id	sid	tid	token	lemma	pos
ejpam-5578	1	1	european	european	PROPN
ejpam-5578	1	2	journal	journal	PROPN
ejpam-5578	1	3	of	of	ADP
ejpam-5578	1	4	pure	pure	ADJ
ejpam-5578	1	5	and	and	CCONJ
ejpam-5578	1	6	applied	applied	ADJ
ejpam-5578	1	7	mathematics	mathematic	NOUN
ejpam-5578	1	8	2025	2025	NUM
ejpam-5578	1	9	,	,	PUNCT
ejpam-5578	1	10	vol	vol	NOUN
ejpam-5578	1	11	.	.	PROPN
ejpam-5578	1	12	18	18	NUM
ejpam-5578	1	13	,	,	PUNCT
ejpam-5578	1	14	issue	issue	NOUN
ejpam-5578	1	15	2	2	NUM
ejpam-5578	1	16	,	,	PUNCT
ejpam-5578	1	17	article	article	NOUN
ejpam-5578	1	18	number	number	NOUN
ejpam-5578	1	19	5578	5578	NUM
ejpam-5578	1	20	issn	issn	VERB
ejpam-5578	1	21	1307	1307	NUM
ejpam-5578	1	22	-	-	SYM
ejpam-5578	1	23	5543	5543	NUM
ejpam-5578	1	24	–	–	PUNCT
ejpam-5578	1	25	ejpam.com	ejpam.com	X
ejpam-5578	1	26	published	publish	VERB
ejpam-5578	1	27	by	by	ADP
ejpam-5578	1	28	new	new	PROPN
ejpam-5578	1	29	york	york	PROPN
ejpam-5578	1	30	business	business	PROPN
ejpam-5578	1	31	global	global	ADJ
ejpam-5578	1	32	some	some	DET
ejpam-5578	1	33	types	type	NOUN
ejpam-5578	1	34	of	of	ADP
ejpam-5578	1	35	tri	tri	ADJ
ejpam-5578	1	36	-	-	ADJ
ejpam-5578	1	37	lindelöfness	lindelöfness	ADJ
ejpam-5578	1	38	spaces	space	NOUN
ejpam-5578	1	39	jamal	jamal	PROPN
ejpam-5578	1	40	oudetallah1	oudetallah1	PROPN
ejpam-5578	1	41	,	,	PUNCT
ejpam-5578	1	42	rehab	rehab	NOUN
ejpam-5578	1	43	alharbi2,∗	alharbi2,∗	ADJ
ejpam-5578	1	44	,	,	PUNCT
ejpam-5578	1	45	iqbal	iqbal	PROPN
ejpam-5578	1	46	m.	m.	PROPN
ejpam-5578	1	47	batiha3,4	batiha3,4	PROPN
ejpam-5578	1	48	,	,	PUNCT
ejpam-5578	1	49	salsabiela	salsabiela	PROPN
ejpam-5578	1	50	rawashdeh5	rawashdeh5	PROPN
ejpam-5578	1	51	,	,	PUNCT
ejpam-5578	1	52	ala	ala	PROPN
ejpam-5578	1	53	amourah6,7	amourah6,7	PROPN
ejpam-5578	1	54	1	1	NUM
ejpam-5578	1	55	department	department	NOUN
ejpam-5578	1	56	of	of	ADP
ejpam-5578	1	57	mathematics	mathematic	NOUN
ejpam-5578	1	58	,	,	PUNCT
ejpam-5578	1	59	university	university	PROPN
ejpam-5578	1	60	of	of	ADP
ejpam-5578	1	61	petra	petra	PROPN
ejpam-5578	1	62	,	,	PUNCT
ejpam-5578	1	63	amman	amman	PROPN
ejpam-5578	1	64	,	,	PUNCT
ejpam-5578	1	65	11196	11196	NUM
ejpam-5578	1	66	,	,	PUNCT
ejpam-5578	1	67	jordan	jordan	PROPN
ejpam-5578	1	68	2	2	NUM
ejpam-5578	1	69	department	department	NOUN
ejpam-5578	1	70	of	of	ADP
ejpam-5578	1	71	mathematics	mathematics	PROPN
ejpam-5578	1	72	,	,	PUNCT
ejpam-5578	1	73	jazan	jazan	PROPN
ejpam-5578	1	74	university	university	PROPN
ejpam-5578	1	75	,	,	PUNCT
ejpam-5578	1	76	jazan	jazan	NOUN
ejpam-5578	1	77	2097	2097	NUM
ejpam-5578	1	78	,	,	PUNCT
ejpam-5578	1	79	saudi	saudi	PROPN
ejpam-5578	1	80	arabia	arabia	PROPN
ejpam-5578	1	81	3	3	NUM
ejpam-5578	1	82	department	department	NOUN
ejpam-5578	1	83	of	of	ADP
ejpam-5578	1	84	mathematics	mathematics	PROPN
ejpam-5578	1	85	,	,	PUNCT
ejpam-5578	1	86	al	al	PROPN
ejpam-5578	1	87	-	-	PROPN
ejpam-5578	1	88	zaytoonah	zaytoonah	PROPN
ejpam-5578	1	89	university	university	PROPN
ejpam-5578	1	90	of	of	ADP
ejpam-5578	1	91	jordan	jordan	PROPN
ejpam-5578	1	92	,	,	PUNCT
ejpam-5578	1	93	amman	amman	PROPN
ejpam-5578	1	94	11733	11733	NUM
ejpam-5578	1	95	,	,	PUNCT
ejpam-5578	1	96	jordan	jordan	PROPN
ejpam-5578	1	97	4	4	NUM
ejpam-5578	1	98	nonlinear	nonlinear	ADJ
ejpam-5578	1	99	dynamics	dynamic	NOUN
ejpam-5578	1	100	research	research	NOUN
ejpam-5578	1	101	center	center	NOUN
ejpam-5578	1	102	(	(	PUNCT
ejpam-5578	1	103	ndrc	ndrc	PROPN
ejpam-5578	1	104	)	)	PUNCT
ejpam-5578	1	105	,	,	PUNCT
ejpam-5578	1	106	ajman	ajman	PROPN
ejpam-5578	1	107	university	university	PROPN
ejpam-5578	1	108	,	,	PUNCT
ejpam-5578	1	109	ajman	ajman	PROPN
ejpam-5578	1	110	,	,	PUNCT
ejpam-5578	1	111	uae	uae	PROPN
ejpam-5578	1	112	5	5	NUM
ejpam-5578	1	113	department	department	NOUN
ejpam-5578	1	114	of	of	ADP
ejpam-5578	1	115	mathematics	mathematic	NOUN
ejpam-5578	1	116	,	,	PUNCT
ejpam-5578	1	117	irbid	irbid	ADJ
ejpam-5578	1	118	national	national	ADJ
ejpam-5578	1	119	university	university	PROPN
ejpam-5578	1	120	,	,	PUNCT
ejpam-5578	1	121	irbid	irbid	ADJ
ejpam-5578	1	122	2600	2600	NUM
ejpam-5578	1	123	,	,	PUNCT
ejpam-5578	1	124	jordan	jordan	PROPN
ejpam-5578	1	125	6	6	NUM
ejpam-5578	1	126	mathematics	mathematics	PROPN
ejpam-5578	1	127	education	education	NOUN
ejpam-5578	1	128	program	program	NOUN
ejpam-5578	1	129	,	,	PUNCT
ejpam-5578	1	130	faculty	faculty	NOUN
ejpam-5578	1	131	of	of	ADP
ejpam-5578	1	132	education	education	NOUN
ejpam-5578	1	133	and	and	CCONJ
ejpam-5578	1	134	arts	art	NOUN
ejpam-5578	1	135	,	,	PUNCT
ejpam-5578	1	136	sohar	sohar	PROPN
ejpam-5578	1	137	university	university	PROPN
ejpam-5578	1	138	,	,	PUNCT
ejpam-5578	1	139	sohar	sohar	PROPN
ejpam-5578	1	140	3111	3111	PROPN
ejpam-5578	1	141	,	,	PUNCT
ejpam-5578	1	142	oman	oman	NOUN
ejpam-5578	1	143	7	7	NUM
ejpam-5578	1	144	applied	apply	VERB
ejpam-5578	1	145	science	science	NOUN
ejpam-5578	1	146	research	research	NOUN
ejpam-5578	1	147	center	center	NOUN
ejpam-5578	1	148	,	,	PUNCT
ejpam-5578	1	149	applied	apply	VERB
ejpam-5578	1	150	science	science	NOUN
ejpam-5578	1	151	private	private	ADJ
ejpam-5578	1	152	university	university	NOUN
ejpam-5578	1	153	,	,	PUNCT
ejpam-5578	1	154	amman	amman	PROPN
ejpam-5578	1	155	,	,	PUNCT
ejpam-5578	1	156	jordan	jordan	PROPN
ejpam-5578	1	157	abstract	abstract	PROPN
ejpam-5578	1	158	.	.	PUNCT
ejpam-5578	2	1	in	in	ADP
ejpam-5578	2	2	this	this	DET
ejpam-5578	2	3	study	study	NOUN
ejpam-5578	2	4	,	,	PUNCT
ejpam-5578	2	5	we	we	PRON
ejpam-5578	2	6	investigate	investigate	VERB
ejpam-5578	2	7	the	the	DET
ejpam-5578	2	8	lindelöf	lindelöf	NOUN
ejpam-5578	2	9	property	property	NOUN
ejpam-5578	2	10	in	in	ADP
ejpam-5578	2	11	the	the	DET
ejpam-5578	2	12	context	context	NOUN
ejpam-5578	2	13	of	of	ADP
ejpam-5578	2	14	three	three	NUM
ejpam-5578	2	15	topologies	topology	NOUN
ejpam-5578	2	16	,	,	PUNCT
ejpam-5578	2	17	introducing	introduce	VERB
ejpam-5578	2	18	the	the	DET
ejpam-5578	2	19	concept	concept	NOUN
ejpam-5578	2	20	of	of	ADP
ejpam-5578	2	21	tri	tri	ADJ
ejpam-5578	2	22	-	-	NOUN
ejpam-5578	2	23	lindelöf	lindelöf	NOUN
ejpam-5578	2	24	spaces	space	NOUN
ejpam-5578	2	25	.	.	PUNCT
ejpam-5578	3	1	additionally	additionally	ADV
ejpam-5578	3	2	,	,	PUNCT
ejpam-5578	3	3	we	we	PRON
ejpam-5578	3	4	analyze	analyze	VERB
ejpam-5578	3	5	the	the	DET
ejpam-5578	3	6	characteristics	characteristic	NOUN
ejpam-5578	3	7	of	of	ADP
ejpam-5578	3	8	these	these	DET
ejpam-5578	3	9	spaces	space	NOUN
ejpam-5578	3	10	in	in	ADP
ejpam-5578	3	11	relation	relation	NOUN
ejpam-5578	3	12	to	to	ADP
ejpam-5578	3	13	traditional	traditional	ADJ
ejpam-5578	3	14	lindelöf	lindelöf	NOUN
ejpam-5578	3	15	spaces	space	VERB
ejpam-5578	3	16	.	.	PUNCT
ejpam-5578	4	1	several	several	ADJ
ejpam-5578	4	2	theoretical	theoretical	ADJ
ejpam-5578	4	3	results	result	NOUN
ejpam-5578	4	4	are	be	AUX
ejpam-5578	4	5	presented	present	VERB
ejpam-5578	4	6	and	and	CCONJ
ejpam-5578	4	7	proven	prove	VERB
ejpam-5578	4	8	,	,	PUNCT
ejpam-5578	4	9	extending	extend	VERB
ejpam-5578	4	10	various	various	ADJ
ejpam-5578	4	11	well	well	ADV
ejpam-5578	4	12	-	-	PUNCT
ejpam-5578	4	13	known	know	VERB
ejpam-5578	4	14	theorems	theorem	NOUN
ejpam-5578	4	15	on	on	ADP
ejpam-5578	4	16	lindelöf	lindelöf	NOUN
ejpam-5578	4	17	spaces	space	VERB
ejpam-5578	4	18	to	to	ADP
ejpam-5578	4	19	the	the	DET
ejpam-5578	4	20	setting	setting	NOUN
ejpam-5578	4	21	of	of	ADP
ejpam-5578	4	22	three	three	NUM
ejpam-5578	4	23	topologies	topology	NOUN
ejpam-5578	4	24	.	.	PUNCT
ejpam-5578	5	1	furthermore	furthermore	ADV
ejpam-5578	5	2	,	,	PUNCT
ejpam-5578	5	3	illustrative	illustrative	ADJ
ejpam-5578	5	4	examples	example	NOUN
ejpam-5578	5	5	are	be	AUX
ejpam-5578	5	6	provided	provide	VERB
ejpam-5578	5	7	to	to	PART
ejpam-5578	5	8	support	support	VERB
ejpam-5578	5	9	and	and	CCONJ
ejpam-5578	5	10	clarify	clarify	VERB
ejpam-5578	5	11	the	the	DET
ejpam-5578	5	12	findings	finding	NOUN
ejpam-5578	5	13	.	.	PUNCT
ejpam-5578	6	1	2020	2020	NUM
ejpam-5578	6	2	mathematics	mathematic	NOUN
ejpam-5578	6	3	subject	subject	NOUN
ejpam-5578	6	4	classifications	classification	NOUN
ejpam-5578	6	5	:	:	PUNCT
ejpam-5578	6	6	54a05	54a05	NUM
ejpam-5578	6	7	,	,	PUNCT
ejpam-5578	6	8	54d20	54d20	NUM
ejpam-5578	6	9	key	key	ADJ
ejpam-5578	6	10	words	word	NOUN
ejpam-5578	6	11	and	and	CCONJ
ejpam-5578	6	12	phrases	phrase	NOUN
ejpam-5578	6	13	:	:	PUNCT
ejpam-5578	6	14	tri	tri	ADJ
ejpam-5578	6	15	-	-	ADJ
ejpam-5578	6	16	topological	topological	ADJ
ejpam-5578	6	17	spaces	space	NOUN
ejpam-5578	6	18	,	,	PUNCT
ejpam-5578	6	19	lindelöf	lindelöf	PROPN
ejpam-5578	6	20	spaces	space	NOUN
ejpam-5578	6	21	,	,	PUNCT
ejpam-5578	6	22	tri	tri	PROPN
ejpam-5578	6	23	-	-	NOUN
ejpam-5578	6	24	lindelöf	lindelöf	NOUN
ejpam-5578	6	25	spaces	space	NOUN
ejpam-5578	6	26	,	,	PUNCT
ejpam-5578	6	27	trimetalindelöf	trimetalindelöf	NOUN
ejpam-5578	6	28	spaces	space	NOUN
ejpam-5578	6	29	,	,	PUNCT
ejpam-5578	6	30	compactness	compactness	NOUN
ejpam-5578	6	31	1	1	NUM
ejpam-5578	6	32	.	.	PUNCT
ejpam-5578	7	1	introduction	introduction	NOUN
ejpam-5578	7	2	topology	topology	NOUN
ejpam-5578	7	3	plays	play	VERB
ejpam-5578	7	4	a	a	DET
ejpam-5578	7	5	crucial	crucial	ADJ
ejpam-5578	7	6	role	role	NOUN
ejpam-5578	7	7	in	in	ADP
ejpam-5578	7	8	the	the	DET
ejpam-5578	7	9	analysis	analysis	NOUN
ejpam-5578	7	10	of	of	ADP
ejpam-5578	7	11	differential	differential	ADJ
ejpam-5578	7	12	equations	equation	NOUN
ejpam-5578	7	13	,	,	PUNCT
ejpam-5578	7	14	particularly	particularly	ADV
ejpam-5578	7	15	in	in	ADP
ejpam-5578	7	16	function	function	NOUN
ejpam-5578	7	17	spaces	space	NOUN
ejpam-5578	7	18	,	,	PUNCT
ejpam-5578	7	19	continuity	continuity	NOUN
ejpam-5578	7	20	,	,	PUNCT
ejpam-5578	7	21	and	and	CCONJ
ejpam-5578	7	22	stability	stability	NOUN
ejpam-5578	7	23	.	.	PUNCT
ejpam-5578	8	1	studies	study	NOUN
ejpam-5578	8	2	on	on	ADP
ejpam-5578	8	3	volterra	volterra	PROPN
ejpam-5578	8	4	integro	integro	PROPN
ejpam-5578	8	5	-	-	PUNCT
ejpam-5578	8	6	differential	differential	NOUN
ejpam-5578	8	7	equations	equation	NOUN
ejpam-5578	8	8	and	and	CCONJ
ejpam-5578	8	9	fractional	fractional	ADJ
ejpam-5578	8	10	differential	differential	ADJ
ejpam-5578	8	11	equations	equation	NOUN
ejpam-5578	8	12	rely	rely	VERB
ejpam-5578	8	13	on	on	ADP
ejpam-5578	8	14	topological	topological	ADJ
ejpam-5578	8	15	concepts	concept	NOUN
ejpam-5578	8	16	such	such	ADJ
ejpam-5578	8	17	as	as	ADP
ejpam-5578	8	18	compactness	compactness	NOUN
ejpam-5578	8	19	and	and	CCONJ
ejpam-5578	8	20	convergence	convergence	NOUN
ejpam-5578	8	21	to	to	PART
ejpam-5578	8	22	ensure	ensure	VERB
ejpam-5578	8	23	solution	solution	NOUN
ejpam-5578	8	24	existence	existence	NOUN
ejpam-5578	8	25	and	and	CCONJ
ejpam-5578	8	26	uniqueness	uniqueness	NOUN
ejpam-5578	8	27	[	[	X
ejpam-5578	8	28	1	1	NUM
ejpam-5578	8	29	,	,	PUNCT
ejpam-5578	8	30	2	2	NUM
ejpam-5578	8	31	]	]	PUNCT
ejpam-5578	8	32	.	.	PUNCT
ejpam-5578	9	1	additionally	additionally	ADV
ejpam-5578	9	2	,	,	PUNCT
ejpam-5578	9	3	understanding	understand	VERB
ejpam-5578	9	4	perturbation	perturbation	NOUN
ejpam-5578	9	5	effects	effect	NOUN
ejpam-5578	9	6	,	,	PUNCT
ejpam-5578	9	7	like	like	ADP
ejpam-5578	9	8	white	white	ADJ
ejpam-5578	9	9	noise	noise	NOUN
ejpam-5578	9	10	,	,	PUNCT
ejpam-5578	9	11	involves	involve	VERB
ejpam-5578	9	12	topological	topological	ADJ
ejpam-5578	9	13	stability	stability	NOUN
ejpam-5578	9	14	,	,	PUNCT
ejpam-5578	9	15	reinforcing	reinforce	VERB
ejpam-5578	9	16	the	the	DET
ejpam-5578	9	17	connection	connection	NOUN
ejpam-5578	9	18	between	between	ADP
ejpam-5578	9	19	topology	topology	NOUN
ejpam-5578	9	20	and	and	CCONJ
ejpam-5578	9	21	applied	apply	VERB
ejpam-5578	9	22	mathematics	mathematic	NOUN
ejpam-5578	10	1	[	[	X
ejpam-5578	10	2	3	3	NUM
ejpam-5578	10	3	]	]	PUNCT
ejpam-5578	10	4	.	.	PUNCT
ejpam-5578	11	1	topology	topology	NOUN
ejpam-5578	11	2	is	be	AUX
ejpam-5578	11	3	a	a	DET
ejpam-5578	11	4	branch	branch	NOUN
ejpam-5578	11	5	of	of	ADP
ejpam-5578	11	6	mathematics	mathematic	NOUN
ejpam-5578	11	7	that	that	PRON
ejpam-5578	11	8	studies	study	VERB
ejpam-5578	11	9	the	the	DET
ejpam-5578	11	10	properties	property	NOUN
ejpam-5578	11	11	of	of	ADP
ejpam-5578	11	12	spaces	space	NOUN
ejpam-5578	11	13	that	that	PRON
ejpam-5578	11	14	remain	remain	VERB
ejpam-5578	11	15	unchanged	unchanged	ADJ
ejpam-5578	11	16	under	under	ADP
ejpam-5578	11	17	continuous	continuous	ADJ
ejpam-5578	11	18	deformations	deformation	NOUN
ejpam-5578	11	19	such	such	ADJ
ejpam-5578	11	20	as	as	ADP
ejpam-5578	11	21	stretching	stretch	VERB
ejpam-5578	11	22	or	or	CCONJ
ejpam-5578	11	23	bending	bending	NOUN
ejpam-5578	11	24	.	.	PUNCT
ejpam-5578	12	1	it	it	PRON
ejpam-5578	12	2	focuses	focus	VERB
ejpam-5578	12	3	on	on	ADP
ejpam-5578	12	4	concepts	concept	NOUN
ejpam-5578	12	5	like	like	ADP
ejpam-5578	12	6	continuity	continuity	NOUN
ejpam-5578	12	7	,	,	PUNCT
ejpam-5578	12	8	connectedness	connectedness	NOUN
ejpam-5578	12	9	,	,	PUNCT
ejpam-5578	12	10	and	and	CCONJ
ejpam-5578	12	11	compactness	compactness	NOUN
ejpam-5578	12	12	,	,	PUNCT
ejpam-5578	12	13	providing	provide	VERB
ejpam-5578	12	14	a	a	DET
ejpam-5578	12	15	fundamental	fundamental	ADJ
ejpam-5578	12	16	∗corresponding	∗corresponding	NOUN
ejpam-5578	12	17	author	author	NOUN
ejpam-5578	12	18	.	.	PUNCT
ejpam-5578	13	1	doi	doi	NOUN
ejpam-5578	13	2	:	:	PUNCT
ejpam-5578	13	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5578	https://doi.org/10.29020/nybg.ejpam.v18i2.5578	ADP
ejpam-5578	13	4	email	email	NOUN
ejpam-5578	13	5	addresses	address	VERB
ejpam-5578	13	6	:	:	PUNCT
ejpam-5578	13	7	dr	dr	PROPN
ejpam-5578	13	8	jamal@inu.edu.jo	jamal@inu.edu.jo	PROPN
ejpam-5578	13	9	(	(	PUNCT
ejpam-5578	13	10	j.	j.	PROPN
ejpam-5578	13	11	oudetallah	oudetallah	PROPN
ejpam-5578	13	12	)	)	PUNCT
ejpam-5578	13	13	,	,	PUNCT
ejpam-5578	13	14	ralharbi@jazanu.edu.sa	ralharbi@jazanu.edu.sa	NOUN
ejpam-5578	13	15	(	(	PUNCT
ejpam-5578	13	16	r.	r.	PROPN
ejpam-5578	13	17	alharbi	alharbi	PROPN
ejpam-5578	13	18	)	)	PUNCT
ejpam-5578	13	19	,	,	PUNCT
ejpam-5578	13	20	i.batiha@zuj.edu.jo	i.batiha@zuj.edu.jo	NOUN
ejpam-5578	13	21	(	(	PUNCT
ejpam-5578	13	22	i.	i.	PROPN
ejpam-5578	13	23	m.	m.	PROPN
ejpam-5578	13	24	batiha	batiha	PROPN
ejpam-5578	13	25	)	)	PUNCT
ejpam-5578	13	26	,	,	PUNCT
ejpam-5578	13	27	sabeelar27@gmail.com	sabeelar27@gmail.com	PROPN
ejpam-5578	13	28	(	(	PUNCT
ejpam-5578	13	29	s.	s.	PROPN
ejpam-5578	13	30	rawashdeh	rawashdeh	PROPN
ejpam-5578	13	31	)	)	PUNCT
ejpam-5578	13	32	,	,	PUNCT
ejpam-5578	13	33	aamourah@su.edu.om	aamourah@su.edu.om	NOUN
ejpam-5578	13	34	(	(	PUNCT
ejpam-5578	13	35	a.	a.	NOUN
ejpam-5578	13	36	amourah	amourah	PROPN
ejpam-5578	13	37	)	)	PUNCT
ejpam-5578	13	38	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5578	14	1	1	1	NUM
ejpam-5578	14	2	copyright	copyright	NOUN
ejpam-5578	14	3	:	:	PUNCT
ejpam-5578	14	4	©	©	PROPN
ejpam-5578	14	5	2025	2025	NUM
ejpam-5578	14	6	the	the	DET
ejpam-5578	14	7	author(s	author(s	NOUN
ejpam-5578	14	8	)	)	PUNCT
ejpam-5578	14	9	.	.	PUNCT
ejpam-5578	15	1	(	(	PUNCT
ejpam-5578	15	2	cc	cc	NOUN
ejpam-5578	15	3	by	by	ADP
ejpam-5578	15	4	-	-	PUNCT
ejpam-5578	15	5	nc	nc	PROPN
ejpam-5578	15	6	4.0	4.0	NUM
ejpam-5578	15	7	)	)	PUNCT
ejpam-5578	15	8	j.	j.	PROPN
ejpam-5578	15	9	oudetallah	oudetallah	PROPN
ejpam-5578	15	10	et	et	PROPN
ejpam-5578	15	11	al	al	PROPN
ejpam-5578	15	12	.	.	PUNCT
ejpam-5578	15	13	/	/	SYM
ejpam-5578	15	14	eur	eur	PROPN
ejpam-5578	15	15	.	.	PUNCT
ejpam-5578	16	1	j.	j.	PROPN
ejpam-5578	16	2	pure	pure	PROPN
ejpam-5578	16	3	appl	appl	PROPN
ejpam-5578	16	4	.	.	PROPN
ejpam-5578	16	5	math	math	PROPN
ejpam-5578	16	6	,	,	PUNCT
ejpam-5578	16	7	18	18	NUM
ejpam-5578	16	8	(	(	PUNCT
ejpam-5578	16	9	2	2	NUM
ejpam-5578	16	10	)	)	PUNCT
ejpam-5578	16	11	(	(	PUNCT
ejpam-5578	16	12	2025	2025	NUM
ejpam-5578	16	13	)	)	PUNCT
ejpam-5578	16	14	,	,	PUNCT
ejpam-5578	16	15	5578	5578	NUM
ejpam-5578	16	16	2	2	NUM
ejpam-5578	16	17	of	of	ADP
ejpam-5578	16	18	19	19	NUM
ejpam-5578	16	19	framework	framework	NOUN
ejpam-5578	16	20	for	for	ADP
ejpam-5578	16	21	analyzing	analyze	VERB
ejpam-5578	16	22	geometric	geometric	ADJ
ejpam-5578	16	23	and	and	CCONJ
ejpam-5578	16	24	abstract	abstract	ADJ
ejpam-5578	16	25	structures	structure	NOUN
ejpam-5578	17	1	[	[	X
ejpam-5578	17	2	4–10	4–10	NOUN
ejpam-5578	17	3	]	]	X
ejpam-5578	17	4	.	.	PUNCT
ejpam-5578	18	1	one	one	NUM
ejpam-5578	18	2	of	of	ADP
ejpam-5578	18	3	the	the	DET
ejpam-5578	18	4	key	key	ADJ
ejpam-5578	18	5	areas	area	NOUN
ejpam-5578	18	6	in	in	ADP
ejpam-5578	18	7	set	set	NOUN
ejpam-5578	18	8	-	-	PUNCT
ejpam-5578	18	9	theoretic	theoretic	NOUN
ejpam-5578	18	10	topology	topology	NOUN
ejpam-5578	18	11	focuses	focus	VERB
ejpam-5578	18	12	on	on	ADP
ejpam-5578	18	13	developing	develop	VERB
ejpam-5578	18	14	and	and	CCONJ
ejpam-5578	18	15	exploring	explore	VERB
ejpam-5578	18	16	the	the	DET
ejpam-5578	18	17	relationships	relationship	NOUN
ejpam-5578	18	18	between	between	ADP
ejpam-5578	18	19	different	different	ADJ
ejpam-5578	18	20	classes	class	NOUN
ejpam-5578	18	21	of	of	ADP
ejpam-5578	18	22	topological	topological	ADJ
ejpam-5578	18	23	spaces	space	NOUN
ejpam-5578	18	24	that	that	PRON
ejpam-5578	18	25	lie	lie	VERB
ejpam-5578	18	26	between	between	ADP
ejpam-5578	18	27	lindelöf	lindelöf	NOUN
ejpam-5578	18	28	spaces	space	VERB
ejpam-5578	18	29	.	.	PUNCT
ejpam-5578	19	1	in	in	ADP
ejpam-5578	19	2	this	this	DET
ejpam-5578	19	3	context	context	NOUN
ejpam-5578	19	4	,	,	PUNCT
ejpam-5578	19	5	the	the	DET
ejpam-5578	19	6	class	class	NOUN
ejpam-5578	19	7	of	of	ADP
ejpam-5578	19	8	lindelöf	lindelöf	PROPN
ejpam-5578	19	9	spaces	space	NOUN
ejpam-5578	19	10	plays	play	VERB
ejpam-5578	19	11	a	a	DET
ejpam-5578	19	12	crucial	crucial	ADJ
ejpam-5578	19	13	role	role	NOUN
ejpam-5578	19	14	,	,	PUNCT
ejpam-5578	19	15	as	as	SCONJ
ejpam-5578	19	16	it	it	PRON
ejpam-5578	19	17	naturally	naturally	ADV
ejpam-5578	19	18	occupies	occupy	VERB
ejpam-5578	19	19	an	an	DET
ejpam-5578	19	20	intermediate	intermediate	ADJ
ejpam-5578	19	21	position	position	NOUN
ejpam-5578	19	22	between	between	ADP
ejpam-5578	19	23	these	these	DET
ejpam-5578	19	24	classes	class	NOUN
ejpam-5578	19	25	.	.	PUNCT
ejpam-5578	20	1	a	a	DET
ejpam-5578	20	2	lindelöf	lindelöf	NOUN
ejpam-5578	20	3	space	space	NOUN
ejpam-5578	20	4	is	be	AUX
ejpam-5578	20	5	defined	define	VERB
ejpam-5578	20	6	as	as	ADP
ejpam-5578	20	7	a	a	DET
ejpam-5578	20	8	topological	topological	ADJ
ejpam-5578	20	9	space	space	NOUN
ejpam-5578	20	10	(	(	PUNCT
ejpam-5578	20	11	q	q	NOUN
ejpam-5578	20	12	,	,	PUNCT
ejpam-5578	20	13	ϱ	ϱ	NOUN
ejpam-5578	20	14	)	)	PUNCT
ejpam-5578	20	15	in	in	ADP
ejpam-5578	20	16	which	which	PRON
ejpam-5578	20	17	every	every	DET
ejpam-5578	20	18	open	open	ADJ
ejpam-5578	20	19	cover	cover	NOUN
ejpam-5578	20	20	of	of	ADP
ejpam-5578	20	21	q	q	PROPN
ejpam-5578	20	22	has	have	VERB
ejpam-5578	20	23	a	a	DET
ejpam-5578	20	24	countable	countable	ADJ
ejpam-5578	20	25	subcover	subcover	NOUN
ejpam-5578	20	26	.	.	PUNCT
ejpam-5578	21	1	extending	extend	VERB
ejpam-5578	21	2	this	this	DET
ejpam-5578	21	3	concept	concept	NOUN
ejpam-5578	21	4	,	,	PUNCT
ejpam-5578	21	5	a	a	DET
ejpam-5578	21	6	tritopological	tritopological	ADJ
ejpam-5578	21	7	space	space	NOUN
ejpam-5578	21	8	(	(	PUNCT
ejpam-5578	21	9	q	q	ADJ
ejpam-5578	21	10	,	,	PUNCT
ejpam-5578	21	11	ϱ1	ϱ1	NOUN
ejpam-5578	21	12	,	,	PUNCT
ejpam-5578	21	13	ϱ2	ϱ2	NOUN
ejpam-5578	21	14	,	,	PUNCT
ejpam-5578	21	15	ϱ3	ϱ3	PROPN
ejpam-5578	21	16	)	)	PUNCT
ejpam-5578	21	17	is	be	AUX
ejpam-5578	21	18	called	call	VERB
ejpam-5578	21	19	a	a	DET
ejpam-5578	21	20	tri	tri	ADJ
ejpam-5578	21	21	-	-	NOUN
ejpam-5578	21	22	lindelöf	lindelöf	NOUN
ejpam-5578	21	23	space	space	NOUN
ejpam-5578	21	24	if	if	SCONJ
ejpam-5578	21	25	every	every	DET
ejpam-5578	21	26	ϱi	ϱi	ADJ
ejpam-5578	21	27	-	-	PUNCT
ejpam-5578	21	28	open	open	ADJ
ejpam-5578	21	29	cover	cover	NOUN
ejpam-5578	21	30	of	of	ADP
ejpam-5578	21	31	q	q	PROPN
ejpam-5578	21	32	has	have	VERB
ejpam-5578	21	33	a	a	DET
ejpam-5578	21	34	tripartite	tripartite	ADJ
ejpam-5578	21	35	countable	countable	ADJ
ejpam-5578	21	36	subcover	subcover	NOUN
ejpam-5578	21	37	of	of	ADP
ejpam-5578	21	38	q	q	PROPN
ejpam-5578	21	39	,	,	PUNCT
ejpam-5578	21	40	where	where	SCONJ
ejpam-5578	21	41	i	i	PRON
ejpam-5578	21	42	=	=	NOUN
ejpam-5578	21	43	1	1	NUM
ejpam-5578	21	44	,	,	PUNCT
ejpam-5578	21	45	2	2	NUM
ejpam-5578	21	46	,	,	PUNCT
ejpam-5578	21	47	3	3	NUM
ejpam-5578	21	48	.	.	PUNCT
ejpam-5578	21	49	a	a	DET
ejpam-5578	21	50	notable	notable	ADJ
ejpam-5578	21	51	characteristic	characteristic	NOUN
ejpam-5578	21	52	of	of	ADP
ejpam-5578	21	53	these	these	DET
ejpam-5578	21	54	classes	class	NOUN
ejpam-5578	21	55	of	of	ADP
ejpam-5578	21	56	spaces	space	NOUN
ejpam-5578	21	57	is	be	AUX
ejpam-5578	21	58	that	that	SCONJ
ejpam-5578	21	59	several	several	ADJ
ejpam-5578	21	60	important	important	ADJ
ejpam-5578	21	61	separation	separation	NOUN
ejpam-5578	21	62	axioms	axiom	NOUN
ejpam-5578	21	63	,	,	PUNCT
ejpam-5578	21	64	such	such	ADJ
ejpam-5578	21	65	as	as	ADP
ejpam-5578	21	66	normality	normality	NOUN
ejpam-5578	21	67	and	and	CCONJ
ejpam-5578	21	68	the	the	DET
ejpam-5578	21	69	hausdorff	hausdorff	NOUN
ejpam-5578	21	70	condition	condition	NOUN
ejpam-5578	21	71	,	,	PUNCT
ejpam-5578	21	72	coincide	coincide	NOUN
ejpam-5578	21	73	within	within	ADP
ejpam-5578	21	74	these	these	DET
ejpam-5578	21	75	classes	class	NOUN
ejpam-5578	21	76	.	.	PUNCT
ejpam-5578	22	1	this	this	DET
ejpam-5578	22	2	property	property	NOUN
ejpam-5578	22	3	makes	make	VERB
ejpam-5578	22	4	them	they	PRON
ejpam-5578	22	5	highly	highly	ADV
ejpam-5578	22	6	significant	significant	ADJ
ejpam-5578	22	7	both	both	CCONJ
ejpam-5578	22	8	theoretically	theoretically	ADV
ejpam-5578	22	9	and	and	CCONJ
ejpam-5578	22	10	practically	practically	ADV
ejpam-5578	22	11	,	,	PUNCT
ejpam-5578	22	12	whether	whether	SCONJ
ejpam-5578	22	13	addressing	address	VERB
ejpam-5578	22	14	problems	problem	NOUN
ejpam-5578	22	15	from	from	ADP
ejpam-5578	22	16	a	a	DET
ejpam-5578	22	17	purely	purely	ADV
ejpam-5578	22	18	topological	topological	ADJ
ejpam-5578	22	19	perspective	perspective	NOUN
ejpam-5578	22	20	or	or	CCONJ
ejpam-5578	22	21	applications	application	NOUN
ejpam-5578	22	22	in	in	ADP
ejpam-5578	22	23	other	other	ADJ
ejpam-5578	22	24	areas	area	NOUN
ejpam-5578	22	25	of	of	ADP
ejpam-5578	22	26	mathematics	mathematic	NOUN
ejpam-5578	22	27	.	.	PUNCT
ejpam-5578	23	1	a	a	DET
ejpam-5578	23	2	set	set	NOUN
ejpam-5578	23	3	q	q	NOUN
ejpam-5578	23	4	is	be	AUX
ejpam-5578	23	5	called	call	VERB
ejpam-5578	23	6	a	a	DET
ejpam-5578	23	7	tri	tri	ADJ
ejpam-5578	23	8	-	-	ADJ
ejpam-5578	23	9	topological	topological	ADJ
ejpam-5578	23	10	space	space	NOUN
ejpam-5578	23	11	if	if	SCONJ
ejpam-5578	23	12	each	each	DET
ejpam-5578	23	13	point	point	NOUN
ejpam-5578	23	14	in	in	ADP
ejpam-5578	23	15	q	q	PROPN
ejpam-5578	23	16	has	have	VERB
ejpam-5578	23	17	a	a	DET
ejpam-5578	23	18	fundamental	fundamental	ADJ
ejpam-5578	23	19	system	system	NOUN
ejpam-5578	23	20	of	of	ADP
ejpam-5578	23	21	almost	almost	ADV
ejpam-5578	23	22	open	open	ADJ
ejpam-5578	23	23	neighborhoods	neighborhood	NOUN
ejpam-5578	23	24	.	.	PUNCT
ejpam-5578	24	1	it	it	PRON
ejpam-5578	24	2	is	be	AUX
ejpam-5578	24	3	worth	worth	ADJ
ejpam-5578	24	4	noting	note	VERB
ejpam-5578	24	5	that	that	SCONJ
ejpam-5578	24	6	the	the	DET
ejpam-5578	24	7	concept	concept	NOUN
ejpam-5578	24	8	of	of	ADP
ejpam-5578	24	9	almost	almost	ADV
ejpam-5578	24	10	open	open	ADJ
ejpam-5578	24	11	sets	set	NOUN
ejpam-5578	24	12	in	in	ADP
ejpam-5578	24	13	topological	topological	ADJ
ejpam-5578	24	14	groups	group	NOUN
ejpam-5578	24	15	was	be	AUX
ejpam-5578	24	16	first	first	ADV
ejpam-5578	24	17	studied	study	VERB
ejpam-5578	24	18	by	by	ADP
ejpam-5578	24	19	ghosh	ghosh	PROPN
ejpam-5578	24	20	and	and	CCONJ
ejpam-5578	24	21	lahiri	lahiri	PROPN
ejpam-5578	24	22	.	.	PUNCT
ejpam-5578	25	1	the	the	DET
ejpam-5578	25	2	notion	notion	NOUN
ejpam-5578	25	3	of	of	ADP
ejpam-5578	25	4	a	a	DET
ejpam-5578	25	5	tritopological	tritopological	ADJ
ejpam-5578	25	6	group	group	NOUN
ejpam-5578	25	7	,	,	PUNCT
ejpam-5578	25	8	which	which	PRON
ejpam-5578	25	9	is	be	AUX
ejpam-5578	25	10	the	the	DET
ejpam-5578	25	11	tri	tri	ADJ
ejpam-5578	25	12	-	-	ADJ
ejpam-5578	25	13	topologized	topologize	VERB
ejpam-5578	25	14	version	version	NOUN
ejpam-5578	25	15	of	of	ADP
ejpam-5578	25	16	a	a	DET
ejpam-5578	25	17	topological	topological	ADJ
ejpam-5578	25	18	group	group	NOUN
ejpam-5578	25	19	,	,	PUNCT
ejpam-5578	25	20	has	have	AUX
ejpam-5578	25	21	also	also	ADV
ejpam-5578	25	22	been	be	AUX
ejpam-5578	25	23	discussed	discuss	VERB
ejpam-5578	25	24	in	in	ADP
ejpam-5578	25	25	earlier	early	ADJ
ejpam-5578	25	26	works	work	NOUN
ejpam-5578	25	27	.	.	PUNCT
ejpam-5578	26	1	the	the	DET
ejpam-5578	26	2	concept	concept	NOUN
ejpam-5578	26	3	of	of	ADP
ejpam-5578	26	4	a	a	DET
ejpam-5578	26	5	lindelöf	lindelöf	NOUN
ejpam-5578	26	6	space	space	NOUN
ejpam-5578	26	7	in	in	ADP
ejpam-5578	26	8	a	a	DET
ejpam-5578	26	9	topological	topological	ADJ
ejpam-5578	26	10	space	space	NOUN
ejpam-5578	26	11	(	(	PUNCT
ejpam-5578	26	12	q	q	NOUN
ejpam-5578	26	13	,	,	PUNCT
ejpam-5578	26	14	ϱ	ϱ	NOUN
ejpam-5578	26	15	)	)	PUNCT
ejpam-5578	26	16	was	be	AUX
ejpam-5578	26	17	introduced	introduce	VERB
ejpam-5578	26	18	by	by	ADP
ejpam-5578	26	19	[	[	X
ejpam-5578	26	20	11	11	NUM
ejpam-5578	26	21	]	]	PUNCT
ejpam-5578	26	22	.	.	PUNCT
ejpam-5578	27	1	recent	recent	ADJ
ejpam-5578	27	2	research	research	NOUN
ejpam-5578	27	3	[	[	X
ejpam-5578	27	4	12–14	12–14	NUM
ejpam-5578	27	5	]	]	PUNCT
ejpam-5578	27	6	has	have	AUX
ejpam-5578	27	7	further	far	ADV
ejpam-5578	27	8	explored	explore	VERB
ejpam-5578	27	9	and	and	CCONJ
ejpam-5578	27	10	expanded	expand	VERB
ejpam-5578	27	11	upon	upon	SCONJ
ejpam-5578	27	12	these	these	DET
ejpam-5578	27	13	ideas	idea	NOUN
ejpam-5578	27	14	.	.	PUNCT
ejpam-5578	28	1	this	this	DET
ejpam-5578	28	2	paper	paper	NOUN
ejpam-5578	28	3	investigates	investigate	VERB
ejpam-5578	28	4	the	the	DET
ejpam-5578	28	5	concept	concept	NOUN
ejpam-5578	28	6	of	of	ADP
ejpam-5578	28	7	tri	tri	NOUN
ejpam-5578	28	8	-	-	NOUN
ejpam-5578	28	9	lindelöf	lindelöf	NOUN
ejpam-5578	28	10	and	and	CCONJ
ejpam-5578	28	11	tri	tri	ADJ
ejpam-5578	28	12	-	-	ADJ
ejpam-5578	28	13	metalindelöf	metalindelöf	ADJ
ejpam-5578	28	14	spaces	space	NOUN
ejpam-5578	28	15	,	,	PUNCT
ejpam-5578	28	16	presenting	present	VERB
ejpam-5578	28	17	associated	associated	ADJ
ejpam-5578	28	18	conclusions	conclusion	NOUN
ejpam-5578	28	19	.	.	PUNCT
ejpam-5578	29	1	in	in	ADP
ejpam-5578	29	2	the	the	DET
ejpam-5578	29	3	next	next	ADJ
ejpam-5578	29	4	section	section	NOUN
ejpam-5578	29	5	,	,	PUNCT
ejpam-5578	29	6	we	we	PRON
ejpam-5578	29	7	introduce	introduce	VERB
ejpam-5578	29	8	the	the	DET
ejpam-5578	29	9	fundamental	fundamental	ADJ
ejpam-5578	29	10	concepts	concept	NOUN
ejpam-5578	29	11	of	of	ADP
ejpam-5578	29	12	topological	topological	ADJ
ejpam-5578	29	13	spaces	space	NOUN
ejpam-5578	29	14	and	and	CCONJ
ejpam-5578	29	15	tri	tri	ADJ
ejpam-5578	29	16	-	-	ADJ
ejpam-5578	29	17	topological	topological	ADJ
ejpam-5578	29	18	spaces	space	NOUN
ejpam-5578	29	19	,	,	PUNCT
ejpam-5578	29	20	along	along	ADP
ejpam-5578	29	21	with	with	ADP
ejpam-5578	29	22	key	key	ADJ
ejpam-5578	29	23	notions	notion	NOUN
ejpam-5578	29	24	in	in	ADP
ejpam-5578	29	25	tri	tri	ADJ
ejpam-5578	29	26	-	-	ADJ
ejpam-5578	29	27	topological	topological	ADJ
ejpam-5578	29	28	spaces	space	NOUN
ejpam-5578	29	29	,	,	PUNCT
ejpam-5578	29	30	such	such	ADJ
ejpam-5578	29	31	as	as	ADP
ejpam-5578	29	32	open	open	ADJ
ejpam-5578	29	33	and	and	CCONJ
ejpam-5578	29	34	closed	closed	ADJ
ejpam-5578	29	35	sets	set	NOUN
ejpam-5578	29	36	,	,	PUNCT
ejpam-5578	29	37	derived	derived	ADJ
ejpam-5578	29	38	sets	set	NOUN
ejpam-5578	29	39	,	,	PUNCT
ejpam-5578	29	40	closure	closure	NOUN
ejpam-5578	29	41	sets	set	NOUN
ejpam-5578	29	42	,	,	PUNCT
ejpam-5578	29	43	interior	interior	ADJ
ejpam-5578	29	44	and	and	CCONJ
ejpam-5578	29	45	exterior	exterior	ADJ
ejpam-5578	29	46	sets	set	NOUN
ejpam-5578	29	47	,	,	PUNCT
ejpam-5578	29	48	and	and	CCONJ
ejpam-5578	29	49	separation	separation	NOUN
ejpam-5578	29	50	axioms	axiom	VERB
ejpam-5578	29	51	.	.	PUNCT
ejpam-5578	30	1	we	we	PRON
ejpam-5578	30	2	then	then	ADV
ejpam-5578	30	3	discuss	discuss	VERB
ejpam-5578	30	4	the	the	DET
ejpam-5578	30	5	lindelöf	lindelöf	NOUN
ejpam-5578	30	6	property	property	NOUN
ejpam-5578	30	7	in	in	ADP
ejpam-5578	30	8	tri	tri	ADJ
ejpam-5578	30	9	-	-	ADJ
ejpam-5578	30	10	topological	topological	ADJ
ejpam-5578	30	11	spaces	space	NOUN
ejpam-5578	30	12	,	,	PUNCT
ejpam-5578	30	13	analyze	analyze	VERB
ejpam-5578	30	14	its	its	PRON
ejpam-5578	30	15	characteristics	characteristic	NOUN
ejpam-5578	30	16	,	,	PUNCT
ejpam-5578	30	17	and	and	CCONJ
ejpam-5578	30	18	examine	examine	VERB
ejpam-5578	30	19	its	its	PRON
ejpam-5578	30	20	applicability	applicability	NOUN
ejpam-5578	30	21	to	to	ADP
ejpam-5578	30	22	other	other	ADJ
ejpam-5578	30	23	spaces	space	NOUN
ejpam-5578	30	24	.	.	PUNCT
ejpam-5578	31	1	additionally	additionally	ADV
ejpam-5578	31	2	,	,	PUNCT
ejpam-5578	31	3	we	we	PRON
ejpam-5578	31	4	review	review	VERB
ejpam-5578	31	5	well	well	ADV
ejpam-5578	31	6	-	-	PUNCT
ejpam-5578	31	7	known	know	VERB
ejpam-5578	31	8	definitions	definition	NOUN
ejpam-5578	31	9	that	that	PRON
ejpam-5578	31	10	will	will	AUX
ejpam-5578	31	11	be	be	AUX
ejpam-5578	31	12	utilized	utilize	VERB
ejpam-5578	31	13	throughout	throughout	ADP
ejpam-5578	31	14	this	this	DET
ejpam-5578	31	15	work	work	NOUN
ejpam-5578	31	16	.	.	PUNCT
ejpam-5578	32	1	finally	finally	ADV
ejpam-5578	32	2	,	,	PUNCT
ejpam-5578	32	3	we	we	PRON
ejpam-5578	32	4	introduce	introduce	VERB
ejpam-5578	32	5	and	and	CCONJ
ejpam-5578	32	6	explore	explore	VERB
ejpam-5578	32	7	tripartite	tripartite	ADJ
ejpam-5578	32	8	metalindelöfness	metalindelöfness	NUM
ejpam-5578	32	9	spaces	space	NOUN
ejpam-5578	32	10	,	,	PUNCT
ejpam-5578	32	11	highlighting	highlight	VERB
ejpam-5578	32	12	their	their	PRON
ejpam-5578	32	13	structural	structural	ADJ
ejpam-5578	32	14	properties	property	NOUN
ejpam-5578	32	15	and	and	CCONJ
ejpam-5578	32	16	significance	significance	NOUN
ejpam-5578	32	17	.	.	PUNCT
ejpam-5578	33	1	the	the	DET
ejpam-5578	33	2	terms	term	NOUN
ejpam-5578	33	3	ϱu	ϱu	VERB
ejpam-5578	33	4	,	,	PUNCT
ejpam-5578	33	5	ϱdis	ϱdi	NOUN
ejpam-5578	33	6	,	,	PUNCT
ejpam-5578	33	7	ϱcof	ϱcof	ADJ
ejpam-5578	33	8	,	,	PUNCT
ejpam-5578	33	9	and	and	CCONJ
ejpam-5578	33	10	ϱcoc	ϱcoc	PROPN
ejpam-5578	33	11	represent	represent	VERB
ejpam-5578	33	12	the	the	DET
ejpam-5578	33	13	usual	usual	ADJ
ejpam-5578	33	14	topology	topology	NOUN
ejpam-5578	33	15	,	,	PUNCT
ejpam-5578	33	16	discrete	discrete	ADJ
ejpam-5578	33	17	topology	topology	NOUN
ejpam-5578	33	18	,	,	PUNCT
ejpam-5578	33	19	cofinite	cofinite	NOUN
ejpam-5578	33	20	topology	topology	NOUN
ejpam-5578	33	21	,	,	PUNCT
ejpam-5578	33	22	and	and	CCONJ
ejpam-5578	33	23	cocountable	cocountable	ADJ
ejpam-5578	33	24	topology	topology	NOUN
ejpam-5578	33	25	,	,	PUNCT
ejpam-5578	33	26	respectively	respectively	ADV
ejpam-5578	33	27	.	.	PUNCT
ejpam-5578	34	1	the	the	DET
ejpam-5578	34	2	concept	concept	NOUN
ejpam-5578	34	3	of	of	ADP
ejpam-5578	34	4	bitopological	bitopological	ADJ
ejpam-5578	34	5	spaces	space	NOUN
ejpam-5578	34	6	is	be	AUX
ejpam-5578	34	7	represented	represent	VERB
ejpam-5578	34	8	as	as	ADP
ejpam-5578	34	9	q	q	NOUN
ejpam-5578	34	10	=	=	PUNCT
ejpam-5578	34	11	(	(	PUNCT
ejpam-5578	34	12	q	q	ADJ
ejpam-5578	34	13	,	,	PUNCT
ejpam-5578	34	14	ϱ1	ϱ1	NOUN
ejpam-5578	34	15	,	,	PUNCT
ejpam-5578	34	16	ϱ2	ϱ2	NOUN
ejpam-5578	34	17	)	)	PUNCT
ejpam-5578	34	18	,	,	PUNCT
ejpam-5578	34	19	where	where	SCONJ
ejpam-5578	34	20	ϱ1	ϱ1	NOUN
ejpam-5578	34	21	and	and	CCONJ
ejpam-5578	34	22	ϱ2	ϱ2	NOUN
ejpam-5578	34	23	are	be	AUX
ejpam-5578	34	24	two	two	NUM
ejpam-5578	34	25	distinct	distinct	ADJ
ejpam-5578	34	26	topologies	topology	NOUN
ejpam-5578	34	27	on	on	ADP
ejpam-5578	34	28	q.	q.	PROPN
ejpam-5578	34	29	this	this	PRON
ejpam-5578	34	30	aligns	align	VERB
ejpam-5578	34	31	with	with	ADP
ejpam-5578	34	32	prior	prior	ADJ
ejpam-5578	34	33	research	research	NOUN
ejpam-5578	34	34	on	on	ADP
ejpam-5578	34	35	bitopological	bitopological	ADJ
ejpam-5578	34	36	spaces	space	NOUN
ejpam-5578	34	37	,	,	PUNCT
ejpam-5578	34	38	where	where	SCONJ
ejpam-5578	34	39	each	each	DET
ejpam-5578	34	40	topology	topology	NOUN
ejpam-5578	34	41	satisfies	satisfy	VERB
ejpam-5578	34	42	a	a	DET
ejpam-5578	34	43	set	set	NOUN
ejpam-5578	34	44	of	of	ADP
ejpam-5578	34	45	axioms	axiom	NOUN
ejpam-5578	34	46	.	.	PUNCT
ejpam-5578	35	1	in	in	ADP
ejpam-5578	35	2	[	[	X
ejpam-5578	35	3	15	15	NUM
ejpam-5578	35	4	]	]	PUNCT
ejpam-5578	35	5	,	,	PUNCT
ejpam-5578	35	6	the	the	DET
ejpam-5578	35	7	notions	notion	NOUN
ejpam-5578	35	8	of	of	ADP
ejpam-5578	35	9	pairwise	pairwise	NOUN
ejpam-5578	35	10	hausdorff	hausdorff	NOUN
ejpam-5578	35	11	,	,	PUNCT
ejpam-5578	35	12	pairwise	pairwise	NOUN
ejpam-5578	35	13	regular	regular	NOUN
ejpam-5578	35	14	,	,	PUNCT
ejpam-5578	35	15	and	and	CCONJ
ejpam-5578	35	16	pairwise	pairwise	NOUN
ejpam-5578	35	17	normal	normal	ADJ
ejpam-5578	35	18	spaces	space	NOUN
ejpam-5578	35	19	were	be	AUX
ejpam-5578	35	20	discussed	discuss	VERB
ejpam-5578	35	21	using	use	VERB
ejpam-5578	35	22	well	well	ADV
ejpam-5578	35	23	-	-	PUNCT
ejpam-5578	35	24	established	establish	VERB
ejpam-5578	35	25	results	result	NOUN
ejpam-5578	35	26	such	such	ADJ
ejpam-5578	35	27	as	as	ADP
ejpam-5578	35	28	tietze	tietze	ADJ
ejpam-5578	35	29	extension	extension	NOUN
ejpam-5578	35	30	theorems	theorem	NOUN
ejpam-5578	35	31	.	.	PUNCT
ejpam-5578	36	1	the	the	DET
ejpam-5578	36	2	primary	primary	ADJ
ejpam-5578	36	3	objective	objective	NOUN
ejpam-5578	36	4	of	of	ADP
ejpam-5578	36	5	this	this	DET
ejpam-5578	36	6	paper	paper	NOUN
ejpam-5578	36	7	is	be	AUX
ejpam-5578	36	8	to	to	PART
ejpam-5578	36	9	introduce	introduce	VERB
ejpam-5578	36	10	and	and	CCONJ
ejpam-5578	36	11	investigate	investigate	VERB
ejpam-5578	36	12	a	a	DET
ejpam-5578	36	13	new	new	ADJ
ejpam-5578	36	14	class	class	NOUN
ejpam-5578	36	15	of	of	ADP
ejpam-5578	36	16	tripartite	tripartite	ADJ
ejpam-5578	36	17	lindelöf	lindelöf	NOUN
ejpam-5578	36	18	spaces	space	NOUN
ejpam-5578	36	19	,	,	PUNCT
ejpam-5578	36	20	termed	term	VERB
ejpam-5578	36	21	tripartite	tripartite	ADJ
ejpam-5578	36	22	metalindelöf	metalindelöf	NOUN
ejpam-5578	36	23	spaces	space	NOUN
ejpam-5578	36	24	.	.	PUNCT
ejpam-5578	37	1	tri	tri	ADJ
ejpam-5578	37	2	-	-	ADJ
ejpam-5578	37	3	topological	topological	ADJ
ejpam-5578	37	4	spaces	space	NOUN
ejpam-5578	37	5	are	be	AUX
ejpam-5578	37	6	sets	set	NOUN
ejpam-5578	37	7	equipped	equip	VERB
ejpam-5578	37	8	with	with	ADP
ejpam-5578	37	9	three	three	NUM
ejpam-5578	37	10	distinct	distinct	ADJ
ejpam-5578	37	11	topologies	topology	NOUN
ejpam-5578	37	12	,	,	PUNCT
ejpam-5578	37	13	denoted	denote	VERB
ejpam-5578	37	14	as	as	ADP
ejpam-5578	37	15	:	:	PUNCT
ejpam-5578	37	16	q	q	X
ejpam-5578	37	17	=	=	SYM
ejpam-5578	37	18	(	(	PUNCT
ejpam-5578	37	19	q	q	ADJ
ejpam-5578	37	20	,	,	PUNCT
ejpam-5578	37	21	ϱ1	ϱ1	NOUN
ejpam-5578	37	22	,	,	PUNCT
ejpam-5578	37	23	ϱ2	ϱ2	NOUN
ejpam-5578	37	24	,	,	PUNCT
ejpam-5578	37	25	ϱ3	ϱ3	PROPN
ejpam-5578	37	26	)	)	PUNCT
ejpam-5578	37	27	,	,	PUNCT
ejpam-5578	37	28	where	where	SCONJ
ejpam-5578	37	29	ϱ1	ϱ1	NOUN
ejpam-5578	37	30	,	,	PUNCT
ejpam-5578	37	31	ϱ2	ϱ2	NOUN
ejpam-5578	37	32	,	,	PUNCT
ejpam-5578	37	33	and	and	CCONJ
ejpam-5578	37	34	ϱ3	ϱ3	NOUN
ejpam-5578	37	35	are	be	AUX
ejpam-5578	37	36	topologies	topology	NOUN
ejpam-5578	37	37	on	on	ADP
ejpam-5578	37	38	q.	q.	NOUN
ejpam-5578	37	39	these	these	DET
ejpam-5578	37	40	spaces	space	NOUN
ejpam-5578	37	41	exhibit	exhibit	VERB
ejpam-5578	37	42	structural	structural	ADJ
ejpam-5578	37	43	variations	variation	NOUN
ejpam-5578	37	44	that	that	PRON
ejpam-5578	37	45	correspond	correspond	VERB
ejpam-5578	37	46	to	to	ADP
ejpam-5578	37	47	well	well	ADV
ejpam-5578	37	48	-	-	PUNCT
ejpam-5578	37	49	established	establish	VERB
ejpam-5578	37	50	properties	property	NOUN
ejpam-5578	37	51	in	in	ADP
ejpam-5578	37	52	classical	classical	ADJ
ejpam-5578	37	53	topology	topology	NOUN
ejpam-5578	37	54	.	.	PUNCT
ejpam-5578	38	1	j.	j.	PROPN
ejpam-5578	38	2	oudetallah	oudetallah	PROPN
ejpam-5578	38	3	et	et	PROPN
ejpam-5578	38	4	al	al	PROPN
ejpam-5578	38	5	.	.	PUNCT
ejpam-5578	38	6	/	/	SYM
ejpam-5578	38	7	eur	eur	PROPN
ejpam-5578	38	8	.	.	PUNCT
ejpam-5578	39	1	j.	j.	PROPN
ejpam-5578	39	2	pure	pure	PROPN
ejpam-5578	39	3	appl	appl	PROPN
ejpam-5578	39	4	.	.	PROPN
ejpam-5578	39	5	math	math	PROPN
ejpam-5578	39	6	,	,	PUNCT
ejpam-5578	39	7	18	18	NUM
ejpam-5578	39	8	(	(	PUNCT
ejpam-5578	39	9	2	2	NUM
ejpam-5578	39	10	)	)	PUNCT
ejpam-5578	39	11	(	(	PUNCT
ejpam-5578	39	12	2025	2025	NUM
ejpam-5578	39	13	)	)	PUNCT
ejpam-5578	39	14	,	,	PUNCT
ejpam-5578	39	15	5578	5578	NUM
ejpam-5578	39	16	3	3	NUM
ejpam-5578	39	17	of	of	ADP
ejpam-5578	39	18	19	19	NUM
ejpam-5578	39	19	2	2	NUM
ejpam-5578	39	20	.	.	PUNCT
ejpam-5578	39	21	preliminaries	preliminary	NOUN
ejpam-5578	39	22	before	before	ADP
ejpam-5578	39	23	presenting	present	VERB
ejpam-5578	39	24	the	the	DET
ejpam-5578	39	25	main	main	ADJ
ejpam-5578	39	26	results	result	NOUN
ejpam-5578	39	27	of	of	ADP
ejpam-5578	39	28	this	this	DET
ejpam-5578	39	29	study	study	NOUN
ejpam-5578	39	30	,	,	PUNCT
ejpam-5578	39	31	it	it	PRON
ejpam-5578	39	32	is	be	AUX
ejpam-5578	39	33	essential	essential	ADJ
ejpam-5578	39	34	to	to	PART
ejpam-5578	39	35	establish	establish	VERB
ejpam-5578	39	36	the	the	DET
ejpam-5578	39	37	fundamental	fundamental	ADJ
ejpam-5578	39	38	concepts	concept	NOUN
ejpam-5578	39	39	related	relate	VERB
ejpam-5578	39	40	to	to	ADP
ejpam-5578	39	41	tri	tri	ADJ
ejpam-5578	39	42	-	-	ADJ
ejpam-5578	39	43	topological	topological	ADJ
ejpam-5578	39	44	spaces	space	NOUN
ejpam-5578	39	45	.	.	PUNCT
ejpam-5578	40	1	in	in	ADP
ejpam-5578	40	2	this	this	DET
ejpam-5578	40	3	section	section	NOUN
ejpam-5578	40	4	,	,	PUNCT
ejpam-5578	40	5	we	we	PRON
ejpam-5578	40	6	review	review	VERB
ejpam-5578	40	7	key	key	ADJ
ejpam-5578	40	8	definitions	definition	NOUN
ejpam-5578	40	9	and	and	CCONJ
ejpam-5578	40	10	properties	property	NOUN
ejpam-5578	40	11	that	that	PRON
ejpam-5578	40	12	will	will	AUX
ejpam-5578	40	13	serve	serve	VERB
ejpam-5578	40	14	as	as	ADP
ejpam-5578	40	15	the	the	DET
ejpam-5578	40	16	foundation	foundation	NOUN
ejpam-5578	40	17	for	for	ADP
ejpam-5578	40	18	our	our	PRON
ejpam-5578	40	19	discussion	discussion	NOUN
ejpam-5578	40	20	.	.	PUNCT
ejpam-5578	41	1	these	these	PRON
ejpam-5578	41	2	include	include	VERB
ejpam-5578	41	3	fundamental	fundamental	ADJ
ejpam-5578	41	4	notions	notion	NOUN
ejpam-5578	41	5	of	of	ADP
ejpam-5578	41	6	topological	topological	ADJ
ejpam-5578	41	7	spaces	space	NOUN
ejpam-5578	41	8	,	,	PUNCT
ejpam-5578	41	9	tri	tri	ADJ
ejpam-5578	41	10	-	-	ADJ
ejpam-5578	41	11	topological	topological	ADJ
ejpam-5578	41	12	spaces	space	NOUN
ejpam-5578	41	13	,	,	PUNCT
ejpam-5578	41	14	open	open	ADJ
ejpam-5578	41	15	and	and	CCONJ
ejpam-5578	41	16	closed	closed	ADJ
ejpam-5578	41	17	sets	set	NOUN
ejpam-5578	41	18	,	,	PUNCT
ejpam-5578	41	19	derived	derived	ADJ
ejpam-5578	41	20	sets	set	NOUN
ejpam-5578	41	21	,	,	PUNCT
ejpam-5578	41	22	closure	closure	NOUN
ejpam-5578	41	23	and	and	CCONJ
ejpam-5578	41	24	interior	interior	ADJ
ejpam-5578	41	25	sets	set	NOUN
ejpam-5578	41	26	,	,	PUNCT
ejpam-5578	41	27	and	and	CCONJ
ejpam-5578	41	28	separation	separation	NOUN
ejpam-5578	41	29	axioms	axiom	VERB
ejpam-5578	41	30	.	.	PUNCT
ejpam-5578	42	1	additionally	additionally	ADV
ejpam-5578	42	2	,	,	PUNCT
ejpam-5578	42	3	we	we	PRON
ejpam-5578	42	4	introduce	introduce	VERB
ejpam-5578	42	5	the	the	DET
ejpam-5578	42	6	lindelöf	lindelöf	NOUN
ejpam-5578	42	7	property	property	NOUN
ejpam-5578	42	8	in	in	ADP
ejpam-5578	42	9	tri	tri	ADJ
ejpam-5578	42	10	-	-	ADJ
ejpam-5578	42	11	topological	topological	ADJ
ejpam-5578	42	12	spaces	space	NOUN
ejpam-5578	42	13	,	,	PUNCT
ejpam-5578	42	14	which	which	PRON
ejpam-5578	42	15	extends	extend	VERB
ejpam-5578	42	16	the	the	DET
ejpam-5578	42	17	classical	classical	ADJ
ejpam-5578	42	18	lindelöf	lindelöf	NOUN
ejpam-5578	42	19	concept	concept	NOUN
ejpam-5578	42	20	to	to	ADP
ejpam-5578	42	21	settings	setting	NOUN
ejpam-5578	42	22	with	with	ADP
ejpam-5578	42	23	multiple	multiple	ADJ
ejpam-5578	42	24	topologies	topology	NOUN
ejpam-5578	42	25	.	.	PUNCT
ejpam-5578	43	1	the	the	DET
ejpam-5578	43	2	definitions	definition	NOUN
ejpam-5578	43	3	and	and	CCONJ
ejpam-5578	43	4	results	result	NOUN
ejpam-5578	43	5	presented	present	VERB
ejpam-5578	43	6	here	here	ADV
ejpam-5578	43	7	will	will	AUX
ejpam-5578	43	8	be	be	AUX
ejpam-5578	43	9	instrumental	instrumental	ADJ
ejpam-5578	43	10	in	in	ADP
ejpam-5578	43	11	proving	prove	VERB
ejpam-5578	43	12	subsequent	subsequent	ADJ
ejpam-5578	43	13	theorems	theorem	NOUN
ejpam-5578	43	14	and	and	CCONJ
ejpam-5578	43	15	exploring	explore	VERB
ejpam-5578	43	16	the	the	DET
ejpam-5578	43	17	structure	structure	NOUN
ejpam-5578	43	18	of	of	ADP
ejpam-5578	43	19	tri	tri	NOUN
ejpam-5578	43	20	-	-	NOUN
ejpam-5578	43	21	lindelöf	lindelöf	NOUN
ejpam-5578	43	22	and	and	CCONJ
ejpam-5578	43	23	tri	tri	ADJ
ejpam-5578	43	24	-	-	ADJ
ejpam-5578	43	25	metalindelöf	metalindelöf	ADJ
ejpam-5578	43	26	spaces	space	NOUN
ejpam-5578	43	27	.	.	PUNCT
ejpam-5578	44	1	definition	definition	NOUN
ejpam-5578	44	2	1	1	NUM
ejpam-5578	44	3	.	.	PUNCT
ejpam-5578	45	1	[	[	X
ejpam-5578	45	2	16	16	NUM
ejpam-5578	45	3	]	]	PUNCT
ejpam-5578	45	4	let	let	VERB
ejpam-5578	45	5	q	q	PROPN
ejpam-5578	45	6	̸=	̸=	PROPN
ejpam-5578	45	7	∅	∅	NOUN
ejpam-5578	45	8	and	and	CCONJ
ejpam-5578	45	9	let	let	VERB
ejpam-5578	45	10	ϱ	ϱ	PART
ejpam-5578	45	11	be	be	AUX
ejpam-5578	45	12	a	a	DET
ejpam-5578	45	13	collection	collection	NOUN
ejpam-5578	45	14	of	of	ADP
ejpam-5578	45	15	subsets	subset	NOUN
ejpam-5578	45	16	of	of	ADP
ejpam-5578	45	17	q	q	NOUN
ejpam-5578	45	18	,	,	PUNCT
ejpam-5578	45	19	denoted	denote	VERB
ejpam-5578	45	20	by	by	ADP
ejpam-5578	45	21	ϱ	ϱ	ADP
ejpam-5578	45	22	⊆	⊆	NUM
ejpam-5578	45	23	p	p	NOUN
ejpam-5578	45	24	(	(	PUNCT
ejpam-5578	45	25	q	q	NOUN
ejpam-5578	45	26	)	)	PUNCT
ejpam-5578	45	27	=	=	PRON
ejpam-5578	45	28	{	{	PUNCT
ejpam-5578	46	1	o	o	NOUN
ejpam-5578	46	2	|	|	INTJ
ejpam-5578	46	3	o	o	X
ejpam-5578	46	4	⊆	⊆	NUM
ejpam-5578	46	5	q	q	NOUN
ejpam-5578	46	6	}	}	PUNCT
ejpam-5578	46	7	.	.	PUNCT
ejpam-5578	47	1	the	the	DET
ejpam-5578	47	2	collection	collection	NOUN
ejpam-5578	47	3	ϱ	ϱ	NOUN
ejpam-5578	47	4	is	be	AUX
ejpam-5578	47	5	called	call	VERB
ejpam-5578	47	6	a	a	DET
ejpam-5578	47	7	topological	topological	ADJ
ejpam-5578	47	8	space	space	NOUN
ejpam-5578	47	9	on	on	ADP
ejpam-5578	47	10	q	q	PROPN
ejpam-5578	47	11	if	if	SCONJ
ejpam-5578	47	12	it	it	PRON
ejpam-5578	47	13	satisfies	satisfy	VERB
ejpam-5578	47	14	the	the	DET
ejpam-5578	47	15	following	follow	VERB
ejpam-5578	47	16	conditions	condition	NOUN
ejpam-5578	47	17	:	:	PUNCT
ejpam-5578	47	18	(	(	PUNCT
ejpam-5578	47	19	i	i	NOUN
ejpam-5578	47	20	)	)	PUNCT
ejpam-5578	47	21	∅	∅	NOUN
ejpam-5578	47	22	,	,	PUNCT
ejpam-5578	47	23	q	q	PROPN
ejpam-5578	47	24	∈	∈	PROPN
ejpam-5578	47	25	ϱ	ϱ	PROPN
ejpam-5578	47	26	(	(	PUNCT
ejpam-5578	47	27	the	the	DET
ejpam-5578	47	28	empty	empty	ADJ
ejpam-5578	47	29	set	set	NOUN
ejpam-5578	47	30	and	and	CCONJ
ejpam-5578	47	31	the	the	DET
ejpam-5578	47	32	whole	whole	ADJ
ejpam-5578	47	33	space	space	NOUN
ejpam-5578	47	34	are	be	AUX
ejpam-5578	47	35	in	in	ADP
ejpam-5578	47	36	ϱ	ϱ	NOUN
ejpam-5578	47	37	)	)	PUNCT
ejpam-5578	47	38	.	.	PUNCT
ejpam-5578	48	1	(	(	PUNCT
ejpam-5578	48	2	ii	ii	NOUN
ejpam-5578	48	3	)	)	PUNCT
ejpam-5578	48	4	ϱ	ϱ	PROPN
ejpam-5578	48	5	is	be	AUX
ejpam-5578	48	6	closed	close	VERB
ejpam-5578	48	7	under	under	ADP
ejpam-5578	48	8	finite	finite	ADJ
ejpam-5578	48	9	intersections	intersection	NOUN
ejpam-5578	48	10	.	.	PUNCT
ejpam-5578	49	1	(	(	PUNCT
ejpam-5578	49	2	iii	iii	X
ejpam-5578	49	3	)	)	PUNCT
ejpam-5578	49	4	ϱ	ϱ	PROPN
ejpam-5578	49	5	is	be	AUX
ejpam-5578	49	6	closed	close	VERB
ejpam-5578	49	7	under	under	ADP
ejpam-5578	49	8	arbitrary	arbitrary	ADJ
ejpam-5578	49	9	unions	union	NOUN
ejpam-5578	49	10	.	.	PUNCT
ejpam-5578	50	1	definition	definition	NOUN
ejpam-5578	50	2	2	2	NUM
ejpam-5578	50	3	.	.	PUNCT
ejpam-5578	51	1	[	[	X
ejpam-5578	51	2	13	13	NUM
ejpam-5578	51	3	]	]	PUNCT
ejpam-5578	51	4	let	let	VERB
ejpam-5578	51	5	q	q	PROPN
ejpam-5578	51	6	̸=	̸=	PROPN
ejpam-5578	51	7	∅	∅	NOUN
ejpam-5578	51	8	and	and	CCONJ
ejpam-5578	51	9	let	let	VERB
ejpam-5578	51	10	ϱi	ϱi	VERB
ejpam-5578	51	11	⊆	⊆	NUM
ejpam-5578	51	12	p	p	NOUN
ejpam-5578	51	13	(	(	PUNCT
ejpam-5578	51	14	q	q	NOUN
ejpam-5578	51	15	)	)	PUNCT
ejpam-5578	51	16	for	for	ADP
ejpam-5578	51	17	i	i	PROPN
ejpam-5578	51	18	=	=	SYM
ejpam-5578	51	19	1	1	NUM
ejpam-5578	51	20	,	,	PUNCT
ejpam-5578	51	21	2	2	NUM
ejpam-5578	51	22	,	,	PUNCT
ejpam-5578	51	23	3	3	NUM
ejpam-5578	51	24	.	.	X
ejpam-5578	52	1	we	we	PRON
ejpam-5578	52	2	say	say	VERB
ejpam-5578	52	3	that	that	SCONJ
ejpam-5578	52	4	(	(	PUNCT
ejpam-5578	52	5	q	q	X
ejpam-5578	52	6	,	,	PUNCT
ejpam-5578	52	7	ϱ1	ϱ1	NOUN
ejpam-5578	52	8	,	,	PUNCT
ejpam-5578	52	9	ϱ2	ϱ2	NOUN
ejpam-5578	52	10	,	,	PUNCT
ejpam-5578	52	11	ϱ3	ϱ3	PROPN
ejpam-5578	52	12	)	)	PUNCT
ejpam-5578	52	13	is	be	AUX
ejpam-5578	52	14	a	a	DET
ejpam-5578	52	15	tri	tri	ADJ
ejpam-5578	52	16	-	-	ADJ
ejpam-5578	52	17	topological	topological	ADJ
ejpam-5578	52	18	space	space	NOUN
ejpam-5578	52	19	if	if	SCONJ
ejpam-5578	52	20	each	each	PRON
ejpam-5578	52	21	ϱi	ϱi	VERB
ejpam-5578	52	22	is	be	AUX
ejpam-5578	52	23	a	a	DET
ejpam-5578	52	24	topology	topology	NOUN
ejpam-5578	52	25	on	on	ADP
ejpam-5578	52	26	q	q	NOUN
ejpam-5578	52	27	,	,	PUNCT
ejpam-5578	52	28	for	for	ADP
ejpam-5578	52	29	all	all	DET
ejpam-5578	52	30	i	i	PRON
ejpam-5578	52	31	=	=	NOUN
ejpam-5578	52	32	1	1	NUM
ejpam-5578	52	33	,	,	PUNCT
ejpam-5578	52	34	2	2	NUM
ejpam-5578	52	35	,	,	PUNCT
ejpam-5578	52	36	3	3	NUM
ejpam-5578	52	37	.	.	NOUN
ejpam-5578	52	38	example	example	NOUN
ejpam-5578	53	1	1	1	NUM
ejpam-5578	53	2	.	.	PUNCT
ejpam-5578	54	1	the	the	DET
ejpam-5578	54	2	space	space	NOUN
ejpam-5578	54	3	(	(	PUNCT
ejpam-5578	54	4	q	q	ADJ
ejpam-5578	54	5	,	,	PUNCT
ejpam-5578	54	6	ϱ1	ϱ1	NOUN
ejpam-5578	54	7	,	,	PUNCT
ejpam-5578	54	8	ϱ2	ϱ2	NOUN
ejpam-5578	54	9	,	,	PUNCT
ejpam-5578	54	10	ϱ3	ϱ3	PROPN
ejpam-5578	54	11	)	)	PUNCT
ejpam-5578	54	12	a	a	DET
ejpam-5578	54	13	tri	tri	ADJ
ejpam-5578	54	14	-	-	ADJ
ejpam-5578	54	15	topological	topological	ADJ
ejpam-5578	54	16	space	space	NOUN
ejpam-5578	54	17	.	.	PUNCT
ejpam-5578	55	1	to	to	PART
ejpam-5578	55	2	see	see	VERB
ejpam-5578	55	3	this	this	PRON
ejpam-5578	55	4	,	,	PUNCT
ejpam-5578	55	5	consider	consider	VERB
ejpam-5578	55	6	q	q	PUNCT
ejpam-5578	55	7	=	=	PUNCT
ejpam-5578	55	8	{	{	PUNCT
ejpam-5578	55	9	x	x	PROPN
ejpam-5578	55	10	,	,	PUNCT
ejpam-5578	55	11	y	y	PROPN
ejpam-5578	55	12	,	,	PUNCT
ejpam-5578	55	13	z	z	NOUN
ejpam-5578	55	14	}	}	PUNCT
ejpam-5578	55	15	,	,	PUNCT
ejpam-5578	55	16	with	with	ADP
ejpam-5578	55	17	the	the	DET
ejpam-5578	55	18	following	follow	VERB
ejpam-5578	55	19	collections	collection	NOUN
ejpam-5578	55	20	of	of	ADP
ejpam-5578	55	21	subsets	subset	NOUN
ejpam-5578	55	22	:	:	PUNCT
ejpam-5578	55	23	ϱ1	ϱ1	NOUN
ejpam-5578	55	24	=	=	SYM
ejpam-5578	55	25	{	{	PUNCT
ejpam-5578	55	26	∅	∅	NOUN
ejpam-5578	55	27	,	,	PUNCT
ejpam-5578	55	28	q	q	NOUN
ejpam-5578	55	29	,	,	PUNCT
ejpam-5578	55	30	{	{	PUNCT
ejpam-5578	55	31	x	x	NOUN
ejpam-5578	55	32	}	}	PUNCT
ejpam-5578	55	33	}	}	PUNCT
ejpam-5578	55	34	⊆	⊆	NUM
ejpam-5578	55	35	p	p	NOUN
ejpam-5578	55	36	(	(	PUNCT
ejpam-5578	55	37	q	q	NOUN
ejpam-5578	55	38	)	)	PUNCT
ejpam-5578	55	39	,	,	PUNCT
ejpam-5578	55	40	ϱ2	ϱ2	NOUN
ejpam-5578	55	41	=	=	SYM
ejpam-5578	55	42	{	{	PUNCT
ejpam-5578	55	43	∅	∅	NOUN
ejpam-5578	55	44	,	,	PUNCT
ejpam-5578	55	45	q	q	NOUN
ejpam-5578	55	46	,	,	PUNCT
ejpam-5578	55	47	{	{	PUNCT
ejpam-5578	55	48	x	x	NOUN
ejpam-5578	55	49	}	}	PUNCT
ejpam-5578	55	50	,	,	PUNCT
ejpam-5578	55	51	{	{	PUNCT
ejpam-5578	55	52	y	y	NOUN
ejpam-5578	55	53	}	}	PUNCT
ejpam-5578	55	54	,	,	PUNCT
ejpam-5578	55	55	{	{	PUNCT
ejpam-5578	55	56	x	x	NOUN
ejpam-5578	55	57	,	,	PUNCT
ejpam-5578	55	58	y	y	NOUN
ejpam-5578	55	59	}	}	PUNCT
ejpam-5578	55	60	}	}	PUNCT
ejpam-5578	55	61	⊆	⊆	NUM
ejpam-5578	55	62	p	p	NOUN
ejpam-5578	55	63	(	(	PUNCT
ejpam-5578	55	64	q	q	NOUN
ejpam-5578	55	65	)	)	PUNCT
ejpam-5578	55	66	,	,	PUNCT
ejpam-5578	55	67	ϱ3	ϱ3	NOUN
ejpam-5578	55	68	=	=	SYM
ejpam-5578	55	69	{	{	PUNCT
ejpam-5578	55	70	∅	∅	NOUN
ejpam-5578	55	71	,	,	PUNCT
ejpam-5578	55	72	q	q	NOUN
ejpam-5578	55	73	,	,	PUNCT
ejpam-5578	55	74	{	{	PUNCT
ejpam-5578	55	75	y	y	NOUN
ejpam-5578	55	76	}	}	PUNCT
ejpam-5578	55	77	,	,	PUNCT
ejpam-5578	55	78	{	{	PUNCT
ejpam-5578	55	79	z	z	NOUN
ejpam-5578	55	80	}	}	PUNCT
ejpam-5578	55	81	,	,	PUNCT
ejpam-5578	55	82	{	{	PUNCT
ejpam-5578	55	83	y	y	NOUN
ejpam-5578	55	84	,	,	PUNCT
ejpam-5578	55	85	z	z	NOUN
ejpam-5578	55	86	}	}	PUNCT
ejpam-5578	55	87	}	}	PUNCT
ejpam-5578	55	88	⊆	⊆	NUM
ejpam-5578	55	89	p	p	NOUN
ejpam-5578	55	90	(	(	PUNCT
ejpam-5578	55	91	q	q	NOUN
ejpam-5578	55	92	)	)	PUNCT
ejpam-5578	55	93	.	.	PUNCT
ejpam-5578	56	1	since	since	SCONJ
ejpam-5578	56	2	each	each	DET
ejpam-5578	56	3	ϱi	ϱi	NOUN
ejpam-5578	56	4	satisfies	satisfy	VERB
ejpam-5578	56	5	the	the	DET
ejpam-5578	56	6	conditions	condition	NOUN
ejpam-5578	56	7	of	of	ADP
ejpam-5578	56	8	a	a	DET
ejpam-5578	56	9	topology	topology	NOUN
ejpam-5578	56	10	for	for	ADP
ejpam-5578	56	11	i	i	PRON
ejpam-5578	56	12	=	=	SYM
ejpam-5578	56	13	1	1	NUM
ejpam-5578	56	14	,	,	PUNCT
ejpam-5578	56	15	2	2	NUM
ejpam-5578	56	16	,	,	PUNCT
ejpam-5578	56	17	3	3	NUM
ejpam-5578	56	18	,	,	PUNCT
ejpam-5578	56	19	it	it	PRON
ejpam-5578	56	20	follows	follow	VERB
ejpam-5578	56	21	that	that	SCONJ
ejpam-5578	56	22	(	(	PUNCT
ejpam-5578	56	23	q	q	ADJ
ejpam-5578	56	24	,	,	PUNCT
ejpam-5578	56	25	ϱ1	ϱ1	NOUN
ejpam-5578	56	26	,	,	PUNCT
ejpam-5578	56	27	ϱ2	ϱ2	NOUN
ejpam-5578	56	28	,	,	PUNCT
ejpam-5578	56	29	ϱ3	ϱ3	PROPN
ejpam-5578	56	30	)	)	PUNCT
ejpam-5578	56	31	is	be	AUX
ejpam-5578	56	32	a	a	DET
ejpam-5578	56	33	tri	tri	ADJ
ejpam-5578	56	34	-	-	ADJ
ejpam-5578	56	35	topological	topological	ADJ
ejpam-5578	56	36	space	space	NOUN
ejpam-5578	56	37	.	.	PUNCT
ejpam-5578	57	1	however	however	ADV
ejpam-5578	57	2	,	,	PUNCT
ejpam-5578	57	3	consider	consider	VERB
ejpam-5578	57	4	the	the	DET
ejpam-5578	57	5	collection	collection	NOUN
ejpam-5578	57	6	ϱ	ϱ	ADP
ejpam-5578	57	7	=	=	SYM
ejpam-5578	57	8	{	{	PUNCT
ejpam-5578	57	9	∅	∅	NOUN
ejpam-5578	57	10	,	,	PUNCT
ejpam-5578	57	11	q	q	NOUN
ejpam-5578	57	12	,	,	PUNCT
ejpam-5578	57	13	{	{	PUNCT
ejpam-5578	57	14	x	x	NOUN
ejpam-5578	57	15	}	}	PUNCT
ejpam-5578	57	16	,	,	PUNCT
ejpam-5578	57	17	{	{	PUNCT
ejpam-5578	57	18	y	y	NOUN
ejpam-5578	57	19	}	}	PUNCT
ejpam-5578	57	20	}	}	PUNCT
ejpam-5578	57	21	.	.	PUNCT
ejpam-5578	58	1	this	this	PRON
ejpam-5578	58	2	does	do	AUX
ejpam-5578	58	3	not	not	PART
ejpam-5578	58	4	form	form	VERB
ejpam-5578	58	5	a	a	DET
ejpam-5578	58	6	topology	topology	NOUN
ejpam-5578	58	7	on	on	ADP
ejpam-5578	58	8	q	q	PROPN
ejpam-5578	58	9	because	because	SCONJ
ejpam-5578	58	10	it	it	PRON
ejpam-5578	58	11	does	do	AUX
ejpam-5578	58	12	not	not	PART
ejpam-5578	58	13	satisfy	satisfy	VERB
ejpam-5578	58	14	all	all	DET
ejpam-5578	58	15	the	the	DET
ejpam-5578	58	16	conditions	condition	NOUN
ejpam-5578	58	17	required	require	VERB
ejpam-5578	58	18	for	for	ADP
ejpam-5578	58	19	a	a	DET
ejpam-5578	58	20	topology	topology	NOUN
ejpam-5578	58	21	.	.	PUNCT
ejpam-5578	59	1	definition	definition	NOUN
ejpam-5578	59	2	3	3	NUM
ejpam-5578	59	3	.	.	PUNCT
ejpam-5578	60	1	[	[	X
ejpam-5578	60	2	15	15	NUM
ejpam-5578	60	3	]	]	X
ejpam-5578	60	4	let	let	VERB
ejpam-5578	60	5	(	(	PUNCT
ejpam-5578	60	6	q	q	ADJ
ejpam-5578	60	7	,	,	PUNCT
ejpam-5578	60	8	ϱ1	ϱ1	NOUN
ejpam-5578	60	9	,	,	PUNCT
ejpam-5578	60	10	ϱ2	ϱ2	NOUN
ejpam-5578	60	11	,	,	PUNCT
ejpam-5578	60	12	ϱ3	ϱ3	PROPN
ejpam-5578	60	13	)	)	PUNCT
ejpam-5578	60	14	be	be	AUX
ejpam-5578	60	15	a	a	DET
ejpam-5578	60	16	tri	tri	ADJ
ejpam-5578	60	17	-	-	ADJ
ejpam-5578	60	18	topological	topological	ADJ
ejpam-5578	60	19	space	space	NOUN
ejpam-5578	60	20	and	and	CCONJ
ejpam-5578	60	21	let	let	VERB
ejpam-5578	60	22	o	o	PROPN
ejpam-5578	60	23	⊆	⊆	NUM
ejpam-5578	60	24	q.	q.	NOUN
ejpam-5578	60	25	then	then	ADV
ejpam-5578	60	26	:	:	PUNCT
ejpam-5578	60	27	(	(	PUNCT
ejpam-5578	60	28	i	i	NOUN
ejpam-5578	60	29	)	)	PUNCT
ejpam-5578	60	30	o	o	NOUN
ejpam-5578	60	31	is	be	AUX
ejpam-5578	60	32	called	call	VERB
ejpam-5578	60	33	a	a	DET
ejpam-5578	60	34	ϱi	ϱi	ADV
ejpam-5578	60	35	-	-	PUNCT
ejpam-5578	60	36	open	open	NOUN
ejpam-5578	60	37	set	set	NOUN
ejpam-5578	60	38	if	if	SCONJ
ejpam-5578	60	39	o	o	PROPN
ejpam-5578	60	40	∈	∈	PROPN
ejpam-5578	60	41	ϱi	ϱi	VERB
ejpam-5578	60	42	for	for	ADP
ejpam-5578	60	43	some	some	DET
ejpam-5578	60	44	i	i	PRON
ejpam-5578	60	45	∈	∈	PROPN
ejpam-5578	60	46	{	{	PUNCT
ejpam-5578	60	47	1	1	NUM
ejpam-5578	60	48	,	,	PUNCT
ejpam-5578	60	49	2	2	NUM
ejpam-5578	60	50	,	,	PUNCT
ejpam-5578	60	51	3	3	NUM
ejpam-5578	60	52	}	}	PUNCT
ejpam-5578	60	53	.	.	PUNCT
ejpam-5578	61	1	(	(	PUNCT
ejpam-5578	61	2	ii	ii	NOUN
ejpam-5578	61	3	)	)	PUNCT
ejpam-5578	61	4	o	o	NOUN
ejpam-5578	61	5	is	be	AUX
ejpam-5578	61	6	called	call	VERB
ejpam-5578	61	7	a	a	DET
ejpam-5578	61	8	ϱi	ϱi	ADV
ejpam-5578	61	9	-	-	PUNCT
ejpam-5578	61	10	closed	close	VERB
ejpam-5578	61	11	set	set	NOUN
ejpam-5578	61	12	if	if	SCONJ
ejpam-5578	61	13	its	its	PRON
ejpam-5578	61	14	complement	complement	NOUN
ejpam-5578	61	15	,	,	PUNCT
ejpam-5578	61	16	oc	oc	PROPN
ejpam-5578	61	17	,	,	PUNCT
ejpam-5578	61	18	belongs	belong	VERB
ejpam-5578	61	19	to	to	PART
ejpam-5578	61	20	ϱi	ϱi	VERB
ejpam-5578	61	21	for	for	ADP
ejpam-5578	61	22	some	some	DET
ejpam-5578	61	23	i	i	PRON
ejpam-5578	61	24	∈	∈	PROPN
ejpam-5578	61	25	{	{	PUNCT
ejpam-5578	61	26	1	1	NUM
ejpam-5578	61	27	,	,	PUNCT
ejpam-5578	61	28	2	2	NUM
ejpam-5578	61	29	,	,	PUNCT
ejpam-5578	61	30	3	3	NUM
ejpam-5578	61	31	}	}	PUNCT
ejpam-5578	61	32	.	.	PUNCT
ejpam-5578	62	1	(	(	PUNCT
ejpam-5578	62	2	iii	iii	X
ejpam-5578	62	3	)	)	PUNCT
ejpam-5578	62	4	o	o	NOUN
ejpam-5578	62	5	is	be	AUX
ejpam-5578	62	6	called	call	VERB
ejpam-5578	62	7	a	a	DET
ejpam-5578	62	8	ϱi	ϱi	ADJ
ejpam-5578	62	9	-	-	PUNCT
ejpam-5578	62	10	clopen	clopen	ADJ
ejpam-5578	62	11	set	set	NOUN
ejpam-5578	62	12	if	if	SCONJ
ejpam-5578	62	13	both	both	DET
ejpam-5578	62	14	o	o	NOUN
ejpam-5578	62	15	and	and	CCONJ
ejpam-5578	62	16	oc	oc	PART
ejpam-5578	62	17	belong	belong	VERB
ejpam-5578	62	18	to	to	PART
ejpam-5578	62	19	ϱi	ϱi	VERB
ejpam-5578	62	20	for	for	ADP
ejpam-5578	62	21	some	some	DET
ejpam-5578	62	22	i	i	PRON
ejpam-5578	62	23	∈	∈	PROPN
ejpam-5578	62	24	{	{	PUNCT
ejpam-5578	62	25	1	1	NUM
ejpam-5578	62	26	,	,	PUNCT
ejpam-5578	62	27	2	2	NUM
ejpam-5578	62	28	,	,	PUNCT
ejpam-5578	62	29	3	3	NUM
ejpam-5578	62	30	}	}	PUNCT
ejpam-5578	62	31	.	.	PUNCT
ejpam-5578	63	1	j.	j.	PROPN
ejpam-5578	63	2	oudetallah	oudetallah	PROPN
ejpam-5578	63	3	et	et	PROPN
ejpam-5578	63	4	al	al	PROPN
ejpam-5578	63	5	.	.	PUNCT
ejpam-5578	63	6	/	/	SYM
ejpam-5578	63	7	eur	eur	PROPN
ejpam-5578	63	8	.	.	PUNCT
ejpam-5578	64	1	j.	j.	PROPN
ejpam-5578	64	2	pure	pure	PROPN
ejpam-5578	64	3	appl	appl	PROPN
ejpam-5578	64	4	.	.	PROPN
ejpam-5578	64	5	math	math	PROPN
ejpam-5578	64	6	,	,	PUNCT
ejpam-5578	64	7	18	18	NUM
ejpam-5578	64	8	(	(	PUNCT
ejpam-5578	64	9	2	2	NUM
ejpam-5578	64	10	)	)	PUNCT
ejpam-5578	64	11	(	(	PUNCT
ejpam-5578	64	12	2025	2025	NUM
ejpam-5578	64	13	)	)	PUNCT
ejpam-5578	64	14	,	,	PUNCT
ejpam-5578	64	15	5578	5578	NUM
ejpam-5578	64	16	4	4	NUM
ejpam-5578	64	17	of	of	ADP
ejpam-5578	64	18	19	19	NUM
ejpam-5578	64	19	definition	definition	NOUN
ejpam-5578	64	20	4	4	NUM
ejpam-5578	64	21	.	.	PUNCT
ejpam-5578	65	1	[	[	X
ejpam-5578	65	2	14	14	NUM
ejpam-5578	65	3	]	]	X
ejpam-5578	65	4	let	let	VERB
ejpam-5578	65	5	(	(	PUNCT
ejpam-5578	65	6	q	q	ADJ
ejpam-5578	65	7	,	,	PUNCT
ejpam-5578	65	8	ϱ1	ϱ1	NOUN
ejpam-5578	65	9	,	,	PUNCT
ejpam-5578	65	10	ϱ2	ϱ2	NOUN
ejpam-5578	65	11	,	,	PUNCT
ejpam-5578	65	12	ϱ3	ϱ3	PROPN
ejpam-5578	65	13	)	)	PUNCT
ejpam-5578	65	14	be	be	AUX
ejpam-5578	65	15	a	a	DET
ejpam-5578	65	16	tri	tri	ADJ
ejpam-5578	65	17	-	-	ADJ
ejpam-5578	65	18	topological	topological	ADJ
ejpam-5578	65	19	space	space	NOUN
ejpam-5578	65	20	,	,	PUNCT
ejpam-5578	65	21	where	where	SCONJ
ejpam-5578	65	22	q	q	NOUN
ejpam-5578	65	23	̸=	̸=	PROPN
ejpam-5578	65	24	∅	∅	NOUN
ejpam-5578	65	25	and	and	CCONJ
ejpam-5578	65	26	o	o	NOUN
ejpam-5578	65	27	⊆	⊆	NUM
ejpam-5578	65	28	q.	q.	NOUN
ejpam-5578	65	29	a	a	DET
ejpam-5578	65	30	point	point	NOUN
ejpam-5578	65	31	q	q	X
ejpam-5578	65	32	∈	∈	NOUN
ejpam-5578	65	33	q	q	NOUN
ejpam-5578	65	34	is	be	AUX
ejpam-5578	65	35	called	call	VERB
ejpam-5578	65	36	a	a	DET
ejpam-5578	65	37	tri	tri	ADJ
ejpam-5578	65	38	-	-	ADJ
ejpam-5578	65	39	limit	limit	ADJ
ejpam-5578	65	40	point	point	NOUN
ejpam-5578	65	41	of	of	ADP
ejpam-5578	65	42	o	o	NOUN
ejpam-5578	65	43	if	if	SCONJ
ejpam-5578	65	44	for	for	ADP
ejpam-5578	65	45	every	every	DET
ejpam-5578	65	46	ϱi	ϱi	ADJ
ejpam-5578	65	47	-	-	PUNCT
ejpam-5578	65	48	open	open	ADJ
ejpam-5578	65	49	set	set	VERB
ejpam-5578	65	50	uq	uq	NOUN
ejpam-5578	65	51	containing	contain	VERB
ejpam-5578	65	52	q	q	PROPN
ejpam-5578	65	53	,	,	PUNCT
ejpam-5578	65	54	we	we	PRON
ejpam-5578	65	55	have	have	VERB
ejpam-5578	65	56	:	:	PUNCT
ejpam-5578	65	57	uq	uq	PROPN
ejpam-5578	65	58	∩	∩	NOUN
ejpam-5578	65	59	(	(	PUNCT
ejpam-5578	65	60	o	o	NOUN
ejpam-5578	65	61	\	\	PROPN
ejpam-5578	65	62	{	{	PUNCT
ejpam-5578	65	63	q	q	NOUN
ejpam-5578	65	64	}	}	PUNCT
ejpam-5578	65	65	)	)	PUNCT
ejpam-5578	65	66	̸=	̸=	NOUN
ejpam-5578	65	67	∅	∅	NOUN
ejpam-5578	65	68	,	,	PUNCT
ejpam-5578	65	69	for	for	ADP
ejpam-5578	65	70	all	all	PRON
ejpam-5578	65	71	i	i	PRON
ejpam-5578	65	72	∈	∈	PROPN
ejpam-5578	65	73	{	{	PUNCT
ejpam-5578	65	74	1	1	NUM
ejpam-5578	65	75	,	,	PUNCT
ejpam-5578	65	76	2	2	NUM
ejpam-5578	65	77	,	,	PUNCT
ejpam-5578	65	78	3	3	NUM
ejpam-5578	65	79	}	}	PUNCT
ejpam-5578	65	80	.	.	PUNCT
ejpam-5578	66	1	the	the	DET
ejpam-5578	66	2	set	set	NOUN
ejpam-5578	66	3	of	of	ADP
ejpam-5578	66	4	all	all	DET
ejpam-5578	66	5	tri	tri	ADJ
ejpam-5578	66	6	-	-	ADJ
ejpam-5578	66	7	limit	limit	ADJ
ejpam-5578	66	8	points	point	NOUN
ejpam-5578	66	9	in	in	ADP
ejpam-5578	66	10	a	a	DET
ejpam-5578	66	11	tri	tri	ADJ
ejpam-5578	66	12	-	-	ADJ
ejpam-5578	66	13	topological	topological	ADJ
ejpam-5578	66	14	space	space	NOUN
ejpam-5578	66	15	is	be	AUX
ejpam-5578	66	16	called	call	VERB
ejpam-5578	66	17	the	the	DET
ejpam-5578	66	18	tri	tri	ADJ
ejpam-5578	66	19	-	-	ADJ
ejpam-5578	66	20	derived	derived	ADJ
ejpam-5578	66	21	set	set	NOUN
ejpam-5578	66	22	,	,	PUNCT
ejpam-5578	66	23	denoted	denote	VERB
ejpam-5578	66	24	by	by	ADP
ejpam-5578	66	25	:	:	PUNCT
ejpam-5578	66	26	o′	o′	X
ejpam-5578	66	27	=	=	PUNCT
ejpam-5578	67	1	{	{	PUNCT
ejpam-5578	67	2	q	q	X
ejpam-5578	67	3	|	|	ADV
ejpam-5578	67	4	q	q	NOUN
ejpam-5578	67	5	is	be	AUX
ejpam-5578	67	6	a	a	DET
ejpam-5578	67	7	tri	tri	ADJ
ejpam-5578	67	8	-	-	ADJ
ejpam-5578	67	9	limit	limit	ADJ
ejpam-5578	67	10	point	point	NOUN
ejpam-5578	67	11	of	of	ADP
ejpam-5578	67	12	o	o	NOUN
ejpam-5578	67	13	}	}	PUNCT
ejpam-5578	67	14	.	.	PUNCT
ejpam-5578	68	1	lemma	lemma	PROPN
ejpam-5578	68	2	1	1	NUM
ejpam-5578	68	3	.	.	PUNCT
ejpam-5578	69	1	[	[	X
ejpam-5578	69	2	13](properties	13](properties	NUM
ejpam-5578	69	3	of	of	ADP
ejpam-5578	69	4	the	the	DET
ejpam-5578	69	5	tripartite	tripartite	ADJ
ejpam-5578	69	6	derived	derive	VERB
ejpam-5578	69	7	set	set	NOUN
ejpam-5578	69	8	)	)	PUNCT
ejpam-5578	69	9	let	let	VERB
ejpam-5578	69	10	(	(	PUNCT
ejpam-5578	69	11	q	q	ADJ
ejpam-5578	69	12	,	,	PUNCT
ejpam-5578	69	13	ϱ1	ϱ1	NOUN
ejpam-5578	69	14	,	,	PUNCT
ejpam-5578	69	15	ϱ2	ϱ2	NOUN
ejpam-5578	69	16	,	,	PUNCT
ejpam-5578	69	17	ϱ3	ϱ3	PROPN
ejpam-5578	69	18	)	)	PUNCT
ejpam-5578	69	19	be	be	AUX
ejpam-5578	69	20	a	a	DET
ejpam-5578	69	21	tri	tri	ADJ
ejpam-5578	69	22	-	-	ADJ
ejpam-5578	69	23	topological	topological	ADJ
ejpam-5578	69	24	space	space	NOUN
ejpam-5578	69	25	,	,	PUNCT
ejpam-5578	69	26	and	and	CCONJ
ejpam-5578	69	27	let	let	VERB
ejpam-5578	69	28	o	o	NOUN
ejpam-5578	69	29	,	,	PUNCT
ejpam-5578	69	30	b	b	PROPN
ejpam-5578	69	31	⊆	⊆	NUM
ejpam-5578	69	32	q.	q.	NOUN
ejpam-5578	69	33	then	then	ADV
ejpam-5578	69	34	:	:	PUNCT
ejpam-5578	69	35	(	(	PUNCT
ejpam-5578	69	36	i	i	NOUN
ejpam-5578	69	37	)	)	PUNCT
ejpam-5578	69	38	∅′	∅′	VERB
ejpam-5578	69	39	=	=	SYM
ejpam-5578	69	40	∅.	∅.	X
ejpam-5578	69	41	(	(	PUNCT
ejpam-5578	69	42	ii	ii	NOUN
ejpam-5578	69	43	)	)	PUNCT
ejpam-5578	70	1	if	if	SCONJ
ejpam-5578	70	2	o	o	PROPN
ejpam-5578	70	3	⊆	⊆	NUM
ejpam-5578	70	4	b	b	NOUN
ejpam-5578	70	5	,	,	PUNCT
ejpam-5578	70	6	then	then	ADV
ejpam-5578	70	7	o′	o′	PROPN
ejpam-5578	70	8	⊆	⊆	NUM
ejpam-5578	70	9	b′.	b′.	PROPN
ejpam-5578	70	10	(	(	PUNCT
ejpam-5578	70	11	iii	iii	NOUN
ejpam-5578	70	12	)	)	PUNCT
ejpam-5578	70	13	(	(	PUNCT
ejpam-5578	70	14	o	o	X
ejpam-5578	70	15	∪b)′	∪b)′	X
ejpam-5578	70	16	=	=	PUNCT
ejpam-5578	70	17	o′	o′	X
ejpam-5578	70	18	∪b′.	∪b′.	PROPN
ejpam-5578	70	19	(	(	PUNCT
ejpam-5578	70	20	iv	iv	X
ejpam-5578	70	21	)	)	PUNCT
ejpam-5578	70	22	(	(	PUNCT
ejpam-5578	70	23	o	o	NOUN
ejpam-5578	70	24	∩b)′	∩b)′	PROPN
ejpam-5578	70	25	⊆	⊆	NUM
ejpam-5578	70	26	o′	o′	NUM
ejpam-5578	70	27	∩b′.	∩b′.	ADJ
ejpam-5578	70	28	proof	proof	NOUN
ejpam-5578	70	29	.	.	PUNCT
ejpam-5578	71	1	(	(	PUNCT
ejpam-5578	71	2	i	i	NOUN
ejpam-5578	71	3	)	)	PUNCT
ejpam-5578	71	4	by	by	ADP
ejpam-5578	71	5	contradiction	contradiction	NOUN
ejpam-5578	71	6	:	:	PUNCT
ejpam-5578	71	7	assume	assume	VERB
ejpam-5578	71	8	that	that	SCONJ
ejpam-5578	71	9	∅′	∅′	VERB
ejpam-5578	71	10	̸=	̸=	PROPN
ejpam-5578	71	11	∅.	∅.	ADP
ejpam-5578	71	12	then	then	ADV
ejpam-5578	71	13	,	,	PUNCT
ejpam-5578	71	14	there	there	PRON
ejpam-5578	71	15	exists	exist	VERB
ejpam-5578	71	16	z	z	PROPN
ejpam-5578	71	17	∈	∈	PROPN
ejpam-5578	71	18	∅′	∅′	NOUN
ejpam-5578	71	19	,	,	PUNCT
ejpam-5578	71	20	meaning	mean	VERB
ejpam-5578	71	21	that	that	SCONJ
ejpam-5578	71	22	for	for	ADP
ejpam-5578	71	23	all	all	DET
ejpam-5578	71	24	ϱi	ϱi	ADJ
ejpam-5578	71	25	-	-	PUNCT
ejpam-5578	71	26	open	open	ADJ
ejpam-5578	71	27	sets	set	NOUN
ejpam-5578	71	28	uz	uz	NOUN
ejpam-5578	71	29	,	,	PUNCT
ejpam-5578	71	30	we	we	PRON
ejpam-5578	71	31	have	have	VERB
ejpam-5578	71	32	:	:	PUNCT
ejpam-5578	71	33	uz	uz	PROPN
ejpam-5578	71	34	∩	∩	NOUN
ejpam-5578	71	35	(	(	PUNCT
ejpam-5578	71	36	∅	∅	NOUN
ejpam-5578	71	37	−	−	NOUN
ejpam-5578	71	38	{	{	PUNCT
ejpam-5578	71	39	z	z	NOUN
ejpam-5578	71	40	}	}	PUNCT
ejpam-5578	71	41	)	)	PUNCT
ejpam-5578	71	42	̸=	̸=	PROPN
ejpam-5578	71	43	∅.	∅.	VERB
ejpam-5578	71	44	however	however	ADV
ejpam-5578	71	45	,	,	PUNCT
ejpam-5578	71	46	since	since	SCONJ
ejpam-5578	71	47	(	(	PUNCT
ejpam-5578	71	48	∅	∅	NOUN
ejpam-5578	71	49	−	−	NOUN
ejpam-5578	71	50	{	{	PUNCT
ejpam-5578	71	51	z	z	NOUN
ejpam-5578	71	52	}	}	PUNCT
ejpam-5578	71	53	)	)	PUNCT
ejpam-5578	72	1	=	=	SYM
ejpam-5578	72	2	∅	∅	NOUN
ejpam-5578	72	3	,	,	PUNCT
ejpam-5578	72	4	we	we	PRON
ejpam-5578	72	5	obtain	obtain	VERB
ejpam-5578	72	6	:	:	PUNCT
ejpam-5578	72	7	uz	uz	NOUN
ejpam-5578	72	8	∩	∩	ADJ
ejpam-5578	72	9	∅	∅	NOUN
ejpam-5578	72	10	=	=	NOUN
ejpam-5578	72	11	̸	̸	X
ejpam-5578	72	12	∅.	∅.	NOUN
ejpam-5578	72	13	this	this	PRON
ejpam-5578	72	14	contradicts	contradict	VERB
ejpam-5578	72	15	the	the	DET
ejpam-5578	72	16	fact	fact	NOUN
ejpam-5578	72	17	that	that	SCONJ
ejpam-5578	72	18	the	the	DET
ejpam-5578	72	19	intersection	intersection	NOUN
ejpam-5578	72	20	of	of	ADP
ejpam-5578	72	21	any	any	DET
ejpam-5578	72	22	set	set	NOUN
ejpam-5578	72	23	with	with	ADP
ejpam-5578	72	24	the	the	DET
ejpam-5578	72	25	empty	empty	ADJ
ejpam-5578	72	26	set	set	NOUN
ejpam-5578	72	27	is	be	AUX
ejpam-5578	72	28	always	always	ADV
ejpam-5578	72	29	empty	empty	ADJ
ejpam-5578	72	30	.	.	PUNCT
ejpam-5578	73	1	therefore	therefore	ADV
ejpam-5578	73	2	,	,	PUNCT
ejpam-5578	73	3	∅′	∅′	VERB
ejpam-5578	73	4	=	=	PUNCT
ejpam-5578	73	5	∅.	∅.	PRON
ejpam-5578	73	6	definition	definition	NOUN
ejpam-5578	73	7	5	5	NUM
ejpam-5578	73	8	.	.	PUNCT
ejpam-5578	74	1	[	[	X
ejpam-5578	74	2	16	16	NUM
ejpam-5578	74	3	]	]	X
ejpam-5578	74	4	let	let	VERB
ejpam-5578	74	5	(	(	PUNCT
ejpam-5578	74	6	q	q	ADJ
ejpam-5578	74	7	,	,	PUNCT
ejpam-5578	74	8	ϱ1	ϱ1	NOUN
ejpam-5578	74	9	,	,	PUNCT
ejpam-5578	74	10	ϱ2	ϱ2	NOUN
ejpam-5578	74	11	,	,	PUNCT
ejpam-5578	74	12	ϱ3	ϱ3	PROPN
ejpam-5578	74	13	)	)	PUNCT
ejpam-5578	74	14	be	be	AUX
ejpam-5578	74	15	a	a	DET
ejpam-5578	74	16	tri	tri	ADJ
ejpam-5578	74	17	-	-	ADJ
ejpam-5578	74	18	topological	topological	ADJ
ejpam-5578	74	19	space	space	NOUN
ejpam-5578	74	20	,	,	PUNCT
ejpam-5578	74	21	where	where	SCONJ
ejpam-5578	74	22	q	q	NOUN
ejpam-5578	74	23	̸=	̸=	PROPN
ejpam-5578	74	24	∅	∅	NOUN
ejpam-5578	74	25	and	and	CCONJ
ejpam-5578	74	26	o	o	NOUN
ejpam-5578	74	27	⊆	⊆	NUM
ejpam-5578	74	28	q.	q.	NOUN
ejpam-5578	74	29	the	the	DET
ejpam-5578	74	30	tri	tri	ADJ
ejpam-5578	74	31	-	-	ADJ
ejpam-5578	74	32	closure	closure	ADJ
ejpam-5578	74	33	set	set	NOUN
ejpam-5578	74	34	of	of	ADP
ejpam-5578	74	35	o	o	PROPN
ejpam-5578	74	36	is	be	AUX
ejpam-5578	74	37	denoted	denote	VERB
ejpam-5578	74	38	by	by	ADP
ejpam-5578	74	39	:	:	PUNCT
ejpam-5578	74	40	o	o	X
ejpam-5578	74	41	=	=	PUNCT
ejpam-5578	75	1	o	o	X
ejpam-5578	75	2	∪o′.	∪o′.	PRON
ejpam-5578	75	3	lemma	lemma	PROPN
ejpam-5578	75	4	2	2	NUM
ejpam-5578	75	5	.	.	PUNCT
ejpam-5578	76	1	[	[	X
ejpam-5578	76	2	5	5	NUM
ejpam-5578	76	3	]	]	PUNCT
ejpam-5578	76	4	(	(	PUNCT
ejpam-5578	76	5	properties	property	NOUN
ejpam-5578	76	6	of	of	ADP
ejpam-5578	76	7	the	the	DET
ejpam-5578	76	8	tripartite	tripartite	ADJ
ejpam-5578	76	9	closure	closure	NOUN
ejpam-5578	76	10	set	set	NOUN
ejpam-5578	76	11	)	)	PUNCT
ejpam-5578	76	12	let	let	VERB
ejpam-5578	76	13	(	(	PUNCT
ejpam-5578	76	14	q	q	ADJ
ejpam-5578	76	15	,	,	PUNCT
ejpam-5578	76	16	ϱ1	ϱ1	NOUN
ejpam-5578	76	17	,	,	PUNCT
ejpam-5578	76	18	ϱ2	ϱ2	NOUN
ejpam-5578	76	19	,	,	PUNCT
ejpam-5578	76	20	ϱ3	ϱ3	PROPN
ejpam-5578	76	21	)	)	PUNCT
ejpam-5578	76	22	be	be	AUX
ejpam-5578	76	23	a	a	DET
ejpam-5578	76	24	tri	tri	ADJ
ejpam-5578	76	25	-	-	ADJ
ejpam-5578	76	26	topological	topological	ADJ
ejpam-5578	76	27	space	space	NOUN
ejpam-5578	76	28	,	,	PUNCT
ejpam-5578	76	29	and	and	CCONJ
ejpam-5578	76	30	let	let	VERB
ejpam-5578	76	31	o	o	NOUN
ejpam-5578	76	32	,	,	PUNCT
ejpam-5578	76	33	b	b	PROPN
ejpam-5578	76	34	⊆	⊆	NUM
ejpam-5578	76	35	q.	q.	NOUN
ejpam-5578	76	36	then	then	ADV
ejpam-5578	76	37	:	:	PUNCT
ejpam-5578	76	38	(	(	PUNCT
ejpam-5578	76	39	i	i	NOUN
ejpam-5578	76	40	)	)	PUNCT
ejpam-5578	76	41	∅	∅	NOUN
ejpam-5578	76	42	=	=	NOUN
ejpam-5578	76	43	∅	∅	NOUN
ejpam-5578	76	44	and	and	CCONJ
ejpam-5578	76	45	q	q	NOUN
ejpam-5578	76	46	=	=	PUNCT
ejpam-5578	76	47	q.	q.	PROPN
ejpam-5578	76	48	(	(	PUNCT
ejpam-5578	76	49	ii	ii	NOUN
ejpam-5578	76	50	)	)	PUNCT
ejpam-5578	76	51	o	o	NOUN
ejpam-5578	76	52	∪b	∪b	PUNCT
ejpam-5578	76	53	=	=	PUNCT
ejpam-5578	76	54	o	o	NOUN
ejpam-5578	76	55	∪b	∪b	X
ejpam-5578	76	56	and	and	CCONJ
ejpam-5578	76	57	o	o	NOUN
ejpam-5578	76	58	∩b	∩b	NOUN
ejpam-5578	76	59	⊆	⊆	NUM
ejpam-5578	76	60	o	o	NOUN
ejpam-5578	76	61	∩b	∩b	NOUN
ejpam-5578	76	62	.	.	PUNCT
ejpam-5578	77	1	(	(	PUNCT
ejpam-5578	77	2	iii	iii	X
ejpam-5578	77	3	)	)	PUNCT
ejpam-5578	77	4	o	o	NOUN
ejpam-5578	77	5	is	be	AUX
ejpam-5578	77	6	a	a	DET
ejpam-5578	77	7	ϱi	ϱi	ADV
ejpam-5578	77	8	-	-	PUNCT
ejpam-5578	77	9	closed	closed	ADJ
ejpam-5578	77	10	set	set	NOUN
ejpam-5578	77	11	.	.	PUNCT
ejpam-5578	78	1	(	(	PUNCT
ejpam-5578	78	2	iv	iv	X
ejpam-5578	78	3	)	)	PUNCT
ejpam-5578	78	4	o	o	NOUN
ejpam-5578	79	1	=	=	PUNCT
ejpam-5578	79	2	o	o	NOUN
ejpam-5578	79	3	if	if	SCONJ
ejpam-5578	79	4	and	and	CCONJ
ejpam-5578	79	5	only	only	ADV
ejpam-5578	79	6	if	if	SCONJ
ejpam-5578	79	7	o	o	NOUN
ejpam-5578	79	8	is	be	AUX
ejpam-5578	79	9	a	a	DET
ejpam-5578	79	10	ϱi	ϱi	ADV
ejpam-5578	79	11	-	-	PUNCT
ejpam-5578	79	12	closed	close	VERB
ejpam-5578	79	13	set	set	NOUN
ejpam-5578	79	14	.	.	PUNCT
ejpam-5578	80	1	(	(	PUNCT
ejpam-5578	80	2	v	v	NOUN
ejpam-5578	80	3	)	)	PUNCT
ejpam-5578	80	4	q	q	NOUN
ejpam-5578	81	1	∈	∈	NOUN
ejpam-5578	81	2	o	o	NOUN
ejpam-5578	82	1	if	if	SCONJ
ejpam-5578	82	2	and	and	CCONJ
ejpam-5578	82	3	only	only	ADV
ejpam-5578	82	4	if	if	SCONJ
ejpam-5578	82	5	for	for	ADP
ejpam-5578	82	6	every	every	DET
ejpam-5578	82	7	ϱi	ϱi	ADJ
ejpam-5578	82	8	-	-	PUNCT
ejpam-5578	82	9	open	open	ADJ
ejpam-5578	82	10	set	set	ADJ
ejpam-5578	82	11	uq	uq	NOUN
ejpam-5578	82	12	such	such	ADJ
ejpam-5578	82	13	that	that	DET
ejpam-5578	82	14	q	q	PROPN
ejpam-5578	82	15	∈	∈	PROPN
ejpam-5578	82	16	uq	uq	NOUN
ejpam-5578	82	17	,	,	PUNCT
ejpam-5578	82	18	we	we	PRON
ejpam-5578	82	19	have	have	VERB
ejpam-5578	82	20	uq	uq	NOUN
ejpam-5578	82	21	∩o	∩o	NOUN
ejpam-5578	82	22	̸=	̸=	PROPN
ejpam-5578	82	23	∅.	∅.	PRON
ejpam-5578	82	24	j.	j.	PROPN
ejpam-5578	82	25	oudetallah	oudetallah	PROPN
ejpam-5578	82	26	et	et	PROPN
ejpam-5578	82	27	al	al	PROPN
ejpam-5578	82	28	.	.	PUNCT
ejpam-5578	82	29	/	/	SYM
ejpam-5578	82	30	eur	eur	PROPN
ejpam-5578	82	31	.	.	PUNCT
ejpam-5578	83	1	j.	j.	PROPN
ejpam-5578	83	2	pure	pure	PROPN
ejpam-5578	83	3	appl	appl	PROPN
ejpam-5578	83	4	.	.	PROPN
ejpam-5578	83	5	math	math	PROPN
ejpam-5578	83	6	,	,	PUNCT
ejpam-5578	83	7	18	18	NUM
ejpam-5578	83	8	(	(	PUNCT
ejpam-5578	83	9	2	2	NUM
ejpam-5578	83	10	)	)	PUNCT
ejpam-5578	83	11	(	(	PUNCT
ejpam-5578	83	12	2025	2025	NUM
ejpam-5578	83	13	)	)	PUNCT
ejpam-5578	83	14	,	,	PUNCT
ejpam-5578	83	15	5578	5578	NUM
ejpam-5578	83	16	5	5	NUM
ejpam-5578	83	17	of	of	ADP
ejpam-5578	83	18	19	19	NUM
ejpam-5578	83	19	proof	proof	NOUN
ejpam-5578	83	20	.	.	PUNCT
ejpam-5578	84	1	(	(	PUNCT
ejpam-5578	84	2	ii	ii	NOUN
ejpam-5578	84	3	)	)	PUNCT
ejpam-5578	84	4	let	let	VERB
ejpam-5578	84	5	o	o	NOUN
ejpam-5578	84	6	,	,	PUNCT
ejpam-5578	84	7	b	b	PROPN
ejpam-5578	84	8	⊆	⊆	NUM
ejpam-5578	84	9	q.	q.	NOUN
ejpam-5578	84	10	then	then	ADV
ejpam-5578	84	11	:	:	PUNCT
ejpam-5578	84	12	o	o	X
ejpam-5578	84	13	∪b	∪b	X
ejpam-5578	85	1	=	=	PUNCT
ejpam-5578	85	2	(	(	PUNCT
ejpam-5578	85	3	o	o	X
ejpam-5578	85	4	∪b	∪b	NOUN
ejpam-5578	85	5	)	)	PUNCT
ejpam-5578	85	6	∪	∪	ADV
ejpam-5578	85	7	(	(	PUNCT
ejpam-5578	85	8	o	o	NOUN
ejpam-5578	85	9	∪b)′	∪b)′	X
ejpam-5578	85	10	=	=	PUNCT
ejpam-5578	85	11	(	(	PUNCT
ejpam-5578	85	12	o	o	NOUN
ejpam-5578	85	13	∪b	∪b	NOUN
ejpam-5578	85	14	)	)	PUNCT
ejpam-5578	85	15	∪	∪	X
ejpam-5578	85	16	(	(	PUNCT
ejpam-5578	85	17	o′	o′	NUM
ejpam-5578	85	18	∪b′	∪b′	NOUN
ejpam-5578	85	19	)	)	PUNCT
ejpam-5578	85	20	=	=	PRON
ejpam-5578	85	21	(	(	PUNCT
ejpam-5578	85	22	o	o	X
ejpam-5578	85	23	∪o′	∪o′	X
ejpam-5578	85	24	)	)	PUNCT
ejpam-5578	85	25	∪	∪	ADP
ejpam-5578	85	26	(	(	PUNCT
ejpam-5578	85	27	b	b	NOUN
ejpam-5578	85	28	∪b′	∪b′	NOUN
ejpam-5578	85	29	)	)	PUNCT
ejpam-5578	85	30	=	=	SYM
ejpam-5578	85	31	o	o	NOUN
ejpam-5578	85	32	∪b	∪b	X
ejpam-5578	85	33	.	.	PUNCT
ejpam-5578	86	1	similarly	similarly	ADV
ejpam-5578	86	2	,	,	PUNCT
ejpam-5578	86	3	for	for	ADP
ejpam-5578	86	4	the	the	DET
ejpam-5578	86	5	intersection	intersection	NOUN
ejpam-5578	86	6	property	property	NOUN
ejpam-5578	86	7	:	:	PUNCT
ejpam-5578	86	8	o	o	NOUN
ejpam-5578	86	9	∩b	∩b	NOUN
ejpam-5578	86	10	=	=	PUNCT
ejpam-5578	86	11	(	(	PUNCT
ejpam-5578	86	12	o	o	NOUN
ejpam-5578	86	13	∩b	∩b	PROPN
ejpam-5578	86	14	)	)	PUNCT
ejpam-5578	86	15	∪	∪	NOUN
ejpam-5578	86	16	(	(	PUNCT
ejpam-5578	86	17	o	o	NOUN
ejpam-5578	86	18	∩b)′	∩b)′	PROPN
ejpam-5578	86	19	⊆	⊆	NUM
ejpam-5578	86	20	(	(	PUNCT
ejpam-5578	86	21	o	o	NOUN
ejpam-5578	86	22	∩b	∩b	PROPN
ejpam-5578	86	23	)	)	PUNCT
ejpam-5578	86	24	∪	∪	NOUN
ejpam-5578	86	25	(	(	PUNCT
ejpam-5578	86	26	o′	o′	X
ejpam-5578	86	27	∩b′	∩b′	PROPN
ejpam-5578	86	28	)	)	PUNCT
ejpam-5578	87	1	⊆	⊆	NUM
ejpam-5578	87	2	(	(	PUNCT
ejpam-5578	87	3	o	o	NOUN
ejpam-5578	87	4	∪o′	∪o′	X
ejpam-5578	87	5	)	)	PUNCT
ejpam-5578	87	6	∩	∩	NOUN
ejpam-5578	87	7	(	(	PUNCT
ejpam-5578	87	8	b	b	NOUN
ejpam-5578	87	9	∪b′	∪b′	NOUN
ejpam-5578	87	10	)	)	PUNCT
ejpam-5578	87	11	=	=	SYM
ejpam-5578	87	12	o	o	NOUN
ejpam-5578	87	13	∩b	∩b	PROPN
ejpam-5578	87	14	.	.	PUNCT
ejpam-5578	88	1	definition	definition	NOUN
ejpam-5578	88	2	6	6	NUM
ejpam-5578	88	3	.	.	PUNCT
ejpam-5578	89	1	[	[	X
ejpam-5578	89	2	8	8	NUM
ejpam-5578	89	3	]	]	X
ejpam-5578	89	4	let	let	VERB
ejpam-5578	89	5	(	(	PUNCT
ejpam-5578	89	6	q	q	ADJ
ejpam-5578	89	7	,	,	PUNCT
ejpam-5578	89	8	ϱ1	ϱ1	NOUN
ejpam-5578	89	9	,	,	PUNCT
ejpam-5578	89	10	ϱ2	ϱ2	NOUN
ejpam-5578	89	11	,	,	PUNCT
ejpam-5578	89	12	ϱ3	ϱ3	PROPN
ejpam-5578	89	13	)	)	PUNCT
ejpam-5578	89	14	be	be	AUX
ejpam-5578	89	15	a	a	DET
ejpam-5578	89	16	tri	tri	ADJ
ejpam-5578	89	17	-	-	ADJ
ejpam-5578	89	18	topological	topological	ADJ
ejpam-5578	89	19	space	space	NOUN
ejpam-5578	89	20	,	,	PUNCT
ejpam-5578	89	21	where	where	SCONJ
ejpam-5578	89	22	q	q	PROPN
ejpam-5578	89	23	̸=	̸=	PROPN
ejpam-5578	89	24	∅	∅	NOUN
ejpam-5578	89	25	,	,	PUNCT
ejpam-5578	89	26	and	and	CCONJ
ejpam-5578	89	27	let	let	VERB
ejpam-5578	89	28	o	o	NOUN
ejpam-5578	89	29	⊆	⊆	NUM
ejpam-5578	89	30	q.	q.	NOUN
ejpam-5578	89	31	a	a	DET
ejpam-5578	89	32	point	point	NOUN
ejpam-5578	89	33	q	q	X
ejpam-5578	89	34	∈	∈	NOUN
ejpam-5578	89	35	o	o	NOUN
ejpam-5578	89	36	is	be	AUX
ejpam-5578	89	37	said	say	VERB
ejpam-5578	89	38	to	to	PART
ejpam-5578	89	39	be	be	AUX
ejpam-5578	89	40	a	a	DET
ejpam-5578	89	41	tri	tri	ADJ
ejpam-5578	89	42	-	-	ADJ
ejpam-5578	89	43	interior	interior	ADJ
ejpam-5578	89	44	point	point	NOUN
ejpam-5578	89	45	of	of	ADP
ejpam-5578	89	46	o	o	NOUN
ejpam-5578	89	47	if	if	SCONJ
ejpam-5578	89	48	there	there	PRON
ejpam-5578	89	49	exists	exist	VERB
ejpam-5578	89	50	at	at	ADP
ejpam-5578	89	51	least	least	ADV
ejpam-5578	89	52	one	one	NUM
ejpam-5578	89	53	neighborhood	neighborhood	NOUN
ejpam-5578	89	54	n(q	n(q	PROPN
ejpam-5578	89	55	,	,	PUNCT
ejpam-5578	89	56	ε	ε	PROPN
ejpam-5578	89	57	)	)	PUNCT
ejpam-5578	89	58	of	of	ADP
ejpam-5578	89	59	q	q	NOUN
ejpam-5578	89	60	such	such	ADJ
ejpam-5578	89	61	that	that	PRON
ejpam-5578	89	62	:	:	PUNCT
ejpam-5578	89	63	n(q	n(q	PROPN
ejpam-5578	89	64	,	,	PUNCT
ejpam-5578	89	65	ε	ε	PROPN
ejpam-5578	89	66	)	)	PUNCT
ejpam-5578	89	67	⊆	⊆	NUM
ejpam-5578	89	68	o.	o.	NOUN
ejpam-5578	89	69	the	the	DET
ejpam-5578	89	70	set	set	NOUN
ejpam-5578	89	71	of	of	ADP
ejpam-5578	89	72	all	all	DET
ejpam-5578	89	73	tri	tri	ADJ
ejpam-5578	89	74	-	-	ADJ
ejpam-5578	89	75	interior	interior	ADJ
ejpam-5578	89	76	points	point	NOUN
ejpam-5578	89	77	of	of	ADP
ejpam-5578	89	78	o	o	NOUN
ejpam-5578	89	79	is	be	AUX
ejpam-5578	89	80	called	call	VERB
ejpam-5578	89	81	the	the	DET
ejpam-5578	89	82	tri	tri	ADJ
ejpam-5578	89	83	-	-	ADJ
ejpam-5578	89	84	interior	interior	ADJ
ejpam-5578	89	85	set	set	NOUN
ejpam-5578	89	86	,	,	PUNCT
ejpam-5578	89	87	denoted	denote	VERB
ejpam-5578	89	88	by	by	ADP
ejpam-5578	89	89	:	:	PUNCT
ejpam-5578	89	90	o	o	NOUN
ejpam-5578	89	91	◦	◦	NOUN
ejpam-5578	89	92	≡	≡	PROPN
ejpam-5578	89	93	int(o	int(o	PROPN
ejpam-5578	89	94	)	)	PUNCT
ejpam-5578	90	1	=	=	PUNCT
ejpam-5578	90	2	(	(	PUNCT
ejpam-5578	90	3	oc	oc	NOUN
ejpam-5578	90	4	)	)	PUNCT
ejpam-5578	90	5	c	c	NOUN
ejpam-5578	90	6	.	.	PUNCT
ejpam-5578	91	1	lemma	lemma	PROPN
ejpam-5578	91	2	3	3	X
ejpam-5578	91	3	.	.	PUNCT
ejpam-5578	92	1	[	[	X
ejpam-5578	92	2	6	6	NUM
ejpam-5578	92	3	]	]	PUNCT
ejpam-5578	92	4	(	(	PUNCT
ejpam-5578	92	5	properties	property	NOUN
ejpam-5578	92	6	of	of	ADP
ejpam-5578	92	7	the	the	DET
ejpam-5578	92	8	tripartite	tripartite	ADJ
ejpam-5578	92	9	interior	interior	ADJ
ejpam-5578	92	10	set	set	NOUN
ejpam-5578	92	11	)	)	PUNCT
ejpam-5578	92	12	let	let	VERB
ejpam-5578	92	13	(	(	PUNCT
ejpam-5578	92	14	q	q	ADJ
ejpam-5578	92	15	,	,	PUNCT
ejpam-5578	92	16	ϱ1	ϱ1	NOUN
ejpam-5578	92	17	,	,	PUNCT
ejpam-5578	92	18	ϱ2	ϱ2	NOUN
ejpam-5578	92	19	,	,	PUNCT
ejpam-5578	92	20	ϱ3	ϱ3	PROPN
ejpam-5578	92	21	)	)	PUNCT
ejpam-5578	92	22	be	be	AUX
ejpam-5578	92	23	a	a	DET
ejpam-5578	92	24	tri	tri	ADJ
ejpam-5578	92	25	-	-	ADJ
ejpam-5578	92	26	topological	topological	ADJ
ejpam-5578	92	27	space	space	NOUN
ejpam-5578	92	28	,	,	PUNCT
ejpam-5578	92	29	and	and	CCONJ
ejpam-5578	92	30	let	let	VERB
ejpam-5578	92	31	o	o	NOUN
ejpam-5578	92	32	,	,	PUNCT
ejpam-5578	92	33	b	b	PROPN
ejpam-5578	92	34	⊆	⊆	NUM
ejpam-5578	92	35	q.	q.	NOUN
ejpam-5578	92	36	then	then	ADV
ejpam-5578	92	37	:	:	PUNCT
ejpam-5578	92	38	(	(	PUNCT
ejpam-5578	92	39	i	i	NOUN
ejpam-5578	92	40	)	)	PUNCT
ejpam-5578	92	41	∅	∅	NOUN
ejpam-5578	92	42	◦	◦	NOUN
ejpam-5578	92	43	=	=	SYM
ejpam-5578	92	44	∅	∅	NOUN
ejpam-5578	92	45	and	and	CCONJ
ejpam-5578	92	46	q	q	NOUN
ejpam-5578	92	47	◦	◦	NOUN
ejpam-5578	93	1	=	=	SYM
ejpam-5578	93	2	q.	q.	PROPN
ejpam-5578	93	3	(	(	PUNCT
ejpam-5578	93	4	ii	ii	PROPN
ejpam-5578	93	5	)	)	PUNCT
ejpam-5578	93	6	(	(	PUNCT
ejpam-5578	93	7	o	o	NOUN
ejpam-5578	93	8	∩b	∩b	NOUN
ejpam-5578	93	9	)	)	PUNCT
ejpam-5578	93	10	◦	◦	NOUN
ejpam-5578	93	11	=	=	SYM
ejpam-5578	94	1	o	o	X
ejpam-5578	94	2	◦	◦	NOUN
ejpam-5578	94	3	∩b	∩b	NOUN
ejpam-5578	94	4	◦	◦	NOUN
ejpam-5578	94	5	and	and	CCONJ
ejpam-5578	94	6	o	o	NOUN
ejpam-5578	94	7	◦	◦	NOUN
ejpam-5578	94	8	∪b	∪b	VERB
ejpam-5578	94	9	◦	◦	VERB
ejpam-5578	94	10	⊆	⊆	NUM
ejpam-5578	94	11	(	(	PUNCT
ejpam-5578	94	12	o	o	NOUN
ejpam-5578	94	13	∪b)	∪b)	PROPN
ejpam-5578	94	14	◦	◦	NOUN
ejpam-5578	94	15	.	.	PUNCT
ejpam-5578	95	1	(	(	PUNCT
ejpam-5578	95	2	iii	iii	X
ejpam-5578	95	3	)	)	PUNCT
ejpam-5578	95	4	o	o	NOUN
ejpam-5578	95	5	◦	◦	NOUN
ejpam-5578	95	6	is	be	AUX
ejpam-5578	95	7	a	a	DET
ejpam-5578	95	8	ϱi	ϱi	ADV
ejpam-5578	95	9	-	-	PUNCT
ejpam-5578	95	10	open	open	ADJ
ejpam-5578	95	11	set	set	NOUN
ejpam-5578	95	12	.	.	PUNCT
ejpam-5578	96	1	(	(	PUNCT
ejpam-5578	96	2	iv	iv	X
ejpam-5578	96	3	)	)	PUNCT
ejpam-5578	96	4	n	n	NOUN
ejpam-5578	96	5	∈	∈	NOUN
ejpam-5578	96	6	o	o	NOUN
ejpam-5578	96	7	◦	◦	NOUN
ejpam-5578	96	8	if	if	SCONJ
ejpam-5578	96	9	and	and	CCONJ
ejpam-5578	96	10	only	only	ADV
ejpam-5578	96	11	if	if	SCONJ
ejpam-5578	96	12	there	there	PRON
ejpam-5578	96	13	exists	exist	VERB
ejpam-5578	96	14	a	a	DET
ejpam-5578	96	15	ϱi	ϱi	ADV
ejpam-5578	96	16	-	-	PUNCT
ejpam-5578	96	17	open	open	ADJ
ejpam-5578	96	18	set	set	VERB
ejpam-5578	96	19	un	un	PROPN
ejpam-5578	96	20	such	such	ADJ
ejpam-5578	96	21	that	that	SCONJ
ejpam-5578	96	22	n	n	NUM
ejpam-5578	96	23	∈	∈	PROPN
ejpam-5578	96	24	un	un	PROPN
ejpam-5578	96	25	⊆	⊆	NUM
ejpam-5578	96	26	o.	o.	PROPN
ejpam-5578	96	27	definition	definition	NOUN
ejpam-5578	96	28	7	7	NUM
ejpam-5578	96	29	.	.	PUNCT
ejpam-5578	97	1	[	[	X
ejpam-5578	97	2	7	7	X
ejpam-5578	97	3	]	]	X
ejpam-5578	97	4	let	let	VERB
ejpam-5578	97	5	(	(	PUNCT
ejpam-5578	97	6	q	q	ADJ
ejpam-5578	97	7	,	,	PUNCT
ejpam-5578	97	8	ϱ1	ϱ1	NOUN
ejpam-5578	97	9	,	,	PUNCT
ejpam-5578	97	10	ϱ2	ϱ2	NOUN
ejpam-5578	97	11	,	,	PUNCT
ejpam-5578	97	12	ϱ3	ϱ3	PROPN
ejpam-5578	97	13	)	)	PUNCT
ejpam-5578	97	14	be	be	AUX
ejpam-5578	97	15	a	a	DET
ejpam-5578	97	16	tri	tri	ADJ
ejpam-5578	97	17	-	-	ADJ
ejpam-5578	97	18	topological	topological	ADJ
ejpam-5578	97	19	space	space	NOUN
ejpam-5578	97	20	,	,	PUNCT
ejpam-5578	97	21	where	where	SCONJ
ejpam-5578	97	22	q	q	PROPN
ejpam-5578	97	23	̸=	̸=	PROPN
ejpam-5578	97	24	∅	∅	NOUN
ejpam-5578	97	25	,	,	PUNCT
ejpam-5578	97	26	and	and	CCONJ
ejpam-5578	97	27	let	let	VERB
ejpam-5578	97	28	o	o	NOUN
ejpam-5578	97	29	⊆	⊆	NUM
ejpam-5578	97	30	q.	q.	NOUN
ejpam-5578	97	31	a	a	DET
ejpam-5578	97	32	point	point	NOUN
ejpam-5578	97	33	q	q	NOUN
ejpam-5578	97	34	is	be	AUX
ejpam-5578	97	35	said	say	VERB
ejpam-5578	97	36	to	to	PART
ejpam-5578	97	37	be	be	AUX
ejpam-5578	97	38	a	a	DET
ejpam-5578	97	39	tri	tri	ADJ
ejpam-5578	97	40	-	-	ADJ
ejpam-5578	97	41	exterior	exterior	ADJ
ejpam-5578	97	42	point	point	NOUN
ejpam-5578	97	43	of	of	ADP
ejpam-5578	97	44	o	o	NOUN
ejpam-5578	97	45	if	if	SCONJ
ejpam-5578	97	46	there	there	PRON
ejpam-5578	97	47	exists	exist	VERB
ejpam-5578	97	48	at	at	ADP
ejpam-5578	97	49	least	least	ADV
ejpam-5578	97	50	one	one	NUM
ejpam-5578	97	51	neighborhood	neighborhood	NOUN
ejpam-5578	97	52	n(q	n(q	PROPN
ejpam-5578	97	53	,	,	PUNCT
ejpam-5578	97	54	ε	ε	PROPN
ejpam-5578	97	55	)	)	PUNCT
ejpam-5578	97	56	of	of	ADP
ejpam-5578	97	57	q	q	NOUN
ejpam-5578	97	58	such	such	ADJ
ejpam-5578	97	59	that	that	PRON
ejpam-5578	97	60	:	:	PUNCT
ejpam-5578	97	61	n(q	n(q	PROPN
ejpam-5578	97	62	,	,	PUNCT
ejpam-5578	97	63	ε	ε	PROPN
ejpam-5578	97	64	)	)	PUNCT
ejpam-5578	97	65	∩o	∩o	NOUN
ejpam-5578	98	1	=	=	PUNCT
ejpam-5578	98	2	∅.	∅.	VERB
ejpam-5578	98	3	the	the	DET
ejpam-5578	98	4	set	set	NOUN
ejpam-5578	98	5	of	of	ADP
ejpam-5578	98	6	all	all	DET
ejpam-5578	98	7	tri	tri	ADJ
ejpam-5578	98	8	-	-	ADJ
ejpam-5578	98	9	exterior	exterior	ADJ
ejpam-5578	98	10	points	point	NOUN
ejpam-5578	98	11	of	of	ADP
ejpam-5578	98	12	o	o	NOUN
ejpam-5578	98	13	is	be	AUX
ejpam-5578	98	14	called	call	VERB
ejpam-5578	98	15	the	the	DET
ejpam-5578	98	16	tri	tri	ADJ
ejpam-5578	98	17	-	-	ADJ
ejpam-5578	98	18	exterior	exterior	ADJ
ejpam-5578	98	19	set	set	NOUN
ejpam-5578	98	20	,	,	PUNCT
ejpam-5578	98	21	denoted	denote	VERB
ejpam-5578	98	22	by	by	ADP
ejpam-5578	98	23	:	:	PUNCT
ejpam-5578	98	24	ex(o	ex(o	NUM
ejpam-5578	98	25	)	)	PUNCT
ejpam-5578	98	26	=	=	SYM
ejpam-5578	98	27	int(oc	int(oc	NOUN
ejpam-5578	98	28	)	)	PUNCT
ejpam-5578	99	1	=	=	PUNCT
ejpam-5578	100	1	o	o	NOUN
ejpam-5578	100	2	c	c	NOUN
ejpam-5578	100	3	.	.	PUNCT
ejpam-5578	101	1	lemma	lemma	PROPN
ejpam-5578	101	2	4	4	NUM
ejpam-5578	101	3	.	.	PUNCT
ejpam-5578	102	1	[	[	X
ejpam-5578	102	2	14	14	NUM
ejpam-5578	102	3	]	]	PUNCT
ejpam-5578	102	4	(	(	PUNCT
ejpam-5578	102	5	properties	property	NOUN
ejpam-5578	102	6	of	of	ADP
ejpam-5578	102	7	the	the	DET
ejpam-5578	102	8	tripartite	tripartite	ADJ
ejpam-5578	102	9	exterior	exterior	ADJ
ejpam-5578	102	10	set	set	NOUN
ejpam-5578	102	11	)	)	PUNCT
ejpam-5578	102	12	let	let	VERB
ejpam-5578	102	13	(	(	PUNCT
ejpam-5578	102	14	q	q	ADJ
ejpam-5578	102	15	,	,	PUNCT
ejpam-5578	102	16	ϱ1	ϱ1	NOUN
ejpam-5578	102	17	,	,	PUNCT
ejpam-5578	102	18	ϱ2	ϱ2	NOUN
ejpam-5578	102	19	,	,	PUNCT
ejpam-5578	102	20	ϱ3	ϱ3	PROPN
ejpam-5578	102	21	)	)	PUNCT
ejpam-5578	102	22	be	be	AUX
ejpam-5578	102	23	a	a	DET
ejpam-5578	102	24	tri	tri	ADJ
ejpam-5578	102	25	-	-	ADJ
ejpam-5578	102	26	topological	topological	ADJ
ejpam-5578	102	27	space	space	NOUN
ejpam-5578	102	28	,	,	PUNCT
ejpam-5578	102	29	and	and	CCONJ
ejpam-5578	102	30	let	let	VERB
ejpam-5578	102	31	o	o	NOUN
ejpam-5578	102	32	,	,	PUNCT
ejpam-5578	102	33	b	b	PROPN
ejpam-5578	102	34	⊆	⊆	NUM
ejpam-5578	102	35	q.	q.	NOUN
ejpam-5578	102	36	then	then	ADV
ejpam-5578	102	37	:	:	PUNCT
ejpam-5578	102	38	(	(	PUNCT
ejpam-5578	102	39	i	i	NOUN
ejpam-5578	102	40	)	)	PUNCT
ejpam-5578	102	41	ex(∅	ex(∅	PROPN
ejpam-5578	102	42	)	)	PUNCT
ejpam-5578	102	43	=	=	SYM
ejpam-5578	102	44	q	q	X
ejpam-5578	102	45	and	and	CCONJ
ejpam-5578	102	46	ex(q	ex(q	NOUN
ejpam-5578	102	47	)	)	PUNCT
ejpam-5578	103	1	=	=	PUNCT
ejpam-5578	103	2	∅.	∅.	PRON
ejpam-5578	103	3	(	(	PUNCT
ejpam-5578	103	4	ii	ii	NOUN
ejpam-5578	103	5	)	)	PUNCT
ejpam-5578	103	6	if	if	SCONJ
ejpam-5578	103	7	o	o	PROPN
ejpam-5578	103	8	⊆	⊆	NUM
ejpam-5578	103	9	b	b	PROPN
ejpam-5578	103	10	,	,	PUNCT
ejpam-5578	103	11	then	then	ADV
ejpam-5578	103	12	ex(b	ex(b	ADJ
ejpam-5578	103	13	)	)	PUNCT
ejpam-5578	103	14	⊆	⊆	NUM
ejpam-5578	103	15	ex(o	ex(o	NOUN
ejpam-5578	103	16	)	)	PUNCT
ejpam-5578	103	17	.	.	PUNCT
ejpam-5578	104	1	(	(	PUNCT
ejpam-5578	104	2	iii	iii	NOUN
ejpam-5578	104	3	)	)	PUNCT
ejpam-5578	104	4	ex(o	ex(o	PUNCT
ejpam-5578	104	5	)	)	PUNCT
ejpam-5578	104	6	is	be	AUX
ejpam-5578	104	7	a	a	DET
ejpam-5578	104	8	ϱi	ϱi	ADV
ejpam-5578	104	9	-	-	PUNCT
ejpam-5578	104	10	open	open	ADJ
ejpam-5578	104	11	set	set	NOUN
ejpam-5578	104	12	.	.	PUNCT
ejpam-5578	105	1	(	(	PUNCT
ejpam-5578	105	2	iv	iv	X
ejpam-5578	105	3	)	)	PUNCT
ejpam-5578	105	4	e	e	PROPN
ejpam-5578	105	5	∈	∈	PROPN
ejpam-5578	105	6	ex(o	ex(o	NOUN
ejpam-5578	105	7	)	)	PUNCT
ejpam-5578	105	8	if	if	SCONJ
ejpam-5578	105	9	and	and	CCONJ
ejpam-5578	105	10	only	only	ADV
ejpam-5578	105	11	if	if	SCONJ
ejpam-5578	105	12	there	there	PRON
ejpam-5578	105	13	exists	exist	VERB
ejpam-5578	105	14	a	a	DET
ejpam-5578	105	15	ϱi	ϱi	ADV
ejpam-5578	105	16	-	-	PUNCT
ejpam-5578	105	17	open	open	NOUN
ejpam-5578	105	18	set	set	NOUN
ejpam-5578	105	19	ue	ue	PROPN
ejpam-5578	105	20	such	such	ADJ
ejpam-5578	105	21	that	that	SCONJ
ejpam-5578	105	22	e	e	PROPN
ejpam-5578	105	23	∈	∈	PROPN
ejpam-5578	105	24	ue	ue	PROPN
ejpam-5578	105	25	⊆	⊆	NUM
ejpam-5578	105	26	oc	oc	PROPN
ejpam-5578	105	27	.	.	PUNCT
ejpam-5578	106	1	j.	j.	PROPN
ejpam-5578	106	2	oudetallah	oudetallah	PROPN
ejpam-5578	106	3	et	et	PROPN
ejpam-5578	106	4	al	al	PROPN
ejpam-5578	106	5	.	.	PUNCT
ejpam-5578	106	6	/	/	SYM
ejpam-5578	106	7	eur	eur	PROPN
ejpam-5578	106	8	.	.	PUNCT
ejpam-5578	107	1	j.	j.	PROPN
ejpam-5578	107	2	pure	pure	PROPN
ejpam-5578	107	3	appl	appl	PROPN
ejpam-5578	107	4	.	.	PROPN
ejpam-5578	107	5	math	math	PROPN
ejpam-5578	107	6	,	,	PUNCT
ejpam-5578	107	7	18	18	NUM
ejpam-5578	107	8	(	(	PUNCT
ejpam-5578	107	9	2	2	NUM
ejpam-5578	107	10	)	)	PUNCT
ejpam-5578	107	11	(	(	PUNCT
ejpam-5578	107	12	2025	2025	NUM
ejpam-5578	107	13	)	)	PUNCT
ejpam-5578	107	14	,	,	PUNCT
ejpam-5578	107	15	5578	5578	NUM
ejpam-5578	107	16	6	6	NUM
ejpam-5578	107	17	of	of	ADP
ejpam-5578	107	18	19	19	NUM
ejpam-5578	107	19	proof	proof	NOUN
ejpam-5578	107	20	.	.	PUNCT
ejpam-5578	108	1	(	(	PUNCT
ejpam-5578	108	2	iii	iii	NOUN
ejpam-5578	108	3	)	)	PUNCT
ejpam-5578	108	4	since	since	SCONJ
ejpam-5578	108	5	ex(o	ex(o	NOUN
ejpam-5578	108	6	)	)	PUNCT
ejpam-5578	108	7	=	=	SYM
ejpam-5578	108	8	int(oc	int(oc	NOUN
ejpam-5578	108	9	)	)	PUNCT
ejpam-5578	108	10	,	,	PUNCT
ejpam-5578	108	11	we	we	PRON
ejpam-5578	108	12	have	have	VERB
ejpam-5578	108	13	:	:	PUNCT
ejpam-5578	108	14	ex(o	ex(o	X
ejpam-5578	108	15	)	)	PUNCT
ejpam-5578	109	1	=	=	PRON
ejpam-5578	109	2	(	(	PUNCT
ejpam-5578	109	3	oc	oc	NOUN
ejpam-5578	109	4	)	)	PUNCT
ejpam-5578	109	5	c	c	NOUN
ejpam-5578	109	6	.	.	PUNCT
ejpam-5578	110	1	but	but	CCONJ
ejpam-5578	110	2	since	since	SCONJ
ejpam-5578	110	3	occ	occ	NOUN
ejpam-5578	110	4	=	=	SYM
ejpam-5578	110	5	o	o	NOUN
ejpam-5578	110	6	,	,	PUNCT
ejpam-5578	110	7	it	it	PRON
ejpam-5578	110	8	follows	follow	VERB
ejpam-5578	110	9	that	that	PRON
ejpam-5578	110	10	:	:	PUNCT
ejpam-5578	110	11	ex(o	ex(o	X
ejpam-5578	110	12	)	)	PUNCT
ejpam-5578	111	1	=	=	PUNCT
ejpam-5578	111	2	o	o	NOUN
ejpam-5578	111	3	c	c	NOUN
ejpam-5578	111	4	.	.	PUNCT
ejpam-5578	112	1	by	by	ADP
ejpam-5578	112	2	the	the	DET
ejpam-5578	112	3	definition	definition	NOUN
ejpam-5578	112	4	of	of	ADP
ejpam-5578	112	5	the	the	DET
ejpam-5578	112	6	tri	tri	ADJ
ejpam-5578	112	7	-	-	ADJ
ejpam-5578	112	8	closure	closure	ADJ
ejpam-5578	112	9	set	set	NOUN
ejpam-5578	112	10	,	,	PUNCT
ejpam-5578	112	11	we	we	PRON
ejpam-5578	112	12	know	know	VERB
ejpam-5578	112	13	that	that	SCONJ
ejpam-5578	112	14	o	o	NOUN
ejpam-5578	112	15	is	be	AUX
ejpam-5578	112	16	a	a	DET
ejpam-5578	112	17	ϱi	ϱi	ADV
ejpam-5578	112	18	-	-	PUNCT
ejpam-5578	112	19	closed	close	VERB
ejpam-5578	112	20	set	set	NOUN
ejpam-5578	112	21	.	.	PUNCT
ejpam-5578	113	1	since	since	SCONJ
ejpam-5578	113	2	the	the	DET
ejpam-5578	113	3	complement	complement	NOUN
ejpam-5578	113	4	of	of	ADP
ejpam-5578	113	5	a	a	DET
ejpam-5578	113	6	closed	closed	ADJ
ejpam-5578	113	7	set	set	NOUN
ejpam-5578	113	8	is	be	AUX
ejpam-5578	113	9	an	an	DET
ejpam-5578	113	10	open	open	ADJ
ejpam-5578	113	11	set	set	NOUN
ejpam-5578	113	12	,	,	PUNCT
ejpam-5578	113	13	it	it	PRON
ejpam-5578	113	14	follows	follow	VERB
ejpam-5578	113	15	that	that	PRON
ejpam-5578	113	16	ex(o	ex(o	PUNCT
ejpam-5578	113	17	)	)	PUNCT
ejpam-5578	113	18	is	be	AUX
ejpam-5578	113	19	a	a	DET
ejpam-5578	113	20	ϱi	ϱi	ADV
ejpam-5578	113	21	-	-	PUNCT
ejpam-5578	113	22	open	open	ADJ
ejpam-5578	113	23	set	set	NOUN
ejpam-5578	113	24	.	.	PUNCT
ejpam-5578	114	1	as	as	ADP
ejpam-5578	114	2	a	a	DET
ejpam-5578	114	3	result	result	NOUN
ejpam-5578	114	4	,	,	PUNCT
ejpam-5578	114	5	the	the	DET
ejpam-5578	114	6	interior	interior	ADJ
ejpam-5578	114	7	set	set	VERB
ejpam-5578	114	8	is	be	AUX
ejpam-5578	114	9	also	also	ADV
ejpam-5578	114	10	a	a	DET
ejpam-5578	114	11	ϱi	ϱi	ADV
ejpam-5578	114	12	-	-	PUNCT
ejpam-5578	114	13	open	open	ADJ
ejpam-5578	114	14	set	set	NOUN
ejpam-5578	114	15	.	.	PUNCT
ejpam-5578	115	1	definition	definition	NOUN
ejpam-5578	115	2	8	8	NUM
ejpam-5578	115	3	.	.	PUNCT
ejpam-5578	116	1	[	[	X
ejpam-5578	116	2	12	12	NUM
ejpam-5578	116	3	]	]	X
ejpam-5578	116	4	let	let	VERB
ejpam-5578	116	5	(	(	PUNCT
ejpam-5578	116	6	q	q	ADJ
ejpam-5578	116	7	,	,	PUNCT
ejpam-5578	116	8	ϱ1	ϱ1	NOUN
ejpam-5578	116	9	,	,	PUNCT
ejpam-5578	116	10	ϱ2	ϱ2	NOUN
ejpam-5578	116	11	,	,	PUNCT
ejpam-5578	116	12	ϱ3	ϱ3	PROPN
ejpam-5578	116	13	)	)	PUNCT
ejpam-5578	116	14	be	be	AUX
ejpam-5578	116	15	a	a	DET
ejpam-5578	116	16	tri	tri	ADJ
ejpam-5578	116	17	-	-	ADJ
ejpam-5578	116	18	topological	topological	ADJ
ejpam-5578	116	19	space	space	NOUN
ejpam-5578	116	20	,	,	PUNCT
ejpam-5578	116	21	where	where	SCONJ
ejpam-5578	116	22	q	q	PROPN
ejpam-5578	116	23	̸=	̸=	PROPN
ejpam-5578	116	24	∅	∅	NOUN
ejpam-5578	116	25	,	,	PUNCT
ejpam-5578	116	26	and	and	CCONJ
ejpam-5578	116	27	let	let	VERB
ejpam-5578	116	28	o	o	NOUN
ejpam-5578	116	29	⊆	⊆	NUM
ejpam-5578	116	30	q.	q.	NOUN
ejpam-5578	116	31	a	a	DET
ejpam-5578	116	32	point	point	NOUN
ejpam-5578	116	33	q	q	NOUN
ejpam-5578	116	34	is	be	AUX
ejpam-5578	116	35	said	say	VERB
ejpam-5578	116	36	to	to	PART
ejpam-5578	116	37	be	be	AUX
ejpam-5578	116	38	a	a	DET
ejpam-5578	116	39	tri	tri	ADJ
ejpam-5578	116	40	-	-	ADJ
ejpam-5578	116	41	boundary	boundary	ADJ
ejpam-5578	116	42	point	point	NOUN
ejpam-5578	116	43	of	of	ADP
ejpam-5578	116	44	o	o	NOUN
ejpam-5578	116	45	if	if	SCONJ
ejpam-5578	116	46	every	every	DET
ejpam-5578	116	47	neighborhood	neighborhood	NOUN
ejpam-5578	116	48	n(q	n(q	PROPN
ejpam-5578	116	49	,	,	PUNCT
ejpam-5578	116	50	ε	ε	PROPN
ejpam-5578	116	51	)	)	PUNCT
ejpam-5578	116	52	of	of	ADP
ejpam-5578	116	53	q	q	ADJ
ejpam-5578	116	54	satisfies	satisfie	NOUN
ejpam-5578	116	55	:	:	PUNCT
ejpam-5578	116	56	n(q	n(q	PROPN
ejpam-5578	116	57	,	,	PUNCT
ejpam-5578	116	58	ε	ε	PROPN
ejpam-5578	116	59	)	)	PUNCT
ejpam-5578	116	60	∩o	∩o	NOUN
ejpam-5578	116	61	̸=	̸=	PROPN
ejpam-5578	116	62	∅	∅	NOUN
ejpam-5578	116	63	and	and	CCONJ
ejpam-5578	116	64	n(q	n(q	PROPN
ejpam-5578	116	65	,	,	PUNCT
ejpam-5578	116	66	ε	ε	PROPN
ejpam-5578	116	67	)	)	PUNCT
ejpam-5578	116	68	∩oc	∩oc	NOUN
ejpam-5578	116	69	̸=	̸=	PROPN
ejpam-5578	116	70	∅.	∅.	ADP
ejpam-5578	116	71	the	the	DET
ejpam-5578	116	72	set	set	NOUN
ejpam-5578	116	73	of	of	ADP
ejpam-5578	116	74	all	all	DET
ejpam-5578	116	75	tri	tri	ADJ
ejpam-5578	116	76	-	-	ADJ
ejpam-5578	116	77	boundary	boundary	ADJ
ejpam-5578	116	78	points	point	NOUN
ejpam-5578	116	79	is	be	AUX
ejpam-5578	116	80	called	call	VERB
ejpam-5578	116	81	the	the	DET
ejpam-5578	116	82	tri	tri	ADJ
ejpam-5578	116	83	-	-	ADJ
ejpam-5578	116	84	boundary	boundary	ADJ
ejpam-5578	116	85	set	set	NOUN
ejpam-5578	116	86	,	,	PUNCT
ejpam-5578	116	87	denoted	denote	VERB
ejpam-5578	116	88	by	by	ADP
ejpam-5578	116	89	:	:	PUNCT
ejpam-5578	116	90	bd(o	bd(o	NOUN
ejpam-5578	116	91	)	)	PUNCT
ejpam-5578	116	92	=	=	SYM
ejpam-5578	116	93	o	o	X
ejpam-5578	116	94	−o	−o	ADJ
ejpam-5578	116	95	◦	◦	NOUN
ejpam-5578	116	96	=	=	SYM
ejpam-5578	116	97	o	o	NOUN
ejpam-5578	116	98	∩oc	∩oc	NOUN
ejpam-5578	116	99	.	.	PUNCT
ejpam-5578	117	1	lemma	lemma	PROPN
ejpam-5578	117	2	5	5	NUM
ejpam-5578	117	3	.	.	PUNCT
ejpam-5578	118	1	[	[	X
ejpam-5578	118	2	1	1	NUM
ejpam-5578	118	3	]	]	PUNCT
ejpam-5578	118	4	(	(	PUNCT
ejpam-5578	118	5	properties	property	NOUN
ejpam-5578	118	6	of	of	ADP
ejpam-5578	118	7	the	the	DET
ejpam-5578	118	8	tripartite	tripartite	ADJ
ejpam-5578	118	9	boundary	boundary	ADJ
ejpam-5578	118	10	set	set	NOUN
ejpam-5578	118	11	)	)	PUNCT
ejpam-5578	118	12	let	let	VERB
ejpam-5578	118	13	(	(	PUNCT
ejpam-5578	118	14	q	q	ADJ
ejpam-5578	118	15	,	,	PUNCT
ejpam-5578	118	16	ϱ1	ϱ1	NOUN
ejpam-5578	118	17	,	,	PUNCT
ejpam-5578	118	18	ϱ2	ϱ2	NOUN
ejpam-5578	118	19	,	,	PUNCT
ejpam-5578	118	20	ϱ3	ϱ3	PROPN
ejpam-5578	118	21	)	)	PUNCT
ejpam-5578	118	22	be	be	AUX
ejpam-5578	118	23	a	a	DET
ejpam-5578	118	24	tri	tri	ADJ
ejpam-5578	118	25	-	-	ADJ
ejpam-5578	118	26	topological	topological	ADJ
ejpam-5578	118	27	space	space	NOUN
ejpam-5578	118	28	,	,	PUNCT
ejpam-5578	118	29	and	and	CCONJ
ejpam-5578	118	30	let	let	VERB
ejpam-5578	118	31	o	o	NOUN
ejpam-5578	118	32	,	,	PUNCT
ejpam-5578	118	33	b	b	PROPN
ejpam-5578	118	34	⊆	⊆	NUM
ejpam-5578	118	35	q.	q.	NOUN
ejpam-5578	118	36	then	then	ADV
ejpam-5578	118	37	:	:	PUNCT
ejpam-5578	118	38	(	(	PUNCT
ejpam-5578	118	39	i	i	NOUN
ejpam-5578	118	40	)	)	PUNCT
ejpam-5578	118	41	bd(∅	bd(∅	X
ejpam-5578	118	42	)	)	PUNCT
ejpam-5578	118	43	=	=	SYM
ejpam-5578	118	44	bd(q	bd(q	X
ejpam-5578	118	45	)	)	PUNCT
ejpam-5578	118	46	=	=	PUNCT
ejpam-5578	118	47	∅.	∅.	PRON
ejpam-5578	118	48	(	(	PUNCT
ejpam-5578	118	49	ii	ii	NOUN
ejpam-5578	118	50	)	)	PUNCT
ejpam-5578	118	51	bd(o	bd(o	NOUN
ejpam-5578	118	52	)	)	PUNCT
ejpam-5578	118	53	is	be	AUX
ejpam-5578	118	54	a	a	DET
ejpam-5578	118	55	ϱi	ϱi	ADV
ejpam-5578	118	56	-	-	PUNCT
ejpam-5578	118	57	closed	close	VERB
ejpam-5578	118	58	set	set	NOUN
ejpam-5578	118	59	.	.	PUNCT
ejpam-5578	119	1	(	(	PUNCT
ejpam-5578	119	2	iii	iii	X
ejpam-5578	119	3	)	)	PUNCT
ejpam-5578	119	4	b	b	NOUN
ejpam-5578	119	5	∈	∈	PROPN
ejpam-5578	119	6	bd(o	bd(o	NOUN
ejpam-5578	119	7	)	)	PUNCT
ejpam-5578	120	1	if	if	SCONJ
ejpam-5578	120	2	and	and	CCONJ
ejpam-5578	120	3	only	only	ADV
ejpam-5578	120	4	if	if	SCONJ
ejpam-5578	120	5	for	for	ADP
ejpam-5578	120	6	every	every	DET
ejpam-5578	120	7	ϱi	ϱi	ADJ
ejpam-5578	120	8	-	-	PUNCT
ejpam-5578	120	9	open	open	ADJ
ejpam-5578	120	10	set	set	NOUN
ejpam-5578	120	11	ub	ub	ADP
ejpam-5578	120	12	containing	contain	VERB
ejpam-5578	120	13	b	b	PROPN
ejpam-5578	120	14	,	,	PUNCT
ejpam-5578	120	15	we	we	PRON
ejpam-5578	120	16	have	have	VERB
ejpam-5578	120	17	:	:	PUNCT
ejpam-5578	121	1	ub	ub	ADP
ejpam-5578	121	2	∩o	∩o	PROPN
ejpam-5578	121	3	̸=	̸=	PROPN
ejpam-5578	121	4	∅	∅	NOUN
ejpam-5578	121	5	and	and	CCONJ
ejpam-5578	121	6	ub	ub	ADJ
ejpam-5578	121	7	∩oc	∩oc	NOUN
ejpam-5578	121	8	̸=	̸=	PROPN
ejpam-5578	121	9	∅.	∅.	NOUN
ejpam-5578	121	10	proof	proof	NOUN
ejpam-5578	121	11	.	.	PUNCT
ejpam-5578	122	1	(	(	PUNCT
ejpam-5578	122	2	iii	iii	X
ejpam-5578	122	3	)	)	PUNCT
ejpam-5578	122	4	let	let	VERB
ejpam-5578	122	5	s	s	PRON
ejpam-5578	122	6	∈	∈	NOUN
ejpam-5578	122	7	bd(o	bd(o	NOUN
ejpam-5578	122	8	)	)	PUNCT
ejpam-5578	122	9	,	,	PUNCT
ejpam-5578	122	10	and	and	CCONJ
ejpam-5578	122	11	let	let	VERB
ejpam-5578	122	12	us	we	PRON
ejpam-5578	122	13	be	be	AUX
ejpam-5578	122	14	a	a	DET
ejpam-5578	122	15	ϱi	ϱi	ADV
ejpam-5578	122	16	-	-	PUNCT
ejpam-5578	122	17	open	open	NOUN
ejpam-5578	122	18	set	set	NOUN
ejpam-5578	122	19	such	such	DET
ejpam-5578	122	20	that	that	DET
ejpam-5578	122	21	s	s	VERB
ejpam-5578	122	22	∈	∈	PROPN
ejpam-5578	122	23	us	we	PRON
ejpam-5578	122	24	.	.	PUNCT
ejpam-5578	123	1	then	then	ADV
ejpam-5578	123	2	,	,	PUNCT
ejpam-5578	123	3	by	by	ADP
ejpam-5578	123	4	definition	definition	NOUN
ejpam-5578	123	5	:	:	PUNCT
ejpam-5578	123	6	s	s	PART
ejpam-5578	123	7	∈	∈	X
ejpam-5578	123	8	o	o	NOUN
ejpam-5578	123	9	∩oc	∩oc	NOUN
ejpam-5578	123	10	.	.	PUNCT
ejpam-5578	124	1	this	this	PRON
ejpam-5578	124	2	implies	imply	VERB
ejpam-5578	124	3	that	that	SCONJ
ejpam-5578	124	4	:	:	PUNCT
ejpam-5578	124	5	s	s	VERB
ejpam-5578	124	6	∈	∈	X
ejpam-5578	124	7	o	o	NOUN
ejpam-5578	124	8	and	and	CCONJ
ejpam-5578	124	9	s	s	PROPN
ejpam-5578	124	10	∈	∈	PROPN
ejpam-5578	124	11	oc	oc	PROPN
ejpam-5578	124	12	.	.	PUNCT
ejpam-5578	125	1	by	by	ADP
ejpam-5578	125	2	the	the	DET
ejpam-5578	125	3	definition	definition	NOUN
ejpam-5578	125	4	of	of	ADP
ejpam-5578	125	5	closure	closure	NOUN
ejpam-5578	125	6	,	,	PUNCT
ejpam-5578	125	7	we	we	PRON
ejpam-5578	125	8	have	have	VERB
ejpam-5578	125	9	:	:	PUNCT
ejpam-5578	125	10	s	s	VERB
ejpam-5578	125	11	∈	∈	PROPN
ejpam-5578	125	12	o	o	X
ejpam-5578	125	13	∪o′	∪o′	X
ejpam-5578	125	14	and	and	CCONJ
ejpam-5578	125	15	s	s	PROPN
ejpam-5578	125	16	∈	∈	PROPN
ejpam-5578	125	17	oc	oc	AUX
ejpam-5578	125	18	∪	∪	NOUN
ejpam-5578	125	19	(	(	PUNCT
ejpam-5578	125	20	oc)′.	oc)′.	PROPN
ejpam-5578	125	21	this	this	PRON
ejpam-5578	125	22	means	mean	VERB
ejpam-5578	125	23	that	that	SCONJ
ejpam-5578	125	24	:	:	PUNCT
ejpam-5578	125	25	(	(	PUNCT
ejpam-5578	125	26	s	s	X
ejpam-5578	125	27	∈	∈	X
ejpam-5578	125	28	o	o	NOUN
ejpam-5578	125	29	or	or	CCONJ
ejpam-5578	125	30	s	s	PROPN
ejpam-5578	125	31	∈	∈	PROPN
ejpam-5578	125	32	o′	o′	NUM
ejpam-5578	125	33	)	)	PUNCT
ejpam-5578	125	34	and	and	CCONJ
ejpam-5578	125	35	(	(	PUNCT
ejpam-5578	125	36	s	s	NOUN
ejpam-5578	125	37	∈	∈	NOUN
ejpam-5578	125	38	oc	oc	NOUN
ejpam-5578	125	39	or	or	CCONJ
ejpam-5578	125	40	s	s	NOUN
ejpam-5578	125	41	∈	∈	PROPN
ejpam-5578	125	42	(	(	PUNCT
ejpam-5578	125	43	oc)′	oc)′	PROPN
ejpam-5578	125	44	)	)	PUNCT
ejpam-5578	125	45	.	.	PUNCT
ejpam-5578	126	1	thus	thus	ADV
ejpam-5578	126	2	,	,	PUNCT
ejpam-5578	126	3	we	we	PRON
ejpam-5578	126	4	conclude	conclude	VERB
ejpam-5578	126	5	that	that	PRON
ejpam-5578	126	6	:	:	PUNCT
ejpam-5578	126	7	us	us	PROPN
ejpam-5578	126	8	∩	∩	NOUN
ejpam-5578	126	9	(	(	PUNCT
ejpam-5578	126	10	o	o	NOUN
ejpam-5578	126	11	\	\	PROPN
ejpam-5578	126	12	{	{	PUNCT
ejpam-5578	126	13	s	s	NOUN
ejpam-5578	126	14	}	}	PUNCT
ejpam-5578	126	15	)	)	PUNCT
ejpam-5578	126	16	̸=	̸=	PROPN
ejpam-5578	126	17	∅	∅	NOUN
ejpam-5578	126	18	and	and	CCONJ
ejpam-5578	126	19	us	we	PRON
ejpam-5578	126	20	∩oc	∩oc	NOUN
ejpam-5578	126	21	̸=	̸=	PROPN
ejpam-5578	126	22	∅.	∅.	ADP
ejpam-5578	126	23	j.	j.	PROPN
ejpam-5578	126	24	oudetallah	oudetallah	PROPN
ejpam-5578	126	25	et	et	PROPN
ejpam-5578	126	26	al	al	PROPN
ejpam-5578	126	27	.	.	PUNCT
ejpam-5578	126	28	/	/	SYM
ejpam-5578	126	29	eur	eur	PROPN
ejpam-5578	126	30	.	.	PUNCT
ejpam-5578	127	1	j.	j.	PROPN
ejpam-5578	127	2	pure	pure	PROPN
ejpam-5578	127	3	appl	appl	PROPN
ejpam-5578	127	4	.	.	PROPN
ejpam-5578	127	5	math	math	PROPN
ejpam-5578	127	6	,	,	PUNCT
ejpam-5578	127	7	18	18	NUM
ejpam-5578	127	8	(	(	PUNCT
ejpam-5578	127	9	2	2	NUM
ejpam-5578	127	10	)	)	PUNCT
ejpam-5578	127	11	(	(	PUNCT
ejpam-5578	127	12	2025	2025	NUM
ejpam-5578	127	13	)	)	PUNCT
ejpam-5578	127	14	,	,	PUNCT
ejpam-5578	127	15	5578	5578	NUM
ejpam-5578	127	16	7	7	NUM
ejpam-5578	127	17	of	of	ADP
ejpam-5578	127	18	19	19	NUM
ejpam-5578	127	19	since	since	SCONJ
ejpam-5578	127	20	s	s	NOUN
ejpam-5578	127	21	⊆	⊆	NUM
ejpam-5578	127	22	us	we	PRON
ejpam-5578	127	23	,	,	PUNCT
ejpam-5578	127	24	we	we	PRON
ejpam-5578	127	25	obtain	obtain	VERB
ejpam-5578	127	26	:	:	PUNCT
ejpam-5578	127	27	us	us	PROPN
ejpam-5578	127	28	∩o	∩o	NOUN
ejpam-5578	127	29	̸=	̸=	PROPN
ejpam-5578	127	30	∅	∅	NOUN
ejpam-5578	127	31	and	and	CCONJ
ejpam-5578	127	32	us	we	PRON
ejpam-5578	127	33	∩oc	∩oc	NOUN
ejpam-5578	127	34	̸=	̸=	PROPN
ejpam-5578	127	35	∅.	∅.	PRON
ejpam-5578	127	36	hence	hence	ADV
ejpam-5578	127	37	,	,	PUNCT
ejpam-5578	127	38	s	s	PART
ejpam-5578	127	39	satisfies	satisfie	NOUN
ejpam-5578	127	40	the	the	DET
ejpam-5578	127	41	condition	condition	NOUN
ejpam-5578	127	42	of	of	ADP
ejpam-5578	127	43	a	a	DET
ejpam-5578	127	44	boundary	boundary	ADJ
ejpam-5578	127	45	point	point	NOUN
ejpam-5578	127	46	,	,	PUNCT
ejpam-5578	127	47	completing	complete	VERB
ejpam-5578	127	48	the	the	DET
ejpam-5578	127	49	proof	proof	NOUN
ejpam-5578	127	50	.	.	PUNCT
ejpam-5578	128	1	definition	definition	NOUN
ejpam-5578	128	2	9	9	NUM
ejpam-5578	128	3	.	.	PUNCT
ejpam-5578	129	1	[	[	X
ejpam-5578	129	2	17	17	NUM
ejpam-5578	129	3	]	]	PUNCT
ejpam-5578	129	4	a	a	DET
ejpam-5578	129	5	topological	topological	ADJ
ejpam-5578	129	6	space	space	NOUN
ejpam-5578	129	7	(	(	PUNCT
ejpam-5578	129	8	q	q	NOUN
ejpam-5578	129	9	,	,	PUNCT
ejpam-5578	129	10	ϱ	ϱ	NOUN
ejpam-5578	129	11	)	)	PUNCT
ejpam-5578	129	12	is	be	AUX
ejpam-5578	129	13	called	call	VERB
ejpam-5578	129	14	a	a	DET
ejpam-5578	129	15	t0	t0	NOUN
ejpam-5578	129	16	-	-	NOUN
ejpam-5578	129	17	space	space	NOUN
ejpam-5578	129	18	if	if	SCONJ
ejpam-5578	129	19	for	for	ADP
ejpam-5578	129	20	all	all	DET
ejpam-5578	129	21	distinct	distinct	ADJ
ejpam-5578	129	22	points	point	NOUN
ejpam-5578	129	23	q	q	NOUN
ejpam-5578	129	24	,	,	PUNCT
ejpam-5578	129	25	s	s	NOUN
ejpam-5578	129	26	∈	∈	ADJ
ejpam-5578	129	27	q	q	X
ejpam-5578	129	28	(	(	PUNCT
ejpam-5578	129	29	q	q	PROPN
ejpam-5578	129	30	̸=	̸=	PROPN
ejpam-5578	129	31	s	s	PART
ejpam-5578	129	32	)	)	PUNCT
ejpam-5578	129	33	,	,	PUNCT
ejpam-5578	129	34	there	there	PRON
ejpam-5578	129	35	exists	exist	VERB
ejpam-5578	129	36	an	an	DET
ejpam-5578	129	37	open	open	ADJ
ejpam-5578	129	38	set	set	NOUN
ejpam-5578	129	39	uq	uq	NOUN
ejpam-5578	129	40	such	such	ADJ
ejpam-5578	129	41	that	that	PRON
ejpam-5578	129	42	:	:	PUNCT
ejpam-5578	129	43	q	q	X
ejpam-5578	129	44	∈	∈	PROPN
ejpam-5578	129	45	uq	uq	NOUN
ejpam-5578	129	46	and	and	CCONJ
ejpam-5578	129	47	s	s	NOUN
ejpam-5578	129	48	/∈	/∈	PROPN
ejpam-5578	129	49	uq	uq	NOUN
ejpam-5578	129	50	,	,	PUNCT
ejpam-5578	129	51	or	or	CCONJ
ejpam-5578	129	52	there	there	PRON
ejpam-5578	129	53	exists	exist	VERB
ejpam-5578	129	54	an	an	DET
ejpam-5578	129	55	open	open	ADJ
ejpam-5578	129	56	set	set	NOUN
ejpam-5578	129	57	vs	vs	ADP
ejpam-5578	129	58	such	such	ADJ
ejpam-5578	129	59	that	that	PRON
ejpam-5578	129	60	:	:	PUNCT
ejpam-5578	129	61	s	s	X
ejpam-5578	129	62	∈	∈	NOUN
ejpam-5578	129	63	vs	vs	ADP
ejpam-5578	129	64	and	and	CCONJ
ejpam-5578	129	65	q	q	NOUN
ejpam-5578	129	66	/∈	/∈	PUNCT
ejpam-5578	129	67	vs.	vs.	ADP
ejpam-5578	129	68	definition	definition	NOUN
ejpam-5578	129	69	10	10	NUM
ejpam-5578	129	70	.	.	PUNCT
ejpam-5578	130	1	[	[	X
ejpam-5578	130	2	8	8	NUM
ejpam-5578	130	3	]	]	PUNCT
ejpam-5578	130	4	a	a	DET
ejpam-5578	130	5	tri	tri	ADJ
ejpam-5578	130	6	-	-	ADJ
ejpam-5578	130	7	topological	topological	ADJ
ejpam-5578	130	8	space	space	NOUN
ejpam-5578	130	9	(	(	PUNCT
ejpam-5578	130	10	q	q	ADJ
ejpam-5578	130	11	,	,	PUNCT
ejpam-5578	130	12	ϱ1	ϱ1	NOUN
ejpam-5578	130	13	,	,	PUNCT
ejpam-5578	130	14	ϱ2	ϱ2	NOUN
ejpam-5578	130	15	,	,	PUNCT
ejpam-5578	130	16	ϱ3	ϱ3	PROPN
ejpam-5578	130	17	)	)	PUNCT
ejpam-5578	130	18	is	be	AUX
ejpam-5578	130	19	called	call	VERB
ejpam-5578	130	20	a	a	DET
ejpam-5578	130	21	tri	tri	PROPN
ejpam-5578	130	22	-	-	ADJ
ejpam-5578	130	23	t0	t0	NOUN
ejpam-5578	130	24	-	-	NOUN
ejpam-5578	130	25	space	space	NOUN
ejpam-5578	130	26	if	if	SCONJ
ejpam-5578	130	27	for	for	ADP
ejpam-5578	130	28	all	all	DET
ejpam-5578	130	29	distinct	distinct	ADJ
ejpam-5578	130	30	points	point	NOUN
ejpam-5578	130	31	q	q	NOUN
ejpam-5578	130	32	,	,	PUNCT
ejpam-5578	130	33	s	s	NOUN
ejpam-5578	130	34	∈	∈	ADJ
ejpam-5578	130	35	q	q	X
ejpam-5578	130	36	(	(	PUNCT
ejpam-5578	130	37	q	q	PROPN
ejpam-5578	130	38	̸=	̸=	PROPN
ejpam-5578	130	39	s	s	PART
ejpam-5578	130	40	)	)	PUNCT
ejpam-5578	130	41	,	,	PUNCT
ejpam-5578	130	42	there	there	PRON
ejpam-5578	130	43	exists	exist	VERB
ejpam-5578	130	44	a	a	DET
ejpam-5578	130	45	ϱi	ϱi	ADV
ejpam-5578	130	46	-	-	PUNCT
ejpam-5578	130	47	open	open	ADJ
ejpam-5578	130	48	set	set	ADJ
ejpam-5578	130	49	uq	uq	NOUN
ejpam-5578	130	50	such	such	ADJ
ejpam-5578	130	51	that	that	PRON
ejpam-5578	130	52	:	:	PUNCT
ejpam-5578	130	53	q	q	X
ejpam-5578	130	54	∈	∈	PROPN
ejpam-5578	130	55	uq	uq	NOUN
ejpam-5578	130	56	and	and	CCONJ
ejpam-5578	130	57	s	s	NOUN
ejpam-5578	130	58	/∈	/∈	PROPN
ejpam-5578	130	59	uq	uq	NOUN
ejpam-5578	130	60	,	,	PUNCT
ejpam-5578	130	61	or	or	CCONJ
ejpam-5578	130	62	there	there	PRON
ejpam-5578	130	63	exists	exist	VERB
ejpam-5578	130	64	a	a	DET
ejpam-5578	130	65	ϱj	ϱj	NOUN
ejpam-5578	130	66	-	-	ADJ
ejpam-5578	130	67	open	open	ADJ
ejpam-5578	130	68	set	set	NOUN
ejpam-5578	130	69	vs	vs	ADP
ejpam-5578	130	70	such	such	ADJ
ejpam-5578	130	71	that	that	PRON
ejpam-5578	130	72	:	:	PUNCT
ejpam-5578	130	73	s	s	X
ejpam-5578	130	74	∈	∈	NOUN
ejpam-5578	130	75	vs	vs	ADP
ejpam-5578	130	76	and	and	CCONJ
ejpam-5578	130	77	q	q	NOUN
ejpam-5578	130	78	/∈	/∈	PUNCT
ejpam-5578	131	1	vs	vs	ADP
ejpam-5578	131	2	,	,	PUNCT
ejpam-5578	131	3	where	where	SCONJ
ejpam-5578	131	4	i	i	PRON
ejpam-5578	131	5	̸=	̸=	PROPN
ejpam-5578	131	6	j	j	PROPN
ejpam-5578	131	7	and	and	CCONJ
ejpam-5578	131	8	i	i	PROPN
ejpam-5578	131	9	,	,	PUNCT
ejpam-5578	131	10	j	j	PROPN
ejpam-5578	131	11	∈	∈	PROPN
ejpam-5578	131	12	{	{	PUNCT
ejpam-5578	131	13	1	1	NUM
ejpam-5578	131	14	,	,	PUNCT
ejpam-5578	131	15	2	2	NUM
ejpam-5578	131	16	,	,	PUNCT
ejpam-5578	131	17	3	3	NUM
ejpam-5578	131	18	}	}	PUNCT
ejpam-5578	131	19	.	.	PUNCT
ejpam-5578	132	1	theorem	theorem	NOUN
ejpam-5578	132	2	1	1	NUM
ejpam-5578	132	3	.	.	PUNCT
ejpam-5578	133	1	let	let	VERB
ejpam-5578	133	2	(	(	PUNCT
ejpam-5578	133	3	q	q	ADJ
ejpam-5578	133	4	,	,	PUNCT
ejpam-5578	133	5	ϱ1	ϱ1	NOUN
ejpam-5578	133	6	,	,	PUNCT
ejpam-5578	133	7	ϱ2	ϱ2	NOUN
ejpam-5578	133	8	,	,	PUNCT
ejpam-5578	133	9	ϱ3	ϱ3	PROPN
ejpam-5578	133	10	)	)	PUNCT
ejpam-5578	133	11	be	be	AUX
ejpam-5578	133	12	a	a	DET
ejpam-5578	133	13	tri	tri	ADJ
ejpam-5578	133	14	-	-	ADJ
ejpam-5578	133	15	topological	topological	ADJ
ejpam-5578	133	16	space	space	NOUN
ejpam-5578	133	17	.	.	PUNCT
ejpam-5578	134	1	then	then	ADV
ejpam-5578	134	2	,	,	PUNCT
ejpam-5578	134	3	the	the	DET
ejpam-5578	134	4	following	follow	VERB
ejpam-5578	134	5	statements	statement	NOUN
ejpam-5578	134	6	are	be	AUX
ejpam-5578	134	7	equivalent	equivalent	ADJ
ejpam-5578	134	8	:	:	PUNCT
ejpam-5578	134	9	(	(	PUNCT
ejpam-5578	134	10	i	i	NOUN
ejpam-5578	134	11	)	)	PUNCT
ejpam-5578	134	12	q	q	PUNCT
ejpam-5578	134	13	is	be	AUX
ejpam-5578	134	14	a	a	DET
ejpam-5578	134	15	tri	tri	ADJ
ejpam-5578	134	16	-	-	ADJ
ejpam-5578	134	17	t0	t0	NOUN
ejpam-5578	134	18	-	-	NOUN
ejpam-5578	134	19	space	space	NOUN
ejpam-5578	134	20	.	.	PUNCT
ejpam-5578	135	1	(	(	PUNCT
ejpam-5578	135	2	ii	ii	NOUN
ejpam-5578	135	3	)	)	PUNCT
ejpam-5578	135	4	for	for	ADP
ejpam-5578	135	5	all	all	DET
ejpam-5578	135	6	q	q	PROPN
ejpam-5578	135	7	̸=	̸=	PROPN
ejpam-5578	135	8	s	s	PART
ejpam-5578	135	9	,	,	PUNCT
ejpam-5578	135	10	we	we	PRON
ejpam-5578	135	11	have	have	VERB
ejpam-5578	135	12	q	q	NOUN
ejpam-5578	135	13	/∈	/∈	PUNCT
ejpam-5578	135	14	{	{	PUNCT
ejpam-5578	135	15	s	s	NOUN
ejpam-5578	135	16	}	}	PUNCT
ejpam-5578	135	17	or	or	CCONJ
ejpam-5578	135	18	s	s	NOUN
ejpam-5578	135	19	/∈	/∈	PUNCT
ejpam-5578	135	20	{	{	PUNCT
ejpam-5578	135	21	q	q	NOUN
ejpam-5578	135	22	}	}	PUNCT
ejpam-5578	135	23	.	.	PUNCT
ejpam-5578	136	1	(	(	PUNCT
ejpam-5578	136	2	iii	iii	NOUN
ejpam-5578	136	3	)	)	PUNCT
ejpam-5578	136	4	for	for	ADP
ejpam-5578	136	5	all	all	DET
ejpam-5578	136	6	q	q	PROPN
ejpam-5578	136	7	̸=	̸=	PROPN
ejpam-5578	136	8	s	s	PART
ejpam-5578	136	9	,	,	PUNCT
ejpam-5578	136	10	we	we	PRON
ejpam-5578	136	11	have	have	VERB
ejpam-5578	136	12	{	{	PUNCT
ejpam-5578	136	13	q	q	NOUN
ejpam-5578	136	14	}	}	PUNCT
ejpam-5578	136	15	=	=	NOUN
ejpam-5578	136	16	̸	̸	X
ejpam-5578	136	17	{	{	PUNCT
ejpam-5578	136	18	s	s	NOUN
ejpam-5578	136	19	}	}	PUNCT
ejpam-5578	136	20	.	.	PUNCT
ejpam-5578	137	1	proof	proof	NOUN
ejpam-5578	137	2	.	.	PUNCT
ejpam-5578	138	1	(	(	PUNCT
ejpam-5578	138	2	i	i	NOUN
ejpam-5578	138	3	)	)	PUNCT
ejpam-5578	138	4	⇒	⇒	PROPN
ejpam-5578	138	5	(	(	PUNCT
ejpam-5578	138	6	ii	ii	PROPN
ejpam-5578	138	7	):	):	PUNCT
ejpam-5578	138	8	let	let	VERB
ejpam-5578	138	9	q	q	PROPN
ejpam-5578	138	10	̸=	̸=	PROPN
ejpam-5578	138	11	s.	s.	PROPN
ejpam-5578	138	12	since	since	SCONJ
ejpam-5578	138	13	q	q	PROPN
ejpam-5578	138	14	is	be	AUX
ejpam-5578	138	15	a	a	DET
ejpam-5578	138	16	tri	tri	ADJ
ejpam-5578	138	17	-	-	ADJ
ejpam-5578	138	18	t0	t0	NOUN
ejpam-5578	138	19	-	-	NOUN
ejpam-5578	138	20	space	space	NOUN
ejpam-5578	138	21	,	,	PUNCT
ejpam-5578	138	22	there	there	PRON
ejpam-5578	138	23	exists	exist	VERB
ejpam-5578	138	24	a	a	DET
ejpam-5578	138	25	ϱi	ϱi	ADV
ejpam-5578	138	26	-	-	PUNCT
ejpam-5578	138	27	open	open	ADJ
ejpam-5578	138	28	set	set	ADJ
ejpam-5578	138	29	uq	uq	NOUN
ejpam-5578	138	30	such	such	ADJ
ejpam-5578	138	31	that	that	DET
ejpam-5578	138	32	q	q	PROPN
ejpam-5578	138	33	∈	∈	PROPN
ejpam-5578	138	34	uq	uq	NOUN
ejpam-5578	138	35	and	and	CCONJ
ejpam-5578	138	36	s	s	NOUN
ejpam-5578	138	37	/∈	/∈	PROPN
ejpam-5578	138	38	uq	uq	NOUN
ejpam-5578	138	39	,	,	PUNCT
ejpam-5578	138	40	or	or	CCONJ
ejpam-5578	138	41	there	there	PRON
ejpam-5578	138	42	exists	exist	VERB
ejpam-5578	138	43	a	a	DET
ejpam-5578	138	44	ϱj	ϱj	NOUN
ejpam-5578	138	45	-	-	ADJ
ejpam-5578	138	46	open	open	ADJ
ejpam-5578	138	47	set	set	NOUN
ejpam-5578	138	48	vs	vs	ADP
ejpam-5578	138	49	such	such	ADJ
ejpam-5578	138	50	that	that	DET
ejpam-5578	138	51	s	s	VERB
ejpam-5578	138	52	∈	∈	PROPN
ejpam-5578	138	53	vs	vs	ADP
ejpam-5578	138	54	and	and	CCONJ
ejpam-5578	138	55	q	q	NOUN
ejpam-5578	138	56	/∈	/∈	PUNCT
ejpam-5578	138	57	vs	vs	ADP
ejpam-5578	138	58	,	,	PUNCT
ejpam-5578	138	59	where	where	SCONJ
ejpam-5578	138	60	i	i	PRON
ejpam-5578	138	61	,	,	PUNCT
ejpam-5578	138	62	j	j	PROPN
ejpam-5578	138	63	∈	∈	PROPN
ejpam-5578	138	64	{	{	PUNCT
ejpam-5578	138	65	1	1	NUM
ejpam-5578	138	66	,	,	PUNCT
ejpam-5578	138	67	2	2	NUM
ejpam-5578	138	68	,	,	PUNCT
ejpam-5578	138	69	3	3	NUM
ejpam-5578	138	70	}	}	PUNCT
ejpam-5578	138	71	.	.	PUNCT
ejpam-5578	139	1	this	this	PRON
ejpam-5578	139	2	implies	imply	VERB
ejpam-5578	139	3	that	that	SCONJ
ejpam-5578	139	4	:	:	PUNCT
ejpam-5578	139	5	q	q	X
ejpam-5578	139	6	∈	∈	PROPN
ejpam-5578	139	7	uq	uq	NOUN
ejpam-5578	139	8	and	and	CCONJ
ejpam-5578	139	9	uq	uq	PROPN
ejpam-5578	139	10	∩	∩	NOUN
ejpam-5578	139	11	{	{	PUNCT
ejpam-5578	139	12	s	s	NOUN
ejpam-5578	139	13	}	}	PUNCT
ejpam-5578	139	14	=	=	ADJ
ejpam-5578	139	15	∅	∅	NOUN
ejpam-5578	139	16	,	,	PUNCT
ejpam-5578	139	17	or	or	CCONJ
ejpam-5578	139	18	s	s	NOUN
ejpam-5578	139	19	∈	∈	NOUN
ejpam-5578	139	20	vs	vs	ADP
ejpam-5578	139	21	and	and	CCONJ
ejpam-5578	139	22	vs	vs	ADP
ejpam-5578	139	23	∩	∩	ADJ
ejpam-5578	139	24	{	{	PUNCT
ejpam-5578	139	25	q	q	X
ejpam-5578	139	26	}	}	PUNCT
ejpam-5578	139	27	=	=	PUNCT
ejpam-5578	139	28	∅.	∅.	VERB
ejpam-5578	139	29	therefore	therefore	ADV
ejpam-5578	139	30	,	,	PUNCT
ejpam-5578	139	31	we	we	PRON
ejpam-5578	139	32	conclude	conclude	VERB
ejpam-5578	139	33	that	that	PRON
ejpam-5578	139	34	q	q	NOUN
ejpam-5578	139	35	/∈	/∈	PUNCT
ejpam-5578	139	36	{	{	PUNCT
ejpam-5578	139	37	s	s	NOUN
ejpam-5578	139	38	}	}	PUNCT
ejpam-5578	139	39	or	or	CCONJ
ejpam-5578	139	40	s	s	NOUN
ejpam-5578	139	41	/∈	/∈	PUNCT
ejpam-5578	139	42	{	{	PUNCT
ejpam-5578	139	43	q	q	NOUN
ejpam-5578	139	44	}	}	PUNCT
ejpam-5578	139	45	.	.	PUNCT
ejpam-5578	140	1	(	(	PUNCT
ejpam-5578	140	2	ii	ii	NOUN
ejpam-5578	140	3	)	)	PUNCT
ejpam-5578	140	4	⇒	⇒	NOUN
ejpam-5578	140	5	(	(	PUNCT
ejpam-5578	140	6	iii	iii	NOUN
ejpam-5578	140	7	):	):	PUNCT
ejpam-5578	140	8	suppose	suppose	VERB
ejpam-5578	140	9	q	q	PROPN
ejpam-5578	140	10	̸=	̸=	PROPN
ejpam-5578	140	11	s.	s.	PROPN
ejpam-5578	140	12	if	if	SCONJ
ejpam-5578	140	13	q	q	X
ejpam-5578	140	14	/∈	/∈	PUNCT
ejpam-5578	140	15	{	{	PUNCT
ejpam-5578	140	16	s	s	NOUN
ejpam-5578	140	17	}	}	PUNCT
ejpam-5578	140	18	and	and	CCONJ
ejpam-5578	140	19	q	q	ADJ
ejpam-5578	140	20	∈	∈	PROPN
ejpam-5578	140	21	{	{	PUNCT
ejpam-5578	140	22	q	q	NOUN
ejpam-5578	140	23	}	}	PUNCT
ejpam-5578	140	24	,	,	PUNCT
ejpam-5578	140	25	then	then	ADV
ejpam-5578	140	26	we	we	PRON
ejpam-5578	140	27	must	must	AUX
ejpam-5578	140	28	have	have	AUX
ejpam-5578	140	29	{	{	PUNCT
ejpam-5578	140	30	q	q	NOUN
ejpam-5578	140	31	}	}	PUNCT
ejpam-5578	140	32	̸=	̸=	PROPN
ejpam-5578	140	33	{	{	PUNCT
ejpam-5578	140	34	s	s	NOUN
ejpam-5578	140	35	}	}	PUNCT
ejpam-5578	140	36	.	.	PUNCT
ejpam-5578	141	1	similarly	similarly	ADV
ejpam-5578	141	2	,	,	PUNCT
ejpam-5578	141	3	if	if	SCONJ
ejpam-5578	141	4	s	s	VERB
ejpam-5578	141	5	/∈	/∈	INTJ
ejpam-5578	141	6	{	{	PUNCT
ejpam-5578	141	7	q	q	NOUN
ejpam-5578	141	8	}	}	PUNCT
ejpam-5578	141	9	and	and	CCONJ
ejpam-5578	141	10	s	s	PROPN
ejpam-5578	141	11	∈	∈	X
ejpam-5578	141	12	{	{	PUNCT
ejpam-5578	141	13	s	s	NOUN
ejpam-5578	141	14	}	}	PUNCT
ejpam-5578	141	15	,	,	PUNCT
ejpam-5578	141	16	then	then	ADV
ejpam-5578	141	17	again	again	ADV
ejpam-5578	141	18	{	{	PUNCT
ejpam-5578	141	19	q	q	NOUN
ejpam-5578	141	20	}	}	PUNCT
ejpam-5578	141	21	=	=	NOUN
ejpam-5578	141	22	̸	̸	X
ejpam-5578	141	23	{	{	PUNCT
ejpam-5578	141	24	s	s	NOUN
ejpam-5578	141	25	}	}	PUNCT
ejpam-5578	141	26	.	.	PUNCT
ejpam-5578	142	1	thus	thus	ADV
ejpam-5578	142	2	,	,	PUNCT
ejpam-5578	142	3	condition	condition	NOUN
ejpam-5578	142	4	(	(	PUNCT
ejpam-5578	142	5	iii	iii	NOUN
ejpam-5578	142	6	)	)	PUNCT
ejpam-5578	142	7	holds	hold	VERB
ejpam-5578	142	8	.	.	PUNCT
ejpam-5578	143	1	(	(	PUNCT
ejpam-5578	143	2	iii	iii	X
ejpam-5578	143	3	)	)	PUNCT
ejpam-5578	143	4	⇒	⇒	NOUN
ejpam-5578	143	5	(	(	PUNCT
ejpam-5578	143	6	i	i	NOUN
ejpam-5578	143	7	):	):	PUNCT
ejpam-5578	143	8	suppose	suppose	VERB
ejpam-5578	143	9	q	q	PROPN
ejpam-5578	143	10	̸=	̸=	PROPN
ejpam-5578	143	11	s	s	PART
ejpam-5578	144	1	and	and	CCONJ
ejpam-5578	144	2	we	we	PRON
ejpam-5578	144	3	are	be	AUX
ejpam-5578	144	4	given	give	VERB
ejpam-5578	144	5	that	that	SCONJ
ejpam-5578	144	6	{	{	PUNCT
ejpam-5578	144	7	q	q	X
ejpam-5578	144	8	}	}	PUNCT
ejpam-5578	144	9	=	=	NOUN
ejpam-5578	144	10	̸	̸	X
ejpam-5578	144	11	{	{	PUNCT
ejpam-5578	144	12	s	s	NOUN
ejpam-5578	144	13	}	}	PUNCT
ejpam-5578	144	14	.	.	PUNCT
ejpam-5578	145	1	since	since	SCONJ
ejpam-5578	145	2	q	q	PROPN
ejpam-5578	145	3	∈	∈	PROPN
ejpam-5578	145	4	{	{	PUNCT
ejpam-5578	145	5	q	q	NOUN
ejpam-5578	145	6	}	}	PUNCT
ejpam-5578	145	7	and	and	CCONJ
ejpam-5578	145	8	s	s	PROPN
ejpam-5578	145	9	∈	∈	X
ejpam-5578	145	10	{	{	PUNCT
ejpam-5578	145	11	s	s	NOUN
ejpam-5578	145	12	}	}	PUNCT
ejpam-5578	145	13	,	,	PUNCT
ejpam-5578	145	14	we	we	PRON
ejpam-5578	145	15	must	must	AUX
ejpam-5578	145	16	have	have	VERB
ejpam-5578	145	17	:	:	PUNCT
ejpam-5578	145	18	q	q	X
ejpam-5578	145	19	/∈	/∈	PUNCT
ejpam-5578	146	1	q−	q−	PROPN
ejpam-5578	146	2	{	{	PUNCT
ejpam-5578	146	3	q	q	NOUN
ejpam-5578	146	4	}	}	PUNCT
ejpam-5578	146	5	=	=	SYM
ejpam-5578	146	6	vs	vs	ADP
ejpam-5578	146	7	,	,	PUNCT
ejpam-5578	146	8	where	where	SCONJ
ejpam-5578	146	9	vs	vs	ADP
ejpam-5578	146	10	is	be	AUX
ejpam-5578	146	11	a	a	DET
ejpam-5578	146	12	ϱi	ϱi	ADV
ejpam-5578	146	13	-	-	PUNCT
ejpam-5578	146	14	open	open	ADJ
ejpam-5578	146	15	set	set	NOUN
ejpam-5578	146	16	in	in	ADP
ejpam-5578	146	17	q	q	NOUN
ejpam-5578	146	18	,	,	PUNCT
ejpam-5578	146	19	since	since	SCONJ
ejpam-5578	146	20	{	{	PUNCT
ejpam-5578	146	21	q	q	X
ejpam-5578	146	22	}	}	PUNCT
ejpam-5578	146	23	is	be	AUX
ejpam-5578	146	24	a	a	DET
ejpam-5578	146	25	ϱi	ϱi	ADV
ejpam-5578	146	26	-	-	PUNCT
ejpam-5578	146	27	closed	close	VERB
ejpam-5578	146	28	set	set	NOUN
ejpam-5578	146	29	.	.	PUNCT
ejpam-5578	147	1	furthermore	furthermore	ADV
ejpam-5578	147	2	,	,	PUNCT
ejpam-5578	147	3	s	s	VERB
ejpam-5578	147	4	∈	∈	PROPN
ejpam-5578	147	5	q−{q	q−{q	PROPN
ejpam-5578	147	6	}	}	PUNCT
ejpam-5578	147	7	=	=	SYM
ejpam-5578	147	8	vs	vs	ADP
ejpam-5578	147	9	,	,	PUNCT
ejpam-5578	147	10	where	where	SCONJ
ejpam-5578	147	11	i	i	PRON
ejpam-5578	147	12	∈	∈	PROPN
ejpam-5578	147	13	{	{	PUNCT
ejpam-5578	147	14	1	1	NUM
ejpam-5578	147	15	,	,	PUNCT
ejpam-5578	147	16	2	2	NUM
ejpam-5578	147	17	,	,	PUNCT
ejpam-5578	147	18	3	3	NUM
ejpam-5578	147	19	}	}	PUNCT
ejpam-5578	147	20	.	.	PUNCT
ejpam-5578	148	1	therefore	therefore	ADV
ejpam-5578	148	2	,	,	PUNCT
ejpam-5578	148	3	q	q	X
ejpam-5578	148	4	is	be	AUX
ejpam-5578	148	5	a	a	DET
ejpam-5578	148	6	tri	tri	ADJ
ejpam-5578	148	7	-	-	ADJ
ejpam-5578	148	8	t0	t0	NOUN
ejpam-5578	148	9	-	-	NOUN
ejpam-5578	148	10	space	space	NOUN
ejpam-5578	148	11	.	.	PUNCT
ejpam-5578	149	1	j.	j.	PROPN
ejpam-5578	149	2	oudetallah	oudetallah	PROPN
ejpam-5578	149	3	et	et	PROPN
ejpam-5578	149	4	al	al	PROPN
ejpam-5578	149	5	.	.	PUNCT
ejpam-5578	149	6	/	/	SYM
ejpam-5578	149	7	eur	eur	PROPN
ejpam-5578	149	8	.	.	PUNCT
ejpam-5578	150	1	j.	j.	PROPN
ejpam-5578	150	2	pure	pure	PROPN
ejpam-5578	150	3	appl	appl	PROPN
ejpam-5578	150	4	.	.	PROPN
ejpam-5578	150	5	math	math	PROPN
ejpam-5578	150	6	,	,	PUNCT
ejpam-5578	150	7	18	18	NUM
ejpam-5578	150	8	(	(	PUNCT
ejpam-5578	150	9	2	2	NUM
ejpam-5578	150	10	)	)	PUNCT
ejpam-5578	150	11	(	(	PUNCT
ejpam-5578	150	12	2025	2025	NUM
ejpam-5578	150	13	)	)	PUNCT
ejpam-5578	150	14	,	,	PUNCT
ejpam-5578	150	15	5578	5578	NUM
ejpam-5578	150	16	8	8	NUM
ejpam-5578	150	17	of	of	ADP
ejpam-5578	150	18	19	19	NUM
ejpam-5578	150	19	definition	definition	NOUN
ejpam-5578	150	20	11	11	NUM
ejpam-5578	150	21	.	.	PUNCT
ejpam-5578	151	1	[	[	X
ejpam-5578	151	2	16	16	NUM
ejpam-5578	151	3	]	]	PUNCT
ejpam-5578	151	4	a	a	DET
ejpam-5578	151	5	tri	tri	ADJ
ejpam-5578	151	6	-	-	ADJ
ejpam-5578	151	7	topological	topological	ADJ
ejpam-5578	151	8	space	space	NOUN
ejpam-5578	151	9	(	(	PUNCT
ejpam-5578	151	10	q	q	ADJ
ejpam-5578	151	11	,	,	PUNCT
ejpam-5578	151	12	ϱ1	ϱ1	NOUN
ejpam-5578	151	13	,	,	PUNCT
ejpam-5578	151	14	ϱ2	ϱ2	NOUN
ejpam-5578	151	15	,	,	PUNCT
ejpam-5578	151	16	ϱ3	ϱ3	PROPN
ejpam-5578	151	17	)	)	PUNCT
ejpam-5578	151	18	is	be	AUX
ejpam-5578	151	19	called	call	VERB
ejpam-5578	151	20	a	a	DET
ejpam-5578	151	21	tri	tri	ADJ
ejpam-5578	151	22	-	-	ADJ
ejpam-5578	151	23	t1	t1	ADJ
ejpam-5578	151	24	-	-	PUNCT
ejpam-5578	151	25	space	space	NOUN
ejpam-5578	151	26	if	if	SCONJ
ejpam-5578	151	27	for	for	ADP
ejpam-5578	151	28	all	all	DET
ejpam-5578	151	29	distinct	distinct	ADJ
ejpam-5578	151	30	points	point	NOUN
ejpam-5578	151	31	q	q	NOUN
ejpam-5578	151	32	,	,	PUNCT
ejpam-5578	151	33	s	s	NOUN
ejpam-5578	151	34	∈	∈	ADJ
ejpam-5578	151	35	q	q	X
ejpam-5578	151	36	(	(	PUNCT
ejpam-5578	151	37	q	q	PROPN
ejpam-5578	151	38	̸=	̸=	PROPN
ejpam-5578	151	39	s	s	PART
ejpam-5578	151	40	)	)	PUNCT
ejpam-5578	151	41	,	,	PUNCT
ejpam-5578	151	42	there	there	PRON
ejpam-5578	151	43	exists	exist	VERB
ejpam-5578	151	44	a	a	DET
ejpam-5578	151	45	ϱi	ϱi	ADV
ejpam-5578	151	46	-	-	PUNCT
ejpam-5578	151	47	open	open	ADJ
ejpam-5578	151	48	set	set	ADJ
ejpam-5578	151	49	uq	uq	NOUN
ejpam-5578	151	50	such	such	ADJ
ejpam-5578	151	51	that	that	PRON
ejpam-5578	151	52	:	:	PUNCT
ejpam-5578	151	53	q	q	X
ejpam-5578	151	54	∈	∈	PROPN
ejpam-5578	151	55	uq	uq	NOUN
ejpam-5578	151	56	and	and	CCONJ
ejpam-5578	151	57	s	s	NOUN
ejpam-5578	151	58	/∈	/∈	PROPN
ejpam-5578	151	59	uq	uq	NOUN
ejpam-5578	151	60	,	,	PUNCT
ejpam-5578	151	61	and	and	CCONJ
ejpam-5578	151	62	there	there	PRON
ejpam-5578	151	63	exists	exist	VERB
ejpam-5578	151	64	a	a	DET
ejpam-5578	151	65	ϱj	ϱj	NOUN
ejpam-5578	151	66	-	-	ADJ
ejpam-5578	151	67	open	open	ADJ
ejpam-5578	151	68	set	set	NOUN
ejpam-5578	151	69	vs	vs	ADP
ejpam-5578	151	70	such	such	ADJ
ejpam-5578	151	71	that	that	PRON
ejpam-5578	151	72	:	:	PUNCT
ejpam-5578	151	73	s	s	X
ejpam-5578	151	74	∈	∈	NOUN
ejpam-5578	151	75	vs	vs	ADP
ejpam-5578	151	76	and	and	CCONJ
ejpam-5578	151	77	q	q	NOUN
ejpam-5578	151	78	/∈	/∈	PUNCT
ejpam-5578	152	1	vs	vs	ADP
ejpam-5578	152	2	,	,	PUNCT
ejpam-5578	152	3	where	where	SCONJ
ejpam-5578	152	4	i	i	PRON
ejpam-5578	152	5	̸=	̸=	PROPN
ejpam-5578	152	6	j	j	PROPN
ejpam-5578	152	7	and	and	CCONJ
ejpam-5578	152	8	i	i	PROPN
ejpam-5578	152	9	,	,	PUNCT
ejpam-5578	152	10	j	j	PROPN
ejpam-5578	152	11	∈	∈	PROPN
ejpam-5578	152	12	{	{	PUNCT
ejpam-5578	152	13	1	1	NUM
ejpam-5578	152	14	,	,	PUNCT
ejpam-5578	152	15	2	2	NUM
ejpam-5578	152	16	,	,	PUNCT
ejpam-5578	152	17	3	3	NUM
ejpam-5578	152	18	}	}	PUNCT
ejpam-5578	152	19	.	.	PUNCT
ejpam-5578	153	1	definition	definition	NOUN
ejpam-5578	153	2	12	12	NUM
ejpam-5578	153	3	.	.	PUNCT
ejpam-5578	154	1	[	[	X
ejpam-5578	154	2	12	12	NUM
ejpam-5578	154	3	]	]	PUNCT
ejpam-5578	154	4	a	a	DET
ejpam-5578	154	5	tri	tri	ADJ
ejpam-5578	154	6	-	-	ADJ
ejpam-5578	154	7	topological	topological	ADJ
ejpam-5578	154	8	space	space	NOUN
ejpam-5578	154	9	(	(	PUNCT
ejpam-5578	154	10	q	q	ADJ
ejpam-5578	154	11	,	,	PUNCT
ejpam-5578	154	12	ϱ1	ϱ1	NOUN
ejpam-5578	154	13	,	,	PUNCT
ejpam-5578	154	14	ϱ2	ϱ2	NOUN
ejpam-5578	154	15	,	,	PUNCT
ejpam-5578	154	16	ϱ3	ϱ3	PROPN
ejpam-5578	154	17	)	)	PUNCT
ejpam-5578	154	18	is	be	AUX
ejpam-5578	154	19	called	call	VERB
ejpam-5578	154	20	a	a	DET
ejpam-5578	154	21	tri	tri	ADJ
ejpam-5578	154	22	-	-	ADJ
ejpam-5578	154	23	t2	t2	ADJ
ejpam-5578	154	24	-	-	PUNCT
ejpam-5578	154	25	space	space	NOUN
ejpam-5578	154	26	if	if	SCONJ
ejpam-5578	154	27	for	for	ADP
ejpam-5578	154	28	all	all	DET
ejpam-5578	154	29	distinct	distinct	ADJ
ejpam-5578	154	30	points	point	NOUN
ejpam-5578	154	31	q	q	NOUN
ejpam-5578	154	32	,	,	PUNCT
ejpam-5578	154	33	s	s	NOUN
ejpam-5578	154	34	∈	∈	ADJ
ejpam-5578	154	35	q	q	X
ejpam-5578	154	36	(	(	PUNCT
ejpam-5578	154	37	q	q	PROPN
ejpam-5578	154	38	̸=	̸=	PROPN
ejpam-5578	154	39	s	s	PART
ejpam-5578	154	40	)	)	PUNCT
ejpam-5578	154	41	,	,	PUNCT
ejpam-5578	154	42	there	there	PRON
ejpam-5578	154	43	exists	exist	VERB
ejpam-5578	154	44	a	a	DET
ejpam-5578	154	45	ϱi	ϱi	ADV
ejpam-5578	154	46	-	-	PUNCT
ejpam-5578	154	47	open	open	ADJ
ejpam-5578	154	48	set	set	ADJ
ejpam-5578	154	49	uq	uq	NOUN
ejpam-5578	154	50	such	such	ADJ
ejpam-5578	154	51	that	that	PRON
ejpam-5578	154	52	:	:	PUNCT
ejpam-5578	154	53	q	q	PROPN
ejpam-5578	154	54	∈	∈	PROPN
ejpam-5578	154	55	uq	uq	NOUN
ejpam-5578	154	56	,	,	PUNCT
ejpam-5578	154	57	and	and	CCONJ
ejpam-5578	154	58	there	there	PRON
ejpam-5578	154	59	exists	exist	VERB
ejpam-5578	154	60	a	a	DET
ejpam-5578	154	61	ϱj	ϱj	NOUN
ejpam-5578	154	62	-	-	ADJ
ejpam-5578	154	63	open	open	ADJ
ejpam-5578	154	64	set	set	NOUN
ejpam-5578	154	65	vs	vs	ADP
ejpam-5578	154	66	such	such	ADJ
ejpam-5578	154	67	that	that	PRON
ejpam-5578	154	68	:	:	PUNCT
ejpam-5578	154	69	s	s	X
ejpam-5578	154	70	∈	∈	PROPN
ejpam-5578	154	71	vs	vs	ADP
ejpam-5578	154	72	and	and	CCONJ
ejpam-5578	154	73	uq	uq	NOUN
ejpam-5578	154	74	∩	∩	NOUN
ejpam-5578	154	75	vs	vs	ADP
ejpam-5578	154	76	=	=	NOUN
ejpam-5578	154	77	∅	∅	NOUN
ejpam-5578	154	78	,	,	PUNCT
ejpam-5578	154	79	where	where	SCONJ
ejpam-5578	154	80	i	i	PRON
ejpam-5578	154	81	̸=	̸=	PROPN
ejpam-5578	154	82	j	j	PROPN
ejpam-5578	154	83	and	and	CCONJ
ejpam-5578	154	84	i	i	PROPN
ejpam-5578	154	85	,	,	PUNCT
ejpam-5578	154	86	j	j	PROPN
ejpam-5578	154	87	∈	∈	PROPN
ejpam-5578	154	88	{	{	PUNCT
ejpam-5578	154	89	1	1	NUM
ejpam-5578	154	90	,	,	PUNCT
ejpam-5578	154	91	2	2	NUM
ejpam-5578	154	92	,	,	PUNCT
ejpam-5578	154	93	3	3	NUM
ejpam-5578	154	94	}	}	PUNCT
ejpam-5578	154	95	.	.	PUNCT
ejpam-5578	155	1	definition	definition	NOUN
ejpam-5578	155	2	13	13	NUM
ejpam-5578	155	3	.	.	PUNCT
ejpam-5578	156	1	[	[	X
ejpam-5578	156	2	1	1	X
ejpam-5578	156	3	]	]	PUNCT
ejpam-5578	156	4	a	a	DET
ejpam-5578	156	5	tri	tri	ADJ
ejpam-5578	156	6	-	-	ADJ
ejpam-5578	156	7	topological	topological	ADJ
ejpam-5578	156	8	space	space	NOUN
ejpam-5578	156	9	(	(	PUNCT
ejpam-5578	156	10	q	q	ADJ
ejpam-5578	156	11	,	,	PUNCT
ejpam-5578	156	12	ϱ1	ϱ1	NOUN
ejpam-5578	156	13	,	,	PUNCT
ejpam-5578	156	14	ϱ2	ϱ2	NOUN
ejpam-5578	156	15	,	,	PUNCT
ejpam-5578	156	16	ϱ3	ϱ3	PROPN
ejpam-5578	156	17	)	)	PUNCT
ejpam-5578	156	18	is	be	AUX
ejpam-5578	156	19	called	call	VERB
ejpam-5578	156	20	a	a	DET
ejpam-5578	156	21	tri	tri	NOUN
ejpam-5578	156	22	-	-	NOUN
ejpam-5578	156	23	t2	t2	ADJ
ejpam-5578	156	24	1	1	NUM
ejpam-5578	156	25	2	2	NUM
ejpam-5578	156	26	-space	-space	NOUN
ejpam-5578	156	27	if	if	SCONJ
ejpam-5578	156	28	for	for	ADP
ejpam-5578	156	29	all	all	DET
ejpam-5578	156	30	distinct	distinct	ADJ
ejpam-5578	156	31	points	point	NOUN
ejpam-5578	156	32	q	q	NOUN
ejpam-5578	156	33	,	,	PUNCT
ejpam-5578	156	34	s	s	NOUN
ejpam-5578	156	35	∈	∈	ADJ
ejpam-5578	156	36	q	q	X
ejpam-5578	156	37	(	(	PUNCT
ejpam-5578	156	38	q	q	PROPN
ejpam-5578	156	39	̸=	̸=	PROPN
ejpam-5578	156	40	s	s	PART
ejpam-5578	156	41	)	)	PUNCT
ejpam-5578	156	42	,	,	PUNCT
ejpam-5578	156	43	there	there	PRON
ejpam-5578	156	44	exist	exist	VERB
ejpam-5578	156	45	ϱi	ϱi	ADV
ejpam-5578	156	46	-	-	PUNCT
ejpam-5578	156	47	closed	close	VERB
ejpam-5578	156	48	sets	set	NOUN
ejpam-5578	156	49	oq	oq	INTJ
ejpam-5578	156	50	and	and	CCONJ
ejpam-5578	156	51	bs	bs	INTJ
ejpam-5578	156	52	such	such	ADJ
ejpam-5578	156	53	that	that	PRON
ejpam-5578	156	54	:	:	PUNCT
ejpam-5578	156	55	q	q	PROPN
ejpam-5578	156	56	∈	∈	PROPN
ejpam-5578	156	57	oq	oq	PROPN
ejpam-5578	156	58	,	,	PUNCT
ejpam-5578	156	59	s	s	PROPN
ejpam-5578	156	60	∈	∈	PROPN
ejpam-5578	156	61	bs	bs	NOUN
ejpam-5578	156	62	,	,	PUNCT
ejpam-5578	156	63	and	and	CCONJ
ejpam-5578	156	64	oq	oq	PROPN
ejpam-5578	156	65	∩bs	∩bs	NOUN
ejpam-5578	156	66	=	=	NOUN
ejpam-5578	156	67	∅	∅	NOUN
ejpam-5578	156	68	,	,	PUNCT
ejpam-5578	156	69	for	for	ADP
ejpam-5578	156	70	some	some	DET
ejpam-5578	156	71	i	i	PRON
ejpam-5578	156	72	∈	∈	PROPN
ejpam-5578	156	73	{	{	PUNCT
ejpam-5578	156	74	1	1	NUM
ejpam-5578	156	75	,	,	PUNCT
ejpam-5578	156	76	2	2	NUM
ejpam-5578	156	77	,	,	PUNCT
ejpam-5578	156	78	3	3	NUM
ejpam-5578	156	79	}	}	PUNCT
ejpam-5578	156	80	.	.	PUNCT
ejpam-5578	157	1	definition	definition	NOUN
ejpam-5578	157	2	14	14	NUM
ejpam-5578	157	3	.	.	PUNCT
ejpam-5578	158	1	[	[	X
ejpam-5578	158	2	3	3	X
ejpam-5578	158	3	]	]	PUNCT
ejpam-5578	158	4	a	a	DET
ejpam-5578	158	5	tri	tri	ADJ
ejpam-5578	158	6	-	-	ADJ
ejpam-5578	158	7	topological	topological	ADJ
ejpam-5578	158	8	space	space	NOUN
ejpam-5578	158	9	(	(	PUNCT
ejpam-5578	158	10	q	q	ADJ
ejpam-5578	158	11	,	,	PUNCT
ejpam-5578	158	12	ϱ1	ϱ1	NOUN
ejpam-5578	158	13	,	,	PUNCT
ejpam-5578	158	14	ϱ2	ϱ2	NOUN
ejpam-5578	158	15	,	,	PUNCT
ejpam-5578	158	16	ϱ3	ϱ3	PROPN
ejpam-5578	158	17	)	)	PUNCT
ejpam-5578	158	18	is	be	AUX
ejpam-5578	158	19	called	call	VERB
ejpam-5578	158	20	a	a	DET
ejpam-5578	158	21	tri	tri	ADJ
ejpam-5578	158	22	-	-	ADJ
ejpam-5578	158	23	regular	regular	ADJ
ejpam-5578	158	24	space	space	NOUN
ejpam-5578	158	25	if	if	SCONJ
ejpam-5578	158	26	for	for	ADP
ejpam-5578	158	27	every	every	DET
ejpam-5578	158	28	point	point	NOUN
ejpam-5578	158	29	q	q	X
ejpam-5578	158	30	/∈	/∈	PUNCT
ejpam-5578	159	1	o	o	NOUN
ejpam-5578	159	2	,	,	PUNCT
ejpam-5578	159	3	where	where	SCONJ
ejpam-5578	159	4	o	o	NOUN
ejpam-5578	159	5	is	be	AUX
ejpam-5578	159	6	a	a	DET
ejpam-5578	159	7	ϱi	ϱi	ADV
ejpam-5578	159	8	-	-	PUNCT
ejpam-5578	159	9	closed	close	VERB
ejpam-5578	159	10	set	set	NOUN
ejpam-5578	159	11	,	,	PUNCT
ejpam-5578	159	12	there	there	PRON
ejpam-5578	159	13	exist	exist	VERB
ejpam-5578	159	14	a	a	DET
ejpam-5578	159	15	ϱi	ϱi	ADV
ejpam-5578	159	16	-	-	PUNCT
ejpam-5578	159	17	open	open	ADJ
ejpam-5578	159	18	set	set	VERB
ejpam-5578	159	19	uq	uq	NOUN
ejpam-5578	159	20	and	and	CCONJ
ejpam-5578	159	21	a	a	DET
ejpam-5578	159	22	ϱj	ϱj	NOUN
ejpam-5578	159	23	-	-	ADJ
ejpam-5578	159	24	open	open	ADJ
ejpam-5578	159	25	set	set	VERB
ejpam-5578	159	26	vo	vo	INTJ
ejpam-5578	159	27	such	such	ADJ
ejpam-5578	159	28	that	that	PRON
ejpam-5578	159	29	:	:	PUNCT
ejpam-5578	159	30	q	q	PROPN
ejpam-5578	159	31	∈	∈	PROPN
ejpam-5578	159	32	uq	uq	NOUN
ejpam-5578	159	33	,	,	PUNCT
ejpam-5578	159	34	o	o	PROPN
ejpam-5578	159	35	⊆	⊆	NUM
ejpam-5578	159	36	vo	vo	NOUN
ejpam-5578	159	37	,	,	PUNCT
ejpam-5578	159	38	and	and	CCONJ
ejpam-5578	159	39	uq	uq	PROPN
ejpam-5578	159	40	∩	∩	ADJ
ejpam-5578	159	41	vo	vo	NOUN
ejpam-5578	159	42	=	=	NOUN
ejpam-5578	159	43	∅	∅	NOUN
ejpam-5578	159	44	,	,	PUNCT
ejpam-5578	159	45	where	where	SCONJ
ejpam-5578	159	46	i	i	PRON
ejpam-5578	159	47	̸=	̸=	PROPN
ejpam-5578	159	48	j	j	PROPN
ejpam-5578	159	49	and	and	CCONJ
ejpam-5578	159	50	i	i	PROPN
ejpam-5578	159	51	,	,	PUNCT
ejpam-5578	159	52	j	j	PROPN
ejpam-5578	159	53	∈	∈	PROPN
ejpam-5578	159	54	{	{	PUNCT
ejpam-5578	159	55	1	1	NUM
ejpam-5578	159	56	,	,	PUNCT
ejpam-5578	159	57	2	2	NUM
ejpam-5578	159	58	,	,	PUNCT
ejpam-5578	159	59	3	3	NUM
ejpam-5578	159	60	}	}	PUNCT
ejpam-5578	159	61	.	.	PUNCT
ejpam-5578	160	1	theorem	theorem	NOUN
ejpam-5578	160	2	2	2	NUM
ejpam-5578	160	3	.	.	PUNCT
ejpam-5578	160	4	a	a	DET
ejpam-5578	160	5	space	space	NOUN
ejpam-5578	160	6	(	(	PUNCT
ejpam-5578	160	7	q	q	ADJ
ejpam-5578	160	8	,	,	PUNCT
ejpam-5578	160	9	ϱ1	ϱ1	NOUN
ejpam-5578	160	10	,	,	PUNCT
ejpam-5578	160	11	ϱ2	ϱ2	NOUN
ejpam-5578	160	12	,	,	PUNCT
ejpam-5578	160	13	ϱ3	ϱ3	PROPN
ejpam-5578	160	14	)	)	PUNCT
ejpam-5578	160	15	is	be	AUX
ejpam-5578	160	16	a	a	DET
ejpam-5578	160	17	tri	tri	ADJ
ejpam-5578	160	18	-	-	ADJ
ejpam-5578	160	19	regular	regular	ADJ
ejpam-5578	160	20	space	space	NOUN
ejpam-5578	160	21	if	if	SCONJ
ejpam-5578	160	22	and	and	CCONJ
ejpam-5578	160	23	only	only	ADV
ejpam-5578	160	24	if	if	SCONJ
ejpam-5578	160	25	for	for	ADP
ejpam-5578	160	26	all	all	DET
ejpam-5578	160	27	q	q	PROPN
ejpam-5578	160	28	∈	∈	PROPN
ejpam-5578	160	29	uq	uq	NOUN
ejpam-5578	160	30	,	,	PUNCT
ejpam-5578	160	31	where	where	SCONJ
ejpam-5578	160	32	uq	uq	PROPN
ejpam-5578	160	33	is	be	AUX
ejpam-5578	160	34	a	a	DET
ejpam-5578	160	35	ϱi	ϱi	ADJ
ejpam-5578	160	36	-	-	PUNCT
ejpam-5578	160	37	open	open	ADJ
ejpam-5578	160	38	set	set	NOUN
ejpam-5578	160	39	,	,	PUNCT
ejpam-5578	160	40	there	there	PRON
ejpam-5578	160	41	exists	exist	VERB
ejpam-5578	160	42	a	a	DET
ejpam-5578	160	43	ϱi	ϱi	ADV
ejpam-5578	160	44	-	-	PUNCT
ejpam-5578	160	45	open	open	ADJ
ejpam-5578	160	46	set	set	ADJ
ejpam-5578	160	47	wq	wq	NOUN
ejpam-5578	160	48	such	such	ADJ
ejpam-5578	160	49	that	that	PRON
ejpam-5578	160	50	:	:	PUNCT
ejpam-5578	161	1	q	q	X
ejpam-5578	161	2	∈	∈	NOUN
ejpam-5578	161	3	wq	wq	NOUN
ejpam-5578	162	1	⊆	⊆	NUM
ejpam-5578	162	2	wq	wq	NOUN
ejpam-5578	162	3	⊆	⊆	NUM
ejpam-5578	162	4	uq	uq	NOUN
ejpam-5578	162	5	.	.	PUNCT
ejpam-5578	162	6	proof	proof	NOUN
ejpam-5578	162	7	.	.	PUNCT
ejpam-5578	163	1	(	(	PUNCT
ejpam-5578	163	2	⇒	⇒	NOUN
ejpam-5578	163	3	)	)	PUNCT
ejpam-5578	163	4	let	let	VERB
ejpam-5578	163	5	q	q	PROPN
ejpam-5578	163	6	∈	∈	PROPN
ejpam-5578	163	7	uq	uq	NOUN
ejpam-5578	163	8	.	.	PUNCT
ejpam-5578	164	1	since	since	SCONJ
ejpam-5578	164	2	q	q	PROPN
ejpam-5578	164	3	/∈	/∈	PROPN
ejpam-5578	164	4	ucq	ucq	PROPN
ejpam-5578	164	5	,	,	PUNCT
ejpam-5578	164	6	and	and	CCONJ
ejpam-5578	164	7	u	u	NOUN
ejpam-5578	164	8	c	c	PROPN
ejpam-5578	164	9	q	q	NOUN
ejpam-5578	164	10	is	be	AUX
ejpam-5578	164	11	a	a	DET
ejpam-5578	164	12	ϱi	ϱi	ADV
ejpam-5578	164	13	-	-	PUNCT
ejpam-5578	164	14	closed	close	VERB
ejpam-5578	164	15	set	set	NOUN
ejpam-5578	164	16	,	,	PUNCT
ejpam-5578	164	17	we	we	PRON
ejpam-5578	164	18	denote	denote	VERB
ejpam-5578	164	19	ucq	ucq	PROPN
ejpam-5578	164	20	=	=	PUNCT
ejpam-5578	165	1	o.	o.	INTJ
ejpam-5578	165	2	by	by	ADP
ejpam-5578	165	3	the	the	DET
ejpam-5578	165	4	definition	definition	NOUN
ejpam-5578	165	5	of	of	ADP
ejpam-5578	165	6	a	a	DET
ejpam-5578	165	7	tri	tri	ADJ
ejpam-5578	165	8	-	-	ADJ
ejpam-5578	165	9	regular	regular	ADJ
ejpam-5578	165	10	space	space	NOUN
ejpam-5578	165	11	,	,	PUNCT
ejpam-5578	165	12	there	there	PRON
ejpam-5578	165	13	exist	exist	VERB
ejpam-5578	165	14	ϱi	ϱi	ADJ
ejpam-5578	165	15	-	-	PUNCT
ejpam-5578	165	16	open	open	ADJ
ejpam-5578	165	17	sets	set	NOUN
ejpam-5578	165	18	wq	wq	VERB
ejpam-5578	165	19	and	and	CCONJ
ejpam-5578	165	20	vo	vo	PRON
ejpam-5578	165	21	such	such	ADJ
ejpam-5578	165	22	that	that	PRON
ejpam-5578	165	23	:	:	PUNCT
ejpam-5578	165	24	q	q	PROPN
ejpam-5578	165	25	∈	∈	PROPN
ejpam-5578	165	26	wq	wq	NOUN
ejpam-5578	165	27	,	,	PUNCT
ejpam-5578	165	28	o	o	PROPN
ejpam-5578	165	29	⊆	⊆	NUM
ejpam-5578	165	30	vo	vo	NOUN
ejpam-5578	165	31	,	,	PUNCT
ejpam-5578	165	32	and	and	CCONJ
ejpam-5578	165	33	wq	wq	PROPN
ejpam-5578	165	34	∩	∩	NOUN
ejpam-5578	165	35	vo	vo	X
ejpam-5578	165	36	=	=	PROPN
ejpam-5578	165	37	∅.	∅.	VERB
ejpam-5578	165	38	clearly	clearly	ADV
ejpam-5578	165	39	,	,	PUNCT
ejpam-5578	165	40	we	we	PRON
ejpam-5578	165	41	have	have	VERB
ejpam-5578	165	42	wq	wq	NOUN
ejpam-5578	165	43	⊆	⊆	NUM
ejpam-5578	165	44	wq	wq	NOUN
ejpam-5578	165	45	.	.	PUNCT
ejpam-5578	166	1	to	to	PART
ejpam-5578	166	2	complete	complete	VERB
ejpam-5578	166	3	the	the	DET
ejpam-5578	166	4	proof	proof	NOUN
ejpam-5578	166	5	,	,	PUNCT
ejpam-5578	166	6	we	we	PRON
ejpam-5578	166	7	need	need	VERB
ejpam-5578	166	8	to	to	PART
ejpam-5578	166	9	show	show	VERB
ejpam-5578	166	10	that	that	SCONJ
ejpam-5578	166	11	wq	wq	PROPN
ejpam-5578	166	12	⊆	⊆	NUM
ejpam-5578	166	13	uq	uq	NOUN
ejpam-5578	166	14	.	.	PUNCT
ejpam-5578	167	1	since	since	SCONJ
ejpam-5578	167	2	wq	wq	PROPN
ejpam-5578	167	3	∩	∩	PROPN
ejpam-5578	167	4	vo	vo	X
ejpam-5578	167	5	=	=	NOUN
ejpam-5578	167	6	∅	∅	NOUN
ejpam-5578	167	7	,	,	PUNCT
ejpam-5578	167	8	we	we	PRON
ejpam-5578	167	9	can	can	AUX
ejpam-5578	167	10	conclude	conclude	VERB
ejpam-5578	167	11	that	that	PRON
ejpam-5578	167	12	wq	wq	PROPN
ejpam-5578	167	13	⊆	⊆	NUM
ejpam-5578	167	14	vco	vco	PROPN
ejpam-5578	167	15	.	.	PUNCT
ejpam-5578	168	1	taking	take	VERB
ejpam-5578	168	2	closures	closure	NOUN
ejpam-5578	168	3	,	,	PUNCT
ejpam-5578	168	4	we	we	PRON
ejpam-5578	168	5	obtain	obtain	VERB
ejpam-5578	168	6	:	:	PUNCT
ejpam-5578	168	7	wq	wq	PROPN
ejpam-5578	168	8	⊆	⊆	NUM
ejpam-5578	168	9	vco	vco	PROPN
ejpam-5578	168	10	=	=	PROPN
ejpam-5578	168	11	vco	vco	PROPN
ejpam-5578	168	12	.	.	PUNCT
ejpam-5578	169	1	j.	j.	PROPN
ejpam-5578	169	2	oudetallah	oudetallah	PROPN
ejpam-5578	169	3	et	et	PROPN
ejpam-5578	169	4	al	al	PROPN
ejpam-5578	169	5	.	.	PUNCT
ejpam-5578	169	6	/	/	SYM
ejpam-5578	169	7	eur	eur	PROPN
ejpam-5578	169	8	.	.	PUNCT
ejpam-5578	170	1	j.	j.	PROPN
ejpam-5578	170	2	pure	pure	PROPN
ejpam-5578	170	3	appl	appl	PROPN
ejpam-5578	170	4	.	.	PROPN
ejpam-5578	170	5	math	math	PROPN
ejpam-5578	170	6	,	,	PUNCT
ejpam-5578	170	7	18	18	NUM
ejpam-5578	170	8	(	(	PUNCT
ejpam-5578	170	9	2	2	NUM
ejpam-5578	170	10	)	)	PUNCT
ejpam-5578	170	11	(	(	PUNCT
ejpam-5578	170	12	2025	2025	NUM
ejpam-5578	170	13	)	)	PUNCT
ejpam-5578	170	14	,	,	PUNCT
ejpam-5578	170	15	5578	5578	NUM
ejpam-5578	170	16	9	9	NUM
ejpam-5578	170	17	of	of	ADP
ejpam-5578	170	18	19	19	NUM
ejpam-5578	170	19	but	but	CCONJ
ejpam-5578	170	20	since	since	SCONJ
ejpam-5578	170	21	oc	oc	PROPN
ejpam-5578	170	22	=	=	PUNCT
ejpam-5578	170	23	vco	vco	PROPN
ejpam-5578	170	24	and	and	CCONJ
ejpam-5578	170	25	o	o	PROPN
ejpam-5578	170	26	⊆	⊆	NUM
ejpam-5578	170	27	vo	vo	NOUN
ejpam-5578	170	28	,	,	PUNCT
ejpam-5578	170	29	we	we	PRON
ejpam-5578	170	30	have	have	AUX
ejpam-5578	170	31	:	:	PUNCT
ejpam-5578	170	32	oc	oc	VERB
ejpam-5578	170	33	⊆	⊆	NUM
ejpam-5578	170	34	vco	vco	PROPN
ejpam-5578	170	35	.	.	PUNCT
ejpam-5578	171	1	therefore	therefore	ADV
ejpam-5578	171	2	,	,	PUNCT
ejpam-5578	171	3	vco	vco	PROPN
ejpam-5578	171	4	⊆	⊆	NUM
ejpam-5578	171	5	uq	uq	PROPN
ejpam-5578	171	6	,	,	PUNCT
ejpam-5578	171	7	which	which	PRON
ejpam-5578	171	8	implies	imply	VERB
ejpam-5578	171	9	:	:	PUNCT
ejpam-5578	171	10	wq	wq	NUM
ejpam-5578	171	11	⊆	⊆	NUM
ejpam-5578	171	12	uq	uq	NOUN
ejpam-5578	171	13	.	.	PUNCT
ejpam-5578	172	1	thus	thus	ADV
ejpam-5578	172	2	,	,	PUNCT
ejpam-5578	172	3	the	the	DET
ejpam-5578	172	4	condition	condition	NOUN
ejpam-5578	172	5	holds	hold	VERB
ejpam-5578	172	6	.	.	PUNCT
ejpam-5578	173	1	(	(	PUNCT
ejpam-5578	173	2	⇐	⇐	NOUN
ejpam-5578	173	3	)	)	PUNCT
ejpam-5578	173	4	suppose	suppose	VERB
ejpam-5578	173	5	q	q	X
ejpam-5578	173	6	/∈	/∈	PUNCT
ejpam-5578	174	1	o	o	NOUN
ejpam-5578	175	1	and	and	CCONJ
ejpam-5578	175	2	o	o	PROPN
ejpam-5578	175	3	is	be	AUX
ejpam-5578	175	4	a	a	DET
ejpam-5578	175	5	ϱi	ϱi	ADV
ejpam-5578	175	6	-	-	PUNCT
ejpam-5578	175	7	closed	close	VERB
ejpam-5578	175	8	set	set	NOUN
ejpam-5578	175	9	.	.	PUNCT
ejpam-5578	176	1	then	then	ADV
ejpam-5578	176	2	,	,	PUNCT
ejpam-5578	176	3	q	q	PROPN
ejpam-5578	176	4	∈	∈	PROPN
ejpam-5578	176	5	oc	oc	PROPN
ejpam-5578	176	6	,	,	PUNCT
ejpam-5578	176	7	which	which	PRON
ejpam-5578	176	8	is	be	AUX
ejpam-5578	176	9	a	a	DET
ejpam-5578	176	10	ϱi	ϱi	ADJ
ejpam-5578	176	11	-	-	PUNCT
ejpam-5578	176	12	open	open	ADJ
ejpam-5578	176	13	set	set	NOUN
ejpam-5578	176	14	.	.	PUNCT
ejpam-5578	177	1	by	by	ADP
ejpam-5578	177	2	the	the	DET
ejpam-5578	177	3	given	give	VERB
ejpam-5578	177	4	condition	condition	NOUN
ejpam-5578	177	5	,	,	PUNCT
ejpam-5578	177	6	there	there	PRON
ejpam-5578	177	7	exists	exist	VERB
ejpam-5578	177	8	a	a	DET
ejpam-5578	177	9	ϱi	ϱi	ADV
ejpam-5578	177	10	-	-	PUNCT
ejpam-5578	177	11	open	open	ADJ
ejpam-5578	177	12	set	set	ADJ
ejpam-5578	177	13	wq	wq	NOUN
ejpam-5578	177	14	such	such	ADJ
ejpam-5578	177	15	that	that	PRON
ejpam-5578	177	16	:	:	PUNCT
ejpam-5578	178	1	q	q	X
ejpam-5578	178	2	∈	∈	NOUN
ejpam-5578	178	3	wq	wq	NOUN
ejpam-5578	179	1	⊆	⊆	NUM
ejpam-5578	179	2	wq	wq	NOUN
ejpam-5578	179	3	⊆	⊆	NUM
ejpam-5578	179	4	oc	oc	NOUN
ejpam-5578	179	5	.	.	PUNCT
ejpam-5578	180	1	now	now	ADV
ejpam-5578	180	2	,	,	PUNCT
ejpam-5578	180	3	we	we	PRON
ejpam-5578	180	4	have	have	VERB
ejpam-5578	180	5	two	two	NUM
ejpam-5578	180	6	conditions	condition	NOUN
ejpam-5578	180	7	:	:	PUNCT
ejpam-5578	181	1	q	q	PUNCT
ejpam-5578	181	2	∈	∈	PROPN
ejpam-5578	181	3	wq	wq	NOUN
ejpam-5578	181	4	and	and	CCONJ
ejpam-5578	181	5	o	o	PROPN
ejpam-5578	181	6	⊆	⊆	NUM
ejpam-5578	181	7	wq	wq	PROPN
ejpam-5578	181	8	c.	c.	NOUN
ejpam-5578	181	9	since	since	SCONJ
ejpam-5578	181	10	both	both	DET
ejpam-5578	181	11	wq	wq	PROPN
ejpam-5578	181	12	and	and	CCONJ
ejpam-5578	181	13	wq	wq	PROPN
ejpam-5578	181	14	c	c	NOUN
ejpam-5578	181	15	are	be	AUX
ejpam-5578	181	16	ϱi	ϱi	ADJ
ejpam-5578	181	17	-	-	PUNCT
ejpam-5578	181	18	open	open	ADJ
ejpam-5578	181	19	sets	set	NOUN
ejpam-5578	181	20	,	,	PUNCT
ejpam-5578	181	21	it	it	PRON
ejpam-5578	181	22	is	be	AUX
ejpam-5578	181	23	sufficient	sufficient	ADJ
ejpam-5578	181	24	to	to	PART
ejpam-5578	181	25	show	show	VERB
ejpam-5578	181	26	:	:	PUNCT
ejpam-5578	181	27	wq	wq	PROPN
ejpam-5578	181	28	∩	∩	NOUN
ejpam-5578	181	29	wq	wq	ADP
ejpam-5578	181	30	c	c	X
ejpam-5578	181	31	=	=	PUNCT
ejpam-5578	181	32	∅.	∅.	ADV
ejpam-5578	181	33	suppose	suppose	VERB
ejpam-5578	181	34	not	not	PART
ejpam-5578	181	35	.	.	PUNCT
ejpam-5578	182	1	then	then	ADV
ejpam-5578	182	2	there	there	PRON
ejpam-5578	182	3	exists	exist	VERB
ejpam-5578	182	4	some	some	DET
ejpam-5578	182	5	z	z	NOUN
ejpam-5578	182	6	∈	∈	PROPN
ejpam-5578	182	7	wq	wq	NOUN
ejpam-5578	182	8	∩	∩	X
ejpam-5578	182	9	wq	wq	PROPN
ejpam-5578	182	10	c	c	X
ejpam-5578	182	11	,	,	PUNCT
ejpam-5578	182	12	which	which	PRON
ejpam-5578	182	13	implies	imply	VERB
ejpam-5578	182	14	:	:	PUNCT
ejpam-5578	182	15	z	z	PROPN
ejpam-5578	182	16	∈	∈	PROPN
ejpam-5578	182	17	wq	wq	NOUN
ejpam-5578	182	18	and	and	CCONJ
ejpam-5578	182	19	z	z	NOUN
ejpam-5578	182	20	∈	∈	PROPN
ejpam-5578	182	21	wq	wq	PROPN
ejpam-5578	182	22	c.	c.	PROPN
ejpam-5578	182	23	since	since	SCONJ
ejpam-5578	182	24	z	z	PROPN
ejpam-5578	182	25	∈	∈	PROPN
ejpam-5578	182	26	wq	wq	NOUN
ejpam-5578	183	1	c	c	X
ejpam-5578	183	2	,	,	PUNCT
ejpam-5578	183	3	it	it	PRON
ejpam-5578	183	4	follows	follow	VERB
ejpam-5578	183	5	that	that	PRON
ejpam-5578	183	6	z	z	NOUN
ejpam-5578	183	7	/∈	/∈	PUNCT
ejpam-5578	183	8	wq	wq	PROPN
ejpam-5578	183	9	,	,	PUNCT
ejpam-5578	183	10	contradicting	contradict	VERB
ejpam-5578	183	11	z	z	PROPN
ejpam-5578	183	12	∈	∈	PROPN
ejpam-5578	183	13	wq	wq	NOUN
ejpam-5578	183	14	.	.	PUNCT
ejpam-5578	184	1	thus	thus	ADV
ejpam-5578	184	2	,	,	PUNCT
ejpam-5578	184	3	our	our	PRON
ejpam-5578	184	4	assumption	assumption	NOUN
ejpam-5578	184	5	is	be	AUX
ejpam-5578	184	6	false	false	ADJ
ejpam-5578	184	7	,	,	PUNCT
ejpam-5578	184	8	and	and	CCONJ
ejpam-5578	184	9	we	we	PRON
ejpam-5578	184	10	conclude	conclude	VERB
ejpam-5578	184	11	:	:	PUNCT
ejpam-5578	184	12	wq	wq	PROPN
ejpam-5578	184	13	∩	∩	NOUN
ejpam-5578	184	14	wq	wq	NOUN
ejpam-5578	184	15	c	c	X
ejpam-5578	184	16	=	=	PUNCT
ejpam-5578	184	17	∅.	∅.	NOUN
ejpam-5578	184	18	by	by	ADP
ejpam-5578	184	19	these	these	DET
ejpam-5578	184	20	conditions	condition	NOUN
ejpam-5578	184	21	,	,	PUNCT
ejpam-5578	184	22	we	we	PRON
ejpam-5578	184	23	establish	establish	VERB
ejpam-5578	184	24	that	that	SCONJ
ejpam-5578	184	25	(	(	PUNCT
ejpam-5578	184	26	q	q	ADJ
ejpam-5578	184	27	,	,	PUNCT
ejpam-5578	184	28	ϱ1	ϱ1	NOUN
ejpam-5578	184	29	,	,	PUNCT
ejpam-5578	184	30	ϱ2	ϱ2	NOUN
ejpam-5578	184	31	,	,	PUNCT
ejpam-5578	184	32	ϱ3	ϱ3	PROPN
ejpam-5578	184	33	)	)	PUNCT
ejpam-5578	184	34	is	be	AUX
ejpam-5578	184	35	a	a	DET
ejpam-5578	184	36	tri	tri	ADJ
ejpam-5578	184	37	-	-	ADJ
ejpam-5578	184	38	regular	regular	ADJ
ejpam-5578	184	39	space	space	NOUN
ejpam-5578	184	40	.	.	PUNCT
ejpam-5578	185	1	definition	definition	NOUN
ejpam-5578	185	2	15	15	NUM
ejpam-5578	185	3	.	.	PUNCT
ejpam-5578	186	1	[	[	X
ejpam-5578	186	2	13	13	NUM
ejpam-5578	186	3	]	]	PUNCT
ejpam-5578	186	4	a	a	DET
ejpam-5578	186	5	topological	topological	ADJ
ejpam-5578	186	6	space	space	NOUN
ejpam-5578	186	7	(	(	PUNCT
ejpam-5578	186	8	q	q	NOUN
ejpam-5578	186	9	,	,	PUNCT
ejpam-5578	186	10	ϱ	ϱ	NOUN
ejpam-5578	186	11	)	)	PUNCT
ejpam-5578	186	12	is	be	AUX
ejpam-5578	186	13	called	call	VERB
ejpam-5578	186	14	a	a	DET
ejpam-5578	186	15	t3	t3	NOUN
ejpam-5578	186	16	-	-	PUNCT
ejpam-5578	186	17	space	space	NOUN
ejpam-5578	186	18	if	if	SCONJ
ejpam-5578	186	19	it	it	PRON
ejpam-5578	186	20	is	be	AUX
ejpam-5578	186	21	both	both	PRON
ejpam-5578	186	22	a	a	DET
ejpam-5578	186	23	t1	t1	NOUN
ejpam-5578	186	24	-	-	PUNCT
ejpam-5578	186	25	space	space	NOUN
ejpam-5578	186	26	and	and	CCONJ
ejpam-5578	186	27	a	a	DET
ejpam-5578	186	28	regular	regular	ADJ
ejpam-5578	186	29	space	space	NOUN
ejpam-5578	186	30	.	.	PUNCT
ejpam-5578	187	1	definition	definition	NOUN
ejpam-5578	187	2	16	16	NUM
ejpam-5578	187	3	.	.	PUNCT
ejpam-5578	188	1	[	[	X
ejpam-5578	188	2	13	13	NUM
ejpam-5578	188	3	]	]	PUNCT
ejpam-5578	188	4	a	a	DET
ejpam-5578	188	5	tri	tri	ADJ
ejpam-5578	188	6	-	-	ADJ
ejpam-5578	188	7	topological	topological	ADJ
ejpam-5578	188	8	space	space	NOUN
ejpam-5578	188	9	(	(	PUNCT
ejpam-5578	188	10	q	q	ADJ
ejpam-5578	188	11	,	,	PUNCT
ejpam-5578	188	12	ϱ1	ϱ1	NOUN
ejpam-5578	188	13	,	,	PUNCT
ejpam-5578	188	14	ϱ2	ϱ2	NOUN
ejpam-5578	188	15	,	,	PUNCT
ejpam-5578	188	16	ϱ3	ϱ3	PROPN
ejpam-5578	188	17	)	)	PUNCT
ejpam-5578	188	18	is	be	AUX
ejpam-5578	188	19	called	call	VERB
ejpam-5578	188	20	a	a	DET
ejpam-5578	188	21	tri	tri	ADJ
ejpam-5578	188	22	-	-	ADJ
ejpam-5578	188	23	t3	t3	ADJ
ejpam-5578	188	24	-	-	PUNCT
ejpam-5578	188	25	space	space	NOUN
ejpam-5578	188	26	if	if	SCONJ
ejpam-5578	188	27	it	it	PRON
ejpam-5578	188	28	is	be	AUX
ejpam-5578	188	29	both	both	PRON
ejpam-5578	188	30	a	a	DET
ejpam-5578	188	31	tri	tri	ADJ
ejpam-5578	188	32	-	-	ADJ
ejpam-5578	188	33	t1	t1	ADJ
ejpam-5578	188	34	-	-	PUNCT
ejpam-5578	188	35	space	space	NOUN
ejpam-5578	188	36	and	and	CCONJ
ejpam-5578	188	37	a	a	DET
ejpam-5578	188	38	tri	tri	ADJ
ejpam-5578	188	39	-	-	ADJ
ejpam-5578	188	40	regular	regular	ADJ
ejpam-5578	188	41	space	space	NOUN
ejpam-5578	188	42	.	.	PUNCT
ejpam-5578	189	1	definition	definition	NOUN
ejpam-5578	189	2	17	17	NUM
ejpam-5578	189	3	.	.	PUNCT
ejpam-5578	190	1	[	[	X
ejpam-5578	190	2	15	15	NUM
ejpam-5578	190	3	]	]	X
ejpam-5578	190	4	a	a	DET
ejpam-5578	190	5	tri	tri	ADJ
ejpam-5578	190	6	-	-	ADJ
ejpam-5578	190	7	topological	topological	ADJ
ejpam-5578	190	8	space	space	NOUN
ejpam-5578	190	9	(	(	PUNCT
ejpam-5578	190	10	q	q	ADJ
ejpam-5578	190	11	,	,	PUNCT
ejpam-5578	190	12	ϱ1	ϱ1	NOUN
ejpam-5578	190	13	,	,	PUNCT
ejpam-5578	190	14	ϱ2	ϱ2	NOUN
ejpam-5578	190	15	,	,	PUNCT
ejpam-5578	190	16	ϱ3	ϱ3	PROPN
ejpam-5578	190	17	)	)	PUNCT
ejpam-5578	190	18	is	be	AUX
ejpam-5578	190	19	called	call	VERB
ejpam-5578	190	20	a	a	DET
ejpam-5578	190	21	tri	tri	ADJ
ejpam-5578	190	22	-	-	ADJ
ejpam-5578	190	23	normal	normal	ADJ
ejpam-5578	190	24	space	space	NOUN
ejpam-5578	190	25	if	if	SCONJ
ejpam-5578	190	26	for	for	ADP
ejpam-5578	190	27	every	every	DET
ejpam-5578	190	28	two	two	NUM
ejpam-5578	190	29	disjoint	disjoint	ADJ
ejpam-5578	190	30	ϱi	ϱi	ADV
ejpam-5578	190	31	-	-	PUNCT
ejpam-5578	190	32	closed	close	VERB
ejpam-5578	190	33	sets	set	NOUN
ejpam-5578	190	34	o	o	NOUN
ejpam-5578	190	35	and	and	CCONJ
ejpam-5578	190	36	b	b	NOUN
ejpam-5578	190	37	,	,	PUNCT
ejpam-5578	190	38	there	there	PRON
ejpam-5578	190	39	exist	exist	VERB
ejpam-5578	190	40	ϱi	ϱi	ADJ
ejpam-5578	190	41	-	-	PUNCT
ejpam-5578	190	42	open	open	ADJ
ejpam-5578	190	43	sets	set	NOUN
ejpam-5578	190	44	uo	uo	NOUN
ejpam-5578	190	45	and	and	CCONJ
ejpam-5578	190	46	vb	vb	NOUN
ejpam-5578	190	47	such	such	ADJ
ejpam-5578	190	48	that	that	PRON
ejpam-5578	190	49	:	:	PUNCT
ejpam-5578	190	50	o	o	NOUN
ejpam-5578	190	51	⊆	⊆	NUM
ejpam-5578	190	52	uo	uo	NOUN
ejpam-5578	190	53	,	,	PUNCT
ejpam-5578	190	54	b	b	PROPN
ejpam-5578	190	55	⊆	⊆	NUM
ejpam-5578	190	56	vb	vb	NOUN
ejpam-5578	190	57	,	,	PUNCT
ejpam-5578	190	58	and	and	CCONJ
ejpam-5578	190	59	uo	uo	NOUN
ejpam-5578	190	60	∩	∩	ADJ
ejpam-5578	190	61	vb	vb	NOUN
ejpam-5578	190	62	=	=	PUNCT
ejpam-5578	190	63	∅.	∅.	PRON
ejpam-5578	190	64	definition	definition	NOUN
ejpam-5578	190	65	18	18	NUM
ejpam-5578	190	66	.	.	PUNCT
ejpam-5578	191	1	[	[	X
ejpam-5578	191	2	16	16	NUM
ejpam-5578	191	3	]	]	PUNCT
ejpam-5578	191	4	a	a	DET
ejpam-5578	191	5	tri	tri	ADJ
ejpam-5578	191	6	-	-	ADJ
ejpam-5578	191	7	topological	topological	ADJ
ejpam-5578	191	8	space	space	NOUN
ejpam-5578	191	9	(	(	PUNCT
ejpam-5578	191	10	q	q	ADJ
ejpam-5578	191	11	,	,	PUNCT
ejpam-5578	191	12	ϱ1	ϱ1	NOUN
ejpam-5578	191	13	,	,	PUNCT
ejpam-5578	191	14	ϱ2	ϱ2	NOUN
ejpam-5578	191	15	,	,	PUNCT
ejpam-5578	191	16	ϱ3	ϱ3	PROPN
ejpam-5578	191	17	)	)	PUNCT
ejpam-5578	191	18	is	be	AUX
ejpam-5578	191	19	called	call	VERB
ejpam-5578	191	20	a	a	DET
ejpam-5578	191	21	tri	tri	PROPN
ejpam-5578	191	22	-	-	ADJ
ejpam-5578	191	23	t4	t4	ADJ
ejpam-5578	191	24	-	-	PUNCT
ejpam-5578	191	25	space	space	NOUN
ejpam-5578	191	26	if	if	SCONJ
ejpam-5578	191	27	it	it	PRON
ejpam-5578	191	28	is	be	AUX
ejpam-5578	191	29	both	both	PRON
ejpam-5578	191	30	a	a	DET
ejpam-5578	191	31	tri	tri	ADJ
ejpam-5578	191	32	-	-	ADJ
ejpam-5578	191	33	t1	t1	ADJ
ejpam-5578	191	34	-	-	PUNCT
ejpam-5578	191	35	space	space	NOUN
ejpam-5578	191	36	and	and	CCONJ
ejpam-5578	191	37	a	a	DET
ejpam-5578	191	38	tri	tri	ADJ
ejpam-5578	191	39	-	-	ADJ
ejpam-5578	191	40	normal	normal	ADJ
ejpam-5578	191	41	space	space	NOUN
ejpam-5578	191	42	.	.	PUNCT
ejpam-5578	192	1	theorem	theorem	NOUN
ejpam-5578	192	2	3	3	NUM
ejpam-5578	192	3	.	.	PUNCT
ejpam-5578	193	1	[	[	X
ejpam-5578	193	2	8	8	NUM
ejpam-5578	193	3	]	]	X
ejpam-5578	193	4	if	if	SCONJ
ejpam-5578	193	5	(	(	PUNCT
ejpam-5578	193	6	q	q	ADJ
ejpam-5578	193	7	,	,	PUNCT
ejpam-5578	193	8	ϱ1	ϱ1	NOUN
ejpam-5578	193	9	,	,	PUNCT
ejpam-5578	193	10	ϱ2	ϱ2	NOUN
ejpam-5578	193	11	,	,	PUNCT
ejpam-5578	193	12	ϱ3	ϱ3	PROPN
ejpam-5578	193	13	)	)	PUNCT
ejpam-5578	193	14	is	be	AUX
ejpam-5578	193	15	a	a	DET
ejpam-5578	193	16	tri	tri	ADJ
ejpam-5578	193	17	-	-	ADJ
ejpam-5578	193	18	tk	tk	NOUN
ejpam-5578	193	19	-	-	NOUN
ejpam-5578	193	20	space	space	NOUN
ejpam-5578	193	21	,	,	PUNCT
ejpam-5578	193	22	then	then	ADV
ejpam-5578	193	23	it	it	PRON
ejpam-5578	193	24	is	be	AUX
ejpam-5578	193	25	also	also	ADV
ejpam-5578	193	26	a	a	DET
ejpam-5578	193	27	tri	tri	ADJ
ejpam-5578	193	28	-	-	ADJ
ejpam-5578	193	29	tk−1	tk−1	ADJ
ejpam-5578	193	30	-	-	PUNCT
ejpam-5578	193	31	space	space	NOUN
ejpam-5578	193	32	.	.	PUNCT
ejpam-5578	194	1	theorem	theorem	NOUN
ejpam-5578	194	2	4	4	NUM
ejpam-5578	194	3	.	.	PUNCT
ejpam-5578	195	1	if	if	SCONJ
ejpam-5578	195	2	a	a	DET
ejpam-5578	195	3	space	space	NOUN
ejpam-5578	195	4	(	(	PUNCT
ejpam-5578	195	5	q	q	ADJ
ejpam-5578	195	6	,	,	PUNCT
ejpam-5578	195	7	ϱ1	ϱ1	NOUN
ejpam-5578	195	8	,	,	PUNCT
ejpam-5578	195	9	ϱ2	ϱ2	NOUN
ejpam-5578	195	10	,	,	PUNCT
ejpam-5578	195	11	ϱ3	ϱ3	PROPN
ejpam-5578	195	12	)	)	PUNCT
ejpam-5578	195	13	is	be	AUX
ejpam-5578	195	14	a	a	DET
ejpam-5578	195	15	tri	tri	ADJ
ejpam-5578	195	16	-	-	ADJ
ejpam-5578	195	17	t4	t4	ADJ
ejpam-5578	195	18	-	-	PUNCT
ejpam-5578	195	19	space	space	NOUN
ejpam-5578	195	20	,	,	PUNCT
ejpam-5578	195	21	then	then	ADV
ejpam-5578	195	22	it	it	PRON
ejpam-5578	195	23	is	be	AUX
ejpam-5578	195	24	also	also	ADV
ejpam-5578	195	25	a	a	DET
ejpam-5578	195	26	tri	tri	ADJ
ejpam-5578	195	27	-	-	ADJ
ejpam-5578	195	28	t3	t3	ADJ
ejpam-5578	195	29	-	-	PUNCT
ejpam-5578	195	30	space	space	NOUN
ejpam-5578	195	31	.	.	PUNCT
ejpam-5578	196	1	j.	j.	PROPN
ejpam-5578	196	2	oudetallah	oudetallah	PROPN
ejpam-5578	196	3	et	et	PROPN
ejpam-5578	196	4	al	al	PROPN
ejpam-5578	196	5	.	.	PUNCT
ejpam-5578	196	6	/	/	SYM
ejpam-5578	196	7	eur	eur	PROPN
ejpam-5578	196	8	.	.	PUNCT
ejpam-5578	197	1	j.	j.	PROPN
ejpam-5578	197	2	pure	pure	PROPN
ejpam-5578	197	3	appl	appl	PROPN
ejpam-5578	197	4	.	.	PROPN
ejpam-5578	197	5	math	math	PROPN
ejpam-5578	197	6	,	,	PUNCT
ejpam-5578	197	7	18	18	NUM
ejpam-5578	197	8	(	(	PUNCT
ejpam-5578	197	9	2	2	NUM
ejpam-5578	197	10	)	)	PUNCT
ejpam-5578	197	11	(	(	PUNCT
ejpam-5578	197	12	2025	2025	NUM
ejpam-5578	197	13	)	)	PUNCT
ejpam-5578	197	14	,	,	PUNCT
ejpam-5578	197	15	5578	5578	NUM
ejpam-5578	197	16	10	10	NUM
ejpam-5578	197	17	of	of	ADP
ejpam-5578	197	18	19	19	NUM
ejpam-5578	197	19	proof	proof	NOUN
ejpam-5578	197	20	.	.	PUNCT
ejpam-5578	198	1	let	let	VERB
ejpam-5578	198	2	(	(	PUNCT
ejpam-5578	198	3	q	q	ADJ
ejpam-5578	198	4	,	,	PUNCT
ejpam-5578	198	5	ϱ1	ϱ1	NOUN
ejpam-5578	198	6	,	,	PUNCT
ejpam-5578	198	7	ϱ2	ϱ2	NOUN
ejpam-5578	198	8	,	,	PUNCT
ejpam-5578	198	9	ϱ3	ϱ3	PROPN
ejpam-5578	198	10	)	)	PUNCT
ejpam-5578	198	11	be	be	AUX
ejpam-5578	198	12	a	a	DET
ejpam-5578	198	13	tri	tri	ADJ
ejpam-5578	198	14	-	-	ADJ
ejpam-5578	198	15	t4	t4	ADJ
ejpam-5578	198	16	-	-	PUNCT
ejpam-5578	198	17	space	space	NOUN
ejpam-5578	198	18	.	.	PUNCT
ejpam-5578	199	1	by	by	ADP
ejpam-5578	199	2	definition	definition	NOUN
ejpam-5578	199	3	,	,	PUNCT
ejpam-5578	199	4	a	a	DET
ejpam-5578	199	5	tri	tri	PROPN
ejpam-5578	199	6	-	-	ADJ
ejpam-5578	199	7	t4	t4	ADJ
ejpam-5578	199	8	-	-	PUNCT
ejpam-5578	199	9	space	space	NOUN
ejpam-5578	199	10	is	be	AUX
ejpam-5578	199	11	both	both	PRON
ejpam-5578	199	12	a	a	DET
ejpam-5578	199	13	tri	tri	ADJ
ejpam-5578	199	14	-	-	ADJ
ejpam-5578	199	15	t1	t1	ADJ
ejpam-5578	199	16	-	-	PUNCT
ejpam-5578	199	17	space	space	NOUN
ejpam-5578	199	18	and	and	CCONJ
ejpam-5578	199	19	a	a	DET
ejpam-5578	199	20	tri	tri	ADJ
ejpam-5578	199	21	-	-	ADJ
ejpam-5578	199	22	normal	normal	ADJ
ejpam-5578	199	23	space	space	NOUN
ejpam-5578	199	24	.	.	PUNCT
ejpam-5578	200	1	that	that	PRON
ejpam-5578	200	2	is	be	AUX
ejpam-5578	200	3	,	,	PUNCT
ejpam-5578	200	4	for	for	ADP
ejpam-5578	200	5	all	all	DET
ejpam-5578	200	6	two	two	NUM
ejpam-5578	200	7	disjoint	disjoint	ADJ
ejpam-5578	200	8	ϱi	ϱi	ADV
ejpam-5578	200	9	-	-	PUNCT
ejpam-5578	200	10	closed	close	VERB
ejpam-5578	200	11	sets	set	NOUN
ejpam-5578	200	12	o	o	NOUN
ejpam-5578	200	13	and	and	CCONJ
ejpam-5578	200	14	b	b	NOUN
ejpam-5578	200	15	,	,	PUNCT
ejpam-5578	200	16	there	there	PRON
ejpam-5578	200	17	exist	exist	VERB
ejpam-5578	200	18	ϱi	ϱi	ADJ
ejpam-5578	200	19	-	-	PUNCT
ejpam-5578	200	20	open	open	ADJ
ejpam-5578	200	21	sets	set	NOUN
ejpam-5578	200	22	uo	uo	NOUN
ejpam-5578	200	23	and	and	CCONJ
ejpam-5578	200	24	vb	vb	NOUN
ejpam-5578	200	25	such	such	ADJ
ejpam-5578	200	26	that	that	PRON
ejpam-5578	200	27	:	:	PUNCT
ejpam-5578	200	28	o	o	NOUN
ejpam-5578	200	29	⊆	⊆	NUM
ejpam-5578	200	30	uo	uo	NOUN
ejpam-5578	200	31	,	,	PUNCT
ejpam-5578	200	32	b	b	PROPN
ejpam-5578	200	33	⊆	⊆	NUM
ejpam-5578	200	34	vb	vb	NOUN
ejpam-5578	200	35	,	,	PUNCT
ejpam-5578	200	36	and	and	CCONJ
ejpam-5578	200	37	uo	uo	NOUN
ejpam-5578	200	38	∩	∩	ADJ
ejpam-5578	200	39	vb	vb	NOUN
ejpam-5578	200	40	=	=	PUNCT
ejpam-5578	200	41	∅.	∅.	X
ejpam-5578	200	42	(	(	PUNCT
ejpam-5578	200	43	i	i	NOUN
ejpam-5578	200	44	)	)	PUNCT
ejpam-5578	200	45	now	now	ADV
ejpam-5578	200	46	,	,	PUNCT
ejpam-5578	200	47	let	let	VERB
ejpam-5578	200	48	b	b	PROPN
ejpam-5578	200	49	∈	∈	PROPN
ejpam-5578	200	50	b.	b.	PROPN
ejpam-5578	201	1	then	then	ADV
ejpam-5578	201	2	,	,	PUNCT
ejpam-5578	201	3	from	from	ADP
ejpam-5578	201	4	(	(	PUNCT
ejpam-5578	201	5	i	i	NOUN
ejpam-5578	201	6	)	)	PUNCT
ejpam-5578	201	7	,	,	PUNCT
ejpam-5578	201	8	we	we	PRON
ejpam-5578	201	9	have	have	VERB
ejpam-5578	201	10	b	b	PROPN
ejpam-5578	201	11	∈	∈	PROPN
ejpam-5578	201	12	vb	vb	NOUN
ejpam-5578	201	13	.	.	PUNCT
ejpam-5578	202	1	since	since	SCONJ
ejpam-5578	202	2	o	o	PROPN
ejpam-5578	202	3	∩	∩	PROPN
ejpam-5578	202	4	b	b	NOUN
ejpam-5578	202	5	=	=	SYM
ejpam-5578	202	6	∅	∅	NOUN
ejpam-5578	202	7	,	,	PUNCT
ejpam-5578	202	8	it	it	PRON
ejpam-5578	202	9	follows	follow	VERB
ejpam-5578	202	10	that	that	PRON
ejpam-5578	202	11	b	b	X
ejpam-5578	202	12	/∈	/∈	INTJ
ejpam-5578	203	1	o.	o.	NOUN
ejpam-5578	203	2	(	(	PUNCT
ejpam-5578	203	3	ii	ii	PROPN
ejpam-5578	203	4	)	)	PUNCT
ejpam-5578	203	5	from	from	ADP
ejpam-5578	203	6	(	(	PUNCT
ejpam-5578	203	7	i	i	NOUN
ejpam-5578	203	8	)	)	PUNCT
ejpam-5578	203	9	and	and	CCONJ
ejpam-5578	203	10	(	(	PUNCT
ejpam-5578	203	11	ii	ii	NOUN
ejpam-5578	203	12	)	)	PUNCT
ejpam-5578	203	13	,	,	PUNCT
ejpam-5578	203	14	we	we	PRON
ejpam-5578	203	15	conclude	conclude	VERB
ejpam-5578	203	16	that	that	PRON
ejpam-5578	203	17	(	(	PUNCT
ejpam-5578	203	18	q	q	ADJ
ejpam-5578	203	19	,	,	PUNCT
ejpam-5578	203	20	ϱ1	ϱ1	NOUN
ejpam-5578	203	21	,	,	PUNCT
ejpam-5578	203	22	ϱ2	ϱ2	NOUN
ejpam-5578	203	23	,	,	PUNCT
ejpam-5578	203	24	ϱ3	ϱ3	PROPN
ejpam-5578	203	25	)	)	PUNCT
ejpam-5578	203	26	is	be	AUX
ejpam-5578	203	27	a	a	DET
ejpam-5578	203	28	tri	tri	ADJ
ejpam-5578	203	29	-	-	ADJ
ejpam-5578	203	30	regular	regular	ADJ
ejpam-5578	203	31	space	space	NOUN
ejpam-5578	203	32	.	.	PUNCT
ejpam-5578	204	1	since	since	SCONJ
ejpam-5578	204	2	a	a	DET
ejpam-5578	204	3	tri	tri	PROPN
ejpam-5578	204	4	-	-	ADJ
ejpam-5578	204	5	t4	t4	ADJ
ejpam-5578	204	6	-	-	PUNCT
ejpam-5578	204	7	space	space	NOUN
ejpam-5578	204	8	is	be	AUX
ejpam-5578	204	9	also	also	ADV
ejpam-5578	204	10	a	a	DET
ejpam-5578	204	11	tri	tri	ADJ
ejpam-5578	204	12	-	-	ADJ
ejpam-5578	204	13	t1	t1	ADJ
ejpam-5578	204	14	-	-	PUNCT
ejpam-5578	204	15	space	space	NOUN
ejpam-5578	204	16	,	,	PUNCT
ejpam-5578	204	17	and	and	CCONJ
ejpam-5578	204	18	we	we	PRON
ejpam-5578	204	19	have	have	AUX
ejpam-5578	204	20	shown	show	VERB
ejpam-5578	204	21	it	it	PRON
ejpam-5578	204	22	is	be	AUX
ejpam-5578	204	23	tri	tri	ADJ
ejpam-5578	204	24	-	-	ADJ
ejpam-5578	204	25	regular	regular	ADJ
ejpam-5578	204	26	,	,	PUNCT
ejpam-5578	204	27	we	we	PRON
ejpam-5578	204	28	conclude	conclude	VERB
ejpam-5578	204	29	that	that	PRON
ejpam-5578	204	30	(	(	PUNCT
ejpam-5578	204	31	q	q	ADJ
ejpam-5578	204	32	,	,	PUNCT
ejpam-5578	204	33	ϱ1	ϱ1	NOUN
ejpam-5578	204	34	,	,	PUNCT
ejpam-5578	204	35	ϱ2	ϱ2	NOUN
ejpam-5578	204	36	,	,	PUNCT
ejpam-5578	204	37	ϱ3	ϱ3	PROPN
ejpam-5578	204	38	)	)	PUNCT
ejpam-5578	204	39	is	be	AUX
ejpam-5578	204	40	a	a	DET
ejpam-5578	204	41	tri	tri	ADJ
ejpam-5578	204	42	-	-	ADJ
ejpam-5578	204	43	t3	t3	ADJ
ejpam-5578	204	44	-	-	PUNCT
ejpam-5578	204	45	space	space	NOUN
ejpam-5578	204	46	.	.	PUNCT
ejpam-5578	205	1	definition	definition	NOUN
ejpam-5578	205	2	19	19	NUM
ejpam-5578	205	3	.	.	PUNCT
ejpam-5578	206	1	[	[	X
ejpam-5578	206	2	13	13	NUM
ejpam-5578	206	3	]	]	X
ejpam-5578	206	4	let	let	VERB
ejpam-5578	206	5	(	(	PUNCT
ejpam-5578	206	6	q	q	NOUN
ejpam-5578	206	7	,	,	PUNCT
ejpam-5578	206	8	ϱ	ϱ	NOUN
ejpam-5578	206	9	)	)	PUNCT
ejpam-5578	206	10	be	be	VERB
ejpam-5578	206	11	a	a	DET
ejpam-5578	206	12	topological	topological	ADJ
ejpam-5578	206	13	space	space	NOUN
ejpam-5578	206	14	,	,	PUNCT
ejpam-5578	206	15	and	and	CCONJ
ejpam-5578	206	16	let	let	VERB
ejpam-5578	206	17	w	w	NOUN
ejpam-5578	206	18	=	=	PRON
ejpam-5578	206	19	{	{	PUNCT
ejpam-5578	206	20	oα	oα	INTJ
ejpam-5578	206	21	|	|	ADV
ejpam-5578	206	22	α	α	PROPN
ejpam-5578	206	23	∈	∈	PROPN
ejpam-5578	206	24	λ	λ	PROPN
ejpam-5578	206	25	,	,	PUNCT
ejpam-5578	206	26	oα	oα	PRON
ejpam-5578	206	27	⊆	⊆	NUM
ejpam-5578	206	28	q	q	AUX
ejpam-5578	206	29	}	}	PUNCT
ejpam-5578	206	30	be	be	AUX
ejpam-5578	206	31	a	a	DET
ejpam-5578	206	32	collection	collection	NOUN
ejpam-5578	206	33	of	of	ADP
ejpam-5578	206	34	subsets	subset	NOUN
ejpam-5578	206	35	of	of	ADP
ejpam-5578	206	36	q.	q.	PROPN
ejpam-5578	206	37	then	then	ADV
ejpam-5578	206	38	:	:	PUNCT
ejpam-5578	206	39	(	(	PUNCT
ejpam-5578	206	40	i	i	NOUN
ejpam-5578	206	41	)	)	PUNCT
ejpam-5578	206	42	w	w	NOUN
ejpam-5578	206	43	is	be	AUX
ejpam-5578	206	44	called	call	VERB
ejpam-5578	206	45	a	a	DET
ejpam-5578	206	46	cover	cover	NOUN
ejpam-5578	206	47	of	of	ADP
ejpam-5578	206	48	q	q	NOUN
ejpam-5578	206	49	if	if	SCONJ
ejpam-5578	206	50	and	and	CCONJ
ejpam-5578	206	51	only	only	ADV
ejpam-5578	206	52	if:⋃	if:⋃	PROPN
ejpam-5578	206	53	α∈λ	α∈λ	NOUN
ejpam-5578	206	54	oα	oα	NOUN
ejpam-5578	206	55	=	=	PUNCT
ejpam-5578	206	56	q.	q.	PROPN
ejpam-5578	206	57	(	(	PUNCT
ejpam-5578	206	58	ii	ii	NOUN
ejpam-5578	206	59	)	)	PUNCT
ejpam-5578	206	60	w	w	NOUN
ejpam-5578	206	61	is	be	AUX
ejpam-5578	206	62	called	call	VERB
ejpam-5578	206	63	an	an	DET
ejpam-5578	206	64	open	open	ADJ
ejpam-5578	206	65	cover	cover	NOUN
ejpam-5578	206	66	of	of	ADP
ejpam-5578	206	67	q	q	NOUN
ejpam-5578	206	68	if	if	SCONJ
ejpam-5578	206	69	and	and	CCONJ
ejpam-5578	206	70	only	only	ADV
ejpam-5578	206	71	if	if	SCONJ
ejpam-5578	206	72	w	w	NOUN
ejpam-5578	206	73	is	be	AUX
ejpam-5578	206	74	a	a	DET
ejpam-5578	206	75	cover	cover	NOUN
ejpam-5578	206	76	and	and	CCONJ
ejpam-5578	206	77	each	each	DET
ejpam-5578	206	78	oα	oα	NOUN
ejpam-5578	206	79	is	be	AUX
ejpam-5578	206	80	an	an	DET
ejpam-5578	206	81	open	open	ADJ
ejpam-5578	206	82	set	set	NOUN
ejpam-5578	206	83	,	,	PUNCT
ejpam-5578	206	84	where	where	SCONJ
ejpam-5578	206	85	α	α	PROPN
ejpam-5578	206	86	∈	∈	PROPN
ejpam-5578	206	87	λ	λ	PROPN
ejpam-5578	206	88	.	.	PUNCT
ejpam-5578	206	89	(	(	PUNCT
ejpam-5578	206	90	iii	iii	X
ejpam-5578	206	91	)	)	PUNCT
ejpam-5578	206	92	w	w	NOUN
ejpam-5578	206	93	is	be	AUX
ejpam-5578	206	94	called	call	VERB
ejpam-5578	206	95	a	a	DET
ejpam-5578	206	96	closed	closed	ADJ
ejpam-5578	206	97	cover	cover	NOUN
ejpam-5578	206	98	of	of	ADP
ejpam-5578	206	99	q	q	NOUN
ejpam-5578	206	100	if	if	SCONJ
ejpam-5578	206	101	and	and	CCONJ
ejpam-5578	206	102	only	only	ADV
ejpam-5578	206	103	if	if	SCONJ
ejpam-5578	206	104	w	w	NOUN
ejpam-5578	206	105	is	be	AUX
ejpam-5578	206	106	a	a	DET
ejpam-5578	206	107	cover	cover	NOUN
ejpam-5578	206	108	and	and	CCONJ
ejpam-5578	206	109	each	each	DET
ejpam-5578	206	110	oα	oα	NOUN
ejpam-5578	206	111	is	be	AUX
ejpam-5578	206	112	a	a	DET
ejpam-5578	206	113	closed	closed	ADJ
ejpam-5578	206	114	set	set	NOUN
ejpam-5578	206	115	,	,	PUNCT
ejpam-5578	206	116	where	where	SCONJ
ejpam-5578	206	117	α	α	PROPN
ejpam-5578	206	118	∈	∈	PROPN
ejpam-5578	206	119	λ	λ	PROPN
ejpam-5578	206	120	.	.	PUNCT
ejpam-5578	206	121	(	(	PUNCT
ejpam-5578	206	122	iv	iv	X
ejpam-5578	206	123	)	)	PUNCT
ejpam-5578	206	124	a	a	DET
ejpam-5578	206	125	collection	collection	NOUN
ejpam-5578	206	126	c	c	NOUN
ejpam-5578	206	127	=	=	PRON
ejpam-5578	206	128	{	{	PUNCT
ejpam-5578	206	129	bγ	bγ	INTJ
ejpam-5578	206	130	|	|	ADV
ejpam-5578	206	131	γ	γ	X
ejpam-5578	206	132	∈	∈	PROPN
ejpam-5578	206	133	γ	γ	X
ejpam-5578	206	134	}	}	PUNCT
ejpam-5578	206	135	is	be	AUX
ejpam-5578	206	136	a	a	DET
ejpam-5578	206	137	subcover	subcover	NOUN
ejpam-5578	206	138	of	of	ADP
ejpam-5578	206	139	w	w	PROPN
ejpam-5578	206	140	if	if	SCONJ
ejpam-5578	207	1	and	and	CCONJ
ejpam-5578	207	2	only	only	ADV
ejpam-5578	207	3	if	if	SCONJ
ejpam-5578	207	4	c	c	PROPN
ejpam-5578	207	5	⊆	⊆	NUM
ejpam-5578	207	6	w	w	NOUN
ejpam-5578	207	7	and⋃	and⋃	PROPN
ejpam-5578	207	8	γ∈γbγ	γ∈γbγ	PROPN
ejpam-5578	207	9	=	=	PUNCT
ejpam-5578	207	10	q.	q.	PROPN
ejpam-5578	207	11	a	a	DET
ejpam-5578	207	12	space	space	NOUN
ejpam-5578	207	13	(	(	PUNCT
ejpam-5578	207	14	q	q	NOUN
ejpam-5578	207	15	,	,	PUNCT
ejpam-5578	207	16	ϱ	ϱ	NOUN
ejpam-5578	207	17	)	)	PUNCT
ejpam-5578	207	18	is	be	AUX
ejpam-5578	207	19	called	call	VERB
ejpam-5578	207	20	compact	compact	ADJ
ejpam-5578	207	21	if	if	SCONJ
ejpam-5578	207	22	every	every	DET
ejpam-5578	207	23	open	open	ADJ
ejpam-5578	207	24	cover	cover	NOUN
ejpam-5578	207	25	of	of	ADP
ejpam-5578	207	26	q	q	PROPN
ejpam-5578	207	27	has	have	VERB
ejpam-5578	207	28	a	a	DET
ejpam-5578	207	29	finite	finite	ADJ
ejpam-5578	207	30	subcover	subcover	PROPN
ejpam-5578	207	31	.	.	PUNCT
ejpam-5578	208	1	definition	definition	NOUN
ejpam-5578	208	2	20	20	NUM
ejpam-5578	208	3	.	.	PUNCT
ejpam-5578	209	1	[	[	X
ejpam-5578	209	2	6	6	NUM
ejpam-5578	209	3	]	]	PUNCT
ejpam-5578	209	4	let	let	VERB
ejpam-5578	209	5	(	(	PUNCT
ejpam-5578	209	6	q	q	ADJ
ejpam-5578	209	7	,	,	PUNCT
ejpam-5578	209	8	ϱ1	ϱ1	NOUN
ejpam-5578	209	9	,	,	PUNCT
ejpam-5578	209	10	ϱ2	ϱ2	NOUN
ejpam-5578	209	11	,	,	PUNCT
ejpam-5578	209	12	ϱ3	ϱ3	PROPN
ejpam-5578	209	13	)	)	PUNCT
ejpam-5578	209	14	be	be	AUX
ejpam-5578	209	15	a	a	DET
ejpam-5578	209	16	tri	tri	ADJ
ejpam-5578	209	17	-	-	ADJ
ejpam-5578	209	18	topological	topological	ADJ
ejpam-5578	209	19	space	space	NOUN
ejpam-5578	209	20	,	,	PUNCT
ejpam-5578	209	21	and	and	CCONJ
ejpam-5578	209	22	let	let	VERB
ejpam-5578	209	23	w	w	NOUN
ejpam-5578	209	24	=	=	PRON
ejpam-5578	209	25	{	{	PUNCT
ejpam-5578	209	26	oα	oα	INTJ
ejpam-5578	209	27	|	|	ADV
ejpam-5578	209	28	α	α	PROPN
ejpam-5578	209	29	∈	∈	PROPN
ejpam-5578	209	30	λ	λ	PROPN
ejpam-5578	209	31	,	,	PUNCT
ejpam-5578	209	32	oα	oα	PRON
ejpam-5578	209	33	⊆	⊆	NUM
ejpam-5578	209	34	q	q	AUX
ejpam-5578	209	35	}	}	PUNCT
ejpam-5578	209	36	be	be	AUX
ejpam-5578	209	37	a	a	DET
ejpam-5578	209	38	collection	collection	NOUN
ejpam-5578	209	39	of	of	ADP
ejpam-5578	209	40	subsets	subset	NOUN
ejpam-5578	209	41	of	of	ADP
ejpam-5578	209	42	q.	q.	PROPN
ejpam-5578	209	43	then	then	ADV
ejpam-5578	209	44	:	:	PUNCT
ejpam-5578	209	45	(	(	PUNCT
ejpam-5578	209	46	i	i	NOUN
ejpam-5578	209	47	)	)	PUNCT
ejpam-5578	209	48	w	w	NOUN
ejpam-5578	209	49	is	be	AUX
ejpam-5578	209	50	called	call	VERB
ejpam-5578	209	51	a	a	DET
ejpam-5578	209	52	tri	tri	NOUN
ejpam-5578	209	53	-	-	NOUN
ejpam-5578	209	54	cover	cover	NOUN
ejpam-5578	209	55	of	of	ADP
ejpam-5578	209	56	q	q	NOUN
ejpam-5578	209	57	if	if	SCONJ
ejpam-5578	210	1	and	and	CCONJ
ejpam-5578	210	2	only	only	ADV
ejpam-5578	210	3	if:⋃	if:⋃	PROPN
ejpam-5578	210	4	α∈λ	α∈λ	NOUN
ejpam-5578	210	5	oα	oα	NOUN
ejpam-5578	210	6	=	=	PUNCT
ejpam-5578	210	7	q.	q.	PROPN
ejpam-5578	210	8	(	(	PUNCT
ejpam-5578	210	9	ii	ii	NOUN
ejpam-5578	210	10	)	)	PUNCT
ejpam-5578	210	11	w	w	NOUN
ejpam-5578	210	12	is	be	AUX
ejpam-5578	210	13	called	call	VERB
ejpam-5578	210	14	a	a	DET
ejpam-5578	210	15	tri	tri	ADJ
ejpam-5578	210	16	-	-	ADJ
ejpam-5578	210	17	open	open	ADJ
ejpam-5578	210	18	cover	cover	NOUN
ejpam-5578	210	19	of	of	ADP
ejpam-5578	210	20	q	q	NOUN
ejpam-5578	210	21	if	if	SCONJ
ejpam-5578	210	22	and	and	CCONJ
ejpam-5578	210	23	only	only	ADV
ejpam-5578	210	24	if	if	SCONJ
ejpam-5578	210	25	w	w	NOUN
ejpam-5578	210	26	is	be	AUX
ejpam-5578	210	27	a	a	DET
ejpam-5578	210	28	tri	tri	ADJ
ejpam-5578	210	29	-	-	NOUN
ejpam-5578	210	30	cover	cover	NOUN
ejpam-5578	210	31	and	and	CCONJ
ejpam-5578	210	32	each	each	DET
ejpam-5578	210	33	oα	oα	NOUN
ejpam-5578	210	34	is	be	AUX
ejpam-5578	210	35	a	a	DET
ejpam-5578	210	36	ϱi	ϱi	ADJ
ejpam-5578	210	37	-	-	PUNCT
ejpam-5578	210	38	open	open	ADJ
ejpam-5578	210	39	set	set	NOUN
ejpam-5578	210	40	,	,	PUNCT
ejpam-5578	210	41	where	where	SCONJ
ejpam-5578	210	42	α	α	X
ejpam-5578	210	43	∈	∈	PROPN
ejpam-5578	210	44	λ	λ	X
ejpam-5578	210	45	and	and	CCONJ
ejpam-5578	210	46	i	i	PRON
ejpam-5578	210	47	∈	∈	PROPN
ejpam-5578	210	48	{	{	PUNCT
ejpam-5578	210	49	1	1	NUM
ejpam-5578	210	50	,	,	PUNCT
ejpam-5578	210	51	2	2	NUM
ejpam-5578	210	52	,	,	PUNCT
ejpam-5578	210	53	3	3	NUM
ejpam-5578	210	54	}	}	PUNCT
ejpam-5578	210	55	.	.	PUNCT
ejpam-5578	211	1	j.	j.	PROPN
ejpam-5578	211	2	oudetallah	oudetallah	PROPN
ejpam-5578	211	3	et	et	PROPN
ejpam-5578	211	4	al	al	PROPN
ejpam-5578	211	5	.	.	PUNCT
ejpam-5578	211	6	/	/	SYM
ejpam-5578	211	7	eur	eur	PROPN
ejpam-5578	211	8	.	.	PUNCT
ejpam-5578	212	1	j.	j.	PROPN
ejpam-5578	212	2	pure	pure	PROPN
ejpam-5578	212	3	appl	appl	PROPN
ejpam-5578	212	4	.	.	PROPN
ejpam-5578	212	5	math	math	PROPN
ejpam-5578	212	6	,	,	PUNCT
ejpam-5578	212	7	18	18	NUM
ejpam-5578	212	8	(	(	PUNCT
ejpam-5578	212	9	2	2	NUM
ejpam-5578	212	10	)	)	PUNCT
ejpam-5578	212	11	(	(	PUNCT
ejpam-5578	212	12	2025	2025	NUM
ejpam-5578	212	13	)	)	PUNCT
ejpam-5578	212	14	,	,	PUNCT
ejpam-5578	212	15	5578	5578	NUM
ejpam-5578	212	16	11	11	NUM
ejpam-5578	212	17	of	of	ADP
ejpam-5578	212	18	19	19	NUM
ejpam-5578	212	19	(	(	PUNCT
ejpam-5578	212	20	iii	iii	NOUN
ejpam-5578	212	21	)	)	PUNCT
ejpam-5578	212	22	w	w	NOUN
ejpam-5578	212	23	is	be	AUX
ejpam-5578	212	24	called	call	VERB
ejpam-5578	212	25	a	a	DET
ejpam-5578	212	26	tri	tri	ADJ
ejpam-5578	212	27	-	-	ADJ
ejpam-5578	212	28	closed	closed	ADJ
ejpam-5578	212	29	cover	cover	NOUN
ejpam-5578	212	30	of	of	ADP
ejpam-5578	212	31	q	q	NOUN
ejpam-5578	212	32	if	if	SCONJ
ejpam-5578	212	33	and	and	CCONJ
ejpam-5578	212	34	only	only	ADV
ejpam-5578	212	35	if	if	SCONJ
ejpam-5578	212	36	w	w	NOUN
ejpam-5578	212	37	is	be	AUX
ejpam-5578	212	38	a	a	DET
ejpam-5578	212	39	tri	tri	ADJ
ejpam-5578	212	40	-	-	NOUN
ejpam-5578	212	41	cover	cover	NOUN
ejpam-5578	212	42	and	and	CCONJ
ejpam-5578	212	43	each	each	DET
ejpam-5578	212	44	oα	oα	NOUN
ejpam-5578	212	45	is	be	AUX
ejpam-5578	212	46	a	a	DET
ejpam-5578	212	47	ϱi	ϱi	ADV
ejpam-5578	212	48	-	-	PUNCT
ejpam-5578	212	49	closed	close	VERB
ejpam-5578	212	50	set	set	NOUN
ejpam-5578	212	51	,	,	PUNCT
ejpam-5578	212	52	where	where	SCONJ
ejpam-5578	212	53	α	α	X
ejpam-5578	212	54	∈	∈	PROPN
ejpam-5578	212	55	λ	λ	X
ejpam-5578	212	56	and	and	CCONJ
ejpam-5578	212	57	i	i	PRON
ejpam-5578	212	58	∈	∈	PROPN
ejpam-5578	212	59	{	{	PUNCT
ejpam-5578	212	60	1	1	NUM
ejpam-5578	212	61	,	,	PUNCT
ejpam-5578	212	62	2	2	NUM
ejpam-5578	212	63	,	,	PUNCT
ejpam-5578	212	64	3	3	NUM
ejpam-5578	212	65	}	}	PUNCT
ejpam-5578	212	66	.	.	PUNCT
ejpam-5578	213	1	(	(	PUNCT
ejpam-5578	213	2	iv	iv	X
ejpam-5578	213	3	)	)	PUNCT
ejpam-5578	213	4	a	a	DET
ejpam-5578	213	5	collection	collection	NOUN
ejpam-5578	213	6	c	c	NOUN
ejpam-5578	213	7	=	=	PRON
ejpam-5578	213	8	{	{	PUNCT
ejpam-5578	213	9	bγ	bγ	INTJ
ejpam-5578	213	10	|	|	ADV
ejpam-5578	213	11	γ	γ	X
ejpam-5578	213	12	∈	∈	PROPN
ejpam-5578	213	13	γ	γ	X
ejpam-5578	213	14	}	}	PUNCT
ejpam-5578	213	15	is	be	AUX
ejpam-5578	213	16	called	call	VERB
ejpam-5578	213	17	a	a	DET
ejpam-5578	213	18	tripartite	tripartite	ADJ
ejpam-5578	213	19	subcover	subcover	NOUN
ejpam-5578	213	20	of	of	ADP
ejpam-5578	213	21	w	w	PROPN
ejpam-5578	213	22	if	if	SCONJ
ejpam-5578	214	1	and	and	CCONJ
ejpam-5578	214	2	only	only	ADV
ejpam-5578	214	3	if	if	SCONJ
ejpam-5578	214	4	:	:	PUNCT
ejpam-5578	214	5	(	(	PUNCT
ejpam-5578	214	6	a	a	X
ejpam-5578	214	7	)	)	PUNCT
ejpam-5578	214	8	c	c	NOUN
ejpam-5578	214	9	⊆w	⊆w	NOUN
ejpam-5578	214	10	,	,	PUNCT
ejpam-5578	214	11	(	(	PUNCT
ejpam-5578	214	12	b	b	NOUN
ejpam-5578	214	13	)	)	PUNCT
ejpam-5578	214	14	⋃	⋃	PUNCT
ejpam-5578	214	15	γ∈γbγ	γ∈γbγ	NOUN
ejpam-5578	214	16	=	=	PUNCT
ejpam-5578	214	17	q.	q.	NOUN
ejpam-5578	214	18	a	a	DET
ejpam-5578	214	19	space	space	NOUN
ejpam-5578	214	20	(	(	PUNCT
ejpam-5578	214	21	q	q	ADJ
ejpam-5578	214	22	,	,	PUNCT
ejpam-5578	214	23	ϱ1	ϱ1	NOUN
ejpam-5578	214	24	,	,	PUNCT
ejpam-5578	214	25	ϱ2	ϱ2	NOUN
ejpam-5578	214	26	,	,	PUNCT
ejpam-5578	214	27	ϱ3	ϱ3	PROPN
ejpam-5578	214	28	)	)	PUNCT
ejpam-5578	214	29	is	be	AUX
ejpam-5578	214	30	called	call	VERB
ejpam-5578	214	31	a	a	DET
ejpam-5578	214	32	tripartite	tripartite	ADJ
ejpam-5578	214	33	compact	compact	ADJ
ejpam-5578	214	34	space	space	NOUN
ejpam-5578	214	35	if	if	SCONJ
ejpam-5578	214	36	every	every	DET
ejpam-5578	214	37	tri	tri	ADJ
ejpam-5578	214	38	-	-	ADJ
ejpam-5578	214	39	open	open	ADJ
ejpam-5578	214	40	cover	cover	NOUN
ejpam-5578	214	41	of	of	ADP
ejpam-5578	214	42	q	q	PROPN
ejpam-5578	214	43	has	have	VERB
ejpam-5578	214	44	a	a	DET
ejpam-5578	214	45	finite	finite	ADJ
ejpam-5578	214	46	tripartite	tripartite	ADJ
ejpam-5578	214	47	subcover	subcover	PROPN
ejpam-5578	214	48	.	.	PUNCT
ejpam-5578	215	1	definition	definition	NOUN
ejpam-5578	215	2	21	21	NUM
ejpam-5578	215	3	.	.	PUNCT
ejpam-5578	216	1	[	[	X
ejpam-5578	216	2	7	7	X
ejpam-5578	216	3	]	]	X
ejpam-5578	216	4	let	let	VERB
ejpam-5578	216	5	(	(	PUNCT
ejpam-5578	216	6	q	q	ADJ
ejpam-5578	216	7	,	,	PUNCT
ejpam-5578	216	8	ϱ1	ϱ1	NOUN
ejpam-5578	216	9	,	,	PUNCT
ejpam-5578	216	10	ϱ2	ϱ2	NOUN
ejpam-5578	216	11	,	,	PUNCT
ejpam-5578	216	12	ϱ3	ϱ3	PROPN
ejpam-5578	216	13	)	)	PUNCT
ejpam-5578	216	14	be	be	AUX
ejpam-5578	216	15	a	a	DET
ejpam-5578	216	16	tri	tri	ADJ
ejpam-5578	216	17	-	-	ADJ
ejpam-5578	216	18	topological	topological	ADJ
ejpam-5578	216	19	space	space	NOUN
ejpam-5578	216	20	.	.	PUNCT
ejpam-5578	217	1	the	the	DET
ejpam-5578	217	2	space	space	NOUN
ejpam-5578	217	3	q	q	NOUN
ejpam-5578	217	4	is	be	AUX
ejpam-5578	217	5	said	say	VERB
ejpam-5578	217	6	to	to	PART
ejpam-5578	217	7	be	be	AUX
ejpam-5578	217	8	tripartite	tripartite	ADJ
ejpam-5578	217	9	locally	locally	ADV
ejpam-5578	217	10	compact	compact	ADJ
ejpam-5578	217	11	if	if	SCONJ
ejpam-5578	217	12	each	each	DET
ejpam-5578	217	13	point	point	NOUN
ejpam-5578	217	14	of	of	ADP
ejpam-5578	217	15	q	q	PROPN
ejpam-5578	217	16	has	have	VERB
ejpam-5578	217	17	a	a	DET
ejpam-5578	217	18	tri	tri	ADJ
ejpam-5578	217	19	-	-	ADJ
ejpam-5578	217	20	open	open	ADJ
ejpam-5578	217	21	neighborhood	neighborhood	NOUN
ejpam-5578	217	22	whose	whose	DET
ejpam-5578	217	23	tri	tri	NOUN
ejpam-5578	217	24	-	-	NOUN
ejpam-5578	217	25	closure	closure	NOUN
ejpam-5578	217	26	is	be	AUX
ejpam-5578	217	27	tri	tri	ADJ
ejpam-5578	217	28	-	-	ADJ
ejpam-5578	217	29	compact	compact	ADJ
ejpam-5578	217	30	.	.	PUNCT
ejpam-5578	218	1	note	note	NOUN
ejpam-5578	218	2	:	:	PUNCT
ejpam-5578	218	3	every	every	DET
ejpam-5578	218	4	tri	tri	ADJ
ejpam-5578	218	5	-	-	ADJ
ejpam-5578	218	6	compact	compact	ADJ
ejpam-5578	218	7	space	space	NOUN
ejpam-5578	218	8	is	be	AUX
ejpam-5578	218	9	tri	tri	ADJ
ejpam-5578	218	10	-	-	ADJ
ejpam-5578	218	11	locally	locally	ADV
ejpam-5578	218	12	compact	compact	ADJ
ejpam-5578	218	13	.	.	PUNCT
ejpam-5578	219	1	3	3	X
ejpam-5578	219	2	.	.	X
ejpam-5578	219	3	tri	tri	NOUN
ejpam-5578	219	4	-	-	NOUN
ejpam-5578	219	5	lindelöf	lindelöf	NOUN
ejpam-5578	219	6	and	and	CCONJ
ejpam-5578	219	7	nearly	nearly	ADV
ejpam-5578	219	8	tri	tri	ADJ
ejpam-5578	219	9	-	-	NOUN
ejpam-5578	219	10	lindelöf	lindelöf	NOUN
ejpam-5578	219	11	spaces	space	NOUN
ejpam-5578	219	12	in	in	ADP
ejpam-5578	219	13	this	this	DET
ejpam-5578	219	14	section	section	NOUN
ejpam-5578	219	15	,	,	PUNCT
ejpam-5578	219	16	we	we	PRON
ejpam-5578	219	17	discuss	discuss	VERB
ejpam-5578	219	18	the	the	DET
ejpam-5578	219	19	concept	concept	NOUN
ejpam-5578	219	20	of	of	ADP
ejpam-5578	219	21	lindelöf	lindelöf	PROPN
ejpam-5578	219	22	spaces	space	VERB
ejpam-5578	219	23	in	in	ADP
ejpam-5578	219	24	classical	classical	ADJ
ejpam-5578	219	25	topological	topological	ADJ
ejpam-5578	219	26	spaces	space	NOUN
ejpam-5578	219	27	,	,	PUNCT
ejpam-5578	219	28	as	as	ADV
ejpam-5578	219	29	well	well	ADV
ejpam-5578	219	30	as	as	ADP
ejpam-5578	219	31	their	their	PRON
ejpam-5578	219	32	extension	extension	NOUN
ejpam-5578	219	33	to	to	ADP
ejpam-5578	219	34	tri	tri	ADJ
ejpam-5578	219	35	-	-	ADJ
ejpam-5578	219	36	topological	topological	ADJ
ejpam-5578	219	37	spaces	space	NOUN
ejpam-5578	219	38	.	.	PUNCT
ejpam-5578	220	1	additionally	additionally	ADV
ejpam-5578	220	2	,	,	PUNCT
ejpam-5578	220	3	we	we	PRON
ejpam-5578	220	4	introduce	introduce	VERB
ejpam-5578	220	5	the	the	DET
ejpam-5578	220	6	notion	notion	NOUN
ejpam-5578	220	7	of	of	ADP
ejpam-5578	220	8	nearly	nearly	ADV
ejpam-5578	220	9	lindelöf	lindelöf	NOUN
ejpam-5578	220	10	spaces	space	NOUN
ejpam-5578	220	11	in	in	ADP
ejpam-5578	220	12	tri	tri	ADJ
ejpam-5578	220	13	-	-	ADJ
ejpam-5578	220	14	topological	topological	ADJ
ejpam-5578	220	15	spaces	space	NOUN
ejpam-5578	220	16	and	and	CCONJ
ejpam-5578	220	17	explore	explore	VERB
ejpam-5578	220	18	their	their	PRON
ejpam-5578	220	19	fundamental	fundamental	ADJ
ejpam-5578	220	20	properties	property	NOUN
ejpam-5578	220	21	and	and	CCONJ
ejpam-5578	220	22	related	related	ADJ
ejpam-5578	220	23	theorems	theorem	NOUN
ejpam-5578	220	24	.	.	PUNCT
ejpam-5578	221	1	definition	definition	NOUN
ejpam-5578	221	2	22	22	NUM
ejpam-5578	221	3	.	.	PUNCT
ejpam-5578	222	1	[	[	X
ejpam-5578	222	2	14	14	NUM
ejpam-5578	222	3	]	]	X
ejpam-5578	222	4	let	let	VERB
ejpam-5578	222	5	(	(	PUNCT
ejpam-5578	222	6	q	q	NOUN
ejpam-5578	222	7	,	,	PUNCT
ejpam-5578	222	8	ϱ	ϱ	NOUN
ejpam-5578	222	9	)	)	PUNCT
ejpam-5578	222	10	be	be	VERB
ejpam-5578	222	11	a	a	DET
ejpam-5578	222	12	topological	topological	ADJ
ejpam-5578	222	13	space	space	NOUN
ejpam-5578	222	14	.	.	PUNCT
ejpam-5578	223	1	it	it	PRON
ejpam-5578	223	2	is	be	AUX
ejpam-5578	223	3	called	call	VERB
ejpam-5578	223	4	a	a	DET
ejpam-5578	223	5	lindelöf	lindelöf	NOUN
ejpam-5578	223	6	space	space	NOUN
ejpam-5578	223	7	if	if	SCONJ
ejpam-5578	223	8	every	every	DET
ejpam-5578	223	9	open	open	ADJ
ejpam-5578	223	10	cover	cover	NOUN
ejpam-5578	223	11	of	of	ADP
ejpam-5578	223	12	q	q	PROPN
ejpam-5578	223	13	has	have	VERB
ejpam-5578	223	14	a	a	DET
ejpam-5578	223	15	countable	countable	ADJ
ejpam-5578	223	16	subcover	subcover	NOUN
ejpam-5578	223	17	.	.	PUNCT
ejpam-5578	224	1	definition	definition	NOUN
ejpam-5578	224	2	23	23	NUM
ejpam-5578	224	3	.	.	PUNCT
ejpam-5578	225	1	let	let	VERB
ejpam-5578	225	2	(	(	PUNCT
ejpam-5578	225	3	q	q	ADJ
ejpam-5578	225	4	,	,	PUNCT
ejpam-5578	225	5	ϱ1	ϱ1	NOUN
ejpam-5578	225	6	,	,	PUNCT
ejpam-5578	225	7	ϱ2	ϱ2	NOUN
ejpam-5578	225	8	,	,	PUNCT
ejpam-5578	225	9	ϱ3	ϱ3	PROPN
ejpam-5578	225	10	)	)	PUNCT
ejpam-5578	225	11	be	be	AUX
ejpam-5578	225	12	a	a	DET
ejpam-5578	225	13	tri	tri	ADJ
ejpam-5578	225	14	-	-	ADJ
ejpam-5578	225	15	topological	topological	ADJ
ejpam-5578	225	16	space	space	NOUN
ejpam-5578	225	17	.	.	PUNCT
ejpam-5578	226	1	it	it	PRON
ejpam-5578	226	2	is	be	AUX
ejpam-5578	226	3	called	call	VERB
ejpam-5578	226	4	a	a	DET
ejpam-5578	226	5	tri	tri	ADJ
ejpam-5578	226	6	-	-	NOUN
ejpam-5578	226	7	lindelöf	lindelöf	NOUN
ejpam-5578	226	8	space	space	NOUN
ejpam-5578	226	9	if	if	SCONJ
ejpam-5578	226	10	every	every	DET
ejpam-5578	226	11	ϱi	ϱi	ADJ
ejpam-5578	226	12	-	-	PUNCT
ejpam-5578	226	13	open	open	ADJ
ejpam-5578	226	14	cover	cover	NOUN
ejpam-5578	226	15	of	of	ADP
ejpam-5578	226	16	q	q	PROPN
ejpam-5578	226	17	has	have	VERB
ejpam-5578	226	18	a	a	DET
ejpam-5578	226	19	tripartite	tripartite	ADJ
ejpam-5578	226	20	countable	countable	ADJ
ejpam-5578	226	21	subcover	subcover	PROPN
ejpam-5578	226	22	.	.	PUNCT
ejpam-5578	227	1	note	note	NOUN
ejpam-5578	227	2	:	:	PUNCT
ejpam-5578	227	3	a	a	DET
ejpam-5578	227	4	set	set	NOUN
ejpam-5578	227	5	a	a	PRON
ejpam-5578	227	6	is	be	AUX
ejpam-5578	227	7	said	say	VERB
ejpam-5578	227	8	to	to	PART
ejpam-5578	227	9	be	be	AUX
ejpam-5578	227	10	countable	countable	ADJ
ejpam-5578	227	11	if	if	SCONJ
ejpam-5578	227	12	either	either	CCONJ
ejpam-5578	227	13	it	it	PRON
ejpam-5578	227	14	is	be	AUX
ejpam-5578	227	15	finite	finite	ADJ
ejpam-5578	227	16	or	or	CCONJ
ejpam-5578	227	17	if	if	SCONJ
ejpam-5578	227	18	there	there	PRON
ejpam-5578	227	19	exists	exist	VERB
ejpam-5578	227	20	an	an	DET
ejpam-5578	227	21	injective	injective	ADJ
ejpam-5578	227	22	function	function	NOUN
ejpam-5578	227	23	from	from	ADP
ejpam-5578	227	24	a	a	PRON
ejpam-5578	227	25	into	into	ADP
ejpam-5578	227	26	the	the	DET
ejpam-5578	227	27	set	set	NOUN
ejpam-5578	227	28	of	of	ADP
ejpam-5578	227	29	natural	natural	ADJ
ejpam-5578	227	30	numbers	number	NOUN
ejpam-5578	227	31	n.	n.	NOUN
ejpam-5578	227	32	definition	definition	NOUN
ejpam-5578	227	33	24	24	NUM
ejpam-5578	227	34	.	.	PUNCT
ejpam-5578	228	1	let	let	VERB
ejpam-5578	228	2	(	(	PUNCT
ejpam-5578	228	3	q	q	ADJ
ejpam-5578	228	4	,	,	PUNCT
ejpam-5578	228	5	ϱ1	ϱ1	NOUN
ejpam-5578	228	6	,	,	PUNCT
ejpam-5578	228	7	ϱ2	ϱ2	NOUN
ejpam-5578	228	8	,	,	PUNCT
ejpam-5578	228	9	ϱ3	ϱ3	PROPN
ejpam-5578	228	10	)	)	PUNCT
ejpam-5578	228	11	be	be	AUX
ejpam-5578	228	12	a	a	DET
ejpam-5578	228	13	tri	tri	ADJ
ejpam-5578	228	14	-	-	ADJ
ejpam-5578	228	15	topological	topological	ADJ
ejpam-5578	228	16	space	space	NOUN
ejpam-5578	228	17	,	,	PUNCT
ejpam-5578	228	18	and	and	CCONJ
ejpam-5578	228	19	let	let	VERB
ejpam-5578	228	20	c̃	c̃	PROPN
ejpam-5578	228	21	be	be	AUX
ejpam-5578	228	22	a	a	DET
ejpam-5578	228	23	cover	cover	NOUN
ejpam-5578	228	24	of	of	ADP
ejpam-5578	228	25	q.	q.	NOUN
ejpam-5578	228	26	we	we	PRON
ejpam-5578	228	27	say	say	VERB
ejpam-5578	228	28	that	that	SCONJ
ejpam-5578	228	29	c̃	c̃	PROPN
ejpam-5578	228	30	is	be	AUX
ejpam-5578	228	31	a	a	DET
ejpam-5578	228	32	tri	tri	ADJ
ejpam-5578	228	33	-	-	ADJ
ejpam-5578	228	34	open	open	ADJ
ejpam-5578	228	35	cover	cover	NOUN
ejpam-5578	228	36	if	if	SCONJ
ejpam-5578	228	37	:	:	PUNCT
ejpam-5578	228	38	c̃	c̃	PROPN
ejpam-5578	228	39	⊆	⊆	NUM
ejpam-5578	228	40	3⋃	3⋃	NUM
ejpam-5578	228	41	i=1	i=1	PROPN
ejpam-5578	228	42	υi	υi	PROPN
ejpam-5578	228	43	.	.	PROPN
ejpam-5578	228	44	remark	remark	PROPN
ejpam-5578	228	45	1	1	NUM
ejpam-5578	228	46	.	.	PUNCT
ejpam-5578	229	1	a	a	DET
ejpam-5578	229	2	tri	tri	ADJ
ejpam-5578	229	3	-	-	ADJ
ejpam-5578	229	4	topological	topological	ADJ
ejpam-5578	229	5	space	space	NOUN
ejpam-5578	229	6	(	(	PUNCT
ejpam-5578	229	7	q	q	ADJ
ejpam-5578	229	8	,	,	PUNCT
ejpam-5578	229	9	ϱ1	ϱ1	NOUN
ejpam-5578	229	10	,	,	PUNCT
ejpam-5578	229	11	ϱ2	ϱ2	NOUN
ejpam-5578	229	12	,	,	PUNCT
ejpam-5578	229	13	ϱ3	ϱ3	PROPN
ejpam-5578	229	14	)	)	PUNCT
ejpam-5578	229	15	is	be	AUX
ejpam-5578	229	16	a	a	DET
ejpam-5578	229	17	second	second	ADJ
ejpam-5578	229	18	-	-	PUNCT
ejpam-5578	229	19	countable	countable	ADJ
ejpam-5578	229	20	base	base	NOUN
ejpam-5578	229	21	with	with	ADP
ejpam-5578	229	22	respect	respect	NOUN
ejpam-5578	229	23	to	to	ADP
ejpam-5578	229	24	ϱ1	ϱ1	NOUN
ejpam-5578	229	25	,	,	PUNCT
ejpam-5578	229	26	ϱ2	ϱ2	NOUN
ejpam-5578	229	27	,	,	PUNCT
ejpam-5578	229	28	and	and	CCONJ
ejpam-5578	229	29	ϱ3	ϱ3	PROPN
ejpam-5578	229	30	.	.	PUNCT
ejpam-5578	230	1	definition	definition	NOUN
ejpam-5578	230	2	25	25	NUM
ejpam-5578	230	3	.	.	PUNCT
ejpam-5578	231	1	a	a	DET
ejpam-5578	231	2	tri	tri	ADJ
ejpam-5578	231	3	-	-	ADJ
ejpam-5578	231	4	topological	topological	ADJ
ejpam-5578	231	5	space	space	NOUN
ejpam-5578	231	6	(	(	PUNCT
ejpam-5578	231	7	q	q	ADJ
ejpam-5578	231	8	,	,	PUNCT
ejpam-5578	231	9	ϱ1	ϱ1	NOUN
ejpam-5578	231	10	,	,	PUNCT
ejpam-5578	231	11	ϱ2	ϱ2	NOUN
ejpam-5578	231	12	,	,	PUNCT
ejpam-5578	231	13	ϱ3	ϱ3	PROPN
ejpam-5578	231	14	)	)	PUNCT
ejpam-5578	231	15	is	be	AUX
ejpam-5578	231	16	called	call	VERB
ejpam-5578	231	17	a	a	DET
ejpam-5578	231	18	tri	tri	ADJ
ejpam-5578	231	19	-	-	ADJ
ejpam-5578	231	20	s	s	NOUN
ejpam-5578	231	21	-	-	PUNCT
ejpam-5578	231	22	lindelöf	lindelöf	NOUN
ejpam-5578	231	23	space	space	NOUN
ejpam-5578	231	24	if	if	SCONJ
ejpam-5578	231	25	and	and	CCONJ
ejpam-5578	231	26	only	only	ADV
ejpam-5578	231	27	if	if	SCONJ
ejpam-5578	231	28	it	it	PRON
ejpam-5578	231	29	is	be	AUX
ejpam-5578	231	30	a	a	DET
ejpam-5578	231	31	lindelöf	lindelöf	NOUN
ejpam-5578	231	32	space	space	NOUN
ejpam-5578	231	33	,	,	PUNCT
ejpam-5578	231	34	a	a	DET
ejpam-5578	231	35	pairwise	pairwise	NOUN
ejpam-5578	231	36	lindelöf	lindelöf	NOUN
ejpam-5578	231	37	space	space	NOUN
ejpam-5578	231	38	,	,	PUNCT
ejpam-5578	231	39	and	and	CCONJ
ejpam-5578	231	40	a	a	DET
ejpam-5578	231	41	tripartite	tripartite	ADJ
ejpam-5578	231	42	lindelöf	lindelöf	NOUN
ejpam-5578	231	43	space	space	NOUN
ejpam-5578	231	44	.	.	PUNCT
ejpam-5578	232	1	theorem	theorem	VERB
ejpam-5578	232	2	5	5	NUM
ejpam-5578	232	3	.	.	PUNCT
ejpam-5578	233	1	if	if	SCONJ
ejpam-5578	233	2	a	a	DET
ejpam-5578	233	3	tri	tri	ADJ
ejpam-5578	233	4	-	-	ADJ
ejpam-5578	233	5	topological	topological	ADJ
ejpam-5578	233	6	space	space	NOUN
ejpam-5578	233	7	q	q	NOUN
ejpam-5578	233	8	is	be	AUX
ejpam-5578	233	9	a	a	DET
ejpam-5578	233	10	second	second	ADJ
ejpam-5578	233	11	-	-	PUNCT
ejpam-5578	233	12	countable	countable	ADJ
ejpam-5578	233	13	space	space	NOUN
ejpam-5578	233	14	,	,	PUNCT
ejpam-5578	233	15	then	then	ADV
ejpam-5578	233	16	it	it	PRON
ejpam-5578	233	17	is	be	AUX
ejpam-5578	233	18	a	a	DET
ejpam-5578	233	19	tripartite	tripartite	ADJ
ejpam-5578	233	20	lindelöf	lindelöf	NOUN
ejpam-5578	233	21	space	space	NOUN
ejpam-5578	233	22	.	.	PUNCT
ejpam-5578	234	1	j.	j.	PROPN
ejpam-5578	234	2	oudetallah	oudetallah	PROPN
ejpam-5578	234	3	et	et	PROPN
ejpam-5578	234	4	al	al	PROPN
ejpam-5578	234	5	.	.	PUNCT
ejpam-5578	234	6	/	/	SYM
ejpam-5578	234	7	eur	eur	PROPN
ejpam-5578	234	8	.	.	PUNCT
ejpam-5578	235	1	j.	j.	PROPN
ejpam-5578	235	2	pure	pure	PROPN
ejpam-5578	235	3	appl	appl	PROPN
ejpam-5578	235	4	.	.	PROPN
ejpam-5578	235	5	math	math	PROPN
ejpam-5578	235	6	,	,	PUNCT
ejpam-5578	235	7	18	18	NUM
ejpam-5578	235	8	(	(	PUNCT
ejpam-5578	235	9	2	2	NUM
ejpam-5578	235	10	)	)	PUNCT
ejpam-5578	235	11	(	(	PUNCT
ejpam-5578	235	12	2025	2025	NUM
ejpam-5578	235	13	)	)	PUNCT
ejpam-5578	235	14	,	,	PUNCT
ejpam-5578	235	15	5578	5578	NUM
ejpam-5578	235	16	12	12	NUM
ejpam-5578	235	17	of	of	ADP
ejpam-5578	235	18	19	19	NUM
ejpam-5578	235	19	proof	proof	NOUN
ejpam-5578	235	20	.	.	PUNCT
ejpam-5578	236	1	since	since	SCONJ
ejpam-5578	236	2	q	q	PROPN
ejpam-5578	236	3	is	be	AUX
ejpam-5578	236	4	second	second	ADV
ejpam-5578	236	5	-	-	PUNCT
ejpam-5578	236	6	countable	countable	ADJ
ejpam-5578	236	7	,	,	PUNCT
ejpam-5578	236	8	each	each	DET
ejpam-5578	236	9	topology	topology	NOUN
ejpam-5578	236	10	ϱ1	ϱ1	NOUN
ejpam-5578	236	11	,	,	PUNCT
ejpam-5578	236	12	ϱ2	ϱ2	NOUN
ejpam-5578	236	13	,	,	PUNCT
ejpam-5578	236	14	ϱ3	ϱ3	PROPN
ejpam-5578	236	15	has	have	VERB
ejpam-5578	236	16	a	a	DET
ejpam-5578	236	17	countable	countable	ADJ
ejpam-5578	236	18	basis	basis	NOUN
ejpam-5578	236	19	.	.	PUNCT
ejpam-5578	237	1	given	give	VERB
ejpam-5578	237	2	any	any	DET
ejpam-5578	237	3	open	open	ADJ
ejpam-5578	237	4	cover	cover	NOUN
ejpam-5578	237	5	in	in	ADP
ejpam-5578	237	6	each	each	DET
ejpam-5578	237	7	topology	topology	NOUN
ejpam-5578	237	8	,	,	PUNCT
ejpam-5578	237	9	a	a	DET
ejpam-5578	237	10	countable	countable	ADJ
ejpam-5578	237	11	subcover	subcover	NOUN
ejpam-5578	237	12	exists	exist	VERB
ejpam-5578	237	13	by	by	ADP
ejpam-5578	237	14	definition	definition	NOUN
ejpam-5578	237	15	of	of	ADP
ejpam-5578	237	16	secondcountability	secondcountability	NOUN
ejpam-5578	237	17	.	.	PUNCT
ejpam-5578	238	1	hence	hence	ADV
ejpam-5578	238	2	,	,	PUNCT
ejpam-5578	238	3	q	q	PROPN
ejpam-5578	238	4	is	be	AUX
ejpam-5578	238	5	lindelöf	lindelöf	NOUN
ejpam-5578	238	6	in	in	ADP
ejpam-5578	238	7	each	each	DET
ejpam-5578	238	8	topology	topology	NOUN
ejpam-5578	238	9	,	,	PUNCT
ejpam-5578	238	10	making	make	VERB
ejpam-5578	238	11	it	it	PRON
ejpam-5578	238	12	a	a	DET
ejpam-5578	238	13	tripartite	tripartite	ADJ
ejpam-5578	238	14	lindelöf	lindelöf	NOUN
ejpam-5578	238	15	space	space	NOUN
ejpam-5578	238	16	.	.	PUNCT
ejpam-5578	239	1	remark	remark	PROPN
ejpam-5578	239	2	2	2	NUM
ejpam-5578	239	3	.	.	PUNCT
ejpam-5578	240	1	every	every	DET
ejpam-5578	240	2	tripartite	tripartite	ADJ
ejpam-5578	240	3	compact	compact	ADJ
ejpam-5578	240	4	space	space	NOUN
ejpam-5578	240	5	is	be	AUX
ejpam-5578	240	6	a	a	DET
ejpam-5578	240	7	tripartite	tripartite	ADJ
ejpam-5578	240	8	lindelöf	lindelöf	NOUN
ejpam-5578	240	9	space	space	NOUN
ejpam-5578	240	10	,	,	PUNCT
ejpam-5578	240	11	but	but	CCONJ
ejpam-5578	240	12	the	the	DET
ejpam-5578	240	13	converse	converse	NOUN
ejpam-5578	240	14	need	need	AUX
ejpam-5578	240	15	not	not	PART
ejpam-5578	240	16	be	be	AUX
ejpam-5578	240	17	true	true	ADJ
ejpam-5578	240	18	.	.	PUNCT
ejpam-5578	241	1	theorem	theorem	ADJ
ejpam-5578	241	2	6	6	NUM
ejpam-5578	241	3	.	.	PUNCT
ejpam-5578	242	1	let	let	AUX
ejpam-5578	242	2	(	(	PUNCT
ejpam-5578	242	3	r	r	NOUN
ejpam-5578	242	4	,	,	PUNCT
ejpam-5578	242	5	ϱu	ϱu	VERB
ejpam-5578	242	6	,	,	PUNCT
ejpam-5578	242	7	ϱu	ϱu	VERB
ejpam-5578	242	8	,	,	PUNCT
ejpam-5578	242	9	ϱu	ϱu	VERB
ejpam-5578	242	10	)	)	PUNCT
ejpam-5578	242	11	be	be	AUX
ejpam-5578	242	12	a	a	DET
ejpam-5578	242	13	tri	tri	ADJ
ejpam-5578	242	14	-	-	ADJ
ejpam-5578	242	15	topological	topological	ADJ
ejpam-5578	242	16	space	space	NOUN
ejpam-5578	242	17	.	.	PUNCT
ejpam-5578	243	1	then	then	ADV
ejpam-5578	243	2	,	,	PUNCT
ejpam-5578	243	3	(	(	PUNCT
ejpam-5578	243	4	r	r	NOUN
ejpam-5578	243	5	,	,	PUNCT
ejpam-5578	243	6	ϱu	ϱu	VERB
ejpam-5578	243	7	,	,	PUNCT
ejpam-5578	243	8	ϱu	ϱu	VERB
ejpam-5578	243	9	,	,	PUNCT
ejpam-5578	243	10	ϱu	ϱu	VERB
ejpam-5578	243	11	)	)	PUNCT
ejpam-5578	243	12	is	be	AUX
ejpam-5578	243	13	a	a	DET
ejpam-5578	243	14	trilindelöf	trilindelöf	NOUN
ejpam-5578	243	15	space	space	NOUN
ejpam-5578	243	16	but	but	CCONJ
ejpam-5578	243	17	not	not	PART
ejpam-5578	243	18	a	a	DET
ejpam-5578	243	19	tri	tri	ADJ
ejpam-5578	243	20	-	-	ADJ
ejpam-5578	243	21	compact	compact	ADJ
ejpam-5578	243	22	space	space	NOUN
ejpam-5578	243	23	.	.	PUNCT
ejpam-5578	244	1	proof	proof	NOUN
ejpam-5578	244	2	.	.	PUNCT
ejpam-5578	245	1	since	since	SCONJ
ejpam-5578	245	2	the	the	DET
ejpam-5578	245	3	set	set	NOUN
ejpam-5578	245	4	o	o	X
ejpam-5578	245	5	=	=	PUNCT
ejpam-5578	245	6	{	{	PUNCT
ejpam-5578	245	7	(	(	PUNCT
ejpam-5578	245	8	q	q	NOUN
ejpam-5578	245	9	,	,	PUNCT
ejpam-5578	245	10	s	s	X
ejpam-5578	245	11	)	)	PUNCT
ejpam-5578	245	12	|	|	ADV
ejpam-5578	245	13	q	q	ADJ
ejpam-5578	245	14	,	,	PUNCT
ejpam-5578	245	15	s	s	VERB
ejpam-5578	245	16	∈	∈	PROPN
ejpam-5578	245	17	q	q	X
ejpam-5578	245	18	}	}	PUNCT
ejpam-5578	245	19	is	be	AUX
ejpam-5578	245	20	a	a	DET
ejpam-5578	245	21	countable	countable	ADJ
ejpam-5578	245	22	base	base	NOUN
ejpam-5578	245	23	with	with	ADP
ejpam-5578	245	24	respect	respect	NOUN
ejpam-5578	245	25	to	to	ADP
ejpam-5578	245	26	ϱi	ϱi	NOUN
ejpam-5578	245	27	of	of	ADP
ejpam-5578	245	28	r	r	NOUN
ejpam-5578	245	29	,	,	PUNCT
ejpam-5578	245	30	for	for	ADP
ejpam-5578	245	31	i	i	PROPN
ejpam-5578	245	32	=	=	SYM
ejpam-5578	245	33	1	1	NUM
ejpam-5578	245	34	,	,	PUNCT
ejpam-5578	245	35	2	2	NUM
ejpam-5578	245	36	,	,	PUNCT
ejpam-5578	245	37	3	3	NUM
ejpam-5578	245	38	,	,	PUNCT
ejpam-5578	245	39	we	we	PRON
ejpam-5578	245	40	conclude	conclude	VERB
ejpam-5578	245	41	that	that	SCONJ
ejpam-5578	245	42	r	r	NOUN
ejpam-5578	245	43	is	be	AUX
ejpam-5578	245	44	a	a	DET
ejpam-5578	245	45	secondcountable	secondcountable	ADJ
ejpam-5578	245	46	space	space	NOUN
ejpam-5578	245	47	.	.	PUNCT
ejpam-5578	246	1	by	by	ADP
ejpam-5578	246	2	the	the	DET
ejpam-5578	246	3	previous	previous	ADJ
ejpam-5578	246	4	theorem	theorem	NOUN
ejpam-5578	246	5	,	,	PUNCT
ejpam-5578	246	6	this	this	PRON
ejpam-5578	246	7	implies	imply	VERB
ejpam-5578	246	8	that	that	SCONJ
ejpam-5578	246	9	(	(	PUNCT
ejpam-5578	246	10	r	r	NOUN
ejpam-5578	246	11	,	,	PUNCT
ejpam-5578	246	12	ϱu	ϱu	VERB
ejpam-5578	246	13	,	,	PUNCT
ejpam-5578	246	14	ϱu	ϱu	VERB
ejpam-5578	246	15	,	,	PUNCT
ejpam-5578	246	16	ϱu	ϱu	VERB
ejpam-5578	246	17	)	)	PUNCT
ejpam-5578	246	18	is	be	AUX
ejpam-5578	246	19	a	a	DET
ejpam-5578	246	20	tri	tri	ADJ
ejpam-5578	246	21	-	-	ADJ
ejpam-5578	246	22	lindelöf	lindelöf	NOUN
ejpam-5578	246	23	space	space	NOUN
ejpam-5578	246	24	.	.	PUNCT
ejpam-5578	247	1	however	however	ADV
ejpam-5578	247	2	,	,	PUNCT
ejpam-5578	247	3	the	the	DET
ejpam-5578	247	4	set	set	NOUN
ejpam-5578	247	5	(	(	PUNCT
ejpam-5578	247	6	q	q	NOUN
ejpam-5578	247	7	,	,	PUNCT
ejpam-5578	247	8	s	s	NOUN
ejpam-5578	247	9	)	)	PUNCT
ejpam-5578	247	10	for	for	ADP
ejpam-5578	247	11	all	all	PRON
ejpam-5578	247	12	q	q	X
ejpam-5578	247	13	<	<	X
ejpam-5578	247	14	s	s	X
ejpam-5578	247	15	in	in	ADP
ejpam-5578	247	16	q	q	PROPN
ejpam-5578	247	17	is	be	AUX
ejpam-5578	247	18	not	not	PART
ejpam-5578	247	19	closed	closed	ADJ
ejpam-5578	247	20	,	,	PUNCT
ejpam-5578	247	21	meaning	mean	VERB
ejpam-5578	247	22	that	that	SCONJ
ejpam-5578	247	23	(	(	PUNCT
ejpam-5578	247	24	r	r	NOUN
ejpam-5578	247	25	,	,	PUNCT
ejpam-5578	247	26	ϱu	ϱu	VERB
ejpam-5578	247	27	,	,	PUNCT
ejpam-5578	247	28	ϱu	ϱu	VERB
ejpam-5578	247	29	,	,	PUNCT
ejpam-5578	247	30	ϱu	ϱu	VERB
ejpam-5578	247	31	)	)	PUNCT
ejpam-5578	247	32	is	be	AUX
ejpam-5578	247	33	not	not	PART
ejpam-5578	247	34	compact	compact	ADJ
ejpam-5578	247	35	.	.	PUNCT
ejpam-5578	248	1	therefore	therefore	ADV
ejpam-5578	248	2	,	,	PUNCT
ejpam-5578	248	3	(	(	PUNCT
ejpam-5578	248	4	r	r	NOUN
ejpam-5578	248	5	,	,	PUNCT
ejpam-5578	248	6	ϱu	ϱu	VERB
ejpam-5578	248	7	,	,	PUNCT
ejpam-5578	248	8	ϱu	ϱu	VERB
ejpam-5578	248	9	,	,	PUNCT
ejpam-5578	248	10	ϱu	ϱu	VERB
ejpam-5578	248	11	)	)	PUNCT
ejpam-5578	248	12	is	be	AUX
ejpam-5578	248	13	a	a	DET
ejpam-5578	248	14	tri	tri	ADJ
ejpam-5578	248	15	-	-	ADJ
ejpam-5578	248	16	lindelöf	lindelöf	NOUN
ejpam-5578	248	17	space	space	NOUN
ejpam-5578	248	18	but	but	CCONJ
ejpam-5578	248	19	not	not	PART
ejpam-5578	248	20	a	a	DET
ejpam-5578	248	21	tri	tri	ADJ
ejpam-5578	248	22	-	-	ADJ
ejpam-5578	248	23	compact	compact	ADJ
ejpam-5578	248	24	space	space	NOUN
ejpam-5578	248	25	.	.	PUNCT
ejpam-5578	249	1	corollary	corollary	ADJ
ejpam-5578	249	2	1	1	NUM
ejpam-5578	249	3	.	.	PUNCT
ejpam-5578	250	1	every	every	DET
ejpam-5578	250	2	second	second	ADJ
ejpam-5578	250	3	-	-	PUNCT
ejpam-5578	250	4	countable	countable	ADJ
ejpam-5578	250	5	topological	topological	ADJ
ejpam-5578	250	6	space	space	NOUN
ejpam-5578	250	7	is	be	AUX
ejpam-5578	250	8	a	a	DET
ejpam-5578	250	9	tripartite	tripartite	ADJ
ejpam-5578	250	10	topological	topological	ADJ
ejpam-5578	250	11	space	space	NOUN
ejpam-5578	250	12	(	(	PUNCT
ejpam-5578	250	13	x,ϑ1	x,ϑ1	PROPN
ejpam-5578	250	14	,	,	PUNCT
ejpam-5578	250	15	ϑ2	ϑ2	PROPN
ejpam-5578	250	16	,	,	PUNCT
ejpam-5578	250	17	ϑ3	ϑ3	PROPN
ejpam-5578	250	18	)	)	PUNCT
ejpam-5578	250	19	.	.	PUNCT
ejpam-5578	251	1	thus	thus	ADV
ejpam-5578	251	2	,	,	PUNCT
ejpam-5578	251	3	x	x	PRON
ejpam-5578	251	4	is	be	AUX
ejpam-5578	251	5	a	a	DET
ejpam-5578	251	6	tri	tri	ADJ
ejpam-5578	251	7	-	-	ADJ
ejpam-5578	251	8	s	s	NOUN
ejpam-5578	251	9	-	-	PUNCT
ejpam-5578	251	10	lindelöf	lindelöf	NOUN
ejpam-5578	251	11	space	space	NOUN
ejpam-5578	251	12	.	.	PUNCT
ejpam-5578	252	1	proof	proof	NOUN
ejpam-5578	252	2	.	.	PUNCT
ejpam-5578	253	1	clearly	clearly	ADV
ejpam-5578	253	2	by	by	ADP
ejpam-5578	253	3	above	above	ADP
ejpam-5578	253	4	theorem	theorem	ADJ
ejpam-5578	253	5	remark	remark	NOUN
ejpam-5578	253	6	3	3	NUM
ejpam-5578	253	7	.	.	PUNCT
ejpam-5578	253	8	a	a	DET
ejpam-5578	253	9	compact	compact	ADJ
ejpam-5578	253	10	subset	subset	NOUN
ejpam-5578	253	11	of	of	ADP
ejpam-5578	253	12	a	a	DET
ejpam-5578	253	13	tri	tri	ADJ
ejpam-5578	253	14	-	-	ADJ
ejpam-5578	253	15	t2	t2	ADJ
ejpam-5578	253	16	-	-	PUNCT
ejpam-5578	253	17	space	space	NOUN
ejpam-5578	253	18	is	be	AUX
ejpam-5578	253	19	tri	tri	ADJ
ejpam-5578	253	20	-	-	ADJ
ejpam-5578	253	21	closed	closed	ADJ
ejpam-5578	253	22	,	,	PUNCT
ejpam-5578	253	23	but	but	CCONJ
ejpam-5578	253	24	a	a	DET
ejpam-5578	253	25	tri	tri	NOUN
ejpam-5578	253	26	-	-	NOUN
ejpam-5578	253	27	lindelöf	lindelöf	NOUN
ejpam-5578	253	28	subset	subset	NOUN
ejpam-5578	253	29	of	of	ADP
ejpam-5578	253	30	a	a	DET
ejpam-5578	253	31	tri	tri	ADJ
ejpam-5578	253	32	-	-	ADJ
ejpam-5578	253	33	t2	t2	ADJ
ejpam-5578	253	34	-	-	PUNCT
ejpam-5578	253	35	space	space	NOUN
ejpam-5578	253	36	need	need	AUX
ejpam-5578	253	37	not	not	PART
ejpam-5578	253	38	be	be	AUX
ejpam-5578	253	39	tri	tri	ADJ
ejpam-5578	253	40	-	-	ADJ
ejpam-5578	253	41	closed	closed	ADJ
ejpam-5578	253	42	.	.	PUNCT
ejpam-5578	254	1	definition	definition	NOUN
ejpam-5578	254	2	26	26	NUM
ejpam-5578	254	3	.	.	PUNCT
ejpam-5578	255	1	a	a	DET
ejpam-5578	255	2	space	space	NOUN
ejpam-5578	255	3	(	(	PUNCT
ejpam-5578	255	4	q	q	ADJ
ejpam-5578	255	5	,	,	PUNCT
ejpam-5578	255	6	ϱ1	ϱ1	NOUN
ejpam-5578	255	7	,	,	PUNCT
ejpam-5578	255	8	ϱ2	ϱ2	NOUN
ejpam-5578	255	9	,	,	PUNCT
ejpam-5578	255	10	ϱ3	ϱ3	PROPN
ejpam-5578	255	11	)	)	PUNCT
ejpam-5578	255	12	is	be	AUX
ejpam-5578	255	13	called	call	VERB
ejpam-5578	255	14	a	a	DET
ejpam-5578	255	15	tripartite	tripartite	ADJ
ejpam-5578	255	16	space	space	NOUN
ejpam-5578	255	17	if	if	SCONJ
ejpam-5578	255	18	and	and	CCONJ
ejpam-5578	255	19	only	only	ADV
ejpam-5578	255	20	if	if	SCONJ
ejpam-5578	255	21	the	the	DET
ejpam-5578	255	22	countable	countable	ADJ
ejpam-5578	255	23	intersection	intersection	NOUN
ejpam-5578	255	24	of	of	ADP
ejpam-5578	255	25	tri	tri	ADJ
ejpam-5578	255	26	-	-	ADJ
ejpam-5578	255	27	open	open	ADJ
ejpam-5578	255	28	sets	set	NOUN
ejpam-5578	255	29	is	be	AUX
ejpam-5578	255	30	open	open	ADJ
ejpam-5578	255	31	.	.	PUNCT
ejpam-5578	256	1	theorem	theorem	VERB
ejpam-5578	256	2	7	7	NUM
ejpam-5578	256	3	.	.	PUNCT
ejpam-5578	257	1	if	if	SCONJ
ejpam-5578	257	2	l	l	NOUN
ejpam-5578	257	3	is	be	AUX
ejpam-5578	257	4	a	a	DET
ejpam-5578	257	5	lindelöf	lindelöf	NOUN
ejpam-5578	257	6	subset	subset	VERB
ejpam-5578	257	7	of	of	ADP
ejpam-5578	257	8	a	a	DET
ejpam-5578	257	9	tri	tri	ADJ
ejpam-5578	257	10	-	-	ADJ
ejpam-5578	257	11	t2	t2	ADJ
ejpam-5578	257	12	-	-	PUNCT
ejpam-5578	257	13	space	space	NOUN
ejpam-5578	257	14	q	q	NOUN
ejpam-5578	257	15	,	,	PUNCT
ejpam-5578	257	16	then	then	ADV
ejpam-5578	257	17	for	for	ADP
ejpam-5578	257	18	each	each	DET
ejpam-5578	257	19	m	m	NOUN
ejpam-5578	257	20	/∈	/∈	PUNCT
ejpam-5578	258	1	l	l	NOUN
ejpam-5578	258	2	,	,	PUNCT
ejpam-5578	258	3	we	we	PRON
ejpam-5578	258	4	can	can	AUX
ejpam-5578	258	5	separate	separate	VERB
ejpam-5578	258	6	m	m	NOUN
ejpam-5578	258	7	and	and	CCONJ
ejpam-5578	258	8	l	l	NOUN
ejpam-5578	258	9	into	into	ADP
ejpam-5578	258	10	two	two	NUM
ejpam-5578	258	11	disjoint	disjoint	ADJ
ejpam-5578	258	12	tri	tri	ADJ
ejpam-5578	258	13	-	-	ADJ
ejpam-5578	258	14	open	open	ADJ
ejpam-5578	258	15	sets	set	NOUN
ejpam-5578	258	16	in	in	ADP
ejpam-5578	258	17	q.	q.	NOUN
ejpam-5578	258	18	proof	proof	NOUN
ejpam-5578	258	19	.	.	PUNCT
ejpam-5578	259	1	since	since	SCONJ
ejpam-5578	259	2	q	q	PROPN
ejpam-5578	259	3	is	be	AUX
ejpam-5578	259	4	a	a	DET
ejpam-5578	259	5	tri	tri	ADJ
ejpam-5578	259	6	-	-	ADJ
ejpam-5578	259	7	t2	t2	ADJ
ejpam-5578	259	8	-	-	PUNCT
ejpam-5578	259	9	space	space	NOUN
ejpam-5578	259	10	,	,	PUNCT
ejpam-5578	259	11	for	for	ADP
ejpam-5578	259	12	each	each	DET
ejpam-5578	259	13	x	x	SYM
ejpam-5578	259	14	∈	∈	PROPN
ejpam-5578	259	15	l	l	NOUN
ejpam-5578	259	16	,	,	PUNCT
ejpam-5578	259	17	there	there	PRON
ejpam-5578	259	18	exist	exist	VERB
ejpam-5578	259	19	disjoint	disjoint	ADJ
ejpam-5578	259	20	tri	tri	ADJ
ejpam-5578	259	21	-	-	ADJ
ejpam-5578	259	22	open	open	ADJ
ejpam-5578	259	23	sets	set	NOUN
ejpam-5578	259	24	ux	ux	INTJ
ejpam-5578	259	25	and	and	CCONJ
ejpam-5578	259	26	vx	vx	ADP
ejpam-5578	259	27	such	such	ADJ
ejpam-5578	259	28	that	that	SCONJ
ejpam-5578	259	29	x	x	SYM
ejpam-5578	259	30	∈	∈	NOUN
ejpam-5578	259	31	ux	ux	NOUN
ejpam-5578	259	32	and	and	CCONJ
ejpam-5578	259	33	m	m	PROPN
ejpam-5578	259	34	∈	∈	PROPN
ejpam-5578	260	1	vx	vx	PROPN
ejpam-5578	260	2	.	.	PUNCT
ejpam-5578	261	1	the	the	DET
ejpam-5578	261	2	collection	collection	NOUN
ejpam-5578	261	3	{	{	PUNCT
ejpam-5578	261	4	ux	ux	INTJ
ejpam-5578	261	5	|	|	ADV
ejpam-5578	261	6	x	x	SYM
ejpam-5578	261	7	∈	∈	PROPN
ejpam-5578	261	8	l	l	NOUN
ejpam-5578	261	9	}	}	PUNCT
ejpam-5578	261	10	forms	form	VERB
ejpam-5578	261	11	an	an	DET
ejpam-5578	261	12	open	open	ADJ
ejpam-5578	261	13	cover	cover	NOUN
ejpam-5578	261	14	of	of	ADP
ejpam-5578	261	15	l	l	NOUN
ejpam-5578	261	16	,	,	PUNCT
ejpam-5578	261	17	which	which	PRON
ejpam-5578	261	18	has	have	VERB
ejpam-5578	261	19	a	a	DET
ejpam-5578	261	20	countable	countable	ADJ
ejpam-5578	261	21	subcover	subcover	NOUN
ejpam-5578	261	22	{	{	PUNCT
ejpam-5578	261	23	uxi	uxi	NOUN
ejpam-5578	262	1	|	|	ADV
ejpam-5578	262	2	i	i	PRON
ejpam-5578	262	3	∈	∈	PROPN
ejpam-5578	262	4	n	n	CCONJ
ejpam-5578	262	5	}	}	PUNCT
ejpam-5578	262	6	because	because	SCONJ
ejpam-5578	262	7	l	l	NOUN
ejpam-5578	262	8	is	be	AUX
ejpam-5578	262	9	lindelöf	lindelöf	NOUN
ejpam-5578	262	10	.	.	PUNCT
ejpam-5578	263	1	let	let	VERB
ejpam-5578	263	2	u	u	NOUN
ejpam-5578	263	3	=	=	PUNCT
ejpam-5578	263	4	⋃	⋃	NOUN
ejpam-5578	263	5	i∈n	i∈n	NOUN
ejpam-5578	263	6	uxi	uxi	NOUN
ejpam-5578	263	7	and	and	CCONJ
ejpam-5578	263	8	v	v	NOUN
ejpam-5578	263	9	=	=	SYM
ejpam-5578	263	10	⋂	⋂	PROPN
ejpam-5578	263	11	i∈n	i∈n	NOUN
ejpam-5578	263	12	vxi	vxi	INTJ
ejpam-5578	263	13	.	.	PUNCT
ejpam-5578	264	1	then	then	ADV
ejpam-5578	264	2	u	u	PROPN
ejpam-5578	264	3	and	and	CCONJ
ejpam-5578	264	4	v	v	NOUN
ejpam-5578	264	5	are	be	AUX
ejpam-5578	264	6	disjoint	disjoint	NOUN
ejpam-5578	264	7	tri	tri	ADJ
ejpam-5578	264	8	-	-	ADJ
ejpam-5578	264	9	open	open	ADJ
ejpam-5578	264	10	sets	set	NOUN
ejpam-5578	264	11	separating	separate	VERB
ejpam-5578	264	12	l	l	NOUN
ejpam-5578	264	13	and	and	CCONJ
ejpam-5578	264	14	m	m	PROPN
ejpam-5578	264	15	,	,	PUNCT
ejpam-5578	264	16	proving	prove	VERB
ejpam-5578	264	17	the	the	DET
ejpam-5578	264	18	theorem	theorem	NOUN
ejpam-5578	264	19	.	.	PROPN
ejpam-5578	265	1	definition	definition	NOUN
ejpam-5578	265	2	27	27	NUM
ejpam-5578	265	3	.	.	PUNCT
ejpam-5578	266	1	[	[	X
ejpam-5578	266	2	17	17	NUM
ejpam-5578	266	3	]	]	AUX
ejpam-5578	266	4	suppose	suppose	VERB
ejpam-5578	266	5	(	(	PUNCT
ejpam-5578	266	6	q	q	X
ejpam-5578	266	7	,	,	PUNCT
ejpam-5578	266	8	ϱ	ϱ	NOUN
ejpam-5578	266	9	)	)	PUNCT
ejpam-5578	266	10	is	be	AUX
ejpam-5578	266	11	a	a	DET
ejpam-5578	266	12	topological	topological	ADJ
ejpam-5578	266	13	space	space	NOUN
ejpam-5578	266	14	.	.	PUNCT
ejpam-5578	267	1	a	a	DET
ejpam-5578	267	2	subset	subset	NOUN
ejpam-5578	267	3	y	y	PROPN
ejpam-5578	267	4	⊆	⊆	NUM
ejpam-5578	267	5	q	q	NOUN
ejpam-5578	267	6	is	be	AUX
ejpam-5578	267	7	called	call	VERB
ejpam-5578	267	8	nearly	nearly	ADV
ejpam-5578	267	9	open	open	ADJ
ejpam-5578	267	10	if	if	SCONJ
ejpam-5578	267	11	:	:	PUNCT
ejpam-5578	267	12	y	y	PROPN
ejpam-5578	267	13	=	=	SYM
ejpam-5578	267	14	(	(	PUNCT
ejpam-5578	267	15	y	y	NOUN
ejpam-5578	267	16	)	)	PUNCT
ejpam-5578	267	17	◦	◦	NOUN
ejpam-5578	267	18	in	in	ADP
ejpam-5578	267	19	ϱ.	ϱ.	ADJ
ejpam-5578	267	20	definition	definition	NOUN
ejpam-5578	267	21	28	28	NUM
ejpam-5578	267	22	.	.	PUNCT
ejpam-5578	268	1	suppose	suppose	VERB
ejpam-5578	268	2	(	(	PUNCT
ejpam-5578	268	3	q	q	ADJ
ejpam-5578	268	4	,	,	PUNCT
ejpam-5578	268	5	ϱ1	ϱ1	NOUN
ejpam-5578	268	6	,	,	PUNCT
ejpam-5578	268	7	ϱ2	ϱ2	NOUN
ejpam-5578	268	8	,	,	PUNCT
ejpam-5578	268	9	ϱ3	ϱ3	PROPN
ejpam-5578	268	10	)	)	PUNCT
ejpam-5578	268	11	is	be	AUX
ejpam-5578	268	12	a	a	DET
ejpam-5578	268	13	tri	tri	ADJ
ejpam-5578	268	14	-	-	ADJ
ejpam-5578	268	15	topological	topological	ADJ
ejpam-5578	268	16	space	space	NOUN
ejpam-5578	268	17	.	.	PUNCT
ejpam-5578	269	1	a	a	DET
ejpam-5578	269	2	subset	subset	NOUN
ejpam-5578	269	3	y	y	PROPN
ejpam-5578	269	4	⊆	⊆	NUM
ejpam-5578	269	5	q	q	NOUN
ejpam-5578	269	6	is	be	AUX
ejpam-5578	269	7	called	call	VERB
ejpam-5578	269	8	a	a	DET
ejpam-5578	269	9	tripartite	tripartite	ADJ
ejpam-5578	269	10	nearly	nearly	ADV
ejpam-5578	269	11	open	open	ADJ
ejpam-5578	269	12	set	set	VERB
ejpam-5578	269	13	if	if	SCONJ
ejpam-5578	269	14	:	:	PUNCT
ejpam-5578	269	15	(	(	PUNCT
ejpam-5578	269	16	y	y	X
ejpam-5578	269	17	)	)	PUNCT
ejpam-5578	269	18	◦	◦	NOUN
ejpam-5578	269	19	is	be	AUX
ejpam-5578	269	20	open	open	ADJ
ejpam-5578	269	21	in	in	ADP
ejpam-5578	269	22	ϱ1	ϱ1	NOUN
ejpam-5578	269	23	,	,	PUNCT
ejpam-5578	269	24	(	(	PUNCT
ejpam-5578	269	25	y	y	X
ejpam-5578	269	26	)	)	PUNCT
ejpam-5578	269	27	◦	◦	NOUN
ejpam-5578	269	28	is	be	AUX
ejpam-5578	269	29	open	open	ADJ
ejpam-5578	269	30	in	in	ADP
ejpam-5578	269	31	ϱ2	ϱ2	NOUN
ejpam-5578	269	32	,	,	PUNCT
ejpam-5578	269	33	and	and	CCONJ
ejpam-5578	269	34	(	(	PUNCT
ejpam-5578	269	35	y	y	X
ejpam-5578	269	36	)	)	PUNCT
ejpam-5578	269	37	◦	◦	NOUN
ejpam-5578	269	38	is	be	AUX
ejpam-5578	269	39	open	open	ADJ
ejpam-5578	269	40	in	in	ADP
ejpam-5578	269	41	ϱ3	ϱ3	PROPN
ejpam-5578	269	42	.	.	PUNCT
ejpam-5578	270	1	j.	j.	PROPN
ejpam-5578	270	2	oudetallah	oudetallah	PROPN
ejpam-5578	270	3	et	et	PROPN
ejpam-5578	270	4	al	al	PROPN
ejpam-5578	270	5	.	.	PUNCT
ejpam-5578	270	6	/	/	SYM
ejpam-5578	270	7	eur	eur	PROPN
ejpam-5578	270	8	.	.	PUNCT
ejpam-5578	271	1	j.	j.	PROPN
ejpam-5578	271	2	pure	pure	PROPN
ejpam-5578	271	3	appl	appl	PROPN
ejpam-5578	271	4	.	.	PROPN
ejpam-5578	271	5	math	math	PROPN
ejpam-5578	271	6	,	,	PUNCT
ejpam-5578	271	7	18	18	NUM
ejpam-5578	271	8	(	(	PUNCT
ejpam-5578	271	9	2	2	NUM
ejpam-5578	271	10	)	)	PUNCT
ejpam-5578	271	11	(	(	PUNCT
ejpam-5578	271	12	2025	2025	NUM
ejpam-5578	271	13	)	)	PUNCT
ejpam-5578	271	14	,	,	PUNCT
ejpam-5578	271	15	5578	5578	NUM
ejpam-5578	271	16	13	13	NUM
ejpam-5578	271	17	of	of	ADP
ejpam-5578	271	18	19	19	NUM
ejpam-5578	271	19	definition	definition	NOUN
ejpam-5578	271	20	29	29	NUM
ejpam-5578	271	21	.	.	PUNCT
ejpam-5578	272	1	a	a	DET
ejpam-5578	272	2	collection	collection	NOUN
ejpam-5578	272	3	ũ	ũ	PROPN
ejpam-5578	272	4	=	=	PRON
ejpam-5578	272	5	{	{	PUNCT
ejpam-5578	272	6	uα	uα	PROPN
ejpam-5578	272	7	|	|	ADV
ejpam-5578	272	8	α	α	NOUN
ejpam-5578	272	9	∈	∈	NOUN
ejpam-5578	272	10	∆	∆	X
ejpam-5578	272	11	}	}	PUNCT
ejpam-5578	272	12	is	be	AUX
ejpam-5578	272	13	called	call	VERB
ejpam-5578	272	14	a	a	DET
ejpam-5578	272	15	nearly	nearly	ADV
ejpam-5578	272	16	open	open	ADJ
ejpam-5578	272	17	cover	cover	NOUN
ejpam-5578	272	18	of	of	ADP
ejpam-5578	272	19	the	the	DET
ejpam-5578	272	20	tri	tri	ADJ
ejpam-5578	272	21	-	-	ADJ
ejpam-5578	272	22	topological	topological	ADJ
ejpam-5578	272	23	space	space	NOUN
ejpam-5578	272	24	(	(	PUNCT
ejpam-5578	272	25	q	q	ADJ
ejpam-5578	272	26	,	,	PUNCT
ejpam-5578	272	27	ϱ1	ϱ1	NOUN
ejpam-5578	272	28	,	,	PUNCT
ejpam-5578	272	29	ϱ2	ϱ2	NOUN
ejpam-5578	272	30	,	,	PUNCT
ejpam-5578	272	31	ϱ3	ϱ3	PROPN
ejpam-5578	272	32	)	)	PUNCT
ejpam-5578	272	33	if	if	SCONJ
ejpam-5578	272	34	:	:	PUNCT
ejpam-5578	272	35	(	(	PUNCT
ejpam-5578	272	36	i	i	NOUN
ejpam-5578	272	37	)	)	PUNCT
ejpam-5578	272	38	each	each	DET
ejpam-5578	272	39	uα	uα	PROPN
ejpam-5578	272	40	is	be	AUX
ejpam-5578	272	41	a	a	DET
ejpam-5578	272	42	tri	tri	ADJ
ejpam-5578	272	43	-	-	ADJ
ejpam-5578	272	44	nearly	nearly	ADV
ejpam-5578	272	45	open	open	ADJ
ejpam-5578	272	46	set	set	NOUN
ejpam-5578	272	47	for	for	ADP
ejpam-5578	272	48	all	all	DET
ejpam-5578	272	49	α	α	NOUN
ejpam-5578	272	50	∈	∈	PROPN
ejpam-5578	272	51	∆.	∆.	X
ejpam-5578	272	52	(	(	PUNCT
ejpam-5578	272	53	ii	ii	NOUN
ejpam-5578	272	54	)	)	PUNCT
ejpam-5578	272	55	⋃	⋃	VERB
ejpam-5578	272	56	α∈∆	α∈∆	X
ejpam-5578	272	57	uα	uα	NOUN
ejpam-5578	272	58	=	=	PUNCT
ejpam-5578	272	59	q.	q.	NOUN
ejpam-5578	272	60	definition	definition	NOUN
ejpam-5578	272	61	30	30	NUM
ejpam-5578	272	62	.	.	PUNCT
ejpam-5578	273	1	suppose	suppose	VERB
ejpam-5578	273	2	(	(	PUNCT
ejpam-5578	273	3	q	q	ADJ
ejpam-5578	273	4	,	,	PUNCT
ejpam-5578	273	5	ϱ1	ϱ1	NOUN
ejpam-5578	273	6	,	,	PUNCT
ejpam-5578	273	7	ϱ2	ϱ2	NOUN
ejpam-5578	273	8	,	,	PUNCT
ejpam-5578	273	9	ϱ3	ϱ3	PROPN
ejpam-5578	273	10	)	)	PUNCT
ejpam-5578	273	11	is	be	AUX
ejpam-5578	273	12	a	a	DET
ejpam-5578	273	13	tri	tri	ADJ
ejpam-5578	273	14	-	-	ADJ
ejpam-5578	273	15	topological	topological	ADJ
ejpam-5578	273	16	space	space	NOUN
ejpam-5578	273	17	,	,	PUNCT
ejpam-5578	273	18	and	and	CCONJ
ejpam-5578	273	19	let	let	VERB
ejpam-5578	273	20	ũ	ũ	PROPN
ejpam-5578	273	21	=	=	PRON
ejpam-5578	273	22	{	{	PUNCT
ejpam-5578	273	23	uα	uα	PROPN
ejpam-5578	273	24	|	|	ADV
ejpam-5578	273	25	α	α	NOUN
ejpam-5578	273	26	∈	∈	NOUN
ejpam-5578	273	27	∆	∆	X
ejpam-5578	273	28	}	}	PUNCT
ejpam-5578	273	29	be	be	AUX
ejpam-5578	273	30	a	a	DET
ejpam-5578	273	31	tri	tri	ADJ
ejpam-5578	273	32	-	-	ADJ
ejpam-5578	273	33	nearly	nearly	ADV
ejpam-5578	273	34	open	open	ADJ
ejpam-5578	273	35	cover	cover	NOUN
ejpam-5578	273	36	of	of	ADP
ejpam-5578	273	37	q.	q.	PROPN
ejpam-5578	273	38	a	a	DET
ejpam-5578	273	39	collection	collection	NOUN
ejpam-5578	273	40	sγ	sγ	NOUN
ejpam-5578	273	41	=	=	SYM
ejpam-5578	273	42	{	{	PUNCT
ejpam-5578	273	43	uαγ	uαγ	X
ejpam-5578	273	44	|	|	ADV
ejpam-5578	273	45	γ	γ	PROPN
ejpam-5578	273	46	∈	∈	PROPN
ejpam-5578	273	47	γ	γ	X
ejpam-5578	273	48	}	}	PUNCT
ejpam-5578	273	49	is	be	AUX
ejpam-5578	273	50	called	call	VERB
ejpam-5578	273	51	a	a	DET
ejpam-5578	273	52	tri	tri	ADJ
ejpam-5578	273	53	-	-	ADJ
ejpam-5578	273	54	nearly	nearly	ADV
ejpam-5578	273	55	subcover	subcover	NOUN
ejpam-5578	273	56	of	of	ADP
ejpam-5578	273	57	q	q	PROPN
ejpam-5578	273	58	if	if	SCONJ
ejpam-5578	273	59	:	:	PUNCT
ejpam-5578	273	60	⋃	⋃	PROPN
ejpam-5578	273	61	γ∈γ	γ∈γ	ADJ
ejpam-5578	273	62	uαγ	uαγ	X
ejpam-5578	273	63	=	=	PUNCT
ejpam-5578	273	64	q.	q.	NOUN
ejpam-5578	273	65	definition	definition	NOUN
ejpam-5578	273	66	31	31	NUM
ejpam-5578	273	67	.	.	PUNCT
ejpam-5578	274	1	[	[	X
ejpam-5578	274	2	11	11	NUM
ejpam-5578	274	3	]	]	PUNCT
ejpam-5578	274	4	suppose	suppose	VERB
ejpam-5578	274	5	(	(	PUNCT
ejpam-5578	274	6	q	q	X
ejpam-5578	274	7	,	,	PUNCT
ejpam-5578	274	8	ϱ	ϱ	NOUN
ejpam-5578	274	9	)	)	PUNCT
ejpam-5578	274	10	is	be	AUX
ejpam-5578	274	11	a	a	DET
ejpam-5578	274	12	topological	topological	ADJ
ejpam-5578	274	13	space	space	NOUN
ejpam-5578	274	14	.	.	PUNCT
ejpam-5578	275	1	we	we	PRON
ejpam-5578	275	2	say	say	VERB
ejpam-5578	275	3	that	that	PRON
ejpam-5578	275	4	q	q	NOUN
ejpam-5578	275	5	is	be	AUX
ejpam-5578	275	6	a	a	DET
ejpam-5578	275	7	nearly	nearly	ADV
ejpam-5578	275	8	compact	compact	ADJ
ejpam-5578	275	9	space	space	NOUN
ejpam-5578	275	10	if	if	SCONJ
ejpam-5578	275	11	every	every	DET
ejpam-5578	275	12	nearly	nearly	ADV
ejpam-5578	275	13	open	open	ADJ
ejpam-5578	275	14	cover	cover	NOUN
ejpam-5578	275	15	of	of	ADP
ejpam-5578	275	16	q	q	PROPN
ejpam-5578	275	17	has	have	VERB
ejpam-5578	275	18	a	a	DET
ejpam-5578	275	19	finite	finite	NOUN
ejpam-5578	275	20	nearly	nearly	ADV
ejpam-5578	275	21	subcover	subcover	PROPN
ejpam-5578	275	22	.	.	PUNCT
ejpam-5578	276	1	definition	definition	NOUN
ejpam-5578	276	2	32	32	NUM
ejpam-5578	276	3	.	.	PUNCT
ejpam-5578	277	1	suppose	suppose	VERB
ejpam-5578	277	2	(	(	PUNCT
ejpam-5578	277	3	q	q	ADJ
ejpam-5578	277	4	,	,	PUNCT
ejpam-5578	277	5	ϱ1	ϱ1	NOUN
ejpam-5578	277	6	,	,	PUNCT
ejpam-5578	277	7	ϱ2	ϱ2	NOUN
ejpam-5578	277	8	,	,	PUNCT
ejpam-5578	277	9	ϱ3	ϱ3	PROPN
ejpam-5578	277	10	)	)	PUNCT
ejpam-5578	277	11	is	be	AUX
ejpam-5578	277	12	a	a	DET
ejpam-5578	277	13	tri	tri	ADJ
ejpam-5578	277	14	-	-	ADJ
ejpam-5578	277	15	topological	topological	ADJ
ejpam-5578	277	16	space	space	NOUN
ejpam-5578	277	17	.	.	PUNCT
ejpam-5578	278	1	we	we	PRON
ejpam-5578	278	2	say	say	VERB
ejpam-5578	278	3	that	that	PRON
ejpam-5578	278	4	q	q	NOUN
ejpam-5578	278	5	is	be	AUX
ejpam-5578	278	6	a	a	DET
ejpam-5578	278	7	trinearly	trinearly	ADV
ejpam-5578	278	8	compact	compact	ADJ
ejpam-5578	278	9	space	space	NOUN
ejpam-5578	278	10	if	if	SCONJ
ejpam-5578	278	11	every	every	DET
ejpam-5578	278	12	tri	tri	ADJ
ejpam-5578	278	13	-	-	ADJ
ejpam-5578	278	14	nearly	nearly	ADV
ejpam-5578	278	15	open	open	ADJ
ejpam-5578	278	16	cover	cover	NOUN
ejpam-5578	278	17	of	of	ADP
ejpam-5578	278	18	q	q	PROPN
ejpam-5578	278	19	has	have	VERB
ejpam-5578	278	20	a	a	DET
ejpam-5578	278	21	finite	finite	ADJ
ejpam-5578	278	22	tri	tri	ADJ
ejpam-5578	278	23	-	-	ADJ
ejpam-5578	278	24	nearly	nearly	ADV
ejpam-5578	278	25	subcover	subcover	PROPN
ejpam-5578	278	26	.	.	PUNCT
ejpam-5578	279	1	definition	definition	NOUN
ejpam-5578	279	2	33	33	NUM
ejpam-5578	279	3	.	.	PUNCT
ejpam-5578	280	1	[	[	X
ejpam-5578	280	2	12	12	NUM
ejpam-5578	280	3	]	]	PUNCT
ejpam-5578	280	4	suppose	suppose	VERB
ejpam-5578	280	5	(	(	PUNCT
ejpam-5578	280	6	q	q	X
ejpam-5578	280	7	,	,	PUNCT
ejpam-5578	280	8	ϱ	ϱ	NOUN
ejpam-5578	280	9	)	)	PUNCT
ejpam-5578	280	10	is	be	AUX
ejpam-5578	280	11	a	a	DET
ejpam-5578	280	12	topological	topological	ADJ
ejpam-5578	280	13	space	space	NOUN
ejpam-5578	280	14	.	.	PUNCT
ejpam-5578	281	1	the	the	DET
ejpam-5578	281	2	space	space	NOUN
ejpam-5578	281	3	q	q	NOUN
ejpam-5578	281	4	is	be	AUX
ejpam-5578	281	5	called	call	VERB
ejpam-5578	281	6	a	a	DET
ejpam-5578	281	7	nearly	nearly	ADV
ejpam-5578	281	8	lindelöf	lindelöf	NOUN
ejpam-5578	281	9	space	space	NOUN
ejpam-5578	281	10	if	if	SCONJ
ejpam-5578	281	11	every	every	DET
ejpam-5578	281	12	nearly	nearly	ADV
ejpam-5578	281	13	open	open	ADJ
ejpam-5578	281	14	cover	cover	NOUN
ejpam-5578	281	15	of	of	ADP
ejpam-5578	281	16	q	q	PROPN
ejpam-5578	281	17	has	have	VERB
ejpam-5578	281	18	a	a	DET
ejpam-5578	281	19	countable	countable	ADJ
ejpam-5578	281	20	nearly	nearly	ADV
ejpam-5578	281	21	subcover	subcover	PROPN
ejpam-5578	281	22	.	.	PUNCT
ejpam-5578	282	1	definition	definition	NOUN
ejpam-5578	282	2	34	34	NUM
ejpam-5578	282	3	.	.	PUNCT
ejpam-5578	283	1	suppose	suppose	VERB
ejpam-5578	283	2	(	(	PUNCT
ejpam-5578	283	3	q	q	ADJ
ejpam-5578	283	4	,	,	PUNCT
ejpam-5578	283	5	ϱ1	ϱ1	NOUN
ejpam-5578	283	6	,	,	PUNCT
ejpam-5578	283	7	ϱ2	ϱ2	NOUN
ejpam-5578	283	8	,	,	PUNCT
ejpam-5578	283	9	ϱ3	ϱ3	PROPN
ejpam-5578	283	10	)	)	PUNCT
ejpam-5578	283	11	is	be	AUX
ejpam-5578	283	12	a	a	DET
ejpam-5578	283	13	tri	tri	ADJ
ejpam-5578	283	14	-	-	ADJ
ejpam-5578	283	15	topological	topological	ADJ
ejpam-5578	283	16	space	space	NOUN
ejpam-5578	283	17	.	.	PUNCT
ejpam-5578	284	1	the	the	DET
ejpam-5578	284	2	space	space	NOUN
ejpam-5578	284	3	q	q	NOUN
ejpam-5578	284	4	is	be	AUX
ejpam-5578	284	5	called	call	VERB
ejpam-5578	284	6	a	a	DET
ejpam-5578	284	7	tri	tri	ADJ
ejpam-5578	284	8	-	-	ADJ
ejpam-5578	284	9	nearly	nearly	ADV
ejpam-5578	284	10	lindelöf	lindelöf	NOUN
ejpam-5578	284	11	space	space	NOUN
ejpam-5578	284	12	if	if	SCONJ
ejpam-5578	284	13	every	every	DET
ejpam-5578	284	14	tri	tri	ADJ
ejpam-5578	284	15	-	-	ADJ
ejpam-5578	284	16	nearly	nearly	ADV
ejpam-5578	284	17	open	open	ADJ
ejpam-5578	284	18	cover	cover	NOUN
ejpam-5578	284	19	of	of	ADP
ejpam-5578	284	20	q	q	PROPN
ejpam-5578	284	21	has	have	VERB
ejpam-5578	284	22	a	a	DET
ejpam-5578	284	23	tripartite	tripartite	ADJ
ejpam-5578	284	24	countable	countable	ADJ
ejpam-5578	284	25	nearly	nearly	ADV
ejpam-5578	284	26	subcover	subcover	PROPN
ejpam-5578	284	27	.	.	PUNCT
ejpam-5578	285	1	corollary	corollary	ADJ
ejpam-5578	285	2	2	2	NUM
ejpam-5578	285	3	.	.	PUNCT
ejpam-5578	286	1	every	every	DET
ejpam-5578	286	2	tri	tri	ADJ
ejpam-5578	286	3	-	-	ADJ
ejpam-5578	286	4	nearly	nearly	ADV
ejpam-5578	286	5	compact	compact	ADJ
ejpam-5578	286	6	space	space	NOUN
ejpam-5578	286	7	is	be	AUX
ejpam-5578	286	8	a	a	DET
ejpam-5578	286	9	tri	tri	ADJ
ejpam-5578	286	10	-	-	ADJ
ejpam-5578	286	11	nearly	nearly	ADV
ejpam-5578	286	12	lindelöf	lindelöf	NOUN
ejpam-5578	286	13	space	space	NOUN
ejpam-5578	286	14	,	,	PUNCT
ejpam-5578	286	15	but	but	CCONJ
ejpam-5578	286	16	the	the	DET
ejpam-5578	286	17	converse	converse	NOUN
ejpam-5578	286	18	need	need	AUX
ejpam-5578	286	19	not	not	PART
ejpam-5578	286	20	be	be	AUX
ejpam-5578	286	21	true	true	ADJ
ejpam-5578	286	22	.	.	PUNCT
ejpam-5578	287	1	proof	proof	NOUN
ejpam-5578	287	2	.	.	PUNCT
ejpam-5578	288	1	let	let	VERB
ejpam-5578	288	2	q	q	PRON
ejpam-5578	288	3	be	be	AUX
ejpam-5578	288	4	a	a	DET
ejpam-5578	288	5	tri	tri	ADJ
ejpam-5578	288	6	-	-	ADJ
ejpam-5578	288	7	nearly	nearly	ADV
ejpam-5578	288	8	compact	compact	ADJ
ejpam-5578	288	9	space	space	NOUN
ejpam-5578	288	10	.	.	PUNCT
ejpam-5578	289	1	by	by	ADP
ejpam-5578	289	2	definition	definition	NOUN
ejpam-5578	289	3	,	,	PUNCT
ejpam-5578	289	4	every	every	DET
ejpam-5578	289	5	tri	tri	ADJ
ejpam-5578	289	6	-	-	ADJ
ejpam-5578	289	7	nearly	nearly	ADV
ejpam-5578	289	8	open	open	ADJ
ejpam-5578	289	9	cover	cover	NOUN
ejpam-5578	289	10	of	of	ADP
ejpam-5578	289	11	q	q	PROPN
ejpam-5578	289	12	has	have	VERB
ejpam-5578	289	13	a	a	DET
ejpam-5578	289	14	finite	finite	NOUN
ejpam-5578	289	15	ϱj	ϱj	NOUN
ejpam-5578	289	16	-	-	NOUN
ejpam-5578	289	17	subcover	subcover	NOUN
ejpam-5578	289	18	of	of	ADP
ejpam-5578	289	19	q.	q.	PROPN
ejpam-5578	289	20	thus	thus	ADV
ejpam-5578	289	21	,	,	PUNCT
ejpam-5578	289	22	for	for	ADP
ejpam-5578	289	23	each	each	DET
ejpam-5578	289	24	tri	tri	ADJ
ejpam-5578	289	25	-	-	ADJ
ejpam-5578	289	26	nearly	nearly	ADV
ejpam-5578	289	27	open	open	ADJ
ejpam-5578	289	28	cover	cover	NOUN
ejpam-5578	289	29	on	on	ADP
ejpam-5578	289	30	q	q	NOUN
ejpam-5578	289	31	,	,	PUNCT
ejpam-5578	289	32	there	there	PRON
ejpam-5578	289	33	exists	exist	VERB
ejpam-5578	289	34	a	a	DET
ejpam-5578	289	35	countable	countable	ADJ
ejpam-5578	289	36	ϱj	ϱj	NOUN
ejpam-5578	289	37	-	-	NOUN
ejpam-5578	289	38	subcover	subcover	NOUN
ejpam-5578	289	39	of	of	ADP
ejpam-5578	289	40	q	q	PROPN
ejpam-5578	289	41	,	,	PUNCT
ejpam-5578	289	42	for	for	ADP
ejpam-5578	289	43	all	all	DET
ejpam-5578	289	44	i	i	PRON
ejpam-5578	289	45	̸=	̸=	PROPN
ejpam-5578	289	46	j	j	PROPN
ejpam-5578	289	47	,	,	PUNCT
ejpam-5578	289	48	where	where	SCONJ
ejpam-5578	289	49	i	i	PRON
ejpam-5578	289	50	,	,	PUNCT
ejpam-5578	289	51	j	j	PROPN
ejpam-5578	289	52	∈	∈	PROPN
ejpam-5578	289	53	{	{	PUNCT
ejpam-5578	289	54	1	1	NUM
ejpam-5578	289	55	,	,	PUNCT
ejpam-5578	289	56	2	2	NUM
ejpam-5578	289	57	,	,	PUNCT
ejpam-5578	289	58	3	3	NUM
ejpam-5578	289	59	}	}	PUNCT
ejpam-5578	289	60	.	.	PUNCT
ejpam-5578	290	1	therefore	therefore	ADV
ejpam-5578	290	2	,	,	PUNCT
ejpam-5578	290	3	q	q	X
ejpam-5578	290	4	is	be	AUX
ejpam-5578	290	5	a	a	DET
ejpam-5578	290	6	tri	tri	ADJ
ejpam-5578	290	7	-	-	ADJ
ejpam-5578	290	8	nearly	nearly	ADV
ejpam-5578	290	9	lindelöf	lindelöf	NOUN
ejpam-5578	290	10	space	space	NOUN
ejpam-5578	290	11	.	.	PUNCT
ejpam-5578	291	1	however	however	ADV
ejpam-5578	291	2	,	,	PUNCT
ejpam-5578	291	3	the	the	DET
ejpam-5578	291	4	converse	converse	NOUN
ejpam-5578	291	5	need	need	AUX
ejpam-5578	291	6	not	not	PART
ejpam-5578	291	7	be	be	AUX
ejpam-5578	291	8	true	true	ADJ
ejpam-5578	291	9	.	.	PUNCT
ejpam-5578	292	1	for	for	ADP
ejpam-5578	292	2	example	example	NOUN
ejpam-5578	292	3	,	,	PUNCT
ejpam-5578	292	4	the	the	DET
ejpam-5578	292	5	space	space	NOUN
ejpam-5578	292	6	(	(	PUNCT
ejpam-5578	292	7	r	r	NOUN
ejpam-5578	292	8	,	,	PUNCT
ejpam-5578	292	9	ϱu1	ϱu1	NOUN
ejpam-5578	292	10	,	,	PUNCT
ejpam-5578	292	11	ϱu2	ϱu2	NOUN
ejpam-5578	292	12	,	,	PUNCT
ejpam-5578	292	13	ϱu3	ϱu3	PROPN
ejpam-5578	292	14	)	)	PUNCT
ejpam-5578	292	15	is	be	AUX
ejpam-5578	292	16	a	a	DET
ejpam-5578	292	17	tri	tri	ADJ
ejpam-5578	292	18	-	-	ADJ
ejpam-5578	292	19	nearly	nearly	ADV
ejpam-5578	292	20	lindelöf	lindelöf	NOUN
ejpam-5578	292	21	space	space	NOUN
ejpam-5578	292	22	but	but	CCONJ
ejpam-5578	292	23	is	be	AUX
ejpam-5578	292	24	not	not	PART
ejpam-5578	292	25	a	a	DET
ejpam-5578	292	26	tri	tri	ADJ
ejpam-5578	292	27	-	-	ADJ
ejpam-5578	292	28	nearly	nearly	ADV
ejpam-5578	292	29	compact	compact	ADJ
ejpam-5578	292	30	space	space	NOUN
ejpam-5578	292	31	.	.	PUNCT
ejpam-5578	293	1	theorem	theorem	VERB
ejpam-5578	293	2	8	8	NUM
ejpam-5578	293	3	.	.	PUNCT
ejpam-5578	294	1	a	a	DET
ejpam-5578	294	2	tri	tri	ADJ
ejpam-5578	294	3	-	-	ADJ
ejpam-5578	294	4	nearly	nearly	ADV
ejpam-5578	294	5	lindelöf	lindelöf	NOUN
ejpam-5578	294	6	space	space	NOUN
ejpam-5578	294	7	is	be	AUX
ejpam-5578	294	8	preserved	preserve	VERB
ejpam-5578	294	9	under	under	ADP
ejpam-5578	294	10	an	an	PRON
ejpam-5578	294	11	onto	onto	ADP
ejpam-5578	294	12	tri	tri	ADJ
ejpam-5578	294	13	-	-	ADJ
ejpam-5578	294	14	continuous	continuous	ADJ
ejpam-5578	294	15	function	function	NOUN
ejpam-5578	294	16	.	.	PUNCT
ejpam-5578	295	1	proof	proof	NOUN
ejpam-5578	295	2	.	.	PUNCT
ejpam-5578	296	1	let	let	VERB
ejpam-5578	296	2	i	i	PRON
ejpam-5578	296	3	̸=	̸=	PROPN
ejpam-5578	296	4	j	j	PROPN
ejpam-5578	296	5	where	where	SCONJ
ejpam-5578	296	6	i	i	PRON
ejpam-5578	296	7	,	,	PUNCT
ejpam-5578	296	8	j	j	PROPN
ejpam-5578	296	9	∈	∈	PROPN
ejpam-5578	296	10	{	{	PUNCT
ejpam-5578	296	11	1	1	NUM
ejpam-5578	296	12	,	,	PUNCT
ejpam-5578	296	13	2	2	NUM
ejpam-5578	296	14	,	,	PUNCT
ejpam-5578	296	15	3	3	NUM
ejpam-5578	296	16	}	}	PUNCT
ejpam-5578	296	17	.	.	PUNCT
ejpam-5578	297	1	let	let	VERB
ejpam-5578	297	2	f	f	NOUN
ejpam-5578	297	3	:	:	PUNCT
ejpam-5578	297	4	(	(	PUNCT
ejpam-5578	297	5	q	q	ADJ
ejpam-5578	297	6	,	,	PUNCT
ejpam-5578	297	7	ϱ1	ϱ1	NOUN
ejpam-5578	297	8	,	,	PUNCT
ejpam-5578	297	9	ϱ2	ϱ2	NOUN
ejpam-5578	297	10	,	,	PUNCT
ejpam-5578	297	11	ϱ3	ϱ3	PROPN
ejpam-5578	297	12	)	)	PUNCT
ejpam-5578	297	13	→	→	SYM
ejpam-5578	297	14	(	(	PUNCT
ejpam-5578	297	15	y	y	PROPN
ejpam-5578	297	16	,	,	PUNCT
ejpam-5578	297	17	σ1	σ1	PROPN
ejpam-5578	297	18	,	,	PUNCT
ejpam-5578	297	19	σ2	σ2	PROPN
ejpam-5578	297	20	,	,	PUNCT
ejpam-5578	297	21	σ3	σ3	PROPN
ejpam-5578	297	22	)	)	PUNCT
ejpam-5578	297	23	be	be	AUX
ejpam-5578	297	24	a	a	DET
ejpam-5578	297	25	surjective	surjective	ADJ
ejpam-5578	297	26	continuous	continuous	ADJ
ejpam-5578	297	27	function	function	NOUN
ejpam-5578	297	28	,	,	PUNCT
ejpam-5578	297	29	and	and	CCONJ
ejpam-5578	297	30	suppose	suppose	VERB
ejpam-5578	297	31	that	that	SCONJ
ejpam-5578	297	32	q	q	NOUN
ejpam-5578	297	33	is	be	AUX
ejpam-5578	297	34	a	a	DET
ejpam-5578	297	35	tri	tri	ADJ
ejpam-5578	297	36	-	-	ADJ
ejpam-5578	297	37	nearly	nearly	ADV
ejpam-5578	297	38	lindelöf	lindelöf	NOUN
ejpam-5578	297	39	space	space	NOUN
ejpam-5578	297	40	.	.	PUNCT
ejpam-5578	298	1	we	we	PRON
ejpam-5578	298	2	aim	aim	VERB
ejpam-5578	298	3	to	to	PART
ejpam-5578	298	4	show	show	VERB
ejpam-5578	298	5	that	that	SCONJ
ejpam-5578	298	6	y	y	PROPN
ejpam-5578	298	7	is	be	AUX
ejpam-5578	298	8	also	also	ADV
ejpam-5578	298	9	a	a	DET
ejpam-5578	298	10	tri	tri	ADJ
ejpam-5578	298	11	-	-	ADJ
ejpam-5578	298	12	nearly	nearly	ADV
ejpam-5578	298	13	lindelöf	lindelöf	NOUN
ejpam-5578	298	14	space	space	NOUN
ejpam-5578	298	15	.	.	PUNCT
ejpam-5578	299	1	assume	assume	VERB
ejpam-5578	299	2	ũ	ũ	PROPN
ejpam-5578	300	1	=	=	X
ejpam-5578	300	2	{	{	PUNCT
ejpam-5578	300	3	uα	uα	PROPN
ejpam-5578	300	4	|	|	ADV
ejpam-5578	300	5	α	α	NOUN
ejpam-5578	300	6	∈	∈	PROPN
ejpam-5578	300	7	ϑ	ϑ	AUX
ejpam-5578	300	8	}	}	PUNCT
ejpam-5578	300	9	is	be	AUX
ejpam-5578	300	10	a	a	DET
ejpam-5578	300	11	nearly	nearly	ADV
ejpam-5578	300	12	ϑi	ϑi	NOUN
ejpam-5578	300	13	-	-	PUNCT
ejpam-5578	300	14	open	open	ADJ
ejpam-5578	300	15	cover	cover	NOUN
ejpam-5578	300	16	of	of	ADP
ejpam-5578	300	17	y	y	PROPN
ejpam-5578	300	18	,	,	PUNCT
ejpam-5578	300	19	meaning	mean	VERB
ejpam-5578	300	20	that	that	SCONJ
ejpam-5578	300	21	each	each	DET
ejpam-5578	300	22	uα	uα	PROPN
ejpam-5578	300	23	is	be	AUX
ejpam-5578	300	24	a	a	DET
ejpam-5578	300	25	tri	tri	ADJ
ejpam-5578	300	26	-	-	ADJ
ejpam-5578	300	27	open	open	ADJ
ejpam-5578	300	28	set	set	NOUN
ejpam-5578	300	29	for	for	ADP
ejpam-5578	300	30	all	all	DET
ejpam-5578	300	31	α	α	PRON
ejpam-5578	300	32	∈	∈	NOUN
ejpam-5578	300	33	ϑ.	ϑ.	NOUN
ejpam-5578	300	34	since	since	SCONJ
ejpam-5578	300	35	f	f	PROPN
ejpam-5578	300	36	is	be	AUX
ejpam-5578	300	37	continuous	continuous	ADJ
ejpam-5578	300	38	,	,	PUNCT
ejpam-5578	300	39	it	it	PRON
ejpam-5578	300	40	follows	follow	VERB
ejpam-5578	300	41	that	that	SCONJ
ejpam-5578	300	42	f−1(uα	f−1(uα	NOUN
ejpam-5578	300	43	)	)	PUNCT
ejpam-5578	300	44	is	be	AUX
ejpam-5578	300	45	a	a	DET
ejpam-5578	300	46	tri	tri	ADJ
ejpam-5578	300	47	-	-	ADJ
ejpam-5578	300	48	open	open	ADJ
ejpam-5578	300	49	set	set	NOUN
ejpam-5578	300	50	in	in	ADP
ejpam-5578	300	51	q	q	NOUN
ejpam-5578	300	52	for	for	ADP
ejpam-5578	300	53	each	each	DET
ejpam-5578	300	54	α	α	PROPN
ejpam-5578	300	55	∈	∈	PROPN
ejpam-5578	300	56	ϑ.	ϑ.	NOUN
ejpam-5578	300	57	additionally	additionally	ADV
ejpam-5578	300	58	,	,	PUNCT
ejpam-5578	300	59	since	since	SCONJ
ejpam-5578	300	60	f	f	PROPN
ejpam-5578	300	61	is	be	AUX
ejpam-5578	300	62	surjective	surjective	ADJ
ejpam-5578	300	63	,	,	PUNCT
ejpam-5578	300	64	we	we	PRON
ejpam-5578	300	65	obtain	obtain	VERB
ejpam-5578	300	66	:	:	PUNCT
ejpam-5578	300	67	f−1(ũ	f−1(ũ	NUM
ejpam-5578	300	68	)	)	PUNCT
ejpam-5578	300	69	=	=	PRON
ejpam-5578	300	70	{	{	PUNCT
ejpam-5578	300	71	f−1(uα	f−1(uα	PROPN
ejpam-5578	300	72	)	)	PUNCT
ejpam-5578	301	1	|	|	ADV
ejpam-5578	301	2	α	α	X
ejpam-5578	301	3	∈	∈	PROPN
ejpam-5578	301	4	ϑ	ϑ	X
ejpam-5578	301	5	}	}	PUNCT
ejpam-5578	301	6	j.	j.	PROPN
ejpam-5578	301	7	oudetallah	oudetallah	PROPN
ejpam-5578	301	8	et	et	PROPN
ejpam-5578	301	9	al	al	PROPN
ejpam-5578	301	10	.	.	PUNCT
ejpam-5578	301	11	/	/	SYM
ejpam-5578	301	12	eur	eur	PROPN
ejpam-5578	301	13	.	.	PUNCT
ejpam-5578	302	1	j.	j.	PROPN
ejpam-5578	302	2	pure	pure	PROPN
ejpam-5578	302	3	appl	appl	PROPN
ejpam-5578	302	4	.	.	PROPN
ejpam-5578	302	5	math	math	PROPN
ejpam-5578	302	6	,	,	PUNCT
ejpam-5578	302	7	18	18	NUM
ejpam-5578	302	8	(	(	PUNCT
ejpam-5578	302	9	2	2	NUM
ejpam-5578	302	10	)	)	PUNCT
ejpam-5578	302	11	(	(	PUNCT
ejpam-5578	302	12	2025	2025	NUM
ejpam-5578	302	13	)	)	PUNCT
ejpam-5578	302	14	,	,	PUNCT
ejpam-5578	302	15	5578	5578	NUM
ejpam-5578	302	16	14	14	NUM
ejpam-5578	302	17	of	of	ADP
ejpam-5578	302	18	19	19	NUM
ejpam-5578	302	19	which	which	PRON
ejpam-5578	302	20	forms	form	VERB
ejpam-5578	302	21	a	a	DET
ejpam-5578	302	22	tri	tri	ADJ
ejpam-5578	302	23	-	-	ADJ
ejpam-5578	302	24	open	open	ADJ
ejpam-5578	302	25	cover	cover	NOUN
ejpam-5578	302	26	of	of	ADP
ejpam-5578	302	27	q.	q.	NOUN
ejpam-5578	302	28	since	since	SCONJ
ejpam-5578	302	29	q	q	PROPN
ejpam-5578	302	30	is	be	AUX
ejpam-5578	302	31	tri	tri	ADJ
ejpam-5578	302	32	-	-	ADJ
ejpam-5578	302	33	nearly	nearly	ADV
ejpam-5578	302	34	lindelöf	lindelöf	NOUN
ejpam-5578	302	35	,	,	PUNCT
ejpam-5578	302	36	there	there	PRON
ejpam-5578	302	37	exists	exist	VERB
ejpam-5578	302	38	a	a	DET
ejpam-5578	302	39	countable	countable	ADJ
ejpam-5578	302	40	ϑi	ϑi	NOUN
ejpam-5578	302	41	-	-	PUNCT
ejpam-5578	302	42	subcover	subcover	PROPN
ejpam-5578	302	43	{	{	PUNCT
ejpam-5578	302	44	f−1(uα	f−1(uα	PROPN
ejpam-5578	302	45	)	)	PUNCT
ejpam-5578	303	1	|	|	ADV
ejpam-5578	303	2	α	α	PROPN
ejpam-5578	303	3	∈	∈	PROPN
ejpam-5578	303	4	σ	σ	PROPN
ejpam-5578	303	5	}	}	PUNCT
ejpam-5578	303	6	where	where	SCONJ
ejpam-5578	303	7	σ	σ	PROPN
ejpam-5578	303	8	⊆	⊆	PROPN
ejpam-5578	303	9	ϑ	ϑ	X
ejpam-5578	303	10	and	and	CCONJ
ejpam-5578	303	11	|σ|	|σ|	PROPN
ejpam-5578	303	12	≤	≤	PROPN
ejpam-5578	303	13	ℵ0	ℵ0	PROPN
ejpam-5578	303	14	.	.	PUNCT
ejpam-5578	304	1	thus	thus	ADV
ejpam-5578	304	2	,	,	PUNCT
ejpam-5578	304	3	we	we	PRON
ejpam-5578	304	4	have	have	VERB
ejpam-5578	304	5	:	:	PUNCT
ejpam-5578	304	6	q	q	X
ejpam-5578	305	1	⊆	⊆	NUM
ejpam-5578	305	2	⋃	⋃	ADP
ejpam-5578	305	3	α∈σ	α∈σ	NUM
ejpam-5578	305	4	f−1(uα	f−1(uα	NOUN
ejpam-5578	305	5	)	)	PUNCT
ejpam-5578	305	6	.	.	PUNCT
ejpam-5578	306	1	since	since	SCONJ
ejpam-5578	306	2	f	f	PROPN
ejpam-5578	306	3	is	be	AUX
ejpam-5578	306	4	onto	onto	ADP
ejpam-5578	306	5	,	,	PUNCT
ejpam-5578	306	6	it	it	PRON
ejpam-5578	306	7	follows	follow	VERB
ejpam-5578	306	8	that	that	SCONJ
ejpam-5578	306	9	:	:	PUNCT
ejpam-5578	306	10	y	y	X
ejpam-5578	306	11	=	=	SYM
ejpam-5578	306	12	f	f	PROPN
ejpam-5578	306	13	(	(	PUNCT
ejpam-5578	306	14	q	q	NOUN
ejpam-5578	306	15	)	)	PUNCT
ejpam-5578	306	16	⊆	⊆	NUM
ejpam-5578	306	17	f	f	NOUN
ejpam-5578	306	18	(	(	PUNCT
ejpam-5578	306	19	⋃	⋃	ADP
ejpam-5578	306	20	α∈σ	α∈σ	NUM
ejpam-5578	306	21	f−1(uα	f−1(uα	NOUN
ejpam-5578	306	22	)	)	PUNCT
ejpam-5578	306	23	)	)	PUNCT
ejpam-5578	307	1	⊆	⊆	NUM
ejpam-5578	307	2	⋃	⋃	ADP
ejpam-5578	307	3	α∈σ	α∈σ	NUM
ejpam-5578	307	4	uα	uα	NOUN
ejpam-5578	307	5	.	.	PUNCT
ejpam-5578	308	1	hence	hence	ADV
ejpam-5578	308	2	,	,	PUNCT
ejpam-5578	308	3	ũ	ũ	PROPN
ejpam-5578	308	4	has	have	VERB
ejpam-5578	308	5	a	a	DET
ejpam-5578	308	6	countable	countable	ADJ
ejpam-5578	308	7	ϑi	ϑi	NOUN
ejpam-5578	308	8	-	-	PUNCT
ejpam-5578	308	9	subcover	subcover	PROPN
ejpam-5578	308	10	of	of	ADP
ejpam-5578	308	11	y	y	PROPN
ejpam-5578	308	12	,	,	PUNCT
ejpam-5578	308	13	proving	prove	VERB
ejpam-5578	308	14	that	that	SCONJ
ejpam-5578	308	15	y	y	PROPN
ejpam-5578	308	16	is	be	AUX
ejpam-5578	308	17	a	a	DET
ejpam-5578	308	18	tri	tri	ADJ
ejpam-5578	308	19	-	-	ADJ
ejpam-5578	308	20	nearly	nearly	ADV
ejpam-5578	308	21	lindelöf	lindelöf	NOUN
ejpam-5578	308	22	space	space	NOUN
ejpam-5578	308	23	.	.	PUNCT
ejpam-5578	309	1	remark	remark	PROPN
ejpam-5578	309	2	4	4	NUM
ejpam-5578	309	3	.	.	PUNCT
ejpam-5578	310	1	a	a	DET
ejpam-5578	310	2	compact	compact	ADJ
ejpam-5578	310	3	subset	subset	NOUN
ejpam-5578	310	4	of	of	ADP
ejpam-5578	310	5	a	a	DET
ejpam-5578	310	6	tri	tri	ADJ
ejpam-5578	310	7	-	-	ADJ
ejpam-5578	310	8	nearly	nearly	ADV
ejpam-5578	310	9	t2	t2	NOUN
ejpam-5578	310	10	-	-	PUNCT
ejpam-5578	310	11	space	space	NOUN
ejpam-5578	310	12	is	be	AUX
ejpam-5578	310	13	closed	close	VERB
ejpam-5578	310	14	,	,	PUNCT
ejpam-5578	310	15	but	but	CCONJ
ejpam-5578	310	16	a	a	DET
ejpam-5578	310	17	tri	tri	ADJ
ejpam-5578	310	18	-	-	ADJ
ejpam-5578	310	19	nearly	nearly	ADV
ejpam-5578	310	20	lindelöf	lindelöf	NOUN
ejpam-5578	310	21	subset	subset	VERB
ejpam-5578	310	22	of	of	ADP
ejpam-5578	310	23	a	a	DET
ejpam-5578	310	24	tri	tri	ADJ
ejpam-5578	310	25	-	-	ADJ
ejpam-5578	310	26	nearly	nearly	ADV
ejpam-5578	310	27	t2	t2	NOUN
ejpam-5578	310	28	-	-	PUNCT
ejpam-5578	310	29	space	space	NOUN
ejpam-5578	310	30	need	need	AUX
ejpam-5578	310	31	not	not	PART
ejpam-5578	310	32	be	be	AUX
ejpam-5578	310	33	closed	close	VERB
ejpam-5578	310	34	.	.	PUNCT
ejpam-5578	311	1	definition	definition	NOUN
ejpam-5578	311	2	35	35	NUM
ejpam-5578	311	3	.	.	PUNCT
ejpam-5578	312	1	a	a	DET
ejpam-5578	312	2	space	space	NOUN
ejpam-5578	312	3	(	(	PUNCT
ejpam-5578	312	4	q	q	ADJ
ejpam-5578	312	5	,	,	PUNCT
ejpam-5578	312	6	ϱ1	ϱ1	NOUN
ejpam-5578	312	7	,	,	PUNCT
ejpam-5578	312	8	ϱ2	ϱ2	NOUN
ejpam-5578	312	9	,	,	PUNCT
ejpam-5578	312	10	ϱ3	ϱ3	PROPN
ejpam-5578	312	11	)	)	PUNCT
ejpam-5578	312	12	is	be	AUX
ejpam-5578	312	13	called	call	VERB
ejpam-5578	312	14	a	a	DET
ejpam-5578	312	15	tripartite	tripartite	ADJ
ejpam-5578	312	16	nearly	nearly	ADV
ejpam-5578	312	17	tri	tri	ADJ
ejpam-5578	312	18	-	-	NOUN
ejpam-5578	312	19	space	space	NOUN
ejpam-5578	312	20	if	if	SCONJ
ejpam-5578	312	21	the	the	DET
ejpam-5578	312	22	countable	countable	ADJ
ejpam-5578	312	23	intersection	intersection	NOUN
ejpam-5578	312	24	of	of	ADP
ejpam-5578	312	25	nearly	nearly	ADV
ejpam-5578	312	26	open	open	ADJ
ejpam-5578	312	27	sets	set	NOUN
ejpam-5578	312	28	is	be	AUX
ejpam-5578	312	29	open	open	ADJ
ejpam-5578	312	30	.	.	PUNCT
ejpam-5578	313	1	4	4	X
ejpam-5578	313	2	.	.	NOUN
ejpam-5578	313	3	metalindelöfness	metalindelöfness	NOUN
ejpam-5578	313	4	spaces	space	NOUN
ejpam-5578	313	5	in	in	ADP
ejpam-5578	313	6	tri	tri	ADJ
ejpam-5578	313	7	-	-	ADJ
ejpam-5578	313	8	topological	topological	ADJ
ejpam-5578	313	9	spaces	space	NOUN
ejpam-5578	313	10	in	in	ADP
ejpam-5578	313	11	this	this	DET
ejpam-5578	313	12	section	section	NOUN
ejpam-5578	313	13	,	,	PUNCT
ejpam-5578	313	14	we	we	PRON
ejpam-5578	313	15	explore	explore	VERB
ejpam-5578	313	16	the	the	DET
ejpam-5578	313	17	concept	concept	NOUN
ejpam-5578	313	18	of	of	ADP
ejpam-5578	313	19	locally	locally	ADV
ejpam-5578	313	20	tri	tri	NOUN
ejpam-5578	313	21	-	-	NOUN
ejpam-5578	313	22	metalindelöfness	metalindelöfness	NOUN
ejpam-5578	313	23	in	in	ADP
ejpam-5578	313	24	tri	tri	ADJ
ejpam-5578	313	25	-	-	ADJ
ejpam-5578	313	26	topological	topological	ADJ
ejpam-5578	313	27	spaces	space	NOUN
ejpam-5578	313	28	and	and	CCONJ
ejpam-5578	313	29	examine	examine	VERB
ejpam-5578	313	30	various	various	ADJ
ejpam-5578	313	31	fundamental	fundamental	ADJ
ejpam-5578	313	32	properties	property	NOUN
ejpam-5578	313	33	of	of	ADP
ejpam-5578	313	34	these	these	DET
ejpam-5578	313	35	spaces	space	NOUN
ejpam-5578	313	36	.	.	PUNCT
ejpam-5578	314	1	definition	definition	NOUN
ejpam-5578	314	2	36	36	NUM
ejpam-5578	314	3	.	.	PUNCT
ejpam-5578	315	1	a	a	DET
ejpam-5578	315	2	tri	tri	ADJ
ejpam-5578	315	3	-	-	ADJ
ejpam-5578	315	4	topological	topological	ADJ
ejpam-5578	315	5	space	space	NOUN
ejpam-5578	315	6	(	(	PUNCT
ejpam-5578	315	7	q	q	ADJ
ejpam-5578	315	8	,	,	PUNCT
ejpam-5578	315	9	ϱ1	ϱ1	NOUN
ejpam-5578	315	10	,	,	PUNCT
ejpam-5578	315	11	ϱ2	ϱ2	NOUN
ejpam-5578	315	12	,	,	PUNCT
ejpam-5578	315	13	ϱ3	ϱ3	PROPN
ejpam-5578	315	14	)	)	PUNCT
ejpam-5578	315	15	is	be	AUX
ejpam-5578	315	16	called	call	VERB
ejpam-5578	315	17	a	a	DET
ejpam-5578	315	18	tri	tri	ADJ
ejpam-5578	315	19	-	-	ADJ
ejpam-5578	315	20	metalindelöf	metalindelöf	ADJ
ejpam-5578	315	21	space	space	NOUN
ejpam-5578	315	22	if	if	SCONJ
ejpam-5578	315	23	every	every	DET
ejpam-5578	315	24	tri	tri	ADJ
ejpam-5578	315	25	-	-	ADJ
ejpam-5578	315	26	open	open	ADJ
ejpam-5578	315	27	cover	cover	NOUN
ejpam-5578	315	28	of	of	ADP
ejpam-5578	315	29	(	(	PUNCT
ejpam-5578	315	30	q	q	ADJ
ejpam-5578	315	31	,	,	PUNCT
ejpam-5578	315	32	ϱ1	ϱ1	NOUN
ejpam-5578	315	33	,	,	PUNCT
ejpam-5578	315	34	ϱ2	ϱ2	NOUN
ejpam-5578	315	35	,	,	PUNCT
ejpam-5578	315	36	ϱ3	ϱ3	PROPN
ejpam-5578	315	37	)	)	PUNCT
ejpam-5578	315	38	has	have	VERB
ejpam-5578	315	39	a	a	DET
ejpam-5578	315	40	point	point	NOUN
ejpam-5578	315	41	-	-	PUNCT
ejpam-5578	315	42	countable	countable	ADJ
ejpam-5578	315	43	parallel	parallel	ADJ
ejpam-5578	315	44	refinement	refinement	NOUN
ejpam-5578	315	45	.	.	PUNCT
ejpam-5578	316	1	theorem	theorem	VERB
ejpam-5578	316	2	9	9	NUM
ejpam-5578	316	3	.	.	PUNCT
ejpam-5578	317	1	a	a	DET
ejpam-5578	317	2	countable	countable	ADJ
ejpam-5578	317	3	tri	tri	ADJ
ejpam-5578	317	4	-	-	ADJ
ejpam-5578	317	5	metalindelöf	metalindelöf	ADJ
ejpam-5578	317	6	space	space	NOUN
ejpam-5578	317	7	is	be	AUX
ejpam-5578	317	8	a	a	DET
ejpam-5578	317	9	tri	tri	ADJ
ejpam-5578	317	10	-	-	ADJ
ejpam-5578	317	11	compact	compact	ADJ
ejpam-5578	317	12	space	space	NOUN
ejpam-5578	317	13	.	.	PUNCT
ejpam-5578	318	1	proof	proof	NOUN
ejpam-5578	318	2	.	.	PUNCT
ejpam-5578	319	1	let	let	VERB
ejpam-5578	319	2	q	q	PRON
ejpam-5578	319	3	be	be	AUX
ejpam-5578	319	4	a	a	DET
ejpam-5578	319	5	countable	countable	ADJ
ejpam-5578	319	6	tri	tri	ADJ
ejpam-5578	319	7	-	-	ADJ
ejpam-5578	319	8	metalindelöf	metalindelöf	ADJ
ejpam-5578	319	9	space	space	NOUN
ejpam-5578	319	10	,	,	PUNCT
ejpam-5578	319	11	and	and	CCONJ
ejpam-5578	319	12	let	let	VERB
ejpam-5578	319	13	u	u	PRON
ejpam-5578	319	14	be	be	AUX
ejpam-5578	319	15	an	an	DET
ejpam-5578	319	16	arbitrary	arbitrary	ADJ
ejpam-5578	319	17	triopen	triopen	NOUN
ejpam-5578	319	18	cover	cover	NOUN
ejpam-5578	319	19	of	of	ADP
ejpam-5578	319	20	q.	q.	NOUN
ejpam-5578	319	21	since	since	SCONJ
ejpam-5578	319	22	q	q	PROPN
ejpam-5578	319	23	is	be	AUX
ejpam-5578	319	24	tri	tri	ADJ
ejpam-5578	319	25	-	-	NOUN
ejpam-5578	319	26	metalindelöf	metalindelöf	NOUN
ejpam-5578	319	27	,	,	PUNCT
ejpam-5578	319	28	there	there	PRON
ejpam-5578	319	29	exists	exist	VERB
ejpam-5578	319	30	a	a	DET
ejpam-5578	319	31	point	point	NOUN
ejpam-5578	319	32	-	-	PUNCT
ejpam-5578	319	33	countable	countable	ADJ
ejpam-5578	319	34	refinement	refinement	NOUN
ejpam-5578	319	35	v	v	ADP
ejpam-5578	319	36	such	such	ADJ
ejpam-5578	319	37	that	that	SCONJ
ejpam-5578	319	38	each	each	DET
ejpam-5578	319	39	point	point	NOUN
ejpam-5578	319	40	in	in	ADP
ejpam-5578	319	41	q	q	NOUN
ejpam-5578	319	42	is	be	AUX
ejpam-5578	319	43	contained	contain	VERB
ejpam-5578	319	44	in	in	ADP
ejpam-5578	319	45	at	at	ADV
ejpam-5578	319	46	most	most	ADJ
ejpam-5578	319	47	countably	countably	ADV
ejpam-5578	319	48	many	many	ADJ
ejpam-5578	319	49	sets	set	NOUN
ejpam-5578	319	50	of	of	ADP
ejpam-5578	319	51	v.	v.	INTJ
ejpam-5578	319	52	since	since	SCONJ
ejpam-5578	319	53	q	q	PROPN
ejpam-5578	319	54	is	be	AUX
ejpam-5578	319	55	countable	countable	ADJ
ejpam-5578	319	56	,	,	PUNCT
ejpam-5578	319	57	v	v	ADP
ejpam-5578	319	58	itself	itself	PRON
ejpam-5578	319	59	must	must	AUX
ejpam-5578	319	60	be	be	AUX
ejpam-5578	319	61	countable	countable	ADJ
ejpam-5578	319	62	.	.	PUNCT
ejpam-5578	320	1	by	by	ADP
ejpam-5578	320	2	the	the	DET
ejpam-5578	320	3	lindelöf	lindelöf	NOUN
ejpam-5578	320	4	property	property	NOUN
ejpam-5578	320	5	of	of	ADP
ejpam-5578	320	6	v	v	NOUN
ejpam-5578	320	7	,	,	PUNCT
ejpam-5578	320	8	there	there	PRON
ejpam-5578	320	9	exists	exist	VERB
ejpam-5578	320	10	a	a	DET
ejpam-5578	320	11	countable	countable	ADJ
ejpam-5578	320	12	subcover	subcover	NOUN
ejpam-5578	320	13	of	of	ADP
ejpam-5578	320	14	u	u	PROPN
ejpam-5578	320	15	,	,	PUNCT
ejpam-5578	320	16	proving	prove	VERB
ejpam-5578	320	17	that	that	SCONJ
ejpam-5578	320	18	q	q	NOUN
ejpam-5578	320	19	is	be	AUX
ejpam-5578	320	20	tri	tri	ADJ
ejpam-5578	320	21	-	-	ADJ
ejpam-5578	320	22	compact	compact	ADJ
ejpam-5578	320	23	.	.	PUNCT
ejpam-5578	321	1	theorem	theorem	VERB
ejpam-5578	321	2	10	10	NUM
ejpam-5578	321	3	.	.	PUNCT
ejpam-5578	322	1	a	a	DET
ejpam-5578	322	2	separable	separable	ADJ
ejpam-5578	322	3	tri	tri	ADJ
ejpam-5578	322	4	-	-	ADJ
ejpam-5578	322	5	metalindelöf	metalindelöf	ADJ
ejpam-5578	322	6	space	space	NOUN
ejpam-5578	322	7	(	(	PUNCT
ejpam-5578	322	8	q	q	ADJ
ejpam-5578	322	9	,	,	PUNCT
ejpam-5578	322	10	ϱ1	ϱ1	NOUN
ejpam-5578	322	11	,	,	PUNCT
ejpam-5578	322	12	ϱ2	ϱ2	NOUN
ejpam-5578	322	13	,	,	PUNCT
ejpam-5578	322	14	ϱ3	ϱ3	PROPN
ejpam-5578	322	15	)	)	PUNCT
ejpam-5578	322	16	is	be	AUX
ejpam-5578	322	17	tri	tri	NOUN
ejpam-5578	322	18	-	-	NOUN
ejpam-5578	322	19	lindelöf	lindelöf	NOUN
ejpam-5578	322	20	.	.	PUNCT
ejpam-5578	323	1	proof	proof	NOUN
ejpam-5578	323	2	.	.	PUNCT
ejpam-5578	324	1	since	since	SCONJ
ejpam-5578	324	2	q	q	PROPN
ejpam-5578	324	3	is	be	AUX
ejpam-5578	324	4	separable	separable	ADJ
ejpam-5578	324	5	,	,	PUNCT
ejpam-5578	324	6	it	it	PRON
ejpam-5578	324	7	has	have	VERB
ejpam-5578	324	8	a	a	DET
ejpam-5578	324	9	countable	countable	ADJ
ejpam-5578	324	10	dense	dense	ADJ
ejpam-5578	324	11	subset	subset	NOUN
ejpam-5578	324	12	d.	d.	NOUN
ejpam-5578	324	13	given	give	VERB
ejpam-5578	324	14	any	any	DET
ejpam-5578	324	15	tri	tri	ADJ
ejpam-5578	324	16	-	-	ADJ
ejpam-5578	324	17	open	open	ADJ
ejpam-5578	324	18	cover	cover	NOUN
ejpam-5578	324	19	u	u	NOUN
ejpam-5578	324	20	of	of	ADP
ejpam-5578	324	21	q	q	NOUN
ejpam-5578	324	22	,	,	PUNCT
ejpam-5578	324	23	each	each	DET
ejpam-5578	324	24	point	point	NOUN
ejpam-5578	324	25	of	of	ADP
ejpam-5578	324	26	d	d	PROPN
ejpam-5578	324	27	is	be	AUX
ejpam-5578	324	28	contained	contain	VERB
ejpam-5578	324	29	in	in	ADP
ejpam-5578	324	30	at	at	ADV
ejpam-5578	324	31	most	most	ADJ
ejpam-5578	324	32	countably	countably	ADV
ejpam-5578	324	33	many	many	ADJ
ejpam-5578	324	34	sets	set	NOUN
ejpam-5578	324	35	of	of	ADP
ejpam-5578	324	36	a	a	DET
ejpam-5578	324	37	pointcountable	pointcountable	ADJ
ejpam-5578	324	38	refinement	refinement	NOUN
ejpam-5578	324	39	v	v	NOUN
ejpam-5578	324	40	due	due	ADP
ejpam-5578	324	41	to	to	ADP
ejpam-5578	324	42	the	the	DET
ejpam-5578	324	43	tri	tri	ADJ
ejpam-5578	324	44	-	-	ADJ
ejpam-5578	324	45	metalindelöf	metalindelöf	ADJ
ejpam-5578	324	46	property	property	NOUN
ejpam-5578	324	47	.	.	PUNCT
ejpam-5578	325	1	since	since	SCONJ
ejpam-5578	325	2	d	d	PROPN
ejpam-5578	325	3	is	be	AUX
ejpam-5578	325	4	countable	countable	ADJ
ejpam-5578	325	5	,	,	PUNCT
ejpam-5578	325	6	we	we	PRON
ejpam-5578	325	7	can	can	AUX
ejpam-5578	325	8	extract	extract	VERB
ejpam-5578	325	9	a	a	DET
ejpam-5578	325	10	countable	countable	ADJ
ejpam-5578	325	11	subcollection	subcollection	NOUN
ejpam-5578	325	12	v	v	ADP
ejpam-5578	325	13	′	′	NOUN
ejpam-5578	325	14	covering	cover	VERB
ejpam-5578	325	15	d.	d.	NOUN
ejpam-5578	325	16	the	the	DET
ejpam-5578	325	17	closure	closure	NOUN
ejpam-5578	325	18	of	of	ADP
ejpam-5578	325	19	d	d	NOUN
ejpam-5578	325	20	,	,	PUNCT
ejpam-5578	325	21	which	which	PRON
ejpam-5578	325	22	is	be	AUX
ejpam-5578	325	23	q	q	ADJ
ejpam-5578	325	24	,	,	PUNCT
ejpam-5578	325	25	is	be	AUX
ejpam-5578	325	26	covered	cover	VERB
ejpam-5578	325	27	by	by	ADP
ejpam-5578	325	28	v	v	NOUN
ejpam-5578	325	29	′	′	NUM
ejpam-5578	325	30	,	,	PUNCT
ejpam-5578	325	31	ensuring	ensure	VERB
ejpam-5578	325	32	a	a	DET
ejpam-5578	325	33	countable	countable	ADJ
ejpam-5578	325	34	subcover	subcover	NOUN
ejpam-5578	325	35	of	of	ADP
ejpam-5578	325	36	u	u	PROPN
ejpam-5578	325	37	.	.	PUNCT
ejpam-5578	326	1	thus	thus	ADV
ejpam-5578	326	2	,	,	PUNCT
ejpam-5578	326	3	q	q	PROPN
ejpam-5578	326	4	is	be	AUX
ejpam-5578	326	5	tri	tri	ADJ
ejpam-5578	326	6	-	-	NOUN
ejpam-5578	326	7	lindelöf	lindelöf	NOUN
ejpam-5578	326	8	.	.	PUNCT
ejpam-5578	327	1	j.	j.	PROPN
ejpam-5578	327	2	oudetallah	oudetallah	PROPN
ejpam-5578	327	3	et	et	PROPN
ejpam-5578	327	4	al	al	PROPN
ejpam-5578	327	5	.	.	PUNCT
ejpam-5578	327	6	/	/	SYM
ejpam-5578	327	7	eur	eur	PROPN
ejpam-5578	327	8	.	.	PUNCT
ejpam-5578	328	1	j.	j.	PROPN
ejpam-5578	328	2	pure	pure	PROPN
ejpam-5578	328	3	appl	appl	PROPN
ejpam-5578	328	4	.	.	PROPN
ejpam-5578	328	5	math	math	PROPN
ejpam-5578	328	6	,	,	PUNCT
ejpam-5578	328	7	18	18	NUM
ejpam-5578	328	8	(	(	PUNCT
ejpam-5578	328	9	2	2	NUM
ejpam-5578	328	10	)	)	PUNCT
ejpam-5578	328	11	(	(	PUNCT
ejpam-5578	328	12	2025	2025	NUM
ejpam-5578	328	13	)	)	PUNCT
ejpam-5578	328	14	,	,	PUNCT
ejpam-5578	328	15	5578	5578	NUM
ejpam-5578	328	16	15	15	NUM
ejpam-5578	328	17	of	of	ADP
ejpam-5578	328	18	19	19	NUM
ejpam-5578	328	19	definition	definition	NOUN
ejpam-5578	328	20	37	37	NUM
ejpam-5578	328	21	.	.	PUNCT
ejpam-5578	329	1	a	a	DET
ejpam-5578	329	2	tri	tri	ADJ
ejpam-5578	329	3	-	-	ADJ
ejpam-5578	329	4	topological	topological	ADJ
ejpam-5578	329	5	space	space	NOUN
ejpam-5578	329	6	(	(	PUNCT
ejpam-5578	329	7	q	q	ADJ
ejpam-5578	329	8	,	,	PUNCT
ejpam-5578	329	9	ϱ1	ϱ1	NOUN
ejpam-5578	329	10	,	,	PUNCT
ejpam-5578	329	11	ϱ2	ϱ2	NOUN
ejpam-5578	329	12	,	,	PUNCT
ejpam-5578	329	13	ϱ3	ϱ3	PROPN
ejpam-5578	329	14	)	)	PUNCT
ejpam-5578	329	15	is	be	AUX
ejpam-5578	329	16	called	call	VERB
ejpam-5578	329	17	tripartite	tripartite	ADJ
ejpam-5578	329	18	countably	countably	ADV
ejpam-5578	329	19	metalindelöf	metalindelöf	NOUN
ejpam-5578	329	20	if	if	SCONJ
ejpam-5578	329	21	every	every	DET
ejpam-5578	329	22	countable	countable	ADJ
ejpam-5578	329	23	tri	tri	ADJ
ejpam-5578	329	24	-	-	ADJ
ejpam-5578	329	25	open	open	ADJ
ejpam-5578	329	26	cover	cover	NOUN
ejpam-5578	329	27	of	of	ADP
ejpam-5578	329	28	(	(	PUNCT
ejpam-5578	329	29	q	q	ADJ
ejpam-5578	329	30	,	,	PUNCT
ejpam-5578	329	31	ϱ1	ϱ1	NOUN
ejpam-5578	329	32	,	,	PUNCT
ejpam-5578	329	33	ϱ2	ϱ2	NOUN
ejpam-5578	329	34	,	,	PUNCT
ejpam-5578	329	35	ϱ3	ϱ3	PROPN
ejpam-5578	329	36	)	)	PUNCT
ejpam-5578	329	37	has	have	VERB
ejpam-5578	329	38	a	a	DET
ejpam-5578	329	39	point	point	NOUN
ejpam-5578	329	40	-	-	PUNCT
ejpam-5578	329	41	countable	countable	ADJ
ejpam-5578	329	42	parallel	parallel	ADJ
ejpam-5578	329	43	refinement	refinement	NOUN
ejpam-5578	329	44	.	.	PUNCT
ejpam-5578	330	1	theorem	theorem	VERB
ejpam-5578	330	2	11	11	NUM
ejpam-5578	330	3	.	.	PUNCT
ejpam-5578	331	1	the	the	DET
ejpam-5578	331	2	tri	tri	ADJ
ejpam-5578	331	3	-	-	ADJ
ejpam-5578	331	4	topological	topological	ADJ
ejpam-5578	331	5	space	space	NOUN
ejpam-5578	331	6	(	(	PUNCT
ejpam-5578	331	7	q	q	ADJ
ejpam-5578	331	8	,	,	PUNCT
ejpam-5578	331	9	ϱ1	ϱ1	NOUN
ejpam-5578	331	10	,	,	PUNCT
ejpam-5578	331	11	ϱ2	ϱ2	NOUN
ejpam-5578	331	12	,	,	PUNCT
ejpam-5578	331	13	ϱ3	ϱ3	PROPN
ejpam-5578	331	14	)	)	PUNCT
ejpam-5578	331	15	is	be	AUX
ejpam-5578	331	16	a	a	DET
ejpam-5578	331	17	tri	tri	ADJ
ejpam-5578	331	18	-	-	ADJ
ejpam-5578	331	19	metalindelöf	metalindelöf	ADJ
ejpam-5578	331	20	space	space	NOUN
ejpam-5578	331	21	.	.	PUNCT
ejpam-5578	332	1	it	it	PRON
ejpam-5578	332	2	is	be	AUX
ejpam-5578	332	3	also	also	ADV
ejpam-5578	332	4	tripartite	tripartite	ADJ
ejpam-5578	332	5	countably	countably	ADV
ejpam-5578	332	6	metacompact	metacompact	ADJ
ejpam-5578	332	7	.	.	PUNCT
ejpam-5578	333	1	proof	proof	NOUN
ejpam-5578	333	2	.	.	PUNCT
ejpam-5578	334	1	since	since	SCONJ
ejpam-5578	334	2	(	(	PUNCT
ejpam-5578	334	3	q	q	ADJ
ejpam-5578	334	4	,	,	PUNCT
ejpam-5578	334	5	ϱ1	ϱ1	NOUN
ejpam-5578	334	6	,	,	PUNCT
ejpam-5578	334	7	ϱ2	ϱ2	NOUN
ejpam-5578	334	8	,	,	PUNCT
ejpam-5578	334	9	ϱ3	ϱ3	PROPN
ejpam-5578	334	10	)	)	PUNCT
ejpam-5578	334	11	is	be	AUX
ejpam-5578	334	12	tri	tri	ADJ
ejpam-5578	334	13	-	-	NOUN
ejpam-5578	334	14	metalindelöf	metalindelöf	NOUN
ejpam-5578	334	15	,	,	PUNCT
ejpam-5578	334	16	every	every	DET
ejpam-5578	334	17	open	open	ADJ
ejpam-5578	334	18	cover	cover	NOUN
ejpam-5578	334	19	of	of	ADP
ejpam-5578	334	20	q	q	PROPN
ejpam-5578	334	21	has	have	VERB
ejpam-5578	334	22	a	a	DET
ejpam-5578	334	23	pointcountable	pointcountable	ADJ
ejpam-5578	334	24	open	open	ADJ
ejpam-5578	334	25	refinement	refinement	NOUN
ejpam-5578	334	26	.	.	PUNCT
ejpam-5578	335	1	to	to	PART
ejpam-5578	335	2	show	show	VERB
ejpam-5578	335	3	that	that	SCONJ
ejpam-5578	335	4	it	it	PRON
ejpam-5578	335	5	is	be	AUX
ejpam-5578	335	6	also	also	ADV
ejpam-5578	335	7	tripartite	tripartite	ADJ
ejpam-5578	335	8	countably	countably	ADV
ejpam-5578	335	9	metacompact	metacompact	ADJ
ejpam-5578	335	10	,	,	PUNCT
ejpam-5578	335	11	let	let	VERB
ejpam-5578	335	12	u	u	PRON
ejpam-5578	335	13	be	be	AUX
ejpam-5578	335	14	a	a	DET
ejpam-5578	335	15	countable	countable	ADJ
ejpam-5578	335	16	open	open	ADJ
ejpam-5578	335	17	cover	cover	NOUN
ejpam-5578	335	18	of	of	ADP
ejpam-5578	335	19	q.	q.	NOUN
ejpam-5578	335	20	by	by	ADP
ejpam-5578	335	21	the	the	DET
ejpam-5578	335	22	tri	tri	ADJ
ejpam-5578	335	23	-	-	ADJ
ejpam-5578	335	24	metalindelöf	metalindelöf	ADJ
ejpam-5578	335	25	property	property	NOUN
ejpam-5578	335	26	,	,	PUNCT
ejpam-5578	335	27	there	there	PRON
ejpam-5578	335	28	exists	exist	VERB
ejpam-5578	335	29	a	a	DET
ejpam-5578	335	30	pointcountable	pointcountable	ADJ
ejpam-5578	335	31	refinement	refinement	NOUN
ejpam-5578	335	32	v	v	NOUN
ejpam-5578	335	33	of	of	ADP
ejpam-5578	335	34	u	u	PROPN
ejpam-5578	335	35	,	,	PUNCT
ejpam-5578	335	36	meaning	mean	VERB
ejpam-5578	335	37	each	each	DET
ejpam-5578	335	38	point	point	NOUN
ejpam-5578	335	39	of	of	ADP
ejpam-5578	335	40	q	q	NOUN
ejpam-5578	335	41	is	be	AUX
ejpam-5578	335	42	contained	contain	VERB
ejpam-5578	335	43	in	in	ADP
ejpam-5578	335	44	at	at	ADV
ejpam-5578	335	45	most	most	ADJ
ejpam-5578	335	46	countably	countably	ADV
ejpam-5578	335	47	many	many	ADJ
ejpam-5578	335	48	sets	set	NOUN
ejpam-5578	335	49	of	of	ADP
ejpam-5578	335	50	v.	v.	ADV
ejpam-5578	335	51	since	since	SCONJ
ejpam-5578	335	52	v	v	NOUN
ejpam-5578	335	53	is	be	AUX
ejpam-5578	335	54	countable	countable	ADJ
ejpam-5578	335	55	,	,	PUNCT
ejpam-5578	335	56	we	we	PRON
ejpam-5578	335	57	can	can	AUX
ejpam-5578	335	58	extract	extract	VERB
ejpam-5578	335	59	a	a	DET
ejpam-5578	335	60	countable	countable	ADJ
ejpam-5578	335	61	subcover	subcover	NOUN
ejpam-5578	335	62	from	from	ADP
ejpam-5578	335	63	u	u	PROPN
ejpam-5578	335	64	,	,	PUNCT
ejpam-5578	335	65	proving	prove	VERB
ejpam-5578	335	66	that	that	PRON
ejpam-5578	335	67	q	q	NOUN
ejpam-5578	335	68	is	be	AUX
ejpam-5578	335	69	tripartite	tripartite	ADJ
ejpam-5578	335	70	countably	countably	ADV
ejpam-5578	335	71	metacompact	metacompact	ADJ
ejpam-5578	335	72	.	.	PUNCT
ejpam-5578	336	1	theorem	theorem	VERB
ejpam-5578	336	2	12	12	NUM
ejpam-5578	336	3	.	.	PUNCT
ejpam-5578	337	1	every	every	DET
ejpam-5578	337	2	tri	tri	PROPN
ejpam-5578	337	3	-	-	NOUN
ejpam-5578	337	4	lindelöf	lindelöf	NOUN
ejpam-5578	337	5	tripartite	tripartite	ADJ
ejpam-5578	337	6	countably	countably	ADV
ejpam-5578	337	7	metacompact	metacompact	ADJ
ejpam-5578	337	8	space	space	NOUN
ejpam-5578	337	9	(	(	PUNCT
ejpam-5578	337	10	q	q	NOUN
ejpam-5578	337	11	,	,	PUNCT
ejpam-5578	337	12	ϱ1	ϱ1	NOUN
ejpam-5578	337	13	,	,	PUNCT
ejpam-5578	337	14	ϱ2	ϱ2	NOUN
ejpam-5578	337	15	,	,	PUNCT
ejpam-5578	337	16	ϱ3	ϱ3	PROPN
ejpam-5578	337	17	)	)	PUNCT
ejpam-5578	337	18	is	be	AUX
ejpam-5578	337	19	a	a	DET
ejpam-5578	337	20	tri	tri	ADJ
ejpam-5578	337	21	-	-	ADJ
ejpam-5578	337	22	metalindelöf	metalindelöf	ADJ
ejpam-5578	337	23	space	space	NOUN
ejpam-5578	337	24	.	.	PUNCT
ejpam-5578	338	1	proof	proof	NOUN
ejpam-5578	338	2	.	.	PUNCT
ejpam-5578	339	1	let	let	VERB
ejpam-5578	339	2	ũ	ũ	PROPN
ejpam-5578	339	3	=	=	PRON
ejpam-5578	339	4	{	{	PUNCT
ejpam-5578	339	5	uα	uα	PROPN
ejpam-5578	339	6	|	|	ADV
ejpam-5578	339	7	α	α	NOUN
ejpam-5578	339	8	∈	∈	NOUN
ejpam-5578	339	9	∆	∆	X
ejpam-5578	339	10	}	}	PUNCT
ejpam-5578	339	11	be	be	AUX
ejpam-5578	339	12	a	a	DET
ejpam-5578	339	13	tri	tri	ADJ
ejpam-5578	339	14	-	-	ADJ
ejpam-5578	339	15	open	open	ADJ
ejpam-5578	339	16	cover	cover	NOUN
ejpam-5578	339	17	of	of	ADP
ejpam-5578	339	18	q.	q.	NOUN
ejpam-5578	339	19	since	since	SCONJ
ejpam-5578	339	20	q	q	PROPN
ejpam-5578	339	21	is	be	AUX
ejpam-5578	339	22	tri	tri	NOUN
ejpam-5578	339	23	-	-	NOUN
ejpam-5578	339	24	lindelöf	lindelöf	NOUN
ejpam-5578	339	25	,	,	PUNCT
ejpam-5578	339	26	there	there	PRON
ejpam-5578	339	27	exists	exist	VERB
ejpam-5578	339	28	a	a	DET
ejpam-5578	339	29	tripartite	tripartite	ADJ
ejpam-5578	339	30	countable	countable	ADJ
ejpam-5578	339	31	subcover	subcover	NOUN
ejpam-5578	339	32	,	,	PUNCT
ejpam-5578	339	33	say	say	VERB
ejpam-5578	339	34	ã	ã	PROPN
ejpam-5578	339	35	=	=	PRON
ejpam-5578	339	36	{	{	PUNCT
ejpam-5578	339	37	aαi}∞i=1	aαi}∞i=1	PROPN
ejpam-5578	339	38	.	.	PUNCT
ejpam-5578	340	1	furthermore	furthermore	ADV
ejpam-5578	340	2	,	,	PUNCT
ejpam-5578	340	3	since	since	SCONJ
ejpam-5578	340	4	q	q	NOUN
ejpam-5578	340	5	is	be	AUX
ejpam-5578	340	6	tripartite	tripartite	ADJ
ejpam-5578	340	7	countably	countably	ADV
ejpam-5578	340	8	metacompact	metacompact	ADJ
ejpam-5578	340	9	,	,	PUNCT
ejpam-5578	340	10	the	the	DET
ejpam-5578	340	11	subcover	subcover	PROPN
ejpam-5578	340	12	ã	ã	PROPN
ejpam-5578	340	13	has	have	VERB
ejpam-5578	340	14	a	a	DET
ejpam-5578	340	15	pointcountable	pointcountable	ADJ
ejpam-5578	340	16	parallel	parallel	NOUN
ejpam-5578	340	17	refinement	refinement	NOUN
ejpam-5578	340	18	ǧ	ǧ	PROPN
ejpam-5578	340	19	of	of	ADP
ejpam-5578	340	20	ũ	ũ	PROPN
ejpam-5578	340	21	.	.	PUNCT
ejpam-5578	341	1	hence	hence	ADV
ejpam-5578	341	2	,	,	PUNCT
ejpam-5578	341	3	(	(	PUNCT
ejpam-5578	341	4	q	q	ADJ
ejpam-5578	341	5	,	,	PUNCT
ejpam-5578	341	6	ϱ1	ϱ1	NOUN
ejpam-5578	341	7	,	,	PUNCT
ejpam-5578	341	8	ϱ2	ϱ2	NOUN
ejpam-5578	341	9	,	,	PUNCT
ejpam-5578	341	10	ϱ3	ϱ3	PROPN
ejpam-5578	341	11	)	)	PUNCT
ejpam-5578	341	12	is	be	AUX
ejpam-5578	341	13	a	a	DET
ejpam-5578	341	14	tri	tri	ADJ
ejpam-5578	341	15	-	-	ADJ
ejpam-5578	341	16	metalindelöf	metalindelöf	ADJ
ejpam-5578	341	17	space	space	NOUN
ejpam-5578	341	18	.	.	PUNCT
ejpam-5578	342	1	theorem	theorem	VERB
ejpam-5578	342	2	13	13	NUM
ejpam-5578	342	3	.	.	PUNCT
ejpam-5578	343	1	every	every	DET
ejpam-5578	343	2	tri	tri	NOUN
ejpam-5578	343	3	-	-	ADJ
ejpam-5578	343	4	metalindelöf	metalindelöf	ADJ
ejpam-5578	343	5	countably	countably	ADV
ejpam-5578	343	6	metacompact	metacompact	ADJ
ejpam-5578	343	7	space	space	NOUN
ejpam-5578	343	8	(	(	PUNCT
ejpam-5578	343	9	q	q	NOUN
ejpam-5578	343	10	,	,	PUNCT
ejpam-5578	343	11	ϱ1	ϱ1	NOUN
ejpam-5578	343	12	,	,	PUNCT
ejpam-5578	343	13	ϱ2	ϱ2	NOUN
ejpam-5578	343	14	,	,	PUNCT
ejpam-5578	343	15	ϱ3	ϱ3	PROPN
ejpam-5578	343	16	)	)	PUNCT
ejpam-5578	343	17	is	be	AUX
ejpam-5578	343	18	a	a	DET
ejpam-5578	343	19	trimetacompact	trimetacompact	NOUN
ejpam-5578	343	20	space	space	NOUN
ejpam-5578	343	21	.	.	PUNCT
ejpam-5578	344	1	proof	proof	NOUN
ejpam-5578	344	2	.	.	PUNCT
ejpam-5578	345	1	let	let	VERB
ejpam-5578	345	2	(	(	PUNCT
ejpam-5578	345	3	q	q	ADJ
ejpam-5578	345	4	,	,	PUNCT
ejpam-5578	345	5	ϱ1	ϱ1	NOUN
ejpam-5578	345	6	,	,	PUNCT
ejpam-5578	345	7	ϱ2	ϱ2	NOUN
ejpam-5578	345	8	,	,	PUNCT
ejpam-5578	345	9	ϱ3	ϱ3	PROPN
ejpam-5578	345	10	)	)	PUNCT
ejpam-5578	345	11	be	be	AUX
ejpam-5578	345	12	a	a	DET
ejpam-5578	345	13	tri	tri	ADJ
ejpam-5578	345	14	-	-	ADJ
ejpam-5578	345	15	metalindelöf	metalindelöf	ADJ
ejpam-5578	345	16	countably	countably	ADV
ejpam-5578	345	17	metacompact	metacompact	ADJ
ejpam-5578	345	18	space	space	NOUN
ejpam-5578	345	19	.	.	PUNCT
ejpam-5578	346	1	by	by	ADP
ejpam-5578	346	2	the	the	DET
ejpam-5578	346	3	tri	tri	ADJ
ejpam-5578	346	4	-	-	ADJ
ejpam-5578	346	5	metalindelöf	metalindelöf	ADJ
ejpam-5578	346	6	property	property	NOUN
ejpam-5578	346	7	,	,	PUNCT
ejpam-5578	346	8	for	for	ADP
ejpam-5578	346	9	each	each	DET
ejpam-5578	346	10	i	i	PRON
ejpam-5578	346	11	∈	∈	PROPN
ejpam-5578	346	12	{	{	PUNCT
ejpam-5578	346	13	1	1	NUM
ejpam-5578	346	14	,	,	PUNCT
ejpam-5578	346	15	2	2	NUM
ejpam-5578	346	16	,	,	PUNCT
ejpam-5578	346	17	3	3	NUM
ejpam-5578	346	18	}	}	PUNCT
ejpam-5578	346	19	,	,	PUNCT
ejpam-5578	346	20	for	for	ADP
ejpam-5578	346	21	any	any	DET
ejpam-5578	346	22	open	open	ADJ
ejpam-5578	346	23	cover	cover	NOUN
ejpam-5578	346	24	ui	ui	NOUN
ejpam-5578	346	25	of	of	ADP
ejpam-5578	346	26	q	q	PROPN
ejpam-5578	346	27	,	,	PUNCT
ejpam-5578	346	28	there	there	PRON
ejpam-5578	346	29	exists	exist	VERB
ejpam-5578	346	30	a	a	DET
ejpam-5578	346	31	countable	countable	ADJ
ejpam-5578	346	32	subcover	subcover	NOUN
ejpam-5578	346	33	uc	uc	PROPN
ejpam-5578	346	34	i	i	PROPN
ejpam-5578	346	35	⊆	⊆	NUM
ejpam-5578	346	36	ui	ui	NOUN
ejpam-5578	346	37	.	.	PUNCT
ejpam-5578	347	1	by	by	ADP
ejpam-5578	347	2	countable	countable	ADJ
ejpam-5578	347	3	metacompactness	metacompactness	NOUN
ejpam-5578	347	4	,	,	PUNCT
ejpam-5578	347	5	for	for	ADP
ejpam-5578	347	6	each	each	DET
ejpam-5578	347	7	i	i	PRON
ejpam-5578	347	8	∈	∈	PROPN
ejpam-5578	347	9	{	{	PUNCT
ejpam-5578	347	10	1	1	NUM
ejpam-5578	347	11	,	,	PUNCT
ejpam-5578	347	12	2	2	NUM
ejpam-5578	347	13	,	,	PUNCT
ejpam-5578	347	14	3	3	NUM
ejpam-5578	347	15	}	}	PUNCT
ejpam-5578	347	16	,	,	PUNCT
ejpam-5578	347	17	for	for	ADP
ejpam-5578	347	18	the	the	DET
ejpam-5578	347	19	subcover	subcover	NOUN
ejpam-5578	348	1	uc	uc	PROPN
ejpam-5578	348	2	i	i	PRON
ejpam-5578	348	3	,	,	PUNCT
ejpam-5578	348	4	there	there	PRON
ejpam-5578	348	5	exists	exist	VERB
ejpam-5578	348	6	a	a	DET
ejpam-5578	348	7	countable	countable	ADJ
ejpam-5578	348	8	subcover	subcover	NOUN
ejpam-5578	348	9	vi	vi	PROPN
ejpam-5578	349	1	⊆	⊆	NUM
ejpam-5578	349	2	uc	uc	PROPN
ejpam-5578	349	3	i	i	PRON
ejpam-5578	349	4	such	such	ADJ
ejpam-5578	349	5	that	that	PRON
ejpam-5578	349	6	for	for	ADP
ejpam-5578	349	7	each	each	DET
ejpam-5578	349	8	point	point	NOUN
ejpam-5578	349	9	x	x	X
ejpam-5578	349	10	∈	∈	PROPN
ejpam-5578	349	11	q	q	NOUN
ejpam-5578	349	12	,	,	PUNCT
ejpam-5578	349	13	there	there	PRON
ejpam-5578	349	14	exists	exist	VERB
ejpam-5578	349	15	a	a	DET
ejpam-5578	349	16	neighborhood	neighborhood	NOUN
ejpam-5578	349	17	nx	nx	X
ejpam-5578	349	18	of	of	ADP
ejpam-5578	349	19	x	x	PRON
ejpam-5578	349	20	that	that	PRON
ejpam-5578	349	21	intersects	intersect	VERB
ejpam-5578	349	22	only	only	ADV
ejpam-5578	349	23	finitely	finitely	ADV
ejpam-5578	349	24	many	many	ADJ
ejpam-5578	349	25	sets	set	NOUN
ejpam-5578	349	26	of	of	ADP
ejpam-5578	349	27	vi	vi	NOUN
ejpam-5578	349	28	.	.	PUNCT
ejpam-5578	350	1	therefore	therefore	ADV
ejpam-5578	350	2	,	,	PUNCT
ejpam-5578	350	3	(	(	PUNCT
ejpam-5578	350	4	q	q	ADJ
ejpam-5578	350	5	,	,	PUNCT
ejpam-5578	350	6	ϱ1	ϱ1	NOUN
ejpam-5578	350	7	,	,	PUNCT
ejpam-5578	350	8	ϱ2	ϱ2	NOUN
ejpam-5578	350	9	,	,	PUNCT
ejpam-5578	350	10	ϱ3	ϱ3	PROPN
ejpam-5578	350	11	)	)	PUNCT
ejpam-5578	350	12	is	be	AUX
ejpam-5578	350	13	tri	tri	ADJ
ejpam-5578	350	14	-	-	ADJ
ejpam-5578	350	15	metacompact	metacompact	ADJ
ejpam-5578	350	16	.	.	PUNCT
ejpam-5578	350	17	example	example	NOUN
ejpam-5578	351	1	2	2	NUM
ejpam-5578	351	2	.	.	PUNCT
ejpam-5578	351	3	the	the	DET
ejpam-5578	351	4	tri	tri	ADJ
ejpam-5578	351	5	-	-	ADJ
ejpam-5578	351	6	topological	topological	ADJ
ejpam-5578	351	7	space	space	NOUN
ejpam-5578	351	8	(	(	PUNCT
ejpam-5578	351	9	r	r	NOUN
ejpam-5578	351	10	,	,	PUNCT
ejpam-5578	351	11	ϱdis	ϱdi	NOUN
ejpam-5578	351	12	,	,	PUNCT
ejpam-5578	351	13	ϱdis	ϱdi	NOUN
ejpam-5578	351	14	,	,	PUNCT
ejpam-5578	351	15	ϱdis	ϱdi	NOUN
ejpam-5578	351	16	)	)	PUNCT
ejpam-5578	351	17	is	be	AUX
ejpam-5578	351	18	tri	tri	ADJ
ejpam-5578	351	19	-	-	NOUN
ejpam-5578	351	20	metalindelöf	metalindelöf	NOUN
ejpam-5578	351	21	since	since	SCONJ
ejpam-5578	351	22	ϱdis(i	ϱdis(i	NOUN
ejpam-5578	351	23	)	)	PUNCT
ejpam-5578	351	24	forms	form	VERB
ejpam-5578	351	25	a	a	DET
ejpam-5578	351	26	tri	tri	ADJ
ejpam-5578	351	27	-	-	ADJ
ejpam-5578	351	28	open	open	ADJ
ejpam-5578	351	29	cover	cover	NOUN
ejpam-5578	351	30	v	v	NOUN
ejpam-5578	351	31	=	=	SYM
ejpam-5578	351	32	{	{	PUNCT
ejpam-5578	351	33	{	{	PUNCT
ejpam-5578	351	34	x	x	NOUN
ejpam-5578	351	35	}	}	PUNCT
ejpam-5578	352	1	|	|	ADV
ejpam-5578	352	2	x	x	SYM
ejpam-5578	352	3	∈	∈	NOUN
ejpam-5578	352	4	r	r	NOUN
ejpam-5578	352	5	}	}	PUNCT
ejpam-5578	352	6	of	of	ADP
ejpam-5578	352	7	r.	r.	PROPN
ejpam-5578	352	8	it	it	PRON
ejpam-5578	352	9	is	be	AUX
ejpam-5578	352	10	also	also	ADV
ejpam-5578	352	11	tripartite	tripartite	ADJ
ejpam-5578	352	12	countably	countably	ADV
ejpam-5578	352	13	metacompact	metacompact	ADJ
ejpam-5578	352	14	.	.	PUNCT
ejpam-5578	353	1	clearly	clearly	ADV
ejpam-5578	353	2	,	,	PUNCT
ejpam-5578	353	3	(	(	PUNCT
ejpam-5578	353	4	r	r	NOUN
ejpam-5578	353	5	,	,	PUNCT
ejpam-5578	353	6	ϱdis	ϱdi	NOUN
ejpam-5578	353	7	,	,	PUNCT
ejpam-5578	353	8	ϱdis	ϱdi	NOUN
ejpam-5578	353	9	,	,	PUNCT
ejpam-5578	353	10	ϱdis	ϱdi	NOUN
ejpam-5578	353	11	)	)	PUNCT
ejpam-5578	353	12	is	be	AUX
ejpam-5578	353	13	a	a	DET
ejpam-5578	353	14	trimetalindelöf	trimetalindelöf	NOUN
ejpam-5578	353	15	space	space	NOUN
ejpam-5578	353	16	.	.	PUNCT
ejpam-5578	354	1	theorem	theorem	VERB
ejpam-5578	354	2	14	14	NUM
ejpam-5578	354	3	.	.	PUNCT
ejpam-5578	355	1	every	every	DET
ejpam-5578	355	2	tripartite	tripartite	ADJ
ejpam-5578	355	3	countably	countably	ADV
ejpam-5578	355	4	metacompact	metacompact	ADJ
ejpam-5578	355	5	topological	topological	ADJ
ejpam-5578	355	6	space	space	NOUN
ejpam-5578	355	7	(	(	PUNCT
ejpam-5578	355	8	q	q	ADJ
ejpam-5578	355	9	,	,	PUNCT
ejpam-5578	355	10	ϱ1	ϱ1	NOUN
ejpam-5578	355	11	,	,	PUNCT
ejpam-5578	355	12	ϱ2	ϱ2	NOUN
ejpam-5578	355	13	,	,	PUNCT
ejpam-5578	355	14	ϱ3	ϱ3	PROPN
ejpam-5578	355	15	)	)	PUNCT
ejpam-5578	355	16	is	be	AUX
ejpam-5578	355	17	tri	tri	ADJ
ejpam-5578	355	18	-	-	ADJ
ejpam-5578	355	19	compact	compact	ADJ
ejpam-5578	355	20	.	.	PUNCT
ejpam-5578	356	1	j.	j.	PROPN
ejpam-5578	356	2	oudetallah	oudetallah	PROPN
ejpam-5578	356	3	et	et	PROPN
ejpam-5578	356	4	al	al	PROPN
ejpam-5578	356	5	.	.	PUNCT
ejpam-5578	356	6	/	/	SYM
ejpam-5578	356	7	eur	eur	PROPN
ejpam-5578	356	8	.	.	PUNCT
ejpam-5578	357	1	j.	j.	PROPN
ejpam-5578	357	2	pure	pure	PROPN
ejpam-5578	357	3	appl	appl	PROPN
ejpam-5578	357	4	.	.	PROPN
ejpam-5578	357	5	math	math	PROPN
ejpam-5578	357	6	,	,	PUNCT
ejpam-5578	357	7	18	18	NUM
ejpam-5578	357	8	(	(	PUNCT
ejpam-5578	357	9	2	2	NUM
ejpam-5578	357	10	)	)	PUNCT
ejpam-5578	357	11	(	(	PUNCT
ejpam-5578	357	12	2025	2025	NUM
ejpam-5578	357	13	)	)	PUNCT
ejpam-5578	357	14	,	,	PUNCT
ejpam-5578	357	15	5578	5578	NUM
ejpam-5578	357	16	16	16	NUM
ejpam-5578	357	17	of	of	ADP
ejpam-5578	357	18	19	19	NUM
ejpam-5578	357	19	proof	proof	NOUN
ejpam-5578	357	20	.	.	PUNCT
ejpam-5578	358	1	let	let	VERB
ejpam-5578	358	2	(	(	PUNCT
ejpam-5578	358	3	q	q	ADJ
ejpam-5578	358	4	,	,	PUNCT
ejpam-5578	358	5	ϱ1	ϱ1	NOUN
ejpam-5578	358	6	,	,	PUNCT
ejpam-5578	358	7	ϱ2	ϱ2	NOUN
ejpam-5578	358	8	,	,	PUNCT
ejpam-5578	358	9	ϱ3	ϱ3	PROPN
ejpam-5578	358	10	)	)	PUNCT
ejpam-5578	358	11	be	be	VERB
ejpam-5578	358	12	a	a	DET
ejpam-5578	358	13	tripartite	tripartite	ADJ
ejpam-5578	358	14	countably	countably	ADV
ejpam-5578	358	15	metacompact	metacompact	ADJ
ejpam-5578	358	16	topological	topological	ADJ
ejpam-5578	358	17	space	space	NOUN
ejpam-5578	358	18	.	.	PUNCT
ejpam-5578	359	1	by	by	ADP
ejpam-5578	359	2	the	the	DET
ejpam-5578	359	3	definition	definition	NOUN
ejpam-5578	359	4	of	of	ADP
ejpam-5578	359	5	countable	countable	ADJ
ejpam-5578	359	6	metacompactness	metacompactness	NOUN
ejpam-5578	359	7	,	,	PUNCT
ejpam-5578	359	8	every	every	DET
ejpam-5578	359	9	countable	countable	ADJ
ejpam-5578	359	10	open	open	ADJ
ejpam-5578	359	11	cover	cover	NOUN
ejpam-5578	359	12	of	of	ADP
ejpam-5578	359	13	q	q	PROPN
ejpam-5578	359	14	has	have	VERB
ejpam-5578	359	15	a	a	DET
ejpam-5578	359	16	finite	finite	ADJ
ejpam-5578	359	17	subcover	subcover	PROPN
ejpam-5578	359	18	.	.	PUNCT
ejpam-5578	360	1	we	we	PRON
ejpam-5578	360	2	are	be	AUX
ejpam-5578	360	3	required	require	VERB
ejpam-5578	360	4	to	to	PART
ejpam-5578	360	5	show	show	VERB
ejpam-5578	360	6	that	that	SCONJ
ejpam-5578	360	7	q	q	NOUN
ejpam-5578	360	8	is	be	AUX
ejpam-5578	360	9	tri	tri	ADJ
ejpam-5578	360	10	-	-	ADJ
ejpam-5578	360	11	compact	compact	ADJ
ejpam-5578	360	12	,	,	PUNCT
ejpam-5578	360	13	which	which	PRON
ejpam-5578	360	14	means	mean	VERB
ejpam-5578	360	15	that	that	SCONJ
ejpam-5578	360	16	every	every	DET
ejpam-5578	360	17	open	open	ADJ
ejpam-5578	360	18	cover	cover	NOUN
ejpam-5578	360	19	of	of	ADP
ejpam-5578	360	20	q	q	PROPN
ejpam-5578	360	21	has	have	VERB
ejpam-5578	360	22	a	a	DET
ejpam-5578	360	23	finite	finite	ADJ
ejpam-5578	360	24	subcover	subcover	NOUN
ejpam-5578	360	25	with	with	ADP
ejpam-5578	360	26	respect	respect	NOUN
ejpam-5578	360	27	to	to	ADP
ejpam-5578	360	28	the	the	DET
ejpam-5578	360	29	topology	topology	NOUN
ejpam-5578	360	30	ϱ1	ϱ1	NOUN
ejpam-5578	360	31	,	,	PUNCT
ejpam-5578	360	32	ϱ2	ϱ2	NOUN
ejpam-5578	360	33	,	,	PUNCT
ejpam-5578	360	34	ϱ3	ϱ3	PROPN
ejpam-5578	360	35	.	.	PUNCT
ejpam-5578	361	1	since	since	SCONJ
ejpam-5578	361	2	q	q	PROPN
ejpam-5578	361	3	is	be	AUX
ejpam-5578	361	4	countably	countably	ADV
ejpam-5578	361	5	metacompact	metacompact	ADJ
ejpam-5578	361	6	,	,	PUNCT
ejpam-5578	361	7	for	for	ADP
ejpam-5578	361	8	any	any	DET
ejpam-5578	361	9	countable	countable	ADJ
ejpam-5578	361	10	collection	collection	NOUN
ejpam-5578	361	11	of	of	ADP
ejpam-5578	361	12	open	open	ADJ
ejpam-5578	361	13	sets	set	NOUN
ejpam-5578	361	14	{	{	PUNCT
ejpam-5578	361	15	ui}i∈n	ui}i∈n	NOUN
ejpam-5578	361	16	that	that	PRON
ejpam-5578	361	17	cover	cover	VERB
ejpam-5578	361	18	q	q	NOUN
ejpam-5578	361	19	,	,	PUNCT
ejpam-5578	361	20	there	there	PRON
ejpam-5578	361	21	exists	exist	VERB
ejpam-5578	361	22	a	a	DET
ejpam-5578	361	23	finite	finite	ADJ
ejpam-5578	361	24	subcollection	subcollection	NOUN
ejpam-5578	361	25	{	{	PUNCT
ejpam-5578	361	26	ui1	ui1	ADV
ejpam-5578	361	27	,	,	PUNCT
ejpam-5578	361	28	ui2	ui2	INTJ
ejpam-5578	361	29	,	,	PUNCT
ejpam-5578	361	30	.	.	PUNCT
ejpam-5578	361	31	.	.	PUNCT
ejpam-5578	362	1	.	.	PUNCT
ejpam-5578	363	1	,	,	PUNCT
ejpam-5578	363	2	uik	uik	NOUN
ejpam-5578	363	3	}	}	PUNCT
ejpam-5578	363	4	such	such	ADJ
ejpam-5578	363	5	that	that	SCONJ
ejpam-5578	363	6	their	their	PRON
ejpam-5578	363	7	union	union	NOUN
ejpam-5578	363	8	covers	cover	VERB
ejpam-5578	363	9	q.	q.	NOUN
ejpam-5578	363	10	for	for	ADP
ejpam-5578	363	11	each	each	PRON
ejpam-5578	363	12	of	of	ADP
ejpam-5578	363	13	the	the	DET
ejpam-5578	363	14	topologies	topology	NOUN
ejpam-5578	363	15	ϱ1	ϱ1	NOUN
ejpam-5578	363	16	,	,	PUNCT
ejpam-5578	363	17	ϱ2	ϱ2	NOUN
ejpam-5578	363	18	,	,	PUNCT
ejpam-5578	363	19	ϱ3	ϱ3	PROPN
ejpam-5578	363	20	,	,	PUNCT
ejpam-5578	363	21	we	we	PRON
ejpam-5578	363	22	have	have	VERB
ejpam-5578	363	23	the	the	DET
ejpam-5578	363	24	same	same	ADJ
ejpam-5578	363	25	result	result	NOUN
ejpam-5578	363	26	since	since	SCONJ
ejpam-5578	363	27	the	the	DET
ejpam-5578	363	28	topologies	topology	NOUN
ejpam-5578	363	29	are	be	AUX
ejpam-5578	363	30	compatible	compatible	ADJ
ejpam-5578	363	31	with	with	ADP
ejpam-5578	363	32	the	the	DET
ejpam-5578	363	33	metacompactness	metacompactness	ADJ
ejpam-5578	363	34	condition	condition	NOUN
ejpam-5578	363	35	.	.	PUNCT
ejpam-5578	364	1	therefore	therefore	ADV
ejpam-5578	364	2	,	,	PUNCT
ejpam-5578	364	3	we	we	PRON
ejpam-5578	364	4	can	can	AUX
ejpam-5578	364	5	find	find	VERB
ejpam-5578	364	6	finite	finite	ADJ
ejpam-5578	364	7	subcovers	subcover	NOUN
ejpam-5578	364	8	for	for	ADP
ejpam-5578	364	9	each	each	PRON
ejpam-5578	364	10	of	of	ADP
ejpam-5578	364	11	the	the	DET
ejpam-5578	364	12	topologies	topology	NOUN
ejpam-5578	364	13	,	,	PUNCT
ejpam-5578	364	14	implying	imply	VERB
ejpam-5578	364	15	that	that	SCONJ
ejpam-5578	364	16	q	q	NOUN
ejpam-5578	364	17	is	be	AUX
ejpam-5578	364	18	tri	tri	ADJ
ejpam-5578	364	19	-	-	ADJ
ejpam-5578	364	20	compact	compact	ADJ
ejpam-5578	364	21	.	.	PUNCT
ejpam-5578	365	1	hence	hence	ADV
ejpam-5578	365	2	,	,	PUNCT
ejpam-5578	365	3	the	the	DET
ejpam-5578	365	4	space	space	NOUN
ejpam-5578	365	5	(	(	PUNCT
ejpam-5578	365	6	q	q	ADJ
ejpam-5578	365	7	,	,	PUNCT
ejpam-5578	365	8	ϱ1	ϱ1	NOUN
ejpam-5578	365	9	,	,	PUNCT
ejpam-5578	365	10	ϱ2	ϱ2	NOUN
ejpam-5578	365	11	,	,	PUNCT
ejpam-5578	365	12	ϱ3	ϱ3	PROPN
ejpam-5578	365	13	)	)	PUNCT
ejpam-5578	365	14	is	be	AUX
ejpam-5578	365	15	tri	tri	ADJ
ejpam-5578	365	16	-	-	ADJ
ejpam-5578	365	17	compact	compact	ADJ
ejpam-5578	365	18	.	.	PUNCT
ejpam-5578	366	1	theorem	theorem	VERB
ejpam-5578	366	2	15	15	NUM
ejpam-5578	366	3	.	.	PUNCT
ejpam-5578	367	1	the	the	DET
ejpam-5578	367	2	product	product	NOUN
ejpam-5578	367	3	of	of	ADP
ejpam-5578	367	4	a	a	DET
ejpam-5578	367	5	tri	tri	ADJ
ejpam-5578	367	6	-	-	ADJ
ejpam-5578	367	7	compact	compact	ADJ
ejpam-5578	367	8	space	space	NOUN
ejpam-5578	367	9	q	q	NOUN
ejpam-5578	367	10	and	and	CCONJ
ejpam-5578	367	11	a	a	DET
ejpam-5578	367	12	tri	tri	ADJ
ejpam-5578	367	13	-	-	ADJ
ejpam-5578	367	14	metalindelöf	metalindelöf	ADJ
ejpam-5578	367	15	space	space	NOUN
ejpam-5578	367	16	y	y	PROPN
ejpam-5578	367	17	is	be	AUX
ejpam-5578	367	18	tri	tri	ADJ
ejpam-5578	367	19	-	-	NOUN
ejpam-5578	367	20	metalindelöf	metalindelöf	NOUN
ejpam-5578	367	21	,	,	PUNCT
ejpam-5578	367	22	where	where	SCONJ
ejpam-5578	367	23	(	(	PUNCT
ejpam-5578	367	24	q	q	ADJ
ejpam-5578	367	25	,	,	PUNCT
ejpam-5578	367	26	ϱ1	ϱ1	NOUN
ejpam-5578	367	27	,	,	PUNCT
ejpam-5578	367	28	ϱ2	ϱ2	NOUN
ejpam-5578	367	29	,	,	PUNCT
ejpam-5578	367	30	ϱ3	ϱ3	PROPN
ejpam-5578	367	31	)	)	PUNCT
ejpam-5578	367	32	and	and	CCONJ
ejpam-5578	367	33	(	(	PUNCT
ejpam-5578	367	34	y	y	PROPN
ejpam-5578	367	35	,	,	PUNCT
ejpam-5578	367	36	σ1	σ1	PROPN
ejpam-5578	367	37	,	,	PUNCT
ejpam-5578	367	38	σ2	σ2	PROPN
ejpam-5578	367	39	,	,	PUNCT
ejpam-5578	367	40	σ3	σ3	PROPN
ejpam-5578	367	41	)	)	PUNCT
ejpam-5578	367	42	are	be	AUX
ejpam-5578	367	43	tri	tri	ADJ
ejpam-5578	367	44	-	-	ADJ
ejpam-5578	367	45	topological	topological	ADJ
ejpam-5578	367	46	spaces	space	NOUN
ejpam-5578	367	47	.	.	PUNCT
ejpam-5578	368	1	proof	proof	NOUN
ejpam-5578	368	2	.	.	PUNCT
ejpam-5578	369	1	let	let	VERB
ejpam-5578	369	2	f	f	NOUN
ejpam-5578	369	3	:	:	PUNCT
ejpam-5578	369	4	q×	q×	PUNCT
ejpam-5578	369	5	y	y	PROPN
ejpam-5578	369	6	→	→	SYM
ejpam-5578	369	7	y	y	PROPN
ejpam-5578	369	8	be	be	AUX
ejpam-5578	369	9	the	the	DET
ejpam-5578	369	10	tri	tri	ADJ
ejpam-5578	369	11	-	-	ADJ
ejpam-5578	369	12	projection	projection	ADJ
ejpam-5578	369	13	function	function	NOUN
ejpam-5578	369	14	,	,	PUNCT
ejpam-5578	369	15	defined	define	VERB
ejpam-5578	369	16	by	by	ADP
ejpam-5578	369	17	f(q	f(q	PROPN
ejpam-5578	369	18	,	,	PUNCT
ejpam-5578	369	19	s	s	PART
ejpam-5578	369	20	)	)	PUNCT
ejpam-5578	369	21	=	=	SYM
ejpam-5578	369	22	s	s	NOUN
ejpam-5578	369	23	,	,	PUNCT
ejpam-5578	369	24	such	such	ADJ
ejpam-5578	369	25	that	that	SCONJ
ejpam-5578	369	26	(	(	PUNCT
ejpam-5578	369	27	q	q	X
ejpam-5578	369	28	,	,	PUNCT
ejpam-5578	369	29	s	s	X
ejpam-5578	369	30	)	)	PUNCT
ejpam-5578	369	31	∈	∈	PROPN
ejpam-5578	369	32	q	q	X
ejpam-5578	369	33	×	×	NOUN
ejpam-5578	369	34	y	y	PROPN
ejpam-5578	369	35	.	.	PUNCT
ejpam-5578	370	1	then	then	ADV
ejpam-5578	370	2	,	,	PUNCT
ejpam-5578	370	3	f	f	X
ejpam-5578	370	4	:	:	PUNCT
ejpam-5578	370	5	q	q	PUNCT
ejpam-5578	370	6	×	×	NOUN
ejpam-5578	370	7	y	y	PROPN
ejpam-5578	370	8	→	→	SYM
ejpam-5578	370	9	y	y	PROPN
ejpam-5578	370	10	is	be	AUX
ejpam-5578	370	11	a	a	DET
ejpam-5578	370	12	tri	tri	ADJ
ejpam-5578	370	13	-	-	ADJ
ejpam-5578	370	14	perfect	perfect	ADJ
ejpam-5578	370	15	function	function	NOUN
ejpam-5578	370	16	.	.	PUNCT
ejpam-5578	371	1	since	since	SCONJ
ejpam-5578	371	2	y	y	PROPN
ejpam-5578	371	3	is	be	AUX
ejpam-5578	371	4	tri	tri	ADJ
ejpam-5578	371	5	-	-	NOUN
ejpam-5578	371	6	metalindelöf	metalindelöf	NOUN
ejpam-5578	371	7	,	,	PUNCT
ejpam-5578	371	8	it	it	PRON
ejpam-5578	371	9	follows	follow	VERB
ejpam-5578	371	10	that	that	SCONJ
ejpam-5578	371	11	q×	q×	PUNCT
ejpam-5578	371	12	y	y	NOUN
ejpam-5578	371	13	is	be	AUX
ejpam-5578	371	14	also	also	ADV
ejpam-5578	371	15	tri	tri	ADJ
ejpam-5578	371	16	-	-	NOUN
ejpam-5578	371	17	metalindelöf	metalindelöf	ADJ
ejpam-5578	371	18	.	.	PUNCT
ejpam-5578	372	1	theorem	theorem	VERB
ejpam-5578	372	2	16	16	NUM
ejpam-5578	372	3	.	.	PUNCT
ejpam-5578	373	1	let	let	VERB
ejpam-5578	373	2	f	f	NOUN
ejpam-5578	373	3	:	:	PUNCT
ejpam-5578	373	4	(	(	PUNCT
ejpam-5578	373	5	q	q	ADJ
ejpam-5578	373	6	,	,	PUNCT
ejpam-5578	373	7	ϱ1	ϱ1	NOUN
ejpam-5578	373	8	,	,	PUNCT
ejpam-5578	373	9	ϱ2	ϱ2	NOUN
ejpam-5578	373	10	,	,	PUNCT
ejpam-5578	373	11	ϱ3	ϱ3	PROPN
ejpam-5578	373	12	)	)	PUNCT
ejpam-5578	373	13	→	→	SYM
ejpam-5578	373	14	(	(	PUNCT
ejpam-5578	373	15	y	y	PROPN
ejpam-5578	373	16	,	,	PUNCT
ejpam-5578	373	17	σ1	σ1	PROPN
ejpam-5578	373	18	,	,	PUNCT
ejpam-5578	373	19	σ2	σ2	PROPN
ejpam-5578	373	20	,	,	PUNCT
ejpam-5578	373	21	σ3	σ3	PROPN
ejpam-5578	373	22	)	)	PUNCT
ejpam-5578	373	23	be	be	AUX
ejpam-5578	373	24	a	a	DET
ejpam-5578	373	25	continuous	continuous	ADJ
ejpam-5578	373	26	,	,	PUNCT
ejpam-5578	373	27	tri	tri	ADJ
ejpam-5578	373	28	-	-	ADJ
ejpam-5578	373	29	closed	closed	ADJ
ejpam-5578	373	30	,	,	PUNCT
ejpam-5578	373	31	and	and	CCONJ
ejpam-5578	373	32	onto	onto	ADP
ejpam-5578	373	33	function	function	NOUN
ejpam-5578	373	34	.	.	PUNCT
ejpam-5578	374	1	then	then	ADV
ejpam-5578	374	2	,	,	PUNCT
ejpam-5578	374	3	if	if	SCONJ
ejpam-5578	374	4	q	q	NOUN
ejpam-5578	374	5	is	be	AUX
ejpam-5578	374	6	tri	tri	ADJ
ejpam-5578	374	7	-	-	NOUN
ejpam-5578	374	8	metalindelöf	metalindelöf	NOUN
ejpam-5578	374	9	,	,	PUNCT
ejpam-5578	374	10	then	then	ADV
ejpam-5578	374	11	y	y	PROPN
ejpam-5578	374	12	is	be	AUX
ejpam-5578	374	13	also	also	ADV
ejpam-5578	374	14	tri	tri	ADJ
ejpam-5578	374	15	-	-	NOUN
ejpam-5578	374	16	metalindelöf	metalindelöf	NOUN
ejpam-5578	374	17	.	.	PUNCT
ejpam-5578	375	1	proof	proof	NOUN
ejpam-5578	375	2	.	.	PUNCT
ejpam-5578	376	1	let	let	VERB
ejpam-5578	376	2	ã	ã	PROPN
ejpam-5578	376	3	=	=	PRON
ejpam-5578	376	4	{	{	PUNCT
ejpam-5578	377	1	uα	uα	X
ejpam-5578	378	1	|	|	ADV
ejpam-5578	379	1	α	α	NOUN
ejpam-5578	379	2	∈	∈	NOUN
ejpam-5578	379	3	∆	∆	X
ejpam-5578	379	4	}	}	PUNCT
ejpam-5578	379	5	∪	∪	X
ejpam-5578	379	6	{	{	PUNCT
ejpam-5578	379	7	vβ	vβ	NOUN
ejpam-5578	379	8	|	|	ADV
ejpam-5578	379	9	β	β	NOUN
ejpam-5578	379	10	∈	∈	PROPN
ejpam-5578	379	11	γ	γ	X
ejpam-5578	379	12	}	}	PUNCT
ejpam-5578	379	13	be	be	VERB
ejpam-5578	379	14	any	any	DET
ejpam-5578	379	15	tri	tri	ADJ
ejpam-5578	379	16	-	-	ADJ
ejpam-5578	379	17	open	open	ADJ
ejpam-5578	379	18	cover	cover	NOUN
ejpam-5578	379	19	of	of	ADP
ejpam-5578	379	20	y	y	PROPN
ejpam-5578	379	21	,	,	PUNCT
ejpam-5578	379	22	where	where	SCONJ
ejpam-5578	379	23	{	{	PUNCT
ejpam-5578	379	24	uα	uα	NOUN
ejpam-5578	379	25	|	|	ADV
ejpam-5578	379	26	α	α	NOUN
ejpam-5578	379	27	∈	∈	NOUN
ejpam-5578	379	28	∆	∆	X
ejpam-5578	379	29	}	}	PUNCT
ejpam-5578	379	30	consists	consist	VERB
ejpam-5578	379	31	of	of	ADP
ejpam-5578	379	32	tripartite	tripartite	ADJ
ejpam-5578	379	33	σ	σ	VERB
ejpam-5578	379	34	-	-	PUNCT
ejpam-5578	379	35	open	open	ADJ
ejpam-5578	379	36	members	member	NOUN
ejpam-5578	379	37	of	of	ADP
ejpam-5578	379	38	ã.	ã.	NOUN
ejpam-5578	379	39	since	since	SCONJ
ejpam-5578	379	40	f	f	PROPN
ejpam-5578	379	41	is	be	AUX
ejpam-5578	379	42	a	a	DET
ejpam-5578	379	43	continuous	continuous	ADJ
ejpam-5578	379	44	and	and	CCONJ
ejpam-5578	379	45	onto	onto	ADP
ejpam-5578	379	46	function	function	NOUN
ejpam-5578	379	47	,	,	PUNCT
ejpam-5578	379	48	the	the	DET
ejpam-5578	379	49	set	set	NOUN
ejpam-5578	379	50	ũ	ũ	PROPN
ejpam-5578	379	51	=	=	X
ejpam-5578	379	52	{	{	PUNCT
ejpam-5578	379	53	f−1(uα	f−1(uα	PROPN
ejpam-5578	379	54	)	)	PUNCT
ejpam-5578	379	55	|	|	ADV
ejpam-5578	379	56	α	α	NUM
ejpam-5578	379	57	∈	∈	NOUN
ejpam-5578	379	58	∆	∆	X
ejpam-5578	379	59	}	}	PUNCT
ejpam-5578	379	60	∪	∪	X
ejpam-5578	379	61	{	{	PUNCT
ejpam-5578	379	62	f−1(vβ	f−1(vβ	PROPN
ejpam-5578	379	63	)	)	PUNCT
ejpam-5578	379	64	|	|	ADV
ejpam-5578	379	65	β	β	PROPN
ejpam-5578	379	66	∈	∈	PROPN
ejpam-5578	379	67	γ	γ	X
ejpam-5578	379	68	}	}	PUNCT
ejpam-5578	379	69	is	be	AUX
ejpam-5578	379	70	a	a	DET
ejpam-5578	379	71	tri	tri	ADJ
ejpam-5578	379	72	-	-	ADJ
ejpam-5578	379	73	open	open	ADJ
ejpam-5578	379	74	cover	cover	NOUN
ejpam-5578	379	75	of	of	ADP
ejpam-5578	379	76	q.	q.	NOUN
ejpam-5578	379	77	given	give	VERB
ejpam-5578	379	78	that	that	PRON
ejpam-5578	379	79	q	q	NOUN
ejpam-5578	379	80	is	be	AUX
ejpam-5578	379	81	tri	tri	ADJ
ejpam-5578	379	82	-	-	NOUN
ejpam-5578	379	83	metalindelöf	metalindelöf	NOUN
ejpam-5578	379	84	,	,	PUNCT
ejpam-5578	379	85	there	there	PRON
ejpam-5578	379	86	exists	exist	VERB
ejpam-5578	379	87	a	a	DET
ejpam-5578	379	88	point	point	NOUN
ejpam-5578	379	89	-	-	PUNCT
ejpam-5578	379	90	countable	countable	ADJ
ejpam-5578	379	91	tri	tri	ADJ
ejpam-5578	379	92	-	-	ADJ
ejpam-5578	379	93	open	open	ADJ
ejpam-5578	379	94	parallel	parallel	ADJ
ejpam-5578	379	95	refinement	refinement	NOUN
ejpam-5578	379	96	of	of	ADP
ejpam-5578	379	97	ũ	ũ	PROPN
ejpam-5578	379	98	,	,	PUNCT
ejpam-5578	379	99	denoted	denote	VERB
ejpam-5578	379	100	by	by	ADP
ejpam-5578	379	101	ũ∗	ũ∗	PROPN
ejpam-5578	380	1	=	=	SYM
ejpam-5578	380	2	{	{	PUNCT
ejpam-5578	380	3	f−1(u∗	f−1(u∗	PROPN
ejpam-5578	380	4	α	α	NOUN
ejpam-5578	380	5	)	)	PUNCT
ejpam-5578	380	6	|	|	ADV
ejpam-5578	380	7	α	α	NUM
ejpam-5578	380	8	∈	∈	NOUN
ejpam-5578	380	9	∆	∆	X
ejpam-5578	380	10	}	}	PUNCT
ejpam-5578	380	11	∪	∪	X
ejpam-5578	380	12	{	{	PUNCT
ejpam-5578	380	13	f−1(v	f−1(v	PROPN
ejpam-5578	380	14	∗	∗	X
ejpam-5578	380	15	β	β	X
ejpam-5578	380	16	)	)	PUNCT
ejpam-5578	381	1	|	|	ADV
ejpam-5578	381	2	β	β	X
ejpam-5578	381	3	∈	∈	PROPN
ejpam-5578	381	4	γ	γ	X
ejpam-5578	381	5	}	}	PUNCT
ejpam-5578	381	6	.	.	PUNCT
ejpam-5578	382	1	thus	thus	ADV
ejpam-5578	382	2	,	,	PUNCT
ejpam-5578	382	3	ã∗	ã∗	PROPN
ejpam-5578	382	4	=	=	PRON
ejpam-5578	382	5	{	{	PUNCT
ejpam-5578	382	6	u∗	u∗	INTJ
ejpam-5578	382	7	α	α	NOUN
ejpam-5578	382	8	|	|	ADV
ejpam-5578	382	9	α	α	NOUN
ejpam-5578	382	10	∈	∈	NOUN
ejpam-5578	382	11	∆	∆	X
ejpam-5578	382	12	}	}	PUNCT
ejpam-5578	382	13	∪	∪	X
ejpam-5578	382	14	{	{	PUNCT
ejpam-5578	382	15	v	v	NOUN
ejpam-5578	382	16	∗	∗	NOUN
ejpam-5578	382	17	β	β	X
ejpam-5578	383	1	|	|	ADV
ejpam-5578	383	2	β	β	X
ejpam-5578	383	3	∈	∈	PROPN
ejpam-5578	383	4	γ	γ	X
ejpam-5578	383	5	}	}	PUNCT
ejpam-5578	383	6	is	be	AUX
ejpam-5578	383	7	a	a	DET
ejpam-5578	383	8	point	point	NOUN
ejpam-5578	383	9	-	-	PUNCT
ejpam-5578	383	10	countable	countable	ADJ
ejpam-5578	383	11	tri	tri	ADJ
ejpam-5578	383	12	-	-	ADJ
ejpam-5578	383	13	open	open	ADJ
ejpam-5578	383	14	parallel	parallel	ADJ
ejpam-5578	383	15	refinement	refinement	NOUN
ejpam-5578	383	16	of	of	ADP
ejpam-5578	383	17	ã.	ã.	PROPN
ejpam-5578	383	18	therefore	therefore	ADV
ejpam-5578	383	19	,	,	PUNCT
ejpam-5578	383	20	y	y	PROPN
ejpam-5578	383	21	is	be	AUX
ejpam-5578	383	22	tri	tri	ADJ
ejpam-5578	383	23	-	-	NOUN
ejpam-5578	383	24	metalindelöf	metalindelöf	NOUN
ejpam-5578	383	25	.	.	PUNCT
ejpam-5578	384	1	lemma	lemma	PROPN
ejpam-5578	384	2	6	6	NUM
ejpam-5578	384	3	.	.	PUNCT
ejpam-5578	385	1	let	let	VERB
ejpam-5578	385	2	f	f	NOUN
ejpam-5578	385	3	:	:	PUNCT
ejpam-5578	385	4	(	(	PUNCT
ejpam-5578	385	5	q	q	ADJ
ejpam-5578	385	6	,	,	PUNCT
ejpam-5578	385	7	ϱ1	ϱ1	NOUN
ejpam-5578	385	8	,	,	PUNCT
ejpam-5578	385	9	ϱ2	ϱ2	NOUN
ejpam-5578	385	10	,	,	PUNCT
ejpam-5578	385	11	ϱ3	ϱ3	PROPN
ejpam-5578	385	12	)	)	PUNCT
ejpam-5578	385	13	→	→	SYM
ejpam-5578	385	14	(	(	PUNCT
ejpam-5578	385	15	y	y	PROPN
ejpam-5578	385	16	,	,	PUNCT
ejpam-5578	385	17	σ1	σ1	PROPN
ejpam-5578	385	18	,	,	PUNCT
ejpam-5578	385	19	σ2	σ2	PROPN
ejpam-5578	385	20	,	,	PUNCT
ejpam-5578	385	21	σ3	σ3	PROPN
ejpam-5578	385	22	)	)	PUNCT
ejpam-5578	385	23	be	be	AUX
ejpam-5578	385	24	a	a	DET
ejpam-5578	385	25	continuous	continuous	ADJ
ejpam-5578	385	26	and	and	CCONJ
ejpam-5578	385	27	onto	onto	ADP
ejpam-5578	385	28	function	function	NOUN
ejpam-5578	385	29	.	.	PUNCT
ejpam-5578	386	1	if	if	SCONJ
ejpam-5578	386	2	ã	ã	PROPN
ejpam-5578	386	3	=	=	PRON
ejpam-5578	386	4	{	{	PUNCT
ejpam-5578	386	5	aα	aα	NOUN
ejpam-5578	386	6	|	|	ADV
ejpam-5578	386	7	α	α	NOUN
ejpam-5578	386	8	∈	∈	NOUN
ejpam-5578	386	9	∆	∆	X
ejpam-5578	386	10	}	}	PUNCT
ejpam-5578	386	11	is	be	AUX
ejpam-5578	386	12	a	a	DET
ejpam-5578	386	13	point	point	NOUN
ejpam-5578	386	14	-	-	PUNCT
ejpam-5578	386	15	countable	countable	ADJ
ejpam-5578	386	16	family	family	NOUN
ejpam-5578	386	17	of	of	ADP
ejpam-5578	386	18	subsets	subset	NOUN
ejpam-5578	386	19	of	of	ADP
ejpam-5578	386	20	q	q	NOUN
ejpam-5578	386	21	,	,	PUNCT
ejpam-5578	386	22	then	then	ADV
ejpam-5578	386	23	{	{	PUNCT
ejpam-5578	386	24	f(aα	f(aα	PROPN
ejpam-5578	386	25	)	)	PUNCT
ejpam-5578	386	26	|	|	ADV
ejpam-5578	386	27	α	α	PROPN
ejpam-5578	386	28	∈	∈	NOUN
ejpam-5578	386	29	∆	∆	X
ejpam-5578	386	30	}	}	PUNCT
ejpam-5578	386	31	is	be	AUX
ejpam-5578	386	32	a	a	DET
ejpam-5578	386	33	point	point	NOUN
ejpam-5578	386	34	-	-	PUNCT
ejpam-5578	386	35	countable	countable	ADJ
ejpam-5578	386	36	family	family	NOUN
ejpam-5578	386	37	of	of	ADP
ejpam-5578	386	38	subsets	subset	NOUN
ejpam-5578	386	39	of	of	ADP
ejpam-5578	386	40	y	y	PROPN
ejpam-5578	386	41	.	.	PUNCT
ejpam-5578	387	1	j.	j.	PROPN
ejpam-5578	387	2	oudetallah	oudetallah	PROPN
ejpam-5578	387	3	et	et	PROPN
ejpam-5578	387	4	al	al	PROPN
ejpam-5578	387	5	.	.	PUNCT
ejpam-5578	387	6	/	/	SYM
ejpam-5578	387	7	eur	eur	PROPN
ejpam-5578	387	8	.	.	PUNCT
ejpam-5578	388	1	j.	j.	PROPN
ejpam-5578	388	2	pure	pure	PROPN
ejpam-5578	388	3	appl	appl	PROPN
ejpam-5578	388	4	.	.	PROPN
ejpam-5578	388	5	math	math	PROPN
ejpam-5578	388	6	,	,	PUNCT
ejpam-5578	388	7	18	18	NUM
ejpam-5578	388	8	(	(	PUNCT
ejpam-5578	388	9	2	2	NUM
ejpam-5578	388	10	)	)	PUNCT
ejpam-5578	388	11	(	(	PUNCT
ejpam-5578	388	12	2025	2025	NUM
ejpam-5578	388	13	)	)	PUNCT
ejpam-5578	388	14	,	,	PUNCT
ejpam-5578	388	15	5578	5578	NUM
ejpam-5578	388	16	17	17	NUM
ejpam-5578	388	17	of	of	ADP
ejpam-5578	388	18	19	19	NUM
ejpam-5578	388	19	proof	proof	NOUN
ejpam-5578	388	20	.	.	PUNCT
ejpam-5578	389	1	let	let	VERB
ejpam-5578	389	2	f	f	NOUN
ejpam-5578	389	3	:	:	PUNCT
ejpam-5578	389	4	(	(	PUNCT
ejpam-5578	389	5	q	q	ADJ
ejpam-5578	389	6	,	,	PUNCT
ejpam-5578	389	7	ϱ1	ϱ1	NOUN
ejpam-5578	389	8	,	,	PUNCT
ejpam-5578	389	9	ϱ2	ϱ2	NOUN
ejpam-5578	389	10	,	,	PUNCT
ejpam-5578	389	11	ϱ3	ϱ3	PROPN
ejpam-5578	389	12	)	)	PUNCT
ejpam-5578	389	13	→	→	SYM
ejpam-5578	389	14	(	(	PUNCT
ejpam-5578	389	15	y	y	PROPN
ejpam-5578	389	16	,	,	PUNCT
ejpam-5578	389	17	σ1	σ1	PROPN
ejpam-5578	389	18	,	,	PUNCT
ejpam-5578	389	19	σ2	σ2	PROPN
ejpam-5578	389	20	,	,	PUNCT
ejpam-5578	389	21	σ3	σ3	PROPN
ejpam-5578	389	22	)	)	PUNCT
ejpam-5578	389	23	be	be	AUX
ejpam-5578	389	24	a	a	DET
ejpam-5578	389	25	continuous	continuous	ADJ
ejpam-5578	389	26	and	and	CCONJ
ejpam-5578	389	27	onto	onto	ADP
ejpam-5578	389	28	function	function	NOUN
ejpam-5578	389	29	.	.	PUNCT
ejpam-5578	390	1	suppose	suppose	VERB
ejpam-5578	390	2	ã	ã	PROPN
ejpam-5578	390	3	=	=	PRON
ejpam-5578	390	4	{	{	PUNCT
ejpam-5578	390	5	aα	aα	NOUN
ejpam-5578	390	6	|	|	ADV
ejpam-5578	390	7	α	α	NOUN
ejpam-5578	390	8	∈	∈	NOUN
ejpam-5578	390	9	∆	∆	X
ejpam-5578	390	10	}	}	PUNCT
ejpam-5578	390	11	is	be	AUX
ejpam-5578	390	12	a	a	DET
ejpam-5578	390	13	point	point	NOUN
ejpam-5578	390	14	-	-	PUNCT
ejpam-5578	390	15	countable	countable	ADJ
ejpam-5578	390	16	family	family	NOUN
ejpam-5578	390	17	of	of	ADP
ejpam-5578	390	18	subsets	subset	NOUN
ejpam-5578	390	19	of	of	ADP
ejpam-5578	390	20	q	q	NOUN
ejpam-5578	390	21	,	,	PUNCT
ejpam-5578	390	22	i.e.	i.e.	X
ejpam-5578	390	23	,	,	PUNCT
ejpam-5578	390	24	for	for	ADP
ejpam-5578	390	25	each	each	DET
ejpam-5578	390	26	point	point	NOUN
ejpam-5578	390	27	x	x	X
ejpam-5578	390	28	∈	∈	PROPN
ejpam-5578	390	29	q	q	NOUN
ejpam-5578	390	30	,	,	PUNCT
ejpam-5578	390	31	the	the	DET
ejpam-5578	390	32	set	set	NOUN
ejpam-5578	390	33	{	{	PUNCT
ejpam-5578	390	34	α	α	NOUN
ejpam-5578	390	35	∈	∈	NOUN
ejpam-5578	390	36	∆	∆	NOUN
ejpam-5578	391	1	|	|	ADV
ejpam-5578	391	2	x	x	SYM
ejpam-5578	391	3	∈	∈	PROPN
ejpam-5578	391	4	aα	aα	NOUN
ejpam-5578	391	5	}	}	PUNCT
ejpam-5578	391	6	is	be	AUX
ejpam-5578	391	7	countable	countable	ADJ
ejpam-5578	391	8	.	.	PUNCT
ejpam-5578	392	1	we	we	PRON
ejpam-5578	392	2	aim	aim	VERB
ejpam-5578	392	3	to	to	PART
ejpam-5578	392	4	prove	prove	VERB
ejpam-5578	392	5	that	that	SCONJ
ejpam-5578	392	6	{	{	PUNCT
ejpam-5578	392	7	f(aα	f(aα	NOUN
ejpam-5578	392	8	)	)	PUNCT
ejpam-5578	392	9	|	|	ADV
ejpam-5578	392	10	α	α	PROPN
ejpam-5578	392	11	∈	∈	NOUN
ejpam-5578	392	12	∆	∆	X
ejpam-5578	392	13	}	}	PUNCT
ejpam-5578	392	14	is	be	AUX
ejpam-5578	392	15	a	a	DET
ejpam-5578	392	16	point	point	NOUN
ejpam-5578	392	17	-	-	PUNCT
ejpam-5578	392	18	countable	countable	ADJ
ejpam-5578	392	19	family	family	NOUN
ejpam-5578	392	20	of	of	ADP
ejpam-5578	392	21	subsets	subset	NOUN
ejpam-5578	392	22	of	of	ADP
ejpam-5578	392	23	y	y	PROPN
ejpam-5578	392	24	.	.	PUNCT
ejpam-5578	393	1	consider	consider	VERB
ejpam-5578	393	2	any	any	DET
ejpam-5578	393	3	point	point	NOUN
ejpam-5578	393	4	y	y	PROPN
ejpam-5578	393	5	∈	∈	PROPN
ejpam-5578	393	6	y	y	PROPN
ejpam-5578	393	7	.	.	PUNCT
ejpam-5578	394	1	since	since	SCONJ
ejpam-5578	394	2	f	f	PROPN
ejpam-5578	394	3	is	be	AUX
ejpam-5578	394	4	onto	onto	ADP
ejpam-5578	394	5	,	,	PUNCT
ejpam-5578	394	6	there	there	PRON
ejpam-5578	394	7	exists	exist	VERB
ejpam-5578	394	8	some	some	DET
ejpam-5578	394	9	x	x	SYM
ejpam-5578	394	10	∈	∈	PROPN
ejpam-5578	394	11	q	q	NOUN
ejpam-5578	394	12	such	such	ADJ
ejpam-5578	394	13	that	that	SCONJ
ejpam-5578	394	14	f(x	f(x	NOUN
ejpam-5578	394	15	)	)	PUNCT
ejpam-5578	395	1	=	=	PUNCT
ejpam-5578	395	2	y.	y.	NOUN
ejpam-5578	395	3	since	since	SCONJ
ejpam-5578	395	4	ã	ã	PROPN
ejpam-5578	395	5	=	=	PRON
ejpam-5578	395	6	{	{	PUNCT
ejpam-5578	395	7	aα	aα	NOUN
ejpam-5578	395	8	|	|	ADV
ejpam-5578	395	9	α	α	NOUN
ejpam-5578	395	10	∈	∈	NOUN
ejpam-5578	395	11	∆	∆	X
ejpam-5578	395	12	}	}	PUNCT
ejpam-5578	395	13	is	be	AUX
ejpam-5578	395	14	a	a	DET
ejpam-5578	395	15	point	point	NOUN
ejpam-5578	395	16	-	-	PUNCT
ejpam-5578	395	17	countable	countable	ADJ
ejpam-5578	395	18	family	family	NOUN
ejpam-5578	395	19	of	of	ADP
ejpam-5578	395	20	subsets	subset	NOUN
ejpam-5578	395	21	of	of	ADP
ejpam-5578	395	22	q	q	NOUN
ejpam-5578	395	23	,	,	PUNCT
ejpam-5578	395	24	the	the	DET
ejpam-5578	395	25	set	set	NOUN
ejpam-5578	395	26	{	{	PUNCT
ejpam-5578	395	27	α	α	NOUN
ejpam-5578	395	28	∈	∈	NOUN
ejpam-5578	395	29	∆	∆	NOUN
ejpam-5578	395	30	|	|	ADV
ejpam-5578	395	31	x	x	SYM
ejpam-5578	395	32	∈	∈	PROPN
ejpam-5578	395	33	aα	aα	NOUN
ejpam-5578	395	34	}	}	PUNCT
ejpam-5578	395	35	is	be	AUX
ejpam-5578	395	36	countable	countable	ADJ
ejpam-5578	395	37	.	.	PUNCT
ejpam-5578	396	1	thus	thus	ADV
ejpam-5578	396	2	,	,	PUNCT
ejpam-5578	396	3	the	the	DET
ejpam-5578	396	4	set	set	NOUN
ejpam-5578	396	5	{	{	PUNCT
ejpam-5578	396	6	α	α	NOUN
ejpam-5578	396	7	∈	∈	PROPN
ejpam-5578	396	8	∆	∆	X
ejpam-5578	396	9	|	|	ADV
ejpam-5578	396	10	f(x	f(x	PROPN
ejpam-5578	396	11	)	)	PUNCT
ejpam-5578	396	12	∈	∈	PROPN
ejpam-5578	396	13	f(aα	f(aα	PROPN
ejpam-5578	396	14	)	)	PUNCT
ejpam-5578	396	15	}	}	PUNCT
ejpam-5578	396	16	is	be	AUX
ejpam-5578	396	17	also	also	ADV
ejpam-5578	396	18	countable	countable	ADJ
ejpam-5578	396	19	,	,	PUNCT
ejpam-5578	396	20	since	since	SCONJ
ejpam-5578	396	21	for	for	ADP
ejpam-5578	396	22	any	any	DET
ejpam-5578	396	23	α	α	NOUN
ejpam-5578	396	24	∈	∈	NOUN
ejpam-5578	396	25	∆	∆	PROPN
ejpam-5578	396	26	,	,	PUNCT
ejpam-5578	396	27	we	we	PRON
ejpam-5578	396	28	have	have	VERB
ejpam-5578	396	29	f(x	f(x	PROPN
ejpam-5578	396	30	)	)	PUNCT
ejpam-5578	396	31	∈	∈	PROPN
ejpam-5578	396	32	f(aα	f(aα	PROPN
ejpam-5578	396	33	)	)	PUNCT
ejpam-5578	397	1	if	if	SCONJ
ejpam-5578	397	2	and	and	CCONJ
ejpam-5578	397	3	only	only	ADV
ejpam-5578	397	4	if	if	SCONJ
ejpam-5578	397	5	x	x	SYM
ejpam-5578	397	6	∈	∈	PROPN
ejpam-5578	397	7	aα	aα	NOUN
ejpam-5578	397	8	.	.	PUNCT
ejpam-5578	398	1	therefore	therefore	ADV
ejpam-5578	398	2	,	,	PUNCT
ejpam-5578	398	3	{	{	PUNCT
ejpam-5578	398	4	f(aα	f(aα	NOUN
ejpam-5578	398	5	)	)	PUNCT
ejpam-5578	398	6	|	|	ADV
ejpam-5578	398	7	α	α	PROPN
ejpam-5578	398	8	∈	∈	NOUN
ejpam-5578	398	9	∆	∆	X
ejpam-5578	398	10	}	}	PUNCT
ejpam-5578	398	11	is	be	AUX
ejpam-5578	398	12	a	a	DET
ejpam-5578	398	13	point	point	NOUN
ejpam-5578	398	14	-	-	PUNCT
ejpam-5578	398	15	countable	countable	ADJ
ejpam-5578	398	16	family	family	NOUN
ejpam-5578	398	17	of	of	ADP
ejpam-5578	398	18	subsets	subset	NOUN
ejpam-5578	398	19	of	of	ADP
ejpam-5578	398	20	y	y	PROPN
ejpam-5578	398	21	.	.	PUNCT
ejpam-5578	399	1	q.e.d	q.e.d	PROPN
ejpam-5578	399	2	.	.	PUNCT
ejpam-5578	400	1	definition	definition	NOUN
ejpam-5578	400	2	38	38	NUM
ejpam-5578	400	3	.	.	PUNCT
ejpam-5578	401	1	a	a	DET
ejpam-5578	401	2	space	space	NOUN
ejpam-5578	401	3	(	(	PUNCT
ejpam-5578	401	4	q	q	ADJ
ejpam-5578	401	5	,	,	PUNCT
ejpam-5578	401	6	ϱ1	ϱ1	NOUN
ejpam-5578	401	7	,	,	PUNCT
ejpam-5578	401	8	ϱ2	ϱ2	NOUN
ejpam-5578	401	9	,	,	PUNCT
ejpam-5578	401	10	ϱ3	ϱ3	PROPN
ejpam-5578	401	11	)	)	PUNCT
ejpam-5578	401	12	is	be	AUX
ejpam-5578	401	13	called	call	VERB
ejpam-5578	401	14	a	a	DET
ejpam-5578	401	15	tri	tri	ADJ
ejpam-5578	401	16	-	-	ADJ
ejpam-5578	401	17	metalindelöf	metalindelöf	ADJ
ejpam-5578	401	18	space	space	NOUN
ejpam-5578	401	19	if	if	SCONJ
ejpam-5578	401	20	every	every	DET
ejpam-5578	401	21	tri	tri	ADJ
ejpam-5578	401	22	-	-	ADJ
ejpam-5578	401	23	open	open	ADJ
ejpam-5578	401	24	cover	cover	NOUN
ejpam-5578	401	25	of	of	ADP
ejpam-5578	401	26	q	q	PROPN
ejpam-5578	401	27	has	have	VERB
ejpam-5578	401	28	a	a	DET
ejpam-5578	401	29	tri	tri	ADJ
ejpam-5578	401	30	-	-	ADJ
ejpam-5578	401	31	open	open	ADJ
ejpam-5578	401	32	locally	locally	ADV
ejpam-5578	401	33	countable	countable	ADJ
ejpam-5578	401	34	refinement	refinement	NOUN
ejpam-5578	401	35	.	.	PUNCT
ejpam-5578	402	1	definition	definition	NOUN
ejpam-5578	402	2	39	39	NUM
ejpam-5578	402	3	.	.	PUNCT
ejpam-5578	403	1	a	a	DET
ejpam-5578	403	2	subset	subset	NOUN
ejpam-5578	403	3	ψ	ψ	NOUN
ejpam-5578	403	4	of	of	ADP
ejpam-5578	403	5	a	a	DET
ejpam-5578	403	6	space	space	NOUN
ejpam-5578	403	7	(	(	PUNCT
ejpam-5578	403	8	q	q	ADJ
ejpam-5578	403	9	,	,	PUNCT
ejpam-5578	403	10	ϱ1	ϱ1	NOUN
ejpam-5578	403	11	,	,	PUNCT
ejpam-5578	403	12	ϱ2	ϱ2	NOUN
ejpam-5578	403	13	,	,	PUNCT
ejpam-5578	403	14	ϱ3	ϱ3	PROPN
ejpam-5578	403	15	)	)	PUNCT
ejpam-5578	403	16	is	be	AUX
ejpam-5578	403	17	said	say	VERB
ejpam-5578	403	18	to	to	PART
ejpam-5578	403	19	be	be	AUX
ejpam-5578	403	20	tri	tri	ADJ
ejpam-5578	403	21	-	-	NOUN
ejpam-5578	403	22	paralindelöf	paralindelöf	NOUN
ejpam-5578	403	23	relative	relative	ADJ
ejpam-5578	403	24	to	to	ADP
ejpam-5578	403	25	q	q	NOUN
ejpam-5578	403	26	if	if	SCONJ
ejpam-5578	403	27	every	every	DET
ejpam-5578	403	28	tri	tri	ADJ
ejpam-5578	403	29	-	-	ADJ
ejpam-5578	403	30	open	open	ADJ
ejpam-5578	403	31	cover	cover	NOUN
ejpam-5578	403	32	of	of	ADP
ejpam-5578	403	33	ψ	ψ	NOUN
ejpam-5578	403	34	by	by	ADP
ejpam-5578	403	35	members	member	NOUN
ejpam-5578	403	36	of	of	ADP
ejpam-5578	403	37	ϱ	ϱ	PROPN
ejpam-5578	403	38	has	have	VERB
ejpam-5578	403	39	a	a	DET
ejpam-5578	403	40	tripartite	tripartite	ADJ
ejpam-5578	403	41	locally	locally	ADV
ejpam-5578	403	42	countable	countable	ADJ
ejpam-5578	403	43	parallel	parallel	ADJ
ejpam-5578	403	44	refinement	refinement	NOUN
ejpam-5578	403	45	in	in	ADP
ejpam-5578	403	46	q	q	NOUN
ejpam-5578	403	47	by	by	ADP
ejpam-5578	403	48	members	member	NOUN
ejpam-5578	403	49	of	of	ADP
ejpam-5578	403	50	ϱ.	ϱ.	PROPN
ejpam-5578	403	51	corollary	corollary	PROPN
ejpam-5578	403	52	3	3	NUM
ejpam-5578	403	53	.	.	PUNCT
ejpam-5578	404	1	every	every	DET
ejpam-5578	404	2	tri	tri	ADJ
ejpam-5578	404	3	-	-	ADJ
ejpam-5578	404	4	paralindelöf	paralindelöf	NOUN
ejpam-5578	404	5	space	space	NOUN
ejpam-5578	404	6	is	be	AUX
ejpam-5578	404	7	tri	tri	ADJ
ejpam-5578	404	8	-	-	ADJ
ejpam-5578	404	9	metalindelöf	metalindelöf	NOUN
ejpam-5578	404	10	.	.	PUNCT
ejpam-5578	405	1	proof	proof	NOUN
ejpam-5578	405	2	.	.	PUNCT
ejpam-5578	406	1	clearly	clearly	ADV
ejpam-5578	406	2	by	by	ADP
ejpam-5578	406	3	above	above	ADP
ejpam-5578	406	4	lemma	lemma	PROPN
ejpam-5578	406	5	theorem	theorem	VERB
ejpam-5578	406	6	17	17	NUM
ejpam-5578	406	7	.	.	PUNCT
ejpam-5578	407	1	every	every	DET
ejpam-5578	407	2	tri	tri	ADJ
ejpam-5578	407	3	-	-	ADJ
ejpam-5578	407	4	closed	closed	ADJ
ejpam-5578	407	5	subspace	subspace	NOUN
ejpam-5578	407	6	of	of	ADP
ejpam-5578	407	7	a	a	DET
ejpam-5578	407	8	tri	tri	ADJ
ejpam-5578	407	9	-	-	ADJ
ejpam-5578	407	10	metalindelöf	metalindelöf	ADJ
ejpam-5578	407	11	space	space	NOUN
ejpam-5578	407	12	(	(	PUNCT
ejpam-5578	407	13	q	q	ADJ
ejpam-5578	407	14	,	,	PUNCT
ejpam-5578	407	15	ϱ1	ϱ1	NOUN
ejpam-5578	407	16	,	,	PUNCT
ejpam-5578	407	17	ϱ2	ϱ2	NOUN
ejpam-5578	407	18	,	,	PUNCT
ejpam-5578	407	19	ϱ3	ϱ3	PROPN
ejpam-5578	407	20	)	)	PUNCT
ejpam-5578	407	21	is	be	AUX
ejpam-5578	407	22	trimetalindelöf	trimetalindelöf	NOUN
ejpam-5578	407	23	.	.	PUNCT
ejpam-5578	408	1	proof	proof	NOUN
ejpam-5578	408	2	.	.	PUNCT
ejpam-5578	409	1	let	let	VERB
ejpam-5578	409	2	x	x	PRON
ejpam-5578	409	3	be	be	AUX
ejpam-5578	409	4	a	a	DET
ejpam-5578	409	5	tri	tri	ADJ
ejpam-5578	409	6	-	-	ADJ
ejpam-5578	409	7	closed	closed	ADJ
ejpam-5578	409	8	subspace	subspace	NOUN
ejpam-5578	409	9	of	of	ADP
ejpam-5578	409	10	the	the	DET
ejpam-5578	409	11	tri	tri	ADJ
ejpam-5578	409	12	-	-	ADJ
ejpam-5578	409	13	metalindelöf	metalindelöf	ADJ
ejpam-5578	409	14	space	space	NOUN
ejpam-5578	409	15	(	(	PUNCT
ejpam-5578	409	16	q	q	ADJ
ejpam-5578	409	17	,	,	PUNCT
ejpam-5578	409	18	ϱ1	ϱ1	NOUN
ejpam-5578	409	19	,	,	PUNCT
ejpam-5578	409	20	ϱ2	ϱ2	NOUN
ejpam-5578	409	21	,	,	PUNCT
ejpam-5578	409	22	ϱ3	ϱ3	PROPN
ejpam-5578	409	23	)	)	PUNCT
ejpam-5578	409	24	.	.	PUNCT
ejpam-5578	410	1	to	to	PART
ejpam-5578	410	2	show	show	VERB
ejpam-5578	410	3	that	that	SCONJ
ejpam-5578	410	4	x	x	PRON
ejpam-5578	410	5	is	be	AUX
ejpam-5578	410	6	tri	tri	ADJ
ejpam-5578	410	7	-	-	NOUN
ejpam-5578	410	8	metalindelöf	metalindelöf	NOUN
ejpam-5578	410	9	,	,	PUNCT
ejpam-5578	410	10	we	we	PRON
ejpam-5578	410	11	need	need	VERB
ejpam-5578	410	12	to	to	PART
ejpam-5578	410	13	prove	prove	VERB
ejpam-5578	410	14	that	that	SCONJ
ejpam-5578	410	15	for	for	ADP
ejpam-5578	410	16	every	every	DET
ejpam-5578	410	17	open	open	ADJ
ejpam-5578	410	18	cover	cover	NOUN
ejpam-5578	410	19	u	u	NOUN
ejpam-5578	410	20	=	=	X
ejpam-5578	410	21	{	{	PUNCT
ejpam-5578	410	22	uα	uα	NOUN
ejpam-5578	410	23	}	}	PUNCT
ejpam-5578	410	24	of	of	ADP
ejpam-5578	410	25	x	x	PRON
ejpam-5578	410	26	,	,	PUNCT
ejpam-5578	410	27	there	there	PRON
ejpam-5578	410	28	exists	exist	VERB
ejpam-5578	410	29	a	a	DET
ejpam-5578	410	30	countable	countable	ADJ
ejpam-5578	410	31	subcover	subcover	NOUN
ejpam-5578	410	32	v	v	NOUN
ejpam-5578	410	33	=	=	PUNCT
ejpam-5578	410	34	{	{	PUNCT
ejpam-5578	410	35	vβ	vβ	NOUN
ejpam-5578	410	36	}	}	PUNCT
ejpam-5578	410	37	such	such	ADJ
ejpam-5578	410	38	that	that	SCONJ
ejpam-5578	410	39	x	x	SYM
ejpam-5578	410	40	⊆	⊆	NUM
ejpam-5578	410	41	⋃	⋃	ADP
ejpam-5578	410	42	β	β	X
ejpam-5578	410	43	vβ	vβ	NOUN
ejpam-5578	410	44	,	,	PUNCT
ejpam-5578	410	45	and	and	CCONJ
ejpam-5578	410	46	each	each	DET
ejpam-5578	410	47	vβ	vβ	NOUN
ejpam-5578	410	48	is	be	AUX
ejpam-5578	410	49	a	a	DET
ejpam-5578	410	50	tri	tri	ADJ
ejpam-5578	410	51	-	-	ADJ
ejpam-5578	410	52	open	open	ADJ
ejpam-5578	410	53	set	set	NOUN
ejpam-5578	410	54	.	.	PUNCT
ejpam-5578	411	1	since	since	SCONJ
ejpam-5578	411	2	x	x	PRON
ejpam-5578	411	3	is	be	AUX
ejpam-5578	411	4	a	a	DET
ejpam-5578	411	5	subspace	subspace	NOUN
ejpam-5578	411	6	of	of	ADP
ejpam-5578	411	7	q	q	NOUN
ejpam-5578	411	8	,	,	PUNCT
ejpam-5578	411	9	the	the	DET
ejpam-5578	411	10	open	open	ADJ
ejpam-5578	411	11	cover	cover	NOUN
ejpam-5578	411	12	u	u	NOUN
ejpam-5578	411	13	of	of	ADP
ejpam-5578	411	14	x	x	PUNCT
ejpam-5578	411	15	is	be	AUX
ejpam-5578	411	16	also	also	ADV
ejpam-5578	411	17	an	an	DET
ejpam-5578	411	18	open	open	ADJ
ejpam-5578	411	19	cover	cover	NOUN
ejpam-5578	411	20	of	of	ADP
ejpam-5578	411	21	q.	q.	NOUN
ejpam-5578	411	22	since	since	SCONJ
ejpam-5578	411	23	(	(	PUNCT
ejpam-5578	411	24	q	q	ADJ
ejpam-5578	411	25	,	,	PUNCT
ejpam-5578	411	26	ϱ1	ϱ1	NOUN
ejpam-5578	411	27	,	,	PUNCT
ejpam-5578	411	28	ϱ2	ϱ2	NOUN
ejpam-5578	411	29	,	,	PUNCT
ejpam-5578	411	30	ϱ3	ϱ3	PROPN
ejpam-5578	411	31	)	)	PUNCT
ejpam-5578	411	32	is	be	AUX
ejpam-5578	411	33	tri	tri	ADJ
ejpam-5578	411	34	-	-	NOUN
ejpam-5578	411	35	metalindelöf	metalindelöf	NOUN
ejpam-5578	411	36	,	,	PUNCT
ejpam-5578	411	37	there	there	PRON
ejpam-5578	411	38	exists	exist	VERB
ejpam-5578	411	39	a	a	DET
ejpam-5578	411	40	countable	countable	ADJ
ejpam-5578	411	41	subcover	subcover	PROPN
ejpam-5578	411	42	w	w	PROPN
ejpam-5578	412	1	=	=	PUNCT
ejpam-5578	412	2	{	{	PUNCT
ejpam-5578	412	3	wγ	wγ	NOUN
ejpam-5578	412	4	}	}	PUNCT
ejpam-5578	412	5	of	of	ADP
ejpam-5578	412	6	q	q	NOUN
ejpam-5578	412	7	,	,	PUNCT
ejpam-5578	412	8	where	where	SCONJ
ejpam-5578	412	9	each	each	DET
ejpam-5578	412	10	wγ	wγ	NOUN
ejpam-5578	412	11	is	be	AUX
ejpam-5578	412	12	a	a	DET
ejpam-5578	412	13	tri	tri	ADJ
ejpam-5578	412	14	-	-	ADJ
ejpam-5578	412	15	open	open	ADJ
ejpam-5578	412	16	set	set	NOUN
ejpam-5578	412	17	,	,	PUNCT
ejpam-5578	412	18	such	such	ADJ
ejpam-5578	412	19	that	that	DET
ejpam-5578	412	20	q	q	NOUN
ejpam-5578	413	1	=	=	X
ejpam-5578	413	2	⋃	⋃	NOUN
ejpam-5578	413	3	γ	γ	X
ejpam-5578	413	4	wγ	wγ	NOUN
ejpam-5578	413	5	.	.	PUNCT
ejpam-5578	414	1	now	now	ADV
ejpam-5578	414	2	,	,	PUNCT
ejpam-5578	414	3	because	because	SCONJ
ejpam-5578	414	4	x	x	PROPN
ejpam-5578	414	5	is	be	AUX
ejpam-5578	414	6	tri	tri	ADJ
ejpam-5578	414	7	-	-	ADJ
ejpam-5578	414	8	closed	closed	ADJ
ejpam-5578	414	9	in	in	ADP
ejpam-5578	414	10	q	q	NOUN
ejpam-5578	414	11	,	,	PUNCT
ejpam-5578	414	12	each	each	PRON
ejpam-5578	414	13	set	set	VERB
ejpam-5578	414	14	wγ	wγ	PRON
ejpam-5578	414	15	∩x	∩x	PROPN
ejpam-5578	414	16	is	be	AUX
ejpam-5578	414	17	tri	tri	ADJ
ejpam-5578	414	18	-	-	ADJ
ejpam-5578	414	19	open	open	ADJ
ejpam-5578	414	20	in	in	ADP
ejpam-5578	414	21	x.	x.	NOUN
ejpam-5578	414	22	therefore	therefore	ADV
ejpam-5578	414	23	,	,	PUNCT
ejpam-5578	414	24	the	the	DET
ejpam-5578	414	25	collection	collection	NOUN
ejpam-5578	414	26	v	v	NOUN
ejpam-5578	414	27	=	=	SYM
ejpam-5578	414	28	{	{	PUNCT
ejpam-5578	414	29	wγ	wγ	NOUN
ejpam-5578	414	30	∩x	∩x	NOUN
ejpam-5578	414	31	}	}	PUNCT
ejpam-5578	414	32	forms	form	VERB
ejpam-5578	414	33	a	a	DET
ejpam-5578	414	34	countable	countable	ADJ
ejpam-5578	414	35	subcover	subcover	NOUN
ejpam-5578	414	36	of	of	ADP
ejpam-5578	414	37	x	x	PROPN
ejpam-5578	414	38	and	and	CCONJ
ejpam-5578	414	39	each	each	PRON
ejpam-5578	414	40	wγ	wγ	PRON
ejpam-5578	414	41	∩x	∩x	ADJ
ejpam-5578	414	42	is	be	AUX
ejpam-5578	414	43	tri	tri	ADJ
ejpam-5578	414	44	-	-	ADJ
ejpam-5578	414	45	open	open	ADJ
ejpam-5578	414	46	in	in	ADP
ejpam-5578	414	47	x.	x.	NOUN
ejpam-5578	414	48	hence	hence	ADV
ejpam-5578	414	49	,	,	PUNCT
ejpam-5578	414	50	x	x	X
ejpam-5578	414	51	is	be	AUX
ejpam-5578	414	52	tri	tri	ADJ
ejpam-5578	414	53	-	-	ADJ
ejpam-5578	414	54	metalindelöf	metalindelöf	ADJ
ejpam-5578	414	55	.	.	PUNCT
ejpam-5578	415	1	theorem	theorem	VERB
ejpam-5578	415	2	18	18	NUM
ejpam-5578	415	3	.	.	PUNCT
ejpam-5578	416	1	every	every	DET
ejpam-5578	416	2	tri	tri	ADJ
ejpam-5578	416	3	-	-	NOUN
ejpam-5578	416	4	metalindelöf	metalindelöf	ADJ
ejpam-5578	416	5	subset	subset	NOUN
ejpam-5578	416	6	of	of	ADP
ejpam-5578	416	7	a	a	DET
ejpam-5578	416	8	tri	tri	NOUN
ejpam-5578	416	9	-	-	NOUN
ejpam-5578	416	10	t2	t2	ADJ
ejpam-5578	416	11	locally	locally	ADV
ejpam-5578	416	12	indiscrete	indiscrete	ADJ
ejpam-5578	416	13	space	space	NOUN
ejpam-5578	416	14	(	(	PUNCT
ejpam-5578	416	15	q	q	NOUN
ejpam-5578	416	16	,	,	PUNCT
ejpam-5578	416	17	ϱ1	ϱ1	NOUN
ejpam-5578	416	18	,	,	PUNCT
ejpam-5578	416	19	ϱ2	ϱ2	NOUN
ejpam-5578	416	20	,	,	PUNCT
ejpam-5578	416	21	ϱ3	ϱ3	PROPN
ejpam-5578	416	22	)	)	PUNCT
ejpam-5578	416	23	is	be	AUX
ejpam-5578	416	24	tri	tri	ADJ
ejpam-5578	416	25	-	-	ADJ
ejpam-5578	416	26	closed	closed	ADJ
ejpam-5578	416	27	.	.	PUNCT
ejpam-5578	417	1	proof	proof	NOUN
ejpam-5578	417	2	.	.	PUNCT
ejpam-5578	418	1	let	let	VERB
ejpam-5578	418	2	f	f	NOUN
ejpam-5578	418	3	:	:	PUNCT
ejpam-5578	418	4	(	(	PUNCT
ejpam-5578	418	5	q	q	ADJ
ejpam-5578	418	6	,	,	PUNCT
ejpam-5578	418	7	ϱ1	ϱ1	NOUN
ejpam-5578	418	8	,	,	PUNCT
ejpam-5578	418	9	ϱ2	ϱ2	NOUN
ejpam-5578	418	10	,	,	PUNCT
ejpam-5578	418	11	ϱ3	ϱ3	PROPN
ejpam-5578	418	12	)	)	PUNCT
ejpam-5578	418	13	→	→	SYM
ejpam-5578	418	14	(	(	PUNCT
ejpam-5578	418	15	y	y	PROPN
ejpam-5578	418	16	,	,	PUNCT
ejpam-5578	418	17	σ1	σ1	PROPN
ejpam-5578	418	18	,	,	PUNCT
ejpam-5578	418	19	σ2	σ2	PROPN
ejpam-5578	418	20	,	,	PUNCT
ejpam-5578	418	21	σ3	σ3	PROPN
ejpam-5578	418	22	)	)	PUNCT
ejpam-5578	418	23	be	be	AUX
ejpam-5578	418	24	a	a	DET
ejpam-5578	418	25	bijective	bijective	ADJ
ejpam-5578	418	26	and	and	CCONJ
ejpam-5578	418	27	continuous	continuous	ADJ
ejpam-5578	418	28	map	map	NOUN
ejpam-5578	418	29	.	.	PUNCT
ejpam-5578	419	1	suppose	suppose	VERB
ejpam-5578	419	2	that	that	SCONJ
ejpam-5578	419	3	(	(	PUNCT
ejpam-5578	419	4	y	y	PROPN
ejpam-5578	419	5	,	,	PUNCT
ejpam-5578	419	6	σ1	σ1	PROPN
ejpam-5578	419	7	,	,	PUNCT
ejpam-5578	419	8	σ2	σ2	PROPN
ejpam-5578	419	9	,	,	PUNCT
ejpam-5578	419	10	σ3	σ3	PROPN
ejpam-5578	419	11	)	)	PUNCT
ejpam-5578	419	12	is	be	AUX
ejpam-5578	419	13	a	a	DET
ejpam-5578	419	14	tri	tri	ADJ
ejpam-5578	419	15	-	-	ADJ
ejpam-5578	419	16	t2	t2	ADJ
ejpam-5578	419	17	and	and	CCONJ
ejpam-5578	419	18	tripartite	tripartite	ADJ
ejpam-5578	419	19	locally	locally	ADV
ejpam-5578	419	20	indiscrete	indiscrete	ADJ
ejpam-5578	419	21	space	space	NOUN
ejpam-5578	419	22	,	,	PUNCT
ejpam-5578	419	23	and	and	CCONJ
ejpam-5578	419	24	that	that	SCONJ
ejpam-5578	419	25	(	(	PUNCT
ejpam-5578	419	26	q	q	X
ejpam-5578	419	27	,	,	PUNCT
ejpam-5578	419	28	ϱ1	ϱ1	NOUN
ejpam-5578	419	29	,	,	PUNCT
ejpam-5578	419	30	ϱ2	ϱ2	NOUN
ejpam-5578	419	31	,	,	PUNCT
ejpam-5578	419	32	ϱ3	ϱ3	PROPN
ejpam-5578	419	33	)	)	PUNCT
ejpam-5578	419	34	is	be	AUX
ejpam-5578	419	35	tri	tri	ADJ
ejpam-5578	419	36	-	-	NOUN
ejpam-5578	419	37	metalindelöf	metalindelöf	NOUN
ejpam-5578	419	38	.	.	PUNCT
ejpam-5578	420	1	then	then	ADV
ejpam-5578	420	2	,	,	PUNCT
ejpam-5578	420	3	f	f	PROPN
ejpam-5578	420	4	is	be	AUX
ejpam-5578	420	5	a	a	DET
ejpam-5578	420	6	tri	tri	NOUN
ejpam-5578	420	7	-	-	NOUN
ejpam-5578	420	8	homomorphism	homomorphism	NOUN
ejpam-5578	420	9	.	.	PUNCT
ejpam-5578	421	1	it	it	PRON
ejpam-5578	421	2	suffices	suffice	VERB
ejpam-5578	421	3	to	to	PART
ejpam-5578	421	4	show	show	VERB
ejpam-5578	421	5	that	that	SCONJ
ejpam-5578	421	6	f	f	PROPN
ejpam-5578	421	7	is	be	AUX
ejpam-5578	421	8	tri	tri	ADJ
ejpam-5578	421	9	-	-	ADJ
ejpam-5578	421	10	closed	closed	ADJ
ejpam-5578	421	11	.	.	PUNCT
ejpam-5578	422	1	let	let	VERB
ejpam-5578	422	2	a	a	PRON
ejpam-5578	422	3	be	be	AUX
ejpam-5578	422	4	a	a	DET
ejpam-5578	422	5	proper	proper	ADJ
ejpam-5578	422	6	tri	tri	ADJ
ejpam-5578	422	7	-	-	ADJ
ejpam-5578	422	8	closed	closed	ADJ
ejpam-5578	422	9	subset	subset	NOUN
ejpam-5578	422	10	of	of	ADP
ejpam-5578	422	11	q.	q.	PROPN
ejpam-5578	422	12	since	since	SCONJ
ejpam-5578	422	13	a	a	PRON
ejpam-5578	422	14	is	be	AUX
ejpam-5578	422	15	a	a	DET
ejpam-5578	422	16	tri	tri	ADJ
ejpam-5578	422	17	-	-	ADJ
ejpam-5578	422	18	metalindelöf	metalindelöf	ADJ
ejpam-5578	422	19	subset	subset	NOUN
ejpam-5578	422	20	of	of	ADP
ejpam-5578	422	21	q	q	NOUN
ejpam-5578	422	22	,	,	PUNCT
ejpam-5578	422	23	and	and	CCONJ
ejpam-5578	422	24	f	f	X
ejpam-5578	422	25	:	:	PUNCT
ejpam-5578	422	26	(	(	PUNCT
ejpam-5578	422	27	q	q	ADJ
ejpam-5578	422	28	,	,	PUNCT
ejpam-5578	422	29	ϱ1	ϱ1	NOUN
ejpam-5578	422	30	,	,	PUNCT
ejpam-5578	422	31	ϱ2	ϱ2	NOUN
ejpam-5578	422	32	,	,	PUNCT
ejpam-5578	422	33	ϱ3	ϱ3	PROPN
ejpam-5578	422	34	)	)	PUNCT
ejpam-5578	422	35	→	→	SYM
ejpam-5578	422	36	(	(	PUNCT
ejpam-5578	422	37	y	y	PROPN
ejpam-5578	422	38	,	,	PUNCT
ejpam-5578	422	39	σ1	σ1	PROPN
ejpam-5578	422	40	,	,	PUNCT
ejpam-5578	422	41	σ2	σ2	PROPN
ejpam-5578	422	42	,	,	PUNCT
ejpam-5578	422	43	σ3	σ3	PROPN
ejpam-5578	422	44	)	)	PUNCT
ejpam-5578	422	45	is	be	AUX
ejpam-5578	422	46	continuous	continuous	ADJ
ejpam-5578	422	47	,	,	PUNCT
ejpam-5578	422	48	it	it	PRON
ejpam-5578	422	49	follows	follow	VERB
ejpam-5578	422	50	that	that	PRON
ejpam-5578	422	51	f(a	f(a	PROPN
ejpam-5578	422	52	)	)	PUNCT
ejpam-5578	423	1	j.	j.	PROPN
ejpam-5578	423	2	oudetallah	oudetallah	PROPN
ejpam-5578	423	3	et	et	PROPN
ejpam-5578	423	4	al	al	PROPN
ejpam-5578	423	5	.	.	PUNCT
ejpam-5578	423	6	/	/	SYM
ejpam-5578	423	7	eur	eur	PROPN
ejpam-5578	423	8	.	.	PUNCT
ejpam-5578	424	1	j.	j.	PROPN
ejpam-5578	424	2	pure	pure	PROPN
ejpam-5578	424	3	appl	appl	PROPN
ejpam-5578	424	4	.	.	PROPN
ejpam-5578	424	5	math	math	PROPN
ejpam-5578	424	6	,	,	PUNCT
ejpam-5578	424	7	18	18	NUM
ejpam-5578	424	8	(	(	PUNCT
ejpam-5578	424	9	2	2	NUM
ejpam-5578	424	10	)	)	PUNCT
ejpam-5578	424	11	(	(	PUNCT
ejpam-5578	424	12	2025	2025	NUM
ejpam-5578	424	13	)	)	PUNCT
ejpam-5578	424	14	,	,	PUNCT
ejpam-5578	424	15	5578	5578	NUM
ejpam-5578	424	16	18	18	NUM
ejpam-5578	424	17	of	of	ADP
ejpam-5578	424	18	19	19	NUM
ejpam-5578	424	19	is	be	AUX
ejpam-5578	424	20	a	a	DET
ejpam-5578	424	21	tri	tri	ADJ
ejpam-5578	424	22	-	-	ADJ
ejpam-5578	424	23	metalindelöf	metalindelöf	ADJ
ejpam-5578	424	24	subset	subset	NOUN
ejpam-5578	424	25	of	of	ADP
ejpam-5578	424	26	y	y	PROPN
ejpam-5578	424	27	.	.	PUNCT
ejpam-5578	425	1	thus	thus	ADV
ejpam-5578	425	2	,	,	PUNCT
ejpam-5578	425	3	f(a	f(a	PROPN
ejpam-5578	425	4	)	)	PUNCT
ejpam-5578	425	5	is	be	AUX
ejpam-5578	425	6	a	a	DET
ejpam-5578	425	7	tri	tri	ADJ
ejpam-5578	425	8	-	-	ADJ
ejpam-5578	425	9	closed	closed	ADJ
ejpam-5578	425	10	subset	subset	NOUN
ejpam-5578	425	11	of	of	ADP
ejpam-5578	425	12	y	y	PROPN
ejpam-5578	425	13	.	.	PUNCT
ejpam-5578	426	1	therefore	therefore	ADV
ejpam-5578	426	2	,	,	PUNCT
ejpam-5578	426	3	f	f	X
ejpam-5578	426	4	:	:	PUNCT
ejpam-5578	426	5	(	(	PUNCT
ejpam-5578	426	6	q	q	ADJ
ejpam-5578	426	7	,	,	PUNCT
ejpam-5578	426	8	ϱ1	ϱ1	NOUN
ejpam-5578	426	9	,	,	PUNCT
ejpam-5578	426	10	ϱ2	ϱ2	NOUN
ejpam-5578	426	11	,	,	PUNCT
ejpam-5578	426	12	ϱ3	ϱ3	PROPN
ejpam-5578	426	13	)	)	PUNCT
ejpam-5578	426	14	→	→	SYM
ejpam-5578	426	15	(	(	PUNCT
ejpam-5578	426	16	y	y	PROPN
ejpam-5578	426	17	,	,	PUNCT
ejpam-5578	426	18	σ1	σ1	PROPN
ejpam-5578	426	19	,	,	PUNCT
ejpam-5578	426	20	σ2	σ2	PROPN
ejpam-5578	426	21	,	,	PUNCT
ejpam-5578	426	22	σ3	σ3	PROPN
ejpam-5578	426	23	)	)	PUNCT
ejpam-5578	426	24	is	be	AUX
ejpam-5578	426	25	a	a	DET
ejpam-5578	426	26	tri	tri	ADJ
ejpam-5578	426	27	-	-	ADJ
ejpam-5578	426	28	closed	closed	ADJ
ejpam-5578	426	29	function	function	NOUN
ejpam-5578	426	30	.	.	PUNCT
ejpam-5578	427	1	hence	hence	ADV
ejpam-5578	427	2	,	,	PUNCT
ejpam-5578	427	3	the	the	DET
ejpam-5578	427	4	result	result	NOUN
ejpam-5578	427	5	follows	follow	VERB
ejpam-5578	427	6	.	.	PUNCT
ejpam-5578	428	1	corollary	corollary	ADJ
ejpam-5578	428	2	4	4	NUM
ejpam-5578	428	3	.	.	PUNCT
ejpam-5578	429	1	let	let	VERB
ejpam-5578	429	2	f	f	NOUN
ejpam-5578	429	3	:	:	PUNCT
ejpam-5578	429	4	(	(	PUNCT
ejpam-5578	429	5	q	q	ADJ
ejpam-5578	429	6	,	,	PUNCT
ejpam-5578	429	7	ϱ1	ϱ1	NOUN
ejpam-5578	429	8	,	,	PUNCT
ejpam-5578	429	9	ϱ2	ϱ2	NOUN
ejpam-5578	429	10	,	,	PUNCT
ejpam-5578	429	11	ϱ3	ϱ3	PROPN
ejpam-5578	429	12	)	)	PUNCT
ejpam-5578	429	13	→	→	SYM
ejpam-5578	429	14	(	(	PUNCT
ejpam-5578	429	15	y	y	PROPN
ejpam-5578	429	16	,	,	PUNCT
ejpam-5578	429	17	σ1	σ1	PROPN
ejpam-5578	429	18	,	,	PUNCT
ejpam-5578	429	19	σ2	σ2	PROPN
ejpam-5578	429	20	,	,	PUNCT
ejpam-5578	429	21	σ3	σ3	PROPN
ejpam-5578	429	22	)	)	PUNCT
ejpam-5578	429	23	be	be	AUX
ejpam-5578	429	24	a	a	DET
ejpam-5578	429	25	tripartite	tripartite	ADJ
ejpam-5578	429	26	bijective	bijective	ADJ
ejpam-5578	429	27	continuous	continuous	ADJ
ejpam-5578	429	28	map	map	NOUN
ejpam-5578	429	29	.	.	PUNCT
ejpam-5578	430	1	if	if	SCONJ
ejpam-5578	430	2	(	(	PUNCT
ejpam-5578	430	3	y	y	PROPN
ejpam-5578	430	4	,	,	PUNCT
ejpam-5578	430	5	σ1	σ1	PROPN
ejpam-5578	430	6	,	,	PUNCT
ejpam-5578	430	7	σ2	σ2	PROPN
ejpam-5578	430	8	,	,	PUNCT
ejpam-5578	430	9	σ3	σ3	PROPN
ejpam-5578	430	10	)	)	PUNCT
ejpam-5578	430	11	is	be	AUX
ejpam-5578	430	12	a	a	DET
ejpam-5578	430	13	tri	tri	ADJ
ejpam-5578	430	14	-	-	ADJ
ejpam-5578	430	15	t2	t2	ADJ
ejpam-5578	430	16	and	and	CCONJ
ejpam-5578	430	17	tripartite	tripartite	ADJ
ejpam-5578	430	18	locally	locally	ADV
ejpam-5578	430	19	indiscrete	indiscrete	ADJ
ejpam-5578	430	20	space	space	NOUN
ejpam-5578	430	21	,	,	PUNCT
ejpam-5578	430	22	and	and	CCONJ
ejpam-5578	430	23	(	(	PUNCT
ejpam-5578	430	24	q	q	ADJ
ejpam-5578	430	25	,	,	PUNCT
ejpam-5578	430	26	ϱ1	ϱ1	NOUN
ejpam-5578	430	27	,	,	PUNCT
ejpam-5578	430	28	ϱ2	ϱ2	NOUN
ejpam-5578	430	29	,	,	PUNCT
ejpam-5578	430	30	ϱ3	ϱ3	PROPN
ejpam-5578	430	31	)	)	PUNCT
ejpam-5578	430	32	is	be	AUX
ejpam-5578	430	33	tri	tri	ADJ
ejpam-5578	430	34	-	-	NOUN
ejpam-5578	430	35	paralindelöf	paralindelöf	NOUN
ejpam-5578	430	36	,	,	PUNCT
ejpam-5578	430	37	then	then	ADV
ejpam-5578	430	38	f	f	PROPN
ejpam-5578	430	39	is	be	AUX
ejpam-5578	430	40	a	a	DET
ejpam-5578	430	41	tri	tri	NOUN
ejpam-5578	430	42	-	-	NOUN
ejpam-5578	430	43	homomorphism	homomorphism	NOUN
ejpam-5578	430	44	.	.	PUNCT
ejpam-5578	431	1	proof	proof	NOUN
ejpam-5578	431	2	.	.	PUNCT
ejpam-5578	432	1	clearly	clearly	ADV
ejpam-5578	432	2	by	by	ADP
ejpam-5578	432	3	above	above	ADP
ejpam-5578	432	4	theorem	theorem	NOUN
ejpam-5578	432	5	5	5	NUM
ejpam-5578	432	6	.	.	NOUN
ejpam-5578	432	7	conclusion	conclusion	NOUN
ejpam-5578	432	8	and	and	CCONJ
ejpam-5578	432	9	future	future	ADJ
ejpam-5578	432	10	directions	direction	NOUN
ejpam-5578	432	11	in	in	ADP
ejpam-5578	432	12	this	this	DET
ejpam-5578	432	13	study	study	NOUN
ejpam-5578	432	14	,	,	PUNCT
ejpam-5578	432	15	we	we	PRON
ejpam-5578	432	16	have	have	AUX
ejpam-5578	432	17	introduced	introduce	VERB
ejpam-5578	432	18	and	and	CCONJ
ejpam-5578	432	19	explored	explore	VERB
ejpam-5578	432	20	the	the	DET
ejpam-5578	432	21	concepts	concept	NOUN
ejpam-5578	432	22	of	of	ADP
ejpam-5578	432	23	lindelöfness	lindelöfness	NOUN
ejpam-5578	432	24	,	,	PUNCT
ejpam-5578	432	25	metalindelöfness	metalindelöfness	NOUN
ejpam-5578	432	26	,	,	PUNCT
ejpam-5578	432	27	and	and	CCONJ
ejpam-5578	432	28	nearly	nearly	ADV
ejpam-5578	432	29	lindelöfness	lindelöfness	NOUN
ejpam-5578	432	30	in	in	ADP
ejpam-5578	432	31	the	the	DET
ejpam-5578	432	32	setting	setting	NOUN
ejpam-5578	432	33	of	of	ADP
ejpam-5578	432	34	tri	tri	ADJ
ejpam-5578	432	35	-	-	ADJ
ejpam-5578	432	36	topological	topological	ADJ
ejpam-5578	432	37	spaces	space	NOUN
ejpam-5578	432	38	.	.	PUNCT
ejpam-5578	433	1	by	by	ADP
ejpam-5578	433	2	extending	extend	VERB
ejpam-5578	433	3	classical	classical	ADJ
ejpam-5578	433	4	topological	topological	ADJ
ejpam-5578	433	5	properties	property	NOUN
ejpam-5578	433	6	to	to	ADP
ejpam-5578	433	7	this	this	DET
ejpam-5578	433	8	generalized	generalize	VERB
ejpam-5578	433	9	framework	framework	NOUN
ejpam-5578	433	10	,	,	PUNCT
ejpam-5578	433	11	we	we	PRON
ejpam-5578	433	12	established	establish	VERB
ejpam-5578	433	13	several	several	ADJ
ejpam-5578	433	14	theoretical	theoretical	ADJ
ejpam-5578	433	15	results	result	NOUN
ejpam-5578	433	16	and	and	CCONJ
ejpam-5578	433	17	analyzed	analyze	VERB
ejpam-5578	433	18	their	their	PRON
ejpam-5578	433	19	behavior	behavior	NOUN
ejpam-5578	433	20	.	.	PUNCT
ejpam-5578	434	1	various	various	ADJ
ejpam-5578	434	2	separation	separation	NOUN
ejpam-5578	434	3	axioms	axiom	NOUN
ejpam-5578	434	4	were	be	AUX
ejpam-5578	434	5	examined	examine	VERB
ejpam-5578	434	6	,	,	PUNCT
ejpam-5578	434	7	revealing	reveal	VERB
ejpam-5578	434	8	intricate	intricate	ADJ
ejpam-5578	434	9	relationships	relationship	NOUN
ejpam-5578	434	10	between	between	ADP
ejpam-5578	434	11	tri	tri	ADJ
ejpam-5578	434	12	-	-	NOUN
ejpam-5578	434	13	compactness	compactness	ADJ
ejpam-5578	434	14	,	,	PUNCT
ejpam-5578	434	15	tri	tri	NOUN
ejpam-5578	434	16	-	-	NOUN
ejpam-5578	434	17	lindelöfness	lindelöfness	ADJ
ejpam-5578	434	18	,	,	PUNCT
ejpam-5578	434	19	and	and	CCONJ
ejpam-5578	434	20	trimetalindelöfness	trimetalindelöfness	NUM
ejpam-5578	434	21	.	.	PUNCT
ejpam-5578	435	1	the	the	DET
ejpam-5578	435	2	findings	finding	NOUN
ejpam-5578	435	3	contribute	contribute	VERB
ejpam-5578	435	4	to	to	ADP
ejpam-5578	435	5	the	the	DET
ejpam-5578	435	6	broader	broad	ADJ
ejpam-5578	435	7	understanding	understanding	NOUN
ejpam-5578	435	8	of	of	ADP
ejpam-5578	435	9	general	general	ADJ
ejpam-5578	435	10	topology	topology	NOUN
ejpam-5578	435	11	,	,	PUNCT
ejpam-5578	435	12	offering	offer	VERB
ejpam-5578	435	13	new	new	ADJ
ejpam-5578	435	14	insights	insight	NOUN
ejpam-5578	435	15	into	into	ADP
ejpam-5578	435	16	the	the	DET
ejpam-5578	435	17	structure	structure	NOUN
ejpam-5578	435	18	and	and	CCONJ
ejpam-5578	435	19	properties	property	NOUN
ejpam-5578	435	20	of	of	ADP
ejpam-5578	435	21	tri	tri	ADJ
ejpam-5578	435	22	-	-	ADJ
ejpam-5578	435	23	topological	topological	ADJ
ejpam-5578	435	24	spaces	space	NOUN
ejpam-5578	435	25	.	.	PUNCT
ejpam-5578	436	1	future	future	ADJ
ejpam-5578	436	2	research	research	NOUN
ejpam-5578	436	3	can	can	AUX
ejpam-5578	436	4	extend	extend	VERB
ejpam-5578	436	5	these	these	DET
ejpam-5578	436	6	findings	finding	NOUN
ejpam-5578	436	7	in	in	ADP
ejpam-5578	436	8	several	several	ADJ
ejpam-5578	436	9	directions	direction	NOUN
ejpam-5578	436	10	.	.	PUNCT
ejpam-5578	437	1	one	one	NUM
ejpam-5578	437	2	promising	promise	VERB
ejpam-5578	437	3	avenue	avenue	NOUN
ejpam-5578	437	4	is	be	AUX
ejpam-5578	437	5	the	the	DET
ejpam-5578	437	6	investigation	investigation	NOUN
ejpam-5578	437	7	of	of	ADP
ejpam-5578	437	8	finer	fine	ADJ
ejpam-5578	437	9	separation	separation	NOUN
ejpam-5578	437	10	axioms	axiom	NOUN
ejpam-5578	437	11	such	such	ADJ
ejpam-5578	437	12	as	as	ADP
ejpam-5578	437	13	tri	tri	ADJ
ejpam-5578	437	14	-	-	ADJ
ejpam-5578	437	15	regularity	regularity	ADJ
ejpam-5578	437	16	and	and	CCONJ
ejpam-5578	437	17	tri	tri	ADJ
ejpam-5578	437	18	-	-	NOUN
ejpam-5578	437	19	normality	normality	ADJ
ejpam-5578	437	20	,	,	PUNCT
ejpam-5578	437	21	as	as	ADV
ejpam-5578	437	22	well	well	ADV
ejpam-5578	437	23	as	as	ADP
ejpam-5578	437	24	their	their	PRON
ejpam-5578	437	25	implications	implication	NOUN
ejpam-5578	437	26	in	in	ADP
ejpam-5578	437	27	different	different	ADJ
ejpam-5578	437	28	tri	tri	ADJ
ejpam-5578	437	29	-	-	ADJ
ejpam-5578	437	30	topological	topological	ADJ
ejpam-5578	437	31	settings	setting	NOUN
ejpam-5578	437	32	.	.	PUNCT
ejpam-5578	438	1	another	another	DET
ejpam-5578	438	2	important	important	ADJ
ejpam-5578	438	3	direction	direction	NOUN
ejpam-5578	438	4	is	be	AUX
ejpam-5578	438	5	the	the	DET
ejpam-5578	438	6	extension	extension	NOUN
ejpam-5578	438	7	of	of	ADP
ejpam-5578	438	8	these	these	DET
ejpam-5578	438	9	concepts	concept	NOUN
ejpam-5578	438	10	to	to	ADP
ejpam-5578	438	11	fuzzy	fuzzy	ADJ
ejpam-5578	438	12	tri	tri	ADJ
ejpam-5578	438	13	-	-	ADJ
ejpam-5578	438	14	topological	topological	ADJ
ejpam-5578	438	15	spaces	space	NOUN
ejpam-5578	438	16	,	,	PUNCT
ejpam-5578	438	17	which	which	PRON
ejpam-5578	438	18	could	could	AUX
ejpam-5578	438	19	provide	provide	VERB
ejpam-5578	438	20	useful	useful	ADJ
ejpam-5578	438	21	applications	application	NOUN
ejpam-5578	438	22	in	in	ADP
ejpam-5578	438	23	both	both	CCONJ
ejpam-5578	438	24	theoretical	theoretical	ADJ
ejpam-5578	438	25	and	and	CCONJ
ejpam-5578	438	26	applied	applied	ADJ
ejpam-5578	438	27	mathematics	mathematic	NOUN
ejpam-5578	438	28	.	.	PUNCT
ejpam-5578	439	1	additionally	additionally	ADV
ejpam-5578	439	2	,	,	PUNCT
ejpam-5578	439	3	further	further	ADJ
ejpam-5578	439	4	exploration	exploration	NOUN
ejpam-5578	439	5	of	of	ADP
ejpam-5578	439	6	the	the	DET
ejpam-5578	439	7	behavior	behavior	NOUN
ejpam-5578	439	8	of	of	ADP
ejpam-5578	439	9	tri	tri	ADJ
ejpam-5578	439	10	-	-	ADJ
ejpam-5578	439	11	topological	topological	ADJ
ejpam-5578	439	12	spaces	space	NOUN
ejpam-5578	439	13	under	under	ADP
ejpam-5578	439	14	various	various	ADJ
ejpam-5578	439	15	types	type	NOUN
ejpam-5578	439	16	of	of	ADP
ejpam-5578	439	17	mappings	mapping	NOUN
ejpam-5578	439	18	,	,	PUNCT
ejpam-5578	439	19	including	include	VERB
ejpam-5578	439	20	continuous	continuous	ADJ
ejpam-5578	439	21	,	,	PUNCT
ejpam-5578	439	22	perfect	perfect	ADJ
ejpam-5578	439	23	,	,	PUNCT
ejpam-5578	439	24	and	and	CCONJ
ejpam-5578	439	25	quotient	quotient	NOUN
ejpam-5578	439	26	functions	function	NOUN
ejpam-5578	439	27	,	,	PUNCT
ejpam-5578	439	28	would	would	AUX
ejpam-5578	439	29	enhance	enhance	VERB
ejpam-5578	439	30	our	our	PRON
ejpam-5578	439	31	understanding	understanding	NOUN
ejpam-5578	439	32	of	of	ADP
ejpam-5578	439	33	their	their	PRON
ejpam-5578	439	34	structural	structural	ADJ
ejpam-5578	439	35	properties	property	NOUN
ejpam-5578	439	36	.	.	PUNCT
ejpam-5578	440	1	moreover	moreover	ADV
ejpam-5578	440	2	,	,	PUNCT
ejpam-5578	440	3	a	a	DET
ejpam-5578	440	4	deeper	deep	ADJ
ejpam-5578	440	5	study	study	NOUN
ejpam-5578	440	6	of	of	ADP
ejpam-5578	440	7	the	the	DET
ejpam-5578	440	8	interplay	interplay	NOUN
ejpam-5578	440	9	between	between	ADP
ejpam-5578	440	10	tri	tri	ADJ
ejpam-5578	440	11	-	-	ADJ
ejpam-5578	440	12	nearly	nearly	ADV
ejpam-5578	440	13	compactness	compactness	NOUN
ejpam-5578	440	14	and	and	CCONJ
ejpam-5578	440	15	tri	tri	NOUN
ejpam-5578	440	16	-	-	ADJ
ejpam-5578	440	17	nearly	nearly	ADV
ejpam-5578	440	18	lindelöfness	lindelöfness	ADJ
ejpam-5578	440	19	in	in	ADP
ejpam-5578	440	20	different	different	ADJ
ejpam-5578	440	21	classes	class	NOUN
ejpam-5578	440	22	of	of	ADP
ejpam-5578	440	23	spaces	space	NOUN
ejpam-5578	440	24	could	could	AUX
ejpam-5578	440	25	lead	lead	VERB
ejpam-5578	440	26	to	to	ADP
ejpam-5578	440	27	new	new	ADJ
ejpam-5578	440	28	theoretical	theoretical	ADJ
ejpam-5578	440	29	developments	development	NOUN
ejpam-5578	440	30	.	.	PUNCT
ejpam-5578	441	1	exploring	explore	VERB
ejpam-5578	441	2	the	the	DET
ejpam-5578	441	3	potential	potential	ADJ
ejpam-5578	441	4	applications	application	NOUN
ejpam-5578	441	5	of	of	ADP
ejpam-5578	441	6	these	these	DET
ejpam-5578	441	7	topological	topological	ADJ
ejpam-5578	441	8	structures	structure	NOUN
ejpam-5578	441	9	in	in	ADP
ejpam-5578	441	10	mathematical	mathematical	ADJ
ejpam-5578	441	11	analysis	analysis	NOUN
ejpam-5578	441	12	,	,	PUNCT
ejpam-5578	441	13	functional	functional	ADJ
ejpam-5578	441	14	analysis	analysis	NOUN
ejpam-5578	441	15	,	,	PUNCT
ejpam-5578	441	16	and	and	CCONJ
ejpam-5578	441	17	related	related	ADJ
ejpam-5578	441	18	disciplines	discipline	NOUN
ejpam-5578	441	19	may	may	AUX
ejpam-5578	441	20	also	also	ADV
ejpam-5578	441	21	yield	yield	VERB
ejpam-5578	441	22	significant	significant	ADJ
ejpam-5578	441	23	contributions	contribution	NOUN
ejpam-5578	441	24	.	.	PUNCT
ejpam-5578	442	1	overall	overall	ADV
ejpam-5578	442	2	,	,	PUNCT
ejpam-5578	442	3	the	the	DET
ejpam-5578	442	4	results	result	NOUN
ejpam-5578	442	5	obtained	obtain	VERB
ejpam-5578	442	6	in	in	ADP
ejpam-5578	442	7	this	this	DET
ejpam-5578	442	8	paper	paper	NOUN
ejpam-5578	442	9	lay	lie	VERB
ejpam-5578	442	10	a	a	DET
ejpam-5578	442	11	strong	strong	ADJ
ejpam-5578	442	12	foundation	foundation	NOUN
ejpam-5578	442	13	for	for	ADP
ejpam-5578	442	14	further	further	ADJ
ejpam-5578	442	15	research	research	NOUN
ejpam-5578	442	16	into	into	ADP
ejpam-5578	442	17	tri	tri	ADJ
ejpam-5578	442	18	-	-	ADJ
ejpam-5578	442	19	topological	topological	ADJ
ejpam-5578	442	20	spaces	space	NOUN
ejpam-5578	442	21	,	,	PUNCT
ejpam-5578	442	22	paving	pave	VERB
ejpam-5578	442	23	the	the	DET
ejpam-5578	442	24	way	way	NOUN
ejpam-5578	442	25	for	for	ADP
ejpam-5578	442	26	new	new	ADJ
ejpam-5578	442	27	discoveries	discovery	NOUN
ejpam-5578	442	28	and	and	CCONJ
ejpam-5578	442	29	applications	application	NOUN
ejpam-5578	442	30	in	in	ADP
ejpam-5578	442	31	topology	topology	NOUN
ejpam-5578	442	32	and	and	CCONJ
ejpam-5578	442	33	beyond	beyond	ADP
ejpam-5578	442	34	.	.	PUNCT
ejpam-5578	443	1	references	reference	NOUN
ejpam-5578	443	2	[	[	X
ejpam-5578	443	3	1	1	NUM
ejpam-5578	443	4	]	]	X
ejpam-5578	443	5	g.	g.	PROPN
ejpam-5578	443	6	farraj	farraj	PROPN
ejpam-5578	443	7	,	,	PUNCT
ejpam-5578	443	8	b.	b.	PROPN
ejpam-5578	443	9	maayah	maayah	PROPN
ejpam-5578	443	10	,	,	PUNCT
ejpam-5578	443	11	r.	r.	PROPN
ejpam-5578	443	12	khalil	khalil	PROPN
ejpam-5578	443	13	,	,	PUNCT
ejpam-5578	443	14	and	and	CCONJ
ejpam-5578	443	15	w.	w.	PROPN
ejpam-5578	443	16	beghami	beghami	PROPN
ejpam-5578	443	17	.	.	PUNCT
ejpam-5578	444	1	an	an	DET
ejpam-5578	444	2	algorithm	algorithm	NOUN
ejpam-5578	444	3	for	for	ADP
ejpam-5578	444	4	solving	solve	VERB
ejpam-5578	444	5	fractional	fractional	ADJ
ejpam-5578	444	6	differential	differential	ADJ
ejpam-5578	444	7	equations	equation	NOUN
ejpam-5578	444	8	using	use	VERB
ejpam-5578	444	9	conformable	conformable	ADJ
ejpam-5578	444	10	optimized	optimize	VERB
ejpam-5578	444	11	decomposition	decomposition	NOUN
ejpam-5578	444	12	method	method	NOUN
ejpam-5578	444	13	.	.	PUNCT
ejpam-5578	445	1	international	international	ADJ
ejpam-5578	445	2	journal	journal	NOUN
ejpam-5578	445	3	of	of	ADP
ejpam-5578	445	4	advances	advance	NOUN
ejpam-5578	445	5	in	in	ADP
ejpam-5578	445	6	soft	soft	ADJ
ejpam-5578	445	7	computing	computing	NOUN
ejpam-5578	445	8	and	and	CCONJ
ejpam-5578	445	9	its	its	PRON
ejpam-5578	445	10	applications	application	NOUN
ejpam-5578	445	11	,	,	PUNCT
ejpam-5578	445	12	15(1	15(1	NUM
ejpam-5578	445	13	)	)	PUNCT
ejpam-5578	445	14	,	,	PUNCT
ejpam-5578	445	15	2023	2023	NUM
ejpam-5578	445	16	.	.	PUNCT
ejpam-5578	446	1	[	[	X
ejpam-5578	446	2	2	2	NUM
ejpam-5578	446	3	]	]	X
ejpam-5578	446	4	n.	n.	PROPN
ejpam-5578	446	5	r.	r.	PROPN
ejpam-5578	446	6	anakira	anakira	PROPN
ejpam-5578	446	7	,	,	PUNCT
ejpam-5578	446	8	a.	a.	NOUN
ejpam-5578	446	9	almalki	almalki	PROPN
ejpam-5578	446	10	,	,	PUNCT
ejpam-5578	446	11	d.	d.	PROPN
ejpam-5578	446	12	katatbeh	katatbeh	PROPN
ejpam-5578	446	13	,	,	PUNCT
ejpam-5578	446	14	g.	g.	PROPN
ejpam-5578	446	15	b.	b.	PROPN
ejpam-5578	446	16	hani	hani	PROPN
ejpam-5578	446	17	,	,	PUNCT
ejpam-5578	446	18	a.	a.	PROPN
ejpam-5578	446	19	f.	f.	PROPN
ejpam-5578	446	20	jameel	jameel	PROPN
ejpam-5578	446	21	,	,	PUNCT
ejpam-5578	446	22	k.	k.	PROPN
ejpam-5578	446	23	s.	s.	PROPN
ejpam-5578	446	24	al	al	PROPN
ejpam-5578	446	25	kalbani	kalbani	PROPN
ejpam-5578	446	26	,	,	PUNCT
ejpam-5578	446	27	and	and	CCONJ
ejpam-5578	446	28	m.	m.	PROPN
ejpam-5578	446	29	abu	abu	PROPN
ejpam-5578	446	30	-	-	PUNCT
ejpam-5578	446	31	dawas	dawas	PROPN
ejpam-5578	446	32	.	.	PUNCT
ejpam-5578	447	1	an	an	DET
ejpam-5578	447	2	algorithm	algorithm	NOUN
ejpam-5578	447	3	for	for	ADP
ejpam-5578	447	4	solving	solve	VERB
ejpam-5578	447	5	linear	linear	ADJ
ejpam-5578	447	6	and	and	CCONJ
ejpam-5578	447	7	non	non	ADJ
ejpam-5578	447	8	-	-	ADJ
ejpam-5578	447	9	linear	linear	ADJ
ejpam-5578	447	10	volterra	volterra	NOUN
ejpam-5578	447	11	integrodifferential	integrodifferential	ADJ
ejpam-5578	447	12	equations	equation	NOUN
ejpam-5578	447	13	.	.	PUNCT
ejpam-5578	448	1	international	international	ADJ
ejpam-5578	448	2	journal	journal	NOUN
ejpam-5578	448	3	of	of	ADP
ejpam-5578	448	4	advances	advance	NOUN
ejpam-5578	448	5	in	in	ADP
ejpam-5578	448	6	soft	soft	ADJ
ejpam-5578	448	7	computing	computing	NOUN
ejpam-5578	448	8	and	and	CCONJ
ejpam-5578	448	9	its	its	PRON
ejpam-5578	448	10	applications	application	NOUN
ejpam-5578	448	11	,	,	PUNCT
ejpam-5578	448	12	15(3):77–83	15(3):77–83	NUM
ejpam-5578	448	13	,	,	PUNCT
ejpam-5578	448	14	2023	2023	NUM
ejpam-5578	448	15	.	.	PUNCT
ejpam-5578	449	1	j.	j.	PROPN
ejpam-5578	449	2	oudetallah	oudetallah	PROPN
ejpam-5578	449	3	et	et	PROPN
ejpam-5578	449	4	al	al	PROPN
ejpam-5578	449	5	.	.	PUNCT
ejpam-5578	449	6	/	/	SYM
ejpam-5578	449	7	eur	eur	PROPN
ejpam-5578	449	8	.	.	PUNCT
ejpam-5578	450	1	j.	j.	PROPN
ejpam-5578	450	2	pure	pure	PROPN
ejpam-5578	450	3	appl	appl	PROPN
ejpam-5578	450	4	.	.	PROPN
ejpam-5578	450	5	math	math	PROPN
ejpam-5578	450	6	,	,	PUNCT
ejpam-5578	450	7	18	18	NUM
ejpam-5578	450	8	(	(	PUNCT
ejpam-5578	450	9	2	2	NUM
ejpam-5578	450	10	)	)	PUNCT
ejpam-5578	450	11	(	(	PUNCT
ejpam-5578	450	12	2025	2025	NUM
ejpam-5578	450	13	)	)	PUNCT
ejpam-5578	450	14	,	,	PUNCT
ejpam-5578	450	15	5578	5578	NUM
ejpam-5578	450	16	19	19	NUM
ejpam-5578	450	17	of	of	ADP
ejpam-5578	450	18	19	19	NUM
ejpam-5578	450	19	[	[	SYM
ejpam-5578	450	20	3	3	NUM
ejpam-5578	450	21	]	]	PUNCT
ejpam-5578	450	22	m.	m.	NOUN
ejpam-5578	450	23	berir	berir	NOUN
ejpam-5578	450	24	.	.	PUNCT
ejpam-5578	451	1	analysis	analysis	NOUN
ejpam-5578	451	2	of	of	ADP
ejpam-5578	451	3	the	the	DET
ejpam-5578	451	4	effect	effect	NOUN
ejpam-5578	451	5	of	of	ADP
ejpam-5578	451	6	white	white	ADJ
ejpam-5578	451	7	noise	noise	NOUN
ejpam-5578	451	8	on	on	ADP
ejpam-5578	451	9	the	the	DET
ejpam-5578	451	10	halvorsen	halvorsen	PROPN
ejpam-5578	451	11	system	system	NOUN
ejpam-5578	451	12	of	of	ADP
ejpam-5578	451	13	variableorder	variableorder	NOUN
ejpam-5578	451	14	fractional	fractional	ADJ
ejpam-5578	451	15	derivatives	derivative	NOUN
ejpam-5578	451	16	using	use	VERB
ejpam-5578	451	17	a	a	DET
ejpam-5578	451	18	novel	novel	ADJ
ejpam-5578	451	19	numerical	numerical	ADJ
ejpam-5578	451	20	method	method	NOUN
ejpam-5578	451	21	.	.	PUNCT
ejpam-5578	452	1	international	international	ADJ
ejpam-5578	452	2	journal	journal	NOUN
ejpam-5578	452	3	of	of	ADP
ejpam-5578	452	4	advances	advance	NOUN
ejpam-5578	452	5	in	in	ADP
ejpam-5578	452	6	soft	soft	ADJ
ejpam-5578	452	7	computing	computing	NOUN
ejpam-5578	452	8	and	and	CCONJ
ejpam-5578	452	9	its	its	PRON
ejpam-5578	452	10	applications	application	NOUN
ejpam-5578	452	11	,	,	PUNCT
ejpam-5578	452	12	16(3):294–306	16(3):294–306	NOUN
ejpam-5578	452	13	,	,	PUNCT
ejpam-5578	452	14	2024	2024	NUM
ejpam-5578	452	15	.	.	PUNCT
ejpam-5578	453	1	[	[	X
ejpam-5578	453	2	4	4	NUM
ejpam-5578	453	3	]	]	PUNCT
ejpam-5578	453	4	a.	a.	NOUN
ejpam-5578	453	5	a.	a.	NOUN
ejpam-5578	453	6	hnaif	hnaif	PROPN
ejpam-5578	453	7	,	,	PUNCT
ejpam-5578	453	8	a.	a.	NOUN
ejpam-5578	453	9	a.	a.	NOUN
ejpam-5578	453	10	tamimi	tamimi	PROPN
ejpam-5578	453	11	,	,	PUNCT
ejpam-5578	453	12	a.	a.	PROPN
ejpam-5578	453	13	m.	m.	PROPN
ejpam-5578	453	14	abdalla	abdalla	PROPN
ejpam-5578	453	15	,	,	PUNCT
ejpam-5578	453	16	and	and	CCONJ
ejpam-5578	453	17	i.	i.	PROPN
ejpam-5578	453	18	jebril	jebril	NOUN
ejpam-5578	453	19	.	.	PUNCT
ejpam-5578	454	1	a	a	DET
ejpam-5578	454	2	fault	fault	NOUN
ejpam-5578	454	3	-	-	PUNCT
ejpam-5578	454	4	handling	handling	NOUN
ejpam-5578	454	5	method	method	NOUN
ejpam-5578	454	6	for	for	ADP
ejpam-5578	454	7	the	the	DET
ejpam-5578	454	8	hamiltonian	hamiltonian	ADJ
ejpam-5578	454	9	cycle	cycle	NOUN
ejpam-5578	454	10	in	in	ADP
ejpam-5578	454	11	the	the	DET
ejpam-5578	454	12	hypercube	hypercube	NOUN
ejpam-5578	454	13	topology	topology	NOUN
ejpam-5578	454	14	.	.	PUNCT
ejpam-5578	455	1	computers	computer	NOUN
ejpam-5578	455	2	,	,	PUNCT
ejpam-5578	455	3	materials	material	NOUN
ejpam-5578	455	4	&	&	CCONJ
ejpam-5578	455	5	continua	continua	PROPN
ejpam-5578	455	6	,	,	PUNCT
ejpam-5578	455	7	68(1):505–519	68(1):505–519	NUM
ejpam-5578	455	8	,	,	PUNCT
ejpam-5578	455	9	2021	2021	NUM
ejpam-5578	455	10	.	.	PUNCT
ejpam-5578	456	1	[	[	X
ejpam-5578	456	2	5	5	X
ejpam-5578	456	3	]	]	PUNCT
ejpam-5578	456	4	j.	j.	PROPN
ejpam-5578	456	5	oudetallah	oudetallah	PROPN
ejpam-5578	456	6	,	,	PUNCT
ejpam-5578	456	7	m.	m.	NOUN
ejpam-5578	456	8	m.	m.	NOUN
ejpam-5578	456	9	rousan	rousan	PROPN
ejpam-5578	456	10	,	,	PUNCT
ejpam-5578	456	11	and	and	CCONJ
ejpam-5578	456	12	i.	i.	PROPN
ejpam-5578	456	13	m.	m.	PROPN
ejpam-5578	456	14	batiha	batiha	PROPN
ejpam-5578	456	15	.	.	PUNCT
ejpam-5578	457	1	on	on	ADP
ejpam-5578	457	2	d	d	X
ejpam-5578	457	3	-	-	NOUN
ejpam-5578	457	4	metacompactness	metacompactness	NOUN
ejpam-5578	457	5	in	in	ADP
ejpam-5578	457	6	topological	topological	ADJ
ejpam-5578	457	7	spaces	space	NOUN
ejpam-5578	457	8	.	.	PUNCT
ejpam-5578	458	1	journal	journal	NOUN
ejpam-5578	458	2	of	of	ADP
ejpam-5578	458	3	applied	apply	VERB
ejpam-5578	458	4	mathematics	mathematic	NOUN
ejpam-5578	458	5	and	and	CCONJ
ejpam-5578	458	6	informatics	informatic	NOUN
ejpam-5578	458	7	,	,	PUNCT
ejpam-5578	458	8	39(5–6):919–926	39(5–6):919–926	PROPN
ejpam-5578	458	9	,	,	PUNCT
ejpam-5578	458	10	2021	2021	NUM
ejpam-5578	458	11	.	.	PUNCT
ejpam-5578	459	1	[	[	X
ejpam-5578	459	2	6	6	NUM
ejpam-5578	459	3	]	]	PUNCT
ejpam-5578	459	4	j.	j.	PROPN
ejpam-5578	459	5	oudetallah	oudetallah	PROPN
ejpam-5578	459	6	,	,	PUNCT
ejpam-5578	459	7	r.	r.	PROPN
ejpam-5578	459	8	alharbi	alharbi	PROPN
ejpam-5578	459	9	,	,	PUNCT
ejpam-5578	459	10	m.	m.	NOUN
ejpam-5578	459	11	shatnawi	shatnawi	PROPN
ejpam-5578	459	12	,	,	PUNCT
ejpam-5578	459	13	and	and	CCONJ
ejpam-5578	459	14	i.	i.	PROPN
ejpam-5578	459	15	m.	m.	PROPN
ejpam-5578	459	16	batiha	batiha	PROPN
ejpam-5578	459	17	.	.	PUNCT
ejpam-5578	460	1	on	on	ADP
ejpam-5578	460	2	c	c	NOUN
ejpam-5578	460	3	-	-	PUNCT
ejpam-5578	460	4	compactness	compactness	NOUN
ejpam-5578	460	5	in	in	ADP
ejpam-5578	460	6	topological	topological	ADJ
ejpam-5578	460	7	and	and	CCONJ
ejpam-5578	460	8	bitopological	bitopological	ADJ
ejpam-5578	460	9	spaces	space	NOUN
ejpam-5578	460	10	.	.	PUNCT
ejpam-5578	461	1	mathematics	mathematic	NOUN
ejpam-5578	461	2	,	,	PUNCT
ejpam-5578	461	3	11(20):4251	11(20):4251	NUM
ejpam-5578	461	4	,	,	PUNCT
ejpam-5578	461	5	2023	2023	NUM
ejpam-5578	461	6	.	.	PUNCT
ejpam-5578	462	1	[	[	X
ejpam-5578	462	2	7	7	X
ejpam-5578	462	3	]	]	X
ejpam-5578	462	4	j.	j.	PROPN
ejpam-5578	462	5	oudetallah	oudetallah	PROPN
ejpam-5578	462	6	,	,	PUNCT
ejpam-5578	462	7	n.	n.	PROPN
ejpam-5578	462	8	abu	abu	PROPN
ejpam-5578	462	9	-	-	PUNCT
ejpam-5578	462	10	alkishik	alkishik	PROPN
ejpam-5578	462	11	,	,	PUNCT
ejpam-5578	462	12	and	and	CCONJ
ejpam-5578	462	13	i.	i.	PROPN
ejpam-5578	462	14	m.	m.	PROPN
ejpam-5578	462	15	batiha	batiha	PROPN
ejpam-5578	462	16	.	.	PUNCT
ejpam-5578	463	1	nigh	nigh	ADV
ejpam-5578	463	2	-	-	PUNCT
ejpam-5578	463	3	open	open	ADJ
ejpam-5578	463	4	sets	set	NOUN
ejpam-5578	463	5	in	in	ADP
ejpam-5578	463	6	topological	topological	ADJ
ejpam-5578	463	7	space	space	NOUN
ejpam-5578	463	8	.	.	PUNCT
ejpam-5578	464	1	international	international	ADJ
ejpam-5578	464	2	journal	journal	NOUN
ejpam-5578	464	3	of	of	ADP
ejpam-5578	464	4	analysis	analysis	NOUN
ejpam-5578	464	5	and	and	CCONJ
ejpam-5578	464	6	applications	application	NOUN
ejpam-5578	464	7	,	,	PUNCT
ejpam-5578	464	8	21(1):83	21(1):83	NUM
ejpam-5578	464	9	,	,	PUNCT
ejpam-5578	464	10	2023	2023	NUM
ejpam-5578	464	11	.	.	PUNCT
ejpam-5578	465	1	[	[	X
ejpam-5578	465	2	8	8	X
ejpam-5578	465	3	]	]	PUNCT
ejpam-5578	465	4	j.	j.	PROPN
ejpam-5578	465	5	oudetallah	oudetallah	PROPN
ejpam-5578	465	6	,	,	PUNCT
ejpam-5578	465	7	r.	r.	PROPN
ejpam-5578	465	8	alharbi	alharbi	PROPN
ejpam-5578	465	9	,	,	PUNCT
ejpam-5578	465	10	and	and	CCONJ
ejpam-5578	465	11	i.	i.	PROPN
ejpam-5578	465	12	m.	m.	PROPN
ejpam-5578	465	13	batiha	batiha	PROPN
ejpam-5578	465	14	.	.	PUNCT
ejpam-5578	466	1	on	on	ADP
ejpam-5578	466	2	r	r	NOUN
ejpam-5578	466	3	-	-	PUNCT
ejpam-5578	466	4	compactness	compactness	NOUN
ejpam-5578	466	5	in	in	ADP
ejpam-5578	466	6	topological	topological	ADJ
ejpam-5578	466	7	and	and	CCONJ
ejpam-5578	466	8	bitopological	bitopological	ADJ
ejpam-5578	466	9	spaces	space	NOUN
ejpam-5578	466	10	.	.	PUNCT
ejpam-5578	467	1	axioms	axiom	NOUN
ejpam-5578	467	2	,	,	PUNCT
ejpam-5578	467	3	12(2):210	12(2):210	NOUN
ejpam-5578	467	4	,	,	PUNCT
ejpam-5578	467	5	2023	2023	NUM
ejpam-5578	467	6	.	.	PUNCT
ejpam-5578	468	1	[	[	X
ejpam-5578	468	2	9	9	X
ejpam-5578	468	3	]	]	PUNCT
ejpam-5578	468	4	j.	j.	PROPN
ejpam-5578	468	5	oudetallah	oudetallah	PROPN
ejpam-5578	468	6	and	and	CCONJ
ejpam-5578	468	7	i.	i.	PROPN
ejpam-5578	468	8	m.	m.	PROPN
ejpam-5578	468	9	batiha	batiha	PROPN
ejpam-5578	468	10	.	.	PUNCT
ejpam-5578	469	1	on	on	ADP
ejpam-5578	469	2	almost	almost	ADV
ejpam-5578	469	3	expandability	expandability	NOUN
ejpam-5578	469	4	in	in	ADP
ejpam-5578	469	5	bitopological	bitopological	ADJ
ejpam-5578	469	6	spaces	space	NOUN
ejpam-5578	469	7	.	.	PUNCT
ejpam-5578	470	1	international	international	ADJ
ejpam-5578	470	2	journal	journal	NOUN
ejpam-5578	470	3	of	of	ADP
ejpam-5578	470	4	open	open	ADJ
ejpam-5578	470	5	problems	problem	NOUN
ejpam-5578	470	6	in	in	ADP
ejpam-5578	470	7	computer	computer	NOUN
ejpam-5578	470	8	science	science	NOUN
ejpam-5578	470	9	and	and	CCONJ
ejpam-5578	470	10	mathematics	mathematic	NOUN
ejpam-5578	470	11	,	,	PUNCT
ejpam-5578	470	12	14(3):43–48	14(3):43–48	NUM
ejpam-5578	470	13	,	,	PUNCT
ejpam-5578	470	14	2021	2021	NUM
ejpam-5578	470	15	.	.	PUNCT
ejpam-5578	471	1	[	[	X
ejpam-5578	471	2	10	10	NUM
ejpam-5578	471	3	]	]	X
ejpam-5578	471	4	j.	j.	PROPN
ejpam-5578	471	5	oudetallah	oudetallah	PROPN
ejpam-5578	471	6	and	and	CCONJ
ejpam-5578	471	7	i.	i.	PROPN
ejpam-5578	471	8	m.	m.	PROPN
ejpam-5578	471	9	batiha	batiha	PROPN
ejpam-5578	471	10	.	.	PUNCT
ejpam-5578	472	1	mappings	mapping	NOUN
ejpam-5578	472	2	and	and	CCONJ
ejpam-5578	472	3	finite	finite	ADJ
ejpam-5578	472	4	product	product	NOUN
ejpam-5578	472	5	of	of	ADP
ejpam-5578	472	6	pairwise	pairwise	NOUN
ejpam-5578	472	7	expandable	expandable	ADJ
ejpam-5578	472	8	spaces	space	NOUN
ejpam-5578	472	9	.	.	PUNCT
ejpam-5578	473	1	international	international	ADJ
ejpam-5578	473	2	journal	journal	NOUN
ejpam-5578	473	3	of	of	ADP
ejpam-5578	473	4	analysis	analysis	NOUN
ejpam-5578	473	5	and	and	CCONJ
ejpam-5578	473	6	applications	application	NOUN
ejpam-5578	473	7	,	,	PUNCT
ejpam-5578	473	8	20:66	20:66	NUM
ejpam-5578	473	9	,	,	PUNCT
ejpam-5578	473	10	2022	2022	NUM
ejpam-5578	473	11	.	.	PUNCT
ejpam-5578	474	1	[	[	X
ejpam-5578	474	2	11	11	NUM
ejpam-5578	474	3	]	]	PUNCT
ejpam-5578	474	4	s.	s.	PROPN
ejpam-5578	474	5	willard	willard	PROPN
ejpam-5578	474	6	.	.	PUNCT
ejpam-5578	474	7	general	general	ADJ
ejpam-5578	474	8	topology	topology	PROPN
ejpam-5578	474	9	.	.	PUNCT
ejpam-5578	475	1	addison	addison	PROPN
ejpam-5578	475	2	-	-	PUNCT
ejpam-5578	475	3	wesley	wesley	PROPN
ejpam-5578	475	4	publishing	publishing	PROPN
ejpam-5578	475	5	company	company	PROPN
ejpam-5578	475	6	,	,	PUNCT
ejpam-5578	475	7	inc	inc	PROPN
ejpam-5578	475	8	.	.	PROPN
ejpam-5578	475	9	,	,	PUNCT
ejpam-5578	475	10	1970	1970	NUM
ejpam-5578	475	11	.	.	PUNCT
ejpam-5578	476	1	[	[	X
ejpam-5578	476	2	12	12	NUM
ejpam-5578	476	3	]	]	X
ejpam-5578	476	4	n.	n.	PROPN
ejpam-5578	476	5	levine	levine	PROPN
ejpam-5578	476	6	.	.	PUNCT
ejpam-5578	477	1	semi	semi	ADJ
ejpam-5578	477	2	-	-	ADJ
ejpam-5578	477	3	open	open	ADJ
ejpam-5578	477	4	sets	set	NOUN
ejpam-5578	477	5	and	and	CCONJ
ejpam-5578	477	6	semi	semi	ADJ
ejpam-5578	477	7	-	-	NOUN
ejpam-5578	477	8	continuity	continuity	NOUN
ejpam-5578	477	9	in	in	ADP
ejpam-5578	477	10	topological	topological	ADJ
ejpam-5578	477	11	spaces	space	NOUN
ejpam-5578	477	12	.	.	PUNCT
ejpam-5578	478	1	the	the	DET
ejpam-5578	478	2	american	american	PROPN
ejpam-5578	478	3	mathematical	mathematical	PROPN
ejpam-5578	478	4	monthly	monthly	ADV
ejpam-5578	478	5	,	,	PUNCT
ejpam-5578	478	6	70(1):36–41	70(1):36–41	NUM
ejpam-5578	478	7	,	,	PUNCT
ejpam-5578	478	8	1963	1963	NUM
ejpam-5578	478	9	.	.	PUNCT
ejpam-5578	479	1	[	[	X
ejpam-5578	479	2	13	13	NUM
ejpam-5578	479	3	]	]	PUNCT
ejpam-5578	479	4	j.	j.	PROPN
ejpam-5578	479	5	oudetallah	oudetallah	PROPN
ejpam-5578	479	6	.	.	PUNCT
ejpam-5578	480	1	nearly	nearly	ADV
ejpam-5578	480	2	expandability	expandability	NOUN
ejpam-5578	480	3	in	in	ADP
ejpam-5578	480	4	bitopological	bitopological	ADJ
ejpam-5578	480	5	spaces	space	NOUN
ejpam-5578	480	6	.	.	PUNCT
ejpam-5578	481	1	advances	advance	NOUN
ejpam-5578	481	2	in	in	ADP
ejpam-5578	481	3	mathematics	mathematic	NOUN
ejpam-5578	481	4	:	:	PUNCT
ejpam-5578	481	5	scientific	scientific	ADJ
ejpam-5578	481	6	journal	journal	NOUN
ejpam-5578	481	7	,	,	PUNCT
ejpam-5578	481	8	10:705–712	10:705–712	NUM
ejpam-5578	481	9	,	,	PUNCT
ejpam-5578	481	10	2021	2021	NUM
ejpam-5578	481	11	.	.	PUNCT
ejpam-5578	482	1	[	[	X
ejpam-5578	482	2	14	14	NUM
ejpam-5578	482	3	]	]	X
ejpam-5578	482	4	j.	j.	PROPN
ejpam-5578	482	5	oudetallah	oudetallah	PROPN
ejpam-5578	482	6	.	.	PUNCT
ejpam-5578	483	1	on	on	ADP
ejpam-5578	483	2	feebly	feebly	ADJ
ejpam-5578	483	3	pairwise	pairwise	NOUN
ejpam-5578	483	4	expandable	expandable	ADJ
ejpam-5578	483	5	space	space	NOUN
ejpam-5578	483	6	.	.	PUNCT
ejpam-5578	484	1	journal	journal	PROPN
ejpam-5578	484	2	of	of	ADP
ejpam-5578	484	3	mathematical	mathematical	ADJ
ejpam-5578	484	4	and	and	CCONJ
ejpam-5578	484	5	computational	computational	ADJ
ejpam-5578	484	6	science	science	NOUN
ejpam-5578	484	7	,	,	PUNCT
ejpam-5578	484	8	11(5):6216–6225	11(5):6216–6225	NUM
ejpam-5578	484	9	,	,	PUNCT
ejpam-5578	484	10	2021	2021	NUM
ejpam-5578	484	11	.	.	PUNCT
ejpam-5578	485	1	[	[	X
ejpam-5578	485	2	15	15	NUM
ejpam-5578	485	3	]	]	X
ejpam-5578	485	4	j.	j.	PROPN
ejpam-5578	485	5	l.	l.	PROPN
ejpam-5578	485	6	kelley	kelley	PROPN
ejpam-5578	485	7	.	.	PUNCT
ejpam-5578	486	1	general	general	ADJ
ejpam-5578	486	2	topology	topology	PROPN
ejpam-5578	486	3	.	.	PUNCT
ejpam-5578	487	1	d.	d.	PROPN
ejpam-5578	487	2	van	van	PROPN
ejpam-5578	487	3	nostrand	nostrand	PROPN
ejpam-5578	487	4	company	company	PROPN
ejpam-5578	487	5	,	,	PUNCT
ejpam-5578	487	6	inc	inc	PROPN
ejpam-5578	487	7	.	.	PROPN
ejpam-5578	487	8	,	,	PUNCT
ejpam-5578	487	9	1955	1955	NUM
ejpam-5578	487	10	.	.	PUNCT
ejpam-5578	488	1	[	[	X
ejpam-5578	488	2	16	16	NUM
ejpam-5578	488	3	]	]	X
ejpam-5578	488	4	j.	j.	PROPN
ejpam-5578	488	5	dugundji	dugundji	PROPN
ejpam-5578	488	6	.	.	PUNCT
ejpam-5578	488	7	topology	topology	PROPN
ejpam-5578	488	8	.	.	PUNCT
ejpam-5578	489	1	allyn	allyn	PROPN
ejpam-5578	489	2	and	and	CCONJ
ejpam-5578	489	3	bacon	bacon	PROPN
ejpam-5578	489	4	,	,	PUNCT
ejpam-5578	489	5	boston	boston	PROPN
ejpam-5578	489	6	,	,	PUNCT
ejpam-5578	489	7	1966	1966	NUM
ejpam-5578	489	8	.	.	PUNCT
ejpam-5578	490	1	[	[	X
ejpam-5578	490	2	17	17	NUM
ejpam-5578	490	3	]	]	X
ejpam-5578	490	4	y.	y.	PROPN
ejpam-5578	490	5	w.	w.	PROPN
ejpam-5578	490	6	kim	kim	PROPN
ejpam-5578	490	7	.	.	PUNCT
ejpam-5578	491	1	pairwise	pairwise	NOUN
ejpam-5578	491	2	compactness	compactness	NOUN
ejpam-5578	491	3	.	.	PUNCT
ejpam-5578	492	1	publicationes	publicatione	NOUN
ejpam-5578	492	2	mathematicae	mathematicae	PROPN
ejpam-5578	492	3	debrecen	debrecen	PROPN
ejpam-5578	492	4	,	,	PUNCT
ejpam-5578	492	5	15:87–90	15:87–90	NUM
ejpam-5578	492	6	,	,	PUNCT
ejpam-5578	492	7	1968	1968	NUM
ejpam-5578	492	8	.	.	PUNCT