id	sid	tid	token	lemma	pos
ejpam-5802	1	1	european	european	PROPN
ejpam-5802	1	2	journal	journal	PROPN
ejpam-5802	1	3	of	of	ADP
ejpam-5802	1	4	pure	pure	ADJ
ejpam-5802	1	5	and	and	CCONJ
ejpam-5802	1	6	applied	applied	ADJ
ejpam-5802	1	7	mathematics	mathematic	NOUN
ejpam-5802	1	8	2025	2025	NUM
ejpam-5802	1	9	,	,	PUNCT
ejpam-5802	1	10	vol	vol	NOUN
ejpam-5802	1	11	.	.	PROPN
ejpam-5802	1	12	18	18	NUM
ejpam-5802	1	13	,	,	PUNCT
ejpam-5802	1	14	issue	issue	NOUN
ejpam-5802	1	15	2	2	NUM
ejpam-5802	1	16	,	,	PUNCT
ejpam-5802	1	17	article	article	NOUN
ejpam-5802	1	18	number	number	NOUN
ejpam-5802	1	19	5802	5802	NUM
ejpam-5802	1	20	issn	issn	VERB
ejpam-5802	1	21	1307	1307	NUM
ejpam-5802	1	22	-	-	SYM
ejpam-5802	1	23	5543	5543	NUM
ejpam-5802	1	24	–	–	PUNCT
ejpam-5802	1	25	ejpam.com	ejpam.com	X
ejpam-5802	1	26	published	publish	VERB
ejpam-5802	1	27	by	by	ADP
ejpam-5802	1	28	new	new	PROPN
ejpam-5802	1	29	york	york	PROPN
ejpam-5802	1	30	business	business	PROPN
ejpam-5802	1	31	global	global	PROPN
ejpam-5802	1	32	σ	σ	PROPN
ejpam-5802	1	33	-	-	ADJ
ejpam-5802	1	34	compact	compact	ADJ
ejpam-5802	1	35	spaces	space	NOUN
ejpam-5802	1	36	in	in	ADP
ejpam-5802	1	37	nth	nth	ADJ
ejpam-5802	1	38	-	-	ADJ
ejpam-5802	1	39	topological	topological	ADJ
ejpam-5802	1	40	space	space	NOUN
ejpam-5802	1	41	jamal	jamal	PROPN
ejpam-5802	1	42	oudetallah1	oudetallah1	PROPN
ejpam-5802	1	43	,	,	PUNCT
ejpam-5802	1	44	ala	ala	PROPN
ejpam-5802	1	45	amourah2,3,∗	amourah2,3,∗	PROPN
ejpam-5802	1	46	,	,	PUNCT
ejpam-5802	1	47	iqbal	iqbal	PROPN
ejpam-5802	1	48	m.	m.	PROPN
ejpam-5802	1	49	batiha4,5	batiha4,5	PROPN
ejpam-5802	1	50	,	,	PUNCT
ejpam-5802	1	51	jamal	jamal	PROPN
ejpam-5802	1	52	salah6,∗	salah6,∗	PROPN
ejpam-5802	1	53	,	,	PUNCT
ejpam-5802	1	54	mutaz	mutaz	NOUN
ejpam-5802	1	55	shatnawi7	shatnawi7	NOUN
ejpam-5802	1	56	1	1	NUM
ejpam-5802	1	57	department	department	NOUN
ejpam-5802	1	58	of	of	ADP
ejpam-5802	1	59	mathematics	mathematics	PROPN
ejpam-5802	1	60	,	,	PUNCT
ejpam-5802	1	61	university	university	PROPN
ejpam-5802	1	62	of	of	ADP
ejpam-5802	1	63	petra	petra	PROPN
ejpam-5802	1	64	,	,	PUNCT
ejpam-5802	1	65	amman	amman	PROPN
ejpam-5802	1	66	,	,	PUNCT
ejpam-5802	1	67	11196	11196	NUM
ejpam-5802	1	68	,	,	PUNCT
ejpam-5802	1	69	jordan	jordan	PROPN
ejpam-5802	1	70	2	2	NUM
ejpam-5802	1	71	mathematics	mathematics	PROPN
ejpam-5802	1	72	education	education	NOUN
ejpam-5802	1	73	program	program	NOUN
ejpam-5802	1	74	,	,	PUNCT
ejpam-5802	1	75	faculty	faculty	NOUN
ejpam-5802	1	76	of	of	ADP
ejpam-5802	1	77	education	education	NOUN
ejpam-5802	1	78	and	and	CCONJ
ejpam-5802	1	79	arts	art	NOUN
ejpam-5802	1	80	,	,	PUNCT
ejpam-5802	1	81	sohar	sohar	PROPN
ejpam-5802	1	82	university	university	PROPN
ejpam-5802	1	83	,	,	PUNCT
ejpam-5802	1	84	sohar	sohar	PROPN
ejpam-5802	1	85	311	311	NUM
ejpam-5802	1	86	,	,	PUNCT
ejpam-5802	1	87	oman	oman	NOUN
ejpam-5802	1	88	3	3	NUM
ejpam-5802	1	89	applied	apply	VERB
ejpam-5802	1	90	science	science	NOUN
ejpam-5802	1	91	research	research	NOUN
ejpam-5802	1	92	center	center	NOUN
ejpam-5802	1	93	,	,	PUNCT
ejpam-5802	1	94	applied	apply	VERB
ejpam-5802	1	95	science	science	NOUN
ejpam-5802	1	96	private	private	ADJ
ejpam-5802	1	97	university	university	NOUN
ejpam-5802	1	98	,	,	PUNCT
ejpam-5802	1	99	amman	amman	PROPN
ejpam-5802	1	100	,	,	PUNCT
ejpam-5802	1	101	jordan	jordan	PROPN
ejpam-5802	1	102	4	4	NUM
ejpam-5802	1	103	department	department	NOUN
ejpam-5802	1	104	of	of	ADP
ejpam-5802	1	105	mathematics	mathematic	NOUN
ejpam-5802	1	106	,	,	PUNCT
ejpam-5802	1	107	al	al	PROPN
ejpam-5802	1	108	zaytoonah	zaytoonah	PROPN
ejpam-5802	1	109	university	university	PROPN
ejpam-5802	1	110	of	of	ADP
ejpam-5802	1	111	jordan	jordan	PROPN
ejpam-5802	1	112	,	,	PUNCT
ejpam-5802	1	113	amman	amman	PROPN
ejpam-5802	1	114	11733	11733	NUM
ejpam-5802	1	115	,	,	PUNCT
ejpam-5802	1	116	jordan	jordan	PROPN
ejpam-5802	1	117	5	5	NUM
ejpam-5802	1	118	nonlinear	nonlinear	ADJ
ejpam-5802	1	119	dynamics	dynamic	NOUN
ejpam-5802	1	120	research	research	NOUN
ejpam-5802	1	121	center	center	NOUN
ejpam-5802	1	122	(	(	PUNCT
ejpam-5802	1	123	ndrc	ndrc	PROPN
ejpam-5802	1	124	)	)	PUNCT
ejpam-5802	1	125	,	,	PUNCT
ejpam-5802	1	126	ajman	ajman	PROPN
ejpam-5802	1	127	university	university	PROPN
ejpam-5802	1	128	,	,	PUNCT
ejpam-5802	1	129	ajman	ajman	NOUN
ejpam-5802	1	130	346	346	NUM
ejpam-5802	1	131	,	,	PUNCT
ejpam-5802	1	132	uae	uae	PROPN
ejpam-5802	1	133	6	6	NUM
ejpam-5802	1	134	college	college	NOUN
ejpam-5802	1	135	of	of	ADP
ejpam-5802	1	136	applied	apply	VERB
ejpam-5802	1	137	and	and	CCONJ
ejpam-5802	1	138	health	health	NOUN
ejpam-5802	1	139	sciences	science	NOUN
ejpam-5802	1	140	,	,	PUNCT
ejpam-5802	1	141	a’sharqiyah	a’sharqiyah	PROPN
ejpam-5802	1	142	university	university	NOUN
ejpam-5802	1	143	,	,	PUNCT
ejpam-5802	1	144	post	post	PROPN
ejpam-5802	1	145	box	box	PROPN
ejpam-5802	1	146	no	no	INTJ
ejpam-5802	1	147	.	.	PROPN
ejpam-5802	1	148	42	42	NUM
ejpam-5802	1	149	,	,	PUNCT
ejpam-5802	1	150	post	post	VERB
ejpam-5802	1	151	code	code	NOUN
ejpam-5802	1	152	no	no	INTJ
ejpam-5802	1	153	.	.	NOUN
ejpam-5802	1	154	400	400	NUM
ejpam-5802	1	155	ibra	ibra	NOUN
ejpam-5802	1	156	,	,	PUNCT
ejpam-5802	1	157	sultanate	sultanate	NOUN
ejpam-5802	1	158	of	of	ADP
ejpam-5802	1	159	oman	oman	PROPN
ejpam-5802	1	160	7	7	NUM
ejpam-5802	1	161	department	department	NOUN
ejpam-5802	1	162	of	of	ADP
ejpam-5802	1	163	mathematics	mathematic	NOUN
ejpam-5802	1	164	,	,	PUNCT
ejpam-5802	1	165	faculty	faculty	NOUN
ejpam-5802	1	166	of	of	ADP
ejpam-5802	1	167	science	science	NOUN
ejpam-5802	1	168	and	and	CCONJ
ejpam-5802	1	169	information	information	NOUN
ejpam-5802	1	170	technology	technology	NOUN
ejpam-5802	1	171	,	,	PUNCT
ejpam-5802	1	172	irbid	irbid	VERB
ejpam-5802	1	173	national	national	ADJ
ejpam-5802	1	174	university	university	PROPN
ejpam-5802	1	175	,	,	PUNCT
ejpam-5802	1	176	irbid	irbid	VERB
ejpam-5802	1	177	21110	21110	NUM
ejpam-5802	1	178	,	,	PUNCT
ejpam-5802	1	179	jordan	jordan	PROPN
ejpam-5802	1	180	abstract	abstract	PROPN
ejpam-5802	1	181	.	.	PUNCT
ejpam-5802	2	1	the	the	DET
ejpam-5802	2	2	principal	principal	NOUN
ejpam-5802	2	3	aims	aim	VERB
ejpam-5802	2	4	of	of	ADP
ejpam-5802	2	5	this	this	DET
ejpam-5802	2	6	paper	paper	NOUN
ejpam-5802	2	7	include	include	VERB
ejpam-5802	2	8	the	the	DET
ejpam-5802	2	9	introduction	introduction	NOUN
ejpam-5802	2	10	of	of	ADP
ejpam-5802	2	11	the	the	DET
ejpam-5802	2	12	concept	concept	NOUN
ejpam-5802	2	13	of	of	ADP
ejpam-5802	2	14	σ	σ	PROPN
ejpam-5802	2	15	-	-	ADJ
ejpam-5802	2	16	compact	compact	ADJ
ejpam-5802	2	17	spaces	space	NOUN
ejpam-5802	2	18	in	in	ADP
ejpam-5802	2	19	nth	nth	ADJ
ejpam-5802	2	20	-	-	ADJ
ejpam-5802	2	21	topological	topological	ADJ
ejpam-5802	2	22	spaces	space	NOUN
ejpam-5802	2	23	,	,	PUNCT
ejpam-5802	2	24	the	the	DET
ejpam-5802	2	25	definition	definition	NOUN
ejpam-5802	2	26	of	of	ADP
ejpam-5802	2	27	compactness	compactness	NOUN
ejpam-5802	2	28	,	,	PUNCT
ejpam-5802	2	29	discussion	discussion	NOUN
ejpam-5802	2	30	of	of	ADP
ejpam-5802	2	31	various	various	ADJ
ejpam-5802	2	32	generalizations	generalization	NOUN
ejpam-5802	2	33	encompassing	encompass	VERB
ejpam-5802	2	34	compactness	compactness	NOUN
ejpam-5802	2	35	in	in	ADP
ejpam-5802	2	36	nth	nth	ADJ
ejpam-5802	2	37	-	-	ADJ
ejpam-5802	2	38	topological	topological	ADJ
ejpam-5802	2	39	space	space	NOUN
ejpam-5802	2	40	,	,	PUNCT
ejpam-5802	2	41	the	the	DET
ejpam-5802	2	42	properties	property	NOUN
ejpam-5802	2	43	of	of	ADP
ejpam-5802	2	44	σ	σ	NOUN
ejpam-5802	2	45	-	-	ADJ
ejpam-5802	2	46	compact	compact	ADJ
ejpam-5802	2	47	spaces	space	NOUN
ejpam-5802	2	48	.	.	PUNCT
ejpam-5802	3	1	furthermore	furthermore	ADV
ejpam-5802	3	2	,	,	PUNCT
ejpam-5802	3	3	our	our	PRON
ejpam-5802	3	4	study	study	NOUN
ejpam-5802	3	5	extends	extend	VERB
ejpam-5802	3	6	to	to	ADP
ejpam-5802	3	7	the	the	DET
ejpam-5802	3	8	analysis	analysis	NOUN
ejpam-5802	3	9	of	of	ADP
ejpam-5802	3	10	the	the	DET
ejpam-5802	3	11	notion	notion	NOUN
ejpam-5802	3	12	of	of	ADP
ejpam-5802	3	13	countable	countable	ADJ
ejpam-5802	3	14	compactness	compactness	NOUN
ejpam-5802	3	15	in	in	ADP
ejpam-5802	3	16	nth	nth	ADJ
ejpam-5802	3	17	-	-	ADJ
ejpam-5802	3	18	topological	topological	ADJ
ejpam-5802	3	19	spaces	space	NOUN
ejpam-5802	3	20	.	.	PUNCT
ejpam-5802	4	1	our	our	PRON
ejpam-5802	4	2	investigation	investigation	NOUN
ejpam-5802	4	3	extends	extend	VERB
ejpam-5802	4	4	to	to	ADP
ejpam-5802	4	5	various	various	ADJ
ejpam-5802	4	6	generalizations	generalization	NOUN
ejpam-5802	4	7	of	of	ADP
ejpam-5802	4	8	these	these	DET
ejpam-5802	4	9	spaces	space	NOUN
ejpam-5802	4	10	.	.	PUNCT
ejpam-5802	5	1	2020	2020	NUM
ejpam-5802	5	2	mathematics	mathematic	NOUN
ejpam-5802	5	3	subject	subject	NOUN
ejpam-5802	5	4	classifications	classification	NOUN
ejpam-5802	5	5	:	:	PUNCT
ejpam-5802	5	6	30c45	30c45	NUM
ejpam-5802	5	7	key	key	ADJ
ejpam-5802	5	8	words	word	NOUN
ejpam-5802	5	9	and	and	CCONJ
ejpam-5802	5	10	phrases	phrase	NOUN
ejpam-5802	5	11	:	:	PUNCT
ejpam-5802	5	12	tri	tri	ADJ
ejpam-5802	5	13	-	-	ADJ
ejpam-5802	5	14	topological	topological	ADJ
ejpam-5802	5	15	spaces	space	NOUN
ejpam-5802	5	16	,	,	PUNCT
ejpam-5802	5	17	compactness	compactness	NOUN
ejpam-5802	5	18	,	,	PUNCT
ejpam-5802	5	19	sigma	sigma	X
ejpam-5802	5	20	compact	compact	ADJ
ejpam-5802	5	21	spaces	space	NOUN
ejpam-5802	5	22	,	,	PUNCT
ejpam-5802	5	23	separation	separation	NOUN
ejpam-5802	5	24	axioms	axiom	VERB
ejpam-5802	5	25	1	1	NUM
ejpam-5802	5	26	.	.	PUNCT
ejpam-5802	6	1	introduction	introduction	NOUN
ejpam-5802	6	2	the	the	DET
ejpam-5802	6	3	study	study	NOUN
ejpam-5802	6	4	of	of	ADP
ejpam-5802	6	5	nth	nth	ADJ
ejpam-5802	6	6	-	-	ADJ
ejpam-5802	6	7	topological	topological	ADJ
ejpam-5802	6	8	spaces	space	NOUN
ejpam-5802	6	9	arises	arise	VERB
ejpam-5802	6	10	as	as	ADP
ejpam-5802	6	11	a	a	DET
ejpam-5802	6	12	natural	natural	ADJ
ejpam-5802	6	13	extension	extension	NOUN
ejpam-5802	6	14	of	of	ADP
ejpam-5802	6	15	the	the	DET
ejpam-5802	6	16	concepts	concept	NOUN
ejpam-5802	6	17	found	find	VERB
ejpam-5802	6	18	in	in	ADP
ejpam-5802	6	19	bi	bi	ADJ
ejpam-5802	6	20	-	-	ADJ
ejpam-5802	6	21	topological	topological	ADJ
ejpam-5802	6	22	and	and	CCONJ
ejpam-5802	6	23	tri	tri	ADJ
ejpam-5802	6	24	-	-	ADJ
ejpam-5802	6	25	topological	topological	ADJ
ejpam-5802	6	26	spaces	space	NOUN
ejpam-5802	6	27	,	,	PUNCT
ejpam-5802	6	28	building	build	VERB
ejpam-5802	6	29	upon	upon	SCONJ
ejpam-5802	6	30	the	the	DET
ejpam-5802	6	31	foundation	foundation	NOUN
ejpam-5802	6	32	of	of	ADP
ejpam-5802	6	33	single	single	ADJ
ejpam-5802	6	34	topological	topological	ADJ
ejpam-5802	6	35	spaces	space	NOUN
ejpam-5802	6	36	.	.	PUNCT
ejpam-5802	7	1	these	these	DET
ejpam-5802	7	2	extensions	extension	NOUN
ejpam-5802	7	3	aim	aim	VERB
ejpam-5802	7	4	to	to	PART
ejpam-5802	7	5	provide	provide	VERB
ejpam-5802	7	6	a	a	DET
ejpam-5802	7	7	more	more	ADV
ejpam-5802	7	8	comprehensive	comprehensive	ADJ
ejpam-5802	7	9	framework	framework	NOUN
ejpam-5802	7	10	for	for	ADP
ejpam-5802	7	11	understanding	understand	VERB
ejpam-5802	7	12	complex	complex	ADJ
ejpam-5802	7	13	structures	structure	NOUN
ejpam-5802	7	14	that	that	PRON
ejpam-5802	7	15	involve	involve	VERB
ejpam-5802	7	16	multiple	multiple	ADJ
ejpam-5802	7	17	interrelated	interrelated	ADJ
ejpam-5802	7	18	topologies	topology	NOUN
ejpam-5802	7	19	.	.	PUNCT
ejpam-5802	8	1	in	in	ADP
ejpam-5802	8	2	this	this	DET
ejpam-5802	8	3	paper	paper	NOUN
ejpam-5802	8	4	,	,	PUNCT
ejpam-5802	8	5	we	we	PRON
ejpam-5802	8	6	define	define	VERB
ejpam-5802	8	7	an	an	DET
ejpam-5802	8	8	nth	nth	ADJ
ejpam-5802	8	9	-	-	ADJ
ejpam-5802	8	10	topological	topological	ADJ
ejpam-5802	8	11	space	space	NOUN
ejpam-5802	8	12	as	as	ADP
ejpam-5802	8	13	a	a	DET
ejpam-5802	8	14	non	non	ADJ
ejpam-5802	8	15	-	-	ADJ
ejpam-5802	8	16	empty	empty	ADJ
ejpam-5802	8	17	set	set	NOUN
ejpam-5802	8	18	k	k	PROPN
ejpam-5802	8	19	equipped	equip	VERB
ejpam-5802	8	20	with	with	ADP
ejpam-5802	8	21	nth	nth	PROPN
ejpam-5802	8	22	distinct	distinct	PROPN
ejpam-5802	8	23	topologies	topology	NOUN
ejpam-5802	8	24	,	,	PUNCT
ejpam-5802	8	25	denoted	denote	VERB
ejpam-5802	8	26	as	as	ADP
ejpam-5802	8	27	η1	η1	NOUN
ejpam-5802	8	28	,	,	PUNCT
ejpam-5802	8	29	η2	η2	NOUN
ejpam-5802	8	30	,	,	PUNCT
ejpam-5802	8	31	...	...	PUNCT
ejpam-5802	8	32	,	,	PUNCT
ejpam-5802	8	33	ηn	ηn	INTJ
ejpam-5802	8	34	,	,	PUNCT
ejpam-5802	8	35	forming	form	VERB
ejpam-5802	8	36	the	the	DET
ejpam-5802	8	37	structure	structure	NOUN
ejpam-5802	8	38	(	(	PUNCT
ejpam-5802	8	39	k	k	X
ejpam-5802	8	40	,	,	PUNCT
ejpam-5802	8	41	η1	η1	NOUN
ejpam-5802	8	42	,	,	PUNCT
ejpam-5802	8	43	η2	η2	NOUN
ejpam-5802	8	44	,	,	PUNCT
ejpam-5802	8	45	...	...	PUNCT
ejpam-5802	8	46	,	,	PUNCT
ejpam-5802	8	47	ηn	ηn	ADJ
ejpam-5802	8	48	)	)	PUNCT
ejpam-5802	8	49	.	.	PUNCT
ejpam-5802	9	1	∗corresponding	∗corresponde	VERB
ejpam-5802	9	2	author	author	NOUN
ejpam-5802	9	3	.	.	PUNCT
ejpam-5802	10	1	∗corresponding	∗corresponde	VERB
ejpam-5802	10	2	author	author	NOUN
ejpam-5802	10	3	.	.	PUNCT
ejpam-5802	11	1	doi	doi	NOUN
ejpam-5802	11	2	:	:	PUNCT
ejpam-5802	11	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5802	https://doi.org/10.29020/nybg.ejpam.v18i2.5802	ADJ
ejpam-5802	11	4	email	email	NOUN
ejpam-5802	11	5	addresses	address	VERB
ejpam-5802	11	6	:	:	PUNCT
ejpam-5802	11	7	jamal.oudetallah@uop.edu.jo	jamal.oudetallah@uop.edu.jo	PROPN
ejpam-5802	11	8	(	(	PUNCT
ejpam-5802	11	9	j.	j.	PROPN
ejpam-5802	11	10	oudetallah	oudetallah	PROPN
ejpam-5802	11	11	)	)	PUNCT
ejpam-5802	11	12	,	,	PUNCT
ejpam-5802	12	1	aamourah@su.edu.om	aamourah@su.edu.om	NOUN
ejpam-5802	12	2	(	(	PUNCT
ejpam-5802	12	3	a.	a.	NOUN
ejpam-5802	12	4	amourah	amourah	PROPN
ejpam-5802	12	5	)	)	PUNCT
ejpam-5802	12	6	,	,	PUNCT
ejpam-5802	12	7	i.batiha@zuj.edu.jo	i.batiha@zuj.edu.jo	NOUN
ejpam-5802	12	8	(	(	PUNCT
ejpam-5802	12	9	i.	i.	PROPN
ejpam-5802	12	10	m.	m.	PROPN
ejpam-5802	12	11	batiha	batiha	PROPN
ejpam-5802	12	12	)	)	PUNCT
ejpam-5802	12	13	,	,	PUNCT
ejpam-5802	12	14	damous73@yahoo.com	damous73@yahoo.com	X
ejpam-5802	12	15	(	(	PUNCT
ejpam-5802	12	16	j.	j.	PROPN
ejpam-5802	12	17	salah	salah	PROPN
ejpam-5802	12	18	)	)	PUNCT
ejpam-5802	12	19	,	,	PUNCT
ejpam-5802	12	20	m.shatnawi@inu.edu.jo	m.shatnawi@inu.edu.jo	PROPN
ejpam-5802	12	21	(	(	PUNCT
ejpam-5802	12	22	m.	m.	NOUN
ejpam-5802	12	23	shatnawi	shatnawi	PROPN
ejpam-5802	12	24	)	)	PUNCT
ejpam-5802	12	25	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5802	13	1	1	1	NUM
ejpam-5802	13	2	copyright	copyright	NOUN
ejpam-5802	13	3	:	:	PUNCT
ejpam-5802	13	4	©	©	PROPN
ejpam-5802	13	5	2025	2025	NUM
ejpam-5802	13	6	the	the	DET
ejpam-5802	13	7	author(s	author(s	NOUN
ejpam-5802	13	8	)	)	PUNCT
ejpam-5802	13	9	.	.	PUNCT
ejpam-5802	14	1	(	(	PUNCT
ejpam-5802	14	2	cc	cc	NOUN
ejpam-5802	14	3	by	by	ADP
ejpam-5802	14	4	-	-	PUNCT
ejpam-5802	14	5	nc	nc	PROPN
ejpam-5802	14	6	4.0	4.0	NUM
ejpam-5802	14	7	)	)	PUNCT
ejpam-5802	14	8	j.	j.	PROPN
ejpam-5802	14	9	oudetallah	oudetallah	PROPN
ejpam-5802	14	10	et	et	PROPN
ejpam-5802	14	11	al	al	PROPN
ejpam-5802	14	12	.	.	PUNCT
ejpam-5802	14	13	/	/	SYM
ejpam-5802	14	14	eur	eur	PROPN
ejpam-5802	14	15	.	.	PUNCT
ejpam-5802	15	1	j.	j.	PROPN
ejpam-5802	15	2	pure	pure	PROPN
ejpam-5802	15	3	appl	appl	PROPN
ejpam-5802	15	4	.	.	PROPN
ejpam-5802	15	5	math	math	PROPN
ejpam-5802	15	6	,	,	PUNCT
ejpam-5802	15	7	18	18	NUM
ejpam-5802	15	8	(	(	PUNCT
ejpam-5802	15	9	2	2	NUM
ejpam-5802	15	10	)	)	PUNCT
ejpam-5802	15	11	(	(	PUNCT
ejpam-5802	15	12	2025	2025	NUM
ejpam-5802	15	13	)	)	PUNCT
ejpam-5802	15	14	,	,	PUNCT
ejpam-5802	15	15	5802	5802	NUM
ejpam-5802	15	16	2	2	NUM
ejpam-5802	15	17	of	of	ADP
ejpam-5802	15	18	14	14	NUM
ejpam-5802	15	19	the	the	DET
ejpam-5802	15	20	idea	idea	NOUN
ejpam-5802	15	21	of	of	ADP
ejpam-5802	15	22	nth	nth	NOUN
ejpam-5802	15	23	-	-	ADJ
ejpam-5802	15	24	topological	topological	ADJ
ejpam-5802	15	25	spaces	space	NOUN
ejpam-5802	15	26	began	begin	VERB
ejpam-5802	15	27	gaining	gain	VERB
ejpam-5802	15	28	attention	attention	NOUN
ejpam-5802	15	29	in	in	ADP
ejpam-5802	15	30	the	the	DET
ejpam-5802	15	31	early	early	ADJ
ejpam-5802	15	32	21st	21st	ADJ
ejpam-5802	15	33	century	century	NOUN
ejpam-5802	15	34	,	,	PUNCT
ejpam-5802	15	35	specifically	specifically	ADV
ejpam-5802	15	36	around	around	ADP
ejpam-5802	15	37	the	the	DET
ejpam-5802	15	38	year	year	NOUN
ejpam-5802	15	39	2000	2000	NUM
ejpam-5802	15	40	,	,	PUNCT
ejpam-5802	15	41	as	as	SCONJ
ejpam-5802	15	42	researchers	researcher	NOUN
ejpam-5802	15	43	sought	seek	VERB
ejpam-5802	15	44	to	to	PART
ejpam-5802	15	45	expand	expand	VERB
ejpam-5802	15	46	the	the	DET
ejpam-5802	15	47	theoretical	theoretical	ADJ
ejpam-5802	15	48	understanding	understanding	NOUN
ejpam-5802	15	49	and	and	CCONJ
ejpam-5802	15	50	practical	practical	ADJ
ejpam-5802	15	51	applications	application	NOUN
ejpam-5802	15	52	of	of	ADP
ejpam-5802	15	53	topological	topological	ADJ
ejpam-5802	15	54	concepts	concept	NOUN
ejpam-5802	15	55	to	to	ADP
ejpam-5802	15	56	more	more	ADJ
ejpam-5802	15	57	intricate	intricate	ADJ
ejpam-5802	15	58	systems	system	NOUN
ejpam-5802	15	59	.	.	PUNCT
ejpam-5802	16	1	central	central	ADJ
ejpam-5802	16	2	to	to	ADP
ejpam-5802	16	3	this	this	DET
ejpam-5802	16	4	study	study	NOUN
ejpam-5802	16	5	is	be	AUX
ejpam-5802	16	6	the	the	DET
ejpam-5802	16	7	notion	notion	NOUN
ejpam-5802	16	8	of	of	ADP
ejpam-5802	16	9	nth	nth	NOUN
ejpam-5802	16	10	-	-	NOUN
ejpam-5802	16	11	compactness	compactness	NOUN
ejpam-5802	16	12	,	,	PUNCT
ejpam-5802	16	13	which	which	PRON
ejpam-5802	16	14	generalizes	generalize	VERB
ejpam-5802	16	15	the	the	DET
ejpam-5802	16	16	classical	classical	ADJ
ejpam-5802	16	17	concept	concept	NOUN
ejpam-5802	16	18	of	of	ADP
ejpam-5802	16	19	compactness	compactness	NOUN
ejpam-5802	16	20	by	by	ADP
ejpam-5802	16	21	requiring	require	VERB
ejpam-5802	16	22	the	the	DET
ejpam-5802	16	23	existence	existence	NOUN
ejpam-5802	16	24	of	of	ADP
ejpam-5802	16	25	a	a	DET
ejpam-5802	16	26	finite	finite	ADJ
ejpam-5802	16	27	subcover	subcover	NOUN
ejpam-5802	16	28	under	under	ADP
ejpam-5802	16	29	the	the	DET
ejpam-5802	16	30	nthtopological	nthtopological	ADJ
ejpam-5802	16	31	framework	framework	NOUN
ejpam-5802	16	32	.	.	PUNCT
ejpam-5802	17	1	this	this	DET
ejpam-5802	17	2	generalization	generalization	NOUN
ejpam-5802	17	3	has	have	AUX
ejpam-5802	17	4	proven	prove	VERB
ejpam-5802	17	5	to	to	PART
ejpam-5802	17	6	be	be	AUX
ejpam-5802	17	7	a	a	DET
ejpam-5802	17	8	powerful	powerful	ADJ
ejpam-5802	17	9	tool	tool	NOUN
ejpam-5802	17	10	in	in	ADP
ejpam-5802	17	11	extending	extend	VERB
ejpam-5802	17	12	well	well	ADV
ejpam-5802	17	13	-	-	PUNCT
ejpam-5802	17	14	established	establish	VERB
ejpam-5802	17	15	results	result	NOUN
ejpam-5802	17	16	to	to	ADP
ejpam-5802	17	17	broader	broad	ADJ
ejpam-5802	17	18	contexts	context	NOUN
ejpam-5802	17	19	.	.	PUNCT
ejpam-5802	18	1	nth	nth	ADJ
ejpam-5802	18	2	-	-	ADJ
ejpam-5802	18	3	topological	topological	ADJ
ejpam-5802	18	4	spaces	space	NOUN
ejpam-5802	18	5	have	have	AUX
ejpam-5802	18	6	shown	show	VERB
ejpam-5802	18	7	particular	particular	ADJ
ejpam-5802	18	8	promise	promise	NOUN
ejpam-5802	18	9	in	in	ADP
ejpam-5802	18	10	their	their	PRON
ejpam-5802	18	11	application	application	NOUN
ejpam-5802	18	12	to	to	ADP
ejpam-5802	18	13	compact	compact	ADJ
ejpam-5802	18	14	and	and	CCONJ
ejpam-5802	18	15	metacompact	metacompact	ADJ
ejpam-5802	18	16	spaces	space	NOUN
ejpam-5802	18	17	,	,	PUNCT
ejpam-5802	18	18	serving	serve	VERB
ejpam-5802	18	19	as	as	ADP
ejpam-5802	18	20	a	a	DET
ejpam-5802	18	21	bridge	bridge	NOUN
ejpam-5802	18	22	between	between	ADP
ejpam-5802	18	23	classical	classical	ADJ
ejpam-5802	18	24	topology	topology	NOUN
ejpam-5802	18	25	and	and	CCONJ
ejpam-5802	18	26	more	more	ADJ
ejpam-5802	18	27	specialized	specialized	ADJ
ejpam-5802	18	28	fields	field	NOUN
ejpam-5802	18	29	.	.	PUNCT
ejpam-5802	19	1	the	the	DET
ejpam-5802	19	2	exploration	exploration	NOUN
ejpam-5802	19	3	of	of	ADP
ejpam-5802	19	4	nth	nth	NOUN
ejpam-5802	19	5	-	-	PUNCT
ejpam-5802	19	6	compactness	compactness	NOUN
ejpam-5802	19	7	has	have	AUX
ejpam-5802	19	8	provided	provide	VERB
ejpam-5802	19	9	new	new	ADJ
ejpam-5802	19	10	insights	insight	NOUN
ejpam-5802	19	11	into	into	ADP
ejpam-5802	19	12	the	the	DET
ejpam-5802	19	13	behavior	behavior	NOUN
ejpam-5802	19	14	of	of	ADP
ejpam-5802	19	15	finite	finite	PROPN
ejpam-5802	19	16	subcovers	subcover	NOUN
ejpam-5802	19	17	and	and	CCONJ
ejpam-5802	19	18	their	their	PRON
ejpam-5802	19	19	interactions	interaction	NOUN
ejpam-5802	19	20	across	across	ADP
ejpam-5802	19	21	multiple	multiple	ADJ
ejpam-5802	19	22	topologies	topology	NOUN
ejpam-5802	19	23	.	.	PUNCT
ejpam-5802	20	1	by	by	ADP
ejpam-5802	20	2	expanding	expand	VERB
ejpam-5802	20	3	upon	upon	SCONJ
ejpam-5802	20	4	existing	exist	VERB
ejpam-5802	20	5	concepts	concept	NOUN
ejpam-5802	20	6	such	such	ADJ
ejpam-5802	20	7	as	as	ADP
ejpam-5802	20	8	nth	nth	NOUN
ejpam-5802	20	9	-	-	NOUN
ejpam-5802	20	10	metacompactness	metacompactness	ADJ
ejpam-5802	20	11	,	,	PUNCT
ejpam-5802	20	12	researchers	researcher	NOUN
ejpam-5802	20	13	have	have	AUX
ejpam-5802	20	14	developed	develop	VERB
ejpam-5802	20	15	a	a	DET
ejpam-5802	20	16	wealth	wealth	NOUN
ejpam-5802	20	17	of	of	ADP
ejpam-5802	20	18	generalized	generalized	ADJ
ejpam-5802	20	19	theorems	theorem	NOUN
ejpam-5802	20	20	and	and	CCONJ
ejpam-5802	20	21	illustrative	illustrative	ADJ
ejpam-5802	20	22	examples	example	NOUN
ejpam-5802	20	23	.	.	PUNCT
ejpam-5802	21	1	this	this	DET
ejpam-5802	21	2	paper	paper	NOUN
ejpam-5802	21	3	builds	build	VERB
ejpam-5802	21	4	on	on	ADP
ejpam-5802	21	5	these	these	DET
ejpam-5802	21	6	advancements	advancement	NOUN
ejpam-5802	21	7	,	,	PUNCT
ejpam-5802	21	8	presenting	present	VERB
ejpam-5802	21	9	several	several	ADJ
ejpam-5802	21	10	significant	significant	ADJ
ejpam-5802	21	11	examples	example	NOUN
ejpam-5802	21	12	and	and	CCONJ
ejpam-5802	21	13	discussing	discuss	VERB
ejpam-5802	21	14	key	key	ADJ
ejpam-5802	21	15	results	result	NOUN
ejpam-5802	21	16	that	that	PRON
ejpam-5802	21	17	extend	extend	VERB
ejpam-5802	21	18	the	the	DET
ejpam-5802	21	19	foundational	foundational	ADJ
ejpam-5802	21	20	theorems	theorem	NOUN
ejpam-5802	21	21	of	of	ADP
ejpam-5802	21	22	topology	topology	NOUN
ejpam-5802	21	23	to	to	ADP
ejpam-5802	21	24	nth	nth	NOUN
ejpam-5802	21	25	-	-	PUNCT
ejpam-5802	21	26	topological	topological	ADJ
ejpam-5802	21	27	spaces	space	NOUN
ejpam-5802	21	28	.	.	PUNCT
ejpam-5802	22	1	the	the	DET
ejpam-5802	22	2	works	work	NOUN
ejpam-5802	22	3	of	of	ADP
ejpam-5802	22	4	[	[	X
ejpam-5802	22	5	j.	j.	PROPN
ejpam-5802	22	6	oudetallah	oudetallah	PROPN
ejpam-5802	22	7	]	]	PUNCT
ejpam-5802	22	8	,	,	PUNCT
ejpam-5802	22	9	[	[	X
ejpam-5802	22	10	jamal	jamal	ADJ
ejpam-5802	22	11	oudetallah	oudetallah	PROPN
ejpam-5802	22	12	(	(	PUNCT
ejpam-5802	22	13	2021	2021	NUM
ejpam-5802	22	14	)	)	PUNCT
ejpam-5802	22	15	]	]	PUNCT
ejpam-5802	22	16	,	,	PUNCT
ejpam-5802	22	17	[	[	X
ejpam-5802	22	18	jamal	jamal	PROPN
ejpam-5802	22	19	oudetallah	oudetallah	PROPN
ejpam-5802	22	20	and	and	CCONJ
ejpam-5802	22	21	m	m	PROPN
ejpam-5802	22	22	al	al	PROPN
ejpam-5802	22	23	-	-	PUNCT
ejpam-5802	22	24	hawari	hawari	PROPN
ejpam-5802	22	25	(	(	PUNCT
ejpam-5802	22	26	2018	2018	NUM
ejpam-5802	22	27	)	)	PUNCT
ejpam-5802	22	28	]	]	PUNCT
ejpam-5802	22	29	,	,	PUNCT
ejpam-5802	22	30	and	and	CCONJ
ejpam-5802	22	31	[	[	X
ejpam-5802	22	32	jamal	jamal	PROPN
ejpam-5802	22	33	oudetallah	oudetallah	PROPN
ejpam-5802	22	34	,	,	PUNCT
ejpam-5802	22	35	mohammad	mohammad	PROPN
ejpam-5802	22	36	m.	m.	PROPN
ejpam-5802	22	37	rousa	rousa	NOUN
ejpam-5802	22	38	(	(	PUNCT
ejpam-5802	22	39	2021	2021	NUM
ejpam-5802	22	40	)	)	PUNCT
ejpam-5802	22	41	]	]	PUNCT
ejpam-5802	22	42	are	be	AUX
ejpam-5802	22	43	particularly	particularly	ADV
ejpam-5802	22	44	noteworthy	noteworthy	ADJ
ejpam-5802	22	45	in	in	ADP
ejpam-5802	22	46	this	this	DET
ejpam-5802	22	47	regard	regard	NOUN
ejpam-5802	22	48	,	,	PUNCT
ejpam-5802	22	49	as	as	SCONJ
ejpam-5802	22	50	they	they	PRON
ejpam-5802	22	51	provide	provide	VERB
ejpam-5802	22	52	a	a	DET
ejpam-5802	22	53	robust	robust	ADJ
ejpam-5802	22	54	theoretical	theoretical	ADJ
ejpam-5802	22	55	underpinning	underpinning	NOUN
ejpam-5802	22	56	for	for	ADP
ejpam-5802	22	57	the	the	DET
ejpam-5802	22	58	concepts	concept	NOUN
ejpam-5802	22	59	discussed	discuss	VERB
ejpam-5802	22	60	here	here	ADV
ejpam-5802	22	61	.	.	PUNCT
ejpam-5802	23	1	these	these	DET
ejpam-5802	23	2	contributions	contribution	NOUN
ejpam-5802	23	3	underline	underline	VERB
ejpam-5802	23	4	the	the	DET
ejpam-5802	23	5	versatility	versatility	NOUN
ejpam-5802	23	6	and	and	CCONJ
ejpam-5802	23	7	applicability	applicability	NOUN
ejpam-5802	23	8	of	of	ADP
ejpam-5802	23	9	nth	nth	NOUN
ejpam-5802	23	10	-	-	ADJ
ejpam-5802	23	11	topological	topological	ADJ
ejpam-5802	23	12	spaces	space	NOUN
ejpam-5802	23	13	in	in	ADP
ejpam-5802	23	14	modern	modern	ADJ
ejpam-5802	23	15	topology	topology	NOUN
ejpam-5802	23	16	,	,	PUNCT
ejpam-5802	23	17	making	make	VERB
ejpam-5802	23	18	them	they	PRON
ejpam-5802	23	19	a	a	DET
ejpam-5802	23	20	crucial	crucial	ADJ
ejpam-5802	23	21	area	area	NOUN
ejpam-5802	23	22	of	of	ADP
ejpam-5802	23	23	study	study	NOUN
ejpam-5802	23	24	for	for	ADP
ejpam-5802	23	25	further	further	ADJ
ejpam-5802	23	26	exploration	exploration	NOUN
ejpam-5802	23	27	and	and	CCONJ
ejpam-5802	23	28	development	development	NOUN
ejpam-5802	23	29	.	.	PUNCT
ejpam-5802	24	1	2	2	X
ejpam-5802	24	2	.	.	X
ejpam-5802	24	3	literature	literature	NOUN
ejpam-5802	24	4	review	review	VERB
ejpam-5802	24	5	the	the	DET
ejpam-5802	24	6	concept	concept	NOUN
ejpam-5802	24	7	of	of	ADP
ejpam-5802	24	8	a	a	DET
ejpam-5802	24	9	σ	σ	NOUN
ejpam-5802	24	10	space	space	NOUN
ejpam-5802	24	11	in	in	ADP
ejpam-5802	24	12	topological	topological	ADJ
ejpam-5802	24	13	space	space	NOUN
ejpam-5802	24	14	(	(	PUNCT
ejpam-5802	24	15	k	k	X
ejpam-5802	24	16	,	,	PUNCT
ejpam-5802	24	17	η	η	NOUN
ejpam-5802	24	18	)	)	PUNCT
ejpam-5802	24	19	was	be	AUX
ejpam-5802	24	20	presented	present	VERB
ejpam-5802	24	21	by	by	ADP
ejpam-5802	24	22	[	[	X
ejpam-5802	24	23	7	7	NUM
ejpam-5802	24	24	]	]	PUNCT
ejpam-5802	24	25	.	.	PUNCT
ejpam-5802	25	1	recent	recent	ADJ
ejpam-5802	25	2	research	research	NOUN
ejpam-5802	25	3	[	[	X
ejpam-5802	25	4	2	2	NUM
ejpam-5802	25	5	]	]	PUNCT
ejpam-5802	25	6	,	,	PUNCT
ejpam-5802	25	7	[	[	X
ejpam-5802	25	8	3	3	NUM
ejpam-5802	25	9	]	]	PUNCT
ejpam-5802	25	10	,	,	PUNCT
ejpam-5802	25	11	[	[	X
ejpam-5802	25	12	6	6	NUM
ejpam-5802	25	13	]	]	PUNCT
ejpam-5802	25	14	has	have	AUX
ejpam-5802	25	15	delved	delve	VERB
ejpam-5802	25	16	deeper	deeply	ADV
ejpam-5802	25	17	into	into	ADP
ejpam-5802	25	18	these	these	DET
ejpam-5802	25	19	areas	area	NOUN
ejpam-5802	25	20	.	.	PUNCT
ejpam-5802	26	1	this	this	DET
ejpam-5802	26	2	paper	paper	NOUN
ejpam-5802	26	3	explores	explore	VERB
ejpam-5802	26	4	the	the	DET
ejpam-5802	26	5	concept	concept	NOUN
ejpam-5802	26	6	of	of	ADP
ejpam-5802	26	7	nth	nth	PROPN
ejpam-5802	26	8	-	-	PUNCT
ejpam-5802	26	9	σ	σ	PROPN
ejpam-5802	26	10	presents	present	NOUN
ejpam-5802	26	11	associated	associate	VERB
ejpam-5802	26	12	conclusions	conclusion	NOUN
ejpam-5802	26	13	.	.	PUNCT
ejpam-5802	27	1	then	then	ADV
ejpam-5802	27	2	,	,	PUNCT
ejpam-5802	27	3	we	we	PRON
ejpam-5802	27	4	introduce	introduce	VERB
ejpam-5802	27	5	the	the	DET
ejpam-5802	27	6	concept	concept	NOUN
ejpam-5802	27	7	of	of	ADP
ejpam-5802	27	8	topological	topological	ADJ
ejpam-5802	27	9	space	space	NOUN
ejpam-5802	27	10	,	,	PUNCT
ejpam-5802	27	11	nth	nth	ADJ
ejpam-5802	27	12	-	-	ADJ
ejpam-5802	27	13	topological	topological	ADJ
ejpam-5802	27	14	space	space	NOUN
ejpam-5802	27	15	and	and	CCONJ
ejpam-5802	27	16	some	some	DET
ejpam-5802	27	17	important	important	ADJ
ejpam-5802	27	18	concept	concept	NOUN
ejpam-5802	27	19	in	in	ADP
ejpam-5802	27	20	nth	nth	ADJ
ejpam-5802	27	21	-	-	ADJ
ejpam-5802	27	22	topological	topological	ADJ
ejpam-5802	27	23	space	space	NOUN
ejpam-5802	27	24	like	like	ADP
ejpam-5802	27	25	:	:	PUNCT
ejpam-5802	27	26	open	open	ADJ
ejpam-5802	27	27	and	and	CCONJ
ejpam-5802	27	28	closed	closed	ADJ
ejpam-5802	27	29	sets	set	NOUN
ejpam-5802	27	30	,	,	PUNCT
ejpam-5802	27	31	derived	derive	VERB
ejpam-5802	27	32	set	set	NOUN
ejpam-5802	27	33	,	,	PUNCT
ejpam-5802	27	34	closure	closure	NOUN
ejpam-5802	27	35	set	set	NOUN
ejpam-5802	27	36	,	,	PUNCT
ejpam-5802	27	37	interior	interior	ADJ
ejpam-5802	27	38	and	and	CCONJ
ejpam-5802	27	39	exterior	exterior	ADJ
ejpam-5802	27	40	sets	set	NOUN
ejpam-5802	27	41	,	,	PUNCT
ejpam-5802	27	42	separation	separation	NOUN
ejpam-5802	27	43	axioms	axiom	NOUN
ejpam-5802	27	44	,	,	PUNCT
ejpam-5802	27	45	etc	etc	X
ejpam-5802	27	46	...	...	X
ejpam-5802	27	47	.	.	PUNCT
ejpam-5802	28	1	then	then	ADV
ejpam-5802	28	2	we	we	PRON
ejpam-5802	28	3	talk	talk	VERB
ejpam-5802	28	4	about	about	ADP
ejpam-5802	28	5	the	the	DET
ejpam-5802	28	6	concept	concept	NOUN
ejpam-5802	28	7	of	of	ADP
ejpam-5802	28	8	σ	σ	PROPN
ejpam-5802	28	9	space	space	NOUN
ejpam-5802	28	10	in	in	ADP
ejpam-5802	28	11	nth	nth	PROPN
ejpam-5802	28	12	-	-	ADJ
ejpam-5802	28	13	topological	topological	ADJ
ejpam-5802	28	14	spaces	space	NOUN
ejpam-5802	28	15	,	,	PUNCT
ejpam-5802	28	16	discuss	discuss	VERB
ejpam-5802	28	17	its	its	PRON
ejpam-5802	28	18	features	feature	NOUN
ejpam-5802	28	19	,	,	PUNCT
ejpam-5802	28	20	and	and	CCONJ
ejpam-5802	28	21	apply	apply	VERB
ejpam-5802	28	22	it	it	PRON
ejpam-5802	28	23	to	to	ADP
ejpam-5802	28	24	other	other	ADJ
ejpam-5802	28	25	spaces	space	NOUN
ejpam-5802	28	26	.	.	PUNCT
ejpam-5802	29	1	we	we	PRON
ejpam-5802	29	2	examine	examine	VERB
ejpam-5802	29	3	well	well	ADV
ejpam-5802	29	4	-	-	PUNCT
ejpam-5802	29	5	known	know	VERB
ejpam-5802	29	6	definitions	definition	NOUN
ejpam-5802	29	7	that	that	PRON
ejpam-5802	29	8	will	will	AUX
ejpam-5802	29	9	be	be	AUX
ejpam-5802	29	10	applied	apply	VERB
ejpam-5802	29	11	in	in	ADP
ejpam-5802	29	12	the	the	DET
ejpam-5802	29	13	sequel	sequel	NOUN
ejpam-5802	29	14	.	.	PUNCT
ejpam-5802	30	1	the	the	DET
ejpam-5802	30	2	terms	term	NOUN
ejpam-5802	30	3	ηu	ηu	ADP
ejpam-5802	30	4	,	,	PUNCT
ejpam-5802	30	5	ηdis	ηdi	NOUN
ejpam-5802	30	6	,	,	PUNCT
ejpam-5802	30	7	ηcof	ηcof	PROPN
ejpam-5802	30	8	and	and	CCONJ
ejpam-5802	30	9	ηcoc	ηcoc	VERB
ejpam-5802	30	10	represent	represent	VERB
ejpam-5802	30	11	the	the	DET
ejpam-5802	30	12	ordinary	ordinary	ADJ
ejpam-5802	30	13	or	or	CCONJ
ejpam-5802	30	14	usual	usual	ADJ
ejpam-5802	30	15	topology	topology	NOUN
ejpam-5802	30	16	,	,	PUNCT
ejpam-5802	30	17	discrete	discrete	ADJ
ejpam-5802	30	18	topology	topology	NOUN
ejpam-5802	30	19	,	,	PUNCT
ejpam-5802	30	20	co	co	ADJ
ejpam-5802	30	21	-	-	ADJ
ejpam-5802	30	22	finite	finite	ADJ
ejpam-5802	30	23	topology	topology	NOUN
ejpam-5802	30	24	,	,	PUNCT
ejpam-5802	30	25	and	and	CCONJ
ejpam-5802	30	26	co	co	ADJ
ejpam-5802	30	27	-	-	ADJ
ejpam-5802	30	28	countable	countable	ADJ
ejpam-5802	30	29	topology	topology	NOUN
ejpam-5802	30	30	,	,	PUNCT
ejpam-5802	30	31	respectively	respectively	ADV
ejpam-5802	30	32	.	.	PUNCT
ejpam-5802	31	1	the	the	DET
ejpam-5802	31	2	concept	concept	NOUN
ejpam-5802	31	3	of	of	ADP
ejpam-5802	31	4	tritopological	tritopological	ADJ
ejpam-5802	31	5	spaces	space	NOUN
ejpam-5802	31	6	can	can	AUX
ejpam-5802	31	7	be	be	AUX
ejpam-5802	31	8	represented	represent	VERB
ejpam-5802	31	9	as	as	ADP
ejpam-5802	31	10	k	k	PROPN
ejpam-5802	31	11	=	=	PRON
ejpam-5802	31	12	(	(	PUNCT
ejpam-5802	31	13	k	k	X
ejpam-5802	31	14	,	,	PUNCT
ejpam-5802	31	15	η1	η1	NOUN
ejpam-5802	31	16	,	,	PUNCT
ejpam-5802	31	17	η2	η2	NOUN
ejpam-5802	31	18	,	,	PUNCT
ejpam-5802	31	19	η3	η3	NOUN
ejpam-5802	31	20	)	)	PUNCT
ejpam-5802	31	21	where	where	SCONJ
ejpam-5802	31	22	η1	η1	NOUN
ejpam-5802	31	23	,	,	PUNCT
ejpam-5802	31	24	η2	η2	PROPN
ejpam-5802	31	25	and	and	CCONJ
ejpam-5802	31	26	η3	η3	NOUN
ejpam-5802	31	27	are	be	AUX
ejpam-5802	31	28	topologies	topology	NOUN
ejpam-5802	31	29	on	on	ADP
ejpam-5802	31	30	k	k	PROPN
ejpam-5802	31	31	and	and	CCONJ
ejpam-5802	31	32	the	the	DET
ejpam-5802	31	33	concept	concept	NOUN
ejpam-5802	31	34	of	of	ADP
ejpam-5802	31	35	nth	nth	ADJ
ejpam-5802	31	36	-	-	ADJ
ejpam-5802	31	37	topological	topological	ADJ
ejpam-5802	31	38	space	space	NOUN
ejpam-5802	31	39	(	(	PUNCT
ejpam-5802	31	40	k	k	X
ejpam-5802	31	41	,	,	PUNCT
ejpam-5802	31	42	η1	η1	NOUN
ejpam-5802	31	43	,	,	PUNCT
ejpam-5802	31	44	η2	η2	NOUN
ejpam-5802	31	45	,	,	PUNCT
ejpam-5802	31	46	...	...	PUNCT
ejpam-5802	31	47	,	,	PUNCT
ejpam-5802	31	48	ηn	ηn	PROPN
ejpam-5802	31	49	)	)	PUNCT
ejpam-5802	31	50	where	where	SCONJ
ejpam-5802	31	51	η1	η1	NOUN
ejpam-5802	31	52	,	,	PUNCT
ejpam-5802	31	53	η2	η2	PROPN
ejpam-5802	31	54	...	...	PUNCT
ejpam-5802	31	55	η3	η3	NOUN
ejpam-5802	31	56	are	be	AUX
ejpam-5802	31	57	topologies	topology	NOUN
ejpam-5802	31	58	on	on	ADP
ejpam-5802	31	59	k	k	PROPN
ejpam-5802	31	60	.	.	PUNCT
ejpam-5802	32	1	this	this	PRON
ejpam-5802	32	2	is	be	AUX
ejpam-5802	32	3	connected	connect	VERB
ejpam-5802	32	4	to	to	ADP
ejpam-5802	32	5	prior	prior	ADJ
ejpam-5802	32	6	research	research	NOUN
ejpam-5802	32	7	on	on	ADP
ejpam-5802	32	8	nth	nth	ADJ
ejpam-5802	32	9	-	-	ADJ
ejpam-5802	32	10	topological	topological	ADJ
ejpam-5802	32	11	spaces	space	NOUN
ejpam-5802	32	12	,	,	PUNCT
ejpam-5802	32	13	where	where	SCONJ
ejpam-5802	32	14	each	each	DET
ejpam-5802	32	15	topology	topology	NOUN
ejpam-5802	32	16	is	be	AUX
ejpam-5802	32	17	a	a	DET
ejpam-5802	32	18	set	set	NOUN
ejpam-5802	32	19	of	of	ADP
ejpam-5802	32	20	points	point	NOUN
ejpam-5802	32	21	that	that	PRON
ejpam-5802	32	22	meet	meet	VERB
ejpam-5802	32	23	a	a	DET
ejpam-5802	32	24	set	set	NOUN
ejpam-5802	32	25	of	of	ADP
ejpam-5802	32	26	axioms	axiom	NOUN
ejpam-5802	32	27	.	.	PUNCT
ejpam-5802	33	1	[	[	X
ejpam-5802	33	2	4	4	X
ejpam-5802	33	3	]	]	PUNCT
ejpam-5802	33	4	explained	explain	VERB
ejpam-5802	33	5	hausdorff	hausdorff	NOUN
ejpam-5802	33	6	,	,	PUNCT
ejpam-5802	33	7	regular	regular	ADJ
ejpam-5802	33	8	and	and	CCONJ
ejpam-5802	33	9	normal	normal	ADJ
ejpam-5802	33	10	spaces	space	NOUN
ejpam-5802	33	11	in	in	ADP
ejpam-5802	33	12	nth	nth	PROPN
ejpam-5802	33	13	topological	topological	ADJ
ejpam-5802	33	14	spaces	space	NOUN
ejpam-5802	33	15	using	use	VERB
ejpam-5802	33	16	a	a	DET
ejpam-5802	33	17	set	set	NOUN
ejpam-5802	33	18	of	of	ADP
ejpam-5802	33	19	standard	standard	ADJ
ejpam-5802	33	20	results	result	NOUN
ejpam-5802	33	21	known	know	VERB
ejpam-5802	33	22	as	as	ADP
ejpam-5802	33	23	tietze	tietze	ADJ
ejpam-5802	33	24	extintion	extintion	NOUN
ejpam-5802	33	25	.	.	PUNCT
ejpam-5802	34	1	the	the	DET
ejpam-5802	34	2	primary	primary	ADJ
ejpam-5802	34	3	goal	goal	NOUN
ejpam-5802	34	4	of	of	ADP
ejpam-5802	34	5	this	this	DET
ejpam-5802	34	6	paper	paper	NOUN
ejpam-5802	34	7	is	be	AUX
ejpam-5802	34	8	to	to	PART
ejpam-5802	34	9	introduce	introduce	VERB
ejpam-5802	34	10	and	and	CCONJ
ejpam-5802	34	11	investigate	investigate	VERB
ejpam-5802	34	12	a	a	DET
ejpam-5802	34	13	novel	novel	ADJ
ejpam-5802	34	14	sort	sort	NOUN
ejpam-5802	34	15	of	of	ADP
ejpam-5802	34	16	nth	nth	NOUN
ejpam-5802	34	17	-	-	PUNCT
ejpam-5802	34	18	σ	σ	NOUN
ejpam-5802	34	19	space	space	NOUN
ejpam-5802	34	20	and	and	CCONJ
ejpam-5802	34	21	nth	nth	ADJ
ejpam-5802	34	22	-	-	ADJ
ejpam-5802	34	23	topological	topological	ADJ
ejpam-5802	34	24	spaces	space	NOUN
ejpam-5802	34	25	are	be	AUX
ejpam-5802	34	26	sets	set	NOUN
ejpam-5802	34	27	containing	contain	VERB
ejpam-5802	34	28	n	n	DET
ejpam-5802	34	29	topologies	topology	NOUN
ejpam-5802	34	30	.	.	PUNCT
ejpam-5802	35	1	j.	j.	PROPN
ejpam-5802	35	2	oudetallah	oudetallah	PROPN
ejpam-5802	35	3	et	et	PROPN
ejpam-5802	35	4	al	al	PROPN
ejpam-5802	35	5	.	.	PUNCT
ejpam-5802	35	6	/	/	SYM
ejpam-5802	35	7	eur	eur	PROPN
ejpam-5802	35	8	.	.	PUNCT
ejpam-5802	36	1	j.	j.	PROPN
ejpam-5802	36	2	pure	pure	PROPN
ejpam-5802	36	3	appl	appl	PROPN
ejpam-5802	36	4	.	.	PROPN
ejpam-5802	36	5	math	math	PROPN
ejpam-5802	36	6	,	,	PUNCT
ejpam-5802	36	7	18	18	NUM
ejpam-5802	36	8	(	(	PUNCT
ejpam-5802	36	9	2	2	NUM
ejpam-5802	36	10	)	)	PUNCT
ejpam-5802	36	11	(	(	PUNCT
ejpam-5802	36	12	2025	2025	NUM
ejpam-5802	36	13	)	)	PUNCT
ejpam-5802	36	14	,	,	PUNCT
ejpam-5802	36	15	5802	5802	NUM
ejpam-5802	36	16	3	3	NUM
ejpam-5802	36	17	of	of	ADP
ejpam-5802	36	18	14	14	NUM
ejpam-5802	36	19	3	3	NUM
ejpam-5802	36	20	.	.	PUNCT
ejpam-5802	37	1	preliminaries	preliminary	NOUN
ejpam-5802	37	2	definition	definition	NOUN
ejpam-5802	37	3	1.1	1.1	NUM
ejpam-5802	38	1	[	[	X
ejpam-5802	38	2	3	3	NUM
ejpam-5802	38	3	]	]	PUNCT
ejpam-5802	38	4	:	:	PUNCT
ejpam-5802	38	5	let	let	VERB
ejpam-5802	38	6	k	k	PROPN
ejpam-5802	38	7	̸=	̸=	PROPN
ejpam-5802	38	8	ϕ	ϕ	PROPN
ejpam-5802	38	9	,	,	PUNCT
ejpam-5802	38	10	η	η	PROPN
ejpam-5802	38	11	⊂	⊂	NOUN
ejpam-5802	38	12	p(k	p(k	NOUN
ejpam-5802	38	13	)	)	PUNCT
ejpam-5802	38	14	=	=	PRON
ejpam-5802	38	15	{	{	PUNCT
ejpam-5802	38	16	a	a	X
ejpam-5802	38	17	:	:	PUNCT
ejpam-5802	38	18	a	a	DET
ejpam-5802	38	19	⊆	⊆	NUM
ejpam-5802	38	20	k	k	NOUN
ejpam-5802	38	21	}	}	PUNCT
ejpam-5802	38	22	,	,	PUNCT
ejpam-5802	38	23	then	then	ADV
ejpam-5802	38	24	η	η	PROPN
ejpam-5802	38	25	is	be	AUX
ejpam-5802	38	26	called	call	VERB
ejpam-5802	38	27	topology	topology	NOUN
ejpam-5802	38	28	on	on	ADP
ejpam-5802	38	29	k	k	PROPN
ejpam-5802	38	30	if	if	SCONJ
ejpam-5802	38	31	the	the	DET
ejpam-5802	38	32	following	follow	VERB
ejpam-5802	38	33	conditions	condition	NOUN
ejpam-5802	38	34	are	be	AUX
ejpam-5802	38	35	satisfied	satisfied	ADJ
ejpam-5802	38	36	:	:	PUNCT
ejpam-5802	38	37	i	i	NOUN
ejpam-5802	38	38	)	)	PUNCT
ejpam-5802	38	39	ϕ	ϕ	PROPN
ejpam-5802	38	40	,	,	PUNCT
ejpam-5802	38	41	k	k	PROPN
ejpam-5802	38	42	∈	∈	PROPN
ejpam-5802	38	43	η	η	PROPN
ejpam-5802	38	44	.	.	PROPN
ejpam-5802	38	45	ii	ii	PROPN
ejpam-5802	38	46	)	)	PUNCT
ejpam-5802	38	47	closed	close	VERB
ejpam-5802	38	48	under	under	ADP
ejpam-5802	38	49	intersection	intersection	NOUN
ejpam-5802	38	50	.	.	PUNCT
ejpam-5802	39	1	iii	iii	X
ejpam-5802	39	2	)	)	PUNCT
ejpam-5802	39	3	the	the	DET
ejpam-5802	39	4	union	union	NOUN
ejpam-5802	39	5	of	of	ADP
ejpam-5802	39	6	any	any	DET
ejpam-5802	39	7	collection	collection	NOUN
ejpam-5802	39	8	of	of	ADP
ejpam-5802	39	9	sets	set	NOUN
ejpam-5802	39	10	in	in	ADP
ejpam-5802	39	11	η	η	PROPN
ejpam-5802	39	12	is	be	AUX
ejpam-5802	39	13	also	also	ADV
ejpam-5802	39	14	in	in	ADP
ejpam-5802	39	15	η	η	PROPN
ejpam-5802	39	16	.	.	PROPN
ejpam-5802	39	17	definition	definition	NOUN
ejpam-5802	39	18	2.1[1	2.1[1	NUM
ejpam-5802	39	19	]	]	PUNCT
ejpam-5802	39	20	:	:	PUNCT
ejpam-5802	39	21	let	let	VERB
ejpam-5802	39	22	k	k	PRON
ejpam-5802	39	23	be	be	AUX
ejpam-5802	39	24	a	a	DET
ejpam-5802	39	25	non	non	X
ejpam-5802	39	26	empty	empty	ADJ
ejpam-5802	39	27	set	set	NOUN
ejpam-5802	39	28	,	,	PUNCT
ejpam-5802	39	29	ηi	ηi	PROPN
ejpam-5802	39	30	⊂	⊂	PROPN
ejpam-5802	39	31	p(k	p(k	NOUN
ejpam-5802	39	32	)	)	PUNCT
ejpam-5802	39	33	=	=	PRON
ejpam-5802	39	34	{	{	PUNCT
ejpam-5802	39	35	a	a	X
ejpam-5802	39	36	:	:	PUNCT
ejpam-5802	39	37	a	a	DET
ejpam-5802	39	38	⊆	⊆	NUM
ejpam-5802	39	39	k	k	NOUN
ejpam-5802	39	40	}	}	PUNCT
ejpam-5802	39	41	,	,	PUNCT
ejpam-5802	39	42	where	where	SCONJ
ejpam-5802	39	43	i=1,2,3,	i=1,2,3,	NOUN
ejpam-5802	39	44	...	...	PUNCT
ejpam-5802	39	45	,n	,n	PUNCT
ejpam-5802	39	46	.	.	PUNCT
ejpam-5802	40	1	we	we	PRON
ejpam-5802	40	2	say	say	VERB
ejpam-5802	40	3	that	that	SCONJ
ejpam-5802	40	4	(	(	PUNCT
ejpam-5802	40	5	k	k	X
ejpam-5802	40	6	,	,	PUNCT
ejpam-5802	40	7	η1	η1	NOUN
ejpam-5802	40	8	,	,	PUNCT
ejpam-5802	40	9	η2	η2	PROPN
ejpam-5802	40	10	,	,	PUNCT
ejpam-5802	40	11	...	...	PUNCT
ejpam-5802	40	12	,	,	PUNCT
ejpam-5802	40	13	ηn	ηn	INTJ
ejpam-5802	40	14	)	)	PUNCT
ejpam-5802	40	15	is	be	AUX
ejpam-5802	40	16	nth	nth	ADJ
ejpam-5802	40	17	-	-	ADJ
ejpam-5802	40	18	topological	topological	ADJ
ejpam-5802	40	19	space	space	NOUN
ejpam-5802	40	20	if	if	SCONJ
ejpam-5802	40	21	ηi	ηi	PROPN
ejpam-5802	40	22	is	be	AUX
ejpam-5802	40	23	topology	topology	NOUN
ejpam-5802	40	24	on	on	ADP
ejpam-5802	40	25	k	k	PROPN
ejpam-5802	40	26	,	,	PUNCT
ejpam-5802	40	27	for	for	ADP
ejpam-5802	40	28	all	all	DET
ejpam-5802	40	29	i=1,2,3,	i=1,2,3,	NOUN
ejpam-5802	40	30	...	...	PUNCT
ejpam-5802	40	31	,n	,n	PUNCT
ejpam-5802	40	32	.	.	PUNCT
ejpam-5802	41	1	example	example	NOUN
ejpam-5802	41	2	consider	consider	VERB
ejpam-5802	41	3	k	k	X
ejpam-5802	41	4	=	=	PUNCT
ejpam-5802	41	5	{	{	PUNCT
ejpam-5802	41	6	1,2,3	1,2,3	NUM
ejpam-5802	41	7	}	}	PUNCT
ejpam-5802	41	8	η1	η1	NOUN
ejpam-5802	41	9	=	=	SYM
ejpam-5802	41	10	{	{	PUNCT
ejpam-5802	41	11	ϕ	ϕ	PROPN
ejpam-5802	41	12	,	,	PUNCT
ejpam-5802	41	13	k	k	PROPN
ejpam-5802	41	14	,	,	PUNCT
ejpam-5802	41	15	{	{	PUNCT
ejpam-5802	41	16	1	1	NUM
ejpam-5802	41	17	}	}	PUNCT
ejpam-5802	41	18	}	}	PUNCT
ejpam-5802	41	19	⊂	⊂	NOUN
ejpam-5802	41	20	p(k	p(k	NOUN
ejpam-5802	41	21	)	)	PUNCT
ejpam-5802	41	22	η2	η2	NOUN
ejpam-5802	41	23	=	=	SYM
ejpam-5802	41	24	{	{	PUNCT
ejpam-5802	41	25	ϕ	ϕ	X
ejpam-5802	41	26	,	,	PUNCT
ejpam-5802	41	27	k	k	PROPN
ejpam-5802	41	28	,	,	PUNCT
ejpam-5802	41	29	{	{	PUNCT
ejpam-5802	41	30	1	1	NUM
ejpam-5802	41	31	}	}	PUNCT
ejpam-5802	41	32	,	,	PUNCT
ejpam-5802	41	33	{	{	PUNCT
ejpam-5802	41	34	2	2	NUM
ejpam-5802	41	35	}	}	PUNCT
ejpam-5802	41	36	,	,	PUNCT
ejpam-5802	41	37	{	{	PUNCT
ejpam-5802	41	38	1,2	1,2	NUM
ejpam-5802	41	39	}	}	PUNCT
ejpam-5802	41	40	}	}	PUNCT
ejpam-5802	41	41	⊂	⊂	NOUN
ejpam-5802	41	42	p(k	p(k	NOUN
ejpam-5802	41	43	)	)	PUNCT
ejpam-5802	41	44	η3	η3	NOUN
ejpam-5802	41	45	=	=	PUNCT
ejpam-5802	41	46	{	{	PUNCT
ejpam-5802	41	47	ϕ	ϕ	X
ejpam-5802	41	48	,	,	PUNCT
ejpam-5802	41	49	k	k	PROPN
ejpam-5802	41	50	,	,	PUNCT
ejpam-5802	41	51	{	{	PUNCT
ejpam-5802	41	52	2	2	NUM
ejpam-5802	41	53	}	}	PUNCT
ejpam-5802	41	54	,	,	PUNCT
ejpam-5802	41	55	{	{	PUNCT
ejpam-5802	41	56	3	3	NUM
ejpam-5802	41	57	}	}	PUNCT
ejpam-5802	41	58	,	,	PUNCT
ejpam-5802	41	59	{	{	PUNCT
ejpam-5802	41	60	2,3	2,3	NUM
ejpam-5802	41	61	}	}	PUNCT
ejpam-5802	41	62	}	}	PUNCT
ejpam-5802	41	63	⊂	⊂	ADJ
ejpam-5802	41	64	p(k	p(k	NOUN
ejpam-5802	41	65	)	)	PUNCT
ejpam-5802	41	66	ηi	ηi	NOUN
ejpam-5802	41	67	’s	’s	PART
ejpam-5802	41	68	satisfies	satisfy	VERB
ejpam-5802	41	69	the	the	DET
ejpam-5802	41	70	condition	condition	NOUN
ejpam-5802	41	71	of	of	ADP
ejpam-5802	41	72	topological	topological	ADJ
ejpam-5802	41	73	space	space	NOUN
ejpam-5802	41	74	,	,	PUNCT
ejpam-5802	41	75	i=1,2,3	i=1,2,3	PRON
ejpam-5802	41	76	so	so	ADV
ejpam-5802	41	77	,	,	PUNCT
ejpam-5802	41	78	(	(	PUNCT
ejpam-5802	41	79	k	k	X
ejpam-5802	41	80	,	,	PUNCT
ejpam-5802	41	81	η1	η1	NOUN
ejpam-5802	41	82	,	,	PUNCT
ejpam-5802	41	83	η2	η2	PROPN
ejpam-5802	41	84	,	,	PUNCT
ejpam-5802	41	85	η3	η3	PROPN
ejpam-5802	41	86	)	)	PUNCT
ejpam-5802	41	87	is	be	AUX
ejpam-5802	41	88	tritopological	tritopological	ADJ
ejpam-5802	41	89	space	space	NOUN
ejpam-5802	41	90	.	.	PUNCT
ejpam-5802	42	1	but	but	CCONJ
ejpam-5802	42	2	,	,	PUNCT
ejpam-5802	42	3	for	for	ADP
ejpam-5802	42	4	example	example	NOUN
ejpam-5802	42	5	η	η	PROPN
ejpam-5802	42	6	=	=	PROPN
ejpam-5802	42	7	{	{	PUNCT
ejpam-5802	42	8	ϕ	ϕ	NOUN
ejpam-5802	42	9	,	,	PUNCT
ejpam-5802	42	10	1	1	NUM
ejpam-5802	42	11	}	}	PUNCT
ejpam-5802	42	12	is	be	AUX
ejpam-5802	42	13	not	not	PART
ejpam-5802	42	14	topological	topological	ADJ
ejpam-5802	42	15	space	space	NOUN
ejpam-5802	42	16	because	because	SCONJ
ejpam-5802	42	17	it	it	PRON
ejpam-5802	42	18	is	be	AUX
ejpam-5802	42	19	not	not	PART
ejpam-5802	42	20	contains	contain	VERB
ejpam-5802	42	21	k.	k.	PROPN
ejpam-5802	42	22	definition	definition	NOUN
ejpam-5802	42	23	3.1	3.1	NUM
ejpam-5802	42	24	:	:	PUNCT
ejpam-5802	42	25	let	let	AUX
ejpam-5802	42	26	(	(	PUNCT
ejpam-5802	42	27	k	k	X
ejpam-5802	42	28	,	,	PUNCT
ejpam-5802	42	29	η1	η1	NOUN
ejpam-5802	42	30	,	,	PUNCT
ejpam-5802	42	31	η2	η2	PROPN
ejpam-5802	42	32	,	,	PUNCT
ejpam-5802	42	33	...	...	PUNCT
ejpam-5802	42	34	,	,	PUNCT
ejpam-5802	42	35	ηn	ηn	INTJ
ejpam-5802	42	36	)	)	PUNCT
ejpam-5802	42	37	be	be	AUX
ejpam-5802	42	38	a	a	DET
ejpam-5802	42	39	nth	nth	ADJ
ejpam-5802	42	40	-	-	ADJ
ejpam-5802	42	41	topological	topological	ADJ
ejpam-5802	42	42	space	space	NOUN
ejpam-5802	42	43	.	.	PUNCT
ejpam-5802	43	1	e	e	X
ejpam-5802	43	2	⊂	⊂	PROPN
ejpam-5802	43	3	k	k	PROPN
ejpam-5802	43	4	,	,	PUNCT
ejpam-5802	43	5	then	then	ADV
ejpam-5802	43	6	:	:	PUNCT
ejpam-5802	43	7	i	i	X
ejpam-5802	43	8	)	)	PUNCT
ejpam-5802	43	9	e	e	NOUN
ejpam-5802	43	10	is	be	AUX
ejpam-5802	43	11	called	call	VERB
ejpam-5802	43	12	nth	nth	ADV
ejpam-5802	43	13	-	-	ADJ
ejpam-5802	43	14	open	open	ADJ
ejpam-5802	43	15	set	set	NOUN
ejpam-5802	43	16	,	,	PUNCT
ejpam-5802	43	17	if	if	SCONJ
ejpam-5802	43	18	e	e	PROPN
ejpam-5802	43	19	∈	∈	NOUN
ejpam-5802	43	20	ηi	ηi	NOUN
ejpam-5802	43	21	for	for	ADP
ejpam-5802	43	22	some	some	DET
ejpam-5802	43	23	i=1,2,3	i=1,2,3	NUM
ejpam-5802	43	24	.	.	PUNCT
ejpam-5802	43	25	ii	ii	X
ejpam-5802	43	26	)	)	PUNCT
ejpam-5802	44	1	e	e	NOUN
ejpam-5802	44	2	is	be	AUX
ejpam-5802	44	3	called	call	VERB
ejpam-5802	44	4	nth	nth	ADV
ejpam-5802	44	5	-	-	PUNCT
ejpam-5802	44	6	cloced	cloced	ADJ
ejpam-5802	44	7	set	set	NOUN
ejpam-5802	44	8	,	,	PUNCT
ejpam-5802	44	9	if	if	SCONJ
ejpam-5802	44	10	ec	ec	PROPN
ejpam-5802	44	11	∈	∈	PROPN
ejpam-5802	44	12	ηi	ηi	NOUN
ejpam-5802	44	13	for	for	ADP
ejpam-5802	44	14	some	some	DET
ejpam-5802	44	15	i=1,2,3	i=1,2,3	NUM
ejpam-5802	44	16	.	.	PUNCT
ejpam-5802	45	1	iii	iii	X
ejpam-5802	45	2	)	)	PUNCT
ejpam-5802	45	3	e	e	NOUN
ejpam-5802	45	4	is	be	AUX
ejpam-5802	45	5	called	call	VERB
ejpam-5802	45	6	nth	nth	ADV
ejpam-5802	45	7	-	-	PUNCT
ejpam-5802	45	8	clopen	clopen	ADJ
ejpam-5802	45	9	set	set	NOUN
ejpam-5802	45	10	,	,	PUNCT
ejpam-5802	45	11	if	if	SCONJ
ejpam-5802	45	12	e	e	PROPN
ejpam-5802	45	13	and	and	CCONJ
ejpam-5802	45	14	ec	ec	PROPN
ejpam-5802	45	15	are	be	AUX
ejpam-5802	45	16	both	both	PRON
ejpam-5802	45	17	in	in	ADP
ejpam-5802	45	18	ηi	ηi	NOUN
ejpam-5802	45	19	for	for	ADP
ejpam-5802	45	20	some	some	DET
ejpam-5802	45	21	i=1,2,3	i=1,2,3	ADJ
ejpam-5802	45	22	.	.	PUNCT
ejpam-5802	46	1	example	example	NOUN
ejpam-5802	46	2	let	let	VERB
ejpam-5802	46	3	k	k	PROPN
ejpam-5802	46	4	=	=	PRON
ejpam-5802	46	5	{	{	PUNCT
ejpam-5802	46	6	x	x	PROPN
ejpam-5802	46	7	,	,	PUNCT
ejpam-5802	46	8	y	y	PROPN
ejpam-5802	46	9	,	,	PUNCT
ejpam-5802	46	10	z	z	NOUN
ejpam-5802	46	11	}	}	PUNCT
ejpam-5802	46	12	,	,	PUNCT
ejpam-5802	46	13	η1	η1	NOUN
ejpam-5802	46	14	=	=	SYM
ejpam-5802	46	15	{	{	PUNCT
ejpam-5802	46	16	ϕ,k	ϕ,k	PROPN
ejpam-5802	46	17	,	,	PUNCT
ejpam-5802	46	18	{	{	PUNCT
ejpam-5802	46	19	x	x	NOUN
ejpam-5802	46	20	}	}	PUNCT
ejpam-5802	46	21	}	}	PUNCT
ejpam-5802	46	22	,	,	PUNCT
ejpam-5802	46	23	η2	η2	PROPN
ejpam-5802	46	24	=	=	SYM
ejpam-5802	46	25	{	{	PUNCT
ejpam-5802	46	26	ϕ,k	ϕ,k	PROPN
ejpam-5802	46	27	,	,	PUNCT
ejpam-5802	46	28	{	{	PUNCT
ejpam-5802	46	29	y	y	NOUN
ejpam-5802	46	30	}	}	PUNCT
ejpam-5802	46	31	}	}	PUNCT
ejpam-5802	46	32	,	,	PUNCT
ejpam-5802	46	33	η3	η3	PROPN
ejpam-5802	46	34	=	=	PUNCT
ejpam-5802	46	35	{	{	PUNCT
ejpam-5802	46	36	ϕ,k	ϕ,k	PROPN
ejpam-5802	46	37	,	,	PUNCT
ejpam-5802	46	38	{	{	PUNCT
ejpam-5802	46	39	z	z	NOUN
ejpam-5802	46	40	}	}	PUNCT
ejpam-5802	46	41	}	}	PUNCT
ejpam-5802	46	42	.	.	PUNCT
ejpam-5802	47	1	the	the	DET
ejpam-5802	47	2	sets	set	NOUN
ejpam-5802	47	3	:	:	PUNCT
ejpam-5802	47	4	ϕ,k	ϕ,k	ADJ
ejpam-5802	47	5	,	,	PUNCT
ejpam-5802	47	6	{	{	PUNCT
ejpam-5802	47	7	x	x	X
ejpam-5802	47	8	}	}	PUNCT
ejpam-5802	47	9	,	,	PUNCT
ejpam-5802	47	10	{	{	PUNCT
ejpam-5802	47	11	y	y	NOUN
ejpam-5802	47	12	}	}	PUNCT
ejpam-5802	47	13	,	,	PUNCT
ejpam-5802	47	14	{	{	PUNCT
ejpam-5802	47	15	z	z	X
ejpam-5802	47	16	}	}	PUNCT
ejpam-5802	47	17	are	be	AUX
ejpam-5802	47	18	nth	nth	ADV
ejpam-5802	47	19	-	-	ADJ
ejpam-5802	47	20	open	open	ADJ
ejpam-5802	47	21	sets	set	NOUN
ejpam-5802	47	22	in	in	ADP
ejpam-5802	47	23	k.	k.	PROPN
ejpam-5802	48	1	the	the	DET
ejpam-5802	48	2	sets	set	NOUN
ejpam-5802	48	3	:	:	PUNCT
ejpam-5802	48	4	ϕ,k	ϕ,k	ADJ
ejpam-5802	48	5	,	,	PUNCT
ejpam-5802	48	6	{	{	PUNCT
ejpam-5802	48	7	y	y	PROPN
ejpam-5802	48	8	,	,	PUNCT
ejpam-5802	48	9	z	z	NOUN
ejpam-5802	48	10	}	}	PUNCT
ejpam-5802	48	11	,	,	PUNCT
ejpam-5802	48	12	{	{	PUNCT
ejpam-5802	48	13	x	x	NOUN
ejpam-5802	48	14	,	,	PUNCT
ejpam-5802	48	15	z	z	NOUN
ejpam-5802	48	16	}	}	PUNCT
ejpam-5802	48	17	,	,	PUNCT
ejpam-5802	48	18	{	{	PUNCT
ejpam-5802	48	19	x	x	NOUN
ejpam-5802	48	20	,	,	PUNCT
ejpam-5802	48	21	y	y	NOUN
ejpam-5802	48	22	}	}	PUNCT
ejpam-5802	48	23	are	be	AUX
ejpam-5802	48	24	nth	nth	ADV
ejpam-5802	48	25	-	-	PUNCT
ejpam-5802	48	26	closed	close	VERB
ejpam-5802	48	27	sets	set	NOUN
ejpam-5802	48	28	in	in	ADP
ejpam-5802	48	29	k.	k.	PROPN
ejpam-5802	49	1	the	the	DET
ejpam-5802	49	2	sets	set	NOUN
ejpam-5802	49	3	:	:	PUNCT
ejpam-5802	49	4	ϕ	ϕ	X
ejpam-5802	49	5	,	,	PUNCT
ejpam-5802	49	6	k	k	PROPN
ejpam-5802	49	7	are	be	AUX
ejpam-5802	49	8	nth	nth	ADV
ejpam-5802	49	9	-	-	PUNCT
ejpam-5802	49	10	clopen	clopen	ADJ
ejpam-5802	49	11	sets	set	NOUN
ejpam-5802	49	12	in	in	ADP
ejpam-5802	49	13	k.	k.	PROPN
ejpam-5802	49	14	definition	definition	NOUN
ejpam-5802	49	15	4.1[5	4.1[5	PROPN
ejpam-5802	49	16	]	]	X
ejpam-5802	49	17	:	:	PUNCT
ejpam-5802	49	18	let	let	VERB
ejpam-5802	49	19	(	(	PUNCT
ejpam-5802	49	20	k	k	X
ejpam-5802	49	21	,	,	PUNCT
ejpam-5802	49	22	η1,η2,	η1,η2,	PROPN
ejpam-5802	49	23	...	...	PUNCT
ejpam-5802	49	24	,ηn	,ηn	PUNCT
ejpam-5802	49	25	)	)	PUNCT
ejpam-5802	49	26	be	be	AUX
ejpam-5802	49	27	a	a	DET
ejpam-5802	49	28	nth	nth	ADJ
ejpam-5802	49	29	-	-	ADJ
ejpam-5802	49	30	topological	topological	ADJ
ejpam-5802	49	31	space	space	NOUN
ejpam-5802	49	32	,	,	PUNCT
ejpam-5802	49	33	k	k	PROPN
ejpam-5802	49	34	̸=	̸=	PROPN
ejpam-5802	49	35	ϕ	ϕ	PROPN
ejpam-5802	49	36	and	and	CCONJ
ejpam-5802	49	37	a	a	PRON
ejpam-5802	49	38	is	be	AUX
ejpam-5802	49	39	subset	subset	VERB
ejpam-5802	49	40	of	of	ADP
ejpam-5802	49	41	k	k	PROPN
ejpam-5802	49	42	,	,	PUNCT
ejpam-5802	49	43	then	then	ADV
ejpam-5802	49	44	q	q	PROPN
ejpam-5802	49	45	∈	∈	PROPN
ejpam-5802	49	46	k	k	PROPN
ejpam-5802	49	47	is	be	AUX
ejpam-5802	49	48	called	call	VERB
ejpam-5802	49	49	nth	nth	NOUN
ejpam-5802	49	50	-	-	PUNCT
ejpam-5802	49	51	limit	limit	NOUN
ejpam-5802	49	52	point	point	NOUN
ejpam-5802	49	53	of	of	ADP
ejpam-5802	49	54	a	a	DET
ejpam-5802	49	55	if	if	NOUN
ejpam-5802	49	56	for	for	ADP
ejpam-5802	49	57	all	all	PRON
ejpam-5802	49	58	ud	ud	ADV
ejpam-5802	49	59	nth	nth	ADV
ejpam-5802	49	60	-	-	ADJ
ejpam-5802	49	61	open	open	ADJ
ejpam-5802	49	62	set	set	NOUN
ejpam-5802	49	63	such	such	ADJ
ejpam-5802	49	64	that	that	SCONJ
ejpam-5802	49	65	ud	ud	ADP
ejpam-5802	49	66	∩	∩	NOUN
ejpam-5802	49	67	(	(	PUNCT
ejpam-5802	49	68	a−	a−	X
ejpam-5802	49	69	{	{	PUNCT
ejpam-5802	49	70	d	d	NOUN
ejpam-5802	49	71	}	}	PUNCT
ejpam-5802	49	72	)	)	PUNCT
ejpam-5802	49	73	̸=	̸=	PROPN
ejpam-5802	49	74	ϕ	ϕ	NOUN
ejpam-5802	49	75	.	.	PUNCT
ejpam-5802	50	1	the	the	DET
ejpam-5802	50	2	set	set	NOUN
ejpam-5802	50	3	of	of	ADP
ejpam-5802	50	4	all	all	DET
ejpam-5802	50	5	nth	nth	NOUN
ejpam-5802	50	6	-	-	PUNCT
ejpam-5802	50	7	limit	limit	NOUN
ejpam-5802	50	8	points	point	NOUN
ejpam-5802	50	9	is	be	AUX
ejpam-5802	50	10	called	call	VERB
ejpam-5802	50	11	nth	nth	ADV
ejpam-5802	50	12	-	-	PUNCT
ejpam-5802	50	13	derived	derive	VERB
ejpam-5802	50	14	set	set	NOUN
ejpam-5802	50	15	and	and	CCONJ
ejpam-5802	50	16	it	it	PRON
ejpam-5802	50	17	is	be	AUX
ejpam-5802	50	18	denoted	denote	VERB
ejpam-5802	50	19	by	by	ADP
ejpam-5802	50	20	a′	a′	PROPN
ejpam-5802	50	21	=	=	SYM
ejpam-5802	50	22	{	{	PUNCT
ejpam-5802	50	23	d	d	NOUN
ejpam-5802	50	24	:	:	PUNCT
ejpam-5802	50	25	d	d	PRON
ejpam-5802	50	26	is	be	AUX
ejpam-5802	50	27	nth	nth	NOUN
ejpam-5802	50	28	-	-	PUNCT
ejpam-5802	50	29	limit	limit	NOUN
ejpam-5802	50	30	point	point	NOUN
ejpam-5802	50	31	of	of	ADP
ejpam-5802	50	32	a	a	PRON
ejpam-5802	50	33	}	}	PUNCT
ejpam-5802	50	34	.	.	PUNCT
ejpam-5802	51	1	properties	property	NOUN
ejpam-5802	51	2	of	of	ADP
ejpam-5802	51	3	derived	derived	ADJ
ejpam-5802	51	4	set	set	NOUN
ejpam-5802	51	5	:	:	PUNCT
ejpam-5802	51	6	let	let	VERB
ejpam-5802	51	7	(	(	PUNCT
ejpam-5802	51	8	k	k	X
ejpam-5802	51	9	,	,	PUNCT
ejpam-5802	51	10	η1,η2	η1,η2	PROPN
ejpam-5802	51	11	,	,	PUNCT
ejpam-5802	51	12	...	...	PUNCT
ejpam-5802	51	13	,	,	PUNCT
ejpam-5802	51	14	ηn	ηn	INTJ
ejpam-5802	51	15	)	)	PUNCT
ejpam-5802	51	16	be	be	AUX
ejpam-5802	51	17	a	a	DET
ejpam-5802	51	18	nth	nth	ADJ
ejpam-5802	51	19	-	-	ADJ
ejpam-5802	51	20	topological	topological	ADJ
ejpam-5802	51	21	space	space	NOUN
ejpam-5802	51	22	and	and	CCONJ
ejpam-5802	51	23	let	let	VERB
ejpam-5802	51	24	w	w	NOUN
ejpam-5802	51	25	,	,	PUNCT
ejpam-5802	51	26	m	m	VERB
ejpam-5802	51	27	⊂	⊂	PROPN
ejpam-5802	51	28	k	k	NOUN
ejpam-5802	51	29	,	,	PUNCT
ejpam-5802	51	30	then	then	ADV
ejpam-5802	51	31	:	:	PUNCT
ejpam-5802	51	32	i	i	X
ejpam-5802	51	33	)	)	PUNCT
ejpam-5802	51	34	the	the	DET
ejpam-5802	51	35	derived	derive	VERB
ejpam-5802	51	36	set	set	NOUN
ejpam-5802	51	37	of	of	ADP
ejpam-5802	51	38	ϕ	ϕ	PROPN
ejpam-5802	51	39	is	be	AUX
ejpam-5802	51	40	ϕ.	ϕ.	PROPN
ejpam-5802	51	41	ii	ii	PROPN
ejpam-5802	51	42	)	)	PUNCT
ejpam-5802	51	43	if	if	SCONJ
ejpam-5802	51	44	w	w	PROPN
ejpam-5802	51	45	subset	subset	NOUN
ejpam-5802	51	46	of	of	ADP
ejpam-5802	51	47	m	m	PROPN
ejpam-5802	51	48	,	,	PUNCT
ejpam-5802	51	49	then	then	ADV
ejpam-5802	51	50	w	w	NOUN
ejpam-5802	51	51	’	'	PUNCT
ejpam-5802	51	52	subset	subset	NOUN
ejpam-5802	51	53	of	of	ADP
ejpam-5802	51	54	m	m	NOUN
ejpam-5802	51	55	’	'	PUNCT
ejpam-5802	51	56	.	.	PUNCT
ejpam-5802	52	1	iii	iii	X
ejpam-5802	52	2	)	)	PUNCT
ejpam-5802	52	3	the	the	DET
ejpam-5802	52	4	derived	derive	VERB
ejpam-5802	52	5	set	set	NOUN
ejpam-5802	52	6	of	of	ADP
ejpam-5802	52	7	union	union	NOUN
ejpam-5802	52	8	of	of	ADP
ejpam-5802	52	9	w	w	PROPN
ejpam-5802	52	10	and	and	CCONJ
ejpam-5802	52	11	m	m	VERB
ejpam-5802	52	12	equal	equal	ADJ
ejpam-5802	52	13	the	the	DET
ejpam-5802	52	14	union	union	NOUN
ejpam-5802	52	15	of	of	ADP
ejpam-5802	52	16	the	the	DET
ejpam-5802	52	17	derived	derive	VERB
ejpam-5802	52	18	set	set	NOUN
ejpam-5802	52	19	of	of	ADP
ejpam-5802	52	20	w	w	PROPN
ejpam-5802	52	21	and	and	CCONJ
ejpam-5802	52	22	the	the	DET
ejpam-5802	52	23	derived	derived	ADJ
ejpam-5802	52	24	set	set	NOUN
ejpam-5802	52	25	of	of	ADP
ejpam-5802	52	26	m.	m.	NOUN
ejpam-5802	52	27	iv	iv	X
ejpam-5802	52	28	)	)	PUNCT
ejpam-5802	52	29	the	the	DET
ejpam-5802	52	30	derived	derive	VERB
ejpam-5802	52	31	set	set	NOUN
ejpam-5802	52	32	of	of	ADP
ejpam-5802	52	33	intersection	intersection	NOUN
ejpam-5802	52	34	of	of	ADP
ejpam-5802	52	35	w	w	PROPN
ejpam-5802	52	36	and	and	CCONJ
ejpam-5802	52	37	m	m	VERB
ejpam-5802	52	38	equal	equal	ADJ
ejpam-5802	52	39	the	the	DET
ejpam-5802	52	40	intersection	intersection	NOUN
ejpam-5802	52	41	of	of	ADP
ejpam-5802	52	42	the	the	DET
ejpam-5802	52	43	derived	derive	VERB
ejpam-5802	52	44	set	set	NOUN
ejpam-5802	52	45	of	of	ADP
ejpam-5802	52	46	j.	j.	PROPN
ejpam-5802	52	47	oudetallah	oudetallah	PROPN
ejpam-5802	52	48	et	et	PROPN
ejpam-5802	52	49	al	al	PROPN
ejpam-5802	52	50	.	.	PUNCT
ejpam-5802	52	51	/	/	SYM
ejpam-5802	52	52	eur	eur	PROPN
ejpam-5802	52	53	.	.	PUNCT
ejpam-5802	53	1	j.	j.	PROPN
ejpam-5802	53	2	pure	pure	PROPN
ejpam-5802	53	3	appl	appl	PROPN
ejpam-5802	53	4	.	.	PROPN
ejpam-5802	53	5	math	math	PROPN
ejpam-5802	53	6	,	,	PUNCT
ejpam-5802	53	7	18	18	NUM
ejpam-5802	53	8	(	(	PUNCT
ejpam-5802	53	9	2	2	NUM
ejpam-5802	53	10	)	)	PUNCT
ejpam-5802	53	11	(	(	PUNCT
ejpam-5802	53	12	2025	2025	NUM
ejpam-5802	53	13	)	)	PUNCT
ejpam-5802	53	14	,	,	PUNCT
ejpam-5802	53	15	5802	5802	NUM
ejpam-5802	53	16	4	4	NUM
ejpam-5802	53	17	of	of	ADP
ejpam-5802	53	18	14	14	NUM
ejpam-5802	53	19	w	w	NOUN
ejpam-5802	53	20	and	and	CCONJ
ejpam-5802	53	21	the	the	DET
ejpam-5802	53	22	derived	derive	VERB
ejpam-5802	53	23	set	set	NOUN
ejpam-5802	53	24	of	of	ADP
ejpam-5802	53	25	m.	m.	NOUN
ejpam-5802	53	26	example	example	NOUN
ejpam-5802	53	27	letk	letk	PROPN
ejpam-5802	53	28	=	=	NOUN
ejpam-5802	53	29	{	{	PUNCT
ejpam-5802	53	30	x	x	NOUN
ejpam-5802	53	31	,	,	PUNCT
ejpam-5802	53	32	y	y	PROPN
ejpam-5802	53	33	,	,	PUNCT
ejpam-5802	53	34	z	z	NOUN
ejpam-5802	53	35	,	,	PUNCT
ejpam-5802	53	36	q	q	ADJ
ejpam-5802	53	37	}	}	PUNCT
ejpam-5802	53	38	,	,	PUNCT
ejpam-5802	53	39	η1={ϕ,k	η1={ϕ,k	NOUN
ejpam-5802	53	40	,	,	PUNCT
ejpam-5802	53	41	{	{	PUNCT
ejpam-5802	53	42	x	x	X
ejpam-5802	53	43	}	}	PUNCT
ejpam-5802	53	44	,	,	PUNCT
ejpam-5802	53	45	{	{	PUNCT
ejpam-5802	53	46	x	x	NOUN
ejpam-5802	53	47	,	,	PUNCT
ejpam-5802	53	48	y	y	NOUN
ejpam-5802	53	49	}	}	PUNCT
ejpam-5802	53	50	}	}	PUNCT
ejpam-5802	53	51	,	,	PUNCT
ejpam-5802	53	52	η2	η2	PROPN
ejpam-5802	53	53	=	=	SYM
ejpam-5802	53	54	{	{	PUNCT
ejpam-5802	53	55	ϕ,k	ϕ,k	PROPN
ejpam-5802	53	56	,	,	PUNCT
ejpam-5802	53	57	{	{	PUNCT
ejpam-5802	53	58	x	x	NOUN
ejpam-5802	53	59	}	}	PUNCT
ejpam-5802	53	60	}	}	PUNCT
ejpam-5802	53	61	,	,	PUNCT
ejpam-5802	53	62	η3	η3	PROPN
ejpam-5802	53	63	=	=	PUNCT
ejpam-5802	53	64	{	{	PUNCT
ejpam-5802	53	65	ϕ,k	ϕ,k	PROPN
ejpam-5802	53	66	,	,	PUNCT
ejpam-5802	53	67	{	{	PUNCT
ejpam-5802	53	68	x	x	X
ejpam-5802	53	69	}	}	PUNCT
ejpam-5802	53	70	,	,	PUNCT
ejpam-5802	53	71	{	{	PUNCT
ejpam-5802	53	72	x	x	NOUN
ejpam-5802	53	73	,	,	PUNCT
ejpam-5802	53	74	z	z	NOUN
ejpam-5802	53	75	}	}	PUNCT
ejpam-5802	53	76	}	}	PUNCT
ejpam-5802	53	77	and	and	CCONJ
ejpam-5802	53	78	a	a	PRON
ejpam-5802	53	79	=	=	X
ejpam-5802	53	80	{	{	PUNCT
ejpam-5802	53	81	x	x	NOUN
ejpam-5802	53	82	,	,	PUNCT
ejpam-5802	53	83	z	z	NOUN
ejpam-5802	53	84	}	}	PUNCT
ejpam-5802	53	85	.	.	PUNCT
ejpam-5802	54	1	now	now	ADV
ejpam-5802	54	2	y	y	PROPN
ejpam-5802	54	3	∈	∈	PROPN
ejpam-5802	54	4	k	k	PROPN
ejpam-5802	54	5	and	and	CCONJ
ejpam-5802	54	6	{	{	PUNCT
ejpam-5802	54	7	x	x	NOUN
ejpam-5802	54	8	,	,	PUNCT
ejpam-5802	54	9	y	y	NOUN
ejpam-5802	54	10	}	}	PUNCT
ejpam-5802	54	11	nth	nth	ADJ
ejpam-5802	54	12	-	-	ADJ
ejpam-5802	54	13	open	open	ADJ
ejpam-5802	54	14	set	set	NOUN
ejpam-5802	54	15	in	in	ADP
ejpam-5802	54	16	η1	η1	NOUN
ejpam-5802	54	17	and	and	CCONJ
ejpam-5802	54	18	y	y	PROPN
ejpam-5802	54	19	∈	∈	PROPN
ejpam-5802	55	1	a	a	PRON
ejpam-5802	55	2	we	we	PRON
ejpam-5802	55	3	have	have	VERB
ejpam-5802	55	4	{	{	PUNCT
ejpam-5802	55	5	x	x	NOUN
ejpam-5802	55	6	,	,	PUNCT
ejpam-5802	55	7	y	y	NOUN
ejpam-5802	55	8	}	}	PUNCT
ejpam-5802	55	9	∩	∩	NOUN
ejpam-5802	55	10	(	(	PUNCT
ejpam-5802	55	11	a−	a−	PROPN
ejpam-5802	55	12	{	{	PUNCT
ejpam-5802	55	13	y	y	NOUN
ejpam-5802	55	14	}	}	PUNCT
ejpam-5802	55	15	)	)	PUNCT
ejpam-5802	56	1	=	=	NOUN
ejpam-5802	56	2	{	{	PUNCT
ejpam-5802	56	3	x	x	NOUN
ejpam-5802	56	4	}	}	PUNCT
ejpam-5802	56	5	̸=	̸=	PROPN
ejpam-5802	56	6	ϕ	ϕ	NOUN
ejpam-5802	56	7	then	then	ADV
ejpam-5802	56	8	y	y	PROPN
ejpam-5802	56	9	is	be	AUX
ejpam-5802	56	10	a	a	DET
ejpam-5802	56	11	nth	nth	NOUN
ejpam-5802	56	12	-	-	PUNCT
ejpam-5802	56	13	limit	limit	NOUN
ejpam-5802	56	14	point	point	NOUN
ejpam-5802	56	15	of	of	ADP
ejpam-5802	56	16	a.	a.	NOUN
ejpam-5802	56	17	and	and	CCONJ
ejpam-5802	56	18	the	the	DET
ejpam-5802	56	19	same	same	ADJ
ejpam-5802	56	20	argement	argement	NOUN
ejpam-5802	56	21	we	we	PRON
ejpam-5802	56	22	get	get	VERB
ejpam-5802	56	23	also	also	ADV
ejpam-5802	56	24	x	x	PRON
ejpam-5802	56	25	and	and	CCONJ
ejpam-5802	56	26	z	z	NOUN
ejpam-5802	56	27	are	be	AUX
ejpam-5802	56	28	limit	limit	NOUN
ejpam-5802	56	29	point	point	NOUN
ejpam-5802	56	30	,	,	PUNCT
ejpam-5802	56	31	and	and	CCONJ
ejpam-5802	56	32	a′=	a′=	PROPN
ejpam-5802	56	33	{	{	PUNCT
ejpam-5802	56	34	x	x	PROPN
ejpam-5802	56	35	,	,	PUNCT
ejpam-5802	56	36	y	y	PROPN
ejpam-5802	56	37	,	,	PUNCT
ejpam-5802	56	38	z	z	NOUN
ejpam-5802	56	39	}	}	PUNCT
ejpam-5802	56	40	.	.	PUNCT
ejpam-5802	57	1	definitio	definitio	NOUN
ejpam-5802	57	2	5.1	5.1	NUM
ejpam-5802	57	3	:	:	PUNCT
ejpam-5802	57	4	let	let	AUX
ejpam-5802	57	5	(	(	PUNCT
ejpam-5802	57	6	k	k	X
ejpam-5802	57	7	,	,	PUNCT
ejpam-5802	57	8	η1	η1	NOUN
ejpam-5802	57	9	,	,	PUNCT
ejpam-5802	57	10	η2	η2	NOUN
ejpam-5802	57	11	,	,	PUNCT
ejpam-5802	57	12	...	...	PUNCT
ejpam-5802	57	13	,	,	PUNCT
ejpam-5802	57	14	ηn	ηn	INTJ
ejpam-5802	57	15	)	)	PUNCT
ejpam-5802	57	16	be	be	AUX
ejpam-5802	57	17	a	a	DET
ejpam-5802	57	18	nth	nth	ADJ
ejpam-5802	57	19	-	-	ADJ
ejpam-5802	57	20	topological	topological	ADJ
ejpam-5802	57	21	space	space	NOUN
ejpam-5802	57	22	,	,	PUNCT
ejpam-5802	57	23	k	k	PROPN
ejpam-5802	57	24	̸=	̸=	PROPN
ejpam-5802	57	25	ϕ	ϕ	PROPN
ejpam-5802	58	1	and	and	CCONJ
ejpam-5802	58	2	w	w	PROPN
ejpam-5802	58	3	is	be	AUX
ejpam-5802	58	4	subset	subset	VERB
ejpam-5802	58	5	of	of	ADP
ejpam-5802	58	6	k	k	PROPN
ejpam-5802	58	7	,	,	PUNCT
ejpam-5802	58	8	then	then	ADV
ejpam-5802	58	9	the	the	DET
ejpam-5802	58	10	nth	nth	NOUN
ejpam-5802	58	11	-	-	ADJ
ejpam-5802	58	12	clousre	clousre	ADJ
ejpam-5802	58	13	set	set	NOUN
ejpam-5802	58	14	is	be	AUX
ejpam-5802	58	15	denoted	denote	VERB
ejpam-5802	58	16	by	by	ADP
ejpam-5802	58	17	w	w	PROPN
ejpam-5802	58	18	=	=	NOUN
ejpam-5802	58	19	w	w	NOUN
ejpam-5802	58	20	∪	∪	ADP
ejpam-5802	58	21	w	w	PROPN
ejpam-5802	58	22	′	′	NUM
ejpam-5802	58	23	note	note	NOUN
ejpam-5802	58	24	that	that	SCONJ
ejpam-5802	58	25	:	:	PUNCT
ejpam-5802	58	26	z	z	NOUN
ejpam-5802	58	27	is	be	AUX
ejpam-5802	58	28	nth	nth	NOUN
ejpam-5802	58	29	-	-	PUNCT
ejpam-5802	58	30	closure	closure	NOUN
ejpam-5802	58	31	set	set	NOUN
ejpam-5802	58	32	.	.	PUNCT
ejpam-5802	59	1	properties	property	NOUN
ejpam-5802	59	2	of	of	ADP
ejpam-5802	59	3	closure	closure	NOUN
ejpam-5802	59	4	set	set	NOUN
ejpam-5802	59	5	:	:	PUNCT
ejpam-5802	59	6	let	let	VERB
ejpam-5802	59	7	(	(	PUNCT
ejpam-5802	59	8	k	k	X
ejpam-5802	59	9	,	,	PUNCT
ejpam-5802	59	10	η1,η2,	η1,η2,	PROPN
ejpam-5802	59	11	...	...	PUNCT
ejpam-5802	59	12	,ηn	,ηn	PUNCT
ejpam-5802	59	13	)	)	PUNCT
ejpam-5802	59	14	be	be	AUX
ejpam-5802	59	15	a	a	DET
ejpam-5802	59	16	nth	nth	ADJ
ejpam-5802	59	17	-	-	ADJ
ejpam-5802	59	18	topological	topological	ADJ
ejpam-5802	59	19	space	space	NOUN
ejpam-5802	59	20	and	and	CCONJ
ejpam-5802	59	21	w	w	NOUN
ejpam-5802	59	22	is	be	AUX
ejpam-5802	59	23	subset	subset	VERB
ejpam-5802	59	24	of	of	ADP
ejpam-5802	59	25	k.	k.	PROPN
ejpam-5802	60	1	then	then	ADV
ejpam-5802	60	2	:	:	PUNCT
ejpam-5802	60	3	i	i	X
ejpam-5802	60	4	)	)	PUNCT
ejpam-5802	60	5	w	w	PROPN
ejpam-5802	60	6	is	be	AUX
ejpam-5802	60	7	nth	nth	ADV
ejpam-5802	60	8	-	-	PUNCT
ejpam-5802	60	9	closed	close	VERB
ejpam-5802	60	10	set	set	NOUN
ejpam-5802	60	11	.	.	PUNCT
ejpam-5802	61	1	ii	ii	PROPN
ejpam-5802	61	2	)	)	PUNCT
ejpam-5802	62	1	w	w	PROPN
ejpam-5802	62	2	c	c	NOUN
ejpam-5802	62	3	is	be	AUX
ejpam-5802	62	4	nthopen	nthopen	ADJ
ejpam-5802	62	5	set	set	VERB
ejpam-5802	62	6	.	.	PUNCT
ejpam-5802	63	1	iii	iii	X
ejpam-5802	63	2	)	)	PUNCT
ejpam-5802	63	3	w	w	PROPN
ejpam-5802	63	4	∈	∈	PROPN
ejpam-5802	63	5	w	w	NOUN
ejpam-5802	64	1	if	if	SCONJ
ejpam-5802	64	2	and	and	CCONJ
ejpam-5802	64	3	only	only	ADV
ejpam-5802	64	4	if	if	SCONJ
ejpam-5802	64	5	for	for	ADP
ejpam-5802	64	6	all	all	DET
ejpam-5802	64	7	ηi	ηi	NOUN
ejpam-5802	64	8	-	-	PUNCT
ejpam-5802	64	9	open	open	ADJ
ejpam-5802	64	10	set	set	NOUN
ejpam-5802	64	11	uw	uw	PROPN
ejpam-5802	64	12	and	and	CCONJ
ejpam-5802	64	13	w	w	PROPN
ejpam-5802	64	14	∈	∈	PROPN
ejpam-5802	64	15	uw	uw	PROPN
ejpam-5802	64	16	,	,	PUNCT
ejpam-5802	64	17	we	we	PRON
ejpam-5802	64	18	have	have	VERB
ejpam-5802	64	19	uw	uw	PROPN
ejpam-5802	64	20	∩	∩	NOUN
ejpam-5802	64	21	w	w	PROPN
ejpam-5802	64	22	̸=	̸=	PROPN
ejpam-5802	64	23	ϕ.	ϕ.	PROPN
ejpam-5802	64	24	iv	iv	X
ejpam-5802	64	25	)	)	PUNCT
ejpam-5802	64	26	w	w	PROPN
ejpam-5802	64	27	/∈	/∈	INTJ
ejpam-5802	65	1	w	w	NOUN
ejpam-5802	65	2	if	if	SCONJ
ejpam-5802	65	3	and	and	CCONJ
ejpam-5802	65	4	only	only	ADV
ejpam-5802	65	5	if	if	SCONJ
ejpam-5802	65	6	for	for	ADP
ejpam-5802	65	7	all	all	DET
ejpam-5802	65	8	ηi	ηi	NOUN
ejpam-5802	65	9	-	-	PUNCT
ejpam-5802	65	10	open	open	ADJ
ejpam-5802	65	11	set	set	ADJ
ejpam-5802	65	12	uw	uw	PROPN
ejpam-5802	65	13	(	(	PUNCT
ejpam-5802	65	14	i=	i=	PROPN
ejpam-5802	65	15	1,2,3,	1,2,3,	NUM
ejpam-5802	65	16	...	...	PUNCT
ejpam-5802	65	17	,n	,n	PUNCT
ejpam-5802	65	18	)	)	PUNCT
ejpam-5802	65	19	and	and	CCONJ
ejpam-5802	65	20	w	w	PROPN
ejpam-5802	65	21	∈	∈	PROPN
ejpam-5802	65	22	uw	uw	PROPN
ejpam-5802	65	23	,	,	PUNCT
ejpam-5802	65	24	we	we	PRON
ejpam-5802	65	25	have	have	VERB
ejpam-5802	65	26	uw	uw	PROPN
ejpam-5802	65	27	∩	∩	NOUN
ejpam-5802	65	28	w	w	PROPN
ejpam-5802	65	29	=	=	PUNCT
ejpam-5802	65	30	ϕ.	ϕ.	PROPN
ejpam-5802	65	31	definition	definition	NOUN
ejpam-5802	65	32	6.1	6.1	NUM
ejpam-5802	65	33	:	:	PUNCT
ejpam-5802	65	34	let	let	VERB
ejpam-5802	65	35	(	(	PUNCT
ejpam-5802	65	36	k	k	X
ejpam-5802	65	37	,	,	PUNCT
ejpam-5802	65	38	η1,η2,	η1,η2,	PROPN
ejpam-5802	65	39	...	...	PUNCT
ejpam-5802	65	40	,ηn	,ηn	PUNCT
ejpam-5802	65	41	)	)	PUNCT
ejpam-5802	65	42	be	be	AUX
ejpam-5802	65	43	a	a	DET
ejpam-5802	65	44	nth	nth	ADJ
ejpam-5802	65	45	-	-	ADJ
ejpam-5802	65	46	topological	topological	ADJ
ejpam-5802	65	47	space	space	NOUN
ejpam-5802	65	48	,	,	PUNCT
ejpam-5802	65	49	k	k	PROPN
ejpam-5802	65	50	̸=	̸=	PROPN
ejpam-5802	65	51	ϕ	ϕ	PROPN
ejpam-5802	65	52	and	and	CCONJ
ejpam-5802	65	53	w	w	PROPN
ejpam-5802	65	54	⊂	⊂	PROPN
ejpam-5802	66	1	d	d	PROPN
ejpam-5802	66	2	,	,	PUNCT
ejpam-5802	66	3	then	then	ADV
ejpam-5802	66	4	a	a	DET
ejpam-5802	66	5	piont	piont	NOUN
ejpam-5802	66	6	d	d	X
ejpam-5802	66	7	∈	∈	PROPN
ejpam-5802	66	8	w	w	NOUN
ejpam-5802	66	9	is	be	AUX
ejpam-5802	66	10	said	say	VERB
ejpam-5802	66	11	to	to	PART
ejpam-5802	66	12	be	be	AUX
ejpam-5802	66	13	nth	nth	ADJ
ejpam-5802	66	14	-	-	ADJ
ejpam-5802	66	15	interior	interior	ADJ
ejpam-5802	66	16	piont	piont	NOUN
ejpam-5802	66	17	of	of	ADP
ejpam-5802	66	18	w	w	NOUN
ejpam-5802	66	19	if	if	SCONJ
ejpam-5802	66	20	there	there	PRON
ejpam-5802	66	21	exist	exist	VERB
ejpam-5802	66	22	at	at	ADV
ejpam-5802	66	23	least	least	ADV
ejpam-5802	66	24	one	one	NUM
ejpam-5802	66	25	neighborhood	neighborhood	NOUN
ejpam-5802	66	26	of	of	ADP
ejpam-5802	66	27	d	d	PROPN
ejpam-5802	66	28	(	(	PUNCT
ejpam-5802	66	29	n(d	n(d	PROPN
ejpam-5802	66	30	,	,	PUNCT
ejpam-5802	66	31	ε	ε	PROPN
ejpam-5802	66	32	)	)	PUNCT
ejpam-5802	66	33	)	)	PUNCT
ejpam-5802	66	34	such	such	ADJ
ejpam-5802	66	35	that	that	SCONJ
ejpam-5802	66	36	n(d	n(d	PROPN
ejpam-5802	66	37	,	,	PUNCT
ejpam-5802	66	38	ε	ε	PROPN
ejpam-5802	66	39	)	)	PUNCT
ejpam-5802	67	1	⊆	⊆	NUM
ejpam-5802	67	2	w.	w.	NOUN
ejpam-5802	67	3	the	the	DET
ejpam-5802	67	4	set	set	NOUN
ejpam-5802	67	5	of	of	ADP
ejpam-5802	67	6	all	all	DET
ejpam-5802	67	7	nth	nth	ADJ
ejpam-5802	67	8	-	-	ADJ
ejpam-5802	67	9	interior	interior	ADJ
ejpam-5802	67	10	piont	piont	NOUN
ejpam-5802	67	11	is	be	AUX
ejpam-5802	67	12	called	call	VERB
ejpam-5802	67	13	the	the	DET
ejpam-5802	67	14	nth	nth	ADJ
ejpam-5802	67	15	-	-	ADJ
ejpam-5802	67	16	interior	interior	ADJ
ejpam-5802	67	17	set	set	NOUN
ejpam-5802	67	18	and	and	CCONJ
ejpam-5802	67	19	it	it	PRON
ejpam-5802	67	20	is	be	AUX
ejpam-5802	67	21	denoted	denote	VERB
ejpam-5802	67	22	by	by	ADP
ejpam-5802	67	23	a	a	DET
ejpam-5802	67	24	◦	◦	NOUN
ejpam-5802	67	25	≡	≡	PROPN
ejpam-5802	67	26	int(w	int(w	PROPN
ejpam-5802	67	27	)	)	PUNCT
ejpam-5802	68	1	=	=	NOUN
ejpam-5802	68	2	ac	ac	PROPN
ejpam-5802	68	3	c	c	PROPN
ejpam-5802	68	4	.	.	PUNCT
ejpam-5802	69	1	note	note	VERB
ejpam-5802	69	2	that	that	SCONJ
ejpam-5802	69	3	:	:	PUNCT
ejpam-5802	69	4	a	a	DET
ejpam-5802	69	5	◦	◦	NOUN
ejpam-5802	69	6	is	be	AUX
ejpam-5802	69	7	nth	nth	ADV
ejpam-5802	69	8	-	-	ADJ
ejpam-5802	69	9	open	open	ADJ
ejpam-5802	69	10	set	set	NOUN
ejpam-5802	69	11	.	.	PUNCT
ejpam-5802	70	1	properties	property	NOUN
ejpam-5802	70	2	of	of	ADP
ejpam-5802	70	3	interior	interior	ADJ
ejpam-5802	70	4	set	set	NOUN
ejpam-5802	70	5	:	:	PUNCT
ejpam-5802	70	6	let	let	VERB
ejpam-5802	70	7	(	(	PUNCT
ejpam-5802	70	8	k	k	X
ejpam-5802	70	9	,	,	PUNCT
ejpam-5802	70	10	η1,η2,	η1,η2,	PROPN
ejpam-5802	70	11	...	...	PUNCT
ejpam-5802	70	12	,ηn	,ηn	PUNCT
ejpam-5802	70	13	)	)	PUNCT
ejpam-5802	70	14	be	be	AUX
ejpam-5802	70	15	a	a	DET
ejpam-5802	70	16	nth	nth	ADJ
ejpam-5802	70	17	-	-	ADJ
ejpam-5802	70	18	topological	topological	ADJ
ejpam-5802	70	19	space	space	NOUN
ejpam-5802	70	20	and	and	CCONJ
ejpam-5802	70	21	let	let	VERB
ejpam-5802	70	22	x	x	PRON
ejpam-5802	70	23	,	,	PUNCT
ejpam-5802	70	24	y	y	PROPN
ejpam-5802	70	25	⊂	⊂	PROPN
ejpam-5802	70	26	k	k	PROPN
ejpam-5802	70	27	,	,	PUNCT
ejpam-5802	70	28	then	then	ADV
ejpam-5802	70	29	:	:	PUNCT
ejpam-5802	70	30	(	(	PUNCT
ejpam-5802	70	31	i	i	NOUN
ejpam-5802	70	32	)	)	PUNCT
ejpam-5802	70	33	ϕ	ϕ	NOUN
ejpam-5802	70	34	◦	◦	NOUN
ejpam-5802	70	35	=	=	SYM
ejpam-5802	70	36	ϕ	ϕ	PROPN
ejpam-5802	70	37	and	and	CCONJ
ejpam-5802	70	38	k	k	PROPN
ejpam-5802	70	39	◦	◦	NOUN
ejpam-5802	70	40	=	=	SYM
ejpam-5802	70	41	k.	k.	PROPN
ejpam-5802	70	42	(	(	PUNCT
ejpam-5802	70	43	ii	ii	PROPN
ejpam-5802	70	44	)	)	PUNCT
ejpam-5802	70	45	(	(	PUNCT
ejpam-5802	70	46	x	x	PROPN
ejpam-5802	70	47	∩	∩	ADJ
ejpam-5802	70	48	y	y	PROPN
ejpam-5802	70	49	)	)	PUNCT
ejpam-5802	70	50	◦	◦	NOUN
ejpam-5802	70	51	=	=	PUNCT
ejpam-5802	70	52	x	x	PUNCT
ejpam-5802	70	53	◦	◦	NOUN
ejpam-5802	70	54	∩y	∩y	NOUN
ejpam-5802	70	55	◦	◦	NOUN
ejpam-5802	70	56	and	and	CCONJ
ejpam-5802	70	57	x	x	PART
ejpam-5802	70	58	◦	◦	NOUN
ejpam-5802	70	59	∪y	∪y	NUM
ejpam-5802	70	60	◦	◦	NOUN
ejpam-5802	70	61	⊂	⊂	X
ejpam-5802	70	62	(	(	PUNCT
ejpam-5802	70	63	x	x	SYM
ejpam-5802	70	64	∪	∪	PROPN
ejpam-5802	70	65	y	y	PROPN
ejpam-5802	70	66	)	)	PUNCT
ejpam-5802	70	67	◦	◦	NOUN
ejpam-5802	70	68	.	.	PUNCT
ejpam-5802	71	1	(	(	PUNCT
ejpam-5802	71	2	iii	iii	NOUN
ejpam-5802	71	3	)	)	PUNCT
ejpam-5802	71	4	x	x	NOUN
ejpam-5802	71	5	◦	◦	NOUN
ejpam-5802	71	6	is	be	AUX
ejpam-5802	71	7	ηi	ηi	NOUN
ejpam-5802	71	8	-	-	PUNCT
ejpam-5802	71	9	open	open	ADJ
ejpam-5802	71	10	set	set	NOUN
ejpam-5802	71	11	.	.	PUNCT
ejpam-5802	72	1	(	(	PUNCT
ejpam-5802	72	2	iv	iv	X
ejpam-5802	72	3	)	)	PUNCT
ejpam-5802	72	4	n	n	NOUN
ejpam-5802	72	5	∈	∈	NOUN
ejpam-5802	72	6	x	x	X
ejpam-5802	72	7	◦	◦	NOUN
ejpam-5802	72	8	if	if	SCONJ
ejpam-5802	72	9	and	and	CCONJ
ejpam-5802	72	10	only	only	ADV
ejpam-5802	72	11	if	if	SCONJ
ejpam-5802	72	12	there	there	PRON
ejpam-5802	72	13	exist	exist	VERB
ejpam-5802	72	14	ηi	ηi	NOUN
ejpam-5802	72	15	-	-	PUNCT
ejpam-5802	72	16	open	open	ADJ
ejpam-5802	72	17	set	set	VERB
ejpam-5802	72	18	un	un	PROPN
ejpam-5802	72	19	such	such	ADJ
ejpam-5802	72	20	that	that	SCONJ
ejpam-5802	72	21	n	n	PROPN
ejpam-5802	72	22	∈	∈	PROPN
ejpam-5802	72	23	un	un	PROPN
ejpam-5802	72	24	⊂	⊂	PROPN
ejpam-5802	72	25	x.	x.	PROPN
ejpam-5802	72	26	definition	definition	NOUN
ejpam-5802	72	27	7.1	7.1	NUM
ejpam-5802	72	28	:	:	PUNCT
ejpam-5802	72	29	let	let	VERB
ejpam-5802	72	30	(	(	PUNCT
ejpam-5802	72	31	k	k	X
ejpam-5802	72	32	,	,	PUNCT
ejpam-5802	72	33	η1,η2,	η1,η2,	PROPN
ejpam-5802	72	34	...	...	PUNCT
ejpam-5802	72	35	,ηn	,ηn	PUNCT
ejpam-5802	72	36	)	)	PUNCT
ejpam-5802	72	37	be	be	AUX
ejpam-5802	72	38	a	a	DET
ejpam-5802	72	39	nth	nth	ADJ
ejpam-5802	72	40	-	-	ADJ
ejpam-5802	72	41	topological	topological	ADJ
ejpam-5802	72	42	space	space	NOUN
ejpam-5802	72	43	,	,	PUNCT
ejpam-5802	72	44	k	k	PROPN
ejpam-5802	72	45	̸=	̸=	PROPN
ejpam-5802	72	46	ϕ	ϕ	PROPN
ejpam-5802	72	47	and	and	CCONJ
ejpam-5802	72	48	w	w	PROPN
ejpam-5802	72	49	is	be	AUX
ejpam-5802	72	50	subset	subset	VERB
ejpam-5802	72	51	of	of	ADP
ejpam-5802	72	52	k	k	NOUN
ejpam-5802	72	53	,	,	PUNCT
ejpam-5802	72	54	then	then	ADV
ejpam-5802	72	55	the	the	DET
ejpam-5802	72	56	point	point	NOUN
ejpam-5802	72	57	d	d	NOUN
ejpam-5802	72	58	is	be	AUX
ejpam-5802	72	59	said	say	VERB
ejpam-5802	72	60	to	to	PART
ejpam-5802	72	61	be	be	AUX
ejpam-5802	72	62	nth	nth	ADJ
ejpam-5802	72	63	-	-	ADJ
ejpam-5802	72	64	exterior	exterior	ADJ
ejpam-5802	72	65	point	point	NOUN
ejpam-5802	72	66	of	of	ADP
ejpam-5802	72	67	w	w	NOUN
ejpam-5802	72	68	,	,	PUNCT
ejpam-5802	72	69	if	if	SCONJ
ejpam-5802	72	70	there	there	PRON
ejpam-5802	72	71	exist	exist	VERB
ejpam-5802	72	72	at	at	ADV
ejpam-5802	72	73	least	least	ADV
ejpam-5802	72	74	one	one	NUM
ejpam-5802	72	75	neighborhood	neighborhood	NOUN
ejpam-5802	72	76	of	of	ADP
ejpam-5802	72	77	d	d	NOUN
ejpam-5802	72	78	such	such	ADJ
ejpam-5802	72	79	that	that	SCONJ
ejpam-5802	72	80	n(d	n(d	PROPN
ejpam-5802	72	81	,	,	PUNCT
ejpam-5802	72	82	ε	ε	PROPN
ejpam-5802	72	83	)	)	PUNCT
ejpam-5802	72	84	∩	∩	NOUN
ejpam-5802	72	85	w	w	PROPN
ejpam-5802	72	86	=	=	PUNCT
ejpam-5802	72	87	ϕ	ϕ	X
ejpam-5802	72	88	the	the	DET
ejpam-5802	72	89	set	set	NOUN
ejpam-5802	72	90	of	of	ADP
ejpam-5802	72	91	all	all	DET
ejpam-5802	72	92	nth	nth	ADJ
ejpam-5802	72	93	-	-	ADJ
ejpam-5802	72	94	exterior	exterior	ADJ
ejpam-5802	72	95	point	point	NOUN
ejpam-5802	72	96	is	be	AUX
ejpam-5802	72	97	called	call	VERB
ejpam-5802	72	98	nth	nth	ADJ
ejpam-5802	72	99	-	-	ADJ
ejpam-5802	72	100	exterior	exterior	ADJ
ejpam-5802	72	101	set	set	NOUN
ejpam-5802	72	102	and	and	CCONJ
ejpam-5802	72	103	it	it	PRON
ejpam-5802	72	104	is	be	AUX
ejpam-5802	72	105	denoted	denote	VERB
ejpam-5802	72	106	by	by	ADP
ejpam-5802	72	107	ex(w)=int(w	ex(w)=int(w	NOUN
ejpam-5802	72	108	c)=	c)=	PROPN
ejpam-5802	72	109	w	w	PROPN
ejpam-5802	72	110	c	c	PROPN
ejpam-5802	72	111	note	note	VERB
ejpam-5802	72	112	that	that	SCONJ
ejpam-5802	72	113	:	:	PUNCT
ejpam-5802	72	114	ex(w)is	ex(w)is	ADJ
ejpam-5802	72	115	nth	nth	NOUN
ejpam-5802	72	116	-	-	PUNCT
ejpam-5802	72	117	close	close	ADJ
ejpam-5802	72	118	set	set	NOUN
ejpam-5802	72	119	.	.	PUNCT
ejpam-5802	73	1	properties	property	NOUN
ejpam-5802	73	2	of	of	ADP
ejpam-5802	73	3	exterior	exterior	ADJ
ejpam-5802	73	4	set	set	NOUN
ejpam-5802	73	5	:	:	PUNCT
ejpam-5802	73	6	let	let	VERB
ejpam-5802	73	7	(	(	PUNCT
ejpam-5802	73	8	k	k	X
ejpam-5802	73	9	,	,	PUNCT
ejpam-5802	73	10	η1,η2,	η1,η2,	PROPN
ejpam-5802	73	11	...	...	PUNCT
ejpam-5802	73	12	,ηn	,ηn	PUNCT
ejpam-5802	73	13	)	)	PUNCT
ejpam-5802	73	14	be	be	AUX
ejpam-5802	73	15	a	a	DET
ejpam-5802	73	16	nth	nth	ADJ
ejpam-5802	73	17	-	-	ADJ
ejpam-5802	73	18	topological	topological	ADJ
ejpam-5802	73	19	space	space	NOUN
ejpam-5802	73	20	and	and	CCONJ
ejpam-5802	73	21	let	let	VERB
ejpam-5802	73	22	w	w	NOUN
ejpam-5802	73	23	,	,	PUNCT
ejpam-5802	73	24	m	m	VERB
ejpam-5802	73	25	⊂	⊂	PROPN
ejpam-5802	73	26	k	k	NOUN
ejpam-5802	73	27	,	,	PUNCT
ejpam-5802	73	28	then	then	ADV
ejpam-5802	73	29	:	:	PUNCT
ejpam-5802	73	30	j.	j.	PROPN
ejpam-5802	73	31	oudetallah	oudetallah	PROPN
ejpam-5802	73	32	et	et	PROPN
ejpam-5802	73	33	al	al	PROPN
ejpam-5802	73	34	.	.	PUNCT
ejpam-5802	73	35	/	/	SYM
ejpam-5802	73	36	eur	eur	PROPN
ejpam-5802	73	37	.	.	PUNCT
ejpam-5802	74	1	j.	j.	PROPN
ejpam-5802	74	2	pure	pure	PROPN
ejpam-5802	74	3	appl	appl	PROPN
ejpam-5802	74	4	.	.	PROPN
ejpam-5802	74	5	math	math	PROPN
ejpam-5802	74	6	,	,	PUNCT
ejpam-5802	74	7	18	18	NUM
ejpam-5802	74	8	(	(	PUNCT
ejpam-5802	74	9	2	2	NUM
ejpam-5802	74	10	)	)	PUNCT
ejpam-5802	74	11	(	(	PUNCT
ejpam-5802	74	12	2025	2025	NUM
ejpam-5802	74	13	)	)	PUNCT
ejpam-5802	74	14	,	,	PUNCT
ejpam-5802	74	15	5802	5802	NUM
ejpam-5802	74	16	5	5	NUM
ejpam-5802	74	17	of	of	ADP
ejpam-5802	74	18	14	14	NUM
ejpam-5802	74	19	(	(	PUNCT
ejpam-5802	74	20	i	i	NOUN
ejpam-5802	74	21	)	)	PUNCT
ejpam-5802	74	22	the	the	DET
ejpam-5802	74	23	exterior	exterior	ADJ
ejpam-5802	74	24	set	set	NOUN
ejpam-5802	74	25	of	of	ADP
ejpam-5802	74	26	ϕ	ϕ	PROPN
ejpam-5802	74	27	is	be	AUX
ejpam-5802	74	28	k	k	PROPN
ejpam-5802	74	29	and	and	CCONJ
ejpam-5802	74	30	the	the	DET
ejpam-5802	74	31	exterior	exterior	ADJ
ejpam-5802	74	32	set	set	NOUN
ejpam-5802	74	33	of	of	ADP
ejpam-5802	74	34	k	k	PROPN
ejpam-5802	74	35	is	be	AUX
ejpam-5802	74	36	ϕ.	ϕ.	PROPN
ejpam-5802	74	37	(	(	PUNCT
ejpam-5802	74	38	ii	ii	PROPN
ejpam-5802	74	39	)	)	PUNCT
ejpam-5802	74	40	if	if	SCONJ
ejpam-5802	74	41	w	w	PROPN
ejpam-5802	74	42	⊂	⊂	PROPN
ejpam-5802	74	43	m	m	PROPN
ejpam-5802	74	44	,	,	PUNCT
ejpam-5802	74	45	then	then	ADV
ejpam-5802	74	46	ex(m	ex(m	NUM
ejpam-5802	74	47	)	)	PUNCT
ejpam-5802	75	1	⊂	⊂	PROPN
ejpam-5802	75	2	ex(w	ex(w	NUM
ejpam-5802	75	3	)	)	PUNCT
ejpam-5802	75	4	.	.	PUNCT
ejpam-5802	76	1	(	(	PUNCT
ejpam-5802	76	2	iii	iii	NOUN
ejpam-5802	76	3	)	)	PUNCT
ejpam-5802	76	4	ex(w	ex(w	NUM
ejpam-5802	76	5	)	)	PUNCT
ejpam-5802	76	6	is	be	AUX
ejpam-5802	76	7	ηi	ηi	NOUN
ejpam-5802	76	8	-	-	PUNCT
ejpam-5802	76	9	open	open	ADJ
ejpam-5802	76	10	set	set	NOUN
ejpam-5802	76	11	,	,	PUNCT
ejpam-5802	76	12	i=1,2,	i=1,2,	NOUN
ejpam-5802	76	13	...	...	PUNCT
ejpam-5802	76	14	,n	,n	PUNCT
ejpam-5802	76	15	.	.	PUNCT
ejpam-5802	77	1	(	(	PUNCT
ejpam-5802	77	2	iv	iv	X
ejpam-5802	77	3	)	)	PUNCT
ejpam-5802	77	4	m	m	VERB
ejpam-5802	77	5	∈	∈	NOUN
ejpam-5802	77	6	ex(w	ex(w	NOUN
ejpam-5802	77	7	)	)	PUNCT
ejpam-5802	77	8	if	if	SCONJ
ejpam-5802	77	9	and	and	CCONJ
ejpam-5802	77	10	only	only	ADV
ejpam-5802	77	11	if	if	SCONJ
ejpam-5802	77	12	there	there	PRON
ejpam-5802	77	13	exsit	exsit	VERB
ejpam-5802	77	14	ηi	ηi	NOUN
ejpam-5802	77	15	-	-	PUNCT
ejpam-5802	77	16	open	open	ADJ
ejpam-5802	77	17	set	set	NOUN
ejpam-5802	77	18	um	um	INTJ
ejpam-5802	77	19	such	such	ADJ
ejpam-5802	77	20	that	that	SCONJ
ejpam-5802	77	21	m	m	PROPN
ejpam-5802	77	22	∈	∈	PROPN
ejpam-5802	77	23	uk	uk	PROPN
ejpam-5802	77	24	⊂	⊂	PROPN
ejpam-5802	77	25	w	w	PROPN
ejpam-5802	77	26	c.	c.	PROPN
ejpam-5802	77	27	proof	proof	NOUN
ejpam-5802	77	28	:	:	PUNCT
ejpam-5802	77	29	(	(	PUNCT
ejpam-5802	77	30	iii	iii	NOUN
ejpam-5802	77	31	)	)	PUNCT
ejpam-5802	77	32	since	since	SCONJ
ejpam-5802	77	33	ex(w	ex(w	NUM
ejpam-5802	77	34	)	)	PUNCT
ejpam-5802	77	35	=	=	PUNCT
ejpam-5802	77	36	int(w	int(w	ADP
ejpam-5802	77	37	c	c	NOUN
ejpam-5802	77	38	)	)	PUNCT
ejpam-5802	77	39	,	,	PUNCT
ejpam-5802	77	40	then	then	ADV
ejpam-5802	77	41	ex(w	ex(w	NUM
ejpam-5802	77	42	)	)	PUNCT
ejpam-5802	77	43	=	=	SYM
ejpam-5802	77	44	w	w	PROPN
ejpam-5802	77	45	ccc	ccc	PROPN
ejpam-5802	77	46	,	,	PUNCT
ejpam-5802	77	47	but	but	CCONJ
ejpam-5802	77	48	w	w	ADP
ejpam-5802	77	49	cc	cc	NOUN
ejpam-5802	77	50	=	=	PUNCT
ejpam-5802	77	51	w	w	PROPN
ejpam-5802	77	52	thus	thus	ADV
ejpam-5802	77	53	,	,	PUNCT
ejpam-5802	77	54	ex(w	ex(w	PUNCT
ejpam-5802	77	55	)	)	PUNCT
ejpam-5802	78	1	=	=	PUNCT
ejpam-5802	78	2	w	w	PROPN
ejpam-5802	78	3	c	c	PROPN
ejpam-5802	78	4	and	and	CCONJ
ejpam-5802	78	5	by	by	ADP
ejpam-5802	78	6	definition	definition	NOUN
ejpam-5802	78	7	of	of	ADP
ejpam-5802	78	8	nth	nth	NOUN
ejpam-5802	78	9	-	-	PUNCT
ejpam-5802	78	10	closure	closure	NOUN
ejpam-5802	78	11	set	set	NOUN
ejpam-5802	78	12	we	we	PRON
ejpam-5802	78	13	have	have	VERB
ejpam-5802	78	14	w	w	PROPN
ejpam-5802	78	15	is	be	AUX
ejpam-5802	78	16	ηi	ηi	NOUN
ejpam-5802	78	17	-	-	PUNCT
ejpam-5802	78	18	closed	closed	ADJ
ejpam-5802	78	19	set	set	NOUN
ejpam-5802	78	20	so	so	ADV
ejpam-5802	78	21	,	,	PUNCT
ejpam-5802	78	22	the	the	DET
ejpam-5802	78	23	complement	complement	NOUN
ejpam-5802	78	24	of	of	ADP
ejpam-5802	78	25	ηi	ηi	NOUN
ejpam-5802	78	26	-	-	PUNCT
ejpam-5802	78	27	closed	close	VERB
ejpam-5802	78	28	set	set	NOUN
ejpam-5802	78	29	is	be	AUX
ejpam-5802	78	30	ηi	ηi	NOUN
ejpam-5802	78	31	-	-	PUNCT
ejpam-5802	78	32	open	open	ADJ
ejpam-5802	78	33	set	set	NOUN
ejpam-5802	78	34	,	,	PUNCT
ejpam-5802	78	35	therefor	therefor	ADP
ejpam-5802	78	36	ex(w	ex(w	NUM
ejpam-5802	78	37	)	)	PUNCT
ejpam-5802	78	38	is	be	AUX
ejpam-5802	78	39	ηi	ηi	NOUN
ejpam-5802	78	40	-	-	PUNCT
ejpam-5802	78	41	open	open	ADJ
ejpam-5802	78	42	set	set	NOUN
ejpam-5802	78	43	,	,	PUNCT
ejpam-5802	78	44	i=1,2,	i=1,2,	NOUN
ejpam-5802	78	45	...	...	PUNCT
ejpam-5802	78	46	,n	,n	PUNCT
ejpam-5802	78	47	.	.	PUNCT
ejpam-5802	79	1	definition	definition	NOUN
ejpam-5802	79	2	8.1	8.1	NUM
ejpam-5802	79	3	:	:	PUNCT
ejpam-5802	79	4	let	let	VERB
ejpam-5802	79	5	(	(	PUNCT
ejpam-5802	79	6	k	k	X
ejpam-5802	79	7	,	,	PUNCT
ejpam-5802	79	8	η1,η2,	η1,η2,	PROPN
ejpam-5802	79	9	...	...	PUNCT
ejpam-5802	79	10	,ηn	,ηn	PUNCT
ejpam-5802	79	11	)	)	PUNCT
ejpam-5802	79	12	be	be	AUX
ejpam-5802	79	13	a	a	DET
ejpam-5802	79	14	nth	nth	ADJ
ejpam-5802	79	15	-	-	ADJ
ejpam-5802	79	16	topological	topological	ADJ
ejpam-5802	79	17	space	space	NOUN
ejpam-5802	79	18	,	,	PUNCT
ejpam-5802	79	19	k	k	PROPN
ejpam-5802	79	20	̸=	̸=	PROPN
ejpam-5802	79	21	ϕ	ϕ	PROPN
ejpam-5802	79	22	and	and	CCONJ
ejpam-5802	79	23	w	w	PROPN
ejpam-5802	79	24	is	be	AUX
ejpam-5802	79	25	subset	subset	VERB
ejpam-5802	79	26	of	of	ADP
ejpam-5802	79	27	k	k	PROPN
ejpam-5802	79	28	,	,	PUNCT
ejpam-5802	79	29	then	then	ADV
ejpam-5802	79	30	the	the	DET
ejpam-5802	79	31	point	point	NOUN
ejpam-5802	79	32	d	d	NOUN
ejpam-5802	79	33	is	be	AUX
ejpam-5802	79	34	said	say	VERB
ejpam-5802	79	35	to	to	PART
ejpam-5802	79	36	be	be	AUX
ejpam-5802	79	37	nth	nth	ADJ
ejpam-5802	79	38	-	-	PUNCT
ejpam-5802	79	39	boundary	boundary	ADJ
ejpam-5802	79	40	point	point	NOUN
ejpam-5802	79	41	of	of	ADP
ejpam-5802	79	42	w	w	NOUN
ejpam-5802	79	43	,	,	PUNCT
ejpam-5802	79	44	if	if	SCONJ
ejpam-5802	79	45	every	every	DET
ejpam-5802	79	46	neighborhood	neighborhood	NOUN
ejpam-5802	79	47	of	of	ADP
ejpam-5802	79	48	d	d	NOUN
ejpam-5802	79	49	satisfy	satisfy	VERB
ejpam-5802	79	50	that	that	SCONJ
ejpam-5802	79	51	n(d	n(d	PROPN
ejpam-5802	79	52	,	,	PUNCT
ejpam-5802	79	53	ε	ε	PROPN
ejpam-5802	79	54	)	)	PUNCT
ejpam-5802	79	55	∩	∩	NOUN
ejpam-5802	79	56	a	a	DET
ejpam-5802	79	57	̸=	̸=	PROPN
ejpam-5802	79	58	ϕ	ϕ	PROPN
ejpam-5802	79	59	and	and	CCONJ
ejpam-5802	79	60	n(d	n(d	PROPN
ejpam-5802	79	61	,	,	PUNCT
ejpam-5802	79	62	ε	ε	PROPN
ejpam-5802	79	63	)	)	PUNCT
ejpam-5802	79	64	∩	∩	PROPN
ejpam-5802	79	65	ac	ac	PROPN
ejpam-5802	79	66	̸=	̸=	PROPN
ejpam-5802	79	67	ϕ.	ϕ.	VERB
ejpam-5802	79	68	the	the	DET
ejpam-5802	79	69	set	set	NOUN
ejpam-5802	79	70	of	of	ADP
ejpam-5802	79	71	all	all	DET
ejpam-5802	79	72	nth	nth	NOUN
ejpam-5802	79	73	-	-	PUNCT
ejpam-5802	79	74	boundary	boundary	ADJ
ejpam-5802	79	75	point	point	NOUN
ejpam-5802	79	76	is	be	AUX
ejpam-5802	79	77	called	call	VERB
ejpam-5802	79	78	nth	nth	ADJ
ejpam-5802	79	79	-	-	PUNCT
ejpam-5802	79	80	boundary	boundary	ADJ
ejpam-5802	79	81	set	set	NOUN
ejpam-5802	79	82	,	,	PUNCT
ejpam-5802	79	83	and	and	CCONJ
ejpam-5802	79	84	it	it	PRON
ejpam-5802	79	85	is	be	AUX
ejpam-5802	79	86	denoted	denote	VERB
ejpam-5802	79	87	by	by	ADP
ejpam-5802	79	88	bd(w	bd(w	NOUN
ejpam-5802	79	89	)	)	PUNCT
ejpam-5802	79	90	=	=	PUNCT
ejpam-5802	80	1	w	w	ADP
ejpam-5802	80	2	−w	−w	ADV
ejpam-5802	80	3	◦	◦	NOUN
ejpam-5802	80	4	=	=	PUNCT
ejpam-5802	80	5	w	w	PROPN
ejpam-5802	80	6	∩w	∩w	PROPN
ejpam-5802	80	7	c.	c.	PROPN
ejpam-5802	80	8	note	note	VERB
ejpam-5802	80	9	that	that	SCONJ
ejpam-5802	80	10	:	:	PUNCT
ejpam-5802	80	11	bd	bd	PROPN
ejpam-5802	80	12	(	(	PUNCT
ejpam-5802	80	13	w	w	NOUN
ejpam-5802	80	14	)	)	PUNCT
ejpam-5802	80	15	is	be	AUX
ejpam-5802	80	16	nth	nth	ADV
ejpam-5802	80	17	-	-	PUNCT
ejpam-5802	80	18	closed	close	VERB
ejpam-5802	80	19	set	set	NOUN
ejpam-5802	80	20	.	.	PUNCT
ejpam-5802	81	1	properties	property	NOUN
ejpam-5802	81	2	of	of	ADP
ejpam-5802	81	3	boundary	boundary	ADJ
ejpam-5802	81	4	set	set	NOUN
ejpam-5802	81	5	:	:	PUNCT
ejpam-5802	81	6	let	let	VERB
ejpam-5802	81	7	(	(	PUNCT
ejpam-5802	81	8	k	k	X
ejpam-5802	81	9	,	,	PUNCT
ejpam-5802	81	10	η1,η2,	η1,η2,	PROPN
ejpam-5802	81	11	...	...	PUNCT
ejpam-5802	81	12	,ηn	,ηn	PUNCT
ejpam-5802	81	13	)	)	PUNCT
ejpam-5802	81	14	be	be	AUX
ejpam-5802	81	15	a	a	DET
ejpam-5802	81	16	nth	nth	ADJ
ejpam-5802	81	17	-	-	ADJ
ejpam-5802	81	18	topological	topological	ADJ
ejpam-5802	81	19	space	space	NOUN
ejpam-5802	81	20	and	and	CCONJ
ejpam-5802	81	21	let	let	VERB
ejpam-5802	81	22	x	x	PRON
ejpam-5802	81	23	,	,	PUNCT
ejpam-5802	81	24	y	y	PROPN
ejpam-5802	81	25	⊂	⊂	PROPN
ejpam-5802	81	26	k	k	PROPN
ejpam-5802	81	27	,	,	PUNCT
ejpam-5802	81	28	then	then	ADV
ejpam-5802	81	29	:	:	PUNCT
ejpam-5802	81	30	(	(	PUNCT
ejpam-5802	81	31	i	i	NOUN
ejpam-5802	81	32	)	)	PUNCT
ejpam-5802	81	33	the	the	DET
ejpam-5802	81	34	boundary	boundary	ADJ
ejpam-5802	81	35	set	set	NOUN
ejpam-5802	81	36	of	of	ADP
ejpam-5802	81	37	the	the	DET
ejpam-5802	81	38	empty	empty	ADJ
ejpam-5802	81	39	set	set	NOUN
ejpam-5802	81	40	and	and	CCONJ
ejpam-5802	81	41	k	k	PROPN
ejpam-5802	81	42	equal	equal	ADJ
ejpam-5802	81	43	ϕ.	ϕ.	PROPN
ejpam-5802	81	44	(	(	PUNCT
ejpam-5802	81	45	ii	ii	PROPN
ejpam-5802	81	46	)	)	PUNCT
ejpam-5802	81	47	bd(x	bd(x	X
ejpam-5802	81	48	)	)	PUNCT
ejpam-5802	81	49	is	be	AUX
ejpam-5802	81	50	ηi	ηi	NOUN
ejpam-5802	81	51	-	-	PUNCT
ejpam-5802	81	52	closed	closed	ADJ
ejpam-5802	81	53	set	set	NOUN
ejpam-5802	81	54	,	,	PUNCT
ejpam-5802	81	55	i=1,2,	i=1,2,	NOUN
ejpam-5802	81	56	...	...	PUNCT
ejpam-5802	81	57	,n	,n	X
ejpam-5802	81	58	.	.	PUNCT
ejpam-5802	82	1	(	(	PUNCT
ejpam-5802	82	2	iii	iii	X
ejpam-5802	82	3	)	)	PUNCT
ejpam-5802	82	4	y	y	PROPN
ejpam-5802	82	5	∈	∈	PROPN
ejpam-5802	82	6	bd(x	bd(x	ADV
ejpam-5802	82	7	)	)	PUNCT
ejpam-5802	82	8	if	if	SCONJ
ejpam-5802	82	9	and	and	CCONJ
ejpam-5802	82	10	only	only	ADV
ejpam-5802	82	11	if	if	SCONJ
ejpam-5802	82	12	for	for	ADP
ejpam-5802	82	13	all	all	DET
ejpam-5802	82	14	ηi	ηi	NOUN
ejpam-5802	82	15	-	-	PUNCT
ejpam-5802	82	16	open	open	ADJ
ejpam-5802	82	17	set	set	NOUN
ejpam-5802	82	18	uy	uy	ADP
ejpam-5802	82	19	such	such	ADJ
ejpam-5802	82	20	that	that	SCONJ
ejpam-5802	82	21	y	y	PROPN
ejpam-5802	82	22	∈	∈	PROPN
ejpam-5802	83	1	uy	uy	INTJ
ejpam-5802	84	1	we	we	PRON
ejpam-5802	84	2	have	have	VERB
ejpam-5802	84	3	uy	uy	NOUN
ejpam-5802	84	4	∩	∩	NOUN
ejpam-5802	84	5	x	x	PROPN
ejpam-5802	84	6	̸=	̸=	PROPN
ejpam-5802	84	7	ϕ	ϕ	PROPN
ejpam-5802	84	8	and	and	CCONJ
ejpam-5802	84	9	uy	uy	PROPN
ejpam-5802	84	10	∩	∩	PROPN
ejpam-5802	84	11	xc	xc	PROPN
ejpam-5802	84	12	̸=	̸=	PROPN
ejpam-5802	84	13	ϕ.	ϕ.	PROPN
ejpam-5802	84	14	proof	proof	NOUN
ejpam-5802	84	15	:	:	PUNCT
ejpam-5802	84	16	(	(	PUNCT
ejpam-5802	84	17	iii	iii	X
ejpam-5802	84	18	)	)	PUNCT
ejpam-5802	84	19	let	let	VERB
ejpam-5802	84	20	y	y	PROPN
ejpam-5802	84	21	∈	∈	PROPN
ejpam-5802	84	22	bd(x	bd(x	X
ejpam-5802	84	23	)	)	PUNCT
ejpam-5802	84	24	and	and	CCONJ
ejpam-5802	84	25	uy	uy	PROPN
ejpam-5802	84	26	be	be	AUX
ejpam-5802	84	27	a	a	DET
ejpam-5802	84	28	ηi	ηi	NOUN
ejpam-5802	84	29	-	-	PUNCT
ejpam-5802	84	30	open	open	NOUN
ejpam-5802	84	31	set	set	NOUN
ejpam-5802	85	1	such	such	ADJ
ejpam-5802	85	2	that	that	SCONJ
ejpam-5802	85	3	y	y	PROPN
ejpam-5802	85	4	uy	uy	INTJ
ejpam-5802	85	5	,	,	PUNCT
ejpam-5802	85	6	then	then	ADV
ejpam-5802	85	7	y	y	PROPN
ejpam-5802	85	8	∈	∈	PROPN
ejpam-5802	85	9	(	(	PUNCT
ejpam-5802	85	10	x∩xc	x∩xc	PROPN
ejpam-5802	85	11	)	)	PUNCT
ejpam-5802	85	12	,	,	PUNCT
ejpam-5802	85	13	if	if	SCONJ
ejpam-5802	85	14	and	and	CCONJ
ejpam-5802	85	15	only	only	ADV
ejpam-5802	85	16	if	if	SCONJ
ejpam-5802	85	17	b	b	PROPN
ejpam-5802	85	18	∈	∈	PROPN
ejpam-5802	85	19	x	x	X
ejpam-5802	85	20	and	and	CCONJ
ejpam-5802	85	21	y	y	PROPN
ejpam-5802	85	22	∈	∈	PROPN
ejpam-5802	85	23	xc	xc	PROPN
ejpam-5802	85	24	,	,	PUNCT
ejpam-5802	85	25	if	if	SCONJ
ejpam-5802	85	26	and	and	CCONJ
ejpam-5802	85	27	only	only	ADV
ejpam-5802	85	28	if	if	SCONJ
ejpam-5802	85	29	y	y	PROPN
ejpam-5802	85	30	∈	∈	PROPN
ejpam-5802	85	31	(	(	PUNCT
ejpam-5802	85	32	x	x	SYM
ejpam-5802	85	33	∪	∪	X
ejpam-5802	85	34	x	x	NOUN
ejpam-5802	85	35	′	′	NUM
ejpam-5802	85	36	)	)	PUNCT
ejpam-5802	85	37	and	and	CCONJ
ejpam-5802	85	38	y	y	PROPN
ejpam-5802	85	39	∈	∈	PROPN
ejpam-5802	85	40	xc	xc	PROPN
ejpam-5802	85	41	∪	∪	PROPN
ejpam-5802	85	42	(	(	PUNCT
ejpam-5802	85	43	xc)′	xc)′	PROPN
ejpam-5802	85	44	,	,	PUNCT
ejpam-5802	85	45	if	if	SCONJ
ejpam-5802	85	46	and	and	CCONJ
ejpam-5802	85	47	only	only	ADV
ejpam-5802	85	48	if	if	SCONJ
ejpam-5802	85	49	(	(	PUNCT
ejpam-5802	85	50	y	y	PROPN
ejpam-5802	85	51	∈	∈	PROPN
ejpam-5802	85	52	x	x	X
ejpam-5802	85	53	or	or	CCONJ
ejpam-5802	85	54	y	y	PROPN
ejpam-5802	85	55	∈	∈	PROPN
ejpam-5802	85	56	x	x	NOUN
ejpam-5802	85	57	’	'	PUNCT
ejpam-5802	85	58	)	)	PUNCT
ejpam-5802	85	59	and	and	CCONJ
ejpam-5802	85	60	(	(	PUNCT
ejpam-5802	85	61	y	y	PROPN
ejpam-5802	85	62	∈	∈	PROPN
ejpam-5802	85	63	xc	xc	PROPN
ejpam-5802	85	64	or	or	CCONJ
ejpam-5802	85	65	y	y	PROPN
ejpam-5802	85	66	∈	∈	PROPN
ejpam-5802	85	67	(	(	PUNCT
ejpam-5802	85	68	xc)′	xc)′	PROPN
ejpam-5802	85	69	,	,	PUNCT
ejpam-5802	85	70	if	if	SCONJ
ejpam-5802	85	71	and	and	CCONJ
ejpam-5802	85	72	only	only	ADV
ejpam-5802	85	73	if	if	SCONJ
ejpam-5802	85	74	y	y	PROPN
ejpam-5802	85	75	∈	∈	PROPN
ejpam-5802	85	76	x	x	PRON
ejpam-5802	85	77	’	'	PUNCT
ejpam-5802	85	78	and	and	CCONJ
ejpam-5802	85	79	y	y	PROPN
ejpam-5802	85	80	∈	∈	PROPN
ejpam-5802	85	81	xc	xc	PROPN
ejpam-5802	85	82	,	,	PUNCT
ejpam-5802	85	83	if	if	SCONJ
ejpam-5802	85	84	and	and	CCONJ
ejpam-5802	85	85	only	only	ADV
ejpam-5802	85	86	if	if	SCONJ
ejpam-5802	85	87	uy	uy	PROPN
ejpam-5802	85	88	∩	∩	NOUN
ejpam-5802	85	89	(	(	PUNCT
ejpam-5802	85	90	x/{y	x/{y	NUM
ejpam-5802	85	91	}	}	PUNCT
ejpam-5802	85	92	)	)	PUNCT
ejpam-5802	85	93	̸=	̸=	PROPN
ejpam-5802	85	94	ϕ	ϕ	PROPN
ejpam-5802	85	95	and	and	CCONJ
ejpam-5802	85	96	y	y	PROPN
ejpam-5802	85	97	∩	∩	PROPN
ejpam-5802	85	98	xc	xc	PROPN
ejpam-5802	85	99	̸=	̸=	PROPN
ejpam-5802	85	100	ϕ	ϕ	PROPN
ejpam-5802	85	101	,	,	PUNCT
ejpam-5802	85	102	but	but	CCONJ
ejpam-5802	85	103	y	y	PROPN
ejpam-5802	85	104	⊂	⊂	PROPN
ejpam-5802	85	105	uy	uy	INTJ
ejpam-5802	85	106	,	,	PUNCT
ejpam-5802	85	107	so	so	ADV
ejpam-5802	85	108	we	we	PRON
ejpam-5802	85	109	have	have	VERB
ejpam-5802	85	110	uy	uy	NOUN
ejpam-5802	85	111	∩	∩	NOUN
ejpam-5802	85	112	x	x	PROPN
ejpam-5802	85	113	̸=	̸=	PROPN
ejpam-5802	85	114	ϕ	ϕ	PROPN
ejpam-5802	85	115	and	and	CCONJ
ejpam-5802	85	116	uy	uy	PROPN
ejpam-5802	85	117	∩	∩	PROPN
ejpam-5802	85	118	xc	xc	PROPN
ejpam-5802	85	119	̸=	̸=	PROPN
ejpam-5802	85	120	ϕ	ϕ	PROPN
ejpam-5802	85	121	.	.	PUNCT
ejpam-5802	86	1	definition	definition	NOUN
ejpam-5802	86	2	9.1	9.1	NUM
ejpam-5802	86	3	:	:	PUNCT
ejpam-5802	86	4	a	a	DET
ejpam-5802	86	5	nth	nth	ADJ
ejpam-5802	86	6	-	-	ADJ
ejpam-5802	86	7	topological	topological	ADJ
ejpam-5802	86	8	space	space	NOUN
ejpam-5802	86	9	(	(	PUNCT
ejpam-5802	86	10	k	k	PROPN
ejpam-5802	86	11	,	,	PUNCT
ejpam-5802	86	12	η1,η2,	η1,η2,	PROPN
ejpam-5802	86	13	...	...	PUNCT
ejpam-5802	86	14	,ηn	,ηn	PUNCT
ejpam-5802	86	15	)	)	PUNCT
ejpam-5802	86	16	is	be	AUX
ejpam-5802	86	17	t	t	PROPN
ejpam-5802	86	18	◦	◦	NOUN
ejpam-5802	86	19	-space	-space	NOUN
ejpam-5802	86	20	,	,	PUNCT
ejpam-5802	86	21	if	if	SCONJ
ejpam-5802	86	22	for	for	ADP
ejpam-5802	86	23	all	all	DET
ejpam-5802	86	24	c	c	NOUN
ejpam-5802	86	25	̸=	̸=	PROPN
ejpam-5802	86	26	d	d	PROPN
ejpam-5802	86	27	in	in	ADP
ejpam-5802	86	28	k	k	PROPN
ejpam-5802	86	29	,	,	PUNCT
ejpam-5802	86	30	there	there	PRON
ejpam-5802	86	31	exists	exist	VERB
ejpam-5802	86	32	ηi	ηi	NOUN
ejpam-5802	86	33	-	-	PUNCT
ejpam-5802	86	34	open	open	ADJ
ejpam-5802	86	35	set	set	NOUN
ejpam-5802	86	36	uc	uc	ADP
ejpam-5802	86	37	such	such	ADJ
ejpam-5802	86	38	that	that	SCONJ
ejpam-5802	86	39	c	c	PROPN
ejpam-5802	86	40	∈	∈	PROPN
ejpam-5802	87	1	uc	uc	X
ejpam-5802	87	2	and	and	CCONJ
ejpam-5802	87	3	d	d	PROPN
ejpam-5802	87	4	/∈	/∈	PUNCT
ejpam-5802	88	1	uc	uc	ADJ
ejpam-5802	88	2	or	or	CCONJ
ejpam-5802	88	3	there	there	PRON
ejpam-5802	88	4	exists	exist	VERB
ejpam-5802	88	5	ηi	ηi	NOUN
ejpam-5802	88	6	-	-	PUNCT
ejpam-5802	88	7	open	open	ADJ
ejpam-5802	88	8	set	set	NOUN
ejpam-5802	88	9	vd	vd	NOUN
ejpam-5802	88	10	such	such	ADJ
ejpam-5802	88	11	that	that	PRON
ejpam-5802	88	12	c	c	NOUN
ejpam-5802	88	13	/∈	/∈	PUNCT
ejpam-5802	89	1	vd	vd	NOUN
ejpam-5802	89	2	and	and	CCONJ
ejpam-5802	89	3	d	d	PROPN
ejpam-5802	89	4	∈	∈	PROPN
ejpam-5802	89	5	vd	vd	NOUN
ejpam-5802	89	6	,	,	PUNCT
ejpam-5802	89	7	for	for	ADP
ejpam-5802	89	8	all	all	DET
ejpam-5802	89	9	i=	i=	PROPN
ejpam-5802	89	10	1,2,	1,2,	NUM
ejpam-5802	89	11	...	...	PUNCT
ejpam-5802	89	12	,n	,n	SYM
ejpam-5802	89	13	.	.	PUNCT
ejpam-5802	90	1	theorem	theorem	NOUN
ejpam-5802	90	2	1	1	NUM
ejpam-5802	90	3	:	:	PUNCT
ejpam-5802	90	4	let	let	VERB
ejpam-5802	90	5	(	(	PUNCT
ejpam-5802	90	6	k	k	X
ejpam-5802	90	7	,	,	PUNCT
ejpam-5802	90	8	η1,η2,	η1,η2,	PROPN
ejpam-5802	90	9	...	...	PUNCT
ejpam-5802	90	10	,ηn	,ηn	PUNCT
ejpam-5802	90	11	)	)	PUNCT
ejpam-5802	90	12	be	be	AUX
ejpam-5802	90	13	a	a	DET
ejpam-5802	90	14	topological	topological	ADJ
ejpam-5802	90	15	space	space	NOUN
ejpam-5802	90	16	,	,	PUNCT
ejpam-5802	90	17	then	then	ADV
ejpam-5802	90	18	the	the	DET
ejpam-5802	90	19	following	following	NOUN
ejpam-5802	90	20	are	be	AUX
ejpam-5802	90	21	equivalent	equivalent	ADJ
ejpam-5802	90	22	:	:	PUNCT
ejpam-5802	90	23	i	i	NOUN
ejpam-5802	90	24	)	)	PUNCT
ejpam-5802	91	1	k	k	X
ejpam-5802	91	2	is	be	AUX
ejpam-5802	91	3	nth	nth	NOUN
ejpam-5802	91	4	-	-	PUNCT
ejpam-5802	91	5	t0	t0	NOUN
ejpam-5802	91	6	-	-	NOUN
ejpam-5802	91	7	space	space	NOUN
ejpam-5802	91	8	.	.	PUNCT
ejpam-5802	92	1	ii	ii	X
ejpam-5802	92	2	)	)	PUNCT
ejpam-5802	92	3	for	for	ADP
ejpam-5802	92	4	all	all	DET
ejpam-5802	92	5	m	m	PROPN
ejpam-5802	92	6	̸=	̸=	PROPN
ejpam-5802	92	7	n	n	NOUN
ejpam-5802	92	8	in	in	ADP
ejpam-5802	92	9	k	k	PROPN
ejpam-5802	92	10	,	,	PUNCT
ejpam-5802	92	11	we	we	PRON
ejpam-5802	92	12	have	have	VERB
ejpam-5802	92	13	m	m	PRON
ejpam-5802	92	14	/∈	/∈	PUNCT
ejpam-5802	92	15	{	{	PUNCT
ejpam-5802	92	16	n	n	CCONJ
ejpam-5802	92	17	}	}	PUNCT
ejpam-5802	92	18	or	or	CCONJ
ejpam-5802	92	19	n	n	ADV
ejpam-5802	92	20	/∈	/∈	PUNCT
ejpam-5802	92	21	{	{	PUNCT
ejpam-5802	92	22	m	m	NOUN
ejpam-5802	92	23	}	}	PUNCT
ejpam-5802	92	24	.	.	PUNCT
ejpam-5802	93	1	iii	iii	X
ejpam-5802	93	2	)	)	PUNCT
ejpam-5802	93	3	for	for	ADP
ejpam-5802	93	4	all	all	DET
ejpam-5802	93	5	m	m	PROPN
ejpam-5802	93	6	̸=	̸=	PROPN
ejpam-5802	93	7	n	n	NOUN
ejpam-5802	93	8	in	in	ADP
ejpam-5802	93	9	k	k	PROPN
ejpam-5802	93	10	,	,	PUNCT
ejpam-5802	93	11	we	we	PRON
ejpam-5802	93	12	have	have	VERB
ejpam-5802	93	13	{	{	PUNCT
ejpam-5802	93	14	m	m	NOUN
ejpam-5802	93	15	}	}	PUNCT
ejpam-5802	93	16	̸=	̸=	PROPN
ejpam-5802	93	17	{	{	PUNCT
ejpam-5802	93	18	n	n	CCONJ
ejpam-5802	93	19	}	}	PUNCT
ejpam-5802	93	20	.	.	PUNCT
ejpam-5802	94	1	proof	proof	NOUN
ejpam-5802	94	2	:	:	PUNCT
ejpam-5802	94	3	(	(	PUNCT
ejpam-5802	94	4	(	(	PUNCT
ejpam-5802	94	5	i	i	NOUN
ejpam-5802	94	6	)	)	PUNCT
ejpam-5802	94	7	implies	imply	VERB
ejpam-5802	94	8	(	(	PUNCT
ejpam-5802	94	9	ii	ii	NOUN
ejpam-5802	94	10	)	)	PUNCT
ejpam-5802	94	11	)	)	PUNCT
ejpam-5802	95	1	let	let	VERB
ejpam-5802	95	2	m	m	PRON
ejpam-5802	95	3	̸=	̸=	PROPN
ejpam-5802	95	4	n	n	CCONJ
ejpam-5802	95	5	,	,	PUNCT
ejpam-5802	95	6	then	then	ADV
ejpam-5802	95	7	there	there	PRON
ejpam-5802	95	8	exist	exist	VERB
ejpam-5802	95	9	ηi	ηi	NOUN
ejpam-5802	95	10	-	-	PUNCT
ejpam-5802	95	11	open	open	NOUN
ejpam-5802	95	12	set	set	NOUN
ejpam-5802	95	13	such	such	ADJ
ejpam-5802	95	14	that	that	SCONJ
ejpam-5802	95	15	m	m	VERB
ejpam-5802	95	16	∈	∈	ADJ
ejpam-5802	95	17	um	um	INTJ
ejpam-5802	95	18	and	and	CCONJ
ejpam-5802	95	19	n	n	ADV
ejpam-5802	95	20	/∈	/∈	PUNCT
ejpam-5802	96	1	u	u	NOUN
ejpam-5802	96	2	−m	−m	NOUN
ejpam-5802	96	3	or	or	CCONJ
ejpam-5802	96	4	there	there	PRON
ejpam-5802	96	5	exist	exist	VERB
ejpam-5802	96	6	ηj	ηj	NOUN
ejpam-5802	96	7	-	-	ADJ
ejpam-5802	96	8	open	open	ADJ
ejpam-5802	96	9	set	set	NOUN
ejpam-5802	96	10	vn	vn	NOUN
ejpam-5802	96	11	such	such	ADJ
ejpam-5802	96	12	that	that	SCONJ
ejpam-5802	96	13	m	m	PROPN
ejpam-5802	96	14	∈	∈	PROPN
ejpam-5802	96	15	vn	vn	NOUN
ejpam-5802	96	16	and	and	CCONJ
ejpam-5802	96	17	m	m	PROPN
ejpam-5802	96	18	/∈	/∈	PUNCT
ejpam-5802	97	1	vn	vn	INTJ
ejpam-5802	97	2	where	where	SCONJ
ejpam-5802	97	3	i=1,2,	i=1,2,	NOUN
ejpam-5802	97	4	...	...	PUNCT
ejpam-5802	97	5	,n	,n	PUNCT
ejpam-5802	97	6	.	.	PUNCT
ejpam-5802	98	1	so	so	ADV
ejpam-5802	98	2	,	,	PUNCT
ejpam-5802	98	3	we	we	PRON
ejpam-5802	98	4	have	have	VERB
ejpam-5802	98	5	m	m	PROPN
ejpam-5802	98	6	∈	∈	ADJ
ejpam-5802	98	7	um	um	INTJ
ejpam-5802	98	8	and	and	CCONJ
ejpam-5802	98	9	um	um	INTJ
ejpam-5802	98	10	∩	∩	ADJ
ejpam-5802	98	11	{	{	PUNCT
ejpam-5802	98	12	n	n	CCONJ
ejpam-5802	98	13	}	}	PUNCT
ejpam-5802	98	14	=	=	SYM
ejpam-5802	98	15	ϕ	ϕ	NOUN
ejpam-5802	98	16	or	or	CCONJ
ejpam-5802	98	17	n	n	PROPN
ejpam-5802	98	18	in	in	ADP
ejpam-5802	98	19	vn	vn	PROPN
ejpam-5802	98	20	and	and	CCONJ
ejpam-5802	98	21	vn	vn	PROPN
ejpam-5802	98	22	∩	∩	PROPN
ejpam-5802	98	23	{	{	PUNCT
ejpam-5802	98	24	m	m	NOUN
ejpam-5802	98	25	}	}	PUNCT
ejpam-5802	98	26	=	=	SYM
ejpam-5802	98	27	ϕ.	ϕ.	PROPN
ejpam-5802	98	28	thus	thus	ADV
ejpam-5802	98	29	,	,	PUNCT
ejpam-5802	98	30	m	m	NOUN
ejpam-5802	98	31	/∈	/∈	PUNCT
ejpam-5802	98	32	{	{	PUNCT
ejpam-5802	98	33	n	n	CCONJ
ejpam-5802	98	34	}	}	PUNCT
ejpam-5802	98	35	or	or	CCONJ
ejpam-5802	98	36	n	n	ADV
ejpam-5802	98	37	/∈	/∈	PUNCT
ejpam-5802	98	38	{	{	PUNCT
ejpam-5802	98	39	m	m	NOUN
ejpam-5802	98	40	}	}	PUNCT
ejpam-5802	98	41	.	.	PUNCT
ejpam-5802	99	1	(	(	PUNCT
ejpam-5802	99	2	(	(	PUNCT
ejpam-5802	99	3	ii	ii	NOUN
ejpam-5802	99	4	)	)	PUNCT
ejpam-5802	99	5	implies	imply	VERB
ejpam-5802	99	6	(	(	PUNCT
ejpam-5802	99	7	iii	iii	NOUN
ejpam-5802	99	8	)	)	PUNCT
ejpam-5802	99	9	)	)	PUNCT
ejpam-5802	100	1	j.	j.	PROPN
ejpam-5802	100	2	oudetallah	oudetallah	PROPN
ejpam-5802	100	3	et	et	PROPN
ejpam-5802	100	4	al	al	PROPN
ejpam-5802	100	5	.	.	PUNCT
ejpam-5802	100	6	/	/	SYM
ejpam-5802	100	7	eur	eur	PROPN
ejpam-5802	100	8	.	.	PUNCT
ejpam-5802	101	1	j.	j.	PROPN
ejpam-5802	101	2	pure	pure	PROPN
ejpam-5802	101	3	appl	appl	PROPN
ejpam-5802	101	4	.	.	PROPN
ejpam-5802	101	5	math	math	PROPN
ejpam-5802	101	6	,	,	PUNCT
ejpam-5802	101	7	18	18	NUM
ejpam-5802	101	8	(	(	PUNCT
ejpam-5802	101	9	2	2	NUM
ejpam-5802	101	10	)	)	PUNCT
ejpam-5802	101	11	(	(	PUNCT
ejpam-5802	101	12	2025	2025	NUM
ejpam-5802	101	13	)	)	PUNCT
ejpam-5802	101	14	,	,	PUNCT
ejpam-5802	101	15	5802	5802	NUM
ejpam-5802	101	16	6	6	NUM
ejpam-5802	101	17	of	of	ADP
ejpam-5802	101	18	14	14	NUM
ejpam-5802	101	19	let	let	VERB
ejpam-5802	101	20	m	m	PRON
ejpam-5802	101	21	̸=	̸=	PROPN
ejpam-5802	101	22	n	n	CCONJ
ejpam-5802	101	23	,	,	PUNCT
ejpam-5802	101	24	then	then	ADV
ejpam-5802	101	25	if	if	SCONJ
ejpam-5802	101	26	m	m	ADV
ejpam-5802	101	27	/∈	/∈	PUNCT
ejpam-5802	101	28	{	{	PUNCT
ejpam-5802	101	29	n	n	CCONJ
ejpam-5802	101	30	}	}	PUNCT
ejpam-5802	101	31	and	and	CCONJ
ejpam-5802	101	32	m	m	PROPN
ejpam-5802	101	33	∈	∈	NOUN
ejpam-5802	101	34	{	{	PUNCT
ejpam-5802	101	35	m	m	NOUN
ejpam-5802	101	36	}	}	PUNCT
ejpam-5802	101	37	,	,	PUNCT
ejpam-5802	101	38	then	then	ADV
ejpam-5802	101	39	we	we	PRON
ejpam-5802	101	40	have	have	VERB
ejpam-5802	101	41	{	{	PUNCT
ejpam-5802	101	42	m	m	NOUN
ejpam-5802	101	43	}	}	PUNCT
ejpam-5802	101	44	=	=	ADJ
ejpam-5802	101	45	̸	̸	NUM
ejpam-5802	101	46	{	{	PUNCT
ejpam-5802	101	47	n	n	X
ejpam-5802	101	48	}	}	PUNCT
ejpam-5802	101	49	.	.	PUNCT
ejpam-5802	102	1	additionally	additionally	ADV
ejpam-5802	102	2	,	,	PUNCT
ejpam-5802	102	3	if	if	SCONJ
ejpam-5802	102	4	n	n	ADV
ejpam-5802	102	5	/∈	/∈	PUNCT
ejpam-5802	102	6	{	{	PUNCT
ejpam-5802	102	7	n	n	CCONJ
ejpam-5802	102	8	}	}	PUNCT
ejpam-5802	102	9	and	and	CCONJ
ejpam-5802	102	10	n	n	PRON
ejpam-5802	102	11	∈	∈	PROPN
ejpam-5802	102	12	{	{	PUNCT
ejpam-5802	102	13	n	n	CCONJ
ejpam-5802	102	14	}	}	PUNCT
ejpam-5802	102	15	,	,	PUNCT
ejpam-5802	102	16	then	then	ADV
ejpam-5802	102	17	we	we	PRON
ejpam-5802	102	18	have	have	VERB
ejpam-5802	102	19	{	{	PUNCT
ejpam-5802	102	20	m	m	NOUN
ejpam-5802	102	21	}	}	PUNCT
ejpam-5802	102	22	̸=	̸=	PROPN
ejpam-5802	102	23	{	{	PUNCT
ejpam-5802	102	24	n	n	CCONJ
ejpam-5802	102	25	}	}	PUNCT
ejpam-5802	102	26	.	.	PUNCT
ejpam-5802	103	1	(	(	PUNCT
ejpam-5802	103	2	(	(	PUNCT
ejpam-5802	103	3	iii	iii	NOUN
ejpam-5802	103	4	)	)	PUNCT
ejpam-5802	103	5	implies	imply	VERB
ejpam-5802	103	6	(	(	PUNCT
ejpam-5802	103	7	i	i	NOUN
ejpam-5802	103	8	)	)	PUNCT
ejpam-5802	103	9	)	)	PUNCT
ejpam-5802	104	1	let	let	VERB
ejpam-5802	104	2	m	m	PRON
ejpam-5802	104	3	̸=	̸=	PROPN
ejpam-5802	104	4	n	n	CCONJ
ejpam-5802	104	5	and	and	CCONJ
ejpam-5802	104	6	by	by	ADP
ejpam-5802	104	7	given	give	VERB
ejpam-5802	104	8	{	{	PUNCT
ejpam-5802	104	9	m	m	NOUN
ejpam-5802	104	10	}	}	PUNCT
ejpam-5802	104	11	=	=	ADJ
ejpam-5802	104	12	̸	̸	NUM
ejpam-5802	104	13	{	{	PUNCT
ejpam-5802	104	14	n	n	CCONJ
ejpam-5802	104	15	}	}	PUNCT
ejpam-5802	104	16	,	,	PUNCT
ejpam-5802	104	17	but	but	CCONJ
ejpam-5802	104	18	m	m	PROPN
ejpam-5802	104	19	∈	∈	PROPN
ejpam-5802	104	20	{	{	PUNCT
ejpam-5802	104	21	m	m	NOUN
ejpam-5802	104	22	}	}	PUNCT
ejpam-5802	104	23	and	and	CCONJ
ejpam-5802	104	24	n	n	PRON
ejpam-5802	104	25	∈	∈	PROPN
ejpam-5802	104	26	{	{	PUNCT
ejpam-5802	104	27	n	n	CCONJ
ejpam-5802	104	28	}	}	PUNCT
ejpam-5802	104	29	,	,	PUNCT
ejpam-5802	104	30	then	then	ADV
ejpam-5802	104	31	m	m	VERB
ejpam-5802	104	32	/∈	/∈	PUNCT
ejpam-5802	105	1	k	k	PROPN
ejpam-5802	106	1	−	−	PROPN
ejpam-5802	106	2	{	{	PUNCT
ejpam-5802	106	3	m	m	NOUN
ejpam-5802	106	4	}	}	PUNCT
ejpam-5802	106	5	=	=	PUNCT
ejpam-5802	106	6	vn	vn	X
ejpam-5802	106	7	which	which	PRON
ejpam-5802	106	8	is	be	AUX
ejpam-5802	106	9	ηi	ηi	PROPN
ejpam-5802	106	10	open	open	ADJ
ejpam-5802	106	11	set	set	NOUN
ejpam-5802	106	12	in	in	ADP
ejpam-5802	106	13	k	k	PROPN
ejpam-5802	106	14	since	since	SCONJ
ejpam-5802	106	15	{	{	PUNCT
ejpam-5802	106	16	m	m	PRON
ejpam-5802	106	17	}	}	PUNCT
ejpam-5802	106	18	is	be	AUX
ejpam-5802	106	19	ηi	ηi	NOUN
ejpam-5802	106	20	-	-	PUNCT
ejpam-5802	106	21	closed	close	VERB
ejpam-5802	106	22	set	set	NOUN
ejpam-5802	106	23	in	in	ADP
ejpam-5802	106	24	k	k	PROPN
ejpam-5802	106	25	and	and	CCONJ
ejpam-5802	106	26	n	n	CCONJ
ejpam-5802	106	27	∈	∈	PROPN
ejpam-5802	107	1	k	k	NOUN
ejpam-5802	107	2	−	−	PROPN
ejpam-5802	107	3	{	{	PUNCT
ejpam-5802	107	4	m	m	NOUN
ejpam-5802	107	5	}	}	PUNCT
ejpam-5802	107	6	=	=	PUNCT
ejpam-5802	107	7	vn	vn	ADP
ejpam-5802	107	8	where	where	SCONJ
ejpam-5802	107	9	i=1,2,	i=1,2,	NOUN
ejpam-5802	107	10	...	...	PUNCT
ejpam-5802	107	11	,n	,n	PUNCT
ejpam-5802	107	12	.	.	PUNCT
ejpam-5802	108	1	thus	thus	ADV
ejpam-5802	108	2	,	,	PUNCT
ejpam-5802	108	3	k	k	PROPN
ejpam-5802	108	4	is	be	AUX
ejpam-5802	108	5	nth	nth	NOUN
ejpam-5802	108	6	-	-	PUNCT
ejpam-5802	108	7	t0	t0	NOUN
ejpam-5802	108	8	-	-	NOUN
ejpam-5802	108	9	space	space	NOUN
ejpam-5802	108	10	.	.	PUNCT
ejpam-5802	109	1	definition	definition	NOUN
ejpam-5802	109	2	10.1	10.1	NUM
ejpam-5802	109	3	:	:	PUNCT
ejpam-5802	109	4	a	a	DET
ejpam-5802	109	5	nth	nth	ADJ
ejpam-5802	109	6	-	-	ADJ
ejpam-5802	109	7	topological	topological	ADJ
ejpam-5802	109	8	space	space	NOUN
ejpam-5802	109	9	(	(	PUNCT
ejpam-5802	109	10	k	k	PROPN
ejpam-5802	109	11	,	,	PUNCT
ejpam-5802	109	12	η1,η2,	η1,η2,	PROPN
ejpam-5802	109	13	...	...	PUNCT
ejpam-5802	109	14	,ηn	,ηn	PUNCT
ejpam-5802	109	15	)	)	PUNCT
ejpam-5802	109	16	is	be	AUX
ejpam-5802	109	17	t1	t1	NOUN
ejpam-5802	109	18	-	-	PUNCT
ejpam-5802	109	19	space	space	NOUN
ejpam-5802	109	20	,	,	PUNCT
ejpam-5802	109	21	if	if	SCONJ
ejpam-5802	109	22	for	for	ADP
ejpam-5802	109	23	all	all	DET
ejpam-5802	109	24	c	c	NOUN
ejpam-5802	109	25	̸=	̸=	PROPN
ejpam-5802	109	26	d	d	PROPN
ejpam-5802	109	27	in	in	ADP
ejpam-5802	109	28	k	k	PROPN
ejpam-5802	109	29	,	,	PUNCT
ejpam-5802	109	30	there	there	PRON
ejpam-5802	109	31	exists	exist	VERB
ejpam-5802	109	32	ηi	ηi	NOUN
ejpam-5802	109	33	-	-	PUNCT
ejpam-5802	109	34	open	open	ADJ
ejpam-5802	109	35	set	set	NOUN
ejpam-5802	109	36	uc	uc	ADP
ejpam-5802	109	37	such	such	ADJ
ejpam-5802	109	38	that	that	SCONJ
ejpam-5802	109	39	c	c	PROPN
ejpam-5802	109	40	∈	∈	PROPN
ejpam-5802	110	1	uc	uc	X
ejpam-5802	110	2	and	and	CCONJ
ejpam-5802	110	3	d	d	PROPN
ejpam-5802	110	4	/∈	/∈	PUNCT
ejpam-5802	111	1	uc	uc	NOUN
ejpam-5802	111	2	and	and	CCONJ
ejpam-5802	111	3	there	there	PRON
ejpam-5802	111	4	exists	exist	VERB
ejpam-5802	111	5	ηi	ηi	NOUN
ejpam-5802	111	6	-	-	PUNCT
ejpam-5802	111	7	open	open	ADJ
ejpam-5802	111	8	set	set	NOUN
ejpam-5802	111	9	vd	vd	NOUN
ejpam-5802	112	1	such	such	ADJ
ejpam-5802	112	2	that	that	PRON
ejpam-5802	112	3	c	c	NOUN
ejpam-5802	112	4	/∈	/∈	PUNCT
ejpam-5802	112	5	vd	vd	NOUN
ejpam-5802	112	6	and	and	CCONJ
ejpam-5802	112	7	d	d	PROPN
ejpam-5802	112	8	∈	∈	PROPN
ejpam-5802	112	9	vd	vd	NOUN
ejpam-5802	112	10	,	,	PUNCT
ejpam-5802	112	11	for	for	ADP
ejpam-5802	112	12	all	all	DET
ejpam-5802	112	13	i=	i=	PROPN
ejpam-5802	112	14	1,2,	1,2,	NUM
ejpam-5802	112	15	...	...	PUNCT
ejpam-5802	112	16	,n	,n	PUNCT
ejpam-5802	112	17	.	.	PUNCT
ejpam-5802	113	1	definition	definition	NOUN
ejpam-5802	113	2	11.1	11.1	NUM
ejpam-5802	113	3	:	:	PUNCT
ejpam-5802	113	4	a	a	DET
ejpam-5802	113	5	nth	nth	ADJ
ejpam-5802	113	6	-	-	ADJ
ejpam-5802	113	7	topological	topological	ADJ
ejpam-5802	113	8	space	space	NOUN
ejpam-5802	113	9	(	(	PUNCT
ejpam-5802	113	10	k	k	PROPN
ejpam-5802	113	11	,	,	PUNCT
ejpam-5802	113	12	η1,η2,	η1,η2,	PROPN
ejpam-5802	113	13	...	...	PUNCT
ejpam-5802	113	14	,ηn	,ηn	PUNCT
ejpam-5802	113	15	)	)	PUNCT
ejpam-5802	113	16	is	be	AUX
ejpam-5802	113	17	t2	t2	NOUN
ejpam-5802	113	18	-	-	PUNCT
ejpam-5802	113	19	space	space	NOUN
ejpam-5802	113	20	,	,	PUNCT
ejpam-5802	113	21	if	if	SCONJ
ejpam-5802	113	22	for	for	ADP
ejpam-5802	113	23	all	all	DET
ejpam-5802	113	24	c	c	NOUN
ejpam-5802	113	25	̸=	̸=	PROPN
ejpam-5802	113	26	d	d	PROPN
ejpam-5802	113	27	in	in	ADP
ejpam-5802	113	28	k	k	PROPN
ejpam-5802	113	29	,	,	PUNCT
ejpam-5802	113	30	there	there	PRON
ejpam-5802	113	31	exists	exist	VERB
ejpam-5802	113	32	ηi	ηi	NOUN
ejpam-5802	113	33	-	-	PUNCT
ejpam-5802	113	34	open	open	ADJ
ejpam-5802	113	35	set	set	NOUN
ejpam-5802	113	36	uc	uc	ADV
ejpam-5802	113	37	and	and	CCONJ
ejpam-5802	113	38	there	there	PRON
ejpam-5802	113	39	exists	exist	VERB
ejpam-5802	113	40	ηi	ηi	NOUN
ejpam-5802	113	41	-	-	PUNCT
ejpam-5802	113	42	open	open	ADJ
ejpam-5802	113	43	set	set	NOUN
ejpam-5802	113	44	vd	vd	NOUN
ejpam-5802	113	45	such	such	ADJ
ejpam-5802	114	1	that	that	SCONJ
ejpam-5802	114	2	c	c	PROPN
ejpam-5802	114	3	∈	∈	PROPN
ejpam-5802	115	1	uc	uc	PROPN
ejpam-5802	115	2	and	and	CCONJ
ejpam-5802	115	3	d	d	PROPN
ejpam-5802	115	4	∈	∈	PROPN
ejpam-5802	115	5	vd	vd	NOUN
ejpam-5802	115	6	and	and	CCONJ
ejpam-5802	115	7	uc	uc	ADV
ejpam-5802	115	8	∩	∩	ADJ
ejpam-5802	115	9	vd	vd	NOUN
ejpam-5802	115	10	.	.	PUNCT
ejpam-5802	116	1	=	=	SYM
ejpam-5802	116	2	θ	θ	PROPN
ejpam-5802	116	3	,	,	PUNCT
ejpam-5802	116	4	for	for	ADP
ejpam-5802	116	5	all	all	DET
ejpam-5802	116	6	i=	i=	PROPN
ejpam-5802	116	7	1,2,	1,2,	NUM
ejpam-5802	116	8	...	...	PUNCT
ejpam-5802	116	9	,n	,n	PUNCT
ejpam-5802	116	10	.	.	PUNCT
ejpam-5802	117	1	definition	definition	NOUN
ejpam-5802	117	2	12.1	12.1	NUM
ejpam-5802	117	3	:	:	PUNCT
ejpam-5802	117	4	a	a	DET
ejpam-5802	117	5	nth	nth	ADJ
ejpam-5802	117	6	-	-	ADJ
ejpam-5802	117	7	topological	topological	ADJ
ejpam-5802	117	8	space	space	NOUN
ejpam-5802	117	9	(	(	PUNCT
ejpam-5802	117	10	k	k	PROPN
ejpam-5802	117	11	,	,	PUNCT
ejpam-5802	117	12	η1,η2,	η1,η2,	PROPN
ejpam-5802	117	13	...	...	PUNCT
ejpam-5802	117	14	,ηn	,ηn	PUNCT
ejpam-5802	117	15	)	)	PUNCT
ejpam-5802	117	16	is	be	AUX
ejpam-5802	117	17	t2	t2	NOUN
ejpam-5802	117	18	1	1	NUM
ejpam-5802	117	19	2	2	NUM
ejpam-5802	117	20	-space	-space	NOUN
ejpam-5802	117	21	,	,	PUNCT
ejpam-5802	117	22	if	if	SCONJ
ejpam-5802	117	23	for	for	ADP
ejpam-5802	117	24	all	all	DET
ejpam-5802	117	25	c	c	NOUN
ejpam-5802	117	26	̸=	̸=	PROPN
ejpam-5802	117	27	d	d	PROPN
ejpam-5802	117	28	in	in	ADP
ejpam-5802	117	29	k	k	NOUN
ejpam-5802	117	30	there	there	PRON
ejpam-5802	117	31	exists	exist	VERB
ejpam-5802	117	32	ηi	ηi	NOUN
ejpam-5802	117	33	-	-	PUNCT
ejpam-5802	117	34	closed	close	VERB
ejpam-5802	117	35	set	set	VERB
ejpam-5802	117	36	ac	ac	PROPN
ejpam-5802	118	1	and	and	CCONJ
ejpam-5802	118	2	there	there	PRON
ejpam-5802	118	3	exists	exist	VERB
ejpam-5802	119	1	ηi	ηi	NOUN
ejpam-5802	119	2	-	-	PUNCT
ejpam-5802	119	3	closed	close	VERB
ejpam-5802	119	4	set	set	NOUN
ejpam-5802	119	5	bd	bd	PROPN
ejpam-5802	119	6	in	in	ADP
ejpam-5802	119	7	k	k	PROPN
ejpam-5802	119	8	,	,	PUNCT
ejpam-5802	119	9	such	such	ADJ
ejpam-5802	119	10	that	that	SCONJ
ejpam-5802	119	11	c	c	PROPN
ejpam-5802	119	12	∈	∈	PROPN
ejpam-5802	119	13	ac	ac	PROPN
ejpam-5802	119	14	,	,	PUNCT
ejpam-5802	119	15	d	d	PROPN
ejpam-5802	119	16	∈	∈	PROPN
ejpam-5802	119	17	bd	bd	PROPN
ejpam-5802	119	18	and	and	CCONJ
ejpam-5802	119	19	ac	ac	PROPN
ejpam-5802	119	20	∩	∩	PROPN
ejpam-5802	119	21	bd	bd	PROPN
ejpam-5802	119	22	=	=	SYM
ejpam-5802	119	23	θ	θ	PROPN
ejpam-5802	119	24	,	,	PUNCT
ejpam-5802	119	25	for	for	ADP
ejpam-5802	119	26	all	all	DET
ejpam-5802	119	27	i=	i=	PROPN
ejpam-5802	119	28	1,2,	1,2,	NUM
ejpam-5802	119	29	...	...	PUNCT
ejpam-5802	119	30	,n	,n	PUNCT
ejpam-5802	119	31	.	.	PUNCT
ejpam-5802	120	1	definition	definition	NOUN
ejpam-5802	120	2	13.1	13.1	NUM
ejpam-5802	120	3	:	:	PUNCT
ejpam-5802	120	4	a	a	DET
ejpam-5802	120	5	nth	nth	ADJ
ejpam-5802	120	6	-	-	ADJ
ejpam-5802	120	7	topological	topological	ADJ
ejpam-5802	120	8	space	space	NOUN
ejpam-5802	120	9	(	(	PUNCT
ejpam-5802	120	10	k	k	PROPN
ejpam-5802	120	11	,	,	PUNCT
ejpam-5802	120	12	η1,η2,	η1,η2,	PROPN
ejpam-5802	120	13	...	...	PUNCT
ejpam-5802	120	14	,ηn	,ηn	PUNCT
ejpam-5802	120	15	)	)	PUNCT
ejpam-5802	120	16	is	be	AUX
ejpam-5802	120	17	nth	nth	ADJ
ejpam-5802	120	18	-	-	ADJ
ejpam-5802	120	19	regular	regular	ADJ
ejpam-5802	120	20	space	space	NOUN
ejpam-5802	120	21	if	if	SCONJ
ejpam-5802	120	22	for	for	ADP
ejpam-5802	120	23	all	all	DET
ejpam-5802	120	24	c	c	NOUN
ejpam-5802	120	25	/∈	/∈	PUNCT
ejpam-5802	121	1	a	a	PRON
ejpam-5802	121	2	and	and	CCONJ
ejpam-5802	121	3	a	a	DET
ejpam-5802	121	4	nth	nth	NOUN
ejpam-5802	121	5	-	-	PUNCT
ejpam-5802	121	6	closed	close	VERB
ejpam-5802	121	7	set	set	NOUN
ejpam-5802	121	8	in	in	ADP
ejpam-5802	121	9	k	k	NOUN
ejpam-5802	121	10	,	,	PUNCT
ejpam-5802	121	11	there	there	PRON
ejpam-5802	121	12	exist	exist	VERB
ejpam-5802	121	13	ηi	ηi	NOUN
ejpam-5802	121	14	-	-	PUNCT
ejpam-5802	121	15	open	open	ADJ
ejpam-5802	121	16	set	set	NOUN
ejpam-5802	121	17	uc	uc	PROPN
ejpam-5802	121	18	and	and	CCONJ
ejpam-5802	121	19	ηi	ηi	NOUN
ejpam-5802	121	20	-	-	PUNCT
ejpam-5802	121	21	open	open	ADJ
ejpam-5802	121	22	set	set	VERB
ejpam-5802	121	23	va	va	NOUN
ejpam-5802	121	24	in	in	ADP
ejpam-5802	121	25	k	k	PROPN
ejpam-5802	121	26	such	such	ADJ
ejpam-5802	122	1	that	that	SCONJ
ejpam-5802	122	2	c	c	PROPN
ejpam-5802	122	3	∈	∈	PROPN
ejpam-5802	123	1	uc	uc	PROPN
ejpam-5802	123	2	,	,	PUNCT
ejpam-5802	123	3	a	a	DET
ejpam-5802	123	4	⊂	⊂	PROPN
ejpam-5802	123	5	va	va	PROPN
ejpam-5802	123	6	and	and	CCONJ
ejpam-5802	123	7	uc	uc	PROPN
ejpam-5802	123	8	∩	∩	PROPN
ejpam-5802	123	9	va	va	PROPN
ejpam-5802	123	10	.	.	PUNCT
ejpam-5802	124	1	=	=	SYM
ejpam-5802	124	2	θ	θ	PROPN
ejpam-5802	124	3	theorem	theorem	VERB
ejpam-5802	124	4	2	2	NUM
ejpam-5802	124	5	:	:	PUNCT
ejpam-5802	124	6	a	a	DET
ejpam-5802	124	7	space	space	NOUN
ejpam-5802	124	8	(	(	PUNCT
ejpam-5802	124	9	k	k	PROPN
ejpam-5802	124	10	,	,	PUNCT
ejpam-5802	124	11	η1,η2,	η1,η2,	PROPN
ejpam-5802	124	12	...	...	PUNCT
ejpam-5802	124	13	,ηn	,ηn	PUNCT
ejpam-5802	124	14	)	)	PUNCT
ejpam-5802	124	15	is	be	AUX
ejpam-5802	124	16	nth	nth	ADJ
ejpam-5802	124	17	-	-	ADJ
ejpam-5802	124	18	regular	regular	ADJ
ejpam-5802	124	19	space	space	NOUN
ejpam-5802	124	20	if	if	SCONJ
ejpam-5802	124	21	and	and	CCONJ
ejpam-5802	124	22	only	only	ADV
ejpam-5802	124	23	if	if	SCONJ
ejpam-5802	124	24	for	for	ADP
ejpam-5802	124	25	all	all	DET
ejpam-5802	124	26	m	m	NOUN
ejpam-5802	124	27	∈	∈	ADJ
ejpam-5802	124	28	um	um	INTJ
ejpam-5802	124	29	,	,	PUNCT
ejpam-5802	124	30	where	where	SCONJ
ejpam-5802	124	31	um	um	INTJ
ejpam-5802	124	32	is	be	AUX
ejpam-5802	124	33	ηi	ηi	NOUN
ejpam-5802	124	34	-	-	PUNCT
ejpam-5802	124	35	open	open	ADJ
ejpam-5802	124	36	set	set	NOUN
ejpam-5802	124	37	,	,	PUNCT
ejpam-5802	124	38	there	there	PRON
ejpam-5802	124	39	exist	exist	VERB
ejpam-5802	124	40	ηi	ηi	NOUN
ejpam-5802	124	41	-	-	PUNCT
ejpam-5802	124	42	open	open	ADJ
ejpam-5802	124	43	set	set	NOUN
ejpam-5802	124	44	wm	wm	ADP
ejpam-5802	124	45	such	such	ADJ
ejpam-5802	124	46	that	that	DET
ejpam-5802	124	47	m∈wm⊂wm⊂um	m∈wm⊂wm⊂um	NOUN
ejpam-5802	124	48	.	.	PUNCT
ejpam-5802	125	1	proof	proof	NOUN
ejpam-5802	125	2	:	:	PUNCT
ejpam-5802	125	3	(	(	PUNCT
ejpam-5802	125	4	→	→	NOUN
ejpam-5802	125	5	)	)	PUNCT
ejpam-5802	125	6	let	let	VERB
ejpam-5802	125	7	m	m	PRON
ejpam-5802	125	8	∈	∈	VERB
ejpam-5802	125	9	um	um	INTJ
ejpam-5802	125	10	,	,	PUNCT
ejpam-5802	125	11	then	then	ADV
ejpam-5802	125	12	m	m	VERB
ejpam-5802	125	13	/∈	/∈	INTJ
ejpam-5802	126	1	um	um	INTJ
ejpam-5802	126	2	c	c	INTJ
ejpam-5802	126	3	,	,	PUNCT
ejpam-5802	126	4	but	but	CCONJ
ejpam-5802	126	5	um	um	INTJ
ejpam-5802	126	6	c	c	NOUN
ejpam-5802	126	7	is	be	AUX
ejpam-5802	126	8	ηi	ηi	NOUN
ejpam-5802	126	9	-	-	PUNCT
ejpam-5802	126	10	closed	close	VERB
ejpam-5802	126	11	set	set	NOUN
ejpam-5802	126	12	,	,	PUNCT
ejpam-5802	126	13	then	then	ADV
ejpam-5802	126	14	we	we	PRON
ejpam-5802	126	15	can	can	AUX
ejpam-5802	126	16	say	say	VERB
ejpam-5802	126	17	that	that	SCONJ
ejpam-5802	126	18	um	um	INTJ
ejpam-5802	126	19	c	c	NOUN
ejpam-5802	126	20	=	=	NOUN
ejpam-5802	126	21	m.	m.	NOUN
ejpam-5802	126	22	so	so	ADV
ejpam-5802	126	23	,	,	PUNCT
ejpam-5802	126	24	by	by	ADP
ejpam-5802	126	25	definition	definition	NOUN
ejpam-5802	126	26	of	of	ADP
ejpam-5802	126	27	nth	nth	NOUN
ejpam-5802	126	28	-	-	ADJ
ejpam-5802	126	29	regular	regular	ADJ
ejpam-5802	126	30	space	space	NOUN
ejpam-5802	126	31	,	,	PUNCT
ejpam-5802	126	32	there	there	PRON
ejpam-5802	126	33	exist	exist	VERB
ejpam-5802	126	34	ηi	ηi	NOUN
ejpam-5802	126	35	-	-	PUNCT
ejpam-5802	126	36	open	open	ADJ
ejpam-5802	126	37	set	set	NOUN
ejpam-5802	126	38	wm	wm	PROPN
ejpam-5802	126	39	and	and	CCONJ
ejpam-5802	126	40	vm	vm	PROPN
ejpam-5802	126	41	such	such	ADJ
ejpam-5802	126	42	that	that	SCONJ
ejpam-5802	126	43	a	a	DET
ejpam-5802	126	44	∈	∈	PROPN
ejpam-5802	126	45	wm	wm	PROPN
ejpam-5802	126	46	,	,	PUNCT
ejpam-5802	126	47	m	m	VERB
ejpam-5802	126	48	⊂	⊂	PROPN
ejpam-5802	126	49	vm	vm	PROPN
ejpam-5802	126	50	and	and	CCONJ
ejpam-5802	126	51	wm	wm	PROPN
ejpam-5802	126	52	∩	∩	PROPN
ejpam-5802	126	53	vm	vm	PROPN
ejpam-5802	127	1	=	=	PROPN
ejpam-5802	127	2	ϕ	ϕ	PROPN
ejpam-5802	127	3	,	,	PUNCT
ejpam-5802	127	4	but	but	CCONJ
ejpam-5802	127	5	clearly	clearly	ADV
ejpam-5802	127	6	wm⊂wm	wm⊂wm	VERB
ejpam-5802	127	7	.	.	PUNCT
ejpam-5802	128	1	it	it	PRON
ejpam-5802	128	2	is	be	AUX
ejpam-5802	128	3	enough	enough	ADJ
ejpam-5802	128	4	to	to	PART
ejpam-5802	128	5	show	show	VERB
ejpam-5802	128	6	wm	wm	PROPN
ejpam-5802	129	1	⊂	⊂	PROPN
ejpam-5802	129	2	um	um	INTJ
ejpam-5802	129	3	,	,	PUNCT
ejpam-5802	129	4	now	now	ADV
ejpam-5802	129	5	wm	wm	VERB
ejpam-5802	129	6	∩	∩	ADJ
ejpam-5802	129	7	vm=ϕ	vm=ϕ	PROPN
ejpam-5802	129	8	,	,	PUNCT
ejpam-5802	129	9	then	then	ADV
ejpam-5802	129	10	we	we	PRON
ejpam-5802	129	11	can	can	AUX
ejpam-5802	129	12	say	say	VERB
ejpam-5802	129	13	that	that	PRON
ejpam-5802	129	14	wm	wm	PROPN
ejpam-5802	129	15	⊂	⊂	PROPN
ejpam-5802	129	16	vm	vm	PROPN
ejpam-5802	130	1	c	c	X
ejpam-5802	130	2	,	,	PUNCT
ejpam-5802	130	3	then	then	ADV
ejpam-5802	130	4	wm	wm	PROPN
ejpam-5802	130	5	⊂	⊂	PROPN
ejpam-5802	130	6	vmc	vmc	PROPN
ejpam-5802	130	7	=	=	PUNCT
ejpam-5802	130	8	vm	vm	PROPN
ejpam-5802	130	9	c	c	PROPN
ejpam-5802	130	10	.	.	PUNCT
ejpam-5802	131	1	so	so	ADV
ejpam-5802	131	2	,	,	PUNCT
ejpam-5802	131	3	we	we	PRON
ejpam-5802	131	4	have	have	VERB
ejpam-5802	131	5	wm	wm	PROPN
ejpam-5802	131	6	⊂	⊂	PROPN
ejpam-5802	131	7	vm	vm	PROPN
ejpam-5802	132	1	c	c	PROPN
ejpam-5802	132	2	,	,	PUNCT
ejpam-5802	132	3	but	but	CCONJ
ejpam-5802	132	4	um	um	INTJ
ejpam-5802	132	5	c=	c=	NOUN
ejpam-5802	132	6	m	m	PROPN
ejpam-5802	132	7	⊂	⊂	PROPN
ejpam-5802	132	8	vm	vm	PROPN
ejpam-5802	132	9	,	,	PUNCT
ejpam-5802	132	10	then	then	ADV
ejpam-5802	132	11	um	um	INTJ
ejpam-5802	132	12	c	c	PROPN
ejpam-5802	132	13	⊂	⊂	PROPN
ejpam-5802	132	14	vm	vm	PROPN
ejpam-5802	132	15	,	,	PUNCT
ejpam-5802	132	16	then	then	ADV
ejpam-5802	132	17	vm	vm	PROPN
ejpam-5802	133	1	c	c	PROPN
ejpam-5802	133	2	⊂	⊂	PROPN
ejpam-5802	133	3	um	um	INTJ
ejpam-5802	133	4	,	,	PUNCT
ejpam-5802	133	5	thus	thus	ADV
ejpam-5802	133	6	wm	wm	PROPN
ejpam-5802	133	7	⊂	⊂	PROPN
ejpam-5802	133	8	um	um	INTJ
ejpam-5802	133	9	.	.	PUNCT
ejpam-5802	133	10	(	(	PUNCT
ejpam-5802	133	11	←	←	PROPN
ejpam-5802	133	12	)	)	PUNCT
ejpam-5802	133	13	let	let	VERB
ejpam-5802	133	14	m	m	PRON
ejpam-5802	133	15	/∈	/∈	VERB
ejpam-5802	134	1	m	m	VERB
ejpam-5802	134	2	and	and	CCONJ
ejpam-5802	134	3	m	m	VERB
ejpam-5802	134	4	is	be	AUX
ejpam-5802	134	5	ηi	ηi	NOUN
ejpam-5802	134	6	-	-	PUNCT
ejpam-5802	134	7	open	open	ADJ
ejpam-5802	134	8	set	set	NOUN
ejpam-5802	134	9	,	,	PUNCT
ejpam-5802	134	10	then	then	ADV
ejpam-5802	134	11	m	m	VERB
ejpam-5802	134	12	∈	∈	ADJ
ejpam-5802	134	13	m	m	NOUN
ejpam-5802	134	14	c	c	NOUN
ejpam-5802	134	15	and	and	CCONJ
ejpam-5802	134	16	m	m	PROPN
ejpam-5802	134	17	c	c	NOUN
ejpam-5802	134	18	is	be	AUX
ejpam-5802	134	19	ηi	ηi	NOUN
ejpam-5802	134	20	-	-	PUNCT
ejpam-5802	134	21	open	open	ADJ
ejpam-5802	134	22	set	set	NOUN
ejpam-5802	134	23	,	,	PUNCT
ejpam-5802	134	24	then	then	ADV
ejpam-5802	134	25	by	by	SCONJ
ejpam-5802	134	26	given	give	VERB
ejpam-5802	134	27	there	there	ADV
ejpam-5802	134	28	exist	exist	VERB
ejpam-5802	134	29	ηi	ηi	NOUN
ejpam-5802	134	30	-	-	PUNCT
ejpam-5802	134	31	open	open	ADJ
ejpam-5802	134	32	set	set	NOUN
ejpam-5802	134	33	wm	wm	ADP
ejpam-5802	134	34	such	such	ADJ
ejpam-5802	135	1	that	that	SCONJ
ejpam-5802	135	2	m	m	PROPN
ejpam-5802	135	3	∈	∈	PROPN
ejpam-5802	135	4	wm	wm	PROPN
ejpam-5802	135	5	⊂	⊂	PROPN
ejpam-5802	135	6	wm	wm	PROPN
ejpam-5802	135	7	⊂	⊂	PROPN
ejpam-5802	135	8	m	m	PROPN
ejpam-5802	135	9	c.	c.	PROPN
ejpam-5802	135	10	now	now	ADV
ejpam-5802	135	11	we	we	PRON
ejpam-5802	135	12	have	have	VERB
ejpam-5802	135	13	two	two	NUM
ejpam-5802	135	14	givens	given	NOUN
ejpam-5802	135	15	,	,	PUNCT
ejpam-5802	135	16	m	m	PROPN
ejpam-5802	135	17	∈	∈	PROPN
ejpam-5802	135	18	wm	wm	PROPN
ejpam-5802	135	19	and	and	CCONJ
ejpam-5802	135	20	m	m	PROPN
ejpam-5802	135	21	⊂	⊂	PROPN
ejpam-5802	135	22	wm	wm	PROPN
ejpam-5802	135	23	c	c	PROPN
ejpam-5802	135	24	,	,	PUNCT
ejpam-5802	135	25	where	where	SCONJ
ejpam-5802	135	26	wm	wm	PROPN
ejpam-5802	135	27	and	and	CCONJ
ejpam-5802	135	28	wm	wm	PROPN
ejpam-5802	135	29	c	c	PROPN
ejpam-5802	135	30	is	be	AUX
ejpam-5802	135	31	ηi	ηi	NOUN
ejpam-5802	135	32	-	-	PUNCT
ejpam-5802	135	33	open	open	ADJ
ejpam-5802	135	34	sets	set	NOUN
ejpam-5802	135	35	,	,	PUNCT
ejpam-5802	135	36	i=1,2,	i=1,2,	NOUN
ejpam-5802	135	37	...	...	PUNCT
ejpam-5802	135	38	,n	,n	PUNCT
ejpam-5802	135	39	.	.	PUNCT
ejpam-5802	136	1	.....	.....	PUNCT
ejpam-5802	137	1	(	(	PUNCT
ejpam-5802	137	2	*	*	NOUN
ejpam-5802	137	3	)	)	PUNCT
ejpam-5802	137	4	.	.	PUNCT
ejpam-5802	138	1	it	it	PRON
ejpam-5802	138	2	is	be	AUX
ejpam-5802	138	3	enough	enough	ADJ
ejpam-5802	138	4	to	to	PART
ejpam-5802	138	5	show	show	VERB
ejpam-5802	138	6	that	that	SCONJ
ejpam-5802	138	7	wm	wm	PROPN
ejpam-5802	138	8	∩	∩	PROPN
ejpam-5802	138	9	wm	wm	PROPN
ejpam-5802	138	10	c	c	PROPN
ejpam-5802	138	11	=	=	SYM
ejpam-5802	138	12	ϕ	ϕ	PROPN
ejpam-5802	138	13	,	,	PUNCT
ejpam-5802	138	14	suppose	suppose	VERB
ejpam-5802	138	15	not	not	PART
ejpam-5802	138	16	,	,	PUNCT
ejpam-5802	138	17	then	then	ADV
ejpam-5802	138	18	there	there	PRON
ejpam-5802	138	19	exist	exist	VERB
ejpam-5802	138	20	y	y	PRON
ejpam-5802	138	21	such	such	ADJ
ejpam-5802	138	22	that	that	SCONJ
ejpam-5802	138	23	y	y	PROPN
ejpam-5802	138	24	∈	∈	PROPN
ejpam-5802	138	25	(	(	PUNCT
ejpam-5802	138	26	wm	wm	PROPN
ejpam-5802	138	27	∩	∩	PROPN
ejpam-5802	138	28	wm	wm	PROPN
ejpam-5802	138	29	c	c	PROPN
ejpam-5802	138	30	)	)	PUNCT
ejpam-5802	138	31	,	,	PUNCT
ejpam-5802	138	32	that	that	PRON
ejpam-5802	138	33	is	be	AUX
ejpam-5802	138	34	implies	imply	VERB
ejpam-5802	138	35	y	y	PROPN
ejpam-5802	138	36	∈	∈	PROPN
ejpam-5802	138	37	w	w	PROPN
ejpam-5802	138	38	and	and	CCONJ
ejpam-5802	138	39	y	y	PROPN
ejpam-5802	138	40	∈	∈	PROPN
ejpam-5802	139	1	wm	wm	PROPN
ejpam-5802	139	2	c	c	X
ejpam-5802	139	3	,	,	PUNCT
ejpam-5802	139	4	then	then	ADV
ejpam-5802	139	5	y	y	PROPN
ejpam-5802	139	6	∈	∈	PROPN
ejpam-5802	139	7	wm	wm	PROPN
ejpam-5802	139	8	and	and	CCONJ
ejpam-5802	139	9	y	y	PROPN
ejpam-5802	139	10	/∈	/∈	PUNCT
ejpam-5802	140	1	w	w	NOUN
ejpam-5802	140	2	and	and	CCONJ
ejpam-5802	140	3	y	y	PROPN
ejpam-5802	140	4	∈	∈	PROPN
ejpam-5802	140	5	wm	wm	PROPN
ejpam-5802	141	1	′	′	NOUN
ejpam-5802	141	2	,	,	PUNCT
ejpam-5802	141	3	then	then	ADV
ejpam-5802	141	4	we	we	PRON
ejpam-5802	141	5	have	have	VERB
ejpam-5802	141	6	y	y	PROPN
ejpam-5802	141	7	∈	∈	PROPN
ejpam-5802	141	8	(	(	PUNCT
ejpam-5802	141	9	wm	wm	PROPN
ejpam-5802	141	10	∩	∩	PROPN
ejpam-5802	141	11	wm	wm	PROPN
ejpam-5802	141	12	c	c	PROPN
ejpam-5802	141	13	)	)	PUNCT
ejpam-5802	141	14	that	that	PRON
ejpam-5802	141	15	is	be	AUX
ejpam-5802	141	16	contradiction	contradiction	NOUN
ejpam-5802	141	17	.	.	PUNCT
ejpam-5802	142	1	j.	j.	PROPN
ejpam-5802	142	2	oudetallah	oudetallah	PROPN
ejpam-5802	142	3	et	et	PROPN
ejpam-5802	142	4	al	al	PROPN
ejpam-5802	142	5	.	.	PUNCT
ejpam-5802	142	6	/	/	SYM
ejpam-5802	142	7	eur	eur	PROPN
ejpam-5802	142	8	.	.	PUNCT
ejpam-5802	143	1	j.	j.	PROPN
ejpam-5802	143	2	pure	pure	PROPN
ejpam-5802	143	3	appl	appl	PROPN
ejpam-5802	143	4	.	.	PROPN
ejpam-5802	143	5	math	math	PROPN
ejpam-5802	143	6	,	,	PUNCT
ejpam-5802	143	7	18	18	NUM
ejpam-5802	143	8	(	(	PUNCT
ejpam-5802	143	9	2	2	NUM
ejpam-5802	143	10	)	)	PUNCT
ejpam-5802	143	11	(	(	PUNCT
ejpam-5802	143	12	2025	2025	NUM
ejpam-5802	143	13	)	)	PUNCT
ejpam-5802	143	14	,	,	PUNCT
ejpam-5802	143	15	5802	5802	NUM
ejpam-5802	143	16	7	7	NUM
ejpam-5802	143	17	of	of	ADP
ejpam-5802	143	18	14	14	NUM
ejpam-5802	143	19	so	so	ADV
ejpam-5802	143	20	,	,	PUNCT
ejpam-5802	143	21	wm	wm	PROPN
ejpam-5802	143	22	∩	∩	PROPN
ejpam-5802	143	23	wm	wm	PROPN
ejpam-5802	143	24	c	c	PROPN
ejpam-5802	143	25	=	=	SYM
ejpam-5802	143	26	ϕ	ϕ	PROPN
ejpam-5802	143	27	.....	.....	PUNCT
ejpam-5802	143	28	(	(	PUNCT
ejpam-5802	143	29	*	*	PUNCT
ejpam-5802	143	30	*	*	PUNCT
ejpam-5802	143	31	)	)	PUNCT
ejpam-5802	143	32	by	by	ADP
ejpam-5802	143	33	(	(	PUNCT
ejpam-5802	143	34	*	*	PUNCT
ejpam-5802	143	35	)	)	PUNCT
ejpam-5802	143	36	and	and	CCONJ
ejpam-5802	143	37	(	(	PUNCT
ejpam-5802	143	38	*	*	PUNCT
ejpam-5802	143	39	*	*	PUNCT
ejpam-5802	143	40	)	)	PUNCT
ejpam-5802	144	1	we	we	PRON
ejpam-5802	144	2	have	have	VERB
ejpam-5802	144	3	,	,	PUNCT
ejpam-5802	144	4	a	a	DET
ejpam-5802	144	5	space	space	NOUN
ejpam-5802	144	6	(	(	PUNCT
ejpam-5802	144	7	k	k	PROPN
ejpam-5802	144	8	,	,	PUNCT
ejpam-5802	144	9	η1,η2,	η1,η2,	PROPN
ejpam-5802	144	10	...	...	PUNCT
ejpam-5802	144	11	,ηn	,ηn	PUNCT
ejpam-5802	144	12	)	)	PUNCT
ejpam-5802	144	13	is	be	AUX
ejpam-5802	144	14	n	n	PRON
ejpam-5802	144	15	th	th	ADV
ejpam-5802	144	16	-	-	PUNCT
ejpam-5802	144	17	regular	regular	ADJ
ejpam-5802	144	18	space	space	NOUN
ejpam-5802	144	19	.	.	PUNCT
ejpam-5802	145	1	definition	definition	NOUN
ejpam-5802	145	2	14.1	14.1	NUM
ejpam-5802	145	3	:	:	PUNCT
ejpam-5802	145	4	a	a	DET
ejpam-5802	145	5	nth	nth	ADJ
ejpam-5802	145	6	-	-	ADJ
ejpam-5802	145	7	topological	topological	ADJ
ejpam-5802	145	8	space	space	NOUN
ejpam-5802	145	9	(	(	PUNCT
ejpam-5802	145	10	k	k	PROPN
ejpam-5802	145	11	,	,	PUNCT
ejpam-5802	145	12	η1,η2,	η1,η2,	PROPN
ejpam-5802	145	13	...	...	PUNCT
ejpam-5802	145	14	,ηn	,ηn	PUNCT
ejpam-5802	145	15	)	)	PUNCT
ejpam-5802	145	16	is	be	AUX
ejpam-5802	145	17	t3	t3	NOUN
ejpam-5802	145	18	-	-	PUNCT
ejpam-5802	145	19	space	space	NOUN
ejpam-5802	145	20	if	if	SCONJ
ejpam-5802	145	21	k	k	PROPN
ejpam-5802	145	22	is	be	AUX
ejpam-5802	145	23	nthregular	nthregular	ADJ
ejpam-5802	145	24	space	space	NOUN
ejpam-5802	145	25	and	and	CCONJ
ejpam-5802	145	26	t1	t1	NOUN
ejpam-5802	145	27	-	-	NOUN
ejpam-5802	145	28	space	space	NOUN
ejpam-5802	145	29	.	.	PUNCT
ejpam-5802	146	1	definition	definition	NOUN
ejpam-5802	146	2	15.1	15.1	NUM
ejpam-5802	146	3	:	:	PUNCT
ejpam-5802	146	4	a	a	DET
ejpam-5802	146	5	nth	nth	ADJ
ejpam-5802	146	6	-	-	ADJ
ejpam-5802	146	7	topological	topological	ADJ
ejpam-5802	146	8	space	space	NOUN
ejpam-5802	146	9	(	(	PUNCT
ejpam-5802	146	10	k	k	PROPN
ejpam-5802	146	11	,	,	PUNCT
ejpam-5802	146	12	η1,η2,	η1,η2,	PROPN
ejpam-5802	146	13	...	...	PUNCT
ejpam-5802	146	14	,ηn	,ηn	PUNCT
ejpam-5802	146	15	)	)	PUNCT
ejpam-5802	146	16	is	be	AUX
ejpam-5802	146	17	nth	nth	ADJ
ejpam-5802	146	18	-	-	ADJ
ejpam-5802	146	19	normal	normal	ADJ
ejpam-5802	146	20	apace	apace	NOUN
ejpam-5802	146	21	if	if	SCONJ
ejpam-5802	146	22	for	for	ADP
ejpam-5802	146	23	all	all	DET
ejpam-5802	146	24	m	m	PROPN
ejpam-5802	146	25	,	,	PUNCT
ejpam-5802	146	26	w	w	PROPN
ejpam-5802	146	27	be	be	AUX
ejpam-5802	146	28	a	a	DET
ejpam-5802	146	29	nthclosed	nthclosed	ADJ
ejpam-5802	146	30	set	set	NOUN
ejpam-5802	146	31	in	in	ADP
ejpam-5802	146	32	k	k	PROPN
ejpam-5802	146	33	and	and	CCONJ
ejpam-5802	146	34	m	m	PROPN
ejpam-5802	146	35	∩	∩	ADJ
ejpam-5802	146	36	w	w	PROPN
ejpam-5802	146	37	=	=	SYM
ejpam-5802	146	38	θ	θ	PROPN
ejpam-5802	146	39	,	,	PUNCT
ejpam-5802	146	40	there	there	PRON
ejpam-5802	146	41	exists	exist	VERB
ejpam-5802	146	42	ηi	ηi	NOUN
ejpam-5802	146	43	-	-	PUNCT
ejpam-5802	146	44	open	open	ADJ
ejpam-5802	146	45	set	set	VERB
ejpam-5802	146	46	um	um	INTJ
ejpam-5802	146	47	and	and	CCONJ
ejpam-5802	146	48	ηi	ηi	NOUN
ejpam-5802	146	49	-	-	PUNCT
ejpam-5802	146	50	open	open	ADJ
ejpam-5802	146	51	set	set	VERB
ejpam-5802	146	52	vw	vw	PROPN
ejpam-5802	146	53	in	in	ADP
ejpam-5802	146	54	m	m	PROPN
ejpam-5802	146	55	.	.	PUNCT
ejpam-5802	147	1	such	such	ADJ
ejpam-5802	147	2	that	that	SCONJ
ejpam-5802	147	3	m	m	VERB
ejpam-5802	147	4	⊂	⊂	ADJ
ejpam-5802	147	5	um	um	INTJ
ejpam-5802	147	6	,	,	PUNCT
ejpam-5802	147	7	w	w	PROPN
ejpam-5802	147	8	⊂	⊂	PROPN
ejpam-5802	147	9	vb	vb	PROPN
ejpam-5802	147	10	and	and	CCONJ
ejpam-5802	147	11	ua	ua	PROPN
ejpam-5802	147	12	∩	∩	NOUN
ejpam-5802	147	13	vb	vb	X
ejpam-5802	147	14	.	.	PUNCT
ejpam-5802	148	1	=	=	SYM
ejpam-5802	148	2	θ	θ	PROPN
ejpam-5802	148	3	.	.	PUNCT
ejpam-5802	148	4	definition	definition	NOUN
ejpam-5802	148	5	16.1	16.1	NUM
ejpam-5802	148	6	:	:	PUNCT
ejpam-5802	148	7	a	a	DET
ejpam-5802	148	8	nthtopological	nthtopological	ADJ
ejpam-5802	148	9	space	space	NOUN
ejpam-5802	148	10	(	(	PUNCT
ejpam-5802	148	11	k	k	PROPN
ejpam-5802	148	12	,	,	PUNCT
ejpam-5802	148	13	η1,η2,	η1,η2,	PROPN
ejpam-5802	148	14	...	...	PUNCT
ejpam-5802	148	15	,ηn	,ηn	PUNCT
ejpam-5802	148	16	)	)	PUNCT
ejpam-5802	148	17	is	be	AUX
ejpam-5802	148	18	t4	t4	PROPN
ejpam-5802	148	19	-	-	PUNCT
ejpam-5802	148	20	space	space	NOUN
ejpam-5802	148	21	if	if	SCONJ
ejpam-5802	148	22	k	k	PROPN
ejpam-5802	148	23	is	be	AUX
ejpam-5802	148	24	nth	nth	ADV
ejpam-5802	148	25	normal	normal	ADJ
ejpam-5802	148	26	space	space	NOUN
ejpam-5802	148	27	and	and	CCONJ
ejpam-5802	148	28	t1	t1	NOUN
ejpam-5802	148	29	-	-	NOUN
ejpam-5802	148	30	space	space	NOUN
ejpam-5802	148	31	.	.	PUNCT
ejpam-5802	149	1	definition	definition	NOUN
ejpam-5802	149	2	17.1	17.1	NUM
ejpam-5802	149	3	:	:	PUNCT
ejpam-5802	149	4	a	a	DET
ejpam-5802	149	5	nth	nth	ADJ
ejpam-5802	149	6	-	-	ADJ
ejpam-5802	149	7	topological	topological	ADJ
ejpam-5802	149	8	space	space	NOUN
ejpam-5802	149	9	(	(	PUNCT
ejpam-5802	149	10	k	k	PROPN
ejpam-5802	149	11	,	,	PUNCT
ejpam-5802	149	12	η1,η2,	η1,η2,	PROPN
ejpam-5802	149	13	...	...	PUNCT
ejpam-5802	149	14	,ηn	,ηn	PUNCT
ejpam-5802	149	15	)	)	PUNCT
ejpam-5802	149	16	and	and	CCONJ
ejpam-5802	149	17	let	let	VERB
ejpam-5802	149	18	a	a	DET
ejpam-5802	149	19	subset	subset	NOUN
ejpam-5802	149	20	of	of	ADP
ejpam-5802	149	21	k.	k.	PROPN
ejpam-5802	149	22	the	the	DET
ejpam-5802	149	23	complement	complement	NOUN
ejpam-5802	149	24	of	of	ADP
ejpam-5802	149	25	nth	nth	NOUN
ejpam-5802	149	26	-	-	PUNCT
ejpam-5802	149	27	α	α	PRON
ejpam-5802	149	28	open	open	ADJ
ejpam-5802	149	29	set	set	NOUN
ejpam-5802	149	30	is	be	AUX
ejpam-5802	149	31	called	call	VERB
ejpam-5802	149	32	nth	nth	PROPN
ejpam-5802	149	33	-	-	PUNCT
ejpam-5802	149	34	α	α	PROPN
ejpam-5802	149	35	closed	closed	ADJ
ejpam-5802	149	36	set	set	NOUN
ejpam-5802	149	37	.	.	PUNCT
ejpam-5802	150	1	4	4	X
ejpam-5802	150	2	.	.	X
ejpam-5802	150	3	nth	nth	ADJ
ejpam-5802	150	4	-	-	ADJ
ejpam-5802	150	5	compact	compact	ADJ
ejpam-5802	150	6	space	space	NOUN
ejpam-5802	150	7	and	and	CCONJ
ejpam-5802	150	8	some	some	DET
ejpam-5802	150	9	type	type	NOUN
ejpam-5802	150	10	of	of	ADP
ejpam-5802	150	11	it	it	PRON
ejpam-5802	150	12	this	this	DET
ejpam-5802	150	13	section	section	NOUN
ejpam-5802	150	14	includes	include	VERB
ejpam-5802	150	15	several	several	ADJ
ejpam-5802	150	16	important	important	ADJ
ejpam-5802	150	17	concepts	concept	NOUN
ejpam-5802	150	18	in	in	ADP
ejpam-5802	150	19	nth	nth	ADJ
ejpam-5802	150	20	-	-	ADJ
ejpam-5802	150	21	topological	topological	ADJ
ejpam-5802	150	22	spaces	space	NOUN
ejpam-5802	150	23	.	.	PUNCT
ejpam-5802	151	1	definition	definition	NOUN
ejpam-5802	151	2	2.1	2.1	NUM
ejpam-5802	152	1	[	[	X
ejpam-5802	152	2	1	1	NUM
ejpam-5802	152	3	]	]	PUNCT
ejpam-5802	152	4	:	:	PUNCT
ejpam-5802	152	5	let	let	VERB
ejpam-5802	152	6	(	(	PUNCT
ejpam-5802	152	7	k	k	X
ejpam-5802	152	8	,	,	PUNCT
ejpam-5802	152	9	η	η	NOUN
ejpam-5802	152	10	)	)	PUNCT
ejpam-5802	152	11	be	be	VERB
ejpam-5802	152	12	a	a	DET
ejpam-5802	152	13	topological	topological	ADJ
ejpam-5802	152	14	space	space	NOUN
ejpam-5802	152	15	and	and	CCONJ
ejpam-5802	152	16	q	q	NOUN
ejpam-5802	152	17	=	=	NOUN
ejpam-5802	152	18	{	{	PUNCT
ejpam-5802	152	19	wα	wα	NOUN
ejpam-5802	152	20	:	:	PUNCT
ejpam-5802	152	21	α	α	PROPN
ejpam-5802	152	22	∈	∈	PROPN
ejpam-5802	152	23	λ	λ	PROPN
ejpam-5802	152	24	,	,	PUNCT
ejpam-5802	152	25	wα	wα	NOUN
ejpam-5802	152	26	⊂	⊂	PROPN
ejpam-5802	152	27	k	k	X
ejpam-5802	152	28	}	}	PUNCT
ejpam-5802	152	29	is	be	AUX
ejpam-5802	152	30	called	call	VERB
ejpam-5802	152	31	:	:	PUNCT
ejpam-5802	152	32	i	i	NOUN
ejpam-5802	152	33	)	)	PUNCT
ejpam-5802	152	34	cover	cover	NOUN
ejpam-5802	152	35	of	of	ADP
ejpam-5802	152	36	k	k	PRON
ejpam-5802	152	37	if	if	SCONJ
ejpam-5802	152	38	and	and	CCONJ
ejpam-5802	152	39	only	only	ADV
ejpam-5802	152	40	if	if	SCONJ
ejpam-5802	152	41	⋃	⋃	ADJ
ejpam-5802	152	42	α∈λ	α∈λ	NOUN
ejpam-5802	152	43	wα	wα	NOUN
ejpam-5802	152	44	=	=	PROPN
ejpam-5802	152	45	k.	k.	PROPN
ejpam-5802	152	46	ii	ii	PROPN
ejpam-5802	152	47	)	)	PUNCT
ejpam-5802	152	48	open	open	ADJ
ejpam-5802	152	49	cover	cover	NOUN
ejpam-5802	152	50	of	of	ADP
ejpam-5802	152	51	k	k	PROPN
ejpam-5802	152	52	if	if	SCONJ
ejpam-5802	153	1	and	and	CCONJ
ejpam-5802	153	2	only	only	ADV
ejpam-5802	153	3	if	if	SCONJ
ejpam-5802	153	4	q	q	NOUN
ejpam-5802	153	5	is	be	AUX
ejpam-5802	153	6	cover	cover	NOUN
ejpam-5802	153	7	and	and	CCONJ
ejpam-5802	153	8	wα	wα	NOUN
ejpam-5802	153	9	is	be	AUX
ejpam-5802	153	10	open	open	ADJ
ejpam-5802	153	11	set	set	VERB
ejpam-5802	153	12	,	,	PUNCT
ejpam-5802	153	13	where	where	SCONJ
ejpam-5802	153	14	α	α	PROPN
ejpam-5802	153	15	∈	∈	PROPN
ejpam-5802	153	16	λ	λ	PROPN
ejpam-5802	153	17	.	.	PUNCT
ejpam-5802	153	18	iii	iii	NOUN
ejpam-5802	153	19	)	)	PUNCT
ejpam-5802	153	20	closed	closed	ADJ
ejpam-5802	153	21	cover	cover	NOUN
ejpam-5802	153	22	of	of	ADP
ejpam-5802	153	23	k	k	PRON
ejpam-5802	153	24	if	if	SCONJ
ejpam-5802	153	25	and	and	CCONJ
ejpam-5802	153	26	only	only	ADV
ejpam-5802	153	27	if	if	SCONJ
ejpam-5802	153	28	q	q	NOUN
ejpam-5802	153	29	is	be	AUX
ejpam-5802	153	30	cover	cover	NOUN
ejpam-5802	153	31	and	and	CCONJ
ejpam-5802	153	32	wα	wα	NOUN
ejpam-5802	153	33	is	be	AUX
ejpam-5802	153	34	closed	close	VERB
ejpam-5802	153	35	set	set	VERB
ejpam-5802	153	36	,	,	PUNCT
ejpam-5802	153	37	where	where	SCONJ
ejpam-5802	153	38	α	α	PROPN
ejpam-5802	153	39	∈	∈	PROPN
ejpam-5802	153	40	λ	λ	PROPN
ejpam-5802	153	41	.	.	NOUN
ejpam-5802	153	42	iv	iv	NUM
ejpam-5802	153	43	)	)	PUNCT
ejpam-5802	153	44	c	c	NOUN
ejpam-5802	154	1	=	=	PRON
ejpam-5802	154	2	{	{	PUNCT
ejpam-5802	154	3	rγ	rγ	NOUN
ejpam-5802	154	4	:	:	PUNCT
ejpam-5802	154	5	γ	γ	PROPN
ejpam-5802	154	6	∈	∈	PROPN
ejpam-5802	154	7	γ	γ	X
ejpam-5802	154	8	}	}	PUNCT
ejpam-5802	154	9	is	be	AUX
ejpam-5802	154	10	a	a	DET
ejpam-5802	154	11	subcover	subcover	NOUN
ejpam-5802	154	12	of	of	ADP
ejpam-5802	154	13	q	q	PROPN
ejpam-5802	154	14	if	if	SCONJ
ejpam-5802	154	15	and	and	CCONJ
ejpam-5802	154	16	only	only	ADV
ejpam-5802	154	17	if	if	SCONJ
ejpam-5802	154	18	:	:	PUNCT
ejpam-5802	154	19	(	(	PUNCT
ejpam-5802	154	20	i	i	NOUN
ejpam-5802	154	21	)	)	PUNCT
ejpam-5802	154	22	c	c	PROPN
ejpam-5802	155	1	⊂	⊂	PROPN
ejpam-5802	155	2	q	q	X
ejpam-5802	155	3	(	(	PUNCT
ejpam-5802	155	4	ii	ii	NOUN
ejpam-5802	155	5	)	)	PUNCT
ejpam-5802	155	6	⋃	⋃	ADV
ejpam-5802	155	7	γ∈γ	γ∈γ	ADJ
ejpam-5802	155	8	rγ	rγ	NOUN
ejpam-5802	156	1	=	=	SYM
ejpam-5802	156	2	k	k	PROPN
ejpam-5802	156	3	a	a	DET
ejpam-5802	156	4	space	space	NOUN
ejpam-5802	156	5	(	(	PUNCT
ejpam-5802	156	6	k	k	X
ejpam-5802	156	7	,	,	PUNCT
ejpam-5802	156	8	η	η	NOUN
ejpam-5802	156	9	)	)	PUNCT
ejpam-5802	156	10	is	be	AUX
ejpam-5802	156	11	called	call	VERB
ejpam-5802	156	12	compact	compact	ADJ
ejpam-5802	156	13	space	space	NOUN
ejpam-5802	156	14	,	,	PUNCT
ejpam-5802	156	15	if	if	SCONJ
ejpam-5802	156	16	every	every	DET
ejpam-5802	156	17	open	open	ADJ
ejpam-5802	156	18	cover	cover	NOUN
ejpam-5802	156	19	of	of	ADP
ejpam-5802	156	20	k	k	PROPN
ejpam-5802	156	21	has	have	VERB
ejpam-5802	156	22	a	a	DET
ejpam-5802	156	23	finite	finite	ADJ
ejpam-5802	156	24	subcover	subcover	PROPN
ejpam-5802	156	25	.	.	PUNCT
ejpam-5802	156	26	example	example	NOUN
ejpam-5802	157	1	[	[	X
ejpam-5802	157	2	7	7	X
ejpam-5802	157	3	]	]	X
ejpam-5802	157	4	(	(	PUNCT
ejpam-5802	157	5	r	r	NOUN
ejpam-5802	157	6	,	,	PUNCT
ejpam-5802	157	7	η	η	NOUN
ejpam-5802	157	8	)	)	PUNCT
ejpam-5802	157	9	is	be	AUX
ejpam-5802	157	10	not	not	PART
ejpam-5802	157	11	compact	compact	ADJ
ejpam-5802	157	12	.	.	PUNCT
ejpam-5802	158	1	proof	proof	NOUN
ejpam-5802	158	2	:	:	PUNCT
ejpam-5802	158	3	by	by	ADP
ejpam-5802	158	4	contradiction	contradiction	NOUN
ejpam-5802	158	5	,	,	PUNCT
ejpam-5802	158	6	assume	assume	VERB
ejpam-5802	158	7	that	that	SCONJ
ejpam-5802	158	8	(	(	PUNCT
ejpam-5802	158	9	r	r	NOUN
ejpam-5802	158	10	,	,	PUNCT
ejpam-5802	158	11	ηu	ηu	NOUN
ejpam-5802	158	12	)	)	PUNCT
ejpam-5802	158	13	is	be	AUX
ejpam-5802	158	14	compact	compact	ADJ
ejpam-5802	158	15	,	,	PUNCT
ejpam-5802	158	16	so	so	CCONJ
ejpam-5802	158	17	every	every	DET
ejpam-5802	158	18	open	open	ADJ
ejpam-5802	158	19	cover	cover	NOUN
ejpam-5802	158	20	of	of	ADP
ejpam-5802	158	21	r	r	NOUN
ejpam-5802	158	22	has	have	VERB
ejpam-5802	158	23	a	a	DET
ejpam-5802	158	24	finite	finite	ADJ
ejpam-5802	158	25	subcover	subcover	NOUN
ejpam-5802	158	26	,	,	PUNCT
ejpam-5802	158	27	but	but	CCONJ
ejpam-5802	158	28	q	q	NOUN
ejpam-5802	158	29	=	=	NOUN
ejpam-5802	158	30	{	{	PUNCT
ejpam-5802	158	31	(	(	PUNCT
ejpam-5802	158	32	−n	−n	ADJ
ejpam-5802	158	33	,	,	PUNCT
ejpam-5802	158	34	n	n	CCONJ
ejpam-5802	158	35	)	)	PUNCT
ejpam-5802	158	36	:	:	PUNCT
ejpam-5802	159	1	n	n	X
ejpam-5802	159	2	=	=	SYM
ejpam-5802	159	3	1	1	NUM
ejpam-5802	159	4	,	,	PUNCT
ejpam-5802	159	5	2	2	NUM
ejpam-5802	159	6	,	,	PUNCT
ejpam-5802	159	7	3	3	NUM
ejpam-5802	159	8	,	,	PUNCT
ejpam-5802	159	9	...	...	PUNCT
ejpam-5802	159	10	}	}	PUNCT
ejpam-5802	159	11	is	be	AUX
ejpam-5802	159	12	open	open	ADJ
ejpam-5802	159	13	cover	cover	NOUN
ejpam-5802	159	14	of	of	ADP
ejpam-5802	159	15	k	k	PROPN
ejpam-5802	159	16	because	because	SCONJ
ejpam-5802	159	17	∞⋃	∞⋃	PROPN
ejpam-5802	159	18	n=1	n=1	PROPN
ejpam-5802	159	19	(	(	PUNCT
ejpam-5802	159	20	−n	−n	PROPN
ejpam-5802	159	21	,	,	PUNCT
ejpam-5802	159	22	n)=r	n)=r	PROPN
ejpam-5802	159	23	and	and	CCONJ
ejpam-5802	159	24	(	(	PUNCT
ejpam-5802	159	25	-n	-n	NOUN
ejpam-5802	159	26	,	,	PUNCT
ejpam-5802	159	27	n	n	CCONJ
ejpam-5802	159	28	)	)	PUNCT
ejpam-5802	159	29	is	be	AUX
ejpam-5802	159	30	open	open	ADJ
ejpam-5802	159	31	set	set	VERB
ejpam-5802	159	32	,	,	PUNCT
ejpam-5802	159	33	so	so	CCONJ
ejpam-5802	159	34	e	e	NOUN
ejpam-5802	159	35	has	have	VERB
ejpam-5802	159	36	a	a	DET
ejpam-5802	159	37	finite	finite	ADJ
ejpam-5802	159	38	subcover	subcover	PROPN
ejpam-5802	159	39	say	say	VERB
ejpam-5802	159	40	c={(−n1	c={(−n1	NOUN
ejpam-5802	159	41	,	,	PUNCT
ejpam-5802	159	42	n1	n1	NOUN
ejpam-5802	159	43	)	)	PUNCT
ejpam-5802	159	44	,	,	PUNCT
ejpam-5802	159	45	(	(	PUNCT
ejpam-5802	159	46	−n2	−n2	PROPN
ejpam-5802	159	47	,	,	PUNCT
ejpam-5802	159	48	n2).(−n3	n2).(−n3	ADP
ejpam-5802	159	49	,	,	PUNCT
ejpam-5802	159	50	n3	n3	NOUN
ejpam-5802	159	51	)	)	PUNCT
ejpam-5802	159	52	,	,	PUNCT
ejpam-5802	159	53	.	.	PUNCT
ejpam-5802	159	54	.	.	PUNCT
ejpam-5802	160	1	.	.	PUNCT
ejpam-5802	161	1	,	,	PUNCT
ejpam-5802	161	2	(	(	PUNCT
ejpam-5802	161	3	−nm	−nm	ADP
ejpam-5802	161	4	,	,	PUNCT
ejpam-5802	161	5	nm	nm	NOUN
ejpam-5802	161	6	)	)	PUNCT
ejpam-5802	161	7	}	}	PUNCT
ejpam-5802	161	8	,	,	PUNCT
ejpam-5802	161	9	then	then	ADV
ejpam-5802	161	10	m⋃	m⋃	PROPN
ejpam-5802	161	11	i=1	i=1	PROPN
ejpam-5802	161	12	(	(	PUNCT
ejpam-5802	161	13	−ni	−ni	PROPN
ejpam-5802	161	14	,	,	PUNCT
ejpam-5802	161	15	ni	ni	PROPN
ejpam-5802	161	16	)	)	PUNCT
ejpam-5802	161	17	=	=	SYM
ejpam-5802	161	18	r	r	NOUN
ejpam-5802	161	19	,	,	PUNCT
ejpam-5802	161	20	then	then	ADV
ejpam-5802	161	21	(	(	PUNCT
ejpam-5802	161	22	a	a	DET
ejpam-5802	161	23	,	,	PUNCT
ejpam-5802	161	24	b	b	NOUN
ejpam-5802	161	25	)	)	PUNCT
ejpam-5802	161	26	=	=	SYM
ejpam-5802	162	1	r	r	NOUN
ejpam-5802	162	2	where	where	SCONJ
ejpam-5802	162	3	a	a	DET
ejpam-5802	162	4	=	=	PUNCT
ejpam-5802	162	5	min{−ni	min{−ni	NOUN
ejpam-5802	162	6	}	}	PUNCT
ejpam-5802	162	7	i=1,	i=1,	NOUN
ejpam-5802	162	8	...	...	PUNCT
ejpam-5802	162	9	,m	,m	PUNCT
ejpam-5802	162	10	and	and	CCONJ
ejpam-5802	162	11	b	b	X
ejpam-5802	162	12	=	=	PUNCT
ejpam-5802	162	13	max{ni	max{ni	ADV
ejpam-5802	162	14	}	}	PUNCT
ejpam-5802	162	15	i=1,	i=1,	NOUN
ejpam-5802	162	16	...	...	PUNCT
ejpam-5802	162	17	,m	,m	PUNCT
ejpam-5802	162	18	,	,	PUNCT
ejpam-5802	162	19	then	then	ADV
ejpam-5802	162	20	r=(a	r=(a	VERB
ejpam-5802	162	21	,	,	PUNCT
ejpam-5802	162	22	b	b	NOUN
ejpam-5802	162	23	)	)	PUNCT
ejpam-5802	162	24	⊂	⊂	PROPN
ejpam-5802	163	1	[	[	X
ejpam-5802	163	2	a	a	X
ejpam-5802	163	3	,	,	PUNCT
ejpam-5802	163	4	b]⇒	b]⇒	PROPN
ejpam-5802	163	5	r	r	NOUN
ejpam-5802	163	6	⊂	⊂	PROPN
ejpam-5802	164	1	[	[	X
ejpam-5802	164	2	a	a	PRON
ejpam-5802	164	3	,	,	PUNCT
ejpam-5802	164	4	b	b	NOUN
ejpam-5802	164	5	]	]	X
ejpam-5802	164	6	≡	≡	PROPN
ejpam-5802	164	7	bounded	bound	VERB
ejpam-5802	164	8	set	set	NOUN
ejpam-5802	164	9	so	so	ADV
ejpam-5802	164	10	,	,	PUNCT
ejpam-5802	164	11	r	r	NOUN
ejpam-5802	164	12	is	be	AUX
ejpam-5802	164	13	bounded	bound	VERB
ejpam-5802	164	14	set	set	VERB
ejpam-5802	164	15	and	and	CCONJ
ejpam-5802	164	16	that	that	PRON
ejpam-5802	164	17	is	be	AUX
ejpam-5802	164	18	contradicted	contradict	VERB
ejpam-5802	164	19	.	.	PUNCT
ejpam-5802	165	1	∴	∴	NOUN
ejpam-5802	165	2	(	(	PUNCT
ejpam-5802	165	3	r	r	NOUN
ejpam-5802	165	4	,	,	PUNCT
ejpam-5802	165	5	ηu	ηu	NOUN
ejpam-5802	165	6	)	)	PUNCT
ejpam-5802	165	7	is	be	AUX
ejpam-5802	165	8	not	not	PART
ejpam-5802	165	9	compact	compact	ADJ
ejpam-5802	165	10	space	space	NOUN
ejpam-5802	165	11	.	.	PUNCT
ejpam-5802	166	1	j.	j.	PROPN
ejpam-5802	166	2	oudetallah	oudetallah	PROPN
ejpam-5802	166	3	et	et	PROPN
ejpam-5802	166	4	al	al	PROPN
ejpam-5802	166	5	.	.	PUNCT
ejpam-5802	166	6	/	/	SYM
ejpam-5802	166	7	eur	eur	PROPN
ejpam-5802	166	8	.	.	PUNCT
ejpam-5802	167	1	j.	j.	PROPN
ejpam-5802	167	2	pure	pure	PROPN
ejpam-5802	167	3	appl	appl	PROPN
ejpam-5802	167	4	.	.	PROPN
ejpam-5802	167	5	math	math	PROPN
ejpam-5802	167	6	,	,	PUNCT
ejpam-5802	167	7	18	18	NUM
ejpam-5802	167	8	(	(	PUNCT
ejpam-5802	167	9	2	2	NUM
ejpam-5802	167	10	)	)	PUNCT
ejpam-5802	167	11	(	(	PUNCT
ejpam-5802	167	12	2025	2025	NUM
ejpam-5802	167	13	)	)	PUNCT
ejpam-5802	167	14	,	,	PUNCT
ejpam-5802	167	15	5802	5802	NUM
ejpam-5802	167	16	8	8	NUM
ejpam-5802	167	17	of	of	ADP
ejpam-5802	167	18	14	14	NUM
ejpam-5802	167	19	definition	definition	NOUN
ejpam-5802	167	20	2.2	2.2	NUM
ejpam-5802	167	21	:	:	PUNCT
ejpam-5802	167	22	let	let	AUX
ejpam-5802	167	23	(	(	PUNCT
ejpam-5802	167	24	k	k	X
ejpam-5802	167	25	,	,	PUNCT
ejpam-5802	167	26	η1,η2,	η1,η2,	PROPN
ejpam-5802	167	27	...	...	PUNCT
ejpam-5802	167	28	,ηn	,ηn	PUNCT
ejpam-5802	167	29	)	)	PUNCT
ejpam-5802	167	30	be	be	AUX
ejpam-5802	167	31	an	an	DET
ejpam-5802	167	32	nth	nth	ADJ
ejpam-5802	167	33	-	-	ADJ
ejpam-5802	167	34	topological	topological	ADJ
ejpam-5802	167	35	space	space	NOUN
ejpam-5802	167	36	and	and	CCONJ
ejpam-5802	167	37	let	let	VERB
ejpam-5802	167	38	w	w	PROPN
ejpam-5802	167	39	subset	subset	NOUN
ejpam-5802	167	40	of	of	ADP
ejpam-5802	167	41	k	k	PROPN
ejpam-5802	167	42	is	be	AUX
ejpam-5802	167	43	called	call	VERB
ejpam-5802	167	44	an	an	DET
ejpam-5802	167	45	nth	nth	NOUN
ejpam-5802	167	46	-	-	PUNCT
ejpam-5802	167	47	α∗-open	α∗-open	NOUN
ejpam-5802	167	48	set	set	VERB
ejpam-5802	167	49	in	in	ADP
ejpam-5802	167	50	k	k	NOUN
ejpam-5802	167	51	,	,	PUNCT
ejpam-5802	167	52	if	if	SCONJ
ejpam-5802	167	53	w	w	PROPN
ejpam-5802	167	54	subset	subset	NOUN
ejpam-5802	167	55	of	of	ADP
ejpam-5802	167	56	η1	η1	NOUN
ejpam-5802	167	57	int∗(η2cl(η3int	int∗(η2cl(η3int	PROPN
ejpam-5802	167	58	∗w	∗w	PROPN
ejpam-5802	167	59	)	)	PUNCT
ejpam-5802	167	60	.	.	PUNCT
ejpam-5802	168	1	example	example	NOUN
ejpam-5802	168	2	let	let	VERB
ejpam-5802	168	3	(	(	PUNCT
ejpam-5802	168	4	k	k	X
ejpam-5802	168	5	,	,	PUNCT
ejpam-5802	168	6	η1,η2,	η1,η2,	PROPN
ejpam-5802	168	7	...	...	PUNCT
ejpam-5802	168	8	,ηn	,ηn	PUNCT
ejpam-5802	168	9	)	)	PUNCT
ejpam-5802	168	10	be	be	AUX
ejpam-5802	168	11	an	an	DET
ejpam-5802	168	12	nth	nth	ADJ
ejpam-5802	168	13	-	-	ADJ
ejpam-5802	168	14	topological	topological	ADJ
ejpam-5802	168	15	space	space	NOUN
ejpam-5802	168	16	where	where	SCONJ
ejpam-5802	168	17	k	k	NOUN
ejpam-5802	168	18	=	=	PUNCT
ejpam-5802	168	19	{	{	PUNCT
ejpam-5802	168	20	1,2,3	1,2,3	NUM
ejpam-5802	168	21	}	}	PUNCT
ejpam-5802	168	22	,	,	PUNCT
ejpam-5802	168	23	η1={ϕ,k,{1	η1={ϕ,k,{1	PROPN
ejpam-5802	168	24	}	}	PUNCT
ejpam-5802	168	25	}	}	PUNCT
ejpam-5802	168	26	,	,	PUNCT
ejpam-5802	168	27	η2={ϕ,k,{1},{1,2	η2={ϕ,k,{1},{1,2	NOUN
ejpam-5802	168	28	}	}	PUNCT
ejpam-5802	168	29	}	}	PUNCT
ejpam-5802	168	30	,	,	PUNCT
ejpam-5802	168	31	η3=	η3=	PROPN
ejpam-5802	168	32	{	{	PUNCT
ejpam-5802	168	33	ϕ,k,{1},{1,3	ϕ,k,{1},{1,3	NUM
ejpam-5802	168	34	}	}	PUNCT
ejpam-5802	168	35	}	}	PUNCT
ejpam-5802	168	36	then	then	ADV
ejpam-5802	168	37	the	the	DET
ejpam-5802	168	38	nth	nth	NOUN
ejpam-5802	168	39	-	-	PUNCT
ejpam-5802	168	40	α∗-open	α∗-open	NUM
ejpam-5802	168	41	set	set	NOUN
ejpam-5802	168	42	are	be	AUX
ejpam-5802	168	43	{	{	PUNCT
ejpam-5802	168	44	ϕ,{1},{1,2},{1,3},k	ϕ,{1},{1,2},{1,3},k	NOUN
ejpam-5802	168	45	}	}	PUNCT
ejpam-5802	168	46	.	.	PUNCT
ejpam-5802	169	1	theorem	theorem	NOUN
ejpam-5802	169	2	1	1	NUM
ejpam-5802	169	3	:	:	PUNCT
ejpam-5802	169	4	if	if	SCONJ
ejpam-5802	169	5	w	w	NOUN
ejpam-5802	169	6	is	be	AUX
ejpam-5802	169	7	nth	nth	ADV
ejpam-5802	169	8	open	open	ADJ
ejpam-5802	169	9	set	set	NOUN
ejpam-5802	169	10	,	,	PUNCT
ejpam-5802	169	11	then	then	ADV
ejpam-5802	169	12	w	w	PROPN
ejpam-5802	169	13	is	be	AUX
ejpam-5802	169	14	nth	nth	PROPN
ejpam-5802	169	15	α∗-open	α∗-open	NUM
ejpam-5802	169	16	set	set	NOUN
ejpam-5802	169	17	.	.	PUNCT
ejpam-5802	170	1	proof	proof	NOUN
ejpam-5802	170	2	:	:	PUNCT
ejpam-5802	170	3	w	w	NOUN
ejpam-5802	170	4	is	be	AUX
ejpam-5802	170	5	nth	nth	ADV
ejpam-5802	170	6	-	-	ADJ
ejpam-5802	170	7	open	open	ADJ
ejpam-5802	170	8	set	set	ADJ
ejpam-5802	170	9	⇒	⇒	PROPN
ejpam-5802	170	10	w	w	PROPN
ejpam-5802	170	11	⊂	⊂	PROPN
ejpam-5802	170	12	η1	η1	PROPN
ejpam-5802	170	13	int(η2int(η3inta	int(η2int(η3inta	PROPN
ejpam-5802	170	14	)	)	PUNCT
ejpam-5802	170	15	⇒	⇒	PROPN
ejpam-5802	170	16	w	w	PROPN
ejpam-5802	170	17	⊂	⊂	PROPN
ejpam-5802	170	18	η1	η1	PROPN
ejpam-5802	170	19	int(η2cl(η3inta	int(η2cl(η3inta	NOUN
ejpam-5802	170	20	)	)	PUNCT
ejpam-5802	170	21	⇒	⇒	NOUN
ejpam-5802	170	22	w	w	PROPN
ejpam-5802	170	23	⊂	⊂	PROPN
ejpam-5802	170	24	η1	η1	PROPN
ejpam-5802	170	25	int∗(η2cl(η3int	int∗(η2cl(η3int	NOUN
ejpam-5802	170	26	∗a	∗a	ADJ
ejpam-5802	170	27	)	)	PUNCT
ejpam-5802	170	28	.	.	PUNCT
ejpam-5802	171	1	⇒	⇒	PROPN
ejpam-5802	171	2	w	w	PROPN
ejpam-5802	171	3	is	be	AUX
ejpam-5802	171	4	nth	nth	PROPN
ejpam-5802	171	5	α∗-open	α∗-open	NUM
ejpam-5802	171	6	set	set	NOUN
ejpam-5802	171	7	.	.	PUNCT
ejpam-5802	172	1	note	note	NOUN
ejpam-5802	172	2	:	:	PUNCT
ejpam-5802	172	3	the	the	DET
ejpam-5802	172	4	converse	converse	NOUN
ejpam-5802	172	5	is	be	AUX
ejpam-5802	172	6	not	not	PART
ejpam-5802	172	7	true	true	ADJ
ejpam-5802	172	8	.	.	PUNCT
ejpam-5802	173	1	example	example	NOUN
ejpam-5802	173	2	:	:	PUNCT
ejpam-5802	173	3	let	let	VERB
ejpam-5802	173	4	(	(	PUNCT
ejpam-5802	173	5	k	k	X
ejpam-5802	173	6	,	,	PUNCT
ejpam-5802	173	7	η1,η2,	η1,η2,	PROPN
ejpam-5802	173	8	...	...	PUNCT
ejpam-5802	173	9	,ηn	,ηn	PUNCT
ejpam-5802	173	10	)	)	PUNCT
ejpam-5802	173	11	be	be	AUX
ejpam-5802	173	12	an	an	DET
ejpam-5802	173	13	nth	nth	ADJ
ejpam-5802	173	14	-	-	ADJ
ejpam-5802	173	15	topological	topological	ADJ
ejpam-5802	173	16	space	space	NOUN
ejpam-5802	173	17	where	where	SCONJ
ejpam-5802	173	18	k	k	NOUN
ejpam-5802	173	19	=	=	PUNCT
ejpam-5802	173	20	{	{	PUNCT
ejpam-5802	173	21	1,2,3	1,2,3	NUM
ejpam-5802	173	22	}	}	PUNCT
ejpam-5802	173	23	,	,	PUNCT
ejpam-5802	173	24	η1	η1	NOUN
ejpam-5802	173	25	=	=	SYM
ejpam-5802	173	26	{	{	PUNCT
ejpam-5802	173	27	ϕ,k	ϕ,k	PROPN
ejpam-5802	173	28	,	,	PUNCT
ejpam-5802	173	29	{	{	PUNCT
ejpam-5802	173	30	1	1	NUM
ejpam-5802	173	31	}	}	PUNCT
ejpam-5802	173	32	}	}	PUNCT
ejpam-5802	173	33	,	,	PUNCT
ejpam-5802	173	34	η2	η2	PROPN
ejpam-5802	173	35	=	=	SYM
ejpam-5802	173	36	{	{	PUNCT
ejpam-5802	173	37	ϕ,k	ϕ,k	PROPN
ejpam-5802	173	38	,	,	PUNCT
ejpam-5802	173	39	{	{	PUNCT
ejpam-5802	173	40	1	1	NUM
ejpam-5802	173	41	}	}	PUNCT
ejpam-5802	173	42	,	,	PUNCT
ejpam-5802	173	43	{	{	PUNCT
ejpam-5802	173	44	1	1	NUM
ejpam-5802	173	45	,	,	PUNCT
ejpam-5802	173	46	2	2	NUM
ejpam-5802	173	47	}	}	PUNCT
ejpam-5802	173	48	}	}	PUNCT
ejpam-5802	173	49	,	,	PUNCT
ejpam-5802	173	50	η3	η3	PROPN
ejpam-5802	173	51	=	=	PUNCT
ejpam-5802	173	52	{	{	PUNCT
ejpam-5802	173	53	ϕ,k	ϕ,k	PROPN
ejpam-5802	173	54	,	,	PUNCT
ejpam-5802	173	55	{	{	PUNCT
ejpam-5802	173	56	1	1	NUM
ejpam-5802	173	57	}	}	PUNCT
ejpam-5802	173	58	,	,	PUNCT
ejpam-5802	173	59	{	{	PUNCT
ejpam-5802	173	60	1	1	NUM
ejpam-5802	173	61	,	,	PUNCT
ejpam-5802	173	62	3	3	NUM
ejpam-5802	173	63	}	}	PUNCT
ejpam-5802	173	64	}	}	PUNCT
ejpam-5802	173	65	,	,	PUNCT
ejpam-5802	173	66	then	then	ADV
ejpam-5802	173	67	:	:	PUNCT
ejpam-5802	173	68	nth	nth	PROPN
ejpam-5802	173	69	α∗-open	α∗-open	PROPN
ejpam-5802	173	70	set	set	VERB
ejpam-5802	173	71	are	be	AUX
ejpam-5802	173	72	{	{	PUNCT
ejpam-5802	173	73	ϕ,{1},{1,2},{1,3},k	ϕ,{1},{1,2},{1,3},k	NOUN
ejpam-5802	173	74	}	}	PUNCT
ejpam-5802	173	75	.	.	PUNCT
ejpam-5802	174	1	nth	nth	PROPN
ejpam-5802	175	1	α∗-closed	α∗-close	VERB
ejpam-5802	175	2	set	set	VERB
ejpam-5802	175	3	are	be	AUX
ejpam-5802	175	4	{	{	PUNCT
ejpam-5802	175	5	ϕ,{2},{3},{2,3},k	ϕ,{2},{3},{2,3},k	PROPN
ejpam-5802	175	6	}	}	PUNCT
ejpam-5802	175	7	.	.	PUNCT
ejpam-5802	176	1	w={1,2	w={1,2	PROPN
ejpam-5802	176	2	}	}	PUNCT
ejpam-5802	176	3	is	be	AUX
ejpam-5802	176	4	nth	nth	NOUN
ejpam-5802	176	5	α∗-open	α∗-open	NUM
ejpam-5802	176	6	set	set	VERB
ejpam-5802	176	7	.	.	PUNCT
ejpam-5802	177	1	but	but	CCONJ
ejpam-5802	177	2	,	,	PUNCT
ejpam-5802	177	3	w={1,2	w={1,2	NOUN
ejpam-5802	177	4	}	}	PUNCT
ejpam-5802	177	5	is	be	AUX
ejpam-5802	177	6	not	not	PART
ejpam-5802	177	7	nth	nth	ADV
ejpam-5802	177	8	open	open	ADJ
ejpam-5802	177	9	set	set	NOUN
ejpam-5802	177	10	.	.	PUNCT
ejpam-5802	178	1	definition	definition	NOUN
ejpam-5802	178	2	3.2	3.2	NUM
ejpam-5802	178	3	:	:	PUNCT
ejpam-5802	178	4	let	let	VERB
ejpam-5802	178	5	(	(	PUNCT
ejpam-5802	178	6	k	k	X
ejpam-5802	178	7	,	,	PUNCT
ejpam-5802	178	8	η1,η2,	η1,η2,	PROPN
ejpam-5802	178	9	...	...	PUNCT
ejpam-5802	178	10	,ηn	,ηn	PUNCT
ejpam-5802	178	11	)	)	PUNCT
ejpam-5802	178	12	be	be	AUX
ejpam-5802	178	13	an	an	DET
ejpam-5802	178	14	nth	nth	ADJ
ejpam-5802	178	15	-	-	ADJ
ejpam-5802	178	16	topological	topological	ADJ
ejpam-5802	178	17	space	space	NOUN
ejpam-5802	178	18	and	and	CCONJ
ejpam-5802	178	19	let	let	VERB
ejpam-5802	178	20	w	w	PROPN
ejpam-5802	178	21	subset	subset	NOUN
ejpam-5802	178	22	of	of	ADP
ejpam-5802	178	23	k	k	PROPN
ejpam-5802	178	24	is	be	AUX
ejpam-5802	178	25	called	call	VERB
ejpam-5802	178	26	an	an	DET
ejpam-5802	178	27	nth	nth	ADV
ejpam-5802	178	28	-	-	PUNCT
ejpam-5802	178	29	α∗-closed	α∗-close	VERB
ejpam-5802	178	30	set	set	NOUN
ejpam-5802	178	31	in	in	ADP
ejpam-5802	178	32	k	k	PROPN
ejpam-5802	178	33	,	,	PUNCT
ejpam-5802	178	34	if	if	SCONJ
ejpam-5802	178	35	w	w	PROPN
ejpam-5802	178	36	⊃	⊃	X
ejpam-5802	178	37	η1	η1	NOUN
ejpam-5802	178	38	int∗(η2cl(η3int	int∗(η2cl(η3int	NOUN
ejpam-5802	178	39	∗a	∗a	ADJ
ejpam-5802	178	40	)	)	PUNCT
ejpam-5802	178	41	.	.	PUNCT
ejpam-5802	179	1	theorem	theorem	VERB
ejpam-5802	179	2	2	2	NUM
ejpam-5802	179	3	:	:	PUNCT
ejpam-5802	179	4	every	every	DET
ejpam-5802	179	5	nth	nth	NOUN
ejpam-5802	179	6	-	-	PUNCT
ejpam-5802	179	7	closed	closed	ADJ
ejpam-5802	179	8	set	set	NOUN
ejpam-5802	179	9	is	be	AUX
ejpam-5802	179	10	nth	nth	NOUN
ejpam-5802	179	11	α∗-closed	α∗-close	VERB
ejpam-5802	179	12	set	set	NOUN
ejpam-5802	179	13	.	.	PUNCT
ejpam-5802	180	1	proof	proof	NOUN
ejpam-5802	180	2	:	:	PUNCT
ejpam-5802	180	3	w	w	NOUN
ejpam-5802	180	4	is	be	AUX
ejpam-5802	180	5	nth	nth	ADV
ejpam-5802	180	6	-	-	PUNCT
ejpam-5802	180	7	closed	close	VERB
ejpam-5802	180	8	set	set	NOUN
ejpam-5802	180	9	implies	imply	VERB
ejpam-5802	180	10	w	w	NOUN
ejpam-5802	180	11	subset	subset	NOUN
ejpam-5802	180	12	of	of	ADP
ejpam-5802	180	13	η1	η1	NOUN
ejpam-5802	180	14	cl	cl	NOUN
ejpam-5802	180	15	η2	η2	VERB
ejpam-5802	180	16	cl	cl	NOUN
ejpam-5802	180	17	η3	η3	NOUN
ejpam-5802	180	18	cl	cl	NOUN
ejpam-5802	180	19	w	w	NOUN
ejpam-5802	180	20	implies	imply	VERB
ejpam-5802	180	21	w	w	PROPN
ejpam-5802	180	22	c	c	PROPN
ejpam-5802	180	23	⊂	⊂	X
ejpam-5802	180	24	η1	η1	PROPN
ejpam-5802	180	25	int	int	PROPN
ejpam-5802	180	26	η2	η2	VERB
ejpam-5802	180	27	int	int	NOUN
ejpam-5802	180	28	η3	η3	NOUN
ejpam-5802	180	29	int	int	VERB
ejpam-5802	180	30	w	w	PROPN
ejpam-5802	180	31	c	c	PROPN
ejpam-5802	180	32	implies	imply	VERB
ejpam-5802	180	33	w	w	PROPN
ejpam-5802	180	34	c	c	X
ejpam-5802	180	35	⊂	⊂	PROPN
ejpam-5802	180	36	η1	η1	PROPN
ejpam-5802	180	37	int∗η2	int∗η2	PROPN
ejpam-5802	180	38	int	int	NOUN
ejpam-5802	180	39	η3	η3	NOUN
ejpam-5802	180	40	int∗	int∗	PROPN
ejpam-5802	180	41	w	w	PROPN
ejpam-5802	180	42	c	c	PROPN
ejpam-5802	180	43	implies	imply	VERB
ejpam-5802	180	44	w	w	PROPN
ejpam-5802	180	45	c	c	X
ejpam-5802	180	46	⊂	⊂	X
ejpam-5802	180	47	η1	η1	PROPN
ejpam-5802	180	48	int∗	int∗	PROPN
ejpam-5802	180	49	η2	η2	VERB
ejpam-5802	180	50	clη3	clη3	VERB
ejpam-5802	180	51	int∗	int∗	PROPN
ejpam-5802	180	52	w	w	PROPN
ejpam-5802	180	53	c	c	PROPN
ejpam-5802	180	54	implies	imply	VERB
ejpam-5802	180	55	w	w	PROPN
ejpam-5802	180	56	c	c	PROPN
ejpam-5802	180	57	is	be	AUX
ejpam-5802	180	58	nth	nth	PROPN
ejpam-5802	180	59	α∗-open	α∗-open	NOUN
ejpam-5802	180	60	implies	imply	VERB
ejpam-5802	180	61	w	w	NOUN
ejpam-5802	181	1	is	be	AUX
ejpam-5802	181	2	nth	nth	ADV
ejpam-5802	181	3	α∗-closed	α∗-close	VERB
ejpam-5802	181	4	set	set	NOUN
ejpam-5802	181	5	.	.	PUNCT
ejpam-5802	182	1	definition	definition	NOUN
ejpam-5802	182	2	4.2	4.2	NUM
ejpam-5802	182	3	:	:	PUNCT
ejpam-5802	182	4	let	let	VERB
ejpam-5802	182	5	(	(	PUNCT
ejpam-5802	182	6	k	k	X
ejpam-5802	182	7	,	,	PUNCT
ejpam-5802	182	8	η1,η2,	η1,η2,	PROPN
ejpam-5802	182	9	...	...	PUNCT
ejpam-5802	182	10	,ηn	,ηn	PUNCT
ejpam-5802	182	11	)	)	PUNCT
ejpam-5802	182	12	be	be	AUX
ejpam-5802	182	13	an	an	DET
ejpam-5802	182	14	nth	nth	ADJ
ejpam-5802	182	15	-	-	ADJ
ejpam-5802	182	16	topological	topological	ADJ
ejpam-5802	182	17	space	space	NOUN
ejpam-5802	182	18	and	and	CCONJ
ejpam-5802	182	19	u	u	NOUN
ejpam-5802	182	20	=	=	NOUN
ejpam-5802	182	21	{	{	PUNCT
ejpam-5802	182	22	wα	wα	NOUN
ejpam-5802	182	23	:	:	PUNCT
ejpam-5802	182	24	α	α	PROPN
ejpam-5802	182	25	∈	∈	PROPN
ejpam-5802	182	26	λ	λ	PROPN
ejpam-5802	182	27	,	,	PUNCT
ejpam-5802	182	28	wα	wα	NOUN
ejpam-5802	182	29	⊂	⊂	PROPN
ejpam-5802	182	30	k	k	X
ejpam-5802	182	31	}	}	PUNCT
ejpam-5802	182	32	is	be	AUX
ejpam-5802	182	33	called	call	VERB
ejpam-5802	182	34	:	:	PUNCT
ejpam-5802	182	35	i	i	PRON
ejpam-5802	182	36	)	)	PUNCT
ejpam-5802	182	37	nth	nth	NOUN
ejpam-5802	182	38	-	-	PUNCT
ejpam-5802	182	39	cover	cover	NOUN
ejpam-5802	182	40	of	of	ADP
ejpam-5802	182	41	k	k	PRON
ejpam-5802	182	42	if	if	SCONJ
ejpam-5802	182	43	and	and	CCONJ
ejpam-5802	182	44	only	only	ADV
ejpam-5802	182	45	if	if	SCONJ
ejpam-5802	182	46	⋃	⋃	ADJ
ejpam-5802	182	47	α∈λ	α∈λ	NOUN
ejpam-5802	182	48	wα	wα	NOUN
ejpam-5802	182	49	=	=	PROPN
ejpam-5802	182	50	k.	k.	PROPN
ejpam-5802	182	51	ii	ii	PROPN
ejpam-5802	182	52	)	)	PUNCT
ejpam-5802	182	53	nth	nth	ADJ
ejpam-5802	182	54	-	-	ADJ
ejpam-5802	182	55	open	open	ADJ
ejpam-5802	182	56	cover	cover	NOUN
ejpam-5802	182	57	of	of	ADP
ejpam-5802	182	58	k	k	PROPN
ejpam-5802	182	59	if	if	SCONJ
ejpam-5802	182	60	and	and	CCONJ
ejpam-5802	182	61	only	only	ADV
ejpam-5802	182	62	if	if	SCONJ
ejpam-5802	182	63	u	u	NOUN
ejpam-5802	182	64	is	be	AUX
ejpam-5802	182	65	nth	nth	NOUN
ejpam-5802	182	66	-	-	PUNCT
ejpam-5802	182	67	cover	cover	NOUN
ejpam-5802	182	68	and	and	CCONJ
ejpam-5802	182	69	wα	wα	NOUN
ejpam-5802	182	70	is	be	AUX
ejpam-5802	182	71	ηi	ηi	NOUN
ejpam-5802	182	72	-	-	PUNCT
ejpam-5802	182	73	open	open	ADJ
ejpam-5802	182	74	set	set	NOUN
ejpam-5802	182	75	,	,	PUNCT
ejpam-5802	182	76	where	where	SCONJ
ejpam-5802	182	77	α	α	X
ejpam-5802	182	78	∈	∈	PROPN
ejpam-5802	182	79	λ	λ	PROPN
ejpam-5802	182	80	,	,	PUNCT
ejpam-5802	182	81	i=1,2,	i=1,2,	NOUN
ejpam-5802	182	82	...	...	PUNCT
ejpam-5802	182	83	,n	,n	PUNCT
ejpam-5802	182	84	.	.	PUNCT
ejpam-5802	182	85	iii	iii	X
ejpam-5802	182	86	)	)	PUNCT
ejpam-5802	182	87	nth	nth	NOUN
ejpam-5802	182	88	-	-	PUNCT
ejpam-5802	182	89	closed	close	VERB
ejpam-5802	182	90	cover	cover	NOUN
ejpam-5802	182	91	of	of	ADP
ejpam-5802	182	92	k	k	PROPN
ejpam-5802	182	93	if	if	SCONJ
ejpam-5802	182	94	and	and	CCONJ
ejpam-5802	182	95	only	only	ADV
ejpam-5802	182	96	if	if	SCONJ
ejpam-5802	182	97	u	u	NOUN
ejpam-5802	182	98	is	be	AUX
ejpam-5802	182	99	nth	nth	NOUN
ejpam-5802	182	100	-	-	PUNCT
ejpam-5802	182	101	cover	cover	NOUN
ejpam-5802	182	102	and	and	CCONJ
ejpam-5802	182	103	wα	wα	NOUN
ejpam-5802	182	104	is	be	AUX
ejpam-5802	182	105	ηi	ηi	NOUN
ejpam-5802	182	106	-	-	PUNCT
ejpam-5802	182	107	closed	close	VERB
ejpam-5802	182	108	set	set	NOUN
ejpam-5802	182	109	,	,	PUNCT
ejpam-5802	182	110	where	where	SCONJ
ejpam-5802	182	111	α	α	PROPN
ejpam-5802	182	112	∈	∈	PROPN
ejpam-5802	182	113	λ	λ	PROPN
ejpam-5802	182	114	,	,	PUNCT
ejpam-5802	182	115	i=1,2,	i=1,2,	NOUN
ejpam-5802	182	116	...	...	PUNCT
ejpam-5802	182	117	,n	,n	PUNCT
ejpam-5802	182	118	.	.	PUNCT
ejpam-5802	183	1	j.	j.	PROPN
ejpam-5802	183	2	oudetallah	oudetallah	PROPN
ejpam-5802	183	3	et	et	PROPN
ejpam-5802	183	4	al	al	PROPN
ejpam-5802	183	5	.	.	PUNCT
ejpam-5802	183	6	/	/	SYM
ejpam-5802	183	7	eur	eur	PROPN
ejpam-5802	183	8	.	.	PUNCT
ejpam-5802	184	1	j.	j.	PROPN
ejpam-5802	184	2	pure	pure	PROPN
ejpam-5802	184	3	appl	appl	PROPN
ejpam-5802	184	4	.	.	PROPN
ejpam-5802	184	5	math	math	PROPN
ejpam-5802	184	6	,	,	PUNCT
ejpam-5802	184	7	18	18	NUM
ejpam-5802	184	8	(	(	PUNCT
ejpam-5802	184	9	2	2	NUM
ejpam-5802	184	10	)	)	PUNCT
ejpam-5802	184	11	(	(	PUNCT
ejpam-5802	184	12	2025	2025	NUM
ejpam-5802	184	13	)	)	PUNCT
ejpam-5802	184	14	,	,	PUNCT
ejpam-5802	184	15	5802	5802	NUM
ejpam-5802	184	16	9	9	NUM
ejpam-5802	184	17	of	of	ADP
ejpam-5802	184	18	14	14	NUM
ejpam-5802	184	19	iv	iv	NOUN
ejpam-5802	184	20	)	)	PUNCT
ejpam-5802	184	21	e	e	NOUN
ejpam-5802	184	22	=	=	PRON
ejpam-5802	184	23	{	{	PUNCT
ejpam-5802	184	24	mγ	mγ	NOUN
ejpam-5802	184	25	:	:	PUNCT
ejpam-5802	184	26	γ	γ	PROPN
ejpam-5802	184	27	∈	∈	PROPN
ejpam-5802	184	28	γ	γ	X
ejpam-5802	184	29	}	}	PUNCT
ejpam-5802	184	30	is	be	AUX
ejpam-5802	184	31	a	a	DET
ejpam-5802	184	32	nthpartite	nthpartite	ADJ
ejpam-5802	184	33	subcover	subcover	NOUN
ejpam-5802	184	34	of	of	ADP
ejpam-5802	184	35	u	u	PROPN
ejpam-5802	184	36	if	if	SCONJ
ejpam-5802	184	37	and	and	CCONJ
ejpam-5802	184	38	only	only	ADV
ejpam-5802	184	39	if	if	SCONJ
ejpam-5802	184	40	:	:	PUNCT
ejpam-5802	184	41	(	(	PUNCT
ejpam-5802	184	42	a	a	X
ejpam-5802	184	43	)	)	PUNCT
ejpam-5802	184	44	e	e	NOUN
ejpam-5802	184	45	⊂	⊂	PROPN
ejpam-5802	184	46	u	u	PROPN
ejpam-5802	184	47	(	(	PUNCT
ejpam-5802	184	48	b	b	NOUN
ejpam-5802	184	49	)	)	PUNCT
ejpam-5802	184	50	⋃	⋃	ADV
ejpam-5802	184	51	γ∈γ	γ∈γ	ADJ
ejpam-5802	184	52	mγ	mγ	NOUN
ejpam-5802	184	53	=	=	SYM
ejpam-5802	184	54	k	k	PROPN
ejpam-5802	184	55	a	a	DET
ejpam-5802	184	56	space	space	NOUN
ejpam-5802	184	57	(	(	PUNCT
ejpam-5802	184	58	k	k	X
ejpam-5802	184	59	,	,	PUNCT
ejpam-5802	184	60	η1	η1	NOUN
ejpam-5802	184	61	,	,	PUNCT
ejpam-5802	184	62	η2	η2	NOUN
ejpam-5802	184	63	,	,	PUNCT
ejpam-5802	184	64	...	...	PUNCT
ejpam-5802	184	65	,	,	PUNCT
ejpam-5802	184	66	ηn	ηn	INTJ
ejpam-5802	184	67	)	)	PUNCT
ejpam-5802	184	68	is	be	AUX
ejpam-5802	184	69	called	call	VERB
ejpam-5802	184	70	nth	nth	ADJ
ejpam-5802	184	71	-	-	ADJ
ejpam-5802	184	72	compact	compact	ADJ
ejpam-5802	184	73	space	space	NOUN
ejpam-5802	184	74	,	,	PUNCT
ejpam-5802	184	75	if	if	SCONJ
ejpam-5802	184	76	every	every	DET
ejpam-5802	184	77	nth	nth	NOUN
ejpam-5802	184	78	-	-	ADJ
ejpam-5802	184	79	open	open	ADJ
ejpam-5802	184	80	cover	cover	NOUN
ejpam-5802	184	81	of	of	ADP
ejpam-5802	184	82	k	k	PROPN
ejpam-5802	184	83	has	have	VERB
ejpam-5802	184	84	a	a	DET
ejpam-5802	184	85	finite	finite	ADJ
ejpam-5802	184	86	nth	nth	PROPN
ejpam-5802	184	87	subcover	subcover	PROPN
ejpam-5802	184	88	.	.	PUNCT
ejpam-5802	185	1	example	example	NOUN
ejpam-5802	185	2	:	:	PUNCT
ejpam-5802	185	3	the	the	DET
ejpam-5802	185	4	nth	nth	ADJ
ejpam-5802	185	5	-	-	ADJ
ejpam-5802	185	6	topological	topological	ADJ
ejpam-5802	185	7	space	space	NOUN
ejpam-5802	185	8	(	(	PUNCT
ejpam-5802	185	9	r	r	NOUN
ejpam-5802	185	10	,	,	PUNCT
ejpam-5802	185	11	ηu1	ηu1	NOUN
ejpam-5802	185	12	,	,	PUNCT
ejpam-5802	185	13	ηu2	ηu2	INTJ
ejpam-5802	185	14	,	,	PUNCT
ejpam-5802	185	15	...	...	PUNCT
ejpam-5802	185	16	,	,	PUNCT
ejpam-5802	185	17	ηun	ηun	PROPN
ejpam-5802	185	18	)	)	PUNCT
ejpam-5802	185	19	is	be	AUX
ejpam-5802	185	20	not	not	PART
ejpam-5802	185	21	n	n	PRON
ejpam-5802	185	22	th	th	ADV
ejpam-5802	185	23	-	-	PUNCT
ejpam-5802	185	24	compact	compact	ADJ
ejpam-5802	185	25	space	space	NOUN
ejpam-5802	185	26	.	.	PUNCT
ejpam-5802	186	1	proof	proof	NOUN
ejpam-5802	186	2	:	:	PUNCT
ejpam-5802	186	3	by	by	ADP
ejpam-5802	186	4	contradiction	contradiction	NOUN
ejpam-5802	186	5	,	,	PUNCT
ejpam-5802	186	6	assume	assume	VERB
ejpam-5802	186	7	that	that	SCONJ
ejpam-5802	186	8	(	(	PUNCT
ejpam-5802	186	9	r	r	NOUN
ejpam-5802	186	10	,	,	PUNCT
ejpam-5802	186	11	η1	η1	NOUN
ejpam-5802	186	12	,	,	PUNCT
ejpam-5802	186	13	η2	η2	NOUN
ejpam-5802	186	14	,	,	PUNCT
ejpam-5802	186	15	...	...	PUNCT
ejpam-5802	186	16	,	,	PUNCT
ejpam-5802	186	17	ηn	ηn	INTJ
ejpam-5802	186	18	)	)	PUNCT
ejpam-5802	186	19	is	be	AUX
ejpam-5802	186	20	nth	nth	ADJ
ejpam-5802	186	21	-	-	ADJ
ejpam-5802	186	22	compact	compact	ADJ
ejpam-5802	186	23	,	,	PUNCT
ejpam-5802	186	24	so	so	CCONJ
ejpam-5802	186	25	every	every	DET
ejpam-5802	186	26	nth	nth	NOUN
ejpam-5802	186	27	-	-	ADJ
ejpam-5802	186	28	open	open	ADJ
ejpam-5802	186	29	cover	cover	NOUN
ejpam-5802	186	30	of	of	ADP
ejpam-5802	186	31	r	r	NOUN
ejpam-5802	186	32	has	have	VERB
ejpam-5802	186	33	a	a	DET
ejpam-5802	186	34	finite	finite	NOUN
ejpam-5802	186	35	nth	nth	PROPN
ejpam-5802	186	36	subcover	subcover	PROPN
ejpam-5802	186	37	,	,	PUNCT
ejpam-5802	186	38	but	but	CCONJ
ejpam-5802	187	1	e	e	X
ejpam-5802	187	2	=	=	PRON
ejpam-5802	187	3	{	{	PUNCT
ejpam-5802	187	4	(	(	PUNCT
ejpam-5802	187	5	−n	−n	ADJ
ejpam-5802	187	6	,	,	PUNCT
ejpam-5802	187	7	n	n	CCONJ
ejpam-5802	187	8	)	)	PUNCT
ejpam-5802	187	9	:	:	PUNCT
ejpam-5802	188	1	n	n	X
ejpam-5802	188	2	=	=	SYM
ejpam-5802	188	3	1	1	NUM
ejpam-5802	188	4	,	,	PUNCT
ejpam-5802	188	5	2	2	NUM
ejpam-5802	188	6	,	,	PUNCT
ejpam-5802	188	7	3	3	NUM
ejpam-5802	188	8	,	,	PUNCT
ejpam-5802	188	9	...	...	PUNCT
ejpam-5802	188	10	}	}	PUNCT
ejpam-5802	188	11	is	be	AUX
ejpam-5802	188	12	nth	nth	ADV
ejpam-5802	188	13	-	-	ADJ
ejpam-5802	188	14	open	open	ADJ
ejpam-5802	188	15	cover	cover	NOUN
ejpam-5802	188	16	of	of	ADP
ejpam-5802	188	17	k	k	PROPN
ejpam-5802	188	18	because	because	SCONJ
ejpam-5802	188	19	∞⋃	∞⋃	PROPN
ejpam-5802	188	20	n=1	n=1	PROPN
ejpam-5802	188	21	(	(	PUNCT
ejpam-5802	188	22	−n	−n	PROPN
ejpam-5802	188	23	,	,	PUNCT
ejpam-5802	188	24	n)=r	n)=r	PROPN
ejpam-5802	188	25	and	and	CCONJ
ejpam-5802	188	26	(	(	PUNCT
ejpam-5802	188	27	-n	-n	NOUN
ejpam-5802	188	28	,	,	PUNCT
ejpam-5802	188	29	n	n	CCONJ
ejpam-5802	188	30	)	)	PUNCT
ejpam-5802	188	31	is	be	AUX
ejpam-5802	188	32	ηui	ηui	NOUN
ejpam-5802	188	33	-	-	PUNCT
ejpam-5802	188	34	open	open	NOUN
ejpam-5802	188	35	set	set	NOUN
ejpam-5802	188	36	,	,	PUNCT
ejpam-5802	188	37	i=1,2,	i=1,2,	NOUN
ejpam-5802	188	38	...	...	PUNCT
ejpam-5802	188	39	,n	,n	PUNCT
ejpam-5802	188	40	,	,	PUNCT
ejpam-5802	188	41	so	so	CCONJ
ejpam-5802	188	42	e	e	NOUN
ejpam-5802	188	43	has	have	VERB
ejpam-5802	188	44	a	a	DET
ejpam-5802	188	45	finite	finite	ADJ
ejpam-5802	188	46	nth	nth	PROPN
ejpam-5802	188	47	-	-	PROPN
ejpam-5802	188	48	subcover	subcover	PROPN
ejpam-5802	188	49	say	say	VERB
ejpam-5802	188	50	c={(−n1	c={(−n1	NOUN
ejpam-5802	188	51	,	,	PUNCT
ejpam-5802	188	52	n1	n1	NOUN
ejpam-5802	188	53	)	)	PUNCT
ejpam-5802	188	54	,	,	PUNCT
ejpam-5802	188	55	(	(	PUNCT
ejpam-5802	188	56	−n2	−n2	PROPN
ejpam-5802	188	57	,	,	PUNCT
ejpam-5802	188	58	n2).(−n3	n2).(−n3	ADP
ejpam-5802	188	59	,	,	PUNCT
ejpam-5802	188	60	n3	n3	NOUN
ejpam-5802	188	61	)	)	PUNCT
ejpam-5802	188	62	,	,	PUNCT
ejpam-5802	188	63	...	...	PUNCT
ejpam-5802	188	64	,	,	PUNCT
ejpam-5802	188	65	(	(	PUNCT
ejpam-5802	188	66	−nm	−nm	ADP
ejpam-5802	188	67	,	,	PUNCT
ejpam-5802	188	68	nm	nm	NOUN
ejpam-5802	188	69	)	)	PUNCT
ejpam-5802	188	70	}	}	PUNCT
ejpam-5802	188	71	,	,	PUNCT
ejpam-5802	188	72	then	then	ADV
ejpam-5802	188	73	m⋃	m⋃	PROPN
ejpam-5802	188	74	i=1	i=1	PROPN
ejpam-5802	188	75	(	(	PUNCT
ejpam-5802	188	76	−ni	−ni	PROPN
ejpam-5802	188	77	,	,	PUNCT
ejpam-5802	188	78	ni	ni	PROPN
ejpam-5802	188	79	)	)	PUNCT
ejpam-5802	188	80	=	=	SYM
ejpam-5802	188	81	r	r	NOUN
ejpam-5802	188	82	,	,	PUNCT
ejpam-5802	188	83	then	then	ADV
ejpam-5802	188	84	(	(	PUNCT
ejpam-5802	188	85	x	x	X
ejpam-5802	188	86	,	,	PUNCT
ejpam-5802	188	87	y	y	NOUN
ejpam-5802	188	88	)	)	PUNCT
ejpam-5802	188	89	=	=	SYM
ejpam-5802	189	1	r	r	NOUN
ejpam-5802	189	2	where	where	SCONJ
ejpam-5802	189	3	x	x	X
ejpam-5802	189	4	=	=	SYM
ejpam-5802	189	5	min{−ni	min{−ni	PROPN
ejpam-5802	189	6	}	}	PUNCT
ejpam-5802	189	7	i=1,	i=1,	NOUN
ejpam-5802	189	8	...	...	PUNCT
ejpam-5802	189	9	,m	,m	PUNCT
ejpam-5802	189	10	and	and	CCONJ
ejpam-5802	189	11	y	y	PROPN
ejpam-5802	189	12	=	=	PUNCT
ejpam-5802	189	13	max{ni	max{ni	ADV
ejpam-5802	189	14	}	}	PUNCT
ejpam-5802	189	15	i=1,	i=1,	NOUN
ejpam-5802	189	16	...	...	PUNCT
ejpam-5802	189	17	,k	,k	PUNCT
ejpam-5802	189	18	,	,	PUNCT
ejpam-5802	189	19	then	then	ADV
ejpam-5802	189	20	r=(x	r=(x	PROPN
ejpam-5802	189	21	,	,	PUNCT
ejpam-5802	189	22	y	y	NOUN
ejpam-5802	189	23	)	)	PUNCT
ejpam-5802	189	24	⊂	⊂	PROPN
ejpam-5802	190	1	[	[	X
ejpam-5802	190	2	x	x	X
ejpam-5802	190	3	,	,	PUNCT
ejpam-5802	190	4	y	y	PROPN
ejpam-5802	190	5	]	]	PUNCT
ejpam-5802	190	6	⇒	⇒	NOUN
ejpam-5802	190	7	r⊂	r⊂	PROPN
ejpam-5802	191	1	[	[	X
ejpam-5802	191	2	x	x	X
ejpam-5802	191	3	,	,	PUNCT
ejpam-5802	191	4	y]≡	y]≡	PROPN
ejpam-5802	191	5	bounded	bound	VERB
ejpam-5802	191	6	set	set	VERB
ejpam-5802	191	7	so	so	ADV
ejpam-5802	191	8	,	,	PUNCT
ejpam-5802	191	9	r	r	NOUN
ejpam-5802	191	10	is	be	AUX
ejpam-5802	191	11	bounded	bound	VERB
ejpam-5802	191	12	set	set	VERB
ejpam-5802	191	13	and	and	CCONJ
ejpam-5802	191	14	that	that	PRON
ejpam-5802	191	15	is	be	AUX
ejpam-5802	191	16	contradicted.∴	contradicted.∴	X
ejpam-5802	191	17	(	(	PUNCT
ejpam-5802	191	18	r	r	NOUN
ejpam-5802	191	19	,	,	PUNCT
ejpam-5802	191	20	ηu1	ηu1	NOUN
ejpam-5802	191	21	,	,	PUNCT
ejpam-5802	191	22	ηu2	ηu2	INTJ
ejpam-5802	191	23	,	,	PUNCT
ejpam-5802	191	24	...	...	PUNCT
ejpam-5802	191	25	,	,	PUNCT
ejpam-5802	191	26	ηun	ηun	PROPN
ejpam-5802	191	27	)	)	PUNCT
ejpam-5802	191	28	is	be	AUX
ejpam-5802	191	29	not	not	PART
ejpam-5802	191	30	nth	nth	ADJ
ejpam-5802	191	31	-	-	ADJ
ejpam-5802	191	32	compact	compact	ADJ
ejpam-5802	191	33	space	space	NOUN
ejpam-5802	191	34	.	.	PUNCT
ejpam-5802	192	1	theorem	theorem	NOUN
ejpam-5802	192	2	3	3	NUM
ejpam-5802	192	3	:	:	PUNCT
ejpam-5802	192	4	let	let	VERB
ejpam-5802	192	5	(	(	PUNCT
ejpam-5802	192	6	k	k	X
ejpam-5802	192	7	,	,	PUNCT
ejpam-5802	192	8	η	η	NOUN
ejpam-5802	192	9	)	)	PUNCT
ejpam-5802	192	10	be	be	VERB
ejpam-5802	192	11	a	a	DET
ejpam-5802	192	12	topological	topological	ADJ
ejpam-5802	192	13	space	space	NOUN
ejpam-5802	192	14	and	and	CCONJ
ejpam-5802	192	15	u	u	NOUN
ejpam-5802	192	16	⊂	⊂	PROPN
ejpam-5802	192	17	k	k	PROPN
ejpam-5802	192	18	,	,	PUNCT
ejpam-5802	192	19	then	then	ADV
ejpam-5802	192	20	u	u	NOUN
ejpam-5802	192	21	is	be	AUX
ejpam-5802	192	22	compact	compact	ADJ
ejpam-5802	192	23	space	space	NOUN
ejpam-5802	192	24	if	if	SCONJ
ejpam-5802	193	1	and	and	CCONJ
ejpam-5802	193	2	only	only	ADV
ejpam-5802	193	3	if	if	SCONJ
ejpam-5802	193	4	u	u	NOUN
ejpam-5802	193	5	is	be	AUX
ejpam-5802	193	6	closed	close	VERB
ejpam-5802	193	7	set	set	VERB
ejpam-5802	193	8	and	and	CCONJ
ejpam-5802	193	9	bounded	bound	VERB
ejpam-5802	193	10	set	set	PROPN
ejpam-5802	193	11	.	.	PUNCT
ejpam-5802	194	1	theorem	theorem	VERB
ejpam-5802	194	2	4	4	NUM
ejpam-5802	194	3	:	:	PUNCT
ejpam-5802	194	4	let	let	VERB
ejpam-5802	194	5	(	(	PUNCT
ejpam-5802	194	6	k	k	X
ejpam-5802	194	7	,	,	PUNCT
ejpam-5802	194	8	η1,η2,	η1,η2,	PROPN
ejpam-5802	194	9	...	...	PUNCT
ejpam-5802	194	10	,ηn	,ηn	PUNCT
ejpam-5802	194	11	)	)	PUNCT
ejpam-5802	194	12	be	be	AUX
ejpam-5802	194	13	a	a	DET
ejpam-5802	194	14	nth	nth	NOUN
ejpam-5802	194	15	topological	topological	ADJ
ejpam-5802	194	16	space	space	NOUN
ejpam-5802	194	17	and	and	CCONJ
ejpam-5802	194	18	u	u	NOUN
ejpam-5802	194	19	⊂	⊂	PROPN
ejpam-5802	194	20	k	k	PROPN
ejpam-5802	194	21	,	,	PUNCT
ejpam-5802	194	22	then	then	ADV
ejpam-5802	194	23	u	u	NOUN
ejpam-5802	194	24	is	be	AUX
ejpam-5802	194	25	nth	nth	ADJ
ejpam-5802	194	26	-	-	ADJ
ejpam-5802	194	27	compact	compact	ADJ
ejpam-5802	194	28	space	space	NOUN
ejpam-5802	194	29	if	if	SCONJ
ejpam-5802	195	1	and	and	CCONJ
ejpam-5802	195	2	only	only	ADV
ejpam-5802	195	3	if	if	SCONJ
ejpam-5802	195	4	u	u	NOUN
ejpam-5802	195	5	is	be	AUX
ejpam-5802	195	6	ηi	ηi	NOUN
ejpam-5802	195	7	-	-	PUNCT
ejpam-5802	195	8	closed	closed	ADJ
ejpam-5802	195	9	set	set	NOUN
ejpam-5802	195	10	and	and	CCONJ
ejpam-5802	195	11	nth	nth	NOUN
ejpam-5802	195	12	-	-	PUNCT
ejpam-5802	195	13	bounded	bound	VERB
ejpam-5802	195	14	set	set	NOUN
ejpam-5802	195	15	.	.	PUNCT
ejpam-5802	196	1	proof	proof	NOUN
ejpam-5802	196	2	:	:	PUNCT
ejpam-5802	196	3	suppose	suppose	VERB
ejpam-5802	196	4	m	m	VERB
ejpam-5802	196	5	⊂	⊂	NOUN
ejpam-5802	196	6	r	r	NOUN
ejpam-5802	196	7	is	be	AUX
ejpam-5802	196	8	nth	nth	NOUN
ejpam-5802	196	9	-	-	ADJ
ejpam-5802	196	10	compact	compact	ADJ
ejpam-5802	196	11	.	.	PUNCT
ejpam-5802	197	1	for	for	ADP
ejpam-5802	197	2	each	each	DET
ejpam-5802	197	3	m	m	PROPN
ejpam-5802	197	4	∈	∈	PROPN
ejpam-5802	197	5	m	m	PRON
ejpam-5802	197	6	,	,	PUNCT
ejpam-5802	197	7	consider	consider	VERB
ejpam-5802	197	8	the	the	DET
ejpam-5802	197	9	open	open	ADJ
ejpam-5802	197	10	interval	interval	NOUN
ejpam-5802	197	11	(	(	PUNCT
ejpam-5802	197	12	m	m	NOUN
ejpam-5802	197	13	−	−	NOUN
ejpam-5802	197	14	1,m	1,m	NOUN
ejpam-5802	198	1	+	+	CCONJ
ejpam-5802	198	2	1	1	X
ejpam-5802	199	1	)	)	PUNCT
ejpam-5802	199	2	=	=	SYM
ejpam-5802	199	3	wm	wm	PROPN
ejpam-5802	199	4	.	.	PUNCT
ejpam-5802	200	1	each	each	DET
ejpam-5802	200	2	wm	wm	PROPN
ejpam-5802	200	3	is	be	AUX
ejpam-5802	200	4	ηi	ηi	NOUN
ejpam-5802	200	5	-	-	PUNCT
ejpam-5802	200	6	open	open	ADJ
ejpam-5802	200	7	in	in	ADP
ejpam-5802	200	8	r	r	NOUN
ejpam-5802	200	9	,	,	PUNCT
ejpam-5802	200	10	so	so	CCONJ
ejpam-5802	200	11	{	{	PUNCT
ejpam-5802	200	12	wm	wm	NOUN
ejpam-5802	200	13	:	:	PUNCT
ejpam-5802	200	14	m	m	VERB
ejpam-5802	200	15	∈	∈	PROPN
ejpam-5802	200	16	m	m	PRON
ejpam-5802	200	17	}	}	PUNCT
ejpam-5802	200	18	forms	form	VERB
ejpam-5802	200	19	an	an	DET
ejpam-5802	200	20	nth	nth	NOUN
ejpam-5802	200	21	-	-	ADJ
ejpam-5802	200	22	open	open	ADJ
ejpam-5802	200	23	cover	cover	NOUN
ejpam-5802	200	24	of	of	ADP
ejpam-5802	200	25	m	m	PROPN
ejpam-5802	200	26	.	.	PUNCT
ejpam-5802	201	1	since	since	SCONJ
ejpam-5802	201	2	m	m	PROPN
ejpam-5802	201	3	is	be	AUX
ejpam-5802	201	4	nth	nth	ADJ
ejpam-5802	201	5	-	-	ADJ
ejpam-5802	201	6	compact	compact	ADJ
ejpam-5802	201	7	,	,	PUNCT
ejpam-5802	201	8	there	there	PRON
ejpam-5802	201	9	exist	exist	VERB
ejpam-5802	201	10	finitely	finitely	ADV
ejpam-5802	201	11	many	many	ADJ
ejpam-5802	201	12	points	point	NOUN
ejpam-5802	201	13	m1,m2	m1,m2	PROPN
ejpam-5802	201	14	,	,	PUNCT
ejpam-5802	201	15	.	.	PUNCT
ejpam-5802	201	16	.	.	PUNCT
ejpam-5802	202	1	.	.	PUNCT
ejpam-5802	203	1	,	,	PUNCT
ejpam-5802	203	2	mn	mn	PROPN
ejpam-5802	203	3	∈m	∈m	NOUN
ejpam-5802	203	4	such	such	ADJ
ejpam-5802	203	5	that	that	SCONJ
ejpam-5802	203	6	m	m	PROPN
ejpam-5802	203	7	⊆	⊆	NUM
ejpam-5802	203	8	⋃n	⋃n	NOUN
ejpam-5802	203	9	i=1wmi	i=1wmi	NOUN
ejpam-5802	203	10	.	.	PUNCT
ejpam-5802	204	1	let	let	VERB
ejpam-5802	204	2	q	q	NOUN
ejpam-5802	204	3	=	=	SYM
ejpam-5802	204	4	max(m1,m2	max(m1,m2	NOUN
ejpam-5802	204	5	,	,	PUNCT
ejpam-5802	204	6	.	.	PUNCT
ejpam-5802	204	7	.	.	PUNCT
ejpam-5802	205	1	.	.	PUNCT
ejpam-5802	206	1	,	,	PUNCT
ejpam-5802	206	2	mn	mn	PROPN
ejpam-5802	206	3	)	)	PUNCT
ejpam-5802	206	4	and	and	CCONJ
ejpam-5802	206	5	e	e	X
ejpam-5802	206	6	=	=	SYM
ejpam-5802	206	7	min(m1,m2	min(m1,m2	PROPN
ejpam-5802	206	8	,	,	PUNCT
ejpam-5802	206	9	.	.	PUNCT
ejpam-5802	206	10	.	.	PUNCT
ejpam-5802	206	11	.	.	PUNCT
ejpam-5802	207	1	,	,	PUNCT
ejpam-5802	207	2	mn	mn	PROPN
ejpam-5802	207	3	)	)	PUNCT
ejpam-5802	207	4	.	.	PUNCT
ejpam-5802	208	1	then	then	ADV
ejpam-5802	208	2	m	m	PROPN
ejpam-5802	208	3	⊆	⊆	NUM
ejpam-5802	208	4	⋃n	⋃n	NOUN
ejpam-5802	208	5	i=1wmi	i=1wmi	NOUN
ejpam-5802	208	6	⊆	⊆	NUM
ejpam-5802	208	7	[	[	X
ejpam-5802	208	8	q	q	X
ejpam-5802	208	9	−	−	PROPN
ejpam-5802	208	10	1	1	NUM
ejpam-5802	208	11	,	,	PUNCT
ejpam-5802	208	12	q	q	X
ejpam-5802	209	1	+	+	NUM
ejpam-5802	209	2	1	1	NUM
ejpam-5802	209	3	]	]	PUNCT
ejpam-5802	209	4	,	,	PUNCT
ejpam-5802	209	5	so	so	CCONJ
ejpam-5802	209	6	y	y	PROPN
ejpam-5802	209	7	is	be	AUX
ejpam-5802	209	8	nth	nth	ADV
ejpam-5802	209	9	-	-	PUNCT
ejpam-5802	209	10	bounded	bound	VERB
ejpam-5802	209	11	.	.	PUNCT
ejpam-5802	210	1	since	since	SCONJ
ejpam-5802	210	2	m	m	PROPN
ejpam-5802	210	3	is	be	AUX
ejpam-5802	210	4	nth	nth	ADJ
ejpam-5802	210	5	-	-	ADJ
ejpam-5802	210	6	compact	compact	ADJ
ejpam-5802	210	7	in	in	ADP
ejpam-5802	210	8	the	the	DET
ejpam-5802	210	9	euclidean	euclidean	ADJ
ejpam-5802	210	10	space	space	NOUN
ejpam-5802	210	11	r	r	NOUN
ejpam-5802	210	12	(	(	PUNCT
ejpam-5802	210	13	denoted	denote	VERB
ejpam-5802	210	14	as	as	ADP
ejpam-5802	210	15	t2	t2	NOUN
ejpam-5802	210	16	space	space	NOUN
ejpam-5802	210	17	)	)	PUNCT
ejpam-5802	210	18	,	,	PUNCT
ejpam-5802	210	19	y	y	PROPN
ejpam-5802	210	20	is	be	AUX
ejpam-5802	210	21	ηi	ηi	NOUN
ejpam-5802	210	22	-	-	PUNCT
ejpam-5802	210	23	closed	close	VERB
ejpam-5802	210	24	set	set	NOUN
ejpam-5802	210	25	.	.	PUNCT
ejpam-5802	211	1	conversely	conversely	ADV
ejpam-5802	211	2	,	,	PUNCT
ejpam-5802	211	3	suppose	suppose	VERB
ejpam-5802	211	4	y	y	PROPN
ejpam-5802	211	5	is	be	AUX
ejpam-5802	211	6	ηi	ηi	NOUN
ejpam-5802	211	7	-	-	PUNCT
ejpam-5802	211	8	closed	closed	ADJ
ejpam-5802	211	9	and	and	CCONJ
ejpam-5802	211	10	nth	nth	NOUN
ejpam-5802	211	11	-	-	PUNCT
ejpam-5802	211	12	bounded	bound	VERB
ejpam-5802	211	13	in	in	ADP
ejpam-5802	211	14	r.	r.	PROPN
ejpam-5802	211	15	if	if	SCONJ
ejpam-5802	211	16	y	y	PROPN
ejpam-5802	211	17	is	be	AUX
ejpam-5802	211	18	nth	nth	NOUN
ejpam-5802	211	19	-	-	PUNCT
ejpam-5802	211	20	bounded	bounded	ADJ
ejpam-5802	211	21	,	,	PUNCT
ejpam-5802	211	22	then	then	ADV
ejpam-5802	211	23	y	y	PROPN
ejpam-5802	211	24	⊂	⊂	PROPN
ejpam-5802	212	1	[	[	X
ejpam-5802	212	2	x	x	X
ejpam-5802	212	3	,	,	PUNCT
ejpam-5802	212	4	y	y	PROPN
ejpam-5802	212	5	]	]	PUNCT
ejpam-5802	212	6	for	for	ADP
ejpam-5802	212	7	some	some	PRON
ejpam-5802	212	8	x	x	SYM
ejpam-5802	212	9	<	<	X
ejpam-5802	212	10	y	y	PROPN
ejpam-5802	212	11	in	in	ADP
ejpam-5802	212	12	r.	r.	PROPN
ejpam-5802	212	13	since	since	SCONJ
ejpam-5802	212	14	y	y	PROPN
ejpam-5802	212	15	is	be	AUX
ejpam-5802	212	16	ηi	ηi	NOUN
ejpam-5802	212	17	-	-	PUNCT
ejpam-5802	212	18	closed	closed	ADJ
ejpam-5802	212	19	in	in	ADP
ejpam-5802	212	20	the	the	DET
ejpam-5802	212	21	nth	nth	NOUN
ejpam-5802	212	22	-	-	ADJ
ejpam-5802	212	23	compact	compact	ADJ
ejpam-5802	212	24	subset	subset	NOUN
ejpam-5802	212	25	[	[	X
ejpam-5802	212	26	x	x	X
ejpam-5802	212	27	,	,	PUNCT
ejpam-5802	212	28	y	y	PROPN
ejpam-5802	212	29	]	]	X
ejpam-5802	212	30	,	,	PUNCT
ejpam-5802	212	31	then	then	ADV
ejpam-5802	212	32	y	y	PROPN
ejpam-5802	212	33	is	be	AUX
ejpam-5802	212	34	nth	nth	ADJ
ejpam-5802	212	35	-	-	ADJ
ejpam-5802	212	36	compact	compact	ADJ
ejpam-5802	212	37	set	set	NOUN
ejpam-5802	212	38	.	.	PUNCT
ejpam-5802	213	1	therefore	therefore	ADV
ejpam-5802	213	2	,	,	PUNCT
ejpam-5802	213	3	y	y	PROPN
ejpam-5802	213	4	is	be	AUX
ejpam-5802	213	5	ηi	ηi	NOUN
ejpam-5802	213	6	-	-	PUNCT
ejpam-5802	213	7	closed	closed	ADJ
ejpam-5802	213	8	and	and	CCONJ
ejpam-5802	213	9	nth	nth	NOUN
ejpam-5802	213	10	-	-	PUNCT
ejpam-5802	213	11	bounded	bound	VERB
ejpam-5802	213	12	if	if	SCONJ
ejpam-5802	213	13	and	and	CCONJ
ejpam-5802	213	14	only	only	ADV
ejpam-5802	213	15	if	if	SCONJ
ejpam-5802	213	16	m	m	NOUN
ejpam-5802	213	17	is	be	AUX
ejpam-5802	213	18	nth	nth	ADJ
ejpam-5802	213	19	-	-	ADJ
ejpam-5802	213	20	compact	compact	ADJ
ejpam-5802	213	21	.	.	PUNCT
ejpam-5802	214	1	definition	definition	NOUN
ejpam-5802	214	2	5.2	5.2	NUM
ejpam-5802	215	1	[	[	X
ejpam-5802	215	2	6	6	NUM
ejpam-5802	215	3	]	]	PUNCT
ejpam-5802	215	4	:	:	PUNCT
ejpam-5802	215	5	let	let	VERB
ejpam-5802	215	6	(	(	PUNCT
ejpam-5802	215	7	k	k	X
ejpam-5802	215	8	,	,	PUNCT
ejpam-5802	215	9	η	η	NOUN
ejpam-5802	215	10	)	)	PUNCT
ejpam-5802	215	11	be	be	VERB
ejpam-5802	215	12	a	a	DET
ejpam-5802	215	13	topological	topological	ADJ
ejpam-5802	215	14	space	space	NOUN
ejpam-5802	215	15	,	,	PUNCT
ejpam-5802	215	16	and	and	CCONJ
ejpam-5802	215	17	let	let	VERB
ejpam-5802	215	18	l	l	NOUN
ejpam-5802	215	19	be	be	AUX
ejpam-5802	215	20	a	a	DET
ejpam-5802	215	21	family	family	NOUN
ejpam-5802	215	22	of	of	ADP
ejpam-5802	215	23	subsets	subset	NOUN
ejpam-5802	215	24	of	of	ADP
ejpam-5802	215	25	k.	k.	PROPN
ejpam-5802	216	1	we	we	PRON
ejpam-5802	216	2	say	say	VERB
ejpam-5802	216	3	that	that	SCONJ
ejpam-5802	216	4	l	l	NOUN
ejpam-5802	216	5	has	have	VERB
ejpam-5802	216	6	a	a	DET
ejpam-5802	216	7	finite	finite	ADJ
ejpam-5802	216	8	intersection	intersection	NOUN
ejpam-5802	216	9	property	property	NOUN
ejpam-5802	216	10	(	(	PUNCT
ejpam-5802	216	11	f.i.p	f.i.p	ADJ
ejpam-5802	216	12	)	)	PUNCT
ejpam-5802	216	13	if	if	SCONJ
ejpam-5802	217	1	and	and	CCONJ
ejpam-5802	217	2	only	only	ADV
ejpam-5802	217	3	if	if	SCONJ
ejpam-5802	217	4	the	the	DET
ejpam-5802	217	5	intersection	intersection	NOUN
ejpam-5802	217	6	of	of	ADP
ejpam-5802	217	7	any	any	DET
ejpam-5802	217	8	finite	finite	ADJ
ejpam-5802	217	9	number	number	NOUN
ejpam-5802	217	10	of	of	ADP
ejpam-5802	217	11	members	member	NOUN
ejpam-5802	217	12	of	of	ADP
ejpam-5802	217	13	l	l	NOUN
ejpam-5802	217	14	is	be	AUX
ejpam-5802	217	15	non	non	ADJ
ejpam-5802	217	16	-	-	ADJ
ejpam-5802	217	17	empty	empty	ADJ
ejpam-5802	217	18	.	.	PUNCT
ejpam-5802	218	1	definition	definition	NOUN
ejpam-5802	218	2	6.2	6.2	NUM
ejpam-5802	218	3	:	:	PUNCT
ejpam-5802	218	4	let	let	VERB
ejpam-5802	218	5	(	(	PUNCT
ejpam-5802	218	6	k	k	X
ejpam-5802	218	7	,	,	PUNCT
ejpam-5802	218	8	η1,η2,	η1,η2,	PROPN
ejpam-5802	218	9	...	...	PUNCT
ejpam-5802	218	10	,ηn	,ηn	PUNCT
ejpam-5802	218	11	)	)	PUNCT
ejpam-5802	218	12	be	be	AUX
ejpam-5802	218	13	a	a	DET
ejpam-5802	218	14	nth	nth	ADJ
ejpam-5802	218	15	-	-	ADJ
ejpam-5802	218	16	topological	topological	ADJ
ejpam-5802	218	17	space	space	NOUN
ejpam-5802	218	18	,	,	PUNCT
ejpam-5802	218	19	and	and	CCONJ
ejpam-5802	218	20	let	let	VERB
ejpam-5802	218	21	l	l	NOUN
ejpam-5802	218	22	be	be	AUX
ejpam-5802	218	23	a	a	DET
ejpam-5802	218	24	family	family	NOUN
ejpam-5802	218	25	of	of	ADP
ejpam-5802	218	26	subsets	subset	NOUN
ejpam-5802	218	27	of	of	ADP
ejpam-5802	218	28	k.	k.	PROPN
ejpam-5802	219	1	we	we	PRON
ejpam-5802	219	2	say	say	VERB
ejpam-5802	219	3	that	that	SCONJ
ejpam-5802	219	4	l	l	NOUN
ejpam-5802	219	5	has	have	VERB
ejpam-5802	219	6	a	a	DET
ejpam-5802	219	7	finite	finite	ADJ
ejpam-5802	219	8	intersection	intersection	NOUN
ejpam-5802	219	9	property	property	NOUN
ejpam-5802	219	10	(	(	PUNCT
ejpam-5802	219	11	f.i.p	f.i.p	ADJ
ejpam-5802	219	12	)	)	PUNCT
ejpam-5802	219	13	if	if	SCONJ
ejpam-5802	219	14	and	and	CCONJ
ejpam-5802	219	15	only	only	ADV
ejpam-5802	219	16	if	if	SCONJ
ejpam-5802	219	17	the	the	DET
ejpam-5802	219	18	j.	j.	PROPN
ejpam-5802	219	19	oudetallah	oudetallah	PROPN
ejpam-5802	219	20	et	et	PROPN
ejpam-5802	219	21	al	al	PROPN
ejpam-5802	219	22	.	.	PUNCT
ejpam-5802	219	23	/	/	SYM
ejpam-5802	219	24	eur	eur	PROPN
ejpam-5802	219	25	.	.	PUNCT
ejpam-5802	220	1	j.	j.	PROPN
ejpam-5802	220	2	pure	pure	PROPN
ejpam-5802	220	3	appl	appl	PROPN
ejpam-5802	220	4	.	.	PROPN
ejpam-5802	220	5	math	math	PROPN
ejpam-5802	220	6	,	,	PUNCT
ejpam-5802	220	7	18	18	NUM
ejpam-5802	220	8	(	(	PUNCT
ejpam-5802	220	9	2	2	NUM
ejpam-5802	220	10	)	)	PUNCT
ejpam-5802	220	11	(	(	PUNCT
ejpam-5802	220	12	2025	2025	NUM
ejpam-5802	220	13	)	)	PUNCT
ejpam-5802	220	14	,	,	PUNCT
ejpam-5802	220	15	5802	5802	NUM
ejpam-5802	220	16	10	10	NUM
ejpam-5802	220	17	of	of	ADP
ejpam-5802	220	18	14	14	NUM
ejpam-5802	220	19	intersection	intersection	NOUN
ejpam-5802	220	20	of	of	ADP
ejpam-5802	220	21	any	any	DET
ejpam-5802	220	22	finite	finite	ADJ
ejpam-5802	220	23	number	number	NOUN
ejpam-5802	220	24	of	of	ADP
ejpam-5802	220	25	members	member	NOUN
ejpam-5802	220	26	of	of	ADP
ejpam-5802	220	27	l	l	NOUN
ejpam-5802	220	28	is	be	AUX
ejpam-5802	220	29	non	non	ADJ
ejpam-5802	220	30	-	-	ADJ
ejpam-5802	220	31	empty	empty	ADJ
ejpam-5802	220	32	.	.	PUNCT
ejpam-5802	221	1	theorem	theorem	NOUN
ejpam-5802	221	2	5	5	NUM
ejpam-5802	221	3	:	:	PUNCT
ejpam-5802	221	4	let	let	VERB
ejpam-5802	221	5	(	(	PUNCT
ejpam-5802	221	6	k	k	X
ejpam-5802	221	7	,	,	PUNCT
ejpam-5802	221	8	η1,η2,	η1,η2,	PROPN
ejpam-5802	221	9	...	...	PUNCT
ejpam-5802	221	10	,ηn	,ηn	PUNCT
ejpam-5802	221	11	)	)	PUNCT
ejpam-5802	221	12	be	be	AUX
ejpam-5802	221	13	a	a	DET
ejpam-5802	221	14	nth	nth	ADJ
ejpam-5802	221	15	-	-	ADJ
ejpam-5802	221	16	topological	topological	ADJ
ejpam-5802	221	17	space	space	NOUN
ejpam-5802	221	18	.	.	PUNCT
ejpam-5802	222	1	then	then	ADV
ejpam-5802	222	2	k	k	PROPN
ejpam-5802	222	3	is	be	AUX
ejpam-5802	222	4	nth	nth	ADJ
ejpam-5802	222	5	-	-	ADJ
ejpam-5802	222	6	compact	compact	ADJ
ejpam-5802	222	7	if	if	SCONJ
ejpam-5802	223	1	and	and	CCONJ
ejpam-5802	223	2	only	only	ADV
ejpam-5802	223	3	if	if	SCONJ
ejpam-5802	223	4	every	every	DET
ejpam-5802	223	5	family	family	NOUN
ejpam-5802	223	6	of	of	ADP
ejpam-5802	223	7	nth	nth	NOUN
ejpam-5802	223	8	-	-	PUNCT
ejpam-5802	223	9	closed	closed	ADJ
ejpam-5802	223	10	subsets	subset	NOUN
ejpam-5802	223	11	of	of	ADP
ejpam-5802	223	12	k	k	PROPN
ejpam-5802	223	13	with	with	ADP
ejpam-5802	223	14	the	the	DET
ejpam-5802	223	15	finite	finite	ADJ
ejpam-5802	223	16	intersection	intersection	NOUN
ejpam-5802	223	17	property	property	NOUN
ejpam-5802	223	18	(	(	PUNCT
ejpam-5802	223	19	f.i.p	f.i.p	ADV
ejpam-5802	223	20	)	)	PUNCT
ejpam-5802	223	21	has	have	VERB
ejpam-5802	223	22	a	a	DET
ejpam-5802	223	23	non	non	ADJ
ejpam-5802	223	24	-	-	ADJ
ejpam-5802	223	25	empty	empty	ADJ
ejpam-5802	223	26	intersection	intersection	NOUN
ejpam-5802	223	27	.	.	PUNCT
ejpam-5802	224	1	proof	proof	NOUN
ejpam-5802	224	2	:	:	PUNCT
ejpam-5802	224	3	suppose	suppose	VERB
ejpam-5802	224	4	k	k	PROPN
ejpam-5802	224	5	is	be	AUX
ejpam-5802	224	6	nth	nth	ADJ
ejpam-5802	224	7	-	-	ADJ
ejpam-5802	224	8	compact	compact	ADJ
ejpam-5802	224	9	space	space	NOUN
ejpam-5802	224	10	.	.	PUNCT
ejpam-5802	225	1	if	if	SCONJ
ejpam-5802	225	2	there	there	PRON
ejpam-5802	225	3	exists	exist	VERB
ejpam-5802	225	4	a	a	DET
ejpam-5802	225	5	family	family	NOUN
ejpam-5802	225	6	of	of	ADP
ejpam-5802	225	7	nth	nth	NOUN
ejpam-5802	225	8	-	-	PUNCT
ejpam-5802	225	9	closed	closed	ADJ
ejpam-5802	225	10	subsets	subset	NOUN
ejpam-5802	225	11	of	of	ADP
ejpam-5802	225	12	k	k	NOUN
ejpam-5802	225	13	,	,	PUNCT
ejpam-5802	225	14	say	say	VERB
ejpam-5802	225	15	{	{	PUNCT
ejpam-5802	225	16	wα	wα	NOUN
ejpam-5802	225	17	:	:	PUNCT
ejpam-5802	225	18	α	α	PROPN
ejpam-5802	225	19	∈	∈	PROPN
ejpam-5802	225	20	λ	λ	NOUN
ejpam-5802	225	21	}	}	PUNCT
ejpam-5802	225	22	,	,	PUNCT
ejpam-5802	225	23	with	with	ADP
ejpam-5802	225	24	f.i.p	f.i.p	ADJ
ejpam-5802	225	25	such	such	ADJ
ejpam-5802	225	26	that	that	SCONJ
ejpam-5802	225	27	⋂	⋂	PROPN
ejpam-5802	225	28	α∈λwα	α∈λwα	PROPN
ejpam-5802	225	29	=	=	SYM
ejpam-5802	225	30	∅	∅	NOUN
ejpam-5802	225	31	,	,	PUNCT
ejpam-5802	225	32	then	then	ADV
ejpam-5802	225	33	⋃	⋃	PUNCT
ejpam-5802	225	34	α∈λ(k	α∈λ(k	PROPN
ejpam-5802	225	35	\wα	\wα	PROPN
ejpam-5802	225	36	)	)	PUNCT
ejpam-5802	225	37	=	=	SYM
ejpam-5802	225	38	k	k	PROPN
ejpam-5802	225	39	\	\	PROPN
ejpam-5802	225	40	⋂	⋂	PROPN
ejpam-5802	225	41	α∈λwα	α∈λwα	PROPN
ejpam-5802	225	42	=	=	SYM
ejpam-5802	225	43	k	k	PROPN
ejpam-5802	225	44	\	\	NOUN
ejpam-5802	225	45	∅	∅	NOUN
ejpam-5802	225	46	=	=	PUNCT
ejpam-5802	225	47	k.	k.	PROPN
ejpam-5802	225	48	since	since	SCONJ
ejpam-5802	225	49	wα	wα	PROPN
ejpam-5802	225	50	is	be	AUX
ejpam-5802	225	51	ηi	ηi	NOUN
ejpam-5802	225	52	-	-	PUNCT
ejpam-5802	225	53	closed	close	VERB
ejpam-5802	225	54	set	set	NOUN
ejpam-5802	225	55	in	in	ADP
ejpam-5802	225	56	k	k	PROPN
ejpam-5802	225	57	for	for	ADP
ejpam-5802	225	58	all	all	DET
ejpam-5802	225	59	α	α	PRON
ejpam-5802	225	60	∈	∈	PROPN
ejpam-5802	225	61	λ	λ	PROPN
ejpam-5802	225	62	,	,	PUNCT
ejpam-5802	225	63	k	k	PROPN
ejpam-5802	225	64	\wα	\wα	PROPN
ejpam-5802	225	65	is	be	AUX
ejpam-5802	225	66	ηi	ηi	NOUN
ejpam-5802	225	67	-	-	PUNCT
ejpam-5802	225	68	open	open	ADJ
ejpam-5802	225	69	set	set	NOUN
ejpam-5802	225	70	in	in	ADP
ejpam-5802	225	71	k	k	PROPN
ejpam-5802	225	72	for	for	ADP
ejpam-5802	225	73	all	all	PRON
ejpam-5802	225	74	α	α	DET
ejpam-5802	225	75	∈	∈	PROPN
ejpam-5802	225	76	λ	λ	PROPN
ejpam-5802	225	77	.	.	PUNCT
ejpam-5802	226	1	therefore	therefore	ADV
ejpam-5802	226	2	,	,	PUNCT
ejpam-5802	226	3	n	n	PROPN
ejpam-5802	226	4	=	=	SYM
ejpam-5802	226	5	{	{	PUNCT
ejpam-5802	226	6	k	k	PROPN
ejpam-5802	226	7	\	\	PROPN
ejpam-5802	226	8	wα	wα	NOUN
ejpam-5802	226	9	:	:	PUNCT
ejpam-5802	226	10	α	α	PROPN
ejpam-5802	226	11	∈	∈	PROPN
ejpam-5802	226	12	λ	λ	PROPN
ejpam-5802	226	13	}	}	PUNCT
ejpam-5802	226	14	is	be	AUX
ejpam-5802	226	15	an	an	DET
ejpam-5802	226	16	nth	nth	NOUN
ejpam-5802	226	17	-	-	ADJ
ejpam-5802	226	18	open	open	ADJ
ejpam-5802	226	19	cover	cover	NOUN
ejpam-5802	226	20	of	of	ADP
ejpam-5802	226	21	k.	k.	NOUN
ejpam-5802	226	22	by	by	ADP
ejpam-5802	226	23	the	the	DET
ejpam-5802	226	24	compactness	compactness	NOUN
ejpam-5802	226	25	of	of	ADP
ejpam-5802	226	26	k	k	PROPN
ejpam-5802	226	27	,	,	PUNCT
ejpam-5802	226	28	n	n	PRON
ejpam-5802	226	29	has	have	VERB
ejpam-5802	226	30	a	a	DET
ejpam-5802	226	31	finite	finite	ADJ
ejpam-5802	226	32	subcover	subcover	NOUN
ejpam-5802	226	33	of	of	ADP
ejpam-5802	226	34	k	k	PROPN
ejpam-5802	226	35	,	,	PUNCT
ejpam-5802	226	36	say	say	VERB
ejpam-5802	226	37	{	{	PUNCT
ejpam-5802	226	38	k	k	PROPN
ejpam-5802	226	39	\wαi	\wαi	PROPN
ejpam-5802	226	40	:	:	PUNCT
ejpam-5802	226	41	i	i	NOUN
ejpam-5802	226	42	=	=	NOUN
ejpam-5802	226	43	1	1	NUM
ejpam-5802	226	44	,	,	PUNCT
ejpam-5802	226	45	2	2	NUM
ejpam-5802	226	46	,	,	PUNCT
ejpam-5802	226	47	.	.	PUNCT
ejpam-5802	226	48	.	.	PUNCT
ejpam-5802	227	1	.	.	PUNCT
ejpam-5802	227	2	,	,	PUNCT
ejpam-5802	227	3	n	n	CCONJ
ejpam-5802	227	4	}	}	PUNCT
ejpam-5802	227	5	.	.	PUNCT
ejpam-5802	228	1	thus	thus	ADV
ejpam-5802	228	2	,	,	PUNCT
ejpam-5802	228	3	k	k	PROPN
ejpam-5802	228	4	=	=	SYM
ejpam-5802	228	5	⋃n	⋃n	PROPN
ejpam-5802	228	6	i=1(k	i=1(k	NOUN
ejpam-5802	228	7	\wαi	\wαi	PROPN
ejpam-5802	228	8	)	)	PUNCT
ejpam-5802	228	9	=	=	SYM
ejpam-5802	228	10	k	k	PROPN
ejpam-5802	228	11	\	\	PROPN
ejpam-5802	228	12	⋂n	⋂n	PROPN
ejpam-5802	228	13	i=1wαi	i=1wαi	NOUN
ejpam-5802	228	14	.	.	PUNCT
ejpam-5802	229	1	this	this	PRON
ejpam-5802	229	2	contradicts	contradict	VERB
ejpam-5802	229	3	⋂	⋂	PROPN
ejpam-5802	229	4	α∈λwα	α∈λwα	PROPN
ejpam-5802	229	5	=	=	SYM
ejpam-5802	229	6	∅	∅	NOUN
ejpam-5802	229	7	,	,	PUNCT
ejpam-5802	229	8	proving	prove	VERB
ejpam-5802	229	9	that	that	SCONJ
ejpam-5802	229	10	every	every	DET
ejpam-5802	229	11	family	family	NOUN
ejpam-5802	229	12	of	of	ADP
ejpam-5802	229	13	nth	nth	NOUN
ejpam-5802	229	14	-	-	PUNCT
ejpam-5802	229	15	closed	closed	ADJ
ejpam-5802	229	16	subsets	subset	NOUN
ejpam-5802	229	17	of	of	ADP
ejpam-5802	229	18	k	k	PROPN
ejpam-5802	229	19	with	with	ADP
ejpam-5802	229	20	f.i.p	f.i.p	ADV
ejpam-5802	229	21	has	have	VERB
ejpam-5802	229	22	a	a	DET
ejpam-5802	229	23	non	non	ADJ
ejpam-5802	229	24	-	-	ADJ
ejpam-5802	229	25	empty	empty	ADJ
ejpam-5802	229	26	intersection	intersection	NOUN
ejpam-5802	229	27	.	.	PUNCT
ejpam-5802	230	1	conversely	conversely	ADV
ejpam-5802	230	2	,	,	PUNCT
ejpam-5802	230	3	suppose	suppose	VERB
ejpam-5802	230	4	every	every	DET
ejpam-5802	230	5	family	family	NOUN
ejpam-5802	230	6	of	of	ADP
ejpam-5802	230	7	nth	nth	NOUN
ejpam-5802	230	8	-	-	PUNCT
ejpam-5802	230	9	closed	closed	ADJ
ejpam-5802	230	10	subsets	subset	NOUN
ejpam-5802	230	11	of	of	ADP
ejpam-5802	230	12	k	k	PROPN
ejpam-5802	230	13	with	with	ADP
ejpam-5802	230	14	f.i.p	f.i.p	ADV
ejpam-5802	230	15	has	have	AUX
ejpam-5802	230	16	a	a	DET
ejpam-5802	230	17	non	non	ADJ
ejpam-5802	230	18	-	-	ADJ
ejpam-5802	230	19	empty	empty	ADJ
ejpam-5802	230	20	intersection	intersection	NOUN
ejpam-5802	230	21	.	.	PUNCT
ejpam-5802	231	1	if	if	SCONJ
ejpam-5802	231	2	k	k	PROPN
ejpam-5802	231	3	is	be	AUX
ejpam-5802	231	4	not	not	PART
ejpam-5802	231	5	nth	nth	ADV
ejpam-5802	231	6	-	-	ADJ
ejpam-5802	231	7	compact	compact	ADJ
ejpam-5802	231	8	,	,	PUNCT
ejpam-5802	231	9	then	then	ADV
ejpam-5802	231	10	there	there	PRON
ejpam-5802	231	11	exists	exist	VERB
ejpam-5802	231	12	an	an	DET
ejpam-5802	231	13	nth	nth	NOUN
ejpam-5802	231	14	-	-	ADJ
ejpam-5802	231	15	open	open	ADJ
ejpam-5802	231	16	cover	cover	NOUN
ejpam-5802	231	17	of	of	ADP
ejpam-5802	231	18	k	k	NOUN
ejpam-5802	231	19	,	,	PUNCT
ejpam-5802	231	20	say	say	VERB
ejpam-5802	231	21	{	{	PUNCT
ejpam-5802	231	22	wα	wα	NOUN
ejpam-5802	231	23	:	:	PUNCT
ejpam-5802	231	24	α	α	PROPN
ejpam-5802	231	25	∈	∈	PROPN
ejpam-5802	231	26	λ	λ	NOUN
ejpam-5802	231	27	}	}	PUNCT
ejpam-5802	231	28	.	.	PUNCT
ejpam-5802	232	1	since	since	SCONJ
ejpam-5802	232	2	wα	wα	NOUN
ejpam-5802	232	3	is	be	AUX
ejpam-5802	232	4	nth	nth	ADV
ejpam-5802	232	5	-	-	ADJ
ejpam-5802	232	6	open	open	ADJ
ejpam-5802	232	7	for	for	ADP
ejpam-5802	232	8	all	all	DET
ejpam-5802	232	9	α	α	PRON
ejpam-5802	232	10	∈	∈	PROPN
ejpam-5802	232	11	λ	λ	PROPN
ejpam-5802	232	12	,	,	PUNCT
ejpam-5802	232	13	{	{	PUNCT
ejpam-5802	232	14	k	k	X
ejpam-5802	232	15	\wα	\wα	PROPN
ejpam-5802	232	16	:	:	PUNCT
ejpam-5802	232	17	α	α	PROPN
ejpam-5802	232	18	∈	∈	PROPN
ejpam-5802	232	19	λ	λ	PROPN
ejpam-5802	232	20	}	}	PUNCT
ejpam-5802	232	21	is	be	AUX
ejpam-5802	232	22	a	a	DET
ejpam-5802	232	23	family	family	NOUN
ejpam-5802	232	24	of	of	ADP
ejpam-5802	232	25	nth	nth	NOUN
ejpam-5802	232	26	-	-	PUNCT
ejpam-5802	232	27	closed	closed	ADJ
ejpam-5802	232	28	subsets	subset	NOUN
ejpam-5802	232	29	of	of	ADP
ejpam-5802	232	30	k.	k.	PROPN
ejpam-5802	232	31	claim	claim	PROPN
ejpam-5802	232	32	:	:	PUNCT
ejpam-5802	232	33	{	{	PUNCT
ejpam-5802	232	34	k	k	PROPN
ejpam-5802	232	35	\	\	PROPN
ejpam-5802	232	36	wα	wα	NOUN
ejpam-5802	232	37	:	:	PUNCT
ejpam-5802	232	38	α	α	PROPN
ejpam-5802	232	39	∈	∈	PROPN
ejpam-5802	232	40	λ	λ	PROPN
ejpam-5802	232	41	}	}	PUNCT
ejpam-5802	232	42	has	have	VERB
ejpam-5802	232	43	f.i.p	f.i.p	ADJ
ejpam-5802	232	44	.	.	PUNCT
ejpam-5802	233	1	if	if	SCONJ
ejpam-5802	233	2	not	not	PART
ejpam-5802	233	3	,	,	PUNCT
ejpam-5802	233	4	there	there	PRON
ejpam-5802	233	5	exist	exist	VERB
ejpam-5802	233	6	w1	w1	NOUN
ejpam-5802	233	7	,	,	PUNCT
ejpam-5802	233	8	w2	w2	NOUN
ejpam-5802	233	9	,	,	PUNCT
ejpam-5802	233	10	.	.	PUNCT
ejpam-5802	233	11	.	.	PUNCT
ejpam-5802	234	1	.	.	PUNCT
ejpam-5802	235	1	,	,	PUNCT
ejpam-5802	235	2	wn	wn	INTJ
ejpam-5802	235	3	such	such	ADJ
ejpam-5802	235	4	that	that	DET
ejpam-5802	235	5	⋂n	⋂n	PROPN
ejpam-5802	235	6	i=1(k	i=1(k	VERB
ejpam-5802	235	7	\	\	PROPN
ejpam-5802	235	8	wi	wi	PROPN
ejpam-5802	235	9	)	)	PUNCT
ejpam-5802	236	1	=	=	NOUN
ejpam-5802	236	2	∅	∅	NOUN
ejpam-5802	236	3	,	,	PUNCT
ejpam-5802	236	4	hence	hence	ADV
ejpam-5802	236	5	⋃n	⋃n	PROPN
ejpam-5802	236	6	i=1wi	i=1wi	NUM
ejpam-5802	236	7	=	=	PUNCT
ejpam-5802	236	8	k.	k.	PROPN
ejpam-5802	237	1	this	this	PRON
ejpam-5802	237	2	implies	imply	VERB
ejpam-5802	237	3	{	{	PUNCT
ejpam-5802	237	4	wi	wi	PROPN
ejpam-5802	237	5	:	:	PUNCT
ejpam-5802	237	6	i	i	NOUN
ejpam-5802	237	7	=	=	NOUN
ejpam-5802	237	8	1	1	NUM
ejpam-5802	237	9	,	,	PUNCT
ejpam-5802	237	10	2	2	NUM
ejpam-5802	237	11	,	,	PUNCT
ejpam-5802	237	12	.	.	PUNCT
ejpam-5802	237	13	.	.	PUNCT
ejpam-5802	237	14	.	.	PUNCT
ejpam-5802	238	1	,	,	PUNCT
ejpam-5802	238	2	n	n	CCONJ
ejpam-5802	238	3	}	}	PUNCT
ejpam-5802	238	4	is	be	AUX
ejpam-5802	238	5	a	a	DET
ejpam-5802	238	6	finite	finite	ADJ
ejpam-5802	238	7	subcover	subcover	NOUN
ejpam-5802	238	8	of	of	ADP
ejpam-5802	238	9	k	k	PROPN
ejpam-5802	238	10	,	,	PUNCT
ejpam-5802	238	11	which	which	PRON
ejpam-5802	238	12	is	be	AUX
ejpam-5802	238	13	a	a	DET
ejpam-5802	238	14	contradiction	contradiction	NOUN
ejpam-5802	238	15	.	.	PUNCT
ejpam-5802	239	1	therefore	therefore	ADV
ejpam-5802	239	2	,	,	PUNCT
ejpam-5802	239	3	{	{	PUNCT
ejpam-5802	239	4	k	k	PROPN
ejpam-5802	239	5	\	\	PROPN
ejpam-5802	239	6	wα	wα	NOUN
ejpam-5802	239	7	:	:	PUNCT
ejpam-5802	239	8	α	α	PROPN
ejpam-5802	239	9	∈	∈	PROPN
ejpam-5802	239	10	λ	λ	PROPN
ejpam-5802	239	11	}	}	PUNCT
ejpam-5802	239	12	has	have	VERB
ejpam-5802	239	13	f.i.p	f.i.p	ADV
ejpam-5802	239	14	.	.	PUNCT
ejpam-5802	240	1	by	by	ADP
ejpam-5802	240	2	assumption	assumption	NOUN
ejpam-5802	240	3	,	,	PUNCT
ejpam-5802	240	4	⋂	⋂	PROPN
ejpam-5802	240	5	α∈λwα	α∈λwα	PROPN
ejpam-5802	240	6	̸=	̸=	PROPN
ejpam-5802	240	7	∅.	∅.	PRON
ejpam-5802	240	8	so	so	ADV
ejpam-5802	240	9	,	,	PUNCT
ejpam-5802	240	10	∅	∅	NOUN
ejpam-5802	240	11	=	=	NOUN
ejpam-5802	240	12	̸	̸	NUM
ejpam-5802	240	13	k	k	NOUN
ejpam-5802	240	14	\	\	PROPN
ejpam-5802	240	15	⋂	⋂	PROPN
ejpam-5802	240	16	α∈λwα	α∈λwα	PROPN
ejpam-5802	240	17	=	=	PUNCT
ejpam-5802	240	18	⋃	⋃	ADP
ejpam-5802	240	19	α∈λ(k	α∈λ(k	VERB
ejpam-5802	240	20	\	\	X
ejpam-5802	241	1	(	(	PUNCT
ejpam-5802	241	2	k	k	PROPN
ejpam-5802	241	3	\	\	PROPN
ejpam-5802	241	4	wα	wα	NOUN
ejpam-5802	241	5	)	)	PUNCT
ejpam-5802	241	6	)	)	PUNCT
ejpam-5802	242	1	=	=	PUNCT
ejpam-5802	242	2	⋃	⋃	NOUN
ejpam-5802	242	3	α∈λwα	α∈λwα	PROPN
ejpam-5802	242	4	,	,	PUNCT
ejpam-5802	242	5	which	which	PRON
ejpam-5802	242	6	is	be	AUX
ejpam-5802	242	7	a	a	DET
ejpam-5802	242	8	contradiction	contradiction	NOUN
ejpam-5802	242	9	.	.	PUNCT
ejpam-5802	243	1	hence	hence	ADV
ejpam-5802	243	2	,	,	PUNCT
ejpam-5802	243	3	k	k	PROPN
ejpam-5802	243	4	must	must	AUX
ejpam-5802	243	5	be	be	AUX
ejpam-5802	243	6	compact	compact	ADJ
ejpam-5802	243	7	.	.	PUNCT
ejpam-5802	244	1	theorem	theorem	VERB
ejpam-5802	244	2	6	6	NUM
ejpam-5802	244	3	:	:	PUNCT
ejpam-5802	244	4	every	every	DET
ejpam-5802	244	5	nth	nth	NOUN
ejpam-5802	244	6	-	-	PUNCT
ejpam-5802	244	7	closed	closed	ADJ
ejpam-5802	244	8	subset	subset	NOUN
ejpam-5802	244	9	of	of	ADP
ejpam-5802	244	10	a	a	DET
ejpam-5802	244	11	nth	nth	ADJ
ejpam-5802	244	12	-	-	ADJ
ejpam-5802	244	13	compact	compact	ADJ
ejpam-5802	244	14	space	space	NOUN
ejpam-5802	244	15	is	be	AUX
ejpam-5802	244	16	nth	nth	NOUN
ejpam-5802	244	17	-	-	ADJ
ejpam-5802	244	18	compact	compact	ADJ
ejpam-5802	244	19	.	.	PUNCT
ejpam-5802	245	1	proof	proof	NOUN
ejpam-5802	245	2	:	:	PUNCT
ejpam-5802	245	3	suppose	suppose	VERB
ejpam-5802	245	4	that	that	SCONJ
ejpam-5802	245	5	t	t	PROPN
ejpam-5802	245	6	is	be	AUX
ejpam-5802	245	7	a	a	DET
ejpam-5802	245	8	nth	nth	NOUN
ejpam-5802	245	9	-	-	PUNCT
ejpam-5802	245	10	closed	close	VERB
ejpam-5802	245	11	subset	subset	NOUN
ejpam-5802	245	12	in	in	ADP
ejpam-5802	245	13	a	a	DET
ejpam-5802	245	14	compact	compact	ADJ
ejpam-5802	245	15	space	space	NOUN
ejpam-5802	246	1	k.	k.	PROPN
ejpam-5802	246	2	let	let	VERB
ejpam-5802	246	3	e	e	NOUN
ejpam-5802	246	4	=	=	PRON
ejpam-5802	246	5	{	{	PUNCT
ejpam-5802	246	6	tα	tα	X
ejpam-5802	246	7	:	:	PUNCT
ejpam-5802	246	8	α	α	PROPN
ejpam-5802	246	9	∈	∈	PROPN
ejpam-5802	246	10	λ	λ	NOUN
ejpam-5802	246	11	}	}	PUNCT
ejpam-5802	246	12	be	be	VERB
ejpam-5802	246	13	an	an	DET
ejpam-5802	246	14	nth	nth	NOUN
ejpam-5802	246	15	-	-	ADJ
ejpam-5802	246	16	open	open	ADJ
ejpam-5802	246	17	cover	cover	NOUN
ejpam-5802	246	18	of	of	ADP
ejpam-5802	246	19	t	t	PROPN
ejpam-5802	246	20	.	.	PUNCT
ejpam-5802	247	1	then	then	ADV
ejpam-5802	247	2	k	k	PROPN
ejpam-5802	247	3	=	=	PUNCT
ejpam-5802	247	4	t	t	PROPN
ejpam-5802	247	5	∪	∪	NOUN
ejpam-5802	247	6	(	(	PUNCT
ejpam-5802	247	7	k	k	PROPN
ejpam-5802	247	8	t	t	PROPN
ejpam-5802	247	9	)	)	PUNCT
ejpam-5802	247	10	=	=	SYM
ejpam-5802	247	11	⋃	⋃	NOUN
ejpam-5802	247	12	α∈λ	α∈λ	NOUN
ejpam-5802	247	13	tα∪	tα∪	NUM
ejpam-5802	247	14	(	(	PUNCT
ejpam-5802	247	15	k	k	PROPN
ejpam-5802	247	16	t	t	PROPN
ejpam-5802	247	17	)	)	PUNCT
ejpam-5802	247	18	is	be	AUX
ejpam-5802	247	19	an	an	DET
ejpam-5802	247	20	nth	nth	NOUN
ejpam-5802	247	21	-	-	ADJ
ejpam-5802	247	22	open	open	ADJ
ejpam-5802	247	23	cover	cover	NOUN
ejpam-5802	247	24	of	of	ADP
ejpam-5802	247	25	k.	k.	PROPN
ejpam-5802	247	26	since	since	SCONJ
ejpam-5802	247	27	k	k	PROPN
ejpam-5802	247	28	is	be	AUX
ejpam-5802	247	29	nth	nth	ADJ
ejpam-5802	247	30	-	-	ADJ
ejpam-5802	247	31	compact	compact	ADJ
ejpam-5802	247	32	,	,	PUNCT
ejpam-5802	247	33	t	t	PROPN
ejpam-5802	247	34	∪	∪	X
ejpam-5802	247	35	(	(	PUNCT
ejpam-5802	247	36	k	k	PROPN
ejpam-5802	247	37	−	−	PROPN
ejpam-5802	247	38	t	t	PROPN
ejpam-5802	247	39	)	)	PUNCT
ejpam-5802	247	40	can	can	AUX
ejpam-5802	247	41	be	be	AUX
ejpam-5802	247	42	reduced	reduce	VERB
ejpam-5802	247	43	to	to	ADP
ejpam-5802	247	44	a	a	DET
ejpam-5802	247	45	nth	nth	NOUN
ejpam-5802	247	46	finite	finite	PROPN
ejpam-5802	247	47	subcover	subcover	PROPN
ejpam-5802	247	48	.	.	PUNCT
ejpam-5802	248	1	say	say	VERB
ejpam-5802	248	2	nth	nth	NOUN
ejpam-5802	248	3	-	-	PUNCT
ejpam-5802	248	4	finite	finite	PROPN
ejpam-5802	248	5	subcover	subcover	PROPN
ejpam-5802	248	6	theorem	theorem	VERB
ejpam-5802	248	7	7	7	NUM
ejpam-5802	248	8	[	[	SYM
ejpam-5802	248	9	4	4	NUM
ejpam-5802	248	10	]	]	PUNCT
ejpam-5802	248	11	:	:	PUNCT
ejpam-5802	248	12	let	let	VERB
ejpam-5802	248	13	w	w	PART
ejpam-5802	248	14	be	be	AUX
ejpam-5802	248	15	a	a	DET
ejpam-5802	248	16	compact	compact	ADJ
ejpam-5802	248	17	subset	subset	NOUN
ejpam-5802	248	18	in	in	ADP
ejpam-5802	248	19	a	a	DET
ejpam-5802	248	20	nth	nth	NOUN
ejpam-5802	248	21	-	-	PUNCT
ejpam-5802	248	22	t2	t2	NOUN
ejpam-5802	248	23	-	-	PUNCT
ejpam-5802	248	24	space	space	NOUN
ejpam-5802	248	25	k.	k.	NOUN
ejpam-5802	248	26	then	then	ADV
ejpam-5802	248	27	for	for	ADP
ejpam-5802	248	28	all	all	DET
ejpam-5802	248	29	n	n	PRON
ejpam-5802	248	30	/∈w	/∈w	PUNCT
ejpam-5802	248	31	there	there	PRON
ejpam-5802	248	32	exists	exist	VERB
ejpam-5802	248	33	an	an	DET
ejpam-5802	248	34	open	open	ADJ
ejpam-5802	248	35	set	set	VERB
ejpam-5802	248	36	un	un	PROPN
ejpam-5802	248	37	containing	contain	VERB
ejpam-5802	248	38	n	n	PRON
ejpam-5802	248	39	such	such	ADJ
ejpam-5802	248	40	that	that	SCONJ
ejpam-5802	248	41	w	w	PROPN
ejpam-5802	248	42	∩	∩	PROPN
ejpam-5802	248	43	un	un	PROPN
ejpam-5802	248	44	=	=	ADJ
ejpam-5802	248	45	∅	∅	NOUN
ejpam-5802	248	46	theorem	theorem	VERB
ejpam-5802	248	47	8	8	NUM
ejpam-5802	248	48	:	:	PUNCT
ejpam-5802	248	49	let	let	VERB
ejpam-5802	248	50	w	w	PART
ejpam-5802	248	51	be	be	AUX
ejpam-5802	248	52	a	a	DET
ejpam-5802	248	53	nth	nth	ADJ
ejpam-5802	248	54	-	-	ADJ
ejpam-5802	248	55	compact	compact	ADJ
ejpam-5802	248	56	subset	subset	NOUN
ejpam-5802	248	57	in	in	ADP
ejpam-5802	248	58	a	a	DET
ejpam-5802	248	59	nth	nth	NOUN
ejpam-5802	248	60	-	-	PUNCT
ejpam-5802	248	61	t2	t2	NOUN
ejpam-5802	248	62	-	-	PUNCT
ejpam-5802	248	63	space	space	NOUN
ejpam-5802	248	64	k.	k.	NOUN
ejpam-5802	248	65	then	then	ADV
ejpam-5802	248	66	for	for	ADP
ejpam-5802	248	67	all	all	DET
ejpam-5802	248	68	n	n	PRON
ejpam-5802	248	69	/∈w	/∈w	PUNCT
ejpam-5802	248	70	there	there	PRON
ejpam-5802	248	71	exists	exist	VERB
ejpam-5802	248	72	a	a	DET
ejpam-5802	248	73	ηi	ηi	NOUN
ejpam-5802	248	74	-	-	PUNCT
ejpam-5802	248	75	open	open	ADJ
ejpam-5802	248	76	set	set	VERB
ejpam-5802	248	77	un	un	PROPN
ejpam-5802	248	78	containing	contain	VERB
ejpam-5802	248	79	n	n	PRON
ejpam-5802	248	80	such	such	ADJ
ejpam-5802	248	81	that	that	SCONJ
ejpam-5802	248	82	w	w	PROPN
ejpam-5802	248	83	∩	∩	PROPN
ejpam-5802	248	84	un	un	PROPN
ejpam-5802	248	85	=	=	NOUN
ejpam-5802	248	86	∅	∅	NOUN
ejpam-5802	248	87	,	,	PUNCT
ejpam-5802	248	88	i=1,2,	i=1,2,	NOUN
ejpam-5802	248	89	...	...	PUNCT
ejpam-5802	248	90	,n	,n	PUNCT
ejpam-5802	248	91	.	.	PUNCT
ejpam-5802	249	1	definition	definition	NOUN
ejpam-5802	249	2	7.2	7.2	NUM
ejpam-5802	249	3	:	:	PUNCT
ejpam-5802	249	4	let	let	VERB
ejpam-5802	249	5	(	(	PUNCT
ejpam-5802	249	6	k	k	X
ejpam-5802	249	7	,	,	PUNCT
ejpam-5802	249	8	η1,η2,	η1,η2,	PROPN
ejpam-5802	249	9	...	...	PUNCT
ejpam-5802	249	10	,ηn	,ηn	PUNCT
ejpam-5802	249	11	)	)	PUNCT
ejpam-5802	249	12	be	be	AUX
ejpam-5802	249	13	a	a	DET
ejpam-5802	249	14	nth	nth	ADJ
ejpam-5802	249	15	-	-	ADJ
ejpam-5802	249	16	topological	topological	ADJ
ejpam-5802	249	17	space	space	NOUN
ejpam-5802	249	18	,	,	PUNCT
ejpam-5802	249	19	then	then	ADV
ejpam-5802	249	20	a	a	DET
ejpam-5802	249	21	set	set	NOUN
ejpam-5802	249	22	g	g	NOUN
ejpam-5802	249	23	in	in	ADP
ejpam-5802	249	24	(	(	PUNCT
ejpam-5802	249	25	k	k	PROPN
ejpam-5802	249	26	,	,	PUNCT
ejpam-5802	249	27	η1,η2,	η1,η2,	PROPN
ejpam-5802	249	28	...	...	PUNCT
ejpam-5802	249	29	,ηn	,ηn	PUNCT
ejpam-5802	249	30	)	)	PUNCT
ejpam-5802	249	31	is	be	AUX
ejpam-5802	249	32	called	call	VERB
ejpam-5802	249	33	nth	nth	ADV
ejpam-5802	249	34	-	-	PUNCT
ejpam-5802	249	35	dense	dense	ADJ
ejpam-5802	249	36	set	set	NOUN
ejpam-5802	249	37	if	if	SCONJ
ejpam-5802	249	38	g	g	PROPN
ejpam-5802	249	39	=	=	PROPN
ejpam-5802	249	40	k.	k.	PROPN
ejpam-5802	249	41	on	on	ADP
ejpam-5802	249	42	another	another	DET
ejpam-5802	249	43	hand	hand	NOUN
ejpam-5802	249	44	,	,	PUNCT
ejpam-5802	249	45	if	if	SCONJ
ejpam-5802	249	46	g	g	PROPN
ejpam-5802	249	47	is	be	AUX
ejpam-5802	249	48	dense	dense	ADJ
ejpam-5802	249	49	in	in	ADP
ejpam-5802	249	50	(	(	PUNCT
ejpam-5802	249	51	k	k	PROPN
ejpam-5802	249	52	,	,	PUNCT
ejpam-5802	249	53	η1,η2,	η1,η2,	PROPN
ejpam-5802	249	54	...	...	PUNCT
ejpam-5802	249	55	,ηn),then	,ηn),then	PUNCT
ejpam-5802	249	56	for	for	ADP
ejpam-5802	249	57	all	all	DET
ejpam-5802	249	58	ηi	ηi	NOUN
ejpam-5802	249	59	-	-	PUNCT
ejpam-5802	249	60	open	open	ADJ
ejpam-5802	249	61	set	set	NOUN
ejpam-5802	249	62	u	u	NOUN
ejpam-5802	249	63	we	we	PRON
ejpam-5802	249	64	have	have	VERB
ejpam-5802	249	65	u	u	NOUN
ejpam-5802	249	66	∩	∩	NOUN
ejpam-5802	249	67	s	s	PART
ejpam-5802	249	68	̸=	̸=	PROPN
ejpam-5802	249	69	ϕ.	ϕ.	PROPN
ejpam-5802	249	70	j.	j.	PROPN
ejpam-5802	249	71	oudetallah	oudetallah	PROPN
ejpam-5802	249	72	et	et	PROPN
ejpam-5802	249	73	al	al	PROPN
ejpam-5802	249	74	.	.	PUNCT
ejpam-5802	249	75	/	/	SYM
ejpam-5802	249	76	eur	eur	PROPN
ejpam-5802	249	77	.	.	PUNCT
ejpam-5802	250	1	j.	j.	PROPN
ejpam-5802	250	2	pure	pure	PROPN
ejpam-5802	250	3	appl	appl	PROPN
ejpam-5802	250	4	.	.	PROPN
ejpam-5802	250	5	math	math	PROPN
ejpam-5802	250	6	,	,	PUNCT
ejpam-5802	250	7	18	18	NUM
ejpam-5802	250	8	(	(	PUNCT
ejpam-5802	250	9	2	2	NUM
ejpam-5802	250	10	)	)	PUNCT
ejpam-5802	250	11	(	(	PUNCT
ejpam-5802	250	12	2025	2025	NUM
ejpam-5802	250	13	)	)	PUNCT
ejpam-5802	250	14	,	,	PUNCT
ejpam-5802	250	15	5802	5802	NUM
ejpam-5802	250	16	11	11	NUM
ejpam-5802	250	17	of	of	ADP
ejpam-5802	250	18	14	14	NUM
ejpam-5802	250	19	definition	definition	NOUN
ejpam-5802	250	20	8.2	8.2	NUM
ejpam-5802	250	21	:	:	PUNCT
ejpam-5802	250	22	let	let	VERB
ejpam-5802	250	23	(	(	PUNCT
ejpam-5802	250	24	k	k	X
ejpam-5802	250	25	,	,	PUNCT
ejpam-5802	250	26	η1,η2,	η1,η2,	PROPN
ejpam-5802	250	27	...	...	PUNCT
ejpam-5802	250	28	,ηn	,ηn	PUNCT
ejpam-5802	250	29	)	)	PUNCT
ejpam-5802	250	30	and	and	CCONJ
ejpam-5802	250	31	(	(	PUNCT
ejpam-5802	250	32	q	q	X
ejpam-5802	250	33	,	,	PUNCT
ejpam-5802	250	34	λ1,λ2	λ1,λ2	PROPN
ejpam-5802	250	35	,	,	PUNCT
ejpam-5802	250	36	...	...	PUNCT
ejpam-5802	250	37	,	,	PUNCT
ejpam-5802	250	38	λn	λn	NOUN
ejpam-5802	250	39	)	)	PUNCT
ejpam-5802	250	40	are	be	AUX
ejpam-5802	250	41	nth	nth	ADJ
ejpam-5802	250	42	-	-	ADJ
ejpam-5802	250	43	topological	topological	ADJ
ejpam-5802	250	44	space	space	NOUN
ejpam-5802	250	45	,	,	PUNCT
ejpam-5802	250	46	then	then	ADV
ejpam-5802	250	47	the	the	DET
ejpam-5802	250	48	function	function	NOUN
ejpam-5802	250	49	h:(k	h:(k	PROPN
ejpam-5802	250	50	,	,	PUNCT
ejpam-5802	250	51	η1,η2,	η1,η2,	PROPN
ejpam-5802	250	52	...	...	PUNCT
ejpam-5802	250	53	,ηn	,ηn	PUNCT
ejpam-5802	250	54	)	)	PUNCT
ejpam-5802	250	55	→	→	PUNCT
ejpam-5802	250	56	(	(	PUNCT
ejpam-5802	250	57	q	q	X
ejpam-5802	250	58	,	,	PUNCT
ejpam-5802	250	59	λ1,λ2	λ1,λ2	PROPN
ejpam-5802	250	60	,	,	PUNCT
ejpam-5802	250	61	...	...	PUNCT
ejpam-5802	250	62	,	,	PUNCT
ejpam-5802	250	63	λn	λn	NOUN
ejpam-5802	250	64	)	)	PUNCT
ejpam-5802	250	65	is	be	AUX
ejpam-5802	250	66	called	call	VERB
ejpam-5802	250	67	nth	nth	ADV
ejpam-5802	250	68	-	-	ADJ
ejpam-5802	250	69	open	open	ADJ
ejpam-5802	250	70	function	function	NOUN
ejpam-5802	250	71	if	if	SCONJ
ejpam-5802	250	72	h(u	h(u	PROPN
ejpam-5802	250	73	)	)	PUNCT
ejpam-5802	251	1	=	=	SYM
ejpam-5802	251	2	v	v	NOUN
ejpam-5802	251	3	,	,	PUNCT
ejpam-5802	251	4	where	where	SCONJ
ejpam-5802	251	5	u	u	NOUN
ejpam-5802	251	6	is	be	AUX
ejpam-5802	251	7	ηi	ηi	NOUN
ejpam-5802	251	8	-	-	PUNCT
ejpam-5802	251	9	open	open	ADJ
ejpam-5802	251	10	set	set	NOUN
ejpam-5802	251	11	and	and	CCONJ
ejpam-5802	251	12	v	v	NOUN
ejpam-5802	251	13	is	be	AUX
ejpam-5802	251	14	σi	σi	NOUN
ejpam-5802	251	15	-	-	PUNCT
ejpam-5802	251	16	open	open	ADJ
ejpam-5802	251	17	set	set	NOUN
ejpam-5802	251	18	.	.	PUNCT
ejpam-5802	252	1	5	5	X
ejpam-5802	252	2	.	.	X
ejpam-5802	252	3	σ	σ	VERB
ejpam-5802	252	4	-	-	ADJ
ejpam-5802	252	5	compact	compact	ADJ
ejpam-5802	252	6	space	space	NOUN
ejpam-5802	252	7	in	in	ADP
ejpam-5802	252	8	nth	nth	ADJ
ejpam-5802	252	9	-	-	ADJ
ejpam-5802	252	10	topological	topological	ADJ
ejpam-5802	252	11	space	space	NOUN
ejpam-5802	252	12	now	now	ADV
ejpam-5802	252	13	,	,	PUNCT
ejpam-5802	252	14	we	we	PRON
ejpam-5802	252	15	will	will	AUX
ejpam-5802	252	16	show	show	VERB
ejpam-5802	252	17	some	some	DET
ejpam-5802	252	18	concept	concept	NOUN
ejpam-5802	252	19	of	of	ADP
ejpam-5802	252	20	σ	σ	NOUN
ejpam-5802	252	21	-	-	ADJ
ejpam-5802	252	22	compact	compact	ADJ
ejpam-5802	252	23	space	space	NOUN
ejpam-5802	252	24	in	in	ADP
ejpam-5802	252	25	topological	topological	ADJ
ejpam-5802	252	26	space	space	NOUN
ejpam-5802	252	27	,	,	PUNCT
ejpam-5802	252	28	σ	σ	NOUN
ejpam-5802	252	29	-	-	ADJ
ejpam-5802	252	30	compact	compact	ADJ
ejpam-5802	252	31	space	space	NOUN
ejpam-5802	252	32	in	in	ADP
ejpam-5802	252	33	nth	nth	ADJ
ejpam-5802	252	34	-	-	ADJ
ejpam-5802	252	35	topological	topological	ADJ
ejpam-5802	252	36	space	space	NOUN
ejpam-5802	252	37	and	and	CCONJ
ejpam-5802	252	38	some	some	DET
ejpam-5802	252	39	theorems	theorem	NOUN
ejpam-5802	252	40	and	and	CCONJ
ejpam-5802	252	41	their	their	PRON
ejpam-5802	252	42	properties	property	NOUN
ejpam-5802	252	43	.	.	PUNCT
ejpam-5802	253	1	definition	definition	NOUN
ejpam-5802	253	2	1.3	1.3	NUM
ejpam-5802	254	1	[	[	X
ejpam-5802	254	2	2	2	NUM
ejpam-5802	254	3	]	]	PUNCT
ejpam-5802	254	4	:	:	PUNCT
ejpam-5802	254	5	let	let	VERB
ejpam-5802	254	6	(	(	PUNCT
ejpam-5802	254	7	k	k	X
ejpam-5802	254	8	,	,	PUNCT
ejpam-5802	254	9	η	η	NOUN
ejpam-5802	254	10	)	)	PUNCT
ejpam-5802	254	11	be	be	VERB
ejpam-5802	254	12	a	a	DET
ejpam-5802	254	13	topological	topological	ADJ
ejpam-5802	254	14	space	space	NOUN
ejpam-5802	254	15	,	,	PUNCT
ejpam-5802	254	16	then	then	ADV
ejpam-5802	254	17	it	it	PRON
ejpam-5802	254	18	is	be	AUX
ejpam-5802	254	19	called	call	VERB
ejpam-5802	254	20	σ	σ	NOUN
ejpam-5802	254	21	-	-	ADJ
ejpam-5802	254	22	compact	compact	ADJ
ejpam-5802	254	23	space	space	NOUN
ejpam-5802	254	24	if	if	SCONJ
ejpam-5802	254	25	every	every	DET
ejpam-5802	254	26	open	open	ADJ
ejpam-5802	254	27	cover	cover	NOUN
ejpam-5802	254	28	of	of	ADP
ejpam-5802	254	29	k	k	PROPN
ejpam-5802	254	30	has	have	VERB
ejpam-5802	254	31	a	a	DET
ejpam-5802	254	32	countable	countable	ADJ
ejpam-5802	254	33	subcover	subcover	NOUN
ejpam-5802	254	34	of	of	ADP
ejpam-5802	254	35	k.on	k.on	PROPN
ejpam-5802	254	36	the	the	DET
ejpam-5802	254	37	same	same	ADJ
ejpam-5802	254	38	time	time	NOUN
ejpam-5802	254	39	a	a	DET
ejpam-5802	254	40	topological	topological	ADJ
ejpam-5802	254	41	space	space	NOUN
ejpam-5802	254	42	k	k	PROPN
ejpam-5802	254	43	is	be	AUX
ejpam-5802	254	44	called	call	VERB
ejpam-5802	254	45	σ	σ	NOUN
ejpam-5802	254	46	-	-	ADJ
ejpam-5802	254	47	compact	compact	ADJ
ejpam-5802	254	48	if	if	SCONJ
ejpam-5802	254	49	it	it	PRON
ejpam-5802	254	50	can	can	AUX
ejpam-5802	254	51	be	be	AUX
ejpam-5802	254	52	expressed	express	VERB
ejpam-5802	254	53	as	as	ADP
ejpam-5802	254	54	a	a	DET
ejpam-5802	254	55	countable	countable	ADJ
ejpam-5802	254	56	union	union	NOUN
ejpam-5802	254	57	of	of	ADP
ejpam-5802	254	58	compact	compact	ADJ
ejpam-5802	254	59	subspaces	subspace	NOUN
ejpam-5802	254	60	.	.	PUNCT
ejpam-5802	255	1	definition	definition	NOUN
ejpam-5802	255	2	2.3	2.3	NUM
ejpam-5802	255	3	:	:	PUNCT
ejpam-5802	255	4	let	let	VERB
ejpam-5802	255	5	(	(	PUNCT
ejpam-5802	255	6	k	k	X
ejpam-5802	255	7	,	,	PUNCT
ejpam-5802	255	8	η1	η1	NOUN
ejpam-5802	255	9	,	,	PUNCT
ejpam-5802	255	10	η2	η2	NOUN
ejpam-5802	255	11	,	,	PUNCT
ejpam-5802	255	12	...	...	PUNCT
ejpam-5802	255	13	,	,	PUNCT
ejpam-5802	255	14	ηn	ηn	INTJ
ejpam-5802	255	15	)	)	PUNCT
ejpam-5802	255	16	be	be	AUX
ejpam-5802	255	17	a	a	DET
ejpam-5802	255	18	nth	nth	ADJ
ejpam-5802	255	19	-	-	ADJ
ejpam-5802	255	20	topological	topological	ADJ
ejpam-5802	255	21	space	space	NOUN
ejpam-5802	255	22	,	,	PUNCT
ejpam-5802	255	23	then	then	ADV
ejpam-5802	255	24	it	it	PRON
ejpam-5802	255	25	is	be	AUX
ejpam-5802	255	26	called	call	VERB
ejpam-5802	255	27	nth	nth	PROPN
ejpam-5802	255	28	σ	σ	PROPN
ejpam-5802	255	29	topological	topological	ADJ
ejpam-5802	255	30	space	space	NOUN
ejpam-5802	255	31	if	if	SCONJ
ejpam-5802	255	32	every	every	DET
ejpam-5802	255	33	ηi	ηi	NOUN
ejpam-5802	255	34	-	-	PUNCT
ejpam-5802	255	35	open	open	ADJ
ejpam-5802	255	36	cover	cover	NOUN
ejpam-5802	255	37	of	of	ADP
ejpam-5802	255	38	k	k	PROPN
ejpam-5802	255	39	has	have	VERB
ejpam-5802	255	40	a	a	DET
ejpam-5802	255	41	nth	nth	NOUN
ejpam-5802	255	42	countable	countable	ADJ
ejpam-5802	255	43	subcover	subcover	PROPN
ejpam-5802	255	44	of	of	ADP
ejpam-5802	255	45	k.	k.	PROPN
ejpam-5802	255	46	theorem	theorem	PROPN
ejpam-5802	255	47	1	1	NUM
ejpam-5802	255	48	:	:	PUNCT
ejpam-5802	255	49	any	any	DET
ejpam-5802	255	50	closed	closed	ADJ
ejpam-5802	255	51	subspace	subspace	NOUN
ejpam-5802	255	52	of	of	ADP
ejpam-5802	255	53	a	a	DET
ejpam-5802	255	54	nth	nth	NOUN
ejpam-5802	255	55	σ	σ	ADJ
ejpam-5802	255	56	-	-	ADJ
ejpam-5802	255	57	compact	compact	ADJ
ejpam-5802	255	58	space	space	NOUN
ejpam-5802	255	59	is	be	AUX
ejpam-5802	255	60	also	also	ADV
ejpam-5802	255	61	nth	nth	PROPN
ejpam-5802	255	62	σ	σ	PROPN
ejpam-5802	255	63	-	-	ADJ
ejpam-5802	255	64	compact	compact	ADJ
ejpam-5802	255	65	.	.	PUNCT
ejpam-5802	256	1	proof	proof	NOUN
ejpam-5802	256	2	:	:	PUNCT
ejpam-5802	256	3	let	let	VERB
ejpam-5802	256	4	(	(	PUNCT
ejpam-5802	256	5	k	k	X
ejpam-5802	256	6	,	,	PUNCT
ejpam-5802	256	7	η1	η1	NOUN
ejpam-5802	256	8	,	,	PUNCT
ejpam-5802	256	9	η2	η2	NOUN
ejpam-5802	256	10	,	,	PUNCT
ejpam-5802	256	11	...	...	PUNCT
ejpam-5802	256	12	,	,	PUNCT
ejpam-5802	256	13	ηn	ηn	INTJ
ejpam-5802	256	14	)	)	PUNCT
ejpam-5802	256	15	be	be	AUX
ejpam-5802	256	16	a	a	DET
ejpam-5802	256	17	nth	nth	NOUN
ejpam-5802	256	18	σ	σ	ADJ
ejpam-5802	256	19	-	-	ADJ
ejpam-5802	256	20	compact	compact	ADJ
ejpam-5802	256	21	space	space	NOUN
ejpam-5802	256	22	,	,	PUNCT
ejpam-5802	256	23	meaning	mean	VERB
ejpam-5802	256	24	k	k	PROPN
ejpam-5802	256	25	=	=	SYM
ejpam-5802	256	26	⋃∞	⋃∞	X
ejpam-5802	256	27	ni=1m(ni	ni=1m(ni	PROPN
ejpam-5802	256	28	)	)	PUNCT
ejpam-5802	256	29	,	,	PUNCT
ejpam-5802	256	30	where	where	SCONJ
ejpam-5802	256	31	each	each	DET
ejpam-5802	256	32	m(ni	m(ni	NOUN
ejpam-5802	256	33	)	)	PUNCT
ejpam-5802	256	34	is	be	AUX
ejpam-5802	256	35	compact	compact	ADJ
ejpam-5802	256	36	in	in	ADP
ejpam-5802	256	37	k.	k.	PROPN
ejpam-5802	256	38	for	for	ADP
ejpam-5802	256	39	any	any	DET
ejpam-5802	256	40	closed	closed	ADJ
ejpam-5802	256	41	subspace	subspace	NOUN
ejpam-5802	256	42	q	q	PROPN
ejpam-5802	256	43	⊆	⊆	NUM
ejpam-5802	256	44	k	k	NOUN
ejpam-5802	256	45	,	,	PUNCT
ejpam-5802	256	46	each	each	DET
ejpam-5802	256	47	mn	mn	PROPN
ejpam-5802	256	48	∩	∩	PROPN
ejpam-5802	256	49	q	q	X
ejpam-5802	256	50	is	be	AUX
ejpam-5802	256	51	compact	compact	ADJ
ejpam-5802	256	52	(	(	PUNCT
ejpam-5802	256	53	since	since	SCONJ
ejpam-5802	256	54	compactness	compactness	NOUN
ejpam-5802	256	55	is	be	AUX
ejpam-5802	256	56	preserved	preserve	VERB
ejpam-5802	256	57	under	under	ADP
ejpam-5802	256	58	closed	closed	ADJ
ejpam-5802	256	59	subspaces	subspace	NOUN
ejpam-5802	256	60	)	)	PUNCT
ejpam-5802	256	61	.	.	PUNCT
ejpam-5802	257	1	thus	thus	ADV
ejpam-5802	257	2	,	,	PUNCT
ejpam-5802	257	3	q	q	X
ejpam-5802	257	4	=	=	SYM
ejpam-5802	257	5	⋃∞	⋃∞	SYM
ejpam-5802	257	6	ni=1m(ni	ni=1m(ni	PROPN
ejpam-5802	257	7	)	)	PUNCT
ejpam-5802	257	8	∩	∩	PROPN
ejpam-5802	257	9	f	f	PROPN
ejpam-5802	257	10	,	,	PUNCT
ejpam-5802	257	11	which	which	PRON
ejpam-5802	257	12	is	be	AUX
ejpam-5802	257	13	a	a	DET
ejpam-5802	257	14	countable	countable	ADJ
ejpam-5802	257	15	union	union	NOUN
ejpam-5802	257	16	of	of	ADP
ejpam-5802	257	17	compact	compact	ADJ
ejpam-5802	257	18	sets	set	NOUN
ejpam-5802	257	19	in	in	ADP
ejpam-5802	257	20	q	q	NOUN
ejpam-5802	257	21	,	,	PUNCT
ejpam-5802	257	22	proving	prove	VERB
ejpam-5802	257	23	that	that	PRON
ejpam-5802	257	24	q	q	NOUN
ejpam-5802	257	25	is	be	AUX
ejpam-5802	257	26	nth	nth	NOUN
ejpam-5802	257	27	σ	σ	PROPN
ejpam-5802	257	28	-	-	ADJ
ejpam-5802	257	29	compact	compact	ADJ
ejpam-5802	257	30	,	,	PUNCT
ejpam-5802	257	31	i=1,2,	i=1,2,	NOUN
ejpam-5802	257	32	...	...	PUNCT
ejpam-5802	257	33	,n	,n	PUNCT
ejpam-5802	257	34	.	.	PUNCT
ejpam-5802	258	1	theorem	theorem	NOUN
ejpam-5802	258	2	2	2	NUM
ejpam-5802	258	3	:	:	PUNCT
ejpam-5802	258	4	the	the	DET
ejpam-5802	258	5	continuous	continuous	ADJ
ejpam-5802	258	6	image	image	NOUN
ejpam-5802	258	7	of	of	ADP
ejpam-5802	258	8	a	a	DET
ejpam-5802	258	9	nth	nth	NOUN
ejpam-5802	258	10	σ	σ	ADJ
ejpam-5802	258	11	-	-	ADJ
ejpam-5802	258	12	compact	compact	ADJ
ejpam-5802	258	13	space	space	NOUN
ejpam-5802	258	14	is	be	AUX
ejpam-5802	258	15	also	also	ADV
ejpam-5802	258	16	nth	nth	PROPN
ejpam-5802	258	17	σ	σ	PROPN
ejpam-5802	258	18	-	-	ADJ
ejpam-5802	258	19	compact	compact	ADJ
ejpam-5802	258	20	space	space	NOUN
ejpam-5802	258	21	.	.	PUNCT
ejpam-5802	259	1	proof	proof	NOUN
ejpam-5802	259	2	:	:	PUNCT
ejpam-5802	259	3	let	let	VERB
ejpam-5802	259	4	h	h	NOUN
ejpam-5802	259	5	:	:	PUNCT
ejpam-5802	259	6	(	(	PUNCT
ejpam-5802	259	7	k	k	X
ejpam-5802	259	8	,	,	PUNCT
ejpam-5802	259	9	η1	η1	NOUN
ejpam-5802	259	10	,	,	PUNCT
ejpam-5802	259	11	η2	η2	NOUN
ejpam-5802	259	12	,	,	PUNCT
ejpam-5802	259	13	...	...	PUNCT
ejpam-5802	259	14	,	,	PUNCT
ejpam-5802	259	15	ηn	ηn	PROPN
ejpam-5802	259	16	)	)	PUNCT
ejpam-5802	259	17	→	→	SYM
ejpam-5802	259	18	(	(	PUNCT
ejpam-5802	259	19	j	j	NOUN
ejpam-5802	259	20	,	,	PUNCT
ejpam-5802	259	21	λ1,λ2,λ3	λ1,λ2,λ3	X
ejpam-5802	259	22	)	)	PUNCT
ejpam-5802	259	23	be	be	AUX
ejpam-5802	259	24	a	a	DET
ejpam-5802	259	25	continuous	continuous	ADJ
ejpam-5802	259	26	map	map	NOUN
ejpam-5802	259	27	and	and	CCONJ
ejpam-5802	259	28	d	d	NOUN
ejpam-5802	259	29	=	=	SYM
ejpam-5802	259	30	⋃∞	⋃∞	X
ejpam-5802	259	31	ni=1	ni=1	PROPN
ejpam-5802	259	32	m(ni	m(ni	PROPN
ejpam-5802	259	33	)	)	PUNCT
ejpam-5802	259	34	,	,	PUNCT
ejpam-5802	259	35	where	where	SCONJ
ejpam-5802	259	36	each	each	DET
ejpam-5802	259	37	m(ni	m(ni	NOUN
ejpam-5802	259	38	)	)	PUNCT
ejpam-5802	259	39	is	be	AUX
ejpam-5802	259	40	compact	compact	ADJ
ejpam-5802	259	41	.	.	PUNCT
ejpam-5802	260	1	since	since	SCONJ
ejpam-5802	260	2	h(m(ni	h(m(ni	NOUN
ejpam-5802	260	3	)	)	PUNCT
ejpam-5802	260	4	)	)	PUNCT
ejpam-5802	260	5	is	be	AUX
ejpam-5802	260	6	compact	compact	ADJ
ejpam-5802	260	7	(	(	PUNCT
ejpam-5802	260	8	compactness	compactness	NOUN
ejpam-5802	260	9	preserved	preserve	VERB
ejpam-5802	260	10	under	under	ADP
ejpam-5802	260	11	continuous	continuous	ADJ
ejpam-5802	260	12	maps	map	NOUN
ejpam-5802	260	13	)	)	PUNCT
ejpam-5802	260	14	,	,	PUNCT
ejpam-5802	260	15	we	we	PRON
ejpam-5802	260	16	have	have	VERB
ejpam-5802	260	17	h(k	h(k	PROPN
ejpam-5802	260	18	)	)	PUNCT
ejpam-5802	261	1	=	=	SYM
ejpam-5802	261	2	⋃∞	⋃∞	X
ejpam-5802	261	3	ni=1	ni=1	X
ejpam-5802	261	4	f(m(ni	f(m(ni	NOUN
ejpam-5802	261	5	)	)	PUNCT
ejpam-5802	261	6	)	)	PUNCT
ejpam-5802	261	7	,	,	PUNCT
ejpam-5802	261	8	which	which	PRON
ejpam-5802	261	9	is	be	AUX
ejpam-5802	261	10	a	a	DET
ejpam-5802	261	11	countable	countable	ADJ
ejpam-5802	261	12	union	union	NOUN
ejpam-5802	261	13	of	of	ADP
ejpam-5802	261	14	compact	compact	ADJ
ejpam-5802	261	15	sets	set	NOUN
ejpam-5802	261	16	in	in	ADP
ejpam-5802	261	17	j.	j.	PROPN
ejpam-5802	261	18	hence	hence	PROPN
ejpam-5802	261	19	,	,	PUNCT
ejpam-5802	261	20	h(k	h(k	PROPN
ejpam-5802	261	21	)	)	PUNCT
ejpam-5802	261	22	is	be	AUX
ejpam-5802	261	23	nth	nth	NOUN
ejpam-5802	261	24	σ	σ	PROPN
ejpam-5802	261	25	-	-	PROPN
ejpam-5802	261	26	compact	compact	ADJ
ejpam-5802	261	27	,	,	PUNCT
ejpam-5802	261	28	for	for	ADP
ejpam-5802	261	29	all	all	DET
ejpam-5802	261	30	i=1,2,	i=1,2,	NOUN
ejpam-5802	261	31	...	...	PUNCT
ejpam-5802	261	32	,n	,n	PUNCT
ejpam-5802	261	33	.	.	PUNCT
ejpam-5802	262	1	theorem	theorem	VERB
ejpam-5802	262	2	3	3	NUM
ejpam-5802	262	3	:	:	PUNCT
ejpam-5802	262	4	the	the	DET
ejpam-5802	262	5	product	product	NOUN
ejpam-5802	262	6	of	of	ADP
ejpam-5802	262	7	a	a	DET
ejpam-5802	262	8	nth	nth	NOUN
ejpam-5802	262	9	σ	σ	ADJ
ejpam-5802	262	10	-	-	ADJ
ejpam-5802	262	11	compact	compact	ADJ
ejpam-5802	262	12	space	space	NOUN
ejpam-5802	262	13	with	with	ADP
ejpam-5802	262	14	a	a	DET
ejpam-5802	262	15	nth	nth	ADJ
ejpam-5802	262	16	compact	compact	ADJ
ejpam-5802	262	17	space	space	NOUN
ejpam-5802	262	18	is	be	AUX
ejpam-5802	262	19	nth	nth	NOUN
ejpam-5802	262	20	σ	σ	PROPN
ejpam-5802	262	21	-	-	PROPN
ejpam-5802	262	22	compact	compact	ADJ
ejpam-5802	262	23	.	.	PUNCT
ejpam-5802	263	1	proof	proof	NOUN
ejpam-5802	263	2	:	:	PUNCT
ejpam-5802	263	3	let	let	VERB
ejpam-5802	263	4	k	k	PROPN
ejpam-5802	263	5	=	=	PUNCT
ejpam-5802	263	6	⋃∞	⋃∞	X
ejpam-5802	263	7	ni=1m(ni	ni=1m(ni	PROPN
ejpam-5802	263	8	)	)	PUNCT
ejpam-5802	263	9	,	,	PUNCT
ejpam-5802	263	10	where	where	SCONJ
ejpam-5802	263	11	each	each	DET
ejpam-5802	263	12	m(ni	m(ni	PROPN
ejpam-5802	263	13	)	)	PUNCT
ejpam-5802	263	14	⊂	⊂	PROPN
ejpam-5802	264	1	k	k	PROPN
ejpam-5802	264	2	is	be	AUX
ejpam-5802	264	3	nth	nth	NOUN
ejpam-5802	264	4	compact	compact	ADJ
ejpam-5802	264	5	,	,	PUNCT
ejpam-5802	264	6	and	and	CCONJ
ejpam-5802	264	7	let	let	VERB
ejpam-5802	264	8	y	y	PRON
ejpam-5802	264	9	be	be	AUX
ejpam-5802	264	10	nth	nth	ADV
ejpam-5802	264	11	compact	compact	ADJ
ejpam-5802	264	12	.	.	PUNCT
ejpam-5802	265	1	then	then	ADV
ejpam-5802	265	2	k	k	PROPN
ejpam-5802	265	3	×	×	PROPN
ejpam-5802	265	4	y	y	PROPN
ejpam-5802	265	5	=	=	PUNCT
ejpam-5802	265	6	⋃∞	⋃∞	X
ejpam-5802	265	7	ni=1	ni=1	X
ejpam-5802	265	8	(	(	PUNCT
ejpam-5802	265	9	m(ni)×	m(ni)×	PROPN
ejpam-5802	265	10	y	y	PROPN
ejpam-5802	265	11	)	)	PUNCT
ejpam-5802	265	12	,	,	PUNCT
ejpam-5802	265	13	where	where	SCONJ
ejpam-5802	265	14	each	each	DET
ejpam-5802	265	15	m(ni)×	m(ni)×	X
ejpam-5802	265	16	y	y	PROPN
ejpam-5802	265	17	is	be	AUX
ejpam-5802	265	18	nth	nth	ADV
ejpam-5802	265	19	compact	compact	ADJ
ejpam-5802	265	20	in	in	ADP
ejpam-5802	265	21	k	k	PROPN
ejpam-5802	265	22	×y	×y	PRON
ejpam-5802	265	23	(	(	PUNCT
ejpam-5802	265	24	since	since	SCONJ
ejpam-5802	265	25	j.	j.	PROPN
ejpam-5802	265	26	oudetallah	oudetallah	PROPN
ejpam-5802	265	27	et	et	PROPN
ejpam-5802	265	28	al	al	PROPN
ejpam-5802	265	29	.	.	PUNCT
ejpam-5802	265	30	/	/	SYM
ejpam-5802	265	31	eur	eur	PROPN
ejpam-5802	265	32	.	.	PUNCT
ejpam-5802	266	1	j.	j.	PROPN
ejpam-5802	266	2	pure	pure	PROPN
ejpam-5802	266	3	appl	appl	PROPN
ejpam-5802	266	4	.	.	PROPN
ejpam-5802	266	5	math	math	PROPN
ejpam-5802	266	6	,	,	PUNCT
ejpam-5802	266	7	18	18	NUM
ejpam-5802	266	8	(	(	PUNCT
ejpam-5802	266	9	2	2	NUM
ejpam-5802	266	10	)	)	PUNCT
ejpam-5802	266	11	(	(	PUNCT
ejpam-5802	266	12	2025	2025	NUM
ejpam-5802	266	13	)	)	PUNCT
ejpam-5802	266	14	,	,	PUNCT
ejpam-5802	266	15	5802	5802	NUM
ejpam-5802	266	16	12	12	NUM
ejpam-5802	266	17	of	of	ADP
ejpam-5802	266	18	14	14	NUM
ejpam-5802	266	19	the	the	DET
ejpam-5802	266	20	product	product	NOUN
ejpam-5802	266	21	of	of	ADP
ejpam-5802	266	22	nth	nth	PROPN
ejpam-5802	266	23	compact	compact	ADJ
ejpam-5802	266	24	spaces	space	NOUN
ejpam-5802	266	25	is	be	AUX
ejpam-5802	266	26	nth	nth	NOUN
ejpam-5802	266	27	compact	compact	ADJ
ejpam-5802	266	28	)	)	PUNCT
ejpam-5802	266	29	.	.	PUNCT
ejpam-5802	267	1	therefore	therefore	ADV
ejpam-5802	267	2	,	,	PUNCT
ejpam-5802	267	3	k	k	PROPN
ejpam-5802	267	4	×	×	PROPN
ejpam-5802	267	5	y	y	PROPN
ejpam-5802	267	6	is	be	AUX
ejpam-5802	267	7	nth	nth	PROPN
ejpam-5802	267	8	σ	σ	PROPN
ejpam-5802	267	9	-	-	PROPN
ejpam-5802	267	10	compact	compact	ADJ
ejpam-5802	267	11	.	.	PUNCT
ejpam-5802	268	1	theorem	theorem	NOUN
ejpam-5802	268	2	5	5	NUM
ejpam-5802	268	3	:	:	PUNCT
ejpam-5802	268	4	the	the	DET
ejpam-5802	268	5	countable	countable	ADJ
ejpam-5802	268	6	union	union	NOUN
ejpam-5802	268	7	of	of	ADP
ejpam-5802	268	8	nth	nth	PROPN
ejpam-5802	268	9	σ	σ	PROPN
ejpam-5802	268	10	-	-	ADJ
ejpam-5802	268	11	compact	compact	ADJ
ejpam-5802	268	12	subspaces	subspace	NOUN
ejpam-5802	268	13	is	be	AUX
ejpam-5802	268	14	nth	nth	NOUN
ejpam-5802	268	15	σ	σ	PROPN
ejpam-5802	268	16	-	-	PROPN
ejpam-5802	268	17	compact	compact	ADJ
ejpam-5802	268	18	.	.	PUNCT
ejpam-5802	269	1	proof	proof	NOUN
ejpam-5802	269	2	:	:	PUNCT
ejpam-5802	269	3	let	let	VERB
ejpam-5802	269	4	k	k	PROPN
ejpam-5802	269	5	=	=	PRON
ejpam-5802	269	6	⋃∞	⋃∞	X
ejpam-5802	269	7	i=1ki	i=1ki	NOUN
ejpam-5802	269	8	,	,	PUNCT
ejpam-5802	269	9	where	where	SCONJ
ejpam-5802	269	10	each	each	DET
ejpam-5802	269	11	di	di	NOUN
ejpam-5802	269	12	is	be	AUX
ejpam-5802	269	13	n	n	ADV
ejpam-5802	269	14	th	th	X
ejpam-5802	269	15	σ	σ	NOUN
ejpam-5802	269	16	-	-	NOUN
ejpam-5802	269	17	compact	compact	ADJ
ejpam-5802	269	18	.	.	PUNCT
ejpam-5802	270	1	then	then	ADV
ejpam-5802	270	2	,	,	PUNCT
ejpam-5802	270	3	for	for	ADP
ejpam-5802	270	4	each	each	DET
ejpam-5802	270	5	i	i	PRON
ejpam-5802	270	6	,	,	PUNCT
ejpam-5802	270	7	we	we	PRON
ejpam-5802	270	8	can	can	AUX
ejpam-5802	270	9	write	write	VERB
ejpam-5802	270	10	ki	ki	PROPN
ejpam-5802	270	11	=	=	NOUN
ejpam-5802	270	12	⋃∞	⋃∞	ADP
ejpam-5802	270	13	j=1	j=1	PROPN
ejpam-5802	270	14	sij	sij	PROPN
ejpam-5802	270	15	,	,	PUNCT
ejpam-5802	270	16	where	where	SCONJ
ejpam-5802	270	17	sij	sij	PROPN
ejpam-5802	270	18	are	be	AUX
ejpam-5802	270	19	nth	nth	ADV
ejpam-5802	270	20	compact	compact	ADJ
ejpam-5802	270	21	.	.	PUNCT
ejpam-5802	271	1	thus	thus	ADV
ejpam-5802	271	2	,	,	PUNCT
ejpam-5802	271	3	k	k	PROPN
ejpam-5802	271	4	=	=	X
ejpam-5802	271	5	⋃∞	⋃∞	X
ejpam-5802	271	6	i=1	i=1	X
ejpam-5802	271	7	⋃∞	⋃∞	PUNCT
ejpam-5802	271	8	j=1	j=1	PROPN
ejpam-5802	271	9	sij	sij	PROPN
ejpam-5802	271	10	,	,	PUNCT
ejpam-5802	271	11	which	which	PRON
ejpam-5802	271	12	is	be	AUX
ejpam-5802	271	13	a	a	DET
ejpam-5802	271	14	nth	nth	NOUN
ejpam-5802	271	15	countable	countable	ADJ
ejpam-5802	271	16	union	union	NOUN
ejpam-5802	271	17	of	of	ADP
ejpam-5802	271	18	nth	nth	PROPN
ejpam-5802	271	19	compact	compact	ADJ
ejpam-5802	271	20	sets	set	NOUN
ejpam-5802	271	21	,	,	PUNCT
ejpam-5802	271	22	proving	prove	VERB
ejpam-5802	271	23	k	k	PROPN
ejpam-5802	271	24	is	be	AUX
ejpam-5802	271	25	nth	nth	PROPN
ejpam-5802	271	26	σ	σ	PROPN
ejpam-5802	271	27	-	-	PROPN
ejpam-5802	271	28	compact	compact	ADJ
ejpam-5802	271	29	.	.	PUNCT
ejpam-5802	272	1	theorem	theorem	VERB
ejpam-5802	272	2	6	6	NUM
ejpam-5802	272	3	:	:	PUNCT
ejpam-5802	272	4	every	every	DET
ejpam-5802	272	5	second	second	ADJ
ejpam-5802	272	6	-	-	PUNCT
ejpam-5802	272	7	countable	countable	ADJ
ejpam-5802	272	8	compact	compact	ADJ
ejpam-5802	272	9	space	space	NOUN
ejpam-5802	272	10	is	be	AUX
ejpam-5802	272	11	nth	nth	NOUN
ejpam-5802	272	12	σ	σ	PROPN
ejpam-5802	272	13	-	-	ADJ
ejpam-5802	272	14	compact	compact	ADJ
ejpam-5802	272	15	space	space	NOUN
ejpam-5802	272	16	.	.	PUNCT
ejpam-5802	273	1	proof	proof	NOUN
ejpam-5802	273	2	:	:	PUNCT
ejpam-5802	273	3	since	since	SCONJ
ejpam-5802	273	4	(	(	PUNCT
ejpam-5802	273	5	k	k	X
ejpam-5802	273	6	,	,	PUNCT
ejpam-5802	273	7	η1	η1	NOUN
ejpam-5802	273	8	,	,	PUNCT
ejpam-5802	273	9	η2	η2	NOUN
ejpam-5802	273	10	,	,	PUNCT
ejpam-5802	273	11	...	...	PUNCT
ejpam-5802	273	12	,	,	PUNCT
ejpam-5802	273	13	ηn	ηn	INTJ
ejpam-5802	273	14	)	)	PUNCT
ejpam-5802	273	15	is	be	AUX
ejpam-5802	273	16	nth	nth	PROPN
ejpam-5802	273	17	topological	topological	ADJ
ejpam-5802	273	18	space	space	NOUN
ejpam-5802	273	19	and	and	CCONJ
ejpam-5802	273	20	k	k	PROPN
ejpam-5802	273	21	is	be	AUX
ejpam-5802	273	22	second	second	ADV
ejpam-5802	273	23	countable	countable	ADJ
ejpam-5802	273	24	,	,	PUNCT
ejpam-5802	273	25	there	there	PRON
ejpam-5802	273	26	exists	exist	VERB
ejpam-5802	273	27	a	a	DET
ejpam-5802	273	28	countable	countable	ADJ
ejpam-5802	273	29	base	base	NOUN
ejpam-5802	273	30	{	{	PUNCT
ejpam-5802	273	31	vi}∞i=1	vi}∞i=1	X
ejpam-5802	273	32	.	.	PUNCT
ejpam-5802	274	1	each	each	DET
ejpam-5802	274	2	compact	compact	ADJ
ejpam-5802	274	3	subset	subset	VERB
ejpam-5802	274	4	mi	mi	PROPN
ejpam-5802	274	5	=	=	PROPN
ejpam-5802	274	6	vi	vi	PROPN
ejpam-5802	274	7	is	be	AUX
ejpam-5802	274	8	compact	compact	ADJ
ejpam-5802	274	9	in	in	ADP
ejpam-5802	274	10	a	a	DET
ejpam-5802	274	11	second	second	ADJ
ejpam-5802	274	12	-	-	PUNCT
ejpam-5802	274	13	countable	countable	ADJ
ejpam-5802	274	14	space	space	NOUN
ejpam-5802	274	15	,	,	PUNCT
ejpam-5802	274	16	and	and	CCONJ
ejpam-5802	274	17	since	since	SCONJ
ejpam-5802	274	18	k	k	PROPN
ejpam-5802	274	19	=	=	PUNCT
ejpam-5802	274	20	⋃∞	⋃∞	X
ejpam-5802	274	21	i=1mi	i=1mi	PROPN
ejpam-5802	274	22	,	,	PUNCT
ejpam-5802	274	23	k	k	PROPN
ejpam-5802	274	24	is	be	AUX
ejpam-5802	274	25	nth	nth	PROPN
ejpam-5802	274	26	σ	σ	PROPN
ejpam-5802	274	27	-	-	ADJ
ejpam-5802	274	28	compact	compact	ADJ
ejpam-5802	274	29	space	space	NOUN
ejpam-5802	274	30	.	.	PUNCT
ejpam-5802	275	1	theorem	theorem	VERB
ejpam-5802	275	2	7	7	NUM
ejpam-5802	275	3	:	:	PUNCT
ejpam-5802	275	4	every	every	DET
ejpam-5802	275	5	compact	compact	ADJ
ejpam-5802	275	6	subspace	subspace	NOUN
ejpam-5802	275	7	of	of	ADP
ejpam-5802	275	8	a	a	DET
ejpam-5802	275	9	nth	nth	NOUN
ejpam-5802	275	10	σ	σ	ADJ
ejpam-5802	275	11	-	-	ADJ
ejpam-5802	275	12	compact	compact	ADJ
ejpam-5802	275	13	space	space	NOUN
ejpam-5802	275	14	is	be	AUX
ejpam-5802	275	15	nth	nth	NOUN
ejpam-5802	275	16	σ	σ	PROPN
ejpam-5802	275	17	-	-	ADJ
ejpam-5802	275	18	compact	compact	ADJ
ejpam-5802	275	19	space	space	NOUN
ejpam-5802	275	20	.	.	PUNCT
ejpam-5802	276	1	proof	proof	NOUN
ejpam-5802	276	2	:	:	PUNCT
ejpam-5802	276	3	let	let	VERB
ejpam-5802	276	4	(	(	PUNCT
ejpam-5802	276	5	k	k	X
ejpam-5802	276	6	,	,	PUNCT
ejpam-5802	276	7	η1	η1	NOUN
ejpam-5802	276	8	,	,	PUNCT
ejpam-5802	276	9	η2	η2	NOUN
ejpam-5802	276	10	,	,	PUNCT
ejpam-5802	276	11	...	...	PUNCT
ejpam-5802	276	12	,	,	PUNCT
ejpam-5802	276	13	ηn	ηn	INTJ
ejpam-5802	276	14	)	)	PUNCT
ejpam-5802	276	15	be	be	AUX
ejpam-5802	276	16	nth	nth	NOUN
ejpam-5802	276	17	σ	σ	PROPN
ejpam-5802	276	18	-	-	ADJ
ejpam-5802	276	19	compact	compact	ADJ
ejpam-5802	276	20	and	and	CCONJ
ejpam-5802	276	21	m	m	VERB
ejpam-5802	276	22	⊂	⊂	PROPN
ejpam-5802	276	23	k	k	PROPN
ejpam-5802	276	24	compact	compact	PROPN
ejpam-5802	276	25	.	.	PUNCT
ejpam-5802	277	1	since	since	SCONJ
ejpam-5802	277	2	k	k	PROPN
ejpam-5802	277	3	=	=	PROPN
ejpam-5802	277	4	⋃∞	⋃∞	SYM
ejpam-5802	277	5	n=1m(ni	n=1m(ni	PROPN
ejpam-5802	277	6	)	)	PUNCT
ejpam-5802	277	7	where	where	SCONJ
ejpam-5802	277	8	each	each	DET
ejpam-5802	277	9	m(ni	m(ni	PROPN
ejpam-5802	277	10	)	)	PUNCT
ejpam-5802	277	11	is	be	AUX
ejpam-5802	277	12	n	n	PRON
ejpam-5802	277	13	th	th	X
ejpam-5802	277	14	compact	compact	ADJ
ejpam-5802	277	15	,	,	PUNCT
ejpam-5802	277	16	m	m	VERB
ejpam-5802	277	17	=	=	NOUN
ejpam-5802	277	18	⋃∞	⋃∞	X
ejpam-5802	277	19	n=1	n=1	PROPN
ejpam-5802	277	20	(	(	PUNCT
ejpam-5802	277	21	m	m	VERB
ejpam-5802	277	22	∩m(ni	∩m(ni	ADJ
ejpam-5802	277	23	)	)	PUNCT
ejpam-5802	277	24	)	)	PUNCT
ejpam-5802	277	25	,	,	PUNCT
ejpam-5802	277	26	which	which	PRON
ejpam-5802	277	27	is	be	AUX
ejpam-5802	277	28	a	a	DET
ejpam-5802	277	29	countable	countable	ADJ
ejpam-5802	277	30	union	union	NOUN
ejpam-5802	277	31	of	of	ADP
ejpam-5802	277	32	compact	compact	ADJ
ejpam-5802	277	33	sets	set	NOUN
ejpam-5802	277	34	.	.	PUNCT
ejpam-5802	278	1	thus	thus	ADV
ejpam-5802	278	2	,	,	PUNCT
ejpam-5802	278	3	m	m	VERB
ejpam-5802	278	4	is	be	AUX
ejpam-5802	278	5	nth	nth	PROPN
ejpam-5802	278	6	σ	σ	PROPN
ejpam-5802	278	7	-	-	ADJ
ejpam-5802	278	8	compact	compact	ADJ
ejpam-5802	278	9	space	space	NOUN
ejpam-5802	278	10	,	,	PUNCT
ejpam-5802	278	11	i=1,2,	i=1,2,	NOUN
ejpam-5802	278	12	...	...	PUNCT
ejpam-5802	278	13	,n	,n	PUNCT
ejpam-5802	278	14	.	.	PUNCT
ejpam-5802	279	1	theorem	theorem	VERB
ejpam-5802	279	2	8	8	NUM
ejpam-5802	279	3	:	:	PUNCT
ejpam-5802	279	4	if	if	SCONJ
ejpam-5802	279	5	k	k	PROPN
ejpam-5802	279	6	is	be	AUX
ejpam-5802	279	7	nth	nth	PROPN
ejpam-5802	279	8	σ	σ	PROPN
ejpam-5802	279	9	-	-	ADJ
ejpam-5802	279	10	compact	compact	ADJ
ejpam-5802	279	11	space	space	NOUN
ejpam-5802	279	12	,	,	PUNCT
ejpam-5802	279	13	then	then	ADV
ejpam-5802	279	14	any	any	DET
ejpam-5802	279	15	quotient	quotient	NOUN
ejpam-5802	279	16	space	space	NOUN
ejpam-5802	279	17	r	r	NOUN
ejpam-5802	279	18	=	=	SYM
ejpam-5802	279	19	k	k	X
ejpam-5802	279	20	∼	∼	NOUN
ejpam-5802	279	21	is	be	AUX
ejpam-5802	279	22	nth	nth	NOUN
ejpam-5802	279	23	σ	σ	PROPN
ejpam-5802	279	24	-	-	ADJ
ejpam-5802	279	25	compact	compact	ADJ
ejpam-5802	279	26	space	space	NOUN
ejpam-5802	279	27	.	.	PUNCT
ejpam-5802	280	1	proof	proof	NOUN
ejpam-5802	280	2	:	:	PUNCT
ejpam-5802	280	3	let	let	VERB
ejpam-5802	280	4	k	k	PROPN
ejpam-5802	280	5	=	=	PRON
ejpam-5802	280	6	⋃∞	⋃∞	X
ejpam-5802	280	7	n=1	n=1	PROPN
ejpam-5802	280	8	m(ni	m(ni	PROPN
ejpam-5802	280	9	)	)	PUNCT
ejpam-5802	280	10	with	with	ADP
ejpam-5802	280	11	each	each	DET
ejpam-5802	280	12	m(ni	m(ni	PROPN
ejpam-5802	280	13	)	)	PUNCT
ejpam-5802	280	14	nth	nth	PROPN
ejpam-5802	280	15	σ	σ	PROPN
ejpam-5802	280	16	-	-	ADJ
ejpam-5802	280	17	compact	compact	ADJ
ejpam-5802	280	18	space	space	NOUN
ejpam-5802	280	19	.	.	PUNCT
ejpam-5802	281	1	since	since	SCONJ
ejpam-5802	281	2	the	the	DET
ejpam-5802	281	3	quotient	quotient	NOUN
ejpam-5802	281	4	map	map	NOUN
ejpam-5802	281	5	q	q	NOUN
ejpam-5802	281	6	:	:	PUNCT
ejpam-5802	281	7	k	k	X
ejpam-5802	281	8	→	→	PUNCT
ejpam-5802	281	9	r	r	NOUN
ejpam-5802	281	10	is	be	AUX
ejpam-5802	281	11	continuous	continuous	ADJ
ejpam-5802	281	12	,	,	PUNCT
ejpam-5802	281	13	q(m(ni	q(m(ni	PROPN
ejpam-5802	281	14	)	)	PUNCT
ejpam-5802	281	15	)	)	PUNCT
ejpam-5802	282	1	is	be	AUX
ejpam-5802	282	2	nth	nth	PROPN
ejpam-5802	282	3	σ	σ	PROPN
ejpam-5802	282	4	-	-	PROPN
ejpam-5802	282	5	compact	compact	ADJ
ejpam-5802	282	6	in	in	ADP
ejpam-5802	282	7	r.	r.	PROPN
ejpam-5802	282	8	thus	thus	ADV
ejpam-5802	282	9	,	,	PUNCT
ejpam-5802	282	10	r	r	NOUN
ejpam-5802	282	11	=	=	SYM
ejpam-5802	282	12	⋃∞	⋃∞	X
ejpam-5802	282	13	n=1q(m(ni	n=1q(m(ni	PROPN
ejpam-5802	282	14	)	)	PUNCT
ejpam-5802	282	15	)	)	PUNCT
ejpam-5802	282	16	,	,	PUNCT
ejpam-5802	282	17	proving	prove	VERB
ejpam-5802	282	18	that	that	SCONJ
ejpam-5802	282	19	r	r	NOUN
ejpam-5802	282	20	is	be	AUX
ejpam-5802	282	21	nth	nth	NOUN
ejpam-5802	282	22	σ	σ	PROPN
ejpam-5802	282	23	-	-	ADJ
ejpam-5802	282	24	compact	compact	ADJ
ejpam-5802	282	25	space	space	NOUN
ejpam-5802	282	26	,	,	PUNCT
ejpam-5802	282	27	i=1,2,	i=1,2,	NOUN
ejpam-5802	282	28	...	...	PUNCT
ejpam-5802	282	29	,n	,n	PUNCT
ejpam-5802	282	30	.	.	PUNCT
ejpam-5802	283	1	theorem	theorem	VERB
ejpam-5802	283	2	9	9	NUM
ejpam-5802	283	3	:	:	PUNCT
ejpam-5802	283	4	every	every	DET
ejpam-5802	283	5	nth	nth	NOUN
ejpam-5802	283	6	σ	σ	ADJ
ejpam-5802	283	7	-	-	ADJ
ejpam-5802	283	8	compact	compact	ADJ
ejpam-5802	283	9	space	space	NOUN
ejpam-5802	283	10	is	be	AUX
ejpam-5802	283	11	separable	separable	ADJ
ejpam-5802	283	12	if	if	SCONJ
ejpam-5802	283	13	it	it	PRON
ejpam-5802	283	14	is	be	AUX
ejpam-5802	283	15	a	a	DET
ejpam-5802	283	16	metric	metric	ADJ
ejpam-5802	283	17	space	space	NOUN
ejpam-5802	283	18	.	.	PUNCT
ejpam-5802	284	1	proof	proof	NOUN
ejpam-5802	284	2	:	:	PUNCT
ejpam-5802	284	3	let	let	VERB
ejpam-5802	284	4	k	k	PRON
ejpam-5802	284	5	be	be	AUX
ejpam-5802	284	6	an	an	DET
ejpam-5802	284	7	nth	nth	NOUN
ejpam-5802	284	8	σ	σ	NOUN
ejpam-5802	284	9	-	-	ADJ
ejpam-5802	284	10	compact	compact	ADJ
ejpam-5802	284	11	metric	metric	ADJ
ejpam-5802	284	12	space	space	NOUN
ejpam-5802	284	13	.	.	PUNCT
ejpam-5802	285	1	since	since	SCONJ
ejpam-5802	285	2	k	k	PROPN
ejpam-5802	285	3	can	can	AUX
ejpam-5802	285	4	be	be	AUX
ejpam-5802	285	5	expressed	express	VERB
ejpam-5802	285	6	as	as	ADP
ejpam-5802	285	7	a	a	DET
ejpam-5802	285	8	countable	countable	ADJ
ejpam-5802	285	9	union	union	NOUN
ejpam-5802	285	10	of	of	ADP
ejpam-5802	285	11	compact	compact	ADJ
ejpam-5802	285	12	sets	set	NOUN
ejpam-5802	285	13	m(ni	m(ni	PROPN
ejpam-5802	285	14	)	)	PUNCT
ejpam-5802	285	15	,	,	PUNCT
ejpam-5802	285	16	each	each	DET
ejpam-5802	285	17	m(ni	m(ni	PROPN
ejpam-5802	285	18	)	)	PUNCT
ejpam-5802	285	19	is	be	AUX
ejpam-5802	285	20	separable	separable	ADJ
ejpam-5802	285	21	(	(	PUNCT
ejpam-5802	285	22	nth	nth	ADJ
ejpam-5802	285	23	compact	compact	ADJ
ejpam-5802	285	24	subsets	subset	NOUN
ejpam-5802	285	25	of	of	ADP
ejpam-5802	285	26	metric	metric	ADJ
ejpam-5802	285	27	spaces	space	NOUN
ejpam-5802	285	28	are	be	AUX
ejpam-5802	285	29	separable	separable	ADJ
ejpam-5802	285	30	)	)	PUNCT
ejpam-5802	285	31	.	.	PUNCT
ejpam-5802	286	1	therefore	therefore	ADV
ejpam-5802	286	2	,	,	PUNCT
ejpam-5802	286	3	we	we	PRON
ejpam-5802	286	4	can	can	AUX
ejpam-5802	286	5	find	find	VERB
ejpam-5802	286	6	a	a	DET
ejpam-5802	286	7	countable	countable	ADJ
ejpam-5802	286	8	dense	dense	ADJ
ejpam-5802	286	9	subset	subset	NOUN
ejpam-5802	286	10	t(ni	t(ni	NUM
ejpam-5802	286	11	)	)	PUNCT
ejpam-5802	286	12	for	for	ADP
ejpam-5802	286	13	each	each	DET
ejpam-5802	286	14	m(ni	m(ni	PROPN
ejpam-5802	286	15	)	)	PUNCT
ejpam-5802	286	16	.	.	PUNCT
ejpam-5802	287	1	the	the	DET
ejpam-5802	287	2	union	union	PROPN
ejpam-5802	287	3	t	t	PROPN
ejpam-5802	287	4	=	=	PUNCT
ejpam-5802	287	5	⋃∞	⋃∞	CCONJ
ejpam-5802	287	6	n=1	n=1	PROPN
ejpam-5802	287	7	t(ni	t(ni	PROPN
ejpam-5802	287	8	)	)	PUNCT
ejpam-5802	287	9	is	be	AUX
ejpam-5802	287	10	dense	dense	ADJ
ejpam-5802	287	11	in	in	ADP
ejpam-5802	287	12	k	k	PROPN
ejpam-5802	287	13	,	,	PUNCT
ejpam-5802	287	14	showing	show	VERB
ejpam-5802	287	15	that	that	SCONJ
ejpam-5802	287	16	k	k	PROPN
ejpam-5802	287	17	is	be	AUX
ejpam-5802	287	18	separable	separable	ADJ
ejpam-5802	287	19	,	,	PUNCT
ejpam-5802	287	20	for	for	ADP
ejpam-5802	287	21	all	all	DET
ejpam-5802	287	22	i=1,2,	i=1,2,	NOUN
ejpam-5802	287	23	...	...	PUNCT
ejpam-5802	287	24	,n	,n	PUNCT
ejpam-5802	287	25	.	.	PUNCT
ejpam-5802	288	1	example	example	NOUN
ejpam-5802	288	2	:	:	PUNCT
ejpam-5802	288	3	the	the	DET
ejpam-5802	288	4	real	real	ADJ
ejpam-5802	288	5	numbers	number	NOUN
ejpam-5802	288	6	r	r	NOUN
ejpam-5802	288	7	with	with	ADP
ejpam-5802	288	8	the	the	DET
ejpam-5802	288	9	standard	standard	ADJ
ejpam-5802	288	10	topology	topology	NOUN
ejpam-5802	288	11	are	be	AUX
ejpam-5802	288	12	nth	nth	NOUN
ejpam-5802	288	13	σ	σ	PROPN
ejpam-5802	288	14	-	-	ADJ
ejpam-5802	288	15	compact	compact	ADJ
ejpam-5802	288	16	and	and	CCONJ
ejpam-5802	288	17	separable	separable	ADJ
ejpam-5802	288	18	(	(	PUNCT
ejpam-5802	288	19	since	since	SCONJ
ejpam-5802	288	20	the	the	DET
ejpam-5802	288	21	set	set	NOUN
ejpam-5802	288	22	of	of	ADP
ejpam-5802	288	23	rational	rational	ADJ
ejpam-5802	288	24	numbers	number	NOUN
ejpam-5802	288	25	q	q	NOUN
ejpam-5802	288	26	is	be	AUX
ejpam-5802	288	27	dense	dense	ADJ
ejpam-5802	288	28	in	in	ADP
ejpam-5802	288	29	r	r	NOUN
ejpam-5802	288	30	)	)	PUNCT
ejpam-5802	288	31	.	.	PUNCT
ejpam-5802	289	1	j.	j.	PROPN
ejpam-5802	289	2	oudetallah	oudetallah	PROPN
ejpam-5802	289	3	et	et	PROPN
ejpam-5802	289	4	al	al	PROPN
ejpam-5802	289	5	.	.	PUNCT
ejpam-5802	289	6	/	/	SYM
ejpam-5802	289	7	eur	eur	PROPN
ejpam-5802	289	8	.	.	PUNCT
ejpam-5802	290	1	j.	j.	PROPN
ejpam-5802	290	2	pure	pure	PROPN
ejpam-5802	290	3	appl	appl	PROPN
ejpam-5802	290	4	.	.	PROPN
ejpam-5802	290	5	math	math	PROPN
ejpam-5802	290	6	,	,	PUNCT
ejpam-5802	290	7	18	18	NUM
ejpam-5802	290	8	(	(	PUNCT
ejpam-5802	290	9	2	2	NUM
ejpam-5802	290	10	)	)	PUNCT
ejpam-5802	290	11	(	(	PUNCT
ejpam-5802	290	12	2025	2025	NUM
ejpam-5802	290	13	)	)	PUNCT
ejpam-5802	290	14	,	,	PUNCT
ejpam-5802	290	15	5802	5802	NUM
ejpam-5802	290	16	13	13	NUM
ejpam-5802	290	17	of	of	ADP
ejpam-5802	290	18	14	14	NUM
ejpam-5802	290	19	theorem	theorem	NOUN
ejpam-5802	290	20	10	10	NUM
ejpam-5802	290	21	:	:	PUNCT
ejpam-5802	290	22	any	any	DET
ejpam-5802	290	23	locally	locally	ADV
ejpam-5802	290	24	compact	compact	ADJ
ejpam-5802	290	25	in	in	ADP
ejpam-5802	290	26	nth	nth	PROPN
ejpam-5802	290	27	σ	σ	PROPN
ejpam-5802	290	28	-	-	ADJ
ejpam-5802	290	29	compact	compact	ADJ
ejpam-5802	290	30	space	space	NOUN
ejpam-5802	290	31	is	be	AUX
ejpam-5802	290	32	nth	nth	NOUN
ejpam-5802	290	33	σ	σ	PROPN
ejpam-5802	290	34	-	-	ADJ
ejpam-5802	290	35	compact	compact	ADJ
ejpam-5802	290	36	space	space	NOUN
ejpam-5802	290	37	.	.	PUNCT
ejpam-5802	291	1	proof	proof	NOUN
ejpam-5802	291	2	:	:	PUNCT
ejpam-5802	291	3	let	let	AUX
ejpam-5802	291	4	(	(	PUNCT
ejpam-5802	291	5	k	k	X
ejpam-5802	291	6	,	,	PUNCT
ejpam-5802	291	7	η1	η1	NOUN
ejpam-5802	291	8	,	,	PUNCT
ejpam-5802	291	9	η2	η2	NOUN
ejpam-5802	291	10	,	,	PUNCT
ejpam-5802	291	11	...	...	PUNCT
ejpam-5802	291	12	,	,	PUNCT
ejpam-5802	291	13	ηn	ηn	INTJ
ejpam-5802	291	14	)	)	PUNCT
ejpam-5802	291	15	be	be	AUX
ejpam-5802	291	16	nth	nth	ADV
ejpam-5802	291	17	topological	topological	ADJ
ejpam-5802	291	18	space	space	NOUN
ejpam-5802	291	19	and	and	CCONJ
ejpam-5802	291	20	k	k	PROPN
ejpam-5802	291	21	is	be	AUX
ejpam-5802	291	22	nth	nth	PROPN
ejpam-5802	291	23	σ	σ	PROPN
ejpam-5802	291	24	-	-	ADJ
ejpam-5802	291	25	compact	compact	ADJ
ejpam-5802	291	26	space	space	NOUN
ejpam-5802	291	27	and	and	CCONJ
ejpam-5802	291	28	let	let	VERB
ejpam-5802	291	29	k	k	PROPN
ejpam-5802	291	30	be	be	AUX
ejpam-5802	291	31	a	a	DET
ejpam-5802	291	32	locally	locally	ADV
ejpam-5802	291	33	compact	compact	ADJ
ejpam-5802	291	34	nth	nth	NOUN
ejpam-5802	291	35	σ	σ	PROPN
ejpam-5802	291	36	-	-	ADJ
ejpam-5802	291	37	compact	compact	ADJ
ejpam-5802	291	38	space	space	NOUN
ejpam-5802	291	39	,	,	PUNCT
ejpam-5802	291	40	and	and	CCONJ
ejpam-5802	291	41	let	let	VERB
ejpam-5802	291	42	k	k	PROPN
ejpam-5802	291	43	=	=	SYM
ejpam-5802	291	44	⋃∞	⋃∞	SYM
ejpam-5802	291	45	n=1m(ni	n=1m(ni	PROPN
ejpam-5802	291	46	)	)	PUNCT
ejpam-5802	291	47	,	,	PUNCT
ejpam-5802	291	48	where	where	SCONJ
ejpam-5802	291	49	each	each	DET
ejpam-5802	291	50	m(ni	m(ni	NOUN
ejpam-5802	291	51	)	)	PUNCT
ejpam-5802	291	52	is	be	AUX
ejpam-5802	291	53	nth	nth	NOUN
ejpam-5802	291	54	compact	compact	ADJ
ejpam-5802	291	55	.	.	PUNCT
ejpam-5802	292	1	for	for	ADP
ejpam-5802	292	2	each	each	DET
ejpam-5802	292	3	point	point	NOUN
ejpam-5802	292	4	di	di	X
ejpam-5802	292	5	∈	∈	PROPN
ejpam-5802	292	6	k	k	NOUN
ejpam-5802	292	7	,	,	PUNCT
ejpam-5802	292	8	there	there	PRON
ejpam-5802	292	9	exists	exist	VERB
ejpam-5802	292	10	a	a	DET
ejpam-5802	292	11	neighborhood	neighborhood	NOUN
ejpam-5802	292	12	v(di	v(di	NOUN
ejpam-5802	292	13	)	)	PUNCT
ejpam-5802	292	14	that	that	PRON
ejpam-5802	292	15	is	be	AUX
ejpam-5802	292	16	compact	compact	ADJ
ejpam-5802	292	17	.	.	PUNCT
ejpam-5802	293	1	thus	thus	ADV
ejpam-5802	293	2	,	,	PUNCT
ejpam-5802	293	3	we	we	PRON
ejpam-5802	293	4	can	can	AUX
ejpam-5802	293	5	cover	cover	VERB
ejpam-5802	293	6	k	k	X
ejpam-5802	293	7	by	by	ADP
ejpam-5802	293	8	a	a	DET
ejpam-5802	293	9	countable	countable	ADJ
ejpam-5802	293	10	union	union	NOUN
ejpam-5802	293	11	of	of	ADP
ejpam-5802	293	12	compact	compact	ADJ
ejpam-5802	293	13	neighborhoods	neighborhood	NOUN
ejpam-5802	293	14	,	,	PUNCT
ejpam-5802	293	15	confirming	confirm	VERB
ejpam-5802	293	16	that	that	SCONJ
ejpam-5802	293	17	k	k	PROPN
ejpam-5802	293	18	is	be	AUX
ejpam-5802	293	19	nth	nth	PROPN
ejpam-5802	293	20	σ	σ	PROPN
ejpam-5802	293	21	-	-	ADJ
ejpam-5802	293	22	compact	compact	ADJ
ejpam-5802	293	23	space	space	NOUN
ejpam-5802	293	24	.	.	PUNCT
ejpam-5802	294	1	example	example	NOUN
ejpam-5802	294	2	:	:	PUNCT
ejpam-5802	294	3	the	the	DET
ejpam-5802	294	4	space	space	NOUN
ejpam-5802	294	5	rn	rn	PROPN
ejpam-5802	294	6	is	be	AUX
ejpam-5802	294	7	locally	locally	ADV
ejpam-5802	294	8	compact	compact	ADJ
ejpam-5802	294	9	and	and	CCONJ
ejpam-5802	294	10	nth	nth	NOUN
ejpam-5802	294	11	σ	σ	PROPN
ejpam-5802	294	12	-	-	ADJ
ejpam-5802	294	13	compact	compact	ADJ
ejpam-5802	294	14	space	space	NOUN
ejpam-5802	294	15	,	,	PUNCT
ejpam-5802	294	16	as	as	SCONJ
ejpam-5802	294	17	it	it	PRON
ejpam-5802	294	18	can	can	AUX
ejpam-5802	294	19	be	be	AUX
ejpam-5802	294	20	covered	cover	VERB
ejpam-5802	294	21	by	by	ADP
ejpam-5802	294	22	compact	compact	ADJ
ejpam-5802	294	23	sets	set	NOUN
ejpam-5802	294	24	(	(	PUNCT
ejpam-5802	294	25	closed	closed	ADJ
ejpam-5802	294	26	balls	ball	NOUN
ejpam-5802	294	27	)	)	PUNCT
ejpam-5802	294	28	in	in	ADP
ejpam-5802	294	29	a	a	DET
ejpam-5802	294	30	countable	countable	ADJ
ejpam-5802	294	31	manner	manner	NOUN
ejpam-5802	294	32	.	.	PUNCT
ejpam-5802	295	1	theorem	theorem	VERB
ejpam-5802	295	2	11	11	NUM
ejpam-5802	295	3	:	:	PUNCT
ejpam-5802	295	4	the	the	DET
ejpam-5802	295	5	space	space	NOUN
ejpam-5802	295	6	c(k	c(k	NOUN
ejpam-5802	295	7	)	)	PUNCT
ejpam-5802	295	8	of	of	ADP
ejpam-5802	295	9	continuous	continuous	ADJ
ejpam-5802	295	10	functions	function	NOUN
ejpam-5802	295	11	on	on	ADP
ejpam-5802	295	12	an	an	DET
ejpam-5802	295	13	nth	nth	NOUN
ejpam-5802	295	14	σ	σ	PROPN
ejpam-5802	295	15	-	-	ADJ
ejpam-5802	295	16	compact	compact	ADJ
ejpam-5802	295	17	space	space	NOUN
ejpam-5802	295	18	,	,	PUNCT
ejpam-5802	295	19	k	k	PROPN
ejpam-5802	295	20	is	be	AUX
ejpam-5802	295	21	nth	nth	PROPN
ejpam-5802	295	22	σ	σ	PROPN
ejpam-5802	295	23	-	-	PROPN
ejpam-5802	295	24	compact	compact	ADJ
ejpam-5802	295	25	under	under	ADP
ejpam-5802	295	26	the	the	DET
ejpam-5802	295	27	compact	compact	ADJ
ejpam-5802	295	28	open	open	ADJ
ejpam-5802	295	29	topology	topology	NOUN
ejpam-5802	295	30	.	.	PUNCT
ejpam-5802	296	1	proof	proof	NOUN
ejpam-5802	296	2	:	:	PUNCT
ejpam-5802	296	3	let	let	VERB
ejpam-5802	296	4	k	k	PROPN
ejpam-5802	296	5	=	=	PUNCT
ejpam-5802	296	6	⋃∞	⋃∞	SYM
ejpam-5802	296	7	n=1m(ni	n=1m(ni	PROPN
ejpam-5802	296	8	)	)	PUNCT
ejpam-5802	296	9	,	,	PUNCT
ejpam-5802	296	10	where	where	SCONJ
ejpam-5802	296	11	each	each	DET
ejpam-5802	296	12	m(ni	m(ni	NOUN
ejpam-5802	296	13	)	)	PUNCT
ejpam-5802	296	14	is	be	AUX
ejpam-5802	296	15	nth	nth	NOUN
ejpam-5802	296	16	compact	compact	ADJ
ejpam-5802	296	17	.	.	PUNCT
ejpam-5802	297	1	the	the	DET
ejpam-5802	297	2	compact	compact	ADJ
ejpam-5802	297	3	open	open	ADJ
ejpam-5802	297	4	topology	topology	NOUN
ejpam-5802	297	5	is	be	AUX
ejpam-5802	297	6	generated	generate	VERB
ejpam-5802	297	7	by	by	ADP
ejpam-5802	297	8	sets	set	NOUN
ejpam-5802	297	9	of	of	ADP
ejpam-5802	297	10	the	the	DET
ejpam-5802	297	11	form	form	NOUN
ejpam-5802	297	12	{	{	PUNCT
ejpam-5802	297	13	h	h	NOUN
ejpam-5802	297	14	:	:	PUNCT
ejpam-5802	297	15	m	m	VERB
ejpam-5802	297	16	→	→	SYM
ejpam-5802	298	1	r	r	NOUN
ejpam-5802	298	2	|	|	ADV
ejpam-5802	298	3	h(m	h(m	ADJ
ejpam-5802	298	4	)	)	PUNCT
ejpam-5802	298	5	⊆	⊆	NUM
ejpam-5802	298	6	u	u	NOUN
ejpam-5802	298	7	}	}	PUNCT
ejpam-5802	298	8	.	.	PUNCT
ejpam-5802	299	1	each	each	DET
ejpam-5802	299	2	nth	nth	PROPN
ejpam-5802	299	3	compact	compact	ADJ
ejpam-5802	299	4	set	set	VERB
ejpam-5802	299	5	m(ni	m(ni	PROPN
ejpam-5802	299	6	)	)	PUNCT
ejpam-5802	299	7	gives	give	VERB
ejpam-5802	299	8	rise	rise	NOUN
ejpam-5802	299	9	to	to	ADP
ejpam-5802	299	10	a	a	DET
ejpam-5802	299	11	countable	countable	ADJ
ejpam-5802	299	12	family	family	NOUN
ejpam-5802	299	13	of	of	ADP
ejpam-5802	299	14	compact	compact	ADJ
ejpam-5802	299	15	sets	set	NOUN
ejpam-5802	299	16	c(m(ni	c(m(ni	NOUN
ejpam-5802	299	17	)	)	PUNCT
ejpam-5802	299	18	)	)	PUNCT
ejpam-5802	299	19	in	in	ADP
ejpam-5802	299	20	c(k	c(k	NOUN
ejpam-5802	299	21	)	)	PUNCT
ejpam-5802	299	22	.	.	PUNCT
ejpam-5802	300	1	thus	thus	ADV
ejpam-5802	300	2	,	,	PUNCT
ejpam-5802	300	3	c(k	c(k	PROPN
ejpam-5802	300	4	)	)	PUNCT
ejpam-5802	300	5	can	can	AUX
ejpam-5802	300	6	be	be	AUX
ejpam-5802	300	7	expressed	express	VERB
ejpam-5802	300	8	as	as	ADP
ejpam-5802	300	9	a	a	DET
ejpam-5802	300	10	countable	countable	ADJ
ejpam-5802	300	11	union	union	NOUN
ejpam-5802	300	12	of	of	ADP
ejpam-5802	300	13	compact	compact	ADJ
ejpam-5802	300	14	sets	set	NOUN
ejpam-5802	300	15	,	,	PUNCT
ejpam-5802	300	16	proving	prove	VERB
ejpam-5802	300	17	it	it	PRON
ejpam-5802	300	18	is	be	AUX
ejpam-5802	300	19	nth	nth	PROPN
ejpam-5802	300	20	σ	σ	PROPN
ejpam-5802	300	21	-	-	PROPN
ejpam-5802	300	22	compact	compact	ADJ
ejpam-5802	300	23	.	.	PUNCT
ejpam-5802	301	1	theorem	theorem	NOUN
ejpam-5802	301	2	12	12	NUM
ejpam-5802	301	3	:	:	PUNCT
ejpam-5802	301	4	if	if	SCONJ
ejpam-5802	301	5	k	k	PROPN
ejpam-5802	301	6	is	be	AUX
ejpam-5802	301	7	nth	nth	PROPN
ejpam-5802	301	8	σ	σ	PROPN
ejpam-5802	301	9	-	-	ADJ
ejpam-5802	301	10	compact	compact	ADJ
ejpam-5802	301	11	space	space	NOUN
ejpam-5802	301	12	and	and	CCONJ
ejpam-5802	301	13	q	q	NOUN
ejpam-5802	301	14	is	be	AUX
ejpam-5802	301	15	a	a	DET
ejpam-5802	301	16	closed	closed	ADJ
ejpam-5802	301	17	subset	subset	NOUN
ejpam-5802	301	18	of	of	ADP
ejpam-5802	301	19	k	k	NOUN
ejpam-5802	301	20	,	,	PUNCT
ejpam-5802	301	21	then	then	ADV
ejpam-5802	301	22	q	q	X
ejpam-5802	301	23	is	be	AUX
ejpam-5802	301	24	nth	nth	PROPN
ejpam-5802	301	25	σ	σ	PROPN
ejpam-5802	301	26	-	-	ADJ
ejpam-5802	301	27	compact	compact	ADJ
ejpam-5802	301	28	space	space	NOUN
ejpam-5802	301	29	.	.	PUNCT
ejpam-5802	302	1	proof	proof	NOUN
ejpam-5802	302	2	:	:	PUNCT
ejpam-5802	302	3	since	since	SCONJ
ejpam-5802	302	4	k	k	PROPN
ejpam-5802	302	5	=	=	SYM
ejpam-5802	302	6	⋃∞	⋃∞	SYM
ejpam-5802	302	7	n=1m(ni	n=1m(ni	PROPN
ejpam-5802	302	8	)	)	PUNCT
ejpam-5802	302	9	is	be	AUX
ejpam-5802	302	10	n	n	PRON
ejpam-5802	302	11	th	th	X
ejpam-5802	302	12	σ	σ	ADJ
ejpam-5802	302	13	-	-	ADJ
ejpam-5802	302	14	compact	compact	ADJ
ejpam-5802	302	15	space	space	NOUN
ejpam-5802	302	16	,	,	PUNCT
ejpam-5802	302	17	the	the	DET
ejpam-5802	302	18	intersection	intersection	NOUN
ejpam-5802	302	19	m(ni	m(ni	NOUN
ejpam-5802	302	20	)	)	PUNCT
ejpam-5802	302	21	∩	∩	NOUN
ejpam-5802	302	22	q	q	X
ejpam-5802	302	23	is	be	AUX
ejpam-5802	302	24	compact	compact	ADJ
ejpam-5802	302	25	for	for	ADP
ejpam-5802	302	26	each	each	DET
ejpam-5802	302	27	ni	ni	PROPN
ejpam-5802	302	28	.	.	PROPN
ejpam-5802	303	1	therefore	therefore	ADV
ejpam-5802	303	2	,	,	PUNCT
ejpam-5802	303	3	q	q	X
ejpam-5802	303	4	=	=	PUNCT
ejpam-5802	303	5	⋃∞	⋃∞	X
ejpam-5802	303	6	n=1	n=1	PROPN
ejpam-5802	303	7	(	(	PUNCT
ejpam-5802	303	8	m(ni	m(ni	PROPN
ejpam-5802	303	9	)	)	PUNCT
ejpam-5802	303	10	∩	∩	ADJ
ejpam-5802	303	11	q	q	NOUN
ejpam-5802	303	12	)	)	PUNCT
ejpam-5802	303	13	,	,	PUNCT
ejpam-5802	303	14	which	which	PRON
ejpam-5802	303	15	is	be	AUX
ejpam-5802	303	16	a	a	DET
ejpam-5802	303	17	countable	countable	ADJ
ejpam-5802	303	18	union	union	NOUN
ejpam-5802	303	19	of	of	ADP
ejpam-5802	303	20	compact	compact	ADJ
ejpam-5802	303	21	sets	set	NOUN
ejpam-5802	303	22	.	.	PUNCT
ejpam-5802	304	1	thus	thus	ADV
ejpam-5802	304	2	,	,	PUNCT
ejpam-5802	304	3	q	q	PROPN
ejpam-5802	304	4	is	be	AUX
ejpam-5802	304	5	nth	nth	PROPN
ejpam-5802	304	6	σ	σ	PROPN
ejpam-5802	304	7	-	-	ADJ
ejpam-5802	304	8	compact	compact	ADJ
ejpam-5802	304	9	space	space	NOUN
ejpam-5802	304	10	,	,	PUNCT
ejpam-5802	304	11	for	for	ADP
ejpam-5802	304	12	all	all	DET
ejpam-5802	304	13	i=1,2,	i=1,2,	NOUN
ejpam-5802	304	14	...	...	PUNCT
ejpam-5802	304	15	,n	,n	PUNCT
ejpam-5802	304	16	.	.	PUNCT
ejpam-5802	305	1	theorem	theorem	VERB
ejpam-5802	305	2	13	13	NUM
ejpam-5802	305	3	:	:	PUNCT
ejpam-5802	305	4	every	every	DET
ejpam-5802	305	5	nth	nth	NOUN
ejpam-5802	305	6	σ	σ	ADJ
ejpam-5802	305	7	-	-	ADJ
ejpam-5802	305	8	compact	compact	ADJ
ejpam-5802	305	9	space	space	NOUN
ejpam-5802	305	10	can	can	AUX
ejpam-5802	305	11	be	be	AUX
ejpam-5802	305	12	expressed	express	VERB
ejpam-5802	305	13	as	as	ADP
ejpam-5802	305	14	a	a	DET
ejpam-5802	305	15	countable	countable	ADJ
ejpam-5802	305	16	union	union	NOUN
ejpam-5802	305	17	of	of	ADP
ejpam-5802	305	18	locally	locally	ADV
ejpam-5802	305	19	finite	finite	VERB
ejpam-5802	305	20	open	open	ADJ
ejpam-5802	305	21	covers	cover	NOUN
ejpam-5802	305	22	.	.	PUNCT
ejpam-5802	306	1	proof	proof	NOUN
ejpam-5802	306	2	:	:	PUNCT
ejpam-5802	306	3	let	let	VERB
ejpam-5802	306	4	k	k	PROPN
ejpam-5802	306	5	=	=	PRON
ejpam-5802	306	6	⋃∞	⋃∞	SYM
ejpam-5802	306	7	n=1m(ni	n=1m(ni	PROPN
ejpam-5802	306	8	)	)	PUNCT
ejpam-5802	306	9	be	be	VERB
ejpam-5802	306	10	nth	nth	NOUN
ejpam-5802	306	11	σ	σ	PROPN
ejpam-5802	306	12	-	-	ADJ
ejpam-5802	306	13	compact	compact	ADJ
ejpam-5802	306	14	space	space	NOUN
ejpam-5802	306	15	.	.	PUNCT
ejpam-5802	307	1	each	each	DET
ejpam-5802	307	2	compact	compact	ADJ
ejpam-5802	307	3	set	set	VERB
ejpam-5802	307	4	m(ni	m(ni	PROPN
ejpam-5802	307	5	)	)	PUNCT
ejpam-5802	307	6	can	can	AUX
ejpam-5802	307	7	be	be	AUX
ejpam-5802	307	8	covered	cover	VERB
ejpam-5802	307	9	by	by	ADP
ejpam-5802	307	10	a	a	DET
ejpam-5802	307	11	locally	locally	ADV
ejpam-5802	307	12	finite	finite	ADJ
ejpam-5802	307	13	collection	collection	NOUN
ejpam-5802	307	14	of	of	ADP
ejpam-5802	307	15	open	open	ADJ
ejpam-5802	307	16	sets	set	NOUN
ejpam-5802	307	17	.	.	PUNCT
ejpam-5802	308	1	the	the	DET
ejpam-5802	308	2	union	union	NOUN
ejpam-5802	308	3	of	of	ADP
ejpam-5802	308	4	these	these	DET
ejpam-5802	308	5	open	open	ADJ
ejpam-5802	308	6	covers	cover	NOUN
ejpam-5802	308	7	from	from	ADP
ejpam-5802	308	8	all	all	DET
ejpam-5802	308	9	m(ni	m(ni	NOUN
ejpam-5802	308	10	)	)	PUNCT
ejpam-5802	308	11	remains	remain	VERB
ejpam-5802	308	12	locally	locally	ADV
ejpam-5802	308	13	finite	finite	ADJ
ejpam-5802	308	14	.	.	PUNCT
ejpam-5802	309	1	thus	thus	ADV
ejpam-5802	309	2	,	,	PUNCT
ejpam-5802	309	3	k	k	PROPN
ejpam-5802	309	4	can	can	AUX
ejpam-5802	309	5	be	be	AUX
ejpam-5802	309	6	expressed	express	VERB
ejpam-5802	309	7	as	as	ADP
ejpam-5802	309	8	a	a	DET
ejpam-5802	309	9	countable	countable	ADJ
ejpam-5802	309	10	union	union	NOUN
ejpam-5802	309	11	of	of	ADP
ejpam-5802	309	12	locally	locally	ADV
ejpam-5802	309	13	finite	finite	VERB
ejpam-5802	309	14	open	open	ADJ
ejpam-5802	309	15	covers	cover	NOUN
ejpam-5802	309	16	,	,	PUNCT
ejpam-5802	309	17	for	for	ADP
ejpam-5802	309	18	all	all	DET
ejpam-5802	309	19	i=1,2,	i=1,2,	NOUN
ejpam-5802	309	20	...	...	PUNCT
ejpam-5802	309	21	,n	,n	PUNCT
ejpam-5802	309	22	.	.	PUNCT
ejpam-5802	310	1	example	example	NOUN
ejpam-5802	310	2	:	:	PUNCT
ejpam-5802	310	3	the	the	DET
ejpam-5802	310	4	space	space	NOUN
ejpam-5802	310	5	r	r	NOUN
ejpam-5802	310	6	can	can	AUX
ejpam-5802	310	7	be	be	AUX
ejpam-5802	310	8	covered	cover	VERB
ejpam-5802	310	9	by	by	ADP
ejpam-5802	310	10	intervals	interval	NOUN
ejpam-5802	310	11	(	(	PUNCT
ejpam-5802	310	12	n	n	CCONJ
ejpam-5802	310	13	,	,	PUNCT
ejpam-5802	310	14	n+	n+	X
ejpam-5802	310	15	1	1	NUM
ejpam-5802	310	16	)	)	PUNCT
ejpam-5802	310	17	for	for	SCONJ
ejpam-5802	310	18	each	each	DET
ejpam-5802	310	19	n	n	PRON
ejpam-5802	310	20	∈	∈	PROPN
ejpam-5802	310	21	z.	z.	PROPN
ejpam-5802	310	22	theorem	theorem	VERB
ejpam-5802	310	23	15	15	NUM
ejpam-5802	310	24	:	:	PUNCT
ejpam-5802	310	25	a	a	DET
ejpam-5802	310	26	nth	nth	NOUN
ejpam-5802	310	27	σ	σ	ADJ
ejpam-5802	310	28	-	-	ADJ
ejpam-5802	310	29	compact	compact	ADJ
ejpam-5802	310	30	hausdorff	hausdorff	NOUN
ejpam-5802	310	31	space	space	NOUN
ejpam-5802	310	32	is	be	AUX
ejpam-5802	310	33	second	second	ADV
ejpam-5802	310	34	-	-	PUNCT
ejpam-5802	310	35	countable	countable	ADJ
ejpam-5802	310	36	.	.	PUNCT
ejpam-5802	311	1	j.	j.	PROPN
ejpam-5802	311	2	oudetallah	oudetallah	PROPN
ejpam-5802	311	3	et	et	PROPN
ejpam-5802	311	4	al	al	PROPN
ejpam-5802	311	5	.	.	PUNCT
ejpam-5802	311	6	/	/	SYM
ejpam-5802	311	7	eur	eur	PROPN
ejpam-5802	311	8	.	.	PUNCT
ejpam-5802	312	1	j.	j.	PROPN
ejpam-5802	312	2	pure	pure	PROPN
ejpam-5802	312	3	appl	appl	PROPN
ejpam-5802	312	4	.	.	PROPN
ejpam-5802	312	5	math	math	PROPN
ejpam-5802	312	6	,	,	PUNCT
ejpam-5802	312	7	18	18	NUM
ejpam-5802	312	8	(	(	PUNCT
ejpam-5802	312	9	2	2	NUM
ejpam-5802	312	10	)	)	PUNCT
ejpam-5802	312	11	(	(	PUNCT
ejpam-5802	312	12	2025	2025	NUM
ejpam-5802	312	13	)	)	PUNCT
ejpam-5802	312	14	,	,	PUNCT
ejpam-5802	312	15	5802	5802	NUM
ejpam-5802	312	16	14	14	NUM
ejpam-5802	312	17	of	of	ADP
ejpam-5802	312	18	14	14	NUM
ejpam-5802	312	19	proof	proof	NOUN
ejpam-5802	312	20	:	:	PUNCT
ejpam-5802	312	21	suppose	suppose	VERB
ejpam-5802	312	22	k	k	PROPN
ejpam-5802	312	23	is	be	AUX
ejpam-5802	312	24	a	a	DET
ejpam-5802	312	25	nth	nth	NOUN
ejpam-5802	312	26	σ	σ	ADJ
ejpam-5802	312	27	-	-	ADJ
ejpam-5802	312	28	compact	compact	ADJ
ejpam-5802	312	29	hausdorff	hausdorff	NOUN
ejpam-5802	312	30	space	space	NOUN
ejpam-5802	312	31	that	that	PRON
ejpam-5802	312	32	may	may	AUX
ejpam-5802	312	33	be	be	AUX
ejpam-5802	312	34	written	write	VERB
ejpam-5802	312	35	as	as	ADP
ejpam-5802	312	36	a	a	DET
ejpam-5802	312	37	countable	countable	ADJ
ejpam-5802	312	38	union	union	NOUN
ejpam-5802	312	39	of	of	ADP
ejpam-5802	312	40	compact	compact	ADJ
ejpam-5802	312	41	sets	set	NOUN
ejpam-5802	312	42	.	.	PUNCT
ejpam-5802	313	1	each	each	DET
ejpam-5802	313	2	compact	compact	ADJ
ejpam-5802	313	3	subset	subset	NOUN
ejpam-5802	313	4	is	be	AUX
ejpam-5802	313	5	second	second	ADV
ejpam-5802	313	6	-	-	PUNCT
ejpam-5802	313	7	countable	countable	ADJ
ejpam-5802	313	8	,	,	PUNCT
ejpam-5802	313	9	resulting	result	VERB
ejpam-5802	313	10	in	in	ADP
ejpam-5802	313	11	a	a	DET
ejpam-5802	313	12	countable	countable	ADJ
ejpam-5802	313	13	base	base	NOUN
ejpam-5802	313	14	for	for	ADP
ejpam-5802	313	15	the	the	DET
ejpam-5802	313	16	topology	topology	NOUN
ejpam-5802	313	17	.	.	PUNCT
ejpam-5802	314	1	the	the	DET
ejpam-5802	314	2	union	union	NOUN
ejpam-5802	314	3	of	of	ADP
ejpam-5802	314	4	these	these	DET
ejpam-5802	314	5	countable	countable	ADJ
ejpam-5802	314	6	bases	basis	NOUN
ejpam-5802	314	7	produces	produce	VERB
ejpam-5802	314	8	a	a	DET
ejpam-5802	314	9	countable	countable	ADJ
ejpam-5802	314	10	base	base	NOUN
ejpam-5802	314	11	for	for	ADP
ejpam-5802	314	12	k	k	PROPN
ejpam-5802	314	13	,	,	PUNCT
ejpam-5802	314	14	indicating	indicate	VERB
ejpam-5802	314	15	that	that	SCONJ
ejpam-5802	314	16	it	it	PRON
ejpam-5802	314	17	is	be	AUX
ejpam-5802	314	18	second	second	ADV
ejpam-5802	314	19	-	-	PUNCT
ejpam-5802	314	20	countable	countable	ADJ
ejpam-5802	314	21	.	.	PUNCT
ejpam-5802	315	1	example	example	NOUN
ejpam-5802	315	2	:	:	PUNCT
ejpam-5802	315	3	the	the	DET
ejpam-5802	315	4	space	space	NOUN
ejpam-5802	315	5	rn	rn	PROPN
ejpam-5802	315	6	is	be	AUX
ejpam-5802	315	7	hausdorff	hausdorff	NOUN
ejpam-5802	315	8	,	,	PUNCT
ejpam-5802	315	9	nth	nth	PROPN
ejpam-5802	315	10	σ	σ	PROPN
ejpam-5802	315	11	-	-	PROPN
ejpam-5802	315	12	compact	compact	ADJ
ejpam-5802	315	13	,	,	PUNCT
ejpam-5802	315	14	and	and	CCONJ
ejpam-5802	315	15	second	second	ADV
ejpam-5802	315	16	-	-	PUNCT
ejpam-5802	315	17	countable	countable	ADJ
ejpam-5802	315	18	,	,	PUNCT
ejpam-5802	315	19	meaning	mean	VERB
ejpam-5802	315	20	it	it	PRON
ejpam-5802	315	21	may	may	AUX
ejpam-5802	315	22	be	be	AUX
ejpam-5802	315	23	covered	cover	VERB
ejpam-5802	315	24	by	by	ADP
ejpam-5802	315	25	balls	ball	NOUN
ejpam-5802	315	26	in	in	ADP
ejpam-5802	315	27	a	a	DET
ejpam-5802	315	28	countable	countable	ADJ
ejpam-5802	315	29	way	way	NOUN
ejpam-5802	315	30	.	.	PUNCT
ejpam-5802	316	1	6	6	X
ejpam-5802	316	2	.	.	X
ejpam-5802	316	3	conclusion	conclusion	NOUN
ejpam-5802	316	4	in	in	ADP
ejpam-5802	316	5	this	this	DET
ejpam-5802	316	6	paper	paper	NOUN
ejpam-5802	316	7	,	,	PUNCT
ejpam-5802	316	8	we	we	PRON
ejpam-5802	316	9	obtained	obtain	VERB
ejpam-5802	316	10	some	some	DET
ejpam-5802	316	11	results	result	NOUN
ejpam-5802	316	12	related	relate	VERB
ejpam-5802	316	13	to	to	ADP
ejpam-5802	316	14	σ	σ	NOUN
ejpam-5802	316	15	-	-	ADJ
ejpam-5802	316	16	compact	compact	ADJ
ejpam-5802	316	17	spaces	space	NOUN
ejpam-5802	316	18	,	,	PUNCT
ejpam-5802	316	19	and	and	CCONJ
ejpam-5802	316	20	applied	apply	VERB
ejpam-5802	316	21	this	this	DET
ejpam-5802	316	22	concept	concept	NOUN
ejpam-5802	316	23	in	in	ADP
ejpam-5802	316	24	nth	nth	ADJ
ejpam-5802	316	25	-	-	ADJ
ejpam-5802	316	26	topological	topological	ADJ
ejpam-5802	316	27	spaces	space	NOUN
ejpam-5802	316	28	.	.	PUNCT
ejpam-5802	317	1	several	several	ADJ
ejpam-5802	317	2	characteristics	characteristic	NOUN
ejpam-5802	317	3	of	of	ADP
ejpam-5802	317	4	these	these	DET
ejpam-5802	317	5	spaces	space	NOUN
ejpam-5802	317	6	and	and	CCONJ
ejpam-5802	317	7	their	their	PRON
ejpam-5802	317	8	interactions	interaction	NOUN
ejpam-5802	317	9	with	with	ADP
ejpam-5802	317	10	other	other	ADJ
ejpam-5802	317	11	topologies	topology	NOUN
ejpam-5802	317	12	are	be	AUX
ejpam-5802	317	13	presented	present	VERB
ejpam-5802	317	14	.	.	PUNCT
ejpam-5802	318	1	also	also	ADV
ejpam-5802	318	2	,	,	PUNCT
ejpam-5802	318	3	our	our	PRON
ejpam-5802	318	4	study	study	NOUN
ejpam-5802	318	5	of	of	ADP
ejpam-5802	318	6	σ	σ	PROPN
ejpam-5802	318	7	-	-	ADJ
ejpam-5802	318	8	compact	compact	ADJ
ejpam-5802	318	9	spaces	space	NOUN
ejpam-5802	318	10	solved	solve	VERB
ejpam-5802	318	11	some	some	DET
ejpam-5802	318	12	important	important	ADJ
ejpam-5802	318	13	mathematical	mathematical	ADJ
ejpam-5802	318	14	problems	problem	NOUN
ejpam-5802	318	15	in	in	ADP
ejpam-5802	318	16	nth	nth	ADJ
ejpam-5802	318	17	-	-	ADJ
ejpam-5802	318	18	topological	topological	ADJ
ejpam-5802	318	19	spaces	space	NOUN
ejpam-5802	318	20	.	.	PUNCT
ejpam-5802	319	1	acknowledgments	acknowledgment	NOUN
ejpam-5802	319	2	we	we	PRON
ejpam-5802	319	3	very	very	ADV
ejpam-5802	319	4	much	much	ADV
ejpam-5802	319	5	appreciate	appreciate	VERB
ejpam-5802	319	6	everyone	everyone	PRON
ejpam-5802	319	7	who	who	PRON
ejpam-5802	319	8	made	make	VERB
ejpam-5802	319	9	a	a	DET
ejpam-5802	319	10	contribution	contribution	NOUN
ejpam-5802	319	11	to	to	ADP
ejpam-5802	319	12	this	this	DET
ejpam-5802	319	13	research	research	NOUN
ejpam-5802	319	14	project	project	NOUN
ejpam-5802	319	15	.	.	PUNCT
ejpam-5802	320	1	their	their	PRON
ejpam-5802	320	2	help	help	NOUN
ejpam-5802	320	3	,	,	PUNCT
ejpam-5802	320	4	guidance	guidance	NOUN
ejpam-5802	320	5	,	,	PUNCT
ejpam-5802	320	6	and	and	CCONJ
ejpam-5802	320	7	teamwork	teamwork	NOUN
ejpam-5802	320	8	have	have	AUX
ejpam-5802	320	9	been	be	AUX
ejpam-5802	320	10	key	key	ADJ
ejpam-5802	320	11	to	to	ADP
ejpam-5802	320	12	the	the	DET
ejpam-5802	320	13	completion	completion	NOUN
ejpam-5802	320	14	of	of	ADP
ejpam-5802	320	15	this	this	DET
ejpam-5802	320	16	research	research	NOUN
ejpam-5802	320	17	.	.	PUNCT
ejpam-5802	321	1	references	reference	NOUN
ejpam-5802	321	2	[	[	X
ejpam-5802	321	3	1	1	NUM
ejpam-5802	321	4	]	]	X
ejpam-5802	321	5	dugundji	dugundji	NOUN
ejpam-5802	321	6	;	;	PUNCT
ejpam-5802	321	7	j.	j.	PROPN
ejpam-5802	321	8	,	,	PUNCT
ejpam-5802	321	9	(	(	PUNCT
ejpam-5802	321	10	1966	1966	NUM
ejpam-5802	321	11	)	)	PUNCT
ejpam-5802	321	12	.	.	PUNCT
ejpam-5802	322	1	topology	topology	NOUN
ejpam-5802	322	2	,	,	PUNCT
ejpam-5802	322	3	allyn	allyn	NOUN
ejpam-5802	322	4	and	and	CCONJ
ejpam-5802	322	5	bacon	bacon	NOUN
ejpam-5802	322	6	,	,	PUNCT
ejpam-5802	322	7	boston	boston	PROPN
ejpam-5802	322	8	.	.	PUNCT
ejpam-5802	323	1	[	[	X
ejpam-5802	323	2	2	2	X
ejpam-5802	323	3	]	]	PUNCT
ejpam-5802	323	4	j.	j.	PROPN
ejpam-5802	323	5	oudetallah	oudetallah	PROPN
ejpam-5802	323	6	,	,	PUNCT
ejpam-5802	323	7	on	on	ADP
ejpam-5802	323	8	feebly	feebly	ADV
ejpam-5802	323	9	pairwiese	pairwiese	ADJ
ejpam-5802	323	10	expandable	expandable	ADJ
ejpam-5802	323	11	space	space	NOUN
ejpam-5802	323	12	,	,	PUNCT
ejpam-5802	323	13	j.	j.	PROPN
ejpam-5802	323	14	math	math	PROPN
ejpam-5802	323	15	.	.	PUNCT
ejpam-5802	324	1	comput	comput	NOUN
ejpam-5802	324	2	.	.	PUNCT
ejpam-5802	325	1	sci	sci	PROPN
ejpam-5802	325	2	.	.	PROPN
ejpam-5802	325	3	11	11	NUM
ejpam-5802	325	4	(	(	PUNCT
ejpam-5802	325	5	2021	2021	NUM
ejpam-5802	325	6	)	)	PUNCT
ejpam-5802	325	7	,	,	PUNCT
ejpam-5802	325	8	no	no	INTJ
ejpam-5802	325	9	.	.	NOUN
ejpam-5802	325	10	5	5	NUM
ejpam-5802	325	11	,	,	PUNCT
ejpam-5802	325	12	6216	6216	NUM
ejpam-5802	325	13	-	-	SYM
ejpam-5802	325	14	6225	6225	NUM
ejpam-5802	325	15	[	[	X
ejpam-5802	325	16	3	3	X
ejpam-5802	325	17	]	]	PUNCT
ejpam-5802	325	18	j.	j.	PROPN
ejpam-5802	325	19	oudetallah	oudetallah	PROPN
ejpam-5802	325	20	,	,	PUNCT
ejpam-5802	325	21	nearly	nearly	ADV
ejpam-5802	325	22	expandability	expandability	NOUN
ejpam-5802	325	23	in	in	ADP
ejpam-5802	325	24	bitopological	bitopological	ADJ
ejpam-5802	325	25	spaces	space	NOUN
ejpam-5802	325	26	,	,	PUNCT
ejpam-5802	325	27	advances	advance	NOUN
ejpam-5802	325	28	in	in	ADP
ejpam-5802	325	29	mathematics	mathematic	NOUN
ejpam-5802	325	30	:	:	PUNCT
ejpam-5802	325	31	scientific	scientific	ADJ
ejpam-5802	325	32	journal	journal	NOUN
ejpam-5802	325	33	10	10	NUM
ejpam-5802	325	34	(	(	PUNCT
ejpam-5802	325	35	2021	2021	NUM
ejpam-5802	325	36	)	)	PUNCT
ejpam-5802	325	37	,	,	PUNCT
ejpam-5802	325	38	705	705	NUM
ejpam-5802	325	39	-	-	SYM
ejpam-5802	325	40	712	712	NUM
ejpam-5802	325	41	.	.	PUNCT
ejpam-5802	326	1	[	[	X
ejpam-5802	326	2	4	4	X
ejpam-5802	326	3	]	]	PUNCT
ejpam-5802	326	4	j.	j.	PROPN
ejpam-5802	326	5	kelley	kelley	PROPN
ejpam-5802	326	6	,	,	PUNCT
ejpam-5802	326	7	general	general	ADJ
ejpam-5802	326	8	topology	topology	NOUN
ejpam-5802	326	9	,	,	PUNCT
ejpam-5802	326	10	van	van	PROPN
ejpam-5802	326	11	nostrand	nostrand	PROPN
ejpam-5802	326	12	company	company	NOUN
ejpam-5802	326	13	,	,	PUNCT
ejpam-5802	326	14	1955	1955	NUM
ejpam-5802	326	15	..	..	PUNCT
ejpam-5802	326	16	kyungpook	kyungpook	PROPN
ejpam-5802	326	17	math.j	math.j	PROPN
ejpam-5802	326	18	.	.	PROPN
ejpam-5802	326	19	,32	,32	PROPN
ejpam-5802	326	20	,	,	PUNCT
ejpam-5802	326	21	no	no	INTJ
ejpam-5802	326	22	.	.	PUNCT
ejpam-5802	327	1	2(1992	2(1992	NUM
ejpam-5802	327	2	)	)	PUNCT
ejpam-5802	328	1	,	,	PUNCT
ejpam-5802	328	2	273	273	NUM
ejpam-5802	328	3	-	-	SYM
ejpam-5802	328	4	284	284	NUM
ejpam-5802	328	5	[	[	X
ejpam-5802	328	6	5	5	NUM
ejpam-5802	328	7	]	]	X
ejpam-5802	328	8	kim	kim	PROPN
ejpam-5802	328	9	,	,	PUNCT
ejpam-5802	328	10	y.	y.	PROPN
ejpam-5802	328	11	w.	w.	PROPN
ejpam-5802	328	12	(	(	PUNCT
ejpam-5802	328	13	1968	1968	NUM
ejpam-5802	328	14	)	)	PUNCT
ejpam-5802	328	15	.	.	PUNCT
ejpam-5802	329	1	pairwise	pairwise	NOUN
ejpam-5802	329	2	compactness	compactness	NOUN
ejpam-5802	329	3	.	.	PUNCT
ejpam-5802	330	1	publ	publ	PROPN
ejpam-5802	330	2	.	.	PUNCT
ejpam-5802	331	1	math	math	NOUN
ejpam-5802	331	2	.	.	PUNCT
ejpam-5802	332	1	debrecen.15	debrecen.15	PROPN
ejpam-5802	332	2	,	,	PUNCT
ejpam-5802	332	3	87	87	NUM
ejpam-5802	332	4	-	-	SYM
ejpam-5802	332	5	90	90	NUM
ejpam-5802	332	6	.	.	PUNCT
ejpam-5802	333	1	[	[	X
ejpam-5802	333	2	6	6	NUM
ejpam-5802	333	3	]	]	PUNCT
ejpam-5802	333	4	levine	levine	PROPN
ejpam-5802	333	5	;	;	PUNCT
ejpam-5802	333	6	n.	n.	NOUN
ejpam-5802	333	7	,	,	PUNCT
ejpam-5802	333	8	(	(	PUNCT
ejpam-5802	333	9	1963	1963	NUM
ejpam-5802	333	10	)	)	PUNCT
ejpam-5802	333	11	.	.	PUNCT
ejpam-5802	334	1	semi	semi	ADJ
ejpam-5802	334	2	-	-	ADJ
ejpam-5802	334	3	open	open	ADJ
ejpam-5802	334	4	sets	set	NOUN
ejpam-5802	334	5	and	and	CCONJ
ejpam-5802	334	6	semi	semi	ADJ
ejpam-5802	334	7	-	-	NOUN
ejpam-5802	334	8	continuity	continuity	NOUN
ejpam-5802	334	9	in	in	ADP
ejpam-5802	334	10	topological	topological	ADJ
ejpam-5802	334	11	spaces	space	NOUN
ejpam-5802	334	12	,	,	PUNCT
ejpam-5802	334	13	amer	amer	PROPN
ejpam-5802	334	14	.	.	PROPN
ejpam-5802	334	15	math	math	PROPN
ejpam-5802	334	16	.	.	PUNCT
ejpam-5802	335	1	monthly	monthly	ADJ
ejpam-5802	335	2	,	,	PUNCT
ejpam-5802	335	3	70	70	NUM
ejpam-5802	335	4	,	,	PUNCT
ejpam-5802	335	5	36	36	NUM
ejpam-5802	335	6	-	-	SYM
ejpam-5802	335	7	41	41	NUM
ejpam-5802	335	8	.	.	PUNCT
ejpam-5802	336	1	[	[	X
ejpam-5802	336	2	7	7	NUM
ejpam-5802	336	3	]	]	X
ejpam-5802	336	4	willard	willard	NOUN
ejpam-5802	336	5	;	;	PUNCT
ejpam-5802	336	6	s.	s.	PROPN
ejpam-5802	336	7	,	,	PUNCT
ejpam-5802	336	8	(	(	PUNCT
ejpam-5802	336	9	1970).general	1970).general	NUM
ejpam-5802	336	10	topology	topology	NOUN
ejpam-5802	336	11	,	,	PUNCT
ejpam-5802	336	12	addisonwesley	addisonwesley	ADJ
ejpam-5802	336	13	publishing	publishing	NOUN
ejpam-5802	336	14	company	company	PROPN
ejpam-5802	336	15	,	,	PUNCT
ejpam-5802	336	16	inc	inc	PROPN
ejpam-5802	336	17	.	.	PUNCT