id	sid	tid	token	lemma	pos
ejpam-5764	1	1	european	european	PROPN
ejpam-5764	1	2	journal	journal	PROPN
ejpam-5764	1	3	of	of	ADP
ejpam-5764	1	4	pure	pure	ADJ
ejpam-5764	1	5	and	and	CCONJ
ejpam-5764	1	6	applied	applied	ADJ
ejpam-5764	1	7	mathematics	mathematic	NOUN
ejpam-5764	1	8	2025	2025	NUM
ejpam-5764	1	9	,	,	PUNCT
ejpam-5764	1	10	vol	vol	NOUN
ejpam-5764	1	11	.	.	PROPN
ejpam-5764	1	12	18	18	NUM
ejpam-5764	1	13	,	,	PUNCT
ejpam-5764	1	14	issue	issue	NOUN
ejpam-5764	1	15	2	2	NUM
ejpam-5764	1	16	,	,	PUNCT
ejpam-5764	1	17	article	article	NOUN
ejpam-5764	1	18	number	number	NOUN
ejpam-5764	1	19	5764	5764	NUM
ejpam-5764	1	20	issn	issn	PROPN
ejpam-5764	1	21	1307	1307	NUM
ejpam-5764	1	22	-	-	SYM
ejpam-5764	1	23	5543	5543	NUM
ejpam-5764	1	24	–	–	PUNCT
ejpam-5764	1	25	ejpam.com	ejpam.com	X
ejpam-5764	1	26	published	publish	VERB
ejpam-5764	1	27	by	by	ADP
ejpam-5764	1	28	new	new	PROPN
ejpam-5764	1	29	york	york	PROPN
ejpam-5764	1	30	business	business	PROPN
ejpam-5764	1	31	global	global	ADJ
ejpam-5764	1	32	some	some	DET
ejpam-5764	1	33	types	type	NOUN
ejpam-5764	1	34	of	of	ADP
ejpam-5764	1	35	tri	tri	ADJ
ejpam-5764	1	36	-	-	ADJ
ejpam-5764	1	37	locally	locally	ADV
ejpam-5764	1	38	compactness	compactness	NOUN
ejpam-5764	1	39	spaces	space	NOUN
ejpam-5764	1	40	jamal	jamal	PROPN
ejpam-5764	1	41	oudetallah1	oudetallah1	PROPN
ejpam-5764	1	42	,	,	PUNCT
ejpam-5764	1	43	ala	ala	PROPN
ejpam-5764	1	44	amourah2,∗	amourah2,∗	ADJ
ejpam-5764	1	45	,	,	PUNCT
ejpam-5764	1	46	sultan	sultan	PROPN
ejpam-5764	1	47	alsaadi2	alsaadi2	PROPN
ejpam-5764	1	48	,	,	PUNCT
ejpam-5764	1	49	iqbal	iqbal	PROPN
ejpam-5764	1	50	m.	m.	PROPN
ejpam-5764	1	51	batiha3	batiha3	PROPN
ejpam-5764	1	52	,	,	PUNCT
ejpam-5764	1	53	jamal	jamal	PROPN
ejpam-5764	1	54	salah4,∗	salah4,∗	PROPN
ejpam-5764	1	55	,	,	PUNCT
ejpam-5764	1	56	tala	tala	PROPN
ejpam-5764	1	57	sasa5	sasa5	PROPN
ejpam-5764	1	58	1	1	NUM
ejpam-5764	1	59	department	department	NOUN
ejpam-5764	1	60	of	of	ADP
ejpam-5764	1	61	mathematics	mathematics	PROPN
ejpam-5764	1	62	,	,	PUNCT
ejpam-5764	1	63	university	university	PROPN
ejpam-5764	1	64	of	of	ADP
ejpam-5764	1	65	petra	petra	PROPN
ejpam-5764	1	66	,	,	PUNCT
ejpam-5764	1	67	amman	amman	PROPN
ejpam-5764	1	68	,	,	PUNCT
ejpam-5764	1	69	11196	11196	NUM
ejpam-5764	1	70	,	,	PUNCT
ejpam-5764	1	71	jordan	jordan	PROPN
ejpam-5764	1	72	2	2	NUM
ejpam-5764	1	73	mathematics	mathematics	PROPN
ejpam-5764	1	74	education	education	NOUN
ejpam-5764	1	75	program	program	NOUN
ejpam-5764	1	76	,	,	PUNCT
ejpam-5764	1	77	faculty	faculty	NOUN
ejpam-5764	1	78	of	of	ADP
ejpam-5764	1	79	education	education	NOUN
ejpam-5764	1	80	and	and	CCONJ
ejpam-5764	1	81	arts	art	NOUN
ejpam-5764	1	82	,	,	PUNCT
ejpam-5764	1	83	sohar	sohar	PROPN
ejpam-5764	1	84	university	university	PROPN
ejpam-5764	1	85	,	,	PUNCT
ejpam-5764	1	86	sohar	sohar	PROPN
ejpam-5764	1	87	311	311	NUM
ejpam-5764	1	88	,	,	PUNCT
ejpam-5764	1	89	oman	oman	PROPN
ejpam-5764	1	90	3	3	NUM
ejpam-5764	1	91	department	department	NOUN
ejpam-5764	1	92	of	of	ADP
ejpam-5764	1	93	mathematics	mathematic	NOUN
ejpam-5764	1	94	,	,	PUNCT
ejpam-5764	1	95	al	al	PROPN
ejpam-5764	1	96	zaytoonah	zaytoonah	PROPN
ejpam-5764	1	97	university	university	PROPN
ejpam-5764	1	98	of	of	ADP
ejpam-5764	1	99	jordan	jordan	PROPN
ejpam-5764	1	100	,	,	PUNCT
ejpam-5764	1	101	amman	amman	PROPN
ejpam-5764	1	102	11733	11733	NUM
ejpam-5764	1	103	,	,	PUNCT
ejpam-5764	1	104	jordan	jordan	PROPN
ejpam-5764	1	105	.	.	PROPN
ejpam-5764	2	1	4	4	NUM
ejpam-5764	2	2	college	college	NOUN
ejpam-5764	2	3	of	of	ADP
ejpam-5764	2	4	applied	apply	VERB
ejpam-5764	2	5	and	and	CCONJ
ejpam-5764	2	6	health	health	NOUN
ejpam-5764	2	7	sciences	science	NOUN
ejpam-5764	2	8	,	,	PUNCT
ejpam-5764	2	9	a’sharqiyah	a’sharqiyah	PROPN
ejpam-5764	2	10	university	university	NOUN
ejpam-5764	2	11	,	,	PUNCT
ejpam-5764	2	12	post	post	PROPN
ejpam-5764	2	13	box	box	PROPN
ejpam-5764	2	14	no	no	INTJ
ejpam-5764	2	15	.	.	PROPN
ejpam-5764	2	16	42	42	NUM
ejpam-5764	2	17	,	,	PUNCT
ejpam-5764	2	18	post	post	VERB
ejpam-5764	2	19	code	code	NOUN
ejpam-5764	2	20	no	no	INTJ
ejpam-5764	2	21	.	.	NOUN
ejpam-5764	2	22	400	400	NUM
ejpam-5764	2	23	ibra	ibra	NOUN
ejpam-5764	2	24	,	,	PUNCT
ejpam-5764	2	25	sultanate	sultanate	NOUN
ejpam-5764	2	26	of	of	ADP
ejpam-5764	2	27	oman	oman	PROPN
ejpam-5764	2	28	5	5	NUM
ejpam-5764	2	29	department	department	NOUN
ejpam-5764	2	30	of	of	ADP
ejpam-5764	2	31	mathematics	mathematic	NOUN
ejpam-5764	2	32	,	,	PUNCT
ejpam-5764	2	33	faculty	faculty	NOUN
ejpam-5764	2	34	of	of	ADP
ejpam-5764	2	35	science	science	NOUN
ejpam-5764	2	36	,	,	PUNCT
ejpam-5764	2	37	applied	apply	VERB
ejpam-5764	2	38	science	science	NOUN
ejpam-5764	2	39	private	private	ADJ
ejpam-5764	2	40	university	university	NOUN
ejpam-5764	2	41	,	,	PUNCT
ejpam-5764	2	42	amman	amman	PROPN
ejpam-5764	2	43	,	,	PUNCT
ejpam-5764	2	44	jordan	jordan	PROPN
ejpam-5764	2	45	abstract	abstract	PROPN
ejpam-5764	2	46	.	.	PUNCT
ejpam-5764	3	1	three	three	NUM
ejpam-5764	3	2	topologies	topology	NOUN
ejpam-5764	3	3	,	,	PUNCT
ejpam-5764	3	4	or	or	CCONJ
ejpam-5764	3	5	tri	tri	ADJ
ejpam-5764	3	6	-	-	ADJ
ejpam-5764	3	7	locally	locally	ADV
ejpam-5764	3	8	compact	compact	ADJ
ejpam-5764	3	9	spaces	space	NOUN
ejpam-5764	3	10	,	,	PUNCT
ejpam-5764	3	11	will	will	AUX
ejpam-5764	3	12	be	be	AUX
ejpam-5764	3	13	examined	examine	VERB
ejpam-5764	3	14	in	in	ADP
ejpam-5764	3	15	this	this	DET
ejpam-5764	3	16	study	study	NOUN
ejpam-5764	3	17	in	in	ADP
ejpam-5764	3	18	order	order	NOUN
ejpam-5764	3	19	to	to	PART
ejpam-5764	3	20	examine	examine	VERB
ejpam-5764	3	21	the	the	DET
ejpam-5764	3	22	locally	locally	ADV
ejpam-5764	3	23	compactness	compactness	NOUN
ejpam-5764	3	24	spaces	space	NOUN
ejpam-5764	3	25	attribute	attribute	NOUN
ejpam-5764	3	26	.	.	PUNCT
ejpam-5764	4	1	furthermore	furthermore	ADV
ejpam-5764	4	2	,	,	PUNCT
ejpam-5764	4	3	these	these	DET
ejpam-5764	4	4	spaces	space	NOUN
ejpam-5764	4	5	’	'	PUNCT
ejpam-5764	4	6	characteristics	characteristic	NOUN
ejpam-5764	4	7	will	will	AUX
ejpam-5764	4	8	be	be	AUX
ejpam-5764	4	9	analyzed	analyze	VERB
ejpam-5764	4	10	in	in	ADP
ejpam-5764	4	11	light	light	NOUN
ejpam-5764	4	12	of	of	ADP
ejpam-5764	4	13	locally	locally	ADV
ejpam-5764	4	14	limited	limited	ADJ
ejpam-5764	4	15	spaces	space	NOUN
ejpam-5764	4	16	.	.	PUNCT
ejpam-5764	5	1	several	several	ADJ
ejpam-5764	5	2	well	well	ADV
ejpam-5764	5	3	-	-	PUNCT
ejpam-5764	5	4	known	know	VERB
ejpam-5764	5	5	theorems	theorem	NOUN
ejpam-5764	5	6	about	about	ADP
ejpam-5764	5	7	locally	locally	ADV
ejpam-5764	5	8	compact	compact	ADJ
ejpam-5764	5	9	spaces	space	NOUN
ejpam-5764	5	10	have	have	AUX
ejpam-5764	5	11	been	be	AUX
ejpam-5764	5	12	expanded	expand	VERB
ejpam-5764	5	13	to	to	PART
ejpam-5764	5	14	apply	apply	VERB
ejpam-5764	5	15	to	to	ADP
ejpam-5764	5	16	three	three	NUM
ejpam-5764	5	17	topologies	topology	NOUN
ejpam-5764	5	18	,	,	PUNCT
ejpam-5764	5	19	and	and	CCONJ
ejpam-5764	5	20	many	many	ADJ
ejpam-5764	5	21	theoretical	theoretical	ADJ
ejpam-5764	5	22	results	result	NOUN
ejpam-5764	5	23	have	have	AUX
ejpam-5764	5	24	been	be	AUX
ejpam-5764	5	25	proposed	propose	VERB
ejpam-5764	5	26	and	and	CCONJ
ejpam-5764	5	27	verified	verify	VERB
ejpam-5764	5	28	.	.	PUNCT
ejpam-5764	6	1	the	the	DET
ejpam-5764	6	2	results	result	NOUN
ejpam-5764	6	3	are	be	AUX
ejpam-5764	6	4	supported	support	VERB
ejpam-5764	6	5	by	by	ADP
ejpam-5764	6	6	illustrative	illustrative	ADJ
ejpam-5764	6	7	instances	instance	NOUN
ejpam-5764	6	8	.	.	PUNCT
ejpam-5764	7	1	2020	2020	NUM
ejpam-5764	7	2	mathematics	mathematic	NOUN
ejpam-5764	7	3	subject	subject	NOUN
ejpam-5764	7	4	classifications	classification	NOUN
ejpam-5764	7	5	:	:	PUNCT
ejpam-5764	7	6	47b38	47b38	NUM
ejpam-5764	7	7	key	key	ADJ
ejpam-5764	7	8	words	word	NOUN
ejpam-5764	7	9	and	and	CCONJ
ejpam-5764	7	10	phrases	phrase	NOUN
ejpam-5764	7	11	:	:	PUNCT
ejpam-5764	7	12	tri	tri	ADJ
ejpam-5764	7	13	-	-	ADJ
ejpam-5764	7	14	locally	locally	ADV
ejpam-5764	7	15	compact	compact	ADJ
ejpam-5764	7	16	spaces	space	NOUN
ejpam-5764	7	17	,	,	PUNCT
ejpam-5764	7	18	tri	tri	ADJ
ejpam-5764	7	19	-	-	ADJ
ejpam-5764	7	20	topological	topological	ADJ
ejpam-5764	7	21	spaces	space	NOUN
ejpam-5764	7	22	,	,	PUNCT
ejpam-5764	7	23	locally	locally	ADV
ejpam-5764	7	24	compactness	compactness	NOUN
ejpam-5764	7	25	,	,	PUNCT
ejpam-5764	7	26	metacompactness	metacompactness	NOUN
ejpam-5764	7	27	1	1	NUM
ejpam-5764	7	28	.	.	PUNCT
ejpam-5764	7	29	introduction	introduction	NOUN
ejpam-5764	7	30	the	the	DET
ejpam-5764	7	31	study	study	NOUN
ejpam-5764	7	32	of	of	ADP
ejpam-5764	7	33	the	the	DET
ejpam-5764	7	34	connections	connection	NOUN
ejpam-5764	7	35	between	between	ADP
ejpam-5764	7	36	different	different	ADJ
ejpam-5764	7	37	classes	class	NOUN
ejpam-5764	7	38	of	of	ADP
ejpam-5764	7	39	topological	topological	ADJ
ejpam-5764	7	40	spaces	space	NOUN
ejpam-5764	7	41	located	locate	VERB
ejpam-5764	7	42	between	between	ADP
ejpam-5764	7	43	countably	countably	ADV
ejpam-5764	7	44	paracompact	paracompact	ADJ
ejpam-5764	7	45	spaces	space	NOUN
ejpam-5764	7	46	is	be	AUX
ejpam-5764	7	47	one	one	NUM
ejpam-5764	7	48	of	of	ADP
ejpam-5764	7	49	the	the	DET
ejpam-5764	7	50	main	main	ADJ
ejpam-5764	7	51	areas	area	NOUN
ejpam-5764	7	52	of	of	ADP
ejpam-5764	7	53	set	set	VERB
ejpam-5764	7	54	theoretic	theoretic	ADJ
ejpam-5764	7	55	topology	topology	NOUN
ejpam-5764	8	1	[	[	X
ejpam-5764	8	2	1–4	1–4	NOUN
ejpam-5764	8	3	]	]	X
ejpam-5764	8	4	.	.	PUNCT
ejpam-5764	9	1	since	since	SCONJ
ejpam-5764	9	2	it	it	PRON
ejpam-5764	9	3	naturally	naturally	ADV
ejpam-5764	9	4	lies	lie	VERB
ejpam-5764	9	5	between	between	ADP
ejpam-5764	9	6	these	these	DET
ejpam-5764	9	7	classes	class	NOUN
ejpam-5764	9	8	,	,	PUNCT
ejpam-5764	9	9	the	the	DET
ejpam-5764	9	10	class	class	NOUN
ejpam-5764	9	11	of	of	ADP
ejpam-5764	9	12	locally	locally	ADV
ejpam-5764	9	13	compact	compact	ADJ
ejpam-5764	9	14	spaces	space	NOUN
ejpam-5764	9	15	is	be	AUX
ejpam-5764	9	16	important	important	ADJ
ejpam-5764	9	17	in	in	ADP
ejpam-5764	9	18	this	this	DET
ejpam-5764	9	19	context	context	NOUN
ejpam-5764	9	20	.	.	PUNCT
ejpam-5764	10	1	according	accord	VERB
ejpam-5764	10	2	to	to	ADP
ejpam-5764	10	3	dugundji	dugundji	NOUN
ejpam-5764	10	4	(	(	PUNCT
ejpam-5764	10	5	1966	1966	NUM
ejpam-5764	10	6	)	)	PUNCT
ejpam-5764	10	7	,	,	PUNCT
ejpam-5764	10	8	a	a	DET
ejpam-5764	10	9	locally	locally	ADV
ejpam-5764	10	10	compact	compact	ADJ
ejpam-5764	10	11	space	space	NOUN
ejpam-5764	10	12	is	be	AUX
ejpam-5764	10	13	a	a	DET
ejpam-5764	10	14	topological	topological	ADJ
ejpam-5764	10	15	space	space	NOUN
ejpam-5764	10	16	(	(	PUNCT
ejpam-5764	10	17	x,ϑ	x,ϑ	PROPN
ejpam-5764	10	18	)	)	PUNCT
ejpam-5764	10	19	in	in	ADP
ejpam-5764	10	20	which	which	PRON
ejpam-5764	10	21	each	each	DET
ejpam-5764	10	22	point	point	VERB
ejpam-5764	10	23	a	a	DET
ejpam-5764	10	24	∈	∈	NOUN
ejpam-5764	10	25	x	x	PUNCT
ejpam-5764	10	26	has	have	AUX
ejpam-5764	10	27	a	a	DET
ejpam-5764	10	28	neighborhood	neighborhood	NOUN
ejpam-5764	10	29	that	that	PRON
ejpam-5764	10	30	is	be	AUX
ejpam-5764	10	31	also	also	ADV
ejpam-5764	10	32	contained	contain	VERB
ejpam-5764	10	33	within	within	ADP
ejpam-5764	10	34	a	a	DET
ejpam-5764	10	35	compact	compact	ADJ
ejpam-5764	10	36	space	space	NOUN
ejpam-5764	10	37	.	.	PUNCT
ejpam-5764	11	1	similarly	similarly	ADV
ejpam-5764	11	2	,	,	PUNCT
ejpam-5764	11	3	a	a	DET
ejpam-5764	11	4	tri	tri	ADJ
ejpam-5764	11	5	-	-	ADJ
ejpam-5764	11	6	topological	topological	ADJ
ejpam-5764	11	7	space	space	NOUN
ejpam-5764	11	8	(	(	PUNCT
ejpam-5764	11	9	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	11	10	,	,	PUNCT
ejpam-5764	11	11	ϑ2	ϑ2	PROPN
ejpam-5764	11	12	,	,	PUNCT
ejpam-5764	11	13	ϑ3	ϑ3	PROPN
ejpam-5764	11	14	)	)	PUNCT
ejpam-5764	11	15	is	be	AUX
ejpam-5764	11	16	called	call	VERB
ejpam-5764	11	17	a	a	DET
ejpam-5764	11	18	tri	tri	ADJ
ejpam-5764	11	19	-	-	ADJ
ejpam-5764	11	20	locally	locally	ADV
ejpam-5764	11	21	metacompact	metacompact	ADJ
ejpam-5764	11	22	space	space	NOUN
ejpam-5764	11	23	if	if	SCONJ
ejpam-5764	11	24	every	every	DET
ejpam-5764	11	25	point	point	NOUN
ejpam-5764	11	26	a	a	DET
ejpam-5764	11	27	∈	∈	NOUN
ejpam-5764	11	28	x	x	PUNCT
ejpam-5764	11	29	has	have	VERB
ejpam-5764	11	30	a	a	DET
ejpam-5764	11	31	neighborhood	neighborhood	NOUN
ejpam-5764	11	32	that	that	PRON
ejpam-5764	11	33	is	be	AUX
ejpam-5764	11	34	contained	contain	VERB
ejpam-5764	11	35	within	within	ADP
ejpam-5764	11	36	a	a	DET
ejpam-5764	11	37	tri	tri	ADJ
ejpam-5764	11	38	-	-	ADJ
ejpam-5764	11	39	compact	compact	ADJ
ejpam-5764	11	40	area	area	NOUN
ejpam-5764	11	41	.	.	PUNCT
ejpam-5764	12	1	∗corresponding	∗corresponde	VERB
ejpam-5764	12	2	author	author	NOUN
ejpam-5764	12	3	.	.	PUNCT
ejpam-5764	13	1	∗corresponding	∗corresponde	VERB
ejpam-5764	13	2	author	author	NOUN
ejpam-5764	13	3	.	.	PUNCT
ejpam-5764	14	1	doi	doi	NOUN
ejpam-5764	14	2	:	:	PUNCT
ejpam-5764	14	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5764	https://doi.org/10.29020/nybg.ejpam.v18i2.5764	NOUN
ejpam-5764	14	4	email	email	NOUN
ejpam-5764	14	5	addresses	address	NOUN
ejpam-5764	14	6	:	:	PUNCT
ejpam-5764	14	7	jamal.oudetallah@uop.edu.jo	jamal.oudetallah@uop.edu.jo	PROPN
ejpam-5764	14	8	(	(	PUNCT
ejpam-5764	14	9	j.	j.	PROPN
ejpam-5764	14	10	oudetallah	oudetallah	PROPN
ejpam-5764	14	11	)	)	PUNCT
ejpam-5764	14	12	,	,	PUNCT
ejpam-5764	15	1	aamourah@su.edu.om	aamourah@su.edu.om	NOUN
ejpam-5764	15	2	(	(	PUNCT
ejpam-5764	15	3	a.	a.	NOUN
ejpam-5764	15	4	amourah),alsaad99@hotmail.com	amourah),alsaad99@hotmail.com	PROPN
ejpam-5764	15	5	(	(	PUNCT
ejpam-5764	15	6	s.	s.	PROPN
ejpam-5764	15	7	alsaadi	alsaadi	PROPN
ejpam-5764	15	8	)	)	PUNCT
ejpam-5764	15	9	,	,	PUNCT
ejpam-5764	15	10	i.batiha@zuj.edu.jo	i.batiha@zuj.edu.jo	NOUN
ejpam-5764	15	11	(	(	PUNCT
ejpam-5764	15	12	i.	i.	PROPN
ejpam-5764	15	13	m.	m.	PROPN
ejpam-5764	15	14	batiha	batiha	PROPN
ejpam-5764	15	15	)	)	PUNCT
ejpam-5764	15	16	,	,	PUNCT
ejpam-5764	15	17	damous73@yahoo.com	damous73@yahoo.com	X
ejpam-5764	15	18	(	(	PUNCT
ejpam-5764	15	19	j.	j.	PROPN
ejpam-5764	15	20	salah	salah	PROPN
ejpam-5764	15	21	)	)	PUNCT
ejpam-5764	15	22	,	,	PUNCT
ejpam-5764	15	23	t	t	NOUN
ejpam-5764	15	24	sasa@asu.edu.jo	sasa@asu.edu.jo	NOUN
ejpam-5764	15	25	(	(	PUNCT
ejpam-5764	15	26	t.	t.	PROPN
ejpam-5764	15	27	sasa	sasa	PROPN
ejpam-5764	15	28	)	)	PUNCT
ejpam-5764	15	29	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5764	15	30	1	1	NUM
ejpam-5764	15	31	copyright	copyright	NOUN
ejpam-5764	15	32	:	:	PUNCT
ejpam-5764	15	33	©	©	PROPN
ejpam-5764	15	34	2025	2025	NUM
ejpam-5764	15	35	the	the	DET
ejpam-5764	15	36	author(s	author(s	NOUN
ejpam-5764	15	37	)	)	PUNCT
ejpam-5764	15	38	.	.	PUNCT
ejpam-5764	16	1	(	(	PUNCT
ejpam-5764	16	2	cc	cc	NOUN
ejpam-5764	16	3	by	by	ADP
ejpam-5764	16	4	-	-	PUNCT
ejpam-5764	16	5	nc	nc	PROPN
ejpam-5764	16	6	4.0	4.0	NUM
ejpam-5764	16	7	)	)	PUNCT
ejpam-5764	16	8	j.	j.	PROPN
ejpam-5764	16	9	oudetallah	oudetallah	PROPN
ejpam-5764	16	10	et	et	PROPN
ejpam-5764	16	11	al	al	PROPN
ejpam-5764	16	12	.	.	PUNCT
ejpam-5764	16	13	/	/	SYM
ejpam-5764	16	14	eur	eur	PROPN
ejpam-5764	16	15	.	.	PUNCT
ejpam-5764	17	1	j.	j.	PROPN
ejpam-5764	17	2	pure	pure	PROPN
ejpam-5764	17	3	appl	appl	PROPN
ejpam-5764	17	4	.	.	PROPN
ejpam-5764	17	5	math	math	PROPN
ejpam-5764	17	6	,	,	PUNCT
ejpam-5764	17	7	18	18	NUM
ejpam-5764	17	8	(	(	PUNCT
ejpam-5764	17	9	2	2	NUM
ejpam-5764	17	10	)	)	PUNCT
ejpam-5764	17	11	(	(	PUNCT
ejpam-5764	17	12	2025	2025	NUM
ejpam-5764	17	13	)	)	PUNCT
ejpam-5764	17	14	,	,	PUNCT
ejpam-5764	17	15	5764	5764	NUM
ejpam-5764	17	16	2	2	NUM
ejpam-5764	17	17	of	of	ADP
ejpam-5764	17	18	11	11	NUM
ejpam-5764	17	19	one	one	NUM
ejpam-5764	17	20	important	important	ADJ
ejpam-5764	17	21	feature	feature	NOUN
ejpam-5764	17	22	of	of	ADP
ejpam-5764	17	23	such	such	ADJ
ejpam-5764	17	24	spaces	space	NOUN
ejpam-5764	17	25	is	be	AUX
ejpam-5764	17	26	that	that	SCONJ
ejpam-5764	17	27	several	several	ADJ
ejpam-5764	17	28	important	important	ADJ
ejpam-5764	17	29	separation	separation	NOUN
ejpam-5764	17	30	axioms	axiom	NOUN
ejpam-5764	17	31	,	,	PUNCT
ejpam-5764	17	32	such	such	ADJ
ejpam-5764	17	33	as	as	ADP
ejpam-5764	17	34	normality	normality	NOUN
ejpam-5764	17	35	and	and	CCONJ
ejpam-5764	17	36	collection	collection	NOUN
ejpam-5764	17	37	-	-	PUNCT
ejpam-5764	17	38	wise	wise	ADJ
ejpam-5764	17	39	hausdorff	hausdorff	NOUN
ejpam-5764	17	40	,	,	PUNCT
ejpam-5764	17	41	agree	agree	VERB
ejpam-5764	17	42	for	for	ADP
ejpam-5764	17	43	them	they	PRON
ejpam-5764	17	44	.	.	PUNCT
ejpam-5764	18	1	there	there	PRON
ejpam-5764	18	2	are	be	VERB
ejpam-5764	18	3	significant	significant	ADJ
ejpam-5764	18	4	theoretical	theoretical	ADJ
ejpam-5764	18	5	and	and	CCONJ
ejpam-5764	18	6	practical	practical	ADJ
ejpam-5764	18	7	implications	implication	NOUN
ejpam-5764	18	8	to	to	ADP
ejpam-5764	18	9	problems	problem	NOUN
ejpam-5764	18	10	that	that	PRON
ejpam-5764	18	11	come	come	VERB
ejpam-5764	18	12	from	from	ADP
ejpam-5764	18	13	other	other	ADJ
ejpam-5764	18	14	areas	area	NOUN
ejpam-5764	18	15	of	of	ADP
ejpam-5764	18	16	mathematics	mathematic	NOUN
ejpam-5764	18	17	or	or	CCONJ
ejpam-5764	18	18	from	from	ADP
ejpam-5764	18	19	a	a	DET
ejpam-5764	18	20	strictly	strictly	ADV
ejpam-5764	18	21	topological	topological	ADJ
ejpam-5764	18	22	standpoint	standpoint	NOUN
ejpam-5764	18	23	.	.	PUNCT
ejpam-5764	19	1	if	if	SCONJ
ejpam-5764	19	2	there	there	PRON
ejpam-5764	19	3	is	be	VERB
ejpam-5764	19	4	a	a	DET
ejpam-5764	19	5	fundamental	fundamental	ADJ
ejpam-5764	19	6	system	system	NOUN
ejpam-5764	19	7	of	of	ADP
ejpam-5764	19	8	nearly	nearly	ADV
ejpam-5764	19	9	open	open	ADJ
ejpam-5764	19	10	neighborhoods	neighborhood	NOUN
ejpam-5764	19	11	for	for	ADP
ejpam-5764	19	12	every	every	DET
ejpam-5764	19	13	point	point	NOUN
ejpam-5764	19	14	in	in	ADP
ejpam-5764	19	15	a	a	DET
ejpam-5764	19	16	set	set	NOUN
ejpam-5764	19	17	x	x	NOUN
ejpam-5764	19	18	,	,	PUNCT
ejpam-5764	19	19	then	then	ADV
ejpam-5764	19	20	x	x	PUNCT
ejpam-5764	19	21	is	be	AUX
ejpam-5764	19	22	a	a	DET
ejpam-5764	19	23	tri	tri	ADJ
ejpam-5764	19	24	-	-	ADJ
ejpam-5764	19	25	topological	topological	ADJ
ejpam-5764	19	26	space	space	NOUN
ejpam-5764	19	27	.	.	PUNCT
ejpam-5764	20	1	keep	keep	VERB
ejpam-5764	20	2	in	in	ADP
ejpam-5764	20	3	mind	mind	NOUN
ejpam-5764	20	4	that	that	SCONJ
ejpam-5764	20	5	the	the	DET
ejpam-5764	20	6	first	first	ADJ
ejpam-5764	20	7	people	people	NOUN
ejpam-5764	20	8	to	to	PART
ejpam-5764	20	9	examine	examine	VERB
ejpam-5764	20	10	almost	almost	ADV
ejpam-5764	20	11	open	open	ADJ
ejpam-5764	20	12	sets	set	NOUN
ejpam-5764	20	13	in	in	ADP
ejpam-5764	20	14	a	a	DET
ejpam-5764	20	15	topological	topological	ADJ
ejpam-5764	20	16	group	group	NOUN
ejpam-5764	20	17	were	be	AUX
ejpam-5764	20	18	ghosh	ghosh	PROPN
ejpam-5764	20	19	and	and	CCONJ
ejpam-5764	20	20	lahiri	lahiri	PRON
ejpam-5764	21	1	[	[	X
ejpam-5764	21	2	5	5	NUM
ejpam-5764	21	3	]	]	PUNCT
ejpam-5764	21	4	.	.	PUNCT
ejpam-5764	22	1	the	the	DET
ejpam-5764	22	2	concept	concept	NOUN
ejpam-5764	22	3	of	of	ADP
ejpam-5764	22	4	a	a	DET
ejpam-5764	22	5	tri	tri	ADJ
ejpam-5764	22	6	-	-	ADJ
ejpam-5764	22	7	topological	topological	ADJ
ejpam-5764	22	8	group	group	NOUN
ejpam-5764	22	9	,	,	PUNCT
ejpam-5764	22	10	or	or	CCONJ
ejpam-5764	22	11	the	the	DET
ejpam-5764	22	12	tri	tri	ADJ
ejpam-5764	22	13	-	-	ADJ
ejpam-5764	22	14	topologized	topologize	VERB
ejpam-5764	22	15	form	form	NOUN
ejpam-5764	22	16	of	of	ADP
ejpam-5764	22	17	a	a	DET
ejpam-5764	22	18	topological	topological	ADJ
ejpam-5764	22	19	group	group	NOUN
ejpam-5764	22	20	,	,	PUNCT
ejpam-5764	22	21	has	have	AUX
ejpam-5764	22	22	previously	previously	ADV
ejpam-5764	22	23	been	be	AUX
ejpam-5764	22	24	discussed	discuss	VERB
ejpam-5764	22	25	in	in	ADP
ejpam-5764	22	26	earlier	early	ADJ
ejpam-5764	22	27	research	research	NOUN
ejpam-5764	22	28	.	.	PUNCT
ejpam-5764	23	1	since	since	SCONJ
ejpam-5764	23	2	all	all	PRON
ejpam-5764	23	3	of	of	ADP
ejpam-5764	23	4	the	the	DET
ejpam-5764	23	5	spaces	space	NOUN
ejpam-5764	23	6	examined	examine	VERB
ejpam-5764	23	7	in	in	ADP
ejpam-5764	23	8	this	this	DET
ejpam-5764	23	9	study	study	NOUN
ejpam-5764	23	10	are	be	AUX
ejpam-5764	23	11	assumed	assume	VERB
ejpam-5764	23	12	to	to	PART
ejpam-5764	23	13	be	be	AUX
ejpam-5764	23	14	nonempty	nonempty	ADJ
ejpam-5764	23	15	and	and	CCONJ
ejpam-5764	23	16	t0	t0	PROPN
ejpam-5764	23	17	spaces	space	VERB
ejpam-5764	23	18	,	,	PUNCT
ejpam-5764	23	19	any	any	DET
ejpam-5764	23	20	two	two	NUM
ejpam-5764	23	21	open	open	ADJ
ejpam-5764	23	22	neighborhoods	neighborhood	NOUN
ejpam-5764	23	23	of	of	ADP
ejpam-5764	23	24	a	a	DET
ejpam-5764	23	25	meet	meet	NOUN
ejpam-5764	23	26	to	to	PART
ejpam-5764	23	27	generate	generate	VERB
ejpam-5764	23	28	another	another	DET
ejpam-5764	23	29	open	open	ADJ
ejpam-5764	23	30	neighborhood	neighborhood	NOUN
ejpam-5764	23	31	of	of	ADP
ejpam-5764	23	32	a	a	PRON
ejpam-5764	23	33	for	for	ADP
ejpam-5764	23	34	any	any	DET
ejpam-5764	23	35	point	point	NOUN
ejpam-5764	23	36	a	a	PRON
ejpam-5764	23	37	in	in	ADP
ejpam-5764	23	38	the	the	DET
ejpam-5764	23	39	space	space	NOUN
ejpam-5764	23	40	.	.	PUNCT
ejpam-5764	24	1	the	the	DET
ejpam-5764	24	2	concept	concept	NOUN
ejpam-5764	24	3	of	of	ADP
ejpam-5764	24	4	a	a	DET
ejpam-5764	24	5	locally	locally	ADV
ejpam-5764	24	6	compact	compact	ADJ
ejpam-5764	24	7	space	space	NOUN
ejpam-5764	24	8	in	in	ADP
ejpam-5764	24	9	topological	topological	ADJ
ejpam-5764	24	10	space	space	NOUN
ejpam-5764	24	11	(	(	PUNCT
ejpam-5764	24	12	x,ϑ	x,ϑ	PROPN
ejpam-5764	24	13	)	)	PUNCT
ejpam-5764	24	14	was	be	AUX
ejpam-5764	24	15	first	first	ADV
ejpam-5764	24	16	proposed	propose	VERB
ejpam-5764	24	17	by	by	ADP
ejpam-5764	24	18	levine	levine	PROPN
ejpam-5764	24	19	[	[	X
ejpam-5764	24	20	6	6	NUM
ejpam-5764	24	21	]	]	PUNCT
ejpam-5764	24	22	.	.	PUNCT
ejpam-5764	25	1	these	these	DET
ejpam-5764	25	2	subjects	subject	NOUN
ejpam-5764	25	3	were	be	AUX
ejpam-5764	25	4	examined	examine	VERB
ejpam-5764	25	5	in	in	ADP
ejpam-5764	25	6	greater	great	ADJ
ejpam-5764	25	7	detail	detail	NOUN
ejpam-5764	25	8	in	in	ADP
ejpam-5764	25	9	more	more	ADV
ejpam-5764	25	10	recent	recent	ADJ
ejpam-5764	25	11	research	research	NOUN
ejpam-5764	25	12	[	[	X
ejpam-5764	25	13	7–10	7–10	X
ejpam-5764	25	14	]	]	X
ejpam-5764	25	15	....	....	PUNCT
ejpam-5764	26	1	the	the	DET
ejpam-5764	26	2	notions	notion	NOUN
ejpam-5764	26	3	of	of	ADP
ejpam-5764	26	4	tri	tri	ADJ
ejpam-5764	26	5	-	-	ADJ
ejpam-5764	26	6	locally	locally	ADV
ejpam-5764	26	7	compact	compact	ADJ
ejpam-5764	26	8	and	and	CCONJ
ejpam-5764	26	9	tri	tri	ADJ
ejpam-5764	26	10	-	-	ADJ
ejpam-5764	26	11	locally	locally	ADV
ejpam-5764	26	12	metacompact	metacompact	NOUN
ejpam-5764	26	13	in	in	ADP
ejpam-5764	26	14	tri	tri	ADJ
ejpam-5764	26	15	-	-	ADJ
ejpam-5764	26	16	topological	topological	ADJ
ejpam-5764	26	17	spaces	space	NOUN
ejpam-5764	26	18	,	,	PUNCT
ejpam-5764	26	19	as	as	ADV
ejpam-5764	26	20	well	well	ADV
ejpam-5764	26	21	as	as	ADP
ejpam-5764	26	22	related	related	ADJ
ejpam-5764	26	23	findings	finding	NOUN
ejpam-5764	26	24	,	,	PUNCT
ejpam-5764	26	25	are	be	AUX
ejpam-5764	26	26	examined	examine	VERB
ejpam-5764	26	27	in	in	ADP
ejpam-5764	26	28	this	this	DET
ejpam-5764	26	29	work	work	NOUN
ejpam-5764	26	30	.	.	PUNCT
ejpam-5764	27	1	in	in	ADP
ejpam-5764	27	2	tri	tri	ADJ
ejpam-5764	27	3	-	-	ADJ
ejpam-5764	27	4	topological	topological	ADJ
ejpam-5764	27	5	spaces	space	NOUN
ejpam-5764	27	6	,	,	PUNCT
ejpam-5764	27	7	we	we	PRON
ejpam-5764	27	8	present	present	VERB
ejpam-5764	27	9	the	the	DET
ejpam-5764	27	10	notion	notion	NOUN
ejpam-5764	27	11	of	of	ADP
ejpam-5764	27	12	tri	tri	ADJ
ejpam-5764	27	13	-	-	ADJ
ejpam-5764	27	14	locally	locally	ADV
ejpam-5764	27	15	compactness	compactness	NOUN
ejpam-5764	27	16	,	,	PUNCT
ejpam-5764	27	17	analyze	analyze	VERB
ejpam-5764	27	18	its	its	PRON
ejpam-5764	27	19	properties	property	NOUN
ejpam-5764	27	20	,	,	PUNCT
ejpam-5764	27	21	and	and	CCONJ
ejpam-5764	27	22	apply	apply	VERB
ejpam-5764	27	23	it	it	PRON
ejpam-5764	27	24	to	to	ADP
ejpam-5764	27	25	different	different	ADJ
ejpam-5764	27	26	spaces	space	NOUN
ejpam-5764	27	27	.	.	PUNCT
ejpam-5764	28	1	we	we	PRON
ejpam-5764	28	2	go	go	VERB
ejpam-5764	28	3	over	over	ADP
ejpam-5764	28	4	common	common	ADJ
ejpam-5764	28	5	definitions	definition	NOUN
ejpam-5764	28	6	that	that	PRON
ejpam-5764	28	7	will	will	AUX
ejpam-5764	28	8	be	be	AUX
ejpam-5764	28	9	used	use	VERB
ejpam-5764	28	10	in	in	ADP
ejpam-5764	28	11	the	the	DET
ejpam-5764	28	12	parts	part	NOUN
ejpam-5764	28	13	that	that	PRON
ejpam-5764	28	14	follow	follow	VERB
ejpam-5764	28	15	.	.	PUNCT
ejpam-5764	29	1	typically	typically	ADV
ejpam-5764	29	2	,	,	PUNCT
ejpam-5764	29	3	ϑu	ϑu	PROPN
ejpam-5764	29	4	,	,	PUNCT
ejpam-5764	29	5	ϑdis	ϑdi	NOUN
ejpam-5764	29	6	,	,	PUNCT
ejpam-5764	29	7	ϑcof	ϑcof	NOUN
ejpam-5764	29	8	,	,	PUNCT
ejpam-5764	29	9	and	and	CCONJ
ejpam-5764	29	10	ϑcoc	ϑcoc	PROPN
ejpam-5764	29	11	represent	represent	VERB
ejpam-5764	29	12	discrete	discrete	NOUN
ejpam-5764	29	13	,	,	PUNCT
ejpam-5764	29	14	co	co	NOUN
ejpam-5764	29	15	-	-	NOUN
ejpam-5764	29	16	finite	finite	ADJ
ejpam-5764	29	17	,	,	PUNCT
ejpam-5764	29	18	and	and	CCONJ
ejpam-5764	29	19	co	co	ADJ
ejpam-5764	29	20	-	-	ADJ
ejpam-5764	29	21	countable	countable	ADJ
ejpam-5764	29	22	topologies	topology	NOUN
ejpam-5764	29	23	,	,	PUNCT
ejpam-5764	29	24	respectively	respectively	ADV
ejpam-5764	29	25	.	.	PUNCT
ejpam-5764	30	1	x	x	X
ejpam-5764	30	2	=	=	SYM
ejpam-5764	30	3	(	(	PUNCT
ejpam-5764	30	4	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	30	5	,	,	PUNCT
ejpam-5764	30	6	ϑ2	ϑ2	PROPN
ejpam-5764	30	7	)	)	PUNCT
ejpam-5764	30	8	is	be	AUX
ejpam-5764	30	9	a	a	DET
ejpam-5764	30	10	representation	representation	NOUN
ejpam-5764	30	11	of	of	ADP
ejpam-5764	30	12	the	the	DET
ejpam-5764	30	13	concept	concept	NOUN
ejpam-5764	30	14	of	of	ADP
ejpam-5764	30	15	bitopological	bitopological	ADJ
ejpam-5764	30	16	spaces	space	NOUN
ejpam-5764	30	17	,	,	PUNCT
ejpam-5764	30	18	where	where	SCONJ
ejpam-5764	30	19	ϑ1	ϑ1	NOUN
ejpam-5764	30	20	,	,	PUNCT
ejpam-5764	30	21	ϑ2	ϑ2	PROPN
ejpam-5764	30	22	are	be	AUX
ejpam-5764	30	23	two	two	NUM
ejpam-5764	30	24	topologies	topology	NOUN
ejpam-5764	30	25	on	on	ADP
ejpam-5764	30	26	x.	x.	NOUN
ejpam-5764	30	27	this	this	PRON
ejpam-5764	30	28	is	be	AUX
ejpam-5764	30	29	related	relate	VERB
ejpam-5764	30	30	to	to	ADP
ejpam-5764	30	31	earlier	early	ADJ
ejpam-5764	30	32	research	research	NOUN
ejpam-5764	30	33	on	on	ADP
ejpam-5764	30	34	bitopological	bitopological	ADJ
ejpam-5764	30	35	spaces	space	NOUN
ejpam-5764	30	36	,	,	PUNCT
ejpam-5764	30	37	where	where	SCONJ
ejpam-5764	30	38	a	a	DET
ejpam-5764	30	39	topology	topology	NOUN
ejpam-5764	30	40	is	be	AUX
ejpam-5764	30	41	a	a	DET
ejpam-5764	30	42	collection	collection	NOUN
ejpam-5764	30	43	of	of	ADP
ejpam-5764	30	44	points	point	NOUN
ejpam-5764	30	45	that	that	PRON
ejpam-5764	30	46	satisfy	satisfy	VERB
ejpam-5764	30	47	a	a	DET
ejpam-5764	30	48	set	set	NOUN
ejpam-5764	30	49	of	of	ADP
ejpam-5764	30	50	axioms	axiom	NOUN
ejpam-5764	30	51	.	.	PUNCT
ejpam-5764	31	1	kim	kim	PROPN
ejpam-5764	31	2	’s	’s	PART
ejpam-5764	31	3	paper	paper	NOUN
ejpam-5764	31	4	[	[	X
ejpam-5764	31	5	5	5	NUM
ejpam-5764	31	6	]	]	PUNCT
ejpam-5764	31	7	described	describe	VERB
ejpam-5764	31	8	pairwise	pairwise	NOUN
ejpam-5764	31	9	hausdorff	hausdorff	NOUN
ejpam-5764	31	10	,	,	PUNCT
ejpam-5764	31	11	pairwise	pairwise	NOUN
ejpam-5764	31	12	regular	regular	NOUN
ejpam-5764	31	13	,	,	PUNCT
ejpam-5764	31	14	and	and	CCONJ
ejpam-5764	31	15	pairwise	pairwise	VERB
ejpam-5764	31	16	normal	normal	ADJ
ejpam-5764	31	17	spaces	space	NOUN
ejpam-5764	31	18	using	use	VERB
ejpam-5764	31	19	a	a	DET
ejpam-5764	31	20	set	set	NOUN
ejpam-5764	31	21	of	of	ADP
ejpam-5764	31	22	standard	standard	ADJ
ejpam-5764	31	23	results	result	NOUN
ejpam-5764	31	24	known	know	VERB
ejpam-5764	31	25	as	as	ADP
ejpam-5764	31	26	the	the	DET
ejpam-5764	31	27	tietze	tietze	NOUN
ejpam-5764	31	28	extension	extension	NOUN
ejpam-5764	31	29	.	.	PUNCT
ejpam-5764	32	1	bitopological	bitopological	ADJ
ejpam-5764	32	2	space	space	NOUN
ejpam-5764	32	3	study	study	NOUN
ejpam-5764	32	4	was	be	AUX
ejpam-5764	32	5	further	far	ADV
ejpam-5764	32	6	explored	explore	VERB
ejpam-5764	32	7	in	in	ADP
ejpam-5764	32	8	[	[	X
ejpam-5764	32	9	11	11	NUM
ejpam-5764	32	10	,	,	PUNCT
ejpam-5764	32	11	12	12	NUM
ejpam-5764	32	12	]	]	PUNCT
ejpam-5764	32	13	.	.	PUNCT
ejpam-5764	33	1	according	accord	VERB
ejpam-5764	33	2	to	to	ADP
ejpam-5764	33	3	[	[	X
ejpam-5764	33	4	7	7	NUM
ejpam-5764	33	5	,	,	PUNCT
ejpam-5764	33	6	8	8	NUM
ejpam-5764	33	7	]	]	PUNCT
ejpam-5764	33	8	,	,	PUNCT
ejpam-5764	33	9	bitopological	bitopological	ADJ
ejpam-5764	33	10	space	space	NOUN
ejpam-5764	33	11	can	can	AUX
ejpam-5764	33	12	expand	expand	VERB
ejpam-5764	33	13	,	,	PUNCT
ejpam-5764	33	14	nearly	nearly	ADV
ejpam-5764	33	15	expand	expand	VERB
ejpam-5764	33	16	,	,	PUNCT
ejpam-5764	33	17	and	and	CCONJ
ejpam-5764	33	18	feebly	feebly	ADV
ejpam-5764	33	19	expand	expand	VERB
ejpam-5764	33	20	.	.	PUNCT
ejpam-5764	34	1	the	the	DET
ejpam-5764	34	2	primary	primary	ADJ
ejpam-5764	34	3	goal	goal	NOUN
ejpam-5764	34	4	of	of	ADP
ejpam-5764	34	5	this	this	DET
ejpam-5764	34	6	paper	paper	NOUN
ejpam-5764	34	7	is	be	AUX
ejpam-5764	34	8	to	to	PART
ejpam-5764	34	9	introduce	introduce	VERB
ejpam-5764	34	10	and	and	CCONJ
ejpam-5764	34	11	investigate	investigate	VERB
ejpam-5764	34	12	a	a	DET
ejpam-5764	34	13	new	new	ADJ
ejpam-5764	34	14	kind	kind	NOUN
ejpam-5764	34	15	of	of	ADP
ejpam-5764	34	16	tripartite	tripartite	ADJ
ejpam-5764	34	17	compact	compact	ADJ
ejpam-5764	34	18	space	space	NOUN
ejpam-5764	34	19	:	:	PUNCT
ejpam-5764	34	20	the	the	DET
ejpam-5764	34	21	tripartite	tripartite	ADJ
ejpam-5764	34	22	locally	locally	ADV
ejpam-5764	34	23	compact	compact	ADJ
ejpam-5764	34	24	space	space	NOUN
ejpam-5764	34	25	.	.	PUNCT
ejpam-5764	35	1	tri	tri	ADJ
ejpam-5764	35	2	-	-	ADJ
ejpam-5764	35	3	topological	topological	ADJ
ejpam-5764	35	4	spaces	space	NOUN
ejpam-5764	35	5	are	be	AUX
ejpam-5764	35	6	sets	set	NOUN
ejpam-5764	35	7	containing	contain	VERB
ejpam-5764	35	8	three	three	NUM
ejpam-5764	35	9	topologies	topology	NOUN
ejpam-5764	35	10	,	,	PUNCT
ejpam-5764	35	11	where	where	SCONJ
ejpam-5764	35	12	ϑ1	ϑ1	NOUN
ejpam-5764	35	13	,	,	PUNCT
ejpam-5764	35	14	ϑ2	ϑ2	PROPN
ejpam-5764	35	15	,	,	PUNCT
ejpam-5764	35	16	and	and	CCONJ
ejpam-5764	35	17	ϑ3	ϑ3	NOUN
ejpam-5764	35	18	are	be	AUX
ejpam-5764	35	19	topologies	topology	NOUN
ejpam-5764	35	20	on	on	ADP
ejpam-5764	35	21	x.	x.	NOUN
ejpam-5764	35	22	they	they	PRON
ejpam-5764	35	23	are	be	AUX
ejpam-5764	35	24	represented	represent	VERB
ejpam-5764	35	25	as	as	ADP
ejpam-5764	35	26	x	x	X
ejpam-5764	35	27	=	=	SYM
ejpam-5764	35	28	(	(	PUNCT
ejpam-5764	35	29	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	35	30	,	,	PUNCT
ejpam-5764	35	31	ϑ2	ϑ2	PROPN
ejpam-5764	35	32	,	,	PUNCT
ejpam-5764	35	33	ϑ3	ϑ3	PROPN
ejpam-5764	35	34	)	)	PUNCT
ejpam-5764	35	35	.	.	PUNCT
ejpam-5764	36	1	tri	tri	ADJ
ejpam-5764	36	2	-	-	ADJ
ejpam-5764	36	3	topological	topological	ADJ
ejpam-5764	36	4	space	space	NOUN
ejpam-5764	36	5	variations	variation	NOUN
ejpam-5764	36	6	match	match	VERB
ejpam-5764	36	7	well	well	ADV
ejpam-5764	36	8	-	-	PUNCT
ejpam-5764	36	9	known	know	VERB
ejpam-5764	36	10	topological	topological	ADJ
ejpam-5764	36	11	space	space	NOUN
ejpam-5764	36	12	features	feature	NOUN
ejpam-5764	36	13	.	.	PUNCT
ejpam-5764	37	1	2	2	X
ejpam-5764	37	2	.	.	X
ejpam-5764	37	3	preliminaries	preliminary	NOUN
ejpam-5764	37	4	we	we	PRON
ejpam-5764	37	5	will	will	AUX
ejpam-5764	37	6	illustrate	illustrate	VERB
ejpam-5764	37	7	some	some	PRON
ejpam-5764	37	8	of	of	ADP
ejpam-5764	37	9	the	the	DET
ejpam-5764	37	10	fundamental	fundamental	ADJ
ejpam-5764	37	11	concepts	concept	NOUN
ejpam-5764	37	12	of	of	ADP
ejpam-5764	37	13	tri	tri	ADJ
ejpam-5764	37	14	-	-	ADJ
ejpam-5764	37	15	topological	topological	ADJ
ejpam-5764	37	16	space	space	NOUN
ejpam-5764	37	17	in	in	ADP
ejpam-5764	37	18	this	this	DET
ejpam-5764	37	19	part	part	NOUN
ejpam-5764	37	20	,	,	PUNCT
ejpam-5764	37	21	including	include	VERB
ejpam-5764	37	22	paracompactness	paracompactness	NOUN
ejpam-5764	37	23	,	,	PUNCT
ejpam-5764	37	24	dense	dense	ADJ
ejpam-5764	37	25	sets	set	NOUN
ejpam-5764	37	26	,	,	PUNCT
ejpam-5764	37	27	and	and	CCONJ
ejpam-5764	37	28	compact	compact	ADJ
ejpam-5764	37	29	space	space	NOUN
ejpam-5764	37	30	.	.	PUNCT
ejpam-5764	38	1	definition	definition	NOUN
ejpam-5764	38	2	1	1	NUM
ejpam-5764	38	3	.	.	PUNCT
ejpam-5764	39	1	[	[	X
ejpam-5764	39	2	1	1	X
ejpam-5764	39	3	]	]	PUNCT
ejpam-5764	39	4	ϑ	ϑ	X
ejpam-5764	39	5	⊂	⊂	PROPN
ejpam-5764	39	6	p(x	p(x	PROPN
ejpam-5764	39	7	)	)	PUNCT
ejpam-5764	39	8	=	=	PRON
ejpam-5764	39	9	{	{	PUNCT
ejpam-5764	39	10	a	a	X
ejpam-5764	39	11	:	:	PUNCT
ejpam-5764	39	12	a	a	DET
ejpam-5764	39	13	⊆	⊆	NUM
ejpam-5764	39	14	x	x	SYM
ejpam-5764	39	15	}	}	PUNCT
ejpam-5764	39	16	is	be	AUX
ejpam-5764	39	17	a	a	DET
ejpam-5764	39	18	collection	collection	NOUN
ejpam-5764	39	19	of	of	ADP
ejpam-5764	39	20	subsets	subset	NOUN
ejpam-5764	39	21	of	of	ADP
ejpam-5764	39	22	x	x	NOUN
ejpam-5764	39	23	,	,	PUNCT
ejpam-5764	39	24	where	where	SCONJ
ejpam-5764	39	25	x	x	PRON
ejpam-5764	39	26	is	be	AUX
ejpam-5764	39	27	a	a	DET
ejpam-5764	39	28	non	non	ADJ
ejpam-5764	39	29	-	-	ADJ
ejpam-5764	39	30	empty	empty	ADJ
ejpam-5764	39	31	set	set	NOUN
ejpam-5764	39	32	.	.	PUNCT
ejpam-5764	40	1	if	if	SCONJ
ejpam-5764	40	2	ϑ	ϑ	PROPN
ejpam-5764	40	3	satisfies	satisfy	VERB
ejpam-5764	40	4	the	the	DET
ejpam-5764	40	5	following	follow	VERB
ejpam-5764	40	6	requirements	requirement	NOUN
ejpam-5764	40	7	,	,	PUNCT
ejpam-5764	40	8	it	it	PRON
ejpam-5764	40	9	is	be	AUX
ejpam-5764	40	10	considered	consider	VERB
ejpam-5764	40	11	a	a	DET
ejpam-5764	40	12	topology	topology	NOUN
ejpam-5764	40	13	on	on	ADP
ejpam-5764	40	14	x	x	NOUN
ejpam-5764	40	15	:	:	PUNCT
ejpam-5764	40	16	(	(	PUNCT
ejpam-5764	40	17	i	i	NOUN
ejpam-5764	40	18	)	)	PUNCT
ejpam-5764	40	19	∅	∅	NOUN
ejpam-5764	40	20	,	,	PUNCT
ejpam-5764	40	21	x	x	SYM
ejpam-5764	40	22	∈	∈	PROPN
ejpam-5764	40	23	ϑ	ϑ	X
ejpam-5764	40	24	(	(	PUNCT
ejpam-5764	40	25	ii	ii	NOUN
ejpam-5764	40	26	)	)	PUNCT
ejpam-5764	40	27	we	we	PRON
ejpam-5764	40	28	have	have	VERB
ejpam-5764	40	29	a	a	DET
ejpam-5764	40	30	∩b	∩b	NOUN
ejpam-5764	40	31	∈	∈	NOUN
ejpam-5764	40	32	ϑ	ϑ	NOUN
ejpam-5764	40	33	for	for	ADP
ejpam-5764	40	34	every	every	DET
ejpam-5764	40	35	a	a	PROPN
ejpam-5764	40	36	,	,	PUNCT
ejpam-5764	40	37	b	b	PROPN
ejpam-5764	40	38	∈	∈	PROPN
ejpam-5764	40	39	ϑ.	ϑ.	NOUN
ejpam-5764	40	40	(	(	PUNCT
ejpam-5764	40	41	iii	iii	NOUN
ejpam-5764	40	42	)	)	PUNCT
ejpam-5764	41	1	⋃	⋃	PUNCT
ejpam-5764	41	2	α∈λaα	α∈λaα	PROPN
ejpam-5764	41	3	∈	∈	PROPN
ejpam-5764	41	4	ϑ	ϑ	X
ejpam-5764	41	5	if	if	SCONJ
ejpam-5764	41	6	e	e	NOUN
ejpam-5764	41	7	=	=	PRON
ejpam-5764	41	8	{	{	PUNCT
ejpam-5764	41	9	aα	aα	NOUN
ejpam-5764	41	10	:	:	PUNCT
ejpam-5764	41	11	α	α	PROPN
ejpam-5764	41	12	∈	∈	PROPN
ejpam-5764	41	13	λ	λ	PROPN
ejpam-5764	41	14	,	,	PUNCT
ejpam-5764	41	15	aα	aα	NOUN
ejpam-5764	41	16	∈	∈	PROPN
ejpam-5764	41	17	ϑ	ϑ	NOUN
ejpam-5764	41	18	}	}	PUNCT
ejpam-5764	41	19	is	be	AUX
ejpam-5764	41	20	any	any	DET
ejpam-5764	41	21	collection	collection	NOUN
ejpam-5764	41	22	of	of	ADP
ejpam-5764	41	23	sets	set	NOUN
ejpam-5764	41	24	in	in	ADP
ejpam-5764	41	25	ϑ	ϑ	PRON
ejpam-5764	41	26	definition	definition	NOUN
ejpam-5764	41	27	2	2	NUM
ejpam-5764	41	28	.	.	PUNCT
ejpam-5764	42	1	[	[	X
ejpam-5764	42	2	10	10	NUM
ejpam-5764	42	3	]	]	PUNCT
ejpam-5764	42	4	.	.	PUNCT
ejpam-5764	43	1	let	let	VERB
ejpam-5764	43	2	x	x	PRON
ejpam-5764	43	3	be	be	AUX
ejpam-5764	43	4	a	a	DET
ejpam-5764	43	5	non	non	ADJ
ejpam-5764	43	6	-	-	ADJ
ejpam-5764	43	7	empty	empty	ADJ
ejpam-5764	43	8	set	set	NOUN
ejpam-5764	43	9	,	,	PUNCT
ejpam-5764	43	10	and	and	CCONJ
ejpam-5764	43	11	for	for	ADP
ejpam-5764	43	12	i	i	PRON
ejpam-5764	43	13	=	=	NOUN
ejpam-5764	43	14	1	1	NUM
ejpam-5764	43	15	,	,	PUNCT
ejpam-5764	43	16	2	2	NUM
ejpam-5764	43	17	,	,	PUNCT
ejpam-5764	43	18	3	3	NUM
ejpam-5764	43	19	,	,	PUNCT
ejpam-5764	43	20	ϑi	ϑi	PROPN
ejpam-5764	43	21	⊂	⊂	PROPN
ejpam-5764	43	22	p(x	p(x	PROPN
ejpam-5764	43	23	)	)	PUNCT
ejpam-5764	43	24	.	.	PUNCT
ejpam-5764	44	1	(	(	PUNCT
ejpam-5764	44	2	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	44	3	,	,	PUNCT
ejpam-5764	44	4	ϑ2	ϑ2	PROPN
ejpam-5764	44	5	,	,	PUNCT
ejpam-5764	44	6	ϑ3	ϑ3	PROPN
ejpam-5764	44	7	)	)	PUNCT
ejpam-5764	44	8	is	be	AUX
ejpam-5764	44	9	a	a	DET
ejpam-5764	44	10	tri	tri	ADJ
ejpam-5764	44	11	-	-	ADJ
ejpam-5764	44	12	topological	topological	ADJ
ejpam-5764	44	13	space	space	NOUN
ejpam-5764	44	14	if	if	SCONJ
ejpam-5764	44	15	ϑi	ϑi	PROPN
ejpam-5764	44	16	is	be	AUX
ejpam-5764	44	17	a	a	DET
ejpam-5764	44	18	topology	topology	NOUN
ejpam-5764	44	19	on	on	ADP
ejpam-5764	44	20	x	x	PUNCT
ejpam-5764	44	21	for	for	ADP
ejpam-5764	44	22	all	all	DET
ejpam-5764	44	23	i	i	PRON
ejpam-5764	44	24	=	=	NOUN
ejpam-5764	44	25	1	1	NUM
ejpam-5764	44	26	,	,	PUNCT
ejpam-5764	44	27	2	2	NUM
ejpam-5764	44	28	,	,	PUNCT
ejpam-5764	44	29	3	3	NUM
ejpam-5764	45	1	.	.	PUNCT
ejpam-5764	45	2	j.	j.	PROPN
ejpam-5764	45	3	oudetallah	oudetallah	PROPN
ejpam-5764	45	4	et	et	PROPN
ejpam-5764	45	5	al	al	PROPN
ejpam-5764	45	6	.	.	PUNCT
ejpam-5764	45	7	/	/	SYM
ejpam-5764	45	8	eur	eur	PROPN
ejpam-5764	45	9	.	.	PUNCT
ejpam-5764	46	1	j.	j.	PROPN
ejpam-5764	46	2	pure	pure	PROPN
ejpam-5764	46	3	appl	appl	PROPN
ejpam-5764	46	4	.	.	PROPN
ejpam-5764	46	5	math	math	PROPN
ejpam-5764	46	6	,	,	PUNCT
ejpam-5764	46	7	18	18	NUM
ejpam-5764	46	8	(	(	PUNCT
ejpam-5764	46	9	2	2	NUM
ejpam-5764	46	10	)	)	PUNCT
ejpam-5764	46	11	(	(	PUNCT
ejpam-5764	46	12	2025	2025	NUM
ejpam-5764	46	13	)	)	PUNCT
ejpam-5764	46	14	,	,	PUNCT
ejpam-5764	46	15	5764	5764	NUM
ejpam-5764	46	16	3	3	NUM
ejpam-5764	46	17	of	of	ADP
ejpam-5764	46	18	11	11	NUM
ejpam-5764	46	19	example	example	NOUN
ejpam-5764	46	20	1	1	NUM
ejpam-5764	46	21	.	.	X
ejpam-5764	46	22	assume	assume	VERB
ejpam-5764	46	23	x	x	X
ejpam-5764	46	24	=	=	X
ejpam-5764	46	25	{	{	PUNCT
ejpam-5764	46	26	a	a	DET
ejpam-5764	46	27	,	,	PUNCT
ejpam-5764	46	28	b	b	NOUN
ejpam-5764	46	29	,	,	PUNCT
ejpam-5764	46	30	c	c	NOUN
ejpam-5764	46	31	}	}	PUNCT
ejpam-5764	46	32	so	so	SCONJ
ejpam-5764	46	33	that	that	SCONJ
ejpam-5764	46	34	they	they	PRON
ejpam-5764	46	35	(	(	PUNCT
ejpam-5764	46	36	i	i	NOUN
ejpam-5764	46	37	)	)	PUNCT
ejpam-5764	46	38	ϑ1	ϑ1	NOUN
ejpam-5764	46	39	=	=	SYM
ejpam-5764	46	40	{	{	PUNCT
ejpam-5764	46	41	∅	∅	NOUN
ejpam-5764	46	42	,	,	PUNCT
ejpam-5764	46	43	x	x	X
ejpam-5764	46	44	,	,	PUNCT
ejpam-5764	46	45	{	{	PUNCT
ejpam-5764	46	46	a	a	X
ejpam-5764	46	47	}	}	PUNCT
ejpam-5764	46	48	}	}	PUNCT
ejpam-5764	46	49	⊂	⊂	PROPN
ejpam-5764	46	50	p(x	p(x	PROPN
ejpam-5764	46	51	)	)	PUNCT
ejpam-5764	46	52	(	(	PUNCT
ejpam-5764	46	53	ii	ii	NOUN
ejpam-5764	46	54	)	)	PUNCT
ejpam-5764	46	55	ϑ2	ϑ2	PROPN
ejpam-5764	46	56	=	=	SYM
ejpam-5764	46	57	{	{	PUNCT
ejpam-5764	46	58	∅	∅	NOUN
ejpam-5764	46	59	,	,	PUNCT
ejpam-5764	46	60	x	x	X
ejpam-5764	46	61	,	,	PUNCT
ejpam-5764	46	62	{	{	PUNCT
ejpam-5764	46	63	a	a	X
ejpam-5764	46	64	}	}	PUNCT
ejpam-5764	46	65	,	,	PUNCT
ejpam-5764	46	66	{	{	PUNCT
ejpam-5764	46	67	b	b	NOUN
ejpam-5764	46	68	}	}	PUNCT
ejpam-5764	46	69	,	,	PUNCT
ejpam-5764	46	70	{	{	PUNCT
ejpam-5764	46	71	a	a	PRON
ejpam-5764	46	72	,	,	PUNCT
ejpam-5764	46	73	b	b	NOUN
ejpam-5764	46	74	}	}	PUNCT
ejpam-5764	46	75	}	}	PUNCT
ejpam-5764	46	76	⊂	⊂	PROPN
ejpam-5764	46	77	p(x	p(x	PROPN
ejpam-5764	46	78	)	)	PUNCT
ejpam-5764	46	79	(	(	PUNCT
ejpam-5764	46	80	iii	iii	X
ejpam-5764	46	81	)	)	PUNCT
ejpam-5764	46	82	ϑ3	ϑ3	NOUN
ejpam-5764	46	83	=	=	SYM
ejpam-5764	46	84	{	{	PUNCT
ejpam-5764	46	85	∅	∅	NOUN
ejpam-5764	46	86	,	,	PUNCT
ejpam-5764	46	87	x	x	X
ejpam-5764	46	88	,	,	PUNCT
ejpam-5764	46	89	{	{	PUNCT
ejpam-5764	46	90	b	b	NOUN
ejpam-5764	46	91	}	}	PUNCT
ejpam-5764	46	92	,	,	PUNCT
ejpam-5764	46	93	{	{	PUNCT
ejpam-5764	46	94	c	c	X
ejpam-5764	46	95	}	}	PUNCT
ejpam-5764	46	96	,	,	PUNCT
ejpam-5764	46	97	{	{	PUNCT
ejpam-5764	46	98	b	b	X
ejpam-5764	46	99	,	,	PUNCT
ejpam-5764	46	100	c	c	NOUN
ejpam-5764	46	101	}	}	PUNCT
ejpam-5764	46	102	}	}	PUNCT
ejpam-5764	46	103	⊂	⊂	PROPN
ejpam-5764	46	104	p(x	p(x	PROPN
ejpam-5764	46	105	)	)	PUNCT
ejpam-5764	46	106	for	for	ADP
ejpam-5764	46	107	i	i	PROPN
ejpam-5764	46	108	=	=	NOUN
ejpam-5764	46	109	1	1	NUM
ejpam-5764	46	110	,	,	PUNCT
ejpam-5764	46	111	2	2	NUM
ejpam-5764	46	112	,	,	PUNCT
ejpam-5764	46	113	3	3	NUM
ejpam-5764	46	114	,	,	PUNCT
ejpam-5764	46	115	ϑi	ϑi	PROPN
ejpam-5764	46	116	satisfies	satisfy	VERB
ejpam-5764	46	117	the	the	DET
ejpam-5764	46	118	requirements	requirement	NOUN
ejpam-5764	46	119	of	of	ADP
ejpam-5764	46	120	a	a	DET
ejpam-5764	46	121	topological	topological	ADJ
ejpam-5764	46	122	space	space	NOUN
ejpam-5764	46	123	.	.	PUNCT
ejpam-5764	47	1	a	a	DET
ejpam-5764	47	2	tri	tri	ADJ
ejpam-5764	47	3	-	-	ADJ
ejpam-5764	47	4	topological	topological	ADJ
ejpam-5764	47	5	space	space	NOUN
ejpam-5764	47	6	is	be	AUX
ejpam-5764	47	7	thus	thus	ADV
ejpam-5764	47	8	(	(	PUNCT
ejpam-5764	47	9	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	47	10	,	,	PUNCT
ejpam-5764	47	11	ϑ2	ϑ2	PROPN
ejpam-5764	47	12	,	,	PUNCT
ejpam-5764	47	13	ϑ3	ϑ3	PROPN
ejpam-5764	47	14	)	)	PUNCT
ejpam-5764	47	15	.	.	PUNCT
ejpam-5764	48	1	for	for	ADP
ejpam-5764	48	2	example	example	NOUN
ejpam-5764	48	3	,	,	PUNCT
ejpam-5764	48	4	{	{	PUNCT
ejpam-5764	48	5	a	a	PRON
ejpam-5764	48	6	}	}	PUNCT
ejpam-5764	48	7	∪	∪	NOUN
ejpam-5764	48	8	{	{	PUNCT
ejpam-5764	48	9	b	b	NOUN
ejpam-5764	48	10	}	}	PUNCT
ejpam-5764	48	11	=	=	SYM
ejpam-5764	48	12	{	{	PUNCT
ejpam-5764	48	13	a	a	PRON
ejpam-5764	48	14	,	,	PUNCT
ejpam-5764	48	15	b	b	NOUN
ejpam-5764	48	16	}	}	PUNCT
ejpam-5764	48	17	̸∈	̸∈	PROPN
ejpam-5764	48	18	ϑ	ϑ	NOUN
ejpam-5764	48	19	,	,	PUNCT
ejpam-5764	48	20	therefore	therefore	ADV
ejpam-5764	48	21	the	the	DET
ejpam-5764	48	22	space	space	NOUN
ejpam-5764	48	23	ϑ	ϑ	X
ejpam-5764	48	24	=	=	PUNCT
ejpam-5764	48	25	{	{	PUNCT
ejpam-5764	48	26	∅	∅	NOUN
ejpam-5764	48	27	,	,	PUNCT
ejpam-5764	48	28	x	x	X
ejpam-5764	48	29	,	,	PUNCT
ejpam-5764	48	30	{	{	PUNCT
ejpam-5764	48	31	a	a	X
ejpam-5764	48	32	}	}	PUNCT
ejpam-5764	48	33	,	,	PUNCT
ejpam-5764	48	34	{	{	PUNCT
ejpam-5764	48	35	b	b	X
ejpam-5764	48	36	}	}	PUNCT
ejpam-5764	48	37	}	}	PUNCT
ejpam-5764	48	38	is	be	AUX
ejpam-5764	48	39	not	not	PART
ejpam-5764	48	40	a	a	DET
ejpam-5764	48	41	topological	topological	ADJ
ejpam-5764	48	42	space	space	NOUN
ejpam-5764	48	43	.	.	PUNCT
ejpam-5764	49	1	definition	definition	NOUN
ejpam-5764	49	2	3	3	NUM
ejpam-5764	49	3	.	.	PUNCT
ejpam-5764	50	1	[	[	X
ejpam-5764	50	2	11	11	NUM
ejpam-5764	50	3	]	]	PUNCT
ejpam-5764	50	4	presuming	presume	VERB
ejpam-5764	50	5	that	that	SCONJ
ejpam-5764	50	6	(	(	PUNCT
ejpam-5764	50	7	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	50	8	,	,	PUNCT
ejpam-5764	50	9	ϑ2	ϑ2	PROPN
ejpam-5764	50	10	,	,	PUNCT
ejpam-5764	50	11	ϑ3	ϑ3	PROPN
ejpam-5764	50	12	)	)	PUNCT
ejpam-5764	50	13	is	be	AUX
ejpam-5764	50	14	a	a	DET
ejpam-5764	50	15	tri	tri	ADJ
ejpam-5764	50	16	-	-	ADJ
ejpam-5764	50	17	topological	topological	ADJ
ejpam-5764	50	18	space	space	NOUN
ejpam-5764	50	19	and	and	CCONJ
ejpam-5764	50	20	that	that	SCONJ
ejpam-5764	50	21	a	a	DET
ejpam-5764	50	22	⊂	⊂	X
ejpam-5764	50	23	x	x	X
ejpam-5764	50	24	(	(	PUNCT
ejpam-5764	50	25	i	i	NOUN
ejpam-5764	50	26	)	)	PUNCT
ejpam-5764	50	27	if	if	SCONJ
ejpam-5764	50	28	a	a	DET
ejpam-5764	50	29	∈	∈	PROPN
ejpam-5764	50	30	ϑi	ϑi	NOUN
ejpam-5764	50	31	for	for	ADP
ejpam-5764	50	32	some	some	DET
ejpam-5764	50	33	i	i	NOUN
ejpam-5764	50	34	=	=	NOUN
ejpam-5764	50	35	1	1	NUM
ejpam-5764	50	36	,	,	PUNCT
ejpam-5764	50	37	2	2	NUM
ejpam-5764	50	38	,	,	PUNCT
ejpam-5764	50	39	3	3	NUM
ejpam-5764	50	40	,	,	PUNCT
ejpam-5764	50	41	then	then	ADV
ejpam-5764	50	42	a	a	PRON
ejpam-5764	50	43	is	be	AUX
ejpam-5764	50	44	a	a	DET
ejpam-5764	50	45	ϑi	ϑi	NOUN
ejpam-5764	50	46	-	-	PUNCT
ejpam-5764	50	47	open	open	NOUN
ejpam-5764	50	48	set	set	NOUN
ejpam-5764	50	49	.	.	PUNCT
ejpam-5764	51	1	(	(	PUNCT
ejpam-5764	51	2	ii	ii	NOUN
ejpam-5764	51	3	)	)	PUNCT
ejpam-5764	51	4	if	if	SCONJ
ejpam-5764	51	5	ac	ac	PROPN
ejpam-5764	51	6	∈	∈	PROPN
ejpam-5764	51	7	ϑi	ϑi	PROPN
ejpam-5764	51	8	for	for	ADP
ejpam-5764	51	9	some	some	DET
ejpam-5764	51	10	i	i	NOUN
ejpam-5764	51	11	=	=	NOUN
ejpam-5764	51	12	1	1	NUM
ejpam-5764	51	13	,	,	PUNCT
ejpam-5764	51	14	2	2	NUM
ejpam-5764	51	15	,	,	PUNCT
ejpam-5764	51	16	3	3	NUM
ejpam-5764	51	17	,	,	PUNCT
ejpam-5764	51	18	then	then	ADV
ejpam-5764	51	19	a	a	PRON
ejpam-5764	51	20	is	be	AUX
ejpam-5764	51	21	a	a	DET
ejpam-5764	51	22	ϑi	ϑi	NOUN
ejpam-5764	51	23	-	-	PUNCT
ejpam-5764	51	24	closed	close	VERB
ejpam-5764	51	25	set	set	NOUN
ejpam-5764	51	26	.	.	PUNCT
ejpam-5764	52	1	(	(	PUNCT
ejpam-5764	52	2	iii	iii	X
ejpam-5764	52	3	)	)	PUNCT
ejpam-5764	52	4	if	if	SCONJ
ejpam-5764	52	5	a	a	PRON
ejpam-5764	52	6	and	and	CCONJ
ejpam-5764	52	7	ac	ac	PROPN
ejpam-5764	52	8	are	be	AUX
ejpam-5764	52	9	both	both	PRON
ejpam-5764	52	10	in	in	ADP
ejpam-5764	52	11	ϑi	ϑi	NOUN
ejpam-5764	52	12	for	for	ADP
ejpam-5764	52	13	some	some	DET
ejpam-5764	52	14	i	i	NOUN
ejpam-5764	52	15	=	=	NOUN
ejpam-5764	52	16	1	1	NUM
ejpam-5764	52	17	,	,	PUNCT
ejpam-5764	52	18	2	2	NUM
ejpam-5764	52	19	,	,	PUNCT
ejpam-5764	52	20	3	3	NUM
ejpam-5764	52	21	,	,	PUNCT
ejpam-5764	52	22	then	then	ADV
ejpam-5764	52	23	a	a	PRON
ejpam-5764	52	24	is	be	AUX
ejpam-5764	52	25	referred	refer	VERB
ejpam-5764	52	26	to	to	ADP
ejpam-5764	52	27	as	as	ADP
ejpam-5764	52	28	a	a	DET
ejpam-5764	52	29	ϑi	ϑi	NOUN
ejpam-5764	52	30	-	-	PUNCT
ejpam-5764	52	31	clopen	clopen	ADJ
ejpam-5764	52	32	set	set	NOUN
ejpam-5764	52	33	.	.	PUNCT
ejpam-5764	53	1	definition	definition	NOUN
ejpam-5764	53	2	4	4	NUM
ejpam-5764	53	3	.	.	PUNCT
ejpam-5764	54	1	[	[	X
ejpam-5764	54	2	7	7	X
ejpam-5764	54	3	]	]	PUNCT
ejpam-5764	54	4	given	give	VERB
ejpam-5764	54	5	a	a	DET
ejpam-5764	54	6	tri	tri	ADJ
ejpam-5764	54	7	-	-	ADJ
ejpam-5764	54	8	topological	topological	ADJ
ejpam-5764	54	9	space	space	NOUN
ejpam-5764	54	10	(	(	PUNCT
ejpam-5764	54	11	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	54	12	,	,	PUNCT
ejpam-5764	54	13	ϑ2	ϑ2	PROPN
ejpam-5764	54	14	,	,	PUNCT
ejpam-5764	54	15	ϑ3	ϑ3	PROPN
ejpam-5764	54	16	)	)	PUNCT
ejpam-5764	54	17	,	,	PUNCT
ejpam-5764	54	18	x	x	X
ejpam-5764	54	19	̸=	̸=	NOUN
ejpam-5764	54	20	∅	∅	NOUN
ejpam-5764	54	21	,	,	PUNCT
ejpam-5764	54	22	and	and	CCONJ
ejpam-5764	54	23	a	a	PRON
ejpam-5764	54	24	as	as	ADP
ejpam-5764	54	25	a	a	DET
ejpam-5764	54	26	subset	subset	NOUN
ejpam-5764	54	27	of	of	ADP
ejpam-5764	54	28	x	x	PRON
ejpam-5764	54	29	,	,	PUNCT
ejpam-5764	54	30	a	a	DET
ejpam-5764	54	31	∈	∈	NOUN
ejpam-5764	54	32	x	x	PUNCT
ejpam-5764	54	33	is	be	AUX
ejpam-5764	54	34	a	a	DET
ejpam-5764	54	35	tri	tri	ADJ
ejpam-5764	54	36	-	-	ADJ
ejpam-5764	54	37	limit	limit	ADJ
ejpam-5764	54	38	point	point	NOUN
ejpam-5764	54	39	of	of	ADP
ejpam-5764	54	40	a	a	DET
ejpam-5764	54	41	if	if	NOUN
ejpam-5764	54	42	,	,	PUNCT
ejpam-5764	54	43	for	for	ADP
ejpam-5764	54	44	any	any	DET
ejpam-5764	54	45	ϑi	ϑi	NOUN
ejpam-5764	54	46	-	-	PUNCT
ejpam-5764	54	47	open	open	NOUN
ejpam-5764	54	48	set	set	VERB
ejpam-5764	54	49	ua	ua	PROPN
ejpam-5764	54	50	containing	contain	VERB
ejpam-5764	54	51	a	a	DET
ejpam-5764	54	52	,	,	PUNCT
ejpam-5764	54	53	ua∩(a−{a	ua∩(a−{a	PROPN
ejpam-5764	54	54	}	}	PUNCT
ejpam-5764	54	55	)	)	PUNCT
ejpam-5764	55	1	̸=	̸=	PROPN
ejpam-5764	55	2	∅	∅	NOUN
ejpam-5764	55	3	..	..	PUNCT
ejpam-5764	55	4	a′	a′	PROPN
ejpam-5764	55	5	=	=	SYM
ejpam-5764	55	6	{	{	PUNCT
ejpam-5764	55	7	a	a	X
ejpam-5764	55	8	:	:	PUNCT
ejpam-5764	55	9	a	a	PRON
ejpam-5764	55	10	is	be	AUX
ejpam-5764	55	11	a	a	DET
ejpam-5764	55	12	tri	tri	ADJ
ejpam-5764	55	13	-	-	ADJ
ejpam-5764	55	14	limit	limit	ADJ
ejpam-5764	55	15	point	point	NOUN
ejpam-5764	55	16	of	of	ADP
ejpam-5764	55	17	a	a	PRON
ejpam-5764	55	18	}	}	PUNCT
ejpam-5764	55	19	is	be	AUX
ejpam-5764	55	20	the	the	DET
ejpam-5764	55	21	representation	representation	NOUN
ejpam-5764	55	22	of	of	ADP
ejpam-5764	55	23	the	the	DET
ejpam-5764	55	24	tri	tri	ADJ
ejpam-5764	55	25	-	-	ADJ
ejpam-5764	55	26	derived	derived	ADJ
ejpam-5764	55	27	set	set	NOUN
ejpam-5764	55	28	,	,	PUNCT
ejpam-5764	55	29	which	which	PRON
ejpam-5764	55	30	is	be	AUX
ejpam-5764	55	31	the	the	DET
ejpam-5764	55	32	set	set	NOUN
ejpam-5764	55	33	of	of	ADP
ejpam-5764	55	34	all	all	DET
ejpam-5764	55	35	tri	tri	ADJ
ejpam-5764	55	36	-	-	ADJ
ejpam-5764	55	37	limit	limit	ADJ
ejpam-5764	55	38	points	point	NOUN
ejpam-5764	55	39	.	.	PUNCT
ejpam-5764	56	1	theorem	theorem	NOUN
ejpam-5764	56	2	1	1	NUM
ejpam-5764	56	3	.	.	PUNCT
ejpam-5764	57	1	[	[	X
ejpam-5764	57	2	8	8	NUM
ejpam-5764	57	3	]	]	X
ejpam-5764	57	4	if	if	SCONJ
ejpam-5764	57	5	(	(	PUNCT
ejpam-5764	57	6	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	57	7	,	,	PUNCT
ejpam-5764	57	8	ϑ2	ϑ2	PROPN
ejpam-5764	57	9	,	,	PUNCT
ejpam-5764	57	10	ϑ3	ϑ3	PROPN
ejpam-5764	57	11	)	)	PUNCT
ejpam-5764	57	12	and	and	CCONJ
ejpam-5764	57	13	a	a	PRON
ejpam-5764	57	14	,	,	PUNCT
ejpam-5764	57	15	b	b	X
ejpam-5764	57	16	⊂	⊂	PROPN
ejpam-5764	57	17	x	x	X
ejpam-5764	57	18	are	be	AUX
ejpam-5764	57	19	tri	tri	ADJ
ejpam-5764	57	20	-	-	ADJ
ejpam-5764	57	21	topological	topological	ADJ
ejpam-5764	57	22	spaces	space	NOUN
ejpam-5764	57	23	,	,	PUNCT
ejpam-5764	57	24	then	then	ADV
ejpam-5764	57	25	:	:	PUNCT
ejpam-5764	57	26	(	(	PUNCT
ejpam-5764	57	27	i	i	NOUN
ejpam-5764	57	28	)	)	PUNCT
ejpam-5764	57	29	∅′	∅′	PART
ejpam-5764	57	30	=	=	SYM
ejpam-5764	58	1	∅	∅	NOUN
ejpam-5764	58	2	(	(	PUNCT
ejpam-5764	58	3	ii	ii	NOUN
ejpam-5764	58	4	)	)	PUNCT
ejpam-5764	58	5	(	(	PUNCT
ejpam-5764	58	6	a	a	DET
ejpam-5764	58	7	∪b)′	∪b)′	NOUN
ejpam-5764	58	8	=	=	PUNCT
ejpam-5764	58	9	a′	a′	PROPN
ejpam-5764	58	10	∪b′	∪b′	NOUN
ejpam-5764	58	11	(	(	PUNCT
ejpam-5764	58	12	iii	iii	NOUN
ejpam-5764	58	13	)	)	PUNCT
ejpam-5764	58	14	(	(	PUNCT
ejpam-5764	58	15	a	a	X
ejpam-5764	58	16	∩b)′	∩b)′	PUNCT
ejpam-5764	58	17	⊂	⊂	PROPN
ejpam-5764	58	18	a′	a′	NOUN
ejpam-5764	58	19	∩b′	∩b′	PROPN
ejpam-5764	58	20	(	(	PUNCT
ejpam-5764	58	21	iv	iv	X
ejpam-5764	58	22	)	)	PUNCT
ejpam-5764	58	23	if	if	SCONJ
ejpam-5764	58	24	a	a	DET
ejpam-5764	58	25	⊂	⊂	PROPN
ejpam-5764	58	26	b	b	PROPN
ejpam-5764	58	27	,	,	PUNCT
ejpam-5764	58	28	then	then	ADV
ejpam-5764	58	29	a′	a′	PROPN
ejpam-5764	58	30	⊂	⊂	PROPN
ejpam-5764	58	31	b′	b′	ADJ
ejpam-5764	58	32	definition	definition	NOUN
ejpam-5764	58	33	5	5	NUM
ejpam-5764	58	34	.	.	PUNCT
ejpam-5764	59	1	[	[	X
ejpam-5764	59	2	9	9	NUM
ejpam-5764	59	3	]	]	X
ejpam-5764	59	4	a	a	DET
ejpam-5764	59	5	=	=	X
ejpam-5764	59	6	a	a	DET
ejpam-5764	59	7	∪a′	∪a′	NOUN
ejpam-5764	59	8	is	be	AUX
ejpam-5764	59	9	the	the	DET
ejpam-5764	59	10	representation	representation	NOUN
ejpam-5764	59	11	of	of	ADP
ejpam-5764	59	12	the	the	DET
ejpam-5764	59	13	tri	tri	ADJ
ejpam-5764	59	14	-	-	NOUN
ejpam-5764	59	15	closure	closure	NOUN
ejpam-5764	59	16	set	set	VERB
ejpam-5764	59	17	if	if	SCONJ
ejpam-5764	59	18	(	(	PUNCT
ejpam-5764	59	19	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	59	20	,	,	PUNCT
ejpam-5764	59	21	ϑ2	ϑ2	PROPN
ejpam-5764	59	22	,	,	PUNCT
ejpam-5764	59	23	ϑ3	ϑ3	PROPN
ejpam-5764	59	24	)	)	PUNCT
ejpam-5764	59	25	is	be	AUX
ejpam-5764	59	26	a	a	DET
ejpam-5764	59	27	tri	tri	ADJ
ejpam-5764	59	28	-	-	ADJ
ejpam-5764	59	29	topological	topological	ADJ
ejpam-5764	59	30	space	space	NOUN
ejpam-5764	59	31	,	,	PUNCT
ejpam-5764	59	32	x	x	PUNCT
ejpam-5764	59	33	̸=	̸=	NOUN
ejpam-5764	59	34	∅	∅	NOUN
ejpam-5764	59	35	,	,	PUNCT
ejpam-5764	59	36	and	and	CCONJ
ejpam-5764	59	37	a	a	PRON
ejpam-5764	59	38	is	be	AUX
ejpam-5764	59	39	a	a	DET
ejpam-5764	59	40	subset	subset	NOUN
ejpam-5764	59	41	of	of	ADP
ejpam-5764	59	42	x.	x.	PROPN
ejpam-5764	59	43	theorem	theorem	NOUN
ejpam-5764	59	44	2	2	NUM
ejpam-5764	59	45	.	.	PUNCT
ejpam-5764	60	1	[	[	X
ejpam-5764	60	2	8	8	NUM
ejpam-5764	60	3	]	]	X
ejpam-5764	60	4	let	let	VERB
ejpam-5764	60	5	(	(	PUNCT
ejpam-5764	60	6	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	60	7	,	,	PUNCT
ejpam-5764	60	8	ϑ2	ϑ2	PROPN
ejpam-5764	60	9	,	,	PUNCT
ejpam-5764	60	10	ϑ3	ϑ3	PROPN
ejpam-5764	60	11	)	)	PUNCT
ejpam-5764	60	12	be	be	AUX
ejpam-5764	60	13	a	a	DET
ejpam-5764	60	14	tri	tri	ADJ
ejpam-5764	60	15	-	-	ADJ
ejpam-5764	60	16	topological	topological	ADJ
ejpam-5764	60	17	space	space	NOUN
ejpam-5764	60	18	and	and	CCONJ
ejpam-5764	60	19	a	a	DET
ejpam-5764	60	20	,	,	PUNCT
ejpam-5764	60	21	b	b	X
ejpam-5764	60	22	⊂	⊂	PROPN
ejpam-5764	60	23	x.	x.	NOUN
ejpam-5764	61	1	then	then	ADV
ejpam-5764	61	2	:	:	PUNCT
ejpam-5764	61	3	(	(	PUNCT
ejpam-5764	61	4	i	i	NOUN
ejpam-5764	61	5	)	)	PUNCT
ejpam-5764	61	6	x	x	X
ejpam-5764	62	1	=	=	PUNCT
ejpam-5764	62	2	x	x	X
ejpam-5764	62	3	and	and	CCONJ
ejpam-5764	62	4	∅	∅	NOUN
ejpam-5764	62	5	=	=	NOUN
ejpam-5764	62	6	∅	∅	NOUN
ejpam-5764	62	7	(	(	PUNCT
ejpam-5764	62	8	ii	ii	NOUN
ejpam-5764	62	9	)	)	PUNCT
ejpam-5764	62	10	a	a	PRON
ejpam-5764	62	11	∪b	∪b	X
ejpam-5764	62	12	=	=	PUNCT
ejpam-5764	62	13	a	a	PRON
ejpam-5764	62	14	∪b	∪b	PUNCT
ejpam-5764	62	15	(	(	PUNCT
ejpam-5764	62	16	iii	iii	NOUN
ejpam-5764	62	17	)	)	PUNCT
ejpam-5764	62	18	a	a	DET
ejpam-5764	62	19	∩b	∩b	X
ejpam-5764	62	20	⊂	⊂	PRON
ejpam-5764	62	21	a	a	DET
ejpam-5764	62	22	∩b	∩b	NOUN
ejpam-5764	62	23	(	(	PUNCT
ejpam-5764	62	24	iv	iv	X
ejpam-5764	62	25	)	)	PUNCT
ejpam-5764	62	26	we	we	PRON
ejpam-5764	62	27	have	have	VERB
ejpam-5764	62	28	ua	ua	PROPN
ejpam-5764	62	29	∩a	∩a	PROPN
ejpam-5764	62	30	̸=	̸=	PROPN
ejpam-5764	62	31	∅	∅	NOUN
ejpam-5764	62	32	for	for	ADP
ejpam-5764	62	33	every	every	DET
ejpam-5764	62	34	point	point	NOUN
ejpam-5764	62	35	a	a	DET
ejpam-5764	62	36	∈	∈	PROPN
ejpam-5764	62	37	a	a	PRON
ejpam-5764	62	38	and	and	CCONJ
ejpam-5764	62	39	every	every	DET
ejpam-5764	62	40	ϑi	ϑi	NOUN
ejpam-5764	62	41	-	-	PUNCT
ejpam-5764	62	42	open	open	NOUN
ejpam-5764	62	43	set	set	VERB
ejpam-5764	62	44	ua	ua	NOUN
ejpam-5764	62	45	containing	contain	VERB
ejpam-5764	62	46	a.	a.	NOUN
ejpam-5764	62	47	(	(	PUNCT
ejpam-5764	62	48	v	v	NOUN
ejpam-5764	62	49	)	)	PUNCT
ejpam-5764	62	50	a	a	PRON
ejpam-5764	62	51	is	be	AUX
ejpam-5764	62	52	a	a	DET
ejpam-5764	62	53	ϑi	ϑi	NOUN
ejpam-5764	62	54	-	-	PUNCT
ejpam-5764	62	55	closed	close	VERB
ejpam-5764	62	56	set	set	NOUN
ejpam-5764	62	57	for	for	ADP
ejpam-5764	62	58	each	each	DET
ejpam-5764	62	59	i	i	PRON
ejpam-5764	62	60	∈	∈	PROPN
ejpam-5764	62	61	{	{	PUNCT
ejpam-5764	62	62	1	1	NUM
ejpam-5764	62	63	,	,	PUNCT
ejpam-5764	62	64	2	2	NUM
ejpam-5764	62	65	,	,	PUNCT
ejpam-5764	62	66	3	3	NUM
ejpam-5764	62	67	}	}	PUNCT
ejpam-5764	62	68	if	if	SCONJ
ejpam-5764	63	1	and	and	CCONJ
ejpam-5764	63	2	only	only	ADV
ejpam-5764	63	3	if	if	SCONJ
ejpam-5764	63	4	a	a	DET
ejpam-5764	63	5	=	=	X
ejpam-5764	63	6	a.	a.	NOUN
ejpam-5764	63	7	j.	j.	PROPN
ejpam-5764	63	8	oudetallah	oudetallah	PROPN
ejpam-5764	63	9	et	et	PROPN
ejpam-5764	63	10	al	al	PROPN
ejpam-5764	63	11	.	.	PUNCT
ejpam-5764	63	12	/	/	SYM
ejpam-5764	63	13	eur	eur	PROPN
ejpam-5764	63	14	.	.	PUNCT
ejpam-5764	64	1	j.	j.	PROPN
ejpam-5764	64	2	pure	pure	PROPN
ejpam-5764	64	3	appl	appl	PROPN
ejpam-5764	64	4	.	.	PROPN
ejpam-5764	64	5	math	math	PROPN
ejpam-5764	64	6	,	,	PUNCT
ejpam-5764	64	7	18	18	NUM
ejpam-5764	64	8	(	(	PUNCT
ejpam-5764	64	9	2	2	NUM
ejpam-5764	64	10	)	)	PUNCT
ejpam-5764	64	11	(	(	PUNCT
ejpam-5764	64	12	2025	2025	NUM
ejpam-5764	64	13	)	)	PUNCT
ejpam-5764	64	14	,	,	PUNCT
ejpam-5764	64	15	5764	5764	NUM
ejpam-5764	64	16	4	4	NUM
ejpam-5764	64	17	of	of	ADP
ejpam-5764	64	18	11	11	NUM
ejpam-5764	64	19	definition	definition	NOUN
ejpam-5764	64	20	6	6	NUM
ejpam-5764	64	21	.	.	PUNCT
ejpam-5764	65	1	[	[	X
ejpam-5764	65	2	4	4	X
ejpam-5764	65	3	]	]	PUNCT
ejpam-5764	65	4	allow	allow	VERB
ejpam-5764	65	5	x	x	PUNCT
ejpam-5764	65	6	̸=	̸=	PROPN
ejpam-5764	65	7	∅	∅	NOUN
ejpam-5764	65	8	,	,	PUNCT
ejpam-5764	65	9	a	a	DET
ejpam-5764	65	10	be	be	AUX
ejpam-5764	65	11	a	a	DET
ejpam-5764	65	12	subset	subset	NOUN
ejpam-5764	65	13	of	of	ADP
ejpam-5764	65	14	x	x	X
ejpam-5764	65	15	,	,	PUNCT
ejpam-5764	65	16	and	and	CCONJ
ejpam-5764	65	17	allow	allow	VERB
ejpam-5764	65	18	(	(	PUNCT
ejpam-5764	65	19	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	65	20	,	,	PUNCT
ejpam-5764	65	21	ϑ2	ϑ2	PROPN
ejpam-5764	65	22	,	,	PUNCT
ejpam-5764	65	23	ϑ3	ϑ3	PROPN
ejpam-5764	65	24	)	)	PUNCT
ejpam-5764	65	25	be	be	AUX
ejpam-5764	65	26	a	a	DET
ejpam-5764	65	27	tritopological	tritopological	ADJ
ejpam-5764	65	28	space	space	NOUN
ejpam-5764	65	29	.	.	PUNCT
ejpam-5764	66	1	if	if	SCONJ
ejpam-5764	66	2	there	there	PRON
ejpam-5764	66	3	is	be	VERB
ejpam-5764	66	4	at	at	ADV
ejpam-5764	66	5	least	least	ADJ
ejpam-5764	66	6	one	one	NUM
ejpam-5764	66	7	ϑi	ϑi	NOUN
ejpam-5764	66	8	-	-	PUNCT
ejpam-5764	66	9	neighborhood	neighborhood	NOUN
ejpam-5764	66	10	n(a	n(a	NOUN
ejpam-5764	66	11	,	,	PUNCT
ejpam-5764	66	12	ϑi	ϑi	PROPN
ejpam-5764	66	13	)	)	PUNCT
ejpam-5764	66	14	of	of	ADP
ejpam-5764	66	15	a	a	PRON
ejpam-5764	66	16	for	for	ADP
ejpam-5764	66	17	some	some	DET
ejpam-5764	66	18	i	i	PRON
ejpam-5764	66	19	∈	∈	PROPN
ejpam-5764	66	20	{	{	PUNCT
ejpam-5764	66	21	1	1	NUM
ejpam-5764	66	22	,	,	PUNCT
ejpam-5764	66	23	2	2	NUM
ejpam-5764	66	24	,	,	PUNCT
ejpam-5764	66	25	3	3	NUM
ejpam-5764	66	26	}	}	PUNCT
ejpam-5764	66	27	such	such	ADJ
ejpam-5764	66	28	that	that	SCONJ
ejpam-5764	66	29	n(a	n(a	PROPN
ejpam-5764	66	30	,	,	PUNCT
ejpam-5764	66	31	ϑi	ϑi	PROPN
ejpam-5764	66	32	)	)	PUNCT
ejpam-5764	66	33	⊆	⊆	NUM
ejpam-5764	66	34	a	a	PRON
ejpam-5764	66	35	,	,	PUNCT
ejpam-5764	66	36	then	then	ADV
ejpam-5764	66	37	a	a	DET
ejpam-5764	66	38	point	point	NOUN
ejpam-5764	66	39	a	a	DET
ejpam-5764	66	40	∈	∈	NOUN
ejpam-5764	66	41	a	a	PRON
ejpam-5764	66	42	is	be	AUX
ejpam-5764	66	43	called	call	VERB
ejpam-5764	66	44	a	a	DET
ejpam-5764	66	45	tri	tri	ADJ
ejpam-5764	66	46	-	-	ADJ
ejpam-5764	66	47	interior	interior	ADJ
ejpam-5764	66	48	point	point	NOUN
ejpam-5764	66	49	of	of	ADP
ejpam-5764	66	50	a.	a.	NOUN
ejpam-5764	66	51	a	a	DET
ejpam-5764	66	52	◦	◦	NOUN
ejpam-5764	66	53	or	or	CCONJ
ejpam-5764	66	54	int(a	int(a	PROPN
ejpam-5764	66	55	)	)	PUNCT
ejpam-5764	66	56	indicate	indicate	VERB
ejpam-5764	66	57	the	the	DET
ejpam-5764	66	58	tri	tri	ADJ
ejpam-5764	66	59	-	-	ADJ
ejpam-5764	66	60	interior	interior	ADJ
ejpam-5764	66	61	of	of	ADP
ejpam-5764	66	62	a	a	PRON
ejpam-5764	66	63	,	,	PUNCT
ejpam-5764	66	64	which	which	PRON
ejpam-5764	66	65	is	be	AUX
ejpam-5764	66	66	the	the	DET
ejpam-5764	66	67	set	set	NOUN
ejpam-5764	66	68	of	of	ADP
ejpam-5764	66	69	all	all	DET
ejpam-5764	66	70	tri	tri	ADJ
ejpam-5764	66	71	-	-	ADJ
ejpam-5764	66	72	interior	interior	ADJ
ejpam-5764	66	73	points	point	NOUN
ejpam-5764	66	74	of	of	ADP
ejpam-5764	66	75	a.	a.	NOUN
ejpam-5764	66	76	a	a	DET
ejpam-5764	66	77	◦	◦	NOUN
ejpam-5764	66	78	=	=	SYM
ejpam-5764	66	79	int(a	int(a	NOUN
ejpam-5764	66	80	)	)	PUNCT
ejpam-5764	66	81	=	=	NOUN
ejpam-5764	67	1	(	(	PUNCT
ejpam-5764	67	2	ac)c	ac)c	PROPN
ejpam-5764	67	3	is	be	AUX
ejpam-5764	67	4	another	another	DET
ejpam-5764	67	5	way	way	NOUN
ejpam-5764	67	6	to	to	PART
ejpam-5764	67	7	express	express	VERB
ejpam-5764	67	8	this	this	PRON
ejpam-5764	67	9	,	,	PUNCT
ejpam-5764	67	10	in	in	ADP
ejpam-5764	67	11	which	which	PRON
ejpam-5764	67	12	ac	ac	PROPN
ejpam-5764	67	13	is	be	AUX
ejpam-5764	67	14	the	the	DET
ejpam-5764	67	15	tri	tri	NOUN
ejpam-5764	67	16	-	-	NOUN
ejpam-5764	67	17	closure	closure	NOUN
ejpam-5764	67	18	of	of	ADP
ejpam-5764	67	19	the	the	DET
ejpam-5764	67	20	complement	complement	NOUN
ejpam-5764	67	21	of	of	ADP
ejpam-5764	67	22	a.	a.	NOUN
ejpam-5764	67	23	theorem	theorem	NOUN
ejpam-5764	67	24	3	3	NUM
ejpam-5764	67	25	.	.	PUNCT
ejpam-5764	68	1	[	[	X
ejpam-5764	68	2	7	7	X
ejpam-5764	68	3	]	]	X
ejpam-5764	68	4	the	the	DET
ejpam-5764	68	5	following	follow	VERB
ejpam-5764	68	6	characteristics	characteristic	NOUN
ejpam-5764	68	7	are	be	AUX
ejpam-5764	68	8	true	true	ADJ
ejpam-5764	68	9	given	give	VERB
ejpam-5764	68	10	a	a	DET
ejpam-5764	68	11	tri	tri	ADJ
ejpam-5764	68	12	-	-	ADJ
ejpam-5764	68	13	topological	topological	ADJ
ejpam-5764	68	14	space	space	NOUN
ejpam-5764	68	15	(	(	PUNCT
ejpam-5764	68	16	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	68	17	,	,	PUNCT
ejpam-5764	68	18	ϑ2	ϑ2	PROPN
ejpam-5764	68	19	,	,	PUNCT
ejpam-5764	68	20	ϑ3	ϑ3	PROPN
ejpam-5764	68	21	)	)	PUNCT
ejpam-5764	68	22	and	and	CCONJ
ejpam-5764	68	23	a	a	PRON
ejpam-5764	68	24	,	,	PUNCT
ejpam-5764	68	25	b	b	X
ejpam-5764	68	26	⊂	⊂	PROPN
ejpam-5764	68	27	x	x	X
ejpam-5764	68	28	:	:	PUNCT
ejpam-5764	68	29	(	(	PUNCT
ejpam-5764	68	30	i	i	NOUN
ejpam-5764	68	31	)	)	PUNCT
ejpam-5764	68	32	x	x	X
ejpam-5764	68	33	◦	◦	NOUN
ejpam-5764	68	34	=	=	SYM
ejpam-5764	68	35	x	x	X
ejpam-5764	68	36	and	and	CCONJ
ejpam-5764	68	37	∅	∅	NOUN
ejpam-5764	68	38	◦	◦	NOUN
ejpam-5764	68	39	=	=	SYM
ejpam-5764	68	40	∅.	∅.	X
ejpam-5764	68	41	(	(	PUNCT
ejpam-5764	68	42	ii	ii	NOUN
ejpam-5764	68	43	)	)	PUNCT
ejpam-5764	68	44	(	(	PUNCT
ejpam-5764	68	45	a	a	DET
ejpam-5764	68	46	∩b	∩b	NOUN
ejpam-5764	68	47	)	)	PUNCT
ejpam-5764	68	48	◦	◦	NOUN
ejpam-5764	68	49	=	=	PUNCT
ejpam-5764	68	50	a	a	DET
ejpam-5764	68	51	◦	◦	NOUN
ejpam-5764	68	52	∩b	∩b	NOUN
ejpam-5764	68	53	◦	◦	NOUN
ejpam-5764	68	54	and	and	CCONJ
ejpam-5764	68	55	a	a	DET
ejpam-5764	68	56	◦	◦	NOUN
ejpam-5764	68	57	∪b	∪b	NOUN
ejpam-5764	68	58	◦	◦	NOUN
ejpam-5764	68	59	⊂	⊂	X
ejpam-5764	68	60	(	(	PUNCT
ejpam-5764	68	61	a	a	DET
ejpam-5764	68	62	∪b)	∪b)	PROPN
ejpam-5764	68	63	◦	◦	NOUN
ejpam-5764	68	64	.	.	PUNCT
ejpam-5764	69	1	(	(	PUNCT
ejpam-5764	69	2	iii	iii	X
ejpam-5764	69	3	)	)	PUNCT
ejpam-5764	69	4	a	a	DET
ejpam-5764	69	5	◦	◦	NOUN
ejpam-5764	69	6	is	be	AUX
ejpam-5764	69	7	a	a	DET
ejpam-5764	69	8	ϑi	ϑi	NOUN
ejpam-5764	69	9	-	-	PUNCT
ejpam-5764	69	10	open	open	NOUN
ejpam-5764	69	11	set	set	NOUN
ejpam-5764	69	12	for	for	ADP
ejpam-5764	69	13	each	each	DET
ejpam-5764	69	14	i	i	PRON
ejpam-5764	69	15	∈	∈	PROPN
ejpam-5764	69	16	{	{	PUNCT
ejpam-5764	69	17	1	1	NUM
ejpam-5764	69	18	,	,	PUNCT
ejpam-5764	69	19	2	2	NUM
ejpam-5764	69	20	,	,	PUNCT
ejpam-5764	69	21	3	3	NUM
ejpam-5764	69	22	}	}	PUNCT
ejpam-5764	69	23	if	if	SCONJ
ejpam-5764	69	24	and	and	CCONJ
ejpam-5764	69	25	only	only	ADV
ejpam-5764	69	26	if	if	SCONJ
ejpam-5764	69	27	there	there	PRON
ejpam-5764	69	28	exists	exist	VERB
ejpam-5764	69	29	a	a	DET
ejpam-5764	69	30	ϑi	ϑi	NOUN
ejpam-5764	69	31	-	-	PUNCT
ejpam-5764	69	32	open	open	NOUN
ejpam-5764	69	33	set	set	VERB
ejpam-5764	69	34	un	un	PROPN
ejpam-5764	69	35	such	such	ADJ
ejpam-5764	69	36	that	that	SCONJ
ejpam-5764	69	37	n	n	NUM
ejpam-5764	69	38	∈	∈	PROPN
ejpam-5764	69	39	un	un	PROPN
ejpam-5764	69	40	⊂	⊂	PROPN
ejpam-5764	69	41	a	a	PROPN
ejpam-5764	69	42	for	for	ADP
ejpam-5764	69	43	each	each	DET
ejpam-5764	69	44	i	i	PRON
ejpam-5764	69	45	∈	∈	PROPN
ejpam-5764	69	46	{	{	PUNCT
ejpam-5764	69	47	1	1	NUM
ejpam-5764	69	48	,	,	PUNCT
ejpam-5764	69	49	2	2	NUM
ejpam-5764	69	50	,	,	PUNCT
ejpam-5764	69	51	3	3	NUM
ejpam-5764	69	52	}	}	PUNCT
ejpam-5764	69	53	.	.	PUNCT
ejpam-5764	70	1	definition	definition	NOUN
ejpam-5764	70	2	7	7	NUM
ejpam-5764	70	3	.	.	PUNCT
ejpam-5764	71	1	[	[	X
ejpam-5764	71	2	8	8	NUM
ejpam-5764	71	3	]	]	PUNCT
ejpam-5764	71	4	since	since	SCONJ
ejpam-5764	71	5	x	x	PROPN
ejpam-5764	71	6	̸=	̸=	PROPN
ejpam-5764	71	7	ϕ	ϕ	PROPN
ejpam-5764	71	8	and	and	CCONJ
ejpam-5764	71	9	a	a	PRON
ejpam-5764	71	10	is	be	AUX
ejpam-5764	71	11	a	a	DET
ejpam-5764	71	12	subset	subset	NOUN
ejpam-5764	71	13	of	of	ADP
ejpam-5764	71	14	x	x	PRON
ejpam-5764	71	15	,	,	PUNCT
ejpam-5764	71	16	let	let	VERB
ejpam-5764	71	17	(	(	PUNCT
ejpam-5764	71	18	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	71	19	,	,	PUNCT
ejpam-5764	71	20	ϑ2	ϑ2	PROPN
ejpam-5764	71	21	,	,	PUNCT
ejpam-5764	71	22	ϑ3	ϑ3	PROPN
ejpam-5764	71	23	)	)	PUNCT
ejpam-5764	71	24	be	be	AUX
ejpam-5764	71	25	a	a	DET
ejpam-5764	71	26	tri	tri	ADJ
ejpam-5764	71	27	-	-	ADJ
ejpam-5764	71	28	topological	topological	ADJ
ejpam-5764	71	29	space	space	NOUN
ejpam-5764	71	30	.	.	PUNCT
ejpam-5764	72	1	if	if	SCONJ
ejpam-5764	72	2	there	there	PRON
ejpam-5764	72	3	is	be	VERB
ejpam-5764	72	4	at	at	ADV
ejpam-5764	72	5	least	least	ADJ
ejpam-5764	72	6	one	one	NUM
ejpam-5764	72	7	neighborhood	neighborhood	NOUN
ejpam-5764	72	8	of	of	ADP
ejpam-5764	72	9	a	a	DET
ejpam-5764	72	10	such	such	ADJ
ejpam-5764	72	11	that	that	SCONJ
ejpam-5764	72	12	n(a	n(a	PROPN
ejpam-5764	72	13	,	,	PUNCT
ejpam-5764	72	14	ε	ε	PROPN
ejpam-5764	72	15	)	)	PUNCT
ejpam-5764	72	16	∩	∩	NOUN
ejpam-5764	72	17	a	a	DET
ejpam-5764	72	18	=	=	SYM
ejpam-5764	72	19	ϕ	ϕ	NOUN
ejpam-5764	72	20	,	,	PUNCT
ejpam-5764	72	21	then	then	ADV
ejpam-5764	72	22	a	a	PRON
ejpam-5764	72	23	is	be	AUX
ejpam-5764	72	24	a	a	DET
ejpam-5764	72	25	tri	tri	ADJ
ejpam-5764	72	26	-	-	ADJ
ejpam-5764	72	27	exterior	exterior	ADJ
ejpam-5764	72	28	point	point	NOUN
ejpam-5764	72	29	of	of	ADP
ejpam-5764	72	30	a.	a.	NOUN
ejpam-5764	72	31	the	the	DET
ejpam-5764	72	32	tri	tri	ADJ
ejpam-5764	72	33	-	-	ADJ
ejpam-5764	72	34	exterior	exterior	ADJ
ejpam-5764	72	35	set	set	NOUN
ejpam-5764	72	36	,	,	PUNCT
ejpam-5764	72	37	which	which	PRON
ejpam-5764	72	38	is	be	AUX
ejpam-5764	72	39	the	the	DET
ejpam-5764	72	40	set	set	NOUN
ejpam-5764	72	41	of	of	ADP
ejpam-5764	72	42	all	all	DET
ejpam-5764	72	43	tri	tri	ADJ
ejpam-5764	72	44	-	-	ADJ
ejpam-5764	72	45	exterior	exterior	ADJ
ejpam-5764	72	46	points	point	NOUN
ejpam-5764	72	47	,	,	PUNCT
ejpam-5764	72	48	is	be	AUX
ejpam-5764	72	49	represented	represent	VERB
ejpam-5764	72	50	by	by	ADP
ejpam-5764	72	51	the	the	DET
ejpam-5764	72	52	equation	equation	NOUN
ejpam-5764	72	53	ex(a	ex(a	NOUN
ejpam-5764	72	54	)	)	PUNCT
ejpam-5764	72	55	=	=	SYM
ejpam-5764	72	56	int(ac	int(ac	NOUN
ejpam-5764	72	57	)	)	PUNCT
ejpam-5764	72	58	=	=	PUNCT
ejpam-5764	73	1	a	a	DET
ejpam-5764	73	2	c	c	NOUN
ejpam-5764	73	3	.	.	PUNCT
ejpam-5764	74	1	theorem	theorem	ADJ
ejpam-5764	74	2	4	4	NUM
ejpam-5764	74	3	.	.	PUNCT
ejpam-5764	75	1	if	if	SCONJ
ejpam-5764	75	2	we	we	PRON
ejpam-5764	75	3	define	define	VERB
ejpam-5764	75	4	ex(a	ex(a	NOUN
ejpam-5764	75	5	)	)	PUNCT
ejpam-5764	75	6	=	=	SYM
ejpam-5764	75	7	int(ac	int(ac	NOUN
ejpam-5764	75	8	)	)	PUNCT
ejpam-5764	75	9	(	(	PUNCT
ejpam-5764	75	10	the	the	DET
ejpam-5764	75	11	interior	interior	NOUN
ejpam-5764	75	12	of	of	ADP
ejpam-5764	75	13	the	the	DET
ejpam-5764	75	14	complement	complement	NOUN
ejpam-5764	75	15	of	of	ADP
ejpam-5764	75	16	a	a	PRON
ejpam-5764	75	17	)	)	PUNCT
ejpam-5764	75	18	given	give	VERB
ejpam-5764	75	19	a	a	DET
ejpam-5764	75	20	tri	tri	ADJ
ejpam-5764	75	21	-	-	ADJ
ejpam-5764	75	22	topological	topological	ADJ
ejpam-5764	75	23	space	space	NOUN
ejpam-5764	75	24	(	(	PUNCT
ejpam-5764	75	25	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	75	26	,	,	PUNCT
ejpam-5764	75	27	ϑ2	ϑ2	PROPN
ejpam-5764	75	28	,	,	PUNCT
ejpam-5764	75	29	ϑ3	ϑ3	PROPN
ejpam-5764	75	30	)	)	PUNCT
ejpam-5764	75	31	and	and	CCONJ
ejpam-5764	75	32	a	a	DET
ejpam-5764	75	33	,	,	PUNCT
ejpam-5764	75	34	b	b	X
ejpam-5764	75	35	⊂	⊂	PROPN
ejpam-5764	75	36	x	x	X
ejpam-5764	75	37	,	,	PUNCT
ejpam-5764	75	38	then	then	ADV
ejpam-5764	75	39	:	:	PUNCT
ejpam-5764	75	40	(	(	PUNCT
ejpam-5764	75	41	i	i	NOUN
ejpam-5764	75	42	)	)	PUNCT
ejpam-5764	75	43	ex(∅	ex(∅	PROPN
ejpam-5764	75	44	)	)	PUNCT
ejpam-5764	76	1	=	=	SYM
ejpam-5764	76	2	x	x	X
ejpam-5764	76	3	and	and	CCONJ
ejpam-5764	76	4	ex(x	ex(x	NOUN
ejpam-5764	76	5	)	)	PUNCT
ejpam-5764	77	1	=	=	PUNCT
ejpam-5764	77	2	∅.	∅.	VERB
ejpam-5764	77	3	if	if	SCONJ
ejpam-5764	77	4	and	and	CCONJ
ejpam-5764	77	5	only	only	ADV
ejpam-5764	77	6	if	if	SCONJ
ejpam-5764	77	7	there	there	PRON
ejpam-5764	77	8	is	be	VERB
ejpam-5764	77	9	a	a	DET
ejpam-5764	77	10	ϑi	ϑi	NOUN
ejpam-5764	77	11	-	-	PUNCT
ejpam-5764	77	12	open	open	NOUN
ejpam-5764	77	13	set	set	VERB
ejpam-5764	77	14	ue	ue	PROPN
ejpam-5764	78	1	such	such	ADJ
ejpam-5764	78	2	that	that	SCONJ
ejpam-5764	78	3	e	e	PROPN
ejpam-5764	78	4	∈	∈	PROPN
ejpam-5764	78	5	ue	ue	PROPN
ejpam-5764	78	6	⊂	⊂	PROPN
ejpam-5764	78	7	ac	ac	PROPN
ejpam-5764	78	8	,	,	PUNCT
ejpam-5764	78	9	then	then	ADV
ejpam-5764	78	10	for	for	ADP
ejpam-5764	78	11	all	all	DET
ejpam-5764	78	12	e	e	NOUN
ejpam-5764	78	13	∈	∈	PROPN
ejpam-5764	78	14	x	x	X
ejpam-5764	78	15	,	,	PUNCT
ejpam-5764	78	16	e	e	PROPN
ejpam-5764	78	17	∈	∈	PROPN
ejpam-5764	78	18	ex(a	ex(a	NOUN
ejpam-5764	78	19	)	)	PUNCT
ejpam-5764	78	20	ex(b	ex(b	X
ejpam-5764	78	21	)	)	PUNCT
ejpam-5764	78	22	⊂	⊂	NOUN
ejpam-5764	78	23	ex(a	ex(a	NOUN
ejpam-5764	78	24	)	)	PUNCT
ejpam-5764	79	1	if	if	SCONJ
ejpam-5764	79	2	a	a	DET
ejpam-5764	79	3	⊂	⊂	PROPN
ejpam-5764	79	4	b.	b.	PROPN
ejpam-5764	79	5	proof	proof	NOUN
ejpam-5764	79	6	.	.	PUNCT
ejpam-5764	80	1	(	(	PUNCT
ejpam-5764	80	2	i	i	NOUN
ejpam-5764	80	3	)	)	PUNCT
ejpam-5764	80	4	ex(∅	ex(∅	PROPN
ejpam-5764	80	5	)	)	PUNCT
ejpam-5764	80	6	=	=	SYM
ejpam-5764	80	7	int(∅c	int(∅c	PROPN
ejpam-5764	80	8	)	)	PUNCT
ejpam-5764	80	9	=	=	PUNCT
ejpam-5764	80	10	int(x	int(x	PROPN
ejpam-5764	80	11	)	)	PUNCT
ejpam-5764	80	12	=	=	SYM
ejpam-5764	80	13	x	x	X
ejpam-5764	80	14	and	and	CCONJ
ejpam-5764	80	15	ex(x	ex(x	NOUN
ejpam-5764	80	16	)	)	PUNCT
ejpam-5764	80	17	=	=	SYM
ejpam-5764	80	18	int(xc	int(xc	NOUN
ejpam-5764	80	19	)	)	PUNCT
ejpam-5764	80	20	=	=	SYM
ejpam-5764	80	21	int(∅	int(∅	NOUN
ejpam-5764	80	22	)	)	PUNCT
ejpam-5764	80	23	=	=	SYM
ejpam-5764	80	24	∅.	∅.	PRON
ejpam-5764	80	25	(	(	PUNCT
ejpam-5764	80	26	ii	ii	NOUN
ejpam-5764	80	27	)	)	PUNCT
ejpam-5764	80	28	if	if	SCONJ
ejpam-5764	81	1	and	and	CCONJ
ejpam-5764	81	2	only	only	ADV
ejpam-5764	81	3	if	if	SCONJ
ejpam-5764	81	4	there	there	PRON
ejpam-5764	81	5	is	be	VERB
ejpam-5764	81	6	a	a	DET
ejpam-5764	81	7	ϑi	ϑi	NOUN
ejpam-5764	81	8	-	-	PUNCT
ejpam-5764	81	9	open	open	NOUN
ejpam-5764	81	10	set	set	VERB
ejpam-5764	81	11	ue	ue	PROPN
ejpam-5764	81	12	such	such	ADJ
ejpam-5764	81	13	that	that	SCONJ
ejpam-5764	81	14	e	e	PROPN
ejpam-5764	81	15	∈	∈	PROPN
ejpam-5764	81	16	ue	ue	PROPN
ejpam-5764	81	17	⊂	⊂	PROPN
ejpam-5764	81	18	ac	ac	PROPN
ejpam-5764	81	19	,	,	PUNCT
ejpam-5764	81	20	then	then	ADV
ejpam-5764	81	21	by	by	ADP
ejpam-5764	81	22	definition	definition	NOUN
ejpam-5764	81	23	of	of	ADP
ejpam-5764	81	24	interior	interior	NOUN
ejpam-5764	81	25	,	,	PUNCT
ejpam-5764	81	26	e	e	PROPN
ejpam-5764	81	27	∈	∈	PROPN
ejpam-5764	81	28	int(ac	int(ac	PROPN
ejpam-5764	81	29	)	)	PUNCT
ejpam-5764	81	30	=	=	NOUN
ejpam-5764	81	31	ex(a	ex(a	NOUN
ejpam-5764	81	32	)	)	PUNCT
ejpam-5764	81	33	.	.	PUNCT
ejpam-5764	82	1	assume	assume	VERB
ejpam-5764	82	2	that	that	SCONJ
ejpam-5764	82	3	a	a	DET
ejpam-5764	82	4	⊂	⊂	PROPN
ejpam-5764	82	5	b.	b.	PROPN
ejpam-5764	82	6	bc	bc	PROPN
ejpam-5764	82	7	⊂	⊂	PROPN
ejpam-5764	82	8	ac	ac	PROPN
ejpam-5764	82	9	,	,	PUNCT
ejpam-5764	82	10	then	then	ADV
ejpam-5764	82	11	.	.	PUNCT
ejpam-5764	83	1	set	set	VERB
ejpam-5764	83	2	inclusion	inclusion	NOUN
ejpam-5764	83	3	is	be	AUX
ejpam-5764	83	4	maintained	maintain	VERB
ejpam-5764	83	5	by	by	ADP
ejpam-5764	83	6	taking	take	VERB
ejpam-5764	83	7	the	the	DET
ejpam-5764	83	8	interior	interior	NOUN
ejpam-5764	83	9	,	,	PUNCT
ejpam-5764	83	10	so	so	ADV
ejpam-5764	83	11	int(bc	int(bc	ADJ
ejpam-5764	83	12	)	)	PUNCT
ejpam-5764	83	13	⊂	⊂	PROPN
ejpam-5764	83	14	int(ac	int(ac	PROPN
ejpam-5764	83	15	)	)	PUNCT
ejpam-5764	83	16	.	.	PUNCT
ejpam-5764	84	1	ex(b	ex(b	PROPN
ejpam-5764	84	2	)	)	PUNCT
ejpam-5764	85	1	⊂	⊂	NOUN
ejpam-5764	85	2	ex(a	ex(a	NOUN
ejpam-5764	85	3	)	)	PUNCT
ejpam-5764	85	4	,	,	PUNCT
ejpam-5764	85	5	so	so	ADV
ejpam-5764	85	6	.	.	PUNCT
ejpam-5764	86	1	definition	definition	NOUN
ejpam-5764	86	2	8	8	NUM
ejpam-5764	86	3	.	.	PUNCT
ejpam-5764	87	1	[	[	X
ejpam-5764	87	2	9	9	NUM
ejpam-5764	87	3	]	]	X
ejpam-5764	87	4	let	let	VERB
ejpam-5764	87	5	(	(	PUNCT
ejpam-5764	87	6	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	87	7	,	,	PUNCT
ejpam-5764	87	8	ϑ2	ϑ2	PROPN
ejpam-5764	87	9	,	,	PUNCT
ejpam-5764	87	10	ϑ3	ϑ3	PROPN
ejpam-5764	87	11	)	)	PUNCT
ejpam-5764	87	12	be	be	AUX
ejpam-5764	87	13	a	a	DET
ejpam-5764	87	14	tri	tri	ADJ
ejpam-5764	87	15	-	-	ADJ
ejpam-5764	87	16	topological	topological	ADJ
ejpam-5764	87	17	space	space	NOUN
ejpam-5764	87	18	,	,	PUNCT
ejpam-5764	87	19	and	and	CCONJ
ejpam-5764	87	20	let	let	VERB
ejpam-5764	87	21	x	x	PRON
ejpam-5764	87	22	̸=	̸=	PROPN
ejpam-5764	87	23	∅	∅	NOUN
ejpam-5764	87	24	,	,	PUNCT
ejpam-5764	87	25	a	a	DET
ejpam-5764	87	26	be	be	AUX
ejpam-5764	87	27	a	a	DET
ejpam-5764	87	28	subset	subset	NOUN
ejpam-5764	87	29	of	of	ADP
ejpam-5764	87	30	x.	x.	NOUN
ejpam-5764	87	31	if	if	SCONJ
ejpam-5764	87	32	every	every	DET
ejpam-5764	87	33	neighborhood	neighborhood	NOUN
ejpam-5764	87	34	n(a	n(a	NOUN
ejpam-5764	87	35	,	,	PUNCT
ejpam-5764	87	36	ϑi	ϑi	PROPN
ejpam-5764	87	37	)	)	PUNCT
ejpam-5764	87	38	of	of	ADP
ejpam-5764	87	39	a	a	PRON
ejpam-5764	87	40	(	(	PUNCT
ejpam-5764	87	41	with	with	ADP
ejpam-5764	87	42	respect	respect	NOUN
ejpam-5764	87	43	to	to	ADP
ejpam-5764	87	44	each	each	DET
ejpam-5764	87	45	topology	topology	NOUN
ejpam-5764	87	46	ϑi	ϑi	PROPN
ejpam-5764	87	47	,	,	PUNCT
ejpam-5764	87	48	i	i	NOUN
ejpam-5764	87	49	=	=	NOUN
ejpam-5764	87	50	1	1	NUM
ejpam-5764	87	51	,	,	PUNCT
ejpam-5764	87	52	2	2	NUM
ejpam-5764	87	53	,	,	PUNCT
ejpam-5764	87	54	3	3	NUM
ejpam-5764	87	55	)	)	PUNCT
ejpam-5764	87	56	fulfills	fulfill	VERB
ejpam-5764	87	57	both	both	DET
ejpam-5764	87	58	n(a	n(a	NOUN
ejpam-5764	87	59	,	,	PUNCT
ejpam-5764	87	60	ϑi)∩a	ϑi)∩a	NOUN
ejpam-5764	87	61	̸=	̸=	PROPN
ejpam-5764	87	62	∅	∅	NOUN
ejpam-5764	87	63	and	and	CCONJ
ejpam-5764	87	64	n(a	n(a	NOUN
ejpam-5764	87	65	,	,	PUNCT
ejpam-5764	87	66	ϑi)∩ac	ϑi)∩ac	PROPN
ejpam-5764	87	67	̸=	̸=	PROPN
ejpam-5764	87	68	∅	∅	NOUN
ejpam-5764	87	69	,	,	PUNCT
ejpam-5764	87	70	then	then	ADV
ejpam-5764	87	71	the	the	DET
ejpam-5764	87	72	point	point	NOUN
ejpam-5764	87	73	a	a	DET
ejpam-5764	87	74	∈	∈	NOUN
ejpam-5764	87	75	x	x	PUNCT
ejpam-5764	87	76	is	be	AUX
ejpam-5764	87	77	a	a	DET
ejpam-5764	87	78	tri	tri	ADJ
ejpam-5764	87	79	-	-	ADJ
ejpam-5764	87	80	boundary	boundary	ADJ
ejpam-5764	87	81	point	point	NOUN
ejpam-5764	87	82	of	of	ADP
ejpam-5764	87	83	a.	a.	NOUN
ejpam-5764	87	84	the	the	DET
ejpam-5764	87	85	collection	collection	NOUN
ejpam-5764	87	86	of	of	ADP
ejpam-5764	87	87	all	all	DET
ejpam-5764	87	88	tri	tri	ADJ
ejpam-5764	87	89	-	-	ADJ
ejpam-5764	87	90	boundary	boundary	ADJ
ejpam-5764	87	91	points	point	NOUN
ejpam-5764	87	92	of	of	ADP
ejpam-5764	87	93	a	a	PRON
ejpam-5764	87	94	is	be	AUX
ejpam-5764	87	95	its	its	PRON
ejpam-5764	87	96	tri	tri	ADJ
ejpam-5764	87	97	-	-	NOUN
ejpam-5764	87	98	boundary	boundary	ADJ
ejpam-5764	87	99	,	,	PUNCT
ejpam-5764	87	100	represented	represent	VERB
ejpam-5764	87	101	by	by	ADP
ejpam-5764	87	102	bd(a	bd(a	NOUN
ejpam-5764	87	103	)	)	PUNCT
ejpam-5764	87	104	.	.	PUNCT
ejpam-5764	88	1	it	it	PRON
ejpam-5764	88	2	may	may	AUX
ejpam-5764	88	3	be	be	AUX
ejpam-5764	88	4	written	write	VERB
ejpam-5764	88	5	as	as	SCONJ
ejpam-5764	88	6	follows	follow	VERB
ejpam-5764	88	7	:	:	PUNCT
ejpam-5764	88	8	bd(a	bd(a	X
ejpam-5764	88	9	)	)	PUNCT
ejpam-5764	88	10	=	=	SYM
ejpam-5764	88	11	a	a	DET
ejpam-5764	88	12	∩	∩	ADJ
ejpam-5764	88	13	ac	ac	NOUN
ejpam-5764	88	14	=	=	SYM
ejpam-5764	88	15	a−	a−	PROPN
ejpam-5764	88	16	a	a	DET
ejpam-5764	88	17	◦	◦	NOUN
ejpam-5764	88	18	,	,	PUNCT
ejpam-5764	88	19	where	where	SCONJ
ejpam-5764	88	20	a	a	PRON
ejpam-5764	88	21	is	be	AUX
ejpam-5764	88	22	the	the	DET
ejpam-5764	88	23	tri	tri	NOUN
ejpam-5764	88	24	-	-	NOUN
ejpam-5764	88	25	closure	closure	NOUN
ejpam-5764	88	26	of	of	ADP
ejpam-5764	88	27	a	a	PRON
ejpam-5764	88	28	and	and	CCONJ
ejpam-5764	88	29	a	a	DET
ejpam-5764	88	30	◦	◦	NOUN
ejpam-5764	88	31	is	be	AUX
ejpam-5764	88	32	the	the	DET
ejpam-5764	88	33	tri	tri	ADJ
ejpam-5764	88	34	-	-	ADJ
ejpam-5764	88	35	interior	interior	ADJ
ejpam-5764	88	36	of	of	ADP
ejpam-5764	88	37	a.	a.	NOUN
ejpam-5764	88	38	theorem	theorem	NOUN
ejpam-5764	88	39	5	5	NUM
ejpam-5764	88	40	.	.	PUNCT
ejpam-5764	88	41	given	give	VERB
ejpam-5764	88	42	a	a	PRON
ejpam-5764	88	43	,	,	PUNCT
ejpam-5764	88	44	b	b	X
ejpam-5764	88	45	⊂	⊂	PROPN
ejpam-5764	88	46	x	x	X
ejpam-5764	88	47	and	and	CCONJ
ejpam-5764	88	48	a	a	DET
ejpam-5764	88	49	tri	tri	ADJ
ejpam-5764	88	50	-	-	ADJ
ejpam-5764	88	51	topological	topological	ADJ
ejpam-5764	88	52	space	space	NOUN
ejpam-5764	88	53	(	(	PUNCT
ejpam-5764	88	54	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	88	55	,	,	PUNCT
ejpam-5764	88	56	ϑ2	ϑ2	PROPN
ejpam-5764	88	57	,	,	PUNCT
ejpam-5764	88	58	ϑ3	ϑ3	PROPN
ejpam-5764	88	59	)	)	PUNCT
ejpam-5764	88	60	,	,	PUNCT
ejpam-5764	88	61	(	(	PUNCT
ejpam-5764	88	62	i	i	NOUN
ejpam-5764	88	63	)	)	PUNCT
ejpam-5764	88	64	bd(∅	bd(∅	X
ejpam-5764	88	65	)	)	PUNCT
ejpam-5764	88	66	=	=	SYM
ejpam-5764	88	67	bd(x	bd(x	X
ejpam-5764	88	68	)	)	PUNCT
ejpam-5764	88	69	=	=	NOUN
ejpam-5764	88	70	∅	∅	NOUN
ejpam-5764	88	71	(	(	PUNCT
ejpam-5764	88	72	ii	ii	NOUN
ejpam-5764	88	73	)	)	PUNCT
ejpam-5764	88	74	bd(a	bd(a	X
ejpam-5764	88	75	)	)	PUNCT
ejpam-5764	88	76	is	be	AUX
ejpam-5764	88	77	a	a	DET
ejpam-5764	88	78	ϑi	ϑi	NOUN
ejpam-5764	88	79	-	-	PUNCT
ejpam-5764	88	80	closed	close	VERB
ejpam-5764	88	81	set	set	NOUN
ejpam-5764	88	82	j.	j.	PROPN
ejpam-5764	88	83	oudetallah	oudetallah	PROPN
ejpam-5764	88	84	et	et	PROPN
ejpam-5764	88	85	al	al	PROPN
ejpam-5764	88	86	.	.	PUNCT
ejpam-5764	88	87	/	/	SYM
ejpam-5764	88	88	eur	eur	PROPN
ejpam-5764	88	89	.	.	PUNCT
ejpam-5764	89	1	j.	j.	PROPN
ejpam-5764	89	2	pure	pure	PROPN
ejpam-5764	89	3	appl	appl	PROPN
ejpam-5764	89	4	.	.	PROPN
ejpam-5764	89	5	math	math	PROPN
ejpam-5764	89	6	,	,	PUNCT
ejpam-5764	89	7	18	18	NUM
ejpam-5764	89	8	(	(	PUNCT
ejpam-5764	89	9	2	2	NUM
ejpam-5764	89	10	)	)	PUNCT
ejpam-5764	89	11	(	(	PUNCT
ejpam-5764	89	12	2025	2025	NUM
ejpam-5764	89	13	)	)	PUNCT
ejpam-5764	89	14	,	,	PUNCT
ejpam-5764	89	15	5764	5764	NUM
ejpam-5764	89	16	5	5	NUM
ejpam-5764	89	17	of	of	ADP
ejpam-5764	89	18	11	11	NUM
ejpam-5764	89	19	(	(	PUNCT
ejpam-5764	89	20	iii	iii	NOUN
ejpam-5764	89	21	)	)	PUNCT
ejpam-5764	89	22	b	b	NOUN
ejpam-5764	89	23	∈	∈	PROPN
ejpam-5764	89	24	bd(a	bd(a	X
ejpam-5764	89	25	)	)	PUNCT
ejpam-5764	89	26	if	if	SCONJ
ejpam-5764	89	27	and	and	CCONJ
ejpam-5764	89	28	only	only	ADV
ejpam-5764	89	29	if	if	SCONJ
ejpam-5764	89	30	for	for	ADP
ejpam-5764	89	31	all	all	DET
ejpam-5764	89	32	ϑi	ϑi	NOUN
ejpam-5764	89	33	-	-	PUNCT
ejpam-5764	89	34	open	open	ADJ
ejpam-5764	89	35	sets	set	NOUN
ejpam-5764	89	36	ub	ub	ADP
ejpam-5764	89	37	containing	contain	VERB
ejpam-5764	89	38	b	b	NOUN
ejpam-5764	89	39	,	,	PUNCT
ejpam-5764	89	40	we	we	PRON
ejpam-5764	89	41	have	have	VERB
ejpam-5764	89	42	ub	ub	VERB
ejpam-5764	89	43	∩a	∩a	PROPN
ejpam-5764	89	44	̸=	̸=	PROPN
ejpam-5764	89	45	∅	∅	NOUN
ejpam-5764	89	46	and	and	CCONJ
ejpam-5764	89	47	ub	ub	INTJ
ejpam-5764	89	48	∩ac	∩ac	PROPN
ejpam-5764	89	49	̸=	̸=	PROPN
ejpam-5764	89	50	∅	∅	NOUN
ejpam-5764	89	51	proof	proof	NOUN
ejpam-5764	89	52	.	.	PUNCT
ejpam-5764	90	1	we	we	PRON
ejpam-5764	90	2	only	only	ADV
ejpam-5764	90	3	prove	prove	VERB
ejpam-5764	90	4	(	(	PUNCT
ejpam-5764	90	5	iii	iii	NOUN
ejpam-5764	90	6	)	)	PUNCT
ejpam-5764	90	7	here	here	ADV
ejpam-5764	90	8	.	.	PUNCT
ejpam-5764	91	1	if	if	SCONJ
ejpam-5764	91	2	b	b	PROPN
ejpam-5764	91	3	∈	∈	PROPN
ejpam-5764	91	4	bd(a	bd(a	NUM
ejpam-5764	91	5	)	)	PUNCT
ejpam-5764	91	6	and	and	CCONJ
ejpam-5764	91	7	ub	ub	ADV
ejpam-5764	91	8	is	be	AUX
ejpam-5764	91	9	a	a	DET
ejpam-5764	91	10	ϑi	ϑi	NOUN
ejpam-5764	91	11	-	-	PUNCT
ejpam-5764	91	12	open	open	NOUN
ejpam-5764	91	13	set	set	NOUN
ejpam-5764	91	14	containing	contain	VERB
ejpam-5764	91	15	b	b	NOUN
ejpam-5764	91	16	,	,	PUNCT
ejpam-5764	91	17	then	then	ADV
ejpam-5764	91	18	:	:	PUNCT
ejpam-5764	91	19	b	b	X
ejpam-5764	91	20	∈	∈	PROPN
ejpam-5764	91	21	bd(a	bd(a	X
ejpam-5764	91	22	)	)	PUNCT
ejpam-5764	91	23	=	=	PUNCT
ejpam-5764	91	24	a	a	DET
ejpam-5764	91	25	∩ac	∩ac	NOUN
ejpam-5764	91	26	if	if	SCONJ
ejpam-5764	91	27	and	and	CCONJ
ejpam-5764	91	28	only	only	ADV
ejpam-5764	91	29	if	if	SCONJ
ejpam-5764	91	30	b	b	PROPN
ejpam-5764	91	31	∈	∈	PROPN
ejpam-5764	91	32	a	a	DET
ejpam-5764	91	33	∧	∧	PROPN
ejpam-5764	91	34	b	b	PROPN
ejpam-5764	91	35	∈	∈	PROPN
ejpam-5764	91	36	ac	ac	VERB
ejpam-5764	92	1	if	if	SCONJ
ejpam-5764	92	2	and	and	CCONJ
ejpam-5764	92	3	only	only	ADV
ejpam-5764	92	4	if	if	SCONJ
ejpam-5764	92	5	b	b	PROPN
ejpam-5764	92	6	∈	∈	PROPN
ejpam-5764	92	7	(	(	PUNCT
ejpam-5764	92	8	a	a	DET
ejpam-5764	92	9	∪a′	∪a′	NOUN
ejpam-5764	92	10	)	)	PUNCT
ejpam-5764	92	11	∧	∧	PROPN
ejpam-5764	92	12	b	b	PROPN
ejpam-5764	92	13	∈	∈	PROPN
ejpam-5764	92	14	ac	ac	PROPN
ejpam-5764	92	15	∪	∪	ADV
ejpam-5764	92	16	(	(	PUNCT
ejpam-5764	92	17	ac)′	ac)′	ADP
ejpam-5764	92	18	if	if	SCONJ
ejpam-5764	92	19	and	and	CCONJ
ejpam-5764	92	20	only	only	ADV
ejpam-5764	92	21	if	if	SCONJ
ejpam-5764	92	22	(	(	PUNCT
ejpam-5764	92	23	b	b	X
ejpam-5764	92	24	∈	∈	PROPN
ejpam-5764	92	25	a	a	DET
ejpam-5764	92	26	∨	∨	NUM
ejpam-5764	92	27	b	b	NOUN
ejpam-5764	92	28	∈	∈	PROPN
ejpam-5764	92	29	a′	a′	PROPN
ejpam-5764	92	30	)	)	PUNCT
ejpam-5764	92	31	∧	∧	PROPN
ejpam-5764	92	32	(	(	PUNCT
ejpam-5764	92	33	b	b	PROPN
ejpam-5764	92	34	∈	∈	PROPN
ejpam-5764	92	35	ac	ac	PROPN
ejpam-5764	93	1	∨	∨	PROPN
ejpam-5764	93	2	b	b	PROPN
ejpam-5764	93	3	∈	∈	PROPN
ejpam-5764	93	4	(	(	PUNCT
ejpam-5764	93	5	ac)′	ac)′	NOUN
ejpam-5764	93	6	)	)	PUNCT
ejpam-5764	93	7	if	if	SCONJ
ejpam-5764	93	8	and	and	CCONJ
ejpam-5764	93	9	only	only	ADV
ejpam-5764	93	10	if	if	SCONJ
ejpam-5764	93	11	b	b	PROPN
ejpam-5764	93	12	∈	∈	PROPN
ejpam-5764	93	13	a′	a′	PROPN
ejpam-5764	93	14	∧	∧	PROPN
ejpam-5764	93	15	b	b	PROPN
ejpam-5764	93	16	∈	∈	PROPN
ejpam-5764	93	17	(	(	PUNCT
ejpam-5764	93	18	ac)′	ac)′	ADP
ejpam-5764	93	19	if	if	SCONJ
ejpam-5764	93	20	and	and	CCONJ
ejpam-5764	93	21	only	only	ADV
ejpam-5764	93	22	if	if	SCONJ
ejpam-5764	93	23	ub	ub	NOUN
ejpam-5764	93	24	∩	∩	NOUN
ejpam-5764	93	25	(	(	PUNCT
ejpam-5764	93	26	a/{b	a/{b	ADP
ejpam-5764	93	27	}	}	PUNCT
ejpam-5764	93	28	)	)	PUNCT
ejpam-5764	93	29	̸=	̸=	PROPN
ejpam-5764	93	30	∅	∅	NOUN
ejpam-5764	93	31	∧	∧	PROPN
ejpam-5764	93	32	ub	ub	NOUN
ejpam-5764	93	33	∩	∩	NOUN
ejpam-5764	93	34	(	(	PUNCT
ejpam-5764	93	35	ac/{b	ac/{b	PROPN
ejpam-5764	93	36	}	}	PUNCT
ejpam-5764	93	37	)	)	PUNCT
ejpam-5764	93	38	̸=	̸=	NOUN
ejpam-5764	93	39	∅	∅	NOUN
ejpam-5764	93	40	but	but	CCONJ
ejpam-5764	93	41	we	we	PRON
ejpam-5764	93	42	have	have	VERB
ejpam-5764	93	43	b	b	PROPN
ejpam-5764	93	44	⊂	⊂	PROPN
ejpam-5764	93	45	ub	ub	PROPN
ejpam-5764	93	46	,	,	PUNCT
ejpam-5764	93	47	so	so	SCONJ
ejpam-5764	93	48	we	we	PRON
ejpam-5764	93	49	obtain	obtain	VERB
ejpam-5764	93	50	ub	ub	ADP
ejpam-5764	93	51	∩a	∩a	PROPN
ejpam-5764	93	52	̸=	̸=	PROPN
ejpam-5764	93	53	∅	∅	NOUN
ejpam-5764	93	54	and	and	CCONJ
ejpam-5764	93	55	ub	ub	INTJ
ejpam-5764	93	56	∩ac	∩ac	NOUN
ejpam-5764	93	57	̸=	̸=	PROPN
ejpam-5764	93	58	∅.	∅.	PRON
ejpam-5764	93	59	definition	definition	NOUN
ejpam-5764	93	60	9	9	NUM
ejpam-5764	93	61	.	.	PUNCT
ejpam-5764	94	1	[	[	X
ejpam-5764	94	2	7	7	X
ejpam-5764	94	3	]	]	X
ejpam-5764	94	4	a	a	DET
ejpam-5764	94	5	tri	tri	ADJ
ejpam-5764	94	6	-	-	ADJ
ejpam-5764	94	7	topological	topological	ADJ
ejpam-5764	94	8	space	space	NOUN
ejpam-5764	94	9	(	(	PUNCT
ejpam-5764	94	10	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	94	11	,	,	PUNCT
ejpam-5764	94	12	ϑ2	ϑ2	PROPN
ejpam-5764	94	13	,	,	PUNCT
ejpam-5764	94	14	ϑ3	ϑ3	NOUN
ejpam-5764	94	15	)	)	PUNCT
ejpam-5764	94	16	functions	function	NOUN
ejpam-5764	94	17	as	as	ADP
ejpam-5764	94	18	a	a	DET
ejpam-5764	94	19	tri	tri	ADJ
ejpam-5764	94	20	-	-	ADJ
ejpam-5764	94	21	t0	t0	NOUN
ejpam-5764	94	22	-	-	NOUN
ejpam-5764	94	23	space	space	NOUN
ejpam-5764	94	24	when	when	SCONJ
ejpam-5764	94	25	it	it	PRON
ejpam-5764	94	26	contains	contain	VERB
ejpam-5764	94	27	either	either	CCONJ
ejpam-5764	94	28	a	a	DET
ejpam-5764	94	29	ϑi	ϑi	NOUN
ejpam-5764	94	30	-	-	PUNCT
ejpam-5764	94	31	open	open	NOUN
ejpam-5764	94	32	set	set	VERB
ejpam-5764	94	33	ua	ua	NOUN
ejpam-5764	94	34	containing	contain	VERB
ejpam-5764	95	1	a	a	PRON
ejpam-5764	95	2	but	but	CCONJ
ejpam-5764	95	3	excluding	exclude	VERB
ejpam-5764	95	4	b	b	NOUN
ejpam-5764	96	1	or	or	CCONJ
ejpam-5764	96	2	it	it	PRON
ejpam-5764	96	3	possesses	possess	VERB
ejpam-5764	96	4	a	a	DET
ejpam-5764	96	5	ϑj	ϑj	ADV
ejpam-5764	96	6	-	-	PUNCT
ejpam-5764	96	7	open	open	ADJ
ejpam-5764	96	8	set	set	VERB
ejpam-5764	96	9	vb	vb	NOUN
ejpam-5764	96	10	with	with	ADP
ejpam-5764	96	11	element	element	NOUN
ejpam-5764	96	12	b	b	PROPN
ejpam-5764	96	13	inside	inside	NOUN
ejpam-5764	96	14	but	but	CCONJ
ejpam-5764	96	15	element	element	VERB
ejpam-5764	96	16	a	a	DET
ejpam-5764	96	17	kept	keep	VERB
ejpam-5764	96	18	outside	outside	ADV
ejpam-5764	96	19	from	from	ADP
ejpam-5764	96	20	vb	vb	NOUN
ejpam-5764	96	21	where	where	SCONJ
ejpam-5764	96	22	i	i	PRON
ejpam-5764	96	23	̸=	̸=	PROPN
ejpam-5764	96	24	j	j	PROPN
ejpam-5764	96	25	and	and	CCONJ
ejpam-5764	96	26	i	i	PROPN
ejpam-5764	96	27	,	,	PUNCT
ejpam-5764	96	28	j	j	PROPN
ejpam-5764	96	29	=	=	SYM
ejpam-5764	96	30	1	1	NUM
ejpam-5764	96	31	,	,	PUNCT
ejpam-5764	96	32	2	2	NUM
ejpam-5764	96	33	,	,	PUNCT
ejpam-5764	96	34	3	3	NUM
ejpam-5764	96	35	for	for	ADP
ejpam-5764	96	36	every	every	DET
ejpam-5764	96	37	pair	pair	NOUN
ejpam-5764	96	38	of	of	ADP
ejpam-5764	96	39	distinct	distinct	ADJ
ejpam-5764	96	40	elements	element	NOUN
ejpam-5764	96	41	a	a	DET
ejpam-5764	96	42	definition	definition	NOUN
ejpam-5764	96	43	10	10	NUM
ejpam-5764	96	44	.	.	PUNCT
ejpam-5764	97	1	[	[	X
ejpam-5764	97	2	8	8	NUM
ejpam-5764	97	3	]	]	X
ejpam-5764	97	4	if	if	SCONJ
ejpam-5764	97	5	,	,	PUNCT
ejpam-5764	97	6	for	for	ADP
ejpam-5764	97	7	each	each	PRON
ejpam-5764	97	8	of	of	ADP
ejpam-5764	97	9	the	the	DET
ejpam-5764	97	10	two	two	NUM
ejpam-5764	97	11	distinct	distinct	ADJ
ejpam-5764	97	12	elements	element	NOUN
ejpam-5764	97	13	a	a	PRON
ejpam-5764	97	14	and	and	CCONJ
ejpam-5764	97	15	b	b	NOUN
ejpam-5764	97	16	in	in	ADP
ejpam-5764	97	17	x	x	SYM
ejpam-5764	97	18	,	,	PUNCT
ejpam-5764	97	19	there	there	PRON
ejpam-5764	97	20	exists	exist	VERB
ejpam-5764	97	21	ϑi	ϑi	NOUN
ejpam-5764	97	22	-	-	PUNCT
ejpam-5764	97	23	open	open	NOUN
ejpam-5764	97	24	set	set	NOUN
ejpam-5764	97	25	ua	ua	PROPN
ejpam-5764	97	26	such	such	ADJ
ejpam-5764	97	27	that	that	SCONJ
ejpam-5764	97	28	a	a	DET
ejpam-5764	97	29	∈	∈	PROPN
ejpam-5764	97	30	ua	ua	PROPN
ejpam-5764	97	31	and	and	CCONJ
ejpam-5764	97	32	b	b	PROPN
ejpam-5764	97	33	/∈	/∈	PUNCT
ejpam-5764	97	34	ua	ua	PROPN
ejpam-5764	97	35	,	,	PUNCT
ejpam-5764	97	36	or	or	CCONJ
ejpam-5764	97	37	ϑj	ϑj	ADV
ejpam-5764	97	38	-	-	PUNCT
ejpam-5764	97	39	open	open	ADJ
ejpam-5764	97	40	set	set	VERB
ejpam-5764	97	41	vb	vb	ADP
ejpam-5764	97	42	such	such	DET
ejpam-5764	97	43	that	that	DET
ejpam-5764	97	44	b	b	PROPN
ejpam-5764	97	45	∈	∈	PROPN
ejpam-5764	97	46	vb	vb	NOUN
ejpam-5764	97	47	and	and	CCONJ
ejpam-5764	97	48	a	a	DET
ejpam-5764	97	49	/∈	/∈	INTJ
ejpam-5764	97	50	vb	vb	NOUN
ejpam-5764	97	51	,	,	PUNCT
ejpam-5764	97	52	where	where	SCONJ
ejpam-5764	97	53	i	i	PRON
ejpam-5764	97	54	̸=	̸=	PROPN
ejpam-5764	97	55	j	j	PROPN
ejpam-5764	97	56	and	and	CCONJ
ejpam-5764	97	57	i	i	PROPN
ejpam-5764	97	58	,	,	PUNCT
ejpam-5764	97	59	j	j	PROPN
ejpam-5764	97	60	=	=	SYM
ejpam-5764	97	61	1	1	NUM
ejpam-5764	97	62	,	,	PUNCT
ejpam-5764	97	63	2	2	NUM
ejpam-5764	97	64	,	,	PUNCT
ejpam-5764	97	65	3	3	NUM
ejpam-5764	97	66	,	,	PUNCT
ejpam-5764	97	67	then	then	ADV
ejpam-5764	97	68	(	(	PUNCT
ejpam-5764	97	69	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	97	70	,	,	PUNCT
ejpam-5764	97	71	ϑ2	ϑ2	PROPN
ejpam-5764	97	72	,	,	PUNCT
ejpam-5764	97	73	ϑ3	ϑ3	PROPN
ejpam-5764	97	74	)	)	PUNCT
ejpam-5764	97	75	is	be	AUX
ejpam-5764	97	76	a	a	DET
ejpam-5764	97	77	tri−	tri−	NUM
ejpam-5764	97	78	t0	t0	NOUN
ejpam-5764	97	79	-	-	NOUN
ejpam-5764	97	80	space	space	NOUN
ejpam-5764	97	81	.	.	PUNCT
ejpam-5764	98	1	theorem	theorem	NOUN
ejpam-5764	98	2	6	6	NUM
ejpam-5764	98	3	.	.	PUNCT
ejpam-5764	99	1	let	let	AUX
ejpam-5764	99	2	(	(	PUNCT
ejpam-5764	99	3	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	99	4	,	,	PUNCT
ejpam-5764	99	5	ϑ2	ϑ2	PROPN
ejpam-5764	99	6	,	,	PUNCT
ejpam-5764	99	7	ϑ3	ϑ3	PROPN
ejpam-5764	99	8	)	)	PUNCT
ejpam-5764	99	9	be	be	AUX
ejpam-5764	99	10	a	a	DET
ejpam-5764	99	11	tri	tri	ADJ
ejpam-5764	99	12	-	-	ADJ
ejpam-5764	99	13	topological	topological	ADJ
ejpam-5764	99	14	space	space	NOUN
ejpam-5764	99	15	.	.	PUNCT
ejpam-5764	100	1	then	then	ADV
ejpam-5764	100	2	thefollowing	thefollowing	NOUN
ejpam-5764	100	3	statements	statement	NOUN
ejpam-5764	100	4	are	be	AUX
ejpam-5764	100	5	equivalent	equivalent	ADJ
ejpam-5764	100	6	:	:	PUNCT
ejpam-5764	100	7	(	(	PUNCT
ejpam-5764	100	8	i	i	NOUN
ejpam-5764	100	9	)	)	PUNCT
ejpam-5764	100	10	x	x	PUNCT
ejpam-5764	100	11	represents	represent	VERB
ejpam-5764	100	12	a	a	DET
ejpam-5764	100	13	tri	tri	ADJ
ejpam-5764	100	14	-	-	ADJ
ejpam-5764	100	15	t0	t0	NOUN
ejpam-5764	100	16	-	-	PUNCT
ejpam-5764	100	17	space	space	NOUN
ejpam-5764	100	18	(	(	PUNCT
ejpam-5764	100	19	ii	ii	NOUN
ejpam-5764	100	20	)	)	PUNCT
ejpam-5764	100	21	for	for	ADP
ejpam-5764	100	22	any	any	DET
ejpam-5764	100	23	two	two	NUM
ejpam-5764	100	24	distinct	distinct	ADJ
ejpam-5764	100	25	elements	element	NOUN
ejpam-5764	100	26	a	a	DET
ejpam-5764	100	27	and	and	CCONJ
ejpam-5764	100	28	b	b	NOUN
ejpam-5764	100	29	,	,	PUNCT
ejpam-5764	100	30	a	a	PRON
ejpam-5764	100	31	/∈	/∈	PUNCT
ejpam-5764	100	32	{	{	PUNCT
ejpam-5764	100	33	b	b	NOUN
ejpam-5764	100	34	}	}	PUNCT
ejpam-5764	100	35	or	or	CCONJ
ejpam-5764	100	36	b	b	NOUN
ejpam-5764	100	37	/∈	/∈	PUNCT
ejpam-5764	100	38	{	{	PUNCT
ejpam-5764	100	39	a	a	NOUN
ejpam-5764	100	40	}	}	PUNCT
ejpam-5764	100	41	(	(	PUNCT
ejpam-5764	100	42	iii	iii	NOUN
ejpam-5764	100	43	)	)	PUNCT
ejpam-5764	100	44	if	if	SCONJ
ejpam-5764	100	45	a	a	PRON
ejpam-5764	100	46	and	and	CCONJ
ejpam-5764	100	47	b	b	NOUN
ejpam-5764	100	48	are	be	AUX
ejpam-5764	100	49	two	two	NUM
ejpam-5764	100	50	distinct	distinct	ADJ
ejpam-5764	100	51	elements	element	NOUN
ejpam-5764	100	52	,	,	PUNCT
ejpam-5764	100	53	we	we	PRON
ejpam-5764	100	54	have	have	VERB
ejpam-5764	100	55	{	{	PUNCT
ejpam-5764	100	56	a	a	NOUN
ejpam-5764	100	57	}	}	PUNCT
ejpam-5764	100	58	=	=	ADJ
ejpam-5764	100	59	̸	̸	NUM
ejpam-5764	100	60	{	{	PUNCT
ejpam-5764	100	61	b	b	NOUN
ejpam-5764	100	62	}	}	PUNCT
ejpam-5764	100	63	proof	proof	NOUN
ejpam-5764	100	64	.	.	PUNCT
ejpam-5764	101	1	(	(	PUNCT
ejpam-5764	101	2	i	i	NOUN
ejpam-5764	101	3	)	)	PUNCT
ejpam-5764	101	4	⇒	⇒	PROPN
ejpam-5764	101	5	(	(	PUNCT
ejpam-5764	101	6	ii	ii	PROPN
ejpam-5764	101	7	):	):	PUNCT
ejpam-5764	101	8	let	let	VERB
ejpam-5764	101	9	a	a	DET
ejpam-5764	101	10	̸=	̸=	PROPN
ejpam-5764	101	11	b	b	NOUN
ejpam-5764	101	12	be	be	AUX
ejpam-5764	101	13	distinct	distinct	ADJ
ejpam-5764	101	14	elements	element	NOUN
ejpam-5764	101	15	of	of	ADP
ejpam-5764	101	16	x	x	X
ejpam-5764	101	17	,	,	PUNCT
ejpam-5764	101	18	and	and	CCONJ
ejpam-5764	101	19	suppose	suppose	VERB
ejpam-5764	101	20	x	x	PRON
ejpam-5764	101	21	is	be	AUX
ejpam-5764	101	22	a	a	DET
ejpam-5764	101	23	tri	tri	ADJ
ejpam-5764	101	24	-	-	ADJ
ejpam-5764	101	25	t0	t0	NOUN
ejpam-5764	101	26	-	-	NOUN
ejpam-5764	101	27	space	space	NOUN
ejpam-5764	101	28	.	.	PUNCT
ejpam-5764	102	1	by	by	ADP
ejpam-5764	102	2	definition	definition	NOUN
ejpam-5764	102	3	of	of	ADP
ejpam-5764	102	4	a	a	DET
ejpam-5764	102	5	tri	tri	ADJ
ejpam-5764	102	6	-	-	ADJ
ejpam-5764	102	7	t0	t0	NOUN
ejpam-5764	102	8	-	-	NOUN
ejpam-5764	102	9	space	space	NOUN
ejpam-5764	102	10	,	,	PUNCT
ejpam-5764	102	11	there	there	PRON
ejpam-5764	102	12	exists	exist	VERB
ejpam-5764	102	13	a	a	DET
ejpam-5764	102	14	ϑi	ϑi	NOUN
ejpam-5764	102	15	-	-	PUNCT
ejpam-5764	102	16	open	open	NOUN
ejpam-5764	102	17	set	set	NOUN
ejpam-5764	102	18	ua	ua	PROPN
ejpam-5764	102	19	such	such	ADJ
ejpam-5764	102	20	that	that	SCONJ
ejpam-5764	102	21	a	a	DET
ejpam-5764	102	22	∈	∈	PROPN
ejpam-5764	102	23	ua	ua	PROPN
ejpam-5764	102	24	and	and	CCONJ
ejpam-5764	102	25	b	b	PROPN
ejpam-5764	102	26	/∈	/∈	PROPN
ejpam-5764	102	27	ua	ua	PROPN
ejpam-5764	102	28	for	for	ADP
ejpam-5764	102	29	some	some	DET
ejpam-5764	102	30	i	i	PRON
ejpam-5764	102	31	∈	∈	PROPN
ejpam-5764	102	32	{	{	PUNCT
ejpam-5764	102	33	1	1	NUM
ejpam-5764	102	34	,	,	PUNCT
ejpam-5764	102	35	2	2	NUM
ejpam-5764	102	36	,	,	PUNCT
ejpam-5764	102	37	3	3	NUM
ejpam-5764	102	38	}	}	PUNCT
ejpam-5764	102	39	,	,	PUNCT
ejpam-5764	102	40	or	or	CCONJ
ejpam-5764	102	41	a	a	DET
ejpam-5764	102	42	ϑj	ϑj	ADV
ejpam-5764	102	43	-	-	PUNCT
ejpam-5764	102	44	open	open	ADJ
ejpam-5764	102	45	set	set	VERB
ejpam-5764	102	46	vb	vb	ADP
ejpam-5764	102	47	such	such	DET
ejpam-5764	102	48	that	that	DET
ejpam-5764	102	49	b	b	PROPN
ejpam-5764	102	50	∈	∈	PROPN
ejpam-5764	102	51	vb	vb	NOUN
ejpam-5764	102	52	and	and	CCONJ
ejpam-5764	102	53	a	a	DET
ejpam-5764	102	54	/∈	/∈	INTJ
ejpam-5764	102	55	vb	vb	NOUN
ejpam-5764	102	56	for	for	ADP
ejpam-5764	102	57	some	some	DET
ejpam-5764	102	58	j	j	PROPN
ejpam-5764	102	59	∈	∈	PROPN
ejpam-5764	102	60	{	{	PUNCT
ejpam-5764	102	61	1	1	NUM
ejpam-5764	102	62	,	,	PUNCT
ejpam-5764	102	63	2	2	NUM
ejpam-5764	102	64	,	,	PUNCT
ejpam-5764	102	65	3	3	NUM
ejpam-5764	102	66	}	}	PUNCT
ejpam-5764	102	67	.	.	PUNCT
ejpam-5764	103	1	in	in	ADP
ejpam-5764	103	2	the	the	DET
ejpam-5764	103	3	first	first	ADJ
ejpam-5764	103	4	case	case	NOUN
ejpam-5764	103	5	,	,	PUNCT
ejpam-5764	103	6	since	since	SCONJ
ejpam-5764	103	7	a	a	DET
ejpam-5764	103	8	∈	∈	PROPN
ejpam-5764	103	9	ua	ua	PROPN
ejpam-5764	103	10	and	and	CCONJ
ejpam-5764	103	11	ua	ua	PROPN
ejpam-5764	103	12	∩	∩	PROPN
ejpam-5764	103	13	{	{	PUNCT
ejpam-5764	103	14	b	b	NOUN
ejpam-5764	103	15	}	}	PUNCT
ejpam-5764	103	16	=	=	NOUN
ejpam-5764	103	17	∅	∅	NOUN
ejpam-5764	103	18	,	,	PUNCT
ejpam-5764	103	19	this	this	PRON
ejpam-5764	103	20	implies	imply	VERB
ejpam-5764	103	21	b	b	X
ejpam-5764	103	22	/∈	/∈	PUNCT
ejpam-5764	103	23	{	{	PUNCT
ejpam-5764	103	24	a	a	NOUN
ejpam-5764	103	25	}	}	PUNCT
ejpam-5764	103	26	.	.	PUNCT
ejpam-5764	104	1	in	in	ADP
ejpam-5764	104	2	the	the	DET
ejpam-5764	104	3	second	second	ADJ
ejpam-5764	104	4	case	case	NOUN
ejpam-5764	104	5	,	,	PUNCT
ejpam-5764	104	6	since	since	SCONJ
ejpam-5764	104	7	b	b	PROPN
ejpam-5764	104	8	∈	∈	PROPN
ejpam-5764	104	9	vb	vb	NOUN
ejpam-5764	104	10	and	and	CCONJ
ejpam-5764	104	11	vb	vb	NOUN
ejpam-5764	104	12	∩	∩	NOUN
ejpam-5764	104	13	{	{	PUNCT
ejpam-5764	104	14	a	a	NOUN
ejpam-5764	104	15	}	}	PUNCT
ejpam-5764	104	16	=	=	SYM
ejpam-5764	104	17	∅	∅	NOUN
ejpam-5764	104	18	,	,	PUNCT
ejpam-5764	104	19	this	this	PRON
ejpam-5764	104	20	implies	imply	VERB
ejpam-5764	104	21	a	a	DET
ejpam-5764	104	22	/∈	/∈	PUNCT
ejpam-5764	104	23	{	{	PUNCT
ejpam-5764	104	24	b	b	NOUN
ejpam-5764	104	25	}	}	PUNCT
ejpam-5764	104	26	.	.	PUNCT
ejpam-5764	105	1	as	as	ADP
ejpam-5764	105	2	a	a	DET
ejpam-5764	105	3	result	result	NOUN
ejpam-5764	105	4	,	,	PUNCT
ejpam-5764	105	5	a	a	DET
ejpam-5764	105	6	/∈	/∈	PUNCT
ejpam-5764	105	7	{	{	PUNCT
ejpam-5764	105	8	b	b	NOUN
ejpam-5764	105	9	}	}	PUNCT
ejpam-5764	105	10	or	or	CCONJ
ejpam-5764	105	11	b	b	NOUN
ejpam-5764	105	12	/∈	/∈	PUNCT
ejpam-5764	105	13	{	{	PUNCT
ejpam-5764	105	14	a	a	NOUN
ejpam-5764	105	15	}	}	PUNCT
ejpam-5764	105	16	.	.	PUNCT
ejpam-5764	106	1	(	(	PUNCT
ejpam-5764	106	2	ii	ii	NOUN
ejpam-5764	106	3	)	)	PUNCT
ejpam-5764	106	4	⇒	⇒	NOUN
ejpam-5764	106	5	(	(	PUNCT
ejpam-5764	106	6	iii	iii	NOUN
ejpam-5764	106	7	):	):	PUNCT
ejpam-5764	106	8	for	for	ADP
ejpam-5764	106	9	distinct	distinct	ADJ
ejpam-5764	106	10	elements	element	NOUN
ejpam-5764	106	11	a	a	PRON
ejpam-5764	106	12	and	and	CCONJ
ejpam-5764	106	13	b	b	NOUN
ejpam-5764	106	14	,	,	PUNCT
ejpam-5764	106	15	we	we	PRON
ejpam-5764	106	16	have	have	VERB
ejpam-5764	106	17	a	a	DET
ejpam-5764	106	18	/∈	/∈	PUNCT
ejpam-5764	106	19	{	{	PUNCT
ejpam-5764	106	20	b	b	NOUN
ejpam-5764	106	21	}	}	PUNCT
ejpam-5764	106	22	or	or	CCONJ
ejpam-5764	106	23	b	b	NOUN
ejpam-5764	106	24	/∈	/∈	PUNCT
ejpam-5764	106	25	{	{	PUNCT
ejpam-5764	106	26	a	a	NOUN
ejpam-5764	106	27	}	}	PUNCT
ejpam-5764	106	28	.	.	PUNCT
ejpam-5764	107	1	without	without	ADP
ejpam-5764	107	2	loss	loss	NOUN
ejpam-5764	107	3	of	of	ADP
ejpam-5764	107	4	generality	generality	NOUN
ejpam-5764	107	5	,	,	PUNCT
ejpam-5764	107	6	assume	assume	VERB
ejpam-5764	107	7	that	that	SCONJ
ejpam-5764	107	8	a	a	DET
ejpam-5764	107	9	/∈	/∈	PUNCT
ejpam-5764	107	10	{	{	PUNCT
ejpam-5764	107	11	b	b	NOUN
ejpam-5764	107	12	}	}	PUNCT
ejpam-5764	107	13	.	.	PUNCT
ejpam-5764	108	1	since	since	SCONJ
ejpam-5764	108	2	a	a	DET
ejpam-5764	108	3	∈	∈	PROPN
ejpam-5764	108	4	{	{	PUNCT
ejpam-5764	108	5	a	a	NOUN
ejpam-5764	108	6	}	}	PUNCT
ejpam-5764	108	7	,	,	PUNCT
ejpam-5764	108	8	we	we	PRON
ejpam-5764	108	9	have	have	VERB
ejpam-5764	108	10	{	{	PUNCT
ejpam-5764	108	11	a	a	NOUN
ejpam-5764	108	12	}	}	PUNCT
ejpam-5764	108	13	=	=	ADJ
ejpam-5764	108	14	̸	̸	NUM
ejpam-5764	108	15	{	{	PUNCT
ejpam-5764	108	16	b	b	NOUN
ejpam-5764	108	17	}	}	PUNCT
ejpam-5764	108	18	.	.	PUNCT
ejpam-5764	109	1	(	(	PUNCT
ejpam-5764	109	2	iii	iii	X
ejpam-5764	109	3	)	)	PUNCT
ejpam-5764	109	4	⇒	⇒	NOUN
ejpam-5764	109	5	(	(	PUNCT
ejpam-5764	109	6	i	i	NOUN
ejpam-5764	109	7	):	):	PUNCT
ejpam-5764	109	8	assume	assume	VERB
ejpam-5764	109	9	a	a	PRON
ejpam-5764	109	10	and	and	CCONJ
ejpam-5764	109	11	b	b	NOUN
ejpam-5764	109	12	are	be	AUX
ejpam-5764	109	13	distinct	distinct	ADJ
ejpam-5764	109	14	elements	element	NOUN
ejpam-5764	110	1	such	such	ADJ
ejpam-5764	110	2	that	that	SCONJ
ejpam-5764	110	3	{	{	PUNCT
ejpam-5764	110	4	a	a	NOUN
ejpam-5764	110	5	}	}	PUNCT
ejpam-5764	110	6	=	=	ADJ
ejpam-5764	110	7	̸	̸	NUM
ejpam-5764	110	8	{	{	PUNCT
ejpam-5764	110	9	b	b	NOUN
ejpam-5764	110	10	}	}	PUNCT
ejpam-5764	110	11	.	.	PUNCT
ejpam-5764	111	1	then	then	ADV
ejpam-5764	111	2	,	,	PUNCT
ejpam-5764	111	3	there	there	PRON
ejpam-5764	111	4	exists	exist	VERB
ejpam-5764	111	5	either	either	CCONJ
ejpam-5764	111	6	c	c	PROPN
ejpam-5764	111	7	∈	∈	PROPN
ejpam-5764	111	8	{	{	PUNCT
ejpam-5764	111	9	a	a	NOUN
ejpam-5764	111	10	}	}	PUNCT
ejpam-5764	111	11	\	\	NOUN
ejpam-5764	111	12	{	{	PUNCT
ejpam-5764	111	13	b	b	NOUN
ejpam-5764	111	14	}	}	PUNCT
ejpam-5764	111	15	or	or	CCONJ
ejpam-5764	111	16	d	d	PROPN
ejpam-5764	111	17	∈	∈	PROPN
ejpam-5764	111	18	{	{	PUNCT
ejpam-5764	111	19	b	b	NOUN
ejpam-5764	111	20	}	}	PUNCT
ejpam-5764	111	21	\	\	NOUN
ejpam-5764	111	22	{	{	PUNCT
ejpam-5764	111	23	a	a	NOUN
ejpam-5764	111	24	}	}	PUNCT
ejpam-5764	111	25	.	.	PUNCT
ejpam-5764	112	1	without	without	ADP
ejpam-5764	112	2	loss	loss	NOUN
ejpam-5764	112	3	of	of	ADP
ejpam-5764	112	4	generality	generality	NOUN
ejpam-5764	112	5	,	,	PUNCT
ejpam-5764	112	6	assume	assume	VERB
ejpam-5764	112	7	b	b	X
ejpam-5764	112	8	/∈	/∈	PUNCT
ejpam-5764	112	9	{	{	PUNCT
ejpam-5764	112	10	a	a	NOUN
ejpam-5764	112	11	}	}	PUNCT
ejpam-5764	112	12	(	(	PUNCT
ejpam-5764	112	13	and	and	CCONJ
ejpam-5764	112	14	obviously	obviously	ADV
ejpam-5764	112	15	b	b	PROPN
ejpam-5764	112	16	∈	∈	PROPN
ejpam-5764	112	17	{	{	PUNCT
ejpam-5764	112	18	b	b	NOUN
ejpam-5764	112	19	}	}	PUNCT
ejpam-5764	112	20	)	)	PUNCT
ejpam-5764	112	21	.	.	PUNCT
ejpam-5764	113	1	since	since	SCONJ
ejpam-5764	113	2	{	{	PUNCT
ejpam-5764	113	3	a	a	PRON
ejpam-5764	113	4	}	}	PUNCT
ejpam-5764	113	5	is	be	AUX
ejpam-5764	113	6	a	a	DET
ejpam-5764	113	7	ϑi	ϑi	NOUN
ejpam-5764	113	8	-	-	PUNCT
ejpam-5764	113	9	closed	close	VERB
ejpam-5764	113	10	set	set	NOUN
ejpam-5764	113	11	in	in	ADP
ejpam-5764	113	12	x	x	PUNCT
ejpam-5764	113	13	for	for	ADP
ejpam-5764	113	14	each	each	DET
ejpam-5764	113	15	i	i	PRON
ejpam-5764	113	16	∈	∈	PROPN
ejpam-5764	113	17	{	{	PUNCT
ejpam-5764	113	18	1	1	NUM
ejpam-5764	113	19	,	,	PUNCT
ejpam-5764	113	20	2	2	NUM
ejpam-5764	113	21	,	,	PUNCT
ejpam-5764	113	22	3	3	NUM
ejpam-5764	113	23	}	}	PUNCT
ejpam-5764	113	24	,	,	PUNCT
ejpam-5764	113	25	the	the	DET
ejpam-5764	113	26	set	set	NOUN
ejpam-5764	113	27	x	x	SYM
ejpam-5764	113	28	\	\	X
ejpam-5764	113	29	{	{	PUNCT
ejpam-5764	113	30	a	a	NOUN
ejpam-5764	113	31	}	}	PUNCT
ejpam-5764	113	32	=	=	SYM
ejpam-5764	113	33	vb	vb	NOUN
ejpam-5764	113	34	is	be	AUX
ejpam-5764	113	35	ϑi	ϑi	NOUN
ejpam-5764	113	36	-	-	PUNCT
ejpam-5764	113	37	open	open	ADJ
ejpam-5764	113	38	in	in	ADP
ejpam-5764	113	39	x	x	PUNCT
ejpam-5764	113	40	for	for	ADP
ejpam-5764	113	41	each	each	DET
ejpam-5764	113	42	i.	i.	NOUN
ejpam-5764	113	43	we	we	PRON
ejpam-5764	113	44	have	have	VERB
ejpam-5764	113	45	b	b	NUM
ejpam-5764	113	46	∈	∈	PROPN
ejpam-5764	113	47	vb	vb	NOUN
ejpam-5764	113	48	and	and	CCONJ
ejpam-5764	113	49	a	a	DET
ejpam-5764	113	50	/∈	/∈	INTJ
ejpam-5764	113	51	vb	vb	NOUN
ejpam-5764	113	52	.	.	PUNCT
ejpam-5764	114	1	as	as	ADP
ejpam-5764	114	2	a	a	DET
ejpam-5764	114	3	result	result	NOUN
ejpam-5764	114	4	,	,	PUNCT
ejpam-5764	114	5	x	x	PRON
ejpam-5764	114	6	is	be	AUX
ejpam-5764	114	7	a	a	DET
ejpam-5764	114	8	tri	tri	ADJ
ejpam-5764	114	9	-	-	ADJ
ejpam-5764	114	10	t0	t0	NOUN
ejpam-5764	114	11	-	-	NOUN
ejpam-5764	114	12	space	space	NOUN
ejpam-5764	114	13	.	.	PUNCT
ejpam-5764	115	1	j.	j.	PROPN
ejpam-5764	115	2	oudetallah	oudetallah	PROPN
ejpam-5764	115	3	et	et	PROPN
ejpam-5764	115	4	al	al	PROPN
ejpam-5764	115	5	.	.	PUNCT
ejpam-5764	115	6	/	/	SYM
ejpam-5764	115	7	eur	eur	PROPN
ejpam-5764	115	8	.	.	PUNCT
ejpam-5764	116	1	j.	j.	PROPN
ejpam-5764	116	2	pure	pure	PROPN
ejpam-5764	116	3	appl	appl	PROPN
ejpam-5764	116	4	.	.	PROPN
ejpam-5764	116	5	math	math	PROPN
ejpam-5764	116	6	,	,	PUNCT
ejpam-5764	116	7	18	18	NUM
ejpam-5764	116	8	(	(	PUNCT
ejpam-5764	116	9	2	2	NUM
ejpam-5764	116	10	)	)	PUNCT
ejpam-5764	116	11	(	(	PUNCT
ejpam-5764	116	12	2025	2025	NUM
ejpam-5764	116	13	)	)	PUNCT
ejpam-5764	116	14	,	,	PUNCT
ejpam-5764	116	15	5764	5764	NUM
ejpam-5764	116	16	6	6	NUM
ejpam-5764	116	17	of	of	ADP
ejpam-5764	116	18	11	11	NUM
ejpam-5764	116	19	definition	definition	NOUN
ejpam-5764	116	20	11	11	NUM
ejpam-5764	116	21	.	.	PUNCT
ejpam-5764	117	1	[	[	X
ejpam-5764	117	2	7	7	NUM
ejpam-5764	117	3	]	]	X
ejpam-5764	117	4	(	(	PUNCT
ejpam-5764	117	5	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	117	6	,	,	PUNCT
ejpam-5764	117	7	ϑ2	ϑ2	PROPN
ejpam-5764	117	8	,	,	PUNCT
ejpam-5764	117	9	ϑ3	ϑ3	PROPN
ejpam-5764	117	10	)	)	PUNCT
ejpam-5764	117	11	is	be	AUX
ejpam-5764	117	12	a	a	DET
ejpam-5764	117	13	tri	tri	ADJ
ejpam-5764	117	14	-	-	ADJ
ejpam-5764	117	15	t1	t1	ADJ
ejpam-5764	117	16	-	-	PUNCT
ejpam-5764	117	17	space	space	NOUN
ejpam-5764	117	18	if	if	SCONJ
ejpam-5764	117	19	,	,	PUNCT
ejpam-5764	117	20	for	for	ADP
ejpam-5764	117	21	each	each	PRON
ejpam-5764	117	22	of	of	ADP
ejpam-5764	117	23	the	the	DET
ejpam-5764	117	24	two	two	NUM
ejpam-5764	117	25	distinct	distinct	ADJ
ejpam-5764	117	26	elements	element	NOUN
ejpam-5764	117	27	a	a	PRON
ejpam-5764	117	28	and	and	CCONJ
ejpam-5764	117	29	b	b	NOUN
ejpam-5764	117	30	in	in	ADP
ejpam-5764	117	31	x	x	SYM
ejpam-5764	117	32	,	,	PUNCT
ejpam-5764	117	33	there	there	PRON
ejpam-5764	117	34	exists	exist	VERB
ejpam-5764	117	35	ϑi	ϑi	NOUN
ejpam-5764	117	36	-	-	PUNCT
ejpam-5764	117	37	open	open	NOUN
ejpam-5764	117	38	set	set	NOUN
ejpam-5764	117	39	ua	ua	PROPN
ejpam-5764	117	40	such	such	ADJ
ejpam-5764	117	41	that	that	SCONJ
ejpam-5764	117	42	a	a	DET
ejpam-5764	117	43	∈	∈	PROPN
ejpam-5764	117	44	ua	ua	PROPN
ejpam-5764	117	45	,	,	PUNCT
ejpam-5764	117	46	b	b	PROPN
ejpam-5764	117	47	/∈	/∈	SYM
ejpam-5764	117	48	ua	ua	PROPN
ejpam-5764	117	49	,	,	PUNCT
ejpam-5764	117	50	and	and	CCONJ
ejpam-5764	117	51	b	b	X
ejpam-5764	117	52	∈	∈	PROPN
ejpam-5764	117	53	vb	vb	NOUN
ejpam-5764	117	54	such	such	DET
ejpam-5764	117	55	that	that	PRON
ejpam-5764	117	56	b	b	PROPN
ejpam-5764	117	57	∈	∈	PROPN
ejpam-5764	117	58	vb	vb	NOUN
ejpam-5764	117	59	and	and	CCONJ
ejpam-5764	117	60	a	a	DET
ejpam-5764	117	61	/∈	/∈	INTJ
ejpam-5764	117	62	vb	vb	NOUN
ejpam-5764	117	63	,	,	PUNCT
ejpam-5764	117	64	where	where	SCONJ
ejpam-5764	117	65	i	i	PRON
ejpam-5764	117	66	̸=	̸=	PROPN
ejpam-5764	117	67	j	j	PROPN
ejpam-5764	117	68	such	such	ADJ
ejpam-5764	117	69	that	that	SCONJ
ejpam-5764	117	70	i	i	PRON
ejpam-5764	117	71	,	,	PUNCT
ejpam-5764	117	72	j	j	PROPN
ejpam-5764	117	73	=	=	SYM
ejpam-5764	117	74	1	1	NUM
ejpam-5764	117	75	,	,	PUNCT
ejpam-5764	117	76	2	2	NUM
ejpam-5764	117	77	,	,	PUNCT
ejpam-5764	117	78	3	3	NUM
ejpam-5764	117	79	.	.	X
ejpam-5764	117	80	definition	definition	NOUN
ejpam-5764	117	81	12	12	NUM
ejpam-5764	117	82	.	.	PUNCT
ejpam-5764	118	1	[	[	X
ejpam-5764	118	2	9	9	NUM
ejpam-5764	118	3	]	]	PUNCT
ejpam-5764	118	4	(	(	PUNCT
ejpam-5764	118	5	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	118	6	,	,	PUNCT
ejpam-5764	118	7	ϑ2	ϑ2	PROPN
ejpam-5764	118	8	,	,	PUNCT
ejpam-5764	118	9	ϑ3	ϑ3	PROPN
ejpam-5764	118	10	)	)	PUNCT
ejpam-5764	118	11	is	be	AUX
ejpam-5764	118	12	a	a	DET
ejpam-5764	118	13	tri	tri	ADJ
ejpam-5764	118	14	-	-	ADJ
ejpam-5764	118	15	t2	t2	ADJ
ejpam-5764	118	16	-	-	PUNCT
ejpam-5764	118	17	space	space	NOUN
ejpam-5764	118	18	if	if	SCONJ
ejpam-5764	118	19	,	,	PUNCT
ejpam-5764	118	20	for	for	ADP
ejpam-5764	118	21	each	each	PRON
ejpam-5764	118	22	of	of	ADP
ejpam-5764	118	23	the	the	DET
ejpam-5764	118	24	two	two	NUM
ejpam-5764	118	25	distinct	distinct	ADJ
ejpam-5764	118	26	elements	element	NOUN
ejpam-5764	118	27	a	a	PRON
ejpam-5764	118	28	and	and	CCONJ
ejpam-5764	118	29	b	b	NOUN
ejpam-5764	118	30	in	in	ADP
ejpam-5764	118	31	x	x	SYM
ejpam-5764	118	32	,	,	PUNCT
ejpam-5764	118	33	there	there	PRON
ejpam-5764	118	34	exists	exist	VERB
ejpam-5764	118	35	ϑi	ϑi	NOUN
ejpam-5764	118	36	-	-	PUNCT
ejpam-5764	118	37	open	open	NOUN
ejpam-5764	118	38	set	set	NOUN
ejpam-5764	118	39	ua	ua	PROPN
ejpam-5764	118	40	such	such	ADJ
ejpam-5764	118	41	that	that	SCONJ
ejpam-5764	118	42	a	a	DET
ejpam-5764	118	43	∈	∈	PROPN
ejpam-5764	118	44	ua	ua	PROPN
ejpam-5764	118	45	and	and	CCONJ
ejpam-5764	118	46	ϑj	ϑj	ADV
ejpam-5764	118	47	-	-	PUNCT
ejpam-5764	118	48	open	open	ADJ
ejpam-5764	118	49	set	set	VERB
ejpam-5764	118	50	vb	vb	ADP
ejpam-5764	118	51	such	such	DET
ejpam-5764	118	52	that	that	PRON
ejpam-5764	118	53	b	b	PROPN
ejpam-5764	118	54	∈	∈	PROPN
ejpam-5764	118	55	vb	vb	NOUN
ejpam-5764	118	56	and	and	CCONJ
ejpam-5764	118	57	ua	ua	PROPN
ejpam-5764	118	58	∩	∩	PROPN
ejpam-5764	118	59	vb	vb	PROPN
ejpam-5764	118	60	=	=	SYM
ejpam-5764	118	61	ϕ	ϕ	PROPN
ejpam-5764	118	62	,	,	PUNCT
ejpam-5764	118	63	where	where	SCONJ
ejpam-5764	118	64	i	i	PRON
ejpam-5764	118	65	̸=	̸=	PROPN
ejpam-5764	118	66	j	j	PROPN
ejpam-5764	118	67	such	such	ADJ
ejpam-5764	118	68	that	that	SCONJ
ejpam-5764	118	69	i	i	PRON
ejpam-5764	118	70	,	,	PUNCT
ejpam-5764	118	71	j	j	PROPN
ejpam-5764	118	72	=	=	SYM
ejpam-5764	118	73	1	1	NUM
ejpam-5764	118	74	,	,	PUNCT
ejpam-5764	118	75	2	2	NUM
ejpam-5764	118	76	,	,	PUNCT
ejpam-5764	118	77	3	3	NUM
ejpam-5764	118	78	.	.	X
ejpam-5764	118	79	definition	definition	NOUN
ejpam-5764	118	80	13	13	NUM
ejpam-5764	118	81	.	.	PUNCT
ejpam-5764	119	1	[	[	X
ejpam-5764	119	2	7	7	X
ejpam-5764	119	3	]	]	PUNCT
ejpam-5764	119	4	for	for	ADP
ejpam-5764	119	5	i	i	PROPN
ejpam-5764	119	6	=	=	NOUN
ejpam-5764	119	7	1	1	NUM
ejpam-5764	119	8	,	,	PUNCT
ejpam-5764	119	9	2	2	NUM
ejpam-5764	119	10	,	,	PUNCT
ejpam-5764	119	11	3	3	NUM
ejpam-5764	119	12	,	,	PUNCT
ejpam-5764	119	13	a	a	DET
ejpam-5764	119	14	topological	topological	ADJ
ejpam-5764	119	15	space	space	NOUN
ejpam-5764	119	16	(	(	PUNCT
ejpam-5764	119	17	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	119	18	,	,	PUNCT
ejpam-5764	119	19	ϑ2	ϑ2	PROPN
ejpam-5764	119	20	,	,	PUNCT
ejpam-5764	119	21	ϑ3	ϑ3	PROPN
ejpam-5764	119	22	)	)	PUNCT
ejpam-5764	119	23	is	be	AUX
ejpam-5764	119	24	a	a	DET
ejpam-5764	119	25	tri	tri	ADJ
ejpam-5764	119	26	-	-	NOUN
ejpam-5764	119	27	t2	t2	ADJ
ejpam-5764	119	28	1	1	NUM
ejpam-5764	119	29	2	2	NUM
ejpam-5764	119	30	-space	-space	NOUN
ejpam-5764	119	31	if	if	SCONJ
ejpam-5764	119	32	,	,	PUNCT
ejpam-5764	119	33	for	for	ADP
ejpam-5764	119	34	each	each	PRON
ejpam-5764	119	35	of	of	ADP
ejpam-5764	119	36	the	the	DET
ejpam-5764	119	37	two	two	NUM
ejpam-5764	119	38	distinct	distinct	ADJ
ejpam-5764	119	39	elements	element	NOUN
ejpam-5764	119	40	a	a	PRON
ejpam-5764	119	41	and	and	CCONJ
ejpam-5764	119	42	b	b	NOUN
ejpam-5764	119	43	in	in	ADP
ejpam-5764	119	44	x	x	NOUN
ejpam-5764	119	45	,	,	PUNCT
ejpam-5764	119	46	there	there	PRON
ejpam-5764	119	47	exists	exist	VERB
ejpam-5764	119	48	a	a	DET
ejpam-5764	119	49	ϑi	ϑi	NOUN
ejpam-5764	119	50	-	-	PUNCT
ejpam-5764	119	51	closed	close	VERB
ejpam-5764	119	52	set	set	NOUN
ejpam-5764	119	53	aa	aa	NOUN
ejpam-5764	119	54	,	,	PUNCT
ejpam-5764	119	55	b	b	PROPN
ejpam-5764	119	56	∈	∈	PROPN
ejpam-5764	119	57	bb	bb	NOUN
ejpam-5764	119	58	,	,	PUNCT
ejpam-5764	119	59	and	and	CCONJ
ejpam-5764	119	60	aa	aa	NOUN
ejpam-5764	119	61	∩bb	∩bb	NOUN
ejpam-5764	119	62	=	=	PUNCT
ejpam-5764	119	63	ϕ.	ϕ.	PROPN
ejpam-5764	119	64	definition	definition	NOUN
ejpam-5764	119	65	14	14	NUM
ejpam-5764	119	66	.	.	PUNCT
ejpam-5764	120	1	[	[	X
ejpam-5764	120	2	8	8	NUM
ejpam-5764	120	3	]	]	PUNCT
ejpam-5764	120	4	(	(	PUNCT
ejpam-5764	120	5	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	120	6	,	,	PUNCT
ejpam-5764	120	7	ϑ2	ϑ2	PROPN
ejpam-5764	120	8	,	,	PUNCT
ejpam-5764	120	9	ϑ3	ϑ3	PROPN
ejpam-5764	120	10	)	)	PUNCT
ejpam-5764	120	11	is	be	AUX
ejpam-5764	120	12	a	a	DET
ejpam-5764	120	13	tri	tri	ADJ
ejpam-5764	120	14	-	-	ADJ
ejpam-5764	120	15	regular	regular	ADJ
ejpam-5764	120	16	space	space	NOUN
ejpam-5764	120	17	.	.	PUNCT
ejpam-5764	121	1	if	if	SCONJ
ejpam-5764	121	2	a	a	PRON
ejpam-5764	121	3	is	be	AUX
ejpam-5764	121	4	a	a	DET
ejpam-5764	121	5	ϑi	ϑi	NOUN
ejpam-5764	121	6	-	-	PUNCT
ejpam-5764	121	7	closed	close	VERB
ejpam-5764	121	8	set	set	NOUN
ejpam-5764	121	9	and	and	CCONJ
ejpam-5764	121	10	a	a	DET
ejpam-5764	121	11	∈	∈	PROPN
ejpam-5764	121	12	ua	ua	PROPN
ejpam-5764	121	13	,	,	PUNCT
ejpam-5764	121	14	a	a	DET
ejpam-5764	121	15	⊂	⊂	PROPN
ejpam-5764	121	16	va	va	PROPN
ejpam-5764	121	17	,	,	PUNCT
ejpam-5764	121	18	and	and	CCONJ
ejpam-5764	121	19	ua	ua	PROPN
ejpam-5764	121	20	∩	∩	PROPN
ejpam-5764	121	21	va	va	PROPN
ejpam-5764	121	22	=	=	SYM
ejpam-5764	121	23	ϕ	ϕ	PROPN
ejpam-5764	121	24	,	,	PUNCT
ejpam-5764	121	25	then	then	ADV
ejpam-5764	121	26	i	i	PRON
ejpam-5764	121	27	̸=	̸=	PROPN
ejpam-5764	121	28	j	j	PROPN
ejpam-5764	121	29	,	,	PUNCT
ejpam-5764	121	30	for	for	ADP
ejpam-5764	121	31	i	i	PRON
ejpam-5764	121	32	,	,	PUNCT
ejpam-5764	121	33	j	j	PROPN
ejpam-5764	121	34	=	=	SYM
ejpam-5764	121	35	1	1	NUM
ejpam-5764	121	36	,	,	PUNCT
ejpam-5764	121	37	2	2	NUM
ejpam-5764	121	38	,	,	PUNCT
ejpam-5764	121	39	3	3	NUM
ejpam-5764	121	40	.	.	X
ejpam-5764	121	41	theorem	theorem	VERB
ejpam-5764	121	42	7	7	NUM
ejpam-5764	121	43	.	.	PUNCT
ejpam-5764	122	1	a	a	DET
ejpam-5764	122	2	tri	tri	ADJ
ejpam-5764	122	3	-	-	ADJ
ejpam-5764	122	4	topological	topological	ADJ
ejpam-5764	122	5	space	space	NOUN
ejpam-5764	122	6	(	(	PUNCT
ejpam-5764	122	7	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	122	8	,	,	PUNCT
ejpam-5764	122	9	ϑ2	ϑ2	PROPN
ejpam-5764	122	10	,	,	PUNCT
ejpam-5764	122	11	ϑ3	ϑ3	PROPN
ejpam-5764	122	12	)	)	PUNCT
ejpam-5764	122	13	is	be	AUX
ejpam-5764	122	14	a	a	DET
ejpam-5764	122	15	tri	tri	ADJ
ejpam-5764	122	16	-	-	ADJ
ejpam-5764	122	17	regular	regular	ADJ
ejpam-5764	122	18	space	space	NOUN
ejpam-5764	122	19	if	if	SCONJ
ejpam-5764	122	20	and	and	CCONJ
ejpam-5764	122	21	only	only	ADV
ejpam-5764	122	22	if	if	SCONJ
ejpam-5764	122	23	,	,	PUNCT
ejpam-5764	122	24	for	for	ADP
ejpam-5764	122	25	every	every	DET
ejpam-5764	122	26	point	point	NOUN
ejpam-5764	122	27	a	a	DET
ejpam-5764	122	28	∈	∈	NOUN
ejpam-5764	122	29	x	x	X
ejpam-5764	122	30	and	and	CCONJ
ejpam-5764	122	31	ϑi	ϑi	NOUN
ejpam-5764	122	32	-	-	PUNCT
ejpam-5764	122	33	open	open	NOUN
ejpam-5764	122	34	set	set	VERB
ejpam-5764	122	35	ua	ua	PROPN
ejpam-5764	122	36	containing	contain	VERB
ejpam-5764	122	37	a	a	PRON
ejpam-5764	122	38	,	,	PUNCT
ejpam-5764	122	39	there	there	PRON
ejpam-5764	122	40	exists	exist	VERB
ejpam-5764	122	41	a	a	DET
ejpam-5764	122	42	ϑi	ϑi	NOUN
ejpam-5764	122	43	-	-	PUNCT
ejpam-5764	122	44	open	open	NOUN
ejpam-5764	122	45	set	set	NOUN
ejpam-5764	122	46	wa	wa	INTJ
ejpam-5764	122	47	such	such	ADJ
ejpam-5764	122	48	that	that	SCONJ
ejpam-5764	122	49	a	a	DET
ejpam-5764	122	50	∈	∈	PROPN
ejpam-5764	122	51	wa	wa	PROPN
ejpam-5764	122	52	⊂	⊂	PROPN
ejpam-5764	122	53	wa	wa	PROPN
ejpam-5764	122	54	⊂	⊂	PROPN
ejpam-5764	122	55	ua	ua	PROPN
ejpam-5764	122	56	.	.	PUNCT
ejpam-5764	122	57	proof	proof	NOUN
ejpam-5764	122	58	.	.	PUNCT
ejpam-5764	123	1	(	(	PUNCT
ejpam-5764	123	2	⇒	⇒	PROPN
ejpam-5764	123	3	)	)	PUNCT
ejpam-5764	123	4	if	if	SCONJ
ejpam-5764	123	5	a	a	DET
ejpam-5764	123	6	∈	∈	PROPN
ejpam-5764	123	7	ua	ua	PROPN
ejpam-5764	123	8	,	,	PUNCT
ejpam-5764	123	9	then	then	ADV
ejpam-5764	123	10	a	a	DET
ejpam-5764	123	11	/∈	/∈	INTJ
ejpam-5764	123	12	uca	uca	NOUN
ejpam-5764	123	13	.	.	PUNCT
ejpam-5764	124	1	since	since	SCONJ
ejpam-5764	124	2	uca	uca	PROPN
ejpam-5764	124	3	is	be	AUX
ejpam-5764	124	4	a	a	DET
ejpam-5764	124	5	ϑi	ϑi	NOUN
ejpam-5764	124	6	-	-	PUNCT
ejpam-5764	124	7	closed	close	VERB
ejpam-5764	124	8	set	set	NOUN
ejpam-5764	124	9	and	and	CCONJ
ejpam-5764	124	10	(	(	PUNCT
ejpam-5764	124	11	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	124	12	,	,	PUNCT
ejpam-5764	124	13	ϑ2	ϑ2	PROPN
ejpam-5764	124	14	,	,	PUNCT
ejpam-5764	124	15	ϑ3	ϑ3	PROPN
ejpam-5764	124	16	)	)	PUNCT
ejpam-5764	124	17	is	be	AUX
ejpam-5764	124	18	a	a	DET
ejpam-5764	124	19	tri	tri	ADJ
ejpam-5764	124	20	-	-	ADJ
ejpam-5764	124	21	regular	regular	ADJ
ejpam-5764	124	22	space	space	NOUN
ejpam-5764	124	23	,	,	PUNCT
ejpam-5764	124	24	there	there	PRON
ejpam-5764	124	25	exist	exist	VERB
ejpam-5764	124	26	ϑi	ϑi	NOUN
ejpam-5764	124	27	-	-	PUNCT
ejpam-5764	124	28	open	open	ADJ
ejpam-5764	124	29	sets	set	NOUN
ejpam-5764	124	30	wa	wa	ADJ
ejpam-5764	124	31	and	and	CCONJ
ejpam-5764	124	32	vuc	vuc	VERB
ejpam-5764	124	33	a	a	DET
ejpam-5764	124	34	such	such	ADJ
ejpam-5764	124	35	that	that	SCONJ
ejpam-5764	124	36	a	a	DET
ejpam-5764	124	37	∈	∈	PROPN
ejpam-5764	124	38	wa	wa	NOUN
ejpam-5764	124	39	,	,	PUNCT
ejpam-5764	124	40	uca	uca	PROPN
ejpam-5764	124	41	⊂	⊂	PROPN
ejpam-5764	124	42	vuc	vuc	VERB
ejpam-5764	124	43	a	a	DET
ejpam-5764	124	44	,	,	PUNCT
ejpam-5764	124	45	and	and	CCONJ
ejpam-5764	124	46	wa	wa	ADJ
ejpam-5764	124	47	∩	∩	PROPN
ejpam-5764	124	48	vuc	vuc	VERB
ejpam-5764	124	49	a	a	DET
ejpam-5764	124	50	=	=	X
ejpam-5764	124	51	∅.	∅.	NOUN
ejpam-5764	124	52	thus	thus	ADV
ejpam-5764	124	53	,	,	PUNCT
ejpam-5764	124	54	wa	wa	PROPN
ejpam-5764	124	55	⊂	⊂	PROPN
ejpam-5764	124	56	vcuc	vcuc	PROPN
ejpam-5764	124	57	a	a	PRON
ejpam-5764	124	58	.	.	PUNCT
ejpam-5764	125	1	since	since	SCONJ
ejpam-5764	125	2	vuc	vuc	NOUN
ejpam-5764	125	3	a	a	PRON
ejpam-5764	125	4	is	be	AUX
ejpam-5764	125	5	ϑi	ϑi	NOUN
ejpam-5764	125	6	-	-	PUNCT
ejpam-5764	125	7	open	open	ADJ
ejpam-5764	125	8	,	,	PUNCT
ejpam-5764	125	9	v	v	NOUN
ejpam-5764	125	10	c	c	NOUN
ejpam-5764	125	11	uc	uc	NOUN
ejpam-5764	125	12	a	a	PRON
ejpam-5764	125	13	is	be	AUX
ejpam-5764	125	14	ϑi	ϑi	NOUN
ejpam-5764	125	15	-	-	PUNCT
ejpam-5764	125	16	closed	close	VERB
ejpam-5764	125	17	,	,	PUNCT
ejpam-5764	125	18	which	which	PRON
ejpam-5764	125	19	means	mean	VERB
ejpam-5764	125	20	wa	wa	PROPN
ejpam-5764	125	21	⊂	⊂	PROPN
ejpam-5764	125	22	vcuc	vcuc	PROPN
ejpam-5764	125	23	a	a	PRON
ejpam-5764	125	24	.	.	PUNCT
ejpam-5764	126	1	moreover	moreover	ADV
ejpam-5764	126	2	,	,	PUNCT
ejpam-5764	126	3	uca	uca	PROPN
ejpam-5764	126	4	⊂	⊂	PROPN
ejpam-5764	126	5	vuc	vuc	VERB
ejpam-5764	126	6	a	a	DET
ejpam-5764	126	7	implies	implie	NOUN
ejpam-5764	126	8	vcuc	vcuc	PROPN
ejpam-5764	126	9	a	a	DET
ejpam-5764	126	10	⊂	⊂	PROPN
ejpam-5764	126	11	ua	ua	PROPN
ejpam-5764	126	12	.	.	PUNCT
ejpam-5764	127	1	consequently	consequently	ADV
ejpam-5764	127	2	,	,	PUNCT
ejpam-5764	127	3	a	a	DET
ejpam-5764	127	4	∈	∈	PROPN
ejpam-5764	127	5	wa	wa	PROPN
ejpam-5764	127	6	⊂	⊂	PROPN
ejpam-5764	127	7	wa	wa	PROPN
ejpam-5764	127	8	⊂	⊂	PROPN
ejpam-5764	127	9	vcuc	vcuc	PROPN
ejpam-5764	127	10	a	a	DET
ejpam-5764	127	11	⊂	⊂	PROPN
ejpam-5764	127	12	ua	ua	PROPN
ejpam-5764	127	13	.	.	PUNCT
ejpam-5764	128	1	(	(	PUNCT
ejpam-5764	128	2	⇐	⇐	NOUN
ejpam-5764	128	3	)	)	PUNCT
ejpam-5764	128	4	let	let	VERB
ejpam-5764	128	5	a	a	DET
ejpam-5764	128	6	∈	∈	PROPN
ejpam-5764	128	7	x	x	X
ejpam-5764	128	8	and	and	CCONJ
ejpam-5764	128	9	f	f	PROPN
ejpam-5764	128	10	be	be	AUX
ejpam-5764	128	11	a	a	DET
ejpam-5764	128	12	ϑi	ϑi	NOUN
ejpam-5764	128	13	-	-	PUNCT
ejpam-5764	128	14	closed	close	VERB
ejpam-5764	128	15	set	set	NOUN
ejpam-5764	128	16	such	such	DET
ejpam-5764	128	17	that	that	SCONJ
ejpam-5764	128	18	a	a	PRON
ejpam-5764	128	19	/∈	/∈	NOUN
ejpam-5764	128	20	f	f	PROPN
ejpam-5764	128	21	.	.	PUNCT
ejpam-5764	129	1	then	then	ADV
ejpam-5764	129	2	a	a	DET
ejpam-5764	129	3	∈	∈	PROPN
ejpam-5764	129	4	f	f	X
ejpam-5764	129	5	c	c	NOUN
ejpam-5764	129	6	,	,	PUNCT
ejpam-5764	129	7	and	and	CCONJ
ejpam-5764	129	8	f	f	PROPN
ejpam-5764	129	9	c	c	PROPN
ejpam-5764	129	10	is	be	AUX
ejpam-5764	129	11	a	a	DET
ejpam-5764	129	12	ϑi	ϑi	NOUN
ejpam-5764	129	13	-	-	PUNCT
ejpam-5764	129	14	open	open	NOUN
ejpam-5764	129	15	set	set	NOUN
ejpam-5764	129	16	containing	contain	VERB
ejpam-5764	129	17	a.	a.	NOUN
ejpam-5764	129	18	by	by	ADP
ejpam-5764	129	19	our	our	PRON
ejpam-5764	129	20	hypothesis	hypothesis	NOUN
ejpam-5764	129	21	,	,	PUNCT
ejpam-5764	129	22	there	there	PRON
ejpam-5764	129	23	exists	exist	VERB
ejpam-5764	129	24	a	a	DET
ejpam-5764	129	25	ϑi	ϑi	NOUN
ejpam-5764	129	26	-	-	PUNCT
ejpam-5764	129	27	open	open	NOUN
ejpam-5764	129	28	set	set	NOUN
ejpam-5764	129	29	wa	wa	INTJ
ejpam-5764	129	30	such	such	ADJ
ejpam-5764	129	31	that	that	SCONJ
ejpam-5764	129	32	a	a	DET
ejpam-5764	129	33	∈	∈	PROPN
ejpam-5764	129	34	wa	wa	PROPN
ejpam-5764	129	35	⊂	⊂	PROPN
ejpam-5764	129	36	wa	wa	PROPN
ejpam-5764	129	37	⊂	⊂	PROPN
ejpam-5764	129	38	f	f	PROPN
ejpam-5764	130	1	c.	c.	PROPN
ejpam-5764	130	2	this	this	PRON
ejpam-5764	130	3	implies	imply	VERB
ejpam-5764	130	4	a	a	DET
ejpam-5764	130	5	∈	∈	PROPN
ejpam-5764	130	6	wa	wa	NOUN
ejpam-5764	130	7	and	and	CCONJ
ejpam-5764	130	8	f	f	PROPN
ejpam-5764	130	9	⊂	⊂	PROPN
ejpam-5764	130	10	(	(	PUNCT
ejpam-5764	130	11	wa	wa	PROPN
ejpam-5764	130	12	)	)	PUNCT
ejpam-5764	130	13	c.	c.	NOUN
ejpam-5764	130	14	since	since	SCONJ
ejpam-5764	130	15	wa	wa	PROPN
ejpam-5764	130	16	is	be	AUX
ejpam-5764	130	17	ϑi	ϑi	NOUN
ejpam-5764	130	18	-	-	PUNCT
ejpam-5764	130	19	closed	close	VERB
ejpam-5764	130	20	,	,	PUNCT
ejpam-5764	130	21	(	(	PUNCT
ejpam-5764	130	22	wa	wa	ADJ
ejpam-5764	130	23	)	)	PUNCT
ejpam-5764	130	24	c	c	PROPN
ejpam-5764	130	25	is	be	AUX
ejpam-5764	130	26	ϑi	ϑi	NOUN
ejpam-5764	130	27	-	-	PUNCT
ejpam-5764	130	28	open	open	ADJ
ejpam-5764	130	29	.	.	PUNCT
ejpam-5764	131	1	we	we	PRON
ejpam-5764	131	2	also	also	ADV
ejpam-5764	131	3	have	have	VERB
ejpam-5764	131	4	wa	wa	ADJ
ejpam-5764	131	5	∩	∩	NOUN
ejpam-5764	131	6	(	(	PUNCT
ejpam-5764	131	7	wa	wa	NOUN
ejpam-5764	131	8	)	)	PUNCT
ejpam-5764	131	9	c	c	NOUN
ejpam-5764	132	1	=	=	PUNCT
ejpam-5764	132	2	∅.	∅.	VERB
ejpam-5764	132	3	therefore	therefore	ADV
ejpam-5764	132	4	,	,	PUNCT
ejpam-5764	132	5	(	(	PUNCT
ejpam-5764	132	6	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	132	7	,	,	PUNCT
ejpam-5764	132	8	ϑ2	ϑ2	PROPN
ejpam-5764	132	9	,	,	PUNCT
ejpam-5764	132	10	ϑ3	ϑ3	PROPN
ejpam-5764	132	11	)	)	PUNCT
ejpam-5764	132	12	is	be	AUX
ejpam-5764	132	13	a	a	DET
ejpam-5764	132	14	tri	tri	ADJ
ejpam-5764	132	15	-	-	ADJ
ejpam-5764	132	16	regular	regular	ADJ
ejpam-5764	132	17	space	space	NOUN
ejpam-5764	132	18	.	.	PUNCT
ejpam-5764	133	1	definition	definition	NOUN
ejpam-5764	133	2	15	15	NUM
ejpam-5764	133	3	.	.	PUNCT
ejpam-5764	134	1	[	[	X
ejpam-5764	134	2	8	8	NUM
ejpam-5764	134	3	]	]	PUNCT
ejpam-5764	134	4	a	a	DET
ejpam-5764	134	5	tri	tri	ADJ
ejpam-5764	134	6	-	-	ADJ
ejpam-5764	134	7	topological	topological	ADJ
ejpam-5764	134	8	space	space	NOUN
ejpam-5764	134	9	(	(	PUNCT
ejpam-5764	134	10	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	134	11	,	,	PUNCT
ejpam-5764	134	12	ϑ2	ϑ2	PROPN
ejpam-5764	134	13	,	,	PUNCT
ejpam-5764	134	14	ϑ3	ϑ3	PROPN
ejpam-5764	134	15	)	)	PUNCT
ejpam-5764	134	16	is	be	AUX
ejpam-5764	134	17	a	a	DET
ejpam-5764	134	18	tri	tri	ADJ
ejpam-5764	134	19	-	-	ADJ
ejpam-5764	134	20	t3	t3	ADJ
ejpam-5764	134	21	-	-	PUNCT
ejpam-5764	134	22	space	space	NOUN
ejpam-5764	134	23	if	if	SCONJ
ejpam-5764	134	24	it	it	PRON
ejpam-5764	134	25	is	be	AUX
ejpam-5764	134	26	both	both	PRON
ejpam-5764	134	27	a	a	DET
ejpam-5764	134	28	tri	tri	ADJ
ejpam-5764	134	29	-	-	ADJ
ejpam-5764	134	30	t1	t1	ADJ
ejpam-5764	134	31	-	-	PUNCT
ejpam-5764	134	32	space	space	NOUN
ejpam-5764	134	33	and	and	CCONJ
ejpam-5764	134	34	tri	tri	ADJ
ejpam-5764	134	35	-	-	ADJ
ejpam-5764	134	36	regular	regular	ADJ
ejpam-5764	134	37	.	.	PUNCT
ejpam-5764	135	1	definition	definition	NOUN
ejpam-5764	135	2	16	16	NUM
ejpam-5764	135	3	.	.	PUNCT
ejpam-5764	136	1	[	[	X
ejpam-5764	136	2	7	7	X
ejpam-5764	136	3	]	]	X
ejpam-5764	136	4	a	a	DET
ejpam-5764	136	5	tri	tri	ADJ
ejpam-5764	136	6	-	-	ADJ
ejpam-5764	136	7	topological	topological	ADJ
ejpam-5764	136	8	space	space	NOUN
ejpam-5764	136	9	(	(	PUNCT
ejpam-5764	136	10	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	136	11	,	,	PUNCT
ejpam-5764	136	12	ϑ2	ϑ2	PROPN
ejpam-5764	136	13	,	,	PUNCT
ejpam-5764	136	14	ϑ3	ϑ3	PROPN
ejpam-5764	136	15	)	)	PUNCT
ejpam-5764	136	16	is	be	AUX
ejpam-5764	136	17	a	a	DET
ejpam-5764	136	18	tri	tri	ADJ
ejpam-5764	136	19	-	-	ADJ
ejpam-5764	136	20	normal	normal	ADJ
ejpam-5764	136	21	space	space	NOUN
ejpam-5764	136	22	if	if	SCONJ
ejpam-5764	136	23	for	for	ADP
ejpam-5764	136	24	any	any	DET
ejpam-5764	136	25	two	two	NUM
ejpam-5764	136	26	disjoint	disjoint	NOUN
ejpam-5764	136	27	ϑi	ϑi	NOUN
ejpam-5764	136	28	-	-	PUNCT
ejpam-5764	136	29	closed	close	VERB
ejpam-5764	136	30	sets	set	NOUN
ejpam-5764	136	31	a	a	PRON
ejpam-5764	136	32	and	and	CCONJ
ejpam-5764	136	33	b	b	NOUN
ejpam-5764	136	34	,	,	PUNCT
ejpam-5764	136	35	there	there	PRON
ejpam-5764	136	36	exist	exist	VERB
ejpam-5764	136	37	ϑi	ϑi	NOUN
ejpam-5764	136	38	-	-	PUNCT
ejpam-5764	136	39	open	open	NOUN
ejpam-5764	136	40	sets	set	NOUN
ejpam-5764	136	41	ua	ua	PROPN
ejpam-5764	136	42	and	and	CCONJ
ejpam-5764	136	43	vb	vb	NOUN
ejpam-5764	137	1	such	such	ADJ
ejpam-5764	137	2	that	that	SCONJ
ejpam-5764	137	3	a	a	DET
ejpam-5764	137	4	⊂	⊂	PROPN
ejpam-5764	137	5	ua	ua	PROPN
ejpam-5764	137	6	,	,	PUNCT
ejpam-5764	137	7	b	b	PROPN
ejpam-5764	137	8	⊂	⊂	PROPN
ejpam-5764	137	9	vb	vb	PROPN
ejpam-5764	137	10	,	,	PUNCT
ejpam-5764	137	11	and	and	CCONJ
ejpam-5764	137	12	ua	ua	PROPN
ejpam-5764	137	13	∩	∩	NOUN
ejpam-5764	137	14	vb	vb	NOUN
ejpam-5764	137	15	=	=	PUNCT
ejpam-5764	137	16	∅.	∅.	NOUN
ejpam-5764	137	17	theorem	theorem	VERB
ejpam-5764	137	18	8	8	NUM
ejpam-5764	137	19	.	.	PUNCT
ejpam-5764	138	1	a	a	DET
ejpam-5764	138	2	tri	tri	ADJ
ejpam-5764	138	3	-	-	ADJ
ejpam-5764	138	4	topological	topological	ADJ
ejpam-5764	138	5	space	space	NOUN
ejpam-5764	138	6	(	(	PUNCT
ejpam-5764	138	7	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	138	8	,	,	PUNCT
ejpam-5764	138	9	ϑ2	ϑ2	PROPN
ejpam-5764	138	10	,	,	PUNCT
ejpam-5764	138	11	ϑ3	ϑ3	PROPN
ejpam-5764	138	12	)	)	PUNCT
ejpam-5764	138	13	is	be	AUX
ejpam-5764	138	14	a	a	DET
ejpam-5764	138	15	tri	tri	ADJ
ejpam-5764	138	16	-	-	ADJ
ejpam-5764	138	17	normal	normal	ADJ
ejpam-5764	138	18	space	space	NOUN
ejpam-5764	138	19	if	if	SCONJ
ejpam-5764	138	20	and	and	CCONJ
ejpam-5764	138	21	only	only	ADV
ejpam-5764	138	22	if	if	SCONJ
ejpam-5764	138	23	for	for	ADP
ejpam-5764	138	24	every	every	DET
ejpam-5764	138	25	ϑi	ϑi	NOUN
ejpam-5764	138	26	-	-	PUNCT
ejpam-5764	138	27	closed	close	VERB
ejpam-5764	138	28	set	set	VERB
ejpam-5764	138	29	f	f	PROPN
ejpam-5764	138	30	and	and	CCONJ
ejpam-5764	138	31	ϑi	ϑi	NOUN
ejpam-5764	138	32	-	-	PUNCT
ejpam-5764	138	33	open	open	VERB
ejpam-5764	138	34	set	set	VERB
ejpam-5764	138	35	u	u	NOUN
ejpam-5764	138	36	containing	contain	VERB
ejpam-5764	138	37	f	f	NOUN
ejpam-5764	138	38	,	,	PUNCT
ejpam-5764	138	39	there	there	PRON
ejpam-5764	138	40	exists	exist	VERB
ejpam-5764	138	41	a	a	DET
ejpam-5764	138	42	ϑi	ϑi	NOUN
ejpam-5764	138	43	-	-	PUNCT
ejpam-5764	138	44	open	open	NOUN
ejpam-5764	138	45	set	set	VERB
ejpam-5764	138	46	v	v	ADP
ejpam-5764	138	47	such	such	DET
ejpam-5764	138	48	that	that	SCONJ
ejpam-5764	138	49	f	f	PROPN
ejpam-5764	138	50	⊂	⊂	PROPN
ejpam-5764	138	51	v	v	ADP
ejpam-5764	138	52	⊂	⊂	PROPN
ejpam-5764	138	53	v	v	ADP
ejpam-5764	138	54	⊂	⊂	PROPN
ejpam-5764	138	55	u	u	PROPN
ejpam-5764	138	56	.	.	PUNCT
ejpam-5764	139	1	proof	proof	NOUN
ejpam-5764	139	2	.	.	PUNCT
ejpam-5764	140	1	(	(	PUNCT
ejpam-5764	140	2	⇒	⇒	PROPN
ejpam-5764	140	3	)	)	PUNCT
ejpam-5764	140	4	let	let	VERB
ejpam-5764	140	5	f	f	PRON
ejpam-5764	140	6	be	be	AUX
ejpam-5764	140	7	a	a	DET
ejpam-5764	140	8	ϑi	ϑi	NOUN
ejpam-5764	140	9	-	-	PUNCT
ejpam-5764	140	10	closed	close	VERB
ejpam-5764	140	11	set	set	NOUN
ejpam-5764	140	12	and	and	CCONJ
ejpam-5764	140	13	u	u	NOUN
ejpam-5764	140	14	be	be	VERB
ejpam-5764	140	15	a	a	DET
ejpam-5764	140	16	ϑi	ϑi	NOUN
ejpam-5764	140	17	-	-	PUNCT
ejpam-5764	140	18	open	open	NOUN
ejpam-5764	140	19	set	set	NOUN
ejpam-5764	140	20	containing	contain	VERB
ejpam-5764	140	21	f	f	PROPN
ejpam-5764	140	22	.	.	PUNCT
ejpam-5764	141	1	then	then	ADV
ejpam-5764	141	2	u	u	X
ejpam-5764	141	3	c	c	PROPN
ejpam-5764	141	4	is	be	AUX
ejpam-5764	141	5	a	a	DET
ejpam-5764	141	6	ϑi	ϑi	NOUN
ejpam-5764	141	7	-	-	PUNCT
ejpam-5764	141	8	closed	close	VERB
ejpam-5764	141	9	set	set	NOUN
ejpam-5764	141	10	and	and	CCONJ
ejpam-5764	141	11	f	f	PROPN
ejpam-5764	141	12	∩	∩	NOUN
ejpam-5764	141	13	u	u	NOUN
ejpam-5764	141	14	c	c	NOUN
ejpam-5764	141	15	=	=	PUNCT
ejpam-5764	141	16	∅.	∅.	NOUN
ejpam-5764	141	17	since	since	SCONJ
ejpam-5764	141	18	(	(	PUNCT
ejpam-5764	141	19	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	141	20	,	,	PUNCT
ejpam-5764	141	21	ϑ2	ϑ2	PROPN
ejpam-5764	141	22	,	,	PUNCT
ejpam-5764	141	23	ϑ3	ϑ3	PROPN
ejpam-5764	141	24	)	)	PUNCT
ejpam-5764	141	25	is	be	AUX
ejpam-5764	141	26	tri	tri	ADJ
ejpam-5764	141	27	-	-	ADJ
ejpam-5764	141	28	normal	normal	ADJ
ejpam-5764	141	29	,	,	PUNCT
ejpam-5764	141	30	there	there	PRON
ejpam-5764	141	31	exist	exist	VERB
ejpam-5764	141	32	ϑi	ϑi	NOUN
ejpam-5764	141	33	-	-	PUNCT
ejpam-5764	141	34	open	open	NOUN
ejpam-5764	141	35	sets	set	NOUN
ejpam-5764	141	36	v	v	ADP
ejpam-5764	141	37	and	and	CCONJ
ejpam-5764	141	38	w	w	ADP
ejpam-5764	141	39	such	such	ADJ
ejpam-5764	141	40	that	that	SCONJ
ejpam-5764	141	41	f	f	PROPN
ejpam-5764	141	42	⊂	⊂	PROPN
ejpam-5764	141	43	v	v	PROPN
ejpam-5764	141	44	,	,	PUNCT
ejpam-5764	141	45	u	u	PROPN
ejpam-5764	141	46	c	c	PROPN
ejpam-5764	141	47	⊂	⊂	PROPN
ejpam-5764	141	48	w	w	PROPN
ejpam-5764	141	49	,	,	PUNCT
ejpam-5764	141	50	and	and	CCONJ
ejpam-5764	141	51	v	v	ADP
ejpam-5764	141	52	∩w	∩w	NOUN
ejpam-5764	141	53	=	=	PUNCT
ejpam-5764	141	54	∅.	∅.	VERB
ejpam-5764	141	55	thus	thus	ADV
ejpam-5764	141	56	,	,	PUNCT
ejpam-5764	141	57	v	v	X
ejpam-5764	141	58	⊂	⊂	PROPN
ejpam-5764	141	59	w	w	PROPN
ejpam-5764	141	60	c.	c.	PROPN
ejpam-5764	141	61	since	since	SCONJ
ejpam-5764	141	62	w	w	PROPN
ejpam-5764	141	63	is	be	AUX
ejpam-5764	141	64	ϑi	ϑi	NOUN
ejpam-5764	141	65	-	-	PUNCT
ejpam-5764	141	66	open	open	ADJ
ejpam-5764	141	67	,	,	PUNCT
ejpam-5764	141	68	w	w	PROPN
ejpam-5764	141	69	c	c	NOUN
ejpam-5764	141	70	is	be	AUX
ejpam-5764	141	71	ϑi	ϑi	NOUN
ejpam-5764	141	72	-	-	PUNCT
ejpam-5764	141	73	closed	close	VERB
ejpam-5764	141	74	,	,	PUNCT
ejpam-5764	141	75	which	which	PRON
ejpam-5764	141	76	means	mean	VERB
ejpam-5764	141	77	v	v	ADP
ejpam-5764	141	78	⊂	⊂	PROPN
ejpam-5764	141	79	w	w	PROPN
ejpam-5764	141	80	c.	c.	PROPN
ejpam-5764	141	81	additionally	additionally	ADV
ejpam-5764	141	82	,	,	PUNCT
ejpam-5764	141	83	u	u	PROPN
ejpam-5764	141	84	c	c	PROPN
ejpam-5764	141	85	⊂	⊂	PROPN
ejpam-5764	141	86	w	w	PROPN
ejpam-5764	141	87	implies	imply	VERB
ejpam-5764	141	88	w	w	PROPN
ejpam-5764	141	89	c	c	NOUN
ejpam-5764	141	90	⊂	⊂	PROPN
ejpam-5764	141	91	u	u	PROPN
ejpam-5764	141	92	.	.	PUNCT
ejpam-5764	142	1	therefore	therefore	ADV
ejpam-5764	142	2	,	,	PUNCT
ejpam-5764	142	3	f	f	PROPN
ejpam-5764	142	4	⊂	⊂	PROPN
ejpam-5764	142	5	v	v	ADP
ejpam-5764	142	6	⊂	⊂	PROPN
ejpam-5764	142	7	v	v	X
ejpam-5764	142	8	⊂	⊂	PROPN
ejpam-5764	142	9	w	w	PROPN
ejpam-5764	142	10	c	c	PROPN
ejpam-5764	142	11	⊂	⊂	PROPN
ejpam-5764	142	12	u	u	PROPN
ejpam-5764	142	13	.	.	PUNCT
ejpam-5764	143	1	(	(	PUNCT
ejpam-5764	143	2	⇐	⇐	NOUN
ejpam-5764	143	3	)	)	PUNCT
ejpam-5764	143	4	let	let	VERB
ejpam-5764	143	5	f	f	PROPN
ejpam-5764	143	6	and	and	CCONJ
ejpam-5764	143	7	g	g	PROPN
ejpam-5764	143	8	be	be	AUX
ejpam-5764	143	9	disjoint	disjoint	PROPN
ejpam-5764	143	10	ϑi	ϑi	NOUN
ejpam-5764	143	11	-	-	PUNCT
ejpam-5764	143	12	closed	close	VERB
ejpam-5764	143	13	sets	set	NOUN
ejpam-5764	143	14	.	.	PUNCT
ejpam-5764	144	1	then	then	ADV
ejpam-5764	144	2	f	f	PROPN
ejpam-5764	144	3	⊂	⊂	PROPN
ejpam-5764	144	4	gc	gc	PROPN
ejpam-5764	144	5	and	and	CCONJ
ejpam-5764	144	6	gc	gc	PROPN
ejpam-5764	144	7	is	be	AUX
ejpam-5764	144	8	a	a	DET
ejpam-5764	144	9	ϑi	ϑi	NOUN
ejpam-5764	144	10	-	-	PUNCT
ejpam-5764	144	11	open	open	NOUN
ejpam-5764	144	12	set	set	NOUN
ejpam-5764	144	13	.	.	PUNCT
ejpam-5764	145	1	by	by	ADP
ejpam-5764	145	2	our	our	PRON
ejpam-5764	145	3	hypothesis	hypothesis	NOUN
ejpam-5764	145	4	,	,	PUNCT
ejpam-5764	145	5	there	there	PRON
ejpam-5764	145	6	exists	exist	VERB
ejpam-5764	145	7	a	a	DET
ejpam-5764	145	8	ϑi	ϑi	NOUN
ejpam-5764	145	9	-	-	PUNCT
ejpam-5764	145	10	open	open	NOUN
ejpam-5764	145	11	set	set	VERB
ejpam-5764	145	12	v	v	ADP
ejpam-5764	145	13	such	such	DET
ejpam-5764	145	14	that	that	SCONJ
ejpam-5764	145	15	f	f	PROPN
ejpam-5764	145	16	⊂	⊂	PROPN
ejpam-5764	145	17	v	v	ADP
ejpam-5764	145	18	⊂	⊂	PROPN
ejpam-5764	145	19	v	v	X
ejpam-5764	145	20	⊂	⊂	PROPN
ejpam-5764	145	21	gc	gc	PROPN
ejpam-5764	145	22	.	.	PROPN
ejpam-5764	146	1	this	this	PRON
ejpam-5764	146	2	implies	imply	VERB
ejpam-5764	146	3	f	f	PROPN
ejpam-5764	146	4	⊂	⊂	PROPN
ejpam-5764	146	5	v	v	PROPN
ejpam-5764	146	6	and	and	CCONJ
ejpam-5764	146	7	g	g	PROPN
ejpam-5764	146	8	⊂	⊂	PROPN
ejpam-5764	146	9	(	(	PUNCT
ejpam-5764	146	10	v	v	NOUN
ejpam-5764	146	11	)	)	PUNCT
ejpam-5764	146	12	c.	c.	NOUN
ejpam-5764	146	13	since	since	SCONJ
ejpam-5764	146	14	v	v	NUM
ejpam-5764	146	15	is	be	AUX
ejpam-5764	146	16	ϑi	ϑi	NOUN
ejpam-5764	146	17	-	-	PUNCT
ejpam-5764	146	18	closed	close	VERB
ejpam-5764	146	19	,	,	PUNCT
ejpam-5764	146	20	(	(	PUNCT
ejpam-5764	146	21	v	v	NOUN
ejpam-5764	146	22	)	)	PUNCT
ejpam-5764	146	23	c	c	PROPN
ejpam-5764	146	24	is	be	AUX
ejpam-5764	146	25	ϑi	ϑi	NOUN
ejpam-5764	146	26	-	-	PUNCT
ejpam-5764	146	27	open	open	ADJ
ejpam-5764	146	28	.	.	PUNCT
ejpam-5764	147	1	we	we	PRON
ejpam-5764	147	2	also	also	ADV
ejpam-5764	147	3	have	have	VERB
ejpam-5764	147	4	v	v	ADP
ejpam-5764	147	5	∩	∩	NOUN
ejpam-5764	147	6	(	(	PUNCT
ejpam-5764	147	7	v	v	NOUN
ejpam-5764	147	8	)	)	PUNCT
ejpam-5764	147	9	c	c	NOUN
ejpam-5764	147	10	=	=	PUNCT
ejpam-5764	147	11	∅.	∅.	VERB
ejpam-5764	147	12	therefore	therefore	ADV
ejpam-5764	147	13	,	,	PUNCT
ejpam-5764	147	14	(	(	PUNCT
ejpam-5764	147	15	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	147	16	,	,	PUNCT
ejpam-5764	147	17	ϑ2	ϑ2	PROPN
ejpam-5764	147	18	,	,	PUNCT
ejpam-5764	147	19	ϑ3	ϑ3	PROPN
ejpam-5764	147	20	)	)	PUNCT
ejpam-5764	147	21	is	be	AUX
ejpam-5764	147	22	tri	tri	ADJ
ejpam-5764	147	23	-	-	ADJ
ejpam-5764	147	24	normal	normal	ADJ
ejpam-5764	147	25	.	.	PUNCT
ejpam-5764	148	1	j.	j.	PROPN
ejpam-5764	148	2	oudetallah	oudetallah	PROPN
ejpam-5764	148	3	et	et	PROPN
ejpam-5764	148	4	al	al	PROPN
ejpam-5764	148	5	.	.	PUNCT
ejpam-5764	148	6	/	/	SYM
ejpam-5764	148	7	eur	eur	PROPN
ejpam-5764	148	8	.	.	PUNCT
ejpam-5764	149	1	j.	j.	PROPN
ejpam-5764	149	2	pure	pure	PROPN
ejpam-5764	149	3	appl	appl	PROPN
ejpam-5764	149	4	.	.	PROPN
ejpam-5764	149	5	math	math	PROPN
ejpam-5764	149	6	,	,	PUNCT
ejpam-5764	149	7	18	18	NUM
ejpam-5764	149	8	(	(	PUNCT
ejpam-5764	149	9	2	2	NUM
ejpam-5764	149	10	)	)	PUNCT
ejpam-5764	149	11	(	(	PUNCT
ejpam-5764	149	12	2025	2025	NUM
ejpam-5764	149	13	)	)	PUNCT
ejpam-5764	149	14	,	,	PUNCT
ejpam-5764	149	15	5764	5764	NUM
ejpam-5764	149	16	7	7	NUM
ejpam-5764	149	17	of	of	ADP
ejpam-5764	149	18	11	11	NUM
ejpam-5764	149	19	definition	definition	NOUN
ejpam-5764	149	20	17	17	NUM
ejpam-5764	149	21	.	.	PUNCT
ejpam-5764	150	1	[	[	X
ejpam-5764	150	2	7	7	X
ejpam-5764	150	3	]	]	X
ejpam-5764	150	4	a	a	DET
ejpam-5764	150	5	tri	tri	ADJ
ejpam-5764	150	6	-	-	ADJ
ejpam-5764	150	7	topological	topological	ADJ
ejpam-5764	150	8	space	space	NOUN
ejpam-5764	150	9	(	(	PUNCT
ejpam-5764	150	10	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	150	11	,	,	PUNCT
ejpam-5764	150	12	ϑ2	ϑ2	PROPN
ejpam-5764	150	13	,	,	PUNCT
ejpam-5764	150	14	ϑ3	ϑ3	PROPN
ejpam-5764	150	15	)	)	PUNCT
ejpam-5764	150	16	is	be	AUX
ejpam-5764	150	17	a	a	DET
ejpam-5764	150	18	tri	tri	ADJ
ejpam-5764	150	19	-	-	ADJ
ejpam-5764	150	20	t4	t4	ADJ
ejpam-5764	150	21	-	-	PUNCT
ejpam-5764	150	22	space	space	NOUN
ejpam-5764	150	23	if	if	SCONJ
ejpam-5764	150	24	it	it	PRON
ejpam-5764	150	25	is	be	AUX
ejpam-5764	150	26	both	both	PRON
ejpam-5764	150	27	a	a	DET
ejpam-5764	150	28	tri	tri	ADJ
ejpam-5764	150	29	-	-	ADJ
ejpam-5764	150	30	t1	t1	ADJ
ejpam-5764	150	31	-	-	PUNCT
ejpam-5764	150	32	space	space	NOUN
ejpam-5764	150	33	and	and	CCONJ
ejpam-5764	150	34	tri	tri	ADJ
ejpam-5764	150	35	-	-	ADJ
ejpam-5764	150	36	normal	normal	ADJ
ejpam-5764	150	37	.	.	PUNCT
ejpam-5764	151	1	theorem	theorem	VERB
ejpam-5764	151	2	9	9	NUM
ejpam-5764	151	3	.	.	PUNCT
ejpam-5764	152	1	[	[	X
ejpam-5764	152	2	8	8	NUM
ejpam-5764	152	3	]	]	X
ejpam-5764	152	4	it	it	PRON
ejpam-5764	152	5	is	be	AUX
ejpam-5764	152	6	tri	tri	ADJ
ejpam-5764	152	7	-	-	ADJ
ejpam-5764	152	8	tk−1	tk−1	ADJ
ejpam-5764	152	9	-	-	PUNCT
ejpam-5764	152	10	space	space	NOUN
ejpam-5764	152	11	if	if	SCONJ
ejpam-5764	152	12	(	(	PUNCT
ejpam-5764	152	13	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	152	14	,	,	PUNCT
ejpam-5764	152	15	ϑ2	ϑ2	PROPN
ejpam-5764	152	16	,	,	PUNCT
ejpam-5764	152	17	ϑ3	ϑ3	PROPN
ejpam-5764	152	18	)	)	PUNCT
ejpam-5764	152	19	is	be	AUX
ejpam-5764	152	20	tri	tri	ADJ
ejpam-5764	152	21	-	-	ADJ
ejpam-5764	152	22	tk	tk	NOUN
ejpam-5764	152	23	-	-	NOUN
ejpam-5764	152	24	space	space	NOUN
ejpam-5764	152	25	.	.	PUNCT
ejpam-5764	153	1	theorem	theorem	ADJ
ejpam-5764	153	2	10	10	NUM
ejpam-5764	153	3	.	.	PUNCT
ejpam-5764	154	1	[	[	X
ejpam-5764	154	2	9	9	NUM
ejpam-5764	154	3	]	]	PUNCT
ejpam-5764	154	4	a	a	DET
ejpam-5764	154	5	space	space	NOUN
ejpam-5764	154	6	is	be	AUX
ejpam-5764	154	7	tri	tri	ADJ
ejpam-5764	154	8	-	-	ADJ
ejpam-5764	154	9	t3	t3	ADJ
ejpam-5764	154	10	-	-	PUNCT
ejpam-5764	154	11	space	space	NOUN
ejpam-5764	154	12	if	if	SCONJ
ejpam-5764	154	13	(	(	PUNCT
ejpam-5764	154	14	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	154	15	,	,	PUNCT
ejpam-5764	154	16	ϑ2	ϑ2	PROPN
ejpam-5764	154	17	,	,	PUNCT
ejpam-5764	154	18	ϑ3	ϑ3	PROPN
ejpam-5764	154	19	)	)	PUNCT
ejpam-5764	154	20	is	be	AUX
ejpam-5764	154	21	tri	tri	ADJ
ejpam-5764	154	22	-	-	ADJ
ejpam-5764	154	23	t4	t4	ADJ
ejpam-5764	154	24	-	-	PUNCT
ejpam-5764	154	25	space	space	NOUN
ejpam-5764	154	26	.	.	PUNCT
ejpam-5764	155	1	proof	proof	NOUN
ejpam-5764	155	2	.	.	PUNCT
ejpam-5764	156	1	by	by	ADP
ejpam-5764	156	2	considering	consider	VERB
ejpam-5764	156	3	(	(	PUNCT
ejpam-5764	156	4	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	156	5	,	,	PUNCT
ejpam-5764	156	6	ϑ2	ϑ2	PROPN
ejpam-5764	156	7	,	,	PUNCT
ejpam-5764	156	8	ϑ3	ϑ3	PROPN
ejpam-5764	156	9	)	)	PUNCT
ejpam-5764	156	10	to	to	PART
ejpam-5764	156	11	be	be	AUX
ejpam-5764	156	12	tri	tri	ADJ
ejpam-5764	156	13	-	-	ADJ
ejpam-5764	156	14	t4	t4	ADJ
ejpam-5764	156	15	-	-	PUNCT
ejpam-5764	156	16	space	space	NOUN
ejpam-5764	156	17	,	,	PUNCT
ejpam-5764	156	18	it	it	PRON
ejpam-5764	156	19	is	be	AUX
ejpam-5764	156	20	tri	tri	ADJ
ejpam-5764	156	21	-	-	ADJ
ejpam-5764	156	22	t1	t1	ADJ
ejpam-5764	156	23	-	-	PUNCT
ejpam-5764	156	24	space	space	NOUN
ejpam-5764	156	25	and	and	CCONJ
ejpam-5764	156	26	tri	tri	ADJ
ejpam-5764	156	27	-	-	ADJ
ejpam-5764	156	28	normal	normal	ADJ
ejpam-5764	156	29	space	space	NOUN
ejpam-5764	156	30	.	.	PUNCT
ejpam-5764	157	1	this	this	PRON
ejpam-5764	157	2	suggests	suggest	VERB
ejpam-5764	157	3	that	that	SCONJ
ejpam-5764	157	4	for	for	ADP
ejpam-5764	157	5	any	any	PRON
ejpam-5764	157	6	of	of	ADP
ejpam-5764	157	7	the	the	DET
ejpam-5764	157	8	two	two	NUM
ejpam-5764	157	9	disjoint	disjoint	NOUN
ejpam-5764	157	10	ϑi	ϑi	NOUN
ejpam-5764	157	11	-	-	PUNCT
ejpam-5764	157	12	closed	close	VERB
ejpam-5764	157	13	sets	set	NOUN
ejpam-5764	157	14	a	a	PRON
ejpam-5764	157	15	and	and	CCONJ
ejpam-5764	157	16	b	b	NOUN
ejpam-5764	157	17	,	,	PUNCT
ejpam-5764	157	18	there	there	PRON
ejpam-5764	157	19	are	be	VERB
ejpam-5764	157	20	ϑiopen	ϑiopen	ADJ
ejpam-5764	157	21	sets	set	NOUN
ejpam-5764	157	22	ua	ua	PROPN
ejpam-5764	157	23	and	and	CCONJ
ejpam-5764	157	24	vb	vb	NOUN
ejpam-5764	157	25	such	such	ADJ
ejpam-5764	157	26	that	that	SCONJ
ejpam-5764	157	27	a	a	DET
ejpam-5764	157	28	⊂	⊂	PROPN
ejpam-5764	157	29	ua	ua	PROPN
ejpam-5764	157	30	and	and	CCONJ
ejpam-5764	157	31	b	b	PROPN
ejpam-5764	157	32	⊂	⊂	PROPN
ejpam-5764	157	33	vb	vb	PROPN
ejpam-5764	157	34	with	with	ADP
ejpam-5764	157	35	ua	ua	PROPN
ejpam-5764	157	36	∩	∩	PROPN
ejpam-5764	157	37	vb	vb	PROPN
ejpam-5764	157	38	=	=	PUNCT
ejpam-5764	157	39	ϕ.	ϕ.	PROPN
ejpam-5764	157	40	(	(	PUNCT
ejpam-5764	157	41	1	1	X
ejpam-5764	157	42	)	)	PUNCT
ejpam-5764	157	43	let	let	VERB
ejpam-5764	157	44	b	b	X
ejpam-5764	157	45	∈	∈	PROPN
ejpam-5764	157	46	b	b	NOUN
ejpam-5764	157	47	now	now	ADV
ejpam-5764	157	48	,	,	PUNCT
ejpam-5764	157	49	followed	follow	VERB
ejpam-5764	157	50	by	by	ADP
ejpam-5764	157	51	b	b	PROPN
ejpam-5764	157	52	∈	∈	PROPN
ejpam-5764	157	53	vb	vb	PROPN
ejpam-5764	157	54	.	.	PUNCT
ejpam-5764	158	1	on	on	ADP
ejpam-5764	158	2	the	the	DET
ejpam-5764	158	3	other	other	ADJ
ejpam-5764	158	4	hand	hand	NOUN
ejpam-5764	158	5	,	,	PUNCT
ejpam-5764	158	6	a	a	DET
ejpam-5764	158	7	∩b	∩b	NOUN
ejpam-5764	158	8	=	=	SYM
ejpam-5764	158	9	ϕ.	ϕ.	PROPN
ejpam-5764	158	10	thus	thus	ADV
ejpam-5764	158	11	,	,	PUNCT
ejpam-5764	158	12	b	b	PROPN
ejpam-5764	158	13	/∈	/∈	PUNCT
ejpam-5764	158	14	aisobtained	aisobtaine	VERB
ejpam-5764	158	15	.	.	PUNCT
ejpam-5764	159	1	(	(	PUNCT
ejpam-5764	159	2	2	2	NUM
ejpam-5764	159	3	)	)	PUNCT
ejpam-5764	159	4	thus	thus	ADV
ejpam-5764	159	5	,	,	PUNCT
ejpam-5764	159	6	(	(	PUNCT
ejpam-5764	159	7	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	159	8	,	,	PUNCT
ejpam-5764	159	9	ϑ2	ϑ2	PROPN
ejpam-5764	159	10	,	,	PUNCT
ejpam-5764	159	11	ϑ3	ϑ3	PROPN
ejpam-5764	159	12	)	)	PUNCT
ejpam-5764	159	13	is	be	AUX
ejpam-5764	159	14	a	a	DET
ejpam-5764	159	15	tri	tri	ADJ
ejpam-5764	159	16	-	-	ADJ
ejpam-5764	159	17	regular	regular	ADJ
ejpam-5764	159	18	space	space	NOUN
ejpam-5764	159	19	according	accord	VERB
ejpam-5764	159	20	to	to	ADP
ejpam-5764	159	21	(	(	PUNCT
ejpam-5764	159	22	1	1	NUM
ejpam-5764	159	23	)	)	PUNCT
ejpam-5764	159	24	and	and	CCONJ
ejpam-5764	159	25	(	(	PUNCT
ejpam-5764	159	26	2	2	NUM
ejpam-5764	159	27	)	)	PUNCT
ejpam-5764	159	28	.	.	PUNCT
ejpam-5764	160	1	thus	thus	ADV
ejpam-5764	160	2	,	,	PUNCT
ejpam-5764	160	3	(	(	PUNCT
ejpam-5764	160	4	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	160	5	,	,	PUNCT
ejpam-5764	160	6	ϑ2	ϑ2	PROPN
ejpam-5764	160	7	,	,	PUNCT
ejpam-5764	160	8	ϑ3	ϑ3	PROPN
ejpam-5764	160	9	)	)	PUNCT
ejpam-5764	160	10	is	be	AUX
ejpam-5764	160	11	obtained	obtain	VERB
ejpam-5764	160	12	.	.	PUNCT
ejpam-5764	161	1	(	(	PUNCT
ejpam-5764	161	2	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	161	3	,	,	PUNCT
ejpam-5764	161	4	ϑ2	ϑ2	PROPN
ejpam-5764	161	5	,	,	PUNCT
ejpam-5764	161	6	ϑ3	ϑ3	PROPN
ejpam-5764	161	7	)	)	PUNCT
ejpam-5764	161	8	is	be	AUX
ejpam-5764	161	9	tri	tri	ADJ
ejpam-5764	161	10	-	-	ADJ
ejpam-5764	161	11	t3	t3	ADJ
ejpam-5764	161	12	-	-	PUNCT
ejpam-5764	161	13	space	space	NOUN
ejpam-5764	161	14	since	since	SCONJ
ejpam-5764	161	15	is	be	AUX
ejpam-5764	161	16	tri	tri	ADJ
ejpam-5764	161	17	-	-	ADJ
ejpam-5764	161	18	t1	t1	ADJ
ejpam-5764	161	19	-	-	PUNCT
ejpam-5764	161	20	space	space	NOUN
ejpam-5764	161	21	and	and	CCONJ
ejpam-5764	161	22	tri	tri	ADJ
ejpam-5764	161	23	-	-	ADJ
ejpam-5764	161	24	regular	regular	ADJ
ejpam-5764	161	25	space	space	NOUN
ejpam-5764	161	26	.	.	PUNCT
ejpam-5764	162	1	theorem	theorem	VERB
ejpam-5764	162	2	11	11	NUM
ejpam-5764	162	3	.	.	PUNCT
ejpam-5764	163	1	[	[	X
ejpam-5764	163	2	8	8	NUM
ejpam-5764	163	3	]	]	X
ejpam-5764	163	4	a	a	DET
ejpam-5764	163	5	space	space	NOUN
ejpam-5764	163	6	is	be	AUX
ejpam-5764	163	7	tri	tri	ADJ
ejpam-5764	163	8	-	-	ADJ
ejpam-5764	163	9	normal	normal	ADJ
ejpam-5764	163	10	if	if	SCONJ
ejpam-5764	163	11	(	(	PUNCT
ejpam-5764	163	12	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	163	13	,	,	PUNCT
ejpam-5764	163	14	ϑ2	ϑ2	PROPN
ejpam-5764	163	15	,	,	PUNCT
ejpam-5764	163	16	ϑ3	ϑ3	PROPN
ejpam-5764	163	17	)	)	PUNCT
ejpam-5764	163	18	is	be	AUX
ejpam-5764	163	19	tri	tri	ADJ
ejpam-5764	163	20	-	-	ADJ
ejpam-5764	163	21	completely	completely	ADV
ejpam-5764	163	22	normal	normal	ADJ
ejpam-5764	163	23	.	.	PUNCT
ejpam-5764	164	1	proof	proof	NOUN
ejpam-5764	164	2	.	.	PUNCT
ejpam-5764	165	1	consider	consider	VERB
ejpam-5764	165	2	the	the	DET
ejpam-5764	165	3	space	space	NOUN
ejpam-5764	165	4	(	(	PUNCT
ejpam-5764	165	5	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	165	6	,	,	PUNCT
ejpam-5764	165	7	ϑ2	ϑ2	PROPN
ejpam-5764	165	8	,	,	PUNCT
ejpam-5764	165	9	ϑ3	ϑ3	PROPN
ejpam-5764	165	10	)	)	PUNCT
ejpam-5764	165	11	to	to	PART
ejpam-5764	165	12	be	be	AUX
ejpam-5764	165	13	tri	tri	ADJ
ejpam-5764	165	14	-	-	ADJ
ejpam-5764	165	15	completely	completely	ADV
ejpam-5764	165	16	normal	normal	ADJ
ejpam-5764	165	17	.	.	PUNCT
ejpam-5764	166	1	by	by	ADP
ejpam-5764	166	2	definition	definition	NOUN
ejpam-5764	166	3	,	,	PUNCT
ejpam-5764	166	4	there	there	PRON
ejpam-5764	166	5	is	be	VERB
ejpam-5764	166	6	a	a	DET
ejpam-5764	166	7	ϑi	ϑi	NOUN
ejpam-5764	166	8	-	-	PUNCT
ejpam-5764	166	9	continuous	continuous	ADJ
ejpam-5764	166	10	function	function	NOUN
ejpam-5764	166	11	fi	fi	NOUN
ejpam-5764	166	12	:	:	PUNCT
ejpam-5764	167	1	x	x	X
ejpam-5764	168	1	→	→	SYM
ejpam-5764	169	1	[	[	X
ejpam-5764	169	2	0	0	NUM
ejpam-5764	169	3	,	,	PUNCT
ejpam-5764	169	4	1	1	NUM
ejpam-5764	169	5	]	]	PUNCT
ejpam-5764	169	6	for	for	ADP
ejpam-5764	169	7	any	any	DET
ejpam-5764	169	8	two	two	NUM
ejpam-5764	169	9	disjoint	disjoint	NOUN
ejpam-5764	169	10	ϑi	ϑi	NOUN
ejpam-5764	169	11	-	-	PUNCT
ejpam-5764	169	12	closed	close	VERB
ejpam-5764	169	13	sets	set	NOUN
ejpam-5764	169	14	a	a	PRON
ejpam-5764	169	15	and	and	CCONJ
ejpam-5764	169	16	b.	b.	NOUN
ejpam-5764	169	17	such	such	ADJ
ejpam-5764	169	18	that	that	DET
ejpam-5764	169	19	fi(b	fi(b	NUM
ejpam-5764	169	20	)	)	PUNCT
ejpam-5764	169	21	=	=	PUNCT
ejpam-5764	169	22	{	{	PUNCT
ejpam-5764	169	23	1	1	NUM
ejpam-5764	169	24	}	}	PUNCT
ejpam-5764	169	25	,	,	PUNCT
ejpam-5764	169	26	fi(a	fi(a	X
ejpam-5764	169	27	)	)	PUNCT
ejpam-5764	169	28	=	=	PRON
ejpam-5764	169	29	{	{	PUNCT
ejpam-5764	169	30	0	0	NUM
ejpam-5764	169	31	}	}	PUNCT
ejpam-5764	169	32	(	(	PUNCT
ejpam-5764	169	33	3	3	X
ejpam-5764	169	34	)	)	PUNCT
ejpam-5764	169	35	we	we	PRON
ejpam-5764	169	36	now	now	ADV
ejpam-5764	169	37	define	define	VERB
ejpam-5764	169	38	the	the	DET
ejpam-5764	169	39	inverse	inverse	NOUN
ejpam-5764	169	40	images	image	NOUN
ejpam-5764	169	41	of	of	ADP
ejpam-5764	169	42	the	the	DET
ejpam-5764	169	43	open	open	ADJ
ejpam-5764	169	44	intervals	interval	NOUN
ejpam-5764	169	45	(	(	PUNCT
ejpam-5764	169	46	0	0	NUM
ejpam-5764	169	47	,	,	PUNCT
ejpam-5764	169	48	12	12	NUM
ejpam-5764	169	49	)	)	PUNCT
ejpam-5764	169	50	and	and	CCONJ
ejpam-5764	169	51	(	(	PUNCT
ejpam-5764	169	52	12	12	NUM
ejpam-5764	169	53	,	,	PUNCT
ejpam-5764	169	54	1	1	NUM
ejpam-5764	169	55	)	)	PUNCT
ejpam-5764	169	56	under	under	ADP
ejpam-5764	169	57	fi	fi	NOUN
ejpam-5764	169	58	,	,	PUNCT
ejpam-5764	169	59	yielding	yield	VERB
ejpam-5764	169	60	two	two	NUM
ejpam-5764	169	61	ϑi	ϑi	NOUN
ejpam-5764	169	62	-	-	PUNCT
ejpam-5764	169	63	open	open	NOUN
ejpam-5764	169	64	sets	set	NOUN
ejpam-5764	169	65	ua	ua	PROPN
ejpam-5764	169	66	and	and	CCONJ
ejpam-5764	169	67	vb	vb	NOUN
ejpam-5764	169	68	such	such	ADJ
ejpam-5764	169	69	that	that	SCONJ
ejpam-5764	169	70	a	a	DET
ejpam-5764	169	71	⊂	⊂	PROPN
ejpam-5764	169	72	ua	ua	PROPN
ejpam-5764	169	73	,	,	PUNCT
ejpam-5764	169	74	b	b	PROPN
ejpam-5764	169	75	⊂	⊂	PROPN
ejpam-5764	169	76	vb	vb	PROPN
ejpam-5764	169	77	,	,	PUNCT
ejpam-5764	169	78	ua	ua	PROPN
ejpam-5764	169	79	∩	∩	PROPN
ejpam-5764	169	80	vb	vb	NOUN
ejpam-5764	169	81	=	=	PUNCT
ejpam-5764	169	82	∅.	∅.	X
ejpam-5764	169	83	(	(	PUNCT
ejpam-5764	169	84	4	4	NUM
ejpam-5764	169	85	)	)	PUNCT
ejpam-5764	169	86	the	the	DET
ejpam-5764	169	87	tri	tri	NOUN
ejpam-5764	169	88	-	-	NOUN
ejpam-5764	169	89	normality	normality	NOUN
ejpam-5764	169	90	of	of	ADP
ejpam-5764	169	91	(	(	PUNCT
ejpam-5764	169	92	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	169	93	,	,	PUNCT
ejpam-5764	169	94	ϑ2	ϑ2	PROPN
ejpam-5764	169	95	,	,	PUNCT
ejpam-5764	169	96	ϑ3	ϑ3	PROPN
ejpam-5764	169	97	)	)	PUNCT
ejpam-5764	169	98	may	may	AUX
ejpam-5764	169	99	be	be	AUX
ejpam-5764	169	100	inferred	infer	VERB
ejpam-5764	169	101	from	from	ADP
ejpam-5764	169	102	(	(	PUNCT
ejpam-5764	169	103	3	3	NUM
ejpam-5764	169	104	)	)	PUNCT
ejpam-5764	169	105	and	and	CCONJ
ejpam-5764	169	106	(	(	PUNCT
ejpam-5764	169	107	4	4	NUM
ejpam-5764	169	108	)	)	PUNCT
ejpam-5764	169	109	.	.	PUNCT
ejpam-5764	170	1	definition	definition	NOUN
ejpam-5764	170	2	18	18	NUM
ejpam-5764	170	3	.	.	PUNCT
ejpam-5764	171	1	given	give	VERB
ejpam-5764	171	2	a	a	DET
ejpam-5764	171	3	tri	tri	ADJ
ejpam-5764	171	4	-	-	ADJ
ejpam-5764	171	5	topological	topological	ADJ
ejpam-5764	171	6	space	space	NOUN
ejpam-5764	171	7	(	(	PUNCT
ejpam-5764	171	8	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	171	9	,	,	PUNCT
ejpam-5764	171	10	ϑ2	ϑ2	PROPN
ejpam-5764	171	11	,	,	PUNCT
ejpam-5764	171	12	ϑ3	ϑ3	PROPN
ejpam-5764	171	13	)	)	PUNCT
ejpam-5764	171	14	,	,	PUNCT
ejpam-5764	171	15	a	a	PRON
ejpam-5764	171	16	set	set	NOUN
ejpam-5764	171	17	d	d	NOUN
ejpam-5764	171	18	in	in	ADP
ejpam-5764	171	19	(	(	PUNCT
ejpam-5764	171	20	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	171	21	,	,	PUNCT
ejpam-5764	171	22	ϑ2	ϑ2	PROPN
ejpam-5764	171	23	,	,	PUNCT
ejpam-5764	171	24	ϑ3	ϑ3	PROPN
ejpam-5764	171	25	)	)	PUNCT
ejpam-5764	171	26	is	be	AUX
ejpam-5764	171	27	referred	refer	VERB
ejpam-5764	171	28	to	to	ADP
ejpam-5764	171	29	as	as	ADP
ejpam-5764	171	30	a	a	DET
ejpam-5764	171	31	tri	tri	ADJ
ejpam-5764	171	32	-	-	ADJ
ejpam-5764	171	33	dense	dense	ADJ
ejpam-5764	171	34	set	set	NOUN
ejpam-5764	171	35	if	if	SCONJ
ejpam-5764	171	36	d	d	PROPN
ejpam-5764	171	37	=	=	SYM
ejpam-5764	171	38	x.	x.	NOUN
ejpam-5764	171	39	conversely	conversely	ADV
ejpam-5764	171	40	,	,	PUNCT
ejpam-5764	171	41	for	for	ADP
ejpam-5764	171	42	every	every	DET
ejpam-5764	171	43	ϑi	ϑi	NOUN
ejpam-5764	171	44	-	-	PUNCT
ejpam-5764	171	45	open	open	NOUN
ejpam-5764	171	46	set	set	NOUN
ejpam-5764	171	47	u	u	NOUN
ejpam-5764	171	48	,	,	PUNCT
ejpam-5764	171	49	we	we	PRON
ejpam-5764	171	50	obtain	obtain	VERB
ejpam-5764	171	51	u	u	NOUN
ejpam-5764	171	52	∩d	∩d	NOUN
ejpam-5764	171	53	̸=	̸=	PROPN
ejpam-5764	171	54	ϕ	ϕ	NOUN
ejpam-5764	171	55	if	if	SCONJ
ejpam-5764	171	56	d	d	NOUN
ejpam-5764	171	57	is	be	AUX
ejpam-5764	171	58	dense	dense	ADJ
ejpam-5764	171	59	in	in	ADP
ejpam-5764	171	60	(	(	PUNCT
ejpam-5764	171	61	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	171	62	,	,	PUNCT
ejpam-5764	171	63	ϑ2	ϑ2	PROPN
ejpam-5764	171	64	,	,	PUNCT
ejpam-5764	171	65	ϑ3	ϑ3	PROPN
ejpam-5764	171	66	)	)	PUNCT
ejpam-5764	171	67	.	.	PUNCT
ejpam-5764	172	1	definition	definition	NOUN
ejpam-5764	172	2	19	19	NUM
ejpam-5764	172	3	.	.	PUNCT
ejpam-5764	173	1	let	let	VERB
ejpam-5764	173	2	(	(	PUNCT
ejpam-5764	173	3	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	173	4	,	,	PUNCT
ejpam-5764	173	5	ϑ2	ϑ2	PROPN
ejpam-5764	173	6	,	,	PUNCT
ejpam-5764	173	7	ϑ3	ϑ3	PROPN
ejpam-5764	173	8	)	)	PUNCT
ejpam-5764	173	9	and	and	CCONJ
ejpam-5764	173	10	(	(	PUNCT
ejpam-5764	173	11	y	y	PROPN
ejpam-5764	173	12	,	,	PUNCT
ejpam-5764	173	13	σ1	σ1	PROPN
ejpam-5764	173	14	,	,	PUNCT
ejpam-5764	173	15	σ2	σ2	PROPN
ejpam-5764	173	16	,	,	PUNCT
ejpam-5764	173	17	σ3	σ3	PROPN
ejpam-5764	173	18	)	)	PUNCT
ejpam-5764	173	19	be	be	VERB
ejpam-5764	173	20	tri	tri	ADJ
ejpam-5764	173	21	-	-	ADJ
ejpam-5764	173	22	topological	topological	ADJ
ejpam-5764	173	23	spaces	space	NOUN
ejpam-5764	173	24	.	.	PUNCT
ejpam-5764	174	1	if	if	SCONJ
ejpam-5764	174	2	f(u	f(u	PROPN
ejpam-5764	174	3	)	)	PUNCT
ejpam-5764	174	4	=	=	SYM
ejpam-5764	174	5	v	v	NOUN
ejpam-5764	174	6	,	,	PUNCT
ejpam-5764	174	7	where	where	SCONJ
ejpam-5764	174	8	u	u	NOUN
ejpam-5764	174	9	is	be	AUX
ejpam-5764	174	10	ϑi	ϑi	NOUN
ejpam-5764	174	11	-	-	PUNCT
ejpam-5764	174	12	open	open	NOUN
ejpam-5764	174	13	set	set	NOUN
ejpam-5764	174	14	and	and	CCONJ
ejpam-5764	174	15	v	v	NOUN
ejpam-5764	174	16	is	be	AUX
ejpam-5764	174	17	σi	σi	NOUN
ejpam-5764	174	18	-	-	PUNCT
ejpam-5764	174	19	open	open	ADJ
ejpam-5764	174	20	set	set	NOUN
ejpam-5764	174	21	,	,	PUNCT
ejpam-5764	174	22	then	then	ADV
ejpam-5764	174	23	f	f	X
ejpam-5764	174	24	:	:	PUNCT
ejpam-5764	174	25	(	(	PUNCT
ejpam-5764	174	26	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	174	27	,	,	PUNCT
ejpam-5764	174	28	ϑ2	ϑ2	PROPN
ejpam-5764	174	29	,	,	PUNCT
ejpam-5764	174	30	ϑ3	ϑ3	PROPN
ejpam-5764	174	31	)	)	PUNCT
ejpam-5764	174	32	is	be	AUX
ejpam-5764	174	33	a	a	DET
ejpam-5764	174	34	tri	tri	ADJ
ejpam-5764	174	35	-	-	ADJ
ejpam-5764	174	36	open	open	ADJ
ejpam-5764	174	37	function	function	NOUN
ejpam-5764	174	38	.	.	PUNCT
ejpam-5764	175	1	j.	j.	PROPN
ejpam-5764	175	2	oudetallah	oudetallah	PROPN
ejpam-5764	175	3	et	et	PROPN
ejpam-5764	175	4	al	al	PROPN
ejpam-5764	175	5	.	.	PUNCT
ejpam-5764	175	6	/	/	SYM
ejpam-5764	175	7	eur	eur	PROPN
ejpam-5764	175	8	.	.	PUNCT
ejpam-5764	176	1	j.	j.	PROPN
ejpam-5764	176	2	pure	pure	PROPN
ejpam-5764	176	3	appl	appl	PROPN
ejpam-5764	176	4	.	.	PROPN
ejpam-5764	176	5	math	math	PROPN
ejpam-5764	176	6	,	,	PUNCT
ejpam-5764	176	7	18	18	NUM
ejpam-5764	176	8	(	(	PUNCT
ejpam-5764	176	9	2	2	NUM
ejpam-5764	176	10	)	)	PUNCT
ejpam-5764	176	11	(	(	PUNCT
ejpam-5764	176	12	2025	2025	NUM
ejpam-5764	176	13	)	)	PUNCT
ejpam-5764	176	14	,	,	PUNCT
ejpam-5764	176	15	5764	5764	NUM
ejpam-5764	176	16	8	8	NUM
ejpam-5764	176	17	of	of	ADP
ejpam-5764	176	18	11	11	NUM
ejpam-5764	176	19	3	3	NUM
ejpam-5764	176	20	.	.	PUNCT
ejpam-5764	177	1	tri	tri	ADJ
ejpam-5764	177	2	-	-	ADJ
ejpam-5764	177	3	locally	locally	ADV
ejpam-5764	177	4	compact	compact	ADJ
ejpam-5764	177	5	spaces	space	NOUN
ejpam-5764	177	6	we	we	PRON
ejpam-5764	177	7	then	then	ADV
ejpam-5764	177	8	introduce	introduce	VERB
ejpam-5764	177	9	the	the	DET
ejpam-5764	177	10	idea	idea	NOUN
ejpam-5764	177	11	of	of	ADP
ejpam-5764	177	12	tri	tri	ADJ
ejpam-5764	177	13	-	-	ADJ
ejpam-5764	177	14	locally	locally	ADV
ejpam-5764	177	15	compact	compact	ADJ
ejpam-5764	177	16	spaces	space	NOUN
ejpam-5764	177	17	and	and	CCONJ
ejpam-5764	177	18	establish	establish	VERB
ejpam-5764	177	19	some	some	PRON
ejpam-5764	177	20	of	of	ADP
ejpam-5764	177	21	their	their	PRON
ejpam-5764	177	22	most	most	ADV
ejpam-5764	177	23	important	important	ADJ
ejpam-5764	177	24	properties	property	NOUN
ejpam-5764	177	25	in	in	ADP
ejpam-5764	177	26	this	this	DET
ejpam-5764	177	27	section	section	NOUN
ejpam-5764	177	28	.	.	PUNCT
ejpam-5764	178	1	definition	definition	NOUN
ejpam-5764	178	2	20	20	NUM
ejpam-5764	178	3	.	.	PUNCT
ejpam-5764	179	1	a	a	DET
ejpam-5764	179	2	subset	subset	NOUN
ejpam-5764	179	3	a	a	PRON
ejpam-5764	179	4	of	of	ADP
ejpam-5764	179	5	a	a	DET
ejpam-5764	179	6	tri	tri	ADJ
ejpam-5764	179	7	-	-	ADJ
ejpam-5764	179	8	topological	topological	ADJ
ejpam-5764	179	9	space	space	NOUN
ejpam-5764	179	10	(	(	PUNCT
ejpam-5764	179	11	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	179	12	,	,	PUNCT
ejpam-5764	179	13	ϑ2	ϑ2	PROPN
ejpam-5764	179	14	,	,	PUNCT
ejpam-5764	179	15	ϑ3	ϑ3	PROPN
ejpam-5764	179	16	)	)	PUNCT
ejpam-5764	179	17	is	be	AUX
ejpam-5764	179	18	tri	tri	ADJ
ejpam-5764	179	19	-	-	ADJ
ejpam-5764	179	20	compact	compact	ADJ
ejpam-5764	179	21	if	if	SCONJ
ejpam-5764	179	22	every	every	DET
ejpam-5764	179	23	cover	cover	NOUN
ejpam-5764	179	24	of	of	ADP
ejpam-5764	179	25	a	a	PRON
ejpam-5764	179	26	by	by	ADP
ejpam-5764	179	27	ϑi	ϑi	NOUN
ejpam-5764	179	28	-	-	PUNCT
ejpam-5764	179	29	open	open	ADJ
ejpam-5764	179	30	sets	set	NOUN
ejpam-5764	179	31	(	(	PUNCT
ejpam-5764	179	32	for	for	ADP
ejpam-5764	179	33	i	i	PRON
ejpam-5764	179	34	=	=	SYM
ejpam-5764	179	35	1	1	NUM
ejpam-5764	179	36	,	,	PUNCT
ejpam-5764	179	37	2	2	NUM
ejpam-5764	179	38	,	,	PUNCT
ejpam-5764	179	39	3	3	NUM
ejpam-5764	179	40	)	)	PUNCT
ejpam-5764	179	41	has	have	VERB
ejpam-5764	179	42	a	a	DET
ejpam-5764	179	43	finite	finite	ADJ
ejpam-5764	179	44	subcover	subcover	PROPN
ejpam-5764	179	45	.	.	PUNCT
ejpam-5764	180	1	definition	definition	NOUN
ejpam-5764	180	2	21	21	NUM
ejpam-5764	180	3	.	.	PUNCT
ejpam-5764	181	1	a	a	DET
ejpam-5764	181	2	tri	tri	ADJ
ejpam-5764	181	3	-	-	ADJ
ejpam-5764	181	4	topological	topological	ADJ
ejpam-5764	181	5	space	space	NOUN
ejpam-5764	181	6	(	(	PUNCT
ejpam-5764	181	7	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	181	8	,	,	PUNCT
ejpam-5764	181	9	ϑ2	ϑ2	PROPN
ejpam-5764	181	10	,	,	PUNCT
ejpam-5764	181	11	ϑ3	ϑ3	PROPN
ejpam-5764	181	12	)	)	PUNCT
ejpam-5764	181	13	is	be	AUX
ejpam-5764	181	14	tri	tri	ADJ
ejpam-5764	181	15	-	-	ADJ
ejpam-5764	181	16	locally	locally	ADV
ejpam-5764	181	17	compact	compact	ADJ
ejpam-5764	181	18	if	if	SCONJ
ejpam-5764	181	19	for	for	ADP
ejpam-5764	181	20	every	every	DET
ejpam-5764	181	21	point	point	NOUN
ejpam-5764	181	22	a	a	DET
ejpam-5764	181	23	∈	∈	NOUN
ejpam-5764	181	24	x	x	NOUN
ejpam-5764	181	25	,	,	PUNCT
ejpam-5764	181	26	there	there	PRON
ejpam-5764	181	27	exists	exist	VERB
ejpam-5764	181	28	a	a	DET
ejpam-5764	181	29	ϑi	ϑi	NOUN
ejpam-5764	181	30	-	-	PUNCT
ejpam-5764	181	31	open	open	NOUN
ejpam-5764	181	32	set	set	VERB
ejpam-5764	181	33	ua	ua	NOUN
ejpam-5764	181	34	containing	contain	VERB
ejpam-5764	181	35	a	a	DET
ejpam-5764	181	36	such	such	ADJ
ejpam-5764	181	37	that	that	SCONJ
ejpam-5764	181	38	ua	ua	PROPN
ejpam-5764	181	39	is	be	AUX
ejpam-5764	181	40	tri	tri	ADJ
ejpam-5764	181	41	-	-	ADJ
ejpam-5764	181	42	compact	compact	ADJ
ejpam-5764	181	43	.	.	PUNCT
ejpam-5764	182	1	theorem	theorem	NOUN
ejpam-5764	182	2	12	12	NUM
ejpam-5764	182	3	.	.	PUNCT
ejpam-5764	183	1	a	a	DET
ejpam-5764	183	2	tri	tri	ADJ
ejpam-5764	183	3	-	-	ADJ
ejpam-5764	183	4	topological	topological	ADJ
ejpam-5764	183	5	space	space	NOUN
ejpam-5764	183	6	(	(	PUNCT
ejpam-5764	183	7	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	183	8	,	,	PUNCT
ejpam-5764	183	9	ϑ2	ϑ2	PROPN
ejpam-5764	183	10	,	,	PUNCT
ejpam-5764	183	11	ϑ3	ϑ3	PROPN
ejpam-5764	183	12	)	)	PUNCT
ejpam-5764	183	13	is	be	AUX
ejpam-5764	183	14	tri	tri	ADJ
ejpam-5764	183	15	-	-	ADJ
ejpam-5764	183	16	locally	locally	ADV
ejpam-5764	183	17	compact	compact	ADJ
ejpam-5764	183	18	if	if	SCONJ
ejpam-5764	184	1	and	and	CCONJ
ejpam-5764	184	2	only	only	ADV
ejpam-5764	184	3	if	if	SCONJ
ejpam-5764	184	4	for	for	ADP
ejpam-5764	184	5	every	every	DET
ejpam-5764	184	6	point	point	NOUN
ejpam-5764	184	7	a	a	DET
ejpam-5764	184	8	∈	∈	NOUN
ejpam-5764	184	9	x	x	X
ejpam-5764	184	10	and	and	CCONJ
ejpam-5764	184	11	every	every	DET
ejpam-5764	184	12	ϑi	ϑi	NOUN
ejpam-5764	184	13	-	-	PUNCT
ejpam-5764	184	14	open	open	NOUN
ejpam-5764	184	15	set	set	NOUN
ejpam-5764	184	16	u	u	NOUN
ejpam-5764	184	17	containing	contain	VERB
ejpam-5764	184	18	a	a	PRON
ejpam-5764	184	19	,	,	PUNCT
ejpam-5764	184	20	there	there	PRON
ejpam-5764	184	21	exists	exist	VERB
ejpam-5764	184	22	a	a	DET
ejpam-5764	184	23	ϑi	ϑi	NOUN
ejpam-5764	184	24	-	-	PUNCT
ejpam-5764	184	25	open	open	NOUN
ejpam-5764	184	26	set	set	VERB
ejpam-5764	184	27	v	v	ADP
ejpam-5764	184	28	such	such	DET
ejpam-5764	184	29	that	that	SCONJ
ejpam-5764	184	30	a	a	DET
ejpam-5764	184	31	∈	∈	PROPN
ejpam-5764	184	32	v	v	ADP
ejpam-5764	184	33	⊂	⊂	PROPN
ejpam-5764	184	34	v	v	ADP
ejpam-5764	184	35	⊂	⊂	PROPN
ejpam-5764	184	36	u	u	PROPN
ejpam-5764	184	37	and	and	CCONJ
ejpam-5764	184	38	v	v	NOUN
ejpam-5764	184	39	is	be	AUX
ejpam-5764	184	40	tri	tri	ADJ
ejpam-5764	184	41	-	-	ADJ
ejpam-5764	184	42	compact	compact	ADJ
ejpam-5764	184	43	.	.	PUNCT
ejpam-5764	185	1	proof	proof	NOUN
ejpam-5764	185	2	.	.	PUNCT
ejpam-5764	186	1	(	(	PUNCT
ejpam-5764	186	2	⇒	⇒	NOUN
ejpam-5764	186	3	)	)	PUNCT
ejpam-5764	186	4	assume	assume	VERB
ejpam-5764	186	5	(	(	PUNCT
ejpam-5764	186	6	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	186	7	,	,	PUNCT
ejpam-5764	186	8	ϑ2	ϑ2	PROPN
ejpam-5764	186	9	,	,	PUNCT
ejpam-5764	186	10	ϑ3	ϑ3	PROPN
ejpam-5764	186	11	)	)	PUNCT
ejpam-5764	186	12	is	be	AUX
ejpam-5764	186	13	tri	tri	ADJ
ejpam-5764	186	14	-	-	ADJ
ejpam-5764	186	15	locally	locally	ADV
ejpam-5764	186	16	compact	compact	ADJ
ejpam-5764	186	17	.	.	PUNCT
ejpam-5764	187	1	let	let	VERB
ejpam-5764	187	2	a	a	DET
ejpam-5764	187	3	∈	∈	PROPN
ejpam-5764	187	4	x	x	X
ejpam-5764	187	5	and	and	CCONJ
ejpam-5764	187	6	u	u	PRON
ejpam-5764	187	7	be	be	VERB
ejpam-5764	187	8	a	a	DET
ejpam-5764	187	9	ϑiopen	ϑiopen	ADJ
ejpam-5764	187	10	set	set	NOUN
ejpam-5764	187	11	containing	contain	VERB
ejpam-5764	187	12	a.	a.	NOUN
ejpam-5764	187	13	by	by	ADP
ejpam-5764	187	14	definition	definition	NOUN
ejpam-5764	187	15	,	,	PUNCT
ejpam-5764	187	16	there	there	PRON
ejpam-5764	187	17	exists	exist	VERB
ejpam-5764	187	18	a	a	DET
ejpam-5764	187	19	ϑj	ϑj	ADV
ejpam-5764	187	20	-	-	PUNCT
ejpam-5764	187	21	open	open	ADJ
ejpam-5764	187	22	set	set	VERB
ejpam-5764	187	23	wa	wa	NOUN
ejpam-5764	187	24	containing	contain	VERB
ejpam-5764	187	25	a	a	DET
ejpam-5764	187	26	such	such	ADJ
ejpam-5764	187	27	that	that	DET
ejpam-5764	187	28	wa	wa	PROPN
ejpam-5764	187	29	is	be	AUX
ejpam-5764	187	30	tri	tri	ADJ
ejpam-5764	187	31	-	-	ADJ
ejpam-5764	187	32	compact	compact	ADJ
ejpam-5764	187	33	.	.	PUNCT
ejpam-5764	188	1	let	let	VERB
ejpam-5764	188	2	v	v	NOUN
ejpam-5764	188	3	=	=	SYM
ejpam-5764	188	4	wa	wa	X
ejpam-5764	188	5	∩	∩	ADJ
ejpam-5764	188	6	u	u	PROPN
ejpam-5764	188	7	,	,	PUNCT
ejpam-5764	188	8	which	which	PRON
ejpam-5764	188	9	is	be	AUX
ejpam-5764	188	10	a	a	DET
ejpam-5764	188	11	ϑi	ϑi	NOUN
ejpam-5764	188	12	-	-	PUNCT
ejpam-5764	188	13	open	open	NOUN
ejpam-5764	188	14	set	set	NOUN
ejpam-5764	188	15	containing	contain	VERB
ejpam-5764	188	16	a.	a.	NOUN
ejpam-5764	188	17	then	then	ADV
ejpam-5764	188	18	v	v	X
ejpam-5764	188	19	⊂	⊂	PROPN
ejpam-5764	188	20	wa	wa	PROPN
ejpam-5764	188	21	∩	∩	PROPN
ejpam-5764	188	22	u	u	PROPN
ejpam-5764	188	23	⊂	⊂	PROPN
ejpam-5764	188	24	wa	wa	PROPN
ejpam-5764	188	25	∩	∩	PROPN
ejpam-5764	188	26	u	u	PROPN
ejpam-5764	188	27	.	.	PUNCT
ejpam-5764	189	1	since	since	SCONJ
ejpam-5764	189	2	v	v	NOUN
ejpam-5764	189	3	is	be	AUX
ejpam-5764	189	4	a	a	DET
ejpam-5764	189	5	closed	closed	ADJ
ejpam-5764	189	6	subset	subset	NOUN
ejpam-5764	189	7	of	of	ADP
ejpam-5764	189	8	the	the	DET
ejpam-5764	189	9	tri	tri	ADJ
ejpam-5764	189	10	-	-	ADJ
ejpam-5764	189	11	compact	compact	ADJ
ejpam-5764	189	12	set	set	NOUN
ejpam-5764	189	13	wa	wa	PROPN
ejpam-5764	189	14	,	,	PUNCT
ejpam-5764	189	15	v	v	NOUN
ejpam-5764	189	16	is	be	AUX
ejpam-5764	189	17	tri	tri	ADJ
ejpam-5764	189	18	-	-	ADJ
ejpam-5764	189	19	compact	compact	ADJ
ejpam-5764	189	20	.	.	PUNCT
ejpam-5764	190	1	therefore	therefore	ADV
ejpam-5764	190	2	,	,	PUNCT
ejpam-5764	190	3	a	a	DET
ejpam-5764	190	4	∈	∈	PROPN
ejpam-5764	190	5	v	v	ADP
ejpam-5764	190	6	⊂	⊂	PROPN
ejpam-5764	190	7	v	v	ADP
ejpam-5764	190	8	⊂	⊂	PROPN
ejpam-5764	190	9	u	u	PROPN
ejpam-5764	190	10	and	and	CCONJ
ejpam-5764	190	11	v	v	NOUN
ejpam-5764	190	12	is	be	AUX
ejpam-5764	190	13	tri	tri	ADJ
ejpam-5764	190	14	-	-	ADJ
ejpam-5764	190	15	compact	compact	ADJ
ejpam-5764	190	16	.	.	PUNCT
ejpam-5764	191	1	(	(	PUNCT
ejpam-5764	191	2	⇐	⇐	NOUN
ejpam-5764	191	3	)	)	PUNCT
ejpam-5764	191	4	this	this	DET
ejpam-5764	191	5	direction	direction	NOUN
ejpam-5764	191	6	follows	follow	VERB
ejpam-5764	191	7	directly	directly	ADV
ejpam-5764	191	8	from	from	ADP
ejpam-5764	191	9	the	the	DET
ejpam-5764	191	10	definition	definition	NOUN
ejpam-5764	191	11	of	of	ADP
ejpam-5764	191	12	tri	tri	ADJ
ejpam-5764	191	13	-	-	ADJ
ejpam-5764	191	14	locally	locally	ADV
ejpam-5764	191	15	compact	compact	ADJ
ejpam-5764	191	16	spaces	space	NOUN
ejpam-5764	191	17	.	.	PUNCT
ejpam-5764	192	1	theorem	theorem	NOUN
ejpam-5764	192	2	13	13	NUM
ejpam-5764	192	3	.	.	PUNCT
ejpam-5764	193	1	let	let	AUX
ejpam-5764	193	2	(	(	PUNCT
ejpam-5764	193	3	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	193	4	,	,	PUNCT
ejpam-5764	193	5	ϑ2	ϑ2	PROPN
ejpam-5764	193	6	,	,	PUNCT
ejpam-5764	193	7	ϑ3	ϑ3	PROPN
ejpam-5764	193	8	)	)	PUNCT
ejpam-5764	193	9	be	be	AUX
ejpam-5764	193	10	a	a	DET
ejpam-5764	193	11	tri	tri	ADJ
ejpam-5764	193	12	-	-	ADJ
ejpam-5764	193	13	t2	t2	ADJ
ejpam-5764	193	14	-	-	PUNCT
ejpam-5764	193	15	space	space	NOUN
ejpam-5764	193	16	.	.	PUNCT
ejpam-5764	194	1	if	if	SCONJ
ejpam-5764	194	2	x	x	PRON
ejpam-5764	194	3	is	be	AUX
ejpam-5764	194	4	tri	tri	ADJ
ejpam-5764	194	5	-	-	ADJ
ejpam-5764	194	6	locally	locally	ADV
ejpam-5764	194	7	compact	compact	ADJ
ejpam-5764	194	8	,	,	PUNCT
ejpam-5764	194	9	then	then	ADV
ejpam-5764	194	10	for	for	ADP
ejpam-5764	194	11	every	every	DET
ejpam-5764	194	12	tri	tri	ADJ
ejpam-5764	194	13	-	-	ADJ
ejpam-5764	194	14	compact	compact	ADJ
ejpam-5764	194	15	set	set	NOUN
ejpam-5764	194	16	k	k	PROPN
ejpam-5764	194	17	and	and	CCONJ
ejpam-5764	194	18	every	every	DET
ejpam-5764	194	19	ϑi	ϑi	NOUN
ejpam-5764	194	20	-	-	PUNCT
ejpam-5764	194	21	open	open	NOUN
ejpam-5764	194	22	set	set	NOUN
ejpam-5764	194	23	u	u	NOUN
ejpam-5764	194	24	containing	contain	VERB
ejpam-5764	194	25	k	k	X
ejpam-5764	194	26	,	,	PUNCT
ejpam-5764	194	27	there	there	PRON
ejpam-5764	194	28	exists	exist	VERB
ejpam-5764	194	29	a	a	DET
ejpam-5764	194	30	ϑi	ϑi	NOUN
ejpam-5764	194	31	-	-	PUNCT
ejpam-5764	194	32	open	open	NOUN
ejpam-5764	194	33	set	set	VERB
ejpam-5764	194	34	v	v	ADP
ejpam-5764	194	35	such	such	ADJ
ejpam-5764	194	36	that	that	SCONJ
ejpam-5764	194	37	k	k	PROPN
ejpam-5764	194	38	⊂	⊂	PROPN
ejpam-5764	194	39	v	v	ADP
ejpam-5764	194	40	⊂	⊂	PROPN
ejpam-5764	194	41	v	v	ADP
ejpam-5764	194	42	⊂	⊂	PROPN
ejpam-5764	194	43	u	u	PROPN
ejpam-5764	194	44	and	and	CCONJ
ejpam-5764	194	45	v	v	NOUN
ejpam-5764	194	46	is	be	AUX
ejpam-5764	194	47	tri	tri	ADJ
ejpam-5764	194	48	-	-	ADJ
ejpam-5764	194	49	compact	compact	ADJ
ejpam-5764	194	50	.	.	PUNCT
ejpam-5764	195	1	proof	proof	NOUN
ejpam-5764	195	2	.	.	PUNCT
ejpam-5764	196	1	let	let	VERB
ejpam-5764	196	2	k	k	PRON
ejpam-5764	196	3	be	be	AUX
ejpam-5764	196	4	a	a	DET
ejpam-5764	196	5	tri	tri	ADJ
ejpam-5764	196	6	-	-	ADJ
ejpam-5764	196	7	compact	compact	ADJ
ejpam-5764	196	8	set	set	NOUN
ejpam-5764	196	9	and	and	CCONJ
ejpam-5764	196	10	u	u	PRON
ejpam-5764	196	11	be	be	VERB
ejpam-5764	196	12	a	a	DET
ejpam-5764	196	13	ϑi	ϑi	NOUN
ejpam-5764	196	14	-	-	PUNCT
ejpam-5764	196	15	open	open	NOUN
ejpam-5764	196	16	set	set	NOUN
ejpam-5764	196	17	containing	contain	VERB
ejpam-5764	196	18	k.	k.	NOUN
ejpam-5764	196	19	for	for	ADP
ejpam-5764	196	20	each	each	PRON
ejpam-5764	196	21	a	a	DET
ejpam-5764	196	22	∈	∈	PROPN
ejpam-5764	196	23	k	k	NOUN
ejpam-5764	196	24	,	,	PUNCT
ejpam-5764	196	25	there	there	PRON
ejpam-5764	196	26	exists	exist	VERB
ejpam-5764	196	27	a	a	DET
ejpam-5764	196	28	ϑi	ϑi	NOUN
ejpam-5764	196	29	-	-	PUNCT
ejpam-5764	196	30	open	open	NOUN
ejpam-5764	196	31	set	set	VERB
ejpam-5764	196	32	va	va	NOUN
ejpam-5764	196	33	such	such	ADJ
ejpam-5764	196	34	that	that	SCONJ
ejpam-5764	196	35	a	a	DET
ejpam-5764	196	36	∈	∈	PROPN
ejpam-5764	196	37	va	va	PROPN
ejpam-5764	196	38	⊂	⊂	PROPN
ejpam-5764	196	39	va	va	PROPN
ejpam-5764	197	1	⊂	⊂	PROPN
ejpam-5764	197	2	u	u	PROPN
ejpam-5764	197	3	and	and	CCONJ
ejpam-5764	197	4	va	va	PROPN
ejpam-5764	197	5	is	be	AUX
ejpam-5764	197	6	tri	tri	ADJ
ejpam-5764	197	7	-	-	ADJ
ejpam-5764	197	8	compact	compact	ADJ
ejpam-5764	197	9	.	.	PUNCT
ejpam-5764	198	1	the	the	DET
ejpam-5764	198	2	collection	collection	NOUN
ejpam-5764	198	3	{	{	PUNCT
ejpam-5764	198	4	va	va	NOUN
ejpam-5764	198	5	:	:	PUNCT
ejpam-5764	198	6	a	a	DET
ejpam-5764	198	7	∈	∈	PROPN
ejpam-5764	198	8	k	k	NOUN
ejpam-5764	198	9	}	}	PUNCT
ejpam-5764	198	10	forms	form	VERB
ejpam-5764	198	11	an	an	DET
ejpam-5764	198	12	open	open	ADJ
ejpam-5764	198	13	cover	cover	NOUN
ejpam-5764	198	14	of	of	ADP
ejpam-5764	198	15	k.	k.	PROPN
ejpam-5764	198	16	since	since	SCONJ
ejpam-5764	198	17	k	k	PROPN
ejpam-5764	198	18	is	be	AUX
ejpam-5764	198	19	tri	tri	ADJ
ejpam-5764	198	20	-	-	ADJ
ejpam-5764	198	21	compact	compact	ADJ
ejpam-5764	198	22	,	,	PUNCT
ejpam-5764	198	23	there	there	PRON
ejpam-5764	198	24	exists	exist	VERB
ejpam-5764	198	25	a	a	DET
ejpam-5764	198	26	finite	finite	NOUN
ejpam-5764	198	27	subset	subset	NOUN
ejpam-5764	198	28	{	{	PUNCT
ejpam-5764	198	29	a1	a1	PROPN
ejpam-5764	198	30	,	,	PUNCT
ejpam-5764	198	31	a2	a2	PROPN
ejpam-5764	198	32	,	,	PUNCT
ejpam-5764	198	33	.	.	PUNCT
ejpam-5764	198	34	.	.	PUNCT
ejpam-5764	199	1	.	.	PUNCT
ejpam-5764	200	1	,	,	PUNCT
ejpam-5764	200	2	an	an	PRON
ejpam-5764	200	3	}	}	PUNCT
ejpam-5764	200	4	⊂	⊂	PROPN
ejpam-5764	201	1	k	k	NOUN
ejpam-5764	202	1	such	such	ADJ
ejpam-5764	202	2	that	that	SCONJ
ejpam-5764	202	3	k	k	PROPN
ejpam-5764	202	4	⊂	⊂	PROPN
ejpam-5764	202	5	⋃n	⋃n	PROPN
ejpam-5764	202	6	j=1	j=1	PROPN
ejpam-5764	202	7	vaj	vaj	PROPN
ejpam-5764	202	8	.	.	PUNCT
ejpam-5764	203	1	let	let	VERB
ejpam-5764	203	2	v	v	NOUN
ejpam-5764	203	3	=	=	SYM
ejpam-5764	203	4	⋃n	⋃n	NOUN
ejpam-5764	203	5	j=1	j=1	PROPN
ejpam-5764	203	6	vaj	vaj	NOUN
ejpam-5764	203	7	.	.	PUNCT
ejpam-5764	204	1	then	then	ADV
ejpam-5764	204	2	v	v	NOUN
ejpam-5764	204	3	is	be	AUX
ejpam-5764	204	4	a	a	DET
ejpam-5764	204	5	ϑi	ϑi	NOUN
ejpam-5764	204	6	-	-	PUNCT
ejpam-5764	204	7	open	open	NOUN
ejpam-5764	204	8	set	set	NOUN
ejpam-5764	204	9	and	and	CCONJ
ejpam-5764	204	10	k	k	PROPN
ejpam-5764	204	11	⊂	⊂	PROPN
ejpam-5764	204	12	v	v	ADP
ejpam-5764	204	13	⊂	⊂	PROPN
ejpam-5764	204	14	v	v	X
ejpam-5764	204	15	⊂	⊂	PROPN
ejpam-5764	204	16	⋃n	⋃n	PROPN
ejpam-5764	204	17	j=1	j=1	PROPN
ejpam-5764	204	18	vaj	vaj	PROPN
ejpam-5764	204	19	⊂	⊂	PROPN
ejpam-5764	204	20	⋃n	⋃n	PROPN
ejpam-5764	204	21	j=1	j=1	PROPN
ejpam-5764	204	22	vaj	vaj	PROPN
ejpam-5764	204	23	⊂	⊂	PROPN
ejpam-5764	204	24	u	u	PROPN
ejpam-5764	204	25	.	.	PUNCT
ejpam-5764	205	1	since	since	SCONJ
ejpam-5764	205	2	v	v	NUM
ejpam-5764	205	3	⊂	⊂	PROPN
ejpam-5764	205	4	⋃n	⋃n	PROPN
ejpam-5764	205	5	j=1	j=1	PROPN
ejpam-5764	205	6	vaj	vaj	NOUN
ejpam-5764	205	7	and	and	CCONJ
ejpam-5764	205	8	each	each	DET
ejpam-5764	205	9	vaj	vaj	NOUN
ejpam-5764	205	10	is	be	AUX
ejpam-5764	205	11	tri	tri	ADJ
ejpam-5764	205	12	-	-	ADJ
ejpam-5764	205	13	compact	compact	ADJ
ejpam-5764	205	14	,	,	PUNCT
ejpam-5764	205	15	their	their	PRON
ejpam-5764	205	16	finite	finite	PROPN
ejpam-5764	205	17	union	union	NOUN
ejpam-5764	205	18	⋃n	⋃n	PROPN
ejpam-5764	205	19	j=1	j=1	PROPN
ejpam-5764	205	20	vaj	vaj	PROPN
ejpam-5764	205	21	is	be	AUX
ejpam-5764	205	22	tricompact	tricompact	ADJ
ejpam-5764	205	23	.	.	PUNCT
ejpam-5764	206	1	therefore	therefore	ADV
ejpam-5764	206	2	,	,	PUNCT
ejpam-5764	206	3	v	v	NOUN
ejpam-5764	206	4	is	be	AUX
ejpam-5764	206	5	tri	tri	ADJ
ejpam-5764	206	6	-	-	ADJ
ejpam-5764	206	7	compact	compact	ADJ
ejpam-5764	206	8	as	as	ADP
ejpam-5764	206	9	a	a	DET
ejpam-5764	206	10	closed	closed	ADJ
ejpam-5764	206	11	subset	subset	NOUN
ejpam-5764	206	12	of	of	ADP
ejpam-5764	206	13	a	a	DET
ejpam-5764	206	14	tri	tri	ADJ
ejpam-5764	206	15	-	-	ADJ
ejpam-5764	206	16	compact	compact	ADJ
ejpam-5764	206	17	set	set	NOUN
ejpam-5764	206	18	.	.	PUNCT
ejpam-5764	207	1	theorem	theorem	VERB
ejpam-5764	207	2	14	14	NUM
ejpam-5764	207	3	.	.	PUNCT
ejpam-5764	208	1	let	let	AUX
ejpam-5764	208	2	(	(	PUNCT
ejpam-5764	208	3	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	208	4	,	,	PUNCT
ejpam-5764	208	5	ϑ2	ϑ2	PROPN
ejpam-5764	208	6	,	,	PUNCT
ejpam-5764	208	7	ϑ3	ϑ3	PROPN
ejpam-5764	208	8	)	)	PUNCT
ejpam-5764	208	9	be	be	AUX
ejpam-5764	208	10	a	a	DET
ejpam-5764	208	11	tri	tri	ADJ
ejpam-5764	208	12	-	-	ADJ
ejpam-5764	208	13	topological	topological	ADJ
ejpam-5764	208	14	space	space	NOUN
ejpam-5764	208	15	.	.	PUNCT
ejpam-5764	209	1	if	if	SCONJ
ejpam-5764	209	2	x	x	PRON
ejpam-5764	209	3	is	be	AUX
ejpam-5764	209	4	tri	tri	ADJ
ejpam-5764	209	5	-	-	ADJ
ejpam-5764	209	6	locally	locally	ADV
ejpam-5764	209	7	compact	compact	ADJ
ejpam-5764	209	8	and	and	CCONJ
ejpam-5764	209	9	tri	tri	ADJ
ejpam-5764	209	10	-	-	NOUN
ejpam-5764	209	11	t2	t2	NOUN
ejpam-5764	209	12	,	,	PUNCT
ejpam-5764	209	13	then	then	ADV
ejpam-5764	209	14	for	for	ADP
ejpam-5764	209	15	any	any	DET
ejpam-5764	209	16	tri	tri	ADJ
ejpam-5764	209	17	-	-	ADJ
ejpam-5764	209	18	compact	compact	ADJ
ejpam-5764	209	19	set	set	NOUN
ejpam-5764	209	20	k	k	PROPN
ejpam-5764	209	21	and	and	CCONJ
ejpam-5764	209	22	any	any	DET
ejpam-5764	209	23	closed	closed	ADJ
ejpam-5764	209	24	set	set	NOUN
ejpam-5764	209	25	f	f	PROPN
ejpam-5764	209	26	such	such	ADJ
ejpam-5764	209	27	that	that	SCONJ
ejpam-5764	209	28	k	k	PROPN
ejpam-5764	209	29	∩	∩	PROPN
ejpam-5764	209	30	f	f	X
ejpam-5764	209	31	=	=	NOUN
ejpam-5764	209	32	∅	∅	NOUN
ejpam-5764	209	33	,	,	PUNCT
ejpam-5764	209	34	there	there	PRON
ejpam-5764	209	35	exist	exist	VERB
ejpam-5764	209	36	ϑi	ϑi	NOUN
ejpam-5764	209	37	-	-	PUNCT
ejpam-5764	209	38	open	open	NOUN
ejpam-5764	209	39	sets	set	VERB
ejpam-5764	209	40	u	u	NOUN
ejpam-5764	209	41	and	and	CCONJ
ejpam-5764	209	42	v	v	ADP
ejpam-5764	209	43	such	such	ADJ
ejpam-5764	209	44	that	that	SCONJ
ejpam-5764	209	45	k	k	PROPN
ejpam-5764	209	46	⊂	⊂	PROPN
ejpam-5764	209	47	u	u	PROPN
ejpam-5764	209	48	,	,	PUNCT
ejpam-5764	209	49	f	f	PROPN
ejpam-5764	209	50	⊂	⊂	PROPN
ejpam-5764	209	51	v	v	PROPN
ejpam-5764	209	52	,	,	PUNCT
ejpam-5764	209	53	and	and	CCONJ
ejpam-5764	209	54	u	u	NOUN
ejpam-5764	209	55	∩	∩	NOUN
ejpam-5764	209	56	v	v	NOUN
ejpam-5764	209	57	=	=	PUNCT
ejpam-5764	209	58	∅.	∅.	NOUN
ejpam-5764	209	59	proof	proof	NOUN
ejpam-5764	209	60	.	.	PUNCT
ejpam-5764	210	1	let	let	VERB
ejpam-5764	210	2	k	k	PRON
ejpam-5764	210	3	be	be	AUX
ejpam-5764	210	4	a	a	DET
ejpam-5764	210	5	tri	tri	ADJ
ejpam-5764	210	6	-	-	ADJ
ejpam-5764	210	7	compact	compact	ADJ
ejpam-5764	210	8	set	set	NOUN
ejpam-5764	210	9	and	and	CCONJ
ejpam-5764	210	10	f	f	PROPN
ejpam-5764	210	11	be	be	AUX
ejpam-5764	210	12	a	a	DET
ejpam-5764	210	13	closed	closed	ADJ
ejpam-5764	210	14	set	set	NOUN
ejpam-5764	210	15	such	such	ADJ
ejpam-5764	210	16	that	that	SCONJ
ejpam-5764	210	17	k	k	PROPN
ejpam-5764	210	18	∩	∩	PROPN
ejpam-5764	210	19	f	f	X
ejpam-5764	210	20	=	=	PUNCT
ejpam-5764	210	21	∅.	∅.	NOUN
ejpam-5764	210	22	for	for	ADP
ejpam-5764	210	23	each	each	PRON
ejpam-5764	210	24	a	a	DET
ejpam-5764	210	25	∈	∈	PROPN
ejpam-5764	210	26	k	k	NOUN
ejpam-5764	210	27	,	,	PUNCT
ejpam-5764	210	28	we	we	PRON
ejpam-5764	210	29	have	have	AUX
ejpam-5764	210	30	a	a	DET
ejpam-5764	210	31	/∈	/∈	NOUN
ejpam-5764	210	32	f	f	NOUN
ejpam-5764	210	33	,	,	PUNCT
ejpam-5764	210	34	which	which	PRON
ejpam-5764	210	35	means	mean	VERB
ejpam-5764	210	36	a	a	DET
ejpam-5764	210	37	∈	∈	PROPN
ejpam-5764	210	38	f	f	PROPN
ejpam-5764	210	39	c.	c.	PROPN
ejpam-5764	210	40	since	since	SCONJ
ejpam-5764	210	41	x	x	PROPN
ejpam-5764	210	42	is	be	AUX
ejpam-5764	210	43	tri	tri	ADJ
ejpam-5764	210	44	-	-	NOUN
ejpam-5764	210	45	t2	t2	NOUN
ejpam-5764	210	46	,	,	PUNCT
ejpam-5764	210	47	for	for	ADP
ejpam-5764	210	48	each	each	DET
ejpam-5764	210	49	a	a	DET
ejpam-5764	210	50	∈	∈	PROPN
ejpam-5764	210	51	k	k	PROPN
ejpam-5764	210	52	and	and	CCONJ
ejpam-5764	210	53	b	b	PROPN
ejpam-5764	210	54	∈	∈	PROPN
ejpam-5764	210	55	f	f	X
ejpam-5764	210	56	,	,	PUNCT
ejpam-5764	210	57	there	there	PRON
ejpam-5764	210	58	exist	exist	VERB
ejpam-5764	210	59	ϑi	ϑi	NOUN
ejpam-5764	210	60	-	-	PUNCT
ejpam-5764	210	61	open	open	NOUN
ejpam-5764	210	62	sets	set	NOUN
ejpam-5764	210	63	ua	ua	PROPN
ejpam-5764	210	64	and	and	CCONJ
ejpam-5764	210	65	vb	vb	NOUN
ejpam-5764	210	66	such	such	ADJ
ejpam-5764	210	67	that	that	SCONJ
ejpam-5764	210	68	a	a	DET
ejpam-5764	210	69	∈	∈	PROPN
ejpam-5764	210	70	ua	ua	PROPN
ejpam-5764	210	71	,	,	PUNCT
ejpam-5764	210	72	b	b	PROPN
ejpam-5764	210	73	∈	∈	PROPN
ejpam-5764	210	74	vb	vb	NOUN
ejpam-5764	210	75	,	,	PUNCT
ejpam-5764	210	76	and	and	CCONJ
ejpam-5764	210	77	ua	ua	PROPN
ejpam-5764	210	78	∩	∩	NOUN
ejpam-5764	210	79	vb	vb	X
ejpam-5764	210	80	=	=	PUNCT
ejpam-5764	210	81	∅.	∅.	NOUN
ejpam-5764	210	82	for	for	ADP
ejpam-5764	210	83	each	each	DET
ejpam-5764	210	84	a	a	DET
ejpam-5764	210	85	∈	∈	PROPN
ejpam-5764	210	86	k	k	NOUN
ejpam-5764	210	87	,	,	PUNCT
ejpam-5764	210	88	the	the	DET
ejpam-5764	210	89	collection	collection	NOUN
ejpam-5764	210	90	{	{	PUNCT
ejpam-5764	210	91	vb	vb	NOUN
ejpam-5764	210	92	:	:	PUNCT
ejpam-5764	210	93	b	b	X
ejpam-5764	210	94	∈	∈	ADJ
ejpam-5764	210	95	f	f	X
ejpam-5764	210	96	}	}	PUNCT
ejpam-5764	210	97	forms	form	VERB
ejpam-5764	210	98	an	an	DET
ejpam-5764	210	99	open	open	ADJ
ejpam-5764	210	100	cover	cover	NOUN
ejpam-5764	210	101	of	of	ADP
ejpam-5764	210	102	f	f	PROPN
ejpam-5764	210	103	.	.	PUNCT
ejpam-5764	211	1	since	since	SCONJ
ejpam-5764	211	2	x	x	PRON
ejpam-5764	211	3	is	be	AUX
ejpam-5764	211	4	trilocally	trilocally	ADV
ejpam-5764	211	5	compact	compact	ADJ
ejpam-5764	211	6	,	,	PUNCT
ejpam-5764	211	7	there	there	PRON
ejpam-5764	211	8	exists	exist	VERB
ejpam-5764	211	9	a	a	DET
ejpam-5764	211	10	finite	finite	NOUN
ejpam-5764	211	11	subset	subset	NOUN
ejpam-5764	211	12	{	{	PUNCT
ejpam-5764	211	13	b1	b1	NOUN
ejpam-5764	211	14	,	,	PUNCT
ejpam-5764	211	15	b2	b2	NOUN
ejpam-5764	211	16	,	,	PUNCT
ejpam-5764	211	17	.	.	PUNCT
ejpam-5764	211	18	.	.	PUNCT
ejpam-5764	212	1	.	.	PUNCT
ejpam-5764	213	1	,	,	PUNCT
ejpam-5764	213	2	bna	bna	PROPN
ejpam-5764	213	3	}	}	PUNCT
ejpam-5764	213	4	⊂	⊂	PROPN
ejpam-5764	213	5	f	f	PROPN
ejpam-5764	214	1	such	such	ADJ
ejpam-5764	214	2	that	that	SCONJ
ejpam-5764	214	3	f	f	PROPN
ejpam-5764	214	4	⊂	⊂	PROPN
ejpam-5764	214	5	⋃na	⋃na	PUNCT
ejpam-5764	214	6	j=1	j=1	ADJ
ejpam-5764	214	7	vbj	vbj	NOUN
ejpam-5764	214	8	.	.	PUNCT
ejpam-5764	215	1	let	let	VERB
ejpam-5764	215	2	va	va	PROPN
ejpam-5764	215	3	=	=	PUNCT
ejpam-5764	215	4	⋃na	⋃na	PUNCT
ejpam-5764	215	5	j=1	j=1	ADJ
ejpam-5764	215	6	vbj	vbj	NOUN
ejpam-5764	215	7	.	.	PUNCT
ejpam-5764	216	1	then	then	ADV
ejpam-5764	216	2	va	va	PROPN
ejpam-5764	216	3	is	be	AUX
ejpam-5764	216	4	a	a	DET
ejpam-5764	216	5	ϑi	ϑi	NOUN
ejpam-5764	216	6	-	-	PUNCT
ejpam-5764	216	7	open	open	NOUN
ejpam-5764	216	8	set	set	NOUN
ejpam-5764	216	9	containing	contain	VERB
ejpam-5764	216	10	f	f	PROPN
ejpam-5764	216	11	.	.	PUNCT
ejpam-5764	217	1	j.	j.	PROPN
ejpam-5764	217	2	oudetallah	oudetallah	PROPN
ejpam-5764	217	3	et	et	PROPN
ejpam-5764	217	4	al	al	PROPN
ejpam-5764	217	5	.	.	PUNCT
ejpam-5764	217	6	/	/	SYM
ejpam-5764	217	7	eur	eur	PROPN
ejpam-5764	217	8	.	.	PUNCT
ejpam-5764	218	1	j.	j.	PROPN
ejpam-5764	218	2	pure	pure	PROPN
ejpam-5764	218	3	appl	appl	PROPN
ejpam-5764	218	4	.	.	PROPN
ejpam-5764	218	5	math	math	PROPN
ejpam-5764	218	6	,	,	PUNCT
ejpam-5764	218	7	18	18	NUM
ejpam-5764	218	8	(	(	PUNCT
ejpam-5764	218	9	2	2	NUM
ejpam-5764	218	10	)	)	PUNCT
ejpam-5764	218	11	(	(	PUNCT
ejpam-5764	218	12	2025	2025	NUM
ejpam-5764	218	13	)	)	PUNCT
ejpam-5764	218	14	,	,	PUNCT
ejpam-5764	218	15	5764	5764	NUM
ejpam-5764	218	16	9	9	NUM
ejpam-5764	218	17	of	of	ADP
ejpam-5764	218	18	11	11	NUM
ejpam-5764	218	19	now	now	ADV
ejpam-5764	218	20	,	,	PUNCT
ejpam-5764	218	21	let	let	VERB
ejpam-5764	218	22	wa	wa	ADV
ejpam-5764	218	23	=	=	NOUN
ejpam-5764	219	1	x	x	SYM
ejpam-5764	219	2	\	\	PROPN
ejpam-5764	219	3	va	va	PROPN
ejpam-5764	219	4	.	.	PUNCT
ejpam-5764	220	1	then	then	ADV
ejpam-5764	220	2	wa	wa	PROPN
ejpam-5764	220	3	is	be	AUX
ejpam-5764	220	4	a	a	DET
ejpam-5764	220	5	ϑi	ϑi	NOUN
ejpam-5764	220	6	-	-	PUNCT
ejpam-5764	220	7	closed	close	VERB
ejpam-5764	220	8	set	set	NOUN
ejpam-5764	220	9	and	and	CCONJ
ejpam-5764	220	10	a	a	DET
ejpam-5764	220	11	∈	∈	PROPN
ejpam-5764	220	12	wa	wa	PROPN
ejpam-5764	220	13	.	.	PROPN
ejpam-5764	221	1	by	by	ADP
ejpam-5764	221	2	the	the	DET
ejpam-5764	221	3	previous	previous	ADJ
ejpam-5764	221	4	theorem	theorem	NOUN
ejpam-5764	221	5	,	,	PUNCT
ejpam-5764	221	6	there	there	PRON
ejpam-5764	221	7	exists	exist	VERB
ejpam-5764	221	8	a	a	DET
ejpam-5764	221	9	ϑi	ϑi	NOUN
ejpam-5764	221	10	-	-	PUNCT
ejpam-5764	221	11	open	open	NOUN
ejpam-5764	221	12	set	set	NOUN
ejpam-5764	221	13	ua	ua	PROPN
ejpam-5764	221	14	such	such	ADJ
ejpam-5764	221	15	that	that	SCONJ
ejpam-5764	221	16	a	a	DET
ejpam-5764	221	17	∈	∈	PROPN
ejpam-5764	222	1	ua	ua	PROPN
ejpam-5764	222	2	⊂	⊂	PROPN
ejpam-5764	222	3	ua	ua	PROPN
ejpam-5764	222	4	⊂	⊂	PROPN
ejpam-5764	222	5	wa	wa	PROPN
ejpam-5764	222	6	and	and	CCONJ
ejpam-5764	222	7	ua	ua	PROPN
ejpam-5764	222	8	is	be	AUX
ejpam-5764	222	9	tri	tri	ADJ
ejpam-5764	222	10	-	-	ADJ
ejpam-5764	222	11	compact	compact	ADJ
ejpam-5764	222	12	.	.	PUNCT
ejpam-5764	223	1	the	the	DET
ejpam-5764	223	2	collection	collection	NOUN
ejpam-5764	223	3	{	{	PUNCT
ejpam-5764	223	4	ua	ua	NOUN
ejpam-5764	223	5	:	:	PUNCT
ejpam-5764	223	6	a	a	DET
ejpam-5764	223	7	∈	∈	PROPN
ejpam-5764	223	8	k	k	NOUN
ejpam-5764	223	9	}	}	PUNCT
ejpam-5764	223	10	forms	form	VERB
ejpam-5764	223	11	an	an	DET
ejpam-5764	223	12	open	open	ADJ
ejpam-5764	223	13	cover	cover	NOUN
ejpam-5764	223	14	of	of	ADP
ejpam-5764	223	15	k.	k.	PROPN
ejpam-5764	223	16	since	since	SCONJ
ejpam-5764	223	17	k	k	PROPN
ejpam-5764	223	18	is	be	AUX
ejpam-5764	223	19	tri	tri	ADJ
ejpam-5764	223	20	-	-	ADJ
ejpam-5764	223	21	compact	compact	ADJ
ejpam-5764	223	22	,	,	PUNCT
ejpam-5764	223	23	there	there	PRON
ejpam-5764	223	24	exists	exist	VERB
ejpam-5764	223	25	a	a	DET
ejpam-5764	223	26	finite	finite	NOUN
ejpam-5764	223	27	subset	subset	NOUN
ejpam-5764	223	28	{	{	PUNCT
ejpam-5764	223	29	a1	a1	PROPN
ejpam-5764	223	30	,	,	PUNCT
ejpam-5764	223	31	a2	a2	PROPN
ejpam-5764	223	32	,	,	PUNCT
ejpam-5764	223	33	.	.	PUNCT
ejpam-5764	223	34	.	.	PUNCT
ejpam-5764	224	1	.	.	PUNCT
ejpam-5764	225	1	,	,	PUNCT
ejpam-5764	225	2	am	be	AUX
ejpam-5764	225	3	}	}	PUNCT
ejpam-5764	225	4	⊂	⊂	PROPN
ejpam-5764	225	5	k	k	PROPN
ejpam-5764	225	6	such	such	ADJ
ejpam-5764	225	7	that	that	SCONJ
ejpam-5764	225	8	k	k	PROPN
ejpam-5764	225	9	⊂	⊂	PROPN
ejpam-5764	225	10	⋃m	⋃m	PROPN
ejpam-5764	225	11	j=1	j=1	PROPN
ejpam-5764	225	12	uaj	uaj	X
ejpam-5764	225	13	.	.	PUNCT
ejpam-5764	226	1	let	let	VERB
ejpam-5764	226	2	u	u	PRON
ejpam-5764	226	3	=	=	SYM
ejpam-5764	226	4	⋃m	⋃m	X
ejpam-5764	226	5	j=1	j=1	PROPN
ejpam-5764	226	6	uaj	uaj	X
ejpam-5764	226	7	and	and	CCONJ
ejpam-5764	226	8	v	v	NOUN
ejpam-5764	226	9	=	=	NOUN
ejpam-5764	226	10	⋂m	⋂m	NOUN
ejpam-5764	226	11	j=1	j=1	PROPN
ejpam-5764	226	12	vaj	vaj	NOUN
ejpam-5764	226	13	.	.	PUNCT
ejpam-5764	227	1	then	then	ADV
ejpam-5764	227	2	u	u	NOUN
ejpam-5764	227	3	is	be	AUX
ejpam-5764	227	4	a	a	DET
ejpam-5764	227	5	ϑi	ϑi	NOUN
ejpam-5764	227	6	-	-	PUNCT
ejpam-5764	227	7	open	open	NOUN
ejpam-5764	227	8	set	set	NOUN
ejpam-5764	227	9	containing	contain	VERB
ejpam-5764	227	10	k	k	PROPN
ejpam-5764	227	11	,	,	PUNCT
ejpam-5764	227	12	and	and	CCONJ
ejpam-5764	227	13	v	v	NOUN
ejpam-5764	227	14	is	be	AUX
ejpam-5764	227	15	a	a	DET
ejpam-5764	227	16	ϑi	ϑi	NOUN
ejpam-5764	227	17	-	-	PUNCT
ejpam-5764	227	18	open	open	NOUN
ejpam-5764	227	19	set	set	NOUN
ejpam-5764	227	20	containing	contain	VERB
ejpam-5764	227	21	f	f	PROPN
ejpam-5764	227	22	.	.	PUNCT
ejpam-5764	228	1	furthermore	furthermore	ADV
ejpam-5764	228	2	,	,	PUNCT
ejpam-5764	228	3	u	u	PROPN
ejpam-5764	228	4	∩	∩	NOUN
ejpam-5764	228	5	v	v	NOUN
ejpam-5764	228	6	=	=	NOUN
ejpam-5764	228	7	∅	∅	NOUN
ejpam-5764	228	8	because	because	SCONJ
ejpam-5764	228	9	uaj	uaj	ADJ
ejpam-5764	228	10	∩	∩	ADJ
ejpam-5764	228	11	vaj	vaj	NOUN
ejpam-5764	228	12	=	=	PUNCT
ejpam-5764	228	13	∅	∅	NOUN
ejpam-5764	228	14	for	for	ADP
ejpam-5764	228	15	each	each	PRON
ejpam-5764	228	16	j	j	PROPN
ejpam-5764	228	17	=	=	SYM
ejpam-5764	228	18	1	1	NUM
ejpam-5764	228	19	,	,	PUNCT
ejpam-5764	228	20	2	2	NUM
ejpam-5764	228	21	,	,	PUNCT
ejpam-5764	228	22	.	.	PUNCT
ejpam-5764	228	23	.	.	PUNCT
ejpam-5764	228	24	.	.	PUNCT
ejpam-5764	229	1	,	,	PUNCT
ejpam-5764	229	2	m.	m.	NOUN
ejpam-5764	229	3	theorem	theorem	VERB
ejpam-5764	229	4	15	15	NUM
ejpam-5764	229	5	.	.	PUNCT
ejpam-5764	230	1	let	let	AUX
ejpam-5764	230	2	(	(	PUNCT
ejpam-5764	230	3	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	230	4	,	,	PUNCT
ejpam-5764	230	5	ϑ2	ϑ2	PROPN
ejpam-5764	230	6	,	,	PUNCT
ejpam-5764	230	7	ϑ3	ϑ3	PROPN
ejpam-5764	230	8	)	)	PUNCT
ejpam-5764	230	9	be	be	AUX
ejpam-5764	230	10	a	a	DET
ejpam-5764	230	11	tri	tri	ADJ
ejpam-5764	230	12	-	-	ADJ
ejpam-5764	230	13	t2	t2	ADJ
ejpam-5764	230	14	-	-	PUNCT
ejpam-5764	230	15	space	space	NOUN
ejpam-5764	230	16	.	.	PUNCT
ejpam-5764	231	1	if	if	SCONJ
ejpam-5764	231	2	x	x	PRON
ejpam-5764	231	3	is	be	AUX
ejpam-5764	231	4	tri	tri	ADJ
ejpam-5764	231	5	-	-	ADJ
ejpam-5764	231	6	locally	locally	ADV
ejpam-5764	231	7	compact	compact	ADJ
ejpam-5764	231	8	,	,	PUNCT
ejpam-5764	231	9	then	then	ADV
ejpam-5764	231	10	for	for	ADP
ejpam-5764	231	11	any	any	DET
ejpam-5764	231	12	tri	tri	ADJ
ejpam-5764	231	13	-	-	ADJ
ejpam-5764	231	14	compact	compact	ADJ
ejpam-5764	231	15	set	set	NOUN
ejpam-5764	231	16	k	k	PROPN
ejpam-5764	231	17	and	and	CCONJ
ejpam-5764	231	18	any	any	DET
ejpam-5764	231	19	ϑi	ϑi	NOUN
ejpam-5764	231	20	-	-	PUNCT
ejpam-5764	231	21	open	open	NOUN
ejpam-5764	231	22	set	set	NOUN
ejpam-5764	231	23	u	u	NOUN
ejpam-5764	231	24	containing	contain	VERB
ejpam-5764	231	25	k	k	X
ejpam-5764	231	26	,	,	PUNCT
ejpam-5764	231	27	there	there	PRON
ejpam-5764	231	28	exists	exist	VERB
ejpam-5764	231	29	a	a	DET
ejpam-5764	231	30	ϑi	ϑi	NOUN
ejpam-5764	231	31	-	-	PUNCT
ejpam-5764	231	32	open	open	NOUN
ejpam-5764	231	33	set	set	VERB
ejpam-5764	231	34	v	v	NOUN
ejpam-5764	231	35	with	with	ADP
ejpam-5764	231	36	compact	compact	ADJ
ejpam-5764	231	37	closure	closure	NOUN
ejpam-5764	231	38	such	such	ADJ
ejpam-5764	231	39	that	that	SCONJ
ejpam-5764	231	40	k	k	PROPN
ejpam-5764	231	41	⊂	⊂	PROPN
ejpam-5764	231	42	v	v	ADP
ejpam-5764	231	43	⊂	⊂	PROPN
ejpam-5764	231	44	v	v	ADP
ejpam-5764	231	45	⊂	⊂	PROPN
ejpam-5764	231	46	u	u	PROPN
ejpam-5764	231	47	.	.	PUNCT
ejpam-5764	232	1	proof	proof	NOUN
ejpam-5764	232	2	.	.	PUNCT
ejpam-5764	233	1	let	let	VERB
ejpam-5764	233	2	k	k	PRON
ejpam-5764	233	3	be	be	AUX
ejpam-5764	233	4	a	a	DET
ejpam-5764	233	5	tri	tri	ADJ
ejpam-5764	233	6	-	-	ADJ
ejpam-5764	233	7	compact	compact	ADJ
ejpam-5764	233	8	set	set	NOUN
ejpam-5764	233	9	and	and	CCONJ
ejpam-5764	233	10	u	u	PRON
ejpam-5764	233	11	be	be	VERB
ejpam-5764	233	12	a	a	DET
ejpam-5764	233	13	ϑi	ϑi	NOUN
ejpam-5764	233	14	-	-	PUNCT
ejpam-5764	233	15	open	open	NOUN
ejpam-5764	233	16	set	set	NOUN
ejpam-5764	233	17	containing	contain	VERB
ejpam-5764	233	18	k.	k.	NOUN
ejpam-5764	233	19	for	for	ADP
ejpam-5764	233	20	each	each	PRON
ejpam-5764	233	21	a	a	DET
ejpam-5764	233	22	∈	∈	PROPN
ejpam-5764	233	23	k	k	NOUN
ejpam-5764	233	24	,	,	PUNCT
ejpam-5764	233	25	by	by	ADP
ejpam-5764	233	26	tri	tri	ADJ
ejpam-5764	233	27	-	-	ADJ
ejpam-5764	233	28	local	local	ADJ
ejpam-5764	233	29	compactness	compactness	NOUN
ejpam-5764	233	30	,	,	PUNCT
ejpam-5764	233	31	there	there	PRON
ejpam-5764	233	32	exists	exist	VERB
ejpam-5764	233	33	a	a	DET
ejpam-5764	233	34	ϑi	ϑi	NOUN
ejpam-5764	233	35	-	-	PUNCT
ejpam-5764	233	36	open	open	NOUN
ejpam-5764	233	37	set	set	VERB
ejpam-5764	233	38	va	va	NOUN
ejpam-5764	233	39	such	such	ADJ
ejpam-5764	233	40	that	that	SCONJ
ejpam-5764	233	41	a	a	DET
ejpam-5764	233	42	∈	∈	PROPN
ejpam-5764	233	43	va	va	PROPN
ejpam-5764	233	44	⊂	⊂	PROPN
ejpam-5764	233	45	va	va	PROPN
ejpam-5764	234	1	⊂	⊂	PROPN
ejpam-5764	234	2	u	u	PROPN
ejpam-5764	234	3	and	and	CCONJ
ejpam-5764	234	4	va	va	PROPN
ejpam-5764	234	5	is	be	AUX
ejpam-5764	234	6	tri	tri	ADJ
ejpam-5764	234	7	-	-	ADJ
ejpam-5764	234	8	compact	compact	ADJ
ejpam-5764	234	9	.	.	PUNCT
ejpam-5764	235	1	the	the	DET
ejpam-5764	235	2	collection	collection	NOUN
ejpam-5764	235	3	{	{	PUNCT
ejpam-5764	235	4	va	va	NOUN
ejpam-5764	235	5	:	:	PUNCT
ejpam-5764	235	6	a	a	DET
ejpam-5764	235	7	∈	∈	PROPN
ejpam-5764	235	8	k	k	NOUN
ejpam-5764	235	9	}	}	PUNCT
ejpam-5764	235	10	forms	form	VERB
ejpam-5764	235	11	an	an	DET
ejpam-5764	235	12	open	open	ADJ
ejpam-5764	235	13	cover	cover	NOUN
ejpam-5764	235	14	of	of	ADP
ejpam-5764	235	15	k.	k.	PROPN
ejpam-5764	235	16	since	since	SCONJ
ejpam-5764	235	17	k	k	PROPN
ejpam-5764	235	18	is	be	AUX
ejpam-5764	235	19	tri	tri	ADJ
ejpam-5764	235	20	-	-	ADJ
ejpam-5764	235	21	compact	compact	ADJ
ejpam-5764	235	22	,	,	PUNCT
ejpam-5764	235	23	there	there	PRON
ejpam-5764	235	24	exists	exist	VERB
ejpam-5764	235	25	a	a	DET
ejpam-5764	235	26	finite	finite	NOUN
ejpam-5764	235	27	subset	subset	NOUN
ejpam-5764	235	28	{	{	PUNCT
ejpam-5764	235	29	a1	a1	PROPN
ejpam-5764	235	30	,	,	PUNCT
ejpam-5764	235	31	a2	a2	PROPN
ejpam-5764	235	32	,	,	PUNCT
ejpam-5764	235	33	.	.	PUNCT
ejpam-5764	235	34	.	.	PUNCT
ejpam-5764	236	1	.	.	PUNCT
ejpam-5764	237	1	,	,	PUNCT
ejpam-5764	237	2	an	an	PRON
ejpam-5764	237	3	}	}	PUNCT
ejpam-5764	237	4	⊂	⊂	PROPN
ejpam-5764	238	1	k	k	NOUN
ejpam-5764	239	1	such	such	ADJ
ejpam-5764	239	2	that	that	SCONJ
ejpam-5764	239	3	k	k	PROPN
ejpam-5764	239	4	⊂	⊂	PROPN
ejpam-5764	239	5	⋃n	⋃n	PROPN
ejpam-5764	239	6	j=1	j=1	PROPN
ejpam-5764	239	7	vaj	vaj	PROPN
ejpam-5764	239	8	.	.	PUNCT
ejpam-5764	240	1	let	let	VERB
ejpam-5764	240	2	v	v	NOUN
ejpam-5764	240	3	=	=	SYM
ejpam-5764	240	4	⋃n	⋃n	NOUN
ejpam-5764	240	5	j=1	j=1	PROPN
ejpam-5764	240	6	vaj	vaj	NOUN
ejpam-5764	240	7	.	.	PUNCT
ejpam-5764	241	1	then	then	ADV
ejpam-5764	241	2	v	v	NOUN
ejpam-5764	241	3	is	be	AUX
ejpam-5764	241	4	a	a	DET
ejpam-5764	241	5	ϑi	ϑi	NOUN
ejpam-5764	241	6	-	-	PUNCT
ejpam-5764	241	7	open	open	NOUN
ejpam-5764	241	8	set	set	NOUN
ejpam-5764	241	9	and	and	CCONJ
ejpam-5764	241	10	k	k	PROPN
ejpam-5764	241	11	⊂	⊂	PROPN
ejpam-5764	241	12	v	v	ADP
ejpam-5764	241	13	⊂	⊂	PROPN
ejpam-5764	241	14	v	v	X
ejpam-5764	241	15	⊂	⊂	PROPN
ejpam-5764	241	16	⋃n	⋃n	PROPN
ejpam-5764	241	17	j=1	j=1	PROPN
ejpam-5764	241	18	vaj	vaj	PROPN
ejpam-5764	241	19	⊂	⊂	PROPN
ejpam-5764	241	20	u	u	PROPN
ejpam-5764	241	21	.	.	PUNCT
ejpam-5764	242	1	since	since	SCONJ
ejpam-5764	242	2	each	each	DET
ejpam-5764	242	3	vaj	vaj	NOUN
ejpam-5764	242	4	is	be	AUX
ejpam-5764	242	5	tri	tri	ADJ
ejpam-5764	242	6	-	-	ADJ
ejpam-5764	242	7	compact	compact	ADJ
ejpam-5764	242	8	,	,	PUNCT
ejpam-5764	242	9	their	their	PRON
ejpam-5764	242	10	finite	finite	PROPN
ejpam-5764	242	11	union	union	NOUN
ejpam-5764	242	12	⋃n	⋃n	PROPN
ejpam-5764	242	13	j=1	j=1	PROPN
ejpam-5764	242	14	vaj	vaj	PROPN
ejpam-5764	242	15	is	be	AUX
ejpam-5764	242	16	tri	tri	ADJ
ejpam-5764	242	17	-	-	ADJ
ejpam-5764	242	18	compact	compact	ADJ
ejpam-5764	242	19	.	.	PUNCT
ejpam-5764	243	1	therefore	therefore	ADV
ejpam-5764	243	2	,	,	PUNCT
ejpam-5764	243	3	v	v	NOUN
ejpam-5764	243	4	is	be	AUX
ejpam-5764	243	5	tri	tri	ADJ
ejpam-5764	243	6	-	-	ADJ
ejpam-5764	243	7	compact	compact	ADJ
ejpam-5764	243	8	as	as	ADP
ejpam-5764	243	9	a	a	DET
ejpam-5764	243	10	closed	closed	ADJ
ejpam-5764	243	11	subset	subset	NOUN
ejpam-5764	243	12	of	of	ADP
ejpam-5764	243	13	a	a	DET
ejpam-5764	243	14	tri	tri	ADJ
ejpam-5764	243	15	-	-	ADJ
ejpam-5764	243	16	compact	compact	ADJ
ejpam-5764	243	17	set	set	NOUN
ejpam-5764	243	18	.	.	PUNCT
ejpam-5764	244	1	theorem	theorem	VERB
ejpam-5764	244	2	16	16	NUM
ejpam-5764	244	3	.	.	PUNCT
ejpam-5764	245	1	let	let	AUX
ejpam-5764	245	2	(	(	PUNCT
ejpam-5764	245	3	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	245	4	,	,	PUNCT
ejpam-5764	245	5	ϑ2	ϑ2	PROPN
ejpam-5764	245	6	,	,	PUNCT
ejpam-5764	245	7	ϑ3	ϑ3	PROPN
ejpam-5764	245	8	)	)	PUNCT
ejpam-5764	245	9	be	be	AUX
ejpam-5764	245	10	a	a	DET
ejpam-5764	245	11	tri	tri	ADJ
ejpam-5764	245	12	-	-	ADJ
ejpam-5764	245	13	topological	topological	ADJ
ejpam-5764	245	14	space	space	NOUN
ejpam-5764	245	15	.	.	PUNCT
ejpam-5764	246	1	if	if	SCONJ
ejpam-5764	246	2	x	x	PRON
ejpam-5764	246	3	is	be	AUX
ejpam-5764	246	4	tri	tri	ADJ
ejpam-5764	246	5	-	-	ADJ
ejpam-5764	246	6	locally	locally	ADV
ejpam-5764	246	7	compact	compact	ADJ
ejpam-5764	246	8	and	and	CCONJ
ejpam-5764	246	9	tri	tri	ADJ
ejpam-5764	246	10	-	-	NOUN
ejpam-5764	246	11	t3	t3	ADJ
ejpam-5764	246	12	,	,	PUNCT
ejpam-5764	246	13	then	then	ADV
ejpam-5764	246	14	x	x	PUNCT
ejpam-5764	246	15	is	be	AUX
ejpam-5764	246	16	tri	tri	ADJ
ejpam-5764	246	17	-	-	ADJ
ejpam-5764	246	18	regular	regular	ADJ
ejpam-5764	246	19	.	.	PUNCT
ejpam-5764	247	1	proof	proof	NOUN
ejpam-5764	247	2	.	.	PUNCT
ejpam-5764	248	1	let	let	VERB
ejpam-5764	248	2	a	a	DET
ejpam-5764	248	3	∈	∈	PROPN
ejpam-5764	248	4	x	x	X
ejpam-5764	248	5	and	and	CCONJ
ejpam-5764	248	6	f	f	PROPN
ejpam-5764	248	7	be	be	AUX
ejpam-5764	248	8	a	a	DET
ejpam-5764	248	9	ϑi	ϑi	NOUN
ejpam-5764	248	10	-	-	PUNCT
ejpam-5764	248	11	closed	close	VERB
ejpam-5764	248	12	set	set	NOUN
ejpam-5764	248	13	such	such	DET
ejpam-5764	248	14	that	that	SCONJ
ejpam-5764	248	15	a	a	DET
ejpam-5764	248	16	/∈	/∈	NOUN
ejpam-5764	248	17	f	f	X
ejpam-5764	248	18	.	.	PUNCT
ejpam-5764	249	1	since	since	SCONJ
ejpam-5764	249	2	x	x	PROPN
ejpam-5764	249	3	is	be	AUX
ejpam-5764	249	4	tri	tri	ADJ
ejpam-5764	249	5	-	-	ADJ
ejpam-5764	249	6	t3	t3	ADJ
ejpam-5764	249	7	,	,	PUNCT
ejpam-5764	249	8	it	it	PRON
ejpam-5764	249	9	is	be	AUX
ejpam-5764	249	10	tri	tri	ADJ
ejpam-5764	249	11	-	-	NOUN
ejpam-5764	249	12	t1	t1	NOUN
ejpam-5764	249	13	,	,	PUNCT
ejpam-5764	249	14	which	which	PRON
ejpam-5764	249	15	means	mean	VERB
ejpam-5764	249	16	{	{	PUNCT
ejpam-5764	249	17	a	a	PRON
ejpam-5764	249	18	}	}	PUNCT
ejpam-5764	249	19	is	be	AUX
ejpam-5764	249	20	a	a	DET
ejpam-5764	249	21	tri	tri	ADJ
ejpam-5764	249	22	-	-	ADJ
ejpam-5764	249	23	compact	compact	ADJ
ejpam-5764	249	24	set	set	NOUN
ejpam-5764	249	25	.	.	PUNCT
ejpam-5764	250	1	by	by	ADP
ejpam-5764	250	2	the	the	DET
ejpam-5764	250	3	previous	previous	ADJ
ejpam-5764	250	4	theorem	theorem	NOUN
ejpam-5764	250	5	,	,	PUNCT
ejpam-5764	250	6	there	there	PRON
ejpam-5764	250	7	exist	exist	VERB
ejpam-5764	250	8	ϑi	ϑi	NOUN
ejpam-5764	250	9	-	-	PUNCT
ejpam-5764	250	10	open	open	NOUN
ejpam-5764	250	11	sets	set	VERB
ejpam-5764	250	12	u	u	NOUN
ejpam-5764	250	13	and	and	CCONJ
ejpam-5764	250	14	v	v	ADP
ejpam-5764	250	15	such	such	ADJ
ejpam-5764	250	16	that	that	SCONJ
ejpam-5764	250	17	{	{	PUNCT
ejpam-5764	250	18	a	a	NOUN
ejpam-5764	250	19	}	}	PUNCT
ejpam-5764	250	20	⊂	⊂	PROPN
ejpam-5764	250	21	u	u	PROPN
ejpam-5764	250	22	,	,	PUNCT
ejpam-5764	250	23	f	f	PROPN
ejpam-5764	250	24	⊂	⊂	PROPN
ejpam-5764	250	25	v	v	PROPN
ejpam-5764	250	26	,	,	PUNCT
ejpam-5764	250	27	and	and	CCONJ
ejpam-5764	250	28	u	u	NOUN
ejpam-5764	250	29	∩	∩	NOUN
ejpam-5764	250	30	v	v	NOUN
ejpam-5764	250	31	=	=	PUNCT
ejpam-5764	250	32	∅.	∅.	VERB
ejpam-5764	250	33	therefore	therefore	ADV
ejpam-5764	250	34	,	,	PUNCT
ejpam-5764	250	35	x	x	X
ejpam-5764	250	36	is	be	AUX
ejpam-5764	250	37	tri	tri	ADJ
ejpam-5764	250	38	-	-	ADJ
ejpam-5764	250	39	regular	regular	ADJ
ejpam-5764	250	40	.	.	PUNCT
ejpam-5764	251	1	theorem	theorem	NOUN
ejpam-5764	251	2	17	17	NUM
ejpam-5764	251	3	.	.	PUNCT
ejpam-5764	252	1	let	let	AUX
ejpam-5764	252	2	(	(	PUNCT
ejpam-5764	252	3	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	252	4	,	,	PUNCT
ejpam-5764	252	5	ϑ2	ϑ2	PROPN
ejpam-5764	252	6	,	,	PUNCT
ejpam-5764	252	7	ϑ3	ϑ3	PROPN
ejpam-5764	252	8	)	)	PUNCT
ejpam-5764	252	9	be	be	AUX
ejpam-5764	252	10	a	a	DET
ejpam-5764	252	11	tri	tri	ADJ
ejpam-5764	252	12	-	-	ADJ
ejpam-5764	252	13	topological	topological	ADJ
ejpam-5764	252	14	space	space	NOUN
ejpam-5764	252	15	.	.	PUNCT
ejpam-5764	253	1	if	if	SCONJ
ejpam-5764	253	2	x	x	PRON
ejpam-5764	253	3	is	be	AUX
ejpam-5764	253	4	tri	tri	ADJ
ejpam-5764	253	5	-	-	ADJ
ejpam-5764	253	6	locally	locally	ADV
ejpam-5764	253	7	compact	compact	ADJ
ejpam-5764	253	8	and	and	CCONJ
ejpam-5764	253	9	tri	tri	ADJ
ejpam-5764	253	10	-	-	NOUN
ejpam-5764	253	11	t2	t2	NOUN
ejpam-5764	253	12	,	,	PUNCT
ejpam-5764	253	13	then	then	ADV
ejpam-5764	253	14	for	for	ADP
ejpam-5764	253	15	any	any	DET
ejpam-5764	253	16	two	two	NUM
ejpam-5764	253	17	disjoint	disjoint	ADJ
ejpam-5764	253	18	tri	tri	ADJ
ejpam-5764	253	19	-	-	ADJ
ejpam-5764	253	20	compact	compact	ADJ
ejpam-5764	253	21	sets	set	NOUN
ejpam-5764	253	22	k1	k1	NOUN
ejpam-5764	253	23	and	and	CCONJ
ejpam-5764	253	24	k2	k2	NOUN
ejpam-5764	253	25	,	,	PUNCT
ejpam-5764	253	26	there	there	PRON
ejpam-5764	253	27	exist	exist	VERB
ejpam-5764	253	28	ϑi	ϑi	NOUN
ejpam-5764	253	29	-	-	PUNCT
ejpam-5764	253	30	open	open	ADJ
ejpam-5764	253	31	sets	set	NOUN
ejpam-5764	253	32	u1	u1	NOUN
ejpam-5764	253	33	and	and	CCONJ
ejpam-5764	253	34	u2	u2	NOUN
ejpam-5764	253	35	such	such	ADJ
ejpam-5764	253	36	that	that	SCONJ
ejpam-5764	253	37	k1	k1	PROPN
ejpam-5764	253	38	⊂	⊂	PROPN
ejpam-5764	253	39	u1	u1	PROPN
ejpam-5764	253	40	,	,	PUNCT
ejpam-5764	253	41	k2	k2	PROPN
ejpam-5764	253	42	⊂	⊂	PROPN
ejpam-5764	253	43	u2	u2	PROPN
ejpam-5764	253	44	,	,	PUNCT
ejpam-5764	253	45	and	and	CCONJ
ejpam-5764	253	46	u1	u1	NOUN
ejpam-5764	253	47	∩	∩	ADJ
ejpam-5764	253	48	u2	u2	NOUN
ejpam-5764	253	49	=	=	PUNCT
ejpam-5764	253	50	∅.	∅.	NOUN
ejpam-5764	253	51	proof	proof	NOUN
ejpam-5764	253	52	.	.	PUNCT
ejpam-5764	254	1	let	let	VERB
ejpam-5764	254	2	k1	k1	NOUN
ejpam-5764	254	3	and	and	CCONJ
ejpam-5764	254	4	k2	k2	PROPN
ejpam-5764	254	5	be	be	PROPN
ejpam-5764	254	6	disjoint	disjoint	ADJ
ejpam-5764	254	7	tri	tri	ADJ
ejpam-5764	254	8	-	-	ADJ
ejpam-5764	254	9	compact	compact	ADJ
ejpam-5764	254	10	sets	set	NOUN
ejpam-5764	254	11	.	.	PUNCT
ejpam-5764	255	1	for	for	ADP
ejpam-5764	255	2	each	each	DET
ejpam-5764	255	3	a	a	DET
ejpam-5764	255	4	∈	∈	PROPN
ejpam-5764	255	5	k1	k1	NOUN
ejpam-5764	255	6	and	and	CCONJ
ejpam-5764	255	7	b	b	NOUN
ejpam-5764	255	8	∈	∈	PROPN
ejpam-5764	255	9	k2	k2	NOUN
ejpam-5764	255	10	,	,	PUNCT
ejpam-5764	255	11	since	since	SCONJ
ejpam-5764	255	12	x	x	PROPN
ejpam-5764	255	13	is	be	AUX
ejpam-5764	255	14	tri	tri	ADJ
ejpam-5764	255	15	-	-	NOUN
ejpam-5764	255	16	t2	t2	ADJ
ejpam-5764	255	17	,	,	PUNCT
ejpam-5764	255	18	there	there	PRON
ejpam-5764	255	19	exist	exist	VERB
ejpam-5764	255	20	ϑi	ϑi	NOUN
ejpam-5764	255	21	-	-	PUNCT
ejpam-5764	255	22	open	open	NOUN
ejpam-5764	255	23	sets	set	NOUN
ejpam-5764	255	24	ua	ua	PROPN
ejpam-5764	255	25	and	and	CCONJ
ejpam-5764	255	26	vb	vb	NOUN
ejpam-5764	255	27	such	such	ADJ
ejpam-5764	255	28	that	that	SCONJ
ejpam-5764	255	29	a	a	DET
ejpam-5764	255	30	∈	∈	PROPN
ejpam-5764	255	31	ua	ua	PROPN
ejpam-5764	255	32	,	,	PUNCT
ejpam-5764	255	33	b	b	PROPN
ejpam-5764	255	34	∈	∈	PROPN
ejpam-5764	255	35	vb	vb	NOUN
ejpam-5764	255	36	,	,	PUNCT
ejpam-5764	255	37	and	and	CCONJ
ejpam-5764	255	38	ua	ua	PROPN
ejpam-5764	255	39	∩	∩	NOUN
ejpam-5764	255	40	vb	vb	X
ejpam-5764	255	41	=	=	PUNCT
ejpam-5764	255	42	∅.	∅.	NOUN
ejpam-5764	255	43	for	for	ADP
ejpam-5764	255	44	each	each	DET
ejpam-5764	255	45	a	a	DET
ejpam-5764	255	46	∈	∈	PROPN
ejpam-5764	255	47	k1	k1	NOUN
ejpam-5764	255	48	,	,	PUNCT
ejpam-5764	255	49	the	the	DET
ejpam-5764	255	50	collection	collection	NOUN
ejpam-5764	255	51	{	{	PUNCT
ejpam-5764	255	52	vb	vb	NOUN
ejpam-5764	255	53	:	:	PUNCT
ejpam-5764	255	54	b	b	X
ejpam-5764	255	55	∈	∈	PROPN
ejpam-5764	255	56	k2	k2	NOUN
ejpam-5764	255	57	}	}	PUNCT
ejpam-5764	255	58	forms	form	VERB
ejpam-5764	255	59	an	an	DET
ejpam-5764	255	60	open	open	ADJ
ejpam-5764	255	61	cover	cover	NOUN
ejpam-5764	255	62	of	of	ADP
ejpam-5764	255	63	k2	k2	NOUN
ejpam-5764	255	64	.	.	PUNCT
ejpam-5764	256	1	since	since	SCONJ
ejpam-5764	256	2	k2	k2	PROPN
ejpam-5764	256	3	is	be	AUX
ejpam-5764	256	4	tri	tri	ADJ
ejpam-5764	256	5	-	-	ADJ
ejpam-5764	256	6	compact	compact	ADJ
ejpam-5764	256	7	,	,	PUNCT
ejpam-5764	256	8	there	there	PRON
ejpam-5764	256	9	exists	exist	VERB
ejpam-5764	256	10	a	a	DET
ejpam-5764	256	11	finite	finite	NOUN
ejpam-5764	256	12	subset	subset	NOUN
ejpam-5764	256	13	{	{	PUNCT
ejpam-5764	256	14	b1	b1	NOUN
ejpam-5764	256	15	,	,	PUNCT
ejpam-5764	256	16	b2	b2	NOUN
ejpam-5764	256	17	,	,	PUNCT
ejpam-5764	256	18	.	.	PUNCT
ejpam-5764	256	19	.	.	PUNCT
ejpam-5764	257	1	.	.	PUNCT
ejpam-5764	258	1	,	,	PUNCT
ejpam-5764	258	2	bna	bna	PROPN
ejpam-5764	258	3	}	}	PUNCT
ejpam-5764	258	4	⊂	⊂	PROPN
ejpam-5764	258	5	k2	k2	PROPN
ejpam-5764	258	6	such	such	ADJ
ejpam-5764	258	7	that	that	SCONJ
ejpam-5764	258	8	k2	k2	PROPN
ejpam-5764	258	9	⊂	⊂	PROPN
ejpam-5764	258	10	⋃na	⋃na	PUNCT
ejpam-5764	258	11	j=1	j=1	PROPN
ejpam-5764	258	12	vbj	vbj	NOUN
ejpam-5764	258	13	.	.	PUNCT
ejpam-5764	259	1	let	let	VERB
ejpam-5764	259	2	va	va	PROPN
ejpam-5764	259	3	=	=	PUNCT
ejpam-5764	259	4	⋃na	⋃na	PUNCT
ejpam-5764	259	5	j=1	j=1	ADJ
ejpam-5764	259	6	vbj	vbj	NOUN
ejpam-5764	259	7	.	.	PUNCT
ejpam-5764	260	1	then	then	ADV
ejpam-5764	260	2	va	va	PROPN
ejpam-5764	260	3	is	be	AUX
ejpam-5764	260	4	a	a	DET
ejpam-5764	260	5	ϑi	ϑi	NOUN
ejpam-5764	260	6	-	-	PUNCT
ejpam-5764	260	7	open	open	NOUN
ejpam-5764	260	8	set	set	NOUN
ejpam-5764	260	9	containing	contain	VERB
ejpam-5764	260	10	k2	k2	PROPN
ejpam-5764	260	11	and	and	CCONJ
ejpam-5764	260	12	ua	ua	PROPN
ejpam-5764	260	13	∩	∩	PROPN
ejpam-5764	260	14	va	va	PROPN
ejpam-5764	260	15	=	=	PROPN
ejpam-5764	260	16	∅.	∅.	VERB
ejpam-5764	260	17	the	the	DET
ejpam-5764	260	18	collection	collection	NOUN
ejpam-5764	260	19	{	{	PUNCT
ejpam-5764	260	20	ua	ua	NOUN
ejpam-5764	260	21	:	:	PUNCT
ejpam-5764	260	22	a	a	DET
ejpam-5764	260	23	∈	∈	PROPN
ejpam-5764	260	24	k1	k1	NOUN
ejpam-5764	260	25	}	}	PUNCT
ejpam-5764	260	26	forms	form	VERB
ejpam-5764	260	27	an	an	DET
ejpam-5764	260	28	open	open	ADJ
ejpam-5764	260	29	cover	cover	NOUN
ejpam-5764	260	30	of	of	ADP
ejpam-5764	260	31	k1	k1	NOUN
ejpam-5764	260	32	.	.	PUNCT
ejpam-5764	261	1	since	since	SCONJ
ejpam-5764	261	2	k1	k1	PROPN
ejpam-5764	261	3	is	be	AUX
ejpam-5764	261	4	tri	tri	ADJ
ejpam-5764	261	5	-	-	ADJ
ejpam-5764	261	6	compact	compact	ADJ
ejpam-5764	261	7	,	,	PUNCT
ejpam-5764	261	8	there	there	PRON
ejpam-5764	261	9	exists	exist	VERB
ejpam-5764	261	10	a	a	DET
ejpam-5764	261	11	finite	finite	NOUN
ejpam-5764	261	12	subset	subset	NOUN
ejpam-5764	261	13	{	{	PUNCT
ejpam-5764	261	14	a1	a1	PROPN
ejpam-5764	261	15	,	,	PUNCT
ejpam-5764	261	16	a2	a2	PROPN
ejpam-5764	261	17	,	,	PUNCT
ejpam-5764	261	18	.	.	PUNCT
ejpam-5764	261	19	.	.	PUNCT
ejpam-5764	262	1	.	.	PUNCT
ejpam-5764	263	1	,	,	PUNCT
ejpam-5764	263	2	am	be	AUX
ejpam-5764	263	3	}	}	PUNCT
ejpam-5764	263	4	⊂	⊂	PROPN
ejpam-5764	263	5	k1	k1	NOUN
ejpam-5764	263	6	such	such	ADJ
ejpam-5764	263	7	that	that	SCONJ
ejpam-5764	263	8	k1	k1	PROPN
ejpam-5764	263	9	⊂	⊂	PROPN
ejpam-5764	263	10	⋃m	⋃m	PROPN
ejpam-5764	263	11	j=1	j=1	PROPN
ejpam-5764	263	12	uaj	uaj	X
ejpam-5764	263	13	.	.	PUNCT
ejpam-5764	264	1	let	let	VERB
ejpam-5764	264	2	u1	u1	NOUN
ejpam-5764	264	3	=	=	SYM
ejpam-5764	264	4	⋃m	⋃m	PROPN
ejpam-5764	264	5	j=1	j=1	PROPN
ejpam-5764	264	6	uaj	uaj	NOUN
ejpam-5764	264	7	and	and	CCONJ
ejpam-5764	264	8	u2	u2	PROPN
ejpam-5764	264	9	=	=	PUNCT
ejpam-5764	264	10	⋂m	⋂m	NOUN
ejpam-5764	264	11	j=1	j=1	PROPN
ejpam-5764	264	12	vaj	vaj	NOUN
ejpam-5764	264	13	.	.	PUNCT
ejpam-5764	265	1	thus	thus	ADV
ejpam-5764	265	2	k1	k1	NOUN
ejpam-5764	265	3	is	be	AUX
ejpam-5764	265	4	an	an	DET
ejpam-5764	265	5	element	element	NOUN
ejpam-5764	265	6	of	of	ADP
ejpam-5764	265	7	u1	u1	NOUN
ejpam-5764	265	8	which	which	PRON
ejpam-5764	265	9	is	be	AUX
ejpam-5764	265	10	a	a	DET
ejpam-5764	265	11	ϑi	ϑi	NOUN
ejpam-5764	265	12	open	open	ADJ
ejpam-5764	265	13	set	set	NOUN
ejpam-5764	265	14	and	and	CCONJ
ejpam-5764	265	15	similarly	similarly	ADV
ejpam-5764	265	16	for	for	ADP
ejpam-5764	265	17	k2	k2	NOUN
ejpam-5764	265	18	and	and	CCONJ
ejpam-5764	265	19	u2	u2	PROPN
ejpam-5764	265	20	.	.	PUNCT
ejpam-5764	266	1	furthermore	furthermore	ADV
ejpam-5764	266	2	,	,	PUNCT
ejpam-5764	266	3	u1	u1	NOUN
ejpam-5764	266	4	∩	∩	ADJ
ejpam-5764	266	5	u2	u2	NOUN
ejpam-5764	266	6	=	=	NOUN
ejpam-5764	266	7	∅	∅	NOUN
ejpam-5764	266	8	because	because	SCONJ
ejpam-5764	266	9	uaj	uaj	ADJ
ejpam-5764	266	10	∩	∩	ADJ
ejpam-5764	266	11	vaj	vaj	NOUN
ejpam-5764	266	12	=	=	PUNCT
ejpam-5764	266	13	∅	∅	NOUN
ejpam-5764	266	14	for	for	ADP
ejpam-5764	266	15	each	each	PRON
ejpam-5764	266	16	j	j	PROPN
ejpam-5764	266	17	=	=	SYM
ejpam-5764	266	18	1	1	NUM
ejpam-5764	266	19	,	,	PUNCT
ejpam-5764	266	20	2	2	NUM
ejpam-5764	266	21	,	,	PUNCT
ejpam-5764	266	22	.	.	PUNCT
ejpam-5764	266	23	.	.	PUNCT
ejpam-5764	266	24	.	.	PUNCT
ejpam-5764	267	1	,	,	PUNCT
ejpam-5764	267	2	m.	m.	NOUN
ejpam-5764	267	3	j.	j.	PROPN
ejpam-5764	267	4	oudetallah	oudetallah	PROPN
ejpam-5764	267	5	et	et	PROPN
ejpam-5764	267	6	al	al	PROPN
ejpam-5764	267	7	.	.	PUNCT
ejpam-5764	267	8	/	/	SYM
ejpam-5764	267	9	eur	eur	PROPN
ejpam-5764	267	10	.	.	PUNCT
ejpam-5764	268	1	j.	j.	PROPN
ejpam-5764	268	2	pure	pure	PROPN
ejpam-5764	268	3	appl	appl	PROPN
ejpam-5764	268	4	.	.	PROPN
ejpam-5764	268	5	math	math	PROPN
ejpam-5764	268	6	,	,	PUNCT
ejpam-5764	268	7	18	18	NUM
ejpam-5764	268	8	(	(	PUNCT
ejpam-5764	268	9	2	2	NUM
ejpam-5764	268	10	)	)	PUNCT
ejpam-5764	268	11	(	(	PUNCT
ejpam-5764	268	12	2025	2025	NUM
ejpam-5764	268	13	)	)	PUNCT
ejpam-5764	268	14	,	,	PUNCT
ejpam-5764	268	15	5764	5764	NUM
ejpam-5764	268	16	10	10	NUM
ejpam-5764	268	17	of	of	ADP
ejpam-5764	268	18	11	11	NUM
ejpam-5764	268	19	4	4	NUM
ejpam-5764	268	20	.	.	PUNCT
ejpam-5764	269	1	tri	tri	ADJ
ejpam-5764	269	2	-	-	ADJ
ejpam-5764	269	3	locally	locally	ADV
ejpam-5764	269	4	metacompact	metacompact	ADJ
ejpam-5764	269	5	spaces	space	NOUN
ejpam-5764	269	6	in	in	ADP
ejpam-5764	269	7	this	this	DET
ejpam-5764	269	8	part	part	NOUN
ejpam-5764	269	9	,	,	PUNCT
ejpam-5764	269	10	we	we	PRON
ejpam-5764	269	11	raise	raise	VERB
ejpam-5764	269	12	the	the	DET
ejpam-5764	269	13	idea	idea	NOUN
ejpam-5764	269	14	of	of	ADP
ejpam-5764	269	15	metacompactness	metacompactness	NOUN
ejpam-5764	269	16	to	to	ADP
ejpam-5764	269	17	tri	tri	VERB
ejpam-5764	269	18	topological	topological	ADJ
ejpam-5764	269	19	space	space	NOUN
ejpam-5764	269	20	and	and	CCONJ
ejpam-5764	269	21	discuss	discuss	VERB
ejpam-5764	269	22	the	the	DET
ejpam-5764	269	23	connection	connection	NOUN
ejpam-5764	269	24	of	of	ADP
ejpam-5764	269	25	tri	tri	PROPN
ejpam-5764	269	26	locally	locally	ADV
ejpam-5764	269	27	compact	compact	ADJ
ejpam-5764	269	28	and	and	CCONJ
ejpam-5764	269	29	tri	tri	VERB
ejpam-5764	269	30	locally	locally	ADV
ejpam-5764	269	31	metacompact	metacompact	NOUN
ejpam-5764	269	32	.	.	PUNCT
ejpam-5764	270	1	definition	definition	NOUN
ejpam-5764	270	2	22	22	NUM
ejpam-5764	270	3	.	.	PUNCT
ejpam-5764	271	1	a	a	DET
ejpam-5764	271	2	family	family	NOUN
ejpam-5764	271	3	u	u	NOUN
ejpam-5764	271	4	of	of	ADP
ejpam-5764	271	5	subsets	subset	NOUN
ejpam-5764	271	6	of	of	ADP
ejpam-5764	271	7	a	a	DET
ejpam-5764	271	8	tri	tri	ADJ
ejpam-5764	271	9	-	-	ADJ
ejpam-5764	271	10	topological	topological	ADJ
ejpam-5764	271	11	space	space	NOUN
ejpam-5764	271	12	(	(	PUNCT
ejpam-5764	271	13	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	271	14	,	,	PUNCT
ejpam-5764	271	15	ϑ2	ϑ2	PROPN
ejpam-5764	271	16	,	,	PUNCT
ejpam-5764	271	17	ϑ3	ϑ3	PROPN
ejpam-5764	271	18	)	)	PUNCT
ejpam-5764	271	19	is	be	AUX
ejpam-5764	271	20	called	call	VERB
ejpam-5764	271	21	point	point	NOUN
ejpam-5764	271	22	-	-	PUNCT
ejpam-5764	271	23	finite	finite	NOUN
ejpam-5764	271	24	if	if	SCONJ
ejpam-5764	271	25	each	each	DET
ejpam-5764	271	26	point	point	NOUN
ejpam-5764	271	27	of	of	ADP
ejpam-5764	271	28	x	x	PUNCT
ejpam-5764	271	29	belongs	belong	VERB
ejpam-5764	271	30	to	to	ADP
ejpam-5764	271	31	at	at	ADP
ejpam-5764	271	32	most	most	ADV
ejpam-5764	271	33	finitely	finitely	ADV
ejpam-5764	271	34	many	many	ADJ
ejpam-5764	271	35	members	member	NOUN
ejpam-5764	271	36	of	of	ADP
ejpam-5764	271	37	u	u	PROPN
ejpam-5764	271	38	.	.	PUNCT
ejpam-5764	272	1	definition	definition	NOUN
ejpam-5764	272	2	23	23	NUM
ejpam-5764	272	3	.	.	PUNCT
ejpam-5764	273	1	a	a	DET
ejpam-5764	273	2	tri	tri	ADJ
ejpam-5764	273	3	-	-	ADJ
ejpam-5764	273	4	topological	topological	ADJ
ejpam-5764	273	5	space	space	NOUN
ejpam-5764	273	6	(	(	PUNCT
ejpam-5764	273	7	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	273	8	,	,	PUNCT
ejpam-5764	273	9	ϑ2	ϑ2	PROPN
ejpam-5764	273	10	,	,	PUNCT
ejpam-5764	273	11	ϑ3	ϑ3	PROPN
ejpam-5764	273	12	)	)	PUNCT
ejpam-5764	273	13	is	be	AUX
ejpam-5764	273	14	tri	tri	ADJ
ejpam-5764	273	15	-	-	ADJ
ejpam-5764	273	16	metacompact	metacompact	ADJ
ejpam-5764	273	17	if	if	SCONJ
ejpam-5764	273	18	every	every	DET
ejpam-5764	273	19	open	open	ADJ
ejpam-5764	273	20	cover	cover	NOUN
ejpam-5764	273	21	of	of	ADP
ejpam-5764	273	22	x	x	PUNCT
ejpam-5764	273	23	has	have	VERB
ejpam-5764	273	24	a	a	DET
ejpam-5764	273	25	point	point	NOUN
ejpam-5764	273	26	-	-	PUNCT
ejpam-5764	273	27	finite	finite	ADJ
ejpam-5764	273	28	open	open	ADJ
ejpam-5764	273	29	refinement	refinement	NOUN
ejpam-5764	273	30	.	.	PUNCT
ejpam-5764	274	1	definition	definition	NOUN
ejpam-5764	274	2	24	24	NUM
ejpam-5764	274	3	.	.	PUNCT
ejpam-5764	275	1	a	a	DET
ejpam-5764	275	2	tri	tri	ADJ
ejpam-5764	275	3	-	-	ADJ
ejpam-5764	275	4	topological	topological	ADJ
ejpam-5764	275	5	space	space	NOUN
ejpam-5764	275	6	(	(	PUNCT
ejpam-5764	275	7	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	275	8	,	,	PUNCT
ejpam-5764	275	9	ϑ2	ϑ2	PROPN
ejpam-5764	275	10	,	,	PUNCT
ejpam-5764	275	11	ϑ3	ϑ3	PROPN
ejpam-5764	275	12	)	)	PUNCT
ejpam-5764	275	13	is	be	AUX
ejpam-5764	275	14	tri	tri	ADJ
ejpam-5764	275	15	-	-	ADJ
ejpam-5764	275	16	locally	locally	ADV
ejpam-5764	275	17	metacompact	metacompact	NOUN
ejpam-5764	275	18	if	if	SCONJ
ejpam-5764	275	19	for	for	ADP
ejpam-5764	275	20	every	every	DET
ejpam-5764	275	21	point	point	NOUN
ejpam-5764	275	22	a	a	DET
ejpam-5764	275	23	∈	∈	NOUN
ejpam-5764	275	24	x	x	NOUN
ejpam-5764	275	25	,	,	PUNCT
ejpam-5764	275	26	there	there	PRON
ejpam-5764	275	27	exists	exist	VERB
ejpam-5764	275	28	a	a	DET
ejpam-5764	275	29	ϑi	ϑi	NOUN
ejpam-5764	275	30	-	-	PUNCT
ejpam-5764	275	31	open	open	NOUN
ejpam-5764	275	32	set	set	VERB
ejpam-5764	275	33	ua	ua	NOUN
ejpam-5764	275	34	containing	contain	VERB
ejpam-5764	275	35	a	a	DET
ejpam-5764	275	36	such	such	ADJ
ejpam-5764	275	37	that	that	SCONJ
ejpam-5764	275	38	ua	ua	PROPN
ejpam-5764	275	39	is	be	AUX
ejpam-5764	275	40	tri	tri	ADJ
ejpam-5764	275	41	-	-	ADJ
ejpam-5764	275	42	metacompact	metacompact	ADJ
ejpam-5764	275	43	.	.	PUNCT
ejpam-5764	276	1	theorem	theorem	VERB
ejpam-5764	276	2	18	18	NUM
ejpam-5764	276	3	.	.	PUNCT
ejpam-5764	277	1	every	every	DET
ejpam-5764	277	2	tri	tri	ADJ
ejpam-5764	277	3	-	-	ADJ
ejpam-5764	277	4	locally	locally	ADV
ejpam-5764	277	5	compact	compact	ADJ
ejpam-5764	277	6	space	space	NOUN
ejpam-5764	277	7	is	be	AUX
ejpam-5764	277	8	tri	tri	ADJ
ejpam-5764	277	9	-	-	ADJ
ejpam-5764	277	10	locally	locally	ADV
ejpam-5764	277	11	metacompact	metacompact	NOUN
ejpam-5764	277	12	.	.	PUNCT
ejpam-5764	278	1	proof	proof	NOUN
ejpam-5764	278	2	.	.	PUNCT
ejpam-5764	279	1	let	let	AUX
ejpam-5764	279	2	(	(	PUNCT
ejpam-5764	279	3	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	279	4	,	,	PUNCT
ejpam-5764	279	5	ϑ2	ϑ2	PROPN
ejpam-5764	279	6	,	,	PUNCT
ejpam-5764	279	7	ϑ3	ϑ3	PROPN
ejpam-5764	279	8	)	)	PUNCT
ejpam-5764	279	9	be	be	AUX
ejpam-5764	279	10	a	a	DET
ejpam-5764	279	11	tri	tri	ADJ
ejpam-5764	279	12	-	-	ADJ
ejpam-5764	279	13	locally	locally	ADV
ejpam-5764	279	14	compact	compact	ADJ
ejpam-5764	279	15	space	space	NOUN
ejpam-5764	279	16	.	.	PUNCT
ejpam-5764	280	1	for	for	ADP
ejpam-5764	280	2	every	every	DET
ejpam-5764	280	3	point	point	NOUN
ejpam-5764	280	4	a	a	DET
ejpam-5764	280	5	∈	∈	NOUN
ejpam-5764	280	6	x	x	NOUN
ejpam-5764	280	7	,	,	PUNCT
ejpam-5764	280	8	there	there	PRON
ejpam-5764	280	9	exists	exist	VERB
ejpam-5764	280	10	a	a	DET
ejpam-5764	280	11	ϑi	ϑi	NOUN
ejpam-5764	280	12	-	-	PUNCT
ejpam-5764	280	13	open	open	NOUN
ejpam-5764	280	14	set	set	VERB
ejpam-5764	280	15	ua	ua	NOUN
ejpam-5764	280	16	containing	contain	VERB
ejpam-5764	280	17	a	a	DET
ejpam-5764	280	18	such	such	ADJ
ejpam-5764	280	19	that	that	SCONJ
ejpam-5764	280	20	ua	ua	PROPN
ejpam-5764	280	21	is	be	AUX
ejpam-5764	280	22	tri	tri	ADJ
ejpam-5764	280	23	-	-	ADJ
ejpam-5764	280	24	compact	compact	ADJ
ejpam-5764	280	25	.	.	PUNCT
ejpam-5764	281	1	since	since	SCONJ
ejpam-5764	281	2	every	every	DET
ejpam-5764	281	3	tri	tri	ADJ
ejpam-5764	281	4	-	-	ADJ
ejpam-5764	281	5	compact	compact	ADJ
ejpam-5764	281	6	space	space	NOUN
ejpam-5764	281	7	is	be	AUX
ejpam-5764	281	8	tri	tri	ADJ
ejpam-5764	281	9	-	-	ADJ
ejpam-5764	281	10	metacompact	metacompact	ADJ
ejpam-5764	281	11	,	,	PUNCT
ejpam-5764	281	12	ua	ua	PROPN
ejpam-5764	281	13	is	be	AUX
ejpam-5764	281	14	tri	tri	ADJ
ejpam-5764	281	15	-	-	ADJ
ejpam-5764	281	16	metacompact	metacompact	ADJ
ejpam-5764	281	17	.	.	PUNCT
ejpam-5764	282	1	therefore	therefore	ADV
ejpam-5764	282	2	,	,	PUNCT
ejpam-5764	282	3	(	(	PUNCT
ejpam-5764	282	4	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	282	5	,	,	PUNCT
ejpam-5764	282	6	ϑ2	ϑ2	PROPN
ejpam-5764	282	7	,	,	PUNCT
ejpam-5764	282	8	ϑ3	ϑ3	PROPN
ejpam-5764	282	9	)	)	PUNCT
ejpam-5764	282	10	is	be	AUX
ejpam-5764	282	11	tri	tri	ADJ
ejpam-5764	282	12	-	-	ADJ
ejpam-5764	282	13	locally	locally	ADV
ejpam-5764	282	14	metacompact	metacompact	NOUN
ejpam-5764	282	15	.	.	PUNCT
ejpam-5764	283	1	theorem	theorem	NOUN
ejpam-5764	283	2	19	19	NUM
ejpam-5764	283	3	.	.	PUNCT
ejpam-5764	284	1	let	let	AUX
ejpam-5764	284	2	(	(	PUNCT
ejpam-5764	284	3	x,ϑ1	x,ϑ1	PROPN
ejpam-5764	284	4	,	,	PUNCT
ejpam-5764	284	5	ϑ2	ϑ2	PROPN
ejpam-5764	284	6	,	,	PUNCT
ejpam-5764	284	7	ϑ3	ϑ3	PROPN
ejpam-5764	284	8	)	)	PUNCT
ejpam-5764	284	9	be	be	AUX
ejpam-5764	284	10	a	a	DET
ejpam-5764	284	11	tri	tri	ADJ
ejpam-5764	284	12	-	-	ADJ
ejpam-5764	284	13	topological	topological	ADJ
ejpam-5764	284	14	space	space	NOUN
ejpam-5764	284	15	.	.	PUNCT
ejpam-5764	285	1	if	if	SCONJ
ejpam-5764	285	2	x	x	PRON
ejpam-5764	285	3	is	be	AUX
ejpam-5764	285	4	tri	tri	ADJ
ejpam-5764	285	5	-	-	ADJ
ejpam-5764	285	6	locally	locally	ADV
ejpam-5764	285	7	metacompact	metacompact	ADJ
ejpam-5764	285	8	and	and	CCONJ
ejpam-5764	285	9	tri	tri	ADJ
ejpam-5764	285	10	-	-	NOUN
ejpam-5764	285	11	t3	t3	ADJ
ejpam-5764	285	12	,	,	PUNCT
ejpam-5764	285	13	then	then	ADV
ejpam-5764	285	14	for	for	ADP
ejpam-5764	285	15	any	any	DET
ejpam-5764	285	16	tri	tri	ADJ
ejpam-5764	285	17	-	-	ADJ
ejpam-5764	285	18	metacompact	metacompact	ADJ
ejpam-5764	285	19	set	set	NOUN
ejpam-5764	285	20	m	m	PROPN
ejpam-5764	285	21	and	and	CCONJ
ejpam-5764	285	22	any	any	DET
ejpam-5764	285	23	ϑi	ϑi	NOUN
ejpam-5764	285	24	-	-	PUNCT
ejpam-5764	285	25	open	open	NOUN
ejpam-5764	285	26	set	set	VERB
ejpam-5764	285	27	u	u	NOUN
ejpam-5764	285	28	containing	contain	VERB
ejpam-5764	285	29	m	m	PRON
ejpam-5764	285	30	,	,	PUNCT
ejpam-5764	285	31	there	there	PRON
ejpam-5764	285	32	exists	exist	VERB
ejpam-5764	285	33	a	a	DET
ejpam-5764	285	34	ϑi	ϑi	NOUN
ejpam-5764	285	35	-	-	PUNCT
ejpam-5764	285	36	open	open	NOUN
ejpam-5764	285	37	set	set	VERB
ejpam-5764	285	38	v	v	ADP
ejpam-5764	285	39	such	such	ADJ
ejpam-5764	285	40	that	that	SCONJ
ejpam-5764	285	41	m	m	PROPN
ejpam-5764	285	42	⊂	⊂	PROPN
ejpam-5764	285	43	v	v	ADP
ejpam-5764	285	44	⊂	⊂	PROPN
ejpam-5764	285	45	v	v	ADP
ejpam-5764	285	46	⊂	⊂	PROPN
ejpam-5764	285	47	u	u	PROPN
ejpam-5764	285	48	and	and	CCONJ
ejpam-5764	285	49	v	v	NOUN
ejpam-5764	285	50	is	be	AUX
ejpam-5764	285	51	tri	tri	ADJ
ejpam-5764	285	52	-	-	ADJ
ejpam-5764	285	53	metacompact	metacompact	ADJ
ejpam-5764	285	54	.	.	PUNCT
ejpam-5764	286	1	proof	proof	NOUN
ejpam-5764	286	2	.	.	PUNCT
ejpam-5764	287	1	let	let	VERB
ejpam-5764	287	2	m	m	PRON
ejpam-5764	287	3	be	be	AUX
ejpam-5764	287	4	a	a	DET
ejpam-5764	287	5	tri	tri	ADJ
ejpam-5764	287	6	-	-	ADJ
ejpam-5764	287	7	metacompact	metacompact	ADJ
ejpam-5764	287	8	set	set	NOUN
ejpam-5764	287	9	and	and	CCONJ
ejpam-5764	287	10	u	u	PRON
ejpam-5764	287	11	be	be	VERB
ejpam-5764	287	12	a	a	DET
ejpam-5764	287	13	ϑi	ϑi	NOUN
ejpam-5764	287	14	-	-	PUNCT
ejpam-5764	287	15	open	open	NOUN
ejpam-5764	287	16	set	set	NOUN
ejpam-5764	287	17	containing	contain	VERB
ejpam-5764	287	18	m	m	PRON
ejpam-5764	287	19	.	.	PUNCT
ejpam-5764	288	1	for	for	ADP
ejpam-5764	288	2	each	each	PRON
ejpam-5764	288	3	a	a	DET
ejpam-5764	288	4	∈	∈	ADJ
ejpam-5764	288	5	m	m	VERB
ejpam-5764	288	6	,	,	PUNCT
ejpam-5764	288	7	by	by	ADP
ejpam-5764	288	8	tri	tri	ADJ
ejpam-5764	288	9	-	-	ADJ
ejpam-5764	288	10	local	local	ADJ
ejpam-5764	288	11	metacompactness	metacompactness	NOUN
ejpam-5764	288	12	,	,	PUNCT
ejpam-5764	288	13	there	there	PRON
ejpam-5764	288	14	exists	exist	VERB
ejpam-5764	288	15	a	a	DET
ejpam-5764	288	16	ϑi	ϑi	NOUN
ejpam-5764	288	17	-	-	PUNCT
ejpam-5764	288	18	open	open	NOUN
ejpam-5764	288	19	set	set	VERB
ejpam-5764	288	20	va	va	NOUN
ejpam-5764	288	21	such	such	ADJ
ejpam-5764	288	22	that	that	SCONJ
ejpam-5764	288	23	a	a	DET
ejpam-5764	288	24	∈	∈	PROPN
ejpam-5764	288	25	va	va	PROPN
ejpam-5764	288	26	⊂	⊂	PROPN
ejpam-5764	288	27	va	va	PROPN
ejpam-5764	289	1	⊂	⊂	PROPN
ejpam-5764	289	2	u	u	PROPN
ejpam-5764	289	3	and	and	CCONJ
ejpam-5764	289	4	va	va	PROPN
ejpam-5764	289	5	is	be	AUX
ejpam-5764	289	6	tri	tri	ADJ
ejpam-5764	289	7	-	-	ADJ
ejpam-5764	289	8	metacompact	metacompact	ADJ
ejpam-5764	289	9	.	.	PUNCT
ejpam-5764	290	1	the	the	DET
ejpam-5764	290	2	collection	collection	NOUN
ejpam-5764	290	3	{	{	PUNCT
ejpam-5764	290	4	va	va	NOUN
ejpam-5764	290	5	:	:	PUNCT
ejpam-5764	290	6	a	a	DET
ejpam-5764	290	7	∈	∈	PROPN
ejpam-5764	290	8	m	m	NOUN
ejpam-5764	290	9	}	}	PUNCT
ejpam-5764	290	10	forms	form	VERB
ejpam-5764	290	11	an	an	DET
ejpam-5764	290	12	open	open	ADJ
ejpam-5764	290	13	cover	cover	NOUN
ejpam-5764	290	14	of	of	ADP
ejpam-5764	290	15	m	m	PROPN
ejpam-5764	290	16	.	.	PUNCT
ejpam-5764	291	1	since	since	SCONJ
ejpam-5764	291	2	m	m	PROPN
ejpam-5764	291	3	is	be	AUX
ejpam-5764	291	4	tri	tri	ADJ
ejpam-5764	291	5	-	-	ADJ
ejpam-5764	291	6	metacompact	metacompact	ADJ
ejpam-5764	291	7	,	,	PUNCT
ejpam-5764	291	8	there	there	PRON
ejpam-5764	291	9	exists	exist	VERB
ejpam-5764	291	10	a	a	DET
ejpam-5764	291	11	point	point	NOUN
ejpam-5764	291	12	-	-	PUNCT
ejpam-5764	291	13	finite	finite	ADJ
ejpam-5764	291	14	open	open	ADJ
ejpam-5764	291	15	refinement	refinement	NOUN
ejpam-5764	291	16	{	{	PUNCT
ejpam-5764	291	17	wα	wα	NOUN
ejpam-5764	291	18	:	:	PUNCT
ejpam-5764	291	19	α	α	PROPN
ejpam-5764	291	20	∈	∈	PROPN
ejpam-5764	291	21	λ	λ	NOUN
ejpam-5764	291	22	}	}	PUNCT
ejpam-5764	291	23	of	of	ADP
ejpam-5764	291	24	{	{	PUNCT
ejpam-5764	291	25	va	va	NOUN
ejpam-5764	291	26	:	:	PUNCT
ejpam-5764	291	27	a	a	DET
ejpam-5764	291	28	∈	∈	PROPN
ejpam-5764	291	29	m	m	NOUN
ejpam-5764	291	30	}	}	PUNCT
ejpam-5764	291	31	.	.	PUNCT
ejpam-5764	292	1	for	for	ADP
ejpam-5764	292	2	each	each	DET
ejpam-5764	292	3	α	α	PROPN
ejpam-5764	292	4	∈	∈	PROPN
ejpam-5764	292	5	λ	λ	NOUN
ejpam-5764	292	6	,	,	PUNCT
ejpam-5764	292	7	there	there	PRON
ejpam-5764	292	8	exists	exist	VERB
ejpam-5764	292	9	aα	aα	NOUN
ejpam-5764	292	10	∈	∈	NOUN
ejpam-5764	292	11	m	m	VERB
ejpam-5764	292	12	such	such	ADJ
ejpam-5764	292	13	that	that	DET
ejpam-5764	292	14	wα	wα	NOUN
ejpam-5764	292	15	⊂	⊂	PROPN
ejpam-5764	292	16	vaα	vaα	PROPN
ejpam-5764	292	17	.	.	PUNCT
ejpam-5764	293	1	let	let	VERB
ejpam-5764	293	2	v	v	NOUN
ejpam-5764	293	3	=	=	PUNCT
ejpam-5764	293	4	⋃	⋃	NOUN
ejpam-5764	293	5	α∈λwα	α∈λwα	PROPN
ejpam-5764	293	6	.	.	PUNCT
ejpam-5764	294	1	then	then	ADV
ejpam-5764	294	2	v	v	NOUN
ejpam-5764	294	3	is	be	AUX
ejpam-5764	294	4	a	a	DET
ejpam-5764	294	5	ϑi	ϑi	NOUN
ejpam-5764	294	6	-	-	PUNCT
ejpam-5764	294	7	open	open	NOUN
ejpam-5764	294	8	set	set	NOUN
ejpam-5764	294	9	and	and	CCONJ
ejpam-5764	294	10	m	m	PROPN
ejpam-5764	294	11	⊂	⊂	PROPN
ejpam-5764	294	12	v	v	ADP
ejpam-5764	294	13	⊂	⊂	PROPN
ejpam-5764	294	14	v	v	ADP
ejpam-5764	294	15	⊂	⊂	PROPN
ejpam-5764	294	16	⋃	⋃	PROPN
ejpam-5764	294	17	α∈λwα	α∈λwα	PROPN
ejpam-5764	294	18	⊂⋃	⊂⋃	X
ejpam-5764	294	19	α∈λ	α∈λ	NOUN
ejpam-5764	294	20	vaα	vaα	PROPN
ejpam-5764	295	1	⊂	⊂	PROPN
ejpam-5764	295	2	u	u	PROPN
ejpam-5764	295	3	.	.	PUNCT
ejpam-5764	296	1	since	since	SCONJ
ejpam-5764	296	2	each	each	DET
ejpam-5764	296	3	vaα	vaα	NOUN
ejpam-5764	296	4	is	be	AUX
ejpam-5764	296	5	tri	tri	ADJ
ejpam-5764	296	6	-	-	ADJ
ejpam-5764	296	7	metacompact	metacompact	ADJ
ejpam-5764	296	8	and	and	CCONJ
ejpam-5764	296	9	the	the	DET
ejpam-5764	296	10	collection	collection	NOUN
ejpam-5764	296	11	{	{	PUNCT
ejpam-5764	296	12	wα	wα	NOUN
ejpam-5764	296	13	:	:	PUNCT
ejpam-5764	296	14	α	α	PROPN
ejpam-5764	296	15	∈	∈	PROPN
ejpam-5764	296	16	λ	λ	NOUN
ejpam-5764	296	17	}	}	PUNCT
ejpam-5764	296	18	is	be	AUX
ejpam-5764	296	19	point	point	NOUN
ejpam-5764	296	20	-	-	PUNCT
ejpam-5764	296	21	finite	finite	ADJ
ejpam-5764	296	22	,	,	PUNCT
ejpam-5764	296	23	v	v	NOUN
ejpam-5764	296	24	is	be	AUX
ejpam-5764	296	25	tri	tri	ADJ
ejpam-5764	296	26	-	-	ADJ
ejpam-5764	296	27	metacompact	metacompact	ADJ
ejpam-5764	296	28	.	.	PUNCT
ejpam-5764	297	1	5	5	X
ejpam-5764	297	2	.	.	X
ejpam-5764	297	3	conclusion	conclusion	NOUN
ejpam-5764	297	4	in	in	ADP
ejpam-5764	297	5	this	this	DET
ejpam-5764	297	6	paper	paper	NOUN
ejpam-5764	297	7	,	,	PUNCT
ejpam-5764	297	8	we	we	PRON
ejpam-5764	297	9	have	have	AUX
ejpam-5764	297	10	introduced	introduce	VERB
ejpam-5764	297	11	and	and	CCONJ
ejpam-5764	297	12	studied	study	VERB
ejpam-5764	297	13	the	the	DET
ejpam-5764	297	14	concept	concept	NOUN
ejpam-5764	297	15	of	of	ADP
ejpam-5764	297	16	tri	tri	ADJ
ejpam-5764	297	17	-	-	ADJ
ejpam-5764	297	18	locally	locally	ADV
ejpam-5764	297	19	compact	compact	ADJ
ejpam-5764	297	20	spaces	space	NOUN
ejpam-5764	297	21	in	in	ADP
ejpam-5764	297	22	the	the	DET
ejpam-5764	297	23	context	context	NOUN
ejpam-5764	297	24	of	of	ADP
ejpam-5764	297	25	tri	tri	ADJ
ejpam-5764	297	26	-	-	ADJ
ejpam-5764	297	27	topological	topological	ADJ
ejpam-5764	297	28	spaces	space	NOUN
ejpam-5764	297	29	.	.	PUNCT
ejpam-5764	298	1	several	several	ADJ
ejpam-5764	298	2	fundamental	fundamental	ADJ
ejpam-5764	298	3	properties	property	NOUN
ejpam-5764	298	4	and	and	CCONJ
ejpam-5764	298	5	theorems	theorem	NOUN
ejpam-5764	298	6	regarding	regard	VERB
ejpam-5764	298	7	tri	tri	ADJ
ejpam-5764	298	8	-	-	ADJ
ejpam-5764	298	9	locally	locally	ADV
ejpam-5764	298	10	compact	compact	ADJ
ejpam-5764	298	11	spaces	space	NOUN
ejpam-5764	298	12	are	be	AUX
ejpam-5764	298	13	proved	prove	VERB
ejpam-5764	298	14	and	and	CCONJ
ejpam-5764	298	15	their	their	PRON
ejpam-5764	298	16	connections	connection	NOUN
ejpam-5764	298	17	with	with	ADP
ejpam-5764	298	18	tri	tri	ADJ
ejpam-5764	298	19	regular	regular	ADJ
ejpam-5764	298	20	spaces	space	NOUN
ejpam-5764	298	21	and	and	CCONJ
ejpam-5764	298	22	tri	tri	ADJ
ejpam-5764	298	23	t3	t3	PROPN
ejpam-5764	298	24	spaces	space	NOUN
ejpam-5764	298	25	are	be	AUX
ejpam-5764	298	26	established	establish	VERB
ejpam-5764	298	27	.	.	PUNCT
ejpam-5764	299	1	for	for	ADP
ejpam-5764	299	2	that	that	PRON
ejpam-5764	299	3	,	,	PUNCT
ejpam-5764	299	4	we	we	PRON
ejpam-5764	299	5	have	have	AUX
ejpam-5764	299	6	also	also	ADV
ejpam-5764	299	7	shown	show	VERB
ejpam-5764	299	8	that	that	SCONJ
ejpam-5764	299	9	every	every	DET
ejpam-5764	299	10	tri	tri	ADJ
ejpam-5764	299	11	-	-	ADJ
ejpam-5764	299	12	locally	locally	ADV
ejpam-5764	299	13	compact	compact	ADJ
ejpam-5764	299	14	space	space	NOUN
ejpam-5764	299	15	is	be	AUX
ejpam-5764	299	16	tri	tri	ADJ
ejpam-5764	299	17	-	-	ADJ
ejpam-5764	299	18	locally	locally	ADV
ejpam-5764	299	19	metacompact	metacompact	NOUN
ejpam-5764	299	20	,	,	PUNCT
ejpam-5764	299	21	and	and	CCONJ
ejpam-5764	299	22	then	then	ADV
ejpam-5764	299	23	we	we	PRON
ejpam-5764	299	24	have	have	AUX
ejpam-5764	299	25	explored	explore	VERB
ejpam-5764	299	26	the	the	DET
ejpam-5764	299	27	connection	connection	NOUN
ejpam-5764	299	28	between	between	ADP
ejpam-5764	299	29	tri	tri	ADJ
ejpam-5764	299	30	-	-	ADJ
ejpam-5764	299	31	locally	locally	ADV
ejpam-5764	299	32	compact	compact	ADJ
ejpam-5764	299	33	spaces	space	NOUN
ejpam-5764	299	34	and	and	CCONJ
ejpam-5764	299	35	tri	tri	ADJ
ejpam-5764	299	36	-	-	ADJ
ejpam-5764	299	37	locally	locally	ADV
ejpam-5764	299	38	metacompact	metacompact	NOUN
ejpam-5764	299	39	spaces	space	NOUN
ejpam-5764	299	40	.	.	PUNCT
ejpam-5764	300	1	the	the	DET
ejpam-5764	300	2	behavior	behavior	NOUN
ejpam-5764	300	3	of	of	ADP
ejpam-5764	300	4	tri	tri	ADJ
ejpam-5764	300	5	-	-	ADJ
ejpam-5764	300	6	locally	locally	ADV
ejpam-5764	300	7	compact	compact	ADJ
ejpam-5764	300	8	spaces	space	NOUN
ejpam-5764	300	9	under	under	ADP
ejpam-5764	300	10	various	various	ADJ
ejpam-5764	300	11	continuous	continuous	ADJ
ejpam-5764	300	12	operations	operation	NOUN
ejpam-5764	300	13	,	,	PUNCT
ejpam-5764	300	14	such	such	ADJ
ejpam-5764	300	15	as	as	ADP
ejpam-5764	300	16	continuous	continuous	ADJ
ejpam-5764	300	17	mappings	mapping	NOUN
ejpam-5764	300	18	,	,	PUNCT
ejpam-5764	300	19	products	product	NOUN
ejpam-5764	300	20	,	,	PUNCT
ejpam-5764	300	21	and	and	CCONJ
ejpam-5764	300	22	quotients	quotient	NOUN
ejpam-5764	300	23	could	could	AUX
ejpam-5764	300	24	be	be	AUX
ejpam-5764	300	25	further	far	ADV
ejpam-5764	300	26	researched	research	VERB
ejpam-5764	300	27	.	.	PUNCT
ejpam-5764	301	1	one	one	PRON
ejpam-5764	301	2	could	could	AUX
ejpam-5764	301	3	also	also	ADV
ejpam-5764	301	4	j.	j.	PROPN
ejpam-5764	301	5	oudetallah	oudetallah	PROPN
ejpam-5764	301	6	et	et	PROPN
ejpam-5764	301	7	al	al	PROPN
ejpam-5764	301	8	.	.	PUNCT
ejpam-5764	301	9	/	/	SYM
ejpam-5764	301	10	eur	eur	PROPN
ejpam-5764	301	11	.	.	PUNCT
ejpam-5764	302	1	j.	j.	PROPN
ejpam-5764	302	2	pure	pure	PROPN
ejpam-5764	302	3	appl	appl	PROPN
ejpam-5764	302	4	.	.	PROPN
ejpam-5764	302	5	math	math	PROPN
ejpam-5764	302	6	,	,	PUNCT
ejpam-5764	302	7	18	18	NUM
ejpam-5764	302	8	(	(	PUNCT
ejpam-5764	302	9	2	2	NUM
ejpam-5764	302	10	)	)	PUNCT
ejpam-5764	302	11	(	(	PUNCT
ejpam-5764	302	12	2025	2025	NUM
ejpam-5764	302	13	)	)	PUNCT
ejpam-5764	302	14	,	,	PUNCT
ejpam-5764	302	15	5764	5764	NUM
ejpam-5764	302	16	11	11	NUM
ejpam-5764	302	17	of	of	ADP
ejpam-5764	302	18	11	11	NUM
ejpam-5764	302	19	explore	explore	VERB
ejpam-5764	302	20	the	the	DET
ejpam-5764	302	21	relationship	relationship	NOUN
ejpam-5764	302	22	between	between	ADP
ejpam-5764	302	23	tri	tri	ADJ
ejpam-5764	302	24	-	-	ADJ
ejpam-5764	302	25	locally	locally	ADV
ejpam-5764	302	26	compact	compact	ADJ
ejpam-5764	302	27	spaces	space	NOUN
ejpam-5764	302	28	and	and	CCONJ
ejpam-5764	302	29	other	other	ADJ
ejpam-5764	302	30	types	type	NOUN
ejpam-5764	302	31	of	of	ADP
ejpam-5764	302	32	tri	tri	ADJ
ejpam-5764	302	33	-	-	ADJ
ejpam-5764	302	34	topological	topological	ADJ
ejpam-5764	302	35	spaces	space	NOUN
ejpam-5764	302	36	in	in	ADP
ejpam-5764	302	37	general	general	ADJ
ejpam-5764	302	38	,	,	PUNCT
ejpam-5764	302	39	i.e.	i.e.	X
ejpam-5764	302	40	between	between	ADP
ejpam-5764	302	41	tri	tri	ADJ
ejpam-5764	302	42	-	-	ADJ
ejpam-5764	302	43	locally	locally	ADV
ejpam-5764	302	44	compact	compact	ADJ
ejpam-5764	302	45	spaces	space	NOUN
ejpam-5764	302	46	and	and	CCONJ
ejpam-5764	302	47	tri	tri	ADJ
ejpam-5764	302	48	-	-	ADJ
ejpam-5764	302	49	paracompact	paracompact	ADJ
ejpam-5764	302	50	spaces	space	NOUN
ejpam-5764	302	51	and	and	CCONJ
ejpam-5764	302	52	tri	tri	ADJ
ejpam-5764	302	53	-	-	ADJ
ejpam-5764	302	54	lindelf	lindelf	ADJ
ejpam-5764	302	55	spaces	space	NOUN
ejpam-5764	302	56	.	.	PUNCT
ejpam-5764	303	1	references	reference	NOUN
ejpam-5764	303	2	[	[	X
ejpam-5764	303	3	1	1	NUM
ejpam-5764	303	4	]	]	PUNCT
ejpam-5764	303	5	stephen	stephen	PROPN
ejpam-5764	303	6	willard	willard	PROPN
ejpam-5764	303	7	.	.	PUNCT
ejpam-5764	304	1	general	general	ADJ
ejpam-5764	304	2	topology	topology	PROPN
ejpam-5764	304	3	.	.	PUNCT
ejpam-5764	305	1	addison	addison	PROPN
ejpam-5764	305	2	-	-	PUNCT
ejpam-5764	305	3	wesley	wesley	PROPN
ejpam-5764	305	4	,	,	PUNCT
ejpam-5764	305	5	reading	reading	NOUN
ejpam-5764	305	6	,	,	PUNCT
ejpam-5764	305	7	ma	ma	PROPN
ejpam-5764	305	8	,	,	PUNCT
ejpam-5764	305	9	1970	1970	NUM
ejpam-5764	305	10	.	.	PUNCT
ejpam-5764	306	1	[	[	X
ejpam-5764	306	2	2	2	X
ejpam-5764	306	3	]	]	X
ejpam-5764	306	4	james	james	PROPN
ejpam-5764	306	5	r.	r.	PROPN
ejpam-5764	306	6	munkres	munkres	PROPN
ejpam-5764	306	7	.	.	PUNCT
ejpam-5764	307	1	topology	topology	NOUN
ejpam-5764	307	2	.	.	PUNCT
ejpam-5764	308	1	prentice	prentice	NOUN
ejpam-5764	308	2	-	-	PUNCT
ejpam-5764	308	3	hall	hall	PROPN
ejpam-5764	308	4	,	,	PUNCT
ejpam-5764	308	5	englewood	englewood	PROPN
ejpam-5764	308	6	cliffs	cliffs	PROPN
ejpam-5764	308	7	,	,	PUNCT
ejpam-5764	308	8	nj	nj	PROPN
ejpam-5764	308	9	,	,	PUNCT
ejpam-5764	308	10	2	2	NUM
ejpam-5764	308	11	edition	edition	NOUN
ejpam-5764	308	12	,	,	PUNCT
ejpam-5764	308	13	2000	2000	NUM
ejpam-5764	308	14	.	.	PUNCT
ejpam-5764	309	1	[	[	X
ejpam-5764	309	2	3	3	X
ejpam-5764	309	3	]	]	X
ejpam-5764	309	4	jun	jun	PROPN
ejpam-5764	309	5	-	-	PUNCT
ejpam-5764	309	6	iti	iti	PROPN
ejpam-5764	309	7	nagata	nagata	PROPN
ejpam-5764	309	8	.	.	PUNCT
ejpam-5764	310	1	modern	modern	ADJ
ejpam-5764	310	2	general	general	ADJ
ejpam-5764	310	3	topology	topology	NOUN
ejpam-5764	310	4	.	.	PUNCT
ejpam-5764	311	1	elsevier	elsevier	PROPN
ejpam-5764	311	2	,	,	PUNCT
ejpam-5764	311	3	amsterdam	amsterdam	PROPN
ejpam-5764	311	4	,	,	PUNCT
ejpam-5764	311	5	1985	1985	NUM
ejpam-5764	311	6	.	.	PUNCT
ejpam-5764	312	1	[	[	X
ejpam-5764	312	2	4	4	X
ejpam-5764	312	3	]	]	X
ejpam-5764	312	4	john	john	PROPN
ejpam-5764	312	5	l.	l.	PROPN
ejpam-5764	312	6	kelley	kelley	PROPN
ejpam-5764	312	7	.	.	PUNCT
ejpam-5764	312	8	general	general	ADJ
ejpam-5764	312	9	topology	topology	PROPN
ejpam-5764	312	10	.	.	PUNCT
ejpam-5764	313	1	graduate	graduate	NOUN
ejpam-5764	313	2	texts	text	NOUN
ejpam-5764	313	3	in	in	ADP
ejpam-5764	313	4	mathematics	mathematic	NOUN
ejpam-5764	313	5	,	,	PUNCT
ejpam-5764	313	6	27	27	NUM
ejpam-5764	313	7	,	,	PUNCT
ejpam-5764	313	8	1955	1955	NUM
ejpam-5764	313	9	.	.	PUNCT
ejpam-5764	314	1	[	[	X
ejpam-5764	314	2	5	5	X
ejpam-5764	314	3	]	]	PUNCT
ejpam-5764	314	4	yong	yong	PROPN
ejpam-5764	314	5	woon	woon	PROPN
ejpam-5764	314	6	kim	kim	PROPN
ejpam-5764	314	7	.	.	PUNCT
ejpam-5764	315	1	pairwise	pairwise	NOUN
ejpam-5764	315	2	compactness	compactness	NOUN
ejpam-5764	315	3	.	.	PUNCT
ejpam-5764	316	1	publicationes	publicatione	NOUN
ejpam-5764	316	2	mathematicae	mathematicae	PROPN
ejpam-5764	316	3	debrecen	debrecen	PROPN
ejpam-5764	316	4	,	,	PUNCT
ejpam-5764	316	5	15:87–90	15:87–90	NUM
ejpam-5764	316	6	,	,	PUNCT
ejpam-5764	316	7	1968	1968	NUM
ejpam-5764	316	8	.	.	PUNCT
ejpam-5764	317	1	[	[	X
ejpam-5764	317	2	6	6	NUM
ejpam-5764	317	3	]	]	PUNCT
ejpam-5764	317	4	norman	norman	PROPN
ejpam-5764	317	5	levine	levine	PROPN
ejpam-5764	317	6	.	.	PUNCT
ejpam-5764	318	1	semi	semi	ADJ
ejpam-5764	318	2	-	-	ADJ
ejpam-5764	318	3	open	open	ADJ
ejpam-5764	318	4	sets	set	NOUN
ejpam-5764	318	5	and	and	CCONJ
ejpam-5764	318	6	semi	semi	ADJ
ejpam-5764	318	7	-	-	NOUN
ejpam-5764	318	8	continuity	continuity	NOUN
ejpam-5764	318	9	in	in	ADP
ejpam-5764	318	10	topological	topological	ADJ
ejpam-5764	318	11	spaces	space	NOUN
ejpam-5764	318	12	.	.	PUNCT
ejpam-5764	319	1	the	the	DET
ejpam-5764	319	2	american	american	PROPN
ejpam-5764	319	3	mathematical	mathematical	PROPN
ejpam-5764	319	4	monthly	monthly	ADV
ejpam-5764	319	5	,	,	PUNCT
ejpam-5764	319	6	70(1):36–41	70(1):36–41	NUM
ejpam-5764	319	7	,	,	PUNCT
ejpam-5764	319	8	1963	1963	NUM
ejpam-5764	319	9	.	.	PUNCT
ejpam-5764	320	1	[	[	X
ejpam-5764	320	2	7	7	X
ejpam-5764	320	3	]	]	X
ejpam-5764	320	4	jamal	jamal	PROPN
ejpam-5764	320	5	oudetallah	oudetallah	PROPN
ejpam-5764	320	6	,	,	PUNCT
ejpam-5764	320	7	rehab	rehab	NOUN
ejpam-5764	320	8	alharbi	alharbi	NOUN
ejpam-5764	320	9	,	,	PUNCT
ejpam-5764	320	10	salsabiela	salsabiela	PROPN
ejpam-5764	320	11	rawashdeh	rawashdeh	PROPN
ejpam-5764	320	12	,	,	PUNCT
ejpam-5764	320	13	and	and	CCONJ
ejpam-5764	320	14	ala	ala	PROPN
ejpam-5764	320	15	amourah	amourah	PROPN
ejpam-5764	320	16	.	.	PUNCT
ejpam-5764	321	1	lindelöfness	lindelöfness	X
ejpam-5764	321	2	spaces	space	NOUN
ejpam-5764	321	3	in	in	ADP
ejpam-5764	321	4	n	n	PRON
ejpam-5764	321	5	th	th	CCONJ
ejpam-5764	321	6	topological	topological	ADJ
ejpam-5764	321	7	spaces	space	NOUN
ejpam-5764	321	8	.	.	PUNCT
ejpam-5764	322	1	international	international	ADJ
ejpam-5764	322	2	journal	journal	PROPN
ejpam-5764	322	3	of	of	ADP
ejpam-5764	322	4	neutrosophic	neutrosophic	ADJ
ejpam-5764	322	5	science	science	NOUN
ejpam-5764	322	6	,	,	PUNCT
ejpam-5764	322	7	25(3):206–216	25(3):206–216	NUM
ejpam-5764	322	8	,	,	PUNCT
ejpam-5764	322	9	2025	2025	NUM
ejpam-5764	322	10	.	.	PUNCT
ejpam-5764	323	1	[	[	X
ejpam-5764	323	2	8	8	NUM
ejpam-5764	323	3	]	]	ADJ
ejpam-5764	323	4	rehab	rehab	NOUN
ejpam-5764	323	5	alharbi	alharbi	NOUN
ejpam-5764	323	6	,	,	PUNCT
ejpam-5764	323	7	jamal	jamal	PROPN
ejpam-5764	323	8	oudetallah	oudetallah	PROPN
ejpam-5764	323	9	,	,	PUNCT
ejpam-5764	323	10	salsabiela	salsabiela	PROPN
ejpam-5764	323	11	rawashdeh	rawashdeh	NOUN
ejpam-5764	323	12	,	,	PUNCT
ejpam-5764	323	13	and	and	CCONJ
ejpam-5764	323	14	ala	ala	PROPN
ejpam-5764	323	15	amourah	amourah	PROPN
ejpam-5764	323	16	.	.	PUNCT
ejpam-5764	324	1	some	some	DET
ejpam-5764	324	2	types	type	NOUN
ejpam-5764	324	3	of	of	ADP
ejpam-5764	324	4	n	n	PRON
ejpam-5764	324	5	th	th	ADV
ejpam-5764	324	6	-	-	PUNCT
ejpam-5764	324	7	locally	locally	ADV
ejpam-5764	324	8	compactness	compactness	NOUN
ejpam-5764	324	9	spaces	space	NOUN
ejpam-5764	324	10	.	.	PUNCT
ejpam-5764	325	1	international	international	ADJ
ejpam-5764	325	2	journal	journal	PROPN
ejpam-5764	325	3	of	of	ADP
ejpam-5764	325	4	neutrosophic	neutrosophic	ADJ
ejpam-5764	325	5	science	science	NOUN
ejpam-5764	325	6	,	,	PUNCT
ejpam-5764	325	7	25(3):217–228	25(3):217–228	PROPN
ejpam-5764	325	8	,	,	PUNCT
ejpam-5764	325	9	2025	2025	NUM
ejpam-5764	325	10	.	.	PUNCT
ejpam-5764	326	1	[	[	X
ejpam-5764	326	2	9	9	NUM
ejpam-5764	326	3	]	]	X
ejpam-5764	326	4	jamal	jamal	PROPN
ejpam-5764	326	5	oudetallah	oudetallah	PROPN
ejpam-5764	326	6	,	,	PUNCT
ejpam-5764	326	7	mohammad	mohammad	PROPN
ejpam-5764	326	8	m.	m.	PROPN
ejpam-5764	326	9	rousan	rousan	PROPN
ejpam-5764	326	10	,	,	PUNCT
ejpam-5764	326	11	and	and	CCONJ
ejpam-5764	326	12	iqbal	iqbal	PROPN
ejpam-5764	326	13	m.	m.	PROPN
ejpam-5764	326	14	batiha	batiha	PROPN
ejpam-5764	326	15	.	.	PUNCT
ejpam-5764	327	1	on	on	ADP
ejpam-5764	327	2	dmetacompactness	dmetacompactness	NOUN
ejpam-5764	327	3	in	in	ADP
ejpam-5764	327	4	topological	topological	ADJ
ejpam-5764	327	5	spaces	space	NOUN
ejpam-5764	327	6	.	.	PUNCT
ejpam-5764	328	1	journal	journal	NOUN
ejpam-5764	328	2	of	of	ADP
ejpam-5764	328	3	applied	apply	VERB
ejpam-5764	328	4	mathematics	mathematics	PROPN
ejpam-5764	328	5	&	&	CCONJ
ejpam-5764	328	6	informatics	informatic	NOUN
ejpam-5764	328	7	,	,	PUNCT
ejpam-5764	328	8	39(5	39(5	PROPN
ejpam-5764	328	9	-	-	SYM
ejpam-5764	328	10	6):919–926	6):919–926	NUM
ejpam-5764	328	11	,	,	PUNCT
ejpam-5764	328	12	2021	2021	NUM
ejpam-5764	328	13	.	.	PUNCT
ejpam-5764	329	1	[	[	X
ejpam-5764	329	2	10	10	NUM
ejpam-5764	329	3	]	]	X
ejpam-5764	329	4	jamal	jamal	PROPN
ejpam-5764	329	5	oudetallah	oudetallah	PROPN
ejpam-5764	329	6	.	.	PUNCT
ejpam-5764	330	1	nearly	nearly	ADV
ejpam-5764	330	2	expandability	expandability	NOUN
ejpam-5764	330	3	in	in	ADP
ejpam-5764	330	4	bitopological	bitopological	ADJ
ejpam-5764	330	5	spaces	space	NOUN
ejpam-5764	330	6	.	.	PUNCT
ejpam-5764	331	1	advances	advance	NOUN
ejpam-5764	331	2	in	in	ADP
ejpam-5764	331	3	mathematics	mathematic	NOUN
ejpam-5764	331	4	:	:	PUNCT
ejpam-5764	331	5	scientific	scientific	ADJ
ejpam-5764	331	6	journal	journal	NOUN
ejpam-5764	331	7	,	,	PUNCT
ejpam-5764	331	8	10(2):705–712	10(2):705–712	ADJ
ejpam-5764	331	9	,	,	PUNCT
ejpam-5764	331	10	2021	2021	NUM
ejpam-5764	331	11	.	.	PUNCT
ejpam-5764	332	1	[	[	X
ejpam-5764	332	2	11	11	NUM
ejpam-5764	332	3	]	]	X
ejpam-5764	332	4	n.	n.	NOUN
ejpam-5764	332	5	alharbi	alharbi	PROPN
ejpam-5764	332	6	,	,	PUNCT
ejpam-5764	332	7	h.	h.	PROPN
ejpam-5764	332	8	shukri	shukri	PROPN
ejpam-5764	332	9	,	,	PUNCT
ejpam-5764	332	10	and	and	CCONJ
ejpam-5764	332	11	m.	m.	PROPN
ejpam-5764	332	12	s.	s.	PROPN
ejpam-5764	332	13	m.	m.	PROPN
ejpam-5764	332	14	noorani	noorani	PROPN
ejpam-5764	332	15	.	.	PUNCT
ejpam-5764	333	1	some	some	DET
ejpam-5764	333	2	properties	property	NOUN
ejpam-5764	333	3	of	of	ADP
ejpam-5764	333	4	pairwise	pairwise	NOUN
ejpam-5764	333	5	β	β	NOUN
ejpam-5764	333	6	-	-	NOUN
ejpam-5764	333	7	irresolute	irresolute	ADJ
ejpam-5764	333	8	and	and	CCONJ
ejpam-5764	333	9	strongly	strongly	ADV
ejpam-5764	333	10	β	β	ADJ
ejpam-5764	333	11	-	-	ADJ
ejpam-5764	333	12	irresolute	irresolute	ADJ
ejpam-5764	333	13	bitopological	bitopological	ADJ
ejpam-5764	333	14	mappings	mapping	NOUN
ejpam-5764	333	15	.	.	PUNCT
ejpam-5764	334	1	symmetry	symmetry	NOUN
ejpam-5764	334	2	,	,	PUNCT
ejpam-5764	334	3	15(2):375	15(2):375	NUM
ejpam-5764	334	4	,	,	PUNCT
ejpam-5764	334	5	2023	2023	NUM
ejpam-5764	334	6	.	.	PUNCT
ejpam-5764	335	1	[	[	X
ejpam-5764	335	2	12	12	NUM
ejpam-5764	335	3	]	]	PUNCT
ejpam-5764	335	4	s.	s.	PROPN
ejpam-5764	335	5	hnaif	hnaif	PROPN
ejpam-5764	335	6	,	,	PUNCT
ejpam-5764	335	7	m.	m.	NOUN
ejpam-5764	335	8	abu	abu	PROPN
ejpam-5764	335	9	-	-	PUNCT
ejpam-5764	335	10	saleem	saleem	PROPN
ejpam-5764	335	11	,	,	PUNCT
ejpam-5764	335	12	and	and	CCONJ
ejpam-5764	335	13	w.	w.	PROPN
ejpam-5764	335	14	shatanawi	shatanawi	PROPN
ejpam-5764	335	15	.	.	PUNCT
ejpam-5764	336	1	on	on	ADP
ejpam-5764	336	2	results	result	NOUN
ejpam-5764	336	3	of	of	ADP
ejpam-5764	336	4	relations	relation	NOUN
ejpam-5764	336	5	between	between	ADP
ejpam-5764	336	6	pairwise	pairwise	NOUN
ejpam-5764	336	7	almost	almost	ADV
ejpam-5764	336	8	s	s	NOUN
ejpam-5764	336	9	-	-	ADJ
ejpam-5764	336	10	regular	regular	ADJ
ejpam-5764	336	11	and	and	CCONJ
ejpam-5764	336	12	related	related	ADJ
ejpam-5764	336	13	bitopological	bitopological	ADJ
ejpam-5764	336	14	spaces	space	NOUN
ejpam-5764	336	15	.	.	PUNCT
ejpam-5764	337	1	journal	journal	NOUN
ejpam-5764	337	2	of	of	ADP
ejpam-5764	337	3	function	function	NOUN
ejpam-5764	337	4	spaces	space	NOUN
ejpam-5764	337	5	,	,	PUNCT
ejpam-5764	337	6	2021:5580806	2021:5580806	NOUN
ejpam-5764	337	7	,	,	PUNCT
ejpam-5764	337	8	2021	2021	NUM
ejpam-5764	337	9	.	.	PUNCT