONJ
ejpam-5223	51	40	shown	show	VERB
ejpam-5223	51	41	by	by	ADP
ejpam-5223	51	42	the	the	DET
ejpam-5223	51	43	following	follow	VERB
ejpam-5223	51	44	example	example	NOUN
ejpam-5223	51	45	.	.	PUNCT
ejpam-5223	52	1	example	example	NOUN
ejpam-5223	53	1	4	4	NUM
ejpam-5223	53	2	.	.	PUNCT
ejpam-5223	54	1	[	[	X
ejpam-5223	54	2	2	2	X
ejpam-5223	54	3	]	]	PUNCT
ejpam-5223	54	4	let	let	VERB
ejpam-5223	54	5	an	an	DET
ejpam-5223	54	6	=	=	SYM
ejpam-5223	54	7	(	(	PUNCT
ejpam-5223	54	8	n	n	CCONJ
ejpam-5223	54	9	,	,	PUNCT
ejpam-5223	54	10	n+	n+	X
ejpam-5223	54	11	1	1	X
ejpam-5223	54	12	)	)	PUNCT
ejpam-5223	54	13	be	be	AUX
ejpam-5223	54	14	a	a	DET
ejpam-5223	54	15	subset	subset	NOUN
ejpam-5223	54	16	of	of	ADP
ejpam-5223	54	17	(	(	PUNCT
ejpam-5223	54	18	r	r	NOUN
ejpam-5223	54	19	,	,	PUNCT
ejpam-5223	54	20	u	u	NOUN
ejpam-5223	54	21	)	)	PUNCT
ejpam-5223	54	22	for	for	ADP
ejpam-5223	54	23	all	all	DET
ejpam-5223	54	24	n	n	PRON
ejpam-5223	54	25	∈	∈	PROPN
ejpam-5223	54	26	n	n	CCONJ
ejpam-5223	54	27	,	,	PUNCT
ejpam-5223	54	28	then	then	ADV
ejpam-5223	54	29	,	,	PUNCT
ejpam-5223	54	30	an	an	DET
ejpam-5223	54	31	=	=	X
ejpam-5223	54	32	(	(	PUNCT
ejpam-5223	54	33	n	n	CCONJ
ejpam-5223	54	34	,	,	PUNCT
ejpam-5223	54	35	n+1	n+1	NOUN
ejpam-5223	54	36	)	)	PUNCT
ejpam-5223	54	37	∈	∈	PROPN
ejpam-5223	54	38	u	u	NOUN
ejpam-5223	54	39	and	and	CCONJ
ejpam-5223	54	40	cl(n	cl(n	NOUN
ejpam-5223	54	41	,	,	PUNCT
ejpam-5223	54	42	n+1	n+1	NOUN
ejpam-5223	54	43	)	)	PUNCT
ejpam-5223	54	44	\	\	PUNCT
ejpam-5223	54	45	(	(	PUNCT
ejpam-5223	54	46	n	n	CCONJ
ejpam-5223	54	47	,	,	PUNCT
ejpam-5223	54	48	n+1	n+1	PROPN
ejpam-5223	54	49	)	)	PUNCT
ejpam-5223	54	50	=	=	SYM
ejpam-5223	54	51	{	{	PUNCT
ejpam-5223	54	52	n	n	CCONJ
ejpam-5223	54	53	,	,	PUNCT
ejpam-5223	54	54	n+1	n+1	VERB
ejpam-5223	54	55	}	}	PUNCT
ejpam-5223	54	56	is	be	AUX
ejpam-5223	54	57	finite	finite	ADJ
ejpam-5223	54	58	for	for	ADP
ejpam-5223	54	59	all	all	DET
ejpam-5223	54	60	n	n	DET
ejpam-5223	54	61	∈	∈	PROPN
ejpam-5223	54	62	n.	n.	NOUN
ejpam-5223	54	63	hence	hence	ADV
ejpam-5223	54	64	,	,	PUNCT
ejpam-5223	54	65	an	an	PRON
ejpam-5223	54	66	=	=	X
ejpam-5223	54	67	(	(	PUNCT
ejpam-5223	54	68	n	n	CCONJ
ejpam-5223	54	69	,	,	PUNCT
ejpam-5223	54	70	n+1	n+1	PROPN
ejpam-5223	54	71	)	)	PUNCT
ejpam-5223	54	72	is	be	AUX
ejpam-5223	54	73	f−open	f−open	ADJ
ejpam-5223	54	74	for	for	ADP
ejpam-5223	54	75	all	all	DET
ejpam-5223	54	76	n	n	PRON
ejpam-5223	54	77	∈	∈	PROPN
ejpam-5223	54	78	n.	n.	NOUN
ejpam-5223	54	79	now	now	ADV
ejpam-5223	54	80	,	,	PUNCT
ejpam-5223	54	81	we	we	PRON
ejpam-5223	54	82	have	have	VERB
ejpam-5223	54	83	⋃	⋃	NOUN
ejpam-5223	54	84	n∈n	n∈n	NOUN
ejpam-5223	54	85	(	(	PUNCT
ejpam-5223	54	86	n	n	CCONJ
ejpam-5223	54	87	,	,	PUNCT
ejpam-5223	54	88	n+	n+	X
ejpam-5223	54	89	1	1	NUM
ejpam-5223	54	90	)	)	PUNCT
ejpam-5223	54	91	=	=	PUNCT
ejpam-5223	55	1	[	[	X
ejpam-5223	55	2	1,∞	1,∞	NUM
ejpam-5223	55	3	)	)	PUNCT
ejpam-5223	55	4	\	\	NOUN
ejpam-5223	56	1	n	n	PRON
ejpam-5223	56	2	is	be	AUX
ejpam-5223	56	3	an	an	DET
ejpam-5223	56	4	open	open	ADJ
ejpam-5223	56	5	set	set	NOUN
ejpam-5223	56	6	.	.	PUNCT
ejpam-5223	57	1	however	however	ADV
ejpam-5223	57	2	,	,	PUNCT
ejpam-5223	57	3	cl	cl	INTJ
ejpam-5223	57	4	(	(	PUNCT
ejpam-5223	57	5	⋃	⋃	NOUN
ejpam-5223	57	6	n∈n	n∈n	NOUN
ejpam-5223	57	7	(	(	PUNCT
ejpam-5223	57	8	n	n	CCONJ
ejpam-5223	57	9	,	,	PUNCT
ejpam-5223	57	10	n+	n+	X
ejpam-5223	57	11	1))\	1))\	NUM
ejpam-5223	57	12	⋃	⋃	NOUN
ejpam-5223	57	13	n∈n	n∈n	NOUN
ejpam-5223	57	14	(	(	PUNCT
ejpam-5223	57	15	n	n	CCONJ
ejpam-5223	57	16	,	,	PUNCT
ejpam-5223	57	17	n+	n+	X
ejpam-5223	57	18	1	1	NUM
ejpam-5223	57	19	)	)	PUNCT
ejpam-5223	57	20	=	=	NOUN
ejpam-5223	57	21	cl([1,∞)\n)\([1,∞)\	cl([1,∞)\n)\([1,∞)\	NOUN
ejpam-5223	57	22	n	n	CCONJ
ejpam-5223	57	23	)	)	PUNCT
ejpam-5223	57	24	=	=	PUNCT
ejpam-5223	58	1	[	[	X
ejpam-5223	58	2	1,∞)\([1,∞)\	1,∞)\([1,∞)\	NUM
ejpam-5223	58	3	n	n	CCONJ
ejpam-5223	58	4	)	)	PUNCT
ejpam-5223	58	5	=	=	PRON
ejpam-5223	59	1	n	n	PROPN
ejpam-5223	59	2	is	be	AUX
ejpam-5223	59	3	not	not	PART
ejpam-5223	59	4	a	a	DET
ejpam-5223	59	5	finite	finite	NOUN
ejpam-5223	59	6	set	set	NOUN
ejpam-5223	59	7	.	.	PUNCT
ejpam-5223	60	1	therefore	therefore	ADV
ejpam-5223	60	2	,	,	PUNCT
ejpam-5223	60	3	⋃	⋃	SCONJ
ejpam-5223	60	4	n∈n	n∈n	NOUN
ejpam-5223	60	5	(	(	PUNCT
ejpam-5223	60	6	n	n	CCONJ
ejpam-5223	60	7	,	,	PUNCT
ejpam-5223	60	8	n+	n+	NUM
ejpam-5223	60	9	1	1	NUM
ejpam-5223	60	10	)	)	PUNCT
ejpam-5223	60	11	is	be	AUX
ejpam-5223	60	12	not	not	PART
ejpam-5223	60	13	f−open	f−open	PROPN
ejpam-5223	60	14	.	.	PUNCT
ejpam-5223	61	1	definition	definition	NOUN
ejpam-5223	61	2	5	5	NUM
ejpam-5223	61	3	.	.	PUNCT
ejpam-5223	62	1	a	a	DET
ejpam-5223	62	2	topological	topological	ADJ
ejpam-5223	62	3	space	space	NOUN
ejpam-5223	62	4	(	(	PUNCT
ejpam-5223	62	5	x	x	X
ejpam-5223	62	6	,	,	PUNCT
ejpam-5223	62	7	τ	τ	X
ejpam-5223	62	8	)	)	PUNCT
ejpam-5223	62	9	is	be	AUX
ejpam-5223	62	10	called	call	VERB
ejpam-5223	62	11	an	an	DET
ejpam-5223	62	12	ft0	ft0	NOUN
ejpam-5223	62	13	−	−	NOUN
ejpam-5223	62	14	space	space	NOUN
ejpam-5223	62	15	if	if	SCONJ
ejpam-5223	62	16	for	for	ADP
ejpam-5223	62	17	any	any	DET
ejpam-5223	62	18	two	two	NUM
ejpam-5223	62	19	distinct	distinct	ADJ
ejpam-5223	62	20	points	point	NOUN
ejpam-5223	62	21	x	x	NOUN
ejpam-5223	62	22	,	,	PUNCT
ejpam-5223	62	23	y	y	PROPN
ejpam-5223	62	24	∈	∈	PROPN
ejpam-5223	62	25	x	x	PUNCT
ejpam-5223	62	26	there	there	PRON
ejpam-5223	62	27	is	be	VERB
ejpam-5223	62	28	an	an	DET
ejpam-5223	62	29	f−open	f−open	PROPN
ejpam-5223	62	30	set	set	NOUN
ejpam-5223	62	31	u	u	NOUN
ejpam-5223	62	32	in	in	ADP
ejpam-5223	62	33	x	x	PUNCT
ejpam-5223	62	34	containing	contain	VERB
ejpam-5223	62	35	x	x	PUNCT
ejpam-5223	62	36	but	but	CCONJ
ejpam-5223	62	37	not	not	PART
ejpam-5223	62	38	y	y	PROPN
ejpam-5223	62	39	or	or	CCONJ
ejpam-5223	62	40	an	an	DET
ejpam-5223	62	41	f−	f−	PROPN
ejpam-5223	62	42	open	open	ADJ
ejpam-5223	62	43	set	set	NOUN
ejpam-5223	62	44	u	u	NOUN
ejpam-5223	62	45	containing	contain	VERB
ejpam-5223	62	46	y	y	NOUN
ejpam-5223	62	47	but	but	CCONJ
ejpam-5223	62	48	not	not	PART
ejpam-5223	62	49	x.	x.	NOUN
ejpam-5223	62	50	example	example	NOUN
ejpam-5223	63	1	5	5	X
ejpam-5223	63	2	.	.	PUNCT
ejpam-5223	64	1	let	let	AUX
ejpam-5223	64	2	(	(	PUNCT
ejpam-5223	64	3	r	r	NOUN
ejpam-5223	64	4	,	,	PUNCT
ejpam-5223	64	5	u	u	NOUN
ejpam-5223	64	6	)	)	PUNCT
ejpam-5223	64	7	be	be	VERB
ejpam-5223	64	8	a	a	DET
ejpam-5223	64	9	topological	topological	ADJ
ejpam-5223	64	10	space	space	NOUN
ejpam-5223	64	11	,	,	PUNCT
ejpam-5223	64	12	where	where	SCONJ
ejpam-5223	64	13	u	u	NOUN
ejpam-5223	64	14	is	be	AUX
ejpam-5223	64	15	the	the	DET
ejpam-5223	64	16	usual	usual	ADJ
ejpam-5223	64	17	topology	topology	NOUN
ejpam-5223	64	18	.	.	PUNCT
ejpam-5223	65	1	let	let	AUX
ejpam-5223	65	2	(	(	PUNCT
ejpam-5223	65	3	a	a	DET
ejpam-5223	65	4	,	,	PUNCT
ejpam-5223	65	5	b	b	NOUN
ejpam-5223	65	6	)	)	PUNCT
ejpam-5223	65	7	be	be	AUX
ejpam-5223	65	8	any	any	DET
ejpam-5223	65	9	open	open	ADJ
ejpam-5223	65	10	interval	interval	NOUN
ejpam-5223	65	11	in	in	ADP
ejpam-5223	65	12	(	(	PUNCT
ejpam-5223	65	13	r	r	NOUN
ejpam-5223	65	14	,	,	PUNCT
ejpam-5223	65	15	u	u	NOUN
ejpam-5223	65	16	)	)	PUNCT
ejpam-5223	65	17	,	,	PUNCT
ejpam-5223	65	18	since	since	SCONJ
ejpam-5223	65	19	cl(a	cl(a	NUM
ejpam-5223	65	20	,	,	PUNCT
ejpam-5223	65	21	b)\(a	b)\(a	PROPN
ejpam-5223	65	22	,	,	PUNCT
ejpam-5223	65	23	b	b	NOUN
ejpam-5223	65	24	)	)	PUNCT
ejpam-5223	65	25	=	=	PUNCT
ejpam-5223	66	1	[	[	X
ejpam-5223	66	2	a	a	DET
ejpam-5223	66	3	,	,	PUNCT
ejpam-5223	66	4	b]\(a	b]\(a	NUM
ejpam-5223	66	5	,	,	PUNCT
ejpam-5223	66	6	b	b	NOUN
ejpam-5223	66	7	)	)	PUNCT
ejpam-5223	66	8	=	=	NOUN
ejpam-5223	66	9	{	{	PUNCT
ejpam-5223	66	10	a	a	PRON
ejpam-5223	66	11	,	,	PUNCT
ejpam-5223	66	12	b	b	NOUN
ejpam-5223	66	13	}	}	PUNCT
ejpam-5223	66	14	is	be	AUX
ejpam-5223	66	15	finte	finte	NOUN
ejpam-5223	66	16	,	,	PUNCT
ejpam-5223	66	17	then	then	ADV
ejpam-5223	66	18	any	any	DET
ejpam-5223	66	19	open	open	ADJ
ejpam-5223	66	20	interval	interval	NOUN
ejpam-5223	66	21	in	in	ADP
ejpam-5223	66	22	(	(	PUNCT
ejpam-5223	66	23	r	r	NOUN
ejpam-5223	66	24	,	,	PUNCT
ejpam-5223	66	25	u	u	NOUN
ejpam-5223	66	26	)	)	PUNCT
ejpam-5223	66	27	is	be	AUX
ejpam-5223	66	28	f	f	PROPN
ejpam-5223	66	29	-open	-open	NOUN
ejpam-5223	66	30	.	.	PUNCT
ejpam-5223	67	1	so	so	ADV
ejpam-5223	67	2	,	,	PUNCT
ejpam-5223	67	3	for	for	ADP
ejpam-5223	67	4	any	any	DET
ejpam-5223	67	5	two	two	NUM
ejpam-5223	67	6	distinct	distinct	ADJ
ejpam-5223	67	7	points	point	NOUN
ejpam-5223	67	8	x	x	NOUN
ejpam-5223	67	9	,	,	PUNCT
ejpam-5223	67	10	y	y	PROPN
ejpam-5223	67	11	∈	∈	PROPN
ejpam-5223	67	12	r	r	NOUN
ejpam-5223	67	13	there	there	PRON
ejpam-5223	67	14	is	be	VERB
ejpam-5223	67	15	an	an	DET
ejpam-5223	67	16	open	open	ADJ
ejpam-5223	67	17	interval	interval	NOUN
ejpam-5223	67	18	(	(	PUNCT
ejpam-5223	67	19	a	a	PRON
ejpam-5223	67	20	,	,	PUNCT
ejpam-5223	67	21	b)containing	b)containe	VERB
ejpam-5223	67	22	x	x	PUNCT
ejpam-5223	67	23	but	but	CCONJ
ejpam-5223	67	24	not	not	PART
ejpam-5223	67	25	y	y	PROPN
ejpam-5223	67	26	or	or	CCONJ
ejpam-5223	67	27	an	an	DET
ejpam-5223	67	28	open	open	ADJ
ejpam-5223	67	29	interval	interval	NOUN
ejpam-5223	67	30	(	(	PUNCT
ejpam-5223	67	31	a	a	DET
ejpam-5223	67	32	,	,	PUNCT
ejpam-5223	67	33	b	b	NOUN
ejpam-5223	67	34	)	)	PUNCT
ejpam-5223	67	35	containing	contain	VERB
ejpam-5223	67	36	y	y	NOUN
ejpam-5223	67	37	but	but	CCONJ
ejpam-5223	67	38	not	not	PART
ejpam-5223	67	39	x.therefore	x.therefore	PROPN
ejpam-5223	67	40	,	,	PUNCT
ejpam-5223	67	41	(	(	PUNCT
ejpam-5223	67	42	r	r	NOUN
ejpam-5223	67	43	,	,	PUNCT
ejpam-5223	67	44	u	u	NOUN
ejpam-5223	67	45	)	)	PUNCT
ejpam-5223	67	46	is	be	AUX
ejpam-5223	67	47	an	an	DET
ejpam-5223	67	48	ft0	ft0	NOUN
ejpam-5223	67	49	−	−	PROPN
ejpam-5223	67	50	space	space	NOUN
ejpam-5223	67	51	.	.	PUNCT
ejpam-5223	68	1	definition	definition	NOUN
ejpam-5223	68	2	6	6	NUM
ejpam-5223	68	3	.	.	PUNCT
ejpam-5223	69	1	a	a	DET
ejpam-5223	69	2	topological	topological	ADJ
ejpam-5223	69	3	space	space	NOUN
ejpam-5223	69	4	(	(	PUNCT
ejpam-5223	69	5	x	x	X
ejpam-5223	69	6	,	,	PUNCT
ejpam-5223	69	7	τ	τ	X
ejpam-5223	69	8	)	)	PUNCT
ejpam-5223	69	9	is	be	AUX
ejpam-5223	69	10	called	call	VERB
ejpam-5223	69	11	an	an	DET
ejpam-5223	69	12	ft1	ft1	NOUN
ejpam-5223	69	13	−	−	PROPN
ejpam-5223	69	14	space	space	NOUN
ejpam-5223	69	15	if	if	SCONJ
ejpam-5223	69	16	for	for	ADP
ejpam-5223	69	17	any	any	DET
ejpam-5223	69	18	two	two	NUM
ejpam-5223	69	19	distinct	distinct	ADJ
ejpam-5223	69	20	points	point	NOUN
ejpam-5223	69	21	x	x	NOUN
ejpam-5223	69	22	,	,	PUNCT
ejpam-5223	69	23	y	y	PROPN
ejpam-5223	69	24	∈	∈	PROPN
ejpam-5223	69	25	x	x	PUNCT
ejpam-5223	69	26	there	there	PRON
ejpam-5223	69	27	is	be	VERB
ejpam-5223	69	28	an	an	DET
ejpam-5223	69	29	f−open	f−open	PROPN
ejpam-5223	69	30	set	set	NOUN
ejpam-5223	69	31	u	u	NOUN
ejpam-5223	69	32	in	in	ADP
ejpam-5223	69	33	x	x	PUNCT
ejpam-5223	69	34	containing	contain	VERB
ejpam-5223	69	35	x	x	NOUN
ejpam-5223	69	36	but	but	CCONJ
ejpam-5223	69	37	not	not	PART
ejpam-5223	69	38	y	y	PROPN
ejpam-5223	69	39	and	and	CCONJ
ejpam-5223	69	40	an	an	DET
ejpam-5223	69	41	f−	f−	NOUN
ejpam-5223	69	42	open	open	ADJ
ejpam-5223	69	43	set	set	VERB
ejpam-5223	69	44	v	v	NOUN
ejpam-5223	69	45	in	in	ADP
ejpam-5223	69	46	x	x	PUNCT
ejpam-5223	69	47	containing	contain	VERB
ejpam-5223	69	48	y	y	NOUN
ejpam-5223	69	49	but	but	CCONJ
ejpam-5223	69	50	not	not	PART
ejpam-5223	69	51	x.	x.	NOUN
ejpam-5223	69	52	example	example	NOUN
ejpam-5223	70	1	6	6	NUM
ejpam-5223	70	2	.	.	PUNCT
ejpam-5223	71	1	let	let	AUX
ejpam-5223	71	2	(	(	PUNCT
ejpam-5223	71	3	r	r	NOUN
ejpam-5223	71	4	,	,	PUNCT
ejpam-5223	71	5	u	u	NOUN
ejpam-5223	71	6	)	)	PUNCT
ejpam-5223	71	7	be	be	VERB
ejpam-5223	71	8	the	the	DET
ejpam-5223	71	9	usual	usual	ADJ
ejpam-5223	71	10	topology	topology	NOUN
ejpam-5223	71	11	for	for	ADP
ejpam-5223	71	12	r.	r.	PROPN
ejpam-5223	71	13	let	let	VERB
ejpam-5223	71	14	x	x	PRON
ejpam-5223	71	15	,	,	PUNCT
ejpam-5223	71	16	y	y	PROPN
ejpam-5223	71	17	∈	∈	PROPN
ejpam-5223	71	18	r	r	PROPN
ejpam-5223	71	19	,	,	PUNCT
ejpam-5223	71	20	y	y	PROPN
ejpam-5223	71	21	>	>	X
ejpam-5223	71	22	x	x	X
ejpam-5223	71	23	,	,	PUNCT
ejpam-5223	71	24	and	and	CCONJ
ejpam-5223	71	25	y	y	PROPN
ejpam-5223	71	26	−	−	NOUN
ejpam-5223	72	1	x	x	SYM
ejpam-5223	72	2	=	=	SYM
ejpam-5223	72	3	c.	c.	NOUN
ejpam-5223	72	4	then	then	ADV
ejpam-5223	72	5	u	u	X
ejpam-5223	72	6	=	=	PUNCT
ejpam-5223	72	7	(	(	PUNCT
ejpam-5223	72	8	x−	x−	PROPN
ejpam-5223	72	9	c	c	PROPN
ejpam-5223	72	10	3	3	NUM
ejpam-5223	72	11	,	,	PUNCT
ejpam-5223	72	12	x+	x+	PROPN
ejpam-5223	72	13	c	c	NOUN
ejpam-5223	72	14	3	3	NUM
ejpam-5223	72	15	)	)	PUNCT
ejpam-5223	72	16	and	and	CCONJ
ejpam-5223	72	17	v	v	X
ejpam-5223	72	18	=	=	SYM
ejpam-5223	72	19	(	(	PUNCT
ejpam-5223	72	20	y	y	PROPN
ejpam-5223	72	21	−	−	PROPN
ejpam-5223	72	22	c	c	NOUN
ejpam-5223	72	23	3	3	NUM
ejpam-5223	72	24	,	,	PUNCT
ejpam-5223	72	25	y	y	PROPN
ejpam-5223	73	1	+	+	CCONJ
ejpam-5223	73	2	c	c	PROPN
ejpam-5223	73	3	3	3	NUM
ejpam-5223	73	4	)	)	PUNCT
ejpam-5223	73	5	are	be	AUX
ejpam-5223	73	6	two	two	NUM
ejpam-5223	73	7	f−open	f−open	NOUN
ejpam-5223	73	8	sets	set	NOUN
ejpam-5223	73	9	where	where	SCONJ
ejpam-5223	73	10	x	x	PUNCT
ejpam-5223	73	11	∈	∈	PROPN
ejpam-5223	73	12	u	u	NOUN
ejpam-5223	73	13	,	,	PUNCT
ejpam-5223	73	14	y	y	PROPN
ejpam-5223	73	15	/∈	/∈	PUNCT
ejpam-5223	73	16	u	u	PROPN
ejpam-5223	73	17	and	and	CCONJ
ejpam-5223	73	18	y	y	PROPN
ejpam-5223	73	19	∈	∈	PROPN
ejpam-5223	73	20	v	v	NOUN
ejpam-5223	73	21	,	,	PUNCT
ejpam-5223	73	22	x	x	PROPN
ejpam-5223	73	23	/∈	/∈	NOUN
ejpam-5223	73	24	v	v	NOUN
ejpam-5223	73	25	.therefore	.therefore	NOUN
ejpam-5223	73	26	,	,	PUNCT
ejpam-5223	73	27	(	(	PUNCT
ejpam-5223	73	28	r	r	NOUN
ejpam-5223	73	29	,	,	PUNCT
ejpam-5223	73	30	u	u	NOUN
ejpam-5223	73	31	)	)	PUNCT
ejpam-5223	73	32	is	be	AUX
ejpam-5223	73	33	an	an	DET
ejpam-5223	73	34	ft1	ft1	NOUN
ejpam-5223	73	35	−	−	PROPN
ejpam-5223	73	36	space	space	NOUN
ejpam-5223	73	37	.	.	PUNCT
ejpam-5223	74	1	theorem	theorem	NOUN
ejpam-5223	74	2	1	1	NUM
ejpam-5223	74	3	.	.	PUNCT
ejpam-5223	74	4	an	an	DET
ejpam-5223	74	5	ft1	ft1	PROPN
ejpam-5223	74	6	−	−	PROPN
ejpam-5223	74	7	space	space	NOUN
ejpam-5223	74	8	is	be	AUX
ejpam-5223	74	9	an	an	DET
ejpam-5223	74	10	ft0	ft0	NOUN
ejpam-5223	74	11	−	−	NOUN
ejpam-5223	74	12	space	space	NOUN
ejpam-5223	74	13	,	,	PUNCT
ejpam-5223	74	14	but	but	CCONJ
ejpam-5223	74	15	the	the	DET
ejpam-5223	74	16	converse	converse	NOUN
ejpam-5223	74	17	is	be	AUX
ejpam-5223	74	18	not	not	PART
ejpam-5223	74	19	true	true	ADJ
ejpam-5223	74	20	.	.	PUNCT
ejpam-5223	75	1	proof	proof	NOUN
ejpam-5223	75	2	.	.	PUNCT
ejpam-5223	76	1	let	let	VERB
ejpam-5223	76	2	(	(	PUNCT
ejpam-5223	76	3	x	x	NOUN
ejpam-5223	76	4	,	,	PUNCT
ejpam-5223	76	5	τ	τ	X
ejpam-5223	76	6	)	)	PUNCT
ejpam-5223	76	7	be	be	VERB
ejpam-5223	76	8	an	an	DET
ejpam-5223	76	9	ft1	ft1	NOUN
ejpam-5223	76	10	−	−	PROPN
ejpam-5223	76	11	space	space	NOUN
ejpam-5223	76	12	.	.	PUNCT
ejpam-5223	77	1	then	then	ADV
ejpam-5223	77	2	for	for	ADP
ejpam-5223	77	3	any	any	DET
ejpam-5223	77	4	distinct	distinct	ADJ
ejpam-5223	77	5	points	point	NOUN
ejpam-5223	77	6	x	x	NOUN
ejpam-5223	77	7	,	,	PUNCT
ejpam-5223	77	8	y	y	PROPN
ejpam-5223	77	9	∈	∈	PROPN
ejpam-5223	77	10	x	x	PRON
ejpam-5223	77	11	,	,	PUNCT
ejpam-5223	77	12	there	there	PRON
ejpam-5223	77	13	exist	exist	VERB
ejpam-5223	77	14	f−open	f−open	PART
ejpam-5223	77	15	sets	set	VERB
ejpam-5223	77	16	u	u	NOUN
ejpam-5223	77	17	,	,	PUNCT
ejpam-5223	77	18	v	v	PROPN
ejpam-5223	77	19	∈	∈	PROPN
ejpam-5223	77	20	τf	τf	ADP
ejpam-5223	77	21	such	such	ADJ
ejpam-5223	77	22	that	that	PRON
ejpam-5223	77	23	:	:	PUNCT
ejpam-5223	77	24	x	x	X
ejpam-5223	77	25	∈	∈	PROPN
ejpam-5223	77	26	u	u	NOUN
ejpam-5223	77	27	,	,	PUNCT
ejpam-5223	77	28	y	y	PROPN
ejpam-5223	77	29	/∈	/∈	PUNCT
ejpam-5223	77	30	u	u	PROPN
ejpam-5223	77	31	and	and	CCONJ
ejpam-5223	77	32	y	y	PROPN
ejpam-5223	77	33	∈	∈	PROPN
ejpam-5223	77	34	v	v	NOUN
ejpam-5223	77	35	,	,	PUNCT
ejpam-5223	77	36	x	x	PROPN
ejpam-5223	77	37	/∈	/∈	PUNCT
ejpam-5223	77	38	v	v	INTJ
ejpam-5223	77	39	hence	hence	ADV
ejpam-5223	77	40	,	,	PUNCT
ejpam-5223	77	41	there	there	PRON
ejpam-5223	77	42	exists	exist	VERB
ejpam-5223	77	43	an	an	DET
ejpam-5223	77	44	f−open	f−open	NOUN
ejpam-5223	77	45	set	set	NOUN
ejpam-5223	77	46	u	u	PROPN
ejpam-5223	77	47	∈	∈	PROPN
ejpam-5223	77	48	τf	τf	ADP
ejpam-5223	77	49	such	such	ADJ
ejpam-5223	77	50	that	that	PRON
ejpam-5223	77	51	:	:	PUNCT
ejpam-5223	77	52	x	x	X
ejpam-5223	77	53	∈	∈	NOUN
ejpam-5223	77	54	u	u	NOUN
ejpam-5223	77	55	and	and	CCONJ
ejpam-5223	77	56	y	y	PROPN
ejpam-5223	77	57	/∈	/∈	PUNCT
ejpam-5223	78	1	u	u	NOUN
ejpam-5223	78	2	or	or	CCONJ
ejpam-5223	78	3	y	y	PROPN
ejpam-5223	78	4	∈	∈	PROPN
ejpam-5223	78	5	u	u	NOUN
ejpam-5223	78	6	and	and	CCONJ
ejpam-5223	78	7	x	x	PROPN
ejpam-5223	78	8	/∈	/∈	PUNCT
ejpam-5223	78	9	u	u	PROPN
ejpam-5223	78	10	therefore,(x	therefore,(x	PROPN
ejpam-5223	78	11	,	,	PUNCT
ejpam-5223	78	12	τ	τ	X
ejpam-5223	78	13	)	)	PUNCT
ejpam-5223	78	14	is	be	AUX
ejpam-5223	78	15	an	an	DET
ejpam-5223	78	16	ft0	ft0	NOUN
ejpam-5223	78	17	−	−	PROPN
ejpam-5223	78	18	space	space	NOUN
ejpam-5223	78	19	.	.	PUNCT
ejpam-5223	79	1	for	for	ADP
ejpam-5223	79	2	the	the	DET
ejpam-5223	79	3	converse	converse	NOUN
ejpam-5223	79	4	,	,	PUNCT
ejpam-5223	79	5	let	let	VERB
ejpam-5223	79	6	us	we	PRON
ejpam-5223	79	7	consider	consider	VERB
ejpam-5223	79	8	the	the	DET
ejpam-5223	79	9	sierpinski	sierpinski	ADJ
ejpam-5223	79	10	space	space	NOUN
ejpam-5223	79	11	,	,	PUNCT
ejpam-5223	79	12	where	where	SCONJ
ejpam-5223	79	13	s	s	VERB
ejpam-5223	79	14	=	=	X
ejpam-5223	79	15	{	{	PUNCT
ejpam-5223	79	16	0	0	NUM
ejpam-5223	79	17	,	,	PUNCT
ejpam-5223	79	18	1	1	NUM
ejpam-5223	79	19	}	}	PUNCT
ejpam-5223	79	20	and	and	CCONJ
ejpam-5223	79	21	τ	τ	PROPN
ejpam-5223	79	22	=	=	SYM
ejpam-5223	79	23	{	{	PUNCT
ejpam-5223	79	24	∅	∅	NOUN
ejpam-5223	79	25	,	,	PUNCT
ejpam-5223	79	26	{	{	PUNCT
ejpam-5223	79	27	1	1	NUM
ejpam-5223	79	28	}	}	PUNCT
ejpam-5223	79	29	,	,	PUNCT
ejpam-5223	79	30	{	{	PUNCT
ejpam-5223	79	31	0	0	NUM
ejpam-5223	79	32	,	,	PUNCT
ejpam-5223	79	33	1	1	NUM
ejpam-5223	79	34	}	}	PUNCT
ejpam-5223	79	35	}	}	PUNCT
ejpam-5223	79	36	.	.	PUNCT
ejpam-5223	80	1	it	it	PRON
ejpam-5223	80	2	is	be	AUX
ejpam-5223	80	3	clear	clear	ADJ
ejpam-5223	80	4	that	that	SCONJ
ejpam-5223	80	5	the	the	DET
ejpam-5223	80	6	sierpinski	sierpinski	ADJ
ejpam-5223	80	7	space	space	NOUN
ejpam-5223	80	8	is	be	AUX
ejpam-5223	80	9	fto	fto	NOUN
ejpam-5223	80	10	but	but	CCONJ
ejpam-5223	80	11	not	not	PART
ejpam-5223	80	12	ft1	ft1	PROPN
ejpam-5223	80	13	.	.	PUNCT
ejpam-5223	81	1	m.	m.	PROPN
ejpam-5223	81	2	baloush	baloush	PROPN
ejpam-5223	81	3	et	et	PROPN
ejpam-5223	81	4	al	al	PROPN
ejpam-5223	81	5	.	.	PUNCT
ejpam-5223	81	6	/	/	SYM
ejpam-5223	81	7	eur	eur	PROPN
ejpam-5223	81	8	.	.	PUNCT
ejpam-5223	82	1	j.	j.	PROPN
ejpam-5223	82	2	pure	pure	PROPN
ejpam-5223	82	3	appl	appl	PROPN
ejpam-5223	82	4	.	.	PROPN
ejpam-5223	82	5	math	math	PROPN
ejpam-5223	82	6	,	,	PUNCT
ejpam-5223	82	7	17	17	NUM
ejpam-5223	82	8	(	(	PUNCT
ejpam-5223	82	9	3	3	NUM
ejpam-5223	82	10	)	)	PUNCT
ejpam-5223	82	11	(	(	PUNCT
ejpam-5223	82	12	2024	2024	NUM
ejpam-5223	82	13	)	)	PUNCT
ejpam-5223	82	14	,	,	PUNCT
ejpam-5223	82	15	1463	1463	NUM
ejpam-5223	82	16	-	-	SYM
ejpam-5223	82	17	1470	1470	NUM
ejpam-5223	82	18	1466	1466	NUM
ejpam-5223	82	19	theorem	theorem	NOUN
ejpam-5223	82	20	2	2	NUM
ejpam-5223	82	21	.	.	PUNCT
ejpam-5223	82	22	a	a	DET
ejpam-5223	82	23	topological	topological	ADJ
ejpam-5223	82	24	space	space	NOUN
ejpam-5223	82	25	(	(	PUNCT
ejpam-5223	82	26	x	x	X
ejpam-5223	82	27	,	,	PUNCT
ejpam-5223	82	28	τ	τ	X
ejpam-5223	82	29	)	)	PUNCT
ejpam-5223	82	30	is	be	AUX
ejpam-5223	82	31	an	an	DET
ejpam-5223	82	32	ft1	ft1	NOUN
ejpam-5223	82	33	space	space	NOUN
ejpam-5223	82	34	if	if	SCONJ
ejpam-5223	82	35	and	and	CCONJ
ejpam-5223	82	36	only	only	ADV
ejpam-5223	82	37	if	if	SCONJ
ejpam-5223	82	38	for	for	ADP
ejpam-5223	82	39	each	each	DET
ejpam-5223	82	40	x	x	SYM
ejpam-5223	82	41	∈	∈	PROPN
ejpam-5223	82	42	x	x	NOUN
ejpam-5223	82	43	,	,	PUNCT
ejpam-5223	82	44	the	the	DET
ejpam-5223	82	45	singleton	singleton	PROPN
ejpam-5223	82	46	set	set	NOUN
ejpam-5223	82	47	{	{	PUNCT
ejpam-5223	82	48	x	x	NOUN
ejpam-5223	82	49	}	}	PUNCT
ejpam-5223	82	50	is	be	AUX
ejpam-5223	82	51	f−closed	f−close	VERB
ejpam-5223	82	52	.	.	PUNCT
ejpam-5223	83	1	proof	proof	NOUN
ejpam-5223	83	2	.	.	PUNCT
ejpam-5223	84	1	let	let	VERB
ejpam-5223	84	2	(	(	PUNCT
ejpam-5223	84	3	x	x	NOUN
ejpam-5223	84	4	,	,	PUNCT
ejpam-5223	84	5	τ	τ	X
ejpam-5223	84	6	)	)	PUNCT
ejpam-5223	84	7	be	be	AUX
ejpam-5223	84	8	an	an	DET
ejpam-5223	84	9	ft1	ft1	NOUN
ejpam-5223	84	10	-	-	PUNCT
ejpam-5223	84	11	space	space	NOUN
ejpam-5223	84	12	and	and	CCONJ
ejpam-5223	84	13	let	let	VERB
ejpam-5223	84	14	x	x	SYM
ejpam-5223	84	15	∈	∈	PROPN
ejpam-5223	84	16	x	x	PUNCT
ejpam-5223	84	17	be	be	AUX
ejpam-5223	84	18	any	any	DET
ejpam-5223	84	19	point	point	NOUN
ejpam-5223	84	20	.	.	PUNCT
ejpam-5223	85	1	we	we	PRON
ejpam-5223	85	2	want	want	VERB
ejpam-5223	85	3	to	to	PART
ejpam-5223	85	4	show	show	VERB
ejpam-5223	85	5	that	that	SCONJ
ejpam-5223	85	6	{	{	PUNCT
ejpam-5223	85	7	x	x	X
ejpam-5223	85	8	}	}	PUNCT
ejpam-5223	85	9	is	be	AUX
ejpam-5223	85	10	f−closed	f−close	VERB
ejpam-5223	85	11	,	,	PUNCT
ejpam-5223	85	12	i.e.	i.e.	X
ejpam-5223	85	13	,	,	PUNCT
ejpam-5223	85	14	{	{	PUNCT
ejpam-5223	85	15	x	x	NOUN
ejpam-5223	85	16	}	}	PUNCT
ejpam-5223	85	17	is	be	AUX
ejpam-5223	85	18	closed	closed	ADJ
ejpam-5223	85	19	and	and	CCONJ
ejpam-5223	85	20	{	{	PUNCT
ejpam-5223	85	21	x}\int({x	x}\int({x	NOUN
ejpam-5223	85	22	}	}	PUNCT
ejpam-5223	85	23	)	)	PUNCT
ejpam-5223	85	24	is	be	AUX
ejpam-5223	85	25	a	a	DET
ejpam-5223	85	26	finite	finite	ADJ
ejpam-5223	85	27	set	set	NOUN
ejpam-5223	85	28	.	.	PUNCT
ejpam-5223	86	1	since	since	SCONJ
ejpam-5223	86	2	x	x	PRON
ejpam-5223	86	3	is	be	AUX
ejpam-5223	86	4	an	an	DET
ejpam-5223	86	5	ft1	ft1	PROPN
ejpam-5223	86	6	space	space	NOUN
ejpam-5223	86	7	,	,	PUNCT
ejpam-5223	86	8	then	then	ADV
ejpam-5223	86	9	it	it	PRON
ejpam-5223	86	10	is	be	AUX
ejpam-5223	86	11	a	a	DET
ejpam-5223	86	12	t1	t1	NOUN
ejpam-5223	86	13	-	-	PUNCT
ejpam-5223	86	14	space	space	NOUN
ejpam-5223	86	15	and	and	CCONJ
ejpam-5223	86	16	every	every	DET
ejpam-5223	86	17	singleton	singleton	NOUN
ejpam-5223	86	18	{	{	PUNCT
ejpam-5223	86	19	x	x	NOUN
ejpam-5223	86	20	}	}	PUNCT
ejpam-5223	86	21	is	be	AUX
ejpam-5223	86	22	closed	closed	ADJ
ejpam-5223	86	23	.	.	PUNCT
ejpam-5223	87	1	now	now	ADV
ejpam-5223	87	2	{	{	PUNCT
ejpam-5223	87	3	x	x	NOUN
ejpam-5223	87	4	}	}	PUNCT
ejpam-5223	87	5	\int	\int	PROPN
ejpam-5223	87	6	(	(	PUNCT
ejpam-5223	87	7	{	{	PUNCT
ejpam-5223	87	8	x	x	NOUN
ejpam-5223	87	9	}	}	PUNCT
ejpam-5223	87	10	)	)	PUNCT
ejpam-5223	87	11	=	=	PRON
ejpam-5223	87	12	{	{	PUNCT
ejpam-5223	87	13	x	x	NOUN
ejpam-5223	87	14	}	}	PUNCT
ejpam-5223	87	15	\∅	\∅	NOUN
ejpam-5223	87	16	=	=	PRON
ejpam-5223	87	17	{	{	PUNCT
ejpam-5223	87	18	x	x	NOUN
ejpam-5223	87	19	}	}	PUNCT
ejpam-5223	87	20	is	be	AUX
ejpam-5223	87	21	finite	finite	ADJ
ejpam-5223	87	22	.	.	PUNCT
ejpam-5223	88	1	therefore	therefore	ADV
ejpam-5223	88	2	,	,	PUNCT
ejpam-5223	88	3	{	{	PUNCT
ejpam-5223	88	4	x	x	X
ejpam-5223	88	5	}	}	PUNCT
ejpam-5223	88	6	is	be	AUX
ejpam-5223	88	7	f−closed	f−close	VERB
ejpam-5223	88	8	.	.	PUNCT
ejpam-5223	89	1	conversely	conversely	ADV
ejpam-5223	89	2	,	,	PUNCT
ejpam-5223	89	3	let	let	VERB
ejpam-5223	89	4	every	every	DET
ejpam-5223	89	5	singleton	singleton	NOUN
ejpam-5223	89	6	{	{	PUNCT
ejpam-5223	89	7	x	x	NOUN
ejpam-5223	89	8	}	}	PUNCT
ejpam-5223	89	9	be	be	AUX
ejpam-5223	89	10	f−closed	f−close	VERB
ejpam-5223	89	11	,	,	PUNCT
ejpam-5223	89	12	and	and	CCONJ
ejpam-5223	89	13	let	let	VERB
ejpam-5223	89	14	x	x	PRON
ejpam-5223	89	15	̸=	̸=	PROPN
ejpam-5223	89	16	y	y	PROPN
ejpam-5223	89	17	be	be	AUX
ejpam-5223	89	18	two	two	NUM
ejpam-5223	89	19	points	point	NOUN
ejpam-5223	89	20	in	in	ADP
ejpam-5223	89	21	x	x	NOUN
ejpam-5223	89	22	,	,	PUNCT
ejpam-5223	89	23	then	then	ADV
ejpam-5223	89	24	since	since	SCONJ
ejpam-5223	89	25	{	{	PUNCT
ejpam-5223	89	26	x	x	X
ejpam-5223	89	27	}	}	PUNCT
ejpam-5223	89	28	is	be	AUX
ejpam-5223	89	29	f−closed	f−close	VERB
ejpam-5223	89	30	,	,	PUNCT
ejpam-5223	89	31	x\{x	x\{x	PRON
ejpam-5223	89	32	}	}	PUNCT
ejpam-5223	89	33	is	be	AUX
ejpam-5223	89	34	f−	f−	NOUN
ejpam-5223	89	35	open	open	ADJ
ejpam-5223	89	36	and	and	CCONJ
ejpam-5223	89	37	contains	contain	VERB
ejpam-5223	89	38	y	y	PROPN
ejpam-5223	89	39	but	but	CCONJ
ejpam-5223	89	40	not	not	PART
ejpam-5223	89	41	x.	x.	NOUN
ejpam-5223	89	42	similarly	similarly	ADV
ejpam-5223	89	43	,	,	PUNCT
ejpam-5223	89	44	x\{y	x\{y	ADV
ejpam-5223	89	45	}	}	PUNCT
ejpam-5223	89	46	is	be	AUX
ejpam-5223	89	47	f−	f−	ADV
ejpam-5223	89	48	open	open	ADJ
ejpam-5223	89	49	and	and	CCONJ
ejpam-5223	89	50	contains	contain	VERB
ejpam-5223	89	51	x	x	PUNCT
ejpam-5223	89	52	but	but	CCONJ
ejpam-5223	89	53	not	not	PART
ejpam-5223	89	54	y.	y.	PROPN
ejpam-5223	89	55	therefore	therefore	ADV
ejpam-5223	89	56	,	,	PUNCT
ejpam-5223	89	57	(	(	PUNCT
ejpam-5223	89	58	x	x	X
ejpam-5223	89	59	,	,	PUNCT
ejpam-5223	89	60	τ	τ	X
ejpam-5223	89	61	)	)	PUNCT
ejpam-5223	89	62	is	be	AUX
ejpam-5223	89	63	an	an	DET
ejpam-5223	89	64	ft1space	ft1space	NOUN
ejpam-5223	89	65	.	.	PUNCT
ejpam-5223	90	1	definition	definition	NOUN
ejpam-5223	90	2	7	7	NUM
ejpam-5223	90	3	.	.	PUNCT
ejpam-5223	91	1	a	a	DET
ejpam-5223	91	2	topological	topological	ADJ
ejpam-5223	91	3	space	space	NOUN
ejpam-5223	91	4	(	(	PUNCT
ejpam-5223	91	5	x	x	X
ejpam-5223	91	6	,	,	PUNCT
ejpam-5223	91	7	τ	τ	X
ejpam-5223	91	8	)	)	PUNCT
ejpam-5223	91	9	is	be	AUX
ejpam-5223	91	10	called	call	VERB
ejpam-5223	91	11	an	an	DET
ejpam-5223	91	12	ft2	ft2	NOUN
ejpam-5223	91	13	−	−	NOUN
ejpam-5223	91	14	space	space	NOUN
ejpam-5223	91	15	if	if	SCONJ
ejpam-5223	91	16	for	for	ADP
ejpam-5223	91	17	any	any	DET
ejpam-5223	91	18	two	two	NUM
ejpam-5223	91	19	distinct	distinct	ADJ
ejpam-5223	91	20	points	point	NOUN
ejpam-5223	91	21	x	x	NOUN
ejpam-5223	91	22	,	,	PUNCT
ejpam-5223	91	23	y	y	PROPN
ejpam-5223	91	24	∈	∈	PROPN
ejpam-5223	91	25	x	x	PUNCT
ejpam-5223	91	26	there	there	PRON
ejpam-5223	91	27	exist	exist	VERB
ejpam-5223	91	28	f−open	f−open	VERB
ejpam-5223	91	29	sets	set	VERB
ejpam-5223	91	30	u	u	NOUN
ejpam-5223	91	31	and	and	CCONJ
ejpam-5223	91	32	v	v	NOUN
ejpam-5223	91	33	in	in	ADP
ejpam-5223	91	34	x	x	NOUN
ejpam-5223	91	35	,	,	PUNCT
ejpam-5223	91	36	such	such	ADJ
ejpam-5223	91	37	that	that	SCONJ
ejpam-5223	91	38	x	x	SYM
ejpam-5223	91	39	∈	∈	PROPN
ejpam-5223	91	40	u	u	NOUN
ejpam-5223	91	41	and	and	CCONJ
ejpam-5223	91	42	y	y	PROPN
ejpam-5223	91	43	∈	∈	PROPN
ejpam-5223	91	44	v	v	NOUN
ejpam-5223	91	45	,	,	PUNCT
ejpam-5223	91	46	and	and	CCONJ
ejpam-5223	91	47	u	u	NOUN
ejpam-5223	91	48	∩	∩	NOUN
ejpam-5223	91	49	v	v	NOUN
ejpam-5223	91	50	=	=	PUNCT
ejpam-5223	91	51	∅.	∅.	NOUN
ejpam-5223	91	52	example	example	NOUN
ejpam-5223	91	53	7	7	NUM
ejpam-5223	91	54	.	.	PUNCT
ejpam-5223	92	1	let	let	VERB
ejpam-5223	92	2	us	we	PRON
ejpam-5223	92	3	consider	consider	VERB
ejpam-5223	92	4	the	the	DET
ejpam-5223	92	5	usual	usual	ADJ
ejpam-5223	92	6	topology	topology	NOUN
ejpam-5223	92	7	for	for	ADP
ejpam-5223	92	8	r	r	NOUN
ejpam-5223	92	9	as	as	ADP
ejpam-5223	92	10	in	in	ADP
ejpam-5223	92	11	example	example	NOUN
ejpam-5223	93	1	5.then	5.then	X
ejpam-5223	93	2	u	u	NOUN
ejpam-5223	93	3	=	=	PUNCT
ejpam-5223	93	4	(	(	PUNCT
ejpam-5223	93	5	x−	x−	PROPN
ejpam-5223	93	6	c	c	PROPN
ejpam-5223	93	7	3	3	NUM
ejpam-5223	93	8	,	,	PUNCT
ejpam-5223	93	9	x+	x+	PROPN
ejpam-5223	93	10	c	c	NOUN
ejpam-5223	93	11	3	3	NUM
ejpam-5223	93	12	)	)	PUNCT
ejpam-5223	93	13	and	and	CCONJ
ejpam-5223	93	14	v	v	X
ejpam-5223	93	15	=	=	SYM
ejpam-5223	93	16	(	(	PUNCT
ejpam-5223	93	17	y	y	PROPN
ejpam-5223	93	18	−	−	PROPN
ejpam-5223	93	19	c	c	NOUN
ejpam-5223	93	20	3	3	NUM
ejpam-5223	93	21	,	,	PUNCT
ejpam-5223	93	22	y	y	PROPN
ejpam-5223	94	1	+	+	CCONJ
ejpam-5223	94	2	c	c	PROPN
ejpam-5223	94	3	3	3	NUM
ejpam-5223	94	4	)	)	PUNCT
ejpam-5223	94	5	are	be	AUX
ejpam-5223	94	6	two	two	NUM
ejpam-5223	94	7	f−open	f−open	NOUN
ejpam-5223	94	8	sets	set	NOUN
ejpam-5223	94	9	where	where	SCONJ
ejpam-5223	94	10	x	x	PUNCT
ejpam-5223	94	11	∈	∈	PROPN
ejpam-5223	94	12	u	u	NOUN
ejpam-5223	94	13	,	,	PUNCT
ejpam-5223	94	14	y	y	PROPN
ejpam-5223	94	15	∈	∈	PROPN
ejpam-5223	94	16	v	v	NOUN
ejpam-5223	94	17	,	,	PUNCT
ejpam-5223	94	18	x	x	PUNCT
ejpam-5223	94	19	and	and	CCONJ
ejpam-5223	94	20	u	u	PROPN
ejpam-5223	94	21	∩	∩	NOUN
ejpam-5223	94	22	v	v	NOUN
ejpam-5223	94	23	=	=	PUNCT
ejpam-5223	94	24	∅.	∅.	VERB
ejpam-5223	94	25	therefore	therefore	ADV
ejpam-5223	94	26	,	,	PUNCT
ejpam-5223	94	27	(	(	PUNCT
ejpam-5223	94	28	r	r	NOUN
ejpam-5223	94	29	,	,	PUNCT
ejpam-5223	94	30	u	u	NOUN
ejpam-5223	94	31	)	)	PUNCT
ejpam-5223	94	32	is	be	AUX
ejpam-5223	94	33	an	an	DET
ejpam-5223	94	34	ft2	ft2	NOUN
ejpam-5223	94	35	−	−	PROPN
ejpam-5223	94	36	space	space	NOUN
ejpam-5223	94	37	.	.	PUNCT
ejpam-5223	95	1	theorem	theorem	NOUN
ejpam-5223	95	2	3	3	NUM
ejpam-5223	95	3	.	.	PUNCT
ejpam-5223	96	1	an	an	DET
ejpam-5223	96	2	ft2	ft2	NOUN
ejpam-5223	96	3	−	−	PROPN
ejpam-5223	96	4	space	space	NOUN
ejpam-5223	96	5	is	be	AUX
ejpam-5223	96	6	an	an	DET
ejpam-5223	96	7	ft1	ft1	NOUN
ejpam-5223	96	8	−	−	PROPN
ejpam-5223	96	9	space	space	NOUN
ejpam-5223	96	10	,	,	PUNCT
ejpam-5223	96	11	but	but	CCONJ
ejpam-5223	96	12	the	the	DET
ejpam-5223	96	13	converse	converse	NOUN
ejpam-5223	96	14	is	be	AUX
ejpam-5223	96	15	not	not	PART
ejpam-5223	96	16	true	true	ADJ
ejpam-5223	96	17	.	.	PUNCT
ejpam-5223	97	1	proof	proof	NOUN
ejpam-5223	97	2	.	.	PUNCT
ejpam-5223	98	1	let	let	VERB
ejpam-5223	98	2	(	(	PUNCT
ejpam-5223	98	3	x	x	NOUN
ejpam-5223	98	4	,	,	PUNCT
ejpam-5223	98	5	τ	τ	X
ejpam-5223	98	6	)	)	PUNCT
ejpam-5223	98	7	be	be	AUX
ejpam-5223	98	8	an	an	DET
ejpam-5223	98	9	ft2−	ft2−	ADJ
ejpam-5223	98	10	space	space	NOUN
ejpam-5223	98	11	.	.	PUNCT
ejpam-5223	99	1	then	then	ADV
ejpam-5223	99	2	∀x	∀x	X
ejpam-5223	99	3	,	,	PUNCT
ejpam-5223	99	4	y	y	PROPN
ejpam-5223	99	5	∈	∈	PROPN
ejpam-5223	99	6	x	x	X
ejpam-5223	99	7	:	:	PUNCT
ejpam-5223	99	8	x	x	SYM
ejpam-5223	99	9	̸=	̸=	PROPN
ejpam-5223	99	10	y	y	PROPN
ejpam-5223	99	11	,	,	PUNCT
ejpam-5223	99	12	there	there	PRON
ejpam-5223	99	13	exist	exist	VERB
ejpam-5223	99	14	f−open	f−open	PART
ejpam-5223	99	15	sets	set	VERB
ejpam-5223	99	16	u	u	NOUN
ejpam-5223	99	17	,	,	PUNCT
ejpam-5223	99	18	v	v	ADP
ejpam-5223	99	19	such	such	ADJ
ejpam-5223	99	20	that	that	PRON
ejpam-5223	99	21	:	:	PUNCT
ejpam-5223	99	22	x	x	X
ejpam-5223	99	23	∈	∈	PROPN
ejpam-5223	99	24	u	u	NOUN
ejpam-5223	99	25	,	,	PUNCT
ejpam-5223	99	26	y	y	PROPN
ejpam-5223	99	27	∈	∈	PROPN
ejpam-5223	99	28	v	v	NOUN
ejpam-5223	99	29	and	and	CCONJ
ejpam-5223	99	30	u	u	NOUN
ejpam-5223	99	31	∩	∩	ADJ
ejpam-5223	99	32	v	v	NOUN
ejpam-5223	99	33	=	=	NOUN
ejpam-5223	99	34	∅	∅	NOUN
ejpam-5223	99	35	therefore	therefore	ADV
ejpam-5223	99	36	,	,	PUNCT
ejpam-5223	99	37	we	we	PRON
ejpam-5223	99	38	have	have	VERB
ejpam-5223	99	39	u	u	NOUN
ejpam-5223	99	40	∈	∈	NOUN
ejpam-5223	99	41	τf	τf	ADP
ejpam-5223	99	42	:	:	PUNCT
ejpam-5223	99	43	x	x	X
ejpam-5223	99	44	∈	∈	PROPN
ejpam-5223	99	45	u	u	NOUN
ejpam-5223	99	46	,	,	PUNCT
ejpam-5223	99	47	y	y	PROPN
ejpam-5223	99	48	/∈	/∈	PUNCT
ejpam-5223	99	49	u	u	NOUN
ejpam-5223	99	50	and	and	CCONJ
ejpam-5223	99	51	v	v	ADP
ejpam-5223	99	52	∈	∈	NOUN
ejpam-5223	100	1	τf	τf	ADP
ejpam-5223	100	2	:	:	PUNCT
ejpam-5223	100	3	y	y	PROPN
ejpam-5223	100	4	∈	∈	PROPN
ejpam-5223	100	5	v	v	PROPN
ejpam-5223	100	6	,	,	PUNCT
ejpam-5223	100	7	x	x	PROPN
ejpam-5223	100	8	/∈	/∈	PUNCT
ejpam-5223	101	1	v	v	ADP
ejpam-5223	101	2	this	this	PRON
ejpam-5223	101	3	shows	show	VERB
ejpam-5223	101	4	that	that	SCONJ
ejpam-5223	101	5	(	(	PUNCT
ejpam-5223	101	6	x	x	X
ejpam-5223	101	7	,	,	PUNCT
ejpam-5223	101	8	τ	τ	X
ejpam-5223	101	9	)	)	PUNCT
ejpam-5223	101	10	is	be	AUX
ejpam-5223	101	11	an	an	DET
ejpam-5223	101	12	ft1	ft1	NOUN
ejpam-5223	101	13	−	−	PROPN
ejpam-5223	101	14	space	space	NOUN
ejpam-5223	101	15	.	.	PUNCT
ejpam-5223	102	1	for	for	ADP
ejpam-5223	102	2	the	the	DET
ejpam-5223	102	3	converse	converse	NOUN
ejpam-5223	102	4	,	,	PUNCT
ejpam-5223	102	5	let	let	VERB
ejpam-5223	102	6	us	we	PRON
ejpam-5223	102	7	consider	consider	VERB
ejpam-5223	102	8	the	the	DET
ejpam-5223	102	9	cofinite	cofinite	NOUN
ejpam-5223	102	10	topology	topology	NOUN
ejpam-5223	102	11	τcof	τcof	NOUN
ejpam-5223	102	12	on	on	ADP
ejpam-5223	102	13	an	an	DET
ejpam-5223	102	14	infinite	infinite	ADJ
ejpam-5223	102	15	set	set	NOUN
ejpam-5223	102	16	x.	x.	NOUN
ejpam-5223	102	17	then	then	ADV
ejpam-5223	102	18	(	(	PUNCT
ejpam-5223	102	19	x	x	X
ejpam-5223	102	20	,	,	PUNCT
ejpam-5223	102	21	τcof	τcof	PROPN
ejpam-5223	102	22	)	)	PUNCT
ejpam-5223	102	23	is	be	AUX
ejpam-5223	102	24	an	an	DET
ejpam-5223	102	25	ft1−space	ft1−space	NOUN
ejpam-5223	102	26	but	but	CCONJ
ejpam-5223	102	27	is	be	AUX
ejpam-5223	102	28	not	not	PART
ejpam-5223	102	29	ft2	ft2	NOUN
ejpam-5223	102	30	.	.	PUNCT
ejpam-5223	103	1	let	let	VERB
ejpam-5223	103	2	x	x	SYM
ejpam-5223	103	3	∈	∈	PROPN
ejpam-5223	103	4	x	x	PUNCT
ejpam-5223	103	5	be	be	AUX
ejpam-5223	103	6	any	any	DET
ejpam-5223	103	7	point	point	NOUN
ejpam-5223	103	8	,	,	PUNCT
ejpam-5223	103	9	since	since	SCONJ
ejpam-5223	103	10	{	{	PUNCT
ejpam-5223	103	11	x	x	NOUN
ejpam-5223	103	12	}	}	PUNCT
ejpam-5223	103	13	\int	\int	PROPN
ejpam-5223	103	14	(	(	PUNCT
ejpam-5223	103	15	{	{	PUNCT
ejpam-5223	103	16	x	x	NOUN
ejpam-5223	103	17	}	}	PUNCT
ejpam-5223	103	18	)	)	PUNCT
ejpam-5223	103	19	=	=	PRON
ejpam-5223	103	20	{	{	PUNCT
ejpam-5223	103	21	x	x	NOUN
ejpam-5223	103	22	}	}	PUNCT
ejpam-5223	103	23	\∅	\∅	NOUN
ejpam-5223	104	1	=	=	PRON
ejpam-5223	104	2	{	{	PUNCT
ejpam-5223	104	3	x	x	NOUN
ejpam-5223	104	4	}	}	PUNCT
ejpam-5223	104	5	is	be	AUX
ejpam-5223	104	6	finite	finite	ADJ
ejpam-5223	104	7	,	,	PUNCT
ejpam-5223	104	8	then	then	ADV
ejpam-5223	104	9	the	the	DET
ejpam-5223	104	10	singleton	singleton	NOUN
ejpam-5223	104	11	{	{	PUNCT
ejpam-5223	104	12	x	x	NOUN
ejpam-5223	104	13	}	}	PUNCT
ejpam-5223	104	14	is	be	AUX
ejpam-5223	104	15	f−closed	f−close	VERB
ejpam-5223	104	16	and	and	CCONJ
ejpam-5223	104	17	hence	hence	ADV
ejpam-5223	104	18	,	,	PUNCT
ejpam-5223	104	19	by	by	ADP
ejpam-5223	104	20	theorem	theorem	NOUN
ejpam-5223	104	21	2	2	NUM
ejpam-5223	104	22	,	,	PUNCT
ejpam-5223	104	23	x	x	X
ejpam-5223	104	24	is	be	AUX
ejpam-5223	104	25	an	an	DET
ejpam-5223	104	26	ft1	ft1	NOUN
ejpam-5223	104	27	−	−	PROPN
ejpam-5223	104	28	space	space	NOUN
ejpam-5223	104	29	.	.	PUNCT
ejpam-5223	105	1	to	to	PART
ejpam-5223	105	2	show	show	VERB
ejpam-5223	105	3	that	that	SCONJ
ejpam-5223	105	4	x	x	PRON
ejpam-5223	105	5	is	be	AUX
ejpam-5223	105	6	not	not	PART
ejpam-5223	105	7	an	an	DET
ejpam-5223	105	8	ft2−space	ft2−space	NOUN
ejpam-5223	105	9	,	,	PUNCT
ejpam-5223	105	10	let	let	VERB
ejpam-5223	105	11	u	u	PRON
ejpam-5223	105	12	and	and	CCONJ
ejpam-5223	105	13	v	v	NOUN
ejpam-5223	105	14	be	be	AUX
ejpam-5223	105	15	any	any	DET
ejpam-5223	105	16	two	two	NUM
ejpam-5223	105	17	open	open	ADJ
ejpam-5223	105	18	subsets	subset	NOUN
ejpam-5223	105	19	of	of	ADP
ejpam-5223	105	20	x	x	SYM
ejpam-5223	105	21	such	such	ADJ
ejpam-5223	105	22	that	that	SCONJ
ejpam-5223	105	23	u	u	PROPN
ejpam-5223	105	24	∩	∩	NOUN
ejpam-5223	105	25	v	v	NOUN
ejpam-5223	105	26	=	=	NOUN
ejpam-5223	105	27	∅.	∅.	NOUN
ejpam-5223	105	28	since	since	ADV
ejpam-5223	105	29	,	,	PUNCT
ejpam-5223	105	30	u	u	NOUN
ejpam-5223	105	31	is	be	AUX
ejpam-5223	105	32	open	open	ADJ
ejpam-5223	105	33	and	and	CCONJ
ejpam-5223	105	34	cl(u)\u⊆	cl(u)\u⊆	INTJ
ejpam-5223	105	35	r\u	r\u	PROPN
ejpam-5223	105	36	,	,	PUNCT
ejpam-5223	105	37	then	then	ADV
ejpam-5223	105	38	cl(u)\u	cl(u)\u	PROPN
ejpam-5223	105	39	is	be	AUX
ejpam-5223	105	40	finite	finite	ADJ
ejpam-5223	105	41	and	and	CCONJ
ejpam-5223	105	42	then	then	ADV
ejpam-5223	105	43	u	u	NOUN
ejpam-5223	105	44	is	be	AUX
ejpam-5223	105	45	f−open	f−open	PROPN
ejpam-5223	105	46	.	.	PUNCT
ejpam-5223	105	47	similarly	similarly	ADV
ejpam-5223	105	48	,	,	PUNCT
ejpam-5223	105	49	v	v	NOUN
ejpam-5223	105	50	is	be	AUX
ejpam-5223	105	51	also	also	ADV
ejpam-5223	105	52	an	an	DET
ejpam-5223	105	53	f−open	f−open	ADV
ejpam-5223	105	54	set	set	NOUN
ejpam-5223	105	55	.	.	PUNCT
ejpam-5223	106	1	now	now	ADV
ejpam-5223	106	2	,	,	PUNCT
ejpam-5223	106	3	since	since	SCONJ
ejpam-5223	106	4	u	u	PROPN
ejpam-5223	106	5	∩	∩	NOUN
ejpam-5223	106	6	v	v	NOUN
ejpam-5223	106	7	=	=	SYM
ejpam-5223	106	8	∅	∅	NOUN
ejpam-5223	106	9	,	,	PUNCT
ejpam-5223	106	10	then	then	ADV
ejpam-5223	106	11	m.	m.	PROPN
ejpam-5223	106	12	baloush	baloush	PROPN
ejpam-5223	106	13	et	et	PROPN
ejpam-5223	106	14	al	al	PROPN
ejpam-5223	106	15	.	.	PUNCT
ejpam-5223	106	16	/	/	SYM
ejpam-5223	106	17	eur	eur	PROPN
ejpam-5223	106	18	.	.	PUNCT
ejpam-5223	107	1	j.	j.	PROPN
ejpam-5223	107	2	pure	pure	PROPN
ejpam-5223	107	3	appl	appl	PROPN
ejpam-5223	107	4	.	.	PROPN
ejpam-5223	107	5	math	math	PROPN
ejpam-5223	107	6	,	,	PUNCT
ejpam-5223	107	7	17	17	NUM
ejpam-5223	107	8	(	(	PUNCT
ejpam-5223	107	9	3	3	NUM
ejpam-5223	107	10	)	)	PUNCT
ejpam-5223	107	11	(	(	PUNCT
ejpam-5223	107	12	2024	2024	NUM
ejpam-5223	107	13	)	)	PUNCT
ejpam-5223	107	14	,	,	PUNCT
ejpam-5223	107	15	1463	1463	NUM
ejpam-5223	107	16	-	-	SYM
ejpam-5223	107	17	1470	1470	NUM
ejpam-5223	107	18	1467	1467	NUM
ejpam-5223	107	19	(	(	PUNCT
ejpam-5223	107	20	x\u	x\u	X
ejpam-5223	107	21	)	)	PUNCT
ejpam-5223	107	22	∪	∪	NOUN
ejpam-5223	107	23	(	(	PUNCT
ejpam-5223	107	24	x\v	x\v	PROPN
ejpam-5223	107	25	)	)	PUNCT
ejpam-5223	108	1	=	=	PUNCT
ejpam-5223	109	1	x	x	PUNCT
ejpam-5223	109	2	this	this	PRON
ejpam-5223	109	3	is	be	AUX
ejpam-5223	109	4	a	a	DET
ejpam-5223	109	5	contradiction	contradiction	NOUN
ejpam-5223	109	6	since	since	SCONJ
ejpam-5223	109	7	x	x	PRON
ejpam-5223	109	8	is	be	AUX
ejpam-5223	109	9	infinite	infinite	ADJ
ejpam-5223	109	10	.	.	PUNCT
ejpam-5223	110	1	hence	hence	ADV
ejpam-5223	110	2	,	,	PUNCT
ejpam-5223	110	3	there	there	PRON
ejpam-5223	110	4	is	be	VERB
ejpam-5223	110	5	no	no	DET
ejpam-5223	110	6	two	two	NUM
ejpam-5223	110	7	distinct	distinct	ADJ
ejpam-5223	110	8	points	point	NOUN
ejpam-5223	110	9	inx	inx	AUX
ejpam-5223	110	10	belong	belong	VERB
ejpam-5223	110	11	to	to	ADP
ejpam-5223	110	12	two	two	NUM
ejpam-5223	110	13	disjoint	disjoint	ADJ
ejpam-5223	110	14	f−open	f−open	NOUN
ejpam-5223	110	15	sets	set	NOUN
ejpam-5223	110	16	.	.	PUNCT
ejpam-5223	111	1	therefore	therefore	ADV
ejpam-5223	111	2	,	,	PUNCT
ejpam-5223	111	3	x	x	X
ejpam-5223	111	4	is	be	AUX
ejpam-5223	111	5	not	not	PART
ejpam-5223	111	6	an	an	DET
ejpam-5223	111	7	ft2−space	ft2−space	NOUN
ejpam-5223	111	8	.	.	PUNCT
ejpam-5223	112	1	definition	definition	NOUN
ejpam-5223	112	2	8	8	NUM
ejpam-5223	112	3	.	.	PUNCT
ejpam-5223	113	1	a	a	DET
ejpam-5223	113	2	topological	topological	ADJ
ejpam-5223	113	3	space	space	NOUN
ejpam-5223	113	4	(	(	PUNCT
ejpam-5223	113	5	x	x	X
ejpam-5223	113	6	,	,	PUNCT
ejpam-5223	113	7	τ	τ	X
ejpam-5223	113	8	)	)	PUNCT
ejpam-5223	113	9	is	be	AUX
ejpam-5223	113	10	called	call	VERB
ejpam-5223	113	11	an	an	DET
ejpam-5223	113	12	f−regular	f−regular	PROPN
ejpam-5223	113	13	space	space	NOUN
ejpam-5223	113	14	(	(	PUNCT
ejpam-5223	113	15	briefly	briefly	ADV
ejpam-5223	114	1	fr	fr	ADP
ejpam-5223	114	2	−	−	PROPN
ejpam-5223	114	3	space	space	NOUN
ejpam-5223	114	4	)	)	PUNCT
ejpam-5223	114	5	if	if	SCONJ
ejpam-5223	114	6	for	for	ADP
ejpam-5223	114	7	each	each	DET
ejpam-5223	114	8	closed	close	VERB
ejpam-5223	114	9	subset	subset	NOUN
ejpam-5223	114	10	w	w	ADP
ejpam-5223	114	11	⊂	⊂	PROPN
ejpam-5223	114	12	x	x	X
ejpam-5223	114	13	and	and	CCONJ
ejpam-5223	114	14	each	each	PRON
ejpam-5223	114	15	x	x	X
ejpam-5223	114	16	/∈	/∈	PUNCT
ejpam-5223	115	1	w	w	X
ejpam-5223	115	2	,	,	PUNCT
ejpam-5223	115	3	there	there	PRON
ejpam-5223	115	4	exist	exist	VERB
ejpam-5223	115	5	f−open	f−open	VERB
ejpam-5223	115	6	sets	set	VERB
ejpam-5223	115	7	u	u	NOUN
ejpam-5223	115	8	and	and	CCONJ
ejpam-5223	115	9	v	v	NOUN
ejpam-5223	115	10	in	in	ADP
ejpam-5223	115	11	x	x	NOUN
ejpam-5223	115	12	,	,	PUNCT
ejpam-5223	115	13	such	such	ADJ
ejpam-5223	115	14	that	that	SCONJ
ejpam-5223	115	15	x	x	SYM
ejpam-5223	115	16	∈	∈	PROPN
ejpam-5223	115	17	u	u	NOUN
ejpam-5223	115	18	,	,	PUNCT
ejpam-5223	115	19	w	w	PROPN
ejpam-5223	115	20	⊆	⊆	NUM
ejpam-5223	115	21	v	v	NOUN
ejpam-5223	115	22	,	,	PUNCT
ejpam-5223	115	23	and	and	CCONJ
ejpam-5223	115	24	u	u	NOUN
ejpam-5223	115	25	∩	∩	NOUN
ejpam-5223	115	26	v	v	NOUN
ejpam-5223	115	27	=	=	PUNCT
ejpam-5223	115	28	∅.	∅.	VERB
ejpam-5223	115	29	an	an	DET
ejpam-5223	115	30	f−	f−	PROPN
ejpam-5223	115	31	regular	regular	ADJ
ejpam-5223	115	32	ft1	ft1	PROPN
ejpam-5223	115	33	−	−	PROPN
ejpam-5223	115	34	space	space	NOUN
ejpam-5223	115	35	is	be	AUX
ejpam-5223	115	36	called	call	VERB
ejpam-5223	115	37	an	an	DET
ejpam-5223	115	38	ft3	ft3	NOUN
ejpam-5223	115	39	−	−	PROPN
ejpam-5223	115	40	space	space	NOUN
ejpam-5223	115	41	.	.	PUNCT
ejpam-5223	116	1	example	example	NOUN
ejpam-5223	116	2	8	8	NUM
ejpam-5223	116	3	.	.	PUNCT
ejpam-5223	117	1	let	let	VERB
ejpam-5223	117	2	us	we	PRON
ejpam-5223	117	3	consider	consider	VERB
ejpam-5223	117	4	the	the	DET
ejpam-5223	117	5	usual	usual	ADJ
ejpam-5223	117	6	topology	topology	NOUN
ejpam-5223	117	7	for	for	ADP
ejpam-5223	117	8	r	r	NOUN
ejpam-5223	117	9	as	as	ADP
ejpam-5223	117	10	in	in	ADP
ejpam-5223	117	11	example	example	NOUN
ejpam-5223	117	12	5	5	X
ejpam-5223	117	13	.	.	PUNCT
ejpam-5223	118	1	it	it	PRON
ejpam-5223	118	2	’s	’	VERB
ejpam-5223	118	3	easy	easy	ADJ
ejpam-5223	118	4	to	to	PART
ejpam-5223	118	5	show	show	VERB
ejpam-5223	118	6	that	that	SCONJ
ejpam-5223	118	7	(	(	PUNCT
ejpam-5223	118	8	r	r	NOUN
ejpam-5223	118	9	,	,	PUNCT
ejpam-5223	118	10	u	u	NOUN
ejpam-5223	118	11	)	)	PUNCT
ejpam-5223	118	12	is	be	AUX
ejpam-5223	118	13	ft3	ft3	NOUN
ejpam-5223	118	14	−	−	PROPN
ejpam-5223	118	15	space	space	NOUN
ejpam-5223	118	16	.	.	PUNCT
ejpam-5223	119	1	theorem	theorem	ADJ
ejpam-5223	119	2	4	4	NUM
ejpam-5223	119	3	.	.	X
ejpam-5223	120	1	for	for	ADP
ejpam-5223	120	2	a	a	DET
ejpam-5223	120	3	topological	topological	ADJ
ejpam-5223	120	4	space	space	NOUN
ejpam-5223	120	5	(	(	PUNCT
ejpam-5223	120	6	x	x	X
ejpam-5223	120	7	,	,	PUNCT
ejpam-5223	120	8	τ	τ	PROPN
ejpam-5223	120	9	)	)	PUNCT
ejpam-5223	120	10	,	,	PUNCT
ejpam-5223	120	11	the	the	DET
ejpam-5223	120	12	following	follow	VERB
ejpam-5223	120	13	properties	property	NOUN
ejpam-5223	120	14	are	be	AUX
ejpam-5223	120	15	equivalent	equivalent	ADJ
ejpam-5223	120	16	:	:	PUNCT
ejpam-5223	120	17	(	(	PUNCT
ejpam-5223	120	18	1	1	X
ejpam-5223	120	19	)	)	PUNCT
ejpam-5223	120	20	(	(	PUNCT
ejpam-5223	120	21	x	x	X
ejpam-5223	120	22	,	,	PUNCT
ejpam-5223	120	23	τ	τ	X
ejpam-5223	120	24	)	)	PUNCT
ejpam-5223	120	25	is	be	AUX
ejpam-5223	120	26	f	f	NOUN
ejpam-5223	120	27	-regular	-regular	ADJ
ejpam-5223	120	28	;	;	PUNCT
ejpam-5223	120	29	(	(	PUNCT
ejpam-5223	120	30	2	2	X
ejpam-5223	120	31	)	)	PUNCT
ejpam-5223	120	32	for	for	ADP
ejpam-5223	120	33	any	any	DET
ejpam-5223	120	34	x	x	SYM
ejpam-5223	120	35	∈	∈	PROPN
ejpam-5223	120	36	x	x	X
ejpam-5223	120	37	and	and	CCONJ
ejpam-5223	120	38	any	any	DET
ejpam-5223	120	39	open	open	ADJ
ejpam-5223	120	40	set	set	NOUN
ejpam-5223	120	41	u	u	NOUN
ejpam-5223	120	42	containing	contain	VERB
ejpam-5223	120	43	x	x	PRON
ejpam-5223	120	44	,	,	PUNCT
ejpam-5223	120	45	there	there	PRON
ejpam-5223	120	46	exists	exist	VERB
ejpam-5223	120	47	an	an	DET
ejpam-5223	120	48	f	f	PROPN
ejpam-5223	120	49	-open	-open	NOUN
ejpam-5223	120	50	set	set	VERB
ejpam-5223	120	51	v	v	ADP
ejpam-5223	120	52	such	such	ADJ
ejpam-5223	120	53	that	that	SCONJ
ejpam-5223	120	54	x	x	SYM
ejpam-5223	120	55	∈	∈	NOUN
ejpam-5223	120	56	v	v	ADP
ejpam-5223	120	57	⊆	⊆	NUM
ejpam-5223	120	58	clf	clf	PROPN
ejpam-5223	120	59	(	(	PUNCT
ejpam-5223	120	60	v	v	NOUN
ejpam-5223	120	61	)	)	PUNCT
ejpam-5223	120	62	⊆	⊆	NUM
ejpam-5223	120	63	u	u	NOUN
ejpam-5223	120	64	;	;	PUNCT
ejpam-5223	120	65	(	(	PUNCT
ejpam-5223	120	66	3	3	X
ejpam-5223	120	67	)	)	PUNCT
ejpam-5223	120	68	for	for	ADP
ejpam-5223	120	69	any	any	DET
ejpam-5223	120	70	x	x	SYM
ejpam-5223	120	71	∈	∈	PROPN
ejpam-5223	120	72	x	x	X
ejpam-5223	120	73	and	and	CCONJ
ejpam-5223	120	74	any	any	DET
ejpam-5223	120	75	closed	closed	ADJ
ejpam-5223	120	76	set	set	NOUN
ejpam-5223	120	77	b	b	NOUN
ejpam-5223	120	78	such	such	ADJ
ejpam-5223	120	79	that	that	PRON
ejpam-5223	120	80	x	x	SYM
ejpam-5223	120	81	/∈	/∈	PUNCT
ejpam-5223	121	1	b	b	NOUN
ejpam-5223	121	2	,	,	PUNCT
ejpam-5223	121	3	there	there	PRON
ejpam-5223	121	4	exists	exist	VERB
ejpam-5223	121	5	an	an	DET
ejpam-5223	121	6	f	f	PROPN
ejpam-5223	121	7	-open	-open	PROPN
ejpam-5223	121	8	set	set	VERB
ejpam-5223	121	9	u	u	PRON
ejpam-5223	121	10	such	such	ADJ
ejpam-5223	121	11	that	that	SCONJ
ejpam-5223	121	12	x	x	SYM
ejpam-5223	121	13	∈	∈	PROPN
ejpam-5223	121	14	u	u	NOUN
ejpam-5223	121	15	and	and	CCONJ
ejpam-5223	121	16	b	b	PROPN
ejpam-5223	121	17	∩	∩	PROPN
ejpam-5223	121	18	clf	clf	PROPN
ejpam-5223	121	19	(	(	PUNCT
ejpam-5223	121	20	u	u	NOUN
ejpam-5223	121	21	)	)	PUNCT
ejpam-5223	121	22	=	=	PUNCT
ejpam-5223	121	23	∅.	∅.	NOUN
ejpam-5223	121	24	proof	proof	NOUN
ejpam-5223	121	25	.	.	PUNCT
ejpam-5223	122	1	(	(	PUNCT
ejpam-5223	122	2	1	1	X
ejpam-5223	122	3	)	)	PUNCT
ejpam-5223	122	4	⇒	⇒	NOUN
ejpam-5223	122	5	(	(	PUNCT
ejpam-5223	122	6	2	2	NUM
ejpam-5223	122	7	):	):	PUNCT
ejpam-5223	122	8	let	let	VERB
ejpam-5223	122	9	x	x	PRON
ejpam-5223	122	10	be	be	AUX
ejpam-5223	122	11	an	an	DET
ejpam-5223	122	12	f	f	NOUN
ejpam-5223	122	13	-regular	-regular	ADJ
ejpam-5223	122	14	space	space	NOUN
ejpam-5223	122	15	and	and	CCONJ
ejpam-5223	122	16	u	u	NOUN
ejpam-5223	122	17	be	be	VERB
ejpam-5223	122	18	any	any	DET
ejpam-5223	122	19	open	open	ADJ
ejpam-5223	122	20	set	set	NOUN
ejpam-5223	122	21	containing	contain	VERB
ejpam-5223	122	22	x.	x.	NOUN
ejpam-5223	122	23	let	let	VERB
ejpam-5223	122	24	k	k	NOUN
ejpam-5223	122	25	=	=	PUNCT
ejpam-5223	122	26	x	x	SYM
ejpam-5223	122	27	\	\	PROPN
ejpam-5223	122	28	u	u	PROPN
ejpam-5223	122	29	,	,	PUNCT
ejpam-5223	122	30	then	then	ADV
ejpam-5223	122	31	k	k	PROPN
ejpam-5223	122	32	is	be	AUX
ejpam-5223	122	33	a	a	DET
ejpam-5223	122	34	closed	closed	ADJ
ejpam-5223	122	35	set	set	VERB
ejpam-5223	122	36	not	not	PART
ejpam-5223	122	37	containing	contain	VERB
ejpam-5223	122	38	x.	x.	NOUN
ejpam-5223	122	39	since	since	SCONJ
ejpam-5223	122	40	(	(	PUNCT
ejpam-5223	122	41	x	x	X
ejpam-5223	122	42	,	,	PUNCT
ejpam-5223	122	43	τ	τ	X
ejpam-5223	122	44	)	)	PUNCT
ejpam-5223	122	45	is	be	AUX
ejpam-5223	122	46	f	f	NOUN
ejpam-5223	122	47	-regular	-regular	ADJ
ejpam-5223	122	48	,	,	PUNCT
ejpam-5223	122	49	then	then	ADV
ejpam-5223	122	50	there	there	PRON
ejpam-5223	122	51	exist	exist	VERB
ejpam-5223	122	52	f	f	PROPN
ejpam-5223	122	53	-open	-open	PROPN
ejpam-5223	122	54	sets	set	NOUN
ejpam-5223	122	55	v	v	ADP
ejpam-5223	122	56	,	,	PUNCT
ejpam-5223	122	57	w	w	NOUN
ejpam-5223	122	58	of	of	ADP
ejpam-5223	122	59	x	x	SYM
ejpam-5223	122	60	such	such	ADJ
ejpam-5223	122	61	that	that	SCONJ
ejpam-5223	122	62	x	x	SYM
ejpam-5223	122	63	∈	∈	PROPN
ejpam-5223	122	64	v	v	NOUN
ejpam-5223	122	65	,	,	PUNCT
ejpam-5223	122	66	k	k	PROPN
ejpam-5223	122	67	⊂	⊂	PROPN
ejpam-5223	122	68	w	w	PROPN
ejpam-5223	122	69	and	and	CCONJ
ejpam-5223	122	70	v	v	ADP
ejpam-5223	122	71	∩w	∩w	ADJ
ejpam-5223	122	72	=	=	PUNCT
ejpam-5223	122	73	∅.	∅.	VERB
ejpam-5223	122	74	hence	hence	ADV
ejpam-5223	122	75	clf	clf	PROPN
ejpam-5223	122	76	(	(	PUNCT
ejpam-5223	122	77	v	v	NOUN
ejpam-5223	122	78	)	)	PUNCT
ejpam-5223	122	79	∩w	∩w	PUNCT
ejpam-5223	123	1	=	=	PUNCT
ejpam-5223	123	2	∅.	∅.	VERB
ejpam-5223	123	3	therefore	therefore	ADV
ejpam-5223	123	4	,	,	PUNCT
ejpam-5223	123	5	we	we	PRON
ejpam-5223	123	6	have	have	VERB
ejpam-5223	123	7	x	x	X
ejpam-5223	123	8	∈	∈	NOUN
ejpam-5223	123	9	v	v	ADP
ejpam-5223	123	10	⊆	⊆	NUM
ejpam-5223	123	11	clf	clf	PROPN
ejpam-5223	123	12	(	(	PUNCT
ejpam-5223	123	13	v	v	NOUN
ejpam-5223	123	14	)	)	PUNCT
ejpam-5223	123	15	⊆	⊆	NUM
ejpam-5223	123	16	u	u	NOUN
ejpam-5223	123	17	.	.	PUNCT
ejpam-5223	124	1	(	(	PUNCT
ejpam-5223	124	2	2	2	X
ejpam-5223	124	3	)	)	PUNCT
ejpam-5223	124	4	⇒	⇒	NOUN
ejpam-5223	124	5	(	(	PUNCT
ejpam-5223	124	6	3	3	NUM
ejpam-5223	124	7	):	):	PUNCT
ejpam-5223	124	8	let	let	VERB
ejpam-5223	124	9	x	x	PRON
ejpam-5223	124	10	be	be	AUX
ejpam-5223	124	11	any	any	DET
ejpam-5223	124	12	point	point	NOUN
ejpam-5223	124	13	of	of	ADP
ejpam-5223	124	14	x	x	PROPN
ejpam-5223	124	15	and	and	CCONJ
ejpam-5223	124	16	b	b	NOUN
ejpam-5223	124	17	be	be	AUX
ejpam-5223	124	18	any	any	DET
ejpam-5223	124	19	closed	closed	ADJ
ejpam-5223	124	20	set	set	VERB
ejpam-5223	124	21	in	in	ADP
ejpam-5223	124	22	x	x	PUNCT
ejpam-5223	124	23	not	not	PART
ejpam-5223	124	24	containing	contain	VERB
ejpam-5223	124	25	x.	x.	NOUN
ejpam-5223	124	26	then	then	ADV
ejpam-5223	124	27	x	x	SYM
ejpam-5223	124	28	\	\	PROPN
ejpam-5223	124	29	b	b	PROPN
ejpam-5223	124	30	is	be	AUX
ejpam-5223	124	31	an	an	DET
ejpam-5223	124	32	open	open	ADJ
ejpam-5223	124	33	set	set	NOUN
ejpam-5223	124	34	containing	contain	VERB
ejpam-5223	124	35	x.	x.	NOUN
ejpam-5223	124	36	by	by	ADP
ejpam-5223	124	37	(	(	PUNCT
ejpam-5223	124	38	2	2	NUM
ejpam-5223	124	39	)	)	PUNCT
ejpam-5223	124	40	,	,	PUNCT
ejpam-5223	124	41	there	there	PRON
ejpam-5223	124	42	exists	exist	VERB
ejpam-5223	124	43	an	an	DET
ejpam-5223	124	44	f	f	PROPN
ejpam-5223	124	45	-open	-open	PROPN
ejpam-5223	124	46	set	set	VERB
ejpam-5223	124	47	u	u	PRON
ejpam-5223	124	48	such	such	ADJ
ejpam-5223	124	49	that	that	SCONJ
ejpam-5223	124	50	x	x	SYM
ejpam-5223	124	51	∈	∈	PROPN
ejpam-5223	124	52	u	u	NOUN
ejpam-5223	124	53	⊆	⊆	PROPN
ejpam-5223	124	54	clf	clf	PROPN
ejpam-5223	124	55	(	(	PUNCT
ejpam-5223	124	56	u	u	NOUN
ejpam-5223	124	57	)	)	PUNCT
ejpam-5223	124	58	⊆	⊆	NUM
ejpam-5223	124	59	(	(	PUNCT
ejpam-5223	124	60	x	x	NOUN
ejpam-5223	124	61	\b	\b	ADJ
ejpam-5223	124	62	)	)	PUNCT
ejpam-5223	124	63	.	.	PUNCT
ejpam-5223	125	1	therefore	therefore	ADV
ejpam-5223	125	2	,	,	PUNCT
ejpam-5223	125	3	there	there	PRON
ejpam-5223	125	4	exists	exist	VERB
ejpam-5223	125	5	an	an	DET
ejpam-5223	125	6	f	f	PROPN
ejpam-5223	125	7	-open	-open	PROPN
ejpam-5223	125	8	set	set	VERB
ejpam-5223	125	9	u	u	PRON
ejpam-5223	125	10	such	such	ADJ
ejpam-5223	125	11	that	that	SCONJ
ejpam-5223	125	12	x	x	SYM
ejpam-5223	125	13	∈	∈	PROPN
ejpam-5223	125	14	u	u	NOUN
ejpam-5223	125	15	and	and	CCONJ
ejpam-5223	125	16	b	b	PROPN
ejpam-5223	125	17	∩	∩	PROPN
ejpam-5223	125	18	clf	clf	PROPN
ejpam-5223	125	19	(	(	PUNCT
ejpam-5223	125	20	u	u	NOUN
ejpam-5223	125	21	)	)	PUNCT
ejpam-5223	125	22	=	=	PUNCT
ejpam-5223	125	23	∅.	∅.	X
ejpam-5223	125	24	(	(	PUNCT
ejpam-5223	125	25	3	3	NUM
ejpam-5223	125	26	)	)	PUNCT
ejpam-5223	125	27	⇒	⇒	NOUN
ejpam-5223	125	28	(	(	PUNCT
ejpam-5223	125	29	1	1	NUM
ejpam-5223	125	30	):	):	PUNCT
ejpam-5223	125	31	let	let	VERB
ejpam-5223	125	32	k	k	PRON
ejpam-5223	125	33	be	be	AUX
ejpam-5223	125	34	a	a	DET
ejpam-5223	125	35	closed	closed	ADJ
ejpam-5223	125	36	set	set	VERB
ejpam-5223	125	37	not	not	PART
ejpam-5223	125	38	containing	contain	VERB
ejpam-5223	125	39	x.	x.	NOUN
ejpam-5223	125	40	then	then	ADV
ejpam-5223	125	41	x	x	SYM
ejpam-5223	125	42	∈	∈	PROPN
ejpam-5223	125	43	x	x	PUNCT
ejpam-5223	125	44	\k	\k	NOUN
ejpam-5223	125	45	and	and	CCONJ
ejpam-5223	125	46	x	x	SYM
ejpam-5223	125	47	\k	\k	NOUN
ejpam-5223	125	48	is	be	AUX
ejpam-5223	125	49	an	an	DET
ejpam-5223	125	50	open	open	ADJ
ejpam-5223	125	51	set	set	NOUN
ejpam-5223	125	52	.	.	PUNCT
ejpam-5223	126	1	hence	hence	ADV
ejpam-5223	126	2	there	there	PRON
ejpam-5223	126	3	exists	exist	VERB
ejpam-5223	126	4	an	an	DET
ejpam-5223	126	5	f	f	PROPN
ejpam-5223	126	6	-open	-open	PROPN
ejpam-5223	126	7	set	set	VERB
ejpam-5223	126	8	u	u	PRON
ejpam-5223	126	9	such	such	ADJ
ejpam-5223	126	10	that	that	SCONJ
ejpam-5223	126	11	x	x	SYM
ejpam-5223	126	12	∈	∈	PROPN
ejpam-5223	126	13	u	u	NOUN
ejpam-5223	126	14	and	and	CCONJ
ejpam-5223	126	15	k	k	PROPN
ejpam-5223	126	16	∩	∩	PROPN
ejpam-5223	126	17	clf	clf	PROPN
ejpam-5223	126	18	(	(	PUNCT
ejpam-5223	126	19	u	u	NOUN
ejpam-5223	126	20	)	)	PUNCT
ejpam-5223	126	21	=	=	PUNCT
ejpam-5223	126	22	∅.	∅.	AUX
ejpam-5223	126	23	let	let	VERB
ejpam-5223	126	24	v	v	NOUN
ejpam-5223	126	25	=	=	SYM
ejpam-5223	126	26	x	x	SYM
ejpam-5223	126	27	\	\	PROPN
ejpam-5223	126	28	clf	clf	PROPN
ejpam-5223	126	29	(	(	PUNCT
ejpam-5223	126	30	u	u	NOUN
ejpam-5223	126	31	)	)	PUNCT
ejpam-5223	126	32	.	.	PUNCT
ejpam-5223	127	1	then	then	ADV
ejpam-5223	127	2	v	v	NOUN
ejpam-5223	127	3	is	be	AUX
ejpam-5223	127	4	f	f	PROPN
ejpam-5223	127	5	-open	-open	PROPN
ejpam-5223	127	6	,	,	PUNCT
ejpam-5223	127	7	k	k	PROPN
ejpam-5223	127	8	⊆	⊆	NUM
ejpam-5223	127	9	v	v	NOUN
ejpam-5223	127	10	and	and	CCONJ
ejpam-5223	127	11	u	u	NOUN
ejpam-5223	127	12	∩	∩	NOUN
ejpam-5223	127	13	v	v	ADP
ejpam-5223	127	14	=	=	SYM
ejpam-5223	127	15	u	u	NOUN
ejpam-5223	127	16	∩	∩	NOUN
ejpam-5223	127	17	(	(	PUNCT
ejpam-5223	127	18	x	x	SYM
ejpam-5223	127	19	\	\	PROPN
ejpam-5223	127	20	cl	cl	NOUN
ejpam-5223	127	21	f	f	X
ejpam-5223	127	22	(	(	PUNCT
ejpam-5223	127	23	u	u	NOUN
ejpam-5223	127	24	)	)	PUNCT
ejpam-5223	127	25	)	)	PUNCT
ejpam-5223	128	1	=	=	PUNCT
ejpam-5223	128	2	∅.	∅.	ADP
ejpam-5223	128	3	this	this	PRON
ejpam-5223	128	4	shows	show	VERB
ejpam-5223	128	5	that	that	SCONJ
ejpam-5223	128	6	(	(	PUNCT
ejpam-5223	128	7	x	x	X
ejpam-5223	128	8	,	,	PUNCT
ejpam-5223	128	9	τ	τ	X
ejpam-5223	128	10	)	)	PUNCT
ejpam-5223	128	11	is	be	AUX
ejpam-5223	128	12	f	f	NOUN
ejpam-5223	128	13	-regular	-regular	NOUN
ejpam-5223	128	14	.	.	PUNCT
ejpam-5223	129	1	definition	definition	NOUN
ejpam-5223	129	2	9	9	NUM
ejpam-5223	129	3	.	.	PUNCT
ejpam-5223	130	1	a	a	DET
ejpam-5223	130	2	topological	topological	ADJ
ejpam-5223	130	3	space	space	NOUN
ejpam-5223	130	4	(	(	PUNCT
ejpam-5223	130	5	x	x	X
ejpam-5223	130	6	,	,	PUNCT
ejpam-5223	130	7	τ	τ	X
ejpam-5223	130	8	)	)	PUNCT
ejpam-5223	130	9	is	be	AUX
ejpam-5223	130	10	called	call	VERB
ejpam-5223	130	11	an	an	DET
ejpam-5223	130	12	f−normal	f−normal	ADJ
ejpam-5223	130	13	space	space	NOUN
ejpam-5223	130	14	(	(	PUNCT
ejpam-5223	130	15	briefly	briefly	NOUN
ejpam-5223	130	16	fn−space	fn−space	NOUN
ejpam-5223	130	17	)	)	PUNCT
ejpam-5223	130	18	if	if	SCONJ
ejpam-5223	130	19	for	for	ADP
ejpam-5223	130	20	each	each	DET
ejpam-5223	130	21	pair	pair	NOUN
ejpam-5223	130	22	of	of	ADP
ejpam-5223	130	23	disjoint	disjoint	NOUN
ejpam-5223	130	24	closed	close	VERB
ejpam-5223	130	25	subsets	subset	NOUN
ejpam-5223	130	26	w1	w1	NOUN
ejpam-5223	130	27	and	and	CCONJ
ejpam-5223	130	28	w2	w2	NOUN
ejpam-5223	130	29	of	of	ADP
ejpam-5223	130	30	x	x	PRON
ejpam-5223	130	31	,	,	PUNCT
ejpam-5223	130	32	there	there	PRON
ejpam-5223	130	33	exist	exist	VERB
ejpam-5223	130	34	f−open	f−open	VERB
ejpam-5223	130	35	sets	set	VERB
ejpam-5223	130	36	u	u	NOUN
ejpam-5223	130	37	and	and	CCONJ
ejpam-5223	130	38	v	v	NOUN
ejpam-5223	130	39	in	in	ADP
ejpam-5223	130	40	x	x	NOUN
ejpam-5223	130	41	,	,	PUNCT
ejpam-5223	130	42	such	such	ADJ
ejpam-5223	130	43	that	that	SCONJ
ejpam-5223	130	44	w1	w1	NOUN
ejpam-5223	130	45	⊆	⊆	NUM
ejpam-5223	130	46	u	u	NOUN
ejpam-5223	130	47	,	,	PUNCT
ejpam-5223	130	48	w2	w2	NOUN
ejpam-5223	130	49	⊆	⊆	NUM
ejpam-5223	130	50	v	v	NOUN
ejpam-5223	130	51	,	,	PUNCT
ejpam-5223	130	52	and	and	CCONJ
ejpam-5223	130	53	u∩v	u∩v	PROPN
ejpam-5223	130	54	=	=	X
ejpam-5223	130	55	∅.	∅.	VERB
ejpam-5223	130	56	an	an	DET
ejpam-5223	130	57	f−	f−	PROPN
ejpam-5223	130	58	normal	normal	ADJ
ejpam-5223	130	59	ft1−space	ft1−space	NOUN
ejpam-5223	130	60	is	be	AUX
ejpam-5223	130	61	called	call	VERB
ejpam-5223	130	62	a	a	DET
ejpam-5223	130	63	ft4	ft4	NOUN
ejpam-5223	130	64	−	−	PROPN
ejpam-5223	130	65	space	space	NOUN
ejpam-5223	130	66	.	.	PUNCT
ejpam-5223	130	67	example	example	NOUN
ejpam-5223	131	1	9	9	NUM
ejpam-5223	131	2	.	.	PUNCT
ejpam-5223	132	1	the	the	DET
ejpam-5223	132	2	usual	usual	ADJ
ejpam-5223	132	3	topology	topology	NOUN
ejpam-5223	132	4	for	for	ADP
ejpam-5223	132	5	r	r	NOUN
ejpam-5223	132	6	as	as	ADP
ejpam-5223	132	7	in	in	ADP
ejpam-5223	132	8	example	example	NOUN
ejpam-5223	132	9	5	5	NUM
ejpam-5223	132	10	is	be	AUX
ejpam-5223	132	11	an	an	DET
ejpam-5223	132	12	fn	fn	NOUN
ejpam-5223	132	13	and	and	CCONJ
ejpam-5223	132	14	ft1	ft1	NOUN
ejpam-5223	132	15	−	−	PROPN
ejpam-5223	132	16	space	space	NOUN
ejpam-5223	132	17	and	and	CCONJ
ejpam-5223	132	18	hence	hence	ADV
ejpam-5223	132	19	it	it	PRON
ejpam-5223	132	20	is	be	AUX
ejpam-5223	132	21	an	an	DET
ejpam-5223	132	22	ft4	ft4	NOUN
ejpam-5223	132	23	−	−	PROPN
ejpam-5223	132	24	space	space	NOUN
ejpam-5223	132	25	.	.	PUNCT
ejpam-5223	133	1	remark	remark	NOUN
ejpam-5223	133	2	2	2	NUM
ejpam-5223	133	3	.	.	PUNCT
ejpam-5223	134	1	every	every	DET
ejpam-5223	134	2	f−normal	f−normal	NOUN
ejpam-5223	134	3	space	space	NOUN
ejpam-5223	134	4	in	in	ADP
ejpam-5223	134	5	not	not	PART
ejpam-5223	134	6	necessarily	necessarily	ADV
ejpam-5223	134	7	f−regular	f−regular	NOUN
ejpam-5223	134	8	.	.	PUNCT
ejpam-5223	135	1	m.	m.	NOUN
ejpam-5223	135	2	baloush	baloush	PROPN
ejpam-5223	135	3	et	et	PROPN
ejpam-5223	135	4	al	al	PROPN
ejpam-5223	135	5	.	.	PUNCT
ejpam-5223	135	6	/	/	SYM
ejpam-5223	135	7	eur	eur	PROPN
ejpam-5223	135	8	.	.	PUNCT
ejpam-5223	136	1	j.	j.	PROPN
ejpam-5223	136	2	pure	pure	PROPN
ejpam-5223	136	3	appl	appl	PROPN
ejpam-5223	136	4	.	.	PROPN
ejpam-5223	136	5	math	math	PROPN
ejpam-5223	136	6	,	,	PUNCT
ejpam-5223	136	7	17	17	NUM
ejpam-5223	136	8	(	(	PUNCT
ejpam-5223	136	9	3	3	NUM
ejpam-5223	136	10	)	)	PUNCT
ejpam-5223	136	11	(	(	PUNCT
ejpam-5223	136	12	2024	2024	NUM
ejpam-5223	136	13	)	)	PUNCT
ejpam-5223	136	14	,	,	PUNCT
ejpam-5223	136	15	1463	1463	NUM
ejpam-5223	136	16	-	-	SYM
ejpam-5223	136	17	1470	1470	NUM
ejpam-5223	136	18	1468	1468	NUM
ejpam-5223	136	19	example	example	NOUN
ejpam-5223	136	20	10	10	NUM
ejpam-5223	136	21	.	.	PUNCT
ejpam-5223	137	1	let	let	VERB
ejpam-5223	137	2	us	we	PRON
ejpam-5223	137	3	consider	consider	VERB
ejpam-5223	137	4	the	the	DET
ejpam-5223	137	5	sierpinski	sierpinski	ADJ
ejpam-5223	137	6	space	space	NOUN
ejpam-5223	137	7	,	,	PUNCT
ejpam-5223	137	8	where	where	SCONJ
ejpam-5223	137	9	s	s	VERB
ejpam-5223	137	10	=	=	X
ejpam-5223	137	11	{	{	PUNCT
ejpam-5223	137	12	0	0	NUM
ejpam-5223	137	13	,	,	PUNCT
ejpam-5223	137	14	1	1	NUM
ejpam-5223	137	15	}	}	PUNCT
ejpam-5223	137	16	and	and	CCONJ
ejpam-5223	137	17	τ	τ	PROPN
ejpam-5223	137	18	=	=	SYM
ejpam-5223	137	19	{	{	PUNCT
ejpam-5223	137	20	∅	∅	NOUN
ejpam-5223	137	21	,	,	PUNCT
ejpam-5223	137	22	{	{	PUNCT
ejpam-5223	137	23	1	1	NUM
ejpam-5223	137	24	}	}	PUNCT
ejpam-5223	137	25	,	,	PUNCT
ejpam-5223	137	26	{	{	PUNCT
ejpam-5223	137	27	0	0	NUM
ejpam-5223	137	28	,	,	PUNCT
ejpam-5223	137	29	1	1	NUM
ejpam-5223	137	30	}	}	PUNCT
ejpam-5223	137	31	}	}	PUNCT
ejpam-5223	137	32	.	.	PUNCT
ejpam-5223	138	1	it	it	PRON
ejpam-5223	138	2	is	be	AUX
ejpam-5223	138	3	clear	clear	ADJ
ejpam-5223	138	4	that	that	SCONJ
ejpam-5223	138	5	the	the	DET
ejpam-5223	138	6	sierpinski	sierpinski	ADJ
ejpam-5223	138	7	space	space	NOUN
ejpam-5223	138	8	is	be	AUX
ejpam-5223	138	9	f−normal	f−normal	ADJ
ejpam-5223	138	10	since	since	SCONJ
ejpam-5223	138	11	the	the	DET
ejpam-5223	138	12	only	only	ADJ
ejpam-5223	138	13	closed	closed	ADJ
ejpam-5223	138	14	subsets	subset	NOUN
ejpam-5223	138	15	of	of	ADP
ejpam-5223	138	16	s	s	PRON
ejpam-5223	138	17	are	be	AUX
ejpam-5223	138	18	{	{	PUNCT
ejpam-5223	138	19	0	0	NUM
ejpam-5223	138	20	}	}	PUNCT
ejpam-5223	138	21	and	and	CCONJ
ejpam-5223	138	22	∅	∅	NOUN
ejpam-5223	138	23	,	,	PUNCT
ejpam-5223	138	24	but	but	CCONJ
ejpam-5223	138	25	s	s	NOUN
ejpam-5223	138	26	is	be	AUX
ejpam-5223	138	27	not	not	PART
ejpam-5223	138	28	f	f	NOUN
ejpam-5223	138	29	-	-	NOUN
ejpam-5223	138	30	regular	regular	ADJ
ejpam-5223	138	31	,	,	PUNCT
ejpam-5223	138	32	because	because	SCONJ
ejpam-5223	138	33	1	1	NUM
ejpam-5223	138	34	and	and	CCONJ
ejpam-5223	138	35	{	{	PUNCT
ejpam-5223	138	36	0	0	NOUN
ejpam-5223	138	37	}	}	PUNCT
ejpam-5223	138	38	which	which	PRON
ejpam-5223	138	39	is	be	AUX
ejpam-5223	138	40	closed	close	VERB
ejpam-5223	138	41	set	set	VERB
ejpam-5223	138	42	can	can	AUX
ejpam-5223	138	43	not	not	PART
ejpam-5223	138	44	be	be	AUX
ejpam-5223	138	45	separated	separate	VERB
ejpam-5223	138	46	by	by	ADP
ejpam-5223	138	47	two	two	NUM
ejpam-5223	138	48	disjoint	disjoint	ADJ
ejpam-5223	138	49	f	f	X
ejpam-5223	138	50	-	-	PUNCT
ejpam-5223	138	51	open	open	ADJ
ejpam-5223	138	52	sets	set	NOUN
ejpam-5223	138	53	,	,	PUNCT
ejpam-5223	138	54	i.e.	i.e.	X
ejpam-5223	138	55	,	,	PUNCT
ejpam-5223	138	56	1	1	NUM
ejpam-5223	138	57	/∈	/∈	PUNCT
ejpam-5223	138	58	{	{	PUNCT
ejpam-5223	138	59	0	0	NUM
ejpam-5223	138	60	}	}	PUNCT
ejpam-5223	138	61	which	which	PRON
ejpam-5223	138	62	is	be	AUX
ejpam-5223	138	63	closed	closed	ADJ
ejpam-5223	138	64	sets	set	NOUN
ejpam-5223	138	65	,	,	PUNCT
ejpam-5223	138	66	1	1	NUM
ejpam-5223	138	67	∈	∈	NOUN
ejpam-5223	138	68	{	{	PUNCT
ejpam-5223	138	69	1	1	NUM
ejpam-5223	138	70	}	}	PUNCT
ejpam-5223	138	71	,	,	PUNCT
ejpam-5223	138	72	{	{	PUNCT
ejpam-5223	138	73	0	0	NUM
ejpam-5223	138	74	}	}	PUNCT
ejpam-5223	138	75	⊆	⊆	NUM
ejpam-5223	138	76	{	{	PUNCT
ejpam-5223	138	77	0	0	NUM
ejpam-5223	138	78	,	,	PUNCT
ejpam-5223	138	79	1	1	NUM
ejpam-5223	138	80	}	}	PUNCT
ejpam-5223	138	81	where	where	SCONJ
ejpam-5223	138	82	{	{	PUNCT
ejpam-5223	138	83	1	1	NUM
ejpam-5223	138	84	}	}	PUNCT
ejpam-5223	138	85	,	,	PUNCT
ejpam-5223	138	86	{	{	PUNCT
ejpam-5223	138	87	0	0	NUM
ejpam-5223	138	88	,	,	PUNCT
ejpam-5223	138	89	1	1	NUM
ejpam-5223	138	90	}	}	PUNCT
ejpam-5223	138	91	are	be	AUX
ejpam-5223	138	92	f−open	f−open	VERB
ejpam-5223	138	93	sets	set	NOUN
ejpam-5223	138	94	and	and	CCONJ
ejpam-5223	138	95	{	{	PUNCT
ejpam-5223	138	96	1	1	NUM
ejpam-5223	138	97	}	}	PUNCT
ejpam-5223	138	98	∩	∩	NOUN
ejpam-5223	138	99	{	{	PUNCT
ejpam-5223	138	100	0	0	NUM
ejpam-5223	138	101	,	,	PUNCT
ejpam-5223	138	102	1	1	NUM
ejpam-5223	138	103	}	}	PUNCT
ejpam-5223	138	104	=	=	SYM
ejpam-5223	138	105	{	{	PUNCT
ejpam-5223	138	106	1	1	NUM
ejpam-5223	138	107	}	}	PUNCT
ejpam-5223	138	108	=	=	NOUN
ejpam-5223	138	109	̸	̸	ADJ
ejpam-5223	138	110	∅	∅	NOUN
ejpam-5223	138	111	theorem	theorem	VERB
ejpam-5223	138	112	5	5	NUM
ejpam-5223	138	113	.	.	PUNCT
ejpam-5223	139	1	every	every	DET
ejpam-5223	139	2	ft4	ft4	NOUN
ejpam-5223	139	3	−	−	PROPN
ejpam-5223	139	4	space	space	NOUN
ejpam-5223	139	5	is	be	AUX
ejpam-5223	139	6	an	an	DET
ejpam-5223	139	7	ft3	ft3	NOUN
ejpam-5223	139	8	−	−	NOUN
ejpam-5223	139	9	space	space	NOUN
ejpam-5223	139	10	.	.	PUNCT
ejpam-5223	140	1	proof	proof	NOUN
ejpam-5223	140	2	.	.	PUNCT
ejpam-5223	141	1	let	let	VERB
ejpam-5223	141	2	(	(	PUNCT
ejpam-5223	141	3	x	x	NOUN
ejpam-5223	141	4	,	,	PUNCT
ejpam-5223	141	5	τ	τ	X
ejpam-5223	141	6	)	)	PUNCT
ejpam-5223	141	7	be	be	VERB
ejpam-5223	141	8	an	an	DET
ejpam-5223	141	9	ft4	ft4	NOUN
ejpam-5223	141	10	−	−	PROPN
ejpam-5223	141	11	space	space	NOUN
ejpam-5223	141	12	.	.	PUNCT
ejpam-5223	142	1	then	then	ADV
ejpam-5223	142	2	(	(	PUNCT
ejpam-5223	142	3	x	x	X
ejpam-5223	142	4	,	,	PUNCT
ejpam-5223	142	5	τ	τ	X
ejpam-5223	142	6	)	)	PUNCT
ejpam-5223	142	7	is	be	AUX
ejpam-5223	142	8	an	an	DET
ejpam-5223	142	9	ft1	ft1	PROPN
ejpam-5223	142	10	space	space	NOUN
ejpam-5223	142	11	,	,	PUNCT
ejpam-5223	142	12	hence	hence	ADV
ejpam-5223	142	13	we	we	PRON
ejpam-5223	142	14	need	need	VERB
ejpam-5223	142	15	only	only	ADV
ejpam-5223	142	16	show	show	VERB
ejpam-5223	142	17	that	that	SCONJ
ejpam-5223	142	18	x	x	PRON
ejpam-5223	142	19	is	be	AUX
ejpam-5223	142	20	an	an	DET
ejpam-5223	142	21	fr−	fr−	PROPN
ejpam-5223	142	22	space	space	NOUN
ejpam-5223	142	23	.	.	PUNCT
ejpam-5223	143	1	for	for	ADP
ejpam-5223	143	2	that	that	PRON
ejpam-5223	143	3	,	,	PUNCT
ejpam-5223	143	4	let	let	VERB
ejpam-5223	143	5	k	k	PROPN
ejpam-5223	143	6	⊆	⊆	NUM
ejpam-5223	143	7	x	x	VERB
ejpam-5223	143	8	be	be	AUX
ejpam-5223	143	9	an	an	DET
ejpam-5223	143	10	f	f	NOUN
ejpam-5223	143	11	−	−	NOUN
ejpam-5223	143	12	closed	closed	ADJ
ejpam-5223	143	13	set	set	VERB
ejpam-5223	143	14	such	such	ADJ
ejpam-5223	143	15	that	that	SCONJ
ejpam-5223	143	16	x	x	PROPN
ejpam-5223	143	17	/∈	/∈	PROPN
ejpam-5223	143	18	k.	k.	PROPN
ejpam-5223	144	1	since	since	SCONJ
ejpam-5223	144	2	x	x	PRON
ejpam-5223	144	3	is	be	AUX
ejpam-5223	144	4	an	an	DET
ejpam-5223	144	5	ft1	ft1	PROPN
ejpam-5223	144	6	space	space	NOUN
ejpam-5223	144	7	,	,	PUNCT
ejpam-5223	144	8	then	then	ADV
ejpam-5223	144	9	{	{	PUNCT
ejpam-5223	144	10	x	x	X
ejpam-5223	144	11	}	}	PUNCT
ejpam-5223	144	12	is	be	AUX
ejpam-5223	144	13	an	an	DET
ejpam-5223	144	14	f	f	PROPN
ejpam-5223	144	15	-closed	-close	VERB
ejpam-5223	144	16	set	set	VERB
ejpam-5223	144	17	such	such	ADJ
ejpam-5223	144	18	that	that	SCONJ
ejpam-5223	144	19	{	{	PUNCT
ejpam-5223	144	20	x	x	NOUN
ejpam-5223	144	21	}	}	PUNCT
ejpam-5223	144	22	∩	∩	NOUN
ejpam-5223	144	23	k	k	NOUN
ejpam-5223	145	1	=	=	PUNCT
ejpam-5223	145	2	∅.	∅.	NOUN
ejpam-5223	145	3	since	since	SCONJ
ejpam-5223	145	4	x	x	PRON
ejpam-5223	145	5	is	be	AUX
ejpam-5223	145	6	an	an	DET
ejpam-5223	145	7	fn−space	fn−space	NOUN
ejpam-5223	145	8	,	,	PUNCT
ejpam-5223	145	9	there	there	PRON
ejpam-5223	145	10	exist	exist	VERB
ejpam-5223	145	11	f−open	f−open	VERB
ejpam-5223	145	12	sets	set	VERB
ejpam-5223	145	13	u	u	NOUN
ejpam-5223	145	14	and	and	CCONJ
ejpam-5223	145	15	v	v	NOUN
ejpam-5223	145	16	in	in	ADP
ejpam-5223	145	17	x	x	NOUN
ejpam-5223	145	18	,	,	PUNCT
ejpam-5223	145	19	such	such	ADJ
ejpam-5223	145	20	that	that	SCONJ
ejpam-5223	145	21	{	{	PUNCT
ejpam-5223	145	22	x	x	NOUN
ejpam-5223	145	23	}	}	PUNCT
ejpam-5223	145	24	⊆	⊆	NUM
ejpam-5223	145	25	u	u	NOUN
ejpam-5223	145	26	,	,	PUNCT
ejpam-5223	145	27	k	k	PROPN
ejpam-5223	145	28	⊆	⊆	NUM
ejpam-5223	145	29	v	v	NOUN
ejpam-5223	145	30	,	,	PUNCT
ejpam-5223	145	31	and	and	CCONJ
ejpam-5223	145	32	u	u	NOUN
ejpam-5223	145	33	∩	∩	NOUN
ejpam-5223	145	34	v	v	NOUN
ejpam-5223	145	35	=	=	PUNCT
ejpam-5223	145	36	∅.	∅.	VERB
ejpam-5223	145	37	hence	hence	ADV
ejpam-5223	145	38	,	,	PUNCT
ejpam-5223	145	39	for	for	SCONJ
ejpam-5223	145	40	each	each	DET
ejpam-5223	145	41	closed	close	VERB
ejpam-5223	145	42	subset	subset	NOUN
ejpam-5223	146	1	k	k	PROPN
ejpam-5223	146	2	⊂	⊂	PROPN
ejpam-5223	146	3	x	x	X
ejpam-5223	146	4	and	and	CCONJ
ejpam-5223	146	5	each	each	PRON
ejpam-5223	146	6	x	x	X
ejpam-5223	146	7	/∈	/∈	PUNCT
ejpam-5223	147	1	k	k	NOUN
ejpam-5223	147	2	,	,	PUNCT
ejpam-5223	147	3	there	there	PRON
ejpam-5223	147	4	exist	exist	VERB
ejpam-5223	147	5	f−open	f−open	VERB
ejpam-5223	147	6	sets	set	VERB
ejpam-5223	147	7	u	u	NOUN
ejpam-5223	147	8	and	and	CCONJ
ejpam-5223	147	9	v	v	NOUN
ejpam-5223	147	10	in	in	ADP
ejpam-5223	147	11	x	x	PUNCT
ejpam-5223	147	12	such	such	ADJ
ejpam-5223	147	13	that	that	SCONJ
ejpam-5223	147	14	x	x	SYM
ejpam-5223	147	15	∈	∈	PROPN
ejpam-5223	147	16	u	u	NOUN
ejpam-5223	147	17	,	,	PUNCT
ejpam-5223	147	18	k	k	PROPN
ejpam-5223	147	19	⊆	⊆	NUM
ejpam-5223	147	20	v	v	NOUN
ejpam-5223	147	21	,	,	PUNCT
ejpam-5223	147	22	and	and	CCONJ
ejpam-5223	147	23	u	u	NOUN
ejpam-5223	147	24	∩	∩	NOUN
ejpam-5223	147	25	v	v	NOUN
ejpam-5223	147	26	=	=	PUNCT
ejpam-5223	147	27	∅.	∅.	VERB
ejpam-5223	147	28	therefore	therefore	ADV
ejpam-5223	147	29	,	,	PUNCT
ejpam-5223	147	30	x	x	X
ejpam-5223	147	31	is	be	AUX
ejpam-5223	147	32	fr−	fr−	PROPN
ejpam-5223	147	33	regular	regular	ADJ
ejpam-5223	147	34	.	.	PUNCT
ejpam-5223	148	1	theorem	theorem	VERB
ejpam-5223	148	2	6	6	NUM
ejpam-5223	148	3	.	.	PUNCT
ejpam-5223	149	1	for	for	ADP
ejpam-5223	149	2	a	a	DET
ejpam-5223	149	3	topological	topological	ADJ
ejpam-5223	149	4	space	space	NOUN
ejpam-5223	149	5	(	(	PUNCT
ejpam-5223	149	6	x	x	X
ejpam-5223	149	7	,	,	PUNCT
ejpam-5223	149	8	τ	τ	PROPN
ejpam-5223	149	9	)	)	PUNCT
ejpam-5223	149	10	,	,	PUNCT
ejpam-5223	149	11	the	the	DET
ejpam-5223	149	12	following	follow	VERB
ejpam-5223	149	13	properties	property	NOUN
ejpam-5223	149	14	are	be	AUX
ejpam-5223	149	15	equivalent	equivalent	ADJ
ejpam-5223	149	16	:	:	PUNCT
ejpam-5223	149	17	(	(	PUNCT
ejpam-5223	149	18	1	1	X
ejpam-5223	149	19	)	)	PUNCT
ejpam-5223	149	20	(	(	PUNCT
ejpam-5223	149	21	x	x	X
ejpam-5223	149	22	,	,	PUNCT
ejpam-5223	149	23	τ	τ	X
ejpam-5223	149	24	)	)	PUNCT
ejpam-5223	149	25	is	be	AUX
ejpam-5223	149	26	f	f	PROPN
ejpam-5223	149	27	-normal	-normal	NOUN
ejpam-5223	149	28	;	;	PUNCT
ejpam-5223	149	29	(	(	PUNCT
ejpam-5223	149	30	2	2	X
ejpam-5223	149	31	)	)	PUNCT
ejpam-5223	149	32	for	for	ADP
ejpam-5223	149	33	any	any	DET
ejpam-5223	149	34	closed	closed	ADJ
ejpam-5223	149	35	set	set	VERB
ejpam-5223	149	36	f	f	NOUN
ejpam-5223	149	37	and	and	CCONJ
ejpam-5223	149	38	any	any	DET
ejpam-5223	149	39	open	open	ADJ
ejpam-5223	149	40	set	set	NOUN
ejpam-5223	149	41	u	u	NOUN
ejpam-5223	149	42	containing	contain	VERB
ejpam-5223	149	43	f	f	NOUN
ejpam-5223	149	44	,	,	PUNCT
ejpam-5223	149	45	there	there	PRON
ejpam-5223	149	46	exists	exist	VERB
ejpam-5223	149	47	an	an	DET
ejpam-5223	149	48	f	f	PROPN
ejpam-5223	149	49	-open	-open	NOUN
ejpam-5223	149	50	set	set	VERB
ejpam-5223	149	51	v	v	ADP
ejpam-5223	149	52	such	such	ADJ
ejpam-5223	149	53	that	that	SCONJ
ejpam-5223	149	54	f	f	PROPN
ejpam-5223	149	55	⊆	⊆	NUM
ejpam-5223	149	56	v	v	ADP
ejpam-5223	149	57	⊆	⊆	NUM
ejpam-5223	149	58	clf	clf	PROPN
ejpam-5223	149	59	(	(	PUNCT
ejpam-5223	149	60	v	v	NOUN
ejpam-5223	149	61	)	)	PUNCT
ejpam-5223	149	62	⊆	⊆	NUM
ejpam-5223	149	63	u	u	NOUN
ejpam-5223	149	64	;	;	PUNCT
ejpam-5223	149	65	(	(	PUNCT
ejpam-5223	149	66	3	3	X
ejpam-5223	149	67	)	)	PUNCT
ejpam-5223	149	68	for	for	ADP
ejpam-5223	149	69	any	any	DET
ejpam-5223	149	70	disjoint	disjoint	NOUN
ejpam-5223	149	71	closed	close	VERB
ejpam-5223	149	72	sets	set	NOUN
ejpam-5223	149	73	a	a	DET
ejpam-5223	149	74	,	,	PUNCT
ejpam-5223	149	75	b	b	NOUN
ejpam-5223	149	76	,	,	PUNCT
ejpam-5223	149	77	there	there	PRON
ejpam-5223	149	78	exists	exist	VERB
ejpam-5223	149	79	an	an	DET
ejpam-5223	149	80	f	f	PROPN
ejpam-5223	149	81	-open	-open	PROPN
ejpam-5223	149	82	set	set	VERB
ejpam-5223	149	83	u	u	NOUN
ejpam-5223	149	84	such	such	ADJ
ejpam-5223	149	85	that	that	SCONJ
ejpam-5223	149	86	a	a	DET
ejpam-5223	149	87	⊆	⊆	NUM
ejpam-5223	149	88	u	u	NOUN
ejpam-5223	149	89	and	and	CCONJ
ejpam-5223	149	90	b	b	PROPN
ejpam-5223	149	91	∩	∩	PROPN
ejpam-5223	149	92	clf	clf	PROPN
ejpam-5223	149	93	(	(	PUNCT
ejpam-5223	149	94	u	u	NOUN
ejpam-5223	149	95	)	)	PUNCT
ejpam-5223	149	96	=	=	PUNCT
ejpam-5223	149	97	∅.	∅.	NOUN
ejpam-5223	149	98	proof	proof	NOUN
ejpam-5223	149	99	.	.	PUNCT
ejpam-5223	150	1	the	the	DET
ejpam-5223	150	2	proof	proof	NOUN
ejpam-5223	150	3	is	be	AUX
ejpam-5223	150	4	similar	similar	ADJ
ejpam-5223	150	5	with	with	ADP
ejpam-5223	150	6	theorem	theorem	ADJ
ejpam-5223	150	7	4	4	NUM
ejpam-5223	150	8	.	.	PUNCT
ejpam-5223	150	9	lemma	lemma	PROPN
ejpam-5223	150	10	1	1	X
ejpam-5223	150	11	.	.	PUNCT
ejpam-5223	151	1	let	let	AUX
ejpam-5223	151	2	(	(	PUNCT
ejpam-5223	151	3	x	x	NOUN
ejpam-5223	151	4	,	,	PUNCT
ejpam-5223	151	5	τ	τ	X
ejpam-5223	151	6	)	)	PUNCT
ejpam-5223	151	7	be	be	VERB
ejpam-5223	151	8	a	a	DET
ejpam-5223	151	9	topological	topological	ADJ
ejpam-5223	151	10	space	space	NOUN
ejpam-5223	151	11	and	and	CCONJ
ejpam-5223	151	12	y	y	PROPN
ejpam-5223	151	13	be	be	AUX
ejpam-5223	151	14	a	a	DET
ejpam-5223	151	15	subset	subset	NOUN
ejpam-5223	151	16	of	of	ADP
ejpam-5223	151	17	x.	x.	NOUN
ejpam-5223	151	18	if	if	SCONJ
ejpam-5223	151	19	u	u	NOUN
ejpam-5223	151	20	is	be	AUX
ejpam-5223	151	21	an	an	DET
ejpam-5223	151	22	f	f	PROPN
ejpam-5223	151	23	-open	-open	NOUN
ejpam-5223	151	24	set	set	NOUN
ejpam-5223	151	25	of	of	ADP
ejpam-5223	151	26	x	x	NOUN
ejpam-5223	151	27	,	,	PUNCT
ejpam-5223	151	28	then	then	ADV
ejpam-5223	151	29	u	u	PROPN
ejpam-5223	151	30	∩	∩	NOUN
ejpam-5223	151	31	y	y	PROPN
ejpam-5223	151	32	is	be	AUX
ejpam-5223	151	33	an	an	DET
ejpam-5223	151	34	f	f	PROPN
ejpam-5223	151	35	-open	-open	NOUN
ejpam-5223	151	36	set	set	NOUN
ejpam-5223	151	37	of	of	ADP
ejpam-5223	151	38	the	the	DET
ejpam-5223	151	39	subspace	subspace	NOUN
ejpam-5223	151	40	y	y	PROPN
ejpam-5223	151	41	.	.	PUNCT
ejpam-5223	152	1	proof	proof	NOUN
ejpam-5223	152	2	.	.	PUNCT
ejpam-5223	153	1	since	since	SCONJ
ejpam-5223	153	2	u	u	NOUN
ejpam-5223	153	3	is	be	AUX
ejpam-5223	153	4	open	open	ADJ
ejpam-5223	153	5	in	in	ADP
ejpam-5223	153	6	x	x	PROPN
ejpam-5223	153	7	,	,	PUNCT
ejpam-5223	153	8	u	u	PROPN
ejpam-5223	153	9	∩	∩	NOUN
ejpam-5223	153	10	y	y	PROPN
ejpam-5223	153	11	is	be	AUX
ejpam-5223	153	12	open	open	ADJ
ejpam-5223	153	13	in	in	ADP
ejpam-5223	153	14	y	y	PROPN
ejpam-5223	153	15	.	.	PUNCT
ejpam-5223	154	1	cly	cly	ADV
ejpam-5223	154	2	(	(	PUNCT
ejpam-5223	154	3	u	u	PROPN
ejpam-5223	154	4	∩	∩	NOUN
ejpam-5223	154	5	y	y	NOUN
ejpam-5223	154	6	)	)	PUNCT
ejpam-5223	154	7	\	\	PUNCT
ejpam-5223	155	1	(	(	PUNCT
ejpam-5223	155	2	u	u	NOUN
ejpam-5223	155	3	∩	∩	NOUN
ejpam-5223	155	4	y	y	NOUN
ejpam-5223	155	5	)	)	PUNCT
ejpam-5223	155	6	=	=	SYM
ejpam-5223	156	1	clx(u	clx(u	PROPN
ejpam-5223	156	2	∩	∩	NOUN
ejpam-5223	156	3	y	y	PROPN
ejpam-5223	156	4	)	)	PUNCT
ejpam-5223	156	5	∩	∩	PROPN
ejpam-5223	156	6	y	y	PROPN
ejpam-5223	156	7	\	\	PROPN
ejpam-5223	156	8	(	(	PUNCT
ejpam-5223	156	9	u	u	NOUN
ejpam-5223	156	10	∩	∩	NOUN
ejpam-5223	156	11	y	y	PROPN
ejpam-5223	156	12	)	)	PUNCT
ejpam-5223	156	13	⊆	⊆	NUM
ejpam-5223	156	14	clx(u	clx(u	NOUN
ejpam-5223	156	15	)	)	PUNCT
ejpam-5223	156	16	∩	∩	NOUN
ejpam-5223	156	17	y	y	PROPN
ejpam-5223	156	18	\	\	PROPN
ejpam-5223	156	19	(	(	PUNCT
ejpam-5223	156	20	u	u	NOUN
ejpam-5223	156	21	∩	∩	NOUN
ejpam-5223	156	22	y	y	PROPN
ejpam-5223	156	23	)	)	PUNCT
ejpam-5223	157	1	⊂	⊂	PROPN
ejpam-5223	157	2	clx(u	clx(u	X
ejpam-5223	157	3	)	)	PUNCT
ejpam-5223	157	4	\	\	PROPN
ejpam-5223	157	5	u	u	NOUN
ejpam-5223	157	6	.	.	PUNCT
ejpam-5223	158	1	since	since	SCONJ
ejpam-5223	158	2	u	u	NOUN
ejpam-5223	158	3	is	be	AUX
ejpam-5223	158	4	an	an	DET
ejpam-5223	158	5	f	f	PROPN
ejpam-5223	158	6	-open	-open	NOUN
ejpam-5223	158	7	set	set	NOUN
ejpam-5223	158	8	of	of	ADP
ejpam-5223	158	9	x	x	PROPN
ejpam-5223	158	10	,	,	PUNCT
ejpam-5223	158	11	clx(u	clx(u	PROPN
ejpam-5223	158	12	)	)	PUNCT
ejpam-5223	158	13	\	\	NOUN
ejpam-5223	159	1	u	u	NOUN
ejpam-5223	159	2	is	be	AUX
ejpam-5223	159	3	a	a	DET
ejpam-5223	159	4	finite	finite	ADJ
ejpam-5223	159	5	set	set	NOUN
ejpam-5223	159	6	.	.	PUNCT
ejpam-5223	160	1	therefore	therefore	ADV
ejpam-5223	160	2	,	,	PUNCT
ejpam-5223	160	3	u	u	PROPN
ejpam-5223	160	4	∩	∩	NOUN
ejpam-5223	160	5	y	y	PROPN
ejpam-5223	160	6	is	be	AUX
ejpam-5223	160	7	f	f	PROPN
ejpam-5223	160	8	-open	-open	PROPN
ejpam-5223	160	9	in	in	ADP
ejpam-5223	160	10	the	the	DET
ejpam-5223	160	11	subspace	subspace	NOUN
ejpam-5223	160	12	y	y	PROPN
ejpam-5223	160	13	.	.	PUNCT
ejpam-5223	161	1	theorem	theorem	VERB
ejpam-5223	161	2	7	7	NUM
ejpam-5223	161	3	.	.	PUNCT
ejpam-5223	162	1	if	if	SCONJ
ejpam-5223	162	2	x	x	PRON
ejpam-5223	162	3	is	be	AUX
ejpam-5223	162	4	an	an	DET
ejpam-5223	162	5	fti	fti	PROPN
ejpam-5223	162	6	−	−	PROPN
ejpam-5223	162	7	space	space	NOUN
ejpam-5223	162	8	,	,	PUNCT
ejpam-5223	162	9	then	then	ADV
ejpam-5223	162	10	any	any	DET
ejpam-5223	162	11	subspace	subspace	NOUN
ejpam-5223	162	12	y	y	PROPN
ejpam-5223	162	13	of	of	ADP
ejpam-5223	162	14	x	x	X
ejpam-5223	162	15	is	be	AUX
ejpam-5223	162	16	an	an	DET
ejpam-5223	162	17	fti	fti	PROPN
ejpam-5223	162	18	−	−	PROPN
ejpam-5223	162	19	space	space	NOUN
ejpam-5223	162	20	for	for	ADP
ejpam-5223	162	21	i	i	PROPN
ejpam-5223	162	22	=	=	SYM
ejpam-5223	162	23	0	0	NUM
ejpam-5223	162	24	,	,	PUNCT
ejpam-5223	162	25	1	1	NUM
ejpam-5223	162	26	,	,	PUNCT
ejpam-5223	162	27	2	2	NUM
ejpam-5223	162	28	,	,	PUNCT
ejpam-5223	162	29	3	3	NUM
ejpam-5223	162	30	,	,	PUNCT
ejpam-5223	162	31	4	4	NUM
ejpam-5223	162	32	.	.	PUNCT
ejpam-5223	162	33	proof	proof	NOUN
ejpam-5223	162	34	.	.	PUNCT
ejpam-5223	163	1	we	we	PRON
ejpam-5223	163	2	consider	consider	VERB
ejpam-5223	163	3	only	only	ADV
ejpam-5223	163	4	the	the	DET
ejpam-5223	163	5	cases	case	NOUN
ejpam-5223	163	6	i	i	PRON
ejpam-5223	163	7	=	=	NOUN
ejpam-5223	163	8	1	1	NUM
ejpam-5223	163	9	,	,	PUNCT
ejpam-5223	163	10	3	3	NUM
ejpam-5223	163	11	and	and	CCONJ
ejpam-5223	163	12	the	the	DET
ejpam-5223	163	13	other	other	ADJ
ejpam-5223	163	14	cases	case	NOUN
ejpam-5223	163	15	can	can	AUX
ejpam-5223	163	16	be	be	AUX
ejpam-5223	163	17	proved	prove	VERB
ejpam-5223	163	18	by	by	ADP
ejpam-5223	163	19	the	the	DET
ejpam-5223	163	20	same	same	ADJ
ejpam-5223	163	21	argument	argument	NOUN
ejpam-5223	163	22	.	.	PUNCT
ejpam-5223	164	1	1	1	X
ejpam-5223	164	2	)	)	PUNCT
ejpam-5223	164	3	let	let	VERB
ejpam-5223	164	4	i	i	PRON
ejpam-5223	164	5	=	=	NOUN
ejpam-5223	164	6	1	1	X
ejpam-5223	164	7	.	.	PUNCT
ejpam-5223	165	1	let	let	VERB
ejpam-5223	165	2	x	x	PRON
ejpam-5223	165	3	,	,	PUNCT
ejpam-5223	165	4	y	y	PROPN
ejpam-5223	165	5	be	be	VERB
ejpam-5223	165	6	any	any	DET
ejpam-5223	165	7	distinct	distinct	ADJ
ejpam-5223	165	8	points	point	NOUN
ejpam-5223	165	9	of	of	ADP
ejpam-5223	165	10	a	a	DET
ejpam-5223	165	11	subspace	subspace	NOUN
ejpam-5223	165	12	y	y	PROPN
ejpam-5223	165	13	of	of	ADP
ejpam-5223	165	14	an	an	DET
ejpam-5223	165	15	ft1	ft1	NOUN
ejpam-5223	165	16	-	-	PUNCT
ejpam-5223	165	17	space	space	NOUN
ejpam-5223	165	18	x.	x.	NOUN
ejpam-5223	165	19	there	there	PRON
ejpam-5223	165	20	exists	exist	VERB
ejpam-5223	165	21	an	an	DET
ejpam-5223	165	22	f	f	PROPN
ejpam-5223	165	23	-open	-open	PROPN
ejpam-5223	165	24	set	set	NOUN
ejpam-5223	165	25	u	u	NOUN
ejpam-5223	165	26	of	of	ADP
ejpam-5223	165	27	x	x	SYM
ejpam-5223	165	28	such	such	ADJ
ejpam-5223	165	29	that	that	SCONJ
ejpam-5223	165	30	x	x	SYM
ejpam-5223	165	31	∈	∈	PROPN
ejpam-5223	165	32	u	u	NOUN
ejpam-5223	165	33	and	and	CCONJ
ejpam-5223	165	34	y	y	PROPN
ejpam-5223	165	35	/∈	/∈	PUNCT
ejpam-5223	165	36	u	u	PROPN
ejpam-5223	165	37	.	.	PUNCT
ejpam-5223	166	1	by	by	ADP
ejpam-5223	166	2	lemma	lemma	PROPN
ejpam-5223	166	3	1	1	NUM
ejpam-5223	166	4	,	,	PUNCT
ejpam-5223	166	5	u	u	NOUN
ejpam-5223	166	6	∩	∩	NOUN
ejpam-5223	166	7	y	y	PROPN
ejpam-5223	166	8	is	be	AUX
ejpam-5223	166	9	an	an	DET
ejpam-5223	166	10	f	f	PROPN
ejpam-5223	166	11	-open	-open	NOUN
ejpam-5223	166	12	set	set	NOUN
ejpam-5223	166	13	of	of	ADP
ejpam-5223	166	14	y	y	PRON
ejpam-5223	166	15	such	such	ADJ
ejpam-5223	166	16	that	that	SCONJ
ejpam-5223	166	17	x	x	SYM
ejpam-5223	166	18	∈	∈	PROPN
ejpam-5223	166	19	u	u	NOUN
ejpam-5223	166	20	∩	∩	NOUN
ejpam-5223	166	21	y	y	PROPN
ejpam-5223	166	22	and	and	CCONJ
ejpam-5223	166	23	y	y	PROPN
ejpam-5223	166	24	/∈	/∈	PUNCT
ejpam-5223	167	1	u	u	PROPN
ejpam-5223	167	2	∩	∩	PROPN
ejpam-5223	167	3	y	y	PROPN
ejpam-5223	167	4	.	.	PUNCT
ejpam-5223	168	1	similarly	similarly	ADV
ejpam-5223	168	2	,	,	PUNCT
ejpam-5223	168	3	we	we	PRON
ejpam-5223	168	4	can	can	AUX
ejpam-5223	168	5	find	find	VERB
ejpam-5223	168	6	an	an	DET
ejpam-5223	168	7	f	f	PROPN
ejpam-5223	168	8	open	open	ADV
ejpam-5223	168	9	set	set	VERB
ejpam-5223	168	10	v	v	NOUN
ejpam-5223	168	11	in	in	ADP
ejpam-5223	168	12	y	y	NOUN
ejpam-5223	168	13	containing	contain	VERB
ejpam-5223	168	14	y	y	PROPN
ejpam-5223	168	15	but	but	CCONJ
ejpam-5223	168	16	not	not	PART
ejpam-5223	168	17	x.	x.	NOUN
ejpam-5223	168	18	therefore	therefore	ADV
ejpam-5223	168	19	,	,	PUNCT
ejpam-5223	168	20	the	the	DET
ejpam-5223	168	21	subspace	subspace	NOUN
ejpam-5223	168	22	y	y	PROPN
ejpam-5223	168	23	is	be	AUX
ejpam-5223	168	24	an	an	DET
ejpam-5223	168	25	ft1−space	ft1−space	NOUN
ejpam-5223	168	26	.	.	PUNCT
ejpam-5223	169	1	m.	m.	NOUN
ejpam-5223	169	2	baloush	baloush	PROPN
ejpam-5223	169	3	et	et	PROPN
ejpam-5223	169	4	al	al	PROPN
ejpam-5223	169	5	.	.	PUNCT
ejpam-5223	169	6	/	/	SYM
ejpam-5223	169	7	eur	eur	PROPN
ejpam-5223	169	8	.	.	PUNCT
ejpam-5223	170	1	j.	j.	PROPN
ejpam-5223	170	2	pure	pure	PROPN
ejpam-5223	170	3	appl	appl	PROPN
ejpam-5223	170	4	.	.	PROPN
ejpam-5223	170	5	math	math	PROPN
ejpam-5223	170	6	,	,	PUNCT
ejpam-5223	170	7	17	17	NUM
ejpam-5223	170	8	(	(	PUNCT
ejpam-5223	170	9	3	3	NUM
ejpam-5223	170	10	)	)	PUNCT
ejpam-5223	170	11	(	(	PUNCT
ejpam-5223	170	12	2024	2024	NUM
ejpam-5223	170	13	)	)	PUNCT
ejpam-5223	170	14	,	,	PUNCT
ejpam-5223	170	15	1463	1463	NUM
ejpam-5223	170	16	-	-	SYM
ejpam-5223	170	17	1470	1470	NUM
ejpam-5223	170	18	1469	1469	NUM
ejpam-5223	170	19	2	2	NUM
ejpam-5223	170	20	)	)	PUNCT
ejpam-5223	170	21	let	let	VERB
ejpam-5223	170	22	i	i	PRON
ejpam-5223	170	23	=	=	NOUN
ejpam-5223	171	1	3	3	X
ejpam-5223	171	2	.	.	PUNCT
ejpam-5223	171	3	let	let	VERB
ejpam-5223	171	4	k	k	PRON
ejpam-5223	171	5	be	be	AUX
ejpam-5223	171	6	any	any	DET
ejpam-5223	171	7	closed	closed	ADJ
ejpam-5223	171	8	set	set	VERB
ejpam-5223	171	9	in	in	ADP
ejpam-5223	171	10	y	y	PROPN
ejpam-5223	171	11	and	and	CCONJ
ejpam-5223	172	1	y	y	PROPN
ejpam-5223	172	2	∈	∈	PROPN
ejpam-5223	172	3	y	y	PROPN
ejpam-5223	172	4	\	\	PROPN
ejpam-5223	172	5	k.	k.	PROPN
ejpam-5223	173	1	then	then	ADV
ejpam-5223	173	2	there	there	PRON
ejpam-5223	173	3	exists	exist	VERB
ejpam-5223	173	4	a	a	DET
ejpam-5223	173	5	closed	closed	ADJ
ejpam-5223	173	6	set	set	VERB
ejpam-5223	173	7	kx	kx	PROPN
ejpam-5223	173	8	in	in	ADP
ejpam-5223	173	9	x	x	PUNCT
ejpam-5223	173	10	such	such	ADJ
ejpam-5223	173	11	that	that	SCONJ
ejpam-5223	173	12	k	k	PROPN
ejpam-5223	173	13	=	=	PUNCT
ejpam-5223	173	14	kx	kx	PROPN
ejpam-5223	173	15	∩	∩	PROPN
ejpam-5223	173	16	y	y	PROPN
ejpam-5223	173	17	,	,	PUNCT
ejpam-5223	173	18	where	where	SCONJ
ejpam-5223	173	19	y	y	PROPN
ejpam-5223	173	20	/∈	/∈	PUNCT
ejpam-5223	173	21	kx	kx	PROPN
ejpam-5223	173	22	.	.	PUNCT
ejpam-5223	174	1	since	since	SCONJ
ejpam-5223	174	2	x	x	PROPN
ejpam-5223	174	3	is	be	AUX
ejpam-5223	174	4	ft3	ft3	NUM
ejpam-5223	174	5	,	,	PUNCT
ejpam-5223	174	6	there	there	PRON
ejpam-5223	174	7	exist	exist	VERB
ejpam-5223	174	8	disjoint	disjoint	NOUN
ejpam-5223	174	9	f	f	X
ejpam-5223	174	10	-open	-open	PROPN
ejpam-5223	174	11	sets	set	NOUN
ejpam-5223	174	12	ux	ux	INTJ
ejpam-5223	174	13	,	,	PUNCT
ejpam-5223	174	14	vx	vx	PROPN
ejpam-5223	174	15	in	in	ADP
ejpam-5223	174	16	x	x	X
ejpam-5223	174	17	such	such	ADJ
ejpam-5223	174	18	that	that	SCONJ
ejpam-5223	174	19	y	y	PROPN
ejpam-5223	174	20	∈	∈	PROPN
ejpam-5223	174	21	vx	vx	PROPN
ejpam-5223	174	22	and	and	CCONJ
ejpam-5223	174	23	kx	kx	PROPN
ejpam-5223	174	24	⊂	⊂	PROPN
ejpam-5223	174	25	ux	ux	PROPN
ejpam-5223	174	26	.	.	PUNCT
ejpam-5223	175	1	now	now	ADV
ejpam-5223	175	2	,	,	PUNCT
ejpam-5223	175	3	let	let	VERB
ejpam-5223	175	4	u	u	PRON
ejpam-5223	175	5	=	=	SYM
ejpam-5223	175	6	ux	ux	PROPN
ejpam-5223	175	7	∩	∩	PROPN
ejpam-5223	175	8	y	y	PROPN
ejpam-5223	175	9	,	,	PUNCT
ejpam-5223	175	10	v	v	NOUN
ejpam-5223	175	11	=	=	SYM
ejpam-5223	175	12	vx	vx	PROPN
ejpam-5223	175	13	∩	∩	PROPN
ejpam-5223	175	14	y	y	PROPN
ejpam-5223	175	15	,	,	PUNCT
ejpam-5223	175	16	then	then	ADV
ejpam-5223	175	17	by	by	ADP
ejpam-5223	175	18	lemma	lemma	PROPN
ejpam-5223	175	19	1	1	NUM
ejpam-5223	175	20	,	,	PUNCT
ejpam-5223	175	21	u	u	NOUN
ejpam-5223	175	22	,	,	PUNCT
ejpam-5223	175	23	v	v	NOUN
ejpam-5223	175	24	are	be	AUX
ejpam-5223	175	25	f	f	NUM
ejpam-5223	175	26	-open	-open	NOUN
ejpam-5223	175	27	sets	set	NOUN
ejpam-5223	175	28	in	in	ADP
ejpam-5223	175	29	y	y	PROPN
ejpam-5223	175	30	and	and	CCONJ
ejpam-5223	175	31	k	k	PROPN
ejpam-5223	175	32	=	=	PROPN
ejpam-5223	175	33	kx	kx	PROPN
ejpam-5223	175	34	∩y	∩y	PROPN
ejpam-5223	175	35	⊂	⊂	PROPN
ejpam-5223	175	36	ux	ux	PROPN
ejpam-5223	175	37	∩y	∩y	PROPN
ejpam-5223	175	38	=	=	SYM
ejpam-5223	175	39	u	u	PROPN
ejpam-5223	175	40	and	and	CCONJ
ejpam-5223	175	41	y	y	PROPN
ejpam-5223	175	42	∈	∈	PROPN
ejpam-5223	175	43	vx	vx	PROPN
ejpam-5223	175	44	∩y	∩y	NOUN
ejpam-5223	175	45	=	=	PUNCT
ejpam-5223	175	46	v	v	PROPN
ejpam-5223	175	47	.	.	PUNCT
ejpam-5223	176	1	moreover	moreover	ADV
ejpam-5223	176	2	,	,	PUNCT
ejpam-5223	176	3	u	u	PROPN
ejpam-5223	176	4	∩v	∩v	NOUN
ejpam-5223	176	5	⊂	⊂	X
ejpam-5223	176	6	ux	ux	ADV
ejpam-5223	176	7	∩vx	∩vx	VERB
ejpam-5223	176	8	=	=	PUNCT
ejpam-5223	176	9	∅.	∅.	VERB
ejpam-5223	176	10	therefore	therefore	ADV
ejpam-5223	176	11	,	,	PUNCT
ejpam-5223	176	12	y	y	PROPN
ejpam-5223	176	13	is	be	AUX
ejpam-5223	176	14	ft3	ft3	PROPN
ejpam-5223	176	15	.	.	PUNCT
ejpam-5223	177	1	lemma	lemma	PROPN
ejpam-5223	177	2	2	2	NUM
ejpam-5223	177	3	.	.	PUNCT
ejpam-5223	178	1	[	[	X
ejpam-5223	178	2	2	2	NUM
ejpam-5223	178	3	]	]	X
ejpam-5223	178	4	let	let	VERB
ejpam-5223	178	5	(	(	PUNCT
ejpam-5223	178	6	x	x	NOUN
ejpam-5223	178	7	,	,	PUNCT
ejpam-5223	178	8	τ	τ	X
ejpam-5223	178	9	)	)	PUNCT
ejpam-5223	178	10	be	be	VERB
ejpam-5223	178	11	a	a	DET
ejpam-5223	178	12	topological	topological	ADJ
ejpam-5223	178	13	space	space	NOUN
ejpam-5223	178	14	.	.	PUNCT
ejpam-5223	179	1	for	for	ADP
ejpam-5223	179	2	f	f	PROPN
ejpam-5223	179	3	-open	-open	PROPN
ejpam-5223	179	4	sets	set	NOUN
ejpam-5223	179	5	of	of	ADP
ejpam-5223	179	6	x	x	PRON
ejpam-5223	179	7	,	,	PUNCT
ejpam-5223	179	8	the	the	DET
ejpam-5223	179	9	following	follow	VERB
ejpam-5223	179	10	properties	property	NOUN
ejpam-5223	179	11	hold	hold	VERB
ejpam-5223	179	12	:	:	PUNCT
ejpam-5223	179	13	(	(	PUNCT
ejpam-5223	179	14	1	1	X
ejpam-5223	179	15	)	)	PUNCT
ejpam-5223	179	16	the	the	DET
ejpam-5223	179	17	finite	finite	PROPN
ejpam-5223	179	18	union	union	PROPN
ejpam-5223	179	19	of	of	ADP
ejpam-5223	179	20	f	f	PROPN
ejpam-5223	179	21	-open	-open	PROPN
ejpam-5223	179	22	sets	set	NOUN
ejpam-5223	179	23	is	be	AUX
ejpam-5223	179	24	f	f	PROPN
ejpam-5223	179	25	-open	-open	PROPN
ejpam-5223	179	26	,	,	PUNCT
ejpam-5223	179	27	(	(	PUNCT
ejpam-5223	179	28	2	2	X
ejpam-5223	179	29	)	)	PUNCT
ejpam-5223	179	30	the	the	DET
ejpam-5223	179	31	finite	finite	ADJ
ejpam-5223	179	32	intersection	intersection	NOUN
ejpam-5223	179	33	of	of	ADP
ejpam-5223	179	34	f	f	PROPN
ejpam-5223	179	35	-open	-open	PROPN
ejpam-5223	179	36	sets	set	NOUN
ejpam-5223	179	37	is	be	AUX
ejpam-5223	179	38	f	f	PROPN
ejpam-5223	179	39	-open	-open	PROPN
ejpam-5223	179	40	.	.	PUNCT
ejpam-5223	180	1	theorem	theorem	NOUN
ejpam-5223	180	2	8	8	NUM
ejpam-5223	180	3	.	.	PUNCT
ejpam-5223	181	1	let	let	AUX
ejpam-5223	181	2	(	(	PUNCT
ejpam-5223	181	3	x	x	NOUN
ejpam-5223	181	4	,	,	PUNCT
ejpam-5223	181	5	τ	τ	X
ejpam-5223	181	6	)	)	PUNCT
ejpam-5223	181	7	be	be	VERB
ejpam-5223	181	8	a	a	DET
ejpam-5223	181	9	topological	topological	ADJ
ejpam-5223	181	10	space	space	NOUN
ejpam-5223	181	11	.	.	PUNCT
ejpam-5223	182	1	then	then	ADV
ejpam-5223	182	2	every	every	DET
ejpam-5223	182	3	fti	fti	PROPN
ejpam-5223	182	4	space	space	NOUN
ejpam-5223	182	5	is	be	AUX
ejpam-5223	182	6	a	a	DET
ejpam-5223	182	7	ti	ti	NOUN
ejpam-5223	182	8	space	space	NOUN
ejpam-5223	182	9	for	for	ADP
ejpam-5223	182	10	i	i	PROPN
ejpam-5223	182	11	=	=	SYM
ejpam-5223	182	12	0	0	NUM
ejpam-5223	182	13	,	,	PUNCT
ejpam-5223	182	14	1	1	NUM
ejpam-5223	182	15	,	,	PUNCT
ejpam-5223	182	16	2	2	NUM
ejpam-5223	182	17	,	,	PUNCT
ejpam-5223	182	18	3	3	NUM
ejpam-5223	182	19	,	,	PUNCT
ejpam-5223	182	20	4	4	NUM
ejpam-5223	182	21	.	.	PUNCT
ejpam-5223	183	1	however	however	ADV
ejpam-5223	183	2	,	,	PUNCT
ejpam-5223	183	3	the	the	DET
ejpam-5223	183	4	converse	converse	NOUN
ejpam-5223	183	5	is	be	AUX
ejpam-5223	183	6	true	true	ADJ
ejpam-5223	183	7	whenever	whenever	SCONJ
ejpam-5223	183	8	x	x	PRON
ejpam-5223	183	9	is	be	AUX
ejpam-5223	183	10	finite	finite	ADJ
ejpam-5223	183	11	.	.	PUNCT
ejpam-5223	184	1	proof	proof	NOUN
ejpam-5223	184	2	.	.	PUNCT
ejpam-5223	185	1	easy	easy	ADJ
ejpam-5223	185	2	,	,	PUNCT
ejpam-5223	185	3	since	since	SCONJ
ejpam-5223	185	4	f−open	f−open	ADP
ejpam-5223	185	5	sets	set	NOUN
ejpam-5223	185	6	are	be	AUX
ejpam-5223	185	7	open	open	ADJ
ejpam-5223	185	8	sets	set	NOUN
ejpam-5223	185	9	.	.	PUNCT
ejpam-5223	186	1	for	for	ADP
ejpam-5223	186	2	the	the	DET
ejpam-5223	186	3	converse	converse	NOUN
ejpam-5223	186	4	,	,	PUNCT
ejpam-5223	186	5	let	let	VERB
ejpam-5223	186	6	x	x	PRON
ejpam-5223	186	7	be	be	AUX
ejpam-5223	186	8	a	a	DET
ejpam-5223	186	9	finite	finite	ADJ
ejpam-5223	186	10	set	set	NOUN
ejpam-5223	186	11	,	,	PUNCT
ejpam-5223	186	12	then	then	ADV
ejpam-5223	186	13	every	every	DET
ejpam-5223	186	14	open	open	ADJ
ejpam-5223	186	15	set	set	NOUN
ejpam-5223	186	16	is	be	AUX
ejpam-5223	186	17	a	a	DET
ejpam-5223	186	18	f−open	f−open	NOUN
ejpam-5223	186	19	set	set	NOUN
ejpam-5223	186	20	and	and	CCONJ
ejpam-5223	186	21	then	then	ADV
ejpam-5223	186	22	every	every	DET
ejpam-5223	186	23	ti	ti	NOUN
ejpam-5223	186	24	space	space	NOUN
ejpam-5223	186	25	is	be	AUX
ejpam-5223	186	26	a	a	DET
ejpam-5223	186	27	fti	fti	PROPN
ejpam-5223	186	28	space	space	NOUN
ejpam-5223	186	29	for	for	ADP
ejpam-5223	186	30	i	i	PROPN
ejpam-5223	186	31	=	=	SYM
ejpam-5223	186	32	0	0	NUM
ejpam-5223	186	33	,	,	PUNCT
ejpam-5223	186	34	1	1	NUM
ejpam-5223	186	35	,	,	PUNCT
ejpam-5223	186	36	2	2	NUM
ejpam-5223	186	37	,	,	PUNCT
ejpam-5223	186	38	3	3	NUM
ejpam-5223	186	39	,	,	PUNCT
ejpam-5223	186	40	4	4	NUM
ejpam-5223	186	41	.	.	PUNCT
ejpam-5223	187	1	theorem	theorem	NOUN
ejpam-5223	187	2	9	9	NUM
ejpam-5223	187	3	.	.	PUNCT
ejpam-5223	188	1	if	if	SCONJ
ejpam-5223	188	2	(	(	PUNCT
ejpam-5223	188	3	x	x	NOUN
ejpam-5223	188	4	,	,	PUNCT
ejpam-5223	188	5	τ	τ	X
ejpam-5223	188	6	)	)	PUNCT
ejpam-5223	188	7	is	be	AUX
ejpam-5223	188	8	f	f	PROPN
ejpam-5223	188	9	-compact	-compact	PROPN
ejpam-5223	188	10	and	and	CCONJ
ejpam-5223	188	11	ft2	ft2	NOUN
ejpam-5223	188	12	,	,	PUNCT
ejpam-5223	188	13	then	then	ADV
ejpam-5223	188	14	(	(	PUNCT
ejpam-5223	188	15	x	x	X
ejpam-5223	188	16	,	,	PUNCT
ejpam-5223	188	17	τ	τ	X
ejpam-5223	188	18	)	)	PUNCT
ejpam-5223	188	19	is	be	AUX
ejpam-5223	188	20	ft4	ft4	PROPN
ejpam-5223	188	21	.	.	PUNCT
ejpam-5223	189	1	proof	proof	NOUN
ejpam-5223	189	2	.	.	PUNCT
ejpam-5223	190	1	let	let	VERB
ejpam-5223	190	2	k	k	NOUN
ejpam-5223	190	3	,	,	PUNCT
ejpam-5223	190	4	l	l	NOUN
ejpam-5223	190	5	be	be	VERB
ejpam-5223	190	6	any	any	DET
ejpam-5223	190	7	disjoint	disjoint	ADJ
ejpam-5223	190	8	closed	close	VERB
ejpam-5223	190	9	sets	set	NOUN
ejpam-5223	190	10	.	.	PUNCT
ejpam-5223	191	1	then	then	ADV
ejpam-5223	191	2	they	they	PRON
ejpam-5223	191	3	are	be	AUX
ejpam-5223	191	4	f	f	PROPN
ejpam-5223	191	5	-compact	-compact	PROPN
ejpam-5223	191	6	.	.	PUNCT
ejpam-5223	192	1	let	let	VERB
ejpam-5223	192	2	k	k	PRON
ejpam-5223	192	3	be	be	AUX
ejpam-5223	192	4	any	any	DET
ejpam-5223	192	5	point	point	NOUN
ejpam-5223	192	6	of	of	ADP
ejpam-5223	192	7	k.	k.	NOUN
ejpam-5223	192	8	for	for	ADP
ejpam-5223	192	9	any	any	DET
ejpam-5223	192	10	pointx	pointx	VERB
ejpam-5223	192	11	∈	∈	PROPN
ejpam-5223	192	12	l	l	NOUN
ejpam-5223	192	13	,	,	PUNCT
ejpam-5223	192	14	x	x	PROPN
ejpam-5223	192	15	/∈	/∈	PUNCT
ejpam-5223	193	1	k	k	PROPN
ejpam-5223	193	2	and	and	CCONJ
ejpam-5223	193	3	x	x	PROPN
ejpam-5223	193	4	̸=	̸=	PROPN
ejpam-5223	193	5	k.	k.	PROPN
ejpam-5223	194	1	since	since	SCONJ
ejpam-5223	194	2	(	(	PUNCT
ejpam-5223	194	3	x	x	X
ejpam-5223	194	4	,	,	PUNCT
ejpam-5223	194	5	τ	τ	X
ejpam-5223	194	6	)	)	PUNCT
ejpam-5223	194	7	is	be	AUX
ejpam-5223	194	8	ft2	ft2	NOUN
ejpam-5223	194	9	,	,	PUNCT
ejpam-5223	194	10	there	there	PRON
ejpam-5223	194	11	exist	exist	VERB
ejpam-5223	194	12	disjoint	disjoint	NOUN
ejpam-5223	194	13	f	f	PROPN
ejpam-5223	194	14	-open	-open	PROPN
ejpam-5223	194	15	sets	set	NOUN
ejpam-5223	194	16	ux(k	ux(k	NOUN
ejpam-5223	194	17	)	)	PUNCT
ejpam-5223	194	18	and	and	CCONJ
ejpam-5223	194	19	vk(x	vk(x	NOUN
ejpam-5223	194	20	)	)	PUNCT
ejpam-5223	194	21	such	such	ADJ
ejpam-5223	194	22	that	that	SCONJ
ejpam-5223	194	23	k	k	PROPN
ejpam-5223	194	24	∈	∈	PROPN
ejpam-5223	194	25	ux(k	ux(k	NOUN
ejpam-5223	194	26	)	)	PUNCT
ejpam-5223	194	27	and	and	CCONJ
ejpam-5223	194	28	x	x	PUNCT
ejpam-5223	194	29	∈	∈	NOUN
ejpam-5223	194	30	vk(x	vk(x	NOUN
ejpam-5223	194	31	)	)	PUNCT
ejpam-5223	194	32	.	.	PUNCT
ejpam-5223	195	1	now	now	ADV
ejpam-5223	195	2	,	,	PUNCT
ejpam-5223	195	3	fix	fix	NOUN
ejpam-5223	195	4	x	x	SYM
ejpam-5223	195	5	,	,	PUNCT
ejpam-5223	195	6	then	then	ADV
ejpam-5223	195	7	∪{ux(k	∪{ux(k	NOUN
ejpam-5223	195	8	)	)	PUNCT
ejpam-5223	195	9	:	:	PUNCT
ejpam-5223	196	1	k	k	PROPN
ejpam-5223	196	2	∈	∈	PROPN
ejpam-5223	196	3	k	k	X
ejpam-5223	196	4	}	}	PUNCT
ejpam-5223	196	5	is	be	AUX
ejpam-5223	196	6	f	f	PROPN
ejpam-5223	196	7	-open	-open	ADJ
ejpam-5223	196	8	cover	cover	NOUN
ejpam-5223	196	9	of	of	ADP
ejpam-5223	196	10	k	k	PROPN
ejpam-5223	196	11	and	and	CCONJ
ejpam-5223	196	12	there	there	PRON
ejpam-5223	196	13	exists	exist	VERB
ejpam-5223	196	14	a	a	DET
ejpam-5223	196	15	finite	finite	NOUN
ejpam-5223	196	16	subset	subset	VERB
ejpam-5223	196	17	k0	k0	PROPN
ejpam-5223	196	18	of	of	ADP
ejpam-5223	196	19	k	k	PROPN
ejpam-5223	196	20	such	such	ADJ
ejpam-5223	196	21	that	that	SCONJ
ejpam-5223	196	22	k	k	PROPN
ejpam-5223	196	23	⊂	⊂	PROPN
ejpam-5223	196	24	∪{ux(k	∪{ux(k	PROPN
ejpam-5223	196	25	)	)	PUNCT
ejpam-5223	196	26	:	:	PUNCT
ejpam-5223	197	1	k	k	PROPN
ejpam-5223	197	2	∈	∈	PROPN
ejpam-5223	197	3	k0	k0	PROPN
ejpam-5223	197	4	}	}	PUNCT
ejpam-5223	197	5	.	.	PUNCT
ejpam-5223	198	1	now	now	ADV
ejpam-5223	198	2	,	,	PUNCT
ejpam-5223	198	3	put	put	VERB
ejpam-5223	198	4	u(x	u(x	NOUN
ejpam-5223	198	5	)	)	PUNCT
ejpam-5223	198	6	=	=	SYM
ejpam-5223	198	7	∪{ux(k	∪{ux(k	NOUN
ejpam-5223	198	8	)	)	PUNCT
ejpam-5223	198	9	:	:	PUNCT
ejpam-5223	199	1	k	k	PROPN
ejpam-5223	199	2	∈	∈	PROPN
ejpam-5223	199	3	k0	k0	PROPN
ejpam-5223	199	4	}	}	PUNCT
ejpam-5223	199	5	and	and	CCONJ
ejpam-5223	199	6	vk0(x	vk0(x	NOUN
ejpam-5223	199	7	)	)	PUNCT
ejpam-5223	199	8	=	=	SYM
ejpam-5223	199	9	∩{vk(x	∩{vk(x	PROPN
ejpam-5223	199	10	)	)	PUNCT
ejpam-5223	199	11	:	:	PUNCT
ejpam-5223	200	1	k	k	PROPN
ejpam-5223	200	2	∈	∈	PROPN
ejpam-5223	200	3	k0	k0	PROPN
ejpam-5223	200	4	}	}	PUNCT
ejpam-5223	200	5	.	.	PUNCT
ejpam-5223	201	1	then	then	ADV
ejpam-5223	201	2	u(x	u(x	NOUN
ejpam-5223	201	3	)	)	PUNCT
ejpam-5223	201	4	∩	∩	NOUN
ejpam-5223	201	5	vk0(x	vk0(x	NOUN
ejpam-5223	201	6	)	)	PUNCT
ejpam-5223	201	7	=	=	NOUN
ejpam-5223	201	8	∅	∅	NOUN
ejpam-5223	201	9	for	for	ADP
ejpam-5223	201	10	each	each	DET
ejpam-5223	201	11	x	x	SYM
ejpam-5223	201	12	∈	∈	PROPN
ejpam-5223	201	13	l.	l.	NOUN
ejpam-5223	201	14	since	since	SCONJ
ejpam-5223	201	15	∪{vk0(x	∪{vk0(x	PROPN
ejpam-5223	201	16	)	)	PUNCT
ejpam-5223	201	17	:	:	PUNCT
ejpam-5223	202	1	x	x	X
ejpam-5223	202	2	∈	∈	PROPN
ejpam-5223	202	3	l	l	NOUN
ejpam-5223	202	4	}	}	PUNCT
ejpam-5223	202	5	is	be	AUX
ejpam-5223	202	6	an	an	DET
ejpam-5223	202	7	f	f	PROPN
ejpam-5223	202	8	-open	-open	ADJ
ejpam-5223	202	9	cover	cover	NOUN
ejpam-5223	202	10	of	of	ADP
ejpam-5223	202	11	l	l	NOUN
ejpam-5223	202	12	and	and	CCONJ
ejpam-5223	202	13	l	l	NOUN
ejpam-5223	202	14	is	be	AUX
ejpam-5223	202	15	f	f	PROPN
ejpam-5223	202	16	-compact	-compact	PROPN
ejpam-5223	202	17	,	,	PUNCT
ejpam-5223	202	18	there	there	PRON
ejpam-5223	202	19	exists	exist	VERB
ejpam-5223	202	20	a	a	DET
ejpam-5223	202	21	finite	finite	NOUN
ejpam-5223	202	22	subset	subset	VERB
ejpam-5223	202	23	l0	l0	PROPN
ejpam-5223	202	24	of	of	ADP
ejpam-5223	202	25	l	l	NOUN
ejpam-5223	202	26	such	such	ADJ
ejpam-5223	202	27	that	that	SCONJ
ejpam-5223	202	28	l	l	NOUN
ejpam-5223	202	29	⊂	⊂	X
ejpam-5223	202	30	∪{vk0(x	∪{vk0(x	PROPN
ejpam-5223	202	31	)	)	PUNCT
ejpam-5223	202	32	:	:	PUNCT
ejpam-5223	203	1	x	x	X
ejpam-5223	203	2	∈	∈	PROPN
ejpam-5223	203	3	l0	l0	PROPN
ejpam-5223	203	4	}	}	PUNCT
ejpam-5223	203	5	.	.	PUNCT
ejpam-5223	204	1	now	now	ADV
ejpam-5223	204	2	,	,	PUNCT
ejpam-5223	204	3	put	put	VERB
ejpam-5223	204	4	vl	vl	ADP
ejpam-5223	204	5	=	=	NOUN
ejpam-5223	204	6	⊂	⊂	NOUN
ejpam-5223	204	7	∪{vk0(x	∪{vk0(x	ADJ
ejpam-5223	204	8	)	)	PUNCT
ejpam-5223	204	9	:	:	PUNCT
ejpam-5223	205	1	x	x	X
ejpam-5223	205	2	∈	∈	PROPN
ejpam-5223	205	3	l0	l0	PROPN
ejpam-5223	205	4	}	}	PUNCT
ejpam-5223	205	5	and	and	CCONJ
ejpam-5223	205	6	uk	uk	PROPN
ejpam-5223	205	7	=	=	SYM
ejpam-5223	205	8	∩{u(x	∩{u(x	PROPN
ejpam-5223	205	9	)	)	PUNCT
ejpam-5223	205	10	:	:	PUNCT
ejpam-5223	205	11	x	x	X
ejpam-5223	205	12	∈	∈	PROPN
ejpam-5223	205	13	l0	l0	PROPN
ejpam-5223	205	14	}	}	PUNCT
ejpam-5223	205	15	.	.	PUNCT
ejpam-5223	206	1	then	then	ADV
ejpam-5223	206	2	,	,	PUNCT
ejpam-5223	206	3	by	by	ADP
ejpam-5223	206	4	lemma	lemma	PROPN
ejpam-5223	206	5	2	2	NUM
ejpam-5223	206	6	,	,	PUNCT
ejpam-5223	206	7	uk	uk	PROPN
ejpam-5223	206	8	,	,	PUNCT
ejpam-5223	206	9	vl	vl	PROPN
ejpam-5223	206	10	are	be	AUX
ejpam-5223	206	11	disjoint	disjoint	NOUN
ejpam-5223	206	12	f	f	X
ejpam-5223	206	13	-open	-open	NOUN
ejpam-5223	206	14	sets	set	VERB
ejpam-5223	206	15	such	such	ADJ
ejpam-5223	206	16	that	that	SCONJ
ejpam-5223	206	17	l	l	PROPN
ejpam-5223	206	18	⊂	⊂	PROPN
ejpam-5223	207	1	vl	vl	PROPN
ejpam-5223	207	2	,	,	PUNCT
ejpam-5223	207	3	k	k	PROPN
ejpam-5223	207	4	⊂	⊂	PROPN
ejpam-5223	207	5	uk	uk	PROPN
ejpam-5223	207	6	.	.	PUNCT
ejpam-5223	207	7	therefore	therefore	ADV
ejpam-5223	207	8	,	,	PUNCT
ejpam-5223	207	9	(	(	PUNCT
ejpam-5223	207	10	x	x	X
ejpam-5223	207	11	,	,	PUNCT
ejpam-5223	207	12	τ	τ	X
ejpam-5223	207	13	)	)	PUNCT
ejpam-5223	207	14	is	be	AUX
ejpam-5223	207	15	ft4	ft4	PROPN
ejpam-5223	207	16	.	.	PUNCT
ejpam-5223	208	1	definition	definition	NOUN
ejpam-5223	208	2	10	10	NUM
ejpam-5223	208	3	.	.	PUNCT
ejpam-5223	209	1	a	a	DET
ejpam-5223	209	2	function	function	NOUN
ejpam-5223	209	3	f	f	NOUN
ejpam-5223	209	4	:	:	PUNCT
ejpam-5223	209	5	(	(	PUNCT
ejpam-5223	209	6	x	x	X
ejpam-5223	209	7	,	,	PUNCT
ejpam-5223	209	8	τ	τ	X
ejpam-5223	209	9	)	)	PUNCT
ejpam-5223	209	10	→	→	SYM
ejpam-5223	209	11	(	(	PUNCT
ejpam-5223	209	12	y	y	PROPN
ejpam-5223	209	13	,	,	PUNCT
ejpam-5223	209	14	σ	σ	PROPN
ejpam-5223	209	15	)	)	PUNCT
ejpam-5223	209	16	is	be	AUX
ejpam-5223	209	17	said	say	VERB
ejpam-5223	209	18	to	to	PART
ejpam-5223	209	19	be	be	AUX
ejpam-5223	209	20	f	f	PROPN
ejpam-5223	209	21	-closed	-close	VERB
ejpam-5223	209	22	preserving	preserve	VERB
ejpam-5223	209	23	if	if	SCONJ
ejpam-5223	209	24	for	for	ADP
ejpam-5223	209	25	any	any	DET
ejpam-5223	209	26	f	f	PROPN
ejpam-5223	209	27	-closed	-close	VERB
ejpam-5223	209	28	set	set	NOUN
ejpam-5223	209	29	k	k	PROPN
ejpam-5223	209	30	of	of	ADP
ejpam-5223	209	31	x	x	PRON
ejpam-5223	209	32	,	,	PUNCT
ejpam-5223	209	33	f(k	f(k	VERB
ejpam-5223	209	34	)	)	PUNCT
ejpam-5223	209	35	is	be	AUX
ejpam-5223	209	36	f	f	PROPN
ejpam-5223	209	37	-closed	-close	VERB
ejpam-5223	209	38	in	in	ADP
ejpam-5223	209	39	y	y	PROPN
ejpam-5223	209	40	.	.	PUNCT
ejpam-5223	210	1	theorem	theorem	ADJ
ejpam-5223	210	2	10	10	NUM
ejpam-5223	210	3	.	.	PUNCT
ejpam-5223	211	1	a	a	DET
ejpam-5223	211	2	surjective	surjective	ADJ
ejpam-5223	211	3	function	function	NOUN
ejpam-5223	211	4	f	f	NOUN
ejpam-5223	211	5	:	:	PUNCT
ejpam-5223	211	6	(	(	PUNCT
ejpam-5223	211	7	x	x	X
ejpam-5223	211	8	,	,	PUNCT
ejpam-5223	211	9	τ	τ	X
ejpam-5223	211	10	)	)	PUNCT
ejpam-5223	211	11	→	→	SYM
ejpam-5223	211	12	(	(	PUNCT
ejpam-5223	211	13	y	y	PROPN
ejpam-5223	211	14	,	,	PUNCT
ejpam-5223	211	15	σ	σ	PROPN
ejpam-5223	211	16	)	)	PUNCT
ejpam-5223	211	17	is	be	AUX
ejpam-5223	211	18	f	f	PROPN
ejpam-5223	211	19	-closed	-close	VERB
ejpam-5223	211	20	preserving	preserve	VERB
ejpam-5223	211	21	if	if	SCONJ
ejpam-5223	211	22	and	and	CCONJ
ejpam-5223	211	23	only	only	ADV
ejpam-5223	211	24	if	if	SCONJ
ejpam-5223	211	25	for	for	ADP
ejpam-5223	211	26	any	any	DET
ejpam-5223	211	27	subset	subset	NOUN
ejpam-5223	211	28	s	s	PROPN
ejpam-5223	211	29	of	of	ADP
ejpam-5223	211	30	y	y	PROPN
ejpam-5223	211	31	and	and	CCONJ
ejpam-5223	211	32	any	any	DET
ejpam-5223	211	33	f	f	PROPN
ejpam-5223	211	34	-open	-open	PROPN
ejpam-5223	211	35	set	set	VERB
ejpam-5223	211	36	u	u	NOUN
ejpam-5223	211	37	such	such	ADJ
ejpam-5223	211	38	that	that	DET
ejpam-5223	211	39	f−1(s	f−1(s	PROPN
ejpam-5223	211	40	)	)	PUNCT
ejpam-5223	211	41	⊆	⊆	NUM
ejpam-5223	211	42	u	u	NOUN
ejpam-5223	211	43	,	,	PUNCT
ejpam-5223	211	44	there	there	PRON
ejpam-5223	211	45	exists	exist	VERB
ejpam-5223	211	46	an	an	DET
ejpam-5223	211	47	f	f	PROPN
ejpam-5223	211	48	-open	-open	NOUN
ejpam-5223	211	49	set	set	VERB
ejpam-5223	211	50	v	v	NOUN
ejpam-5223	211	51	in	in	ADP
ejpam-5223	211	52	y	y	PROPN
ejpam-5223	211	53	such	such	ADJ
ejpam-5223	211	54	that	that	PRON
ejpam-5223	211	55	s	s	PROPN
ejpam-5223	211	56	⊂	⊂	X
ejpam-5223	211	57	v	v	NOUN
ejpam-5223	211	58	and	and	CCONJ
ejpam-5223	211	59	f−1(v	f−1(v	PROPN
ejpam-5223	211	60	)	)	PUNCT
ejpam-5223	212	1	⊆	⊆	NUM
ejpam-5223	212	2	u	u	NOUN
ejpam-5223	212	3	.	.	PUNCT
ejpam-5223	213	1	proof	proof	NOUN
ejpam-5223	213	2	.	.	PUNCT
ejpam-5223	214	1	(	(	PUNCT
ejpam-5223	214	2	⇒	⇒	PROPN
ejpam-5223	214	3	)	)	PUNCT
ejpam-5223	214	4	let	let	VERB
ejpam-5223	214	5	s	s	PRON
ejpam-5223	214	6	be	be	AUX
ejpam-5223	214	7	any	any	DET
ejpam-5223	214	8	subset	subset	NOUN
ejpam-5223	214	9	of	of	ADP
ejpam-5223	214	10	y	y	PROPN
ejpam-5223	214	11	and	and	CCONJ
ejpam-5223	214	12	u	u	NOUN
ejpam-5223	214	13	be	be	VERB
ejpam-5223	214	14	any	any	DET
ejpam-5223	214	15	f	f	PROPN
ejpam-5223	214	16	-open	-open	NOUN
ejpam-5223	214	17	set	set	VERB
ejpam-5223	214	18	such	such	ADJ
ejpam-5223	214	19	that	that	DET
ejpam-5223	214	20	f−1(s	f−1(s	PROPN
ejpam-5223	214	21	)	)	PUNCT
ejpam-5223	214	22	⊆	⊆	NUM
ejpam-5223	214	23	u	u	NOUN
ejpam-5223	214	24	.	.	PUNCT
ejpam-5223	215	1	since	since	SCONJ
ejpam-5223	215	2	x	x	PROPN
ejpam-5223	215	3	\u	\u	X
ejpam-5223	215	4	is	be	AUX
ejpam-5223	215	5	f	f	PROPN
ejpam-5223	215	6	-closed	-closed	PROPN
ejpam-5223	215	7	,	,	PUNCT
ejpam-5223	215	8	f(x	f(x	PROPN
ejpam-5223	215	9	\u	\u	NUM
ejpam-5223	215	10	)	)	PUNCT
ejpam-5223	215	11	is	be	AUX
ejpam-5223	215	12	f	f	PROPN
ejpam-5223	215	13	-closed	-close	VERB
ejpam-5223	215	14	in	in	ADP
ejpam-5223	215	15	y	y	PROPN
ejpam-5223	215	16	.	.	PUNCT
ejpam-5223	216	1	since	since	SCONJ
ejpam-5223	216	2	f−1(s	f−1(s	PROPN
ejpam-5223	216	3	)	)	PUNCT
ejpam-5223	216	4	⊆	⊆	NUM
ejpam-5223	216	5	u	u	NOUN
ejpam-5223	216	6	,	,	PUNCT
ejpam-5223	216	7	x	x	X
ejpam-5223	216	8	\u	\u	X
ejpam-5223	216	9	⊆	⊆	NUM
ejpam-5223	216	10	x	x	SYM
ejpam-5223	216	11	\f−1(s	\f−1(s	NOUN
ejpam-5223	216	12	)	)	PUNCT
ejpam-5223	216	13	.	.	PUNCT
ejpam-5223	217	1	let	let	VERB
ejpam-5223	217	2	v	v	VERB
ejpam-5223	217	3	=	=	SYM
ejpam-5223	217	4	y	y	PROPN
ejpam-5223	217	5	\	\	PROPN
ejpam-5223	217	6	f(x	f(x	PROPN
ejpam-5223	217	7	\	\	PROPN
ejpam-5223	217	8	u	u	NOUN
ejpam-5223	217	9	)	)	PUNCT
ejpam-5223	217	10	.	.	PUNCT
ejpam-5223	218	1	then	then	ADV
ejpam-5223	218	2	we	we	PRON
ejpam-5223	218	3	have	have	VERB
ejpam-5223	218	4	s	s	VERB
ejpam-5223	218	5	⊆	⊆	NUM
ejpam-5223	218	6	y	y	PROPN
ejpam-5223	218	7	\	\	PROPN
ejpam-5223	218	8	f(x	f(x	PROPN
ejpam-5223	218	9	\	\	PROPN
ejpam-5223	218	10	u	u	NOUN
ejpam-5223	218	11	)	)	PUNCT
ejpam-5223	218	12	=	=	SYM
ejpam-5223	218	13	v	v	NOUN
ejpam-5223	218	14	and	and	CCONJ
ejpam-5223	218	15	f−1(v	f−1(v	NOUN
ejpam-5223	218	16	)	)	PUNCT
ejpam-5223	219	1	⊆	⊆	NUM
ejpam-5223	219	2	u	u	NOUN
ejpam-5223	219	3	.	.	PUNCT
ejpam-5223	220	1	(	(	PUNCT
ejpam-5223	220	2	⇐	⇐	ADJ
ejpam-5223	220	3	)	)	PUNCT
ejpam-5223	220	4	let	let	VERB
ejpam-5223	220	5	k	k	X
ejpam-5223	220	6	be	be	AUX
ejpam-5223	220	7	any	any	DET
ejpam-5223	220	8	f	f	NOUN
ejpam-5223	220	9	-closed	-close	VERB
ejpam-5223	220	10	in	in	ADP
ejpam-5223	220	11	x.	x.	NOUN
ejpam-5223	220	12	we	we	PRON
ejpam-5223	220	13	show	show	VERB
ejpam-5223	220	14	that	that	SCONJ
ejpam-5223	220	15	f(k	f(k	VERB
ejpam-5223	220	16	)	)	PUNCT
ejpam-5223	220	17	is	be	AUX
ejpam-5223	220	18	f	f	PROPN
ejpam-5223	220	19	-closed	-close	VERB
ejpam-5223	220	20	in	in	ADP
ejpam-5223	220	21	y	y	PROPN
ejpam-5223	220	22	.	.	PUNCT
ejpam-5223	221	1	let	let	VERB
ejpam-5223	221	2	s	s	PRON
ejpam-5223	221	3	=	=	VERB
ejpam-5223	221	4	y	y	PROPN
ejpam-5223	221	5	\f(k	\f(k	PROPN
ejpam-5223	221	6	)	)	PUNCT
ejpam-5223	221	7	.	.	PUNCT
ejpam-5223	222	1	then	then	ADV
ejpam-5223	222	2	f−1(s	f−1(s	PROPN
ejpam-5223	222	3	)	)	PUNCT
ejpam-5223	222	4	=	=	SYM
ejpam-5223	222	5	f−1(y	f−1(y	PROPN
ejpam-5223	222	6	\f(k	\f(k	PROPN
ejpam-5223	222	7	)	)	PUNCT
ejpam-5223	222	8	)	)	PUNCT
ejpam-5223	223	1	⊆	⊆	NUM
ejpam-5223	223	2	x	x	PUNCT
ejpam-5223	223	3	\k	\k	NOUN
ejpam-5223	223	4	.	.	PUNCT
ejpam-5223	224	1	since	since	SCONJ
ejpam-5223	224	2	x	x	SYM
ejpam-5223	224	3	\k	\k	NOUN
ejpam-5223	224	4	is	be	AUX
ejpam-5223	224	5	f	f	PROPN
ejpam-5223	224	6	-open	-open	PROPN
ejpam-5223	224	7	,	,	PUNCT
ejpam-5223	224	8	there	there	PRON
ejpam-5223	224	9	exists	exist	VERB
ejpam-5223	224	10	an	an	DET
ejpam-5223	224	11	f	f	PROPN
ejpam-5223	224	12	-open	-open	NOUN
ejpam-5223	224	13	set	set	VERB
ejpam-5223	224	14	v	v	ADP
ejpam-5223	224	15	such	such	ADJ
ejpam-5223	224	16	that	that	SCONJ
ejpam-5223	224	17	y	y	PROPN
ejpam-5223	224	18	\	\	PROPN
ejpam-5223	224	19	f(k	f(k	PROPN
ejpam-5223	224	20	)	)	PUNCT
ejpam-5223	224	21	⊂	⊂	PROPN
ejpam-5223	224	22	v	v	NOUN
ejpam-5223	224	23	and	and	CCONJ
ejpam-5223	224	24	f−1(v	f−1(v	PROPN
ejpam-5223	224	25	)	)	PUNCT
ejpam-5223	225	1	⊂	⊂	X
ejpam-5223	225	2	x	x	PUNCT
ejpam-5223	225	3	\k	\k	NOUN
ejpam-5223	225	4	.	.	PUNCT
ejpam-5223	226	1	hence	hence	ADV
ejpam-5223	226	2	k	k	X
ejpam-5223	226	3	⊂	⊂	PROPN
ejpam-5223	226	4	x	x	PUNCT
ejpam-5223	226	5	\	\	PROPN
ejpam-5223	226	6	f−1(v	f−1(v	PROPN
ejpam-5223	226	7	)	)	PUNCT
ejpam-5223	227	1	=	=	PUNCT
ejpam-5223	227	2	f−1(y	f−1(y	PROPN
ejpam-5223	227	3	\	\	PROPN
ejpam-5223	227	4	v	v	NOUN
ejpam-5223	227	5	)	)	PUNCT
ejpam-5223	227	6	and	and	CCONJ
ejpam-5223	227	7	f(k	f(k	VERB
ejpam-5223	227	8	)	)	PUNCT
ejpam-5223	227	9	⊆	⊆	NUM
ejpam-5223	227	10	y	y	PROPN
ejpam-5223	227	11	\	\	PROPN
ejpam-5223	227	12	v	v	NOUN
ejpam-5223	227	13	.	.	PUNCT
ejpam-5223	228	1	on	on	ADP
ejpam-5223	228	2	the	the	DET
ejpam-5223	228	3	other	other	ADJ
ejpam-5223	228	4	hand	hand	NOUN
ejpam-5223	228	5	,	,	PUNCT
ejpam-5223	228	6	we	we	PRON
ejpam-5223	228	7	have	have	VERB
ejpam-5223	228	8	y	y	PROPN
ejpam-5223	228	9	\	\	PROPN
ejpam-5223	228	10	v	v	ADP
ejpam-5223	228	11	⊆	⊆	NUM
ejpam-5223	228	12	f(k	f(k	NUM
ejpam-5223	228	13	)	)	PUNCT
ejpam-5223	228	14	.	.	PUNCT
ejpam-5223	229	1	therefore	therefore	ADV
ejpam-5223	229	2	,	,	PUNCT
ejpam-5223	229	3	y	y	PROPN
ejpam-5223	229	4	\	\	PROPN
ejpam-5223	229	5	v	v	X
ejpam-5223	229	6	=	=	SYM
ejpam-5223	229	7	f(k	f(k	VERB
ejpam-5223	229	8	)	)	PUNCT
ejpam-5223	229	9	and	and	CCONJ
ejpam-5223	229	10	f(k	f(k	VERB
ejpam-5223	229	11	)	)	PUNCT
ejpam-5223	229	12	is	be	AUX
ejpam-5223	229	13	f	f	PROPN
ejpam-5223	229	14	-closed	-close	VERB
ejpam-5223	229	15	in	in	ADP
ejpam-5223	229	16	y	y	PROPN
ejpam-5223	229	17	.	.	PUNCT
ejpam-5223	230	1	references	reference	NOUN
ejpam-5223	230	2	1470	1470	NUM
ejpam-5223	230	3	theorem	theorem	VERB
ejpam-5223	230	4	11	11	NUM
ejpam-5223	230	5	.	.	PUNCT
ejpam-5223	231	1	let	let	VERB
ejpam-5223	231	2	f	f	NOUN
ejpam-5223	231	3	:	:	PUNCT
ejpam-5223	231	4	(	(	PUNCT
ejpam-5223	231	5	x	x	X
ejpam-5223	231	6	,	,	PUNCT
ejpam-5223	231	7	τ	τ	X
ejpam-5223	231	8	)	)	PUNCT
ejpam-5223	231	9	→	→	SYM
ejpam-5223	231	10	(	(	PUNCT
ejpam-5223	231	11	y	y	PROPN
ejpam-5223	231	12	,	,	PUNCT
ejpam-5223	231	13	σ	σ	PROPN
ejpam-5223	231	14	)	)	PUNCT
ejpam-5223	231	15	be	be	VERB
ejpam-5223	231	16	an	an	DET
ejpam-5223	231	17	f	f	NOUN
ejpam-5223	231	18	-closed	-close	VERB
ejpam-5223	231	19	preserving	preserve	VERB
ejpam-5223	231	20	continuous	continuous	ADJ
ejpam-5223	231	21	surjection	surjection	NOUN
ejpam-5223	231	22	.	.	PUNCT
ejpam-5223	232	1	if	if	SCONJ
ejpam-5223	232	2	(	(	PUNCT
ejpam-5223	232	3	x	x	NOUN
ejpam-5223	232	4	,	,	PUNCT
ejpam-5223	232	5	τ	τ	X
ejpam-5223	232	6	)	)	PUNCT
ejpam-5223	232	7	is	be	AUX
ejpam-5223	232	8	f	f	PROPN
ejpam-5223	232	9	-normal	-normal	NOUN
ejpam-5223	232	10	,	,	PUNCT
ejpam-5223	232	11	then	then	ADV
ejpam-5223	232	12	(	(	PUNCT
ejpam-5223	232	13	y	y	PROPN
ejpam-5223	232	14	,	,	PUNCT
ejpam-5223	232	15	σ	σ	PROPN
ejpam-5223	232	16	)	)	PUNCT
ejpam-5223	232	17	is	be	AUX
ejpam-5223	232	18	f	f	PROPN
ejpam-5223	232	19	-normal	-normal	NOUN
ejpam-5223	232	20	.	.	PUNCT
ejpam-5223	233	1	proof	proof	NOUN
ejpam-5223	233	2	.	.	PUNCT
ejpam-5223	234	1	let	let	VERB
ejpam-5223	234	2	(	(	PUNCT
ejpam-5223	234	3	x	x	NOUN
ejpam-5223	234	4	,	,	PUNCT
ejpam-5223	234	5	τ	τ	X
ejpam-5223	234	6	)	)	PUNCT
ejpam-5223	234	7	be	be	VERB
ejpam-5223	234	8	f	f	NOUN
ejpam-5223	234	9	-normal	-normal	PROPN
ejpam-5223	234	10	.	.	PUNCT
ejpam-5223	235	1	for	for	ADP
ejpam-5223	235	2	any	any	DET
ejpam-5223	235	3	disjoint	disjoint	NOUN
ejpam-5223	235	4	closed	close	VERB
ejpam-5223	235	5	sets	set	NOUN
ejpam-5223	235	6	k1	k1	NOUN
ejpam-5223	235	7	and	and	CCONJ
ejpam-5223	235	8	k2	k2	NOUN
ejpam-5223	235	9	in	in	ADP
ejpam-5223	235	10	y	y	PROPN
ejpam-5223	235	11	,	,	PUNCT
ejpam-5223	235	12	f−1(k1	f−1(k1	NOUN
ejpam-5223	235	13	)	)	PUNCT
ejpam-5223	235	14	and	and	CCONJ
ejpam-5223	235	15	f−1(k2	f−1(k2	NOUN
ejpam-5223	235	16	)	)	PUNCT
ejpam-5223	235	17	are	be	AUX
ejpam-5223	235	18	disjoint	disjoint	NOUN
ejpam-5223	235	19	closed	close	VERB
ejpam-5223	235	20	sets	set	NOUN
ejpam-5223	235	21	in	in	ADP
ejpam-5223	235	22	x	x	PUNCT
ejpam-5223	235	23	since	since	SCONJ
ejpam-5223	235	24	f	f	PROPN
ejpam-5223	235	25	is	be	AUX
ejpam-5223	235	26	cotinuous	cotinuous	ADJ
ejpam-5223	235	27	.	.	PUNCT
ejpam-5223	236	1	since	since	SCONJ
ejpam-5223	236	2	(	(	PUNCT
ejpam-5223	236	3	x	x	X
ejpam-5223	236	4	,	,	PUNCT
ejpam-5223	236	5	τ	τ	X
ejpam-5223	236	6	)	)	PUNCT
ejpam-5223	236	7	is	be	AUX
ejpam-5223	236	8	f	f	PROPN
ejpam-5223	236	9	-normal	-normal	NOUN
ejpam-5223	236	10	,	,	PUNCT
ejpam-5223	236	11	there	there	PRON
ejpam-5223	236	12	exist	exist	VERB
ejpam-5223	236	13	f	f	PROPN
ejpam-5223	236	14	-open	-open	PROPN
ejpam-5223	236	15	sets	set	NOUN
ejpam-5223	236	16	u1	u1	NOUN
ejpam-5223	236	17	,	,	PUNCT
ejpam-5223	236	18	u2	u2	NOUN
ejpam-5223	236	19	in	in	ADP
ejpam-5223	236	20	x	x	PROPN
ejpam-5223	236	21	such	such	ADJ
ejpam-5223	236	22	that	that	SCONJ
ejpam-5223	236	23	f−1(ki	f−1(ki	PROPN
ejpam-5223	236	24	)	)	PUNCT
ejpam-5223	236	25	⊆	⊆	NUM
ejpam-5223	236	26	ui	ui	NOUN
ejpam-5223	236	27	(	(	PUNCT
ejpam-5223	236	28	i	i	NOUN
ejpam-5223	236	29	=	=	NOUN
ejpam-5223	236	30	1	1	NUM
ejpam-5223	236	31	,	,	PUNCT
ejpam-5223	236	32	2	2	NUM
ejpam-5223	236	33	)	)	PUNCT
ejpam-5223	236	34	and	and	CCONJ
ejpam-5223	236	35	u1∩u2	u1∩u2	PROPN
ejpam-5223	236	36	=	=	PUNCT
ejpam-5223	236	37	∅.	∅.	X
ejpam-5223	236	38	by	by	ADP
ejpam-5223	236	39	theorem	theorem	NOUN
ejpam-5223	236	40	10	10	NUM
ejpam-5223	236	41	,	,	PUNCT
ejpam-5223	236	42	there	there	PRON
ejpam-5223	236	43	exist	exist	VERB
ejpam-5223	236	44	f	f	PROPN
ejpam-5223	236	45	-open	-open	NOUN
ejpam-5223	236	46	sets	set	NOUN
ejpam-5223	236	47	vi	vi	NOUN
ejpam-5223	236	48	such	such	ADJ
ejpam-5223	236	49	that	that	SCONJ
ejpam-5223	236	50	ki	ki	PROPN
ejpam-5223	236	51	⊂	⊂	PROPN
ejpam-5223	236	52	vi	vi	PROPN
ejpam-5223	236	53	,	,	PUNCT
ejpam-5223	236	54	f	f	PROPN
ejpam-5223	236	55	−1vi	−1vi	NOUN
ejpam-5223	236	56	)	)	PUNCT
ejpam-5223	236	57	⊆	⊆	NUM
ejpam-5223	236	58	ui	ui	NOUN
ejpam-5223	236	59	(	(	PUNCT
ejpam-5223	236	60	i	i	NOUN
ejpam-5223	236	61	=	=	NOUN
ejpam-5223	236	62	1	1	NUM
ejpam-5223	236	63	,	,	PUNCT
ejpam-5223	236	64	2	2	NUM
ejpam-5223	236	65	)	)	PUNCT
ejpam-5223	236	66	.	.	PUNCT
ejpam-5223	237	1	since	since	SCONJ
ejpam-5223	237	2	u1	u1	NOUN
ejpam-5223	237	3	∩	∩	ADJ
ejpam-5223	237	4	u2	u2	NOUN
ejpam-5223	237	5	=	=	PUNCT
ejpam-5223	237	6	∅	∅	NOUN
ejpam-5223	237	7	and	and	CCONJ
ejpam-5223	237	8	f	f	PROPN
ejpam-5223	237	9	is	be	AUX
ejpam-5223	237	10	surjective	surjective	ADJ
ejpam-5223	237	11	,	,	PUNCT
ejpam-5223	237	12	v1	v1	NOUN
ejpam-5223	237	13	∩	∩	ADJ
ejpam-5223	237	14	v2	v2	NOUN
ejpam-5223	237	15	=	=	PUNCT
ejpam-5223	237	16	∅.	∅.	VERB
ejpam-5223	237	17	therefore	therefore	ADV
ejpam-5223	237	18	,	,	PUNCT
ejpam-5223	237	19	(	(	PUNCT
ejpam-5223	237	20	y	y	PROPN
ejpam-5223	237	21	,	,	PUNCT
ejpam-5223	237	22	σ	σ	PROPN
ejpam-5223	237	23	)	)	PUNCT
ejpam-5223	237	24	is	be	AUX
ejpam-5223	237	25	f	f	PROPN
ejpam-5223	237	26	-normal	-normal	PROPN
ejpam-5223	237	27	.	.	PUNCT
ejpam-5223	238	1	corollary	corollary	ADJ
ejpam-5223	238	2	1	1	NUM
ejpam-5223	238	3	.	.	PUNCT
ejpam-5223	239	1	let	let	VERB
ejpam-5223	239	2	f	f	NOUN
ejpam-5223	239	3	:	:	PUNCT
ejpam-5223	239	4	(	(	PUNCT
ejpam-5223	239	5	x	x	X
ejpam-5223	239	6	,	,	PUNCT
ejpam-5223	239	7	τ	τ	X
ejpam-5223	239	8	)	)	PUNCT
ejpam-5223	239	9	→	→	SYM
ejpam-5223	239	10	(	(	PUNCT
ejpam-5223	239	11	y	y	PROPN
ejpam-5223	239	12	,	,	PUNCT
ejpam-5223	239	13	σ	σ	PROPN
ejpam-5223	239	14	)	)	PUNCT
ejpam-5223	239	15	be	be	VERB
ejpam-5223	239	16	an	an	DET
ejpam-5223	239	17	f	f	NOUN
ejpam-5223	239	18	-closed	-close	VERB
ejpam-5223	239	19	preserving	preserve	VERB
ejpam-5223	239	20	continuous	continuous	ADJ
ejpam-5223	239	21	surjection	surjection	NOUN
ejpam-5223	239	22	.	.	PUNCT
ejpam-5223	240	1	if	if	SCONJ
ejpam-5223	240	2	(	(	PUNCT
ejpam-5223	240	3	x	x	NOUN
ejpam-5223	240	4	,	,	PUNCT
ejpam-5223	240	5	τ	τ	X
ejpam-5223	240	6	)	)	PUNCT
ejpam-5223	240	7	is	be	AUX
ejpam-5223	240	8	ft4	ft4	PROPN
ejpam-5223	240	9	,	,	PUNCT
ejpam-5223	240	10	then	then	ADV
ejpam-5223	240	11	(	(	PUNCT
ejpam-5223	240	12	y	y	PROPN
ejpam-5223	240	13	,	,	PUNCT
ejpam-5223	240	14	σ	σ	PROPN
ejpam-5223	240	15	)	)	PUNCT
ejpam-5223	240	16	is	be	AUX
ejpam-5223	240	17	ft4	ft4	PROPN
ejpam-5223	240	18	.	.	PUNCT
ejpam-5223	240	19	proof	proof	NOUN
ejpam-5223	240	20	.	.	PUNCT
ejpam-5223	241	1	it	it	PRON
ejpam-5223	241	2	is	be	AUX
ejpam-5223	241	3	necessary	necessary	ADJ
ejpam-5223	241	4	to	to	PART
ejpam-5223	241	5	show	show	VERB
ejpam-5223	241	6	that	that	SCONJ
ejpam-5223	241	7	if	if	SCONJ
ejpam-5223	241	8	(	(	PUNCT
ejpam-5223	241	9	x	x	NOUN
ejpam-5223	241	10	,	,	PUNCT
ejpam-5223	241	11	τ	τ	X
ejpam-5223	241	12	)	)	PUNCT
ejpam-5223	241	13	is	be	AUX
ejpam-5223	241	14	ft1	ft1	PROPN
ejpam-5223	241	15	,	,	PUNCT
ejpam-5223	241	16	then	then	ADV
ejpam-5223	241	17	(	(	PUNCT
ejpam-5223	241	18	y	y	PROPN
ejpam-5223	241	19	,	,	PUNCT
ejpam-5223	241	20	σ	σ	PROPN
ejpam-5223	241	21	)	)	PUNCT
ejpam-5223	241	22	is	be	AUX
ejpam-5223	241	23	ft1	ft1	PROPN
ejpam-5223	241	24	.	.	PUNCT
ejpam-5223	242	1	for	for	ADP
ejpam-5223	242	2	any	any	DET
ejpam-5223	242	3	point	point	NOUN
ejpam-5223	242	4	y	y	PROPN
ejpam-5223	242	5	∈	∈	PROPN
ejpam-5223	242	6	y	y	PROPN
ejpam-5223	242	7	,	,	PUNCT
ejpam-5223	242	8	there	there	PRON
ejpam-5223	242	9	exists	exist	VERB
ejpam-5223	242	10	x	x	X
ejpam-5223	242	11	∈	∈	PROPN
ejpam-5223	242	12	x	x	PUNCT
ejpam-5223	242	13	such	such	ADJ
ejpam-5223	242	14	that	that	SCONJ
ejpam-5223	242	15	f(x	f(x	NOUN
ejpam-5223	242	16	)	)	PUNCT
ejpam-5223	243	1	=	=	PUNCT
ejpam-5223	243	2	y.	y.	NOUN
ejpam-5223	243	3	since	since	SCONJ
ejpam-5223	243	4	x	x	PROPN
ejpam-5223	243	5	is	be	AUX
ejpam-5223	243	6	ft1	ft1	PROPN
ejpam-5223	243	7	,	,	PUNCT
ejpam-5223	243	8	by	by	ADP
ejpam-5223	243	9	theorem	theorem	NOUN
ejpam-5223	243	10	?	?	PUNCT
ejpam-5223	243	11	?	?	PUNCT
ejpam-5223	243	12	,	,	PUNCT
ejpam-5223	243	13	{	{	PUNCT
ejpam-5223	243	14	x	x	X
ejpam-5223	243	15	}	}	PUNCT
ejpam-5223	243	16	is	be	AUX
ejpam-5223	243	17	f	f	PROPN
ejpam-5223	243	18	-closed	-close	VERB
ejpam-5223	243	19	in	in	ADP
ejpam-5223	243	20	x	x	NOUN
ejpam-5223	243	21	and	and	CCONJ
ejpam-5223	243	22	f({x	f({x	NOUN
ejpam-5223	243	23	}	}	PUNCT
ejpam-5223	243	24	)	)	PUNCT
ejpam-5223	244	1	=	=	PRON
ejpam-5223	244	2	{	{	PUNCT
ejpam-5223	244	3	y	y	NOUN
ejpam-5223	244	4	}	}	PUNCT
ejpam-5223	244	5	is	be	AUX
ejpam-5223	244	6	f	f	PROPN
ejpam-5223	244	7	-closed	-close	VERB
ejpam-5223	244	8	in	in	ADP
ejpam-5223	244	9	y	y	PROPN
ejpam-5223	244	10	.	.	PUNCT
ejpam-5223	245	1	conclusion	conclusion	NOUN
ejpam-5223	245	2	.	.	PUNCT
ejpam-5223	246	1	by	by	ADP
ejpam-5223	246	2	using	use	VERB
ejpam-5223	246	3	f	f	PROPN
ejpam-5223	246	4	-open	-open	ADJ
ejpam-5223	246	5	sets	set	NOUN
ejpam-5223	246	6	in	in	ADP
ejpam-5223	246	7	a	a	DET
ejpam-5223	246	8	topological	topological	ADJ
ejpam-5223	246	9	space	space	NOUN
ejpam-5223	246	10	,	,	PUNCT
ejpam-5223	246	11	we	we	PRON
ejpam-5223	246	12	defined	define	VERB
ejpam-5223	246	13	separation	separation	NOUN
ejpam-5223	246	14	axioms	axiom	VERB
ejpam-5223	246	15	fti(i	fti(i	NOUN
ejpam-5223	246	16	=	=	SYM
ejpam-5223	246	17	0	0	NUM
ejpam-5223	246	18	,	,	PUNCT
ejpam-5223	246	19	1	1	NUM
ejpam-5223	246	20	,	,	PUNCT
ejpam-5223	246	21	2	2	NUM
ejpam-5223	246	22	,	,	PUNCT
ejpam-5223	246	23	3	3	NUM
ejpam-5223	246	24	,	,	PUNCT
ejpam-5223	246	25	4	4	NUM
ejpam-5223	246	26	)	)	PUNCT
ejpam-5223	246	27	and	and	CCONJ
ejpam-5223	246	28	obtained	obtain	VERB
ejpam-5223	246	29	their	their	PRON
ejpam-5223	246	30	properties	property	NOUN
ejpam-5223	246	31	,	,	PUNCT
ejpam-5223	246	32	characterization	characterization	NOUN
ejpam-5223	246	33	and	and	CCONJ
ejpam-5223	246	34	relationships	relationship	NOUN
ejpam-5223	246	35	.	.	PUNCT
ejpam-5223	247	1	furthermore	furthermore	ADV
ejpam-5223	247	2	,	,	PUNCT
ejpam-5223	247	3	it	it	PRON
ejpam-5223	247	4	was	be	AUX
ejpam-5223	247	5	shown	show	VERB
ejpam-5223	247	6	that	that	SCONJ
ejpam-5223	247	7	(	(	PUNCT
ejpam-5223	247	8	1	1	X
ejpam-5223	247	9	)	)	PUNCT
ejpam-5223	247	10	f	f	PROPN
ejpam-5223	247	11	-compact	-compact	PROPN
ejpam-5223	247	12	ft2	ft2	NOUN
ejpam-5223	247	13	-	-	PUNCT
ejpam-5223	247	14	spaces	space	NOUN
ejpam-5223	247	15	are	be	AUX
ejpam-5223	247	16	ft4	ft4	NOUN
ejpam-5223	247	17	,	,	PUNCT
ejpam-5223	247	18	(	(	PUNCT
ejpam-5223	247	19	2	2	X
ejpam-5223	247	20	)	)	PUNCT
ejpam-5223	247	21	f	f	PROPN
ejpam-5223	247	22	-normality	-normality	PROPN
ejpam-5223	247	23	is	be	AUX
ejpam-5223	247	24	preserved	preserve	VERB
ejpam-5223	247	25	under	under	ADP
ejpam-5223	247	26	f	f	PROPN
ejpam-5223	247	27	-closed	-close	VERB
ejpam-5223	247	28	preserving	preserve	VERB
ejpam-5223	247	29	continuous	continuous	ADJ
ejpam-5223	247	30	surjections	surjection	NOUN
ejpam-5223	247	31	,	,	PUNCT
ejpam-5223	247	32	(	(	PUNCT
ejpam-5223	247	33	3	3	X
ejpam-5223	247	34	)	)	PUNCT
ejpam-5223	247	35	for	for	ADP
ejpam-5223	247	36	fti(i	fti(i	NOUN
ejpam-5223	247	37	=	=	SYM
ejpam-5223	247	38	0	0	NUM
ejpam-5223	247	39	,	,	PUNCT
ejpam-5223	247	40	1	1	NUM
ejpam-5223	247	41	,	,	PUNCT
ejpam-5223	247	42	2	2	NUM
ejpam-5223	247	43	,	,	PUNCT
ejpam-5223	247	44	3	3	NUM
ejpam-5223	247	45	,	,	PUNCT
ejpam-5223	247	46	4	4	NUM
ejpam-5223	247	47	)	)	PUNCT
ejpam-5223	247	48	the	the	DET
ejpam-5223	247	49	following	follow	VERB
ejpam-5223	247	50	diagram	diagram	NOUN
ejpam-5223	247	51	holds	hold	VERB
ejpam-5223	247	52	:	:	PUNCT
ejpam-5223	247	53	ft4	ft4	PROPN
ejpam-5223	247	54	⇒	⇒	PROPN
ejpam-5223	247	55	ft3	ft3	PROPN
ejpam-5223	247	56	⇒	⇒	PROPN
ejpam-5223	248	1	ft2	ft2	PROPN
ejpam-5223	248	2	⇒	⇒	PROPN
ejpam-5223	248	3	ft1	ft1	PROPN
ejpam-5223	248	4	⇒	⇒	PROPN
ejpam-5223	248	5	ft0	ft0	VERB
ejpam-5223	248	6	⇓	⇓	PROPN
ejpam-5223	248	7	⇓	⇓	PROPN
ejpam-5223	248	8	⇓	⇓	PROPN
ejpam-5223	248	9	⇓	⇓	PROPN
ejpam-5223	248	10	⇓	⇓	PROPN
ejpam-5223	248	11	t4	t4	PROPN
ejpam-5223	248	12	⇒	⇒	PROPN
ejpam-5223	248	13	t3	t3	PROPN
ejpam-5223	248	14	⇒	⇒	PROPN
ejpam-5223	248	15	t2	t2	PROPN
ejpam-5223	248	16	⇒	⇒	PROPN
ejpam-5223	248	17	t1	t1	PROPN
ejpam-5223	248	18	⇒	⇒	PROPN
ejpam-5223	248	19	t0	t0	PROPN
ejpam-5223	248	20	acknowledgements	acknowledgement	VERB
ejpam-5223	248	21	the	the	DET
ejpam-5223	248	22	authors	author	NOUN
ejpam-5223	248	23	extend	extend	VERB
ejpam-5223	248	24	their	their	PRON
ejpam-5223	248	25	appreciation	appreciation	NOUN
ejpam-5223	248	26	to	to	ADP
ejpam-5223	248	27	the	the	DET
ejpam-5223	248	28	national	national	PROPN
ejpam-5223	248	29	university	university	PROPN
ejpam-5223	248	30	of	of	ADP
ejpam-5223	248	31	malaysia	malaysia	PROPN
ejpam-5223	248	32	for	for	ADP
ejpam-5223	248	33	supporting	support	VERB
ejpam-5223	248	34	this	this	DET
ejpam-5223	248	35	work	work	NOUN
ejpam-5223	248	36	under	under	ADP
ejpam-5223	248	37	the	the	DET
ejpam-5223	248	38	research	research	NOUN
ejpam-5223	248	39	grant	grant	NOUN
ejpam-5223	248	40	:	:	PUNCT
ejpam-5223	248	41	gp-2021	gp-2021	NOUN
ejpam-5223	248	42	-	-	PUNCT
ejpam-5223	248	43	k014049	k014049	PROPN
ejpam-5223	248	44	ganjaran	ganjaran	NOUN
ejpam-5223	248	45	penerbitan	penerbitan	PROPN
ejpam-5223	248	46	.	.	PUNCT
ejpam-5223	249	1	references	reference	NOUN
ejpam-5223	249	2	[	[	X
ejpam-5223	249	3	1	1	NUM
ejpam-5223	249	4	]	]	PUNCT
ejpam-5223	249	5	m.	m.	NOUN
ejpam-5223	249	6	h.	h.	PROPN
ejpam-5223	249	7	alqahtani	alqahtani	PROPN
ejpam-5223	249	8	and	and	CCONJ
ejpam-5223	249	9	a.m.	a.m.	PROPN
ejpam-5223	250	1	abd	abd	PROPN
ejpam-5223	250	2	el	el	PROPN
ejpam-5223	250	3	-	-	PROPN
ejpam-5223	250	4	latif	latif	PROPN
ejpam-5223	250	5	.	.	PUNCT
ejpam-5223	251	1	separation	separation	NOUN
ejpam-5223	251	2	axioms	axiom	NOUN
ejpam-5223	251	3	via	via	ADP
ejpam-5223	251	4	novel	novel	ADJ
ejpam-5223	251	5	operators	operator	NOUN
ejpam-5223	251	6	in	in	ADP
ejpam-5223	251	7	the	the	DET
ejpam-5223	251	8	frame	frame	NOUN
ejpam-5223	251	9	of	of	ADP
ejpam-5223	251	10	topological	topological	ADJ
ejpam-5223	251	11	spaces	space	NOUN
ejpam-5223	251	12	and	and	CCONJ
ejpam-5223	251	13	applications	application	NOUN
ejpam-5223	251	14	.	.	PUNCT
ejpam-5223	252	1	aims	aim	VERB
ejpam-5223	252	2	mathematicsl	mathematicsl	NOUN
ejpam-5223	252	3	,	,	PUNCT
ejpam-5223	252	4	9(6):14213–14227	9(6):14213–14227	NUM
ejpam-5223	252	5	,	,	PUNCT
ejpam-5223	252	6	2024	2024	NUM
ejpam-5223	252	7	.	.	PUNCT
ejpam-5223	253	1	[	[	X
ejpam-5223	253	2	2	2	X
ejpam-5223	253	3	]	]	X
ejpam-5223	253	4	m.h	m.h	PROPN
ejpam-5223	253	5	.	.	PROPN
ejpam-5223	253	6	alqahtani	alqahtani	PROPN
ejpam-5223	253	7	.	.	PUNCT
ejpam-5223	254	1	f	f	X
ejpam-5223	254	2	-	-	PUNCT
ejpam-5223	254	3	open	open	ADJ
ejpam-5223	254	4	and	and	CCONJ
ejpam-5223	254	5	f	f	X
ejpam-5223	254	6	-	-	PUNCT
ejpam-5223	254	7	closed	close	VERB
ejpam-5223	254	8	sets	set	NOUN
ejpam-5223	254	9	in	in	ADP
ejpam-5223	254	10	topological	topological	ADJ
ejpam-5223	254	11	spaces	space	NOUN
ejpam-5223	254	12	.	.	PUNCT
ejpam-5223	255	1	eur	eur	PROPN
ejpam-5223	255	2	.	.	PUNCT
ejpam-5223	256	1	j.	j.	PROPN
ejpam-5223	256	2	pure	pure	PROPN
ejpam-5223	256	3	appl	appl	PROPN
ejpam-5223	256	4	.	.	PUNCT
ejpam-5223	256	5	math	math	PROPN
ejpam-5223	256	6	.	.	PUNCT
ejpam-5223	256	7	,	,	PUNCT
ejpam-5223	256	8	6(2):819–832	6(2):819–832	NOUN
ejpam-5223	256	9	,	,	PUNCT
ejpam-5223	256	10	2023	2023	NUM
ejpam-5223	256	11	.	.	PUNCT
ejpam-5223	257	1	[	[	X
ejpam-5223	257	2	3	3	NUM
ejpam-5223	257	3	]	]	SYM
ejpam-5223	257	4	a.b	a.b	PROPN
ejpam-5223	257	5	.	.	PROPN
ejpam-5223	257	6	khalaf	khalaf	PROPN
ejpam-5223	257	7	,	,	PUNCT
ejpam-5223	257	8	h.m	h.m	PROPN
ejpam-5223	257	9	.	.	PROPN
ejpam-5223	257	10	darwesh	darwesh	PROPN
ejpam-5223	257	11	,	,	PUNCT
ejpam-5223	257	12	and	and	CCONJ
ejpam-5223	257	13	k.	k.	PROPN
ejpam-5223	257	14	kannan	kannan	PROPN
ejpam-5223	257	15	.	.	PUNCT
ejpam-5223	258	1	some	some	DET
ejpam-5223	258	2	types	type	NOUN
ejpam-5223	258	3	of	of	ADP
ejpam-5223	258	4	separation	separation	NOUN
ejpam-5223	258	5	axioms	axiom	NOUN
ejpam-5223	258	6	in	in	ADP
ejpam-5223	258	7	topological	topological	ADJ
ejpam-5223	258	8	spaces	space	NOUN
ejpam-5223	258	9	.	.	PUNCT
ejpam-5223	259	1	tamsui	tamsui	PROPN
ejpam-5223	259	2	oxford	oxford	PROPN
ejpam-5223	259	3	journal	journal	PROPN
ejpam-5223	259	4	of	of	ADP
ejpam-5223	259	5	information	information	NOUN
ejpam-5223	259	6	and	and	CCONJ
ejpam-5223	259	7	mathematical	mathematical	ADJ
ejpam-5223	259	8	sciences	science	NOUN
ejpam-5223	259	9	,	,	PUNCT
ejpam-5223	259	10	28(3):303–326	28(3):303–326	NOUN
ejpam-5223	259	11	,	,	PUNCT
ejpam-5223	259	12	2012	2012	NUM
ejpam-5223	259	13	.	.	PUNCT