id	sid	tid	token	lemma	pos
ejpam-6497	1	1	european	european	PROPN
ejpam-6497	1	2	journal	journal	PROPN
ejpam-6497	1	3	of	of	ADP
ejpam-6497	1	4	pure	pure	ADJ
ejpam-6497	1	5	and	and	CCONJ
ejpam-6497	1	6	applied	applied	ADJ
ejpam-6497	1	7	mathematics	mathematic	NOUN
ejpam-6497	1	8	2025	2025	NUM
ejpam-6497	1	9	,	,	PUNCT
ejpam-6497	1	10	vol	vol	NOUN
ejpam-6497	1	11	.	.	PROPN
ejpam-6497	1	12	18	18	NUM
ejpam-6497	1	13	,	,	PUNCT
ejpam-6497	1	14	issue	issue	NOUN
ejpam-6497	1	15	3	3	NUM
ejpam-6497	1	16	,	,	PUNCT
ejpam-6497	1	17	article	article	NOUN
ejpam-6497	1	18	number	number	NOUN
ejpam-6497	1	19	6497	6497	NUM
ejpam-6497	1	20	issn	issn	PROPN
ejpam-6497	1	21	1307	1307	NUM
ejpam-6497	1	22	-	-	SYM
ejpam-6497	1	23	5543	5543	NUM
ejpam-6497	1	24	–	–	PUNCT
ejpam-6497	1	25	ejpam.com	ejpam.com	X
ejpam-6497	1	26	published	publish	VERB
ejpam-6497	1	27	by	by	ADP
ejpam-6497	1	28	new	new	PROPN
ejpam-6497	1	29	york	york	PROPN
ejpam-6497	1	30	business	business	NOUN
ejpam-6497	1	31	global	global	PROPN
ejpam-6497	1	32	almost	almost	ADV
ejpam-6497	1	33	,	,	PUNCT
ejpam-6497	1	34	weakly	weakly	ADJ
ejpam-6497	1	35	,	,	PUNCT
ejpam-6497	1	36	and	and	CCONJ
ejpam-6497	1	37	nearly	nearly	ADV
ejpam-6497	1	38	lindelöf	lindelöf	PROPN
ejpam-6497	1	39	ideal	ideal	ADJ
ejpam-6497	1	40	topological	topological	PROPN
ejpam-6497	1	41	spaces	space	NOUN
ejpam-6497	1	42	eman	eman	PROPN
ejpam-6497	1	43	almuhur1,∗	almuhur1,∗	PROPN
ejpam-6497	1	44	,	,	PUNCT
ejpam-6497	1	45	manal	manal	PROPN
ejpam-6497	1	46	al	al	PROPN
ejpam-6497	1	47	-	-	PUNCT
ejpam-6497	1	48	labadi2	labadi2	PROPN
ejpam-6497	1	49	,	,	PUNCT
ejpam-6497	1	50	enoch	enoch	PROPN
ejpam-6497	1	51	suleiman3	suleiman3	PROPN
ejpam-6497	1	52	,	,	PUNCT
ejpam-6497	1	53	nazneen	nazneen	PROPN
ejpam-6497	1	54	khan4	khan4	PROPN
ejpam-6497	1	55	,	,	PUNCT
ejpam-6497	1	56	mohammad	mohammad	PROPN
ejpam-6497	1	57	esmael	esmael	PROPN
ejpam-6497	1	58	samei5	samei5	PROPN
ejpam-6497	1	59	1	1	NUM
ejpam-6497	1	60	department	department	NOUN
ejpam-6497	1	61	of	of	ADP
ejpam-6497	1	62	mathematics	mathematic	NOUN
ejpam-6497	1	63	,	,	PUNCT
ejpam-6497	1	64	applied	apply	VERB
ejpam-6497	1	65	science	science	NOUN
ejpam-6497	1	66	private	private	ADJ
ejpam-6497	1	67	university	university	NOUN
ejpam-6497	1	68	,	,	PUNCT
ejpam-6497	1	69	amman	amman	PROPN
ejpam-6497	1	70	,	,	PUNCT
ejpam-6497	1	71	jordan	jordan	PROPN
ejpam-6497	1	72	2	2	NUM
ejpam-6497	1	73	department	department	NOUN
ejpam-6497	1	74	of	of	ADP
ejpam-6497	1	75	mathematics	mathematics	PROPN
ejpam-6497	1	76	,	,	PUNCT
ejpam-6497	1	77	university	university	PROPN
ejpam-6497	1	78	of	of	ADP
ejpam-6497	1	79	petra	petra	PROPN
ejpam-6497	1	80	,	,	PUNCT
ejpam-6497	1	81	amman	amman	PROPN
ejpam-6497	1	82	,	,	PUNCT
ejpam-6497	1	83	jordan	jordan	PROPN
ejpam-6497	1	84	3	3	NUM
ejpam-6497	1	85	department	department	PROPN
ejpam-6497	1	86	of	of	ADP
ejpam-6497	1	87	mathematics	mathematics	PROPN
ejpam-6497	1	88	,	,	PUNCT
ejpam-6497	1	89	federal	federal	ADJ
ejpam-6497	1	90	university	university	NOUN
ejpam-6497	1	91	gashua	gashua	PROPN
ejpam-6497	1	92	,	,	PUNCT
ejpam-6497	1	93	yobe	yobe	PROPN
ejpam-6497	1	94	state	state	PROPN
ejpam-6497	1	95	,	,	PUNCT
ejpam-6497	1	96	nigeria	nigeria	PROPN
ejpam-6497	1	97	4	4	NUM
ejpam-6497	1	98	department	department	NOUN
ejpam-6497	1	99	of	of	ADP
ejpam-6497	1	100	mathematics	mathematic	NOUN
ejpam-6497	1	101	,	,	PUNCT
ejpam-6497	1	102	taibah	taibah	PROPN
ejpam-6497	1	103	university	university	PROPN
ejpam-6497	1	104	,	,	PUNCT
ejpam-6497	1	105	madina	madina	PROPN
ejpam-6497	1	106	munawwara	munawwara	PROPN
ejpam-6497	1	107	,	,	PUNCT
ejpam-6497	1	108	saudi	saudi	PROPN
ejpam-6497	1	109	arabia	arabia	PROPN
ejpam-6497	1	110	5	5	NUM
ejpam-6497	1	111	department	department	NOUN
ejpam-6497	1	112	of	of	ADP
ejpam-6497	1	113	mathematics	mathematic	NOUN
ejpam-6497	1	114	,	,	PUNCT
ejpam-6497	1	115	faculty	faculty	NOUN
ejpam-6497	1	116	of	of	ADP
ejpam-6497	1	117	science	science	NOUN
ejpam-6497	1	118	,	,	PUNCT
ejpam-6497	1	119	bu	bu	PROPN
ejpam-6497	1	120	-	-	PUNCT
ejpam-6497	1	121	ali	ali	PROPN
ejpam-6497	1	122	sina	sina	PROPN
ejpam-6497	1	123	university	university	PROPN
ejpam-6497	1	124	,	,	PUNCT
ejpam-6497	1	125	hamedan	hamedan	PROPN
ejpam-6497	1	126	,	,	PUNCT
ejpam-6497	1	127	iran	iran	PROPN
ejpam-6497	1	128	abstract	abstract	ADJ
ejpam-6497	1	129	.	.	PUNCT
ejpam-6497	2	1	the	the	DET
ejpam-6497	2	2	concepts	concept	NOUN
ejpam-6497	2	3	of	of	ADP
ejpam-6497	2	4	almost	almost	ADV
ejpam-6497	2	5	,	,	PUNCT
ejpam-6497	2	6	weakly	weakly	ADJ
ejpam-6497	2	7	and	and	CCONJ
ejpam-6497	2	8	nearly	nearly	ADV
ejpam-6497	2	9	lindelöf	lindelöf	NOUN
ejpam-6497	2	10	closed	close	VERB
ejpam-6497	2	11	ideal	ideal	ADJ
ejpam-6497	2	12	topological	topological	ADJ
ejpam-6497	2	13	spaces	space	NOUN
ejpam-6497	2	14	are	be	AUX
ejpam-6497	2	15	introduced	introduce	VERB
ejpam-6497	2	16	in	in	ADP
ejpam-6497	2	17	this	this	DET
ejpam-6497	2	18	work	work	NOUN
ejpam-6497	2	19	.	.	PUNCT
ejpam-6497	3	1	we	we	PRON
ejpam-6497	3	2	examine	examine	VERB
ejpam-6497	3	3	their	their	PRON
ejpam-6497	3	4	subspaces	subspace	NOUN
ejpam-6497	3	5	and	and	CCONJ
ejpam-6497	3	6	the	the	DET
ejpam-6497	3	7	connection	connection	NOUN
ejpam-6497	3	8	between	between	ADP
ejpam-6497	3	9	the	the	DET
ejpam-6497	3	10	subspaces	subspace	NOUN
ejpam-6497	3	11	and	and	CCONJ
ejpam-6497	3	12	their	their	PRON
ejpam-6497	3	13	topological	topological	ADJ
ejpam-6497	3	14	characteristics	characteristic	NOUN
ejpam-6497	3	15	and	and	CCONJ
ejpam-6497	3	16	explain	explain	VERB
ejpam-6497	3	17	how	how	SCONJ
ejpam-6497	3	18	countable	countable	ADJ
ejpam-6497	3	19	covers	cover	NOUN
ejpam-6497	3	20	affect	affect	VERB
ejpam-6497	3	21	almost	almost	ADV
ejpam-6497	3	22	lindelöf	lindelöf	NOUN
ejpam-6497	3	23	spaces	space	VERB
ejpam-6497	3	24	and	and	CCONJ
ejpam-6497	3	25	concentrate	concentrate	VERB
ejpam-6497	3	26	on	on	ADP
ejpam-6497	3	27	the	the	DET
ejpam-6497	3	28	significance	significance	NOUN
ejpam-6497	3	29	of	of	ADP
ejpam-6497	3	30	these	these	DET
ejpam-6497	3	31	covers	cover	NOUN
ejpam-6497	3	32	.	.	PUNCT
ejpam-6497	4	1	these	these	DET
ejpam-6497	4	2	covers	cover	NOUN
ejpam-6497	4	3	are	be	AUX
ejpam-6497	4	4	made	make	VERB
ejpam-6497	4	5	up	up	ADP
ejpam-6497	4	6	of	of	ADP
ejpam-6497	4	7	countable	countable	ADJ
ejpam-6497	4	8	subfamilies	subfamily	NOUN
ejpam-6497	4	9	whose	whose	DET
ejpam-6497	4	10	closures	closure	NOUN
ejpam-6497	4	11	cover	cover	VERB
ejpam-6497	4	12	the	the	DET
ejpam-6497	4	13	ideal	ideal	ADJ
ejpam-6497	4	14	spaces	space	NOUN
ejpam-6497	4	15	.	.	PUNCT
ejpam-6497	5	1	definitions	definition	NOUN
ejpam-6497	5	2	,	,	PUNCT
ejpam-6497	5	3	claims	claim	NOUN
ejpam-6497	5	4	,	,	PUNCT
ejpam-6497	5	5	characterizations	characterization	NOUN
ejpam-6497	5	6	,	,	PUNCT
ejpam-6497	5	7	and	and	CCONJ
ejpam-6497	5	8	observations	observation	NOUN
ejpam-6497	5	9	pertaining	pertain	VERB
ejpam-6497	5	10	to	to	ADP
ejpam-6497	5	11	the	the	DET
ejpam-6497	5	12	recently	recently	ADV
ejpam-6497	5	13	presented	present	VERB
ejpam-6497	5	14	concepts	concept	NOUN
ejpam-6497	5	15	of	of	ADP
ejpam-6497	5	16	almost	almost	ADV
ejpam-6497	5	17	and	and	CCONJ
ejpam-6497	5	18	weakly	weakly	ADJ
ejpam-6497	5	19	lindelöf	lindelöf	PROPN
ejpam-6497	5	20	ideal	ideal	PROPN
ejpam-6497	5	21	topological	topological	ADJ
ejpam-6497	5	22	spaces	space	NOUN
ejpam-6497	5	23	are	be	AUX
ejpam-6497	5	24	stated	state	VERB
ejpam-6497	5	25	,	,	PUNCT
ejpam-6497	5	26	examined	examine	VERB
ejpam-6497	5	27	,	,	PUNCT
ejpam-6497	5	28	and	and	CCONJ
ejpam-6497	5	29	discussed	discuss	VERB
ejpam-6497	5	30	.	.	PUNCT
ejpam-6497	6	1	additionally	additionally	ADV
ejpam-6497	6	2	,	,	PUNCT
ejpam-6497	6	3	the	the	DET
ejpam-6497	6	4	connections	connection	NOUN
ejpam-6497	6	5	among	among	ADP
ejpam-6497	6	6	various	various	ADJ
ejpam-6497	6	7	ideal	ideal	ADJ
ejpam-6497	6	8	topological	topological	ADJ
ejpam-6497	6	9	spaces	space	NOUN
ejpam-6497	6	10	are	be	AUX
ejpam-6497	6	11	analyzed	analyze	VERB
ejpam-6497	6	12	and	and	CCONJ
ejpam-6497	6	13	explored	explore	VERB
ejpam-6497	6	14	.	.	PUNCT
ejpam-6497	7	1	we	we	PRON
ejpam-6497	7	2	provide	provide	VERB
ejpam-6497	7	3	examples	example	NOUN
ejpam-6497	7	4	of	of	ADP
ejpam-6497	7	5	the	the	DET
ejpam-6497	7	6	consequences	consequence	NOUN
ejpam-6497	7	7	of	of	ADP
ejpam-6497	7	8	these	these	DET
ejpam-6497	7	9	novel	novel	ADJ
ejpam-6497	7	10	ideal	ideal	ADJ
ejpam-6497	7	11	spaces	space	NOUN
ejpam-6497	7	12	.	.	PUNCT
ejpam-6497	8	1	2020	2020	NUM
ejpam-6497	8	2	mathematics	mathematic	NOUN
ejpam-6497	8	3	subject	subject	NOUN
ejpam-6497	8	4	classifications	classification	NOUN
ejpam-6497	8	5	:	:	PUNCT
ejpam-6497	8	6	54a05	54a05	NUM
ejpam-6497	8	7	,	,	PUNCT
ejpam-6497	8	8	54a10	54a10	NUM
ejpam-6497	8	9	key	key	ADJ
ejpam-6497	8	10	words	word	NOUN
ejpam-6497	8	11	and	and	CCONJ
ejpam-6497	8	12	phrases	phrase	NOUN
ejpam-6497	8	13	:	:	PUNCT
ejpam-6497	8	14	almost	almost	ADV
ejpam-6497	8	15	lindelöf	lindelöf	NOUN
ejpam-6497	8	16	,	,	PUNCT
ejpam-6497	8	17	weakly	weakly	ADJ
ejpam-6497	8	18	lindelöf	lindelöf	NOUN
ejpam-6497	8	19	,	,	PUNCT
ejpam-6497	8	20	nearly	nearly	ADV
ejpam-6497	8	21	lindelöf	lindelöf	NOUN
ejpam-6497	8	22	,	,	PUNCT
ejpam-6497	8	23	ideal	ideal	ADJ
ejpam-6497	8	24	spaces	space	NOUN
ejpam-6497	8	25	1	1	NUM
ejpam-6497	8	26	.	.	X
ejpam-6497	8	27	introduction	introduction	NOUN
ejpam-6497	8	28	the	the	DET
ejpam-6497	8	29	ideal	ideal	ADJ
ejpam-6497	8	30	j	j	PROPN
ejpam-6497	8	31	on	on	ADP
ejpam-6497	8	32	the	the	DET
ejpam-6497	8	33	(	(	PUNCT
ejpam-6497	8	34	x	x	PROPN
ejpam-6497	8	35	,	,	PUNCT
ejpam-6497	8	36	τ	τ	X
ejpam-6497	8	37	)	)	PUNCT
ejpam-6497	8	38	is	be	AUX
ejpam-6497	8	39	a	a	DET
ejpam-6497	8	40	non	non	ADJ
ejpam-6497	8	41	-	-	ADJ
ejpam-6497	8	42	empty	empty	ADJ
ejpam-6497	8	43	collection	collection	NOUN
ejpam-6497	8	44	of	of	ADP
ejpam-6497	8	45	℘(x	℘(x	ADJ
ejpam-6497	8	46	)	)	PUNCT
ejpam-6497	8	47	subsets	subset	NOUN
ejpam-6497	8	48	satisfying	satisfy	VERB
ejpam-6497	8	49	:	:	PUNCT
ejpam-6497	8	50	i	i	X
ejpam-6497	8	51	)	)	PUNCT
ejpam-6497	9	1	if	if	SCONJ
ejpam-6497	9	2	z	z	PROPN
ejpam-6497	9	3	∈	∈	PROPN
ejpam-6497	9	4	j	j	PROPN
ejpam-6497	9	5	and	and	CCONJ
ejpam-6497	9	6	w	w	PROPN
ejpam-6497	9	7	⊂	⊂	PROPN
ejpam-6497	9	8	z	z	PROPN
ejpam-6497	9	9	,	,	PUNCT
ejpam-6497	9	10	then	then	ADV
ejpam-6497	9	11	w	w	PROPN
ejpam-6497	9	12	∈	∈	PROPN
ejpam-6497	9	13	j	j	PROPN
ejpam-6497	9	14	;	;	PUNCT
ejpam-6497	9	15	ii	ii	X
ejpam-6497	9	16	)	)	PUNCT
ejpam-6497	9	17	if	if	SCONJ
ejpam-6497	9	18	z	z	PROPN
ejpam-6497	9	19	∈	∈	PROPN
ejpam-6497	9	20	j	j	PROPN
ejpam-6497	9	21	and	and	CCONJ
ejpam-6497	9	22	w	w	PROPN
ejpam-6497	9	23	∈	∈	PROPN
ejpam-6497	9	24	j	j	PROPN
ejpam-6497	9	25	,	,	PUNCT
ejpam-6497	9	26	then	then	ADV
ejpam-6497	9	27	z	z	PROPN
ejpam-6497	9	28	∪w	∪w	PROPN
ejpam-6497	9	29	∈	∈	PROPN
ejpam-6497	9	30	j	j	PROPN
ejpam-6497	9	31	.	.	PUNCT
ejpam-6497	10	1	hamlett	hamlett	PROPN
ejpam-6497	10	2	and	and	CCONJ
ejpam-6497	10	3	jankovic	jankovic	PROPN
ejpam-6497	11	1	[	[	X
ejpam-6497	11	2	1	1	NUM
ejpam-6497	11	3	,	,	PUNCT
ejpam-6497	11	4	2	2	NUM
ejpam-6497	11	5	]	]	PUNCT
ejpam-6497	11	6	created	create	VERB
ejpam-6497	11	7	the	the	DET
ejpam-6497	11	8	first	first	ADJ
ejpam-6497	11	9	generalization	generalization	NOUN
ejpam-6497	11	10	of	of	ADP
ejpam-6497	11	11	several	several	ADJ
ejpam-6497	11	12	important	important	ADJ
ejpam-6497	11	13	features	feature	NOUN
ejpam-6497	11	14	of	of	ADP
ejpam-6497	11	15	general	general	ADJ
ejpam-6497	11	16	topology	topology	NOUN
ejpam-6497	11	17	via	via	ADP
ejpam-6497	11	18	topological	topological	ADJ
ejpam-6497	11	19	ideals	ideal	NOUN
ejpam-6497	11	20	in	in	ADP
ejpam-6497	11	21	ideal	ideal	ADJ
ejpam-6497	11	22	topological	topological	ADJ
ejpam-6497	11	23	spaces	space	NOUN
ejpam-6497	11	24	.	.	PUNCT
ejpam-6497	12	1	features	feature	NOUN
ejpam-6497	12	2	like	like	ADP
ejpam-6497	12	3	separation	separation	NOUN
ejpam-6497	12	4	axioms	axiom	NOUN
ejpam-6497	12	5	,	,	PUNCT
ejpam-6497	12	6	decomposition	decomposition	NOUN
ejpam-6497	12	7	of	of	ADP
ejpam-6497	12	8	continuity	continuity	NOUN
ejpam-6497	12	9	,	,	PUNCT
ejpam-6497	12	10	connectedness	connectedness	NOUN
ejpam-6497	12	11	,	,	PUNCT
ejpam-6497	12	12	compactness	compactness	NOUN
ejpam-6497	12	13	,	,	PUNCT
ejpam-6497	12	14	and	and	CCONJ
ejpam-6497	12	15	resolvability	resolvability	NOUN
ejpam-6497	12	16	have	have	AUX
ejpam-6497	12	17	all	all	ADV
ejpam-6497	12	18	been	be	AUX
ejpam-6497	12	19	generalized	generalize	VERB
ejpam-6497	12	20	using	use	VERB
ejpam-6497	12	21	the	the	DET
ejpam-6497	12	22	concept	concept	NOUN
ejpam-6497	12	23	of	of	ADP
ejpam-6497	12	24	ideals	ideal	NOUN
ejpam-6497	12	25	[	[	X
ejpam-6497	12	26	3	3	NUM
ejpam-6497	12	27	,	,	PUNCT
ejpam-6497	12	28	4	4	NUM
ejpam-6497	12	29	]	]	PUNCT
ejpam-6497	12	30	.	.	PUNCT
ejpam-6497	13	1	historically	historically	ADV
ejpam-6497	13	2	,	,	PUNCT
ejpam-6497	13	3	there	there	PRON
ejpam-6497	13	4	have	have	AUX
ejpam-6497	13	5	been	be	AUX
ejpam-6497	13	6	two	two	NUM
ejpam-6497	13	7	∗corresponding	∗corresponde	VERB
ejpam-6497	13	8	author	author	NOUN
ejpam-6497	13	9	.	.	PUNCT
ejpam-6497	14	1	doi	doi	NOUN
ejpam-6497	14	2	:	:	PUNCT
ejpam-6497	14	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6497	https://doi.org/10.29020/nybg.ejpam.v18i3.6497	ADJ
ejpam-6497	14	4	email	email	NOUN
ejpam-6497	14	5	addresses	address	NOUN
ejpam-6497	14	6	:	:	PUNCT
ejpam-6497	14	7	e	e	X
ejpam-6497	14	8	almuhur@asu.edu.jo	almuhur@asu.edu.jo	NOUN
ejpam-6497	14	9	(	(	PUNCT
ejpam-6497	14	10	e.	e.	PROPN
ejpam-6497	14	11	almuhur	almuhur	PROPN
ejpam-6497	14	12	)	)	PUNCT
ejpam-6497	14	13	,	,	PUNCT
ejpam-6497	14	14	manal.allabadi@uop.edu.jo	manal.allabadi@uop.edu.jo	X
ejpam-6497	14	15	(	(	PUNCT
ejpam-6497	14	16	m.	m.	NOUN
ejpam-6497	14	17	al	al	PROPN
ejpam-6497	14	18	-	-	PUNCT
ejpam-6497	14	19	labadi	labadi	NOUN
ejpam-6497	14	20	)	)	PUNCT
ejpam-6497	14	21	,	,	PUNCT
ejpam-6497	14	22	enochsuleiman@gmail.com	enochsuleiman@gmail.com	X
ejpam-6497	14	23	(	(	PUNCT
ejpam-6497	14	24	e.	e.	PROPN
ejpam-6497	14	25	suleiman	suleiman	PROPN
ejpam-6497	14	26	)	)	PUNCT
ejpam-6497	14	27	,	,	PUNCT
ejpam-6497	14	28	nkkhan@taibahu.edu.sa	nkkhan@taibahu.edu.sa	PROPN
ejpam-6497	14	29	(	(	PUNCT
ejpam-6497	14	30	n.	n.	PROPN
ejpam-6497	14	31	khan	khan	PROPN
ejpam-6497	14	32	)	)	PUNCT
ejpam-6497	14	33	,	,	PUNCT
ejpam-6497	14	34	mesamei@basu.ac.ir	mesamei@basu.ac.ir	PROPN
ejpam-6497	14	35	(	(	PUNCT
ejpam-6497	14	36	m.e	m.e	PROPN
ejpam-6497	14	37	.	.	PROPN
ejpam-6497	14	38	samei	samei	PROPN
ejpam-6497	14	39	)	)	PUNCT
ejpam-6497	14	40	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6497	15	1	1	1	NUM
ejpam-6497	15	2	copyright	copyright	NOUN
ejpam-6497	15	3	:	:	PUNCT
ejpam-6497	15	4	©	©	PROPN
ejpam-6497	15	5	2025	2025	NUM
ejpam-6497	15	6	the	the	DET
ejpam-6497	15	7	author(s	author(s	NOUN
ejpam-6497	15	8	)	)	PUNCT
ejpam-6497	15	9	.	.	PUNCT
ejpam-6497	16	1	(	(	PUNCT
ejpam-6497	16	2	cc	cc	NOUN
ejpam-6497	16	3	by	by	ADP
ejpam-6497	16	4	-	-	PUNCT
ejpam-6497	16	5	nc	nc	PROPN
ejpam-6497	16	6	4.0	4.0	NUM
ejpam-6497	16	7	)	)	PUNCT
ejpam-6497	16	8	e.	e.	PROPN
ejpam-6497	16	9	almuhur	almuhur	PROPN
ejpam-6497	16	10	et	et	PROPN
ejpam-6497	16	11	al	al	PROPN
ejpam-6497	16	12	.	.	PUNCT
ejpam-6497	16	13	/	/	SYM
ejpam-6497	16	14	eur	eur	PROPN
ejpam-6497	16	15	.	.	PUNCT
ejpam-6497	17	1	j.	j.	PROPN
ejpam-6497	17	2	pure	pure	PROPN
ejpam-6497	17	3	appl	appl	PROPN
ejpam-6497	17	4	.	.	PROPN
ejpam-6497	17	5	math	math	PROPN
ejpam-6497	17	6	,	,	PUNCT
ejpam-6497	17	7	18	18	NUM
ejpam-6497	17	8	(	(	PUNCT
ejpam-6497	17	9	3	3	NUM
ejpam-6497	17	10	)	)	PUNCT
ejpam-6497	17	11	(	(	PUNCT
ejpam-6497	17	12	2025	2025	NUM
ejpam-6497	17	13	)	)	PUNCT
ejpam-6497	17	14	,	,	PUNCT
ejpam-6497	17	15	6497	6497	NUM
ejpam-6497	17	16	2	2	NUM
ejpam-6497	17	17	of	of	ADP
ejpam-6497	17	18	11	11	NUM
ejpam-6497	17	19	primary	primary	ADJ
ejpam-6497	17	20	developments	development	NOUN
ejpam-6497	17	21	in	in	ADP
ejpam-6497	17	22	the	the	DET
ejpam-6497	17	23	application	application	NOUN
ejpam-6497	17	24	of	of	ADP
ejpam-6497	17	25	ideals	ideal	NOUN
ejpam-6497	17	26	in	in	ADP
ejpam-6497	17	27	general	general	ADJ
ejpam-6497	17	28	topology	topology	NOUN
ejpam-6497	17	29	.	.	PUNCT
ejpam-6497	18	1	the	the	DET
ejpam-6497	18	2	study	study	NOUN
ejpam-6497	18	3	of	of	ADP
ejpam-6497	18	4	topological	topological	ADJ
ejpam-6497	18	5	spaces	space	NOUN
ejpam-6497	18	6	’	'	PUNCT
ejpam-6497	18	7	local	local	ADJ
ejpam-6497	18	8	properties	property	NOUN
ejpam-6497	18	9	,	,	PUNCT
ejpam-6497	18	10	which	which	PRON
ejpam-6497	18	11	can	can	AUX
ejpam-6497	18	12	be	be	AUX
ejpam-6497	18	13	extended	extend	VERB
ejpam-6497	18	14	to	to	ADP
ejpam-6497	18	15	their	their	PRON
ejpam-6497	18	16	global	global	ADJ
ejpam-6497	18	17	properties	property	NOUN
ejpam-6497	18	18	,	,	PUNCT
ejpam-6497	18	19	is	be	AUX
ejpam-6497	18	20	the	the	DET
ejpam-6497	18	21	focus	focus	NOUN
ejpam-6497	18	22	of	of	ADP
ejpam-6497	18	23	the	the	DET
ejpam-6497	18	24	first	first	ADJ
ejpam-6497	18	25	line	line	NOUN
ejpam-6497	18	26	[	[	X
ejpam-6497	18	27	5	5	NUM
ejpam-6497	18	28	,	,	PUNCT
ejpam-6497	18	29	6	6	NUM
ejpam-6497	18	30	]	]	PUNCT
ejpam-6497	18	31	.	.	PUNCT
ejpam-6497	19	1	the	the	DET
ejpam-6497	19	2	compatibility	compatibility	NOUN
ejpam-6497	19	3	of	of	ADP
ejpam-6497	19	4	an	an	DET
ejpam-6497	19	5	ideal	ideal	NOUN
ejpam-6497	19	6	with	with	ADP
ejpam-6497	19	7	a	a	DET
ejpam-6497	19	8	topology	topology	NOUN
ejpam-6497	19	9	is	be	AUX
ejpam-6497	19	10	the	the	DET
ejpam-6497	19	11	main	main	ADJ
ejpam-6497	19	12	idea	idea	NOUN
ejpam-6497	19	13	in	in	ADP
ejpam-6497	19	14	these	these	DET
ejpam-6497	19	15	studies	study	NOUN
ejpam-6497	19	16	.	.	PUNCT
ejpam-6497	20	1	an	an	DET
ejpam-6497	20	2	example	example	NOUN
ejpam-6497	20	3	of	of	ADP
ejpam-6497	20	4	an	an	DET
ejpam-6497	20	5	immediate	immediate	ADJ
ejpam-6497	20	6	corollary	corollary	NOUN
ejpam-6497	20	7	of	of	ADP
ejpam-6497	20	8	the	the	DET
ejpam-6497	20	9	σ	σ	PROPN
ejpam-6497	20	10	-	-	PUNCT
ejpam-6497	20	11	extension	extension	NOUN
ejpam-6497	20	12	theorem	theorem	NOUN
ejpam-6497	20	13	is	be	AUX
ejpam-6497	20	14	the	the	DET
ejpam-6497	20	15	well	well	ADV
ejpam-6497	20	16	-	-	PUNCT
ejpam-6497	20	17	known	know	VERB
ejpam-6497	20	18	banach	banach	NOUN
ejpam-6497	20	19	category	category	NOUN
ejpam-6497	20	20	theorem	theorem	VERB
ejpam-6497	20	21	[	[	X
ejpam-6497	20	22	5	5	NUM
ejpam-6497	20	23	]	]	PUNCT
ejpam-6497	20	24	.	.	PUNCT
ejpam-6497	21	1	the	the	DET
ejpam-6497	21	2	second	second	ADJ
ejpam-6497	21	3	-	-	PUNCT
ejpam-6497	21	4	line	line	NOUN
ejpam-6497	21	5	works	work	NOUN
ejpam-6497	21	6	employ	employ	VERB
ejpam-6497	21	7	ideals	ideal	NOUN
ejpam-6497	21	8	to	to	PART
ejpam-6497	21	9	generalize	generalize	VERB
ejpam-6497	21	10	some	some	DET
ejpam-6497	21	11	topological	topological	ADJ
ejpam-6497	21	12	space	space	NOUN
ejpam-6497	21	13	features	feature	NOUN
ejpam-6497	21	14	,	,	PUNCT
ejpam-6497	21	15	like	like	ADP
ejpam-6497	21	16	the	the	DET
ejpam-6497	21	17	separation	separation	NOUN
ejpam-6497	21	18	axioms	axiom	VERB
ejpam-6497	21	19	[	[	X
ejpam-6497	21	20	7	7	X
ejpam-6497	21	21	]	]	PUNCT
ejpam-6497	21	22	and	and	CCONJ
ejpam-6497	21	23	compactness	compactness	NOUN
ejpam-6497	22	1	[	[	X
ejpam-6497	22	2	8	8	NUM
ejpam-6497	22	3	]	]	PUNCT
ejpam-6497	22	4	.	.	PUNCT
ejpam-6497	23	1	in	in	ADP
ejpam-6497	23	2	1996	1996	NUM
ejpam-6497	23	3	,	,	PUNCT
ejpam-6497	23	4	santoro	santoro	PROPN
ejpam-6497	23	5	and	and	CCONJ
ejpam-6497	23	6	cammaroto	cammaroto	NOUN
ejpam-6497	23	7	[	[	X
ejpam-6497	23	8	9	9	NUM
ejpam-6497	23	9	]	]	PUNCT
ejpam-6497	23	10	presented	present	VERB
ejpam-6497	23	11	the	the	DET
ejpam-6497	23	12	concept	concept	NOUN
ejpam-6497	23	13	of	of	ADP
ejpam-6497	23	14	weakly	weakly	ADJ
ejpam-6497	23	15	lindelöf	lindelöf	NOUN
ejpam-6497	23	16	spaces	space	NOUN
ejpam-6497	23	17	(	(	PUNCT
ejpam-6497	23	18	sl	sl	NOUN
ejpam-6497	23	19	)	)	PUNCT
ejpam-6497	23	20	.	.	PUNCT
ejpam-6497	24	1	the	the	DET
ejpam-6497	24	2	well	well	ADV
ejpam-6497	24	3	-	-	PUNCT
ejpam-6497	24	4	known	know	VERB
ejpam-6497	24	5	lindelöf	lindelöf	NOUN
ejpam-6497	24	6	property	property	NOUN
ejpam-6497	24	7	naturally	naturally	ADV
ejpam-6497	24	8	deteriorates	deteriorate	VERB
ejpam-6497	24	9	into	into	ADP
ejpam-6497	24	10	the	the	DET
ejpam-6497	24	11	weak	weak	ADJ
ejpam-6497	24	12	lindelöf	lindelöf	NOUN
ejpam-6497	24	13	property	property	NOUN
ejpam-6497	24	14	.	.	PUNCT
ejpam-6497	25	1	the	the	DET
ejpam-6497	25	2	fact	fact	NOUN
ejpam-6497	25	3	that	that	SCONJ
ejpam-6497	25	4	we	we	PRON
ejpam-6497	25	5	only	only	ADV
ejpam-6497	25	6	need	need	VERB
ejpam-6497	25	7	the	the	DET
ejpam-6497	25	8	countable	countable	ADJ
ejpam-6497	25	9	set	set	NOUN
ejpam-6497	25	10	ŵ	ŵ	NUM
ejpam-6497	25	11	to	to	PART
ejpam-6497	25	12	cover	cover	VERB
ejpam-6497	25	13	a	a	DET
ejpam-6497	25	14	dense	dense	ADJ
ejpam-6497	25	15	subset	subset	NOUN
ejpam-6497	25	16	of	of	ADP
ejpam-6497	25	17	the	the	DET
ejpam-6497	25	18	space	space	NOUN
ejpam-6497	25	19	x	x	PUNCT
ejpam-6497	25	20	naturally	naturally	ADV
ejpam-6497	25	21	weakens	weaken	VERB
ejpam-6497	25	22	the	the	DET
ejpam-6497	25	23	lindelöf	lindelöf	NOUN
ejpam-6497	25	24	criterion	criterion	NOUN
ejpam-6497	25	25	.	.	PUNCT
ejpam-6497	26	1	in	in	ADP
ejpam-6497	26	2	particular	particular	ADJ
ejpam-6497	26	3	,	,	PUNCT
ejpam-6497	26	4	if	if	SCONJ
ejpam-6497	26	5	there	there	PRON
ejpam-6497	26	6	exists	exist	VERB
ejpam-6497	26	7	a	a	DET
ejpam-6497	26	8	countable	countable	ADJ
ejpam-6497	26	9	ŵ	ŵ	NUM
ejpam-6497	26	10	û	û	NUM
ejpam-6497	26	11	such	such	ADJ
ejpam-6497	26	12	that	that	DET
ejpam-6497	26	13	∪ŵ	∪ŵ	NOUN
ejpam-6497	26	14	is	be	AUX
ejpam-6497	26	15	dense	dense	ADJ
ejpam-6497	26	16	in	in	ADP
ejpam-6497	26	17	x	x	PUNCT
ejpam-6497	26	18	for	for	ADP
ejpam-6497	26	19	each	each	DET
ejpam-6497	26	20	open	open	ADJ
ejpam-6497	26	21	cover	cover	NOUN
ejpam-6497	26	22	û	û	NUM
ejpam-6497	26	23	of	of	ADP
ejpam-6497	26	24	x	x	PRON
ejpam-6497	26	25	,	,	PUNCT
ejpam-6497	26	26	then	then	ADV
ejpam-6497	26	27	x	x	PUNCT
ejpam-6497	26	28	is	be	AUX
ejpam-6497	26	29	a	a	DET
ejpam-6497	26	30	weakly	weakly	ADJ
ejpam-6497	26	31	sl	sl	NOUN
ejpam-6497	26	32	[	[	X
ejpam-6497	26	33	10	10	NUM
ejpam-6497	26	34	]	]	PUNCT
ejpam-6497	26	35	.	.	PUNCT
ejpam-6497	27	1	the	the	DET
ejpam-6497	27	2	traditional	traditional	ADJ
ejpam-6497	27	3	idea	idea	NOUN
ejpam-6497	27	4	of	of	ADP
ejpam-6497	27	5	sls	sls	PROPN
ejpam-6497	27	6	in	in	ADP
ejpam-6497	27	7	topology	topology	NOUN
ejpam-6497	27	8	is	be	AUX
ejpam-6497	27	9	generalized	generalize	VERB
ejpam-6497	27	10	by	by	ADP
ejpam-6497	27	11	the	the	DET
ejpam-6497	27	12	concept	concept	NOUN
ejpam-6497	27	13	of	of	ADP
ejpam-6497	27	14	almost	almost	ADV
ejpam-6497	27	15	sls	sls	PROPN
ejpam-6497	27	16	.	.	PUNCT
ejpam-6497	28	1	an	an	DET
ejpam-6497	28	2	almost	almost	ADV
ejpam-6497	28	3	sl	sl	NOUN
ejpam-6497	28	4	is	be	AUX
ejpam-6497	28	5	a	a	DET
ejpam-6497	28	6	topological	topological	ADJ
ejpam-6497	28	7	space	space	NOUN
ejpam-6497	28	8	where	where	SCONJ
ejpam-6497	28	9	a	a	DET
ejpam-6497	28	10	little	little	ADJ
ejpam-6497	28	11	weaker	weak	ADJ
ejpam-6497	28	12	requirement	requirement	NOUN
ejpam-6497	28	13	is	be	AUX
ejpam-6497	28	14	satisfied	satisfied	ADJ
ejpam-6497	28	15	:	:	PUNCT
ejpam-6497	28	16	we	we	PRON
ejpam-6497	28	17	just	just	ADV
ejpam-6497	28	18	need	need	VERB
ejpam-6497	28	19	that	that	SCONJ
ejpam-6497	28	20	each	each	DET
ejpam-6497	28	21	open	open	ADJ
ejpam-6497	28	22	cover	cover	NOUN
ejpam-6497	28	23	has	have	VERB
ejpam-6497	28	24	a	a	DET
ejpam-6497	28	25	”	"	PUNCT
ejpam-6497	28	26	countable	countable	ADJ
ejpam-6497	28	27	refinement	refinement	NOUN
ejpam-6497	28	28	”	"	PUNCT
ejpam-6497	28	29	that	that	PRON
ejpam-6497	28	30	covers	cover	VERB
ejpam-6497	28	31	the	the	DET
ejpam-6497	28	32	space	space	NOUN
ejpam-6497	28	33	,	,	PUNCT
ejpam-6497	28	34	rather	rather	ADV
ejpam-6497	28	35	than	than	ADP
ejpam-6497	28	36	that	that	SCONJ
ejpam-6497	28	37	each	each	DET
ejpam-6497	28	38	open	open	ADJ
ejpam-6497	28	39	cover	cover	NOUN
ejpam-6497	28	40	has	have	VERB
ejpam-6497	28	41	a	a	DET
ejpam-6497	28	42	countable	countable	ADJ
ejpam-6497	28	43	subcover	subcover	NOUN
ejpam-6497	28	44	.	.	PUNCT
ejpam-6497	29	1	definition	definition	NOUN
ejpam-6497	29	2	1	1	NUM
ejpam-6497	29	3	.	.	PUNCT
ejpam-6497	30	1	the	the	DET
ejpam-6497	30	2	space	space	NOUN
ejpam-6497	30	3	x	x	PUNCT
ejpam-6497	30	4	is	be	AUX
ejpam-6497	30	5	almost	almost	ADV
ejpam-6497	30	6	lindelöf	lindelöf	NOUN
ejpam-6497	30	7	if	if	SCONJ
ejpam-6497	30	8	for	for	ADP
ejpam-6497	30	9	each	each	DET
ejpam-6497	30	10	family	family	NOUN
ejpam-6497	30	11	of	of	ADP
ejpam-6497	30	12	open	open	ADJ
ejpam-6497	30	13	subsets	subset	NOUN
ejpam-6497	30	14	{	{	PUNCT
ejpam-6497	30	15	uα	uα	NOUN
ejpam-6497	30	16	:	:	PUNCT
ejpam-6497	30	17	α	α	PROPN
ejpam-6497	30	18	∈	∈	PROPN
ejpam-6497	30	19	λ	λ	PROPN
ejpam-6497	30	20	}	}	PUNCT
ejpam-6497	30	21	,	,	PUNCT
ejpam-6497	30	22	covering	cover	VERB
ejpam-6497	30	23	it	it	PRON
ejpam-6497	30	24	,	,	PUNCT
ejpam-6497	30	25	there	there	PRON
ejpam-6497	30	26	exists	exist	VERB
ejpam-6497	30	27	{	{	PUNCT
ejpam-6497	30	28	u	u	NOUN
ejpam-6497	30	29	′	′	NOUN
ejpam-6497	30	30	n	n	NOUN
ejpam-6497	30	31	:	:	PUNCT
ejpam-6497	30	32	n	n	CCONJ
ejpam-6497	30	33	∈	∈	PROPN
ejpam-6497	30	34	n	n	CCONJ
ejpam-6497	30	35	}	}	PUNCT
ejpam-6497	30	36	a	a	DET
ejpam-6497	30	37	countable	countable	ADJ
ejpam-6497	30	38	collection	collection	NOUN
ejpam-6497	30	39	of	of	ADP
ejpam-6497	30	40	open	open	ADJ
ejpam-6497	30	41	sets	set	NOUN
ejpam-6497	30	42	:	:	PUNCT
ejpam-6497	30	43	i	i	NOUN
ejpam-6497	30	44	)	)	PUNCT
ejpam-6497	30	45	there	there	PRON
ejpam-6497	30	46	exists	exist	VERB
ejpam-6497	30	47	α	α	PRON
ejpam-6497	30	48	∈	∈	PROPN
ejpam-6497	30	49	λ	λ	X
ejpam-6497	30	50	:	:	PUNCT
ejpam-6497	30	51	u	u	NOUN
ejpam-6497	30	52	′	′	NOUN
ejpam-6497	30	53	n	n	NUM
ejpam-6497	30	54	⊂	⊂	PROPN
ejpam-6497	30	55	uα	uα	PROPN
ejpam-6497	30	56	;	;	PUNCT
ejpam-6497	30	57	ii	ii	X
ejpam-6497	30	58	)	)	PUNCT
ejpam-6497	30	59	x	x	X
ejpam-6497	31	1	=	=	PUNCT
ejpam-6497	31	2	∪n∈nu	∪n∈nu	ADJ
ejpam-6497	31	3	′	′	NUM
ejpam-6497	31	4	n.	n.	NOUN
ejpam-6497	31	5	remark	remark	NOUN
ejpam-6497	31	6	1	1	NUM
ejpam-6497	31	7	.	.	PUNCT
ejpam-6497	31	8	important	important	ADJ
ejpam-6497	31	9	differences	difference	NOUN
ejpam-6497	31	10	between	between	ADP
ejpam-6497	31	11	almost	almost	ADV
ejpam-6497	31	12	lindelöf	lindelöf	NOUN
ejpam-6497	31	13	and	and	CCONJ
ejpam-6497	31	14	lindelöf	lindelöf	NOUN
ejpam-6497	31	15	spaces	space	VERB
ejpam-6497	31	16	a	a	DET
ejpam-6497	31	17	)	)	PUNCT
ejpam-6497	31	18	countable	countable	ADJ
ejpam-6497	31	19	subcovers	subcover	NOUN
ejpam-6497	31	20	are	be	AUX
ejpam-6497	31	21	directly	directly	ADV
ejpam-6497	31	22	extracted	extract	VERB
ejpam-6497	31	23	from	from	ADP
ejpam-6497	31	24	the	the	DET
ejpam-6497	31	25	original	original	ADJ
ejpam-6497	31	26	open	open	ADJ
ejpam-6497	31	27	cover	cover	NOUN
ejpam-6497	31	28	in	in	ADP
ejpam-6497	31	29	a	a	DET
ejpam-6497	31	30	sl	sl	NOUN
ejpam-6497	31	31	;	;	PUNCT
ejpam-6497	31	32	b	b	X
ejpam-6497	31	33	)	)	PUNCT
ejpam-6497	31	34	before	before	ADP
ejpam-6497	31	35	extracting	extract	VERB
ejpam-6497	31	36	a	a	DET
ejpam-6497	31	37	countable	countable	ADJ
ejpam-6497	31	38	subcover	subcover	NOUN
ejpam-6497	31	39	,	,	PUNCT
ejpam-6497	31	40	we	we	PRON
ejpam-6497	31	41	decrease	decrease	VERB
ejpam-6497	31	42	the	the	DET
ejpam-6497	31	43	sets	set	NOUN
ejpam-6497	31	44	(	(	PUNCT
ejpam-6497	31	45	while	while	SCONJ
ejpam-6497	31	46	keeping	keep	VERB
ejpam-6497	31	47	them	they	PRON
ejpam-6497	31	48	open	open	ADJ
ejpam-6497	31	49	)	)	PUNCT
ejpam-6497	31	50	in	in	ADP
ejpam-6497	31	51	an	an	DET
ejpam-6497	31	52	almost	almost	ADV
ejpam-6497	31	53	sl	sl	NOUN
ejpam-6497	31	54	,	,	PUNCT
ejpam-6497	31	55	allowing	allow	VERB
ejpam-6497	31	56	us	we	PRON
ejpam-6497	31	57	to	to	PART
ejpam-6497	31	58	modify	modify	VERB
ejpam-6497	31	59	the	the	DET
ejpam-6497	31	60	original	original	ADJ
ejpam-6497	31	61	open	open	ADJ
ejpam-6497	31	62	cover	cover	NOUN
ejpam-6497	31	63	.	.	PUNCT
ejpam-6497	32	1	as	as	ADP
ejpam-6497	32	2	a	a	DET
ejpam-6497	32	3	result	result	NOUN
ejpam-6497	32	4	,	,	PUNCT
ejpam-6497	32	5	all	all	DET
ejpam-6497	32	6	sls	sls	NOUN
ejpam-6497	32	7	are	be	AUX
ejpam-6497	32	8	almost	almost	ADV
ejpam-6497	32	9	lindelöf	lindelöf	NOUN
ejpam-6497	32	10	,	,	PUNCT
ejpam-6497	32	11	albeit	albeit	SCONJ
ejpam-6497	32	12	this	this	PRON
ejpam-6497	32	13	is	be	AUX
ejpam-6497	32	14	not	not	PART
ejpam-6497	32	15	always	always	ADV
ejpam-6497	32	16	the	the	DET
ejpam-6497	32	17	case	case	NOUN
ejpam-6497	32	18	.	.	PUNCT
ejpam-6497	33	1	moreover	moreover	ADV
ejpam-6497	33	2	,	,	PUNCT
ejpam-6497	33	3	compact	compact	ADJ
ejpam-6497	33	4	spaces	space	NOUN
ejpam-6497	33	5	are	be	AUX
ejpam-6497	33	6	lindelöf	lindelöf	NOUN
ejpam-6497	33	7	and	and	CCONJ
ejpam-6497	33	8	so	so	ADV
ejpam-6497	33	9	,	,	PUNCT
ejpam-6497	33	10	they	they	PRON
ejpam-6497	33	11	are	be	AUX
ejpam-6497	33	12	almost	almost	ADV
ejpam-6497	33	13	lindelöf	lindelöf	NOUN
ejpam-6497	33	14	.	.	PUNCT
ejpam-6497	34	1	(	(	PUNCT
ejpam-6497	34	2	[	[	X
ejpam-6497	34	3	0	0	NUM
ejpam-6497	34	4	,	,	PUNCT
ejpam-6497	34	5	1	1	NUM
ejpam-6497	34	6	]	]	PUNCT
ejpam-6497	34	7	,	,	PUNCT
ejpam-6497	34	8	τu	τu	ADP
ejpam-6497	34	9	)	)	PUNCT
ejpam-6497	34	10	and	and	CCONJ
ejpam-6497	34	11	(	(	PUNCT
ejpam-6497	34	12	r	r	NOUN
ejpam-6497	34	13	,	,	PUNCT
ejpam-6497	34	14	τu	τu	PRON
ejpam-6497	34	15	)	)	PUNCT
ejpam-6497	34	16	are	be	AUX
ejpam-6497	34	17	lindelöf	lindelöf	NOUN
ejpam-6497	34	18	and	and	CCONJ
ejpam-6497	34	19	hence	hence	ADV
ejpam-6497	34	20	almost	almost	ADV
ejpam-6497	34	21	sls	sls	PROPN
ejpam-6497	34	22	.	.	PROPN
ejpam-6497	35	1	examine	examine	PROPN
ejpam-6497	35	2	r	r	NOUN
ejpam-6497	35	3	that	that	PRON
ejpam-6497	35	4	has	have	VERB
ejpam-6497	35	5	the	the	DET
ejpam-6497	35	6	lower	low	ADJ
ejpam-6497	35	7	limit	limit	NOUN
ejpam-6497	35	8	topology	topology	NOUN
ejpam-6497	35	9	,	,	PUNCT
ejpam-6497	35	10	which	which	PRON
ejpam-6497	35	11	is	be	AUX
ejpam-6497	35	12	produced	produce	VERB
ejpam-6497	35	13	by	by	ADP
ejpam-6497	35	14	intervals	interval	NOUN
ejpam-6497	35	15	of	of	ADP
ejpam-6497	35	16	the	the	DET
ejpam-6497	35	17	[	[	X
ejpam-6497	35	18	a	a	PRON
ejpam-6497	35	19	,	,	PUNCT
ejpam-6497	35	20	b	b	NOUN
ejpam-6497	35	21	)	)	PUNCT
ejpam-6497	35	22	type	type	NOUN
ejpam-6497	35	23	a	a	PRON
ejpam-6497	35	24	,	,	PUNCT
ejpam-6497	35	25	b	b	PROPN
ejpam-6497	35	26	∈	∈	PROPN
ejpam-6497	35	27	r.	r.	NOUN
ejpam-6497	35	28	because	because	SCONJ
ejpam-6497	35	29	some	some	DET
ejpam-6497	35	30	open	open	ADJ
ejpam-6497	35	31	covers	cover	NOUN
ejpam-6497	35	32	can	can	AUX
ejpam-6497	35	33	not	not	PART
ejpam-6497	35	34	have	have	VERB
ejpam-6497	35	35	a	a	DET
ejpam-6497	35	36	countable	countable	ADJ
ejpam-6497	35	37	subcover	subcover	NOUN
ejpam-6497	35	38	extracted	extract	VERB
ejpam-6497	35	39	,	,	PUNCT
ejpam-6497	35	40	this	this	DET
ejpam-6497	35	41	space	space	NOUN
ejpam-6497	35	42	is	be	AUX
ejpam-6497	35	43	not	not	PART
ejpam-6497	35	44	lindelöf	lindelöf	NOUN
ejpam-6497	35	45	.	.	PUNCT
ejpam-6497	36	1	nonetheless	nonetheless	ADV
ejpam-6497	36	2	,	,	PUNCT
ejpam-6497	36	3	it	it	PRON
ejpam-6497	36	4	is	be	AUX
ejpam-6497	36	5	almost	almost	ADV
ejpam-6497	36	6	lindelöf	lindelöf	NOUN
ejpam-6497	36	7	since	since	SCONJ
ejpam-6497	36	8	a	a	DET
ejpam-6497	36	9	countable	countable	ADJ
ejpam-6497	36	10	subfamily	subfamily	ADV
ejpam-6497	36	11	spanning	span	VERB
ejpam-6497	36	12	r	r	NOUN
ejpam-6497	36	13	may	may	AUX
ejpam-6497	36	14	be	be	AUX
ejpam-6497	36	15	created	create	VERB
ejpam-6497	36	16	using	use	VERB
ejpam-6497	36	17	the	the	DET
ejpam-6497	36	18	closures	closure	NOUN
ejpam-6497	36	19	of	of	ADP
ejpam-6497	36	20	the	the	DET
ejpam-6497	36	21	intervals	interval	NOUN
ejpam-6497	36	22	[	[	X
ejpam-6497	36	23	a	a	X
ejpam-6497	36	24	,	,	PUNCT
ejpam-6497	36	25	b	b	NOUN
ejpam-6497	36	26	]	]	X
ejpam-6497	36	27	.	.	PUNCT
ejpam-6497	37	1	if	if	SCONJ
ejpam-6497	37	2	each	each	DET
ejpam-6497	37	3	open	open	ADJ
ejpam-6497	37	4	cover	cover	NOUN
ejpam-6497	37	5	in	in	ADP
ejpam-6497	37	6	the	the	DET
ejpam-6497	37	7	space	space	NOUN
ejpam-6497	37	8	x	x	PRON
ejpam-6497	37	9	has	have	VERB
ejpam-6497	37	10	a	a	DET
ejpam-6497	37	11	countable	countable	ADJ
ejpam-6497	37	12	subcollection	subcollection	NOUN
ejpam-6497	37	13	whose	whose	DET
ejpam-6497	37	14	union	union	NOUN
ejpam-6497	37	15	is	be	AUX
ejpam-6497	37	16	dense	dense	ADJ
ejpam-6497	37	17	in	in	ADP
ejpam-6497	37	18	x	x	PRON
ejpam-6497	37	19	,	,	PUNCT
ejpam-6497	37	20	then	then	ADV
ejpam-6497	37	21	the	the	DET
ejpam-6497	37	22	space	space	NOUN
ejpam-6497	37	23	is	be	AUX
ejpam-6497	37	24	weakly	weakly	ADJ
ejpam-6497	37	25	lindelöf	lindelöf	NOUN
ejpam-6497	37	26	.	.	PUNCT
ejpam-6497	38	1	this	this	DET
ejpam-6497	38	2	trait	trait	NOUN
ejpam-6497	38	3	is	be	AUX
ejpam-6497	38	4	stronger	strong	ADJ
ejpam-6497	38	5	than	than	ADP
ejpam-6497	38	6	separability	separability	NOUN
ejpam-6497	38	7	but	but	CCONJ
ejpam-6497	38	8	weaker	weak	ADJ
ejpam-6497	38	9	than	than	ADP
ejpam-6497	38	10	the	the	DET
ejpam-6497	38	11	lindelöf	lindelöf	NOUN
ejpam-6497	38	12	property	property	NOUN
ejpam-6497	38	13	.	.	PUNCT
ejpam-6497	39	1	understanding	understand	VERB
ejpam-6497	39	2	how	how	SCONJ
ejpam-6497	39	3	compactness	compactness	NOUN
ejpam-6497	39	4	,	,	PUNCT
ejpam-6497	39	5	separability	separability	NOUN
ejpam-6497	39	6	,	,	PUNCT
ejpam-6497	39	7	and	and	CCONJ
ejpam-6497	39	8	covering	cover	VERB
ejpam-6497	39	9	qualities	quality	NOUN
ejpam-6497	39	10	interact	interact	VERB
ejpam-6497	39	11	in	in	ADP
ejpam-6497	39	12	topology	topology	NOUN
ejpam-6497	39	13	requires	require	VERB
ejpam-6497	39	14	an	an	DET
ejpam-6497	39	15	understanding	understanding	NOUN
ejpam-6497	39	16	of	of	ADP
ejpam-6497	39	17	weakly	weakly	ADJ
ejpam-6497	39	18	sls	sls	PROPN
ejpam-6497	39	19	.	.	PUNCT
ejpam-6497	40	1	the	the	DET
ejpam-6497	40	2	study	study	NOUN
ejpam-6497	40	3	of	of	ADP
ejpam-6497	40	4	functional	functional	ADJ
ejpam-6497	40	5	analysis	analysis	NOUN
ejpam-6497	40	6	and	and	CCONJ
ejpam-6497	40	7	general	general	ADJ
ejpam-6497	40	8	topology	topology	NOUN
ejpam-6497	40	9	naturally	naturally	ADV
ejpam-6497	40	10	leads	lead	VERB
ejpam-6497	40	11	to	to	ADP
ejpam-6497	40	12	weakly	weakly	ADJ
ejpam-6497	40	13	sls	sls	PROPN
ejpam-6497	40	14	.	.	PUNCT
ejpam-6497	41	1	they	they	PRON
ejpam-6497	41	2	offer	offer	VERB
ejpam-6497	41	3	a	a	DET
ejpam-6497	41	4	helpful	helpful	ADJ
ejpam-6497	41	5	compromise	compromise	NOUN
ejpam-6497	41	6	between	between	ADP
ejpam-6497	41	7	the	the	DET
ejpam-6497	41	8	lindelöf	lindelöf	NOUN
ejpam-6497	41	9	characteristic	characteristic	ADJ
ejpam-6497	41	10	and	and	CCONJ
ejpam-6497	41	11	separability	separability	NOUN
ejpam-6497	41	12	.	.	PUNCT
ejpam-6497	42	1	they	they	PRON
ejpam-6497	42	2	are	be	AUX
ejpam-6497	42	3	e.	e.	PROPN
ejpam-6497	42	4	almuhur	almuhur	PROPN
ejpam-6497	43	1	et	et	PROPN
ejpam-6497	43	2	al	al	PROPN
ejpam-6497	43	3	.	.	PUNCT
ejpam-6497	43	4	/	/	SYM
ejpam-6497	43	5	eur	eur	PROPN
ejpam-6497	43	6	.	.	PUNCT
ejpam-6497	44	1	j.	j.	PROPN
ejpam-6497	44	2	pure	pure	PROPN
ejpam-6497	44	3	appl	appl	PROPN
ejpam-6497	44	4	.	.	PROPN
ejpam-6497	44	5	math	math	PROPN
ejpam-6497	44	6	,	,	PUNCT
ejpam-6497	44	7	18	18	NUM
ejpam-6497	44	8	(	(	PUNCT
ejpam-6497	44	9	3	3	NUM
ejpam-6497	44	10	)	)	PUNCT
ejpam-6497	44	11	(	(	PUNCT
ejpam-6497	44	12	2025	2025	NUM
ejpam-6497	44	13	)	)	PUNCT
ejpam-6497	44	14	,	,	PUNCT
ejpam-6497	44	15	6497	6497	NUM
ejpam-6497	44	16	3	3	NUM
ejpam-6497	44	17	of	of	ADP
ejpam-6497	44	18	11	11	NUM
ejpam-6497	44	19	especially	especially	ADV
ejpam-6497	44	20	pertinent	pertinent	ADJ
ejpam-6497	44	21	in	in	ADP
ejpam-6497	44	22	areas	area	NOUN
ejpam-6497	44	23	like	like	ADP
ejpam-6497	44	24	measure	measure	NOUN
ejpam-6497	44	25	theory	theory	NOUN
ejpam-6497	44	26	and	and	CCONJ
ejpam-6497	44	27	function	function	NOUN
ejpam-6497	44	28	space	space	NOUN
ejpam-6497	44	29	analysis	analysis	NOUN
ejpam-6497	44	30	where	where	SCONJ
ejpam-6497	44	31	density	density	NOUN
ejpam-6497	44	32	arguments	argument	NOUN
ejpam-6497	44	33	are	be	AUX
ejpam-6497	44	34	crucial	crucial	ADJ
ejpam-6497	44	35	.	.	PUNCT
ejpam-6497	45	1	comparison	comparison	NOUN
ejpam-6497	45	2	with	with	ADP
ejpam-6497	45	3	sls	sls	PROPN
ejpam-6497	45	4	:	:	PUNCT
ejpam-6497	45	5	if	if	SCONJ
ejpam-6497	45	6	a	a	DET
ejpam-6497	45	7	countable	countable	ADJ
ejpam-6497	45	8	subcover	subcover	NOUN
ejpam-6497	45	9	exists	exist	VERB
ejpam-6497	45	10	,	,	PUNCT
ejpam-6497	45	11	its	its	PRON
ejpam-6497	45	12	union	union	NOUN
ejpam-6497	45	13	is	be	AUX
ejpam-6497	45	14	the	the	DET
ejpam-6497	45	15	entire	entire	ADJ
ejpam-6497	45	16	space	space	NOUN
ejpam-6497	45	17	(	(	PUNCT
ejpam-6497	45	18	and	and	CCONJ
ejpam-6497	45	19	hence	hence	ADV
ejpam-6497	45	20	dense	dense	ADJ
ejpam-6497	45	21	)	)	PUNCT
ejpam-6497	45	22	,	,	PUNCT
ejpam-6497	45	23	making	make	VERB
ejpam-6497	45	24	every	every	DET
ejpam-6497	45	25	sl	sl	NOUN
ejpam-6497	45	26	,	,	PUNCT
ejpam-6497	45	27	weakly	weakly	ADJ
ejpam-6497	45	28	lindelöf	lindelöf	NOUN
ejpam-6497	45	29	.	.	PUNCT
ejpam-6497	46	1	the	the	DET
ejpam-6497	46	2	opposite	opposite	NOUN
ejpam-6497	46	3	is	be	AUX
ejpam-6497	46	4	n’t	not	PART
ejpam-6497	46	5	true	true	ADJ
ejpam-6497	46	6	,	,	PUNCT
ejpam-6497	46	7	though	though	ADV
ejpam-6497	46	8	.	.	PUNCT
ejpam-6497	47	1	weakly	weakly	ADJ
ejpam-6497	47	2	lindelöf	lindelöf	NOUN
ejpam-6497	47	3	areas	area	NOUN
ejpam-6497	47	4	that	that	PRON
ejpam-6497	47	5	are	be	AUX
ejpam-6497	47	6	not	not	PART
ejpam-6497	47	7	lindelöf	lindelöf	NOUN
ejpam-6497	47	8	do	do	AUX
ejpam-6497	47	9	exist	exist	VERB
ejpam-6497	47	10	[	[	PUNCT
ejpam-6497	47	11	11	11	NUM
ejpam-6497	47	12	]	]	PUNCT
ejpam-6497	47	13	.	.	PUNCT
ejpam-6497	48	1	example	example	NOUN
ejpam-6497	49	1	1	1	NUM
ejpam-6497	49	2	.	.	X
ejpam-6497	49	3	i	i	PRON
ejpam-6497	49	4	)	)	PUNCT
ejpam-6497	49	5	weakly	weakly	ADJ
ejpam-6497	49	6	lindelöf	lindelöf	NOUN
ejpam-6497	49	7	is	be	AUX
ejpam-6497	49	8	any	any	DET
ejpam-6497	49	9	separable	separable	ADJ
ejpam-6497	49	10	space	space	NOUN
ejpam-6497	49	11	.	.	PUNCT
ejpam-6497	50	1	this	this	PRON
ejpam-6497	50	2	is	be	AUX
ejpam-6497	50	3	due	due	ADJ
ejpam-6497	50	4	to	to	ADP
ejpam-6497	50	5	the	the	DET
ejpam-6497	50	6	fact	fact	NOUN
ejpam-6497	50	7	that	that	SCONJ
ejpam-6497	50	8	a	a	DET
ejpam-6497	50	9	countable	countable	ADJ
ejpam-6497	50	10	subcollection	subcollection	NOUN
ejpam-6497	50	11	of	of	ADP
ejpam-6497	50	12	an	an	DET
ejpam-6497	50	13	open	open	ADJ
ejpam-6497	50	14	cover	cover	NOUN
ejpam-6497	50	15	whose	whose	DET
ejpam-6497	50	16	union	union	NOUN
ejpam-6497	50	17	is	be	AUX
ejpam-6497	50	18	dense	dense	ADJ
ejpam-6497	50	19	may	may	AUX
ejpam-6497	50	20	always	always	ADV
ejpam-6497	50	21	be	be	AUX
ejpam-6497	50	22	constructed	construct	VERB
ejpam-6497	50	23	from	from	ADP
ejpam-6497	50	24	a	a	DET
ejpam-6497	50	25	countable	countable	ADJ
ejpam-6497	50	26	dense	dense	ADJ
ejpam-6497	50	27	subset	subset	NOUN
ejpam-6497	50	28	.	.	PUNCT
ejpam-6497	51	1	ii	ii	PROPN
ejpam-6497	51	2	)	)	PUNCT
ejpam-6497	51	3	with	with	ADP
ejpam-6497	51	4	the	the	DET
ejpam-6497	51	5	conventional	conventional	ADJ
ejpam-6497	51	6	topology	topology	NOUN
ejpam-6497	51	7	,	,	PUNCT
ejpam-6497	51	8	the	the	DET
ejpam-6497	51	9	real	real	ADJ
ejpam-6497	51	10	line	line	NOUN
ejpam-6497	51	11	r	r	NOUN
ejpam-6497	51	12	is	be	AUX
ejpam-6497	51	13	both	both	DET
ejpam-6497	51	14	lindelöf	lindelöf	NOUN
ejpam-6497	51	15	and	and	CCONJ
ejpam-6497	51	16	weakly	weakly	ADJ
ejpam-6497	51	17	lindelöf	lindelöf	PROPN
ejpam-6497	51	18	.	.	PUNCT
ejpam-6497	52	1	iii	iii	X
ejpam-6497	52	2	)	)	PUNCT
ejpam-6497	52	3	the	the	DET
ejpam-6497	52	4	true	true	ADJ
ejpam-6497	52	5	line	line	NOUN
ejpam-6497	52	6	with	with	ADP
ejpam-6497	52	7	the	the	DET
ejpam-6497	52	8	lower	low	ADJ
ejpam-6497	52	9	limit	limit	NOUN
ejpam-6497	52	10	topology	topology	NOUN
ejpam-6497	52	11	,	,	PUNCT
ejpam-6497	52	12	the	the	DET
ejpam-6497	52	13	sorgenfrey	sorgenfrey	PROPN
ejpam-6497	52	14	line	line	NOUN
ejpam-6497	52	15	,	,	PUNCT
ejpam-6497	52	16	is	be	AUX
ejpam-6497	52	17	not	not	PART
ejpam-6497	52	18	lindelöf	lindelöf	NOUN
ejpam-6497	52	19	but	but	CCONJ
ejpam-6497	52	20	faintly	faintly	ADV
ejpam-6497	52	21	so	so	ADV
ejpam-6497	52	22	.	.	PUNCT
ejpam-6497	53	1	remark	remark	PROPN
ejpam-6497	53	2	2	2	NUM
ejpam-6497	53	3	.	.	PUNCT
ejpam-6497	53	4	relation	relation	NOUN
ejpam-6497	53	5	to	to	ADP
ejpam-6497	53	6	further	further	ADJ
ejpam-6497	53	7	topological	topological	ADJ
ejpam-6497	53	8	features	feature	NOUN
ejpam-6497	53	9	:	:	PUNCT
ejpam-6497	53	10	a	a	X
ejpam-6497	53	11	)	)	PUNCT
ejpam-6497	53	12	separability	separability	NOUN
ejpam-6497	53	13	:	:	PUNCT
ejpam-6497	53	14	while	while	SCONJ
ejpam-6497	53	15	the	the	DET
ejpam-6497	53	16	opposite	opposite	NOUN
ejpam-6497	53	17	is	be	AUX
ejpam-6497	53	18	not	not	PART
ejpam-6497	53	19	true	true	ADJ
ejpam-6497	53	20	,	,	PUNCT
ejpam-6497	53	21	any	any	DET
ejpam-6497	53	22	separable	separable	ADJ
ejpam-6497	53	23	space	space	NOUN
ejpam-6497	53	24	is	be	AUX
ejpam-6497	53	25	weakly	weakly	ADJ
ejpam-6497	53	26	lindelöf	lindelöf	NOUN
ejpam-6497	53	27	.	.	PUNCT
ejpam-6497	54	1	for	for	ADP
ejpam-6497	54	2	instance	instance	NOUN
ejpam-6497	54	3	,	,	PUNCT
ejpam-6497	54	4	the	the	DET
ejpam-6497	54	5	one	one	NUM
ejpam-6497	54	6	-	-	PUNCT
ejpam-6497	54	7	point	point	NOUN
ejpam-6497	54	8	compactification	compactification	NOUN
ejpam-6497	54	9	of	of	ADP
ejpam-6497	54	10	a	a	DET
ejpam-6497	54	11	discrete	discrete	ADJ
ejpam-6497	54	12	uncountable	uncountable	ADJ
ejpam-6497	54	13	space	space	NOUN
ejpam-6497	54	14	is	be	AUX
ejpam-6497	54	15	weakly	weakly	ADJ
ejpam-6497	54	16	lindelöf	lindelöf	NOUN
ejpam-6497	54	17	but	but	CCONJ
ejpam-6497	54	18	not	not	PART
ejpam-6497	54	19	separable	separable	ADJ
ejpam-6497	54	20	;	;	PUNCT
ejpam-6497	54	21	b	b	X
ejpam-6497	54	22	)	)	PUNCT
ejpam-6497	54	23	first	first	ADJ
ejpam-6497	54	24	countability	countability	NOUN
ejpam-6497	54	25	:	:	PUNCT
ejpam-6497	54	26	neither	neither	CCONJ
ejpam-6497	54	27	first	first	ADJ
ejpam-6497	54	28	countability	countability	NOUN
ejpam-6497	54	29	nor	nor	CCONJ
ejpam-6497	54	30	weak	weak	ADJ
ejpam-6497	54	31	lindelöfness	lindelöfness	PUNCT
ejpam-6497	54	32	are	be	AUX
ejpam-6497	54	33	a	a	DET
ejpam-6497	54	34	prerequisite	prerequisite	NOUN
ejpam-6497	54	35	for	for	ADP
ejpam-6497	54	36	the	the	DET
ejpam-6497	54	37	other	other	ADJ
ejpam-6497	54	38	;	;	PUNCT
ejpam-6497	54	39	c	c	X
ejpam-6497	54	40	)	)	PUNCT
ejpam-6497	54	41	normality	normality	NOUN
ejpam-6497	54	42	:	:	PUNCT
ejpam-6497	54	43	a	a	DET
ejpam-6497	54	44	weakly	weakly	ADJ
ejpam-6497	54	45	sl	sl	INTJ
ejpam-6497	54	46	that	that	PRON
ejpam-6497	54	47	is	be	AUX
ejpam-6497	54	48	normal	normal	ADJ
ejpam-6497	54	49	is	be	AUX
ejpam-6497	54	50	not	not	PART
ejpam-6497	54	51	always	always	ADV
ejpam-6497	54	52	lindelöf	lindelöf	PROPN
ejpam-6497	54	53	.	.	PUNCT
ejpam-6497	55	1	the	the	DET
ejpam-6497	55	2	moore	moore	PROPN
ejpam-6497	55	3	(	(	PUNCT
ejpam-6497	55	4	niemytzki	niemytzki	NOUN
ejpam-6497	55	5	)	)	PUNCT
ejpam-6497	55	6	plane	plane	NOUN
ejpam-6497	55	7	,	,	PUNCT
ejpam-6497	55	8	for	for	ADP
ejpam-6497	55	9	instance	instance	NOUN
ejpam-6497	55	10	,	,	PUNCT
ejpam-6497	55	11	is	be	AUX
ejpam-6497	55	12	normal	normal	ADJ
ejpam-6497	55	13	and	and	CCONJ
ejpam-6497	55	14	weakly	weakly	ADJ
ejpam-6497	55	15	lindelöf	lindelöf	NOUN
ejpam-6497	55	16	but	but	CCONJ
ejpam-6497	55	17	not	not	PART
ejpam-6497	55	18	lindelöf	lindelöf	PROPN
ejpam-6497	55	19	.	.	PUNCT
ejpam-6497	56	1	typically	typically	ADV
ejpam-6497	56	2	,	,	PUNCT
ejpam-6497	56	3	the	the	DET
ejpam-6497	56	4	extent	extent	NOUN
ejpam-6497	56	5	e(x	e(x	NUM
ejpam-6497	56	6	)	)	PUNCT
ejpam-6497	56	7	of	of	ADP
ejpam-6497	56	8	x	x	PUNCT
ejpam-6497	56	9	represents	represent	VERB
ejpam-6497	56	10	the	the	DET
ejpam-6497	56	11	smallest	small	ADJ
ejpam-6497	56	12	cardinal	cardinal	ADJ
ejpam-6497	56	13	number	number	NOUN
ejpam-6497	56	14	κ	κ	NOUN
ejpam-6497	56	15	(	(	PUNCT
ejpam-6497	56	16	the	the	DET
ejpam-6497	56	17	smallest	small	ADJ
ejpam-6497	56	18	cardinal	cardinal	ADJ
ejpam-6497	56	19	number	number	NOUN
ejpam-6497	56	20	in	in	ADP
ejpam-6497	56	21	set	set	NOUN
ejpam-6497	56	22	theory	theory	NOUN
ejpam-6497	56	23	is	be	AUX
ejpam-6497	56	24	represented	represent	VERB
ejpam-6497	56	25	by	by	ADP
ejpam-6497	56	26	the	the	DET
ejpam-6497	56	27	formula	formula	NOUN
ejpam-6497	56	28	κ	κ	NOUN
ejpam-6497	56	29	=	=	PUNCT
ejpam-6497	56	30	ℵ	ℵ	PROPN
ejpam-6497	56	31	◦	◦	NOUN
ejpam-6497	56	32	=	=	SYM
ejpam-6497	57	1	|n|	|n|	NUM
ejpam-6497	58	1	[	[	X
ejpam-6497	58	2	12	12	NUM
ejpam-6497	58	3	]	]	PUNCT
ejpam-6497	58	4	)	)	PUNCT
ejpam-6497	58	5	for	for	ADP
ejpam-6497	58	6	which	which	PRON
ejpam-6497	58	7	the	the	DET
ejpam-6497	58	8	cardinality	cardinality	NOUN
ejpam-6497	58	9	of	of	ADP
ejpam-6497	58	10	each	each	DET
ejpam-6497	58	11	discrete	discrete	ADJ
ejpam-6497	58	12	closed	closed	ADJ
ejpam-6497	58	13	subset	subset	NOUN
ejpam-6497	58	14	of	of	ADP
ejpam-6497	58	15	x	x	PUNCT
ejpam-6497	58	16	is	be	AUX
ejpam-6497	58	17	less	less	ADJ
ejpam-6497	58	18	than	than	ADP
ejpam-6497	58	19	or	or	CCONJ
ejpam-6497	58	20	equal	equal	ADJ
ejpam-6497	58	21	κ	κ	NOUN
ejpam-6497	58	22	.	.	PUNCT
ejpam-6497	59	1	if	if	SCONJ
ejpam-6497	59	2	a	a	PRON
ejpam-6497	59	3	⊂	⊂	PROPN
ejpam-6497	59	4	x	x	NOUN
ejpam-6497	59	5	,	,	PUNCT
ejpam-6497	59	6	then	then	ADV
ejpam-6497	59	7	|a|	|a|	NOUN
ejpam-6497	59	8	denotes	denote	VERB
ejpam-6497	59	9	the	the	DET
ejpam-6497	59	10	cardinality	cardinality	NOUN
ejpam-6497	59	11	of	of	ADP
ejpam-6497	59	12	a.	a.	NOUN
ejpam-6497	59	13	definitely	definitely	ADV
ejpam-6497	59	14	,	,	PUNCT
ejpam-6497	59	15	ω	ω	PROPN
ejpam-6497	59	16	is	be	AUX
ejpam-6497	59	17	the	the	DET
ejpam-6497	59	18	first	first	ADJ
ejpam-6497	59	19	infinite	infinite	ADJ
ejpam-6497	59	20	cardinal	cardinal	ADJ
ejpam-6497	59	21	number	number	NOUN
ejpam-6497	59	22	,	,	PUNCT
ejpam-6497	59	23	ω1is	ω1is	PUNCT
ejpam-6497	59	24	the	the	DET
ejpam-6497	59	25	first	first	ADJ
ejpam-6497	59	26	uncountable	uncountable	ADJ
ejpam-6497	59	27	cardinal	cardinal	ADJ
ejpam-6497	59	28	number	number	NOUN
ejpam-6497	59	29	and	and	CCONJ
ejpam-6497	59	30	c	c	NOUN
ejpam-6497	59	31	represents	represent	VERB
ejpam-6497	59	32	the	the	DET
ejpam-6497	59	33	cardinality	cardinality	NOUN
ejpam-6497	59	34	of	of	ADP
ejpam-6497	59	35	r.	r.	PROPN
ejpam-6497	59	36	additionally	additionally	ADV
ejpam-6497	59	37	,	,	PUNCT
ejpam-6497	59	38	cammaroto	cammaroto	NOUN
ejpam-6497	59	39	and	and	CCONJ
ejpam-6497	59	40	santoro	santoro	PROPN
ejpam-6497	60	1	[	[	X
ejpam-6497	60	2	9	9	NUM
ejpam-6497	60	3	]	]	PUNCT
ejpam-6497	60	4	created	create	VERB
ejpam-6497	60	5	an	an	DET
ejpam-6497	60	6	example	example	NOUN
ejpam-6497	60	7	(	(	PUNCT
ejpam-6497	60	8	see	see	VERB
ejpam-6497	60	9	[	[	X
ejpam-6497	60	10	9	9	NUM
ejpam-6497	60	11	,	,	PUNCT
ejpam-6497	60	12	example	example	NOUN
ejpam-6497	60	13	3.11	3.11	NUM
ejpam-6497	60	14	]	]	PUNCT
ejpam-6497	60	15	)	)	PUNCT
ejpam-6497	60	16	demonstrating	demonstrate	VERB
ejpam-6497	60	17	that	that	SCONJ
ejpam-6497	60	18	there	there	PRON
ejpam-6497	60	19	is	be	VERB
ejpam-6497	60	20	a	a	DET
ejpam-6497	60	21	tychonoff	tychonoff	NOUN
ejpam-6497	60	22	weakly	weakly	ADJ
ejpam-6497	61	1	sl	sl	INTJ
ejpam-6497	61	2	that	that	PRON
ejpam-6497	61	3	is	be	AUX
ejpam-6497	61	4	not	not	PART
ejpam-6497	61	5	nearly	nearly	ADV
ejpam-6497	61	6	lindelöf	lindelöf	NOUN
ejpam-6497	61	7	.	.	PUNCT
ejpam-6497	62	1	a	a	DET
ejpam-6497	62	2	generalization	generalization	NOUN
ejpam-6497	62	3	or	or	CCONJ
ejpam-6497	62	4	relaxation	relaxation	NOUN
ejpam-6497	62	5	of	of	ADP
ejpam-6497	62	6	the	the	DET
ejpam-6497	62	7	concept	concept	NOUN
ejpam-6497	62	8	is	be	AUX
ejpam-6497	62	9	a	a	DET
ejpam-6497	62	10	nearly	nearly	ADV
ejpam-6497	62	11	sl	sl	NOUN
ejpam-6497	62	12	,	,	PUNCT
ejpam-6497	62	13	which	which	PRON
ejpam-6497	62	14	is	be	AUX
ejpam-6497	62	15	frequently	frequently	ADV
ejpam-6497	62	16	described	describe	VERB
ejpam-6497	62	17	in	in	ADP
ejpam-6497	62	18	terms	term	NOUN
ejpam-6497	62	19	of	of	ADP
ejpam-6497	62	20	specific	specific	ADJ
ejpam-6497	62	21	“	"	PUNCT
ejpam-6497	62	22	almost	almost	ADV
ejpam-6497	62	23	”	"	PUNCT
ejpam-6497	62	24	requirements	requirement	NOUN
ejpam-6497	62	25	pertaining	pertain	VERB
ejpam-6497	62	26	to	to	ADP
ejpam-6497	62	27	lindelöfness	lindelöfness	NOUN
ejpam-6497	62	28	.	.	PUNCT
ejpam-6497	63	1	the	the	DET
ejpam-6497	63	2	exact	exact	ADJ
ejpam-6497	63	3	concept	concept	NOUN
ejpam-6497	63	4	of	of	ADP
ejpam-6497	63	5	nearly	nearly	ADV
ejpam-6497	63	6	sls	sls	PROPN
ejpam-6497	63	7	depends	depend	VERB
ejpam-6497	63	8	on	on	ADP
ejpam-6497	63	9	the	the	DET
ejpam-6497	63	10	context	context	NOUN
ejpam-6497	63	11	and	and	CCONJ
ejpam-6497	63	12	the	the	DET
ejpam-6497	63	13	specific	specific	ADJ
ejpam-6497	63	14	generalization	generalization	NOUN
ejpam-6497	63	15	being	be	AUX
ejpam-6497	63	16	studied	study	VERB
ejpam-6497	63	17	.	.	PUNCT
ejpam-6497	64	1	2	2	X
ejpam-6497	64	2	.	.	X
ejpam-6497	64	3	main	main	ADJ
ejpam-6497	64	4	results	result	NOUN
ejpam-6497	64	5	definition	definition	NOUN
ejpam-6497	64	6	2	2	NUM
ejpam-6497	64	7	.	.	PUNCT
ejpam-6497	65	1	a	a	DET
ejpam-6497	65	2	topological	topological	ADJ
ejpam-6497	65	3	space	space	NOUN
ejpam-6497	65	4	x	x	PUNCT
ejpam-6497	65	5	is	be	AUX
ejpam-6497	65	6	an	an	DET
ejpam-6497	65	7	almost	almost	ADV
ejpam-6497	65	8	lindelöf	lindelöf	PROPN
ejpam-6497	65	9	ideal	ideal	ADJ
ejpam-6497	65	10	space	space	NOUN
ejpam-6497	65	11	modulo	modulo	PROPN
ejpam-6497	65	12	j	j	PROPN
ejpam-6497	65	13	if	if	SCONJ
ejpam-6497	65	14	each	each	PRON
ejpam-6497	65	15	ü	ü	VERB
ejpam-6497	65	16	=	=	PRON
ejpam-6497	65	17	{	{	PUNCT
ejpam-6497	65	18	uα	uα	X
ejpam-6497	65	19	:	:	PUNCT
ejpam-6497	65	20	α	α	PROPN
ejpam-6497	65	21	∈	∈	PROPN
ejpam-6497	65	22	λ	λ	PROPN
ejpam-6497	65	23	}	}	PUNCT
ejpam-6497	65	24	,	,	PUNCT
ejpam-6497	65	25	an	an	DET
ejpam-6497	65	26	open	open	ADJ
ejpam-6497	65	27	cover	cover	NOUN
ejpam-6497	65	28	of	of	ADP
ejpam-6497	65	29	x	x	X
ejpam-6497	65	30	admits	admit	VERB
ejpam-6497	65	31	countable	countable	ADJ
ejpam-6497	65	32	subfamily	subfamily	ADV
ejpam-6497	65	33	:	:	PUNCT
ejpam-6497	65	34	x	x	SYM
ejpam-6497	65	35	=	=	SYM
ejpam-6497	65	36	∪n∈ncl	∪n∈ncl	NOUN
ejpam-6497	65	37	(	(	PUNCT
ejpam-6497	65	38	uαn	uαn	PROPN
ejpam-6497	65	39	)	)	PUNCT
ejpam-6497	66	1	[	[	X
ejpam-6497	66	2	13	13	NUM
ejpam-6497	66	3	]	]	PUNCT
ejpam-6497	66	4	.	.	PUNCT
ejpam-6497	67	1	definition	definition	NOUN
ejpam-6497	67	2	3	3	NUM
ejpam-6497	67	3	.	.	PUNCT
ejpam-6497	68	1	the	the	DET
ejpam-6497	68	2	space	space	NOUN
ejpam-6497	68	3	x	x	PUNCT
ejpam-6497	68	4	is	be	AUX
ejpam-6497	68	5	an	an	DET
ejpam-6497	68	6	almost	almost	ADV
ejpam-6497	68	7	ideal	ideal	ADJ
ejpam-6497	68	8	space	space	NOUN
ejpam-6497	68	9	modulo	modulo	NOUN
ejpam-6497	68	10	j	j	PROPN
ejpam-6497	68	11	if	if	SCONJ
ejpam-6497	68	12	every	every	DET
ejpam-6497	68	13	almost	almost	ADV
ejpam-6497	68	14	lindelöf	lindelöf	NOUN
ejpam-6497	68	15	subset	subset	VERB
ejpam-6497	68	16	of	of	ADP
ejpam-6497	68	17	x	x	SYM
ejpam-6497	68	18	modulo	modulo	PROPN
ejpam-6497	68	19	j	j	PROPN
ejpam-6497	68	20	is	be	AUX
ejpam-6497	68	21	closed	closed	ADJ
ejpam-6497	68	22	.	.	PUNCT
ejpam-6497	69	1	e.	e.	PROPN
ejpam-6497	69	2	almuhur	almuhur	PROPN
ejpam-6497	69	3	et	et	PROPN
ejpam-6497	69	4	al	al	PROPN
ejpam-6497	69	5	.	.	PUNCT
ejpam-6497	69	6	/	/	SYM
ejpam-6497	69	7	eur	eur	PROPN
ejpam-6497	69	8	.	.	PUNCT
ejpam-6497	70	1	j.	j.	PROPN
ejpam-6497	70	2	pure	pure	PROPN
ejpam-6497	70	3	appl	appl	PROPN
ejpam-6497	70	4	.	.	PROPN
ejpam-6497	70	5	math	math	PROPN
ejpam-6497	70	6	,	,	PUNCT
ejpam-6497	70	7	18	18	NUM
ejpam-6497	70	8	(	(	PUNCT
ejpam-6497	70	9	3	3	NUM
ejpam-6497	70	10	)	)	PUNCT
ejpam-6497	70	11	(	(	PUNCT
ejpam-6497	70	12	2025	2025	NUM
ejpam-6497	70	13	)	)	PUNCT
ejpam-6497	70	14	,	,	PUNCT
ejpam-6497	70	15	6497	6497	NUM
ejpam-6497	70	16	4	4	NUM
ejpam-6497	70	17	of	of	ADP
ejpam-6497	70	18	11	11	NUM
ejpam-6497	70	19	theorem	theorem	NOUN
ejpam-6497	70	20	1	1	NUM
ejpam-6497	70	21	.	.	PUNCT
ejpam-6497	71	1	a	a	DET
ejpam-6497	71	2	topological	topological	ADJ
ejpam-6497	71	3	space	space	NOUN
ejpam-6497	71	4	x	x	PRON
ejpam-6497	71	5	is	be	AUX
ejpam-6497	71	6	almost	almost	ADV
ejpam-6497	71	7	sl	sl	ADP
ejpam-6497	71	8	modulo	modulo	ADJ
ejpam-6497	71	9	j	j	PROPN
ejpam-6497	72	1	if	if	SCONJ
ejpam-6497	72	2	and	and	CCONJ
ejpam-6497	72	3	only	only	ADV
ejpam-6497	72	4	if	if	SCONJ
ejpam-6497	72	5	ĥ	ĥ	PUNCT
ejpam-6497	72	6	=	=	PUNCT
ejpam-6497	72	7	{	{	PUNCT
ejpam-6497	72	8	hα	hα	X
ejpam-6497	72	9	:	:	PUNCT
ejpam-6497	72	10	α	α	PROPN
ejpam-6497	72	11	∈	∈	PROPN
ejpam-6497	72	12	λ	λ	PROPN
ejpam-6497	72	13	}	}	PUNCT
ejpam-6497	72	14	,	,	PUNCT
ejpam-6497	72	15	the	the	DET
ejpam-6497	72	16	family	family	NOUN
ejpam-6497	72	17	of	of	ADP
ejpam-6497	72	18	closed	closed	ADJ
ejpam-6497	72	19	subsets	subset	NOUN
ejpam-6497	72	20	of	of	ADP
ejpam-6497	72	21	x	x	PRON
ejpam-6497	72	22	:	:	PUNCT
ejpam-6497	72	23	∩α∈λhα	∩α∈λhα	NOUN
ejpam-6497	72	24	=	=	PUNCT
ejpam-6497	72	25	∅	∅	NOUN
ejpam-6497	72	26	admits	admit	VERB
ejpam-6497	72	27	the	the	DET
ejpam-6497	72	28	countable	countable	ADJ
ejpam-6497	72	29	subfamily	subfamily	ADV
ejpam-6497	72	30	∩	∩	ADJ
ejpam-6497	72	31	n∈n	n∈n	NOUN
ejpam-6497	72	32	hαn	hαn	NOUN
ejpam-6497	72	33	=	=	PUNCT
ejpam-6497	72	34	∅.	∅.	NOUN
ejpam-6497	72	35	proof	proof	NOUN
ejpam-6497	72	36	.	.	PUNCT
ejpam-6497	73	1	let	let	VERB
ejpam-6497	73	2	ĥ	ĥ	X
ejpam-6497	73	3	=	=	PUNCT
ejpam-6497	73	4	{	{	PUNCT
ejpam-6497	73	5	hα	hα	X
ejpam-6497	73	6	:	:	PUNCT
ejpam-6497	73	7	α	α	PROPN
ejpam-6497	73	8	∈	∈	PROPN
ejpam-6497	73	9	λ	λ	X
ejpam-6497	73	10	}	}	PUNCT
ejpam-6497	73	11	be	be	AUX
ejpam-6497	73	12	a	a	DET
ejpam-6497	73	13	family	family	NOUN
ejpam-6497	73	14	consisting	consist	VERB
ejpam-6497	73	15	of	of	ADP
ejpam-6497	73	16	closed	closed	ADJ
ejpam-6497	73	17	subsets	subset	NOUN
ejpam-6497	73	18	of	of	ADP
ejpam-6497	73	19	x	x	PRON
ejpam-6497	73	20	:	:	PUNCT
ejpam-6497	73	21	∩α∈λhα	∩α∈λhα	X
ejpam-6497	73	22	=	=	PUNCT
ejpam-6497	73	23	∅.	∅.	VERB
ejpam-6497	73	24	so	so	ADV
ejpam-6497	73	25	,	,	PUNCT
ejpam-6497	73	26	{	{	PUNCT
ejpam-6497	73	27	x	x	SYM
ejpam-6497	73	28	\	\	NOUN
ejpam-6497	73	29	hα	hα	ADP
ejpam-6497	73	30	:	:	PUNCT
ejpam-6497	73	31	α	α	PROPN
ejpam-6497	73	32	∈	∈	PROPN
ejpam-6497	73	33	λ	λ	PROPN
ejpam-6497	73	34	}	}	PUNCT
ejpam-6497	73	35	covers	cover	VERB
ejpam-6497	73	36	x.	x.	NOUN
ejpam-6497	73	37	since	since	SCONJ
ejpam-6497	73	38	x	x	PRON
ejpam-6497	73	39	is	be	AUX
ejpam-6497	73	40	almost	almost	ADV
ejpam-6497	73	41	lindelöf	lindelöf	NOUN
ejpam-6497	73	42	modulo	modulo	PROPN
ejpam-6497	73	43	j	j	PROPN
ejpam-6497	73	44	,	,	PUNCT
ejpam-6497	73	45	there	there	PRON
ejpam-6497	73	46	exists	exist	VERB
ejpam-6497	73	47	{	{	PUNCT
ejpam-6497	73	48	α1	α1	PROPN
ejpam-6497	73	49	,	,	PUNCT
ejpam-6497	73	50	α2	α2	ADJ
ejpam-6497	73	51	,	,	PUNCT
ejpam-6497	73	52	.	.	PUNCT
ejpam-6497	73	53	.	.	PUNCT
ejpam-6497	73	54	.	.	PUNCT
ejpam-6497	74	1	}	}	PUNCT
ejpam-6497	74	2	a	a	DET
ejpam-6497	74	3	countable	countable	ADJ
ejpam-6497	74	4	subfamily	subfamily	NOUN
ejpam-6497	74	5	:	:	PUNCT
ejpam-6497	74	6	x	x	SYM
ejpam-6497	74	7	=	=	SYM
ejpam-6497	74	8	∪n∈ncl	∪n∈ncl	NOUN
ejpam-6497	74	9	(	(	PUNCT
ejpam-6497	74	10	x	x	X
ejpam-6497	74	11	\hαn	\hαn	PROPN
ejpam-6497	74	12	)	)	PUNCT
ejpam-6497	74	13	.	.	PUNCT
ejpam-6497	75	1	hence	hence	ADV
ejpam-6497	75	2	,	,	PUNCT
ejpam-6497	75	3	∩	∩	ADJ
ejpam-6497	75	4	n∈n	n∈n	NOUN
ejpam-6497	75	5	int	int	NOUN
ejpam-6497	75	6	(	(	PUNCT
ejpam-6497	75	7	hαn	hαn	NOUN
ejpam-6497	75	8	)	)	PUNCT
ejpam-6497	75	9	=	=	PUNCT
ejpam-6497	75	10	∅.	∅.	NOUN
ejpam-6497	75	11	on	on	ADP
ejpam-6497	75	12	the	the	DET
ejpam-6497	75	13	other	other	ADJ
ejpam-6497	75	14	hand	hand	NOUN
ejpam-6497	75	15	,	,	PUNCT
ejpam-6497	75	16	if	if	SCONJ
ejpam-6497	75	17	ü	ü	PRON
ejpam-6497	75	18	=	=	PRON
ejpam-6497	75	19	{	{	PUNCT
ejpam-6497	75	20	uα	uα	X
ejpam-6497	75	21	:	:	PUNCT
ejpam-6497	75	22	α	α	PROPN
ejpam-6497	75	23	∈	∈	PROPN
ejpam-6497	75	24	λ	λ	PROPN
ejpam-6497	75	25	}	}	PUNCT
ejpam-6497	75	26	forms	form	VERB
ejpam-6497	75	27	an	an	DET
ejpam-6497	75	28	open	open	ADJ
ejpam-6497	75	29	cover	cover	NOUN
ejpam-6497	75	30	of	of	ADP
ejpam-6497	75	31	x	x	SYM
ejpam-6497	75	32	modulo	modulo	PROPN
ejpam-6497	75	33	j	j	PROPN
ejpam-6497	75	34	.	.	PUNCT
ejpam-6497	76	1	therefore	therefore	ADV
ejpam-6497	76	2	,	,	PUNCT
ejpam-6497	76	3	{	{	PUNCT
ejpam-6497	76	4	x	x	SYM
ejpam-6497	76	5	\	\	PROPN
ejpam-6497	76	6	uα	uα	PROPN
ejpam-6497	76	7	:	:	PUNCT
ejpam-6497	76	8	α	α	PROPN
ejpam-6497	76	9	∈	∈	PROPN
ejpam-6497	76	10	λ	λ	PROPN
ejpam-6497	76	11	}	}	PUNCT
ejpam-6497	76	12	forms	form	VERB
ejpam-6497	76	13	a	a	DET
ejpam-6497	76	14	family	family	NOUN
ejpam-6497	76	15	of	of	ADP
ejpam-6497	76	16	closed	closed	ADJ
ejpam-6497	76	17	subsets	subset	NOUN
ejpam-6497	76	18	of	of	ADP
ejpam-6497	76	19	x	x	PRON
ejpam-6497	76	20	:	:	PUNCT
ejpam-6497	76	21	∩α∈λ	∩α∈λ	NOUN
ejpam-6497	76	22	(	(	PUNCT
ejpam-6497	76	23	x	x	SYM
ejpam-6497	76	24	\	\	PROPN
ejpam-6497	76	25	uα	uα	PROPN
ejpam-6497	76	26	)	)	PUNCT
ejpam-6497	77	1	=	=	PUNCT
ejpam-6497	77	2	∅.	∅.	VERB
ejpam-6497	77	3	thus	thus	ADV
ejpam-6497	77	4	,	,	PUNCT
ejpam-6497	77	5	there	there	PRON
ejpam-6497	77	6	is	be	VERB
ejpam-6497	77	7	{	{	PUNCT
ejpam-6497	77	8	α1	α1	PROPN
ejpam-6497	77	9	,	,	PUNCT
ejpam-6497	77	10	α2	α2	ADJ
ejpam-6497	77	11	,	,	PUNCT
ejpam-6497	77	12	.	.	PUNCT
ejpam-6497	77	13	.	.	PUNCT
ejpam-6497	77	14	.	.	PUNCT
ejpam-6497	78	1	}	}	PUNCT
ejpam-6497	78	2	a	a	DET
ejpam-6497	78	3	countable	countable	ADJ
ejpam-6497	78	4	subfamily	subfamily	NOUN
ejpam-6497	78	5	:	:	PUNCT
ejpam-6497	78	6	∩	∩	NOUN
ejpam-6497	78	7	n∈n	n∈n	NOUN
ejpam-6497	78	8	(	(	PUNCT
ejpam-6497	78	9	x	x	SYM
ejpam-6497	78	10	\	\	PROPN
ejpam-6497	78	11	uαn	uαn	PROPN
ejpam-6497	78	12	)	)	PUNCT
ejpam-6497	78	13	=	=	NOUN
ejpam-6497	78	14	∅	∅	NOUN
ejpam-6497	78	15	,	,	PUNCT
ejpam-6497	78	16	i.e	i.e	X
ejpam-6497	78	17	x	x	SYM
ejpam-6497	78	18	=	=	SYM
ejpam-6497	78	19	∪n∈ncl	∪n∈ncl	NOUN
ejpam-6497	78	20	(	(	PUNCT
ejpam-6497	78	21	uαn	uαn	PROPN
ejpam-6497	78	22	)	)	PUNCT
ejpam-6497	78	23	.	.	PUNCT
ejpam-6497	79	1	theorem	theorem	NOUN
ejpam-6497	79	2	2	2	NUM
ejpam-6497	79	3	.	.	PUNCT
ejpam-6497	80	1	if	if	SCONJ
ejpam-6497	80	2	x	x	PRON
ejpam-6497	80	3	is	be	AUX
ejpam-6497	80	4	an	an	DET
ejpam-6497	80	5	almost	almost	ADV
ejpam-6497	80	6	regular	regular	ADJ
ejpam-6497	80	7	sl	sl	NUM
ejpam-6497	80	8	modulo	modulo	PROPN
ejpam-6497	80	9	j	j	PROPN
ejpam-6497	80	10	,	,	PUNCT
ejpam-6497	80	11	then	then	ADV
ejpam-6497	80	12	it	it	PRON
ejpam-6497	80	13	is	be	AUX
ejpam-6497	80	14	lindelöf	lindelöf	NOUN
ejpam-6497	80	15	.	.	PUNCT
ejpam-6497	81	1	proof	proof	NOUN
ejpam-6497	81	2	.	.	PUNCT
ejpam-6497	82	1	suppose	suppose	VERB
ejpam-6497	82	2	that	that	SCONJ
ejpam-6497	82	3	ũ	ũ	PROPN
ejpam-6497	82	4	=	=	X
ejpam-6497	82	5	{	{	PUNCT
ejpam-6497	82	6	uα	uα	X
ejpam-6497	82	7	:	:	PUNCT
ejpam-6497	82	8	α	α	PROPN
ejpam-6497	82	9	∈	∈	PROPN
ejpam-6497	82	10	λ	λ	PROPN
ejpam-6497	82	11	}	}	PUNCT
ejpam-6497	82	12	forms	form	VERB
ejpam-6497	82	13	an	an	DET
ejpam-6497	82	14	open	open	ADJ
ejpam-6497	82	15	cover	cover	NOUN
ejpam-6497	82	16	of	of	ADP
ejpam-6497	82	17	x	x	PUNCT
ejpam-6497	82	18	for	for	ADP
ejpam-6497	82	19	each	each	DET
ejpam-6497	82	20	uα	uα	PROPN
ejpam-6497	82	21	a	a	DET
ejpam-6497	82	22	regularly	regularly	ADV
ejpam-6497	82	23	open	open	ADJ
ejpam-6497	82	24	subset	subset	NOUN
ejpam-6497	82	25	.	.	PUNCT
ejpam-6497	83	1	but	but	CCONJ
ejpam-6497	83	2	x	x	X
ejpam-6497	83	3	is	be	AUX
ejpam-6497	83	4	almost	almost	ADV
ejpam-6497	83	5	regular	regular	ADJ
ejpam-6497	83	6	lindelöf	lindelöf	NOUN
ejpam-6497	84	1	modulo	modulo	PROPN
ejpam-6497	84	2	j	j	PROPN
ejpam-6497	84	3	,	,	PUNCT
ejpam-6497	84	4	then	then	ADV
ejpam-6497	84	5	for	for	ADP
ejpam-6497	84	6	every	every	DET
ejpam-6497	84	7	a	a	DET
ejpam-6497	84	8	∈	∈	PROPN
ejpam-6497	84	9	x	x	NOUN
ejpam-6497	84	10	,	,	PUNCT
ejpam-6497	84	11	there	there	PRON
ejpam-6497	84	12	exists	exist	VERB
ejpam-6497	84	13	αa	αa	PROPN
ejpam-6497	84	14	∈	∈	PROPN
ejpam-6497	84	15	λ	λ	PROPN
ejpam-6497	84	16	:	:	PUNCT
ejpam-6497	84	17	a	a	DET
ejpam-6497	84	18	∈	∈	PROPN
ejpam-6497	84	19	uαa	uαa	NOUN
ejpam-6497	84	20	.	.	PUNCT
ejpam-6497	85	1	for	for	ADP
ejpam-6497	85	2	the	the	DET
ejpam-6497	85	3	regularly	regularly	ADV
ejpam-6497	85	4	open	open	VERB
ejpam-6497	85	5	a	a	DET
ejpam-6497	85	6	-	-	PUNCT
ejpam-6497	85	7	neighborhood	neighborhood	NOUN
ejpam-6497	85	8	vαa	vαa	NOUN
ejpam-6497	85	9	,	,	PUNCT
ejpam-6497	85	10	a	a	DET
ejpam-6497	85	11	∈	∈	PROPN
ejpam-6497	85	12	vαa	vαa	NOUN
ejpam-6497	85	13	⊂	⊂	X
ejpam-6497	85	14	cl(vαa	cl(vαa	PROPN
ejpam-6497	85	15	)	)	PUNCT
ejpam-6497	86	1	⊂	⊂	PROPN
ejpam-6497	86	2	uαa	uαa	PROPN
ejpam-6497	86	3	.	.	PUNCT
ejpam-6497	87	1	for	for	ADP
ejpam-6497	87	2	x	x	X
ejpam-6497	87	3	,	,	PUNCT
ejpam-6497	87	4	being	be	AUX
ejpam-6497	87	5	a	a	DET
ejpam-6497	87	6	nearly	nearly	ADV
ejpam-6497	87	7	l	l	NOUN
ejpam-6497	87	8	-	-	ADJ
ejpam-6497	87	9	closed	closed	ADJ
ejpam-6497	87	10	,	,	PUNCT
ejpam-6497	87	11	there	there	PRON
ejpam-6497	87	12	is	be	VERB
ejpam-6497	87	13	{	{	PUNCT
ejpam-6497	87	14	a1	a1	PROPN
ejpam-6497	87	15	,	,	PUNCT
ejpam-6497	87	16	a2	a2	PROPN
ejpam-6497	87	17	,	,	PUNCT
ejpam-6497	87	18	.	.	PUNCT
ejpam-6497	87	19	.	.	PUNCT
ejpam-6497	87	20	.	.	PUNCT
ejpam-6497	88	1	}	}	PUNCT
ejpam-6497	88	2	a	a	DET
ejpam-6497	88	3	countable	countable	ADJ
ejpam-6497	88	4	subfamily	subfamily	ADV
ejpam-6497	88	5	:	:	PUNCT
ejpam-6497	88	6	x	x	SYM
ejpam-6497	88	7	=	=	PUNCT
ejpam-6497	88	8	∪	∪	ADP
ejpam-6497	88	9	n∈n	n∈n	X
ejpam-6497	88	10	cl(vαa	cl(vαa	PROPN
ejpam-6497	88	11	)	)	PUNCT
ejpam-6497	88	12	.	.	PUNCT
ejpam-6497	89	1	thus	thus	ADV
ejpam-6497	89	2	,	,	PUNCT
ejpam-6497	89	3	ṽ	ṽ	PROPN
ejpam-6497	89	4	=	=	SYM
ejpam-6497	89	5	{	{	PUNCT
ejpam-6497	89	6	vαa	vαa	NOUN
ejpam-6497	89	7	:	:	PUNCT
ejpam-6497	89	8	α	α	PROPN
ejpam-6497	89	9	∈	∈	PROPN
ejpam-6497	89	10	λ	λ	PROPN
ejpam-6497	89	11	}	}	PUNCT
ejpam-6497	89	12	covers	cover	VERB
ejpam-6497	89	13	x	x	PUNCT
ejpam-6497	89	14	regularly	regularly	ADV
ejpam-6497	89	15	because	because	SCONJ
ejpam-6497	89	16	x	x	PRON
ejpam-6497	89	17	is	be	AUX
ejpam-6497	89	18	almost	almost	ADV
ejpam-6497	89	19	modulo	modulo	ADJ
ejpam-6497	89	20	j	j	PROPN
ejpam-6497	89	21	.	.	PUNCT
ejpam-6497	90	1	therefore	therefore	ADV
ejpam-6497	90	2	,	,	PUNCT
ejpam-6497	90	3	x	x	X
ejpam-6497	90	4	is	be	AUX
ejpam-6497	90	5	lindelöf	lindelöf	NOUN
ejpam-6497	90	6	modulo	modulo	PROPN
ejpam-6497	90	7	j	j	PROPN
ejpam-6497	90	8	.	.	PUNCT
ejpam-6497	91	1	corollary	corollary	ADJ
ejpam-6497	91	2	1	1	NUM
ejpam-6497	91	3	.	.	PUNCT
ejpam-6497	92	1	x	x	PRON
ejpam-6497	92	2	is	be	AUX
ejpam-6497	92	3	an	an	DET
ejpam-6497	92	4	almost	almost	ADV
ejpam-6497	92	5	sl	sl	NOUN
ejpam-6497	92	6	modulo	modulo	ADJ
ejpam-6497	92	7	j	j	PROPN
ejpam-6497	93	1	if	if	SCONJ
ejpam-6497	93	2	and	and	CCONJ
ejpam-6497	93	3	only	only	ADV
ejpam-6497	93	4	if	if	SCONJ
ejpam-6497	93	5	it	it	PRON
ejpam-6497	93	6	is	be	AUX
ejpam-6497	93	7	nearly	nearly	ADV
ejpam-6497	93	8	lindelöf	lindelöf	NOUN
ejpam-6497	93	9	.	.	PUNCT
ejpam-6497	94	1	theorem	theorem	VERB
ejpam-6497	94	2	3	3	NUM
ejpam-6497	94	3	.	.	NUM
ejpam-6497	95	1	x	x	PUNCT
ejpam-6497	95	2	is	be	AUX
ejpam-6497	95	3	an	an	DET
ejpam-6497	95	4	almost	almost	ADV
ejpam-6497	95	5	sl	sl	NOUN
ejpam-6497	95	6	modulo	modulo	ADJ
ejpam-6497	95	7	j	j	PROPN
ejpam-6497	96	1	if	if	SCONJ
ejpam-6497	96	2	and	and	CCONJ
ejpam-6497	96	3	only	only	ADV
ejpam-6497	96	4	if	if	SCONJ
ejpam-6497	96	5	for	for	ADP
ejpam-6497	96	6	every	every	DET
ejpam-6497	96	7	family	family	NOUN
ejpam-6497	96	8	m̃	m̃	PROPN
ejpam-6497	96	9	=	=	PUNCT
ejpam-6497	96	10	{	{	PUNCT
ejpam-6497	96	11	mα	mα	X
ejpam-6497	96	12	:	:	PUNCT
ejpam-6497	96	13	α	α	PROPN
ejpam-6497	96	14	∈	∈	PROPN
ejpam-6497	96	15	λ	λ	PROPN
ejpam-6497	96	16	}	}	PUNCT
ejpam-6497	96	17	of	of	ADP
ejpam-6497	96	18	closed	closed	ADJ
ejpam-6497	96	19	subsets	subset	NOUN
ejpam-6497	96	20	of	of	ADP
ejpam-6497	96	21	x	x	SYM
ejpam-6497	96	22	modulo	modulo	PROPN
ejpam-6497	96	23	j	j	PROPN
ejpam-6497	96	24	,	,	PUNCT
ejpam-6497	96	25	there	there	PRON
ejpam-6497	96	26	is	be	VERB
ejpam-6497	96	27	ũ	ũ	PROPN
ejpam-6497	96	28	=	=	X
ejpam-6497	96	29	{	{	PUNCT
ejpam-6497	96	30	uα	uα	X
ejpam-6497	96	31	:	:	PUNCT
ejpam-6497	96	32	α	α	PROPN
ejpam-6497	96	33	∈	∈	PROPN
ejpam-6497	96	34	λ	λ	X
ejpam-6497	96	35	}	}	PUNCT
ejpam-6497	96	36	a	a	DET
ejpam-6497	96	37	family	family	NOUN
ejpam-6497	96	38	of	of	ADP
ejpam-6497	96	39	open	open	ADJ
ejpam-6497	96	40	subsets	subset	NOUN
ejpam-6497	96	41	with	with	ADP
ejpam-6497	96	42	∩	∩	ADJ
ejpam-6497	96	43	α∈λ	α∈λ	NOUN
ejpam-6497	96	44	cl(uα	cl(uα	NOUN
ejpam-6497	96	45	)	)	PUNCT
ejpam-6497	97	1	=	=	NOUN
ejpam-6497	97	2	∅	∅	NOUN
ejpam-6497	97	3	:	:	PUNCT
ejpam-6497	97	4	mα	mα	PROPN
ejpam-6497	97	5	⊂	⊂	PROPN
ejpam-6497	97	6	uα	uα	PROPN
ejpam-6497	97	7	,	,	PUNCT
ejpam-6497	97	8	and	and	CCONJ
ejpam-6497	97	9	there	there	PRON
ejpam-6497	97	10	exists	exist	VERB
ejpam-6497	97	11	{	{	PUNCT
ejpam-6497	97	12	α1	α1	PROPN
ejpam-6497	97	13	,	,	PUNCT
ejpam-6497	97	14	α2	α2	ADJ
ejpam-6497	97	15	,	,	PUNCT
ejpam-6497	97	16	.	.	PUNCT
ejpam-6497	97	17	.	.	PUNCT
ejpam-6497	97	18	.	.	PUNCT
ejpam-6497	98	1	}	}	PUNCT
ejpam-6497	98	2	a	a	DET
ejpam-6497	98	3	countable	countable	ADJ
ejpam-6497	98	4	subfamily	subfamily	ADV
ejpam-6497	98	5	such	such	ADJ
ejpam-6497	98	6	that	that	SCONJ
ejpam-6497	98	7	∩n∈n	∩n∈n	PROPN
ejpam-6497	98	8	int(mαn	int(mαn	PROPN
ejpam-6497	98	9	)	)	PUNCT
ejpam-6497	98	10	=	=	PUNCT
ejpam-6497	98	11	∅.	∅.	PROPN
ejpam-6497	98	12	e.	e.	PROPN
ejpam-6497	98	13	almuhur	almuhur	PROPN
ejpam-6497	98	14	et	et	PROPN
ejpam-6497	98	15	al	al	PROPN
ejpam-6497	98	16	.	.	PUNCT
ejpam-6497	98	17	/	/	SYM
ejpam-6497	98	18	eur	eur	PROPN
ejpam-6497	98	19	.	.	PUNCT
ejpam-6497	99	1	j.	j.	PROPN
ejpam-6497	99	2	pure	pure	PROPN
ejpam-6497	99	3	appl	appl	PROPN
ejpam-6497	99	4	.	.	PROPN
ejpam-6497	99	5	math	math	PROPN
ejpam-6497	99	6	,	,	PUNCT
ejpam-6497	99	7	18	18	NUM
ejpam-6497	99	8	(	(	PUNCT
ejpam-6497	99	9	3	3	NUM
ejpam-6497	99	10	)	)	PUNCT
ejpam-6497	99	11	(	(	PUNCT
ejpam-6497	99	12	2025	2025	NUM
ejpam-6497	99	13	)	)	PUNCT
ejpam-6497	99	14	,	,	PUNCT
ejpam-6497	99	15	6497	6497	NUM
ejpam-6497	99	16	5	5	NUM
ejpam-6497	99	17	of	of	ADP
ejpam-6497	99	18	11	11	NUM
ejpam-6497	99	19	proof	proof	NOUN
ejpam-6497	99	20	.	.	PUNCT
ejpam-6497	100	1	direct	direct	ADJ
ejpam-6497	100	2	part	part	NOUN
ejpam-6497	100	3	:	:	PUNCT
ejpam-6497	100	4	assume	assume	VERB
ejpam-6497	100	5	that	that	SCONJ
ejpam-6497	100	6	m̃	m̃	PROPN
ejpam-6497	100	7	=	=	PRON
ejpam-6497	100	8	{	{	PUNCT
ejpam-6497	100	9	mα	mα	X
ejpam-6497	100	10	:	:	PUNCT
ejpam-6497	100	11	α	α	PROPN
ejpam-6497	100	12	∈	∈	PROPN
ejpam-6497	100	13	λ	λ	PROPN
ejpam-6497	100	14	}	}	PUNCT
ejpam-6497	100	15	is	be	AUX
ejpam-6497	100	16	a	a	DET
ejpam-6497	100	17	family	family	NOUN
ejpam-6497	100	18	of	of	ADP
ejpam-6497	100	19	closed	closed	ADJ
ejpam-6497	100	20	subsets	subset	NOUN
ejpam-6497	100	21	of	of	ADP
ejpam-6497	100	22	x	x	SYM
ejpam-6497	100	23	modulo	modulo	PROPN
ejpam-6497	100	24	j	j	PROPN
ejpam-6497	100	25	.	.	PUNCT
ejpam-6497	101	1	if	if	SCONJ
ejpam-6497	101	2	ũ	ũ	PROPN
ejpam-6497	101	3	=	=	X
ejpam-6497	101	4	{	{	PUNCT
ejpam-6497	101	5	uα	uα	X
ejpam-6497	101	6	:	:	PUNCT
ejpam-6497	101	7	α	α	PROPN
ejpam-6497	101	8	∈	∈	PROPN
ejpam-6497	101	9	λ	λ	PROPN
ejpam-6497	101	10	}	}	PUNCT
ejpam-6497	101	11	is	be	AUX
ejpam-6497	101	12	a	a	DET
ejpam-6497	101	13	family	family	NOUN
ejpam-6497	101	14	of	of	ADP
ejpam-6497	101	15	open	open	ADJ
ejpam-6497	101	16	subsets	subset	NOUN
ejpam-6497	101	17	with	with	ADP
ejpam-6497	101	18	∩α∈λcl(uα∈λ	∩α∈λcl(uα∈λ	NOUN
ejpam-6497	101	19	)	)	PUNCT
ejpam-6497	101	20	=	=	SYM
ejpam-6497	101	21	∅	∅	NOUN
ejpam-6497	101	22	,	,	PUNCT
ejpam-6497	101	23	then	then	ADV
ejpam-6497	101	24	mα	mα	PROPN
ejpam-6497	101	25	∈	∈	PROPN
ejpam-6497	102	1	ũ	ũ	PROPN
ejpam-6497	102	2	.	.	PUNCT
ejpam-6497	103	1	since	since	SCONJ
ejpam-6497	103	2	x	x	PRON
ejpam-6497	103	3	is	be	AUX
ejpam-6497	103	4	regular	regular	ADJ
ejpam-6497	103	5	modulo	modulo	PROPN
ejpam-6497	103	6	j	j	PROPN
ejpam-6497	103	7	,	,	PUNCT
ejpam-6497	103	8	then	then	ADV
ejpam-6497	103	9	mα	mα	PROPN
ejpam-6497	103	10	⊂	⊂	PROPN
ejpam-6497	103	11	uα	uα	PROPN
ejpam-6497	103	12	⊂	⊂	PROPN
ejpam-6497	103	13	cl(uα	cl(uα	PROPN
ejpam-6497	103	14	)	)	PUNCT
ejpam-6497	103	15	.	.	PUNCT
ejpam-6497	104	1	so	so	ADV
ejpam-6497	104	2	,	,	PUNCT
ejpam-6497	104	3	x	x	SYM
ejpam-6497	104	4	\	\	PROPN
ejpam-6497	104	5	uα	uα	PROPN
ejpam-6497	104	6	⊂	⊂	PROPN
ejpam-6497	104	7	x	x	PROPN
ejpam-6497	104	8	\mα	\mα	PROPN
ejpam-6497	104	9	,	,	PUNCT
ejpam-6497	104	10	and	and	CCONJ
ejpam-6497	104	11	x	x	X
ejpam-6497	104	12	=	=	SYM
ejpam-6497	104	13	∪α∈λ	∪α∈λ	NUM
ejpam-6497	104	14	(	(	PUNCT
ejpam-6497	104	15	x	x	SYM
ejpam-6497	104	16	\mα	\mα	PROPN
ejpam-6497	104	17	)	)	PUNCT
ejpam-6497	104	18	,	,	PUNCT
ejpam-6497	104	19	because	because	SCONJ
ejpam-6497	104	20	of	of	ADP
ejpam-6497	104	21	being	be	AUX
ejpam-6497	104	22	an	an	DET
ejpam-6497	104	23	almost	almost	ADV
ejpam-6497	104	24	regular	regular	ADJ
ejpam-6497	104	25	space	space	NOUN
ejpam-6497	104	26	modulo	modulo	PROPN
ejpam-6497	104	27	j	j	PROPN
ejpam-6497	104	28	.	.	PUNCT
ejpam-6497	105	1	but	but	CCONJ
ejpam-6497	105	2	x	x	X
ejpam-6497	105	3	is	be	AUX
ejpam-6497	105	4	a	a	DET
ejpam-6497	105	5	sl	sl	NOUN
ejpam-6497	105	6	modulo	modulo	PROPN
ejpam-6497	105	7	j	j	NOUN
ejpam-6497	105	8	,	,	PUNCT
ejpam-6497	105	9	there	there	PRON
ejpam-6497	105	10	exists	exist	VERB
ejpam-6497	105	11	a	a	DET
ejpam-6497	105	12	countable	countable	ADJ
ejpam-6497	105	13	subset	subset	NOUN
ejpam-6497	105	14	{	{	PUNCT
ejpam-6497	105	15	α1	α1	PROPN
ejpam-6497	105	16	,	,	PUNCT
ejpam-6497	105	17	α2	α2	ADJ
ejpam-6497	105	18	,	,	PUNCT
ejpam-6497	105	19	.	.	PUNCT
ejpam-6497	105	20	.	.	PUNCT
ejpam-6497	105	21	.	.	PUNCT
ejpam-6497	106	1	}	}	PUNCT
ejpam-6497	106	2	:	:	PUNCT
ejpam-6497	107	1	x	x	X
ejpam-6497	107	2	=	=	PUNCT
ejpam-6497	107	3	∪	∪	ADP
ejpam-6497	107	4	n∈n	n∈n	X
ejpam-6497	107	5	cl	cl	NOUN
ejpam-6497	107	6	(	(	PUNCT
ejpam-6497	107	7	x	x	X
ejpam-6497	107	8	\mαn	\mαn	ADJ
ejpam-6497	107	9	)	)	PUNCT
ejpam-6497	107	10	=	=	PUNCT
ejpam-6497	107	11	∪	∪	ADP
ejpam-6497	107	12	n∈n	n∈n	NOUN
ejpam-6497	107	13	(	(	PUNCT
ejpam-6497	107	14	x	x	SYM
ejpam-6497	107	15	\	\	PROPN
ejpam-6497	107	16	int(mαn	int(mαn	PROPN
ejpam-6497	107	17	)	)	PUNCT
ejpam-6497	107	18	)	)	PUNCT
ejpam-6497	108	1	=	=	PUNCT
ejpam-6497	108	2	x	x	SYM
ejpam-6497	108	3	\	\	PROPN
ejpam-6497	108	4	∩	∩	PROPN
ejpam-6497	108	5	n∈n	n∈n	NOUN
ejpam-6497	108	6	int(mαn	int(mαn	NOUN
ejpam-6497	108	7	)	)	PUNCT
ejpam-6497	108	8	.	.	PUNCT
ejpam-6497	109	1	thus	thus	ADV
ejpam-6497	109	2	,	,	PUNCT
ejpam-6497	109	3	∩n∈n	∩n∈n	PROPN
ejpam-6497	109	4	int(mαn	int(mαn	PROPN
ejpam-6497	109	5	)	)	PUNCT
ejpam-6497	109	6	=	=	PUNCT
ejpam-6497	109	7	∅.	∅.	PRON
ejpam-6497	109	8	converse	converse	NOUN
ejpam-6497	109	9	part	part	NOUN
ejpam-6497	109	10	:	:	PUNCT
ejpam-6497	109	11	if	if	SCONJ
ejpam-6497	109	12	the	the	DET
ejpam-6497	109	13	family	family	NOUN
ejpam-6497	109	14	ũ	ũ	PROPN
ejpam-6497	109	15	=	=	X
ejpam-6497	109	16	{	{	PUNCT
ejpam-6497	109	17	uα	uα	X
ejpam-6497	109	18	:	:	PUNCT
ejpam-6497	109	19	α	α	PROPN
ejpam-6497	109	20	∈	∈	PROPN
ejpam-6497	109	21	λ	λ	PROPN
ejpam-6497	109	22	}	}	PUNCT
ejpam-6497	109	23	comprises	comprise	VERB
ejpam-6497	109	24	regular	regular	ADJ
ejpam-6497	109	25	open	open	ADJ
ejpam-6497	109	26	subsets	subset	NOUN
ejpam-6497	109	27	of	of	ADP
ejpam-6497	109	28	x	x	SYM
ejpam-6497	109	29	modulo	modulo	PROPN
ejpam-6497	109	30	j	j	PROPN
ejpam-6497	109	31	with	with	ADP
ejpam-6497	109	32	the	the	DET
ejpam-6497	109	33	empty	empty	ADJ
ejpam-6497	109	34	set	set	NOUN
ejpam-6497	109	35	∩n∈n	∩n∈n	NOUN
ejpam-6497	109	36	int(mαn	int(mαn	PROPN
ejpam-6497	109	37	)	)	PUNCT
ejpam-6497	109	38	.	.	PUNCT
ejpam-6497	110	1	then	then	ADV
ejpam-6497	110	2	,	,	PUNCT
ejpam-6497	110	3	for	for	ADP
ejpam-6497	110	4	every	every	DET
ejpam-6497	110	5	α	α	PROPN
ejpam-6497	110	6	∈	∈	PROPN
ejpam-6497	110	7	λ	λ	NOUN
ejpam-6497	110	8	,	,	PUNCT
ejpam-6497	110	9	there	there	PRON
ejpam-6497	110	10	is	be	VERB
ejpam-6497	110	11	mα	mα	PROPN
ejpam-6497	110	12	⊂	⊂	PROPN
ejpam-6497	110	13	x	x	X
ejpam-6497	110	14	:	:	PUNCT
ejpam-6497	110	15	mα	mα	PROPN
ejpam-6497	110	16	⊂	⊂	X
ejpam-6497	110	17	uα	uα	PROPN
ejpam-6497	110	18	where	where	SCONJ
ejpam-6497	110	19	mα	mα	PROPN
ejpam-6497	110	20	is	be	AUX
ejpam-6497	110	21	regular	regular	ADJ
ejpam-6497	110	22	and	and	CCONJ
ejpam-6497	110	23	closed	closed	ADJ
ejpam-6497	110	24	modulo	modulo	PROPN
ejpam-6497	110	25	j	j	NOUN
ejpam-6497	110	26	with	with	ADP
ejpam-6497	110	27	the	the	DET
ejpam-6497	110	28	empty	empty	ADJ
ejpam-6497	110	29	set	set	NOUN
ejpam-6497	110	30	∪n∈n	∪n∈n	PROPN
ejpam-6497	110	31	int(mαn	int(mαn	PROPN
ejpam-6497	110	32	)	)	PUNCT
ejpam-6497	110	33	.	.	PUNCT
ejpam-6497	111	1	thus	thus	ADV
ejpam-6497	111	2	,	,	PUNCT
ejpam-6497	111	3	∩	∩	ADJ
ejpam-6497	111	4	n∈n	n∈n	NOUN
ejpam-6497	111	5	cl(x	cl(x	PUNCT
ejpam-6497	111	6	\mαn	\mαn	NOUN
ejpam-6497	111	7	)	)	PUNCT
ejpam-6497	111	8	=	=	NOUN
ejpam-6497	111	9	∩	∩	NOUN
ejpam-6497	111	10	n∈n	n∈n	X
ejpam-6497	111	11	(	(	PUNCT
ejpam-6497	111	12	x	x	SYM
ejpam-6497	111	13	\	\	PROPN
ejpam-6497	111	14	int(mαn	int(mαn	PROPN
ejpam-6497	111	15	)	)	PUNCT
ejpam-6497	111	16	)	)	PUNCT
ejpam-6497	111	17	=	=	PUNCT
ejpam-6497	111	18	x	x	SYM
ejpam-6497	111	19	\	\	PROPN
ejpam-6497	111	20	∩	∩	PROPN
ejpam-6497	111	21	n∈n	n∈n	X
ejpam-6497	111	22	int(mαn	int(mαn	ADJ
ejpam-6497	111	23	)	)	PUNCT
ejpam-6497	111	24	=	=	PUNCT
ejpam-6497	112	1	x	x	SYM
ejpam-6497	112	2	\	\	X
ejpam-6497	112	3	x	x	PUNCT
ejpam-6497	112	4	=	=	PRON
ejpam-6497	112	5	∅.	∅.	PRON
ejpam-6497	112	6	hence	hence	ADV
ejpam-6497	112	7	,	,	PUNCT
ejpam-6497	112	8	there	there	PRON
ejpam-6497	112	9	exists	exist	VERB
ejpam-6497	112	10	{	{	PUNCT
ejpam-6497	112	11	α1	α1	PROPN
ejpam-6497	112	12	,	,	PUNCT
ejpam-6497	112	13	α2	α2	ADJ
ejpam-6497	112	14	,	,	PUNCT
ejpam-6497	112	15	.	.	PUNCT
ejpam-6497	112	16	.	.	PUNCT
ejpam-6497	112	17	.	.	PUNCT
ejpam-6497	113	1	}	}	PUNCT
ejpam-6497	113	2	:	:	PUNCT
ejpam-6497	113	3	∩n∈n	∩n∈n	PROPN
ejpam-6497	113	4	int(x	int(x	PROPN
ejpam-6497	113	5	\	\	PROPN
ejpam-6497	113	6	uαn	uαn	PROPN
ejpam-6497	113	7	)	)	PUNCT
ejpam-6497	113	8	is	be	AUX
ejpam-6497	113	9	empty	empty	ADJ
ejpam-6497	113	10	.	.	PUNCT
ejpam-6497	114	1	consequently	consequently	ADV
ejpam-6497	114	2	,	,	PUNCT
ejpam-6497	114	3	x	x	SYM
ejpam-6497	114	4	\	\	PROPN
ejpam-6497	114	5	∪	∪	X
ejpam-6497	114	6	n∈n	n∈n	X
ejpam-6497	114	7	cl(uαn	cl(uαn	NOUN
ejpam-6497	114	8	)	)	PUNCT
ejpam-6497	114	9	=	=	SYM
ejpam-6497	114	10	∅	∅	NOUN
ejpam-6497	114	11	,	,	PUNCT
ejpam-6497	114	12	too	too	ADV
ejpam-6497	114	13	and	and	CCONJ
ejpam-6497	114	14	x	x	X
ejpam-6497	114	15	=	=	SYM
ejpam-6497	114	16	∪n∈ncl(uαn	∪n∈ncl(uαn	NOUN
ejpam-6497	114	17	)	)	PUNCT
ejpam-6497	114	18	.	.	PUNCT
ejpam-6497	115	1	definition	definition	NOUN
ejpam-6497	115	2	4	4	NUM
ejpam-6497	115	3	.	.	PUNCT
ejpam-6497	116	1	x	x	PUNCT
ejpam-6497	116	2	is	be	AUX
ejpam-6497	116	3	a	a	DET
ejpam-6497	116	4	hereditarily	hereditarily	NOUN
ejpam-6497	116	5	almost	almost	ADV
ejpam-6497	116	6	sl	sl	VERB
ejpam-6497	116	7	modulo	modulo	ADJ
ejpam-6497	116	8	j	j	PROPN
ejpam-6497	116	9	if	if	SCONJ
ejpam-6497	116	10	each	each	PRON
ejpam-6497	116	11	of	of	ADP
ejpam-6497	116	12	its	its	PRON
ejpam-6497	116	13	subspaces	subspace	NOUN
ejpam-6497	116	14	is	be	AUX
ejpam-6497	116	15	almost	almost	ADV
ejpam-6497	116	16	sl	sl	ADP
ejpam-6497	116	17	modulo	modulo	PROPN
ejpam-6497	116	18	j	j	PROPN
ejpam-6497	116	19	.	.	PUNCT
ejpam-6497	116	20	remark	remark	PROPN
ejpam-6497	116	21	3	3	NUM
ejpam-6497	116	22	.	.	PUNCT
ejpam-6497	117	1	if	if	SCONJ
ejpam-6497	117	2	x	x	PRON
ejpam-6497	117	3	is	be	AUX
ejpam-6497	117	4	a	a	DET
ejpam-6497	117	5	hereditarily	hereditarily	NOUN
ejpam-6497	117	6	almost	almost	ADV
ejpam-6497	117	7	sl	sl	VERB
ejpam-6497	117	8	modulo	modulo	PROPN
ejpam-6497	117	9	j	j	PROPN
ejpam-6497	117	10	,	,	PUNCT
ejpam-6497	117	11	then	then	ADV
ejpam-6497	117	12	x	x	PUNCT
ejpam-6497	117	13	is	be	AUX
ejpam-6497	117	14	countable	countable	ADJ
ejpam-6497	117	15	discrete	discrete	ADJ
ejpam-6497	117	16	if	if	SCONJ
ejpam-6497	117	17	and	and	CCONJ
ejpam-6497	117	18	only	only	ADV
ejpam-6497	117	19	if	if	SCONJ
ejpam-6497	117	20	x	x	PRON
ejpam-6497	117	21	is	be	AUX
ejpam-6497	117	22	hereditarily	hereditarily	ADJ
ejpam-6497	117	23	lindelöf	lindelöf	NOUN
ejpam-6497	117	24	.	.	PUNCT
ejpam-6497	118	1	definition	definition	NOUN
ejpam-6497	118	2	5	5	NUM
ejpam-6497	118	3	.	.	PUNCT
ejpam-6497	119	1	x	x	PUNCT
ejpam-6497	119	2	is	be	AUX
ejpam-6497	119	3	an	an	DET
ejpam-6497	119	4	almost	almost	ADV
ejpam-6497	119	5	sl	sl	NOUN
ejpam-6497	119	6	modulo	modulo	ADJ
ejpam-6497	119	7	j	j	PROPN
ejpam-6497	119	8	if	if	SCONJ
ejpam-6497	119	9	each	each	DET
ejpam-6497	119	10	almost	almost	ADV
ejpam-6497	119	11	regular	regular	ADJ
ejpam-6497	119	12	lindelöf	lindelöf	NOUN
ejpam-6497	119	13	subset	subset	VERB
ejpam-6497	119	14	of	of	ADP
ejpam-6497	119	15	x	x	SYM
ejpam-6497	119	16	modulo	modulo	PROPN
ejpam-6497	119	17	j	j	PROPN
ejpam-6497	119	18	is	be	AUX
ejpam-6497	119	19	closed	closed	ADJ
ejpam-6497	119	20	.	.	PUNCT
ejpam-6497	120	1	definition	definition	NOUN
ejpam-6497	120	2	6	6	NUM
ejpam-6497	120	3	.	.	PUNCT
ejpam-6497	121	1	if	if	SCONJ
ejpam-6497	121	2	x	x	PRON
ejpam-6497	121	3	is	be	AUX
ejpam-6497	121	4	an	an	DET
ejpam-6497	121	5	almost	almost	ADV
ejpam-6497	121	6	regular	regular	ADJ
ejpam-6497	121	7	space	space	NOUN
ejpam-6497	121	8	modulo	modulo	NOUN
ejpam-6497	121	9	j	j	PROPN
ejpam-6497	121	10	,	,	PUNCT
ejpam-6497	121	11	then	then	ADV
ejpam-6497	121	12	a	a	DET
ejpam-6497	121	13	subspace	subspace	NOUN
ejpam-6497	121	14	y	y	PROPN
ejpam-6497	121	15	is	be	AUX
ejpam-6497	121	16	almost	almost	ADV
ejpam-6497	121	17	regular	regular	ADJ
ejpam-6497	121	18	relative	relative	ADJ
ejpam-6497	121	19	to	to	ADP
ejpam-6497	121	20	x	x	PROPN
ejpam-6497	121	21	modulo	modulo	PROPN
ejpam-6497	121	22	j	j	PROPN
ejpam-6497	121	23	′	′	NOUN
ejpam-6497	122	1	if	if	SCONJ
ejpam-6497	122	2	for	for	ADP
ejpam-6497	122	3	each	each	DET
ejpam-6497	122	4	ŏ	ŏ	ADJ
ejpam-6497	122	5	=	=	PRON
ejpam-6497	122	6	{	{	PUNCT
ejpam-6497	122	7	oα	oα	X
ejpam-6497	122	8	:	:	PUNCT
ejpam-6497	122	9	α	α	PROPN
ejpam-6497	122	10	∈	∈	PROPN
ejpam-6497	122	11	λ	λ	X
ejpam-6497	122	12	}	}	PUNCT
ejpam-6497	122	13	the	the	DET
ejpam-6497	122	14	collection	collection	NOUN
ejpam-6497	122	15	of	of	ADP
ejpam-6497	122	16	open	open	ADJ
ejpam-6497	122	17	subsets	subset	NOUN
ejpam-6497	122	18	of	of	ADP
ejpam-6497	122	19	x	x	SYM
ejpam-6497	122	20	modulo	modulo	PROPN
ejpam-6497	122	21	j	j	PROPN
ejpam-6497	122	22	:	:	PUNCT
ejpam-6497	122	23	⊂	⊂	PROPN
ejpam-6497	122	24	∪α∈λoα	∪α∈λoα	PROPN
ejpam-6497	122	25	,	,	PUNCT
ejpam-6497	122	26	there	there	PRON
ejpam-6497	122	27	exists	exist	VERB
ejpam-6497	122	28	kα	kα	PROPN
ejpam-6497	122	29	⊂	⊂	PROPN
ejpam-6497	122	30	x	x	PUNCT
ejpam-6497	123	1	a	a	DET
ejpam-6497	123	2	regularly	regularly	ADV
ejpam-6497	123	3	closed	close	VERB
ejpam-6497	123	4	subset	subset	ADJ
ejpam-6497	123	5	moulo	moulo	PROPN
ejpam-6497	123	6	j	j	PROPN
ejpam-6497	123	7	:	:	PUNCT
ejpam-6497	123	8	kα	kα	PROPN
ejpam-6497	123	9	⊂	⊂	PROPN
ejpam-6497	123	10	oα	oα	PROPN
ejpam-6497	123	11	and	and	CCONJ
ejpam-6497	123	12	y	y	PROPN
ejpam-6497	123	13	⊂	⊂	PROPN
ejpam-6497	123	14	∪α∈λ	∪α∈λ	PROPN
ejpam-6497	123	15	int(kα	int(kα	PROPN
ejpam-6497	123	16	)	)	PUNCT
ejpam-6497	123	17	.	.	PUNCT
ejpam-6497	124	1	in	in	ADP
ejpam-6497	124	2	addition	addition	NOUN
ejpam-6497	124	3	,	,	PUNCT
ejpam-6497	124	4	there	there	PRON
ejpam-6497	124	5	exists	exist	VERB
ejpam-6497	124	6	{	{	PUNCT
ejpam-6497	124	7	αn	αn	NOUN
ejpam-6497	124	8	:	:	PUNCT
ejpam-6497	124	9	n	n	CCONJ
ejpam-6497	124	10	∈	∈	PROPN
ejpam-6497	124	11	n	n	CCONJ
ejpam-6497	124	12	}	}	PUNCT
ejpam-6497	124	13	the	the	DET
ejpam-6497	124	14	countable	countable	ADJ
ejpam-6497	124	15	subset	subset	NOUN
ejpam-6497	124	16	of	of	ADP
ejpam-6497	124	17	x	x	PROPN
ejpam-6497	124	18	modulo	modulo	PROPN
ejpam-6497	124	19	j	j	NOUN
ejpam-6497	124	20	:	:	PUNCT
ejpam-6497	124	21	y	y	PROPN
ejpam-6497	124	22	⊂	⊂	PROPN
ejpam-6497	124	23	∪n∈ncl(oα	∪n∈ncl(oα	PROPN
ejpam-6497	124	24	)	)	PUNCT
ejpam-6497	124	25	.	.	PUNCT
ejpam-6497	125	1	remark	remark	NOUN
ejpam-6497	125	2	4	4	NUM
ejpam-6497	125	3	.	.	PUNCT
ejpam-6497	126	1	if	if	SCONJ
ejpam-6497	126	2	x	x	PRON
ejpam-6497	126	3	is	be	AUX
ejpam-6497	126	4	almost	almost	ADV
ejpam-6497	126	5	regular	regular	ADJ
ejpam-6497	126	6	modulo	modulo	ADJ
ejpam-6497	126	7	j	j	PROPN
ejpam-6497	126	8	,	,	PUNCT
ejpam-6497	126	9	then	then	ADV
ejpam-6497	126	10	x	x	PUNCT
ejpam-6497	126	11	sl	sl	PROPN
ejpam-6497	126	12	modulo	modulo	X
ejpam-6497	126	13	j	j	PROPN
ejpam-6497	126	14	.	.	PUNCT
ejpam-6497	127	1	the	the	DET
ejpam-6497	127	2	remark	remark	NOUN
ejpam-6497	127	3	above	above	ADV
ejpam-6497	127	4	is	be	AUX
ejpam-6497	127	5	not	not	PART
ejpam-6497	127	6	true	true	ADJ
ejpam-6497	127	7	for	for	ADP
ejpam-6497	127	8	the	the	DET
ejpam-6497	127	9	urysohn	urysohn	PROPN
ejpam-6497	127	10	space	space	NOUN
ejpam-6497	127	11	[	[	X
ejpam-6497	127	12	14	14	NUM
ejpam-6497	127	13	]	]	PUNCT
ejpam-6497	127	14	.	.	PUNCT
ejpam-6497	128	1	e.	e.	PROPN
ejpam-6497	128	2	almuhur	almuhur	PROPN
ejpam-6497	128	3	et	et	PROPN
ejpam-6497	128	4	al	al	PROPN
ejpam-6497	128	5	.	.	PUNCT
ejpam-6497	128	6	/	/	SYM
ejpam-6497	128	7	eur	eur	PROPN
ejpam-6497	128	8	.	.	PUNCT
ejpam-6497	129	1	j.	j.	PROPN
ejpam-6497	129	2	pure	pure	PROPN
ejpam-6497	129	3	appl	appl	PROPN
ejpam-6497	129	4	.	.	PROPN
ejpam-6497	129	5	math	math	PROPN
ejpam-6497	129	6	,	,	PUNCT
ejpam-6497	129	7	18	18	NUM
ejpam-6497	129	8	(	(	PUNCT
ejpam-6497	129	9	3	3	NUM
ejpam-6497	129	10	)	)	PUNCT
ejpam-6497	129	11	(	(	PUNCT
ejpam-6497	129	12	2025	2025	NUM
ejpam-6497	129	13	)	)	PUNCT
ejpam-6497	129	14	,	,	PUNCT
ejpam-6497	129	15	6497	6497	NUM
ejpam-6497	129	16	6	6	NUM
ejpam-6497	129	17	of	of	ADP
ejpam-6497	129	18	11	11	NUM
ejpam-6497	129	19	example	example	NOUN
ejpam-6497	129	20	2	2	NUM
ejpam-6497	129	21	.	.	PUNCT
ejpam-6497	130	1	let	let	VERB
ejpam-6497	130	2	ℵ	ℵ	NOUN
ejpam-6497	130	3	=	=	PUNCT
ejpam-6497	130	4	{	{	PUNCT
ejpam-6497	130	5	nα	nα	NOUN
ejpam-6497	130	6	:	:	PUNCT
ejpam-6497	130	7	α	α	PROPN
ejpam-6497	130	8	<	<	X
ejpam-6497	130	9	ω1	ω1	PROPN
ejpam-6497	130	10	}	}	PUNCT
ejpam-6497	130	11	,	,	PUNCT
ejpam-6497	130	12	ℵ̀	ℵ̀	PROPN
ejpam-6497	130	13	=	=	PRON
ejpam-6497	130	14	{	{	PUNCT
ejpam-6497	130	15	mi	mi	NOUN
ejpam-6497	130	16	:	:	PUNCT
ejpam-6497	130	17	i	i	PROPN
ejpam-6497	130	18	∈	∈	PROPN
ejpam-6497	130	19	ω	ω	X
ejpam-6497	130	20	}	}	PUNCT
ejpam-6497	130	21	and	and	CCONJ
ejpam-6497	130	22	y	y	PROPN
ejpam-6497	130	23	=	=	PRON
ejpam-6497	130	24	{	{	PUNCT
ejpam-6497	130	25	(	(	PUNCT
ejpam-6497	130	26	nα	nα	PROPN
ejpam-6497	130	27	,	,	PUNCT
ejpam-6497	130	28	mi	mi	PROPN
ejpam-6497	130	29	)	)	PUNCT
ejpam-6497	130	30	}	}	PUNCT
ejpam-6497	130	31	α	α	X
ejpam-6497	130	32	<	<	X
ejpam-6497	130	33	ω1	ω1	PROPN
ejpam-6497	130	34	for	for	ADP
ejpam-6497	130	35	each	each	PRON
ejpam-6497	130	36	i	i	PROPN
ejpam-6497	130	37	∈	∈	PROPN
ejpam-6497	131	1	ω	ω	INTJ
ejpam-6497	131	2	.	.	PUNCT
ejpam-6497	132	1	if	if	SCONJ
ejpam-6497	132	2	x	x	PRON
ejpam-6497	132	3	=	=	SYM
ejpam-6497	132	4	y	y	PROPN
ejpam-6497	132	5	∪	∪	VERB
ejpam-6497	132	6	ℵ	ℵ	ADP
ejpam-6497	132	7	∪	∪	X
ejpam-6497	132	8	{	{	PUNCT
ejpam-6497	132	9	n	n	ADV
ejpam-6497	132	10	}	}	PUNCT
ejpam-6497	132	11	for	for	ADP
ejpam-6497	132	12	each	each	DET
ejpam-6497	132	13	n	n	NOUN
ejpam-6497	132	14	/∈	/∈	PUNCT
ejpam-6497	133	1	y	y	PROPN
ejpam-6497	133	2	∪	∪	ADJ
ejpam-6497	133	3	ℵ	ℵ	NOUN
ejpam-6497	133	4	,	,	PUNCT
ejpam-6497	133	5	then	then	ADV
ejpam-6497	133	6	x	x	PART
ejpam-6497	133	7	modulo	modulo	PROPN
ejpam-6497	133	8	j	j	PROPN
ejpam-6497	133	9	is	be	AUX
ejpam-6497	133	10	topologized	topologize	VERB
ejpam-6497	133	11	as	as	SCONJ
ejpam-6497	133	12	follows	follow	VERB
ejpam-6497	133	13	:	:	PUNCT
ejpam-6497	133	14	each	each	DET
ejpam-6497	133	15	y	y	PROPN
ejpam-6497	133	16	∈	∈	PROPN
ejpam-6497	133	17	y	y	PROPN
ejpam-6497	133	18	is	be	AUX
ejpam-6497	133	19	an	an	DET
ejpam-6497	133	20	isolated	isolated	ADJ
ejpam-6497	133	21	point	point	NOUN
ejpam-6497	133	22	.	.	PUNCT
ejpam-6497	134	1	the	the	DET
ejpam-6497	134	2	neighborhood	neighborhood	NOUN
ejpam-6497	134	3	of	of	ADP
ejpam-6497	134	4	nα	nα	NOUN
ejpam-6497	134	5	∈	∈	PROPN
ejpam-6497	134	6	ℵ	ℵ	NOUN
ejpam-6497	134	7	has	have	VERB
ejpam-6497	134	8	the	the	DET
ejpam-6497	134	9	form	form	NOUN
ejpam-6497	134	10	:	:	PUNCT
ejpam-6497	134	11	unα(i	unα(i	X
ejpam-6497	134	12	)	)	PUNCT
ejpam-6497	135	1	=	=	PRON
ejpam-6497	135	2	{	{	PUNCT
ejpam-6497	135	3	nα	nα	NOUN
ejpam-6497	135	4	}	}	PUNCT
ejpam-6497	135	5	∪	∪	NOUN
ejpam-6497	135	6	{	{	PUNCT
ejpam-6497	135	7	(	(	PUNCT
ejpam-6497	135	8	nα	nα	NOUN
ejpam-6497	135	9	,	,	PUNCT
ejpam-6497	135	10	mi	mi	NOUN
ejpam-6497	135	11	)	)	PUNCT
ejpam-6497	135	12	}	}	PUNCT
ejpam-6497	136	1	α	α	X
ejpam-6497	136	2	<	<	X
ejpam-6497	136	3	ω1	ω1	ADJ
ejpam-6497	136	4	,	,	PUNCT
ejpam-6497	136	5	∀i	∀i	NOUN
ejpam-6497	136	6	∈	∈	PROPN
ejpam-6497	136	7	ω	ω	NOUN
ejpam-6497	136	8	.	.	PUNCT
ejpam-6497	137	1	the	the	DET
ejpam-6497	137	2	neighborhood	neighborhood	NOUN
ejpam-6497	137	3	of	of	ADP
ejpam-6497	137	4	n	n	NUM
ejpam-6497	137	5	is	be	AUX
ejpam-6497	137	6	un(α	un(α	PRON
ejpam-6497	137	7	)	)	PUNCT
ejpam-6497	138	1	=	=	PRON
ejpam-6497	138	2	{	{	PUNCT
ejpam-6497	138	3	nα	nα	NOUN
ejpam-6497	138	4	}	}	PUNCT
ejpam-6497	138	5	∪	∪	NOUN
ejpam-6497	138	6	{	{	PUNCT
ejpam-6497	138	7	(	(	PUNCT
ejpam-6497	138	8	nγ	nγ	PROPN
ejpam-6497	138	9	,	,	PUNCT
ejpam-6497	138	10	mi	mi	PROPN
ejpam-6497	138	11	)	)	PUNCT
ejpam-6497	138	12	:	:	PUNCT
ejpam-6497	138	13	γ	γ	X
ejpam-6497	138	14	>	>	X
ejpam-6497	138	15	α	α	PROPN
ejpam-6497	138	16	}	}	PUNCT
ejpam-6497	138	17	α	α	PRON
ejpam-6497	138	18	<	<	X
ejpam-6497	138	19	ω1	ω1	PROPN
ejpam-6497	138	20	,	,	PUNCT
ejpam-6497	138	21	∀i	∀i	NOUN
ejpam-6497	138	22	∈	∈	PROPN
ejpam-6497	138	23	ω	ω	NOUN
ejpam-6497	138	24	.	.	PUNCT
ejpam-6497	139	1	now	now	ADV
ejpam-6497	139	2	,	,	PUNCT
ejpam-6497	139	3	x	x	X
ejpam-6497	139	4	is	be	AUX
ejpam-6497	139	5	a	a	DET
ejpam-6497	139	6	not	not	PART
ejpam-6497	139	7	regular	regular	ADJ
ejpam-6497	139	8	urysohn	urysohn	PROPN
ejpam-6497	139	9	space	space	NOUN
ejpam-6497	139	10	modulo	modulo	PROPN
ejpam-6497	139	11	j	j	PROPN
ejpam-6497	139	12	because	because	SCONJ
ejpam-6497	139	13	n	n	PRON
ejpam-6497	139	14	can	can	AUX
ejpam-6497	139	15	not	not	PART
ejpam-6497	139	16	be	be	AUX
ejpam-6497	139	17	separated	separate	VERB
ejpam-6497	139	18	from	from	ADP
ejpam-6497	139	19	the	the	DET
ejpam-6497	139	20	uncountable	uncountable	ADJ
ejpam-6497	139	21	discrete	discrete	ADJ
ejpam-6497	139	22	closed	close	VERB
ejpam-6497	139	23	set	set	NOUN
ejpam-6497	139	24	ℵ.	ℵ.	PROPN
ejpam-6497	139	25	hence	hence	ADV
ejpam-6497	139	26	,	,	PUNCT
ejpam-6497	139	27	x	x	X
ejpam-6497	139	28	is	be	AUX
ejpam-6497	139	29	not	not	PART
ejpam-6497	139	30	a	a	DET
ejpam-6497	139	31	sl	sl	NOUN
ejpam-6497	139	32	modulo	modulo	NOUN
ejpam-6497	139	33	j	j	PROPN
ejpam-6497	139	34	.	.	PUNCT
ejpam-6497	140	1	if	if	SCONJ
ejpam-6497	140	2	u	u	PRON
ejpam-6497	140	3	covers	cover	VERB
ejpam-6497	140	4	x	x	X
ejpam-6497	140	5	modulo	modulo	PROPN
ejpam-6497	140	6	j	j	PROPN
ejpam-6497	140	7	,	,	PUNCT
ejpam-6497	140	8	so	so	ADV
ejpam-6497	140	9	there	there	PRON
ejpam-6497	140	10	exists	exist	VERB
ejpam-6497	140	11	un	un	PROPN
ejpam-6497	140	12	∈	∈	PROPN
ejpam-6497	140	13	u	u	PROPN
ejpam-6497	140	14	for	for	ADP
ejpam-6497	140	15	each	each	DET
ejpam-6497	140	16	n	n	PROPN
ejpam-6497	140	17	∈	∈	PROPN
ejpam-6497	140	18	un	un	PROPN
ejpam-6497	140	19	and	and	CCONJ
ejpam-6497	140	20	there	there	PRON
ejpam-6497	140	21	is	be	VERB
ejpam-6497	140	22	γ	γ	X
ejpam-6497	140	23	<	<	X
ejpam-6497	140	24	ω1	ω1	PROPN
ejpam-6497	140	25	:	:	PUNCT
ejpam-6497	140	26	un(γ	un(γ	NUM
ejpam-6497	140	27	)	)	PUNCT
ejpam-6497	140	28	⊂	⊂	PROPN
ejpam-6497	140	29	un	un	PROPN
ejpam-6497	140	30	.	.	PROPN
ejpam-6497	141	1	now	now	ADV
ejpam-6497	141	2	,	,	PUNCT
ejpam-6497	141	3	{	{	PUNCT
ejpam-6497	141	4	nα	nα	X
ejpam-6497	141	5	:	:	PUNCT
ejpam-6497	141	6	α	α	X
ejpam-6497	141	7	>	>	X
ejpam-6497	141	8	γ	γ	X
ejpam-6497	141	9	}	}	PUNCT
ejpam-6497	141	10	∪	∪	X
ejpam-6497	141	11	{	{	PUNCT
ejpam-6497	141	12	n	n	CCONJ
ejpam-6497	141	13	}	}	PUNCT
ejpam-6497	141	14	∪	∪	NOUN
ejpam-6497	141	15	{	{	PUNCT
ejpam-6497	141	16	(	(	PUNCT
ejpam-6497	141	17	nγ	nγ	PROPN
ejpam-6497	141	18	,	,	PUNCT
ejpam-6497	141	19	mi	mi	PROPN
ejpam-6497	141	20	)	)	PUNCT
ejpam-6497	141	21	:	:	PUNCT
ejpam-6497	141	22	γ	γ	X
ejpam-6497	141	23	>	>	X
ejpam-6497	141	24	α	α	PROPN
ejpam-6497	141	25	}	}	PUNCT
ejpam-6497	141	26	α	α	PRON
ejpam-6497	141	27	<	<	X
ejpam-6497	141	28	ω1	ω1	PROPN
ejpam-6497	141	29	⊂	⊂	PROPN
ejpam-6497	141	30	un	un	PROPN
ejpam-6497	141	31	,	,	PUNCT
ejpam-6497	141	32	∀	∀	VERB
ejpam-6497	141	33	i	i	NOUN
ejpam-6497	141	34	∈	∈	PROPN
ejpam-6497	141	35	ω	ω	PROPN
ejpam-6497	141	36	,	,	PUNCT
ejpam-6497	141	37	and	and	CCONJ
ejpam-6497	141	38	x	x	SYM
ejpam-6497	141	39	\	\	PROPN
ejpam-6497	141	40	un	un	PROPN
ejpam-6497	141	41	is	be	AUX
ejpam-6497	141	42	countable	countable	ADJ
ejpam-6497	141	43	.	.	PUNCT
ejpam-6497	142	1	so	so	ADV
ejpam-6497	142	2	there	there	PRON
ejpam-6497	142	3	is	be	VERB
ejpam-6497	142	4	ŵ	ŵ	X
ejpam-6497	142	5	⊂	⊂	PROPN
ejpam-6497	142	6	u	u	PROPN
ejpam-6497	142	7	countable	countable	VERB
ejpam-6497	142	8	such	such	ADJ
ejpam-6497	142	9	that	that	SCONJ
ejpam-6497	142	10	x	x	SYM
ejpam-6497	142	11	\	\	PROPN
ejpam-6497	142	12	un	un	PROPN
ejpam-6497	142	13	⊂	⊂	PROPN
ejpam-6497	142	14	∪ŵ	∪ŵ	VERB
ejpam-6497	142	15	.	.	PUNCT
ejpam-6497	143	1	if	if	SCONJ
ejpam-6497	143	2	õ	õ	PRON
ejpam-6497	143	3	=	=	SYM
ejpam-6497	143	4	ŵ	ŵ	X
ejpam-6497	143	5	∪	∪	X
ejpam-6497	143	6	{	{	PUNCT
ejpam-6497	143	7	un	un	PROPN
ejpam-6497	143	8	}	}	PUNCT
ejpam-6497	143	9	,	,	PUNCT
ejpam-6497	143	10	then	then	ADV
ejpam-6497	143	11	õ	õ	PROPN
ejpam-6497	143	12	⊂	⊂	PROPN
ejpam-6497	143	13	u	u	PROPN
ejpam-6497	143	14	is	be	AUX
ejpam-6497	143	15	a	a	DET
ejpam-6497	143	16	countable	countable	ADJ
ejpam-6497	143	17	subfamily	subfamily	ADV
ejpam-6497	143	18	.	.	PUNCT
ejpam-6497	144	1	theorem	theorem	ADJ
ejpam-6497	144	2	4	4	NUM
ejpam-6497	144	3	.	.	PUNCT
ejpam-6497	145	1	if	if	SCONJ
ejpam-6497	145	2	x	x	PRON
ejpam-6497	145	3	is	be	AUX
ejpam-6497	145	4	almost	almost	ADV
ejpam-6497	145	5	regular	regular	ADJ
ejpam-6497	145	6	modulo	modulo	ADJ
ejpam-6497	145	7	j	j	PROPN
ejpam-6497	145	8	,	,	PUNCT
ejpam-6497	145	9	and	and	CCONJ
ejpam-6497	145	10	y	y	PROPN
ejpam-6497	145	11	is	be	AUX
ejpam-6497	145	12	an	an	DET
ejpam-6497	145	13	almost	almost	ADV
ejpam-6497	145	14	regular	regular	ADJ
ejpam-6497	145	15	subspace	subspace	NOUN
ejpam-6497	145	16	of	of	ADP
ejpam-6497	145	17	x	x	PROPN
ejpam-6497	145	18	modulo	modulo	PROPN
ejpam-6497	145	19	j	j	PROPN
ejpam-6497	145	20	′	′	PROPN
ejpam-6497	145	21	,	,	PUNCT
ejpam-6497	145	22	then	then	ADV
ejpam-6497	145	23	y	y	PROPN
ejpam-6497	145	24	is	be	AUX
ejpam-6497	145	25	almost	almost	ADV
ejpam-6497	145	26	regular	regular	ADJ
ejpam-6497	145	27	relative	relative	ADJ
ejpam-6497	145	28	to	to	ADP
ejpam-6497	145	29	x	x	PROPN
ejpam-6497	145	30	modulo	modulo	PROPN
ejpam-6497	145	31	j	j	PROPN
ejpam-6497	145	32	′.	′.	PROPN
ejpam-6497	145	33	proof	proof	NOUN
ejpam-6497	145	34	.	.	PUNCT
ejpam-6497	146	1	if	if	SCONJ
ejpam-6497	146	2	ŏ	ŏ	ADV
ejpam-6497	146	3	=	=	PRON
ejpam-6497	146	4	{	{	PUNCT
ejpam-6497	146	5	oα	oα	X
ejpam-6497	146	6	:	:	PUNCT
ejpam-6497	146	7	α	α	PROPN
ejpam-6497	146	8	∈	∈	PROPN
ejpam-6497	146	9	λ	λ	PROPN
ejpam-6497	146	10	}	}	PUNCT
ejpam-6497	146	11	forms	form	VERB
ejpam-6497	146	12	an	an	DET
ejpam-6497	146	13	open	open	ADJ
ejpam-6497	146	14	cover	cover	NOUN
ejpam-6497	146	15	of	of	ADP
ejpam-6497	146	16	y	y	PROPN
ejpam-6497	146	17	modulo	modulo	PROPN
ejpam-6497	146	18	j	j	PROPN
ejpam-6497	146	19	′	′	PROPN
ejpam-6497	146	20	,	,	PUNCT
ejpam-6497	146	21	then	then	ADV
ejpam-6497	146	22	there	there	PRON
ejpam-6497	146	23	exists	exist	VERB
ejpam-6497	146	24	fα	fα	ADP
ejpam-6497	146	25	⊂	⊂	PROPN
ejpam-6497	146	26	x	x	PUNCT
ejpam-6497	146	27	regularly	regularly	ADV
ejpam-6497	146	28	closed	close	VERB
ejpam-6497	146	29	subset	subset	VERB
ejpam-6497	146	30	fα	fα	ADP
ejpam-6497	146	31	⊂	⊂	PROPN
ejpam-6497	146	32	oα	oα	PROPN
ejpam-6497	146	33	,	,	PUNCT
ejpam-6497	146	34	y	y	PROPN
ejpam-6497	146	35	⊂	⊂	PROPN
ejpam-6497	146	36	∪α∈λ	∪α∈λ	PROPN
ejpam-6497	146	37	int(fα	int(fα	ADV
ejpam-6497	146	38	)	)	PUNCT
ejpam-6497	146	39	,	,	PUNCT
ejpam-6497	146	40	and	and	CCONJ
ejpam-6497	146	41	there	there	PRON
ejpam-6497	146	42	is	be	VERB
ejpam-6497	146	43	{	{	PUNCT
ejpam-6497	146	44	αn	αn	NOUN
ejpam-6497	146	45	:	:	PUNCT
ejpam-6497	146	46	n	n	CCONJ
ejpam-6497	146	47	∈	∈	PROPN
ejpam-6497	146	48	n	n	CCONJ
ejpam-6497	146	49	}	}	PUNCT
ejpam-6497	146	50	the	the	DET
ejpam-6497	146	51	countable	countable	ADJ
ejpam-6497	146	52	subset	subset	NOUN
ejpam-6497	146	53	of	of	ADP
ejpam-6497	146	54	x	x	PROPN
ejpam-6497	146	55	modulo	modulo	PROPN
ejpam-6497	146	56	j	j	NOUN
ejpam-6497	146	57	:	:	PUNCT
ejpam-6497	146	58	y	y	PROPN
ejpam-6497	146	59	⊂	⊂	PROPN
ejpam-6497	146	60	∪n∈ncl(oα	∪n∈ncl(oα	PROPN
ejpam-6497	146	61	)	)	PUNCT
ejpam-6497	146	62	.	.	PUNCT
ejpam-6497	147	1	if	if	SCONJ
ejpam-6497	147	2	uα	uα	PROPN
ejpam-6497	147	3	=	=	PUNCT
ejpam-6497	147	4	int(fα	int(fα	NOUN
ejpam-6497	147	5	)	)	PUNCT
ejpam-6497	147	6	∩	∩	ADJ
ejpam-6497	147	7	y	y	PROPN
ejpam-6497	147	8	,	,	PUNCT
ejpam-6497	147	9	wα	wα	NOUN
ejpam-6497	147	10	=	=	SYM
ejpam-6497	147	11	oα	oα	PROPN
ejpam-6497	147	12	∩	∩	PROPN
ejpam-6497	147	13	y	y	PROPN
ejpam-6497	147	14	,	,	PUNCT
ejpam-6497	147	15	both	both	PRON
ejpam-6497	147	16	are	be	AUX
ejpam-6497	147	17	open	open	ADJ
ejpam-6497	147	18	subsets	subset	NOUN
ejpam-6497	147	19	of	of	ADP
ejpam-6497	147	20	y	y	PROPN
ejpam-6497	147	21	:	:	PUNCT
ejpam-6497	147	22	cl(uα	cl(uα	NOUN
ejpam-6497	147	23	)	)	PUNCT
ejpam-6497	147	24	is	be	AUX
ejpam-6497	147	25	regularly	regularly	ADV
ejpam-6497	147	26	closed	close	VERB
ejpam-6497	147	27	subset	subset	NOUN
ejpam-6497	147	28	of	of	ADP
ejpam-6497	147	29	y	y	PROPN
ejpam-6497	147	30	modulo	modulo	PROPN
ejpam-6497	147	31	j	j	PROPN
ejpam-6497	147	32	′.	′.	PROPN
ejpam-6497	147	33	so	so	ADV
ejpam-6497	147	34	,	,	PUNCT
ejpam-6497	147	35	cl(uα	cl(uα	PROPN
ejpam-6497	147	36	)	)	PUNCT
ejpam-6497	148	1	⊂	⊂	PROPN
ejpam-6497	148	2	fα	fα	ADP
ejpam-6497	148	3	∩	∩	PROPN
ejpam-6497	148	4	y	y	PROPN
ejpam-6497	148	5	⊂	⊂	PROPN
ejpam-6497	148	6	oα	oα	PROPN
ejpam-6497	148	7	∩	∩	PROPN
ejpam-6497	148	8	y	y	PROPN
ejpam-6497	148	9	,	,	PUNCT
ejpam-6497	148	10	∀α	∀α	VERB
ejpam-6497	148	11	∈	∈	PROPN
ejpam-6497	148	12	λ	λ	NOUN
ejpam-6497	148	13	.	.	PUNCT
ejpam-6497	149	1	now	now	ADV
ejpam-6497	149	2	,	,	PUNCT
ejpam-6497	149	3	x	x	X
ejpam-6497	149	4	=	=	PUNCT
ejpam-6497	149	5	∩α∈λuα	∩α∈λuα	NOUN
ejpam-6497	149	6	and	and	CCONJ
ejpam-6497	149	7	uα	uα	PROPN
ejpam-6497	149	8	⊂	⊂	PROPN
ejpam-6497	149	9	int(cl	int(cl	X
ejpam-6497	149	10	(	(	PUNCT
ejpam-6497	149	11	uα	uα	NOUN
ejpam-6497	149	12	)	)	PUNCT
ejpam-6497	149	13	)	)	PUNCT
ejpam-6497	149	14	,	,	PUNCT
ejpam-6497	149	15	hence	hence	ADV
ejpam-6497	149	16	y	y	PROPN
ejpam-6497	149	17	=	=	SYM
ejpam-6497	149	18	∪α∈λ	∪α∈λ	NUM
ejpam-6497	149	19	int	int	NOUN
ejpam-6497	149	20	(	(	PUNCT
ejpam-6497	149	21	cl(uα	cl(uα	PROPN
ejpam-6497	149	22	)	)	PUNCT
ejpam-6497	149	23	)	)	PUNCT
ejpam-6497	149	24	.	.	PUNCT
ejpam-6497	150	1	since	since	SCONJ
ejpam-6497	150	2	y	y	PROPN
ejpam-6497	150	3	is	be	AUX
ejpam-6497	150	4	almost	almost	ADV
ejpam-6497	150	5	regular	regular	ADJ
ejpam-6497	150	6	l	l	ADV
ejpam-6497	150	7	-	-	ADJ
ejpam-6497	150	8	closed	closed	ADJ
ejpam-6497	150	9	modulo	modulo	NOUN
ejpam-6497	150	10	j	j	PROPN
ejpam-6497	150	11	′	′	PROPN
ejpam-6497	150	12	,	,	PUNCT
ejpam-6497	150	13	∃	∃	PROPN
ejpam-6497	150	14	{	{	PUNCT
ejpam-6497	150	15	αn	αn	NOUN
ejpam-6497	150	16	:	:	PUNCT
ejpam-6497	150	17	n	n	CCONJ
ejpam-6497	150	18	∈	∈	PROPN
ejpam-6497	150	19	n	n	NOUN
ejpam-6497	150	20	}	}	PUNCT
ejpam-6497	150	21	:	:	PUNCT
ejpam-6497	150	22	x	x	X
ejpam-6497	150	23	=	=	PUNCT
ejpam-6497	150	24	∪	∪	ADP
ejpam-6497	150	25	n∈n	n∈n	NUM
ejpam-6497	150	26	cl(wαn	cl(wαn	NOUN
ejpam-6497	150	27	)	)	PUNCT
ejpam-6497	150	28	.	.	PUNCT
ejpam-6497	151	1	but	but	CCONJ
ejpam-6497	151	2	cl(wαn	cl(wαn	ADJ
ejpam-6497	151	3	)	)	PUNCT
ejpam-6497	151	4	⊂	⊂	PROPN
ejpam-6497	151	5	cl(uα	cl(uα	PROPN
ejpam-6497	151	6	)	)	PUNCT
ejpam-6497	151	7	,	,	PUNCT
ejpam-6497	151	8	so	so	CCONJ
ejpam-6497	151	9	y	y	PROPN
ejpam-6497	151	10	=	=	SYM
ejpam-6497	151	11	∪n∈ncl(oαn	∪n∈ncl(oαn	PROPN
ejpam-6497	151	12	)	)	PUNCT
ejpam-6497	151	13	.	.	PUNCT
ejpam-6497	152	1	as	as	ADP
ejpam-6497	152	2	a	a	DET
ejpam-6497	152	3	consequence	consequence	NOUN
ejpam-6497	152	4	,	,	PUNCT
ejpam-6497	152	5	y	y	PROPN
ejpam-6497	152	6	is	be	AUX
ejpam-6497	152	7	almost	almost	ADV
ejpam-6497	152	8	regular	regular	ADJ
ejpam-6497	152	9	subspace	subspace	NOUN
ejpam-6497	152	10	relative	relative	ADJ
ejpam-6497	152	11	to	to	ADP
ejpam-6497	152	12	x	x	PROPN
ejpam-6497	152	13	modulo	modulo	PROPN
ejpam-6497	152	14	j	j	PROPN
ejpam-6497	152	15	′.	′.	PROPN
ejpam-6497	152	16	corollary	corollary	ADJ
ejpam-6497	153	1	2	2	NUM
ejpam-6497	153	2	.	.	PUNCT
ejpam-6497	154	1	if	if	SCONJ
ejpam-6497	154	2	x	x	PRON
ejpam-6497	154	3	is	be	AUX
ejpam-6497	154	4	an	an	DET
ejpam-6497	154	5	almost	almost	ADV
ejpam-6497	154	6	regular	regular	ADJ
ejpam-6497	154	7	space	space	NOUN
ejpam-6497	154	8	modulo	modulo	NOUN
ejpam-6497	154	9	j	j	PROPN
ejpam-6497	154	10	and	and	CCONJ
ejpam-6497	154	11	each	each	PRON
ejpam-6497	154	12	of	of	ADP
ejpam-6497	154	13	its	its	PRON
ejpam-6497	154	14	proper	proper	ADJ
ejpam-6497	154	15	regularly	regularly	ADV
ejpam-6497	154	16	closed	closed	ADJ
ejpam-6497	154	17	subset	subset	NOUN
ejpam-6497	154	18	is	be	AUX
ejpam-6497	154	19	almost	almost	ADV
ejpam-6497	154	20	regular	regular	ADJ
ejpam-6497	154	21	l	l	ADV
ejpam-6497	154	22	-	-	ADJ
ejpam-6497	154	23	closed	closed	ADJ
ejpam-6497	154	24	modulo	modulo	NOUN
ejpam-6497	154	25	j	j	PROPN
ejpam-6497	154	26	,	,	PUNCT
ejpam-6497	154	27	then	then	ADV
ejpam-6497	154	28	x	x	PUNCT
ejpam-6497	154	29	is	be	AUX
ejpam-6497	154	30	almost	almost	ADV
ejpam-6497	154	31	regular	regular	ADJ
ejpam-6497	154	32	modulo	modulo	PROPN
ejpam-6497	154	33	j	j	PROPN
ejpam-6497	154	34	.	.	PUNCT
ejpam-6497	155	1	theorem	theorem	VERB
ejpam-6497	155	2	5	5	NUM
ejpam-6497	155	3	.	.	PUNCT
ejpam-6497	156	1	if	if	SCONJ
ejpam-6497	156	2	x	x	PRON
ejpam-6497	156	3	is	be	AUX
ejpam-6497	156	4	almost	almost	ADV
ejpam-6497	156	5	regular	regular	ADJ
ejpam-6497	156	6	modulo	modulo	ADJ
ejpam-6497	156	7	j	j	NOUN
ejpam-6497	156	8	,	,	PUNCT
ejpam-6497	156	9	then	then	ADV
ejpam-6497	156	10	each	each	PRON
ejpam-6497	156	11	of	of	ADP
ejpam-6497	156	12	its	its	PRON
ejpam-6497	156	13	proper	proper	ADJ
ejpam-6497	156	14	clopen	clopen	ADJ
ejpam-6497	156	15	subsets	subset	NOUN
ejpam-6497	156	16	is	be	AUX
ejpam-6497	156	17	almost	almost	ADV
ejpam-6497	156	18	regular	regular	ADJ
ejpam-6497	156	19	relative	relative	ADJ
ejpam-6497	156	20	to	to	ADP
ejpam-6497	156	21	x	x	PROPN
ejpam-6497	156	22	modulo	modulo	PROPN
ejpam-6497	156	23	j	j	PROPN
ejpam-6497	156	24	.	.	PUNCT
ejpam-6497	157	1	e.	e.	PROPN
ejpam-6497	157	2	almuhur	almuhur	PROPN
ejpam-6497	157	3	et	et	PROPN
ejpam-6497	157	4	al	al	PROPN
ejpam-6497	157	5	.	.	PUNCT
ejpam-6497	157	6	/	/	SYM
ejpam-6497	157	7	eur	eur	PROPN
ejpam-6497	157	8	.	.	PUNCT
ejpam-6497	158	1	j.	j.	PROPN
ejpam-6497	158	2	pure	pure	PROPN
ejpam-6497	158	3	appl	appl	PROPN
ejpam-6497	158	4	.	.	PROPN
ejpam-6497	158	5	math	math	PROPN
ejpam-6497	158	6	,	,	PUNCT
ejpam-6497	158	7	18	18	NUM
ejpam-6497	158	8	(	(	PUNCT
ejpam-6497	158	9	3	3	NUM
ejpam-6497	158	10	)	)	PUNCT
ejpam-6497	158	11	(	(	PUNCT
ejpam-6497	158	12	2025	2025	NUM
ejpam-6497	158	13	)	)	PUNCT
ejpam-6497	158	14	,	,	PUNCT
ejpam-6497	158	15	6497	6497	NUM
ejpam-6497	158	16	7	7	NUM
ejpam-6497	158	17	of	of	ADP
ejpam-6497	158	18	11	11	NUM
ejpam-6497	158	19	proof	proof	NOUN
ejpam-6497	158	20	.	.	PUNCT
ejpam-6497	159	1	if	if	SCONJ
ejpam-6497	159	2	k	k	PROPN
ejpam-6497	159	3	⊂	⊂	PROPN
ejpam-6497	159	4	x	x	X
ejpam-6497	159	5	and	and	CCONJ
ejpam-6497	159	6	ü	ü	VERB
ejpam-6497	159	7	=	=	SYM
ejpam-6497	159	8	{	{	PUNCT
ejpam-6497	159	9	uα	uα	X
ejpam-6497	159	10	:	:	PUNCT
ejpam-6497	159	11	α	α	PROPN
ejpam-6497	159	12	∈	∈	PROPN
ejpam-6497	159	13	λ	λ	PROPN
ejpam-6497	159	14	}	}	PUNCT
ejpam-6497	159	15	covers	cover	VERB
ejpam-6497	159	16	k	k	X
ejpam-6497	159	17	:	:	PUNCT
ejpam-6497	159	18	∀α	∀α	NOUN
ejpam-6497	159	19	∈	∈	PROPN
ejpam-6497	159	20	λ	λ	NOUN
ejpam-6497	159	21	,	,	PUNCT
ejpam-6497	159	22	there	there	PRON
ejpam-6497	159	23	is	be	VERB
ejpam-6497	159	24	aα	aα	ADV
ejpam-6497	159	25	regularly	regularly	ADV
ejpam-6497	159	26	closed	close	VERB
ejpam-6497	159	27	and	and	CCONJ
ejpam-6497	159	28	aα	aα	NOUN
ejpam-6497	159	29	⊂	⊂	PROPN
ejpam-6497	159	30	uα	uα	PROPN
ejpam-6497	159	31	.	.	PUNCT
ejpam-6497	160	1	since	since	SCONJ
ejpam-6497	160	2	k	k	PROPN
ejpam-6497	160	3	⊂	⊂	PROPN
ejpam-6497	160	4	∪	∪	ADP
ejpam-6497	160	5	α∈λ	α∈λ	NOUN
ejpam-6497	160	6	int(aα	int(aα	NOUN
ejpam-6497	160	7	)	)	PUNCT
ejpam-6497	160	8	,	,	PUNCT
ejpam-6497	160	9	there	there	PRON
ejpam-6497	160	10	exists	exist	VERB
ejpam-6497	160	11	{	{	PUNCT
ejpam-6497	160	12	α1	α1	PROPN
ejpam-6497	160	13	,	,	PUNCT
ejpam-6497	160	14	α2	α2	ADJ
ejpam-6497	160	15	,	,	PUNCT
ejpam-6497	160	16	.	.	PUNCT
ejpam-6497	160	17	.	.	PUNCT
ejpam-6497	161	1	.	.	PUNCT
ejpam-6497	162	1	}	}	PUNCT
ejpam-6497	163	1	a	a	DET
ejpam-6497	163	2	countable	countable	ADJ
ejpam-6497	163	3	subset	subset	NOUN
ejpam-6497	163	4	such	such	ADJ
ejpam-6497	163	5	that	that	SCONJ
ejpam-6497	163	6	k	k	PROPN
ejpam-6497	163	7	⊂	⊂	PROPN
ejpam-6497	163	8	∪n∈ncl(uαn	∪n∈ncl(uαn	PROPN
ejpam-6497	163	9	)	)	PUNCT
ejpam-6497	163	10	.	.	PUNCT
ejpam-6497	164	1	but	but	CCONJ
ejpam-6497	164	2	,	,	PUNCT
ejpam-6497	164	3	{	{	PUNCT
ejpam-6497	164	4	uα	uα	PROPN
ejpam-6497	164	5	}	}	PUNCT
ejpam-6497	164	6	α∈λ	α∈λ	NOUN
ejpam-6497	164	7	∪	∪	ADV
ejpam-6497	164	8	(	(	PUNCT
ejpam-6497	164	9	x	x	NOUN
ejpam-6497	164	10	\k	\k	NOUN
ejpam-6497	164	11	)	)	PUNCT
ejpam-6497	164	12	,	,	PUNCT
ejpam-6497	164	13	covers	cover	VERB
ejpam-6497	164	14	x	x	PUNCT
ejpam-6497	164	15	regularly	regularly	ADV
ejpam-6497	164	16	,	,	PUNCT
ejpam-6497	164	17	and	and	CCONJ
ejpam-6497	164	18	x	x	X
ejpam-6497	164	19	is	be	AUX
ejpam-6497	164	20	almost	almost	ADV
ejpam-6497	164	21	regular	regular	ADJ
ejpam-6497	164	22	l	l	ADV
ejpam-6497	164	23	-	-	ADJ
ejpam-6497	164	24	closed	closed	ADJ
ejpam-6497	164	25	modulo	modulo	PROPN
ejpam-6497	164	26	j	j	PROPN
ejpam-6497	164	27	.	.	PUNCT
ejpam-6497	165	1	hence	hence	ADV
ejpam-6497	165	2	,	,	PUNCT
ejpam-6497	165	3	x	x	PUNCT
ejpam-6497	165	4	=	=	SYM
ejpam-6497	165	5	∪n∈n	∪n∈n	PROPN
ejpam-6497	165	6	(	(	PUNCT
ejpam-6497	165	7	x	x	PROPN
ejpam-6497	165	8	\k	\k	NOUN
ejpam-6497	165	9	)	)	PUNCT
ejpam-6497	165	10	.	.	PUNCT
ejpam-6497	166	1	definition	definition	NOUN
ejpam-6497	166	2	7	7	NUM
ejpam-6497	166	3	.	.	PUNCT
ejpam-6497	167	1	the	the	DET
ejpam-6497	167	2	space	space	NOUN
ejpam-6497	167	3	x	x	X
ejpam-6497	167	4	modulo	modulo	PROPN
ejpam-6497	167	5	j	j	PROPN
ejpam-6497	167	6	is	be	AUX
ejpam-6497	167	7	weakly	weakly	ADJ
ejpam-6497	167	8	lindelöf	lindelöf	NOUN
ejpam-6497	167	9	if	if	SCONJ
ejpam-6497	167	10	for	for	ADP
ejpam-6497	167	11	each	each	DET
ejpam-6497	167	12	cover	cover	NOUN
ejpam-6497	167	13	õ	õ	NOUN
ejpam-6497	167	14	=	=	SYM
ejpam-6497	167	15	{	{	PUNCT
ejpam-6497	167	16	oβ	oβ	X
ejpam-6497	167	17	:	:	PUNCT
ejpam-6497	167	18	β	β	X
ejpam-6497	167	19	∈	∈	PROPN
ejpam-6497	167	20	γ	γ	X
ejpam-6497	167	21	}	}	PUNCT
ejpam-6497	167	22	,	,	PUNCT
ejpam-6497	167	23	of	of	ADP
ejpam-6497	167	24	its	its	PRON
ejpam-6497	167	25	subsets	subset	NOUN
ejpam-6497	167	26	,	,	PUNCT
ejpam-6497	167	27	there	there	PRON
ejpam-6497	167	28	is	be	VERB
ejpam-6497	167	29	{	{	PUNCT
ejpam-6497	167	30	α1	α1	PROPN
ejpam-6497	167	31	,	,	PUNCT
ejpam-6497	167	32	α2	α2	ADJ
ejpam-6497	167	33	,	,	PUNCT
ejpam-6497	167	34	.	.	PUNCT
ejpam-6497	167	35	.	.	PUNCT
ejpam-6497	167	36	.	.	PUNCT
ejpam-6497	168	1	}	}	PUNCT
ejpam-6497	168	2	a	a	DET
ejpam-6497	168	3	countable	countable	ADJ
ejpam-6497	168	4	subset	subset	NOUN
ejpam-6497	168	5	such	such	ADJ
ejpam-6497	168	6	that	that	SCONJ
ejpam-6497	168	7	x	x	X
ejpam-6497	168	8	=	=	PUNCT
ejpam-6497	168	9	cl	cl	NOUN
ejpam-6497	168	10	(	(	PUNCT
ejpam-6497	168	11	∪n∈n	∪n∈n	X
ejpam-6497	168	12	(	(	PUNCT
ejpam-6497	168	13	oβn	oβn	NOUN
ejpam-6497	168	14	)	)	PUNCT
ejpam-6497	168	15	)	)	PUNCT
ejpam-6497	168	16	.	.	PUNCT
ejpam-6497	169	1	definition	definition	NOUN
ejpam-6497	169	2	8	8	NUM
ejpam-6497	169	3	.	.	PUNCT
ejpam-6497	170	1	the	the	DET
ejpam-6497	170	2	space	space	NOUN
ejpam-6497	170	3	x	x	X
ejpam-6497	170	4	modulo	modulo	PROPN
ejpam-6497	170	5	j	j	PROPN
ejpam-6497	170	6	is	be	AUX
ejpam-6497	170	7	weakly	weakly	ADV
ejpam-6497	170	8	regular	regular	ADJ
ejpam-6497	170	9	if	if	SCONJ
ejpam-6497	170	10	for	for	ADP
ejpam-6497	170	11	each	each	PRON
ejpam-6497	170	12	of	of	ADP
ejpam-6497	170	13	its	its	PRON
ejpam-6497	170	14	covers	cover	NOUN
ejpam-6497	170	15	by	by	ADP
ejpam-6497	170	16	the	the	DET
ejpam-6497	170	17	regular	regular	ADJ
ejpam-6497	170	18	open	open	ADJ
ejpam-6497	170	19	subsets	subset	NOUN
ejpam-6497	170	20	{	{	PUNCT
ejpam-6497	170	21	uβ	uβ	X
ejpam-6497	170	22	:	:	PUNCT
ejpam-6497	170	23	β	β	X
ejpam-6497	170	24	∈	∈	PROPN
ejpam-6497	170	25	γ	γ	X
ejpam-6497	170	26	}	}	PUNCT
ejpam-6497	170	27	,	,	PUNCT
ejpam-6497	170	28	there	there	PRON
ejpam-6497	170	29	exists	exist	VERB
ejpam-6497	170	30	{	{	PUNCT
ejpam-6497	170	31	α1	α1	PROPN
ejpam-6497	170	32	,	,	PUNCT
ejpam-6497	170	33	α2	α2	ADJ
ejpam-6497	170	34	,	,	PUNCT
ejpam-6497	170	35	.	.	PUNCT
ejpam-6497	170	36	.	.	PUNCT
ejpam-6497	170	37	.	.	PUNCT
ejpam-6497	171	1	}	}	PUNCT
ejpam-6497	171	2	a	a	DET
ejpam-6497	171	3	countable	countable	ADJ
ejpam-6497	171	4	subset	subset	NOUN
ejpam-6497	171	5	:	:	PUNCT
ejpam-6497	171	6	x	x	SYM
ejpam-6497	171	7	=	=	SYM
ejpam-6497	171	8	cl(∪n∈n	cl(∪n∈n	PROPN
ejpam-6497	171	9	(	(	PUNCT
ejpam-6497	171	10	uβn	uβn	PROPN
ejpam-6497	171	11	)	)	PUNCT
ejpam-6497	171	12	)	)	PUNCT
ejpam-6497	171	13	.	.	PUNCT
ejpam-6497	172	1	theorem	theorem	VERB
ejpam-6497	172	2	6	6	NUM
ejpam-6497	172	3	.	.	PUNCT
ejpam-6497	173	1	the	the	DET
ejpam-6497	173	2	space	space	NOUN
ejpam-6497	173	3	x	x	X
ejpam-6497	173	4	modulo	modulo	PROPN
ejpam-6497	173	5	j	j	PROPN
ejpam-6497	173	6	is	be	AUX
ejpam-6497	173	7	weakly	weakly	ADJ
ejpam-6497	173	8	if	if	SCONJ
ejpam-6497	173	9	and	and	CCONJ
ejpam-6497	173	10	only	only	ADV
ejpam-6497	173	11	if	if	SCONJ
ejpam-6497	173	12	for	for	ADP
ejpam-6497	173	13	the	the	DET
ejpam-6497	173	14	family	family	NOUN
ejpam-6497	173	15	k	k	NOUN
ejpam-6497	173	16	∼	∼	NOUN
ejpam-6497	174	1	=	=	PUNCT
ejpam-6497	174	2	{	{	PUNCT
ejpam-6497	174	3	kβ	kβ	INTJ
ejpam-6497	174	4	:	:	PUNCT
ejpam-6497	174	5	β	β	X
ejpam-6497	174	6	∈	∈	PROPN
ejpam-6497	174	7	γ	γ	X
ejpam-6497	174	8	}	}	PUNCT
ejpam-6497	174	9	,	,	PUNCT
ejpam-6497	174	10	of	of	ADP
ejpam-6497	174	11	closed	closed	ADJ
ejpam-6497	174	12	subsets	subset	NOUN
ejpam-6497	174	13	:	:	PUNCT
ejpam-6497	174	14	∩β∈γ(kβ	∩β∈γ(kβ	NUM
ejpam-6497	174	15	)	)	PUNCT
ejpam-6497	174	16	is	be	AUX
ejpam-6497	174	17	empty	empty	ADJ
ejpam-6497	174	18	,	,	PUNCT
ejpam-6497	174	19	there	there	PRON
ejpam-6497	174	20	exists	exist	VERB
ejpam-6497	174	21	{	{	PUNCT
ejpam-6497	174	22	α1	α1	PROPN
ejpam-6497	174	23	,	,	PUNCT
ejpam-6497	174	24	α2	α2	ADJ
ejpam-6497	174	25	,	,	PUNCT
ejpam-6497	174	26	.	.	PUNCT
ejpam-6497	174	27	.	.	PUNCT
ejpam-6497	174	28	.	.	PUNCT
ejpam-6497	175	1	}	}	PUNCT
ejpam-6497	175	2	a	a	DET
ejpam-6497	175	3	countable	countable	ADJ
ejpam-6497	175	4	subset	subset	NOUN
ejpam-6497	175	5	such	such	ADJ
ejpam-6497	175	6	that	that	DET
ejpam-6497	175	7	int	int	NOUN
ejpam-6497	175	8	(	(	PUNCT
ejpam-6497	175	9	∩n∈n	∩n∈n	NOUN
ejpam-6497	175	10	(	(	PUNCT
ejpam-6497	175	11	kβn	kβn	PROPN
ejpam-6497	175	12	)	)	PUNCT
ejpam-6497	175	13	)	)	PUNCT
ejpam-6497	175	14	is	be	AUX
ejpam-6497	175	15	empty	empty	ADJ
ejpam-6497	175	16	.	.	PUNCT
ejpam-6497	176	1	proof	proof	NOUN
ejpam-6497	176	2	.	.	PUNCT
ejpam-6497	177	1	let	let	VERB
ejpam-6497	177	2	k	k	NOUN
ejpam-6497	177	3	∼	∼	VERB
ejpam-6497	177	4	=	=	PUNCT
ejpam-6497	177	5	{	{	PUNCT
ejpam-6497	177	6	kβ	kβ	INTJ
ejpam-6497	177	7	:	:	PUNCT
ejpam-6497	177	8	β	β	X
ejpam-6497	177	9	∈	∈	PROPN
ejpam-6497	177	10	γ	γ	NOUN
ejpam-6497	177	11	}	}	PUNCT
ejpam-6497	177	12	consists	consist	VERB
ejpam-6497	177	13	of	of	ADP
ejpam-6497	177	14	closed	closed	ADJ
ejpam-6497	177	15	subsets	subset	NOUN
ejpam-6497	177	16	of	of	ADP
ejpam-6497	177	17	x	x	X
ejpam-6497	177	18	modulo	modulo	PROPN
ejpam-6497	177	19	j	j	PROPN
ejpam-6497	177	20	:	:	PUNCT
ejpam-6497	177	21	∩β∈γ(kβ	∩β∈γ(kβ	NUM
ejpam-6497	177	22	)	)	PUNCT
ejpam-6497	177	23	.	.	PUNCT
ejpam-6497	178	1	now	now	ADV
ejpam-6497	178	2	,	,	PUNCT
ejpam-6497	178	3	x	x	SYM
ejpam-6497	178	4	=	=	SYM
ejpam-6497	178	5	∪β∈γ(x	∪β∈γ(x	NUM
ejpam-6497	178	6	\	\	NOUN
ejpam-6497	178	7	kβ	kβ	PROPN
ejpam-6497	178	8	)	)	PUNCT
ejpam-6497	178	9	,	,	PUNCT
ejpam-6497	178	10	there	there	PRON
ejpam-6497	178	11	exists	exist	VERB
ejpam-6497	178	12	{	{	PUNCT
ejpam-6497	178	13	α1	α1	PROPN
ejpam-6497	178	14	,	,	PUNCT
ejpam-6497	178	15	α2	α2	ADJ
ejpam-6497	178	16	,	,	PUNCT
ejpam-6497	178	17	.	.	PUNCT
ejpam-6497	178	18	.	.	PUNCT
ejpam-6497	178	19	.	.	PUNCT
ejpam-6497	179	1	}	}	PUNCT
ejpam-6497	179	2	a	a	DET
ejpam-6497	179	3	countable	countable	ADJ
ejpam-6497	179	4	subset	subset	NOUN
ejpam-6497	179	5	such	such	ADJ
ejpam-6497	179	6	that	that	SCONJ
ejpam-6497	179	7	x	x	SYM
ejpam-6497	179	8	=	=	SYM
ejpam-6497	179	9	cl(x	cl(x	X
ejpam-6497	179	10	\kβn	\kβn	NOUN
ejpam-6497	179	11	)	)	PUNCT
ejpam-6497	179	12	.	.	PUNCT
ejpam-6497	180	1	hence	hence	ADV
ejpam-6497	180	2	,	,	PUNCT
ejpam-6497	180	3	x	x	SYM
ejpam-6497	180	4	\	\	PROPN
ejpam-6497	180	5	cl(x	cl(x	X
ejpam-6497	180	6	\kβn	\kβn	PROPN
ejpam-6497	180	7	)	)	PUNCT
ejpam-6497	181	1	=	=	PUNCT
ejpam-6497	181	2	∅.	∅.	ADP
ejpam-6497	181	3	thus	thus	ADV
ejpam-6497	181	4	,	,	PUNCT
ejpam-6497	181	5	int	int	NOUN
ejpam-6497	181	6	(	(	PUNCT
ejpam-6497	181	7	x	x	SYM
ejpam-6497	181	8	\	\	PROPN
ejpam-6497	181	9	∪	∪	X
ejpam-6497	181	10	n∈n	n∈n	NOUN
ejpam-6497	181	11	(	(	PUNCT
ejpam-6497	181	12	x	x	X
ejpam-6497	181	13	\kβn	\kβn	PROPN
ejpam-6497	181	14	)	)	PUNCT
ejpam-6497	181	15	)	)	PUNCT
ejpam-6497	182	1	=	=	PUNCT
ejpam-6497	182	2	int	int	NOUN
ejpam-6497	182	3	(	(	PUNCT
ejpam-6497	182	4	∩	∩	ADJ
ejpam-6497	182	5	n∈n	n∈n	X
ejpam-6497	182	6	(	(	PUNCT
ejpam-6497	182	7	kβn	kβn	PROPN
ejpam-6497	182	8	)	)	PUNCT
ejpam-6497	182	9	)	)	PUNCT
ejpam-6497	182	10	,	,	PUNCT
ejpam-6497	182	11	is	be	AUX
ejpam-6497	182	12	empty	empty	ADJ
ejpam-6497	182	13	.	.	PUNCT
ejpam-6497	183	1	theorem	theorem	ADJ
ejpam-6497	183	2	7	7	NUM
ejpam-6497	183	3	.	.	X
ejpam-6497	184	1	there	there	PRON
ejpam-6497	184	2	is	be	VERB
ejpam-6497	184	3	a	a	DET
ejpam-6497	184	4	tychonoff	tychonoff	NOUN
ejpam-6497	184	5	weakly	weakly	ADJ
ejpam-6497	184	6	sl	sl	NOUN
ejpam-6497	184	7	modulo	modulo	X
ejpam-6497	185	1	j	j	PROPN
ejpam-6497	186	1	that	that	PRON
ejpam-6497	186	2	is	be	AUX
ejpam-6497	186	3	not	not	PART
ejpam-6497	186	4	almost	almost	ADV
ejpam-6497	186	5	lindelöf	lindelöf	NOUN
ejpam-6497	186	6	.	.	PUNCT
ejpam-6497	187	1	proof	proof	NOUN
ejpam-6497	187	2	.	.	PUNCT
ejpam-6497	188	1	if	if	SCONJ
ejpam-6497	188	2	y	y	PROPN
ejpam-6497	188	3	is	be	AUX
ejpam-6497	188	4	a	a	DET
ejpam-6497	188	5	discrete	discrete	ADJ
ejpam-6497	188	6	space	space	NOUN
ejpam-6497	188	7	modulo	modulo	NOUN
ejpam-6497	188	8	j	j	PROPN
ejpam-6497	188	9	:	:	PUNCT
ejpam-6497	188	10	|y|	|y|	PROPN
ejpam-6497	188	11	=	=	SYM
ejpam-6497	188	12	ω1	ω1	PROPN
ejpam-6497	188	13	,	,	PUNCT
ejpam-6497	188	14	x	x	SYM
ejpam-6497	188	15	=	=	PUNCT
ejpam-6497	188	16	(	(	PUNCT
ejpam-6497	188	17	βy	βy	PRON
ejpam-6497	188	18	×	×	NOUN
ejpam-6497	188	19	(	(	PUNCT
ejpam-6497	188	20	ω	ω	NOUN
ejpam-6497	188	21	+	+	NOUN
ejpam-6497	188	22	1	1	NUM
ejpam-6497	188	23	)	)	PUNCT
ejpam-6497	188	24	)	)	PUNCT
ejpam-6497	189	1	−	−	PROPN
ejpam-6497	189	2	(	(	PUNCT
ejpam-6497	189	3	(	(	PUNCT
ejpam-6497	189	4	βy	βy	PRON
ejpam-6497	189	5	\	\	X
ejpam-6497	189	6	y)×	y)×	NOUN
ejpam-6497	189	7	{	{	PUNCT
ejpam-6497	189	8	ω	ω	NOUN
ejpam-6497	189	9	}	}	PUNCT
ejpam-6497	189	10	)	)	PUNCT
ejpam-6497	189	11	,	,	PUNCT
ejpam-6497	189	12	is	be	AUX
ejpam-6497	189	13	a	a	DET
ejpam-6497	189	14	subspace	subspace	NOUN
ejpam-6497	189	15	of	of	ADP
ejpam-6497	189	16	βy×(ω+1	βy×(ω+1	NOUN
ejpam-6497	189	17	)	)	PUNCT
ejpam-6497	189	18	modulo	modulo	PROPN
ejpam-6497	189	19	j	j	PROPN
ejpam-6497	189	20	,	,	PUNCT
ejpam-6497	189	21	and	and	CCONJ
ejpam-6497	189	22	ü	ü	PRON
ejpam-6497	189	23	is	be	AUX
ejpam-6497	189	24	an	an	DET
ejpam-6497	189	25	open	open	ADJ
ejpam-6497	189	26	cover	cover	NOUN
ejpam-6497	189	27	of	of	ADP
ejpam-6497	189	28	x	x	SYM
ejpam-6497	189	29	modulo	modulo	PROPN
ejpam-6497	189	30	j	j	PROPN
ejpam-6497	189	31	.	.	PUNCT
ejpam-6497	190	1	βy×ω	βy×ω	PROPN
ejpam-6497	190	2	is	be	AUX
ejpam-6497	190	3	a	a	DET
ejpam-6497	190	4	σ	σ	ADJ
ejpam-6497	190	5	-	-	ADJ
ejpam-6497	190	6	compact	compact	ADJ
ejpam-6497	190	7	dense	dense	NOUN
ejpam-6497	190	8	in	in	ADP
ejpam-6497	190	9	x	x	PROPN
ejpam-6497	190	10	modulo	modulo	PROPN
ejpam-6497	190	11	j	j	PROPN
ejpam-6497	190	12	,	,	PUNCT
ejpam-6497	190	13	there	there	PRON
ejpam-6497	190	14	exists	exist	VERB
ejpam-6497	190	15	ŵ	ŵ	NUM
ejpam-6497	190	16	a	a	DET
ejpam-6497	190	17	countable	countable	ADJ
ejpam-6497	190	18	subset	subset	NOUN
ejpam-6497	190	19	of	of	ADP
ejpam-6497	190	20	ü	ü	NOUN
ejpam-6497	190	21	:	:	PUNCT
ejpam-6497	190	22	βy×ω	βy×ω	PROPN
ejpam-6497	190	23	⊂	⊂	PROPN
ejpam-6497	190	24	∪ŵ	∪ŵ	VERB
ejpam-6497	190	25	.	.	PUNCT
ejpam-6497	191	1	e.	e.	PROPN
ejpam-6497	191	2	almuhur	almuhur	PROPN
ejpam-6497	191	3	et	et	PROPN
ejpam-6497	191	4	al	al	PROPN
ejpam-6497	191	5	.	.	PUNCT
ejpam-6497	191	6	/	/	SYM
ejpam-6497	191	7	eur	eur	PROPN
ejpam-6497	191	8	.	.	PUNCT
ejpam-6497	192	1	j.	j.	PROPN
ejpam-6497	192	2	pure	pure	PROPN
ejpam-6497	192	3	appl	appl	PROPN
ejpam-6497	192	4	.	.	PROPN
ejpam-6497	192	5	math	math	PROPN
ejpam-6497	192	6	,	,	PUNCT
ejpam-6497	192	7	18	18	NUM
ejpam-6497	192	8	(	(	PUNCT
ejpam-6497	192	9	3	3	NUM
ejpam-6497	192	10	)	)	PUNCT
ejpam-6497	192	11	(	(	PUNCT
ejpam-6497	192	12	2025	2025	NUM
ejpam-6497	192	13	)	)	PUNCT
ejpam-6497	192	14	,	,	PUNCT
ejpam-6497	192	15	6497	6497	NUM
ejpam-6497	192	16	8	8	NUM
ejpam-6497	192	17	of	of	ADP
ejpam-6497	192	18	11	11	NUM
ejpam-6497	192	19	hence	hence	ADV
ejpam-6497	192	20	,	,	PUNCT
ejpam-6497	192	21	x	x	PUNCT
ejpam-6497	192	22	=	=	PRON
ejpam-6497	192	23	∪ŵ	∪ŵ	NOUN
ejpam-6497	193	1	and	and	CCONJ
ejpam-6497	193	2	so	so	ADV
ejpam-6497	193	3	x	x	PRON
ejpam-6497	193	4	is	be	AUX
ejpam-6497	193	5	a	a	DET
ejpam-6497	193	6	weakly	weakly	ADJ
ejpam-6497	193	7	sl	sl	NOUN
ejpam-6497	193	8	modulo	modulo	NOUN
ejpam-6497	193	9	j	j	PROPN
ejpam-6497	193	10	.	.	PUNCT
ejpam-6497	194	1	since	since	SCONJ
ejpam-6497	194	2	|y|	|y|	PROPN
ejpam-6497	194	3	=	=	SYM
ejpam-6497	194	4	ω1	ω1	PROPN
ejpam-6497	194	5	,	,	PUNCT
ejpam-6497	194	6	y	y	PROPN
ejpam-6497	194	7	can	can	AUX
ejpam-6497	194	8	be	be	AUX
ejpam-6497	194	9	enumerated	enumerate	VERB
ejpam-6497	194	10	by	by	ADP
ejpam-6497	194	11	{	{	PUNCT
ejpam-6497	194	12	yγ	yγ	INTJ
ejpam-6497	194	13	:	:	PUNCT
ejpam-6497	194	14	γ	γ	PROPN
ejpam-6497	194	15	<	<	X
ejpam-6497	194	16	ω1	ω1	PROPN
ejpam-6497	194	17	}	}	PUNCT
ejpam-6497	194	18	and	and	CCONJ
ejpam-6497	194	19	for	for	ADP
ejpam-6497	194	20	every	every	DET
ejpam-6497	194	21	n	n	PRON
ejpam-6497	194	22	∈	∈	PROPN
ejpam-6497	194	23	ω	ω	PROPN
ejpam-6497	194	24	.	.	PUNCT
ejpam-6497	195	1	let	let	VERB
ejpam-6497	195	2	uγ	uγ	ADV
ejpam-6497	195	3	=	=	PUNCT
ejpam-6497	195	4	{	{	PUNCT
ejpam-6497	195	5	yγ	yγ	PROPN
ejpam-6497	195	6	}	}	PUNCT
ejpam-6497	195	7	×	×	NOUN
ejpam-6497	195	8	(	(	PUNCT
ejpam-6497	195	9	ω	ω	NOUN
ejpam-6497	195	10	+	+	NOUN
ejpam-6497	195	11	1	1	NUM
ejpam-6497	195	12	)	)	PUNCT
ejpam-6497	195	13	and	and	CCONJ
ejpam-6497	196	1	wn	wn	NOUN
ejpam-6497	196	2	=	=	NOUN
ejpam-6497	196	3	βy	βy	PROPN
ejpam-6497	196	4	×	×	NOUN
ejpam-6497	196	5	{	{	PUNCT
ejpam-6497	196	6	n	n	CCONJ
ejpam-6497	196	7	}	}	PUNCT
ejpam-6497	196	8	.	.	PUNCT
ejpam-6497	197	1	if	if	SCONJ
ejpam-6497	197	2	ü	ü	PRON
ejpam-6497	197	3	=	=	PRON
ejpam-6497	197	4	{	{	PUNCT
ejpam-6497	197	5	uγ	uγ	ADV
ejpam-6497	197	6	:	:	PUNCT
ejpam-6497	197	7	γ	γ	X
ejpam-6497	197	8	<	<	X
ejpam-6497	197	9	ω1	ω1	PROPN
ejpam-6497	197	10	}	}	PUNCT
ejpam-6497	197	11	∪	∪	NOUN
ejpam-6497	197	12	{	{	PUNCT
ejpam-6497	197	13	wn	wn	NOUN
ejpam-6497	197	14	:	:	PUNCT
ejpam-6497	197	15	n	n	PROPN
ejpam-6497	197	16	∈	∈	PROPN
ejpam-6497	197	17	ω	ω	PROPN
ejpam-6497	197	18	}	}	PUNCT
ejpam-6497	197	19	,	,	PUNCT
ejpam-6497	197	20	then	then	ADV
ejpam-6497	197	21	∪ŵ	∪ŵ	VERB
ejpam-6497	197	22	=	=	SYM
ejpam-6497	197	23	∪	∪	X
ejpam-6497	197	24	{	{	PUNCT
ejpam-6497	197	25	w	w	NOUN
ejpam-6497	197	26	:	:	PUNCT
ejpam-6497	197	27	w	w	PROPN
ejpam-6497	197	28	∈	∈	NOUN
ejpam-6497	197	29	ŵ	ŵ	X
ejpam-6497	197	30	}	}	PUNCT
ejpam-6497	197	31	.	.	PUNCT
ejpam-6497	198	1	if	if	SCONJ
ejpam-6497	198	2	γ	γ	X
ejpam-6497	198	3	◦	◦	NOUN
ejpam-6497	198	4	=	=	SYM
ejpam-6497	198	5	sup	sup	NOUN
ejpam-6497	198	6	{	{	PUNCT
ejpam-6497	198	7	γ	γ	NOUN
ejpam-6497	198	8	:	:	PUNCT
ejpam-6497	198	9	uγ	uγ	PROPN
ejpam-6497	198	10	∈	∈	PROPN
ejpam-6497	198	11	ŵ	ŵ	X
ejpam-6497	198	12	}	}	PUNCT
ejpam-6497	198	13	,	,	PUNCT
ejpam-6497	198	14	then	then	ADV
ejpam-6497	198	15	γ	γ	X
ejpam-6497	198	16	◦	◦	NOUN
ejpam-6497	198	17	<	<	X
ejpam-6497	198	18	ω1	ω1	PROPN
ejpam-6497	198	19	because	because	SCONJ
ejpam-6497	198	20	ŵ	ŵ	PROPN
ejpam-6497	198	21	is	be	AUX
ejpam-6497	198	22	countable	countable	ADJ
ejpam-6497	198	23	.	.	PUNCT
ejpam-6497	199	1	considering	consider	VERB
ejpam-6497	199	2	γ′	γ′	PROPN
ejpam-6497	199	3	>	>	X
ejpam-6497	199	4	γ	γ	PROPN
ejpam-6497	199	5	◦	◦	NOUN
ejpam-6497	199	6	,	,	PUNCT
ejpam-6497	199	7	then	then	ADV
ejpam-6497	199	8	(	(	PUNCT
ejpam-6497	199	9	yγ′	yγ′	PROPN
ejpam-6497	199	10	,	,	PUNCT
ejpam-6497	199	11	ω	ω	PROPN
ejpam-6497	199	12	)	)	PUNCT
ejpam-6497	199	13	/∈	/∈	PUNCT
ejpam-6497	200	1	{	{	PUNCT
ejpam-6497	200	2	w	w	NOUN
ejpam-6497	200	3	:	:	PUNCT
ejpam-6497	200	4	w	w	PROPN
ejpam-6497	200	5	∈	∈	PROPN
ejpam-6497	200	6	ŵ	ŵ	X
ejpam-6497	200	7	}	}	PUNCT
ejpam-6497	200	8	.	.	PUNCT
ejpam-6497	201	1	but	but	CCONJ
ejpam-6497	201	2	(	(	PUNCT
ejpam-6497	201	3	yγ′	yγ′	INTJ
ejpam-6497	201	4	,	,	PUNCT
ejpam-6497	201	5	ω	ω	NUM
ejpam-6497	201	6	)	)	PUNCT
ejpam-6497	201	7	∈	∈	PROPN
ejpam-6497	201	8	uγ′	uγ′	VERB
ejpam-6497	202	1	⊂	⊂	X
ejpam-6497	202	2	ü	ü	X
ejpam-6497	202	3	,	,	PUNCT
ejpam-6497	202	4	hence	hence	ADV
ejpam-6497	202	5	x	x	PUNCT
ejpam-6497	202	6	is	be	AUX
ejpam-6497	202	7	not	not	PART
ejpam-6497	202	8	an	an	DET
ejpam-6497	202	9	almost	almost	ADV
ejpam-6497	202	10	sl	sl	VERB
ejpam-6497	202	11	modulo	modulo	PROPN
ejpam-6497	202	12	j	j	PROPN
ejpam-6497	202	13	.	.	PUNCT
ejpam-6497	203	1	theorem	theorem	VERB
ejpam-6497	203	2	8	8	NUM
ejpam-6497	203	3	.	.	PUNCT
ejpam-6497	204	1	for	for	ADP
ejpam-6497	204	2	each	each	DET
ejpam-6497	204	3	infinite	infinite	ADJ
ejpam-6497	204	4	cardinal	cardinal	ADJ
ejpam-6497	204	5	κ	κ	NOUN
ejpam-6497	204	6	,	,	PUNCT
ejpam-6497	204	7	there	there	PRON
ejpam-6497	204	8	is	be	VERB
ejpam-6497	204	9	a	a	DET
ejpam-6497	204	10	tychonoff	tychonoff	NOUN
ejpam-6497	204	11	weakly	weakly	ADJ
ejpam-6497	204	12	sl	sl	NOUN
ejpam-6497	204	13	,	,	PUNCT
ejpam-6497	204	14	x	x	PROPN
ejpam-6497	204	15	modulo	modulo	PROPN
ejpam-6497	204	16	j	j	NOUN
ejpam-6497	204	17	with	with	ADP
ejpam-6497	204	18	e(x	e(x	NUM
ejpam-6497	204	19	)	)	PUNCT
ejpam-6497	204	20	>	>	X
ejpam-6497	205	1	κ	κ	X
ejpam-6497	205	2	.	.	PUNCT
ejpam-6497	206	1	although	although	SCONJ
ejpam-6497	206	2	there	there	PRON
ejpam-6497	206	3	are	be	VERB
ejpam-6497	206	4	other	other	ADJ
ejpam-6497	206	5	methods	method	NOUN
ejpam-6497	206	6	for	for	ADP
ejpam-6497	206	7	defining	define	VERB
ejpam-6497	206	8	nearly	nearly	ADV
ejpam-6497	206	9	lindelöf	lindelöf	NOUN
ejpam-6497	206	10	ideal	ideal	ADJ
ejpam-6497	206	11	spaces	space	NOUN
ejpam-6497	206	12	,	,	PUNCT
ejpam-6497	206	13	weakening	weaken	VERB
ejpam-6497	206	14	the	the	DET
ejpam-6497	206	15	lindelöf	lindelöf	NOUN
ejpam-6497	206	16	condition	condition	NOUN
ejpam-6497	206	17	is	be	AUX
ejpam-6497	206	18	a	a	DET
ejpam-6497	206	19	popular	popular	ADJ
ejpam-6497	206	20	strategy	strategy	NOUN
ejpam-6497	206	21	.	.	PUNCT
ejpam-6497	207	1	the	the	DET
ejpam-6497	207	2	following	follow	VERB
ejpam-6497	207	3	are	be	AUX
ejpam-6497	207	4	two	two	NUM
ejpam-6497	207	5	common	common	ADJ
ejpam-6497	207	6	definitions	definition	NOUN
ejpam-6497	207	7	.	.	PUNCT
ejpam-6497	208	1	i	i	PRON
ejpam-6497	208	2	)	)	PUNCT
ejpam-6497	208	3	dense	dense	ADJ
ejpam-6497	208	4	subsets	subset	NOUN
ejpam-6497	208	5	definition	definition	NOUN
ejpam-6497	208	6	:	:	PUNCT
ejpam-6497	208	7	the	the	DET
ejpam-6497	208	8	ideal	ideal	ADJ
ejpam-6497	208	9	space	space	NOUN
ejpam-6497	208	10	x	x	PUNCT
ejpam-6497	208	11	is	be	AUX
ejpam-6497	208	12	nearly	nearly	ADV
ejpam-6497	208	13	lindelöf	lindelöf	NOUN
ejpam-6497	208	14	if	if	SCONJ
ejpam-6497	208	15	,	,	PUNCT
ejpam-6497	208	16	for	for	ADP
ejpam-6497	208	17	each	each	DET
ejpam-6497	208	18	open	open	ADJ
ejpam-6497	208	19	cover	cover	NOUN
ejpam-6497	208	20	û	û	NUM
ejpam-6497	208	21	of	of	ADP
ejpam-6497	208	22	x	x	SYM
ejpam-6497	208	23	modulo	modulo	PROPN
ejpam-6497	208	24	j	j	PROPN
ejpam-6497	208	25	,	,	PUNCT
ejpam-6497	208	26	there	there	PRON
ejpam-6497	208	27	is	be	VERB
ejpam-6497	208	28	a	a	DET
ejpam-6497	208	29	dense	dense	ADJ
ejpam-6497	208	30	subset	subset	NOUN
ejpam-6497	209	1	d	d	NOUN
ejpam-6497	209	2	⊆	⊆	NUM
ejpam-6497	209	3	x	x	SYM
ejpam-6497	209	4	such	such	ADJ
ejpam-6497	209	5	that	that	SCONJ
ejpam-6497	209	6	a	a	DET
ejpam-6497	209	7	countable	countable	ADJ
ejpam-6497	209	8	subcollection	subcollection	NOUN
ejpam-6497	209	9	of	of	ADP
ejpam-6497	209	10	û	û	NUM
ejpam-6497	209	11	may	may	AUX
ejpam-6497	209	12	cover	cover	VERB
ejpam-6497	209	13	d.	d.	PROPN
ejpam-6497	209	14	ii	ii	PROPN
ejpam-6497	209	15	)	)	PUNCT
ejpam-6497	209	16	definition	definition	NOUN
ejpam-6497	209	17	via	via	ADP
ejpam-6497	209	18	nearly	nearly	ADV
ejpam-6497	209	19	covers	cover	VERB
ejpam-6497	209	20	:	:	PUNCT
ejpam-6497	209	21	if	if	SCONJ
ejpam-6497	209	22	there	there	PRON
ejpam-6497	209	23	exists	exist	VERB
ejpam-6497	209	24	a	a	DET
ejpam-6497	209	25	countable	countable	ADJ
ejpam-6497	209	26	subcollection	subcollection	NOUN
ejpam-6497	209	27	õ	õ	VERB
ejpam-6497	209	28	⊆	⊆	NUM
ejpam-6497	209	29	û	û	NUM
ejpam-6497	209	30	where	where	SCONJ
ejpam-6497	209	31	the	the	DET
ejpam-6497	209	32	union	union	NOUN
ejpam-6497	209	33	of	of	ADP
ejpam-6497	209	34	the	the	DET
ejpam-6497	209	35	sets	set	NOUN
ejpam-6497	209	36	in	in	ADP
ejpam-6497	209	37	õ	õ	PROPN
ejpam-6497	209	38	is	be	AUX
ejpam-6497	209	39	dense	dense	ADJ
ejpam-6497	209	40	in	in	ADP
ejpam-6497	209	41	x	x	PROPN
ejpam-6497	209	42	modulo	modulo	PROPN
ejpam-6497	209	43	j	j	PROPN
ejpam-6497	209	44	for	for	ADP
ejpam-6497	209	45	each	each	DET
ejpam-6497	209	46	open	open	ADJ
ejpam-6497	209	47	cover	cover	NOUN
ejpam-6497	209	48	û	û	NUM
ejpam-6497	209	49	of	of	ADP
ejpam-6497	209	50	x	x	PRON
ejpam-6497	209	51	,	,	PUNCT
ejpam-6497	209	52	then	then	ADV
ejpam-6497	209	53	the	the	DET
ejpam-6497	209	54	topological	topological	ADJ
ejpam-6497	209	55	space	space	NOUN
ejpam-6497	209	56	x	x	PUNCT
ejpam-6497	209	57	is	be	AUX
ejpam-6497	209	58	nearly	nearly	ADV
ejpam-6497	209	59	sl	sl	ADP
ejpam-6497	209	60	modulo	modulo	PROPN
ejpam-6497	209	61	j	j	PROPN
ejpam-6497	209	62	.	.	PUNCT
ejpam-6497	210	1	since	since	SCONJ
ejpam-6497	210	2	any	any	DET
ejpam-6497	210	3	open	open	ADJ
ejpam-6497	210	4	cover	cover	NOUN
ejpam-6497	210	5	has	have	VERB
ejpam-6497	210	6	a	a	DET
ejpam-6497	210	7	countable	countable	ADJ
ejpam-6497	210	8	subcover	subcover	NOUN
ejpam-6497	210	9	if	if	SCONJ
ejpam-6497	210	10	x	x	PRON
ejpam-6497	210	11	is	be	AUX
ejpam-6497	210	12	lindelöf	lindelöf	NOUN
ejpam-6497	210	13	ideal	ideal	ADJ
ejpam-6497	210	14	space	space	NOUN
ejpam-6497	210	15	,	,	PUNCT
ejpam-6497	210	16	this	this	PRON
ejpam-6497	210	17	trivially	trivially	ADV
ejpam-6497	210	18	satisfies	satisfy	VERB
ejpam-6497	210	19	the	the	DET
ejpam-6497	210	20	nearly	nearly	ADJ
ejpam-6497	210	21	lindelöf	lindelöf	NOUN
ejpam-6497	210	22	condition	condition	NOUN
ejpam-6497	210	23	,	,	PUNCT
ejpam-6497	210	24	making	make	VERB
ejpam-6497	210	25	any	any	DET
ejpam-6497	210	26	lindelöf	lindelöf	NOUN
ejpam-6497	210	27	ideal	ideal	ADJ
ejpam-6497	210	28	space	space	NOUN
ejpam-6497	210	29	nearly	nearly	ADV
ejpam-6497	210	30	lindelöf	lindelöf	PUNCT
ejpam-6497	210	31	[	[	X
ejpam-6497	210	32	15	15	NUM
ejpam-6497	210	33	]	]	PUNCT
ejpam-6497	210	34	.	.	PUNCT
ejpam-6497	211	1	according	accord	VERB
ejpam-6497	211	2	to	to	ADP
ejpam-6497	211	3	some	some	DET
ejpam-6497	211	4	definitions	definition	NOUN
ejpam-6497	211	5	,	,	PUNCT
ejpam-6497	211	6	any	any	DET
ejpam-6497	211	7	ideal	ideal	ADJ
ejpam-6497	211	8	space	space	NOUN
ejpam-6497	211	9	that	that	PRON
ejpam-6497	211	10	has	have	VERB
ejpam-6497	211	11	a	a	DET
ejpam-6497	211	12	countable	countable	ADJ
ejpam-6497	211	13	dense	dense	ADJ
ejpam-6497	211	14	subset	subset	NOUN
ejpam-6497	211	15	—	—	PUNCT
ejpam-6497	211	16	such	such	ADJ
ejpam-6497	211	17	as	as	ADP
ejpam-6497	211	18	separable	separable	ADJ
ejpam-6497	211	19	spaces	space	NOUN
ejpam-6497	211	20	—	—	PUNCT
ejpam-6497	211	21	is	be	AUX
ejpam-6497	211	22	nearly	nearly	ADV
ejpam-6497	211	23	lindelöf	lindelöf	NOUN
ejpam-6497	211	24	because	because	SCONJ
ejpam-6497	211	25	the	the	DET
ejpam-6497	211	26	dense	dense	ADJ
ejpam-6497	211	27	subset	subset	NOUN
ejpam-6497	211	28	is	be	AUX
ejpam-6497	211	29	frequently	frequently	ADV
ejpam-6497	211	30	covered	cover	VERB
ejpam-6497	211	31	by	by	ADP
ejpam-6497	211	32	a	a	DET
ejpam-6497	211	33	countable	countable	ADJ
ejpam-6497	211	34	subcollection	subcollection	NOUN
ejpam-6497	211	35	of	of	ADP
ejpam-6497	211	36	any	any	DET
ejpam-6497	211	37	open	open	ADJ
ejpam-6497	211	38	cover	cover	NOUN
ejpam-6497	211	39	.	.	PUNCT
ejpam-6497	212	1	furthermore	furthermore	ADV
ejpam-6497	212	2	,	,	PUNCT
ejpam-6497	212	3	if	if	SCONJ
ejpam-6497	212	4	and	and	CCONJ
ejpam-6497	212	5	only	only	ADV
ejpam-6497	212	6	if	if	SCONJ
ejpam-6497	212	7	a	a	DET
ejpam-6497	212	8	discrete	discrete	ADJ
ejpam-6497	212	9	ideal	ideal	ADJ
ejpam-6497	212	10	space	space	NOUN
ejpam-6497	212	11	is	be	AUX
ejpam-6497	212	12	countable	countable	ADJ
ejpam-6497	212	13	,	,	PUNCT
ejpam-6497	212	14	it	it	PRON
ejpam-6497	212	15	is	be	AUX
ejpam-6497	212	16	lindelöf	lindelöf	NOUN
ejpam-6497	212	17	.	.	PUNCT
ejpam-6497	213	1	depending	depend	VERB
ejpam-6497	213	2	on	on	ADP
ejpam-6497	213	3	the	the	DET
ejpam-6497	213	4	definition	definition	NOUN
ejpam-6497	213	5	,	,	PUNCT
ejpam-6497	213	6	anything	anything	PRON
ejpam-6497	213	7	that	that	PRON
ejpam-6497	213	8	is	be	AUX
ejpam-6497	213	9	uncountable	uncountable	ADJ
ejpam-6497	213	10	may	may	AUX
ejpam-6497	213	11	nevertheless	nevertheless	ADV
ejpam-6497	213	12	meet	meet	VERB
ejpam-6497	213	13	certain	certain	ADJ
ejpam-6497	213	14	weakened	weakened	ADJ
ejpam-6497	213	15	kinds	kind	NOUN
ejpam-6497	213	16	of	of	ADP
ejpam-6497	213	17	lindelöfness	lindelöfness	NOUN
ejpam-6497	213	18	even	even	ADV
ejpam-6497	213	19	though	though	SCONJ
ejpam-6497	213	20	it	it	PRON
ejpam-6497	213	21	is	be	AUX
ejpam-6497	213	22	not	not	PART
ejpam-6497	213	23	lindelöf	lindelöf	PUNCT
ejpam-6497	214	1	[	[	X
ejpam-6497	214	2	16	16	NUM
ejpam-6497	214	3	]	]	PUNCT
ejpam-6497	214	4	.	.	PUNCT
ejpam-6497	215	1	the	the	DET
ejpam-6497	215	2	study	study	NOUN
ejpam-6497	215	3	of	of	ADP
ejpam-6497	215	4	covering	cover	VERB
ejpam-6497	215	5	qualities	quality	NOUN
ejpam-6497	215	6	and	and	CCONJ
ejpam-6497	215	7	their	their	PRON
ejpam-6497	215	8	generalizations	generalization	NOUN
ejpam-6497	215	9	in	in	ADP
ejpam-6497	215	10	general	general	ADJ
ejpam-6497	215	11	topology	topology	NOUN
ejpam-6497	215	12	inevitably	inevitably	ADV
ejpam-6497	215	13	leads	lead	VERB
ejpam-6497	215	14	to	to	ADP
ejpam-6497	215	15	the	the	DET
ejpam-6497	215	16	emergence	emergence	NOUN
ejpam-6497	215	17	of	of	ADP
ejpam-6497	215	18	nearly	nearly	ADV
ejpam-6497	215	19	lindelöf	lindelöf	NOUN
ejpam-6497	215	20	ideal	ideal	ADJ
ejpam-6497	215	21	spaces	space	VERB
ejpam-6497	215	22	.	.	PUNCT
ejpam-6497	216	1	they	they	PRON
ejpam-6497	216	2	are	be	AUX
ejpam-6497	216	3	especially	especially	ADV
ejpam-6497	216	4	helpful	helpful	ADJ
ejpam-6497	216	5	in	in	ADP
ejpam-6497	216	6	situations	situation	NOUN
ejpam-6497	216	7	when	when	SCONJ
ejpam-6497	216	8	density	density	NOUN
ejpam-6497	216	9	-	-	PUNCT
ejpam-6497	216	10	based	base	VERB
ejpam-6497	216	11	covering	covering	NOUN
ejpam-6497	216	12	or	or	CCONJ
ejpam-6497	216	13	a	a	DET
ejpam-6497	216	14	weaker	weak	ADJ
ejpam-6497	216	15	type	type	NOUN
ejpam-6497	216	16	of	of	ADP
ejpam-6497	216	17	countability	countability	NOUN
ejpam-6497	216	18	is	be	AUX
ejpam-6497	216	19	still	still	ADV
ejpam-6497	216	20	preferred	preferred	ADJ
ejpam-6497	216	21	but	but	CCONJ
ejpam-6497	216	22	lindelöfness	lindelöfness	X
ejpam-6497	216	23	is	be	AUX
ejpam-6497	216	24	an	an	DET
ejpam-6497	216	25	excessively	excessively	ADV
ejpam-6497	216	26	strong	strong	ADJ
ejpam-6497	216	27	condition	condition	NOUN
ejpam-6497	217	1	[	[	X
ejpam-6497	217	2	17	17	NUM
ejpam-6497	217	3	,	,	PUNCT
ejpam-6497	217	4	18	18	NUM
ejpam-6497	217	5	]	]	PUNCT
ejpam-6497	217	6	.	.	PUNCT
ejpam-6497	218	1	e.	e.	PROPN
ejpam-6497	218	2	almuhur	almuhur	PROPN
ejpam-6497	218	3	et	et	PROPN
ejpam-6497	218	4	al	al	PROPN
ejpam-6497	218	5	.	.	PUNCT
ejpam-6497	218	6	/	/	SYM
ejpam-6497	218	7	eur	eur	PROPN
ejpam-6497	218	8	.	.	PUNCT
ejpam-6497	219	1	j.	j.	PROPN
ejpam-6497	219	2	pure	pure	PROPN
ejpam-6497	219	3	appl	appl	PROPN
ejpam-6497	219	4	.	.	PROPN
ejpam-6497	219	5	math	math	PROPN
ejpam-6497	219	6	,	,	PUNCT
ejpam-6497	219	7	18	18	NUM
ejpam-6497	219	8	(	(	PUNCT
ejpam-6497	219	9	3	3	NUM
ejpam-6497	219	10	)	)	PUNCT
ejpam-6497	219	11	(	(	PUNCT
ejpam-6497	219	12	2025	2025	NUM
ejpam-6497	219	13	)	)	PUNCT
ejpam-6497	219	14	,	,	PUNCT
ejpam-6497	219	15	6497	6497	NUM
ejpam-6497	219	16	9	9	NUM
ejpam-6497	219	17	of	of	ADP
ejpam-6497	219	18	11	11	NUM
ejpam-6497	219	19	applications	application	NOUN
ejpam-6497	219	20	i	i	NOUN
ejpam-6497	219	21	)	)	PUNCT
ejpam-6497	219	22	functional	functional	ADJ
ejpam-6497	219	23	analysis	analysis	NOUN
ejpam-6497	219	24	:	:	PUNCT
ejpam-6497	219	25	the	the	DET
ejpam-6497	219	26	study	study	NOUN
ejpam-6497	219	27	of	of	ADP
ejpam-6497	219	28	function	function	NOUN
ejpam-6497	219	29	spaces	space	NOUN
ejpam-6497	219	30	and	and	CCONJ
ejpam-6497	219	31	their	their	PRON
ejpam-6497	219	32	topological	topological	ADJ
ejpam-6497	219	33	characteristics	characteristic	NOUN
ejpam-6497	219	34	involves	involve	VERB
ejpam-6497	219	35	the	the	DET
ejpam-6497	219	36	use	use	NOUN
ejpam-6497	219	37	of	of	ADP
ejpam-6497	219	38	nearly	nearly	ADV
ejpam-6497	219	39	l	l	NOUN
ejpam-6497	219	40	-	-	PUNCT
ejpam-6497	219	41	closed	closed	ADJ
ejpam-6497	219	42	ideal	ideal	ADJ
ejpam-6497	219	43	sls	sls	PROPN
ejpam-6497	219	44	.	.	PROPN
ejpam-6497	219	45	ii	ii	PROPN
ejpam-6497	219	46	)	)	PUNCT
ejpam-6497	219	47	set	set	NOUN
ejpam-6497	219	48	-	-	PUNCT
ejpam-6497	219	49	theoretic	theoretic	NOUN
ejpam-6497	219	50	topology	topology	NOUN
ejpam-6497	219	51	:	:	PUNCT
ejpam-6497	219	52	cardinal	cardinal	ADJ
ejpam-6497	219	53	invariants	invariant	NOUN
ejpam-6497	219	54	and	and	CCONJ
ejpam-6497	219	55	combinatorial	combinatorial	ADJ
ejpam-6497	219	56	principles	principle	NOUN
ejpam-6497	219	57	are	be	AUX
ejpam-6497	219	58	examined	examine	VERB
ejpam-6497	219	59	in	in	ADP
ejpam-6497	219	60	relation	relation	NOUN
ejpam-6497	219	61	to	to	ADP
ejpam-6497	219	62	these	these	DET
ejpam-6497	219	63	spaces	space	NOUN
ejpam-6497	219	64	.	.	PUNCT
ejpam-6497	220	1	iii	iii	X
ejpam-6497	220	2	)	)	PUNCT
ejpam-6497	220	3	generalized	generalize	VERB
ejpam-6497	220	4	metric	metric	ADJ
ejpam-6497	220	5	spaces	space	NOUN
ejpam-6497	220	6	:	:	PUNCT
ejpam-6497	220	7	nearly	nearly	ADV
ejpam-6497	220	8	lindelöf	lindelöf	NOUN
ejpam-6497	220	9	ideal	ideal	ADJ
ejpam-6497	220	10	spaces	space	NOUN
ejpam-6497	220	11	serve	serve	VERB
ejpam-6497	220	12	as	as	ADP
ejpam-6497	220	13	a	a	DET
ejpam-6497	220	14	link	link	NOUN
ejpam-6497	220	15	between	between	ADP
ejpam-6497	220	16	more	more	ADV
ejpam-6497	220	17	generic	generic	ADJ
ejpam-6497	220	18	ideal	ideal	ADJ
ejpam-6497	220	19	topological	topological	ADJ
ejpam-6497	220	20	spaces	space	NOUN
ejpam-6497	220	21	and	and	CCONJ
ejpam-6497	220	22	metric	metric	ADJ
ejpam-6497	220	23	-	-	PUNCT
ejpam-6497	220	24	like	like	ADJ
ejpam-6497	220	25	spaces	space	NOUN
ejpam-6497	220	26	.	.	PUNCT
ejpam-6497	221	1	theorem	theorem	NOUN
ejpam-6497	221	2	9	9	NUM
ejpam-6497	221	3	.	.	PUNCT
ejpam-6497	222	1	if	if	SCONJ
ejpam-6497	222	2	x	x	PRON
ejpam-6497	222	3	is	be	AUX
ejpam-6497	222	4	lindelöf	lindelöf	NOUN
ejpam-6497	222	5	ideal	ideal	ADJ
ejpam-6497	222	6	and	and	CCONJ
ejpam-6497	222	7	a	a	DET
ejpam-6497	222	8	⊆	⊆	NUM
ejpam-6497	222	9	x	x	SYM
ejpam-6497	222	10	,	,	PUNCT
ejpam-6497	222	11	then	then	ADV
ejpam-6497	222	12	the	the	DET
ejpam-6497	222	13	following	following	NOUN
ejpam-6497	222	14	are	be	AUX
ejpam-6497	222	15	equivalent	equivalent	ADJ
ejpam-6497	222	16	:	:	PUNCT
ejpam-6497	222	17	a	a	X
ejpam-6497	222	18	)	)	PUNCT
ejpam-6497	222	19	a	a	PRON
ejpam-6497	222	20	is	be	AUX
ejpam-6497	222	21	an	an	DET
ejpam-6497	222	22	almost	almost	ADV
ejpam-6497	222	23	lindelöf	lindelöf	NOUN
ejpam-6497	222	24	subset	subset	VERB
ejpam-6497	222	25	modulo	modulo	PROPN
ejpam-6497	222	26	j	j	PROPN
ejpam-6497	222	27	.	.	PUNCT
ejpam-6497	223	1	b	b	X
ejpam-6497	223	2	)	)	PUNCT
ejpam-6497	223	3	a	a	PRON
ejpam-6497	223	4	is	be	AUX
ejpam-6497	223	5	weakly	weakly	ADJ
ejpam-6497	223	6	lindelöf	lindelöf	NOUN
ejpam-6497	223	7	subset	subset	VERB
ejpam-6497	223	8	modulo	modulo	PROPN
ejpam-6497	223	9	j	j	PROPN
ejpam-6497	223	10	.	.	PUNCT
ejpam-6497	224	1	proof	proof	NOUN
ejpam-6497	224	2	.	.	PUNCT
ejpam-6497	225	1	(	(	PUNCT
ejpam-6497	225	2	a	a	DET
ejpam-6497	225	3	⇒	⇒	NOUN
ejpam-6497	225	4	b	b	X
ejpam-6497	225	5	)	)	PUNCT
ejpam-6497	225	6	clear	clear	ADJ
ejpam-6497	225	7	.	.	PUNCT
ejpam-6497	226	1	(	(	PUNCT
ejpam-6497	226	2	b	b	X
ejpam-6497	226	3	⇒a	⇒a	X
ejpam-6497	226	4	)	)	PUNCT
ejpam-6497	226	5	if	if	SCONJ
ejpam-6497	226	6	x	x	PRON
ejpam-6497	226	7	is	be	AUX
ejpam-6497	226	8	not	not	PART
ejpam-6497	226	9	a	a	DET
ejpam-6497	226	10	sl	sl	NOUN
ejpam-6497	226	11	modulo	modulo	ADJ
ejpam-6497	226	12	j	j	PROPN
ejpam-6497	226	13	and	and	CCONJ
ejpam-6497	226	14	õ	õ	PROPN
ejpam-6497	226	15	covers	cover	VERB
ejpam-6497	226	16	x.	x.	NOUN
ejpam-6497	226	17	then	then	ADV
ejpam-6497	226	18	,	,	PUNCT
ejpam-6497	226	19	for	for	SCONJ
ejpam-6497	226	20	every	every	DET
ejpam-6497	226	21	o	o	NOUN
ejpam-6497	226	22	∈	∈	PROPN
ejpam-6497	226	23	õ	õ	PROPN
ejpam-6497	226	24	,	,	PUNCT
ejpam-6497	226	25	{	{	PUNCT
ejpam-6497	226	26	o	o	NOUN
ejpam-6497	226	27	×	×	NOUN
ejpam-6497	226	28	{	{	PUNCT
ejpam-6497	226	29	0	0	NUM
ejpam-6497	226	30	,	,	PUNCT
ejpam-6497	226	31	1	1	NUM
ejpam-6497	226	32	}	}	PUNCT
ejpam-6497	226	33	}	}	PUNCT
ejpam-6497	226	34	covers	cover	VERB
ejpam-6497	226	35	a.	a.	NOUN
ejpam-6497	226	36	hence	hence	ADV
ejpam-6497	226	37	,	,	PUNCT
ejpam-6497	226	38	a	a	PRON
ejpam-6497	226	39	is	be	AUX
ejpam-6497	226	40	not	not	PART
ejpam-6497	226	41	a	a	DET
ejpam-6497	226	42	weakly	weakly	ADJ
ejpam-6497	226	43	lindelöf	lindelöf	NOUN
ejpam-6497	226	44	subset	subset	VERB
ejpam-6497	226	45	modulo	modulo	PROPN
ejpam-6497	226	46	j	j	PROPN
ejpam-6497	226	47	because	because	SCONJ
ejpam-6497	226	48	all	all	DET
ejpam-6497	226	49	points	point	NOUN
ejpam-6497	226	50	of	of	ADP
ejpam-6497	226	51	x×	x×	PROPN
ejpam-6497	226	52	{	{	PUNCT
ejpam-6497	226	53	1	1	X
ejpam-6497	226	54	}	}	PUNCT
ejpam-6497	226	55	are	be	AUX
ejpam-6497	226	56	isolated	isolate	VERB
ejpam-6497	226	57	in	in	ADP
ejpam-6497	226	58	a.	a.	NOUN
ejpam-6497	226	59	3	3	NUM
ejpam-6497	226	60	.	.	PUNCT
ejpam-6497	227	1	conclusion	conclusion	NOUN
ejpam-6497	227	2	this	this	DET
ejpam-6497	227	3	paper	paper	NOUN
ejpam-6497	227	4	introduces	introduce	VERB
ejpam-6497	227	5	the	the	DET
ejpam-6497	227	6	notions	notion	NOUN
ejpam-6497	227	7	of	of	ADP
ejpam-6497	227	8	virtually	virtually	ADV
ejpam-6497	227	9	,	,	PUNCT
ejpam-6497	227	10	weakly	weakly	ADJ
ejpam-6497	227	11	,	,	PUNCT
ejpam-6497	227	12	and	and	CCONJ
ejpam-6497	227	13	almost	almost	ADV
ejpam-6497	227	14	lindelöf	lindelöf	NOUN
ejpam-6497	227	15	closed	close	VERB
ejpam-6497	227	16	ideal	ideal	ADJ
ejpam-6497	227	17	topological	topological	ADJ
ejpam-6497	227	18	spaces	space	NOUN
ejpam-6497	227	19	.	.	PUNCT
ejpam-6497	228	1	in	in	ADP
ejpam-6497	228	2	addition	addition	NOUN
ejpam-6497	228	3	to	to	ADP
ejpam-6497	228	4	explaining	explain	VERB
ejpam-6497	228	5	how	how	SCONJ
ejpam-6497	228	6	countable	countable	ADJ
ejpam-6497	228	7	covers	cover	VERB
ejpam-6497	228	8	impact	impact	NOUN
ejpam-6497	228	9	almost	almost	ADV
ejpam-6497	228	10	lindelöf	lindelöf	NOUN
ejpam-6497	228	11	spaces	space	VERB
ejpam-6497	228	12	and	and	CCONJ
ejpam-6497	228	13	focusing	focus	VERB
ejpam-6497	228	14	on	on	ADP
ejpam-6497	228	15	their	their	PRON
ejpam-6497	228	16	importance	importance	NOUN
ejpam-6497	228	17	,	,	PUNCT
ejpam-6497	228	18	we	we	PRON
ejpam-6497	228	19	also	also	ADV
ejpam-6497	228	20	look	look	VERB
ejpam-6497	228	21	at	at	ADP
ejpam-6497	228	22	their	their	PRON
ejpam-6497	228	23	subspaces	subspace	NOUN
ejpam-6497	228	24	and	and	CCONJ
ejpam-6497	228	25	the	the	DET
ejpam-6497	228	26	relationship	relationship	NOUN
ejpam-6497	228	27	between	between	ADP
ejpam-6497	228	28	the	the	DET
ejpam-6497	228	29	subspaces	subspace	NOUN
ejpam-6497	228	30	and	and	CCONJ
ejpam-6497	228	31	their	their	PRON
ejpam-6497	228	32	topological	topological	ADJ
ejpam-6497	228	33	properties	property	NOUN
ejpam-6497	228	34	.	.	PUNCT
ejpam-6497	229	1	the	the	DET
ejpam-6497	229	2	ideal	ideal	ADJ
ejpam-6497	229	3	spaces	space	NOUN
ejpam-6497	229	4	are	be	AUX
ejpam-6497	229	5	covered	cover	VERB
ejpam-6497	229	6	by	by	ADP
ejpam-6497	229	7	the	the	DET
ejpam-6497	229	8	closures	closure	NOUN
ejpam-6497	229	9	of	of	ADP
ejpam-6497	229	10	countable	countable	ADJ
ejpam-6497	229	11	subfamilies	subfamily	NOUN
ejpam-6497	229	12	that	that	PRON
ejpam-6497	229	13	make	make	VERB
ejpam-6497	229	14	up	up	ADP
ejpam-6497	229	15	these	these	DET
ejpam-6497	229	16	covers	cover	NOUN
ejpam-6497	229	17	.	.	PUNCT
ejpam-6497	230	1	we	we	PRON
ejpam-6497	230	2	begin	begin	VERB
ejpam-6497	230	3	,	,	PUNCT
ejpam-6497	230	4	analyze	analyze	VERB
ejpam-6497	230	5	,	,	PUNCT
ejpam-6497	230	6	and	and	CCONJ
ejpam-6497	230	7	discuss	discuss	VERB
ejpam-6497	230	8	definitions	definition	NOUN
ejpam-6497	230	9	,	,	PUNCT
ejpam-6497	230	10	assertions	assertion	NOUN
ejpam-6497	230	11	,	,	PUNCT
ejpam-6497	230	12	characterizations	characterization	NOUN
ejpam-6497	230	13	,	,	PUNCT
ejpam-6497	230	14	and	and	CCONJ
ejpam-6497	230	15	observations	observation	NOUN
ejpam-6497	230	16	related	relate	VERB
ejpam-6497	230	17	to	to	ADP
ejpam-6497	230	18	the	the	DET
ejpam-6497	230	19	recently	recently	ADV
ejpam-6497	230	20	introduced	introduce	VERB
ejpam-6497	230	21	notions	notion	NOUN
ejpam-6497	230	22	of	of	ADP
ejpam-6497	230	23	almost	almost	ADV
ejpam-6497	230	24	and	and	CCONJ
ejpam-6497	230	25	weakly	weakly	ADJ
ejpam-6497	230	26	lindelöf	lindelöf	PUNCT
ejpam-6497	230	27	ideal	ideal	ADJ
ejpam-6497	230	28	topological	topological	ADJ
ejpam-6497	230	29	spaces	space	NOUN
ejpam-6497	230	30	.	.	PUNCT
ejpam-6497	231	1	the	the	DET
ejpam-6497	231	2	relationships	relationship	NOUN
ejpam-6497	231	3	between	between	ADP
ejpam-6497	231	4	different	different	ADJ
ejpam-6497	231	5	ideal	ideal	ADJ
ejpam-6497	231	6	topological	topological	ADJ
ejpam-6497	231	7	spaces	space	NOUN
ejpam-6497	231	8	are	be	AUX
ejpam-6497	231	9	also	also	ADV
ejpam-6497	231	10	examined	examine	VERB
ejpam-6497	231	11	and	and	CCONJ
ejpam-6497	231	12	studied	study	VERB
ejpam-6497	231	13	.	.	PUNCT
ejpam-6497	232	1	we	we	PRON
ejpam-6497	232	2	illustrate	illustrate	VERB
ejpam-6497	232	3	the	the	DET
ejpam-6497	232	4	implications	implication	NOUN
ejpam-6497	232	5	of	of	ADP
ejpam-6497	232	6	these	these	DET
ejpam-6497	232	7	new	new	ADJ
ejpam-6497	232	8	ideal	ideal	ADJ
ejpam-6497	232	9	environments	environment	NOUN
ejpam-6497	232	10	.	.	PUNCT
ejpam-6497	233	1	declarations	declaration	NOUN
ejpam-6497	233	2	availability	availability	NOUN
ejpam-6497	233	3	of	of	ADP
ejpam-6497	233	4	data	datum	NOUN
ejpam-6497	233	5	and	and	CCONJ
ejpam-6497	233	6	materials	material	NOUN
ejpam-6497	233	7	data	datum	NOUN
ejpam-6497	233	8	sharing	sharing	NOUN
ejpam-6497	233	9	is	be	AUX
ejpam-6497	233	10	not	not	PART
ejpam-6497	233	11	applicable	applicable	ADJ
ejpam-6497	233	12	to	to	ADP
ejpam-6497	233	13	this	this	DET
ejpam-6497	233	14	article	article	NOUN
ejpam-6497	233	15	as	as	SCONJ
ejpam-6497	233	16	no	no	DET
ejpam-6497	233	17	datasets	dataset	NOUN
ejpam-6497	233	18	were	be	AUX
ejpam-6497	233	19	generated	generate	VERB
ejpam-6497	233	20	or	or	CCONJ
ejpam-6497	233	21	analyzed	analyze	VERB
ejpam-6497	233	22	during	during	ADP
ejpam-6497	233	23	the	the	DET
ejpam-6497	233	24	current	current	ADJ
ejpam-6497	233	25	study	study	NOUN
ejpam-6497	233	26	.	.	PUNCT
ejpam-6497	234	1	competing	compete	VERB
ejpam-6497	234	2	interests	interest	NOUN
ejpam-6497	234	3	the	the	DET
ejpam-6497	234	4	authors	author	NOUN
ejpam-6497	234	5	declare	declare	VERB
ejpam-6497	234	6	that	that	SCONJ
ejpam-6497	234	7	they	they	PRON
ejpam-6497	234	8	have	have	VERB
ejpam-6497	234	9	no	no	DET
ejpam-6497	234	10	competing	compete	VERB
ejpam-6497	234	11	interests	interest	NOUN
ejpam-6497	234	12	.	.	PUNCT
ejpam-6497	235	1	conflict	conflict	NOUN
ejpam-6497	235	2	of	of	ADP
ejpam-6497	235	3	interest	interest	NOUN
ejpam-6497	235	4	no	no	DET
ejpam-6497	235	5	conflicts	conflict	NOUN
ejpam-6497	235	6	of	of	ADP
ejpam-6497	235	7	interest	interest	NOUN
ejpam-6497	235	8	are	be	AUX
ejpam-6497	235	9	disclosed	disclose	VERB
ejpam-6497	235	10	by	by	ADP
ejpam-6497	235	11	the	the	DET
ejpam-6497	235	12	authors	author	NOUN
ejpam-6497	235	13	.	.	PUNCT
ejpam-6497	236	1	funding	fund	VERB
ejpam-6497	236	2	no	no	DET
ejpam-6497	236	3	particular	particular	ADJ
ejpam-6497	236	4	grant	grant	NOUN
ejpam-6497	236	5	for	for	ADP
ejpam-6497	236	6	this	this	DET
ejpam-6497	236	7	study	study	NOUN
ejpam-6497	236	8	was	be	AUX
ejpam-6497	236	9	provided	provide	VERB
ejpam-6497	236	10	by	by	ADP
ejpam-6497	236	11	funding	fund	VERB
ejpam-6497	236	12	agencies	agency	NOUN
ejpam-6497	236	13	from	from	ADP
ejpam-6497	236	14	the	the	DET
ejpam-6497	236	15	commercial	commercial	ADJ
ejpam-6497	236	16	,	,	PUNCT
ejpam-6497	236	17	nonprofit	nonprofit	ADJ
ejpam-6497	236	18	sectors	sector	NOUN
ejpam-6497	236	19	,	,	PUNCT
ejpam-6497	236	20	or	or	CCONJ
ejpam-6497	236	21	public	public	NOUN
ejpam-6497	236	22	.	.	PUNCT
ejpam-6497	237	1	e.	e.	PROPN
ejpam-6497	237	2	almuhur	almuhur	PROPN
ejpam-6497	237	3	et	et	PROPN
ejpam-6497	237	4	al	al	PROPN
ejpam-6497	237	5	.	.	PUNCT
ejpam-6497	237	6	/	/	SYM
ejpam-6497	237	7	eur	eur	PROPN
ejpam-6497	237	8	.	.	PUNCT
ejpam-6497	238	1	j.	j.	PROPN
ejpam-6497	238	2	pure	pure	PROPN
ejpam-6497	238	3	appl	appl	PROPN
ejpam-6497	238	4	.	.	PROPN
ejpam-6497	238	5	math	math	PROPN
ejpam-6497	238	6	,	,	PUNCT
ejpam-6497	238	7	18	18	NUM
ejpam-6497	238	8	(	(	PUNCT
ejpam-6497	238	9	3	3	NUM
ejpam-6497	238	10	)	)	PUNCT
ejpam-6497	238	11	(	(	PUNCT
ejpam-6497	238	12	2025	2025	NUM
ejpam-6497	238	13	)	)	PUNCT
ejpam-6497	238	14	,	,	PUNCT
ejpam-6497	238	15	6497	6497	NUM
ejpam-6497	238	16	10	10	NUM
ejpam-6497	238	17	of	of	ADP
ejpam-6497	238	18	11	11	NUM
ejpam-6497	238	19	authors	author	NOUN
ejpam-6497	238	20	’	'	PUNCT
ejpam-6497	238	21	contributions	contribution	NOUN
ejpam-6497	238	22	all	all	DET
ejpam-6497	238	23	authors	author	NOUN
ejpam-6497	238	24	have	have	AUX
ejpam-6497	238	25	equally	equally	ADV
ejpam-6497	238	26	contributed	contribute	VERB
ejpam-6497	238	27	,	,	PUNCT
ejpam-6497	238	28	read	read	VERB
ejpam-6497	238	29	,	,	PUNCT
ejpam-6497	238	30	and	and	CCONJ
ejpam-6497	238	31	approved	approve	VERB
ejpam-6497	238	32	the	the	DET
ejpam-6497	238	33	final	final	ADJ
ejpam-6497	238	34	manuscript	manuscript	NOUN
ejpam-6497	238	35	.	.	PUNCT
ejpam-6497	239	1	references	reference	NOUN
ejpam-6497	239	2	[	[	X
ejpam-6497	239	3	1	1	X
ejpam-6497	239	4	]	]	PUNCT
ejpam-6497	239	5	t.	t.	PROPN
ejpam-6497	239	6	r.	r.	PROPN
ejpam-6497	239	7	hamlett	hamlett	PROPN
ejpam-6497	239	8	and	and	CCONJ
ejpam-6497	239	9	d.	d.	PROPN
ejpam-6497	239	10	janković.	janković.	PROPN
ejpam-6497	239	11	ideals	ideal	NOUN
ejpam-6497	239	12	in	in	ADP
ejpam-6497	239	13	general	general	ADJ
ejpam-6497	239	14	topology	topology	NOUN
ejpam-6497	239	15	,	,	PUNCT
ejpam-6497	239	16	general	general	ADJ
ejpam-6497	239	17	topology	topology	NOUN
ejpam-6497	239	18	and	and	CCONJ
ejpam-6497	239	19	applications	application	NOUN
ejpam-6497	239	20	.	.	PUNCT
ejpam-6497	240	1	springer	springer	NOUN
ejpam-6497	240	2	,	,	PUNCT
ejpam-6497	240	3	new	new	PROPN
ejpam-6497	240	4	york	york	PROPN
ejpam-6497	240	5	,	,	PUNCT
ejpam-6497	240	6	1988	1988	NUM
ejpam-6497	240	7	.	.	PUNCT
ejpam-6497	241	1	[	[	X
ejpam-6497	241	2	2	2	X
ejpam-6497	241	3	]	]	X
ejpam-6497	241	4	d.	d.	PROPN
ejpam-6497	241	5	janković	janković	PROPN
ejpam-6497	241	6	and	and	CCONJ
ejpam-6497	241	7	t.	t.	PROPN
ejpam-6497	241	8	r.	r.	PROPN
ejpam-6497	241	9	hamlett	hamlett	PROPN
ejpam-6497	241	10	.	.	PUNCT
ejpam-6497	242	1	new	new	ADJ
ejpam-6497	242	2	topologies	topology	NOUN
ejpam-6497	242	3	from	from	ADP
ejpam-6497	242	4	old	old	ADJ
ejpam-6497	242	5	via	via	ADP
ejpam-6497	242	6	ideals	ideal	NOUN
ejpam-6497	242	7	.	.	PUNCT
ejpam-6497	243	1	the	the	DET
ejpam-6497	243	2	american	american	PROPN
ejpam-6497	243	3	mathematical	mathematical	PROPN
ejpam-6497	243	4	monthly	monthly	PROPN
ejpam-6497	243	5	,	,	PUNCT
ejpam-6497	243	6	97(4):295–310	97(4):295–310	PROPN
ejpam-6497	243	7	,	,	PUNCT
ejpam-6497	243	8	1990	1990	NUM
ejpam-6497	243	9	.	.	PUNCT
ejpam-6497	244	1	[	[	X
ejpam-6497	244	2	3	3	X
ejpam-6497	244	3	]	]	X
ejpam-6497	244	4	g.	g.	PROPN
ejpam-6497	244	5	aslim	aslim	PROPN
ejpam-6497	244	6	,	,	PUNCT
ejpam-6497	244	7	a.	a.	NOUN
ejpam-6497	244	8	caksu	caksu	NOUN
ejpam-6497	244	9	guler	guler	NOUN
ejpam-6497	244	10	,	,	PUNCT
ejpam-6497	244	11	and	and	CCONJ
ejpam-6497	244	12	t.	t.	PROPN
ejpam-6497	244	13	noiri	noiri	PROPN
ejpam-6497	244	14	.	.	PUNCT
ejpam-6497	245	1	on	on	ADP
ejpam-6497	245	2	decompositions	decomposition	NOUN
ejpam-6497	245	3	of	of	ADP
ejpam-6497	245	4	continuity	continuity	NOUN
ejpam-6497	245	5	and	and	CCONJ
ejpam-6497	245	6	some	some	DET
ejpam-6497	245	7	weaker	weak	ADJ
ejpam-6497	245	8	forms	form	NOUN
ejpam-6497	245	9	of	of	ADP
ejpam-6497	245	10	continuity	continuity	NOUN
ejpam-6497	245	11	via	via	ADP
ejpam-6497	245	12	idealization	idealization	NOUN
ejpam-6497	245	13	.	.	PUNCT
ejpam-6497	246	1	acta	acta	PROPN
ejpam-6497	246	2	mathematica	mathematica	PROPN
ejpam-6497	246	3	hungarica	hungarica	PROPN
ejpam-6497	246	4	,	,	PUNCT
ejpam-6497	246	5	109:183	109:183	NUM
ejpam-6497	246	6	–	–	PUNCT
ejpam-6497	246	7	190	190	NUM
ejpam-6497	246	8	,	,	PUNCT
ejpam-6497	246	9	2005	2005	NUM
ejpam-6497	246	10	.	.	PUNCT
ejpam-6497	247	1	[	[	X
ejpam-6497	247	2	4	4	X
ejpam-6497	247	3	]	]	PUNCT
ejpam-6497	247	4	e.	e.	PROPN
ejpam-6497	247	5	ekici	ekici	PROPN
ejpam-6497	247	6	and	and	CCONJ
ejpam-6497	247	7	t.	t.	PROPN
ejpam-6497	247	8	noiri	noiri	PROPN
ejpam-6497	247	9	.	.	PUNCT
ejpam-6497	248	1	connectedness	connectedness	NOUN
ejpam-6497	248	2	in	in	ADP
ejpam-6497	248	3	ideal	ideal	ADJ
ejpam-6497	248	4	topological	topological	ADJ
ejpam-6497	248	5	spaces	space	NOUN
ejpam-6497	248	6	.	.	PUNCT
ejpam-6497	249	1	novi	novi	PROPN
ejpam-6497	249	2	sad	sad	PROPN
ejpam-6497	249	3	journal	journal	PROPN
ejpam-6497	249	4	of	of	ADP
ejpam-6497	249	5	mathematics	mathematic	NOUN
ejpam-6497	249	6	,	,	PUNCT
ejpam-6497	249	7	38(2):65–70	38(2):65–70	NUM
ejpam-6497	249	8	,	,	PUNCT
ejpam-6497	249	9	2008	2008	NUM
ejpam-6497	249	10	.	.	PUNCT
ejpam-6497	250	1	[	[	X
ejpam-6497	250	2	5	5	X
ejpam-6497	250	3	]	]	X
ejpam-6497	250	4	d.	d.	PROPN
ejpam-6497	250	5	janković	janković	PROPN
ejpam-6497	250	6	,	,	PUNCT
ejpam-6497	250	7	t.	t.	PROPN
ejpam-6497	250	8	r.	r.	PROPN
ejpam-6497	250	9	hamlett	hamlett	PROPN
ejpam-6497	250	10	,	,	PUNCT
ejpam-6497	250	11	and	and	CCONJ
ejpam-6497	250	12	c.	c.	PROPN
ejpam-6497	250	13	konstadilaki	konstadilaki	PROPN
ejpam-6497	250	14	.	.	PUNCT
ejpam-6497	251	1	local	local	ADJ
ejpam-6497	251	2	-	-	PUNCT
ejpam-6497	251	3	to	to	ADP
ejpam-6497	251	4	-	-	PUNCT
ejpam-6497	251	5	global	global	ADJ
ejpam-6497	251	6	topological	topological	ADJ
ejpam-6497	251	7	properties	property	NOUN
ejpam-6497	251	8	.	.	PUNCT
ejpam-6497	252	1	mathematica	mathematica	PROPN
ejpam-6497	252	2	japonica	japonica	PROPN
ejpam-6497	252	3	,	,	PUNCT
ejpam-6497	252	4	52(1):79–81	52(1):79–81	NUM
ejpam-6497	252	5	,	,	PUNCT
ejpam-6497	252	6	2000	2000	NUM
ejpam-6497	252	7	.	.	PUNCT
ejpam-6497	253	1	[	[	X
ejpam-6497	253	2	6	6	NUM
ejpam-6497	253	3	]	]	PUNCT
ejpam-6497	253	4	a.	a.	NOUN
ejpam-6497	253	5	s.	s.	PROPN
ejpam-6497	253	6	mashhour	mashhour	PROPN
ejpam-6497	253	7	,	,	PUNCT
ejpam-6497	253	8	a.	a.	PROPN
ejpam-6497	253	9	a.	a.	PROPN
ejpam-6497	253	10	allam	allam	PROPN
ejpam-6497	253	11	,	,	PUNCT
ejpam-6497	253	12	f.	f.	PROPN
ejpam-6497	253	13	s.	s.	PROPN
ejpam-6497	253	14	mahmoud	mahmoud	PROPN
ejpam-6497	253	15	,	,	PUNCT
ejpam-6497	253	16	and	and	CCONJ
ejpam-6497	253	17	f.	f.	PROPN
ejpam-6497	253	18	h.	h.	PROPN
ejpam-6497	253	19	khedr	khedr	PROPN
ejpam-6497	253	20	.	.	PUNCT
ejpam-6497	254	1	on	on	ADP
ejpam-6497	254	2	supratopological	supratopological	ADJ
ejpam-6497	254	3	spaces	space	NOUN
ejpam-6497	254	4	.	.	PUNCT
ejpam-6497	255	1	indian	indian	ADJ
ejpam-6497	255	2	journal	journal	PROPN
ejpam-6497	255	3	of	of	ADP
ejpam-6497	255	4	pure	pure	ADJ
ejpam-6497	255	5	and	and	CCONJ
ejpam-6497	255	6	applied	applied	ADJ
ejpam-6497	255	7	mathematics	mathematic	NOUN
ejpam-6497	255	8	,	,	PUNCT
ejpam-6497	255	9	14:502–510	14:502–510	NUM
ejpam-6497	255	10	,	,	PUNCT
ejpam-6497	255	11	1983	1983	NUM
ejpam-6497	255	12	.	.	PUNCT
ejpam-6497	256	1	[	[	X
ejpam-6497	256	2	7	7	X
ejpam-6497	256	3	]	]	X
ejpam-6497	256	4	f.	f.	PROPN
ejpam-6497	256	5	g.	g.	PROPN
ejpam-6497	256	6	arenas	arenas	PROPN
ejpam-6497	256	7	,	,	PUNCT
ejpam-6497	256	8	j.	j.	PROPN
ejpam-6497	256	9	dontchev	dontchev	PROPN
ejpam-6497	256	10	,	,	PUNCT
ejpam-6497	256	11	and	and	CCONJ
ejpam-6497	256	12	m.	m.	PROPN
ejpam-6497	256	13	l.	l.	PROPN
ejpam-6497	256	14	puertas	puertas	PROPN
ejpam-6497	256	15	.	.	PUNCT
ejpam-6497	257	1	idealization	idealization	NOUN
ejpam-6497	257	2	of	of	ADP
ejpam-6497	257	3	some	some	DET
ejpam-6497	257	4	weak	weak	ADJ
ejpam-6497	257	5	separation	separation	NOUN
ejpam-6497	257	6	axioms	axiom	NOUN
ejpam-6497	257	7	.	.	PUNCT
ejpam-6497	258	1	acta	acta	PROPN
ejpam-6497	258	2	mathematica	mathematica	PROPN
ejpam-6497	258	3	hungarica	hungarica	PROPN
ejpam-6497	258	4	,	,	PUNCT
ejpam-6497	258	5	89:47–53	89:47–53	NUM
ejpam-6497	258	6	,	,	PUNCT
ejpam-6497	258	7	2000	2000	NUM
ejpam-6497	258	8	.	.	PUNCT
ejpam-6497	259	1	[	[	X
ejpam-6497	259	2	8	8	X
ejpam-6497	259	3	]	]	PUNCT
ejpam-6497	259	4	s.	s.	PROPN
ejpam-6497	259	5	solovjovs	solovjovs	PROPN
ejpam-6497	259	6	.	.	PUNCT
ejpam-6497	260	1	topological	topological	ADJ
ejpam-6497	260	2	spaces	space	NOUN
ejpam-6497	260	3	with	with	ADP
ejpam-6497	260	4	a	a	DET
ejpam-6497	260	5	countable	countable	ADJ
ejpam-6497	260	6	compactness	compactness	NOUN
ejpam-6497	260	7	defect	defect	NOUN
ejpam-6497	260	8	(	(	PUNCT
ejpam-6497	260	9	in	in	ADP
ejpam-6497	260	10	latvian	latvian	NOUN
ejpam-6497	260	11	)	)	PUNCT
ejpam-6497	260	12	.	.	PUNCT
ejpam-6497	261	1	bachelor	bachelor	NOUN
ejpam-6497	261	2	thesis	thesis	NOUN
ejpam-6497	261	3	,	,	PUNCT
ejpam-6497	261	4	univ	univ	PROPN
ejpam-6497	261	5	.	.	PROPN
ejpam-6497	261	6	of	of	ADP
ejpam-6497	261	7	latvia	latvia	PROPN
ejpam-6497	261	8	,	,	PUNCT
ejpam-6497	261	9	riga	riga	PROPN
ejpam-6497	261	10	,	,	PUNCT
ejpam-6497	261	11	1999	1999	NUM
ejpam-6497	261	12	.	.	PUNCT
ejpam-6497	262	1	[	[	X
ejpam-6497	262	2	9	9	NUM
ejpam-6497	262	3	]	]	PUNCT
ejpam-6497	262	4	f.	f.	PROPN
ejpam-6497	262	5	cammaroto	cammaroto	PROPN
ejpam-6497	262	6	and	and	CCONJ
ejpam-6497	262	7	g.	g.	PROPN
ejpam-6497	262	8	santoro	santoro	PROPN
ejpam-6497	262	9	.	.	PUNCT
ejpam-6497	263	1	some	some	DET
ejpam-6497	263	2	counterexamples	counterexample	NOUN
ejpam-6497	263	3	and	and	CCONJ
ejpam-6497	263	4	properties	property	NOUN
ejpam-6497	263	5	on	on	ADP
ejpam-6497	263	6	generalizations	generalization	NOUN
ejpam-6497	263	7	of	of	ADP
ejpam-6497	263	8	lindelöf	lindelöf	PROPN
ejpam-6497	263	9	spaces	space	VERB
ejpam-6497	263	10	.	.	PUNCT
ejpam-6497	264	1	international	international	ADJ
ejpam-6497	264	2	journal	journal	PROPN
ejpam-6497	264	3	of	of	ADP
ejpam-6497	264	4	mathematics	mathematics	PROPN
ejpam-6497	264	5	&	&	CCONJ
ejpam-6497	264	6	mathematical	mathematical	PROPN
ejpam-6497	264	7	sciences	sciences	PROPN
ejpam-6497	264	8	,	,	PUNCT
ejpam-6497	264	9	9:10	9:10	NUM
ejpam-6497	264	10	pages	page	NOUN
ejpam-6497	264	11	,	,	PUNCT
ejpam-6497	264	12	1996	1996	NUM
ejpam-6497	264	13	.	.	PUNCT
ejpam-6497	265	1	[	[	X
ejpam-6497	265	2	10	10	NUM
ejpam-6497	265	3	]	]	PUNCT
ejpam-6497	265	4	k.	k.	PROPN
ejpam-6497	266	1	p.	p.	PROPN
ejpam-6497	266	2	hart	hart	PROPN
ejpam-6497	266	3	,	,	PUNCT
ejpam-6497	266	4	j.	j.	PROPN
ejpam-6497	266	5	i.	i.	PROPN
ejpam-6497	266	6	nagata	nagata	PROPN
ejpam-6497	266	7	,	,	PUNCT
ejpam-6497	266	8	and	and	CCONJ
ejpam-6497	266	9	j.	j.	PROPN
ejpam-6497	266	10	e.	e.	PROPN
ejpam-6497	266	11	vaughan	vaughan	PROPN
ejpam-6497	266	12	.	.	PUNCT
ejpam-6497	267	1	encyclopedia	encyclopedia	PROPN
ejpam-6497	267	2	of	of	ADP
ejpam-6497	267	3	general	general	ADJ
ejpam-6497	267	4	topology	topology	NOUN
ejpam-6497	267	5	.	.	PUNCT
ejpam-6497	268	1	first	first	PROPN
ejpam-6497	268	2	edition	edition	PROPN
ejpam-6497	268	3	,	,	PUNCT
ejpam-6497	268	4	elsevier	elsevier	PROPN
ejpam-6497	268	5	science	science	NOUN
ejpam-6497	268	6	publishers	publisher	NOUN
ejpam-6497	268	7	,	,	PUNCT
ejpam-6497	268	8	amsterdam	amsterdam	PROPN
ejpam-6497	268	9	,	,	PUNCT
ejpam-6497	268	10	2003	2003	NUM
ejpam-6497	268	11	.	.	PUNCT
ejpam-6497	269	1	[	[	X
ejpam-6497	269	2	11	11	NUM
ejpam-6497	269	3	]	]	PUNCT
ejpam-6497	269	4	a.	a.	NOUN
ejpam-6497	269	5	j.	j.	PROPN
ejpam-6497	269	6	fawakhreh	fawakhreh	PROPN
ejpam-6497	269	7	and	and	CCONJ
ejpam-6497	269	8	a.	a.	NOUN
ejpam-6497	269	9	kiliçman	kiliçman	PROPN
ejpam-6497	269	10	.	.	PUNCT
ejpam-6497	269	11	mappings	mapping	NOUN
ejpam-6497	269	12	on	on	ADP
ejpam-6497	269	13	weakly	weakly	ADJ
ejpam-6497	269	14	lindelöf	lindelöf	NOUN
ejpam-6497	269	15	and	and	CCONJ
ejpam-6497	269	16	weakly	weakly	ADJ
ejpam-6497	269	17	regularlindelöf	regularlindelöf	NOUN
ejpam-6497	269	18	spaces	space	NOUN
ejpam-6497	269	19	.	.	PUNCT
ejpam-6497	270	1	applied	apply	VERB
ejpam-6497	270	2	general	general	ADJ
ejpam-6497	270	3	topology	topology	NOUN
ejpam-6497	270	4	,	,	PUNCT
ejpam-6497	270	5	12(2):135–141	12(2):135–141	NUM
ejpam-6497	270	6	,	,	PUNCT
ejpam-6497	270	7	2011	2011	NUM
ejpam-6497	270	8	.	.	PUNCT
ejpam-6497	271	1	[	[	X
ejpam-6497	271	2	12	12	NUM
ejpam-6497	271	3	]	]	X
ejpam-6497	271	4	s.	s.	PROPN
ejpam-6497	271	5	willard	willard	PROPN
ejpam-6497	271	6	and	and	CCONJ
ejpam-6497	271	7	u.	u.	PROPN
ejpam-6497	271	8	n.	n.	PROPN
ejpam-6497	271	9	b.	b.	PROPN
ejpam-6497	271	10	dissanayake	dissanayake	PROPN
ejpam-6497	271	11	.	.	PUNCT
ejpam-6497	272	1	the	the	DET
ejpam-6497	272	2	almost	almost	ADV
ejpam-6497	272	3	lindelöf	lindelöf	NOUN
ejpam-6497	272	4	degree	degree	NOUN
ejpam-6497	272	5	.	.	PUNCT
ejpam-6497	273	1	canadian	canadian	ADJ
ejpam-6497	273	2	mathematical	mathematical	ADJ
ejpam-6497	273	3	bulletin	bulletin	NOUN
ejpam-6497	273	4	,	,	PUNCT
ejpam-6497	273	5	27(4):452–455	27(4):452–455	PROPN
ejpam-6497	273	6	,	,	PUNCT
ejpam-6497	273	7	1984	1984	NUM
ejpam-6497	273	8	.	.	PUNCT
ejpam-6497	274	1	[	[	X
ejpam-6497	274	2	13	13	NUM
ejpam-6497	274	3	]	]	X
ejpam-6497	274	4	y.	y.	NOUN
ejpam-6497	274	5	song	song	PROPN
ejpam-6497	274	6	.	.	PUNCT
ejpam-6497	275	1	on	on	ADP
ejpam-6497	275	2	relatively	relatively	ADV
ejpam-6497	275	3	almost	almost	ADV
ejpam-6497	275	4	lindelöf	lindelöf	NOUN
ejpam-6497	275	5	subsets	subset	NOUN
ejpam-6497	275	6	.	.	PUNCT
ejpam-6497	276	1	mathematica	mathematica	PROPN
ejpam-6497	276	2	bohemica	bohemica	PROPN
ejpam-6497	276	3	,	,	PUNCT
ejpam-6497	276	4	134(2):183	134(2):183	NUM
ejpam-6497	276	5	–	–	PUNCT
ejpam-6497	276	6	190	190	NUM
ejpam-6497	276	7	,	,	PUNCT
ejpam-6497	276	8	2009	2009	NUM
ejpam-6497	276	9	.	.	PUNCT
ejpam-6497	277	1	[	[	X
ejpam-6497	277	2	14	14	NUM
ejpam-6497	277	3	]	]	PUNCT
ejpam-6497	277	4	j.	j.	PROPN
ejpam-6497	277	5	thomas	thomas	PROPN
ejpam-6497	277	6	.	.	PUNCT
ejpam-6497	278	1	set	set	PROPN
ejpam-6497	278	2	theory	theory	NOUN
ejpam-6497	278	3	.	.	PUNCT
ejpam-6497	279	1	springer	springer	NOUN
ejpam-6497	279	2	monographs	monograph	NOUN
ejpam-6497	279	3	in	in	ADP
ejpam-6497	279	4	mathematics	mathematics	PROPN
ejpam-6497	279	5	,	,	PUNCT
ejpam-6497	279	6	berlin	berlin	PROPN
ejpam-6497	279	7	,	,	PUNCT
ejpam-6497	279	8	new	new	PROPN
ejpam-6497	279	9	york	york	PROPN
ejpam-6497	279	10	,	,	PUNCT
ejpam-6497	279	11	2003	2003	NUM
ejpam-6497	279	12	.	.	PUNCT
ejpam-6497	280	1	[	[	X
ejpam-6497	280	2	15	15	NUM
ejpam-6497	280	3	]	]	X
ejpam-6497	280	4	b.	b.	PROPN
ejpam-6497	280	5	roy	roy	PROPN
ejpam-6497	280	6	.	.	PROPN
ejpam-6497	281	1	on	on	ADP
ejpam-6497	281	2	nearly	nearly	ADV
ejpam-6497	281	3	lindelöf	lindelöf	NOUN
ejpam-6497	281	4	spaces	space	NOUN
ejpam-6497	281	5	via	via	ADP
ejpam-6497	281	6	generalized	generalized	ADJ
ejpam-6497	281	7	topology	topology	NOUN
ejpam-6497	281	8	.	.	PUNCT
ejpam-6497	282	1	proyecciones	proyecciones	PROPN
ejpam-6497	282	2	journal	journal	PROPN
ejpam-6497	282	3	of	of	ADP
ejpam-6497	282	4	mathematics	mathematic	NOUN
ejpam-6497	282	5	,	,	PUNCT
ejpam-6497	282	6	38(1):49–57	38(1):49–57	NUM
ejpam-6497	282	7	,	,	PUNCT
ejpam-6497	282	8	2019	2019	NUM
ejpam-6497	282	9	.	.	PUNCT
ejpam-6497	283	1	[	[	X
ejpam-6497	283	2	16	16	NUM
ejpam-6497	283	3	]	]	PUNCT
ejpam-6497	283	4	a.	a.	PROPN
ejpam-6497	283	5	al	al	PROPN
ejpam-6497	283	6	-	-	PUNCT
ejpam-6497	283	7	omari	omari	PROPN
ejpam-6497	283	8	and	and	CCONJ
ejpam-6497	283	9	t.	t.	PROPN
ejpam-6497	283	10	noiri	noiri	PROPN
ejpam-6497	283	11	.	.	PUNCT
ejpam-6497	284	1	characterizations	characterization	NOUN
ejpam-6497	284	2	of	of	ADP
ejpam-6497	284	3	nearly	nearly	ADV
ejpam-6497	284	4	lindelöf	lindelöf	NOUN
ejpam-6497	284	5	spaces	space	NOUN
ejpam-6497	284	6	.	.	PUNCT
ejpam-6497	285	1	jordan	jordan	PROPN
ejpam-6497	285	2	journal	journal	PROPN
ejpam-6497	285	3	of	of	ADP
ejpam-6497	285	4	mathematics	mathematics	PROPN
ejpam-6497	285	5	and	and	CCONJ
ejpam-6497	285	6	statistics	statistic	NOUN
ejpam-6497	285	7	,	,	PUNCT
ejpam-6497	285	8	3(2):81–92	3(2):81–92	NUM
ejpam-6497	285	9	,	,	PUNCT
ejpam-6497	285	10	2010	2010	NUM
ejpam-6497	285	11	.	.	PUNCT
ejpam-6497	286	1	[	[	X
ejpam-6497	286	2	17	17	NUM
ejpam-6497	286	3	]	]	X
ejpam-6497	286	4	e.	e.	PROPN
ejpam-6497	286	5	almuhur	almuhur	PROPN
ejpam-6497	286	6	,	,	PUNCT
ejpam-6497	286	7	m.	m.	PROPN
ejpam-6497	286	8	al	al	PROPN
ejpam-6497	286	9	-	-	PUNCT
ejpam-6497	286	10	labadi	labadi	PROPN
ejpam-6497	286	11	,	,	PUNCT
ejpam-6497	286	12	a.	a.	NOUN
ejpam-6497	286	13	shatarah	shatarah	PROPN
ejpam-6497	286	14	,	,	PUNCT
ejpam-6497	286	15	s.	s.	PROPN
ejpam-6497	286	16	khamis	khamis	PROPN
ejpam-6497	286	17	,	,	PUNCT
ejpam-6497	286	18	and	and	CCONJ
ejpam-6497	286	19	n.	n.	PROPN
ejpam-6497	286	20	omar	omar	PROPN
ejpam-6497	286	21	.	.	PUNCT
ejpam-6497	287	1	almost	almost	ADV
ejpam-6497	287	2	,	,	PUNCT
ejpam-6497	287	3	weakly	weakly	ADJ
ejpam-6497	287	4	and	and	CCONJ
ejpam-6497	287	5	nearly	nearly	ADV
ejpam-6497	287	6	l	l	NOUN
ejpam-6497	287	7	-	-	ADJ
ejpam-6497	287	8	closed	closed	ADJ
ejpam-6497	287	9	topological	topological	ADJ
ejpam-6497	287	10	spaces	space	NOUN
ejpam-6497	287	11	.	.	PUNCT
ejpam-6497	288	1	2021	2021	NUM
ejpam-6497	288	2	international	international	ADJ
ejpam-6497	288	3	conference	conference	NOUN
ejpam-6497	288	4	on	on	ADP
ejpam-6497	288	5	information	information	NOUN
ejpam-6497	288	6	technology	technology	NOUN
ejpam-6497	288	7	,	,	PUNCT
ejpam-6497	288	8	2021	2021	NUM
ejpam-6497	288	9	:	:	PUNCT
ejpam-6497	288	10	icit	icit	ADJ
ejpam-6497	288	11	2021	2021	NUM
ejpam-6497	288	12	–	–	PUNCT
ejpam-6497	288	13	proceedings	proceeding	NOUN
ejpam-6497	288	14	,	,	PUNCT
ejpam-6497	288	15	2021	2021	NUM
ejpam-6497	288	16	.	.	PUNCT
ejpam-6497	289	1	e.	e.	PROPN
ejpam-6497	289	2	almuhur	almuhur	PROPN
ejpam-6497	289	3	et	et	PROPN
ejpam-6497	289	4	al	al	PROPN
ejpam-6497	289	5	.	.	PUNCT
ejpam-6497	289	6	/	/	SYM
ejpam-6497	289	7	eur	eur	PROPN
ejpam-6497	289	8	.	.	PUNCT
ejpam-6497	290	1	j.	j.	PROPN
ejpam-6497	290	2	pure	pure	PROPN
ejpam-6497	290	3	appl	appl	PROPN
ejpam-6497	290	4	.	.	PROPN
ejpam-6497	290	5	math	math	PROPN
ejpam-6497	290	6	,	,	PUNCT
ejpam-6497	290	7	18	18	NUM
ejpam-6497	290	8	(	(	PUNCT
ejpam-6497	290	9	3	3	NUM
ejpam-6497	290	10	)	)	PUNCT
ejpam-6497	290	11	(	(	PUNCT
ejpam-6497	290	12	2025	2025	NUM
ejpam-6497	290	13	)	)	PUNCT
ejpam-6497	290	14	,	,	PUNCT
ejpam-6497	290	15	6497	6497	NUM
ejpam-6497	290	16	11	11	NUM
ejpam-6497	290	17	of	of	ADP
ejpam-6497	290	18	11	11	NUM
ejpam-6497	291	1	[	[	SYM
ejpam-6497	291	2	18	18	NUM
ejpam-6497	291	3	]	]	X
ejpam-6497	291	4	e.	e.	PROPN
ejpam-6497	291	5	almuhur	almuhur	PROPN
ejpam-6497	291	6	and	and	CCONJ
ejpam-6497	291	7	m.	m.	PROPN
ejpam-6497	291	8	al	al	PROPN
ejpam-6497	291	9	-	-	PUNCT
ejpam-6497	291	10	labadi	labadi	NOUN
ejpam-6497	291	11	.	.	PUNCT
ejpam-6497	292	1	on	on	ADP
ejpam-6497	292	2	irresolute	irresolute	ADJ
ejpam-6497	292	3	functions	function	NOUN
ejpam-6497	292	4	in	in	ADP
ejpam-6497	292	5	ideal	ideal	ADJ
ejpam-6497	292	6	topological	topological	ADJ
ejpam-6497	292	7	spaces	space	NOUN
ejpam-6497	292	8	.	.	PUNCT
ejpam-6497	293	1	thermal	thermal	ADJ
ejpam-6497	293	2	science	science	NOUN
ejpam-6497	293	3	,	,	PUNCT
ejpam-6497	293	4	26(s2):s703	26(s2):s703	NUM
ejpam-6497	293	5	–	–	PUNCT
ejpam-6497	293	6	s709	s709	NUM
ejpam-6497	293	7	,	,	PUNCT
ejpam-6497	293	8	2022	2022	NUM
ejpam-6497	293	9	.	.	PUNCT