id	sid	tid	token	lemma	pos
ejpam-5362	1	1	european	european	PROPN
ejpam-5362	1	2	journal	journal	PROPN
ejpam-5362	1	3	of	of	ADP
ejpam-5362	1	4	pure	pure	ADJ
ejpam-5362	1	5	and	and	CCONJ
ejpam-5362	1	6	applied	applied	ADJ
ejpam-5362	1	7	mathematics	mathematic	NOUN
ejpam-5362	1	8	2025	2025	NUM
ejpam-5362	1	9	,	,	PUNCT
ejpam-5362	1	10	vol	vol	NOUN
ejpam-5362	1	11	.	.	PROPN
ejpam-5362	1	12	18	18	NUM
ejpam-5362	1	13	,	,	PUNCT
ejpam-5362	1	14	issue	issue	NOUN
ejpam-5362	1	15	1	1	NUM
ejpam-5362	1	16	,	,	PUNCT
ejpam-5362	1	17	article	article	NOUN
ejpam-5362	1	18	number	number	NOUN
ejpam-5362	1	19	5362	5362	NUM
ejpam-5362	1	20	issn	issn	VERB
ejpam-5362	1	21	1307	1307	NUM
ejpam-5362	1	22	-	-	SYM
ejpam-5362	1	23	5543	5543	NUM
ejpam-5362	1	24	–	–	PUNCT
ejpam-5362	1	25	ejpam.com	ejpam.com	X
ejpam-5362	1	26	published	publish	VERB
ejpam-5362	1	27	by	by	ADP
ejpam-5362	1	28	new	new	PROPN
ejpam-5362	1	29	york	york	PROPN
ejpam-5362	1	30	business	business	PROPN
ejpam-5362	1	31	global	global	PROPN
ejpam-5362	1	32	on	on	ADP
ejpam-5362	1	33	the	the	DET
ejpam-5362	1	34	category	category	NOUN
ejpam-5362	1	35	of	of	ADP
ejpam-5362	1	36	(	(	PUNCT
ejpam-5362	1	37	i	i	PROPN
ejpam-5362	1	38	,	,	PUNCT
ejpam-5362	1	39	j)-baire	j)-baire	PROPN
ejpam-5362	1	40	bilocales	bilocale	NOUN
ejpam-5362	1	41	mbekezeli	mbekezeli	PROPN
ejpam-5362	1	42	nxumalo	nxumalo	PROPN
ejpam-5362	1	43	department	department	PROPN
ejpam-5362	1	44	of	of	ADP
ejpam-5362	1	45	mathematics	mathematics	PROPN
ejpam-5362	1	46	(	(	PUNCT
ejpam-5362	1	47	pure	pure	ADJ
ejpam-5362	1	48	and	and	CCONJ
ejpam-5362	1	49	applied	apply	VERB
ejpam-5362	1	50	)	)	PUNCT
ejpam-5362	1	51	,	,	PUNCT
ejpam-5362	1	52	faculty	faculty	NOUN
ejpam-5362	1	53	of	of	ADP
ejpam-5362	1	54	science	science	NOUN
ejpam-5362	1	55	,	,	PUNCT
ejpam-5362	1	56	rhodes	rhode	VERB
ejpam-5362	1	57	university	university	PROPN
ejpam-5362	1	58	,	,	PUNCT
ejpam-5362	1	59	makhanda	makhanda	NOUN
ejpam-5362	1	60	,	,	PUNCT
ejpam-5362	1	61	eastern	eastern	ADJ
ejpam-5362	1	62	cape	cape	NOUN
ejpam-5362	1	63	,	,	PUNCT
ejpam-5362	1	64	south	south	PROPN
ejpam-5362	1	65	africa	africa	PROPN
ejpam-5362	1	66	abstract	abstract	PROPN
ejpam-5362	1	67	.	.	PUNCT
ejpam-5362	2	1	we	we	PRON
ejpam-5362	2	2	define	define	VERB
ejpam-5362	2	3	and	and	CCONJ
ejpam-5362	2	4	characterize	characterize	VERB
ejpam-5362	2	5	the	the	DET
ejpam-5362	2	6	notion	notion	NOUN
ejpam-5362	2	7	of	of	ADP
ejpam-5362	2	8	(	(	PUNCT
ejpam-5362	2	9	i	i	PROPN
ejpam-5362	2	10	,	,	PUNCT
ejpam-5362	2	11	j)-baireness	j)-baireness	NOUN
ejpam-5362	2	12	for	for	ADP
ejpam-5362	2	13	bilocales	bilocale	NOUN
ejpam-5362	2	14	.	.	PUNCT
ejpam-5362	3	1	we	we	PRON
ejpam-5362	3	2	also	also	ADV
ejpam-5362	3	3	give	give	VERB
ejpam-5362	3	4	internal	internal	ADJ
ejpam-5362	3	5	properties	property	NOUN
ejpam-5362	3	6	of	of	ADP
ejpam-5362	3	7	(	(	PUNCT
ejpam-5362	3	8	i	i	PROPN
ejpam-5362	3	9	,	,	PUNCT
ejpam-5362	3	10	j)-baire	j)-baire	PROPN
ejpam-5362	3	11	bilocales	bilocale	NOUN
ejpam-5362	3	12	which	which	PRON
ejpam-5362	3	13	are	be	AUX
ejpam-5362	3	14	not	not	PART
ejpam-5362	3	15	translated	translate	VERB
ejpam-5362	3	16	from	from	ADP
ejpam-5362	3	17	properties	property	NOUN
ejpam-5362	3	18	of	of	ADP
ejpam-5362	3	19	(	(	PUNCT
ejpam-5362	3	20	i	i	INTJ
ejpam-5362	3	21	,	,	PUNCT
ejpam-5362	3	22	j)-baireness	j)-baireness	ADJ
ejpam-5362	3	23	in	in	ADP
ejpam-5362	3	24	bispaces	bispace	NOUN
ejpam-5362	3	25	.	.	PUNCT
ejpam-5362	4	1	it	it	PRON
ejpam-5362	4	2	turns	turn	VERB
ejpam-5362	4	3	out	out	ADP
ejpam-5362	4	4	(	(	PUNCT
ejpam-5362	4	5	i	i	PROPN
ejpam-5362	4	6	,	,	PUNCT
ejpam-5362	4	7	j)-baire	j)-baire	PROPN
ejpam-5362	4	8	bilocales	bilocale	NOUN
ejpam-5362	4	9	are	be	AUX
ejpam-5362	4	10	conservative	conservative	ADJ
ejpam-5362	4	11	in	in	ADP
ejpam-5362	4	12	bilocales	bilocale	NOUN
ejpam-5362	4	13	,	,	PUNCT
ejpam-5362	4	14	in	in	ADP
ejpam-5362	4	15	the	the	DET
ejpam-5362	4	16	sense	sense	NOUN
ejpam-5362	4	17	that	that	SCONJ
ejpam-5362	4	18	a	a	DET
ejpam-5362	4	19	bitopological	bitopological	ADJ
ejpam-5362	4	20	space	space	NOUN
ejpam-5362	4	21	is	be	AUX
ejpam-5362	4	22	almost	almost	ADV
ejpam-5362	4	23	(	(	PUNCT
ejpam-5362	4	24	i	i	NOUN
ejpam-5362	4	25	,	,	PUNCT
ejpam-5362	4	26	j)-baire	j)-baire	VERB
ejpam-5362	4	27	if	if	SCONJ
ejpam-5362	4	28	and	and	CCONJ
ejpam-5362	4	29	only	only	ADV
ejpam-5362	4	30	if	if	SCONJ
ejpam-5362	4	31	the	the	DET
ejpam-5362	4	32	bilocale	bilocale	NOUN
ejpam-5362	4	33	it	it	PRON
ejpam-5362	4	34	induces	induce	VERB
ejpam-5362	4	35	is	be	AUX
ejpam-5362	4	36	(	(	PUNCT
ejpam-5362	4	37	i	i	NOUN
ejpam-5362	4	38	,	,	PUNCT
ejpam-5362	4	39	j)-baire	j)-baire	NOUN
ejpam-5362	4	40	.	.	PUNCT
ejpam-5362	5	1	furthermore	furthermore	ADV
ejpam-5362	5	2	,	,	PUNCT
ejpam-5362	5	3	in	in	ADP
ejpam-5362	5	4	the	the	DET
ejpam-5362	5	5	class	class	NOUN
ejpam-5362	5	6	of	of	ADP
ejpam-5362	5	7	noetherian	noetherian	ADJ
ejpam-5362	5	8	bilocales	bilocale	NOUN
ejpam-5362	5	9	,	,	PUNCT
ejpam-5362	5	10	(	(	PUNCT
ejpam-5362	5	11	i	i	PRON
ejpam-5362	5	12	,	,	PUNCT
ejpam-5362	5	13	j)-baireness	j)-baireness	NOUN
ejpam-5362	5	14	of	of	ADP
ejpam-5362	5	15	a	a	DET
ejpam-5362	5	16	bilocale	bilocale	NOUN
ejpam-5362	5	17	coincides	coincide	VERB
ejpam-5362	5	18	with	with	ADP
ejpam-5362	5	19	(	(	PUNCT
ejpam-5362	5	20	i	i	NOUN
ejpam-5362	5	21	,	,	PUNCT
ejpam-5362	5	22	j)baireness	j)baireness	NOUN
ejpam-5362	5	23	of	of	ADP
ejpam-5362	5	24	its	its	PRON
ejpam-5362	5	25	ideal	ideal	ADJ
ejpam-5362	5	26	bilocale	bilocale	NOUN
ejpam-5362	5	27	.	.	PUNCT
ejpam-5362	6	1	we	we	PRON
ejpam-5362	6	2	also	also	ADV
ejpam-5362	6	3	consider	consider	VERB
ejpam-5362	6	4	relative	relative	ADJ
ejpam-5362	6	5	versions	version	NOUN
ejpam-5362	6	6	of	of	ADP
ejpam-5362	6	7	(	(	PUNCT
ejpam-5362	6	8	i	i	PROPN
ejpam-5362	6	9	,	,	PUNCT
ejpam-5362	6	10	j)-baire	j)-baire	VERB
ejpam-5362	6	11	where	where	SCONJ
ejpam-5362	6	12	we	we	PRON
ejpam-5362	6	13	show	show	VERB
ejpam-5362	6	14	that	that	SCONJ
ejpam-5362	6	15	a	a	DET
ejpam-5362	6	16	bilocale	bilocale	NOUN
ejpam-5362	6	17	is	be	AUX
ejpam-5362	6	18	(	(	PUNCT
ejpam-5362	6	19	i	i	NOUN
ejpam-5362	6	20	,	,	PUNCT
ejpam-5362	6	21	j)-baire	j)-baire	VERB
ejpam-5362	6	22	only	only	ADV
ejpam-5362	6	23	if	if	SCONJ
ejpam-5362	6	24	the	the	DET
ejpam-5362	6	25	subbilocale	subbilocale	NOUN
ejpam-5362	6	26	induced	induce	VERB
ejpam-5362	6	27	by	by	ADP
ejpam-5362	6	28	the	the	DET
ejpam-5362	6	29	booleanization	booleanization	NOUN
ejpam-5362	6	30	is	be	AUX
ejpam-5362	6	31	(	(	PUNCT
ejpam-5362	6	32	i	i	NOUN
ejpam-5362	6	33	,	,	PUNCT
ejpam-5362	6	34	j)-baire	j)-baire	PROPN
ejpam-5362	6	35	.	.	PUNCT
ejpam-5362	7	1	we	we	PRON
ejpam-5362	7	2	use	use	VERB
ejpam-5362	7	3	the	the	DET
ejpam-5362	7	4	characterization	characterization	NOUN
ejpam-5362	7	5	of	of	ADP
ejpam-5362	7	6	(	(	PUNCT
ejpam-5362	7	7	i	i	PROPN
ejpam-5362	7	8	,	,	PUNCT
ejpam-5362	7	9	j)-baire	j)-baire	NOUN
ejpam-5362	7	10	bilocales	bilocale	NOUN
ejpam-5362	7	11	to	to	PART
ejpam-5362	7	12	introduce	introduce	VERB
ejpam-5362	7	13	and	and	CCONJ
ejpam-5362	7	14	characterize	characterize	VERB
ejpam-5362	7	15	(	(	PUNCT
ejpam-5362	7	16	τi	τi	ADP
ejpam-5362	7	17	,	,	PUNCT
ejpam-5362	7	18	τj)-baireness	τj)-baireness	NOUN
ejpam-5362	7	19	in	in	ADP
ejpam-5362	7	20	the	the	DET
ejpam-5362	7	21	category	category	NOUN
ejpam-5362	7	22	of	of	ADP
ejpam-5362	7	23	topobilocales	topobilocale	NOUN
ejpam-5362	7	24	.	.	PUNCT
ejpam-5362	8	1	2020	2020	NUM
ejpam-5362	8	2	mathematics	mathematic	NOUN
ejpam-5362	8	3	subject	subject	NOUN
ejpam-5362	8	4	classifications	classification	NOUN
ejpam-5362	8	5	:	:	PUNCT
ejpam-5362	8	6	06d22	06d22	NOUN
ejpam-5362	8	7	,	,	PUNCT
ejpam-5362	8	8	54e52	54e52	NUM
ejpam-5362	8	9	,	,	PUNCT
ejpam-5362	8	10	54e55	54e55	NUM
ejpam-5362	8	11	key	key	ADJ
ejpam-5362	8	12	words	word	NOUN
ejpam-5362	8	13	and	and	CCONJ
ejpam-5362	8	14	phrases	phrase	NOUN
ejpam-5362	8	15	:	:	PUNCT
ejpam-5362	8	16	(	(	PUNCT
ejpam-5362	8	17	i	i	NOUN
ejpam-5362	8	18	,	,	PUNCT
ejpam-5362	8	19	j)-baire	j)-baire	ADJ
ejpam-5362	8	20	,	,	PUNCT
ejpam-5362	8	21	topobilocale	topobilocale	NOUN
ejpam-5362	8	22	,	,	PUNCT
ejpam-5362	8	23	i	i	PRON
ejpam-5362	8	24	-	-	PUNCT
ejpam-5362	8	25	prefit	prefit	VERB
ejpam-5362	8	26	,	,	PUNCT
ejpam-5362	8	27	i	i	NOUN
ejpam-5362	8	28	-	-	PUNCT
ejpam-5362	8	29	pseudocomplete	pseudocomplete	NOUN
ejpam-5362	8	30	,	,	PUNCT
ejpam-5362	8	31	ideal	ideal	ADJ
ejpam-5362	8	32	bilocale	bilocale	NOUN
ejpam-5362	8	33	,	,	PUNCT
ejpam-5362	8	34	relatively	relatively	ADV
ejpam-5362	8	35	(	(	PUNCT
ejpam-5362	8	36	i	i	NOUN
ejpam-5362	8	37	,	,	PUNCT
ejpam-5362	8	38	j)-baire	j)-baire	PROPN
ejpam-5362	8	39	1	1	NUM
ejpam-5362	8	40	.	.	PUNCT
ejpam-5362	8	41	introduction	introduction	NOUN
ejpam-5362	8	42	in	in	ADP
ejpam-5362	8	43	classical	classical	ADJ
ejpam-5362	8	44	topology	topology	NOUN
ejpam-5362	8	45	,	,	PUNCT
ejpam-5362	8	46	a	a	DET
ejpam-5362	8	47	space	space	NOUN
ejpam-5362	8	48	is	be	AUX
ejpam-5362	8	49	called	call	VERB
ejpam-5362	8	50	baire	baire	NOUN
ejpam-5362	8	51	if	if	SCONJ
ejpam-5362	8	52	the	the	DET
ejpam-5362	8	53	intersection	intersection	NOUN
ejpam-5362	8	54	of	of	ADP
ejpam-5362	8	55	every	every	DET
ejpam-5362	8	56	sequence	sequence	NOUN
ejpam-5362	8	57	of	of	ADP
ejpam-5362	8	58	dense	dense	ADJ
ejpam-5362	8	59	open	open	ADJ
ejpam-5362	8	60	sets	set	NOUN
ejpam-5362	8	61	is	be	AUX
ejpam-5362	8	62	dense	dense	ADJ
ejpam-5362	8	63	.	.	PUNCT
ejpam-5362	9	1	baire	baire	NOUN
ejpam-5362	9	2	spaces	space	NOUN
ejpam-5362	9	3	play	play	VERB
ejpam-5362	9	4	an	an	DET
ejpam-5362	9	5	important	important	ADJ
ejpam-5362	9	6	role	role	NOUN
ejpam-5362	9	7	in	in	ADP
ejpam-5362	9	8	different	different	ADJ
ejpam-5362	9	9	areas	area	NOUN
ejpam-5362	9	10	of	of	ADP
ejpam-5362	9	11	mathematics	mathematic	NOUN
ejpam-5362	9	12	such	such	ADJ
ejpam-5362	9	13	as	as	ADP
ejpam-5362	9	14	analysis	analysis	NOUN
ejpam-5362	9	15	and	and	CCONJ
ejpam-5362	9	16	mathematical	mathematical	ADJ
ejpam-5362	9	17	logic	logic	NOUN
ejpam-5362	9	18	.	.	PUNCT
ejpam-5362	10	1	the	the	DET
ejpam-5362	10	2	concept	concept	NOUN
ejpam-5362	10	3	of	of	ADP
ejpam-5362	10	4	baire	baire	NOUN
ejpam-5362	10	5	spaces	space	NOUN
ejpam-5362	10	6	has	have	AUX
ejpam-5362	10	7	also	also	ADV
ejpam-5362	10	8	appeared	appear	VERB
ejpam-5362	10	9	in	in	ADP
ejpam-5362	10	10	fuzzy	fuzzy	ADJ
ejpam-5362	10	11	set	set	NOUN
ejpam-5362	10	12	theory	theory	NOUN
ejpam-5362	10	13	as	as	ADV
ejpam-5362	10	14	well	well	ADV
ejpam-5362	10	15	as	as	ADP
ejpam-5362	10	16	soft	soft	ADJ
ejpam-5362	10	17	set	set	NOUN
ejpam-5362	10	18	theory	theory	NOUN
ejpam-5362	10	19	,	,	PUNCT
ejpam-5362	10	20	see	see	VERB
ejpam-5362	10	21	[	[	X
ejpam-5362	10	22	22	22	NUM
ejpam-5362	10	23	]	]	PUNCT
ejpam-5362	10	24	and	and	CCONJ
ejpam-5362	11	1	[	[	X
ejpam-5362	11	2	2	2	NUM
ejpam-5362	11	3	]	]	PUNCT
ejpam-5362	11	4	.	.	PUNCT
ejpam-5362	12	1	fuzzy	fuzzy	ADJ
ejpam-5362	12	2	sets	set	NOUN
ejpam-5362	12	3	were	be	AUX
ejpam-5362	12	4	introduced	introduce	VERB
ejpam-5362	12	5	by	by	ADP
ejpam-5362	12	6	zadeh	zadeh	PROPN
ejpam-5362	13	1	[	[	X
ejpam-5362	13	2	23	23	NUM
ejpam-5362	13	3	]	]	PUNCT
ejpam-5362	13	4	and	and	CCONJ
ejpam-5362	13	5	soft	soft	ADJ
ejpam-5362	13	6	sets	set	NOUN
ejpam-5362	13	7	were	be	AUX
ejpam-5362	13	8	initially	initially	ADV
ejpam-5362	13	9	introduced	introduce	VERB
ejpam-5362	13	10	by	by	ADP
ejpam-5362	13	11	molodtsov	molodtsov	NOUN
ejpam-5362	13	12	[	[	X
ejpam-5362	13	13	13	13	NUM
ejpam-5362	13	14	]	]	PUNCT
ejpam-5362	13	15	.	.	PUNCT
ejpam-5362	14	1	both	both	PRON
ejpam-5362	14	2	of	of	ADP
ejpam-5362	14	3	these	these	DET
ejpam-5362	14	4	sets	set	NOUN
ejpam-5362	14	5	were	be	AUX
ejpam-5362	14	6	developed	develop	VERB
ejpam-5362	14	7	to	to	PART
ejpam-5362	14	8	solve	solve	VERB
ejpam-5362	14	9	the	the	DET
ejpam-5362	14	10	problem	problem	NOUN
ejpam-5362	14	11	of	of	ADP
ejpam-5362	14	12	modeling	model	VERB
ejpam-5362	14	13	vagueness	vagueness	NOUN
ejpam-5362	14	14	in	in	ADP
ejpam-5362	14	15	real	real	ADJ
ejpam-5362	14	16	-	-	PUNCT
ejpam-5362	14	17	life	life	NOUN
ejpam-5362	14	18	problems	problem	NOUN
ejpam-5362	14	19	.	.	PUNCT
ejpam-5362	15	1	fuzzy	fuzzy	ADJ
ejpam-5362	15	2	sets	set	NOUN
ejpam-5362	15	3	have	have	AUX
ejpam-5362	15	4	been	be	AUX
ejpam-5362	15	5	applied	apply	VERB
ejpam-5362	15	6	in	in	ADP
ejpam-5362	15	7	medical	medical	ADJ
ejpam-5362	15	8	diagnosis	diagnosis	NOUN
ejpam-5362	15	9	[	[	X
ejpam-5362	15	10	1	1	X
ejpam-5362	15	11	]	]	PUNCT
ejpam-5362	15	12	while	while	SCONJ
ejpam-5362	15	13	fuzzy	fuzzy	ADJ
ejpam-5362	15	14	soft	soft	ADJ
ejpam-5362	15	15	sets	set	NOUN
ejpam-5362	15	16	have	have	AUX
ejpam-5362	15	17	been	be	AUX
ejpam-5362	15	18	used	use	VERB
ejpam-5362	15	19	to	to	PART
ejpam-5362	15	20	classify	classify	VERB
ejpam-5362	15	21	wood	wood	NOUN
ejpam-5362	15	22	materials	material	NOUN
ejpam-5362	15	23	to	to	PART
ejpam-5362	15	24	prevent	prevent	VERB
ejpam-5362	15	25	fire	fire	NOUN
ejpam-5362	15	26	-	-	PUNCT
ejpam-5362	15	27	related	relate	VERB
ejpam-5362	15	28	injuries	injury	NOUN
ejpam-5362	15	29	and	and	CCONJ
ejpam-5362	15	30	deaths	death	NOUN
ejpam-5362	16	1	[	[	X
ejpam-5362	16	2	9	9	NUM
ejpam-5362	16	3	]	]	PUNCT
ejpam-5362	16	4	.	.	PUNCT
ejpam-5362	17	1	in	in	ADP
ejpam-5362	17	2	bispaces	bispace	NOUN
ejpam-5362	17	3	(	(	PUNCT
ejpam-5362	17	4	spaces	space	NOUN
ejpam-5362	17	5	endowed	endow	VERB
ejpam-5362	17	6	with	with	ADP
ejpam-5362	17	7	two	two	NUM
ejpam-5362	17	8	topologies	topology	NOUN
ejpam-5362	17	9	)	)	PUNCT
ejpam-5362	17	10	,	,	PUNCT
ejpam-5362	17	11	an	an	DET
ejpam-5362	17	12	almost	almost	ADV
ejpam-5362	17	13	(	(	PUNCT
ejpam-5362	17	14	i	i	NOUN
ejpam-5362	17	15	,	,	PUNCT
ejpam-5362	17	16	j)-baire	j)-baire	PROPN
ejpam-5362	17	17	bispace	bispace	NOUN
ejpam-5362	17	18	refers	refer	VERB
ejpam-5362	17	19	to	to	ADP
ejpam-5362	17	20	a	a	DET
ejpam-5362	17	21	bispace	bispace	NOUN
ejpam-5362	17	22	(	(	PUNCT
ejpam-5362	17	23	x	x	NOUN
ejpam-5362	17	24	,	,	PUNCT
ejpam-5362	17	25	τ1	τ1	NOUN
ejpam-5362	17	26	,	,	PUNCT
ejpam-5362	17	27	τ2	τ2	NOUN
ejpam-5362	17	28	)	)	PUNCT
ejpam-5362	17	29	in	in	ADP
ejpam-5362	17	30	which	which	PRON
ejpam-5362	17	31	the	the	DET
ejpam-5362	17	32	intersection	intersection	NOUN
ejpam-5362	17	33	of	of	ADP
ejpam-5362	17	34	any	any	DET
ejpam-5362	17	35	sequence	sequence	NOUN
ejpam-5362	17	36	of	of	ADP
ejpam-5362	17	37	τi	τi	NOUN
ejpam-5362	17	38	-	-	PUNCT
ejpam-5362	17	39	dense	dense	ADJ
ejpam-5362	17	40	τj	τj	ADP
ejpam-5362	17	41	-	-	PUNCT
ejpam-5362	17	42	open	open	ADJ
ejpam-5362	17	43	subsets	subset	NOUN
ejpam-5362	17	44	is	be	AUX
ejpam-5362	17	45	τi	τi	ADJ
ejpam-5362	17	46	-	-	ADV
ejpam-5362	17	47	open	open	ADJ
ejpam-5362	17	48	.	.	PUNCT
ejpam-5362	18	1	a	a	DET
ejpam-5362	18	2	study	study	NOUN
ejpam-5362	18	3	of	of	ADP
ejpam-5362	18	4	almost	almost	ADV
ejpam-5362	18	5	(	(	PUNCT
ejpam-5362	18	6	i	i	NOUN
ejpam-5362	18	7	,	,	PUNCT
ejpam-5362	18	8	j)-baire	j)-baire	NOUN
ejpam-5362	18	9	bispaces	bispace	NOUN
ejpam-5362	18	10	is	be	AUX
ejpam-5362	18	11	documented	document	VERB
ejpam-5362	18	12	in	in	ADP
ejpam-5362	18	13	[	[	X
ejpam-5362	18	14	8	8	NUM
ejpam-5362	18	15	]	]	PUNCT
ejpam-5362	18	16	.	.	PUNCT
ejpam-5362	19	1	these	these	DET
ejpam-5362	19	2	bispaces	bispace	NOUN
ejpam-5362	19	3	also	also	ADV
ejpam-5362	19	4	appear	appear	VERB
ejpam-5362	19	5	in	in	ADP
ejpam-5362	19	6	a	a	DET
ejpam-5362	19	7	number	number	NOUN
ejpam-5362	19	8	of	of	ADP
ejpam-5362	19	9	articles	article	NOUN
ejpam-5362	19	10	such	such	ADJ
ejpam-5362	19	11	as	as	ADP
ejpam-5362	19	12	[	[	X
ejpam-5362	19	13	7	7	NUM
ejpam-5362	19	14	]	]	PUNCT
ejpam-5362	19	15	and	and	CCONJ
ejpam-5362	19	16	[	[	X
ejpam-5362	19	17	6	6	NUM
ejpam-5362	19	18	]	]	PUNCT
ejpam-5362	19	19	.	.	PUNCT
ejpam-5362	20	1	in	in	ADP
ejpam-5362	20	2	locale	locale	PROPN
ejpam-5362	20	3	theory	theory	NOUN
ejpam-5362	20	4	,	,	PUNCT
ejpam-5362	20	5	a	a	DET
ejpam-5362	20	6	baire	baire	NOUN
ejpam-5362	20	7	locale	locale	NOUN
ejpam-5362	20	8	was	be	AUX
ejpam-5362	20	9	introduced	introduce	VERB
ejpam-5362	20	10	by	by	ADP
ejpam-5362	20	11	isbell	isbell	NOUN
ejpam-5362	20	12	[	[	X
ejpam-5362	20	13	10	10	NUM
ejpam-5362	20	14	]	]	PUNCT
ejpam-5362	20	15	as	as	ADP
ejpam-5362	20	16	one	one	NUM
ejpam-5362	20	17	in	in	ADP
ejpam-5362	20	18	which	which	PRON
ejpam-5362	20	19	every	every	DET
ejpam-5362	20	20	non	non	ADJ
ejpam-5362	20	21	-	-	ADJ
ejpam-5362	20	22	void	void	ADJ
ejpam-5362	20	23	open	open	ADJ
ejpam-5362	20	24	sublocale	sublocale	NOUN
ejpam-5362	20	25	is	be	AUX
ejpam-5362	20	26	of	of	ADP
ejpam-5362	20	27	second	second	ADJ
ejpam-5362	20	28	category	category	NOUN
ejpam-5362	20	29	.	.	PUNCT
ejpam-5362	21	1	to	to	ADP
ejpam-5362	21	2	our	our	PRON
ejpam-5362	21	3	knowledge	knowledge	NOUN
ejpam-5362	21	4	,	,	PUNCT
ejpam-5362	21	5	(	(	PUNCT
ejpam-5362	21	6	i	i	PRON
ejpam-5362	21	7	,	,	PUNCT
ejpam-5362	21	8	j)-baireness	j)-baireness	PROPN
ejpam-5362	21	9	has	have	AUX
ejpam-5362	21	10	not	not	PART
ejpam-5362	21	11	yet	yet	ADV
ejpam-5362	21	12	appeared	appear	VERB
ejpam-5362	21	13	in	in	ADP
ejpam-5362	21	14	the	the	DET
ejpam-5362	21	15	category	category	NOUN
ejpam-5362	21	16	of	of	ADP
ejpam-5362	21	17	doi	doi	NOUN
ejpam-5362	21	18	:	:	PUNCT
ejpam-5362	21	19	https://doi.org/10.29020/nybg.ejpam.v18i1.5362	https://doi.org/10.29020/nybg.ejpam.v18i1.5362	ADJ
ejpam-5362	21	20	email	email	NOUN
ejpam-5362	21	21	address	address	NOUN
ejpam-5362	21	22	:	:	PUNCT
ejpam-5362	21	23	sibahlezwide@gmail.com	sibahlezwide@gmail.com	X
ejpam-5362	21	24	(	(	PUNCT
ejpam-5362	21	25	m.	m.	NOUN
ejpam-5362	21	26	nxumalo	nxumalo	PROPN
ejpam-5362	21	27	)	)	PUNCT
ejpam-5362	21	28	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5362	22	1	1	1	NUM
ejpam-5362	22	2	copyright	copyright	NOUN
ejpam-5362	22	3	:	:	PUNCT
ejpam-5362	22	4	©	©	PROPN
ejpam-5362	22	5	2025	2025	NUM
ejpam-5362	22	6	the	the	DET
ejpam-5362	22	7	author(s	author(s	NOUN
ejpam-5362	22	8	)	)	PUNCT
ejpam-5362	22	9	.	.	PUNCT
ejpam-5362	23	1	(	(	PUNCT
ejpam-5362	23	2	cc	cc	NOUN
ejpam-5362	23	3	by	by	ADP
ejpam-5362	23	4	-	-	PUNCT
ejpam-5362	23	5	nc	nc	PROPN
ejpam-5362	23	6	4.0	4.0	NUM
ejpam-5362	23	7	)	)	PUNCT
ejpam-5362	23	8	m.	m.	NOUN
ejpam-5362	23	9	nxumalo	nxumalo	PROPN
ejpam-5362	23	10	/	/	SYM
ejpam-5362	23	11	eur	eur	PROPN
ejpam-5362	23	12	.	.	PUNCT
ejpam-5362	24	1	j.	j.	PROPN
ejpam-5362	24	2	pure	pure	PROPN
ejpam-5362	24	3	appl	appl	PROPN
ejpam-5362	24	4	.	.	PROPN
ejpam-5362	24	5	math	math	PROPN
ejpam-5362	24	6	,	,	PUNCT
ejpam-5362	24	7	18	18	NUM
ejpam-5362	24	8	(	(	PUNCT
ejpam-5362	24	9	1	1	NUM
ejpam-5362	24	10	)	)	PUNCT
ejpam-5362	24	11	(	(	PUNCT
ejpam-5362	24	12	2025	2025	NUM
ejpam-5362	24	13	)	)	PUNCT
ejpam-5362	24	14	,	,	PUNCT
ejpam-5362	24	15	5362	5362	NUM
ejpam-5362	24	16	2	2	NUM
ejpam-5362	24	17	of	of	ADP
ejpam-5362	24	18	21	21	NUM
ejpam-5362	24	19	bilocales	bilocale	NOUN
ejpam-5362	24	20	.	.	PUNCT
ejpam-5362	25	1	in	in	ADP
ejpam-5362	25	2	this	this	DET
ejpam-5362	25	3	paper	paper	NOUN
ejpam-5362	25	4	,	,	PUNCT
ejpam-5362	25	5	we	we	PRON
ejpam-5362	25	6	introduce	introduce	VERB
ejpam-5362	25	7	and	and	CCONJ
ejpam-5362	25	8	study	study	VERB
ejpam-5362	25	9	(	(	PUNCT
ejpam-5362	25	10	i	i	PROPN
ejpam-5362	25	11	,	,	PUNCT
ejpam-5362	25	12	j)-baire	j)-baire	PROPN
ejpam-5362	25	13	bilocales	bilocale	NOUN
ejpam-5362	25	14	.	.	PUNCT
ejpam-5362	26	1	our	our	PRON
ejpam-5362	26	2	definition	definition	NOUN
ejpam-5362	26	3	is	be	AUX
ejpam-5362	26	4	rather	rather	ADV
ejpam-5362	26	5	an	an	DET
ejpam-5362	26	6	extension	extension	NOUN
ejpam-5362	26	7	of	of	ADP
ejpam-5362	26	8	almost	almost	ADV
ejpam-5362	26	9	(	(	PUNCT
ejpam-5362	26	10	i	i	NOUN
ejpam-5362	26	11	,	,	PUNCT
ejpam-5362	26	12	j)-baire	j)-baire	NOUN
ejpam-5362	26	13	bispaces	bispace	NOUN
ejpam-5362	26	14	instead	instead	ADV
ejpam-5362	26	15	of	of	ADP
ejpam-5362	26	16	baire	baire	NOUN
ejpam-5362	26	17	locales	locale	NOUN
ejpam-5362	26	18	,	,	PUNCT
ejpam-5362	26	19	with	with	ADP
ejpam-5362	26	20	the	the	DET
ejpam-5362	26	21	prefix	prefix	NOUN
ejpam-5362	26	22	“	"	PUNCT
ejpam-5362	26	23	almost	almost	ADV
ejpam-5362	26	24	”	"	PUNCT
ejpam-5362	26	25	being	be	AUX
ejpam-5362	26	26	dropped	drop	VERB
ejpam-5362	26	27	.	.	PUNCT
ejpam-5362	27	1	since	since	SCONJ
ejpam-5362	27	2	the	the	DET
ejpam-5362	27	3	definition	definition	NOUN
ejpam-5362	27	4	of	of	ADP
ejpam-5362	27	5	almost	almost	ADV
ejpam-5362	27	6	(	(	PUNCT
ejpam-5362	27	7	i	i	NOUN
ejpam-5362	27	8	,	,	PUNCT
ejpam-5362	27	9	j)-baire	j)-baire	ADJ
ejpam-5362	27	10	bispace	bispace	NOUN
ejpam-5362	27	11	is	be	AUX
ejpam-5362	27	12	purely	purely	ADV
ejpam-5362	27	13	in	in	ADP
ejpam-5362	27	14	terms	term	NOUN
ejpam-5362	27	15	of	of	ADP
ejpam-5362	27	16	open	open	ADJ
ejpam-5362	27	17	subsets	subset	NOUN
ejpam-5362	27	18	,	,	PUNCT
ejpam-5362	27	19	we	we	PRON
ejpam-5362	27	20	extend	extend	VERB
ejpam-5362	27	21	it	it	PRON
ejpam-5362	27	22	to	to	ADP
ejpam-5362	27	23	bilocales	bilocale	NOUN
ejpam-5362	27	24	almost	almost	ADV
ejpam-5362	27	25	verbatim	verbatim	ADJ
ejpam-5362	27	26	.	.	PUNCT
ejpam-5362	28	1	we	we	PRON
ejpam-5362	28	2	aim	aim	VERB
ejpam-5362	28	3	to	to	PART
ejpam-5362	28	4	extend	extend	VERB
ejpam-5362	28	5	some	some	DET
ejpam-5362	28	6	known	know	VERB
ejpam-5362	28	7	bispaces	bispace	NOUN
ejpam-5362	28	8	results	result	NOUN
ejpam-5362	28	9	and	and	CCONJ
ejpam-5362	28	10	also	also	ADV
ejpam-5362	28	11	give	give	VERB
ejpam-5362	28	12	some	some	DET
ejpam-5362	28	13	natural	natural	ADJ
ejpam-5362	28	14	properties	property	NOUN
ejpam-5362	28	15	of	of	ADP
ejpam-5362	28	16	(	(	PUNCT
ejpam-5362	28	17	i	i	PROPN
ejpam-5362	28	18	,	,	PUNCT
ejpam-5362	28	19	j)-baire	j)-baire	NOUN
ejpam-5362	28	20	bilocales	bilocale	NOUN
ejpam-5362	28	21	.	.	PUNCT
ejpam-5362	29	1	some	some	PRON
ejpam-5362	29	2	of	of	ADP
ejpam-5362	29	3	the	the	DET
ejpam-5362	29	4	natural	natural	ADJ
ejpam-5362	29	5	results	result	NOUN
ejpam-5362	29	6	include	include	VERB
ejpam-5362	29	7	(	(	PUNCT
ejpam-5362	29	8	i	i	INTJ
ejpam-5362	29	9	,	,	PUNCT
ejpam-5362	29	10	j)-baireness	j)-baireness	NOUN
ejpam-5362	29	11	of	of	ADP
ejpam-5362	29	12	both	both	CCONJ
ejpam-5362	29	13	the	the	DET
ejpam-5362	29	14	ideal	ideal	ADJ
ejpam-5362	29	15	bilocale	bilocale	NOUN
ejpam-5362	29	16	and	and	CCONJ
ejpam-5362	29	17	the	the	DET
ejpam-5362	29	18	subbilocale	subbilocale	NOUN
ejpam-5362	29	19	induced	induce	VERB
ejpam-5362	29	20	by	by	ADP
ejpam-5362	29	21	the	the	DET
ejpam-5362	29	22	smallest	small	ADJ
ejpam-5362	29	23	dense	dense	ADJ
ejpam-5362	29	24	sublocale	sublocale	NOUN
ejpam-5362	29	25	.	.	PUNCT
ejpam-5362	30	1	extending	extend	VERB
ejpam-5362	30	2	results	result	NOUN
ejpam-5362	30	3	from	from	ADP
ejpam-5362	30	4	spaces	space	NOUN
ejpam-5362	30	5	or	or	CCONJ
ejpam-5362	30	6	bispaces	bispace	NOUN
ejpam-5362	30	7	to	to	ADP
ejpam-5362	30	8	bilocales	bilocale	NOUN
ejpam-5362	30	9	/	/	SYM
ejpam-5362	30	10	biframes	biframe	NOUN
ejpam-5362	30	11	is	be	AUX
ejpam-5362	30	12	not	not	PART
ejpam-5362	30	13	outrageous	outrageous	ADJ
ejpam-5362	30	14	.	.	PUNCT
ejpam-5362	31	1	for	for	ADP
ejpam-5362	31	2	instance	instance	NOUN
ejpam-5362	31	3	,	,	PUNCT
ejpam-5362	31	4	schauerte	schauerte	VERB
ejpam-5362	31	5	in	in	ADP
ejpam-5362	31	6	[	[	X
ejpam-5362	31	7	21	21	NUM
ejpam-5362	31	8	]	]	PUNCT
ejpam-5362	31	9	extended	extend	VERB
ejpam-5362	31	10	the	the	DET
ejpam-5362	31	11	notion	notion	NOUN
ejpam-5362	31	12	of	of	ADP
ejpam-5362	31	13	a	a	DET
ejpam-5362	31	14	normal	normal	ADJ
ejpam-5362	31	15	space	space	NOUN
ejpam-5362	31	16	to	to	ADP
ejpam-5362	31	17	a	a	DET
ejpam-5362	31	18	normal	normal	ADJ
ejpam-5362	31	19	biframe	biframe	NOUN
ejpam-5362	31	20	.	.	PUNCT
ejpam-5362	32	1	this	this	DET
ejpam-5362	32	2	paper	paper	NOUN
ejpam-5362	32	3	contributes	contribute	VERB
ejpam-5362	32	4	to	to	ADP
ejpam-5362	32	5	the	the	DET
ejpam-5362	32	6	theory	theory	NOUN
ejpam-5362	32	7	of	of	ADP
ejpam-5362	32	8	bilocales	bilocale	NOUN
ejpam-5362	32	9	.	.	PUNCT
ejpam-5362	33	1	this	this	DET
ejpam-5362	33	2	paper	paper	NOUN
ejpam-5362	33	3	is	be	AUX
ejpam-5362	33	4	organized	organize	VERB
ejpam-5362	33	5	as	as	SCONJ
ejpam-5362	33	6	follows	follow	VERB
ejpam-5362	33	7	.	.	PUNCT
ejpam-5362	34	1	section	section	NOUN
ejpam-5362	34	2	two	two	NUM
ejpam-5362	34	3	consists	consist	NOUN
ejpam-5362	34	4	of	of	ADP
ejpam-5362	34	5	the	the	DET
ejpam-5362	34	6	necessary	necessary	ADJ
ejpam-5362	34	7	background	background	NOUN
ejpam-5362	34	8	.	.	PUNCT
ejpam-5362	35	1	in	in	ADP
ejpam-5362	35	2	section	section	NOUN
ejpam-5362	35	3	three	three	NUM
ejpam-5362	35	4	we	we	PRON
ejpam-5362	35	5	introduce	introduce	VERB
ejpam-5362	35	6	and	and	CCONJ
ejpam-5362	35	7	characterize	characterize	VERB
ejpam-5362	35	8	(	(	PUNCT
ejpam-5362	35	9	i	i	PROPN
ejpam-5362	35	10	,	,	PUNCT
ejpam-5362	35	11	j)-baire	j)-baire	NOUN
ejpam-5362	35	12	bilocales	bilocale	NOUN
ejpam-5362	35	13	.	.	PUNCT
ejpam-5362	36	1	we	we	PRON
ejpam-5362	36	2	also	also	ADV
ejpam-5362	36	3	show	show	VERB
ejpam-5362	36	4	that	that	SCONJ
ejpam-5362	36	5	the	the	DET
ejpam-5362	36	6	class	class	NOUN
ejpam-5362	36	7	of	of	ADP
ejpam-5362	36	8	(	(	PUNCT
ejpam-5362	36	9	i	i	PROPN
ejpam-5362	36	10	,	,	PUNCT
ejpam-5362	36	11	j)-baire	j)-baire	PROPN
ejpam-5362	36	12	bilocales	bilocale	NOUN
ejpam-5362	36	13	includes	include	VERB
ejpam-5362	36	14	the	the	DET
ejpam-5362	36	15	following	follow	VERB
ejpam-5362	36	16	classes	class	NOUN
ejpam-5362	36	17	:	:	PUNCT
ejpam-5362	36	18	(	(	PUNCT
ejpam-5362	36	19	i	i	NOUN
ejpam-5362	36	20	)	)	PUNCT
ejpam-5362	36	21	compact	compact	PROPN
ejpam-5362	36	22	i	i	NOUN
ejpam-5362	36	23	-	-	PUNCT
ejpam-5362	36	24	prefit	prefit	PROPN
ejpam-5362	36	25	bilocales	bilocale	NOUN
ejpam-5362	36	26	,	,	PUNCT
ejpam-5362	36	27	(	(	PUNCT
ejpam-5362	36	28	ii	ii	NOUN
ejpam-5362	36	29	)	)	PUNCT
ejpam-5362	36	30	bilocales	bilocale	NOUN
ejpam-5362	36	31	(	(	PUNCT
ejpam-5362	36	32	l	l	NOUN
ejpam-5362	36	33	,	,	PUNCT
ejpam-5362	36	34	l1	l1	PROPN
ejpam-5362	36	35	,	,	PUNCT
ejpam-5362	36	36	l2	l2	NOUN
ejpam-5362	36	37	)	)	PUNCT
ejpam-5362	36	38	where	where	SCONJ
ejpam-5362	36	39	there	there	PRON
ejpam-5362	36	40	is	be	VERB
ejpam-5362	36	41	an	an	DET
ejpam-5362	36	42	i	i	NOUN
ejpam-5362	36	43	-	-	PUNCT
ejpam-5362	36	44	prefit	prefit	NOUN
ejpam-5362	36	45	compactification	compactification	NOUN
ejpam-5362	36	46	h	h	NOUN
ejpam-5362	36	47	:	:	PUNCT
ejpam-5362	36	48	(	(	PUNCT
ejpam-5362	36	49	m	m	NOUN
ejpam-5362	36	50	,	,	PUNCT
ejpam-5362	36	51	m1,m2	m1,m2	PROPN
ejpam-5362	36	52	)	)	PUNCT
ejpam-5362	36	53	→	→	SYM
ejpam-5362	36	54	(	(	PUNCT
ejpam-5362	36	55	l	l	NOUN
ejpam-5362	36	56	,	,	PUNCT
ejpam-5362	36	57	l1	l1	PROPN
ejpam-5362	36	58	,	,	PUNCT
ejpam-5362	36	59	l2	l2	NOUN
ejpam-5362	36	60	)	)	PUNCT
ejpam-5362	36	61	with	with	ADP
ejpam-5362	36	62	which	which	PRON
ejpam-5362	36	63	h∗[l	h∗[l	NOUN
ejpam-5362	36	64	]	]	PUNCT
ejpam-5362	36	65	is	be	AUX
ejpam-5362	36	66	i	i	PROPN
ejpam-5362	36	67	-	-	PUNCT
ejpam-5362	36	68	gδ	gδ	NOUN
ejpam-5362	36	69	-	-	PUNCT
ejpam-5362	36	70	dense	dense	ADJ
ejpam-5362	36	71	inm	inm	NOUN
ejpam-5362	36	72	,	,	PUNCT
ejpam-5362	36	73	and	and	CCONJ
ejpam-5362	36	74	(	(	PUNCT
ejpam-5362	36	75	iii	iii	X
ejpam-5362	36	76	)	)	PUNCT
ejpam-5362	36	77	i	i	NOUN
ejpam-5362	36	78	-	-	PUNCT
ejpam-5362	36	79	pseudocomplete	pseudocomplete	NOUN
ejpam-5362	36	80	bilocales	bilocale	NOUN
ejpam-5362	36	81	.	.	PUNCT
ejpam-5362	37	1	in	in	ADP
ejpam-5362	37	2	the	the	DET
ejpam-5362	37	3	class	class	NOUN
ejpam-5362	37	4	of	of	ADP
ejpam-5362	37	5	noetherian	noetherian	ADJ
ejpam-5362	37	6	bilocales	bilocale	NOUN
ejpam-5362	37	7	,	,	PUNCT
ejpam-5362	37	8	a	a	DET
ejpam-5362	37	9	bilocale	bilocale	NOUN
ejpam-5362	37	10	is	be	AUX
ejpam-5362	37	11	(	(	PUNCT
ejpam-5362	37	12	i	i	NOUN
ejpam-5362	37	13	,	,	PUNCT
ejpam-5362	37	14	j)-baire	j)-baire	VERB
ejpam-5362	37	15	if	if	SCONJ
ejpam-5362	37	16	and	and	CCONJ
ejpam-5362	37	17	only	only	ADV
ejpam-5362	37	18	if	if	SCONJ
ejpam-5362	37	19	the	the	DET
ejpam-5362	37	20	induced	induced	ADJ
ejpam-5362	37	21	ideal	ideal	ADJ
ejpam-5362	37	22	bilocale	bilocale	NOUN
ejpam-5362	37	23	is	be	AUX
ejpam-5362	37	24	(	(	PUNCT
ejpam-5362	37	25	i	i	NOUN
ejpam-5362	37	26	,	,	PUNCT
ejpam-5362	37	27	j)-baire	j)-baire	NOUN
ejpam-5362	37	28	.	.	PUNCT
ejpam-5362	38	1	in	in	ADP
ejpam-5362	38	2	section	section	NOUN
ejpam-5362	38	3	four	four	NUM
ejpam-5362	38	4	,	,	PUNCT
ejpam-5362	38	5	we	we	PRON
ejpam-5362	38	6	investigate	investigate	VERB
ejpam-5362	38	7	relative	relative	ADJ
ejpam-5362	38	8	versions	version	NOUN
ejpam-5362	38	9	of	of	ADP
ejpam-5362	38	10	(	(	PUNCT
ejpam-5362	38	11	i	i	NOUN
ejpam-5362	38	12	,	,	PUNCT
ejpam-5362	38	13	j)-baireness	j)-baireness	ADJ
ejpam-5362	38	14	.	.	PUNCT
ejpam-5362	39	1	we	we	PRON
ejpam-5362	39	2	show	show	VERB
ejpam-5362	39	3	that	that	SCONJ
ejpam-5362	39	4	a	a	DET
ejpam-5362	39	5	bilocale	bilocale	NOUN
ejpam-5362	39	6	is	be	AUX
ejpam-5362	39	7	(	(	PUNCT
ejpam-5362	39	8	i	i	NOUN
ejpam-5362	39	9	,	,	PUNCT
ejpam-5362	39	10	j)-baire	j)-baire	VERB
ejpam-5362	39	11	only	only	ADV
ejpam-5362	39	12	if	if	SCONJ
ejpam-5362	39	13	the	the	DET
ejpam-5362	39	14	subbilocale	subbilocale	NOUN
ejpam-5362	39	15	induced	induce	VERB
ejpam-5362	39	16	by	by	ADP
ejpam-5362	39	17	the	the	DET
ejpam-5362	39	18	smallest	small	ADJ
ejpam-5362	39	19	dense	dense	ADJ
ejpam-5362	39	20	sublocale	sublocale	NOUN
ejpam-5362	39	21	is	be	AUX
ejpam-5362	39	22	(	(	PUNCT
ejpam-5362	39	23	i	i	NOUN
ejpam-5362	39	24	,	,	PUNCT
ejpam-5362	39	25	j)-baire	j)-baire	PROPN
ejpam-5362	39	26	.	.	PUNCT
ejpam-5362	40	1	we	we	PRON
ejpam-5362	40	2	also	also	ADV
ejpam-5362	40	3	introduce	introduce	VERB
ejpam-5362	40	4	and	and	CCONJ
ejpam-5362	40	5	characterize	characterize	VERB
ejpam-5362	40	6	relatively	relatively	ADV
ejpam-5362	40	7	(	(	PUNCT
ejpam-5362	40	8	i	i	NOUN
ejpam-5362	40	9	,	,	PUNCT
ejpam-5362	40	10	j)-baire	j)-baire	NOUN
ejpam-5362	40	11	subbilocales	subbilocale	NOUN
ejpam-5362	40	12	.	.	PUNCT
ejpam-5362	41	1	it	it	PRON
ejpam-5362	41	2	turns	turn	VERB
ejpam-5362	41	3	out	out	ADP
ejpam-5362	41	4	that	that	SCONJ
ejpam-5362	41	5	in	in	ADP
ejpam-5362	41	6	a	a	DET
ejpam-5362	41	7	class	class	NOUN
ejpam-5362	41	8	of	of	ADP
ejpam-5362	41	9	dense	dense	ADJ
ejpam-5362	41	10	subbilocales	subbilocale	NOUN
ejpam-5362	41	11	,	,	PUNCT
ejpam-5362	41	12	(	(	PUNCT
ejpam-5362	41	13	i	i	PRON
ejpam-5362	41	14	,	,	PUNCT
ejpam-5362	41	15	j)-baire	j)-baire	VERB
ejpam-5362	41	16	coincides	coincide	VERB
ejpam-5362	41	17	with	with	ADP
ejpam-5362	41	18	relatively	relatively	ADV
ejpam-5362	41	19	(	(	PUNCT
ejpam-5362	41	20	i	i	NOUN
ejpam-5362	41	21	,	,	PUNCT
ejpam-5362	41	22	j)baire	j)baire	PROPN
ejpam-5362	41	23	.	.	PUNCT
ejpam-5362	42	1	in	in	ADP
ejpam-5362	42	2	section	section	NOUN
ejpam-5362	42	3	five	five	NUM
ejpam-5362	42	4	,	,	PUNCT
ejpam-5362	42	5	we	we	PRON
ejpam-5362	42	6	define	define	VERB
ejpam-5362	42	7	and	and	CCONJ
ejpam-5362	42	8	characterize	characterize	VERB
ejpam-5362	42	9	(	(	PUNCT
ejpam-5362	42	10	τi	τi	ADP
ejpam-5362	42	11	,	,	PUNCT
ejpam-5362	42	12	τj)-baire	τj)-baire	ADJ
ejpam-5362	42	13	topobilocales	topobilocale	NOUN
ejpam-5362	42	14	.	.	PUNCT
ejpam-5362	43	1	2	2	X
ejpam-5362	43	2	.	.	X
ejpam-5362	43	3	preliminaries	preliminary	NOUN
ejpam-5362	43	4	the	the	DET
ejpam-5362	43	5	book	book	NOUN
ejpam-5362	43	6	[	[	X
ejpam-5362	43	7	17	17	NUM
ejpam-5362	43	8	]	]	PUNCT
ejpam-5362	43	9	is	be	AUX
ejpam-5362	43	10	our	our	PRON
ejpam-5362	43	11	main	main	ADJ
ejpam-5362	43	12	reference	reference	NOUN
ejpam-5362	43	13	for	for	ADP
ejpam-5362	43	14	notions	notion	NOUN
ejpam-5362	43	15	of	of	ADP
ejpam-5362	43	16	locales	locale	NOUN
ejpam-5362	43	17	and	and	CCONJ
ejpam-5362	43	18	sublocales	sublocale	NOUN
ejpam-5362	43	19	.	.	PUNCT
ejpam-5362	44	1	see	see	VERB
ejpam-5362	44	2	[	[	X
ejpam-5362	44	3	4	4	NUM
ejpam-5362	44	4	,	,	PUNCT
ejpam-5362	44	5	15	15	NUM
ejpam-5362	44	6	,	,	PUNCT
ejpam-5362	44	7	18	18	NUM
ejpam-5362	44	8	]	]	PUNCT
ejpam-5362	44	9	for	for	ADP
ejpam-5362	44	10	the	the	DET
ejpam-5362	44	11	theory	theory	NOUN
ejpam-5362	44	12	of	of	ADP
ejpam-5362	44	13	bilocales	bilocale	NOUN
ejpam-5362	44	14	.	.	PUNCT
ejpam-5362	45	1	2.1	2.1	NUM
ejpam-5362	45	2	.	.	PUNCT
ejpam-5362	45	3	locales	locale	NOUN
ejpam-5362	45	4	a	a	DET
ejpam-5362	45	5	locale	locale	PROPN
ejpam-5362	45	6	l	l	NOUN
ejpam-5362	45	7	is	be	AUX
ejpam-5362	45	8	a	a	DET
ejpam-5362	45	9	complete	complete	ADJ
ejpam-5362	45	10	lattice	lattice	NOUN
ejpam-5362	45	11	in	in	ADP
ejpam-5362	45	12	which	which	PRON
ejpam-5362	45	13	a	a	DET
ejpam-5362	45	14	∧	∧	PROPN
ejpam-5362	45	15	∨	∨	NUM
ejpam-5362	45	16	b	b	NOUN
ejpam-5362	45	17	=	=	SYM
ejpam-5362	45	18	∨	∨	X
ejpam-5362	45	19	{	{	PUNCT
ejpam-5362	45	20	a	a	DET
ejpam-5362	45	21	∧	∧	PROPN
ejpam-5362	45	22	b	b	PROPN
ejpam-5362	45	23	:	:	PUNCT
ejpam-5362	45	24	b	b	X
ejpam-5362	45	25	∈	∈	PROPN
ejpam-5362	45	26	b	b	NOUN
ejpam-5362	45	27	}	}	PUNCT
ejpam-5362	45	28	for	for	ADP
ejpam-5362	45	29	all	all	DET
ejpam-5362	45	30	a	a	DET
ejpam-5362	45	31	∈	∈	PROPN
ejpam-5362	45	32	l	l	NOUN
ejpam-5362	45	33	,	,	PUNCT
ejpam-5362	45	34	b	b	PROPN
ejpam-5362	45	35	⊆	⊆	NUM
ejpam-5362	45	36	l.	l.	PROPN
ejpam-5362	45	37	1l	1l	PROPN
ejpam-5362	45	38	and	and	CCONJ
ejpam-5362	45	39	0l	0l	NUM
ejpam-5362	45	40	,	,	PUNCT
ejpam-5362	45	41	with	with	SCONJ
ejpam-5362	45	42	subscripts	subscript	NOUN
ejpam-5362	45	43	dropped	drop	VERB
ejpam-5362	45	44	if	if	SCONJ
ejpam-5362	45	45	there	there	PRON
ejpam-5362	45	46	is	be	VERB
ejpam-5362	45	47	no	no	DET
ejpam-5362	45	48	possibility	possibility	NOUN
ejpam-5362	45	49	of	of	ADP
ejpam-5362	45	50	confusion	confusion	NOUN
ejpam-5362	45	51	,	,	PUNCT
ejpam-5362	45	52	respectively	respectively	ADV
ejpam-5362	45	53	denote	denote	VERB
ejpam-5362	45	54	the	the	DET
ejpam-5362	45	55	top	top	ADJ
ejpam-5362	45	56	element	element	NOUN
ejpam-5362	45	57	and	and	CCONJ
ejpam-5362	45	58	the	the	DET
ejpam-5362	45	59	bottom	bottom	ADJ
ejpam-5362	45	60	element	element	NOUN
ejpam-5362	45	61	of	of	ADP
ejpam-5362	45	62	a	a	DET
ejpam-5362	45	63	locale	locale	NOUN
ejpam-5362	45	64	l.	l.	NOUN
ejpam-5362	45	65	by	by	ADP
ejpam-5362	45	66	a	a	DET
ejpam-5362	45	67	point	point	NOUN
ejpam-5362	45	68	of	of	ADP
ejpam-5362	45	69	a	a	DET
ejpam-5362	45	70	locale	locale	ADJ
ejpam-5362	45	71	l	l	NOUN
ejpam-5362	45	72	we	we	PRON
ejpam-5362	45	73	mean	mean	VERB
ejpam-5362	45	74	an	an	DET
ejpam-5362	45	75	element	element	NOUN
ejpam-5362	45	76	a	a	PRON
ejpam-5362	45	77	of	of	ADP
ejpam-5362	45	78	l	l	NOUN
ejpam-5362	46	1	such	such	ADJ
ejpam-5362	46	2	that	that	SCONJ
ejpam-5362	46	3	a	a	DET
ejpam-5362	46	4	̸=	̸=	PROPN
ejpam-5362	46	5	1	1	NUM
ejpam-5362	46	6	and	and	CCONJ
ejpam-5362	46	7	b∧	b∧	PROPN
ejpam-5362	46	8	c	c	NOUN
ejpam-5362	46	9	≤	≤	NOUN
ejpam-5362	46	10	a	a	PRON
ejpam-5362	46	11	implies	implie	NOUN
ejpam-5362	46	12	b	b	NOUN
ejpam-5362	46	13	≤	≤	NOUN
ejpam-5362	46	14	a	a	PRON
ejpam-5362	46	15	or	or	CCONJ
ejpam-5362	46	16	c	c	NOUN
ejpam-5362	46	17	≤	≤	NOUN
ejpam-5362	46	18	a	a	PRON
ejpam-5362	46	19	for	for	ADP
ejpam-5362	46	20	all	all	DET
ejpam-5362	46	21	b	b	NOUN
ejpam-5362	46	22	,	,	PUNCT
ejpam-5362	46	23	c	c	PROPN
ejpam-5362	46	24	∈	∈	PROPN
ejpam-5362	46	25	l.	l.	NOUN
ejpam-5362	46	26	we	we	PRON
ejpam-5362	46	27	denote	denote	VERB
ejpam-5362	46	28	by	by	ADP
ejpam-5362	46	29	a∗	a∗	PROPN
ejpam-5362	46	30	the	the	DET
ejpam-5362	46	31	pseudocomplement	pseudocomplement	NOUN
ejpam-5362	46	32	of	of	ADP
ejpam-5362	46	33	an	an	DET
ejpam-5362	46	34	element	element	NOUN
ejpam-5362	46	35	a	a	DET
ejpam-5362	46	36	∈	∈	PROPN
ejpam-5362	46	37	l.	l.	NOUN
ejpam-5362	46	38	an	an	DET
ejpam-5362	46	39	element	element	NOUN
ejpam-5362	46	40	a	a	DET
ejpam-5362	46	41	∈	∈	PROPN
ejpam-5362	46	42	l	l	NOUN
ejpam-5362	46	43	is	be	AUX
ejpam-5362	46	44	said	say	VERB
ejpam-5362	46	45	to	to	PART
ejpam-5362	46	46	be	be	AUX
ejpam-5362	46	47	dense	dense	ADJ
ejpam-5362	46	48	and	and	CCONJ
ejpam-5362	46	49	complemented	complement	VERB
ejpam-5362	46	50	in	in	ADP
ejpam-5362	46	51	case	case	NOUN
ejpam-5362	46	52	a∗	a∗	NOUN
ejpam-5362	46	53	=	=	SYM
ejpam-5362	46	54	0	0	NUM
ejpam-5362	46	55	and	and	CCONJ
ejpam-5362	46	56	a	a	DET
ejpam-5362	46	57	∨	∨	NOUN
ejpam-5362	46	58	a∗	a∗	NOUN
ejpam-5362	46	59	=	=	SYM
ejpam-5362	46	60	1	1	NUM
ejpam-5362	46	61	,	,	PUNCT
ejpam-5362	46	62	respectively	respectively	ADV
ejpam-5362	46	63	.	.	PUNCT
ejpam-5362	47	1	an	an	DET
ejpam-5362	47	2	element	element	NOUN
ejpam-5362	47	3	x	x	SYM
ejpam-5362	47	4	∈	∈	NOUN
ejpam-5362	47	5	l	l	NOUN
ejpam-5362	47	6	is	be	AUX
ejpam-5362	47	7	compact	compact	ADJ
ejpam-5362	47	8	if	if	SCONJ
ejpam-5362	47	9	x	x	SYM
ejpam-5362	47	10	≤	≤	X
ejpam-5362	47	11	∨	∨	NUM
ejpam-5362	47	12	a	a	PRON
ejpam-5362	47	13	for	for	ADP
ejpam-5362	47	14	a	a	DET
ejpam-5362	47	15	⊆	⊆	NUM
ejpam-5362	47	16	l	l	NOUN
ejpam-5362	47	17	implies	imply	VERB
ejpam-5362	47	18	x	x	PUNCT
ejpam-5362	47	19	≤	≤	X
ejpam-5362	47	20	∨	∨	NUM
ejpam-5362	47	21	f	f	NOUN
ejpam-5362	47	22	for	for	ADP
ejpam-5362	47	23	some	some	DET
ejpam-5362	47	24	finite	finite	NOUN
ejpam-5362	47	25	f	f	PROPN
ejpam-5362	47	26	⊆	⊆	NUM
ejpam-5362	47	27	a.	a.	NOUN
ejpam-5362	47	28	by	by	ADP
ejpam-5362	47	29	a	a	DET
ejpam-5362	47	30	compact	compact	ADJ
ejpam-5362	47	31	locale	locale	NOUN
ejpam-5362	47	32	l	l	NOUN
ejpam-5362	47	33	we	we	PRON
ejpam-5362	47	34	mean	mean	VERB
ejpam-5362	47	35	a	a	DET
ejpam-5362	47	36	locale	locale	NOUN
ejpam-5362	47	37	in	in	ADP
ejpam-5362	47	38	which	which	PRON
ejpam-5362	47	39	the	the	DET
ejpam-5362	47	40	top	top	ADJ
ejpam-5362	47	41	element	element	NOUN
ejpam-5362	47	42	is	be	AUX
ejpam-5362	47	43	compact	compact	ADJ
ejpam-5362	47	44	.	.	PUNCT
ejpam-5362	48	1	a	a	DET
ejpam-5362	48	2	regular	regular	ADJ
ejpam-5362	48	3	locale	locale	NOUN
ejpam-5362	48	4	is	be	AUX
ejpam-5362	48	5	a	a	DET
ejpam-5362	48	6	locale	locale	NOUN
ejpam-5362	48	7	l	l	NOUN
ejpam-5362	48	8	in	in	ADP
ejpam-5362	48	9	which	which	PRON
ejpam-5362	48	10	a	a	DET
ejpam-5362	48	11	=	=	SYM
ejpam-5362	48	12	∨	∨	X
ejpam-5362	48	13	{	{	PUNCT
ejpam-5362	48	14	x	x	SYM
ejpam-5362	48	15	∈	∈	NOUN
ejpam-5362	48	16	l	l	NOUN
ejpam-5362	48	17	:	:	PUNCT
ejpam-5362	48	18	x	x	SYM
ejpam-5362	48	19	≺	≺	NOUN
ejpam-5362	48	20	a	a	PRON
ejpam-5362	48	21	}	}	PUNCT
ejpam-5362	48	22	for	for	ADP
ejpam-5362	48	23	every	every	DET
ejpam-5362	48	24	a	a	DET
ejpam-5362	48	25	∈	∈	PROPN
ejpam-5362	48	26	l	l	NOUN
ejpam-5362	48	27	,	,	PUNCT
ejpam-5362	48	28	where	where	SCONJ
ejpam-5362	48	29	x	x	PUNCT
ejpam-5362	48	30	≺	≺	VERB
ejpam-5362	48	31	a	a	DET
ejpam-5362	48	32	means	means	NOUN
ejpam-5362	48	33	that	that	PRON
ejpam-5362	48	34	x∗	x∗	PROPN
ejpam-5362	48	35	∨	∨	NUM
ejpam-5362	48	36	a	a	PRON
ejpam-5362	48	37	=	=	ADJ
ejpam-5362	48	38	1	1	X
ejpam-5362	48	39	.	.	PUNCT
ejpam-5362	48	40	m.	m.	NOUN
ejpam-5362	48	41	nxumalo	nxumalo	PROPN
ejpam-5362	48	42	/	/	SYM
ejpam-5362	48	43	eur	eur	PROPN
ejpam-5362	48	44	.	.	PUNCT
ejpam-5362	49	1	j.	j.	PROPN
ejpam-5362	49	2	pure	pure	PROPN
ejpam-5362	49	3	appl	appl	PROPN
ejpam-5362	49	4	.	.	PROPN
ejpam-5362	49	5	math	math	PROPN
ejpam-5362	49	6	,	,	PUNCT
ejpam-5362	49	7	18	18	NUM
ejpam-5362	49	8	(	(	PUNCT
ejpam-5362	49	9	1	1	NUM
ejpam-5362	49	10	)	)	PUNCT
ejpam-5362	49	11	(	(	PUNCT
ejpam-5362	49	12	2025	2025	NUM
ejpam-5362	49	13	)	)	PUNCT
ejpam-5362	49	14	,	,	PUNCT
ejpam-5362	49	15	5362	5362	NUM
ejpam-5362	49	16	3	3	NUM
ejpam-5362	49	17	of	of	ADP
ejpam-5362	49	18	21	21	NUM
ejpam-5362	49	19	by	by	ADP
ejpam-5362	49	20	a	a	DET
ejpam-5362	49	21	subframe	subframe	NOUN
ejpam-5362	49	22	of	of	ADP
ejpam-5362	49	23	a	a	DET
ejpam-5362	49	24	locale	locale	NOUN
ejpam-5362	49	25	l	l	NOUN
ejpam-5362	49	26	,	,	PUNCT
ejpam-5362	49	27	we	we	PRON
ejpam-5362	49	28	mean	mean	VERB
ejpam-5362	49	29	a	a	DET
ejpam-5362	49	30	subset	subset	NOUN
ejpam-5362	49	31	which	which	PRON
ejpam-5362	49	32	is	be	AUX
ejpam-5362	49	33	closed	close	VERB
ejpam-5362	49	34	under	under	ADP
ejpam-5362	49	35	joins	join	NOUN
ejpam-5362	49	36	and	and	CCONJ
ejpam-5362	49	37	finite	finite	NOUN
ejpam-5362	49	38	meets	meet	NOUN
ejpam-5362	49	39	.	.	PUNCT
ejpam-5362	50	1	we	we	PRON
ejpam-5362	50	2	denote	denote	VERB
ejpam-5362	50	3	by	by	ADP
ejpam-5362	50	4	ox	ox	NOUN
ejpam-5362	50	5	the	the	DET
ejpam-5362	50	6	locale	locale	NOUN
ejpam-5362	50	7	of	of	ADP
ejpam-5362	50	8	open	open	ADJ
ejpam-5362	50	9	subsets	subset	NOUN
ejpam-5362	50	10	of	of	ADP
ejpam-5362	50	11	a	a	DET
ejpam-5362	50	12	topological	topological	ADJ
ejpam-5362	50	13	space	space	NOUN
ejpam-5362	50	14	x.	x.	NOUN
ejpam-5362	51	1	a	a	DET
ejpam-5362	51	2	localic	localic	ADJ
ejpam-5362	51	3	map	map	NOUN
ejpam-5362	51	4	is	be	AUX
ejpam-5362	51	5	an	an	DET
ejpam-5362	51	6	infima	infima	NOUN
ejpam-5362	51	7	-	-	PUNCT
ejpam-5362	51	8	preserving	preserve	VERB
ejpam-5362	51	9	function	function	NOUN
ejpam-5362	51	10	f	f	NOUN
ejpam-5362	51	11	:	:	PUNCT
ejpam-5362	51	12	l	l	X
ejpam-5362	51	13	→	→	PUNCT
ejpam-5362	51	14	m	m	VERB
ejpam-5362	51	15	between	between	ADP
ejpam-5362	51	16	locales	locale	NOUN
ejpam-5362	51	17	such	such	ADJ
ejpam-5362	51	18	that	that	SCONJ
ejpam-5362	51	19	the	the	DET
ejpam-5362	51	20	corresponding	corresponding	ADJ
ejpam-5362	51	21	left	left	ADJ
ejpam-5362	51	22	adjoint	adjoint	PROPN
ejpam-5362	51	23	f∗	f∗	NOUN
ejpam-5362	51	24	,	,	PUNCT
ejpam-5362	51	25	called	call	VERB
ejpam-5362	51	26	the	the	DET
ejpam-5362	51	27	frame	frame	NOUN
ejpam-5362	51	28	homomorphism	homomorphism	NOUN
ejpam-5362	51	29	,	,	PUNCT
ejpam-5362	51	30	preserves	preserve	VERB
ejpam-5362	51	31	binary	binary	NOUN
ejpam-5362	51	32	meets	meet	NOUN
ejpam-5362	51	33	.	.	PUNCT
ejpam-5362	52	1	a	a	DET
ejpam-5362	52	2	frame	frame	NOUN
ejpam-5362	52	3	homomorphism	homomorphism	PROPN
ejpam-5362	52	4	h	h	NOUN
ejpam-5362	52	5	:	:	PUNCT
ejpam-5362	52	6	m	m	VERB
ejpam-5362	52	7	→	→	SYM
ejpam-5362	52	8	l	l	NOUN
ejpam-5362	52	9	is	be	AUX
ejpam-5362	52	10	dense	dense	ADJ
ejpam-5362	52	11	if	if	SCONJ
ejpam-5362	52	12	h(x	h(x	PROPN
ejpam-5362	52	13	)	)	PUNCT
ejpam-5362	53	1	=	=	SYM
ejpam-5362	53	2	0	0	NUM
ejpam-5362	53	3	implies	imply	VERB
ejpam-5362	53	4	x	x	PUNCT
ejpam-5362	53	5	=	=	SYM
ejpam-5362	53	6	0	0	NUM
ejpam-5362	53	7	for	for	ADP
ejpam-5362	53	8	all	all	PRON
ejpam-5362	53	9	x	x	SYM
ejpam-5362	53	10	∈	∈	PROPN
ejpam-5362	53	11	m	m	NOUN
ejpam-5362	53	12	.	.	PUNCT
ejpam-5362	54	1	a	a	DET
ejpam-5362	54	2	sublocale	sublocale	NOUN
ejpam-5362	54	3	of	of	ADP
ejpam-5362	54	4	a	a	DET
ejpam-5362	54	5	locale	locale	PROPN
ejpam-5362	54	6	l	l	NOUN
ejpam-5362	54	7	is	be	AUX
ejpam-5362	54	8	a	a	DET
ejpam-5362	54	9	subset	subset	NOUN
ejpam-5362	54	10	s	s	AUX
ejpam-5362	54	11	closed	close	VERB
ejpam-5362	54	12	under	under	ADP
ejpam-5362	54	13	all	all	DET
ejpam-5362	54	14	meets	meet	NOUN
ejpam-5362	54	15	and	and	CCONJ
ejpam-5362	54	16	x	x	PUNCT
ejpam-5362	54	17	↠	↠	PRON
ejpam-5362	54	18	s	s	PART
ejpam-5362	54	19	∈	∈	NOUN
ejpam-5362	54	20	s	s	NOUN
ejpam-5362	54	21	for	for	ADP
ejpam-5362	54	22	every	every	DET
ejpam-5362	54	23	x	x	SYM
ejpam-5362	54	24	∈	∈	PROPN
ejpam-5362	54	25	l	l	NOUN
ejpam-5362	54	26	and	and	CCONJ
ejpam-5362	54	27	s	s	PROPN
ejpam-5362	54	28	∈	∈	PROPN
ejpam-5362	54	29	s	s	NOUN
ejpam-5362	54	30	,	,	PUNCT
ejpam-5362	54	31	where	where	SCONJ
ejpam-5362	54	32	↠	↠	PROPN
ejpam-5362	54	33	is	be	AUX
ejpam-5362	54	34	a	a	DET
ejpam-5362	54	35	heyting	heyte	VERB
ejpam-5362	54	36	operation	operation	NOUN
ejpam-5362	54	37	on	on	ADP
ejpam-5362	54	38	l	l	PROPN
ejpam-5362	54	39	satisfying	satisfy	VERB
ejpam-5362	54	40	that	that	SCONJ
ejpam-5362	54	41	a	a	DET
ejpam-5362	54	42	≤	≤	PROPN
ejpam-5362	54	43	b	b	NOUN
ejpam-5362	54	44	↠	↠	NOUN
ejpam-5362	55	1	c	c	NOUN
ejpam-5362	55	2	if	if	SCONJ
ejpam-5362	55	3	and	and	CCONJ
ejpam-5362	55	4	only	only	ADV
ejpam-5362	55	5	if	if	SCONJ
ejpam-5362	55	6	a	a	DET
ejpam-5362	55	7	∧	∧	PROPN
ejpam-5362	55	8	b	b	PROPN
ejpam-5362	55	9	≤	≤	NUM
ejpam-5362	55	10	c	c	NOUN
ejpam-5362	55	11	for	for	ADP
ejpam-5362	55	12	all	all	DET
ejpam-5362	55	13	a	a	DET
ejpam-5362	55	14	,	,	PUNCT
ejpam-5362	55	15	b	b	NOUN
ejpam-5362	55	16	,	,	PUNCT
ejpam-5362	55	17	c	c	PROPN
ejpam-5362	55	18	∈	∈	PROPN
ejpam-5362	55	19	l.	l.	NOUN
ejpam-5362	55	20	we	we	PRON
ejpam-5362	55	21	denote	denote	VERB
ejpam-5362	55	22	by	by	ADP
ejpam-5362	55	23	o	o	PROPN
ejpam-5362	55	24	the	the	DET
ejpam-5362	55	25	smallest	small	ADJ
ejpam-5362	55	26	sublocale	sublocale	NOUN
ejpam-5362	55	27	of	of	ADP
ejpam-5362	55	28	a	a	DET
ejpam-5362	55	29	locale	locale	NOUN
ejpam-5362	55	30	l.	l.	NOUN
ejpam-5362	55	31	we	we	PRON
ejpam-5362	55	32	use	use	VERB
ejpam-5362	55	33	s(l	s(l	ADV
ejpam-5362	55	34	)	)	PUNCT
ejpam-5362	55	35	to	to	PART
ejpam-5362	55	36	represent	represent	VERB
ejpam-5362	55	37	the	the	DET
ejpam-5362	55	38	coframe	coframe	NOUN
ejpam-5362	55	39	of	of	ADP
ejpam-5362	55	40	sublocales	sublocale	NOUN
ejpam-5362	55	41	of	of	ADP
ejpam-5362	55	42	a	a	DET
ejpam-5362	55	43	locale	locale	NOUN
ejpam-5362	55	44	l.	l.	NOUN
ejpam-5362	55	45	for	for	ADP
ejpam-5362	55	46	each	each	DET
ejpam-5362	55	47	s	s	PROPN
ejpam-5362	55	48	∈	∈	PROPN
ejpam-5362	55	49	s(l	s(l	NUM
ejpam-5362	55	50	)	)	PUNCT
ejpam-5362	55	51	,	,	PUNCT
ejpam-5362	55	52	we	we	PRON
ejpam-5362	55	53	define	define	VERB
ejpam-5362	55	54	l∖	l∖	PROPN
ejpam-5362	55	55	s	s	PART
ejpam-5362	55	56	:	:	PUNCT
ejpam-5362	55	57	=	=	SYM
ejpam-5362	55	58	∨	∨	X
ejpam-5362	55	59	{	{	PUNCT
ejpam-5362	55	60	t	t	PROPN
ejpam-5362	55	61	∈	∈	PROPN
ejpam-5362	55	62	s(l	s(l	PROPN
ejpam-5362	55	63	)	)	PUNCT
ejpam-5362	55	64	:	:	PUNCT
ejpam-5362	55	65	t	t	PROPN
ejpam-5362	55	66	∩	∩	PROPN
ejpam-5362	55	67	s	s	PART
ejpam-5362	55	68	=	=	ADJ
ejpam-5362	55	69	o	o	NOUN
ejpam-5362	55	70	}	}	PUNCT
ejpam-5362	55	71	.	.	PUNCT
ejpam-5362	56	1	the	the	DET
ejpam-5362	56	2	sublocales	sublocale	NOUN
ejpam-5362	56	3	c(a	c(a	ADV
ejpam-5362	56	4	)	)	PUNCT
ejpam-5362	56	5	=	=	PRON
ejpam-5362	56	6	{	{	PUNCT
ejpam-5362	56	7	x	x	PUNCT
ejpam-5362	56	8	∈	∈	PROPN
ejpam-5362	56	9	l	l	NOUN
ejpam-5362	56	10	:	:	PUNCT
ejpam-5362	56	11	a	a	DET
ejpam-5362	56	12	≤	≤	NUM
ejpam-5362	56	13	x	x	SYM
ejpam-5362	56	14	}	}	PUNCT
ejpam-5362	56	15	and	and	CCONJ
ejpam-5362	56	16	o(a	o(a	NOUN
ejpam-5362	56	17	)	)	PUNCT
ejpam-5362	56	18	=	=	PRON
ejpam-5362	56	19	{	{	PUNCT
ejpam-5362	56	20	a	a	DET
ejpam-5362	56	21	↠	↠	NOUN
ejpam-5362	56	22	x	x	NOUN
ejpam-5362	56	23	:	:	PUNCT
ejpam-5362	56	24	x	x	SYM
ejpam-5362	56	25	∈	∈	NOUN
ejpam-5362	56	26	l	l	NOUN
ejpam-5362	56	27	}	}	PUNCT
ejpam-5362	56	28	,	,	PUNCT
ejpam-5362	56	29	of	of	ADP
ejpam-5362	56	30	a	a	DET
ejpam-5362	56	31	locale	locale	ADJ
ejpam-5362	56	32	l	l	NOUN
ejpam-5362	56	33	are	be	AUX
ejpam-5362	56	34	respectively	respectively	ADV
ejpam-5362	56	35	the	the	DET
ejpam-5362	56	36	closed	closed	ADJ
ejpam-5362	56	37	and	and	CCONJ
ejpam-5362	56	38	open	open	ADJ
ejpam-5362	56	39	sublocales	sublocale	NOUN
ejpam-5362	56	40	induced	induce	VERB
ejpam-5362	56	41	by	by	ADP
ejpam-5362	56	42	an	an	DET
ejpam-5362	56	43	element	element	NOUN
ejpam-5362	56	44	a	a	PRON
ejpam-5362	56	45	of	of	ADP
ejpam-5362	56	46	l.	l.	NOUN
ejpam-5362	56	47	they	they	PRON
ejpam-5362	56	48	are	be	AUX
ejpam-5362	56	49	complements	complement	NOUN
ejpam-5362	56	50	of	of	ADP
ejpam-5362	56	51	each	each	DET
ejpam-5362	56	52	other	other	ADJ
ejpam-5362	56	53	.	.	PUNCT
ejpam-5362	57	1	the	the	DET
ejpam-5362	57	2	smallest	small	ADJ
ejpam-5362	57	3	closed	close	VERB
ejpam-5362	57	4	sublocale	sublocale	NOUN
ejpam-5362	57	5	of	of	ADP
ejpam-5362	57	6	l	l	NOUN
ejpam-5362	57	7	that	that	PRON
ejpam-5362	57	8	contains	contain	VERB
ejpam-5362	57	9	a	a	DET
ejpam-5362	57	10	sublocale	sublocale	NOUN
ejpam-5362	57	11	s	s	VERB
ejpam-5362	57	12	is	be	AUX
ejpam-5362	57	13	called	call	VERB
ejpam-5362	57	14	the	the	DET
ejpam-5362	57	15	closure	closure	NOUN
ejpam-5362	57	16	of	of	ADP
ejpam-5362	57	17	s	s	PRON
ejpam-5362	57	18	and	and	CCONJ
ejpam-5362	57	19	denoted	denote	VERB
ejpam-5362	57	20	by	by	ADP
ejpam-5362	57	21	s	s	PRON
ejpam-5362	57	22	or	or	CCONJ
ejpam-5362	57	23	cll(s	cll(s	PROPN
ejpam-5362	57	24	)	)	PUNCT
ejpam-5362	57	25	with	with	ADP
ejpam-5362	57	26	subscript	subscript	NOUN
ejpam-5362	57	27	l	l	PROPN
ejpam-5362	57	28	dropped	drop	VERB
ejpam-5362	57	29	when	when	SCONJ
ejpam-5362	57	30	the	the	DET
ejpam-5362	57	31	locale	locale	NOUN
ejpam-5362	57	32	is	be	AUX
ejpam-5362	57	33	clear	clear	ADJ
ejpam-5362	57	34	from	from	ADP
ejpam-5362	57	35	the	the	DET
ejpam-5362	57	36	context	context	NOUN
ejpam-5362	57	37	.	.	PUNCT
ejpam-5362	58	1	for	for	ADP
ejpam-5362	58	2	every	every	DET
ejpam-5362	58	3	λ	λ	PROPN
ejpam-5362	58	4	,	,	PUNCT
ejpam-5362	58	5	c	c	PROPN
ejpam-5362	58	6	(	(	PUNCT
ejpam-5362	58	7	∨	∨	NUM
ejpam-5362	58	8	α∈λ	α∈λ	NOUN
ejpam-5362	58	9	xα	xα	PUNCT
ejpam-5362	58	10	)	)	PUNCT
ejpam-5362	59	1	=	=	PUNCT
ejpam-5362	59	2	∧	∧	NOUN
ejpam-5362	59	3	α∈λ	α∈λ	NOUN
ejpam-5362	59	4	c(xα	c(xα	NOUN
ejpam-5362	59	5	)	)	PUNCT
ejpam-5362	59	6	.	.	PUNCT
ejpam-5362	60	1	a	a	DET
ejpam-5362	60	2	sublocale	sublocale	NOUN
ejpam-5362	60	3	s	s	X
ejpam-5362	60	4	of	of	ADP
ejpam-5362	60	5	a	a	DET
ejpam-5362	60	6	locale	locale	ADJ
ejpam-5362	60	7	l	l	NOUN
ejpam-5362	60	8	is	be	AUX
ejpam-5362	60	9	dense	dense	ADJ
ejpam-5362	60	10	and	and	CCONJ
ejpam-5362	60	11	nowhere	nowhere	ADV
ejpam-5362	60	12	dense	dense	ADJ
ejpam-5362	60	13	if	if	SCONJ
ejpam-5362	60	14	s	s	PART
ejpam-5362	60	15	=	=	NOUN
ejpam-5362	60	16	l	l	NOUN
ejpam-5362	60	17	and	and	CCONJ
ejpam-5362	60	18	s	s	X
ejpam-5362	60	19	∩	∩	X
ejpam-5362	60	20	bl	bl	NOUN
ejpam-5362	60	21	=	=	SYM
ejpam-5362	60	22	o	o	PROPN
ejpam-5362	60	23	,	,	PUNCT
ejpam-5362	60	24	respectively	respectively	ADV
ejpam-5362	60	25	,	,	PUNCT
ejpam-5362	60	26	where	where	SCONJ
ejpam-5362	60	27	b(l	b(l	PROPN
ejpam-5362	60	28	)	)	PUNCT
ejpam-5362	61	1	=	=	PRON
ejpam-5362	61	2	{	{	PUNCT
ejpam-5362	62	1	x	x	X
ejpam-5362	62	2	↠	↠	PROPN
ejpam-5362	62	3	0	0	NUM
ejpam-5362	62	4	:	:	PUNCT
ejpam-5362	62	5	x	x	SYM
ejpam-5362	62	6	∈	∈	PROPN
ejpam-5362	62	7	l	l	NOUN
ejpam-5362	62	8	}	}	PUNCT
ejpam-5362	62	9	is	be	AUX
ejpam-5362	62	10	the	the	DET
ejpam-5362	62	11	smallest	small	ADJ
ejpam-5362	62	12	dense	dense	ADJ
ejpam-5362	62	13	sublocale	sublocale	NOUN
ejpam-5362	62	14	of	of	ADP
ejpam-5362	62	15	l.	l.	NOUN
ejpam-5362	62	16	we	we	PRON
ejpam-5362	62	17	refer	refer	VERB
ejpam-5362	62	18	a	a	DET
ejpam-5362	62	19	reader	reader	NOUN
ejpam-5362	62	20	to	to	ADP
ejpam-5362	62	21	[	[	X
ejpam-5362	62	22	14	14	NUM
ejpam-5362	62	23	]	]	PUNCT
ejpam-5362	62	24	for	for	ADP
ejpam-5362	62	25	a	a	DET
ejpam-5362	62	26	comprehensive	comprehensive	ADJ
ejpam-5362	62	27	study	study	NOUN
ejpam-5362	62	28	of	of	ADP
ejpam-5362	62	29	nowhere	nowhere	ADJ
ejpam-5362	62	30	dense	dense	ADJ
ejpam-5362	62	31	sublocales	sublocale	NOUN
ejpam-5362	62	32	.	.	PUNCT
ejpam-5362	63	1	by	by	ADP
ejpam-5362	63	2	a	a	DET
ejpam-5362	63	3	gδ	gδ	NOUN
ejpam-5362	63	4	-	-	PUNCT
ejpam-5362	63	5	sublocale	sublocale	NOUN
ejpam-5362	63	6	of	of	ADP
ejpam-5362	63	7	a	a	DET
ejpam-5362	63	8	locale	locale	NOUN
ejpam-5362	63	9	l	l	NOUN
ejpam-5362	63	10	,	,	PUNCT
ejpam-5362	63	11	we	we	PRON
ejpam-5362	63	12	mean	mean	VERB
ejpam-5362	63	13	a	a	DET
ejpam-5362	63	14	sublocale	sublocale	NOUN
ejpam-5362	63	15	of	of	ADP
ejpam-5362	63	16	the	the	DET
ejpam-5362	63	17	form	form	NOUN
ejpam-5362	63	18	s	s	PART
ejpam-5362	63	19	=	=	NOUN
ejpam-5362	63	20	∧	∧	PROPN
ejpam-5362	63	21	n∈n	n∈n	NOUN
ejpam-5362	63	22	o(xn	o(xn	NUM
ejpam-5362	63	23	)	)	PUNCT
ejpam-5362	63	24	.	.	PUNCT
ejpam-5362	64	1	for	for	ADP
ejpam-5362	64	2	each	each	DET
ejpam-5362	64	3	sublocale	sublocale	NOUN
ejpam-5362	64	4	s	s	PART
ejpam-5362	64	5	⊆	⊆	NUM
ejpam-5362	64	6	l	l	NOUN
ejpam-5362	64	7	there	there	PRON
ejpam-5362	64	8	is	be	VERB
ejpam-5362	64	9	an	an	PRON
ejpam-5362	64	10	onto	onto	ADP
ejpam-5362	64	11	frame	frame	NOUN
ejpam-5362	64	12	homomorphism	homomorphism	NOUN
ejpam-5362	64	13	νs	νs	PRON
ejpam-5362	64	14	:	:	PUNCT
ejpam-5362	64	15	l	l	X
ejpam-5362	64	16	→	→	SYM
ejpam-5362	64	17	s	s	AUX
ejpam-5362	64	18	defined	define	VERB
ejpam-5362	64	19	by	by	ADP
ejpam-5362	64	20	νs(a	νs(a	NOUN
ejpam-5362	64	21	)	)	PUNCT
ejpam-5362	65	1	=	=	SYM
ejpam-5362	65	2	∧	∧	NOUN
ejpam-5362	65	3	{	{	PUNCT
ejpam-5362	65	4	s	s	NOUN
ejpam-5362	65	5	∈	∈	NOUN
ejpam-5362	65	6	s	s	PART
ejpam-5362	65	7	:	:	PUNCT
ejpam-5362	65	8	a	a	DET
ejpam-5362	65	9	≤	≤	NUM
ejpam-5362	65	10	s	s	PART
ejpam-5362	65	11	}	}	PUNCT
ejpam-5362	65	12	.	.	PUNCT
ejpam-5362	66	1	open	open	ADJ
ejpam-5362	66	2	sublocales	sublocale	NOUN
ejpam-5362	66	3	and	and	CCONJ
ejpam-5362	66	4	closed	close	VERB
ejpam-5362	66	5	sublocales	sublocale	NOUN
ejpam-5362	66	6	of	of	ADP
ejpam-5362	66	7	a	a	DET
ejpam-5362	66	8	sublocale	sublocale	NOUN
ejpam-5362	66	9	s	s	NOUN
ejpam-5362	66	10	of	of	ADP
ejpam-5362	66	11	l	l	NOUN
ejpam-5362	66	12	are	be	AUX
ejpam-5362	66	13	given	give	VERB
ejpam-5362	66	14	by	by	ADP
ejpam-5362	66	15	os(νs(a	os(νs(a	NOUN
ejpam-5362	66	16	)	)	PUNCT
ejpam-5362	66	17	)	)	PUNCT
ejpam-5362	67	1	=	=	SYM
ejpam-5362	67	2	s	s	NOUN
ejpam-5362	67	3	∩	∩	NOUN
ejpam-5362	67	4	o(a	o(a	NOUN
ejpam-5362	67	5	)	)	PUNCT
ejpam-5362	67	6	and	and	CCONJ
ejpam-5362	67	7	cs(νs(a	cs(νs(a	NUM
ejpam-5362	67	8	)	)	PUNCT
ejpam-5362	67	9	)	)	PUNCT
ejpam-5362	68	1	=	=	SYM
ejpam-5362	68	2	s	s	NOUN
ejpam-5362	68	3	∩	∩	NOUN
ejpam-5362	68	4	c(a	c(a	NOUN
ejpam-5362	68	5	)	)	PUNCT
ejpam-5362	68	6	,	,	PUNCT
ejpam-5362	68	7	respectively	respectively	ADV
ejpam-5362	68	8	,	,	PUNCT
ejpam-5362	68	9	for	for	ADP
ejpam-5362	68	10	a	a	DET
ejpam-5362	68	11	∈	∈	PROPN
ejpam-5362	68	12	l.	l.	NOUN
ejpam-5362	68	13	each	each	DET
ejpam-5362	68	14	localic	localic	ADJ
ejpam-5362	68	15	map	map	NOUN
ejpam-5362	69	1	f	f	NOUN
ejpam-5362	69	2	:	:	PUNCT
ejpam-5362	69	3	l	l	X
ejpam-5362	69	4	→	→	PUNCT
ejpam-5362	69	5	m	m	NOUN
ejpam-5362	69	6	induces	induce	VERB
ejpam-5362	69	7	the	the	DET
ejpam-5362	69	8	functions	function	NOUN
ejpam-5362	69	9	f	f	X
ejpam-5362	70	1	[	[	X
ejpam-5362	70	2	−	−	X
ejpam-5362	70	3	]	]	X
ejpam-5362	70	4	:	:	PUNCT
ejpam-5362	70	5	s(l	s(l	X
ejpam-5362	70	6	)	)	PUNCT
ejpam-5362	70	7	→	→	SYM
ejpam-5362	70	8	s(m	s(m	NOUN
ejpam-5362	70	9	)	)	PUNCT
ejpam-5362	70	10	given	give	VERB
ejpam-5362	70	11	by	by	ADP
ejpam-5362	70	12	the	the	DET
ejpam-5362	70	13	set	set	NOUN
ejpam-5362	70	14	-	-	PUNCT
ejpam-5362	70	15	theoretic	theoretic	NOUN
ejpam-5362	70	16	image	image	NOUN
ejpam-5362	70	17	of	of	ADP
ejpam-5362	70	18	each	each	DET
ejpam-5362	70	19	sublocale	sublocale	NOUN
ejpam-5362	70	20	of	of	ADP
ejpam-5362	70	21	l	l	NOUN
ejpam-5362	70	22	under	under	ADP
ejpam-5362	70	23	f	f	PROPN
ejpam-5362	70	24	,	,	PUNCT
ejpam-5362	70	25	and	and	CCONJ
ejpam-5362	70	26	f−1[−	f−1[−	NOUN
ejpam-5362	70	27	]	]	PUNCT
ejpam-5362	70	28	:	:	PUNCT
ejpam-5362	70	29	s(m	s(m	NOUN
ejpam-5362	70	30	)	)	PUNCT
ejpam-5362	70	31	→	→	SYM
ejpam-5362	70	32	s(l	s(l	X
ejpam-5362	70	33	)	)	PUNCT
ejpam-5362	70	34	given	give	VERB
ejpam-5362	70	35	by	by	ADP
ejpam-5362	70	36	f−1[t	f−1[t	NOUN
ejpam-5362	70	37	]	]	PUNCT
ejpam-5362	70	38	=	=	SYM
ejpam-5362	70	39	∨	∨	X
ejpam-5362	70	40	{	{	PUNCT
ejpam-5362	70	41	a	a	DET
ejpam-5362	70	42	∈	∈	PROPN
ejpam-5362	70	43	s(l	s(l	NUM
ejpam-5362	70	44	)	)	PUNCT
ejpam-5362	70	45	:	:	PUNCT
ejpam-5362	70	46	a	a	DET
ejpam-5362	70	47	⊆	⊆	NUM
ejpam-5362	70	48	f−1(t	f−1(t	NOUN
ejpam-5362	70	49	)	)	PUNCT
ejpam-5362	70	50	}	}	PUNCT
ejpam-5362	70	51	.	.	PUNCT
ejpam-5362	71	1	for	for	ADP
ejpam-5362	71	2	a	a	DET
ejpam-5362	71	3	localic	localic	ADJ
ejpam-5362	71	4	map	map	NOUN
ejpam-5362	71	5	f	f	NOUN
ejpam-5362	71	6	:	:	PUNCT
ejpam-5362	71	7	l	l	X
ejpam-5362	71	8	→	→	PUNCT
ejpam-5362	71	9	m	m	VERB
ejpam-5362	71	10	and	and	CCONJ
ejpam-5362	71	11	x	x	SYM
ejpam-5362	71	12	∈	∈	NOUN
ejpam-5362	71	13	m	m	NOUN
ejpam-5362	71	14	,	,	PUNCT
ejpam-5362	71	15	f−1[cm	f−1[cm	X
ejpam-5362	71	16	(	(	PUNCT
ejpam-5362	71	17	x	x	X
ejpam-5362	71	18	)	)	PUNCT
ejpam-5362	71	19	]	]	PUNCT
ejpam-5362	71	20	=	=	SYM
ejpam-5362	71	21	cl(h(x	cl(h(x	NOUN
ejpam-5362	71	22	)	)	PUNCT
ejpam-5362	71	23	)	)	PUNCT
ejpam-5362	71	24	and	and	CCONJ
ejpam-5362	71	25	f−1[om	f−1[om	NOUN
ejpam-5362	71	26	(	(	PUNCT
ejpam-5362	71	27	x	x	NOUN
ejpam-5362	71	28	)	)	PUNCT
ejpam-5362	71	29	]	]	PUNCT
ejpam-5362	71	30	=	=	SYM
ejpam-5362	71	31	ol(h(x	ol(h(x	NOUN
ejpam-5362	71	32	)	)	PUNCT
ejpam-5362	71	33	)	)	PUNCT
ejpam-5362	71	34	.	.	PUNCT
ejpam-5362	72	1	we	we	PRON
ejpam-5362	72	2	denote	denote	VERB
ejpam-5362	72	3	by	by	ADP
ejpam-5362	72	4	ã	ã	PROPN
ejpam-5362	72	5	the	the	DET
ejpam-5362	72	6	sublocale	sublocale	NOUN
ejpam-5362	72	7	of	of	ADP
ejpam-5362	72	8	ox	ox	NOUN
ejpam-5362	72	9	induced	induce	VERB
ejpam-5362	72	10	by	by	ADP
ejpam-5362	72	11	a	a	DET
ejpam-5362	72	12	subset	subset	NOUN
ejpam-5362	72	13	a	a	PRON
ejpam-5362	72	14	of	of	ADP
ejpam-5362	72	15	a	a	DET
ejpam-5362	72	16	topological	topological	ADJ
ejpam-5362	72	17	space	space	NOUN
ejpam-5362	72	18	x.	x.	NOUN
ejpam-5362	72	19	m.	m.	PROPN
ejpam-5362	72	20	nxumalo	nxumalo	PROPN
ejpam-5362	72	21	/	/	SYM
ejpam-5362	72	22	eur	eur	PROPN
ejpam-5362	72	23	.	.	PUNCT
ejpam-5362	73	1	j.	j.	PROPN
ejpam-5362	73	2	pure	pure	PROPN
ejpam-5362	73	3	appl	appl	PROPN
ejpam-5362	73	4	.	.	PROPN
ejpam-5362	73	5	math	math	PROPN
ejpam-5362	73	6	,	,	PUNCT
ejpam-5362	73	7	18	18	NUM
ejpam-5362	73	8	(	(	PUNCT
ejpam-5362	73	9	1	1	NUM
ejpam-5362	73	10	)	)	PUNCT
ejpam-5362	73	11	(	(	PUNCT
ejpam-5362	73	12	2025	2025	NUM
ejpam-5362	73	13	)	)	PUNCT
ejpam-5362	73	14	,	,	PUNCT
ejpam-5362	73	15	5362	5362	NUM
ejpam-5362	73	16	4	4	NUM
ejpam-5362	73	17	of	of	ADP
ejpam-5362	73	18	21	21	NUM
ejpam-5362	73	19	2.2	2.2	NUM
ejpam-5362	73	20	.	.	PUNCT
ejpam-5362	74	1	bilocales	bilocale	NOUN
ejpam-5362	74	2	a	a	DET
ejpam-5362	74	3	bilocale	bilocale	NOUN
ejpam-5362	74	4	is	be	AUX
ejpam-5362	74	5	a	a	DET
ejpam-5362	74	6	triple	triple	ADJ
ejpam-5362	74	7	(	(	PUNCT
ejpam-5362	74	8	l	l	NOUN
ejpam-5362	74	9	,	,	PUNCT
ejpam-5362	74	10	l1	l1	PROPN
ejpam-5362	74	11	,	,	PUNCT
ejpam-5362	74	12	l2	l2	NOUN
ejpam-5362	74	13	)	)	PUNCT
ejpam-5362	74	14	where	where	SCONJ
ejpam-5362	74	15	l1	l1	PROPN
ejpam-5362	74	16	,	,	PUNCT
ejpam-5362	74	17	l2	l2	NOUN
ejpam-5362	74	18	are	be	AUX
ejpam-5362	74	19	subframes	subframe	NOUN
ejpam-5362	74	20	of	of	ADP
ejpam-5362	74	21	a	a	DET
ejpam-5362	74	22	locale	locale	ADJ
ejpam-5362	74	23	l	l	NOUN
ejpam-5362	74	24	and	and	CCONJ
ejpam-5362	74	25	for	for	ADP
ejpam-5362	74	26	all	all	DET
ejpam-5362	74	27	a	a	DET
ejpam-5362	74	28	∈	∈	PROPN
ejpam-5362	74	29	l	l	NOUN
ejpam-5362	74	30	,	,	PUNCT
ejpam-5362	74	31	a	a	DET
ejpam-5362	74	32	=	=	SYM
ejpam-5362	74	33	∨	∨	X
ejpam-5362	74	34	{	{	PUNCT
ejpam-5362	74	35	a1	a1	NOUN
ejpam-5362	74	36	∧	∧	PROPN
ejpam-5362	74	37	a2	a2	PROPN
ejpam-5362	74	38	:	:	PUNCT
ejpam-5362	74	39	a1	a1	PROPN
ejpam-5362	74	40	∈	∈	PROPN
ejpam-5362	74	41	l1	l1	PROPN
ejpam-5362	74	42	,	,	PUNCT
ejpam-5362	74	43	a2	a2	PROPN
ejpam-5362	74	44	∈	∈	PROPN
ejpam-5362	74	45	l2	l2	NOUN
ejpam-5362	74	46	and	and	CCONJ
ejpam-5362	74	47	a1	a1	NOUN
ejpam-5362	74	48	∧	∧	PROPN
ejpam-5362	74	49	a2	a2	PROPN
ejpam-5362	74	50	≤	≤	NOUN
ejpam-5362	74	51	a	a	PRON
ejpam-5362	74	52	}	}	PUNCT
ejpam-5362	74	53	.	.	PUNCT
ejpam-5362	75	1	we	we	PRON
ejpam-5362	75	2	call	call	VERB
ejpam-5362	75	3	l	l	NOUN
ejpam-5362	75	4	the	the	DET
ejpam-5362	75	5	total	total	ADJ
ejpam-5362	75	6	part	part	NOUN
ejpam-5362	75	7	of	of	ADP
ejpam-5362	75	8	(	(	PUNCT
ejpam-5362	75	9	l	l	NOUN
ejpam-5362	75	10	,	,	PUNCT
ejpam-5362	75	11	l1	l1	PROPN
ejpam-5362	75	12	,	,	PUNCT
ejpam-5362	75	13	l2	l2	NOUN
ejpam-5362	75	14	)	)	PUNCT
ejpam-5362	75	15	,	,	PUNCT
ejpam-5362	75	16	and	and	CCONJ
ejpam-5362	75	17	l1	l1	PROPN
ejpam-5362	75	18	and	and	CCONJ
ejpam-5362	75	19	l2	l2	VERB
ejpam-5362	75	20	the	the	DET
ejpam-5362	75	21	first	first	ADJ
ejpam-5362	75	22	and	and	CCONJ
ejpam-5362	75	23	second	second	ADJ
ejpam-5362	75	24	parts	part	NOUN
ejpam-5362	75	25	,	,	PUNCT
ejpam-5362	75	26	respectively	respectively	ADV
ejpam-5362	75	27	.	.	PUNCT
ejpam-5362	76	1	we	we	PRON
ejpam-5362	76	2	use	use	VERB
ejpam-5362	76	3	the	the	DET
ejpam-5362	76	4	notations	notation	NOUN
ejpam-5362	76	5	li	li	X
ejpam-5362	76	6	,	,	PUNCT
ejpam-5362	76	7	lj	lj	PROPN
ejpam-5362	76	8	to	to	PART
ejpam-5362	76	9	denote	denote	VERB
ejpam-5362	76	10	the	the	DET
ejpam-5362	76	11	first	first	ADJ
ejpam-5362	76	12	or	or	CCONJ
ejpam-5362	76	13	second	second	ADJ
ejpam-5362	76	14	parts	part	NOUN
ejpam-5362	76	15	of	of	ADP
ejpam-5362	76	16	(	(	PUNCT
ejpam-5362	76	17	l	l	NOUN
ejpam-5362	76	18	,	,	PUNCT
ejpam-5362	76	19	l1	l1	PROPN
ejpam-5362	76	20	,	,	PUNCT
ejpam-5362	76	21	l2	l2	NOUN
ejpam-5362	76	22	)	)	PUNCT
ejpam-5362	76	23	,	,	PUNCT
ejpam-5362	76	24	always	always	ADV
ejpam-5362	76	25	assuming	assume	VERB
ejpam-5362	76	26	that	that	SCONJ
ejpam-5362	76	27	i	i	PRON
ejpam-5362	76	28	,	,	PUNCT
ejpam-5362	76	29	j	j	PROPN
ejpam-5362	76	30	=	=	SYM
ejpam-5362	76	31	1	1	NUM
ejpam-5362	76	32	,	,	PUNCT
ejpam-5362	76	33	2	2	NUM
ejpam-5362	76	34	,	,	PUNCT
ejpam-5362	76	35	i	i	PRON
ejpam-5362	76	36	̸=	̸=	PROPN
ejpam-5362	76	37	j.	j.	PROPN
ejpam-5362	76	38	for	for	ADP
ejpam-5362	76	39	every	every	DET
ejpam-5362	76	40	bispace	bispace	NOUN
ejpam-5362	76	41	(	(	PUNCT
ejpam-5362	76	42	x	x	NOUN
ejpam-5362	76	43	,	,	PUNCT
ejpam-5362	76	44	τ1	τ1	NOUN
ejpam-5362	76	45	,	,	PUNCT
ejpam-5362	76	46	τ2	τ2	NOUN
ejpam-5362	76	47	)	)	PUNCT
ejpam-5362	76	48	,	,	PUNCT
ejpam-5362	76	49	there	there	PRON
ejpam-5362	76	50	is	be	VERB
ejpam-5362	76	51	a	a	DET
ejpam-5362	76	52	corresponding	correspond	VERB
ejpam-5362	76	53	bilocale	bilocale	NOUN
ejpam-5362	76	54	(	(	PUNCT
ejpam-5362	76	55	τ1	τ1	PROPN
ejpam-5362	76	56	∨	∨	NUM
ejpam-5362	76	57	τ2	τ2	NOUN
ejpam-5362	76	58	,	,	PUNCT
ejpam-5362	76	59	τ1	τ1	NOUN
ejpam-5362	76	60	,	,	PUNCT
ejpam-5362	76	61	τ2	τ2	NOUN
ejpam-5362	76	62	)	)	PUNCT
ejpam-5362	76	63	.	.	PUNCT
ejpam-5362	77	1	for	for	ADP
ejpam-5362	77	2	example	example	NOUN
ejpam-5362	77	3	,	,	PUNCT
ejpam-5362	77	4	let	let	VERB
ejpam-5362	77	5	(	(	PUNCT
ejpam-5362	77	6	x	x	NOUN
ejpam-5362	77	7	,	,	PUNCT
ejpam-5362	77	8	τ1	τ1	NOUN
ejpam-5362	77	9	,	,	PUNCT
ejpam-5362	77	10	τ2	τ2	PROPN
ejpam-5362	77	11	)	)	PUNCT
ejpam-5362	77	12	be	be	VERB
ejpam-5362	77	13	a	a	DET
ejpam-5362	77	14	bispace	bispace	NOUN
ejpam-5362	77	15	where	where	SCONJ
ejpam-5362	77	16	x	x	X
ejpam-5362	77	17	=	=	PRON
ejpam-5362	77	18	{	{	PUNCT
ejpam-5362	77	19	a	a	PRON
ejpam-5362	77	20	,	,	PUNCT
ejpam-5362	77	21	b	b	NOUN
ejpam-5362	77	22	}	}	PUNCT
ejpam-5362	77	23	,	,	PUNCT
ejpam-5362	77	24	τ1	τ1	NOUN
ejpam-5362	77	25	=	=	SYM
ejpam-5362	77	26	{	{	PUNCT
ejpam-5362	77	27	∅	∅	NOUN
ejpam-5362	77	28	,	,	PUNCT
ejpam-5362	77	29	x	x	NOUN
ejpam-5362	77	30	}	}	PUNCT
ejpam-5362	77	31	and	and	CCONJ
ejpam-5362	77	32	τ2	τ2	NOUN
ejpam-5362	77	33	=	=	SYM
ejpam-5362	77	34	{	{	PUNCT
ejpam-5362	77	35	∅	∅	NOUN
ejpam-5362	77	36	,	,	PUNCT
ejpam-5362	77	37	x	x	X
ejpam-5362	77	38	,	,	PUNCT
ejpam-5362	77	39	{	{	PUNCT
ejpam-5362	77	40	a	a	X
ejpam-5362	77	41	}	}	PUNCT
ejpam-5362	77	42	}	}	PUNCT
ejpam-5362	77	43	.	.	PUNCT
ejpam-5362	78	1	then	then	ADV
ejpam-5362	78	2	(	(	PUNCT
ejpam-5362	78	3	τ1	τ1	ADP
ejpam-5362	78	4	∨	∨	NUM
ejpam-5362	78	5	τ2	τ2	NOUN
ejpam-5362	78	6	=	=	SYM
ejpam-5362	78	7	τ2	τ2	PROPN
ejpam-5362	78	8	,	,	PUNCT
ejpam-5362	78	9	τ1	τ1	NOUN
ejpam-5362	78	10	,	,	PUNCT
ejpam-5362	78	11	τ2	τ2	NOUN
ejpam-5362	78	12	)	)	PUNCT
ejpam-5362	78	13	is	be	AUX
ejpam-5362	78	14	a	a	DET
ejpam-5362	78	15	bilocale	bilocale	NOUN
ejpam-5362	78	16	.	.	PUNCT
ejpam-5362	79	1	the	the	DET
ejpam-5362	79	2	bilocale	bilocale	NOUN
ejpam-5362	79	3	pseudocomplement	pseudocomplement	NOUN
ejpam-5362	79	4	of	of	ADP
ejpam-5362	79	5	c	c	PROPN
ejpam-5362	79	6	∈	∈	PROPN
ejpam-5362	79	7	li	li	PROPN
ejpam-5362	79	8	is	be	AUX
ejpam-5362	79	9	given	give	VERB
ejpam-5362	79	10	by	by	ADP
ejpam-5362	79	11	c•	c•	NOUN
ejpam-5362	79	12	=	=	PUNCT
ejpam-5362	79	13	∨	∨	X
ejpam-5362	79	14	{	{	PUNCT
ejpam-5362	79	15	x	x	SYM
ejpam-5362	79	16	∈	∈	NOUN
ejpam-5362	79	17	lj	lj	NOUN
ejpam-5362	79	18	:	:	PUNCT
ejpam-5362	80	1	x	x	PUNCT
ejpam-5362	80	2	∧	∧	NOUN
ejpam-5362	80	3	c	c	NOUN
ejpam-5362	80	4	=	=	NOUN
ejpam-5362	80	5	0	0	NUM
ejpam-5362	80	6	}	}	PUNCT
ejpam-5362	80	7	.	.	PUNCT
ejpam-5362	81	1	for	for	ADP
ejpam-5362	81	2	all	all	DET
ejpam-5362	81	3	a	a	DET
ejpam-5362	81	4	∈	∈	NOUN
ejpam-5362	81	5	lj	lj	NOUN
ejpam-5362	81	6	,	,	PUNCT
ejpam-5362	81	7	b	b	PROPN
ejpam-5362	81	8	∈	∈	PROPN
ejpam-5362	81	9	li	li	PROPN
ejpam-5362	81	10	,	,	PUNCT
ejpam-5362	81	11	a	a	DET
ejpam-5362	81	12	∧	∧	PROPN
ejpam-5362	81	13	b	b	NOUN
ejpam-5362	81	14	=	=	SYM
ejpam-5362	81	15	0	0	PUNCT
ejpam-5362	81	16	if	if	SCONJ
ejpam-5362	81	17	and	and	CCONJ
ejpam-5362	81	18	only	only	ADV
ejpam-5362	81	19	if	if	SCONJ
ejpam-5362	81	20	a	a	DET
ejpam-5362	81	21	≤	≤	NOUN
ejpam-5362	81	22	b•.	b•.	VERB
ejpam-5362	81	23	a	a	DET
ejpam-5362	81	24	bilocale	bilocale	NOUN
ejpam-5362	81	25	(	(	PUNCT
ejpam-5362	81	26	l	l	NOUN
ejpam-5362	81	27	,	,	PUNCT
ejpam-5362	81	28	l1	l1	PROPN
ejpam-5362	81	29	,	,	PUNCT
ejpam-5362	81	30	l2	l2	NOUN
ejpam-5362	81	31	)	)	PUNCT
ejpam-5362	81	32	is	be	AUX
ejpam-5362	81	33	compact	compact	ADJ
ejpam-5362	81	34	if	if	SCONJ
ejpam-5362	81	35	its	its	PRON
ejpam-5362	81	36	total	total	ADJ
ejpam-5362	81	37	part	part	NOUN
ejpam-5362	81	38	is	be	AUX
ejpam-5362	81	39	compact	compact	ADJ
ejpam-5362	81	40	,	,	PUNCT
ejpam-5362	81	41	and	and	CCONJ
ejpam-5362	81	42	regular	regular	ADJ
ejpam-5362	81	43	provided	provide	VERB
ejpam-5362	81	44	that	that	SCONJ
ejpam-5362	81	45	x	x	X
ejpam-5362	81	46	=	=	SYM
ejpam-5362	81	47	∨	∨	X
ejpam-5362	81	48	{	{	PUNCT
ejpam-5362	81	49	a	a	DET
ejpam-5362	81	50	∈	∈	PROPN
ejpam-5362	81	51	li	li	NOUN
ejpam-5362	81	52	:	:	PUNCT
ejpam-5362	81	53	a	a	DET
ejpam-5362	81	54	≺i	≺i	PROPN
ejpam-5362	81	55	x	x	NOUN
ejpam-5362	81	56	}	}	PUNCT
ejpam-5362	81	57	for	for	ADP
ejpam-5362	81	58	every	every	DET
ejpam-5362	81	59	x	x	PROPN
ejpam-5362	81	60	∈	∈	PROPN
ejpam-5362	81	61	li	li	PROPN
ejpam-5362	81	62	,	,	PUNCT
ejpam-5362	81	63	where	where	SCONJ
ejpam-5362	81	64	a	a	DET
ejpam-5362	81	65	≺i	≺i	PROPN
ejpam-5362	81	66	x	x	PUNCT
ejpam-5362	81	67	means	mean	VERB
ejpam-5362	81	68	that	that	SCONJ
ejpam-5362	81	69	there	there	PRON
ejpam-5362	81	70	is	be	VERB
ejpam-5362	81	71	c	c	NOUN
ejpam-5362	81	72	∈	∈	PROPN
ejpam-5362	81	73	lj	lj	ADV
ejpam-5362	81	74	such	such	ADJ
ejpam-5362	81	75	that	that	DET
ejpam-5362	81	76	a∧c	a∧c	NOUN
ejpam-5362	81	77	=	=	SYM
ejpam-5362	81	78	0	0	NUM
ejpam-5362	81	79	and	and	CCONJ
ejpam-5362	81	80	c∨x	c∨x	PROPN
ejpam-5362	81	81	=	=	PUNCT
ejpam-5362	82	1	1	1	X
ejpam-5362	82	2	.	.	PUNCT
ejpam-5362	82	3	a	a	DET
ejpam-5362	82	4	biframe	biframe	NOUN
ejpam-5362	82	5	homomorphism	homomorphism	NOUN
ejpam-5362	82	6	(	(	PUNCT
ejpam-5362	82	7	or	or	CCONJ
ejpam-5362	82	8	biframe	biframe	NOUN
ejpam-5362	82	9	map	map	NOUN
ejpam-5362	82	10	)	)	PUNCT
ejpam-5362	82	11	h	h	NOUN
ejpam-5362	82	12	:	:	PUNCT
ejpam-5362	82	13	(	(	PUNCT
ejpam-5362	82	14	m	m	NOUN
ejpam-5362	82	15	,	,	PUNCT
ejpam-5362	82	16	m1,m2	m1,m2	PROPN
ejpam-5362	82	17	)	)	PUNCT
ejpam-5362	82	18	→	→	SYM
ejpam-5362	82	19	(	(	PUNCT
ejpam-5362	82	20	l	l	NOUN
ejpam-5362	82	21	,	,	PUNCT
ejpam-5362	82	22	l1	l1	PROPN
ejpam-5362	82	23	,	,	PUNCT
ejpam-5362	82	24	l2	l2	NOUN
ejpam-5362	82	25	)	)	PUNCT
ejpam-5362	82	26	is	be	AUX
ejpam-5362	82	27	a	a	DET
ejpam-5362	82	28	frame	frame	NOUN
ejpam-5362	82	29	homomorphism	homomorphism	NOUN
ejpam-5362	82	30	h	h	NOUN
ejpam-5362	82	31	:	:	PUNCT
ejpam-5362	82	32	m	m	VERB
ejpam-5362	82	33	→	→	SYM
ejpam-5362	82	34	l	l	NOUN
ejpam-5362	82	35	for	for	ADP
ejpam-5362	82	36	which	which	PRON
ejpam-5362	82	37	h(mi	h(mi	PROPN
ejpam-5362	82	38	)	)	PUNCT
ejpam-5362	82	39	⊆	⊆	NUM
ejpam-5362	82	40	li	li	X
ejpam-5362	82	41	(	(	PUNCT
ejpam-5362	82	42	i	i	NOUN
ejpam-5362	82	43	=	=	NOUN
ejpam-5362	82	44	1	1	NUM
ejpam-5362	82	45	,	,	PUNCT
ejpam-5362	82	46	2	2	NUM
ejpam-5362	82	47	)	)	PUNCT
ejpam-5362	82	48	.	.	PUNCT
ejpam-5362	83	1	the	the	DET
ejpam-5362	83	2	map	map	NOUN
ejpam-5362	83	3	h	h	NOUN
ejpam-5362	83	4	:	:	PUNCT
ejpam-5362	83	5	m	m	VERB
ejpam-5362	83	6	→	→	SYM
ejpam-5362	83	7	l	l	NOUN
ejpam-5362	83	8	is	be	AUX
ejpam-5362	83	9	called	call	VERB
ejpam-5362	83	10	the	the	DET
ejpam-5362	83	11	total	total	ADJ
ejpam-5362	83	12	part	part	NOUN
ejpam-5362	83	13	of	of	ADP
ejpam-5362	83	14	h	h	NOUN
ejpam-5362	83	15	:	:	PUNCT
ejpam-5362	83	16	(	(	PUNCT
ejpam-5362	83	17	m	m	NOUN
ejpam-5362	83	18	,	,	PUNCT
ejpam-5362	83	19	m1,m2	m1,m2	PROPN
ejpam-5362	83	20	)	)	PUNCT
ejpam-5362	83	21	→	→	SYM
ejpam-5362	83	22	(	(	PUNCT
ejpam-5362	83	23	l	l	NOUN
ejpam-5362	83	24	,	,	PUNCT
ejpam-5362	83	25	l1	l1	PROPN
ejpam-5362	83	26	,	,	PUNCT
ejpam-5362	83	27	l2	l2	NOUN
ejpam-5362	83	28	)	)	PUNCT
ejpam-5362	83	29	.	.	PUNCT
ejpam-5362	84	1	by	by	ADP
ejpam-5362	84	2	a	a	DET
ejpam-5362	84	3	biframe	biframe	NOUN
ejpam-5362	84	4	map	map	NOUN
ejpam-5362	84	5	we	we	PRON
ejpam-5362	84	6	mean	mean	VERB
ejpam-5362	84	7	a	a	DET
ejpam-5362	84	8	function	function	NOUN
ejpam-5362	84	9	h	h	NOUN
ejpam-5362	84	10	:	:	PUNCT
ejpam-5362	84	11	(	(	PUNCT
ejpam-5362	84	12	m	m	NOUN
ejpam-5362	84	13	,	,	PUNCT
ejpam-5362	84	14	m1,m2	m1,m2	PROPN
ejpam-5362	84	15	)	)	PUNCT
ejpam-5362	84	16	→	→	SYM
ejpam-5362	84	17	(	(	PUNCT
ejpam-5362	84	18	l	l	NOUN
ejpam-5362	84	19	,	,	PUNCT
ejpam-5362	84	20	l1	l1	PROPN
ejpam-5362	84	21	,	,	PUNCT
ejpam-5362	84	22	l2	l2	NOUN
ejpam-5362	84	23	)	)	PUNCT
ejpam-5362	84	24	with	with	ADP
ejpam-5362	84	25	a	a	DET
ejpam-5362	84	26	dense	dense	ADJ
ejpam-5362	84	27	total	total	ADJ
ejpam-5362	84	28	part	part	NOUN
ejpam-5362	84	29	h	h	NOUN
ejpam-5362	84	30	:	:	PUNCT
ejpam-5362	84	31	m	m	AUX
ejpam-5362	84	32	→	→	SYM
ejpam-5362	84	33	l.	l.	PROPN
ejpam-5362	84	34	it	it	PRON
ejpam-5362	84	35	is	be	AUX
ejpam-5362	84	36	onto	onto	ADP
ejpam-5362	84	37	if	if	SCONJ
ejpam-5362	84	38	h[mi	h[mi	PROPN
ejpam-5362	84	39	]	]	X
ejpam-5362	84	40	=	=	SYM
ejpam-5362	84	41	li	li	PROPN
ejpam-5362	84	42	for	for	ADP
ejpam-5362	84	43	i	i	PROPN
ejpam-5362	84	44	=	=	SYM
ejpam-5362	84	45	1	1	NUM
ejpam-5362	84	46	,	,	PUNCT
ejpam-5362	84	47	2	2	NUM
ejpam-5362	84	48	.	.	PUNCT
ejpam-5362	84	49	a	a	DET
ejpam-5362	84	50	subbilocale	subbilocale	NOUN
ejpam-5362	84	51	of	of	ADP
ejpam-5362	84	52	a	a	DET
ejpam-5362	84	53	bilocale	bilocale	NOUN
ejpam-5362	84	54	(	(	PUNCT
ejpam-5362	84	55	l	l	NOUN
ejpam-5362	84	56	,	,	PUNCT
ejpam-5362	84	57	l1	l1	PROPN
ejpam-5362	84	58	,	,	PUNCT
ejpam-5362	84	59	l2	l2	NOUN
ejpam-5362	84	60	)	)	PUNCT
ejpam-5362	84	61	is	be	AUX
ejpam-5362	84	62	a	a	DET
ejpam-5362	84	63	triple	triple	ADJ
ejpam-5362	84	64	(	(	PUNCT
ejpam-5362	84	65	s	s	NOUN
ejpam-5362	84	66	,	,	PUNCT
ejpam-5362	84	67	s1	s1	NOUN
ejpam-5362	84	68	,	,	PUNCT
ejpam-5362	84	69	s2	s2	PROPN
ejpam-5362	84	70	)	)	PUNCT
ejpam-5362	84	71	where	where	SCONJ
ejpam-5362	84	72	s	s	NOUN
ejpam-5362	84	73	is	be	AUX
ejpam-5362	84	74	a	a	DET
ejpam-5362	84	75	sublocale	sublocale	NOUN
ejpam-5362	84	76	of	of	ADP
ejpam-5362	84	77	l	l	NOUN
ejpam-5362	84	78	and	and	CCONJ
ejpam-5362	84	79	si	si	X
ejpam-5362	84	80	=	=	SYM
ejpam-5362	84	81	νs	νs	PRON
ejpam-5362	85	1	[	[	X
ejpam-5362	85	2	li	li	X
ejpam-5362	85	3	]	]	X
ejpam-5362	85	4	for	for	ADP
ejpam-5362	85	5	i	i	PROPN
ejpam-5362	85	6	=	=	NOUN
ejpam-5362	85	7	1	1	NUM
ejpam-5362	85	8	,	,	PUNCT
ejpam-5362	85	9	2	2	NUM
ejpam-5362	85	10	.	.	X
ejpam-5362	86	1	we	we	PRON
ejpam-5362	86	2	shall	shall	AUX
ejpam-5362	86	3	say	say	VERB
ejpam-5362	86	4	that	that	SCONJ
ejpam-5362	86	5	(	(	PUNCT
ejpam-5362	86	6	s	s	X
ejpam-5362	86	7	,	,	PUNCT
ejpam-5362	86	8	s1	s1	NOUN
ejpam-5362	86	9	,	,	PUNCT
ejpam-5362	86	10	s2	s2	PROPN
ejpam-5362	86	11	)	)	PUNCT
ejpam-5362	86	12	is	be	AUX
ejpam-5362	86	13	a	a	DET
ejpam-5362	86	14	p	p	ADV
ejpam-5362	86	15	-subbilocale	-subbilocale	ADJ
ejpam-5362	86	16	in	in	ADP
ejpam-5362	86	17	case	case	NOUN
ejpam-5362	86	18	s	s	PART
ejpam-5362	86	19	has	have	VERB
ejpam-5362	86	20	property	property	NOUN
ejpam-5362	86	21	p	p	PROPN
ejpam-5362	86	22	.	.	PUNCT
ejpam-5362	87	1	recall	recall	VERB
ejpam-5362	87	2	that	that	PRON
ejpam-5362	87	3	for	for	ADP
ejpam-5362	87	4	a	a	DET
ejpam-5362	87	5	bilocale	bilocale	NOUN
ejpam-5362	87	6	(	(	PUNCT
ejpam-5362	87	7	l	l	NOUN
ejpam-5362	87	8	,	,	PUNCT
ejpam-5362	87	9	l1	l1	PROPN
ejpam-5362	87	10	,	,	PUNCT
ejpam-5362	87	11	l2	l2	NOUN
ejpam-5362	87	12	)	)	PUNCT
ejpam-5362	87	13	and	and	CCONJ
ejpam-5362	87	14	a	a	DET
ejpam-5362	87	15	sublocale	sublocale	NOUN
ejpam-5362	87	16	s	s	X
ejpam-5362	87	17	of	of	ADP
ejpam-5362	87	18	l	l	NOUN
ejpam-5362	87	19	:	:	PUNCT
ejpam-5362	88	1	[	[	X
ejpam-5362	88	2	15	15	NUM
ejpam-5362	88	3	]	]	SYM
ejpam-5362	88	4	inti(s	inti(s	NOUN
ejpam-5362	88	5	)	)	PUNCT
ejpam-5362	88	6	=	=	SYM
ejpam-5362	88	7	∨	∨	X
ejpam-5362	88	8	{	{	PUNCT
ejpam-5362	88	9	o(a	o(a	PROPN
ejpam-5362	88	10	)	)	PUNCT
ejpam-5362	88	11	:	:	PUNCT
ejpam-5362	88	12	a	a	DET
ejpam-5362	88	13	∈	∈	PROPN
ejpam-5362	88	14	li	li	X
ejpam-5362	88	15	,	,	PUNCT
ejpam-5362	88	16	o(a	o(a	NOUN
ejpam-5362	88	17	)	)	PUNCT
ejpam-5362	88	18	⊆	⊆	NUM
ejpam-5362	88	19	s	s	X
ejpam-5362	88	20	}	}	PUNCT
ejpam-5362	88	21	(	(	PUNCT
ejpam-5362	88	22	i	i	NOUN
ejpam-5362	88	23	=	=	NOUN
ejpam-5362	88	24	1	1	NUM
ejpam-5362	88	25	,	,	PUNCT
ejpam-5362	88	26	2	2	NUM
ejpam-5362	88	27	)	)	PUNCT
ejpam-5362	88	28	.	.	PUNCT
ejpam-5362	89	1	and	and	CCONJ
ejpam-5362	90	1	[	[	X
ejpam-5362	90	2	18	18	NUM
ejpam-5362	90	3	]	]	SYM
ejpam-5362	90	4	cli(s	cli(s	NOUN
ejpam-5362	90	5	)	)	PUNCT
ejpam-5362	90	6	=	=	SYM
ejpam-5362	90	7	∧	∧	PROPN
ejpam-5362	90	8	{	{	PUNCT
ejpam-5362	90	9	c(a	c(a	PROPN
ejpam-5362	90	10	)	)	PUNCT
ejpam-5362	90	11	:	:	PUNCT
ejpam-5362	90	12	a	a	DET
ejpam-5362	90	13	∈	∈	PROPN
ejpam-5362	90	14	li	li	X
ejpam-5362	90	15	,	,	PUNCT
ejpam-5362	90	16	s	s	VERB
ejpam-5362	90	17	⊆	⊆	NUM
ejpam-5362	90	18	c(a	c(a	NOUN
ejpam-5362	90	19	)	)	PUNCT
ejpam-5362	90	20	}	}	PUNCT
ejpam-5362	91	1	=	=	SYM
ejpam-5362	91	2	c	c	X
ejpam-5362	91	3	(	(	PUNCT
ejpam-5362	91	4	∨	∨	X
ejpam-5362	91	5	{	{	PUNCT
ejpam-5362	91	6	a	a	DET
ejpam-5362	91	7	∈	∈	PROPN
ejpam-5362	91	8	li	li	NOUN
ejpam-5362	91	9	:	:	PUNCT
ejpam-5362	91	10	s	s	VERB
ejpam-5362	91	11	⊆	⊆	NUM
ejpam-5362	91	12	c(a	c(a	NOUN
ejpam-5362	91	13	)	)	PUNCT
ejpam-5362	91	14	}	}	PUNCT
ejpam-5362	91	15	)	)	PUNCT
ejpam-5362	92	1	(	(	PUNCT
ejpam-5362	92	2	i	i	NOUN
ejpam-5362	92	3	=	=	NOUN
ejpam-5362	92	4	1	1	NUM
ejpam-5362	92	5	,	,	PUNCT
ejpam-5362	92	6	2	2	NUM
ejpam-5362	92	7	)	)	PUNCT
ejpam-5362	92	8	.	.	PUNCT
ejpam-5362	93	1	for	for	ADP
ejpam-5362	93	2	each	each	DET
ejpam-5362	93	3	a	a	DET
ejpam-5362	93	4	∈	∈	PROPN
ejpam-5362	93	5	li	li	PROPN
ejpam-5362	93	6	,	,	PUNCT
ejpam-5362	93	7	c(a	c(a	PROPN
ejpam-5362	93	8	•	•	NUM
ejpam-5362	93	9	)	)	PUNCT
ejpam-5362	93	10	=	=	SYM
ejpam-5362	93	11	clj(o(a	clj(o(a	NOUN
ejpam-5362	93	12	)	)	PUNCT
ejpam-5362	93	13	)	)	PUNCT
ejpam-5362	93	14	.	.	PUNCT
ejpam-5362	94	1	a	a	DET
ejpam-5362	94	2	sublocale	sublocale	NOUN
ejpam-5362	94	3	a	a	PRON
ejpam-5362	94	4	of	of	ADP
ejpam-5362	94	5	a	a	DET
ejpam-5362	94	6	bilocale	bilocale	NOUN
ejpam-5362	94	7	(	(	PUNCT
ejpam-5362	94	8	l	l	NOUN
ejpam-5362	94	9	,	,	PUNCT
ejpam-5362	94	10	l1	l1	PROPN
ejpam-5362	94	11	,	,	PUNCT
ejpam-5362	94	12	l2	l2	NOUN
ejpam-5362	94	13	)	)	PUNCT
ejpam-5362	94	14	is	be	AUX
ejpam-5362	94	15	i	i	PRON
ejpam-5362	94	16	-	-	PUNCT
ejpam-5362	94	17	dense	dense	ADJ
ejpam-5362	94	18	if	if	SCONJ
ejpam-5362	94	19	cli(a	cli(a	PROPN
ejpam-5362	94	20	)	)	PUNCT
ejpam-5362	94	21	=	=	PUNCT
ejpam-5362	95	1	l.	l.	NOUN
ejpam-5362	95	2	this	this	PRON
ejpam-5362	95	3	is	be	AUX
ejpam-5362	95	4	equivalent	equivalent	ADJ
ejpam-5362	95	5	to	to	ADP
ejpam-5362	95	6	saying	say	VERB
ejpam-5362	95	7	that	that	SCONJ
ejpam-5362	95	8	s	s	VERB
ejpam-5362	95	9	is	be	AUX
ejpam-5362	95	10	i	i	PRON
ejpam-5362	95	11	-	-	PUNCT
ejpam-5362	95	12	dense	dense	ADJ
ejpam-5362	95	13	if	if	SCONJ
ejpam-5362	96	1	and	and	CCONJ
ejpam-5362	96	2	only	only	ADV
ejpam-5362	96	3	if	if	SCONJ
ejpam-5362	96	4	for	for	ADP
ejpam-5362	96	5	each	each	DET
ejpam-5362	96	6	non	non	ADJ
ejpam-5362	96	7	-	-	ADJ
ejpam-5362	96	8	zero	zero	NUM
ejpam-5362	96	9	x	x	SYM
ejpam-5362	96	10	∈	∈	PROPN
ejpam-5362	96	11	li	li	PROPN
ejpam-5362	96	12	,	,	PUNCT
ejpam-5362	96	13	o(x	o(x	PROPN
ejpam-5362	96	14	)	)	PUNCT
ejpam-5362	96	15	∩	∩	NOUN
ejpam-5362	96	16	s	s	PART
ejpam-5362	96	17	̸=	̸=	PROPN
ejpam-5362	96	18	o.	o.	NOUN
ejpam-5362	96	19	every	every	DET
ejpam-5362	96	20	sublocale	sublocale	NOUN
ejpam-5362	96	21	containing	contain	VERB
ejpam-5362	96	22	an	an	DET
ejpam-5362	96	23	i	i	NOUN
ejpam-5362	96	24	-	-	PUNCT
ejpam-5362	96	25	dense	dense	ADJ
ejpam-5362	96	26	sublocale	sublocale	NOUN
ejpam-5362	96	27	is	be	AUX
ejpam-5362	96	28	i	i	PRON
ejpam-5362	96	29	-	-	PUNCT
ejpam-5362	96	30	dense	dense	ADJ
ejpam-5362	96	31	.	.	PUNCT
ejpam-5362	97	1	given	give	VERB
ejpam-5362	97	2	a	a	DET
ejpam-5362	97	3	bilocale	bilocale	NOUN
ejpam-5362	97	4	(	(	PUNCT
ejpam-5362	97	5	l	l	NOUN
ejpam-5362	97	6	,	,	PUNCT
ejpam-5362	97	7	l1	l1	PROPN
ejpam-5362	97	8	,	,	PUNCT
ejpam-5362	97	9	l2	l2	NOUN
ejpam-5362	97	10	)	)	PUNCT
ejpam-5362	97	11	,	,	PUNCT
ejpam-5362	97	12	a	a	DET
ejpam-5362	97	13	sublocale	sublocale	NOUN
ejpam-5362	97	14	s	s	X
ejpam-5362	97	15	of	of	ADP
ejpam-5362	97	16	l	l	NOUN
ejpam-5362	97	17	is	be	AUX
ejpam-5362	97	18	(	(	PUNCT
ejpam-5362	97	19	i	i	NOUN
ejpam-5362	97	20	,	,	PUNCT
ejpam-5362	97	21	j)-nowhere	j)-nowhere	ADV
ejpam-5362	97	22	dense	dense	ADJ
ejpam-5362	97	23	if	if	SCONJ
ejpam-5362	97	24	intj(cli(s	intj(cli(s	NUM
ejpam-5362	97	25	)	)	PUNCT
ejpam-5362	97	26	)	)	PUNCT
ejpam-5362	98	1	=	=	SYM
ejpam-5362	98	2	o	o	X
ejpam-5362	98	3	(	(	PUNCT
ejpam-5362	98	4	i	i	PRON
ejpam-5362	98	5	̸=	̸=	PROPN
ejpam-5362	98	6	j	j	PROPN
ejpam-5362	98	7	∈	∈	PROPN
ejpam-5362	98	8	{	{	PUNCT
ejpam-5362	98	9	1	1	NUM
ejpam-5362	98	10	,	,	PUNCT
ejpam-5362	98	11	2	2	NUM
ejpam-5362	98	12	}	}	PUNCT
ejpam-5362	98	13	)	)	PUNCT
ejpam-5362	98	14	.	.	PUNCT
ejpam-5362	99	1	as	as	ADP
ejpam-5362	99	2	a	a	DET
ejpam-5362	99	3	result	result	NOUN
ejpam-5362	99	4	,	,	PUNCT
ejpam-5362	99	5	a	a	DET
ejpam-5362	99	6	sublocale	sublocale	NOUN
ejpam-5362	99	7	s	s	X
ejpam-5362	99	8	of	of	ADP
ejpam-5362	99	9	a	a	DET
ejpam-5362	99	10	bilocale	bilocale	NOUN
ejpam-5362	99	11	(	(	PUNCT
ejpam-5362	99	12	l	l	NOUN
ejpam-5362	99	13	,	,	PUNCT
ejpam-5362	99	14	l1	l1	PROPN
ejpam-5362	99	15	,	,	PUNCT
ejpam-5362	99	16	l2	l2	NOUN
ejpam-5362	99	17	)	)	PUNCT
ejpam-5362	99	18	is	be	AUX
ejpam-5362	99	19	(	(	PUNCT
ejpam-5362	99	20	i	i	NOUN
ejpam-5362	99	21	,	,	PUNCT
ejpam-5362	99	22	j)-nowhere	j)-nowhere	ADV
ejpam-5362	99	23	dense	dense	ADJ
ejpam-5362	99	24	m.	m.	NOUN
ejpam-5362	99	25	nxumalo	nxumalo	PROPN
ejpam-5362	99	26	/	/	SYM
ejpam-5362	99	27	eur	eur	PROPN
ejpam-5362	99	28	.	.	PUNCT
ejpam-5362	100	1	j.	j.	PROPN
ejpam-5362	100	2	pure	pure	PROPN
ejpam-5362	100	3	appl	appl	PROPN
ejpam-5362	100	4	.	.	PROPN
ejpam-5362	100	5	math	math	PROPN
ejpam-5362	100	6	,	,	PUNCT
ejpam-5362	100	7	18	18	NUM
ejpam-5362	100	8	(	(	PUNCT
ejpam-5362	100	9	1	1	NUM
ejpam-5362	100	10	)	)	PUNCT
ejpam-5362	100	11	(	(	PUNCT
ejpam-5362	100	12	2025	2025	NUM
ejpam-5362	100	13	)	)	PUNCT
ejpam-5362	100	14	,	,	PUNCT
ejpam-5362	100	15	5362	5362	NUM
ejpam-5362	100	16	5	5	NUM
ejpam-5362	100	17	of	of	ADP
ejpam-5362	100	18	21	21	NUM
ejpam-5362	100	19	if	if	SCONJ
ejpam-5362	100	20	and	and	CCONJ
ejpam-5362	100	21	only	only	ADV
ejpam-5362	100	22	if	if	SCONJ
ejpam-5362	100	23	l	l	NOUN
ejpam-5362	100	24	∖	∖	X
ejpam-5362	100	25	cli(s	cli(s	NOUN
ejpam-5362	100	26	)	)	PUNCT
ejpam-5362	100	27	is	be	AUX
ejpam-5362	100	28	j	j	NOUN
ejpam-5362	100	29	-	-	PUNCT
ejpam-5362	100	30	dense	dense	ADJ
ejpam-5362	100	31	if	if	SCONJ
ejpam-5362	101	1	and	and	CCONJ
ejpam-5362	101	2	only	only	ADV
ejpam-5362	101	3	if	if	SCONJ
ejpam-5362	101	4	s	s	X
ejpam-5362	101	5	is	be	AUX
ejpam-5362	101	6	(	(	PUNCT
ejpam-5362	101	7	i	i	NOUN
ejpam-5362	101	8	,	,	PUNCT
ejpam-5362	101	9	j)-nowhere	j)-nowhere	ADV
ejpam-5362	101	10	dense	dense	ADJ
ejpam-5362	101	11	.	.	PUNCT
ejpam-5362	102	1	furthermore	furthermore	ADV
ejpam-5362	102	2	,	,	PUNCT
ejpam-5362	102	3	an	an	DET
ejpam-5362	102	4	element	element	NOUN
ejpam-5362	102	5	a	a	DET
ejpam-5362	102	6	∈	∈	PROPN
ejpam-5362	102	7	li	li	PROPN
ejpam-5362	102	8	is	be	AUX
ejpam-5362	102	9	j	j	NOUN
ejpam-5362	102	10	-	-	PUNCT
ejpam-5362	102	11	dense	dense	ADJ
ejpam-5362	102	12	if	if	SCONJ
ejpam-5362	103	1	and	and	CCONJ
ejpam-5362	103	2	only	only	ADV
ejpam-5362	103	3	if	if	SCONJ
ejpam-5362	103	4	c(a	c(a	NOUN
ejpam-5362	103	5	)	)	PUNCT
ejpam-5362	103	6	is	be	AUX
ejpam-5362	103	7	(	(	PUNCT
ejpam-5362	103	8	i	i	NOUN
ejpam-5362	103	9	,	,	PUNCT
ejpam-5362	103	10	j)-nowhere	j)-nowhere	ADV
ejpam-5362	103	11	dense	dense	ADJ
ejpam-5362	103	12	.	.	PUNCT
ejpam-5362	104	1	when	when	SCONJ
ejpam-5362	104	2	dealing	deal	VERB
ejpam-5362	104	3	with	with	ADP
ejpam-5362	104	4	subbilocales	subbilocale	NOUN
ejpam-5362	104	5	,	,	PUNCT
ejpam-5362	104	6	say	say	VERB
ejpam-5362	104	7	(	(	PUNCT
ejpam-5362	104	8	s	s	X
ejpam-5362	104	9	,	,	PUNCT
ejpam-5362	104	10	s1	s1	NOUN
ejpam-5362	104	11	,	,	PUNCT
ejpam-5362	104	12	s2	s2	PROPN
ejpam-5362	104	13	)	)	PUNCT
ejpam-5362	104	14	,	,	PUNCT
ejpam-5362	104	15	we	we	PRON
ejpam-5362	104	16	write	write	VERB
ejpam-5362	104	17	is	be	AUX
ejpam-5362	104	18	-	-	PUNCT
ejpam-5362	104	19	dense	dense	ADJ
ejpam-5362	104	20	,	,	PUNCT
ejpam-5362	104	21	is	be	AUX
ejpam-5362	104	22	-	-	PUNCT
ejpam-5362	104	23	open	open	ADJ
ejpam-5362	104	24	and	and	CCONJ
ejpam-5362	104	25	(	(	PUNCT
ejpam-5362	104	26	is	be	AUX
ejpam-5362	104	27	,	,	PUNCT
ejpam-5362	104	28	js)nowhere	js)nowhere	VERB
ejpam-5362	104	29	dense	dense	ADJ
ejpam-5362	104	30	instead	instead	ADV
ejpam-5362	104	31	of	of	ADP
ejpam-5362	104	32	i	i	NOUN
ejpam-5362	104	33	-	-	PUNCT
ejpam-5362	104	34	dense	dense	ADJ
ejpam-5362	104	35	,	,	PUNCT
ejpam-5362	104	36	i	i	PRON
ejpam-5362	104	37	-	-	PUNCT
ejpam-5362	104	38	open	open	ADJ
ejpam-5362	104	39	and	and	CCONJ
ejpam-5362	104	40	(	(	PUNCT
ejpam-5362	104	41	i	i	NOUN
ejpam-5362	104	42	,	,	PUNCT
ejpam-5362	104	43	j)-nowhere	j)-nowhere	ADV
ejpam-5362	104	44	dense	dense	ADJ
ejpam-5362	104	45	.	.	PUNCT
ejpam-5362	105	1	by	by	ADP
ejpam-5362	105	2	an	an	DET
ejpam-5362	105	3	i	i	PROPN
ejpam-5362	105	4	-	-	PUNCT
ejpam-5362	105	5	gδ	gδ	NOUN
ejpam-5362	105	6	-	-	PUNCT
ejpam-5362	105	7	sublocale	sublocale	NOUN
ejpam-5362	105	8	of	of	ADP
ejpam-5362	105	9	a	a	DET
ejpam-5362	105	10	bilocale	bilocale	NOUN
ejpam-5362	105	11	(	(	PUNCT
ejpam-5362	105	12	l	l	NOUN
ejpam-5362	105	13	,	,	PUNCT
ejpam-5362	105	14	l1	l1	PROPN
ejpam-5362	105	15	,	,	PUNCT
ejpam-5362	105	16	l2	l2	NOUN
ejpam-5362	105	17	)	)	PUNCT
ejpam-5362	105	18	,	,	PUNCT
ejpam-5362	105	19	we	we	PRON
ejpam-5362	105	20	mean	mean	VERB
ejpam-5362	105	21	a	a	DET
ejpam-5362	105	22	sublocale	sublocale	NOUN
ejpam-5362	105	23	of	of	ADP
ejpam-5362	105	24	the	the	DET
ejpam-5362	105	25	form	form	NOUN
ejpam-5362	105	26	s	s	PART
ejpam-5362	105	27	=	=	NOUN
ejpam-5362	105	28	∧	∧	NOUN
ejpam-5362	105	29	n∈n	n∈n	NOUN
ejpam-5362	105	30	o(xn	o(xn	NOUN
ejpam-5362	105	31	)	)	PUNCT
ejpam-5362	105	32	where	where	SCONJ
ejpam-5362	105	33	each	each	DET
ejpam-5362	105	34	xn	xn	PROPN
ejpam-5362	105	35	∈	∈	PROPN
ejpam-5362	105	36	li	li	PROPN
ejpam-5362	105	37	.	.	PUNCT
ejpam-5362	106	1	a	a	DET
ejpam-5362	106	2	sublocale	sublocale	NOUN
ejpam-5362	106	3	of	of	ADP
ejpam-5362	106	4	a	a	DET
ejpam-5362	106	5	bilocale	bilocale	NOUN
ejpam-5362	106	6	(	(	PUNCT
ejpam-5362	106	7	l	l	NOUN
ejpam-5362	106	8	,	,	PUNCT
ejpam-5362	106	9	l1	l1	PROPN
ejpam-5362	106	10	,	,	PUNCT
ejpam-5362	106	11	l2	l2	NOUN
ejpam-5362	106	12	)	)	PUNCT
ejpam-5362	106	13	is	be	AUX
ejpam-5362	106	14	i	i	PROPN
ejpam-5362	106	15	-	-	PUNCT
ejpam-5362	106	16	gδ	gδ	NOUN
ejpam-5362	106	17	-	-	PUNCT
ejpam-5362	106	18	dense	dense	ADJ
ejpam-5362	106	19	if	if	SCONJ
ejpam-5362	106	20	it	it	PRON
ejpam-5362	106	21	meets	meet	VERB
ejpam-5362	106	22	every	every	DET
ejpam-5362	106	23	nonvoid	nonvoid	NOUN
ejpam-5362	106	24	i	i	PROPN
ejpam-5362	106	25	-	-	PUNCT
ejpam-5362	106	26	gδ	gδ	NOUN
ejpam-5362	106	27	-	-	PUNCT
ejpam-5362	106	28	sublocales	sublocale	NOUN
ejpam-5362	106	29	.	.	PUNCT
ejpam-5362	107	1	for	for	ADP
ejpam-5362	107	2	the	the	DET
ejpam-5362	107	3	bilocale	bilocale	NOUN
ejpam-5362	107	4	(	(	PUNCT
ejpam-5362	107	5	τ1	τ1	PROPN
ejpam-5362	107	6	∨	∨	NUM
ejpam-5362	107	7	τ2	τ2	NOUN
ejpam-5362	107	8	,	,	PUNCT
ejpam-5362	107	9	τ1	τ1	NOUN
ejpam-5362	107	10	,	,	PUNCT
ejpam-5362	107	11	τ2	τ2	NOUN
ejpam-5362	107	12	)	)	PUNCT
ejpam-5362	107	13	induced	induce	VERB
ejpam-5362	107	14	by	by	ADP
ejpam-5362	107	15	a	a	DET
ejpam-5362	107	16	bispace	bispace	NOUN
ejpam-5362	107	17	(	(	PUNCT
ejpam-5362	107	18	x	x	NOUN
ejpam-5362	107	19	,	,	PUNCT
ejpam-5362	107	20	τ1	τ1	NOUN
ejpam-5362	107	21	,	,	PUNCT
ejpam-5362	107	22	τ2	τ2	NOUN
ejpam-5362	107	23	)	)	PUNCT
ejpam-5362	107	24	,	,	PUNCT
ejpam-5362	107	25	we	we	PRON
ejpam-5362	107	26	shall	shall	AUX
ejpam-5362	107	27	write	write	VERB
ejpam-5362	107	28	u	u	PROPN
ejpam-5362	107	29	is	be	AUX
ejpam-5362	107	30	τi	τi	ADJ
ejpam-5362	107	31	-	-	PUNCT
ejpam-5362	107	32	open	open	ADJ
ejpam-5362	107	33	if	if	SCONJ
ejpam-5362	107	34	u	u	PROPN
ejpam-5362	107	35	∈	∈	PROPN
ejpam-5362	107	36	τi	τi	X
ejpam-5362	107	37	and	and	CCONJ
ejpam-5362	107	38	u	u	NOUN
ejpam-5362	107	39	is	be	AUX
ejpam-5362	107	40	τi	τi	ADJ
ejpam-5362	107	41	-	-	PUNCT
ejpam-5362	107	42	dense	dense	ADJ
ejpam-5362	107	43	if	if	SCONJ
ejpam-5362	107	44	u	u	NOUN
ejpam-5362	107	45	is	be	AUX
ejpam-5362	107	46	dense	dense	ADJ
ejpam-5362	107	47	with	with	ADP
ejpam-5362	107	48	respect	respect	NOUN
ejpam-5362	107	49	to	to	ADP
ejpam-5362	107	50	the	the	DET
ejpam-5362	107	51	topological	topological	ADJ
ejpam-5362	107	52	space	space	NOUN
ejpam-5362	107	53	(	(	PUNCT
ejpam-5362	107	54	x	x	NOUN
ejpam-5362	107	55	,	,	PUNCT
ejpam-5362	107	56	τi	τi	NOUN
ejpam-5362	107	57	)	)	PUNCT
ejpam-5362	107	58	.	.	PUNCT
ejpam-5362	108	1	3	3	X
ejpam-5362	108	2	.	.	X
ejpam-5362	108	3	(	(	PUNCT
ejpam-5362	108	4	i	i	NOUN
ejpam-5362	108	5	,	,	PUNCT
ejpam-5362	108	6	j)-baire	j)-baire	PROPN
ejpam-5362	108	7	bilocales	bilocale	NOUN
ejpam-5362	108	8	recall	recall	VERB
ejpam-5362	108	9	that	that	SCONJ
ejpam-5362	108	10	a	a	DET
ejpam-5362	108	11	bispace	bispace	NOUN
ejpam-5362	108	12	(	(	PUNCT
ejpam-5362	108	13	x	x	NOUN
ejpam-5362	108	14	,	,	PUNCT
ejpam-5362	108	15	τ1	τ1	NOUN
ejpam-5362	108	16	,	,	PUNCT
ejpam-5362	108	17	τ2	τ2	NOUN
ejpam-5362	108	18	)	)	PUNCT
ejpam-5362	108	19	is	be	AUX
ejpam-5362	108	20	almost	almost	ADV
ejpam-5362	108	21	(	(	PUNCT
ejpam-5362	108	22	i	i	NOUN
ejpam-5362	108	23	,	,	PUNCT
ejpam-5362	108	24	j)-baire	j)-baire	PROPN
ejpam-5362	109	1	[	[	X
ejpam-5362	109	2	8	8	X
ejpam-5362	109	3	]	]	X
ejpam-5362	109	4	if	if	SCONJ
ejpam-5362	109	5	any	any	DET
ejpam-5362	109	6	collection	collection	NOUN
ejpam-5362	109	7	{	{	PUNCT
ejpam-5362	109	8	un	un	PROPN
ejpam-5362	109	9	:	:	PUNCT
ejpam-5362	109	10	n	n	CCONJ
ejpam-5362	109	11	∈	∈	PROPN
ejpam-5362	109	12	n	n	CCONJ
ejpam-5362	109	13	}	}	PUNCT
ejpam-5362	109	14	of	of	ADP
ejpam-5362	109	15	τi	τi	NOUN
ejpam-5362	109	16	-	-	PUNCT
ejpam-5362	109	17	dense	dense	ADJ
ejpam-5362	109	18	τj	τj	ADP
ejpam-5362	109	19	-	-	PUNCT
ejpam-5362	109	20	open	open	ADJ
ejpam-5362	109	21	subsets	subset	NOUN
ejpam-5362	109	22	ofx	ofx	NOUN
ejpam-5362	109	23	satisfies	satisfy	VERB
ejpam-5362	109	24	the	the	DET
ejpam-5362	109	25	condition	condition	NOUN
ejpam-5362	109	26	⋂	⋂	PROPN
ejpam-5362	109	27	n∈n	n∈n	PROPN
ejpam-5362	109	28	un	un	PROPN
ejpam-5362	109	29	is	be	AUX
ejpam-5362	109	30	τi	τi	ADJ
ejpam-5362	109	31	-	-	PUNCT
ejpam-5362	109	32	dense	dense	ADJ
ejpam-5362	109	33	.	.	PUNCT
ejpam-5362	110	1	in	in	ADP
ejpam-5362	110	2	this	this	DET
ejpam-5362	110	3	section	section	NOUN
ejpam-5362	110	4	,	,	PUNCT
ejpam-5362	110	5	we	we	PRON
ejpam-5362	110	6	extend	extend	VERB
ejpam-5362	110	7	the	the	DET
ejpam-5362	110	8	definition	definition	NOUN
ejpam-5362	110	9	of	of	ADP
ejpam-5362	110	10	almost	almost	ADV
ejpam-5362	110	11	(	(	PUNCT
ejpam-5362	110	12	i	i	NOUN
ejpam-5362	110	13	,	,	PUNCT
ejpam-5362	110	14	j)-baire	j)-baire	VERB
ejpam-5362	110	15	bispaces	bispace	NOUN
ejpam-5362	110	16	to	to	ADP
ejpam-5362	110	17	bilocales	bilocale	NOUN
ejpam-5362	110	18	where	where	SCONJ
ejpam-5362	110	19	the	the	DET
ejpam-5362	110	20	prefix	prefix	NOUN
ejpam-5362	110	21	“	"	PUNCT
ejpam-5362	110	22	almost	almost	ADV
ejpam-5362	110	23	”	"	PUNCT
ejpam-5362	110	24	shall	shall	AUX
ejpam-5362	110	25	be	be	AUX
ejpam-5362	110	26	dropped	drop	VERB
ejpam-5362	110	27	.	.	PUNCT
ejpam-5362	111	1	we	we	PRON
ejpam-5362	111	2	aim	aim	VERB
ejpam-5362	111	3	to	to	PART
ejpam-5362	111	4	define	define	VERB
ejpam-5362	111	5	(	(	PUNCT
ejpam-5362	111	6	i	i	NOUN
ejpam-5362	111	7	,	,	PUNCT
ejpam-5362	111	8	j)-baire	j)-baire	NOUN
ejpam-5362	111	9	bilocales	bilocale	NOUN
ejpam-5362	111	10	in	in	ADP
ejpam-5362	111	11	such	such	DET
ejpam-5362	111	12	a	a	DET
ejpam-5362	111	13	way	way	NOUN
ejpam-5362	111	14	that	that	PRON
ejpam-5362	111	15	a	a	DET
ejpam-5362	111	16	bispace	bispace	NOUN
ejpam-5362	111	17	(	(	PUNCT
ejpam-5362	111	18	x	x	NOUN
ejpam-5362	111	19	,	,	PUNCT
ejpam-5362	111	20	τ1	τ1	NOUN
ejpam-5362	111	21	,	,	PUNCT
ejpam-5362	111	22	τ2	τ2	NOUN
ejpam-5362	111	23	)	)	PUNCT
ejpam-5362	111	24	is	be	AUX
ejpam-5362	111	25	almost	almost	ADV
ejpam-5362	111	26	(	(	PUNCT
ejpam-5362	111	27	i	i	NOUN
ejpam-5362	111	28	,	,	PUNCT
ejpam-5362	111	29	j)-baire	j)-baire	VERB
ejpam-5362	111	30	if	if	SCONJ
ejpam-5362	111	31	and	and	CCONJ
ejpam-5362	111	32	only	only	ADV
ejpam-5362	111	33	if	if	SCONJ
ejpam-5362	111	34	the	the	DET
ejpam-5362	111	35	bilocale	bilocale	NOUN
ejpam-5362	111	36	(	(	PUNCT
ejpam-5362	111	37	τ1	τ1	PROPN
ejpam-5362	111	38	∨	∨	NUM
ejpam-5362	111	39	τ2	τ2	NOUN
ejpam-5362	111	40	,	,	PUNCT
ejpam-5362	111	41	τ1	τ1	NOUN
ejpam-5362	111	42	,	,	PUNCT
ejpam-5362	111	43	τ2	τ2	NOUN
ejpam-5362	111	44	)	)	PUNCT
ejpam-5362	111	45	is	be	AUX
ejpam-5362	111	46	(	(	PUNCT
ejpam-5362	111	47	i	i	NOUN
ejpam-5362	111	48	,	,	PUNCT
ejpam-5362	111	49	j)-baire	j)-baire	PROPN
ejpam-5362	111	50	.	.	PUNCT
ejpam-5362	112	1	we	we	PRON
ejpam-5362	112	2	shall	shall	AUX
ejpam-5362	112	3	call	call	VERB
ejpam-5362	112	4	an	an	DET
ejpam-5362	112	5	open	open	ADJ
ejpam-5362	112	6	(	(	PUNCT
ejpam-5362	112	7	resp	resp	NOUN
ejpam-5362	112	8	.	.	PUNCT
ejpam-5362	113	1	closed	closed	ADJ
ejpam-5362	113	2	)	)	PUNCT
ejpam-5362	113	3	sublocale	sublocale	NOUN
ejpam-5362	113	4	i	i	NOUN
ejpam-5362	113	5	-	-	PUNCT
ejpam-5362	113	6	open	open	ADJ
ejpam-5362	113	7	(	(	PUNCT
ejpam-5362	113	8	resp	resp	NOUN
ejpam-5362	113	9	.	.	PUNCT
ejpam-5362	114	1	i	i	PRON
ejpam-5362	114	2	-	-	PUNCT
ejpam-5362	114	3	closed	closed	ADJ
ejpam-5362	114	4	)	)	PUNCT
ejpam-5362	114	5	in	in	ADP
ejpam-5362	114	6	case	case	NOUN
ejpam-5362	114	7	the	the	DET
ejpam-5362	114	8	inducing	induce	VERB
ejpam-5362	114	9	element	element	NOUN
ejpam-5362	114	10	is	be	AUX
ejpam-5362	114	11	an	an	DET
ejpam-5362	114	12	element	element	NOUN
ejpam-5362	114	13	of	of	ADP
ejpam-5362	114	14	li	li	PROPN
ejpam-5362	114	15	.	.	PROPN
ejpam-5362	114	16	definition	definition	NOUN
ejpam-5362	114	17	1	1	NUM
ejpam-5362	114	18	.	.	PUNCT
ejpam-5362	115	1	a	a	DET
ejpam-5362	115	2	bilocale	bilocale	NOUN
ejpam-5362	115	3	(	(	PUNCT
ejpam-5362	115	4	l	l	NOUN
ejpam-5362	115	5	,	,	PUNCT
ejpam-5362	115	6	l1	l1	PROPN
ejpam-5362	115	7	,	,	PUNCT
ejpam-5362	115	8	l2	l2	NOUN
ejpam-5362	115	9	)	)	PUNCT
ejpam-5362	115	10	is	be	AUX
ejpam-5362	115	11	said	say	VERB
ejpam-5362	115	12	to	to	PART
ejpam-5362	115	13	be	be	AUX
ejpam-5362	115	14	(	(	PUNCT
ejpam-5362	115	15	i	i	NOUN
ejpam-5362	115	16	,	,	PUNCT
ejpam-5362	115	17	j)-baire	j)-baire	VERB
ejpam-5362	115	18	if	if	SCONJ
ejpam-5362	115	19	the	the	DET
ejpam-5362	115	20	intersection	intersection	NOUN
ejpam-5362	115	21	of	of	ADP
ejpam-5362	115	22	countably	countably	ADV
ejpam-5362	115	23	many	many	ADJ
ejpam-5362	115	24	i	i	PRON
ejpam-5362	115	25	-	-	PUNCT
ejpam-5362	115	26	dense	dense	ADJ
ejpam-5362	115	27	j	j	NOUN
ejpam-5362	115	28	-	-	ADJ
ejpam-5362	115	29	open	open	ADJ
ejpam-5362	115	30	sublocales	sublocale	NOUN
ejpam-5362	115	31	is	be	AUX
ejpam-5362	115	32	i	i	PRON
ejpam-5362	115	33	-	-	PUNCT
ejpam-5362	115	34	dense	dense	ADJ
ejpam-5362	115	35	.	.	PUNCT
ejpam-5362	116	1	example	example	NOUN
ejpam-5362	117	1	1	1	NUM
ejpam-5362	117	2	.	.	PUNCT
ejpam-5362	117	3	since	since	ADV
ejpam-5362	117	4	,	,	PUNCT
ejpam-5362	117	5	in	in	ADP
ejpam-5362	117	6	locales	locale	NOUN
ejpam-5362	117	7	,	,	PUNCT
ejpam-5362	117	8	the	the	DET
ejpam-5362	117	9	intersection	intersection	NOUN
ejpam-5362	117	10	of	of	ADP
ejpam-5362	117	11	dense	dense	ADJ
ejpam-5362	117	12	sublocales	sublocale	NOUN
ejpam-5362	117	13	is	be	AUX
ejpam-5362	117	14	dense	dense	ADJ
ejpam-5362	117	15	,	,	PUNCT
ejpam-5362	117	16	every	every	DET
ejpam-5362	117	17	symmetric	symmetric	ADJ
ejpam-5362	117	18	bilocale	bilocale	NOUN
ejpam-5362	117	19	(	(	PUNCT
ejpam-5362	117	20	bilocale	bilocale	NOUN
ejpam-5362	117	21	of	of	ADP
ejpam-5362	117	22	the	the	DET
ejpam-5362	117	23	form	form	NOUN
ejpam-5362	117	24	(	(	PUNCT
ejpam-5362	117	25	l	l	NOUN
ejpam-5362	117	26	,	,	PUNCT
ejpam-5362	117	27	l	l	NOUN
ejpam-5362	117	28	,	,	PUNCT
ejpam-5362	117	29	l	l	NOUN
ejpam-5362	117	30	)	)	PUNCT
ejpam-5362	117	31	)	)	PUNCT
ejpam-5362	117	32	is	be	AUX
ejpam-5362	117	33	(	(	PUNCT
ejpam-5362	117	34	i	i	NOUN
ejpam-5362	117	35	,	,	PUNCT
ejpam-5362	117	36	j)-baire	j)-baire	NOUN
ejpam-5362	117	37	.	.	PUNCT
ejpam-5362	118	1	for	for	ADP
ejpam-5362	118	2	a	a	DET
ejpam-5362	118	3	bispace	bispace	NOUN
ejpam-5362	118	4	(	(	PUNCT
ejpam-5362	118	5	x	x	NOUN
ejpam-5362	118	6	,	,	PUNCT
ejpam-5362	118	7	τ1	τ1	NOUN
ejpam-5362	118	8	,	,	PUNCT
ejpam-5362	118	9	τ2	τ2	NOUN
ejpam-5362	118	10	)	)	PUNCT
ejpam-5362	118	11	and	and	CCONJ
ejpam-5362	118	12	a	a	DET
ejpam-5362	118	13	⊆	⊆	NUM
ejpam-5362	118	14	x	x	NOUN
ejpam-5362	118	15	,	,	PUNCT
ejpam-5362	118	16	define	define	VERB
ejpam-5362	118	17	ã	ã	PROPN
ejpam-5362	118	18	=	=	SYM
ejpam-5362	118	19	{	{	PUNCT
ejpam-5362	118	20	intτ1∨τ2((x	intτ1∨τ2((x	NOUN
ejpam-5362	118	21	∖a	∖a	NOUN
ejpam-5362	118	22	)	)	PUNCT
ejpam-5362	118	23	∪g	∪g	NUM
ejpam-5362	118	24	)	)	PUNCT
ejpam-5362	118	25	:	:	PUNCT
ejpam-5362	118	26	g	g	PROPN
ejpam-5362	118	27	∈	∈	PROPN
ejpam-5362	118	28	τ1	τ1	PROPN
ejpam-5362	118	29	∨	∨	NUM
ejpam-5362	118	30	τ2	τ2	NOUN
ejpam-5362	118	31	}	}	PUNCT
ejpam-5362	118	32	.	.	PUNCT
ejpam-5362	119	1	it	it	PRON
ejpam-5362	119	2	is	be	AUX
ejpam-5362	119	3	clear	clear	ADJ
ejpam-5362	119	4	that	that	SCONJ
ejpam-5362	119	5	ã	ã	PROPN
ejpam-5362	119	6	is	be	AUX
ejpam-5362	119	7	a	a	DET
ejpam-5362	119	8	sublocale	sublocale	NOUN
ejpam-5362	119	9	of	of	ADP
ejpam-5362	119	10	τ1	τ1	PROPN
ejpam-5362	119	11	∨	∨	NUM
ejpam-5362	119	12	τ2	τ2	NOUN
ejpam-5362	119	13	.	.	PUNCT
ejpam-5362	120	1	for	for	ADP
ejpam-5362	120	2	each	each	DET
ejpam-5362	120	3	x	x	SYM
ejpam-5362	120	4	∈	∈	PROPN
ejpam-5362	120	5	x	x	NOUN
ejpam-5362	120	6	,	,	PUNCT
ejpam-5362	120	7	x̃	x̃	PROPN
ejpam-5362	120	8	=	=	PUNCT
ejpam-5362	120	9	x	x	SYM
ejpam-5362	120	10	∖	∖	X
ejpam-5362	120	11	clτ1∨τ2	clτ1∨τ2	PROPN
ejpam-5362	120	12	{	{	PUNCT
ejpam-5362	120	13	x	x	NOUN
ejpam-5362	120	14	}	}	PUNCT
ejpam-5362	120	15	is	be	AUX
ejpam-5362	120	16	a	a	DET
ejpam-5362	120	17	point	point	NOUN
ejpam-5362	120	18	of	of	ADP
ejpam-5362	120	19	τ1	τ1	PROPN
ejpam-5362	120	20	∨	∨	NUM
ejpam-5362	120	21	τ2	τ2	NOUN
ejpam-5362	120	22	.	.	PUNCT
ejpam-5362	121	1	just	just	ADV
ejpam-5362	121	2	like	like	INTJ
ejpam-5362	121	3	in	in	ADP
ejpam-5362	121	4	the	the	DET
ejpam-5362	121	5	case	case	NOUN
ejpam-5362	121	6	of	of	ADP
ejpam-5362	121	7	locales	locale	NOUN
ejpam-5362	121	8	,	,	PUNCT
ejpam-5362	121	9	o(u	o(u	ADJ
ejpam-5362	121	10	)	)	PUNCT
ejpam-5362	121	11	=	=	SYM
ejpam-5362	121	12	ũ	ũ	PROPN
ejpam-5362	121	13	for	for	ADP
ejpam-5362	121	14	every	every	DET
ejpam-5362	121	15	u	u	PROPN
ejpam-5362	121	16	∈	∈	PROPN
ejpam-5362	121	17	τ1	τ1	PROPN
ejpam-5362	121	18	∨	∨	NUM
ejpam-5362	121	19	τ2	τ2	PROPN
ejpam-5362	121	20	.	.	PUNCT
ejpam-5362	122	1	recall	recall	NOUN
ejpam-5362	122	2	from	from	ADP
ejpam-5362	122	3	[	[	X
ejpam-5362	122	4	11	11	NUM
ejpam-5362	122	5	]	]	PUNCT
ejpam-5362	122	6	that	that	SCONJ
ejpam-5362	122	7	given	give	VERB
ejpam-5362	122	8	a	a	DET
ejpam-5362	122	9	topological	topological	ADJ
ejpam-5362	122	10	property	property	NOUN
ejpam-5362	122	11	p	p	NOUN
ejpam-5362	122	12	,	,	PUNCT
ejpam-5362	122	13	a	a	DET
ejpam-5362	122	14	bispace	bispace	NOUN
ejpam-5362	122	15	(	(	PUNCT
ejpam-5362	122	16	x	x	NOUN
ejpam-5362	122	17	,	,	PUNCT
ejpam-5362	122	18	τ1	τ1	NOUN
ejpam-5362	122	19	,	,	PUNCT
ejpam-5362	122	20	τ2	τ2	NOUN
ejpam-5362	122	21	)	)	PUNCT
ejpam-5362	122	22	is	be	AUX
ejpam-5362	122	23	sup	sup	NOUN
ejpam-5362	122	24	-	-	PUNCT
ejpam-5362	122	25	p	p	NOUN
ejpam-5362	122	26	if	if	SCONJ
ejpam-5362	122	27	(	(	PUNCT
ejpam-5362	122	28	x	x	NOUN
ejpam-5362	122	29	,	,	PUNCT
ejpam-5362	122	30	τ1	τ1	ADP
ejpam-5362	122	31	∨	∨	NUM
ejpam-5362	122	32	τ2	τ2	NOUN
ejpam-5362	122	33	)	)	PUNCT
ejpam-5362	122	34	has	have	AUX
ejpam-5362	122	35	property	property	NOUN
ejpam-5362	122	36	p	p	NOUN
ejpam-5362	122	37	.	.	PUNCT
ejpam-5362	123	1	in	in	ADP
ejpam-5362	123	2	[	[	X
ejpam-5362	123	3	16	16	NUM
ejpam-5362	123	4	]	]	PUNCT
ejpam-5362	123	5	,	,	PUNCT
ejpam-5362	123	6	we	we	PRON
ejpam-5362	123	7	proved	prove	VERB
ejpam-5362	123	8	the	the	DET
ejpam-5362	123	9	following	follow	VERB
ejpam-5362	123	10	result	result	NOUN
ejpam-5362	123	11	.	.	PUNCT
ejpam-5362	124	1	lemma	lemma	PROPN
ejpam-5362	124	2	1	1	X
ejpam-5362	124	3	.	.	PUNCT
ejpam-5362	125	1	let	let	AUX
ejpam-5362	125	2	(	(	PUNCT
ejpam-5362	125	3	x	x	NOUN
ejpam-5362	125	4	,	,	PUNCT
ejpam-5362	125	5	τ1	τ1	NOUN
ejpam-5362	125	6	,	,	PUNCT
ejpam-5362	125	7	τ2	τ2	PROPN
ejpam-5362	125	8	)	)	PUNCT
ejpam-5362	125	9	be	be	VERB
ejpam-5362	125	10	a	a	DET
ejpam-5362	125	11	sup	sup	ADJ
ejpam-5362	125	12	-	-	PUNCT
ejpam-5362	125	13	td	td	NOUN
ejpam-5362	125	14	-	-	PUNCT
ejpam-5362	125	15	bispace	bispace	NOUN
ejpam-5362	125	16	.	.	PUNCT
ejpam-5362	126	1	then	then	ADV
ejpam-5362	126	2	a	a	DET
ejpam-5362	126	3	⊆	⊆	NUM
ejpam-5362	126	4	x	x	X
ejpam-5362	126	5	is	be	AUX
ejpam-5362	126	6	τi	τi	ADJ
ejpam-5362	126	7	-	-	PUNCT
ejpam-5362	126	8	dense	dense	ADJ
ejpam-5362	126	9	in	in	ADP
ejpam-5362	126	10	(	(	PUNCT
ejpam-5362	126	11	x	x	NOUN
ejpam-5362	126	12	,	,	PUNCT
ejpam-5362	126	13	τ1	τ1	NOUN
ejpam-5362	126	14	,	,	PUNCT
ejpam-5362	126	15	τ2	τ2	PROPN
ejpam-5362	126	16	)	)	PUNCT
ejpam-5362	126	17	iff	iff	PROPN
ejpam-5362	126	18	ã	ã	PROPN
ejpam-5362	126	19	is	be	AUX
ejpam-5362	126	20	i	i	PRON
ejpam-5362	126	21	-	-	PUNCT
ejpam-5362	126	22	dense	dense	ADJ
ejpam-5362	126	23	in	in	ADP
ejpam-5362	126	24	(	(	PUNCT
ejpam-5362	126	25	τ1	τ1	PROPN
ejpam-5362	126	26	∨	∨	NUM
ejpam-5362	126	27	τ2	τ2	NOUN
ejpam-5362	126	28	,	,	PUNCT
ejpam-5362	126	29	τ1	τ1	NOUN
ejpam-5362	126	30	,	,	PUNCT
ejpam-5362	126	31	τ2	τ2	NOUN
ejpam-5362	126	32	)	)	PUNCT
ejpam-5362	126	33	.	.	PUNCT
ejpam-5362	127	1	in	in	ADP
ejpam-5362	127	2	[	[	X
ejpam-5362	127	3	19	19	NUM
ejpam-5362	127	4	]	]	PUNCT
ejpam-5362	127	5	,	,	PUNCT
ejpam-5362	127	6	the	the	DET
ejpam-5362	127	7	authors	author	NOUN
ejpam-5362	127	8	show	show	VERB
ejpam-5362	127	9	that	that	SCONJ
ejpam-5362	127	10	if	if	SCONJ
ejpam-5362	127	11	x	x	PRON
ejpam-5362	127	12	is	be	AUX
ejpam-5362	127	13	a	a	DET
ejpam-5362	127	14	topological	topological	ADJ
ejpam-5362	127	15	space	space	NOUN
ejpam-5362	127	16	and	and	CCONJ
ejpam-5362	127	17	y	y	PROPN
ejpam-5362	127	18	⊆	⊆	NUM
ejpam-5362	127	19	x	x	ADP
ejpam-5362	127	20	,	,	PUNCT
ejpam-5362	127	21	then	then	ADV
ejpam-5362	127	22	ỹ	ỹ	PROPN
ejpam-5362	127	23	=	=	SYM
ejpam-5362	127	24	∨	∨	X
ejpam-5362	127	25	{	{	PUNCT
ejpam-5362	127	26	{	{	PUNCT
ejpam-5362	127	27	x	x	X
ejpam-5362	127	28	∖	∖	X
ejpam-5362	127	29	{	{	PUNCT
ejpam-5362	127	30	y	y	NOUN
ejpam-5362	127	31	}	}	PUNCT
ejpam-5362	127	32	,	,	PUNCT
ejpam-5362	127	33	1ox	1ox	ADJ
ejpam-5362	127	34	}	}	PUNCT
ejpam-5362	127	35	:	:	PUNCT
ejpam-5362	128	1	y	y	PROPN
ejpam-5362	128	2	∈	∈	PROPN
ejpam-5362	128	3	y	y	PROPN
ejpam-5362	128	4	}	}	PUNCT
ejpam-5362	128	5	.	.	PUNCT
ejpam-5362	129	1	proposition	proposition	NOUN
ejpam-5362	129	2	1	1	NUM
ejpam-5362	129	3	.	.	PUNCT
ejpam-5362	130	1	let	let	AUX
ejpam-5362	130	2	(	(	PUNCT
ejpam-5362	130	3	x	x	NOUN
ejpam-5362	130	4	,	,	PUNCT
ejpam-5362	130	5	τ1	τ1	NOUN
ejpam-5362	130	6	,	,	PUNCT
ejpam-5362	130	7	τ2	τ2	PROPN
ejpam-5362	130	8	)	)	PUNCT
ejpam-5362	130	9	be	be	VERB
ejpam-5362	130	10	a	a	DET
ejpam-5362	130	11	sup	sup	ADJ
ejpam-5362	130	12	-	-	PUNCT
ejpam-5362	130	13	td	td	NOUN
ejpam-5362	130	14	-	-	PUNCT
ejpam-5362	130	15	bispace	bispace	NOUN
ejpam-5362	130	16	in	in	ADP
ejpam-5362	130	17	which	which	PRON
ejpam-5362	130	18	gδ	gδ	NOUN
ejpam-5362	130	19	-	-	PUNCT
ejpam-5362	130	20	sublocales	sublocale	NOUN
ejpam-5362	130	21	of	of	ADP
ejpam-5362	130	22	(	(	PUNCT
ejpam-5362	130	23	τ1∨τ2	τ1∨τ2	PROPN
ejpam-5362	130	24	,	,	PUNCT
ejpam-5362	130	25	τ1	τ1	NOUN
ejpam-5362	130	26	,	,	PUNCT
ejpam-5362	130	27	τ2	τ2	NOUN
ejpam-5362	130	28	)	)	PUNCT
ejpam-5362	130	29	are	be	AUX
ejpam-5362	130	30	complemented	complement	VERB
ejpam-5362	130	31	.	.	PUNCT
ejpam-5362	131	1	then	then	ADV
ejpam-5362	131	2	(	(	PUNCT
ejpam-5362	131	3	x	x	NOUN
ejpam-5362	131	4	,	,	PUNCT
ejpam-5362	131	5	τ1	τ1	NOUN
ejpam-5362	131	6	,	,	PUNCT
ejpam-5362	131	7	τ2	τ2	NOUN
ejpam-5362	131	8	)	)	PUNCT
ejpam-5362	131	9	is	be	AUX
ejpam-5362	131	10	almost	almost	ADV
ejpam-5362	131	11	(	(	PUNCT
ejpam-5362	131	12	i	i	NOUN
ejpam-5362	131	13	,	,	PUNCT
ejpam-5362	131	14	j)-baire	j)-baire	PROPN
ejpam-5362	131	15	iff	iff	PROPN
ejpam-5362	131	16	(	(	PUNCT
ejpam-5362	131	17	τ1	τ1	PROPN
ejpam-5362	131	18	∨	∨	NUM
ejpam-5362	131	19	τ2	τ2	NOUN
ejpam-5362	131	20	,	,	PUNCT
ejpam-5362	131	21	τ1	τ1	NOUN
ejpam-5362	131	22	,	,	PUNCT
ejpam-5362	131	23	τ2	τ2	NOUN
ejpam-5362	131	24	)	)	PUNCT
ejpam-5362	131	25	is	be	AUX
ejpam-5362	131	26	(	(	PUNCT
ejpam-5362	131	27	i	i	NOUN
ejpam-5362	131	28	,	,	PUNCT
ejpam-5362	131	29	j)-baire	j)-baire	NOUN
ejpam-5362	131	30	.	.	PUNCT
ejpam-5362	132	1	m.	m.	NOUN
ejpam-5362	132	2	nxumalo	nxumalo	PROPN
ejpam-5362	132	3	/	/	SYM
ejpam-5362	132	4	eur	eur	PROPN
ejpam-5362	132	5	.	.	PUNCT
ejpam-5362	133	1	j.	j.	PROPN
ejpam-5362	133	2	pure	pure	PROPN
ejpam-5362	133	3	appl	appl	PROPN
ejpam-5362	133	4	.	.	PROPN
ejpam-5362	133	5	math	math	PROPN
ejpam-5362	133	6	,	,	PUNCT
ejpam-5362	133	7	18	18	NUM
ejpam-5362	133	8	(	(	PUNCT
ejpam-5362	133	9	1	1	NUM
ejpam-5362	133	10	)	)	PUNCT
ejpam-5362	133	11	(	(	PUNCT
ejpam-5362	133	12	2025	2025	NUM
ejpam-5362	133	13	)	)	PUNCT
ejpam-5362	133	14	,	,	PUNCT
ejpam-5362	133	15	5362	5362	NUM
ejpam-5362	133	16	6	6	NUM
ejpam-5362	133	17	of	of	ADP
ejpam-5362	133	18	21	21	NUM
ejpam-5362	133	19	proof	proof	NOUN
ejpam-5362	133	20	.	.	PUNCT
ejpam-5362	134	1	(=	(=	AUX
ejpam-5362	134	2	⇒	⇒	NOUN
ejpam-5362	134	3	):	):	PUNCT
ejpam-5362	134	4	let	let	VERB
ejpam-5362	134	5	{	{	PUNCT
ejpam-5362	134	6	o(un	o(un	NUM
ejpam-5362	134	7	)	)	PUNCT
ejpam-5362	134	8	:	:	PUNCT
ejpam-5362	134	9	n	n	CCONJ
ejpam-5362	134	10	∈	∈	PROPN
ejpam-5362	134	11	n	n	CCONJ
ejpam-5362	134	12	}	}	PUNCT
ejpam-5362	134	13	be	be	AUX
ejpam-5362	134	14	a	a	DET
ejpam-5362	134	15	collection	collection	NOUN
ejpam-5362	134	16	of	of	ADP
ejpam-5362	134	17	i	i	NOUN
ejpam-5362	134	18	-	-	PUNCT
ejpam-5362	134	19	dense	dense	ADJ
ejpam-5362	134	20	j	j	NOUN
ejpam-5362	134	21	-	-	ADJ
ejpam-5362	134	22	open	open	ADJ
ejpam-5362	134	23	sublocales	sublocale	NOUN
ejpam-5362	134	24	.	.	PUNCT
ejpam-5362	135	1	it	it	PRON
ejpam-5362	135	2	follows	follow	VERB
ejpam-5362	135	3	that	that	SCONJ
ejpam-5362	135	4	{	{	PUNCT
ejpam-5362	135	5	un	un	PROPN
ejpam-5362	135	6	:	:	PUNCT
ejpam-5362	135	7	n	n	CCONJ
ejpam-5362	135	8	∈	∈	PROPN
ejpam-5362	135	9	n	n	CCONJ
ejpam-5362	135	10	}	}	PUNCT
ejpam-5362	135	11	is	be	AUX
ejpam-5362	135	12	a	a	DET
ejpam-5362	135	13	collection	collection	NOUN
ejpam-5362	135	14	of	of	ADP
ejpam-5362	135	15	τi	τi	NOUN
ejpam-5362	135	16	-	-	PUNCT
ejpam-5362	135	17	dense	dense	ADJ
ejpam-5362	135	18	τj	τj	ADP
ejpam-5362	135	19	-	-	PUNCT
ejpam-5362	135	20	open	open	ADJ
ejpam-5362	135	21	subsets	subset	NOUN
ejpam-5362	135	22	of	of	ADP
ejpam-5362	135	23	x.	x.	NOUN
ejpam-5362	135	24	it	it	PRON
ejpam-5362	135	25	follows	follow	VERB
ejpam-5362	135	26	that⋂	that⋂	X
ejpam-5362	136	1	n∈n	n∈n	PROPN
ejpam-5362	136	2	un	un	PROPN
ejpam-5362	136	3	is	be	AUX
ejpam-5362	136	4	τi	τi	ADJ
ejpam-5362	136	5	-	-	PUNCT
ejpam-5362	136	6	dense	dense	ADJ
ejpam-5362	136	7	.	.	PUNCT
ejpam-5362	137	1	claim	claim	NOUN
ejpam-5362	137	2	:	:	PUNCT
ejpam-5362	137	3	∧	∧	NOUN
ejpam-5362	137	4	n∈n	n∈n	NOUN
ejpam-5362	137	5	o(un	o(un	NUM
ejpam-5362	137	6	)	)	PUNCT
ejpam-5362	137	7	is	be	AUX
ejpam-5362	137	8	i	i	PRON
ejpam-5362	137	9	-	-	PUNCT
ejpam-5362	137	10	dense	dense	ADJ
ejpam-5362	137	11	.	.	PUNCT
ejpam-5362	138	1	proof	proof	NOUN
ejpam-5362	138	2	:	:	PUNCT
ejpam-5362	138	3	let	let	VERB
ejpam-5362	138	4	o(v	o(v	PROPN
ejpam-5362	138	5	)	)	PUNCT
ejpam-5362	138	6	be	be	AUX
ejpam-5362	138	7	an	an	DET
ejpam-5362	138	8	i	i	NOUN
ejpam-5362	138	9	-	-	PUNCT
ejpam-5362	138	10	open	open	ADJ
ejpam-5362	138	11	sublocale	sublocale	NOUN
ejpam-5362	138	12	such	such	ADJ
ejpam-5362	138	13	that	that	SCONJ
ejpam-5362	138	14	o(v	o(v	NOUN
ejpam-5362	138	15	)	)	PUNCT
ejpam-5362	138	16	∩	∩	NOUN
ejpam-5362	138	17	∧	∧	NOUN
ejpam-5362	138	18	n∈n	n∈n	NOUN
ejpam-5362	138	19	o(un	o(un	NUM
ejpam-5362	138	20	)	)	PUNCT
ejpam-5362	138	21	=	=	SYM
ejpam-5362	139	1	o.	o.	NOUN
ejpam-5362	139	2	then∧	then∧	PROPN
ejpam-5362	139	3	n∈n	n∈n	PUNCT
ejpam-5362	139	4	o(v	o(v	PROPN
ejpam-5362	139	5	∩	∩	ADJ
ejpam-5362	139	6	un	un	ADJ
ejpam-5362	139	7	)	)	PUNCT
ejpam-5362	139	8	=	=	VERB
ejpam-5362	140	1	o.	o.	NOUN
ejpam-5362	140	2	we	we	PRON
ejpam-5362	140	3	must	must	AUX
ejpam-5362	140	4	have	have	VERB
ejpam-5362	140	5	that	that	SCONJ
ejpam-5362	140	6	⋂	⋂	PROPN
ejpam-5362	140	7	n∈n(v	n∈n(v	PROPN
ejpam-5362	140	8	∩	∩	NOUN
ejpam-5362	140	9	un	un	NOUN
ejpam-5362	140	10	)	)	PUNCT
ejpam-5362	140	11	=	=	PUNCT
ejpam-5362	140	12	∅.	∅.	VERB
ejpam-5362	140	13	otherwise	otherwise	ADV
ejpam-5362	140	14	,	,	PUNCT
ejpam-5362	140	15	there	there	PRON
ejpam-5362	140	16	is	be	VERB
ejpam-5362	140	17	x	x	X
ejpam-5362	140	18	∈	∈	PROPN
ejpam-5362	140	19	v	v	NUM
ejpam-5362	140	20	∩	∩	X
ejpam-5362	140	21	un	un	PROPN
ejpam-5362	140	22	for	for	ADP
ejpam-5362	140	23	each	each	DET
ejpam-5362	140	24	n	n	PRON
ejpam-5362	140	25	∈	∈	PROPN
ejpam-5362	140	26	n.	n.	NOUN
ejpam-5362	140	27	since	since	SCONJ
ejpam-5362	140	28	each	each	DET
ejpam-5362	140	29	v	v	PROPN
ejpam-5362	140	30	∩	∩	X
ejpam-5362	140	31	un	un	PROPN
ejpam-5362	140	32	is	be	AUX
ejpam-5362	140	33	τ1	τ1	ADP
ejpam-5362	140	34	∨	∨	NUM
ejpam-5362	140	35	τ2	τ2	PROPN
ejpam-5362	140	36	,	,	PUNCT
ejpam-5362	140	37	ṽ	ṽ	PROPN
ejpam-5362	140	38	∩	∩	NOUN
ejpam-5362	140	39	un	un	PROPN
ejpam-5362	140	40	=	=	PROPN
ejpam-5362	140	41	o(v	o(v	PROPN
ejpam-5362	140	42	∩	∩	ADJ
ejpam-5362	140	43	un	un	NOUN
ejpam-5362	140	44	)	)	PUNCT
ejpam-5362	140	45	∋	∋	NOUN
ejpam-5362	140	46	x̃	x̃	PROPN
ejpam-5362	140	47	for	for	ADP
ejpam-5362	140	48	each	each	DET
ejpam-5362	140	49	n	n	PRON
ejpam-5362	140	50	∈	∈	PROPN
ejpam-5362	140	51	n.	n.	NOUN
ejpam-5362	140	52	therefore	therefore	ADV
ejpam-5362	140	53	x̃	x̃	PROPN
ejpam-5362	140	54	∈	∈	PROPN
ejpam-5362	140	55	∧	∧	PROPN
ejpam-5362	140	56	n∈n	n∈n	PUNCT
ejpam-5362	140	57	o(v	o(v	PROPN
ejpam-5362	140	58	∩	∩	ADJ
ejpam-5362	140	59	un	un	PROPN
ejpam-5362	140	60	)	)	PUNCT
ejpam-5362	140	61	which	which	PRON
ejpam-5362	140	62	is	be	AUX
ejpam-5362	140	63	impossible	impossible	ADJ
ejpam-5362	140	64	.	.	PUNCT
ejpam-5362	141	1	therefore	therefore	ADV
ejpam-5362	141	2	v	v	X
ejpam-5362	141	3	=	=	NOUN
ejpam-5362	141	4	∅	∅	NOUN
ejpam-5362	141	5	so	so	SCONJ
ejpam-5362	141	6	that	that	SCONJ
ejpam-5362	141	7	o(v	o(v	NOUN
ejpam-5362	141	8	)	)	PUNCT
ejpam-5362	141	9	=	=	SYM
ejpam-5362	142	1	o.	o.	NOUN
ejpam-5362	142	2	thus	thus	ADV
ejpam-5362	142	3	∧	∧	PROPN
ejpam-5362	142	4	n∈n	n∈n	NOUN
ejpam-5362	142	5	o(un	o(un	NUM
ejpam-5362	142	6	)	)	PUNCT
ejpam-5362	142	7	is	be	AUX
ejpam-5362	142	8	i	i	PRON
ejpam-5362	142	9	-	-	PUNCT
ejpam-5362	142	10	dense	dense	ADJ
ejpam-5362	142	11	.	.	PUNCT
ejpam-5362	143	1	(	(	PUNCT
ejpam-5362	143	2	⇐	⇐	NOUN
ejpam-5362	143	3	=)	=)	PROPN
ejpam-5362	143	4	:	:	PUNCT
ejpam-5362	143	5	let	let	VERB
ejpam-5362	143	6	{	{	PUNCT
ejpam-5362	143	7	un	un	PROPN
ejpam-5362	143	8	:	:	PUNCT
ejpam-5362	143	9	n	n	CCONJ
ejpam-5362	143	10	∈	∈	PROPN
ejpam-5362	143	11	n	n	CCONJ
ejpam-5362	143	12	}	}	PUNCT
ejpam-5362	143	13	be	be	AUX
ejpam-5362	143	14	a	a	DET
ejpam-5362	143	15	collection	collection	NOUN
ejpam-5362	143	16	of	of	ADP
ejpam-5362	143	17	τi	τi	NOUN
ejpam-5362	143	18	-	-	PUNCT
ejpam-5362	143	19	dense	dense	ADJ
ejpam-5362	143	20	τj	τj	ADP
ejpam-5362	143	21	-	-	PUNCT
ejpam-5362	143	22	open	open	ADJ
ejpam-5362	143	23	subsets	subset	NOUN
ejpam-5362	143	24	of	of	ADP
ejpam-5362	143	25	x.	x.	NOUN
ejpam-5362	143	26	then	then	ADV
ejpam-5362	143	27	{	{	PUNCT
ejpam-5362	143	28	o(un	o(un	PROPN
ejpam-5362	143	29	)	)	PUNCT
ejpam-5362	143	30	:	:	PUNCT
ejpam-5362	143	31	n	n	CCONJ
ejpam-5362	143	32	∈	∈	PROPN
ejpam-5362	143	33	n	n	CCONJ
ejpam-5362	143	34	}	}	PUNCT
ejpam-5362	143	35	is	be	AUX
ejpam-5362	143	36	a	a	DET
ejpam-5362	143	37	collection	collection	NOUN
ejpam-5362	143	38	of	of	ADP
ejpam-5362	143	39	i	i	NOUN
ejpam-5362	143	40	-	-	PUNCT
ejpam-5362	143	41	dense	dense	ADJ
ejpam-5362	143	42	j	j	NOUN
ejpam-5362	143	43	-	-	ADJ
ejpam-5362	143	44	open	open	ADJ
ejpam-5362	143	45	sublocales	sublocale	NOUN
ejpam-5362	143	46	of	of	ADP
ejpam-5362	143	47	τ1	τ1	PROPN
ejpam-5362	143	48	∨	∨	NUM
ejpam-5362	143	49	τ2	τ2	NOUN
ejpam-5362	143	50	.	.	PUNCT
ejpam-5362	144	1	it	it	PRON
ejpam-5362	144	2	follows	follow	VERB
ejpam-5362	144	3	that∧	that∧	PROPN
ejpam-5362	144	4	n∈n	n∈n	ADV
ejpam-5362	144	5	o(un	o(un	NUM
ejpam-5362	144	6	)	)	PUNCT
ejpam-5362	144	7	is	be	AUX
ejpam-5362	144	8	τi	τi	ADJ
ejpam-5362	144	9	-	-	PUNCT
ejpam-5362	144	10	dense	dense	ADJ
ejpam-5362	144	11	.	.	PUNCT
ejpam-5362	145	1	to	to	PART
ejpam-5362	145	2	show	show	VERB
ejpam-5362	145	3	that	that	SCONJ
ejpam-5362	145	4	⋂	⋂	PROPN
ejpam-5362	145	5	n∈n	n∈n	PROPN
ejpam-5362	145	6	un	un	PROPN
ejpam-5362	145	7	is	be	AUX
ejpam-5362	145	8	τi	τi	ADJ
ejpam-5362	145	9	-	-	PUNCT
ejpam-5362	145	10	dense	dense	ADJ
ejpam-5362	145	11	,	,	PUNCT
ejpam-5362	145	12	let	let	VERB
ejpam-5362	145	13	v	v	PART
ejpam-5362	145	14	be	be	AUX
ejpam-5362	145	15	a	a	DET
ejpam-5362	145	16	nonempty	nonempty	ADJ
ejpam-5362	145	17	τi	τi	NOUN
ejpam-5362	145	18	-	-	PUNCT
ejpam-5362	145	19	open	open	ADJ
ejpam-5362	145	20	subset	subset	NOUN
ejpam-5362	145	21	of	of	ADP
ejpam-5362	145	22	x	x	SYM
ejpam-5362	145	23	such	such	ADJ
ejpam-5362	145	24	that	that	DET
ejpam-5362	145	25	v	v	NOUN
ejpam-5362	145	26	∩	∩	NOUN
ejpam-5362	145	27	(	(	PUNCT
ejpam-5362	145	28	⋂	⋂	PROPN
ejpam-5362	145	29	n∈n	n∈n	NOUN
ejpam-5362	145	30	un	un	PROPN
ejpam-5362	145	31	)	)	PUNCT
ejpam-5362	146	1	=	=	PUNCT
ejpam-5362	146	2	∅.	∅.	VERB
ejpam-5362	146	3	then⋃	then⋃	PROPN
ejpam-5362	146	4	n∈n	n∈n	ADV
ejpam-5362	146	5	(	(	PUNCT
ejpam-5362	146	6	x	x	X
ejpam-5362	146	7	∖	∖	PROPN
ejpam-5362	146	8	(	(	PUNCT
ejpam-5362	146	9	v	v	PROPN
ejpam-5362	146	10	∩	∩	X
ejpam-5362	146	11	un	un	NOUN
ejpam-5362	146	12	)	)	PUNCT
ejpam-5362	146	13	)	)	PUNCT
ejpam-5362	147	1	=	=	PUNCT
ejpam-5362	147	2	x.	x.	NOUN
ejpam-5362	147	3	observe	observe	VERB
ejpam-5362	147	4	that	that	SCONJ
ejpam-5362	147	5	∨	∨	NUM
ejpam-5362	147	6	n∈n	n∈n	NOUN
ejpam-5362	147	7	c(v	c(v	PROPN
ejpam-5362	147	8	∩	∩	ADJ
ejpam-5362	147	9	un	un	ADJ
ejpam-5362	147	10	)	)	PUNCT
ejpam-5362	147	11	=	=	SYM
ejpam-5362	147	12	ox	ox	NOUN
ejpam-5362	147	13	:	:	PUNCT
ejpam-5362	147	14	let	let	VERB
ejpam-5362	147	15	p	p	X
ejpam-5362	147	16	∈	∈	PROPN
ejpam-5362	147	17	x.	x.	NOUN
ejpam-5362	148	1	then	then	ADV
ejpam-5362	148	2	p	p	PROPN
ejpam-5362	148	3	∈	∈	PROPN
ejpam-5362	148	4	x	x	PRON
ejpam-5362	148	5	∖	∖	X
ejpam-5362	148	6	(	(	PUNCT
ejpam-5362	148	7	v	v	PROPN
ejpam-5362	148	8	∩	∩	X
ejpam-5362	148	9	un	un	NOUN
ejpam-5362	148	10	)	)	PUNCT
ejpam-5362	148	11	for	for	ADP
ejpam-5362	148	12	some	some	DET
ejpam-5362	148	13	n	n	PRON
ejpam-5362	148	14	∈	∈	PROPN
ejpam-5362	148	15	n.	n.	NOUN
ejpam-5362	148	16	therefore	therefore	ADV
ejpam-5362	148	17	{	{	PUNCT
ejpam-5362	148	18	p	p	NOUN
ejpam-5362	148	19	}	}	PUNCT
ejpam-5362	148	20	⊆	⊆	NUM
ejpam-5362	148	21	x	x	SYM
ejpam-5362	148	22	∖	∖	X
ejpam-5362	148	23	(	(	PUNCT
ejpam-5362	148	24	v	v	PROPN
ejpam-5362	148	25	∩	∩	X
ejpam-5362	148	26	un	un	NOUN
ejpam-5362	148	27	)	)	PUNCT
ejpam-5362	148	28	for	for	ADP
ejpam-5362	148	29	some	some	DET
ejpam-5362	148	30	n	n	PRON
ejpam-5362	148	31	∈	∈	NOUN
ejpam-5362	148	32	n	n	NOUN
ejpam-5362	148	33	so	so	ADV
ejpam-5362	148	34	that	that	SCONJ
ejpam-5362	148	35	v	v	NUM
ejpam-5362	148	36	∩	∩	PROPN
ejpam-5362	148	37	un	un	PROPN
ejpam-5362	148	38	⊆	⊆	X
ejpam-5362	148	39	x	x	X
ejpam-5362	148	40	∖	∖	X
ejpam-5362	148	41	{	{	PUNCT
ejpam-5362	148	42	p	p	X
ejpam-5362	148	43	}	}	PUNCT
ejpam-5362	148	44	.	.	PUNCT
ejpam-5362	149	1	this	this	PRON
ejpam-5362	149	2	implies	imply	VERB
ejpam-5362	149	3	that	that	SCONJ
ejpam-5362	149	4	x	x	PRON
ejpam-5362	149	5	∖	∖	X
ejpam-5362	149	6	{	{	PUNCT
ejpam-5362	149	7	p	p	PROPN
ejpam-5362	149	8	}	}	PUNCT
ejpam-5362	149	9	∈	∈	PROPN
ejpam-5362	149	10	c(v	c(v	PROPN
ejpam-5362	149	11	∩	∩	NOUN
ejpam-5362	149	12	un	un	PROPN
ejpam-5362	149	13	)	)	PUNCT
ejpam-5362	149	14	.	.	PUNCT
ejpam-5362	150	1	as	as	ADP
ejpam-5362	150	2	a	a	DET
ejpam-5362	150	3	result	result	NOUN
ejpam-5362	150	4	,	,	PUNCT
ejpam-5362	150	5	{	{	PUNCT
ejpam-5362	150	6	x	x	X
ejpam-5362	150	7	∖	∖	X
ejpam-5362	150	8	{	{	PUNCT
ejpam-5362	150	9	p	p	X
ejpam-5362	150	10	}	}	PUNCT
ejpam-5362	150	11	,	,	PUNCT
ejpam-5362	150	12	1τ1∨τ2	1τ1∨τ2	NUM
ejpam-5362	150	13	}	}	SYM
ejpam-5362	150	14	⊆	⊆	NUM
ejpam-5362	150	15	c(v	c(v	PROPN
ejpam-5362	150	16	∩	∩	NOUN
ejpam-5362	150	17	un	un	PROPN
ejpam-5362	150	18	)	)	PUNCT
ejpam-5362	150	19	.	.	PUNCT
ejpam-5362	151	1	therefore	therefore	ADV
ejpam-5362	151	2	τ1	τ1	ADP
ejpam-5362	151	3	∨	∨	NUM
ejpam-5362	151	4	τ2	τ2	PROPN
ejpam-5362	151	5	=	=	SYM
ejpam-5362	151	6	∨	∨	X
ejpam-5362	151	7	{	{	PUNCT
ejpam-5362	151	8	{	{	PUNCT
ejpam-5362	151	9	x	x	X
ejpam-5362	151	10	∖	∖	NOUN
ejpam-5362	151	11	{	{	PUNCT
ejpam-5362	151	12	p	p	X
ejpam-5362	151	13	}	}	PUNCT
ejpam-5362	151	14	,	,	PUNCT
ejpam-5362	151	15	1τ1∨τ2	1τ1∨τ2	NUM
ejpam-5362	151	16	}	}	PUNCT
ejpam-5362	151	17	:	:	PUNCT
ejpam-5362	151	18	p	p	X
ejpam-5362	151	19	∈	∈	PROPN
ejpam-5362	151	20	x	x	PRON
ejpam-5362	151	21	}	}	PUNCT
ejpam-5362	151	22	⊆	⊆	NUM
ejpam-5362	151	23	∨	∨	NUM
ejpam-5362	151	24	{	{	PUNCT
ejpam-5362	151	25	c(v	c(v	PROPN
ejpam-5362	151	26	∩	∩	NOUN
ejpam-5362	151	27	un	un	PROPN
ejpam-5362	151	28	)	)	PUNCT
ejpam-5362	151	29	:	:	PUNCT
ejpam-5362	151	30	n	n	X
ejpam-5362	151	31	∈	∈	PROPN
ejpam-5362	151	32	n	n	CCONJ
ejpam-5362	151	33	}	}	PUNCT
ejpam-5362	151	34	⊆	⊆	NUM
ejpam-5362	151	35	τ1	τ1	ADP
ejpam-5362	151	36	∨	∨	NUM
ejpam-5362	151	37	τ2	τ2	NOUN
ejpam-5362	151	38	.	.	PUNCT
ejpam-5362	152	1	since	since	SCONJ
ejpam-5362	152	2	∧	∧	PROPN
ejpam-5362	152	3	n∈n	n∈n	NOUN
ejpam-5362	152	4	o(un	o(un	NUM
ejpam-5362	152	5	)	)	PUNCT
ejpam-5362	152	6	is	be	AUX
ejpam-5362	152	7	i	i	PRON
ejpam-5362	152	8	-	-	PUNCT
ejpam-5362	152	9	dense	dense	ADJ
ejpam-5362	152	10	and	and	CCONJ
ejpam-5362	152	11	o(v	o(v	NOUN
ejpam-5362	152	12	)	)	PUNCT
ejpam-5362	152	13	is	be	AUX
ejpam-5362	152	14	non	non	ADJ
ejpam-5362	152	15	-	-	ADJ
ejpam-5362	152	16	void	void	ADJ
ejpam-5362	152	17	i	i	NOUN
ejpam-5362	152	18	-	-	PUNCT
ejpam-5362	152	19	open	open	ADJ
ejpam-5362	152	20	,	,	PUNCT
ejpam-5362	152	21	o(v	o(v	NOUN
ejpam-5362	152	22	)	)	PUNCT
ejpam-5362	152	23	∩	∩	NOUN
ejpam-5362	152	24	∧	∧	NOUN
ejpam-5362	152	25	n∈n	n∈n	NOUN
ejpam-5362	152	26	o(un	o(un	NUM
ejpam-5362	152	27	)	)	PUNCT
ejpam-5362	152	28	̸=	̸=	PROPN
ejpam-5362	152	29	o	o	NOUN
ejpam-5362	152	30	,	,	PUNCT
ejpam-5362	152	31	so	so	SCONJ
ejpam-5362	152	32	that	that	SCONJ
ejpam-5362	152	33	o	o	NOUN
ejpam-5362	152	34	̸=	̸=	PROPN
ejpam-5362	152	35	∧	∧	PROPN
ejpam-5362	152	36	n∈n	n∈n	PUNCT
ejpam-5362	152	37	o(v	o(v	PROPN
ejpam-5362	152	38	∩	∩	NOUN
ejpam-5362	152	39	un	un	PROPN
ejpam-5362	152	40	)	)	PUNCT
ejpam-5362	152	41	.	.	PUNCT
ejpam-5362	153	1	m.	m.	NOUN
ejpam-5362	153	2	nxumalo	nxumalo	PROPN
ejpam-5362	153	3	/	/	SYM
ejpam-5362	153	4	eur	eur	PROPN
ejpam-5362	153	5	.	.	PUNCT
ejpam-5362	154	1	j.	j.	PROPN
ejpam-5362	154	2	pure	pure	PROPN
ejpam-5362	154	3	appl	appl	PROPN
ejpam-5362	154	4	.	.	PROPN
ejpam-5362	154	5	math	math	PROPN
ejpam-5362	154	6	,	,	PUNCT
ejpam-5362	154	7	18	18	NUM
ejpam-5362	154	8	(	(	PUNCT
ejpam-5362	154	9	1	1	NUM
ejpam-5362	154	10	)	)	PUNCT
ejpam-5362	154	11	(	(	PUNCT
ejpam-5362	154	12	2025	2025	NUM
ejpam-5362	154	13	)	)	PUNCT
ejpam-5362	154	14	,	,	PUNCT
ejpam-5362	154	15	5362	5362	NUM
ejpam-5362	154	16	7	7	NUM
ejpam-5362	154	17	of	of	ADP
ejpam-5362	154	18	21	21	NUM
ejpam-5362	154	19	because	because	SCONJ
ejpam-5362	154	20	∧	∧	PROPN
ejpam-5362	154	21	n∈n	n∈n	PUNCT
ejpam-5362	154	22	o(v	o(v	PROPN
ejpam-5362	154	23	∩	∩	ADJ
ejpam-5362	154	24	un	un	VERB
ejpam-5362	154	25	)	)	PUNCT
ejpam-5362	154	26	is	be	AUX
ejpam-5362	154	27	a	a	DET
ejpam-5362	154	28	complemented	complement	VERB
ejpam-5362	154	29	gδ	gδ	NOUN
ejpam-5362	154	30	-	-	PUNCT
ejpam-5362	154	31	sublocale	sublocale	NOUN
ejpam-5362	155	1	,	,	PUNCT
ejpam-5362	155	2	we	we	PRON
ejpam-5362	155	3	have	have	VERB
ejpam-5362	155	4	that∨	that∨	PROPN
ejpam-5362	155	5	n∈n	n∈n	NOUN
ejpam-5362	155	6	c(v	c(v	PROPN
ejpam-5362	155	7	∩	∩	ADJ
ejpam-5362	155	8	un	un	NOUN
ejpam-5362	155	9	)	)	PUNCT
ejpam-5362	155	10	̸=	̸=	PROPN
ejpam-5362	155	11	τ1	τ1	ADP
ejpam-5362	155	12	∨	∨	NUM
ejpam-5362	155	13	τ2	τ2	NOUN
ejpam-5362	155	14	,	,	PUNCT
ejpam-5362	155	15	which	which	PRON
ejpam-5362	155	16	is	be	AUX
ejpam-5362	155	17	impossible	impossible	ADJ
ejpam-5362	155	18	.	.	PUNCT
ejpam-5362	156	1	definition	definition	NOUN
ejpam-5362	156	2	2	2	NUM
ejpam-5362	156	3	.	.	PUNCT
ejpam-5362	157	1	let	let	VERB
ejpam-5362	157	2	(	(	PUNCT
ejpam-5362	157	3	l	l	NOUN
ejpam-5362	157	4	,	,	PUNCT
ejpam-5362	157	5	l1	l1	PROPN
ejpam-5362	157	6	,	,	PUNCT
ejpam-5362	157	7	l2	l2	NOUN
ejpam-5362	157	8	)	)	PUNCT
ejpam-5362	157	9	be	be	AUX
ejpam-5362	157	10	a	a	DET
ejpam-5362	157	11	bilocale	bilocale	NOUN
ejpam-5362	157	12	.	.	PUNCT
ejpam-5362	158	1	a	a	DET
ejpam-5362	158	2	sublocale	sublocale	NOUN
ejpam-5362	158	3	s	s	NOUN
ejpam-5362	158	4	of	of	ADP
ejpam-5362	158	5	l	l	NOUN
ejpam-5362	158	6	is	be	AUX
ejpam-5362	158	7	said	say	VERB
ejpam-5362	158	8	to	to	PART
ejpam-5362	158	9	be	be	AUX
ejpam-5362	158	10	of	of	ADP
ejpam-5362	158	11	(	(	PUNCT
ejpam-5362	158	12	i	i	PROPN
ejpam-5362	158	13	,	,	PUNCT
ejpam-5362	158	14	j)-first	j)-first	PROPN
ejpam-5362	158	15	category	category	NOUN
ejpam-5362	158	16	if	if	SCONJ
ejpam-5362	158	17	there	there	PRON
ejpam-5362	158	18	are	be	VERB
ejpam-5362	158	19	countably	countably	ADV
ejpam-5362	158	20	many	many	ADJ
ejpam-5362	158	21	(	(	PUNCT
ejpam-5362	158	22	i	i	NOUN
ejpam-5362	158	23	,	,	PUNCT
ejpam-5362	158	24	j)-nowhere	j)-nowhere	X
ejpam-5362	158	25	dense	dense	ADJ
ejpam-5362	158	26	sublocales	sublocale	NOUN
ejpam-5362	158	27	sn	sn	PROPN
ejpam-5362	158	28	,	,	PUNCT
ejpam-5362	158	29	n	n	PROPN
ejpam-5362	158	30	∈	∈	PROPN
ejpam-5362	158	31	n	n	CCONJ
ejpam-5362	158	32	,	,	PUNCT
ejpam-5362	158	33	such	such	ADJ
ejpam-5362	158	34	that	that	PRON
ejpam-5362	158	35	s	s	VERB
ejpam-5362	158	36	⊆	⊆	NUM
ejpam-5362	158	37	∨	∨	NUM
ejpam-5362	158	38	n∈n	n∈n	X
ejpam-5362	158	39	sn	sn	PROPN
ejpam-5362	158	40	.	.	PUNCT
ejpam-5362	159	1	it	it	PRON
ejpam-5362	159	2	is	be	AUX
ejpam-5362	159	3	of	of	ADP
ejpam-5362	159	4	(	(	PUNCT
ejpam-5362	159	5	i	i	PROPN
ejpam-5362	159	6	,	,	PUNCT
ejpam-5362	159	7	j)-second	j)-second	PROPN
ejpam-5362	159	8	category	category	NOUN
ejpam-5362	159	9	if	if	SCONJ
ejpam-5362	159	10	it	it	PRON
ejpam-5362	159	11	is	be	AUX
ejpam-5362	159	12	not	not	PART
ejpam-5362	159	13	of	of	ADP
ejpam-5362	159	14	(	(	PUNCT
ejpam-5362	159	15	i	i	PROPN
ejpam-5362	159	16	,	,	PUNCT
ejpam-5362	159	17	j)-first	j)-first	PROPN
ejpam-5362	159	18	category	category	NOUN
ejpam-5362	159	19	.	.	PUNCT
ejpam-5362	160	1	theorem	theorem	NOUN
ejpam-5362	160	2	1	1	NUM
ejpam-5362	160	3	.	.	PUNCT
ejpam-5362	161	1	let	let	VERB
ejpam-5362	161	2	(	(	PUNCT
ejpam-5362	161	3	l	l	NOUN
ejpam-5362	161	4	,	,	PUNCT
ejpam-5362	161	5	l1	l1	PROPN
ejpam-5362	161	6	,	,	PUNCT
ejpam-5362	161	7	l2	l2	NOUN
ejpam-5362	161	8	)	)	PUNCT
ejpam-5362	161	9	be	be	AUX
ejpam-5362	161	10	a	a	DET
ejpam-5362	161	11	bilocale	bilocale	NOUN
ejpam-5362	161	12	whose	whose	DET
ejpam-5362	161	13	j	j	NOUN
ejpam-5362	161	14	-	-	PUNCT
ejpam-5362	161	15	gδ	gδ	NOUN
ejpam-5362	161	16	-	-	PUNCT
ejpam-5362	161	17	sublocales	sublocale	NOUN
ejpam-5362	161	18	are	be	AUX
ejpam-5362	161	19	complemented	complement	VERB
ejpam-5362	161	20	in	in	ADP
ejpam-5362	161	21	l.	l.	PROPN
ejpam-5362	161	22	the	the	DET
ejpam-5362	161	23	following	follow	VERB
ejpam-5362	161	24	statements	statement	NOUN
ejpam-5362	161	25	are	be	AUX
ejpam-5362	161	26	equivalent	equivalent	ADJ
ejpam-5362	161	27	:	:	PUNCT
ejpam-5362	161	28	(	(	PUNCT
ejpam-5362	161	29	i	i	NOUN
ejpam-5362	161	30	)	)	PUNCT
ejpam-5362	161	31	(	(	PUNCT
ejpam-5362	161	32	l	l	NOUN
ejpam-5362	161	33	,	,	PUNCT
ejpam-5362	161	34	l1	l1	PROPN
ejpam-5362	161	35	,	,	PUNCT
ejpam-5362	161	36	l2	l2	NOUN
ejpam-5362	161	37	)	)	PUNCT
ejpam-5362	161	38	is	be	AUX
ejpam-5362	161	39	(	(	PUNCT
ejpam-5362	161	40	i	i	NOUN
ejpam-5362	161	41	,	,	PUNCT
ejpam-5362	161	42	j)-baire	j)-baire	NOUN
ejpam-5362	161	43	.	.	PUNCT
ejpam-5362	162	1	(	(	PUNCT
ejpam-5362	162	2	ii	ii	NOUN
ejpam-5362	162	3	)	)	PUNCT
ejpam-5362	162	4	each	each	DET
ejpam-5362	162	5	non	non	ADJ
ejpam-5362	162	6	-	-	ADJ
ejpam-5362	162	7	void	void	ADJ
ejpam-5362	162	8	i	i	NOUN
ejpam-5362	162	9	-	-	PUNCT
ejpam-5362	162	10	open	open	ADJ
ejpam-5362	162	11	sublocale	sublocale	NOUN
ejpam-5362	162	12	is	be	AUX
ejpam-5362	162	13	of	of	ADP
ejpam-5362	162	14	(	(	PUNCT
ejpam-5362	162	15	j	j	NOUN
ejpam-5362	162	16	,	,	PUNCT
ejpam-5362	162	17	i)-second	i)-second	ADP
ejpam-5362	162	18	category	category	NOUN
ejpam-5362	162	19	.	.	PUNCT
ejpam-5362	163	1	(	(	PUNCT
ejpam-5362	163	2	iii	iii	X
ejpam-5362	163	3	)	)	PUNCT
ejpam-5362	163	4	every	every	DET
ejpam-5362	163	5	sublocale	sublocale	NOUN
ejpam-5362	163	6	of	of	ADP
ejpam-5362	163	7	(	(	PUNCT
ejpam-5362	163	8	j	j	PROPN
ejpam-5362	163	9	,	,	PUNCT
ejpam-5362	163	10	i)-first	i)-first	PUNCT
ejpam-5362	163	11	category	category	NOUN
ejpam-5362	163	12	has	have	AUX
ejpam-5362	163	13	void	void	VERB
ejpam-5362	163	14	i	i	NOUN
ejpam-5362	163	15	-	-	NOUN
ejpam-5362	163	16	interior	interior	NOUN
ejpam-5362	163	17	.	.	PUNCT
ejpam-5362	164	1	(	(	PUNCT
ejpam-5362	164	2	iv	iv	X
ejpam-5362	164	3	)	)	PUNCT
ejpam-5362	164	4	the	the	DET
ejpam-5362	164	5	supplement	supplement	NOUN
ejpam-5362	164	6	of	of	ADP
ejpam-5362	164	7	every	every	DET
ejpam-5362	164	8	sublocale	sublocale	NOUN
ejpam-5362	164	9	of	of	ADP
ejpam-5362	164	10	(	(	PUNCT
ejpam-5362	164	11	j	j	PROPN
ejpam-5362	164	12	,	,	PUNCT
ejpam-5362	164	13	i)-first	i)-first	PUNCT
ejpam-5362	164	14	category	category	NOUN
ejpam-5362	164	15	is	be	AUX
ejpam-5362	164	16	i	i	PRON
ejpam-5362	164	17	-	-	PUNCT
ejpam-5362	164	18	dense	dense	ADJ
ejpam-5362	164	19	.	.	PUNCT
ejpam-5362	165	1	proof	proof	NOUN
ejpam-5362	165	2	.	.	PUNCT
ejpam-5362	166	1	(	(	PUNCT
ejpam-5362	166	2	i	i	NOUN
ejpam-5362	166	3	)	)	PUNCT
ejpam-5362	167	1	=	=	NOUN
ejpam-5362	167	2	⇒	⇒	NOUN
ejpam-5362	167	3	(	(	PUNCT
ejpam-5362	167	4	ii	ii	NOUN
ejpam-5362	167	5	):	):	PUNCT
ejpam-5362	167	6	let	let	VERB
ejpam-5362	167	7	u	u	PRON
ejpam-5362	167	8	be	be	AUX
ejpam-5362	167	9	a	a	DET
ejpam-5362	167	10	non	non	ADJ
ejpam-5362	167	11	-	-	ADJ
ejpam-5362	167	12	void	void	ADJ
ejpam-5362	167	13	i	i	NOUN
ejpam-5362	167	14	-	-	PUNCT
ejpam-5362	167	15	open	open	ADJ
ejpam-5362	167	16	sublocale	sublocale	NOUN
ejpam-5362	167	17	of	of	ADP
ejpam-5362	167	18	l	l	NOUN
ejpam-5362	167	19	and	and	CCONJ
ejpam-5362	167	20	assume	assume	VERB
ejpam-5362	167	21	that	that	SCONJ
ejpam-5362	167	22	u	u	PROPN
ejpam-5362	167	23	⊆	⊆	NUM
ejpam-5362	167	24	∨	∨	NUM
ejpam-5362	167	25	n∈n	n∈n	X
ejpam-5362	167	26	sn	sn	NOUN
ejpam-5362	167	27	for	for	ADP
ejpam-5362	167	28	some	some	DET
ejpam-5362	167	29	collection	collection	NOUN
ejpam-5362	167	30	{	{	PUNCT
ejpam-5362	167	31	sn	sn	NOUN
ejpam-5362	167	32	:	:	PUNCT
ejpam-5362	167	33	n	n	CCONJ
ejpam-5362	167	34	∈	∈	PROPN
ejpam-5362	167	35	n	n	CCONJ
ejpam-5362	167	36	}	}	PUNCT
ejpam-5362	167	37	of	of	ADP
ejpam-5362	167	38	(	(	PUNCT
ejpam-5362	167	39	j	j	NOUN
ejpam-5362	167	40	,	,	PUNCT
ejpam-5362	167	41	i)-nowhere	i)-nowhere	ADP
ejpam-5362	167	42	dense	dense	ADJ
ejpam-5362	167	43	sublocales	sublocale	NOUN
ejpam-5362	167	44	.	.	PUNCT
ejpam-5362	168	1	then	then	ADV
ejpam-5362	168	2	u	u	NOUN
ejpam-5362	168	3	⊆	⊆	NUM
ejpam-5362	168	4	∨	∨	NUM
ejpam-5362	168	5	n∈n	n∈n	X
ejpam-5362	168	6	sn	sn	PROPN
ejpam-5362	169	1	where	where	SCONJ
ejpam-5362	169	2	members	member	NOUN
ejpam-5362	169	3	of	of	ADP
ejpam-5362	169	4	the	the	DET
ejpam-5362	169	5	collection	collection	NOUN
ejpam-5362	169	6	{	{	PUNCT
ejpam-5362	169	7	sn	sn	NOUN
ejpam-5362	169	8	:	:	PUNCT
ejpam-5362	169	9	n	n	CCONJ
ejpam-5362	169	10	∈	∈	PROPN
ejpam-5362	169	11	n	n	CCONJ
ejpam-5362	169	12	}	}	PUNCT
ejpam-5362	169	13	are	be	AUX
ejpam-5362	169	14	(	(	PUNCT
ejpam-5362	169	15	j	j	NOUN
ejpam-5362	169	16	,	,	PUNCT
ejpam-5362	169	17	i)-nowhere	i)-nowhere	ADP
ejpam-5362	169	18	dense	dense	ADJ
ejpam-5362	169	19	.	.	PUNCT
ejpam-5362	170	1	it	it	PRON
ejpam-5362	170	2	follows	follow	VERB
ejpam-5362	170	3	that	that	SCONJ
ejpam-5362	170	4	members	member	NOUN
ejpam-5362	170	5	of	of	ADP
ejpam-5362	170	6	the	the	DET
ejpam-5362	170	7	collection	collection	NOUN
ejpam-5362	170	8	{	{	PUNCT
ejpam-5362	170	9	l∖	l∖	PROPN
ejpam-5362	170	10	clj(sn	clj(sn	VERB
ejpam-5362	170	11	)	)	PUNCT
ejpam-5362	170	12	:	:	PUNCT
ejpam-5362	170	13	n	n	X
ejpam-5362	170	14	∈	∈	PROPN
ejpam-5362	170	15	n	n	CCONJ
ejpam-5362	170	16	}	}	PUNCT
ejpam-5362	170	17	are	be	AUX
ejpam-5362	170	18	i	i	PRON
ejpam-5362	170	19	-	-	PUNCT
ejpam-5362	170	20	dense	dense	ADJ
ejpam-5362	170	21	j	j	NOUN
ejpam-5362	170	22	-	-	ADJ
ejpam-5362	170	23	open	open	ADJ
ejpam-5362	170	24	sublocales	sublocale	NOUN
ejpam-5362	170	25	.	.	PUNCT
ejpam-5362	171	1	by	by	ADP
ejpam-5362	171	2	hypothesis	hypothesis	NOUN
ejpam-5362	171	3	,	,	PUNCT
ejpam-5362	171	4	∧	∧	PROPN
ejpam-5362	171	5	n∈n(l∖	n∈n(l∖	PROPN
ejpam-5362	171	6	clj(sn	clj(sn	ADJ
ejpam-5362	171	7	)	)	PUNCT
ejpam-5362	171	8	is	be	AUX
ejpam-5362	171	9	i	i	PRON
ejpam-5362	171	10	-	-	PUNCT
ejpam-5362	171	11	dense	dense	ADJ
ejpam-5362	171	12	so	so	SCONJ
ejpam-5362	171	13	that	that	SCONJ
ejpam-5362	171	14	u	u	PROPN
ejpam-5362	171	15	∩	∩	NOUN
ejpam-5362	171	16	(	(	PUNCT
ejpam-5362	171	17	∧	∧	PROPN
ejpam-5362	171	18	n∈n	n∈n	NOUN
ejpam-5362	171	19	(	(	PUNCT
ejpam-5362	171	20	l∖	l∖	PROPN
ejpam-5362	171	21	clj(sn	clj(sn	VERB
ejpam-5362	171	22	)	)	PUNCT
ejpam-5362	171	23	)	)	PUNCT
ejpam-5362	171	24	)	)	PUNCT
ejpam-5362	172	1	̸=	̸=	PROPN
ejpam-5362	172	2	o.	o.	NOUN
ejpam-5362	172	3	therefore	therefore	ADV
ejpam-5362	172	4	o	o	X
ejpam-5362	172	5	̸=	̸=	PROPN
ejpam-5362	172	6	(	(	PUNCT
ejpam-5362	172	7	∨	∨	PROPN
ejpam-5362	172	8	k∈n	k∈n	PROPN
ejpam-5362	172	9	sk	sk	PROPN
ejpam-5362	172	10	)	)	PUNCT
ejpam-5362	172	11	∩	∩	NOUN
ejpam-5362	172	12	(	(	PUNCT
ejpam-5362	172	13	∧	∧	PROPN
ejpam-5362	172	14	n∈n	n∈n	NOUN
ejpam-5362	172	15	(	(	PUNCT
ejpam-5362	172	16	l∖	l∖	PROPN
ejpam-5362	172	17	clj(sn	clj(sn	VERB
ejpam-5362	172	18	)	)	PUNCT
ejpam-5362	172	19	)	)	PUNCT
ejpam-5362	172	20	)	)	PUNCT
ejpam-5362	173	1	=	=	PUNCT
ejpam-5362	173	2	∨	∨	NUM
ejpam-5362	173	3	k∈n	k∈n	PROPN
ejpam-5362	173	4	(	(	PUNCT
ejpam-5362	173	5	sk	sk	PROPN
ejpam-5362	173	6	∩	∩	NOUN
ejpam-5362	173	7	(	(	PUNCT
ejpam-5362	173	8	∧	∧	PROPN
ejpam-5362	173	9	n∈n	n∈n	NOUN
ejpam-5362	173	10	(	(	PUNCT
ejpam-5362	173	11	l∖	l∖	PROPN
ejpam-5362	173	12	sn	sn	PROPN
ejpam-5362	173	13	)	)	PUNCT
ejpam-5362	173	14	)	)	PUNCT
ejpam-5362	173	15	)	)	PUNCT
ejpam-5362	174	1	⊆	⊆	NUM
ejpam-5362	174	2	∨	∨	NUM
ejpam-5362	174	3	k∈n	k∈n	PROPN
ejpam-5362	174	4	(	(	PUNCT
ejpam-5362	174	5	sk	sk	NOUN
ejpam-5362	174	6	∩	∩	NOUN
ejpam-5362	174	7	(	(	PUNCT
ejpam-5362	174	8	l∖	l∖	PROPN
ejpam-5362	174	9	sk	sk	VERB
ejpam-5362	174	10	)	)	PUNCT
ejpam-5362	174	11	)	)	PUNCT
ejpam-5362	175	1	=	=	PUNCT
ejpam-5362	175	2	o	o	NOUN
ejpam-5362	175	3	which	which	PRON
ejpam-5362	175	4	is	be	AUX
ejpam-5362	175	5	impossible	impossible	ADJ
ejpam-5362	175	6	.	.	PUNCT
ejpam-5362	176	1	(	(	PUNCT
ejpam-5362	176	2	ii	ii	NOUN
ejpam-5362	176	3	)	)	PUNCT
ejpam-5362	176	4	=	=	NOUN
ejpam-5362	176	5	⇒	⇒	NOUN
ejpam-5362	176	6	(	(	PUNCT
ejpam-5362	176	7	iii	iii	NOUN
ejpam-5362	176	8	):	):	PUNCT
ejpam-5362	176	9	let	let	VERB
ejpam-5362	176	10	s	s	PRON
ejpam-5362	176	11	be	be	AUX
ejpam-5362	176	12	a	a	DET
ejpam-5362	176	13	sublocale	sublocale	NOUN
ejpam-5362	176	14	of	of	ADP
ejpam-5362	176	15	(	(	PUNCT
ejpam-5362	176	16	j	j	PROPN
ejpam-5362	176	17	,	,	PUNCT
ejpam-5362	176	18	i)-first	i)-first	ADJ
ejpam-5362	176	19	category	category	NOUN
ejpam-5362	176	20	with	with	ADP
ejpam-5362	176	21	a	a	DET
ejpam-5362	176	22	non	non	ADJ
ejpam-5362	176	23	-	-	ADJ
ejpam-5362	176	24	void	void	ADJ
ejpam-5362	176	25	i	i	NOUN
ejpam-5362	176	26	-	-	NOUN
ejpam-5362	176	27	interior	interior	ADJ
ejpam-5362	176	28	.	.	PUNCT
ejpam-5362	177	1	we	we	PRON
ejpam-5362	177	2	then	then	ADV
ejpam-5362	177	3	get	get	VERB
ejpam-5362	177	4	that	that	DET
ejpam-5362	177	5	inti(s	inti(s	NOUN
ejpam-5362	177	6	)	)	PUNCT
ejpam-5362	177	7	is	be	AUX
ejpam-5362	177	8	a	a	DET
ejpam-5362	177	9	non	non	ADJ
ejpam-5362	177	10	-	-	ADJ
ejpam-5362	177	11	void	void	ADJ
ejpam-5362	177	12	i	i	NOUN
ejpam-5362	177	13	-	-	PUNCT
ejpam-5362	177	14	open	open	ADJ
ejpam-5362	177	15	sublocale	sublocale	NOUN
ejpam-5362	177	16	which	which	PRON
ejpam-5362	177	17	must	must	AUX
ejpam-5362	177	18	be	be	AUX
ejpam-5362	177	19	of	of	ADP
ejpam-5362	177	20	(	(	PUNCT
ejpam-5362	177	21	j	j	NOUN
ejpam-5362	177	22	,	,	PUNCT
ejpam-5362	177	23	i)-second	i)-second	ADP
ejpam-5362	177	24	category	category	NOUN
ejpam-5362	177	25	by	by	ADP
ejpam-5362	177	26	(	(	PUNCT
ejpam-5362	177	27	ii	ii	NOUN
ejpam-5362	177	28	)	)	PUNCT
ejpam-5362	177	29	.	.	PUNCT
ejpam-5362	178	1	this	this	PRON
ejpam-5362	178	2	is	be	AUX
ejpam-5362	178	3	a	a	DET
ejpam-5362	178	4	contradiction	contradiction	NOUN
ejpam-5362	178	5	.	.	PUNCT
ejpam-5362	179	1	m.	m.	NOUN
ejpam-5362	179	2	nxumalo	nxumalo	PROPN
ejpam-5362	179	3	/	/	SYM
ejpam-5362	179	4	eur	eur	PROPN
ejpam-5362	179	5	.	.	PUNCT
ejpam-5362	180	1	j.	j.	PROPN
ejpam-5362	180	2	pure	pure	PROPN
ejpam-5362	180	3	appl	appl	PROPN
ejpam-5362	180	4	.	.	PROPN
ejpam-5362	180	5	math	math	PROPN
ejpam-5362	180	6	,	,	PUNCT
ejpam-5362	180	7	18	18	NUM
ejpam-5362	180	8	(	(	PUNCT
ejpam-5362	180	9	1	1	NUM
ejpam-5362	180	10	)	)	PUNCT
ejpam-5362	180	11	(	(	PUNCT
ejpam-5362	180	12	2025	2025	NUM
ejpam-5362	180	13	)	)	PUNCT
ejpam-5362	180	14	,	,	PUNCT
ejpam-5362	180	15	5362	5362	NUM
ejpam-5362	180	16	8	8	NUM
ejpam-5362	180	17	of	of	ADP
ejpam-5362	180	18	21	21	NUM
ejpam-5362	180	19	(	(	PUNCT
ejpam-5362	180	20	iii	iii	NOUN
ejpam-5362	180	21	)	)	PUNCT
ejpam-5362	180	22	=	=	NOUN
ejpam-5362	180	23	⇒	⇒	NOUN
ejpam-5362	180	24	(	(	PUNCT
ejpam-5362	180	25	iv	iv	NUM
ejpam-5362	180	26	):	):	PUNCT
ejpam-5362	180	27	let	let	VERB
ejpam-5362	180	28	s	s	PRON
ejpam-5362	180	29	be	be	AUX
ejpam-5362	180	30	a	a	DET
ejpam-5362	180	31	sublocale	sublocale	NOUN
ejpam-5362	180	32	of	of	ADP
ejpam-5362	180	33	l	l	NOUN
ejpam-5362	180	34	which	which	PRON
ejpam-5362	180	35	is	be	AUX
ejpam-5362	180	36	of	of	ADP
ejpam-5362	180	37	(	(	PUNCT
ejpam-5362	180	38	j	j	PROPN
ejpam-5362	180	39	,	,	PUNCT
ejpam-5362	180	40	i)-first	i)-first	NOUN
ejpam-5362	180	41	category	category	NOUN
ejpam-5362	180	42	and	and	CCONJ
ejpam-5362	180	43	choose	choose	VERB
ejpam-5362	180	44	x	x	PUNCT
ejpam-5362	180	45	∈	∈	PROPN
ejpam-5362	180	46	li	li	NOUN
ejpam-5362	180	47	with	with	ADP
ejpam-5362	180	48	o(x	o(x	PROPN
ejpam-5362	180	49	)	)	PUNCT
ejpam-5362	180	50	∩	∩	NOUN
ejpam-5362	180	51	(	(	PUNCT
ejpam-5362	180	52	l	l	X
ejpam-5362	180	53	∖	∖	X
ejpam-5362	180	54	s	s	PART
ejpam-5362	180	55	)	)	PUNCT
ejpam-5362	180	56	=	=	SYM
ejpam-5362	181	1	o.	o.	NOUN
ejpam-5362	181	2	then	then	ADV
ejpam-5362	181	3	o(x	o(x	PROPN
ejpam-5362	181	4	)	)	PUNCT
ejpam-5362	182	1	⊆	⊆	NUM
ejpam-5362	182	2	s.	s.	PROPN
ejpam-5362	182	3	since	since	SCONJ
ejpam-5362	182	4	s	s	PART
ejpam-5362	182	5	satisfies	satisfie	NOUN
ejpam-5362	182	6	the	the	DET
ejpam-5362	182	7	conditions	condition	NOUN
ejpam-5362	182	8	hypothesized	hypothesize	VERB
ejpam-5362	182	9	in	in	ADP
ejpam-5362	182	10	(	(	PUNCT
ejpam-5362	182	11	iii	iii	NOUN
ejpam-5362	182	12	)	)	PUNCT
ejpam-5362	182	13	,	,	PUNCT
ejpam-5362	182	14	inti(s	inti(s	NOUN
ejpam-5362	182	15	)	)	PUNCT
ejpam-5362	182	16	̸=	̸=	PROPN
ejpam-5362	182	17	o	o	NOUN
ejpam-5362	182	18	,	,	PUNCT
ejpam-5362	182	19	so	so	SCONJ
ejpam-5362	182	20	that	that	SCONJ
ejpam-5362	182	21	the	the	DET
ejpam-5362	182	22	i	i	NOUN
ejpam-5362	182	23	-	-	PUNCT
ejpam-5362	182	24	open	open	ADJ
ejpam-5362	182	25	sublocale	sublocale	NOUN
ejpam-5362	182	26	o(x	o(x	PROPN
ejpam-5362	182	27	)	)	PUNCT
ejpam-5362	182	28	is	be	AUX
ejpam-5362	182	29	void	void	ADJ
ejpam-5362	182	30	.	.	PUNCT
ejpam-5362	183	1	(	(	PUNCT
ejpam-5362	183	2	iv	iv	X
ejpam-5362	183	3	)	)	PUNCT
ejpam-5362	183	4	=	=	NOUN
ejpam-5362	183	5	⇒	⇒	NOUN
ejpam-5362	183	6	(	(	PUNCT
ejpam-5362	183	7	i	i	NOUN
ejpam-5362	183	8	):	):	PUNCT
ejpam-5362	183	9	let	let	VERB
ejpam-5362	183	10	{	{	PUNCT
ejpam-5362	183	11	o(xn	o(xn	X
ejpam-5362	183	12	)	)	PUNCT
ejpam-5362	183	13	:	:	PUNCT
ejpam-5362	184	1	n	n	CCONJ
ejpam-5362	184	2	∈	∈	PROPN
ejpam-5362	184	3	n	n	CCONJ
ejpam-5362	184	4	}	}	PUNCT
ejpam-5362	184	5	be	be	AUX
ejpam-5362	184	6	a	a	DET
ejpam-5362	184	7	collection	collection	NOUN
ejpam-5362	184	8	of	of	ADP
ejpam-5362	184	9	i	i	NOUN
ejpam-5362	184	10	-	-	PUNCT
ejpam-5362	184	11	dense	dense	ADJ
ejpam-5362	184	12	j	j	NOUN
ejpam-5362	184	13	-	-	ADJ
ejpam-5362	184	14	open	open	ADJ
ejpam-5362	184	15	sublocales	sublocale	NOUN
ejpam-5362	184	16	and	and	CCONJ
ejpam-5362	184	17	assume	assume	VERB
ejpam-5362	184	18	that	that	SCONJ
ejpam-5362	184	19	there	there	PRON
ejpam-5362	184	20	is	be	VERB
ejpam-5362	184	21	an	an	DET
ejpam-5362	184	22	i	i	NOUN
ejpam-5362	184	23	-	-	PUNCT
ejpam-5362	184	24	open	open	ADJ
ejpam-5362	184	25	sublocale	sublocale	NOUN
ejpam-5362	184	26	o(y	o(y	NOUN
ejpam-5362	184	27	)	)	PUNCT
ejpam-5362	184	28	with	with	ADP
ejpam-5362	184	29	o(y	o(y	NOUN
ejpam-5362	184	30	)	)	PUNCT
ejpam-5362	184	31	∩	∩	NOUN
ejpam-5362	184	32	(	(	PUNCT
ejpam-5362	184	33	∧	∧	PROPN
ejpam-5362	184	34	n∈n	n∈n	NOUN
ejpam-5362	184	35	o(xn	o(xn	NUM
ejpam-5362	184	36	)	)	PUNCT
ejpam-5362	184	37	)	)	PUNCT
ejpam-5362	185	1	=	=	PUNCT
ejpam-5362	185	2	o	o	X
ejpam-5362	185	3	then	then	ADV
ejpam-5362	185	4	o(y	o(y	PROPN
ejpam-5362	185	5	)	)	PUNCT
ejpam-5362	185	6	⊆	⊆	NUM
ejpam-5362	185	7	∨	∨	NUM
ejpam-5362	185	8	n∈n	n∈n	X
ejpam-5362	185	9	c(xn	c(xn	NOUN
ejpam-5362	185	10	)	)	PUNCT
ejpam-5362	185	11	,	,	PUNCT
ejpam-5362	185	12	making	make	VERB
ejpam-5362	185	13	o(y	o(y	NOUN
ejpam-5362	185	14	)	)	PUNCT
ejpam-5362	185	15	a	a	DET
ejpam-5362	185	16	sublocale	sublocale	NOUN
ejpam-5362	185	17	of	of	ADP
ejpam-5362	185	18	(	(	PUNCT
ejpam-5362	185	19	j	j	PROPN
ejpam-5362	185	20	,	,	PUNCT
ejpam-5362	185	21	i)-first	i)-first	NOUN
ejpam-5362	185	22	category	category	NOUN
ejpam-5362	185	23	.	.	PUNCT
ejpam-5362	186	1	by	by	ADP
ejpam-5362	186	2	(	(	PUNCT
ejpam-5362	186	3	iv	iv	X
ejpam-5362	186	4	)	)	PUNCT
ejpam-5362	186	5	,	,	PUNCT
ejpam-5362	186	6	l∖o(y	l∖o(y	PROPN
ejpam-5362	186	7	)	)	PUNCT
ejpam-5362	186	8	=	=	SYM
ejpam-5362	186	9	c(y	c(y	PROPN
ejpam-5362	186	10	)	)	PUNCT
ejpam-5362	186	11	is	be	AUX
ejpam-5362	186	12	i	i	PRON
ejpam-5362	186	13	-	-	PUNCT
ejpam-5362	186	14	dense	dense	ADJ
ejpam-5362	186	15	,	,	PUNCT
ejpam-5362	186	16	i.e.	i.e.	X
ejpam-5362	186	17	,	,	PUNCT
ejpam-5362	186	18	cli(c(y	cli(c(y	NOUN
ejpam-5362	186	19	)	)	PUNCT
ejpam-5362	186	20	)	)	PUNCT
ejpam-5362	187	1	=	=	SYM
ejpam-5362	187	2	c(y	c(y	PROPN
ejpam-5362	187	3	)	)	PUNCT
ejpam-5362	187	4	=	=	SYM
ejpam-5362	188	1	1	1	X
ejpam-5362	188	2	.	.	X
ejpam-5362	188	3	therefore	therefore	ADV
ejpam-5362	188	4	y	y	PROPN
ejpam-5362	188	5	=	=	PUNCT
ejpam-5362	188	6	0	0	PUNCT
ejpam-5362	189	1	so	so	SCONJ
ejpam-5362	189	2	that	that	SCONJ
ejpam-5362	189	3	o(y	o(y	ADV
ejpam-5362	189	4	)	)	PUNCT
ejpam-5362	189	5	=	=	SYM
ejpam-5362	190	1	o.	o.	NOUN
ejpam-5362	190	2	hence(∧	hence(∧	VERB
ejpam-5362	190	3	n∈n	n∈n	NOUN
ejpam-5362	190	4	o(xn	o(xn	NOUN
ejpam-5362	190	5	)	)	PUNCT
ejpam-5362	190	6	)	)	PUNCT
ejpam-5362	190	7	is	be	AUX
ejpam-5362	190	8	i	i	PRON
ejpam-5362	190	9	-	-	PUNCT
ejpam-5362	190	10	dense	dense	ADJ
ejpam-5362	190	11	.	.	PUNCT
ejpam-5362	191	1	we	we	PRON
ejpam-5362	191	2	shall	shall	AUX
ejpam-5362	191	3	say	say	VERB
ejpam-5362	191	4	that	that	SCONJ
ejpam-5362	191	5	a	a	DET
ejpam-5362	191	6	collection	collection	NOUN
ejpam-5362	191	7	c	c	NOUN
ejpam-5362	191	8	of	of	ADP
ejpam-5362	191	9	sublocales	sublocale	NOUN
ejpam-5362	191	10	of	of	ADP
ejpam-5362	191	11	l	l	NOUN
ejpam-5362	191	12	has	have	VERB
ejpam-5362	191	13	the	the	DET
ejpam-5362	191	14	finite	finite	ADJ
ejpam-5362	191	15	intersection	intersection	NOUN
ejpam-5362	191	16	property	property	NOUN
ejpam-5362	191	17	(	(	PUNCT
ejpam-5362	191	18	fip	fip	PROPN
ejpam-5362	191	19	)	)	PUNCT
ejpam-5362	191	20	if	if	SCONJ
ejpam-5362	191	21	the	the	DET
ejpam-5362	191	22	intersection	intersection	NOUN
ejpam-5362	191	23	of	of	ADP
ejpam-5362	191	24	every	every	DET
ejpam-5362	191	25	finite	finite	ADJ
ejpam-5362	191	26	subcollection	subcollection	NOUN
ejpam-5362	191	27	of	of	ADP
ejpam-5362	191	28	c	c	PROPN
ejpam-5362	191	29	has	have	VERB
ejpam-5362	191	30	a	a	DET
ejpam-5362	191	31	non	non	ADJ
ejpam-5362	191	32	-	-	ADJ
ejpam-5362	191	33	void	void	ADJ
ejpam-5362	191	34	intersection	intersection	NOUN
ejpam-5362	191	35	.	.	PUNCT
ejpam-5362	192	1	proposition	proposition	NOUN
ejpam-5362	192	2	2	2	NUM
ejpam-5362	192	3	.	.	PUNCT
ejpam-5362	193	1	if	if	SCONJ
ejpam-5362	193	2	a	a	DET
ejpam-5362	193	3	bilocale	bilocale	NOUN
ejpam-5362	193	4	(	(	PUNCT
ejpam-5362	193	5	l	l	NOUN
ejpam-5362	193	6	,	,	PUNCT
ejpam-5362	193	7	l1	l1	PROPN
ejpam-5362	193	8	,	,	PUNCT
ejpam-5362	193	9	l2	l2	NOUN
ejpam-5362	193	10	)	)	PUNCT
ejpam-5362	193	11	is	be	AUX
ejpam-5362	193	12	compact	compact	ADJ
ejpam-5362	193	13	,	,	PUNCT
ejpam-5362	193	14	then	then	ADV
ejpam-5362	193	15	every	every	DET
ejpam-5362	193	16	collection	collection	NOUN
ejpam-5362	193	17	of	of	ADP
ejpam-5362	193	18	closed	close	VERB
ejpam-5362	193	19	sublocales	sublocale	NOUN
ejpam-5362	193	20	with	with	ADP
ejpam-5362	193	21	the	the	DET
ejpam-5362	193	22	fip	fip	PROPN
ejpam-5362	193	23	has	have	VERB
ejpam-5362	193	24	a	a	DET
ejpam-5362	193	25	non	non	ADJ
ejpam-5362	193	26	-	-	ADJ
ejpam-5362	193	27	void	void	ADJ
ejpam-5362	193	28	intersection	intersection	NOUN
ejpam-5362	193	29	.	.	PUNCT
ejpam-5362	194	1	proof	proof	NOUN
ejpam-5362	194	2	.	.	PUNCT
ejpam-5362	195	1	let	let	VERB
ejpam-5362	195	2	{	{	PUNCT
ejpam-5362	195	3	c(xα	c(xα	NUM
ejpam-5362	195	4	)	)	PUNCT
ejpam-5362	195	5	:	:	PUNCT
ejpam-5362	195	6	α	α	PROPN
ejpam-5362	195	7	∈	∈	PROPN
ejpam-5362	195	8	λ	λ	NOUN
ejpam-5362	195	9	}	}	PUNCT
ejpam-5362	195	10	be	be	VERB
ejpam-5362	195	11	a	a	DET
ejpam-5362	195	12	collection	collection	NOUN
ejpam-5362	195	13	with	with	ADP
ejpam-5362	195	14	the	the	DET
ejpam-5362	195	15	fip	fip	PROPN
ejpam-5362	195	16	and	and	CCONJ
ejpam-5362	195	17	assume	assume	VERB
ejpam-5362	195	18	that	that	SCONJ
ejpam-5362	195	19	∧	∧	PROPN
ejpam-5362	195	20	α∈λ	α∈λ	NOUN
ejpam-5362	195	21	c(xα	c(xα	NOUN
ejpam-5362	195	22	)	)	PUNCT
ejpam-5362	196	1	=	=	SYM
ejpam-5362	196	2	o.	o.	NOUN
ejpam-5362	196	3	then	then	ADV
ejpam-5362	196	4	l	l	PROPN
ejpam-5362	197	1	=	=	PUNCT
ejpam-5362	198	1	l∖	l∖	PROPN
ejpam-5362	198	2	∧	∧	PROPN
ejpam-5362	198	3	α∈λ	α∈λ	NOUN
ejpam-5362	198	4	c(xα	c(xα	NOUN
ejpam-5362	198	5	)	)	PUNCT
ejpam-5362	198	6	=	=	PUNCT
ejpam-5362	199	1	∨	∨	NUM
ejpam-5362	199	2	α∈λ	α∈λ	NOUN
ejpam-5362	199	3	o(xα	o(xα	NUM
ejpam-5362	199	4	)	)	PUNCT
ejpam-5362	199	5	,	,	PUNCT
ejpam-5362	199	6	making	make	VERB
ejpam-5362	199	7	o	o	PROPN
ejpam-5362	199	8	(	(	PUNCT
ejpam-5362	199	9	∨	∨	NUM
ejpam-5362	199	10	α∈λ	α∈λ	NOUN
ejpam-5362	199	11	xα	xα	PUNCT
ejpam-5362	199	12	)	)	PUNCT
ejpam-5362	200	1	=	=	PUNCT
ejpam-5362	200	2	l.	l.	PROPN
ejpam-5362	200	3	therefore	therefore	ADV
ejpam-5362	200	4	∨	∨	NUM
ejpam-5362	200	5	α∈λ	α∈λ	NOUN
ejpam-5362	200	6	xα	xα	PUNCT
ejpam-5362	201	1	=	=	NOUN
ejpam-5362	201	2	1	1	X
ejpam-5362	201	3	.	.	PUNCT
ejpam-5362	202	1	since	since	SCONJ
ejpam-5362	202	2	(	(	PUNCT
ejpam-5362	202	3	l	l	NOUN
ejpam-5362	202	4	,	,	PUNCT
ejpam-5362	202	5	l1	l1	PROPN
ejpam-5362	202	6	,	,	PUNCT
ejpam-5362	202	7	l2	l2	NOUN
ejpam-5362	202	8	)	)	PUNCT
ejpam-5362	202	9	is	be	AUX
ejpam-5362	202	10	compact	compact	ADJ
ejpam-5362	202	11	,	,	PUNCT
ejpam-5362	202	12	there	there	PRON
ejpam-5362	202	13	is	be	VERB
ejpam-5362	202	14	a	a	DET
ejpam-5362	202	15	finite	finite	NOUN
ejpam-5362	202	16	set	set	VERB
ejpam-5362	202	17	f	f	PROPN
ejpam-5362	202	18	⊆	⊆	NUM
ejpam-5362	202	19	λ	λ	X
ejpam-5362	202	20	such	such	ADJ
ejpam-5362	202	21	that	that	SCONJ
ejpam-5362	202	22	∨	∨	NUM
ejpam-5362	202	23	α∈f	α∈f	NOUN
ejpam-5362	202	24	xα	xα	PUNCT
ejpam-5362	203	1	=	=	NOUN
ejpam-5362	203	2	1	1	X
ejpam-5362	203	3	.	.	X
ejpam-5362	204	1	we	we	PRON
ejpam-5362	204	2	get	get	VERB
ejpam-5362	204	3	that	that	PRON
ejpam-5362	204	4	o	o	NOUN
ejpam-5362	205	1	=	=	PUNCT
ejpam-5362	205	2	c	c	X
ejpam-5362	205	3	(	(	PUNCT
ejpam-5362	205	4	∨	∨	NUM
ejpam-5362	205	5	α∈f	α∈f	NOUN
ejpam-5362	205	6	xα	xα	PUNCT
ejpam-5362	205	7	)	)	PUNCT
ejpam-5362	206	1	=	=	PUNCT
ejpam-5362	206	2	∧	∧	NOUN
ejpam-5362	206	3	α∈f	α∈f	NOUN
ejpam-5362	206	4	c(xα	c(xα	NOUN
ejpam-5362	206	5	)	)	PUNCT
ejpam-5362	206	6	,	,	PUNCT
ejpam-5362	206	7	which	which	PRON
ejpam-5362	206	8	contradicts	contradict	VERB
ejpam-5362	206	9	that	that	SCONJ
ejpam-5362	206	10	{	{	PUNCT
ejpam-5362	206	11	c(xα	c(xα	NOUN
ejpam-5362	206	12	)	)	PUNCT
ejpam-5362	206	13	:	:	PUNCT
ejpam-5362	206	14	α	α	PROPN
ejpam-5362	206	15	∈	∈	PROPN
ejpam-5362	206	16	λ	λ	PROPN
ejpam-5362	206	17	}	}	PUNCT
ejpam-5362	206	18	has	have	VERB
ejpam-5362	206	19	the	the	DET
ejpam-5362	206	20	fip	fip	PROPN
ejpam-5362	206	21	.	.	PROPN
ejpam-5362	206	22	remark	remark	PROPN
ejpam-5362	206	23	1	1	NUM
ejpam-5362	206	24	.	.	PUNCT
ejpam-5362	207	1	the	the	DET
ejpam-5362	207	2	converse	converse	NOUN
ejpam-5362	207	3	of	of	ADP
ejpam-5362	207	4	the	the	DET
ejpam-5362	207	5	preceding	precede	VERB
ejpam-5362	207	6	result	result	NOUN
ejpam-5362	207	7	holds	hold	VERB
ejpam-5362	207	8	.	.	PUNCT
ejpam-5362	208	1	we	we	PRON
ejpam-5362	208	2	are	be	AUX
ejpam-5362	208	3	however	however	ADV
ejpam-5362	208	4	interested	interested	ADJ
ejpam-5362	208	5	in	in	ADP
ejpam-5362	208	6	the	the	DET
ejpam-5362	208	7	forward	forward	ADJ
ejpam-5362	208	8	direction	direction	NOUN
ejpam-5362	208	9	,	,	PUNCT
ejpam-5362	208	10	that	that	PRON
ejpam-5362	208	11	is	be	AUX
ejpam-5362	208	12	why	why	SCONJ
ejpam-5362	208	13	we	we	PRON
ejpam-5362	208	14	only	only	ADV
ejpam-5362	208	15	proved	prove	VERB
ejpam-5362	208	16	it	it	PRON
ejpam-5362	208	17	.	.	PUNCT
ejpam-5362	209	1	recall	recall	VERB
ejpam-5362	209	2	from	from	ADP
ejpam-5362	209	3	[	[	X
ejpam-5362	209	4	20	20	NUM
ejpam-5362	209	5	]	]	PUNCT
ejpam-5362	209	6	that	that	SCONJ
ejpam-5362	209	7	a	a	DET
ejpam-5362	209	8	locale	locale	NOUN
ejpam-5362	209	9	l	l	NOUN
ejpam-5362	209	10	is	be	AUX
ejpam-5362	209	11	prefit	prefit	ADJ
ejpam-5362	209	12	if	if	SCONJ
ejpam-5362	209	13	for	for	ADP
ejpam-5362	209	14	each	each	DET
ejpam-5362	209	15	nonzero	nonzero	NOUN
ejpam-5362	210	1	x	x	SYM
ejpam-5362	210	2	∈	∈	ADJ
ejpam-5362	210	3	l	l	NOUN
ejpam-5362	210	4	there	there	PRON
ejpam-5362	210	5	is	be	VERB
ejpam-5362	210	6	a	a	DET
ejpam-5362	210	7	nonzero	nonzero	NOUN
ejpam-5362	210	8	y	y	PROPN
ejpam-5362	210	9	∈	∈	PROPN
ejpam-5362	210	10	l	l	NOUN
ejpam-5362	210	11	such	such	ADJ
ejpam-5362	210	12	that	that	SCONJ
ejpam-5362	210	13	y⋆	y⋆	NOUN
ejpam-5362	210	14	∨	∨	NOUN
ejpam-5362	210	15	x	x	X
ejpam-5362	210	16	=	=	SYM
ejpam-5362	210	17	1	1	X
ejpam-5362	210	18	.	.	PUNCT
ejpam-5362	211	1	a	a	DET
ejpam-5362	211	2	bispace	bispace	NOUN
ejpam-5362	211	3	(	(	PUNCT
ejpam-5362	211	4	x	x	NOUN
ejpam-5362	211	5	,	,	PUNCT
ejpam-5362	211	6	τ1	τ1	NOUN
ejpam-5362	211	7	,	,	PUNCT
ejpam-5362	211	8	τ2	τ2	NOUN
ejpam-5362	211	9	)	)	PUNCT
ejpam-5362	211	10	is	be	AUX
ejpam-5362	211	11	almost	almost	ADV
ejpam-5362	211	12	regular	regular	ADJ
ejpam-5362	211	13	if	if	SCONJ
ejpam-5362	211	14	for	for	ADP
ejpam-5362	211	15	each	each	DET
ejpam-5362	211	16	nonempty	nonempty	ADJ
ejpam-5362	211	17	u	u	NOUN
ejpam-5362	211	18	∈	∈	NOUN
ejpam-5362	211	19	τi	τi	NOUN
ejpam-5362	211	20	,	,	PUNCT
ejpam-5362	211	21	there	there	PRON
ejpam-5362	211	22	is	be	VERB
ejpam-5362	211	23	nonempty	nonempty	X
ejpam-5362	211	24	v	v	ADP
ejpam-5362	211	25	∈	∈	NOUN
ejpam-5362	211	26	τi	τi	ADP
ejpam-5362	211	27	such	such	ADJ
ejpam-5362	211	28	that	that	SCONJ
ejpam-5362	211	29	clτj	clτj	NOUN
ejpam-5362	211	30	(	(	PUNCT
ejpam-5362	211	31	v	v	NOUN
ejpam-5362	211	32	)	)	PUNCT
ejpam-5362	211	33	⊆	⊆	NUM
ejpam-5362	211	34	u	u	NOUN
ejpam-5362	211	35	.	.	PUNCT
ejpam-5362	212	1	since	since	SCONJ
ejpam-5362	212	2	prefitness	prefitness	ADV
ejpam-5362	212	3	is	be	AUX
ejpam-5362	212	4	a	a	DET
ejpam-5362	212	5	localic	localic	ADJ
ejpam-5362	212	6	version	version	NOUN
ejpam-5362	212	7	of	of	ADP
ejpam-5362	212	8	almost	almost	ADV
ejpam-5362	212	9	regularity	regularity	NOUN
ejpam-5362	212	10	in	in	ADP
ejpam-5362	212	11	spaces	space	NOUN
ejpam-5362	212	12	(	(	PUNCT
ejpam-5362	212	13	spaces	space	NOUN
ejpam-5362	212	14	in	in	ADP
ejpam-5362	212	15	which	which	PRON
ejpam-5362	212	16	every	every	DET
ejpam-5362	212	17	nonempty	nonempty	NOUN
ejpam-5362	212	18	open	open	ADJ
ejpam-5362	212	19	set	set	NOUN
ejpam-5362	212	20	contains	contain	VERB
ejpam-5362	212	21	some	some	DET
ejpam-5362	212	22	closure	closure	NOUN
ejpam-5362	212	23	of	of	ADP
ejpam-5362	212	24	a	a	DET
ejpam-5362	212	25	nonempty	nonempty	ADJ
ejpam-5362	212	26	open	open	ADJ
ejpam-5362	212	27	subset	subset	NOUN
ejpam-5362	212	28	)	)	PUNCT
ejpam-5362	212	29	,	,	PUNCT
ejpam-5362	212	30	we	we	PRON
ejpam-5362	212	31	define	define	VERB
ejpam-5362	212	32	a	a	DET
ejpam-5362	212	33	prefit	prefit	ADJ
ejpam-5362	212	34	bilocale	bilocale	NOUN
ejpam-5362	212	35	(	(	PUNCT
ejpam-5362	212	36	l	l	NOUN
ejpam-5362	212	37	,	,	PUNCT
ejpam-5362	212	38	l1	l1	PROPN
ejpam-5362	212	39	,	,	PUNCT
ejpam-5362	212	40	l2	l2	NOUN
ejpam-5362	212	41	)	)	PUNCT
ejpam-5362	212	42	using	use	VERB
ejpam-5362	212	43	the	the	DET
ejpam-5362	212	44	notion	notion	NOUN
ejpam-5362	212	45	of	of	ADP
ejpam-5362	212	46	almost	almost	ADV
ejpam-5362	212	47	regular	regular	ADJ
ejpam-5362	212	48	bispace	bispace	NOUN
ejpam-5362	212	49	as	as	ADP
ejpam-5362	212	50	one	one	NUM
ejpam-5362	212	51	in	in	ADP
ejpam-5362	212	52	which	which	PRON
ejpam-5362	212	53	for	for	ADP
ejpam-5362	212	54	each	each	DET
ejpam-5362	212	55	x	x	PROPN
ejpam-5362	212	56	∈	∈	PROPN
ejpam-5362	212	57	li	li	PROPN
ejpam-5362	212	58	,	,	PUNCT
ejpam-5362	212	59	i	i	PRON
ejpam-5362	212	60	=	=	NOUN
ejpam-5362	212	61	1	1	NUM
ejpam-5362	212	62	,	,	PUNCT
ejpam-5362	212	63	2	2	NUM
ejpam-5362	212	64	,	,	PUNCT
ejpam-5362	212	65	there	there	PRON
ejpam-5362	212	66	is	be	VERB
ejpam-5362	212	67	y	y	PROPN
ejpam-5362	212	68	∈	∈	PROPN
ejpam-5362	212	69	li	li	PROPN
ejpam-5362	213	1	such	such	ADJ
ejpam-5362	213	2	that	that	SCONJ
ejpam-5362	213	3	y•	y•	NOUN
ejpam-5362	213	4	∨	∨	NUM
ejpam-5362	213	5	x	x	SYM
ejpam-5362	213	6	=	=	SYM
ejpam-5362	213	7	1	1	X
ejpam-5362	213	8	.	.	PUNCT
ejpam-5362	213	9	related	relate	VERB
ejpam-5362	213	10	to	to	ADP
ejpam-5362	213	11	prefit	prefit	VERB
ejpam-5362	213	12	bilocales	bilocale	NOUN
ejpam-5362	213	13	,	,	PUNCT
ejpam-5362	213	14	we	we	PRON
ejpam-5362	213	15	give	give	VERB
ejpam-5362	213	16	the	the	DET
ejpam-5362	213	17	following	follow	VERB
ejpam-5362	213	18	definition	definition	NOUN
ejpam-5362	213	19	.	.	PUNCT
ejpam-5362	214	1	definition	definition	NOUN
ejpam-5362	214	2	3	3	NUM
ejpam-5362	214	3	.	.	PUNCT
ejpam-5362	214	4	call	call	VERB
ejpam-5362	214	5	a	a	DET
ejpam-5362	214	6	bilocale	bilocale	NOUN
ejpam-5362	214	7	(	(	PUNCT
ejpam-5362	214	8	l	l	NOUN
ejpam-5362	214	9	,	,	PUNCT
ejpam-5362	214	10	l1	l1	PROPN
ejpam-5362	214	11	,	,	PUNCT
ejpam-5362	214	12	l2	l2	NOUN
ejpam-5362	214	13	)	)	PUNCT
ejpam-5362	215	1	i	i	PRON
ejpam-5362	215	2	-	-	PUNCT
ejpam-5362	215	3	prefit	prefit	VERB
ejpam-5362	215	4	in	in	ADP
ejpam-5362	215	5	case	case	NOUN
ejpam-5362	215	6	for	for	ADP
ejpam-5362	215	7	every	every	DET
ejpam-5362	215	8	nonzero	nonzero	NOUN
ejpam-5362	215	9	x	x	SYM
ejpam-5362	215	10	∈	∈	PROPN
ejpam-5362	215	11	l	l	NOUN
ejpam-5362	215	12	,	,	PUNCT
ejpam-5362	215	13	there	there	PRON
ejpam-5362	215	14	is	be	VERB
ejpam-5362	215	15	a	a	DET
ejpam-5362	215	16	nonzero	nonzero	ADJ
ejpam-5362	215	17	y	y	PROPN
ejpam-5362	215	18	∈	∈	PROPN
ejpam-5362	215	19	li	li	PROPN
ejpam-5362	216	1	such	such	ADJ
ejpam-5362	216	2	that	that	SCONJ
ejpam-5362	216	3	y•	y•	NOUN
ejpam-5362	216	4	∨	∨	NUM
ejpam-5362	216	5	x	x	SYM
ejpam-5362	216	6	=	=	SYM
ejpam-5362	216	7	1	1	X
ejpam-5362	216	8	.	.	PUNCT
ejpam-5362	216	9	m.	m.	NOUN
ejpam-5362	216	10	nxumalo	nxumalo	PROPN
ejpam-5362	216	11	/	/	SYM
ejpam-5362	216	12	eur	eur	PROPN
ejpam-5362	216	13	.	.	PUNCT
ejpam-5362	217	1	j.	j.	PROPN
ejpam-5362	217	2	pure	pure	PROPN
ejpam-5362	217	3	appl	appl	PROPN
ejpam-5362	217	4	.	.	PROPN
ejpam-5362	217	5	math	math	PROPN
ejpam-5362	217	6	,	,	PUNCT
ejpam-5362	217	7	18	18	NUM
ejpam-5362	217	8	(	(	PUNCT
ejpam-5362	217	9	1	1	NUM
ejpam-5362	217	10	)	)	PUNCT
ejpam-5362	217	11	(	(	PUNCT
ejpam-5362	217	12	2025	2025	NUM
ejpam-5362	217	13	)	)	PUNCT
ejpam-5362	217	14	,	,	PUNCT
ejpam-5362	217	15	5362	5362	NUM
ejpam-5362	217	16	9	9	NUM
ejpam-5362	217	17	of	of	ADP
ejpam-5362	217	18	21	21	NUM
ejpam-5362	217	19	we	we	PRON
ejpam-5362	217	20	consider	consider	VERB
ejpam-5362	217	21	some	some	DET
ejpam-5362	217	22	examples	example	NOUN
ejpam-5362	217	23	.	.	PUNCT
ejpam-5362	218	1	example	example	NOUN
ejpam-5362	219	1	2	2	NUM
ejpam-5362	219	2	.	.	PUNCT
ejpam-5362	219	3	(	(	PUNCT
ejpam-5362	219	4	i	i	NOUN
ejpam-5362	219	5	)	)	PUNCT
ejpam-5362	219	6	the	the	DET
ejpam-5362	219	7	bilocale	bilocale	NOUN
ejpam-5362	219	8	of	of	ADP
ejpam-5362	219	9	reals	real	NOUN
ejpam-5362	219	10	is	be	AUX
ejpam-5362	219	11	an	an	DET
ejpam-5362	219	12	example	example	NOUN
ejpam-5362	219	13	of	of	ADP
ejpam-5362	219	14	a	a	DET
ejpam-5362	219	15	prefit	prefit	ADJ
ejpam-5362	219	16	bilocale	bilocale	NOUN
ejpam-5362	219	17	which	which	PRON
ejpam-5362	219	18	is	be	AUX
ejpam-5362	219	19	not	not	PART
ejpam-5362	219	20	i	i	PRON
ejpam-5362	219	21	-	-	PUNCT
ejpam-5362	219	22	prefit	prefit	ADJ
ejpam-5362	219	23	.	.	PUNCT
ejpam-5362	220	1	(	(	PUNCT
ejpam-5362	220	2	ii	ii	NOUN
ejpam-5362	220	3	)	)	PUNCT
ejpam-5362	220	4	for	for	ADP
ejpam-5362	220	5	any	any	DET
ejpam-5362	220	6	almost	almost	ADV
ejpam-5362	220	7	regular	regular	ADJ
ejpam-5362	220	8	bispace	bispace	NOUN
ejpam-5362	220	9	(	(	PUNCT
ejpam-5362	220	10	x	x	NOUN
ejpam-5362	220	11	,	,	PUNCT
ejpam-5362	220	12	τ1	τ1	NOUN
ejpam-5362	220	13	,	,	PUNCT
ejpam-5362	220	14	τ2	τ2	NOUN
ejpam-5362	220	15	)	)	PUNCT
ejpam-5362	220	16	with	with	ADP
ejpam-5362	220	17	τ1	τ1	ADP
ejpam-5362	220	18	⊆	⊆	NUM
ejpam-5362	220	19	τ2	τ2	NOUN
ejpam-5362	220	20	,	,	PUNCT
ejpam-5362	220	21	the	the	DET
ejpam-5362	220	22	bilocale	bilocale	NOUN
ejpam-5362	220	23	(	(	PUNCT
ejpam-5362	220	24	τ1	τ1	PROPN
ejpam-5362	220	25	∨	∨	NUM
ejpam-5362	220	26	τ2	τ2	NOUN
ejpam-5362	220	27	,	,	PUNCT
ejpam-5362	220	28	τ1	τ1	NOUN
ejpam-5362	220	29	,	,	PUNCT
ejpam-5362	220	30	τ2	τ2	NOUN
ejpam-5362	220	31	)	)	PUNCT
ejpam-5362	220	32	is	be	AUX
ejpam-5362	220	33	2	2	NUM
ejpam-5362	220	34	-	-	PUNCT
ejpam-5362	220	35	prefit	prefit	NOUN
ejpam-5362	220	36	.	.	PUNCT
ejpam-5362	221	1	in	in	ADP
ejpam-5362	221	2	particular	particular	ADJ
ejpam-5362	221	3	,	,	PUNCT
ejpam-5362	221	4	if	if	SCONJ
ejpam-5362	221	5	l	l	NOUN
ejpam-5362	221	6	is	be	AUX
ejpam-5362	221	7	prefit	prefit	ADJ
ejpam-5362	221	8	,	,	PUNCT
ejpam-5362	221	9	then	then	ADV
ejpam-5362	221	10	(	(	PUNCT
ejpam-5362	221	11	l	l	NOUN
ejpam-5362	221	12	,	,	PUNCT
ejpam-5362	221	13	l	l	NOUN
ejpam-5362	221	14	,	,	PUNCT
ejpam-5362	221	15	l	l	NOUN
ejpam-5362	221	16	)	)	PUNCT
ejpam-5362	221	17	is	be	AUX
ejpam-5362	221	18	i	i	PRON
ejpam-5362	221	19	-	-	NOUN
ejpam-5362	221	20	prefit	prefit	NOUN
ejpam-5362	222	1	(	(	PUNCT
ejpam-5362	222	2	i	i	NOUN
ejpam-5362	222	3	=	=	NOUN
ejpam-5362	222	4	1	1	NUM
ejpam-5362	222	5	,	,	PUNCT
ejpam-5362	222	6	2	2	NUM
ejpam-5362	222	7	)	)	PUNCT
ejpam-5362	222	8	.	.	PUNCT
ejpam-5362	223	1	(	(	PUNCT
ejpam-5362	223	2	iii	iii	NOUN
ejpam-5362	223	3	)	)	PUNCT
ejpam-5362	223	4	by	by	ADP
ejpam-5362	223	5	[	[	X
ejpam-5362	223	6	21	21	NUM
ejpam-5362	223	7	]	]	X
ejpam-5362	223	8	,	,	PUNCT
ejpam-5362	223	9	a	a	DET
ejpam-5362	223	10	bilocale	bilocale	NOUN
ejpam-5362	223	11	(	(	PUNCT
ejpam-5362	223	12	l	l	NOUN
ejpam-5362	223	13	,	,	PUNCT
ejpam-5362	223	14	l1	l1	PROPN
ejpam-5362	223	15	,	,	PUNCT
ejpam-5362	223	16	l2	l2	NOUN
ejpam-5362	223	17	)	)	PUNCT
ejpam-5362	223	18	is	be	AUX
ejpam-5362	223	19	boolean	boolean	ADJ
ejpam-5362	223	20	if	if	SCONJ
ejpam-5362	223	21	for	for	ADP
ejpam-5362	223	22	each	each	DET
ejpam-5362	223	23	x	x	PROPN
ejpam-5362	223	24	∈	∈	PROPN
ejpam-5362	223	25	li	li	PROPN
ejpam-5362	223	26	,	,	PUNCT
ejpam-5362	223	27	i	i	PRON
ejpam-5362	223	28	=	=	NOUN
ejpam-5362	223	29	1	1	NUM
ejpam-5362	223	30	,	,	PUNCT
ejpam-5362	223	31	2	2	NUM
ejpam-5362	223	32	,	,	PUNCT
ejpam-5362	223	33	there	there	PRON
ejpam-5362	223	34	is	be	VERB
ejpam-5362	223	35	c	c	NOUN
ejpam-5362	223	36	∈	∈	NOUN
ejpam-5362	223	37	lj	lj	INTJ
ejpam-5362	223	38	(	(	PUNCT
ejpam-5362	223	39	i	i	PROPN
ejpam-5362	223	40	̸=	̸=	PROPN
ejpam-5362	223	41	j	j	PROPN
ejpam-5362	223	42	)	)	PUNCT
ejpam-5362	223	43	such	such	ADJ
ejpam-5362	223	44	that	that	SCONJ
ejpam-5362	223	45	x	x	X
ejpam-5362	223	46	∧	∧	NOUN
ejpam-5362	223	47	c	c	NOUN
ejpam-5362	223	48	=	=	SYM
ejpam-5362	223	49	0	0	PROPN
ejpam-5362	223	50	and	and	CCONJ
ejpam-5362	223	51	x	x	SYM
ejpam-5362	223	52	∨	∨	NUM
ejpam-5362	223	53	c	c	NOUN
ejpam-5362	223	54	=	=	SYM
ejpam-5362	223	55	1	1	X
ejpam-5362	223	56	.	.	PUNCT
ejpam-5362	223	57	boolean	boolean	ADJ
ejpam-5362	223	58	and	and	CCONJ
ejpam-5362	223	59	i	i	PRON
ejpam-5362	223	60	-	-	PUNCT
ejpam-5362	223	61	prefit	prefit	PROPN
ejpam-5362	223	62	are	be	AUX
ejpam-5362	223	63	incomparable	incomparable	ADJ
ejpam-5362	223	64	:	:	PUNCT
ejpam-5362	223	65	consider	consider	VERB
ejpam-5362	223	66	the	the	DET
ejpam-5362	223	67	set	set	NOUN
ejpam-5362	223	68	x	x	PUNCT
ejpam-5362	223	69	=	=	X
ejpam-5362	223	70	{	{	PUNCT
ejpam-5362	223	71	a	a	PRON
ejpam-5362	223	72	,	,	PUNCT
ejpam-5362	223	73	b	b	NOUN
ejpam-5362	223	74	,	,	PUNCT
ejpam-5362	223	75	c	c	NOUN
ejpam-5362	223	76	,	,	PUNCT
ejpam-5362	223	77	d	d	NOUN
ejpam-5362	223	78	}	}	PUNCT
ejpam-5362	223	79	endowed	endow	VERB
ejpam-5362	223	80	with	with	ADP
ejpam-5362	223	81	topologies	topology	NOUN
ejpam-5362	223	82	τ1	τ1	NOUN
ejpam-5362	223	83	=	=	SYM
ejpam-5362	223	84	{	{	PUNCT
ejpam-5362	223	85	∅	∅	NOUN
ejpam-5362	223	86	,	,	PUNCT
ejpam-5362	223	87	x	x	X
ejpam-5362	223	88	,	,	PUNCT
ejpam-5362	223	89	{	{	PUNCT
ejpam-5362	223	90	a	a	X
ejpam-5362	223	91	}	}	PUNCT
ejpam-5362	223	92	,	,	PUNCT
ejpam-5362	223	93	{	{	PUNCT
ejpam-5362	223	94	b	b	NOUN
ejpam-5362	223	95	}	}	PUNCT
ejpam-5362	223	96	,	,	PUNCT
ejpam-5362	223	97	{	{	PUNCT
ejpam-5362	223	98	a	a	PRON
ejpam-5362	223	99	,	,	PUNCT
ejpam-5362	223	100	b	b	NOUN
ejpam-5362	223	101	}	}	PUNCT
ejpam-5362	223	102	}	}	PUNCT
ejpam-5362	223	103	and	and	CCONJ
ejpam-5362	223	104	τ2	τ2	NOUN
ejpam-5362	223	105	=	=	SYM
ejpam-5362	223	106	{	{	PUNCT
ejpam-5362	223	107	∅	∅	NOUN
ejpam-5362	223	108	,	,	PUNCT
ejpam-5362	223	109	x	x	X
ejpam-5362	223	110	,	,	PUNCT
ejpam-5362	223	111	{	{	PUNCT
ejpam-5362	223	112	b	b	NOUN
ejpam-5362	223	113	,	,	PUNCT
ejpam-5362	223	114	c	c	NOUN
ejpam-5362	223	115	,	,	PUNCT
ejpam-5362	223	116	d	d	NOUN
ejpam-5362	223	117	}	}	PUNCT
ejpam-5362	223	118	,	,	PUNCT
ejpam-5362	223	119	{	{	PUNCT
ejpam-5362	223	120	a	a	PRON
ejpam-5362	223	121	,	,	PUNCT
ejpam-5362	223	122	c	c	NOUN
ejpam-5362	223	123	,	,	PUNCT
ejpam-5362	223	124	d	d	NOUN
ejpam-5362	223	125	}	}	PUNCT
ejpam-5362	223	126	,	,	PUNCT
ejpam-5362	223	127	{	{	PUNCT
ejpam-5362	223	128	c	c	X
ejpam-5362	223	129	,	,	PUNCT
ejpam-5362	223	130	d	d	NOUN
ejpam-5362	223	131	}	}	PUNCT
ejpam-5362	223	132	}	}	PUNCT
ejpam-5362	223	133	.	.	PUNCT
ejpam-5362	224	1	it	it	PRON
ejpam-5362	224	2	is	be	AUX
ejpam-5362	224	3	clear	clear	ADJ
ejpam-5362	224	4	that	that	SCONJ
ejpam-5362	224	5	(	(	PUNCT
ejpam-5362	224	6	τ1	τ1	PROPN
ejpam-5362	224	7	∨	∨	NUM
ejpam-5362	224	8	τ2	τ2	NOUN
ejpam-5362	224	9	,	,	PUNCT
ejpam-5362	224	10	τ1	τ1	NOUN
ejpam-5362	224	11	,	,	PUNCT
ejpam-5362	224	12	τ2	τ2	NOUN
ejpam-5362	224	13	)	)	PUNCT
ejpam-5362	224	14	is	be	AUX
ejpam-5362	224	15	boolean	boolean	ADJ
ejpam-5362	224	16	.	.	PUNCT
ejpam-5362	225	1	this	this	DET
ejpam-5362	225	2	bilocale	bilocale	NOUN
ejpam-5362	225	3	is	be	AUX
ejpam-5362	225	4	not	not	PART
ejpam-5362	225	5	i	i	PRON
ejpam-5362	225	6	-	-	NOUN
ejpam-5362	225	7	prefit	prefit	NOUN
ejpam-5362	226	1	(	(	PUNCT
ejpam-5362	226	2	i	i	NOUN
ejpam-5362	226	3	=	=	NOUN
ejpam-5362	226	4	1	1	NUM
ejpam-5362	226	5	,	,	PUNCT
ejpam-5362	226	6	2	2	NUM
ejpam-5362	226	7	)	)	PUNCT
ejpam-5362	226	8	since	since	SCONJ
ejpam-5362	226	9	for	for	ADP
ejpam-5362	226	10	the	the	DET
ejpam-5362	226	11	set	set	NOUN
ejpam-5362	226	12	{	{	PUNCT
ejpam-5362	226	13	a	a	DET
ejpam-5362	226	14	}	}	PUNCT
ejpam-5362	226	15	∈	∈	PROPN
ejpam-5362	226	16	τ1	τ1	PROPN
ejpam-5362	226	17	∨	∨	NUM
ejpam-5362	226	18	τ2	τ2	NOUN
ejpam-5362	226	19	,	,	PUNCT
ejpam-5362	226	20	there	there	PRON
ejpam-5362	226	21	is	be	VERB
ejpam-5362	226	22	no	no	DET
ejpam-5362	226	23	nonempty	nonempty	ADJ
ejpam-5362	226	24	u	u	NOUN
ejpam-5362	226	25	∈	∈	NOUN
ejpam-5362	226	26	τi	τi	VERB
ejpam-5362	226	27	satisfying	satisfy	VERB
ejpam-5362	226	28	that	that	SCONJ
ejpam-5362	226	29	u•	u•	NOUN
ejpam-5362	226	30	∨	∨	X
ejpam-5362	226	31	{	{	PUNCT
ejpam-5362	226	32	a	a	NOUN
ejpam-5362	226	33	}	}	PUNCT
ejpam-5362	226	34	=	=	SYM
ejpam-5362	226	35	x.	x.	NOUN
ejpam-5362	226	36	for	for	ADP
ejpam-5362	226	37	any	any	DET
ejpam-5362	226	38	non	non	ADJ
ejpam-5362	226	39	-	-	ADJ
ejpam-5362	226	40	boolean	boolean	ADJ
ejpam-5362	226	41	prefit	prefit	NOUN
ejpam-5362	226	42	locale	locale	PROPN
ejpam-5362	226	43	l	l	PROPN
ejpam-5362	226	44	,	,	PUNCT
ejpam-5362	226	45	(	(	PUNCT
ejpam-5362	226	46	l	l	NOUN
ejpam-5362	226	47	,	,	PUNCT
ejpam-5362	226	48	l	l	NOUN
ejpam-5362	226	49	,	,	PUNCT
ejpam-5362	226	50	l	l	NOUN
ejpam-5362	226	51	)	)	PUNCT
ejpam-5362	226	52	is	be	AUX
ejpam-5362	226	53	an	an	DET
ejpam-5362	226	54	example	example	NOUN
ejpam-5362	226	55	of	of	ADP
ejpam-5362	226	56	a	a	DET
ejpam-5362	226	57	non	non	ADJ
ejpam-5362	226	58	-	-	ADJ
ejpam-5362	226	59	boolean	boolean	ADJ
ejpam-5362	226	60	i	i	NOUN
ejpam-5362	226	61	-	-	NOUN
ejpam-5362	226	62	prefit	prefit	NOUN
ejpam-5362	227	1	(	(	PUNCT
ejpam-5362	227	2	i	i	NOUN
ejpam-5362	227	3	=	=	NOUN
ejpam-5362	227	4	1	1	NUM
ejpam-5362	227	5	,	,	PUNCT
ejpam-5362	227	6	2	2	NUM
ejpam-5362	227	7	)	)	PUNCT
ejpam-5362	227	8	bilocale	bilocale	NOUN
ejpam-5362	227	9	.	.	PUNCT
ejpam-5362	228	1	in	in	ADP
ejpam-5362	228	2	the	the	DET
ejpam-5362	228	3	following	follow	VERB
ejpam-5362	228	4	result	result	NOUN
ejpam-5362	228	5	,	,	PUNCT
ejpam-5362	228	6	we	we	PRON
ejpam-5362	228	7	show	show	VERB
ejpam-5362	228	8	that	that	SCONJ
ejpam-5362	228	9	the	the	DET
ejpam-5362	228	10	class	class	NOUN
ejpam-5362	228	11	of	of	ADP
ejpam-5362	228	12	(	(	PUNCT
ejpam-5362	228	13	i	i	PROPN
ejpam-5362	228	14	,	,	PUNCT
ejpam-5362	228	15	j)-baire	j)-baire	PROPN
ejpam-5362	228	16	bilocales	bilocale	NOUN
ejpam-5362	228	17	contains	contain	VERB
ejpam-5362	228	18	compact	compact	ADJ
ejpam-5362	228	19	i	i	NOUN
ejpam-5362	228	20	-	-	PUNCT
ejpam-5362	228	21	prefit	prefit	NOUN
ejpam-5362	228	22	bilocales	bilocale	NOUN
ejpam-5362	228	23	.	.	PUNCT
ejpam-5362	229	1	proposition	proposition	NOUN
ejpam-5362	229	2	3	3	NUM
ejpam-5362	229	3	.	.	PUNCT
ejpam-5362	230	1	every	every	DET
ejpam-5362	230	2	compact	compact	ADJ
ejpam-5362	230	3	i	i	NOUN
ejpam-5362	230	4	-	-	PUNCT
ejpam-5362	230	5	prefit	prefit	NOUN
ejpam-5362	230	6	bilocale	bilocale	NOUN
ejpam-5362	230	7	is	be	AUX
ejpam-5362	230	8	(	(	PUNCT
ejpam-5362	230	9	i	i	NOUN
ejpam-5362	230	10	,	,	PUNCT
ejpam-5362	230	11	j)-baire	j)-baire	NOUN
ejpam-5362	230	12	.	.	PUNCT
ejpam-5362	231	1	proof	proof	NOUN
ejpam-5362	231	2	.	.	PUNCT
ejpam-5362	232	1	let	let	VERB
ejpam-5362	232	2	(	(	PUNCT
ejpam-5362	232	3	l	l	NOUN
ejpam-5362	232	4	,	,	PUNCT
ejpam-5362	232	5	l1	l1	PROPN
ejpam-5362	232	6	,	,	PUNCT
ejpam-5362	232	7	l2	l2	NOUN
ejpam-5362	232	8	)	)	PUNCT
ejpam-5362	232	9	be	be	AUX
ejpam-5362	232	10	a	a	DET
ejpam-5362	232	11	compact	compact	ADJ
ejpam-5362	232	12	i	i	NOUN
ejpam-5362	232	13	-	-	PUNCT
ejpam-5362	232	14	prefit	prefit	ADJ
ejpam-5362	232	15	bilocale	bilocale	NOUN
ejpam-5362	232	16	and	and	CCONJ
ejpam-5362	232	17	choose	choose	VERB
ejpam-5362	232	18	a	a	DET
ejpam-5362	232	19	collection	collection	NOUN
ejpam-5362	232	20	{	{	PUNCT
ejpam-5362	232	21	o(xn	o(xn	NOUN
ejpam-5362	232	22	)	)	PUNCT
ejpam-5362	232	23	:	:	PUNCT
ejpam-5362	232	24	n	n	X
ejpam-5362	232	25	∈	∈	PROPN
ejpam-5362	232	26	n	n	CCONJ
ejpam-5362	232	27	,	,	PUNCT
ejpam-5362	232	28	xn	xn	PROPN
ejpam-5362	232	29	∈	∈	PROPN
ejpam-5362	232	30	li	li	PROPN
ejpam-5362	232	31	}	}	PUNCT
ejpam-5362	232	32	of	of	ADP
ejpam-5362	232	33	i	i	NOUN
ejpam-5362	232	34	-	-	PUNCT
ejpam-5362	232	35	dense	dense	ADJ
ejpam-5362	232	36	j	j	NOUN
ejpam-5362	232	37	-	-	ADJ
ejpam-5362	232	38	open	open	ADJ
ejpam-5362	232	39	sublocales	sublocale	NOUN
ejpam-5362	232	40	and	and	CCONJ
ejpam-5362	232	41	a	a	DET
ejpam-5362	232	42	non	non	ADJ
ejpam-5362	232	43	-	-	ADJ
ejpam-5362	232	44	void	void	ADJ
ejpam-5362	232	45	j	j	NOUN
ejpam-5362	232	46	-	-	ADJ
ejpam-5362	232	47	open	open	ADJ
ejpam-5362	232	48	sublocale	sublocale	NOUN
ejpam-5362	232	49	o(y	o(y	NOUN
ejpam-5362	232	50	)	)	PUNCT
ejpam-5362	232	51	.	.	PUNCT
ejpam-5362	233	1	then	then	ADV
ejpam-5362	233	2	o(y	o(y	PROPN
ejpam-5362	233	3	)	)	PUNCT
ejpam-5362	233	4	∩	∩	NOUN
ejpam-5362	233	5	o(xn	o(xn	NOUN
ejpam-5362	233	6	)	)	PUNCT
ejpam-5362	233	7	̸=	̸=	PROPN
ejpam-5362	233	8	o	o	NOUN
ejpam-5362	233	9	for	for	ADP
ejpam-5362	233	10	each	each	DET
ejpam-5362	233	11	n	n	PRON
ejpam-5362	233	12	∈	∈	PROPN
ejpam-5362	233	13	n.	n.	NOUN
ejpam-5362	233	14	this	this	PRON
ejpam-5362	233	15	makes	make	VERB
ejpam-5362	233	16	y∧xn	y∧xn	PROPN
ejpam-5362	233	17	̸=	̸=	PROPN
ejpam-5362	233	18	0	0	NUM
ejpam-5362	233	19	.	.	PUNCT
ejpam-5362	234	1	since	since	SCONJ
ejpam-5362	234	2	(	(	PUNCT
ejpam-5362	234	3	l	l	NOUN
ejpam-5362	234	4	,	,	PUNCT
ejpam-5362	234	5	l1	l1	PROPN
ejpam-5362	234	6	,	,	PUNCT
ejpam-5362	234	7	l2	l2	NOUN
ejpam-5362	234	8	)	)	PUNCT
ejpam-5362	234	9	is	be	AUX
ejpam-5362	234	10	i	i	NOUN
ejpam-5362	234	11	-	-	PUNCT
ejpam-5362	234	12	prefit	prefit	ADJ
ejpam-5362	234	13	,	,	PUNCT
ejpam-5362	234	14	there	there	PRON
ejpam-5362	234	15	is	be	VERB
ejpam-5362	234	16	nozero	nozero	NOUN
ejpam-5362	234	17	b1	b1	PROPN
ejpam-5362	234	18	∈	∈	PROPN
ejpam-5362	234	19	li	li	PROPN
ejpam-5362	234	20	such	such	ADJ
ejpam-5362	234	21	that	that	PRON
ejpam-5362	234	22	b•1	b•1	PROPN
ejpam-5362	234	23	∨	∨	NOUN
ejpam-5362	234	24	(	(	PUNCT
ejpam-5362	234	25	y	y	PROPN
ejpam-5362	234	26	∧	∧	PROPN
ejpam-5362	234	27	x1	x1	PROPN
ejpam-5362	234	28	)	)	PUNCT
ejpam-5362	234	29	=	=	SYM
ejpam-5362	235	1	1	1	X
ejpam-5362	235	2	.	.	PUNCT
ejpam-5362	235	3	because	because	SCONJ
ejpam-5362	235	4	o(x2	o(x2	NOUN
ejpam-5362	235	5	)	)	PUNCT
ejpam-5362	235	6	is	be	AUX
ejpam-5362	235	7	i	i	PRON
ejpam-5362	235	8	-	-	PUNCT
ejpam-5362	235	9	dense	dense	ADJ
ejpam-5362	235	10	,	,	PUNCT
ejpam-5362	235	11	we	we	PRON
ejpam-5362	235	12	have	have	VERB
ejpam-5362	235	13	that	that	DET
ejpam-5362	235	14	o(x2	o(x2	NOUN
ejpam-5362	235	15	)	)	PUNCT
ejpam-5362	235	16	∩	∩	NOUN
ejpam-5362	235	17	o(b1	o(b1	VERB
ejpam-5362	235	18	)	)	PUNCT
ejpam-5362	235	19	̸=	̸=	PROPN
ejpam-5362	235	20	o	o	NOUN
ejpam-5362	236	1	so	so	SCONJ
ejpam-5362	236	2	that	that	SCONJ
ejpam-5362	236	3	x2	x2	PROPN
ejpam-5362	236	4	∧	∧	PROPN
ejpam-5362	236	5	b1	b1	NOUN
ejpam-5362	236	6	is	be	AUX
ejpam-5362	236	7	a	a	DET
ejpam-5362	236	8	nonzero	nonzero	ADJ
ejpam-5362	236	9	element	element	NOUN
ejpam-5362	236	10	of	of	ADP
ejpam-5362	236	11	l.	l.	PROPN
ejpam-5362	236	12	by	by	ADP
ejpam-5362	236	13	i	i	PROPN
ejpam-5362	236	14	-	-	PUNCT
ejpam-5362	236	15	prefitness	prefitness	ADV
ejpam-5362	236	16	again	again	ADV
ejpam-5362	236	17	,	,	PUNCT
ejpam-5362	236	18	there	there	PRON
ejpam-5362	236	19	is	be	VERB
ejpam-5362	236	20	nonzero	nonzero	PROPN
ejpam-5362	236	21	b2	b2	PROPN
ejpam-5362	236	22	∈	∈	PROPN
ejpam-5362	236	23	li	li	NOUN
ejpam-5362	237	1	such	such	ADJ
ejpam-5362	237	2	that	that	SCONJ
ejpam-5362	237	3	b•2	b•2	PROPN
ejpam-5362	237	4	∨	∨	PROPN
ejpam-5362	237	5	(	(	PUNCT
ejpam-5362	237	6	x2	x2	PROPN
ejpam-5362	237	7	∧	∧	PROPN
ejpam-5362	237	8	b1	b1	NOUN
ejpam-5362	237	9	)	)	PUNCT
ejpam-5362	237	10	=	=	SYM
ejpam-5362	237	11	1	1	X
ejpam-5362	237	12	.	.	X
ejpam-5362	237	13	continuing	continue	VERB
ejpam-5362	237	14	like	like	ADP
ejpam-5362	237	15	this	this	PRON
ejpam-5362	237	16	for	for	ADP
ejpam-5362	237	17	n	n	NOUN
ejpam-5362	237	18	=	=	SYM
ejpam-5362	237	19	3	3	NUM
ejpam-5362	237	20	,	,	PUNCT
ejpam-5362	237	21	4	4	NUM
ejpam-5362	237	22	,	,	PUNCT
ejpam-5362	237	23	..	..	PUNCT
ejpam-5362	237	24	,	,	PUNCT
ejpam-5362	237	25	we	we	PRON
ejpam-5362	237	26	find	find	VERB
ejpam-5362	237	27	bn	bn	NUM
ejpam-5362	237	28	∈	∈	PROPN
ejpam-5362	237	29	li	li	NOUN
ejpam-5362	237	30	such	such	ADJ
ejpam-5362	237	31	that	that	SCONJ
ejpam-5362	237	32	b•n	b•n	PROPN
ejpam-5362	237	33	∨	∨	PROPN
ejpam-5362	237	34	(	(	PUNCT
ejpam-5362	237	35	xn	xn	PROPN
ejpam-5362	237	36	∧	∧	PROPN
ejpam-5362	237	37	bn−1	bn−1	PROPN
ejpam-5362	237	38	)	)	PUNCT
ejpam-5362	237	39	=	=	SYM
ejpam-5362	238	1	1	1	X
ejpam-5362	238	2	.	.	X
ejpam-5362	238	3	therefore	therefore	ADV
ejpam-5362	238	4	c(b•n	c(b•n	PROPN
ejpam-5362	238	5	)	)	PUNCT
ejpam-5362	238	6	⊆	⊆	NUM
ejpam-5362	238	7	o(xn	o(xn	NUM
ejpam-5362	238	8	)	)	PUNCT
ejpam-5362	238	9	∩	∩	NOUN
ejpam-5362	238	10	o(bn−1	o(bn−1	ADJ
ejpam-5362	238	11	)	)	PUNCT
ejpam-5362	238	12	.	.	PUNCT
ejpam-5362	239	1	since	since	SCONJ
ejpam-5362	239	2	each	each	DET
ejpam-5362	239	3	bn	bn	PROPN
ejpam-5362	239	4	∈	∈	PROPN
ejpam-5362	239	5	li	li	NOUN
ejpam-5362	239	6	,	,	PUNCT
ejpam-5362	239	7	we	we	PRON
ejpam-5362	239	8	have	have	VERB
ejpam-5362	239	9	that	that	DET
ejpam-5362	239	10	c(b•n	c(b•n	PROPN
ejpam-5362	239	11	)	)	PUNCT
ejpam-5362	239	12	=	=	PUNCT
ejpam-5362	239	13	clj(o(bn	clj(o(bn	NOUN
ejpam-5362	239	14	)	)	PUNCT
ejpam-5362	239	15	)	)	PUNCT
ejpam-5362	239	16	.	.	PUNCT
ejpam-5362	240	1	therefore	therefore	ADV
ejpam-5362	240	2	...	...	PUNCT
ejpam-5362	240	3	⊆	⊆	NUM
ejpam-5362	240	4	c(b•3	c(b•3	NOUN
ejpam-5362	240	5	)	)	PUNCT
ejpam-5362	240	6	=	=	SYM
ejpam-5362	240	7	clj(o(b3	clj(o(b3	PROPN
ejpam-5362	240	8	)	)	PUNCT
ejpam-5362	240	9	)	)	PUNCT
ejpam-5362	241	1	⊆	⊆	NUM
ejpam-5362	241	2	c(b•2	c(b•2	NOUN
ejpam-5362	241	3	)	)	PUNCT
ejpam-5362	241	4	=	=	SYM
ejpam-5362	241	5	clj(o(b2	clj(o(b2	PROPN
ejpam-5362	241	6	)	)	PUNCT
ejpam-5362	241	7	)	)	PUNCT
ejpam-5362	242	1	⊆	⊆	NUM
ejpam-5362	242	2	c(b•1	c(b•1	NOUN
ejpam-5362	242	3	)	)	PUNCT
ejpam-5362	242	4	=	=	SYM
ejpam-5362	242	5	clj(o(b1	clj(o(b1	NOUN
ejpam-5362	242	6	)	)	PUNCT
ejpam-5362	242	7	)	)	PUNCT
ejpam-5362	242	8	⊆	⊆	NUM
ejpam-5362	242	9	o(y	o(y	NOUN
ejpam-5362	242	10	)	)	PUNCT
ejpam-5362	242	11	∩	∩	NOUN
ejpam-5362	242	12	o(x1	o(x1	NOUN
ejpam-5362	242	13	)	)	PUNCT
ejpam-5362	242	14	.	.	PUNCT
ejpam-5362	243	1	we	we	PRON
ejpam-5362	243	2	now	now	ADV
ejpam-5362	243	3	have	have	VERB
ejpam-5362	243	4	the	the	DET
ejpam-5362	243	5	decreasing	decrease	VERB
ejpam-5362	243	6	sequence	sequence	NOUN
ejpam-5362	243	7	c(b•1	c(b•1	NOUN
ejpam-5362	243	8	)	)	PUNCT
ejpam-5362	243	9	,	,	PUNCT
ejpam-5362	243	10	c(b	c(b	PROPN
ejpam-5362	243	11	•	•	NOUN
ejpam-5362	243	12	2	2	NUM
ejpam-5362	243	13	)	)	PUNCT
ejpam-5362	243	14	,	,	PUNCT
ejpam-5362	243	15	c(b	c(b	PROPN
ejpam-5362	243	16	•	•	NOUN
ejpam-5362	243	17	3	3	NUM
ejpam-5362	243	18	)	)	PUNCT
ejpam-5362	243	19	,	,	PUNCT
ejpam-5362	243	20	...	...	PUNCT
ejpam-5362	243	21	of	of	ADP
ejpam-5362	243	22	closed	close	VERB
ejpam-5362	243	23	sublocales	sublocale	NOUN
ejpam-5362	243	24	,	,	PUNCT
ejpam-5362	243	25	so	so	SCONJ
ejpam-5362	243	26	that	that	SCONJ
ejpam-5362	243	27	the	the	DET
ejpam-5362	243	28	collection	collection	NOUN
ejpam-5362	243	29	{	{	PUNCT
ejpam-5362	243	30	c(b•n	c(b•n	PROPN
ejpam-5362	243	31	)	)	PUNCT
ejpam-5362	243	32	:	:	PUNCT
ejpam-5362	243	33	n	n	X
ejpam-5362	243	34	∈	∈	PROPN
ejpam-5362	243	35	n	n	CCONJ
ejpam-5362	243	36	}	}	PUNCT
ejpam-5362	243	37	has	have	VERB
ejpam-5362	243	38	the	the	DET
ejpam-5362	243	39	fip	fip	PROPN
ejpam-5362	243	40	.	.	PUNCT
ejpam-5362	244	1	by	by	ADP
ejpam-5362	244	2	compactness	compactness	NOUN
ejpam-5362	244	3	of	of	ADP
ejpam-5362	244	4	(	(	PUNCT
ejpam-5362	244	5	l	l	NOUN
ejpam-5362	244	6	,	,	PUNCT
ejpam-5362	244	7	l1	l1	PROPN
ejpam-5362	244	8	,	,	PUNCT
ejpam-5362	244	9	l2	l2	NOUN
ejpam-5362	244	10	)	)	PUNCT
ejpam-5362	244	11	,	,	PUNCT
ejpam-5362	244	12	∧	∧	PROPN
ejpam-5362	244	13	n∈n	n∈n	PUNCT
ejpam-5362	244	14	c(b•n	c(b•n	PROPN
ejpam-5362	244	15	)	)	PUNCT
ejpam-5362	245	1	̸=	̸=	PROPN
ejpam-5362	245	2	o.	o.	NOUN
ejpam-5362	245	3	because	because	SCONJ
ejpam-5362	245	4	∧	∧	PROPN
ejpam-5362	245	5	n∈n	n∈n	NOUN
ejpam-5362	245	6	c(b•n	c(b•n	PROPN
ejpam-5362	245	7	)	)	PUNCT
ejpam-5362	245	8	⊆	⊆	NUM
ejpam-5362	245	9	o(y	o(y	NOUN
ejpam-5362	245	10	)	)	PUNCT
ejpam-5362	245	11	∩	∩	NOUN
ejpam-5362	245	12	∧	∧	NOUN
ejpam-5362	245	13	n∈n	n∈n	NOUN
ejpam-5362	245	14	o(xn	o(xn	NOUN
ejpam-5362	245	15	)	)	PUNCT
ejpam-5362	245	16	,	,	PUNCT
ejpam-5362	245	17	we	we	PRON
ejpam-5362	245	18	then	then	ADV
ejpam-5362	245	19	have	have	VERB
ejpam-5362	245	20	that	that	DET
ejpam-5362	245	21	o(y	o(y	NOUN
ejpam-5362	245	22	)	)	PUNCT
ejpam-5362	245	23	∩	∩	NOUN
ejpam-5362	245	24	∧	∧	NOUN
ejpam-5362	245	25	n∈n	n∈n	NOUN
ejpam-5362	245	26	o(xn	o(xn	NOUN
ejpam-5362	245	27	)	)	PUNCT
ejpam-5362	245	28	̸=	̸=	PROPN
ejpam-5362	245	29	o	o	NOUN
ejpam-5362	245	30	,	,	PUNCT
ejpam-5362	245	31	making	make	VERB
ejpam-5362	245	32	∧	∧	PROPN
ejpam-5362	245	33	n∈n	n∈n	NOUN
ejpam-5362	245	34	o(xn	o(xn	NOUN
ejpam-5362	245	35	)	)	PUNCT
ejpam-5362	245	36	an	an	DET
ejpam-5362	245	37	i	i	NOUN
ejpam-5362	245	38	-	-	PUNCT
ejpam-5362	245	39	dense	dense	ADJ
ejpam-5362	245	40	sublocale	sublocale	NOUN
ejpam-5362	245	41	.	.	PUNCT
ejpam-5362	246	1	the	the	DET
ejpam-5362	246	2	converse	converse	NOUN
ejpam-5362	246	3	of	of	ADP
ejpam-5362	246	4	proposition	proposition	NOUN
ejpam-5362	246	5	3	3	NUM
ejpam-5362	246	6	is	be	AUX
ejpam-5362	246	7	not	not	PART
ejpam-5362	246	8	always	always	ADV
ejpam-5362	246	9	true	true	ADJ
ejpam-5362	246	10	,	,	PUNCT
ejpam-5362	246	11	as	as	SCONJ
ejpam-5362	246	12	shown	show	VERB
ejpam-5362	246	13	below	below	ADP
ejpam-5362	246	14	.	.	PUNCT
ejpam-5362	247	1	m.	m.	NOUN
ejpam-5362	247	2	nxumalo	nxumalo	PROPN
ejpam-5362	247	3	/	/	SYM
ejpam-5362	247	4	eur	eur	PROPN
ejpam-5362	247	5	.	.	PUNCT
ejpam-5362	248	1	j.	j.	PROPN
ejpam-5362	248	2	pure	pure	PROPN
ejpam-5362	248	3	appl	appl	PROPN
ejpam-5362	248	4	.	.	PROPN
ejpam-5362	248	5	math	math	PROPN
ejpam-5362	248	6	,	,	PUNCT
ejpam-5362	248	7	18	18	NUM
ejpam-5362	248	8	(	(	PUNCT
ejpam-5362	248	9	1	1	NUM
ejpam-5362	248	10	)	)	PUNCT
ejpam-5362	248	11	(	(	PUNCT
ejpam-5362	248	12	2025	2025	NUM
ejpam-5362	248	13	)	)	PUNCT
ejpam-5362	248	14	,	,	PUNCT
ejpam-5362	248	15	5362	5362	NUM
ejpam-5362	248	16	10	10	NUM
ejpam-5362	248	17	of	of	ADP
ejpam-5362	248	18	21	21	NUM
ejpam-5362	248	19	example	example	NOUN
ejpam-5362	248	20	3	3	NUM
ejpam-5362	248	21	.	.	X
ejpam-5362	249	1	for	for	ADP
ejpam-5362	249	2	the	the	DET
ejpam-5362	249	3	bispace	bispace	NOUN
ejpam-5362	249	4	(	(	PUNCT
ejpam-5362	249	5	n	n	CCONJ
ejpam-5362	249	6	,	,	PUNCT
ejpam-5362	249	7	τd	τd	INTJ
ejpam-5362	249	8	,	,	PUNCT
ejpam-5362	249	9	τcf	τcf	PROPN
ejpam-5362	249	10	)	)	PUNCT
ejpam-5362	249	11	,	,	PUNCT
ejpam-5362	249	12	(	(	PUNCT
ejpam-5362	249	13	τd	τd	ADV
ejpam-5362	249	14	∨	∨	NUM
ejpam-5362	249	15	τcf	τcf	NOUN
ejpam-5362	249	16	=	=	NOUN
ejpam-5362	249	17	τd	τd	NOUN
ejpam-5362	249	18	,	,	PUNCT
ejpam-5362	249	19	τd	τd	ADV
ejpam-5362	249	20	,	,	PUNCT
ejpam-5362	249	21	τcf	τcf	PROPN
ejpam-5362	249	22	)	)	PUNCT
ejpam-5362	249	23	is	be	AUX
ejpam-5362	249	24	(	(	PUNCT
ejpam-5362	249	25	τd	τd	INTJ
ejpam-5362	249	26	,	,	PUNCT
ejpam-5362	249	27	τcf	τcf	ADJ
ejpam-5362	249	28	)	)	PUNCT
ejpam-5362	249	29	-baire	-baire	PROPN
ejpam-5362	249	30	but	but	CCONJ
ejpam-5362	249	31	not	not	PART
ejpam-5362	249	32	compact	compact	ADJ
ejpam-5362	249	33	.	.	PUNCT
ejpam-5362	250	1	its	its	PRON
ejpam-5362	250	2	(	(	PUNCT
ejpam-5362	250	3	τd	τd	INTJ
ejpam-5362	250	4	,	,	PUNCT
ejpam-5362	250	5	τcf	τcf	ADJ
ejpam-5362	250	6	)	)	PUNCT
ejpam-5362	250	7	-baireness	-baireness	NOUN
ejpam-5362	250	8	follows	follow	VERB
ejpam-5362	250	9	since	since	SCONJ
ejpam-5362	250	10	n	n	NUM
ejpam-5362	250	11	is	be	AUX
ejpam-5362	250	12	the	the	DET
ejpam-5362	250	13	only	only	ADJ
ejpam-5362	250	14	τd	τd	ADJ
ejpam-5362	250	15	-	-	PUNCT
ejpam-5362	250	16	dense	dense	ADJ
ejpam-5362	250	17	member	member	NOUN
ejpam-5362	250	18	of	of	ADP
ejpam-5362	250	19	τcf	τcf	PROPN
ejpam-5362	250	20	.	.	PUNCT
ejpam-5362	251	1	recall	recall	VERB
ejpam-5362	251	2	that	that	PRON
ejpam-5362	251	3	for	for	ADP
ejpam-5362	251	4	any	any	PRON
ejpam-5362	251	5	onto	onto	ADP
ejpam-5362	251	6	frame	frame	NOUN
ejpam-5362	251	7	homomorphism	homomorphism	PROPN
ejpam-5362	251	8	h	h	NOUN
ejpam-5362	251	9	:	:	PUNCT
ejpam-5362	251	10	m	m	VERB
ejpam-5362	251	11	→	→	SYM
ejpam-5362	251	12	l	l	NOUN
ejpam-5362	251	13	,	,	PUNCT
ejpam-5362	251	14	h∗	h∗	NOUN
ejpam-5362	251	15	:	:	PUNCT
ejpam-5362	251	16	l	l	X
ejpam-5362	251	17	→	→	SYM
ejpam-5362	251	18	h∗[l	h∗[l	PROPN
ejpam-5362	251	19	]	]	PUNCT
ejpam-5362	251	20	is	be	AUX
ejpam-5362	251	21	a	a	DET
ejpam-5362	251	22	frame	frame	NOUN
ejpam-5362	251	23	isomorphism	isomorphism	NOUN
ejpam-5362	251	24	.	.	PUNCT
ejpam-5362	252	1	if	if	SCONJ
ejpam-5362	252	2	h	h	NOUN
ejpam-5362	252	3	is	be	AUX
ejpam-5362	252	4	further	far	ADV
ejpam-5362	252	5	dense	dense	ADJ
ejpam-5362	252	6	,	,	PUNCT
ejpam-5362	252	7	then	then	ADV
ejpam-5362	252	8	h∗(0	h∗(0	NOUN
ejpam-5362	252	9	)	)	PUNCT
ejpam-5362	253	1	=	=	SYM
ejpam-5362	253	2	0	0	X
ejpam-5362	253	3	.	.	PUNCT
ejpam-5362	254	1	lemma	lemma	PROPN
ejpam-5362	254	2	2	2	X
ejpam-5362	254	3	.	.	PUNCT
ejpam-5362	255	1	let	let	VERB
ejpam-5362	255	2	h	h	NOUN
ejpam-5362	255	3	:	:	PUNCT
ejpam-5362	255	4	(	(	PUNCT
ejpam-5362	255	5	m	m	NOUN
ejpam-5362	255	6	,	,	PUNCT
ejpam-5362	255	7	m1,m2	m1,m2	PROPN
ejpam-5362	255	8	)	)	PUNCT
ejpam-5362	255	9	→	→	SYM
ejpam-5362	255	10	(	(	PUNCT
ejpam-5362	255	11	l	l	NOUN
ejpam-5362	255	12	,	,	PUNCT
ejpam-5362	255	13	l1	l1	PROPN
ejpam-5362	255	14	,	,	PUNCT
ejpam-5362	255	15	l2	l2	NOUN
ejpam-5362	255	16	)	)	PUNCT
ejpam-5362	255	17	be	be	AUX
ejpam-5362	255	18	a	a	DET
ejpam-5362	255	19	dense	dense	ADJ
ejpam-5362	255	20	and	and	CCONJ
ejpam-5362	255	21	onto	onto	ADP
ejpam-5362	255	22	biframe	biframe	NOUN
ejpam-5362	255	23	map	map	NOUN
ejpam-5362	255	24	.	.	PUNCT
ejpam-5362	256	1	if	if	SCONJ
ejpam-5362	256	2	x	x	SYM
ejpam-5362	256	3	∈	∈	PROPN
ejpam-5362	256	4	li	li	PROPN
ejpam-5362	256	5	is	be	AUX
ejpam-5362	256	6	j	j	NOUN
ejpam-5362	256	7	-	-	PUNCT
ejpam-5362	256	8	dense	dense	ADJ
ejpam-5362	256	9	,	,	PUNCT
ejpam-5362	256	10	then	then	ADV
ejpam-5362	256	11	h∗(x	h∗(x	PROPN
ejpam-5362	256	12	)	)	PUNCT
ejpam-5362	256	13	∧	∧	PROPN
ejpam-5362	256	14	a	a	DET
ejpam-5362	256	15	̸=	̸=	PROPN
ejpam-5362	256	16	0	0	NUM
ejpam-5362	256	17	whenever	whenever	SCONJ
ejpam-5362	256	18	a	a	DET
ejpam-5362	256	19	∈	∈	PROPN
ejpam-5362	256	20	mi	mi	PROPN
ejpam-5362	256	21	is	be	AUX
ejpam-5362	256	22	nonzero	nonzero	NOUN
ejpam-5362	256	23	.	.	PUNCT
ejpam-5362	257	1	proof	proof	NOUN
ejpam-5362	257	2	.	.	PUNCT
ejpam-5362	258	1	let	let	VERB
ejpam-5362	258	2	a	a	DET
ejpam-5362	258	3	∈	∈	PROPN
ejpam-5362	258	4	mi	mi	NOUN
ejpam-5362	258	5	be	be	AUX
ejpam-5362	258	6	nonzero	nonzero	NOUN
ejpam-5362	258	7	such	such	ADJ
ejpam-5362	258	8	that	that	SCONJ
ejpam-5362	258	9	a	a	DET
ejpam-5362	258	10	∧	∧	PROPN
ejpam-5362	258	11	h∗(x	h∗(x	NOUN
ejpam-5362	258	12	)	)	PUNCT
ejpam-5362	258	13	=	=	SYM
ejpam-5362	259	1	0	0	X
ejpam-5362	259	2	.	.	PUNCT
ejpam-5362	260	1	then	then	ADV
ejpam-5362	260	2	0	0	X
ejpam-5362	260	3	=	=	SYM
ejpam-5362	260	4	h(a	h(a	PROPN
ejpam-5362	260	5	)	)	PUNCT
ejpam-5362	260	6	∧	∧	PROPN
ejpam-5362	260	7	h(h∗(x	h(h∗(x	PROPN
ejpam-5362	260	8	)	)	PUNCT
ejpam-5362	260	9	)	)	PUNCT
ejpam-5362	261	1	=	=	SYM
ejpam-5362	261	2	h(a	h(a	PROPN
ejpam-5362	261	3	)	)	PUNCT
ejpam-5362	262	1	∧	∧	NOUN
ejpam-5362	262	2	x.	x.	NOUN
ejpam-5362	262	3	since	since	SCONJ
ejpam-5362	262	4	h[mi	h[mi	PROPN
ejpam-5362	262	5	]	]	PUNCT
ejpam-5362	262	6	⊆	⊆	NUM
ejpam-5362	262	7	li	li	PROPN
ejpam-5362	262	8	,	,	PUNCT
ejpam-5362	262	9	h(a	h(a	PROPN
ejpam-5362	262	10	)	)	PUNCT
ejpam-5362	263	1	∈	∈	PROPN
ejpam-5362	263	2	li	li	PROPN
ejpam-5362	264	1	so	so	SCONJ
ejpam-5362	264	2	that	that	PRON
ejpam-5362	264	3	h(a	h(a	PROPN
ejpam-5362	264	4	)	)	PUNCT
ejpam-5362	265	1	=	=	PUNCT
ejpam-5362	265	2	0	0	X
ejpam-5362	265	3	.	.	PUNCT
ejpam-5362	266	1	therefore	therefore	ADV
ejpam-5362	266	2	a	a	DET
ejpam-5362	266	3	≤	≤	NUM
ejpam-5362	266	4	h∗(h(a	h∗(h(a	NOUN
ejpam-5362	266	5	)	)	PUNCT
ejpam-5362	266	6	)	)	PUNCT
ejpam-5362	267	1	=	=	PUNCT
ejpam-5362	267	2	h∗(0	h∗(0	NOUN
ejpam-5362	267	3	)	)	PUNCT
ejpam-5362	267	4	=	=	SYM
ejpam-5362	268	1	0	0	X
ejpam-5362	268	2	.	.	PUNCT
ejpam-5362	268	3	proposition	proposition	NOUN
ejpam-5362	268	4	4	4	NUM
ejpam-5362	268	5	.	.	PUNCT
ejpam-5362	269	1	let	let	VERB
ejpam-5362	269	2	(	(	PUNCT
ejpam-5362	269	3	l	l	NOUN
ejpam-5362	269	4	,	,	PUNCT
ejpam-5362	269	5	l1	l1	PROPN
ejpam-5362	269	6	,	,	PUNCT
ejpam-5362	269	7	l2	l2	NOUN
ejpam-5362	269	8	)	)	PUNCT
ejpam-5362	269	9	be	be	AUX
ejpam-5362	269	10	a	a	DET
ejpam-5362	269	11	bilocale	bilocale	NOUN
ejpam-5362	269	12	.	.	PUNCT
ejpam-5362	270	1	if	if	SCONJ
ejpam-5362	270	2	there	there	PRON
ejpam-5362	270	3	is	be	VERB
ejpam-5362	270	4	a	a	DET
ejpam-5362	270	5	dense	dense	ADJ
ejpam-5362	270	6	onto	onto	ADP
ejpam-5362	270	7	biframe	biframe	NOUN
ejpam-5362	270	8	map	map	NOUN
ejpam-5362	270	9	h	h	NOUN
ejpam-5362	270	10	:	:	PUNCT
ejpam-5362	270	11	(	(	PUNCT
ejpam-5362	270	12	m	m	NOUN
ejpam-5362	270	13	,	,	PUNCT
ejpam-5362	270	14	m1,m2	m1,m2	PROPN
ejpam-5362	270	15	)	)	PUNCT
ejpam-5362	270	16	→	→	SYM
ejpam-5362	270	17	(	(	PUNCT
ejpam-5362	270	18	l	l	NOUN
ejpam-5362	270	19	,	,	PUNCT
ejpam-5362	270	20	l1	l1	PROPN
ejpam-5362	270	21	,	,	PUNCT
ejpam-5362	270	22	l2	l2	NOUN
ejpam-5362	270	23	)	)	PUNCT
ejpam-5362	270	24	from	from	ADP
ejpam-5362	270	25	an	an	DET
ejpam-5362	270	26	(	(	PUNCT
ejpam-5362	270	27	i	i	NOUN
ejpam-5362	270	28	,	,	PUNCT
ejpam-5362	270	29	j)-baire	j)-baire	NOUN
ejpam-5362	270	30	bilocale	bilocale	NOUN
ejpam-5362	270	31	(	(	PUNCT
ejpam-5362	270	32	m	m	PROPN
ejpam-5362	270	33	,	,	PUNCT
ejpam-5362	270	34	m1,m2	m1,m2	PROPN
ejpam-5362	270	35	)	)	PUNCT
ejpam-5362	270	36	with	with	ADP
ejpam-5362	270	37	which	which	PRON
ejpam-5362	270	38	h∗[l	h∗[l	NOUN
ejpam-5362	270	39	]	]	PUNCT
ejpam-5362	270	40	is	be	AUX
ejpam-5362	270	41	i	i	PROPN
ejpam-5362	270	42	-	-	PUNCT
ejpam-5362	270	43	gδ	gδ	NOUN
ejpam-5362	270	44	-	-	PUNCT
ejpam-5362	270	45	dense	dense	NOUN
ejpam-5362	270	46	in	in	ADP
ejpam-5362	270	47	m	m	PROPN
ejpam-5362	270	48	,	,	PUNCT
ejpam-5362	270	49	then	then	ADV
ejpam-5362	270	50	(	(	PUNCT
ejpam-5362	270	51	l	l	NOUN
ejpam-5362	270	52	,	,	PUNCT
ejpam-5362	270	53	l1	l1	PROPN
ejpam-5362	270	54	,	,	PUNCT
ejpam-5362	270	55	l2	l2	NOUN
ejpam-5362	270	56	)	)	PUNCT
ejpam-5362	270	57	is	be	AUX
ejpam-5362	270	58	(	(	PUNCT
ejpam-5362	270	59	i	i	NOUN
ejpam-5362	270	60	,	,	PUNCT
ejpam-5362	270	61	j)-baire	j)-baire	NOUN
ejpam-5362	270	62	.	.	PUNCT
ejpam-5362	271	1	proof	proof	NOUN
ejpam-5362	271	2	.	.	PUNCT
ejpam-5362	272	1	suppose	suppose	VERB
ejpam-5362	272	2	that	that	SCONJ
ejpam-5362	272	3	the	the	DET
ejpam-5362	272	4	hypothesized	hypothesized	ADJ
ejpam-5362	272	5	statement	statement	NOUN
ejpam-5362	272	6	is	be	AUX
ejpam-5362	272	7	true	true	ADJ
ejpam-5362	272	8	and	and	CCONJ
ejpam-5362	272	9	let	let	VERB
ejpam-5362	272	10	{	{	PUNCT
ejpam-5362	272	11	o(xn	o(xn	NUM
ejpam-5362	272	12	)	)	PUNCT
ejpam-5362	272	13	:	:	PUNCT
ejpam-5362	272	14	n	n	CCONJ
ejpam-5362	272	15	∈	∈	PROPN
ejpam-5362	272	16	n	n	CCONJ
ejpam-5362	272	17	}	}	PUNCT
ejpam-5362	272	18	be	be	AUX
ejpam-5362	272	19	a	a	DET
ejpam-5362	272	20	collection	collection	NOUN
ejpam-5362	272	21	of	of	ADP
ejpam-5362	272	22	i	i	NOUN
ejpam-5362	272	23	-	-	PUNCT
ejpam-5362	272	24	dense	dense	ADJ
ejpam-5362	272	25	j	j	NOUN
ejpam-5362	272	26	-	-	ADJ
ejpam-5362	272	27	open	open	ADJ
ejpam-5362	272	28	sublocales	sublocale	NOUN
ejpam-5362	272	29	of	of	ADP
ejpam-5362	272	30	l.	l.	PROPN
ejpam-5362	272	31	now	now	ADV
ejpam-5362	272	32	,	,	PUNCT
ejpam-5362	272	33	if	if	SCONJ
ejpam-5362	272	34	o(y	o(y	NOUN
ejpam-5362	272	35	)	)	PUNCT
ejpam-5362	272	36	∩	∩	NOUN
ejpam-5362	272	37	(	(	PUNCT
ejpam-5362	272	38	∧	∧	PROPN
ejpam-5362	272	39	n∈n	n∈n	NOUN
ejpam-5362	272	40	o(xn	o(xn	NUM
ejpam-5362	272	41	)	)	PUNCT
ejpam-5362	272	42	)	)	PUNCT
ejpam-5362	273	1	=	=	PUNCT
ejpam-5362	273	2	o	o	NOUN
ejpam-5362	273	3	for	for	ADP
ejpam-5362	273	4	some	some	DET
ejpam-5362	273	5	i	i	PRON
ejpam-5362	273	6	-	-	PUNCT
ejpam-5362	273	7	open	open	ADJ
ejpam-5362	273	8	sublocale	sublocale	NOUN
ejpam-5362	273	9	o(y	o(y	NOUN
ejpam-5362	273	10	)	)	PUNCT
ejpam-5362	273	11	of	of	ADP
ejpam-5362	273	12	l	l	NOUN
ejpam-5362	273	13	,	,	PUNCT
ejpam-5362	273	14	then	then	ADV
ejpam-5362	273	15	o	o	X
ejpam-5362	273	16	=	=	PUNCT
ejpam-5362	273	17	h∗[o(y	h∗[o(y	ADJ
ejpam-5362	273	18	)	)	PUNCT
ejpam-5362	273	19	]	]	PUNCT
ejpam-5362	273	20	∩	∩	PROPN
ejpam-5362	273	21	h∗	h∗	PROPN
ejpam-5362	274	1	[	[	X
ejpam-5362	274	2	∧	∧	PROPN
ejpam-5362	274	3	n∈n	n∈n	ADV
ejpam-5362	274	4	o(xn	o(xn	NOUN
ejpam-5362	274	5	)	)	PUNCT
ejpam-5362	274	6	]	]	PUNCT
ejpam-5362	275	1	=	=	PUNCT
ejpam-5362	275	2	h∗[o(y	h∗[o(y	X
ejpam-5362	275	3	)	)	PUNCT
ejpam-5362	275	4	]	]	PUNCT
ejpam-5362	276	1	∩	∩	NOUN
ejpam-5362	276	2	(	(	PUNCT
ejpam-5362	276	3	∧	∧	PROPN
ejpam-5362	276	4	n∈n	n∈n	NOUN
ejpam-5362	276	5	h∗[o(xn	h∗[o(xn	NUM
ejpam-5362	276	6	)	)	PUNCT
ejpam-5362	276	7	]	]	PUNCT
ejpam-5362	276	8	)	)	PUNCT
ejpam-5362	276	9	where	where	SCONJ
ejpam-5362	276	10	the	the	DET
ejpam-5362	276	11	first	first	ADJ
ejpam-5362	276	12	equality	equality	NOUN
ejpam-5362	276	13	follows	follow	VERB
ejpam-5362	276	14	since	since	SCONJ
ejpam-5362	276	15	h∗[o	h∗[o	NOUN
ejpam-5362	276	16	]	]	X
ejpam-5362	276	17	=	=	SYM
ejpam-5362	276	18	o	o	NOUN
ejpam-5362	276	19	and	and	CCONJ
ejpam-5362	276	20	h∗	h∗	PROPN
ejpam-5362	276	21	is	be	AUX
ejpam-5362	276	22	injective	injective	ADJ
ejpam-5362	276	23	,	,	PUNCT
ejpam-5362	276	24	and	and	CCONJ
ejpam-5362	276	25	the	the	DET
ejpam-5362	276	26	second	second	ADJ
ejpam-5362	276	27	equality	equality	NOUN
ejpam-5362	276	28	follows	follow	VERB
ejpam-5362	276	29	since	since	SCONJ
ejpam-5362	276	30	the	the	DET
ejpam-5362	276	31	total	total	ADJ
ejpam-5362	276	32	part	part	NOUN
ejpam-5362	276	33	h∗	h∗	NOUN
ejpam-5362	276	34	:	:	PUNCT
ejpam-5362	276	35	l	l	X
ejpam-5362	276	36	→	→	PUNCT
ejpam-5362	276	37	m	m	NOUN
ejpam-5362	276	38	is	be	AUX
ejpam-5362	276	39	a	a	DET
ejpam-5362	276	40	right	right	ADJ
ejpam-5362	276	41	adjoint	adjoint	NOUN
ejpam-5362	276	42	.	.	PUNCT
ejpam-5362	277	1	by	by	ADP
ejpam-5362	277	2	virtue	virtue	NOUN
ejpam-5362	277	3	of	of	ADP
ejpam-5362	277	4	h∗	h∗	PROPN
ejpam-5362	277	5	:	:	PUNCT
ejpam-5362	277	6	l	l	X
ejpam-5362	277	7	→	→	SYM
ejpam-5362	277	8	h∗[l	h∗[l	PROPN
ejpam-5362	277	9	]	]	PUNCT
ejpam-5362	277	10	being	be	AUX
ejpam-5362	277	11	a	a	DET
ejpam-5362	277	12	frame	frame	NOUN
ejpam-5362	277	13	isomorphism	isomorphism	NOUN
ejpam-5362	277	14	and	and	CCONJ
ejpam-5362	277	15	hence	hence	ADV
ejpam-5362	277	16	open	open	ADJ
ejpam-5362	277	17	,	,	PUNCT
ejpam-5362	277	18	we	we	PRON
ejpam-5362	277	19	get	get	VERB
ejpam-5362	277	20	that	that	DET
ejpam-5362	277	21	oh∗[l](h∗(y	oh∗[l](h∗(y	PROPN
ejpam-5362	277	22	)	)	PUNCT
ejpam-5362	277	23	)	)	PUNCT
ejpam-5362	277	24	∩	∩	NOUN
ejpam-5362	277	25	(	(	PUNCT
ejpam-5362	277	26	∧	∧	PROPN
ejpam-5362	277	27	n∈n	n∈n	NOUN
ejpam-5362	277	28	oh∗[l](h∗(xn	oh∗[l](h∗(xn	NUM
ejpam-5362	277	29	)	)	PUNCT
ejpam-5362	277	30	)	)	PUNCT
ejpam-5362	277	31	)	)	PUNCT
ejpam-5362	278	1	=	=	SYM
ejpam-5362	278	2	o.	o.	INTJ
ejpam-5362	278	3	for	for	ADP
ejpam-5362	278	4	each	each	DET
ejpam-5362	278	5	n	n	PRON
ejpam-5362	278	6	∈	∈	PROPN
ejpam-5362	278	7	n	n	CCONJ
ejpam-5362	278	8	,	,	PUNCT
ejpam-5362	278	9	h∗(xn	h∗(xn	PROPN
ejpam-5362	278	10	)	)	PUNCT
ejpam-5362	278	11	=	=	SYM
ejpam-5362	278	12	h∗(h(an	h∗(h(an	NOUN
ejpam-5362	278	13	)	)	PUNCT
ejpam-5362	278	14	)	)	PUNCT
ejpam-5362	278	15	for	for	ADP
ejpam-5362	278	16	some	some	DET
ejpam-5362	278	17	an	an	DET
ejpam-5362	278	18	∈	∈	PROPN
ejpam-5362	278	19	mi	mi	PROPN
ejpam-5362	278	20	.	.	PROPN
ejpam-5362	278	21	therefore	therefore	ADV
ejpam-5362	278	22	o	o	X
ejpam-5362	278	23	=	=	PUNCT
ejpam-5362	278	24	oh∗[l](h∗(y	oh∗[l](h∗(y	PROPN
ejpam-5362	278	25	)	)	PUNCT
ejpam-5362	278	26	)	)	PUNCT
ejpam-5362	278	27	∩	∩	NOUN
ejpam-5362	278	28	(	(	PUNCT
ejpam-5362	278	29	∧	∧	PROPN
ejpam-5362	278	30	n∈n	n∈n	NOUN
ejpam-5362	278	31	oh∗[l](h∗(h(an	oh∗[l](h∗(h(an	NUM
ejpam-5362	278	32	)	)	PUNCT
ejpam-5362	278	33	)	)	PUNCT
ejpam-5362	278	34	)	)	PUNCT
ejpam-5362	278	35	)	)	PUNCT
ejpam-5362	279	1	=	=	PUNCT
ejpam-5362	279	2	h∗[l	h∗[l	ADJ
ejpam-5362	279	3	]	]	PUNCT
ejpam-5362	279	4	∩	∩	X
ejpam-5362	279	5	o(h∗(y	o(h∗(y	NUM
ejpam-5362	279	6	)	)	PUNCT
ejpam-5362	279	7	)	)	PUNCT
ejpam-5362	279	8	∩	∩	NOUN
ejpam-5362	279	9	(	(	PUNCT
ejpam-5362	279	10	∧	∧	PROPN
ejpam-5362	279	11	n∈n	n∈n	NOUN
ejpam-5362	279	12	(	(	PUNCT
ejpam-5362	279	13	h∗[l	h∗[l	PROPN
ejpam-5362	279	14	]	]	PUNCT
ejpam-5362	279	15	∩	∩	NOUN
ejpam-5362	279	16	o(h∗(h(an	o(h∗(h(an	PROPN
ejpam-5362	279	17	)	)	PUNCT
ejpam-5362	279	18	)	)	PUNCT
ejpam-5362	279	19	)	)	PUNCT
ejpam-5362	279	20	)	)	PUNCT
ejpam-5362	279	21	)	)	PUNCT
ejpam-5362	280	1	=	=	PUNCT
ejpam-5362	280	2	h∗[l	h∗[l	ADJ
ejpam-5362	280	3	]	]	PUNCT
ejpam-5362	280	4	∩	∩	X
ejpam-5362	280	5	o(h∗(y	o(h∗(y	NUM
ejpam-5362	280	6	)	)	PUNCT
ejpam-5362	280	7	)	)	PUNCT
ejpam-5362	280	8	∩	∩	NOUN
ejpam-5362	280	9	(	(	PUNCT
ejpam-5362	280	10	∧	∧	PROPN
ejpam-5362	280	11	n∈n	n∈n	VERB
ejpam-5362	280	12	o(h∗(h(an	o(h∗(h(an	PROPN
ejpam-5362	280	13	)	)	PUNCT
ejpam-5362	280	14	)	)	PUNCT
ejpam-5362	280	15	)	)	PUNCT
ejpam-5362	280	16	)	)	PUNCT
ejpam-5362	280	17	⊇	⊇	PROPN
ejpam-5362	280	18	h∗[l	h∗[l	PROPN
ejpam-5362	280	19	]	]	PUNCT
ejpam-5362	280	20	∩	∩	X
ejpam-5362	280	21	o(h∗(y	o(h∗(y	NUM
ejpam-5362	280	22	)	)	PUNCT
ejpam-5362	280	23	)	)	PUNCT
ejpam-5362	280	24	∩	∩	NOUN
ejpam-5362	280	25	(	(	PUNCT
ejpam-5362	280	26	∧	∧	PROPN
ejpam-5362	280	27	n∈n	n∈n	NOUN
ejpam-5362	280	28	o(an	o(an	NUM
ejpam-5362	280	29	)	)	PUNCT
ejpam-5362	280	30	)	)	PUNCT
ejpam-5362	280	31	.	.	PUNCT
ejpam-5362	281	1	m.	m.	NOUN
ejpam-5362	281	2	nxumalo	nxumalo	PROPN
ejpam-5362	281	3	/	/	SYM
ejpam-5362	281	4	eur	eur	PROPN
ejpam-5362	281	5	.	.	PUNCT
ejpam-5362	282	1	j.	j.	PROPN
ejpam-5362	282	2	pure	pure	PROPN
ejpam-5362	282	3	appl	appl	PROPN
ejpam-5362	282	4	.	.	PROPN
ejpam-5362	282	5	math	math	PROPN
ejpam-5362	282	6	,	,	PUNCT
ejpam-5362	282	7	18	18	NUM
ejpam-5362	282	8	(	(	PUNCT
ejpam-5362	282	9	1	1	NUM
ejpam-5362	282	10	)	)	PUNCT
ejpam-5362	282	11	(	(	PUNCT
ejpam-5362	282	12	2025	2025	NUM
ejpam-5362	282	13	)	)	PUNCT
ejpam-5362	282	14	,	,	PUNCT
ejpam-5362	282	15	5362	5362	NUM
ejpam-5362	282	16	11	11	NUM
ejpam-5362	282	17	of	of	ADP
ejpam-5362	282	18	21	21	NUM
ejpam-5362	282	19	since	since	SCONJ
ejpam-5362	282	20	i	i	PRON
ejpam-5362	282	21	-	-	PUNCT
ejpam-5362	282	22	gδ	gδ	NOUN
ejpam-5362	282	23	-	-	PUNCT
ejpam-5362	282	24	dense	dense	ADJ
ejpam-5362	282	25	sublocales	sublocale	NOUN
ejpam-5362	282	26	are	be	AUX
ejpam-5362	282	27	dense	dense	ADJ
ejpam-5362	282	28	,	,	PUNCT
ejpam-5362	282	29	h∗[l	h∗[l	PROPN
ejpam-5362	282	30	]	]	PUNCT
ejpam-5362	282	31	is	be	AUX
ejpam-5362	282	32	a	a	DET
ejpam-5362	282	33	dense	dense	ADJ
ejpam-5362	282	34	sublocale	sublocale	NOUN
ejpam-5362	282	35	of	of	ADP
ejpam-5362	282	36	m	m	PROPN
ejpam-5362	282	37	.	.	PUNCT
ejpam-5362	283	1	each	each	PRON
ejpam-5362	283	2	of	of	ADP
ejpam-5362	283	3	the	the	DET
ejpam-5362	283	4	an	an	PRON
ejpam-5362	283	5	’s	’s	NOUN
ejpam-5362	283	6	is	be	AUX
ejpam-5362	283	7	i	i	PRON
ejpam-5362	283	8	-	-	PUNCT
ejpam-5362	283	9	dense	dense	ADJ
ejpam-5362	283	10	:	:	PUNCT
ejpam-5362	283	11	pick	pick	VERB
ejpam-5362	283	12	b	b	PROPN
ejpam-5362	283	13	∈	∈	PROPN
ejpam-5362	283	14	mi	mi	NOUN
ejpam-5362	283	15	such	such	ADJ
ejpam-5362	283	16	that	that	DET
ejpam-5362	283	17	b	b	PROPN
ejpam-5362	283	18	∧	∧	NOUN
ejpam-5362	283	19	an	an	PRON
ejpam-5362	283	20	=	=	NOUN
ejpam-5362	283	21	0	0	PROPN
ejpam-5362	283	22	.	.	PUNCT
ejpam-5362	284	1	then	then	ADV
ejpam-5362	284	2	h(b	h(b	NUM
ejpam-5362	284	3	)	)	PUNCT
ejpam-5362	284	4	∧	∧	PROPN
ejpam-5362	284	5	h(an	h(an	PROPN
ejpam-5362	284	6	)	)	PUNCT
ejpam-5362	284	7	=	=	SYM
ejpam-5362	284	8	0	0	PUNCT
ejpam-5362	285	1	so	so	SCONJ
ejpam-5362	285	2	that	that	SCONJ
ejpam-5362	285	3	h∗(h(b	h∗(h(b	PROPN
ejpam-5362	285	4	)	)	PUNCT
ejpam-5362	285	5	)	)	PUNCT
ejpam-5362	286	1	∧	∧	NOUN
ejpam-5362	286	2	h∗(h(an	h∗(h(an	NOUN
ejpam-5362	286	3	)	)	PUNCT
ejpam-5362	286	4	)	)	PUNCT
ejpam-5362	287	1	=	=	PUNCT
ejpam-5362	287	2	h∗(0	h∗(0	NOUN
ejpam-5362	287	3	)	)	PUNCT
ejpam-5362	287	4	=	=	SYM
ejpam-5362	288	1	0	0	NUM
ejpam-5362	288	2	,	,	PUNCT
ejpam-5362	288	3	where	where	SCONJ
ejpam-5362	288	4	the	the	DET
ejpam-5362	288	5	latter	latter	ADJ
ejpam-5362	288	6	equality	equality	NOUN
ejpam-5362	288	7	follows	follow	VERB
ejpam-5362	288	8	since	since	SCONJ
ejpam-5362	288	9	h∗	h∗	PROPN
ejpam-5362	288	10	:	:	PUNCT
ejpam-5362	288	11	l	l	X
ejpam-5362	288	12	→	→	PUNCT
ejpam-5362	288	13	m	m	VERB
ejpam-5362	288	14	is	be	AUX
ejpam-5362	288	15	a	a	DET
ejpam-5362	288	16	dense	dense	ADJ
ejpam-5362	288	17	localic	localic	ADJ
ejpam-5362	288	18	map	map	NOUN
ejpam-5362	288	19	.	.	PUNCT
ejpam-5362	289	1	therefore	therefore	ADV
ejpam-5362	289	2	b	b	X
ejpam-5362	289	3	∧	∧	PROPN
ejpam-5362	289	4	h∗(xn	h∗(xn	PROPN
ejpam-5362	289	5	)	)	PUNCT
ejpam-5362	289	6	=	=	SYM
ejpam-5362	290	1	0	0	X
ejpam-5362	290	2	.	.	PUNCT
ejpam-5362	290	3	by	by	ADP
ejpam-5362	290	4	lemma	lemma	PROPN
ejpam-5362	290	5	2	2	NUM
ejpam-5362	290	6	,	,	PUNCT
ejpam-5362	290	7	b	b	NOUN
ejpam-5362	290	8	=	=	SYM
ejpam-5362	290	9	0	0	PROPN
ejpam-5362	291	1	and	and	CCONJ
ejpam-5362	291	2	hence	hence	ADV
ejpam-5362	291	3	each	each	DET
ejpam-5362	291	4	an	an	PRON
ejpam-5362	291	5	is	be	AUX
ejpam-5362	291	6	i	i	PRON
ejpam-5362	291	7	-	-	PUNCT
ejpam-5362	291	8	dense	dense	ADJ
ejpam-5362	291	9	.	.	PUNCT
ejpam-5362	292	1	therefore	therefore	ADV
ejpam-5362	292	2	the	the	DET
ejpam-5362	292	3	collection	collection	NOUN
ejpam-5362	292	4	{	{	PUNCT
ejpam-5362	292	5	o(an	o(an	PROPN
ejpam-5362	292	6	)	)	PUNCT
ejpam-5362	292	7	:	:	PUNCT
ejpam-5362	293	1	n	n	CCONJ
ejpam-5362	293	2	∈	∈	PROPN
ejpam-5362	293	3	n	n	CCONJ
ejpam-5362	293	4	}	}	PUNCT
ejpam-5362	293	5	consists	consist	VERB
ejpam-5362	293	6	of	of	ADP
ejpam-5362	293	7	i	i	NOUN
ejpam-5362	293	8	-	-	PUNCT
ejpam-5362	293	9	dense	dense	ADJ
ejpam-5362	293	10	j	j	NOUN
ejpam-5362	293	11	-	-	ADJ
ejpam-5362	293	12	open	open	ADJ
ejpam-5362	293	13	sublocales	sublocale	NOUN
ejpam-5362	293	14	of	of	ADP
ejpam-5362	293	15	m	m	PROPN
ejpam-5362	293	16	.	.	PUNCT
ejpam-5362	294	1	we	we	PRON
ejpam-5362	294	2	then	then	ADV
ejpam-5362	294	3	get	get	VERB
ejpam-5362	294	4	that	that	DET
ejpam-5362	294	5	o(h∗(y))∩	o(h∗(y))∩	NOUN
ejpam-5362	294	6	(	(	PUNCT
ejpam-5362	294	7	∧	∧	PROPN
ejpam-5362	294	8	n∈n	n∈n	NOUN
ejpam-5362	294	9	(	(	PUNCT
ejpam-5362	294	10	o(an	o(an	PROPN
ejpam-5362	294	11	)	)	PUNCT
ejpam-5362	294	12	)	)	PUNCT
ejpam-5362	294	13	)	)	PUNCT
ejpam-5362	294	14	is	be	AUX
ejpam-5362	294	15	an	an	DET
ejpam-5362	294	16	i	i	NOUN
ejpam-5362	294	17	-	-	PUNCT
ejpam-5362	294	18	gδ	gδ	NOUN
ejpam-5362	294	19	-	-	PUNCT
ejpam-5362	294	20	sublocale	sublocale	NOUN
ejpam-5362	294	21	.	.	PUNCT
ejpam-5362	295	1	because	because	SCONJ
ejpam-5362	295	2	h∗[l	h∗[l	PROPN
ejpam-5362	295	3	]	]	PUNCT
ejpam-5362	295	4	is	be	AUX
ejpam-5362	295	5	i	i	PROPN
ejpam-5362	295	6	-	-	PUNCT
ejpam-5362	295	7	gδ	gδ	NOUN
ejpam-5362	295	8	-	-	PUNCT
ejpam-5362	295	9	dense	dense	ADJ
ejpam-5362	295	10	,	,	PUNCT
ejpam-5362	295	11	so	so	ADV
ejpam-5362	295	12	o(h∗(y	o(h∗(y	ADJ
ejpam-5362	295	13	)	)	PUNCT
ejpam-5362	295	14	)	)	PUNCT
ejpam-5362	295	15	∩	∩	NOUN
ejpam-5362	295	16	(	(	PUNCT
ejpam-5362	295	17	∧	∧	PROPN
ejpam-5362	295	18	n∈n	n∈n	NOUN
ejpam-5362	295	19	o(an	o(an	NUM
ejpam-5362	295	20	)	)	PUNCT
ejpam-5362	295	21	)	)	PUNCT
ejpam-5362	296	1	=	=	SYM
ejpam-5362	296	2	o.	o.	INTJ
ejpam-5362	296	3	since	since	SCONJ
ejpam-5362	296	4	(	(	PUNCT
ejpam-5362	296	5	m	m	PROPN
ejpam-5362	296	6	,	,	PUNCT
ejpam-5362	296	7	m1,m2	m1,m2	PROPN
ejpam-5362	296	8	)	)	PUNCT
ejpam-5362	296	9	is	be	AUX
ejpam-5362	296	10	(	(	PUNCT
ejpam-5362	296	11	i	i	NOUN
ejpam-5362	296	12	,	,	PUNCT
ejpam-5362	296	13	j)-baire	j)-baire	PROPN
ejpam-5362	296	14	,	,	PUNCT
ejpam-5362	296	15	it	it	PRON
ejpam-5362	296	16	follows	follow	VERB
ejpam-5362	296	17	that	that	SCONJ
ejpam-5362	296	18	∧	∧	PROPN
ejpam-5362	296	19	n∈n	n∈n	ADP
ejpam-5362	296	20	o(an	o(an	NUM
ejpam-5362	296	21	)	)	PUNCT
ejpam-5362	296	22	is	be	AUX
ejpam-5362	296	23	i	i	PRON
ejpam-5362	296	24	-	-	PUNCT
ejpam-5362	296	25	dense	dense	ADJ
ejpam-5362	296	26	,	,	PUNCT
ejpam-5362	296	27	so	so	SCONJ
ejpam-5362	296	28	that	that	SCONJ
ejpam-5362	296	29	o(h∗(y	o(h∗(y	PROPN
ejpam-5362	296	30	)	)	PUNCT
ejpam-5362	296	31	)	)	PUNCT
ejpam-5362	297	1	=	=	SYM
ejpam-5362	297	2	o.	o.	PROPN
ejpam-5362	297	3	therefore	therefore	ADV
ejpam-5362	297	4	h∗(y	h∗(y	PROPN
ejpam-5362	297	5	)	)	PUNCT
ejpam-5362	298	1	=	=	PUNCT
ejpam-5362	298	2	0	0	NUM
ejpam-5362	298	3	,	,	PUNCT
ejpam-5362	298	4	so	so	SCONJ
ejpam-5362	298	5	that	that	SCONJ
ejpam-5362	298	6	0	0	X
ejpam-5362	298	7	=	=	SYM
ejpam-5362	298	8	h(h∗(y	h(h∗(y	PROPN
ejpam-5362	298	9	)	)	PUNCT
ejpam-5362	298	10	)	)	PUNCT
ejpam-5362	299	1	=	=	VERB
ejpam-5362	300	1	y.	y.	NOUN
ejpam-5362	300	2	this	this	PRON
ejpam-5362	300	3	means	mean	VERB
ejpam-5362	300	4	that	that	SCONJ
ejpam-5362	300	5	o(y	o(y	ADV
ejpam-5362	300	6	)	)	PUNCT
ejpam-5362	300	7	=	=	SYM
ejpam-5362	301	1	o.	o.	NOUN
ejpam-5362	301	2	thus	thus	ADV
ejpam-5362	301	3	∧	∧	PROPN
ejpam-5362	301	4	n∈n	n∈n	NOUN
ejpam-5362	301	5	o(xn	o(xn	NUM
ejpam-5362	301	6	)	)	PUNCT
ejpam-5362	301	7	is	be	AUX
ejpam-5362	301	8	i	i	NOUN
ejpam-5362	301	9	-	-	PUNCT
ejpam-5362	301	10	dense	dense	ADJ
ejpam-5362	301	11	,	,	PUNCT
ejpam-5362	301	12	and	and	CCONJ
ejpam-5362	301	13	hence	hence	ADV
ejpam-5362	301	14	(	(	PUNCT
ejpam-5362	301	15	l	l	NOUN
ejpam-5362	301	16	,	,	PUNCT
ejpam-5362	301	17	l1	l1	PROPN
ejpam-5362	301	18	,	,	PUNCT
ejpam-5362	301	19	l2	l2	NOUN
ejpam-5362	301	20	)	)	PUNCT
ejpam-5362	301	21	is	be	AUX
ejpam-5362	301	22	(	(	PUNCT
ejpam-5362	301	23	i	i	PROPN
ejpam-5362	301	24	,	,	PUNCT
ejpam-5362	301	25	j)baire	j)baire	PROPN
ejpam-5362	301	26	.	.	PUNCT
ejpam-5362	302	1	a	a	DET
ejpam-5362	302	2	compactification	compactification	NOUN
ejpam-5362	302	3	of	of	ADP
ejpam-5362	302	4	a	a	DET
ejpam-5362	302	5	bilocale	bilocale	NOUN
ejpam-5362	302	6	(	(	PUNCT
ejpam-5362	302	7	l	l	NOUN
ejpam-5362	302	8	,	,	PUNCT
ejpam-5362	302	9	l1	l1	PROPN
ejpam-5362	302	10	,	,	PUNCT
ejpam-5362	302	11	l2	l2	NOUN
ejpam-5362	302	12	)	)	PUNCT
ejpam-5362	302	13	is	be	AUX
ejpam-5362	302	14	a	a	DET
ejpam-5362	302	15	dense	dense	ADJ
ejpam-5362	302	16	and	and	CCONJ
ejpam-5362	302	17	onto	onto	ADP
ejpam-5362	302	18	biframe	biframe	NOUN
ejpam-5362	302	19	map	map	NOUN
ejpam-5362	302	20	h	h	NOUN
ejpam-5362	302	21	:	:	PUNCT
ejpam-5362	302	22	(	(	PUNCT
ejpam-5362	302	23	m	m	NOUN
ejpam-5362	302	24	,	,	PUNCT
ejpam-5362	302	25	m1,m2	m1,m2	PROPN
ejpam-5362	302	26	)	)	PUNCT
ejpam-5362	302	27	→	→	SYM
ejpam-5362	302	28	(	(	PUNCT
ejpam-5362	302	29	l	l	NOUN
ejpam-5362	302	30	,	,	PUNCT
ejpam-5362	302	31	l1	l1	PROPN
ejpam-5362	302	32	,	,	PUNCT
ejpam-5362	302	33	l2	l2	NOUN
ejpam-5362	302	34	)	)	PUNCT
ejpam-5362	302	35	from	from	ADP
ejpam-5362	302	36	a	a	DET
ejpam-5362	302	37	compact	compact	ADJ
ejpam-5362	302	38	regular	regular	ADJ
ejpam-5362	302	39	bilocale	bilocale	NOUN
ejpam-5362	302	40	(	(	PUNCT
ejpam-5362	302	41	m	m	PROPN
ejpam-5362	302	42	,	,	PUNCT
ejpam-5362	302	43	m1,m2	m1,m2	PROPN
ejpam-5362	302	44	)	)	PUNCT
ejpam-5362	302	45	.	.	PUNCT
ejpam-5362	303	1	so	so	ADV
ejpam-5362	303	2	,	,	PUNCT
ejpam-5362	303	3	for	for	ADP
ejpam-5362	303	4	a	a	DET
ejpam-5362	303	5	bilocalic	bilocalic	ADJ
ejpam-5362	303	6	property	property	NOUN
ejpam-5362	303	7	p	p	NOUN
ejpam-5362	303	8	,	,	PUNCT
ejpam-5362	303	9	we	we	PRON
ejpam-5362	303	10	shall	shall	AUX
ejpam-5362	303	11	say	say	VERB
ejpam-5362	303	12	that	that	PRON
ejpam-5362	303	13	(	(	PUNCT
ejpam-5362	303	14	l	l	NOUN
ejpam-5362	303	15	,	,	PUNCT
ejpam-5362	303	16	l1	l1	PROPN
ejpam-5362	303	17	,	,	PUNCT
ejpam-5362	303	18	l2	l2	NOUN
ejpam-5362	303	19	)	)	PUNCT
ejpam-5362	303	20	has	have	AUX
ejpam-5362	303	21	a	a	DET
ejpam-5362	303	22	p	p	NOUN
ejpam-5362	303	23	-compactification	-compactification	NOUN
ejpam-5362	303	24	in	in	ADP
ejpam-5362	303	25	case	case	NOUN
ejpam-5362	303	26	(	(	PUNCT
ejpam-5362	303	27	m	m	NOUN
ejpam-5362	303	28	,	,	PUNCT
ejpam-5362	303	29	m1,m2	m1,m2	PROPN
ejpam-5362	303	30	)	)	PUNCT
ejpam-5362	303	31	has	have	VERB
ejpam-5362	303	32	property	property	NOUN
ejpam-5362	303	33	p	p	NOUN
ejpam-5362	303	34	.	.	PUNCT
ejpam-5362	304	1	corollary	corollary	ADJ
ejpam-5362	304	2	1	1	NUM
ejpam-5362	304	3	.	.	PUNCT
ejpam-5362	305	1	let	let	VERB
ejpam-5362	305	2	(	(	PUNCT
ejpam-5362	305	3	l	l	NOUN
ejpam-5362	305	4	,	,	PUNCT
ejpam-5362	305	5	l1	l1	PROPN
ejpam-5362	305	6	,	,	PUNCT
ejpam-5362	305	7	l2	l2	NOUN
ejpam-5362	305	8	)	)	PUNCT
ejpam-5362	305	9	be	be	AUX
ejpam-5362	305	10	a	a	DET
ejpam-5362	305	11	bilocale	bilocale	NOUN
ejpam-5362	305	12	.	.	PUNCT
ejpam-5362	306	1	if	if	SCONJ
ejpam-5362	306	2	there	there	PRON
ejpam-5362	306	3	is	be	VERB
ejpam-5362	306	4	a	a	DET
ejpam-5362	306	5	i	i	NOUN
ejpam-5362	306	6	-	-	PUNCT
ejpam-5362	306	7	prefit	prefit	NOUN
ejpam-5362	306	8	compactification	compactification	NOUN
ejpam-5362	306	9	h	h	NOUN
ejpam-5362	306	10	:	:	PUNCT
ejpam-5362	306	11	(	(	PUNCT
ejpam-5362	306	12	m	m	NOUN
ejpam-5362	306	13	,	,	PUNCT
ejpam-5362	306	14	m1,m2	m1,m2	PROPN
ejpam-5362	306	15	)	)	PUNCT
ejpam-5362	306	16	→	→	SYM
ejpam-5362	306	17	(	(	PUNCT
ejpam-5362	306	18	l	l	NOUN
ejpam-5362	306	19	,	,	PUNCT
ejpam-5362	306	20	l1	l1	PROPN
ejpam-5362	306	21	,	,	PUNCT
ejpam-5362	306	22	l2	l2	NOUN
ejpam-5362	306	23	)	)	PUNCT
ejpam-5362	306	24	with	with	ADP
ejpam-5362	306	25	which	which	PRON
ejpam-5362	306	26	h∗[l	h∗[l	NOUN
ejpam-5362	306	27	]	]	PUNCT
ejpam-5362	306	28	is	be	AUX
ejpam-5362	306	29	i	i	PROPN
ejpam-5362	306	30	-	-	PUNCT
ejpam-5362	306	31	gδ	gδ	NOUN
ejpam-5362	306	32	-	-	PUNCT
ejpam-5362	306	33	dense	dense	NOUN
ejpam-5362	306	34	in	in	ADP
ejpam-5362	306	35	m	m	PROPN
ejpam-5362	306	36	,	,	PUNCT
ejpam-5362	306	37	then	then	ADV
ejpam-5362	306	38	(	(	PUNCT
ejpam-5362	306	39	l	l	NOUN
ejpam-5362	306	40	,	,	PUNCT
ejpam-5362	306	41	l1	l1	PROPN
ejpam-5362	306	42	,	,	PUNCT
ejpam-5362	306	43	l2	l2	NOUN
ejpam-5362	306	44	)	)	PUNCT
ejpam-5362	306	45	is	be	AUX
ejpam-5362	306	46	(	(	PUNCT
ejpam-5362	306	47	i	i	PROPN
ejpam-5362	306	48	,	,	PUNCT
ejpam-5362	306	49	j)baire	j)baire	PROPN
ejpam-5362	306	50	.	.	PUNCT
ejpam-5362	307	1	definition	definition	NOUN
ejpam-5362	307	2	4	4	NUM
ejpam-5362	307	3	.	.	PUNCT
ejpam-5362	308	1	let	let	VERB
ejpam-5362	308	2	(	(	PUNCT
ejpam-5362	308	3	l	l	NOUN
ejpam-5362	308	4	,	,	PUNCT
ejpam-5362	308	5	l1	l1	PROPN
ejpam-5362	308	6	,	,	PUNCT
ejpam-5362	308	7	l2	l2	NOUN
ejpam-5362	308	8	)	)	PUNCT
ejpam-5362	308	9	be	be	AUX
ejpam-5362	308	10	a	a	DET
ejpam-5362	308	11	bilocale	bilocale	NOUN
ejpam-5362	308	12	.	.	PUNCT
ejpam-5362	309	1	an	an	DET
ejpam-5362	309	2	i	i	PROPN
ejpam-5362	309	3	-	-	PUNCT
ejpam-5362	309	4	π	π	NOUN
ejpam-5362	309	5	-	-	NOUN
ejpam-5362	309	6	base	base	NOUN
ejpam-5362	309	7	for	for	ADP
ejpam-5362	309	8	(	(	PUNCT
ejpam-5362	309	9	l	l	NOUN
ejpam-5362	309	10	,	,	PUNCT
ejpam-5362	309	11	l1	l1	PROPN
ejpam-5362	309	12	,	,	PUNCT
ejpam-5362	309	13	l2	l2	NOUN
ejpam-5362	309	14	)	)	PUNCT
ejpam-5362	309	15	is	be	AUX
ejpam-5362	309	16	a	a	DET
ejpam-5362	309	17	collection	collection	NOUN
ejpam-5362	309	18	c	c	NOUN
ejpam-5362	309	19	of	of	ADP
ejpam-5362	309	20	non	non	ADJ
ejpam-5362	309	21	-	-	ADJ
ejpam-5362	309	22	void	void	ADJ
ejpam-5362	309	23	i	i	PRON
ejpam-5362	309	24	-	-	PUNCT
ejpam-5362	309	25	open	open	ADJ
ejpam-5362	309	26	sublocales	sublocale	VERB
ejpam-5362	309	27	such	such	ADJ
ejpam-5362	309	28	that	that	SCONJ
ejpam-5362	309	29	each	each	DET
ejpam-5362	309	30	non	non	ADJ
ejpam-5362	309	31	-	-	ADJ
ejpam-5362	309	32	void	void	ADJ
ejpam-5362	309	33	i	i	NOUN
ejpam-5362	309	34	-	-	PUNCT
ejpam-5362	309	35	open	open	ADJ
ejpam-5362	309	36	sublocale	sublocale	NOUN
ejpam-5362	309	37	of	of	ADP
ejpam-5362	309	38	l	l	NOUN
ejpam-5362	309	39	contains	contain	VERB
ejpam-5362	309	40	a	a	DET
ejpam-5362	309	41	member	member	NOUN
ejpam-5362	309	42	of	of	ADP
ejpam-5362	309	43	c.	c.	PROPN
ejpam-5362	309	44	a	a	DET
ejpam-5362	309	45	bilocale	bilocale	NOUN
ejpam-5362	309	46	is	be	AUX
ejpam-5362	309	47	said	say	VERB
ejpam-5362	309	48	to	to	PART
ejpam-5362	309	49	be	be	AUX
ejpam-5362	309	50	i	i	NOUN
ejpam-5362	309	51	-	-	NOUN
ejpam-5362	309	52	pseudocomplete	pseudocomplete	ADJ
ejpam-5362	309	53	if	if	SCONJ
ejpam-5362	309	54	it	it	PRON
ejpam-5362	309	55	is	be	AUX
ejpam-5362	309	56	i	i	PRON
ejpam-5362	309	57	-	-	NOUN
ejpam-5362	309	58	prefit	prefit	NOUN
ejpam-5362	309	59	and	and	CCONJ
ejpam-5362	309	60	it	it	PRON
ejpam-5362	309	61	has	have	VERB
ejpam-5362	309	62	a	a	DET
ejpam-5362	309	63	sequence	sequence	NOUN
ejpam-5362	309	64	(	(	PUNCT
ejpam-5362	309	65	cn)n∈n	cn)n∈n	PROPN
ejpam-5362	309	66	of	of	ADP
ejpam-5362	309	67	i	i	PROPN
ejpam-5362	309	68	-	-	PUNCT
ejpam-5362	309	69	π	π	NOUN
ejpam-5362	309	70	-	-	NOUN
ejpam-5362	309	71	bases	basis	NOUN
ejpam-5362	309	72	such	such	ADJ
ejpam-5362	309	73	that	that	SCONJ
ejpam-5362	309	74	whenever	whenever	SCONJ
ejpam-5362	309	75	o(xn	o(xn	X
ejpam-5362	309	76	)	)	PUNCT
ejpam-5362	309	77	∈	∈	PROPN
ejpam-5362	309	78	cn	cn	PROPN
ejpam-5362	309	79	and	and	CCONJ
ejpam-5362	309	80	clj(o(xn+1	clj(o(xn+1	PROPN
ejpam-5362	309	81	)	)	PUNCT
ejpam-5362	309	82	)	)	PUNCT
ejpam-5362	310	1	⊆	⊆	NUM
ejpam-5362	310	2	o(xn	o(xn	NOUN
ejpam-5362	310	3	)	)	PUNCT
ejpam-5362	310	4	for	for	ADP
ejpam-5362	310	5	each	each	DET
ejpam-5362	310	6	n	n	CCONJ
ejpam-5362	310	7	,	,	PUNCT
ejpam-5362	310	8	then	then	ADV
ejpam-5362	310	9	∧	∧	PROPN
ejpam-5362	310	10	n∈n	n∈n	NOUN
ejpam-5362	310	11	o(xn	o(xn	NOUN
ejpam-5362	310	12	)	)	PUNCT
ejpam-5362	310	13	̸=	̸=	PROPN
ejpam-5362	310	14	o.	o.	NOUN
ejpam-5362	310	15	proposition	proposition	NOUN
ejpam-5362	310	16	5	5	NUM
ejpam-5362	310	17	.	.	PUNCT
ejpam-5362	311	1	every	every	DET
ejpam-5362	311	2	i	i	NOUN
ejpam-5362	311	3	-	-	PUNCT
ejpam-5362	311	4	pseudocomplete	pseudocomplete	NOUN
ejpam-5362	311	5	bilocale	bilocale	NOUN
ejpam-5362	311	6	is	be	AUX
ejpam-5362	311	7	(	(	PUNCT
ejpam-5362	311	8	i	i	NOUN
ejpam-5362	311	9	,	,	PUNCT
ejpam-5362	311	10	j)-baire	j)-baire	NOUN
ejpam-5362	311	11	.	.	PUNCT
ejpam-5362	312	1	proof	proof	NOUN
ejpam-5362	312	2	.	.	PUNCT
ejpam-5362	313	1	let	let	VERB
ejpam-5362	313	2	(	(	PUNCT
ejpam-5362	313	3	l	l	NOUN
ejpam-5362	313	4	,	,	PUNCT
ejpam-5362	313	5	l1	l1	PROPN
ejpam-5362	313	6	,	,	PUNCT
ejpam-5362	313	7	l2	l2	NOUN
ejpam-5362	313	8	)	)	PUNCT
ejpam-5362	313	9	be	be	AUX
ejpam-5362	313	10	a	a	DET
ejpam-5362	313	11	pseudocomplete	pseudocomplete	ADJ
ejpam-5362	313	12	bilocale	bilocale	NOUN
ejpam-5362	313	13	and	and	CCONJ
ejpam-5362	313	14	pick	pick	VERB
ejpam-5362	313	15	a	a	DET
ejpam-5362	313	16	collection	collection	NOUN
ejpam-5362	313	17	{	{	PUNCT
ejpam-5362	313	18	o(xn	o(xn	NOUN
ejpam-5362	313	19	)	)	PUNCT
ejpam-5362	313	20	:	:	PUNCT
ejpam-5362	313	21	n	n	CCONJ
ejpam-5362	313	22	∈	∈	PROPN
ejpam-5362	313	23	n	n	CCONJ
ejpam-5362	313	24	}	}	PUNCT
ejpam-5362	313	25	of	of	ADP
ejpam-5362	313	26	i	i	NOUN
ejpam-5362	313	27	-	-	PUNCT
ejpam-5362	313	28	dense	dense	ADJ
ejpam-5362	313	29	j	j	NOUN
ejpam-5362	313	30	-	-	ADJ
ejpam-5362	313	31	open	open	ADJ
ejpam-5362	313	32	sublocales	sublocale	NOUN
ejpam-5362	313	33	.	.	PUNCT
ejpam-5362	314	1	since	since	SCONJ
ejpam-5362	314	2	(	(	PUNCT
ejpam-5362	314	3	l	l	NOUN
ejpam-5362	314	4	,	,	PUNCT
ejpam-5362	314	5	l1	l1	PROPN
ejpam-5362	314	6	,	,	PUNCT
ejpam-5362	314	7	l2	l2	NOUN
ejpam-5362	314	8	)	)	PUNCT
ejpam-5362	314	9	is	be	AUX
ejpam-5362	314	10	pseudocomplete	pseudocomplete	ADJ
ejpam-5362	314	11	,	,	PUNCT
ejpam-5362	314	12	there	there	PRON
ejpam-5362	314	13	is	be	VERB
ejpam-5362	314	14	a	a	DET
ejpam-5362	314	15	sequence	sequence	NOUN
ejpam-5362	314	16	(	(	PUNCT
ejpam-5362	314	17	cn)n∈n	cn)n∈n	PROPN
ejpam-5362	314	18	of	of	ADP
ejpam-5362	314	19	i	i	PROPN
ejpam-5362	314	20	-	-	PUNCT
ejpam-5362	314	21	π	π	NOUN
ejpam-5362	314	22	-	-	NOUN
ejpam-5362	314	23	bases	basis	NOUN
ejpam-5362	314	24	with	with	ADP
ejpam-5362	314	25	the	the	DET
ejpam-5362	314	26	corresponding	corresponding	ADJ
ejpam-5362	314	27	pseudocompleteness	pseudocompleteness	NOUN
ejpam-5362	314	28	property	property	NOUN
ejpam-5362	314	29	.	.	PUNCT
ejpam-5362	315	1	for	for	ADP
ejpam-5362	315	2	each	each	DET
ejpam-5362	315	3	nonvoid	nonvoid	PROPN
ejpam-5362	315	4	i	i	NOUN
ejpam-5362	315	5	-	-	PUNCT
ejpam-5362	315	6	open	open	ADJ
ejpam-5362	315	7	sublocale	sublocale	NOUN
ejpam-5362	315	8	o(y	o(y	NOUN
ejpam-5362	315	9	)	)	PUNCT
ejpam-5362	315	10	,	,	PUNCT
ejpam-5362	315	11	we	we	PRON
ejpam-5362	315	12	have	have	VERB
ejpam-5362	315	13	that	that	SCONJ
ejpam-5362	315	14	each	each	DET
ejpam-5362	315	15	o(y	o(y	NOUN
ejpam-5362	315	16	)	)	PUNCT
ejpam-5362	315	17	∩	∩	NOUN
ejpam-5362	315	18	o(xn	o(xn	X
ejpam-5362	315	19	)	)	PUNCT
ejpam-5362	315	20	is	be	AUX
ejpam-5362	315	21	a	a	DET
ejpam-5362	315	22	non	non	ADJ
ejpam-5362	315	23	-	-	ADJ
ejpam-5362	315	24	void	void	ADJ
ejpam-5362	315	25	open	open	ADJ
ejpam-5362	315	26	sublocale	sublocale	NOUN
ejpam-5362	315	27	,	,	PUNCT
ejpam-5362	315	28	so	so	SCONJ
ejpam-5362	315	29	that	that	SCONJ
ejpam-5362	315	30	y	y	PROPN
ejpam-5362	315	31	∧	∧	PROPN
ejpam-5362	315	32	xn	xn	PROPN
ejpam-5362	315	33	̸=	̸=	PROPN
ejpam-5362	315	34	0	0	NUM
ejpam-5362	315	35	.	.	PUNCT
ejpam-5362	316	1	since	since	SCONJ
ejpam-5362	316	2	(	(	PUNCT
ejpam-5362	316	3	l	l	NOUN
ejpam-5362	316	4	,	,	PUNCT
ejpam-5362	316	5	l1	l1	PROPN
ejpam-5362	316	6	,	,	PUNCT
ejpam-5362	316	7	l2	l2	NOUN
ejpam-5362	316	8	)	)	PUNCT
ejpam-5362	316	9	is	be	AUX
ejpam-5362	316	10	i	i	NOUN
ejpam-5362	316	11	-	-	PUNCT
ejpam-5362	316	12	prefit	prefit	ADJ
ejpam-5362	316	13	,	,	PUNCT
ejpam-5362	316	14	for	for	ADP
ejpam-5362	316	15	n	n	NOUN
ejpam-5362	316	16	=	=	SYM
ejpam-5362	316	17	1	1	NUM
ejpam-5362	316	18	,	,	PUNCT
ejpam-5362	316	19	there	there	PRON
ejpam-5362	316	20	is	be	VERB
ejpam-5362	316	21	nonzero	nonzero	ADJ
ejpam-5362	316	22	a1	a1	PROPN
ejpam-5362	316	23	∈	∈	PROPN
ejpam-5362	316	24	li	li	NOUN
ejpam-5362	316	25	such	such	ADJ
ejpam-5362	316	26	that	that	SCONJ
ejpam-5362	316	27	a•1	a•1	ADV
ejpam-5362	316	28	∨	∨	NUM
ejpam-5362	316	29	(	(	PUNCT
ejpam-5362	316	30	y	y	PROPN
ejpam-5362	316	31	∧	∧	PROPN
ejpam-5362	316	32	x1	x1	PROPN
ejpam-5362	316	33	)	)	PUNCT
ejpam-5362	316	34	=	=	SYM
ejpam-5362	317	1	1	1	X
ejpam-5362	317	2	.	.	PUNCT
ejpam-5362	317	3	this	this	PRON
ejpam-5362	317	4	makes	make	VERB
ejpam-5362	317	5	o	o	PROPN
ejpam-5362	317	6	̸=	̸=	PROPN
ejpam-5362	317	7	o(a1	o(a1	NOUN
ejpam-5362	317	8	)	)	PUNCT
ejpam-5362	317	9	⊆	⊆	NUM
ejpam-5362	317	10	clj(o(a1	clj(o(a1	NOUN
ejpam-5362	317	11	)	)	PUNCT
ejpam-5362	317	12	)	)	PUNCT
ejpam-5362	318	1	⊆	⊆	NUM
ejpam-5362	318	2	o(y	o(y	NOUN
ejpam-5362	318	3	)	)	PUNCT
ejpam-5362	318	4	∩	∩	NOUN
ejpam-5362	318	5	o(x1	o(x1	PROPN
ejpam-5362	318	6	)	)	PUNCT
ejpam-5362	318	7	.	.	PUNCT
ejpam-5362	319	1	m.	m.	NOUN
ejpam-5362	319	2	nxumalo	nxumalo	PROPN
ejpam-5362	319	3	/	/	SYM
ejpam-5362	319	4	eur	eur	PROPN
ejpam-5362	319	5	.	.	PUNCT
ejpam-5362	320	1	j.	j.	PROPN
ejpam-5362	320	2	pure	pure	PROPN
ejpam-5362	320	3	appl	appl	PROPN
ejpam-5362	320	4	.	.	PROPN
ejpam-5362	320	5	math	math	PROPN
ejpam-5362	320	6	,	,	PUNCT
ejpam-5362	320	7	18	18	NUM
ejpam-5362	320	8	(	(	PUNCT
ejpam-5362	320	9	1	1	NUM
ejpam-5362	320	10	)	)	PUNCT
ejpam-5362	320	11	(	(	PUNCT
ejpam-5362	320	12	2025	2025	NUM
ejpam-5362	320	13	)	)	PUNCT
ejpam-5362	320	14	,	,	PUNCT
ejpam-5362	320	15	5362	5362	NUM
ejpam-5362	320	16	12	12	NUM
ejpam-5362	320	17	of	of	ADP
ejpam-5362	320	18	21	21	NUM
ejpam-5362	320	19	for	for	ADP
ejpam-5362	320	20	the	the	DET
ejpam-5362	320	21	i	i	PROPN
ejpam-5362	320	22	-	-	PUNCT
ejpam-5362	320	23	π	π	PROPN
ejpam-5362	320	24	-	-	PUNCT
ejpam-5362	320	25	base	base	ADJ
ejpam-5362	320	26	c1	c1	NOUN
ejpam-5362	320	27	,	,	PUNCT
ejpam-5362	320	28	there	there	PRON
ejpam-5362	320	29	is	be	VERB
ejpam-5362	320	30	o(c1	o(c1	NOUN
ejpam-5362	320	31	)	)	PUNCT
ejpam-5362	320	32	∈	∈	PROPN
ejpam-5362	320	33	c1	c1	PROPN
ejpam-5362	320	34	with	with	ADP
ejpam-5362	320	35	o(c1	o(c1	PROPN
ejpam-5362	320	36	)	)	PUNCT
ejpam-5362	320	37	⊆	⊆	NUM
ejpam-5362	320	38	clj(o(c1	clj(o(c1	NOUN
ejpam-5362	320	39	)	)	PUNCT
ejpam-5362	320	40	)	)	PUNCT
ejpam-5362	321	1	⊆	⊆	NUM
ejpam-5362	321	2	o(a1	o(a1	NOUN
ejpam-5362	321	3	)	)	PUNCT
ejpam-5362	321	4	⊆	⊆	NUM
ejpam-5362	321	5	o(y	o(y	NOUN
ejpam-5362	321	6	)	)	PUNCT
ejpam-5362	321	7	∩	∩	NOUN
ejpam-5362	321	8	o(x1	o(x1	NOUN
ejpam-5362	321	9	)	)	PUNCT
ejpam-5362	321	10	.	.	PUNCT
ejpam-5362	322	1	using	use	VERB
ejpam-5362	322	2	the	the	DET
ejpam-5362	322	3	fact	fact	NOUN
ejpam-5362	322	4	that	that	SCONJ
ejpam-5362	322	5	o(x2	o(x2	NOUN
ejpam-5362	322	6	)	)	PUNCT
ejpam-5362	322	7	is	be	AUX
ejpam-5362	322	8	i	i	PRON
ejpam-5362	322	9	-	-	PUNCT
ejpam-5362	322	10	dense	dense	ADJ
ejpam-5362	322	11	and	and	CCONJ
ejpam-5362	322	12	o(c1	o(c1	NOUN
ejpam-5362	322	13	)	)	PUNCT
ejpam-5362	322	14	is	be	AUX
ejpam-5362	322	15	non	non	ADJ
ejpam-5362	322	16	-	-	ADJ
ejpam-5362	322	17	void	void	ADJ
ejpam-5362	322	18	i	i	NOUN
ejpam-5362	322	19	-	-	PUNCT
ejpam-5362	322	20	open	open	ADJ
ejpam-5362	322	21	,	,	PUNCT
ejpam-5362	322	22	we	we	PRON
ejpam-5362	322	23	get	get	VERB
ejpam-5362	322	24	that	that	DET
ejpam-5362	322	25	o(c1)∩	o(c1)∩	ADJ
ejpam-5362	322	26	o(x2	o(x2	NOUN
ejpam-5362	322	27	)	)	PUNCT
ejpam-5362	322	28	is	be	AUX
ejpam-5362	322	29	a	a	DET
ejpam-5362	322	30	non	non	ADJ
ejpam-5362	322	31	-	-	ADJ
ejpam-5362	322	32	void	void	ADJ
ejpam-5362	322	33	open	open	ADJ
ejpam-5362	322	34	sublocale	sublocale	NOUN
ejpam-5362	322	35	.	.	PUNCT
ejpam-5362	323	1	since	since	SCONJ
ejpam-5362	323	2	(	(	PUNCT
ejpam-5362	323	3	l	l	NOUN
ejpam-5362	323	4	,	,	PUNCT
ejpam-5362	323	5	l1	l1	PROPN
ejpam-5362	323	6	,	,	PUNCT
ejpam-5362	323	7	l2	l2	NOUN
ejpam-5362	323	8	)	)	PUNCT
ejpam-5362	323	9	is	be	AUX
ejpam-5362	323	10	i	i	NOUN
ejpam-5362	323	11	-	-	PUNCT
ejpam-5362	323	12	prefit	prefit	ADJ
ejpam-5362	323	13	,	,	PUNCT
ejpam-5362	323	14	there	there	PRON
ejpam-5362	323	15	is	be	VERB
ejpam-5362	323	16	nonzero	nonzero	PROPN
ejpam-5362	323	17	a2	a2	PROPN
ejpam-5362	323	18	∈	∈	PROPN
ejpam-5362	323	19	li	li	PROPN
ejpam-5362	323	20	such	such	ADJ
ejpam-5362	323	21	that	that	SCONJ
ejpam-5362	323	22	o	o	PROPN
ejpam-5362	323	23	̸=	̸=	PROPN
ejpam-5362	323	24	o(a2	o(a2	NOUN
ejpam-5362	323	25	)	)	PUNCT
ejpam-5362	323	26	⊆	⊆	NUM
ejpam-5362	323	27	clj(o(a2	clj(o(a2	PROPN
ejpam-5362	323	28	)	)	PUNCT
ejpam-5362	323	29	)	)	PUNCT
ejpam-5362	324	1	⊆	⊆	NUM
ejpam-5362	324	2	o(c1	o(c1	NUM
ejpam-5362	324	3	)	)	PUNCT
ejpam-5362	324	4	∩	∩	ADJ
ejpam-5362	324	5	o(x2	o(x2	NOUN
ejpam-5362	324	6	)	)	PUNCT
ejpam-5362	324	7	.	.	PUNCT
ejpam-5362	325	1	an	an	DET
ejpam-5362	325	2	application	application	NOUN
ejpam-5362	325	3	of	of	ADP
ejpam-5362	325	4	pseudocompleteness	pseudocompleteness	NOUN
ejpam-5362	325	5	to	to	ADP
ejpam-5362	325	6	the	the	DET
ejpam-5362	325	7	i	i	PROPN
ejpam-5362	325	8	-	-	PUNCT
ejpam-5362	325	9	π	π	NOUN
ejpam-5362	325	10	-	-	PUNCT
ejpam-5362	325	11	base	base	ADJ
ejpam-5362	325	12	c2	c2	PROPN
ejpam-5362	325	13	yields	yield	VERB
ejpam-5362	325	14	an	an	DET
ejpam-5362	325	15	existence	existence	NOUN
ejpam-5362	325	16	of	of	ADP
ejpam-5362	325	17	o(c2	o(c2	ADJ
ejpam-5362	325	18	)	)	PUNCT
ejpam-5362	325	19	∈	∈	PROPN
ejpam-5362	325	20	c2	c2	PROPN
ejpam-5362	325	21	such	such	ADJ
ejpam-5362	325	22	that	that	SCONJ
ejpam-5362	325	23	o(c2	o(c2	ADJ
ejpam-5362	325	24	)	)	PUNCT
ejpam-5362	325	25	⊆	⊆	NUM
ejpam-5362	325	26	clj(o(c2	clj(o(c2	NOUN
ejpam-5362	325	27	)	)	PUNCT
ejpam-5362	325	28	)	)	PUNCT
ejpam-5362	326	1	⊆	⊆	NUM
ejpam-5362	326	2	o(a2	o(a2	NOUN
ejpam-5362	326	3	)	)	PUNCT
ejpam-5362	326	4	⊆	⊆	NUM
ejpam-5362	326	5	o(c1	o(c1	NOUN
ejpam-5362	326	6	)	)	PUNCT
ejpam-5362	326	7	∩	∩	ADJ
ejpam-5362	326	8	o(x2	o(x2	NOUN
ejpam-5362	326	9	)	)	PUNCT
ejpam-5362	326	10	.	.	PUNCT
ejpam-5362	327	1	since	since	SCONJ
ejpam-5362	327	2	o(x3	o(x3	ADV
ejpam-5362	327	3	)	)	PUNCT
ejpam-5362	327	4	is	be	AUX
ejpam-5362	327	5	i	i	PRON
ejpam-5362	327	6	-	-	PUNCT
ejpam-5362	327	7	dense	dense	ADJ
ejpam-5362	327	8	and	and	CCONJ
ejpam-5362	327	9	o(c2	o(c2	NUM
ejpam-5362	327	10	)	)	PUNCT
ejpam-5362	327	11	is	be	AUX
ejpam-5362	327	12	a	a	DET
ejpam-5362	327	13	non	non	ADJ
ejpam-5362	327	14	-	-	ADJ
ejpam-5362	327	15	void	void	ADJ
ejpam-5362	327	16	i	i	NOUN
ejpam-5362	327	17	-	-	PUNCT
ejpam-5362	327	18	open	open	ADJ
ejpam-5362	327	19	sublocale	sublocale	NOUN
ejpam-5362	327	20	,	,	PUNCT
ejpam-5362	327	21	it	it	PRON
ejpam-5362	327	22	follows	follow	VERB
ejpam-5362	327	23	that	that	SCONJ
ejpam-5362	327	24	o(c2)∩o(x3	o(c2)∩o(x3	NOUN
ejpam-5362	327	25	)	)	PUNCT
ejpam-5362	327	26	̸=	̸=	PROPN
ejpam-5362	327	27	o.	o.	NOUN
ejpam-5362	327	28	applying	apply	VERB
ejpam-5362	327	29	that	that	PRON
ejpam-5362	327	30	(	(	PUNCT
ejpam-5362	327	31	l	l	NOUN
ejpam-5362	327	32	,	,	PUNCT
ejpam-5362	327	33	l1	l1	PROPN
ejpam-5362	327	34	,	,	PUNCT
ejpam-5362	327	35	l2	l2	NOUN
ejpam-5362	327	36	)	)	PUNCT
ejpam-5362	327	37	is	be	AUX
ejpam-5362	327	38	i	i	PRON
ejpam-5362	327	39	-	-	NOUN
ejpam-5362	327	40	prefit	prefit	ADJ
ejpam-5362	327	41	again	again	ADV
ejpam-5362	327	42	implies	imply	VERB
ejpam-5362	327	43	that	that	SCONJ
ejpam-5362	327	44	there	there	PRON
ejpam-5362	327	45	is	be	VERB
ejpam-5362	327	46	a	a	DET
ejpam-5362	327	47	nonzero	nonzero	NOUN
ejpam-5362	327	48	a3	a3	NOUN
ejpam-5362	327	49	∈	∈	PROPN
ejpam-5362	327	50	li	li	PROPN
ejpam-5362	327	51	such	such	ADJ
ejpam-5362	327	52	that	that	SCONJ
ejpam-5362	327	53	o	o	PROPN
ejpam-5362	327	54	̸=	̸=	PROPN
ejpam-5362	327	55	o(a3	o(a3	NOUN
ejpam-5362	327	56	)	)	PUNCT
ejpam-5362	327	57	⊆	⊆	NUM
ejpam-5362	327	58	cli(o(a3	cli(o(a3	PROPN
ejpam-5362	327	59	)	)	PUNCT
ejpam-5362	327	60	)	)	PUNCT
ejpam-5362	328	1	⊆	⊆	NUM
ejpam-5362	328	2	o(c2	o(c2	NUM
ejpam-5362	328	3	)	)	PUNCT
ejpam-5362	328	4	∩	∩	NOUN
ejpam-5362	328	5	o(x3	o(x3	ADV
ejpam-5362	328	6	)	)	PUNCT
ejpam-5362	328	7	.	.	PUNCT
ejpam-5362	329	1	therefore	therefore	ADV
ejpam-5362	329	2	,	,	PUNCT
ejpam-5362	329	3	for	for	ADP
ejpam-5362	329	4	the	the	DET
ejpam-5362	329	5	i	i	PROPN
ejpam-5362	329	6	-	-	PUNCT
ejpam-5362	329	7	π	π	PROPN
ejpam-5362	329	8	-	-	PUNCT
ejpam-5362	329	9	base	base	ADJ
ejpam-5362	329	10	c3	c3	NOUN
ejpam-5362	329	11	,	,	PUNCT
ejpam-5362	329	12	there	there	PRON
ejpam-5362	329	13	is	be	VERB
ejpam-5362	329	14	o(c3	o(c3	NOUN
ejpam-5362	329	15	)	)	PUNCT
ejpam-5362	329	16	∈	∈	PROPN
ejpam-5362	329	17	c3	c3	NOUN
ejpam-5362	329	18	such	such	ADJ
ejpam-5362	330	1	that	that	SCONJ
ejpam-5362	330	2	o(c3	o(c3	NOUN
ejpam-5362	330	3	)	)	PUNCT
ejpam-5362	330	4	⊆	⊆	NUM
ejpam-5362	330	5	clj(o(c3	clj(o(c3	NOUN
ejpam-5362	330	6	)	)	PUNCT
ejpam-5362	330	7	)	)	PUNCT
ejpam-5362	330	8	⊆	⊆	NUM
ejpam-5362	330	9	o(a3	o(a3	NOUN
ejpam-5362	330	10	)	)	PUNCT
ejpam-5362	330	11	⊆	⊆	NUM
ejpam-5362	330	12	o(c2	o(c2	NUM
ejpam-5362	330	13	)	)	PUNCT
ejpam-5362	330	14	∩	∩	NOUN
ejpam-5362	330	15	o(x3	o(x3	ADV
ejpam-5362	330	16	)	)	PUNCT
ejpam-5362	330	17	.	.	PUNCT
ejpam-5362	331	1	continuing	continue	VERB
ejpam-5362	331	2	like	like	ADP
ejpam-5362	331	3	this	this	PRON
ejpam-5362	331	4	for	for	ADP
ejpam-5362	331	5	n	n	NOUN
ejpam-5362	331	6	=	=	SYM
ejpam-5362	331	7	4	4	NUM
ejpam-5362	331	8	,	,	PUNCT
ejpam-5362	331	9	5	5	NUM
ejpam-5362	331	10	,	,	PUNCT
ejpam-5362	331	11	....	....	PUNCT
ejpam-5362	331	12	,	,	PUNCT
ejpam-5362	331	13	we	we	PRON
ejpam-5362	331	14	get	get	VERB
ejpam-5362	331	15	that	that	PRON
ejpam-5362	331	16	for	for	ADP
ejpam-5362	331	17	each	each	DET
ejpam-5362	331	18	i	i	PROPN
ejpam-5362	331	19	-	-	PUNCT
ejpam-5362	331	20	π	π	PROPN
ejpam-5362	331	21	-	-	PUNCT
ejpam-5362	331	22	base	base	ADJ
ejpam-5362	331	23	cn	cn	NOUN
ejpam-5362	331	24	,	,	PUNCT
ejpam-5362	331	25	there	there	PRON
ejpam-5362	331	26	is	be	VERB
ejpam-5362	331	27	o(cn	o(cn	NUM
ejpam-5362	331	28	)	)	PUNCT
ejpam-5362	331	29	∈	∈	PROPN
ejpam-5362	332	1	cn	cn	PROPN
ejpam-5362	332	2	such	such	ADJ
ejpam-5362	332	3	that	that	SCONJ
ejpam-5362	332	4	o(cn	o(cn	PROPN
ejpam-5362	332	5	)	)	PUNCT
ejpam-5362	332	6	⊆	⊆	NUM
ejpam-5362	332	7	clj(o(cn	clj(o(cn	NOUN
ejpam-5362	332	8	)	)	PUNCT
ejpam-5362	332	9	)	)	PUNCT
ejpam-5362	333	1	⊆	⊆	NUM
ejpam-5362	333	2	o(cn−1	o(cn−1	NUM
ejpam-5362	333	3	)	)	PUNCT
ejpam-5362	333	4	∩	∩	NOUN
ejpam-5362	333	5	o(xn	o(xn	NOUN
ejpam-5362	333	6	)	)	PUNCT
ejpam-5362	333	7	.	.	PUNCT
ejpam-5362	334	1	since	since	SCONJ
ejpam-5362	334	2	(	(	PUNCT
ejpam-5362	334	3	l	l	NOUN
ejpam-5362	334	4	,	,	PUNCT
ejpam-5362	334	5	l1	l1	PROPN
ejpam-5362	334	6	,	,	PUNCT
ejpam-5362	334	7	l2	l2	NOUN
ejpam-5362	334	8	)	)	PUNCT
ejpam-5362	334	9	is	be	AUX
ejpam-5362	334	10	i	i	NOUN
ejpam-5362	334	11	-	-	PUNCT
ejpam-5362	334	12	pseudocomplete	pseudocomplete	NOUN
ejpam-5362	334	13	,	,	PUNCT
ejpam-5362	334	14	∧	∧	PROPN
ejpam-5362	334	15	n∈n	n∈n	NOUN
ejpam-5362	334	16	o(cn	o(cn	NUM
ejpam-5362	334	17	)	)	PUNCT
ejpam-5362	334	18	̸=	̸=	PROPN
ejpam-5362	334	19	o.	o.	NOUN
ejpam-5362	334	20	because	because	SCONJ
ejpam-5362	334	21	o(cn	o(cn	PROPN
ejpam-5362	334	22	)	)	PUNCT
ejpam-5362	334	23	⊆	⊆	NUM
ejpam-5362	334	24	o(y	o(y	NOUN
ejpam-5362	334	25	)	)	PUNCT
ejpam-5362	334	26	∩	∩	NOUN
ejpam-5362	334	27	o(xn	o(xn	NOUN
ejpam-5362	334	28	)	)	PUNCT
ejpam-5362	334	29	for	for	ADP
ejpam-5362	334	30	each	each	DET
ejpam-5362	334	31	n	n	PRON
ejpam-5362	334	32	∈	∈	PROPN
ejpam-5362	334	33	n	n	CCONJ
ejpam-5362	334	34	,	,	PUNCT
ejpam-5362	334	35	we	we	PRON
ejpam-5362	334	36	have	have	VERB
ejpam-5362	334	37	o	o	NOUN
ejpam-5362	334	38	̸=	̸=	PROPN
ejpam-5362	334	39	∧	∧	PROPN
ejpam-5362	334	40	n∈n	n∈n	DET
ejpam-5362	334	41	o(cn	o(cn	PROPN
ejpam-5362	334	42	)	)	PUNCT
ejpam-5362	334	43	⊆	⊆	NUM
ejpam-5362	334	44	o(y	o(y	NOUN
ejpam-5362	334	45	)	)	PUNCT
ejpam-5362	334	46	∩	∩	NOUN
ejpam-5362	334	47	∧	∧	NOUN
ejpam-5362	334	48	n∈n	n∈n	NOUN
ejpam-5362	334	49	o(xn	o(xn	NUM
ejpam-5362	334	50	)	)	PUNCT
ejpam-5362	334	51	,	,	PUNCT
ejpam-5362	334	52	making	make	VERB
ejpam-5362	334	53	∧	∧	PROPN
ejpam-5362	334	54	n∈n	n∈n	NOUN
ejpam-5362	334	55	o(xn	o(xn	NOUN
ejpam-5362	334	56	)	)	PUNCT
ejpam-5362	334	57	an	an	DET
ejpam-5362	334	58	i	i	NOUN
ejpam-5362	334	59	-	-	PUNCT
ejpam-5362	334	60	dense	dense	ADJ
ejpam-5362	334	61	sublocale	sublocale	NOUN
ejpam-5362	334	62	.	.	PUNCT
ejpam-5362	335	1	thus	thus	ADV
ejpam-5362	335	2	(	(	PUNCT
ejpam-5362	335	3	l	l	NOUN
ejpam-5362	335	4	,	,	PUNCT
ejpam-5362	335	5	l1	l1	PROPN
ejpam-5362	335	6	,	,	PUNCT
ejpam-5362	335	7	l2	l2	NOUN
ejpam-5362	335	8	)	)	PUNCT
ejpam-5362	335	9	is	be	AUX
ejpam-5362	335	10	(	(	PUNCT
ejpam-5362	335	11	i	i	NOUN
ejpam-5362	335	12	,	,	PUNCT
ejpam-5362	335	13	j)-baire	j)-baire	PROPN
ejpam-5362	335	14	.	.	PUNCT
ejpam-5362	336	1	recall	recall	VERB
ejpam-5362	336	2	from	from	ADP
ejpam-5362	336	3	[	[	X
ejpam-5362	336	4	5	5	NUM
ejpam-5362	336	5	]	]	PUNCT
ejpam-5362	336	6	that	that	SCONJ
ejpam-5362	336	7	the	the	DET
ejpam-5362	336	8	triple	triple	ADJ
ejpam-5362	336	9	(	(	PUNCT
ejpam-5362	336	10	jl	jl	NOUN
ejpam-5362	336	11	,	,	PUNCT
ejpam-5362	336	12	(	(	PUNCT
ejpam-5362	336	13	jl)1	jl)1	PROPN
ejpam-5362	336	14	,	,	PUNCT
ejpam-5362	336	15	(	(	PUNCT
ejpam-5362	336	16	jl)2	jl)2	PROPN
ejpam-5362	336	17	)	)	PUNCT
ejpam-5362	336	18	,	,	PUNCT
ejpam-5362	336	19	where	where	SCONJ
ejpam-5362	336	20	jl	jl	PROPN
ejpam-5362	336	21	is	be	AUX
ejpam-5362	336	22	the	the	DET
ejpam-5362	336	23	locale	locale	NOUN
ejpam-5362	336	24	of	of	ADP
ejpam-5362	336	25	all	all	DET
ejpam-5362	336	26	ideals	ideal	NOUN
ejpam-5362	336	27	of	of	ADP
ejpam-5362	336	28	l	l	NOUN
ejpam-5362	336	29	and	and	CCONJ
ejpam-5362	336	30	(	(	PUNCT
ejpam-5362	336	31	jl)i	jl)i	PROPN
ejpam-5362	336	32	(	(	PUNCT
ejpam-5362	336	33	i	i	NOUN
ejpam-5362	336	34	=	=	NOUN
ejpam-5362	336	35	1	1	NUM
ejpam-5362	336	36	,	,	PUNCT
ejpam-5362	336	37	2	2	NUM
ejpam-5362	336	38	)	)	PUNCT
ejpam-5362	336	39	is	be	AUX
ejpam-5362	336	40	the	the	DET
ejpam-5362	336	41	subframe	subframe	NOUN
ejpam-5362	336	42	of	of	ADP
ejpam-5362	336	43	jl	jl	PROPN
ejpam-5362	336	44	consisting	consist	VERB
ejpam-5362	336	45	of	of	ADP
ejpam-5362	336	46	all	all	DET
ejpam-5362	336	47	ideals	ideal	NOUN
ejpam-5362	336	48	j	j	PROPN
ejpam-5362	336	49	⊆	⊆	NUM
ejpam-5362	336	50	l	l	NOUN
ejpam-5362	336	51	generated	generate	VERB
ejpam-5362	336	52	by	by	ADP
ejpam-5362	336	53	j	j	PROPN
ejpam-5362	336	54	∩	∩	PROPN
ejpam-5362	336	55	li	li	PROPN
ejpam-5362	336	56	,	,	PUNCT
ejpam-5362	336	57	is	be	AUX
ejpam-5362	336	58	a	a	DET
ejpam-5362	336	59	bilocale	bilocale	NOUN
ejpam-5362	336	60	called	call	VERB
ejpam-5362	336	61	the	the	DET
ejpam-5362	336	62	ideal	ideal	ADJ
ejpam-5362	336	63	bilocale	bilocale	NOUN
ejpam-5362	336	64	.	.	PUNCT
ejpam-5362	337	1	call	call	VERB
ejpam-5362	337	2	a	a	DET
ejpam-5362	337	3	bilocale	bilocale	NOUN
ejpam-5362	337	4	(	(	PUNCT
ejpam-5362	337	5	l	l	NOUN
ejpam-5362	337	6	,	,	PUNCT
ejpam-5362	337	7	l1	l1	PROPN
ejpam-5362	337	8	,	,	PUNCT
ejpam-5362	337	9	l2	l2	NOUN
ejpam-5362	337	10	)	)	PUNCT
ejpam-5362	337	11	noetherian	noetherian	NOUN
ejpam-5362	337	12	in	in	ADP
ejpam-5362	337	13	case	case	NOUN
ejpam-5362	337	14	its	its	PRON
ejpam-5362	337	15	total	total	ADJ
ejpam-5362	337	16	part	part	NOUN
ejpam-5362	337	17	l	l	NOUN
ejpam-5362	337	18	is	be	AUX
ejpam-5362	337	19	noetherian	noetherian	ADJ
ejpam-5362	337	20	,	,	PUNCT
ejpam-5362	337	21	i.e.	i.e.	X
ejpam-5362	337	22	,	,	PUNCT
ejpam-5362	337	23	all	all	PRON
ejpam-5362	337	24	of	of	ADP
ejpam-5362	337	25	its	its	PRON
ejpam-5362	337	26	elements	element	NOUN
ejpam-5362	337	27	are	be	AUX
ejpam-5362	337	28	compact	compact	ADJ
ejpam-5362	337	29	.	.	PUNCT
ejpam-5362	338	1	in	in	ADP
ejpam-5362	338	2	a	a	DET
ejpam-5362	338	3	noetherian	noetherian	ADJ
ejpam-5362	338	4	locale	locale	NOUN
ejpam-5362	338	5	,	,	PUNCT
ejpam-5362	338	6	all	all	DET
ejpam-5362	338	7	ideals	ideal	NOUN
ejpam-5362	338	8	are	be	AUX
ejpam-5362	338	9	principal	principal	ADJ
ejpam-5362	338	10	[	[	X
ejpam-5362	338	11	3	3	NUM
ejpam-5362	338	12	]	]	PUNCT
ejpam-5362	338	13	.	.	PUNCT
ejpam-5362	339	1	this	this	PRON
ejpam-5362	339	2	suggests	suggest	VERB
ejpam-5362	339	3	that	that	SCONJ
ejpam-5362	339	4	in	in	ADP
ejpam-5362	339	5	a	a	DET
ejpam-5362	339	6	noetherian	noetherian	ADJ
ejpam-5362	339	7	locale	locale	NOUN
ejpam-5362	339	8	,	,	PUNCT
ejpam-5362	339	9	the	the	DET
ejpam-5362	339	10	locale	locale	NOUN
ejpam-5362	339	11	jl	jl	NOUN
ejpam-5362	339	12	of	of	ADP
ejpam-5362	339	13	ideals	ideal	NOUN
ejpam-5362	339	14	of	of	ADP
ejpam-5362	339	15	a	a	DET
ejpam-5362	339	16	locale	locale	ADJ
ejpam-5362	339	17	l	l	NOUN
ejpam-5362	339	18	is	be	AUX
ejpam-5362	339	19	isomorphic	isomorphic	ADJ
ejpam-5362	339	20	to	to	ADP
ejpam-5362	339	21	l.	l.	NOUN
ejpam-5362	339	22	for	for	ADP
ejpam-5362	339	23	use	use	NOUN
ejpam-5362	339	24	below	below	ADV
ejpam-5362	339	25	,	,	PUNCT
ejpam-5362	339	26	we	we	PRON
ejpam-5362	339	27	recall	recall	VERB
ejpam-5362	339	28	from	from	ADP
ejpam-5362	339	29	[	[	X
ejpam-5362	339	30	15	15	NUM
ejpam-5362	339	31	,	,	PUNCT
ejpam-5362	339	32	proposition	proposition	NOUN
ejpam-5362	339	33	6.9	6.9	NUM
ejpam-5362	339	34	.	.	PUNCT
ejpam-5362	339	35	]	]	PUNCT
ejpam-5362	340	1	that	that	SCONJ
ejpam-5362	340	2	in	in	ADP
ejpam-5362	340	3	a	a	DET
ejpam-5362	340	4	bilocale	bilocale	NOUN
ejpam-5362	340	5	(	(	PUNCT
ejpam-5362	340	6	l	l	NOUN
ejpam-5362	340	7	,	,	PUNCT
ejpam-5362	340	8	l1	l1	PROPN
ejpam-5362	340	9	,	,	PUNCT
ejpam-5362	340	10	l2	l2	NOUN
ejpam-5362	340	11	)	)	PUNCT
ejpam-5362	340	12	,	,	PUNCT
ejpam-5362	340	13	if	if	SCONJ
ejpam-5362	340	14	x	x	PROPN
ejpam-5362	340	15	∈	∈	PROPN
ejpam-5362	340	16	li	li	PROPN
ejpam-5362	340	17	is	be	AUX
ejpam-5362	340	18	j	j	NOUN
ejpam-5362	340	19	-	-	PUNCT
ejpam-5362	340	20	dense	dense	ADJ
ejpam-5362	340	21	,	,	PUNCT
ejpam-5362	340	22	then	then	ADV
ejpam-5362	340	23	↓x	↓x	PUNCT
ejpam-5362	340	24	∈	∈	PROPN
ejpam-5362	340	25	jli	jli	PROPN
ejpam-5362	340	26	is	be	AUX
ejpam-5362	340	27	jlj	jlj	NOUN
ejpam-5362	340	28	-	-	PUNCT
ejpam-5362	340	29	dense	dense	ADJ
ejpam-5362	340	30	.	.	PUNCT
ejpam-5362	341	1	furthermore	furthermore	ADV
ejpam-5362	341	2	,	,	PUNCT
ejpam-5362	341	3	for	for	ADP
ejpam-5362	341	4	a	a	DET
ejpam-5362	341	5	noetherian	noetherian	ADJ
ejpam-5362	341	6	bilocale	bilocale	NOUN
ejpam-5362	341	7	(	(	PUNCT
ejpam-5362	341	8	l	l	NOUN
ejpam-5362	341	9	,	,	PUNCT
ejpam-5362	341	10	l1	l1	PROPN
ejpam-5362	341	11	,	,	PUNCT
ejpam-5362	341	12	l2	l2	NOUN
ejpam-5362	341	13	)	)	PUNCT
ejpam-5362	341	14	,	,	PUNCT
ejpam-5362	341	15	∨	∨	NUM
ejpam-5362	341	16	j	j	PROPN
ejpam-5362	341	17	∈	∈	PROPN
ejpam-5362	341	18	li	li	PROPN
ejpam-5362	341	19	is	be	AUX
ejpam-5362	341	20	j	j	NOUN
ejpam-5362	341	21	-	-	ADJ
ejpam-5362	341	22	dense	dense	ADJ
ejpam-5362	341	23	whenever	whenever	SCONJ
ejpam-5362	341	24	j	j	PROPN
ejpam-5362	341	25	∈	∈	PROPN
ejpam-5362	341	26	jli	jli	PROPN
ejpam-5362	341	27	is	be	AUX
ejpam-5362	341	28	jlj	jlj	NOUN
ejpam-5362	341	29	-	-	PUNCT
ejpam-5362	341	30	dense	dense	ADJ
ejpam-5362	341	31	.	.	PUNCT
ejpam-5362	342	1	m.	m.	NOUN
ejpam-5362	342	2	nxumalo	nxumalo	PROPN
ejpam-5362	342	3	/	/	SYM
ejpam-5362	342	4	eur	eur	PROPN
ejpam-5362	342	5	.	.	PUNCT
ejpam-5362	343	1	j.	j.	PROPN
ejpam-5362	343	2	pure	pure	PROPN
ejpam-5362	343	3	appl	appl	PROPN
ejpam-5362	343	4	.	.	PROPN
ejpam-5362	343	5	math	math	PROPN
ejpam-5362	343	6	,	,	PUNCT
ejpam-5362	343	7	18	18	NUM
ejpam-5362	343	8	(	(	PUNCT
ejpam-5362	343	9	1	1	NUM
ejpam-5362	343	10	)	)	PUNCT
ejpam-5362	343	11	(	(	PUNCT
ejpam-5362	343	12	2025	2025	NUM
ejpam-5362	343	13	)	)	PUNCT
ejpam-5362	343	14	,	,	PUNCT
ejpam-5362	343	15	5362	5362	NUM
ejpam-5362	343	16	13	13	NUM
ejpam-5362	343	17	of	of	ADP
ejpam-5362	343	18	21	21	NUM
ejpam-5362	343	19	proposition	proposition	NOUN
ejpam-5362	343	20	6	6	NUM
ejpam-5362	343	21	.	.	PUNCT
ejpam-5362	344	1	let	let	VERB
ejpam-5362	344	2	(	(	PUNCT
ejpam-5362	344	3	l	l	NOUN
ejpam-5362	344	4	,	,	PUNCT
ejpam-5362	344	5	l1	l1	PROPN
ejpam-5362	344	6	,	,	PUNCT
ejpam-5362	344	7	l2	l2	NOUN
ejpam-5362	344	8	)	)	PUNCT
ejpam-5362	344	9	be	be	AUX
ejpam-5362	344	10	a	a	DET
ejpam-5362	344	11	bilocale	bilocale	NOUN
ejpam-5362	344	12	.	.	PUNCT
ejpam-5362	345	1	then	then	ADV
ejpam-5362	345	2	(	(	PUNCT
ejpam-5362	345	3	l	l	NOUN
ejpam-5362	345	4	,	,	PUNCT
ejpam-5362	345	5	l1	l1	PROPN
ejpam-5362	345	6	,	,	PUNCT
ejpam-5362	345	7	l2	l2	NOUN
ejpam-5362	345	8	)	)	PUNCT
ejpam-5362	345	9	is	be	AUX
ejpam-5362	345	10	(	(	PUNCT
ejpam-5362	345	11	i	i	PROPN
ejpam-5362	345	12	,	,	PUNCT
ejpam-5362	345	13	j)-baire	j)-baire	VERB
ejpam-5362	345	14	only	only	ADV
ejpam-5362	345	15	if	if	SCONJ
ejpam-5362	345	16	(	(	PUNCT
ejpam-5362	345	17	jl	jl	NOUN
ejpam-5362	345	18	,	,	PUNCT
ejpam-5362	345	19	(	(	PUNCT
ejpam-5362	345	20	jl)1	jl)1	PROPN
ejpam-5362	345	21	,	,	PUNCT
ejpam-5362	345	22	(	(	PUNCT
ejpam-5362	345	23	jl)2	jl)2	PROPN
ejpam-5362	345	24	)	)	PUNCT
ejpam-5362	345	25	is	be	AUX
ejpam-5362	345	26	(	(	PUNCT
ejpam-5362	345	27	i	i	NOUN
ejpam-5362	345	28	,	,	PUNCT
ejpam-5362	345	29	j)-baire	j)-baire	NOUN
ejpam-5362	345	30	.	.	PUNCT
ejpam-5362	346	1	moreover	moreover	ADV
ejpam-5362	346	2	,	,	PUNCT
ejpam-5362	346	3	if	if	SCONJ
ejpam-5362	346	4	(	(	PUNCT
ejpam-5362	346	5	l	l	NOUN
ejpam-5362	346	6	,	,	PUNCT
ejpam-5362	346	7	l1	l1	PROPN
ejpam-5362	346	8	,	,	PUNCT
ejpam-5362	346	9	l2	l2	NOUN
ejpam-5362	346	10	)	)	PUNCT
ejpam-5362	346	11	is	be	AUX
ejpam-5362	346	12	noetherian	noetherian	ADJ
ejpam-5362	346	13	,	,	PUNCT
ejpam-5362	346	14	then	then	ADV
ejpam-5362	346	15	(	(	PUNCT
ejpam-5362	346	16	l	l	NOUN
ejpam-5362	346	17	,	,	PUNCT
ejpam-5362	346	18	l1	l1	PROPN
ejpam-5362	346	19	,	,	PUNCT
ejpam-5362	346	20	l2	l2	NOUN
ejpam-5362	346	21	)	)	PUNCT
ejpam-5362	346	22	is	be	AUX
ejpam-5362	346	23	(	(	PUNCT
ejpam-5362	346	24	i	i	PROPN
ejpam-5362	346	25	,	,	PUNCT
ejpam-5362	346	26	j)-baire	j)-baire	PROPN
ejpam-5362	346	27	iff	iff	PROPN
ejpam-5362	346	28	(	(	PUNCT
ejpam-5362	346	29	jl	jl	PROPN
ejpam-5362	346	30	,	,	PUNCT
ejpam-5362	346	31	(	(	PUNCT
ejpam-5362	346	32	jl)1	jl)1	PROPN
ejpam-5362	346	33	,	,	PUNCT
ejpam-5362	346	34	(	(	PUNCT
ejpam-5362	346	35	jl)2	jl)2	PROPN
ejpam-5362	346	36	)	)	PUNCT
ejpam-5362	346	37	is	be	AUX
ejpam-5362	346	38	(	(	PUNCT
ejpam-5362	346	39	i	i	NOUN
ejpam-5362	346	40	,	,	PUNCT
ejpam-5362	346	41	j)-baire	j)-baire	NOUN
ejpam-5362	346	42	.	.	PUNCT
ejpam-5362	347	1	proof	proof	NOUN
ejpam-5362	347	2	.	.	PUNCT
ejpam-5362	348	1	choose	choose	VERB
ejpam-5362	348	2	a	a	DET
ejpam-5362	348	3	collection	collection	NOUN
ejpam-5362	348	4	{	{	PUNCT
ejpam-5362	348	5	o(xn	o(xn	NOUN
ejpam-5362	348	6	)	)	PUNCT
ejpam-5362	348	7	:	:	PUNCT
ejpam-5362	348	8	n	n	CCONJ
ejpam-5362	348	9	∈	∈	PROPN
ejpam-5362	348	10	n	n	CCONJ
ejpam-5362	348	11	}	}	PUNCT
ejpam-5362	348	12	of	of	ADP
ejpam-5362	348	13	i	i	NOUN
ejpam-5362	348	14	-	-	PUNCT
ejpam-5362	348	15	dense	dense	ADJ
ejpam-5362	348	16	j	j	NOUN
ejpam-5362	348	17	-	-	ADJ
ejpam-5362	348	18	open	open	ADJ
ejpam-5362	348	19	sublocales	sublocale	NOUN
ejpam-5362	348	20	.	.	PUNCT
ejpam-5362	349	1	then	then	ADV
ejpam-5362	349	2	{	{	PUNCT
ejpam-5362	349	3	ojl(↓xn	ojl(↓xn	NOUN
ejpam-5362	349	4	)	)	PUNCT
ejpam-5362	349	5	:	:	PUNCT
ejpam-5362	349	6	n	n	CCONJ
ejpam-5362	349	7	∈	∈	PROPN
ejpam-5362	349	8	n	n	CCONJ
ejpam-5362	349	9	}	}	PUNCT
ejpam-5362	349	10	is	be	AUX
ejpam-5362	349	11	a	a	DET
ejpam-5362	349	12	collection	collection	NOUN
ejpam-5362	349	13	of	of	ADP
ejpam-5362	349	14	jli	jli	PROPN
ejpam-5362	349	15	-	-	PUNCT
ejpam-5362	349	16	dense	dense	ADJ
ejpam-5362	349	17	jlj	jlj	NOUN
ejpam-5362	349	18	-	-	PUNCT
ejpam-5362	349	19	open	open	ADJ
ejpam-5362	349	20	sublocales	sublocale	NOUN
ejpam-5362	349	21	.	.	PUNCT
ejpam-5362	350	1	by	by	ADP
ejpam-5362	350	2	hypothesis	hypothesis	NOUN
ejpam-5362	350	3	,	,	PUNCT
ejpam-5362	350	4	∧	∧	NOUN
ejpam-5362	350	5	n∈n	n∈n	ADJ
ejpam-5362	350	6	ojl(↓xn	ojl(↓xn	NOUN
ejpam-5362	350	7	)	)	PUNCT
ejpam-5362	350	8	is	be	AUX
ejpam-5362	350	9	jli	jli	NOUN
ejpam-5362	350	10	-	-	PUNCT
ejpam-5362	350	11	dense	dense	ADJ
ejpam-5362	350	12	.	.	PUNCT
ejpam-5362	351	1	to	to	PART
ejpam-5362	351	2	show	show	VERB
ejpam-5362	351	3	that	that	SCONJ
ejpam-5362	351	4	∧	∧	PROPN
ejpam-5362	351	5	n∈n	n∈n	ADV
ejpam-5362	351	6	o(xn	o(xn	NUM
ejpam-5362	351	7	)	)	PUNCT
ejpam-5362	351	8	is	be	AUX
ejpam-5362	351	9	i	i	PRON
ejpam-5362	351	10	-	-	PUNCT
ejpam-5362	351	11	dense	dense	ADJ
ejpam-5362	351	12	,	,	PUNCT
ejpam-5362	351	13	let	let	VERB
ejpam-5362	351	14	o(y	o(y	NOUN
ejpam-5362	351	15	)	)	PUNCT
ejpam-5362	351	16	be	be	AUX
ejpam-5362	351	17	an	an	DET
ejpam-5362	351	18	i	i	NOUN
ejpam-5362	351	19	-	-	PUNCT
ejpam-5362	351	20	open	open	ADJ
ejpam-5362	351	21	sublocale	sublocale	NOUN
ejpam-5362	351	22	such	such	ADJ
ejpam-5362	351	23	that	that	SCONJ
ejpam-5362	351	24	o(y	o(y	PROPN
ejpam-5362	351	25	)	)	PUNCT
ejpam-5362	351	26	∩	∩	NOUN
ejpam-5362	351	27	(	(	PUNCT
ejpam-5362	351	28	∧	∧	PROPN
ejpam-5362	351	29	n∈n	n∈n	NOUN
ejpam-5362	351	30	o(xn	o(xn	NUM
ejpam-5362	351	31	)	)	PUNCT
ejpam-5362	351	32	)	)	PUNCT
ejpam-5362	352	1	=	=	SYM
ejpam-5362	352	2	o.	o.	NOUN
ejpam-5362	352	3	claim	claim	NOUN
ejpam-5362	352	4	:	:	PUNCT
ejpam-5362	352	5	ojl(↓y	ojl(↓y	ADJ
ejpam-5362	352	6	)	)	PUNCT
ejpam-5362	352	7	∩	∩	NOUN
ejpam-5362	352	8	(	(	PUNCT
ejpam-5362	352	9	∧	∧	PROPN
ejpam-5362	352	10	n∈n	n∈n	NOUN
ejpam-5362	352	11	ojl	ojl	VERB
ejpam-5362	352	12	(	(	PUNCT
ejpam-5362	352	13	∨	∨	NUM
ejpam-5362	352	14	↓xn	↓xn	NOUN
ejpam-5362	352	15	)	)	PUNCT
ejpam-5362	352	16	)	)	PUNCT
ejpam-5362	353	1	=	=	SYM
ejpam-5362	353	2	o.	o.	NOUN
ejpam-5362	353	3	proof	proof	NOUN
ejpam-5362	353	4	:	:	PUNCT
ejpam-5362	353	5	otherwise	otherwise	ADV
ejpam-5362	353	6	,	,	PUNCT
ejpam-5362	353	7	∧	∧	PROPN
ejpam-5362	353	8	n∈n	n∈n	NOUN
ejpam-5362	353	9	o(↓y	o(↓y	NUM
ejpam-5362	353	10	∩	∩	ADJ
ejpam-5362	353	11	↓xn	↓xn	NOUN
ejpam-5362	353	12	)	)	PUNCT
ejpam-5362	353	13	̸=	̸=	PROPN
ejpam-5362	353	14	o	o	NOUN
ejpam-5362	353	15	which	which	PRON
ejpam-5362	353	16	implies	imply	VERB
ejpam-5362	353	17	that	that	SCONJ
ejpam-5362	353	18	o	o	PROPN
ejpam-5362	353	19	̸=	̸=	PROPN
ejpam-5362	353	20	↓y	↓y	X
ejpam-5362	353	21	∩	∩	ADJ
ejpam-5362	353	22	↓xn	↓xn	NOUN
ejpam-5362	353	23	=	=	SYM
ejpam-5362	353	24	↓(y	↓(y	NOUN
ejpam-5362	353	25	∧	∧	PROPN
ejpam-5362	353	26	xn	xn	X
ejpam-5362	353	27	)	)	PUNCT
ejpam-5362	353	28	for	for	ADP
ejpam-5362	353	29	each	each	DET
ejpam-5362	353	30	n	n	DET
ejpam-5362	353	31	∈	∈	PROPN
ejpam-5362	353	32	n.	n.	NOUN
ejpam-5362	353	33	therefore	therefore	ADV
ejpam-5362	353	34	y	y	PROPN
ejpam-5362	353	35	∧	∧	PROPN
ejpam-5362	353	36	xn	xn	PROPN
ejpam-5362	353	37	̸=	̸=	PROPN
ejpam-5362	353	38	0	0	NUM
ejpam-5362	353	39	for	for	ADP
ejpam-5362	353	40	each	each	DET
ejpam-5362	353	41	n	n	PRON
ejpam-5362	353	42	∈	∈	PROPN
ejpam-5362	353	43	n	n	NOUN
ejpam-5362	353	44	so	so	ADV
ejpam-5362	353	45	that	that	SCONJ
ejpam-5362	353	46	o	o	NOUN
ejpam-5362	353	47	̸=	̸=	PROPN
ejpam-5362	353	48	∧	∧	PROPN
ejpam-5362	353	49	n∈n	n∈n	VERB
ejpam-5362	353	50	o(y	o(y	PROPN
ejpam-5362	353	51	∧	∧	PROPN
ejpam-5362	353	52	xn	xn	X
ejpam-5362	353	53	)	)	PUNCT
ejpam-5362	353	54	=	=	SYM
ejpam-5362	353	55	o(y	o(y	NOUN
ejpam-5362	353	56	)	)	PUNCT
ejpam-5362	353	57	∩	∩	NOUN
ejpam-5362	353	58	(	(	PUNCT
ejpam-5362	353	59	∧	∧	PROPN
ejpam-5362	353	60	n∈n	n∈n	NOUN
ejpam-5362	353	61	o(xn	o(xn	NOUN
ejpam-5362	353	62	)	)	PUNCT
ejpam-5362	353	63	)	)	PUNCT
ejpam-5362	353	64	which	which	PRON
ejpam-5362	353	65	is	be	AUX
ejpam-5362	353	66	a	a	DET
ejpam-5362	353	67	contradiction	contradiction	NOUN
ejpam-5362	353	68	.	.	PUNCT
ejpam-5362	354	1	thus	thus	ADV
ejpam-5362	354	2	ojl(↓y	ojl(↓y	PROPN
ejpam-5362	354	3	)	)	PUNCT
ejpam-5362	354	4	=	=	PUNCT
ejpam-5362	355	1	o	o	NOUN
ejpam-5362	355	2	implying	imply	VERB
ejpam-5362	355	3	that	that	SCONJ
ejpam-5362	355	4	↓y	↓y	PUNCT
ejpam-5362	355	5	=	=	SYM
ejpam-5362	355	6	o.	o.	NOUN
ejpam-5362	355	7	therefore	therefore	ADV
ejpam-5362	355	8	o(y	o(y	PROPN
ejpam-5362	355	9	)	)	PUNCT
ejpam-5362	356	1	=	=	SYM
ejpam-5362	356	2	o	o	NOUN
ejpam-5362	356	3	and	and	CCONJ
ejpam-5362	356	4	hence	hence	ADV
ejpam-5362	356	5	∧	∧	PROPN
ejpam-5362	356	6	n∈n	n∈n	NOUN
ejpam-5362	356	7	o(xn	o(xn	NUM
ejpam-5362	356	8	)	)	PUNCT
ejpam-5362	356	9	is	be	AUX
ejpam-5362	356	10	i	i	PRON
ejpam-5362	356	11	-	-	PUNCT
ejpam-5362	356	12	dense	dense	ADJ
ejpam-5362	356	13	.	.	PUNCT
ejpam-5362	357	1	the	the	DET
ejpam-5362	357	2	particular	particular	ADJ
ejpam-5362	357	3	case	case	NOUN
ejpam-5362	357	4	follows	follow	VERB
ejpam-5362	357	5	since	since	SCONJ
ejpam-5362	357	6	l	l	NOUN
ejpam-5362	357	7	is	be	AUX
ejpam-5362	357	8	isomorphic	isomorphic	ADJ
ejpam-5362	357	9	to	to	ADP
ejpam-5362	357	10	jl	jl	PROPN
ejpam-5362	357	11	.	.	PROPN
ejpam-5362	358	1	4	4	NUM
ejpam-5362	358	2	.	.	X
ejpam-5362	358	3	concerning	concern	VERB
ejpam-5362	358	4	relative	relative	ADJ
ejpam-5362	358	5	versions	version	NOUN
ejpam-5362	358	6	of	of	ADP
ejpam-5362	358	7	(	(	PUNCT
ejpam-5362	358	8	i	i	PROPN
ejpam-5362	358	9	,	,	PUNCT
ejpam-5362	358	10	j)-baire	j)-baire	NOUN
ejpam-5362	358	11	bilocales	bilocale	NOUN
ejpam-5362	358	12	in	in	ADP
ejpam-5362	358	13	this	this	DET
ejpam-5362	358	14	section	section	NOUN
ejpam-5362	358	15	,	,	PUNCT
ejpam-5362	358	16	we	we	PRON
ejpam-5362	358	17	consider	consider	VERB
ejpam-5362	358	18	(	(	PUNCT
ejpam-5362	358	19	i	i	NOUN
ejpam-5362	358	20	,	,	PUNCT
ejpam-5362	358	21	j)-baireness	j)-baireness	NOUN
ejpam-5362	358	22	of	of	ADP
ejpam-5362	358	23	subbilocales	subbilocale	NOUN
ejpam-5362	358	24	.	.	PUNCT
ejpam-5362	359	1	we	we	PRON
ejpam-5362	359	2	recall	recall	VERB
ejpam-5362	359	3	the	the	DET
ejpam-5362	359	4	following	follow	VERB
ejpam-5362	359	5	lemma	lemma	PROPN
ejpam-5362	359	6	from	from	ADP
ejpam-5362	359	7	[	[	X
ejpam-5362	359	8	16	16	NUM
ejpam-5362	359	9	]	]	PUNCT
ejpam-5362	359	10	.	.	PUNCT
ejpam-5362	360	1	lemma	lemma	PROPN
ejpam-5362	360	2	3	3	X
ejpam-5362	360	3	.	.	PUNCT
ejpam-5362	361	1	let	let	VERB
ejpam-5362	361	2	(	(	PUNCT
ejpam-5362	361	3	s	s	X
ejpam-5362	361	4	,	,	PUNCT
ejpam-5362	361	5	s1	s1	NOUN
ejpam-5362	361	6	,	,	PUNCT
ejpam-5362	361	7	s2	s2	PROPN
ejpam-5362	361	8	)	)	PUNCT
ejpam-5362	361	9	be	be	VERB
ejpam-5362	361	10	a	a	DET
ejpam-5362	361	11	dense	dense	ADJ
ejpam-5362	361	12	subbilocale	subbilocale	NOUN
ejpam-5362	361	13	of	of	ADP
ejpam-5362	361	14	a	a	DET
ejpam-5362	361	15	bilocale	bilocale	NOUN
ejpam-5362	361	16	(	(	PUNCT
ejpam-5362	361	17	l	l	NOUN
ejpam-5362	361	18	,	,	PUNCT
ejpam-5362	361	19	l1	l1	PROPN
ejpam-5362	361	20	,	,	PUNCT
ejpam-5362	361	21	l2	l2	NOUN
ejpam-5362	361	22	)	)	PUNCT
ejpam-5362	361	23	.	.	PUNCT
ejpam-5362	362	1	an	an	DET
ejpam-5362	362	2	element	element	NOUN
ejpam-5362	362	3	y	y	PROPN
ejpam-5362	362	4	of	of	ADP
ejpam-5362	362	5	li	li	PROPN
ejpam-5362	362	6	is	be	AUX
ejpam-5362	362	7	j	j	NOUN
ejpam-5362	362	8	-	-	PUNCT
ejpam-5362	362	9	dense	dense	ADJ
ejpam-5362	362	10	iff	iff	PROPN
ejpam-5362	362	11	νs(y	νs(y	NOUN
ejpam-5362	362	12	)	)	PUNCT
ejpam-5362	362	13	is	be	AUX
ejpam-5362	362	14	js	js	ADJ
ejpam-5362	362	15	-	-	PUNCT
ejpam-5362	362	16	dense	dense	ADJ
ejpam-5362	362	17	.	.	PUNCT
ejpam-5362	363	1	corollary	corollary	ADJ
ejpam-5362	363	2	2	2	NUM
ejpam-5362	363	3	.	.	PUNCT
ejpam-5362	364	1	let	let	VERB
ejpam-5362	364	2	(	(	PUNCT
ejpam-5362	364	3	s	s	X
ejpam-5362	364	4	,	,	PUNCT
ejpam-5362	364	5	s1	s1	NOUN
ejpam-5362	364	6	,	,	PUNCT
ejpam-5362	364	7	s2	s2	PROPN
ejpam-5362	364	8	)	)	PUNCT
ejpam-5362	364	9	be	be	VERB
ejpam-5362	364	10	a	a	DET
ejpam-5362	364	11	dense	dense	ADJ
ejpam-5362	364	12	subbilocale	subbilocale	NOUN
ejpam-5362	364	13	of	of	ADP
ejpam-5362	364	14	a	a	DET
ejpam-5362	364	15	bilocale	bilocale	NOUN
ejpam-5362	364	16	(	(	PUNCT
ejpam-5362	364	17	l	l	NOUN
ejpam-5362	364	18	,	,	PUNCT
ejpam-5362	364	19	l1	l1	PROPN
ejpam-5362	364	20	,	,	PUNCT
ejpam-5362	364	21	l2	l2	NOUN
ejpam-5362	364	22	)	)	PUNCT
ejpam-5362	364	23	.	.	PUNCT
ejpam-5362	365	1	an	an	DET
ejpam-5362	365	2	element	element	NOUN
ejpam-5362	365	3	y	y	PROPN
ejpam-5362	365	4	of	of	ADP
ejpam-5362	365	5	li	li	PROPN
ejpam-5362	365	6	is	be	AUX
ejpam-5362	365	7	j	j	NOUN
ejpam-5362	365	8	-	-	PUNCT
ejpam-5362	365	9	dense	dense	ADJ
ejpam-5362	365	10	iff	iff	PROPN
ejpam-5362	365	11	os(νs(y	os(νs(y	NUM
ejpam-5362	365	12	)	)	PUNCT
ejpam-5362	365	13	)	)	PUNCT
ejpam-5362	366	1	=	=	SYM
ejpam-5362	366	2	s	s	NOUN
ejpam-5362	366	3	∩	∩	NOUN
ejpam-5362	366	4	o(y	o(y	X
ejpam-5362	366	5	)	)	PUNCT
ejpam-5362	366	6	is	be	AUX
ejpam-5362	366	7	js	js	ADJ
ejpam-5362	366	8	-	-	PUNCT
ejpam-5362	366	9	dense	dense	ADJ
ejpam-5362	366	10	is	be	AUX
ejpam-5362	366	11	-	-	PUNCT
ejpam-5362	366	12	open	open	ADJ
ejpam-5362	366	13	.	.	PUNCT
ejpam-5362	367	1	we	we	PRON
ejpam-5362	367	2	also	also	ADV
ejpam-5362	367	3	have	have	VERB
ejpam-5362	367	4	the	the	DET
ejpam-5362	367	5	following	follow	VERB
ejpam-5362	367	6	result	result	NOUN
ejpam-5362	367	7	.	.	PUNCT
ejpam-5362	368	1	lemma	lemma	PROPN
ejpam-5362	368	2	4	4	X
ejpam-5362	368	3	.	.	PUNCT
ejpam-5362	369	1	let	let	VERB
ejpam-5362	369	2	(	(	PUNCT
ejpam-5362	369	3	l	l	NOUN
ejpam-5362	369	4	,	,	PUNCT
ejpam-5362	369	5	l1	l1	PROPN
ejpam-5362	369	6	,	,	PUNCT
ejpam-5362	369	7	l2	l2	NOUN
ejpam-5362	369	8	)	)	PUNCT
ejpam-5362	369	9	be	be	AUX
ejpam-5362	369	10	a	a	DET
ejpam-5362	369	11	bilocale	bilocale	NOUN
ejpam-5362	369	12	with	with	ADP
ejpam-5362	369	13	(	(	PUNCT
ejpam-5362	369	14	s	s	PROPN
ejpam-5362	369	15	,	,	PUNCT
ejpam-5362	369	16	s1	s1	NOUN
ejpam-5362	369	17	,	,	PUNCT
ejpam-5362	369	18	s2	s2	PROPN
ejpam-5362	369	19	)	)	PUNCT
ejpam-5362	369	20	as	as	ADP
ejpam-5362	369	21	its	its	PRON
ejpam-5362	369	22	dense	dense	ADJ
ejpam-5362	369	23	subbilocale	subbilocale	NOUN
ejpam-5362	369	24	.	.	PUNCT
ejpam-5362	370	1	a	a	DET
ejpam-5362	370	2	sublocale	sublocale	NOUN
ejpam-5362	370	3	a	a	PRON
ejpam-5362	370	4	of	of	ADP
ejpam-5362	370	5	s	s	NOUN
ejpam-5362	370	6	is	be	AUX
ejpam-5362	370	7	is	be	AUX
ejpam-5362	370	8	-	-	PUNCT
ejpam-5362	370	9	dense	dense	ADJ
ejpam-5362	370	10	iff	iff	PROPN
ejpam-5362	371	1	it	it	PRON
ejpam-5362	371	2	is	be	AUX
ejpam-5362	371	3	i	i	PRON
ejpam-5362	371	4	-	-	PUNCT
ejpam-5362	371	5	dense	dense	ADJ
ejpam-5362	371	6	.	.	PUNCT
ejpam-5362	372	1	proof	proof	NOUN
ejpam-5362	372	2	.	.	PUNCT
ejpam-5362	373	1	(=	(=	AUX
ejpam-5362	373	2	⇒	⇒	NOUN
ejpam-5362	373	3	):	):	PUNCT
ejpam-5362	373	4	choose	choose	VERB
ejpam-5362	373	5	a	a	DET
ejpam-5362	373	6	non	non	ADJ
ejpam-5362	373	7	-	-	ADJ
ejpam-5362	373	8	void	void	ADJ
ejpam-5362	373	9	i	i	NOUN
ejpam-5362	373	10	-	-	PUNCT
ejpam-5362	373	11	open	open	ADJ
ejpam-5362	373	12	sublocale	sublocale	NOUN
ejpam-5362	373	13	o(x	o(x	PROPN
ejpam-5362	373	14	)	)	PUNCT
ejpam-5362	373	15	of	of	ADP
ejpam-5362	373	16	l.	l.	PROPN
ejpam-5362	373	17	then	then	ADV
ejpam-5362	373	18	o	o	PROPN
ejpam-5362	373	19	̸=	̸=	PROPN
ejpam-5362	373	20	s	s	PART
ejpam-5362	373	21	∩	∩	ADJ
ejpam-5362	373	22	o(x	o(x	PROPN
ejpam-5362	373	23	)	)	PUNCT
ejpam-5362	373	24	=	=	SYM
ejpam-5362	374	1	o(νs(x	o(νs(x	PROPN
ejpam-5362	374	2	)	)	PUNCT
ejpam-5362	374	3	)	)	PUNCT
ejpam-5362	375	1	where	where	SCONJ
ejpam-5362	375	2	νs(x	νs(x	X
ejpam-5362	375	3	)	)	PUNCT
ejpam-5362	375	4	∈	∈	PROPN
ejpam-5362	376	1	si	si	AUX
ejpam-5362	376	2	.	.	PROPN
ejpam-5362	377	1	this	this	PRON
ejpam-5362	377	2	makes	make	VERB
ejpam-5362	377	3	os(νs(x	os(νs(x	NOUN
ejpam-5362	377	4	)	)	PUNCT
ejpam-5362	377	5	)	)	PUNCT
ejpam-5362	378	1	an	an	DET
ejpam-5362	378	2	non	non	ADJ
ejpam-5362	378	3	-	-	ADJ
ejpam-5362	378	4	void	void	ADJ
ejpam-5362	378	5	is	be	AUX
ejpam-5362	378	6	-	-	PUNCT
ejpam-5362	378	7	open	open	ADJ
ejpam-5362	378	8	sublocale	sublocale	NOUN
ejpam-5362	378	9	of	of	ADP
ejpam-5362	378	10	s.	s.	PROPN
ejpam-5362	378	11	since	since	SCONJ
ejpam-5362	378	12	a	a	PRON
ejpam-5362	378	13	is	be	AUX
ejpam-5362	378	14	is	be	AUX
ejpam-5362	378	15	-	-	PUNCT
ejpam-5362	378	16	open	open	ADJ
ejpam-5362	378	17	,	,	PUNCT
ejpam-5362	378	18	o	o	PROPN
ejpam-5362	378	19	̸=	̸=	PROPN
ejpam-5362	378	20	a	a	DET
ejpam-5362	378	21	∩	∩	NOUN
ejpam-5362	378	22	os(νs(x	os(νs(x	NOUN
ejpam-5362	378	23	)	)	PUNCT
ejpam-5362	378	24	)	)	PUNCT
ejpam-5362	379	1	=	=	PUNCT
ejpam-5362	379	2	a	a	DET
ejpam-5362	379	3	∩	∩	NOUN
ejpam-5362	379	4	o(x	o(x	PROPN
ejpam-5362	379	5	)	)	PUNCT
ejpam-5362	379	6	.	.	PUNCT
ejpam-5362	380	1	m.	m.	NOUN
ejpam-5362	380	2	nxumalo	nxumalo	PROPN
ejpam-5362	380	3	/	/	SYM
ejpam-5362	380	4	eur	eur	PROPN
ejpam-5362	380	5	.	.	PUNCT
ejpam-5362	381	1	j.	j.	PROPN
ejpam-5362	381	2	pure	pure	PROPN
ejpam-5362	381	3	appl	appl	PROPN
ejpam-5362	381	4	.	.	PROPN
ejpam-5362	381	5	math	math	PROPN
ejpam-5362	381	6	,	,	PUNCT
ejpam-5362	381	7	18	18	NUM
ejpam-5362	381	8	(	(	PUNCT
ejpam-5362	381	9	1	1	NUM
ejpam-5362	381	10	)	)	PUNCT
ejpam-5362	381	11	(	(	PUNCT
ejpam-5362	381	12	2025	2025	NUM
ejpam-5362	381	13	)	)	PUNCT
ejpam-5362	381	14	,	,	PUNCT
ejpam-5362	381	15	5362	5362	NUM
ejpam-5362	381	16	14	14	NUM
ejpam-5362	381	17	of	of	ADP
ejpam-5362	381	18	21	21	NUM
ejpam-5362	381	19	thus	thus	ADV
ejpam-5362	381	20	a	a	PRON
ejpam-5362	381	21	is	be	AUX
ejpam-5362	381	22	i	i	PRON
ejpam-5362	381	23	-	-	PUNCT
ejpam-5362	381	24	dense	dense	ADJ
ejpam-5362	381	25	.	.	PUNCT
ejpam-5362	382	1	(	(	PUNCT
ejpam-5362	382	2	⇐	⇐	NOUN
ejpam-5362	382	3	=)	=)	PROPN
ejpam-5362	382	4	:	:	PUNCT
ejpam-5362	382	5	let	let	AUX
ejpam-5362	382	6	os(x	os(x	NOUN
ejpam-5362	382	7	)	)	PUNCT
ejpam-5362	382	8	be	be	AUX
ejpam-5362	382	9	a	a	DET
ejpam-5362	382	10	non	non	ADJ
ejpam-5362	382	11	-	-	ADJ
ejpam-5362	382	12	void	void	ADJ
ejpam-5362	382	13	is	be	AUX
ejpam-5362	382	14	-	-	PUNCT
ejpam-5362	382	15	open	open	ADJ
ejpam-5362	382	16	sublocale	sublocale	NOUN
ejpam-5362	382	17	of	of	ADP
ejpam-5362	382	18	s.	s.	PROPN
ejpam-5362	382	19	then	then	ADV
ejpam-5362	382	20	x	x	X
ejpam-5362	382	21	=	=	SYM
ejpam-5362	382	22	νs(y	νs(y	NOUN
ejpam-5362	382	23	)	)	PUNCT
ejpam-5362	382	24	for	for	ADP
ejpam-5362	382	25	some	some	DET
ejpam-5362	382	26	y	y	PROPN
ejpam-5362	382	27	∈	∈	PROPN
ejpam-5362	382	28	li	li	PROPN
ejpam-5362	382	29	.	.	PUNCT
ejpam-5362	383	1	it	it	PRON
ejpam-5362	383	2	follows	follow	VERB
ejpam-5362	383	3	from	from	ADP
ejpam-5362	383	4	lemma	lemma	PROPN
ejpam-5362	383	5	3	3	NUM
ejpam-5362	383	6	that	that	PRON
ejpam-5362	383	7	y	y	PROPN
ejpam-5362	383	8	is	be	AUX
ejpam-5362	383	9	i	i	PRON
ejpam-5362	383	10	-	-	PUNCT
ejpam-5362	383	11	dense	dense	ADJ
ejpam-5362	383	12	.	.	PUNCT
ejpam-5362	384	1	therefore	therefore	ADV
ejpam-5362	384	2	o	o	X
ejpam-5362	384	3	̸=	̸=	PROPN
ejpam-5362	384	4	a	a	DET
ejpam-5362	384	5	∩	∩	NOUN
ejpam-5362	384	6	o(y	o(y	X
ejpam-5362	384	7	)	)	PUNCT
ejpam-5362	384	8	=	=	SYM
ejpam-5362	384	9	a	a	DET
ejpam-5362	384	10	∩	∩	ADJ
ejpam-5362	384	11	os(x	os(x	NOUN
ejpam-5362	384	12	)	)	PUNCT
ejpam-5362	384	13	.	.	PUNCT
ejpam-5362	385	1	thus	thus	ADV
ejpam-5362	385	2	a	a	DET
ejpam-5362	385	3	is	be	AUX
ejpam-5362	385	4	is	be	AUX
ejpam-5362	385	5	-	-	PUNCT
ejpam-5362	385	6	dense	dense	ADJ
ejpam-5362	385	7	.	.	PUNCT
ejpam-5362	386	1	proposition	proposition	NOUN
ejpam-5362	386	2	7	7	NUM
ejpam-5362	386	3	.	.	PUNCT
ejpam-5362	387	1	a	a	DET
ejpam-5362	387	2	bilocale	bilocale	NOUN
ejpam-5362	387	3	(	(	PUNCT
ejpam-5362	387	4	l	l	NOUN
ejpam-5362	387	5	,	,	PUNCT
ejpam-5362	387	6	l1	l1	PROPN
ejpam-5362	387	7	,	,	PUNCT
ejpam-5362	387	8	l2	l2	NOUN
ejpam-5362	387	9	)	)	PUNCT
ejpam-5362	387	10	is	be	AUX
ejpam-5362	387	11	(	(	PUNCT
ejpam-5362	387	12	i	i	PROPN
ejpam-5362	387	13	,	,	PUNCT
ejpam-5362	387	14	j)-baire	j)-baire	VERB
ejpam-5362	387	15	only	only	ADV
ejpam-5362	387	16	if	if	SCONJ
ejpam-5362	387	17	it	it	PRON
ejpam-5362	387	18	contains	contain	VERB
ejpam-5362	387	19	some	some	DET
ejpam-5362	387	20	dense	dense	ADJ
ejpam-5362	387	21	(	(	PUNCT
ejpam-5362	387	22	i	i	NOUN
ejpam-5362	387	23	,	,	PUNCT
ejpam-5362	387	24	j)baire	j)baire	PROPN
ejpam-5362	387	25	subbilocale	subbilocale	NOUN
ejpam-5362	387	26	.	.	PUNCT
ejpam-5362	388	1	proof	proof	NOUN
ejpam-5362	388	2	.	.	PUNCT
ejpam-5362	389	1	let	let	VERB
ejpam-5362	389	2	(	(	PUNCT
ejpam-5362	389	3	s	s	X
ejpam-5362	389	4	,	,	PUNCT
ejpam-5362	389	5	s1	s1	NOUN
ejpam-5362	389	6	,	,	PUNCT
ejpam-5362	389	7	s2	s2	PROPN
ejpam-5362	389	8	)	)	PUNCT
ejpam-5362	389	9	be	be	VERB
ejpam-5362	389	10	a	a	DET
ejpam-5362	389	11	dense	dense	ADJ
ejpam-5362	389	12	and	and	CCONJ
ejpam-5362	389	13	(	(	PUNCT
ejpam-5362	389	14	i	i	NOUN
ejpam-5362	389	15	,	,	PUNCT
ejpam-5362	389	16	j)-baire	j)-baire	NOUN
ejpam-5362	389	17	subbilocale	subbilocale	NOUN
ejpam-5362	389	18	of	of	ADP
ejpam-5362	389	19	(	(	PUNCT
ejpam-5362	389	20	l	l	NOUN
ejpam-5362	389	21	,	,	PUNCT
ejpam-5362	389	22	l1	l1	PROPN
ejpam-5362	389	23	,	,	PUNCT
ejpam-5362	389	24	l2	l2	NOUN
ejpam-5362	389	25	)	)	PUNCT
ejpam-5362	389	26	and	and	CCONJ
ejpam-5362	389	27	pick	pick	VERB
ejpam-5362	389	28	a	a	DET
ejpam-5362	389	29	collection	collection	NOUN
ejpam-5362	389	30	{	{	PUNCT
ejpam-5362	389	31	o(xn	o(xn	NOUN
ejpam-5362	389	32	)	)	PUNCT
ejpam-5362	389	33	:	:	PUNCT
ejpam-5362	389	34	n	n	CCONJ
ejpam-5362	389	35	∈	∈	PROPN
ejpam-5362	389	36	n	n	CCONJ
ejpam-5362	389	37	}	}	PUNCT
ejpam-5362	389	38	of	of	ADP
ejpam-5362	389	39	i	i	NOUN
ejpam-5362	389	40	-	-	PUNCT
ejpam-5362	389	41	dense	dense	ADJ
ejpam-5362	389	42	j	j	NOUN
ejpam-5362	389	43	-	-	ADJ
ejpam-5362	389	44	open	open	ADJ
ejpam-5362	389	45	sublocales	sublocale	NOUN
ejpam-5362	389	46	.	.	PUNCT
ejpam-5362	390	1	since	since	SCONJ
ejpam-5362	390	2	the	the	DET
ejpam-5362	390	3	subbilocale	subbilocale	NOUN
ejpam-5362	390	4	(	(	PUNCT
ejpam-5362	390	5	s	s	PROPN
ejpam-5362	390	6	,	,	PUNCT
ejpam-5362	390	7	s1	s1	NOUN
ejpam-5362	390	8	,	,	PUNCT
ejpam-5362	390	9	s2	s2	PROPN
ejpam-5362	390	10	)	)	PUNCT
ejpam-5362	390	11	is	be	AUX
ejpam-5362	390	12	dense	dense	ADJ
ejpam-5362	390	13	,	,	PUNCT
ejpam-5362	390	14	it	it	PRON
ejpam-5362	390	15	follows	follow	VERB
ejpam-5362	390	16	from	from	ADP
ejpam-5362	390	17	corollary	corollary	ADJ
ejpam-5362	390	18	2	2	NUM
ejpam-5362	390	19	that	that	SCONJ
ejpam-5362	390	20	{	{	PUNCT
ejpam-5362	390	21	s	s	X
ejpam-5362	390	22	∩	∩	NOUN
ejpam-5362	390	23	o(xn	o(xn	X
ejpam-5362	390	24	)	)	PUNCT
ejpam-5362	390	25	:	:	PUNCT
ejpam-5362	391	1	n	n	CCONJ
ejpam-5362	391	2	∈	∈	PROPN
ejpam-5362	391	3	n	n	CCONJ
ejpam-5362	391	4	}	}	PUNCT
ejpam-5362	391	5	is	be	AUX
ejpam-5362	391	6	a	a	DET
ejpam-5362	391	7	collection	collection	NOUN
ejpam-5362	391	8	of	of	ADP
ejpam-5362	391	9	is	be	AUX
ejpam-5362	391	10	-	-	PUNCT
ejpam-5362	391	11	dense	dense	ADJ
ejpam-5362	391	12	js	js	ADJ
ejpam-5362	391	13	-	-	PUNCT
ejpam-5362	391	14	open	open	ADJ
ejpam-5362	391	15	sublocales	sublocale	NOUN
ejpam-5362	391	16	.	.	PUNCT
ejpam-5362	392	1	by	by	ADP
ejpam-5362	392	2	hypothesis	hypothesis	NOUN
ejpam-5362	392	3	,	,	PUNCT
ejpam-5362	392	4	∧	∧	PROPN
ejpam-5362	392	5	n∈n(s	n∈n(s	PROPN
ejpam-5362	392	6	∩	∩	ADJ
ejpam-5362	392	7	o(xn	o(xn	X
ejpam-5362	392	8	)	)	PUNCT
ejpam-5362	392	9	)	)	PUNCT
ejpam-5362	392	10	is	be	AUX
ejpam-5362	392	11	is	be	AUX
ejpam-5362	392	12	-	-	PUNCT
ejpam-5362	392	13	dense	dense	ADJ
ejpam-5362	392	14	,	,	PUNCT
ejpam-5362	392	15	so	so	SCONJ
ejpam-5362	392	16	that	that	SCONJ
ejpam-5362	392	17	it	it	PRON
ejpam-5362	392	18	is	be	AUX
ejpam-5362	392	19	i	i	PRON
ejpam-5362	392	20	-	-	PUNCT
ejpam-5362	392	21	dense	dense	ADJ
ejpam-5362	392	22	by	by	ADP
ejpam-5362	392	23	lemma	lemma	PROPN
ejpam-5362	392	24	4	4	NUM
ejpam-5362	392	25	.	.	PUNCT
ejpam-5362	393	1	since	since	SCONJ
ejpam-5362	393	2	∧	∧	PROPN
ejpam-5362	393	3	n∈n	n∈n	ADV
ejpam-5362	393	4	(	(	PUNCT
ejpam-5362	393	5	s	s	X
ejpam-5362	393	6	∩	∩	NOUN
ejpam-5362	393	7	o(xn	o(xn	X
ejpam-5362	393	8	)	)	PUNCT
ejpam-5362	393	9	)	)	PUNCT
ejpam-5362	394	1	⊆	⊆	NUM
ejpam-5362	394	2	∧	∧	PROPN
ejpam-5362	394	3	n∈n	n∈n	ADV
ejpam-5362	394	4	o(xn	o(xn	NOUN
ejpam-5362	394	5	)	)	PUNCT
ejpam-5362	394	6	,	,	PUNCT
ejpam-5362	394	7	it	it	PRON
ejpam-5362	394	8	follows	follow	VERB
ejpam-5362	394	9	that	that	SCONJ
ejpam-5362	394	10	∧	∧	PROPN
ejpam-5362	394	11	n∈n	n∈n	ADV
ejpam-5362	394	12	o(xn	o(xn	NUM
ejpam-5362	394	13	)	)	PUNCT
ejpam-5362	394	14	is	be	AUX
ejpam-5362	394	15	i	i	PRON
ejpam-5362	394	16	-	-	PUNCT
ejpam-5362	394	17	dense	dense	ADJ
ejpam-5362	394	18	.	.	PUNCT
ejpam-5362	395	1	corollary	corollary	ADJ
ejpam-5362	395	2	3	3	NUM
ejpam-5362	395	3	.	.	PUNCT
ejpam-5362	396	1	a	a	DET
ejpam-5362	396	2	bilocale	bilocale	NOUN
ejpam-5362	396	3	(	(	PUNCT
ejpam-5362	396	4	l	l	NOUN
ejpam-5362	396	5	,	,	PUNCT
ejpam-5362	396	6	l1	l1	PROPN
ejpam-5362	396	7	,	,	PUNCT
ejpam-5362	396	8	l2	l2	NOUN
ejpam-5362	396	9	)	)	PUNCT
ejpam-5362	396	10	is	be	AUX
ejpam-5362	396	11	(	(	PUNCT
ejpam-5362	396	12	i	i	PROPN
ejpam-5362	396	13	,	,	PUNCT
ejpam-5362	396	14	j)-baire	j)-baire	VERB
ejpam-5362	396	15	only	only	ADV
ejpam-5362	396	16	if	if	SCONJ
ejpam-5362	396	17	(	(	PUNCT
ejpam-5362	396	18	bl	bl	INTJ
ejpam-5362	396	19	,	,	PUNCT
ejpam-5362	396	20	νb[l1	νb[l1	PROPN
ejpam-5362	396	21	]	]	PUNCT
ejpam-5362	396	22	,	,	PUNCT
ejpam-5362	396	23	νb[l2	νb[l2	PROPN
ejpam-5362	396	24	]	]	PUNCT
ejpam-5362	396	25	)	)	PUNCT
ejpam-5362	396	26	is	be	AUX
ejpam-5362	396	27	(	(	PUNCT
ejpam-5362	396	28	i	i	NOUN
ejpam-5362	396	29	,	,	PUNCT
ejpam-5362	396	30	j)baire	j)baire	ADV
ejpam-5362	396	31	as	as	ADP
ejpam-5362	396	32	a	a	DET
ejpam-5362	396	33	bilocale	bilocale	NOUN
ejpam-5362	396	34	.	.	PUNCT
ejpam-5362	397	1	call	call	VERB
ejpam-5362	397	2	a	a	DET
ejpam-5362	397	3	bilocale	bilocale	NOUN
ejpam-5362	397	4	(	(	PUNCT
ejpam-5362	397	5	l	l	NOUN
ejpam-5362	397	6	,	,	PUNCT
ejpam-5362	397	7	l1	l1	PROPN
ejpam-5362	397	8	,	,	PUNCT
ejpam-5362	397	9	l2	l2	NOUN
ejpam-5362	397	10	)	)	PUNCT
ejpam-5362	397	11	(	(	PUNCT
ejpam-5362	397	12	i	i	NOUN
ejpam-5362	397	13	,	,	PUNCT
ejpam-5362	397	14	j)-submaximal	j)-submaximal	PROPN
ejpam-5362	397	15	if	if	SCONJ
ejpam-5362	397	16	every	every	DET
ejpam-5362	397	17	i	i	NOUN
ejpam-5362	397	18	-	-	PUNCT
ejpam-5362	397	19	dense	dense	ADJ
ejpam-5362	397	20	sublocale	sublocale	NOUN
ejpam-5362	397	21	of	of	ADP
ejpam-5362	397	22	l	l	NOUN
ejpam-5362	397	23	is	be	AUX
ejpam-5362	397	24	j	j	NOUN
ejpam-5362	397	25	-	-	ADJ
ejpam-5362	397	26	open	open	ADJ
ejpam-5362	397	27	proposition	proposition	NOUN
ejpam-5362	397	28	8	8	NUM
ejpam-5362	397	29	.	.	PUNCT
ejpam-5362	398	1	let	let	VERB
ejpam-5362	398	2	(	(	PUNCT
ejpam-5362	398	3	l	l	NOUN
ejpam-5362	398	4	,	,	PUNCT
ejpam-5362	398	5	l1	l1	PROPN
ejpam-5362	398	6	,	,	PUNCT
ejpam-5362	398	7	l2	l2	NOUN
ejpam-5362	398	8	)	)	PUNCT
ejpam-5362	398	9	be	be	VERB
ejpam-5362	398	10	an	an	DET
ejpam-5362	398	11	(	(	PUNCT
ejpam-5362	398	12	i	i	NOUN
ejpam-5362	398	13	,	,	PUNCT
ejpam-5362	398	14	j)-submaximal	j)-submaximal	ADJ
ejpam-5362	398	15	bilocale	bilocale	NOUN
ejpam-5362	398	16	.	.	PUNCT
ejpam-5362	399	1	then	then	ADV
ejpam-5362	399	2	(	(	PUNCT
ejpam-5362	399	3	l	l	NOUN
ejpam-5362	399	4	,	,	PUNCT
ejpam-5362	399	5	l1	l1	PROPN
ejpam-5362	399	6	,	,	PUNCT
ejpam-5362	399	7	l2	l2	NOUN
ejpam-5362	399	8	)	)	PUNCT
ejpam-5362	399	9	is	be	AUX
ejpam-5362	399	10	(	(	PUNCT
ejpam-5362	399	11	i	i	PROPN
ejpam-5362	399	12	,	,	PUNCT
ejpam-5362	399	13	j)baire	j)baire	PROPN
ejpam-5362	399	14	iff	iff	PROPN
ejpam-5362	399	15	(	(	PUNCT
ejpam-5362	399	16	bl	bl	INTJ
ejpam-5362	399	17	,	,	PUNCT
ejpam-5362	399	18	νb[l1	νb[l1	PROPN
ejpam-5362	399	19	]	]	PUNCT
ejpam-5362	399	20	,	,	PUNCT
ejpam-5362	399	21	νb[l2	νb[l2	PROPN
ejpam-5362	399	22	]	]	PUNCT
ejpam-5362	399	23	)	)	PUNCT
ejpam-5362	400	1	is	be	AUX
ejpam-5362	400	2	(	(	PUNCT
ejpam-5362	400	3	i	i	NOUN
ejpam-5362	400	4	,	,	PUNCT
ejpam-5362	400	5	j)-baire	j)-baire	NOUN
ejpam-5362	400	6	as	as	ADP
ejpam-5362	400	7	a	a	DET
ejpam-5362	400	8	bilocale	bilocale	NOUN
ejpam-5362	400	9	.	.	PUNCT
ejpam-5362	401	1	proof	proof	NOUN
ejpam-5362	401	2	.	.	PUNCT
ejpam-5362	402	1	we	we	PRON
ejpam-5362	402	2	only	only	ADV
ejpam-5362	402	3	prove	prove	VERB
ejpam-5362	402	4	the	the	DET
ejpam-5362	402	5	forward	forward	ADJ
ejpam-5362	402	6	implication	implication	NOUN
ejpam-5362	402	7	:	:	PUNCT
ejpam-5362	402	8	let	let	VERB
ejpam-5362	402	9	{	{	PUNCT
ejpam-5362	402	10	obl(xn	obl(xn	NOUN
ejpam-5362	402	11	)	)	PUNCT
ejpam-5362	402	12	:	:	PUNCT
ejpam-5362	402	13	n	n	CCONJ
ejpam-5362	402	14	∈	∈	PROPN
ejpam-5362	402	15	n	n	CCONJ
ejpam-5362	402	16	}	}	PUNCT
ejpam-5362	402	17	be	be	AUX
ejpam-5362	402	18	a	a	DET
ejpam-5362	402	19	collection	collection	NOUN
ejpam-5362	402	20	of	of	ADP
ejpam-5362	402	21	ibl	ibl	PROPN
ejpam-5362	402	22	-	-	ADJ
ejpam-5362	402	23	dense	dense	ADJ
ejpam-5362	402	24	jbl	jbl	NOUN
ejpam-5362	402	25	-	-	PUNCT
ejpam-5362	402	26	open	open	ADJ
ejpam-5362	402	27	sublocales	sublocale	NOUN
ejpam-5362	402	28	.	.	PUNCT
ejpam-5362	403	1	it	it	PRON
ejpam-5362	403	2	follows	follow	VERB
ejpam-5362	403	3	that	that	SCONJ
ejpam-5362	403	4	{	{	PUNCT
ejpam-5362	403	5	o(xn	o(xn	X
ejpam-5362	403	6	)	)	PUNCT
ejpam-5362	403	7	:	:	PUNCT
ejpam-5362	403	8	n	n	CCONJ
ejpam-5362	403	9	∈	∈	PROPN
ejpam-5362	403	10	n	n	CCONJ
ejpam-5362	403	11	}	}	PUNCT
ejpam-5362	403	12	is	be	AUX
ejpam-5362	403	13	a	a	DET
ejpam-5362	403	14	collection	collection	NOUN
ejpam-5362	403	15	of	of	ADP
ejpam-5362	403	16	i	i	NOUN
ejpam-5362	403	17	-	-	PUNCT
ejpam-5362	403	18	dense	dense	ADJ
ejpam-5362	403	19	j	j	NOUN
ejpam-5362	403	20	-	-	ADJ
ejpam-5362	403	21	open	open	ADJ
ejpam-5362	403	22	sublocales	sublocale	NOUN
ejpam-5362	403	23	.	.	PUNCT
ejpam-5362	404	1	since	since	SCONJ
ejpam-5362	404	2	(	(	PUNCT
ejpam-5362	404	3	l	l	NOUN
ejpam-5362	404	4	,	,	PUNCT
ejpam-5362	404	5	l1	l1	PROPN
ejpam-5362	404	6	,	,	PUNCT
ejpam-5362	404	7	l2	l2	NOUN
ejpam-5362	404	8	)	)	PUNCT
ejpam-5362	404	9	is	be	AUX
ejpam-5362	404	10	(	(	PUNCT
ejpam-5362	404	11	i	i	PRON
ejpam-5362	404	12	,	,	PUNCT
ejpam-5362	404	13	j)-baire,∧	j)-baire,∧	PROPN
ejpam-5362	404	14	n∈n	n∈n	ADV
ejpam-5362	404	15	o(xn	o(xn	NUM
ejpam-5362	404	16	)	)	PUNCT
ejpam-5362	404	17	is	be	AUX
ejpam-5362	404	18	i	i	PRON
ejpam-5362	404	19	-	-	PUNCT
ejpam-5362	404	20	dense	dense	ADJ
ejpam-5362	404	21	.	.	PUNCT
ejpam-5362	405	1	we	we	PRON
ejpam-5362	405	2	must	must	AUX
ejpam-5362	405	3	have	have	VERB
ejpam-5362	405	4	that	that	DET
ejpam-5362	405	5	∧	∧	PROPN
ejpam-5362	405	6	n∈n	n∈n	NOUN
ejpam-5362	405	7	obl(xn	obl(xn	ADP
ejpam-5362	405	8	)	)	PUNCT
ejpam-5362	405	9	is	be	AUX
ejpam-5362	405	10	ibl	ibl	PROPN
ejpam-5362	405	11	-	-	ADJ
ejpam-5362	405	12	dense	dense	ADJ
ejpam-5362	405	13	,	,	PUNCT
ejpam-5362	405	14	otherwise	otherwise	ADV
ejpam-5362	405	15	there	there	PRON
ejpam-5362	405	16	is	be	VERB
ejpam-5362	405	17	a	a	DET
ejpam-5362	405	18	non	non	ADJ
ejpam-5362	405	19	-	-	ADJ
ejpam-5362	405	20	void	void	ADJ
ejpam-5362	405	21	νbl[li]-open	νbl[li]-open	NOUN
ejpam-5362	405	22	sublocale	sublocale	ADJ
ejpam-5362	405	23	obl(y	obl(y	PROPN
ejpam-5362	405	24	)	)	PUNCT
ejpam-5362	405	25	such	such	ADJ
ejpam-5362	405	26	that	that	DET
ejpam-5362	405	27	obl(y	obl(y	NOUN
ejpam-5362	405	28	)	)	PUNCT
ejpam-5362	405	29	∩	∩	NOUN
ejpam-5362	405	30	(	(	PUNCT
ejpam-5362	405	31	∧	∧	PROPN
ejpam-5362	405	32	n∈n	n∈n	NOUN
ejpam-5362	405	33	obl(xn	obl(xn	ADP
ejpam-5362	405	34	)	)	PUNCT
ejpam-5362	405	35	)	)	PUNCT
ejpam-5362	406	1	=	=	SYM
ejpam-5362	406	2	o.	o.	INTJ
ejpam-5362	406	3	therefore	therefore	ADV
ejpam-5362	406	4	obl(y	obl(y	PROPN
ejpam-5362	406	5	)	)	PUNCT
ejpam-5362	406	6	∩	∩	NOUN
ejpam-5362	406	7	(	(	PUNCT
ejpam-5362	406	8	∧	∧	PROPN
ejpam-5362	406	9	n∈n	n∈n	NOUN
ejpam-5362	406	10	o(xn	o(xn	NUM
ejpam-5362	406	11	)	)	PUNCT
ejpam-5362	406	12	)	)	PUNCT
ejpam-5362	407	1	=	=	SYM
ejpam-5362	407	2	o.	o.	INTJ
ejpam-5362	407	3	since	since	SCONJ
ejpam-5362	407	4	every	every	DET
ejpam-5362	407	5	dense	dense	ADJ
ejpam-5362	407	6	sublocale	sublocale	NOUN
ejpam-5362	407	7	is	be	AUX
ejpam-5362	407	8	i	i	PRON
ejpam-5362	407	9	-	-	PUNCT
ejpam-5362	407	10	dense	dense	ADJ
ejpam-5362	407	11	and	and	CCONJ
ejpam-5362	407	12	(	(	PUNCT
ejpam-5362	407	13	l	l	NOUN
ejpam-5362	407	14	,	,	PUNCT
ejpam-5362	407	15	l1	l1	PROPN
ejpam-5362	407	16	,	,	PUNCT
ejpam-5362	407	17	l2	l2	NOUN
ejpam-5362	407	18	)	)	PUNCT
ejpam-5362	407	19	is	be	AUX
ejpam-5362	407	20	(	(	PUNCT
ejpam-5362	407	21	i	i	NOUN
ejpam-5362	407	22	,	,	PUNCT
ejpam-5362	407	23	j)-submaximal	j)-submaximal	PROPN
ejpam-5362	407	24	,	,	PUNCT
ejpam-5362	407	25	we	we	PRON
ejpam-5362	407	26	have	have	VERB
ejpam-5362	407	27	that	that	PRON
ejpam-5362	407	28	bl	bl	PROPN
ejpam-5362	407	29	is	be	AUX
ejpam-5362	407	30	j	j	NOUN
ejpam-5362	407	31	-	-	VERB
ejpam-5362	407	32	open	open	ADJ
ejpam-5362	407	33	so	so	SCONJ
ejpam-5362	407	34	that	that	SCONJ
ejpam-5362	407	35	obl(y	obl(y	PROPN
ejpam-5362	407	36	)	)	PUNCT
ejpam-5362	407	37	=	=	SYM
ejpam-5362	407	38	bl	bl	NOUN
ejpam-5362	407	39	∩	∩	NOUN
ejpam-5362	407	40	o(y	o(y	NOUN
ejpam-5362	407	41	)	)	PUNCT
ejpam-5362	407	42	is	be	AUX
ejpam-5362	407	43	a	a	DET
ejpam-5362	407	44	j	j	NOUN
ejpam-5362	407	45	-	-	PUNCT
ejpam-5362	407	46	open	open	ADJ
ejpam-5362	407	47	sublocale	sublocale	NOUN
ejpam-5362	407	48	.	.	PUNCT
ejpam-5362	408	1	therefore	therefore	ADV
ejpam-5362	408	2	obl(y	obl(y	PROPN
ejpam-5362	408	3	)	)	PUNCT
ejpam-5362	408	4	=	=	SYM
ejpam-5362	408	5	0	0	NUM
ejpam-5362	408	6	which	which	PRON
ejpam-5362	408	7	is	be	AUX
ejpam-5362	408	8	impossible	impossible	ADJ
ejpam-5362	408	9	.	.	PUNCT
ejpam-5362	409	1	m.	m.	NOUN
ejpam-5362	409	2	nxumalo	nxumalo	PROPN
ejpam-5362	409	3	/	/	SYM
ejpam-5362	409	4	eur	eur	PROPN
ejpam-5362	409	5	.	.	PUNCT
ejpam-5362	410	1	j.	j.	PROPN
ejpam-5362	410	2	pure	pure	PROPN
ejpam-5362	410	3	appl	appl	PROPN
ejpam-5362	410	4	.	.	PROPN
ejpam-5362	410	5	math	math	PROPN
ejpam-5362	410	6	,	,	PUNCT
ejpam-5362	410	7	18	18	NUM
ejpam-5362	410	8	(	(	PUNCT
ejpam-5362	410	9	1	1	NUM
ejpam-5362	410	10	)	)	PUNCT
ejpam-5362	410	11	(	(	PUNCT
ejpam-5362	410	12	2025	2025	NUM
ejpam-5362	410	13	)	)	PUNCT
ejpam-5362	410	14	,	,	PUNCT
ejpam-5362	410	15	5362	5362	NUM
ejpam-5362	410	16	15	15	NUM
ejpam-5362	410	17	of	of	ADP
ejpam-5362	410	18	21	21	NUM
ejpam-5362	410	19	proposition	proposition	NOUN
ejpam-5362	410	20	9	9	NUM
ejpam-5362	410	21	.	.	PUNCT
ejpam-5362	411	1	every	every	DET
ejpam-5362	411	2	i	i	NOUN
ejpam-5362	411	3	-	-	PUNCT
ejpam-5362	411	4	open	open	ADJ
ejpam-5362	411	5	subbilocale	subbilocale	NOUN
ejpam-5362	411	6	of	of	ADP
ejpam-5362	411	7	an	an	DET
ejpam-5362	411	8	(	(	PUNCT
ejpam-5362	411	9	i	i	NOUN
ejpam-5362	411	10	,	,	PUNCT
ejpam-5362	411	11	j)-baire	j)-baire	NOUN
ejpam-5362	411	12	bilocale	bilocale	NOUN
ejpam-5362	411	13	is	be	AUX
ejpam-5362	411	14	(	(	PUNCT
ejpam-5362	411	15	i	i	NOUN
ejpam-5362	411	16	,	,	PUNCT
ejpam-5362	411	17	j)-baire	j)-baire	NOUN
ejpam-5362	411	18	.	.	PUNCT
ejpam-5362	412	1	proof	proof	NOUN
ejpam-5362	412	2	.	.	PUNCT
ejpam-5362	413	1	let	let	AUX
ejpam-5362	413	2	(	(	PUNCT
ejpam-5362	413	3	s	s	X
ejpam-5362	413	4	,	,	PUNCT
ejpam-5362	413	5	s1	s1	NOUN
ejpam-5362	413	6	,	,	PUNCT
ejpam-5362	413	7	s2	s2	PROPN
ejpam-5362	413	8	)	)	PUNCT
ejpam-5362	413	9	be	be	VERB
ejpam-5362	413	10	an	an	DET
ejpam-5362	413	11	i	i	NOUN
ejpam-5362	413	12	-	-	PUNCT
ejpam-5362	413	13	open	open	ADJ
ejpam-5362	413	14	subbilocale	subbilocale	NOUN
ejpam-5362	413	15	of	of	ADP
ejpam-5362	413	16	an	an	DET
ejpam-5362	413	17	(	(	PUNCT
ejpam-5362	413	18	i	i	NOUN
ejpam-5362	413	19	,	,	PUNCT
ejpam-5362	413	20	j)-baire	j)-baire	NOUN
ejpam-5362	413	21	bilocale	bilocale	NOUN
ejpam-5362	413	22	(	(	PUNCT
ejpam-5362	413	23	l	l	NOUN
ejpam-5362	413	24	,	,	PUNCT
ejpam-5362	413	25	l1	l1	PROPN
ejpam-5362	413	26	,	,	PUNCT
ejpam-5362	413	27	l2	l2	NOUN
ejpam-5362	413	28	)	)	PUNCT
ejpam-5362	413	29	.	.	PUNCT
ejpam-5362	414	1	choose	choose	VERB
ejpam-5362	414	2	a	a	DET
ejpam-5362	414	3	collection	collection	NOUN
ejpam-5362	414	4	{	{	PUNCT
ejpam-5362	414	5	os(xn	os(xn	PROPN
ejpam-5362	414	6	)	)	PUNCT
ejpam-5362	414	7	:	:	PUNCT
ejpam-5362	414	8	n	n	CCONJ
ejpam-5362	414	9	∈	∈	PROPN
ejpam-5362	414	10	n	n	CCONJ
ejpam-5362	414	11	}	}	PUNCT
ejpam-5362	414	12	of	of	ADP
ejpam-5362	414	13	is	be	AUX
ejpam-5362	414	14	-	-	PUNCT
ejpam-5362	414	15	dense	dense	ADJ
ejpam-5362	414	16	js	js	ADJ
ejpam-5362	414	17	-	-	PUNCT
ejpam-5362	414	18	open	open	ADJ
ejpam-5362	414	19	sublocales	sublocale	NOUN
ejpam-5362	414	20	.	.	PUNCT
ejpam-5362	415	1	we	we	PRON
ejpam-5362	415	2	show	show	VERB
ejpam-5362	415	3	that∧	that∧	PROPN
ejpam-5362	415	4	n∈n	n∈n	ADJ
ejpam-5362	415	5	os(xn	os(xn	PROPN
ejpam-5362	415	6	)	)	PUNCT
ejpam-5362	415	7	is	be	AUX
ejpam-5362	415	8	is	be	AUX
ejpam-5362	415	9	-	-	PUNCT
ejpam-5362	415	10	dense	dense	ADJ
ejpam-5362	415	11	.	.	PUNCT
ejpam-5362	416	1	pick	pick	VERB
ejpam-5362	416	2	an	an	DET
ejpam-5362	416	3	is	be	AUX
ejpam-5362	416	4	-	-	PUNCT
ejpam-5362	416	5	open	open	ADJ
ejpam-5362	416	6	sublocale	sublocale	NOUN
ejpam-5362	416	7	os(y	os(y	NUM
ejpam-5362	416	8	)	)	PUNCT
ejpam-5362	416	9	such	such	ADJ
ejpam-5362	416	10	that(∧	that(∧	NUM
ejpam-5362	416	11	n∈n	n∈n	ADJ
ejpam-5362	416	12	os(xn	os(xn	NOUN
ejpam-5362	416	13	)	)	PUNCT
ejpam-5362	416	14	)	)	PUNCT
ejpam-5362	416	15	∩	∩	NOUN
ejpam-5362	416	16	os(y	os(y	NUM
ejpam-5362	416	17	)	)	PUNCT
ejpam-5362	417	1	=	=	SYM
ejpam-5362	417	2	o.	o.	NOUN
ejpam-5362	417	3	since	since	SCONJ
ejpam-5362	417	4	os(y	os(y	NUM
ejpam-5362	417	5	)	)	PUNCT
ejpam-5362	417	6	⊆	⊆	NUM
ejpam-5362	417	7	s	s	NOUN
ejpam-5362	417	8	,	,	PUNCT
ejpam-5362	417	9	os(y	os(y	NUM
ejpam-5362	417	10	)	)	PUNCT
ejpam-5362	417	11	∩	∩	NOUN
ejpam-5362	417	12	(	(	PUNCT
ejpam-5362	417	13	l∖	l∖	PROPN
ejpam-5362	417	14	s	s	PART
ejpam-5362	417	15	)	)	PUNCT
ejpam-5362	417	16	=	=	SYM
ejpam-5362	418	1	o.	o.	NOUN
ejpam-5362	418	2	therefore	therefore	ADV
ejpam-5362	418	3	os(y	os(y	NUM
ejpam-5362	418	4	)	)	PUNCT
ejpam-5362	418	5	∩	∩	NOUN
ejpam-5362	418	6	(	(	PUNCT
ejpam-5362	418	7	(	(	PUNCT
ejpam-5362	418	8	∧	∧	PROPN
ejpam-5362	418	9	n∈n	n∈n	ADJ
ejpam-5362	418	10	os(xn	os(xn	NOUN
ejpam-5362	418	11	)	)	PUNCT
ejpam-5362	418	12	)	)	PUNCT
ejpam-5362	418	13	∨	∨	NUM
ejpam-5362	418	14	(	(	PUNCT
ejpam-5362	418	15	l∖	l∖	PROPN
ejpam-5362	418	16	s	s	PART
ejpam-5362	418	17	)	)	PUNCT
ejpam-5362	418	18	)	)	PUNCT
ejpam-5362	419	1	=	=	SYM
ejpam-5362	419	2	(	(	PUNCT
ejpam-5362	419	3	(	(	PUNCT
ejpam-5362	419	4	∧	∧	PROPN
ejpam-5362	419	5	n∈n	n∈n	ADJ
ejpam-5362	419	6	os(xn	os(xn	NOUN
ejpam-5362	419	7	)	)	PUNCT
ejpam-5362	419	8	)	)	PUNCT
ejpam-5362	419	9	∩	∩	NOUN
ejpam-5362	419	10	os(y	os(y	NUM
ejpam-5362	419	11	)	)	PUNCT
ejpam-5362	419	12	)	)	PUNCT
ejpam-5362	419	13	∨	∨	NUM
ejpam-5362	419	14	(	(	PUNCT
ejpam-5362	419	15	os(y	os(y	NUM
ejpam-5362	419	16	)	)	PUNCT
ejpam-5362	419	17	∩	∩	NOUN
ejpam-5362	419	18	(	(	PUNCT
ejpam-5362	419	19	l∖	l∖	PROPN
ejpam-5362	419	20	s	s	PART
ejpam-5362	419	21	)	)	PUNCT
ejpam-5362	419	22	)	)	PUNCT
ejpam-5362	420	1	=	=	PUNCT
ejpam-5362	420	2	(	(	PUNCT
ejpam-5362	420	3	∧	∧	PROPN
ejpam-5362	420	4	n∈n	n∈n	ADJ
ejpam-5362	420	5	os(xn	os(xn	NOUN
ejpam-5362	420	6	)	)	PUNCT
ejpam-5362	420	7	)	)	PUNCT
ejpam-5362	420	8	∩	∩	NOUN
ejpam-5362	420	9	os(y	os(y	NUM
ejpam-5362	420	10	)	)	PUNCT
ejpam-5362	421	1	=	=	SYM
ejpam-5362	421	2	o.	o.	INTJ
ejpam-5362	421	3	because	because	SCONJ
ejpam-5362	421	4	os(xn	os(xn	PROPN
ejpam-5362	421	5	)	)	PUNCT
ejpam-5362	421	6	∨	∨	NUM
ejpam-5362	421	7	(	(	PUNCT
ejpam-5362	421	8	l∖	l∖	PROPN
ejpam-5362	421	9	s	s	PART
ejpam-5362	421	10	)	)	PUNCT
ejpam-5362	421	11	is	be	AUX
ejpam-5362	421	12	i	i	PRON
ejpam-5362	421	13	-	-	PUNCT
ejpam-5362	421	14	dense	dense	ADJ
ejpam-5362	421	15	,	,	PUNCT
ejpam-5362	421	16	it	it	PRON
ejpam-5362	421	17	follows	follow	VERB
ejpam-5362	421	18	that∧	that∧	PROPN
ejpam-5362	421	19	n∈n	n∈n	NOUN
ejpam-5362	421	20	(	(	PUNCT
ejpam-5362	421	21	os(xn	os(xn	PROPN
ejpam-5362	421	22	)	)	PUNCT
ejpam-5362	421	23	∨	∨	NUM
ejpam-5362	421	24	(	(	PUNCT
ejpam-5362	421	25	l∖	l∖	PROPN
ejpam-5362	421	26	s	s	PART
ejpam-5362	421	27	)	)	PUNCT
ejpam-5362	421	28	)	)	PUNCT
ejpam-5362	422	1	=	=	PUNCT
ejpam-5362	422	2	(	(	PUNCT
ejpam-5362	422	3	l∖	l∖	PROPN
ejpam-5362	422	4	s	s	PART
ejpam-5362	422	5	)	)	PUNCT
ejpam-5362	422	6	∨	∨	NUM
ejpam-5362	422	7	∧	∧	PROPN
ejpam-5362	422	8	n∈n	n∈n	ADJ
ejpam-5362	422	9	os(xn	os(xn	PROPN
ejpam-5362	422	10	)	)	PUNCT
ejpam-5362	422	11	is	be	AUX
ejpam-5362	422	12	i	i	PRON
ejpam-5362	422	13	-	-	PUNCT
ejpam-5362	422	14	dense	dense	ADJ
ejpam-5362	422	15	.	.	PUNCT
ejpam-5362	423	1	therefore	therefore	ADV
ejpam-5362	423	2	os(y	os(y	NUM
ejpam-5362	423	3	)	)	PUNCT
ejpam-5362	424	1	=	=	SYM
ejpam-5362	424	2	o.	o.	NOUN
ejpam-5362	424	3	thus	thus	ADV
ejpam-5362	424	4	∧	∧	PROPN
ejpam-5362	424	5	n∈n	n∈n	ADJ
ejpam-5362	424	6	os(xn	os(xn	PROPN
ejpam-5362	424	7	)	)	PUNCT
ejpam-5362	424	8	is	be	AUX
ejpam-5362	424	9	is	be	AUX
ejpam-5362	424	10	-	-	PUNCT
ejpam-5362	424	11	dense	dense	ADJ
ejpam-5362	424	12	.	.	PUNCT
ejpam-5362	425	1	definition	definition	NOUN
ejpam-5362	425	2	5	5	NUM
ejpam-5362	425	3	.	.	PUNCT
ejpam-5362	426	1	let	let	VERB
ejpam-5362	426	2	(	(	PUNCT
ejpam-5362	426	3	l	l	NOUN
ejpam-5362	426	4	,	,	PUNCT
ejpam-5362	426	5	l1	l1	PROPN
ejpam-5362	426	6	,	,	PUNCT
ejpam-5362	426	7	l2	l2	NOUN
ejpam-5362	426	8	)	)	PUNCT
ejpam-5362	426	9	be	be	AUX
ejpam-5362	426	10	a	a	DET
ejpam-5362	426	11	bilocale	bilocale	NOUN
ejpam-5362	426	12	.	.	PUNCT
ejpam-5362	427	1	a	a	DET
ejpam-5362	427	2	subbilocale	subbilocale	NOUN
ejpam-5362	427	3	(	(	PUNCT
ejpam-5362	427	4	s	s	NOUN
ejpam-5362	427	5	,	,	PUNCT
ejpam-5362	427	6	s1	s1	NOUN
ejpam-5362	427	7	,	,	PUNCT
ejpam-5362	427	8	s2	s2	PROPN
ejpam-5362	427	9	)	)	PUNCT
ejpam-5362	427	10	of	of	ADP
ejpam-5362	427	11	(	(	PUNCT
ejpam-5362	427	12	l	l	NOUN
ejpam-5362	427	13	,	,	PUNCT
ejpam-5362	427	14	l1	l1	PROPN
ejpam-5362	427	15	,	,	PUNCT
ejpam-5362	427	16	l2	l2	NOUN
ejpam-5362	427	17	)	)	PUNCT
ejpam-5362	427	18	is	be	AUX
ejpam-5362	427	19	relatively	relatively	ADV
ejpam-5362	427	20	(	(	PUNCT
ejpam-5362	427	21	i	i	NOUN
ejpam-5362	427	22	,	,	PUNCT
ejpam-5362	427	23	j)-baire	j)-baire	VERB
ejpam-5362	427	24	if	if	SCONJ
ejpam-5362	427	25	for	for	ADP
ejpam-5362	427	26	every	every	DET
ejpam-5362	427	27	collection	collection	NOUN
ejpam-5362	427	28	{	{	PUNCT
ejpam-5362	427	29	o(xn	o(xn	NOUN
ejpam-5362	427	30	)	)	PUNCT
ejpam-5362	427	31	:	:	PUNCT
ejpam-5362	427	32	n	n	CCONJ
ejpam-5362	427	33	∈	∈	PROPN
ejpam-5362	427	34	n	n	CCONJ
ejpam-5362	427	35	}	}	PUNCT
ejpam-5362	427	36	of	of	ADP
ejpam-5362	427	37	i	i	NOUN
ejpam-5362	427	38	-	-	PUNCT
ejpam-5362	427	39	dense	dense	ADJ
ejpam-5362	427	40	j	j	NOUN
ejpam-5362	427	41	-	-	ADJ
ejpam-5362	427	42	open	open	ADJ
ejpam-5362	427	43	sublocales	sublocale	NOUN
ejpam-5362	427	44	,	,	PUNCT
ejpam-5362	427	45	s	s	NOUN
ejpam-5362	427	46	∩	∩	NOUN
ejpam-5362	427	47	(	(	PUNCT
ejpam-5362	427	48	∧	∧	PROPN
ejpam-5362	427	49	n∈n	n∈n	NOUN
ejpam-5362	427	50	o(xn	o(xn	NUM
ejpam-5362	427	51	)	)	PUNCT
ejpam-5362	427	52	)	)	PUNCT
ejpam-5362	427	53	is	be	AUX
ejpam-5362	427	54	is	be	AUX
ejpam-5362	427	55	-	-	PUNCT
ejpam-5362	427	56	dense	dense	ADJ
ejpam-5362	427	57	.	.	PUNCT
ejpam-5362	428	1	proposition	proposition	NOUN
ejpam-5362	428	2	10	10	NUM
ejpam-5362	428	3	.	.	PUNCT
ejpam-5362	429	1	in	in	ADP
ejpam-5362	429	2	a	a	DET
ejpam-5362	429	3	class	class	NOUN
ejpam-5362	429	4	of	of	ADP
ejpam-5362	429	5	dense	dense	ADJ
ejpam-5362	429	6	subbilocales	subbilocale	NOUN
ejpam-5362	429	7	,	,	PUNCT
ejpam-5362	429	8	(	(	PUNCT
ejpam-5362	429	9	i	i	PRON
ejpam-5362	429	10	,	,	PUNCT
ejpam-5362	429	11	j)-baire	j)-baire	VERB
ejpam-5362	429	12	coincides	coincide	VERB
ejpam-5362	429	13	with	with	ADP
ejpam-5362	429	14	relatively	relatively	ADV
ejpam-5362	429	15	(	(	PUNCT
ejpam-5362	429	16	i	i	NOUN
ejpam-5362	429	17	,	,	PUNCT
ejpam-5362	429	18	j)-baire	j)-baire	NOUN
ejpam-5362	429	19	.	.	PUNCT
ejpam-5362	430	1	proof	proof	NOUN
ejpam-5362	430	2	.	.	PUNCT
ejpam-5362	431	1	let	let	AUX
ejpam-5362	431	2	(	(	PUNCT
ejpam-5362	431	3	s	s	X
ejpam-5362	431	4	,	,	PUNCT
ejpam-5362	431	5	s1	s1	NOUN
ejpam-5362	431	6	,	,	PUNCT
ejpam-5362	431	7	s2	s2	PROPN
ejpam-5362	431	8	)	)	PUNCT
ejpam-5362	431	9	be	be	VERB
ejpam-5362	431	10	an	an	DET
ejpam-5362	431	11	(	(	PUNCT
ejpam-5362	431	12	i	i	NOUN
ejpam-5362	431	13	,	,	PUNCT
ejpam-5362	431	14	j)-baire	j)-baire	NOUN
ejpam-5362	431	15	subbilocale	subbilocale	NOUN
ejpam-5362	431	16	of	of	ADP
ejpam-5362	431	17	a	a	DET
ejpam-5362	431	18	bilocale	bilocale	NOUN
ejpam-5362	431	19	(	(	PUNCT
ejpam-5362	431	20	l	l	NOUN
ejpam-5362	431	21	,	,	PUNCT
ejpam-5362	431	22	l1	l1	PROPN
ejpam-5362	431	23	,	,	PUNCT
ejpam-5362	431	24	l2	l2	NOUN
ejpam-5362	431	25	)	)	PUNCT
ejpam-5362	431	26	and	and	CCONJ
ejpam-5362	431	27	choose	choose	VERB
ejpam-5362	431	28	a	a	DET
ejpam-5362	431	29	collection	collection	NOUN
ejpam-5362	431	30	{	{	PUNCT
ejpam-5362	431	31	o(xn	o(xn	NOUN
ejpam-5362	431	32	)	)	PUNCT
ejpam-5362	431	33	:	:	PUNCT
ejpam-5362	431	34	n	n	CCONJ
ejpam-5362	431	35	∈	∈	PROPN
ejpam-5362	431	36	n	n	CCONJ
ejpam-5362	431	37	}	}	PUNCT
ejpam-5362	431	38	of	of	ADP
ejpam-5362	431	39	i	i	NOUN
ejpam-5362	431	40	-	-	PUNCT
ejpam-5362	431	41	dense	dense	ADJ
ejpam-5362	431	42	j	j	NOUN
ejpam-5362	431	43	-	-	ADJ
ejpam-5362	431	44	open	open	ADJ
ejpam-5362	431	45	sublocales	sublocale	NOUN
ejpam-5362	431	46	of	of	ADP
ejpam-5362	431	47	l.	l.	PROPN
ejpam-5362	431	48	if	if	SCONJ
ejpam-5362	431	49	os(y	os(y	NUM
ejpam-5362	431	50	)	)	PUNCT
ejpam-5362	431	51	∩	∩	NOUN
ejpam-5362	431	52	s	s	PART
ejpam-5362	431	53	∩	∩	NOUN
ejpam-5362	431	54	(	(	PUNCT
ejpam-5362	431	55	∧	∧	PROPN
ejpam-5362	431	56	n∈n	n∈n	NOUN
ejpam-5362	431	57	o(xn	o(xn	NUM
ejpam-5362	431	58	)	)	PUNCT
ejpam-5362	431	59	)	)	PUNCT
ejpam-5362	432	1	=	=	PUNCT
ejpam-5362	432	2	o	o	NOUN
ejpam-5362	432	3	,	,	PUNCT
ejpam-5362	432	4	then	then	ADV
ejpam-5362	432	5	o	o	NOUN
ejpam-5362	432	6	=	=	SYM
ejpam-5362	432	7	os(y	os(y	X
ejpam-5362	432	8	)	)	PUNCT
ejpam-5362	432	9	∩	∩	NOUN
ejpam-5362	432	10	(	(	PUNCT
ejpam-5362	432	11	∧	∧	PROPN
ejpam-5362	432	12	n∈n	n∈n	NOUN
ejpam-5362	432	13	(	(	PUNCT
ejpam-5362	432	14	s	s	X
ejpam-5362	432	15	∩	∩	NOUN
ejpam-5362	432	16	o(xn	o(xn	X
ejpam-5362	432	17	)	)	PUNCT
ejpam-5362	432	18	)	)	PUNCT
ejpam-5362	432	19	)	)	PUNCT
ejpam-5362	433	1	=	=	SYM
ejpam-5362	433	2	os(y	os(y	X
ejpam-5362	433	3	)	)	PUNCT
ejpam-5362	433	4	∩	∩	NOUN
ejpam-5362	433	5	(	(	PUNCT
ejpam-5362	433	6	∧	∧	PROPN
ejpam-5362	433	7	n∈n	n∈n	NOUN
ejpam-5362	433	8	os(νs(xn	os(νs(xn	NUM
ejpam-5362	433	9	)	)	PUNCT
ejpam-5362	433	10	)	)	PUNCT
ejpam-5362	433	11	)	)	PUNCT
ejpam-5362	433	12	where	where	SCONJ
ejpam-5362	433	13	each	each	DET
ejpam-5362	433	14	os(νs(xn	os(νs(xn	NOUN
ejpam-5362	433	15	)	)	PUNCT
ejpam-5362	433	16	)	)	PUNCT
ejpam-5362	433	17	is	be	AUX
ejpam-5362	433	18	is	be	AUX
ejpam-5362	433	19	-	-	PUNCT
ejpam-5362	433	20	dense	dense	ADJ
ejpam-5362	433	21	and	and	CCONJ
ejpam-5362	433	22	js	js	ADV
ejpam-5362	433	23	-	-	PUNCT
ejpam-5362	433	24	open	open	ADJ
ejpam-5362	433	25	.	.	PUNCT
ejpam-5362	434	1	since	since	SCONJ
ejpam-5362	434	2	(	(	PUNCT
ejpam-5362	434	3	s	s	PROPN
ejpam-5362	434	4	,	,	PUNCT
ejpam-5362	434	5	s1	s1	NOUN
ejpam-5362	434	6	,	,	PUNCT
ejpam-5362	434	7	s2	s2	PROPN
ejpam-5362	434	8	)	)	PUNCT
ejpam-5362	434	9	is	be	AUX
ejpam-5362	434	10	(	(	PUNCT
ejpam-5362	434	11	i	i	NOUN
ejpam-5362	434	12	,	,	PUNCT
ejpam-5362	434	13	j)-baire	j)-baire	NOUN
ejpam-5362	434	14	as	as	ADP
ejpam-5362	434	15	a	a	DET
ejpam-5362	434	16	bilocale,∧	bilocale,∧	PROPN
ejpam-5362	434	17	n∈n	n∈n	ADV
ejpam-5362	434	18	os(νs(xn	os(νs(xn	NUM
ejpam-5362	434	19	)	)	PUNCT
ejpam-5362	434	20	)	)	PUNCT
ejpam-5362	435	1	is	be	AUX
ejpam-5362	435	2	is	be	AUX
ejpam-5362	435	3	-	-	PUNCT
ejpam-5362	435	4	dense	dense	ADJ
ejpam-5362	435	5	so	so	SCONJ
ejpam-5362	435	6	that	that	SCONJ
ejpam-5362	435	7	os(y	os(y	NUM
ejpam-5362	435	8	)	)	PUNCT
ejpam-5362	436	1	=	=	SYM
ejpam-5362	436	2	o.	o.	NOUN
ejpam-5362	436	3	thus	thus	ADV
ejpam-5362	436	4	s	s	VERB
ejpam-5362	436	5	∩	∩	NOUN
ejpam-5362	436	6	(	(	PUNCT
ejpam-5362	436	7	∧	∧	PROPN
ejpam-5362	436	8	n∈n	n∈n	NOUN
ejpam-5362	436	9	o(xn	o(xn	NUM
ejpam-5362	436	10	)	)	PUNCT
ejpam-5362	436	11	)	)	PUNCT
ejpam-5362	436	12	is	be	AUX
ejpam-5362	436	13	is	be	AUX
ejpam-5362	436	14	-	-	PUNCT
ejpam-5362	436	15	dense	dense	ADJ
ejpam-5362	436	16	.	.	PUNCT
ejpam-5362	437	1	m.	m.	NOUN
ejpam-5362	437	2	nxumalo	nxumalo	PROPN
ejpam-5362	437	3	/	/	SYM
ejpam-5362	437	4	eur	eur	PROPN
ejpam-5362	437	5	.	.	PUNCT
ejpam-5362	438	1	j.	j.	PROPN
ejpam-5362	438	2	pure	pure	PROPN
ejpam-5362	438	3	appl	appl	PROPN
ejpam-5362	438	4	.	.	PROPN
ejpam-5362	438	5	math	math	PROPN
ejpam-5362	438	6	,	,	PUNCT
ejpam-5362	438	7	18	18	NUM
ejpam-5362	438	8	(	(	PUNCT
ejpam-5362	438	9	1	1	NUM
ejpam-5362	438	10	)	)	PUNCT
ejpam-5362	438	11	(	(	PUNCT
ejpam-5362	438	12	2025	2025	NUM
ejpam-5362	438	13	)	)	PUNCT
ejpam-5362	438	14	,	,	PUNCT
ejpam-5362	438	15	5362	5362	NUM
ejpam-5362	438	16	16	16	NUM
ejpam-5362	438	17	of	of	ADP
ejpam-5362	438	18	21	21	NUM
ejpam-5362	438	19	on	on	ADP
ejpam-5362	438	20	the	the	DET
ejpam-5362	438	21	other	other	ADJ
ejpam-5362	438	22	hand	hand	NOUN
ejpam-5362	438	23	,	,	PUNCT
ejpam-5362	438	24	let	let	VERB
ejpam-5362	438	25	(	(	PUNCT
ejpam-5362	438	26	s	s	X
ejpam-5362	438	27	,	,	PUNCT
ejpam-5362	438	28	s1	s1	NOUN
ejpam-5362	438	29	,	,	PUNCT
ejpam-5362	438	30	s2	s2	PROPN
ejpam-5362	438	31	)	)	PUNCT
ejpam-5362	438	32	be	be	VERB
ejpam-5362	438	33	a	a	DET
ejpam-5362	438	34	relatively	relatively	ADV
ejpam-5362	438	35	(	(	PUNCT
ejpam-5362	438	36	i	i	NOUN
ejpam-5362	438	37	,	,	PUNCT
ejpam-5362	438	38	j)-baire	j)-baire	NOUN
ejpam-5362	438	39	subbilocale	subbilocale	VERB
ejpam-5362	438	40	and	and	CCONJ
ejpam-5362	438	41	pick	pick	VERB
ejpam-5362	438	42	a	a	DET
ejpam-5362	438	43	collection	collection	NOUN
ejpam-5362	438	44	{	{	PUNCT
ejpam-5362	438	45	os(xn	os(xn	PROPN
ejpam-5362	438	46	)	)	PUNCT
ejpam-5362	438	47	:	:	PUNCT
ejpam-5362	439	1	n	n	CCONJ
ejpam-5362	439	2	∈	∈	PROPN
ejpam-5362	439	3	n	n	CCONJ
ejpam-5362	439	4	}	}	PUNCT
ejpam-5362	439	5	of	of	ADP
ejpam-5362	439	6	is	be	AUX
ejpam-5362	439	7	-	-	PUNCT
ejpam-5362	439	8	dense	dense	ADJ
ejpam-5362	439	9	js	js	ADJ
ejpam-5362	439	10	-	-	PUNCT
ejpam-5362	439	11	open	open	ADJ
ejpam-5362	439	12	sublocales	sublocale	NOUN
ejpam-5362	439	13	of	of	ADP
ejpam-5362	439	14	s.	s.	PROPN
ejpam-5362	439	15	for	for	ADP
ejpam-5362	439	16	each	each	DET
ejpam-5362	439	17	xn	xn	PROPN
ejpam-5362	439	18	,	,	PUNCT
ejpam-5362	439	19	there	there	PRON
ejpam-5362	439	20	is	be	VERB
ejpam-5362	439	21	an	an	DET
ejpam-5362	439	22	∈	∈	NOUN
ejpam-5362	439	23	lj	lj	INTJ
ejpam-5362	439	24	such	such	ADJ
ejpam-5362	439	25	that	that	PRON
ejpam-5362	439	26	xn	xn	PUNCT
ejpam-5362	440	1	=	=	PUNCT
ejpam-5362	441	1	νs(an	νs(an	ADJ
ejpam-5362	441	2	)	)	PUNCT
ejpam-5362	441	3	.	.	PUNCT
ejpam-5362	442	1	now	now	ADV
ejpam-5362	442	2	,	,	PUNCT
ejpam-5362	442	3	members	member	NOUN
ejpam-5362	442	4	of	of	ADP
ejpam-5362	442	5	the	the	DET
ejpam-5362	442	6	collection	collection	NOUN
ejpam-5362	442	7	{	{	PUNCT
ejpam-5362	442	8	os(an	os(an	PROPN
ejpam-5362	442	9	)	)	PUNCT
ejpam-5362	442	10	:	:	PUNCT
ejpam-5362	442	11	n	n	X
ejpam-5362	442	12	∈	∈	PROPN
ejpam-5362	442	13	n	n	CCONJ
ejpam-5362	442	14	}	}	PUNCT
ejpam-5362	442	15	are	be	AUX
ejpam-5362	442	16	i	i	PRON
ejpam-5362	442	17	-	-	PUNCT
ejpam-5362	442	18	dense	dense	ADJ
ejpam-5362	442	19	j	j	NOUN
ejpam-5362	442	20	-	-	VERB
ejpam-5362	442	21	open	open	ADJ
ejpam-5362	442	22	in	in	ADP
ejpam-5362	442	23	(	(	PUNCT
ejpam-5362	442	24	l	l	NOUN
ejpam-5362	442	25	,	,	PUNCT
ejpam-5362	442	26	l1	l1	PROPN
ejpam-5362	442	27	,	,	PUNCT
ejpam-5362	442	28	l2	l2	NOUN
ejpam-5362	442	29	)	)	PUNCT
ejpam-5362	442	30	.	.	PUNCT
ejpam-5362	443	1	since	since	SCONJ
ejpam-5362	443	2	(	(	PUNCT
ejpam-5362	443	3	s	s	PROPN
ejpam-5362	443	4	,	,	PUNCT
ejpam-5362	443	5	s1	s1	NOUN
ejpam-5362	443	6	,	,	PUNCT
ejpam-5362	443	7	s2	s2	PROPN
ejpam-5362	443	8	)	)	PUNCT
ejpam-5362	443	9	is	be	AUX
ejpam-5362	443	10	relatively	relatively	ADV
ejpam-5362	443	11	(	(	PUNCT
ejpam-5362	443	12	i	i	NOUN
ejpam-5362	443	13	,	,	PUNCT
ejpam-5362	443	14	j)-baire	j)-baire	ADJ
ejpam-5362	443	15	,	,	PUNCT
ejpam-5362	443	16	s	s	VERB
ejpam-5362	443	17	∩	∩	NOUN
ejpam-5362	443	18	(	(	PUNCT
ejpam-5362	443	19	∧	∧	PROPN
ejpam-5362	443	20	n∈n	n∈n	NOUN
ejpam-5362	443	21	o(an	o(an	NUM
ejpam-5362	443	22	)	)	PUNCT
ejpam-5362	443	23	)	)	PUNCT
ejpam-5362	444	1	=	=	PUNCT
ejpam-5362	444	2	∧	∧	NOUN
ejpam-5362	444	3	n∈n	n∈n	ADJ
ejpam-5362	444	4	os(xn	os(xn	PROPN
ejpam-5362	444	5	)	)	PUNCT
ejpam-5362	444	6	is	be	AUX
ejpam-5362	444	7	is	be	AUX
ejpam-5362	444	8	-	-	PUNCT
ejpam-5362	444	9	dense	dense	ADJ
ejpam-5362	444	10	.	.	PUNCT
ejpam-5362	445	1	thus	thus	ADV
ejpam-5362	445	2	(	(	PUNCT
ejpam-5362	445	3	s	s	X
ejpam-5362	445	4	,	,	PUNCT
ejpam-5362	445	5	s1	s1	NOUN
ejpam-5362	445	6	,	,	PUNCT
ejpam-5362	445	7	s2	s2	PROPN
ejpam-5362	445	8	)	)	PUNCT
ejpam-5362	445	9	is	be	AUX
ejpam-5362	445	10	(	(	PUNCT
ejpam-5362	445	11	i	i	NOUN
ejpam-5362	445	12	,	,	PUNCT
ejpam-5362	445	13	j)-baire	j)-baire	PROPN
ejpam-5362	445	14	.	.	PUNCT
ejpam-5362	446	1	here	here	ADV
ejpam-5362	446	2	is	be	AUX
ejpam-5362	446	3	an	an	DET
ejpam-5362	446	4	example	example	NOUN
ejpam-5362	446	5	of	of	ADP
ejpam-5362	446	6	what	what	PRON
ejpam-5362	446	7	is	be	AUX
ejpam-5362	446	8	illustrated	illustrate	VERB
ejpam-5362	446	9	in	in	ADP
ejpam-5362	446	10	proposition	proposition	NOUN
ejpam-5362	446	11	10	10	NUM
ejpam-5362	446	12	.	.	PUNCT
ejpam-5362	446	13	example	example	NOUN
ejpam-5362	446	14	4	4	NUM
ejpam-5362	446	15	.	.	PUNCT
ejpam-5362	446	16	given	give	VERB
ejpam-5362	446	17	a	a	DET
ejpam-5362	446	18	bilocale	bilocale	NOUN
ejpam-5362	446	19	(	(	PUNCT
ejpam-5362	446	20	l	l	NOUN
ejpam-5362	446	21	,	,	PUNCT
ejpam-5362	446	22	l1	l1	PROPN
ejpam-5362	446	23	,	,	PUNCT
ejpam-5362	446	24	l2	l2	NOUN
ejpam-5362	446	25	)	)	PUNCT
ejpam-5362	446	26	,	,	PUNCT
ejpam-5362	446	27	the	the	DET
ejpam-5362	446	28	subbilocale	subbilocale	NOUN
ejpam-5362	446	29	(	(	PUNCT
ejpam-5362	446	30	bl	bl	INTJ
ejpam-5362	446	31	,	,	PUNCT
ejpam-5362	446	32	νb[l1	νb[l1	PROPN
ejpam-5362	446	33	]	]	PUNCT
ejpam-5362	446	34	,	,	PUNCT
ejpam-5362	446	35	νb[l2	νb[l2	PROPN
ejpam-5362	446	36	]	]	PUNCT
ejpam-5362	446	37	)	)	PUNCT
ejpam-5362	446	38	of	of	ADP
ejpam-5362	446	39	(	(	PUNCT
ejpam-5362	446	40	l	l	NOUN
ejpam-5362	446	41	,	,	PUNCT
ejpam-5362	446	42	l1	l1	PROPN
ejpam-5362	446	43	,	,	PUNCT
ejpam-5362	446	44	l2	l2	NOUN
ejpam-5362	446	45	)	)	PUNCT
ejpam-5362	446	46	is	be	AUX
ejpam-5362	446	47	(	(	PUNCT
ejpam-5362	446	48	i	i	NOUN
ejpam-5362	446	49	,	,	PUNCT
ejpam-5362	446	50	j)-baire	j)-baire	VERB
ejpam-5362	446	51	if	if	SCONJ
ejpam-5362	446	52	and	and	CCONJ
ejpam-5362	446	53	only	only	ADV
ejpam-5362	446	54	if	if	SCONJ
ejpam-5362	446	55	it	it	PRON
ejpam-5362	446	56	is	be	AUX
ejpam-5362	446	57	relatively	relatively	ADV
ejpam-5362	446	58	(	(	PUNCT
ejpam-5362	446	59	i	i	NOUN
ejpam-5362	446	60	,	,	PUNCT
ejpam-5362	446	61	j)-baire	j)-baire	PROPN
ejpam-5362	446	62	.	.	PUNCT
ejpam-5362	447	1	we	we	PRON
ejpam-5362	447	2	close	close	VERB
ejpam-5362	447	3	this	this	DET
ejpam-5362	447	4	section	section	NOUN
ejpam-5362	447	5	with	with	ADP
ejpam-5362	447	6	a	a	DET
ejpam-5362	447	7	characterization	characterization	NOUN
ejpam-5362	447	8	of	of	ADP
ejpam-5362	447	9	relatively	relatively	ADV
ejpam-5362	447	10	(	(	PUNCT
ejpam-5362	447	11	i	i	NOUN
ejpam-5362	447	12	,	,	PUNCT
ejpam-5362	447	13	j)-baire	j)-baire	NOUN
ejpam-5362	447	14	subbilocales	subbilocale	NOUN
ejpam-5362	447	15	.	.	PUNCT
ejpam-5362	448	1	proposition	proposition	NOUN
ejpam-5362	448	2	11	11	NUM
ejpam-5362	448	3	.	.	PUNCT
ejpam-5362	449	1	let	let	AUX
ejpam-5362	449	2	(	(	PUNCT
ejpam-5362	449	3	s	s	X
ejpam-5362	449	4	,	,	PUNCT
ejpam-5362	449	5	s1	s1	NOUN
ejpam-5362	449	6	,	,	PUNCT
ejpam-5362	449	7	s2	s2	PROPN
ejpam-5362	449	8	)	)	PUNCT
ejpam-5362	449	9	be	be	VERB
ejpam-5362	449	10	a	a	DET
ejpam-5362	449	11	dense	dense	ADJ
ejpam-5362	449	12	and	and	CCONJ
ejpam-5362	449	13	complemented	complemented	ADJ
ejpam-5362	449	14	subbilocale	subbilocale	NOUN
ejpam-5362	449	15	of	of	ADP
ejpam-5362	449	16	a	a	DET
ejpam-5362	449	17	bilocale	bilocale	NOUN
ejpam-5362	449	18	(	(	PUNCT
ejpam-5362	449	19	l	l	NOUN
ejpam-5362	449	20	,	,	PUNCT
ejpam-5362	449	21	l1	l1	PROPN
ejpam-5362	449	22	,	,	PUNCT
ejpam-5362	449	23	l2	l2	NOUN
ejpam-5362	449	24	)	)	PUNCT
ejpam-5362	449	25	whose	whose	DET
ejpam-5362	449	26	j	j	NOUN
ejpam-5362	449	27	-	-	PUNCT
ejpam-5362	449	28	gδ	gδ	NOUN
ejpam-5362	449	29	-	-	PUNCT
ejpam-5362	449	30	sublocales	sublocale	NOUN
ejpam-5362	449	31	are	be	AUX
ejpam-5362	449	32	complemented	complement	VERB
ejpam-5362	449	33	.	.	PUNCT
ejpam-5362	450	1	the	the	DET
ejpam-5362	450	2	following	follow	VERB
ejpam-5362	450	3	statements	statement	NOUN
ejpam-5362	450	4	are	be	AUX
ejpam-5362	450	5	equivalent	equivalent	ADJ
ejpam-5362	450	6	:	:	PUNCT
ejpam-5362	450	7	(	(	PUNCT
ejpam-5362	450	8	i	i	NOUN
ejpam-5362	450	9	)	)	PUNCT
ejpam-5362	450	10	(	(	PUNCT
ejpam-5362	450	11	s	s	X
ejpam-5362	450	12	,	,	PUNCT
ejpam-5362	450	13	s1	s1	NOUN
ejpam-5362	450	14	,	,	PUNCT
ejpam-5362	450	15	s2	s2	PROPN
ejpam-5362	450	16	)	)	PUNCT
ejpam-5362	450	17	is	be	AUX
ejpam-5362	450	18	relatively	relatively	ADV
ejpam-5362	450	19	(	(	PUNCT
ejpam-5362	450	20	i	i	NOUN
ejpam-5362	450	21	,	,	PUNCT
ejpam-5362	450	22	j)-baire	j)-baire	NOUN
ejpam-5362	450	23	.	.	PUNCT
ejpam-5362	451	1	(	(	PUNCT
ejpam-5362	451	2	ii	ii	NOUN
ejpam-5362	451	3	)	)	PUNCT
ejpam-5362	451	4	for	for	ADP
ejpam-5362	451	5	every	every	DET
ejpam-5362	451	6	non	non	ADJ
ejpam-5362	451	7	-	-	ADJ
ejpam-5362	451	8	void	void	ADJ
ejpam-5362	451	9	i	i	NOUN
ejpam-5362	451	10	-	-	PUNCT
ejpam-5362	451	11	open	open	ADJ
ejpam-5362	451	12	sublocale	sublocale	NOUN
ejpam-5362	451	13	u	u	NOUN
ejpam-5362	451	14	of	of	ADP
ejpam-5362	451	15	l	l	PROPN
ejpam-5362	451	16	,	,	PUNCT
ejpam-5362	451	17	s	s	PART
ejpam-5362	451	18	∩	∩	ADJ
ejpam-5362	451	19	u	u	NOUN
ejpam-5362	451	20	is	be	AUX
ejpam-5362	451	21	of	of	ADP
ejpam-5362	451	22	(	(	PUNCT
ejpam-5362	451	23	j	j	NOUN
ejpam-5362	451	24	,	,	PUNCT
ejpam-5362	451	25	i)-second	i)-second	ADP
ejpam-5362	451	26	category	category	NOUN
ejpam-5362	451	27	in	in	ADP
ejpam-5362	451	28	(	(	PUNCT
ejpam-5362	451	29	s	s	PROPN
ejpam-5362	451	30	,	,	PUNCT
ejpam-5362	451	31	s1	s1	NOUN
ejpam-5362	451	32	,	,	PUNCT
ejpam-5362	451	33	s2	s2	PROPN
ejpam-5362	451	34	)	)	PUNCT
ejpam-5362	451	35	.	.	PUNCT
ejpam-5362	452	1	(	(	PUNCT
ejpam-5362	452	2	iii	iii	X
ejpam-5362	452	3	)	)	PUNCT
ejpam-5362	452	4	for	for	ADP
ejpam-5362	452	5	every	every	DET
ejpam-5362	452	6	sublocale	sublocale	ADJ
ejpam-5362	452	7	u	u	NOUN
ejpam-5362	452	8	of	of	ADP
ejpam-5362	452	9	(	(	PUNCT
ejpam-5362	452	10	j	j	PROPN
ejpam-5362	452	11	,	,	PUNCT
ejpam-5362	452	12	i)-first	i)-first	PUNCT
ejpam-5362	452	13	category	category	NOUN
ejpam-5362	452	14	in	in	ADP
ejpam-5362	452	15	(	(	PUNCT
ejpam-5362	452	16	l	l	NOUN
ejpam-5362	452	17	,	,	PUNCT
ejpam-5362	452	18	l1	l1	PROPN
ejpam-5362	452	19	,	,	PUNCT
ejpam-5362	452	20	l2	l2	NOUN
ejpam-5362	452	21	)	)	PUNCT
ejpam-5362	452	22	,	,	PUNCT
ejpam-5362	452	23	intis	intis	NOUN
ejpam-5362	452	24	(	(	PUNCT
ejpam-5362	452	25	s	s	X
ejpam-5362	452	26	∩	∩	ADJ
ejpam-5362	452	27	u	u	NOUN
ejpam-5362	452	28	)	)	PUNCT
ejpam-5362	452	29	=	=	SYM
ejpam-5362	453	1	o.	o.	NOUN
ejpam-5362	453	2	(	(	PUNCT
ejpam-5362	453	3	iv	iv	X
ejpam-5362	453	4	)	)	PUNCT
ejpam-5362	453	5	if	if	SCONJ
ejpam-5362	453	6	v	v	NOUN
ejpam-5362	453	7	is	be	AUX
ejpam-5362	453	8	a	a	DET
ejpam-5362	453	9	sublocale	sublocale	NOUN
ejpam-5362	453	10	of	of	ADP
ejpam-5362	453	11	(	(	PUNCT
ejpam-5362	453	12	j	j	PROPN
ejpam-5362	453	13	,	,	PUNCT
ejpam-5362	453	14	i)-first	i)-first	PUNCT
ejpam-5362	453	15	category	category	NOUN
ejpam-5362	453	16	in	in	ADP
ejpam-5362	453	17	(	(	PUNCT
ejpam-5362	453	18	l	l	NOUN
ejpam-5362	453	19	,	,	PUNCT
ejpam-5362	453	20	l1	l1	PROPN
ejpam-5362	453	21	,	,	PUNCT
ejpam-5362	453	22	l2	l2	NOUN
ejpam-5362	453	23	)	)	PUNCT
ejpam-5362	453	24	,	,	PUNCT
ejpam-5362	453	25	then	then	ADV
ejpam-5362	453	26	s	s	VERB
ejpam-5362	453	27	∩	∩	NOUN
ejpam-5362	453	28	(	(	PUNCT
ejpam-5362	453	29	l∖v	l∖v	INTJ
ejpam-5362	453	30	)	)	PUNCT
ejpam-5362	453	31	is	be	AUX
ejpam-5362	453	32	is	be	AUX
ejpam-5362	453	33	-	-	PUNCT
ejpam-5362	453	34	dense	dense	ADJ
ejpam-5362	453	35	.	.	PUNCT
ejpam-5362	454	1	proof	proof	NOUN
ejpam-5362	454	2	.	.	PUNCT
ejpam-5362	455	1	(	(	PUNCT
ejpam-5362	455	2	i	i	NOUN
ejpam-5362	455	3	)	)	PUNCT
ejpam-5362	456	1	=	=	NOUN
ejpam-5362	456	2	⇒	⇒	NOUN
ejpam-5362	456	3	(	(	PUNCT
ejpam-5362	456	4	ii	ii	NOUN
ejpam-5362	456	5	):	):	PUNCT
ejpam-5362	456	6	let	let	VERB
ejpam-5362	456	7	o(x	o(x	PROPN
ejpam-5362	456	8	)	)	PUNCT
ejpam-5362	456	9	be	be	AUX
ejpam-5362	456	10	non	non	ADJ
ejpam-5362	456	11	-	-	ADJ
ejpam-5362	456	12	void	void	ADJ
ejpam-5362	456	13	i	i	PRON
ejpam-5362	456	14	-	-	PUNCT
ejpam-5362	456	15	open	open	ADJ
ejpam-5362	456	16	and	and	CCONJ
ejpam-5362	456	17	assume	assume	VERB
ejpam-5362	456	18	that	that	SCONJ
ejpam-5362	456	19	s	s	VERB
ejpam-5362	456	20	∩	∩	NOUN
ejpam-5362	456	21	o(x	o(x	NUM
ejpam-5362	456	22	)	)	PUNCT
ejpam-5362	456	23	⊆	⊆	NUM
ejpam-5362	456	24	s∨	s∨	PROPN
ejpam-5362	456	25	n∈n	n∈n	ADJ
ejpam-5362	456	26	cs(xn	cs(xn	NOUN
ejpam-5362	456	27	)	)	PUNCT
ejpam-5362	456	28	for	for	ADP
ejpam-5362	456	29	some	some	DET
ejpam-5362	456	30	collection	collection	NOUN
ejpam-5362	456	31	{	{	PUNCT
ejpam-5362	456	32	cs(xn	cs(xn	PROPN
ejpam-5362	456	33	)	)	PUNCT
ejpam-5362	456	34	:	:	PUNCT
ejpam-5362	457	1	n	n	X
ejpam-5362	457	2	∈	∈	PROPN
ejpam-5362	457	3	n	n	CCONJ
ejpam-5362	457	4	}	}	PUNCT
ejpam-5362	457	5	of	of	ADP
ejpam-5362	457	6	(	(	PUNCT
ejpam-5362	457	7	js	js	INTJ
ejpam-5362	457	8	,	,	PUNCT
ejpam-5362	457	9	is)-nowhere	is)-nowhere	VERB
ejpam-5362	457	10	dense	dense	ADJ
ejpam-5362	457	11	sublocales	sublocale	NOUN
ejpam-5362	457	12	of	of	ADP
ejpam-5362	457	13	s.	s.	PROPN
ejpam-5362	457	14	then	then	ADV
ejpam-5362	457	15	s	s	VERB
ejpam-5362	457	16	∩	∩	ADJ
ejpam-5362	457	17	o(x	o(x	NUM
ejpam-5362	457	18	)	)	PUNCT
ejpam-5362	457	19	⊆	⊆	NUM
ejpam-5362	457	20	∨	∨	NUM
ejpam-5362	457	21	n∈n	n∈n	X
ejpam-5362	457	22	c(xn	c(xn	NOUN
ejpam-5362	457	23	)	)	PUNCT
ejpam-5362	457	24	where	where	SCONJ
ejpam-5362	457	25	each	each	DET
ejpam-5362	457	26	c(xn	c(xn	X
ejpam-5362	457	27	)	)	PUNCT
ejpam-5362	457	28	is	be	AUX
ejpam-5362	457	29	(	(	PUNCT
ejpam-5362	457	30	j	j	NOUN
ejpam-5362	457	31	,	,	PUNCT
ejpam-5362	457	32	i)-nowhere	i)-nowhere	ADP
ejpam-5362	457	33	dense	dense	ADJ
ejpam-5362	457	34	because	because	SCONJ
ejpam-5362	457	35	(	(	PUNCT
ejpam-5362	457	36	s	s	X
ejpam-5362	457	37	,	,	PUNCT
ejpam-5362	457	38	s1	s1	NOUN
ejpam-5362	457	39	,	,	PUNCT
ejpam-5362	457	40	s2	s2	PROPN
ejpam-5362	457	41	)	)	PUNCT
ejpam-5362	457	42	is	be	AUX
ejpam-5362	457	43	dense	dense	ADJ
ejpam-5362	457	44	.	.	PUNCT
ejpam-5362	458	1	it	it	PRON
ejpam-5362	458	2	is	be	AUX
ejpam-5362	458	3	clear	clear	ADJ
ejpam-5362	458	4	that	that	SCONJ
ejpam-5362	458	5	the	the	DET
ejpam-5362	458	6	collection	collection	NOUN
ejpam-5362	458	7	{	{	PUNCT
ejpam-5362	458	8	o(xn	o(xn	NOUN
ejpam-5362	458	9	)	)	PUNCT
ejpam-5362	458	10	:	:	PUNCT
ejpam-5362	458	11	n	n	CCONJ
ejpam-5362	458	12	∈	∈	PROPN
ejpam-5362	458	13	n	n	CCONJ
ejpam-5362	458	14	}	}	PUNCT
ejpam-5362	458	15	consists	consist	VERB
ejpam-5362	458	16	of	of	ADP
ejpam-5362	458	17	i	i	NOUN
ejpam-5362	458	18	-	-	PUNCT
ejpam-5362	458	19	dense	dense	ADJ
ejpam-5362	458	20	j	j	NOUN
ejpam-5362	458	21	-	-	ADJ
ejpam-5362	458	22	open	open	ADJ
ejpam-5362	458	23	sublocales	sublocale	NOUN
ejpam-5362	458	24	.	.	PUNCT
ejpam-5362	459	1	it	it	PRON
ejpam-5362	459	2	follows	follow	VERB
ejpam-5362	459	3	from	from	ADP
ejpam-5362	459	4	(	(	PUNCT
ejpam-5362	459	5	i	i	NOUN
ejpam-5362	459	6	)	)	PUNCT
ejpam-5362	459	7	that	that	PRON
ejpam-5362	459	8	s∩	s∩	VERB
ejpam-5362	459	9	(	(	PUNCT
ejpam-5362	459	10	∧	∧	PROPN
ejpam-5362	459	11	n∈n	n∈n	NOUN
ejpam-5362	459	12	o(xn	o(xn	NUM
ejpam-5362	459	13	)	)	PUNCT
ejpam-5362	459	14	)	)	PUNCT
ejpam-5362	459	15	is	be	AUX
ejpam-5362	459	16	is	be	AUX
ejpam-5362	459	17	-	-	PUNCT
ejpam-5362	459	18	dense	dense	ADJ
ejpam-5362	459	19	.	.	PUNCT
ejpam-5362	460	1	since	since	SCONJ
ejpam-5362	460	2	s∩o(x	s∩o(x	ADJ
ejpam-5362	460	3	)	)	PUNCT
ejpam-5362	460	4	̸=	̸=	PROPN
ejpam-5362	460	5	o	o	NOUN
ejpam-5362	460	6	because	because	SCONJ
ejpam-5362	460	7	of	of	ADP
ejpam-5362	460	8	density	density	NOUN
ejpam-5362	460	9	of	of	ADP
ejpam-5362	460	10	(	(	PUNCT
ejpam-5362	460	11	s	s	PROPN
ejpam-5362	460	12	,	,	PUNCT
ejpam-5362	460	13	s1	s1	NOUN
ejpam-5362	460	14	,	,	PUNCT
ejpam-5362	460	15	s2	s2	PROPN
ejpam-5362	460	16	)	)	PUNCT
ejpam-5362	460	17	,	,	PUNCT
ejpam-5362	460	18	we	we	PRON
ejpam-5362	460	19	have	have	VERB
ejpam-5362	460	20	that	that	PRON
ejpam-5362	460	21	s	s	ADP
ejpam-5362	460	22	∩	∩	ADJ
ejpam-5362	460	23	o(x	o(x	ADJ
ejpam-5362	460	24	)	)	PUNCT
ejpam-5362	460	25	∩	∩	NOUN
ejpam-5362	460	26	s	s	PART
ejpam-5362	460	27	∩	∩	NOUN
ejpam-5362	460	28	(	(	PUNCT
ejpam-5362	460	29	∧	∧	PROPN
ejpam-5362	460	30	n∈n	n∈n	NOUN
ejpam-5362	460	31	o(xn	o(xn	NOUN
ejpam-5362	460	32	)	)	PUNCT
ejpam-5362	460	33	)	)	PUNCT
ejpam-5362	461	1	̸=	̸=	PROPN
ejpam-5362	461	2	o.	o.	NOUN
ejpam-5362	461	3	m.	m.	NOUN
ejpam-5362	461	4	nxumalo	nxumalo	PROPN
ejpam-5362	461	5	/	/	SYM
ejpam-5362	461	6	eur	eur	PROPN
ejpam-5362	461	7	.	.	PUNCT
ejpam-5362	462	1	j.	j.	PROPN
ejpam-5362	462	2	pure	pure	PROPN
ejpam-5362	462	3	appl	appl	PROPN
ejpam-5362	462	4	.	.	PROPN
ejpam-5362	462	5	math	math	PROPN
ejpam-5362	462	6	,	,	PUNCT
ejpam-5362	462	7	18	18	NUM
ejpam-5362	462	8	(	(	PUNCT
ejpam-5362	462	9	1	1	NUM
ejpam-5362	462	10	)	)	PUNCT
ejpam-5362	462	11	(	(	PUNCT
ejpam-5362	462	12	2025	2025	NUM
ejpam-5362	462	13	)	)	PUNCT
ejpam-5362	462	14	,	,	PUNCT
ejpam-5362	462	15	5362	5362	NUM
ejpam-5362	462	16	17	17	NUM
ejpam-5362	462	17	of	of	ADP
ejpam-5362	462	18	21	21	NUM
ejpam-5362	462	19	therefore	therefore	ADV
ejpam-5362	462	20	(	(	PUNCT
ejpam-5362	462	21	∨	∨	PROPN
ejpam-5362	462	22	k∈n	k∈n	PROPN
ejpam-5362	462	23	c(xk	c(xk	NUM
ejpam-5362	462	24	)	)	PUNCT
ejpam-5362	462	25	)	)	PUNCT
ejpam-5362	462	26	∩	∩	NOUN
ejpam-5362	462	27	(	(	PUNCT
ejpam-5362	462	28	∧	∧	PROPN
ejpam-5362	462	29	n∈n	n∈n	NOUN
ejpam-5362	462	30	o(xn	o(xn	NOUN
ejpam-5362	462	31	)	)	PUNCT
ejpam-5362	462	32	)	)	PUNCT
ejpam-5362	463	1	̸=	̸=	PROPN
ejpam-5362	463	2	o.	o.	NOUN
ejpam-5362	463	3	since	since	SCONJ
ejpam-5362	463	4	∧	∧	PROPN
ejpam-5362	463	5	n∈n	n∈n	NOUN
ejpam-5362	463	6	o(xn	o(xn	NUM
ejpam-5362	463	7	)	)	PUNCT
ejpam-5362	463	8	is	be	AUX
ejpam-5362	463	9	a	a	DET
ejpam-5362	463	10	j	j	PROPN
ejpam-5362	463	11	-	-	PUNCT
ejpam-5362	463	12	gδ	gδ	NOUN
ejpam-5362	463	13	-	-	PUNCT
ejpam-5362	463	14	sublocale	sublocale	NOUN
ejpam-5362	463	15	of	of	ADP
ejpam-5362	463	16	l	l	NOUN
ejpam-5362	463	17	,	,	PUNCT
ejpam-5362	463	18	it	it	PRON
ejpam-5362	463	19	follows	follow	VERB
ejpam-5362	463	20	that	that	SCONJ
ejpam-5362	463	21	it	it	PRON
ejpam-5362	463	22	is	be	AUX
ejpam-5362	463	23	complemented	complement	VERB
ejpam-5362	463	24	.	.	PUNCT
ejpam-5362	464	1	therefore	therefore	ADV
ejpam-5362	464	2	o	o	X
ejpam-5362	464	3	̸=	̸=	PROPN
ejpam-5362	464	4	∨	∨	NUM
ejpam-5362	464	5	k∈n	k∈n	PROPN
ejpam-5362	464	6	(	(	PUNCT
ejpam-5362	464	7	c(xk	c(xk	NOUN
ejpam-5362	464	8	)	)	PUNCT
ejpam-5362	464	9	∩	∩	NOUN
ejpam-5362	464	10	(	(	PUNCT
ejpam-5362	464	11	∧	∧	PROPN
ejpam-5362	464	12	n∈n	n∈n	NOUN
ejpam-5362	464	13	o(xn	o(xn	NUM
ejpam-5362	464	14	)	)	PUNCT
ejpam-5362	464	15	)	)	PUNCT
ejpam-5362	464	16	)	)	PUNCT
ejpam-5362	465	1	⊆	⊆	NUM
ejpam-5362	465	2	∨	∨	NUM
ejpam-5362	465	3	k∈n	k∈n	PROPN
ejpam-5362	465	4	(	(	PUNCT
ejpam-5362	465	5	c(xk	c(xk	NOUN
ejpam-5362	465	6	)	)	PUNCT
ejpam-5362	465	7	∩	∩	NOUN
ejpam-5362	465	8	o(xk	o(xk	NUM
ejpam-5362	465	9	)	)	PUNCT
ejpam-5362	465	10	)	)	PUNCT
ejpam-5362	465	11	=	=	PUNCT
ejpam-5362	466	1	∨	∨	NUM
ejpam-5362	466	2	n∈n	n∈n	X
ejpam-5362	466	3	(	(	PUNCT
ejpam-5362	466	4	o	o	NOUN
ejpam-5362	466	5	)	)	PUNCT
ejpam-5362	466	6	=	=	SYM
ejpam-5362	466	7	o	o	NOUN
ejpam-5362	466	8	which	which	PRON
ejpam-5362	466	9	is	be	AUX
ejpam-5362	466	10	impossible	impossible	ADJ
ejpam-5362	466	11	.	.	PUNCT
ejpam-5362	467	1	thus	thus	ADV
ejpam-5362	467	2	s	s	VERB
ejpam-5362	467	3	∩	∩	ADJ
ejpam-5362	467	4	o(x	o(x	PROPN
ejpam-5362	467	5	)	)	PUNCT
ejpam-5362	467	6	is	be	AUX
ejpam-5362	467	7	(	(	PUNCT
ejpam-5362	467	8	j	j	NOUN
ejpam-5362	467	9	,	,	PUNCT
ejpam-5362	467	10	i)-second	i)-second	ADP
ejpam-5362	467	11	category	category	NOUN
ejpam-5362	467	12	.	.	PUNCT
ejpam-5362	468	1	(	(	PUNCT
ejpam-5362	468	2	ii	ii	NOUN
ejpam-5362	468	3	)	)	PUNCT
ejpam-5362	469	1	=	=	NOUN
ejpam-5362	469	2	⇒	⇒	NOUN
ejpam-5362	469	3	(	(	PUNCT
ejpam-5362	469	4	i	i	NOUN
ejpam-5362	469	5	):	):	PUNCT
ejpam-5362	469	6	let	let	VERB
ejpam-5362	469	7	{	{	PUNCT
ejpam-5362	469	8	o(xn	o(xn	X
ejpam-5362	469	9	)	)	PUNCT
ejpam-5362	469	10	:	:	PUNCT
ejpam-5362	470	1	n	n	CCONJ
ejpam-5362	470	2	∈	∈	PROPN
ejpam-5362	470	3	n	n	CCONJ
ejpam-5362	470	4	}	}	PUNCT
ejpam-5362	470	5	be	be	AUX
ejpam-5362	470	6	a	a	DET
ejpam-5362	470	7	collection	collection	NOUN
ejpam-5362	470	8	of	of	ADP
ejpam-5362	470	9	i	i	NOUN
ejpam-5362	470	10	-	-	PUNCT
ejpam-5362	470	11	dense	dense	ADJ
ejpam-5362	470	12	j	j	NOUN
ejpam-5362	470	13	-	-	ADJ
ejpam-5362	470	14	open	open	ADJ
ejpam-5362	470	15	sublocales	sublocale	NOUN
ejpam-5362	470	16	and	and	CCONJ
ejpam-5362	470	17	assume	assume	VERB
ejpam-5362	470	18	that	that	SCONJ
ejpam-5362	470	19	there	there	PRON
ejpam-5362	470	20	is	be	VERB
ejpam-5362	470	21	non	non	ADJ
ejpam-5362	470	22	-	-	ADJ
ejpam-5362	470	23	void	void	ADJ
ejpam-5362	470	24	is	be	AUX
ejpam-5362	470	25	-	-	PUNCT
ejpam-5362	470	26	open	open	ADJ
ejpam-5362	470	27	sublocale	sublocale	NOUN
ejpam-5362	470	28	os(y	os(y	NUM
ejpam-5362	470	29	)	)	PUNCT
ejpam-5362	470	30	of	of	ADP
ejpam-5362	470	31	s	s	PRON
ejpam-5362	470	32	such	such	ADJ
ejpam-5362	470	33	that	that	DET
ejpam-5362	470	34	os(y	os(y	NUM
ejpam-5362	470	35	)	)	PUNCT
ejpam-5362	470	36	∩	∩	NOUN
ejpam-5362	470	37	s	s	PART
ejpam-5362	470	38	∩	∩	NOUN
ejpam-5362	470	39	(	(	PUNCT
ejpam-5362	470	40	∧	∧	PROPN
ejpam-5362	470	41	n∈n	n∈n	NOUN
ejpam-5362	470	42	o(xn	o(xn	NUM
ejpam-5362	470	43	)	)	PUNCT
ejpam-5362	470	44	)	)	PUNCT
ejpam-5362	471	1	=	=	SYM
ejpam-5362	471	2	o.	o.	NOUN
ejpam-5362	471	3	then	then	ADV
ejpam-5362	471	4	o(y	o(y	PROPN
ejpam-5362	471	5	)	)	PUNCT
ejpam-5362	471	6	is	be	AUX
ejpam-5362	471	7	non	non	ADJ
ejpam-5362	471	8	-	-	ADJ
ejpam-5362	471	9	void	void	ADJ
ejpam-5362	471	10	i	i	PRON
ejpam-5362	471	11	-	-	PUNCT
ejpam-5362	471	12	open	open	ADJ
ejpam-5362	471	13	and	and	CCONJ
ejpam-5362	471	14	os(y	os(y	NUM
ejpam-5362	471	15	)	)	PUNCT
ejpam-5362	471	16	∩	∩	NOUN
ejpam-5362	471	17	(	(	PUNCT
ejpam-5362	471	18	∧	∧	PROPN
ejpam-5362	471	19	n∈n	n∈n	NOUN
ejpam-5362	471	20	o(xn	o(xn	NUM
ejpam-5362	471	21	)	)	PUNCT
ejpam-5362	471	22	)	)	PUNCT
ejpam-5362	472	1	=	=	PUNCT
ejpam-5362	472	2	o	o	NOUN
ejpam-5362	472	3	which	which	PRON
ejpam-5362	472	4	implies	imply	VERB
ejpam-5362	472	5	os(y	os(y	NUM
ejpam-5362	472	6	)	)	PUNCT
ejpam-5362	472	7	⊆	⊆	NUM
ejpam-5362	472	8	s	s	NOUN
ejpam-5362	472	9	∩	∩	NOUN
ejpam-5362	472	10	(	(	PUNCT
ejpam-5362	472	11	∨	∨	NUM
ejpam-5362	472	12	n∈n	n∈n	X
ejpam-5362	472	13	o(xn	o(xn	NUM
ejpam-5362	472	14	)	)	PUNCT
ejpam-5362	472	15	)	)	PUNCT
ejpam-5362	473	1	=	=	PUNCT
ejpam-5362	473	2	∨	∨	NUM
ejpam-5362	473	3	n∈n	n∈n	X
ejpam-5362	473	4	cs(νs(xn	cs(νs(xn	NOUN
ejpam-5362	473	5	)	)	PUNCT
ejpam-5362	473	6	)	)	PUNCT
ejpam-5362	473	7	where	where	SCONJ
ejpam-5362	473	8	the	the	DET
ejpam-5362	473	9	latter	latter	ADJ
ejpam-5362	473	10	equality	equality	NOUN
ejpam-5362	473	11	holds	hold	VERB
ejpam-5362	473	12	since	since	SCONJ
ejpam-5362	473	13	s	s	PRON
ejpam-5362	473	14	is	be	AUX
ejpam-5362	473	15	complemented	complement	VERB
ejpam-5362	473	16	.	.	PUNCT
ejpam-5362	474	1	since	since	SCONJ
ejpam-5362	474	2	each	each	DET
ejpam-5362	474	3	cs(νs(xn	cs(νs(xn	NOUN
ejpam-5362	474	4	)	)	PUNCT
ejpam-5362	474	5	)	)	PUNCT
ejpam-5362	474	6	is	be	AUX
ejpam-5362	474	7	(	(	PUNCT
ejpam-5362	474	8	js	js	INTJ
ejpam-5362	474	9	,	,	PUNCT
ejpam-5362	474	10	is)nowhere	is)nowhere	ADV
ejpam-5362	474	11	dense	dense	ADJ
ejpam-5362	474	12	,	,	PUNCT
ejpam-5362	474	13	s	s	NOUN
ejpam-5362	474	14	∩	∩	NOUN
ejpam-5362	474	15	o(y	o(y	X
ejpam-5362	474	16	)	)	PUNCT
ejpam-5362	474	17	=	=	SYM
ejpam-5362	474	18	os(y	os(y	X
ejpam-5362	474	19	)	)	PUNCT
ejpam-5362	474	20	is	be	AUX
ejpam-5362	474	21	of	of	ADP
ejpam-5362	474	22	(	(	PUNCT
ejpam-5362	474	23	j	j	NOUN
ejpam-5362	474	24	,	,	PUNCT
ejpam-5362	474	25	i)-first	i)-first	PUNCT
ejpam-5362	474	26	category	category	NOUN
ejpam-5362	474	27	in	in	ADP
ejpam-5362	474	28	(	(	PUNCT
ejpam-5362	474	29	s	s	PROPN
ejpam-5362	474	30	,	,	PUNCT
ejpam-5362	474	31	s1	s1	NOUN
ejpam-5362	474	32	,	,	PUNCT
ejpam-5362	474	33	s2	s2	PROPN
ejpam-5362	474	34	)	)	PUNCT
ejpam-5362	474	35	which	which	PRON
ejpam-5362	474	36	is	be	AUX
ejpam-5362	474	37	a	a	DET
ejpam-5362	474	38	contradiction	contradiction	NOUN
ejpam-5362	474	39	.	.	PUNCT
ejpam-5362	475	1	(	(	PUNCT
ejpam-5362	475	2	ii	ii	NOUN
ejpam-5362	475	3	)	)	PUNCT
ejpam-5362	475	4	=	=	NOUN
ejpam-5362	475	5	⇒	⇒	NOUN
ejpam-5362	475	6	(	(	PUNCT
ejpam-5362	475	7	iii	iii	NOUN
ejpam-5362	475	8	):	):	PUNCT
ejpam-5362	475	9	let	let	VERB
ejpam-5362	475	10	u	u	PRON
ejpam-5362	475	11	be	be	AUX
ejpam-5362	475	12	a	a	DET
ejpam-5362	475	13	sublocale	sublocale	NOUN
ejpam-5362	475	14	of	of	ADP
ejpam-5362	475	15	l	l	NOUN
ejpam-5362	475	16	which	which	PRON
ejpam-5362	475	17	is	be	AUX
ejpam-5362	475	18	of	of	ADP
ejpam-5362	475	19	(	(	PUNCT
ejpam-5362	475	20	j	j	NOUN
ejpam-5362	475	21	,	,	PUNCT
ejpam-5362	475	22	i)-first	i)-first	PUNCT
ejpam-5362	475	23	category	category	NOUN
ejpam-5362	475	24	in	in	ADP
ejpam-5362	475	25	(	(	PUNCT
ejpam-5362	475	26	l	l	NOUN
ejpam-5362	475	27	,	,	PUNCT
ejpam-5362	475	28	l1	l1	PROPN
ejpam-5362	475	29	,	,	PUNCT
ejpam-5362	475	30	l2	l2	NOUN
ejpam-5362	475	31	)	)	PUNCT
ejpam-5362	475	32	and	and	CCONJ
ejpam-5362	475	33	assume	assume	VERB
ejpam-5362	475	34	that	that	SCONJ
ejpam-5362	475	35	intis	intis	NOUN
ejpam-5362	475	36	(	(	PUNCT
ejpam-5362	475	37	s	s	X
ejpam-5362	475	38	∩	∩	ADJ
ejpam-5362	475	39	u	u	NOUN
ejpam-5362	475	40	)	)	PUNCT
ejpam-5362	475	41	̸=	̸=	PROPN
ejpam-5362	475	42	o.	o.	NOUN
ejpam-5362	475	43	then	then	ADV
ejpam-5362	475	44	intis	intis	PROPN
ejpam-5362	475	45	(	(	PUNCT
ejpam-5362	475	46	s	s	X
ejpam-5362	475	47	∩	∩	ADJ
ejpam-5362	475	48	u	u	NOUN
ejpam-5362	475	49	)	)	PUNCT
ejpam-5362	475	50	=	=	SYM
ejpam-5362	475	51	o(x	o(x	ADJ
ejpam-5362	475	52	)	)	PUNCT
ejpam-5362	475	53	∩	∩	NOUN
ejpam-5362	475	54	s	s	PART
ejpam-5362	475	55	for	for	ADP
ejpam-5362	475	56	some	some	DET
ejpam-5362	475	57	x	x	SYM
ejpam-5362	475	58	∈	∈	PROPN
ejpam-5362	475	59	li	li	PROPN
ejpam-5362	475	60	.	.	PUNCT
ejpam-5362	476	1	such	such	ADJ
ejpam-5362	476	2	o(x	o(x	PROPN
ejpam-5362	476	3	)	)	PUNCT
ejpam-5362	476	4	is	be	AUX
ejpam-5362	476	5	a	a	DET
ejpam-5362	476	6	non	non	ADJ
ejpam-5362	476	7	-	-	ADJ
ejpam-5362	476	8	void	void	ADJ
ejpam-5362	476	9	i	i	NOUN
ejpam-5362	476	10	-	-	PUNCT
ejpam-5362	476	11	open	open	ADJ
ejpam-5362	476	12	sublocale	sublocale	NOUN
ejpam-5362	476	13	of	of	ADP
ejpam-5362	476	14	l	l	NOUN
ejpam-5362	476	15	,	,	PUNCT
ejpam-5362	476	16	so	so	ADV
ejpam-5362	476	17	intis	intis	NOUN
ejpam-5362	476	18	(	(	PUNCT
ejpam-5362	476	19	s	s	X
ejpam-5362	476	20	∩	∩	ADJ
ejpam-5362	476	21	u	u	NOUN
ejpam-5362	476	22	)	)	PUNCT
ejpam-5362	476	23	=	=	SYM
ejpam-5362	476	24	s	s	X
ejpam-5362	476	25	∩	∩	ADJ
ejpam-5362	476	26	o(x	o(x	NUM
ejpam-5362	476	27	)	)	PUNCT
ejpam-5362	476	28	must	must	AUX
ejpam-5362	476	29	be	be	AUX
ejpam-5362	476	30	of	of	ADP
ejpam-5362	476	31	(	(	PUNCT
ejpam-5362	476	32	j	j	NOUN
ejpam-5362	476	33	,	,	PUNCT
ejpam-5362	476	34	i)-second	i)-second	ADP
ejpam-5362	476	35	category	category	NOUN
ejpam-5362	476	36	in	in	ADP
ejpam-5362	476	37	(	(	PUNCT
ejpam-5362	476	38	s	s	PROPN
ejpam-5362	476	39	,	,	PUNCT
ejpam-5362	476	40	s1	s1	NOUN
ejpam-5362	476	41	,	,	PUNCT
ejpam-5362	476	42	s2	s2	PROPN
ejpam-5362	476	43	)	)	PUNCT
ejpam-5362	476	44	by	by	ADP
ejpam-5362	476	45	(	(	PUNCT
ejpam-5362	476	46	ii	ii	NOUN
ejpam-5362	476	47	)	)	PUNCT
ejpam-5362	476	48	.	.	PUNCT
ejpam-5362	477	1	but	but	CCONJ
ejpam-5362	477	2	u	u	NOUN
ejpam-5362	477	3	⊆	⊆	NUM
ejpam-5362	477	4	∨	∨	NUM
ejpam-5362	477	5	n∈n	n∈n	X
ejpam-5362	477	6	c(xn	c(xn	NOUN
ejpam-5362	477	7	)	)	PUNCT
ejpam-5362	477	8	for	for	ADP
ejpam-5362	477	9	some	some	DET
ejpam-5362	477	10	collection	collection	NOUN
ejpam-5362	477	11	{	{	PUNCT
ejpam-5362	477	12	c(xn	c(xn	PROPN
ejpam-5362	477	13	)	)	PUNCT
ejpam-5362	477	14	:	:	PUNCT
ejpam-5362	477	15	n	n	CCONJ
ejpam-5362	477	16	∈	∈	PROPN
ejpam-5362	477	17	n	n	CCONJ
ejpam-5362	477	18	}	}	PUNCT
ejpam-5362	477	19	of	of	ADP
ejpam-5362	477	20	(	(	PUNCT
ejpam-5362	477	21	j	j	NOUN
ejpam-5362	477	22	,	,	PUNCT
ejpam-5362	477	23	i)-nowhere	i)-nowhere	ADP
ejpam-5362	477	24	dense	dense	ADJ
ejpam-5362	477	25	sublocales	sublocale	NOUN
ejpam-5362	477	26	of	of	ADP
ejpam-5362	477	27	l	l	NOUN
ejpam-5362	477	28	,	,	PUNCT
ejpam-5362	477	29	so	so	ADV
ejpam-5362	477	30	intis	intis	NOUN
ejpam-5362	477	31	(	(	PUNCT
ejpam-5362	477	32	s	s	X
ejpam-5362	477	33	∩	∩	ADJ
ejpam-5362	477	34	u	u	NOUN
ejpam-5362	477	35	)	)	PUNCT
ejpam-5362	477	36	=	=	SYM
ejpam-5362	477	37	o(x	o(x	ADJ
ejpam-5362	477	38	)	)	PUNCT
ejpam-5362	477	39	∩	∩	NOUN
ejpam-5362	477	40	s	s	PART
ejpam-5362	477	41	⊆	⊆	NUM
ejpam-5362	477	42	u	u	NOUN
ejpam-5362	477	43	∩	∩	NOUN
ejpam-5362	477	44	s	s	VERB
ejpam-5362	477	45	⊆	⊆	NUM
ejpam-5362	477	46	s	s	NOUN
ejpam-5362	477	47	∩	∩	NOUN
ejpam-5362	477	48	∨	∨	NUM
ejpam-5362	477	49	n∈n	n∈n	X
ejpam-5362	477	50	c(xn	c(xn	NOUN
ejpam-5362	477	51	)	)	PUNCT
ejpam-5362	477	52	=	=	PUNCT
ejpam-5362	478	1	∨	∨	NUM
ejpam-5362	478	2	n∈n	n∈n	X
ejpam-5362	478	3	cs(νs(xn	cs(νs(xn	NOUN
ejpam-5362	478	4	)	)	PUNCT
ejpam-5362	478	5	)	)	PUNCT
ejpam-5362	478	6	where	where	SCONJ
ejpam-5362	478	7	each	each	DET
ejpam-5362	478	8	cs(νs(xn	cs(νs(xn	NOUN
ejpam-5362	478	9	)	)	PUNCT
ejpam-5362	478	10	)	)	PUNCT
ejpam-5362	478	11	is	be	AUX
ejpam-5362	478	12	(	(	PUNCT
ejpam-5362	478	13	js	js	INTJ
ejpam-5362	478	14	,	,	PUNCT
ejpam-5362	478	15	is)-nowhere	is)-nowhere	VERB
ejpam-5362	478	16	dense	dense	ADJ
ejpam-5362	478	17	in	in	ADP
ejpam-5362	478	18	(	(	PUNCT
ejpam-5362	478	19	s	s	PROPN
ejpam-5362	478	20	,	,	PUNCT
ejpam-5362	478	21	s1	s1	NOUN
ejpam-5362	478	22	,	,	PUNCT
ejpam-5362	478	23	s2	s2	PROPN
ejpam-5362	478	24	)	)	PUNCT
ejpam-5362	478	25	.	.	PUNCT
ejpam-5362	479	1	this	this	PRON
ejpam-5362	479	2	makes	make	VERB
ejpam-5362	479	3	o(x	o(x	PROPN
ejpam-5362	479	4	)	)	PUNCT
ejpam-5362	479	5	∩	∩	NOUN
ejpam-5362	479	6	s	s	VERB
ejpam-5362	479	7	a	a	DET
ejpam-5362	479	8	sublocale	sublocale	NOUN
ejpam-5362	479	9	of	of	ADP
ejpam-5362	479	10	(	(	PUNCT
ejpam-5362	479	11	j	j	PROPN
ejpam-5362	479	12	,	,	PUNCT
ejpam-5362	479	13	i)-first	i)-first	PUNCT
ejpam-5362	479	14	category	category	NOUN
ejpam-5362	479	15	in	in	ADP
ejpam-5362	479	16	(	(	PUNCT
ejpam-5362	479	17	s	s	PROPN
ejpam-5362	479	18	,	,	PUNCT
ejpam-5362	479	19	s1	s1	NOUN
ejpam-5362	479	20	,	,	PUNCT
ejpam-5362	479	21	s2	s2	PROPN
ejpam-5362	479	22	)	)	PUNCT
ejpam-5362	479	23	which	which	PRON
ejpam-5362	479	24	is	be	AUX
ejpam-5362	479	25	impossible	impossible	ADJ
ejpam-5362	479	26	.	.	PUNCT
ejpam-5362	480	1	m.	m.	NOUN
ejpam-5362	480	2	nxumalo	nxumalo	PROPN
ejpam-5362	480	3	/	/	SYM
ejpam-5362	480	4	eur	eur	PROPN
ejpam-5362	480	5	.	.	PUNCT
ejpam-5362	481	1	j.	j.	PROPN
ejpam-5362	481	2	pure	pure	PROPN
ejpam-5362	481	3	appl	appl	PROPN
ejpam-5362	481	4	.	.	PROPN
ejpam-5362	481	5	math	math	PROPN
ejpam-5362	481	6	,	,	PUNCT
ejpam-5362	481	7	18	18	NUM
ejpam-5362	481	8	(	(	PUNCT
ejpam-5362	481	9	1	1	NUM
ejpam-5362	481	10	)	)	PUNCT
ejpam-5362	481	11	(	(	PUNCT
ejpam-5362	481	12	2025	2025	NUM
ejpam-5362	481	13	)	)	PUNCT
ejpam-5362	481	14	,	,	PUNCT
ejpam-5362	481	15	5362	5362	NUM
ejpam-5362	481	16	18	18	NUM
ejpam-5362	481	17	of	of	ADP
ejpam-5362	481	18	21	21	NUM
ejpam-5362	481	19	(	(	PUNCT
ejpam-5362	481	20	iii	iii	NOUN
ejpam-5362	481	21	)	)	PUNCT
ejpam-5362	481	22	=	=	NOUN
ejpam-5362	481	23	⇒	⇒	NOUN
ejpam-5362	481	24	(	(	PUNCT
ejpam-5362	481	25	iv	iv	NUM
ejpam-5362	481	26	):	):	PUNCT
ejpam-5362	481	27	let	let	VERB
ejpam-5362	481	28	v	v	PART
ejpam-5362	481	29	be	be	AUX
ejpam-5362	481	30	a	a	DET
ejpam-5362	481	31	sublocale	sublocale	NOUN
ejpam-5362	481	32	of	of	ADP
ejpam-5362	481	33	l	l	NOUN
ejpam-5362	481	34	which	which	PRON
ejpam-5362	481	35	is	be	AUX
ejpam-5362	481	36	of	of	ADP
ejpam-5362	481	37	(	(	PUNCT
ejpam-5362	481	38	j	j	NOUN
ejpam-5362	481	39	,	,	PUNCT
ejpam-5362	481	40	i)-first	i)-first	PUNCT
ejpam-5362	481	41	category	category	NOUN
ejpam-5362	481	42	in	in	ADP
ejpam-5362	481	43	(	(	PUNCT
ejpam-5362	481	44	l	l	NOUN
ejpam-5362	481	45	,	,	PUNCT
ejpam-5362	481	46	l1	l1	PROPN
ejpam-5362	481	47	,	,	PUNCT
ejpam-5362	481	48	l2	l2	NOUN
ejpam-5362	481	49	)	)	PUNCT
ejpam-5362	481	50	and	and	CCONJ
ejpam-5362	481	51	choose	choose	VERB
ejpam-5362	481	52	an	an	DET
ejpam-5362	481	53	is	be	AUX
ejpam-5362	481	54	-	-	PUNCT
ejpam-5362	481	55	open	open	ADJ
ejpam-5362	481	56	sublocale	sublocale	NOUN
ejpam-5362	481	57	os(x	os(x	NOUN
ejpam-5362	481	58	)	)	PUNCT
ejpam-5362	481	59	such	such	ADJ
ejpam-5362	481	60	that	that	SCONJ
ejpam-5362	481	61	os(x	os(x	NOUN
ejpam-5362	481	62	)	)	PUNCT
ejpam-5362	481	63	∩	∩	NOUN
ejpam-5362	481	64	s	s	PART
ejpam-5362	481	65	∩	∩	NOUN
ejpam-5362	481	66	(	(	PUNCT
ejpam-5362	481	67	l∖	l∖	PROPN
ejpam-5362	481	68	v	v	PROPN
ejpam-5362	481	69	)	)	PUNCT
ejpam-5362	481	70	=	=	SYM
ejpam-5362	482	1	o.	o.	NOUN
ejpam-5362	482	2	then	then	ADV
ejpam-5362	482	3	os(x	os(x	NOUN
ejpam-5362	482	4	)	)	PUNCT
ejpam-5362	482	5	⊆	⊆	NUM
ejpam-5362	482	6	s	s	NOUN
ejpam-5362	482	7	∩	∩	NOUN
ejpam-5362	482	8	v.	v.	CCONJ
ejpam-5362	482	9	by	by	ADP
ejpam-5362	482	10	(	(	PUNCT
ejpam-5362	482	11	iii	iii	NOUN
ejpam-5362	482	12	)	)	PUNCT
ejpam-5362	482	13	,	,	PUNCT
ejpam-5362	482	14	intis(s	intis(s	NOUN
ejpam-5362	482	15	∩	∩	ADJ
ejpam-5362	482	16	v	v	NOUN
ejpam-5362	482	17	)	)	PUNCT
ejpam-5362	483	1	=	=	SYM
ejpam-5362	483	2	o	o	NOUN
ejpam-5362	483	3	,	,	PUNCT
ejpam-5362	483	4	making	make	VERB
ejpam-5362	483	5	os(x	os(x	NOUN
ejpam-5362	483	6	)	)	PUNCT
ejpam-5362	483	7	=	=	SYM
ejpam-5362	484	1	o.	o.	NOUN
ejpam-5362	484	2	(	(	PUNCT
ejpam-5362	484	3	iv	iv	X
ejpam-5362	484	4	)	)	PUNCT
ejpam-5362	484	5	=	=	NOUN
ejpam-5362	484	6	⇒	⇒	NOUN
ejpam-5362	484	7	(	(	PUNCT
ejpam-5362	484	8	ii	ii	NOUN
ejpam-5362	484	9	):	):	PUNCT
ejpam-5362	484	10	let	let	VERB
ejpam-5362	484	11	o(x	o(x	PROPN
ejpam-5362	484	12	)	)	PUNCT
ejpam-5362	484	13	be	be	AUX
ejpam-5362	484	14	a	a	DET
ejpam-5362	484	15	non	non	ADJ
ejpam-5362	484	16	-	-	ADJ
ejpam-5362	484	17	void	void	ADJ
ejpam-5362	484	18	i	i	NOUN
ejpam-5362	484	19	-	-	PUNCT
ejpam-5362	484	20	open	open	ADJ
ejpam-5362	484	21	sublocale	sublocale	NOUN
ejpam-5362	484	22	of	of	ADP
ejpam-5362	484	23	l	l	NOUN
ejpam-5362	484	24	and	and	CCONJ
ejpam-5362	484	25	assume	assume	VERB
ejpam-5362	484	26	that	that	SCONJ
ejpam-5362	484	27	s	s	VERB
ejpam-5362	484	28	∩	∩	NOUN
ejpam-5362	484	29	o(x	o(x	PROPN
ejpam-5362	484	30	)	)	PUNCT
ejpam-5362	484	31	is	be	AUX
ejpam-5362	484	32	of	of	ADP
ejpam-5362	484	33	(	(	PUNCT
ejpam-5362	484	34	j	j	PROPN
ejpam-5362	484	35	,	,	PUNCT
ejpam-5362	484	36	i)-first	i)-first	NOUN
ejpam-5362	484	37	category	category	NOUN
ejpam-5362	484	38	.	.	PUNCT
ejpam-5362	485	1	by	by	ADP
ejpam-5362	485	2	(	(	PUNCT
ejpam-5362	485	3	iv	iv	X
ejpam-5362	485	4	)	)	PUNCT
ejpam-5362	485	5	,	,	PUNCT
ejpam-5362	485	6	s	s	VERB
ejpam-5362	485	7	∩	∩	NOUN
ejpam-5362	485	8	(	(	PUNCT
ejpam-5362	485	9	l∖	l∖	PROPN
ejpam-5362	485	10	o(x	o(x	PROPN
ejpam-5362	485	11	)	)	PUNCT
ejpam-5362	485	12	)	)	PUNCT
ejpam-5362	486	1	=	=	SYM
ejpam-5362	486	2	s	s	PART
ejpam-5362	486	3	∩	∩	ADJ
ejpam-5362	486	4	c(x	c(x	NOUN
ejpam-5362	486	5	)	)	PUNCT
ejpam-5362	486	6	=	=	SYM
ejpam-5362	486	7	cs(νs(x	cs(νs(x	NOUN
ejpam-5362	486	8	)	)	PUNCT
ejpam-5362	486	9	)	)	PUNCT
ejpam-5362	486	10	is	be	AUX
ejpam-5362	486	11	is	be	AUX
ejpam-5362	486	12	-	-	PUNCT
ejpam-5362	486	13	dense	dense	ADJ
ejpam-5362	486	14	which	which	PRON
ejpam-5362	486	15	implies	imply	VERB
ejpam-5362	486	16	that	that	PRON
ejpam-5362	486	17	νs(x	νs(x	NOUN
ejpam-5362	486	18	)	)	PUNCT
ejpam-5362	486	19	=	=	SYM
ejpam-5362	487	1	0	0	X
ejpam-5362	487	2	.	.	PUNCT
ejpam-5362	487	3	therefore	therefore	ADV
ejpam-5362	487	4	o(x	o(x	PROPN
ejpam-5362	487	5	)	)	PUNCT
ejpam-5362	488	1	=	=	SYM
ejpam-5362	488	2	o	o	NOUN
ejpam-5362	488	3	which	which	PRON
ejpam-5362	488	4	is	be	AUX
ejpam-5362	488	5	a	a	DET
ejpam-5362	488	6	contradiction	contradiction	NOUN
ejpam-5362	488	7	.	.	PUNCT
ejpam-5362	489	1	5	5	X
ejpam-5362	489	2	.	.	X
ejpam-5362	489	3	baireness	baireness	NOUN
ejpam-5362	489	4	of	of	ADP
ejpam-5362	489	5	topobilocales	topobilocale	NOUN
ejpam-5362	489	6	the	the	DET
ejpam-5362	489	7	aim	aim	NOUN
ejpam-5362	489	8	of	of	ADP
ejpam-5362	489	9	this	this	DET
ejpam-5362	489	10	section	section	NOUN
ejpam-5362	489	11	is	be	AUX
ejpam-5362	489	12	to	to	PART
ejpam-5362	489	13	introduce	introduce	VERB
ejpam-5362	489	14	and	and	CCONJ
ejpam-5362	489	15	characterize	characterize	VERB
ejpam-5362	489	16	baireness	baireness	NOUN
ejpam-5362	489	17	in	in	ADP
ejpam-5362	489	18	the	the	DET
ejpam-5362	489	19	category	category	NOUN
ejpam-5362	489	20	of	of	ADP
ejpam-5362	489	21	topobilocales	topobilocale	NOUN
ejpam-5362	489	22	.	.	PUNCT
ejpam-5362	490	1	a	a	DET
ejpam-5362	490	2	topobilocale	topobilocale	NOUN
ejpam-5362	490	3	[	[	X
ejpam-5362	490	4	12	12	NUM
ejpam-5362	490	5	]	]	PUNCT
ejpam-5362	490	6	is	be	AUX
ejpam-5362	490	7	a	a	DET
ejpam-5362	490	8	triple	triple	ADJ
ejpam-5362	490	9	(	(	PUNCT
ejpam-5362	490	10	l	l	NOUN
ejpam-5362	490	11	,	,	PUNCT
ejpam-5362	490	12	τ1	τ1	NOUN
ejpam-5362	490	13	,	,	PUNCT
ejpam-5362	490	14	τ2	τ2	NOUN
ejpam-5362	490	15	)	)	PUNCT
ejpam-5362	490	16	where	where	SCONJ
ejpam-5362	490	17	l	l	NOUN
ejpam-5362	490	18	is	be	AUX
ejpam-5362	490	19	a	a	DET
ejpam-5362	490	20	locale	locale	NOUN
ejpam-5362	490	21	,	,	PUNCT
ejpam-5362	490	22	l1	l1	PROPN
ejpam-5362	490	23	and	and	CCONJ
ejpam-5362	490	24	l2	l2	NOUN
ejpam-5362	490	25	are	be	AUX
ejpam-5362	490	26	subframes	subframe	NOUN
ejpam-5362	490	27	of	of	ADP
ejpam-5362	490	28	l	l	NOUN
ejpam-5362	490	29	all	all	PRON
ejpam-5362	490	30	of	of	ADP
ejpam-5362	490	31	whose	whose	DET
ejpam-5362	490	32	elements	element	NOUN
ejpam-5362	490	33	are	be	AUX
ejpam-5362	490	34	complemented	complement	VERB
ejpam-5362	490	35	in	in	ADP
ejpam-5362	490	36	l.	l.	PROPN
ejpam-5362	490	37	each	each	DET
ejpam-5362	490	38	member	member	NOUN
ejpam-5362	490	39	of	of	ADP
ejpam-5362	490	40	τi	τi	PROPN
ejpam-5362	490	41	(	(	PUNCT
ejpam-5362	490	42	i	i	NOUN
ejpam-5362	490	43	=	=	NOUN
ejpam-5362	490	44	1	1	NUM
ejpam-5362	490	45	,	,	PUNCT
ejpam-5362	490	46	2	2	NUM
ejpam-5362	490	47	)	)	PUNCT
ejpam-5362	490	48	is	be	AUX
ejpam-5362	490	49	called	call	VERB
ejpam-5362	490	50	τi	τi	ADV
ejpam-5362	490	51	-	-	PUNCT
ejpam-5362	490	52	open	open	ADJ
ejpam-5362	490	53	.	.	PUNCT
ejpam-5362	491	1	for	for	ADP
ejpam-5362	491	2	each	each	DET
ejpam-5362	491	3	a	a	DET
ejpam-5362	491	4	∈	∈	PROPN
ejpam-5362	491	5	l	l	NOUN
ejpam-5362	491	6	,	,	PUNCT
ejpam-5362	491	7	the	the	DET
ejpam-5362	491	8	τi	τi	NOUN
ejpam-5362	491	9	-	-	PUNCT
ejpam-5362	491	10	closure	closure	NOUN
ejpam-5362	491	11	(	(	PUNCT
ejpam-5362	491	12	i	i	NOUN
ejpam-5362	491	13	=	=	NOUN
ejpam-5362	491	14	1	1	NUM
ejpam-5362	491	15	,	,	PUNCT
ejpam-5362	491	16	2	2	NUM
ejpam-5362	491	17	)	)	PUNCT
ejpam-5362	491	18	of	of	ADP
ejpam-5362	491	19	a	a	PRON
ejpam-5362	491	20	in	in	ADP
ejpam-5362	491	21	l	l	NOUN
ejpam-5362	491	22	is	be	AUX
ejpam-5362	491	23	defined	define	VERB
ejpam-5362	491	24	by	by	ADP
ejpam-5362	491	25	cl(l	cl(l	NOUN
ejpam-5362	491	26	,	,	PUNCT
ejpam-5362	491	27	τi)(a	τi)(a	NUM
ejpam-5362	491	28	)	)	PUNCT
ejpam-5362	492	1	=	=	PUNCT
ejpam-5362	492	2	∧	∧	NOUN
ejpam-5362	492	3	{	{	PUNCT
ejpam-5362	492	4	b	b	PROPN
ejpam-5362	492	5	∈	∈	X
ejpam-5362	492	6	τ	τ	X
ejpam-5362	492	7	′i	′i	NOUN
ejpam-5362	492	8	:	:	PUNCT
ejpam-5362	492	9	a	a	DET
ejpam-5362	492	10	≤	≤	PROPN
ejpam-5362	492	11	b	b	NOUN
ejpam-5362	492	12	}	}	PUNCT
ejpam-5362	492	13	and	and	CCONJ
ejpam-5362	492	14	the	the	DET
ejpam-5362	492	15	τi	τi	NOUN
ejpam-5362	492	16	-	-	NOUN
ejpam-5362	492	17	interior	interior	NOUN
ejpam-5362	492	18	of	of	ADP
ejpam-5362	492	19	a	a	PRON
ejpam-5362	492	20	is	be	AUX
ejpam-5362	492	21	defined	define	VERB
ejpam-5362	492	22	by	by	ADP
ejpam-5362	492	23	int(l	int(l	PROPN
ejpam-5362	492	24	,	,	PUNCT
ejpam-5362	492	25	τi)(a	τi)(a	NUM
ejpam-5362	492	26	)	)	PUNCT
ejpam-5362	493	1	=	=	SYM
ejpam-5362	493	2	∨	∨	X
ejpam-5362	493	3	{	{	PUNCT
ejpam-5362	493	4	b	b	PROPN
ejpam-5362	493	5	∈	∈	PROPN
ejpam-5362	493	6	τi	τi	ADP
ejpam-5362	493	7	:	:	PUNCT
ejpam-5362	493	8	b	b	X
ejpam-5362	493	9	≤	≤	ADV
ejpam-5362	493	10	a	a	PRON
ejpam-5362	493	11	}	}	PUNCT
ejpam-5362	493	12	.	.	PUNCT
ejpam-5362	494	1	we	we	PRON
ejpam-5362	494	2	have	have	VERB
ejpam-5362	494	3	the	the	DET
ejpam-5362	494	4	following	follow	VERB
ejpam-5362	494	5	result	result	NOUN
ejpam-5362	494	6	.	.	PUNCT
ejpam-5362	495	1	see	see	VERB
ejpam-5362	495	2	[	[	X
ejpam-5362	495	3	24	24	NUM
ejpam-5362	495	4	]	]	PUNCT
ejpam-5362	495	5	for	for	ADP
ejpam-5362	495	6	the	the	DET
ejpam-5362	495	7	proofs	proof	NOUN
ejpam-5362	495	8	of	of	ADP
ejpam-5362	495	9	some	some	PRON
ejpam-5362	495	10	of	of	ADP
ejpam-5362	495	11	the	the	DET
ejpam-5362	495	12	statements	statement	NOUN
ejpam-5362	495	13	.	.	PUNCT
ejpam-5362	496	1	for	for	ADP
ejpam-5362	496	2	the	the	DET
ejpam-5362	496	3	rest	rest	NOUN
ejpam-5362	496	4	of	of	ADP
ejpam-5362	496	5	the	the	DET
ejpam-5362	496	6	statements	statement	NOUN
ejpam-5362	496	7	,	,	PUNCT
ejpam-5362	496	8	the	the	DET
ejpam-5362	496	9	proofs	proof	NOUN
ejpam-5362	496	10	resemble	resemble	VERB
ejpam-5362	496	11	that	that	PRON
ejpam-5362	496	12	of	of	ADP
ejpam-5362	496	13	[	[	X
ejpam-5362	496	14	16	16	NUM
ejpam-5362	496	15	,	,	PUNCT
ejpam-5362	496	16	proposition	proposition	NOUN
ejpam-5362	496	17	5.1.3	5.1.3	NUM
ejpam-5362	496	18	.	.	NUM
ejpam-5362	496	19	]	]	PUNCT
ejpam-5362	496	20	.	.	PUNCT
ejpam-5362	497	1	proposition	proposition	NOUN
ejpam-5362	497	2	12	12	NUM
ejpam-5362	497	3	.	.	PUNCT
ejpam-5362	498	1	let	let	VERB
ejpam-5362	498	2	(	(	PUNCT
ejpam-5362	498	3	l	l	NOUN
ejpam-5362	498	4	,	,	PUNCT
ejpam-5362	498	5	τi	τi	ADJ
ejpam-5362	498	6	,	,	PUNCT
ejpam-5362	498	7	τj	τj	ADV
ejpam-5362	498	8	)	)	PUNCT
ejpam-5362	498	9	be	be	AUX
ejpam-5362	498	10	a	a	DET
ejpam-5362	498	11	topobilocale	topobilocale	NOUN
ejpam-5362	498	12	.	.	PUNCT
ejpam-5362	499	1	then	then	ADV
ejpam-5362	499	2	(	(	PUNCT
ejpam-5362	499	3	i	i	NOUN
ejpam-5362	499	4	)	)	PUNCT
ejpam-5362	499	5	cl(l	cl(l	NOUN
ejpam-5362	499	6	,	,	PUNCT
ejpam-5362	499	7	τi)(0	τi)(0	X
ejpam-5362	499	8	)	)	PUNCT
ejpam-5362	499	9	=	=	SYM
ejpam-5362	499	10	int(l	int(l	PROPN
ejpam-5362	499	11	,	,	PUNCT
ejpam-5362	499	12	τi)(0	τi)(0	NOUN
ejpam-5362	499	13	)	)	PUNCT
ejpam-5362	499	14	=	=	SYM
ejpam-5362	499	15	0	0	X
ejpam-5362	499	16	.	.	PUNCT
ejpam-5362	499	17	(	(	PUNCT
ejpam-5362	499	18	ii	ii	NOUN
ejpam-5362	499	19	)	)	PUNCT
ejpam-5362	499	20	cl(l	cl(l	NOUN
ejpam-5362	499	21	,	,	PUNCT
ejpam-5362	499	22	τi)(1	τi)(1	NOUN
ejpam-5362	499	23	)	)	PUNCT
ejpam-5362	499	24	=	=	SYM
ejpam-5362	499	25	int(l	int(l	PROPN
ejpam-5362	499	26	,	,	PUNCT
ejpam-5362	499	27	τi)(1	τi)(1	NOUN
ejpam-5362	499	28	)	)	PUNCT
ejpam-5362	499	29	=	=	SYM
ejpam-5362	499	30	1	1	X
ejpam-5362	499	31	.	.	PUNCT
ejpam-5362	499	32	(	(	PUNCT
ejpam-5362	499	33	iii	iii	X
ejpam-5362	499	34	)	)	PUNCT
ejpam-5362	499	35	a	a	DET
ejpam-5362	499	36	≤	≤	NUM
ejpam-5362	499	37	cl(l	cl(l	NOUN
ejpam-5362	499	38	,	,	PUNCT
ejpam-5362	499	39	τi)(a	τi)(a	NUM
ejpam-5362	499	40	)	)	PUNCT
ejpam-5362	499	41	.	.	PUNCT
ejpam-5362	500	1	(	(	PUNCT
ejpam-5362	500	2	iv	iv	X
ejpam-5362	500	3	)	)	PUNCT
ejpam-5362	500	4	if	if	SCONJ
ejpam-5362	500	5	a	a	DET
ejpam-5362	500	6	≤	≤	NUM
ejpam-5362	500	7	b	b	NOUN
ejpam-5362	500	8	,	,	PUNCT
ejpam-5362	500	9	then	then	ADV
ejpam-5362	500	10	cl(l	cl(l	NOUN
ejpam-5362	500	11	,	,	PUNCT
ejpam-5362	500	12	τi)(a	τi)(a	NUM
ejpam-5362	500	13	)	)	PUNCT
ejpam-5362	500	14	≤	≤	NOUN
ejpam-5362	500	15	cl(l	cl(l	NOUN
ejpam-5362	500	16	,	,	PUNCT
ejpam-5362	500	17	τi)(b	τi)(b	PROPN
ejpam-5362	500	18	)	)	PUNCT
ejpam-5362	500	19	.	.	PUNCT
ejpam-5362	501	1	(	(	PUNCT
ejpam-5362	501	2	v	v	X
ejpam-5362	501	3	)	)	PUNCT
ejpam-5362	501	4	int(l	int(l	PROPN
ejpam-5362	501	5	,	,	PUNCT
ejpam-5362	501	6	τi)(a	τi)(a	NUM
ejpam-5362	501	7	)	)	PUNCT
ejpam-5362	501	8	≤	≤	NUM
ejpam-5362	501	9	a.	a.	NOUN
ejpam-5362	501	10	(	(	PUNCT
ejpam-5362	501	11	vi	vi	NOUN
ejpam-5362	501	12	)	)	PUNCT
ejpam-5362	501	13	if	if	SCONJ
ejpam-5362	501	14	a	a	DET
ejpam-5362	501	15	≤	≤	NUM
ejpam-5362	501	16	b	b	NOUN
ejpam-5362	501	17	,	,	PUNCT
ejpam-5362	501	18	then	then	ADV
ejpam-5362	501	19	int(l	int(l	PROPN
ejpam-5362	501	20	,	,	PUNCT
ejpam-5362	501	21	τi)(a	τi)(a	NUM
ejpam-5362	501	22	)	)	PUNCT
ejpam-5362	501	23	≤	≤	PROPN
ejpam-5362	501	24	int(l	int(l	PROPN
ejpam-5362	501	25	,	,	PUNCT
ejpam-5362	501	26	τi)(b	τi)(b	PROPN
ejpam-5362	501	27	)	)	PUNCT
ejpam-5362	501	28	.	.	PUNCT
ejpam-5362	502	1	m.	m.	NOUN
ejpam-5362	502	2	nxumalo	nxumalo	PROPN
ejpam-5362	502	3	/	/	SYM
ejpam-5362	502	4	eur	eur	PROPN
ejpam-5362	502	5	.	.	PUNCT
ejpam-5362	503	1	j.	j.	PROPN
ejpam-5362	503	2	pure	pure	PROPN
ejpam-5362	503	3	appl	appl	PROPN
ejpam-5362	503	4	.	.	PROPN
ejpam-5362	503	5	math	math	PROPN
ejpam-5362	503	6	,	,	PUNCT
ejpam-5362	503	7	18	18	NUM
ejpam-5362	503	8	(	(	PUNCT
ejpam-5362	503	9	1	1	NUM
ejpam-5362	503	10	)	)	PUNCT
ejpam-5362	503	11	(	(	PUNCT
ejpam-5362	503	12	2025	2025	NUM
ejpam-5362	503	13	)	)	PUNCT
ejpam-5362	503	14	,	,	PUNCT
ejpam-5362	503	15	5362	5362	NUM
ejpam-5362	503	16	19	19	NUM
ejpam-5362	503	17	of	of	ADP
ejpam-5362	503	18	21	21	NUM
ejpam-5362	503	19	(	(	PUNCT
ejpam-5362	503	20	vii	vii	PROPN
ejpam-5362	503	21	)	)	PUNCT
ejpam-5362	503	22	for	for	ADP
ejpam-5362	503	23	each	each	DET
ejpam-5362	503	24	a	a	DET
ejpam-5362	503	25	∈	∈	PROPN
ejpam-5362	503	26	l	l	NOUN
ejpam-5362	503	27	,	,	PUNCT
ejpam-5362	503	28	(	(	PUNCT
ejpam-5362	503	29	cl(l	cl(l	ADJ
ejpam-5362	503	30	,	,	PUNCT
ejpam-5362	503	31	τi)(a	τi)(a	NUM
ejpam-5362	503	32	)	)	PUNCT
ejpam-5362	503	33	)	)	PUNCT
ejpam-5362	504	1	′	′	NUM
ejpam-5362	505	1	=	=	PUNCT
ejpam-5362	505	2	int(l	int(l	PROPN
ejpam-5362	505	3	,	,	PUNCT
ejpam-5362	505	4	τi)(a	τi)(a	PUNCT
ejpam-5362	505	5	′	′	NUM
ejpam-5362	505	6	)	)	PUNCT
ejpam-5362	505	7	.	.	PUNCT
ejpam-5362	506	1	(	(	PUNCT
ejpam-5362	506	2	viii	viii	NOUN
ejpam-5362	506	3	)	)	PUNCT
ejpam-5362	506	4	for	for	ADP
ejpam-5362	506	5	each	each	DET
ejpam-5362	506	6	a	a	DET
ejpam-5362	506	7	∈	∈	PROPN
ejpam-5362	506	8	l	l	NOUN
ejpam-5362	506	9	,	,	PUNCT
ejpam-5362	506	10	(	(	PUNCT
ejpam-5362	506	11	int(l	int(l	PROPN
ejpam-5362	506	12	,	,	PUNCT
ejpam-5362	506	13	τi)(a	τi)(a	NUM
ejpam-5362	506	14	)	)	PUNCT
ejpam-5362	506	15	)	)	PUNCT
ejpam-5362	506	16	′	′	NUM
ejpam-5362	507	1	=	=	PUNCT
ejpam-5362	507	2	cl(l	cl(l	NOUN
ejpam-5362	507	3	,	,	PUNCT
ejpam-5362	507	4	τi)(a	τi)(a	PUNCT
ejpam-5362	507	5	′	′	NUM
ejpam-5362	507	6	)	)	PUNCT
ejpam-5362	507	7	.	.	PUNCT
ejpam-5362	508	1	call	call	VERB
ejpam-5362	508	2	an	an	DET
ejpam-5362	508	3	element	element	NOUN
ejpam-5362	508	4	a	a	DET
ejpam-5362	508	5	∈	∈	PROPN
ejpam-5362	508	6	l	l	NOUN
ejpam-5362	508	7	τi	τi	NOUN
ejpam-5362	508	8	-	-	PUNCT
ejpam-5362	508	9	dense	dense	ADJ
ejpam-5362	508	10	if	if	SCONJ
ejpam-5362	508	11	cl(l	cl(l	NOUN
ejpam-5362	508	12	,	,	PUNCT
ejpam-5362	508	13	τi)(a	τi)(a	NUM
ejpam-5362	508	14	)	)	PUNCT
ejpam-5362	509	1	=	=	SYM
ejpam-5362	509	2	1	1	X
ejpam-5362	509	3	.	.	PUNCT
ejpam-5362	509	4	clearly	clearly	ADV
ejpam-5362	509	5	,	,	PUNCT
ejpam-5362	509	6	a	a	DET
ejpam-5362	509	7	∈	∈	PROPN
ejpam-5362	509	8	l	l	NOUN
ejpam-5362	509	9	is	be	AUX
ejpam-5362	509	10	τi	τi	ADJ
ejpam-5362	509	11	-	-	PUNCT
ejpam-5362	509	12	dense	dense	ADJ
ejpam-5362	509	13	if	if	SCONJ
ejpam-5362	509	14	and	and	CCONJ
ejpam-5362	509	15	only	only	ADV
ejpam-5362	509	16	if	if	SCONJ
ejpam-5362	509	17	a	a	DET
ejpam-5362	509	18	∧	∧	PROPN
ejpam-5362	509	19	x	x	X
ejpam-5362	509	20	̸=	̸=	PROPN
ejpam-5362	509	21	0	0	NUM
ejpam-5362	509	22	for	for	ADP
ejpam-5362	509	23	all	all	DET
ejpam-5362	509	24	nonzero	nonzero	NOUN
ejpam-5362	509	25	x	x	SYM
ejpam-5362	509	26	∈	∈	NOUN
ejpam-5362	509	27	τi	τi	NOUN
ejpam-5362	509	28	,	,	PUNCT
ejpam-5362	509	29	see	see	VERB
ejpam-5362	509	30	[	[	X
ejpam-5362	509	31	15	15	NUM
ejpam-5362	509	32	,	,	PUNCT
ejpam-5362	509	33	proposition	proposition	NOUN
ejpam-5362	509	34	2.8	2.8	NUM
ejpam-5362	509	35	.	.	PUNCT
ejpam-5362	509	36	]	]	PUNCT
ejpam-5362	509	37	for	for	ADP
ejpam-5362	509	38	the	the	DET
ejpam-5362	509	39	proof	proof	NOUN
ejpam-5362	509	40	.	.	PUNCT
ejpam-5362	510	1	definition	definition	NOUN
ejpam-5362	510	2	6	6	NUM
ejpam-5362	510	3	.	.	PUNCT
ejpam-5362	510	4	call	call	VERB
ejpam-5362	510	5	a	a	DET
ejpam-5362	510	6	topobilocale	topobilocale	NOUN
ejpam-5362	510	7	(	(	PUNCT
ejpam-5362	510	8	l	l	NOUN
ejpam-5362	510	9	,	,	PUNCT
ejpam-5362	510	10	τ1	τ1	NOUN
ejpam-5362	510	11	,	,	PUNCT
ejpam-5362	510	12	τ2	τ2	NOUN
ejpam-5362	510	13	)	)	PUNCT
ejpam-5362	510	14	(	(	PUNCT
ejpam-5362	510	15	τi	τi	ADP
ejpam-5362	510	16	,	,	PUNCT
ejpam-5362	510	17	τj)-baire	τj)-baire	VERB
ejpam-5362	510	18	if	if	SCONJ
ejpam-5362	510	19	any	any	DET
ejpam-5362	510	20	sequence	sequence	NOUN
ejpam-5362	510	21	(	(	PUNCT
ejpam-5362	510	22	xn)n∈n	xn)n∈n	NUM
ejpam-5362	510	23	of	of	ADP
ejpam-5362	510	24	τidense	τidense	NOUN
ejpam-5362	510	25	elements	element	NOUN
ejpam-5362	510	26	of	of	ADP
ejpam-5362	510	27	τj	τj	ADP
ejpam-5362	510	28	satisfies	satisfie	NOUN
ejpam-5362	510	29	the	the	DET
ejpam-5362	510	30	condition	condition	NOUN
ejpam-5362	510	31	∧	∧	PROPN
ejpam-5362	510	32	n∈n	n∈n	ADV
ejpam-5362	510	33	xn	xn	PROPN
ejpam-5362	510	34	is	be	AUX
ejpam-5362	510	35	τi	τi	ADJ
ejpam-5362	510	36	-	-	PUNCT
ejpam-5362	510	37	dense	dense	ADJ
ejpam-5362	510	38	.	.	PUNCT
ejpam-5362	511	1	call	call	VERB
ejpam-5362	511	2	an	an	DET
ejpam-5362	511	3	element	element	NOUN
ejpam-5362	511	4	a	a	DET
ejpam-5362	511	5	∈	∈	NOUN
ejpam-5362	511	6	l	l	NOUN
ejpam-5362	511	7	(	(	PUNCT
ejpam-5362	511	8	τi	τi	ADP
ejpam-5362	511	9	,	,	PUNCT
ejpam-5362	511	10	τj)-nowhere	τj)-nowhere	ADV
ejpam-5362	511	11	dense	dense	ADJ
ejpam-5362	511	12	if	if	SCONJ
ejpam-5362	511	13	int(l	int(l	PROPN
ejpam-5362	511	14	,	,	PUNCT
ejpam-5362	511	15	τj)(cl(l	τj)(cl(l	X
ejpam-5362	511	16	,	,	PUNCT
ejpam-5362	511	17	τi)(a	τi)(a	NUM
ejpam-5362	511	18	)	)	PUNCT
ejpam-5362	511	19	)	)	PUNCT
ejpam-5362	512	1	=	=	PUNCT
ejpam-5362	512	2	0	0	X
ejpam-5362	512	3	.	.	PUNCT
ejpam-5362	513	1	an	an	DET
ejpam-5362	513	2	element	element	NOUN
ejpam-5362	513	3	a	a	DET
ejpam-5362	513	4	∈	∈	PROPN
ejpam-5362	513	5	l	l	NOUN
ejpam-5362	513	6	is	be	AUX
ejpam-5362	513	7	of	of	ADP
ejpam-5362	513	8	(	(	PUNCT
ejpam-5362	513	9	τi	τi	ADP
ejpam-5362	513	10	,	,	PUNCT
ejpam-5362	513	11	τj)-first	τj)-first	ADV
ejpam-5362	513	12	category	category	NOUN
ejpam-5362	513	13	if	if	SCONJ
ejpam-5362	513	14	a	a	DET
ejpam-5362	513	15	≤	≤	NOUN
ejpam-5362	513	16	∨	∨	NUM
ejpam-5362	513	17	n∈n	n∈n	NOUN
ejpam-5362	513	18	xn	xn	PUNCT
ejpam-5362	513	19	for	for	ADP
ejpam-5362	513	20	some	some	DET
ejpam-5362	513	21	collection	collection	NOUN
ejpam-5362	513	22	{	{	PUNCT
ejpam-5362	513	23	xn	xn	NOUN
ejpam-5362	513	24	:	:	PUNCT
ejpam-5362	513	25	n	n	CCONJ
ejpam-5362	513	26	∈	∈	PROPN
ejpam-5362	513	27	n	n	CCONJ
ejpam-5362	513	28	}	}	PUNCT
ejpam-5362	513	29	of	of	ADP
ejpam-5362	513	30	(	(	PUNCT
ejpam-5362	513	31	τi	τi	ADP
ejpam-5362	513	32	,	,	PUNCT
ejpam-5362	513	33	τj)-nowhere	τj)-nowhere	ADP
ejpam-5362	513	34	dense	dense	ADJ
ejpam-5362	513	35	elements	element	NOUN
ejpam-5362	513	36	of	of	ADP
ejpam-5362	513	37	l.	l.	PROPN
ejpam-5362	513	38	otherwise	otherwise	ADV
ejpam-5362	513	39	it	it	PRON
ejpam-5362	513	40	is	be	AUX
ejpam-5362	513	41	of	of	ADP
ejpam-5362	513	42	(	(	PUNCT
ejpam-5362	513	43	τi	τi	ADJ
ejpam-5362	513	44	,	,	PUNCT
ejpam-5362	513	45	τj)-second	τj)-second	ADJ
ejpam-5362	513	46	category	category	NOUN
ejpam-5362	513	47	.	.	PUNCT
ejpam-5362	514	1	it	it	PRON
ejpam-5362	514	2	is	be	AUX
ejpam-5362	514	3	clear	clear	ADJ
ejpam-5362	514	4	that	that	SCONJ
ejpam-5362	514	5	if	if	SCONJ
ejpam-5362	514	6	a	a	PRON
ejpam-5362	514	7	is	be	AUX
ejpam-5362	514	8	of	of	ADP
ejpam-5362	514	9	(	(	PUNCT
ejpam-5362	514	10	τi	τi	ADP
ejpam-5362	514	11	,	,	PUNCT
ejpam-5362	514	12	τj)-first	τj)-first	ADV
ejpam-5362	514	13	category	category	NOUN
ejpam-5362	514	14	and	and	CCONJ
ejpam-5362	514	15	b	b	PROPN
ejpam-5362	514	16	≤	≤	PROPN
ejpam-5362	514	17	a	a	PRON
ejpam-5362	514	18	,	,	PUNCT
ejpam-5362	514	19	then	then	ADV
ejpam-5362	514	20	b	b	PROPN
ejpam-5362	514	21	is	be	AUX
ejpam-5362	514	22	of	of	ADP
ejpam-5362	514	23	(	(	PUNCT
ejpam-5362	514	24	τi	τi	ADP
ejpam-5362	514	25	,	,	PUNCT
ejpam-5362	514	26	τj)-first	τj)-first	ADJ
ejpam-5362	514	27	category	category	NOUN
ejpam-5362	514	28	.	.	PUNCT
ejpam-5362	515	1	for	for	ADP
ejpam-5362	515	2	use	use	NOUN
ejpam-5362	515	3	below	below	ADV
ejpam-5362	515	4	,	,	PUNCT
ejpam-5362	515	5	we	we	PRON
ejpam-5362	515	6	give	give	VERB
ejpam-5362	515	7	the	the	DET
ejpam-5362	515	8	following	follow	VERB
ejpam-5362	515	9	result	result	NOUN
ejpam-5362	515	10	with	with	ADP
ejpam-5362	515	11	a	a	DET
ejpam-5362	515	12	proof	proof	NOUN
ejpam-5362	515	13	similar	similar	ADJ
ejpam-5362	515	14	to	to	ADP
ejpam-5362	515	15	that	that	PRON
ejpam-5362	515	16	of	of	ADP
ejpam-5362	515	17	[	[	X
ejpam-5362	515	18	16	16	NUM
ejpam-5362	515	19	,	,	PUNCT
ejpam-5362	515	20	proposition	proposition	NOUN
ejpam-5362	515	21	2.1.4	2.1.4	NUM
ejpam-5362	515	22	.	.	PUNCT
ejpam-5362	515	23	]	]	PUNCT
ejpam-5362	516	1	proposition	proposition	NOUN
ejpam-5362	516	2	13	13	NUM
ejpam-5362	516	3	.	.	PUNCT
ejpam-5362	517	1	let	let	VERB
ejpam-5362	517	2	(	(	PUNCT
ejpam-5362	517	3	l	l	NOUN
ejpam-5362	517	4	,	,	PUNCT
ejpam-5362	517	5	τ1	τ1	NOUN
ejpam-5362	517	6	,	,	PUNCT
ejpam-5362	517	7	τ2	τ2	PROPN
ejpam-5362	517	8	)	)	PUNCT
ejpam-5362	517	9	be	be	VERB
ejpam-5362	517	10	a	a	DET
ejpam-5362	517	11	topobilocale	topobilocale	NOUN
ejpam-5362	517	12	.	.	PUNCT
ejpam-5362	518	1	then	then	ADV
ejpam-5362	518	2	a	a	DET
ejpam-5362	518	3	∈	∈	PROPN
ejpam-5362	518	4	l	l	NOUN
ejpam-5362	518	5	is	be	AUX
ejpam-5362	518	6	(	(	PUNCT
ejpam-5362	518	7	τi	τi	ADP
ejpam-5362	518	8	,	,	PUNCT
ejpam-5362	518	9	τj)-nowhere	τj)-nowhere	ADP
ejpam-5362	518	10	dense	dense	ADJ
ejpam-5362	518	11	iff	iff	PROPN
ejpam-5362	518	12	(	(	PUNCT
ejpam-5362	518	13	cl(l	cl(l	ADJ
ejpam-5362	518	14	,	,	PUNCT
ejpam-5362	518	15	τi)(a	τi)(a	NUM
ejpam-5362	518	16	)	)	PUNCT
ejpam-5362	518	17	)	)	PUNCT
ejpam-5362	519	1	′	′	NUM
ejpam-5362	519	2	is	be	AUX
ejpam-5362	519	3	τj	τj	ADV
ejpam-5362	519	4	-	-	PUNCT
ejpam-5362	519	5	dense	dense	ADJ
ejpam-5362	519	6	.	.	PUNCT
ejpam-5362	520	1	proposition	proposition	NOUN
ejpam-5362	520	2	14	14	NUM
ejpam-5362	520	3	.	.	PUNCT
ejpam-5362	521	1	let	let	VERB
ejpam-5362	521	2	(	(	PUNCT
ejpam-5362	521	3	l	l	NOUN
ejpam-5362	521	4	,	,	PUNCT
ejpam-5362	521	5	τ1	τ1	NOUN
ejpam-5362	521	6	,	,	PUNCT
ejpam-5362	521	7	τ2	τ2	PROPN
ejpam-5362	521	8	)	)	PUNCT
ejpam-5362	521	9	be	be	VERB
ejpam-5362	521	10	a	a	DET
ejpam-5362	521	11	topobilocale	topobilocale	NOUN
ejpam-5362	521	12	.	.	PUNCT
ejpam-5362	522	1	the	the	DET
ejpam-5362	522	2	following	follow	VERB
ejpam-5362	522	3	statements	statement	NOUN
ejpam-5362	522	4	are	be	AUX
ejpam-5362	522	5	equivalent	equivalent	ADJ
ejpam-5362	522	6	.	.	PUNCT
ejpam-5362	523	1	(	(	PUNCT
ejpam-5362	523	2	i	i	NOUN
ejpam-5362	523	3	)	)	PUNCT
ejpam-5362	523	4	(	(	PUNCT
ejpam-5362	523	5	l	l	NOUN
ejpam-5362	523	6	,	,	PUNCT
ejpam-5362	523	7	τ1	τ1	NOUN
ejpam-5362	523	8	,	,	PUNCT
ejpam-5362	523	9	τ2	τ2	NOUN
ejpam-5362	523	10	)	)	PUNCT
ejpam-5362	523	11	is	be	AUX
ejpam-5362	523	12	(	(	PUNCT
ejpam-5362	523	13	τi	τi	ADJ
ejpam-5362	523	14	,	,	PUNCT
ejpam-5362	523	15	τj)-baire	τj)-baire	NOUN
ejpam-5362	523	16	.	.	PUNCT
ejpam-5362	524	1	(	(	PUNCT
ejpam-5362	524	2	ii	ii	NOUN
ejpam-5362	524	3	)	)	PUNCT
ejpam-5362	524	4	each	each	DET
ejpam-5362	524	5	nonzero	nonzero	PROPN
ejpam-5362	524	6	τi	τi	PROPN
ejpam-5362	524	7	element	element	NOUN
ejpam-5362	524	8	is	be	AUX
ejpam-5362	524	9	of	of	ADP
ejpam-5362	524	10	(	(	PUNCT
ejpam-5362	524	11	τj	τj	ADP
ejpam-5362	524	12	,	,	PUNCT
ejpam-5362	524	13	τi)-second	τi)-second	ADJ
ejpam-5362	524	14	category	category	NOUN
ejpam-5362	524	15	.	.	PUNCT
ejpam-5362	525	1	(	(	PUNCT
ejpam-5362	525	2	iii	iii	X
ejpam-5362	525	3	)	)	PUNCT
ejpam-5362	525	4	every	every	DET
ejpam-5362	525	5	element	element	NOUN
ejpam-5362	525	6	of	of	ADP
ejpam-5362	525	7	(	(	PUNCT
ejpam-5362	525	8	τj	τj	ADP
ejpam-5362	525	9	,	,	PUNCT
ejpam-5362	525	10	τi)-first	τi)-first	ADJ
ejpam-5362	525	11	category	category	NOUN
ejpam-5362	525	12	has	have	VERB
ejpam-5362	525	13	a	a	DET
ejpam-5362	525	14	zero	zero	NUM
ejpam-5362	525	15	τi	τi	NOUN
ejpam-5362	525	16	-	-	PUNCT
ejpam-5362	525	17	interior	interior	NOUN
ejpam-5362	525	18	.	.	PUNCT
ejpam-5362	526	1	(	(	PUNCT
ejpam-5362	526	2	iv	iv	X
ejpam-5362	526	3	)	)	PUNCT
ejpam-5362	526	4	the	the	DET
ejpam-5362	526	5	complement	complement	NOUN
ejpam-5362	526	6	an	an	DET
ejpam-5362	526	7	element	element	NOUN
ejpam-5362	526	8	of	of	ADP
ejpam-5362	526	9	(	(	PUNCT
ejpam-5362	526	10	τj	τj	ADP
ejpam-5362	526	11	,	,	PUNCT
ejpam-5362	526	12	τi)-first	τi)-first	ADJ
ejpam-5362	526	13	category	category	NOUN
ejpam-5362	526	14	is	be	AUX
ejpam-5362	526	15	τi	τi	NOUN
ejpam-5362	526	16	-	-	PUNCT
ejpam-5362	526	17	dense	dense	ADJ
ejpam-5362	526	18	.	.	PUNCT
ejpam-5362	527	1	proof	proof	NOUN
ejpam-5362	527	2	.	.	PUNCT
ejpam-5362	528	1	(	(	PUNCT
ejpam-5362	528	2	i	i	NOUN
ejpam-5362	528	3	)	)	PUNCT
ejpam-5362	529	1	=	=	NOUN
ejpam-5362	529	2	⇒	⇒	NOUN
ejpam-5362	529	3	(	(	PUNCT
ejpam-5362	529	4	ii	ii	NOUN
ejpam-5362	529	5	):	):	PUNCT
ejpam-5362	529	6	assume	assume	VERB
ejpam-5362	529	7	that	that	SCONJ
ejpam-5362	529	8	there	there	PRON
ejpam-5362	529	9	is	be	VERB
ejpam-5362	529	10	a	a	DET
ejpam-5362	529	11	nonzero	nonzero	NOUN
ejpam-5362	529	12	element	element	NOUN
ejpam-5362	529	13	a	a	DET
ejpam-5362	529	14	∈	∈	NOUN
ejpam-5362	529	15	τi	τi	X
ejpam-5362	529	16	which	which	PRON
ejpam-5362	529	17	is	be	AUX
ejpam-5362	529	18	of	of	ADP
ejpam-5362	529	19	(	(	PUNCT
ejpam-5362	529	20	τj	τj	ADP
ejpam-5362	529	21	,	,	PUNCT
ejpam-5362	529	22	τi)first	τi)first	NOUN
ejpam-5362	529	23	category	category	NOUN
ejpam-5362	529	24	.	.	PUNCT
ejpam-5362	530	1	then	then	ADV
ejpam-5362	530	2	a	a	DET
ejpam-5362	530	3	≤	≤	NOUN
ejpam-5362	530	4	∨	∨	NUM
ejpam-5362	530	5	n∈n	n∈n	NOUN
ejpam-5362	530	6	xn	xn	PUNCT
ejpam-5362	531	1	for	for	ADP
ejpam-5362	531	2	some	some	DET
ejpam-5362	531	3	collection	collection	NOUN
ejpam-5362	531	4	{	{	PUNCT
ejpam-5362	531	5	xn	xn	NOUN
ejpam-5362	531	6	:	:	PUNCT
ejpam-5362	531	7	n	n	CCONJ
ejpam-5362	531	8	∈	∈	PROPN
ejpam-5362	531	9	n	n	CCONJ
ejpam-5362	531	10	}	}	PUNCT
ejpam-5362	531	11	of	of	ADP
ejpam-5362	531	12	(	(	PUNCT
ejpam-5362	531	13	τj	τj	ADP
ejpam-5362	531	14	,	,	PUNCT
ejpam-5362	531	15	τi)-nowhere	τi)-nowhere	ADP
ejpam-5362	531	16	dense	dense	ADJ
ejpam-5362	531	17	elements	element	NOUN
ejpam-5362	531	18	.	.	PUNCT
ejpam-5362	532	1	it	it	PRON
ejpam-5362	532	2	is	be	AUX
ejpam-5362	532	3	clear	clear	ADJ
ejpam-5362	532	4	members	member	NOUN
ejpam-5362	532	5	of	of	ADP
ejpam-5362	532	6	the	the	DET
ejpam-5362	532	7	collection	collection	NOUN
ejpam-5362	532	8	{	{	PUNCT
ejpam-5362	532	9	(	(	PUNCT
ejpam-5362	532	10	cl(l	cl(l	NOUN
ejpam-5362	532	11	,	,	PUNCT
ejpam-5362	532	12	τj)(xn))′	τj)(xn))′	NOUN
ejpam-5362	532	13	:	:	PUNCT
ejpam-5362	532	14	n	n	X
ejpam-5362	532	15	∈	∈	PROPN
ejpam-5362	532	16	n	n	CCONJ
ejpam-5362	532	17	}	}	PUNCT
ejpam-5362	532	18	are	be	AUX
ejpam-5362	532	19	τi	τi	ADJ
ejpam-5362	532	20	-	-	PUNCT
ejpam-5362	532	21	dense	dense	ADJ
ejpam-5362	532	22	.	.	PUNCT
ejpam-5362	533	1	by	by	ADP
ejpam-5362	533	2	(	(	PUNCT
ejpam-5362	533	3	i	i	NOUN
ejpam-5362	533	4	)	)	PUNCT
ejpam-5362	533	5	,	,	PUNCT
ejpam-5362	533	6	∧	∧	PROPN
ejpam-5362	533	7	n∈n(cl(l	n∈n(cl(l	PROPN
ejpam-5362	533	8	,	,	PUNCT
ejpam-5362	533	9	τj)(xn	τj)(xn	PUNCT
ejpam-5362	533	10	)	)	PUNCT
ejpam-5362	533	11	)	)	PUNCT
ejpam-5362	534	1	′	′	NUM
ejpam-5362	534	2	is	be	AUX
ejpam-5362	534	3	τi	τi	ADJ
ejpam-5362	534	4	-	-	PUNCT
ejpam-5362	534	5	dense	dense	ADJ
ejpam-5362	534	6	.	.	PUNCT
ejpam-5362	535	1	it	it	PRON
ejpam-5362	535	2	follows	follow	VERB
ejpam-5362	535	3	that	that	SCONJ
ejpam-5362	535	4	a	a	DET
ejpam-5362	535	5	∧	∧	PROPN
ejpam-5362	535	6	(	(	PUNCT
ejpam-5362	535	7	∧	∧	PROPN
ejpam-5362	535	8	n∈n	n∈n	NOUN
ejpam-5362	535	9	(	(	PUNCT
ejpam-5362	535	10	cl(l	cl(l	NOUN
ejpam-5362	535	11	,	,	PUNCT
ejpam-5362	535	12	τj)(xn	τj)(xn	PUNCT
ejpam-5362	535	13	)	)	PUNCT
ejpam-5362	535	14	)	)	PUNCT
ejpam-5362	535	15	′	′	X
ejpam-5362	535	16	)	)	PUNCT
ejpam-5362	536	1	̸=	̸=	PROPN
ejpam-5362	536	2	0	0	NUM
ejpam-5362	536	3	.	.	PUNCT
ejpam-5362	537	1	therefore	therefore	ADV
ejpam-5362	537	2	0	0	X
ejpam-5362	537	3	̸=	̸=	PROPN
ejpam-5362	537	4	(	(	PUNCT
ejpam-5362	537	5	∨	∨	PROPN
ejpam-5362	537	6	k∈n	k∈n	PROPN
ejpam-5362	537	7	xk	xk	PROPN
ejpam-5362	537	8	)	)	PUNCT
ejpam-5362	538	1	∧	∧	PROPN
ejpam-5362	538	2	(	(	PUNCT
ejpam-5362	538	3	∧	∧	PROPN
ejpam-5362	538	4	n∈n	n∈n	NOUN
ejpam-5362	538	5	(	(	PUNCT
ejpam-5362	538	6	cl(l	cl(l	NOUN
ejpam-5362	538	7	,	,	PUNCT
ejpam-5362	538	8	τj)(xn	τj)(xn	PUNCT
ejpam-5362	538	9	)	)	PUNCT
ejpam-5362	538	10	)	)	PUNCT
ejpam-5362	539	1	′	′	X
ejpam-5362	539	2	)	)	PUNCT
ejpam-5362	540	1	=	=	PUNCT
ejpam-5362	540	2	∨	∨	NUM
ejpam-5362	540	3	k∈n	k∈n	PROPN
ejpam-5362	540	4	(	(	PUNCT
ejpam-5362	540	5	xk	xk	PROPN
ejpam-5362	540	6	∧	∧	PROPN
ejpam-5362	540	7	(	(	PUNCT
ejpam-5362	540	8	∧	∧	PROPN
ejpam-5362	540	9	n∈n	n∈n	NOUN
ejpam-5362	540	10	(	(	PUNCT
ejpam-5362	540	11	cl(l	cl(l	NOUN
ejpam-5362	540	12	,	,	PUNCT
ejpam-5362	540	13	τj)(xn	τj)(xn	PUNCT
ejpam-5362	540	14	)	)	PUNCT
ejpam-5362	540	15	)	)	PUNCT
ejpam-5362	540	16	′	′	NUM
ejpam-5362	540	17	)	)	PUNCT
ejpam-5362	540	18	)	)	PUNCT
ejpam-5362	540	19	since	since	SCONJ
ejpam-5362	540	20	l	l	NOUN
ejpam-5362	540	21	is	be	AUX
ejpam-5362	540	22	a	a	DET
ejpam-5362	540	23	locale	locale	NOUN
ejpam-5362	540	24	≤	≤	PROPN
ejpam-5362	540	25	∨	∨	NUM
ejpam-5362	540	26	k∈n	k∈n	PROPN
ejpam-5362	540	27	(	(	PUNCT
ejpam-5362	540	28	xk	xk	PROPN
ejpam-5362	540	29	∧	∧	PROPN
ejpam-5362	540	30	(	(	PUNCT
ejpam-5362	540	31	cl(l	cl(l	X
ejpam-5362	540	32	,	,	PUNCT
ejpam-5362	540	33	τj)(xk	τj)(xk	PUNCT
ejpam-5362	540	34	)	)	PUNCT
ejpam-5362	540	35	)	)	PUNCT
ejpam-5362	541	1	′	′	X
ejpam-5362	541	2	)	)	PUNCT
ejpam-5362	542	1	m.	m.	NOUN
ejpam-5362	542	2	nxumalo	nxumalo	PROPN
ejpam-5362	542	3	/	/	SYM
ejpam-5362	542	4	eur	eur	PROPN
ejpam-5362	542	5	.	.	PUNCT
ejpam-5362	543	1	j.	j.	PROPN
ejpam-5362	543	2	pure	pure	PROPN
ejpam-5362	543	3	appl	appl	PROPN
ejpam-5362	543	4	.	.	PROPN
ejpam-5362	543	5	math	math	PROPN
ejpam-5362	543	6	,	,	PUNCT
ejpam-5362	543	7	18	18	NUM
ejpam-5362	543	8	(	(	PUNCT
ejpam-5362	543	9	1	1	NUM
ejpam-5362	543	10	)	)	PUNCT
ejpam-5362	543	11	(	(	PUNCT
ejpam-5362	543	12	2025	2025	NUM
ejpam-5362	543	13	)	)	PUNCT
ejpam-5362	543	14	,	,	PUNCT
ejpam-5362	543	15	5362	5362	NUM
ejpam-5362	543	16	20	20	NUM
ejpam-5362	543	17	of	of	ADP
ejpam-5362	543	18	21	21	NUM
ejpam-5362	543	19	≤	≤	NUM
ejpam-5362	543	20	∨	∨	NUM
ejpam-5362	543	21	k∈n	k∈n	PROPN
ejpam-5362	543	22	(	(	PUNCT
ejpam-5362	543	23	cl(l	cl(l	NOUN
ejpam-5362	543	24	,	,	PUNCT
ejpam-5362	543	25	τi)(xk	τi)(xk	PUNCT
ejpam-5362	543	26	)	)	PUNCT
ejpam-5362	543	27	∧	∧	NOUN
ejpam-5362	543	28	cl(l	cl(l	NOUN
ejpam-5362	543	29	,	,	PUNCT
ejpam-5362	543	30	τj)(xk	τj)(xk	PUNCT
ejpam-5362	543	31	)	)	PUNCT
ejpam-5362	543	32	)	)	PUNCT
ejpam-5362	544	1	=	=	SYM
ejpam-5362	544	2	0	0	NUM
ejpam-5362	544	3	which	which	PRON
ejpam-5362	544	4	is	be	AUX
ejpam-5362	544	5	a	a	DET
ejpam-5362	544	6	contradiction	contradiction	NOUN
ejpam-5362	544	7	.	.	PUNCT
ejpam-5362	545	1	(	(	PUNCT
ejpam-5362	545	2	ii	ii	NOUN
ejpam-5362	545	3	)	)	PUNCT
ejpam-5362	545	4	⇒	⇒	NOUN
ejpam-5362	545	5	(	(	PUNCT
ejpam-5362	545	6	iii	iii	NOUN
ejpam-5362	545	7	):	):	PUNCT
ejpam-5362	545	8	let	let	VERB
ejpam-5362	545	9	a	a	DET
ejpam-5362	545	10	∈	∈	PROPN
ejpam-5362	545	11	l	l	NOUN
ejpam-5362	545	12	be	be	NOUN
ejpam-5362	545	13	of	of	ADP
ejpam-5362	545	14	(	(	PUNCT
ejpam-5362	545	15	τj	τj	ADP
ejpam-5362	545	16	,	,	PUNCT
ejpam-5362	545	17	τi)-first	τi)-first	ADJ
ejpam-5362	545	18	category	category	NOUN
ejpam-5362	545	19	and	and	CCONJ
ejpam-5362	545	20	assume	assume	VERB
ejpam-5362	545	21	that	that	SCONJ
ejpam-5362	545	22	int(l	int(l	PROPN
ejpam-5362	545	23	,	,	PUNCT
ejpam-5362	545	24	τi)(a	τi)(a	NUM
ejpam-5362	545	25	)	)	PUNCT
ejpam-5362	545	26	̸=	̸=	PROPN
ejpam-5362	545	27	0	0	NUM
ejpam-5362	545	28	.	.	PUNCT
ejpam-5362	546	1	we	we	PRON
ejpam-5362	546	2	now	now	ADV
ejpam-5362	546	3	have	have	VERB
ejpam-5362	546	4	int(l	int(l	PROPN
ejpam-5362	546	5	,	,	PUNCT
ejpam-5362	546	6	τi)(a	τi)(a	NUM
ejpam-5362	546	7	)	)	PUNCT
ejpam-5362	546	8	as	as	ADP
ejpam-5362	546	9	a	a	DET
ejpam-5362	546	10	nonzero	nonzero	NOUN
ejpam-5362	546	11	τi	τi	NOUN
ejpam-5362	546	12	element	element	NOUN
ejpam-5362	546	13	.	.	PUNCT
ejpam-5362	547	1	it	it	PRON
ejpam-5362	547	2	follows	follow	VERB
ejpam-5362	547	3	from	from	ADP
ejpam-5362	547	4	(	(	PUNCT
ejpam-5362	547	5	ii	ii	NOUN
ejpam-5362	547	6	)	)	PUNCT
ejpam-5362	547	7	that	that	PRON
ejpam-5362	547	8	int(l	int(l	PROPN
ejpam-5362	547	9	,	,	PUNCT
ejpam-5362	547	10	τi)(a	τi)(a	NUM
ejpam-5362	547	11	)	)	PUNCT
ejpam-5362	547	12	is	be	AUX
ejpam-5362	547	13	of	of	ADP
ejpam-5362	547	14	(	(	PUNCT
ejpam-5362	547	15	τj	τj	ADP
ejpam-5362	547	16	,	,	PUNCT
ejpam-5362	547	17	τi)-second	τi)-second	ADJ
ejpam-5362	547	18	category	category	NOUN
ejpam-5362	547	19	.	.	PUNCT
ejpam-5362	548	1	this	this	PRON
ejpam-5362	548	2	is	be	AUX
ejpam-5362	548	3	not	not	PART
ejpam-5362	548	4	possible	possible	ADJ
ejpam-5362	548	5	.	.	PUNCT
ejpam-5362	549	1	(	(	PUNCT
ejpam-5362	549	2	iii	iii	X
ejpam-5362	549	3	)	)	PUNCT
ejpam-5362	549	4	⇒	⇒	NOUN
ejpam-5362	549	5	(	(	PUNCT
ejpam-5362	549	6	iv	iv	NUM
ejpam-5362	549	7	):	):	PUNCT
ejpam-5362	549	8	let	let	VERB
ejpam-5362	549	9	a	a	DET
ejpam-5362	549	10	∈	∈	PROPN
ejpam-5362	549	11	l	l	NOUN
ejpam-5362	549	12	be	be	NOUN
ejpam-5362	549	13	of	of	ADP
ejpam-5362	549	14	(	(	PUNCT
ejpam-5362	549	15	τj	τj	ADP
ejpam-5362	549	16	,	,	PUNCT
ejpam-5362	549	17	τi)-first	τi)-first	ADJ
ejpam-5362	549	18	category	category	NOUN
ejpam-5362	549	19	and	and	CCONJ
ejpam-5362	549	20	suppose	suppose	VERB
ejpam-5362	549	21	that	that	SCONJ
ejpam-5362	549	22	a′	a′	PROPN
ejpam-5362	549	23	is	be	AUX
ejpam-5362	549	24	not	not	PART
ejpam-5362	549	25	τi	τi	NOUN
ejpam-5362	549	26	-	-	PUNCT
ejpam-5362	549	27	dense	dense	ADJ
ejpam-5362	549	28	.	.	PUNCT
ejpam-5362	550	1	then	then	ADV
ejpam-5362	550	2	cl(l	cl(l	VERB
ejpam-5362	550	3	,	,	PUNCT
ejpam-5362	550	4	τi)(a	τi)(a	PUNCT
ejpam-5362	550	5	′	′	X
ejpam-5362	550	6	)	)	PUNCT
ejpam-5362	550	7	̸=	̸=	PROPN
ejpam-5362	550	8	1	1	NUM
ejpam-5362	550	9	.	.	PUNCT
ejpam-5362	551	1	because	because	SCONJ
ejpam-5362	551	2	cl(l	cl(l	NOUN
ejpam-5362	551	3	,	,	PUNCT
ejpam-5362	551	4	τi)(a	τi)(a	PUNCT
ejpam-5362	551	5	′	′	NUM
ejpam-5362	551	6	)	)	PUNCT
ejpam-5362	552	1	=	=	PRON
ejpam-5362	552	2	(	(	PUNCT
ejpam-5362	552	3	int(l	int(l	PROPN
ejpam-5362	552	4	,	,	PUNCT
ejpam-5362	552	5	τi)(a	τi)(a	NUM
ejpam-5362	552	6	)	)	PUNCT
ejpam-5362	552	7	)	)	PUNCT
ejpam-5362	553	1	′	′	NOUN
ejpam-5362	553	2	,	,	PUNCT
ejpam-5362	553	3	we	we	PRON
ejpam-5362	553	4	have	have	VERB
ejpam-5362	553	5	that	that	PRON
ejpam-5362	553	6	(	(	PUNCT
ejpam-5362	553	7	int(l	int(l	PROPN
ejpam-5362	553	8	,	,	PUNCT
ejpam-5362	553	9	τi)(a	τi)(a	NUM
ejpam-5362	553	10	)	)	PUNCT
ejpam-5362	553	11	)	)	PUNCT
ejpam-5362	554	1	′	′	NUM
ejpam-5362	555	1	̸=	̸=	PROPN
ejpam-5362	555	2	1	1	NUM
ejpam-5362	555	3	.	.	PUNCT
ejpam-5362	556	1	since	since	SCONJ
ejpam-5362	556	2	a	a	DET
ejpam-5362	556	3	is	is	NOUN
ejpam-5362	556	4	of	of	ADP
ejpam-5362	556	5	(	(	PUNCT
ejpam-5362	556	6	τj	τj	ADP
ejpam-5362	556	7	,	,	PUNCT
ejpam-5362	556	8	τi)-first	τi)-first	ADJ
ejpam-5362	556	9	category	category	NOUN
ejpam-5362	556	10	,	,	PUNCT
ejpam-5362	556	11	it	it	PRON
ejpam-5362	556	12	follows	follow	VERB
ejpam-5362	556	13	from	from	ADP
ejpam-5362	556	14	(	(	PUNCT
ejpam-5362	556	15	iii	iii	NOUN
ejpam-5362	556	16	)	)	PUNCT
ejpam-5362	557	1	that	that	PRON
ejpam-5362	557	2	int(l	int(l	PROPN
ejpam-5362	557	3	,	,	PUNCT
ejpam-5362	557	4	τi)(a	τi)(a	NUM
ejpam-5362	557	5	)	)	PUNCT
ejpam-5362	558	1	=	=	SYM
ejpam-5362	558	2	0	0	PUNCT
ejpam-5362	559	1	so	so	SCONJ
ejpam-5362	559	2	that	that	SCONJ
ejpam-5362	559	3	(	(	PUNCT
ejpam-5362	559	4	int(l	int(l	PROPN
ejpam-5362	559	5	,	,	PUNCT
ejpam-5362	559	6	τi)(a	τi)(a	NUM
ejpam-5362	559	7	)	)	PUNCT
ejpam-5362	559	8	)	)	PUNCT
ejpam-5362	559	9	′	′	NUM
ejpam-5362	559	10	=	=	SYM
ejpam-5362	559	11	1	1	NUM
ejpam-5362	559	12	,	,	PUNCT
ejpam-5362	559	13	which	which	PRON
ejpam-5362	559	14	is	be	AUX
ejpam-5362	559	15	a	a	DET
ejpam-5362	559	16	contradiction	contradiction	NOUN
ejpam-5362	559	17	.	.	PUNCT
ejpam-5362	559	18	(	(	PUNCT
ejpam-5362	559	19	iv	iv	X
ejpam-5362	559	20	)	)	PUNCT
ejpam-5362	559	21	⇒	⇒	NOUN
ejpam-5362	559	22	(	(	PUNCT
ejpam-5362	559	23	i	i	NOUN
ejpam-5362	559	24	):	):	PUNCT
ejpam-5362	559	25	let	let	VERB
ejpam-5362	559	26	(	(	PUNCT
ejpam-5362	559	27	xn)n∈n	xn)n∈n	NUM
ejpam-5362	559	28	be	be	AUX
ejpam-5362	559	29	a	a	DET
ejpam-5362	559	30	sequence	sequence	NOUN
ejpam-5362	559	31	of	of	ADP
ejpam-5362	559	32	τi	τi	NOUN
ejpam-5362	559	33	-	-	PUNCT
ejpam-5362	559	34	dense	dense	ADJ
ejpam-5362	559	35	elements	element	NOUN
ejpam-5362	559	36	of	of	ADP
ejpam-5362	559	37	τj	τj	ADV
ejpam-5362	559	38	and	and	CCONJ
ejpam-5362	559	39	assume	assume	VERB
ejpam-5362	559	40	that	that	SCONJ
ejpam-5362	559	41	there	there	PRON
ejpam-5362	559	42	is	be	VERB
ejpam-5362	559	43	y	y	PROPN
ejpam-5362	559	44	∈	∈	PROPN
ejpam-5362	559	45	τi	τi	VERB
ejpam-5362	559	46	such	such	ADJ
ejpam-5362	559	47	that	that	SCONJ
ejpam-5362	559	48	y	y	PROPN
ejpam-5362	559	49	∧	∧	PROPN
ejpam-5362	559	50	(	(	PUNCT
ejpam-5362	559	51	∧	∧	PROPN
ejpam-5362	559	52	n∈n	n∈n	ADV
ejpam-5362	559	53	xn	xn	PUNCT
ejpam-5362	559	54	)	)	PUNCT
ejpam-5362	560	1	=	=	PUNCT
ejpam-5362	560	2	0	0	X
ejpam-5362	560	3	.	.	PUNCT
ejpam-5362	561	1	then	then	ADV
ejpam-5362	561	2	y	y	PROPN
ejpam-5362	561	3	≤	≤	PROPN
ejpam-5362	561	4	(	(	PUNCT
ejpam-5362	561	5	∧	∧	PROPN
ejpam-5362	561	6	n∈n	n∈n	NOUN
ejpam-5362	561	7	xn	xn	PUNCT
ejpam-5362	561	8	)	)	PUNCT
ejpam-5362	562	1	′	′	NUM
ejpam-5362	563	1	=	=	PUNCT
ejpam-5362	563	2	∨	∨	NUM
ejpam-5362	563	3	n∈n	n∈n	ADV
ejpam-5362	563	4	x′n	x′n	PUNCT
ejpam-5362	564	1	since	since	SCONJ
ejpam-5362	564	2	each	each	DET
ejpam-5362	564	3	xn	xn	PROPN
ejpam-5362	564	4	is	be	AUX
ejpam-5362	564	5	complemented	complement	VERB
ejpam-5362	564	6	.	.	PUNCT
ejpam-5362	565	1	this	this	PRON
ejpam-5362	565	2	makes	make	VERB
ejpam-5362	565	3	y	y	PRON
ejpam-5362	565	4	to	to	PART
ejpam-5362	565	5	be	be	AUX
ejpam-5362	565	6	of	of	ADP
ejpam-5362	565	7	(	(	PUNCT
ejpam-5362	565	8	τj	τj	ADP
ejpam-5362	565	9	,	,	PUNCT
ejpam-5362	565	10	τi)-first	τi)-first	ADJ
ejpam-5362	565	11	category	category	NOUN
ejpam-5362	565	12	.	.	PUNCT
ejpam-5362	566	1	by	by	ADP
ejpam-5362	566	2	(	(	PUNCT
ejpam-5362	566	3	iv	iv	X
ejpam-5362	566	4	)	)	PUNCT
ejpam-5362	566	5	,	,	PUNCT
ejpam-5362	566	6	y′	y′	PROPN
ejpam-5362	566	7	is	be	AUX
ejpam-5362	566	8	τi	τi	ADJ
ejpam-5362	566	9	-	-	PUNCT
ejpam-5362	566	10	dense	dense	ADJ
ejpam-5362	566	11	so	so	SCONJ
ejpam-5362	566	12	that	that	SCONJ
ejpam-5362	566	13	y	y	PROPN
ejpam-5362	566	14	=	=	NOUN
ejpam-5362	566	15	0	0	PROPN
ejpam-5362	566	16	.	.	PUNCT
ejpam-5362	567	1	thus	thus	ADV
ejpam-5362	567	2	∧	∧	PROPN
ejpam-5362	567	3	n∈n	n∈n	ADV
ejpam-5362	567	4	xn	xn	PROPN
ejpam-5362	567	5	is	be	AUX
ejpam-5362	567	6	τi	τi	ADJ
ejpam-5362	567	7	-	-	PUNCT
ejpam-5362	567	8	dense	dense	ADJ
ejpam-5362	567	9	.	.	PUNCT
ejpam-5362	568	1	hence	hence	ADV
ejpam-5362	568	2	(	(	PUNCT
ejpam-5362	568	3	l	l	NOUN
ejpam-5362	568	4	,	,	PUNCT
ejpam-5362	568	5	τ1	τ1	NOUN
ejpam-5362	568	6	,	,	PUNCT
ejpam-5362	568	7	τ2	τ2	NOUN
ejpam-5362	568	8	)	)	PUNCT
ejpam-5362	568	9	is	be	AUX
ejpam-5362	568	10	(	(	PUNCT
ejpam-5362	568	11	τi	τi	ADJ
ejpam-5362	568	12	,	,	PUNCT
ejpam-5362	568	13	τj)-baire	τj)-baire	NOUN
ejpam-5362	568	14	.	.	PUNCT
ejpam-5362	569	1	acknowledgements	acknowledgement	NOUN
ejpam-5362	569	2	the	the	DET
ejpam-5362	569	3	author	author	NOUN
ejpam-5362	569	4	is	be	AUX
ejpam-5362	569	5	indebted	indebte	VERB
ejpam-5362	569	6	to	to	ADP
ejpam-5362	569	7	the	the	DET
ejpam-5362	569	8	referee	referee	NOUN
ejpam-5362	569	9	for	for	ADP
ejpam-5362	569	10	helpful	helpful	ADJ
ejpam-5362	569	11	comments	comment	NOUN
ejpam-5362	569	12	.	.	PUNCT
ejpam-5362	570	1	references	reference	NOUN
ejpam-5362	570	2	[	[	X
ejpam-5362	570	3	1	1	NUM
ejpam-5362	570	4	]	]	PUNCT
ejpam-5362	570	5	k.	k.	PROPN
ejpam-5362	570	6	p.	p.	PROPN
ejpam-5362	570	7	adlassnig	adlassnig	PROPN
ejpam-5362	570	8	.	.	PUNCT
ejpam-5362	571	1	fuzzy	fuzzy	ADJ
ejpam-5362	571	2	set	set	PROPN
ejpam-5362	571	3	theory	theory	NOUN
ejpam-5362	571	4	in	in	ADP
ejpam-5362	571	5	medical	medical	ADJ
ejpam-5362	571	6	diagnosis	diagnosis	NOUN
ejpam-5362	571	7	.	.	PUNCT
ejpam-5362	572	1	ieee	ieee	NOUN
ejpam-5362	572	2	transactions	transaction	NOUN
ejpam-5362	572	3	on	on	ADP
ejpam-5362	572	4	systems	system	NOUN
ejpam-5362	572	5	,	,	PUNCT
ejpam-5362	572	6	man	man	NOUN
ejpam-5362	572	7	,	,	PUNCT
ejpam-5362	572	8	and	and	CCONJ
ejpam-5362	572	9	cybernetics	cybernetic	NOUN
ejpam-5362	572	10	,	,	PUNCT
ejpam-5362	572	11	16(2):260–265	16(2):260–265	NOUN
ejpam-5362	572	12	,	,	PUNCT
ejpam-5362	572	13	1986	1986	NUM
ejpam-5362	572	14	.	.	PUNCT
ejpam-5362	573	1	[	[	X
ejpam-5362	573	2	2	2	NUM
ejpam-5362	573	3	]	]	X
ejpam-5362	573	4	z.a	z.a	PROPN
ejpam-5362	573	5	.	.	PROPN
ejpam-5362	573	6	ameen	ameen	PROPN
ejpam-5362	573	7	and	and	CCONJ
ejpam-5362	573	8	a.b	a.b	PROPN
ejpam-5362	573	9	.	.	PROPN
ejpam-5362	573	10	khalaf	khalaf	PROPN
ejpam-5362	573	11	.	.	PUNCT
ejpam-5362	574	1	the	the	DET
ejpam-5362	574	2	invariance	invariance	NOUN
ejpam-5362	574	3	of	of	ADP
ejpam-5362	574	4	soft	soft	ADJ
ejpam-5362	574	5	baire	baire	NOUN
ejpam-5362	574	6	spaces	space	NOUN
ejpam-5362	574	7	under	under	ADP
ejpam-5362	574	8	soft	soft	ADJ
ejpam-5362	574	9	weak	weak	ADJ
ejpam-5362	574	10	functions	function	NOUN
ejpam-5362	574	11	.	.	PUNCT
ejpam-5362	575	1	journal	journal	NOUN
ejpam-5362	575	2	of	of	ADP
ejpam-5362	575	3	interdisciplinary	interdisciplinary	ADJ
ejpam-5362	575	4	mathematics	mathematic	NOUN
ejpam-5362	575	5	,	,	PUNCT
ejpam-5362	575	6	25(2):1295–1306	25(2):1295–1306	NUM
ejpam-5362	575	7	,	,	PUNCT
ejpam-5362	575	8	2022	2022	NUM
ejpam-5362	575	9	.	.	PUNCT
ejpam-5362	576	1	[	[	X
ejpam-5362	576	2	3	3	X
ejpam-5362	576	3	]	]	PUNCT
ejpam-5362	576	4	c.r.a	c.r.a	NOUN
ejpam-5362	576	5	gilmour	gilmour	PROPN
ejpam-5362	576	6	b	b	PROPN
ejpam-5362	576	7	banaschewski	banaschewski	PROPN
ejpam-5362	576	8	,	,	PUNCT
ejpam-5362	576	9	j.l	j.l	PROPN
ejpam-5362	576	10	.	.	PROPN
ejpam-5362	576	11	frith	frith	PROPN
ejpam-5362	576	12	.	.	PUNCT
ejpam-5362	577	1	on	on	ADP
ejpam-5362	577	2	the	the	DET
ejpam-5362	577	3	congruence	congruence	PROPN
ejpam-5362	577	4	lattice	lattice	NOUN
ejpam-5362	577	5	of	of	ADP
ejpam-5362	577	6	a	a	DET
ejpam-5362	577	7	frame	frame	NOUN
ejpam-5362	577	8	.	.	PUNCT
ejpam-5362	578	1	pacific	pacific	PROPN
ejpam-5362	578	2	journal	journal	PROPN
ejpam-5362	578	3	of	of	ADP
ejpam-5362	578	4	mathematics	mathematic	NOUN
ejpam-5362	578	5	,	,	PUNCT
ejpam-5362	578	6	130(2):209–213	130(2):209–213	NUM
ejpam-5362	578	7	,	,	PUNCT
ejpam-5362	578	8	1987	1987	NUM
ejpam-5362	578	9	.	.	PUNCT
ejpam-5362	579	1	[	[	X
ejpam-5362	579	2	4	4	X
ejpam-5362	579	3	]	]	X
ejpam-5362	579	4	g.c.l	g.c.l	NOUN
ejpam-5362	579	5	.	.	PUNCT
ejpam-5362	580	1	brümmer	brümmer	PROPN
ejpam-5362	580	2	b	b	PROPN
ejpam-5362	580	3	banaschewski	banaschewski	PROPN
ejpam-5362	580	4	and	and	CCONJ
ejpam-5362	580	5	k.a	k.a	PROPN
ejpam-5362	580	6	.	.	PROPN
ejpam-5362	580	7	hardie	hardie	PROPN
ejpam-5362	580	8	.	.	PUNCT
ejpam-5362	581	1	biframes	biframe	NOUN
ejpam-5362	581	2	and	and	CCONJ
ejpam-5362	581	3	bispaces	bispace	NOUN
ejpam-5362	581	4	.	.	PUNCT
ejpam-5362	582	1	quaestiones	quaestione	NOUN
ejpam-5362	582	2	mathematicae	mathematicae	PROPN
ejpam-5362	582	3	,	,	PUNCT
ejpam-5362	582	4	6(1	6(1	NUM
ejpam-5362	582	5	-	-	SYM
ejpam-5362	582	6	3):13–25	3):13–25	NUM
ejpam-5362	582	7	,	,	PUNCT
ejpam-5362	582	8	1983	1983	NUM
ejpam-5362	582	9	.	.	PUNCT
ejpam-5362	583	1	[	[	X
ejpam-5362	583	2	5	5	NUM
ejpam-5362	583	3	]	]	SYM
ejpam-5362	583	4	b	b	X
ejpam-5362	583	5	banaschewski	banaschewski	NOUN
ejpam-5362	583	6	and	and	CCONJ
ejpam-5362	583	7	g.c.l	g.c.l	NOUN
ejpam-5362	583	8	.	.	PUNCT
ejpam-5362	584	1	brümmer	brümmer	NOUN
ejpam-5362	584	2	.	.	PUNCT
ejpam-5362	585	1	strong	strong	ADJ
ejpam-5362	585	2	zero	zero	NUM
ejpam-5362	585	3	-	-	PUNCT
ejpam-5362	585	4	dimensionality	dimensionality	NOUN
ejpam-5362	585	5	of	of	ADP
ejpam-5362	585	6	biframes	biframe	NOUN
ejpam-5362	585	7	and	and	CCONJ
ejpam-5362	585	8	bispaces	bispace	NOUN
ejpam-5362	585	9	:	:	PUNCT
ejpam-5362	585	10	for	for	ADP
ejpam-5362	585	11	the	the	DET
ejpam-5362	585	12	sixtieth	sixtieth	ADJ
ejpam-5362	585	13	birthday	birthday	NOUN
ejpam-5362	585	14	of	of	ADP
ejpam-5362	585	15	keith	keith	PROPN
ejpam-5362	585	16	hardie	hardie	PROPN
ejpam-5362	585	17	.	.	PUNCT
ejpam-5362	586	1	quaestiones	quaestione	NOUN
ejpam-5362	586	2	mathematicae	mathematicae	PROPN
ejpam-5362	586	3	,	,	PUNCT
ejpam-5362	586	4	13(34):273–290	13(34):273–290	NUM
ejpam-5362	586	5	,	,	PUNCT
ejpam-5362	586	6	1990	1990	NUM
ejpam-5362	586	7	.	.	PUNCT
ejpam-5362	587	1	[	[	X
ejpam-5362	587	2	6	6	NUM
ejpam-5362	587	3	]	]	PUNCT
ejpam-5362	587	4	i	i	PRON
ejpam-5362	587	5	dochviri	dochviri	VERB
ejpam-5362	587	6	.	.	PUNCT
ejpam-5362	588	1	a	a	DET
ejpam-5362	588	2	note	note	NOUN
ejpam-5362	588	3	on	on	ADP
ejpam-5362	588	4	almost	almost	ADV
ejpam-5362	588	5	baire	baire	VERB
ejpam-5362	588	6	bitopological	bitopological	ADJ
ejpam-5362	588	7	spaces	space	NOUN
ejpam-5362	588	8	.	.	PUNCT
ejpam-5362	589	1	missouri	missouri	PROPN
ejpam-5362	589	2	journal	journal	PROPN
ejpam-5362	589	3	of	of	ADP
ejpam-5362	589	4	mathematical	mathematical	ADJ
ejpam-5362	589	5	sciences	sciences	PROPN
ejpam-5362	589	6	,	,	PUNCT
ejpam-5362	589	7	22(2):139–141	22(2):139–141	PROPN
ejpam-5362	589	8	,	,	PUNCT
ejpam-5362	589	9	2010	2010	NUM
ejpam-5362	589	10	.	.	PUNCT
ejpam-5362	590	1	[	[	X
ejpam-5362	590	2	7	7	X
ejpam-5362	590	3	]	]	X
ejpam-5362	590	4	i	i	PRON
ejpam-5362	590	5	dochviri	dochviri	NOUN
ejpam-5362	590	6	.	.	PUNCT
ejpam-5362	591	1	on	on	ADP
ejpam-5362	591	2	submaximality	submaximality	NOUN
ejpam-5362	591	3	of	of	ADP
ejpam-5362	591	4	bitopological	bitopological	ADJ
ejpam-5362	591	5	spaces	space	NOUN
ejpam-5362	591	6	.	.	PUNCT
ejpam-5362	592	1	kochi	kochi	PROPN
ejpam-5362	592	2	journal	journal	PROPN
ejpam-5362	592	3	of	of	ADP
ejpam-5362	592	4	mathematics	mathematic	NOUN
ejpam-5362	592	5	,	,	PUNCT
ejpam-5362	592	6	5:121–128	5:121–128	NUM
ejpam-5362	592	7	,	,	PUNCT
ejpam-5362	592	8	2010	2010	NUM
ejpam-5362	592	9	.	.	PUNCT
ejpam-5362	593	1	m.	m.	NOUN
ejpam-5362	593	2	nxumalo	nxumalo	PROPN
ejpam-5362	593	3	/	/	SYM
ejpam-5362	593	4	eur	eur	PROPN
ejpam-5362	593	5	.	.	PUNCT
ejpam-5362	594	1	j.	j.	PROPN
ejpam-5362	594	2	pure	pure	PROPN
ejpam-5362	594	3	appl	appl	PROPN
ejpam-5362	594	4	.	.	PROPN
ejpam-5362	594	5	math	math	PROPN
ejpam-5362	594	6	,	,	PUNCT
ejpam-5362	594	7	18	18	NUM
ejpam-5362	594	8	(	(	PUNCT
ejpam-5362	594	9	1	1	NUM
ejpam-5362	594	10	)	)	PUNCT
ejpam-5362	594	11	(	(	PUNCT
ejpam-5362	594	12	2025	2025	NUM
ejpam-5362	594	13	)	)	PUNCT
ejpam-5362	594	14	,	,	PUNCT
ejpam-5362	594	15	5362	5362	NUM
ejpam-5362	594	16	21	21	NUM
ejpam-5362	594	17	of	of	ADP
ejpam-5362	594	18	21	21	NUM
ejpam-5362	594	19	[	[	SYM
ejpam-5362	594	20	8	8	NUM
ejpam-5362	594	21	]	]	SYM
ejpam-5362	594	22	b	b	NOUN
ejpam-5362	594	23	dvalishvili	dvalishvili	NOUN
ejpam-5362	594	24	.	.	PUNCT
ejpam-5362	595	1	bitopological	bitopological	ADJ
ejpam-5362	595	2	spaces	space	NOUN
ejpam-5362	595	3	:	:	PUNCT
ejpam-5362	595	4	theory	theory	NOUN
ejpam-5362	595	5	,	,	PUNCT
ejpam-5362	595	6	relations	relation	NOUN
ejpam-5362	595	7	with	with	ADP
ejpam-5362	595	8	generalized	generalized	ADJ
ejpam-5362	595	9	algebraic	algebraic	ADJ
ejpam-5362	595	10	structures	structure	NOUN
ejpam-5362	595	11	and	and	CCONJ
ejpam-5362	595	12	applications	application	NOUN
ejpam-5362	595	13	.	.	PUNCT
ejpam-5362	596	1	elsevier	elsevier	NOUN
ejpam-5362	596	2	,	,	PUNCT
ejpam-5362	596	3	2005	2005	NUM
ejpam-5362	596	4	.	.	PUNCT
ejpam-5362	597	1	[	[	X
ejpam-5362	597	2	9	9	NUM
ejpam-5362	597	3	]	]	SYM
ejpam-5362	597	4	c	c	NOUN
ejpam-5362	597	5	özcan	özcan	PROPN
ejpam-5362	597	6	e	e	NOUN
ejpam-5362	597	7	korkmaz	korkmaz	NOUN
ejpam-5362	597	8	and	and	CCONJ
ejpam-5362	597	9	m	m	PROPN
ejpam-5362	597	10	korkmaz	korkmaz	PROPN
ejpam-5362	597	11	.	.	PUNCT
ejpam-5362	598	1	an	an	DET
ejpam-5362	598	2	application	application	NOUN
ejpam-5362	598	3	of	of	ADP
ejpam-5362	598	4	fuzzy	fuzzy	ADJ
ejpam-5362	598	5	soft	soft	ADJ
ejpam-5362	598	6	sets	set	NOUN
ejpam-5362	598	7	to	to	ADP
ejpam-5362	598	8	a	a	DET
ejpam-5362	598	9	real	real	ADJ
ejpam-5362	598	10	-	-	PUNCT
ejpam-5362	598	11	life	life	NOUN
ejpam-5362	598	12	problem	problem	NOUN
ejpam-5362	598	13	:	:	PUNCT
ejpam-5362	598	14	classification	classification	NOUN
ejpam-5362	598	15	of	of	ADP
ejpam-5362	598	16	wood	wood	NOUN
ejpam-5362	598	17	materials	material	NOUN
ejpam-5362	598	18	to	to	PART
ejpam-5362	598	19	prevent	prevent	VERB
ejpam-5362	598	20	fire	fire	NOUN
ejpam-5362	598	21	-	-	PUNCT
ejpam-5362	598	22	related	relate	VERB
ejpam-5362	598	23	injuries	injury	NOUN
ejpam-5362	598	24	and	and	CCONJ
ejpam-5362	598	25	deaths	death	NOUN
ejpam-5362	598	26	.	.	PUNCT
ejpam-5362	599	1	applied	apply	VERB
ejpam-5362	599	2	soft	soft	ADJ
ejpam-5362	599	3	computing	computing	NOUN
ejpam-5362	599	4	,	,	PUNCT
ejpam-5362	599	5	132:109875	132:109875	NUM
ejpam-5362	599	6	,	,	PUNCT
ejpam-5362	599	7	2023	2023	NUM
ejpam-5362	599	8	.	.	PUNCT
ejpam-5362	600	1	[	[	X
ejpam-5362	600	2	10	10	NUM
ejpam-5362	600	3	]	]	X
ejpam-5362	600	4	j.r	j.r	PROPN
ejpam-5362	600	5	.	.	PROPN
ejpam-5362	600	6	isbell	isbell	PROPN
ejpam-5362	600	7	.	.	PUNCT
ejpam-5362	601	1	some	some	DET
ejpam-5362	601	2	problems	problem	NOUN
ejpam-5362	601	3	in	in	ADP
ejpam-5362	601	4	descriptive	descriptive	ADJ
ejpam-5362	601	5	locale	locale	PROPN
ejpam-5362	601	6	theory	theory	NOUN
ejpam-5362	601	7	.	.	PUNCT
ejpam-5362	602	1	canadian	canadian	PROPN
ejpam-5362	602	2	mathematical	mathematical	ADJ
ejpam-5362	602	3	society	society	NOUN
ejpam-5362	602	4	conference	conference	NOUN
ejpam-5362	602	5	proceedings	proceeding	NOUN
ejpam-5362	602	6	,	,	PUNCT
ejpam-5362	602	7	13:243–265	13:243–265	NUM
ejpam-5362	602	8	,	,	PUNCT
ejpam-5362	602	9	1992	1992	NUM
ejpam-5362	602	10	.	.	PUNCT
ejpam-5362	603	1	[	[	X
ejpam-5362	603	2	11	11	NUM
ejpam-5362	603	3	]	]	X
ejpam-5362	603	4	s	s	PART
ejpam-5362	603	5	lal	lal	PROPN
ejpam-5362	603	6	.	.	PUNCT
ejpam-5362	604	1	pairwise	pairwise	NOUN
ejpam-5362	604	2	concepts	concept	NOUN
ejpam-5362	604	3	in	in	ADP
ejpam-5362	604	4	bitopological	bitopological	ADJ
ejpam-5362	604	5	spaces	space	NOUN
ejpam-5362	604	6	.	.	PUNCT
ejpam-5362	605	1	journal	journal	NOUN
ejpam-5362	605	2	of	of	ADP
ejpam-5362	605	3	the	the	DET
ejpam-5362	605	4	australian	australian	ADJ
ejpam-5362	605	5	mathematical	mathematical	ADJ
ejpam-5362	605	6	society	society	NOUN
ejpam-5362	605	7	,	,	PUNCT
ejpam-5362	605	8	26(2):241–250	26(2):241–250	PROPN
ejpam-5362	605	9	,	,	PUNCT
ejpam-5362	605	10	1978	1978	NUM
ejpam-5362	605	11	.	.	PUNCT
ejpam-5362	606	1	[	[	X
ejpam-5362	606	2	12	12	NUM
ejpam-5362	606	3	]	]	X
ejpam-5362	606	4	a.k	a.k	PROPN
ejpam-5362	606	5	.	.	PROPN
ejpam-5362	606	6	feizabadi	feizabadi	PROPN
ejpam-5362	606	7	m	m	PROPN
ejpam-5362	606	8	zarghani	zarghani	PROPN
ejpam-5362	606	9	,	,	PUNCT
ejpam-5362	606	10	a.a	a.a	PROPN
ejpam-5362	606	11	.	.	PROPN
ejpam-5362	606	12	estaji	estaji	PROPN
ejpam-5362	606	13	and	and	CCONJ
ejpam-5362	606	14	g	g	PROPN
ejpam-5362	606	15	branch	branch	NOUN
ejpam-5362	606	16	.	.	PUNCT
ejpam-5362	607	1	a	a	DET
ejpam-5362	607	2	new	new	ADJ
ejpam-5362	607	3	pointfree	pointfree	ADJ
ejpam-5362	607	4	form	form	NOUN
ejpam-5362	607	5	of	of	ADP
ejpam-5362	607	6	topology	topology	NOUN
ejpam-5362	607	7	.	.	PUNCT
ejpam-5362	608	1	in	in	ADP
ejpam-5362	608	2	47th	47th	ADJ
ejpam-5362	608	3	annual	annual	ADJ
ejpam-5362	608	4	iranian	iranian	ADJ
ejpam-5362	608	5	math	math	NOUN
ejpam-5362	608	6	.	.	PUNCT
ejpam-5362	608	7	conf.(aimc47	conf.(aimc47	NOUN
ejpam-5362	608	8	)	)	PUNCT
ejpam-5362	608	9	.	.	PUNCT
ejpam-5362	608	10	,	,	PUNCT
ejpam-5362	608	11	pages	page	NOUN
ejpam-5362	608	12	885–889	885–889	NUM
ejpam-5362	608	13	,	,	PUNCT
ejpam-5362	608	14	karaj	karaj	PROPN
ejpam-5362	608	15	,	,	PUNCT
ejpam-5362	608	16	iran	iran	PROPN
ejpam-5362	608	17	,	,	PUNCT
ejpam-5362	608	18	2016	2016	NUM
ejpam-5362	608	19	.	.	PUNCT
ejpam-5362	609	1	kharazmi	kharazmi	PROPN
ejpam-5362	609	2	university	university	PROPN
ejpam-5362	609	3	.	.	PUNCT
ejpam-5362	610	1	[	[	X
ejpam-5362	610	2	13	13	NUM
ejpam-5362	610	3	]	]	X
ejpam-5362	610	4	d	d	X
ejpam-5362	610	5	molodtsov	molodtsov	PROPN
ejpam-5362	610	6	.	.	PUNCT
ejpam-5362	611	1	soft	soft	ADJ
ejpam-5362	611	2	set	set	NOUN
ejpam-5362	611	3	theory	theory	NOUN
ejpam-5362	611	4	-	-	PUNCT
ejpam-5362	611	5	first	first	ADJ
ejpam-5362	611	6	results	result	NOUN
ejpam-5362	611	7	.	.	PUNCT
ejpam-5362	612	1	computers	computer	NOUN
ejpam-5362	612	2	&	&	CCONJ
ejpam-5362	612	3	mathematics	mathematics	PROPN
ejpam-5362	612	4	with	with	ADP
ejpam-5362	612	5	applications	application	NOUN
ejpam-5362	612	6	,	,	PUNCT
ejpam-5362	612	7	37(4	37(4	PROPN
ejpam-5362	612	8	-	-	PUNCT
ejpam-5362	612	9	5):19–31	5):19–31	NUM
ejpam-5362	612	10	,	,	PUNCT
ejpam-5362	612	11	1999	1999	NUM
ejpam-5362	612	12	.	.	PUNCT
ejpam-5362	613	1	[	[	X
ejpam-5362	613	2	14	14	NUM
ejpam-5362	613	3	]	]	X
ejpam-5362	613	4	m	m	VERB
ejpam-5362	613	5	nxumalo	nxumalo	PROPN
ejpam-5362	613	6	.	.	PUNCT
ejpam-5362	614	1	remote	remote	ADJ
ejpam-5362	614	2	sublocales	sublocale	NOUN
ejpam-5362	614	3	.	.	PUNCT
ejpam-5362	615	1	quaestiones	quaestione	NOUN
ejpam-5362	615	2	mathematicae	mathematicae	PROPN
ejpam-5362	615	3	,	,	PUNCT
ejpam-5362	615	4	47(6):1177–1194	47(6):1177–1194	PROPN
ejpam-5362	615	5	,	,	PUNCT
ejpam-5362	615	6	2024	2024	NUM
ejpam-5362	615	7	.	.	PUNCT
ejpam-5362	616	1	[	[	X
ejpam-5362	616	2	15	15	NUM
ejpam-5362	616	3	]	]	PUNCT
ejpam-5362	616	4	m.	m.	NOUN
ejpam-5362	616	5	nxumalo	nxumalo	PROPN
ejpam-5362	616	6	.	.	PUNCT
ejpam-5362	617	1	remoteness	remoteness	NOUN
ejpam-5362	617	2	in	in	ADP
ejpam-5362	617	3	the	the	DET
ejpam-5362	617	4	category	category	NOUN
ejpam-5362	617	5	of	of	ADP
ejpam-5362	617	6	bilocales	bilocale	NOUN
ejpam-5362	617	7	.	.	PUNCT
ejpam-5362	618	1	filomat	filomat	PROPN
ejpam-5362	618	2	,	,	PUNCT
ejpam-5362	618	3	38(22):7991–8009	38(22):7991–8009	NUM
ejpam-5362	618	4	,	,	PUNCT
ejpam-5362	618	5	2024	2024	NUM
ejpam-5362	618	6	.	.	PUNCT
ejpam-5362	619	1	[	[	X
ejpam-5362	619	2	16	16	NUM
ejpam-5362	619	3	]	]	X
ejpam-5362	619	4	m.s	m.s	PROPN
ejpam-5362	619	5	.	.	PROPN
ejpam-5362	619	6	nxumalo	nxumalo	PROPN
ejpam-5362	619	7	.	.	PUNCT
ejpam-5362	620	1	remoteness	remoteness	NOUN
ejpam-5362	620	2	in	in	ADP
ejpam-5362	620	3	the	the	DET
ejpam-5362	620	4	category	category	NOUN
ejpam-5362	620	5	of	of	ADP
ejpam-5362	620	6	locales	locale	NOUN
ejpam-5362	620	7	.	.	PUNCT
ejpam-5362	621	1	phd	phd	NOUN
ejpam-5362	621	2	thesis	thesis	PROPN
ejpam-5362	621	3	,	,	PUNCT
ejpam-5362	621	4	university	university	NOUN
ejpam-5362	621	5	of	of	ADP
ejpam-5362	621	6	south	south	PROPN
ejpam-5362	621	7	africa	africa	PROPN
ejpam-5362	621	8	,	,	PUNCT
ejpam-5362	621	9	2023	2023	NUM
ejpam-5362	621	10	.	.	PUNCT
ejpam-5362	622	1	[	[	X
ejpam-5362	622	2	17	17	NUM
ejpam-5362	622	3	]	]	X
ejpam-5362	622	4	j	j	PROPN
ejpam-5362	622	5	picado	picado	NOUN
ejpam-5362	622	6	and	and	CCONJ
ejpam-5362	622	7	a	a	DET
ejpam-5362	622	8	pultr	pultr	NOUN
ejpam-5362	622	9	.	.	PUNCT
ejpam-5362	623	1	frames	frame	NOUN
ejpam-5362	623	2	and	and	CCONJ
ejpam-5362	623	3	locales	locale	NOUN
ejpam-5362	623	4	:	:	PUNCT
ejpam-5362	623	5	topology	topology	NOUN
ejpam-5362	623	6	without	without	ADP
ejpam-5362	623	7	points	point	NOUN
ejpam-5362	623	8	.	.	PUNCT
ejpam-5362	624	1	springer	springer	NOUN
ejpam-5362	624	2	science	science	NOUN
ejpam-5362	624	3	and	and	CCONJ
ejpam-5362	624	4	business	business	NOUN
ejpam-5362	624	5	media	medium	NOUN
ejpam-5362	624	6	,	,	PUNCT
ejpam-5362	624	7	2011	2011	NUM
ejpam-5362	624	8	.	.	PUNCT
ejpam-5362	625	1	[	[	X
ejpam-5362	625	2	18	18	NUM
ejpam-5362	625	3	]	]	X
ejpam-5362	625	4	j	j	X
ejpam-5362	625	5	picado	picado	NOUN
ejpam-5362	625	6	and	and	CCONJ
ejpam-5362	625	7	a	a	DET
ejpam-5362	625	8	pultr	pultr	NOUN
ejpam-5362	625	9	.	.	PUNCT
ejpam-5362	626	1	(	(	PUNCT
ejpam-5362	626	2	sub	sub	NOUN
ejpam-5362	626	3	)	)	PUNCT
ejpam-5362	626	4	fit	fit	ADJ
ejpam-5362	626	5	biframes	biframe	NOUN
ejpam-5362	626	6	and	and	CCONJ
ejpam-5362	626	7	non	non	ADJ
ejpam-5362	626	8	-	-	ADJ
ejpam-5362	626	9	symmetric	symmetric	ADJ
ejpam-5362	626	10	nearness	nearness	NOUN
ejpam-5362	626	11	.	.	PUNCT
ejpam-5362	627	1	topology	topology	NOUN
ejpam-5362	627	2	and	and	CCONJ
ejpam-5362	627	3	its	its	PRON
ejpam-5362	627	4	applications	application	NOUN
ejpam-5362	627	5	,	,	PUNCT
ejpam-5362	627	6	168:66–81	168:66–81	NUM
ejpam-5362	627	7	,	,	PUNCT
ejpam-5362	627	8	2014	2014	NUM
ejpam-5362	627	9	.	.	PUNCT
ejpam-5362	628	1	[	[	X
ejpam-5362	628	2	19	19	NUM
ejpam-5362	628	3	]	]	X
ejpam-5362	628	4	j	j	NOUN
ejpam-5362	628	5	picado	picado	NOUN
ejpam-5362	628	6	and	and	CCONJ
ejpam-5362	628	7	a	a	DET
ejpam-5362	628	8	pultr	pultr	NOUN
ejpam-5362	628	9	.	.	PUNCT
ejpam-5362	629	1	axiom	axiom	NOUN
ejpam-5362	629	2	td	td	NOUN
ejpam-5362	629	3	and	and	CCONJ
ejpam-5362	629	4	the	the	DET
ejpam-5362	629	5	simmons	simmon	NOUN
ejpam-5362	629	6	sublocale	sublocale	NOUN
ejpam-5362	629	7	theorem	theorem	VERB
ejpam-5362	629	8	.	.	PUNCT
ejpam-5362	630	1	commentationes	commentatione	NOUN
ejpam-5362	630	2	mathematicae	mathematicae	VERB
ejpam-5362	630	3	universitatis	universitatis	PROPN
ejpam-5362	630	4	carolinae	carolinae	PROPN
ejpam-5362	630	5	,	,	PUNCT
ejpam-5362	630	6	60(4):541–551	60(4):541–551	PROPN
ejpam-5362	630	7	,	,	PUNCT
ejpam-5362	630	8	2019	2019	NUM
ejpam-5362	630	9	.	.	PUNCT
ejpam-5362	631	1	[	[	X
ejpam-5362	631	2	20	20	NUM
ejpam-5362	631	3	]	]	X
ejpam-5362	631	4	j	j	NOUN
ejpam-5362	631	5	picado	picado	NOUN
ejpam-5362	631	6	and	and	CCONJ
ejpam-5362	631	7	a	a	DET
ejpam-5362	631	8	pultr	pultr	NOUN
ejpam-5362	631	9	.	.	PUNCT
ejpam-5362	632	1	separation	separation	NOUN
ejpam-5362	632	2	in	in	ADP
ejpam-5362	632	3	point	point	NOUN
ejpam-5362	632	4	-	-	PUNCT
ejpam-5362	632	5	free	free	ADJ
ejpam-5362	632	6	topology	topology	NOUN
ejpam-5362	632	7	.	.	PUNCT
ejpam-5362	633	1	birkhäuser	birkhäuser	NOUN
ejpam-5362	633	2	,	,	PUNCT
ejpam-5362	633	3	2021	2021	NUM
ejpam-5362	633	4	.	.	PUNCT
ejpam-5362	634	1	[	[	X
ejpam-5362	634	2	21	21	NUM
ejpam-5362	634	3	]	]	X
ejpam-5362	634	4	s	s	VERB
ejpam-5362	634	5	schauerte	schauerte	NOUN
ejpam-5362	634	6	.	.	PUNCT
ejpam-5362	635	1	normality	normality	NOUN
ejpam-5362	635	2	for	for	ADP
ejpam-5362	635	3	biframes	biframe	NOUN
ejpam-5362	635	4	.	.	PUNCT
ejpam-5362	636	1	applied	apply	VERB
ejpam-5362	636	2	categorical	categorical	ADJ
ejpam-5362	636	3	structures	structure	NOUN
ejpam-5362	636	4	,	,	PUNCT
ejpam-5362	636	5	3:1–9	3:1–9	NUM
ejpam-5362	636	6	,	,	PUNCT
ejpam-5362	636	7	1995	1995	NUM
ejpam-5362	636	8	.	.	PUNCT
ejpam-5362	637	1	[	[	X
ejpam-5362	637	2	22	22	NUM
ejpam-5362	637	3	]	]	X
ejpam-5362	637	4	g	g	PROPN
ejpam-5362	637	5	thangaraj	thangaraj	NOUN
ejpam-5362	637	6	and	and	CCONJ
ejpam-5362	637	7	s	s	VERB
ejpam-5362	637	8	anjalmose	anjalmose	ADJ
ejpam-5362	637	9	.	.	PUNCT
ejpam-5362	638	1	on	on	ADP
ejpam-5362	638	2	fuzzy	fuzzy	ADJ
ejpam-5362	638	3	baire	baire	NOUN
ejpam-5362	638	4	spaces	space	NOUN
ejpam-5362	638	5	.	.	PUNCT
ejpam-5362	639	1	the	the	DET
ejpam-5362	639	2	journal	journal	NOUN
ejpam-5362	639	3	of	of	ADP
ejpam-5362	639	4	fuzzy	fuzzy	ADJ
ejpam-5362	639	5	mathematics	mathematic	NOUN
ejpam-5362	639	6	,	,	PUNCT
ejpam-5362	639	7	21(3):667–676	21(3):667–676	NUM
ejpam-5362	639	8	,	,	PUNCT
ejpam-5362	639	9	2013	2013	NUM
ejpam-5362	639	10	.	.	PUNCT
ejpam-5362	640	1	[	[	X
ejpam-5362	640	2	23	23	NUM
ejpam-5362	640	3	]	]	X
ejpam-5362	640	4	l.a	l.a	PROPN
ejpam-5362	640	5	.	.	PROPN
ejpam-5362	640	6	zadeh	zadeh	PROPN
ejpam-5362	640	7	.	.	PUNCT
ejpam-5362	640	8	fuzzy	fuzzy	ADJ
ejpam-5362	640	9	sets	set	NOUN
ejpam-5362	640	10	.	.	PUNCT
ejpam-5362	641	1	information	information	NOUN
ejpam-5362	641	2	and	and	CCONJ
ejpam-5362	641	3	control	control	NOUN
ejpam-5362	641	4	,	,	PUNCT
ejpam-5362	641	5	8(3):338–353	8(3):338–353	NUM
ejpam-5362	641	6	,	,	PUNCT
ejpam-5362	641	7	1965	1965	NUM
ejpam-5362	641	8	.	.	PUNCT
ejpam-5362	642	1	[	[	X
ejpam-5362	642	2	24	24	NUM
ejpam-5362	642	3	]	]	PUNCT
ejpam-5362	642	4	m	m	NOUN
ejpam-5362	642	5	zarghani	zarghani	NOUN
ejpam-5362	642	6	and	and	CCONJ
ejpam-5362	642	7	a.a	a.a	PROPN
ejpam-5362	642	8	.	.	PROPN
ejpam-5362	642	9	estaji	estaji	PROPN
ejpam-5362	642	10	.	.	PUNCT
ejpam-5362	643	1	a	a	DET
ejpam-5362	643	2	new	new	ADJ
ejpam-5362	643	3	pointfree	pointfree	ADJ
ejpam-5362	643	4	form	form	NOUN
ejpam-5362	643	5	of	of	ADP
ejpam-5362	643	6	topology	topology	NOUN
ejpam-5362	643	7	.	.	PUNCT
ejpam-5362	644	1	filomat	filomat	PROPN
ejpam-5362	644	2	,	,	PUNCT
ejpam-5362	644	3	32(8):2721	32(8):2721	NUM
ejpam-5362	644	4	–	–	PUNCT
ejpam-5362	644	5	2733	2733	NUM
ejpam-5362	644	6	,	,	PUNCT
ejpam-5362	644	7	2018	2018	NUM
ejpam-5362	644	8	.	.	PUNCT