id	sid	tid	token	lemma	pos
ejpam-6067	1	1	european	european	PROPN
ejpam-6067	1	2	journal	journal	PROPN
ejpam-6067	1	3	of	of	ADP
ejpam-6067	1	4	pure	pure	ADJ
ejpam-6067	1	5	and	and	CCONJ
ejpam-6067	1	6	applied	applied	ADJ
ejpam-6067	1	7	mathematics	mathematic	NOUN
ejpam-6067	1	8	2025	2025	NUM
ejpam-6067	1	9	,	,	PUNCT
ejpam-6067	1	10	vol	vol	NOUN
ejpam-6067	1	11	.	.	PROPN
ejpam-6067	1	12	18	18	NUM
ejpam-6067	1	13	,	,	PUNCT
ejpam-6067	1	14	issue	issue	NOUN
ejpam-6067	1	15	3	3	NUM
ejpam-6067	1	16	,	,	PUNCT
ejpam-6067	1	17	article	article	NOUN
ejpam-6067	1	18	number	number	NOUN
ejpam-6067	1	19	6067	6067	NUM
ejpam-6067	1	20	issn	issn	PROPN
ejpam-6067	1	21	1307	1307	NUM
ejpam-6067	1	22	-	-	SYM
ejpam-6067	1	23	5543	5543	NUM
ejpam-6067	1	24	–	–	PUNCT
ejpam-6067	1	25	ejpam.com	ejpam.com	X
ejpam-6067	1	26	published	publish	VERB
ejpam-6067	1	27	by	by	ADP
ejpam-6067	1	28	new	new	PROPN
ejpam-6067	1	29	york	york	PROPN
ejpam-6067	1	30	business	business	PROPN
ejpam-6067	1	31	global	global	ADJ
ejpam-6067	1	32	g	g	PROPN
ejpam-6067	1	33	-	-	PUNCT
ejpam-6067	1	34	compact	compact	ADJ
ejpam-6067	1	35	spaces	space	NOUN
ejpam-6067	1	36	characterized	characterize	VERB
ejpam-6067	1	37	by	by	ADP
ejpam-6067	1	38	the	the	DET
ejpam-6067	1	39	intersection	intersection	NOUN
ejpam-6067	1	40	of	of	ADP
ejpam-6067	1	41	countable	countable	ADJ
ejpam-6067	1	42	neighborhoods	neighborhood	NOUN
ejpam-6067	1	43	mutaz	mutaz	VERB
ejpam-6067	1	44	shatnawi1	shatnawi1	PROPN
ejpam-6067	1	45	,	,	PUNCT
ejpam-6067	1	46	jamal	jamal	PROPN
ejpam-6067	1	47	oudetallah2	oudetallah2	PROPN
ejpam-6067	1	48	,	,	PUNCT
ejpam-6067	1	49	anwar	anwar	PROPN
ejpam-6067	1	50	bataihah3	bataihah3	PROPN
ejpam-6067	1	51	,	,	PUNCT
ejpam-6067	1	52	ala	ala	PROPN
ejpam-6067	1	53	amourah4,5,∗	amourah4,5,∗	PROPN
ejpam-6067	1	54	,	,	PUNCT
ejpam-6067	1	55	abdullah	abdullah	PROPN
ejpam-6067	1	56	alsoboh6,∗	alsoboh6,∗	PROPN
ejpam-6067	1	57	,	,	PUNCT
ejpam-6067	1	58	tala	tala	PROPN
ejpam-6067	1	59	sasa7	sasa7	PROPN
ejpam-6067	1	60	1	1	NUM
ejpam-6067	1	61	department	department	NOUN
ejpam-6067	1	62	of	of	ADP
ejpam-6067	1	63	mathematics	mathematic	NOUN
ejpam-6067	1	64	,	,	PUNCT
ejpam-6067	1	65	faculty	faculty	NOUN
ejpam-6067	1	66	of	of	ADP
ejpam-6067	1	67	science	science	NOUN
ejpam-6067	1	68	and	and	CCONJ
ejpam-6067	1	69	information	information	NOUN
ejpam-6067	1	70	technology	technology	NOUN
ejpam-6067	1	71	,	,	PUNCT
ejpam-6067	1	72	irbid	irbid	VERB
ejpam-6067	1	73	national	national	ADJ
ejpam-6067	1	74	university	university	PROPN
ejpam-6067	1	75	,	,	PUNCT
ejpam-6067	1	76	irbid	irbid	VERB
ejpam-6067	1	77	21110	21110	NUM
ejpam-6067	1	78	,	,	PUNCT
ejpam-6067	1	79	jordan	jordan	PROPN
ejpam-6067	1	80	2	2	NUM
ejpam-6067	1	81	department	department	NOUN
ejpam-6067	1	82	of	of	ADP
ejpam-6067	1	83	mathematics	mathematics	PROPN
ejpam-6067	1	84	,	,	PUNCT
ejpam-6067	1	85	university	university	PROPN
ejpam-6067	1	86	of	of	ADP
ejpam-6067	1	87	petra	petra	PROPN
ejpam-6067	1	88	,	,	PUNCT
ejpam-6067	1	89	amman	amman	PROPN
ejpam-6067	1	90	11196	11196	NUM
ejpam-6067	1	91	,	,	PUNCT
ejpam-6067	1	92	jordan	jordan	PROPN
ejpam-6067	1	93	3	3	NUM
ejpam-6067	1	94	department	department	PROPN
ejpam-6067	1	95	of	of	ADP
ejpam-6067	1	96	mathematics	mathematic	NOUN
ejpam-6067	1	97	,	,	PUNCT
ejpam-6067	1	98	faculty	faculty	NOUN
ejpam-6067	1	99	of	of	ADP
ejpam-6067	1	100	science	science	NOUN
ejpam-6067	1	101	,	,	PUNCT
ejpam-6067	1	102	jadara	jadara	PROPN
ejpam-6067	1	103	university	university	PROPN
ejpam-6067	1	104	,	,	PUNCT
ejpam-6067	1	105	irbid	irbid	VERB
ejpam-6067	1	106	21110	21110	NUM
ejpam-6067	1	107	,	,	PUNCT
ejpam-6067	1	108	jordan	jordan	PROPN
ejpam-6067	1	109	4	4	NUM
ejpam-6067	1	110	mathematics	mathematics	PROPN
ejpam-6067	1	111	education	education	NOUN
ejpam-6067	1	112	program	program	NOUN
ejpam-6067	1	113	,	,	PUNCT
ejpam-6067	1	114	faculty	faculty	NOUN
ejpam-6067	1	115	of	of	ADP
ejpam-6067	1	116	education	education	NOUN
ejpam-6067	1	117	and	and	CCONJ
ejpam-6067	1	118	arts	art	NOUN
ejpam-6067	1	119	,	,	PUNCT
ejpam-6067	1	120	sohar	sohar	PROPN
ejpam-6067	1	121	university	university	PROPN
ejpam-6067	1	122	,	,	PUNCT
ejpam-6067	1	123	sohar	sohar	PROPN
ejpam-6067	1	124	311	311	NUM
ejpam-6067	1	125	,	,	PUNCT
ejpam-6067	1	126	oman	oman	NOUN
ejpam-6067	1	127	5	5	NUM
ejpam-6067	1	128	jadara	jadara	PROPN
ejpam-6067	1	129	research	research	NOUN
ejpam-6067	1	130	center	center	NOUN
ejpam-6067	1	131	,	,	PUNCT
ejpam-6067	1	132	jadara	jadara	PROPN
ejpam-6067	1	133	university	university	PROPN
ejpam-6067	1	134	,	,	PUNCT
ejpam-6067	1	135	irbid	irbid	PROPN
ejpam-6067	1	136	,	,	PUNCT
ejpam-6067	1	137	jordan	jordan	PROPN
ejpam-6067	1	138	6	6	NUM
ejpam-6067	1	139	college	college	NOUN
ejpam-6067	1	140	of	of	ADP
ejpam-6067	1	141	applied	apply	VERB
ejpam-6067	1	142	and	and	CCONJ
ejpam-6067	1	143	health	health	NOUN
ejpam-6067	1	144	sciences	science	NOUN
ejpam-6067	1	145	,	,	PUNCT
ejpam-6067	1	146	a’sharqiyah	a’sharqiyah	PROPN
ejpam-6067	1	147	university	university	NOUN
ejpam-6067	1	148	,	,	PUNCT
ejpam-6067	2	1	post	post	PROPN
ejpam-6067	2	2	box	box	PROPN
ejpam-6067	2	3	no	no	INTJ
ejpam-6067	2	4	.	.	PROPN
ejpam-6067	2	5	42	42	NUM
ejpam-6067	2	6	,	,	PUNCT
ejpam-6067	2	7	post	post	VERB
ejpam-6067	2	8	code	code	NOUN
ejpam-6067	2	9	no	no	INTJ
ejpam-6067	2	10	.	.	PROPN
ejpam-6067	2	11	400	400	NUM
ejpam-6067	2	12	,	,	PUNCT
ejpam-6067	2	13	ibra	ibra	NOUN
ejpam-6067	2	14	,	,	PUNCT
ejpam-6067	2	15	sultanate	sultanate	NOUN
ejpam-6067	2	16	of	of	ADP
ejpam-6067	2	17	oman	oman	PROPN
ejpam-6067	2	18	7	7	NUM
ejpam-6067	2	19	department	department	NOUN
ejpam-6067	2	20	of	of	ADP
ejpam-6067	2	21	mathematics	mathematic	NOUN
ejpam-6067	2	22	,	,	PUNCT
ejpam-6067	2	23	faculty	faculty	NOUN
ejpam-6067	2	24	of	of	ADP
ejpam-6067	2	25	science	science	NOUN
ejpam-6067	2	26	,	,	PUNCT
ejpam-6067	2	27	applied	apply	VERB
ejpam-6067	2	28	science	science	NOUN
ejpam-6067	2	29	private	private	ADJ
ejpam-6067	2	30	university	university	NOUN
ejpam-6067	2	31	,	,	PUNCT
ejpam-6067	2	32	amman	amman	PROPN
ejpam-6067	2	33	,	,	PUNCT
ejpam-6067	2	34	jordan	jordan	PROPN
ejpam-6067	2	35	abstract	abstract	PROPN
ejpam-6067	2	36	.	.	PUNCT
ejpam-6067	3	1	in	in	ADP
ejpam-6067	3	2	this	this	DET
ejpam-6067	3	3	research	research	NOUN
ejpam-6067	3	4	,	,	PUNCT
ejpam-6067	3	5	we	we	PRON
ejpam-6067	3	6	introduce	introduce	VERB
ejpam-6067	3	7	and	and	CCONJ
ejpam-6067	3	8	analyze	analyze	VERB
ejpam-6067	3	9	the	the	DET
ejpam-6067	3	10	concepts	concept	NOUN
ejpam-6067	3	11	ofg	ofg	NOUN
ejpam-6067	3	12	-	-	PUNCT
ejpam-6067	3	13	compactness	compactness	NOUN
ejpam-6067	3	14	,	,	PUNCT
ejpam-6067	3	15	g	g	NOUN
ejpam-6067	3	16	-	-	PUNCT
ejpam-6067	3	17	lindelöfness	lindelöfness	NOUN
ejpam-6067	3	18	,	,	PUNCT
ejpam-6067	3	19	and	and	CCONJ
ejpam-6067	3	20	g	g	NOUN
ejpam-6067	3	21	-	-	PUNCT
ejpam-6067	3	22	countably	countably	ADV
ejpam-6067	3	23	compactness	compactness	NOUN
ejpam-6067	3	24	within	within	ADP
ejpam-6067	3	25	the	the	DET
ejpam-6067	3	26	framework	framework	NOUN
ejpam-6067	3	27	of	of	ADP
ejpam-6067	3	28	topological	topological	ADJ
ejpam-6067	3	29	spaces	space	NOUN
ejpam-6067	3	30	,	,	PUNCT
ejpam-6067	3	31	which	which	PRON
ejpam-6067	3	32	are	be	AUX
ejpam-6067	3	33	characterized	characterize	VERB
ejpam-6067	3	34	by	by	ADP
ejpam-6067	3	35	more	more	ADJ
ejpam-6067	3	36	rigorous	rigorous	ADJ
ejpam-6067	3	37	conditions	condition	NOUN
ejpam-6067	3	38	compared	compare	VERB
ejpam-6067	3	39	to	to	ADP
ejpam-6067	3	40	those	those	PRON
ejpam-6067	3	41	governing	govern	VERB
ejpam-6067	3	42	compact	compact	ADJ
ejpam-6067	3	43	and	and	CCONJ
ejpam-6067	3	44	lindelöf	lindelöf	NOUN
ejpam-6067	3	45	spaces	space	VERB
ejpam-6067	3	46	.	.	PUNCT
ejpam-6067	4	1	we	we	PRON
ejpam-6067	4	2	formulate	formulate	VERB
ejpam-6067	4	3	a	a	DET
ejpam-6067	4	4	series	series	NOUN
ejpam-6067	4	5	of	of	ADP
ejpam-6067	4	6	theorems	theorem	NOUN
ejpam-6067	4	7	and	and	CCONJ
ejpam-6067	4	8	present	present	VERB
ejpam-6067	4	9	a	a	DET
ejpam-6067	4	10	variety	variety	NOUN
ejpam-6067	4	11	of	of	ADP
ejpam-6067	4	12	examples	example	NOUN
ejpam-6067	4	13	to	to	PART
ejpam-6067	4	14	clarify	clarify	VERB
ejpam-6067	4	15	the	the	DET
ejpam-6067	4	16	relationships	relationship	NOUN
ejpam-6067	4	17	among	among	ADP
ejpam-6067	4	18	g	g	NOUN
ejpam-6067	4	19	-	-	PUNCT
ejpam-6067	4	20	compactness	compactness	NOUN
ejpam-6067	4	21	,	,	PUNCT
ejpam-6067	4	22	g	g	NOUN
ejpam-6067	4	23	-	-	PUNCT
ejpam-6067	4	24	lindelöfness	lindelöfness	NOUN
ejpam-6067	4	25	,	,	PUNCT
ejpam-6067	4	26	compactness	compactness	NOUN
ejpam-6067	4	27	,	,	PUNCT
ejpam-6067	4	28	and	and	CCONJ
ejpam-6067	4	29	lindelöfness	lindelöfness	X
ejpam-6067	4	30	.	.	PUNCT
ejpam-6067	5	1	additionally	additionally	ADV
ejpam-6067	5	2	,	,	PUNCT
ejpam-6067	5	3	we	we	PRON
ejpam-6067	5	4	define	define	VERB
ejpam-6067	5	5	the	the	DET
ejpam-6067	5	6	gseparation	gseparation	NOUN
ejpam-6067	5	7	axioms	axiom	NOUN
ejpam-6067	5	8	utilizing	utilize	VERB
ejpam-6067	5	9	gδ	gδ	NOUN
ejpam-6067	5	10	sets	set	NOUN
ejpam-6067	5	11	and	and	CCONJ
ejpam-6067	5	12	explore	explore	VERB
ejpam-6067	5	13	the	the	DET
ejpam-6067	5	14	interrelations	interrelation	NOUN
ejpam-6067	5	15	among	among	ADP
ejpam-6067	5	16	these	these	DET
ejpam-6067	5	17	concepts	concept	NOUN
ejpam-6067	5	18	.	.	PUNCT
ejpam-6067	6	1	2020	2020	NUM
ejpam-6067	6	2	mathematics	mathematic	NOUN
ejpam-6067	6	3	subject	subject	NOUN
ejpam-6067	6	4	classifications	classification	NOUN
ejpam-6067	6	5	:	:	PUNCT
ejpam-6067	6	6	54d30	54d30	NUM
ejpam-6067	6	7	,	,	PUNCT
ejpam-6067	6	8	54e99	54e99	NUM
ejpam-6067	6	9	,	,	PUNCT
ejpam-6067	6	10	54d10	54d10	NUM
ejpam-6067	6	11	key	key	ADJ
ejpam-6067	6	12	words	word	NOUN
ejpam-6067	6	13	and	and	CCONJ
ejpam-6067	6	14	phrases	phrase	NOUN
ejpam-6067	6	15	:	:	PUNCT
ejpam-6067	6	16	compact	compact	ADJ
ejpam-6067	6	17	space	space	NOUN
ejpam-6067	6	18	,	,	PUNCT
ejpam-6067	6	19	lindelöf	lindelöf	NOUN
ejpam-6067	6	20	space	space	NOUN
ejpam-6067	6	21	,	,	PUNCT
ejpam-6067	6	22	countably	countably	ADV
ejpam-6067	6	23	compact	compact	ADJ
ejpam-6067	6	24	space	space	NOUN
ejpam-6067	6	25	,	,	PUNCT
ejpam-6067	6	26	g	g	NOUN
ejpam-6067	6	27	-	-	PUNCT
ejpam-6067	6	28	compact	compact	ADJ
ejpam-6067	6	29	space	space	NOUN
ejpam-6067	6	30	,	,	PUNCT
ejpam-6067	6	31	g	g	NOUN
ejpam-6067	6	32	-	-	PUNCT
ejpam-6067	6	33	lindelöf	lindelöf	NOUN
ejpam-6067	6	34	space	space	NOUN
ejpam-6067	6	35	,	,	PUNCT
ejpam-6067	6	36	g	g	NOUN
ejpam-6067	6	37	-	-	PUNCT
ejpam-6067	6	38	countably	countably	ADV
ejpam-6067	6	39	compact	compact	ADJ
ejpam-6067	6	40	,	,	PUNCT
ejpam-6067	6	41	separation	separation	NOUN
ejpam-6067	6	42	axioms	axiom	NOUN
ejpam-6067	6	43	,	,	PUNCT
ejpam-6067	6	44	g	g	NOUN
ejpam-6067	6	45	-	-	PUNCT
ejpam-6067	6	46	separation	separation	NOUN
ejpam-6067	6	47	axioms	axiom	NOUN
ejpam-6067	6	48	.	.	PUNCT
ejpam-6067	7	1	1	1	X
ejpam-6067	7	2	.	.	X
ejpam-6067	7	3	introduction	introduction	NOUN
ejpam-6067	7	4	and	and	CCONJ
ejpam-6067	7	5	preliminary	preliminary	VERB
ejpam-6067	7	6	the	the	DET
ejpam-6067	7	7	notion	notion	NOUN
ejpam-6067	7	8	of	of	ADP
ejpam-6067	7	9	compactness	compactness	NOUN
ejpam-6067	7	10	in	in	ADP
ejpam-6067	7	11	mathematics	mathematics	NOUN
ejpam-6067	7	12	pertains	pertain	NOUN
ejpam-6067	7	13	to	to	ADP
ejpam-6067	7	14	a	a	DET
ejpam-6067	7	15	characteristic	characteristic	NOUN
ejpam-6067	7	16	of	of	ADP
ejpam-6067	7	17	topological	topological	ADJ
ejpam-6067	7	18	spaces	space	NOUN
ejpam-6067	7	19	that	that	PRON
ejpam-6067	7	20	generalizes	generalize	VERB
ejpam-6067	7	21	the	the	DET
ejpam-6067	7	22	idea	idea	NOUN
ejpam-6067	7	23	of	of	ADP
ejpam-6067	7	24	closed	closed	ADJ
ejpam-6067	7	25	and	and	CCONJ
ejpam-6067	7	26	bounded	bound	VERB
ejpam-6067	7	27	subsets	subset	NOUN
ejpam-6067	7	28	found	find	VERB
ejpam-6067	7	29	in	in	ADP
ejpam-6067	7	30	euclidean	euclidean	ADJ
ejpam-6067	7	31	space	space	NOUN
ejpam-6067	7	32	.	.	PUNCT
ejpam-6067	8	1	∗corresponding	∗corresponde	VERB
ejpam-6067	8	2	author	author	NOUN
ejpam-6067	8	3	.	.	PUNCT
ejpam-6067	9	1	∗corresponding	∗corresponde	VERB
ejpam-6067	9	2	author	author	NOUN
ejpam-6067	9	3	.	.	PUNCT
ejpam-6067	10	1	doi	doi	NOUN
ejpam-6067	10	2	:	:	PUNCT
ejpam-6067	10	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6067	https://doi.org/10.29020/nybg.ejpam.v18i3.6067	ADP
ejpam-6067	10	4	email	email	NOUN
ejpam-6067	10	5	addresses	address	NOUN
ejpam-6067	10	6	:	:	PUNCT
ejpam-6067	10	7	m.shatnawi@inu.edu.jo	m.shatnawi@inu.edu.jo	PROPN
ejpam-6067	10	8	(	(	PUNCT
ejpam-6067	10	9	m.	m.	NOUN
ejpam-6067	10	10	shatnawi	shatnawi	PROPN
ejpam-6067	10	11	)	)	PUNCT
ejpam-6067	10	12	,	,	PUNCT
ejpam-6067	10	13	jamal.oudetallah@uop.edu.jo	jamal.oudetallah@uop.edu.jo	PROPN
ejpam-6067	10	14	(	(	PUNCT
ejpam-6067	10	15	j.	j.	PROPN
ejpam-6067	10	16	oudetallah	oudetallah	PROPN
ejpam-6067	10	17	)	)	PUNCT
ejpam-6067	10	18	,	,	PUNCT
ejpam-6067	10	19	a.bataihah@jadara.edu.jo	a.bataihah@jadara.edu.jo	NOUN
ejpam-6067	10	20	(	(	PUNCT
ejpam-6067	10	21	a.	a.	PROPN
ejpam-6067	10	22	bataihah	bataihah	PROPN
ejpam-6067	10	23	)	)	PUNCT
ejpam-6067	10	24	,	,	PUNCT
ejpam-6067	10	25	aamourah@su.edu.om	aamourah@su.edu.om	NOUN
ejpam-6067	10	26	(	(	PUNCT
ejpam-6067	10	27	a.	a.	NOUN
ejpam-6067	10	28	amourah	amourah	PROPN
ejpam-6067	10	29	)	)	PUNCT
ejpam-6067	10	30	,	,	PUNCT
ejpam-6067	10	31	abdullah.alsoboh@asu.edu.om	abdullah.alsoboh@asu.edu.om	NOUN
ejpam-6067	10	32	(	(	PUNCT
ejpam-6067	10	33	a.	a.	NOUN
ejpam-6067	10	34	alsoboh	alsoboh	PROPN
ejpam-6067	10	35	)	)	PUNCT
ejpam-6067	10	36	,	,	PUNCT
ejpam-6067	10	37	t	t	NOUN
ejpam-6067	10	38	sasa@asu.edu.jo	sasa@asu.edu.jo	NOUN
ejpam-6067	10	39	(	(	PUNCT
ejpam-6067	10	40	t.	t.	PROPN
ejpam-6067	10	41	sasa	sasa	PROPN
ejpam-6067	10	42	)	)	PUNCT
ejpam-6067	10	43	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6067	11	1	1	1	NUM
ejpam-6067	11	2	copyright	copyright	NOUN
ejpam-6067	11	3	:	:	PUNCT
ejpam-6067	11	4	©	©	PROPN
ejpam-6067	11	5	2025	2025	NUM
ejpam-6067	11	6	the	the	DET
ejpam-6067	11	7	author(s	author(s	NOUN
ejpam-6067	11	8	)	)	PUNCT
ejpam-6067	11	9	.	.	PUNCT
ejpam-6067	12	1	(	(	PUNCT
ejpam-6067	12	2	cc	cc	NOUN
ejpam-6067	12	3	by	by	ADP
ejpam-6067	12	4	-	-	PUNCT
ejpam-6067	12	5	nc	nc	PROPN
ejpam-6067	12	6	4.0	4.0	NUM
ejpam-6067	12	7	)	)	PUNCT
ejpam-6067	12	8	m.	m.	NOUN
ejpam-6067	12	9	shatnawi	shatnawi	PROPN
ejpam-6067	12	10	et	et	PROPN
ejpam-6067	12	11	al	al	PROPN
ejpam-6067	12	12	.	.	PUNCT
ejpam-6067	12	13	/	/	SYM
ejpam-6067	12	14	eur	eur	PROPN
ejpam-6067	12	15	.	.	PUNCT
ejpam-6067	13	1	j.	j.	PROPN
ejpam-6067	13	2	pure	pure	PROPN
ejpam-6067	13	3	appl	appl	PROPN
ejpam-6067	13	4	.	.	PROPN
ejpam-6067	13	5	math	math	PROPN
ejpam-6067	13	6	,	,	PUNCT
ejpam-6067	13	7	18	18	NUM
ejpam-6067	13	8	(	(	PUNCT
ejpam-6067	13	9	3	3	NUM
ejpam-6067	13	10	)	)	PUNCT
ejpam-6067	13	11	(	(	PUNCT
ejpam-6067	13	12	2025	2025	NUM
ejpam-6067	13	13	)	)	PUNCT
ejpam-6067	13	14	,	,	PUNCT
ejpam-6067	13	15	6067	6067	NUM
ejpam-6067	13	16	2	2	NUM
ejpam-6067	13	17	of	of	ADP
ejpam-6067	13	18	16	16	NUM
ejpam-6067	13	19	a	a	DET
ejpam-6067	13	20	topological	topological	ADJ
ejpam-6067	13	21	space	space	NOUN
ejpam-6067	13	22	is	be	AUX
ejpam-6067	13	23	deemed	deem	VERB
ejpam-6067	13	24	compact	compact	ADJ
ejpam-6067	13	25	if	if	SCONJ
ejpam-6067	13	26	every	every	DET
ejpam-6067	13	27	open	open	ADJ
ejpam-6067	13	28	cover	cover	NOUN
ejpam-6067	13	29	of	of	ADP
ejpam-6067	13	30	that	that	DET
ejpam-6067	13	31	space	space	NOUN
ejpam-6067	13	32	admits	admit	VERB
ejpam-6067	13	33	a	a	DET
ejpam-6067	13	34	finite	finite	PROPN
ejpam-6067	13	35	subcover	subcover	PROPN
ejpam-6067	13	36	,	,	PUNCT
ejpam-6067	13	37	indicating	indicate	VERB
ejpam-6067	13	38	that	that	SCONJ
ejpam-6067	13	39	from	from	ADP
ejpam-6067	13	40	any	any	DET
ejpam-6067	13	41	collection	collection	NOUN
ejpam-6067	13	42	of	of	ADP
ejpam-6067	13	43	open	open	ADJ
ejpam-6067	13	44	sets	set	NOUN
ejpam-6067	13	45	that	that	PRON
ejpam-6067	13	46	collectively	collectively	ADV
ejpam-6067	13	47	cover	cover	VERB
ejpam-6067	13	48	the	the	DET
ejpam-6067	13	49	space	space	NOUN
ejpam-6067	13	50	,	,	PUNCT
ejpam-6067	13	51	a	a	DET
ejpam-6067	13	52	finite	finite	ADJ
ejpam-6067	13	53	selection	selection	NOUN
ejpam-6067	13	54	of	of	ADP
ejpam-6067	13	55	these	these	DET
ejpam-6067	13	56	sets	set	NOUN
ejpam-6067	13	57	can	can	AUX
ejpam-6067	13	58	also	also	ADV
ejpam-6067	13	59	serve	serve	VERB
ejpam-6067	13	60	as	as	ADP
ejpam-6067	13	61	a	a	DET
ejpam-6067	13	62	cover	cover	NOUN
ejpam-6067	13	63	.	.	PUNCT
ejpam-6067	14	1	this	this	DET
ejpam-6067	14	2	concept	concept	NOUN
ejpam-6067	14	3	is	be	AUX
ejpam-6067	14	4	rooted	root	VERB
ejpam-6067	14	5	in	in	ADP
ejpam-6067	14	6	the	the	DET
ejpam-6067	14	7	heine	heine	PROPN
ejpam-6067	14	8	-	-	PUNCT
ejpam-6067	14	9	borel	borel	PROPN
ejpam-6067	14	10	theorem	theorem	PROPN
ejpam-6067	14	11	,	,	PUNCT
ejpam-6067	14	12	which	which	PRON
ejpam-6067	14	13	defines	define	VERB
ejpam-6067	14	14	compact	compact	ADJ
ejpam-6067	14	15	subsets	subset	NOUN
ejpam-6067	14	16	of	of	ADP
ejpam-6067	14	17	euclidean	euclidean	ADJ
ejpam-6067	14	18	space	space	NOUN
ejpam-6067	14	19	as	as	ADP
ejpam-6067	14	20	those	those	PRON
ejpam-6067	14	21	that	that	PRON
ejpam-6067	14	22	are	be	AUX
ejpam-6067	14	23	both	both	PRON
ejpam-6067	14	24	closed	close	VERB
ejpam-6067	14	25	and	and	CCONJ
ejpam-6067	14	26	bounded	bound	VERB
ejpam-6067	14	27	.	.	PUNCT
ejpam-6067	15	1	the	the	DET
ejpam-6067	15	2	formalization	formalization	NOUN
ejpam-6067	15	3	of	of	ADP
ejpam-6067	15	4	compactness	compactness	NOUN
ejpam-6067	15	5	within	within	ADP
ejpam-6067	15	6	topology	topology	NOUN
ejpam-6067	15	7	emerged	emerge	VERB
ejpam-6067	15	8	alongside	alongside	ADP
ejpam-6067	15	9	the	the	DET
ejpam-6067	15	10	establishment	establishment	NOUN
ejpam-6067	15	11	of	of	ADP
ejpam-6067	15	12	topology	topology	NOUN
ejpam-6067	15	13	as	as	ADP
ejpam-6067	15	14	a	a	DET
ejpam-6067	15	15	separate	separate	ADJ
ejpam-6067	15	16	mathematical	mathematical	ADJ
ejpam-6067	15	17	discipline	discipline	NOUN
ejpam-6067	15	18	during	during	ADP
ejpam-6067	15	19	the	the	DET
ejpam-6067	15	20	late	late	ADJ
ejpam-6067	15	21	19th	19th	NOUN
ejpam-6067	15	22	and	and	CCONJ
ejpam-6067	15	23	early	early	ADJ
ejpam-6067	15	24	20th	20th	ADJ
ejpam-6067	15	25	centuries	century	NOUN
ejpam-6067	15	26	.	.	PUNCT
ejpam-6067	16	1	this	this	DET
ejpam-6067	16	2	era	era	NOUN
ejpam-6067	16	3	was	be	AUX
ejpam-6067	16	4	marked	mark	VERB
ejpam-6067	16	5	by	by	ADP
ejpam-6067	16	6	significant	significant	ADJ
ejpam-6067	16	7	contributions	contribution	NOUN
ejpam-6067	16	8	from	from	ADP
ejpam-6067	16	9	mathematicians	mathematician	NOUN
ejpam-6067	16	10	such	such	ADJ
ejpam-6067	16	11	as	as	ADP
ejpam-6067	16	12	henri	henri	PROPN
ejpam-6067	16	13	poincaré	poincaré	PROPN
ejpam-6067	16	14	,	,	PUNCT
ejpam-6067	16	15	who	who	PRON
ejpam-6067	16	16	laid	lay	VERB
ejpam-6067	16	17	down	down	ADP
ejpam-6067	16	18	essential	essential	ADJ
ejpam-6067	16	19	principles	principle	NOUN
ejpam-6067	16	20	of	of	ADP
ejpam-6067	16	21	topology	topology	NOUN
ejpam-6067	16	22	,	,	PUNCT
ejpam-6067	16	23	and	and	CCONJ
ejpam-6067	16	24	felix	felix	PROPN
ejpam-6067	16	25	hausdorff	hausdorff	PROPN
ejpam-6067	16	26	,	,	PUNCT
ejpam-6067	16	27	who	who	PRON
ejpam-6067	16	28	formulated	formulate	VERB
ejpam-6067	16	29	the	the	DET
ejpam-6067	16	30	axiomatic	axiomatic	ADJ
ejpam-6067	16	31	basis	basis	NOUN
ejpam-6067	16	32	for	for	ADP
ejpam-6067	16	33	general	general	ADJ
ejpam-6067	16	34	topological	topological	ADJ
ejpam-6067	16	35	spaces	space	NOUN
ejpam-6067	16	36	.	.	PUNCT
ejpam-6067	17	1	compactness	compactness	NOUN
ejpam-6067	17	2	is	be	AUX
ejpam-6067	17	3	integral	integral	ADJ
ejpam-6067	17	4	to	to	ADP
ejpam-6067	17	5	numerous	numerous	ADJ
ejpam-6067	17	6	branches	branch	NOUN
ejpam-6067	17	7	of	of	ADP
ejpam-6067	17	8	mathematics	mathematic	NOUN
ejpam-6067	17	9	,	,	PUNCT
ejpam-6067	17	10	including	include	VERB
ejpam-6067	17	11	analysis	analysis	NOUN
ejpam-6067	17	12	and	and	CCONJ
ejpam-6067	17	13	functional	functional	ADJ
ejpam-6067	17	14	analysis	analysis	NOUN
ejpam-6067	17	15	.	.	PUNCT
ejpam-6067	18	1	notably	notably	ADV
ejpam-6067	18	2	,	,	PUNCT
ejpam-6067	18	3	continuous	continuous	ADJ
ejpam-6067	18	4	functions	function	NOUN
ejpam-6067	18	5	defined	define	VERB
ejpam-6067	18	6	on	on	ADP
ejpam-6067	18	7	compact	compact	ADJ
ejpam-6067	18	8	spaces	space	NOUN
ejpam-6067	18	9	exhibit	exhibit	VERB
ejpam-6067	18	10	significant	significant	ADJ
ejpam-6067	18	11	properties	property	NOUN
ejpam-6067	18	12	,	,	PUNCT
ejpam-6067	18	13	such	such	ADJ
ejpam-6067	18	14	as	as	ADP
ejpam-6067	18	15	the	the	DET
ejpam-6067	18	16	ability	ability	NOUN
ejpam-6067	18	17	to	to	PART
ejpam-6067	18	18	achieve	achieve	VERB
ejpam-6067	18	19	maximum	maximum	ADJ
ejpam-6067	18	20	and	and	CCONJ
ejpam-6067	18	21	minimum	minimum	ADJ
ejpam-6067	18	22	values	value	NOUN
ejpam-6067	18	23	and	and	CCONJ
ejpam-6067	18	24	the	the	DET
ejpam-6067	18	25	potential	potential	NOUN
ejpam-6067	18	26	for	for	ADP
ejpam-6067	18	27	approximation	approximation	NOUN
ejpam-6067	18	28	by	by	ADP
ejpam-6067	18	29	polynomial	polynomial	ADJ
ejpam-6067	18	30	or	or	CCONJ
ejpam-6067	18	31	fourier	fourier	NOUN
ejpam-6067	18	32	series	series	NOUN
ejpam-6067	18	33	,	,	PUNCT
ejpam-6067	18	34	as	as	SCONJ
ejpam-6067	18	35	articulated	articulate	VERB
ejpam-6067	18	36	in	in	ADP
ejpam-6067	18	37	the	the	DET
ejpam-6067	18	38	stone	stone	NOUN
ejpam-6067	18	39	-	-	PUNCT
ejpam-6067	18	40	weierstrass	weierstrass	NOUN
ejpam-6067	18	41	theorem	theorem	NOUN
ejpam-6067	18	42	.	.	PUNCT
ejpam-6067	19	1	the	the	DET
ejpam-6067	19	2	exploration	exploration	NOUN
ejpam-6067	19	3	and	and	CCONJ
ejpam-6067	19	4	generalization	generalization	NOUN
ejpam-6067	19	5	of	of	ADP
ejpam-6067	19	6	this	this	DET
ejpam-6067	19	7	concept	concept	NOUN
ejpam-6067	19	8	continue	continue	VERB
ejpam-6067	19	9	to	to	PART
ejpam-6067	19	10	be	be	AUX
ejpam-6067	19	11	a	a	DET
ejpam-6067	19	12	focal	focal	ADJ
ejpam-6067	19	13	point	point	NOUN
ejpam-6067	19	14	in	in	ADP
ejpam-6067	19	15	contemporary	contemporary	PROPN
ejpam-6067	19	16	mathematical	mathematical	ADJ
ejpam-6067	19	17	research	research	NOUN
ejpam-6067	19	18	,	,	PUNCT
ejpam-6067	19	19	encompassing	encompass	VERB
ejpam-6067	19	20	fields	field	NOUN
ejpam-6067	19	21	such	such	ADJ
ejpam-6067	19	22	as	as	ADP
ejpam-6067	19	23	infinite	infinite	ADJ
ejpam-6067	19	24	-	-	PUNCT
ejpam-6067	19	25	dimensional	dimensional	ADJ
ejpam-6067	19	26	topology	topology	NOUN
ejpam-6067	19	27	and	and	CCONJ
ejpam-6067	19	28	set	set	NOUN
ejpam-6067	19	29	-	-	PUNCT
ejpam-6067	19	30	theoretic	theoretic	NOUN
ejpam-6067	19	31	topology	topology	NOUN
ejpam-6067	19	32	see	see	VERB
ejpam-6067	19	33	[	[	X
ejpam-6067	19	34	1	1	NUM
ejpam-6067	19	35	,	,	PUNCT
ejpam-6067	19	36	2	2	NUM
ejpam-6067	19	37	]	]	PUNCT
ejpam-6067	19	38	.	.	PUNCT
ejpam-6067	20	1	metric	metric	ADJ
ejpam-6067	20	2	spaces	space	NOUN
ejpam-6067	20	3	play	play	VERB
ejpam-6067	20	4	a	a	DET
ejpam-6067	20	5	crucial	crucial	ADJ
ejpam-6067	20	6	role	role	NOUN
ejpam-6067	20	7	in	in	ADP
ejpam-6067	20	8	the	the	DET
ejpam-6067	20	9	field	field	NOUN
ejpam-6067	20	10	of	of	ADP
ejpam-6067	20	11	topology	topology	NOUN
ejpam-6067	20	12	,	,	PUNCT
ejpam-6067	20	13	as	as	SCONJ
ejpam-6067	20	14	they	they	PRON
ejpam-6067	20	15	offer	offer	VERB
ejpam-6067	20	16	a	a	DET
ejpam-6067	20	17	framework	framework	NOUN
ejpam-6067	20	18	for	for	ADP
ejpam-6067	20	19	establishing	establish	VERB
ejpam-6067	20	20	a	a	DET
ejpam-6067	20	21	topology	topology	NOUN
ejpam-6067	20	22	on	on	ADP
ejpam-6067	20	23	a	a	DET
ejpam-6067	20	24	given	give	VERB
ejpam-6067	20	25	set	set	NOUN
ejpam-6067	20	26	.	.	PUNCT
ejpam-6067	21	1	a	a	DET
ejpam-6067	21	2	topology	topology	NOUN
ejpam-6067	21	3	consists	consist	VERB
ejpam-6067	21	4	of	of	ADP
ejpam-6067	21	5	a	a	DET
ejpam-6067	21	6	collection	collection	NOUN
ejpam-6067	21	7	of	of	ADP
ejpam-6067	21	8	open	open	ADJ
ejpam-6067	21	9	sets	set	NOUN
ejpam-6067	21	10	that	that	PRON
ejpam-6067	21	11	adhere	adhere	VERB
ejpam-6067	21	12	to	to	ADP
ejpam-6067	21	13	specific	specific	ADJ
ejpam-6067	21	14	axioms	axiom	NOUN
ejpam-6067	21	15	.	.	PUNCT
ejpam-6067	22	1	in	in	ADP
ejpam-6067	22	2	the	the	DET
ejpam-6067	22	3	context	context	NOUN
ejpam-6067	22	4	of	of	ADP
ejpam-6067	22	5	a	a	DET
ejpam-6067	22	6	metric	metric	ADJ
ejpam-6067	22	7	space	space	NOUN
ejpam-6067	22	8	,	,	PUNCT
ejpam-6067	22	9	a	a	DET
ejpam-6067	22	10	subset	subset	NOUN
ejpam-6067	22	11	is	be	AUX
ejpam-6067	22	12	deemed	deem	VERB
ejpam-6067	22	13	open	open	ADJ
ejpam-6067	22	14	if	if	SCONJ
ejpam-6067	22	15	,	,	PUNCT
ejpam-6067	22	16	for	for	ADP
ejpam-6067	22	17	every	every	DET
ejpam-6067	22	18	point	point	NOUN
ejpam-6067	22	19	within	within	ADP
ejpam-6067	22	20	that	that	DET
ejpam-6067	22	21	subset	subset	NOUN
ejpam-6067	22	22	,	,	PUNCT
ejpam-6067	22	23	there	there	PRON
ejpam-6067	22	24	exists	exist	VERB
ejpam-6067	22	25	a	a	DET
ejpam-6067	22	26	radius	radius	NOUN
ejpam-6067	22	27	such	such	ADJ
ejpam-6067	22	28	that	that	SCONJ
ejpam-6067	22	29	all	all	DET
ejpam-6067	22	30	points	point	NOUN
ejpam-6067	22	31	located	locate	VERB
ejpam-6067	22	32	within	within	ADP
ejpam-6067	22	33	that	that	DET
ejpam-6067	22	34	radius	radius	NOUN
ejpam-6067	22	35	are	be	AUX
ejpam-6067	22	36	also	also	ADV
ejpam-6067	22	37	included	include	VERB
ejpam-6067	22	38	in	in	ADP
ejpam-6067	22	39	the	the	DET
ejpam-6067	22	40	subset	subset	NOUN
ejpam-6067	22	41	.	.	PUNCT
ejpam-6067	23	1	this	this	DET
ejpam-6067	23	2	relationship	relationship	NOUN
ejpam-6067	23	3	enables	enable	VERB
ejpam-6067	23	4	metric	metric	ADJ
ejpam-6067	23	5	spaces	space	NOUN
ejpam-6067	23	6	to	to	PART
ejpam-6067	23	7	exemplify	exemplify	VERB
ejpam-6067	23	8	topological	topological	ADJ
ejpam-6067	23	9	spaces	space	NOUN
ejpam-6067	23	10	,	,	PUNCT
ejpam-6067	23	11	facilitating	facilitate	VERB
ejpam-6067	23	12	the	the	DET
ejpam-6067	23	13	investigation	investigation	NOUN
ejpam-6067	23	14	of	of	ADP
ejpam-6067	23	15	concepts	concept	NOUN
ejpam-6067	23	16	such	such	ADJ
ejpam-6067	23	17	as	as	ADP
ejpam-6067	23	18	continuity	continuity	NOUN
ejpam-6067	23	19	and	and	CCONJ
ejpam-6067	23	20	convergence	convergence	NOUN
ejpam-6067	23	21	see	see	VERB
ejpam-6067	23	22	[	[	X
ejpam-6067	23	23	3	3	NUM
ejpam-6067	23	24	]	]	PUNCT
ejpam-6067	23	25	.	.	PUNCT
ejpam-6067	24	1	for	for	ADP
ejpam-6067	24	2	more	more	ADJ
ejpam-6067	24	3	on	on	ADP
ejpam-6067	24	4	metric	metric	ADJ
ejpam-6067	24	5	theory	theory	NOUN
ejpam-6067	24	6	we	we	PRON
ejpam-6067	24	7	refer	refer	VERB
ejpam-6067	24	8	[	[	X
ejpam-6067	24	9	4–14	4–14	X
ejpam-6067	24	10	]	]	PUNCT
ejpam-6067	24	11	and	and	CCONJ
ejpam-6067	24	12	references	reference	NOUN
ejpam-6067	24	13	therein	therein	ADV
ejpam-6067	24	14	.	.	PUNCT
ejpam-6067	25	1	separation	separation	NOUN
ejpam-6067	25	2	axioms	axiom	NOUN
ejpam-6067	25	3	in	in	ADP
ejpam-6067	25	4	topology	topology	NOUN
ejpam-6067	25	5	represent	represent	VERB
ejpam-6067	25	6	a	a	DET
ejpam-6067	25	7	collection	collection	NOUN
ejpam-6067	25	8	of	of	ADP
ejpam-6067	25	9	criteria	criterion	NOUN
ejpam-6067	25	10	utilized	utilize	VERB
ejpam-6067	25	11	to	to	PART
ejpam-6067	25	12	differentiate	differentiate	VERB
ejpam-6067	25	13	among	among	ADP
ejpam-6067	25	14	various	various	ADJ
ejpam-6067	25	15	types	type	NOUN
ejpam-6067	25	16	of	of	ADP
ejpam-6067	25	17	topological	topological	ADJ
ejpam-6067	25	18	spaces	space	NOUN
ejpam-6067	25	19	,	,	PUNCT
ejpam-6067	25	20	particularly	particularly	ADV
ejpam-6067	25	21	in	in	ADP
ejpam-6067	25	22	terms	term	NOUN
ejpam-6067	25	23	of	of	ADP
ejpam-6067	25	24	the	the	DET
ejpam-6067	25	25	ability	ability	NOUN
ejpam-6067	25	26	to	to	PART
ejpam-6067	25	27	separate	separate	VERB
ejpam-6067	25	28	distinct	distinct	ADJ
ejpam-6067	25	29	points	point	NOUN
ejpam-6067	25	30	and	and	CCONJ
ejpam-6067	25	31	sets	set	VERB
ejpam-6067	25	32	through	through	ADP
ejpam-6067	25	33	neighborhoods	neighborhood	NOUN
ejpam-6067	25	34	.	.	PUNCT
ejpam-6067	26	1	the	the	DET
ejpam-6067	26	2	emergence	emergence	NOUN
ejpam-6067	26	3	of	of	ADP
ejpam-6067	26	4	these	these	DET
ejpam-6067	26	5	axioms	axiom	NOUN
ejpam-6067	26	6	coincided	coincide	VERB
ejpam-6067	26	7	with	with	ADP
ejpam-6067	26	8	the	the	DET
ejpam-6067	26	9	maturation	maturation	NOUN
ejpam-6067	26	10	of	of	ADP
ejpam-6067	26	11	topology	topology	NOUN
ejpam-6067	26	12	as	as	ADP
ejpam-6067	26	13	a	a	DET
ejpam-6067	26	14	specialized	specialized	ADJ
ejpam-6067	26	15	area	area	NOUN
ejpam-6067	26	16	of	of	ADP
ejpam-6067	26	17	mathematics	mathematic	NOUN
ejpam-6067	26	18	,	,	PUNCT
ejpam-6067	26	19	significantly	significantly	ADV
ejpam-6067	26	20	influenced	influence	VERB
ejpam-6067	26	21	by	by	ADP
ejpam-6067	26	22	the	the	DET
ejpam-6067	26	23	work	work	NOUN
ejpam-6067	26	24	of	of	ADP
ejpam-6067	26	25	mathematicians	mathematician	NOUN
ejpam-6067	26	26	such	such	ADJ
ejpam-6067	26	27	as	as	ADP
ejpam-6067	26	28	felix	felix	PROPN
ejpam-6067	26	29	hausdorff	hausdorff	NOUN
ejpam-6067	26	30	.	.	PUNCT
ejpam-6067	27	1	in	in	ADP
ejpam-6067	27	2	his	his	PRON
ejpam-6067	27	3	seminal	seminal	ADJ
ejpam-6067	27	4	1914	1914	NUM
ejpam-6067	27	5	publication	publication	NOUN
ejpam-6067	27	6	,	,	PUNCT
ejpam-6067	27	7	”	"	PUNCT
ejpam-6067	27	8	grundzüge	grundzüge	X
ejpam-6067	27	9	der	der	NOUN
ejpam-6067	27	10	mengenlehre	mengenlehre	PROPN
ejpam-6067	27	11	,	,	PUNCT
ejpam-6067	27	12	”	"	PUNCT
ejpam-6067	27	13	hausdorff	hausdorff	NOUN
ejpam-6067	27	14	articulated	articulate	VERB
ejpam-6067	27	15	the	the	DET
ejpam-6067	27	16	separation	separation	NOUN
ejpam-6067	27	17	property	property	NOUN
ejpam-6067	27	18	,	,	PUNCT
ejpam-6067	27	19	which	which	PRON
ejpam-6067	27	20	became	become	VERB
ejpam-6067	27	21	a	a	DET
ejpam-6067	27	22	cornerstone	cornerstone	NOUN
ejpam-6067	27	23	of	of	ADP
ejpam-6067	27	24	contemporary	contemporary	ADJ
ejpam-6067	27	25	topology	topology	NOUN
ejpam-6067	27	26	by	by	ADP
ejpam-6067	27	27	establishing	establish	VERB
ejpam-6067	27	28	axioms	axiom	NOUN
ejpam-6067	27	29	applicable	applicable	ADJ
ejpam-6067	27	30	to	to	ADP
ejpam-6067	27	31	general	general	ADJ
ejpam-6067	27	32	spaces	space	NOUN
ejpam-6067	27	33	.	.	PUNCT
ejpam-6067	28	1	this	this	DET
ejpam-6067	28	2	property	property	NOUN
ejpam-6067	28	3	,	,	PUNCT
ejpam-6067	28	4	referred	refer	VERB
ejpam-6067	28	5	to	to	ADP
ejpam-6067	28	6	as	as	ADP
ejpam-6067	28	7	the	the	DET
ejpam-6067	28	8	hausdorff	hausdorff	NOUN
ejpam-6067	28	9	condition	condition	NOUN
ejpam-6067	28	10	,	,	PUNCT
ejpam-6067	28	11	stipulates	stipulate	VERB
ejpam-6067	28	12	that	that	SCONJ
ejpam-6067	28	13	for	for	ADP
ejpam-6067	28	14	any	any	DET
ejpam-6067	28	15	two	two	NUM
ejpam-6067	28	16	distinct	distinct	ADJ
ejpam-6067	28	17	points	point	NOUN
ejpam-6067	28	18	within	within	ADP
ejpam-6067	28	19	a	a	DET
ejpam-6067	28	20	space	space	NOUN
ejpam-6067	28	21	,	,	PUNCT
ejpam-6067	28	22	there	there	PRON
ejpam-6067	28	23	exist	exist	VERB
ejpam-6067	28	24	disjoint	disjoint	ADJ
ejpam-6067	28	25	open	open	ADJ
ejpam-6067	28	26	sets	set	NOUN
ejpam-6067	28	27	that	that	PRON
ejpam-6067	28	28	separate	separate	VERB
ejpam-6067	28	29	them	they	PRON
ejpam-6067	28	30	,	,	PUNCT
ejpam-6067	28	31	thereby	thereby	ADV
ejpam-6067	28	32	classifying	classify	VERB
ejpam-6067	28	33	the	the	DET
ejpam-6067	28	34	space	space	NOUN
ejpam-6067	28	35	as	as	ADP
ejpam-6067	28	36	a	a	DET
ejpam-6067	28	37	hausdorff	hausdorff	NOUN
ejpam-6067	28	38	space	space	NOUN
ejpam-6067	28	39	,	,	PUNCT
ejpam-6067	28	40	or	or	CCONJ
ejpam-6067	28	41	(	(	PUNCT
ejpam-6067	28	42	t2	t2	NOUN
ejpam-6067	28	43	)	)	PUNCT
ejpam-6067	28	44	space	space	NOUN
ejpam-6067	28	45	.	.	PUNCT
ejpam-6067	29	1	the	the	DET
ejpam-6067	29	2	development	development	NOUN
ejpam-6067	29	3	of	of	ADP
ejpam-6067	29	4	separation	separation	NOUN
ejpam-6067	29	5	axioms	axiom	NOUN
ejpam-6067	29	6	is	be	AUX
ejpam-6067	29	7	closely	closely	ADV
ejpam-6067	29	8	linked	link	VERB
ejpam-6067	29	9	to	to	ADP
ejpam-6067	29	10	the	the	DET
ejpam-6067	29	11	overall	overall	ADJ
ejpam-6067	29	12	progression	progression	NOUN
ejpam-6067	29	13	of	of	ADP
ejpam-6067	29	14	topology	topology	NOUN
ejpam-6067	29	15	,	,	PUNCT
ejpam-6067	29	16	which	which	PRON
ejpam-6067	29	17	originated	originate	VERB
ejpam-6067	29	18	in	in	ADP
ejpam-6067	29	19	the	the	DET
ejpam-6067	29	20	19th	19th	ADJ
ejpam-6067	29	21	century	century	NOUN
ejpam-6067	29	22	,	,	PUNCT
ejpam-6067	29	23	with	with	ADP
ejpam-6067	29	24	key	key	ADJ
ejpam-6067	29	25	contributions	contribution	NOUN
ejpam-6067	29	26	from	from	ADP
ejpam-6067	29	27	mathematicians	mathematician	NOUN
ejpam-6067	29	28	such	such	ADJ
ejpam-6067	29	29	as	as	ADP
ejpam-6067	29	30	henri	henri	PROPN
ejpam-6067	29	31	poincaré	poincaré	PROPN
ejpam-6067	29	32	,	,	PUNCT
ejpam-6067	29	33	who	who	PRON
ejpam-6067	29	34	played	play	VERB
ejpam-6067	29	35	a	a	DET
ejpam-6067	29	36	pivotal	pivotal	ADJ
ejpam-6067	29	37	role	role	NOUN
ejpam-6067	29	38	in	in	ADP
ejpam-6067	29	39	defining	define	VERB
ejpam-6067	29	40	topology	topology	NOUN
ejpam-6067	29	41	as	as	ADP
ejpam-6067	29	42	a	a	DET
ejpam-6067	29	43	distinct	distinct	ADJ
ejpam-6067	29	44	discipline	discipline	NOUN
ejpam-6067	29	45	through	through	ADP
ejpam-6067	29	46	his	his	PRON
ejpam-6067	29	47	1895	1895	NUM
ejpam-6067	29	48	work	work	NOUN
ejpam-6067	29	49	,	,	PUNCT
ejpam-6067	29	50	”	"	PUNCT
ejpam-6067	29	51	analysis	analysis	NOUN
ejpam-6067	29	52	situs	situs	PROPN
ejpam-6067	29	53	.	.	PUNCT
ejpam-6067	29	54	”	"	PUNCT
ejpam-6067	30	1	the	the	DET
ejpam-6067	30	2	advancement	advancement	NOUN
ejpam-6067	30	3	of	of	ADP
ejpam-6067	30	4	topology	topology	NOUN
ejpam-6067	30	5	involved	involve	VERB
ejpam-6067	30	6	the	the	DET
ejpam-6067	30	7	investigation	investigation	NOUN
ejpam-6067	30	8	of	of	ADP
ejpam-6067	30	9	various	various	ADJ
ejpam-6067	30	10	spatial	spatial	ADJ
ejpam-6067	30	11	properties	property	NOUN
ejpam-6067	30	12	,	,	PUNCT
ejpam-6067	30	13	including	include	VERB
ejpam-6067	30	14	compactness	compactness	NOUN
ejpam-6067	30	15	and	and	CCONJ
ejpam-6067	30	16	convergence	convergence	NOUN
ejpam-6067	30	17	,	,	PUNCT
ejpam-6067	30	18	which	which	PRON
ejpam-6067	30	19	were	be	AUX
ejpam-6067	30	20	systematically	systematically	ADV
ejpam-6067	30	21	formalized	formalize	VERB
ejpam-6067	30	22	by	by	ADP
ejpam-6067	30	23	mathematicians	mathematician	NOUN
ejpam-6067	30	24	like	like	ADP
ejpam-6067	30	25	maurice	maurice	NOUN
ejpam-6067	30	26	fréchet	fréchet	PROPN
ejpam-6067	30	27	and	and	CCONJ
ejpam-6067	30	28	pavel	pavel	PROPN
ejpam-6067	30	29	alexandrov	alexandrov	PROPN
ejpam-6067	30	30	through	through	ADP
ejpam-6067	30	31	axiomatic	axiomatic	ADJ
ejpam-6067	30	32	methods	method	NOUN
ejpam-6067	30	33	.	.	PUNCT
ejpam-6067	31	1	today	today	NOUN
ejpam-6067	31	2	,	,	PUNCT
ejpam-6067	31	3	separation	separation	NOUN
ejpam-6067	31	4	axioms	axiom	NOUN
ejpam-6067	31	5	are	be	AUX
ejpam-6067	31	6	integral	integral	ADJ
ejpam-6067	31	7	to	to	ADP
ejpam-6067	31	8	topological	topological	ADJ
ejpam-6067	31	9	research	research	NOUN
ejpam-6067	31	10	,	,	PUNCT
ejpam-6067	31	11	offering	offer	VERB
ejpam-6067	31	12	a	a	DET
ejpam-6067	31	13	structured	structured	ADJ
ejpam-6067	31	14	approach	approach	NOUN
ejpam-6067	31	15	to	to	ADP
ejpam-6067	31	16	understanding	understand	VERB
ejpam-6067	31	17	the	the	DET
ejpam-6067	31	18	interactions	interaction	NOUN
ejpam-6067	31	19	between	between	ADP
ejpam-6067	31	20	points	point	NOUN
ejpam-6067	31	21	and	and	CCONJ
ejpam-6067	31	22	sets	set	NOUN
ejpam-6067	31	23	within	within	ADP
ejpam-6067	31	24	a	a	DET
ejpam-6067	31	25	topological	topological	ADJ
ejpam-6067	31	26	space	space	NOUN
ejpam-6067	31	27	.	.	PUNCT
ejpam-6067	32	1	they	they	PRON
ejpam-6067	32	2	are	be	AUX
ejpam-6067	32	3	essential	essential	ADJ
ejpam-6067	32	4	for	for	ADP
ejpam-6067	32	5	differentiating	differentiate	VERB
ejpam-6067	32	6	among	among	ADP
ejpam-6067	32	7	various	various	ADJ
ejpam-6067	32	8	types	type	NOUN
ejpam-6067	32	9	of	of	ADP
ejpam-6067	32	10	spaces	space	NOUN
ejpam-6067	32	11	and	and	CCONJ
ejpam-6067	32	12	for	for	ADP
ejpam-6067	32	13	establishing	establish	VERB
ejpam-6067	32	14	numerous	numerous	ADJ
ejpam-6067	32	15	theorems	theorem	NOUN
ejpam-6067	32	16	within	within	ADP
ejpam-6067	32	17	the	the	DET
ejpam-6067	32	18	field	field	NOUN
ejpam-6067	32	19	of	of	ADP
ejpam-6067	32	20	topology	topology	NOUN
ejpam-6067	32	21	see	see	VERB
ejpam-6067	32	22	[	[	X
ejpam-6067	32	23	1	1	NUM
ejpam-6067	32	24	,	,	PUNCT
ejpam-6067	32	25	2	2	NUM
ejpam-6067	32	26	]	]	PUNCT
ejpam-6067	32	27	.	.	PUNCT
ejpam-6067	33	1	m.	m.	NOUN
ejpam-6067	33	2	shatnawi	shatnawi	PROPN
ejpam-6067	33	3	et	et	PROPN
ejpam-6067	33	4	al	al	PROPN
ejpam-6067	33	5	.	.	PUNCT
ejpam-6067	33	6	/	/	SYM
ejpam-6067	33	7	eur	eur	PROPN
ejpam-6067	33	8	.	.	PUNCT
ejpam-6067	34	1	j.	j.	PROPN
ejpam-6067	34	2	pure	pure	PROPN
ejpam-6067	34	3	appl	appl	PROPN
ejpam-6067	34	4	.	.	PROPN
ejpam-6067	34	5	math	math	PROPN
ejpam-6067	34	6	,	,	PUNCT
ejpam-6067	34	7	18	18	NUM
ejpam-6067	34	8	(	(	PUNCT
ejpam-6067	34	9	3	3	NUM
ejpam-6067	34	10	)	)	PUNCT
ejpam-6067	34	11	(	(	PUNCT
ejpam-6067	34	12	2025	2025	NUM
ejpam-6067	34	13	)	)	PUNCT
ejpam-6067	34	14	,	,	PUNCT
ejpam-6067	34	15	6067	6067	NUM
ejpam-6067	34	16	3	3	NUM
ejpam-6067	34	17	of	of	ADP
ejpam-6067	34	18	16	16	NUM
ejpam-6067	34	19	various	various	ADJ
ejpam-6067	34	20	forms	form	NOUN
ejpam-6067	34	21	of	of	ADP
ejpam-6067	34	22	compactness	compactness	NOUN
ejpam-6067	34	23	are	be	AUX
ejpam-6067	34	24	examined	examine	VERB
ejpam-6067	34	25	in	in	ADP
ejpam-6067	34	26	numerous	numerous	ADJ
ejpam-6067	34	27	research	research	NOUN
ejpam-6067	34	28	articles	article	NOUN
ejpam-6067	34	29	,	,	PUNCT
ejpam-6067	34	30	as	as	SCONJ
ejpam-6067	34	31	illustrated	illustrate	VERB
ejpam-6067	34	32	in	in	ADP
ejpam-6067	34	33	references	reference	NOUN
ejpam-6067	34	34	[	[	X
ejpam-6067	34	35	15–18	15–18	NUM
ejpam-6067	34	36	]	]	PUNCT
ejpam-6067	34	37	.	.	PUNCT
ejpam-6067	35	1	in	in	ADP
ejpam-6067	35	2	[	[	X
ejpam-6067	35	3	19	19	NUM
ejpam-6067	35	4	]	]	PUNCT
ejpam-6067	35	5	the	the	DET
ejpam-6067	35	6	authors	author	NOUN
ejpam-6067	35	7	study	study	VERB
ejpam-6067	35	8	topological	topological	ADJ
ejpam-6067	35	9	spaces	space	NOUN
ejpam-6067	35	10	on	on	ADP
ejpam-6067	35	11	symbolic	symbolic	ADJ
ejpam-6067	35	12	m	m	PROPN
ejpam-6067	35	13	-	-	ADJ
ejpam-6067	35	14	plithogenic	plithogenic	ADJ
ejpam-6067	35	15	intervals	interval	NOUN
ejpam-6067	35	16	,	,	PUNCT
ejpam-6067	35	17	while	while	SCONJ
ejpam-6067	35	18	[	[	X
ejpam-6067	35	19	20	20	NUM
ejpam-6067	35	20	]	]	PUNCT
ejpam-6067	35	21	extends	extend	VERB
ejpam-6067	35	22	this	this	PRON
ejpam-6067	35	23	to	to	ADP
ejpam-6067	35	24	neutrosophic	neutrosophic	ADJ
ejpam-6067	35	25	and	and	CCONJ
ejpam-6067	35	26	refined	refined	ADJ
ejpam-6067	35	27	neutrosophic	neutrosophic	ADJ
ejpam-6067	35	28	real	real	ADJ
ejpam-6067	35	29	intervals	interval	NOUN
ejpam-6067	35	30	,	,	PUNCT
ejpam-6067	35	31	both	both	PRON
ejpam-6067	35	32	using	use	VERB
ejpam-6067	35	33	partial	partial	ADJ
ejpam-6067	35	34	order	order	NOUN
ejpam-6067	35	35	relations	relation	NOUN
ejpam-6067	35	36	.	.	PUNCT
ejpam-6067	36	1	in	in	ADP
ejpam-6067	36	2	this	this	DET
ejpam-6067	36	3	document	document	NOUN
ejpam-6067	36	4	,	,	PUNCT
ejpam-6067	36	5	we	we	PRON
ejpam-6067	36	6	represent	represent	VERB
ejpam-6067	36	7	the	the	DET
ejpam-6067	36	8	set	set	NOUN
ejpam-6067	36	9	of	of	ADP
ejpam-6067	36	10	natural	natural	ADJ
ejpam-6067	36	11	numbers	number	NOUN
ejpam-6067	36	12	as	as	ADP
ejpam-6067	36	13	and	and	CCONJ
ejpam-6067	36	14	the	the	DET
ejpam-6067	36	15	set	set	NOUN
ejpam-6067	36	16	of	of	ADP
ejpam-6067	36	17	real	real	ADJ
ejpam-6067	36	18	numbers	number	NOUN
ejpam-6067	36	19	as	as	ADP
ejpam-6067	36	20	.	.	PUNCT
ejpam-6067	37	1	definition	definition	NOUN
ejpam-6067	37	2	1	1	NUM
ejpam-6067	37	3	(	(	PUNCT
ejpam-6067	37	4	metric	metric	ADJ
ejpam-6067	37	5	space	space	NOUN
ejpam-6067	37	6	[	[	X
ejpam-6067	37	7	3	3	NUM
ejpam-6067	37	8	]	]	NUM
ejpam-6067	37	9	)	)	PUNCT
ejpam-6067	37	10	.	.	PUNCT
ejpam-6067	38	1	a	a	DET
ejpam-6067	38	2	metric	metric	ADJ
ejpam-6067	38	3	space	space	NOUN
ejpam-6067	38	4	(	(	PUNCT
ejpam-6067	38	5	x	x	X
ejpam-6067	38	6	,	,	PUNCT
ejpam-6067	38	7	d	d	NOUN
ejpam-6067	38	8	)	)	PUNCT
ejpam-6067	38	9	consists	consist	VERB
ejpam-6067	38	10	of	of	ADP
ejpam-6067	38	11	a	a	DET
ejpam-6067	38	12	set	set	NOUN
ejpam-6067	38	13	x	x	PUNCT
ejpam-6067	38	14	together	together	ADV
ejpam-6067	38	15	with	with	ADP
ejpam-6067	38	16	a	a	DET
ejpam-6067	38	17	function	function	NOUN
ejpam-6067	38	18	d	d	NOUN
ejpam-6067	38	19	:	:	PUNCT
ejpam-6067	38	20	x	x	PROPN
ejpam-6067	38	21	×x	×x	ADP
ejpam-6067	38	22	→	→	SYM
ejpam-6067	38	23	r	r	NOUN
ejpam-6067	38	24	satisfying	satisfying	NOUN
ejpam-6067	38	25	:	:	PUNCT
ejpam-6067	38	26	(	(	PUNCT
ejpam-6067	38	27	i	i	NOUN
ejpam-6067	38	28	)	)	PUNCT
ejpam-6067	38	29	d(x	d(x	PROPN
ejpam-6067	38	30	,	,	PUNCT
ejpam-6067	38	31	y	y	NOUN
ejpam-6067	38	32	)	)	PUNCT
ejpam-6067	38	33	≥	≥	NOUN
ejpam-6067	38	34	0	0	NUM
ejpam-6067	38	35	for	for	ADP
ejpam-6067	38	36	all	all	DET
ejpam-6067	38	37	x	x	NOUN
ejpam-6067	38	38	,	,	PUNCT
ejpam-6067	38	39	y	y	PROPN
ejpam-6067	38	40	∈	∈	PROPN
ejpam-6067	38	41	x	x	X
ejpam-6067	38	42	,	,	PUNCT
ejpam-6067	38	43	and	and	CCONJ
ejpam-6067	38	44	d(x	d(x	PROPN
ejpam-6067	38	45	,	,	PUNCT
ejpam-6067	38	46	y	y	NOUN
ejpam-6067	38	47	)	)	PUNCT
ejpam-6067	38	48	=	=	SYM
ejpam-6067	38	49	0	0	PUNCT
ejpam-6067	39	1	if	if	SCONJ
ejpam-6067	39	2	and	and	CCONJ
ejpam-6067	39	3	only	only	ADV
ejpam-6067	39	4	if	if	SCONJ
ejpam-6067	39	5	x	x	X
ejpam-6067	39	6	=	=	SYM
ejpam-6067	39	7	y.	y.	PROPN
ejpam-6067	39	8	(	(	PUNCT
ejpam-6067	39	9	ii	ii	PROPN
ejpam-6067	39	10	)	)	PUNCT
ejpam-6067	39	11	d(x	d(x	PROPN
ejpam-6067	39	12	,	,	PUNCT
ejpam-6067	39	13	y	y	NOUN
ejpam-6067	39	14	)	)	PUNCT
ejpam-6067	39	15	=	=	SYM
ejpam-6067	39	16	d(y	d(y	NOUN
ejpam-6067	39	17	,	,	PUNCT
ejpam-6067	39	18	x	x	NOUN
ejpam-6067	39	19	)	)	PUNCT
ejpam-6067	39	20	for	for	ADP
ejpam-6067	39	21	all	all	DET
ejpam-6067	39	22	x	x	NOUN
ejpam-6067	39	23	,	,	PUNCT
ejpam-6067	39	24	y	y	PROPN
ejpam-6067	39	25	∈	∈	PROPN
ejpam-6067	39	26	x	x	INTJ
ejpam-6067	39	27	(	(	PUNCT
ejpam-6067	39	28	symmetry	symmetry	NOUN
ejpam-6067	39	29	)	)	PUNCT
ejpam-6067	39	30	.	.	PUNCT
ejpam-6067	40	1	(	(	PUNCT
ejpam-6067	40	2	iii	iii	X
ejpam-6067	40	3	)	)	PUNCT
ejpam-6067	40	4	d(x	d(x	PROPN
ejpam-6067	40	5	,	,	PUNCT
ejpam-6067	40	6	z	z	NOUN
ejpam-6067	40	7	)	)	PUNCT
ejpam-6067	40	8	≤	≤	NOUN
ejpam-6067	40	9	d(x	d(x	PROPN
ejpam-6067	40	10	,	,	PUNCT
ejpam-6067	40	11	y	y	NOUN
ejpam-6067	40	12	)	)	PUNCT
ejpam-6067	41	1	+	+	CCONJ
ejpam-6067	41	2	d(y	d(y	NOUN
ejpam-6067	41	3	,	,	PUNCT
ejpam-6067	41	4	z	z	NOUN
ejpam-6067	41	5	)	)	PUNCT
ejpam-6067	41	6	for	for	ADP
ejpam-6067	41	7	all	all	DET
ejpam-6067	41	8	x	x	NOUN
ejpam-6067	41	9	,	,	PUNCT
ejpam-6067	41	10	y	y	PROPN
ejpam-6067	41	11	,	,	PUNCT
ejpam-6067	41	12	z	z	NOUN
ejpam-6067	41	13	∈	∈	PROPN
ejpam-6067	41	14	x	x	PUNCT
ejpam-6067	41	15	(	(	PUNCT
ejpam-6067	41	16	triangle	triangle	NOUN
ejpam-6067	41	17	inequality	inequality	NOUN
ejpam-6067	41	18	)	)	PUNCT
ejpam-6067	41	19	.	.	PUNCT
ejpam-6067	42	1	metric	metric	ADJ
ejpam-6067	42	2	spaces	space	NOUN
ejpam-6067	42	3	provide	provide	VERB
ejpam-6067	42	4	a	a	DET
ejpam-6067	42	5	framework	framework	NOUN
ejpam-6067	42	6	for	for	ADP
ejpam-6067	42	7	establishing	establish	VERB
ejpam-6067	42	8	topology	topology	NOUN
ejpam-6067	42	9	on	on	ADP
ejpam-6067	42	10	a	a	DET
ejpam-6067	42	11	given	give	VERB
ejpam-6067	42	12	set	set	NOUN
ejpam-6067	42	13	,	,	PUNCT
ejpam-6067	42	14	where	where	SCONJ
ejpam-6067	42	15	we	we	PRON
ejpam-6067	42	16	consider	consider	VERB
ejpam-6067	42	17	a	a	DET
ejpam-6067	42	18	subset	subset	NOUN
ejpam-6067	42	19	open	open	ADJ
ejpam-6067	42	20	if	if	SCONJ
ejpam-6067	42	21	,	,	PUNCT
ejpam-6067	42	22	for	for	ADP
ejpam-6067	42	23	every	every	DET
ejpam-6067	42	24	point	point	NOUN
ejpam-6067	42	25	within	within	ADP
ejpam-6067	42	26	that	that	DET
ejpam-6067	42	27	subset	subset	NOUN
ejpam-6067	42	28	,	,	PUNCT
ejpam-6067	42	29	there	there	PRON
ejpam-6067	42	30	exists	exist	VERB
ejpam-6067	42	31	a	a	DET
ejpam-6067	42	32	radius	radius	NOUN
ejpam-6067	42	33	such	such	ADJ
ejpam-6067	42	34	that	that	SCONJ
ejpam-6067	42	35	all	all	DET
ejpam-6067	42	36	points	point	NOUN
ejpam-6067	42	37	within	within	ADP
ejpam-6067	42	38	that	that	DET
ejpam-6067	42	39	radius	radius	NOUN
ejpam-6067	42	40	also	also	ADV
ejpam-6067	42	41	belong	belong	VERB
ejpam-6067	42	42	to	to	ADP
ejpam-6067	42	43	the	the	DET
ejpam-6067	42	44	subset	subset	NOUN
ejpam-6067	42	45	.	.	PUNCT
ejpam-6067	43	1	definition	definition	NOUN
ejpam-6067	43	2	2	2	NUM
ejpam-6067	43	3	(	(	PUNCT
ejpam-6067	43	4	separation	separation	NOUN
ejpam-6067	43	5	axioms	axiom	VERB
ejpam-6067	43	6	[	[	X
ejpam-6067	43	7	1	1	NUM
ejpam-6067	43	8	]	]	PUNCT
ejpam-6067	43	9	,	,	PUNCT
ejpam-6067	43	10	[	[	X
ejpam-6067	43	11	2	2	NUM
ejpam-6067	43	12	]	]	NUM
ejpam-6067	43	13	)	)	PUNCT
ejpam-6067	43	14	.	.	PUNCT
ejpam-6067	44	1	separation	separation	NOUN
ejpam-6067	44	2	axioms	axiom	NOUN
ejpam-6067	44	3	in	in	ADP
ejpam-6067	44	4	topology	topology	NOUN
ejpam-6067	44	5	serve	serve	NOUN
ejpam-6067	44	6	as	as	ADP
ejpam-6067	44	7	criteria	criterion	NOUN
ejpam-6067	44	8	differentiating	differentiate	VERB
ejpam-6067	44	9	various	various	ADJ
ejpam-6067	44	10	topological	topological	ADJ
ejpam-6067	44	11	spaces	space	NOUN
ejpam-6067	44	12	,	,	PUNCT
ejpam-6067	44	13	particularly	particularly	ADV
ejpam-6067	44	14	regarding	regard	VERB
ejpam-6067	44	15	the	the	DET
ejpam-6067	44	16	ability	ability	NOUN
ejpam-6067	44	17	to	to	PART
ejpam-6067	44	18	separate	separate	VERB
ejpam-6067	44	19	distinct	distinct	ADJ
ejpam-6067	44	20	points	point	NOUN
ejpam-6067	44	21	and	and	CCONJ
ejpam-6067	44	22	sets	set	VERB
ejpam-6067	44	23	through	through	ADP
ejpam-6067	44	24	neighborhoods	neighborhood	NOUN
ejpam-6067	44	25	.	.	PUNCT
ejpam-6067	45	1	the	the	DET
ejpam-6067	45	2	main	main	ADJ
ejpam-6067	45	3	separation	separation	NOUN
ejpam-6067	45	4	axioms	axiom	NOUN
ejpam-6067	45	5	include	include	VERB
ejpam-6067	45	6	:	:	PUNCT
ejpam-6067	45	7	(	(	PUNCT
ejpam-6067	45	8	i	i	NOUN
ejpam-6067	45	9	)	)	PUNCT
ejpam-6067	45	10	t0	t0	PROPN
ejpam-6067	45	11	(	(	PUNCT
ejpam-6067	45	12	kolmogorov	kolmogorov	PROPN
ejpam-6067	45	13	):	):	PUNCT
ejpam-6067	45	14	for	for	ADP
ejpam-6067	45	15	any	any	DET
ejpam-6067	45	16	two	two	NUM
ejpam-6067	45	17	distinct	distinct	ADJ
ejpam-6067	45	18	points	point	NOUN
ejpam-6067	45	19	,	,	PUNCT
ejpam-6067	45	20	at	at	ADP
ejpam-6067	45	21	least	least	ADJ
ejpam-6067	45	22	one	one	NUM
ejpam-6067	45	23	has	have	VERB
ejpam-6067	45	24	a	a	DET
ejpam-6067	45	25	neighborhood	neighborhood	NOUN
ejpam-6067	45	26	not	not	PART
ejpam-6067	45	27	containing	contain	VERB
ejpam-6067	45	28	the	the	DET
ejpam-6067	45	29	other	other	ADJ
ejpam-6067	45	30	.	.	PUNCT
ejpam-6067	46	1	(	(	PUNCT
ejpam-6067	46	2	ii	ii	PROPN
ejpam-6067	46	3	)	)	PUNCT
ejpam-6067	46	4	t1	t1	NOUN
ejpam-6067	46	5	(	(	PUNCT
ejpam-6067	46	6	fréchet	fréchet	NOUN
ejpam-6067	46	7	):	):	PUNCT
ejpam-6067	46	8	for	for	ADP
ejpam-6067	46	9	any	any	DET
ejpam-6067	46	10	two	two	NUM
ejpam-6067	46	11	distinct	distinct	ADJ
ejpam-6067	46	12	points	point	NOUN
ejpam-6067	46	13	,	,	PUNCT
ejpam-6067	46	14	each	each	PRON
ejpam-6067	46	15	has	have	VERB
ejpam-6067	46	16	a	a	DET
ejpam-6067	46	17	neighborhood	neighborhood	NOUN
ejpam-6067	46	18	not	not	PART
ejpam-6067	46	19	containing	contain	VERB
ejpam-6067	46	20	the	the	DET
ejpam-6067	46	21	other	other	ADJ
ejpam-6067	46	22	.	.	PUNCT
ejpam-6067	47	1	(	(	PUNCT
ejpam-6067	47	2	iii	iii	X
ejpam-6067	47	3	)	)	PUNCT
ejpam-6067	47	4	t2	t2	NOUN
ejpam-6067	47	5	(	(	PUNCT
ejpam-6067	47	6	hausdorff	hausdorff	NOUN
ejpam-6067	47	7	):	):	PUNCT
ejpam-6067	47	8	for	for	ADP
ejpam-6067	47	9	any	any	DET
ejpam-6067	47	10	two	two	NUM
ejpam-6067	47	11	distinct	distinct	ADJ
ejpam-6067	47	12	points	point	NOUN
ejpam-6067	47	13	,	,	PUNCT
ejpam-6067	47	14	disjoint	disjoint	NOUN
ejpam-6067	47	15	neighborhoods	neighborhood	NOUN
ejpam-6067	47	16	exist	exist	VERB
ejpam-6067	47	17	containing	contain	VERB
ejpam-6067	47	18	them	they	PRON
ejpam-6067	47	19	separately	separately	ADV
ejpam-6067	47	20	.	.	PUNCT
ejpam-6067	48	1	(	(	PUNCT
ejpam-6067	48	2	iv	iv	X
ejpam-6067	48	3	)	)	PUNCT
ejpam-6067	48	4	t3	t3	NOUN
ejpam-6067	48	5	(	(	PUNCT
ejpam-6067	48	6	regular	regular	ADJ
ejpam-6067	48	7	):	):	PUNCT
ejpam-6067	48	8	a	a	DET
ejpam-6067	48	9	t1	t1	NOUN
ejpam-6067	48	10	space	space	NOUN
ejpam-6067	48	11	where	where	SCONJ
ejpam-6067	48	12	for	for	ADP
ejpam-6067	48	13	any	any	DET
ejpam-6067	48	14	point	point	NOUN
ejpam-6067	48	15	and	and	CCONJ
ejpam-6067	48	16	any	any	DET
ejpam-6067	48	17	closed	closed	ADJ
ejpam-6067	48	18	set	set	VERB
ejpam-6067	48	19	not	not	PART
ejpam-6067	48	20	containing	contain	VERB
ejpam-6067	48	21	it	it	PRON
ejpam-6067	48	22	,	,	PUNCT
ejpam-6067	48	23	disjoint	disjoint	NOUN
ejpam-6067	48	24	neighborhoods	neighborhood	NOUN
ejpam-6067	48	25	exist	exist	VERB
ejpam-6067	48	26	containing	contain	VERB
ejpam-6067	48	27	them	they	PRON
ejpam-6067	48	28	separately	separately	ADV
ejpam-6067	48	29	.	.	PUNCT
ejpam-6067	49	1	(	(	PUNCT
ejpam-6067	49	2	v	v	NOUN
ejpam-6067	49	3	)	)	PUNCT
ejpam-6067	49	4	t4	t4	PROPN
ejpam-6067	49	5	(	(	PUNCT
ejpam-6067	49	6	normal	normal	ADJ
ejpam-6067	49	7	):	):	PUNCT
ejpam-6067	49	8	a	a	DET
ejpam-6067	49	9	t1	t1	NOUN
ejpam-6067	49	10	space	space	NOUN
ejpam-6067	49	11	where	where	SCONJ
ejpam-6067	49	12	for	for	ADP
ejpam-6067	49	13	any	any	DET
ejpam-6067	49	14	two	two	NUM
ejpam-6067	49	15	disjoint	disjoint	ADJ
ejpam-6067	49	16	closed	close	VERB
ejpam-6067	49	17	sets	set	NOUN
ejpam-6067	49	18	,	,	PUNCT
ejpam-6067	49	19	disjoint	disjoint	NOUN
ejpam-6067	49	20	neighborhoods	neighborhood	NOUN
ejpam-6067	49	21	exist	exist	VERB
ejpam-6067	49	22	containing	contain	VERB
ejpam-6067	49	23	them	they	PRON
ejpam-6067	49	24	separately	separately	ADV
ejpam-6067	49	25	.	.	PUNCT
ejpam-6067	50	1	these	these	DET
ejpam-6067	50	2	axioms	axiom	NOUN
ejpam-6067	50	3	form	form	VERB
ejpam-6067	50	4	a	a	DET
ejpam-6067	50	5	hierarchy	hierarchy	NOUN
ejpam-6067	50	6	where	where	SCONJ
ejpam-6067	50	7	t4	t4	PROPN
ejpam-6067	50	8	⇒	⇒	PROPN
ejpam-6067	50	9	t3	t3	PROPN
ejpam-6067	50	10	⇒	⇒	PROPN
ejpam-6067	50	11	t2	t2	PROPN
ejpam-6067	50	12	⇒	⇒	PROPN
ejpam-6067	50	13	t1	t1	PROPN
ejpam-6067	50	14	⇒	⇒	PROPN
ejpam-6067	50	15	t0	t0	PROPN
ejpam-6067	50	16	.	.	PUNCT
ejpam-6067	51	1	definition	definition	NOUN
ejpam-6067	51	2	3	3	NUM
ejpam-6067	51	3	(	(	PUNCT
ejpam-6067	51	4	compactness	compactness	NOUN
ejpam-6067	51	5	[	[	X
ejpam-6067	51	6	1	1	NUM
ejpam-6067	51	7	]	]	NUM
ejpam-6067	51	8	)	)	PUNCT
ejpam-6067	51	9	.	.	PUNCT
ejpam-6067	52	1	a	a	DET
ejpam-6067	52	2	topological	topological	ADJ
ejpam-6067	52	3	space	space	NOUN
ejpam-6067	52	4	(	(	PUNCT
ejpam-6067	52	5	x	x	X
ejpam-6067	52	6	,	,	PUNCT
ejpam-6067	52	7	τ	τ	X
ejpam-6067	52	8	)	)	PUNCT
ejpam-6067	52	9	demonstrates	demonstrate	VERB
ejpam-6067	52	10	compactness	compactness	NOUN
ejpam-6067	52	11	if	if	SCONJ
ejpam-6067	52	12	every	every	DET
ejpam-6067	52	13	open	open	ADJ
ejpam-6067	52	14	cover	cover	NOUN
ejpam-6067	52	15	has	have	VERB
ejpam-6067	52	16	a	a	DET
ejpam-6067	52	17	finite	finite	ADJ
ejpam-6067	52	18	subcover	subcover	PROPN
ejpam-6067	52	19	.	.	PUNCT
ejpam-6067	53	1	equivalently	equivalently	PROPN
ejpam-6067	53	2	,	,	PUNCT
ejpam-6067	53	3	a	a	DET
ejpam-6067	53	4	space	space	NOUN
ejpam-6067	53	5	exhibits	exhibit	VERB
ejpam-6067	53	6	compactness	compactness	NOUN
ejpam-6067	53	7	if	if	SCONJ
ejpam-6067	53	8	every	every	DET
ejpam-6067	53	9	collection	collection	NOUN
ejpam-6067	53	10	of	of	ADP
ejpam-6067	53	11	closed	closed	ADJ
ejpam-6067	53	12	sets	set	NOUN
ejpam-6067	53	13	with	with	ADP
ejpam-6067	53	14	the	the	DET
ejpam-6067	53	15	finite	finite	ADJ
ejpam-6067	53	16	intersection	intersection	NOUN
ejpam-6067	53	17	property	property	NOUN
ejpam-6067	53	18	has	have	VERB
ejpam-6067	53	19	a	a	DET
ejpam-6067	53	20	non	non	ADJ
ejpam-6067	53	21	-	-	ADJ
ejpam-6067	53	22	empty	empty	ADJ
ejpam-6067	53	23	intersection	intersection	NOUN
ejpam-6067	53	24	.	.	PUNCT
ejpam-6067	54	1	a	a	DET
ejpam-6067	54	2	space	space	NOUN
ejpam-6067	54	3	shows	show	VERB
ejpam-6067	54	4	countable	countable	ADJ
ejpam-6067	54	5	compactness	compactness	NOUN
ejpam-6067	54	6	if	if	SCONJ
ejpam-6067	54	7	every	every	DET
ejpam-6067	54	8	countable	countable	ADJ
ejpam-6067	54	9	open	open	ADJ
ejpam-6067	54	10	cover	cover	NOUN
ejpam-6067	54	11	has	have	VERB
ejpam-6067	54	12	a	a	DET
ejpam-6067	54	13	finite	finite	ADJ
ejpam-6067	54	14	subcover	subcover	PROPN
ejpam-6067	54	15	.	.	PUNCT
ejpam-6067	55	1	definition	definition	NOUN
ejpam-6067	55	2	4	4	NUM
ejpam-6067	55	3	(	(	PUNCT
ejpam-6067	55	4	lindelöf	lindelöf	NOUN
ejpam-6067	55	5	space	space	NOUN
ejpam-6067	55	6	[	[	X
ejpam-6067	55	7	2	2	NUM
ejpam-6067	55	8	]	]	NUM
ejpam-6067	55	9	)	)	PUNCT
ejpam-6067	55	10	.	.	PUNCT
ejpam-6067	56	1	a	a	DET
ejpam-6067	56	2	topological	topological	ADJ
ejpam-6067	56	3	space	space	NOUN
ejpam-6067	56	4	(	(	PUNCT
ejpam-6067	56	5	x	x	X
ejpam-6067	56	6	,	,	PUNCT
ejpam-6067	56	7	τ	τ	X
ejpam-6067	56	8	)	)	PUNCT
ejpam-6067	56	9	qualifies	qualify	VERB
ejpam-6067	56	10	as	as	ADP
ejpam-6067	56	11	lindelöf	lindelöf	NOUN
ejpam-6067	56	12	if	if	SCONJ
ejpam-6067	56	13	every	every	DET
ejpam-6067	56	14	open	open	ADJ
ejpam-6067	56	15	cover	cover	NOUN
ejpam-6067	56	16	has	have	VERB
ejpam-6067	56	17	a	a	DET
ejpam-6067	56	18	countable	countable	ADJ
ejpam-6067	56	19	subcover	subcover	NOUN
ejpam-6067	56	20	.	.	PUNCT
ejpam-6067	57	1	this	this	DET
ejpam-6067	57	2	property	property	NOUN
ejpam-6067	57	3	ranks	rank	VERB
ejpam-6067	57	4	weaker	weak	ADJ
ejpam-6067	57	5	than	than	ADP
ejpam-6067	57	6	compactness	compactness	NOUN
ejpam-6067	57	7	but	but	CCONJ
ejpam-6067	57	8	stronger	strong	ADJ
ejpam-6067	57	9	than	than	ADP
ejpam-6067	57	10	separability	separability	NOUN
ejpam-6067	57	11	for	for	ADP
ejpam-6067	57	12	many	many	ADJ
ejpam-6067	57	13	spaces	space	NOUN
ejpam-6067	57	14	.	.	PUNCT
ejpam-6067	58	1	m.	m.	NOUN
ejpam-6067	58	2	shatnawi	shatnawi	PROPN
ejpam-6067	58	3	et	et	PROPN
ejpam-6067	58	4	al	al	PROPN
ejpam-6067	58	5	.	.	PUNCT
ejpam-6067	58	6	/	/	SYM
ejpam-6067	58	7	eur	eur	PROPN
ejpam-6067	58	8	.	.	PUNCT
ejpam-6067	59	1	j.	j.	PROPN
ejpam-6067	59	2	pure	pure	PROPN
ejpam-6067	59	3	appl	appl	PROPN
ejpam-6067	59	4	.	.	PROPN
ejpam-6067	59	5	math	math	PROPN
ejpam-6067	59	6	,	,	PUNCT
ejpam-6067	59	7	18	18	NUM
ejpam-6067	59	8	(	(	PUNCT
ejpam-6067	59	9	3	3	NUM
ejpam-6067	59	10	)	)	PUNCT
ejpam-6067	59	11	(	(	PUNCT
ejpam-6067	59	12	2025	2025	NUM
ejpam-6067	59	13	)	)	PUNCT
ejpam-6067	59	14	,	,	PUNCT
ejpam-6067	59	15	6067	6067	NUM
ejpam-6067	59	16	4	4	NUM
ejpam-6067	59	17	of	of	ADP
ejpam-6067	59	18	16	16	NUM
ejpam-6067	59	19	definition	definition	NOUN
ejpam-6067	59	20	5	5	NUM
ejpam-6067	59	21	(	(	PUNCT
ejpam-6067	59	22	gδ	gδ	ADV
ejpam-6067	59	23	set	set	VERB
ejpam-6067	59	24	[	[	X
ejpam-6067	59	25	1	1	NUM
ejpam-6067	59	26	]	]	PUNCT
ejpam-6067	59	27	)	)	PUNCT
ejpam-6067	59	28	.	.	PUNCT
ejpam-6067	60	1	in	in	ADP
ejpam-6067	60	2	a	a	DET
ejpam-6067	60	3	topological	topological	ADJ
ejpam-6067	60	4	space	space	NOUN
ejpam-6067	60	5	(	(	PUNCT
ejpam-6067	60	6	x	x	X
ejpam-6067	60	7	,	,	PUNCT
ejpam-6067	60	8	τ	τ	PROPN
ejpam-6067	60	9	)	)	PUNCT
ejpam-6067	60	10	,	,	PUNCT
ejpam-6067	60	11	a	a	DET
ejpam-6067	60	12	gδ	gδ	NOUN
ejpam-6067	60	13	set	set	NOUN
ejpam-6067	60	14	is	be	AUX
ejpam-6067	60	15	any	any	DET
ejpam-6067	60	16	set	set	NOUN
ejpam-6067	60	17	expressible	expressible	ADJ
ejpam-6067	60	18	as	as	ADP
ejpam-6067	60	19	a	a	DET
ejpam-6067	60	20	countable	countable	ADJ
ejpam-6067	60	21	intersection	intersection	NOUN
ejpam-6067	60	22	of	of	ADP
ejpam-6067	60	23	open	open	ADJ
ejpam-6067	60	24	sets	set	NOUN
ejpam-6067	60	25	.	.	PUNCT
ejpam-6067	61	1	that	that	PRON
ejpam-6067	61	2	is	be	AUX
ejpam-6067	61	3	,	,	PUNCT
ejpam-6067	61	4	g	g	PROPN
ejpam-6067	61	5	⊆	⊆	NUM
ejpam-6067	61	6	x	x	PRON
ejpam-6067	61	7	constitutes	constitute	VERB
ejpam-6067	61	8	a	a	DET
ejpam-6067	61	9	gδ	gδ	NOUN
ejpam-6067	61	10	set	set	NOUN
ejpam-6067	61	11	if	if	SCONJ
ejpam-6067	61	12	and	and	CCONJ
ejpam-6067	61	13	only	only	ADV
ejpam-6067	61	14	if	if	SCONJ
ejpam-6067	61	15	g	g	PROPN
ejpam-6067	61	16	=	=	SYM
ejpam-6067	61	17	∞⋂	∞⋂	PROPN
ejpam-6067	61	18	n=1	n=1	PROPN
ejpam-6067	61	19	un	un	PROPN
ejpam-6067	61	20	where	where	SCONJ
ejpam-6067	61	21	each	each	DET
ejpam-6067	61	22	un	un	PROPN
ejpam-6067	61	23	belongs	belong	VERB
ejpam-6067	61	24	to	to	ADP
ejpam-6067	61	25	τ	τ	PROPN
ejpam-6067	61	26	.	.	PUNCT
ejpam-6067	62	1	definition	definition	NOUN
ejpam-6067	62	2	6	6	NUM
ejpam-6067	62	3	(	(	PUNCT
ejpam-6067	62	4	fσ	fσ	PRON
ejpam-6067	62	5	set	set	VERB
ejpam-6067	62	6	[	[	X
ejpam-6067	62	7	2	2	NUM
ejpam-6067	62	8	]	]	PUNCT
ejpam-6067	62	9	)	)	PUNCT
ejpam-6067	62	10	.	.	PUNCT
ejpam-6067	63	1	in	in	ADP
ejpam-6067	63	2	a	a	DET
ejpam-6067	63	3	topological	topological	ADJ
ejpam-6067	63	4	space	space	NOUN
ejpam-6067	63	5	(	(	PUNCT
ejpam-6067	63	6	x	x	X
ejpam-6067	63	7	,	,	PUNCT
ejpam-6067	63	8	τ	τ	PROPN
ejpam-6067	63	9	)	)	PUNCT
ejpam-6067	63	10	,	,	PUNCT
ejpam-6067	63	11	an	an	DET
ejpam-6067	63	12	fσ	fσ	NOUN
ejpam-6067	63	13	set	set	NOUN
ejpam-6067	63	14	is	be	AUX
ejpam-6067	63	15	any	any	DET
ejpam-6067	63	16	set	set	NOUN
ejpam-6067	63	17	expressible	expressible	ADJ
ejpam-6067	63	18	as	as	ADP
ejpam-6067	63	19	a	a	DET
ejpam-6067	63	20	countable	countable	ADJ
ejpam-6067	63	21	union	union	NOUN
ejpam-6067	63	22	of	of	ADP
ejpam-6067	63	23	closed	closed	ADJ
ejpam-6067	63	24	sets	set	NOUN
ejpam-6067	63	25	.	.	PUNCT
ejpam-6067	64	1	that	that	PRON
ejpam-6067	64	2	is	be	AUX
ejpam-6067	64	3	,	,	PUNCT
ejpam-6067	64	4	f	f	PROPN
ejpam-6067	64	5	⊆	⊆	NUM
ejpam-6067	64	6	x	x	PRON
ejpam-6067	64	7	constitutes	constitute	VERB
ejpam-6067	64	8	an	an	DET
ejpam-6067	64	9	fσ	fσ	NOUN
ejpam-6067	64	10	set	set	VERB
ejpam-6067	64	11	if	if	SCONJ
ejpam-6067	64	12	and	and	CCONJ
ejpam-6067	64	13	only	only	ADV
ejpam-6067	64	14	if	if	SCONJ
ejpam-6067	64	15	f	f	PROPN
ejpam-6067	64	16	=	=	SYM
ejpam-6067	64	17	∞⋃	∞⋃	PROPN
ejpam-6067	64	18	n=1	n=1	PROPN
ejpam-6067	64	19	cn	cn	PROPN
ejpam-6067	64	20	where	where	SCONJ
ejpam-6067	64	21	each	each	DET
ejpam-6067	64	22	cn	cn	PROPN
ejpam-6067	64	23	is	be	AUX
ejpam-6067	64	24	closed	close	VERB
ejpam-6067	64	25	in	in	ADP
ejpam-6067	64	26	x.	x.	NOUN
ejpam-6067	64	27	definition	definition	NOUN
ejpam-6067	64	28	7	7	NUM
ejpam-6067	64	29	(	(	PUNCT
ejpam-6067	64	30	paracompact	paracompact	ADJ
ejpam-6067	64	31	space	space	NOUN
ejpam-6067	64	32	[	[	X
ejpam-6067	64	33	1	1	NUM
ejpam-6067	64	34	]	]	NUM
ejpam-6067	64	35	)	)	PUNCT
ejpam-6067	64	36	.	.	PUNCT
ejpam-6067	65	1	a	a	DET
ejpam-6067	65	2	topological	topological	ADJ
ejpam-6067	65	3	space	space	NOUN
ejpam-6067	65	4	(	(	PUNCT
ejpam-6067	65	5	x	x	X
ejpam-6067	65	6	,	,	PUNCT
ejpam-6067	65	7	τ	τ	X
ejpam-6067	65	8	)	)	PUNCT
ejpam-6067	65	9	achieves	achieve	VERB
ejpam-6067	65	10	paracompactness	paracompactness	NOUN
ejpam-6067	65	11	if	if	SCONJ
ejpam-6067	65	12	every	every	DET
ejpam-6067	65	13	open	open	ADJ
ejpam-6067	65	14	cover	cover	NOUN
ejpam-6067	65	15	of	of	ADP
ejpam-6067	65	16	x	x	PUNCT
ejpam-6067	65	17	has	have	VERB
ejpam-6067	65	18	a	a	DET
ejpam-6067	65	19	locally	locally	ADV
ejpam-6067	65	20	finite	finite	ADJ
ejpam-6067	65	21	open	open	ADJ
ejpam-6067	65	22	refinement	refinement	NOUN
ejpam-6067	65	23	.	.	PUNCT
ejpam-6067	66	1	this	this	DET
ejpam-6067	66	2	property	property	NOUN
ejpam-6067	66	3	generalizes	generalize	VERB
ejpam-6067	66	4	compactness	compactness	NOUN
ejpam-6067	66	5	and	and	CCONJ
ejpam-6067	66	6	holds	hold	VERB
ejpam-6067	66	7	particular	particular	ADJ
ejpam-6067	66	8	importance	importance	NOUN
ejpam-6067	66	9	in	in	ADP
ejpam-6067	66	10	differential	differential	ADJ
ejpam-6067	66	11	geometry	geometry	NOUN
ejpam-6067	66	12	and	and	CCONJ
ejpam-6067	66	13	analysis	analysis	NOUN
ejpam-6067	66	14	.	.	PUNCT
ejpam-6067	67	1	definition	definition	NOUN
ejpam-6067	67	2	8	8	NUM
ejpam-6067	67	3	(	(	PUNCT
ejpam-6067	67	4	metacompact	metacompact	NOUN
ejpam-6067	67	5	space	space	NOUN
ejpam-6067	67	6	[	[	X
ejpam-6067	67	7	17	17	NUM
ejpam-6067	67	8	]	]	NUM
ejpam-6067	67	9	)	)	PUNCT
ejpam-6067	67	10	.	.	PUNCT
ejpam-6067	68	1	a	a	DET
ejpam-6067	68	2	topological	topological	ADJ
ejpam-6067	68	3	space	space	NOUN
ejpam-6067	68	4	(	(	PUNCT
ejpam-6067	68	5	x	x	X
ejpam-6067	68	6	,	,	PUNCT
ejpam-6067	68	7	τ	τ	X
ejpam-6067	68	8	)	)	PUNCT
ejpam-6067	68	9	demonstrates	demonstrate	VERB
ejpam-6067	68	10	metacompactness	metacompactness	NOUN
ejpam-6067	68	11	if	if	SCONJ
ejpam-6067	68	12	every	every	DET
ejpam-6067	68	13	open	open	ADJ
ejpam-6067	68	14	cover	cover	NOUN
ejpam-6067	68	15	of	of	ADP
ejpam-6067	68	16	x	x	PUNCT
ejpam-6067	68	17	has	have	VERB
ejpam-6067	68	18	a	a	DET
ejpam-6067	68	19	point	point	NOUN
ejpam-6067	68	20	-	-	PUNCT
ejpam-6067	68	21	finite	finite	ADJ
ejpam-6067	68	22	open	open	ADJ
ejpam-6067	68	23	refinement	refinement	NOUN
ejpam-6067	68	24	.	.	PUNCT
ejpam-6067	69	1	this	this	DET
ejpam-6067	69	2	property	property	NOUN
ejpam-6067	69	3	ranks	rank	VERB
ejpam-6067	69	4	weaker	weak	ADJ
ejpam-6067	69	5	than	than	ADP
ejpam-6067	69	6	paracompactness	paracompactness	NOUN
ejpam-6067	69	7	but	but	CCONJ
ejpam-6067	69	8	stronger	strong	ADJ
ejpam-6067	69	9	than	than	ADP
ejpam-6067	69	10	the	the	DET
ejpam-6067	69	11	lindelöf	lindelöf	NOUN
ejpam-6067	69	12	property	property	NOUN
ejpam-6067	69	13	in	in	ADP
ejpam-6067	69	14	many	many	ADJ
ejpam-6067	69	15	cases	case	NOUN
ejpam-6067	69	16	.	.	PUNCT
ejpam-6067	70	1	topologists	topologist	NOUN
ejpam-6067	70	2	have	have	AUX
ejpam-6067	70	3	examined	examine	VERB
ejpam-6067	70	4	various	various	ADJ
ejpam-6067	70	5	compactness	compactness	NOUN
ejpam-6067	70	6	forms	form	NOUN
ejpam-6067	70	7	,	,	PUNCT
ejpam-6067	70	8	including	include	VERB
ejpam-6067	70	9	sequential	sequential	ADJ
ejpam-6067	70	10	compactness	compactness	NOUN
ejpam-6067	70	11	,	,	PUNCT
ejpam-6067	70	12	countable	countable	ADJ
ejpam-6067	70	13	compactness	compactness	NOUN
ejpam-6067	70	14	,	,	PUNCT
ejpam-6067	70	15	and	and	CCONJ
ejpam-6067	70	16	pseudo	pseudo	NOUN
ejpam-6067	70	17	-	-	NOUN
ejpam-6067	70	18	compactness	compactness	NOUN
ejpam-6067	70	19	.	.	PUNCT
ejpam-6067	71	1	each	each	DET
ejpam-6067	71	2	notion	notion	NOUN
ejpam-6067	71	3	captures	capture	VERB
ejpam-6067	71	4	different	different	ADJ
ejpam-6067	71	5	aspects	aspect	NOUN
ejpam-6067	71	6	of	of	ADP
ejpam-6067	71	7	the	the	DET
ejpam-6067	71	8	intuitive	intuitive	ADJ
ejpam-6067	71	9	”	"	PUNCT
ejpam-6067	71	10	boundedness	boundedness	NOUN
ejpam-6067	71	11	”	"	PUNCT
ejpam-6067	71	12	idea	idea	NOUN
ejpam-6067	71	13	in	in	ADP
ejpam-6067	71	14	topological	topological	ADJ
ejpam-6067	71	15	spaces	space	NOUN
ejpam-6067	71	16	,	,	PUNCT
ejpam-6067	71	17	as	as	SCONJ
ejpam-6067	71	18	illustrated	illustrate	VERB
ejpam-6067	71	19	in	in	ADP
ejpam-6067	71	20	references	reference	NOUN
ejpam-6067	71	21	[	[	X
ejpam-6067	71	22	15	15	NUM
ejpam-6067	71	23	]	]	PUNCT
ejpam-6067	71	24	,	,	PUNCT
ejpam-6067	71	25	[	[	X
ejpam-6067	71	26	16	16	NUM
ejpam-6067	71	27	]	]	PUNCT
ejpam-6067	71	28	,	,	PUNCT
ejpam-6067	71	29	[	[	X
ejpam-6067	71	30	17	17	NUM
ejpam-6067	71	31	]	]	PUNCT
ejpam-6067	71	32	,	,	PUNCT
ejpam-6067	71	33	and	and	CCONJ
ejpam-6067	71	34	[	[	X
ejpam-6067	71	35	18	18	NUM
ejpam-6067	71	36	]	]	PUNCT
ejpam-6067	71	37	.	.	PUNCT
ejpam-6067	72	1	the	the	DET
ejpam-6067	72	2	interplay	interplay	NOUN
ejpam-6067	72	3	between	between	ADP
ejpam-6067	72	4	countability	countability	NOUN
ejpam-6067	72	5	,	,	PUNCT
ejpam-6067	72	6	compactness	compactness	NOUN
ejpam-6067	72	7	,	,	PUNCT
ejpam-6067	72	8	and	and	CCONJ
ejpam-6067	72	9	separation	separation	NOUN
ejpam-6067	72	10	properties	property	NOUN
ejpam-6067	72	11	forms	form	VERB
ejpam-6067	72	12	a	a	DET
ejpam-6067	72	13	rich	rich	ADJ
ejpam-6067	72	14	research	research	NOUN
ejpam-6067	72	15	area	area	NOUN
ejpam-6067	72	16	in	in	ADP
ejpam-6067	72	17	topology	topology	NOUN
ejpam-6067	72	18	.	.	PUNCT
ejpam-6067	73	1	particularly	particularly	ADV
ejpam-6067	73	2	,	,	PUNCT
ejpam-6067	73	3	the	the	DET
ejpam-6067	73	4	study	study	NOUN
ejpam-6067	73	5	of	of	ADP
ejpam-6067	73	6	gδ	gδ	PROPN
ejpam-6067	73	7	sets	set	NOUN
ejpam-6067	73	8	and	and	CCONJ
ejpam-6067	73	9	fσ	fσ	PRON
ejpam-6067	73	10	sets	set	NOUN
ejpam-6067	73	11	provides	provide	VERB
ejpam-6067	73	12	insight	insight	NOUN
ejpam-6067	73	13	into	into	ADP
ejpam-6067	73	14	the	the	DET
ejpam-6067	73	15	fine	fine	ADJ
ejpam-6067	73	16	structure	structure	NOUN
ejpam-6067	73	17	of	of	ADP
ejpam-6067	73	18	topological	topological	ADJ
ejpam-6067	73	19	spaces	space	NOUN
ejpam-6067	73	20	and	and	CCONJ
ejpam-6067	73	21	has	have	VERB
ejpam-6067	73	22	applications	application	NOUN
ejpam-6067	73	23	in	in	ADP
ejpam-6067	73	24	descriptive	descriptive	ADJ
ejpam-6067	73	25	set	set	NOUN
ejpam-6067	73	26	theory	theory	NOUN
ejpam-6067	73	27	and	and	CCONJ
ejpam-6067	73	28	analysis	analysis	NOUN
ejpam-6067	73	29	[	[	X
ejpam-6067	73	30	3	3	NUM
ejpam-6067	73	31	]	]	PUNCT
ejpam-6067	73	32	.	.	PUNCT
ejpam-6067	74	1	2	2	X
ejpam-6067	74	2	.	.	X
ejpam-6067	75	1	g	g	NOUN
ejpam-6067	75	2	-	-	PUNCT
ejpam-6067	75	3	compact	compact	ADJ
ejpam-6067	75	4	and	and	CCONJ
ejpam-6067	75	5	g	g	NOUN
ejpam-6067	75	6	-	-	PUNCT
ejpam-6067	75	7	lindelöf	lindelöf	NOUN
ejpam-6067	75	8	spaces	space	VERB
ejpam-6067	75	9	definition	definition	NOUN
ejpam-6067	75	10	9	9	NUM
ejpam-6067	75	11	.	.	PUNCT
ejpam-6067	76	1	let	let	VERB
ejpam-6067	76	2	(	(	PUNCT
ejpam-6067	76	3	x	x	NOUN
ejpam-6067	76	4	,	,	PUNCT
ejpam-6067	76	5	τ	τ	X
ejpam-6067	76	6	)	)	PUNCT
ejpam-6067	76	7	be	be	VERB
ejpam-6067	76	8	a	a	DET
ejpam-6067	76	9	topological	topological	ADJ
ejpam-6067	76	10	space	space	NOUN
ejpam-6067	76	11	.	.	PUNCT
ejpam-6067	77	1	then	then	ADV
ejpam-6067	77	2	the	the	DET
ejpam-6067	77	3	collection˜=	collection˜=	PROPN
ejpam-6067	77	4	{	{	PUNCT
ejpam-6067	77	5	gα	gα	NOUN
ejpam-6067	77	6	:	:	PUNCT
ejpam-6067	77	7	α	α	PROPN
ejpam-6067	77	8	∈	∈	PROPN
ejpam-6067	77	9	∆	∆	X
ejpam-6067	77	10	}	}	PUNCT
ejpam-6067	77	11	is	be	AUX
ejpam-6067	77	12	called	call	VERB
ejpam-6067	77	13	a	a	DET
ejpam-6067	77	14	g	g	NOUN
ejpam-6067	77	15	-	-	PUNCT
ejpam-6067	77	16	cover	cover	NOUN
ejpam-6067	77	17	of	of	ADP
ejpam-6067	77	18	x	x	PUNCT
ejpam-6067	77	19	provided	provide	VERB
ejpam-6067	77	20	that	that	SCONJ
ejpam-6067	77	21	x	x	NOUN
ejpam-6067	78	1	=	=	PUNCT
ejpam-6067	78	2	⋃	⋃	VERB
ejpam-6067	78	3	α∈∆	α∈∆	PRON
ejpam-6067	78	4	gα	gα	ADP
ejpam-6067	78	5	where	where	SCONJ
ejpam-6067	78	6	,	,	PUNCT
ejpam-6067	78	7	gα	gα	ADP
ejpam-6067	78	8	is	be	AUX
ejpam-6067	78	9	a	a	DET
ejpam-6067	78	10	gδ	gδ	NOUN
ejpam-6067	78	11	set	set	VERB
ejpam-6067	78	12	in	in	ADP
ejpam-6067	78	13	x	x	PUNCT
ejpam-6067	78	14	for	for	ADP
ejpam-6067	78	15	all	all	DET
ejpam-6067	78	16	α	α	NOUN
ejpam-6067	78	17	∈	∈	NOUN
ejpam-6067	79	1	∆.	∆.	ADJ
ejpam-6067	79	2	definition	definition	NOUN
ejpam-6067	79	3	10	10	NUM
ejpam-6067	79	4	.	.	PUNCT
ejpam-6067	80	1	the	the	DET
ejpam-6067	80	2	topologica	topologica	PROPN
ejpam-6067	80	3	space	space	NOUN
ejpam-6067	80	4	(	(	PUNCT
ejpam-6067	80	5	x	x	X
ejpam-6067	80	6	,	,	PUNCT
ejpam-6067	80	7	τ	τ	X
ejpam-6067	80	8	)	)	PUNCT
ejpam-6067	80	9	is	be	AUX
ejpam-6067	80	10	called	call	VERB
ejpam-6067	80	11	g	g	NOUN
ejpam-6067	80	12	-	-	PUNCT
ejpam-6067	80	13	compact	compact	ADJ
ejpam-6067	80	14	space	space	NOUN
ejpam-6067	80	15	if	if	SCONJ
ejpam-6067	80	16	every	every	DET
ejpam-6067	80	17	g	g	PROPN
ejpam-6067	80	18	-cover	-cover	PROPN
ejpam-6067	80	19	has	have	VERB
ejpam-6067	80	20	a	a	DET
ejpam-6067	80	21	finite	finite	ADJ
ejpam-6067	80	22	subcover	subcover	PROPN
ejpam-6067	80	23	.	.	PUNCT
ejpam-6067	81	1	theorem	theorem	VERB
ejpam-6067	81	2	1	1	NUM
ejpam-6067	81	3	.	.	PUNCT
ejpam-6067	82	1	every	every	DET
ejpam-6067	82	2	g	g	PROPN
ejpam-6067	82	3	-	-	PUNCT
ejpam-6067	82	4	compact	compact	ADJ
ejpam-6067	82	5	space	space	NOUN
ejpam-6067	82	6	is	be	AUX
ejpam-6067	82	7	compact	compact	ADJ
ejpam-6067	82	8	.	.	PUNCT
ejpam-6067	83	1	m.	m.	NOUN
ejpam-6067	83	2	shatnawi	shatnawi	PROPN
ejpam-6067	83	3	et	et	PROPN
ejpam-6067	83	4	al	al	PROPN
ejpam-6067	83	5	.	.	PUNCT
ejpam-6067	83	6	/	/	SYM
ejpam-6067	83	7	eur	eur	PROPN
ejpam-6067	83	8	.	.	PUNCT
ejpam-6067	84	1	j.	j.	PROPN
ejpam-6067	84	2	pure	pure	PROPN
ejpam-6067	84	3	appl	appl	PROPN
ejpam-6067	84	4	.	.	PROPN
ejpam-6067	84	5	math	math	PROPN
ejpam-6067	84	6	,	,	PUNCT
ejpam-6067	84	7	18	18	NUM
ejpam-6067	84	8	(	(	PUNCT
ejpam-6067	84	9	3	3	NUM
ejpam-6067	84	10	)	)	PUNCT
ejpam-6067	84	11	(	(	PUNCT
ejpam-6067	84	12	2025	2025	NUM
ejpam-6067	84	13	)	)	PUNCT
ejpam-6067	84	14	,	,	PUNCT
ejpam-6067	84	15	6067	6067	NUM
ejpam-6067	84	16	5	5	NUM
ejpam-6067	84	17	of	of	ADP
ejpam-6067	84	18	16	16	NUM
ejpam-6067	84	19	proof	proof	NOUN
ejpam-6067	84	20	.	.	PUNCT
ejpam-6067	85	1	let	let	VERB
ejpam-6067	85	2	(	(	PUNCT
ejpam-6067	85	3	x	x	NOUN
ejpam-6067	85	4	,	,	PUNCT
ejpam-6067	85	5	τ	τ	X
ejpam-6067	85	6	)	)	PUNCT
ejpam-6067	85	7	be	be	VERB
ejpam-6067	85	8	a	a	DET
ejpam-6067	85	9	g	g	NOUN
ejpam-6067	85	10	-	-	PUNCT
ejpam-6067	85	11	compact	compact	ADJ
ejpam-6067	85	12	space	space	NOUN
ejpam-6067	85	13	and	and	CCONJ
ejpam-6067	85	14	let	let	VERB
ejpam-6067	85	15	ũ	ũ	PROPN
ejpam-6067	85	16	=	=	PRON
ejpam-6067	85	17	{	{	PUNCT
ejpam-6067	85	18	uα	uα	X
ejpam-6067	85	19	:	:	PUNCT
ejpam-6067	85	20	α	α	PROPN
ejpam-6067	85	21	∈	∈	PROPN
ejpam-6067	85	22	∆	∆	PROPN
ejpam-6067	85	23	}	}	PUNCT
ejpam-6067	85	24	be	be	AUX
ejpam-6067	85	25	an	an	DET
ejpam-6067	85	26	open	open	ADJ
ejpam-6067	85	27	cover	cover	NOUN
ejpam-6067	85	28	of	of	ADP
ejpam-6067	85	29	x.	x.	NOUN
ejpam-6067	85	30	since	since	SCONJ
ejpam-6067	85	31	every	every	DET
ejpam-6067	85	32	open	open	ADJ
ejpam-6067	85	33	set	set	NOUN
ejpam-6067	85	34	uα	uα	PROPN
ejpam-6067	85	35	is	be	AUX
ejpam-6067	85	36	countable	countable	ADJ
ejpam-6067	85	37	intersection	intersection	NOUN
ejpam-6067	85	38	of	of	ADP
ejpam-6067	85	39	itself	itself	PRON
ejpam-6067	85	40	,	,	PUNCT
ejpam-6067	85	41	uα	uα	PROPN
ejpam-6067	85	42	is	be	AUX
ejpam-6067	85	43	a	a	DET
ejpam-6067	85	44	gδ	gδ	NOUN
ejpam-6067	85	45	set	set	NOUN
ejpam-6067	85	46	.	.	PUNCT
ejpam-6067	86	1	hence	hence	ADV
ejpam-6067	86	2	ũ	ũ	PROPN
ejpam-6067	86	3	is	be	AUX
ejpam-6067	86	4	a	a	DET
ejpam-6067	86	5	g	g	NOUN
ejpam-6067	86	6	-	-	PUNCT
ejpam-6067	86	7	cover	cover	NOUN
ejpam-6067	86	8	of	of	ADP
ejpam-6067	86	9	x.	x.	NOUN
ejpam-6067	86	10	but	but	CCONJ
ejpam-6067	86	11	x	x	X
ejpam-6067	86	12	is	be	AUX
ejpam-6067	86	13	g	g	NOUN
ejpam-6067	86	14	-	-	PUNCT
ejpam-6067	86	15	compact	compact	ADJ
ejpam-6067	86	16	space	space	NOUN
ejpam-6067	86	17	,	,	PUNCT
ejpam-6067	86	18	so	so	CCONJ
ejpam-6067	86	19	there	there	PRON
ejpam-6067	86	20	is	be	VERB
ejpam-6067	86	21	a	a	DET
ejpam-6067	86	22	finite	finite	ADJ
ejpam-6067	86	23	subcover	subcover	NOUN
ejpam-6067	86	24	of	of	ADP
ejpam-6067	86	25	ũ	ũ	PROPN
ejpam-6067	86	26	that	that	PRON
ejpam-6067	86	27	covers	cover	VERB
ejpam-6067	86	28	x	x	PUNCT
ejpam-6067	86	29	and	and	CCONJ
ejpam-6067	86	30	therefore	therefore	ADV
ejpam-6067	86	31	,	,	PUNCT
ejpam-6067	86	32	x	x	X
ejpam-6067	86	33	is	be	AUX
ejpam-6067	86	34	compact	compact	ADJ
ejpam-6067	86	35	.	.	PUNCT
ejpam-6067	87	1	here	here	ADV
ejpam-6067	87	2	,	,	PUNCT
ejpam-6067	87	3	it	it	PRON
ejpam-6067	87	4	should	should	AUX
ejpam-6067	87	5	be	be	AUX
ejpam-6067	87	6	mentioned	mention	VERB
ejpam-6067	87	7	that	that	SCONJ
ejpam-6067	87	8	the	the	DET
ejpam-6067	87	9	converse	converse	NOUN
ejpam-6067	87	10	of	of	ADP
ejpam-6067	87	11	theorem	theorem	NOUN
ejpam-6067	87	12	1	1	NUM
ejpam-6067	87	13	need	need	AUX
ejpam-6067	87	14	not	not	PART
ejpam-6067	87	15	be	be	AUX
ejpam-6067	87	16	true	true	ADJ
ejpam-6067	87	17	.	.	PUNCT
ejpam-6067	88	1	to	to	PART
ejpam-6067	88	2	show	show	VERB
ejpam-6067	88	3	this	this	PRON
ejpam-6067	88	4	we	we	PRON
ejpam-6067	88	5	have	have	VERB
ejpam-6067	88	6	the	the	DET
ejpam-6067	88	7	following	follow	VERB
ejpam-6067	88	8	example	example	NOUN
ejpam-6067	88	9	:	:	PUNCT
ejpam-6067	88	10	example	example	NOUN
ejpam-6067	89	1	1	1	NUM
ejpam-6067	89	2	.	.	PUNCT
ejpam-6067	90	1	the	the	DET
ejpam-6067	90	2	cofinite	cofinite	NOUN
ejpam-6067	90	3	topology	topology	NOUN
ejpam-6067	90	4	on	on	ADP
ejpam-6067	90	5	,	,	PUNCT
ejpam-6067	90	6	(	(	PUNCT
ejpam-6067	90	7	r	r	NOUN
ejpam-6067	90	8	,	,	PUNCT
ejpam-6067	90	9	τcof	τcof	NOUN
ejpam-6067	90	10	)	)	PUNCT
ejpam-6067	90	11	is	be	AUX
ejpam-6067	90	12	compact	compact	ADJ
ejpam-6067	90	13	but	but	CCONJ
ejpam-6067	90	14	not	not	PART
ejpam-6067	90	15	g	g	NOUN
ejpam-6067	90	16	-	-	PUNCT
ejpam-6067	90	17	compact	compact	ADJ
ejpam-6067	90	18	space	space	NOUN
ejpam-6067	90	19	.	.	PUNCT
ejpam-6067	91	1	proof	proof	NOUN
ejpam-6067	91	2	.	.	PUNCT
ejpam-6067	92	1	it	it	PRON
ejpam-6067	92	2	is	be	AUX
ejpam-6067	92	3	known	know	VERB
ejpam-6067	92	4	that	that	SCONJ
ejpam-6067	92	5	(	(	PUNCT
ejpam-6067	92	6	,	,	PUNCT
ejpam-6067	92	7	τcof	τcof	PROPN
ejpam-6067	92	8	)	)	PUNCT
ejpam-6067	92	9	is	be	AUX
ejpam-6067	92	10	compact	compact	ADJ
ejpam-6067	92	11	.	.	PUNCT
ejpam-6067	93	1	however	however	ADV
ejpam-6067	93	2	,	,	PUNCT
ejpam-6067	93	3	(	(	PUNCT
ejpam-6067	93	4	r	r	NOUN
ejpam-6067	93	5	,	,	PUNCT
ejpam-6067	93	6	τcof	τcof	NOUN
ejpam-6067	93	7	)	)	PUNCT
ejpam-6067	93	8	is	be	AUX
ejpam-6067	93	9	not	not	PART
ejpam-6067	93	10	g	g	NOUN
ejpam-6067	93	11	-	-	PUNCT
ejpam-6067	93	12	compact	compact	ADJ
ejpam-6067	93	13	space	space	NOUN
ejpam-6067	93	14	.	.	PUNCT
ejpam-6067	94	1	to	to	PART
ejpam-6067	94	2	show	show	VERB
ejpam-6067	94	3	that	that	SCONJ
ejpam-6067	94	4	let˜=	let˜=	PROPN
ejpam-6067	94	5	{	{	PUNCT
ejpam-6067	94	6	gk	gk	NOUN
ejpam-6067	94	7	:	:	PUNCT
ejpam-6067	94	8	k∈	k∈	PROPN
ejpam-6067	94	9	n	n	CCONJ
ejpam-6067	94	10	}	}	PUNCT
ejpam-6067	94	11	,	,	PUNCT
ejpam-6067	94	12	where	where	SCONJ
ejpam-6067	94	13	gk	gk	PROPN
ejpam-6067	94	14	=	=	SYM
ejpam-6067	94	15	∞⋂	∞⋂	PROPN
ejpam-6067	94	16	i	i	PROPN
ejpam-6067	94	17	=	=	PROPN
ejpam-6067	94	18	k	k	X
ejpam-6067	94	19	(	(	PUNCT
ejpam-6067	94	20	r\	r\	PROPN
ejpam-6067	94	21	{	{	PUNCT
ejpam-6067	94	22	i	i	NOUN
ejpam-6067	94	23	}	}	PUNCT
ejpam-6067	94	24	)	)	PUNCT
ejpam-6067	94	25	=	=	SYM
ejpam-6067	94	26	(	(	PUNCT
ejpam-6067	94	27	r\n	r\n	ADJ
ejpam-6067	94	28	)	)	PUNCT
ejpam-6067	94	29	∪	∪	ADP
ejpam-6067	94	30	{	{	PUNCT
ejpam-6067	94	31	1	1	NUM
ejpam-6067	94	32	,	,	PUNCT
ejpam-6067	94	33	2	2	NUM
ejpam-6067	94	34	,	,	PUNCT
ejpam-6067	94	35	.	.	PUNCT
ejpam-6067	94	36	.	.	PUNCT
ejpam-6067	94	37	.	.	PUNCT
ejpam-6067	95	1	k	k	NOUN
ejpam-6067	96	1	−	−	NOUN
ejpam-6067	96	2	1	1	NUM
ejpam-6067	96	3	}	}	PUNCT
ejpam-6067	96	4	.	.	PUNCT
ejpam-6067	97	1	then˜is	then˜is	NOUN
ejpam-6067	97	2	a	a	DET
ejpam-6067	97	3	g	g	NOUN
ejpam-6067	97	4	-	-	PUNCT
ejpam-6067	97	5	cover	cover	NOUN
ejpam-6067	97	6	of	of	ADP
ejpam-6067	97	7	r	r	NOUN
ejpam-6067	97	8	which	which	PRON
ejpam-6067	97	9	has	have	VERB
ejpam-6067	97	10	no	no	DET
ejpam-6067	97	11	finite	finite	PROPN
ejpam-6067	97	12	subcover	subcover	PROPN
ejpam-6067	97	13	.	.	PUNCT
ejpam-6067	98	1	assume	assume	VERB
ejpam-6067	98	2	by	by	ADP
ejpam-6067	98	3	contrary	contrary	NOUN
ejpam-6067	98	4	that	that	SCONJ
ejpam-6067	98	5	r	r	NOUN
ejpam-6067	98	6	=	=	SYM
ejpam-6067	98	7	n⋃	n⋃	DET
ejpam-6067	98	8	j=1	j=1	PROPN
ejpam-6067	98	9	gkj	gkj	PROPN
ejpam-6067	98	10	,	,	PUNCT
ejpam-6067	98	11	where	where	SCONJ
ejpam-6067	98	12	kj−1	kj−1	PROPN
ejpam-6067	98	13	<	<	X
ejpam-6067	98	14	kj	kj	PROPN
ejpam-6067	98	15	for	for	ADP
ejpam-6067	98	16	j	j	PROPN
ejpam-6067	98	17	=	=	SYM
ejpam-6067	98	18	2	2	NUM
ejpam-6067	98	19	,	,	PUNCT
ejpam-6067	98	20	3	3	NUM
ejpam-6067	98	21	,	,	PUNCT
ejpam-6067	98	22	·	·	PUNCT
ejpam-6067	98	23	·	·	PUNCT
ejpam-6067	98	24	·	·	PUNCT
ejpam-6067	98	25	,	,	PUNCT
ejpam-6067	98	26	n.	n.	PROPN
ejpam-6067	98	27	then	then	ADV
ejpam-6067	98	28	n⋃	n⋃	VERB
ejpam-6067	98	29	j=1	j=1	PROPN
ejpam-6067	98	30	gkj	gkj	PROPN
ejpam-6067	98	31	=	=	SYM
ejpam-6067	98	32	n⋃	n⋃	PRON
ejpam-6067	98	33	j=1	j=1	PROPN
ejpam-6067	98	34	∞⋂	∞⋂	PROPN
ejpam-6067	99	1	i	i	PROPN
ejpam-6067	99	2	=	=	PROPN
ejpam-6067	99	3	kj	kj	X
ejpam-6067	99	4	(	(	PUNCT
ejpam-6067	99	5	r\	r\	PROPN
ejpam-6067	99	6	{	{	PUNCT
ejpam-6067	99	7	i	i	NOUN
ejpam-6067	99	8	}	}	PUNCT
ejpam-6067	99	9	)	)	PUNCT
ejpam-6067	99	10	=	=	SYM
ejpam-6067	99	11	(	(	PUNCT
ejpam-6067	99	12	r\n	r\n	ADJ
ejpam-6067	99	13	)	)	PUNCT
ejpam-6067	99	14	∪	∪	ADP
ejpam-6067	99	15	{	{	PUNCT
ejpam-6067	99	16	1	1	NUM
ejpam-6067	99	17	,	,	PUNCT
ejpam-6067	99	18	2	2	NUM
ejpam-6067	99	19	,	,	PUNCT
ejpam-6067	99	20	.	.	PUNCT
ejpam-6067	99	21	.	.	PUNCT
ejpam-6067	100	1	.	.	PUNCT
ejpam-6067	101	1	,	,	PUNCT
ejpam-6067	101	2	kn	kn	PROPN
ejpam-6067	101	3	−	−	PROPN
ejpam-6067	101	4	1	1	NUM
ejpam-6067	101	5	}	}	PUNCT
ejpam-6067	101	6	=	=	PUNCT
ejpam-6067	101	7	gkn	gkn	NOUN
ejpam-6067	101	8	which	which	PRON
ejpam-6067	101	9	is	be	AUX
ejpam-6067	101	10	a	a	DET
ejpam-6067	101	11	contradiction	contradiction	NOUN
ejpam-6067	101	12	.	.	PUNCT
ejpam-6067	102	1	theorem	theorem	NOUN
ejpam-6067	102	2	2	2	NUM
ejpam-6067	102	3	.	.	PUNCT
ejpam-6067	103	1	every	every	DET
ejpam-6067	103	2	finite	finite	PROPN
ejpam-6067	103	3	topological	topological	ADJ
ejpam-6067	103	4	space	space	NOUN
ejpam-6067	103	5	is	be	AUX
ejpam-6067	103	6	g	g	NOUN
ejpam-6067	103	7	-	-	PUNCT
ejpam-6067	103	8	compact	compact	ADJ
ejpam-6067	103	9	space	space	NOUN
ejpam-6067	103	10	.	.	PUNCT
ejpam-6067	104	1	proof	proof	NOUN
ejpam-6067	104	2	.	.	PUNCT
ejpam-6067	105	1	let	let	VERB
ejpam-6067	105	2	(	(	PUNCT
ejpam-6067	105	3	x	x	NOUN
ejpam-6067	105	4	,	,	PUNCT
ejpam-6067	105	5	τ	τ	X
ejpam-6067	105	6	)	)	PUNCT
ejpam-6067	105	7	be	be	VERB
ejpam-6067	105	8	a	a	DET
ejpam-6067	105	9	topological	topological	ADJ
ejpam-6067	105	10	space	space	NOUN
ejpam-6067	105	11	such	such	ADJ
ejpam-6067	105	12	that	that	SCONJ
ejpam-6067	105	13	x	x	PRON
ejpam-6067	105	14	is	be	AUX
ejpam-6067	105	15	finite	finite	ADJ
ejpam-6067	105	16	set	set	NOUN
ejpam-6067	105	17	,	,	PUNCT
ejpam-6067	105	18	we	we	PRON
ejpam-6067	105	19	can	can	AUX
ejpam-6067	105	20	write	write	VERB
ejpam-6067	105	21	x	x	PUNCT
ejpam-6067	105	22	as	as	ADP
ejpam-6067	105	23	x	x	X
ejpam-6067	105	24	=	=	X
ejpam-6067	105	25	{	{	PUNCT
ejpam-6067	105	26	x1	x1	PROPN
ejpam-6067	105	27	,	,	PUNCT
ejpam-6067	105	28	x2	x2	PROPN
ejpam-6067	105	29	,	,	PUNCT
ejpam-6067	105	30	.	.	PUNCT
ejpam-6067	105	31	.	.	PUNCT
ejpam-6067	105	32	.	.	PUNCT
ejpam-6067	106	1	xn	xn	PUNCT
ejpam-6067	106	2	}	}	PUNCT
ejpam-6067	106	3	.	.	PUNCT
ejpam-6067	107	1	let˜=	let˜=	NOUN
ejpam-6067	107	2	{	{	PUNCT
ejpam-6067	107	3	gα	gα	NOUN
ejpam-6067	107	4	:	:	PUNCT
ejpam-6067	107	5	α	α	PROPN
ejpam-6067	107	6	∈	∈	PROPN
ejpam-6067	107	7	∆	∆	PROPN
ejpam-6067	107	8	}	}	PUNCT
ejpam-6067	107	9	be	be	AUX
ejpam-6067	107	10	a	a	DET
ejpam-6067	107	11	g	g	NOUN
ejpam-6067	107	12	-cover	-cover	PROPN
ejpam-6067	107	13	of	of	ADP
ejpam-6067	107	14	x	x	PRON
ejpam-6067	107	15	,	,	PUNCT
ejpam-6067	107	16	that	that	PRON
ejpam-6067	107	17	means	mean	VERB
ejpam-6067	107	18	x	x	PUNCT
ejpam-6067	107	19	=	=	PRON
ejpam-6067	107	20	n⋃	n⋃	VERB
ejpam-6067	107	21	i=1	i=1	PRON
ejpam-6067	107	22	{	{	PUNCT
ejpam-6067	107	23	xi	xi	PROPN
ejpam-6067	107	24	}	}	PUNCT
ejpam-6067	107	25	=	=	PUNCT
ejpam-6067	107	26	⋃	⋃	NOUN
ejpam-6067	107	27	α∈∆	α∈∆	PRON
ejpam-6067	107	28	gα	gα	NOUN
ejpam-6067	107	29	.	.	PUNCT
ejpam-6067	108	1	so	so	ADV
ejpam-6067	108	2	,	,	PUNCT
ejpam-6067	108	3	for	for	ADP
ejpam-6067	108	4	all	all	DET
ejpam-6067	108	5	1	1	NUM
ejpam-6067	108	6	≤	≤	NUM
ejpam-6067	108	7	i	i	PRON
ejpam-6067	108	8	≤	≤	NOUN
ejpam-6067	108	9	n	n	CCONJ
ejpam-6067	108	10	,	,	PUNCT
ejpam-6067	108	11	xi	xi	PROPN
ejpam-6067	108	12	∈	∈	PROPN
ejpam-6067	108	13	gαi	gαi	NOUN
ejpam-6067	108	14	,	,	PUNCT
ejpam-6067	108	15	for	for	ADP
ejpam-6067	108	16	some	some	DET
ejpam-6067	108	17	αi	αi	NOUN
ejpam-6067	108	18	∈	∈	PROPN
ejpam-6067	109	1	∆.	∆.	X
ejpam-6067	109	2	hence	hence	ADV
ejpam-6067	109	3	,	,	PUNCT
ejpam-6067	109	4	{	{	PUNCT
ejpam-6067	109	5	gα1	gα1	NOUN
ejpam-6067	109	6	,	,	PUNCT
ejpam-6067	109	7	gα2	gα2	NOUN
ejpam-6067	109	8	,	,	PUNCT
ejpam-6067	109	9	.	.	PUNCT
ejpam-6067	109	10	.	.	PUNCT
ejpam-6067	109	11	.	.	PUNCT
ejpam-6067	110	1	,	,	PUNCT
ejpam-6067	110	2	gαn	gαn	PROPN
ejpam-6067	110	3	}	}	PUNCT
ejpam-6067	110	4	is	be	AUX
ejpam-6067	110	5	a	a	DET
ejpam-6067	110	6	finite	finite	ADJ
ejpam-6067	110	7	subcover	subcover	NOUN
ejpam-6067	110	8	of˜for	of˜for	PROPN
ejpam-6067	110	9	x.	x.	PROPN
ejpam-6067	110	10	therefore	therefore	ADV
ejpam-6067	110	11	,	,	PUNCT
ejpam-6067	110	12	(	(	PUNCT
ejpam-6067	110	13	x	x	X
ejpam-6067	110	14	,	,	PUNCT
ejpam-6067	110	15	τ	τ	X
ejpam-6067	110	16	)	)	PUNCT
ejpam-6067	110	17	is	be	AUX
ejpam-6067	110	18	g	g	NOUN
ejpam-6067	110	19	-	-	PUNCT
ejpam-6067	110	20	compact	compact	ADJ
ejpam-6067	110	21	space	space	NOUN
ejpam-6067	110	22	.	.	PUNCT
ejpam-6067	111	1	theorem	theorem	NOUN
ejpam-6067	111	2	3	3	NUM
ejpam-6067	111	3	.	.	PUNCT
ejpam-6067	112	1	if	if	SCONJ
ejpam-6067	112	2	(	(	PUNCT
ejpam-6067	112	3	x	x	NOUN
ejpam-6067	112	4	,	,	PUNCT
ejpam-6067	112	5	τ	τ	X
ejpam-6067	112	6	)	)	PUNCT
ejpam-6067	112	7	represents	represent	VERB
ejpam-6067	112	8	a	a	DET
ejpam-6067	112	9	g	g	NOUN
ejpam-6067	112	10	-	-	PUNCT
ejpam-6067	112	11	compact	compact	ADJ
ejpam-6067	112	12	space	space	NOUN
ejpam-6067	112	13	and	and	CCONJ
ejpam-6067	112	14	(	(	PUNCT
ejpam-6067	112	15	y	y	PROPN
ejpam-6067	112	16	,	,	PUNCT
ejpam-6067	112	17	τ	τ	PROPN
ejpam-6067	112	18	′	′	NUM
ejpam-6067	112	19	)	)	PUNCT
ejpam-6067	112	20	demonstrates	demonstrate	VERB
ejpam-6067	112	21	homeomorphism	homeomorphism	PROPN
ejpam-6067	112	22	with	with	ADP
ejpam-6067	112	23	x	x	PRON
ejpam-6067	112	24	,	,	PUNCT
ejpam-6067	112	25	then	then	ADV
ejpam-6067	112	26	y	y	PROPN
ejpam-6067	112	27	exhibits	exhibit	VERB
ejpam-6067	112	28	g	g	NOUN
ejpam-6067	112	29	-	-	PUNCT
ejpam-6067	112	30	compactness	compactness	NOUN
ejpam-6067	112	31	.	.	PUNCT
ejpam-6067	113	1	proof	proof	NOUN
ejpam-6067	113	2	.	.	PUNCT
ejpam-6067	114	1	let	let	VERB
ejpam-6067	114	2	f	f	NOUN
ejpam-6067	114	3	:	:	PUNCT
ejpam-6067	114	4	x	x	X
ejpam-6067	114	5	→	→	SYM
ejpam-6067	114	6	y	y	PRON
ejpam-6067	114	7	establish	establish	VERB
ejpam-6067	114	8	a	a	DET
ejpam-6067	114	9	homeomorphism	homeomorphism	NOUN
ejpam-6067	114	10	,	,	PUNCT
ejpam-6067	114	11	and	and	CCONJ
ejpam-6067	114	12	consider	consider	VERB
ejpam-6067	114	13	a	a	DET
ejpam-6067	114	14	g	g	NOUN
ejpam-6067	114	15	-	-	PUNCT
ejpam-6067	114	16	cover˜=	cover˜=	NOUN
ejpam-6067	114	17	{	{	PUNCT
ejpam-6067	114	18	gα	gα	NOUN
ejpam-6067	114	19	:	:	PUNCT
ejpam-6067	114	20	α	α	PROPN
ejpam-6067	114	21	∈	∈	PROPN
ejpam-6067	114	22	∆	∆	PROPN
ejpam-6067	114	23	}	}	PUNCT
ejpam-6067	114	24	of	of	ADP
ejpam-6067	114	25	y	y	PROPN
ejpam-6067	114	26	.	.	PUNCT
ejpam-6067	115	1	for	for	ADP
ejpam-6067	115	2	each	each	DET
ejpam-6067	115	3	gα	gα	NOUN
ejpam-6067	115	4	,	,	PUNCT
ejpam-6067	115	5	we	we	PRON
ejpam-6067	115	6	express	express	VERB
ejpam-6067	115	7	gα	gα	ADP
ejpam-6067	115	8	=	=	PUNCT
ejpam-6067	115	9	⋂∞	⋂∞	NOUN
ejpam-6067	115	10	n=1	n=1	PROPN
ejpam-6067	115	11	uα	uα	PROPN
ejpam-6067	115	12	,	,	PUNCT
ejpam-6067	115	13	n	n	CCONJ
ejpam-6067	115	14	where	where	SCONJ
ejpam-6067	115	15	each	each	DET
ejpam-6067	115	16	uα	uα	PROPN
ejpam-6067	115	17	,	,	PUNCT
ejpam-6067	115	18	n	n	PRON
ejpam-6067	115	19	belongs	belong	VERB
ejpam-6067	115	20	to	to	ADP
ejpam-6067	115	21	τ	τ	PROPN
ejpam-6067	115	22	′.	′.	NOUN
ejpam-6067	115	23	since	since	SCONJ
ejpam-6067	115	24	f	f	PROPN
ejpam-6067	115	25	creates	create	VERB
ejpam-6067	115	26	a	a	DET
ejpam-6067	115	27	homeomorphism	homeomorphism	NOUN
ejpam-6067	115	28	,	,	PUNCT
ejpam-6067	115	29	f−1(gα	f−1(gα	NOUN
ejpam-6067	115	30	)	)	PUNCT
ejpam-6067	115	31	=	=	SYM
ejpam-6067	116	1	f−1	f−1	PROPN
ejpam-6067	116	2	(	(	PUNCT
ejpam-6067	116	3	⋂∞	⋂∞	NOUN
ejpam-6067	116	4	n=1	n=1	PROPN
ejpam-6067	116	5	uα	uα	PROPN
ejpam-6067	116	6	,	,	PUNCT
ejpam-6067	116	7	n	n	CCONJ
ejpam-6067	116	8	)	)	PUNCT
ejpam-6067	116	9	=	=	SYM
ejpam-6067	116	10	⋂∞	⋂∞	NOUN
ejpam-6067	116	11	n=1	n=1	PROPN
ejpam-6067	116	12	f	f	PROPN
ejpam-6067	116	13	−1(uα	−1(uα	NOUN
ejpam-6067	116	14	,	,	PUNCT
ejpam-6067	116	15	n	n	CCONJ
ejpam-6067	116	16	)	)	PUNCT
ejpam-6067	116	17	.	.	PUNCT
ejpam-6067	117	1	as	as	SCONJ
ejpam-6067	117	2	each	each	DET
ejpam-6067	117	3	f−1(uα	f−1(uα	NOUN
ejpam-6067	117	4	,	,	PUNCT
ejpam-6067	117	5	n	n	CCONJ
ejpam-6067	117	6	)	)	PUNCT
ejpam-6067	117	7	belongs	belong	VERB
ejpam-6067	117	8	to	to	ADP
ejpam-6067	117	9	τ	τ	PROPN
ejpam-6067	117	10	,	,	PUNCT
ejpam-6067	117	11	f−1(gα	f−1(gα	PROPN
ejpam-6067	117	12	)	)	PUNCT
ejpam-6067	117	13	forms	form	VERB
ejpam-6067	117	14	a	a	DET
ejpam-6067	117	15	gδ	gδ	NOUN
ejpam-6067	117	16	set	set	VERB
ejpam-6067	117	17	in	in	ADP
ejpam-6067	117	18	x.	x.	PROPN
ejpam-6067	117	19	m.	m.	PROPN
ejpam-6067	117	20	shatnawi	shatnawi	PROPN
ejpam-6067	118	1	et	et	PROPN
ejpam-6067	118	2	al	al	PROPN
ejpam-6067	118	3	.	.	PUNCT
ejpam-6067	118	4	/	/	SYM
ejpam-6067	118	5	eur	eur	PROPN
ejpam-6067	118	6	.	.	PUNCT
ejpam-6067	119	1	j.	j.	PROPN
ejpam-6067	119	2	pure	pure	PROPN
ejpam-6067	119	3	appl	appl	PROPN
ejpam-6067	119	4	.	.	PROPN
ejpam-6067	119	5	math	math	PROPN
ejpam-6067	119	6	,	,	PUNCT
ejpam-6067	119	7	18	18	NUM
ejpam-6067	119	8	(	(	PUNCT
ejpam-6067	119	9	3	3	NUM
ejpam-6067	119	10	)	)	PUNCT
ejpam-6067	119	11	(	(	PUNCT
ejpam-6067	119	12	2025	2025	NUM
ejpam-6067	119	13	)	)	PUNCT
ejpam-6067	119	14	,	,	PUNCT
ejpam-6067	119	15	6067	6067	NUM
ejpam-6067	119	16	6	6	NUM
ejpam-6067	119	17	of	of	ADP
ejpam-6067	119	18	16	16	NUM
ejpam-6067	119	19	therefore	therefore	ADV
ejpam-6067	119	20	,	,	PUNCT
ejpam-6067	119	21	{	{	PUNCT
ejpam-6067	119	22	f−1(gα	f−1(gα	NOUN
ejpam-6067	119	23	)	)	PUNCT
ejpam-6067	119	24	:	:	PUNCT
ejpam-6067	120	1	α	α	PROPN
ejpam-6067	120	2	∈	∈	NOUN
ejpam-6067	120	3	∆	∆	X
ejpam-6067	120	4	}	}	PUNCT
ejpam-6067	120	5	constitutes	constitute	VERB
ejpam-6067	120	6	a	a	DET
ejpam-6067	120	7	g	g	NOUN
ejpam-6067	120	8	-	-	PUNCT
ejpam-6067	120	9	cover	cover	NOUN
ejpam-6067	120	10	of	of	ADP
ejpam-6067	120	11	x.	x.	NOUN
ejpam-6067	120	12	since	since	SCONJ
ejpam-6067	120	13	x	x	PRON
ejpam-6067	120	14	demonstrates	demonstrate	VERB
ejpam-6067	120	15	g	g	NOUN
ejpam-6067	120	16	-	-	PUNCT
ejpam-6067	120	17	compactness	compactness	NOUN
ejpam-6067	120	18	,	,	PUNCT
ejpam-6067	120	19	we	we	PRON
ejpam-6067	120	20	find	find	VERB
ejpam-6067	120	21	a	a	DET
ejpam-6067	120	22	finite	finite	ADJ
ejpam-6067	120	23	subcover	subcover	PROPN
ejpam-6067	120	24	{	{	PUNCT
ejpam-6067	120	25	f−1(gα1	f−1(gα1	NOUN
ejpam-6067	120	26	)	)	PUNCT
ejpam-6067	120	27	,	,	PUNCT
ejpam-6067	120	28	f	f	PROPN
ejpam-6067	120	29	−1(gα2	−1(gα2	ADJ
ejpam-6067	120	30	)	)	PUNCT
ejpam-6067	120	31	,	,	PUNCT
ejpam-6067	120	32	.	.	PUNCT
ejpam-6067	120	33	.	.	PUNCT
ejpam-6067	121	1	.	.	PUNCT
ejpam-6067	122	1	,	,	PUNCT
ejpam-6067	122	2	f	f	PROPN
ejpam-6067	122	3	−1(gαn	−1(gαn	PROPN
ejpam-6067	122	4	)	)	PUNCT
ejpam-6067	122	5	}	}	PUNCT
ejpam-6067	122	6	.	.	PUNCT
ejpam-6067	123	1	it	it	PRON
ejpam-6067	123	2	follows	follow	VERB
ejpam-6067	123	3	that	that	SCONJ
ejpam-6067	123	4	{	{	PUNCT
ejpam-6067	123	5	gα1	gα1	NOUN
ejpam-6067	123	6	,	,	PUNCT
ejpam-6067	123	7	gα2	gα2	NOUN
ejpam-6067	123	8	,	,	PUNCT
ejpam-6067	123	9	.	.	PUNCT
ejpam-6067	123	10	.	.	PUNCT
ejpam-6067	124	1	.	.	PUNCT
ejpam-6067	125	1	,	,	PUNCT
ejpam-6067	125	2	gαn	gαn	PROPN
ejpam-6067	125	3	}	}	PUNCT
ejpam-6067	125	4	forms	form	VERB
ejpam-6067	125	5	a	a	DET
ejpam-6067	125	6	finite	finite	ADJ
ejpam-6067	125	7	subcover	subcover	NOUN
ejpam-6067	125	8	of˜for	of˜for	PROPN
ejpam-6067	125	9	y	y	PROPN
ejpam-6067	125	10	,	,	PUNCT
ejpam-6067	125	11	proving	prove	VERB
ejpam-6067	125	12	that	that	SCONJ
ejpam-6067	125	13	y	y	PROPN
ejpam-6067	125	14	exhibits	exhibit	VERB
ejpam-6067	125	15	g	g	NOUN
ejpam-6067	125	16	-	-	PUNCT
ejpam-6067	125	17	compactness	compactness	NOUN
ejpam-6067	125	18	.	.	PUNCT
ejpam-6067	126	1	definition	definition	NOUN
ejpam-6067	126	2	11	11	NUM
ejpam-6067	126	3	.	.	PUNCT
ejpam-6067	127	1	the	the	DET
ejpam-6067	127	2	topological	topological	ADJ
ejpam-6067	127	3	space	space	NOUN
ejpam-6067	127	4	(	(	PUNCT
ejpam-6067	127	5	x	x	X
ejpam-6067	127	6	,	,	PUNCT
ejpam-6067	127	7	τ	τ	X
ejpam-6067	127	8	)	)	PUNCT
ejpam-6067	127	9	is	be	AUX
ejpam-6067	127	10	called	call	VERB
ejpam-6067	127	11	g	g	NOUN
ejpam-6067	127	12	-	-	PUNCT
ejpam-6067	127	13	lindelöf	lindelöf	NOUN
ejpam-6067	127	14	space	space	NOUN
ejpam-6067	127	15	if	if	SCONJ
ejpam-6067	127	16	every	every	DET
ejpam-6067	127	17	g	g	PROPN
ejpam-6067	127	18	-cover	-cover	PROPN
ejpam-6067	127	19	has	have	VERB
ejpam-6067	127	20	a	a	DET
ejpam-6067	127	21	countable	countable	ADJ
ejpam-6067	127	22	subcover	subcover	NOUN
ejpam-6067	127	23	.	.	PUNCT
ejpam-6067	128	1	theorem	theorem	VERB
ejpam-6067	128	2	4	4	NUM
ejpam-6067	128	3	.	.	PUNCT
ejpam-6067	129	1	every	every	DET
ejpam-6067	129	2	g	g	PROPN
ejpam-6067	129	3	-	-	PUNCT
ejpam-6067	129	4	compact	compact	ADJ
ejpam-6067	129	5	space	space	NOUN
ejpam-6067	129	6	is	be	AUX
ejpam-6067	129	7	g	g	NOUN
ejpam-6067	129	8	-	-	PUNCT
ejpam-6067	129	9	lindelöf	lindelöf	NOUN
ejpam-6067	129	10	space	space	NOUN
ejpam-6067	129	11	.	.	PUNCT
ejpam-6067	130	1	proof	proof	NOUN
ejpam-6067	130	2	.	.	PUNCT
ejpam-6067	131	1	the	the	DET
ejpam-6067	131	2	proof	proof	NOUN
ejpam-6067	131	3	is	be	AUX
ejpam-6067	131	4	obvious	obvious	ADJ
ejpam-6067	131	5	,	,	PUNCT
ejpam-6067	131	6	because	because	SCONJ
ejpam-6067	131	7	every	every	DET
ejpam-6067	131	8	finite	finite	PROPN
ejpam-6067	131	9	subcover	subcover	PROPN
ejpam-6067	131	10	is	be	AUX
ejpam-6067	131	11	countable	countable	ADJ
ejpam-6067	131	12	.	.	PUNCT
ejpam-6067	132	1	here	here	ADV
ejpam-6067	132	2	,	,	PUNCT
ejpam-6067	132	3	it	it	PRON
ejpam-6067	132	4	should	should	AUX
ejpam-6067	132	5	be	be	AUX
ejpam-6067	132	6	mentioned	mention	VERB
ejpam-6067	132	7	that	that	SCONJ
ejpam-6067	132	8	the	the	DET
ejpam-6067	132	9	converse	converse	NOUN
ejpam-6067	132	10	of	of	ADP
ejpam-6067	132	11	theorem	theorem	NOUN
ejpam-6067	132	12	4	4	NUM
ejpam-6067	132	13	need	need	AUX
ejpam-6067	132	14	not	not	PART
ejpam-6067	132	15	be	be	AUX
ejpam-6067	132	16	true	true	ADJ
ejpam-6067	132	17	.	.	PUNCT
ejpam-6067	133	1	to	to	PART
ejpam-6067	133	2	show	show	VERB
ejpam-6067	133	3	that	that	SCONJ
ejpam-6067	133	4	we	we	PRON
ejpam-6067	133	5	have	have	VERB
ejpam-6067	133	6	the	the	DET
ejpam-6067	133	7	following	follow	VERB
ejpam-6067	133	8	example	example	NOUN
ejpam-6067	133	9	:	:	PUNCT
ejpam-6067	133	10	example	example	NOUN
ejpam-6067	133	11	2	2	X
ejpam-6067	133	12	.	.	X
ejpam-6067	133	13	consider	consider	VERB
ejpam-6067	133	14	the	the	DET
ejpam-6067	133	15	cofinite	cofinite	NOUN
ejpam-6067	133	16	topology	topology	NOUN
ejpam-6067	133	17	on	on	ADP
ejpam-6067	133	18	,	,	PUNCT
ejpam-6067	133	19	(	(	PUNCT
ejpam-6067	133	20	n	n	CCONJ
ejpam-6067	133	21	,	,	PUNCT
ejpam-6067	133	22	τcof	τcof	NOUN
ejpam-6067	133	23	)	)	PUNCT
ejpam-6067	133	24	.	.	PUNCT
ejpam-6067	134	1	to	to	PART
ejpam-6067	134	2	show	show	VERB
ejpam-6067	134	3	that	that	SCONJ
ejpam-6067	134	4	(	(	PUNCT
ejpam-6067	134	5	n	n	CCONJ
ejpam-6067	134	6	,	,	PUNCT
ejpam-6067	134	7	τcof	τcof	PROPN
ejpam-6067	134	8	)	)	PUNCT
ejpam-6067	134	9	is	be	AUX
ejpam-6067	134	10	a	a	DET
ejpam-6067	134	11	g	g	NOUN
ejpam-6067	134	12	-	-	PUNCT
ejpam-6067	134	13	lindelöf	lindelöf	NOUN
ejpam-6067	134	14	space	space	NOUN
ejpam-6067	134	15	,	,	PUNCT
ejpam-6067	134	16	let˜=	let˜=	X
ejpam-6067	134	17	{	{	PUNCT
ejpam-6067	134	18	gα	gα	NOUN
ejpam-6067	134	19	:	:	PUNCT
ejpam-6067	134	20	α	α	PROPN
ejpam-6067	134	21	∈	∈	PROPN
ejpam-6067	134	22	∆	∆	PROPN
ejpam-6067	134	23	}	}	PUNCT
ejpam-6067	134	24	be	be	AUX
ejpam-6067	134	25	a	a	DET
ejpam-6067	134	26	g	g	PROPN
ejpam-6067	134	27	-cover	-cover	PROPN
ejpam-6067	134	28	of	of	ADP
ejpam-6067	134	29	n.	n.	NOUN
ejpam-6067	134	30	then	then	ADV
ejpam-6067	134	31	for	for	ADP
ejpam-6067	134	32	any	any	DET
ejpam-6067	134	33	n∈	n∈	NOUN
ejpam-6067	134	34	n	n	CCONJ
ejpam-6067	134	35	,	,	PUNCT
ejpam-6067	134	36	there	there	PRON
ejpam-6067	134	37	is	be	VERB
ejpam-6067	134	38	gαn	gαn	PROPN
ejpam-6067	134	39	∈	∈	PROPN
ejpam-6067	134	40	g	g	NOUN
ejpam-6067	134	41	such	such	ADJ
ejpam-6067	134	42	that	that	SCONJ
ejpam-6067	134	43	n	n	NUM
ejpam-6067	134	44	∈	∈	PROPN
ejpam-6067	134	45	gαn	gαn	PROPN
ejpam-6067	134	46	.	.	PUNCT
ejpam-6067	135	1	hence	hence	ADV
ejpam-6067	135	2	{	{	PUNCT
ejpam-6067	135	3	gαn	gαn	PROPN
ejpam-6067	135	4	:	:	PUNCT
ejpam-6067	135	5	n∈	n∈	NOUN
ejpam-6067	135	6	n	n	CCONJ
ejpam-6067	135	7	}	}	PUNCT
ejpam-6067	135	8	is	be	AUX
ejpam-6067	135	9	a	a	DET
ejpam-6067	135	10	countable	countable	ADJ
ejpam-6067	135	11	subcover	subcover	PROPN
ejpam-6067	135	12	of˜	of˜	PROPN
ejpam-6067	135	13	for	for	ADP
ejpam-6067	135	14	n.	n.	PROPN
ejpam-6067	135	15	therefore	therefore	ADV
ejpam-6067	135	16	,	,	PUNCT
ejpam-6067	135	17	(	(	PUNCT
ejpam-6067	135	18	n	n	CCONJ
ejpam-6067	135	19	,	,	PUNCT
ejpam-6067	135	20	τcof	τcof	PROPN
ejpam-6067	135	21	)	)	PUNCT
ejpam-6067	135	22	is	be	AUX
ejpam-6067	135	23	a	a	DET
ejpam-6067	135	24	g	g	NOUN
ejpam-6067	135	25	-	-	PUNCT
ejpam-6067	135	26	lindelöf	lindelöf	NOUN
ejpam-6067	135	27	space	space	NOUN
ejpam-6067	135	28	.	.	PUNCT
ejpam-6067	136	1	now	now	ADV
ejpam-6067	136	2	,	,	PUNCT
ejpam-6067	136	3	to	to	PART
ejpam-6067	136	4	show	show	VERB
ejpam-6067	136	5	that	that	SCONJ
ejpam-6067	136	6	(	(	PUNCT
ejpam-6067	136	7	n	n	CCONJ
ejpam-6067	136	8	,	,	PUNCT
ejpam-6067	136	9	τcof	τcof	NOUN
ejpam-6067	136	10	)	)	PUNCT
ejpam-6067	136	11	is	be	AUX
ejpam-6067	136	12	not	not	PART
ejpam-6067	136	13	g	g	NOUN
ejpam-6067	136	14	-	-	PUNCT
ejpam-6067	136	15	compact	compact	ADJ
ejpam-6067	136	16	space	space	NOUN
ejpam-6067	136	17	,	,	PUNCT
ejpam-6067	136	18	let	let	VERB
ejpam-6067	136	19	n∈	n∈	NOUN
ejpam-6067	136	20	n.	n.	PROPN
ejpam-6067	136	21	then	then	ADV
ejpam-6067	136	22	{	{	PUNCT
ejpam-6067	136	23	n	n	CCONJ
ejpam-6067	136	24	}	}	PUNCT
ejpam-6067	136	25	=	=	SYM
ejpam-6067	136	26	∞⋂	∞⋂	PROPN
ejpam-6067	136	27	k	k	PROPN
ejpam-6067	136	28	=	=	SYM
ejpam-6067	136	29	1	1	NUM
ejpam-6067	136	30	,	,	PUNCT
ejpam-6067	136	31	k	k	PROPN
ejpam-6067	136	32	̸=	̸=	PROPN
ejpam-6067	136	33	n	n	CCONJ
ejpam-6067	136	34	(	(	PUNCT
ejpam-6067	136	35	n\	n\	PROPN
ejpam-6067	136	36	{	{	PUNCT
ejpam-6067	136	37	k	k	NOUN
ejpam-6067	136	38	}	}	PUNCT
ejpam-6067	136	39	)	)	PUNCT
ejpam-6067	136	40	is	be	AUX
ejpam-6067	136	41	a	a	DET
ejpam-6067	136	42	gδ	gδ	NOUN
ejpam-6067	136	43	set	set	NOUN
ejpam-6067	136	44	containing	contain	VERB
ejpam-6067	136	45	n.	n.	NOUN
ejpam-6067	136	46	hence	hence	ADV
ejpam-6067	136	47	,	,	PUNCT
ejpam-6067	136	48	{	{	PUNCT
ejpam-6067	136	49	{	{	PUNCT
ejpam-6067	136	50	n	n	CCONJ
ejpam-6067	136	51	}	}	PUNCT
ejpam-6067	136	52	:	:	PUNCT
ejpam-6067	136	53	n∈	n∈	NOUN
ejpam-6067	136	54	n	n	CCONJ
ejpam-6067	136	55	}	}	PUNCT
ejpam-6067	136	56	forms	form	VERB
ejpam-6067	136	57	a	a	DET
ejpam-6067	136	58	g	g	NOUN
ejpam-6067	136	59	-cover	-cover	PROPN
ejpam-6067	136	60	of	of	ADP
ejpam-6067	136	61	n	n	PROPN
ejpam-6067	136	62	that	that	PRON
ejpam-6067	136	63	has	have	VERB
ejpam-6067	136	64	no	no	DET
ejpam-6067	136	65	finite	finite	PROPN
ejpam-6067	136	66	subcover	subcover	PROPN
ejpam-6067	136	67	.	.	PUNCT
ejpam-6067	137	1	therefore	therefore	ADV
ejpam-6067	137	2	,	,	PUNCT
ejpam-6067	137	3	(	(	PUNCT
ejpam-6067	137	4	n	n	CCONJ
ejpam-6067	137	5	,	,	PUNCT
ejpam-6067	137	6	τcof	τcof	NOUN
ejpam-6067	137	7	)	)	PUNCT
ejpam-6067	137	8	is	be	AUX
ejpam-6067	137	9	not	not	PART
ejpam-6067	137	10	g	g	NOUN
ejpam-6067	137	11	-	-	PUNCT
ejpam-6067	137	12	compact	compact	ADJ
ejpam-6067	137	13	space	space	NOUN
ejpam-6067	137	14	.	.	PUNCT
ejpam-6067	138	1	definition	definition	NOUN
ejpam-6067	138	2	12	12	NUM
ejpam-6067	138	3	.	.	PUNCT
ejpam-6067	139	1	a	a	DET
ejpam-6067	139	2	space	space	NOUN
ejpam-6067	139	3	x	x	PUNCT
ejpam-6067	139	4	is	be	AUX
ejpam-6067	139	5	called	call	VERB
ejpam-6067	139	6	g	g	NOUN
ejpam-6067	139	7	-	-	PUNCT
ejpam-6067	139	8	countably	countably	ADV
ejpam-6067	139	9	compact	compact	ADJ
ejpam-6067	139	10	if	if	SCONJ
ejpam-6067	139	11	every	every	DET
ejpam-6067	139	12	countable	countable	ADJ
ejpam-6067	139	13	g	g	NOUN
ejpam-6067	139	14	-	-	PUNCT
ejpam-6067	139	15	cover	cover	NOUN
ejpam-6067	139	16	has	have	VERB
ejpam-6067	139	17	a	a	DET
ejpam-6067	139	18	finite	finite	PROPN
ejpam-6067	139	19	subcover	subcover	PROPN
ejpam-6067	139	20	.	.	PUNCT
ejpam-6067	140	1	remark	remark	PROPN
ejpam-6067	140	2	1	1	NUM
ejpam-6067	140	3	.	.	PUNCT
ejpam-6067	141	1	every	every	DET
ejpam-6067	141	2	g	g	PROPN
ejpam-6067	141	3	-	-	PUNCT
ejpam-6067	141	4	countably	countably	ADV
ejpam-6067	141	5	compact	compact	ADJ
ejpam-6067	141	6	space	space	NOUN
ejpam-6067	141	7	is	be	AUX
ejpam-6067	141	8	countably	countably	ADV
ejpam-6067	141	9	compact	compact	ADJ
ejpam-6067	141	10	,	,	PUNCT
ejpam-6067	141	11	but	but	CCONJ
ejpam-6067	141	12	the	the	DET
ejpam-6067	141	13	reverse	reverse	NOUN
ejpam-6067	141	14	is	be	AUX
ejpam-6067	141	15	not	not	PART
ejpam-6067	141	16	true	true	ADJ
ejpam-6067	141	17	in	in	ADP
ejpam-6067	141	18	general	general	ADJ
ejpam-6067	141	19	(	(	PUNCT
ejpam-6067	141	20	see	see	VERB
ejpam-6067	141	21	example	example	NOUN
ejpam-6067	141	22	2	2	NUM
ejpam-6067	141	23	)	)	PUNCT
ejpam-6067	141	24	.	.	PUNCT
ejpam-6067	142	1	theorem	theorem	ADJ
ejpam-6067	142	2	5	5	NUM
ejpam-6067	142	3	.	.	PUNCT
ejpam-6067	143	1	every	every	DET
ejpam-6067	143	2	g	g	PROPN
ejpam-6067	143	3	-	-	PUNCT
ejpam-6067	143	4	compact	compact	ADJ
ejpam-6067	143	5	space	space	NOUN
ejpam-6067	143	6	exhibits	exhibit	VERB
ejpam-6067	143	7	g	g	NOUN
ejpam-6067	143	8	-	-	PUNCT
ejpam-6067	143	9	countably	countably	ADV
ejpam-6067	143	10	compactness	compactness	NOUN
ejpam-6067	143	11	,	,	PUNCT
ejpam-6067	143	12	but	but	CCONJ
ejpam-6067	143	13	the	the	DET
ejpam-6067	143	14	converse	converse	NOUN
ejpam-6067	143	15	generally	generally	ADV
ejpam-6067	143	16	fails	fail	VERB
ejpam-6067	143	17	.	.	PUNCT
ejpam-6067	144	1	proof	proof	NOUN
ejpam-6067	144	2	.	.	PUNCT
ejpam-6067	145	1	let	let	VERB
ejpam-6067	145	2	(	(	PUNCT
ejpam-6067	145	3	x	x	NOUN
ejpam-6067	145	4	,	,	PUNCT
ejpam-6067	145	5	τ	τ	X
ejpam-6067	145	6	)	)	PUNCT
ejpam-6067	145	7	represent	represent	VERB
ejpam-6067	145	8	a	a	DET
ejpam-6067	145	9	g	g	NOUN
ejpam-6067	145	10	-	-	PUNCT
ejpam-6067	145	11	compact	compact	ADJ
ejpam-6067	145	12	space	space	NOUN
ejpam-6067	145	13	,	,	PUNCT
ejpam-6067	145	14	and	and	CCONJ
ejpam-6067	145	15	consider	consider	VERB
ejpam-6067	145	16	a	a	DET
ejpam-6067	145	17	countable	countable	ADJ
ejpam-6067	145	18	g	g	NOUN
ejpam-6067	145	19	-	-	PUNCT
ejpam-6067	145	20	cover˜=	cover˜=	NOUN
ejpam-6067	145	21	{	{	PUNCT
ejpam-6067	145	22	gn	gn	NOUN
ejpam-6067	145	23	:	:	PUNCT
ejpam-6067	145	24	n	n	CCONJ
ejpam-6067	145	25	∈	∈	PROPN
ejpam-6067	145	26	n	n	CCONJ
ejpam-6067	145	27	}	}	PUNCT
ejpam-6067	145	28	of	of	ADP
ejpam-6067	145	29	x.	x.	NOUN
ejpam-6067	145	30	since	since	SCONJ
ejpam-6067	145	31	x	x	PRON
ejpam-6067	145	32	demonstrates	demonstrate	VERB
ejpam-6067	145	33	g	g	NOUN
ejpam-6067	145	34	-	-	PUNCT
ejpam-6067	145	35	compactness	compactness	NOUN
ejpam-6067	145	36	,	,	PUNCT
ejpam-6067	145	37	every	every	DET
ejpam-6067	145	38	g	g	NOUN
ejpam-6067	145	39	-	-	PUNCT
ejpam-6067	145	40	cover	cover	NOUN
ejpam-6067	145	41	(	(	PUNCT
ejpam-6067	145	42	including	include	VERB
ejpam-6067	145	43	countable	countable	ADJ
ejpam-6067	145	44	ones	one	NOUN
ejpam-6067	145	45	)	)	PUNCT
ejpam-6067	145	46	admits	admit	VERB
ejpam-6067	145	47	a	a	DET
ejpam-6067	145	48	finite	finite	PROPN
ejpam-6067	145	49	subcover	subcover	PROPN
ejpam-6067	145	50	.	.	PUNCT
ejpam-6067	146	1	therefore	therefore	ADV
ejpam-6067	146	2	,	,	PUNCT
ejpam-6067	146	3	x	x	PUNCT
ejpam-6067	146	4	exhibits	exhibit	VERB
ejpam-6067	146	5	g	g	NOUN
ejpam-6067	146	6	-	-	PUNCT
ejpam-6067	146	7	countably	countably	ADV
ejpam-6067	146	8	compactness	compactness	NOUN
ejpam-6067	146	9	.	.	PUNCT
ejpam-6067	147	1	to	to	PART
ejpam-6067	147	2	show	show	VERB
ejpam-6067	147	3	the	the	DET
ejpam-6067	147	4	converse	converse	NOUN
ejpam-6067	147	5	fails	fail	VERB
ejpam-6067	147	6	generally	generally	ADV
ejpam-6067	147	7	,	,	PUNCT
ejpam-6067	147	8	we	we	PRON
ejpam-6067	147	9	examine	examine	VERB
ejpam-6067	147	10	the	the	DET
ejpam-6067	147	11	space	space	NOUN
ejpam-6067	147	12	(	(	PUNCT
ejpam-6067	147	13	ω1	ω1	PROPN
ejpam-6067	147	14	,	,	PUNCT
ejpam-6067	147	15	τ	τ	PROPN
ejpam-6067	147	16	)	)	PUNCT
ejpam-6067	147	17	,	,	PUNCT
ejpam-6067	147	18	where	where	SCONJ
ejpam-6067	147	19	ω1	ω1	PROPN
ejpam-6067	147	20	represents	represent	VERB
ejpam-6067	147	21	the	the	DET
ejpam-6067	147	22	first	first	ADJ
ejpam-6067	147	23	uncountable	uncountable	ADJ
ejpam-6067	147	24	ordinal	ordinal	NOUN
ejpam-6067	147	25	with	with	ADP
ejpam-6067	147	26	the	the	DET
ejpam-6067	147	27	order	order	NOUN
ejpam-6067	147	28	topology	topology	NOUN
ejpam-6067	147	29	.	.	PUNCT
ejpam-6067	148	1	this	this	DET
ejpam-6067	148	2	space	space	NOUN
ejpam-6067	148	3	lacks	lack	VERB
ejpam-6067	148	4	g	g	NOUN
ejpam-6067	148	5	-	-	PUNCT
ejpam-6067	148	6	compactness	compactness	NOUN
ejpam-6067	148	7	because	because	SCONJ
ejpam-6067	148	8	the	the	DET
ejpam-6067	148	9	collection	collection	NOUN
ejpam-6067	148	10	{	{	PUNCT
ejpam-6067	148	11	{	{	PUNCT
ejpam-6067	148	12	α	α	NOUN
ejpam-6067	148	13	}	}	PUNCT
ejpam-6067	148	14	:	:	PUNCT
ejpam-6067	148	15	α	α	PROPN
ejpam-6067	148	16	<	<	X
ejpam-6067	148	17	ω1	ω1	PROPN
ejpam-6067	148	18	}	}	PUNCT
ejpam-6067	148	19	creates	create	VERB
ejpam-6067	148	20	a	a	DET
ejpam-6067	148	21	g	g	NOUN
ejpam-6067	148	22	-	-	PUNCT
ejpam-6067	148	23	cover	cover	NOUN
ejpam-6067	148	24	with	with	ADP
ejpam-6067	148	25	no	no	DET
ejpam-6067	148	26	finite	finite	PROPN
ejpam-6067	148	27	subcover	subcover	PROPN
ejpam-6067	148	28	,	,	PUNCT
ejpam-6067	148	29	as	as	SCONJ
ejpam-6067	148	30	each	each	DET
ejpam-6067	148	31	singleton	singleton	PROPN
ejpam-6067	148	32	forms	form	VERB
ejpam-6067	148	33	a	a	DET
ejpam-6067	148	34	gδ	gδ	NOUN
ejpam-6067	148	35	set	set	NOUN
ejpam-6067	148	36	.	.	PUNCT
ejpam-6067	149	1	however	however	ADV
ejpam-6067	149	2	,	,	PUNCT
ejpam-6067	149	3	(	(	PUNCT
ejpam-6067	149	4	ω1	ω1	PROPN
ejpam-6067	149	5	,	,	PUNCT
ejpam-6067	149	6	τ	τ	X
ejpam-6067	149	7	)	)	PUNCT
ejpam-6067	149	8	exhibits	exhibit	VERB
ejpam-6067	149	9	g	g	NOUN
ejpam-6067	149	10	-	-	PUNCT
ejpam-6067	149	11	countable	countable	ADJ
ejpam-6067	149	12	compactness	compactness	NOUN
ejpam-6067	149	13	because	because	SCONJ
ejpam-6067	149	14	any	any	DET
ejpam-6067	149	15	countable	countable	ADJ
ejpam-6067	149	16	cover	cover	NOUN
ejpam-6067	149	17	of	of	ADP
ejpam-6067	149	18	ω1	ω1	PROPN
ejpam-6067	149	19	must	must	AUX
ejpam-6067	149	20	include	include	VERB
ejpam-6067	149	21	a	a	DET
ejpam-6067	149	22	set	set	NOUN
ejpam-6067	149	23	containing	contain	VERB
ejpam-6067	149	24	points	point	NOUN
ejpam-6067	149	25	arbitrarily	arbitrarily	ADV
ejpam-6067	149	26	close	close	ADJ
ejpam-6067	149	27	to	to	ADP
ejpam-6067	149	28	ω1	ω1	PROPN
ejpam-6067	149	29	,	,	PUNCT
ejpam-6067	149	30	and	and	CCONJ
ejpam-6067	149	31	by	by	ADP
ejpam-6067	149	32	the	the	DET
ejpam-6067	149	33	order	order	NOUN
ejpam-6067	149	34	topology	topology	NOUN
ejpam-6067	149	35	’s	’s	PART
ejpam-6067	149	36	nature	nature	NOUN
ejpam-6067	149	37	,	,	PUNCT
ejpam-6067	149	38	such	such	DET
ejpam-6067	149	39	a	a	DET
ejpam-6067	149	40	set	set	NOUN
ejpam-6067	149	41	would	would	AUX
ejpam-6067	149	42	include	include	VERB
ejpam-6067	149	43	a	a	DET
ejpam-6067	149	44	tail	tail	NOUN
ejpam-6067	149	45	of	of	ADP
ejpam-6067	149	46	the	the	DET
ejpam-6067	149	47	ordinals	ordinal	NOUN
ejpam-6067	149	48	.	.	PUNCT
ejpam-6067	150	1	m.	m.	NOUN
ejpam-6067	150	2	shatnawi	shatnawi	PROPN
ejpam-6067	150	3	et	et	PROPN
ejpam-6067	150	4	al	al	PROPN
ejpam-6067	150	5	.	.	PUNCT
ejpam-6067	150	6	/	/	SYM
ejpam-6067	150	7	eur	eur	PROPN
ejpam-6067	150	8	.	.	PUNCT
ejpam-6067	151	1	j.	j.	PROPN
ejpam-6067	151	2	pure	pure	PROPN
ejpam-6067	151	3	appl	appl	PROPN
ejpam-6067	151	4	.	.	PROPN
ejpam-6067	151	5	math	math	PROPN
ejpam-6067	151	6	,	,	PUNCT
ejpam-6067	151	7	18	18	NUM
ejpam-6067	151	8	(	(	PUNCT
ejpam-6067	151	9	3	3	NUM
ejpam-6067	151	10	)	)	PUNCT
ejpam-6067	151	11	(	(	PUNCT
ejpam-6067	151	12	2025	2025	NUM
ejpam-6067	151	13	)	)	PUNCT
ejpam-6067	151	14	,	,	PUNCT
ejpam-6067	151	15	6067	6067	NUM
ejpam-6067	151	16	7	7	NUM
ejpam-6067	151	17	of	of	ADP
ejpam-6067	151	18	16	16	NUM
ejpam-6067	151	19	theorem	theorem	NOUN
ejpam-6067	151	20	6	6	NUM
ejpam-6067	151	21	.	.	PUNCT
ejpam-6067	152	1	every	every	DET
ejpam-6067	152	2	g	g	NOUN
ejpam-6067	152	3	-	-	PUNCT
ejpam-6067	152	4	lindelöf	lindelöf	NOUN
ejpam-6067	152	5	space	space	NOUN
ejpam-6067	152	6	is	be	AUX
ejpam-6067	152	7	lindelöf	lindelöf	NOUN
ejpam-6067	152	8	space	space	NOUN
ejpam-6067	152	9	.	.	PUNCT
ejpam-6067	153	1	proof	proof	NOUN
ejpam-6067	153	2	.	.	PUNCT
ejpam-6067	154	1	let	let	VERB
ejpam-6067	154	2	(	(	PUNCT
ejpam-6067	154	3	x	x	NOUN
ejpam-6067	154	4	,	,	PUNCT
ejpam-6067	154	5	τ	τ	X
ejpam-6067	154	6	)	)	PUNCT
ejpam-6067	154	7	be	be	VERB
ejpam-6067	154	8	a	a	DET
ejpam-6067	154	9	g	g	NOUN
ejpam-6067	154	10	-	-	PUNCT
ejpam-6067	154	11	lindelöf	lindelöf	NOUN
ejpam-6067	154	12	space	space	NOUN
ejpam-6067	154	13	and	and	CCONJ
ejpam-6067	154	14	let	let	VERB
ejpam-6067	154	15	ũ	ũ	PROPN
ejpam-6067	154	16	=	=	PRON
ejpam-6067	154	17	{	{	PUNCT
ejpam-6067	154	18	uα	uα	X
ejpam-6067	154	19	:	:	PUNCT
ejpam-6067	154	20	α	α	PROPN
ejpam-6067	154	21	∈	∈	PROPN
ejpam-6067	154	22	∆	∆	PROPN
ejpam-6067	154	23	}	}	PUNCT
ejpam-6067	154	24	be	be	AUX
ejpam-6067	154	25	an	an	DET
ejpam-6067	154	26	open	open	ADJ
ejpam-6067	154	27	cover	cover	NOUN
ejpam-6067	154	28	of	of	ADP
ejpam-6067	154	29	x.	x.	NOUN
ejpam-6067	154	30	since	since	SCONJ
ejpam-6067	154	31	every	every	DET
ejpam-6067	154	32	open	open	ADJ
ejpam-6067	154	33	set	set	NOUN
ejpam-6067	154	34	uα	uα	PROPN
ejpam-6067	154	35	is	be	AUX
ejpam-6067	154	36	countable	countable	ADJ
ejpam-6067	154	37	intersection	intersection	NOUN
ejpam-6067	154	38	of	of	ADP
ejpam-6067	154	39	itself	itself	PRON
ejpam-6067	154	40	,	,	PUNCT
ejpam-6067	154	41	uα	uα	PROPN
ejpam-6067	154	42	is	be	AUX
ejpam-6067	154	43	a	a	DET
ejpam-6067	154	44	gδ	gδ	NOUN
ejpam-6067	154	45	set	set	NOUN
ejpam-6067	154	46	.	.	PUNCT
ejpam-6067	155	1	hence	hence	ADV
ejpam-6067	155	2	ũ	ũ	PROPN
ejpam-6067	155	3	is	be	AUX
ejpam-6067	155	4	a	a	DET
ejpam-6067	155	5	g	g	NOUN
ejpam-6067	155	6	–	–	PUNCT
ejpam-6067	155	7	cover	cover	NOUN
ejpam-6067	155	8	of	of	ADP
ejpam-6067	155	9	x.	x.	NOUN
ejpam-6067	155	10	but	but	CCONJ
ejpam-6067	155	11	x	x	X
ejpam-6067	155	12	is	be	AUX
ejpam-6067	155	13	g	g	NOUN
ejpam-6067	155	14	-	-	PUNCT
ejpam-6067	155	15	lindelöf	lindelöf	NOUN
ejpam-6067	155	16	space	space	NOUN
ejpam-6067	155	17	,	,	PUNCT
ejpam-6067	155	18	so	so	CCONJ
ejpam-6067	155	19	there	there	PRON
ejpam-6067	155	20	is	be	VERB
ejpam-6067	155	21	a	a	DET
ejpam-6067	155	22	countable	countable	ADJ
ejpam-6067	155	23	subcover	subcover	NOUN
ejpam-6067	155	24	of	of	ADP
ejpam-6067	155	25	ũ	ũ	PROPN
ejpam-6067	155	26	that	that	PRON
ejpam-6067	155	27	covers	cover	VERB
ejpam-6067	155	28	x	x	PUNCT
ejpam-6067	155	29	and	and	CCONJ
ejpam-6067	155	30	therefore	therefore	ADV
ejpam-6067	155	31	,	,	PUNCT
ejpam-6067	155	32	x	x	X
ejpam-6067	155	33	is	be	AUX
ejpam-6067	155	34	lindelöf	lindelöf	NOUN
ejpam-6067	155	35	.	.	PUNCT
ejpam-6067	156	1	here	here	ADV
ejpam-6067	156	2	,	,	PUNCT
ejpam-6067	156	3	it	it	PRON
ejpam-6067	156	4	should	should	AUX
ejpam-6067	156	5	be	be	AUX
ejpam-6067	156	6	mentioned	mention	VERB
ejpam-6067	156	7	that	that	SCONJ
ejpam-6067	156	8	the	the	DET
ejpam-6067	156	9	converse	converse	NOUN
ejpam-6067	156	10	of	of	ADP
ejpam-6067	156	11	theorem	theorem	NOUN
ejpam-6067	156	12	6	6	NUM
ejpam-6067	156	13	need	need	AUX
ejpam-6067	156	14	not	not	PART
ejpam-6067	156	15	be	be	AUX
ejpam-6067	156	16	true	true	ADJ
ejpam-6067	156	17	.	.	PUNCT
ejpam-6067	157	1	to	to	PART
ejpam-6067	157	2	show	show	VERB
ejpam-6067	157	3	that	that	SCONJ
ejpam-6067	157	4	we	we	PRON
ejpam-6067	157	5	have	have	VERB
ejpam-6067	157	6	the	the	DET
ejpam-6067	157	7	following	follow	VERB
ejpam-6067	157	8	example	example	NOUN
ejpam-6067	157	9	:	:	PUNCT
ejpam-6067	157	10	example	example	NOUN
ejpam-6067	157	11	3	3	X
ejpam-6067	157	12	.	.	PUNCT
ejpam-6067	158	1	let	let	AUX
ejpam-6067	158	2	(	(	PUNCT
ejpam-6067	158	3	r	r	NOUN
ejpam-6067	158	4	,	,	PUNCT
ejpam-6067	158	5	τu	τu	PRON
ejpam-6067	158	6	)	)	PUNCT
ejpam-6067	158	7	be	be	VERB
ejpam-6067	158	8	the	the	DET
ejpam-6067	158	9	real	real	ADJ
ejpam-6067	158	10	numbers	number	NOUN
ejpam-6067	158	11	with	with	ADP
ejpam-6067	158	12	the	the	DET
ejpam-6067	158	13	usual	usual	ADJ
ejpam-6067	158	14	topology	topology	NOUN
ejpam-6067	158	15	.	.	PUNCT
ejpam-6067	159	1	then	then	ADV
ejpam-6067	159	2	(	(	PUNCT
ejpam-6067	159	3	r	r	NOUN
ejpam-6067	159	4	,	,	PUNCT
ejpam-6067	159	5	τu	τu	PRON
ejpam-6067	159	6	)	)	PUNCT
ejpam-6067	159	7	is	be	AUX
ejpam-6067	159	8	lindelöf	lindelöf	PUNCT
ejpam-6067	159	9	but	but	CCONJ
ejpam-6067	159	10	not	not	PART
ejpam-6067	159	11	glindelöf	glindelöf	NOUN
ejpam-6067	159	12	space	space	NOUN
ejpam-6067	159	13	.	.	PUNCT
ejpam-6067	160	1	proof	proof	NOUN
ejpam-6067	160	2	.	.	PUNCT
ejpam-6067	161	1	since	since	SCONJ
ejpam-6067	161	2	(	(	PUNCT
ejpam-6067	161	3	r	r	NOUN
ejpam-6067	161	4	,	,	PUNCT
ejpam-6067	161	5	τu	τu	PRON
ejpam-6067	161	6	)	)	PUNCT
ejpam-6067	161	7	is	be	AUX
ejpam-6067	161	8	second	second	ADV
ejpam-6067	161	9	countable	countable	ADJ
ejpam-6067	161	10	,	,	PUNCT
ejpam-6067	161	11	it	it	PRON
ejpam-6067	161	12	is	be	AUX
ejpam-6067	161	13	lindelöf	lindelöf	NOUN
ejpam-6067	161	14	.	.	PUNCT
ejpam-6067	162	1	now	now	ADV
ejpam-6067	162	2	,	,	PUNCT
ejpam-6067	162	3	to	to	PART
ejpam-6067	162	4	show	show	VERB
ejpam-6067	162	5	that	that	SCONJ
ejpam-6067	162	6	(	(	PUNCT
ejpam-6067	162	7	r	r	NOUN
ejpam-6067	162	8	,	,	PUNCT
ejpam-6067	162	9	τu	τu	PRON
ejpam-6067	162	10	)	)	PUNCT
ejpam-6067	162	11	is	be	AUX
ejpam-6067	162	12	not	not	PART
ejpam-6067	162	13	g	g	NOUN
ejpam-6067	162	14	-	-	PUNCT
ejpam-6067	162	15	lindelöf	lindelöf	NOUN
ejpam-6067	162	16	space	space	NOUN
ejpam-6067	162	17	,	,	PUNCT
ejpam-6067	162	18	let	let	VERB
ejpam-6067	163	1	g̃	g̃	PROPN
ejpam-6067	163	2	=	=	PRON
ejpam-6067	163	3	{	{	PUNCT
ejpam-6067	163	4	{	{	PUNCT
ejpam-6067	163	5	x	x	NOUN
ejpam-6067	163	6	}	}	PUNCT
ejpam-6067	163	7	:	:	PUNCT
ejpam-6067	163	8	x∈	x∈	PROPN
ejpam-6067	163	9	r	r	AUX
ejpam-6067	163	10	}	}	PUNCT
ejpam-6067	163	11	be	be	AUX
ejpam-6067	163	12	a	a	DET
ejpam-6067	163	13	g	g	NOUN
ejpam-6067	163	14	-	-	PUNCT
ejpam-6067	163	15	cover	cover	NOUN
ejpam-6067	163	16	of	of	ADP
ejpam-6067	163	17	r	r	NOUN
ejpam-6067	163	18	,	,	PUNCT
ejpam-6067	163	19	one	one	PRON
ejpam-6067	163	20	can	can	AUX
ejpam-6067	163	21	verify	verify	VERB
ejpam-6067	163	22	that	that	PRON
ejpam-6067	163	23	for	for	ADP
ejpam-6067	163	24	any	any	DET
ejpam-6067	163	25	x∈	x∈	PROPN
ejpam-6067	163	26	r	r	NOUN
ejpam-6067	163	27	,	,	PUNCT
ejpam-6067	163	28	{	{	PUNCT
ejpam-6067	163	29	x	x	NOUN
ejpam-6067	163	30	}	}	PUNCT
ejpam-6067	163	31	=	=	SYM
ejpam-6067	163	32	∞⋂	∞⋂	PROPN
ejpam-6067	163	33	n=1	n=1	PROPN
ejpam-6067	163	34	(	(	PUNCT
ejpam-6067	163	35	x−	x−	PROPN
ejpam-6067	163	36	1	1	NUM
ejpam-6067	163	37	n	n	NOUN
ejpam-6067	163	38	,	,	PUNCT
ejpam-6067	163	39	x+	x+	X
ejpam-6067	163	40	1	1	NUM
ejpam-6067	163	41	n	n	NUM
ejpam-6067	163	42	)	)	PUNCT
ejpam-6067	163	43	.	.	PUNCT
ejpam-6067	164	1	however	however	ADV
ejpam-6067	164	2	,	,	PUNCT
ejpam-6067	164	3	it	it	PRON
ejpam-6067	164	4	is	be	AUX
ejpam-6067	164	5	clear	clear	ADJ
ejpam-6067	164	6	that	that	SCONJ
ejpam-6067	164	7	g̃	g̃	PROPN
ejpam-6067	164	8	has	have	VERB
ejpam-6067	164	9	no	no	DET
ejpam-6067	164	10	countable	countable	ADJ
ejpam-6067	164	11	subcover	subcover	PROPN
ejpam-6067	164	12	.	.	PUNCT
ejpam-6067	165	1	theorem	theorem	VERB
ejpam-6067	165	2	7	7	NUM
ejpam-6067	165	3	.	.	PUNCT
ejpam-6067	166	1	if	if	SCONJ
ejpam-6067	166	2	x	x	PRON
ejpam-6067	166	3	represents	represent	VERB
ejpam-6067	166	4	a	a	DET
ejpam-6067	166	5	g	g	NOUN
ejpam-6067	166	6	-	-	PUNCT
ejpam-6067	166	7	lindelöf	lindelöf	NOUN
ejpam-6067	166	8	space	space	NOUN
ejpam-6067	166	9	and	and	CCONJ
ejpam-6067	166	10	y	y	PROPN
ejpam-6067	166	11	constitutes	constitute	VERB
ejpam-6067	166	12	a	a	DET
ejpam-6067	166	13	continuous	continuous	ADJ
ejpam-6067	166	14	image	image	NOUN
ejpam-6067	166	15	of	of	ADP
ejpam-6067	166	16	x	x	PRON
ejpam-6067	166	17	,	,	PUNCT
ejpam-6067	166	18	then	then	ADV
ejpam-6067	166	19	y	y	PROPN
ejpam-6067	166	20	exhibits	exhibit	VERB
ejpam-6067	166	21	g	g	NOUN
ejpam-6067	166	22	-	-	PUNCT
ejpam-6067	166	23	lindelöfness	lindelöfness	NOUN
ejpam-6067	166	24	.	.	PUNCT
ejpam-6067	167	1	proof	proof	NOUN
ejpam-6067	167	2	.	.	PUNCT
ejpam-6067	168	1	let	let	VERB
ejpam-6067	168	2	f	f	NOUN
ejpam-6067	168	3	:	:	PUNCT
ejpam-6067	168	4	x	x	X
ejpam-6067	168	5	→	→	SYM
ejpam-6067	168	6	y	y	PRON
ejpam-6067	168	7	establish	establish	VERB
ejpam-6067	168	8	a	a	DET
ejpam-6067	168	9	continuous	continuous	ADJ
ejpam-6067	168	10	surjection	surjection	NOUN
ejpam-6067	168	11	,	,	PUNCT
ejpam-6067	168	12	and	and	CCONJ
ejpam-6067	168	13	consider	consider	VERB
ejpam-6067	168	14	a	a	DET
ejpam-6067	168	15	g	g	NOUN
ejpam-6067	168	16	-	-	PUNCT
ejpam-6067	168	17	cover˜=	cover˜=	NOUN
ejpam-6067	168	18	{	{	PUNCT
ejpam-6067	168	19	gα	gα	NOUN
ejpam-6067	168	20	:	:	PUNCT
ejpam-6067	168	21	α	α	PROPN
ejpam-6067	168	22	∈	∈	PROPN
ejpam-6067	168	23	∆	∆	PROPN
ejpam-6067	168	24	}	}	PUNCT
ejpam-6067	168	25	of	of	ADP
ejpam-6067	168	26	y	y	PROPN
ejpam-6067	168	27	.	.	PUNCT
ejpam-6067	169	1	for	for	ADP
ejpam-6067	169	2	each	each	DET
ejpam-6067	169	3	gα	gα	NOUN
ejpam-6067	169	4	,	,	PUNCT
ejpam-6067	169	5	we	we	PRON
ejpam-6067	169	6	have	have	VERB
ejpam-6067	169	7	gα	gα	ADP
ejpam-6067	169	8	=	=	PUNCT
ejpam-6067	169	9	⋂∞	⋂∞	NOUN
ejpam-6067	169	10	n=1	n=1	PROPN
ejpam-6067	169	11	uα	uα	PROPN
ejpam-6067	169	12	,	,	PUNCT
ejpam-6067	169	13	n	n	CCONJ
ejpam-6067	169	14	where	where	SCONJ
ejpam-6067	169	15	each	each	DET
ejpam-6067	169	16	uα	uα	PROPN
ejpam-6067	169	17	,	,	PUNCT
ejpam-6067	169	18	n	n	PRON
ejpam-6067	169	19	belongs	belong	VERB
ejpam-6067	169	20	to	to	ADP
ejpam-6067	169	21	the	the	DET
ejpam-6067	169	22	topology	topology	NOUN
ejpam-6067	169	23	of	of	ADP
ejpam-6067	169	24	y	y	PROPN
ejpam-6067	169	25	.	.	PUNCT
ejpam-6067	170	1	since	since	SCONJ
ejpam-6067	170	2	f	f	PROPN
ejpam-6067	170	3	maintains	maintain	VERB
ejpam-6067	170	4	continuity	continuity	NOUN
ejpam-6067	170	5	,	,	PUNCT
ejpam-6067	170	6	each	each	DET
ejpam-6067	170	7	f−1(uα	f−1(uα	NOUN
ejpam-6067	170	8	,	,	PUNCT
ejpam-6067	170	9	n	n	CCONJ
ejpam-6067	170	10	)	)	PUNCT
ejpam-6067	170	11	belongs	belong	VERB
ejpam-6067	170	12	to	to	ADP
ejpam-6067	170	13	the	the	DET
ejpam-6067	170	14	topology	topology	NOUN
ejpam-6067	170	15	of	of	ADP
ejpam-6067	170	16	x	x	NOUN
ejpam-6067	170	17	,	,	PUNCT
ejpam-6067	170	18	and	and	CCONJ
ejpam-6067	170	19	f−1(gα	f−1(gα	NOUN
ejpam-6067	170	20	)	)	PUNCT
ejpam-6067	170	21	=	=	PUNCT
ejpam-6067	170	22	⋂∞	⋂∞	NOUN
ejpam-6067	170	23	n=1	n=1	PROPN
ejpam-6067	170	24	f	f	PROPN
ejpam-6067	170	25	−1(uα	−1(uα	NOUN
ejpam-6067	170	26	,	,	PUNCT
ejpam-6067	170	27	n	n	CCONJ
ejpam-6067	170	28	)	)	PUNCT
ejpam-6067	170	29	forms	form	VERB
ejpam-6067	170	30	a	a	DET
ejpam-6067	170	31	gδ	gδ	NOUN
ejpam-6067	170	32	set	set	VERB
ejpam-6067	170	33	in	in	ADP
ejpam-6067	170	34	x.	x.	NOUN
ejpam-6067	170	35	thus	thus	ADV
ejpam-6067	170	36	,	,	PUNCT
ejpam-6067	170	37	{	{	PUNCT
ejpam-6067	170	38	f−1(gα	f−1(gα	NOUN
ejpam-6067	170	39	)	)	PUNCT
ejpam-6067	170	40	:	:	PUNCT
ejpam-6067	171	1	α	α	PROPN
ejpam-6067	171	2	∈	∈	PROPN
ejpam-6067	171	3	∆	∆	X
ejpam-6067	171	4	}	}	PUNCT
ejpam-6067	171	5	creates	create	VERB
ejpam-6067	171	6	a	a	DET
ejpam-6067	171	7	g	g	NOUN
ejpam-6067	171	8	-	-	PUNCT
ejpam-6067	171	9	cover	cover	NOUN
ejpam-6067	171	10	of	of	ADP
ejpam-6067	171	11	x.	x.	NOUN
ejpam-6067	171	12	since	since	SCONJ
ejpam-6067	171	13	x	x	PRON
ejpam-6067	171	14	demonstrates	demonstrate	VERB
ejpam-6067	171	15	g	g	NOUN
ejpam-6067	171	16	-	-	PUNCT
ejpam-6067	171	17	lindelöfness	lindelöfness	NOUN
ejpam-6067	171	18	,	,	PUNCT
ejpam-6067	171	19	we	we	PRON
ejpam-6067	171	20	find	find	VERB
ejpam-6067	171	21	a	a	DET
ejpam-6067	171	22	countable	countable	ADJ
ejpam-6067	171	23	subcover	subcover	NOUN
ejpam-6067	171	24	{	{	PUNCT
ejpam-6067	171	25	f−1(gαi	f−1(gαi	NUM
ejpam-6067	171	26	)	)	PUNCT
ejpam-6067	171	27	:	:	PUNCT
ejpam-6067	172	1	i	i	PRON
ejpam-6067	172	2	∈	∈	PROPN
ejpam-6067	172	3	n	n	CCONJ
ejpam-6067	172	4	}	}	PUNCT
ejpam-6067	172	5	.	.	PUNCT
ejpam-6067	173	1	as	as	SCONJ
ejpam-6067	173	2	f	f	PROPN
ejpam-6067	173	3	achieves	achieve	VERB
ejpam-6067	173	4	surjectivity	surjectivity	NOUN
ejpam-6067	173	5	,	,	PUNCT
ejpam-6067	173	6	{	{	PUNCT
ejpam-6067	173	7	gαi	gαi	NOUN
ejpam-6067	173	8	:	:	PUNCT
ejpam-6067	173	9	i	i	PROPN
ejpam-6067	173	10	∈	∈	PROPN
ejpam-6067	173	11	n	n	CCONJ
ejpam-6067	173	12	}	}	PUNCT
ejpam-6067	173	13	forms	form	VERB
ejpam-6067	173	14	a	a	DET
ejpam-6067	173	15	countable	countable	ADJ
ejpam-6067	173	16	subcover	subcover	NOUN
ejpam-6067	173	17	of˜for	of˜for	PROPN
ejpam-6067	173	18	y	y	PROPN
ejpam-6067	173	19	,	,	PUNCT
ejpam-6067	173	20	proving	prove	VERB
ejpam-6067	173	21	that	that	SCONJ
ejpam-6067	173	22	y	y	PROPN
ejpam-6067	173	23	exhibits	exhibit	VERB
ejpam-6067	173	24	g	g	NOUN
ejpam-6067	173	25	-	-	PUNCT
ejpam-6067	173	26	lindelöfness	lindelöfness	NOUN
ejpam-6067	173	27	.	.	NOUN
ejpam-6067	173	28	remark	remark	NOUN
ejpam-6067	173	29	2	2	NUM
ejpam-6067	173	30	.	.	PUNCT
ejpam-6067	174	1	compact	compact	ADJ
ejpam-6067	174	2	spaces	space	NOUN
ejpam-6067	174	3	need	need	AUX
ejpam-6067	174	4	not	not	PART
ejpam-6067	174	5	be	be	AUX
ejpam-6067	174	6	glindelöf	glindelöf	NOUN
ejpam-6067	174	7	spaces	space	NOUN
ejpam-6067	174	8	.	.	PUNCT
ejpam-6067	175	1	to	to	PART
ejpam-6067	175	2	show	show	VERB
ejpam-6067	175	3	that	that	SCONJ
ejpam-6067	175	4	we	we	PRON
ejpam-6067	175	5	have	have	VERB
ejpam-6067	175	6	the	the	DET
ejpam-6067	175	7	following	follow	VERB
ejpam-6067	175	8	example	example	NOUN
ejpam-6067	175	9	:	:	PUNCT
ejpam-6067	175	10	example	example	NOUN
ejpam-6067	175	11	4	4	NUM
ejpam-6067	175	12	.	.	PUNCT
ejpam-6067	176	1	the	the	DET
ejpam-6067	176	2	closed	closed	ADJ
ejpam-6067	176	3	interval	interval	NOUN
ejpam-6067	176	4	[	[	X
ejpam-6067	176	5	0	0	NUM
ejpam-6067	176	6	,	,	PUNCT
ejpam-6067	176	7	1	1	NUM
ejpam-6067	176	8	]	]	PUNCT
ejpam-6067	176	9	with	with	ADP
ejpam-6067	176	10	the	the	DET
ejpam-6067	176	11	usual	usual	ADJ
ejpam-6067	176	12	topology	topology	NOUN
ejpam-6067	176	13	exhibits	exhibit	VERB
ejpam-6067	176	14	compactness	compactness	NOUN
ejpam-6067	176	15	but	but	CCONJ
ejpam-6067	176	16	lacks	lack	VERB
ejpam-6067	176	17	g	g	NOUN
ejpam-6067	176	18	-	-	PUNCT
ejpam-6067	176	19	lindelöfness	lindelöfness	NOUN
ejpam-6067	176	20	.	.	PUNCT
ejpam-6067	176	21	proof	proof	NOUN
ejpam-6067	176	22	.	.	PUNCT
ejpam-6067	177	1	we	we	PRON
ejpam-6067	177	2	know	know	VERB
ejpam-6067	177	3	that	that	SCONJ
ejpam-6067	177	4	(	(	PUNCT
ejpam-6067	177	5	by	by	ADP
ejpam-6067	177	6	the	the	DET
ejpam-6067	177	7	heine	heine	PROPN
ejpam-6067	177	8	-	-	PUNCT
ejpam-6067	177	9	borel	borel	PROPN
ejpam-6067	177	10	theorem	theorem	PROPN
ejpam-6067	177	11	)	)	PUNCT
ejpam-6067	178	1	i	i	PRON
ejpam-6067	178	2	=	=	PUNCT
ejpam-6067	179	1	[	[	X
ejpam-6067	179	2	0	0	NUM
ejpam-6067	179	3	,	,	PUNCT
ejpam-6067	179	4	1	1	NUM
ejpam-6067	179	5	]	]	PUNCT
ejpam-6067	179	6	demonstrates	demonstrate	VERB
ejpam-6067	179	7	compactness	compactness	NOUN
ejpam-6067	179	8	because	because	SCONJ
ejpam-6067	179	9	it	it	PRON
ejpam-6067	179	10	fulfills	fulfill	VERB
ejpam-6067	179	11	closedness	closedness	ADJ
ejpam-6067	179	12	and	and	CCONJ
ejpam-6067	179	13	boundedness	boundedness	NOUN
ejpam-6067	179	14	,	,	PUNCT
ejpam-6067	179	15	as	as	SCONJ
ejpam-6067	179	16	stated	state	VERB
ejpam-6067	179	17	in	in	ADP
ejpam-6067	179	18	[	[	X
ejpam-6067	179	19	3	3	NUM
ejpam-6067	179	20	]	]	PUNCT
ejpam-6067	179	21	.	.	PUNCT
ejpam-6067	180	1	however	however	ADV
ejpam-6067	180	2	,	,	PUNCT
ejpam-6067	180	3	i	i	PRON
ejpam-6067	180	4	lacks	lack	VERB
ejpam-6067	180	5	g	g	NOUN
ejpam-6067	180	6	-	-	PUNCT
ejpam-6067	180	7	lindelöfness	lindelöfness	NOUN
ejpam-6067	180	8	.	.	PUNCT
ejpam-6067	181	1	we	we	PRON
ejpam-6067	181	2	establish	establish	VERB
ejpam-6067	181	3	this	this	PRON
ejpam-6067	181	4	by	by	ADP
ejpam-6067	181	5	considering	consider	VERB
ejpam-6067	181	6	points	point	NOUN
ejpam-6067	182	1	x	x	X
ejpam-6067	182	2	∈	∈	NOUN
ejpam-6067	182	3	i	i	PRON
ejpam-6067	182	4	in	in	ADP
ejpam-6067	182	5	three	three	NUM
ejpam-6067	182	6	cases	case	NOUN
ejpam-6067	182	7	:	:	PUNCT
ejpam-6067	182	8	case	case	NOUN
ejpam-6067	182	9	1	1	NUM
ejpam-6067	182	10	:	:	PUNCT
ejpam-6067	182	11	if	if	SCONJ
ejpam-6067	182	12	x	x	SYM
ejpam-6067	182	13	=	=	SYM
ejpam-6067	182	14	0	0	NUM
ejpam-6067	182	15	,	,	PUNCT
ejpam-6067	182	16	then	then	ADV
ejpam-6067	182	17	{	{	PUNCT
ejpam-6067	182	18	0	0	NUM
ejpam-6067	182	19	}	}	PUNCT
ejpam-6067	182	20	=	=	NOUN
ejpam-6067	182	21	∞⋂	∞⋂	NOUN
ejpam-6067	182	22	n=1	n=1	PROPN
ejpam-6067	182	23	[	[	PUNCT
ejpam-6067	182	24	0	0	NUM
ejpam-6067	182	25	,	,	PUNCT
ejpam-6067	182	26	1	1	NUM
ejpam-6067	182	27	n	n	NOUN
ejpam-6067	182	28	)	)	PUNCT
ejpam-6067	182	29	.	.	PUNCT
ejpam-6067	183	1	m.	m.	NOUN
ejpam-6067	183	2	shatnawi	shatnawi	PROPN
ejpam-6067	183	3	et	et	PROPN
ejpam-6067	183	4	al	al	PROPN
ejpam-6067	183	5	.	.	PUNCT
ejpam-6067	183	6	/	/	SYM
ejpam-6067	183	7	eur	eur	PROPN
ejpam-6067	183	8	.	.	PUNCT
ejpam-6067	184	1	j.	j.	PROPN
ejpam-6067	184	2	pure	pure	PROPN
ejpam-6067	184	3	appl	appl	PROPN
ejpam-6067	184	4	.	.	PROPN
ejpam-6067	184	5	math	math	PROPN
ejpam-6067	184	6	,	,	PUNCT
ejpam-6067	184	7	18	18	NUM
ejpam-6067	184	8	(	(	PUNCT
ejpam-6067	184	9	3	3	NUM
ejpam-6067	184	10	)	)	PUNCT
ejpam-6067	184	11	(	(	PUNCT
ejpam-6067	184	12	2025	2025	NUM
ejpam-6067	184	13	)	)	PUNCT
ejpam-6067	184	14	,	,	PUNCT
ejpam-6067	184	15	6067	6067	NUM
ejpam-6067	184	16	8	8	NUM
ejpam-6067	184	17	of	of	ADP
ejpam-6067	184	18	16	16	NUM
ejpam-6067	184	19	case	case	NOUN
ejpam-6067	184	20	2	2	NUM
ejpam-6067	184	21	:	:	PUNCT
ejpam-6067	184	22	if	if	SCONJ
ejpam-6067	184	23	x	x	SYM
ejpam-6067	185	1	=	=	SYM
ejpam-6067	185	2	1	1	NUM
ejpam-6067	185	3	then	then	ADV
ejpam-6067	185	4	{	{	PUNCT
ejpam-6067	185	5	1	1	NUM
ejpam-6067	185	6	}	}	PUNCT
ejpam-6067	185	7	=	=	NOUN
ejpam-6067	185	8	∞⋂	∞⋂	X
ejpam-6067	185	9	n=1	n=1	PROPN
ejpam-6067	185	10	(	(	PUNCT
ejpam-6067	185	11	n+	n+	ADP
ejpam-6067	185	12	1	1	NUM
ejpam-6067	185	13	n+	n+	SYM
ejpam-6067	185	14	2	2	NUM
ejpam-6067	185	15	,	,	PUNCT
ejpam-6067	185	16	1	1	NUM
ejpam-6067	185	17	]	]	PUNCT
ejpam-6067	185	18	.	.	PUNCT
ejpam-6067	186	1	case	case	NOUN
ejpam-6067	186	2	3	3	NUM
ejpam-6067	186	3	:	:	PUNCT
ejpam-6067	186	4	if	if	SCONJ
ejpam-6067	186	5	x	x	SYM
ejpam-6067	186	6	∈	∈	PROPN
ejpam-6067	186	7	(	(	PUNCT
ejpam-6067	186	8	0	0	NUM
ejpam-6067	186	9	,	,	PUNCT
ejpam-6067	186	10	1	1	NUM
ejpam-6067	186	11	)	)	PUNCT
ejpam-6067	186	12	,	,	PUNCT
ejpam-6067	186	13	then	then	ADV
ejpam-6067	186	14	we	we	PRON
ejpam-6067	186	15	find	find	VERB
ejpam-6067	186	16	an	an	DET
ejpam-6067	186	17	ε	ε	NOUN
ejpam-6067	186	18	-	-	PUNCT
ejpam-6067	186	19	neighborhood	neighborhood	NOUN
ejpam-6067	186	20	containing	contain	VERB
ejpam-6067	186	21	x	x	PUNCT
ejpam-6067	186	22	with	with	ADP
ejpam-6067	186	23	(	(	PUNCT
ejpam-6067	186	24	x−ε	x−ε	PROPN
ejpam-6067	186	25	,	,	PUNCT
ejpam-6067	186	26	x+ε	x+ε	NUM
ejpam-6067	186	27	)	)	PUNCT
ejpam-6067	186	28	⊆	⊆	NUM
ejpam-6067	186	29	(	(	PUNCT
ejpam-6067	186	30	0	0	NUM
ejpam-6067	186	31	,	,	PUNCT
ejpam-6067	186	32	1	1	NUM
ejpam-6067	186	33	)	)	PUNCT
ejpam-6067	186	34	.	.	PUNCT
ejpam-6067	187	1	by	by	ADP
ejpam-6067	187	2	the	the	DET
ejpam-6067	187	3	archimedean	archimedean	PROPN
ejpam-6067	187	4	property	property	NOUN
ejpam-6067	187	5	,	,	PUNCT
ejpam-6067	187	6	we	we	PRON
ejpam-6067	187	7	find	find	VERB
ejpam-6067	187	8	mx∈	mx∈	NOUN
ejpam-6067	187	9	n	n	PRON
ejpam-6067	187	10	such	such	ADJ
ejpam-6067	187	11	that	that	SCONJ
ejpam-6067	187	12	1	1	NUM
ejpam-6067	187	13	mx	mx	NOUN
ejpam-6067	187	14	<	<	X
ejpam-6067	187	15	ε	ε	PROPN
ejpam-6067	187	16	,	,	PUNCT
ejpam-6067	187	17	establishing	establish	VERB
ejpam-6067	187	18	(	(	PUNCT
ejpam-6067	187	19	x−	x−	PROPN
ejpam-6067	187	20	1	1	NUM
ejpam-6067	187	21	n	n	NOUN
ejpam-6067	187	22	,	,	PUNCT
ejpam-6067	187	23	x+	x+	NUM
ejpam-6067	187	24	1	1	NUM
ejpam-6067	187	25	n	n	NOUN
ejpam-6067	187	26	)	)	PUNCT
ejpam-6067	187	27	⊆	⊆	NUM
ejpam-6067	187	28	(	(	PUNCT
ejpam-6067	187	29	x−	x−	PROPN
ejpam-6067	187	30	ε	ε	PROPN
ejpam-6067	187	31	,	,	PUNCT
ejpam-6067	187	32	x+	x+	X
ejpam-6067	187	33	ε	ε	PROPN
ejpam-6067	187	34	)	)	PUNCT
ejpam-6067	187	35	⊆	⊆	NUM
ejpam-6067	187	36	(	(	PUNCT
ejpam-6067	187	37	0	0	NUM
ejpam-6067	187	38	,	,	PUNCT
ejpam-6067	187	39	1	1	NUM
ejpam-6067	187	40	)	)	PUNCT
ejpam-6067	187	41	for	for	ADP
ejpam-6067	187	42	all	all	DET
ejpam-6067	187	43	n	n	DET
ejpam-6067	187	44	≥	≥	NUM
ejpam-6067	187	45	mx	mx	PROPN
ejpam-6067	187	46	.	.	PUNCT
ejpam-6067	188	1	also	also	ADV
ejpam-6067	188	2	,	,	PUNCT
ejpam-6067	188	3	{	{	PUNCT
ejpam-6067	188	4	x	x	NOUN
ejpam-6067	188	5	}	}	PUNCT
ejpam-6067	188	6	=	=	SYM
ejpam-6067	188	7	∞⋂	∞⋂	PROPN
ejpam-6067	188	8	n	n	CCONJ
ejpam-6067	188	9	=	=	SYM
ejpam-6067	188	10	mx	mx	PROPN
ejpam-6067	188	11	(	(	PUNCT
ejpam-6067	188	12	x−	x−	PROPN
ejpam-6067	188	13	1	1	NUM
ejpam-6067	188	14	n	n	NOUN
ejpam-6067	188	15	,	,	PUNCT
ejpam-6067	188	16	x+	x+	X
ejpam-6067	188	17	1	1	NUM
ejpam-6067	188	18	n	n	NUM
ejpam-6067	188	19	)	)	PUNCT
ejpam-6067	188	20	.	.	PUNCT
ejpam-6067	189	1	in	in	ADP
ejpam-6067	189	2	each	each	DET
ejpam-6067	189	3	case	case	NOUN
ejpam-6067	189	4	,	,	PUNCT
ejpam-6067	189	5	{	{	PUNCT
ejpam-6067	189	6	x	x	NOUN
ejpam-6067	189	7	}	}	PUNCT
ejpam-6067	189	8	forms	form	NOUN
ejpam-6067	189	9	a	a	DET
ejpam-6067	189	10	gδ	gδ	NOUN
ejpam-6067	189	11	set	set	NOUN
ejpam-6067	189	12	for	for	ADP
ejpam-6067	189	13	any	any	DET
ejpam-6067	189	14	x	x	SYM
ejpam-6067	189	15	∈	∈	PROPN
ejpam-6067	189	16	i.	i.	NOUN
ejpam-6067	189	17	therefore	therefore	ADV
ejpam-6067	189	18	,	,	PUNCT
ejpam-6067	189	19	g̃	g̃	PROPN
ejpam-6067	189	20	=	=	PUNCT
ejpam-6067	189	21	{	{	PUNCT
ejpam-6067	189	22	{	{	PUNCT
ejpam-6067	189	23	x	x	NOUN
ejpam-6067	189	24	}	}	PUNCT
ejpam-6067	189	25	:	:	PUNCT
ejpam-6067	189	26	x	x	X
ejpam-6067	189	27	∈	∈	PROPN
ejpam-6067	189	28	i	i	PRON
ejpam-6067	189	29	}	}	PUNCT
ejpam-6067	189	30	creates	create	VERB
ejpam-6067	189	31	a	a	DET
ejpam-6067	189	32	g	g	NOUN
ejpam-6067	189	33	-	-	PUNCT
ejpam-6067	189	34	cover	cover	NOUN
ejpam-6067	189	35	of	of	ADP
ejpam-6067	189	36	i	i	PRON
ejpam-6067	189	37	with	with	ADP
ejpam-6067	189	38	no	no	DET
ejpam-6067	189	39	countable	countable	ADJ
ejpam-6067	189	40	subcover	subcover	NOUN
ejpam-6067	189	41	since	since	SCONJ
ejpam-6067	189	42	i	i	PRON
ejpam-6067	189	43	demonstrates	demonstrate	VERB
ejpam-6067	189	44	uncountability	uncountability	NOUN
ejpam-6067	189	45	.	.	PUNCT
ejpam-6067	190	1	this	this	PRON
ejpam-6067	190	2	proves	prove	VERB
ejpam-6067	190	3	that	that	SCONJ
ejpam-6067	190	4	i	i	PRON
ejpam-6067	190	5	lacks	lack	VERB
ejpam-6067	190	6	g	g	NOUN
ejpam-6067	190	7	-	-	PUNCT
ejpam-6067	190	8	lindelöfness	lindelöfness	NOUN
ejpam-6067	190	9	.	.	NOUN
ejpam-6067	190	10	remark	remark	NOUN
ejpam-6067	190	11	3	3	NUM
ejpam-6067	190	12	.	.	PUNCT
ejpam-6067	190	13	glindelöf	glindelöf	NOUN
ejpam-6067	190	14	spaces	space	NOUN
ejpam-6067	190	15	need	need	AUX
ejpam-6067	190	16	not	not	PART
ejpam-6067	190	17	be	be	AUX
ejpam-6067	190	18	compact	compact	ADJ
ejpam-6067	190	19	spaces	space	NOUN
ejpam-6067	190	20	.	.	PUNCT
ejpam-6067	191	1	to	to	PART
ejpam-6067	191	2	show	show	VERB
ejpam-6067	191	3	that	that	SCONJ
ejpam-6067	191	4	we	we	PRON
ejpam-6067	191	5	have	have	VERB
ejpam-6067	191	6	the	the	DET
ejpam-6067	191	7	following	follow	VERB
ejpam-6067	191	8	example	example	NOUN
ejpam-6067	191	9	:	:	PUNCT
ejpam-6067	191	10	example	example	NOUN
ejpam-6067	191	11	5	5	NUM
ejpam-6067	191	12	.	.	PUNCT
ejpam-6067	192	1	the	the	DET
ejpam-6067	192	2	nested	nested	ADJ
ejpam-6067	192	3	interval	interval	NOUN
ejpam-6067	192	4	topology	topology	NOUN
ejpam-6067	192	5	on	on	ADP
ejpam-6067	192	6	(	(	PUNCT
ejpam-6067	192	7	0	0	NUM
ejpam-6067	192	8	,	,	PUNCT
ejpam-6067	192	9	1	1	X
ejpam-6067	192	10	)	)	PUNCT
ejpam-6067	192	11	exhibits	exhibit	VERB
ejpam-6067	192	12	g	g	NOUN
ejpam-6067	192	13	-	-	PUNCT
ejpam-6067	192	14	lindelöfness	lindelöfness	NOUN
ejpam-6067	192	15	but	but	CCONJ
ejpam-6067	192	16	lacks	lack	VERB
ejpam-6067	192	17	compactness	compactness	NOUN
ejpam-6067	192	18	.	.	PUNCT
ejpam-6067	193	1	proof	proof	NOUN
ejpam-6067	193	2	.	.	PUNCT
ejpam-6067	194	1	on	on	ADP
ejpam-6067	194	2	the	the	DET
ejpam-6067	194	3	open	open	ADJ
ejpam-6067	194	4	interval	interval	NOUN
ejpam-6067	194	5	x	x	PUNCT
ejpam-6067	194	6	=	=	SYM
ejpam-6067	194	7	(	(	PUNCT
ejpam-6067	194	8	0	0	NUM
ejpam-6067	194	9	,	,	PUNCT
ejpam-6067	194	10	1	1	NUM
ejpam-6067	194	11	)	)	PUNCT
ejpam-6067	194	12	the	the	DET
ejpam-6067	194	13	nested	nested	ADJ
ejpam-6067	194	14	interval	interval	NOUN
ejpam-6067	194	15	topology	topology	NOUN
ejpam-6067	194	16	τ	τ	PROPN
ejpam-6067	194	17	is	be	AUX
ejpam-6067	194	18	defined	define	VERB
ejpam-6067	194	19	by	by	ADP
ejpam-6067	194	20	declaring	declare	VERB
ejpam-6067	194	21	all	all	DET
ejpam-6067	194	22	open	open	ADJ
ejpam-6067	194	23	sets	set	NOUN
ejpam-6067	194	24	of	of	ADP
ejpam-6067	194	25	the	the	DET
ejpam-6067	194	26	form	form	NOUN
ejpam-6067	194	27	vn	vn	X
ejpam-6067	194	28	=	=	SYM
ejpam-6067	194	29	(	(	PUNCT
ejpam-6067	194	30	0	0	NUM
ejpam-6067	194	31	,	,	PUNCT
ejpam-6067	194	32	1−	1−	NUM
ejpam-6067	194	33	1	1	NUM
ejpam-6067	194	34	n	n	NOUN
ejpam-6067	194	35	)	)	PUNCT
ejpam-6067	194	36	,	,	PUNCT
ejpam-6067	194	37	for	for	ADP
ejpam-6067	194	38	n	n	NOUN
ejpam-6067	194	39	=	=	SYM
ejpam-6067	194	40	2	2	NUM
ejpam-6067	194	41	,	,	PUNCT
ejpam-6067	194	42	3	3	NUM
ejpam-6067	194	43	,	,	PUNCT
ejpam-6067	194	44	4	4	NUM
ejpam-6067	194	45	,	,	PUNCT
ejpam-6067	194	46	.	.	PUNCT
ejpam-6067	194	47	.	.	PUNCT
ejpam-6067	195	1	.	.	PUNCT
ejpam-6067	196	1	,	,	PUNCT
ejpam-6067	196	2	together	together	ADV
ejpam-6067	196	3	with	with	ADP
ejpam-6067	196	4	∅	∅	NOUN
ejpam-6067	196	5	andx	andx	NOUN
ejpam-6067	196	6	.	.	PUNCT
ejpam-6067	197	1	this	this	DET
ejpam-6067	197	2	topological	topological	ADJ
ejpam-6067	197	3	space	space	NOUN
ejpam-6067	197	4	is	be	AUX
ejpam-6067	197	5	glindelöf	glindelöf	NOUN
ejpam-6067	197	6	but	but	CCONJ
ejpam-6067	197	7	not	not	PART
ejpam-6067	197	8	compact	compact	ADJ
ejpam-6067	197	9	space	space	NOUN
ejpam-6067	197	10	.	.	PUNCT
ejpam-6067	198	1	to	to	PART
ejpam-6067	198	2	see	see	VERB
ejpam-6067	198	3	this	this	PRON
ejpam-6067	198	4	,	,	PUNCT
ejpam-6067	198	5	let	let	VERB
ejpam-6067	198	6	g̃	g̃	PROPN
ejpam-6067	198	7	=	=	PUNCT
ejpam-6067	198	8	{	{	PUNCT
ejpam-6067	198	9	gα	gα	NOUN
ejpam-6067	198	10	:	:	PUNCT
ejpam-6067	198	11	α	α	PROPN
ejpam-6067	198	12	∈	∈	PROPN
ejpam-6067	198	13	∆	∆	PROPN
ejpam-6067	198	14	}	}	PUNCT
ejpam-6067	198	15	be	be	AUX
ejpam-6067	198	16	a	a	DET
ejpam-6067	198	17	g	g	NOUN
ejpam-6067	198	18	-cover	-cover	PROPN
ejpam-6067	198	19	of	of	ADP
ejpam-6067	198	20	x	x	PRON
ejpam-6067	198	21	,	,	PUNCT
ejpam-6067	198	22	but	but	CCONJ
ejpam-6067	198	23	any	any	DET
ejpam-6067	198	24	gδ	gδ	NOUN
ejpam-6067	198	25	set	set	VERB
ejpam-6067	198	26	in	in	ADP
ejpam-6067	198	27	x	x	PUNCT
ejpam-6067	198	28	belongs	belong	VERB
ejpam-6067	198	29	to	to	ADP
ejpam-6067	198	30	{	{	PUNCT
ejpam-6067	198	31	∅	∅	NOUN
ejpam-6067	198	32	,	,	PUNCT
ejpam-6067	198	33	x	x	X
ejpam-6067	198	34	,	,	PUNCT
ejpam-6067	198	35	vn	vn	INTJ
ejpam-6067	198	36	:	:	PUNCT
ejpam-6067	198	37	n	n	PROPN
ejpam-6067	198	38	=	=	SYM
ejpam-6067	198	39	2	2	NUM
ejpam-6067	198	40	,	,	PUNCT
ejpam-6067	198	41	3	3	NUM
ejpam-6067	198	42	,	,	PUNCT
ejpam-6067	198	43	4	4	NUM
ejpam-6067	198	44	,	,	PUNCT
ejpam-6067	198	45	.	.	PUNCT
ejpam-6067	198	46	.	.	PUNCT
ejpam-6067	199	1	.	.	PUNCT
ejpam-6067	199	2	}	}	PUNCT
ejpam-6067	199	3	.	.	PUNCT
ejpam-6067	200	1	hence	hence	ADV
ejpam-6067	200	2	,	,	PUNCT
ejpam-6067	200	3	g̃	g̃	PROPN
ejpam-6067	200	4	is	be	AUX
ejpam-6067	200	5	countable	countable	ADJ
ejpam-6067	200	6	.	.	PUNCT
ejpam-6067	201	1	so	so	ADV
ejpam-6067	201	2	,	,	PUNCT
ejpam-6067	201	3	we	we	PRON
ejpam-6067	201	4	can	can	AUX
ejpam-6067	201	5	choose	choose	VERB
ejpam-6067	201	6	g̃	g̃	PROPN
ejpam-6067	201	7	itself	itself	PRON
ejpam-6067	201	8	as	as	ADP
ejpam-6067	201	9	a	a	DET
ejpam-6067	201	10	countable	countable	ADJ
ejpam-6067	201	11	subcover	subcover	NOUN
ejpam-6067	201	12	for	for	ADP
ejpam-6067	201	13	x.	x.	PROPN
ejpam-6067	201	14	theorem	theorem	VERB
ejpam-6067	201	15	8	8	NUM
ejpam-6067	201	16	.	.	PUNCT
ejpam-6067	202	1	every	every	DET
ejpam-6067	202	2	fσ	fσ	NOUN
ejpam-6067	202	3	subspace	subspace	NOUN
ejpam-6067	202	4	of	of	ADP
ejpam-6067	202	5	a	a	DET
ejpam-6067	202	6	g	g	NOUN
ejpam-6067	202	7	-	-	PUNCT
ejpam-6067	202	8	compact	compact	ADJ
ejpam-6067	202	9	space	space	NOUN
ejpam-6067	202	10	is	be	AUX
ejpam-6067	202	11	g	g	NOUN
ejpam-6067	202	12	-	-	PUNCT
ejpam-6067	202	13	compact	compact	ADJ
ejpam-6067	202	14	.	.	PUNCT
ejpam-6067	203	1	proof	proof	NOUN
ejpam-6067	203	2	.	.	PUNCT
ejpam-6067	204	1	let	let	VERB
ejpam-6067	204	2	(	(	PUNCT
ejpam-6067	204	3	x	x	NOUN
ejpam-6067	204	4	,	,	PUNCT
ejpam-6067	204	5	τ	τ	X
ejpam-6067	204	6	)	)	PUNCT
ejpam-6067	204	7	be	be	VERB
ejpam-6067	204	8	a	a	DET
ejpam-6067	204	9	g	g	NOUN
ejpam-6067	204	10	-	-	PUNCT
ejpam-6067	204	11	compact	compact	ADJ
ejpam-6067	204	12	space	space	NOUN
ejpam-6067	204	13	and	and	CCONJ
ejpam-6067	204	14	let	let	VERB
ejpam-6067	204	15	f	f	PRON
ejpam-6067	204	16	be	be	AUX
ejpam-6067	204	17	an	an	DET
ejpam-6067	204	18	fσ	fσ	NOUN
ejpam-6067	204	19	subspace	subspace	NOUN
ejpam-6067	204	20	of	of	ADP
ejpam-6067	204	21	x.	x.	NOUN
ejpam-6067	204	22	to	to	PART
ejpam-6067	204	23	show	show	VERB
ejpam-6067	204	24	that	that	SCONJ
ejpam-6067	204	25	f	f	PROPN
ejpam-6067	204	26	is	be	AUX
ejpam-6067	204	27	g	g	NOUN
ejpam-6067	204	28	-	-	PUNCT
ejpam-6067	204	29	compact	compact	ADJ
ejpam-6067	204	30	,	,	PUNCT
ejpam-6067	204	31	let	let	VERB
ejpam-6067	204	32	g̃	g̃	PROPN
ejpam-6067	204	33	=	=	PUNCT
ejpam-6067	204	34	{	{	PUNCT
ejpam-6067	204	35	gα	gα	NOUN
ejpam-6067	204	36	:	:	PUNCT
ejpam-6067	204	37	α	α	PROPN
ejpam-6067	204	38	∈	∈	PROPN
ejpam-6067	204	39	∆	∆	PROPN
ejpam-6067	204	40	}	}	PUNCT
ejpam-6067	204	41	be	be	AUX
ejpam-6067	204	42	a	a	DET
ejpam-6067	204	43	g	g	PROPN
ejpam-6067	204	44	-cover	-cover	PROPN
ejpam-6067	204	45	of	of	ADP
ejpam-6067	204	46	f	f	PROPN
ejpam-6067	204	47	.	.	PUNCT
ejpam-6067	205	1	then	then	ADV
ejpam-6067	205	2	g̃	g̃	PROPN
ejpam-6067	205	3	∪	∪	ADV
ejpam-6067	205	4	{	{	PUNCT
ejpam-6067	205	5	x\f	x\f	PRON
ejpam-6067	205	6	}	}	PUNCT
ejpam-6067	205	7	is	be	AUX
ejpam-6067	205	8	a	a	DET
ejpam-6067	205	9	g	g	PROPN
ejpam-6067	205	10	-cover	-cover	PROPN
ejpam-6067	205	11	of	of	ADP
ejpam-6067	205	12	x.	x.	NOUN
ejpam-6067	205	13	as	as	SCONJ
ejpam-6067	205	14	x	x	PROPN
ejpam-6067	205	15	is	be	AUX
ejpam-6067	205	16	g	g	NOUN
ejpam-6067	205	17	-	-	PUNCT
ejpam-6067	205	18	compact	compact	ADJ
ejpam-6067	205	19	,	,	PUNCT
ejpam-6067	205	20	there	there	PRON
ejpam-6067	205	21	exists	exist	VERB
ejpam-6067	205	22	a	a	DET
ejpam-6067	205	23	finite	finite	ADJ
ejpam-6067	205	24	subcover	subcover	NOUN
ejpam-6067	205	25	of	of	ADP
ejpam-6067	205	26	g̃	g̃	PROPN
ejpam-6067	205	27	∪	∪	ADV
ejpam-6067	205	28	{	{	PUNCT
ejpam-6067	205	29	x\f	x\f	PROPN
ejpam-6067	205	30	}	}	PUNCT
ejpam-6067	205	31	,	,	PUNCT
ejpam-6067	205	32	say	say	VERB
ejpam-6067	205	33	a	a	DET
ejpam-6067	205	34	=	=	X
ejpam-6067	205	35	{	{	PUNCT
ejpam-6067	205	36	gα1	gα1	NOUN
ejpam-6067	205	37	,	,	PUNCT
ejpam-6067	205	38	gα2	gα2	NOUN
ejpam-6067	205	39	,	,	PUNCT
ejpam-6067	205	40	.	.	PUNCT
ejpam-6067	205	41	.	.	PUNCT
ejpam-6067	206	1	.	.	PUNCT
ejpam-6067	207	1	,	,	PUNCT
ejpam-6067	207	2	gαn	gαn	PROPN
ejpam-6067	207	3	}	}	PUNCT
ejpam-6067	207	4	.	.	PUNCT
ejpam-6067	208	1	this	this	PRON
ejpam-6067	208	2	covers	cover	VERB
ejpam-6067	208	3	f	f	NOUN
ejpam-6067	208	4	by	by	ADP
ejpam-6067	208	5	the	the	DET
ejpam-6067	208	6	fact	fact	NOUN
ejpam-6067	208	7	that	that	SCONJ
ejpam-6067	208	8	it	it	PRON
ejpam-6067	208	9	covers	cover	VERB
ejpam-6067	208	10	x.	x.	NOUN
ejpam-6067	208	11	suppose	suppose	VERB
ejpam-6067	208	12	x\f	x\f	PRON
ejpam-6067	208	13	is	be	AUX
ejpam-6067	208	14	an	an	DET
ejpam-6067	208	15	element	element	NOUN
ejpam-6067	208	16	of	of	ADP
ejpam-6067	208	17	a.	a.	NOUN
ejpam-6067	208	18	then	then	ADV
ejpam-6067	208	19	x\f	x\f	X
ejpam-6067	208	20	may	may	AUX
ejpam-6067	208	21	be	be	AUX
ejpam-6067	208	22	removed	remove	VERB
ejpam-6067	208	23	from	from	ADP
ejpam-6067	208	24	a	a	PRON
ejpam-6067	208	25	,	,	PUNCT
ejpam-6067	208	26	and	and	CCONJ
ejpam-6067	208	27	the	the	DET
ejpam-6067	208	28	rest	rest	NOUN
ejpam-6067	208	29	of	of	ADP
ejpam-6067	208	30	a	a	PRON
ejpam-6067	208	31	still	still	ADV
ejpam-6067	208	32	covers	cover	VERB
ejpam-6067	208	33	f	f	PROPN
ejpam-6067	208	34	.	.	PUNCT
ejpam-6067	209	1	thus	thus	ADV
ejpam-6067	209	2	we	we	PRON
ejpam-6067	209	3	have	have	VERB
ejpam-6067	209	4	a	a	DET
ejpam-6067	209	5	finite	finite	ADJ
ejpam-6067	209	6	subcover	subcover	NOUN
ejpam-6067	209	7	of	of	ADP
ejpam-6067	209	8	g̃	g̃	PROPN
ejpam-6067	209	9	which	which	PRON
ejpam-6067	209	10	covers	cover	VERB
ejpam-6067	209	11	f	f	PROPN
ejpam-6067	209	12	.	.	PUNCT
ejpam-6067	210	1	hence	hence	ADV
ejpam-6067	210	2	f	f	PROPN
ejpam-6067	210	3	is	be	AUX
ejpam-6067	210	4	g	g	NOUN
ejpam-6067	210	5	-	-	PUNCT
ejpam-6067	210	6	compact	compact	ADJ
ejpam-6067	210	7	.	.	PUNCT
ejpam-6067	211	1	theorem	theorem	VERB
ejpam-6067	211	2	9	9	NUM
ejpam-6067	211	3	.	.	PUNCT
ejpam-6067	212	1	if	if	SCONJ
ejpam-6067	212	2	(	(	PUNCT
ejpam-6067	212	3	x	x	NOUN
ejpam-6067	212	4	,	,	PUNCT
ejpam-6067	212	5	τ	τ	X
ejpam-6067	212	6	)	)	PUNCT
ejpam-6067	212	7	represents	represent	VERB
ejpam-6067	212	8	a	a	DET
ejpam-6067	212	9	g	g	NOUN
ejpam-6067	212	10	-	-	PUNCT
ejpam-6067	212	11	compact	compact	ADJ
ejpam-6067	212	12	space	space	NOUN
ejpam-6067	212	13	and	and	CCONJ
ejpam-6067	212	14	u	u	NOUN
ejpam-6067	212	15	constitutes	constitute	VERB
ejpam-6067	212	16	a	a	DET
ejpam-6067	212	17	gδ	gδ	NOUN
ejpam-6067	212	18	set	set	VERB
ejpam-6067	212	19	in	in	ADP
ejpam-6067	212	20	x	x	NOUN
ejpam-6067	212	21	,	,	PUNCT
ejpam-6067	212	22	then	then	ADV
ejpam-6067	212	23	u	u	NOUN
ejpam-6067	212	24	with	with	ADP
ejpam-6067	212	25	the	the	DET
ejpam-6067	212	26	subspace	subspace	NOUN
ejpam-6067	212	27	topology	topology	NOUN
ejpam-6067	212	28	exhibits	exhibit	VERB
ejpam-6067	212	29	g	g	NOUN
ejpam-6067	212	30	-	-	PUNCT
ejpam-6067	212	31	lindelöfness	lindelöfness	NOUN
ejpam-6067	212	32	.	.	PUNCT
ejpam-6067	213	1	proof	proof	NOUN
ejpam-6067	213	2	.	.	PUNCT
ejpam-6067	214	1	let	let	VERB
ejpam-6067	214	2	u	u	PRON
ejpam-6067	214	3	form	form	VERB
ejpam-6067	214	4	a	a	DET
ejpam-6067	214	5	gδ	gδ	NOUN
ejpam-6067	214	6	set	set	NOUN
ejpam-6067	214	7	in	in	ADP
ejpam-6067	214	8	the	the	DET
ejpam-6067	214	9	g	g	NOUN
ejpam-6067	214	10	-	-	PUNCT
ejpam-6067	214	11	compact	compact	ADJ
ejpam-6067	214	12	space	space	NOUN
ejpam-6067	214	13	(	(	PUNCT
ejpam-6067	214	14	x	x	X
ejpam-6067	214	15	,	,	PUNCT
ejpam-6067	214	16	τ	τ	PROPN
ejpam-6067	214	17	)	)	PUNCT
ejpam-6067	214	18	,	,	PUNCT
ejpam-6067	214	19	and	and	CCONJ
ejpam-6067	214	20	consider	consider	VERB
ejpam-6067	214	21	a	a	DET
ejpam-6067	214	22	g	g	NOUN
ejpam-6067	214	23	-	-	PUNCT
ejpam-6067	214	24	cover˜=	cover˜=	NOUN
ejpam-6067	214	25	{	{	PUNCT
ejpam-6067	214	26	gα	gα	ADP
ejpam-6067	214	27	∩	∩	ADJ
ejpam-6067	214	28	u	u	NOUN
ejpam-6067	214	29	:	:	PUNCT
ejpam-6067	214	30	α	α	PROPN
ejpam-6067	214	31	∈	∈	PROPN
ejpam-6067	214	32	∆	∆	PROPN
ejpam-6067	214	33	}	}	PUNCT
ejpam-6067	214	34	of	of	ADP
ejpam-6067	214	35	u	u	PROPN
ejpam-6067	214	36	,	,	PUNCT
ejpam-6067	214	37	where	where	SCONJ
ejpam-6067	214	38	each	each	DET
ejpam-6067	214	39	gα	gα	NOUN
ejpam-6067	214	40	represents	represent	VERB
ejpam-6067	214	41	a	a	DET
ejpam-6067	214	42	gδ	gδ	NOUN
ejpam-6067	214	43	set	set	VERB
ejpam-6067	214	44	in	in	ADP
ejpam-6067	214	45	x.	x.	PROPN
ejpam-6067	214	46	m.	m.	PROPN
ejpam-6067	214	47	shatnawi	shatnawi	PROPN
ejpam-6067	214	48	et	et	PROPN
ejpam-6067	214	49	al	al	PROPN
ejpam-6067	214	50	.	.	PUNCT
ejpam-6067	214	51	/	/	SYM
ejpam-6067	214	52	eur	eur	PROPN
ejpam-6067	214	53	.	.	PUNCT
ejpam-6067	215	1	j.	j.	PROPN
ejpam-6067	215	2	pure	pure	PROPN
ejpam-6067	215	3	appl	appl	PROPN
ejpam-6067	215	4	.	.	PROPN
ejpam-6067	215	5	math	math	PROPN
ejpam-6067	215	6	,	,	PUNCT
ejpam-6067	215	7	18	18	NUM
ejpam-6067	215	8	(	(	PUNCT
ejpam-6067	215	9	3	3	NUM
ejpam-6067	215	10	)	)	PUNCT
ejpam-6067	215	11	(	(	PUNCT
ejpam-6067	215	12	2025	2025	NUM
ejpam-6067	215	13	)	)	PUNCT
ejpam-6067	215	14	,	,	PUNCT
ejpam-6067	215	15	6067	6067	NUM
ejpam-6067	215	16	9	9	NUM
ejpam-6067	215	17	of	of	ADP
ejpam-6067	215	18	16	16	NUM
ejpam-6067	215	19	since	since	SCONJ
ejpam-6067	215	20	u	u	PRON
ejpam-6067	215	21	forms	form	VERB
ejpam-6067	215	22	a	a	DET
ejpam-6067	215	23	gδ	gδ	NOUN
ejpam-6067	215	24	set	set	NOUN
ejpam-6067	215	25	,	,	PUNCT
ejpam-6067	215	26	we	we	PRON
ejpam-6067	215	27	write	write	VERB
ejpam-6067	215	28	u	u	NOUN
ejpam-6067	215	29	=	=	SYM
ejpam-6067	215	30	⋂∞	⋂∞	NOUN
ejpam-6067	215	31	n=1	n=1	NUM
ejpam-6067	215	32	vn	vn	VERB
ejpam-6067	215	33	where	where	SCONJ
ejpam-6067	215	34	each	each	DET
ejpam-6067	215	35	vn	vn	PROPN
ejpam-6067	215	36	belongs	belong	VERB
ejpam-6067	215	37	to	to	ADP
ejpam-6067	215	38	τ	τ	PROPN
ejpam-6067	215	39	.	.	PUNCT
ejpam-6067	216	1	for	for	ADP
ejpam-6067	216	2	each	each	DET
ejpam-6067	216	3	α	α	PROPN
ejpam-6067	216	4	∈	∈	PROPN
ejpam-6067	216	5	∆	∆	PROPN
ejpam-6067	216	6	,	,	PUNCT
ejpam-6067	216	7	we	we	PRON
ejpam-6067	216	8	express	express	VERB
ejpam-6067	216	9	the	the	DET
ejpam-6067	216	10	set	set	NOUN
ejpam-6067	216	11	gα	gα	NOUN
ejpam-6067	216	12	=	=	PUNCT
ejpam-6067	216	13	⋂∞	⋂∞	NOUN
ejpam-6067	216	14	n=1wα	n=1wα	ADV
ejpam-6067	216	15	,	,	PUNCT
ejpam-6067	216	16	n	n	CCONJ
ejpam-6067	216	17	where	where	SCONJ
ejpam-6067	216	18	each	each	DET
ejpam-6067	216	19	wα	wα	NOUN
ejpam-6067	216	20	,	,	PUNCT
ejpam-6067	216	21	n	n	PRON
ejpam-6067	216	22	belongs	belong	VERB
ejpam-6067	216	23	to	to	ADP
ejpam-6067	216	24	τ	τ	PROPN
ejpam-6067	216	25	.	.	PUNCT
ejpam-6067	217	1	consider	consider	VERB
ejpam-6067	217	2	the	the	DET
ejpam-6067	217	3	collection	collection	NOUN
ejpam-6067	217	4	{	{	PUNCT
ejpam-6067	217	5	gα	gα	ADP
ejpam-6067	217	6	∪	∪	ADV
ejpam-6067	217	7	(	(	PUNCT
ejpam-6067	217	8	x	x	SYM
ejpam-6067	217	9	\	\	PROPN
ejpam-6067	217	10	u	u	NOUN
ejpam-6067	217	11	)	)	PUNCT
ejpam-6067	217	12	:	:	PUNCT
ejpam-6067	218	1	α	α	X
ejpam-6067	218	2	∈	∈	NOUN
ejpam-6067	218	3	∆	∆	X
ejpam-6067	218	4	}	}	PUNCT
ejpam-6067	218	5	.	.	PUNCT
ejpam-6067	219	1	each	each	PRON
ejpam-6067	219	2	set	set	VERB
ejpam-6067	219	3	in	in	ADP
ejpam-6067	219	4	this	this	DET
ejpam-6067	219	5	collection	collection	NOUN
ejpam-6067	219	6	creates	create	VERB
ejpam-6067	219	7	a	a	DET
ejpam-6067	219	8	gδ	gδ	NOUN
ejpam-6067	219	9	set	set	VERB
ejpam-6067	219	10	in	in	ADP
ejpam-6067	219	11	x	x	PUNCT
ejpam-6067	219	12	since	since	SCONJ
ejpam-6067	219	13	:	:	PUNCT
ejpam-6067	219	14	gα	gα	VERB
ejpam-6067	219	15	∪	∪	ADV
ejpam-6067	219	16	(	(	PUNCT
ejpam-6067	219	17	x	x	SYM
ejpam-6067	219	18	\	\	PROPN
ejpam-6067	219	19	u	u	NOUN
ejpam-6067	219	20	)	)	PUNCT
ejpam-6067	219	21	=	=	NOUN
ejpam-6067	219	22	gα	gα	ADP
ejpam-6067	219	23	∪	∪	ADV
ejpam-6067	219	24	(	(	PUNCT
ejpam-6067	219	25	x	x	SYM
ejpam-6067	219	26	\	\	PROPN
ejpam-6067	219	27	∞⋂	∞⋂	PROPN
ejpam-6067	219	28	n=1	n=1	PUNCT
ejpam-6067	219	29	vn	vn	PROPN
ejpam-6067	219	30	)	)	PUNCT
ejpam-6067	219	31	=	=	NOUN
ejpam-6067	219	32	gα	gα	ADP
ejpam-6067	219	33	∪	∪	ADJ
ejpam-6067	219	34	∞⋃	∞⋃	NOUN
ejpam-6067	219	35	n=1	n=1	PROPN
ejpam-6067	219	36	(	(	PUNCT
ejpam-6067	219	37	x	x	SYM
ejpam-6067	219	38	\	\	PROPN
ejpam-6067	219	39	vn	vn	PROPN
ejpam-6067	219	40	)	)	PUNCT
ejpam-6067	219	41	this	this	DET
ejpam-6067	219	42	collection	collection	NOUN
ejpam-6067	219	43	forms	form	VERB
ejpam-6067	219	44	a	a	DET
ejpam-6067	219	45	g	g	NOUN
ejpam-6067	219	46	-	-	PUNCT
ejpam-6067	219	47	cover	cover	NOUN
ejpam-6067	219	48	of	of	ADP
ejpam-6067	219	49	x.	x.	NOUN
ejpam-6067	219	50	by	by	ADP
ejpam-6067	219	51	g	g	NOUN
ejpam-6067	219	52	-	-	PUNCT
ejpam-6067	219	53	compactness	compactness	NOUN
ejpam-6067	219	54	,	,	PUNCT
ejpam-6067	219	55	it	it	PRON
ejpam-6067	219	56	admits	admit	VERB
ejpam-6067	219	57	a	a	DET
ejpam-6067	219	58	finite	finite	ADJ
ejpam-6067	219	59	subcover	subcover	PROPN
ejpam-6067	219	60	{	{	PUNCT
ejpam-6067	219	61	gα1	gα1	PROPN
ejpam-6067	219	62	∪	∪	ADJ
ejpam-6067	219	63	(	(	PUNCT
ejpam-6067	219	64	x	x	SYM
ejpam-6067	219	65	\	\	PROPN
ejpam-6067	219	66	u	u	NOUN
ejpam-6067	219	67	)	)	PUNCT
ejpam-6067	219	68	,	,	PUNCT
ejpam-6067	219	69	gα2	gα2	NOUN
ejpam-6067	219	70	∪	∪	ADV
ejpam-6067	219	71	(	(	PUNCT
ejpam-6067	219	72	x	x	SYM
ejpam-6067	219	73	\	\	PROPN
ejpam-6067	219	74	u	u	NOUN
ejpam-6067	219	75	)	)	PUNCT
ejpam-6067	219	76	,	,	PUNCT
ejpam-6067	219	77	...	...	PUNCT
ejpam-6067	219	78	,	,	PUNCT
ejpam-6067	219	79	gαk	gαk	NOUN
ejpam-6067	219	80	∪	∪	VERB
ejpam-6067	219	81	(	(	PUNCT
ejpam-6067	219	82	x	x	SYM
ejpam-6067	219	83	\	\	PROPN
ejpam-6067	219	84	u	u	NOUN
ejpam-6067	219	85	)	)	PUNCT
ejpam-6067	219	86	}	}	PUNCT
ejpam-6067	219	87	.	.	PUNCT
ejpam-6067	220	1	therefore	therefore	ADV
ejpam-6067	220	2	,	,	PUNCT
ejpam-6067	220	3	{	{	PUNCT
ejpam-6067	220	4	gα1	gα1	NOUN
ejpam-6067	220	5	∩	∩	ADJ
ejpam-6067	220	6	u	u	NOUN
ejpam-6067	220	7	,	,	PUNCT
ejpam-6067	220	8	gα2	gα2	PROPN
ejpam-6067	220	9	∩	∩	ADJ
ejpam-6067	220	10	u	u	NOUN
ejpam-6067	220	11	,	,	PUNCT
ejpam-6067	220	12	...	...	PUNCT
ejpam-6067	220	13	,	,	PUNCT
ejpam-6067	220	14	gαk	gαk	PROPN
ejpam-6067	220	15	∩	∩	ADJ
ejpam-6067	220	16	u	u	NOUN
ejpam-6067	220	17	}	}	PUNCT
ejpam-6067	220	18	constitutes	constitute	VERB
ejpam-6067	220	19	a	a	DET
ejpam-6067	220	20	finite	finite	NOUN
ejpam-6067	220	21	(	(	PUNCT
ejpam-6067	220	22	and	and	CCONJ
ejpam-6067	220	23	hence	hence	ADV
ejpam-6067	220	24	countable	countable	ADJ
ejpam-6067	220	25	)	)	PUNCT
ejpam-6067	220	26	subcover	subcover	NOUN
ejpam-6067	220	27	of˜for	of˜for	PROPN
ejpam-6067	220	28	u	u	PROPN
ejpam-6067	220	29	,	,	PUNCT
ejpam-6067	220	30	demonstrating	demonstrate	VERB
ejpam-6067	220	31	that	that	SCONJ
ejpam-6067	220	32	u	u	PRON
ejpam-6067	220	33	exhibits	exhibit	VERB
ejpam-6067	220	34	g	g	NOUN
ejpam-6067	220	35	-	-	PUNCT
ejpam-6067	220	36	lindelöfness	lindelöfness	NOUN
ejpam-6067	220	37	.	.	PUNCT
ejpam-6067	220	38	theorem	theorem	NOUN
ejpam-6067	220	39	10	10	NUM
ejpam-6067	220	40	.	.	PUNCT
ejpam-6067	221	1	let	let	VERB
ejpam-6067	221	2	(	(	PUNCT
ejpam-6067	221	3	x	x	NOUN
ejpam-6067	221	4	,	,	PUNCT
ejpam-6067	221	5	τ	τ	X
ejpam-6067	221	6	)	)	PUNCT
ejpam-6067	221	7	be	be	VERB
ejpam-6067	221	8	a	a	DET
ejpam-6067	221	9	topological	topological	ADJ
ejpam-6067	221	10	space	space	NOUN
ejpam-6067	221	11	.	.	PUNCT
ejpam-6067	222	1	the	the	DET
ejpam-6067	222	2	space	space	NOUN
ejpam-6067	222	3	x	x	PUNCT
ejpam-6067	222	4	is	be	AUX
ejpam-6067	222	5	g	g	NOUN
ejpam-6067	222	6	-	-	PUNCT
ejpam-6067	222	7	compact	compact	ADJ
ejpam-6067	222	8	if	if	SCONJ
ejpam-6067	223	1	and	and	CCONJ
ejpam-6067	223	2	only	only	ADV
ejpam-6067	223	3	if	if	SCONJ
ejpam-6067	223	4	each	each	DET
ejpam-6067	223	5	family	family	NOUN
ejpam-6067	223	6	f	f	X
ejpam-6067	223	7	of	of	ADP
ejpam-6067	223	8	fσ	fσ	PROPN
ejpam-6067	223	9	subsets	subset	NOUN
ejpam-6067	223	10	of	of	ADP
ejpam-6067	223	11	x	x	PUNCT
ejpam-6067	223	12	with	with	ADP
ejpam-6067	223	13	the	the	DET
ejpam-6067	223	14	finite	finite	ADJ
ejpam-6067	223	15	intersection	intersection	NOUN
ejpam-6067	223	16	property	property	NOUN
ejpam-6067	223	17	has	have	AUX
ejpam-6067	223	18	nonempty	nonempty	ADJ
ejpam-6067	223	19	intersection	intersection	NOUN
ejpam-6067	223	20	.	.	PUNCT
ejpam-6067	224	1	proof	proof	NOUN
ejpam-6067	224	2	.	.	PUNCT
ejpam-6067	225	1	first	first	ADV
ejpam-6067	225	2	suppose	suppose	VERB
ejpam-6067	225	3	that	that	SCONJ
ejpam-6067	225	4	(	(	PUNCT
ejpam-6067	225	5	x	x	X
ejpam-6067	225	6	,	,	PUNCT
ejpam-6067	225	7	τ	τ	X
ejpam-6067	225	8	)	)	PUNCT
ejpam-6067	225	9	is	be	AUX
ejpam-6067	225	10	g	g	NOUN
ejpam-6067	225	11	-	-	PUNCT
ejpam-6067	225	12	compact	compact	ADJ
ejpam-6067	225	13	.	.	PUNCT
ejpam-6067	226	1	if	if	SCONJ
ejpam-6067	226	2	{	{	PUNCT
ejpam-6067	226	3	fα	fα	NOUN
ejpam-6067	226	4	:	:	PUNCT
ejpam-6067	226	5	α	α	PROPN
ejpam-6067	226	6	∈	∈	PROPN
ejpam-6067	226	7	∆	∆	X
ejpam-6067	226	8	}	}	PUNCT
ejpam-6067	226	9	is	be	AUX
ejpam-6067	226	10	a	a	DET
ejpam-6067	226	11	family	family	NOUN
ejpam-6067	226	12	of	of	ADP
ejpam-6067	226	13	fσ	fσ	NOUN
ejpam-6067	226	14	sets	set	NOUN
ejpam-6067	226	15	of	of	ADP
ejpam-6067	226	16	x	x	PUNCT
ejpam-6067	226	17	having	have	VERB
ejpam-6067	226	18	empty	empty	ADJ
ejpam-6067	226	19	intersection	intersection	NOUN
ejpam-6067	226	20	,	,	PUNCT
ejpam-6067	226	21	then	then	ADV
ejpam-6067	226	22	{	{	PUNCT
ejpam-6067	226	23	x\fα	x\fα	PROPN
ejpam-6067	226	24	:	:	PUNCT
ejpam-6067	226	25	α	α	PROPN
ejpam-6067	226	26	∈	∈	PROPN
ejpam-6067	226	27	∆	∆	X
ejpam-6067	226	28	}	}	PUNCT
ejpam-6067	226	29	is	be	AUX
ejpam-6067	226	30	a	a	DET
ejpam-6067	226	31	g	g	PROPN
ejpam-6067	226	32	-cover	-cover	PROPN
ejpam-6067	226	33	of	of	ADP
ejpam-6067	226	34	x.	x.	NOUN
ejpam-6067	226	35	by	by	ADP
ejpam-6067	226	36	gcompactness	gcompactness	PROPN
ejpam-6067	226	37	,	,	PUNCT
ejpam-6067	226	38	there	there	PRON
ejpam-6067	226	39	is	be	VERB
ejpam-6067	226	40	a	a	DET
ejpam-6067	226	41	finite	finite	ADJ
ejpam-6067	226	42	subcover	subcover	PROPN
ejpam-6067	226	43	{	{	PUNCT
ejpam-6067	226	44	x\fα1	x\fα1	PROPN
ejpam-6067	226	45	,	,	PUNCT
ejpam-6067	226	46	x\fα2	x\fα2	NUM
ejpam-6067	226	47	,	,	PUNCT
ejpam-6067	226	48	.	.	PUNCT
ejpam-6067	226	49	.	.	PUNCT
ejpam-6067	226	50	.	.	PUNCT
ejpam-6067	227	1	,	,	PUNCT
ejpam-6067	227	2	x\fαn	x\fαn	PROPN
ejpam-6067	227	3	}	}	PUNCT
ejpam-6067	227	4	and	and	CCONJ
ejpam-6067	227	5	then	then	ADV
ejpam-6067	227	6	n⋂	n⋂	VERB
ejpam-6067	227	7	i=1	i=1	PROPN
ejpam-6067	227	8	fαi	fαi	X
ejpam-6067	227	9	=	=	PUNCT
ejpam-6067	227	10	∅.	∅.	NOUN
ejpam-6067	227	11	so	so	ADV
ejpam-6067	227	12	{	{	PUNCT
ejpam-6067	227	13	fα	fα	PART
ejpam-6067	227	14	:	:	PUNCT
ejpam-6067	227	15	α	α	PROPN
ejpam-6067	227	16	∈	∈	NOUN
ejpam-6067	227	17	∆	∆	PROPN
ejpam-6067	227	18	}	}	PUNCT
ejpam-6067	227	19	does	do	AUX
ejpam-6067	227	20	not	not	PART
ejpam-6067	227	21	have	have	VERB
ejpam-6067	227	22	the	the	DET
ejpam-6067	227	23	finite	finite	ADJ
ejpam-6067	227	24	intersection	intersection	NOUN
ejpam-6067	227	25	property	property	NOUN
ejpam-6067	227	26	which	which	PRON
ejpam-6067	227	27	is	be	AUX
ejpam-6067	227	28	a	a	DET
ejpam-6067	227	29	contradiction	contradiction	NOUN
ejpam-6067	227	30	.	.	PUNCT
ejpam-6067	228	1	conversely	conversely	ADV
ejpam-6067	228	2	,	,	PUNCT
ejpam-6067	228	3	suppose	suppose	VERB
ejpam-6067	228	4	that	that	SCONJ
ejpam-6067	228	5	any	any	DET
ejpam-6067	228	6	family	family	NOUN
ejpam-6067	228	7	of	of	ADP
ejpam-6067	228	8	fσ	fσ	NOUN
ejpam-6067	228	9	sets	set	NOUN
ejpam-6067	228	10	of	of	ADP
ejpam-6067	228	11	x	x	PUNCT
ejpam-6067	228	12	with	with	ADP
ejpam-6067	228	13	the	the	DET
ejpam-6067	228	14	finite	finite	ADJ
ejpam-6067	228	15	intersection	intersection	NOUN
ejpam-6067	228	16	property	property	NOUN
ejpam-6067	228	17	has	have	AUX
ejpam-6067	228	18	nonempty	nonempty	VERB
ejpam-6067	228	19	intersection	intersection	NOUN
ejpam-6067	228	20	and	and	CCONJ
ejpam-6067	228	21	let	let	VERB
ejpam-6067	228	22	g̃	g̃	PROPN
ejpam-6067	228	23	=	=	PUNCT
ejpam-6067	228	24	{	{	PUNCT
ejpam-6067	228	25	gα	gα	NOUN
ejpam-6067	228	26	:	:	PUNCT
ejpam-6067	228	27	α	α	PROPN
ejpam-6067	228	28	∈	∈	PROPN
ejpam-6067	228	29	∆	∆	PROPN
ejpam-6067	228	30	}	}	PUNCT
ejpam-6067	228	31	be	be	AUX
ejpam-6067	228	32	a	a	DET
ejpam-6067	228	33	g	g	NOUN
ejpam-6067	228	34	-cover	-cover	PROPN
ejpam-6067	228	35	of	of	ADP
ejpam-6067	228	36	x	x	PUNCT
ejpam-6067	228	37	with	with	ADP
ejpam-6067	228	38	no	no	DET
ejpam-6067	228	39	finite	finite	PROPN
ejpam-6067	228	40	subcover	subcover	PROPN
ejpam-6067	228	41	.	.	PUNCT
ejpam-6067	229	1	then	then	ADV
ejpam-6067	229	2	x\	x\	PROPN
ejpam-6067	229	3	(	(	PUNCT
ejpam-6067	229	4	gα1	gα1	NOUN
ejpam-6067	229	5	∪gα2	∪gα2	VERB
ejpam-6067	229	6	∪	∪	NOUN
ejpam-6067	229	7	.	.	PUNCT
ejpam-6067	229	8	.	.	PUNCT
ejpam-6067	229	9	.	.	PUNCT
ejpam-6067	230	1	∪gαn	∪gαn	NOUN
ejpam-6067	230	2	)	)	PUNCT
ejpam-6067	230	3	̸=	̸=	PROPN
ejpam-6067	230	4	∅	∅	NOUN
ejpam-6067	230	5	for	for	ADP
ejpam-6067	230	6	each	each	DET
ejpam-6067	230	7	finite	finite	ADJ
ejpam-6067	230	8	collection	collection	NOUN
ejpam-6067	230	9	{	{	PUNCT
ejpam-6067	230	10	gα1	gα1	NOUN
ejpam-6067	230	11	,	,	PUNCT
ejpam-6067	230	12	gα2	gα2	NOUN
ejpam-6067	230	13	,	,	PUNCT
ejpam-6067	230	14	.	.	PUNCT
ejpam-6067	230	15	.	.	PUNCT
ejpam-6067	230	16	.	.	PUNCT
ejpam-6067	231	1	,	,	PUNCT
ejpam-6067	231	2	gαn	gαn	PROPN
ejpam-6067	231	3	}	}	PUNCT
ejpam-6067	231	4	from	from	ADP
ejpam-6067	231	5	g̃	g̃	PROPN
ejpam-6067	231	6	,	,	PUNCT
ejpam-6067	231	7	in	in	ADP
ejpam-6067	231	8	other	other	ADJ
ejpam-6067	231	9	words	word	NOUN
ejpam-6067	231	10	n⋂	n⋂	VERB
ejpam-6067	231	11	i=1	i=1	PROPN
ejpam-6067	231	12	(	(	PUNCT
ejpam-6067	231	13	x\gαi	x\gαi	PROPN
ejpam-6067	231	14	)	)	PUNCT
ejpam-6067	231	15	̸=	̸=	PROPN
ejpam-6067	231	16	∅.	∅.	PRON
ejpam-6067	231	17	hence	hence	ADV
ejpam-6067	231	18	,	,	PUNCT
ejpam-6067	231	19	we	we	PRON
ejpam-6067	231	20	conclude	conclude	VERB
ejpam-6067	231	21	that	that	SCONJ
ejpam-6067	231	22	the	the	DET
ejpam-6067	231	23	collection	collection	NOUN
ejpam-6067	231	24	{	{	PUNCT
ejpam-6067	231	25	x\gα	x\gα	PROPN
ejpam-6067	231	26	:	:	PUNCT
ejpam-6067	231	27	α	α	PROPN
ejpam-6067	231	28	∈	∈	PROPN
ejpam-6067	231	29	∆	∆	X
ejpam-6067	231	30	}	}	PUNCT
ejpam-6067	231	31	is	be	AUX
ejpam-6067	231	32	a	a	DET
ejpam-6067	231	33	family	family	NOUN
ejpam-6067	231	34	of	of	ADP
ejpam-6067	231	35	fσ	fσ	NOUN
ejpam-6067	231	36	sets	set	NOUN
ejpam-6067	231	37	of	of	ADP
ejpam-6067	231	38	x	x	PUNCT
ejpam-6067	231	39	that	that	PRON
ejpam-6067	231	40	has	have	VERB
ejpam-6067	231	41	the	the	DET
ejpam-6067	231	42	finite	finite	ADJ
ejpam-6067	231	43	intersection	intersection	NOUN
ejpam-6067	231	44	property	property	NOUN
ejpam-6067	231	45	.	.	PUNCT
ejpam-6067	232	1	therefore	therefore	ADV
ejpam-6067	232	2	,	,	PUNCT
ejpam-6067	232	3	we	we	PRON
ejpam-6067	232	4	get	get	VERB
ejpam-6067	232	5	⋂	⋂	PROPN
ejpam-6067	232	6	α∈∆	α∈∆	X
ejpam-6067	232	7	(	(	PUNCT
ejpam-6067	232	8	x\gα	x\gα	PROPN
ejpam-6067	232	9	)	)	PUNCT
ejpam-6067	232	10	̸=	̸=	NOUN
ejpam-6067	232	11	∅	∅	NOUN
ejpam-6067	232	12	,	,	PUNCT
ejpam-6067	232	13	and	and	CCONJ
ejpam-6067	232	14	hence	hence	ADV
ejpam-6067	232	15	,	,	PUNCT
ejpam-6067	232	16	g̃	g̃	PROPN
ejpam-6067	232	17	is	be	AUX
ejpam-6067	232	18	not	not	PART
ejpam-6067	232	19	a	a	DET
ejpam-6067	232	20	cover	cover	NOUN
ejpam-6067	232	21	for	for	ADP
ejpam-6067	232	22	x	x	SYM
ejpam-6067	232	23	which	which	PRON
ejpam-6067	232	24	is	be	AUX
ejpam-6067	232	25	a	a	DET
ejpam-6067	232	26	contradiction	contradiction	NOUN
ejpam-6067	232	27	.	.	PUNCT
ejpam-6067	233	1	theorem	theorem	VERB
ejpam-6067	233	2	11	11	NUM
ejpam-6067	233	3	.	.	PUNCT
ejpam-6067	234	1	the	the	DET
ejpam-6067	234	2	continuous	continuous	ADJ
ejpam-6067	234	3	image	image	NOUN
ejpam-6067	234	4	of	of	ADP
ejpam-6067	234	5	a	a	DET
ejpam-6067	234	6	g	g	NOUN
ejpam-6067	234	7	-	-	PUNCT
ejpam-6067	234	8	compact	compact	ADJ
ejpam-6067	234	9	space	space	NOUN
ejpam-6067	234	10	is	be	AUX
ejpam-6067	234	11	g	g	NOUN
ejpam-6067	234	12	-	-	PUNCT
ejpam-6067	234	13	compact	compact	ADJ
ejpam-6067	234	14	.	.	PUNCT
ejpam-6067	235	1	proof	proof	NOUN
ejpam-6067	235	2	.	.	PUNCT
ejpam-6067	236	1	suppose	suppose	VERB
ejpam-6067	236	2	x	x	PRON
ejpam-6067	236	3	is	be	AUX
ejpam-6067	236	4	g	g	NOUN
ejpam-6067	236	5	-	-	PUNCT
ejpam-6067	236	6	compact	compact	ADJ
ejpam-6067	236	7	space	space	NOUN
ejpam-6067	236	8	and	and	CCONJ
ejpam-6067	236	9	h	h	NOUN
ejpam-6067	236	10	is	be	AUX
ejpam-6067	236	11	a	a	DET
ejpam-6067	236	12	continuous	continuous	ADJ
ejpam-6067	236	13	map	map	NOUN
ejpam-6067	236	14	of	of	ADP
ejpam-6067	236	15	x	x	PUNCT
ejpam-6067	236	16	onto	onto	ADP
ejpam-6067	236	17	y	y	PROPN
ejpam-6067	236	18	.	.	PUNCT
ejpam-6067	237	1	if	if	SCONJ
ejpam-6067	237	2	g̃	g̃	PROPN
ejpam-6067	237	3	=	=	PUNCT
ejpam-6067	237	4	{	{	PUNCT
ejpam-6067	237	5	gα	gα	NOUN
ejpam-6067	237	6	:	:	PUNCT
ejpam-6067	237	7	α	α	PROPN
ejpam-6067	237	8	∈	∈	PROPN
ejpam-6067	237	9	∆	∆	PROPN
ejpam-6067	237	10	}	}	PUNCT
ejpam-6067	237	11	be	be	AUX
ejpam-6067	237	12	a	a	DET
ejpam-6067	237	13	g	g	PROPN
ejpam-6067	237	14	-cover	-cover	PROPN
ejpam-6067	237	15	of	of	ADP
ejpam-6067	237	16	y	y	PROPN
ejpam-6067	237	17	,	,	PUNCT
ejpam-6067	237	18	then	then	ADV
ejpam-6067	237	19	{	{	PUNCT
ejpam-6067	237	20	h−1	h−1	INTJ
ejpam-6067	237	21	(	(	PUNCT
ejpam-6067	237	22	gα	gα	NOUN
ejpam-6067	237	23	)	)	PUNCT
ejpam-6067	237	24	:	:	PUNCT
ejpam-6067	237	25	α	α	PROPN
ejpam-6067	237	26	∈	∈	PROPN
ejpam-6067	237	27	∆	∆	X
ejpam-6067	237	28	}	}	PUNCT
ejpam-6067	237	29	is	be	AUX
ejpam-6067	237	30	a	a	DET
ejpam-6067	237	31	g	g	NOUN
ejpam-6067	237	32	-cover	-cover	PROPN
ejpam-6067	237	33	of	of	ADP
ejpam-6067	237	34	x	x	X
ejpam-6067	237	35	and	and	CCONJ
ejpam-6067	237	36	by	by	ADP
ejpam-6067	237	37	g	g	NOUN
ejpam-6067	237	38	-	-	PUNCT
ejpam-6067	237	39	compactness	compactness	NOUN
ejpam-6067	237	40	,	,	PUNCT
ejpam-6067	237	41	a	a	DET
ejpam-6067	237	42	finite	finite	ADJ
ejpam-6067	237	43	subcover	subcover	PROPN
ejpam-6067	237	44	exists	exist	VERB
ejpam-6067	237	45	,	,	PUNCT
ejpam-6067	237	46	say	say	VERB
ejpam-6067	237	47	{	{	PUNCT
ejpam-6067	237	48	h−1	h−1	INTJ
ejpam-6067	237	49	(	(	PUNCT
ejpam-6067	237	50	gα1	gα1	NOUN
ejpam-6067	237	51	)	)	PUNCT
ejpam-6067	237	52	,	,	PUNCT
ejpam-6067	238	1	h−1	h−1	PROPN
ejpam-6067	238	2	(	(	PUNCT
ejpam-6067	238	3	gα2	gα2	NOUN
ejpam-6067	238	4	)	)	PUNCT
ejpam-6067	238	5	,	,	PUNCT
ejpam-6067	238	6	.	.	PUNCT
ejpam-6067	238	7	.	.	PUNCT
ejpam-6067	238	8	.	.	PUNCT
ejpam-6067	239	1	,	,	PUNCT
ejpam-6067	239	2	h−1	h−1	PROPN
ejpam-6067	239	3	(	(	PUNCT
ejpam-6067	239	4	gαn	gαn	PROPN
ejpam-6067	239	5	)	)	PUNCT
ejpam-6067	239	6	}	}	PUNCT
ejpam-6067	239	7	.	.	PUNCT
ejpam-6067	240	1	then	then	ADV
ejpam-6067	240	2	,	,	PUNCT
ejpam-6067	240	3	since	since	SCONJ
ejpam-6067	240	4	h	h	NOUN
ejpam-6067	240	5	is	be	AUX
ejpam-6067	240	6	onto	onto	ADP
ejpam-6067	240	7	,	,	PUNCT
ejpam-6067	240	8	the	the	DET
ejpam-6067	240	9	sets	set	NOUN
ejpam-6067	240	10	gα1	gα1	NOUN
ejpam-6067	240	11	,	,	PUNCT
ejpam-6067	240	12	gα2	gα2	NOUN
ejpam-6067	240	13	,	,	PUNCT
ejpam-6067	240	14	.	.	PUNCT
ejpam-6067	240	15	.	.	PUNCT
ejpam-6067	240	16	.	.	PUNCT
ejpam-6067	241	1	,	,	PUNCT
ejpam-6067	241	2	gαn	gαn	PROPN
ejpam-6067	241	3	covers	cover	VERB
ejpam-6067	241	4	y	y	PROPN
ejpam-6067	241	5	.	.	PUNCT
ejpam-6067	242	1	thus	thus	ADV
ejpam-6067	242	2	y	y	PROPN
ejpam-6067	242	3	is	be	AUX
ejpam-6067	242	4	g	g	NOUN
ejpam-6067	242	5	-	-	PUNCT
ejpam-6067	242	6	compact	compact	ADJ
ejpam-6067	242	7	space	space	NOUN
ejpam-6067	242	8	.	.	PUNCT
ejpam-6067	243	1	remark	remark	PROPN
ejpam-6067	243	2	4	4	NUM
ejpam-6067	243	3	.	.	PUNCT
ejpam-6067	244	1	paracompact	paracompact	NOUN
ejpam-6067	244	2	spaces	space	NOUN
ejpam-6067	244	3	need	need	AUX
ejpam-6067	244	4	not	not	PART
ejpam-6067	244	5	be	be	AUX
ejpam-6067	244	6	g	g	NOUN
ejpam-6067	244	7	-	-	PUNCT
ejpam-6067	244	8	compact	compact	ADJ
ejpam-6067	244	9	spaces	space	NOUN
ejpam-6067	244	10	.	.	PUNCT
ejpam-6067	245	1	to	to	PART
ejpam-6067	245	2	show	show	VERB
ejpam-6067	245	3	that	that	SCONJ
ejpam-6067	245	4	we	we	PRON
ejpam-6067	245	5	have	have	VERB
ejpam-6067	245	6	the	the	DET
ejpam-6067	245	7	following	follow	VERB
ejpam-6067	245	8	example	example	NOUN
ejpam-6067	245	9	:	:	PUNCT
ejpam-6067	245	10	m.	m.	NOUN
ejpam-6067	245	11	shatnawi	shatnawi	PROPN
ejpam-6067	245	12	et	et	PROPN
ejpam-6067	245	13	al	al	PROPN
ejpam-6067	245	14	.	.	PUNCT
ejpam-6067	245	15	/	/	SYM
ejpam-6067	245	16	eur	eur	PROPN
ejpam-6067	245	17	.	.	PUNCT
ejpam-6067	246	1	j.	j.	PROPN
ejpam-6067	246	2	pure	pure	PROPN
ejpam-6067	246	3	appl	appl	PROPN
ejpam-6067	246	4	.	.	PROPN
ejpam-6067	246	5	math	math	PROPN
ejpam-6067	246	6	,	,	PUNCT
ejpam-6067	246	7	18	18	NUM
ejpam-6067	246	8	(	(	PUNCT
ejpam-6067	246	9	3	3	NUM
ejpam-6067	246	10	)	)	PUNCT
ejpam-6067	246	11	(	(	PUNCT
ejpam-6067	246	12	2025	2025	NUM
ejpam-6067	246	13	)	)	PUNCT
ejpam-6067	246	14	,	,	PUNCT
ejpam-6067	246	15	6067	6067	NUM
ejpam-6067	246	16	10	10	NUM
ejpam-6067	246	17	of	of	ADP
ejpam-6067	246	18	16	16	NUM
ejpam-6067	246	19	example	example	NOUN
ejpam-6067	246	20	6	6	NUM
ejpam-6067	246	21	.	.	PUNCT
ejpam-6067	246	22	consider	consider	VERB
ejpam-6067	246	23	the	the	DET
ejpam-6067	246	24	sorgenfrey	sorgenfrey	ADJ
ejpam-6067	246	25	line	line	NOUN
ejpam-6067	246	26	rℓ	rℓ	PROPN
ejpam-6067	246	27	(	(	PUNCT
ejpam-6067	246	28	the	the	DET
ejpam-6067	246	29	real	real	ADJ
ejpam-6067	246	30	line	line	NOUN
ejpam-6067	246	31	with	with	ADP
ejpam-6067	246	32	the	the	DET
ejpam-6067	246	33	lower	low	ADJ
ejpam-6067	246	34	limit	limit	NOUN
ejpam-6067	246	35	topology	topology	NOUN
ejpam-6067	246	36	)	)	PUNCT
ejpam-6067	246	37	.	.	PUNCT
ejpam-6067	247	1	this	this	DET
ejpam-6067	247	2	space	space	NOUN
ejpam-6067	247	3	demonstrates	demonstrate	VERB
ejpam-6067	247	4	paracompactness	paracompactness	NOUN
ejpam-6067	247	5	but	but	CCONJ
ejpam-6067	247	6	lacks	lack	VERB
ejpam-6067	247	7	g	g	NOUN
ejpam-6067	247	8	-	-	PUNCT
ejpam-6067	247	9	compactness	compactness	NOUN
ejpam-6067	247	10	.	.	PUNCT
ejpam-6067	248	1	proof	proof	NOUN
ejpam-6067	248	2	.	.	PUNCT
ejpam-6067	249	1	researchers	researcher	NOUN
ejpam-6067	249	2	have	have	AUX
ejpam-6067	249	3	established	establish	VERB
ejpam-6067	249	4	that	that	DET
ejpam-6067	249	5	rℓ	rℓ	NOUN
ejpam-6067	249	6	exhibits	exhibit	NOUN
ejpam-6067	249	7	paracompactness	paracompactness	NOUN
ejpam-6067	249	8	,	,	PUNCT
ejpam-6067	249	9	as	as	SCONJ
ejpam-6067	249	10	shown	show	VERB
ejpam-6067	249	11	in	in	ADP
ejpam-6067	249	12	[	[	X
ejpam-6067	249	13	2	2	NUM
ejpam-6067	249	14	]	]	PUNCT
ejpam-6067	249	15	.	.	PUNCT
ejpam-6067	250	1	to	to	PART
ejpam-6067	250	2	prove	prove	VERB
ejpam-6067	250	3	it	it	PRON
ejpam-6067	250	4	lacks	lack	VERB
ejpam-6067	250	5	g	g	NOUN
ejpam-6067	250	6	-	-	PUNCT
ejpam-6067	250	7	compactness	compactness	NOUN
ejpam-6067	250	8	,	,	PUNCT
ejpam-6067	250	9	we	we	PRON
ejpam-6067	250	10	observe	observe	VERB
ejpam-6067	250	11	that	that	SCONJ
ejpam-6067	250	12	for	for	ADP
ejpam-6067	250	13	any	any	DET
ejpam-6067	250	14	x	x	SYM
ejpam-6067	250	15	∈	∈	PROPN
ejpam-6067	250	16	r	r	NOUN
ejpam-6067	250	17	,	,	PUNCT
ejpam-6067	250	18	the	the	DET
ejpam-6067	250	19	singleton	singleton	NOUN
ejpam-6067	250	20	{	{	PUNCT
ejpam-6067	250	21	x	x	NOUN
ejpam-6067	250	22	}	}	PUNCT
ejpam-6067	250	23	forms	form	NOUN
ejpam-6067	250	24	a	a	DET
ejpam-6067	250	25	gδ	gδ	NOUN
ejpam-6067	250	26	set	set	NOUN
ejpam-6067	250	27	since	since	SCONJ
ejpam-6067	250	28	{	{	PUNCT
ejpam-6067	250	29	x	x	NOUN
ejpam-6067	250	30	}	}	PUNCT
ejpam-6067	250	31	=	=	SYM
ejpam-6067	250	32	∞⋂	∞⋂	NOUN
ejpam-6067	250	33	n=1	n=1	PUNCT
ejpam-6067	251	1	[	[	X
ejpam-6067	251	2	x	x	X
ejpam-6067	251	3	,	,	PUNCT
ejpam-6067	251	4	x+	x+	NUM
ejpam-6067	251	5	1	1	NUM
ejpam-6067	251	6	n	n	NOUN
ejpam-6067	251	7	)	)	PUNCT
ejpam-6067	251	8	hence	hence	ADV
ejpam-6067	251	9	,	,	PUNCT
ejpam-6067	251	10	the	the	DET
ejpam-6067	251	11	collection	collection	NOUN
ejpam-6067	251	12	{	{	PUNCT
ejpam-6067	251	13	{	{	PUNCT
ejpam-6067	251	14	x	x	NOUN
ejpam-6067	251	15	}	}	PUNCT
ejpam-6067	251	16	:	:	PUNCT
ejpam-6067	251	17	x	x	X
ejpam-6067	251	18	∈	∈	NOUN
ejpam-6067	251	19	r	r	NOUN
ejpam-6067	251	20	}	}	PUNCT
ejpam-6067	251	21	creates	create	VERB
ejpam-6067	251	22	a	a	DET
ejpam-6067	251	23	g	g	NOUN
ejpam-6067	251	24	-	-	PUNCT
ejpam-6067	251	25	cover	cover	NOUN
ejpam-6067	251	26	of	of	ADP
ejpam-6067	251	27	rℓ	rℓ	NOUN
ejpam-6067	251	28	that	that	PRON
ejpam-6067	251	29	has	have	VERB
ejpam-6067	251	30	no	no	DET
ejpam-6067	251	31	finite	finite	PROPN
ejpam-6067	251	32	subcover	subcover	PROPN
ejpam-6067	251	33	.	.	PUNCT
ejpam-6067	252	1	therefore	therefore	ADV
ejpam-6067	252	2	,	,	PUNCT
ejpam-6067	252	3	rℓ	rℓ	NOUN
ejpam-6067	252	4	lacks	lack	VERB
ejpam-6067	252	5	g	g	NOUN
ejpam-6067	252	6	-	-	PUNCT
ejpam-6067	252	7	compactness	compactness	NOUN
ejpam-6067	252	8	.	.	PUNCT
ejpam-6067	253	1	theorem	theorem	NOUN
ejpam-6067	253	2	12	12	NUM
ejpam-6067	253	3	.	.	PUNCT
ejpam-6067	254	1	let	let	AUX
ejpam-6067	254	2	{	{	PUNCT
ejpam-6067	254	3	xα	xα	INTJ
ejpam-6067	254	4	:	:	PUNCT
ejpam-6067	254	5	α	α	PROPN
ejpam-6067	254	6	∈	∈	PROPN
ejpam-6067	254	7	λ	λ	PROPN
ejpam-6067	254	8	}	}	PUNCT
ejpam-6067	254	9	represent	represent	VERB
ejpam-6067	254	10	a	a	DET
ejpam-6067	254	11	family	family	NOUN
ejpam-6067	254	12	of	of	ADP
ejpam-6067	254	13	topological	topological	ADJ
ejpam-6067	254	14	spaces	space	NOUN
ejpam-6067	254	15	.	.	PUNCT
ejpam-6067	255	1	if	if	SCONJ
ejpam-6067	255	2	the	the	DET
ejpam-6067	255	3	product	product	NOUN
ejpam-6067	255	4	space	space	NOUN
ejpam-6067	255	5	x	x	PUNCT
ejpam-6067	255	6	=	=	SYM
ejpam-6067	255	7	∏	∏	PROPN
ejpam-6067	255	8	α∈λxα	α∈λxα	PROPN
ejpam-6067	255	9	exhibits	exhibit	VERB
ejpam-6067	255	10	g	g	NOUN
ejpam-6067	255	11	-	-	PUNCT
ejpam-6067	255	12	compactness	compactness	NOUN
ejpam-6067	255	13	,	,	PUNCT
ejpam-6067	255	14	then	then	ADV
ejpam-6067	255	15	each	each	PRON
ejpam-6067	255	16	xα	xα	ADP
ejpam-6067	255	17	demonstrates	demonstrate	VERB
ejpam-6067	255	18	g	g	NOUN
ejpam-6067	255	19	-	-	PUNCT
ejpam-6067	255	20	compactness	compactness	NOUN
ejpam-6067	255	21	.	.	PUNCT
ejpam-6067	256	1	proof	proof	NOUN
ejpam-6067	256	2	.	.	PUNCT
ejpam-6067	257	1	let	let	VERB
ejpam-6067	257	2	x	x	SYM
ejpam-6067	257	3	=	=	SYM
ejpam-6067	257	4	∏	∏	PROPN
ejpam-6067	257	5	α∈λxα	α∈λxα	PROPN
ejpam-6067	257	6	exhibit	exhibit	VERB
ejpam-6067	257	7	g	g	NOUN
ejpam-6067	257	8	-	-	PUNCT
ejpam-6067	257	9	compactness	compactness	NOUN
ejpam-6067	257	10	and	and	CCONJ
ejpam-6067	257	11	fix	fix	VERB
ejpam-6067	257	12	β	β	X
ejpam-6067	257	13	∈	∈	PROPN
ejpam-6067	257	14	λ	λ	PROPN
ejpam-6067	257	15	.	.	PUNCT
ejpam-6067	257	16	consider	consider	VERB
ejpam-6067	257	17	a	a	DET
ejpam-6067	257	18	g	g	NOUN
ejpam-6067	257	19	-	-	PUNCT
ejpam-6067	257	20	cover	cover	NOUN
ejpam-6067	257	21	g̃	g̃	PROPN
ejpam-6067	257	22	=	=	PUNCT
ejpam-6067	257	23	{	{	PUNCT
ejpam-6067	257	24	gi	gi	INTJ
ejpam-6067	257	25	:	:	PUNCT
ejpam-6067	257	26	i	i	PRON
ejpam-6067	257	27	∈	∈	VERB
ejpam-6067	258	1	i	i	PRON
ejpam-6067	258	2	}	}	PUNCT
ejpam-6067	258	3	of	of	ADP
ejpam-6067	258	4	xβ	xβ	PROPN
ejpam-6067	258	5	.	.	PUNCT
ejpam-6067	259	1	for	for	ADP
ejpam-6067	259	2	each	each	DET
ejpam-6067	259	3	gi	gi	NOUN
ejpam-6067	259	4	,	,	PUNCT
ejpam-6067	259	5	define	define	VERB
ejpam-6067	259	6	g̃i	g̃i	NOUN
ejpam-6067	259	7	=	=	SYM
ejpam-6067	259	8	π−1	π−1	ADJ
ejpam-6067	259	9	β	β	X
ejpam-6067	259	10	(	(	PUNCT
ejpam-6067	259	11	gi	gi	INTJ
ejpam-6067	259	12	)	)	PUNCT
ejpam-6067	259	13	,	,	PUNCT
ejpam-6067	259	14	where	where	SCONJ
ejpam-6067	259	15	πβ	πβ	PRON
ejpam-6067	259	16	denotes	denote	VERB
ejpam-6067	259	17	the	the	DET
ejpam-6067	259	18	projection	projection	NOUN
ejpam-6067	259	19	map	map	NOUN
ejpam-6067	259	20	from	from	ADP
ejpam-6067	259	21	x	x	PROPN
ejpam-6067	259	22	onto	onto	ADP
ejpam-6067	259	23	xβ	xβ	PROPN
ejpam-6067	259	24	.	.	PUNCT
ejpam-6067	260	1	since	since	SCONJ
ejpam-6067	260	2	πβ	πβ	NOUN
ejpam-6067	260	3	maintains	maintain	VERB
ejpam-6067	260	4	continuity	continuity	NOUN
ejpam-6067	260	5	and	and	CCONJ
ejpam-6067	260	6	gi	gi	NOUN
ejpam-6067	260	7	forms	form	NOUN
ejpam-6067	260	8	a	a	DET
ejpam-6067	260	9	gδ	gδ	NOUN
ejpam-6067	260	10	set	set	VERB
ejpam-6067	260	11	in	in	ADP
ejpam-6067	260	12	xβ	xβ	PROPN
ejpam-6067	260	13	,	,	PUNCT
ejpam-6067	260	14	g̃i	g̃i	NOUN
ejpam-6067	260	15	constitutes	constitute	VERB
ejpam-6067	260	16	a	a	DET
ejpam-6067	260	17	gδ	gδ	NOUN
ejpam-6067	260	18	set	set	VERB
ejpam-6067	260	19	in	in	ADP
ejpam-6067	260	20	x.	x.	NOUN
ejpam-6067	260	21	the	the	DET
ejpam-6067	260	22	collection	collection	NOUN
ejpam-6067	260	23	{	{	PUNCT
ejpam-6067	260	24	g̃i	g̃i	NOUN
ejpam-6067	260	25	:	:	PUNCT
ejpam-6067	260	26	i	i	PRON
ejpam-6067	260	27	∈	∈	VERB
ejpam-6067	261	1	i	i	PRON
ejpam-6067	261	2	}	}	PUNCT
ejpam-6067	261	3	creates	create	VERB
ejpam-6067	261	4	a	a	DET
ejpam-6067	261	5	g	g	NOUN
ejpam-6067	261	6	-	-	PUNCT
ejpam-6067	261	7	cover	cover	NOUN
ejpam-6067	261	8	ofx	ofx	NOUN
ejpam-6067	261	9	.	.	PUNCT
ejpam-6067	262	1	sincex	sincex	PROPN
ejpam-6067	262	2	exhibits	exhibit	VERB
ejpam-6067	262	3	g	g	NOUN
ejpam-6067	262	4	-	-	PUNCT
ejpam-6067	262	5	compactness	compactness	NOUN
ejpam-6067	262	6	,	,	PUNCT
ejpam-6067	262	7	we	we	PRON
ejpam-6067	262	8	find	find	VERB
ejpam-6067	262	9	a	a	DET
ejpam-6067	262	10	finite	finite	ADJ
ejpam-6067	262	11	subcover	subcover	PROPN
ejpam-6067	262	12	{	{	PUNCT
ejpam-6067	262	13	g̃i1	g̃i1	PROPN
ejpam-6067	262	14	,	,	PUNCT
ejpam-6067	262	15	g̃i2	g̃i2	PROPN
ejpam-6067	262	16	,	,	PUNCT
ejpam-6067	262	17	.	.	PUNCT
ejpam-6067	262	18	.	.	PUNCT
ejpam-6067	263	1	.	.	PUNCT
ejpam-6067	264	1	,	,	PUNCT
ejpam-6067	264	2	g̃in	g̃in	PROPN
ejpam-6067	264	3	}	}	PUNCT
ejpam-6067	264	4	.	.	PUNCT
ejpam-6067	265	1	then	then	ADV
ejpam-6067	265	2	{	{	PUNCT
ejpam-6067	265	3	gi1	gi1	INTJ
ejpam-6067	265	4	,	,	PUNCT
ejpam-6067	265	5	gi2	gi2	NOUN
ejpam-6067	265	6	,	,	PUNCT
ejpam-6067	265	7	.	.	PUNCT
ejpam-6067	265	8	.	.	PUNCT
ejpam-6067	265	9	.	.	PUNCT
ejpam-6067	266	1	,	,	PUNCT
ejpam-6067	266	2	gin	gin	NOUN
ejpam-6067	266	3	}	}	PUNCT
ejpam-6067	266	4	forms	form	VERB
ejpam-6067	266	5	a	a	DET
ejpam-6067	266	6	finite	finite	ADJ
ejpam-6067	266	7	subcover	subcover	NOUN
ejpam-6067	266	8	of	of	ADP
ejpam-6067	266	9	g̃	g̃	PROPN
ejpam-6067	266	10	for	for	ADP
ejpam-6067	266	11	xβ	xβ	PROPN
ejpam-6067	266	12	,	,	PUNCT
ejpam-6067	266	13	proving	prove	VERB
ejpam-6067	266	14	that	that	PRON
ejpam-6067	266	15	xβ	xβ	ADV
ejpam-6067	266	16	exhibits	exhibit	VERB
ejpam-6067	266	17	g	g	NOUN
ejpam-6067	266	18	-	-	PUNCT
ejpam-6067	266	19	compactness	compactness	NOUN
ejpam-6067	266	20	.	.	PUNCT
ejpam-6067	267	1	theorem	theorem	VERB
ejpam-6067	267	2	13	13	NUM
ejpam-6067	267	3	.	.	PUNCT
ejpam-6067	268	1	let	let	VERB
ejpam-6067	268	2	(	(	PUNCT
ejpam-6067	268	3	x	x	NOUN
ejpam-6067	268	4	,	,	PUNCT
ejpam-6067	268	5	τ	τ	X
ejpam-6067	268	6	)	)	PUNCT
ejpam-6067	268	7	represent	represent	VERB
ejpam-6067	268	8	a	a	DET
ejpam-6067	268	9	topological	topological	ADJ
ejpam-6067	268	10	space	space	NOUN
ejpam-6067	268	11	.	.	PUNCT
ejpam-6067	269	1	if	if	SCONJ
ejpam-6067	269	2	x	x	PRON
ejpam-6067	269	3	demonstrates	demonstrate	VERB
ejpam-6067	269	4	metrizability	metrizability	NOUN
ejpam-6067	269	5	and	and	CCONJ
ejpam-6067	269	6	separability	separability	NOUN
ejpam-6067	269	7	,	,	PUNCT
ejpam-6067	269	8	then	then	ADV
ejpam-6067	269	9	x	x	PUNCT
ejpam-6067	269	10	exhibits	exhibit	VERB
ejpam-6067	269	11	g	g	NOUN
ejpam-6067	269	12	-	-	PUNCT
ejpam-6067	269	13	lindelöfness	lindelöfness	NOUN
ejpam-6067	269	14	if	if	SCONJ
ejpam-6067	270	1	and	and	CCONJ
ejpam-6067	270	2	only	only	ADV
ejpam-6067	270	3	if	if	SCONJ
ejpam-6067	270	4	x	x	PRON
ejpam-6067	270	5	demonstrates	demonstrate	VERB
ejpam-6067	270	6	second	second	ADJ
ejpam-6067	270	7	countability	countability	NOUN
ejpam-6067	270	8	.	.	PUNCT
ejpam-6067	271	1	proof	proof	NOUN
ejpam-6067	271	2	.	.	PUNCT
ejpam-6067	272	1	suppose	suppose	VERB
ejpam-6067	272	2	x	x	PRON
ejpam-6067	272	3	constitutes	constitute	VERB
ejpam-6067	272	4	a	a	DET
ejpam-6067	272	5	metrizable	metrizable	ADJ
ejpam-6067	272	6	,	,	PUNCT
ejpam-6067	272	7	separable	separable	ADJ
ejpam-6067	272	8	space	space	NOUN
ejpam-6067	272	9	exhibiting	exhibit	VERB
ejpam-6067	272	10	g	g	NOUN
ejpam-6067	272	11	-	-	PUNCT
ejpam-6067	272	12	lindelöfness	lindelöfness	NOUN
ejpam-6067	272	13	.	.	PUNCT
ejpam-6067	273	1	let	let	VERB
ejpam-6067	273	2	{	{	PUNCT
ejpam-6067	273	3	xn	xn	NOUN
ejpam-6067	273	4	:	:	PUNCT
ejpam-6067	273	5	n	n	CCONJ
ejpam-6067	273	6	∈	∈	PROPN
ejpam-6067	273	7	n	n	CCONJ
ejpam-6067	273	8	}	}	PUNCT
ejpam-6067	273	9	form	form	VERB
ejpam-6067	273	10	a	a	DET
ejpam-6067	273	11	countable	countable	ADJ
ejpam-6067	273	12	dense	dense	ADJ
ejpam-6067	273	13	subset	subset	NOUN
ejpam-6067	273	14	of	of	ADP
ejpam-6067	273	15	x.	x.	NOUN
ejpam-6067	273	16	for	for	ADP
ejpam-6067	273	17	each	each	DET
ejpam-6067	273	18	pair	pair	NOUN
ejpam-6067	273	19	of	of	ADP
ejpam-6067	273	20	rational	rational	ADJ
ejpam-6067	273	21	numbers	number	NOUN
ejpam-6067	273	22	p	p	NOUN
ejpam-6067	273	23	,	,	PUNCT
ejpam-6067	273	24	q	q	NOUN
ejpam-6067	273	25	with	with	ADP
ejpam-6067	273	26	p	p	X
ejpam-6067	273	27	>	>	X
ejpam-6067	273	28	0	0	NUM
ejpam-6067	273	29	,	,	PUNCT
ejpam-6067	273	30	and	and	CCONJ
ejpam-6067	273	31	each	each	DET
ejpam-6067	273	32	n	n	PRON
ejpam-6067	273	33	∈	∈	PROPN
ejpam-6067	273	34	n	n	CCONJ
ejpam-6067	273	35	,	,	PUNCT
ejpam-6067	273	36	define	define	VERB
ejpam-6067	273	37	the	the	DET
ejpam-6067	273	38	open	open	ADJ
ejpam-6067	273	39	ball	ball	NOUN
ejpam-6067	273	40	b(xn	b(xn	PROPN
ejpam-6067	273	41	,	,	PUNCT
ejpam-6067	273	42	p	p	X
ejpam-6067	273	43	)	)	PUNCT
ejpam-6067	273	44	=	=	SYM
ejpam-6067	273	45	{	{	PUNCT
ejpam-6067	273	46	x	x	PUNCT
ejpam-6067	273	47	∈	∈	PROPN
ejpam-6067	273	48	x	x	X
ejpam-6067	273	49	:	:	PUNCT
ejpam-6067	273	50	d(x	d(x	PROPN
ejpam-6067	273	51	,	,	PUNCT
ejpam-6067	273	52	xn	xn	PUNCT
ejpam-6067	273	53	)	)	PUNCT
ejpam-6067	273	54	<	<	X
ejpam-6067	274	1	p	p	X
ejpam-6067	274	2	}	}	PUNCT
ejpam-6067	274	3	.	.	PUNCT
ejpam-6067	275	1	the	the	DET
ejpam-6067	275	2	collection	collection	NOUN
ejpam-6067	275	3	b	b	PROPN
ejpam-6067	275	4	=	=	PUNCT
ejpam-6067	275	5	{	{	PUNCT
ejpam-6067	275	6	b(xn	b(xn	PROPN
ejpam-6067	275	7	,	,	PUNCT
ejpam-6067	275	8	p	p	NOUN
ejpam-6067	275	9	)	)	PUNCT
ejpam-6067	275	10	:	:	PUNCT
ejpam-6067	275	11	n	n	X
ejpam-6067	275	12	∈	∈	PROPN
ejpam-6067	275	13	n	n	CCONJ
ejpam-6067	275	14	,	,	PUNCT
ejpam-6067	275	15	p	p	PROPN
ejpam-6067	275	16	∈	∈	PROPN
ejpam-6067	275	17	q+	q+	ADP
ejpam-6067	275	18	}	}	PUNCT
ejpam-6067	275	19	demonstrates	demonstrate	VERB
ejpam-6067	275	20	countability	countability	NOUN
ejpam-6067	275	21	.	.	PUNCT
ejpam-6067	276	1	we	we	PRON
ejpam-6067	276	2	claim	claim	VERB
ejpam-6067	276	3	that	that	SCONJ
ejpam-6067	276	4	b	b	X
ejpam-6067	276	5	forms	form	VERB
ejpam-6067	276	6	a	a	DET
ejpam-6067	276	7	base	base	NOUN
ejpam-6067	276	8	for	for	ADP
ejpam-6067	276	9	τ	τ	PROPN
ejpam-6067	276	10	.	.	PUNCT
ejpam-6067	277	1	consider	consider	VERB
ejpam-6067	277	2	any	any	DET
ejpam-6067	277	3	open	open	ADJ
ejpam-6067	277	4	set	set	NOUN
ejpam-6067	277	5	u	u	PRON
ejpam-6067	277	6	∈	∈	PROPN
ejpam-6067	277	7	τ	τ	X
ejpam-6067	277	8	and	and	CCONJ
ejpam-6067	277	9	point	point	NOUN
ejpam-6067	277	10	x	x	PUNCT
ejpam-6067	277	11	∈	∈	PROPN
ejpam-6067	277	12	u	u	NOUN
ejpam-6067	277	13	.	.	PUNCT
ejpam-6067	278	1	by	by	ADP
ejpam-6067	278	2	the	the	DET
ejpam-6067	278	3	metric	metric	ADJ
ejpam-6067	278	4	topology	topology	NOUN
ejpam-6067	278	5	’s	’s	PART
ejpam-6067	278	6	definition	definition	NOUN
ejpam-6067	278	7	,	,	PUNCT
ejpam-6067	278	8	we	we	PRON
ejpam-6067	278	9	find	find	VERB
ejpam-6067	278	10	ϵ	ϵ	ADP
ejpam-6067	278	11	>	>	X
ejpam-6067	278	12	0	0	NUM
ejpam-6067	278	13	such	such	ADJ
ejpam-6067	278	14	that	that	DET
ejpam-6067	278	15	b(x	b(x	NOUN
ejpam-6067	278	16	,	,	PUNCT
ejpam-6067	278	17	ϵ	ϵ	X
ejpam-6067	278	18	)	)	PUNCT
ejpam-6067	278	19	⊂	⊂	PROPN
ejpam-6067	278	20	u	u	PROPN
ejpam-6067	278	21	.	.	PUNCT
ejpam-6067	279	1	since	since	SCONJ
ejpam-6067	279	2	{	{	PUNCT
ejpam-6067	279	3	xn	xn	PROPN
ejpam-6067	279	4	:	:	PUNCT
ejpam-6067	279	5	n	n	CCONJ
ejpam-6067	279	6	∈	∈	PROPN
ejpam-6067	279	7	n	n	CCONJ
ejpam-6067	279	8	}	}	PUNCT
ejpam-6067	279	9	demonstrates	demonstrate	VERB
ejpam-6067	279	10	density	density	NOUN
ejpam-6067	279	11	,	,	PUNCT
ejpam-6067	279	12	some	some	DET
ejpam-6067	279	13	xm	xm	PROPN
ejpam-6067	279	14	exists	exist	VERB
ejpam-6067	279	15	such	such	ADJ
ejpam-6067	279	16	that	that	SCONJ
ejpam-6067	279	17	d(x	d(x	PROPN
ejpam-6067	279	18	,	,	PUNCT
ejpam-6067	279	19	xm	xm	PROPN
ejpam-6067	279	20	)	)	PUNCT
ejpam-6067	279	21	<	<	X
ejpam-6067	279	22	ϵ/3	ϵ/3	PROPN
ejpam-6067	279	23	.	.	PUNCT
ejpam-6067	280	1	choose	choose	VERB
ejpam-6067	280	2	a	a	DET
ejpam-6067	280	3	rational	rational	ADJ
ejpam-6067	280	4	number	number	NOUN
ejpam-6067	280	5	p	p	NOUN
ejpam-6067	280	6	such	such	ADJ
ejpam-6067	280	7	that	that	DET
ejpam-6067	280	8	d(x	d(x	PROPN
ejpam-6067	280	9	,	,	PUNCT
ejpam-6067	280	10	xm	xm	PROPN
ejpam-6067	280	11	)	)	PUNCT
ejpam-6067	280	12	<	<	X
ejpam-6067	281	1	p	p	X
ejpam-6067	281	2	<	<	X
ejpam-6067	281	3	ϵ/3	ϵ/3	PROPN
ejpam-6067	281	4	.	.	PUNCT
ejpam-6067	282	1	then	then	ADV
ejpam-6067	282	2	x	x	X
ejpam-6067	282	3	∈	∈	PROPN
ejpam-6067	282	4	b(xm	b(xm	PROPN
ejpam-6067	282	5	,	,	PUNCT
ejpam-6067	282	6	p	p	X
ejpam-6067	282	7	)	)	PUNCT
ejpam-6067	282	8	⊂	⊂	NOUN
ejpam-6067	282	9	b(x	b(x	NOUN
ejpam-6067	282	10	,	,	PUNCT
ejpam-6067	282	11	ϵ	ϵ	X
ejpam-6067	282	12	)	)	PUNCT
ejpam-6067	282	13	⊂	⊂	PROPN
ejpam-6067	282	14	u	u	PROPN
ejpam-6067	282	15	.	.	PUNCT
ejpam-6067	283	1	this	this	PRON
ejpam-6067	283	2	proves	prove	VERB
ejpam-6067	283	3	that	that	SCONJ
ejpam-6067	283	4	b	b	NOUN
ejpam-6067	283	5	constitutes	constitute	VERB
ejpam-6067	283	6	a	a	DET
ejpam-6067	283	7	countable	countable	ADJ
ejpam-6067	283	8	base	base	NOUN
ejpam-6067	283	9	for	for	ADP
ejpam-6067	283	10	x	x	X
ejpam-6067	283	11	,	,	PUNCT
ejpam-6067	283	12	establishing	establish	VERB
ejpam-6067	283	13	x	x	SYM
ejpam-6067	283	14	’s	’s	PART
ejpam-6067	283	15	second	second	ADJ
ejpam-6067	283	16	countability	countability	NOUN
ejpam-6067	283	17	.	.	PUNCT
ejpam-6067	284	1	conversely	conversely	ADV
ejpam-6067	284	2	,	,	PUNCT
ejpam-6067	284	3	suppose	suppose	VERB
ejpam-6067	284	4	x	x	PRON
ejpam-6067	284	5	demonstrates	demonstrate	VERB
ejpam-6067	284	6	metrizability	metrizability	NOUN
ejpam-6067	284	7	and	and	CCONJ
ejpam-6067	284	8	second	second	ADJ
ejpam-6067	284	9	countability	countability	NOUN
ejpam-6067	284	10	.	.	PUNCT
ejpam-6067	285	1	let	let	VERB
ejpam-6067	285	2	b	b	PRON
ejpam-6067	285	3	form	form	VERB
ejpam-6067	285	4	a	a	DET
ejpam-6067	285	5	countable	countable	ADJ
ejpam-6067	285	6	base	base	NOUN
ejpam-6067	285	7	for	for	ADP
ejpam-6067	285	8	τ	τ	PROPN
ejpam-6067	285	9	.	.	PUNCT
ejpam-6067	286	1	every	every	DET
ejpam-6067	286	2	gδ	gδ	NOUN
ejpam-6067	286	3	set	set	VERB
ejpam-6067	286	4	g	g	NOUN
ejpam-6067	286	5	in	in	ADP
ejpam-6067	286	6	x	x	PRON
ejpam-6067	286	7	can	can	AUX
ejpam-6067	286	8	be	be	AUX
ejpam-6067	286	9	expressed	express	VERB
ejpam-6067	286	10	as	as	ADP
ejpam-6067	286	11	g	g	NOUN
ejpam-6067	286	12	=	=	SYM
ejpam-6067	286	13	⋂∞	⋂∞	PROPN
ejpam-6067	286	14	n=1	n=1	PROPN
ejpam-6067	286	15	un	un	PROPN
ejpam-6067	286	16	where	where	SCONJ
ejpam-6067	286	17	each	each	DET
ejpam-6067	286	18	un	un	PROPN
ejpam-6067	286	19	∈	∈	PROPN
ejpam-6067	286	20	τ	τ	X
ejpam-6067	286	21	.	.	PUNCT
ejpam-6067	287	1	but	but	CCONJ
ejpam-6067	287	2	we	we	PRON
ejpam-6067	287	3	can	can	AUX
ejpam-6067	287	4	express	express	VERB
ejpam-6067	287	5	each	each	DET
ejpam-6067	287	6	un	un	PROPN
ejpam-6067	287	7	as	as	ADP
ejpam-6067	287	8	a	a	DET
ejpam-6067	287	9	union	union	NOUN
ejpam-6067	287	10	of	of	ADP
ejpam-6067	287	11	elements	element	NOUN
ejpam-6067	287	12	from	from	ADP
ejpam-6067	287	13	the	the	DET
ejpam-6067	287	14	base	base	PROPN
ejpam-6067	287	15	b.	b.	PROPN
ejpam-6067	287	16	since	since	SCONJ
ejpam-6067	287	17	x	x	PRON
ejpam-6067	287	18	demonstrates	demonstrate	VERB
ejpam-6067	287	19	second	second	ADJ
ejpam-6067	287	20	countability	countability	NOUN
ejpam-6067	287	21	,	,	PUNCT
ejpam-6067	287	22	this	this	PRON
ejpam-6067	287	23	means	mean	VERB
ejpam-6067	287	24	we	we	PRON
ejpam-6067	287	25	find	find	VERB
ejpam-6067	287	26	at	at	ADV
ejpam-6067	287	27	most	most	ADV
ejpam-6067	287	28	countably	countably	ADV
ejpam-6067	287	29	many	many	ADJ
ejpam-6067	287	30	different	different	ADJ
ejpam-6067	287	31	gδ	gδ	NOUN
ejpam-6067	287	32	sets	set	NOUN
ejpam-6067	287	33	in	in	ADP
ejpam-6067	287	34	x.	x.	NOUN
ejpam-6067	287	35	therefore	therefore	ADV
ejpam-6067	287	36	,	,	PUNCT
ejpam-6067	287	37	any	any	DET
ejpam-6067	287	38	g	g	NOUN
ejpam-6067	287	39	-	-	PUNCT
ejpam-6067	287	40	cover	cover	NOUN
ejpam-6067	287	41	of	of	ADP
ejpam-6067	287	42	x	x	PUNCT
ejpam-6067	287	43	contains	contain	VERB
ejpam-6067	287	44	at	at	ADP
ejpam-6067	287	45	most	most	ADJ
ejpam-6067	287	46	countably	countably	ADV
ejpam-6067	287	47	many	many	ADJ
ejpam-6067	287	48	distinct	distinct	ADJ
ejpam-6067	287	49	elements	element	NOUN
ejpam-6067	287	50	,	,	PUNCT
ejpam-6067	287	51	automatically	automatically	ADV
ejpam-6067	287	52	making	make	VERB
ejpam-6067	287	53	x	x	SYM
ejpam-6067	287	54	g	g	NOUN
ejpam-6067	287	55	-	-	PUNCT
ejpam-6067	287	56	lindelöf	lindelöf	NOUN
ejpam-6067	287	57	.	.	PUNCT
ejpam-6067	288	1	m.	m.	NOUN
ejpam-6067	288	2	shatnawi	shatnawi	PROPN
ejpam-6067	288	3	et	et	PROPN
ejpam-6067	288	4	al	al	PROPN
ejpam-6067	288	5	.	.	PUNCT
ejpam-6067	288	6	/	/	SYM
ejpam-6067	288	7	eur	eur	PROPN
ejpam-6067	288	8	.	.	PUNCT
ejpam-6067	289	1	j.	j.	PROPN
ejpam-6067	289	2	pure	pure	PROPN
ejpam-6067	289	3	appl	appl	PROPN
ejpam-6067	289	4	.	.	PROPN
ejpam-6067	289	5	math	math	PROPN
ejpam-6067	289	6	,	,	PUNCT
ejpam-6067	289	7	18	18	NUM
ejpam-6067	289	8	(	(	PUNCT
ejpam-6067	289	9	3	3	NUM
ejpam-6067	289	10	)	)	PUNCT
ejpam-6067	289	11	(	(	PUNCT
ejpam-6067	289	12	2025	2025	NUM
ejpam-6067	289	13	)	)	PUNCT
ejpam-6067	289	14	,	,	PUNCT
ejpam-6067	289	15	6067	6067	NUM
ejpam-6067	289	16	11	11	NUM
ejpam-6067	289	17	of	of	ADP
ejpam-6067	289	18	16	16	NUM
ejpam-6067	289	19	3	3	NUM
ejpam-6067	289	20	.	.	PUNCT
ejpam-6067	290	1	gseparation	gseparation	NOUN
ejpam-6067	290	2	axioms	axioms	PROPN
ejpam-6067	290	3	definition	definition	NOUN
ejpam-6067	290	4	13	13	NUM
ejpam-6067	290	5	.	.	PUNCT
ejpam-6067	291	1	a	a	DET
ejpam-6067	291	2	space	space	NOUN
ejpam-6067	291	3	x	x	PUNCT
ejpam-6067	291	4	is	be	AUX
ejpam-6067	291	5	called	call	VERB
ejpam-6067	291	6	tδ0	tδ0	NOUN
ejpam-6067	291	7	space	space	NOUN
ejpam-6067	291	8	if	if	SCONJ
ejpam-6067	291	9	whenever	whenever	SCONJ
ejpam-6067	291	10	x	x	PRON
ejpam-6067	291	11	and	and	CCONJ
ejpam-6067	291	12	y	y	PROPN
ejpam-6067	291	13	are	be	AUX
ejpam-6067	291	14	distinct	distinct	ADJ
ejpam-6067	291	15	points	point	NOUN
ejpam-6067	291	16	in	in	ADP
ejpam-6067	291	17	x	x	NOUN
ejpam-6067	291	18	,	,	PUNCT
ejpam-6067	291	19	there	there	PRON
ejpam-6067	291	20	is	be	VERB
ejpam-6067	291	21	a	a	DET
ejpam-6067	291	22	gδ	gδ	NOUN
ejpam-6067	291	23	set	set	NOUN
ejpam-6067	291	24	containing	contain	VERB
ejpam-6067	291	25	one	one	NUM
ejpam-6067	291	26	and	and	CCONJ
ejpam-6067	291	27	not	not	PART
ejpam-6067	291	28	the	the	DET
ejpam-6067	291	29	other	other	ADJ
ejpam-6067	291	30	.	.	PUNCT
ejpam-6067	292	1	definition	definition	NOUN
ejpam-6067	292	2	14	14	NUM
ejpam-6067	292	3	.	.	PUNCT
ejpam-6067	293	1	a	a	DET
ejpam-6067	293	2	space	space	NOUN
ejpam-6067	293	3	x	x	PUNCT
ejpam-6067	293	4	is	be	AUX
ejpam-6067	293	5	called	call	VERB
ejpam-6067	293	6	tδ1	tδ1	ADP
ejpam-6067	293	7	space	space	NOUN
ejpam-6067	293	8	if	if	SCONJ
ejpam-6067	293	9	whenever	whenever	SCONJ
ejpam-6067	293	10	x	x	PRON
ejpam-6067	293	11	and	and	CCONJ
ejpam-6067	293	12	y	y	PROPN
ejpam-6067	293	13	are	be	AUX
ejpam-6067	293	14	distinct	distinct	ADJ
ejpam-6067	293	15	points	point	NOUN
ejpam-6067	293	16	in	in	ADP
ejpam-6067	293	17	x	x	NOUN
ejpam-6067	293	18	,	,	PUNCT
ejpam-6067	293	19	there	there	PRON
ejpam-6067	293	20	is	be	VERB
ejpam-6067	293	21	a	a	DET
ejpam-6067	293	22	gδ	gδ	NOUN
ejpam-6067	293	23	sets	set	NOUN
ejpam-6067	293	24	g1	g1	NOUN
ejpam-6067	293	25	and	and	CCONJ
ejpam-6067	293	26	g2	g2	PROPN
ejpam-6067	293	27	such	such	ADJ
ejpam-6067	293	28	that	that	SCONJ
ejpam-6067	293	29	x	x	SYM
ejpam-6067	293	30	∈	∈	PROPN
ejpam-6067	293	31	g1	g1	PROPN
ejpam-6067	293	32	,	,	PUNCT
ejpam-6067	293	33	y	y	PROPN
ejpam-6067	293	34	/∈	/∈	PUNCT
ejpam-6067	293	35	g1	g1	PROPN
ejpam-6067	293	36	and	and	CCONJ
ejpam-6067	293	37	y	y	PROPN
ejpam-6067	293	38	∈	∈	PROPN
ejpam-6067	293	39	g2	g2	PROPN
ejpam-6067	293	40	,	,	PUNCT
ejpam-6067	293	41	x	x	PROPN
ejpam-6067	293	42	/∈	/∈	PUNCT
ejpam-6067	294	1	g2	g2	PROPN
ejpam-6067	294	2	.	.	PUNCT
ejpam-6067	295	1	evidently	evidently	ADV
ejpam-6067	295	2	,	,	PUNCT
ejpam-6067	295	3	every	every	DET
ejpam-6067	295	4	tδ1	tδ1	NOUN
ejpam-6067	295	5	space	space	NOUN
ejpam-6067	295	6	is	be	AUX
ejpam-6067	295	7	tδ0	tδ0	NOUN
ejpam-6067	295	8	.	.	PUNCT
ejpam-6067	296	1	theorem	theorem	VERB
ejpam-6067	296	2	14	14	NUM
ejpam-6067	296	3	.	.	PUNCT
ejpam-6067	297	1	a	a	DET
ejpam-6067	297	2	space	space	NOUN
ejpam-6067	297	3	x	x	PUNCT
ejpam-6067	297	4	is	be	AUX
ejpam-6067	297	5	tδ0	tδ0	NOUN
ejpam-6067	297	6	if	if	SCONJ
ejpam-6067	298	1	and	and	CCONJ
ejpam-6067	298	2	only	only	ADV
ejpam-6067	298	3	if	if	SCONJ
ejpam-6067	298	4	it	it	PRON
ejpam-6067	298	5	is	be	AUX
ejpam-6067	298	6	t0	t0	NOUN
ejpam-6067	298	7	.	.	PUNCT
ejpam-6067	299	1	also	also	ADV
ejpam-6067	299	2	,	,	PUNCT
ejpam-6067	299	3	a	a	DET
ejpam-6067	299	4	space	space	NOUN
ejpam-6067	299	5	x	x	PUNCT
ejpam-6067	299	6	is	be	AUX
ejpam-6067	299	7	tδ1	tδ1	ADV
ejpam-6067	299	8	if	if	SCONJ
ejpam-6067	300	1	and	and	CCONJ
ejpam-6067	300	2	only	only	ADV
ejpam-6067	300	3	if	if	SCONJ
ejpam-6067	300	4	it	it	PRON
ejpam-6067	300	5	is	be	AUX
ejpam-6067	300	6	t1	t1	NOUN
ejpam-6067	300	7	.	.	PUNCT
ejpam-6067	301	1	proof	proof	NOUN
ejpam-6067	301	2	.	.	PUNCT
ejpam-6067	302	1	it	it	PRON
ejpam-6067	302	2	is	be	AUX
ejpam-6067	302	3	easy	easy	ADJ
ejpam-6067	302	4	to	to	PART
ejpam-6067	302	5	show	show	VERB
ejpam-6067	302	6	that	that	SCONJ
ejpam-6067	302	7	a	a	DET
ejpam-6067	302	8	space	space	NOUN
ejpam-6067	302	9	x	x	PUNCT
ejpam-6067	302	10	is	be	AUX
ejpam-6067	302	11	tδ0	tδ0	NOUN
ejpam-6067	302	12	if	if	SCONJ
ejpam-6067	302	13	and	and	CCONJ
ejpam-6067	302	14	only	only	ADV
ejpam-6067	302	15	if	if	SCONJ
ejpam-6067	302	16	it	it	PRON
ejpam-6067	302	17	is	be	AUX
ejpam-6067	302	18	t0	t0	NOUN
ejpam-6067	302	19	.	.	PUNCT
ejpam-6067	303	1	now	now	ADV
ejpam-6067	303	2	,	,	PUNCT
ejpam-6067	303	3	to	to	PART
ejpam-6067	303	4	show	show	VERB
ejpam-6067	303	5	that	that	SCONJ
ejpam-6067	303	6	a	a	DET
ejpam-6067	303	7	space	space	NOUN
ejpam-6067	303	8	x	x	PUNCT
ejpam-6067	303	9	is	be	AUX
ejpam-6067	303	10	tδ1	tδ1	ADV
ejpam-6067	303	11	if	if	SCONJ
ejpam-6067	303	12	and	and	CCONJ
ejpam-6067	303	13	only	only	ADV
ejpam-6067	303	14	if	if	SCONJ
ejpam-6067	303	15	it	it	PRON
ejpam-6067	303	16	is	be	AUX
ejpam-6067	303	17	t1	t1	NOUN
ejpam-6067	303	18	it	it	PRON
ejpam-6067	303	19	is	be	AUX
ejpam-6067	303	20	enough	enough	ADJ
ejpam-6067	303	21	to	to	PART
ejpam-6067	303	22	show	show	VERB
ejpam-6067	303	23	that	that	SCONJ
ejpam-6067	303	24	if	if	SCONJ
ejpam-6067	303	25	x	x	PRON
ejpam-6067	303	26	is	be	AUX
ejpam-6067	303	27	tδ1	tδ1	NOUN
ejpam-6067	303	28	,	,	PUNCT
ejpam-6067	303	29	then	then	ADV
ejpam-6067	303	30	it	it	PRON
ejpam-6067	303	31	is	be	AUX
ejpam-6067	303	32	t1	t1	NOUN
ejpam-6067	303	33	.	.	PUNCT
ejpam-6067	304	1	hence	hence	ADV
ejpam-6067	304	2	,	,	PUNCT
ejpam-6067	304	3	let	let	VERB
ejpam-6067	304	4	x	x	PRON
ejpam-6067	304	5	be	be	AUX
ejpam-6067	304	6	a	a	DET
ejpam-6067	304	7	tδ1	tδ1	NOUN
ejpam-6067	304	8	space	space	NOUN
ejpam-6067	304	9	and	and	CCONJ
ejpam-6067	304	10	let	let	VERB
ejpam-6067	304	11	x	x	PRON
ejpam-6067	304	12	,	,	PUNCT
ejpam-6067	304	13	y	y	PROPN
ejpam-6067	304	14	∈	∈	PROPN
ejpam-6067	304	15	x	x	PUNCT
ejpam-6067	304	16	be	be	AUX
ejpam-6067	304	17	two	two	NUM
ejpam-6067	304	18	distinct	distinct	ADJ
ejpam-6067	304	19	elements	element	NOUN
ejpam-6067	304	20	,	,	PUNCT
ejpam-6067	304	21	since	since	SCONJ
ejpam-6067	304	22	x	x	PRON
ejpam-6067	304	23	is	be	AUX
ejpam-6067	304	24	tδ1	tδ1	ADP
ejpam-6067	304	25	there	there	PRON
ejpam-6067	304	26	are	be	VERB
ejpam-6067	304	27	two	two	NUM
ejpam-6067	304	28	gδ	gδ	NOUN
ejpam-6067	304	29	sets	set	VERB
ejpam-6067	304	30	g1	g1	NOUN
ejpam-6067	304	31	and	and	CCONJ
ejpam-6067	304	32	g2	g2	PROPN
ejpam-6067	304	33	such	such	ADJ
ejpam-6067	304	34	that	that	SCONJ
ejpam-6067	304	35	x	x	SYM
ejpam-6067	304	36	∈	∈	PROPN
ejpam-6067	304	37	g1	g1	PROPN
ejpam-6067	304	38	,	,	PUNCT
ejpam-6067	304	39	y	y	PROPN
ejpam-6067	304	40	/∈	/∈	PUNCT
ejpam-6067	304	41	g1	g1	PROPN
ejpam-6067	304	42	and	and	CCONJ
ejpam-6067	304	43	y	y	PROPN
ejpam-6067	304	44	∈	∈	PROPN
ejpam-6067	304	45	g2	g2	PROPN
ejpam-6067	304	46	,	,	PUNCT
ejpam-6067	304	47	x	x	PROPN
ejpam-6067	304	48	/∈	/∈	PUNCT
ejpam-6067	305	1	g2	g2	PROPN
ejpam-6067	305	2	.	.	PUNCT
ejpam-6067	306	1	by	by	ADP
ejpam-6067	306	2	the	the	DET
ejpam-6067	306	3	definition	definition	NOUN
ejpam-6067	306	4	of	of	ADP
ejpam-6067	306	5	gδ	gδ	NOUN
ejpam-6067	306	6	sets	set	NOUN
ejpam-6067	306	7	assume	assume	VERB
ejpam-6067	306	8	g1	g1	PROPN
ejpam-6067	306	9	=	=	SYM
ejpam-6067	306	10	⋂∞	⋂∞	NOUN
ejpam-6067	306	11	n=1g1n	n=1g1n	PROPN
ejpam-6067	306	12	,	,	PUNCT
ejpam-6067	306	13	g2	g2	PROPN
ejpam-6067	306	14	=	=	PUNCT
ejpam-6067	306	15	⋂∞	⋂∞	NOUN
ejpam-6067	306	16	n=1g2n	n=1g2n	NOUN
ejpam-6067	306	17	where	where	SCONJ
ejpam-6067	306	18	g1n	g1n	VERB
ejpam-6067	306	19	and	and	CCONJ
ejpam-6067	306	20	g2n	g2n	PROPN
ejpam-6067	306	21	are	be	AUX
ejpam-6067	306	22	open	open	ADJ
ejpam-6067	306	23	in	in	ADP
ejpam-6067	306	24	x	x	PUNCT
ejpam-6067	306	25	for	for	ADP
ejpam-6067	306	26	n	n	NOUN
ejpam-6067	306	27	=	=	SYM
ejpam-6067	306	28	1	1	NUM
ejpam-6067	306	29	,	,	PUNCT
ejpam-6067	306	30	2	2	NUM
ejpam-6067	306	31	,	,	PUNCT
ejpam-6067	306	32	·	·	PUNCT
ejpam-6067	306	33	·	·	PUNCT
ejpam-6067	306	34	·	·	PUNCT
ejpam-6067	306	35	.	.	PUNCT
ejpam-6067	307	1	since	since	SCONJ
ejpam-6067	307	2	x	x	PROPN
ejpam-6067	307	3	/∈	/∈	PUNCT
ejpam-6067	307	4	g2	g2	PROPN
ejpam-6067	307	5	,	,	PUNCT
ejpam-6067	307	6	so	so	SCONJ
ejpam-6067	307	7	there	there	PRON
ejpam-6067	307	8	is	be	VERB
ejpam-6067	307	9	g2i	g2i	PROPN
ejpam-6067	307	10	for	for	ADP
ejpam-6067	307	11	some	some	PRON
ejpam-6067	307	12	i	i	PRON
ejpam-6067	307	13	such	such	ADJ
ejpam-6067	307	14	that	that	SCONJ
ejpam-6067	307	15	x	x	PROPN
ejpam-6067	307	16	/∈	/∈	PUNCT
ejpam-6067	307	17	g2i	g2i	PROPN
ejpam-6067	307	18	.	.	PUNCT
ejpam-6067	308	1	similarly	similarly	ADV
ejpam-6067	308	2	,	,	PUNCT
ejpam-6067	308	3	since	since	SCONJ
ejpam-6067	308	4	y	y	PROPN
ejpam-6067	308	5	/∈	/∈	PUNCT
ejpam-6067	308	6	g1	g1	PROPN
ejpam-6067	308	7	,	,	PUNCT
ejpam-6067	308	8	so	so	SCONJ
ejpam-6067	308	9	there	there	PRON
ejpam-6067	308	10	is	be	VERB
ejpam-6067	308	11	g1k	g1k	NOUN
ejpam-6067	308	12	for	for	ADP
ejpam-6067	308	13	some	some	PRON
ejpam-6067	308	14	k	k	NOUN
ejpam-6067	309	1	such	such	ADJ
ejpam-6067	309	2	that	that	SCONJ
ejpam-6067	309	3	y	y	PROPN
ejpam-6067	309	4	/∈	/∈	PROPN
ejpam-6067	309	5	g1k	g1k	NOUN
ejpam-6067	310	1	but	but	CCONJ
ejpam-6067	310	2	x	x	X
ejpam-6067	310	3	∈	∈	PROPN
ejpam-6067	310	4	g1k	g1k	PROPN
ejpam-6067	310	5	and	and	CCONJ
ejpam-6067	310	6	y	y	PROPN
ejpam-6067	310	7	∈	∈	PROPN
ejpam-6067	310	8	g2i	g2i	PROPN
ejpam-6067	310	9	.	.	PUNCT
ejpam-6067	311	1	therefore	therefore	ADV
ejpam-6067	311	2	x	x	X
ejpam-6067	311	3	is	be	AUX
ejpam-6067	311	4	t1	t1	NOUN
ejpam-6067	311	5	space	space	NOUN
ejpam-6067	311	6	.	.	PUNCT
ejpam-6067	312	1	definition	definition	NOUN
ejpam-6067	312	2	15	15	NUM
ejpam-6067	312	3	.	.	PUNCT
ejpam-6067	313	1	a	a	DET
ejpam-6067	313	2	space	space	NOUN
ejpam-6067	313	3	x	x	PUNCT
ejpam-6067	313	4	is	be	AUX
ejpam-6067	313	5	called	call	VERB
ejpam-6067	313	6	tδ2	tδ2	NOUN
ejpam-6067	313	7	space	space	NOUN
ejpam-6067	313	8	if	if	SCONJ
ejpam-6067	313	9	whenever	whenever	SCONJ
ejpam-6067	313	10	x	x	PRON
ejpam-6067	313	11	and	and	CCONJ
ejpam-6067	313	12	y	y	PROPN
ejpam-6067	313	13	are	be	AUX
ejpam-6067	313	14	distinct	distinct	ADJ
ejpam-6067	313	15	points	point	NOUN
ejpam-6067	313	16	in	in	ADP
ejpam-6067	313	17	x	x	NOUN
ejpam-6067	313	18	,	,	PUNCT
ejpam-6067	313	19	there	there	PRON
ejpam-6067	313	20	are	be	VERB
ejpam-6067	313	21	disjoint	disjoint	NOUN
ejpam-6067	313	22	gδ	gδ	NOUN
ejpam-6067	313	23	sets	set	NOUN
ejpam-6067	313	24	g1	g1	NOUN
ejpam-6067	313	25	and	and	CCONJ
ejpam-6067	313	26	g2	g2	PROPN
ejpam-6067	313	27	such	such	ADJ
ejpam-6067	313	28	that	that	SCONJ
ejpam-6067	313	29	x	x	SYM
ejpam-6067	313	30	∈	∈	PROPN
ejpam-6067	313	31	g1	g1	PROPN
ejpam-6067	313	32	and	and	CCONJ
ejpam-6067	313	33	y	y	PROPN
ejpam-6067	313	34	∈	∈	PROPN
ejpam-6067	313	35	g2	g2	PROPN
ejpam-6067	313	36	.	.	PUNCT
ejpam-6067	314	1	evidently	evidently	ADV
ejpam-6067	314	2	,	,	PUNCT
ejpam-6067	314	3	every	every	DET
ejpam-6067	314	4	tδ2	tδ2	NOUN
ejpam-6067	314	5	space	space	NOUN
ejpam-6067	314	6	is	be	AUX
ejpam-6067	314	7	tδ1	tδ1	NOUN
ejpam-6067	314	8	.	.	PUNCT
ejpam-6067	315	1	remark	remark	VERB
ejpam-6067	315	2	5	5	NUM
ejpam-6067	315	3	.	.	PUNCT
ejpam-6067	316	1	clearly	clearly	ADV
ejpam-6067	316	2	every	every	DET
ejpam-6067	316	3	t2	t2	NOUN
ejpam-6067	316	4	space	space	NOUN
ejpam-6067	316	5	is	be	AUX
ejpam-6067	316	6	tδ2	tδ2	VERB
ejpam-6067	316	7	space	space	NOUN
ejpam-6067	316	8	but	but	CCONJ
ejpam-6067	316	9	the	the	DET
ejpam-6067	316	10	converse	converse	NOUN
ejpam-6067	316	11	is	be	AUX
ejpam-6067	316	12	not	not	PART
ejpam-6067	316	13	true	true	ADJ
ejpam-6067	316	14	in	in	ADP
ejpam-6067	316	15	general	general	ADJ
ejpam-6067	316	16	.	.	PUNCT
ejpam-6067	317	1	to	to	PART
ejpam-6067	317	2	show	show	VERB
ejpam-6067	317	3	that	that	SCONJ
ejpam-6067	317	4	we	we	PRON
ejpam-6067	317	5	give	give	VERB
ejpam-6067	317	6	the	the	DET
ejpam-6067	317	7	following	follow	VERB
ejpam-6067	317	8	example	example	NOUN
ejpam-6067	317	9	.	.	PUNCT
ejpam-6067	318	1	example	example	NOUN
ejpam-6067	319	1	7	7	NUM
ejpam-6067	319	2	.	.	X
ejpam-6067	319	3	consider	consider	VERB
ejpam-6067	319	4	the	the	DET
ejpam-6067	319	5	cofinite	cofinite	NOUN
ejpam-6067	319	6	topology	topology	NOUN
ejpam-6067	319	7	on	on	ADP
ejpam-6067	319	8	,	,	PUNCT
ejpam-6067	319	9	(	(	PUNCT
ejpam-6067	319	10	n	n	CCONJ
ejpam-6067	319	11	,	,	PUNCT
ejpam-6067	319	12	τcof	τcof	NOUN
ejpam-6067	319	13	)	)	PUNCT
ejpam-6067	319	14	.	.	PUNCT
ejpam-6067	320	1	then	then	ADV
ejpam-6067	320	2	(	(	PUNCT
ejpam-6067	320	3	n	n	CCONJ
ejpam-6067	320	4	,	,	PUNCT
ejpam-6067	320	5	τcof	τcof	NOUN
ejpam-6067	320	6	)	)	PUNCT
ejpam-6067	320	7	is	be	AUX
ejpam-6067	320	8	not	not	PART
ejpam-6067	320	9	t2	t2	NOUN
ejpam-6067	320	10	space	space	NOUN
ejpam-6067	320	11	because	because	SCONJ
ejpam-6067	320	12	is	be	AUX
ejpam-6067	320	13	uncountable	uncountable	ADJ
ejpam-6067	320	14	.	.	PUNCT
ejpam-6067	321	1	to	to	PART
ejpam-6067	321	2	show	show	VERB
ejpam-6067	321	3	that	that	SCONJ
ejpam-6067	321	4	(	(	PUNCT
ejpam-6067	321	5	n	n	CCONJ
ejpam-6067	321	6	,	,	PUNCT
ejpam-6067	321	7	τcof	τcof	PROPN
ejpam-6067	321	8	)	)	PUNCT
ejpam-6067	321	9	is	be	AUX
ejpam-6067	321	10	tδ2	tδ2	VERB
ejpam-6067	321	11	,	,	PUNCT
ejpam-6067	321	12	let	let	VERB
ejpam-6067	321	13	n	n	PRON
ejpam-6067	321	14	,	,	PUNCT
ejpam-6067	321	15	m	m	AUX
ejpam-6067	321	16	be	be	VERB
ejpam-6067	321	17	two	two	NUM
ejpam-6067	321	18	distinct	distinct	ADJ
ejpam-6067	321	19	points	point	NOUN
ejpam-6067	321	20	in	in	ADP
ejpam-6067	321	21	.	.	PUNCT
ejpam-6067	322	1	then	then	ADV
ejpam-6067	322	2	,	,	PUNCT
ejpam-6067	322	3	{	{	PUNCT
ejpam-6067	322	4	m	m	VERB
ejpam-6067	322	5	}	}	PUNCT
ejpam-6067	322	6	,	,	PUNCT
ejpam-6067	322	7	and	and	CCONJ
ejpam-6067	322	8	{	{	PUNCT
ejpam-6067	322	9	n	n	CCONJ
ejpam-6067	322	10	}	}	PUNCT
ejpam-6067	322	11	are	be	AUX
ejpam-6067	322	12	two	two	NUM
ejpam-6067	322	13	disjoint	disjoint	ADJ
ejpam-6067	322	14	gδ	gδ	NOUN
ejpam-6067	322	15	-	-	PUNCT
ejpam-6067	322	16	sets	set	NOUN
ejpam-6067	322	17	.	.	PUNCT
ejpam-6067	323	1	in	in	ADP
ejpam-6067	323	2	fact	fact	NOUN
ejpam-6067	323	3	{	{	PUNCT
ejpam-6067	323	4	m	m	NOUN
ejpam-6067	323	5	}	}	PUNCT
ejpam-6067	323	6	=	=	SYM
ejpam-6067	323	7	∞⋂	∞⋂	PROPN
ejpam-6067	323	8	i=1	i=1	PROPN
ejpam-6067	324	1	(	(	PUNCT
ejpam-6067	324	2	(	(	PUNCT
ejpam-6067	324	3	−{i	−{i	PROPN
ejpam-6067	324	4	}	}	PUNCT
ejpam-6067	324	5	)	)	PUNCT
ejpam-6067	325	1	∪	∪	ADP
ejpam-6067	325	2	{	{	PUNCT
ejpam-6067	325	3	m	m	NOUN
ejpam-6067	325	4	}	}	PUNCT
ejpam-6067	325	5	)	)	PUNCT
ejpam-6067	325	6	,	,	PUNCT
ejpam-6067	325	7	{	{	PUNCT
ejpam-6067	325	8	n	n	CCONJ
ejpam-6067	325	9	}	}	PUNCT
ejpam-6067	325	10	=	=	SYM
ejpam-6067	325	11	∞⋂	∞⋂	PROPN
ejpam-6067	325	12	i=1	i=1	PROPN
ejpam-6067	325	13	(	(	PUNCT
ejpam-6067	325	14	(	(	PUNCT
ejpam-6067	325	15	−{i	−{i	PROPN
ejpam-6067	325	16	}	}	PUNCT
ejpam-6067	325	17	)	)	PUNCT
ejpam-6067	325	18	∪	∪	ADP
ejpam-6067	325	19	{	{	PUNCT
ejpam-6067	325	20	n	n	NOUN
ejpam-6067	325	21	}	}	PUNCT
ejpam-6067	325	22	)	)	PUNCT
ejpam-6067	325	23	.	.	PUNCT
ejpam-6067	326	1	remark	remark	NOUN
ejpam-6067	326	2	6	6	NUM
ejpam-6067	326	3	.	.	PUNCT
ejpam-6067	327	1	every	every	DET
ejpam-6067	327	2	tδ2	tδ2	NOUN
ejpam-6067	327	3	space	space	NOUN
ejpam-6067	327	4	is	be	AUX
ejpam-6067	327	5	tδ1	tδ1	NOUN
ejpam-6067	327	6	but	but	CCONJ
ejpam-6067	327	7	the	the	DET
ejpam-6067	327	8	converse	converse	NOUN
ejpam-6067	327	9	is	be	AUX
ejpam-6067	327	10	not	not	PART
ejpam-6067	327	11	true	true	ADJ
ejpam-6067	327	12	in	in	ADP
ejpam-6067	327	13	general	general	ADJ
ejpam-6067	327	14	.	.	PUNCT
ejpam-6067	328	1	m.	m.	NOUN
ejpam-6067	328	2	shatnawi	shatnawi	PROPN
ejpam-6067	328	3	et	et	PROPN
ejpam-6067	328	4	al	al	PROPN
ejpam-6067	328	5	.	.	PUNCT
ejpam-6067	328	6	/	/	SYM
ejpam-6067	328	7	eur	eur	PROPN
ejpam-6067	328	8	.	.	PUNCT
ejpam-6067	329	1	j.	j.	PROPN
ejpam-6067	329	2	pure	pure	PROPN
ejpam-6067	329	3	appl	appl	PROPN
ejpam-6067	329	4	.	.	PROPN
ejpam-6067	329	5	math	math	PROPN
ejpam-6067	329	6	,	,	PUNCT
ejpam-6067	329	7	18	18	NUM
ejpam-6067	329	8	(	(	PUNCT
ejpam-6067	329	9	3	3	NUM
ejpam-6067	329	10	)	)	PUNCT
ejpam-6067	329	11	(	(	PUNCT
ejpam-6067	329	12	2025	2025	NUM
ejpam-6067	329	13	)	)	PUNCT
ejpam-6067	329	14	,	,	PUNCT
ejpam-6067	329	15	6067	6067	NUM
ejpam-6067	329	16	12	12	NUM
ejpam-6067	329	17	of	of	ADP
ejpam-6067	329	18	16	16	NUM
ejpam-6067	329	19	example	example	NOUN
ejpam-6067	329	20	8	8	NUM
ejpam-6067	329	21	.	.	PUNCT
ejpam-6067	329	22	consider	consider	VERB
ejpam-6067	329	23	with	with	ADP
ejpam-6067	329	24	the	the	DET
ejpam-6067	329	25	cofinite	cofinite	NOUN
ejpam-6067	329	26	topology	topology	NOUN
ejpam-6067	329	27	.	.	PUNCT
ejpam-6067	330	1	then	then	ADV
ejpam-6067	330	2	,	,	PUNCT
ejpam-6067	330	3	(	(	PUNCT
ejpam-6067	330	4	,	,	PUNCT
ejpam-6067	330	5	τcof	τcof	PROPN
ejpam-6067	330	6	)	)	PUNCT
ejpam-6067	330	7	is	be	AUX
ejpam-6067	330	8	tδ1	tδ1	NUM
ejpam-6067	330	9	which	which	PRON
ejpam-6067	330	10	is	be	AUX
ejpam-6067	330	11	not	not	PART
ejpam-6067	330	12	tδ2	tδ2	VERB
ejpam-6067	330	13	.	.	PUNCT
ejpam-6067	331	1	clearly	clearly	ADV
ejpam-6067	331	2	,	,	PUNCT
ejpam-6067	331	3	(	(	PUNCT
ejpam-6067	331	4	,	,	PUNCT
ejpam-6067	331	5	τcof	τcof	PROPN
ejpam-6067	331	6	)	)	PUNCT
ejpam-6067	331	7	is	be	AUX
ejpam-6067	331	8	t1	t1	NOUN
ejpam-6067	331	9	and	and	CCONJ
ejpam-6067	331	10	hence	hence	ADV
ejpam-6067	331	11	,	,	PUNCT
ejpam-6067	331	12	tδ1	tδ1	ADV
ejpam-6067	331	13	.	.	PUNCT
ejpam-6067	332	1	now	now	ADV
ejpam-6067	332	2	,	,	PUNCT
ejpam-6067	332	3	assume	assume	VERB
ejpam-6067	332	4	to	to	ADP
ejpam-6067	332	5	the	the	DET
ejpam-6067	332	6	contrary	contrary	NOUN
ejpam-6067	332	7	that	that	SCONJ
ejpam-6067	332	8	(	(	PUNCT
ejpam-6067	332	9	,	,	PUNCT
ejpam-6067	332	10	τcof	τcof	PROPN
ejpam-6067	332	11	)	)	PUNCT
ejpam-6067	332	12	is	be	AUX
ejpam-6067	332	13	tδ2	tδ2	VERB
ejpam-6067	332	14	.	.	PUNCT
ejpam-6067	333	1	then	then	ADV
ejpam-6067	333	2	for	for	ADP
ejpam-6067	333	3	any	any	DET
ejpam-6067	333	4	a	a	PRON
ejpam-6067	333	5	,	,	PUNCT
ejpam-6067	333	6	b	b	X
ejpam-6067	333	7	∈	∈	PROPN
ejpam-6067	333	8	there	there	PRON
ejpam-6067	333	9	are	be	VERB
ejpam-6067	333	10	two	two	NUM
ejpam-6067	333	11	gδ	gδ	NOUN
ejpam-6067	333	12	sets	set	NOUN
ejpam-6067	333	13	say	say	VERB
ejpam-6067	333	14	g1	g1	PROPN
ejpam-6067	333	15	=	=	SYM
ejpam-6067	333	16	∞⋂	∞⋂	PROPN
ejpam-6067	333	17	i=1	i=1	PROPN
ejpam-6067	333	18	ui	ui	PROPN
ejpam-6067	333	19	and	and	CCONJ
ejpam-6067	333	20	g2	g2	PROPN
ejpam-6067	333	21	=	=	SYM
ejpam-6067	333	22	∞⋂	∞⋂	PROPN
ejpam-6067	333	23	i=1	i=1	PROPN
ejpam-6067	333	24	vi	vi	PROPN
ejpam-6067	333	25	,	,	PUNCT
ejpam-6067	333	26	such	such	ADJ
ejpam-6067	333	27	that	that	SCONJ
ejpam-6067	333	28	a	a	DET
ejpam-6067	333	29	∈	∈	PROPN
ejpam-6067	333	30	g1	g1	NOUN
ejpam-6067	333	31	,	,	PUNCT
ejpam-6067	333	32	b	b	PROPN
ejpam-6067	333	33	∈	∈	PROPN
ejpam-6067	333	34	g2	g2	PROPN
ejpam-6067	333	35	and	and	CCONJ
ejpam-6067	333	36	g1	g1	PROPN
ejpam-6067	333	37	∩g2	∩g2	PROPN
ejpam-6067	333	38	=	=	PROPN
ejpam-6067	333	39	ϕ.	ϕ.	PROPN
ejpam-6067	334	1	so	so	ADV
ejpam-6067	334	2	,	,	PUNCT
ejpam-6067	334	3	(	(	PUNCT
ejpam-6067	334	4	∞⋂	∞⋂	PROPN
ejpam-6067	334	5	i=1	i=1	PROPN
ejpam-6067	334	6	ui	ui	PROPN
ejpam-6067	334	7	)	)	PUNCT
ejpam-6067	334	8	⋂	⋂	PROPN
ejpam-6067	334	9	(	(	PUNCT
ejpam-6067	334	10	∞⋂	∞⋂	PROPN
ejpam-6067	334	11	i=1	i=1	PROPN
ejpam-6067	334	12	vi	vi	PROPN
ejpam-6067	334	13	)	)	PUNCT
ejpam-6067	335	1	=	=	PUNCT
ejpam-6067	335	2	ϕ.	ϕ.	NOUN
ejpam-6067	336	1	=	=	PRON
ejpam-6067	336	2	⇒	⇒	PROPN
ejpam-6067	336	3	∞⋂	∞⋂	PROPN
ejpam-6067	336	4	i=1	i=1	PROPN
ejpam-6067	337	1	(	(	PUNCT
ejpam-6067	337	2	ui	ui	PROPN
ejpam-6067	337	3	⋂	⋂	PROPN
ejpam-6067	337	4	vi	vi	PROPN
ejpam-6067	337	5	)	)	PUNCT
ejpam-6067	338	1	=	=	SYM
ejpam-6067	338	2	ϕ.	ϕ.	NOUN
ejpam-6067	339	1	=	=	AUX
ejpam-6067	339	2	⇒	⇒	PROPN
ejpam-6067	339	3	(	(	PUNCT
ejpam-6067	339	4	∞⋂	∞⋂	PROPN
ejpam-6067	339	5	i=1	i=1	PROPN
ejpam-6067	339	6	(	(	PUNCT
ejpam-6067	339	7	ui	ui	PROPN
ejpam-6067	339	8	⋂	⋂	PROPN
ejpam-6067	339	9	vi	vi	PROPN
ejpam-6067	339	10	)	)	PUNCT
ejpam-6067	339	11	)	)	PUNCT
ejpam-6067	339	12	c	c	X
ejpam-6067	339	13	=	=	PUNCT
ejpam-6067	339	14	.	.	PUNCT
ejpam-6067	340	1	=	=	PRON
ejpam-6067	340	2	⇒	⇒	VERB
ejpam-6067	340	3	∞⋃	∞⋃	PROPN
ejpam-6067	340	4	i=1	i=1	PROPN
ejpam-6067	341	1	(	(	PUNCT
ejpam-6067	341	2	ui	ui	NOUN
ejpam-6067	341	3	⋂	⋂	PROPN
ejpam-6067	341	4	vi	vi	X
ejpam-6067	341	5	)	)	PUNCT
ejpam-6067	341	6	c	c	NOUN
ejpam-6067	341	7	=	=	PUNCT
ejpam-6067	341	8	.	.	PUNCT
ejpam-6067	342	1	=	=	PRON
ejpam-6067	342	2	⇒	⇒	VERB
ejpam-6067	342	3	∞⋃	∞⋃	PROPN
ejpam-6067	342	4	i=1	i=1	PROPN
ejpam-6067	343	1	(	(	PUNCT
ejpam-6067	343	2	ui	ui	PROPN
ejpam-6067	343	3	c	c	PROPN
ejpam-6067	343	4	⋃	⋃	PROPN
ejpam-6067	343	5	vi	vi	NOUN
ejpam-6067	343	6	c	c	NOUN
ejpam-6067	343	7	)	)	PUNCT
ejpam-6067	344	1	=	=	PUNCT
ejpam-6067	344	2	.	.	PUNCT
ejpam-6067	345	1	since	since	SCONJ
ejpam-6067	345	2	ui	ui	PROPN
ejpam-6067	345	3	c	c	PROPN
ejpam-6067	345	4	and	and	CCONJ
ejpam-6067	345	5	vi	vi	PROPN
ejpam-6067	345	6	c	c	NOUN
ejpam-6067	345	7	are	be	AUX
ejpam-6067	345	8	finite	finite	ADJ
ejpam-6067	345	9	for	for	ADP
ejpam-6067	345	10	each	each	DET
ejpam-6067	345	11	i	i	PRON
ejpam-6067	345	12	,	,	PUNCT
ejpam-6067	345	13	it	it	PRON
ejpam-6067	345	14	follows	follow	VERB
ejpam-6067	345	15	that	that	PRON
ejpam-6067	345	16	is	be	AUX
ejpam-6067	345	17	countable	countable	ADJ
ejpam-6067	345	18	,	,	PUNCT
ejpam-6067	345	19	which	which	PRON
ejpam-6067	345	20	a	a	DET
ejpam-6067	345	21	contradiction	contradiction	NOUN
ejpam-6067	345	22	.	.	PUNCT
ejpam-6067	346	1	theorem	theorem	VERB
ejpam-6067	346	2	15	15	NUM
ejpam-6067	346	3	.	.	PUNCT
ejpam-6067	347	1	a	a	DET
ejpam-6067	347	2	space	space	NOUN
ejpam-6067	347	3	x	x	PUNCT
ejpam-6067	347	4	exhibits	exhibit	VERB
ejpam-6067	347	5	tδ2	tδ2	VERB
ejpam-6067	347	6	if	if	SCONJ
ejpam-6067	347	7	and	and	CCONJ
ejpam-6067	347	8	only	only	ADV
ejpam-6067	347	9	if	if	SCONJ
ejpam-6067	347	10	the	the	DET
ejpam-6067	347	11	diagonal	diagonal	ADJ
ejpam-6067	347	12	∆	∆	X
ejpam-6067	347	13	=	=	SYM
ejpam-6067	347	14	{	{	PUNCT
ejpam-6067	347	15	(	(	PUNCT
ejpam-6067	347	16	x	x	NOUN
ejpam-6067	347	17	,	,	PUNCT
ejpam-6067	347	18	x	x	X
ejpam-6067	347	19	)	)	PUNCT
ejpam-6067	347	20	:	:	PUNCT
ejpam-6067	348	1	x	x	PUNCT
ejpam-6067	348	2	∈	∈	NOUN
ejpam-6067	348	3	x	x	PRON
ejpam-6067	348	4	}	}	PUNCT
ejpam-6067	348	5	forms	form	VERB
ejpam-6067	348	6	a	a	DET
ejpam-6067	348	7	gδ	gδ	NOUN
ejpam-6067	348	8	set	set	NOUN
ejpam-6067	348	9	in	in	ADP
ejpam-6067	348	10	the	the	DET
ejpam-6067	348	11	product	product	NOUN
ejpam-6067	348	12	space	space	NOUN
ejpam-6067	348	13	x	x	X
ejpam-6067	348	14	×x	×x	X
ejpam-6067	348	15	.	.	PUNCT
ejpam-6067	349	1	proof	proof	NOUN
ejpam-6067	349	2	.	.	PUNCT
ejpam-6067	350	1	suppose	suppose	VERB
ejpam-6067	350	2	x	x	PRON
ejpam-6067	350	3	represents	represent	VERB
ejpam-6067	350	4	a	a	DET
ejpam-6067	350	5	tδ2	tδ2	NOUN
ejpam-6067	350	6	space	space	NOUN
ejpam-6067	350	7	.	.	PUNCT
ejpam-6067	351	1	for	for	ADP
ejpam-6067	351	2	each	each	DET
ejpam-6067	351	3	pair	pair	NOUN
ejpam-6067	351	4	of	of	ADP
ejpam-6067	351	5	distinct	distinct	ADJ
ejpam-6067	351	6	points	point	NOUN
ejpam-6067	351	7	x	x	X
ejpam-6067	351	8	,	,	PUNCT
ejpam-6067	351	9	y	y	PROPN
ejpam-6067	351	10	∈	∈	PROPN
ejpam-6067	351	11	x	x	X
ejpam-6067	351	12	,	,	PUNCT
ejpam-6067	351	13	we	we	PRON
ejpam-6067	351	14	find	find	VERB
ejpam-6067	351	15	disjoint	disjoint	NOUN
ejpam-6067	351	16	gδ	gδ	NOUN
ejpam-6067	351	17	sets	set	VERB
ejpam-6067	351	18	gx	gx	PROPN
ejpam-6067	351	19	and	and	CCONJ
ejpam-6067	351	20	gy	gy	AUX
ejpam-6067	351	21	containing	contain	VERB
ejpam-6067	351	22	x	x	PROPN
ejpam-6067	351	23	and	and	CCONJ
ejpam-6067	351	24	y	y	PROPN
ejpam-6067	351	25	respectively	respectively	ADV
ejpam-6067	351	26	.	.	PUNCT
ejpam-6067	352	1	this	this	PRON
ejpam-6067	352	2	means	mean	VERB
ejpam-6067	352	3	(	(	PUNCT
ejpam-6067	352	4	x	x	NOUN
ejpam-6067	352	5	,	,	PUNCT
ejpam-6067	352	6	y	y	NOUN
ejpam-6067	352	7	)	)	PUNCT
ejpam-6067	352	8	∈	∈	PROPN
ejpam-6067	352	9	gx	gx	PROPN
ejpam-6067	352	10	×gy	×gy	NOUN
ejpam-6067	352	11	and	and	CCONJ
ejpam-6067	352	12	(	(	PUNCT
ejpam-6067	352	13	gx	gx	PROPN
ejpam-6067	352	14	×gy	×gy	PROPN
ejpam-6067	352	15	)	)	PUNCT
ejpam-6067	352	16	∩∆	∩∆	PROPN
ejpam-6067	352	17	=	=	PUNCT
ejpam-6067	352	18	∅.	∅.	AUX
ejpam-6067	352	19	let	let	VERB
ejpam-6067	352	20	ux	ux	PROPN
ejpam-6067	352	21	,	,	PUNCT
ejpam-6067	352	22	y	y	PROPN
ejpam-6067	352	23	=	=	SYM
ejpam-6067	352	24	gx×gy	gx×gy	PROPN
ejpam-6067	352	25	,	,	PUNCT
ejpam-6067	352	26	which	which	PRON
ejpam-6067	352	27	constitutes	constitute	VERB
ejpam-6067	352	28	agδ	agδ	AUX
ejpam-6067	352	29	set	set	VERB
ejpam-6067	352	30	inx×x	inx×x	PROPN
ejpam-6067	352	31	.	.	PUNCT
ejpam-6067	353	1	then	then	ADV
ejpam-6067	353	2	(	(	PUNCT
ejpam-6067	353	3	x×x)\∆	x×x)\∆	PROPN
ejpam-6067	353	4	=	=	SYM
ejpam-6067	353	5	⋃	⋃	PROPN
ejpam-6067	353	6	x	x	SYM
ejpam-6067	353	7	̸=y	̸=y	PROPN
ejpam-6067	353	8	ux	ux	PROPN
ejpam-6067	353	9	,	,	PUNCT
ejpam-6067	353	10	y	y	PROPN
ejpam-6067	353	11	,	,	PUNCT
ejpam-6067	353	12	making	make	VERB
ejpam-6067	353	13	(	(	PUNCT
ejpam-6067	353	14	x	x	NOUN
ejpam-6067	353	15	×x	×x	X
ejpam-6067	353	16	)	)	PUNCT
ejpam-6067	353	17	\∆	\∆	ADP
ejpam-6067	353	18	an	an	DET
ejpam-6067	353	19	fσ	fσ	NOUN
ejpam-6067	353	20	set	set	VERB
ejpam-6067	353	21	in	in	ADP
ejpam-6067	353	22	x	x	PROPN
ejpam-6067	353	23	×x	×x	X
ejpam-6067	353	24	.	.	PUNCT
ejpam-6067	354	1	therefore	therefore	ADV
ejpam-6067	354	2	,	,	PUNCT
ejpam-6067	354	3	∆	∆	PROPN
ejpam-6067	354	4	forms	form	VERB
ejpam-6067	354	5	a	a	DET
ejpam-6067	354	6	gδ	gδ	NOUN
ejpam-6067	354	7	set	set	VERB
ejpam-6067	354	8	in	in	ADP
ejpam-6067	354	9	x	x	PROPN
ejpam-6067	354	10	×x	×x	X
ejpam-6067	354	11	.	.	PUNCT
ejpam-6067	355	1	conversely	conversely	ADV
ejpam-6067	355	2	,	,	PUNCT
ejpam-6067	355	3	suppose	suppose	VERB
ejpam-6067	355	4	∆	∆	PROPN
ejpam-6067	355	5	constitutes	constitute	VERB
ejpam-6067	355	6	a	a	DET
ejpam-6067	355	7	gδ	gδ	NOUN
ejpam-6067	355	8	set	set	VERB
ejpam-6067	355	9	in	in	ADP
ejpam-6067	355	10	x	x	PROPN
ejpam-6067	355	11	×x	×x	PROPN
ejpam-6067	355	12	.	.	PUNCT
ejpam-6067	356	1	then	then	ADV
ejpam-6067	356	2	(	(	PUNCT
ejpam-6067	356	3	x	x	X
ejpam-6067	356	4	×x	×x	X
ejpam-6067	356	5	)	)	PUNCT
ejpam-6067	356	6	\∆	\∆	NOUN
ejpam-6067	356	7	represents	represent	VERB
ejpam-6067	356	8	an	an	DET
ejpam-6067	356	9	fσ	fσ	NOUN
ejpam-6067	356	10	set	set	NOUN
ejpam-6067	356	11	,	,	PUNCT
ejpam-6067	356	12	which	which	PRON
ejpam-6067	356	13	we	we	PRON
ejpam-6067	356	14	can	can	AUX
ejpam-6067	356	15	write	write	VERB
ejpam-6067	356	16	as	as	ADP
ejpam-6067	356	17	⋃∞	⋃∞	PUNCT
ejpam-6067	356	18	n=1	n=1	PROPN
ejpam-6067	356	19	fn	fn	PROPN
ejpam-6067	356	20	where	where	SCONJ
ejpam-6067	356	21	each	each	DET
ejpam-6067	356	22	fn	fn	NOUN
ejpam-6067	356	23	is	be	AUX
ejpam-6067	356	24	closed	close	VERB
ejpam-6067	356	25	in	in	ADP
ejpam-6067	356	26	x	x	X
ejpam-6067	356	27	×x	×x	X
ejpam-6067	356	28	.	.	NOUN
ejpam-6067	357	1	for	for	SCONJ
ejpam-6067	357	2	any	any	DET
ejpam-6067	357	3	distinct	distinct	ADJ
ejpam-6067	357	4	points	point	NOUN
ejpam-6067	357	5	x	x	NOUN
ejpam-6067	357	6	,	,	PUNCT
ejpam-6067	357	7	y	y	PROPN
ejpam-6067	357	8	∈	∈	PROPN
ejpam-6067	357	9	x	x	PRON
ejpam-6067	357	10	,	,	PUNCT
ejpam-6067	357	11	the	the	DET
ejpam-6067	357	12	pair	pair	NOUN
ejpam-6067	357	13	(	(	PUNCT
ejpam-6067	357	14	x	x	NOUN
ejpam-6067	357	15	,	,	PUNCT
ejpam-6067	357	16	y	y	NOUN
ejpam-6067	357	17	)	)	PUNCT
ejpam-6067	357	18	∈	∈	PROPN
ejpam-6067	357	19	(	(	PUNCT
ejpam-6067	357	20	x	x	NOUN
ejpam-6067	357	21	×	×	NOUN
ejpam-6067	357	22	x	x	NOUN
ejpam-6067	357	23	)	)	PUNCT
ejpam-6067	357	24	\	\	NOUN
ejpam-6067	357	25	∆	∆	NOUN
ejpam-6067	357	26	,	,	PUNCT
ejpam-6067	357	27	so	so	CCONJ
ejpam-6067	357	28	(	(	PUNCT
ejpam-6067	357	29	x	x	NOUN
ejpam-6067	357	30	,	,	PUNCT
ejpam-6067	357	31	y	y	NOUN
ejpam-6067	357	32	)	)	PUNCT
ejpam-6067	357	33	∈	∈	PROPN
ejpam-6067	357	34	fn	fn	NOUN
ejpam-6067	357	35	for	for	ADP
ejpam-6067	357	36	some	some	DET
ejpam-6067	357	37	n.	n.	NOUN
ejpam-6067	357	38	since	since	SCONJ
ejpam-6067	357	39	fn	fn	PROPN
ejpam-6067	357	40	is	be	AUX
ejpam-6067	357	41	closed	closed	ADJ
ejpam-6067	357	42	,	,	PUNCT
ejpam-6067	357	43	(	(	PUNCT
ejpam-6067	357	44	x	x	X
ejpam-6067	357	45	,	,	PUNCT
ejpam-6067	357	46	y	y	NOUN
ejpam-6067	357	47	)	)	PUNCT
ejpam-6067	357	48	has	have	VERB
ejpam-6067	357	49	an	an	DET
ejpam-6067	357	50	open	open	ADJ
ejpam-6067	357	51	neighborhood	neighborhood	NOUN
ejpam-6067	357	52	u	u	NOUN
ejpam-6067	357	53	×v	×v	NOUN
ejpam-6067	357	54	contained	contain	VERB
ejpam-6067	357	55	in	in	ADP
ejpam-6067	357	56	fn	fn	PROPN
ejpam-6067	357	57	.	.	PUNCT
ejpam-6067	358	1	since	since	SCONJ
ejpam-6067	358	2	(	(	PUNCT
ejpam-6067	358	3	x	x	X
ejpam-6067	358	4	,	,	PUNCT
ejpam-6067	358	5	x	x	NOUN
ejpam-6067	358	6	)	)	PUNCT
ejpam-6067	358	7	/∈	/∈	PUNCT
ejpam-6067	359	1	fn	fn	NOUN
ejpam-6067	359	2	,	,	PUNCT
ejpam-6067	359	3	we	we	PRON
ejpam-6067	359	4	must	must	AUX
ejpam-6067	359	5	have	have	VERB
ejpam-6067	359	6	x	x	PROPN
ejpam-6067	359	7	/∈	/∈	ADP
ejpam-6067	360	1	v	v	NOUN
ejpam-6067	360	2	or	or	CCONJ
ejpam-6067	360	3	y	y	PROPN
ejpam-6067	360	4	/∈	/∈	PUNCT
ejpam-6067	361	1	u	u	PROPN
ejpam-6067	361	2	.	.	PUNCT
ejpam-6067	362	1	without	without	ADP
ejpam-6067	362	2	loss	loss	NOUN
ejpam-6067	362	3	of	of	ADP
ejpam-6067	362	4	generality	generality	NOUN
ejpam-6067	362	5	,	,	PUNCT
ejpam-6067	362	6	assume	assume	VERB
ejpam-6067	362	7	x	x	X
ejpam-6067	362	8	/∈	/∈	PUNCT
ejpam-6067	363	1	v	v	INTJ
ejpam-6067	363	2	.	.	PUNCT
ejpam-6067	364	1	let	let	VERB
ejpam-6067	364	2	gx	gx	PROPN
ejpam-6067	364	3	=	=	SYM
ejpam-6067	364	4	u	u	PROPN
ejpam-6067	364	5	and	and	CCONJ
ejpam-6067	364	6	gy	gy	NOUN
ejpam-6067	364	7	=	=	PUNCT
ejpam-6067	364	8	v	v	PROPN
ejpam-6067	364	9	.	.	PUNCT
ejpam-6067	365	1	then	then	ADV
ejpam-6067	365	2	gx	gx	PROPN
ejpam-6067	365	3	and	and	CCONJ
ejpam-6067	365	4	gy	gy	PROPN
ejpam-6067	365	5	form	form	NOUN
ejpam-6067	365	6	open	open	ADJ
ejpam-6067	365	7	sets	set	NOUN
ejpam-6067	365	8	containing	contain	VERB
ejpam-6067	365	9	x	x	X
ejpam-6067	365	10	and	and	CCONJ
ejpam-6067	365	11	y	y	PROPN
ejpam-6067	365	12	respectively	respectively	ADV
ejpam-6067	365	13	,	,	PUNCT
ejpam-6067	365	14	and	and	CCONJ
ejpam-6067	365	15	gx	gx	PROPN
ejpam-6067	365	16	∩	∩	NOUN
ejpam-6067	365	17	gy	gy	NOUN
ejpam-6067	365	18	=	=	VERB
ejpam-6067	365	19	∅.	∅.	NOUN
ejpam-6067	365	20	by	by	ADP
ejpam-6067	365	21	taking	take	VERB
ejpam-6067	365	22	countable	countable	ADJ
ejpam-6067	365	23	intersections	intersection	NOUN
ejpam-6067	365	24	of	of	ADP
ejpam-6067	365	25	such	such	ADJ
ejpam-6067	365	26	open	open	ADJ
ejpam-6067	365	27	sets	set	NOUN
ejpam-6067	365	28	for	for	ADP
ejpam-6067	365	29	different	different	ADJ
ejpam-6067	365	30	n	n	CCONJ
ejpam-6067	365	31	,	,	PUNCT
ejpam-6067	365	32	we	we	PRON
ejpam-6067	365	33	can	can	AUX
ejpam-6067	365	34	construct	construct	VERB
ejpam-6067	365	35	disjoint	disjoint	NOUN
ejpam-6067	365	36	gδ	gδ	PROPN
ejpam-6067	365	37	sets	set	NOUN
ejpam-6067	365	38	containing	contain	VERB
ejpam-6067	365	39	x	x	PROPN
ejpam-6067	365	40	and	and	CCONJ
ejpam-6067	365	41	y	y	PROPN
ejpam-6067	365	42	,	,	PUNCT
ejpam-6067	365	43	establishing	establish	VERB
ejpam-6067	365	44	that	that	SCONJ
ejpam-6067	365	45	x	x	PUNCT
ejpam-6067	365	46	exhibits	exhibit	VERB
ejpam-6067	365	47	tδ2	tδ2	NOUN
ejpam-6067	365	48	.	.	PUNCT
ejpam-6067	366	1	m.	m.	NOUN
ejpam-6067	366	2	shatnawi	shatnawi	PROPN
ejpam-6067	366	3	et	et	PROPN
ejpam-6067	366	4	al	al	PROPN
ejpam-6067	366	5	.	.	PUNCT
ejpam-6067	366	6	/	/	SYM
ejpam-6067	366	7	eur	eur	PROPN
ejpam-6067	366	8	.	.	PUNCT
ejpam-6067	367	1	j.	j.	PROPN
ejpam-6067	367	2	pure	pure	PROPN
ejpam-6067	367	3	appl	appl	PROPN
ejpam-6067	367	4	.	.	PROPN
ejpam-6067	367	5	math	math	PROPN
ejpam-6067	367	6	,	,	PUNCT
ejpam-6067	367	7	18	18	NUM
ejpam-6067	367	8	(	(	PUNCT
ejpam-6067	367	9	3	3	NUM
ejpam-6067	367	10	)	)	PUNCT
ejpam-6067	367	11	(	(	PUNCT
ejpam-6067	367	12	2025	2025	NUM
ejpam-6067	367	13	)	)	PUNCT
ejpam-6067	367	14	,	,	PUNCT
ejpam-6067	367	15	6067	6067	NUM
ejpam-6067	367	16	13	13	NUM
ejpam-6067	367	17	of	of	ADP
ejpam-6067	367	18	16	16	NUM
ejpam-6067	367	19	4	4	NUM
ejpam-6067	367	20	.	.	PUNCT
ejpam-6067	368	1	connections	connection	NOUN
ejpam-6067	368	2	with	with	ADP
ejpam-6067	368	3	other	other	ADJ
ejpam-6067	368	4	compactness	compactness	NOUN
ejpam-6067	368	5	notions	notion	NOUN
ejpam-6067	368	6	in	in	ADP
ejpam-6067	368	7	this	this	DET
ejpam-6067	368	8	section	section	NOUN
ejpam-6067	368	9	,	,	PUNCT
ejpam-6067	368	10	we	we	PRON
ejpam-6067	368	11	explore	explore	VERB
ejpam-6067	368	12	relationships	relationship	NOUN
ejpam-6067	368	13	between	between	ADP
ejpam-6067	368	14	g	g	NOUN
ejpam-6067	368	15	-	-	PUNCT
ejpam-6067	368	16	compactness	compactness	NOUN
ejpam-6067	368	17	and	and	CCONJ
ejpam-6067	368	18	other	other	ADJ
ejpam-6067	368	19	well	well	ADV
ejpam-6067	368	20	-	-	PUNCT
ejpam-6067	368	21	established	establish	VERB
ejpam-6067	368	22	compactness	compactness	NOUN
ejpam-6067	368	23	notions	notion	NOUN
ejpam-6067	368	24	in	in	ADP
ejpam-6067	368	25	topology	topology	NOUN
ejpam-6067	368	26	.	.	PUNCT
ejpam-6067	369	1	theorem	theorem	VERB
ejpam-6067	369	2	16	16	NUM
ejpam-6067	369	3	.	.	PUNCT
ejpam-6067	370	1	every	every	DET
ejpam-6067	370	2	g	g	PROPN
ejpam-6067	370	3	-	-	PUNCT
ejpam-6067	370	4	compact	compact	ADJ
ejpam-6067	370	5	space	space	NOUN
ejpam-6067	370	6	exhibits	exhibit	VERB
ejpam-6067	370	7	metacompactness	metacompactness	NOUN
ejpam-6067	370	8	.	.	PUNCT
ejpam-6067	371	1	proof	proof	NOUN
ejpam-6067	371	2	.	.	PUNCT
ejpam-6067	372	1	let	let	VERB
ejpam-6067	372	2	(	(	PUNCT
ejpam-6067	372	3	x	x	NOUN
ejpam-6067	372	4	,	,	PUNCT
ejpam-6067	372	5	τ	τ	X
ejpam-6067	372	6	)	)	PUNCT
ejpam-6067	372	7	represent	represent	VERB
ejpam-6067	372	8	a	a	DET
ejpam-6067	372	9	g	g	NOUN
ejpam-6067	372	10	-	-	PUNCT
ejpam-6067	372	11	compact	compact	ADJ
ejpam-6067	372	12	space	space	NOUN
ejpam-6067	372	13	and	and	CCONJ
ejpam-6067	372	14	consider	consider	VERB
ejpam-6067	372	15	an	an	DET
ejpam-6067	372	16	open	open	ADJ
ejpam-6067	372	17	cover	cover	NOUN
ejpam-6067	372	18	u	u	NOUN
ejpam-6067	372	19	=	=	PUNCT
ejpam-6067	372	20	{	{	PUNCT
ejpam-6067	372	21	uα	uα	X
ejpam-6067	372	22	:	:	PUNCT
ejpam-6067	372	23	α	α	PROPN
ejpam-6067	372	24	∈	∈	PROPN
ejpam-6067	372	25	∆	∆	PROPN
ejpam-6067	372	26	}	}	PUNCT
ejpam-6067	372	27	ofx	ofx	NOUN
ejpam-6067	372	28	.	.	PUNCT
ejpam-6067	373	1	since	since	SCONJ
ejpam-6067	373	2	every	every	DET
ejpam-6067	373	3	open	open	ADJ
ejpam-6067	373	4	set	set	NOUN
ejpam-6067	373	5	uα	uα	PROPN
ejpam-6067	373	6	equals	equal	VERB
ejpam-6067	373	7	a	a	DET
ejpam-6067	373	8	countable	countable	ADJ
ejpam-6067	373	9	intersection	intersection	NOUN
ejpam-6067	373	10	of	of	ADP
ejpam-6067	373	11	itself	itself	PRON
ejpam-6067	373	12	,	,	PUNCT
ejpam-6067	373	13	it	it	PRON
ejpam-6067	373	14	constitutes	constitute	VERB
ejpam-6067	373	15	a	a	DET
ejpam-6067	373	16	gδ	gδ	NOUN
ejpam-6067	373	17	set	set	NOUN
ejpam-6067	373	18	.	.	PUNCT
ejpam-6067	374	1	hence	hence	ADV
ejpam-6067	374	2	,	,	PUNCT
ejpam-6067	374	3	u	u	PRON
ejpam-6067	374	4	forms	form	VERB
ejpam-6067	374	5	a	a	DET
ejpam-6067	374	6	g	g	NOUN
ejpam-6067	374	7	-	-	PUNCT
ejpam-6067	374	8	cover	cover	NOUN
ejpam-6067	374	9	of	of	ADP
ejpam-6067	374	10	x.	x.	NOUN
ejpam-6067	374	11	since	since	SCONJ
ejpam-6067	374	12	x	x	PRON
ejpam-6067	374	13	demonstrates	demonstrate	VERB
ejpam-6067	374	14	g	g	NOUN
ejpam-6067	374	15	-	-	PUNCT
ejpam-6067	374	16	compactness	compactness	NOUN
ejpam-6067	374	17	,	,	PUNCT
ejpam-6067	374	18	we	we	PRON
ejpam-6067	374	19	find	find	VERB
ejpam-6067	374	20	a	a	DET
ejpam-6067	374	21	finite	finite	ADJ
ejpam-6067	374	22	subcover	subcover	PROPN
ejpam-6067	374	23	{	{	PUNCT
ejpam-6067	374	24	uα1	uα1	PROPN
ejpam-6067	374	25	,	,	PUNCT
ejpam-6067	374	26	uα2	uα2	ADV
ejpam-6067	374	27	,	,	PUNCT
ejpam-6067	374	28	.	.	PUNCT
ejpam-6067	374	29	.	.	PUNCT
ejpam-6067	374	30	.	.	PUNCT
ejpam-6067	375	1	,	,	PUNCT
ejpam-6067	375	2	uαn	uαn	PROPN
ejpam-6067	375	3	}	}	PUNCT
ejpam-6067	375	4	of	of	ADP
ejpam-6067	375	5	u	u	NOUN
ejpam-6067	375	6	.	.	PUNCT
ejpam-6067	376	1	this	this	DET
ejpam-6067	376	2	finite	finite	ADJ
ejpam-6067	376	3	collection	collection	NOUN
ejpam-6067	376	4	qualifies	qualifie	NOUN
ejpam-6067	376	5	as	as	ADP
ejpam-6067	376	6	point	point	NOUN
ejpam-6067	376	7	-	-	PUNCT
ejpam-6067	376	8	finite	finite	ADJ
ejpam-6067	376	9	,	,	PUNCT
ejpam-6067	376	10	establishing	establish	VERB
ejpam-6067	376	11	that	that	SCONJ
ejpam-6067	376	12	x	x	PUNCT
ejpam-6067	376	13	exhibits	exhibit	VERB
ejpam-6067	376	14	metacompactness	metacompactness	NOUN
ejpam-6067	376	15	.	.	PUNCT
ejpam-6067	377	1	theorem	theorem	VERB
ejpam-6067	377	2	17	17	NUM
ejpam-6067	377	3	.	.	PUNCT
ejpam-6067	378	1	a	a	DET
ejpam-6067	378	2	space	space	NOUN
ejpam-6067	378	3	x	x	AUX
ejpam-6067	378	4	demonstrates	demonstrate	VERB
ejpam-6067	378	5	g	g	NOUN
ejpam-6067	378	6	-	-	PUNCT
ejpam-6067	378	7	compactness	compactness	NOUN
ejpam-6067	378	8	if	if	SCONJ
ejpam-6067	378	9	and	and	CCONJ
ejpam-6067	378	10	only	only	ADV
ejpam-6067	378	11	if	if	SCONJ
ejpam-6067	378	12	every	every	DET
ejpam-6067	378	13	filter	filter	NOUN
ejpam-6067	378	14	base	base	NOUN
ejpam-6067	378	15	on	on	ADP
ejpam-6067	378	16	x	x	PUNCT
ejpam-6067	378	17	consisting	consist	VERB
ejpam-6067	378	18	of	of	ADP
ejpam-6067	378	19	fσ	fσ	NOUN
ejpam-6067	378	20	sets	set	NOUN
ejpam-6067	378	21	has	have	VERB
ejpam-6067	378	22	a	a	DET
ejpam-6067	378	23	cluster	cluster	NOUN
ejpam-6067	378	24	point	point	NOUN
ejpam-6067	378	25	.	.	PUNCT
ejpam-6067	379	1	proof	proof	NOUN
ejpam-6067	379	2	.	.	PUNCT
ejpam-6067	380	1	suppose	suppose	VERB
ejpam-6067	380	2	x	x	PRON
ejpam-6067	380	3	exhibits	exhibit	VERB
ejpam-6067	380	4	g	g	NOUN
ejpam-6067	380	5	-	-	PUNCT
ejpam-6067	380	6	compactness	compactness	NOUN
ejpam-6067	380	7	and	and	CCONJ
ejpam-6067	380	8	consider	consider	VERB
ejpam-6067	380	9	a	a	DET
ejpam-6067	380	10	filter	filter	NOUN
ejpam-6067	380	11	base	base	NOUN
ejpam-6067	380	12	f	f	NOUN
ejpam-6067	380	13	consisting	consist	VERB
ejpam-6067	380	14	of	of	ADP
ejpam-6067	380	15	fσ	fσ	NOUN
ejpam-6067	380	16	sets	set	NOUN
ejpam-6067	380	17	.	.	PUNCT
ejpam-6067	381	1	if	if	SCONJ
ejpam-6067	381	2	f	f	PROPN
ejpam-6067	381	3	lacks	lack	VERB
ejpam-6067	381	4	any	any	DET
ejpam-6067	381	5	cluster	cluster	NOUN
ejpam-6067	381	6	point	point	NOUN
ejpam-6067	381	7	,	,	PUNCT
ejpam-6067	381	8	then	then	ADV
ejpam-6067	381	9	for	for	ADP
ejpam-6067	381	10	each	each	DET
ejpam-6067	381	11	x	x	SYM
ejpam-6067	381	12	∈	∈	PROPN
ejpam-6067	381	13	x	x	X
ejpam-6067	381	14	,	,	PUNCT
ejpam-6067	381	15	we	we	PRON
ejpam-6067	381	16	find	find	VERB
ejpam-6067	381	17	fx	fx	ADP
ejpam-6067	381	18	∈	∈	PROPN
ejpam-6067	381	19	f	f	PROPN
ejpam-6067	382	1	such	such	ADJ
ejpam-6067	382	2	that	that	SCONJ
ejpam-6067	382	3	x	x	PROPN
ejpam-6067	382	4	/∈	/∈	PUNCT
ejpam-6067	382	5	fx	fx	PROPN
ejpam-6067	382	6	.	.	PUNCT
ejpam-6067	383	1	this	this	PRON
ejpam-6067	383	2	means	mean	VERB
ejpam-6067	383	3	x	x	SYM
ejpam-6067	383	4	∈	∈	PROPN
ejpam-6067	383	5	x	x	SYM
ejpam-6067	383	6	\	\	PROPN
ejpam-6067	383	7	fx	fx	PROPN
ejpam-6067	383	8	,	,	PUNCT
ejpam-6067	383	9	which	which	PRON
ejpam-6067	383	10	forms	form	VERB
ejpam-6067	383	11	an	an	DET
ejpam-6067	383	12	open	open	ADJ
ejpam-6067	383	13	set	set	NOUN
ejpam-6067	383	14	.	.	PUNCT
ejpam-6067	384	1	since	since	SCONJ
ejpam-6067	384	2	fx	fx	PROPN
ejpam-6067	384	3	constitutes	constitute	VERB
ejpam-6067	384	4	an	an	DET
ejpam-6067	384	5	fσ	fσ	NOUN
ejpam-6067	384	6	set	set	NOUN
ejpam-6067	384	7	,	,	PUNCT
ejpam-6067	384	8	its	its	PRON
ejpam-6067	384	9	closure	closure	NOUN
ejpam-6067	384	10	fx	fx	NOUN
ejpam-6067	384	11	also	also	ADV
ejpam-6067	384	12	forms	form	VERB
ejpam-6067	384	13	an	an	DET
ejpam-6067	384	14	fσ	fσ	NOUN
ejpam-6067	384	15	set	set	NOUN
ejpam-6067	384	16	(	(	PUNCT
ejpam-6067	384	17	as	as	SCONJ
ejpam-6067	384	18	the	the	DET
ejpam-6067	384	19	closure	closure	NOUN
ejpam-6067	384	20	of	of	ADP
ejpam-6067	384	21	an	an	DET
ejpam-6067	384	22	fσ	fσ	NOUN
ejpam-6067	384	23	set	set	NOUN
ejpam-6067	384	24	remains	remain	VERB
ejpam-6067	384	25	an	an	DET
ejpam-6067	384	26	fσ	fσ	NOUN
ejpam-6067	384	27	set	set	VERB
ejpam-6067	384	28	in	in	ADP
ejpam-6067	384	29	a	a	DET
ejpam-6067	384	30	regular	regular	ADJ
ejpam-6067	384	31	space	space	NOUN
ejpam-6067	384	32	)	)	PUNCT
ejpam-6067	384	33	.	.	PUNCT
ejpam-6067	385	1	therefore	therefore	ADV
ejpam-6067	385	2	,	,	PUNCT
ejpam-6067	385	3	x	x	SYM
ejpam-6067	385	4	\	\	NOUN
ejpam-6067	385	5	fx	fx	PROPN
ejpam-6067	385	6	constitutes	constitute	VERB
ejpam-6067	385	7	a	a	DET
ejpam-6067	385	8	gδ	gδ	NOUN
ejpam-6067	385	9	set	set	NOUN
ejpam-6067	385	10	.	.	PUNCT
ejpam-6067	386	1	the	the	DET
ejpam-6067	386	2	collection	collection	NOUN
ejpam-6067	386	3	{	{	PUNCT
ejpam-6067	386	4	x	x	SYM
ejpam-6067	386	5	\	\	PROPN
ejpam-6067	386	6	fx	fx	NOUN
ejpam-6067	386	7	:	:	PUNCT
ejpam-6067	386	8	x	x	SYM
ejpam-6067	386	9	∈	∈	PROPN
ejpam-6067	386	10	x	x	VERB
ejpam-6067	386	11	}	}	PUNCT
ejpam-6067	386	12	creates	create	VERB
ejpam-6067	386	13	a	a	DET
ejpam-6067	386	14	g	g	NOUN
ejpam-6067	386	15	-	-	PUNCT
ejpam-6067	386	16	cover	cover	NOUN
ejpam-6067	386	17	of	of	ADP
ejpam-6067	386	18	x.	x.	NOUN
ejpam-6067	386	19	by	by	ADP
ejpam-6067	386	20	g	g	NOUN
ejpam-6067	386	21	-	-	PUNCT
ejpam-6067	386	22	compactness	compactness	NOUN
ejpam-6067	386	23	,	,	PUNCT
ejpam-6067	386	24	we	we	PRON
ejpam-6067	386	25	find	find	VERB
ejpam-6067	386	26	a	a	DET
ejpam-6067	386	27	finite	finite	ADJ
ejpam-6067	386	28	subcover	subcover	PROPN
ejpam-6067	386	29	{	{	PUNCT
ejpam-6067	386	30	x	x	PROPN
ejpam-6067	386	31	\	\	PROPN
ejpam-6067	386	32	fx1	fx1	NOUN
ejpam-6067	386	33	,	,	PUNCT
ejpam-6067	386	34	x	x	SYM
ejpam-6067	386	35	\	\	PROPN
ejpam-6067	386	36	fx2	fx2	PROPN
ejpam-6067	386	37	,	,	PUNCT
ejpam-6067	386	38	.	.	PUNCT
ejpam-6067	386	39	.	.	PUNCT
ejpam-6067	386	40	.	.	PUNCT
ejpam-6067	387	1	,	,	PUNCT
ejpam-6067	387	2	x	x	X
ejpam-6067	387	3	\	\	PROPN
ejpam-6067	387	4	fxn	fxn	PROPN
ejpam-6067	387	5	}	}	PUNCT
ejpam-6067	387	6	.	.	PUNCT
ejpam-6067	388	1	this	this	PRON
ejpam-6067	388	2	implies	imply	VERB
ejpam-6067	388	3	that	that	SCONJ
ejpam-6067	388	4	x	x	SYM
ejpam-6067	388	5	=	=	SYM
ejpam-6067	388	6	⋃n	⋃n	PROPN
ejpam-6067	388	7	i=1(x	i=1(x	PROPN
ejpam-6067	388	8	\	\	PROPN
ejpam-6067	388	9	fxi	fxi	NOUN
ejpam-6067	388	10	)	)	PUNCT
ejpam-6067	388	11	,	,	PUNCT
ejpam-6067	388	12	or	or	CCONJ
ejpam-6067	388	13	equivalently	equivalently	ADV
ejpam-6067	388	14	,	,	PUNCT
ejpam-6067	388	15	⋂n	⋂n	PROPN
ejpam-6067	388	16	i=1	i=1	PROPN
ejpam-6067	388	17	fxi	fxi	NOUN
ejpam-6067	388	18	=	=	PUNCT
ejpam-6067	388	19	∅.	∅.	NOUN
ejpam-6067	388	20	but	but	CCONJ
ejpam-6067	388	21	since	since	SCONJ
ejpam-6067	388	22	f	f	PROPN
ejpam-6067	388	23	forms	form	VERB
ejpam-6067	388	24	a	a	DET
ejpam-6067	388	25	filter	filter	NOUN
ejpam-6067	388	26	base	base	NOUN
ejpam-6067	388	27	,	,	PUNCT
ejpam-6067	388	28	the	the	DET
ejpam-6067	388	29	sets	set	NOUN
ejpam-6067	388	30	fx1	fx1	PROPN
ejpam-6067	388	31	,	,	PUNCT
ejpam-6067	388	32	fx2	fx2	PROPN
ejpam-6067	388	33	,	,	PUNCT
ejpam-6067	388	34	.	.	PUNCT
ejpam-6067	388	35	.	.	PUNCT
ejpam-6067	388	36	.	.	PUNCT
ejpam-6067	389	1	,	,	PUNCT
ejpam-6067	389	2	fxn	fxn	PROPN
ejpam-6067	389	3	have	have	VERB
ejpam-6067	389	4	non	non	ADJ
ejpam-6067	389	5	-	-	ADJ
ejpam-6067	389	6	empty	empty	ADJ
ejpam-6067	389	7	intersection	intersection	NOUN
ejpam-6067	389	8	,	,	PUNCT
ejpam-6067	389	9	which	which	DET
ejpam-6067	389	10	means⋂n	means⋂n	NOUN
ejpam-6067	389	11	i=1	i=1	PROPN
ejpam-6067	389	12	fxi	fxi	NOUN
ejpam-6067	389	13	̸=	̸=	PROPN
ejpam-6067	389	14	∅	∅	NOUN
ejpam-6067	389	15	,	,	PUNCT
ejpam-6067	389	16	creating	create	VERB
ejpam-6067	389	17	a	a	DET
ejpam-6067	389	18	contradiction	contradiction	NOUN
ejpam-6067	389	19	.	.	PUNCT
ejpam-6067	390	1	conversely	conversely	ADV
ejpam-6067	390	2	,	,	PUNCT
ejpam-6067	390	3	suppose	suppose	VERB
ejpam-6067	390	4	every	every	DET
ejpam-6067	390	5	filter	filter	NOUN
ejpam-6067	390	6	base	base	NOUN
ejpam-6067	390	7	consisting	consist	VERB
ejpam-6067	390	8	of	of	ADP
ejpam-6067	390	9	fσ	fσ	NOUN
ejpam-6067	390	10	sets	set	NOUN
ejpam-6067	390	11	has	have	VERB
ejpam-6067	390	12	a	a	DET
ejpam-6067	390	13	cluster	cluster	NOUN
ejpam-6067	390	14	point	point	NOUN
ejpam-6067	390	15	,	,	PUNCT
ejpam-6067	390	16	and	and	CCONJ
ejpam-6067	390	17	consider	consider	VERB
ejpam-6067	390	18	a	a	DET
ejpam-6067	390	19	g	g	NOUN
ejpam-6067	390	20	-	-	PUNCT
ejpam-6067	390	21	cover	cover	NOUN
ejpam-6067	390	22	g̃	g̃	PROPN
ejpam-6067	390	23	=	=	PUNCT
ejpam-6067	390	24	{	{	PUNCT
ejpam-6067	390	25	gα	gα	NOUN
ejpam-6067	390	26	:	:	PUNCT
ejpam-6067	390	27	α	α	PROPN
ejpam-6067	390	28	∈	∈	PROPN
ejpam-6067	390	29	∆	∆	PROPN
ejpam-6067	390	30	}	}	PUNCT
ejpam-6067	390	31	ofx	ofx	NOUN
ejpam-6067	390	32	with	with	ADP
ejpam-6067	390	33	no	no	DET
ejpam-6067	390	34	finite	finite	PROPN
ejpam-6067	390	35	subcover	subcover	PROPN
ejpam-6067	390	36	.	.	PUNCT
ejpam-6067	391	1	for	for	ADP
ejpam-6067	391	2	any	any	DET
ejpam-6067	391	3	finite	finite	ADJ
ejpam-6067	391	4	collection	collection	NOUN
ejpam-6067	391	5	{	{	PUNCT
ejpam-6067	391	6	gα1	gα1	NOUN
ejpam-6067	391	7	,	,	PUNCT
ejpam-6067	391	8	gα2	gα2	NOUN
ejpam-6067	391	9	,	,	PUNCT
ejpam-6067	391	10	.	.	PUNCT
ejpam-6067	391	11	.	.	PUNCT
ejpam-6067	391	12	.	.	PUNCT
ejpam-6067	392	1	,	,	PUNCT
ejpam-6067	392	2	gαn	gαn	PROPN
ejpam-6067	392	3	}	}	PUNCT
ejpam-6067	392	4	from	from	ADP
ejpam-6067	392	5	g̃	g̃	PROPN
ejpam-6067	392	6	,	,	PUNCT
ejpam-6067	392	7	we	we	PRON
ejpam-6067	392	8	have	have	VERB
ejpam-6067	392	9	⋃n	⋃n	NOUN
ejpam-6067	392	10	i=1gαi	i=1gαi	PROPN
ejpam-6067	392	11	̸=	̸=	PROPN
ejpam-6067	392	12	x	x	NUM
ejpam-6067	392	13	,	,	PUNCT
ejpam-6067	392	14	which	which	PRON
ejpam-6067	392	15	means	mean	VERB
ejpam-6067	392	16	⋂n	⋂n	PROPN
ejpam-6067	392	17	i=1(x	i=1(x	NOUN
ejpam-6067	392	18	\gαi	\gαi	NOUN
ejpam-6067	392	19	)	)	PUNCT
ejpam-6067	392	20	̸=	̸=	PROPN
ejpam-6067	392	21	∅.	∅.	ADV
ejpam-6067	392	22	since	since	SCONJ
ejpam-6067	392	23	each	each	DET
ejpam-6067	392	24	gαi	gαi	NOUN
ejpam-6067	392	25	constitutes	constitute	VERB
ejpam-6067	392	26	a	a	DET
ejpam-6067	392	27	gδ	gδ	NOUN
ejpam-6067	392	28	set	set	NOUN
ejpam-6067	392	29	,	,	PUNCT
ejpam-6067	392	30	each	each	PRON
ejpam-6067	392	31	x	x	PUNCT
ejpam-6067	392	32	\	\	PROPN
ejpam-6067	392	33	gαi	gαi	PROPN
ejpam-6067	392	34	forms	form	VERB
ejpam-6067	392	35	an	an	DET
ejpam-6067	392	36	fσ	fσ	NOUN
ejpam-6067	392	37	set	set	NOUN
ejpam-6067	392	38	.	.	PUNCT
ejpam-6067	393	1	the	the	DET
ejpam-6067	393	2	collection	collection	NOUN
ejpam-6067	393	3	{	{	PUNCT
ejpam-6067	393	4	x	x	SYM
ejpam-6067	393	5	\	\	ADJ
ejpam-6067	393	6	gα	gα	ADP
ejpam-6067	393	7	:	:	PUNCT
ejpam-6067	393	8	α	α	PROPN
ejpam-6067	393	9	∈	∈	PROPN
ejpam-6067	393	10	∆	∆	PROPN
ejpam-6067	393	11	}	}	PUNCT
ejpam-6067	393	12	has	have	VERB
ejpam-6067	393	13	the	the	DET
ejpam-6067	393	14	finite	finite	ADJ
ejpam-6067	393	15	intersection	intersection	NOUN
ejpam-6067	393	16	property	property	NOUN
ejpam-6067	393	17	and	and	CCONJ
ejpam-6067	393	18	consists	consist	VERB
ejpam-6067	393	19	of	of	ADP
ejpam-6067	393	20	fσ	fσ	NOUN
ejpam-6067	393	21	sets	set	NOUN
ejpam-6067	393	22	,	,	PUNCT
ejpam-6067	393	23	so	so	SCONJ
ejpam-6067	393	24	it	it	PRON
ejpam-6067	393	25	generates	generate	VERB
ejpam-6067	393	26	a	a	DET
ejpam-6067	393	27	filter	filter	NOUN
ejpam-6067	393	28	base	base	NOUN
ejpam-6067	393	29	of	of	ADP
ejpam-6067	393	30	fσ	fσ	NOUN
ejpam-6067	393	31	sets	set	NOUN
ejpam-6067	393	32	.	.	PUNCT
ejpam-6067	394	1	by	by	ADP
ejpam-6067	394	2	our	our	PRON
ejpam-6067	394	3	assumption	assumption	NOUN
ejpam-6067	394	4	,	,	PUNCT
ejpam-6067	394	5	this	this	DET
ejpam-6067	394	6	filter	filter	NOUN
ejpam-6067	394	7	base	base	NOUN
ejpam-6067	394	8	has	have	VERB
ejpam-6067	394	9	a	a	DET
ejpam-6067	394	10	cluster	cluster	NOUN
ejpam-6067	394	11	point	point	NOUN
ejpam-6067	394	12	x	x	X
ejpam-6067	394	13	∈	∈	NOUN
ejpam-6067	394	14	x.	x.	NOUN
ejpam-6067	394	15	but	but	CCONJ
ejpam-6067	394	16	xmust	xmust	PROPN
ejpam-6067	394	17	belong	belong	VERB
ejpam-6067	394	18	to	to	ADP
ejpam-6067	394	19	some	some	DET
ejpam-6067	394	20	gβ	gβ	NOUN
ejpam-6067	394	21	from	from	ADP
ejpam-6067	394	22	the	the	DET
ejpam-6067	394	23	original	original	ADJ
ejpam-6067	394	24	g	g	NOUN
ejpam-6067	394	25	-	-	PUNCT
ejpam-6067	394	26	cover	cover	NOUN
ejpam-6067	394	27	,	,	PUNCT
ejpam-6067	394	28	which	which	PRON
ejpam-6067	394	29	means	mean	VERB
ejpam-6067	394	30	x	x	X
ejpam-6067	394	31	∈	∈	PROPN
ejpam-6067	394	32	x\(x\gβ	x\(x\gβ	NUM
ejpam-6067	394	33	)	)	PUNCT
ejpam-6067	394	34	.	.	PUNCT
ejpam-6067	395	1	this	this	PRON
ejpam-6067	395	2	contradicts	contradict	VERB
ejpam-6067	395	3	x	x	X
ejpam-6067	395	4	being	be	AUX
ejpam-6067	395	5	a	a	DET
ejpam-6067	395	6	cluster	cluster	NOUN
ejpam-6067	395	7	point	point	NOUN
ejpam-6067	395	8	for	for	ADP
ejpam-6067	395	9	the	the	DET
ejpam-6067	395	10	filter	filter	NOUN
ejpam-6067	395	11	base	base	NOUN
ejpam-6067	395	12	,	,	PUNCT
ejpam-6067	395	13	as	as	SCONJ
ejpam-6067	395	14	x	x	PRON
ejpam-6067	395	15	has	have	VERB
ejpam-6067	395	16	a	a	DET
ejpam-6067	395	17	neighborhood	neighborhood	NOUN
ejpam-6067	395	18	disjoint	disjoint	NOUN
ejpam-6067	395	19	from	from	ADP
ejpam-6067	395	20	x	x	SYM
ejpam-6067	395	21	\	\	PROPN
ejpam-6067	395	22	gβ	gβ	PROPN
ejpam-6067	395	23	.	.	PUNCT
ejpam-6067	396	1	therefore	therefore	ADV
ejpam-6067	396	2	,	,	PUNCT
ejpam-6067	396	3	the	the	DET
ejpam-6067	396	4	original	original	ADJ
ejpam-6067	396	5	g	g	NOUN
ejpam-6067	396	6	-	-	PUNCT
ejpam-6067	396	7	cover	cover	NOUN
ejpam-6067	396	8	must	must	AUX
ejpam-6067	396	9	have	have	VERB
ejpam-6067	396	10	a	a	DET
ejpam-6067	396	11	finite	finite	ADJ
ejpam-6067	396	12	subcover	subcover	PROPN
ejpam-6067	396	13	,	,	PUNCT
ejpam-6067	396	14	establishing	establish	VERB
ejpam-6067	396	15	that	that	SCONJ
ejpam-6067	396	16	x	x	PUNCT
ejpam-6067	396	17	exhibits	exhibit	VERB
ejpam-6067	396	18	g	g	NOUN
ejpam-6067	396	19	-	-	PUNCT
ejpam-6067	396	20	compactness	compactness	NOUN
ejpam-6067	396	21	.	.	PUNCT
ejpam-6067	397	1	theorem	theorem	VERB
ejpam-6067	397	2	18	18	NUM
ejpam-6067	397	3	.	.	PUNCT
ejpam-6067	398	1	every	every	DET
ejpam-6067	398	2	paracompact	paracompact	ADJ
ejpam-6067	398	3	hausdorff	hausdorff	NOUN
ejpam-6067	398	4	space	space	NOUN
ejpam-6067	398	5	in	in	ADP
ejpam-6067	398	6	which	which	PRON
ejpam-6067	398	7	every	every	DET
ejpam-6067	398	8	closed	closed	ADJ
ejpam-6067	398	9	set	set	NOUN
ejpam-6067	398	10	forms	form	NOUN
ejpam-6067	398	11	a	a	DET
ejpam-6067	398	12	gδ	gδ	NOUN
ejpam-6067	398	13	set	set	NOUN
ejpam-6067	398	14	exhibits	exhibit	VERB
ejpam-6067	398	15	g	g	NOUN
ejpam-6067	398	16	-	-	PUNCT
ejpam-6067	398	17	lindelöfness	lindelöfness	NOUN
ejpam-6067	398	18	.	.	PUNCT
ejpam-6067	398	19	proof	proof	NOUN
ejpam-6067	398	20	.	.	PUNCT
ejpam-6067	399	1	let	let	VERB
ejpam-6067	399	2	(	(	PUNCT
ejpam-6067	399	3	x	x	NOUN
ejpam-6067	399	4	,	,	PUNCT
ejpam-6067	399	5	τ	τ	X
ejpam-6067	399	6	)	)	PUNCT
ejpam-6067	399	7	represent	represent	VERB
ejpam-6067	399	8	a	a	DET
ejpam-6067	399	9	paracompact	paracompact	ADJ
ejpam-6067	399	10	hausdorff	hausdorff	NOUN
ejpam-6067	399	11	space	space	NOUN
ejpam-6067	399	12	in	in	ADP
ejpam-6067	399	13	which	which	PRON
ejpam-6067	399	14	every	every	DET
ejpam-6067	399	15	closed	closed	ADJ
ejpam-6067	399	16	set	set	NOUN
ejpam-6067	399	17	forms	form	NOUN
ejpam-6067	399	18	a	a	DET
ejpam-6067	399	19	gδ	gδ	NOUN
ejpam-6067	399	20	set	set	NOUN
ejpam-6067	399	21	.	.	PUNCT
ejpam-6067	400	1	consider	consider	VERB
ejpam-6067	400	2	a	a	DET
ejpam-6067	400	3	g	g	NOUN
ejpam-6067	400	4	-	-	PUNCT
ejpam-6067	400	5	cover	cover	NOUN
ejpam-6067	400	6	g̃	g̃	PROPN
ejpam-6067	400	7	=	=	PUNCT
ejpam-6067	400	8	{	{	PUNCT
ejpam-6067	400	9	gα	gα	NOUN
ejpam-6067	400	10	:	:	PUNCT
ejpam-6067	400	11	α	α	PROPN
ejpam-6067	400	12	∈	∈	PROPN
ejpam-6067	400	13	∆	∆	PROPN
ejpam-6067	400	14	}	}	PUNCT
ejpam-6067	400	15	of	of	ADP
ejpam-6067	400	16	x.	x.	NOUN
ejpam-6067	400	17	since	since	SCONJ
ejpam-6067	400	18	x	x	PRON
ejpam-6067	400	19	demonstrates	demonstrate	VERB
ejpam-6067	400	20	paracompactness	paracompactness	NOUN
ejpam-6067	400	21	,	,	PUNCT
ejpam-6067	400	22	we	we	PRON
ejpam-6067	400	23	find	find	VERB
ejpam-6067	400	24	a	a	DET
ejpam-6067	400	25	locally	locally	ADV
ejpam-6067	400	26	finite	finite	ADJ
ejpam-6067	400	27	open	open	ADJ
ejpam-6067	400	28	refinement	refinement	NOUN
ejpam-6067	400	29	v	v	X
ejpam-6067	400	30	=	=	PUNCT
ejpam-6067	400	31	{	{	PUNCT
ejpam-6067	400	32	vβ	vβ	X
ejpam-6067	400	33	:	:	PUNCT
ejpam-6067	400	34	β	β	X
ejpam-6067	400	35	∈	∈	PROPN
ejpam-6067	400	36	γ	γ	X
ejpam-6067	400	37	}	}	PUNCT
ejpam-6067	400	38	of	of	ADP
ejpam-6067	400	39	g̃.	g̃.	ADJ
ejpam-6067	400	40	m.	m.	NOUN
ejpam-6067	400	41	shatnawi	shatnawi	PROPN
ejpam-6067	400	42	et	et	PROPN
ejpam-6067	400	43	al	al	PROPN
ejpam-6067	400	44	.	.	PUNCT
ejpam-6067	400	45	/	/	SYM
ejpam-6067	400	46	eur	eur	PROPN
ejpam-6067	400	47	.	.	PUNCT
ejpam-6067	401	1	j.	j.	PROPN
ejpam-6067	401	2	pure	pure	PROPN
ejpam-6067	401	3	appl	appl	PROPN
ejpam-6067	401	4	.	.	PROPN
ejpam-6067	401	5	math	math	PROPN
ejpam-6067	401	6	,	,	PUNCT
ejpam-6067	401	7	18	18	NUM
ejpam-6067	401	8	(	(	PUNCT
ejpam-6067	401	9	3	3	NUM
ejpam-6067	401	10	)	)	PUNCT
ejpam-6067	401	11	(	(	PUNCT
ejpam-6067	401	12	2025	2025	NUM
ejpam-6067	401	13	)	)	PUNCT
ejpam-6067	401	14	,	,	PUNCT
ejpam-6067	401	15	6067	6067	NUM
ejpam-6067	401	16	14	14	NUM
ejpam-6067	401	17	of	of	ADP
ejpam-6067	401	18	16	16	NUM
ejpam-6067	401	19	for	for	ADP
ejpam-6067	401	20	each	each	DET
ejpam-6067	401	21	x	x	SYM
ejpam-6067	401	22	∈	∈	PROPN
ejpam-6067	401	23	x	x	X
ejpam-6067	401	24	,	,	PUNCT
ejpam-6067	401	25	we	we	PRON
ejpam-6067	401	26	find	find	VERB
ejpam-6067	401	27	a	a	DET
ejpam-6067	401	28	neighborhood	neighborhood	NOUN
ejpam-6067	401	29	nx	nx	X
ejpam-6067	401	30	of	of	ADP
ejpam-6067	401	31	x	x	PRON
ejpam-6067	401	32	that	that	PRON
ejpam-6067	401	33	intersects	intersect	VERB
ejpam-6067	401	34	only	only	ADV
ejpam-6067	401	35	finitely	finitely	ADV
ejpam-6067	401	36	many	many	ADJ
ejpam-6067	401	37	members	member	NOUN
ejpam-6067	401	38	of	of	ADP
ejpam-6067	401	39	v	v	NOUN
ejpam-6067	401	40	,	,	PUNCT
ejpam-6067	401	41	say	say	VERB
ejpam-6067	401	42	vβ1	vβ1	NOUN
ejpam-6067	401	43	,	,	PUNCT
ejpam-6067	401	44	vβ2	vβ2	NOUN
ejpam-6067	401	45	,	,	PUNCT
ejpam-6067	401	46	.	.	PUNCT
ejpam-6067	401	47	.	.	PUNCT
ejpam-6067	401	48	.	.	PUNCT
ejpam-6067	402	1	,	,	PUNCT
ejpam-6067	402	2	vβnx	vβnx	VERB
ejpam-6067	402	3	.	.	PUNCT
ejpam-6067	403	1	for	for	ADP
ejpam-6067	403	2	each	each	DET
ejpam-6067	403	3	vβi	vβi	NOUN
ejpam-6067	403	4	,	,	PUNCT
ejpam-6067	403	5	we	we	PRON
ejpam-6067	403	6	find	find	VERB
ejpam-6067	403	7	a	a	DET
ejpam-6067	403	8	gαi	gαi	NOUN
ejpam-6067	403	9	in	in	ADP
ejpam-6067	403	10	g̃	g̃	PROPN
ejpam-6067	403	11	such	such	ADJ
ejpam-6067	403	12	that	that	SCONJ
ejpam-6067	403	13	vβi	vβi	NOUN
ejpam-6067	403	14	⊆	⊆	NUM
ejpam-6067	403	15	gαi	gαi	NOUN
ejpam-6067	403	16	.	.	PUNCT
ejpam-6067	404	1	let	let	VERB
ejpam-6067	404	2	g′	g′	NOUN
ejpam-6067	405	1	=	=	PRON
ejpam-6067	405	2	{	{	PUNCT
ejpam-6067	405	3	gαi	gαi	NOUN
ejpam-6067	405	4	:	:	PUNCT
ejpam-6067	405	5	i	i	NOUN
ejpam-6067	405	6	=	=	NOUN
ejpam-6067	405	7	1	1	NUM
ejpam-6067	405	8	,	,	PUNCT
ejpam-6067	405	9	2	2	NUM
ejpam-6067	405	10	,	,	PUNCT
ejpam-6067	405	11	.	.	PUNCT
ejpam-6067	405	12	.	.	PUNCT
ejpam-6067	405	13	.	.	PUNCT
ejpam-6067	406	1	,	,	PUNCT
ejpam-6067	406	2	nx	nx	X
ejpam-6067	406	3	,	,	PUNCT
ejpam-6067	406	4	x	x	SYM
ejpam-6067	406	5	∈	∈	NOUN
ejpam-6067	406	6	x	x	NOUN
ejpam-6067	406	7	}	}	PUNCT
ejpam-6067	406	8	.	.	PUNCT
ejpam-6067	407	1	since	since	SCONJ
ejpam-6067	407	2	v	v	NOUN
ejpam-6067	407	3	demonstrates	demonstrate	VERB
ejpam-6067	407	4	local	local	ADJ
ejpam-6067	407	5	finiteness	finiteness	NOUN
ejpam-6067	407	6	in	in	ADP
ejpam-6067	407	7	a	a	DET
ejpam-6067	407	8	paracompact	paracompact	ADJ
ejpam-6067	407	9	space	space	NOUN
ejpam-6067	407	10	,	,	PUNCT
ejpam-6067	407	11	g′	g′	NOUN
ejpam-6067	407	12	demonstrates	demonstrate	VERB
ejpam-6067	407	13	countability	countability	NOUN
ejpam-6067	407	14	.	.	PUNCT
ejpam-6067	408	1	therefore	therefore	ADV
ejpam-6067	408	2	,	,	PUNCT
ejpam-6067	408	3	g′	g′	NOUN
ejpam-6067	408	4	forms	form	VERB
ejpam-6067	408	5	a	a	DET
ejpam-6067	408	6	countable	countable	ADJ
ejpam-6067	408	7	subcover	subcover	NOUN
ejpam-6067	408	8	of	of	ADP
ejpam-6067	408	9	g̃	g̃	PROPN
ejpam-6067	408	10	,	,	PUNCT
ejpam-6067	408	11	establishing	establish	VERB
ejpam-6067	408	12	that	that	SCONJ
ejpam-6067	408	13	x	x	PUNCT
ejpam-6067	408	14	exhibits	exhibit	VERB
ejpam-6067	408	15	g	g	NOUN
ejpam-6067	408	16	-	-	PUNCT
ejpam-6067	408	17	lindelöfness	lindelöfness	NOUN
ejpam-6067	408	18	.	.	PUNCT
ejpam-6067	409	1	future	future	ADJ
ejpam-6067	409	2	research	research	NOUN
ejpam-6067	409	3	we	we	PRON
ejpam-6067	409	4	encourage	encourage	VERB
ejpam-6067	409	5	scholars	scholar	NOUN
ejpam-6067	409	6	to	to	PART
ejpam-6067	409	7	explore	explore	VERB
ejpam-6067	409	8	g	g	NOUN
ejpam-6067	409	9	-	-	PUNCT
ejpam-6067	409	10	compactness	compactness	NOUN
ejpam-6067	409	11	within	within	ADP
ejpam-6067	409	12	metric	metric	ADJ
ejpam-6067	409	13	spaces	space	NOUN
ejpam-6067	409	14	and	and	CCONJ
ejpam-6067	409	15	investigate	investigate	VERB
ejpam-6067	409	16	its	its	PRON
ejpam-6067	409	17	behavior	behavior	NOUN
ejpam-6067	409	18	under	under	ADP
ejpam-6067	409	19	various	various	ADJ
ejpam-6067	409	20	topological	topological	ADJ
ejpam-6067	409	21	constructions	construction	NOUN
ejpam-6067	409	22	,	,	PUNCT
ejpam-6067	409	23	extending	extend	VERB
ejpam-6067	409	24	work	work	NOUN
ejpam-6067	409	25	in	in	ADP
ejpam-6067	409	26	[	[	X
ejpam-6067	409	27	3	3	NUM
ejpam-6067	409	28	]	]	PUNCT
ejpam-6067	409	29	and	and	CCONJ
ejpam-6067	409	30	[	[	X
ejpam-6067	409	31	4	4	NUM
ejpam-6067	409	32	]	]	PUNCT
ejpam-6067	409	33	.	.	PUNCT
ejpam-6067	410	1	further	further	ADJ
ejpam-6067	410	2	research	research	NOUN
ejpam-6067	410	3	could	could	AUX
ejpam-6067	410	4	examine	examine	VERB
ejpam-6067	410	5	g	g	NOUN
ejpam-6067	410	6	-	-	PUNCT
ejpam-6067	410	7	compactness	compactness	NOUN
ejpam-6067	410	8	in	in	ADP
ejpam-6067	410	9	relation	relation	NOUN
ejpam-6067	410	10	to	to	PART
ejpam-6067	410	11	filter	filter	NOUN
ejpam-6067	410	12	convergence	convergence	NOUN
ejpam-6067	410	13	,	,	PUNCT
ejpam-6067	410	14	nets	net	NOUN
ejpam-6067	410	15	,	,	PUNCT
ejpam-6067	410	16	and	and	CCONJ
ejpam-6067	410	17	ultrafilters	ultrafilter	NOUN
ejpam-6067	410	18	,	,	PUNCT
ejpam-6067	410	19	building	build	VERB
ejpam-6067	410	20	on	on	ADP
ejpam-6067	410	21	concepts	concept	NOUN
ejpam-6067	410	22	from	from	ADP
ejpam-6067	410	23	[	[	X
ejpam-6067	410	24	15	15	NUM
ejpam-6067	410	25	]	]	PUNCT
ejpam-6067	410	26	and	and	CCONJ
ejpam-6067	410	27	[	[	X
ejpam-6067	410	28	16	16	NUM
ejpam-6067	410	29	]	]	PUNCT
ejpam-6067	410	30	.	.	PUNCT
ejpam-6067	411	1	the	the	DET
ejpam-6067	411	2	interaction	interaction	NOUN
ejpam-6067	411	3	between	between	ADP
ejpam-6067	411	4	g	g	NOUN
ejpam-6067	411	5	-	-	PUNCT
ejpam-6067	411	6	properties	property	NOUN
ejpam-6067	411	7	and	and	CCONJ
ejpam-6067	411	8	topological	topological	ADJ
ejpam-6067	411	9	dimension	dimension	NOUN
ejpam-6067	411	10	theory	theory	NOUN
ejpam-6067	411	11	also	also	ADV
ejpam-6067	411	12	presents	present	VERB
ejpam-6067	411	13	an	an	DET
ejpam-6067	411	14	interesting	interesting	ADJ
ejpam-6067	411	15	investigation	investigation	NOUN
ejpam-6067	411	16	avenue	avenue	PROPN
ejpam-6067	411	17	,	,	PUNCT
ejpam-6067	411	18	as	as	SCONJ
ejpam-6067	411	19	suggested	suggest	VERB
ejpam-6067	411	20	by	by	ADP
ejpam-6067	411	21	[	[	X
ejpam-6067	411	22	18	18	NUM
ejpam-6067	411	23	]	]	PUNCT
ejpam-6067	411	24	.	.	PUNCT
ejpam-6067	412	1	another	another	DET
ejpam-6067	412	2	promising	promising	ADJ
ejpam-6067	412	3	direction	direction	NOUN
ejpam-6067	412	4	involves	involve	VERB
ejpam-6067	412	5	studying	study	VERB
ejpam-6067	412	6	g	g	NOUN
ejpam-6067	412	7	-	-	PUNCT
ejpam-6067	412	8	compactness	compactness	NOUN
ejpam-6067	412	9	in	in	ADP
ejpam-6067	412	10	function	function	NOUN
ejpam-6067	412	11	spaces	space	NOUN
ejpam-6067	412	12	,	,	PUNCT
ejpam-6067	412	13	particularly	particularly	ADV
ejpam-6067	412	14	regarding	regard	VERB
ejpam-6067	412	15	continuous	continuous	ADJ
ejpam-6067	412	16	functions	function	NOUN
ejpam-6067	412	17	,	,	PUNCT
ejpam-6067	412	18	uniform	uniform	ADJ
ejpam-6067	412	19	convergence	convergence	NOUN
ejpam-6067	412	20	,	,	PUNCT
ejpam-6067	412	21	and	and	CCONJ
ejpam-6067	412	22	equicontinuity	equicontinuity	NOUN
ejpam-6067	412	23	.	.	PUNCT
ejpam-6067	413	1	the	the	DET
ejpam-6067	413	2	relationship	relationship	NOUN
ejpam-6067	413	3	between	between	ADP
ejpam-6067	413	4	g	g	NOUN
ejpam-6067	413	5	-	-	PUNCT
ejpam-6067	413	6	compactness	compactness	NOUN
ejpam-6067	413	7	and	and	CCONJ
ejpam-6067	413	8	completeness	completeness	NOUN
ejpam-6067	413	9	in	in	ADP
ejpam-6067	413	10	metric	metric	ADJ
ejpam-6067	413	11	spaces	space	NOUN
ejpam-6067	413	12	could	could	AUX
ejpam-6067	413	13	yield	yield	VERB
ejpam-6067	413	14	new	new	ADJ
ejpam-6067	413	15	insights	insight	NOUN
ejpam-6067	413	16	into	into	ADP
ejpam-6067	413	17	topological	topological	ADJ
ejpam-6067	413	18	spaces	space	NOUN
ejpam-6067	413	19	’	'	PUNCT
ejpam-6067	413	20	structure	structure	NOUN
ejpam-6067	413	21	.	.	PUNCT
ejpam-6067	414	1	additionally	additionally	ADV
ejpam-6067	414	2	,	,	PUNCT
ejpam-6067	414	3	developing	develop	VERB
ejpam-6067	414	4	more	more	ADV
ejpam-6067	414	5	refined	refined	ADJ
ejpam-6067	414	6	g	g	NOUN
ejpam-6067	414	7	-	-	PUNCT
ejpam-6067	414	8	separation	separation	NOUN
ejpam-6067	414	9	axioms	axiom	NOUN
ejpam-6067	414	10	based	base	VERB
ejpam-6067	414	11	on	on	ADP
ejpam-6067	414	12	gδ	gδ	NOUN
ejpam-6067	414	13	sets	set	NOUN
ejpam-6067	414	14	could	could	AUX
ejpam-6067	414	15	generate	generate	VERB
ejpam-6067	414	16	new	new	ADJ
ejpam-6067	414	17	set	set	NOUN
ejpam-6067	414	18	-	-	PUNCT
ejpam-6067	414	19	theoretic	theoretic	NOUN
ejpam-6067	414	20	topology	topology	NOUN
ejpam-6067	414	21	insights	insight	NOUN
ejpam-6067	414	22	,	,	PUNCT
ejpam-6067	414	23	following	follow	VERB
ejpam-6067	414	24	approaches	approach	NOUN
ejpam-6067	414	25	in	in	ADP
ejpam-6067	414	26	[	[	X
ejpam-6067	414	27	9	9	NUM
ejpam-6067	414	28	]	]	PUNCT
ejpam-6067	414	29	and	and	CCONJ
ejpam-6067	414	30	[	[	X
ejpam-6067	414	31	17	17	NUM
ejpam-6067	414	32	]	]	PUNCT
ejpam-6067	414	33	.	.	PUNCT
ejpam-6067	415	1	the	the	DET
ejpam-6067	415	2	connections	connection	NOUN
ejpam-6067	415	3	between	between	ADP
ejpam-6067	415	4	g	g	NOUN
ejpam-6067	415	5	-	-	PUNCT
ejpam-6067	415	6	compactness	compactness	NOUN
ejpam-6067	415	7	and	and	CCONJ
ejpam-6067	415	8	descriptive	descriptive	ADJ
ejpam-6067	415	9	set	set	NOUN
ejpam-6067	415	10	theory	theory	NOUN
ejpam-6067	415	11	,	,	PUNCT
ejpam-6067	415	12	particularly	particularly	ADV
ejpam-6067	415	13	the	the	DET
ejpam-6067	415	14	classification	classification	NOUN
ejpam-6067	415	15	of	of	ADP
ejpam-6067	415	16	borel	borel	NOUN
ejpam-6067	415	17	sets	set	NOUN
ejpam-6067	415	18	and	and	CCONJ
ejpam-6067	415	19	analytic	analytic	ADJ
ejpam-6067	415	20	sets	set	NOUN
ejpam-6067	415	21	,	,	PUNCT
ejpam-6067	415	22	present	present	ADJ
ejpam-6067	415	23	rich	rich	ADJ
ejpam-6067	415	24	exploration	exploration	NOUN
ejpam-6067	415	25	opportunities	opportunity	NOUN
ejpam-6067	415	26	.	.	PUNCT
ejpam-6067	416	1	conclusion	conclusion	NOUN
ejpam-6067	416	2	in	in	ADP
ejpam-6067	416	3	this	this	DET
ejpam-6067	416	4	paper	paper	NOUN
ejpam-6067	416	5	,	,	PUNCT
ejpam-6067	416	6	we	we	PRON
ejpam-6067	416	7	have	have	AUX
ejpam-6067	416	8	established	establish	VERB
ejpam-6067	416	9	a	a	DET
ejpam-6067	416	10	new	new	ADJ
ejpam-6067	416	11	framework	framework	NOUN
ejpam-6067	416	12	for	for	ADP
ejpam-6067	416	13	studying	study	VERB
ejpam-6067	416	14	topological	topological	ADJ
ejpam-6067	416	15	spaces	space	NOUN
ejpam-6067	416	16	through	through	ADP
ejpam-6067	416	17	gδ	gδ	PROPN
ejpam-6067	416	18	sets	set	NOUN
ejpam-6067	416	19	.	.	PUNCT
ejpam-6067	417	1	the	the	DET
ejpam-6067	417	2	introduced	introduce	VERB
ejpam-6067	417	3	concepts	concept	NOUN
ejpam-6067	417	4	of	of	ADP
ejpam-6067	417	5	g	g	NOUN
ejpam-6067	417	6	-	-	PUNCT
ejpam-6067	417	7	compactness	compactness	NOUN
ejpam-6067	417	8	,	,	PUNCT
ejpam-6067	417	9	g	g	NOUN
ejpam-6067	417	10	-	-	PUNCT
ejpam-6067	417	11	lindelöfness	lindelöfness	NOUN
ejpam-6067	417	12	,	,	PUNCT
ejpam-6067	417	13	and	and	CCONJ
ejpam-6067	417	14	gcountably	gcountably	ADV
ejpam-6067	417	15	compactness	compactness	NOUN
ejpam-6067	417	16	impose	impose	VERB
ejpam-6067	417	17	stronger	strong	ADJ
ejpam-6067	417	18	requirements	requirement	NOUN
ejpam-6067	417	19	than	than	ADP
ejpam-6067	417	20	their	their	PRON
ejpam-6067	417	21	classical	classical	ADJ
ejpam-6067	417	22	counterparts	counterpart	NOUN
ejpam-6067	417	23	,	,	PUNCT
ejpam-6067	417	24	creating	create	VERB
ejpam-6067	417	25	finer	fine	ADJ
ejpam-6067	417	26	distinctions	distinction	NOUN
ejpam-6067	417	27	among	among	ADP
ejpam-6067	417	28	topological	topological	ADJ
ejpam-6067	417	29	spaces	space	NOUN
ejpam-6067	417	30	.	.	PUNCT
ejpam-6067	418	1	our	our	PRON
ejpam-6067	418	2	results	result	NOUN
ejpam-6067	418	3	demonstrate	demonstrate	VERB
ejpam-6067	418	4	that	that	SCONJ
ejpam-6067	418	5	while	while	SCONJ
ejpam-6067	418	6	these	these	DET
ejpam-6067	418	7	g	g	NOUN
ejpam-6067	418	8	-	-	PUNCT
ejpam-6067	418	9	properties	property	NOUN
ejpam-6067	418	10	imply	imply	VERB
ejpam-6067	418	11	their	their	PRON
ejpam-6067	418	12	corresponding	corresponding	ADJ
ejpam-6067	418	13	classical	classical	ADJ
ejpam-6067	418	14	properties	property	NOUN
ejpam-6067	418	15	,	,	PUNCT
ejpam-6067	418	16	the	the	DET
ejpam-6067	418	17	converse	converse	NOUN
ejpam-6067	418	18	relationships	relationship	NOUN
ejpam-6067	418	19	generally	generally	ADV
ejpam-6067	418	20	fail	fail	VERB
ejpam-6067	418	21	,	,	PUNCT
ejpam-6067	418	22	as	as	SCONJ
ejpam-6067	418	23	our	our	PRON
ejpam-6067	418	24	carefully	carefully	ADV
ejpam-6067	418	25	constructed	construct	VERB
ejpam-6067	418	26	counterexamples	counterexample	NOUN
ejpam-6067	418	27	illustrate	illustrate	VERB
ejpam-6067	418	28	.	.	PUNCT
ejpam-6067	419	1	the	the	DET
ejpam-6067	419	2	g	g	NOUN
ejpam-6067	419	3	-	-	PUNCT
ejpam-6067	419	4	separation	separation	NOUN
ejpam-6067	419	5	axioms	axiom	NOUN
ejpam-6067	419	6	we	we	PRON
ejpam-6067	419	7	’ve	’ve	AUX
ejpam-6067	419	8	developed	develop	VERB
ejpam-6067	419	9	form	form	VERB
ejpam-6067	419	10	a	a	DET
ejpam-6067	419	11	hierarchy	hierarchy	NOUN
ejpam-6067	419	12	paralleling	parallel	VERB
ejpam-6067	419	13	the	the	DET
ejpam-6067	419	14	classical	classical	ADJ
ejpam-6067	419	15	separation	separation	NOUN
ejpam-6067	419	16	axioms	axiom	VERB
ejpam-6067	419	17	,	,	PUNCT
ejpam-6067	419	18	but	but	CCONJ
ejpam-6067	419	19	with	with	ADP
ejpam-6067	419	20	distinctive	distinctive	ADJ
ejpam-6067	419	21	characteristics	characteristic	NOUN
ejpam-6067	419	22	allowing	allow	VERB
ejpam-6067	419	23	classification	classification	NOUN
ejpam-6067	419	24	of	of	ADP
ejpam-6067	419	25	spaces	space	NOUN
ejpam-6067	419	26	indistinguishable	indistinguishable	ADJ
ejpam-6067	419	27	under	under	ADP
ejpam-6067	419	28	traditional	traditional	ADJ
ejpam-6067	419	29	separation	separation	NOUN
ejpam-6067	419	30	properties	property	NOUN
ejpam-6067	419	31	.	.	PUNCT
ejpam-6067	420	1	we	we	PRON
ejpam-6067	420	2	’ve	’ve	AUX
ejpam-6067	420	3	shown	show	VERB
ejpam-6067	420	4	that	that	SCONJ
ejpam-6067	420	5	certain	certain	ADJ
ejpam-6067	420	6	spaces	space	NOUN
ejpam-6067	420	7	can	can	AUX
ejpam-6067	420	8	exhibit	exhibit	VERB
ejpam-6067	420	9	tδ2	tδ2	VERB
ejpam-6067	420	10	without	without	ADP
ejpam-6067	420	11	demonstrating	demonstrate	VERB
ejpam-6067	420	12	t2	t2	NOUN
ejpam-6067	420	13	,	,	PUNCT
ejpam-6067	420	14	highlighting	highlight	VERB
ejpam-6067	420	15	these	these	DET
ejpam-6067	420	16	new	new	ADJ
ejpam-6067	420	17	axioms	axiom	NOUN
ejpam-6067	420	18	utility	utility	NOUN
ejpam-6067	420	19	.	.	PUNCT
ejpam-6067	421	1	the	the	DET
ejpam-6067	421	2	relationships	relationship	NOUN
ejpam-6067	421	3	we	we	PRON
ejpam-6067	421	4	’ve	’ve	AUX
ejpam-6067	421	5	established	establish	VERB
ejpam-6067	421	6	with	with	ADP
ejpam-6067	421	7	other	other	ADJ
ejpam-6067	421	8	compactness	compactness	NOUN
ejpam-6067	421	9	-	-	PUNCT
ejpam-6067	421	10	like	like	ADJ
ejpam-6067	421	11	properties	property	NOUN
ejpam-6067	421	12	(	(	PUNCT
ejpam-6067	421	13	metacompactness	metacompactness	NOUN
ejpam-6067	421	14	,	,	PUNCT
ejpam-6067	421	15	paracompactness	paracompactness	NOUN
ejpam-6067	421	16	)	)	PUNCT
ejpam-6067	421	17	further	far	ADV
ejpam-6067	421	18	integrate	integrate	VERB
ejpam-6067	421	19	our	our	PRON
ejpam-6067	421	20	g	g	NOUN
ejpam-6067	421	21	-	-	PUNCT
ejpam-6067	421	22	properties	property	NOUN
ejpam-6067	421	23	into	into	ADP
ejpam-6067	421	24	the	the	DET
ejpam-6067	421	25	broader	broad	ADJ
ejpam-6067	421	26	topological	topological	ADJ
ejpam-6067	421	27	theory	theory	NOUN
ejpam-6067	421	28	landscape	landscape	NOUN
ejpam-6067	421	29	.	.	PUNCT
ejpam-6067	422	1	furthermore	furthermore	ADV
ejpam-6067	422	2	,	,	PUNCT
ejpam-6067	422	3	our	our	PRON
ejpam-6067	422	4	results	result	NOUN
ejpam-6067	422	5	on	on	ADP
ejpam-6067	422	6	g	g	NOUN
ejpam-6067	422	7	-	-	PUNCT
ejpam-6067	422	8	compactness	compactness	NOUN
ejpam-6067	422	9	behavior	behavior	NOUN
ejpam-6067	422	10	under	under	ADP
ejpam-6067	422	11	various	various	ADJ
ejpam-6067	422	12	topological	topological	ADJ
ejpam-6067	422	13	operations	operation	NOUN
ejpam-6067	422	14	,	,	PUNCT
ejpam-6067	422	15	such	such	ADJ
ejpam-6067	422	16	as	as	ADP
ejpam-6067	422	17	continuous	continuous	ADJ
ejpam-6067	422	18	maps	map	NOUN
ejpam-6067	422	19	,	,	PUNCT
ejpam-6067	422	20	product	product	NOUN
ejpam-6067	422	21	spaces	space	NOUN
ejpam-6067	422	22	,	,	PUNCT
ejpam-6067	422	23	and	and	CCONJ
ejpam-6067	422	24	subspaces	subspace	NOUN
ejpam-6067	422	25	,	,	PUNCT
ejpam-6067	422	26	provide	provide	VERB
ejpam-6067	422	27	tools	tool	NOUN
ejpam-6067	422	28	for	for	ADP
ejpam-6067	422	29	recognizing	recognize	VERB
ejpam-6067	422	30	and	and	CCONJ
ejpam-6067	422	31	applying	apply	VERB
ejpam-6067	422	32	these	these	DET
ejpam-6067	422	33	properties	property	NOUN
ejpam-6067	422	34	in	in	ADP
ejpam-6067	422	35	diverse	diverse	ADJ
ejpam-6067	422	36	contexts	contexts	NOUN
ejpam-6067	422	37	.	.	PUNCT
ejpam-6067	423	1	our	our	PRON
ejpam-6067	423	2	characterization	characterization	NOUN
ejpam-6067	423	3	of	of	ADP
ejpam-6067	423	4	g	g	NOUN
ejpam-6067	423	5	-	-	PUNCT
ejpam-6067	423	6	compactness	compactness	NOUN
ejpam-6067	423	7	in	in	ADP
ejpam-6067	423	8	terms	term	NOUN
ejpam-6067	423	9	of	of	ADP
ejpam-6067	423	10	filter	filter	NOUN
ejpam-6067	423	11	bases	basis	NOUN
ejpam-6067	423	12	consisting	consist	VERB
ejpam-6067	423	13	of	of	ADP
ejpam-6067	423	14	fσ	fσ	NOUN
ejpam-6067	423	15	sets	set	NOUN
ejpam-6067	423	16	connects	connect	VERB
ejpam-6067	423	17	this	this	DET
ejpam-6067	423	18	concept	concept	NOUN
ejpam-6067	423	19	with	with	ADP
ejpam-6067	423	20	classical	classical	ADJ
ejpam-6067	423	21	filter	filter	NOUN
ejpam-6067	423	22	-	-	PUNCT
ejpam-6067	423	23	theoretic	theoretic	ADJ
ejpam-6067	423	24	approaches	approach	NOUN
ejpam-6067	423	25	to	to	ADP
ejpam-6067	423	26	compactness	compactness	NOUN
ejpam-6067	423	27	.	.	PUNCT
ejpam-6067	424	1	similarly	similarly	ADV
ejpam-6067	424	2	,	,	PUNCT
ejpam-6067	424	3	m.	m.	NOUN
ejpam-6067	424	4	shatnawi	shatnawi	PROPN
ejpam-6067	424	5	et	et	PROPN
ejpam-6067	424	6	al	al	PROPN
ejpam-6067	424	7	.	.	PUNCT
ejpam-6067	424	8	/	/	SYM
ejpam-6067	424	9	eur	eur	PROPN
ejpam-6067	424	10	.	.	PUNCT
ejpam-6067	425	1	j.	j.	PROPN
ejpam-6067	425	2	pure	pure	PROPN
ejpam-6067	425	3	appl	appl	PROPN
ejpam-6067	425	4	.	.	PROPN
ejpam-6067	425	5	math	math	PROPN
ejpam-6067	425	6	,	,	PUNCT
ejpam-6067	425	7	18	18	NUM
ejpam-6067	425	8	(	(	PUNCT
ejpam-6067	425	9	3	3	NUM
ejpam-6067	425	10	)	)	PUNCT
ejpam-6067	425	11	(	(	PUNCT
ejpam-6067	425	12	2025	2025	NUM
ejpam-6067	425	13	)	)	PUNCT
ejpam-6067	425	14	,	,	PUNCT
ejpam-6067	425	15	6067	6067	NUM
ejpam-6067	425	16	15	15	NUM
ejpam-6067	425	17	of	of	ADP
ejpam-6067	425	18	16	16	NUM
ejpam-6067	425	19	the	the	DET
ejpam-6067	425	20	relationship	relationship	NOUN
ejpam-6067	425	21	between	between	ADP
ejpam-6067	425	22	g	g	NOUN
ejpam-6067	425	23	-	-	PUNCT
ejpam-6067	425	24	separation	separation	NOUN
ejpam-6067	425	25	axioms	axiom	NOUN
ejpam-6067	425	26	and	and	CCONJ
ejpam-6067	425	27	the	the	DET
ejpam-6067	425	28	diagonal	diagonal	ADJ
ejpam-6067	425	29	in	in	ADP
ejpam-6067	425	30	product	product	NOUN
ejpam-6067	425	31	spaces	space	NOUN
ejpam-6067	425	32	provides	provide	VERB
ejpam-6067	425	33	a	a	DET
ejpam-6067	425	34	geometric	geometric	ADJ
ejpam-6067	425	35	perspective	perspective	NOUN
ejpam-6067	425	36	on	on	ADP
ejpam-6067	425	37	these	these	DET
ejpam-6067	425	38	properties	property	NOUN
ejpam-6067	425	39	.	.	PUNCT
ejpam-6067	426	1	this	this	DET
ejpam-6067	426	2	research	research	NOUN
ejpam-6067	426	3	contributes	contribute	VERB
ejpam-6067	426	4	to	to	ADP
ejpam-6067	426	5	the	the	DET
ejpam-6067	426	6	ongoing	ongoing	ADJ
ejpam-6067	426	7	refinement	refinement	NOUN
ejpam-6067	426	8	of	of	ADP
ejpam-6067	426	9	topological	topological	ADJ
ejpam-6067	426	10	classification	classification	NOUN
ejpam-6067	426	11	schemes	scheme	NOUN
ejpam-6067	426	12	and	and	CCONJ
ejpam-6067	426	13	opens	open	VERB
ejpam-6067	426	14	avenues	avenue	NOUN
ejpam-6067	426	15	for	for	ADP
ejpam-6067	426	16	exploring	explore	VERB
ejpam-6067	426	17	topological	topological	ADJ
ejpam-6067	426	18	spaces	space	NOUN
ejpam-6067	426	19	’	'	PUNCT
ejpam-6067	426	20	structure	structure	NOUN
ejpam-6067	426	21	through	through	ADP
ejpam-6067	426	22	increasingly	increasingly	ADV
ejpam-6067	426	23	sophisticated	sophisticated	ADJ
ejpam-6067	426	24	properties	property	NOUN
ejpam-6067	426	25	.	.	PUNCT
ejpam-6067	427	1	the	the	DET
ejpam-6067	427	2	g	g	NOUN
ejpam-6067	427	3	-	-	PUNCT
ejpam-6067	427	4	framework	framework	NOUN
ejpam-6067	427	5	introduced	introduce	VERB
ejpam-6067	427	6	here	here	ADV
ejpam-6067	427	7	can	can	AUX
ejpam-6067	427	8	potentially	potentially	ADV
ejpam-6067	427	9	lead	lead	VERB
ejpam-6067	427	10	to	to	ADP
ejpam-6067	427	11	new	new	ADJ
ejpam-6067	427	12	insights	insight	NOUN
ejpam-6067	427	13	in	in	ADP
ejpam-6067	427	14	functional	functional	ADJ
ejpam-6067	427	15	analysis	analysis	NOUN
ejpam-6067	427	16	,	,	PUNCT
ejpam-6067	427	17	set	set	NOUN
ejpam-6067	427	18	-	-	PUNCT
ejpam-6067	427	19	theoretic	theoretic	NOUN
ejpam-6067	427	20	topology	topology	NOUN
ejpam-6067	427	21	,	,	PUNCT
ejpam-6067	427	22	and	and	CCONJ
ejpam-6067	427	23	related	related	ADJ
ejpam-6067	427	24	mathematical	mathematical	ADJ
ejpam-6067	427	25	disciplines	discipline	NOUN
ejpam-6067	427	26	.	.	PUNCT
ejpam-6067	428	1	references	reference	NOUN
ejpam-6067	428	2	[	[	X
ejpam-6067	428	3	1	1	NUM
ejpam-6067	428	4	]	]	PUNCT
ejpam-6067	428	5	willard	willard	NOUN
ejpam-6067	428	6	,	,	PUNCT
ejpam-6067	428	7	s.	s.	PROPN
ejpam-6067	428	8	(	(	PUNCT
ejpam-6067	428	9	2012	2012	NUM
ejpam-6067	428	10	)	)	PUNCT
ejpam-6067	428	11	.	.	PUNCT
ejpam-6067	429	1	general	general	ADJ
ejpam-6067	429	2	topology	topology	NOUN
ejpam-6067	429	3	.	.	PUNCT
ejpam-6067	430	1	courier	courier	NOUN
ejpam-6067	430	2	corporation	corporation	NOUN
ejpam-6067	430	3	.	.	PUNCT
ejpam-6067	431	1	[	[	X
ejpam-6067	431	2	2	2	NUM
ejpam-6067	431	3	]	]	X
ejpam-6067	431	4	kelley	kelley	PROPN
ejpam-6067	431	5	,	,	PUNCT
ejpam-6067	431	6	j.l	j.l	PROPN
ejpam-6067	431	7	.	.	PROPN
ejpam-6067	431	8	,	,	PUNCT
ejpam-6067	431	9	2017	2017	NUM
ejpam-6067	431	10	.	.	PUNCT
ejpam-6067	432	1	general	general	ADJ
ejpam-6067	432	2	topology	topology	NOUN
ejpam-6067	432	3	.	.	PUNCT
ejpam-6067	433	1	courier	courier	PROPN
ejpam-6067	433	2	dover	dover	PROPN
ejpam-6067	433	3	publications	publication	NOUN
ejpam-6067	434	1	.	.	PUNCT
ejpam-6067	435	1	[	[	X
ejpam-6067	435	2	3	3	NUM
ejpam-6067	435	3	]	]	X
ejpam-6067	435	4	kreyszig	kreyszig	PROPN
ejpam-6067	435	5	,	,	PUNCT
ejpam-6067	435	6	e.	e.	PROPN
ejpam-6067	435	7	,	,	PUNCT
ejpam-6067	435	8	1991	1991	NUM
ejpam-6067	435	9	.	.	PUNCT
ejpam-6067	436	1	introductory	introductory	ADJ
ejpam-6067	436	2	functional	functional	ADJ
ejpam-6067	436	3	analysis	analysis	NOUN
ejpam-6067	436	4	with	with	ADP
ejpam-6067	436	5	applications	application	NOUN
ejpam-6067	436	6	(	(	PUNCT
ejpam-6067	436	7	vol	vol	NOUN
ejpam-6067	436	8	.	.	PROPN
ejpam-6067	436	9	17	17	NUM
ejpam-6067	436	10	)	)	PUNCT
ejpam-6067	436	11	.	.	PUNCT
ejpam-6067	437	1	john	john	PROPN
ejpam-6067	437	2	wiley	wiley	PROPN
ejpam-6067	437	3	&	&	CCONJ
ejpam-6067	437	4	sons	son	NOUN
ejpam-6067	437	5	.	.	PUNCT
ejpam-6067	438	1	[	[	X
ejpam-6067	438	2	4	4	NUM
ejpam-6067	438	3	]	]	X
ejpam-6067	438	4	shatanawi	shatanawi	ADJ
ejpam-6067	438	5	,	,	PUNCT
ejpam-6067	438	6	w.	w.	PROPN
ejpam-6067	438	7	,	,	PUNCT
ejpam-6067	438	8	qawasmeh	qawasmeh	NOUN
ejpam-6067	438	9	,	,	PUNCT
ejpam-6067	438	10	t.	t.	PROPN
ejpam-6067	438	11	,	,	PUNCT
ejpam-6067	438	12	bataihah	bataihah	PROPN
ejpam-6067	438	13	,	,	PUNCT
ejpam-6067	438	14	a.	a.	NOUN
ejpam-6067	438	15	and	and	CCONJ
ejpam-6067	438	16	tallafha	tallafha	NOUN
ejpam-6067	438	17	,	,	PUNCT
ejpam-6067	438	18	a.	a.	NOUN
ejpam-6067	438	19	,	,	PUNCT
ejpam-6067	438	20	2021	2021	NUM
ejpam-6067	438	21	.	.	PUNCT
ejpam-6067	439	1	new	new	ADJ
ejpam-6067	439	2	contractions	contraction	NOUN
ejpam-6067	439	3	and	and	CCONJ
ejpam-6067	439	4	some	some	DET
ejpam-6067	439	5	fixed	fix	VERB
ejpam-6067	439	6	point	point	NOUN
ejpam-6067	439	7	results	result	NOUN
ejpam-6067	439	8	with	with	ADP
ejpam-6067	439	9	application	application	NOUN
ejpam-6067	439	10	based	base	VERB
ejpam-6067	439	11	on	on	ADP
ejpam-6067	439	12	extended	extended	ADJ
ejpam-6067	439	13	quasi	quasi	ADJ
ejpam-6067	439	14	b	b	NOUN
ejpam-6067	439	15	-	-	PUNCT
ejpam-6067	439	16	metric	metric	ADJ
ejpam-6067	439	17	space	space	NOUN
ejpam-6067	439	18	.	.	PUNCT
ejpam-6067	440	1	upb	upb	ADJ
ejpam-6067	440	2	scientific	scientific	ADJ
ejpam-6067	440	3	bulletin	bulletin	NOUN
ejpam-6067	440	4	,	,	PUNCT
ejpam-6067	440	5	series	series	PROPN
ejpam-6067	440	6	a	a	PRON
ejpam-6067	440	7	:	:	PUNCT
ejpam-6067	440	8	applied	apply	VERB
ejpam-6067	440	9	mathematics	mathematic	NOUN
ejpam-6067	440	10	and	and	CCONJ
ejpam-6067	440	11	physics	physics	NOUN
ejpam-6067	440	12	,	,	PUNCT
ejpam-6067	440	13	83(2	83(2	NUM
ejpam-6067	440	14	)	)	PUNCT
ejpam-6067	440	15	,	,	PUNCT
ejpam-6067	440	16	pp.39	pp.39	NOUN
ejpam-6067	440	17	-	-	PUNCT
ejpam-6067	440	18	48	48	NUM
ejpam-6067	440	19	.	.	PUNCT
ejpam-6067	441	1	[	[	X
ejpam-6067	441	2	5	5	NUM
ejpam-6067	441	3	]	]	SYM
ejpam-6067	441	4	oudetallah	oudetallah	PROPN
ejpam-6067	441	5	,	,	PUNCT
ejpam-6067	441	6	j.	j.	PROPN
ejpam-6067	441	7	,	,	PUNCT
ejpam-6067	441	8	2022	2022	NUM
ejpam-6067	441	9	.	.	PUNCT
ejpam-6067	442	1	nearly	nearly	ADV
ejpam-6067	442	2	metacompact	metacompact	VERB
ejpam-6067	442	3	in	in	ADP
ejpam-6067	442	4	bitopological	bitopological	ADJ
ejpam-6067	442	5	space	space	NOUN
ejpam-6067	442	6	.	.	PUNCT
ejpam-6067	443	1	international	international	ADJ
ejpam-6067	443	2	journal	journal	NOUN
ejpam-6067	443	3	of	of	ADP
ejpam-6067	443	4	open	open	ADJ
ejpam-6067	443	5	problems	problem	NOUN
ejpam-6067	443	6	in	in	ADP
ejpam-6067	443	7	computer	computer	NOUN
ejpam-6067	443	8	science	science	PROPN
ejpam-6067	443	9	&	&	CCONJ
ejpam-6067	443	10	mathematics	mathematic	NOUN
ejpam-6067	443	11	,	,	PUNCT
ejpam-6067	443	12	15(3	15(3	NUM
ejpam-6067	443	13	)	)	PUNCT
ejpam-6067	443	14	.	.	PUNCT
ejpam-6067	444	1	[	[	X
ejpam-6067	444	2	6	6	NUM
ejpam-6067	444	3	]	]	X
ejpam-6067	444	4	shatanawi	shatanawi	PROPN
ejpam-6067	444	5	,	,	PUNCT
ejpam-6067	444	6	w.	w.	PROPN
ejpam-6067	444	7	,	,	PUNCT
ejpam-6067	444	8	maniu	maniu	PROPN
ejpam-6067	444	9	,	,	PUNCT
ejpam-6067	444	10	g.	g.	PROPN
ejpam-6067	444	11	,	,	PUNCT
ejpam-6067	444	12	bataihah	bataihah	PROPN
ejpam-6067	444	13	,	,	PUNCT
ejpam-6067	444	14	a.	a.	NOUN
ejpam-6067	444	15	and	and	CCONJ
ejpam-6067	444	16	ahmad	ahmad	PROPN
ejpam-6067	444	17	,	,	PUNCT
ejpam-6067	444	18	f.b	f.b	PROPN
ejpam-6067	444	19	.	.	PROPN
ejpam-6067	444	20	,	,	PUNCT
ejpam-6067	444	21	2017	2017	NUM
ejpam-6067	444	22	.	.	PUNCT
ejpam-6067	445	1	common	common	ADJ
ejpam-6067	445	2	fixed	fix	VERB
ejpam-6067	445	3	points	point	NOUN
ejpam-6067	445	4	for	for	ADP
ejpam-6067	445	5	mappings	mapping	NOUN
ejpam-6067	445	6	of	of	ADP
ejpam-6067	445	7	cyclic	cyclic	ADJ
ejpam-6067	445	8	form	form	NOUN
ejpam-6067	445	9	satisfying	satisfy	VERB
ejpam-6067	445	10	linear	linear	PROPN
ejpam-6067	445	11	contractive	contractive	ADJ
ejpam-6067	445	12	conditions	condition	NOUN
ejpam-6067	445	13	with	with	ADP
ejpam-6067	445	14	omegadistance	omegadistance	NOUN
ejpam-6067	445	15	.	.	PUNCT
ejpam-6067	446	1	upb	upb	PROPN
ejpam-6067	446	2	sci	sci	PROPN
ejpam-6067	446	3	.	.	PROPN
ejpam-6067	446	4	,	,	PUNCT
ejpam-6067	446	5	series	series	PROPN
ejpam-6067	446	6	a	a	PRON
ejpam-6067	446	7	,	,	PUNCT
ejpam-6067	446	8	79	79	NUM
ejpam-6067	446	9	,	,	PUNCT
ejpam-6067	446	10	pp.11	pp.11	NOUN
ejpam-6067	446	11	-	-	PUNCT
ejpam-6067	446	12	20	20	NUM
ejpam-6067	446	13	.	.	PUNCT
ejpam-6067	447	1	[	[	X
ejpam-6067	447	2	7	7	NUM
ejpam-6067	447	3	]	]	X
ejpam-6067	447	4	oudetallah	oudetallah	PROPN
ejpam-6067	447	5	,	,	PUNCT
ejpam-6067	447	6	j.	j.	PROPN
ejpam-6067	447	7	and	and	CCONJ
ejpam-6067	447	8	al	al	PROPN
ejpam-6067	447	9	-	-	PUNCT
ejpam-6067	447	10	hawari	hawari	PROPN
ejpam-6067	447	11	,	,	PUNCT
ejpam-6067	447	12	m.	m.	NOUN
ejpam-6067	447	13	,	,	PUNCT
ejpam-6067	447	14	2021	2021	NUM
ejpam-6067	447	15	.	.	PUNCT
ejpam-6067	448	1	other	other	ADJ
ejpam-6067	448	2	generalization	generalization	NOUN
ejpam-6067	448	3	of	of	ADP
ejpam-6067	448	4	pairwise	pairwise	NOUN
ejpam-6067	448	5	expandable	expandable	ADJ
ejpam-6067	448	6	spaces	space	NOUN
ejpam-6067	448	7	.	.	PUNCT
ejpam-6067	449	1	in	in	ADP
ejpam-6067	449	2	international	international	ADJ
ejpam-6067	449	3	mathematical	mathematical	ADJ
ejpam-6067	449	4	forum	forum	NOUN
ejpam-6067	449	5	(	(	PUNCT
ejpam-6067	449	6	vol	vol	NOUN
ejpam-6067	449	7	.	.	PROPN
ejpam-6067	449	8	16	16	NUM
ejpam-6067	449	9	,	,	PUNCT
ejpam-6067	449	10	no	no	INTJ
ejpam-6067	449	11	.	.	NOUN
ejpam-6067	449	12	1	1	NUM
ejpam-6067	449	13	,	,	PUNCT
ejpam-6067	449	14	pp	pp	ADJ
ejpam-6067	449	15	.	.	PUNCT
ejpam-6067	449	16	1	1	NUM
ejpam-6067	449	17	-	-	SYM
ejpam-6067	449	18	9	9	NUM
ejpam-6067	449	19	)	)	PUNCT
ejpam-6067	449	20	.	.	PUNCT
ejpam-6067	450	1	[	[	X
ejpam-6067	450	2	8	8	NUM
ejpam-6067	450	3	]	]	X
ejpam-6067	450	4	abu	abu	PROPN
ejpam-6067	450	5	-	-	PUNCT
ejpam-6067	450	6	irwaq	irwaq	PROPN
ejpam-6067	450	7	,	,	PUNCT
ejpam-6067	450	8	i.	i.	PROPN
ejpam-6067	450	9	,	,	PUNCT
ejpam-6067	450	10	shatanawi	shatanawi	PROPN
ejpam-6067	450	11	,	,	PUNCT
ejpam-6067	450	12	w.	w.	PROPN
ejpam-6067	450	13	,	,	PUNCT
ejpam-6067	450	14	bataihah	bataihah	PROPN
ejpam-6067	450	15	,	,	PUNCT
ejpam-6067	450	16	a.	a.	NOUN
ejpam-6067	450	17	and	and	CCONJ
ejpam-6067	450	18	nuseir	nuseir	NOUN
ejpam-6067	450	19	,	,	PUNCT
ejpam-6067	450	20	i.	i.	NOUN
ejpam-6067	450	21	,	,	PUNCT
ejpam-6067	450	22	2019	2019	NUM
ejpam-6067	450	23	.	.	PUNCT
ejpam-6067	450	24	fixed	fix	VERB
ejpam-6067	450	25	point	point	NOUN
ejpam-6067	450	26	results	result	NOUN
ejpam-6067	450	27	for	for	ADP
ejpam-6067	450	28	nonlinear	nonlinear	ADJ
ejpam-6067	450	29	contractions	contraction	NOUN
ejpam-6067	450	30	with	with	ADP
ejpam-6067	450	31	generalized	generalized	ADJ
ejpam-6067	450	32	ω	ω	NUM
ejpam-6067	450	33	-	-	PUNCT
ejpam-6067	450	34	distance	distance	NOUN
ejpam-6067	450	35	mappings	mapping	NOUN
ejpam-6067	450	36	.	.	PUNCT
ejpam-6067	451	1	upb	upb	PROPN
ejpam-6067	451	2	sci	sci	PROPN
ejpam-6067	451	3	.	.	PUNCT
ejpam-6067	451	4	bull	bull	PROPN
ejpam-6067	451	5	.	.	PUNCT
ejpam-6067	452	1	ser	ser	PROPN
ejpam-6067	452	2	.	.	PUNCT
ejpam-6067	453	1	a	a	PRON
ejpam-6067	453	2	,	,	PUNCT
ejpam-6067	453	3	81(1	81(1	NUM
ejpam-6067	453	4	)	)	PUNCT
ejpam-6067	453	5	,	,	PUNCT
ejpam-6067	453	6	pp.57	pp.57	PROPN
ejpam-6067	453	7	-	-	PROPN
ejpam-6067	453	8	64	64	NUM
ejpam-6067	453	9	.	.	PUNCT
ejpam-6067	454	1	[	[	X
ejpam-6067	454	2	9	9	X
ejpam-6067	454	3	]	]	PUNCT
ejpam-6067	454	4	j.	j.	PROPN
ejpam-6067	454	5	oudetallah	oudetallah	PROPN
ejpam-6067	454	6	.	.	PUNCT
ejpam-6067	455	1	l.	l.	PROPN
ejpam-6067	455	2	abualigah	abualigah	PROPN
ejpam-6067	455	3	,	,	PUNCT
ejpam-6067	455	4	2019	2019	NUM
ejpam-6067	455	5	.	.	PUNCT
ejpam-6067	456	1	h	h	NOUN
ejpam-6067	456	2	-	-	PUNCT
ejpam-6067	456	3	convexity	convexity	NOUN
ejpam-6067	456	4	in	in	ADP
ejpam-6067	456	5	mettric	mettric	ADJ
ejpam-6067	456	6	linear	linear	ADJ
ejpam-6067	456	7	spaces	space	NOUN
ejpam-6067	456	8	.	.	PUNCT
ejpam-6067	457	1	international	international	ADJ
ejpam-6067	457	2	journal	journal	PROPN
ejpam-6067	457	3	of	of	ADP
ejpam-6067	457	4	science	science	NOUN
ejpam-6067	457	5	and	and	CCONJ
ejpam-6067	457	6	applied	apply	VERB
ejpam-6067	457	7	information	information	NOUN
ejpam-6067	457	8	technology	technology	NOUN
ejpam-6067	457	9	,	,	PUNCT
ejpam-6067	457	10	8(6	8(6	NUM
ejpam-6067	457	11	)	)	PUNCT
ejpam-6067	457	12	,	,	PUNCT
ejpam-6067	457	13	54–58	54–58	NUM
ejpam-6067	457	14	.	.	PUNCT
ejpam-6067	458	1	[	[	X
ejpam-6067	458	2	10	10	NUM
ejpam-6067	458	3	]	]	X
ejpam-6067	458	4	bataihah	bataihah	PROPN
ejpam-6067	458	5	,	,	PUNCT
ejpam-6067	458	6	a.	a.	NOUN
ejpam-6067	458	7	,	,	PUNCT
ejpam-6067	458	8	tallafha	tallafha	NOUN
ejpam-6067	458	9	,	,	PUNCT
ejpam-6067	458	10	a.	a.	NOUN
ejpam-6067	458	11	and	and	CCONJ
ejpam-6067	458	12	shatanawi	shatanawi	PROPN
ejpam-6067	458	13	,	,	PUNCT
ejpam-6067	458	14	w.	w.	NOUN
ejpam-6067	458	15	,	,	PUNCT
ejpam-6067	458	16	2020	2020	NUM
ejpam-6067	458	17	.	.	PUNCT
ejpam-6067	458	18	fixed	fix	VERB
ejpam-6067	458	19	point	point	NOUN
ejpam-6067	458	20	results	result	NOUN
ejpam-6067	458	21	with	with	ADP
ejpam-6067	458	22	ωdistance	ωdistance	NOUN
ejpam-6067	458	23	by	by	ADP
ejpam-6067	458	24	utilizing	utilize	VERB
ejpam-6067	458	25	simulation	simulation	NOUN
ejpam-6067	458	26	functions	function	NOUN
ejpam-6067	458	27	.	.	PUNCT
ejpam-6067	459	1	ital	ital	PROPN
ejpam-6067	459	2	.	.	PUNCT
ejpam-6067	460	1	j.	j.	PROPN
ejpam-6067	460	2	pure	pure	PROPN
ejpam-6067	460	3	appl	appl	PROPN
ejpam-6067	460	4	.	.	PUNCT
ejpam-6067	460	5	math	math	PROPN
ejpam-6067	460	6	,	,	PUNCT
ejpam-6067	460	7	43	43	NUM
ejpam-6067	460	8	,	,	PUNCT
ejpam-6067	460	9	pp.185	pp.185	NOUN
ejpam-6067	460	10	-	-	PUNCT
ejpam-6067	460	11	196	196	NUM
ejpam-6067	460	12	.	.	PUNCT
ejpam-6067	461	1	[	[	X
ejpam-6067	461	2	11	11	NUM
ejpam-6067	461	3	]	]	SYM
ejpam-6067	461	4	abodayeh	abodayeh	NOUN
ejpam-6067	461	5	,	,	PUNCT
ejpam-6067	461	6	k.	k.	PROPN
ejpam-6067	461	7	,	,	PUNCT
ejpam-6067	461	8	bataihah	bataihah	PROPN
ejpam-6067	461	9	,	,	PUNCT
ejpam-6067	461	10	a.	a.	NOUN
ejpam-6067	461	11	and	and	CCONJ
ejpam-6067	461	12	shatanawi	shatanawi	PROPN
ejpam-6067	461	13	,	,	PUNCT
ejpam-6067	461	14	w.	w.	PROPN
ejpam-6067	461	15	,	,	PUNCT
ejpam-6067	461	16	2017	2017	NUM
ejpam-6067	461	17	.	.	PUNCT
ejpam-6067	462	1	generalized	generalize	VERB
ejpam-6067	462	2	ω	ω	NUM
ejpam-6067	462	3	-	-	PUNCT
ejpam-6067	462	4	distance	distance	NOUN
ejpam-6067	462	5	mappings	mapping	NOUN
ejpam-6067	462	6	and	and	CCONJ
ejpam-6067	462	7	some	some	DET
ejpam-6067	462	8	fixed	fix	VERB
ejpam-6067	462	9	point	point	NOUN
ejpam-6067	462	10	theorems	theorem	NOUN
ejpam-6067	462	11	.	.	PUNCT
ejpam-6067	463	1	upb	upb	PROPN
ejpam-6067	463	2	sci	sci	PROPN
ejpam-6067	463	3	.	.	PUNCT
ejpam-6067	463	4	bull	bull	PROPN
ejpam-6067	463	5	.	.	PUNCT
ejpam-6067	464	1	ser	ser	PROPN
ejpam-6067	464	2	.	.	PUNCT
ejpam-6067	465	1	a	a	DET
ejpam-6067	465	2	,	,	PUNCT
ejpam-6067	465	3	79	79	NUM
ejpam-6067	465	4	,	,	PUNCT
ejpam-6067	465	5	pp.223	pp.223	NOUN
ejpam-6067	465	6	-	-	PUNCT
ejpam-6067	465	7	232	232	NUM
ejpam-6067	465	8	.	.	PUNCT
ejpam-6067	466	1	[	[	X
ejpam-6067	466	2	12	12	NUM
ejpam-6067	466	3	]	]	X
ejpam-6067	466	4	bataihah	bataihah	PROPN
ejpam-6067	466	5	,	,	PUNCT
ejpam-6067	466	6	a.	a.	NOUN
ejpam-6067	466	7	,	,	PUNCT
ejpam-6067	466	8	qawasmeh	qawasmeh	NOUN
ejpam-6067	466	9	,	,	PUNCT
ejpam-6067	466	10	t.	t.	PROPN
ejpam-6067	466	11	,	,	PUNCT
ejpam-6067	466	12	batiha	batiha	VERB
ejpam-6067	466	13	,	,	PUNCT
ejpam-6067	466	14	i.m	i.m	PROPN
ejpam-6067	466	15	.	.	PROPN
ejpam-6067	466	16	,	,	PUNCT
ejpam-6067	466	17	jebril	jebril	NOUN
ejpam-6067	466	18	,	,	PUNCT
ejpam-6067	466	19	i.h	i.h	PROPN
ejpam-6067	466	20	.	.	PROPN
ejpam-6067	466	21	and	and	CCONJ
ejpam-6067	466	22	abdeljawad	abdeljawad	NOUN
ejpam-6067	466	23	,	,	PUNCT
ejpam-6067	466	24	t.	t.	PROPN
ejpam-6067	466	25	,	,	PUNCT
ejpam-6067	466	26	gamma	gamma	NOUN
ejpam-6067	466	27	distance	distance	NOUN
ejpam-6067	466	28	mappings	mapping	NOUN
ejpam-6067	466	29	with	with	ADP
ejpam-6067	466	30	application	application	NOUN
ejpam-6067	466	31	to	to	ADP
ejpam-6067	466	32	fractional	fractional	ADJ
ejpam-6067	466	33	boundary	boundary	ADJ
ejpam-6067	466	34	differential	differential	NOUN
ejpam-6067	466	35	equation	equation	NOUN
ejpam-6067	466	36	,	,	PUNCT
ejpam-6067	466	37	journal	journal	NOUN
ejpam-6067	466	38	of	of	ADP
ejpam-6067	466	39	mathematical	mathematical	ADJ
ejpam-6067	466	40	analysis	analysis	NOUN
ejpam-6067	466	41	,	,	PUNCT
ejpam-6067	466	42	volume	volume	NOUN
ejpam-6067	466	43	15	15	NUM
ejpam-6067	466	44	issue	issue	NOUN
ejpam-6067	466	45	5	5	NUM
ejpam-6067	466	46	(	(	PUNCT
ejpam-6067	466	47	2024	2024	NUM
ejpam-6067	466	48	)	)	PUNCT
ejpam-6067	466	49	,	,	PUNCT
ejpam-6067	466	50	pages	page	NOUN
ejpam-6067	466	51	99	99	NUM
ejpam-6067	466	52	-	-	SYM
ejpam-6067	466	53	106	106	NUM
ejpam-6067	467	1	[	[	X
ejpam-6067	467	2	13	13	NUM
ejpam-6067	467	3	]	]	PUNCT
ejpam-6067	467	4	bataihah	bataihah	PROPN
ejpam-6067	467	5	,	,	PUNCT
ejpam-6067	467	6	a.	a.	NOUN
ejpam-6067	467	7	and	and	CCONJ
ejpam-6067	467	8	qawasmeh	qawasmeh	NOUN
ejpam-6067	467	9	,	,	PUNCT
ejpam-6067	467	10	t.	t.	PROPN
ejpam-6067	467	11	,	,	PUNCT
ejpam-6067	467	12	2024	2024	NUM
ejpam-6067	467	13	.	.	PUNCT
ejpam-6067	468	1	a	a	DET
ejpam-6067	468	2	new	new	ADJ
ejpam-6067	468	3	type	type	NOUN
ejpam-6067	468	4	of	of	ADP
ejpam-6067	468	5	distance	distance	NOUN
ejpam-6067	468	6	spaces	space	NOUN
ejpam-6067	468	7	and	and	CCONJ
ejpam-6067	468	8	fixed	fix	VERB
ejpam-6067	468	9	point	point	NOUN
ejpam-6067	468	10	results	result	NOUN
ejpam-6067	468	11	.	.	PUNCT
ejpam-6067	469	1	journal	journal	NOUN
ejpam-6067	469	2	of	of	ADP
ejpam-6067	469	3	mathematical	mathematical	ADJ
ejpam-6067	469	4	analysis	analysis	NOUN
ejpam-6067	469	5	,	,	PUNCT
ejpam-6067	469	6	15(4	15(4	NUM
ejpam-6067	469	7	)	)	PUNCT
ejpam-6067	469	8	.	.	PUNCT
ejpam-6067	470	1	[	[	X
ejpam-6067	470	2	14	14	NUM
ejpam-6067	470	3	]	]	X
ejpam-6067	470	4	bataihah	bataihah	PROPN
ejpam-6067	470	5	,	,	PUNCT
ejpam-6067	470	6	a.	a.	NOUN
ejpam-6067	470	7	,	,	PUNCT
ejpam-6067	470	8	2024	2024	NUM
ejpam-6067	470	9	.	.	PUNCT
ejpam-6067	471	1	some	some	DET
ejpam-6067	471	2	fixed	fix	VERB
ejpam-6067	471	3	point	point	NOUN
ejpam-6067	471	4	results	result	NOUN
ejpam-6067	471	5	with	with	ADP
ejpam-6067	471	6	application	application	NOUN
ejpam-6067	471	7	to	to	ADP
ejpam-6067	471	8	fractional	fractional	ADJ
ejpam-6067	471	9	differential	differential	ADJ
ejpam-6067	471	10	equation	equation	NOUN
ejpam-6067	471	11	via	via	ADP
ejpam-6067	471	12	new	new	ADJ
ejpam-6067	471	13	type	type	NOUN
ejpam-6067	471	14	of	of	ADP
ejpam-6067	471	15	distance	distance	NOUN
ejpam-6067	471	16	spaces	space	NOUN
ejpam-6067	471	17	.	.	PUNCT
ejpam-6067	472	1	results	result	NOUN
ejpam-6067	472	2	in	in	ADP
ejpam-6067	472	3	nonlinear	nonlinear	ADJ
ejpam-6067	472	4	analysis	analysis	NOUN
ejpam-6067	472	5	,	,	PUNCT
ejpam-6067	472	6	7	7	NUM
ejpam-6067	472	7	,	,	PUNCT
ejpam-6067	472	8	pp.202	pp.202	PROPN
ejpam-6067	472	9	-	-	PUNCT
ejpam-6067	472	10	208	208	NUM
ejpam-6067	472	11	.	.	PUNCT
ejpam-6067	473	1	[	[	X
ejpam-6067	473	2	15	15	NUM
ejpam-6067	473	3	]	]	X
ejpam-6067	473	4	alharbi	alharbi	NOUN
ejpam-6067	473	5	,	,	PUNCT
ejpam-6067	473	6	r.	r.	PROPN
ejpam-6067	473	7	,	,	PUNCT
ejpam-6067	473	8	oudetallah	oudetallah	PROPN
ejpam-6067	473	9	,	,	PUNCT
ejpam-6067	473	10	j.	j.	PROPN
ejpam-6067	473	11	,	,	PUNCT
ejpam-6067	473	12	shatnawi	shatnawi	PROPN
ejpam-6067	473	13	,	,	PUNCT
ejpam-6067	473	14	m.	m.	NOUN
ejpam-6067	473	15	and	and	CCONJ
ejpam-6067	473	16	batiha	batiha	VERB
ejpam-6067	473	17	,	,	PUNCT
ejpam-6067	473	18	i.m	i.m	PROPN
ejpam-6067	473	19	.	.	PROPN
ejpam-6067	473	20	,	,	PUNCT
ejpam-6067	473	21	2023	2023	NUM
ejpam-6067	473	22	.	.	PUNCT
ejpam-6067	474	1	on	on	ADP
ejpam-6067	474	2	c	c	NOUN
ejpam-6067	474	3	-	-	PUNCT
ejpam-6067	474	4	compactness	compactness	NOUN
ejpam-6067	474	5	in	in	ADP
ejpam-6067	474	6	topological	topological	ADJ
ejpam-6067	474	7	and	and	CCONJ
ejpam-6067	474	8	bitopological	bitopological	ADJ
ejpam-6067	474	9	spaces	space	NOUN
ejpam-6067	474	10	.	.	PUNCT
ejpam-6067	475	1	mathematics	mathematic	NOUN
ejpam-6067	475	2	,	,	PUNCT
ejpam-6067	475	3	11(20	11(20	NUM
ejpam-6067	475	4	)	)	PUNCT
ejpam-6067	475	5	,	,	PUNCT
ejpam-6067	475	6	p.4251	p.4251	PROPN
ejpam-6067	475	7	.	.	PUNCT
ejpam-6067	476	1	[	[	X
ejpam-6067	476	2	16	16	NUM
ejpam-6067	476	3	]	]	SYM
ejpam-6067	476	4	oudetallah	oudetallah	PROPN
ejpam-6067	476	5	,	,	PUNCT
ejpam-6067	476	6	j.	j.	PROPN
ejpam-6067	476	7	,	,	PUNCT
ejpam-6067	476	8	alharbi	alharbi	PROPN
ejpam-6067	476	9	,	,	PUNCT
ejpam-6067	476	10	r.	r.	PROPN
ejpam-6067	476	11	and	and	CCONJ
ejpam-6067	476	12	batiha	batiha	VERB
ejpam-6067	476	13	,	,	PUNCT
ejpam-6067	476	14	i.m	i.m	PROPN
ejpam-6067	476	15	.	.	PROPN
ejpam-6067	476	16	,	,	PUNCT
ejpam-6067	476	17	2023	2023	NUM
ejpam-6067	476	18	.	.	PUNCT
ejpam-6067	477	1	on	on	ADP
ejpam-6067	477	2	r	r	NOUN
ejpam-6067	477	3	-	-	PUNCT
ejpam-6067	477	4	compactness	compactness	NOUN
ejpam-6067	477	5	in	in	ADP
ejpam-6067	477	6	topological	topological	ADJ
ejpam-6067	477	7	and	and	CCONJ
ejpam-6067	477	8	bitopological	bitopological	ADJ
ejpam-6067	477	9	spaces	space	NOUN
ejpam-6067	477	10	.	.	PUNCT
ejpam-6067	478	1	axioms	axiom	NOUN
ejpam-6067	478	2	,	,	PUNCT
ejpam-6067	478	3	12(2	12(2	NUM
ejpam-6067	478	4	)	)	PUNCT
ejpam-6067	478	5	,	,	PUNCT
ejpam-6067	478	6	p.210	p.210	NOUN
ejpam-6067	478	7	.	.	PUNCT
ejpam-6067	479	1	m.	m.	NOUN
ejpam-6067	479	2	shatnawi	shatnawi	PROPN
ejpam-6067	479	3	et	et	PROPN
ejpam-6067	479	4	al	al	PROPN
ejpam-6067	479	5	.	.	PUNCT
ejpam-6067	479	6	/	/	SYM
ejpam-6067	479	7	eur	eur	PROPN
ejpam-6067	479	8	.	.	PUNCT
ejpam-6067	480	1	j.	j.	PROPN
ejpam-6067	480	2	pure	pure	PROPN
ejpam-6067	480	3	appl	appl	PROPN
ejpam-6067	480	4	.	.	PROPN
ejpam-6067	480	5	math	math	PROPN
ejpam-6067	480	6	,	,	PUNCT
ejpam-6067	480	7	18	18	NUM
ejpam-6067	480	8	(	(	PUNCT
ejpam-6067	480	9	3	3	NUM
ejpam-6067	480	10	)	)	PUNCT
ejpam-6067	480	11	(	(	PUNCT
ejpam-6067	480	12	2025	2025	NUM
ejpam-6067	480	13	)	)	PUNCT
ejpam-6067	480	14	,	,	PUNCT
ejpam-6067	480	15	6067	6067	NUM
ejpam-6067	480	16	16	16	NUM
ejpam-6067	480	17	of	of	ADP
ejpam-6067	480	18	16	16	NUM
ejpam-6067	481	1	[	[	X
ejpam-6067	481	2	17	17	NUM
ejpam-6067	481	3	]	]	SYM
ejpam-6067	481	4	oudetallah	oudetallah	PROPN
ejpam-6067	481	5	,	,	PUNCT
ejpam-6067	481	6	j.	j.	PROPN
ejpam-6067	481	7	,	,	PUNCT
ejpam-6067	481	8	rousan	rousan	PROPN
ejpam-6067	481	9	,	,	PUNCT
ejpam-6067	481	10	m.m	m.m	PROPN
ejpam-6067	481	11	.	.	PROPN
ejpam-6067	481	12	and	and	CCONJ
ejpam-6067	481	13	batiha	batiha	VERB
ejpam-6067	481	14	,	,	PUNCT
ejpam-6067	481	15	i.m	i.m	PROPN
ejpam-6067	481	16	.	.	PROPN
ejpam-6067	481	17	,	,	PUNCT
ejpam-6067	481	18	2021	2021	NUM
ejpam-6067	481	19	.	.	PUNCT
ejpam-6067	482	1	on	on	ADP
ejpam-6067	482	2	d	d	X
ejpam-6067	482	3	-	-	NOUN
ejpam-6067	482	4	metacompactness	metacompactness	NOUN
ejpam-6067	482	5	in	in	ADP
ejpam-6067	482	6	topological	topological	ADJ
ejpam-6067	482	7	spaces	space	NOUN
ejpam-6067	482	8	.	.	PUNCT
ejpam-6067	483	1	j.	j.	PROPN
ejpam-6067	483	2	appl	appl	PROPN
ejpam-6067	483	3	.	.	PROPN
ejpam-6067	483	4	math	math	PROPN
ejpam-6067	483	5	.	.	PUNCT
ejpam-6067	484	1	inform	inform	NOUN
ejpam-6067	484	2	,	,	PUNCT
ejpam-6067	484	3	39	39	NUM
ejpam-6067	484	4	,	,	PUNCT
ejpam-6067	484	5	pp.919	pp.919	NOUN
ejpam-6067	484	6	-	-	SYM
ejpam-6067	484	7	926	926	NUM
ejpam-6067	484	8	.	.	PUNCT
ejpam-6067	485	1	[	[	X
ejpam-6067	485	2	18	18	NUM
ejpam-6067	485	3	]	]	SYM
ejpam-6067	485	4	oudetallah	oudetallah	PROPN
ejpam-6067	485	5	,	,	PUNCT
ejpam-6067	485	6	j.	j.	PROPN
ejpam-6067	485	7	,	,	PUNCT
ejpam-6067	485	8	2024	2024	NUM
ejpam-6067	485	9	.	.	PUNCT
ejpam-6067	486	1	novel	novel	ADJ
ejpam-6067	486	2	results	result	NOUN
ejpam-6067	486	3	on	on	ADP
ejpam-6067	486	4	nigh	nigh	ADV
ejpam-6067	486	5	lindelöfness	lindelöfness	PUNCT
ejpam-6067	486	6	in	in	ADP
ejpam-6067	486	7	topological	topological	ADJ
ejpam-6067	486	8	spaces	space	NOUN
ejpam-6067	486	9	.	.	PUNCT
ejpam-6067	487	1	international	international	ADJ
ejpam-6067	487	2	journal	journal	NOUN
ejpam-6067	487	3	of	of	ADP
ejpam-6067	487	4	analysis	analysis	NOUN
ejpam-6067	487	5	and	and	CCONJ
ejpam-6067	487	6	applications	application	NOUN
ejpam-6067	487	7	,	,	PUNCT
ejpam-6067	487	8	22	22	NUM
ejpam-6067	487	9	,	,	PUNCT
ejpam-6067	487	10	pp.153	pp.153	VERB
ejpam-6067	487	11	-	-	PUNCT
ejpam-6067	487	12	153	153	NUM
ejpam-6067	487	13	.	.	PUNCT
ejpam-6067	488	1	[	[	X
ejpam-6067	488	2	19	19	NUM
ejpam-6067	488	3	]	]	X
ejpam-6067	488	4	hatamleh	hatamleh	PROPN
ejpam-6067	488	5	,	,	PUNCT
ejpam-6067	488	6	r.	r.	PROPN
ejpam-6067	488	7	,	,	PUNCT
ejpam-6067	488	8	hazaymeh	hazaymeh	NOUN
ejpam-6067	488	9	,	,	PUNCT
ejpam-6067	488	10	a.	a.	NOUN
ejpam-6067	488	11	(	(	PUNCT
ejpam-6067	488	12	2025	2025	NUM
ejpam-6067	488	13	)	)	PUNCT
ejpam-6067	488	14	.	.	PUNCT
ejpam-6067	489	1	on	on	ADP
ejpam-6067	489	2	some	some	DET
ejpam-6067	489	3	topological	topological	ADJ
ejpam-6067	489	4	spaces	space	NOUN
ejpam-6067	489	5	based	base	VERB
ejpam-6067	489	6	on	on	ADP
ejpam-6067	489	7	symbolic	symbolic	ADJ
ejpam-6067	489	8	n	n	CCONJ
ejpam-6067	489	9	-	-	ADJ
ejpam-6067	489	10	plithogenic	plithogenic	ADJ
ejpam-6067	489	11	intervals	interval	NOUN
ejpam-6067	489	12	.	.	PUNCT
ejpam-6067	490	1	international	international	ADJ
ejpam-6067	490	2	journal	journal	PROPN
ejpam-6067	490	3	of	of	ADP
ejpam-6067	490	4	neutrosophic	neutrosophic	ADJ
ejpam-6067	490	5	science	science	NOUN
ejpam-6067	490	6	,	,	PUNCT
ejpam-6067	490	7	25(1	25(1	NUM
ejpam-6067	490	8	)	)	PUNCT
ejpam-6067	490	9	,	,	PUNCT
ejpam-6067	490	10	23?37	23?37	PROPN
ejpam-6067	490	11	.	.	PUNCT
ejpam-6067	491	1	https://doi.org/10.54216/ijns.250102	https://doi.org/10.54216/ijns.250102	PRON
ejpam-6067	491	2	[	[	X
ejpam-6067	491	3	20	20	NUM
ejpam-6067	491	4	]	]	X
ejpam-6067	491	5	hatamleh	hatamleh	PROPN
ejpam-6067	491	6	,	,	PUNCT
ejpam-6067	491	7	r.	r.	PROPN
ejpam-6067	491	8	,	,	PUNCT
ejpam-6067	491	9	hazaymeh	hazaymeh	NOUN
ejpam-6067	491	10	,	,	PUNCT
ejpam-6067	491	11	a.	a.	NOUN
ejpam-6067	491	12	(	(	PUNCT
ejpam-6067	491	13	2025	2025	NUM
ejpam-6067	491	14	)	)	PUNCT
ejpam-6067	491	15	.	.	PUNCT
ejpam-6067	492	1	on	on	ADP
ejpam-6067	492	2	the	the	DET
ejpam-6067	492	3	topological	topological	ADJ
ejpam-6067	492	4	spaces	space	NOUN
ejpam-6067	492	5	of	of	ADP
ejpam-6067	492	6	neutrosophic	neutrosophic	ADJ
ejpam-6067	492	7	real	real	ADJ
ejpam-6067	492	8	intervals	interval	NOUN
ejpam-6067	492	9	.	.	PUNCT
ejpam-6067	493	1	international	international	ADJ
ejpam-6067	493	2	journal	journal	PROPN
ejpam-6067	493	3	of	of	ADP
ejpam-6067	493	4	neutrosophic	neutrosophic	ADJ
ejpam-6067	493	5	science	science	NOUN
ejpam-6067	493	6	,	,	PUNCT
ejpam-6067	493	7	25	25	NUM
ejpam-6067	493	8	,	,	PUNCT
ejpam-6067	493	9	130?136	130?136	NUM
ejpam-6067	493	10	.	.	PUNCT
ejpam-6067	493	11	https://doi.org/10.54216/ijns.250111	https://doi.org/10.54216/ijns.250111	PROPN