id	sid	tid	token	lemma	pos
ejpam-3758	1	1	european	european	PROPN
ejpam-3758	1	2	journal	journal	PROPN
ejpam-3758	1	3	of	of	ADP
ejpam-3758	1	4	pure	pure	ADJ
ejpam-3758	1	5	and	and	CCONJ
ejpam-3758	1	6	applied	apply	VERB
ejpam-3758	1	7	mathematics	mathematic	NOUN
ejpam-3758	1	8	vol	vol	NOUN
ejpam-3758	1	9	.	.	PROPN
ejpam-3758	2	1	13	13	NUM
ejpam-3758	2	2	,	,	PUNCT
ejpam-3758	2	3	no	no	INTJ
ejpam-3758	2	4	.	.	NOUN
ejpam-3758	2	5	4	4	NUM
ejpam-3758	2	6	,	,	PUNCT
ejpam-3758	2	7	2020	2020	NUM
ejpam-3758	2	8	,	,	PUNCT
ejpam-3758	2	9	977	977	NUM
ejpam-3758	2	10	-	-	SYM
ejpam-3758	2	11	986	986	NUM
ejpam-3758	2	12	issn	issn	PROPN
ejpam-3758	2	13	1307	1307	NUM
ejpam-3758	2	14	-	-	SYM
ejpam-3758	2	15	5543	5543	NUM
ejpam-3758	2	16	–	–	PUNCT
ejpam-3758	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3758	2	18	published	publish	VERB
ejpam-3758	2	19	by	by	ADP
ejpam-3758	2	20	new	new	PROPN
ejpam-3758	2	21	york	york	PROPN
ejpam-3758	2	22	business	business	PROPN
ejpam-3758	2	23	global	global	PROPN
ejpam-3758	2	24	on	on	ADP
ejpam-3758	2	25	(	(	PUNCT
ejpam-3758	2	26	µ1	µ1	PROPN
ejpam-3758	2	27	,	,	PUNCT
ejpam-3758	2	28	µ2	µ2	PROPN
ejpam-3758	2	29	,	,	PUNCT
ejpam-3758	2	30	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	2	31	generalized	generalize	VERB
ejpam-3758	2	32	closed	close	VERB
ejpam-3758	2	33	sets	set	NOUN
ejpam-3758	2	34	breix	breix	VERB
ejpam-3758	2	35	michael	michael	PROPN
ejpam-3758	2	36	g.	g.	PROPN
ejpam-3758	2	37	agua1,∗	agua1,∗	PROPN
ejpam-3758	2	38	,	,	PUNCT
ejpam-3758	2	39	rolando	rolando	PROPN
ejpam-3758	2	40	n.	n.	PROPN
ejpam-3758	2	41	paluga1	paluga1	PROPN
ejpam-3758	2	42	1	1	NUM
ejpam-3758	2	43	department	department	NOUN
ejpam-3758	2	44	of	of	ADP
ejpam-3758	2	45	mathematics	mathematic	NOUN
ejpam-3758	2	46	,	,	PUNCT
ejpam-3758	2	47	caraga	caraga	PROPN
ejpam-3758	2	48	state	state	PROPN
ejpam-3758	2	49	university	university	PROPN
ejpam-3758	2	50	,	,	PUNCT
ejpam-3758	2	51	ampayon	ampayon	NOUN
ejpam-3758	2	52	,	,	PUNCT
ejpam-3758	2	53	butuan	butuan	PROPN
ejpam-3758	2	54	city	city	PROPN
ejpam-3758	2	55	,	,	PUNCT
ejpam-3758	2	56	philippines	philippine	NOUN
ejpam-3758	2	57	abstract	abstract	ADJ
ejpam-3758	2	58	.	.	PUNCT
ejpam-3758	3	1	this	this	DET
ejpam-3758	3	2	paper	paper	NOUN
ejpam-3758	3	3	defines	define	VERB
ejpam-3758	3	4	a	a	DET
ejpam-3758	3	5	new	new	ADJ
ejpam-3758	3	6	generalization	generalization	NOUN
ejpam-3758	3	7	of	of	ADP
ejpam-3758	3	8	closed	closed	ADJ
ejpam-3758	3	9	sets	set	NOUN
ejpam-3758	3	10	in	in	ADP
ejpam-3758	3	11	a	a	DET
ejpam-3758	3	12	tri	tri	ADJ
ejpam-3758	3	13	-	-	ADJ
ejpam-3758	3	14	generalized	generalized	ADJ
ejpam-3758	3	15	topological	topological	ADJ
ejpam-3758	3	16	space	space	NOUN
ejpam-3758	3	17	called	call	VERB
ejpam-3758	3	18	(	(	PUNCT
ejpam-3758	3	19	µ1	µ1	PROPN
ejpam-3758	3	20	,	,	PUNCT
ejpam-3758	3	21	µ2	µ2	PROPN
ejpam-3758	3	22	,	,	PUNCT
ejpam-3758	3	23	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	3	24	generalized	generalize	VERB
ejpam-3758	3	25	closed	close	VERB
ejpam-3758	3	26	set	set	NOUN
ejpam-3758	3	27	(	(	PUNCT
ejpam-3758	3	28	or	or	CCONJ
ejpam-3758	3	29	briefly	briefly	ADV
ejpam-3758	3	30	(	(	PUNCT
ejpam-3758	3	31	µ1	µ1	PROPN
ejpam-3758	3	32	,	,	PUNCT
ejpam-3758	3	33	µ2	µ2	ADJ
ejpam-3758	3	34	,	,	PUNCT
ejpam-3758	3	35	µ3)-wg	µ3)-wg	NOUN
ejpam-3758	3	36	closed	close	VERB
ejpam-3758	3	37	set	set	NOUN
ejpam-3758	3	38	)	)	PUNCT
ejpam-3758	3	39	which	which	PRON
ejpam-3758	3	40	is	be	AUX
ejpam-3758	3	41	defined	define	VERB
ejpam-3758	3	42	as	as	SCONJ
ejpam-3758	3	43	follows	follow	VERB
ejpam-3758	3	44	:	:	PUNCT
ejpam-3758	3	45	a	a	DET
ejpam-3758	3	46	subset	subset	NOUN
ejpam-3758	3	47	a	a	PRON
ejpam-3758	3	48	of	of	ADP
ejpam-3758	3	49	x	x	SYM
ejpam-3758	3	50	is	be	AUX
ejpam-3758	3	51	(	(	PUNCT
ejpam-3758	3	52	µ1	µ1	PROPN
ejpam-3758	3	53	,	,	PUNCT
ejpam-3758	3	54	µ2	µ2	PROPN
ejpam-3758	3	55	,	,	PUNCT
ejpam-3758	3	56	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	3	57	generalized	generalize	VERB
ejpam-3758	3	58	closed	close	VERB
ejpam-3758	3	59	set	set	VERB
ejpam-3758	3	60	if	if	SCONJ
ejpam-3758	3	61	clµ	clµ	NOUN
ejpam-3758	3	62	1	1	NUM
ejpam-3758	3	63	(	(	PUNCT
ejpam-3758	3	64	intµ	intµ	NOUN
ejpam-3758	3	65	2	2	NUM
ejpam-3758	3	66	(	(	PUNCT
ejpam-3758	3	67	a	a	NOUN
ejpam-3758	3	68	)	)	PUNCT
ejpam-3758	3	69	)	)	PUNCT
ejpam-3758	4	1	⊆	⊆	X
ejpam-3758	4	2	u	u	NOUN
ejpam-3758	4	3	whenever	whenever	SCONJ
ejpam-3758	4	4	a	a	DET
ejpam-3758	4	5	⊆	⊆	NUM
ejpam-3758	4	6	u	u	NOUN
ejpam-3758	4	7	and	and	CCONJ
ejpam-3758	4	8	u	u	NOUN
ejpam-3758	4	9	is	be	AUX
ejpam-3758	4	10	µ3	µ3	NOUN
ejpam-3758	4	11	-	-	PUNCT
ejpam-3758	4	12	open	open	ADJ
ejpam-3758	4	13	in	in	ADP
ejpam-3758	4	14	x.	x.	NOUN
ejpam-3758	4	15	at	at	ADP
ejpam-3758	4	16	least	least	ADJ
ejpam-3758	4	17	fifteen	fifteen	NUM
ejpam-3758	4	18	defined	define	VERB
ejpam-3758	4	19	closed	closed	ADJ
ejpam-3758	4	20	sets	set	NOUN
ejpam-3758	4	21	found	find	VERB
ejpam-3758	4	22	in	in	ADP
ejpam-3758	4	23	literature	literature	NOUN
ejpam-3758	4	24	are	be	AUX
ejpam-3758	4	25	considered	consider	VERB
ejpam-3758	4	26	special	special	ADJ
ejpam-3758	4	27	cases	case	NOUN
ejpam-3758	4	28	of	of	ADP
ejpam-3758	4	29	(	(	PUNCT
ejpam-3758	4	30	µ1	µ1	PROPN
ejpam-3758	4	31	,	,	PUNCT
ejpam-3758	4	32	µ2	µ2	PROPN
ejpam-3758	4	33	,	,	PUNCT
ejpam-3758	4	34	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	4	35	generalized	generalize	VERB
ejpam-3758	4	36	closed	close	VERB
ejpam-3758	4	37	set	set	VERB
ejpam-3758	4	38	under	under	ADP
ejpam-3758	4	39	some	some	DET
ejpam-3758	4	40	conditions	condition	NOUN
ejpam-3758	4	41	.	.	PUNCT
ejpam-3758	5	1	furthermore	furthermore	ADV
ejpam-3758	5	2	,	,	PUNCT
ejpam-3758	5	3	some	some	DET
ejpam-3758	5	4	properties	property	NOUN
ejpam-3758	5	5	of	of	ADP
ejpam-3758	5	6	(	(	PUNCT
ejpam-3758	5	7	µ1	µ1	PROPN
ejpam-3758	5	8	,	,	PUNCT
ejpam-3758	5	9	µ2	µ2	PROPN
ejpam-3758	5	10	,	,	PUNCT
ejpam-3758	5	11	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	5	12	generalized	generalize	VERB
ejpam-3758	5	13	closed	closed	ADJ
ejpam-3758	5	14	sets	set	NOUN
ejpam-3758	5	15	are	be	AUX
ejpam-3758	5	16	obtained	obtain	VERB
ejpam-3758	5	17	.	.	PUNCT
ejpam-3758	6	1	2020	2020	NUM
ejpam-3758	6	2	mathematics	mathematic	NOUN
ejpam-3758	6	3	subject	subject	NOUN
ejpam-3758	6	4	classifications	classification	NOUN
ejpam-3758	6	5	:	:	PUNCT
ejpam-3758	6	6	54a05	54a05	NUM
ejpam-3758	6	7	,	,	PUNCT
ejpam-3758	6	8	54a10	54a10	NUM
ejpam-3758	6	9	key	key	ADJ
ejpam-3758	6	10	words	word	NOUN
ejpam-3758	6	11	and	and	CCONJ
ejpam-3758	6	12	phrases	phrase	NOUN
ejpam-3758	6	13	:	:	PUNCT
ejpam-3758	6	14	tri	tri	ADJ
ejpam-3758	6	15	-	-	ADJ
ejpam-3758	6	16	generalized	generalized	ADJ
ejpam-3758	6	17	topological	topological	ADJ
ejpam-3758	6	18	space	space	NOUN
ejpam-3758	6	19	,	,	PUNCT
ejpam-3758	6	20	generalized	generalize	VERB
ejpam-3758	6	21	topological	topological	ADJ
ejpam-3758	6	22	space	space	NOUN
ejpam-3758	6	23	,	,	PUNCT
ejpam-3758	6	24	weakly	weakly	ADV
ejpam-3758	6	25	generalized	generalize	VERB
ejpam-3758	6	26	closed	close	VERB
ejpam-3758	6	27	set	set	VERB
ejpam-3758	6	28	1	1	NUM
ejpam-3758	6	29	.	.	PUNCT
ejpam-3758	7	1	introduction	introduction	NOUN
ejpam-3758	7	2	studies	study	NOUN
ejpam-3758	7	3	concerning	concern	VERB
ejpam-3758	7	4	generalized	generalized	ADJ
ejpam-3758	7	5	topologies	topology	NOUN
ejpam-3758	7	6	have	have	AUX
ejpam-3758	7	7	been	be	AUX
ejpam-3758	7	8	in	in	ADP
ejpam-3758	7	9	literature	literature	NOUN
ejpam-3758	7	10	since	since	SCONJ
ejpam-3758	7	11	its	its	PRON
ejpam-3758	7	12	introduction	introduction	NOUN
ejpam-3758	7	13	in	in	ADP
ejpam-3758	7	14	2002	2002	NUM
ejpam-3758	7	15	by	by	ADP
ejpam-3758	7	16	csaszar	csaszar	NOUN
ejpam-3758	7	17	as	as	SCONJ
ejpam-3758	7	18	cited	cite	VERB
ejpam-3758	7	19	in	in	ADP
ejpam-3758	7	20	[	[	X
ejpam-3758	7	21	1	1	NUM
ejpam-3758	7	22	]	]	PUNCT
ejpam-3758	7	23	.	.	PUNCT
ejpam-3758	8	1	topological	topological	ADJ
ejpam-3758	8	2	properties	property	NOUN
ejpam-3758	8	3	of	of	ADP
ejpam-3758	8	4	generalized	generalized	ADJ
ejpam-3758	8	5	topologies	topology	NOUN
ejpam-3758	8	6	have	have	AUX
ejpam-3758	8	7	also	also	ADV
ejpam-3758	8	8	been	be	AUX
ejpam-3758	8	9	explored	explore	VERB
ejpam-3758	8	10	by	by	ADP
ejpam-3758	8	11	some	some	DET
ejpam-3758	8	12	researchers	researcher	NOUN
ejpam-3758	8	13	including	include	VERB
ejpam-3758	8	14	those	those	PRON
ejpam-3758	8	15	by	by	ADP
ejpam-3758	8	16	tabadkan	tabadkan	ADJ
ejpam-3758	8	17	and	and	CCONJ
ejpam-3758	8	18	taghavi	taghavi	VERB
ejpam-3758	8	19	in	in	ADP
ejpam-3758	8	20	2011	2011	NUM
ejpam-3758	8	21	[	[	X
ejpam-3758	8	22	2	2	NUM
ejpam-3758	8	23	]	]	PUNCT
ejpam-3758	8	24	,	,	PUNCT
ejpam-3758	8	25	and	and	CCONJ
ejpam-3758	8	26	those	those	PRON
ejpam-3758	8	27	by	by	ADP
ejpam-3758	8	28	khayyeri	khayyeri	NOUN
ejpam-3758	8	29	and	and	CCONJ
ejpam-3758	8	30	mohamadian	mohamadian	NOUN
ejpam-3758	8	31	also	also	ADV
ejpam-3758	8	32	in	in	ADP
ejpam-3758	8	33	2011	2011	NUM
ejpam-3758	8	34	[	[	X
ejpam-3758	8	35	3	3	NUM
ejpam-3758	8	36	]	]	PUNCT
ejpam-3758	8	37	.	.	PUNCT
ejpam-3758	9	1	other	other	ADJ
ejpam-3758	9	2	authors	author	NOUN
ejpam-3758	9	3	named	name	VERB
ejpam-3758	9	4	a	a	DET
ejpam-3758	9	5	generalized	generalized	ADJ
ejpam-3758	9	6	topology	topology	NOUN
ejpam-3758	9	7	as	as	ADP
ejpam-3758	9	8	a	a	DET
ejpam-3758	9	9	supra	supra	ADJ
ejpam-3758	9	10	topology	topology	NOUN
ejpam-3758	9	11	and	and	CCONJ
ejpam-3758	9	12	derived	derive	VERB
ejpam-3758	9	13	some	some	DET
ejpam-3758	9	14	important	important	ADJ
ejpam-3758	9	15	definitions	definition	NOUN
ejpam-3758	9	16	and	and	CCONJ
ejpam-3758	9	17	properties	property	NOUN
ejpam-3758	9	18	such	such	ADJ
ejpam-3758	9	19	as	as	ADP
ejpam-3758	9	20	those	those	PRON
ejpam-3758	9	21	of	of	ADP
ejpam-3758	9	22	al	al	PROPN
ejpam-3758	9	23	-	-	PUNCT
ejpam-3758	9	24	shami	shami	PROPN
ejpam-3758	9	25	in	in	ADP
ejpam-3758	9	26	2016	2016	NUM
ejpam-3758	9	27	and	and	CCONJ
ejpam-3758	9	28	2018	2018	NUM
ejpam-3758	10	1	[	[	X
ejpam-3758	10	2	11,12	11,12	NUM
ejpam-3758	10	3	]	]	PUNCT
ejpam-3758	10	4	,	,	PUNCT
ejpam-3758	10	5	and	and	CCONJ
ejpam-3758	10	6	el	el	NOUN
ejpam-3758	10	7	-	-	NOUN
ejpam-3758	10	8	shafie	shafie	NOUN
ejpam-3758	10	9	,	,	PUNCT
ejpam-3758	10	10	et	et	PROPN
ejpam-3758	10	11	al	al	PROPN
ejpam-3758	10	12	.	.	PROPN
ejpam-3758	11	1	in	in	ADP
ejpam-3758	11	2	2020	2020	NUM
ejpam-3758	11	3	[	[	X
ejpam-3758	11	4	13	13	NUM
ejpam-3758	11	5	]	]	PUNCT
ejpam-3758	11	6	.	.	PUNCT
ejpam-3758	12	1	new	new	ADJ
ejpam-3758	12	2	developments	development	NOUN
ejpam-3758	12	3	of	of	ADP
ejpam-3758	12	4	researches	research	NOUN
ejpam-3758	12	5	pertaining	pertain	VERB
ejpam-3758	12	6	to	to	ADP
ejpam-3758	12	7	generalized	generalized	ADJ
ejpam-3758	12	8	topologies	topology	NOUN
ejpam-3758	12	9	have	have	AUX
ejpam-3758	12	10	been	be	AUX
ejpam-3758	12	11	extended	extend	VERB
ejpam-3758	12	12	to	to	ADP
ejpam-3758	12	13	bi	bi	ADJ
ejpam-3758	12	14	-	-	ADJ
ejpam-3758	12	15	generalized	generalize	VERB
ejpam-3758	12	16	topologies	topology	NOUN
ejpam-3758	12	17	wherein	wherein	SCONJ
ejpam-3758	12	18	two	two	NUM
ejpam-3758	12	19	generalized	generalized	ADJ
ejpam-3758	12	20	topologies	topology	NOUN
ejpam-3758	12	21	were	be	AUX
ejpam-3758	12	22	considered	consider	VERB
ejpam-3758	12	23	in	in	ADP
ejpam-3758	12	24	the	the	DET
ejpam-3758	12	25	study	study	NOUN
ejpam-3758	12	26	.	.	PUNCT
ejpam-3758	13	1	two	two	NUM
ejpam-3758	13	2	of	of	ADP
ejpam-3758	13	3	which	which	PRON
ejpam-3758	13	4	include	include	VERB
ejpam-3758	13	5	the	the	DET
ejpam-3758	13	6	researches	research	NOUN
ejpam-3758	13	7	of	of	ADP
ejpam-3758	13	8	dungthaisong	dungthaisong	NOUN
ejpam-3758	13	9	,	,	PUNCT
ejpam-3758	13	10	et	et	PROPN
ejpam-3758	13	11	al	al	PROPN
ejpam-3758	13	12	.	.	PROPN
ejpam-3758	14	1	in	in	ADP
ejpam-3758	14	2	2011	2011	NUM
ejpam-3758	14	3	[	[	X
ejpam-3758	14	4	4	4	NUM
ejpam-3758	14	5	]	]	PUNCT
ejpam-3758	14	6	and	and	CCONJ
ejpam-3758	14	7	of	of	ADP
ejpam-3758	14	8	rara	rara	NOUN
ejpam-3758	14	9	and	and	CCONJ
ejpam-3758	14	10	baculta	baculta	NOUN
ejpam-3758	14	11	in	in	ADP
ejpam-3758	14	12	2015	2015	NUM
ejpam-3758	14	13	[	[	X
ejpam-3758	14	14	5	5	NUM
ejpam-3758	14	15	]	]	PUNCT
ejpam-3758	14	16	.	.	PUNCT
ejpam-3758	15	1	several	several	ADJ
ejpam-3758	15	2	researches	research	NOUN
ejpam-3758	15	3	involving	involve	VERB
ejpam-3758	15	4	closed	closed	ADJ
ejpam-3758	15	5	sets	set	NOUN
ejpam-3758	15	6	,	,	PUNCT
ejpam-3758	15	7	generalized	generalize	VERB
ejpam-3758	15	8	closed	closed	ADJ
ejpam-3758	15	9	sets	set	NOUN
ejpam-3758	15	10	and	and	CCONJ
ejpam-3758	15	11	many	many	ADJ
ejpam-3758	15	12	more	more	ADJ
ejpam-3758	15	13	have	have	AUX
ejpam-3758	15	14	been	be	AUX
ejpam-3758	15	15	available	available	ADJ
ejpam-3758	15	16	in	in	ADP
ejpam-3758	15	17	literature	literature	NOUN
ejpam-3758	15	18	.	.	PUNCT
ejpam-3758	16	1	in	in	ADP
ejpam-3758	16	2	the	the	DET
ejpam-3758	16	3	paper	paper	NOUN
ejpam-3758	16	4	of	of	ADP
ejpam-3758	16	5	mishra	mishra	PROPN
ejpam-3758	16	6	,	,	PUNCT
ejpam-3758	16	7	et	et	PROPN
ejpam-3758	16	8	al	al	PROPN
ejpam-3758	16	9	.	.	PUNCT
ejpam-3758	17	1	[	[	X
ejpam-3758	17	2	6	6	NUM
ejpam-3758	17	3	]	]	PUNCT
ejpam-3758	17	4	,	,	PUNCT
ejpam-3758	17	5	sixteen	sixteen	NUM
ejpam-3758	17	6	(	(	PUNCT
ejpam-3758	17	7	16	16	NUM
ejpam-3758	17	8	)	)	PUNCT
ejpam-3758	17	9	definitions	definition	NOUN
ejpam-3758	17	10	of	of	ADP
ejpam-3758	17	11	closed	closed	ADJ
ejpam-3758	17	12	sets	set	NOUN
ejpam-3758	17	13	were	be	AUX
ejpam-3758	17	14	enumerated	enumerate	VERB
ejpam-3758	17	15	.	.	PUNCT
ejpam-3758	18	1	seven	seven	NUM
ejpam-3758	18	2	(	(	PUNCT
ejpam-3758	18	3	7	7	NUM
ejpam-3758	18	4	)	)	PUNCT
ejpam-3758	18	5	definitions	definition	NOUN
ejpam-3758	18	6	of	of	ADP
ejpam-3758	18	7	closed	closed	ADJ
ejpam-3758	18	8	sets	set	NOUN
ejpam-3758	18	9	were	be	AUX
ejpam-3758	18	10	also	also	ADV
ejpam-3758	18	11	listed	list	VERB
ejpam-3758	18	12	in	in	ADP
ejpam-3758	18	13	the	the	DET
ejpam-3758	18	14	paper	paper	NOUN
ejpam-3758	18	15	of	of	ADP
ejpam-3758	18	16	cao	cao	PROPN
ejpam-3758	18	17	,	,	PUNCT
ejpam-3758	18	18	et	et	NOUN
ejpam-3758	18	19	al.[7	al.[7	PROPN
ejpam-3758	18	20	]	]	X
ejpam-3758	18	21	in	in	ADP
ejpam-3758	18	22	1999	1999	NUM
ejpam-3758	18	23	.	.	PUNCT
ejpam-3758	19	1	in	in	ADP
ejpam-3758	19	2	this	this	DET
ejpam-3758	19	3	paper	paper	NOUN
ejpam-3758	19	4	,	,	PUNCT
ejpam-3758	19	5	the	the	DET
ejpam-3758	19	6	researcher	researcher	NOUN
ejpam-3758	19	7	defines	define	VERB
ejpam-3758	19	8	a	a	DET
ejpam-3758	19	9	new	new	ADJ
ejpam-3758	19	10	generalization	generalization	NOUN
ejpam-3758	19	11	of	of	ADP
ejpam-3758	19	12	closed	closed	ADJ
ejpam-3758	19	13	sets	set	NOUN
ejpam-3758	19	14	called	call	VERB
ejpam-3758	19	15	(	(	PUNCT
ejpam-3758	19	16	µ1	µ1	PROPN
ejpam-3758	19	17	,	,	PUNCT
ejpam-3758	19	18	µ2	µ2	PROPN
ejpam-3758	19	19	,	,	PUNCT
ejpam-3758	19	20	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	19	21	generalized	generalize	VERB
ejpam-3758	19	22	closed	close	VERB
ejpam-3758	19	23	set	set	NOUN
ejpam-3758	19	24	containing	contain	VERB
ejpam-3758	19	25	fifteen	fifteen	NUM
ejpam-3758	19	26	literature	literature	NOUN
ejpam-3758	19	27	-	-	PUNCT
ejpam-3758	19	28	defined	define	VERB
ejpam-3758	19	29	closed	closed	ADJ
ejpam-3758	19	30	sets	set	NOUN
ejpam-3758	19	31	.	.	PUNCT
ejpam-3758	20	1	furthermore	furthermore	ADV
ejpam-3758	20	2	,	,	PUNCT
ejpam-3758	20	3	the	the	DET
ejpam-3758	20	4	corresponding	correspond	VERB
ejpam-3758	20	5	(	(	PUNCT
ejpam-3758	20	6	µ1	µ1	PROPN
ejpam-3758	20	7	,	,	PUNCT
ejpam-3758	20	8	µ2	µ2	PROPN
ejpam-3758	20	9	,	,	PUNCT
ejpam-3758	20	10	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	20	11	generalized	generalize	VERB
ejpam-3758	20	12	open	open	ADJ
ejpam-3758	20	13	sets	set	NOUN
ejpam-3758	20	14	are	be	AUX
ejpam-3758	20	15	characterized	characterize	VERB
ejpam-3758	20	16	.	.	PUNCT
ejpam-3758	21	1	moreover	moreover	ADV
ejpam-3758	21	2	,	,	PUNCT
ejpam-3758	21	3	some	some	DET
ejpam-3758	21	4	properties	property	NOUN
ejpam-3758	21	5	of	of	ADP
ejpam-3758	21	6	(	(	PUNCT
ejpam-3758	21	7	µ1	µ1	PROPN
ejpam-3758	21	8	,	,	PUNCT
ejpam-3758	21	9	µ2	µ2	PROPN
ejpam-3758	21	10	,	,	PUNCT
ejpam-3758	21	11	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	21	12	generalized	generalize	VERB
ejpam-3758	21	13	closed	closed	ADJ
ejpam-3758	21	14	sets	set	NOUN
ejpam-3758	21	15	are	be	AUX
ejpam-3758	21	16	obtained	obtain	VERB
ejpam-3758	21	17	.	.	PUNCT
ejpam-3758	22	1	∗corresponding	∗corresponde	VERB
ejpam-3758	22	2	author	author	NOUN
ejpam-3758	22	3	.	.	PUNCT
ejpam-3758	23	1	doi	doi	NOUN
ejpam-3758	23	2	:	:	PUNCT
ejpam-3758	23	3	https://doi.org/10.29020/nybg.ejpam.v13i4.3758	https://doi.org/10.29020/nybg.ejpam.v13i4.3758	NOUN
ejpam-3758	23	4	email	email	NOUN
ejpam-3758	23	5	addresses	address	VERB
ejpam-3758	23	6	:	:	PUNCT
ejpam-3758	23	7	bgagua@carsu.edu.ph	bgagua@carsu.edu.ph	PROPN
ejpam-3758	23	8	(	(	PUNCT
ejpam-3758	23	9	b.	b.	PROPN
ejpam-3758	23	10	agua	agua	PROPN
ejpam-3758	23	11	)	)	PUNCT
ejpam-3758	23	12	,	,	PUNCT
ejpam-3758	23	13	rnpaluga@carsu.edu.ph	rnpaluga@carsu.edu.ph	NOUN
ejpam-3758	23	14	(	(	PUNCT
ejpam-3758	23	15	r.	r.	PROPN
ejpam-3758	23	16	paluga	paluga	PROPN
ejpam-3758	23	17	)	)	PUNCT
ejpam-3758	23	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-3758	24	1	977	977	NUM
ejpam-3758	24	2	c	c	NOUN
ejpam-3758	24	3	©	©	NOUN
ejpam-3758	24	4	2020	2020	NUM
ejpam-3758	24	5	ejpam	ejpam	VERB
ejpam-3758	24	6	all	all	DET
ejpam-3758	24	7	rights	right	NOUN
ejpam-3758	24	8	reserved	reserve	VERB
ejpam-3758	24	9	.	.	PUNCT
ejpam-3758	25	1	b.	b.	PROPN
ejpam-3758	25	2	agua	agua	PROPN
ejpam-3758	25	3	,	,	PUNCT
ejpam-3758	25	4	r.	r.	PROPN
ejpam-3758	25	5	paluga	paluga	PROPN
ejpam-3758	25	6	/	/	SYM
ejpam-3758	25	7	eur	eur	PROPN
ejpam-3758	25	8	.	.	PUNCT
ejpam-3758	26	1	j.	j.	PROPN
ejpam-3758	26	2	pure	pure	PROPN
ejpam-3758	26	3	appl	appl	PROPN
ejpam-3758	26	4	.	.	PROPN
ejpam-3758	26	5	math	math	PROPN
ejpam-3758	26	6	,	,	PUNCT
ejpam-3758	26	7	13	13	NUM
ejpam-3758	26	8	(	(	PUNCT
ejpam-3758	26	9	4	4	NUM
ejpam-3758	26	10	)	)	PUNCT
ejpam-3758	26	11	(	(	PUNCT
ejpam-3758	26	12	2020	2020	NUM
ejpam-3758	26	13	)	)	PUNCT
ejpam-3758	26	14	,	,	PUNCT
ejpam-3758	26	15	977	977	NUM
ejpam-3758	26	16	-	-	SYM
ejpam-3758	26	17	986	986	NUM
ejpam-3758	26	18	978	978	NUM
ejpam-3758	26	19	2	2	NUM
ejpam-3758	26	20	.	.	PUNCT
ejpam-3758	26	21	preliminaries	preliminary	NOUN
ejpam-3758	26	22	definition	definition	NOUN
ejpam-3758	26	23	1	1	NUM
ejpam-3758	26	24	.	.	PUNCT
ejpam-3758	27	1	[	[	X
ejpam-3758	27	2	1	1	X
ejpam-3758	27	3	]	]	PUNCT
ejpam-3758	27	4	let	let	VERB
ejpam-3758	27	5	x	x	PRON
ejpam-3758	27	6	be	be	AUX
ejpam-3758	27	7	a	a	DET
ejpam-3758	27	8	nonempty	nonempty	ADV
ejpam-3758	27	9	set	set	VERB
ejpam-3758	27	10	.	.	PUNCT
ejpam-3758	28	1	a	a	DET
ejpam-3758	28	2	collection	collection	NOUN
ejpam-3758	28	3	µ	µ	X
ejpam-3758	28	4	of	of	ADP
ejpam-3758	28	5	subsets	subset	NOUN
ejpam-3758	28	6	of	of	ADP
ejpam-3758	28	7	x	x	X
ejpam-3758	28	8	is	be	AUX
ejpam-3758	28	9	a	a	DET
ejpam-3758	28	10	generalized	generalized	ADJ
ejpam-3758	28	11	topology	topology	NOUN
ejpam-3758	28	12	(	(	PUNCT
ejpam-3758	28	13	or	or	CCONJ
ejpam-3758	28	14	briefly	briefly	ADV
ejpam-3758	28	15	gt	gt	INTJ
ejpam-3758	28	16	)	)	PUNCT
ejpam-3758	28	17	in	in	ADP
ejpam-3758	28	18	x	x	SYM
ejpam-3758	28	19	if	if	SCONJ
ejpam-3758	28	20	it	it	PRON
ejpam-3758	28	21	satisfies	satisfy	VERB
ejpam-3758	28	22	:	:	PUNCT
ejpam-3758	28	23	i.	i.	NOUN
ejpam-3758	28	24	∅	∅	NOUN
ejpam-3758	28	25	∈	∈	PROPN
ejpam-3758	28	26	µ	µ	PROPN
ejpam-3758	28	27	,	,	PUNCT
ejpam-3758	28	28	and	and	CCONJ
ejpam-3758	28	29	ii	ii	NOUN
ejpam-3758	28	30	.	.	PUNCT
ejpam-3758	29	1	if	if	SCONJ
ejpam-3758	29	2	{	{	PUNCT
ejpam-3758	29	3	mi	mi	NOUN
ejpam-3758	29	4	:	:	PUNCT
ejpam-3758	29	5	i	i	PROPN
ejpam-3758	29	6	∈	∈	VERB
ejpam-3758	29	7	i	i	PRON
ejpam-3758	29	8	}	}	PUNCT
ejpam-3758	29	9	⊆	⊆	NUM
ejpam-3758	29	10	µ	µ	NUM
ejpam-3758	29	11	,	,	PUNCT
ejpam-3758	29	12	then⋃	then⋃	PROPN
ejpam-3758	29	13	i∈imi	i∈imi	PROPN
ejpam-3758	29	14	∈	∈	PROPN
ejpam-3758	29	15	µ.	µ.	NOUN
ejpam-3758	29	16	if	if	SCONJ
ejpam-3758	29	17	µ	µ	NOUN
ejpam-3758	29	18	is	be	AUX
ejpam-3758	29	19	a	a	DET
ejpam-3758	29	20	gt	gt	PROPN
ejpam-3758	29	21	in	in	ADP
ejpam-3758	29	22	x	x	NOUN
ejpam-3758	29	23	,	,	PUNCT
ejpam-3758	29	24	then	then	ADV
ejpam-3758	29	25	(	(	PUNCT
ejpam-3758	29	26	x,µ	x,µ	NOUN
ejpam-3758	29	27	)	)	PUNCT
ejpam-3758	29	28	is	be	AUX
ejpam-3758	29	29	called	call	VERB
ejpam-3758	29	30	a	a	DET
ejpam-3758	29	31	generalized	generalized	ADJ
ejpam-3758	29	32	topological	topological	ADJ
ejpam-3758	29	33	space	space	NOUN
ejpam-3758	29	34	(	(	PUNCT
ejpam-3758	29	35	or	or	CCONJ
ejpam-3758	29	36	briefly	briefly	ADV
ejpam-3758	29	37	gt	gt	PROPN
ejpam-3758	29	38	space	space	NOUN
ejpam-3758	29	39	)	)	PUNCT
ejpam-3758	29	40	,	,	PUNCT
ejpam-3758	29	41	and	and	CCONJ
ejpam-3758	29	42	the	the	DET
ejpam-3758	29	43	elements	element	NOUN
ejpam-3758	29	44	of	of	ADP
ejpam-3758	29	45	µ	µ	NOUN
ejpam-3758	29	46	are	be	AUX
ejpam-3758	29	47	called	call	VERB
ejpam-3758	29	48	µ-open	µ-open	NOUN
ejpam-3758	29	49	sets	set	NOUN
ejpam-3758	29	50	in	in	ADP
ejpam-3758	29	51	x.	x.	NOUN
ejpam-3758	29	52	if	if	SCONJ
ejpam-3758	29	53	µ1	µ1	PROPN
ejpam-3758	29	54	and	and	CCONJ
ejpam-3758	29	55	µ2	µ2	PROPN
ejpam-3758	29	56	are	be	AUX
ejpam-3758	29	57	gts	gts	NOUN
ejpam-3758	29	58	in	in	ADP
ejpam-3758	29	59	x	x	NOUN
ejpam-3758	29	60	,	,	PUNCT
ejpam-3758	29	61	then	then	ADV
ejpam-3758	29	62	(	(	PUNCT
ejpam-3758	29	63	x,µ1	x,µ1	PROPN
ejpam-3758	29	64	,	,	PUNCT
ejpam-3758	29	65	µ2	µ2	PROPN
ejpam-3758	29	66	)	)	PUNCT
ejpam-3758	29	67	is	be	AUX
ejpam-3758	29	68	called	call	VERB
ejpam-3758	29	69	a	a	DET
ejpam-3758	29	70	bi	bi	ADJ
ejpam-3758	29	71	-	-	ADJ
ejpam-3758	29	72	generalized	generalized	ADJ
ejpam-3758	29	73	topological	topological	ADJ
ejpam-3758	29	74	space.if	space.if	NUM
ejpam-3758	29	75	µ1	µ1	PROPN
ejpam-3758	29	76	µ2	µ2	PROPN
ejpam-3758	29	77	and	and	CCONJ
ejpam-3758	29	78	µ3	µ3	NOUN
ejpam-3758	29	79	are	be	AUX
ejpam-3758	29	80	gts	gts	NOUN
ejpam-3758	29	81	in	in	ADP
ejpam-3758	29	82	x	x	NOUN
ejpam-3758	29	83	,	,	PUNCT
ejpam-3758	29	84	then	then	ADV
ejpam-3758	29	85	(	(	PUNCT
ejpam-3758	29	86	x,µ1	x,µ1	PROPN
ejpam-3758	29	87	,	,	PUNCT
ejpam-3758	29	88	µ2	µ2	ADJ
ejpam-3758	29	89	,	,	PUNCT
ejpam-3758	29	90	µ3	µ3	NUM
ejpam-3758	29	91	)	)	PUNCT
ejpam-3758	29	92	is	be	AUX
ejpam-3758	29	93	called	call	VERB
ejpam-3758	29	94	a	a	DET
ejpam-3758	29	95	tri	tri	ADJ
ejpam-3758	29	96	-	-	ADJ
ejpam-3758	29	97	generalized	generalized	ADJ
ejpam-3758	29	98	topological	topological	ADJ
ejpam-3758	29	99	space	space	NOUN
ejpam-3758	29	100	.	.	PUNCT
ejpam-3758	30	1	definition	definition	NOUN
ejpam-3758	30	2	2	2	NUM
ejpam-3758	30	3	.	.	PUNCT
ejpam-3758	31	1	[	[	X
ejpam-3758	31	2	1,3	1,3	X
ejpam-3758	31	3	]	]	X
ejpam-3758	31	4	let	let	VERB
ejpam-3758	31	5	µ	µ	X
ejpam-3758	31	6	be	be	AUX
ejpam-3758	31	7	a	a	DET
ejpam-3758	31	8	gt	gt	PROPN
ejpam-3758	31	9	in	in	ADP
ejpam-3758	31	10	x.	x.	PROPN
ejpam-3758	31	11	a	a	DET
ejpam-3758	31	12	subset	subset	NOUN
ejpam-3758	31	13	f	f	PROPN
ejpam-3758	31	14	of	of	ADP
ejpam-3758	31	15	x	x	PROPN
ejpam-3758	31	16	is	be	AUX
ejpam-3758	31	17	said	say	VERB
ejpam-3758	31	18	to	to	PART
ejpam-3758	31	19	be	be	AUX
ejpam-3758	31	20	a	a	DET
ejpam-3758	31	21	µ-closed	µ-close	VERB
ejpam-3758	31	22	set	set	VERB
ejpam-3758	31	23	if	if	SCONJ
ejpam-3758	31	24	the	the	DET
ejpam-3758	31	25	complement	complement	NOUN
ejpam-3758	31	26	of	of	ADP
ejpam-3758	31	27	f	f	PROPN
ejpam-3758	31	28	(	(	PUNCT
ejpam-3758	31	29	f	f	PROPN
ejpam-3758	31	30	c	c	X
ejpam-3758	31	31	)	)	PUNCT
ejpam-3758	31	32	is	be	AUX
ejpam-3758	31	33	µ-open	µ-open	NOUN
ejpam-3758	31	34	.	.	PUNCT
ejpam-3758	32	1	the	the	DET
ejpam-3758	32	2	µ-closure	µ-closure	NOUN
ejpam-3758	32	3	of	of	ADP
ejpam-3758	32	4	a	a	DET
ejpam-3758	32	5	subset	subset	NOUN
ejpam-3758	32	6	a	a	PRON
ejpam-3758	32	7	of	of	ADP
ejpam-3758	32	8	x	x	PRON
ejpam-3758	32	9	,	,	PUNCT
ejpam-3758	32	10	denoted	denote	VERB
ejpam-3758	32	11	by	by	ADP
ejpam-3758	32	12	clµ(a	clµ(a	PROPN
ejpam-3758	32	13	)	)	PUNCT
ejpam-3758	32	14	,	,	PUNCT
ejpam-3758	32	15	is	be	AUX
ejpam-3758	32	16	the	the	DET
ejpam-3758	32	17	intersection	intersection	NOUN
ejpam-3758	32	18	of	of	ADP
ejpam-3758	32	19	all	all	DET
ejpam-3758	32	20	µ-closed	µ-close	VERB
ejpam-3758	32	21	sets	set	NOUN
ejpam-3758	32	22	in	in	ADP
ejpam-3758	32	23	x	x	PUNCT
ejpam-3758	32	24	containing	contain	VERB
ejpam-3758	32	25	a	a	DET
ejpam-3758	32	26	while	while	NOUN
ejpam-3758	32	27	the	the	DET
ejpam-3758	32	28	µ-interior	µ-interior	NOUN
ejpam-3758	32	29	of	of	ADP
ejpam-3758	32	30	a	a	DET
ejpam-3758	32	31	subset	subset	NOUN
ejpam-3758	32	32	a	a	PRON
ejpam-3758	32	33	of	of	ADP
ejpam-3758	32	34	x	x	PRON
ejpam-3758	32	35	,	,	PUNCT
ejpam-3758	32	36	denoted	denote	VERB
ejpam-3758	32	37	by	by	ADP
ejpam-3758	32	38	intµ(a	intµ(a	PROPN
ejpam-3758	32	39	)	)	PUNCT
ejpam-3758	32	40	,	,	PUNCT
ejpam-3758	32	41	is	be	AUX
ejpam-3758	32	42	the	the	DET
ejpam-3758	32	43	union	union	NOUN
ejpam-3758	32	44	of	of	ADP
ejpam-3758	32	45	all	all	DET
ejpam-3758	32	46	µ-open	µ-open	PROPN
ejpam-3758	32	47	subsets	subset	NOUN
ejpam-3758	32	48	of	of	ADP
ejpam-3758	32	49	a	a	PRON
ejpam-3758	32	50	in	in	ADP
ejpam-3758	32	51	x.	x.	NOUN
ejpam-3758	32	52	the	the	DET
ejpam-3758	32	53	succeeding	succeed	VERB
ejpam-3758	32	54	theorems	theorem	NOUN
ejpam-3758	32	55	1	1	NUM
ejpam-3758	32	56	to	to	PART
ejpam-3758	32	57	5	5	NUM
ejpam-3758	32	58	are	be	AUX
ejpam-3758	32	59	fundamental	fundamental	ADJ
ejpam-3758	32	60	properties	property	NOUN
ejpam-3758	32	61	of	of	ADP
ejpam-3758	32	62	any	any	DET
ejpam-3758	32	63	gt	gt	PROPN
ejpam-3758	32	64	µ	µ	NOUN
ejpam-3758	32	65	and	and	CCONJ
ejpam-3758	32	66	can	can	AUX
ejpam-3758	32	67	be	be	AUX
ejpam-3758	32	68	easily	easily	ADV
ejpam-3758	32	69	proven	prove	VERB
ejpam-3758	32	70	.	.	PUNCT
ejpam-3758	33	1	theorem	theorem	NOUN
ejpam-3758	33	2	1	1	NUM
ejpam-3758	33	3	.	.	PUNCT
ejpam-3758	34	1	let	let	VERB
ejpam-3758	34	2	x	x	SYM
ejpam-3758	34	3	6=	6=	ADP
ejpam-3758	34	4	∅	∅	NOUN
ejpam-3758	34	5	and	and	CCONJ
ejpam-3758	34	6	µ	µ	PRON
ejpam-3758	34	7	be	be	AUX
ejpam-3758	34	8	a	a	DET
ejpam-3758	34	9	gt	gt	NOUN
ejpam-3758	34	10	in	in	ADP
ejpam-3758	34	11	x.	x.	NOUN
ejpam-3758	34	12	if	if	SCONJ
ejpam-3758	34	13	{	{	PUNCT
ejpam-3758	34	14	ai	ai	VERB
ejpam-3758	34	15	:	:	PUNCT
ejpam-3758	34	16	i	i	PRON
ejpam-3758	34	17	∈	∈	PROPN
ejpam-3758	35	1	i	i	PRON
ejpam-3758	35	2	}	}	PUNCT
ejpam-3758	35	3	is	be	AUX
ejpam-3758	35	4	a	a	DET
ejpam-3758	35	5	collection	collection	NOUN
ejpam-3758	35	6	of	of	ADP
ejpam-3758	35	7	µ-closed	µ-close	VERB
ejpam-3758	35	8	sets	set	NOUN
ejpam-3758	35	9	,	,	PUNCT
ejpam-3758	35	10	then	then	ADV
ejpam-3758	35	11	⋂	⋂	PROPN
ejpam-3758	35	12	i∈i	i∈i	NOUN
ejpam-3758	35	13	ai	ai	VERB
ejpam-3758	35	14	is	be	AUX
ejpam-3758	35	15	a	a	DET
ejpam-3758	35	16	µ-closed	µ-close	VERB
ejpam-3758	35	17	set	set	NOUN
ejpam-3758	35	18	.	.	PUNCT
ejpam-3758	36	1	theorem	theorem	NOUN
ejpam-3758	36	2	2	2	NUM
ejpam-3758	36	3	.	.	PUNCT
ejpam-3758	37	1	let	let	VERB
ejpam-3758	37	2	x	x	SYM
ejpam-3758	37	3	6=	6=	ADP
ejpam-3758	37	4	∅	∅	NOUN
ejpam-3758	37	5	and	and	CCONJ
ejpam-3758	37	6	µ	µ	PRON
ejpam-3758	37	7	be	be	AUX
ejpam-3758	37	8	a	a	DET
ejpam-3758	37	9	gt	gt	PROPN
ejpam-3758	37	10	in	in	ADP
ejpam-3758	37	11	x.	x.	PROPN
ejpam-3758	37	12	suppose	suppose	VERB
ejpam-3758	37	13	also	also	ADV
ejpam-3758	37	14	that	that	SCONJ
ejpam-3758	37	15	a	a	PRON
ejpam-3758	37	16	and	and	CCONJ
ejpam-3758	37	17	b	b	NOUN
ejpam-3758	37	18	are	be	AUX
ejpam-3758	37	19	subsets	subset	NOUN
ejpam-3758	37	20	of	of	ADP
ejpam-3758	37	21	x.	x.	NOUN
ejpam-3758	37	22	then	then	ADV
ejpam-3758	37	23	,	,	PUNCT
ejpam-3758	37	24	i.	i.	NOUN
ejpam-3758	37	25	if	if	SCONJ
ejpam-3758	37	26	a	a	DET
ejpam-3758	37	27	⊆	⊆	NUM
ejpam-3758	37	28	x	x	SYM
ejpam-3758	37	29	,	,	PUNCT
ejpam-3758	37	30	then	then	ADV
ejpam-3758	37	31	intµ(a	intµ(a	NOUN
ejpam-3758	37	32	)	)	PUNCT
ejpam-3758	37	33	⊆	⊆	NUM
ejpam-3758	37	34	a.	a.	NOUN
ejpam-3758	37	35	ii	ii	PROPN
ejpam-3758	37	36	.	.	PUNCT
ejpam-3758	38	1	intµ(a	intµ(a	NOUN
ejpam-3758	38	2	)	)	PUNCT
ejpam-3758	38	3	is	be	AUX
ejpam-3758	38	4	the	the	DET
ejpam-3758	38	5	largest	large	ADJ
ejpam-3758	38	6	open	open	ADJ
ejpam-3758	38	7	subset	subset	NOUN
ejpam-3758	38	8	of	of	ADP
ejpam-3758	38	9	a.	a.	PROPN
ejpam-3758	38	10	iii	iii	PROPN
ejpam-3758	38	11	.	.	PUNCT
ejpam-3758	39	1	a	a	PRON
ejpam-3758	39	2	is	be	AUX
ejpam-3758	39	3	µ-open	µ-open	NOUN
ejpam-3758	39	4	if	if	SCONJ
ejpam-3758	39	5	and	and	CCONJ
ejpam-3758	39	6	only	only	ADV
ejpam-3758	39	7	if	if	SCONJ
ejpam-3758	39	8	intµ(a	intµ(a	ADJ
ejpam-3758	39	9	)	)	PUNCT
ejpam-3758	39	10	=	=	SYM
ejpam-3758	39	11	a.	a.	NOUN
ejpam-3758	39	12	iv	iv	NUM
ejpam-3758	39	13	.	.	PUNCT
ejpam-3758	40	1	if	if	SCONJ
ejpam-3758	40	2	a	a	DET
ejpam-3758	40	3	⊆	⊆	NUM
ejpam-3758	40	4	b	b	NOUN
ejpam-3758	40	5	,	,	PUNCT
ejpam-3758	40	6	then	then	ADV
ejpam-3758	40	7	intµ(a	intµ(a	NOUN
ejpam-3758	40	8	)	)	PUNCT
ejpam-3758	40	9	⊆	⊆	NUM
ejpam-3758	40	10	intµ(b	intµ(b	NOUN
ejpam-3758	40	11	)	)	PUNCT
ejpam-3758	40	12	.	.	PUNCT
ejpam-3758	40	13	theorem	theorem	NOUN
ejpam-3758	40	14	3	3	X
ejpam-3758	40	15	.	.	PUNCT
ejpam-3758	41	1	let	let	VERB
ejpam-3758	41	2	x	x	SYM
ejpam-3758	41	3	6=	6=	ADP
ejpam-3758	41	4	∅	∅	NOUN
ejpam-3758	41	5	and	and	CCONJ
ejpam-3758	41	6	µ	µ	PRON
ejpam-3758	41	7	be	be	AUX
ejpam-3758	41	8	a	a	DET
ejpam-3758	41	9	gt	gt	PROPN
ejpam-3758	41	10	in	in	ADP
ejpam-3758	41	11	x.	x.	PROPN
ejpam-3758	41	12	suppose	suppose	VERB
ejpam-3758	41	13	also	also	ADV
ejpam-3758	41	14	that	that	SCONJ
ejpam-3758	41	15	a	a	PRON
ejpam-3758	41	16	and	and	CCONJ
ejpam-3758	41	17	b	b	NOUN
ejpam-3758	41	18	are	be	AUX
ejpam-3758	41	19	subsets	subset	NOUN
ejpam-3758	41	20	of	of	ADP
ejpam-3758	41	21	x.	x.	NOUN
ejpam-3758	41	22	then	then	ADV
ejpam-3758	41	23	,	,	PUNCT
ejpam-3758	41	24	i.	i.	NOUN
ejpam-3758	41	25	if	if	SCONJ
ejpam-3758	41	26	a	a	DET
ejpam-3758	41	27	⊆	⊆	NUM
ejpam-3758	41	28	x	x	NOUN
ejpam-3758	41	29	,	,	PUNCT
ejpam-3758	41	30	then	then	ADV
ejpam-3758	41	31	a	a	DET
ejpam-3758	41	32	⊆	⊆	NUM
ejpam-3758	41	33	clµ(a	clµ(a	ADJ
ejpam-3758	41	34	)	)	PUNCT
ejpam-3758	41	35	.	.	PUNCT
ejpam-3758	42	1	ii	ii	PROPN
ejpam-3758	42	2	.	.	PUNCT
ejpam-3758	43	1	clµ(a	clµ(a	PROPN
ejpam-3758	43	2	)	)	PUNCT
ejpam-3758	44	1	is	be	AUX
ejpam-3758	44	2	the	the	DET
ejpam-3758	44	3	smallest	small	ADJ
ejpam-3758	44	4	closed	closed	ADJ
ejpam-3758	44	5	superset	superset	NOUN
ejpam-3758	44	6	of	of	ADP
ejpam-3758	44	7	a.	a.	PROPN
ejpam-3758	44	8	iii	iii	PROPN
ejpam-3758	44	9	.	.	PUNCT
ejpam-3758	45	1	a	a	PRON
ejpam-3758	45	2	is	be	AUX
ejpam-3758	45	3	µ-closed	µ-close	VERB
ejpam-3758	45	4	if	if	SCONJ
ejpam-3758	45	5	and	and	CCONJ
ejpam-3758	45	6	only	only	ADV
ejpam-3758	45	7	if	if	SCONJ
ejpam-3758	45	8	clµ(a	clµ(a	PROPN
ejpam-3758	45	9	)	)	PUNCT
ejpam-3758	45	10	=	=	SYM
ejpam-3758	45	11	a.	a.	NOUN
ejpam-3758	45	12	iv	iv	NUM
ejpam-3758	45	13	.	.	PUNCT
ejpam-3758	46	1	if	if	SCONJ
ejpam-3758	46	2	a	a	DET
ejpam-3758	46	3	⊆	⊆	NUM
ejpam-3758	46	4	b	b	NOUN
ejpam-3758	46	5	,	,	PUNCT
ejpam-3758	46	6	then	then	ADV
ejpam-3758	46	7	clµ(a	clµ(a	PROPN
ejpam-3758	46	8	)	)	PUNCT
ejpam-3758	46	9	⊆	⊆	NUM
ejpam-3758	46	10	clµ(b	clµ(b	PROPN
ejpam-3758	46	11	)	)	PUNCT
ejpam-3758	46	12	.	.	PUNCT
ejpam-3758	47	1	theorem	theorem	ADJ
ejpam-3758	47	2	4	4	NUM
ejpam-3758	47	3	.	.	PUNCT
ejpam-3758	48	1	let	let	VERB
ejpam-3758	48	2	x	x	SYM
ejpam-3758	48	3	6=	6=	ADP
ejpam-3758	48	4	∅	∅	NOUN
ejpam-3758	48	5	and	and	CCONJ
ejpam-3758	48	6	µ1	µ1	PROPN
ejpam-3758	48	7	⊆	⊆	NUM
ejpam-3758	48	8	µ2	µ2	PROPN
ejpam-3758	48	9	where	where	SCONJ
ejpam-3758	48	10	µ1	µ1	PROPN
ejpam-3758	48	11	and	and	CCONJ
ejpam-3758	48	12	µ2	µ2	PROPN
ejpam-3758	48	13	are	be	AUX
ejpam-3758	48	14	gts	gts	NOUN
ejpam-3758	48	15	in	in	ADP
ejpam-3758	48	16	x.	x.	NOUN
ejpam-3758	48	17	then	then	ADV
ejpam-3758	48	18	a	a	PRON
ejpam-3758	48	19	is	be	AUX
ejpam-3758	48	20	µ2	µ2	ADJ
ejpam-3758	48	21	-	-	PUNCT
ejpam-3758	48	22	open	open	ADJ
ejpam-3758	48	23	(	(	PUNCT
ejpam-3758	48	24	µ2	µ2	NOUN
ejpam-3758	48	25	-	-	PUNCT
ejpam-3758	48	26	closed	close	VERB
ejpam-3758	48	27	)	)	PUNCT
ejpam-3758	48	28	whenever	whenever	SCONJ
ejpam-3758	48	29	a	a	PRON
ejpam-3758	48	30	is	be	AUX
ejpam-3758	48	31	µ1	µ1	NOUN
ejpam-3758	48	32	-	-	PUNCT
ejpam-3758	48	33	open	open	ADJ
ejpam-3758	48	34	(	(	PUNCT
ejpam-3758	48	35	µ1	µ1	NOUN
ejpam-3758	48	36	-	-	PUNCT
ejpam-3758	48	37	closed	closed	ADJ
ejpam-3758	48	38	)	)	PUNCT
ejpam-3758	48	39	.	.	PUNCT
ejpam-3758	49	1	theorem	theorem	NOUN
ejpam-3758	49	2	5	5	NUM
ejpam-3758	49	3	.	.	PUNCT
ejpam-3758	50	1	let	let	VERB
ejpam-3758	50	2	x	x	SYM
ejpam-3758	50	3	6=	6=	ADP
ejpam-3758	50	4	∅	∅	NOUN
ejpam-3758	50	5	,	,	PUNCT
ejpam-3758	50	6	a	a	DET
ejpam-3758	50	7	⊆	⊆	NUM
ejpam-3758	50	8	x	x	NOUN
ejpam-3758	50	9	,	,	PUNCT
ejpam-3758	50	10	and	and	CCONJ
ejpam-3758	50	11	µ	µ	PRON
ejpam-3758	50	12	be	be	AUX
ejpam-3758	50	13	a	a	DET
ejpam-3758	50	14	generalized	generalized	ADJ
ejpam-3758	50	15	topology	topology	NOUN
ejpam-3758	50	16	.	.	PUNCT
ejpam-3758	51	1	then	then	ADV
ejpam-3758	51	2	,	,	PUNCT
ejpam-3758	51	3	[	[	X
ejpam-3758	51	4	intµ(a)]c	intµ(a)]c	NOUN
ejpam-3758	51	5	=	=	SYM
ejpam-3758	51	6	clµ(ac	clµ(ac	PROPN
ejpam-3758	51	7	)	)	PUNCT
ejpam-3758	51	8	.	.	PUNCT
ejpam-3758	52	1	b.	b.	PROPN
ejpam-3758	52	2	agua	agua	PROPN
ejpam-3758	52	3	,	,	PUNCT
ejpam-3758	52	4	r.	r.	PROPN
ejpam-3758	52	5	paluga	paluga	PROPN
ejpam-3758	52	6	/	/	SYM
ejpam-3758	52	7	eur	eur	PROPN
ejpam-3758	52	8	.	.	PUNCT
ejpam-3758	53	1	j.	j.	PROPN
ejpam-3758	53	2	pure	pure	PROPN
ejpam-3758	53	3	appl	appl	PROPN
ejpam-3758	53	4	.	.	PROPN
ejpam-3758	53	5	math	math	PROPN
ejpam-3758	53	6	,	,	PUNCT
ejpam-3758	53	7	13	13	NUM
ejpam-3758	53	8	(	(	PUNCT
ejpam-3758	53	9	4	4	NUM
ejpam-3758	53	10	)	)	PUNCT
ejpam-3758	53	11	(	(	PUNCT
ejpam-3758	53	12	2020	2020	NUM
ejpam-3758	53	13	)	)	PUNCT
ejpam-3758	53	14	,	,	PUNCT
ejpam-3758	53	15	977	977	NUM
ejpam-3758	53	16	-	-	SYM
ejpam-3758	53	17	986	986	NUM
ejpam-3758	53	18	979	979	NUM
ejpam-3758	53	19	definition	definition	NOUN
ejpam-3758	53	20	3	3	NUM
ejpam-3758	53	21	.	.	PUNCT
ejpam-3758	54	1	[	[	X
ejpam-3758	54	2	8	8	NUM
ejpam-3758	54	3	]	]	PUNCT
ejpam-3758	54	4	let	let	VERB
ejpam-3758	54	5	x	x	PRON
ejpam-3758	54	6	be	be	AUX
ejpam-3758	54	7	a	a	DET
ejpam-3758	54	8	non	non	X
ejpam-3758	54	9	empty	empty	ADJ
ejpam-3758	54	10	set	set	NOUN
ejpam-3758	54	11	,	,	PUNCT
ejpam-3758	54	12	then	then	ADV
ejpam-3758	54	13	the	the	DET
ejpam-3758	54	14	collection	collection	NOUN
ejpam-3758	54	15	of	of	ADP
ejpam-3758	54	16	all	all	DET
ejpam-3758	54	17	subsets	subset	NOUN
ejpam-3758	54	18	of	of	ADP
ejpam-3758	54	19	x	x	SYM
ejpam-3758	54	20	is	be	AUX
ejpam-3758	54	21	called	call	VERB
ejpam-3758	54	22	the	the	DET
ejpam-3758	54	23	discrete	discrete	ADJ
ejpam-3758	54	24	topology	topology	NOUN
ejpam-3758	54	25	.	.	PUNCT
ejpam-3758	55	1	we	we	PRON
ejpam-3758	55	2	denote	denote	VERB
ejpam-3758	55	3	this	this	DET
ejpam-3758	55	4	collection	collection	NOUN
ejpam-3758	55	5	as	as	ADP
ejpam-3758	55	6	d.	d.	PROPN
ejpam-3758	55	7	definition	definition	NOUN
ejpam-3758	55	8	4	4	NUM
ejpam-3758	55	9	.	.	PUNCT
ejpam-3758	56	1	let	let	VERB
ejpam-3758	56	2	y	y	PRON
ejpam-3758	56	3	be	be	AUX
ejpam-3758	56	4	a	a	DET
ejpam-3758	56	5	subset	subset	NOUN
ejpam-3758	56	6	of	of	ADP
ejpam-3758	56	7	x.	x.	NOUN
ejpam-3758	56	8	a	a	DET
ejpam-3758	56	9	set	set	NOUN
ejpam-3758	56	10	a	a	PRON
ejpam-3758	56	11	is	be	AUX
ejpam-3758	56	12	called	call	VERB
ejpam-3758	56	13	a	a	DET
ejpam-3758	56	14	µ-open	µ-open	NOUN
ejpam-3758	56	15	set	set	VERB
ejpam-3758	56	16	in	in	ADP
ejpam-3758	56	17	y	y	PROPN
ejpam-3758	56	18	if	if	SCONJ
ejpam-3758	56	19	a	a	DET
ejpam-3758	56	20	=	=	VERB
ejpam-3758	56	21	y	y	PROPN
ejpam-3758	56	22	⋂	⋂	PROPN
ejpam-3758	56	23	g	g	NOUN
ejpam-3758	56	24	for	for	ADP
ejpam-3758	56	25	some	some	DET
ejpam-3758	56	26	µ-open	µ-open	NOUN
ejpam-3758	56	27	set	set	VERB
ejpam-3758	56	28	g	g	NOUN
ejpam-3758	56	29	in	in	ADP
ejpam-3758	56	30	x.	x.	NOUN
ejpam-3758	56	31	definition	definition	NOUN
ejpam-3758	56	32	5	5	NUM
ejpam-3758	56	33	.	.	PUNCT
ejpam-3758	57	1	[	[	X
ejpam-3758	57	2	1,5,6,10	1,5,6,10	X
ejpam-3758	57	3	]	]	X
ejpam-3758	57	4	let	let	VERB
ejpam-3758	57	5	x	x	PRON
ejpam-3758	57	6	be	be	AUX
ejpam-3758	57	7	a	a	DET
ejpam-3758	57	8	non	non	X
ejpam-3758	57	9	empty	empty	ADJ
ejpam-3758	57	10	set	set	NOUN
ejpam-3758	57	11	and	and	CCONJ
ejpam-3758	57	12	µ	µ	PRON
ejpam-3758	57	13	be	be	AUX
ejpam-3758	57	14	a	a	DET
ejpam-3758	57	15	generalized	generalized	ADJ
ejpam-3758	57	16	topology	topology	NOUN
ejpam-3758	57	17	in	in	ADP
ejpam-3758	57	18	x.	x.	NOUN
ejpam-3758	57	19	then	then	ADV
ejpam-3758	57	20	,	,	PUNCT
ejpam-3758	57	21	i.	i.	PROPN
ejpam-3758	57	22	a	a	DET
ejpam-3758	57	23	subset	subset	VERB
ejpam-3758	57	24	a	a	DET
ejpam-3758	57	25	ofx	ofx	NOUN
ejpam-3758	57	26	is	be	AUX
ejpam-3758	57	27	called	call	VERB
ejpam-3758	57	28	generalized	generalized	ADJ
ejpam-3758	57	29	open	open	ADJ
ejpam-3758	57	30	(	(	PUNCT
ejpam-3758	57	31	briefly	briefly	NOUN
ejpam-3758	57	32	g	g	NOUN
ejpam-3758	57	33	-	-	PUNCT
ejpam-3758	57	34	open	open	ADJ
ejpam-3758	57	35	)	)	PUNCT
ejpam-3758	57	36	set	set	VERB
ejpam-3758	57	37	if	if	SCONJ
ejpam-3758	57	38	f	f	PROPN
ejpam-3758	57	39	⊆	⊆	NUM
ejpam-3758	57	40	int(a	int(a	NOUN
ejpam-3758	57	41	)	)	PUNCT
ejpam-3758	57	42	whenever	whenever	SCONJ
ejpam-3758	57	43	f	f	PROPN
ejpam-3758	57	44	⊆	⊆	PROPN
ejpam-3758	57	45	a	a	PRON
ejpam-3758	57	46	and	and	CCONJ
ejpam-3758	57	47	f	f	PROPN
ejpam-3758	57	48	is	be	AUX
ejpam-3758	57	49	closed	closed	ADJ
ejpam-3758	57	50	.	.	PUNCT
ejpam-3758	58	1	we	we	PRON
ejpam-3758	58	2	denote	denote	VERB
ejpam-3758	58	3	the	the	DET
ejpam-3758	58	4	collection	collection	NOUN
ejpam-3758	58	5	of	of	ADP
ejpam-3758	58	6	g	g	NOUN
ejpam-3758	58	7	-	-	PUNCT
ejpam-3758	58	8	open	open	ADJ
ejpam-3758	58	9	sets	set	NOUN
ejpam-3758	58	10	in	in	ADP
ejpam-3758	58	11	x	x	PUNCT
ejpam-3758	58	12	as	as	ADP
ejpam-3758	58	13	g(x	g(x	NOUN
ejpam-3758	58	14	)	)	PUNCT
ejpam-3758	58	15	.	.	PUNCT
ejpam-3758	59	1	ii	ii	PROPN
ejpam-3758	59	2	.	.	PUNCT
ejpam-3758	60	1	a	a	DET
ejpam-3758	60	2	subset	subset	NOUN
ejpam-3758	60	3	a	a	PRON
ejpam-3758	60	4	of	of	ADP
ejpam-3758	60	5	x	x	PRON
ejpam-3758	60	6	is	be	AUX
ejpam-3758	60	7	called	call	VERB
ejpam-3758	60	8	semi	semi	ADJ
ejpam-3758	60	9	-	-	ADJ
ejpam-3758	60	10	open	open	ADJ
ejpam-3758	60	11	set	set	NOUN
ejpam-3758	60	12	if	if	SCONJ
ejpam-3758	60	13	a	a	DET
ejpam-3758	60	14	⊆	⊆	NUM
ejpam-3758	60	15	cl(int(a	cl(int(a	NOUN
ejpam-3758	60	16	)	)	PUNCT
ejpam-3758	60	17	)	)	PUNCT
ejpam-3758	60	18	.	.	PUNCT
ejpam-3758	61	1	we	we	PRON
ejpam-3758	61	2	denote	denote	VERB
ejpam-3758	61	3	the	the	DET
ejpam-3758	61	4	collection	collection	NOUN
ejpam-3758	61	5	of	of	ADP
ejpam-3758	61	6	semi	semi	ADJ
ejpam-3758	61	7	-	-	ADJ
ejpam-3758	61	8	open	open	ADJ
ejpam-3758	61	9	sets	set	NOUN
ejpam-3758	61	10	in	in	ADP
ejpam-3758	61	11	x	x	PUNCT
ejpam-3758	61	12	as	as	ADP
ejpam-3758	61	13	so(x	so(x	NOUN
ejpam-3758	61	14	)	)	PUNCT
ejpam-3758	61	15	.	.	PUNCT
ejpam-3758	62	1	iii	iii	X
ejpam-3758	62	2	.	.	PUNCT
ejpam-3758	63	1	a	a	DET
ejpam-3758	63	2	subset	subset	NOUN
ejpam-3758	63	3	a	a	PRON
ejpam-3758	63	4	of	of	ADP
ejpam-3758	63	5	x	x	PRON
ejpam-3758	63	6	is	be	AUX
ejpam-3758	63	7	called	call	VERB
ejpam-3758	63	8	α	α	DET
ejpam-3758	63	9	-	-	ADJ
ejpam-3758	63	10	open	open	ADJ
ejpam-3758	63	11	set	set	NOUN
ejpam-3758	63	12	if	if	SCONJ
ejpam-3758	63	13	a	a	DET
ejpam-3758	63	14	⊆	⊆	NUM
ejpam-3758	63	15	int(cl(int(a	int(cl(int(a	NOUN
ejpam-3758	63	16	)	)	PUNCT
ejpam-3758	63	17	)	)	PUNCT
ejpam-3758	63	18	)	)	PUNCT
ejpam-3758	63	19	.	.	PUNCT
ejpam-3758	64	1	we	we	PRON
ejpam-3758	64	2	denote	denote	VERB
ejpam-3758	64	3	the	the	DET
ejpam-3758	64	4	collection	collection	NOUN
ejpam-3758	64	5	of	of	ADP
ejpam-3758	64	6	α	α	NOUN
ejpam-3758	64	7	-	-	ADJ
ejpam-3758	64	8	open	open	ADJ
ejpam-3758	64	9	sets	set	NOUN
ejpam-3758	64	10	in	in	ADP
ejpam-3758	64	11	x	x	PUNCT
ejpam-3758	64	12	as	as	ADP
ejpam-3758	64	13	ao(x	ao(x	NUM
ejpam-3758	64	14	)	)	PUNCT
ejpam-3758	64	15	.	.	PUNCT
ejpam-3758	65	1	iv	iv	X
ejpam-3758	65	2	.	.	PUNCT
ejpam-3758	66	1	a	a	DET
ejpam-3758	66	2	subset	subset	NOUN
ejpam-3758	66	3	a	a	PRON
ejpam-3758	66	4	of	of	ADP
ejpam-3758	66	5	x	x	PRON
ejpam-3758	66	6	is	be	AUX
ejpam-3758	66	7	called	call	VERB
ejpam-3758	66	8	semi	semi	ADJ
ejpam-3758	66	9	-	-	ADJ
ejpam-3758	66	10	preopen	preopen	ADJ
ejpam-3758	66	11	set	set	VERB
ejpam-3758	66	12	if	if	SCONJ
ejpam-3758	66	13	a	a	DET
ejpam-3758	66	14	⊆	⊆	NUM
ejpam-3758	66	15	cl(int(cl(a	cl(int(cl(a	NOUN
ejpam-3758	66	16	)	)	PUNCT
ejpam-3758	66	17	)	)	PUNCT
ejpam-3758	66	18	)	)	PUNCT
ejpam-3758	66	19	.	.	PUNCT
ejpam-3758	67	1	we	we	PRON
ejpam-3758	67	2	denote	denote	VERB
ejpam-3758	67	3	the	the	DET
ejpam-3758	67	4	collection	collection	NOUN
ejpam-3758	67	5	of	of	ADP
ejpam-3758	67	6	semi	semi	ADJ
ejpam-3758	67	7	-	-	ADJ
ejpam-3758	67	8	preopen	preopen	ADJ
ejpam-3758	67	9	sets	set	NOUN
ejpam-3758	67	10	in	in	ADP
ejpam-3758	67	11	x	x	PUNCT
ejpam-3758	67	12	as	as	ADP
ejpam-3758	67	13	spo(x	spo(x	PROPN
ejpam-3758	67	14	)	)	PUNCT
ejpam-3758	67	15	.	.	PUNCT
ejpam-3758	68	1	v.	v.	ADP
ejpam-3758	68	2	a	a	DET
ejpam-3758	68	3	subset	subset	NOUN
ejpam-3758	68	4	a	a	PRON
ejpam-3758	68	5	of	of	ADP
ejpam-3758	68	6	x	x	PRON
ejpam-3758	68	7	is	be	AUX
ejpam-3758	68	8	called	call	VERB
ejpam-3758	68	9	b	b	NOUN
ejpam-3758	68	10	-	-	PUNCT
ejpam-3758	68	11	open	open	ADJ
ejpam-3758	68	12	set	set	NOUN
ejpam-3758	68	13	if	if	SCONJ
ejpam-3758	68	14	a	a	DET
ejpam-3758	68	15	⊆	⊆	NUM
ejpam-3758	68	16	cl(int(a	cl(int(a	NOUN
ejpam-3758	68	17	)	)	PUNCT
ejpam-3758	68	18	)	)	PUNCT
ejpam-3758	69	1	⋃	⋃	SCONJ
ejpam-3758	69	2	int(cl(a	int(cl(a	PROPN
ejpam-3758	69	3	)	)	PUNCT
ejpam-3758	69	4	)	)	PUNCT
ejpam-3758	69	5	.	.	PUNCT
ejpam-3758	70	1	we	we	PRON
ejpam-3758	70	2	denote	denote	VERB
ejpam-3758	70	3	the	the	DET
ejpam-3758	70	4	collection	collection	NOUN
ejpam-3758	70	5	of	of	ADP
ejpam-3758	70	6	b	b	NOUN
ejpam-3758	70	7	-	-	PUNCT
ejpam-3758	70	8	open	open	ADJ
ejpam-3758	70	9	sets	set	NOUN
ejpam-3758	70	10	in	in	ADP
ejpam-3758	70	11	x	x	PUNCT
ejpam-3758	70	12	as	as	ADP
ejpam-3758	70	13	bo(x	bo(x	NUM
ejpam-3758	70	14	)	)	PUNCT
ejpam-3758	70	15	.	.	PUNCT
ejpam-3758	71	1	the	the	DET
ejpam-3758	71	2	complements	complement	NOUN
ejpam-3758	71	3	of	of	ADP
ejpam-3758	71	4	the	the	DET
ejpam-3758	71	5	above	above	ADV
ejpam-3758	71	6	-	-	PUNCT
ejpam-3758	71	7	mentioned	mention	VERB
ejpam-3758	71	8	open	open	ADJ
ejpam-3758	71	9	sets	set	NOUN
ejpam-3758	71	10	are	be	AUX
ejpam-3758	71	11	their	their	PRON
ejpam-3758	71	12	respective	respective	ADJ
ejpam-3758	71	13	closed	closed	ADJ
ejpam-3758	71	14	sets	set	NOUN
ejpam-3758	71	15	.	.	PUNCT
ejpam-3758	72	1	theorem	theorem	NOUN
ejpam-3758	72	2	6	6	NUM
ejpam-3758	72	3	.	.	PUNCT
ejpam-3758	73	1	let	let	VERB
ejpam-3758	73	2	x	x	SYM
ejpam-3758	73	3	6=	6=	ADP
ejpam-3758	73	4	∅.	∅.	ADP
ejpam-3758	73	5	the	the	DET
ejpam-3758	73	6	following	following	NOUN
ejpam-3758	73	7	can	can	AUX
ejpam-3758	73	8	be	be	AUX
ejpam-3758	73	9	shown	show	VERB
ejpam-3758	73	10	using	use	VERB
ejpam-3758	73	11	definitions	definition	NOUN
ejpam-3758	73	12	1	1	NUM
ejpam-3758	73	13	and	and	CCONJ
ejpam-3758	73	14	5	5	NUM
ejpam-3758	73	15	,	,	PUNCT
ejpam-3758	73	16	and	and	CCONJ
ejpam-3758	73	17	theorems	theorem	NOUN
ejpam-3758	73	18	2	2	NUM
ejpam-3758	73	19	and	and	CCONJ
ejpam-3758	73	20	3	3	NUM
ejpam-3758	73	21	.	.	X
ejpam-3758	74	1	i.	i.	NOUN
ejpam-3758	74	2	the	the	DET
ejpam-3758	74	3	collection	collection	NOUN
ejpam-3758	74	4	of	of	ADP
ejpam-3758	74	5	g	g	NOUN
ejpam-3758	74	6	-	-	PUNCT
ejpam-3758	74	7	open	open	ADJ
ejpam-3758	74	8	sets	set	NOUN
ejpam-3758	74	9	in	in	ADP
ejpam-3758	74	10	x	x	SYM
ejpam-3758	74	11	is	be	AUX
ejpam-3758	74	12	a	a	DET
ejpam-3758	74	13	generalized	generalized	ADJ
ejpam-3758	74	14	topology	topology	NOUN
ejpam-3758	74	15	.	.	PUNCT
ejpam-3758	75	1	ii	ii	PROPN
ejpam-3758	75	2	.	.	PUNCT
ejpam-3758	76	1	the	the	DET
ejpam-3758	76	2	collection	collection	NOUN
ejpam-3758	76	3	of	of	ADP
ejpam-3758	76	4	semi	semi	ADJ
ejpam-3758	76	5	-	-	ADJ
ejpam-3758	76	6	open	open	ADJ
ejpam-3758	76	7	sets	set	NOUN
ejpam-3758	76	8	in	in	ADP
ejpam-3758	76	9	x	x	SYM
ejpam-3758	76	10	is	be	AUX
ejpam-3758	76	11	a	a	DET
ejpam-3758	76	12	generalized	generalized	ADJ
ejpam-3758	76	13	topology	topology	NOUN
ejpam-3758	76	14	.	.	PUNCT
ejpam-3758	77	1	iii	iii	X
ejpam-3758	77	2	.	.	PUNCT
ejpam-3758	78	1	the	the	DET
ejpam-3758	78	2	collection	collection	NOUN
ejpam-3758	78	3	of	of	ADP
ejpam-3758	78	4	α	α	NOUN
ejpam-3758	78	5	-	-	ADJ
ejpam-3758	78	6	open	open	ADJ
ejpam-3758	78	7	sets	set	NOUN
ejpam-3758	78	8	in	in	ADP
ejpam-3758	78	9	x	x	SYM
ejpam-3758	78	10	is	be	AUX
ejpam-3758	78	11	a	a	DET
ejpam-3758	78	12	generalized	generalized	ADJ
ejpam-3758	78	13	topology	topology	NOUN
ejpam-3758	78	14	.	.	PUNCT
ejpam-3758	79	1	iv	iv	X
ejpam-3758	79	2	.	.	PUNCT
ejpam-3758	80	1	the	the	DET
ejpam-3758	80	2	collection	collection	NOUN
ejpam-3758	80	3	of	of	ADP
ejpam-3758	80	4	semi	semi	ADJ
ejpam-3758	80	5	-	-	ADJ
ejpam-3758	80	6	preopen	preopen	ADJ
ejpam-3758	80	7	sets	set	NOUN
ejpam-3758	80	8	in	in	ADP
ejpam-3758	80	9	x	x	SYM
ejpam-3758	80	10	is	be	AUX
ejpam-3758	80	11	a	a	DET
ejpam-3758	80	12	generalized	generalized	ADJ
ejpam-3758	80	13	topology	topology	NOUN
ejpam-3758	80	14	.	.	PUNCT
ejpam-3758	81	1	v.	v.	ADP
ejpam-3758	81	2	the	the	DET
ejpam-3758	81	3	collection	collection	NOUN
ejpam-3758	81	4	of	of	ADP
ejpam-3758	81	5	pre	pre	ADJ
ejpam-3758	81	6	-	-	ADJ
ejpam-3758	81	7	open	open	ADJ
ejpam-3758	81	8	sets	set	NOUN
ejpam-3758	81	9	in	in	ADP
ejpam-3758	81	10	x	x	SYM
ejpam-3758	81	11	is	be	AUX
ejpam-3758	81	12	a	a	DET
ejpam-3758	81	13	generalized	generalized	ADJ
ejpam-3758	81	14	topology	topology	NOUN
ejpam-3758	81	15	.	.	PUNCT
ejpam-3758	82	1	vi	vi	X
ejpam-3758	82	2	.	.	PUNCT
ejpam-3758	83	1	the	the	DET
ejpam-3758	83	2	collection	collection	NOUN
ejpam-3758	83	3	of	of	ADP
ejpam-3758	83	4	b	b	NOUN
ejpam-3758	83	5	-	-	PUNCT
ejpam-3758	83	6	open	open	ADJ
ejpam-3758	83	7	sets	set	NOUN
ejpam-3758	83	8	in	in	ADP
ejpam-3758	83	9	x	x	SYM
ejpam-3758	83	10	is	be	AUX
ejpam-3758	83	11	a	a	DET
ejpam-3758	83	12	generalized	generalized	ADJ
ejpam-3758	83	13	topology	topology	NOUN
ejpam-3758	83	14	.	.	PUNCT
ejpam-3758	84	1	definition	definition	NOUN
ejpam-3758	84	2	6	6	NUM
ejpam-3758	84	3	.	.	PUNCT
ejpam-3758	85	1	[	[	X
ejpam-3758	85	2	1,6,7,9	1,6,7,9	NUM
ejpam-3758	85	3	]	]	X
ejpam-3758	85	4	let	let	NOUN
ejpam-3758	85	5	x	x	SYM
ejpam-3758	85	6	6=	6=	ADP
ejpam-3758	85	7	∅	∅	NOUN
ejpam-3758	85	8	and	and	CCONJ
ejpam-3758	85	9	µ	µ	PRON
ejpam-3758	85	10	be	be	AUX
ejpam-3758	85	11	a	a	DET
ejpam-3758	85	12	topology	topology	NOUN
ejpam-3758	85	13	on	on	ADP
ejpam-3758	85	14	x.	x.	NOUN
ejpam-3758	85	15	then	then	ADV
ejpam-3758	85	16	,	,	PUNCT
ejpam-3758	85	17	a	a	DET
ejpam-3758	85	18	subset	subset	NOUN
ejpam-3758	85	19	a	a	PRON
ejpam-3758	85	20	of	of	ADP
ejpam-3758	85	21	x	x	SYM
ejpam-3758	85	22	is	be	AUX
ejpam-3758	85	23	:	:	PUNCT
ejpam-3758	85	24	i.	i.	PROPN
ejpam-3758	85	25	generalized	generalize	VERB
ejpam-3758	85	26	closed	close	VERB
ejpam-3758	85	27	(	(	PUNCT
ejpam-3758	85	28	briefly	briefly	NOUN
ejpam-3758	85	29	g	g	NOUN
ejpam-3758	85	30	-	-	PUNCT
ejpam-3758	85	31	closed	closed	ADJ
ejpam-3758	85	32	)	)	PUNCT
ejpam-3758	85	33	set	set	VERB
ejpam-3758	85	34	if	if	SCONJ
ejpam-3758	85	35	cl(a	cl(a	NUM
ejpam-3758	85	36	)	)	PUNCT
ejpam-3758	85	37	⊆	⊆	NUM
ejpam-3758	85	38	u	u	NOUN
ejpam-3758	85	39	whenever	whenever	SCONJ
ejpam-3758	85	40	a	a	DET
ejpam-3758	85	41	⊆	⊆	NUM
ejpam-3758	85	42	u	u	NOUN
ejpam-3758	85	43	and	and	CCONJ
ejpam-3758	85	44	u	u	NOUN
ejpam-3758	85	45	is	be	AUX
ejpam-3758	85	46	open	open	ADJ
ejpam-3758	85	47	in	in	ADP
ejpam-3758	85	48	x.	x.	PROPN
ejpam-3758	85	49	ii	ii	PROPN
ejpam-3758	85	50	.	.	PUNCT
ejpam-3758	86	1	strongly	strongly	ADV
ejpam-3758	86	2	generalized	generalize	VERB
ejpam-3758	86	3	closed	close	VERB
ejpam-3758	86	4	(	(	PUNCT
ejpam-3758	86	5	or	or	CCONJ
ejpam-3758	86	6	briefly	briefly	ADV
ejpam-3758	86	7	g*-closed	g*-close	VERB
ejpam-3758	86	8	)	)	PUNCT
ejpam-3758	86	9	set	set	VERB
ejpam-3758	86	10	if	if	SCONJ
ejpam-3758	86	11	cl(a	cl(a	NUM
ejpam-3758	86	12	)	)	PUNCT
ejpam-3758	86	13	⊆	⊆	NUM
ejpam-3758	86	14	u	u	NOUN
ejpam-3758	86	15	whenever	whenever	SCONJ
ejpam-3758	86	16	a	a	DET
ejpam-3758	86	17	⊆	⊆	NUM
ejpam-3758	86	18	u	u	NOUN
ejpam-3758	86	19	and	and	CCONJ
ejpam-3758	86	20	u	u	NOUN
ejpam-3758	86	21	is	be	AUX
ejpam-3758	86	22	g	g	NOUN
ejpam-3758	86	23	-	-	PUNCT
ejpam-3758	86	24	open	open	ADJ
ejpam-3758	86	25	in	in	ADP
ejpam-3758	86	26	x.	x.	PROPN
ejpam-3758	86	27	iii	iii	PROPN
ejpam-3758	86	28	.	.	PROPN
ejpam-3758	86	29	generalized	generalize	VERB
ejpam-3758	86	30	preclosed	preclose	VERB
ejpam-3758	86	31	(	(	PUNCT
ejpam-3758	86	32	or	or	CCONJ
ejpam-3758	86	33	briefly	briefly	ADV
ejpam-3758	86	34	gp	gp	NOUN
ejpam-3758	86	35	-	-	PUNCT
ejpam-3758	86	36	closed	closed	ADJ
ejpam-3758	86	37	)	)	PUNCT
ejpam-3758	86	38	set	set	VERB
ejpam-3758	86	39	if	if	SCONJ
ejpam-3758	86	40	pcl(a	pcl(a	NUM
ejpam-3758	86	41	)	)	PUNCT
ejpam-3758	87	1	⊆	⊆	NUM
ejpam-3758	87	2	u	u	NOUN
ejpam-3758	87	3	whenever	whenever	SCONJ
ejpam-3758	87	4	a	a	DET
ejpam-3758	87	5	⊆	⊆	NUM
ejpam-3758	87	6	u	u	NOUN
ejpam-3758	87	7	and	and	CCONJ
ejpam-3758	87	8	u	u	NOUN
ejpam-3758	87	9	is	be	AUX
ejpam-3758	87	10	open	open	ADJ
ejpam-3758	87	11	in	in	ADP
ejpam-3758	87	12	x.	x.	PROPN
ejpam-3758	87	13	b.	b.	PROPN
ejpam-3758	87	14	agua	agua	PROPN
ejpam-3758	87	15	,	,	PUNCT
ejpam-3758	87	16	r.	r.	PROPN
ejpam-3758	87	17	paluga	paluga	PROPN
ejpam-3758	87	18	/	/	SYM
ejpam-3758	87	19	eur	eur	PROPN
ejpam-3758	87	20	.	.	PUNCT
ejpam-3758	88	1	j.	j.	PROPN
ejpam-3758	88	2	pure	pure	PROPN
ejpam-3758	88	3	appl	appl	PROPN
ejpam-3758	88	4	.	.	PROPN
ejpam-3758	88	5	math	math	PROPN
ejpam-3758	88	6	,	,	PUNCT
ejpam-3758	88	7	13	13	NUM
ejpam-3758	88	8	(	(	PUNCT
ejpam-3758	88	9	4	4	NUM
ejpam-3758	88	10	)	)	PUNCT
ejpam-3758	88	11	(	(	PUNCT
ejpam-3758	88	12	2020	2020	NUM
ejpam-3758	88	13	)	)	PUNCT
ejpam-3758	88	14	,	,	PUNCT
ejpam-3758	88	15	977	977	NUM
ejpam-3758	88	16	-	-	SYM
ejpam-3758	88	17	986	986	NUM
ejpam-3758	88	18	980	980	NUM
ejpam-3758	88	19	iv	iv	NOUN
ejpam-3758	88	20	.	.	PUNCT
ejpam-3758	89	1	semi	semi	ADJ
ejpam-3758	89	2	-	-	ADJ
ejpam-3758	89	3	generalized	generalized	ADJ
ejpam-3758	89	4	closed	close	VERB
ejpam-3758	89	5	(	(	PUNCT
ejpam-3758	89	6	or	or	CCONJ
ejpam-3758	89	7	briefly	briefly	ADV
ejpam-3758	89	8	sg	sg	NOUN
ejpam-3758	89	9	-	-	PUNCT
ejpam-3758	89	10	closed	closed	ADJ
ejpam-3758	89	11	)	)	PUNCT
ejpam-3758	89	12	set	set	VERB
ejpam-3758	89	13	if	if	SCONJ
ejpam-3758	89	14	scl(a	scl(a	PROPN
ejpam-3758	89	15	)	)	PUNCT
ejpam-3758	89	16	⊆	⊆	NUM
ejpam-3758	89	17	u	u	NOUN
ejpam-3758	89	18	whenever	whenever	SCONJ
ejpam-3758	89	19	a	a	DET
ejpam-3758	89	20	⊆	⊆	NUM
ejpam-3758	89	21	u	u	NOUN
ejpam-3758	89	22	and	and	CCONJ
ejpam-3758	89	23	u	u	NOUN
ejpam-3758	89	24	is	be	AUX
ejpam-3758	89	25	semi	semi	ADJ
ejpam-3758	89	26	-	-	ADJ
ejpam-3758	89	27	open	open	ADJ
ejpam-3758	89	28	in	in	ADP
ejpam-3758	89	29	x.	x.	PROPN
ejpam-3758	89	30	v.	v.	ADP
ejpam-3758	89	31	generalized	generalize	VERB
ejpam-3758	89	32	semiclosed	semiclose	VERB
ejpam-3758	89	33	(	(	PUNCT
ejpam-3758	89	34	or	or	CCONJ
ejpam-3758	89	35	briefly	briefly	ADV
ejpam-3758	89	36	gs	gs	NOUN
ejpam-3758	89	37	-	-	PUNCT
ejpam-3758	89	38	closed	closed	ADJ
ejpam-3758	89	39	)	)	PUNCT
ejpam-3758	89	40	set	set	VERB
ejpam-3758	89	41	if	if	SCONJ
ejpam-3758	89	42	scl(a	scl(a	PROPN
ejpam-3758	89	43	)	)	PUNCT
ejpam-3758	89	44	⊆	⊆	NUM
ejpam-3758	89	45	u	u	NOUN
ejpam-3758	89	46	whenever	whenever	SCONJ
ejpam-3758	89	47	a	a	DET
ejpam-3758	89	48	⊆	⊆	NUM
ejpam-3758	89	49	u	u	NOUN
ejpam-3758	89	50	and	and	CCONJ
ejpam-3758	89	51	u	u	NOUN
ejpam-3758	89	52	is	be	AUX
ejpam-3758	89	53	open	open	ADJ
ejpam-3758	89	54	in	in	ADP
ejpam-3758	89	55	x.	x.	PROPN
ejpam-3758	89	56	vi	vi	PROPN
ejpam-3758	89	57	.	.	PROPN
ejpam-3758	90	1	generalized	generalize	VERB
ejpam-3758	90	2	b	b	X
ejpam-3758	90	3	-	-	PUNCT
ejpam-3758	90	4	closed	closed	ADJ
ejpam-3758	90	5	(	(	PUNCT
ejpam-3758	90	6	or	or	CCONJ
ejpam-3758	90	7	briefly	briefly	ADV
ejpam-3758	90	8	gb	gb	ADV
ejpam-3758	90	9	-	-	PUNCT
ejpam-3758	90	10	closed	closed	ADJ
ejpam-3758	90	11	)	)	PUNCT
ejpam-3758	90	12	set	set	VERB
ejpam-3758	90	13	if	if	SCONJ
ejpam-3758	90	14	bcl(a	bcl(a	VERB
ejpam-3758	90	15	)	)	PUNCT
ejpam-3758	90	16	⊆	⊆	NUM
ejpam-3758	90	17	u	u	NOUN
ejpam-3758	90	18	whenever	whenever	SCONJ
ejpam-3758	90	19	a	a	DET
ejpam-3758	90	20	⊆	⊆	NUM
ejpam-3758	90	21	u	u	NOUN
ejpam-3758	90	22	and	and	CCONJ
ejpam-3758	90	23	u	u	NOUN
ejpam-3758	90	24	is	be	AUX
ejpam-3758	90	25	open	open	ADJ
ejpam-3758	90	26	in	in	ADP
ejpam-3758	90	27	x.	x.	PROPN
ejpam-3758	90	28	vii	vii	PROPN
ejpam-3758	90	29	.	.	PROPN
ejpam-3758	91	1	generalized	generalize	VERB
ejpam-3758	91	2	α	α	PROPN
ejpam-3758	91	3	-	-	PUNCT
ejpam-3758	91	4	b	b	NOUN
ejpam-3758	91	5	-	-	PUNCT
ejpam-3758	91	6	closed	closed	ADJ
ejpam-3758	91	7	(	(	PUNCT
ejpam-3758	91	8	or	or	CCONJ
ejpam-3758	91	9	briefly	briefly	ADV
ejpam-3758	91	10	gαb	gαb	ADV
ejpam-3758	91	11	-	-	PUNCT
ejpam-3758	91	12	closed	closed	ADJ
ejpam-3758	91	13	)	)	PUNCT
ejpam-3758	91	14	set	set	VERB
ejpam-3758	91	15	if	if	SCONJ
ejpam-3758	91	16	scl(a	scl(a	PROPN
ejpam-3758	91	17	)	)	PUNCT
ejpam-3758	91	18	⊆	⊆	NUM
ejpam-3758	91	19	u	u	NOUN
ejpam-3758	91	20	whenever	whenever	SCONJ
ejpam-3758	91	21	a	a	DET
ejpam-3758	91	22	⊆	⊆	NUM
ejpam-3758	91	23	u	u	NOUN
ejpam-3758	91	24	and	and	CCONJ
ejpam-3758	91	25	u	u	NOUN
ejpam-3758	91	26	is	be	AUX
ejpam-3758	91	27	α	α	NOUN
ejpam-3758	91	28	-	-	NOUN
ejpam-3758	91	29	open	open	ADJ
ejpam-3758	91	30	in	in	ADP
ejpam-3758	91	31	x.	x.	PROPN
ejpam-3758	91	32	viii	viii	PROPN
ejpam-3758	91	33	.	.	PUNCT
ejpam-3758	92	1	semi	semi	ADJ
ejpam-3758	92	2	generalized	generalized	ADJ
ejpam-3758	92	3	b	b	X
ejpam-3758	92	4	-	-	PUNCT
ejpam-3758	92	5	closed	closed	ADJ
ejpam-3758	92	6	set	set	NOUN
ejpam-3758	92	7	(	(	PUNCT
ejpam-3758	92	8	or	or	CCONJ
ejpam-3758	92	9	briefly	briefly	ADV
ejpam-3758	92	10	sbg	sbg	NOUN
ejpam-3758	92	11	-	-	PUNCT
ejpam-3758	92	12	closed	closed	ADJ
ejpam-3758	92	13	)	)	PUNCT
ejpam-3758	92	14	set	set	VERB
ejpam-3758	92	15	if	if	SCONJ
ejpam-3758	92	16	bcl(a	bcl(a	VERB
ejpam-3758	92	17	)	)	PUNCT
ejpam-3758	92	18	⊆	⊆	NUM
ejpam-3758	92	19	u	u	NOUN
ejpam-3758	92	20	whenever	whenever	SCONJ
ejpam-3758	92	21	a	a	DET
ejpam-3758	92	22	⊆	⊆	NUM
ejpam-3758	92	23	u	u	NOUN
ejpam-3758	92	24	and	and	CCONJ
ejpam-3758	92	25	u	u	NOUN
ejpam-3758	92	26	is	be	AUX
ejpam-3758	92	27	semi	semi	ADJ
ejpam-3758	92	28	-	-	ADJ
ejpam-3758	92	29	open	open	ADJ
ejpam-3758	92	30	in	in	ADP
ejpam-3758	92	31	x.	x.	PROPN
ejpam-3758	92	32	ix	ix	PROPN
ejpam-3758	92	33	.	.	PUNCT
ejpam-3758	93	1	weakly	weakly	ADV
ejpam-3758	93	2	closed	closed	ADJ
ejpam-3758	93	3	(	(	PUNCT
ejpam-3758	93	4	or	or	CCONJ
ejpam-3758	93	5	briefly	briefly	ADV
ejpam-3758	93	6	w	w	NOUN
ejpam-3758	93	7	-	-	PUNCT
ejpam-3758	93	8	closed	closed	ADJ
ejpam-3758	93	9	)	)	PUNCT
ejpam-3758	93	10	set	set	VERB
ejpam-3758	93	11	if	if	SCONJ
ejpam-3758	93	12	cl(a	cl(a	NUM
ejpam-3758	93	13	)	)	PUNCT
ejpam-3758	93	14	⊆	⊆	NUM
ejpam-3758	93	15	u	u	NOUN
ejpam-3758	93	16	whenever	whenever	SCONJ
ejpam-3758	93	17	a	a	DET
ejpam-3758	93	18	⊆	⊆	NUM
ejpam-3758	93	19	u	u	NOUN
ejpam-3758	93	20	and	and	CCONJ
ejpam-3758	93	21	u	u	NOUN
ejpam-3758	93	22	is	be	AUX
ejpam-3758	93	23	semi	semi	ADJ
ejpam-3758	93	24	-	-	ADJ
ejpam-3758	93	25	open	open	ADJ
ejpam-3758	93	26	in	in	ADP
ejpam-3758	93	27	x.	x.	PROPN
ejpam-3758	93	28	x.	x.	PROPN
ejpam-3758	93	29	generalized	generalize	VERB
ejpam-3758	93	30	semi	semi	ADV
ejpam-3758	93	31	-	-	ADJ
ejpam-3758	93	32	preclosed	preclosed	ADJ
ejpam-3758	93	33	(	(	PUNCT
ejpam-3758	93	34	or	or	CCONJ
ejpam-3758	93	35	briefly	briefly	ADV
ejpam-3758	93	36	gsp	gsp	VERB
ejpam-3758	93	37	-	-	PUNCT
ejpam-3758	93	38	closed	closed	ADJ
ejpam-3758	93	39	)	)	PUNCT
ejpam-3758	93	40	set	set	VERB
ejpam-3758	93	41	if	if	SCONJ
ejpam-3758	93	42	spcl(a	spcl(a	NUM
ejpam-3758	93	43	)	)	PUNCT
ejpam-3758	93	44	⊆	⊆	NUM
ejpam-3758	93	45	u	u	NOUN
ejpam-3758	93	46	whenever	whenever	SCONJ
ejpam-3758	93	47	a	a	DET
ejpam-3758	93	48	⊆	⊆	NUM
ejpam-3758	93	49	u	u	NOUN
ejpam-3758	93	50	and	and	CCONJ
ejpam-3758	93	51	u	u	NOUN
ejpam-3758	93	52	is	be	AUX
ejpam-3758	93	53	open	open	ADJ
ejpam-3758	93	54	in	in	ADP
ejpam-3758	93	55	x.	x.	PROPN
ejpam-3758	93	56	xi	xi	PROPN
ejpam-3758	93	57	.	.	PUNCT
ejpam-3758	94	1	generalized	generalize	VERB
ejpam-3758	94	2	α	α	NOUN
ejpam-3758	94	3	closed	close	VERB
ejpam-3758	94	4	(	(	PUNCT
ejpam-3758	94	5	or	or	CCONJ
ejpam-3758	94	6	briefly	briefly	ADV
ejpam-3758	94	7	g	g	NOUN
ejpam-3758	94	8	-	-	PUNCT
ejpam-3758	94	9	α	α	NOUN
ejpam-3758	94	10	-	-	PUNCT
ejpam-3758	94	11	closed	closed	ADJ
ejpam-3758	94	12	)	)	PUNCT
ejpam-3758	94	13	set	set	VERB
ejpam-3758	94	14	if	if	SCONJ
ejpam-3758	94	15	α−cl(int(a	α−cl(int(a	NOUN
ejpam-3758	94	16	)	)	PUNCT
ejpam-3758	94	17	)	)	PUNCT
ejpam-3758	95	1	⊆	⊆	NUM
ejpam-3758	95	2	u	u	NOUN
ejpam-3758	95	3	whenever	whenever	SCONJ
ejpam-3758	95	4	a	a	DET
ejpam-3758	95	5	⊆	⊆	NUM
ejpam-3758	95	6	u	u	NOUN
ejpam-3758	95	7	and	and	CCONJ
ejpam-3758	95	8	u	u	NOUN
ejpam-3758	95	9	is	be	AUX
ejpam-3758	95	10	α	α	NOUN
ejpam-3758	95	11	-	-	NOUN
ejpam-3758	95	12	open	open	ADJ
ejpam-3758	95	13	in	in	ADP
ejpam-3758	95	14	x.	x.	PROPN
ejpam-3758	95	15	xii	xii	PROPN
ejpam-3758	95	16	.	.	PUNCT
ejpam-3758	96	1	α	α	X
ejpam-3758	96	2	-	-	PUNCT
ejpam-3758	96	3	generalized	generalize	VERB
ejpam-3758	96	4	closed	close	VERB
ejpam-3758	96	5	(	(	PUNCT
ejpam-3758	96	6	or	or	CCONJ
ejpam-3758	96	7	briefly	briefly	ADV
ejpam-3758	96	8	αg	αg	NOUN
ejpam-3758	96	9	-	-	PUNCT
ejpam-3758	96	10	closed	closed	ADJ
ejpam-3758	96	11	)	)	PUNCT
ejpam-3758	96	12	set	set	VERB
ejpam-3758	96	13	if	if	SCONJ
ejpam-3758	96	14	α−	α−	ADP
ejpam-3758	96	15	cl(int(a	cl(int(a	NOUN
ejpam-3758	96	16	)	)	PUNCT
ejpam-3758	96	17	)	)	PUNCT
ejpam-3758	97	1	⊆	⊆	X
ejpam-3758	97	2	u	u	NOUN
ejpam-3758	97	3	whenever	whenever	SCONJ
ejpam-3758	97	4	a	a	DET
ejpam-3758	97	5	⊆	⊆	NUM
ejpam-3758	97	6	u	u	NOUN
ejpam-3758	97	7	and	and	CCONJ
ejpam-3758	97	8	u	u	NOUN
ejpam-3758	97	9	is	be	AUX
ejpam-3758	97	10	open	open	ADJ
ejpam-3758	97	11	in	in	ADP
ejpam-3758	97	12	x.	x.	PROPN
ejpam-3758	97	13	xiii	xiii	PROPN
ejpam-3758	97	14	.	.	PUNCT
ejpam-3758	98	1	weakly	weakly	ADJ
ejpam-3758	98	2	generalized	generalize	VERB
ejpam-3758	98	3	closed	close	VERB
ejpam-3758	98	4	(	(	PUNCT
ejpam-3758	98	5	or	or	CCONJ
ejpam-3758	98	6	briefly	briefly	ADV
ejpam-3758	98	7	wg	wg	NOUN
ejpam-3758	98	8	-	-	PUNCT
ejpam-3758	98	9	closed	closed	ADJ
ejpam-3758	98	10	)	)	PUNCT
ejpam-3758	98	11	set	set	VERB
ejpam-3758	98	12	if	if	SCONJ
ejpam-3758	98	13	cl(int(a	cl(int(a	NOUN
ejpam-3758	98	14	)	)	PUNCT
ejpam-3758	98	15	)	)	PUNCT
ejpam-3758	99	1	⊆	⊆	X
ejpam-3758	99	2	u	u	NOUN
ejpam-3758	99	3	whenever	whenever	SCONJ
ejpam-3758	99	4	a	a	DET
ejpam-3758	99	5	⊆	⊆	NUM
ejpam-3758	99	6	u	u	NOUN
ejpam-3758	99	7	and	and	CCONJ
ejpam-3758	99	8	u	u	NOUN
ejpam-3758	99	9	is	be	AUX
ejpam-3758	99	10	open	open	ADJ
ejpam-3758	99	11	in	in	ADP
ejpam-3758	99	12	x.	x.	PROPN
ejpam-3758	99	13	xiv	xiv	PROPN
ejpam-3758	99	14	.	.	PUNCT
ejpam-3758	99	15	mildly	mildly	ADV
ejpam-3758	99	16	generalized	generalize	VERB
ejpam-3758	99	17	closed	close	VERB
ejpam-3758	99	18	(	(	PUNCT
ejpam-3758	99	19	or	or	CCONJ
ejpam-3758	99	20	briefly	briefly	ADV
ejpam-3758	99	21	mildly	mildly	ADV
ejpam-3758	99	22	g	g	NOUN
ejpam-3758	99	23	-	-	PUNCT
ejpam-3758	99	24	closed	closed	ADJ
ejpam-3758	99	25	)	)	PUNCT
ejpam-3758	99	26	set	set	VERB
ejpam-3758	99	27	if	if	SCONJ
ejpam-3758	99	28	cl(int(a	cl(int(a	NOUN
ejpam-3758	99	29	)	)	PUNCT
ejpam-3758	99	30	)	)	PUNCT
ejpam-3758	100	1	⊆	⊆	X
ejpam-3758	100	2	u	u	NOUN
ejpam-3758	100	3	whenever	whenever	SCONJ
ejpam-3758	100	4	a	a	DET
ejpam-3758	100	5	⊆	⊆	NUM
ejpam-3758	100	6	u	u	NOUN
ejpam-3758	100	7	and	and	CCONJ
ejpam-3758	100	8	u	u	NOUN
ejpam-3758	100	9	is	be	AUX
ejpam-3758	100	10	g	g	NOUN
ejpam-3758	100	11	-	-	PUNCT
ejpam-3758	100	12	open	open	ADJ
ejpam-3758	100	13	in	in	ADP
ejpam-3758	100	14	x.	x.	PROPN
ejpam-3758	100	15	xv	xv	PROPN
ejpam-3758	100	16	.	.	PUNCT
ejpam-3758	100	17	semi	semi	ADP
ejpam-3758	100	18	weakly	weakly	ADJ
ejpam-3758	100	19	generalized	generalized	ADJ
ejpam-3758	100	20	closed	close	VERB
ejpam-3758	100	21	(	(	PUNCT
ejpam-3758	100	22	or	or	CCONJ
ejpam-3758	100	23	briefly	briefly	ADV
ejpam-3758	100	24	swg	swg	NOUN
ejpam-3758	100	25	-	-	PUNCT
ejpam-3758	100	26	closed	closed	ADJ
ejpam-3758	100	27	)	)	PUNCT
ejpam-3758	100	28	set	set	VERB
ejpam-3758	100	29	if	if	SCONJ
ejpam-3758	100	30	cl(int(a	cl(int(a	NOUN
ejpam-3758	100	31	)	)	PUNCT
ejpam-3758	100	32	)	)	PUNCT
ejpam-3758	101	1	⊆	⊆	X
ejpam-3758	101	2	u	u	NOUN
ejpam-3758	101	3	whenever	whenever	SCONJ
ejpam-3758	101	4	a	a	DET
ejpam-3758	101	5	⊆	⊆	NUM
ejpam-3758	101	6	u	u	NOUN
ejpam-3758	101	7	and	and	CCONJ
ejpam-3758	101	8	u	u	NOUN
ejpam-3758	101	9	is	be	AUX
ejpam-3758	101	10	semi	semi	ADJ
ejpam-3758	101	11	-	-	ADJ
ejpam-3758	101	12	open	open	ADJ
ejpam-3758	101	13	in	in	ADP
ejpam-3758	101	14	x.	x.	NOUN
ejpam-3758	101	15	3	3	NUM
ejpam-3758	101	16	.	.	PUNCT
ejpam-3758	101	17	main	main	ADJ
ejpam-3758	101	18	results	result	NOUN
ejpam-3758	101	19	3.1	3.1	NUM
ejpam-3758	101	20	.	.	PUNCT
ejpam-3758	102	1	(	(	PUNCT
ejpam-3758	102	2	µ1	µ1	PROPN
ejpam-3758	102	3	,	,	PUNCT
ejpam-3758	102	4	µ2	µ2	PROPN
ejpam-3758	102	5	,	,	PUNCT
ejpam-3758	102	6	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	102	7	generalized	generalize	VERB
ejpam-3758	102	8	closed	closed	ADJ
ejpam-3758	102	9	sets	set	NOUN
ejpam-3758	102	10	definition	definition	NOUN
ejpam-3758	102	11	7	7	NUM
ejpam-3758	102	12	.	.	PUNCT
ejpam-3758	103	1	let	let	VERB
ejpam-3758	103	2	a	a	DET
ejpam-3758	103	3	be	be	AUX
ejpam-3758	103	4	a	a	DET
ejpam-3758	103	5	subset	subset	NOUN
ejpam-3758	103	6	of	of	ADP
ejpam-3758	103	7	a	a	PRON
ejpam-3758	103	8	nonempty	nonempty	ADV
ejpam-3758	103	9	set	set	VERB
ejpam-3758	103	10	x	x	PUNCT
ejpam-3758	103	11	and	and	CCONJ
ejpam-3758	103	12	µ1	µ1	PROPN
ejpam-3758	103	13	,	,	PUNCT
ejpam-3758	103	14	µ2	µ2	NOUN
ejpam-3758	103	15	,	,	PUNCT
ejpam-3758	103	16	and	and	CCONJ
ejpam-3758	104	1	µ3	µ3	NOUN
ejpam-3758	104	2	be	be	AUX
ejpam-3758	104	3	generalized	generalize	VERB
ejpam-3758	104	4	topologies	topology	NOUN
ejpam-3758	104	5	in	in	ADP
ejpam-3758	104	6	x.	x.	NOUN
ejpam-3758	104	7	we	we	PRON
ejpam-3758	104	8	say	say	VERB
ejpam-3758	104	9	that	that	SCONJ
ejpam-3758	104	10	a	a	PRON
ejpam-3758	104	11	is	be	AUX
ejpam-3758	104	12	(	(	PUNCT
ejpam-3758	104	13	µ1	µ1	PROPN
ejpam-3758	104	14	,	,	PUNCT
ejpam-3758	104	15	µ2	µ2	PROPN
ejpam-3758	104	16	,	,	PUNCT
ejpam-3758	104	17	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	104	18	generalized	generalize	VERB
ejpam-3758	104	19	closed	close	VERB
ejpam-3758	104	20	(	(	PUNCT
ejpam-3758	104	21	or	or	CCONJ
ejpam-3758	104	22	briefly	briefly	ADV
ejpam-3758	104	23	(	(	PUNCT
ejpam-3758	104	24	µ1	µ1	PROPN
ejpam-3758	104	25	,	,	PUNCT
ejpam-3758	104	26	µ2	µ2	ADJ
ejpam-3758	104	27	,	,	PUNCT
ejpam-3758	104	28	µ3)-wg	µ3)-wg	NOUN
ejpam-3758	104	29	closed	closed	ADJ
ejpam-3758	104	30	)	)	PUNCT
ejpam-3758	104	31	set	set	VERB
ejpam-3758	104	32	if	if	SCONJ
ejpam-3758	104	33	clµ1	clµ1	PROPN
ejpam-3758	104	34	(	(	PUNCT
ejpam-3758	104	35	intµ2	intµ2	NOUN
ejpam-3758	104	36	(	(	PUNCT
ejpam-3758	104	37	a	a	NOUN
ejpam-3758	104	38	)	)	PUNCT
ejpam-3758	104	39	)	)	PUNCT
ejpam-3758	105	1	⊆	⊆	X
ejpam-3758	105	2	u	u	NOUN
ejpam-3758	105	3	whenever	whenever	SCONJ
ejpam-3758	105	4	a	a	DET
ejpam-3758	105	5	⊆	⊆	NUM
ejpam-3758	105	6	u	u	NOUN
ejpam-3758	105	7	and	and	CCONJ
ejpam-3758	105	8	u	u	NOUN
ejpam-3758	105	9	is	be	AUX
ejpam-3758	105	10	µ3	µ3	NOUN
ejpam-3758	105	11	-	-	PUNCT
ejpam-3758	105	12	open	open	ADJ
ejpam-3758	105	13	in	in	ADP
ejpam-3758	105	14	x.	x.	NOUN
ejpam-3758	105	15	we	we	PRON
ejpam-3758	105	16	call	call	VERB
ejpam-3758	105	17	the	the	DET
ejpam-3758	105	18	complement	complement	NOUN
ejpam-3758	105	19	of	of	ADP
ejpam-3758	105	20	every	every	PRON
ejpam-3758	105	21	(	(	PUNCT
ejpam-3758	105	22	µ1	µ1	PROPN
ejpam-3758	105	23	,	,	PUNCT
ejpam-3758	105	24	µ2	µ2	PROPN
ejpam-3758	105	25	,	,	PUNCT
ejpam-3758	105	26	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	105	27	generalized	generalize	VERB
ejpam-3758	105	28	closed	close	VERB
ejpam-3758	105	29	set	set	VERB
ejpam-3758	105	30	as	as	ADP
ejpam-3758	105	31	(	(	PUNCT
ejpam-3758	105	32	µ1	µ1	PROPN
ejpam-3758	105	33	,	,	PUNCT
ejpam-3758	105	34	µ2	µ2	ADJ
ejpam-3758	105	35	,	,	PUNCT
ejpam-3758	105	36	µ3)weakly	µ3)weakly	ADV
ejpam-3758	105	37	generalized	generalize	VERB
ejpam-3758	105	38	open	open	ADJ
ejpam-3758	105	39	(	(	PUNCT
ejpam-3758	105	40	or	or	CCONJ
ejpam-3758	105	41	briefly	briefly	ADV
ejpam-3758	105	42	(	(	PUNCT
ejpam-3758	105	43	µ1	µ1	PROPN
ejpam-3758	105	44	,	,	PUNCT
ejpam-3758	105	45	µ2	µ2	ADJ
ejpam-3758	105	46	,	,	PUNCT
ejpam-3758	105	47	µ3)-wg	µ3)-wg	NOUN
ejpam-3758	105	48	open	open	ADJ
ejpam-3758	105	49	)	)	PUNCT
ejpam-3758	105	50	set	set	VERB
ejpam-3758	105	51	in	in	ADP
ejpam-3758	105	52	x.	x.	PROPN
ejpam-3758	105	53	b.	b.	PROPN
ejpam-3758	105	54	agua	agua	PROPN
ejpam-3758	105	55	,	,	PUNCT
ejpam-3758	105	56	r.	r.	PROPN
ejpam-3758	105	57	paluga	paluga	PROPN
ejpam-3758	105	58	/	/	SYM
ejpam-3758	105	59	eur	eur	PROPN
ejpam-3758	105	60	.	.	PUNCT
ejpam-3758	106	1	j.	j.	PROPN
ejpam-3758	106	2	pure	pure	PROPN
ejpam-3758	106	3	appl	appl	PROPN
ejpam-3758	106	4	.	.	PROPN
ejpam-3758	106	5	math	math	PROPN
ejpam-3758	106	6	,	,	PUNCT
ejpam-3758	106	7	13	13	NUM
ejpam-3758	106	8	(	(	PUNCT
ejpam-3758	106	9	4	4	NUM
ejpam-3758	106	10	)	)	PUNCT
ejpam-3758	106	11	(	(	PUNCT
ejpam-3758	106	12	2020	2020	NUM
ejpam-3758	106	13	)	)	PUNCT
ejpam-3758	106	14	,	,	PUNCT
ejpam-3758	106	15	977	977	NUM
ejpam-3758	106	16	-	-	SYM
ejpam-3758	106	17	986	986	NUM
ejpam-3758	106	18	981	981	NUM
ejpam-3758	106	19	3.2	3.2	NUM
ejpam-3758	106	20	.	.	PUNCT
ejpam-3758	107	1	special	special	ADJ
ejpam-3758	107	2	cases	case	NOUN
ejpam-3758	107	3	of	of	ADP
ejpam-3758	107	4	(	(	PUNCT
ejpam-3758	107	5	µ1	µ1	PROPN
ejpam-3758	107	6	,	,	PUNCT
ejpam-3758	107	7	µ2	µ2	PROPN
ejpam-3758	107	8	,	,	PUNCT
ejpam-3758	107	9	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	107	10	generalized	generalize	VERB
ejpam-3758	107	11	closed	closed	ADJ
ejpam-3758	107	12	sets	set	NOUN
ejpam-3758	107	13	let	let	VERB
ejpam-3758	107	14	x	x	PRON
ejpam-3758	107	15	be	be	AUX
ejpam-3758	107	16	a	a	DET
ejpam-3758	107	17	non	non	X
ejpam-3758	107	18	empty	empty	ADJ
ejpam-3758	107	19	set	set	NOUN
ejpam-3758	107	20	and	and	CCONJ
ejpam-3758	107	21	a	a	DET
ejpam-3758	107	22	⊆	⊆	NUM
ejpam-3758	107	23	x.	x.	NOUN
ejpam-3758	107	24	then	then	ADV
ejpam-3758	107	25	the	the	DET
ejpam-3758	107	26	following	follow	VERB
ejpam-3758	107	27	are	be	AUX
ejpam-3758	107	28	special	special	ADJ
ejpam-3758	107	29	cases	case	NOUN
ejpam-3758	107	30	of	of	ADP
ejpam-3758	107	31	(	(	PUNCT
ejpam-3758	107	32	µ1	µ1	PROPN
ejpam-3758	107	33	,	,	PUNCT
ejpam-3758	107	34	µ2	µ2	PROPN
ejpam-3758	107	35	,	,	PUNCT
ejpam-3758	107	36	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	107	37	generalized	generalize	VERB
ejpam-3758	107	38	closed	closed	ADJ
ejpam-3758	107	39	sets	set	NOUN
ejpam-3758	107	40	with	with	ADP
ejpam-3758	107	41	the	the	DET
ejpam-3758	107	42	corresponding	corresponding	ADJ
ejpam-3758	107	43	conditions	condition	NOUN
ejpam-3758	107	44	.	.	PUNCT
ejpam-3758	108	1	i.	i.	PROPN
ejpam-3758	108	2	generalized	generalize	VERB
ejpam-3758	108	3	closed	close	VERB
ejpam-3758	108	4	(	(	PUNCT
ejpam-3758	108	5	or	or	CCONJ
ejpam-3758	108	6	briefly	briefly	ADV
ejpam-3758	108	7	g	g	NOUN
ejpam-3758	108	8	-	-	PUNCT
ejpam-3758	108	9	closed	closed	ADJ
ejpam-3758	108	10	)	)	PUNCT
ejpam-3758	108	11	set	set	VERB
ejpam-3758	108	12	if	if	SCONJ
ejpam-3758	108	13	µ1	µ1	PROPN
ejpam-3758	108	14	=	=	PUNCT
ejpam-3758	108	15	µ3	µ3	PROPN
ejpam-3758	108	16	is	be	AUX
ejpam-3758	108	17	a	a	DET
ejpam-3758	108	18	topology	topology	NOUN
ejpam-3758	108	19	for	for	ADP
ejpam-3758	108	20	x	x	PUNCT
ejpam-3758	108	21	and	and	CCONJ
ejpam-3758	108	22	µ2	µ2	PROPN
ejpam-3758	108	23	is	be	AUX
ejpam-3758	108	24	the	the	DET
ejpam-3758	108	25	discrete	discrete	ADJ
ejpam-3758	108	26	topology	topology	NOUN
ejpam-3758	108	27	,	,	PUNCT
ejpam-3758	108	28	then	then	ADV
ejpam-3758	108	29	a	a	DET
ejpam-3758	108	30	(	(	PUNCT
ejpam-3758	108	31	µ1	µ1	PROPN
ejpam-3758	108	32	,	,	PUNCT
ejpam-3758	108	33	µ2	µ2	ADJ
ejpam-3758	108	34	,	,	PUNCT
ejpam-3758	108	35	µ3)weakly	µ3)weakly	ADV
ejpam-3758	108	36	generalized	generalize	VERB
ejpam-3758	108	37	closed	close	VERB
ejpam-3758	108	38	set	set	NOUN
ejpam-3758	108	39	is	be	AUX
ejpam-3758	108	40	just	just	ADV
ejpam-3758	108	41	a	a	DET
ejpam-3758	108	42	g	g	NOUN
ejpam-3758	108	43	-	-	PUNCT
ejpam-3758	108	44	closed	close	VERB
ejpam-3758	108	45	set	set	NOUN
ejpam-3758	108	46	since	since	SCONJ
ejpam-3758	108	47	the	the	DET
ejpam-3758	108	48	condition	condition	NOUN
ejpam-3758	108	49	“	"	PUNCT
ejpam-3758	108	50	clµ1	clµ1	NOUN
ejpam-3758	108	51	(	(	PUNCT
ejpam-3758	108	52	intµ2	intµ2	NOUN
ejpam-3758	108	53	(	(	PUNCT
ejpam-3758	108	54	a	a	NOUN
ejpam-3758	108	55	)	)	PUNCT
ejpam-3758	108	56	)	)	PUNCT
ejpam-3758	109	1	⊆	⊆	X
ejpam-3758	109	2	u	u	NOUN
ejpam-3758	109	3	whenever	whenever	SCONJ
ejpam-3758	109	4	a	a	DET
ejpam-3758	109	5	⊆	⊆	NUM
ejpam-3758	109	6	u	u	NOUN
ejpam-3758	109	7	and	and	CCONJ
ejpam-3758	109	8	u	u	NOUN
ejpam-3758	109	9	is	be	AUX
ejpam-3758	109	10	µ3	µ3	NOUN
ejpam-3758	109	11	-	-	PUNCT
ejpam-3758	109	12	open	open	ADJ
ejpam-3758	109	13	in	in	ADP
ejpam-3758	109	14	x	x	NOUN
ejpam-3758	109	15	”	"	PUNCT
ejpam-3758	109	16	becomes	become	VERB
ejpam-3758	109	17	“	"	PUNCT
ejpam-3758	109	18	cl(a	cl(a	NUM
ejpam-3758	109	19	)	)	PUNCT
ejpam-3758	109	20	⊆	⊆	NUM
ejpam-3758	109	21	u	u	NOUN
ejpam-3758	109	22	whenever	whenever	SCONJ
ejpam-3758	109	23	a	a	DET
ejpam-3758	109	24	⊆	⊆	NUM
ejpam-3758	109	25	u	u	NOUN
ejpam-3758	109	26	and	and	CCONJ
ejpam-3758	109	27	u	u	NOUN
ejpam-3758	109	28	is	be	AUX
ejpam-3758	109	29	open	open	ADJ
ejpam-3758	109	30	in	in	ADP
ejpam-3758	109	31	x	x	NOUN
ejpam-3758	109	32	”	"	PUNCT
ejpam-3758	109	33	.	.	PUNCT
ejpam-3758	110	1	ii	ii	X
ejpam-3758	110	2	.	.	PUNCT
ejpam-3758	111	1	strongly	strongly	ADV
ejpam-3758	111	2	generalized	generalize	VERB
ejpam-3758	111	3	closed	close	VERB
ejpam-3758	111	4	(	(	PUNCT
ejpam-3758	111	5	or	or	CCONJ
ejpam-3758	111	6	briefly	briefly	ADV
ejpam-3758	111	7	g*-closed	g*-close	VERB
ejpam-3758	111	8	)	)	PUNCT
ejpam-3758	111	9	set	set	VERB
ejpam-3758	111	10	if	if	SCONJ
ejpam-3758	111	11	µ1	µ1	PROPN
ejpam-3758	111	12	is	be	AUX
ejpam-3758	111	13	a	a	DET
ejpam-3758	111	14	topology	topology	NOUN
ejpam-3758	111	15	in	in	ADP
ejpam-3758	111	16	x	x	X
ejpam-3758	111	17	,	,	PUNCT
ejpam-3758	111	18	µ2	µ2	PROPN
ejpam-3758	111	19	is	be	AUX
ejpam-3758	111	20	the	the	DET
ejpam-3758	111	21	discrete	discrete	ADJ
ejpam-3758	111	22	topology	topology	NOUN
ejpam-3758	111	23	in	in	ADP
ejpam-3758	111	24	x	x	NOUN
ejpam-3758	111	25	,	,	PUNCT
ejpam-3758	111	26	and	and	CCONJ
ejpam-3758	111	27	µ3	µ3	NOUN
ejpam-3758	111	28	=	=	SYM
ejpam-3758	111	29	g(x	g(x	NOUN
ejpam-3758	111	30	)	)	PUNCT
ejpam-3758	111	31	where	where	SCONJ
ejpam-3758	111	32	g(x	g(x	NOUN
ejpam-3758	111	33	)	)	PUNCT
ejpam-3758	111	34	is	be	AUX
ejpam-3758	111	35	the	the	DET
ejpam-3758	111	36	collection	collection	NOUN
ejpam-3758	111	37	of	of	ADP
ejpam-3758	111	38	g	g	NOUN
ejpam-3758	111	39	-	-	PUNCT
ejpam-3758	111	40	open	open	ADJ
ejpam-3758	111	41	sets	set	NOUN
ejpam-3758	111	42	in	in	ADP
ejpam-3758	111	43	x	x	NOUN
ejpam-3758	111	44	,	,	PUNCT
ejpam-3758	111	45	then	then	ADV
ejpam-3758	111	46	a	a	DET
ejpam-3758	111	47	(	(	PUNCT
ejpam-3758	111	48	µ1	µ1	PROPN
ejpam-3758	111	49	,	,	PUNCT
ejpam-3758	111	50	µ2	µ2	PROPN
ejpam-3758	111	51	,	,	PUNCT
ejpam-3758	111	52	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	111	53	generalized	generalize	VERB
ejpam-3758	111	54	closed	close	VERB
ejpam-3758	111	55	set	set	NOUN
ejpam-3758	111	56	is	be	AUX
ejpam-3758	111	57	just	just	ADV
ejpam-3758	111	58	the	the	DET
ejpam-3758	111	59	strongly	strongly	ADV
ejpam-3758	111	60	generalized	generalize	VERB
ejpam-3758	111	61	closed	close	VERB
ejpam-3758	111	62	set	set	NOUN
ejpam-3758	111	63	since	since	SCONJ
ejpam-3758	111	64	the	the	DET
ejpam-3758	111	65	condition	condition	NOUN
ejpam-3758	111	66	“	"	PUNCT
ejpam-3758	111	67	clµ1	clµ1	NOUN
ejpam-3758	111	68	(	(	PUNCT
ejpam-3758	111	69	intµ2	intµ2	NOUN
ejpam-3758	111	70	(	(	PUNCT
ejpam-3758	111	71	a	a	NOUN
ejpam-3758	111	72	)	)	PUNCT
ejpam-3758	111	73	)	)	PUNCT
ejpam-3758	112	1	⊆	⊆	X
ejpam-3758	112	2	u	u	NOUN
ejpam-3758	112	3	whenever	whenever	SCONJ
ejpam-3758	112	4	a	a	DET
ejpam-3758	112	5	⊆	⊆	NUM
ejpam-3758	112	6	u	u	NOUN
ejpam-3758	112	7	and	and	CCONJ
ejpam-3758	112	8	u	u	NOUN
ejpam-3758	112	9	is	be	AUX
ejpam-3758	112	10	µ3	µ3	NOUN
ejpam-3758	112	11	-	-	PUNCT
ejpam-3758	112	12	open	open	ADJ
ejpam-3758	112	13	in	in	ADP
ejpam-3758	112	14	x	x	NOUN
ejpam-3758	112	15	”	"	PUNCT
ejpam-3758	112	16	becomes	become	VERB
ejpam-3758	112	17	“	"	PUNCT
ejpam-3758	112	18	cl(a	cl(a	NUM
ejpam-3758	112	19	)	)	PUNCT
ejpam-3758	112	20	⊆	⊆	NUM
ejpam-3758	112	21	u	u	NOUN
ejpam-3758	112	22	whenever	whenever	SCONJ
ejpam-3758	112	23	a	a	DET
ejpam-3758	112	24	⊆	⊆	NUM
ejpam-3758	112	25	u	u	NOUN
ejpam-3758	112	26	and	and	CCONJ
ejpam-3758	112	27	u	u	NOUN
ejpam-3758	112	28	is	be	AUX
ejpam-3758	112	29	g	g	NOUN
ejpam-3758	112	30	-	-	PUNCT
ejpam-3758	112	31	open	open	ADJ
ejpam-3758	112	32	in	in	ADP
ejpam-3758	112	33	x	x	NOUN
ejpam-3758	112	34	”	"	PUNCT
ejpam-3758	112	35	.	.	PUNCT
ejpam-3758	113	1	iii	iii	X
ejpam-3758	113	2	.	.	NOUN
ejpam-3758	113	3	generalized	generalize	VERB
ejpam-3758	113	4	preclosed	preclose	VERB
ejpam-3758	113	5	(	(	PUNCT
ejpam-3758	113	6	or	or	CCONJ
ejpam-3758	113	7	briefly	briefly	ADV
ejpam-3758	113	8	gp	gp	NOUN
ejpam-3758	113	9	-	-	PUNCT
ejpam-3758	113	10	closed	closed	ADJ
ejpam-3758	113	11	)	)	PUNCT
ejpam-3758	113	12	set	set	VERB
ejpam-3758	113	13	if	if	SCONJ
ejpam-3758	113	14	µ1	µ1	NOUN
ejpam-3758	113	15	=	=	SYM
ejpam-3758	113	16	po(x	po(x	X
ejpam-3758	113	17	)	)	PUNCT
ejpam-3758	113	18	where	where	SCONJ
ejpam-3758	113	19	po(x	po(x	NUM
ejpam-3758	113	20	)	)	PUNCT
ejpam-3758	113	21	is	be	AUX
ejpam-3758	113	22	the	the	DET
ejpam-3758	113	23	collection	collection	NOUN
ejpam-3758	113	24	of	of	ADP
ejpam-3758	113	25	pre	pre	ADJ
ejpam-3758	113	26	-	-	ADJ
ejpam-3758	113	27	open	open	ADJ
ejpam-3758	113	28	sets	set	NOUN
ejpam-3758	113	29	sets	set	NOUN
ejpam-3758	113	30	inx	inx	VERB
ejpam-3758	113	31	,	,	PUNCT
ejpam-3758	113	32	µ2	µ2	PROPN
ejpam-3758	113	33	is	be	AUX
ejpam-3758	113	34	the	the	DET
ejpam-3758	113	35	discrete	discrete	ADJ
ejpam-3758	113	36	topology	topology	NOUN
ejpam-3758	113	37	in	in	ADP
ejpam-3758	113	38	x	x	NOUN
ejpam-3758	113	39	,	,	PUNCT
ejpam-3758	113	40	and	and	CCONJ
ejpam-3758	113	41	µ3	µ3	PROPN
ejpam-3758	113	42	is	be	AUX
ejpam-3758	113	43	a	a	DET
ejpam-3758	113	44	topology	topology	NOUN
ejpam-3758	113	45	in	in	ADP
ejpam-3758	113	46	x	x	NOUN
ejpam-3758	113	47	,	,	PUNCT
ejpam-3758	113	48	then	then	ADV
ejpam-3758	113	49	a	a	DET
ejpam-3758	113	50	(	(	PUNCT
ejpam-3758	113	51	µ1	µ1	PROPN
ejpam-3758	113	52	,	,	PUNCT
ejpam-3758	113	53	µ2	µ2	PROPN
ejpam-3758	113	54	,	,	PUNCT
ejpam-3758	113	55	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	113	56	generalized	generalize	VERB
ejpam-3758	113	57	closed	close	VERB
ejpam-3758	113	58	set	set	NOUN
ejpam-3758	113	59	is	be	AUX
ejpam-3758	113	60	just	just	ADV
ejpam-3758	113	61	the	the	DET
ejpam-3758	113	62	generalized	generalize	VERB
ejpam-3758	113	63	preclosed	preclose	VERB
ejpam-3758	113	64	set	set	NOUN
ejpam-3758	113	65	since	since	SCONJ
ejpam-3758	113	66	the	the	DET
ejpam-3758	113	67	condition	condition	NOUN
ejpam-3758	113	68	“	"	PUNCT
ejpam-3758	113	69	clµ1	clµ1	NOUN
ejpam-3758	113	70	(	(	PUNCT
ejpam-3758	113	71	intµ2	intµ2	NOUN
ejpam-3758	113	72	(	(	PUNCT
ejpam-3758	113	73	a	a	NOUN
ejpam-3758	113	74	)	)	PUNCT
ejpam-3758	113	75	)	)	PUNCT
ejpam-3758	114	1	⊆	⊆	X
ejpam-3758	114	2	u	u	NOUN
ejpam-3758	114	3	whenever	whenever	SCONJ
ejpam-3758	114	4	a	a	DET
ejpam-3758	114	5	⊆	⊆	NUM
ejpam-3758	114	6	u	u	NOUN
ejpam-3758	114	7	and	and	CCONJ
ejpam-3758	114	8	u	u	NOUN
ejpam-3758	114	9	is	be	AUX
ejpam-3758	114	10	µ3	µ3	NOUN
ejpam-3758	114	11	-	-	PUNCT
ejpam-3758	114	12	open	open	ADJ
ejpam-3758	114	13	in	in	ADP
ejpam-3758	114	14	x	x	NOUN
ejpam-3758	114	15	”	"	PUNCT
ejpam-3758	114	16	becomes	become	VERB
ejpam-3758	114	17	“	"	PUNCT
ejpam-3758	114	18	pcl(a	pcl(a	PROPN
ejpam-3758	114	19	)	)	PUNCT
ejpam-3758	114	20	⊆	⊆	NUM
ejpam-3758	114	21	u	u	NOUN
ejpam-3758	114	22	whenever	whenever	SCONJ
ejpam-3758	114	23	a	a	DET
ejpam-3758	114	24	⊆	⊆	NUM
ejpam-3758	114	25	u	u	NOUN
ejpam-3758	114	26	and	and	CCONJ
ejpam-3758	114	27	u	u	NOUN
ejpam-3758	114	28	is	be	AUX
ejpam-3758	114	29	open	open	ADJ
ejpam-3758	114	30	in	in	ADP
ejpam-3758	114	31	x	x	NOUN
ejpam-3758	114	32	”	"	PUNCT
ejpam-3758	114	33	.	.	PUNCT
ejpam-3758	115	1	iv	iv	X
ejpam-3758	115	2	.	.	PUNCT
ejpam-3758	115	3	semi	semi	ADJ
ejpam-3758	115	4	-	-	ADJ
ejpam-3758	115	5	generalized	generalized	ADJ
ejpam-3758	115	6	closed	close	VERB
ejpam-3758	115	7	(	(	PUNCT
ejpam-3758	115	8	or	or	CCONJ
ejpam-3758	115	9	briefly	briefly	ADV
ejpam-3758	115	10	sg	sg	NOUN
ejpam-3758	115	11	-	-	PUNCT
ejpam-3758	115	12	closed	closed	ADJ
ejpam-3758	115	13	)	)	PUNCT
ejpam-3758	115	14	set	set	VERB
ejpam-3758	115	15	if	if	SCONJ
ejpam-3758	115	16	µ1	µ1	PROPN
ejpam-3758	115	17	=	=	SYM
ejpam-3758	115	18	µ3	µ3	NOUN
ejpam-3758	115	19	=	=	SYM
ejpam-3758	115	20	so(x	so(x	X
ejpam-3758	115	21	)	)	PUNCT
ejpam-3758	116	1	where	where	SCONJ
ejpam-3758	116	2	so(x	so(x	NOUN
ejpam-3758	116	3	)	)	PUNCT
ejpam-3758	116	4	is	be	AUX
ejpam-3758	116	5	the	the	DET
ejpam-3758	116	6	collection	collection	NOUN
ejpam-3758	116	7	of	of	ADP
ejpam-3758	116	8	semi	semi	ADJ
ejpam-3758	116	9	-	-	ADJ
ejpam-3758	116	10	open	open	ADJ
ejpam-3758	116	11	sets	set	NOUN
ejpam-3758	116	12	in	in	ADP
ejpam-3758	116	13	x	x	NOUN
ejpam-3758	116	14	,	,	PUNCT
ejpam-3758	116	15	and	and	CCONJ
ejpam-3758	116	16	µ2	µ2	PROPN
ejpam-3758	116	17	is	be	AUX
ejpam-3758	116	18	a	a	DET
ejpam-3758	116	19	discrete	discrete	ADJ
ejpam-3758	116	20	topology	topology	NOUN
ejpam-3758	116	21	in	in	ADP
ejpam-3758	116	22	x	x	NOUN
ejpam-3758	116	23	,	,	PUNCT
ejpam-3758	116	24	then	then	ADV
ejpam-3758	116	25	a	a	DET
ejpam-3758	116	26	(	(	PUNCT
ejpam-3758	116	27	µ1	µ1	PROPN
ejpam-3758	116	28	,	,	PUNCT
ejpam-3758	116	29	µ2	µ2	PROPN
ejpam-3758	116	30	,	,	PUNCT
ejpam-3758	116	31	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	116	32	generalized	generalize	VERB
ejpam-3758	116	33	closed	close	VERB
ejpam-3758	116	34	set	set	NOUN
ejpam-3758	116	35	is	be	AUX
ejpam-3758	116	36	just	just	ADV
ejpam-3758	116	37	a	a	DET
ejpam-3758	116	38	semi	semi	ADJ
ejpam-3758	116	39	-	-	ADJ
ejpam-3758	116	40	generalized	generalized	ADJ
ejpam-3758	116	41	closed	close	VERB
ejpam-3758	116	42	set	set	NOUN
ejpam-3758	116	43	since	since	SCONJ
ejpam-3758	116	44	the	the	DET
ejpam-3758	116	45	condition	condition	NOUN
ejpam-3758	116	46	“	"	PUNCT
ejpam-3758	116	47	clµ1	clµ1	NOUN
ejpam-3758	116	48	(	(	PUNCT
ejpam-3758	116	49	intµ2	intµ2	NOUN
ejpam-3758	116	50	(	(	PUNCT
ejpam-3758	116	51	a	a	NOUN
ejpam-3758	116	52	)	)	PUNCT
ejpam-3758	116	53	)	)	PUNCT
ejpam-3758	117	1	⊆	⊆	X
ejpam-3758	117	2	u	u	NOUN
ejpam-3758	117	3	whenever	whenever	SCONJ
ejpam-3758	117	4	a	a	DET
ejpam-3758	117	5	⊆	⊆	NUM
ejpam-3758	117	6	u	u	NOUN
ejpam-3758	117	7	and	and	CCONJ
ejpam-3758	117	8	u	u	NOUN
ejpam-3758	117	9	is	be	AUX
ejpam-3758	117	10	µ3	µ3	NOUN
ejpam-3758	117	11	-	-	PUNCT
ejpam-3758	117	12	open	open	ADJ
ejpam-3758	117	13	in	in	ADP
ejpam-3758	117	14	x	x	NOUN
ejpam-3758	117	15	”	"	PUNCT
ejpam-3758	117	16	becomes	become	VERB
ejpam-3758	117	17	“	"	PUNCT
ejpam-3758	117	18	scl(a	scl(a	X
ejpam-3758	117	19	)	)	PUNCT
ejpam-3758	117	20	⊆	⊆	NUM
ejpam-3758	117	21	u	u	NOUN
ejpam-3758	117	22	whenever	whenever	SCONJ
ejpam-3758	117	23	a	a	DET
ejpam-3758	117	24	⊆	⊆	NUM
ejpam-3758	117	25	u	u	NOUN
ejpam-3758	117	26	and	and	CCONJ
ejpam-3758	117	27	u	u	NOUN
ejpam-3758	117	28	is	be	AUX
ejpam-3758	117	29	semi	semi	ADJ
ejpam-3758	117	30	-	-	ADJ
ejpam-3758	117	31	open	open	ADJ
ejpam-3758	117	32	in	in	ADP
ejpam-3758	117	33	x	x	NOUN
ejpam-3758	117	34	”	"	PUNCT
ejpam-3758	117	35	.	.	PUNCT
ejpam-3758	118	1	v.	v.	ADP
ejpam-3758	118	2	generalized	generalize	VERB
ejpam-3758	118	3	b	b	X
ejpam-3758	118	4	-	-	PUNCT
ejpam-3758	118	5	closed	closed	ADJ
ejpam-3758	118	6	(	(	PUNCT
ejpam-3758	118	7	or	or	CCONJ
ejpam-3758	118	8	briefly	briefly	ADV
ejpam-3758	118	9	gs	gs	NOUN
ejpam-3758	118	10	-	-	PUNCT
ejpam-3758	118	11	closed	closed	ADJ
ejpam-3758	118	12	)	)	PUNCT
ejpam-3758	118	13	set	set	VERB
ejpam-3758	118	14	if	if	SCONJ
ejpam-3758	118	15	µ1	µ1	NOUN
ejpam-3758	118	16	=	=	SYM
ejpam-3758	118	17	so(x	so(x	NOUN
ejpam-3758	118	18	)	)	PUNCT
ejpam-3758	119	1	where	where	SCONJ
ejpam-3758	119	2	so(x	so(x	NOUN
ejpam-3758	119	3	)	)	PUNCT
ejpam-3758	119	4	is	be	AUX
ejpam-3758	119	5	the	the	DET
ejpam-3758	119	6	collection	collection	NOUN
ejpam-3758	119	7	of	of	ADP
ejpam-3758	119	8	semi	semi	ADJ
ejpam-3758	119	9	-	-	ADJ
ejpam-3758	119	10	open	open	ADJ
ejpam-3758	119	11	sets	set	NOUN
ejpam-3758	119	12	in	in	ADP
ejpam-3758	119	13	x	x	NOUN
ejpam-3758	119	14	,	,	PUNCT
ejpam-3758	119	15	µ2	µ2	PROPN
ejpam-3758	119	16	is	be	AUX
ejpam-3758	119	17	the	the	DET
ejpam-3758	119	18	discrete	discrete	ADJ
ejpam-3758	119	19	topology	topology	NOUN
ejpam-3758	119	20	in	in	ADP
ejpam-3758	119	21	x	x	NOUN
ejpam-3758	119	22	,	,	PUNCT
ejpam-3758	119	23	and	and	CCONJ
ejpam-3758	119	24	µ3	µ3	PROPN
ejpam-3758	119	25	is	be	AUX
ejpam-3758	119	26	a	a	DET
ejpam-3758	119	27	topology	topology	NOUN
ejpam-3758	119	28	in	in	ADP
ejpam-3758	119	29	x	x	NOUN
ejpam-3758	119	30	,	,	PUNCT
ejpam-3758	119	31	then	then	ADV
ejpam-3758	119	32	a	a	DET
ejpam-3758	119	33	(	(	PUNCT
ejpam-3758	119	34	µ1	µ1	PROPN
ejpam-3758	119	35	,	,	PUNCT
ejpam-3758	119	36	µ2	µ2	PROPN
ejpam-3758	119	37	,	,	PUNCT
ejpam-3758	119	38	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	119	39	generalized	generalize	VERB
ejpam-3758	119	40	closed	close	VERB
ejpam-3758	119	41	set	set	NOUN
ejpam-3758	119	42	is	be	AUX
ejpam-3758	119	43	just	just	ADV
ejpam-3758	119	44	a	a	DET
ejpam-3758	119	45	generalized	generalized	ADJ
ejpam-3758	119	46	semi	semi	ADJ
ejpam-3758	119	47	-	-	ADJ
ejpam-3758	119	48	closed	closed	ADJ
ejpam-3758	119	49	set	set	NOUN
ejpam-3758	119	50	since	since	SCONJ
ejpam-3758	119	51	the	the	DET
ejpam-3758	119	52	condition	condition	NOUN
ejpam-3758	119	53	“	"	PUNCT
ejpam-3758	119	54	clµ1	clµ1	NOUN
ejpam-3758	119	55	(	(	PUNCT
ejpam-3758	119	56	intµ2	intµ2	NOUN
ejpam-3758	119	57	(	(	PUNCT
ejpam-3758	119	58	a	a	NOUN
ejpam-3758	119	59	)	)	PUNCT
ejpam-3758	119	60	)	)	PUNCT
ejpam-3758	120	1	⊆	⊆	X
ejpam-3758	120	2	u	u	NOUN
ejpam-3758	120	3	whenever	whenever	SCONJ
ejpam-3758	120	4	a	a	DET
ejpam-3758	120	5	⊆	⊆	NUM
ejpam-3758	120	6	u	u	NOUN
ejpam-3758	120	7	and	and	CCONJ
ejpam-3758	120	8	u	u	NOUN
ejpam-3758	120	9	is	be	AUX
ejpam-3758	120	10	µ3	µ3	NOUN
ejpam-3758	120	11	-	-	PUNCT
ejpam-3758	120	12	open	open	ADJ
ejpam-3758	120	13	in	in	ADP
ejpam-3758	120	14	x	x	NOUN
ejpam-3758	120	15	”	"	PUNCT
ejpam-3758	120	16	becomes	become	VERB
ejpam-3758	120	17	“	"	PUNCT
ejpam-3758	120	18	scl(a	scl(a	X
ejpam-3758	120	19	)	)	PUNCT
ejpam-3758	120	20	⊆	⊆	NUM
ejpam-3758	120	21	u	u	NOUN
ejpam-3758	120	22	whenever	whenever	SCONJ
ejpam-3758	120	23	a	a	DET
ejpam-3758	120	24	⊆	⊆	NUM
ejpam-3758	120	25	u	u	NOUN
ejpam-3758	120	26	and	and	CCONJ
ejpam-3758	120	27	u	u	NOUN
ejpam-3758	120	28	is	be	AUX
ejpam-3758	120	29	open	open	ADJ
ejpam-3758	120	30	in	in	ADP
ejpam-3758	120	31	x	x	NOUN
ejpam-3758	120	32	”	"	PUNCT
ejpam-3758	120	33	.	.	PUNCT
ejpam-3758	121	1	vi	vi	X
ejpam-3758	121	2	.	.	NOUN
ejpam-3758	121	3	generalized	generalize	VERB
ejpam-3758	121	4	semi	semi	ADV
ejpam-3758	121	5	-	-	ADJ
ejpam-3758	121	6	closed	closed	ADJ
ejpam-3758	121	7	(	(	PUNCT
ejpam-3758	121	8	or	or	CCONJ
ejpam-3758	121	9	briefly	briefly	ADV
ejpam-3758	121	10	gb	gb	ADV
ejpam-3758	121	11	-	-	PUNCT
ejpam-3758	121	12	closed	closed	ADJ
ejpam-3758	121	13	)	)	PUNCT
ejpam-3758	121	14	set	set	VERB
ejpam-3758	121	15	if	if	SCONJ
ejpam-3758	121	16	µ1	µ1	PROPN
ejpam-3758	121	17	=	=	SYM
ejpam-3758	121	18	bo(x	bo(x	X
ejpam-3758	121	19	)	)	PUNCT
ejpam-3758	122	1	where	where	SCONJ
ejpam-3758	122	2	bo(x	bo(x	NUM
ejpam-3758	122	3	)	)	PUNCT
ejpam-3758	122	4	is	be	AUX
ejpam-3758	122	5	the	the	DET
ejpam-3758	122	6	collection	collection	NOUN
ejpam-3758	122	7	of	of	ADP
ejpam-3758	122	8	b	b	NOUN
ejpam-3758	122	9	-	-	PUNCT
ejpam-3758	122	10	open	open	ADJ
ejpam-3758	122	11	sets	set	NOUN
ejpam-3758	122	12	sets	set	NOUN
ejpam-3758	122	13	in	in	ADP
ejpam-3758	122	14	x	x	NOUN
ejpam-3758	122	15	,	,	PUNCT
ejpam-3758	122	16	µ2	µ2	PROPN
ejpam-3758	122	17	is	be	AUX
ejpam-3758	122	18	the	the	DET
ejpam-3758	122	19	discrete	discrete	ADJ
ejpam-3758	122	20	topology	topology	NOUN
ejpam-3758	122	21	in	in	ADP
ejpam-3758	122	22	x	x	NOUN
ejpam-3758	122	23	,	,	PUNCT
ejpam-3758	122	24	and	and	CCONJ
ejpam-3758	122	25	µ3	µ3	PROPN
ejpam-3758	122	26	is	be	AUX
ejpam-3758	122	27	a	a	DET
ejpam-3758	122	28	topology	topology	NOUN
ejpam-3758	122	29	in	in	ADP
ejpam-3758	122	30	x	x	NOUN
ejpam-3758	122	31	,	,	PUNCT
ejpam-3758	122	32	then	then	ADV
ejpam-3758	122	33	a	a	DET
ejpam-3758	122	34	(	(	PUNCT
ejpam-3758	122	35	µ1	µ1	PROPN
ejpam-3758	122	36	,	,	PUNCT
ejpam-3758	122	37	µ2	µ2	PROPN
ejpam-3758	122	38	,	,	PUNCT
ejpam-3758	122	39	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	122	40	generalized	generalize	VERB
ejpam-3758	122	41	closed	close	VERB
ejpam-3758	122	42	set	set	NOUN
ejpam-3758	122	43	is	be	AUX
ejpam-3758	122	44	just	just	ADV
ejpam-3758	122	45	the	the	DET
ejpam-3758	122	46	generalized	generalized	ADJ
ejpam-3758	122	47	b	b	X
ejpam-3758	122	48	-	-	PUNCT
ejpam-3758	122	49	closed	closed	ADJ
ejpam-3758	122	50	set	set	NOUN
ejpam-3758	122	51	since	since	SCONJ
ejpam-3758	122	52	the	the	DET
ejpam-3758	122	53	condition	condition	NOUN
ejpam-3758	122	54	“	"	PUNCT
ejpam-3758	122	55	clµ1	clµ1	NOUN
ejpam-3758	122	56	(	(	PUNCT
ejpam-3758	122	57	intµ2	intµ2	NOUN
ejpam-3758	122	58	(	(	PUNCT
ejpam-3758	122	59	a	a	NOUN
ejpam-3758	122	60	)	)	PUNCT
ejpam-3758	122	61	)	)	PUNCT
ejpam-3758	123	1	⊆	⊆	X
ejpam-3758	123	2	u	u	NOUN
ejpam-3758	123	3	whenever	whenever	SCONJ
ejpam-3758	123	4	a	a	DET
ejpam-3758	123	5	⊆	⊆	NUM
ejpam-3758	123	6	u	u	NOUN
ejpam-3758	123	7	and	and	CCONJ
ejpam-3758	123	8	u	u	NOUN
ejpam-3758	123	9	is	be	AUX
ejpam-3758	123	10	µ3	µ3	NOUN
ejpam-3758	123	11	-	-	PUNCT
ejpam-3758	123	12	open	open	ADJ
ejpam-3758	123	13	in	in	ADP
ejpam-3758	123	14	x	x	NOUN
ejpam-3758	123	15	”	"	PUNCT
ejpam-3758	123	16	becomes	become	VERB
ejpam-3758	123	17	“	"	PUNCT
ejpam-3758	123	18	bcl(a	bcl(a	PROPN
ejpam-3758	123	19	)	)	PUNCT
ejpam-3758	123	20	⊆	⊆	NUM
ejpam-3758	123	21	u	u	NOUN
ejpam-3758	123	22	whenever	whenever	SCONJ
ejpam-3758	123	23	a	a	DET
ejpam-3758	123	24	⊆	⊆	NUM
ejpam-3758	123	25	u	u	NOUN
ejpam-3758	123	26	and	and	CCONJ
ejpam-3758	123	27	u	u	NOUN
ejpam-3758	123	28	is	be	AUX
ejpam-3758	123	29	open	open	ADJ
ejpam-3758	123	30	in	in	ADP
ejpam-3758	123	31	x	x	NOUN
ejpam-3758	123	32	”	"	PUNCT
ejpam-3758	123	33	.	.	PUNCT
ejpam-3758	124	1	b.	b.	PROPN
ejpam-3758	124	2	agua	agua	PROPN
ejpam-3758	124	3	,	,	PUNCT
ejpam-3758	124	4	r.	r.	PROPN
ejpam-3758	124	5	paluga	paluga	PROPN
ejpam-3758	124	6	/	/	SYM
ejpam-3758	124	7	eur	eur	PROPN
ejpam-3758	124	8	.	.	PUNCT
ejpam-3758	125	1	j.	j.	PROPN
ejpam-3758	125	2	pure	pure	PROPN
ejpam-3758	125	3	appl	appl	PROPN
ejpam-3758	125	4	.	.	PROPN
ejpam-3758	125	5	math	math	PROPN
ejpam-3758	125	6	,	,	PUNCT
ejpam-3758	125	7	13	13	NUM
ejpam-3758	125	8	(	(	PUNCT
ejpam-3758	125	9	4	4	NUM
ejpam-3758	125	10	)	)	PUNCT
ejpam-3758	125	11	(	(	PUNCT
ejpam-3758	125	12	2020	2020	NUM
ejpam-3758	125	13	)	)	PUNCT
ejpam-3758	125	14	,	,	PUNCT
ejpam-3758	125	15	977	977	NUM
ejpam-3758	125	16	-	-	SYM
ejpam-3758	125	17	986	986	NUM
ejpam-3758	125	18	982	982	NUM
ejpam-3758	125	19	vii	vii	PROPN
ejpam-3758	125	20	.	.	PROPN
ejpam-3758	126	1	generalized	generalize	VERB
ejpam-3758	126	2	αb	αb	NOUN
ejpam-3758	126	3	-	-	PUNCT
ejpam-3758	126	4	closed	closed	ADJ
ejpam-3758	126	5	(	(	PUNCT
ejpam-3758	126	6	or	or	CCONJ
ejpam-3758	126	7	briefly	briefly	ADV
ejpam-3758	126	8	gαb	gαb	ADV
ejpam-3758	126	9	-	-	PUNCT
ejpam-3758	126	10	closed	closed	ADJ
ejpam-3758	126	11	)	)	PUNCT
ejpam-3758	126	12	set	set	VERB
ejpam-3758	126	13	if	if	SCONJ
ejpam-3758	126	14	µ1	µ1	PROPN
ejpam-3758	126	15	=	=	SYM
ejpam-3758	126	16	bo(x	bo(x	X
ejpam-3758	126	17	)	)	PUNCT
ejpam-3758	126	18	where	where	SCONJ
ejpam-3758	126	19	bo(x	bo(x	NUM
ejpam-3758	126	20	)	)	PUNCT
ejpam-3758	126	21	is	be	AUX
ejpam-3758	126	22	the	the	DET
ejpam-3758	126	23	collection	collection	NOUN
ejpam-3758	126	24	of	of	ADP
ejpam-3758	126	25	b	b	NOUN
ejpam-3758	126	26	-	-	PUNCT
ejpam-3758	126	27	open	open	ADJ
ejpam-3758	126	28	sets	set	NOUN
ejpam-3758	126	29	sets	set	NOUN
ejpam-3758	126	30	in	in	ADP
ejpam-3758	126	31	x	x	NOUN
ejpam-3758	126	32	,	,	PUNCT
ejpam-3758	126	33	µ2	µ2	PROPN
ejpam-3758	126	34	is	be	AUX
ejpam-3758	126	35	the	the	DET
ejpam-3758	126	36	discrete	discrete	ADJ
ejpam-3758	126	37	topology	topology	NOUN
ejpam-3758	126	38	in	in	ADP
ejpam-3758	126	39	x	x	NOUN
ejpam-3758	126	40	,	,	PUNCT
ejpam-3758	126	41	and	and	CCONJ
ejpam-3758	126	42	µ3	µ3	NOUN
ejpam-3758	126	43	=	=	PUNCT
ejpam-3758	126	44	ao(x	ao(x	X
ejpam-3758	126	45	)	)	PUNCT
ejpam-3758	126	46	where	where	SCONJ
ejpam-3758	126	47	ao(x	ao(x	PUNCT
ejpam-3758	126	48	)	)	PUNCT
ejpam-3758	126	49	is	be	AUX
ejpam-3758	126	50	the	the	DET
ejpam-3758	126	51	collection	collection	NOUN
ejpam-3758	126	52	of	of	ADP
ejpam-3758	126	53	α	α	NOUN
ejpam-3758	126	54	-	-	ADJ
ejpam-3758	126	55	open	open	ADJ
ejpam-3758	126	56	sets	set	NOUN
ejpam-3758	126	57	in	in	ADP
ejpam-3758	126	58	x	x	NOUN
ejpam-3758	126	59	,	,	PUNCT
ejpam-3758	126	60	then	then	ADV
ejpam-3758	126	61	a	a	DET
ejpam-3758	126	62	(	(	PUNCT
ejpam-3758	126	63	µ1	µ1	PROPN
ejpam-3758	126	64	,	,	PUNCT
ejpam-3758	126	65	µ2	µ2	PROPN
ejpam-3758	126	66	,	,	PUNCT
ejpam-3758	126	67	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	126	68	generalized	generalize	VERB
ejpam-3758	126	69	closed	close	VERB
ejpam-3758	126	70	set	set	NOUN
ejpam-3758	126	71	is	be	AUX
ejpam-3758	126	72	just	just	ADV
ejpam-3758	126	73	the	the	DET
ejpam-3758	126	74	generalized	generalized	ADJ
ejpam-3758	126	75	b	b	X
ejpam-3758	126	76	-	-	PUNCT
ejpam-3758	126	77	closed	closed	ADJ
ejpam-3758	126	78	set	set	NOUN
ejpam-3758	126	79	since	since	SCONJ
ejpam-3758	126	80	the	the	DET
ejpam-3758	126	81	condition	condition	NOUN
ejpam-3758	126	82	“	"	PUNCT
ejpam-3758	126	83	clµ1	clµ1	NOUN
ejpam-3758	126	84	(	(	PUNCT
ejpam-3758	126	85	intµ2	intµ2	NOUN
ejpam-3758	126	86	(	(	PUNCT
ejpam-3758	126	87	a	a	NOUN
ejpam-3758	126	88	)	)	PUNCT
ejpam-3758	126	89	)	)	PUNCT
ejpam-3758	127	1	⊆	⊆	X
ejpam-3758	127	2	u	u	NOUN
ejpam-3758	127	3	whenever	whenever	SCONJ
ejpam-3758	127	4	a	a	DET
ejpam-3758	127	5	⊆	⊆	NUM
ejpam-3758	127	6	u	u	NOUN
ejpam-3758	127	7	and	and	CCONJ
ejpam-3758	127	8	u	u	NOUN
ejpam-3758	127	9	is	be	AUX
ejpam-3758	127	10	µ3	µ3	NOUN
ejpam-3758	127	11	-	-	PUNCT
ejpam-3758	127	12	open	open	ADJ
ejpam-3758	127	13	in	in	ADP
ejpam-3758	127	14	x	x	NOUN
ejpam-3758	127	15	”	"	PUNCT
ejpam-3758	127	16	becomes	become	VERB
ejpam-3758	127	17	“	"	PUNCT
ejpam-3758	127	18	scl(a	scl(a	X
ejpam-3758	127	19	)	)	PUNCT
ejpam-3758	127	20	⊆	⊆	NUM
ejpam-3758	127	21	u	u	NOUN
ejpam-3758	127	22	whenever	whenever	SCONJ
ejpam-3758	127	23	a	a	DET
ejpam-3758	127	24	⊆	⊆	NUM
ejpam-3758	127	25	u	u	NOUN
ejpam-3758	127	26	and	and	CCONJ
ejpam-3758	127	27	u	u	NOUN
ejpam-3758	127	28	is	be	AUX
ejpam-3758	127	29	α	α	NOUN
ejpam-3758	127	30	-	-	NOUN
ejpam-3758	127	31	open	open	ADJ
ejpam-3758	127	32	in	in	ADP
ejpam-3758	127	33	x	x	NOUN
ejpam-3758	127	34	”	"	PUNCT
ejpam-3758	127	35	.	.	PUNCT
ejpam-3758	128	1	viii	viii	PROPN
ejpam-3758	128	2	.	.	PUNCT
ejpam-3758	129	1	semi	semi	ADJ
ejpam-3758	129	2	generalized	generalized	ADJ
ejpam-3758	129	3	b	b	X
ejpam-3758	129	4	-	-	PUNCT
ejpam-3758	129	5	closed	closed	ADJ
ejpam-3758	129	6	(	(	PUNCT
ejpam-3758	129	7	or	or	CCONJ
ejpam-3758	129	8	briefly	briefly	ADV
ejpam-3758	129	9	sbg	sbg	NOUN
ejpam-3758	129	10	-	-	PUNCT
ejpam-3758	129	11	closed	closed	ADJ
ejpam-3758	129	12	)	)	PUNCT
ejpam-3758	129	13	set	set	VERB
ejpam-3758	129	14	if	if	SCONJ
ejpam-3758	129	15	µ1	µ1	PROPN
ejpam-3758	129	16	=	=	SYM
ejpam-3758	129	17	bo(x	bo(x	X
ejpam-3758	129	18	)	)	PUNCT
ejpam-3758	129	19	where	where	SCONJ
ejpam-3758	129	20	bo(x	bo(x	NUM
ejpam-3758	129	21	)	)	PUNCT
ejpam-3758	129	22	is	be	AUX
ejpam-3758	129	23	the	the	DET
ejpam-3758	129	24	collection	collection	NOUN
ejpam-3758	129	25	of	of	ADP
ejpam-3758	129	26	b	b	NOUN
ejpam-3758	129	27	-	-	PUNCT
ejpam-3758	129	28	open	open	ADJ
ejpam-3758	129	29	sets	set	NOUN
ejpam-3758	129	30	sets	set	NOUN
ejpam-3758	129	31	in	in	ADP
ejpam-3758	129	32	x	x	NOUN
ejpam-3758	129	33	,	,	PUNCT
ejpam-3758	129	34	µ2	µ2	PROPN
ejpam-3758	129	35	is	be	AUX
ejpam-3758	129	36	the	the	DET
ejpam-3758	129	37	discrete	discrete	ADJ
ejpam-3758	129	38	topology	topology	NOUN
ejpam-3758	129	39	in	in	ADP
ejpam-3758	129	40	x	x	NOUN
ejpam-3758	129	41	,	,	PUNCT
ejpam-3758	129	42	and	and	CCONJ
ejpam-3758	129	43	µ3	µ3	NOUN
ejpam-3758	129	44	=	=	SYM
ejpam-3758	129	45	so(x	so(x	X
ejpam-3758	129	46	)	)	PUNCT
ejpam-3758	129	47	where	where	SCONJ
ejpam-3758	129	48	so(x	so(x	NOUN
ejpam-3758	129	49	)	)	PUNCT
ejpam-3758	129	50	is	be	AUX
ejpam-3758	129	51	the	the	DET
ejpam-3758	129	52	collection	collection	NOUN
ejpam-3758	129	53	of	of	ADP
ejpam-3758	129	54	semi	semi	ADJ
ejpam-3758	129	55	-	-	ADJ
ejpam-3758	129	56	open	open	ADJ
ejpam-3758	129	57	sets	set	NOUN
ejpam-3758	129	58	inx	inx	VERB
ejpam-3758	129	59	,	,	PUNCT
ejpam-3758	129	60	then	then	ADV
ejpam-3758	129	61	a	a	DET
ejpam-3758	129	62	(	(	PUNCT
ejpam-3758	129	63	µ1	µ1	PROPN
ejpam-3758	129	64	,	,	PUNCT
ejpam-3758	129	65	µ2	µ2	PROPN
ejpam-3758	129	66	,	,	PUNCT
ejpam-3758	129	67	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	129	68	generalized	generalize	VERB
ejpam-3758	129	69	closed	close	VERB
ejpam-3758	129	70	set	set	NOUN
ejpam-3758	129	71	is	be	AUX
ejpam-3758	129	72	just	just	ADV
ejpam-3758	129	73	the	the	DET
ejpam-3758	129	74	semi	semi	ADJ
ejpam-3758	129	75	-	-	ADJ
ejpam-3758	129	76	generalized	generalized	ADJ
ejpam-3758	129	77	b	b	X
ejpam-3758	129	78	-	-	PUNCT
ejpam-3758	129	79	closed	closed	ADJ
ejpam-3758	129	80	set	set	NOUN
ejpam-3758	129	81	since	since	SCONJ
ejpam-3758	129	82	the	the	DET
ejpam-3758	129	83	condition	condition	NOUN
ejpam-3758	129	84	“	"	PUNCT
ejpam-3758	129	85	clµ1	clµ1	NOUN
ejpam-3758	129	86	(	(	PUNCT
ejpam-3758	129	87	intµ2	intµ2	NOUN
ejpam-3758	129	88	(	(	PUNCT
ejpam-3758	129	89	a	a	NOUN
ejpam-3758	129	90	)	)	PUNCT
ejpam-3758	129	91	)	)	PUNCT
ejpam-3758	130	1	⊆	⊆	X
ejpam-3758	130	2	u	u	NOUN
ejpam-3758	130	3	whenever	whenever	SCONJ
ejpam-3758	130	4	a	a	DET
ejpam-3758	130	5	⊆	⊆	NUM
ejpam-3758	130	6	u	u	NOUN
ejpam-3758	130	7	and	and	CCONJ
ejpam-3758	130	8	u	u	NOUN
ejpam-3758	130	9	is	be	AUX
ejpam-3758	130	10	µ3open	µ3open	ADJ
ejpam-3758	130	11	in	in	ADP
ejpam-3758	130	12	x	x	NOUN
ejpam-3758	130	13	”	"	PUNCT
ejpam-3758	130	14	becomes	become	VERB
ejpam-3758	130	15	“	"	PUNCT
ejpam-3758	130	16	bcl(a	bcl(a	PROPN
ejpam-3758	130	17	)	)	PUNCT
ejpam-3758	130	18	⊆	⊆	NUM
ejpam-3758	130	19	u	u	NOUN
ejpam-3758	130	20	whenever	whenever	SCONJ
ejpam-3758	130	21	a	a	DET
ejpam-3758	130	22	⊆	⊆	NUM
ejpam-3758	130	23	u	u	NOUN
ejpam-3758	130	24	and	and	CCONJ
ejpam-3758	130	25	u	u	NOUN
ejpam-3758	130	26	is	be	AUX
ejpam-3758	130	27	semi	semi	ADJ
ejpam-3758	130	28	-	-	ADJ
ejpam-3758	130	29	open	open	ADJ
ejpam-3758	130	30	in	in	ADP
ejpam-3758	130	31	x	x	NOUN
ejpam-3758	130	32	”	"	PUNCT
ejpam-3758	130	33	.	.	PUNCT
ejpam-3758	131	1	ix	ix	INTJ
ejpam-3758	131	2	.	.	PUNCT
ejpam-3758	132	1	weakly	weakly	ADV
ejpam-3758	132	2	closed	closed	ADJ
ejpam-3758	132	3	(	(	PUNCT
ejpam-3758	132	4	or	or	CCONJ
ejpam-3758	132	5	briefly	briefly	ADV
ejpam-3758	132	6	w	w	NOUN
ejpam-3758	132	7	-	-	PUNCT
ejpam-3758	132	8	closed	closed	ADJ
ejpam-3758	132	9	)	)	PUNCT
ejpam-3758	132	10	set	set	VERB
ejpam-3758	132	11	if	if	SCONJ
ejpam-3758	132	12	µ1	µ1	PROPN
ejpam-3758	132	13	is	be	AUX
ejpam-3758	132	14	a	a	DET
ejpam-3758	132	15	topology	topology	NOUN
ejpam-3758	132	16	in	in	ADP
ejpam-3758	132	17	x	x	X
ejpam-3758	132	18	,	,	PUNCT
ejpam-3758	132	19	µ2	µ2	PROPN
ejpam-3758	132	20	is	be	AUX
ejpam-3758	132	21	the	the	DET
ejpam-3758	132	22	discrete	discrete	ADJ
ejpam-3758	132	23	topology	topology	NOUN
ejpam-3758	132	24	in	in	ADP
ejpam-3758	132	25	x	x	NOUN
ejpam-3758	132	26	,	,	PUNCT
ejpam-3758	132	27	and	and	CCONJ
ejpam-3758	132	28	µ3	µ3	NOUN
ejpam-3758	132	29	=	=	SYM
ejpam-3758	132	30	so(x	so(x	X
ejpam-3758	132	31	)	)	PUNCT
ejpam-3758	132	32	where	where	SCONJ
ejpam-3758	132	33	so(x	so(x	NOUN
ejpam-3758	132	34	)	)	PUNCT
ejpam-3758	132	35	is	be	AUX
ejpam-3758	132	36	the	the	DET
ejpam-3758	132	37	collection	collection	NOUN
ejpam-3758	132	38	of	of	ADP
ejpam-3758	132	39	semi	semi	ADJ
ejpam-3758	132	40	-	-	ADJ
ejpam-3758	132	41	open	open	ADJ
ejpam-3758	132	42	sets	set	NOUN
ejpam-3758	132	43	in	in	ADP
ejpam-3758	132	44	x	x	NOUN
ejpam-3758	132	45	,	,	PUNCT
ejpam-3758	132	46	then	then	ADV
ejpam-3758	132	47	a	a	DET
ejpam-3758	132	48	(	(	PUNCT
ejpam-3758	132	49	µ1	µ1	PROPN
ejpam-3758	132	50	,	,	PUNCT
ejpam-3758	132	51	µ2	µ2	PROPN
ejpam-3758	132	52	,	,	PUNCT
ejpam-3758	132	53	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	132	54	generalized	generalize	VERB
ejpam-3758	132	55	closed	close	VERB
ejpam-3758	132	56	set	set	NOUN
ejpam-3758	132	57	is	be	AUX
ejpam-3758	132	58	just	just	ADV
ejpam-3758	132	59	the	the	DET
ejpam-3758	132	60	weakly	weakly	ADJ
ejpam-3758	132	61	closed	closed	ADJ
ejpam-3758	132	62	set	set	NOUN
ejpam-3758	132	63	since	since	SCONJ
ejpam-3758	132	64	the	the	DET
ejpam-3758	132	65	condition	condition	NOUN
ejpam-3758	132	66	“	"	PUNCT
ejpam-3758	132	67	clµ1	clµ1	NOUN
ejpam-3758	132	68	(	(	PUNCT
ejpam-3758	132	69	intµ2	intµ2	NOUN
ejpam-3758	132	70	(	(	PUNCT
ejpam-3758	132	71	a	a	NOUN
ejpam-3758	132	72	)	)	PUNCT
ejpam-3758	132	73	)	)	PUNCT
ejpam-3758	133	1	⊆	⊆	X
ejpam-3758	133	2	u	u	NOUN
ejpam-3758	133	3	whenever	whenever	SCONJ
ejpam-3758	133	4	a	a	DET
ejpam-3758	133	5	⊆	⊆	NUM
ejpam-3758	133	6	u	u	NOUN
ejpam-3758	133	7	and	and	CCONJ
ejpam-3758	133	8	u	u	NOUN
ejpam-3758	133	9	is	be	AUX
ejpam-3758	133	10	µ3	µ3	NOUN
ejpam-3758	133	11	-	-	PUNCT
ejpam-3758	133	12	open	open	ADJ
ejpam-3758	133	13	in	in	ADP
ejpam-3758	133	14	x	x	NOUN
ejpam-3758	133	15	”	"	PUNCT
ejpam-3758	133	16	becomes	become	VERB
ejpam-3758	133	17	“	"	PUNCT
ejpam-3758	133	18	cl(a	cl(a	NUM
ejpam-3758	133	19	)	)	PUNCT
ejpam-3758	133	20	⊆	⊆	NUM
ejpam-3758	133	21	u	u	NOUN
ejpam-3758	133	22	whenever	whenever	SCONJ
ejpam-3758	133	23	a	a	DET
ejpam-3758	133	24	⊆	⊆	NUM
ejpam-3758	133	25	u	u	NOUN
ejpam-3758	133	26	and	and	CCONJ
ejpam-3758	133	27	u	u	NOUN
ejpam-3758	133	28	is	be	AUX
ejpam-3758	133	29	semi	semi	ADJ
ejpam-3758	133	30	-	-	ADJ
ejpam-3758	133	31	open	open	ADJ
ejpam-3758	133	32	in	in	ADP
ejpam-3758	133	33	x	x	NOUN
ejpam-3758	133	34	”	"	PUNCT
ejpam-3758	133	35	.	.	PUNCT
ejpam-3758	134	1	x.	x.	PROPN
ejpam-3758	134	2	generalized	generalize	VERB
ejpam-3758	134	3	semi	semi	ADV
ejpam-3758	134	4	-	-	ADJ
ejpam-3758	134	5	preclosed	preclosed	ADJ
ejpam-3758	134	6	(	(	PUNCT
ejpam-3758	134	7	or	or	CCONJ
ejpam-3758	134	8	briefly	briefly	ADV
ejpam-3758	134	9	gsp	gsp	VERB
ejpam-3758	134	10	-	-	PUNCT
ejpam-3758	134	11	closed	closed	ADJ
ejpam-3758	134	12	)	)	PUNCT
ejpam-3758	134	13	set	set	VERB
ejpam-3758	134	14	if	if	SCONJ
ejpam-3758	134	15	µ1	µ1	PROPN
ejpam-3758	134	16	=	=	SYM
ejpam-3758	134	17	spo(x	spo(x	PROPN
ejpam-3758	134	18	)	)	PUNCT
ejpam-3758	134	19	where	where	SCONJ
ejpam-3758	134	20	spo(x	spo(x	X
ejpam-3758	134	21	)	)	PUNCT
ejpam-3758	134	22	is	be	AUX
ejpam-3758	134	23	the	the	DET
ejpam-3758	134	24	collection	collection	NOUN
ejpam-3758	134	25	of	of	ADP
ejpam-3758	134	26	semi	semi	ADJ
ejpam-3758	134	27	-	-	ADJ
ejpam-3758	134	28	preopen	preopen	ADJ
ejpam-3758	134	29	sets	set	NOUN
ejpam-3758	134	30	in	in	ADP
ejpam-3758	134	31	x	x	NOUN
ejpam-3758	134	32	,	,	PUNCT
ejpam-3758	134	33	µ2	µ2	PROPN
ejpam-3758	134	34	is	be	AUX
ejpam-3758	134	35	the	the	DET
ejpam-3758	134	36	discrete	discrete	ADJ
ejpam-3758	134	37	topology	topology	NOUN
ejpam-3758	134	38	in	in	ADP
ejpam-3758	134	39	x	x	NOUN
ejpam-3758	134	40	,	,	PUNCT
ejpam-3758	134	41	then	then	ADV
ejpam-3758	134	42	a	a	DET
ejpam-3758	134	43	(	(	PUNCT
ejpam-3758	134	44	µ1	µ1	PROPN
ejpam-3758	134	45	,	,	PUNCT
ejpam-3758	134	46	µ2	µ2	PROPN
ejpam-3758	134	47	,	,	PUNCT
ejpam-3758	134	48	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	134	49	generalized	generalize	VERB
ejpam-3758	134	50	closed	close	VERB
ejpam-3758	134	51	set	set	NOUN
ejpam-3758	134	52	is	be	AUX
ejpam-3758	134	53	just	just	ADV
ejpam-3758	134	54	the	the	DET
ejpam-3758	134	55	generalized	generalized	ADJ
ejpam-3758	134	56	semi	semi	ADJ
ejpam-3758	134	57	-	-	ADJ
ejpam-3758	134	58	preclosed	preclosed	ADJ
ejpam-3758	134	59	set	set	NOUN
ejpam-3758	134	60	since	since	SCONJ
ejpam-3758	134	61	the	the	DET
ejpam-3758	134	62	condition	condition	NOUN
ejpam-3758	134	63	“	"	PUNCT
ejpam-3758	134	64	clµ1	clµ1	NOUN
ejpam-3758	134	65	(	(	PUNCT
ejpam-3758	134	66	intµ2	intµ2	NOUN
ejpam-3758	134	67	(	(	PUNCT
ejpam-3758	134	68	a	a	NOUN
ejpam-3758	134	69	)	)	PUNCT
ejpam-3758	134	70	)	)	PUNCT
ejpam-3758	135	1	⊆	⊆	X
ejpam-3758	135	2	u	u	NOUN
ejpam-3758	135	3	whenever	whenever	SCONJ
ejpam-3758	135	4	a	a	DET
ejpam-3758	135	5	⊆	⊆	NUM
ejpam-3758	135	6	u	u	NOUN
ejpam-3758	135	7	and	and	CCONJ
ejpam-3758	135	8	u	u	NOUN
ejpam-3758	135	9	is	be	AUX
ejpam-3758	135	10	µ3	µ3	NOUN
ejpam-3758	135	11	-	-	PUNCT
ejpam-3758	135	12	open	open	ADJ
ejpam-3758	135	13	in	in	ADP
ejpam-3758	135	14	x	x	NOUN
ejpam-3758	135	15	”	"	PUNCT
ejpam-3758	135	16	becomes	become	VERB
ejpam-3758	135	17	“	"	PUNCT
ejpam-3758	135	18	spcl(a	spcl(a	NUM
ejpam-3758	135	19	)	)	PUNCT
ejpam-3758	135	20	⊆	⊆	NUM
ejpam-3758	135	21	u	u	NOUN
ejpam-3758	135	22	whenever	whenever	SCONJ
ejpam-3758	135	23	a	a	DET
ejpam-3758	135	24	⊆	⊆	NUM
ejpam-3758	135	25	u	u	NOUN
ejpam-3758	135	26	and	and	CCONJ
ejpam-3758	135	27	u	u	NOUN
ejpam-3758	135	28	is	be	AUX
ejpam-3758	135	29	open	open	ADJ
ejpam-3758	135	30	in	in	ADP
ejpam-3758	135	31	x	x	NOUN
ejpam-3758	135	32	”	"	PUNCT
ejpam-3758	135	33	.	.	PUNCT
ejpam-3758	136	1	xi	xi	PROPN
ejpam-3758	136	2	.	.	PUNCT
ejpam-3758	137	1	generalized	generalize	VERB
ejpam-3758	137	2	α	α	NOUN
ejpam-3758	137	3	closed	close	VERB
ejpam-3758	137	4	(	(	PUNCT
ejpam-3758	137	5	or	or	CCONJ
ejpam-3758	137	6	briefly	briefly	ADV
ejpam-3758	137	7	gα	gα	NOUN
ejpam-3758	137	8	-	-	PUNCT
ejpam-3758	137	9	closed	closed	ADJ
ejpam-3758	137	10	)	)	PUNCT
ejpam-3758	137	11	set	set	VERB
ejpam-3758	137	12	if	if	SCONJ
ejpam-3758	137	13	µ1	µ1	PROPN
ejpam-3758	137	14	=	=	SYM
ejpam-3758	137	15	µ3	µ3	NOUN
ejpam-3758	137	16	=	=	PUNCT
ejpam-3758	137	17	ao(x	ao(x	X
ejpam-3758	137	18	)	)	PUNCT
ejpam-3758	137	19	where	where	SCONJ
ejpam-3758	137	20	ao(x	ao(x	PUNCT
ejpam-3758	137	21	)	)	PUNCT
ejpam-3758	137	22	is	be	AUX
ejpam-3758	137	23	the	the	DET
ejpam-3758	137	24	collection	collection	NOUN
ejpam-3758	137	25	of	of	ADP
ejpam-3758	137	26	α	α	NOUN
ejpam-3758	137	27	-	-	ADJ
ejpam-3758	137	28	open	open	ADJ
ejpam-3758	137	29	sets	set	NOUN
ejpam-3758	137	30	in	in	ADP
ejpam-3758	137	31	x	x	NOUN
ejpam-3758	137	32	,	,	PUNCT
ejpam-3758	137	33	and	and	CCONJ
ejpam-3758	137	34	µ2	µ2	PROPN
ejpam-3758	137	35	is	be	AUX
ejpam-3758	137	36	a	a	DET
ejpam-3758	137	37	topology	topology	NOUN
ejpam-3758	137	38	in	in	ADP
ejpam-3758	137	39	x	x	NOUN
ejpam-3758	137	40	,	,	PUNCT
ejpam-3758	137	41	then	then	ADV
ejpam-3758	137	42	a	a	DET
ejpam-3758	137	43	(	(	PUNCT
ejpam-3758	137	44	µ1	µ1	PROPN
ejpam-3758	137	45	,	,	PUNCT
ejpam-3758	137	46	µ2	µ2	PROPN
ejpam-3758	137	47	,	,	PUNCT
ejpam-3758	137	48	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	137	49	generalized	generalize	VERB
ejpam-3758	137	50	closed	close	VERB
ejpam-3758	137	51	set	set	NOUN
ejpam-3758	137	52	is	be	AUX
ejpam-3758	137	53	just	just	ADV
ejpam-3758	137	54	the	the	DET
ejpam-3758	137	55	generalized	generalized	ADJ
ejpam-3758	137	56	gα	gα	NOUN
ejpam-3758	137	57	-	-	PUNCT
ejpam-3758	137	58	closed	close	VERB
ejpam-3758	137	59	set	set	NOUN
ejpam-3758	137	60	since	since	SCONJ
ejpam-3758	137	61	the	the	DET
ejpam-3758	137	62	condition	condition	NOUN
ejpam-3758	137	63	“	"	PUNCT
ejpam-3758	137	64	clµ1	clµ1	NOUN
ejpam-3758	137	65	(	(	PUNCT
ejpam-3758	137	66	intµ2	intµ2	NOUN
ejpam-3758	137	67	(	(	PUNCT
ejpam-3758	137	68	a	a	NOUN
ejpam-3758	137	69	)	)	PUNCT
ejpam-3758	137	70	)	)	PUNCT
ejpam-3758	138	1	⊆	⊆	X
ejpam-3758	138	2	u	u	NOUN
ejpam-3758	138	3	whenever	whenever	SCONJ
ejpam-3758	138	4	a	a	DET
ejpam-3758	138	5	⊆	⊆	NUM
ejpam-3758	138	6	u	u	NOUN
ejpam-3758	138	7	and	and	CCONJ
ejpam-3758	138	8	u	u	NOUN
ejpam-3758	138	9	is	be	AUX
ejpam-3758	138	10	µ3	µ3	NOUN
ejpam-3758	138	11	-	-	PUNCT
ejpam-3758	138	12	open	open	ADJ
ejpam-3758	138	13	in	in	ADP
ejpam-3758	138	14	x	x	NOUN
ejpam-3758	138	15	”	"	PUNCT
ejpam-3758	138	16	becomes	become	VERB
ejpam-3758	138	17	“	"	PUNCT
ejpam-3758	138	18	αcl(int(a	αcl(int(a	PROPN
ejpam-3758	138	19	)	)	PUNCT
ejpam-3758	138	20	)	)	PUNCT
ejpam-3758	139	1	⊆	⊆	NUM
ejpam-3758	139	2	u	u	NOUN
ejpam-3758	139	3	whenever	whenever	SCONJ
ejpam-3758	139	4	a	a	DET
ejpam-3758	139	5	⊆	⊆	NUM
ejpam-3758	139	6	u	u	NOUN
ejpam-3758	139	7	and	and	CCONJ
ejpam-3758	139	8	u	u	NOUN
ejpam-3758	139	9	is	be	AUX
ejpam-3758	139	10	α	α	NOUN
ejpam-3758	139	11	-	-	NOUN
ejpam-3758	139	12	open	open	ADJ
ejpam-3758	139	13	in	in	ADP
ejpam-3758	139	14	x	x	NOUN
ejpam-3758	139	15	”	"	PUNCT
ejpam-3758	139	16	.	.	PUNCT
ejpam-3758	140	1	xii	xii	NOUN
ejpam-3758	140	2	.	.	PUNCT
ejpam-3758	141	1	α	α	X
ejpam-3758	141	2	-	-	PUNCT
ejpam-3758	141	3	generalized	generalize	VERB
ejpam-3758	141	4	closed	close	VERB
ejpam-3758	141	5	(	(	PUNCT
ejpam-3758	141	6	or	or	CCONJ
ejpam-3758	141	7	briefly	briefly	ADV
ejpam-3758	141	8	αg	αg	NOUN
ejpam-3758	141	9	-	-	PUNCT
ejpam-3758	141	10	closed	closed	ADJ
ejpam-3758	141	11	)	)	PUNCT
ejpam-3758	141	12	set	set	VERB
ejpam-3758	141	13	if	if	SCONJ
ejpam-3758	141	14	µ1	µ1	PROPN
ejpam-3758	141	15	=	=	SYM
ejpam-3758	141	16	ao(x	ao(x	X
ejpam-3758	141	17	)	)	PUNCT
ejpam-3758	141	18	where	where	SCONJ
ejpam-3758	141	19	ao(x	ao(x	PUNCT
ejpam-3758	141	20	)	)	PUNCT
ejpam-3758	141	21	is	be	AUX
ejpam-3758	141	22	the	the	DET
ejpam-3758	141	23	collection	collection	NOUN
ejpam-3758	141	24	of	of	ADP
ejpam-3758	141	25	α	α	NOUN
ejpam-3758	141	26	-	-	ADJ
ejpam-3758	141	27	open	open	ADJ
ejpam-3758	141	28	sets	set	NOUN
ejpam-3758	141	29	in	in	ADP
ejpam-3758	141	30	x	x	NOUN
ejpam-3758	141	31	,	,	PUNCT
ejpam-3758	141	32	µ2	µ2	PROPN
ejpam-3758	141	33	is	be	AUX
ejpam-3758	141	34	the	the	DET
ejpam-3758	141	35	discrete	discrete	ADJ
ejpam-3758	141	36	topology	topology	NOUN
ejpam-3758	141	37	in	in	ADP
ejpam-3758	141	38	x	x	NOUN
ejpam-3758	141	39	,	,	PUNCT
ejpam-3758	141	40	and	and	CCONJ
ejpam-3758	141	41	µ3	µ3	PROPN
ejpam-3758	141	42	is	be	AUX
ejpam-3758	141	43	a	a	DET
ejpam-3758	141	44	topology	topology	NOUN
ejpam-3758	141	45	in	in	ADP
ejpam-3758	141	46	x	x	NOUN
ejpam-3758	141	47	,	,	PUNCT
ejpam-3758	141	48	then	then	ADV
ejpam-3758	141	49	a	a	DET
ejpam-3758	141	50	(	(	PUNCT
ejpam-3758	141	51	µ1	µ1	PROPN
ejpam-3758	141	52	,	,	PUNCT
ejpam-3758	141	53	µ2	µ2	PROPN
ejpam-3758	141	54	,	,	PUNCT
ejpam-3758	141	55	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	141	56	generalized	generalize	VERB
ejpam-3758	141	57	closed	close	VERB
ejpam-3758	141	58	set	set	NOUN
ejpam-3758	141	59	is	be	AUX
ejpam-3758	141	60	just	just	ADV
ejpam-3758	142	1	the	the	DET
ejpam-3758	142	2	generalized	generalized	ADJ
ejpam-3758	142	3	α	α	PROPN
ejpam-3758	142	4	generalized	generalize	VERB
ejpam-3758	142	5	closed	close	VERB
ejpam-3758	142	6	set	set	VERB
ejpam-3758	142	7	since	since	SCONJ
ejpam-3758	142	8	the	the	DET
ejpam-3758	142	9	condition	condition	NOUN
ejpam-3758	142	10	“	"	PUNCT
ejpam-3758	142	11	clµ1	clµ1	NOUN
ejpam-3758	142	12	(	(	PUNCT
ejpam-3758	142	13	intµ2	intµ2	NOUN
ejpam-3758	142	14	(	(	PUNCT
ejpam-3758	142	15	a	a	NOUN
ejpam-3758	142	16	)	)	PUNCT
ejpam-3758	142	17	)	)	PUNCT
ejpam-3758	143	1	⊆	⊆	X
ejpam-3758	143	2	u	u	NOUN
ejpam-3758	143	3	whenever	whenever	SCONJ
ejpam-3758	143	4	a	a	DET
ejpam-3758	143	5	⊆	⊆	NUM
ejpam-3758	143	6	u	u	NOUN
ejpam-3758	143	7	and	and	CCONJ
ejpam-3758	143	8	u	u	NOUN
ejpam-3758	143	9	is	be	AUX
ejpam-3758	143	10	µ3	µ3	NOUN
ejpam-3758	143	11	-	-	PUNCT
ejpam-3758	143	12	open	open	ADJ
ejpam-3758	143	13	in	in	ADP
ejpam-3758	143	14	x	x	NOUN
ejpam-3758	143	15	”	"	PUNCT
ejpam-3758	143	16	becomes	become	VERB
ejpam-3758	143	17	“	"	PUNCT
ejpam-3758	143	18	αcl(int(a	αcl(int(a	PROPN
ejpam-3758	143	19	)	)	PUNCT
ejpam-3758	143	20	)	)	PUNCT
ejpam-3758	144	1	⊆	⊆	NUM
ejpam-3758	144	2	u	u	NOUN
ejpam-3758	144	3	whenever	whenever	SCONJ
ejpam-3758	144	4	a	a	DET
ejpam-3758	144	5	⊆	⊆	NUM
ejpam-3758	144	6	u	u	NOUN
ejpam-3758	144	7	and	and	CCONJ
ejpam-3758	144	8	u	u	NOUN
ejpam-3758	144	9	is	be	AUX
ejpam-3758	144	10	open	open	ADJ
ejpam-3758	144	11	in	in	ADP
ejpam-3758	144	12	x	x	NOUN
ejpam-3758	144	13	”	"	PUNCT
ejpam-3758	144	14	.	.	PUNCT
ejpam-3758	145	1	xiii	xiii	PROPN
ejpam-3758	145	2	.	.	PUNCT
ejpam-3758	146	1	weakly	weakly	ADJ
ejpam-3758	146	2	generalized	generalize	VERB
ejpam-3758	146	3	closed	close	VERB
ejpam-3758	146	4	(	(	PUNCT
ejpam-3758	146	5	or	or	CCONJ
ejpam-3758	146	6	briefly	briefly	ADV
ejpam-3758	146	7	wg	wg	NOUN
ejpam-3758	146	8	-	-	PUNCT
ejpam-3758	146	9	closed	closed	ADJ
ejpam-3758	146	10	)	)	PUNCT
ejpam-3758	146	11	set	set	VERB
ejpam-3758	146	12	if	if	SCONJ
ejpam-3758	146	13	µ1	µ1	PROPN
ejpam-3758	146	14	=	=	SYM
ejpam-3758	146	15	µ2	µ2	PROPN
ejpam-3758	146	16	=	=	PUNCT
ejpam-3758	146	17	µ3	µ3	PROPN
ejpam-3758	146	18	is	be	AUX
ejpam-3758	146	19	a	a	DET
ejpam-3758	146	20	topology	topology	NOUN
ejpam-3758	146	21	in	in	ADP
ejpam-3758	146	22	x	x	NOUN
ejpam-3758	146	23	,	,	PUNCT
ejpam-3758	146	24	then	then	ADV
ejpam-3758	146	25	a	a	DET
ejpam-3758	146	26	(	(	PUNCT
ejpam-3758	146	27	µ1	µ1	PROPN
ejpam-3758	146	28	,	,	PUNCT
ejpam-3758	146	29	µ2	µ2	PROPN
ejpam-3758	146	30	,	,	PUNCT
ejpam-3758	146	31	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	146	32	generalized	generalize	VERB
ejpam-3758	146	33	closed	close	VERB
ejpam-3758	146	34	set	set	NOUN
ejpam-3758	146	35	is	be	AUX
ejpam-3758	146	36	just	just	ADV
ejpam-3758	146	37	the	the	DET
ejpam-3758	146	38	weakly	weakly	ADJ
ejpam-3758	146	39	generalized	generalized	ADJ
ejpam-3758	146	40	closed	close	VERB
ejpam-3758	146	41	set	set	NOUN
ejpam-3758	146	42	since	since	SCONJ
ejpam-3758	146	43	the	the	DET
ejpam-3758	146	44	condition	condition	NOUN
ejpam-3758	146	45	“	"	PUNCT
ejpam-3758	146	46	clµ1	clµ1	NOUN
ejpam-3758	146	47	(	(	PUNCT
ejpam-3758	146	48	intµ2	intµ2	NOUN
ejpam-3758	146	49	(	(	PUNCT
ejpam-3758	146	50	a	a	NOUN
ejpam-3758	146	51	)	)	PUNCT
ejpam-3758	146	52	)	)	PUNCT
ejpam-3758	146	53	⊆	⊆	NUM
ejpam-3758	146	54	u	u	PROPN
ejpam-3758	146	55	b.	b.	PROPN
ejpam-3758	146	56	agua	agua	PROPN
ejpam-3758	146	57	,	,	PUNCT
ejpam-3758	146	58	r.	r.	PROPN
ejpam-3758	146	59	paluga	paluga	PROPN
ejpam-3758	146	60	/	/	SYM
ejpam-3758	146	61	eur	eur	PROPN
ejpam-3758	146	62	.	.	PUNCT
ejpam-3758	147	1	j.	j.	PROPN
ejpam-3758	147	2	pure	pure	PROPN
ejpam-3758	147	3	appl	appl	PROPN
ejpam-3758	147	4	.	.	PROPN
ejpam-3758	147	5	math	math	PROPN
ejpam-3758	147	6	,	,	PUNCT
ejpam-3758	147	7	13	13	NUM
ejpam-3758	147	8	(	(	PUNCT
ejpam-3758	147	9	4	4	NUM
ejpam-3758	147	10	)	)	PUNCT
ejpam-3758	147	11	(	(	PUNCT
ejpam-3758	147	12	2020	2020	NUM
ejpam-3758	147	13	)	)	PUNCT
ejpam-3758	147	14	,	,	PUNCT
ejpam-3758	147	15	977	977	NUM
ejpam-3758	147	16	-	-	SYM
ejpam-3758	147	17	986	986	NUM
ejpam-3758	147	18	983	983	NUM
ejpam-3758	147	19	whenever	whenever	SCONJ
ejpam-3758	147	20	a	a	DET
ejpam-3758	147	21	⊆	⊆	NUM
ejpam-3758	147	22	u	u	NOUN
ejpam-3758	147	23	and	and	CCONJ
ejpam-3758	147	24	u	u	NOUN
ejpam-3758	147	25	is	be	AUX
ejpam-3758	147	26	µ3	µ3	NOUN
ejpam-3758	147	27	-	-	PUNCT
ejpam-3758	147	28	open	open	ADJ
ejpam-3758	147	29	in	in	ADP
ejpam-3758	147	30	x	x	NOUN
ejpam-3758	147	31	”	"	PUNCT
ejpam-3758	147	32	becomes	become	VERB
ejpam-3758	147	33	“	"	PUNCT
ejpam-3758	147	34	cl(int(a	cl(int(a	NOUN
ejpam-3758	147	35	)	)	PUNCT
ejpam-3758	147	36	)	)	PUNCT
ejpam-3758	148	1	⊆	⊆	X
ejpam-3758	148	2	u	u	NOUN
ejpam-3758	148	3	whenever	whenever	SCONJ
ejpam-3758	148	4	a	a	DET
ejpam-3758	148	5	⊆	⊆	NUM
ejpam-3758	148	6	u	u	NOUN
ejpam-3758	148	7	and	and	CCONJ
ejpam-3758	148	8	u	u	NOUN
ejpam-3758	148	9	is	be	AUX
ejpam-3758	148	10	open	open	ADJ
ejpam-3758	148	11	in	in	ADP
ejpam-3758	148	12	x	x	NOUN
ejpam-3758	148	13	”	"	PUNCT
ejpam-3758	148	14	.	.	PUNCT
ejpam-3758	149	1	xiv	xiv	PROPN
ejpam-3758	149	2	.	.	PUNCT
ejpam-3758	150	1	mildly	mildly	ADV
ejpam-3758	150	2	generalized	generalize	VERB
ejpam-3758	150	3	closed	close	VERB
ejpam-3758	150	4	(	(	PUNCT
ejpam-3758	150	5	or	or	CCONJ
ejpam-3758	150	6	briefly	briefly	ADV
ejpam-3758	150	7	mildly	mildly	ADV
ejpam-3758	150	8	g	g	NOUN
ejpam-3758	150	9	-	-	PUNCT
ejpam-3758	150	10	closed	closed	ADJ
ejpam-3758	150	11	)	)	PUNCT
ejpam-3758	150	12	set	set	VERB
ejpam-3758	150	13	if	if	SCONJ
ejpam-3758	150	14	µ1	µ1	PROPN
ejpam-3758	150	15	=	=	PUNCT
ejpam-3758	150	16	µ2	µ2	PROPN
ejpam-3758	150	17	is	be	AUX
ejpam-3758	150	18	a	a	DET
ejpam-3758	150	19	topology	topology	NOUN
ejpam-3758	150	20	in	in	ADP
ejpam-3758	150	21	x	x	NOUN
ejpam-3758	150	22	,	,	PUNCT
ejpam-3758	150	23	and	and	CCONJ
ejpam-3758	150	24	µ3	µ3	NOUN
ejpam-3758	150	25	=	=	SYM
ejpam-3758	150	26	g(x	g(x	NOUN
ejpam-3758	150	27	)	)	PUNCT
ejpam-3758	150	28	where	where	SCONJ
ejpam-3758	150	29	g(x	g(x	NOUN
ejpam-3758	150	30	)	)	PUNCT
ejpam-3758	150	31	is	be	AUX
ejpam-3758	150	32	the	the	DET
ejpam-3758	150	33	collection	collection	NOUN
ejpam-3758	150	34	of	of	ADP
ejpam-3758	150	35	g	g	NOUN
ejpam-3758	150	36	-	-	PUNCT
ejpam-3758	150	37	open	open	ADJ
ejpam-3758	150	38	sets	set	NOUN
ejpam-3758	150	39	in	in	ADP
ejpam-3758	150	40	x	x	NOUN
ejpam-3758	150	41	,	,	PUNCT
ejpam-3758	150	42	then	then	ADV
ejpam-3758	150	43	a	a	DET
ejpam-3758	150	44	(	(	PUNCT
ejpam-3758	150	45	µ1	µ1	PROPN
ejpam-3758	150	46	,	,	PUNCT
ejpam-3758	150	47	µ2	µ2	PROPN
ejpam-3758	150	48	,	,	PUNCT
ejpam-3758	150	49	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	150	50	generalized	generalize	VERB
ejpam-3758	150	51	closed	close	VERB
ejpam-3758	150	52	set	set	NOUN
ejpam-3758	150	53	is	be	AUX
ejpam-3758	150	54	just	just	ADV
ejpam-3758	150	55	the	the	DET
ejpam-3758	150	56	weakly	weakly	ADJ
ejpam-3758	150	57	closed	closed	ADJ
ejpam-3758	150	58	set	set	NOUN
ejpam-3758	150	59	since	since	SCONJ
ejpam-3758	150	60	the	the	DET
ejpam-3758	150	61	condition	condition	NOUN
ejpam-3758	150	62	“	"	PUNCT
ejpam-3758	150	63	clµ1	clµ1	NOUN
ejpam-3758	150	64	(	(	PUNCT
ejpam-3758	150	65	intµ2	intµ2	NOUN
ejpam-3758	150	66	(	(	PUNCT
ejpam-3758	150	67	a	a	NOUN
ejpam-3758	150	68	)	)	PUNCT
ejpam-3758	150	69	)	)	PUNCT
ejpam-3758	151	1	⊆	⊆	X
ejpam-3758	151	2	u	u	NOUN
ejpam-3758	151	3	whenever	whenever	SCONJ
ejpam-3758	151	4	a	a	DET
ejpam-3758	151	5	⊆	⊆	NUM
ejpam-3758	151	6	u	u	NOUN
ejpam-3758	151	7	and	and	CCONJ
ejpam-3758	151	8	u	u	NOUN
ejpam-3758	151	9	is	be	AUX
ejpam-3758	151	10	µ3	µ3	NOUN
ejpam-3758	151	11	-	-	PUNCT
ejpam-3758	151	12	open	open	ADJ
ejpam-3758	151	13	in	in	ADP
ejpam-3758	151	14	x	x	NOUN
ejpam-3758	151	15	”	"	PUNCT
ejpam-3758	151	16	becomes	become	VERB
ejpam-3758	151	17	“	"	PUNCT
ejpam-3758	151	18	cl(int(a	cl(int(a	NOUN
ejpam-3758	151	19	)	)	PUNCT
ejpam-3758	151	20	)	)	PUNCT
ejpam-3758	152	1	⊆	⊆	X
ejpam-3758	152	2	u	u	NOUN
ejpam-3758	152	3	whenever	whenever	SCONJ
ejpam-3758	152	4	a	a	DET
ejpam-3758	152	5	⊆	⊆	NUM
ejpam-3758	152	6	u	u	NOUN
ejpam-3758	152	7	and	and	CCONJ
ejpam-3758	152	8	u	u	NOUN
ejpam-3758	152	9	is	be	AUX
ejpam-3758	152	10	g	g	NOUN
ejpam-3758	152	11	-	-	PUNCT
ejpam-3758	152	12	open	open	ADJ
ejpam-3758	152	13	in	in	ADP
ejpam-3758	152	14	x	x	NOUN
ejpam-3758	152	15	”	"	PUNCT
ejpam-3758	152	16	.	.	PUNCT
ejpam-3758	153	1	xv	xv	PROPN
ejpam-3758	153	2	.	.	PUNCT
ejpam-3758	153	3	semi	semi	ADJ
ejpam-3758	153	4	-	-	ADJ
ejpam-3758	153	5	weakly	weakly	ADJ
ejpam-3758	153	6	generalized	generalized	ADJ
ejpam-3758	153	7	closed	close	VERB
ejpam-3758	153	8	(	(	PUNCT
ejpam-3758	153	9	or	or	CCONJ
ejpam-3758	153	10	briefly	briefly	ADV
ejpam-3758	153	11	swg	swg	NOUN
ejpam-3758	153	12	-	-	PUNCT
ejpam-3758	153	13	closed	closed	ADJ
ejpam-3758	153	14	)	)	PUNCT
ejpam-3758	153	15	set	set	VERB
ejpam-3758	153	16	if	if	SCONJ
ejpam-3758	153	17	µ1	µ1	PROPN
ejpam-3758	153	18	=	=	SYM
ejpam-3758	153	19	µ2	µ2	PROPN
ejpam-3758	153	20	in	in	ADP
ejpam-3758	153	21	x	x	NOUN
ejpam-3758	153	22	,	,	PUNCT
ejpam-3758	153	23	and	and	CCONJ
ejpam-3758	153	24	µ3	µ3	NOUN
ejpam-3758	153	25	=	=	SYM
ejpam-3758	153	26	so(x	so(x	X
ejpam-3758	153	27	)	)	PUNCT
ejpam-3758	153	28	where	where	SCONJ
ejpam-3758	153	29	so(x	so(x	NOUN
ejpam-3758	153	30	)	)	PUNCT
ejpam-3758	153	31	is	be	AUX
ejpam-3758	153	32	the	the	DET
ejpam-3758	153	33	collection	collection	NOUN
ejpam-3758	153	34	of	of	ADP
ejpam-3758	153	35	semi	semi	ADJ
ejpam-3758	153	36	-	-	ADJ
ejpam-3758	153	37	open	open	ADJ
ejpam-3758	153	38	sets	set	NOUN
ejpam-3758	153	39	in	in	ADP
ejpam-3758	153	40	x	x	NOUN
ejpam-3758	153	41	,	,	PUNCT
ejpam-3758	153	42	then	then	ADV
ejpam-3758	153	43	a	a	DET
ejpam-3758	153	44	(	(	PUNCT
ejpam-3758	153	45	µ1	µ1	PROPN
ejpam-3758	153	46	,	,	PUNCT
ejpam-3758	153	47	µ2	µ2	PROPN
ejpam-3758	153	48	,	,	PUNCT
ejpam-3758	153	49	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	153	50	generalized	generalize	VERB
ejpam-3758	153	51	closed	close	VERB
ejpam-3758	153	52	set	set	NOUN
ejpam-3758	153	53	is	be	AUX
ejpam-3758	153	54	just	just	ADV
ejpam-3758	153	55	the	the	DET
ejpam-3758	153	56	weakly	weakly	ADJ
ejpam-3758	153	57	closed	closed	ADJ
ejpam-3758	153	58	set	set	NOUN
ejpam-3758	153	59	since	since	SCONJ
ejpam-3758	153	60	the	the	DET
ejpam-3758	153	61	condition	condition	NOUN
ejpam-3758	153	62	“	"	PUNCT
ejpam-3758	153	63	clµ1	clµ1	NOUN
ejpam-3758	153	64	(	(	PUNCT
ejpam-3758	153	65	intµ2	intµ2	NOUN
ejpam-3758	153	66	(	(	PUNCT
ejpam-3758	153	67	a	a	NOUN
ejpam-3758	153	68	)	)	PUNCT
ejpam-3758	153	69	)	)	PUNCT
ejpam-3758	154	1	⊆	⊆	X
ejpam-3758	154	2	u	u	NOUN
ejpam-3758	154	3	whenever	whenever	SCONJ
ejpam-3758	154	4	a	a	DET
ejpam-3758	154	5	⊆	⊆	NUM
ejpam-3758	154	6	u	u	NOUN
ejpam-3758	154	7	and	and	CCONJ
ejpam-3758	154	8	u	u	NOUN
ejpam-3758	154	9	is	be	AUX
ejpam-3758	154	10	µ3	µ3	NOUN
ejpam-3758	154	11	-	-	PUNCT
ejpam-3758	154	12	open	open	ADJ
ejpam-3758	154	13	in	in	ADP
ejpam-3758	154	14	x	x	NOUN
ejpam-3758	154	15	”	"	PUNCT
ejpam-3758	154	16	becomes	become	VERB
ejpam-3758	154	17	“	"	PUNCT
ejpam-3758	154	18	cl(int(a	cl(int(a	NOUN
ejpam-3758	154	19	)	)	PUNCT
ejpam-3758	154	20	)	)	PUNCT
ejpam-3758	155	1	⊆	⊆	X
ejpam-3758	155	2	u	u	NOUN
ejpam-3758	155	3	whenever	whenever	SCONJ
ejpam-3758	155	4	a	a	DET
ejpam-3758	155	5	⊆	⊆	NUM
ejpam-3758	155	6	u	u	NOUN
ejpam-3758	155	7	and	and	CCONJ
ejpam-3758	155	8	u	u	NOUN
ejpam-3758	155	9	is	be	AUX
ejpam-3758	155	10	semi	semi	ADJ
ejpam-3758	155	11	-	-	ADJ
ejpam-3758	155	12	open	open	ADJ
ejpam-3758	155	13	in	in	ADP
ejpam-3758	155	14	x	x	NOUN
ejpam-3758	155	15	”	"	PUNCT
ejpam-3758	155	16	.	.	PUNCT
ejpam-3758	155	17	theorem	theorem	VERB
ejpam-3758	155	18	7	7	NUM
ejpam-3758	155	19	.	.	PUNCT
ejpam-3758	156	1	let	let	VERB
ejpam-3758	156	2	(	(	PUNCT
ejpam-3758	156	3	x,µ1	x,µ1	NOUN
ejpam-3758	156	4	,	,	PUNCT
ejpam-3758	156	5	µ2	µ2	ADJ
ejpam-3758	156	6	,	,	PUNCT
ejpam-3758	156	7	µ3	µ3	NUM
ejpam-3758	156	8	)	)	PUNCT
ejpam-3758	156	9	be	be	AUX
ejpam-3758	156	10	a	a	DET
ejpam-3758	156	11	trigeneralized	trigeneralize	VERB
ejpam-3758	156	12	space	space	NOUN
ejpam-3758	156	13	and	and	CCONJ
ejpam-3758	156	14	a	a	DET
ejpam-3758	156	15	⊆	⊆	NUM
ejpam-3758	156	16	x.	x.	NOUN
ejpam-3758	156	17	then	then	ADV
ejpam-3758	156	18	,	,	PUNCT
ejpam-3758	156	19	a	a	PRON
ejpam-3758	156	20	is	be	AUX
ejpam-3758	156	21	(	(	PUNCT
ejpam-3758	156	22	µ1	µ1	PROPN
ejpam-3758	156	23	,	,	PUNCT
ejpam-3758	156	24	µ2	µ2	PROPN
ejpam-3758	156	25	,	,	PUNCT
ejpam-3758	156	26	µ3)-weakly	µ3)-weakly	ADV
ejpam-3758	156	27	generalized	generalize	VERB
ejpam-3758	156	28	open	open	ADJ
ejpam-3758	156	29	set	set	NOUN
ejpam-3758	156	30	if	if	SCONJ
ejpam-3758	156	31	and	and	CCONJ
ejpam-3758	156	32	only	only	ADV
ejpam-3758	157	1	if	if	SCONJ
ejpam-3758	157	2	f	f	PROPN
ejpam-3758	157	3	⊆	⊆	NUM
ejpam-3758	157	4	intµ1	intµ1	PROPN
ejpam-3758	158	1	(	(	PUNCT
ejpam-3758	158	2	clµ2	clµ2	PROPN
ejpam-3758	158	3	(	(	PUNCT
ejpam-3758	158	4	a	a	X
ejpam-3758	158	5	)	)	PUNCT
ejpam-3758	158	6	)	)	PUNCT
ejpam-3758	158	7	whenever	whenever	SCONJ
ejpam-3758	158	8	f	f	PROPN
ejpam-3758	158	9	⊆	⊆	PROPN
ejpam-3758	158	10	a	a	PRON
ejpam-3758	158	11	and	and	CCONJ
ejpam-3758	158	12	f	f	PROPN
ejpam-3758	158	13	is	be	AUX
ejpam-3758	158	14	µ3	µ3	NOUN
ejpam-3758	158	15	-	-	PUNCT
ejpam-3758	158	16	closed	close	VERB
ejpam-3758	158	17	in	in	ADP
ejpam-3758	158	18	x.	x.	NOUN
ejpam-3758	158	19	proof	proof	NOUN
ejpam-3758	158	20	.	.	PUNCT
ejpam-3758	159	1	let	let	VERB
ejpam-3758	159	2	a	a	DET
ejpam-3758	159	3	be	be	AUX
ejpam-3758	159	4	(	(	PUNCT
ejpam-3758	159	5	µ1	µ1	PROPN
ejpam-3758	159	6	,	,	PUNCT
ejpam-3758	159	7	µ2	µ2	ADJ
ejpam-3758	159	8	,	,	PUNCT
ejpam-3758	159	9	µ3)-wg	µ3)-wg	VERB
ejpam-3758	159	10	open	open	ADJ
ejpam-3758	159	11	set	set	NOUN
ejpam-3758	159	12	and	and	CCONJ
ejpam-3758	159	13	f	f	PROPN
ejpam-3758	159	14	⊆	⊆	NUM
ejpam-3758	159	15	a	a	DET
ejpam-3758	159	16	such	such	ADJ
ejpam-3758	159	17	that	that	SCONJ
ejpam-3758	159	18	f	f	PROPN
ejpam-3758	159	19	is	be	AUX
ejpam-3758	159	20	µ3	µ3	NOUN
ejpam-3758	159	21	-	-	PUNCT
ejpam-3758	159	22	closed	closed	ADJ
ejpam-3758	159	23	.	.	PUNCT
ejpam-3758	160	1	then	then	ADV
ejpam-3758	160	2	ac	ac	PROPN
ejpam-3758	160	3	is	be	AUX
ejpam-3758	160	4	(	(	PUNCT
ejpam-3758	160	5	µ1	µ1	PROPN
ejpam-3758	160	6	,	,	PUNCT
ejpam-3758	160	7	µ2	µ2	ADJ
ejpam-3758	160	8	,	,	PUNCT
ejpam-3758	160	9	µ3)-wg	µ3)-wg	NOUN
ejpam-3758	160	10	closed	closed	ADJ
ejpam-3758	160	11	,	,	PUNCT
ejpam-3758	160	12	f	f	PROPN
ejpam-3758	160	13	c	c	PROPN
ejpam-3758	160	14	is	be	AUX
ejpam-3758	160	15	µ3	µ3	NOUN
ejpam-3758	160	16	-	-	PUNCT
ejpam-3758	160	17	open	open	ADJ
ejpam-3758	160	18	,	,	PUNCT
ejpam-3758	160	19	and	and	CCONJ
ejpam-3758	160	20	ac	ac	PROPN
ejpam-3758	160	21	⊆	⊆	NUM
ejpam-3758	160	22	f	f	PROPN
ejpam-3758	160	23	c.	c.	NOUN
ejpam-3758	160	24	that	that	PRON
ejpam-3758	160	25	is	be	AUX
ejpam-3758	160	26	f	f	PROPN
ejpam-3758	160	27	⊆	⊆	NUM
ejpam-3758	160	28	[	[	X
ejpam-3758	160	29	clµ1(intµ2)]c	clµ1(intµ2)]c	NOUN
ejpam-3758	160	30	=	=	SYM
ejpam-3758	160	31	intµ1(clµ2(a	intµ1(clµ2(a	NOUN
ejpam-3758	160	32	)	)	PUNCT
ejpam-3758	160	33	)	)	PUNCT
ejpam-3758	160	34	.	.	PUNCT
ejpam-3758	161	1	hence	hence	ADV
ejpam-3758	161	2	,	,	PUNCT
ejpam-3758	161	3	f	f	PROPN
ejpam-3758	161	4	⊆	⊆	NUM
ejpam-3758	161	5	intµ1	intµ1	PROPN
ejpam-3758	161	6	(	(	PUNCT
ejpam-3758	161	7	clµ2	clµ2	PROPN
ejpam-3758	161	8	(	(	PUNCT
ejpam-3758	161	9	a	a	X
ejpam-3758	161	10	)	)	PUNCT
ejpam-3758	161	11	)	)	PUNCT
ejpam-3758	162	1	whenever	whenever	SCONJ
ejpam-3758	162	2	f	f	PROPN
ejpam-3758	162	3	⊆	⊆	PROPN
ejpam-3758	162	4	a	a	PRON
ejpam-3758	162	5	and	and	CCONJ
ejpam-3758	162	6	f	f	PROPN
ejpam-3758	162	7	is	be	AUX
ejpam-3758	162	8	µ3	µ3	NOUN
ejpam-3758	162	9	-	-	PUNCT
ejpam-3758	162	10	closed	closed	ADJ
ejpam-3758	162	11	.	.	PUNCT
ejpam-3758	163	1	now	now	ADV
ejpam-3758	163	2	,	,	PUNCT
ejpam-3758	163	3	let	let	VERB
ejpam-3758	163	4	f	f	PROPN
ejpam-3758	163	5	⊆	⊆	NUM
ejpam-3758	163	6	a	a	PRON
ejpam-3758	163	7	and	and	CCONJ
ejpam-3758	163	8	f	f	AUX
ejpam-3758	163	9	be	be	AUX
ejpam-3758	163	10	µ3	µ3	VERB
ejpam-3758	163	11	-	-	PUNCT
ejpam-3758	163	12	closed	close	VERB
ejpam-3758	163	13	set	set	NOUN
ejpam-3758	163	14	in	in	ADP
ejpam-3758	163	15	x	x	PUNCT
ejpam-3758	163	16	such	such	ADJ
ejpam-3758	163	17	that	that	SCONJ
ejpam-3758	163	18	f	f	PROPN
ejpam-3758	163	19	⊆	⊆	NUM
ejpam-3758	163	20	intµ1	intµ1	PROPN
ejpam-3758	163	21	(	(	PUNCT
ejpam-3758	163	22	clµ2	clµ2	PROPN
ejpam-3758	163	23	(	(	PUNCT
ejpam-3758	163	24	a	a	NOUN
ejpam-3758	163	25	)	)	PUNCT
ejpam-3758	163	26	)	)	PUNCT
ejpam-3758	163	27	.	.	PUNCT
ejpam-3758	164	1	taking	take	VERB
ejpam-3758	164	2	complementation	complementation	NOUN
ejpam-3758	164	3	,	,	PUNCT
ejpam-3758	164	4	we	we	PRON
ejpam-3758	164	5	have	have	VERB
ejpam-3758	164	6	[	[	PUNCT
ejpam-3758	164	7	intµ1	intµ1	PROPN
ejpam-3758	164	8	(	(	PUNCT
ejpam-3758	164	9	clµ2	clµ2	PROPN
ejpam-3758	164	10	(	(	PUNCT
ejpam-3758	164	11	a	a	NOUN
ejpam-3758	164	12	)	)	PUNCT
ejpam-3758	164	13	)	)	PUNCT
ejpam-3758	164	14	]	]	PUNCT
ejpam-3758	165	1	c	c	X
ejpam-3758	166	1	⊆	⊆	NUM
ejpam-3758	166	2	f	f	X
ejpam-3758	166	3	c	c	PROPN
ejpam-3758	166	4	whenever	whenever	SCONJ
ejpam-3758	166	5	ac	ac	PROPN
ejpam-3758	166	6	⊆	⊆	NUM
ejpam-3758	166	7	f	f	PROPN
ejpam-3758	166	8	c	c	PROPN
ejpam-3758	167	1	and	and	CCONJ
ejpam-3758	167	2	f	f	PROPN
ejpam-3758	167	3	c	c	PROPN
ejpam-3758	167	4	is	be	AUX
ejpam-3758	167	5	µ3	µ3	NOUN
ejpam-3758	167	6	-	-	PUNCT
ejpam-3758	167	7	open	open	ADJ
ejpam-3758	167	8	in	in	ADP
ejpam-3758	167	9	x.	x.	NOUN
ejpam-3758	167	10	but	but	CCONJ
ejpam-3758	167	11	[	[	PUNCT
ejpam-3758	167	12	intµ1	intµ1	PROPN
ejpam-3758	167	13	(	(	PUNCT
ejpam-3758	167	14	clµ2	clµ2	PROPN
ejpam-3758	167	15	(	(	PUNCT
ejpam-3758	167	16	a	a	NOUN
ejpam-3758	167	17	)	)	PUNCT
ejpam-3758	167	18	)	)	PUNCT
ejpam-3758	168	1	]	]	PUNCT
ejpam-3758	168	2	c	c	X
ejpam-3758	168	3	=	=	PUNCT
ejpam-3758	168	4	clµ1	clµ1	PROPN
ejpam-3758	168	5	[	[	PUNCT
ejpam-3758	168	6	(	(	PUNCT
ejpam-3758	168	7	clµ2	clµ2	PROPN
ejpam-3758	168	8	(	(	PUNCT
ejpam-3758	168	9	a))c	a))c	NOUN
ejpam-3758	168	10	]	]	X
ejpam-3758	168	11	=	=	PUNCT
ejpam-3758	168	12	clµ1	clµ1	NOUN
ejpam-3758	168	13	(	(	PUNCT
ejpam-3758	168	14	intµ2	intµ2	PROPN
ejpam-3758	168	15	(	(	PUNCT
ejpam-3758	168	16	ac	ac	PROPN
ejpam-3758	168	17	)	)	PUNCT
ejpam-3758	168	18	)	)	PUNCT
ejpam-3758	169	1	so	so	ADV
ejpam-3758	169	2	clµ1	clµ1	PROPN
ejpam-3758	169	3	(	(	PUNCT
ejpam-3758	169	4	intµ2	intµ2	PROPN
ejpam-3758	169	5	(	(	PUNCT
ejpam-3758	169	6	ac	ac	PROPN
ejpam-3758	169	7	)	)	PUNCT
ejpam-3758	169	8	)	)	PUNCT
ejpam-3758	170	1	⊆	⊆	NUM
ejpam-3758	170	2	f	f	X
ejpam-3758	170	3	c	c	PROPN
ejpam-3758	170	4	whenever	whenever	SCONJ
ejpam-3758	170	5	ac	ac	PROPN
ejpam-3758	170	6	⊆	⊆	NUM
ejpam-3758	170	7	f	f	PROPN
ejpam-3758	170	8	c	c	PROPN
ejpam-3758	171	1	and	and	CCONJ
ejpam-3758	171	2	f	f	PROPN
ejpam-3758	171	3	c	c	PROPN
ejpam-3758	171	4	is	be	AUX
ejpam-3758	171	5	µ3	µ3	NOUN
ejpam-3758	171	6	-	-	PUNCT
ejpam-3758	171	7	open	open	ADJ
ejpam-3758	171	8	in	in	ADP
ejpam-3758	171	9	x.	x.	NOUN
ejpam-3758	171	10	this	this	PRON
ejpam-3758	171	11	means	mean	VERB
ejpam-3758	171	12	that	that	SCONJ
ejpam-3758	171	13	ac	ac	PROPN
ejpam-3758	171	14	is	be	AUX
ejpam-3758	171	15	(	(	PUNCT
ejpam-3758	171	16	µ1	µ1	PROPN
ejpam-3758	171	17	,	,	PUNCT
ejpam-3758	171	18	µ2	µ2	ADJ
ejpam-3758	171	19	,	,	PUNCT
ejpam-3758	171	20	µ3)-wg	µ3)-wg	PROPN
ejpam-3758	171	21	closed	closed	ADJ
ejpam-3758	171	22	set	set	NOUN
ejpam-3758	171	23	.	.	PUNCT
ejpam-3758	172	1	therefore	therefore	ADV
ejpam-3758	172	2	a	a	DET
ejpam-3758	172	3	is	be	AUX
ejpam-3758	172	4	(	(	PUNCT
ejpam-3758	172	5	µ1	µ1	PROPN
ejpam-3758	172	6	,	,	PUNCT
ejpam-3758	172	7	µ2	µ2	ADJ
ejpam-3758	172	8	,	,	PUNCT
ejpam-3758	172	9	µ3)-wg	µ3)-wg	VERB
ejpam-3758	172	10	open	open	ADJ
ejpam-3758	172	11	set	set	NOUN
ejpam-3758	172	12	.	.	PUNCT
ejpam-3758	173	1	theorem	theorem	VERB
ejpam-3758	173	2	8	8	NUM
ejpam-3758	173	3	.	.	PUNCT
ejpam-3758	174	1	if	if	SCONJ
ejpam-3758	174	2	a	a	PRON
ejpam-3758	174	3	is	be	AUX
ejpam-3758	174	4	µ1	µ1	NOUN
ejpam-3758	174	5	-	-	PUNCT
ejpam-3758	174	6	closed	closed	ADJ
ejpam-3758	174	7	then	then	ADV
ejpam-3758	174	8	a	a	DET
ejpam-3758	174	9	is	be	AUX
ejpam-3758	174	10	(	(	PUNCT
ejpam-3758	174	11	µ1	µ1	PROPN
ejpam-3758	174	12	,	,	PUNCT
ejpam-3758	174	13	µ2	µ2	ADJ
ejpam-3758	174	14	,	,	PUNCT
ejpam-3758	174	15	µ3)-wg	µ3)-wg	NOUN
ejpam-3758	174	16	closed	close	VERB
ejpam-3758	174	17	set	set	NOUN
ejpam-3758	174	18	.	.	PUNCT
ejpam-3758	175	1	proof	proof	NOUN
ejpam-3758	175	2	.	.	PUNCT
ejpam-3758	176	1	let	let	VERB
ejpam-3758	176	2	a	a	DET
ejpam-3758	176	3	be	be	AUX
ejpam-3758	176	4	µ1	µ1	NOUN
ejpam-3758	176	5	-	-	PUNCT
ejpam-3758	176	6	closed	closed	ADJ
ejpam-3758	176	7	and	and	CCONJ
ejpam-3758	176	8	u	u	NOUN
ejpam-3758	176	9	be	be	AUX
ejpam-3758	176	10	µ3	µ3	VERB
ejpam-3758	176	11	-	-	PUNCT
ejpam-3758	176	12	open	open	ADJ
ejpam-3758	176	13	such	such	ADJ
ejpam-3758	176	14	that	that	SCONJ
ejpam-3758	176	15	a	a	DET
ejpam-3758	176	16	⊆	⊆	NUM
ejpam-3758	176	17	u	u	NOUN
ejpam-3758	176	18	.	.	PUNCT
ejpam-3758	177	1	by	by	ADP
ejpam-3758	177	2	theorem	theorem	NOUN
ejpam-3758	177	3	2(i	2(i	NUM
ejpam-3758	177	4	.	.	PUNCT
ejpam-3758	177	5	)	)	PUNCT
ejpam-3758	177	6	,	,	PUNCT
ejpam-3758	177	7	intµ2	intµ2	NOUN
ejpam-3758	177	8	(	(	PUNCT
ejpam-3758	177	9	a	a	X
ejpam-3758	177	10	)	)	PUNCT
ejpam-3758	177	11	⊆	⊆	PROPN
ejpam-3758	177	12	a	a	PRON
ejpam-3758	177	13	and	and	CCONJ
ejpam-3758	177	14	applying	applying	NOUN
ejpam-3758	177	15	theorem	theorem	NOUN
ejpam-3758	177	16	3(iv	3(iv	NUM
ejpam-3758	177	17	.	.	PUNCT
ejpam-3758	177	18	)	)	PUNCT
ejpam-3758	177	19	,	,	PUNCT
ejpam-3758	177	20	clµ1	clµ1	PROPN
ejpam-3758	177	21	(	(	PUNCT
ejpam-3758	177	22	intµ2	intµ2	NOUN
ejpam-3758	177	23	(	(	PUNCT
ejpam-3758	177	24	a	a	NOUN
ejpam-3758	177	25	)	)	PUNCT
ejpam-3758	177	26	)	)	PUNCT
ejpam-3758	177	27	⊆	⊆	NUM
ejpam-3758	177	28	clµ1(a	clµ1(a	NUM
ejpam-3758	177	29	)	)	PUNCT
ejpam-3758	177	30	.	.	PUNCT
ejpam-3758	178	1	since	since	SCONJ
ejpam-3758	178	2	a	a	PRON
ejpam-3758	178	3	is	be	AUX
ejpam-3758	178	4	µ1	µ1	NOUN
ejpam-3758	178	5	closed	closed	ADJ
ejpam-3758	178	6	,	,	PUNCT
ejpam-3758	178	7	clµ1(a	clµ1(a	NUM
ejpam-3758	178	8	)	)	PUNCT
ejpam-3758	179	1	=	=	SYM
ejpam-3758	179	2	a.	a.	NOUN
ejpam-3758	179	3	thus	thus	ADV
ejpam-3758	179	4	,	,	PUNCT
ejpam-3758	179	5	clµ1	clµ1	PROPN
ejpam-3758	179	6	(	(	PUNCT
ejpam-3758	179	7	intµ2	intµ2	NOUN
ejpam-3758	179	8	(	(	PUNCT
ejpam-3758	179	9	a	a	NOUN
ejpam-3758	179	10	)	)	PUNCT
ejpam-3758	179	11	)	)	PUNCT
ejpam-3758	180	1	⊆	⊆	NUM
ejpam-3758	180	2	a	a	DET
ejpam-3758	180	3	⊆	⊆	NUM
ejpam-3758	180	4	u	u	NOUN
ejpam-3758	180	5	.	.	PUNCT
ejpam-3758	181	1	therefore	therefore	ADV
ejpam-3758	181	2	,	,	PUNCT
ejpam-3758	181	3	a	a	DET
ejpam-3758	181	4	is	be	AUX
ejpam-3758	181	5	(	(	PUNCT
ejpam-3758	181	6	µ1	µ1	PROPN
ejpam-3758	181	7	,	,	PUNCT
ejpam-3758	181	8	µ2	µ2	ADJ
ejpam-3758	181	9	,	,	PUNCT
ejpam-3758	181	10	µ3)-wg	µ3)-wg	PROPN
ejpam-3758	181	11	closed	close	VERB
ejpam-3758	181	12	set	set	NOUN
ejpam-3758	181	13	.	.	PUNCT
ejpam-3758	182	1	theorem	theorem	VERB
ejpam-3758	182	2	9	9	NUM
ejpam-3758	182	3	.	.	PUNCT
ejpam-3758	183	1	if	if	SCONJ
ejpam-3758	183	2	f	f	PROPN
ejpam-3758	183	3	⊆	⊆	SYM
ejpam-3758	183	4	a	a	PRON
ejpam-3758	183	5	and	and	CCONJ
ejpam-3758	183	6	a	a	PRON
ejpam-3758	183	7	is	be	AUX
ejpam-3758	183	8	µ1	µ1	NOUN
ejpam-3758	183	9	-	-	PUNCT
ejpam-3758	183	10	closed	closed	ADJ
ejpam-3758	183	11	,	,	PUNCT
ejpam-3758	183	12	then	then	ADV
ejpam-3758	183	13	f	f	PROPN
ejpam-3758	183	14	is	be	AUX
ejpam-3758	183	15	(	(	PUNCT
ejpam-3758	183	16	µ1	µ1	PROPN
ejpam-3758	183	17	,	,	PUNCT
ejpam-3758	183	18	µ2	µ2	ADJ
ejpam-3758	183	19	,	,	PUNCT
ejpam-3758	183	20	µ3)-wg	µ3)-wg	NOUN
ejpam-3758	183	21	closed	close	VERB
ejpam-3758	183	22	set	set	NOUN
ejpam-3758	183	23	.	.	PUNCT
ejpam-3758	184	1	proof	proof	NOUN
ejpam-3758	184	2	.	.	PUNCT
ejpam-3758	185	1	let	let	VERB
ejpam-3758	185	2	a	a	DET
ejpam-3758	185	3	be	be	AUX
ejpam-3758	185	4	µ1	µ1	NOUN
ejpam-3758	185	5	-	-	PUNCT
ejpam-3758	185	6	closed	closed	ADJ
ejpam-3758	185	7	and	and	CCONJ
ejpam-3758	185	8	f	f	PROPN
ejpam-3758	185	9	⊆	⊆	NUM
ejpam-3758	185	10	a.	a.	NOUN
ejpam-3758	185	11	suppose	suppose	VERB
ejpam-3758	185	12	a	a	DET
ejpam-3758	185	13	⊆	⊆	NUM
ejpam-3758	185	14	u	u	NOUN
ejpam-3758	185	15	and	and	CCONJ
ejpam-3758	185	16	u	u	NOUN
ejpam-3758	185	17	is	be	AUX
ejpam-3758	185	18	µ3	µ3	NOUN
ejpam-3758	185	19	-	-	PUNCT
ejpam-3758	185	20	open	open	ADJ
ejpam-3758	185	21	.	.	PUNCT
ejpam-3758	186	1	since	since	SCONJ
ejpam-3758	186	2	f	f	PROPN
ejpam-3758	186	3	⊆	⊆	PROPN
ejpam-3758	186	4	a	a	PRON
ejpam-3758	186	5	,	,	PUNCT
ejpam-3758	186	6	intµ2(f	intµ2(f	ADJ
ejpam-3758	186	7	)	)	PUNCT
ejpam-3758	186	8	⊆	⊆	NUM
ejpam-3758	186	9	intµ2(a	intµ2(a	NOUN
ejpam-3758	186	10	)	)	PUNCT
ejpam-3758	186	11	using	use	VERB
ejpam-3758	186	12	theorem	theorem	ADJ
ejpam-3758	186	13	2(iv	2(iv	NUM
ejpam-3758	186	14	.	.	PUNCT
ejpam-3758	186	15	)	)	PUNCT
ejpam-3758	186	16	.	.	PUNCT
ejpam-3758	187	1	consequently	consequently	ADV
ejpam-3758	187	2	,	,	PUNCT
ejpam-3758	187	3	by	by	ADP
ejpam-3758	187	4	theorem	theorem	NOUN
ejpam-3758	187	5	3(iv	3(iv	NUM
ejpam-3758	187	6	.	.	PUNCT
ejpam-3758	187	7	)	)	PUNCT
ejpam-3758	187	8	,	,	PUNCT
ejpam-3758	187	9	clµ1	clµ1	PROPN
ejpam-3758	187	10	(	(	PUNCT
ejpam-3758	187	11	intµ2	intµ2	PROPN
ejpam-3758	187	12	(	(	PUNCT
ejpam-3758	187	13	f	f	PROPN
ejpam-3758	187	14	)	)	PUNCT
ejpam-3758	187	15	)	)	PUNCT
ejpam-3758	188	1	⊆	⊆	NUM
ejpam-3758	188	2	clµ1	clµ1	NOUN
ejpam-3758	188	3	(	(	PUNCT
ejpam-3758	188	4	intµ2	intµ2	NOUN
ejpam-3758	188	5	(	(	PUNCT
ejpam-3758	188	6	a	a	NOUN
ejpam-3758	188	7	)	)	PUNCT
ejpam-3758	188	8	)	)	PUNCT
ejpam-3758	188	9	.	.	PUNCT
ejpam-3758	189	1	moreover	moreover	ADV
ejpam-3758	189	2	,	,	PUNCT
ejpam-3758	189	3	by	by	ADP
ejpam-3758	189	4	theorem	theorem	NOUN
ejpam-3758	189	5	8	8	NUM
ejpam-3758	189	6	,	,	PUNCT
ejpam-3758	189	7	clµ1	clµ1	NOUN
ejpam-3758	189	8	(	(	PUNCT
ejpam-3758	189	9	intµ2	intµ2	NOUN
ejpam-3758	189	10	(	(	PUNCT
ejpam-3758	189	11	a	a	NOUN
ejpam-3758	189	12	)	)	PUNCT
ejpam-3758	189	13	)	)	PUNCT
ejpam-3758	190	1	⊆	⊆	NUM
ejpam-3758	190	2	u	u	NOUN
ejpam-3758	190	3	,	,	PUNCT
ejpam-3758	190	4	thus	thus	ADV
ejpam-3758	190	5	clµ1	clµ1	NOUN
ejpam-3758	190	6	(	(	PUNCT
ejpam-3758	190	7	intµ2	intµ2	PROPN
ejpam-3758	190	8	(	(	PUNCT
ejpam-3758	190	9	f	f	PROPN
ejpam-3758	190	10	)	)	PUNCT
ejpam-3758	190	11	)	)	PUNCT
ejpam-3758	191	1	⊆	⊆	NUM
ejpam-3758	191	2	u	u	NOUN
ejpam-3758	191	3	.	.	PUNCT
ejpam-3758	192	1	therefore	therefore	ADV
ejpam-3758	192	2	,	,	PUNCT
ejpam-3758	192	3	f	f	PROPN
ejpam-3758	192	4	is	be	AUX
ejpam-3758	192	5	(	(	PUNCT
ejpam-3758	192	6	µ1	µ1	PROPN
ejpam-3758	192	7	,	,	PUNCT
ejpam-3758	192	8	µ2	µ2	ADJ
ejpam-3758	192	9	,	,	PUNCT
ejpam-3758	192	10	µ3)-wg	µ3)-wg	PROPN
ejpam-3758	192	11	closed	close	VERB
ejpam-3758	192	12	set	set	NOUN
ejpam-3758	192	13	.	.	PUNCT
ejpam-3758	193	1	theorem	theorem	VERB
ejpam-3758	193	2	10	10	NUM
ejpam-3758	193	3	.	.	PUNCT
ejpam-3758	194	1	if	if	SCONJ
ejpam-3758	194	2	a	a	PRON
ejpam-3758	194	3	is	be	AUX
ejpam-3758	194	4	(	(	PUNCT
ejpam-3758	194	5	µ1	µ1	PROPN
ejpam-3758	194	6	,	,	PUNCT
ejpam-3758	194	7	µ2	µ2	ADJ
ejpam-3758	194	8	,	,	PUNCT
ejpam-3758	194	9	µ3)-wg	µ3)-wg	NOUN
ejpam-3758	194	10	closed	close	VERB
ejpam-3758	194	11	subset	subset	NOUN
ejpam-3758	194	12	of	of	ADP
ejpam-3758	194	13	x	x	X
ejpam-3758	194	14	and	and	CCONJ
ejpam-3758	194	15	a	a	DET
ejpam-3758	194	16	⊆	⊆	NUM
ejpam-3758	194	17	b	b	NOUN
ejpam-3758	194	18	⊆	⊆	NUM
ejpam-3758	194	19	clµ1	clµ1	NOUN
ejpam-3758	194	20	(	(	PUNCT
ejpam-3758	194	21	intµ2	intµ2	NOUN
ejpam-3758	194	22	(	(	PUNCT
ejpam-3758	194	23	a	a	NOUN
ejpam-3758	194	24	)	)	PUNCT
ejpam-3758	194	25	)	)	PUNCT
ejpam-3758	194	26	,	,	PUNCT
ejpam-3758	194	27	then	then	ADV
ejpam-3758	194	28	b	b	X
ejpam-3758	194	29	is	be	AUX
ejpam-3758	194	30	(	(	PUNCT
ejpam-3758	194	31	µ1	µ1	PROPN
ejpam-3758	194	32	,	,	PUNCT
ejpam-3758	194	33	µ2	µ2	ADJ
ejpam-3758	194	34	,	,	PUNCT
ejpam-3758	194	35	µ3)-wg	µ3)-wg	PROPN
ejpam-3758	194	36	closed	closed	ADJ
ejpam-3758	194	37	set	set	NOUN
ejpam-3758	194	38	.	.	PUNCT
ejpam-3758	195	1	b.	b.	PROPN
ejpam-3758	195	2	agua	agua	PROPN
ejpam-3758	195	3	,	,	PUNCT
ejpam-3758	195	4	r.	r.	PROPN
ejpam-3758	195	5	paluga	paluga	PROPN
ejpam-3758	195	6	/	/	SYM
ejpam-3758	195	7	eur	eur	PROPN
ejpam-3758	195	8	.	.	PUNCT
ejpam-3758	196	1	j.	j.	PROPN
ejpam-3758	196	2	pure	pure	PROPN
ejpam-3758	196	3	appl	appl	PROPN
ejpam-3758	196	4	.	.	PROPN
ejpam-3758	196	5	math	math	PROPN
ejpam-3758	196	6	,	,	PUNCT
ejpam-3758	196	7	13	13	NUM
ejpam-3758	196	8	(	(	PUNCT
ejpam-3758	196	9	4	4	NUM
ejpam-3758	196	10	)	)	PUNCT
ejpam-3758	196	11	(	(	PUNCT
ejpam-3758	196	12	2020	2020	NUM
ejpam-3758	196	13	)	)	PUNCT
ejpam-3758	196	14	,	,	PUNCT
ejpam-3758	196	15	977	977	NUM
ejpam-3758	196	16	-	-	SYM
ejpam-3758	196	17	986	986	NUM
ejpam-3758	196	18	984	984	NUM
ejpam-3758	196	19	proof	proof	NOUN
ejpam-3758	196	20	.	.	PUNCT
ejpam-3758	197	1	suppose	suppose	VERB
ejpam-3758	197	2	thata	thata	PROPN
ejpam-3758	197	3	is	be	AUX
ejpam-3758	197	4	(	(	PUNCT
ejpam-3758	197	5	µ1	µ1	PROPN
ejpam-3758	197	6	,	,	PUNCT
ejpam-3758	197	7	µ2	µ2	ADJ
ejpam-3758	197	8	,	,	PUNCT
ejpam-3758	197	9	µ3)-wg	µ3)-wg	NOUN
ejpam-3758	197	10	closed	close	VERB
ejpam-3758	197	11	subset	subset	ADJ
ejpam-3758	197	12	ofx	ofx	NOUN
ejpam-3758	197	13	anda	anda	PROPN
ejpam-3758	197	14	⊆	⊆	NUM
ejpam-3758	197	15	b	b	PROPN
ejpam-3758	197	16	⊆	⊆	NUM
ejpam-3758	197	17	clµ1	clµ1	NOUN
ejpam-3758	197	18	(	(	PUNCT
ejpam-3758	197	19	intµ2	intµ2	NOUN
ejpam-3758	197	20	(	(	PUNCT
ejpam-3758	197	21	a	a	NOUN
ejpam-3758	197	22	)	)	PUNCT
ejpam-3758	197	23	)	)	PUNCT
ejpam-3758	197	24	.	.	PUNCT
ejpam-3758	198	1	let	let	VERB
ejpam-3758	198	2	u	u	PRON
ejpam-3758	198	3	be	be	AUX
ejpam-3758	198	4	µ3	µ3	VERB
ejpam-3758	198	5	-	-	PUNCT
ejpam-3758	198	6	open	open	ADJ
ejpam-3758	198	7	and	and	CCONJ
ejpam-3758	198	8	b	b	NOUN
ejpam-3758	198	9	⊆	⊆	NUM
ejpam-3758	198	10	u	u	NOUN
ejpam-3758	198	11	.	.	PUNCT
ejpam-3758	199	1	since	since	SCONJ
ejpam-3758	199	2	a	a	DET
ejpam-3758	199	3	⊆	⊆	NUM
ejpam-3758	199	4	b	b	NOUN
ejpam-3758	199	5	,	,	PUNCT
ejpam-3758	199	6	then	then	ADV
ejpam-3758	199	7	a	a	DET
ejpam-3758	199	8	⊆	⊆	NUM
ejpam-3758	199	9	u	u	NOUN
ejpam-3758	199	10	.	.	PUNCT
ejpam-3758	200	1	also	also	ADV
ejpam-3758	200	2	,	,	PUNCT
ejpam-3758	200	3	since	since	SCONJ
ejpam-3758	200	4	a	a	DET
ejpam-3758	200	5	is	is	NOUN
ejpam-3758	200	6	(	(	PUNCT
ejpam-3758	200	7	µ1	µ1	PROPN
ejpam-3758	200	8	,	,	PUNCT
ejpam-3758	200	9	µ2	µ2	PROPN
ejpam-3758	200	10	,	,	PUNCT
ejpam-3758	200	11	µ3)wg	µ3)wg	NOUN
ejpam-3758	200	12	closed	close	VERB
ejpam-3758	200	13	set	set	VERB
ejpam-3758	200	14	,	,	PUNCT
ejpam-3758	200	15	clµ1	clµ1	PROPN
ejpam-3758	200	16	(	(	PUNCT
ejpam-3758	200	17	intµ2	intµ2	NOUN
ejpam-3758	200	18	(	(	PUNCT
ejpam-3758	200	19	a	a	NOUN
ejpam-3758	200	20	)	)	PUNCT
ejpam-3758	200	21	)	)	PUNCT
ejpam-3758	201	1	⊆	⊆	NUM
ejpam-3758	201	2	u	u	NOUN
ejpam-3758	201	3	.	.	PUNCT
ejpam-3758	202	1	now	now	ADV
ejpam-3758	202	2	,	,	PUNCT
ejpam-3758	202	3	since	since	SCONJ
ejpam-3758	202	4	b	b	PROPN
ejpam-3758	202	5	⊆	⊆	NUM
ejpam-3758	202	6	clµ1	clµ1	NOUN
ejpam-3758	202	7	(	(	PUNCT
ejpam-3758	202	8	intµ2	intµ2	NOUN
ejpam-3758	202	9	(	(	PUNCT
ejpam-3758	202	10	a	a	NOUN
ejpam-3758	202	11	)	)	PUNCT
ejpam-3758	202	12	)	)	PUNCT
ejpam-3758	202	13	and	and	CCONJ
ejpam-3758	202	14	using	use	VERB
ejpam-3758	202	15	theorem	theorem	ADJ
ejpam-3758	202	16	2(i	2(i	NUM
ejpam-3758	202	17	.	.	PUNCT
ejpam-3758	202	18	)	)	PUNCT
ejpam-3758	202	19	,	,	PUNCT
ejpam-3758	202	20	intµ2	intµ2	NOUN
ejpam-3758	202	21	(	(	PUNCT
ejpam-3758	202	22	b	b	NOUN
ejpam-3758	202	23	)	)	PUNCT
ejpam-3758	202	24	⊆	⊆	NUM
ejpam-3758	202	25	b	b	NOUN
ejpam-3758	202	26	⊆	⊆	NUM
ejpam-3758	202	27	clµ1	clµ1	NOUN
ejpam-3758	202	28	(	(	PUNCT
ejpam-3758	202	29	intµ2	intµ2	NOUN
ejpam-3758	202	30	(	(	PUNCT
ejpam-3758	202	31	a	a	NOUN
ejpam-3758	202	32	)	)	PUNCT
ejpam-3758	202	33	)	)	PUNCT
ejpam-3758	202	34	.	.	PUNCT
ejpam-3758	203	1	consequently	consequently	ADV
ejpam-3758	203	2	,	,	PUNCT
ejpam-3758	203	3	by	by	ADP
ejpam-3758	203	4	theorem	theorem	NOUN
ejpam-3758	203	5	3(iv	3(iv	NUM
ejpam-3758	203	6	.	.	PUNCT
ejpam-3758	203	7	)	)	PUNCT
ejpam-3758	203	8	,	,	PUNCT
ejpam-3758	203	9	clµ1(intµ2	clµ1(intµ2	NOUN
ejpam-3758	203	10	(	(	PUNCT
ejpam-3758	203	11	b	b	NOUN
ejpam-3758	203	12	)	)	PUNCT
ejpam-3758	203	13	)	)	PUNCT
ejpam-3758	204	1	⊆	⊆	NUM
ejpam-3758	204	2	clµ1(b	clµ1(b	NUM
ejpam-3758	204	3	)	)	PUNCT
ejpam-3758	204	4	⊆	⊆	NUM
ejpam-3758	204	5	clµ1	clµ1	NOUN
ejpam-3758	204	6	(	(	PUNCT
ejpam-3758	204	7	intµ2	intµ2	NOUN
ejpam-3758	204	8	(	(	PUNCT
ejpam-3758	204	9	a	a	NOUN
ejpam-3758	204	10	)	)	PUNCT
ejpam-3758	204	11	)	)	PUNCT
ejpam-3758	204	12	.	.	PUNCT
ejpam-3758	205	1	in	in	ADP
ejpam-3758	205	2	effect	effect	NOUN
ejpam-3758	205	3	,	,	PUNCT
ejpam-3758	205	4	clµ1	clµ1	PROPN
ejpam-3758	205	5	(	(	PUNCT
ejpam-3758	205	6	intµ2	intµ2	PROPN
ejpam-3758	205	7	(	(	PUNCT
ejpam-3758	205	8	b	b	NOUN
ejpam-3758	205	9	)	)	PUNCT
ejpam-3758	205	10	)	)	PUNCT
ejpam-3758	205	11	⊆	⊆	NUM
ejpam-3758	205	12	u	u	NOUN
ejpam-3758	205	13	.	.	PUNCT
ejpam-3758	206	1	hence	hence	ADV
ejpam-3758	206	2	,	,	PUNCT
ejpam-3758	206	3	b	b	PROPN
ejpam-3758	206	4	is	be	AUX
ejpam-3758	206	5	(	(	PUNCT
ejpam-3758	206	6	µ1	µ1	PROPN
ejpam-3758	206	7	,	,	PUNCT
ejpam-3758	206	8	µ2	µ2	ADJ
ejpam-3758	206	9	,	,	PUNCT
ejpam-3758	206	10	µ3)-wg	µ3)-wg	PROPN
ejpam-3758	206	11	closed	close	VERB
ejpam-3758	206	12	set	set	NOUN
ejpam-3758	206	13	.	.	PUNCT
ejpam-3758	207	1	theorem	theorem	VERB
ejpam-3758	207	2	11	11	NUM
ejpam-3758	207	3	.	.	PUNCT
ejpam-3758	208	1	if	if	SCONJ
ejpam-3758	208	2	a	a	PRON
ejpam-3758	208	3	is	be	AUX
ejpam-3758	208	4	(	(	PUNCT
ejpam-3758	208	5	µ1	µ1	PROPN
ejpam-3758	208	6	,	,	PUNCT
ejpam-3758	208	7	µ2	µ2	ADJ
ejpam-3758	208	8	,	,	PUNCT
ejpam-3758	208	9	µ3)-wg	µ3)-wg	NOUN
ejpam-3758	208	10	closed	close	VERB
ejpam-3758	208	11	set	set	NOUN
ejpam-3758	208	12	,	,	PUNCT
ejpam-3758	208	13	then	then	ADV
ejpam-3758	208	14	clµ1	clµ1	PROPN
ejpam-3758	208	15	(	(	PUNCT
ejpam-3758	208	16	intµ2	intµ2	NOUN
ejpam-3758	208	17	(	(	PUNCT
ejpam-3758	208	18	a	a	NOUN
ejpam-3758	208	19	)	)	PUNCT
ejpam-3758	208	20	)	)	PUNCT
ejpam-3758	208	21	−	−	ADP
ejpam-3758	209	1	a	a	PRON
ejpam-3758	209	2	contains	contain	VERB
ejpam-3758	209	3	no	no	DET
ejpam-3758	209	4	nonempty	nonempty	ADV
ejpam-3758	209	5	µ3	µ3	NOUN
ejpam-3758	209	6	-	-	PUNCT
ejpam-3758	209	7	closed	close	VERB
ejpam-3758	209	8	set	set	NOUN
ejpam-3758	209	9	.	.	PUNCT
ejpam-3758	210	1	proof	proof	NOUN
ejpam-3758	210	2	.	.	PUNCT
ejpam-3758	211	1	let	let	VERB
ejpam-3758	211	2	a	a	DET
ejpam-3758	211	3	be	be	AUX
ejpam-3758	211	4	(	(	PUNCT
ejpam-3758	211	5	µ1	µ1	PROPN
ejpam-3758	211	6	,	,	PUNCT
ejpam-3758	211	7	µ2	µ2	ADJ
ejpam-3758	211	8	,	,	PUNCT
ejpam-3758	211	9	µ3)-wg	µ3)-wg	NOUN
ejpam-3758	211	10	closed	close	VERB
ejpam-3758	211	11	set	set	ADJ
ejpam-3758	211	12	and	and	CCONJ
ejpam-3758	211	13	f	f	PROPN
ejpam-3758	211	14	be	be	AUX
ejpam-3758	211	15	a	a	DET
ejpam-3758	211	16	nonempty	nonempty	ADJ
ejpam-3758	211	17	µ3	µ3	NOUN
ejpam-3758	211	18	-	-	PUNCT
ejpam-3758	211	19	closed	close	VERB
ejpam-3758	211	20	set	set	NOUN
ejpam-3758	212	1	such	such	ADJ
ejpam-3758	212	2	that	that	SCONJ
ejpam-3758	212	3	f	f	PROPN
ejpam-3758	212	4	⊆	⊆	NUM
ejpam-3758	212	5	clµ1	clµ1	NOUN
ejpam-3758	212	6	(	(	PUNCT
ejpam-3758	212	7	intµ2	intµ2	NOUN
ejpam-3758	212	8	(	(	PUNCT
ejpam-3758	212	9	a	a	NOUN
ejpam-3758	212	10	)	)	PUNCT
ejpam-3758	212	11	−	−	NOUN
ejpam-3758	212	12	a.	a.	NOUN
ejpam-3758	212	13	then	then	ADV
ejpam-3758	212	14	f	f	PROPN
ejpam-3758	212	15	⊆	⊆	NUM
ejpam-3758	212	16	clµ1	clµ1	NOUN
ejpam-3758	212	17	(	(	PUNCT
ejpam-3758	212	18	intµ2	intµ2	NOUN
ejpam-3758	212	19	(	(	PUNCT
ejpam-3758	212	20	a	a	NOUN
ejpam-3758	212	21	)	)	PUNCT
ejpam-3758	212	22	)	)	PUNCT
ejpam-3758	213	1	⋂	⋂	PROPN
ejpam-3758	213	2	ac	ac	PROPN
ejpam-3758	213	3	.	.	PUNCT
ejpam-3758	214	1	this	this	PRON
ejpam-3758	214	2	implies	imply	VERB
ejpam-3758	214	3	that	that	SCONJ
ejpam-3758	214	4	f	f	PROPN
ejpam-3758	214	5	⊆	⊆	NUM
ejpam-3758	214	6	clµ1	clµ1	NOUN
ejpam-3758	214	7	(	(	PUNCT
ejpam-3758	214	8	intµ2	intµ2	NOUN
ejpam-3758	214	9	(	(	PUNCT
ejpam-3758	214	10	a	a	NOUN
ejpam-3758	214	11	)	)	PUNCT
ejpam-3758	214	12	)	)	PUNCT
ejpam-3758	214	13	and	and	CCONJ
ejpam-3758	214	14	f	f	PROPN
ejpam-3758	214	15	⊆	⊆	NUM
ejpam-3758	214	16	⋂	⋂	PROPN
ejpam-3758	214	17	ac	ac	PROPN
ejpam-3758	214	18	.	.	PUNCT
ejpam-3758	214	19	note	note	VERB
ejpam-3758	214	20	that	that	SCONJ
ejpam-3758	214	21	f	f	PROPN
ejpam-3758	214	22	c	c	PROPN
ejpam-3758	214	23	is	be	AUX
ejpam-3758	214	24	µ3	µ3	NOUN
ejpam-3758	214	25	-	-	PUNCT
ejpam-3758	214	26	open	open	ADJ
ejpam-3758	214	27	and	and	CCONJ
ejpam-3758	214	28	a	a	DET
ejpam-3758	214	29	⊆	⊆	NUM
ejpam-3758	214	30	f	f	PROPN
ejpam-3758	214	31	c.	c.	PROPN
ejpam-3758	214	32	now	now	ADV
ejpam-3758	214	33	,	,	PUNCT
ejpam-3758	214	34	since	since	SCONJ
ejpam-3758	214	35	a	a	DET
ejpam-3758	214	36	is	is	NOUN
ejpam-3758	214	37	(	(	PUNCT
ejpam-3758	214	38	µ1	µ1	PROPN
ejpam-3758	214	39	,	,	PUNCT
ejpam-3758	214	40	µ2	µ2	ADJ
ejpam-3758	214	41	,	,	PUNCT
ejpam-3758	214	42	µ3)-wg	µ3)-wg	NOUN
ejpam-3758	214	43	closed	closed	ADJ
ejpam-3758	214	44	,	,	PUNCT
ejpam-3758	214	45	then	then	ADV
ejpam-3758	214	46	clµ1	clµ1	PROPN
ejpam-3758	214	47	(	(	PUNCT
ejpam-3758	214	48	intµ2	intµ2	NOUN
ejpam-3758	214	49	(	(	PUNCT
ejpam-3758	214	50	a	a	NOUN
ejpam-3758	214	51	)	)	PUNCT
ejpam-3758	214	52	)	)	PUNCT
ejpam-3758	215	1	⊆	⊆	NUM
ejpam-3758	215	2	f	f	PROPN
ejpam-3758	215	3	c.	c.	PROPN
ejpam-3758	215	4	thus	thus	ADV
ejpam-3758	215	5	,	,	PUNCT
ejpam-3758	215	6	f	f	PROPN
ejpam-3758	215	7	⊆	⊆	NUM
ejpam-3758	215	8	clµ1	clµ1	NOUN
ejpam-3758	215	9	(	(	PUNCT
ejpam-3758	215	10	intµ2	intµ2	NOUN
ejpam-3758	215	11	(	(	PUNCT
ejpam-3758	215	12	a	a	NOUN
ejpam-3758	215	13	)	)	PUNCT
ejpam-3758	215	14	)	)	PUNCT
ejpam-3758	216	1	⊆	⊆	NUM
ejpam-3758	216	2	f	f	PROPN
ejpam-3758	216	3	c.	c.	PROPN
ejpam-3758	216	4	this	this	PRON
ejpam-3758	216	5	means	mean	VERB
ejpam-3758	216	6	that	that	SCONJ
ejpam-3758	216	7	f	f	PROPN
ejpam-3758	217	1	=	=	SYM
ejpam-3758	217	2	f	f	PROPN
ejpam-3758	217	3	⋂	⋂	PROPN
ejpam-3758	217	4	f	f	X
ejpam-3758	217	5	c	c	PROPN
ejpam-3758	217	6	=	=	PUNCT
ejpam-3758	217	7	∅.	∅.	NOUN
ejpam-3758	217	8	this	this	PRON
ejpam-3758	217	9	is	be	AUX
ejpam-3758	217	10	a	a	DET
ejpam-3758	217	11	contradiction	contradiction	NOUN
ejpam-3758	217	12	.	.	PUNCT
ejpam-3758	218	1	hence	hence	ADV
ejpam-3758	218	2	if	if	SCONJ
ejpam-3758	218	3	a	a	PRON
ejpam-3758	218	4	is	be	AUX
ejpam-3758	218	5	(	(	PUNCT
ejpam-3758	218	6	µ1	µ1	PROPN
ejpam-3758	218	7	,	,	PUNCT
ejpam-3758	218	8	µ2	µ2	ADJ
ejpam-3758	218	9	,	,	PUNCT
ejpam-3758	218	10	µ3)-wg	µ3)-wg	NOUN
ejpam-3758	218	11	closed	close	VERB
ejpam-3758	218	12	set	set	NOUN
ejpam-3758	218	13	,	,	PUNCT
ejpam-3758	218	14	then	then	ADV
ejpam-3758	218	15	clµ1	clµ1	PROPN
ejpam-3758	218	16	(	(	PUNCT
ejpam-3758	218	17	intµ2	intµ2	PROPN
ejpam-3758	218	18	(	(	PUNCT
ejpam-3758	218	19	a))−a	a))−a	PROPN
ejpam-3758	218	20	contains	contain	VERB
ejpam-3758	218	21	no	no	DET
ejpam-3758	218	22	nonempty	nonempty	ADV
ejpam-3758	218	23	µ3	µ3	NOUN
ejpam-3758	218	24	-	-	PUNCT
ejpam-3758	218	25	closed	close	VERB
ejpam-3758	218	26	set	set	NOUN
ejpam-3758	218	27	.	.	PUNCT
ejpam-3758	219	1	remark	remark	PROPN
ejpam-3758	219	2	1	1	NUM
ejpam-3758	219	3	.	.	PUNCT
ejpam-3758	220	1	the	the	DET
ejpam-3758	220	2	converse	converse	NOUN
ejpam-3758	220	3	of	of	ADP
ejpam-3758	220	4	theorem	theorem	NOUN
ejpam-3758	220	5	11	11	NUM
ejpam-3758	220	6	is	be	AUX
ejpam-3758	220	7	not	not	PART
ejpam-3758	220	8	necessarily	necessarily	ADV
ejpam-3758	220	9	true	true	ADJ
ejpam-3758	220	10	.	.	PUNCT
ejpam-3758	220	11	example	example	NOUN
ejpam-3758	221	1	1	1	NUM
ejpam-3758	221	2	.	.	PUNCT
ejpam-3758	221	3	let	let	VERB
ejpam-3758	221	4	x	x	PUNCT
ejpam-3758	221	5	=	=	PRON
ejpam-3758	221	6	{	{	PUNCT
ejpam-3758	221	7	1	1	NUM
ejpam-3758	221	8	,	,	PUNCT
ejpam-3758	221	9	2	2	NUM
ejpam-3758	221	10	,	,	PUNCT
ejpam-3758	221	11	3	3	NUM
ejpam-3758	221	12	}	}	PUNCT
ejpam-3758	221	13	,	,	PUNCT
ejpam-3758	221	14	µ1	µ1	PROPN
ejpam-3758	221	15	=	=	SYM
ejpam-3758	221	16	{	{	PUNCT
ejpam-3758	221	17	∅	∅	NOUN
ejpam-3758	221	18	,	,	PUNCT
ejpam-3758	221	19	{	{	PUNCT
ejpam-3758	221	20	1	1	NUM
ejpam-3758	221	21	}	}	PUNCT
ejpam-3758	221	22	,	,	PUNCT
ejpam-3758	221	23	{	{	PUNCT
ejpam-3758	221	24	1	1	NUM
ejpam-3758	221	25	,	,	PUNCT
ejpam-3758	221	26	3	3	NUM
ejpam-3758	221	27	}	}	PUNCT
ejpam-3758	221	28	}	}	PUNCT
ejpam-3758	221	29	,	,	PUNCT
ejpam-3758	221	30	µ2	µ2	PROPN
ejpam-3758	221	31	=	=	PUNCT
ejpam-3758	221	32	{	{	PUNCT
ejpam-3758	221	33	∅	∅	NOUN
ejpam-3758	221	34	,	,	PUNCT
ejpam-3758	221	35	{	{	PUNCT
ejpam-3758	221	36	1	1	NUM
ejpam-3758	221	37	}	}	PUNCT
ejpam-3758	221	38	,	,	PUNCT
ejpam-3758	221	39	{	{	PUNCT
ejpam-3758	221	40	2	2	NUM
ejpam-3758	221	41	}	}	PUNCT
ejpam-3758	221	42	,	,	PUNCT
ejpam-3758	221	43	{	{	PUNCT
ejpam-3758	221	44	1	1	NUM
ejpam-3758	221	45	,	,	PUNCT
ejpam-3758	221	46	2	2	NUM
ejpam-3758	221	47	}	}	PUNCT
ejpam-3758	221	48	}	}	PUNCT
ejpam-3758	221	49	,	,	PUNCT
ejpam-3758	221	50	and	and	CCONJ
ejpam-3758	221	51	µ3	µ3	NOUN
ejpam-3758	221	52	=	=	SYM
ejpam-3758	221	53	{	{	PUNCT
ejpam-3758	221	54	∅	∅	NOUN
ejpam-3758	221	55	,	,	PUNCT
ejpam-3758	221	56	{	{	PUNCT
ejpam-3758	221	57	2	2	NUM
ejpam-3758	221	58	}	}	PUNCT
ejpam-3758	221	59	,	,	PUNCT
ejpam-3758	221	60	{	{	PUNCT
ejpam-3758	221	61	3	3	NUM
ejpam-3758	221	62	}	}	PUNCT
ejpam-3758	221	63	,	,	PUNCT
ejpam-3758	221	64	{	{	PUNCT
ejpam-3758	221	65	2	2	NUM
ejpam-3758	221	66	,	,	PUNCT
ejpam-3758	221	67	3	3	NUM
ejpam-3758	221	68	}	}	PUNCT
ejpam-3758	221	69	}	}	PUNCT
ejpam-3758	221	70	.	.	PUNCT
ejpam-3758	222	1	the	the	DET
ejpam-3758	222	2	µ1	µ1	NOUN
ejpam-3758	222	3	-	-	PUNCT
ejpam-3758	222	4	closed	close	VERB
ejpam-3758	222	5	sets	set	NOUN
ejpam-3758	222	6	are	be	AUX
ejpam-3758	222	7	x	x	X
ejpam-3758	222	8	,	,	PUNCT
ejpam-3758	222	9	{	{	PUNCT
ejpam-3758	222	10	2	2	NUM
ejpam-3758	222	11	,	,	PUNCT
ejpam-3758	222	12	3	3	NUM
ejpam-3758	222	13	}	}	PUNCT
ejpam-3758	222	14	and	and	CCONJ
ejpam-3758	222	15	{	{	PUNCT
ejpam-3758	222	16	2	2	NUM
ejpam-3758	222	17	}	}	PUNCT
ejpam-3758	222	18	.	.	PUNCT
ejpam-3758	223	1	also	also	ADV
ejpam-3758	223	2	,	,	PUNCT
ejpam-3758	223	3	the	the	DET
ejpam-3758	223	4	µ2	µ2	ADJ
ejpam-3758	223	5	-	-	PUNCT
ejpam-3758	223	6	open	open	ADJ
ejpam-3758	223	7	sets	set	NOUN
ejpam-3758	223	8	are	be	AUX
ejpam-3758	223	9	∅	∅	NOUN
ejpam-3758	223	10	,	,	PUNCT
ejpam-3758	223	11	{	{	PUNCT
ejpam-3758	223	12	1	1	NUM
ejpam-3758	223	13	}	}	PUNCT
ejpam-3758	223	14	,	,	PUNCT
ejpam-3758	223	15	{	{	PUNCT
ejpam-3758	223	16	2	2	NUM
ejpam-3758	223	17	}	}	PUNCT
ejpam-3758	223	18	,	,	PUNCT
ejpam-3758	223	19	and	and	CCONJ
ejpam-3758	223	20	{	{	PUNCT
ejpam-3758	223	21	1	1	NUM
ejpam-3758	223	22	,	,	PUNCT
ejpam-3758	223	23	2	2	NUM
ejpam-3758	223	24	}	}	PUNCT
ejpam-3758	223	25	.	.	PUNCT
ejpam-3758	224	1	the	the	DET
ejpam-3758	224	2	µ3	µ3	NUM
ejpam-3758	224	3	-	-	PUNCT
ejpam-3758	224	4	open	open	ADJ
ejpam-3758	224	5	sets	set	NOUN
ejpam-3758	224	6	on	on	ADP
ejpam-3758	224	7	the	the	DET
ejpam-3758	224	8	other	other	ADJ
ejpam-3758	224	9	hand	hand	NOUN
ejpam-3758	224	10	are	be	AUX
ejpam-3758	224	11	∅	∅	NOUN
ejpam-3758	224	12	,	,	PUNCT
ejpam-3758	224	13	{	{	PUNCT
ejpam-3758	224	14	2	2	NUM
ejpam-3758	224	15	}	}	PUNCT
ejpam-3758	224	16	,	,	PUNCT
ejpam-3758	224	17	{	{	PUNCT
ejpam-3758	224	18	3	3	NUM
ejpam-3758	224	19	}	}	PUNCT
ejpam-3758	224	20	,	,	PUNCT
ejpam-3758	224	21	and	and	CCONJ
ejpam-3758	224	22	{	{	PUNCT
ejpam-3758	224	23	2	2	NUM
ejpam-3758	224	24	,	,	PUNCT
ejpam-3758	224	25	3	3	NUM
ejpam-3758	224	26	}	}	PUNCT
ejpam-3758	224	27	whose	whose	DET
ejpam-3758	224	28	corresponding	corresponding	ADJ
ejpam-3758	224	29	µ3	µ3	NOUN
ejpam-3758	224	30	-	-	PUNCT
ejpam-3758	224	31	closed	close	VERB
ejpam-3758	224	32	sets	set	NOUN
ejpam-3758	224	33	are	be	AUX
ejpam-3758	224	34	x	x	X
ejpam-3758	224	35	,	,	PUNCT
ejpam-3758	224	36	{	{	PUNCT
ejpam-3758	224	37	1	1	NUM
ejpam-3758	224	38	,	,	PUNCT
ejpam-3758	224	39	3	3	NUM
ejpam-3758	224	40	}	}	PUNCT
ejpam-3758	224	41	,	,	PUNCT
ejpam-3758	224	42	{	{	PUNCT
ejpam-3758	224	43	1	1	NUM
ejpam-3758	224	44	,	,	PUNCT
ejpam-3758	224	45	2	2	NUM
ejpam-3758	224	46	}	}	PUNCT
ejpam-3758	224	47	,	,	PUNCT
ejpam-3758	224	48	and	and	CCONJ
ejpam-3758	224	49	{	{	PUNCT
ejpam-3758	224	50	1	1	NUM
ejpam-3758	224	51	}	}	PUNCT
ejpam-3758	224	52	.	.	PUNCT
ejpam-3758	225	1	observe	observe	VERB
ejpam-3758	225	2	that	that	SCONJ
ejpam-3758	225	3	considering	consider	VERB
ejpam-3758	225	4	all	all	DET
ejpam-3758	225	5	the	the	DET
ejpam-3758	225	6	possible	possible	ADJ
ejpam-3758	225	7	subsets	subset	NOUN
ejpam-3758	225	8	of	of	ADP
ejpam-3758	225	9	x	x	NOUN
ejpam-3758	225	10	,	,	PUNCT
ejpam-3758	225	11	only	only	ADV
ejpam-3758	225	12	the	the	DET
ejpam-3758	225	13	sets	set	NOUN
ejpam-3758	225	14	:	:	PUNCT
ejpam-3758	225	15	∅	∅	NOUN
ejpam-3758	225	16	and	and	CCONJ
ejpam-3758	225	17	{	{	PUNCT
ejpam-3758	225	18	3	3	X
ejpam-3758	225	19	}	}	PUNCT
ejpam-3758	225	20	are	be	AUX
ejpam-3758	225	21	not	not	PART
ejpam-3758	225	22	(	(	PUNCT
ejpam-3758	225	23	µ1	µ1	ADJ
ejpam-3758	225	24	,	,	PUNCT
ejpam-3758	225	25	µ2	µ2	ADJ
ejpam-3758	225	26	,	,	PUNCT
ejpam-3758	225	27	µ3)-wg	µ3)-wg	VERB
ejpam-3758	225	28	closed	closed	ADJ
ejpam-3758	225	29	sets	set	NOUN
ejpam-3758	225	30	.	.	PUNCT
ejpam-3758	226	1	if	if	SCONJ
ejpam-3758	226	2	a	a	DET
ejpam-3758	226	3	=	=	NOUN
ejpam-3758	226	4	∅	∅	NOUN
ejpam-3758	226	5	,	,	PUNCT
ejpam-3758	226	6	intµ2(∅	intµ2(∅	ADJ
ejpam-3758	226	7	)	)	PUNCT
ejpam-3758	226	8	=	=	NOUN
ejpam-3758	226	9	∅.	∅.	ADP
ejpam-3758	226	10	consequently	consequently	ADV
ejpam-3758	226	11	,	,	PUNCT
ejpam-3758	226	12	clµ1(intµ2(∅	clµ1(intµ2(∅	PROPN
ejpam-3758	226	13	)	)	PUNCT
ejpam-3758	226	14	)	)	PUNCT
ejpam-3758	227	1	=	=	PRON
ejpam-3758	227	2	{	{	PUNCT
ejpam-3758	227	3	2	2	NUM
ejpam-3758	227	4	}	}	PUNCT
ejpam-3758	227	5	.	.	PUNCT
ejpam-3758	228	1	hence	hence	ADV
ejpam-3758	228	2	,	,	PUNCT
ejpam-3758	228	3	clµ1(intµ2(∅))\∅	clµ1(intµ2(∅))\∅	PROPN
ejpam-3758	228	4	=	=	PUNCT
ejpam-3758	228	5	{	{	PUNCT
ejpam-3758	228	6	2	2	NUM
ejpam-3758	228	7	}	}	PUNCT
ejpam-3758	228	8	which	which	PRON
ejpam-3758	228	9	is	be	AUX
ejpam-3758	228	10	not	not	PART
ejpam-3758	228	11	a	a	DET
ejpam-3758	228	12	µ3	µ3	NOUN
ejpam-3758	228	13	-	-	PUNCT
ejpam-3758	228	14	closed	close	VERB
ejpam-3758	228	15	set	set	NOUN
ejpam-3758	228	16	.	.	PUNCT
ejpam-3758	229	1	so	so	ADV
ejpam-3758	229	2	“	"	PUNCT
ejpam-3758	229	3	clµ1(intµ2(a))\a	clµ1(intµ2(a))\a	NOUN
ejpam-3758	229	4	contains	contain	VERB
ejpam-3758	229	5	no	no	DET
ejpam-3758	229	6	nonempty	nonempty	ADV
ejpam-3758	229	7	µ3	µ3	NOUN
ejpam-3758	229	8	-	-	PUNCT
ejpam-3758	229	9	closed	close	VERB
ejpam-3758	229	10	set	set	NOUN
ejpam-3758	229	11	”	"	PUNCT
ejpam-3758	229	12	is	be	AUX
ejpam-3758	229	13	satisfied	satisfied	ADJ
ejpam-3758	229	14	.	.	PUNCT
ejpam-3758	230	1	thus	thus	ADV
ejpam-3758	230	2	,	,	PUNCT
ejpam-3758	230	3	when	when	SCONJ
ejpam-3758	230	4	a	a	DET
ejpam-3758	230	5	=	=	NOUN
ejpam-3758	230	6	∅	∅	NOUN
ejpam-3758	230	7	the	the	DET
ejpam-3758	230	8	statement	statement	NOUN
ejpam-3758	230	9	“	"	PUNCT
ejpam-3758	230	10	if	if	SCONJ
ejpam-3758	230	11	clµ1(intµ2(a))\a	clµ1(intµ2(a))\a	NOUN
ejpam-3758	230	12	contains	contain	VERB
ejpam-3758	230	13	no	no	DET
ejpam-3758	230	14	nonempty	nonempty	ADV
ejpam-3758	230	15	µ3	µ3	NOUN
ejpam-3758	230	16	-	-	PUNCT
ejpam-3758	230	17	closed	close	VERB
ejpam-3758	230	18	set	set	NOUN
ejpam-3758	230	19	,	,	PUNCT
ejpam-3758	230	20	then	then	ADV
ejpam-3758	230	21	a	a	DET
ejpam-3758	230	22	is	be	AUX
ejpam-3758	230	23	(	(	PUNCT
ejpam-3758	230	24	µ1	µ1	PROPN
ejpam-3758	230	25	,	,	PUNCT
ejpam-3758	230	26	µ2	µ2	ADJ
ejpam-3758	230	27	,	,	PUNCT
ejpam-3758	230	28	µ3)-wg	µ3)-wg	VERB
ejpam-3758	230	29	closed	closed	ADJ
ejpam-3758	230	30	sets	set	NOUN
ejpam-3758	230	31	.	.	PUNCT
ejpam-3758	230	32	”	"	PUNCT
ejpam-3758	230	33	is	be	AUX
ejpam-3758	230	34	false	false	ADJ
ejpam-3758	230	35	.	.	PUNCT
ejpam-3758	231	1	moreover	moreover	ADV
ejpam-3758	231	2	,	,	PUNCT
ejpam-3758	231	3	if	if	SCONJ
ejpam-3758	231	4	a	a	PRON
ejpam-3758	231	5	=	=	X
ejpam-3758	231	6	{	{	PUNCT
ejpam-3758	231	7	3	3	NUM
ejpam-3758	231	8	}	}	PUNCT
ejpam-3758	231	9	,	,	PUNCT
ejpam-3758	231	10	intµ2({3	intµ2({3	PROPN
ejpam-3758	231	11	}	}	PUNCT
ejpam-3758	231	12	)	)	PUNCT
ejpam-3758	232	1	=	=	PUNCT
ejpam-3758	232	2	∅.	∅.	ADP
ejpam-3758	232	3	consequently	consequently	ADV
ejpam-3758	232	4	,	,	PUNCT
ejpam-3758	232	5	clµ1(intµ2({3	clµ1(intµ2({3	ADV
ejpam-3758	232	6	}	}	PUNCT
ejpam-3758	232	7	)	)	PUNCT
ejpam-3758	232	8	)	)	PUNCT
ejpam-3758	233	1	=	=	PRON
ejpam-3758	233	2	{	{	PUNCT
ejpam-3758	233	3	2	2	NUM
ejpam-3758	233	4	}	}	PUNCT
ejpam-3758	233	5	.	.	PUNCT
ejpam-3758	234	1	thus	thus	ADV
ejpam-3758	234	2	,	,	PUNCT
ejpam-3758	234	3	clµ1(intµ2({3}))\{3	clµ1(intµ2({3}))\{3	PROPN
ejpam-3758	234	4	}	}	PUNCT
ejpam-3758	234	5	=	=	SYM
ejpam-3758	234	6	{	{	PUNCT
ejpam-3758	234	7	2	2	NUM
ejpam-3758	234	8	}	}	PUNCT
ejpam-3758	234	9	which	which	PRON
ejpam-3758	234	10	is	be	AUX
ejpam-3758	234	11	not	not	PART
ejpam-3758	234	12	a	a	DET
ejpam-3758	234	13	µ3	µ3	NOUN
ejpam-3758	234	14	-	-	PUNCT
ejpam-3758	234	15	closed	close	VERB
ejpam-3758	234	16	set	set	NOUN
ejpam-3758	234	17	.	.	PUNCT
ejpam-3758	235	1	that	that	PRON
ejpam-3758	235	2	is	be	AUX
ejpam-3758	235	3	,	,	PUNCT
ejpam-3758	235	4	“	"	PUNCT
ejpam-3758	235	5	clµ1(intµ2(a))\a	clµ1(intµ2(a))\a	NOUN
ejpam-3758	235	6	contains	contain	VERB
ejpam-3758	235	7	no	no	DET
ejpam-3758	235	8	nonempty	nonempty	ADV
ejpam-3758	235	9	µ3	µ3	NOUN
ejpam-3758	235	10	-	-	PUNCT
ejpam-3758	235	11	closed	close	VERB
ejpam-3758	235	12	”	"	PUNCT
ejpam-3758	235	13	is	be	AUX
ejpam-3758	235	14	satisfied	satisfied	ADJ
ejpam-3758	235	15	.	.	PUNCT
ejpam-3758	236	1	thus	thus	ADV
ejpam-3758	236	2	,	,	PUNCT
ejpam-3758	236	3	ifa	ifa	PROPN
ejpam-3758	236	4	=	=	PUNCT
ejpam-3758	236	5	{	{	PUNCT
ejpam-3758	236	6	3	3	NUM
ejpam-3758	236	7	}	}	PUNCT
ejpam-3758	236	8	the	the	DET
ejpam-3758	236	9	statement	statement	NOUN
ejpam-3758	236	10	“	"	PUNCT
ejpam-3758	236	11	clµ1(intµ2(a))\a	clµ1(intµ2(a))\a	NOUN
ejpam-3758	236	12	contains	contain	VERB
ejpam-3758	236	13	no	no	DET
ejpam-3758	236	14	nonempty	nonempty	ADV
ejpam-3758	236	15	µ3	µ3	NOUN
ejpam-3758	236	16	-	-	PUNCT
ejpam-3758	236	17	closed	close	VERB
ejpam-3758	236	18	set	set	NOUN
ejpam-3758	236	19	,	,	PUNCT
ejpam-3758	236	20	then	then	ADV
ejpam-3758	236	21	a	a	DET
ejpam-3758	236	22	is	be	AUX
ejpam-3758	236	23	(	(	PUNCT
ejpam-3758	236	24	µ1	µ1	PROPN
ejpam-3758	236	25	,	,	PUNCT
ejpam-3758	236	26	µ2	µ2	ADJ
ejpam-3758	236	27	,	,	PUNCT
ejpam-3758	236	28	µ3)-wg	µ3)-wg	VERB
ejpam-3758	236	29	closed	closed	ADJ
ejpam-3758	236	30	sets	set	NOUN
ejpam-3758	236	31	.	.	PUNCT
ejpam-3758	236	32	”	"	PUNCT
ejpam-3758	236	33	is	be	AUX
ejpam-3758	236	34	false	false	ADJ
ejpam-3758	236	35	.	.	PUNCT
ejpam-3758	236	36	remark	remark	NOUN
ejpam-3758	236	37	1	1	NUM
ejpam-3758	236	38	.	.	PUNCT
ejpam-3758	236	39	states	state	VERB
ejpam-3758	236	40	that	that	SCONJ
ejpam-3758	236	41	the	the	DET
ejpam-3758	236	42	converse	converse	NOUN
ejpam-3758	236	43	of	of	ADP
ejpam-3758	236	44	theorem	theorem	NOUN
ejpam-3758	236	45	11	11	NUM
ejpam-3758	236	46	is	be	AUX
ejpam-3758	236	47	not	not	PART
ejpam-3758	236	48	necessarily	necessarily	ADV
ejpam-3758	236	49	true	true	ADJ
ejpam-3758	236	50	.	.	PUNCT
ejpam-3758	237	1	this	this	PRON
ejpam-3758	237	2	is	be	AUX
ejpam-3758	237	3	illustrated	illustrate	VERB
ejpam-3758	237	4	by	by	ADP
ejpam-3758	237	5	example	example	NOUN
ejpam-3758	237	6	1	1	NUM
ejpam-3758	237	7	.	.	PUNCT
ejpam-3758	238	1	however	however	ADV
ejpam-3758	238	2	,	,	PUNCT
ejpam-3758	238	3	considering	consider	VERB
ejpam-3758	238	4	µ1	µ1	PROPN
ejpam-3758	238	5	⊆	⊆	NUM
ejpam-3758	238	6	µ3	µ3	NOUN
ejpam-3758	238	7	where	where	SCONJ
ejpam-3758	238	8	µ1	µ1	PROPN
ejpam-3758	238	9	and	and	CCONJ
ejpam-3758	238	10	µ3	µ3	NOUN
ejpam-3758	238	11	are	be	AUX
ejpam-3758	238	12	gts	gts	NOUN
ejpam-3758	238	13	in	in	ADP
ejpam-3758	238	14	x	x	NOUN
ejpam-3758	238	15	,	,	PUNCT
ejpam-3758	238	16	then	then	ADV
ejpam-3758	238	17	we	we	PRON
ejpam-3758	238	18	can	can	AUX
ejpam-3758	238	19	consider	consider	VERB
ejpam-3758	238	20	the	the	DET
ejpam-3758	238	21	statement	statement	NOUN
ejpam-3758	238	22	“	"	PUNCT
ejpam-3758	238	23	if	if	SCONJ
ejpam-3758	238	24	clµ1	clµ1	PROPN
ejpam-3758	238	25	(	(	PUNCT
ejpam-3758	238	26	intµ2	intµ2	PROPN
ejpam-3758	238	27	(	(	PUNCT
ejpam-3758	238	28	a))−a	a))−a	PROPN
ejpam-3758	238	29	contains	contain	VERB
ejpam-3758	238	30	no	no	DET
ejpam-3758	238	31	nonempty	nonempty	ADV
ejpam-3758	238	32	µ3	µ3	NOUN
ejpam-3758	238	33	-	-	PUNCT
ejpam-3758	238	34	closed	close	VERB
ejpam-3758	238	35	set	set	NOUN
ejpam-3758	238	36	,	,	PUNCT
ejpam-3758	238	37	then	then	ADV
ejpam-3758	238	38	a	a	PRON
ejpam-3758	238	39	is	be	AUX
ejpam-3758	238	40	(	(	PUNCT
ejpam-3758	238	41	µ1	µ1	PROPN
ejpam-3758	238	42	,	,	PUNCT
ejpam-3758	238	43	µ2	µ2	ADJ
ejpam-3758	238	44	,	,	PUNCT
ejpam-3758	238	45	µ3)-wg	µ3)-wg	PROPN
ejpam-3758	238	46	closed	closed	ADJ
ejpam-3758	238	47	set	set	NOUN
ejpam-3758	238	48	.	.	PUNCT
ejpam-3758	238	49	”	"	PUNCT
ejpam-3758	238	50	theorem	theorem	VERB
ejpam-3758	238	51	12	12	NUM
ejpam-3758	238	52	.	.	PUNCT
ejpam-3758	239	1	let	let	VERB
ejpam-3758	239	2	µ1	µ1	NOUN
ejpam-3758	239	3	⊆	⊆	NUM
ejpam-3758	239	4	µ3	µ3	NOUN
ejpam-3758	239	5	.	.	PUNCT
ejpam-3758	240	1	if	if	SCONJ
ejpam-3758	240	2	clµ1	clµ1	PROPN
ejpam-3758	240	3	(	(	PUNCT
ejpam-3758	240	4	intµ2	intµ2	NOUN
ejpam-3758	240	5	(	(	PUNCT
ejpam-3758	240	6	a	a	NOUN
ejpam-3758	240	7	)	)	PUNCT
ejpam-3758	240	8	)	)	PUNCT
ejpam-3758	240	9	−	−	ADP
ejpam-3758	241	1	a	a	PRON
ejpam-3758	241	2	contains	contain	VERB
ejpam-3758	241	3	no	no	DET
ejpam-3758	241	4	nonempty	nonempty	ADV
ejpam-3758	241	5	µ3	µ3	NOUN
ejpam-3758	241	6	-	-	PUNCT
ejpam-3758	241	7	closed	close	VERB
ejpam-3758	241	8	set	set	NOUN
ejpam-3758	241	9	,	,	PUNCT
ejpam-3758	241	10	then	then	ADV
ejpam-3758	241	11	a	a	PRON
ejpam-3758	241	12	is	be	AUX
ejpam-3758	241	13	(	(	PUNCT
ejpam-3758	241	14	µ1	µ1	PROPN
ejpam-3758	241	15	,	,	PUNCT
ejpam-3758	241	16	µ2	µ2	ADJ
ejpam-3758	241	17	,	,	PUNCT
ejpam-3758	241	18	µ3)-wg	µ3)-wg	NOUN
ejpam-3758	241	19	closed	close	VERB
ejpam-3758	241	20	set	set	NOUN
ejpam-3758	241	21	.	.	PUNCT
ejpam-3758	242	1	proof	proof	NOUN
ejpam-3758	242	2	.	.	PUNCT
ejpam-3758	243	1	let	let	VERB
ejpam-3758	243	2	a	a	DET
ejpam-3758	243	3	⊆	⊆	NUM
ejpam-3758	243	4	x.	x.	NOUN
ejpam-3758	243	5	suppose	suppose	VERB
ejpam-3758	243	6	clµ1	clµ1	PROPN
ejpam-3758	243	7	(	(	PUNCT
ejpam-3758	243	8	intµ2	intµ2	PROPN
ejpam-3758	243	9	(	(	PUNCT
ejpam-3758	243	10	a))−a	a))−a	PROPN
ejpam-3758	243	11	contains	contain	VERB
ejpam-3758	243	12	no	no	DET
ejpam-3758	243	13	nonempty	nonempty	ADV
ejpam-3758	243	14	µ3	µ3	NOUN
ejpam-3758	243	15	-	-	PUNCT
ejpam-3758	243	16	closed	close	VERB
ejpam-3758	243	17	set	set	NOUN
ejpam-3758	243	18	and	and	CCONJ
ejpam-3758	243	19	a	a	PRON
ejpam-3758	243	20	is	be	AUX
ejpam-3758	243	21	not	not	PART
ejpam-3758	243	22	a	a	DET
ejpam-3758	243	23	(	(	PUNCT
ejpam-3758	243	24	µ1	µ1	PROPN
ejpam-3758	243	25	,	,	PUNCT
ejpam-3758	243	26	µ2	µ2	ADJ
ejpam-3758	243	27	,	,	PUNCT
ejpam-3758	243	28	µ3)-wg	µ3)-wg	NOUN
ejpam-3758	243	29	closed	closed	ADJ
ejpam-3758	243	30	set	set	NOUN
ejpam-3758	243	31	.	.	PUNCT
ejpam-3758	244	1	then	then	ADV
ejpam-3758	244	2	there	there	PRON
ejpam-3758	244	3	exists	exist	VERB
ejpam-3758	244	4	µ3	µ3	NOUN
ejpam-3758	244	5	-	-	PUNCT
ejpam-3758	244	6	open	open	ADV
ejpam-3758	244	7	set	set	VERB
ejpam-3758	244	8	u	u	PRON
ejpam-3758	244	9	such	such	ADJ
ejpam-3758	244	10	that	that	SCONJ
ejpam-3758	244	11	a	a	DET
ejpam-3758	244	12	⊆	⊆	NUM
ejpam-3758	244	13	u	u	NOUN
ejpam-3758	244	14	and	and	CCONJ
ejpam-3758	244	15	clµ1	clµ1	PROPN
ejpam-3758	244	16	(	(	PUNCT
ejpam-3758	244	17	intµ2	intµ2	NOUN
ejpam-3758	244	18	(	(	PUNCT
ejpam-3758	244	19	a	a	NOUN
ejpam-3758	244	20	)	)	PUNCT
ejpam-3758	244	21	)	)	PUNCT
ejpam-3758	245	1	*	*	PUNCT
ejpam-3758	245	2	u	u	NOUN
ejpam-3758	245	3	.	.	PUNCT
ejpam-3758	246	1	now	now	ADV
ejpam-3758	246	2	,	,	PUNCT
ejpam-3758	246	3	clµ1	clµ1	PROPN
ejpam-3758	246	4	(	(	PUNCT
ejpam-3758	246	5	intµ2	intµ2	NOUN
ejpam-3758	246	6	(	(	PUNCT
ejpam-3758	246	7	a	a	NOUN
ejpam-3758	246	8	)	)	PUNCT
ejpam-3758	246	9	)	)	PUNCT
ejpam-3758	247	1	*	*	PUNCT
ejpam-3758	247	2	u	u	NOUN
ejpam-3758	247	3	implies	imply	VERB
ejpam-3758	247	4	that	that	DET
ejpam-3758	247	5	clµ1	clµ1	PROPN
ejpam-3758	247	6	(	(	PUNCT
ejpam-3758	247	7	intµ2	intµ2	NOUN
ejpam-3758	247	8	(	(	PUNCT
ejpam-3758	247	9	a	a	NOUN
ejpam-3758	247	10	)	)	PUNCT
ejpam-3758	247	11	)	)	PUNCT
ejpam-3758	248	1	⋂	⋂	PROPN
ejpam-3758	248	2	u	u	X
ejpam-3758	248	3	c	c	PROPN
ejpam-3758	248	4	6=	6=	ADP
ejpam-3758	248	5	∅.	∅.	ADV
ejpam-3758	248	6	let	let	VERB
ejpam-3758	248	7	f	f	NOUN
ejpam-3758	248	8	=	=	PUNCT
ejpam-3758	248	9	clµ1	clµ1	PROPN
ejpam-3758	248	10	(	(	PUNCT
ejpam-3758	248	11	intµ2	intµ2	NOUN
ejpam-3758	248	12	(	(	PUNCT
ejpam-3758	248	13	a	a	NOUN
ejpam-3758	248	14	)	)	PUNCT
ejpam-3758	248	15	)	)	PUNCT
ejpam-3758	249	1	⋂	⋂	PROPN
ejpam-3758	249	2	u	u	PROPN
ejpam-3758	249	3	c.	c.	PROPN
ejpam-3758	249	4	by	by	ADP
ejpam-3758	249	5	theorem	theorem	ADJ
ejpam-3758	249	6	3(ii	3(ii	NUM
ejpam-3758	249	7	.	.	PUNCT
ejpam-3758	249	8	)	)	PUNCT
ejpam-3758	250	1	,	,	PUNCT
ejpam-3758	250	2	clµ1	clµ1	PROPN
ejpam-3758	250	3	(	(	PUNCT
ejpam-3758	250	4	intµ2	intµ2	NOUN
ejpam-3758	250	5	(	(	PUNCT
ejpam-3758	250	6	a	a	NOUN
ejpam-3758	250	7	)	)	PUNCT
ejpam-3758	250	8	)	)	PUNCT
ejpam-3758	250	9	is	be	AUX
ejpam-3758	250	10	µ1	µ1	NOUN
ejpam-3758	250	11	-	-	PUNCT
ejpam-3758	250	12	closed	closed	ADJ
ejpam-3758	250	13	.	.	PUNCT
ejpam-3758	251	1	since	since	SCONJ
ejpam-3758	251	2	µ1	µ1	PROPN
ejpam-3758	251	3	⊆	⊆	NUM
ejpam-3758	251	4	µ3	µ3	NOUN
ejpam-3758	251	5	,	,	PUNCT
ejpam-3758	251	6	references	reference	NOUN
ejpam-3758	251	7	985	985	NUM
ejpam-3758	251	8	applying	apply	VERB
ejpam-3758	251	9	theorem	theorem	NOUN
ejpam-3758	251	10	4	4	NUM
ejpam-3758	251	11	,	,	PUNCT
ejpam-3758	251	12	clµ1	clµ1	NOUN
ejpam-3758	251	13	(	(	PUNCT
ejpam-3758	251	14	intµ2	intµ2	NOUN
ejpam-3758	251	15	(	(	PUNCT
ejpam-3758	251	16	a	a	NOUN
ejpam-3758	251	17	)	)	PUNCT
ejpam-3758	251	18	)	)	PUNCT
ejpam-3758	251	19	is	be	AUX
ejpam-3758	251	20	µ3	µ3	NOUN
ejpam-3758	251	21	-	-	PUNCT
ejpam-3758	251	22	closed	closed	ADJ
ejpam-3758	251	23	.	.	PUNCT
ejpam-3758	252	1	thus	thus	ADV
ejpam-3758	252	2	since	since	SCONJ
ejpam-3758	252	3	u	u	PROPN
ejpam-3758	252	4	c	c	PROPN
ejpam-3758	252	5	is	be	AUX
ejpam-3758	252	6	µ3	µ3	NOUN
ejpam-3758	252	7	-	-	PUNCT
ejpam-3758	252	8	closed	close	VERB
ejpam-3758	252	9	and	and	CCONJ
ejpam-3758	252	10	using	use	VERB
ejpam-3758	252	11	theorem	theorem	NOUN
ejpam-3758	252	12	1	1	NUM
ejpam-3758	252	13	,	,	PUNCT
ejpam-3758	252	14	f	f	PROPN
ejpam-3758	252	15	=	=	PUNCT
ejpam-3758	252	16	clµ1	clµ1	PROPN
ejpam-3758	252	17	(	(	PUNCT
ejpam-3758	252	18	intµ2	intµ2	NOUN
ejpam-3758	252	19	(	(	PUNCT
ejpam-3758	252	20	a	a	NOUN
ejpam-3758	252	21	)	)	PUNCT
ejpam-3758	252	22	)	)	PUNCT
ejpam-3758	253	1	⋂	⋂	PROPN
ejpam-3758	253	2	u	u	NOUN
ejpam-3758	253	3	c	c	PROPN
ejpam-3758	253	4	is	be	AUX
ejpam-3758	253	5	µ3	µ3	NOUN
ejpam-3758	253	6	-	-	PUNCT
ejpam-3758	253	7	closed	closed	ADJ
ejpam-3758	253	8	.	.	PUNCT
ejpam-3758	254	1	now	now	ADV
ejpam-3758	254	2	,	,	PUNCT
ejpam-3758	254	3	f	f	PROPN
ejpam-3758	254	4	6=	6=	PROPN
ejpam-3758	254	5	∅	∅	NOUN
ejpam-3758	254	6	and	and	CCONJ
ejpam-3758	254	7	f	f	NOUN
ejpam-3758	254	8	=	=	SYM
ejpam-3758	254	9	clµ1	clµ1	PROPN
ejpam-3758	254	10	(	(	PUNCT
ejpam-3758	254	11	intµ2	intµ2	NOUN
ejpam-3758	254	12	(	(	PUNCT
ejpam-3758	254	13	a	a	NOUN
ejpam-3758	254	14	)	)	PUNCT
ejpam-3758	254	15	)	)	PUNCT
ejpam-3758	255	1	⋂	⋂	PROPN
ejpam-3758	255	2	u	u	NOUN
ejpam-3758	255	3	c	c	PROPN
ejpam-3758	255	4	⊆	⊆	NUM
ejpam-3758	255	5	clµ1	clµ1	NOUN
ejpam-3758	255	6	(	(	PUNCT
ejpam-3758	255	7	intµ2	intµ2	NOUN
ejpam-3758	255	8	(	(	PUNCT
ejpam-3758	255	9	a	a	NOUN
ejpam-3758	255	10	)	)	PUNCT
ejpam-3758	255	11	)	)	PUNCT
ejpam-3758	256	1	⋂	⋂	PROPN
ejpam-3758	256	2	ac	ac	PROPN
ejpam-3758	256	3	=	=	PROPN
ejpam-3758	256	4	clµ1	clµ1	PROPN
ejpam-3758	256	5	(	(	PUNCT
ejpam-3758	256	6	intµ2	intµ2	PROPN
ejpam-3758	256	7	(	(	PUNCT
ejpam-3758	256	8	a))−a	a))−a	PROPN
ejpam-3758	256	9	.	.	PUNCT
ejpam-3758	257	1	this	this	PRON
ejpam-3758	257	2	is	be	AUX
ejpam-3758	257	3	a	a	DET
ejpam-3758	257	4	contradiction	contradiction	NOUN
ejpam-3758	257	5	.	.	PUNCT
ejpam-3758	258	1	therefore	therefore	ADV
ejpam-3758	258	2	,	,	PUNCT
ejpam-3758	258	3	if	if	SCONJ
ejpam-3758	258	4	clµ1	clµ1	PROPN
ejpam-3758	258	5	(	(	PUNCT
ejpam-3758	258	6	intµ2	intµ2	NOUN
ejpam-3758	258	7	(	(	PUNCT
ejpam-3758	258	8	a))−	a))−	ADP
ejpam-3758	258	9	a	a	DET
ejpam-3758	258	10	contains	contain	VERB
ejpam-3758	258	11	no	no	DET
ejpam-3758	258	12	nonempty	nonempty	ADV
ejpam-3758	258	13	µ3	µ3	NOUN
ejpam-3758	258	14	-	-	PUNCT
ejpam-3758	258	15	closed	close	VERB
ejpam-3758	258	16	set	set	NOUN
ejpam-3758	258	17	,	,	PUNCT
ejpam-3758	258	18	then	then	ADV
ejpam-3758	258	19	a	a	PRON
ejpam-3758	258	20	is	be	AUX
ejpam-3758	258	21	(	(	PUNCT
ejpam-3758	258	22	µ1	µ1	PROPN
ejpam-3758	258	23	,	,	PUNCT
ejpam-3758	258	24	µ2	µ2	ADJ
ejpam-3758	258	25	,	,	PUNCT
ejpam-3758	258	26	µ3)-wg	µ3)-wg	PROPN
ejpam-3758	258	27	closed	close	VERB
ejpam-3758	258	28	set	set	NOUN
ejpam-3758	258	29	.	.	PUNCT
ejpam-3758	259	1	theorem	theorem	VERB
ejpam-3758	259	2	13	13	NUM
ejpam-3758	259	3	.	.	PUNCT
ejpam-3758	260	1	if	if	SCONJ
ejpam-3758	260	2	a	a	PRON
ejpam-3758	260	3	be	be	AUX
ejpam-3758	260	4	µ1	µ1	NOUN
ejpam-3758	260	5	-	-	PUNCT
ejpam-3758	260	6	closed	closed	ADJ
ejpam-3758	260	7	and	and	CCONJ
ejpam-3758	260	8	µ2	µ2	ADJ
ejpam-3758	260	9	-	-	PUNCT
ejpam-3758	260	10	open	open	ADJ
ejpam-3758	260	11	,	,	PUNCT
ejpam-3758	260	12	then	then	ADV
ejpam-3758	260	13	a	a	DET
ejpam-3758	260	14	is	be	AUX
ejpam-3758	260	15	(	(	PUNCT
ejpam-3758	260	16	µ1	µ1	PROPN
ejpam-3758	260	17	,	,	PUNCT
ejpam-3758	260	18	µ2	µ2	ADJ
ejpam-3758	260	19	,	,	PUNCT
ejpam-3758	260	20	µ3)-wg	µ3)-wg	NOUN
ejpam-3758	260	21	closed	close	VERB
ejpam-3758	260	22	set	set	NOUN
ejpam-3758	260	23	.	.	PUNCT
ejpam-3758	261	1	proof	proof	NOUN
ejpam-3758	261	2	.	.	PUNCT
ejpam-3758	262	1	let	let	VERB
ejpam-3758	262	2	a	a	DET
ejpam-3758	262	3	⊆	⊆	NUM
ejpam-3758	262	4	u	u	NOUN
ejpam-3758	262	5	such	such	ADJ
ejpam-3758	262	6	that	that	SCONJ
ejpam-3758	262	7	a	a	PRON
ejpam-3758	262	8	is	be	AUX
ejpam-3758	262	9	both	both	PRON
ejpam-3758	262	10	µ1	µ1	NOUN
ejpam-3758	262	11	-	-	PUNCT
ejpam-3758	262	12	closed	closed	ADJ
ejpam-3758	262	13	and	and	CCONJ
ejpam-3758	262	14	µ2	µ2	ADJ
ejpam-3758	262	15	-	-	PUNCT
ejpam-3758	262	16	open	open	ADJ
ejpam-3758	262	17	,	,	PUNCT
ejpam-3758	262	18	and	and	CCONJ
ejpam-3758	262	19	u	u	NOUN
ejpam-3758	262	20	is	be	AUX
ejpam-3758	262	21	µ3	µ3	NOUN
ejpam-3758	262	22	-	-	PUNCT
ejpam-3758	262	23	open	open	ADJ
ejpam-3758	262	24	such	such	ADJ
ejpam-3758	262	25	that	that	SCONJ
ejpam-3758	262	26	a	a	DET
ejpam-3758	262	27	⊆	⊆	NUM
ejpam-3758	262	28	u	u	NOUN
ejpam-3758	262	29	.	.	PUNCT
ejpam-3758	263	1	since	since	SCONJ
ejpam-3758	263	2	a	a	PRON
ejpam-3758	263	3	is	be	AUX
ejpam-3758	263	4	µ2	µ2	ADJ
ejpam-3758	263	5	-	-	PUNCT
ejpam-3758	263	6	open	open	ADJ
ejpam-3758	263	7	and	and	CCONJ
ejpam-3758	263	8	µ1	µ1	NOUN
ejpam-3758	263	9	-	-	PUNCT
ejpam-3758	263	10	closed	closed	ADJ
ejpam-3758	263	11	,	,	PUNCT
ejpam-3758	263	12	then	then	ADV
ejpam-3758	263	13	applying	apply	VERB
ejpam-3758	263	14	theorem	theorem	ADJ
ejpam-3758	263	15	2(iii	2(iii	NOUN
ejpam-3758	263	16	.	.	PUNCT
ejpam-3758	263	17	)	)	PUNCT
ejpam-3758	264	1	and	and	CCONJ
ejpam-3758	264	2	theorem	theorem	VERB
ejpam-3758	264	3	3(iii	3(iii	NUM
ejpam-3758	264	4	.	.	PUNCT
ejpam-3758	264	5	)	)	PUNCT
ejpam-3758	264	6	,	,	PUNCT
ejpam-3758	264	7	intµ2(a	intµ2(a	NOUN
ejpam-3758	264	8	)	)	PUNCT
ejpam-3758	264	9	=	=	SYM
ejpam-3758	264	10	a	a	PRON
ejpam-3758	264	11	and	and	CCONJ
ejpam-3758	264	12	clµ1(a	clµ1(a	NUM
ejpam-3758	264	13	)	)	PUNCT
ejpam-3758	265	1	=	=	SYM
ejpam-3758	265	2	a.	a.	NOUN
ejpam-3758	265	3	thus	thus	ADV
ejpam-3758	265	4	,	,	PUNCT
ejpam-3758	265	5	clµ1	clµ1	PROPN
ejpam-3758	265	6	(	(	PUNCT
ejpam-3758	265	7	intµ2	intµ2	NOUN
ejpam-3758	265	8	(	(	PUNCT
ejpam-3758	265	9	a	a	NOUN
ejpam-3758	265	10	)	)	PUNCT
ejpam-3758	265	11	)	)	PUNCT
ejpam-3758	266	1	=	=	SYM
ejpam-3758	266	2	clµ1	clµ1	NOUN
ejpam-3758	266	3	(	(	PUNCT
ejpam-3758	266	4	a	a	X
ejpam-3758	266	5	)	)	PUNCT
ejpam-3758	266	6	=	=	SYM
ejpam-3758	266	7	a.	a.	NOUN
ejpam-3758	266	8	in	in	ADP
ejpam-3758	266	9	effect	effect	NOUN
ejpam-3758	266	10	,	,	PUNCT
ejpam-3758	266	11	clµ1	clµ1	PROPN
ejpam-3758	266	12	(	(	PUNCT
ejpam-3758	266	13	intµ2	intµ2	NOUN
ejpam-3758	266	14	(	(	PUNCT
ejpam-3758	266	15	a	a	NOUN
ejpam-3758	266	16	)	)	PUNCT
ejpam-3758	266	17	)	)	PUNCT
ejpam-3758	266	18	⊆	⊆	NUM
ejpam-3758	266	19	u	u	NOUN
ejpam-3758	266	20	.	.	PUNCT
ejpam-3758	267	1	hence	hence	ADV
ejpam-3758	267	2	,	,	PUNCT
ejpam-3758	267	3	a	a	PRON
ejpam-3758	267	4	is	be	AUX
ejpam-3758	267	5	(	(	PUNCT
ejpam-3758	267	6	µ1	µ1	PROPN
ejpam-3758	267	7	,	,	PUNCT
ejpam-3758	267	8	µ2	µ2	ADJ
ejpam-3758	267	9	,	,	PUNCT
ejpam-3758	267	10	µ3)-wg	µ3)-wg	NOUN
ejpam-3758	267	11	closed	closed	ADJ
ejpam-3758	267	12	set	set	NOUN
ejpam-3758	267	13	.	.	PUNCT
ejpam-3758	268	1	definition	definition	NOUN
ejpam-3758	268	2	8	8	NUM
ejpam-3758	268	3	.	.	PUNCT
ejpam-3758	269	1	let	let	VERB
ejpam-3758	269	2	a	a	DET
ejpam-3758	269	3	⊆	⊆	NUM
ejpam-3758	269	4	y	y	SYM
ejpam-3758	269	5	⊆	⊆	NUM
ejpam-3758	269	6	x.then	x.then	NOUN
ejpam-3758	270	1	a	a	PRON
ejpam-3758	270	2	is	be	AUX
ejpam-3758	270	3	(	(	PUNCT
ejpam-3758	270	4	µ1	µ1	PROPN
ejpam-3758	270	5	,	,	PUNCT
ejpam-3758	270	6	µ2	µ2	ADJ
ejpam-3758	270	7	,	,	PUNCT
ejpam-3758	270	8	µ3)-wg	µ3)-wg	NOUN
ejpam-3758	270	9	closed	close	VERB
ejpam-3758	270	10	set	set	VERB
ejpam-3758	270	11	in	in	ADP
ejpam-3758	270	12	y	y	PROPN
ejpam-3758	270	13	if	if	SCONJ
ejpam-3758	270	14	clµ1	clµ1	PROPN
ejpam-3758	270	15	(	(	PUNCT
ejpam-3758	270	16	intµ2	intµ2	NOUN
ejpam-3758	270	17	(	(	PUNCT
ejpam-3758	270	18	a	a	NOUN
ejpam-3758	270	19	)	)	PUNCT
ejpam-3758	270	20	)	)	PUNCT
ejpam-3758	271	1	⊆	⊆	X
ejpam-3758	271	2	u	u	NOUN
ejpam-3758	271	3	whenever	whenever	SCONJ
ejpam-3758	271	4	a	a	DET
ejpam-3758	271	5	⊆	⊆	NUM
ejpam-3758	271	6	u	u	NOUN
ejpam-3758	271	7	and	and	CCONJ
ejpam-3758	271	8	u	u	NOUN
ejpam-3758	271	9	is	be	AUX
ejpam-3758	271	10	µ3	µ3	NOUN
ejpam-3758	271	11	-	-	PUNCT
ejpam-3758	271	12	open	open	ADJ
ejpam-3758	271	13	in	in	ADP
ejpam-3758	271	14	y	y	PROPN
ejpam-3758	271	15	.	.	PUNCT
ejpam-3758	271	16	theorem	theorem	PROPN
ejpam-3758	271	17	14	14	NUM
ejpam-3758	271	18	.	.	PUNCT
ejpam-3758	272	1	let	let	VERB
ejpam-3758	272	2	x	x	SYM
ejpam-3758	272	3	6=	6=	ADP
ejpam-3758	272	4	∅	∅	NOUN
ejpam-3758	272	5	and	and	CCONJ
ejpam-3758	272	6	a	a	DET
ejpam-3758	272	7	⊆	⊆	NUM
ejpam-3758	272	8	y	y	SYM
ejpam-3758	272	9	⊆	⊆	NUM
ejpam-3758	272	10	x.	x.	NOUN
ejpam-3758	272	11	if	if	SCONJ
ejpam-3758	272	12	a	a	PRON
ejpam-3758	272	13	is	be	AUX
ejpam-3758	272	14	(	(	PUNCT
ejpam-3758	272	15	µ1	µ1	PROPN
ejpam-3758	272	16	,	,	PUNCT
ejpam-3758	272	17	µ2	µ2	ADJ
ejpam-3758	272	18	,	,	PUNCT
ejpam-3758	272	19	µ3)-wg	µ3)-wg	NOUN
ejpam-3758	272	20	closed	close	VERB
ejpam-3758	272	21	set	set	VERB
ejpam-3758	272	22	in	in	ADP
ejpam-3758	272	23	x	x	PUNCT
ejpam-3758	272	24	and	and	CCONJ
ejpam-3758	272	25	y	y	PROPN
ejpam-3758	272	26	is	be	AUX
ejpam-3758	272	27	µ1	µ1	ADV
ejpam-3758	272	28	-	-	PUNCT
ejpam-3758	272	29	closed	close	VERB
ejpam-3758	272	30	set	set	NOUN
ejpam-3758	272	31	in	in	ADP
ejpam-3758	272	32	x	x	NOUN
ejpam-3758	272	33	,	,	PUNCT
ejpam-3758	272	34	then	then	ADV
ejpam-3758	272	35	a	a	DET
ejpam-3758	272	36	is	be	AUX
ejpam-3758	272	37	(	(	PUNCT
ejpam-3758	272	38	µ1	µ1	PROPN
ejpam-3758	272	39	,	,	PUNCT
ejpam-3758	272	40	µ2	µ2	ADJ
ejpam-3758	272	41	,	,	PUNCT
ejpam-3758	272	42	µ3)-wg	µ3)-wg	NOUN
ejpam-3758	272	43	closed	close	VERB
ejpam-3758	272	44	set	set	VERB
ejpam-3758	272	45	in	in	ADP
ejpam-3758	272	46	y	y	PROPN
ejpam-3758	272	47	.	.	PUNCT
ejpam-3758	273	1	proof	proof	NOUN
ejpam-3758	273	2	.	.	PUNCT
ejpam-3758	274	1	let	let	VERB
ejpam-3758	274	2	a	a	DET
ejpam-3758	274	3	⊆	⊆	NUM
ejpam-3758	274	4	u	u	NOUN
ejpam-3758	274	5	such	such	ADJ
ejpam-3758	274	6	that	that	SCONJ
ejpam-3758	274	7	u	u	PROPN
ejpam-3758	274	8	is	be	AUX
ejpam-3758	274	9	µ3	µ3	NOUN
ejpam-3758	274	10	-	-	PUNCT
ejpam-3758	274	11	open	open	ADJ
ejpam-3758	274	12	in	in	ADP
ejpam-3758	274	13	y	y	PROPN
ejpam-3758	274	14	.	.	PUNCT
ejpam-3758	275	1	then	then	ADV
ejpam-3758	275	2	u	u	X
ejpam-3758	275	3	=	=	PROPN
ejpam-3758	275	4	y	y	PROPN
ejpam-3758	275	5	⋂	⋂	PROPN
ejpam-3758	275	6	g	g	NOUN
ejpam-3758	275	7	for	for	ADP
ejpam-3758	275	8	some	some	DET
ejpam-3758	275	9	µ3	µ3	NOUN
ejpam-3758	275	10	-	-	PUNCT
ejpam-3758	275	11	open	open	NOUN
ejpam-3758	275	12	set	set	VERB
ejpam-3758	275	13	g	g	NOUN
ejpam-3758	275	14	in	in	ADP
ejpam-3758	275	15	x.	x.	PROPN
ejpam-3758	275	16	note	note	VERB
ejpam-3758	275	17	that	that	SCONJ
ejpam-3758	275	18	a	a	DET
ejpam-3758	275	19	⊆	⊆	NUM
ejpam-3758	275	20	g.	g.	NOUN
ejpam-3758	275	21	since	since	SCONJ
ejpam-3758	275	22	a	a	DET
ejpam-3758	275	23	is	is	NOUN
ejpam-3758	275	24	(	(	PUNCT
ejpam-3758	275	25	µ1	µ1	PROPN
ejpam-3758	275	26	,	,	PUNCT
ejpam-3758	275	27	µ2	µ2	ADJ
ejpam-3758	275	28	,	,	PUNCT
ejpam-3758	275	29	µ3)-wg	µ3)-wg	NOUN
ejpam-3758	275	30	closed	close	VERB
ejpam-3758	275	31	in	in	ADP
ejpam-3758	275	32	x	x	NOUN
ejpam-3758	275	33	,	,	PUNCT
ejpam-3758	275	34	then	then	ADV
ejpam-3758	275	35	clµ1	clµ1	PROPN
ejpam-3758	275	36	(	(	PUNCT
ejpam-3758	275	37	intµ2	intµ2	NOUN
ejpam-3758	275	38	(	(	PUNCT
ejpam-3758	275	39	a	a	NOUN
ejpam-3758	275	40	)	)	PUNCT
ejpam-3758	275	41	)	)	PUNCT
ejpam-3758	276	1	⊆	⊆	NUM
ejpam-3758	276	2	g.	g.	NOUN
ejpam-3758	276	3	now	now	ADV
ejpam-3758	276	4	,	,	PUNCT
ejpam-3758	276	5	by	by	ADP
ejpam-3758	276	6	theorem	theorem	NOUN
ejpam-3758	276	7	2(i	2(i	NUM
ejpam-3758	276	8	.	.	PUNCT
ejpam-3758	276	9	)	)	PUNCT
ejpam-3758	276	10	,	,	PUNCT
ejpam-3758	276	11	intµ2	intµ2	NOUN
ejpam-3758	276	12	(	(	PUNCT
ejpam-3758	276	13	a	a	X
ejpam-3758	276	14	)	)	PUNCT
ejpam-3758	276	15	⊆	⊆	NUM
ejpam-3758	276	16	a.	a.	NOUN
ejpam-3758	276	17	since	since	SCONJ
ejpam-3758	276	18	a	a	DET
ejpam-3758	276	19	⊆	⊆	NUM
ejpam-3758	276	20	y	y	PROPN
ejpam-3758	276	21	,	,	PUNCT
ejpam-3758	276	22	intµ2	intµ2	PROPN
ejpam-3758	276	23	(	(	PUNCT
ejpam-3758	276	24	a	a	X
ejpam-3758	276	25	)	)	PUNCT
ejpam-3758	276	26	⊆	⊆	NUM
ejpam-3758	276	27	y	y	NOUN
ejpam-3758	276	28	.	.	PUNCT
ejpam-3758	277	1	by	by	ADP
ejpam-3758	277	2	theorem	theorem	NOUN
ejpam-3758	277	3	3(iv	3(iv	NUM
ejpam-3758	277	4	.	.	PUNCT
ejpam-3758	277	5	)	)	PUNCT
ejpam-3758	277	6	,	,	PUNCT
ejpam-3758	277	7	clµ1	clµ1	PROPN
ejpam-3758	277	8	(	(	PUNCT
ejpam-3758	277	9	intµ2	intµ2	NOUN
ejpam-3758	277	10	(	(	PUNCT
ejpam-3758	277	11	a	a	NOUN
ejpam-3758	277	12	)	)	PUNCT
ejpam-3758	277	13	)	)	PUNCT
ejpam-3758	277	14	⊆	⊆	NUM
ejpam-3758	277	15	clµ1	clµ1	NOUN
ejpam-3758	277	16	(	(	PUNCT
ejpam-3758	277	17	y	y	PROPN
ejpam-3758	277	18	)	)	PUNCT
ejpam-3758	277	19	.	.	PUNCT
ejpam-3758	278	1	but	but	CCONJ
ejpam-3758	278	2	y	y	PROPN
ejpam-3758	278	3	is	be	AUX
ejpam-3758	278	4	µ1	µ1	NOUN
ejpam-3758	278	5	-	-	PUNCT
ejpam-3758	278	6	closed	closed	ADJ
ejpam-3758	278	7	,	,	PUNCT
ejpam-3758	278	8	so	so	ADV
ejpam-3758	278	9	clµ1	clµ1	PROPN
ejpam-3758	278	10	(	(	PUNCT
ejpam-3758	278	11	y	y	PROPN
ejpam-3758	278	12	)	)	PUNCT
ejpam-3758	279	1	=	=	SYM
ejpam-3758	279	2	y	y	PROPN
ejpam-3758	279	3	.	.	PUNCT
ejpam-3758	280	1	thus	thus	ADV
ejpam-3758	280	2	,	,	PUNCT
ejpam-3758	280	3	clµ1	clµ1	PROPN
ejpam-3758	280	4	(	(	PUNCT
ejpam-3758	280	5	intµ2	intµ2	NOUN
ejpam-3758	280	6	(	(	PUNCT
ejpam-3758	280	7	a	a	NOUN
ejpam-3758	280	8	)	)	PUNCT
ejpam-3758	280	9	)	)	PUNCT
ejpam-3758	281	1	⊆	⊆	NUM
ejpam-3758	281	2	y	y	PROPN
ejpam-3758	281	3	.	.	PUNCT
ejpam-3758	282	1	accordingly	accordingly	ADV
ejpam-3758	282	2	,	,	PUNCT
ejpam-3758	282	3	clµ1	clµ1	PROPN
ejpam-3758	282	4	(	(	PUNCT
ejpam-3758	282	5	intµ2	intµ2	NOUN
ejpam-3758	282	6	(	(	PUNCT
ejpam-3758	282	7	a	a	NOUN
ejpam-3758	282	8	)	)	PUNCT
ejpam-3758	282	9	)	)	PUNCT
ejpam-3758	283	1	=	=	SYM
ejpam-3758	283	2	clµ1	clµ1	NOUN
ejpam-3758	283	3	(	(	PUNCT
ejpam-3758	283	4	intµ2	intµ2	NOUN
ejpam-3758	283	5	(	(	PUNCT
ejpam-3758	283	6	a	a	NOUN
ejpam-3758	283	7	)	)	PUNCT
ejpam-3758	283	8	)	)	PUNCT
ejpam-3758	284	1	⋂	⋂	PROPN
ejpam-3758	284	2	y	y	PROPN
ejpam-3758	284	3	⊆	⊆	NUM
ejpam-3758	284	4	g	g	PROPN
ejpam-3758	284	5	⋂	⋂	PROPN
ejpam-3758	284	6	y	y	PROPN
ejpam-3758	284	7	=	=	PROPN
ejpam-3758	284	8	u	u	PROPN
ejpam-3758	284	9	.	.	PUNCT
ejpam-3758	285	1	therefore	therefore	ADV
ejpam-3758	285	2	,	,	PUNCT
ejpam-3758	285	3	a	a	DET
ejpam-3758	285	4	is	be	AUX
ejpam-3758	285	5	(	(	PUNCT
ejpam-3758	285	6	µ1	µ1	PROPN
ejpam-3758	285	7	,	,	PUNCT
ejpam-3758	285	8	µ2	µ2	ADJ
ejpam-3758	285	9	,	,	PUNCT
ejpam-3758	285	10	µ3)-wg	µ3)-wg	NOUN
ejpam-3758	285	11	closed	close	VERB
ejpam-3758	285	12	set	set	VERB
ejpam-3758	285	13	in	in	ADP
ejpam-3758	285	14	y	y	PROPN
ejpam-3758	285	15	.	.	PUNCT
ejpam-3758	286	1	acknowledgements	acknowledgement	NOUN
ejpam-3758	286	2	the	the	DET
ejpam-3758	286	3	authors	author	NOUN
ejpam-3758	286	4	would	would	AUX
ejpam-3758	286	5	like	like	VERB
ejpam-3758	286	6	to	to	PART
ejpam-3758	286	7	express	express	VERB
ejpam-3758	286	8	their	their	PRON
ejpam-3758	286	9	thanks	thank	NOUN
ejpam-3758	286	10	to	to	ADP
ejpam-3758	286	11	the	the	DET
ejpam-3758	286	12	referees	referee	NOUN
ejpam-3758	286	13	who	who	PRON
ejpam-3758	286	14	gave	give	VERB
ejpam-3758	286	15	their	their	PRON
ejpam-3758	286	16	suggestions	suggestion	NOUN
ejpam-3758	286	17	for	for	ADP
ejpam-3758	286	18	the	the	DET
ejpam-3758	286	19	improvement	improvement	NOUN
ejpam-3758	286	20	of	of	ADP
ejpam-3758	286	21	the	the	DET
ejpam-3758	286	22	paper	paper	NOUN
ejpam-3758	286	23	.	.	PUNCT
ejpam-3758	287	1	references	reference	NOUN
ejpam-3758	287	2	[	[	X
ejpam-3758	287	3	1	1	NUM
ejpam-3758	287	4	]	]	X
ejpam-3758	287	5	fm	fm	PROPN
ejpam-3758	287	6	valenzuela	valenzuela	PROPN
ejpam-3758	287	7	and	and	CCONJ
ejpam-3758	287	8	h	h	PROPN
ejpam-3758	287	9	rara	rara	NOUN
ejpam-3758	287	10	.	.	PUNCT
ejpam-3758	288	1	µ-rgb	µ-rgb	NOUN
ejpam-3758	288	2	-	-	NOUN
ejpam-3758	288	3	sets	set	NOUN
ejpam-3758	288	4	in	in	ADP
ejpam-3758	288	5	a	a	DET
ejpam-3758	288	6	generalized	generalized	ADJ
ejpam-3758	288	7	topological	topological	ADJ
ejpam-3758	288	8	space	space	NOUN
ejpam-3758	288	9	.	.	PUNCT
ejpam-3758	289	1	international	international	ADJ
ejpam-3758	289	2	journal	journal	PROPN
ejpam-3758	289	3	of	of	ADP
ejpam-3758	289	4	mathematical	mathematical	ADJ
ejpam-3758	289	5	analysis	analysis	NOUN
ejpam-3758	289	6	,	,	PUNCT
ejpam-3758	289	7	volume	volume	NOUN
ejpam-3758	289	8	8	8	NUM
ejpam-3758	289	9	,	,	PUNCT
ejpam-3758	289	10	no	no	INTJ
ejpam-3758	289	11	.	.	NOUN
ejpam-3758	289	12	36	36	NUM
ejpam-3758	289	13	,	,	PUNCT
ejpam-3758	289	14	1791	1791	NUM
ejpam-3758	289	15	-	-	SYM
ejpam-3758	289	16	1797	1797	NUM
ejpam-3758	289	17	,	,	PUNCT
ejpam-3758	289	18	2014	2014	NUM
ejpam-3758	289	19	.	.	PUNCT
ejpam-3758	290	1	[	[	X
ejpam-3758	290	2	2	2	NUM
ejpam-3758	290	3	]	]	X
ejpam-3758	290	4	gh	gh	PROPN
ejpam-3758	290	5	tabadkan	tabadkan	PROPN
ejpam-3758	290	6	and	and	CCONJ
ejpam-3758	290	7	a	a	DET
ejpam-3758	290	8	raghavi	raghavi	NOUN
ejpam-3758	290	9	.	.	PUNCT
ejpam-3758	291	1	a	a	DET
ejpam-3758	291	2	note	note	NOUN
ejpam-3758	291	3	on	on	ADP
ejpam-3758	291	4	generalized	generalized	ADJ
ejpam-3758	291	5	topology	topology	NOUN
ejpam-3758	291	6	.	.	PUNCT
ejpam-3758	292	1	international	international	ADJ
ejpam-3758	292	2	mathematical	mathematical	PROPN
ejpam-3758	292	3	forum	forum	PROPN
ejpam-3758	292	4	,	,	PUNCT
ejpam-3758	292	5	volume	volume	NOUN
ejpam-3758	292	6	6	6	NUM
ejpam-3758	292	7	,	,	PUNCT
ejpam-3758	292	8	no	no	INTJ
ejpam-3758	292	9	.	.	NOUN
ejpam-3758	292	10	1	1	NUM
ejpam-3758	292	11	,	,	PUNCT
ejpam-3758	292	12	19	19	NUM
ejpam-3758	292	13	-	-	SYM
ejpam-3758	292	14	24	24	NUM
ejpam-3758	292	15	,	,	PUNCT
ejpam-3758	292	16	2011	2011	NUM
ejpam-3758	292	17	.	.	PUNCT
ejpam-3758	293	1	[	[	X
ejpam-3758	293	2	3	3	NUM
ejpam-3758	293	3	]	]	X
ejpam-3758	293	4	r	r	NOUN
ejpam-3758	293	5	khayyeri	khayyeri	NOUN
ejpam-3758	293	6	and	and	CCONJ
ejpam-3758	293	7	r	r	PROPN
ejpam-3758	293	8	mohamadian	mohamadian	NOUN
ejpam-3758	293	9	.	.	PUNCT
ejpam-3758	294	1	on	on	ADP
ejpam-3758	294	2	base	base	NOUN
ejpam-3758	294	3	for	for	ADP
ejpam-3758	294	4	generalized	generalized	ADJ
ejpam-3758	294	5	topological	topological	ADJ
ejpam-3758	294	6	spaces	space	NOUN
ejpam-3758	294	7	.	.	PUNCT
ejpam-3758	295	1	international	international	ADJ
ejpam-3758	295	2	journal	journal	PROPN
ejpam-3758	295	3	of	of	ADP
ejpam-3758	295	4	contemporary	contemporary	PROPN
ejpam-3758	295	5	mathematical	mathematical	PROPN
ejpam-3758	295	6	sciences	sciences	PROPN
ejpam-3758	295	7	,	,	PUNCT
ejpam-3758	295	8	volume	volume	NOUN
ejpam-3758	295	9	6	6	NUM
ejpam-3758	295	10	,	,	PUNCT
ejpam-3758	295	11	no	no	INTJ
ejpam-3758	295	12	.	.	NOUN
ejpam-3758	295	13	48	48	NUM
ejpam-3758	295	14	,	,	PUNCT
ejpam-3758	295	15	23772383	23772383	NUM
ejpam-3758	295	16	,	,	PUNCT
ejpam-3758	295	17	2011	2011	NUM
ejpam-3758	295	18	.	.	PUNCT
ejpam-3758	296	1	[	[	X
ejpam-3758	296	2	4	4	X
ejpam-3758	296	3	]	]	X
ejpam-3758	296	4	w	w	NOUN
ejpam-3758	296	5	dungthaisong	dungthaisong	NOUN
ejpam-3758	296	6	,	,	PUNCT
ejpam-3758	296	7	et.al	et.al	PROPN
ejpam-3758	296	8	.	.	PUNCT
ejpam-3758	297	1	generalized	generalize	VERB
ejpam-3758	297	2	closed	close	VERB
ejpam-3758	297	3	sets	set	NOUN
ejpam-3758	297	4	in	in	ADP
ejpam-3758	297	5	bigeneralized	bigeneralize	VERB
ejpam-3758	297	6	topological	topological	ADJ
ejpam-3758	297	7	spaces	space	NOUN
ejpam-3758	297	8	.	.	PUNCT
ejpam-3758	298	1	international	international	ADJ
ejpam-3758	298	2	journal	journal	PROPN
ejpam-3758	298	3	of	of	ADP
ejpam-3758	298	4	mathematical	mathematical	ADJ
ejpam-3758	298	5	analysis	analysis	NOUN
ejpam-3758	298	6	,	,	PUNCT
ejpam-3758	298	7	volume	volume	NOUN
ejpam-3758	298	8	5	5	NUM
ejpam-3758	298	9	,	,	PUNCT
ejpam-3758	298	10	no	no	INTJ
ejpam-3758	298	11	.	.	NOUN
ejpam-3758	298	12	24	24	NUM
ejpam-3758	298	13	,	,	PUNCT
ejpam-3758	298	14	1175	1175	NUM
ejpam-3758	298	15	-	-	SYM
ejpam-3758	298	16	1184	1184	NUM
ejpam-3758	298	17	,	,	PUNCT
ejpam-3758	298	18	2011	2011	NUM
ejpam-3758	298	19	.	.	PUNCT
ejpam-3758	299	1	references	reference	NOUN
ejpam-3758	299	2	986	986	NUM
ejpam-3758	299	3	[	[	X
ejpam-3758	299	4	5	5	NUM
ejpam-3758	299	5	]	]	PUNCT
ejpam-3758	299	6	j	j	PROPN
ejpam-3758	299	7	baculta	baculta	PROPN
ejpam-3758	299	8	and	and	CCONJ
ejpam-3758	299	9	h	h	PROPN
ejpam-3758	299	10	rara	rara	NOUN
ejpam-3758	299	11	.	.	PUNCT
ejpam-3758	300	1	regular	regular	ADJ
ejpam-3758	300	2	generalized	generalize	VERB
ejpam-3758	300	3	star	star	NOUN
ejpam-3758	300	4	b	b	NOUN
ejpam-3758	300	5	-	-	PUNCT
ejpam-3758	300	6	sets	set	NOUN
ejpam-3758	300	7	in	in	ADP
ejpam-3758	300	8	bigeneralized	bigeneralize	VERB
ejpam-3758	300	9	topological	topological	ADJ
ejpam-3758	300	10	space	space	NOUN
ejpam-3758	300	11	.	.	PUNCT
ejpam-3758	301	1	applied	apply	VERB
ejpam-3758	301	2	mathematical	mathematical	ADJ
ejpam-3758	301	3	sciences	science	NOUN
ejpam-3758	301	4	,	,	PUNCT
ejpam-3758	301	5	volume	volume	NOUN
ejpam-3758	301	6	9	9	NUM
ejpam-3758	301	7	,	,	PUNCT
ejpam-3758	301	8	no	no	INTJ
ejpam-3758	301	9	.	.	NOUN
ejpam-3758	301	10	15	15	NUM
ejpam-3758	301	11	,	,	PUNCT
ejpam-3758	301	12	703	703	NUM
ejpam-3758	301	13	-	-	SYM
ejpam-3758	301	14	711	711	NUM
ejpam-3758	301	15	,	,	PUNCT
ejpam-3758	301	16	2015	2015	NUM
ejpam-3758	301	17	.	.	PUNCT
ejpam-3758	302	1	[	[	X
ejpam-3758	302	2	6	6	NUM
ejpam-3758	302	3	]	]	X
ejpam-3758	302	4	s	s	PART
ejpam-3758	302	5	mishra	mishra	PROPN
ejpam-3758	302	6	,	,	PUNCT
ejpam-3758	302	7	et.al	et.al	PROPN
ejpam-3758	302	8	.	.	PUNCT
ejpam-3758	303	1	on	on	ADP
ejpam-3758	303	2	regular	regular	ADJ
ejpam-3758	303	3	generalized	generalize	VERB
ejpam-3758	303	4	weakly	weakly	ADJ
ejpam-3758	303	5	(	(	PUNCT
ejpam-3758	303	6	rgw)-closed	rgw)-closed	ADJ
ejpam-3758	303	7	sets	set	NOUN
ejpam-3758	303	8	in	in	ADP
ejpam-3758	303	9	topological	topological	ADJ
ejpam-3758	303	10	spaces	space	NOUN
ejpam-3758	303	11	.	.	PUNCT
ejpam-3758	304	1	international	international	ADJ
ejpam-3758	304	2	journal	journal	PROPN
ejpam-3758	304	3	of	of	ADP
ejpam-3758	304	4	mathematical	mathematical	ADJ
ejpam-3758	304	5	analysis	analysis	NOUN
ejpam-3758	304	6	,	,	PUNCT
ejpam-3758	304	7	volume	volume	NOUN
ejpam-3758	304	8	6	6	NUM
ejpam-3758	304	9	,	,	PUNCT
ejpam-3758	304	10	no	no	INTJ
ejpam-3758	304	11	.	.	NOUN
ejpam-3758	304	12	39	39	NUM
ejpam-3758	304	13	,	,	PUNCT
ejpam-3758	304	14	19391952	19391952	NUM
ejpam-3758	304	15	,	,	PUNCT
ejpam-3758	304	16	2012	2012	NUM
ejpam-3758	304	17	.	.	PUNCT
ejpam-3758	305	1	[	[	X
ejpam-3758	305	2	7	7	X
ejpam-3758	305	3	]	]	X
ejpam-3758	305	4	j	j	PROPN
ejpam-3758	305	5	cao	cao	PROPN
ejpam-3758	305	6	,	,	PUNCT
ejpam-3758	305	7	et.al	et.al	PROPN
ejpam-3758	305	8	.	.	PUNCT
ejpam-3758	306	1	on	on	ADP
ejpam-3758	306	2	generalized	generalized	ADJ
ejpam-3758	306	3	closed	closed	ADJ
ejpam-3758	306	4	sets	set	NOUN
ejpam-3758	306	5	.	.	PUNCT
ejpam-3758	307	1	topology	topology	NOUN
ejpam-3758	307	2	and	and	CCONJ
ejpam-3758	307	3	its	its	PRON
ejpam-3758	307	4	applications	application	NOUN
ejpam-3758	307	5	,	,	PUNCT
ejpam-3758	307	6	no	no	INTJ
ejpam-3758	307	7	.	.	NOUN
ejpam-3758	307	8	123	123	NUM
ejpam-3758	307	9	,	,	PUNCT
ejpam-3758	307	10	37	37	NUM
ejpam-3758	307	11	-	-	SYM
ejpam-3758	307	12	46	46	NUM
ejpam-3758	307	13	,	,	PUNCT
ejpam-3758	307	14	2002	2002	NUM
ejpam-3758	307	15	.	.	PUNCT
ejpam-3758	308	1	[	[	X
ejpam-3758	308	2	8	8	NUM
ejpam-3758	308	3	]	]	X
ejpam-3758	308	4	j	j	PROPN
ejpam-3758	308	5	dugundji	dugundji	PROPN
ejpam-3758	308	6	.	.	PUNCT
ejpam-3758	308	7	topology	topology	PROPN
ejpam-3758	308	8	.	.	PUNCT
ejpam-3758	309	1	allyn	allyn	PROPN
ejpam-3758	309	2	and	and	CCONJ
ejpam-3758	309	3	bacon	bacon	PROPN
ejpam-3758	309	4	,	,	PUNCT
ejpam-3758	309	5	inc	inc	PROPN
ejpam-3758	309	6	.	.	PROPN
ejpam-3758	309	7	,	,	PUNCT
ejpam-3758	309	8	470	470	NUM
ejpam-3758	309	9	atlantic	atlantic	PROPN
ejpam-3758	309	10	avenue	avenue	PROPN
ejpam-3758	309	11	,	,	PUNCT
ejpam-3758	309	12	boston	boston	PROPN
ejpam-3758	309	13	,	,	PUNCT
ejpam-3758	309	14	1978	1978	NUM
ejpam-3758	309	15	.	.	PUNCT
ejpam-3758	310	1	[	[	X
ejpam-3758	310	2	9	9	NUM
ejpam-3758	310	3	]	]	X
ejpam-3758	310	4	s	s	PART
ejpam-3758	310	5	mishra	mishra	PROPN
ejpam-3758	310	6	,	,	PUNCT
ejpam-3758	310	7	et.al	et.al	PROPN
ejpam-3758	310	8	.	.	PUNCT
ejpam-3758	311	1	on	on	ADP
ejpam-3758	311	2	generalized	generalize	VERB
ejpam-3758	311	3	pre	pre	NOUN
ejpam-3758	311	4	regular	regular	ADJ
ejpam-3758	311	5	weakly	weakly	ADJ
ejpam-3758	311	6	(	(	PUNCT
ejpam-3758	311	7	gprw)-closed	gprw)-closed	ADJ
ejpam-3758	311	8	sets	set	NOUN
ejpam-3758	311	9	in	in	ADP
ejpam-3758	311	10	topological	topological	ADJ
ejpam-3758	311	11	spaces	space	NOUN
ejpam-3758	311	12	.	.	PUNCT
ejpam-3758	312	1	international	international	ADJ
ejpam-3758	312	2	mathematical	mathematical	PROPN
ejpam-3758	312	3	forum	forum	PROPN
ejpam-3758	312	4	,	,	PUNCT
ejpam-3758	312	5	no	no	INTJ
ejpam-3758	312	6	.	.	PROPN
ejpam-3758	312	7	40	40	NUM
ejpam-3758	312	8	,	,	PUNCT
ejpam-3758	312	9	1981	1981	NUM
ejpam-3758	312	10	-	-	SYM
ejpam-3758	312	11	1992	1992	NUM
ejpam-3758	312	12	,	,	PUNCT
ejpam-3758	312	13	2012	2012	NUM
ejpam-3758	312	14	.	.	PUNCT
ejpam-3758	313	1	[	[	X
ejpam-3758	313	2	10	10	NUM
ejpam-3758	313	3	]	]	X
ejpam-3758	313	4	m	m	VERB
ejpam-3758	313	5	sarsak	sarsak	ADJ
ejpam-3758	313	6	.	.	PUNCT
ejpam-3758	314	1	on	on	ADP
ejpam-3758	314	2	some	some	DET
ejpam-3758	314	3	properties	property	NOUN
ejpam-3758	314	4	of	of	ADP
ejpam-3758	314	5	generalized	generalized	ADJ
ejpam-3758	314	6	open	open	ADJ
ejpam-3758	314	7	sets	set	NOUN
ejpam-3758	314	8	in	in	ADP
ejpam-3758	314	9	generalized	generalized	ADJ
ejpam-3758	314	10	topological	topological	ADJ
ejpam-3758	314	11	spaces	space	NOUN
ejpam-3758	314	12	.	.	PUNCT
ejpam-3758	315	1	demonstratio	demonstratio	PROPN
ejpam-3758	315	2	mathematica	mathematica	PROPN
ejpam-3758	315	3	,	,	PUNCT
ejpam-3758	315	4	no	no	INTJ
ejpam-3758	315	5	.	.	PUNCT
ejpam-3758	315	6	46(2	46(2	NOUN
ejpam-3758	315	7	)	)	PUNCT
ejpam-3758	315	8	.	.	PUNCT
ejpam-3758	316	1	doi:10.1515	doi:10.1515	NOUN
ejpam-3758	316	2	/	/	SYM
ejpam-3758	316	3	dema-2013	dema-2013	NOUN
ejpam-3758	316	4	-	-	PUNCT
ejpam-3758	316	5	0453	0453	NUM
ejpam-3758	316	6	,	,	PUNCT
ejpam-3758	316	7	2013	2013	NUM
ejpam-3758	316	8	.	.	PUNCT
ejpam-3758	317	1	[	[	X
ejpam-3758	317	2	11	11	NUM
ejpam-3758	317	3	]	]	PUNCT
ejpam-3758	317	4	t	t	PROPN
ejpam-3758	317	5	al	al	PROPN
ejpam-3758	317	6	-	-	PUNCT
ejpam-3758	317	7	shami	shami	PROPN
ejpam-3758	317	8	.	.	PUNCT
ejpam-3758	318	1	supra	supra	ADJ
ejpam-3758	318	2	semi	semi	NOUN
ejpam-3758	318	3	-	-	NOUN
ejpam-3758	318	4	compactness	compactness	NOUN
ejpam-3758	318	5	via	via	ADP
ejpam-3758	318	6	supra	supra	PROPN
ejpam-3758	318	7	topological	topological	PROPN
ejpam-3758	318	8	spaces	space	NOUN
ejpam-3758	318	9	.	.	PUNCT
ejpam-3758	319	1	journal	journal	PROPN
ejpam-3758	319	2	of	of	ADP
ejpam-3758	319	3	taibah	taibah	PROPN
ejpam-3758	319	4	university	university	PROPN
ejpam-3758	319	5	for	for	ADP
ejpam-3758	319	6	science	science	NOUN
ejpam-3758	319	7	,	,	PUNCT
ejpam-3758	319	8	no	no	INTJ
ejpam-3758	319	9	.	.	NOUN
ejpam-3758	319	10	12	12	NUM
ejpam-3758	319	11	(	(	PUNCT
ejpam-3758	319	12	3	3	NUM
ejpam-3758	319	13	)	)	PUNCT
ejpam-3758	319	14	(	(	PUNCT
ejpam-3758	319	15	2018	2018	NUM
ejpam-3758	319	16	)	)	PUNCT
ejpam-3758	319	17	338	338	NUM
ejpam-3758	319	18	-	-	SYM
ejpam-3758	319	19	343	343	NUM
ejpam-3758	319	20	.	.	PUNCT
ejpam-3758	320	1	[	[	X
ejpam-3758	320	2	12	12	NUM
ejpam-3758	320	3	]	]	PUNCT
ejpam-3758	320	4	t	t	PROPN
ejpam-3758	320	5	al	al	PROPN
ejpam-3758	320	6	-	-	PUNCT
ejpam-3758	320	7	shami	shami	PROPN
ejpam-3758	320	8	.	.	PUNCT
ejpam-3758	321	1	some	some	DET
ejpam-3758	321	2	results	result	NOUN
ejpam-3758	321	3	related	relate	VERB
ejpam-3758	321	4	to	to	ADP
ejpam-3758	321	5	supra	supra	PROPN
ejpam-3758	321	6	topological	topological	ADJ
ejpam-3758	321	7	spaces	space	NOUN
ejpam-3758	321	8	.	.	PUNCT
ejpam-3758	322	1	journal	journal	NOUN
ejpam-3758	322	2	of	of	ADP
ejpam-3758	322	3	advanced	advanced	ADJ
ejpam-3758	322	4	studies	study	NOUN
ejpam-3758	322	5	in	in	ADP
ejpam-3758	322	6	topology	topology	NOUN
ejpam-3758	322	7	,	,	PUNCT
ejpam-3758	322	8	no	no	INTJ
ejpam-3758	322	9	.	.	NOUN
ejpam-3758	322	10	7	7	NUM
ejpam-3758	322	11	(	(	PUNCT
ejpam-3758	322	12	4	4	NUM
ejpam-3758	322	13	)	)	PUNCT
ejpam-3758	322	14	(	(	PUNCT
ejpam-3758	322	15	2016	2016	NUM
ejpam-3758	322	16	)	)	PUNCT
ejpam-3758	322	17	283	283	NUM
ejpam-3758	322	18	-	-	SYM
ejpam-3758	322	19	294	294	NUM
ejpam-3758	322	20	.	.	PUNCT
ejpam-3758	323	1	[	[	X
ejpam-3758	323	2	13	13	NUM
ejpam-3758	323	3	]	]	SYM
ejpam-3758	323	4	m	m	PROPN
ejpam-3758	323	5	el	el	PROPN
ejpam-3758	323	6	-	-	PUNCT
ejpam-3758	323	7	shafei	shafei	PROPN
ejpam-3758	323	8	,	,	PUNCT
ejpam-3758	323	9	a	a	DET
ejpam-3758	323	10	zakari	zakari	NOUN
ejpam-3758	323	11	and	and	CCONJ
ejpam-3758	323	12	t	t	PROPN
ejpam-3758	323	13	al	al	PROPN
ejpam-3758	323	14	-	-	PUNCT
ejpam-3758	323	15	shami	shami	PROPN
ejpam-3758	323	16	.	.	PUNCT
ejpam-3758	324	1	some	some	DET
ejpam-3758	324	2	applications	application	NOUN
ejpam-3758	324	3	of	of	ADP
ejpam-3758	324	4	suprapreopen	suprapreopen	ADJ
ejpam-3758	324	5	sets	set	NOUN
ejpam-3758	324	6	.	.	PUNCT
ejpam-3758	325	1	journal	journal	NOUN
ejpam-3758	325	2	of	of	ADP
ejpam-3758	325	3	mathematics	mathematic	NOUN
ejpam-3758	325	4	,	,	PUNCT
ejpam-3758	325	5	volume	volume	NOUN
ejpam-3758	325	6	2020	2020	NUM
ejpam-3758	325	7	,	,	PUNCT
ejpam-3758	325	8	article	article	NOUN
ejpam-3758	325	9	i	i	PROPN
ejpam-3758	325	10	d	d	PROPN
ejpam-3758	325	11	9634206	9634206	NUM
ejpam-3758	325	12	,	,	PUNCT
ejpam-3758	325	13	11	11	NUM
ejpam-3758	325	14	pages	page	NOUN
ejpam-3758	325	15	.	.	PUNCT