id	sid	tid	token	lemma	pos
ejpam-4944	1	1	european	european	PROPN
ejpam-4944	1	2	journal	journal	PROPN
ejpam-4944	1	3	of	of	ADP
ejpam-4944	1	4	pure	pure	ADJ
ejpam-4944	1	5	and	and	CCONJ
ejpam-4944	1	6	applied	apply	VERB
ejpam-4944	1	7	mathematics	mathematic	NOUN
ejpam-4944	1	8	vol	vol	NOUN
ejpam-4944	1	9	.	.	PUNCT
ejpam-4944	2	1	16	16	NUM
ejpam-4944	2	2	,	,	PUNCT
ejpam-4944	2	3	no	no	INTJ
ejpam-4944	2	4	.	.	NOUN
ejpam-4944	2	5	4	4	NUM
ejpam-4944	2	6	,	,	PUNCT
ejpam-4944	2	7	2023	2023	NUM
ejpam-4944	2	8	,	,	PUNCT
ejpam-4944	2	9	2286	2286	NUM
ejpam-4944	2	10	-	-	SYM
ejpam-4944	2	11	2305	2305	NUM
ejpam-4944	2	12	issn	issn	PROPN
ejpam-4944	2	13	1307	1307	NUM
ejpam-4944	2	14	-	-	SYM
ejpam-4944	2	15	5543	5543	NUM
ejpam-4944	2	16	–	–	PUNCT
ejpam-4944	2	17	ejpam.com	ejpam.com	X
ejpam-4944	2	18	published	publish	VERB
ejpam-4944	2	19	by	by	ADP
ejpam-4944	2	20	new	new	PROPN
ejpam-4944	2	21	york	york	PROPN
ejpam-4944	2	22	business	business	PROPN
ejpam-4944	2	23	global	global	ADJ
ejpam-4944	2	24	on	on	ADP
ejpam-4944	2	25	dense	dense	ADJ
ejpam-4944	2	26	sets	set	NOUN
ejpam-4944	2	27	diaa	diaa	ADJ
ejpam-4944	2	28	elgezouli1	elgezouli1	NOUN
ejpam-4944	2	29	,	,	PUNCT
ejpam-4944	2	30	mutaz	mutaz	NOUN
ejpam-4944	2	31	omer2	omer2	NOUN
ejpam-4944	2	32	,	,	PUNCT
ejpam-4944	2	33	yasser	yasser	PROPN
ejpam-4944	2	34	farhat3,∗	farhat3,∗	PROPN
ejpam-4944	2	35	,	,	PUNCT
ejpam-4944	2	36	elmhadi	elmhadi	NOUN
ejpam-4944	2	37	afif4	afif4	PROPN
ejpam-4944	2	38	,	,	PUNCT
ejpam-4944	2	39	vadakasi	vadakasi	NOUN
ejpam-4944	2	40	subramanian5	subramanian5	PROPN
ejpam-4944	2	41	1	1	NUM
ejpam-4944	2	42	department	department	NOUN
ejpam-4944	2	43	of	of	ADP
ejpam-4944	2	44	basic	basic	ADJ
ejpam-4944	2	45	sciences	science	NOUN
ejpam-4944	2	46	,	,	PUNCT
ejpam-4944	2	47	king	king	NOUN
ejpam-4944	2	48	saud	saud	PROPN
ejpam-4944	2	49	university	university	PROPN
ejpam-4944	2	50	,	,	PUNCT
ejpam-4944	2	51	saudi	saudi	PROPN
ejpam-4944	2	52	arabia	arabia	PROPN
ejpam-4944	2	53	2	2	NUM
ejpam-4944	2	54	university	university	NOUN
ejpam-4944	2	55	of	of	ADP
ejpam-4944	2	56	khartoum	khartoum	PROPN
ejpam-4944	2	57	,	,	PUNCT
ejpam-4944	2	58	khartoum	khartoum	PROPN
ejpam-4944	2	59	,	,	PUNCT
ejpam-4944	2	60	sudan	sudan	PROPN
ejpam-4944	2	61	3	3	NUM
ejpam-4944	2	62	academic	academic	PROPN
ejpam-4944	2	63	support	support	NOUN
ejpam-4944	2	64	department	department	NOUN
ejpam-4944	2	65	,	,	PUNCT
ejpam-4944	3	1	abu	abu	PROPN
ejpam-4944	3	2	dhabi	dhabi	PROPN
ejpam-4944	3	3	polytechnic	polytechnic	PROPN
ejpam-4944	3	4	,	,	PUNCT
ejpam-4944	3	5	p.	p.	PROPN
ejpam-4944	3	6	o.	o.	PROPN
ejpam-4944	3	7	box	box	PROPN
ejpam-4944	3	8	111499	111499	NUM
ejpam-4944	3	9	,	,	PUNCT
ejpam-4944	3	10	abu	abu	PROPN
ejpam-4944	3	11	dhabi	dhabi	PROPN
ejpam-4944	3	12	,	,	PUNCT
ejpam-4944	3	13	uae	uae	PROPN
ejpam-4944	3	14	.	.	PROPN
ejpam-4944	3	15	4	4	NUM
ejpam-4944	3	16	university	university	NOUN
ejpam-4944	3	17	of	of	ADP
ejpam-4944	3	18	gezira	gezira	PROPN
ejpam-4944	3	19	,	,	PUNCT
ejpam-4944	3	20	sudan	sudan	PROPN
ejpam-4944	3	21	5	5	NUM
ejpam-4944	3	22	department	department	NOUN
ejpam-4944	3	23	of	of	ADP
ejpam-4944	3	24	mathematics	mathematic	NOUN
ejpam-4944	3	25	,	,	PUNCT
ejpam-4944	3	26	a.k.d.dharma	a.k.d.dharma	PROPN
ejpam-4944	3	27	raja	raja	PROPN
ejpam-4944	3	28	women	woman	NOUN
ejpam-4944	3	29	’s	’s	PART
ejpam-4944	3	30	college	college	PROPN
ejpam-4944	3	31	,	,	PUNCT
ejpam-4944	3	32	rajapalayam	rajapalayam	PROPN
ejpam-4944	3	33	.	.	PUNCT
ejpam-4944	3	34	,	,	PUNCT
ejpam-4944	3	35	india	india	PROPN
ejpam-4944	3	36	abstract	abstract	NOUN
ejpam-4944	3	37	.	.	PUNCT
ejpam-4944	4	1	in	in	ADP
ejpam-4944	4	2	this	this	DET
ejpam-4944	4	3	paper	paper	NOUN
ejpam-4944	4	4	,	,	PUNCT
ejpam-4944	4	5	we	we	PRON
ejpam-4944	4	6	introduce	introduce	VERB
ejpam-4944	4	7	one	one	NUM
ejpam-4944	4	8	interesting	interesting	ADJ
ejpam-4944	4	9	mathematical	mathematical	ADJ
ejpam-4944	4	10	tool	tool	NOUN
ejpam-4944	4	11	namely	namely	ADV
ejpam-4944	4	12	,	,	PUNCT
ejpam-4944	4	13	(	(	PUNCT
ejpam-4944	4	14	s	s	X
ejpam-4944	4	15	,	,	PUNCT
ejpam-4944	4	16	v)⋆-dense	v)⋆-dense	NOUN
ejpam-4944	4	17	,	,	PUNCT
ejpam-4944	4	18	and	and	CCONJ
ejpam-4944	4	19	analyze	analyze	VERB
ejpam-4944	4	20	its	its	PRON
ejpam-4944	4	21	nature	nature	NOUN
ejpam-4944	4	22	in	in	ADP
ejpam-4944	4	23	a	a	DET
ejpam-4944	4	24	bigeneralized	bigeneralize	VERB
ejpam-4944	4	25	topological	topological	ADJ
ejpam-4944	4	26	space	space	NOUN
ejpam-4944	4	27	.	.	PUNCT
ejpam-4944	5	1	further	far	ADV
ejpam-4944	5	2	,	,	PUNCT
ejpam-4944	5	3	we	we	PRON
ejpam-4944	5	4	prove	prove	VERB
ejpam-4944	5	5	some	some	DET
ejpam-4944	5	6	properties	property	NOUN
ejpam-4944	5	7	of	of	ADP
ejpam-4944	5	8	this	this	DET
ejpam-4944	5	9	set	set	NOUN
ejpam-4944	5	10	and	and	CCONJ
ejpam-4944	5	11	give	give	VERB
ejpam-4944	5	12	the	the	DET
ejpam-4944	5	13	relationship	relationship	NOUN
ejpam-4944	5	14	between	between	ADP
ejpam-4944	5	15	(	(	PUNCT
ejpam-4944	5	16	s	s	X
ejpam-4944	5	17	,	,	PUNCT
ejpam-4944	5	18	v)-dense	v)-dense	PUNCT
ejpam-4944	5	19	and	and	CCONJ
ejpam-4944	5	20	(	(	PUNCT
ejpam-4944	5	21	s	s	X
ejpam-4944	5	22	,	,	PUNCT
ejpam-4944	5	23	v)⋆-dense	v)⋆-dense	PROPN
ejpam-4944	5	24	sets	set	NOUN
ejpam-4944	5	25	.	.	PUNCT
ejpam-4944	6	1	finally	finally	ADV
ejpam-4944	6	2	,	,	PUNCT
ejpam-4944	6	3	we	we	PRON
ejpam-4944	6	4	give	give	VERB
ejpam-4944	6	5	applications	application	NOUN
ejpam-4944	6	6	for	for	ADP
ejpam-4944	6	7	various	various	ADJ
ejpam-4944	6	8	sets	set	NOUN
ejpam-4944	6	9	defined	define	VERB
ejpam-4944	6	10	in	in	ADP
ejpam-4944	6	11	a	a	DET
ejpam-4944	6	12	bigeneralized	bigeneralize	VERB
ejpam-4944	6	13	topological	topological	ADJ
ejpam-4944	6	14	space	space	NOUN
ejpam-4944	6	15	.	.	PUNCT
ejpam-4944	7	1	2020	2020	NUM
ejpam-4944	7	2	mathematics	mathematic	NOUN
ejpam-4944	7	3	subject	subject	NOUN
ejpam-4944	7	4	classifications	classification	NOUN
ejpam-4944	7	5	:	:	PUNCT
ejpam-4944	7	6	ams	am	NOUN
ejpam-4944	7	7	subject	subject	ADJ
ejpam-4944	7	8	classification(2020):primary	classification(2020):primary	PROPN
ejpam-4944	7	9	:	:	PUNCT
ejpam-4944	7	10	54a05	54a05	NUM
ejpam-4944	7	11	,	,	PUNCT
ejpam-4944	7	12	54a10	54a10	NUM
ejpam-4944	7	13	.	.	PUNCT
ejpam-4944	8	1	key	key	ADJ
ejpam-4944	8	2	words	word	NOUN
ejpam-4944	8	3	and	and	CCONJ
ejpam-4944	8	4	phrases	phrase	NOUN
ejpam-4944	8	5	:	:	PUNCT
ejpam-4944	8	6	bigeneralized	bigeneralize	VERB
ejpam-4944	8	7	topological	topological	ADJ
ejpam-4944	8	8	space	space	NOUN
ejpam-4944	8	9	,	,	PUNCT
ejpam-4944	8	10	µ(s	µ(	NOUN
ejpam-4944	8	11	,	,	PUNCT
ejpam-4944	8	12	v)-open	v)-open	NOUN
ejpam-4944	8	13	,	,	PUNCT
ejpam-4944	8	14	(	(	PUNCT
ejpam-4944	8	15	s	s	X
ejpam-4944	8	16	,	,	PUNCT
ejpam-4944	8	17	v)-open	v)-open	ADJ
ejpam-4944	8	18	,	,	PUNCT
ejpam-4944	8	19	(	(	PUNCT
ejpam-4944	8	20	s	s	X
ejpam-4944	8	21	,	,	PUNCT
ejpam-4944	8	22	v)-nowhere	v)-nowhere	SCONJ
ejpam-4944	8	23	dense	dense	ADJ
ejpam-4944	8	24	.	.	PUNCT
ejpam-4944	9	1	1	1	X
ejpam-4944	9	2	.	.	X
ejpam-4944	9	3	introduction	introduction	NOUN
ejpam-4944	9	4	the	the	DET
ejpam-4944	9	5	concept	concept	NOUN
ejpam-4944	9	6	of	of	ADP
ejpam-4944	9	7	a	a	DET
ejpam-4944	9	8	generalized	generalized	ADJ
ejpam-4944	9	9	topological	topological	ADJ
ejpam-4944	9	10	space	space	NOUN
ejpam-4944	9	11	was	be	AUX
ejpam-4944	9	12	introduced	introduce	VERB
ejpam-4944	9	13	by	by	ADP
ejpam-4944	9	14	császár	császár	NOUN
ejpam-4944	9	15	in	in	ADP
ejpam-4944	9	16	[	[	X
ejpam-4944	9	17	3	3	NUM
ejpam-4944	9	18	]	]	PUNCT
ejpam-4944	9	19	.	.	PUNCT
ejpam-4944	10	1	some	some	DET
ejpam-4944	10	2	researchers	researcher	NOUN
ejpam-4944	10	3	have	have	AUX
ejpam-4944	10	4	defined	define	VERB
ejpam-4944	10	5	various	various	ADJ
ejpam-4944	10	6	concepts	concept	NOUN
ejpam-4944	10	7	in	in	ADP
ejpam-4944	10	8	this	this	DET
ejpam-4944	10	9	space	space	NOUN
ejpam-4944	10	10	and	and	CCONJ
ejpam-4944	10	11	examined	examine	VERB
ejpam-4944	10	12	their	their	PRON
ejpam-4944	10	13	significance	significance	NOUN
ejpam-4944	10	14	in	in	ADP
ejpam-4944	10	15	a	a	DET
ejpam-4944	10	16	generalized	generalized	ADJ
ejpam-4944	10	17	topological	topological	ADJ
ejpam-4944	10	18	space	space	NOUN
ejpam-4944	10	19	.	.	PUNCT
ejpam-4944	11	1	especially	especially	ADV
ejpam-4944	11	2	,	,	PUNCT
ejpam-4944	11	3	in	in	ADP
ejpam-4944	11	4	a	a	DET
ejpam-4944	11	5	generalized	generalized	ADJ
ejpam-4944	11	6	topological	topological	ADJ
ejpam-4944	11	7	space	space	NOUN
ejpam-4944	11	8	,	,	PUNCT
ejpam-4944	11	9	dense	dense	ADJ
ejpam-4944	11	10	sets	set	NOUN
ejpam-4944	11	11	were	be	AUX
ejpam-4944	11	12	introduced	introduce	VERB
ejpam-4944	11	13	by	by	ADP
ejpam-4944	11	14	ekici	ekici	NOUN
ejpam-4944	11	15	[	[	X
ejpam-4944	11	16	8	8	NUM
ejpam-4944	11	17	]	]	PUNCT
ejpam-4944	11	18	.	.	PUNCT
ejpam-4944	12	1	he	he	PRON
ejpam-4944	12	2	has	have	AUX
ejpam-4944	12	3	proven	prove	VERB
ejpam-4944	12	4	few	few	ADJ
ejpam-4944	12	5	results	result	NOUN
ejpam-4944	12	6	for	for	ADP
ejpam-4944	12	7	dense	dense	ADJ
ejpam-4944	12	8	sets	set	NOUN
ejpam-4944	12	9	in	in	ADP
ejpam-4944	12	10	a	a	DET
ejpam-4944	12	11	generalized	generalized	ADJ
ejpam-4944	12	12	topological	topological	ADJ
ejpam-4944	12	13	space	space	NOUN
ejpam-4944	12	14	.	.	PUNCT
ejpam-4944	13	1	based	base	VERB
ejpam-4944	13	2	on	on	ADP
ejpam-4944	13	3	this	this	PRON
ejpam-4944	13	4	,	,	PUNCT
ejpam-4944	13	5	some	some	DET
ejpam-4944	13	6	mathematicians	mathematician	NOUN
ejpam-4944	13	7	have	have	AUX
ejpam-4944	13	8	proved	prove	VERB
ejpam-4944	13	9	various	various	ADJ
ejpam-4944	13	10	properties	property	NOUN
ejpam-4944	13	11	for	for	ADP
ejpam-4944	13	12	dense	dense	ADJ
ejpam-4944	13	13	sets	set	NOUN
ejpam-4944	13	14	e.g.	e.g.	ADV
ejpam-4944	13	15	[	[	X
ejpam-4944	13	16	11	11	NUM
ejpam-4944	13	17	,	,	PUNCT
ejpam-4944	13	18	12	12	NUM
ejpam-4944	13	19	,	,	PUNCT
ejpam-4944	13	20	15	15	NUM
ejpam-4944	13	21	,	,	PUNCT
ejpam-4944	13	22	17	17	NUM
ejpam-4944	13	23	,	,	PUNCT
ejpam-4944	13	24	19	19	NUM
ejpam-4944	13	25	]	]	PUNCT
ejpam-4944	13	26	.	.	PUNCT
ejpam-4944	14	1	in	in	ADP
ejpam-4944	14	2	[	[	X
ejpam-4944	14	3	10	10	NUM
ejpam-4944	14	4	]	]	PUNCT
ejpam-4944	14	5	,	,	PUNCT
ejpam-4944	14	6	j.c	j.c	PROPN
ejpam-4944	14	7	.	.	PROPN
ejpam-4944	14	8	kelly	kelly	PROPN
ejpam-4944	14	9	introduced	introduce	VERB
ejpam-4944	14	10	the	the	DET
ejpam-4944	14	11	concept	concept	NOUN
ejpam-4944	14	12	namely	namely	ADV
ejpam-4944	14	13	,	,	PUNCT
ejpam-4944	14	14	a	a	DET
ejpam-4944	14	15	bitopological	bitopological	ADJ
ejpam-4944	14	16	space	space	NOUN
ejpam-4944	14	17	.	.	PUNCT
ejpam-4944	15	1	using	use	VERB
ejpam-4944	15	2	these	these	DET
ejpam-4944	15	3	aspects	aspect	NOUN
ejpam-4944	15	4	,	,	PUNCT
ejpam-4944	15	5	boonpok	boonpok	PROPN
ejpam-4944	15	6	founded	found	VERB
ejpam-4944	15	7	the	the	DET
ejpam-4944	15	8	notion	notion	NOUN
ejpam-4944	15	9	of	of	ADP
ejpam-4944	15	10	a	a	DET
ejpam-4944	15	11	bigeneralized	bigeneralize	VERB
ejpam-4944	15	12	topological	topological	ADJ
ejpam-4944	15	13	space	space	NOUN
ejpam-4944	15	14	in	in	ADP
ejpam-4944	15	15	2010	2010	NUM
ejpam-4944	15	16	[	[	X
ejpam-4944	15	17	2	2	NUM
ejpam-4944	15	18	]	]	PUNCT
ejpam-4944	15	19	.	.	PUNCT
ejpam-4944	16	1	he	he	PRON
ejpam-4944	16	2	examines	examine	VERB
ejpam-4944	16	3	the	the	DET
ejpam-4944	16	4	significance	significance	NOUN
ejpam-4944	16	5	of	of	ADP
ejpam-4944	16	6	(	(	PUNCT
ejpam-4944	16	7	m	m	PROPN
ejpam-4944	16	8	,	,	PUNCT
ejpam-4944	16	9	n)-closed	n)-close	VERB
ejpam-4944	16	10	sets	set	NOUN
ejpam-4944	16	11	in	in	ADP
ejpam-4944	16	12	a	a	DET
ejpam-4944	16	13	bigeneralized	bigeneralize	VERB
ejpam-4944	16	14	topological	topological	ADJ
ejpam-4944	16	15	space	space	NOUN
ejpam-4944	16	16	.	.	PUNCT
ejpam-4944	17	1	∗corresponding	∗corresponde	VERB
ejpam-4944	17	2	author	author	NOUN
ejpam-4944	17	3	.	.	PUNCT
ejpam-4944	18	1	doi	doi	NOUN
ejpam-4944	18	2	:	:	PUNCT
ejpam-4944	18	3	https://doi.org/10.29020/nybg.ejpam.v16i4.4944	https://doi.org/10.29020/nybg.ejpam.v16i4.4944	ADJ
ejpam-4944	18	4	email	email	NOUN
ejpam-4944	18	5	addresses	address	VERB
ejpam-4944	18	6	:	:	PUNCT
ejpam-4944	18	7	dbushra.c@ksu.edu.sa	dbushra.c@ksu.edu.sa	PROPN
ejpam-4944	18	8	(	(	PUNCT
ejpam-4944	18	9	d.	d.	PROPN
ejpam-4944	18	10	elgezouli	elgezouli	PROPN
ejpam-4944	18	11	)	)	PUNCT
ejpam-4944	18	12	,	,	PUNCT
ejpam-4944	18	13	farhat.yasser.1@gmail.com	farhat.yasser.1@gmail.com	X
ejpam-4944	18	14	(	(	PUNCT
ejpam-4944	18	15	y.	y.	PROPN
ejpam-4944	18	16	farhat	farhat	PROPN
ejpam-4944	18	17	)	)	PUNCT
ejpam-4944	18	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4944	18	19	2286	2286	NUM
ejpam-4944	19	1	©	©	ADP
ejpam-4944	19	2	2023	2023	NUM
ejpam-4944	19	3	ejpam	ejpam	NOUN
ejpam-4944	19	4	all	all	DET
ejpam-4944	19	5	rights	right	NOUN
ejpam-4944	19	6	reserved	reserve	VERB
ejpam-4944	19	7	.	.	PUNCT
ejpam-4944	20	1	d.	d.	PROPN
ejpam-4944	20	2	elgezouli	elgezouli	PROPN
ejpam-4944	20	3	et	et	PROPN
ejpam-4944	20	4	al	al	PROPN
ejpam-4944	20	5	.	.	PUNCT
ejpam-4944	20	6	/	/	SYM
ejpam-4944	20	7	eur	eur	PROPN
ejpam-4944	20	8	.	.	PUNCT
ejpam-4944	21	1	j.	j.	PROPN
ejpam-4944	21	2	pure	pure	PROPN
ejpam-4944	21	3	appl	appl	PROPN
ejpam-4944	21	4	.	.	PROPN
ejpam-4944	21	5	math	math	PROPN
ejpam-4944	21	6	,	,	PUNCT
ejpam-4944	21	7	16	16	NUM
ejpam-4944	21	8	(	(	PUNCT
ejpam-4944	21	9	4	4	NUM
ejpam-4944	21	10	)	)	PUNCT
ejpam-4944	21	11	(	(	PUNCT
ejpam-4944	21	12	2023	2023	NUM
ejpam-4944	21	13	)	)	PUNCT
ejpam-4944	21	14	,	,	PUNCT
ejpam-4944	21	15	2286	2286	NUM
ejpam-4944	21	16	-	-	SYM
ejpam-4944	21	17	2305	2305	NUM
ejpam-4944	21	18	2287	2287	NUM
ejpam-4944	21	19	inspired	inspire	VERB
ejpam-4944	21	20	by	by	ADP
ejpam-4944	21	21	all	all	DET
ejpam-4944	21	22	this	this	PRON
ejpam-4944	22	1	,	,	PUNCT
ejpam-4944	22	2	we	we	PRON
ejpam-4944	22	3	define	define	VERB
ejpam-4944	22	4	a	a	DET
ejpam-4944	22	5	new	new	ADJ
ejpam-4944	22	6	dense	dense	ADJ
ejpam-4944	22	7	set	set	NOUN
ejpam-4944	22	8	,	,	PUNCT
ejpam-4944	22	9	namely	namely	ADV
ejpam-4944	22	10	,	,	PUNCT
ejpam-4944	22	11	(	(	PUNCT
ejpam-4944	22	12	s	s	X
ejpam-4944	22	13	,	,	PUNCT
ejpam-4944	22	14	v)⋆-dense	v)⋆-dense	PROPN
ejpam-4944	22	15	set	set	NOUN
ejpam-4944	22	16	using	use	VERB
ejpam-4944	22	17	semi	semi	ADJ
ejpam-4944	22	18	-	-	ADJ
ejpam-4944	22	19	open	open	ADJ
ejpam-4944	22	20	sets	set	NOUN
ejpam-4944	22	21	in	in	ADP
ejpam-4944	22	22	a	a	DET
ejpam-4944	22	23	bigeneralized	bigeneralize	VERB
ejpam-4944	22	24	topological	topological	ADJ
ejpam-4944	22	25	space	space	NOUN
ejpam-4944	22	26	.	.	PUNCT
ejpam-4944	23	1	find	find	VERB
ejpam-4944	23	2	various	various	ADJ
ejpam-4944	23	3	interesting	interesting	ADJ
ejpam-4944	23	4	results	result	NOUN
ejpam-4944	23	5	for	for	ADP
ejpam-4944	23	6	(	(	PUNCT
ejpam-4944	23	7	s	s	X
ejpam-4944	23	8	,	,	PUNCT
ejpam-4944	23	9	v)⋆-dense	v)⋆-dense	NOUN
ejpam-4944	23	10	sets	set	NOUN
ejpam-4944	23	11	.	.	PUNCT
ejpam-4944	24	1	next	next	ADJ
ejpam-4944	24	2	section	section	NOUN
ejpam-4944	24	3	,	,	PUNCT
ejpam-4944	24	4	the	the	DET
ejpam-4944	24	5	preliminary	preliminary	ADJ
ejpam-4944	24	6	definitions	definition	NOUN
ejpam-4944	24	7	,	,	PUNCT
ejpam-4944	24	8	and	and	CCONJ
ejpam-4944	24	9	lemmas	lemma	NOUN
ejpam-4944	24	10	are	be	AUX
ejpam-4944	24	11	remembered	remember	VERB
ejpam-4944	24	12	.	.	PUNCT
ejpam-4944	25	1	in	in	ADP
ejpam-4944	25	2	sections	section	NOUN
ejpam-4944	25	3	3	3	NUM
ejpam-4944	25	4	&	&	CCONJ
ejpam-4944	25	5	4	4	NUM
ejpam-4944	25	6	,	,	PUNCT
ejpam-4944	25	7	in	in	ADP
ejpam-4944	25	8	a	a	DET
ejpam-4944	25	9	bigenerlized	bigenerlize	VERB
ejpam-4944	25	10	topological	topological	ADJ
ejpam-4944	25	11	space	space	NOUN
ejpam-4944	25	12	,	,	PUNCT
ejpam-4944	25	13	examined	examine	VERB
ejpam-4944	25	14	the	the	DET
ejpam-4944	25	15	significance	significance	NOUN
ejpam-4944	25	16	of	of	ADP
ejpam-4944	25	17	(	(	PUNCT
ejpam-4944	25	18	s	s	X
ejpam-4944	25	19	,	,	PUNCT
ejpam-4944	25	20	v)⋆-dense	v)⋆-dense	PROPN
ejpam-4944	25	21	set	set	NOUN
ejpam-4944	25	22	.	.	PUNCT
ejpam-4944	26	1	the	the	DET
ejpam-4944	26	2	relationship	relationship	NOUN
ejpam-4944	26	3	between	between	ADP
ejpam-4944	26	4	µ-dense	µ-dense	PROPN
ejpam-4944	26	5	and	and	CCONJ
ejpam-4944	26	6	(	(	PUNCT
ejpam-4944	26	7	s	s	X
ejpam-4944	26	8	,	,	PUNCT
ejpam-4944	26	9	v)⋆-dense	v)⋆-dense	ADJ
ejpam-4944	26	10	sets	set	NOUN
ejpam-4944	26	11	are	be	AUX
ejpam-4944	26	12	proven	prove	VERB
ejpam-4944	26	13	.	.	PUNCT
ejpam-4944	27	1	further	far	ADV
ejpam-4944	27	2	,	,	PUNCT
ejpam-4944	27	3	few	few	ADJ
ejpam-4944	27	4	results	result	NOUN
ejpam-4944	27	5	for	for	ADP
ejpam-4944	27	6	(	(	PUNCT
ejpam-4944	27	7	s	s	X
ejpam-4944	27	8	,	,	PUNCT
ejpam-4944	27	9	v)⋆-dense	v)⋆-dense	PROPN
ejpam-4944	27	10	sets	set	NOUN
ejpam-4944	27	11	using	use	VERB
ejpam-4944	27	12	functions	function	NOUN
ejpam-4944	27	13	are	be	AUX
ejpam-4944	27	14	launched	launch	VERB
ejpam-4944	27	15	.	.	PUNCT
ejpam-4944	28	1	in	in	ADP
ejpam-4944	28	2	the	the	DET
ejpam-4944	28	3	last	last	ADJ
ejpam-4944	28	4	section	section	NOUN
ejpam-4944	28	5	,	,	PUNCT
ejpam-4944	28	6	we	we	PRON
ejpam-4944	28	7	defined	define	VERB
ejpam-4944	28	8	a	a	DET
ejpam-4944	28	9	soft	soft	ADJ
ejpam-4944	28	10	set	set	NOUN
ejpam-4944	28	11	using	use	VERB
ejpam-4944	28	12	(	(	PUNCT
ejpam-4944	28	13	s	s	NOUN
ejpam-4944	28	14	,	,	PUNCT
ejpam-4944	28	15	v)⋆-dense	v)⋆-dense	ADJ
ejpam-4944	28	16	sets	set	NOUN
ejpam-4944	28	17	and	and	CCONJ
ejpam-4944	28	18	various	various	ADJ
ejpam-4944	28	19	types	type	NOUN
ejpam-4944	28	20	of	of	ADP
ejpam-4944	28	21	open	open	ADJ
ejpam-4944	28	22	sets	set	NOUN
ejpam-4944	28	23	defined	define	VERB
ejpam-4944	28	24	in	in	ADP
ejpam-4944	28	25	a	a	DET
ejpam-4944	28	26	bigeneralized	bigeneralize	VERB
ejpam-4944	28	27	topological	topological	ADJ
ejpam-4944	28	28	space	space	NOUN
ejpam-4944	28	29	.	.	PUNCT
ejpam-4944	29	1	2	2	X
ejpam-4944	29	2	.	.	X
ejpam-4944	29	3	preliminaries	preliminary	NOUN
ejpam-4944	29	4	in	in	ADP
ejpam-4944	29	5	[	[	X
ejpam-4944	29	6	3	3	NUM
ejpam-4944	29	7	]	]	PUNCT
ejpam-4944	29	8	,	,	PUNCT
ejpam-4944	29	9	let	let	VERB
ejpam-4944	29	10	x	x	PRON
ejpam-4944	29	11	be	be	AUX
ejpam-4944	29	12	any	any	DET
ejpam-4944	29	13	non	non	ADJ
ejpam-4944	29	14	-	-	ADJ
ejpam-4944	29	15	null	null	ADJ
ejpam-4944	29	16	set	set	NOUN
ejpam-4944	29	17	.	.	PUNCT
ejpam-4944	30	1	a	a	DET
ejpam-4944	30	2	family	family	NOUN
ejpam-4944	30	3	µ	µ	X
ejpam-4944	30	4	of	of	ADP
ejpam-4944	30	5	subsets	subset	NOUN
ejpam-4944	30	6	of	of	ADP
ejpam-4944	30	7	x	x	X
ejpam-4944	30	8	is	be	AUX
ejpam-4944	30	9	a	a	DET
ejpam-4944	30	10	generalized	generalized	ADJ
ejpam-4944	30	11	topology	topology	NOUN
ejpam-4944	30	12	in	in	ADP
ejpam-4944	30	13	x	x	PRON
ejpam-4944	30	14	if	if	SCONJ
ejpam-4944	30	15	it	it	PRON
ejpam-4944	30	16	contains	contain	VERB
ejpam-4944	30	17	the	the	DET
ejpam-4944	30	18	empty	empty	ADJ
ejpam-4944	30	19	set	set	NOUN
ejpam-4944	30	20	and	and	CCONJ
ejpam-4944	30	21	is	be	AUX
ejpam-4944	30	22	closed	close	VERB
ejpam-4944	30	23	under	under	ADP
ejpam-4944	30	24	arbitrary	arbitrary	ADJ
ejpam-4944	30	25	union	union	NOUN
ejpam-4944	30	26	.	.	PUNCT
ejpam-4944	31	1	the	the	DET
ejpam-4944	31	2	pair	pair	NOUN
ejpam-4944	31	3	(	(	PUNCT
ejpam-4944	31	4	x,µ	x,µ	NOUN
ejpam-4944	31	5	)	)	PUNCT
ejpam-4944	31	6	is	be	AUX
ejpam-4944	31	7	called	call	VERB
ejpam-4944	31	8	a	a	DET
ejpam-4944	31	9	generalized	generalized	ADJ
ejpam-4944	31	10	topological	topological	ADJ
ejpam-4944	31	11	space	space	NOUN
ejpam-4944	31	12	(	(	PUNCT
ejpam-4944	31	13	gts	gts	NOUN
ejpam-4944	31	14	)	)	PUNCT
ejpam-4944	31	15	.	.	PUNCT
ejpam-4944	32	1	if	if	SCONJ
ejpam-4944	32	2	x	x	PROPN
ejpam-4944	32	3	∈	∈	PROPN
ejpam-4944	32	4	µ	µ	PROPN
ejpam-4944	32	5	,	,	PUNCT
ejpam-4944	32	6	then	then	ADV
ejpam-4944	32	7	(	(	PUNCT
ejpam-4944	32	8	x,µ	x,µ	NOUN
ejpam-4944	32	9	)	)	PUNCT
ejpam-4944	32	10	is	be	AUX
ejpam-4944	32	11	called	call	VERB
ejpam-4944	32	12	a	a	DET
ejpam-4944	32	13	strong	strong	ADJ
ejpam-4944	32	14	generalized	generalized	ADJ
ejpam-4944	32	15	topological	topological	ADJ
ejpam-4944	32	16	space	space	NOUN
ejpam-4944	32	17	(	(	PUNCT
ejpam-4944	32	18	sgts	sgts	NOUN
ejpam-4944	32	19	)	)	PUNCT
ejpam-4944	32	20	.	.	PUNCT
ejpam-4944	33	1	in	in	ADP
ejpam-4944	33	2	[	[	X
ejpam-4944	33	3	6	6	NUM
ejpam-4944	33	4	]	]	PUNCT
ejpam-4944	33	5	,	,	PUNCT
ejpam-4944	33	6	if	if	SCONJ
ejpam-4944	33	7	q	q	X
ejpam-4944	33	8	∈	∈	PROPN
ejpam-4944	33	9	µ	µ	NOUN
ejpam-4944	33	10	,	,	PUNCT
ejpam-4944	33	11	then	then	ADV
ejpam-4944	33	12	q	q	X
ejpam-4944	33	13	is	be	AUX
ejpam-4944	33	14	called	call	VERB
ejpam-4944	33	15	a	a	DET
ejpam-4944	33	16	µ-open	µ-open	NOUN
ejpam-4944	33	17	set	set	VERB
ejpam-4944	33	18	and	and	CCONJ
ejpam-4944	33	19	if	if	SCONJ
ejpam-4944	33	20	x	x	PRON
ejpam-4944	33	21	−q	−q	NOUN
ejpam-4944	33	22	∈	∈	PROPN
ejpam-4944	33	23	µ	µ	NOUN
ejpam-4944	33	24	,	,	PUNCT
ejpam-4944	33	25	then	then	ADV
ejpam-4944	33	26	q	q	X
ejpam-4944	33	27	is	be	AUX
ejpam-4944	33	28	said	say	VERB
ejpam-4944	33	29	to	to	PART
ejpam-4944	33	30	be	be	AUX
ejpam-4944	33	31	a	a	DET
ejpam-4944	33	32	µ-closed	µ-close	VERB
ejpam-4944	33	33	set	set	NOUN
ejpam-4944	33	34	.	.	PUNCT
ejpam-4944	34	1	the	the	DET
ejpam-4944	34	2	interior	interior	NOUN
ejpam-4944	34	3	of	of	ADP
ejpam-4944	34	4	q	q	PROPN
ejpam-4944	34	5	⊂	⊂	PROPN
ejpam-4944	34	6	x	x	PUNCT
ejpam-4944	34	7	denoted	denote	VERB
ejpam-4944	34	8	by	by	ADP
ejpam-4944	34	9	iµ(d	iµ(d	NOUN
ejpam-4944	34	10	)	)	PUNCT
ejpam-4944	34	11	,	,	PUNCT
ejpam-4944	34	12	is	be	AUX
ejpam-4944	34	13	the	the	DET
ejpam-4944	34	14	union	union	NOUN
ejpam-4944	34	15	of	of	ADP
ejpam-4944	34	16	all	all	DET
ejpam-4944	34	17	µ-open	µ-open	NOUN
ejpam-4944	34	18	sets	set	NOUN
ejpam-4944	34	19	contained	contain	VERB
ejpam-4944	34	20	in	in	ADP
ejpam-4944	34	21	d	d	PROPN
ejpam-4944	34	22	and	and	CCONJ
ejpam-4944	34	23	the	the	DET
ejpam-4944	34	24	closure	closure	NOUN
ejpam-4944	34	25	of	of	ADP
ejpam-4944	34	26	d	d	NOUN
ejpam-4944	34	27	denoted	denote	VERB
ejpam-4944	34	28	by	by	ADP
ejpam-4944	34	29	cµ(d	cµ(d	NOUN
ejpam-4944	34	30	)	)	PUNCT
ejpam-4944	34	31	,	,	PUNCT
ejpam-4944	34	32	is	be	AUX
ejpam-4944	34	33	the	the	DET
ejpam-4944	34	34	intersection	intersection	NOUN
ejpam-4944	34	35	of	of	ADP
ejpam-4944	34	36	all	all	DET
ejpam-4944	34	37	µ-closed	µ-close	VERB
ejpam-4944	34	38	sets	set	NOUN
ejpam-4944	34	39	containing	contain	VERB
ejpam-4944	34	40	d	d	PROPN
ejpam-4944	34	41	[	[	X
ejpam-4944	34	42	12	12	NUM
ejpam-4944	34	43	]	]	PUNCT
ejpam-4944	34	44	.	.	PUNCT
ejpam-4944	35	1	here	here	ADV
ejpam-4944	35	2	,	,	PUNCT
ejpam-4944	35	3	the	the	DET
ejpam-4944	35	4	interior	interior	ADJ
ejpam-4944	35	5	and	and	CCONJ
ejpam-4944	35	6	closure	closure	NOUN
ejpam-4944	35	7	of	of	ADP
ejpam-4944	35	8	the	the	DET
ejpam-4944	35	9	set	set	NOUN
ejpam-4944	35	10	q	q	NOUN
ejpam-4944	35	11	are	be	AUX
ejpam-4944	35	12	notated	notate	VERB
ejpam-4944	35	13	by	by	ADP
ejpam-4944	35	14	iq	iq	NOUN
ejpam-4944	35	15	and	and	CCONJ
ejpam-4944	35	16	cq	cq	NOUN
ejpam-4944	35	17	,	,	PUNCT
ejpam-4944	35	18	respectively	respectively	ADV
ejpam-4944	35	19	,	,	PUNCT
ejpam-4944	35	20	when	when	SCONJ
ejpam-4944	35	21	no	no	DET
ejpam-4944	35	22	confusion	confusion	NOUN
ejpam-4944	35	23	can	can	AUX
ejpam-4944	35	24	arise	arise	VERB
ejpam-4944	35	25	.	.	PUNCT
ejpam-4944	36	1	in	in	ADP
ejpam-4944	36	2	[	[	X
ejpam-4944	36	3	11	11	NUM
ejpam-4944	36	4	]	]	PUNCT
ejpam-4944	36	5	,	,	PUNCT
ejpam-4944	36	6	notated	notate	VERB
ejpam-4944	36	7	by	by	ADP
ejpam-4944	36	8	;	;	PUNCT
ejpam-4944	36	9	µ̃	µ̃	PROPN
ejpam-4944	36	10	=	=	SYM
ejpam-4944	36	11	{	{	PUNCT
ejpam-4944	36	12	d	d	X
ejpam-4944	36	13	∈	∈	PROPN
ejpam-4944	36	14	µ	µ	PRON
ejpam-4944	36	15	|	|	NOUN
ejpam-4944	36	16	d	d	PROPN
ejpam-4944	36	17	̸=	̸=	PROPN
ejpam-4944	36	18	∅	∅	NOUN
ejpam-4944	36	19	}	}	PUNCT
ejpam-4944	36	20	;	;	PUNCT
ejpam-4944	36	21	µ(x	µ(x	X
ejpam-4944	36	22	)	)	PUNCT
ejpam-4944	36	23	=	=	SYM
ejpam-4944	36	24	{	{	PUNCT
ejpam-4944	36	25	d	d	X
ejpam-4944	36	26	∈	∈	PROPN
ejpam-4944	36	27	µ	µ	NOUN
ejpam-4944	36	28	|	|	NOUN
ejpam-4944	36	29	x	x	SYM
ejpam-4944	36	30	∈	∈	PROPN
ejpam-4944	36	31	d	d	NOUN
ejpam-4944	36	32	}	}	PUNCT
ejpam-4944	36	33	.	.	PUNCT
ejpam-4944	37	1	definition	definition	NOUN
ejpam-4944	37	2	1	1	NUM
ejpam-4944	37	3	.	.	PUNCT
ejpam-4944	38	1	[	[	X
ejpam-4944	38	2	8	8	NUM
ejpam-4944	38	3	]	]	PUNCT
ejpam-4944	38	4	a	a	DET
ejpam-4944	38	5	subset	subset	NOUN
ejpam-4944	38	6	q	q	NOUN
ejpam-4944	38	7	of	of	ADP
ejpam-4944	38	8	a	a	DET
ejpam-4944	38	9	gts	gts	NOUN
ejpam-4944	38	10	(	(	PUNCT
ejpam-4944	38	11	x,µ	x,µ	NOUN
ejpam-4944	38	12	)	)	PUNCT
ejpam-4944	38	13	is	be	AUX
ejpam-4944	38	14	said	say	VERB
ejpam-4944	38	15	to	to	PART
ejpam-4944	38	16	be	be	AUX
ejpam-4944	38	17	;	;	PUNCT
ejpam-4944	38	18	•	•	ADP
ejpam-4944	38	19	µ-nowhere	µ-nowhere	ADP
ejpam-4944	38	20	dense	dense	ADJ
ejpam-4944	38	21	if	if	SCONJ
ejpam-4944	38	22	icq	icq	NOUN
ejpam-4944	38	23	=	=	PUNCT
ejpam-4944	38	24	∅.	∅.	NUM
ejpam-4944	38	25	•	•	NUM
ejpam-4944	38	26	µ-dense	µ-dense	NOUN
ejpam-4944	38	27	if	if	SCONJ
ejpam-4944	38	28	cq	cq	PROPN
ejpam-4944	38	29	=	=	PUNCT
ejpam-4944	38	30	x.	x.	NOUN
ejpam-4944	38	31	•	•	NOUN
ejpam-4944	38	32	µ-codense	µ-codense	NOUN
ejpam-4944	39	1	[	[	X
ejpam-4944	39	2	7	7	X
ejpam-4944	39	3	]	]	X
ejpam-4944	39	4	if	if	SCONJ
ejpam-4944	39	5	c(x	c(x	NOUN
ejpam-4944	39	6	−q	−q	NOUN
ejpam-4944	39	7	)	)	PUNCT
ejpam-4944	39	8	=	=	PUNCT
ejpam-4944	40	1	x.	x.	NOUN
ejpam-4944	40	2	definition	definition	NOUN
ejpam-4944	40	3	2	2	NUM
ejpam-4944	40	4	.	.	PUNCT
ejpam-4944	41	1	[	[	X
ejpam-4944	41	2	11	11	NUM
ejpam-4944	41	3	]	]	PUNCT
ejpam-4944	41	4	a	a	DET
ejpam-4944	41	5	subset	subset	NOUN
ejpam-4944	41	6	q	q	NOUN
ejpam-4944	41	7	of	of	ADP
ejpam-4944	41	8	x	x	PROPN
ejpam-4944	41	9	is	be	AUX
ejpam-4944	41	10	called	call	VERB
ejpam-4944	41	11	as	as	ADP
ejpam-4944	41	12	;	;	PUNCT
ejpam-4944	41	13	•	•	NUM
ejpam-4944	41	14	µ-meager	µ-meager	NOUN
ejpam-4944	41	15	if	if	SCONJ
ejpam-4944	41	16	q	q	PROPN
ejpam-4944	41	17	=	=	SYM
ejpam-4944	41	18	⋃	⋃	PROPN
ejpam-4944	41	19	m∈nqm	m∈nqm	PROPN
ejpam-4944	41	20	where	where	SCONJ
ejpam-4944	41	21	each	each	DET
ejpam-4944	41	22	qm	qm	PROPN
ejpam-4944	41	23	is	be	AUX
ejpam-4944	41	24	a	a	DET
ejpam-4944	41	25	µ-nowhere	µ-nowhere	ADV
ejpam-4944	41	26	dense	dense	ADJ
ejpam-4944	41	27	set	set	NOUN
ejpam-4944	41	28	.	.	PUNCT
ejpam-4944	42	1	•	•	NUM
ejpam-4944	42	2	µ-second	µ-second	NOUN
ejpam-4944	42	3	category	category	NOUN
ejpam-4944	42	4	if	if	SCONJ
ejpam-4944	42	5	q	q	NOUN
ejpam-4944	42	6	is	be	AUX
ejpam-4944	42	7	not	not	PART
ejpam-4944	42	8	µ-meager	µ-meager	NOUN
ejpam-4944	42	9	.	.	PUNCT
ejpam-4944	43	1	in	in	ADP
ejpam-4944	43	2	[	[	X
ejpam-4944	43	3	11	11	NUM
ejpam-4944	43	4	]	]	PUNCT
ejpam-4944	43	5	,	,	PUNCT
ejpam-4944	43	6	defined	define	VERB
ejpam-4944	43	7	two	two	NUM
ejpam-4944	43	8	new	new	ADJ
ejpam-4944	43	9	generalized	generalized	ADJ
ejpam-4944	43	10	topologies	topology	NOUN
ejpam-4944	43	11	;	;	PUNCT
ejpam-4944	43	12	µ⋆	µ⋆	PUNCT
ejpam-4944	43	13	=	=	PRON
ejpam-4944	43	14	{	{	PUNCT
ejpam-4944	43	15	⋃	⋃	PROPN
ejpam-4944	43	16	t(l	t(l	PROPN
ejpam-4944	43	17	t	t	PROPN
ejpam-4944	43	18	1	1	NUM
ejpam-4944	43	19	∩	∩	NOUN
ejpam-4944	43	20	lt	lt	PRON
ejpam-4944	43	21	2	2	NUM
ejpam-4944	43	22	∩	∩	X
ejpam-4944	43	23	lt	lt	PRON
ejpam-4944	43	24	3	3	NUM
ejpam-4944	43	25	∩	∩	X
ejpam-4944	43	26	...	...	PUNCT
ejpam-4944	43	27	∩	∩	NOUN
ejpam-4944	43	28	lt	lt	VERB
ejpam-4944	43	29	nt	not	PART
ejpam-4944	43	30	)	)	PUNCT
ejpam-4944	44	1	|	|	ADV
ejpam-4944	44	2	lt	lt	DET
ejpam-4944	44	3	1	1	NUM
ejpam-4944	44	4	,	,	PUNCT
ejpam-4944	44	5	l	l	PROPN
ejpam-4944	44	6	t	t	NOUN
ejpam-4944	44	7	2	2	NUM
ejpam-4944	44	8	,	,	PUNCT
ejpam-4944	44	9	...	...	PUNCT
ejpam-4944	44	10	,	,	PUNCT
ejpam-4944	44	11	l	l	NOUN
ejpam-4944	44	12	t	t	X
ejpam-4944	44	13	nt	not	PART
ejpam-4944	44	14	∈	∈	PROPN
ejpam-4944	44	15	µ	µ	X
ejpam-4944	44	16	}	}	PUNCT
ejpam-4944	44	17	;	;	PUNCT
ejpam-4944	44	18	µ⋆⋆	µ⋆⋆	ADJ
ejpam-4944	44	19	=	=	PUNCT
ejpam-4944	44	20	{	{	PUNCT
ejpam-4944	44	21	d	d	X
ejpam-4944	44	22	⊂	⊂	PROPN
ejpam-4944	44	23	x	x	PUNCT
ejpam-4944	45	1	|	|	ADV
ejpam-4944	45	2	d	d	NOUN
ejpam-4944	45	3	is	be	AUX
ejpam-4944	45	4	of	of	ADP
ejpam-4944	45	5	µ-ii	µ-ii	PROPN
ejpam-4944	45	6	category	category	NOUN
ejpam-4944	45	7	}	}	PUNCT
ejpam-4944	45	8	.	.	PUNCT
ejpam-4944	46	1	d.	d.	PROPN
ejpam-4944	46	2	elgezouli	elgezouli	PROPN
ejpam-4944	46	3	et	et	PROPN
ejpam-4944	46	4	al	al	PROPN
ejpam-4944	46	5	.	.	PUNCT
ejpam-4944	46	6	/	/	SYM
ejpam-4944	46	7	eur	eur	PROPN
ejpam-4944	46	8	.	.	PUNCT
ejpam-4944	47	1	j.	j.	PROPN
ejpam-4944	47	2	pure	pure	PROPN
ejpam-4944	47	3	appl	appl	PROPN
ejpam-4944	47	4	.	.	PROPN
ejpam-4944	47	5	math	math	PROPN
ejpam-4944	47	6	,	,	PUNCT
ejpam-4944	47	7	16	16	NUM
ejpam-4944	47	8	(	(	PUNCT
ejpam-4944	47	9	4	4	NUM
ejpam-4944	47	10	)	)	PUNCT
ejpam-4944	47	11	(	(	PUNCT
ejpam-4944	47	12	2023	2023	NUM
ejpam-4944	47	13	)	)	PUNCT
ejpam-4944	47	14	,	,	PUNCT
ejpam-4944	47	15	2286	2286	NUM
ejpam-4944	47	16	-	-	SYM
ejpam-4944	47	17	2305	2305	NUM
ejpam-4944	47	18	2288	2288	NUM
ejpam-4944	47	19	obviously	obviously	ADV
ejpam-4944	47	20	,	,	PUNCT
ejpam-4944	47	21	µ	µ	X
ejpam-4944	47	22	⊂	⊂	X
ejpam-4944	47	23	µ⋆	µ⋆	X
ejpam-4944	47	24	and	and	CCONJ
ejpam-4944	47	25	µ⋆	µ⋆	PUNCT
ejpam-4944	47	26	is	be	AUX
ejpam-4944	47	27	closed	close	VERB
ejpam-4944	47	28	under	under	ADP
ejpam-4944	47	29	finite	finite	ADJ
ejpam-4944	47	30	intersection	intersection	NOUN
ejpam-4944	47	31	[	[	X
ejpam-4944	47	32	11	11	NUM
ejpam-4944	47	33	]	]	PUNCT
ejpam-4944	47	34	.	.	PUNCT
ejpam-4944	48	1	definition	definition	NOUN
ejpam-4944	48	2	3	3	NUM
ejpam-4944	48	3	.	.	PUNCT
ejpam-4944	49	1	[	[	X
ejpam-4944	49	2	6	6	NUM
ejpam-4944	49	3	]	]	PUNCT
ejpam-4944	49	4	let	let	VERB
ejpam-4944	49	5	(	(	PUNCT
ejpam-4944	49	6	x,µ	x,µ	NOUN
ejpam-4944	49	7	)	)	PUNCT
ejpam-4944	49	8	be	be	VERB
ejpam-4944	49	9	a	a	DET
ejpam-4944	49	10	gts	gts	NOUN
ejpam-4944	49	11	and	and	CCONJ
ejpam-4944	49	12	q	q	NOUN
ejpam-4944	49	13	⊂	⊂	PROPN
ejpam-4944	49	14	x	x	X
ejpam-4944	49	15	is	be	AUX
ejpam-4944	49	16	called	call	VERB
ejpam-4944	49	17	;	;	PUNCT
ejpam-4944	49	18	•	•	NUM
ejpam-4944	49	19	µ-semi	µ-semi	NOUN
ejpam-4944	49	20	-	-	ADJ
ejpam-4944	49	21	open	open	ADJ
ejpam-4944	49	22	if	if	SCONJ
ejpam-4944	49	23	q	q	X
ejpam-4944	49	24	⊂	⊂	PROPN
ejpam-4944	49	25	cµ(iµ(q	cµ(iµ(q	PROPN
ejpam-4944	49	26	)	)	PUNCT
ejpam-4944	49	27	)	)	PUNCT
ejpam-4944	49	28	.	.	PUNCT
ejpam-4944	50	1	•	•	NUM
ejpam-4944	50	2	µ-pre	µ-pre	ADV
ejpam-4944	50	3	-	-	PUNCT
ejpam-4944	50	4	open	open	ADJ
ejpam-4944	50	5	if	if	SCONJ
ejpam-4944	50	6	q	q	X
ejpam-4944	50	7	⊂	⊂	PROPN
ejpam-4944	50	8	iµ(cµ(q	iµ(cµ(q	NUM
ejpam-4944	50	9	)	)	PUNCT
ejpam-4944	50	10	)	)	PUNCT
ejpam-4944	50	11	.	.	PUNCT
ejpam-4944	51	1	•	•	NUM
ejpam-4944	51	2	µ-α	µ-α	NOUN
ejpam-4944	51	3	-	-	PUNCT
ejpam-4944	51	4	open	open	ADJ
ejpam-4944	51	5	if	if	SCONJ
ejpam-4944	51	6	q	q	X
ejpam-4944	51	7	⊂	⊂	PROPN
ejpam-4944	51	8	iµ(cµ(iµ(q	iµ(cµ(iµ(q	NOUN
ejpam-4944	51	9	)	)	PUNCT
ejpam-4944	51	10	)	)	PUNCT
ejpam-4944	51	11	)	)	PUNCT
ejpam-4944	51	12	.	.	PUNCT
ejpam-4944	52	1	•	•	NUM
ejpam-4944	52	2	µ-β	µ-β	ADV
ejpam-4944	52	3	-	-	PUNCT
ejpam-4944	52	4	open	open	ADJ
ejpam-4944	52	5	if	if	SCONJ
ejpam-4944	52	6	q	q	X
ejpam-4944	52	7	⊂	⊂	X
ejpam-4944	52	8	cµ(iµ(cµ(q	cµ(iµ(cµ(q	ADJ
ejpam-4944	52	9	)	)	PUNCT
ejpam-4944	52	10	)	)	PUNCT
ejpam-4944	52	11	)	)	PUNCT
ejpam-4944	52	12	.	.	PUNCT
ejpam-4944	53	1	•	•	NUM
ejpam-4944	53	2	µ-b	µ-b	ADV
ejpam-4944	53	3	-	-	ADJ
ejpam-4944	53	4	open	open	ADJ
ejpam-4944	53	5	[	[	X
ejpam-4944	53	6	1	1	NUM
ejpam-4944	53	7	]	]	PUNCT
ejpam-4944	53	8	if	if	SCONJ
ejpam-4944	53	9	q	q	PROPN
ejpam-4944	53	10	⊂	⊂	PROPN
ejpam-4944	53	11	cµ(iµ(q	cµ(iµ(q	PROPN
ejpam-4944	53	12	)	)	PUNCT
ejpam-4944	53	13	)	)	PUNCT
ejpam-4944	53	14	∪	∪	ADP
ejpam-4944	53	15	iµ(cµ(q	iµ(cµ(q	NOUN
ejpam-4944	53	16	)	)	PUNCT
ejpam-4944	53	17	)	)	PUNCT
ejpam-4944	53	18	.	.	PUNCT
ejpam-4944	54	1	moreover	moreover	ADV
ejpam-4944	54	2	,	,	PUNCT
ejpam-4944	54	3	σ(µ	σ(µ	PROPN
ejpam-4944	54	4	)	)	PUNCT
ejpam-4944	54	5	or	or	CCONJ
ejpam-4944	54	6	σ(µ(x	σ(µ(x	PROPN
ejpam-4944	54	7	)	)	PUNCT
ejpam-4944	54	8	)	)	PUNCT
ejpam-4944	55	1	=	=	PRON
ejpam-4944	55	2	{	{	PUNCT
ejpam-4944	55	3	q	q	X
ejpam-4944	55	4	⊂	⊂	X
ejpam-4944	55	5	x	x	PUNCT
ejpam-4944	56	1	|	|	ADV
ejpam-4944	56	2	q	q	NOUN
ejpam-4944	56	3	is	be	AUX
ejpam-4944	56	4	µ-semi	µ-semi	NOUN
ejpam-4944	56	5	-	-	ADJ
ejpam-4944	56	6	open	open	ADJ
ejpam-4944	56	7	set	set	NOUN
ejpam-4944	56	8	in	in	ADP
ejpam-4944	56	9	x	x	X
ejpam-4944	56	10	}	}	PUNCT
ejpam-4944	56	11	[	[	X
ejpam-4944	56	12	12	12	NUM
ejpam-4944	56	13	]	]	PUNCT
ejpam-4944	56	14	.	.	PUNCT
ejpam-4944	57	1	the	the	DET
ejpam-4944	57	2	µsemi	µsemi	NOUN
ejpam-4944	57	3	-	-	NOUN
ejpam-4944	57	4	interior	interior	NOUN
ejpam-4944	57	5	of	of	ADP
ejpam-4944	57	6	a	a	DET
ejpam-4944	57	7	subset	subset	NOUN
ejpam-4944	57	8	q	q	NOUN
ejpam-4944	57	9	of	of	ADP
ejpam-4944	57	10	(	(	PUNCT
ejpam-4944	57	11	x,µ	x,µ	NOUN
ejpam-4944	57	12	)	)	PUNCT
ejpam-4944	57	13	,	,	PUNCT
ejpam-4944	57	14	denoted	denote	VERB
ejpam-4944	57	15	by	by	ADP
ejpam-4944	57	16	iσ(q	iσ(q	NOUN
ejpam-4944	57	17	)	)	PUNCT
ejpam-4944	57	18	,	,	PUNCT
ejpam-4944	57	19	is	be	AUX
ejpam-4944	57	20	defined	define	VERB
ejpam-4944	57	21	by	by	ADP
ejpam-4944	57	22	the	the	DET
ejpam-4944	57	23	union	union	NOUN
ejpam-4944	57	24	of	of	ADP
ejpam-4944	57	25	all	all	DET
ejpam-4944	57	26	µ-semi	µ-semi	NOUN
ejpam-4944	57	27	-	-	ADJ
ejpam-4944	57	28	open	open	ADJ
ejpam-4944	57	29	subsets	subset	NOUN
ejpam-4944	57	30	of	of	ADP
ejpam-4944	57	31	x	x	PUNCT
ejpam-4944	57	32	contained	contain	VERB
ejpam-4944	57	33	in	in	ADP
ejpam-4944	57	34	q	q	NOUN
ejpam-4944	58	1	[	[	X
ejpam-4944	58	2	12	12	NUM
ejpam-4944	58	3	]	]	PUNCT
ejpam-4944	58	4	.	.	PUNCT
ejpam-4944	59	1	definition	definition	NOUN
ejpam-4944	59	2	4	4	NUM
ejpam-4944	59	3	.	.	PUNCT
ejpam-4944	60	1	[	[	X
ejpam-4944	60	2	2	2	X
ejpam-4944	60	3	]	]	PUNCT
ejpam-4944	60	4	let	let	VERB
ejpam-4944	60	5	µ1	µ1	NOUN
ejpam-4944	60	6	and	and	CCONJ
ejpam-4944	60	7	µ2	µ2	PROPN
ejpam-4944	60	8	be	be	AUX
ejpam-4944	60	9	two	two	NUM
ejpam-4944	60	10	generalized	generalized	ADJ
ejpam-4944	60	11	topologies	topology	NOUN
ejpam-4944	60	12	defined	define	VERB
ejpam-4944	60	13	a	a	DET
ejpam-4944	60	14	non	non	ADJ
ejpam-4944	60	15	-	-	ADJ
ejpam-4944	60	16	null	null	ADJ
ejpam-4944	60	17	set	set	NOUN
ejpam-4944	60	18	x.	x.	NOUN
ejpam-4944	60	19	a	a	DET
ejpam-4944	60	20	triple	triple	ADJ
ejpam-4944	60	21	(	(	PUNCT
ejpam-4944	60	22	x,µ1	x,µ1	NOUN
ejpam-4944	60	23	,	,	PUNCT
ejpam-4944	60	24	µ2	µ2	PROPN
ejpam-4944	60	25	)	)	PUNCT
ejpam-4944	60	26	is	be	AUX
ejpam-4944	60	27	called	call	VERB
ejpam-4944	60	28	a	a	DET
ejpam-4944	60	29	bigeneralized	bigeneralize	VERB
ejpam-4944	60	30	topological	topological	ADJ
ejpam-4944	60	31	space	space	NOUN
ejpam-4944	60	32	(	(	PUNCT
ejpam-4944	60	33	briefly	briefly	ADV
ejpam-4944	60	34	,	,	PUNCT
ejpam-4944	60	35	bgts	bgts	PROPN
ejpam-4944	60	36	)	)	PUNCT
ejpam-4944	60	37	.	.	PUNCT
ejpam-4944	61	1	•	•	NUM
ejpam-4944	61	2	the	the	DET
ejpam-4944	61	3	closure	closure	NOUN
ejpam-4944	61	4	and	and	CCONJ
ejpam-4944	61	5	interior	interior	NOUN
ejpam-4944	61	6	of	of	ADP
ejpam-4944	61	7	q	q	PROPN
ejpam-4944	61	8	⊂	⊂	PROPN
ejpam-4944	61	9	x	x	PUNCT
ejpam-4944	61	10	with	with	SCONJ
ejpam-4944	61	11	respect	respect	NOUN
ejpam-4944	61	12	to	to	ADP
ejpam-4944	61	13	µs	µs	NOUN
ejpam-4944	61	14	are	be	AUX
ejpam-4944	61	15	denoted	denote	VERB
ejpam-4944	61	16	by	by	ADP
ejpam-4944	61	17	cs(q	cs(q	NOUN
ejpam-4944	61	18	)	)	PUNCT
ejpam-4944	61	19	and	and	CCONJ
ejpam-4944	61	20	is(q	is(q	NOUN
ejpam-4944	61	21	)	)	PUNCT
ejpam-4944	61	22	,	,	PUNCT
ejpam-4944	61	23	respectively	respectively	ADV
ejpam-4944	61	24	,	,	PUNCT
ejpam-4944	61	25	for	for	ADP
ejpam-4944	61	26	s	s	NOUN
ejpam-4944	61	27	=	=	SYM
ejpam-4944	61	28	1	1	NUM
ejpam-4944	61	29	,	,	PUNCT
ejpam-4944	61	30	2	2	NUM
ejpam-4944	61	31	.	.	NOUN
ejpam-4944	61	32	•	•	NUM
ejpam-4944	61	33	q	q	NOUN
ejpam-4944	61	34	is	be	AUX
ejpam-4944	61	35	called	call	VERB
ejpam-4944	61	36	(	(	PUNCT
ejpam-4944	61	37	s	s	PROPN
ejpam-4944	61	38	,	,	PUNCT
ejpam-4944	61	39	v)-closed	v)-close	VERB
ejpam-4944	61	40	if	if	SCONJ
ejpam-4944	61	41	cs(cv(q	cs(cv(q	NOUN
ejpam-4944	61	42	)	)	PUNCT
ejpam-4944	61	43	)	)	PUNCT
ejpam-4944	62	1	=	=	PUNCT
ejpam-4944	62	2	d	d	NOUN
ejpam-4944	62	3	,	,	PUNCT
ejpam-4944	62	4	where	where	SCONJ
ejpam-4944	62	5	s	s	X
ejpam-4944	62	6	,	,	PUNCT
ejpam-4944	62	7	v	v	NOUN
ejpam-4944	62	8	=	=	SYM
ejpam-4944	62	9	1	1	NUM
ejpam-4944	62	10	or	or	CCONJ
ejpam-4944	62	11	2	2	NUM
ejpam-4944	62	12	;	;	PUNCT
ejpam-4944	62	13	s	s	VERB
ejpam-4944	62	14	̸=	̸=	PROPN
ejpam-4944	62	15	v.	v.	ADP
ejpam-4944	62	16	•	•	NUM
ejpam-4944	62	17	q	q	NOUN
ejpam-4944	62	18	is	be	AUX
ejpam-4944	62	19	called	call	VERB
ejpam-4944	62	20	(	(	PUNCT
ejpam-4944	62	21	s	s	NOUN
ejpam-4944	62	22	,	,	PUNCT
ejpam-4944	62	23	v)-open	v)-open	VERB
ejpam-4944	62	24	if	if	SCONJ
ejpam-4944	62	25	x	x	PRON
ejpam-4944	62	26	−q	−q	NOUN
ejpam-4944	62	27	is	be	AUX
ejpam-4944	62	28	(	(	PUNCT
ejpam-4944	62	29	s	s	PROPN
ejpam-4944	62	30	,	,	PUNCT
ejpam-4944	62	31	v)-closed	v)-close	VERB
ejpam-4944	62	32	where	where	SCONJ
ejpam-4944	62	33	s	s	X
ejpam-4944	62	34	,	,	PUNCT
ejpam-4944	62	35	v	v	NOUN
ejpam-4944	62	36	=	=	SYM
ejpam-4944	62	37	1	1	NUM
ejpam-4944	62	38	or	or	CCONJ
ejpam-4944	62	39	2	2	NUM
ejpam-4944	62	40	;	;	PUNCT
ejpam-4944	62	41	s	s	VERB
ejpam-4944	62	42	̸=	̸=	PROPN
ejpam-4944	62	43	v.	v.	ADP
ejpam-4944	62	44	a	a	DET
ejpam-4944	62	45	subset	subset	NOUN
ejpam-4944	62	46	q	q	NOUN
ejpam-4944	62	47	of	of	ADP
ejpam-4944	62	48	a	a	DET
ejpam-4944	62	49	bgts	bgts	NOUN
ejpam-4944	62	50	(	(	PUNCT
ejpam-4944	62	51	x,µ1	x,µ1	PROPN
ejpam-4944	62	52	,	,	PUNCT
ejpam-4944	62	53	µ2	µ2	PROPN
ejpam-4944	62	54	)	)	PUNCT
ejpam-4944	62	55	is	be	AUX
ejpam-4944	62	56	said	say	VERB
ejpam-4944	62	57	to	to	PART
ejpam-4944	62	58	be	be	AUX
ejpam-4944	62	59	(	(	PUNCT
ejpam-4944	62	60	1	1	NUM
ejpam-4944	62	61	)	)	PUNCT
ejpam-4944	62	62	(	(	PUNCT
ejpam-4944	62	63	s	s	X
ejpam-4944	62	64	,	,	PUNCT
ejpam-4944	62	65	v)-µ-regular	v)-µ-regular	ADV
ejpam-4944	62	66	open	open	ADJ
ejpam-4944	62	67	if	if	SCONJ
ejpam-4944	62	68	q	q	NOUN
ejpam-4944	62	69	=	=	NOUN
ejpam-4944	62	70	is(cv(q	is(cv(q	NOUN
ejpam-4944	62	71	)	)	PUNCT
ejpam-4944	62	72	)	)	PUNCT
ejpam-4944	62	73	where	where	SCONJ
ejpam-4944	62	74	s	s	X
ejpam-4944	62	75	,	,	PUNCT
ejpam-4944	62	76	v	v	NOUN
ejpam-4944	62	77	=	=	SYM
ejpam-4944	62	78	1	1	NUM
ejpam-4944	62	79	or	or	CCONJ
ejpam-4944	62	80	2	2	NUM
ejpam-4944	62	81	;	;	PUNCT
ejpam-4944	62	82	s	s	VERB
ejpam-4944	62	83	̸=	̸=	PROPN
ejpam-4944	62	84	v.	v.	CCONJ
ejpam-4944	62	85	(	(	PUNCT
ejpam-4944	62	86	2	2	NUM
ejpam-4944	62	87	)	)	PUNCT
ejpam-4944	62	88	(	(	PUNCT
ejpam-4944	62	89	s	s	X
ejpam-4944	62	90	,	,	PUNCT
ejpam-4944	62	91	v)-µ-semi	v)-µ-semi	NOUN
ejpam-4944	62	92	-	-	PUNCT
ejpam-4944	62	93	open	open	ADJ
ejpam-4944	62	94	if	if	SCONJ
ejpam-4944	62	95	q	q	NOUN
ejpam-4944	62	96	⊆	⊆	NUM
ejpam-4944	62	97	cv(is(q	cv(is(q	NOUN
ejpam-4944	62	98	)	)	PUNCT
ejpam-4944	62	99	)	)	PUNCT
ejpam-4944	62	100	where	where	SCONJ
ejpam-4944	62	101	s	s	X
ejpam-4944	62	102	,	,	PUNCT
ejpam-4944	62	103	v	v	NOUN
ejpam-4944	62	104	=	=	SYM
ejpam-4944	62	105	1	1	NUM
ejpam-4944	62	106	or	or	CCONJ
ejpam-4944	62	107	2	2	NUM
ejpam-4944	62	108	;	;	PUNCT
ejpam-4944	62	109	s	s	VERB
ejpam-4944	62	110	̸=	̸=	PROPN
ejpam-4944	62	111	v.	v.	CCONJ
ejpam-4944	62	112	(	(	PUNCT
ejpam-4944	62	113	3	3	NUM
ejpam-4944	62	114	)	)	PUNCT
ejpam-4944	62	115	(	(	PUNCT
ejpam-4944	62	116	s	s	X
ejpam-4944	62	117	,	,	PUNCT
ejpam-4944	62	118	v)-µ-preopen	v)-µ-preopen	VERB
ejpam-4944	62	119	if	if	SCONJ
ejpam-4944	62	120	q	q	NOUN
ejpam-4944	62	121	⊆	⊆	NUM
ejpam-4944	62	122	is(cv(q	is(cv(q	NOUN
ejpam-4944	62	123	)	)	PUNCT
ejpam-4944	62	124	)	)	PUNCT
ejpam-4944	62	125	where	where	SCONJ
ejpam-4944	62	126	s	s	X
ejpam-4944	62	127	,	,	PUNCT
ejpam-4944	62	128	v	v	NOUN
ejpam-4944	62	129	=	=	SYM
ejpam-4944	62	130	1	1	NUM
ejpam-4944	62	131	or	or	CCONJ
ejpam-4944	62	132	2	2	NUM
ejpam-4944	62	133	;	;	PUNCT
ejpam-4944	62	134	s	s	VERB
ejpam-4944	62	135	̸=	̸=	PROPN
ejpam-4944	62	136	v.	v.	CCONJ
ejpam-4944	62	137	(	(	PUNCT
ejpam-4944	62	138	4	4	NUM
ejpam-4944	62	139	)	)	PUNCT
ejpam-4944	62	140	(	(	PUNCT
ejpam-4944	62	141	s	s	X
ejpam-4944	62	142	,	,	PUNCT
ejpam-4944	62	143	v)-µ-α	v)-µ-α	NOUN
ejpam-4944	62	144	-	-	PUNCT
ejpam-4944	62	145	open	open	ADJ
ejpam-4944	62	146	if	if	SCONJ
ejpam-4944	62	147	q	q	PROPN
ejpam-4944	62	148	⊆	⊆	NUM
ejpam-4944	62	149	is(cv(is(q	is(cv(is(q	NOUN
ejpam-4944	62	150	)	)	PUNCT
ejpam-4944	62	151	)	)	PUNCT
ejpam-4944	62	152	)	)	PUNCT
ejpam-4944	62	153	where	where	SCONJ
ejpam-4944	62	154	s	s	X
ejpam-4944	62	155	,	,	PUNCT
ejpam-4944	62	156	v	v	NOUN
ejpam-4944	62	157	=	=	SYM
ejpam-4944	62	158	1	1	NUM
ejpam-4944	62	159	or	or	CCONJ
ejpam-4944	62	160	2	2	NUM
ejpam-4944	62	161	;	;	PUNCT
ejpam-4944	62	162	s	s	VERB
ejpam-4944	62	163	̸=	̸=	PROPN
ejpam-4944	62	164	v	v	NOUN
ejpam-4944	62	165	[	[	X
ejpam-4944	62	166	2	2	NUM
ejpam-4944	62	167	]	]	PUNCT
ejpam-4944	62	168	.	.	PUNCT
ejpam-4944	63	1	lemma	lemma	PROPN
ejpam-4944	63	2	1	1	NUM
ejpam-4944	63	3	.	.	PUNCT
ejpam-4944	64	1	[	[	X
ejpam-4944	64	2	2	2	NUM
ejpam-4944	64	3	,	,	PUNCT
ejpam-4944	64	4	proposition	proposition	NOUN
ejpam-4944	64	5	3.4	3.4	NUM
ejpam-4944	64	6	]	]	PUNCT
ejpam-4944	64	7	let	let	NOUN
ejpam-4944	64	8	(	(	PUNCT
ejpam-4944	64	9	x,µ1	x,µ1	NOUN
ejpam-4944	64	10	,	,	PUNCT
ejpam-4944	64	11	µ2	µ2	PROPN
ejpam-4944	64	12	)	)	PUNCT
ejpam-4944	64	13	be	be	VERB
ejpam-4944	64	14	a	a	DET
ejpam-4944	64	15	bgts	bgts	NOUN
ejpam-4944	64	16	and	and	CCONJ
ejpam-4944	64	17	q	q	PROPN
ejpam-4944	64	18	⊂	⊂	PROPN
ejpam-4944	64	19	x.	x.	NOUN
ejpam-4944	65	1	then	then	ADV
ejpam-4944	65	2	q	q	X
ejpam-4944	65	3	is	be	AUX
ejpam-4944	65	4	(	(	PUNCT
ejpam-4944	65	5	s	s	X
ejpam-4944	65	6	,	,	PUNCT
ejpam-4944	65	7	v)closed	v)close	VERB
ejpam-4944	65	8	if	if	SCONJ
ejpam-4944	65	9	and	and	CCONJ
ejpam-4944	65	10	only	only	ADV
ejpam-4944	65	11	if	if	SCONJ
ejpam-4944	65	12	q	q	NOUN
ejpam-4944	65	13	is	be	AUX
ejpam-4944	65	14	both	both	PRON
ejpam-4944	65	15	µ-closed	µ-close	VERB
ejpam-4944	65	16	in	in	ADP
ejpam-4944	65	17	(	(	PUNCT
ejpam-4944	65	18	x,µs	x,µs	NUM
ejpam-4944	65	19	)	)	PUNCT
ejpam-4944	65	20	and	and	CCONJ
ejpam-4944	65	21	(	(	PUNCT
ejpam-4944	65	22	x,µv	x,µv	PROPN
ejpam-4944	65	23	)	)	PUNCT
ejpam-4944	65	24	where	where	SCONJ
ejpam-4944	65	25	s	s	X
ejpam-4944	65	26	,	,	PUNCT
ejpam-4944	65	27	v	v	NOUN
ejpam-4944	65	28	=	=	SYM
ejpam-4944	65	29	1	1	NUM
ejpam-4944	65	30	,	,	PUNCT
ejpam-4944	65	31	2	2	NUM
ejpam-4944	65	32	;	;	PUNCT
ejpam-4944	65	33	s	s	VERB
ejpam-4944	65	34	̸=	̸=	PROPN
ejpam-4944	65	35	v.	v.	ADP
ejpam-4944	65	36	lemma	lemma	PROPN
ejpam-4944	65	37	2	2	NUM
ejpam-4944	65	38	.	.	PUNCT
ejpam-4944	66	1	[	[	X
ejpam-4944	66	2	5	5	NUM
ejpam-4944	66	3	]	]	PUNCT
ejpam-4944	66	4	in	in	ADP
ejpam-4944	66	5	a	a	DET
ejpam-4944	66	6	gts	gts	NOUN
ejpam-4944	66	7	(	(	PUNCT
ejpam-4944	66	8	x,µ	x,µ	NOUN
ejpam-4944	66	9	)	)	PUNCT
ejpam-4944	66	10	,	,	PUNCT
ejpam-4944	66	11	r	r	NOUN
ejpam-4944	66	12	∈	∈	PROPN
ejpam-4944	66	13	cp	cp	INTJ
ejpam-4944	66	14	if	if	SCONJ
ejpam-4944	66	15	and	and	CCONJ
ejpam-4944	66	16	only	only	ADV
ejpam-4944	66	17	if	if	SCONJ
ejpam-4944	66	18	l	l	NOUN
ejpam-4944	66	19	∩	∩	NOUN
ejpam-4944	66	20	p	p	X
ejpam-4944	66	21	̸=	̸=	PROPN
ejpam-4944	66	22	∅	∅	NOUN
ejpam-4944	66	23	for	for	ADP
ejpam-4944	66	24	all	all	DET
ejpam-4944	66	25	l	l	NOUN
ejpam-4944	66	26	∈	∈	PROPN
ejpam-4944	66	27	µ̃(r	µ̃(r	PROPN
ejpam-4944	66	28	)	)	PUNCT
ejpam-4944	66	29	.	.	PUNCT
ejpam-4944	67	1	lemma	lemma	PROPN
ejpam-4944	67	2	3	3	X
ejpam-4944	67	3	.	.	PUNCT
ejpam-4944	68	1	[	[	X
ejpam-4944	68	2	12	12	NUM
ejpam-4944	68	3	,	,	PUNCT
ejpam-4944	68	4	lemma	lemma	PROPN
ejpam-4944	68	5	3.2	3.2	NUM
ejpam-4944	68	6	]	]	PUNCT
ejpam-4944	68	7	let	let	VERB
ejpam-4944	68	8	(	(	PUNCT
ejpam-4944	68	9	x,µ	x,µ	NOUN
ejpam-4944	68	10	)	)	PUNCT
ejpam-4944	68	11	be	be	VERB
ejpam-4944	68	12	a	a	DET
ejpam-4944	68	13	gts	gts	NOUN
ejpam-4944	68	14	and	and	CCONJ
ejpam-4944	68	15	k	k	NOUN
ejpam-4944	68	16	,	,	PUNCT
ejpam-4944	68	17	p	p	PROPN
ejpam-4944	68	18	⊂	⊂	PROPN
ejpam-4944	68	19	x.	x.	NOUN
ejpam-4944	69	1	if	if	SCONJ
ejpam-4944	69	2	k	k	PROPN
ejpam-4944	69	3	∈	∈	PROPN
ejpam-4944	69	4	µ̃	µ̃	PROPN
ejpam-4944	69	5	and	and	CCONJ
ejpam-4944	69	6	k∩p	k∩p	NOUN
ejpam-4944	69	7	=	=	NOUN
ejpam-4944	69	8	∅	∅	NOUN
ejpam-4944	69	9	,	,	PUNCT
ejpam-4944	69	10	then	then	ADV
ejpam-4944	69	11	k	k	PROPN
ejpam-4944	69	12	∩	∩	ADJ
ejpam-4944	69	13	cp	cp	PROPN
ejpam-4944	69	14	=	=	PROPN
ejpam-4944	69	15	∅.	∅.	PRON
ejpam-4944	69	16	lemma	lemma	PROPN
ejpam-4944	69	17	4	4	NUM
ejpam-4944	69	18	.	.	PUNCT
ejpam-4944	70	1	[	[	X
ejpam-4944	70	2	13	13	NUM
ejpam-4944	70	3	,	,	PUNCT
ejpam-4944	70	4	proposition	proposition	NOUN
ejpam-4944	70	5	2.2	2.2	NUM
ejpam-4944	70	6	]	]	PUNCT
ejpam-4944	70	7	let	let	VERB
ejpam-4944	70	8	(	(	PUNCT
ejpam-4944	70	9	x,µ	x,µ	NOUN
ejpam-4944	70	10	)	)	PUNCT
ejpam-4944	70	11	be	be	AUX
ejpam-4944	70	12	a	a	DET
ejpam-4944	70	13	gts	gts	NOUN
ejpam-4944	70	14	.	.	PUNCT
ejpam-4944	71	1	for	for	ADP
ejpam-4944	71	2	subsets	subset	NOUN
ejpam-4944	71	3	q	q	PROPN
ejpam-4944	71	4	,	,	PUNCT
ejpam-4944	71	5	p	p	PROPN
ejpam-4944	71	6	⊂	⊂	PROPN
ejpam-4944	71	7	x	x	NOUN
ejpam-4944	71	8	,	,	PUNCT
ejpam-4944	71	9	then	then	ADV
ejpam-4944	71	10	the	the	DET
ejpam-4944	71	11	following	follow	VERB
ejpam-4944	71	12	properties	property	NOUN
ejpam-4944	71	13	holds	hold	VERB
ejpam-4944	71	14	:	:	PUNCT
ejpam-4944	71	15	(	(	PUNCT
ejpam-4944	71	16	a	a	X
ejpam-4944	71	17	)	)	PUNCT
ejpam-4944	71	18	cµ(x	cµ(x	NOUN
ejpam-4944	71	19	−q	−q	NOUN
ejpam-4944	71	20	)	)	PUNCT
ejpam-4944	71	21	=	=	PUNCT
ejpam-4944	72	1	x	x	X
ejpam-4944	72	2	−	−	NOUN
ejpam-4944	72	3	iµ(q	iµ(q	NUM
ejpam-4944	72	4	)	)	PUNCT
ejpam-4944	72	5	and	and	CCONJ
ejpam-4944	72	6	iµ(x	iµ(x	VERB
ejpam-4944	72	7	−q	−q	NOUN
ejpam-4944	72	8	)	)	PUNCT
ejpam-4944	72	9	=	=	PUNCT
ejpam-4944	73	1	x	x	X
ejpam-4944	73	2	−	−	NOUN
ejpam-4944	73	3	cµ(q	cµ(q	NUM
ejpam-4944	73	4	)	)	PUNCT
ejpam-4944	73	5	.	.	PUNCT
ejpam-4944	74	1	(	(	PUNCT
ejpam-4944	74	2	b	b	X
ejpam-4944	74	3	)	)	PUNCT
ejpam-4944	74	4	if	if	SCONJ
ejpam-4944	74	5	x	x	PRON
ejpam-4944	74	6	−q	−q	NOUN
ejpam-4944	74	7	∈	∈	PROPN
ejpam-4944	74	8	µ	µ	NOUN
ejpam-4944	74	9	,	,	PUNCT
ejpam-4944	74	10	then	then	ADV
ejpam-4944	74	11	cµ(q	cµ(q	NOUN
ejpam-4944	74	12	)	)	PUNCT
ejpam-4944	75	1	=	=	SYM
ejpam-4944	75	2	q	q	NOUN
ejpam-4944	76	1	and	and	CCONJ
ejpam-4944	76	2	if	if	SCONJ
ejpam-4944	76	3	q	q	X
ejpam-4944	76	4	∈	∈	PROPN
ejpam-4944	76	5	µ	µ	NOUN
ejpam-4944	76	6	,	,	PUNCT
ejpam-4944	76	7	then	then	ADV
ejpam-4944	76	8	iµ(q	iµ(q	NUM
ejpam-4944	76	9	)	)	PUNCT
ejpam-4944	76	10	=	=	SYM
ejpam-4944	76	11	q.	q.	NOUN
ejpam-4944	76	12	(	(	PUNCT
ejpam-4944	76	13	c	c	X
ejpam-4944	76	14	)	)	PUNCT
ejpam-4944	76	15	if	if	SCONJ
ejpam-4944	76	16	q	q	PROPN
ejpam-4944	76	17	⊆	⊆	NUM
ejpam-4944	76	18	p	p	NOUN
ejpam-4944	76	19	,	,	PUNCT
ejpam-4944	76	20	then	then	ADV
ejpam-4944	76	21	cµ(q	cµ(q	NOUN
ejpam-4944	76	22	)	)	PUNCT
ejpam-4944	76	23	⊆	⊆	NUM
ejpam-4944	76	24	cµ(p	cµ(p	NUM
ejpam-4944	76	25	)	)	PUNCT
ejpam-4944	76	26	and	and	CCONJ
ejpam-4944	76	27	iµ(q	iµ(q	NUM
ejpam-4944	76	28	)	)	PUNCT
ejpam-4944	76	29	⊆	⊆	NUM
ejpam-4944	76	30	iµ(p	iµ(p	NUM
ejpam-4944	76	31	)	)	PUNCT
ejpam-4944	76	32	.	.	PUNCT
ejpam-4944	77	1	(	(	PUNCT
ejpam-4944	77	2	d	d	X
ejpam-4944	77	3	)	)	PUNCT
ejpam-4944	77	4	q	q	NOUN
ejpam-4944	78	1	⊆	⊆	NUM
ejpam-4944	78	2	cµ(q	cµ(q	NOUN
ejpam-4944	78	3	)	)	PUNCT
ejpam-4944	78	4	and	and	CCONJ
ejpam-4944	78	5	iµ(q	iµ(q	NUM
ejpam-4944	78	6	)	)	PUNCT
ejpam-4944	78	7	⊆	⊆	NUM
ejpam-4944	78	8	q.	q.	NOUN
ejpam-4944	78	9	(	(	PUNCT
ejpam-4944	78	10	e	e	NOUN
ejpam-4944	78	11	)	)	PUNCT
ejpam-4944	78	12	cµ(cµ(q	cµ(cµ(q	NOUN
ejpam-4944	78	13	)	)	PUNCT
ejpam-4944	78	14	)	)	PUNCT
ejpam-4944	79	1	=	=	PUNCT
ejpam-4944	80	1	cµ(q	cµ(q	X
ejpam-4944	80	2	)	)	PUNCT
ejpam-4944	80	3	and	and	CCONJ
ejpam-4944	80	4	iµ(iµ(q	iµ(iµ(q	ADJ
ejpam-4944	80	5	)	)	PUNCT
ejpam-4944	80	6	)	)	PUNCT
ejpam-4944	81	1	=	=	SYM
ejpam-4944	81	2	iµ(q	iµ(q	NUM
ejpam-4944	81	3	)	)	PUNCT
ejpam-4944	81	4	.	.	PUNCT
ejpam-4944	82	1	3	3	X
ejpam-4944	82	2	.	.	X
ejpam-4944	82	3	nature	nature	NOUN
ejpam-4944	82	4	of	of	ADP
ejpam-4944	82	5	(	(	PUNCT
ejpam-4944	82	6	s	s	X
ejpam-4944	82	7	,	,	PUNCT
ejpam-4944	82	8	v)⋆-dense	v)⋆-dense	ADJ
ejpam-4944	82	9	sets	set	NOUN
ejpam-4944	82	10	here	here	ADV
ejpam-4944	82	11	,	,	PUNCT
ejpam-4944	82	12	we	we	PRON
ejpam-4944	82	13	define	define	VERB
ejpam-4944	82	14	another	another	DET
ejpam-4944	82	15	branch	branch	NOUN
ejpam-4944	82	16	of	of	ADP
ejpam-4944	82	17	dense	dense	ADJ
ejpam-4944	82	18	set	set	NOUN
ejpam-4944	82	19	namely	namely	ADV
ejpam-4944	82	20	,	,	PUNCT
ejpam-4944	82	21	(	(	PUNCT
ejpam-4944	82	22	s	s	X
ejpam-4944	82	23	,	,	PUNCT
ejpam-4944	82	24	v)⋆-dense	v)⋆-dense	PROPN
ejpam-4944	82	25	set	set	NOUN
ejpam-4944	82	26	and	and	CCONJ
ejpam-4944	82	27	study	study	VERB
ejpam-4944	82	28	its	its	PRON
ejpam-4944	82	29	significance	significance	NOUN
ejpam-4944	82	30	in	in	ADP
ejpam-4944	82	31	a	a	DET
ejpam-4944	82	32	bgts	bgts	NOUN
ejpam-4944	82	33	.	.	PUNCT
ejpam-4944	83	1	d.	d.	PROPN
ejpam-4944	83	2	elgezouli	elgezouli	PROPN
ejpam-4944	83	3	et	et	PROPN
ejpam-4944	83	4	al	al	PROPN
ejpam-4944	83	5	.	.	PUNCT
ejpam-4944	83	6	/	/	SYM
ejpam-4944	83	7	eur	eur	PROPN
ejpam-4944	83	8	.	.	PUNCT
ejpam-4944	84	1	j.	j.	PROPN
ejpam-4944	84	2	pure	pure	PROPN
ejpam-4944	84	3	appl	appl	PROPN
ejpam-4944	84	4	.	.	PROPN
ejpam-4944	84	5	math	math	PROPN
ejpam-4944	84	6	,	,	PUNCT
ejpam-4944	84	7	16	16	NUM
ejpam-4944	84	8	(	(	PUNCT
ejpam-4944	84	9	4	4	NUM
ejpam-4944	84	10	)	)	PUNCT
ejpam-4944	84	11	(	(	PUNCT
ejpam-4944	84	12	2023	2023	NUM
ejpam-4944	84	13	)	)	PUNCT
ejpam-4944	84	14	,	,	PUNCT
ejpam-4944	84	15	2286	2286	NUM
ejpam-4944	84	16	-	-	SYM
ejpam-4944	84	17	2305	2305	NUM
ejpam-4944	84	18	2289	2289	NUM
ejpam-4944	84	19	in	in	ADP
ejpam-4944	84	20	a	a	DET
ejpam-4944	84	21	bigeneralized	bigeneralize	VERB
ejpam-4944	84	22	topological	topological	ADJ
ejpam-4944	84	23	space	space	NOUN
ejpam-4944	84	24	,	,	PUNCT
ejpam-4944	84	25	various	various	ADJ
ejpam-4944	84	26	interesting	interesting	ADJ
ejpam-4944	84	27	results	result	NOUN
ejpam-4944	84	28	for	for	ADP
ejpam-4944	84	29	(	(	PUNCT
ejpam-4944	84	30	s	s	X
ejpam-4944	84	31	,	,	PUNCT
ejpam-4944	84	32	v)⋆-dense	v)⋆-dense	ADJ
ejpam-4944	84	33	sets	set	NOUN
ejpam-4944	84	34	are	be	AUX
ejpam-4944	84	35	derived	derive	VERB
ejpam-4944	84	36	which	which	PRON
ejpam-4944	84	37	is	be	AUX
ejpam-4944	84	38	helpful	helpful	ADJ
ejpam-4944	84	39	for	for	ADP
ejpam-4944	84	40	examining	examine	VERB
ejpam-4944	84	41	the	the	DET
ejpam-4944	84	42	given	give	VERB
ejpam-4944	84	43	set	set	NOUN
ejpam-4944	84	44	is	be	AUX
ejpam-4944	84	45	(	(	PUNCT
ejpam-4944	84	46	s	s	X
ejpam-4944	84	47	,	,	PUNCT
ejpam-4944	84	48	v)⋆-dense	v)⋆-dense	NOUN
ejpam-4944	84	49	or	or	CCONJ
ejpam-4944	84	50	not	not	PART
ejpam-4944	84	51	.	.	PUNCT
ejpam-4944	85	1	definition	definition	NOUN
ejpam-4944	85	2	5	5	NUM
ejpam-4944	85	3	.	.	PUNCT
ejpam-4944	86	1	a	a	DET
ejpam-4944	86	2	gts	gts	NOUN
ejpam-4944	86	3	(	(	PUNCT
ejpam-4944	86	4	x,µ	x,µ	NOUN
ejpam-4944	86	5	)	)	PUNCT
ejpam-4944	86	6	is	be	AUX
ejpam-4944	86	7	called	call	VERB
ejpam-4944	86	8	as	as	ADP
ejpam-4944	86	9	;	;	PUNCT
ejpam-4944	86	10	•	•	X
ejpam-4944	86	11	hyperconnected	hyperconnecte	VERB
ejpam-4944	86	12	[	[	X
ejpam-4944	86	13	8	8	NUM
ejpam-4944	86	14	]	]	X
ejpam-4944	86	15	if	if	SCONJ
ejpam-4944	86	16	cµ(q	cµ(q	NOUN
ejpam-4944	86	17	)	)	PUNCT
ejpam-4944	86	18	=	=	PUNCT
ejpam-4944	87	1	x	x	X
ejpam-4944	87	2	whenever	whenever	SCONJ
ejpam-4944	87	3	q	q	X
ejpam-4944	87	4	∈	∈	PROPN
ejpam-4944	87	5	µ̃.	µ̃.	NOUN
ejpam-4944	87	6	•	•	NOUN
ejpam-4944	87	7	generalized	generalize	VERB
ejpam-4944	87	8	submaximal	submaximal	ADJ
ejpam-4944	87	9	[	[	X
ejpam-4944	87	10	7	7	NUM
ejpam-4944	87	11	]	]	X
ejpam-4944	87	12	if	if	SCONJ
ejpam-4944	87	13	q	q	PROPN
ejpam-4944	87	14	∈	∈	PROPN
ejpam-4944	87	15	µ̃	µ̃	PROPN
ejpam-4944	87	16	whenever	whenever	SCONJ
ejpam-4944	87	17	cµ(q	cµ(q	X
ejpam-4944	87	18	)	)	PUNCT
ejpam-4944	87	19	=	=	PUNCT
ejpam-4944	87	20	x.	x.	NOUN
ejpam-4944	87	21	definition	definition	NOUN
ejpam-4944	87	22	6	6	NUM
ejpam-4944	87	23	.	.	PUNCT
ejpam-4944	88	1	[	[	X
ejpam-4944	88	2	16	16	NUM
ejpam-4944	88	3	]	]	X
ejpam-4944	88	4	a	a	DET
ejpam-4944	88	5	gt	gt	PROPN
ejpam-4944	88	6	µ	µ	X
ejpam-4944	88	7	onx	onx	PROPN
ejpam-4944	88	8	is	be	AUX
ejpam-4944	88	9	said	say	VERB
ejpam-4944	88	10	to	to	PART
ejpam-4944	88	11	satisfy	satisfy	VERB
ejpam-4944	88	12	the	the	DET
ejpam-4944	88	13	i	i	NOUN
ejpam-4944	88	14	-	-	PUNCT
ejpam-4944	88	15	property	property	NOUN
ejpam-4944	88	16	wheneverw1,w2	wheneverw1,w2	NOUN
ejpam-4944	88	17	,	,	PUNCT
ejpam-4944	88	18	..	..	PUNCT
ejpam-4944	88	19	,	,	PUNCT
ejpam-4944	88	20	wm	wm	PROPN
ejpam-4944	88	21	∈	∈	PROPN
ejpam-4944	88	22	µ	µ	X
ejpam-4944	88	23	with	with	ADP
ejpam-4944	88	24	w1	w1	NOUN
ejpam-4944	88	25	∩w2	∩w2	PROPN
ejpam-4944	88	26	∩	∩	X
ejpam-4944	88	27	·	·	PUNCT
ejpam-4944	88	28	·	·	PUNCT
ejpam-4944	88	29	·	·	PUNCT
ejpam-4944	89	1	∩wm	∩wm	NOUN
ejpam-4944	89	2	̸=	̸=	PROPN
ejpam-4944	89	3	∅	∅	NOUN
ejpam-4944	89	4	,	,	PUNCT
ejpam-4944	89	5	iµ(w1	iµ(w1	NOUN
ejpam-4944	89	6	∩w2	∩w2	X
ejpam-4944	89	7	∩	∩	X
ejpam-4944	89	8	·	·	PUNCT
ejpam-4944	89	9	·	·	PUNCT
ejpam-4944	89	10	·	·	PUNCT
ejpam-4944	89	11	∩wm	∩wm	NOUN
ejpam-4944	89	12	)	)	PUNCT
ejpam-4944	89	13	̸=	̸=	PROPN
ejpam-4944	89	14	∅.	∅.	PRON
ejpam-4944	89	15	definition	definition	NOUN
ejpam-4944	89	16	7	7	NUM
ejpam-4944	89	17	.	.	PUNCT
ejpam-4944	90	1	[	[	X
ejpam-4944	90	2	9	9	NUM
ejpam-4944	90	3	]	]	X
ejpam-4944	90	4	a	a	DET
ejpam-4944	90	5	non	non	ADJ
ejpam-4944	90	6	-	-	ADJ
ejpam-4944	90	7	null	null	ADJ
ejpam-4944	90	8	subset	subset	NOUN
ejpam-4944	90	9	q	q	NOUN
ejpam-4944	90	10	of	of	ADP
ejpam-4944	90	11	a	a	DET
ejpam-4944	90	12	bgts	bgts	NOUN
ejpam-4944	90	13	(	(	PUNCT
ejpam-4944	90	14	x,µ1	x,µ1	PROPN
ejpam-4944	90	15	,	,	PUNCT
ejpam-4944	90	16	µ2	µ2	PROPN
ejpam-4944	90	17	)	)	PUNCT
ejpam-4944	90	18	is	be	AUX
ejpam-4944	90	19	called	call	VERB
ejpam-4944	90	20	(	(	PUNCT
ejpam-4944	90	21	s	s	NOUN
ejpam-4944	90	22	,	,	PUNCT
ejpam-4944	90	23	v)-dense	v)-dense	NOUN
ejpam-4944	90	24	if	if	SCONJ
ejpam-4944	90	25	cs(cv(q	cs(cv(q	NOUN
ejpam-4944	90	26	)	)	PUNCT
ejpam-4944	90	27	)	)	PUNCT
ejpam-4944	91	1	=	=	PUNCT
ejpam-4944	92	1	x	x	X
ejpam-4944	92	2	where	where	SCONJ
ejpam-4944	92	3	s	s	X
ejpam-4944	92	4	,	,	PUNCT
ejpam-4944	92	5	v	v	NOUN
ejpam-4944	92	6	=	=	SYM
ejpam-4944	92	7	1	1	NUM
ejpam-4944	92	8	,	,	PUNCT
ejpam-4944	92	9	2	2	NUM
ejpam-4944	92	10	and	and	CCONJ
ejpam-4944	92	11	s	s	VERB
ejpam-4944	92	12	̸=	̸=	PROPN
ejpam-4944	92	13	v.	v.	ADP
ejpam-4944	92	14	moreover	moreover	ADV
ejpam-4944	92	15	,	,	PUNCT
ejpam-4944	92	16	(	(	PUNCT
ejpam-4944	92	17	s	s	X
ejpam-4944	92	18	,	,	PUNCT
ejpam-4944	92	19	v	v	NOUN
ejpam-4944	92	20	)	)	PUNCT
ejpam-4944	92	21	−	−	PROPN
ejpam-4944	92	22	d(x	d(x	NOUN
ejpam-4944	92	23	)	)	PUNCT
ejpam-4944	92	24	=	=	PRON
ejpam-4944	92	25	{	{	PUNCT
ejpam-4944	92	26	q	q	X
ejpam-4944	92	27	⊂	⊂	X
ejpam-4944	92	28	x	x	PUNCT
ejpam-4944	92	29	|	|	ADV
ejpam-4944	92	30	q	q	NOUN
ejpam-4944	92	31	is	be	AUX
ejpam-4944	92	32	a	a	DET
ejpam-4944	92	33	(	(	PUNCT
ejpam-4944	92	34	s	s	NOUN
ejpam-4944	92	35	,	,	PUNCT
ejpam-4944	92	36	v)-dense	v)-dense	NOUN
ejpam-4944	92	37	set	set	VERB
ejpam-4944	92	38	in	in	ADP
ejpam-4944	92	39	x	x	NOUN
ejpam-4944	92	40	}	}	PUNCT
ejpam-4944	92	41	where	where	SCONJ
ejpam-4944	92	42	s	s	X
ejpam-4944	92	43	,	,	PUNCT
ejpam-4944	92	44	v	v	NOUN
ejpam-4944	92	45	=	=	SYM
ejpam-4944	92	46	1	1	NUM
ejpam-4944	92	47	,	,	PUNCT
ejpam-4944	92	48	2	2	NUM
ejpam-4944	92	49	;	;	PUNCT
ejpam-4944	92	50	s	s	VERB
ejpam-4944	92	51	̸=	̸=	PROPN
ejpam-4944	92	52	v.	v.	ADP
ejpam-4944	92	53	definition	definition	NOUN
ejpam-4944	92	54	8	8	NUM
ejpam-4944	92	55	.	.	PUNCT
ejpam-4944	93	1	let	let	VERB
ejpam-4944	93	2	q	q	PART
ejpam-4944	93	3	be	be	AUX
ejpam-4944	93	4	a	a	DET
ejpam-4944	93	5	non	non	ADJ
ejpam-4944	93	6	-	-	ADJ
ejpam-4944	93	7	null	null	ADJ
ejpam-4944	93	8	subset	subset	NOUN
ejpam-4944	93	9	of	of	ADP
ejpam-4944	93	10	a	a	DET
ejpam-4944	93	11	bigeneralized	bigeneralize	VERB
ejpam-4944	93	12	topological	topological	ADJ
ejpam-4944	93	13	space	space	NOUN
ejpam-4944	93	14	(	(	PUNCT
ejpam-4944	93	15	x,µ1	x,µ1	PROPN
ejpam-4944	93	16	,	,	PUNCT
ejpam-4944	93	17	µ2	µ2	PROPN
ejpam-4944	93	18	)	)	PUNCT
ejpam-4944	93	19	.	.	PUNCT
ejpam-4944	94	1	then	then	ADV
ejpam-4944	94	2	q	q	X
ejpam-4944	94	3	is	be	AUX
ejpam-4944	94	4	called	call	VERB
ejpam-4944	94	5	(	(	PUNCT
ejpam-4944	94	6	µs	µs	NOUN
ejpam-4944	94	7	,	,	PUNCT
ejpam-4944	94	8	µv	µv	NOUN
ejpam-4944	94	9	)	)	PUNCT
ejpam-4944	94	10	⋆-dense	⋆-dense	NOUN
ejpam-4944	94	11	(	(	PUNCT
ejpam-4944	94	12	briefly	briefly	ADV
ejpam-4944	94	13	,	,	PUNCT
ejpam-4944	94	14	(	(	PUNCT
ejpam-4944	94	15	s	s	X
ejpam-4944	94	16	,	,	PUNCT
ejpam-4944	94	17	v)⋆-dense	v)⋆-dense	PROPN
ejpam-4944	94	18	)	)	PUNCT
ejpam-4944	94	19	if	if	SCONJ
ejpam-4944	94	20	cv(q)∩m	cv(q)∩m	ADP
ejpam-4944	94	21	̸=	̸=	PROPN
ejpam-4944	94	22	∅	∅	NOUN
ejpam-4944	94	23	for	for	ADP
ejpam-4944	94	24	every	every	DET
ejpam-4944	94	25	m	m	PROPN
ejpam-4944	94	26	∈	∈	NOUN
ejpam-4944	94	27	σ̃s	σ̃s	NOUN
ejpam-4944	94	28	where	where	SCONJ
ejpam-4944	94	29	s	s	X
ejpam-4944	94	30	,	,	PUNCT
ejpam-4944	94	31	v	v	NOUN
ejpam-4944	94	32	=	=	SYM
ejpam-4944	94	33	1	1	NUM
ejpam-4944	94	34	,	,	PUNCT
ejpam-4944	94	35	2	2	NUM
ejpam-4944	94	36	;	;	PUNCT
ejpam-4944	94	37	s	s	VERB
ejpam-4944	94	38	̸=	̸=	PROPN
ejpam-4944	94	39	v;σs	v;σ	NOUN
ejpam-4944	94	40	=	=	PUNCT
ejpam-4944	94	41	σ(µs	σ(µs	X
ejpam-4944	94	42	)	)	PUNCT
ejpam-4944	94	43	.	.	PUNCT
ejpam-4944	95	1	for	for	ADP
ejpam-4944	95	2	simplification	simplification	NOUN
ejpam-4944	95	3	we	we	PRON
ejpam-4944	95	4	noted	note	VERB
ejpam-4944	95	5	;	;	PUNCT
ejpam-4944	95	6	(	(	PUNCT
ejpam-4944	95	7	s	s	X
ejpam-4944	95	8	,	,	PUNCT
ejpam-4944	95	9	v)⋆	v)⋆	PROPN
ejpam-4944	95	10	−d(x	−d(x	NOUN
ejpam-4944	95	11	)	)	PUNCT
ejpam-4944	95	12	=	=	PRON
ejpam-4944	95	13	{	{	PUNCT
ejpam-4944	95	14	q	q	X
ejpam-4944	95	15	⊂	⊂	X
ejpam-4944	95	16	x	x	PUNCT
ejpam-4944	96	1	|	|	ADV
ejpam-4944	96	2	q	q	NOUN
ejpam-4944	96	3	is	be	AUX
ejpam-4944	96	4	a	a	DET
ejpam-4944	96	5	(	(	PUNCT
ejpam-4944	96	6	s	s	NOUN
ejpam-4944	96	7	,	,	PUNCT
ejpam-4944	96	8	v)⋆-dense	v)⋆-dense	PROPN
ejpam-4944	96	9	set	set	NOUN
ejpam-4944	96	10	in	in	ADP
ejpam-4944	96	11	x	x	NOUN
ejpam-4944	96	12	}	}	PUNCT
ejpam-4944	96	13	where	where	SCONJ
ejpam-4944	96	14	s	s	X
ejpam-4944	96	15	,	,	PUNCT
ejpam-4944	96	16	v	v	NOUN
ejpam-4944	96	17	=	=	SYM
ejpam-4944	96	18	1	1	NUM
ejpam-4944	96	19	,	,	PUNCT
ejpam-4944	96	20	2	2	NUM
ejpam-4944	96	21	;	;	PUNCT
ejpam-4944	96	22	s	s	VERB
ejpam-4944	96	23	̸=	̸=	PROPN
ejpam-4944	96	24	v.	v.	ADP
ejpam-4944	96	25	remark	remark	NOUN
ejpam-4944	96	26	9	9	NUM
ejpam-4944	96	27	.	.	PUNCT
ejpam-4944	97	1	in	in	ADP
ejpam-4944	97	2	a	a	DET
ejpam-4944	97	3	bgts	bgts	NOUN
ejpam-4944	97	4	,	,	PUNCT
ejpam-4944	97	5	if	if	SCONJ
ejpam-4944	97	6	p	p	X
ejpam-4944	97	7	∈	∈	PROPN
ejpam-4944	97	8	(	(	PUNCT
ejpam-4944	97	9	s	s	PROPN
ejpam-4944	97	10	,	,	PUNCT
ejpam-4944	97	11	v)⋆	v)⋆	PROPN
ejpam-4944	97	12	−d(x	−d(x	NOUN
ejpam-4944	97	13	)	)	PUNCT
ejpam-4944	97	14	and	and	CCONJ
ejpam-4944	97	15	p	p	X
ejpam-4944	97	16	⊂	⊂	PROPN
ejpam-4944	97	17	q	q	X
ejpam-4944	97	18	,	,	PUNCT
ejpam-4944	97	19	then	then	ADV
ejpam-4944	97	20	q(s	q(s	PROPN
ejpam-4944	97	21	,	,	PUNCT
ejpam-4944	97	22	v)⋆	v)⋆	PROPN
ejpam-4944	97	23	−d(x	−d(x	NOUN
ejpam-4944	97	24	)	)	PUNCT
ejpam-4944	97	25	.	.	PUNCT
ejpam-4944	97	26	example	example	NOUN
ejpam-4944	98	1	10	10	NUM
ejpam-4944	98	2	.	.	PUNCT
ejpam-4944	99	1	consider	consider	VERB
ejpam-4944	99	2	the	the	DET
ejpam-4944	99	3	bigeneralized	bigeneralized	ADJ
ejpam-4944	99	4	topological	topological	ADJ
ejpam-4944	99	5	space	space	NOUN
ejpam-4944	99	6	(	(	PUNCT
ejpam-4944	99	7	x,µ1	x,µ1	PROPN
ejpam-4944	99	8	,	,	PUNCT
ejpam-4944	99	9	µ2	µ2	ADJ
ejpam-4944	99	10	)	)	PUNCT
ejpam-4944	99	11	wherex	wherex	PROPN
ejpam-4944	99	12	=	=	PUNCT
ejpam-4944	99	13	{	{	PUNCT
ejpam-4944	99	14	p	p	X
ejpam-4944	99	15	,	,	PUNCT
ejpam-4944	99	16	q	q	ADJ
ejpam-4944	99	17	,	,	PUNCT
ejpam-4944	99	18	r	r	NOUN
ejpam-4944	99	19	,	,	PUNCT
ejpam-4944	99	20	s	s	PART
ejpam-4944	99	21	}	}	PUNCT
ejpam-4944	99	22	;	;	PUNCT
ejpam-4944	99	23	µ1	µ1	PROPN
ejpam-4944	99	24	=	=	SYM
ejpam-4944	99	25	{	{	PUNCT
ejpam-4944	99	26	∅	∅	NOUN
ejpam-4944	99	27	,	,	PUNCT
ejpam-4944	99	28	{	{	PUNCT
ejpam-4944	99	29	p	p	X
ejpam-4944	99	30	,	,	PUNCT
ejpam-4944	99	31	q	q	NOUN
ejpam-4944	99	32	}	}	PUNCT
ejpam-4944	99	33	,	,	PUNCT
ejpam-4944	99	34	{	{	PUNCT
ejpam-4944	99	35	q	q	X
ejpam-4944	99	36	,	,	PUNCT
ejpam-4944	99	37	r	r	NOUN
ejpam-4944	99	38	}	}	PUNCT
ejpam-4944	99	39	,	,	PUNCT
ejpam-4944	99	40	{	{	PUNCT
ejpam-4944	99	41	p	p	X
ejpam-4944	99	42	,	,	PUNCT
ejpam-4944	99	43	q	q	ADJ
ejpam-4944	99	44	,	,	PUNCT
ejpam-4944	99	45	r	r	NOUN
ejpam-4944	99	46	}	}	PUNCT
ejpam-4944	99	47	}	}	PUNCT
ejpam-4944	99	48	and	and	CCONJ
ejpam-4944	99	49	µ2	µ2	PROPN
ejpam-4944	99	50	=	=	PUNCT
ejpam-4944	99	51	{	{	PUNCT
ejpam-4944	99	52	∅	∅	NOUN
ejpam-4944	99	53	,	,	PUNCT
ejpam-4944	99	54	{	{	PUNCT
ejpam-4944	99	55	p	p	X
ejpam-4944	99	56	,	,	PUNCT
ejpam-4944	99	57	s	s	PART
ejpam-4944	99	58	}	}	PUNCT
ejpam-4944	99	59	,	,	PUNCT
ejpam-4944	99	60	{	{	PUNCT
ejpam-4944	99	61	q	q	X
ejpam-4944	99	62	,	,	PUNCT
ejpam-4944	99	63	s	s	PART
ejpam-4944	99	64	}	}	PUNCT
ejpam-4944	99	65	,	,	PUNCT
ejpam-4944	99	66	{	{	PUNCT
ejpam-4944	99	67	p	p	X
ejpam-4944	99	68	,	,	PUNCT
ejpam-4944	99	69	q	q	ADJ
ejpam-4944	99	70	,	,	PUNCT
ejpam-4944	99	71	s	s	PART
ejpam-4944	99	72	}	}	PUNCT
ejpam-4944	99	73	}	}	PUNCT
ejpam-4944	99	74	.	.	PUNCT
ejpam-4944	100	1	then	then	ADV
ejpam-4944	100	2	σ1	σ1	PROPN
ejpam-4944	100	3	=	=	PUNCT
ejpam-4944	100	4	{	{	PUNCT
ejpam-4944	100	5	∅	∅	NOUN
ejpam-4944	100	6	,	,	PUNCT
ejpam-4944	100	7	{	{	PUNCT
ejpam-4944	100	8	p	p	X
ejpam-4944	100	9	,	,	PUNCT
ejpam-4944	100	10	q	q	NOUN
ejpam-4944	100	11	}	}	PUNCT
ejpam-4944	100	12	,	,	PUNCT
ejpam-4944	100	13	{	{	PUNCT
ejpam-4944	100	14	q	q	X
ejpam-4944	100	15	,	,	PUNCT
ejpam-4944	100	16	r	r	NOUN
ejpam-4944	100	17	}	}	PUNCT
ejpam-4944	100	18	,	,	PUNCT
ejpam-4944	100	19	{	{	PUNCT
ejpam-4944	100	20	p	p	X
ejpam-4944	100	21	,	,	PUNCT
ejpam-4944	100	22	q	q	ADJ
ejpam-4944	100	23	,	,	PUNCT
ejpam-4944	100	24	r	r	NOUN
ejpam-4944	100	25	}	}	PUNCT
ejpam-4944	100	26	,	,	PUNCT
ejpam-4944	100	27	{	{	PUNCT
ejpam-4944	100	28	p	p	X
ejpam-4944	100	29	,	,	PUNCT
ejpam-4944	100	30	q	q	X
ejpam-4944	100	31	,	,	PUNCT
ejpam-4944	100	32	s	s	PART
ejpam-4944	100	33	}	}	PUNCT
ejpam-4944	100	34	,	,	PUNCT
ejpam-4944	100	35	{	{	PUNCT
ejpam-4944	100	36	q	q	X
ejpam-4944	100	37	,	,	PUNCT
ejpam-4944	100	38	r	r	NOUN
ejpam-4944	100	39	,	,	PUNCT
ejpam-4944	100	40	s	s	PART
ejpam-4944	100	41	}	}	PUNCT
ejpam-4944	100	42	,	,	PUNCT
ejpam-4944	100	43	x	x	NOUN
ejpam-4944	100	44	}	}	PUNCT
ejpam-4944	100	45	.	.	PUNCT
ejpam-4944	101	1	take	take	VERB
ejpam-4944	101	2	k	k	NOUN
ejpam-4944	101	3	=	=	PRON
ejpam-4944	101	4	{	{	PUNCT
ejpam-4944	101	5	q	q	NOUN
ejpam-4944	101	6	,	,	PUNCT
ejpam-4944	101	7	r	r	NOUN
ejpam-4944	101	8	}	}	PUNCT
ejpam-4944	101	9	.	.	PUNCT
ejpam-4944	102	1	then	then	ADV
ejpam-4944	102	2	c2(k	c2(k	PROPN
ejpam-4944	102	3	)	)	PUNCT
ejpam-4944	102	4	=	=	SYM
ejpam-4944	102	5	k.	k.	PROPN
ejpam-4944	103	1	also	also	ADV
ejpam-4944	103	2	,	,	PUNCT
ejpam-4944	103	3	k	k	PROPN
ejpam-4944	103	4	∩m	∩m	PROPN
ejpam-4944	103	5	̸=	̸=	PROPN
ejpam-4944	103	6	∅	∅	NOUN
ejpam-4944	103	7	for	for	ADP
ejpam-4944	103	8	all	all	DET
ejpam-4944	103	9	m	m	PROPN
ejpam-4944	103	10	∈	∈	ADJ
ejpam-4944	103	11	σ̃1	σ̃1	PROPN
ejpam-4944	103	12	.	.	PUNCT
ejpam-4944	104	1	thus	thus	ADV
ejpam-4944	104	2	,	,	PUNCT
ejpam-4944	104	3	c2(k)∩m	c2(k)∩m	NOUN
ejpam-4944	104	4	̸=	̸=	PROPN
ejpam-4944	104	5	∅	∅	NOUN
ejpam-4944	104	6	for	for	ADP
ejpam-4944	104	7	all	all	DET
ejpam-4944	104	8	m	m	PROPN
ejpam-4944	104	9	∈	∈	ADJ
ejpam-4944	104	10	σ̃1	σ̃1	PROPN
ejpam-4944	104	11	.	.	PUNCT
ejpam-4944	105	1	therefore	therefore	ADV
ejpam-4944	105	2	,	,	PUNCT
ejpam-4944	105	3	k	k	PROPN
ejpam-4944	105	4	∈	∈	PROPN
ejpam-4944	105	5	(	(	PUNCT
ejpam-4944	105	6	1	1	NUM
ejpam-4944	105	7	,	,	PUNCT
ejpam-4944	105	8	2)⋆	2)⋆	PROPN
ejpam-4944	105	9	−d(x	−d(x	NOUN
ejpam-4944	105	10	)	)	PUNCT
ejpam-4944	105	11	.	.	PUNCT
ejpam-4944	106	1	(	(	PUNCT
ejpam-4944	106	2	b	b	X
ejpam-4944	106	3	)	)	PUNCT
ejpam-4944	106	4	consider	consider	VERB
ejpam-4944	106	5	the	the	DET
ejpam-4944	106	6	bigeneralized	bigeneralized	ADJ
ejpam-4944	106	7	topological	topological	ADJ
ejpam-4944	106	8	space	space	NOUN
ejpam-4944	106	9	(	(	PUNCT
ejpam-4944	106	10	x,µ1	x,µ1	PROPN
ejpam-4944	106	11	,	,	PUNCT
ejpam-4944	106	12	µ2	µ2	PROPN
ejpam-4944	106	13	)	)	PUNCT
ejpam-4944	106	14	where	where	SCONJ
ejpam-4944	106	15	x	x	X
ejpam-4944	106	16	=	=	PRON
ejpam-4944	106	17	{	{	PUNCT
ejpam-4944	106	18	p	p	X
ejpam-4944	106	19	,	,	PUNCT
ejpam-4944	106	20	q	q	ADJ
ejpam-4944	106	21	,	,	PUNCT
ejpam-4944	106	22	r	r	NOUN
ejpam-4944	106	23	,	,	PUNCT
ejpam-4944	106	24	s	s	PART
ejpam-4944	106	25	}	}	PUNCT
ejpam-4944	106	26	;	;	PUNCT
ejpam-4944	106	27	µ1	µ1	PROPN
ejpam-4944	106	28	=	=	SYM
ejpam-4944	106	29	{	{	PUNCT
ejpam-4944	106	30	∅	∅	NOUN
ejpam-4944	106	31	,	,	PUNCT
ejpam-4944	106	32	{	{	PUNCT
ejpam-4944	106	33	q	q	NOUN
ejpam-4944	106	34	,	,	PUNCT
ejpam-4944	106	35	r	r	NOUN
ejpam-4944	106	36	}	}	PUNCT
ejpam-4944	106	37	,	,	PUNCT
ejpam-4944	106	38	{	{	PUNCT
ejpam-4944	106	39	q	q	X
ejpam-4944	106	40	,	,	PUNCT
ejpam-4944	106	41	s	s	PART
ejpam-4944	106	42	}	}	PUNCT
ejpam-4944	106	43	,	,	PUNCT
ejpam-4944	106	44	{	{	PUNCT
ejpam-4944	106	45	q	q	X
ejpam-4944	106	46	,	,	PUNCT
ejpam-4944	106	47	r	r	NOUN
ejpam-4944	106	48	,	,	PUNCT
ejpam-4944	106	49	s	s	PART
ejpam-4944	106	50	}	}	PUNCT
ejpam-4944	106	51	}	}	PUNCT
ejpam-4944	106	52	and	and	CCONJ
ejpam-4944	106	53	µ2	µ2	PROPN
ejpam-4944	106	54	=	=	PUNCT
ejpam-4944	106	55	{	{	PUNCT
ejpam-4944	106	56	∅	∅	NOUN
ejpam-4944	106	57	,	,	PUNCT
ejpam-4944	106	58	{	{	PUNCT
ejpam-4944	106	59	p	p	X
ejpam-4944	106	60	,	,	PUNCT
ejpam-4944	106	61	q	q	NOUN
ejpam-4944	106	62	}	}	PUNCT
ejpam-4944	106	63	,	,	PUNCT
ejpam-4944	106	64	{	{	PUNCT
ejpam-4944	106	65	p	p	X
ejpam-4944	106	66	,	,	PUNCT
ejpam-4944	106	67	r	r	NOUN
ejpam-4944	106	68	}	}	PUNCT
ejpam-4944	106	69	,	,	PUNCT
ejpam-4944	106	70	{	{	PUNCT
ejpam-4944	106	71	p	p	X
ejpam-4944	106	72	,	,	PUNCT
ejpam-4944	106	73	q	q	ADJ
ejpam-4944	106	74	,	,	PUNCT
ejpam-4944	106	75	r	r	NOUN
ejpam-4944	106	76	}	}	PUNCT
ejpam-4944	106	77	}	}	PUNCT
ejpam-4944	106	78	.	.	PUNCT
ejpam-4944	107	1	d.	d.	PROPN
ejpam-4944	107	2	elgezouli	elgezouli	PROPN
ejpam-4944	107	3	et	et	PROPN
ejpam-4944	107	4	al	al	PROPN
ejpam-4944	107	5	.	.	PUNCT
ejpam-4944	107	6	/	/	SYM
ejpam-4944	107	7	eur	eur	PROPN
ejpam-4944	107	8	.	.	PUNCT
ejpam-4944	108	1	j.	j.	PROPN
ejpam-4944	108	2	pure	pure	PROPN
ejpam-4944	108	3	appl	appl	PROPN
ejpam-4944	108	4	.	.	PROPN
ejpam-4944	108	5	math	math	PROPN
ejpam-4944	108	6	,	,	PUNCT
ejpam-4944	108	7	16	16	NUM
ejpam-4944	108	8	(	(	PUNCT
ejpam-4944	108	9	4	4	NUM
ejpam-4944	108	10	)	)	PUNCT
ejpam-4944	108	11	(	(	PUNCT
ejpam-4944	108	12	2023	2023	NUM
ejpam-4944	108	13	)	)	PUNCT
ejpam-4944	108	14	,	,	PUNCT
ejpam-4944	108	15	2286	2286	NUM
ejpam-4944	108	16	-	-	SYM
ejpam-4944	108	17	2305	2305	NUM
ejpam-4944	108	18	2290	2290	NUM
ejpam-4944	108	19	then	then	ADV
ejpam-4944	108	20	σ2	σ2	PROPN
ejpam-4944	108	21	=	=	SYM
ejpam-4944	108	22	{	{	PUNCT
ejpam-4944	108	23	∅	∅	NOUN
ejpam-4944	108	24	,	,	PUNCT
ejpam-4944	108	25	{	{	PUNCT
ejpam-4944	108	26	p	p	X
ejpam-4944	108	27	,	,	PUNCT
ejpam-4944	108	28	q	q	NOUN
ejpam-4944	108	29	}	}	PUNCT
ejpam-4944	108	30	,	,	PUNCT
ejpam-4944	108	31	{	{	PUNCT
ejpam-4944	108	32	p	p	X
ejpam-4944	108	33	,	,	PUNCT
ejpam-4944	108	34	r	r	NOUN
ejpam-4944	108	35	}	}	PUNCT
ejpam-4944	108	36	,	,	PUNCT
ejpam-4944	108	37	{	{	PUNCT
ejpam-4944	108	38	p	p	X
ejpam-4944	108	39	,	,	PUNCT
ejpam-4944	108	40	q	q	ADJ
ejpam-4944	108	41	,	,	PUNCT
ejpam-4944	108	42	r	r	NOUN
ejpam-4944	108	43	}	}	PUNCT
ejpam-4944	108	44	,	,	PUNCT
ejpam-4944	108	45	{	{	PUNCT
ejpam-4944	108	46	p	p	X
ejpam-4944	108	47	,	,	PUNCT
ejpam-4944	108	48	q	q	X
ejpam-4944	108	49	,	,	PUNCT
ejpam-4944	108	50	s	s	PART
ejpam-4944	108	51	}	}	PUNCT
ejpam-4944	108	52	,	,	PUNCT
ejpam-4944	108	53	{	{	PUNCT
ejpam-4944	108	54	p	p	X
ejpam-4944	108	55	,	,	PUNCT
ejpam-4944	108	56	r	r	NOUN
ejpam-4944	108	57	,	,	PUNCT
ejpam-4944	108	58	s	s	PART
ejpam-4944	108	59	}	}	PUNCT
ejpam-4944	108	60	,	,	PUNCT
ejpam-4944	108	61	x	x	NOUN
ejpam-4944	108	62	}	}	PUNCT
ejpam-4944	108	63	.	.	PUNCT
ejpam-4944	109	1	take	take	VERB
ejpam-4944	109	2	j	j	NOUN
ejpam-4944	109	3	=	=	PUNCT
ejpam-4944	109	4	{	{	PUNCT
ejpam-4944	109	5	p	p	X
ejpam-4944	109	6	,	,	PUNCT
ejpam-4944	109	7	r	r	NOUN
ejpam-4944	109	8	}	}	PUNCT
ejpam-4944	109	9	.	.	PUNCT
ejpam-4944	110	1	here	here	ADV
ejpam-4944	110	2	c1(j	c1(j	NOUN
ejpam-4944	110	3	)	)	PUNCT
ejpam-4944	110	4	∩h	∩h	PROPN
ejpam-4944	110	5	̸=	̸=	PROPN
ejpam-4944	110	6	∅	∅	NOUN
ejpam-4944	110	7	for	for	ADP
ejpam-4944	110	8	all	all	DET
ejpam-4944	110	9	h	h	NOUN
ejpam-4944	110	10	∈	∈	PROPN
ejpam-4944	110	11	σ̃2	σ̃2	PROPN
ejpam-4944	110	12	.	.	PUNCT
ejpam-4944	111	1	hence	hence	ADV
ejpam-4944	111	2	j	j	PROPN
ejpam-4944	111	3	∈	∈	PROPN
ejpam-4944	111	4	(	(	PUNCT
ejpam-4944	111	5	2	2	NUM
ejpam-4944	111	6	,	,	PUNCT
ejpam-4944	111	7	1)⋆	1)⋆	PROPN
ejpam-4944	111	8	−d(x	−d(x	NOUN
ejpam-4944	111	9	)	)	PUNCT
ejpam-4944	111	10	.	.	PUNCT
ejpam-4944	112	1	theorem	theorem	NOUN
ejpam-4944	112	2	11	11	NUM
ejpam-4944	112	3	.	.	PUNCT
ejpam-4944	113	1	let	let	AUX
ejpam-4944	113	2	(	(	PUNCT
ejpam-4944	113	3	x,µ1	x,µ1	NOUN
ejpam-4944	113	4	,	,	PUNCT
ejpam-4944	113	5	µ2	µ2	PROPN
ejpam-4944	113	6	)	)	PUNCT
ejpam-4944	113	7	be	be	VERB
ejpam-4944	113	8	a	a	DET
ejpam-4944	113	9	bgts	bgts	NOUN
ejpam-4944	113	10	and	and	CCONJ
ejpam-4944	113	11	cµs(q	cµs(q	PROPN
ejpam-4944	113	12	)	)	PUNCT
ejpam-4944	113	13	=	=	PUNCT
ejpam-4944	114	1	x.	x.	NOUN
ejpam-4944	114	2	if	if	SCONJ
ejpam-4944	114	3	µs	µs	NOUN
ejpam-4944	114	4	is	be	AUX
ejpam-4944	114	5	a	a	DET
ejpam-4944	114	6	sgt	sgt	NOUN
ejpam-4944	114	7	,	,	PUNCT
ejpam-4944	114	8	then	then	ADV
ejpam-4944	114	9	q	q	PROPN
ejpam-4944	114	10	∈	∈	PROPN
ejpam-4944	114	11	(	(	PUNCT
ejpam-4944	114	12	s	s	PROPN
ejpam-4944	114	13	,	,	PUNCT
ejpam-4944	114	14	v)⋆	v)⋆	PROPN
ejpam-4944	114	15	−d(x	−d(x	NOUN
ejpam-4944	114	16	)	)	PUNCT
ejpam-4944	114	17	where	where	SCONJ
ejpam-4944	114	18	s	s	X
ejpam-4944	114	19	,	,	PUNCT
ejpam-4944	114	20	v	v	NOUN
ejpam-4944	114	21	=	=	SYM
ejpam-4944	114	22	1	1	NUM
ejpam-4944	114	23	,	,	PUNCT
ejpam-4944	114	24	2	2	NUM
ejpam-4944	114	25	;	;	PUNCT
ejpam-4944	114	26	s	s	VERB
ejpam-4944	114	27	̸=	̸=	PROPN
ejpam-4944	114	28	v.	v.	ADP
ejpam-4944	114	29	proof	proof	NOUN
ejpam-4944	114	30	.	.	PUNCT
ejpam-4944	115	1	take	take	VERB
ejpam-4944	115	2	s	s	NOUN
ejpam-4944	115	3	=	=	SYM
ejpam-4944	115	4	1	1	NUM
ejpam-4944	115	5	and	and	CCONJ
ejpam-4944	115	6	v	v	NOUN
ejpam-4944	115	7	=	=	SYM
ejpam-4944	115	8	2	2	X
ejpam-4944	115	9	.	.	X
ejpam-4944	115	10	assume	assume	VERB
ejpam-4944	115	11	that	that	SCONJ
ejpam-4944	115	12	,	,	PUNCT
ejpam-4944	115	13	cµ1(q	cµ1(q	ADJ
ejpam-4944	115	14	)	)	PUNCT
ejpam-4944	115	15	=	=	SYM
ejpam-4944	116	1	x	x	PUNCT
ejpam-4944	116	2	and	and	CCONJ
ejpam-4944	116	3	µ1	µ1	PROPN
ejpam-4944	116	4	is	be	AUX
ejpam-4944	116	5	a	a	DET
ejpam-4944	116	6	sgt	sgt	PROPN
ejpam-4944	116	7	.	.	PUNCT
ejpam-4944	117	1	let	let	VERB
ejpam-4944	117	2	p	p	PRON
ejpam-4944	117	3	∈	∈	PROPN
ejpam-4944	117	4	σ̃1	σ̃1	PROPN
ejpam-4944	117	5	.	.	PUNCT
ejpam-4944	118	1	then	then	ADV
ejpam-4944	118	2	p	p	X
ejpam-4944	118	3	⊂	⊂	PROPN
ejpam-4944	118	4	cµ1(iµ1(p	cµ1(iµ1(p	NOUN
ejpam-4944	118	5	)	)	PUNCT
ejpam-4944	118	6	)	)	PUNCT
ejpam-4944	119	1	and	and	CCONJ
ejpam-4944	119	2	so	so	ADV
ejpam-4944	119	3	iµ1(p	iµ1(p	ADJ
ejpam-4944	119	4	)	)	PUNCT
ejpam-4944	119	5	̸=	̸=	NOUN
ejpam-4944	119	6	∅	∅	NOUN
ejpam-4944	119	7	,	,	PUNCT
ejpam-4944	119	8	since	since	SCONJ
ejpam-4944	119	9	µ1	µ1	PROPN
ejpam-4944	119	10	is	be	AUX
ejpam-4944	119	11	a	a	DET
ejpam-4944	119	12	sgt	sgt	PROPN
ejpam-4944	119	13	.	.	PUNCT
ejpam-4944	120	1	this	this	PRON
ejpam-4944	120	2	implies	imply	VERB
ejpam-4944	120	3	iµ1(p	iµ1(p	PROPN
ejpam-4944	120	4	)	)	PUNCT
ejpam-4944	120	5	∈	∈	PROPN
ejpam-4944	120	6	µ̃1	µ̃1	NOUN
ejpam-4944	120	7	which	which	PRON
ejpam-4944	120	8	implies	imply	VERB
ejpam-4944	120	9	that	that	SCONJ
ejpam-4944	120	10	iµ1(p	iµ1(p	ADV
ejpam-4944	120	11	)	)	PUNCT
ejpam-4944	120	12	∩q	∩q	PROPN
ejpam-4944	121	1	̸=	̸=	PROPN
ejpam-4944	121	2	∅.	∅.	ADP
ejpam-4944	121	3	thus	thus	ADV
ejpam-4944	121	4	,	,	PUNCT
ejpam-4944	121	5	q	q	PROPN
ejpam-4944	121	6	∩	∩	NOUN
ejpam-4944	121	7	p	p	X
ejpam-4944	121	8	̸=	̸=	PROPN
ejpam-4944	121	9	∅.	∅.	PRON
ejpam-4944	121	10	therefore	therefore	ADV
ejpam-4944	121	11	,	,	PUNCT
ejpam-4944	121	12	q	q	PROPN
ejpam-4944	121	13	∈	∈	PROPN
ejpam-4944	121	14	(	(	PUNCT
ejpam-4944	121	15	1	1	NUM
ejpam-4944	121	16	,	,	PUNCT
ejpam-4944	121	17	2)⋆	2)⋆	PROPN
ejpam-4944	121	18	−d(x	−d(x	NOUN
ejpam-4944	121	19	)	)	PUNCT
ejpam-4944	121	20	.	.	PUNCT
ejpam-4944	122	1	take	take	VERB
ejpam-4944	122	2	s	s	NOUN
ejpam-4944	122	3	=	=	SYM
ejpam-4944	122	4	2	2	NUM
ejpam-4944	122	5	and	and	CCONJ
ejpam-4944	122	6	v	v	NOUN
ejpam-4944	122	7	=	=	SYM
ejpam-4944	122	8	1	1	X
ejpam-4944	122	9	.	.	PUNCT
ejpam-4944	122	10	suppose	suppose	VERB
ejpam-4944	122	11	cµ2(q	cµ2(q	PROPN
ejpam-4944	122	12	)	)	PUNCT
ejpam-4944	123	1	=	=	SYM
ejpam-4944	124	1	x	x	PUNCT
ejpam-4944	124	2	and	and	CCONJ
ejpam-4944	124	3	µ2	µ2	PROPN
ejpam-4944	124	4	is	be	AUX
ejpam-4944	124	5	a	a	DET
ejpam-4944	124	6	sgt	sgt	PROPN
ejpam-4944	124	7	.	.	PUNCT
ejpam-4944	125	1	let	let	VERB
ejpam-4944	125	2	m	m	PROPN
ejpam-4944	125	3	∈	∈	PROPN
ejpam-4944	125	4	σ̃2	σ̃2	PROPN
ejpam-4944	125	5	.	.	PUNCT
ejpam-4944	126	1	then	then	ADV
ejpam-4944	126	2	m	m	PROPN
ejpam-4944	126	3	⊂	⊂	PROPN
ejpam-4944	126	4	cµ2(iµ2(m	cµ2(iµ2(m	NOUN
ejpam-4944	126	5	)	)	PUNCT
ejpam-4944	126	6	)	)	PUNCT
ejpam-4944	127	1	and	and	CCONJ
ejpam-4944	127	2	so	so	ADV
ejpam-4944	127	3	iµ2(m	iµ2(m	NOUN
ejpam-4944	127	4	)	)	PUNCT
ejpam-4944	127	5	̸=	̸=	NOUN
ejpam-4944	127	6	∅	∅	NOUN
ejpam-4944	127	7	,	,	PUNCT
ejpam-4944	127	8	since	since	SCONJ
ejpam-4944	127	9	µ2	µ2	PROPN
ejpam-4944	127	10	is	be	AUX
ejpam-4944	127	11	a	a	DET
ejpam-4944	127	12	sgt	sgt	PROPN
ejpam-4944	127	13	.	.	PUNCT
ejpam-4944	128	1	thus	thus	ADV
ejpam-4944	128	2	,	,	PUNCT
ejpam-4944	128	3	iµ2(m	iµ2(m	NOUN
ejpam-4944	128	4	)	)	PUNCT
ejpam-4944	128	5	∈	∈	PROPN
ejpam-4944	128	6	µ̃2	µ̃2	PROPN
ejpam-4944	128	7	so	so	SCONJ
ejpam-4944	128	8	that	that	SCONJ
ejpam-4944	128	9	iµ2(m	iµ2(m	NOUN
ejpam-4944	128	10	)	)	PUNCT
ejpam-4944	128	11	∩q	∩q	PROPN
ejpam-4944	129	1	̸=	̸=	PROPN
ejpam-4944	129	2	∅.	∅.	ADP
ejpam-4944	129	3	this	this	PRON
ejpam-4944	129	4	implies	imply	VERB
ejpam-4944	129	5	q	q	PROPN
ejpam-4944	129	6	∩m	∩m	PROPN
ejpam-4944	129	7	̸=	̸=	PROPN
ejpam-4944	129	8	∅	∅	NOUN
ejpam-4944	129	9	which	which	PRON
ejpam-4944	129	10	implies	imply	VERB
ejpam-4944	129	11	that	that	SCONJ
ejpam-4944	129	12	q	q	PUNCT
ejpam-4944	129	13	∈	∈	NOUN
ejpam-4944	129	14	(	(	PUNCT
ejpam-4944	129	15	2	2	NUM
ejpam-4944	129	16	,	,	PUNCT
ejpam-4944	129	17	1)⋆	1)⋆	PROPN
ejpam-4944	129	18	−d(x	−d(x	NOUN
ejpam-4944	129	19	)	)	PUNCT
ejpam-4944	129	20	.	.	PUNCT
ejpam-4944	130	1	the	the	DET
ejpam-4944	130	2	below	below	ADP
ejpam-4944	130	3	example	example	NOUN
ejpam-4944	130	4	12	12	NUM
ejpam-4944	130	5	shows	show	VERB
ejpam-4944	130	6	that	that	SCONJ
ejpam-4944	130	7	the	the	DET
ejpam-4944	130	8	hypothesis	hypothesis	NOUN
ejpam-4944	130	9	in	in	ADP
ejpam-4944	130	10	theorem	theorem	NOUN
ejpam-4944	130	11	11	11	NUM
ejpam-4944	130	12	can	can	AUX
ejpam-4944	130	13	not	not	PART
ejpam-4944	130	14	be	be	AUX
ejpam-4944	130	15	dropped	drop	VERB
ejpam-4944	130	16	.	.	PUNCT
ejpam-4944	130	17	example	example	NOUN
ejpam-4944	131	1	12	12	NUM
ejpam-4944	131	2	.	.	PUNCT
ejpam-4944	132	1	(	(	PUNCT
ejpam-4944	132	2	a	a	X
ejpam-4944	132	3	)	)	PUNCT
ejpam-4944	132	4	.	.	PUNCT
ejpam-4944	133	1	consider	consider	VERB
ejpam-4944	133	2	the	the	DET
ejpam-4944	133	3	bgts	bgts	NOUN
ejpam-4944	133	4	(	(	PUNCT
ejpam-4944	133	5	x,µ1	x,µ1	PROPN
ejpam-4944	133	6	,	,	PUNCT
ejpam-4944	133	7	µ2	µ2	PROPN
ejpam-4944	133	8	)	)	PUNCT
ejpam-4944	133	9	where	where	SCONJ
ejpam-4944	133	10	x	x	X
ejpam-4944	133	11	=	=	PRON
ejpam-4944	133	12	{	{	PUNCT
ejpam-4944	133	13	p	p	X
ejpam-4944	133	14	,	,	PUNCT
ejpam-4944	133	15	q	q	ADJ
ejpam-4944	133	16	,	,	PUNCT
ejpam-4944	133	17	r	r	NOUN
ejpam-4944	133	18	,	,	PUNCT
ejpam-4944	133	19	s	s	PART
ejpam-4944	133	20	}	}	PUNCT
ejpam-4944	133	21	;	;	PUNCT
ejpam-4944	133	22	µ1	µ1	PROPN
ejpam-4944	133	23	=	=	SYM
ejpam-4944	133	24	{	{	PUNCT
ejpam-4944	133	25	∅	∅	NOUN
ejpam-4944	133	26	,	,	PUNCT
ejpam-4944	133	27	{	{	PUNCT
ejpam-4944	133	28	q	q	X
ejpam-4944	133	29	,	,	PUNCT
ejpam-4944	133	30	s	s	PART
ejpam-4944	133	31	}	}	PUNCT
ejpam-4944	133	32	,	,	PUNCT
ejpam-4944	133	33	{	{	PUNCT
ejpam-4944	133	34	r	r	NOUN
ejpam-4944	133	35	,	,	PUNCT
ejpam-4944	133	36	s	s	PART
ejpam-4944	133	37	}	}	PUNCT
ejpam-4944	133	38	,	,	PUNCT
ejpam-4944	133	39	{	{	PUNCT
ejpam-4944	133	40	q	q	X
ejpam-4944	133	41	,	,	PUNCT
ejpam-4944	133	42	r	r	NOUN
ejpam-4944	133	43	,	,	PUNCT
ejpam-4944	133	44	s	s	PART
ejpam-4944	133	45	}	}	PUNCT
ejpam-4944	133	46	}	}	PUNCT
ejpam-4944	133	47	and	and	CCONJ
ejpam-4944	133	48	µ2	µ2	PROPN
ejpam-4944	133	49	=	=	PUNCT
ejpam-4944	133	50	{	{	PUNCT
ejpam-4944	133	51	∅	∅	NOUN
ejpam-4944	133	52	,	,	PUNCT
ejpam-4944	133	53	{	{	PUNCT
ejpam-4944	133	54	p	p	X
ejpam-4944	133	55	,	,	PUNCT
ejpam-4944	133	56	r	r	NOUN
ejpam-4944	133	57	}	}	PUNCT
ejpam-4944	133	58	,	,	PUNCT
ejpam-4944	133	59	{	{	PUNCT
ejpam-4944	133	60	q	q	X
ejpam-4944	133	61	,	,	PUNCT
ejpam-4944	133	62	r	r	NOUN
ejpam-4944	133	63	}	}	PUNCT
ejpam-4944	133	64	,	,	PUNCT
ejpam-4944	133	65	{	{	PUNCT
ejpam-4944	133	66	p	p	X
ejpam-4944	133	67	,	,	PUNCT
ejpam-4944	133	68	q	q	ADJ
ejpam-4944	133	69	,	,	PUNCT
ejpam-4944	133	70	r	r	NOUN
ejpam-4944	133	71	}	}	PUNCT
ejpam-4944	133	72	,	,	PUNCT
ejpam-4944	133	73	{	{	PUNCT
ejpam-4944	133	74	p	p	X
ejpam-4944	133	75	,	,	PUNCT
ejpam-4944	133	76	q	q	X
ejpam-4944	133	77	,	,	PUNCT
ejpam-4944	133	78	s	s	PART
ejpam-4944	133	79	}	}	PUNCT
ejpam-4944	133	80	,	,	PUNCT
ejpam-4944	133	81	x	x	NOUN
ejpam-4944	133	82	}	}	PUNCT
ejpam-4944	133	83	.	.	PUNCT
ejpam-4944	134	1	fix	fix	NOUN
ejpam-4944	134	2	s	s	PART
ejpam-4944	134	3	=	=	NOUN
ejpam-4944	134	4	1	1	NUM
ejpam-4944	134	5	;	;	PUNCT
ejpam-4944	134	6	v	v	NOUN
ejpam-4944	134	7	=	=	SYM
ejpam-4944	134	8	2	2	NUM
ejpam-4944	134	9	.	.	PUNCT
ejpam-4944	135	1	obviously	obviously	ADV
ejpam-4944	135	2	,	,	PUNCT
ejpam-4944	135	3	σ1	σ1	PROPN
ejpam-4944	135	4	=	=	PUNCT
ejpam-4944	135	5	{	{	PUNCT
ejpam-4944	135	6	∅	∅	NOUN
ejpam-4944	135	7	,	,	PUNCT
ejpam-4944	135	8	{	{	PUNCT
ejpam-4944	135	9	p	p	X
ejpam-4944	135	10	}	}	PUNCT
ejpam-4944	135	11	,	,	PUNCT
ejpam-4944	135	12	{	{	PUNCT
ejpam-4944	135	13	q	q	X
ejpam-4944	135	14	,	,	PUNCT
ejpam-4944	135	15	s	s	PART
ejpam-4944	135	16	}	}	PUNCT
ejpam-4944	135	17	,	,	PUNCT
ejpam-4944	135	18	{	{	PUNCT
ejpam-4944	135	19	r	r	NOUN
ejpam-4944	135	20	,	,	PUNCT
ejpam-4944	135	21	s	s	PART
ejpam-4944	135	22	}	}	PUNCT
ejpam-4944	135	23	,	,	PUNCT
ejpam-4944	135	24	{	{	PUNCT
ejpam-4944	135	25	p	p	X
ejpam-4944	135	26	,	,	PUNCT
ejpam-4944	135	27	q	q	X
ejpam-4944	135	28	,	,	PUNCT
ejpam-4944	135	29	s	s	PART
ejpam-4944	135	30	}	}	PUNCT
ejpam-4944	135	31	,	,	PUNCT
ejpam-4944	135	32	{	{	PUNCT
ejpam-4944	135	33	p	p	X
ejpam-4944	135	34	,	,	PUNCT
ejpam-4944	135	35	r	r	NOUN
ejpam-4944	135	36	,	,	PUNCT
ejpam-4944	135	37	s	s	PART
ejpam-4944	135	38	}	}	PUNCT
ejpam-4944	135	39	,	,	PUNCT
ejpam-4944	135	40	{	{	PUNCT
ejpam-4944	135	41	q	q	X
ejpam-4944	135	42	,	,	PUNCT
ejpam-4944	135	43	r	r	NOUN
ejpam-4944	135	44	,	,	PUNCT
ejpam-4944	135	45	s	s	PART
ejpam-4944	135	46	}	}	PUNCT
ejpam-4944	135	47	,	,	PUNCT
ejpam-4944	135	48	x	x	NOUN
ejpam-4944	135	49	}	}	PUNCT
ejpam-4944	135	50	.	.	PUNCT
ejpam-4944	136	1	choose	choose	VERB
ejpam-4944	136	2	l	l	NOUN
ejpam-4944	136	3	=	=	SYM
ejpam-4944	136	4	{	{	PUNCT
ejpam-4944	136	5	q	q	X
ejpam-4944	136	6	,	,	PUNCT
ejpam-4944	136	7	s	s	PART
ejpam-4944	136	8	}	}	PUNCT
ejpam-4944	136	9	so	so	SCONJ
ejpam-4944	136	10	that	that	SCONJ
ejpam-4944	136	11	cµ1l	cµ1l	VERB
ejpam-4944	136	12	=	=	SYM
ejpam-4944	136	13	x	x	NOUN
ejpam-4944	136	14	and	and	CCONJ
ejpam-4944	136	15	cµ2l	cµ2l	PROPN
ejpam-4944	136	16	=	=	SYM
ejpam-4944	136	17	l.	l.	PROPN
ejpam-4944	136	18	thus	thus	ADV
ejpam-4944	136	19	,	,	PUNCT
ejpam-4944	136	20	l	l	PROPN
ejpam-4944	136	21	=	=	SYM
ejpam-4944	136	22	{	{	PUNCT
ejpam-4944	136	23	q	q	X
ejpam-4944	136	24	,	,	PUNCT
ejpam-4944	136	25	s	s	AUX
ejpam-4944	136	26	}	}	PUNCT
ejpam-4944	136	27	is	be	AUX
ejpam-4944	136	28	µ1	µ1	NOUN
ejpam-4944	136	29	-	-	PUNCT
ejpam-4944	136	30	dense	dense	ADJ
ejpam-4944	136	31	.	.	PUNCT
ejpam-4944	137	1	but	but	CCONJ
ejpam-4944	137	2	cµ2l	cµ2l	NOUN
ejpam-4944	137	3	∩	∩	NOUN
ejpam-4944	137	4	{	{	PUNCT
ejpam-4944	137	5	p	p	X
ejpam-4944	137	6	}	}	PUNCT
ejpam-4944	137	7	=	=	NOUN
ejpam-4944	137	8	∅	∅	NOUN
ejpam-4944	137	9	where	where	SCONJ
ejpam-4944	137	10	{	{	PUNCT
ejpam-4944	137	11	p	p	NOUN
ejpam-4944	137	12	}	}	PUNCT
ejpam-4944	137	13	∈	∈	PROPN
ejpam-4944	137	14	σ̃1	σ̃1	PROPN
ejpam-4944	137	15	for	for	ADP
ejpam-4944	137	16	that	that	DET
ejpam-4944	137	17	l	l	NOUN
ejpam-4944	137	18	/∈	/∈	PUNCT
ejpam-4944	138	1	(	(	PUNCT
ejpam-4944	138	2	1	1	NUM
ejpam-4944	138	3	,	,	PUNCT
ejpam-4944	138	4	2)⋆	2)⋆	PROPN
ejpam-4944	138	5	−d(x	−d(x	NOUN
ejpam-4944	138	6	)	)	PUNCT
ejpam-4944	138	7	.	.	PUNCT
ejpam-4944	139	1	(	(	PUNCT
ejpam-4944	139	2	b	b	X
ejpam-4944	139	3	)	)	PUNCT
ejpam-4944	139	4	.	.	PUNCT
ejpam-4944	140	1	consider	consider	VERB
ejpam-4944	140	2	the	the	DET
ejpam-4944	140	3	bgts	bgts	NOUN
ejpam-4944	140	4	(	(	PUNCT
ejpam-4944	140	5	x,µ1	x,µ1	PROPN
ejpam-4944	140	6	,	,	PUNCT
ejpam-4944	140	7	µ2	µ2	PROPN
ejpam-4944	140	8	)	)	PUNCT
ejpam-4944	140	9	where	where	SCONJ
ejpam-4944	140	10	x	x	X
ejpam-4944	140	11	=	=	PRON
ejpam-4944	140	12	{	{	PUNCT
ejpam-4944	140	13	p	p	X
ejpam-4944	140	14	,	,	PUNCT
ejpam-4944	140	15	q	q	ADJ
ejpam-4944	140	16	,	,	PUNCT
ejpam-4944	140	17	r	r	NOUN
ejpam-4944	140	18	,	,	PUNCT
ejpam-4944	140	19	s	s	PART
ejpam-4944	140	20	}	}	PUNCT
ejpam-4944	140	21	;	;	PUNCT
ejpam-4944	140	22	µ1	µ1	PROPN
ejpam-4944	140	23	=	=	SYM
ejpam-4944	140	24	{	{	PUNCT
ejpam-4944	140	25	∅	∅	NOUN
ejpam-4944	140	26	,	,	PUNCT
ejpam-4944	140	27	{	{	PUNCT
ejpam-4944	140	28	p	p	X
ejpam-4944	140	29	,	,	PUNCT
ejpam-4944	140	30	r	r	NOUN
ejpam-4944	140	31	}	}	PUNCT
ejpam-4944	140	32	,	,	PUNCT
ejpam-4944	140	33	{	{	PUNCT
ejpam-4944	140	34	q	q	X
ejpam-4944	140	35	,	,	PUNCT
ejpam-4944	140	36	r	r	NOUN
ejpam-4944	140	37	}	}	PUNCT
ejpam-4944	140	38	,	,	PUNCT
ejpam-4944	140	39	{	{	PUNCT
ejpam-4944	140	40	r	r	NOUN
ejpam-4944	140	41	,	,	PUNCT
ejpam-4944	140	42	s	s	PART
ejpam-4944	140	43	}	}	PUNCT
ejpam-4944	140	44	,	,	PUNCT
ejpam-4944	140	45	{	{	PUNCT
ejpam-4944	140	46	p	p	X
ejpam-4944	140	47	,	,	PUNCT
ejpam-4944	140	48	q	q	ADJ
ejpam-4944	140	49	,	,	PUNCT
ejpam-4944	140	50	r	r	NOUN
ejpam-4944	140	51	}	}	PUNCT
ejpam-4944	140	52	,	,	PUNCT
ejpam-4944	140	53	{	{	PUNCT
ejpam-4944	140	54	p	p	X
ejpam-4944	140	55	,	,	PUNCT
ejpam-4944	140	56	r	r	NOUN
ejpam-4944	140	57	,	,	PUNCT
ejpam-4944	140	58	s	s	PART
ejpam-4944	140	59	}	}	PUNCT
ejpam-4944	140	60	,	,	PUNCT
ejpam-4944	140	61	{	{	PUNCT
ejpam-4944	140	62	q	q	X
ejpam-4944	140	63	,	,	PUNCT
ejpam-4944	140	64	r	r	NOUN
ejpam-4944	140	65	,	,	PUNCT
ejpam-4944	140	66	s	s	PART
ejpam-4944	140	67	}	}	PUNCT
ejpam-4944	140	68	,	,	PUNCT
ejpam-4944	140	69	x	x	NOUN
ejpam-4944	140	70	}	}	PUNCT
ejpam-4944	140	71	and	and	CCONJ
ejpam-4944	140	72	µ2	µ2	PROPN
ejpam-4944	140	73	=	=	PUNCT
ejpam-4944	140	74	{	{	PUNCT
ejpam-4944	140	75	∅	∅	NOUN
ejpam-4944	140	76	,	,	PUNCT
ejpam-4944	140	77	{	{	PUNCT
ejpam-4944	140	78	p	p	X
ejpam-4944	140	79	,	,	PUNCT
ejpam-4944	140	80	s	s	PART
ejpam-4944	140	81	}	}	PUNCT
ejpam-4944	140	82	,	,	PUNCT
ejpam-4944	140	83	{	{	PUNCT
ejpam-4944	140	84	q	q	X
ejpam-4944	140	85	,	,	PUNCT
ejpam-4944	140	86	s	s	PART
ejpam-4944	140	87	}	}	PUNCT
ejpam-4944	140	88	,	,	PUNCT
ejpam-4944	140	89	{	{	PUNCT
ejpam-4944	140	90	p	p	X
ejpam-4944	140	91	,	,	PUNCT
ejpam-4944	140	92	q	q	ADJ
ejpam-4944	140	93	,	,	PUNCT
ejpam-4944	140	94	s	s	PART
ejpam-4944	140	95	}	}	PUNCT
ejpam-4944	140	96	}	}	PUNCT
ejpam-4944	140	97	.	.	PUNCT
ejpam-4944	141	1	fix	fix	NOUN
ejpam-4944	141	2	s	s	PART
ejpam-4944	141	3	=	=	NOUN
ejpam-4944	141	4	2	2	NUM
ejpam-4944	141	5	;	;	PUNCT
ejpam-4944	141	6	v	v	NOUN
ejpam-4944	141	7	=	=	SYM
ejpam-4944	141	8	1	1	X
ejpam-4944	141	9	.	.	PUNCT
ejpam-4944	142	1	obviously	obviously	ADV
ejpam-4944	142	2	,	,	PUNCT
ejpam-4944	142	3	σ2	σ2	PROPN
ejpam-4944	142	4	=	=	SYM
ejpam-4944	142	5	{	{	PUNCT
ejpam-4944	142	6	∅	∅	NOUN
ejpam-4944	142	7	,	,	PUNCT
ejpam-4944	142	8	{	{	PUNCT
ejpam-4944	142	9	r	r	NOUN
ejpam-4944	142	10	}	}	PUNCT
ejpam-4944	142	11	,	,	PUNCT
ejpam-4944	142	12	{	{	PUNCT
ejpam-4944	142	13	p	p	X
ejpam-4944	142	14	,	,	PUNCT
ejpam-4944	142	15	s	s	PART
ejpam-4944	142	16	}	}	PUNCT
ejpam-4944	142	17	,	,	PUNCT
ejpam-4944	142	18	{	{	PUNCT
ejpam-4944	142	19	q	q	X
ejpam-4944	142	20	,	,	PUNCT
ejpam-4944	142	21	s	s	PART
ejpam-4944	142	22	}	}	PUNCT
ejpam-4944	142	23	,	,	PUNCT
ejpam-4944	142	24	{	{	PUNCT
ejpam-4944	142	25	p	p	X
ejpam-4944	142	26	,	,	PUNCT
ejpam-4944	142	27	q	q	X
ejpam-4944	142	28	,	,	PUNCT
ejpam-4944	142	29	s	s	PART
ejpam-4944	142	30	}	}	PUNCT
ejpam-4944	142	31	,	,	PUNCT
ejpam-4944	142	32	{	{	PUNCT
ejpam-4944	142	33	p	p	X
ejpam-4944	142	34	,	,	PUNCT
ejpam-4944	142	35	r	r	NOUN
ejpam-4944	142	36	,	,	PUNCT
ejpam-4944	142	37	s	s	PART
ejpam-4944	142	38	}	}	PUNCT
ejpam-4944	142	39	,	,	PUNCT
ejpam-4944	142	40	{	{	PUNCT
ejpam-4944	142	41	q	q	X
ejpam-4944	142	42	,	,	PUNCT
ejpam-4944	142	43	r	r	NOUN
ejpam-4944	142	44	,	,	PUNCT
ejpam-4944	142	45	s	s	PART
ejpam-4944	142	46	}	}	PUNCT
ejpam-4944	142	47	,	,	PUNCT
ejpam-4944	142	48	x	x	NOUN
ejpam-4944	142	49	}	}	PUNCT
ejpam-4944	142	50	.	.	PUNCT
ejpam-4944	143	1	choose	choose	VERB
ejpam-4944	143	2	k	k	X
ejpam-4944	143	3	=	=	PRON
ejpam-4944	143	4	{	{	PUNCT
ejpam-4944	143	5	s	s	NOUN
ejpam-4944	143	6	}	}	PUNCT
ejpam-4944	143	7	so	so	SCONJ
ejpam-4944	143	8	that	that	SCONJ
ejpam-4944	143	9	cµ1k	cµ1k	PROPN
ejpam-4944	143	10	=	=	SYM
ejpam-4944	143	11	k	k	PROPN
ejpam-4944	143	12	and	and	CCONJ
ejpam-4944	143	13	cµ2k	cµ2k	PROPN
ejpam-4944	143	14	=	=	SYM
ejpam-4944	143	15	x.	x.	NOUN
ejpam-4944	143	16	here	here	ADV
ejpam-4944	143	17	,	,	PUNCT
ejpam-4944	143	18	k	k	PROPN
ejpam-4944	143	19	=	=	PRON
ejpam-4944	143	20	{	{	PUNCT
ejpam-4944	143	21	s	s	X
ejpam-4944	143	22	}	}	PUNCT
ejpam-4944	143	23	is	be	AUX
ejpam-4944	143	24	µ2	µ2	ADJ
ejpam-4944	143	25	-	-	PUNCT
ejpam-4944	143	26	dense	dense	ADJ
ejpam-4944	143	27	.	.	PUNCT
ejpam-4944	144	1	but	but	CCONJ
ejpam-4944	144	2	cµ1k	cµ1k	PROPN
ejpam-4944	144	3	∩	∩	NOUN
ejpam-4944	144	4	{	{	PUNCT
ejpam-4944	144	5	r	r	NOUN
ejpam-4944	144	6	}	}	PUNCT
ejpam-4944	144	7	=	=	NOUN
ejpam-4944	144	8	∅	∅	NOUN
ejpam-4944	144	9	where	where	SCONJ
ejpam-4944	144	10	{	{	PUNCT
ejpam-4944	144	11	r	r	NOUN
ejpam-4944	144	12	}	}	PUNCT
ejpam-4944	144	13	∈	∈	NOUN
ejpam-4944	144	14	σ̃2	σ̃2	PROPN
ejpam-4944	144	15	for	for	ADP
ejpam-4944	144	16	that	that	PRON
ejpam-4944	144	17	k	k	PROPN
ejpam-4944	144	18	/∈	/∈	PUNCT
ejpam-4944	145	1	(	(	PUNCT
ejpam-4944	145	2	2	2	NUM
ejpam-4944	145	3	,	,	PUNCT
ejpam-4944	145	4	1)⋆	1)⋆	PROPN
ejpam-4944	145	5	−d(x	−d(x	NOUN
ejpam-4944	145	6	)	)	PUNCT
ejpam-4944	145	7	.	.	PUNCT
ejpam-4944	146	1	d.	d.	PROPN
ejpam-4944	146	2	elgezouli	elgezouli	PROPN
ejpam-4944	146	3	et	et	PROPN
ejpam-4944	146	4	al	al	PROPN
ejpam-4944	146	5	.	.	PUNCT
ejpam-4944	146	6	/	/	SYM
ejpam-4944	146	7	eur	eur	PROPN
ejpam-4944	146	8	.	.	PUNCT
ejpam-4944	147	1	j.	j.	PROPN
ejpam-4944	147	2	pure	pure	PROPN
ejpam-4944	147	3	appl	appl	PROPN
ejpam-4944	147	4	.	.	PROPN
ejpam-4944	147	5	math	math	PROPN
ejpam-4944	147	6	,	,	PUNCT
ejpam-4944	147	7	16	16	NUM
ejpam-4944	147	8	(	(	PUNCT
ejpam-4944	147	9	4	4	NUM
ejpam-4944	147	10	)	)	PUNCT
ejpam-4944	147	11	(	(	PUNCT
ejpam-4944	147	12	2023	2023	NUM
ejpam-4944	147	13	)	)	PUNCT
ejpam-4944	147	14	,	,	PUNCT
ejpam-4944	147	15	2286	2286	NUM
ejpam-4944	147	16	-	-	SYM
ejpam-4944	147	17	2305	2305	NUM
ejpam-4944	147	18	2291	2291	NUM
ejpam-4944	147	19	theorem	theorem	VERB
ejpam-4944	147	20	13	13	NUM
ejpam-4944	147	21	.	.	PUNCT
ejpam-4944	148	1	let	let	AUX
ejpam-4944	148	2	(	(	PUNCT
ejpam-4944	148	3	x,µ1	x,µ1	NOUN
ejpam-4944	148	4	,	,	PUNCT
ejpam-4944	148	5	µ2	µ2	PROPN
ejpam-4944	148	6	)	)	PUNCT
ejpam-4944	148	7	be	be	AUX
ejpam-4944	148	8	a	a	DET
ejpam-4944	148	9	bgts	bgts	NOUN
ejpam-4944	148	10	.	.	PUNCT
ejpam-4944	149	1	then	then	ADV
ejpam-4944	149	2	the	the	DET
ejpam-4944	149	3	following	follow	VERB
ejpam-4944	149	4	are	be	AUX
ejpam-4944	149	5	true	true	ADJ
ejpam-4944	149	6	.	.	PUNCT
ejpam-4944	150	1	(	(	PUNCT
ejpam-4944	150	2	a	a	X
ejpam-4944	150	3	)	)	PUNCT
ejpam-4944	150	4	if	if	SCONJ
ejpam-4944	150	5	cµv(q	cµv(q	NOUN
ejpam-4944	150	6	)	)	PUNCT
ejpam-4944	150	7	=	=	SYM
ejpam-4944	150	8	x	x	NOUN
ejpam-4944	150	9	,	,	PUNCT
ejpam-4944	150	10	then	then	ADV
ejpam-4944	150	11	q	q	PROPN
ejpam-4944	150	12	∈	∈	PROPN
ejpam-4944	150	13	(	(	PUNCT
ejpam-4944	150	14	s	s	PROPN
ejpam-4944	150	15	,	,	PUNCT
ejpam-4944	150	16	v)⋆	v)⋆	PROPN
ejpam-4944	150	17	−d(x	−d(x	NOUN
ejpam-4944	150	18	)	)	PUNCT
ejpam-4944	150	19	where	where	SCONJ
ejpam-4944	150	20	s	s	X
ejpam-4944	150	21	,	,	PUNCT
ejpam-4944	150	22	v	v	NOUN
ejpam-4944	150	23	=	=	SYM
ejpam-4944	150	24	1	1	NUM
ejpam-4944	150	25	,	,	PUNCT
ejpam-4944	150	26	2	2	NUM
ejpam-4944	150	27	;	;	PUNCT
ejpam-4944	150	28	s	s	VERB
ejpam-4944	150	29	̸=	̸=	PROPN
ejpam-4944	150	30	v.	v.	ADP
ejpam-4944	150	31	(	(	PUNCT
ejpam-4944	150	32	b	b	NOUN
ejpam-4944	150	33	)	)	PUNCT
ejpam-4944	150	34	if	if	SCONJ
ejpam-4944	150	35	µs	µs	X
ejpam-4944	150	36	⊂	⊂	PROPN
ejpam-4944	150	37	µv	µv	PROPN
ejpam-4944	150	38	,	,	PUNCT
ejpam-4944	150	39	then	then	ADV
ejpam-4944	150	40	every	every	DET
ejpam-4944	150	41	(	(	PUNCT
ejpam-4944	150	42	s	s	X
ejpam-4944	150	43	,	,	PUNCT
ejpam-4944	150	44	v)⋆-dense	v)⋆-dense	PROPN
ejpam-4944	150	45	is	be	AUX
ejpam-4944	150	46	µs	µs	NOUN
ejpam-4944	150	47	-	-	ADJ
ejpam-4944	150	48	dense	dense	ADJ
ejpam-4944	150	49	where	where	SCONJ
ejpam-4944	150	50	s	s	X
ejpam-4944	150	51	,	,	PUNCT
ejpam-4944	150	52	v	v	NOUN
ejpam-4944	150	53	=	=	SYM
ejpam-4944	150	54	1	1	NUM
ejpam-4944	150	55	,	,	PUNCT
ejpam-4944	150	56	2	2	NUM
ejpam-4944	150	57	;	;	PUNCT
ejpam-4944	150	58	s	s	VERB
ejpam-4944	150	59	̸=	̸=	PROPN
ejpam-4944	150	60	v.	v.	ADP
ejpam-4944	150	61	proof	proof	NOUN
ejpam-4944	150	62	.	.	PUNCT
ejpam-4944	151	1	(	(	PUNCT
ejpam-4944	151	2	a	a	X
ejpam-4944	151	3	)	)	PUNCT
ejpam-4944	151	4	.	.	PUNCT
ejpam-4944	152	1	assume	assume	VERB
ejpam-4944	152	2	that	that	SCONJ
ejpam-4944	152	3	,	,	PUNCT
ejpam-4944	152	4	cµv(q	cµv(q	PROPN
ejpam-4944	152	5	)	)	PUNCT
ejpam-4944	152	6	=	=	PUNCT
ejpam-4944	153	1	x	x	PUNCT
ejpam-4944	153	2	for	for	ADP
ejpam-4944	153	3	v	v	NOUN
ejpam-4944	153	4	=	=	SYM
ejpam-4944	153	5	1	1	NUM
ejpam-4944	153	6	,	,	PUNCT
ejpam-4944	153	7	2	2	NUM
ejpam-4944	153	8	.	.	PUNCT
ejpam-4944	154	1	fix	fix	NOUN
ejpam-4944	154	2	s	s	PART
ejpam-4944	154	3	=	=	SYM
ejpam-4944	154	4	1	1	NUM
ejpam-4944	154	5	and	and	CCONJ
ejpam-4944	154	6	v	v	NOUN
ejpam-4944	154	7	=	=	SYM
ejpam-4944	154	8	2	2	X
ejpam-4944	154	9	.	.	X
ejpam-4944	155	1	we	we	PRON
ejpam-4944	155	2	get	get	VERB
ejpam-4944	155	3	cµ2(q	cµ2(q	PROPN
ejpam-4944	155	4	)	)	PUNCT
ejpam-4944	156	1	=	=	PUNCT
ejpam-4944	157	1	x	x	PUNCT
ejpam-4944	157	2	so	so	ADV
ejpam-4944	157	3	that	that	SCONJ
ejpam-4944	157	4	cµ2(q)∩h	cµ2(q)∩h	NOUN
ejpam-4944	157	5	̸=	̸=	PROPN
ejpam-4944	157	6	∅	∅	NOUN
ejpam-4944	157	7	for	for	ADP
ejpam-4944	157	8	all	all	DET
ejpam-4944	157	9	h	h	NOUN
ejpam-4944	157	10	∈	∈	PROPN
ejpam-4944	157	11	σ̃1	σ̃1	PROPN
ejpam-4944	157	12	.	.	PUNCT
ejpam-4944	158	1	therefore	therefore	ADV
ejpam-4944	158	2	,	,	PUNCT
ejpam-4944	158	3	q	q	X
ejpam-4944	158	4	is	be	AUX
ejpam-4944	158	5	(	(	PUNCT
ejpam-4944	158	6	1	1	NUM
ejpam-4944	158	7	,	,	PUNCT
ejpam-4944	158	8	2)⋆	2)⋆	PROPN
ejpam-4944	158	9	−d(x	−d(x	NOUN
ejpam-4944	158	10	)	)	PUNCT
ejpam-4944	158	11	.	.	PUNCT
ejpam-4944	159	1	take	take	VERB
ejpam-4944	159	2	s	s	NOUN
ejpam-4944	159	3	=	=	SYM
ejpam-4944	159	4	2	2	NUM
ejpam-4944	159	5	and	and	CCONJ
ejpam-4944	159	6	v	v	NOUN
ejpam-4944	159	7	=	=	SYM
ejpam-4944	159	8	1	1	NUM
ejpam-4944	159	9	.	.	PUNCT
ejpam-4944	160	1	then	then	ADV
ejpam-4944	160	2	cµ1(q	cµ1(q	ADJ
ejpam-4944	160	3	)	)	PUNCT
ejpam-4944	160	4	=	=	SYM
ejpam-4944	161	1	x	x	PUNCT
ejpam-4944	161	2	and	and	CCONJ
ejpam-4944	161	3	so	so	ADV
ejpam-4944	161	4	cµ1(q)∩k	cµ1(q)∩k	PROPN
ejpam-4944	161	5	̸=	̸=	PROPN
ejpam-4944	161	6	∅	∅	NOUN
ejpam-4944	161	7	for	for	ADP
ejpam-4944	161	8	all	all	DET
ejpam-4944	161	9	k	k	PROPN
ejpam-4944	161	10	∈	∈	PROPN
ejpam-4944	161	11	σ̃2	σ̃2	PROPN
ejpam-4944	161	12	.	.	PUNCT
ejpam-4944	162	1	therefore	therefore	ADV
ejpam-4944	162	2	,	,	PUNCT
ejpam-4944	162	3	q	q	X
ejpam-4944	162	4	is	be	AUX
ejpam-4944	162	5	(	(	PUNCT
ejpam-4944	162	6	2	2	NUM
ejpam-4944	162	7	,	,	PUNCT
ejpam-4944	162	8	1)⋆	1)⋆	PROPN
ejpam-4944	162	9	−d(x	−d(x	NOUN
ejpam-4944	162	10	)	)	PUNCT
ejpam-4944	162	11	.	.	PUNCT
ejpam-4944	163	1	(	(	PUNCT
ejpam-4944	163	2	b	b	X
ejpam-4944	163	3	)	)	PUNCT
ejpam-4944	163	4	.	.	PUNCT
ejpam-4944	164	1	suppose	suppose	VERB
ejpam-4944	164	2	that	that	SCONJ
ejpam-4944	164	3	µs	µs	PROPN
ejpam-4944	164	4	⊂	⊂	PROPN
ejpam-4944	164	5	µv	µv	VERB
ejpam-4944	164	6	for	for	ADP
ejpam-4944	164	7	s	s	PROPN
ejpam-4944	164	8	,	,	PUNCT
ejpam-4944	164	9	v	v	NOUN
ejpam-4944	164	10	=	=	SYM
ejpam-4944	164	11	1	1	NUM
ejpam-4944	164	12	,	,	PUNCT
ejpam-4944	164	13	2	2	NUM
ejpam-4944	164	14	;	;	PUNCT
ejpam-4944	164	15	s	s	VERB
ejpam-4944	164	16	̸=	̸=	PROPN
ejpam-4944	164	17	v.	v.	CCONJ
ejpam-4944	164	18	let	let	VERB
ejpam-4944	164	19	k	k	PROPN
ejpam-4944	164	20	∈	∈	PROPN
ejpam-4944	164	21	(	(	PUNCT
ejpam-4944	164	22	s	s	PROPN
ejpam-4944	164	23	,	,	PUNCT
ejpam-4944	164	24	v)⋆	v)⋆	PROPN
ejpam-4944	164	25	−d(x	−d(x	NOUN
ejpam-4944	164	26	)	)	PUNCT
ejpam-4944	164	27	where	where	SCONJ
ejpam-4944	164	28	s	s	X
ejpam-4944	164	29	,	,	PUNCT
ejpam-4944	164	30	v	v	NOUN
ejpam-4944	164	31	=	=	SYM
ejpam-4944	164	32	1	1	NUM
ejpam-4944	164	33	,	,	PUNCT
ejpam-4944	164	34	2	2	NUM
ejpam-4944	164	35	;	;	PUNCT
ejpam-4944	164	36	s	s	VERB
ejpam-4944	164	37	̸=	̸=	PROPN
ejpam-4944	164	38	v.	v.	ADP
ejpam-4944	164	39	consider	consider	VERB
ejpam-4944	164	40	s	s	NOUN
ejpam-4944	164	41	=	=	SYM
ejpam-4944	164	42	1	1	NUM
ejpam-4944	164	43	and	and	CCONJ
ejpam-4944	164	44	v	v	NOUN
ejpam-4944	164	45	=	=	SYM
ejpam-4944	164	46	2	2	NUM
ejpam-4944	164	47	.	.	PUNCT
ejpam-4944	164	48	then	then	ADV
ejpam-4944	164	49	µ1	µ1	PROPN
ejpam-4944	164	50	⊂	⊂	PROPN
ejpam-4944	164	51	µ2	µ2	PROPN
ejpam-4944	164	52	and	and	CCONJ
ejpam-4944	164	53	k	k	PROPN
ejpam-4944	164	54	∈	∈	PROPN
ejpam-4944	164	55	(	(	PUNCT
ejpam-4944	164	56	1	1	NUM
ejpam-4944	164	57	,	,	PUNCT
ejpam-4944	164	58	2)⋆	2)⋆	NOUN
ejpam-4944	164	59	−	−	NOUN
ejpam-4944	164	60	d(x	d(x	NOUN
ejpam-4944	164	61	)	)	PUNCT
ejpam-4944	164	62	.	.	PUNCT
ejpam-4944	165	1	let	let	VERB
ejpam-4944	165	2	g	g	PROPN
ejpam-4944	165	3	∈	∈	PROPN
ejpam-4944	165	4	µ̃1	µ̃1	PROPN
ejpam-4944	165	5	.	.	PUNCT
ejpam-4944	166	1	then	then	ADV
ejpam-4944	166	2	g	g	PROPN
ejpam-4944	166	3	∈	∈	PROPN
ejpam-4944	166	4	σ̃1	σ̃1	PROPN
ejpam-4944	166	5	so	so	SCONJ
ejpam-4944	166	6	that	that	DET
ejpam-4944	166	7	g∩cµ2k	g∩cµ2k	NOUN
ejpam-4944	166	8	̸=	̸=	PROPN
ejpam-4944	166	9	∅.	∅.	NOUN
ejpam-4944	166	10	by	by	ADP
ejpam-4944	166	11	hypothesis	hypothesis	NOUN
ejpam-4944	166	12	and	and	CCONJ
ejpam-4944	166	13	lemma	lemma	PROPN
ejpam-4944	166	14	3	3	NUM
ejpam-4944	166	15	,	,	PUNCT
ejpam-4944	166	16	g∩k	g∩k	PROPN
ejpam-4944	166	17	̸=	̸=	PROPN
ejpam-4944	166	18	∅.	∅.	NOUN
ejpam-4944	166	19	hencek	hencek	ADV
ejpam-4944	166	20	is	be	AUX
ejpam-4944	166	21	µ1	µ1	NOUN
ejpam-4944	166	22	-	-	PUNCT
ejpam-4944	166	23	dense	dense	ADJ
ejpam-4944	166	24	.	.	PUNCT
ejpam-4944	167	1	take	take	VERB
ejpam-4944	167	2	s	s	NOUN
ejpam-4944	167	3	=	=	SYM
ejpam-4944	167	4	2	2	NUM
ejpam-4944	167	5	and	and	CCONJ
ejpam-4944	167	6	v	v	NOUN
ejpam-4944	167	7	=	=	SYM
ejpam-4944	167	8	1	1	NUM
ejpam-4944	167	9	.	.	PUNCT
ejpam-4944	168	1	then	then	ADV
ejpam-4944	168	2	µ2	µ2	PROPN
ejpam-4944	168	3	⊂	⊂	PROPN
ejpam-4944	168	4	µ1	µ1	PROPN
ejpam-4944	168	5	and	and	CCONJ
ejpam-4944	168	6	k	k	PROPN
ejpam-4944	168	7	∈	∈	PROPN
ejpam-4944	168	8	(	(	PUNCT
ejpam-4944	168	9	2	2	NUM
ejpam-4944	168	10	,	,	PUNCT
ejpam-4944	168	11	1)⋆	1)⋆	PROPN
ejpam-4944	168	12	−d(x	−d(x	NOUN
ejpam-4944	168	13	)	)	PUNCT
ejpam-4944	168	14	.	.	PUNCT
ejpam-4944	169	1	let	let	VERB
ejpam-4944	169	2	h	h	NOUN
ejpam-4944	169	3	∈	∈	PROPN
ejpam-4944	169	4	µ̃2	µ̃2	PROPN
ejpam-4944	169	5	.	.	PUNCT
ejpam-4944	170	1	then	then	ADV
ejpam-4944	170	2	h	h	PROPN
ejpam-4944	170	3	∈	∈	PROPN
ejpam-4944	170	4	σ̃2	σ̃2	PROPN
ejpam-4944	170	5	so	so	SCONJ
ejpam-4944	170	6	that	that	SCONJ
ejpam-4944	170	7	h	h	PROPN
ejpam-4944	170	8	∩	∩	X
ejpam-4944	170	9	cµ1k	cµ1k	PROPN
ejpam-4944	170	10	̸=	̸=	PROPN
ejpam-4944	170	11	∅.	∅.	NOUN
ejpam-4944	170	12	by	by	ADP
ejpam-4944	170	13	hypothesis	hypothesis	NOUN
ejpam-4944	170	14	and	and	CCONJ
ejpam-4944	170	15	lemma	lemma	PROPN
ejpam-4944	170	16	3	3	NUM
ejpam-4944	170	17	,	,	PUNCT
ejpam-4944	170	18	h	h	NOUN
ejpam-4944	170	19	∩k	∩k	NOUN
ejpam-4944	170	20	̸=	̸=	PROPN
ejpam-4944	170	21	∅.	∅.	PRON
ejpam-4944	170	22	hence	hence	ADV
ejpam-4944	170	23	k	k	PROPN
ejpam-4944	170	24	is	be	AUX
ejpam-4944	170	25	µ2	µ2	ADJ
ejpam-4944	170	26	-	-	PUNCT
ejpam-4944	170	27	dense	dense	ADJ
ejpam-4944	170	28	.	.	PUNCT
ejpam-4944	171	1	the	the	DET
ejpam-4944	171	2	below	below	ADP
ejpam-4944	171	3	example	example	NOUN
ejpam-4944	171	4	14	14	NUM
ejpam-4944	171	5	(	(	PUNCT
ejpam-4944	171	6	b	b	NOUN
ejpam-4944	171	7	)	)	PUNCT
ejpam-4944	171	8	shows	show	VERB
ejpam-4944	171	9	that	that	SCONJ
ejpam-4944	171	10	the	the	DET
ejpam-4944	171	11	converse	converse	NOUN
ejpam-4944	171	12	part	part	NOUN
ejpam-4944	171	13	of	of	ADP
ejpam-4944	171	14	theorem	theorem	ADJ
ejpam-4944	171	15	13	13	NUM
ejpam-4944	171	16	(	(	PUNCT
ejpam-4944	171	17	a	a	NOUN
ejpam-4944	171	18	)	)	PUNCT
ejpam-4944	171	19	need	need	AUX
ejpam-4944	171	20	not	not	PART
ejpam-4944	171	21	be	be	AUX
ejpam-4944	171	22	true	true	ADJ
ejpam-4944	171	23	and	and	CCONJ
ejpam-4944	171	24	the	the	DET
ejpam-4944	171	25	hypothesis	hypothesis	NOUN
ejpam-4944	171	26	of	of	ADP
ejpam-4944	171	27	theorem	theorem	ADJ
ejpam-4944	171	28	13	13	NUM
ejpam-4944	171	29	(	(	PUNCT
ejpam-4944	171	30	b	b	NOUN
ejpam-4944	171	31	)	)	PUNCT
ejpam-4944	171	32	can	can	AUX
ejpam-4944	171	33	not	not	PART
ejpam-4944	171	34	be	be	AUX
ejpam-4944	171	35	neglected	neglect	VERB
ejpam-4944	171	36	as	as	SCONJ
ejpam-4944	171	37	shown	show	VERB
ejpam-4944	171	38	by	by	ADP
ejpam-4944	171	39	example	example	NOUN
ejpam-4944	171	40	14	14	NUM
ejpam-4944	171	41	(	(	PUNCT
ejpam-4944	171	42	a	a	NOUN
ejpam-4944	171	43	)	)	PUNCT
ejpam-4944	171	44	.	.	PUNCT
ejpam-4944	172	1	example	example	NOUN
ejpam-4944	173	1	14	14	NUM
ejpam-4944	173	2	.	.	PUNCT
ejpam-4944	174	1	consider	consider	VERB
ejpam-4944	174	2	the	the	DET
ejpam-4944	174	3	bigeneralized	bigeneralized	ADJ
ejpam-4944	174	4	topological	topological	ADJ
ejpam-4944	174	5	space	space	NOUN
ejpam-4944	174	6	(	(	PUNCT
ejpam-4944	174	7	x,µ1	x,µ1	PROPN
ejpam-4944	174	8	,	,	PUNCT
ejpam-4944	174	9	µ2	µ2	ADJ
ejpam-4944	174	10	)	)	PUNCT
ejpam-4944	174	11	wherex	wherex	PROPN
ejpam-4944	174	12	=	=	PUNCT
ejpam-4944	174	13	{	{	PUNCT
ejpam-4944	174	14	p	p	X
ejpam-4944	174	15	,	,	PUNCT
ejpam-4944	174	16	q	q	ADJ
ejpam-4944	174	17	,	,	PUNCT
ejpam-4944	174	18	r	r	NOUN
ejpam-4944	174	19	,	,	PUNCT
ejpam-4944	174	20	s	s	PART
ejpam-4944	174	21	}	}	PUNCT
ejpam-4944	174	22	;	;	PUNCT
ejpam-4944	174	23	µ1	µ1	PROPN
ejpam-4944	174	24	=	=	SYM
ejpam-4944	174	25	{	{	PUNCT
ejpam-4944	174	26	∅	∅	NOUN
ejpam-4944	174	27	,	,	PUNCT
ejpam-4944	174	28	{	{	PUNCT
ejpam-4944	174	29	p	p	X
ejpam-4944	174	30	,	,	PUNCT
ejpam-4944	174	31	r	r	NOUN
ejpam-4944	174	32	}	}	PUNCT
ejpam-4944	174	33	,	,	PUNCT
ejpam-4944	174	34	{	{	PUNCT
ejpam-4944	174	35	p	p	X
ejpam-4944	174	36	,	,	PUNCT
ejpam-4944	174	37	s	s	PART
ejpam-4944	174	38	}	}	PUNCT
ejpam-4944	174	39	,	,	PUNCT
ejpam-4944	174	40	{	{	PUNCT
ejpam-4944	174	41	p	p	X
ejpam-4944	174	42	,	,	PUNCT
ejpam-4944	174	43	r	r	NOUN
ejpam-4944	174	44	,	,	PUNCT
ejpam-4944	174	45	s	s	PART
ejpam-4944	174	46	}	}	PUNCT
ejpam-4944	174	47	}	}	PUNCT
ejpam-4944	174	48	and	and	CCONJ
ejpam-4944	174	49	µ2	µ2	PROPN
ejpam-4944	174	50	=	=	PUNCT
ejpam-4944	174	51	{	{	PUNCT
ejpam-4944	174	52	∅	∅	NOUN
ejpam-4944	174	53	,	,	PUNCT
ejpam-4944	174	54	{	{	PUNCT
ejpam-4944	174	55	q	q	NOUN
ejpam-4944	174	56	,	,	PUNCT
ejpam-4944	174	57	r	r	NOUN
ejpam-4944	174	58	}	}	PUNCT
ejpam-4944	174	59	,	,	PUNCT
ejpam-4944	174	60	{	{	PUNCT
ejpam-4944	174	61	q	q	X
ejpam-4944	174	62	,	,	PUNCT
ejpam-4944	174	63	s	s	PART
ejpam-4944	174	64	}	}	PUNCT
ejpam-4944	174	65	,	,	PUNCT
ejpam-4944	174	66	{	{	PUNCT
ejpam-4944	174	67	r	r	NOUN
ejpam-4944	174	68	,	,	PUNCT
ejpam-4944	174	69	s	s	PART
ejpam-4944	174	70	}	}	PUNCT
ejpam-4944	174	71	,	,	PUNCT
ejpam-4944	174	72	{	{	PUNCT
ejpam-4944	174	73	q	q	X
ejpam-4944	174	74	,	,	PUNCT
ejpam-4944	174	75	r	r	NOUN
ejpam-4944	174	76	,	,	PUNCT
ejpam-4944	174	77	s	s	PART
ejpam-4944	174	78	}	}	PUNCT
ejpam-4944	174	79	}	}	PUNCT
ejpam-4944	174	80	.	.	PUNCT
ejpam-4944	175	1	we	we	PRON
ejpam-4944	175	2	get	get	VERB
ejpam-4944	175	3	σ1	σ1	NOUN
ejpam-4944	175	4	=	=	SYM
ejpam-4944	175	5	{	{	PUNCT
ejpam-4944	175	6	∅	∅	NOUN
ejpam-4944	175	7	,	,	PUNCT
ejpam-4944	175	8	{	{	PUNCT
ejpam-4944	175	9	q	q	X
ejpam-4944	175	10	}	}	PUNCT
ejpam-4944	175	11	,	,	PUNCT
ejpam-4944	175	12	{	{	PUNCT
ejpam-4944	175	13	p	p	X
ejpam-4944	175	14	,	,	PUNCT
ejpam-4944	175	15	r	r	NOUN
ejpam-4944	175	16	}	}	PUNCT
ejpam-4944	175	17	,	,	PUNCT
ejpam-4944	175	18	{	{	PUNCT
ejpam-4944	175	19	p	p	X
ejpam-4944	175	20	,	,	PUNCT
ejpam-4944	175	21	s	s	PART
ejpam-4944	175	22	}	}	PUNCT
ejpam-4944	175	23	,	,	PUNCT
ejpam-4944	175	24	{	{	PUNCT
ejpam-4944	175	25	p	p	X
ejpam-4944	175	26	,	,	PUNCT
ejpam-4944	175	27	q	q	ADJ
ejpam-4944	175	28	,	,	PUNCT
ejpam-4944	175	29	r	r	NOUN
ejpam-4944	175	30	}	}	PUNCT
ejpam-4944	175	31	,	,	PUNCT
ejpam-4944	175	32	{	{	PUNCT
ejpam-4944	175	33	p	p	X
ejpam-4944	175	34	,	,	PUNCT
ejpam-4944	175	35	q	q	X
ejpam-4944	175	36	,	,	PUNCT
ejpam-4944	175	37	s	s	PART
ejpam-4944	175	38	}	}	PUNCT
ejpam-4944	175	39	,	,	PUNCT
ejpam-4944	175	40	{	{	PUNCT
ejpam-4944	175	41	p	p	X
ejpam-4944	175	42	,	,	PUNCT
ejpam-4944	175	43	r	r	NOUN
ejpam-4944	175	44	,	,	PUNCT
ejpam-4944	175	45	s	s	PART
ejpam-4944	175	46	}	}	PUNCT
ejpam-4944	175	47	,	,	PUNCT
ejpam-4944	175	48	x	x	NOUN
ejpam-4944	175	49	}	}	PUNCT
ejpam-4944	175	50	and	and	CCONJ
ejpam-4944	175	51	σ2	σ2	PROPN
ejpam-4944	175	52	=	=	SYM
ejpam-4944	175	53	{	{	PUNCT
ejpam-4944	175	54	∅	∅	NOUN
ejpam-4944	175	55	,	,	PUNCT
ejpam-4944	175	56	{	{	PUNCT
ejpam-4944	175	57	p	p	X
ejpam-4944	175	58	}	}	PUNCT
ejpam-4944	175	59	,	,	PUNCT
ejpam-4944	175	60	{	{	PUNCT
ejpam-4944	175	61	q	q	X
ejpam-4944	175	62	,	,	PUNCT
ejpam-4944	175	63	r	r	NOUN
ejpam-4944	175	64	}	}	PUNCT
ejpam-4944	175	65	,	,	PUNCT
ejpam-4944	175	66	{	{	PUNCT
ejpam-4944	175	67	q	q	X
ejpam-4944	175	68	,	,	PUNCT
ejpam-4944	175	69	s	s	PART
ejpam-4944	175	70	}	}	PUNCT
ejpam-4944	175	71	,	,	PUNCT
ejpam-4944	175	72	{	{	PUNCT
ejpam-4944	175	73	r	r	NOUN
ejpam-4944	175	74	,	,	PUNCT
ejpam-4944	175	75	s	s	PART
ejpam-4944	175	76	}	}	PUNCT
ejpam-4944	175	77	,	,	PUNCT
ejpam-4944	175	78	{	{	PUNCT
ejpam-4944	175	79	p	p	X
ejpam-4944	175	80	,	,	PUNCT
ejpam-4944	175	81	q	q	ADJ
ejpam-4944	175	82	,	,	PUNCT
ejpam-4944	175	83	r	r	NOUN
ejpam-4944	175	84	}	}	PUNCT
ejpam-4944	175	85	,	,	PUNCT
ejpam-4944	175	86	{	{	PUNCT
ejpam-4944	175	87	p	p	X
ejpam-4944	175	88	,	,	PUNCT
ejpam-4944	175	89	q	q	X
ejpam-4944	175	90	,	,	PUNCT
ejpam-4944	175	91	s	s	PART
ejpam-4944	175	92	}	}	PUNCT
ejpam-4944	175	93	,	,	PUNCT
ejpam-4944	175	94	{	{	PUNCT
ejpam-4944	175	95	p	p	X
ejpam-4944	175	96	,	,	PUNCT
ejpam-4944	175	97	r	r	NOUN
ejpam-4944	175	98	,	,	PUNCT
ejpam-4944	175	99	s	s	PART
ejpam-4944	175	100	}	}	PUNCT
ejpam-4944	175	101	,	,	PUNCT
ejpam-4944	175	102	{	{	PUNCT
ejpam-4944	175	103	q	q	X
ejpam-4944	175	104	,	,	PUNCT
ejpam-4944	175	105	r	r	NOUN
ejpam-4944	175	106	,	,	PUNCT
ejpam-4944	175	107	s	s	PART
ejpam-4944	175	108	}	}	PUNCT
ejpam-4944	175	109	,	,	PUNCT
ejpam-4944	175	110	x	x	NOUN
ejpam-4944	175	111	}	}	PUNCT
ejpam-4944	175	112	.	.	PUNCT
ejpam-4944	176	1	(	(	PUNCT
ejpam-4944	176	2	a	a	X
ejpam-4944	176	3	)	)	PUNCT
ejpam-4944	176	4	.	.	PUNCT
ejpam-4944	177	1	fix	fix	NOUN
ejpam-4944	177	2	s	s	PART
ejpam-4944	177	3	=	=	NOUN
ejpam-4944	177	4	1	1	NUM
ejpam-4944	177	5	;	;	PUNCT
ejpam-4944	177	6	v	v	NOUN
ejpam-4944	177	7	=	=	SYM
ejpam-4944	177	8	2	2	NUM
ejpam-4944	177	9	.	.	PUNCT
ejpam-4944	178	1	here	here	ADV
ejpam-4944	178	2	,	,	PUNCT
ejpam-4944	178	3	µ1	µ1	PROPN
ejpam-4944	178	4	⊈	⊈	PROPN
ejpam-4944	178	5	µ2	µ2	PROPN
ejpam-4944	178	6	.	.	PUNCT
ejpam-4944	179	1	choose	choose	VERB
ejpam-4944	179	2	q	q	NOUN
ejpam-4944	179	3	=	=	PUNCT
ejpam-4944	179	4	{	{	PUNCT
ejpam-4944	179	5	q	q	NOUN
ejpam-4944	179	6	,	,	PUNCT
ejpam-4944	179	7	r	r	NOUN
ejpam-4944	179	8	}	}	PUNCT
ejpam-4944	179	9	we	we	PRON
ejpam-4944	179	10	get	get	VERB
ejpam-4944	179	11	q	q	X
ejpam-4944	179	12	∈	∈	NOUN
ejpam-4944	179	13	(	(	PUNCT
ejpam-4944	179	14	1	1	NUM
ejpam-4944	179	15	,	,	PUNCT
ejpam-4944	179	16	2)⋆	2)⋆	NOUN
ejpam-4944	179	17	−	−	NOUN
ejpam-4944	179	18	d(x	d(x	NOUN
ejpam-4944	179	19	)	)	PUNCT
ejpam-4944	179	20	.	.	PUNCT
ejpam-4944	180	1	because	because	SCONJ
ejpam-4944	180	2	,	,	PUNCT
ejpam-4944	180	3	c2q	c2q	NOUN
ejpam-4944	180	4	∩	∩	ADJ
ejpam-4944	180	5	l	l	PROPN
ejpam-4944	180	6	̸=	̸=	PROPN
ejpam-4944	180	7	∅	∅	NOUN
ejpam-4944	180	8	for	for	ADP
ejpam-4944	180	9	all	all	DET
ejpam-4944	180	10	l	l	NOUN
ejpam-4944	180	11	∈	∈	PROPN
ejpam-4944	180	12	σ̃1	σ̃1	PROPN
ejpam-4944	180	13	.	.	PUNCT
ejpam-4944	181	1	but	but	CCONJ
ejpam-4944	181	2	c1q	c1q	PROPN
ejpam-4944	181	3	=	=	SYM
ejpam-4944	181	4	q	q	PROPN
ejpam-4944	181	5	̸=	̸=	PROPN
ejpam-4944	181	6	x	x	PUNCT
ejpam-4944	181	7	so	so	ADV
ejpam-4944	181	8	that	that	PRON
ejpam-4944	181	9	q	q	NOUN
ejpam-4944	181	10	is	be	AUX
ejpam-4944	181	11	not	not	PART
ejpam-4944	181	12	µ1	µ1	NOUN
ejpam-4944	181	13	-	-	PUNCT
ejpam-4944	181	14	dense	dense	ADJ
ejpam-4944	181	15	.	.	PUNCT
ejpam-4944	182	1	take	take	VERB
ejpam-4944	182	2	s	s	NOUN
ejpam-4944	182	3	=	=	SYM
ejpam-4944	182	4	2	2	NUM
ejpam-4944	182	5	,	,	PUNCT
ejpam-4944	182	6	v	v	NOUN
ejpam-4944	182	7	=	=	SYM
ejpam-4944	182	8	1	1	NUM
ejpam-4944	182	9	and	and	CCONJ
ejpam-4944	182	10	l	l	NOUN
ejpam-4944	182	11	=	=	PUNCT
ejpam-4944	182	12	{	{	PUNCT
ejpam-4944	182	13	p	p	X
ejpam-4944	182	14	,	,	PUNCT
ejpam-4944	182	15	q	q	NOUN
ejpam-4944	182	16	}	}	PUNCT
ejpam-4944	182	17	.	.	PUNCT
ejpam-4944	183	1	here	here	ADV
ejpam-4944	183	2	,	,	PUNCT
ejpam-4944	183	3	c1l	c1l	PROPN
ejpam-4944	183	4	∩	∩	PROPN
ejpam-4944	183	5	d	d	PROPN
ejpam-4944	183	6	̸=	̸=	PROPN
ejpam-4944	183	7	∅	∅	NOUN
ejpam-4944	183	8	for	for	ADP
ejpam-4944	183	9	each	each	DET
ejpam-4944	183	10	d	d	PROPN
ejpam-4944	183	11	∈	∈	PROPN
ejpam-4944	183	12	σ̃2	σ̃2	PROPN
ejpam-4944	183	13	so	so	SCONJ
ejpam-4944	183	14	that	that	SCONJ
ejpam-4944	183	15	l	l	PROPN
ejpam-4944	183	16	∈	∈	PROPN
ejpam-4944	183	17	(	(	PUNCT
ejpam-4944	183	18	2	2	NUM
ejpam-4944	183	19	,	,	PUNCT
ejpam-4944	183	20	1)⋆	1)⋆	PROPN
ejpam-4944	183	21	−d(x	−d(x	NOUN
ejpam-4944	183	22	)	)	PUNCT
ejpam-4944	183	23	.	.	PUNCT
ejpam-4944	184	1	since	since	SCONJ
ejpam-4944	184	2	c2l	c2l	NOUN
ejpam-4944	184	3	=	=	SYM
ejpam-4944	184	4	l	l	NOUN
ejpam-4944	184	5	̸=	̸=	PROPN
ejpam-4944	184	6	∅	∅	NOUN
ejpam-4944	184	7	we	we	PRON
ejpam-4944	184	8	have	have	VERB
ejpam-4944	184	9	l	l	NOUN
ejpam-4944	184	10	is	be	AUX
ejpam-4944	184	11	not	not	PART
ejpam-4944	184	12	µ2	µ2	ADJ
ejpam-4944	184	13	-	-	PUNCT
ejpam-4944	184	14	dense	dense	ADJ
ejpam-4944	184	15	.	.	PUNCT
ejpam-4944	185	1	d.	d.	PROPN
ejpam-4944	185	2	elgezouli	elgezouli	PROPN
ejpam-4944	185	3	et	et	PROPN
ejpam-4944	185	4	al	al	PROPN
ejpam-4944	185	5	.	.	PUNCT
ejpam-4944	185	6	/	/	SYM
ejpam-4944	185	7	eur	eur	PROPN
ejpam-4944	185	8	.	.	PUNCT
ejpam-4944	186	1	j.	j.	PROPN
ejpam-4944	186	2	pure	pure	PROPN
ejpam-4944	186	3	appl	appl	PROPN
ejpam-4944	186	4	.	.	PROPN
ejpam-4944	186	5	math	math	PROPN
ejpam-4944	186	6	,	,	PUNCT
ejpam-4944	186	7	16	16	NUM
ejpam-4944	186	8	(	(	PUNCT
ejpam-4944	186	9	4	4	NUM
ejpam-4944	186	10	)	)	PUNCT
ejpam-4944	186	11	(	(	PUNCT
ejpam-4944	186	12	2023	2023	NUM
ejpam-4944	186	13	)	)	PUNCT
ejpam-4944	186	14	,	,	PUNCT
ejpam-4944	186	15	2286	2286	NUM
ejpam-4944	186	16	-	-	SYM
ejpam-4944	186	17	2305	2305	NUM
ejpam-4944	186	18	2292	2292	NUM
ejpam-4944	186	19	(	(	PUNCT
ejpam-4944	186	20	b	b	NOUN
ejpam-4944	186	21	)	)	PUNCT
ejpam-4944	186	22	.	.	PUNCT
ejpam-4944	187	1	fix	fix	NOUN
ejpam-4944	187	2	s	s	PART
ejpam-4944	187	3	=	=	NOUN
ejpam-4944	187	4	1	1	NUM
ejpam-4944	187	5	;	;	PUNCT
ejpam-4944	187	6	v	v	NOUN
ejpam-4944	187	7	=	=	SYM
ejpam-4944	187	8	2	2	X
ejpam-4944	187	9	.	.	X
ejpam-4944	187	10	choose	choose	VERB
ejpam-4944	187	11	w	w	NOUN
ejpam-4944	187	12	=	=	PUNCT
ejpam-4944	187	13	{	{	PUNCT
ejpam-4944	187	14	p	p	X
ejpam-4944	187	15	,	,	PUNCT
ejpam-4944	187	16	q	q	NOUN
ejpam-4944	187	17	}	}	PUNCT
ejpam-4944	187	18	we	we	PRON
ejpam-4944	187	19	get	get	VERB
ejpam-4944	187	20	w	w	PRON
ejpam-4944	187	21	∈	∈	PROPN
ejpam-4944	187	22	(	(	PUNCT
ejpam-4944	187	23	1	1	NUM
ejpam-4944	187	24	,	,	PUNCT
ejpam-4944	187	25	2)⋆	2)⋆	PROPN
ejpam-4944	187	26	−d(x	−d(x	NOUN
ejpam-4944	187	27	)	)	PUNCT
ejpam-4944	187	28	,	,	PUNCT
ejpam-4944	187	29	since	since	SCONJ
ejpam-4944	187	30	c2w	c2w	NOUN
ejpam-4944	187	31	∩	∩	PROPN
ejpam-4944	187	32	l	l	PROPN
ejpam-4944	187	33	̸=	̸=	PROPN
ejpam-4944	187	34	∅	∅	NOUN
ejpam-4944	187	35	for	for	ADP
ejpam-4944	187	36	all	all	DET
ejpam-4944	187	37	l	l	NOUN
ejpam-4944	187	38	∈	∈	PROPN
ejpam-4944	187	39	σ̃1	σ̃1	PROPN
ejpam-4944	187	40	.	.	PUNCT
ejpam-4944	188	1	here	here	ADV
ejpam-4944	188	2	,	,	PUNCT
ejpam-4944	188	3	c2w	c2w	NOUN
ejpam-4944	188	4	=	=	SYM
ejpam-4944	188	5	w	w	PROPN
ejpam-4944	188	6	̸=	̸=	PROPN
ejpam-4944	188	7	x	x	PUNCT
ejpam-4944	188	8	so	so	SCONJ
ejpam-4944	188	9	that	that	SCONJ
ejpam-4944	188	10	w	w	NOUN
ejpam-4944	188	11	is	be	AUX
ejpam-4944	188	12	not	not	PART
ejpam-4944	188	13	a	a	DET
ejpam-4944	188	14	µ2	µ2	ADJ
ejpam-4944	188	15	-	-	PUNCT
ejpam-4944	188	16	dense	dense	ADJ
ejpam-4944	188	17	set	set	NOUN
ejpam-4944	188	18	.	.	PUNCT
ejpam-4944	189	1	take	take	VERB
ejpam-4944	189	2	s	s	NOUN
ejpam-4944	189	3	=	=	SYM
ejpam-4944	189	4	2	2	NUM
ejpam-4944	189	5	;	;	PUNCT
ejpam-4944	189	6	v	v	NOUN
ejpam-4944	189	7	=	=	SYM
ejpam-4944	189	8	1	1	X
ejpam-4944	189	9	.	.	PUNCT
ejpam-4944	190	1	consider	consider	VERB
ejpam-4944	190	2	the	the	DET
ejpam-4944	190	3	bgts	bgts	NOUN
ejpam-4944	190	4	(	(	PUNCT
ejpam-4944	190	5	x,µ1	x,µ1	PROPN
ejpam-4944	190	6	,	,	PUNCT
ejpam-4944	190	7	µ2	µ2	PROPN
ejpam-4944	190	8	)	)	PUNCT
ejpam-4944	190	9	where	where	SCONJ
ejpam-4944	190	10	x	x	X
ejpam-4944	190	11	=	=	PRON
ejpam-4944	190	12	{	{	PUNCT
ejpam-4944	190	13	p	p	X
ejpam-4944	190	14	,	,	PUNCT
ejpam-4944	190	15	q	q	ADJ
ejpam-4944	190	16	,	,	PUNCT
ejpam-4944	190	17	r	r	NOUN
ejpam-4944	190	18	,	,	PUNCT
ejpam-4944	190	19	s	s	PART
ejpam-4944	190	20	}	}	PUNCT
ejpam-4944	190	21	;	;	PUNCT
ejpam-4944	190	22	µ1	µ1	PROPN
ejpam-4944	190	23	=	=	SYM
ejpam-4944	190	24	{	{	PUNCT
ejpam-4944	190	25	∅	∅	NOUN
ejpam-4944	190	26	,	,	PUNCT
ejpam-4944	190	27	{	{	PUNCT
ejpam-4944	190	28	p	p	X
ejpam-4944	190	29	,	,	PUNCT
ejpam-4944	190	30	r	r	NOUN
ejpam-4944	190	31	}	}	PUNCT
ejpam-4944	190	32	,	,	PUNCT
ejpam-4944	190	33	{	{	PUNCT
ejpam-4944	190	34	p	p	X
ejpam-4944	190	35	,	,	PUNCT
ejpam-4944	190	36	s	s	PART
ejpam-4944	190	37	}	}	PUNCT
ejpam-4944	190	38	,	,	PUNCT
ejpam-4944	190	39	{	{	PUNCT
ejpam-4944	190	40	r	r	NOUN
ejpam-4944	190	41	,	,	PUNCT
ejpam-4944	190	42	s	s	PART
ejpam-4944	190	43	}	}	PUNCT
ejpam-4944	190	44	,	,	PUNCT
ejpam-4944	190	45	{	{	PUNCT
ejpam-4944	190	46	p	p	X
ejpam-4944	190	47	,	,	PUNCT
ejpam-4944	190	48	r	r	NOUN
ejpam-4944	190	49	,	,	PUNCT
ejpam-4944	190	50	s	s	PART
ejpam-4944	190	51	}	}	PUNCT
ejpam-4944	190	52	}	}	PUNCT
ejpam-4944	190	53	and	and	CCONJ
ejpam-4944	190	54	µ2	µ2	PROPN
ejpam-4944	190	55	=	=	PUNCT
ejpam-4944	190	56	{	{	PUNCT
ejpam-4944	190	57	∅	∅	NOUN
ejpam-4944	190	58	,	,	PUNCT
ejpam-4944	190	59	{	{	PUNCT
ejpam-4944	190	60	q	q	NOUN
ejpam-4944	190	61	,	,	PUNCT
ejpam-4944	190	62	r	r	NOUN
ejpam-4944	190	63	}	}	PUNCT
ejpam-4944	190	64	,	,	PUNCT
ejpam-4944	190	65	{	{	PUNCT
ejpam-4944	190	66	q	q	X
ejpam-4944	190	67	,	,	PUNCT
ejpam-4944	190	68	s	s	PART
ejpam-4944	190	69	}	}	PUNCT
ejpam-4944	190	70	,	,	PUNCT
ejpam-4944	190	71	{	{	PUNCT
ejpam-4944	190	72	q	q	X
ejpam-4944	190	73	,	,	PUNCT
ejpam-4944	190	74	r	r	NOUN
ejpam-4944	190	75	,	,	PUNCT
ejpam-4944	190	76	s	s	PART
ejpam-4944	190	77	}	}	PUNCT
ejpam-4944	190	78	}	}	PUNCT
ejpam-4944	190	79	.	.	PUNCT
ejpam-4944	191	1	clearly	clearly	ADV
ejpam-4944	191	2	,	,	PUNCT
ejpam-4944	191	3	we	we	PRON
ejpam-4944	191	4	have	have	VERB
ejpam-4944	191	5	σ1	σ1	NOUN
ejpam-4944	191	6	=	=	SYM
ejpam-4944	191	7	{	{	PUNCT
ejpam-4944	191	8	∅	∅	NOUN
ejpam-4944	191	9	,	,	PUNCT
ejpam-4944	191	10	{	{	PUNCT
ejpam-4944	191	11	q	q	X
ejpam-4944	191	12	}	}	PUNCT
ejpam-4944	191	13	,	,	PUNCT
ejpam-4944	191	14	{	{	PUNCT
ejpam-4944	191	15	p	p	X
ejpam-4944	191	16	,	,	PUNCT
ejpam-4944	191	17	r	r	NOUN
ejpam-4944	191	18	}	}	PUNCT
ejpam-4944	191	19	,	,	PUNCT
ejpam-4944	191	20	{	{	PUNCT
ejpam-4944	191	21	p	p	X
ejpam-4944	191	22	,	,	PUNCT
ejpam-4944	191	23	s	s	PART
ejpam-4944	191	24	}	}	PUNCT
ejpam-4944	191	25	,	,	PUNCT
ejpam-4944	191	26	{	{	PUNCT
ejpam-4944	191	27	r	r	NOUN
ejpam-4944	191	28	,	,	PUNCT
ejpam-4944	191	29	s	s	PART
ejpam-4944	191	30	}	}	PUNCT
ejpam-4944	191	31	,	,	PUNCT
ejpam-4944	191	32	{	{	PUNCT
ejpam-4944	191	33	p	p	X
ejpam-4944	191	34	,	,	PUNCT
ejpam-4944	191	35	q	q	ADJ
ejpam-4944	191	36	,	,	PUNCT
ejpam-4944	191	37	r	r	NOUN
ejpam-4944	191	38	}	}	PUNCT
ejpam-4944	191	39	,	,	PUNCT
ejpam-4944	191	40	{	{	PUNCT
ejpam-4944	191	41	p	p	X
ejpam-4944	191	42	,	,	PUNCT
ejpam-4944	191	43	q	q	X
ejpam-4944	191	44	,	,	PUNCT
ejpam-4944	191	45	s	s	PART
ejpam-4944	191	46	}	}	PUNCT
ejpam-4944	191	47	,	,	PUNCT
ejpam-4944	191	48	{	{	PUNCT
ejpam-4944	191	49	p	p	X
ejpam-4944	191	50	,	,	PUNCT
ejpam-4944	191	51	r	r	NOUN
ejpam-4944	191	52	,	,	PUNCT
ejpam-4944	191	53	s	s	PART
ejpam-4944	191	54	}	}	PUNCT
ejpam-4944	191	55	,	,	PUNCT
ejpam-4944	191	56	{	{	PUNCT
ejpam-4944	191	57	q	q	X
ejpam-4944	191	58	,	,	PUNCT
ejpam-4944	191	59	r	r	NOUN
ejpam-4944	191	60	,	,	PUNCT
ejpam-4944	191	61	s	s	PART
ejpam-4944	191	62	}	}	PUNCT
ejpam-4944	191	63	,	,	PUNCT
ejpam-4944	191	64	x	x	NOUN
ejpam-4944	191	65	}	}	PUNCT
ejpam-4944	191	66	and	and	CCONJ
ejpam-4944	191	67	σ2	σ2	PROPN
ejpam-4944	191	68	=	=	SYM
ejpam-4944	191	69	{	{	PUNCT
ejpam-4944	191	70	∅	∅	NOUN
ejpam-4944	191	71	,	,	PUNCT
ejpam-4944	191	72	{	{	PUNCT
ejpam-4944	191	73	p	p	X
ejpam-4944	191	74	}	}	PUNCT
ejpam-4944	191	75	,	,	PUNCT
ejpam-4944	191	76	{	{	PUNCT
ejpam-4944	191	77	q	q	X
ejpam-4944	191	78	,	,	PUNCT
ejpam-4944	191	79	r	r	NOUN
ejpam-4944	191	80	}	}	PUNCT
ejpam-4944	191	81	,	,	PUNCT
ejpam-4944	191	82	{	{	PUNCT
ejpam-4944	191	83	q	q	X
ejpam-4944	191	84	,	,	PUNCT
ejpam-4944	191	85	s	s	PART
ejpam-4944	191	86	}	}	PUNCT
ejpam-4944	191	87	,	,	PUNCT
ejpam-4944	191	88	{	{	PUNCT
ejpam-4944	191	89	p	p	X
ejpam-4944	191	90	,	,	PUNCT
ejpam-4944	191	91	q	q	ADJ
ejpam-4944	191	92	,	,	PUNCT
ejpam-4944	191	93	r	r	NOUN
ejpam-4944	191	94	}	}	PUNCT
ejpam-4944	191	95	,	,	PUNCT
ejpam-4944	191	96	{	{	PUNCT
ejpam-4944	191	97	p	p	X
ejpam-4944	191	98	,	,	PUNCT
ejpam-4944	191	99	q	q	X
ejpam-4944	191	100	,	,	PUNCT
ejpam-4944	191	101	s	s	PART
ejpam-4944	191	102	}	}	PUNCT
ejpam-4944	191	103	,	,	PUNCT
ejpam-4944	191	104	{	{	PUNCT
ejpam-4944	191	105	q	q	X
ejpam-4944	191	106	,	,	PUNCT
ejpam-4944	191	107	r	r	NOUN
ejpam-4944	191	108	,	,	PUNCT
ejpam-4944	191	109	s	s	PART
ejpam-4944	191	110	}	}	PUNCT
ejpam-4944	191	111	,	,	PUNCT
ejpam-4944	191	112	x	x	NOUN
ejpam-4944	191	113	}	}	PUNCT
ejpam-4944	191	114	.	.	PUNCT
ejpam-4944	192	1	consider	consider	VERB
ejpam-4944	192	2	k	k	NOUN
ejpam-4944	192	3	=	=	PRON
ejpam-4944	192	4	{	{	PUNCT
ejpam-4944	192	5	p	p	X
ejpam-4944	192	6	,	,	PUNCT
ejpam-4944	192	7	q	q	NOUN
ejpam-4944	192	8	}	}	PUNCT
ejpam-4944	192	9	.	.	PUNCT
ejpam-4944	193	1	since	since	SCONJ
ejpam-4944	193	2	c1k	c1k	NOUN
ejpam-4944	193	3	∩m	∩m	PROPN
ejpam-4944	193	4	̸=	̸=	PROPN
ejpam-4944	193	5	∅	∅	NOUN
ejpam-4944	193	6	for	for	ADP
ejpam-4944	193	7	all	all	DET
ejpam-4944	193	8	m	m	NOUN
ejpam-4944	193	9	∈	∈	NOUN
ejpam-4944	193	10	σ̃2	σ̃2	PROPN
ejpam-4944	193	11	we	we	PRON
ejpam-4944	193	12	get	get	VERB
ejpam-4944	193	13	k	k	PRON
ejpam-4944	193	14	∈	∈	PROPN
ejpam-4944	193	15	(	(	PUNCT
ejpam-4944	193	16	2	2	NUM
ejpam-4944	193	17	,	,	PUNCT
ejpam-4944	193	18	1)⋆	1)⋆	PROPN
ejpam-4944	193	19	−d(x	−d(x	NOUN
ejpam-4944	193	20	)	)	PUNCT
ejpam-4944	193	21	.	.	PUNCT
ejpam-4944	194	1	but	but	CCONJ
ejpam-4944	194	2	c1k	c1k	NOUN
ejpam-4944	194	3	=	=	SYM
ejpam-4944	194	4	k	k	PROPN
ejpam-4944	194	5	̸=	̸=	PROPN
ejpam-4944	194	6	x.	x.	PUNCT
ejpam-4944	194	7	thus	thus	ADV
ejpam-4944	194	8	,	,	PUNCT
ejpam-4944	194	9	k	k	PROPN
ejpam-4944	194	10	is	be	AUX
ejpam-4944	194	11	not	not	PART
ejpam-4944	194	12	µ1	µ1	NOUN
ejpam-4944	194	13	-	-	PUNCT
ejpam-4944	194	14	dense	dense	ADJ
ejpam-4944	194	15	.	.	PUNCT
ejpam-4944	195	1	theorem	theorem	ADJ
ejpam-4944	195	2	15	15	NUM
ejpam-4944	195	3	.	.	PUNCT
ejpam-4944	196	1	let	let	AUX
ejpam-4944	196	2	(	(	PUNCT
ejpam-4944	196	3	x,µ1	x,µ1	NOUN
ejpam-4944	196	4	,	,	PUNCT
ejpam-4944	196	5	µ2	µ2	PROPN
ejpam-4944	196	6	)	)	PUNCT
ejpam-4944	196	7	be	be	AUX
ejpam-4944	196	8	a	a	DET
ejpam-4944	196	9	bgts	bgts	NOUN
ejpam-4944	196	10	.	.	PUNCT
ejpam-4944	197	1	then	then	ADV
ejpam-4944	197	2	(	(	PUNCT
ejpam-4944	197	3	s	s	X
ejpam-4944	197	4	,	,	PUNCT
ejpam-4944	197	5	v)⋆	v)⋆	PROPN
ejpam-4944	197	6	−	−	PROPN
ejpam-4944	197	7	d(x	d(x	PROPN
ejpam-4944	197	8	)	)	PUNCT
ejpam-4944	198	1	⊂	⊂	PROPN
ejpam-4944	198	2	(	(	PUNCT
ejpam-4944	198	3	s	s	PROPN
ejpam-4944	198	4	,	,	PUNCT
ejpam-4944	198	5	v	v	NOUN
ejpam-4944	198	6	)	)	PUNCT
ejpam-4944	198	7	−	−	PROPN
ejpam-4944	198	8	d(x	d(x	NOUN
ejpam-4944	198	9	)	)	PUNCT
ejpam-4944	198	10	where	where	SCONJ
ejpam-4944	198	11	s	s	X
ejpam-4944	198	12	,	,	PUNCT
ejpam-4944	198	13	v	v	NOUN
ejpam-4944	198	14	=	=	SYM
ejpam-4944	198	15	1	1	NUM
ejpam-4944	198	16	,	,	PUNCT
ejpam-4944	198	17	2	2	NUM
ejpam-4944	198	18	;	;	PUNCT
ejpam-4944	198	19	s	s	VERB
ejpam-4944	198	20	̸=	̸=	PROPN
ejpam-4944	198	21	v.	v.	ADP
ejpam-4944	198	22	proof	proof	NOUN
ejpam-4944	198	23	.	.	PUNCT
ejpam-4944	199	1	let	let	VERB
ejpam-4944	199	2	q	q	PROPN
ejpam-4944	199	3	∈	∈	PROPN
ejpam-4944	199	4	(	(	PUNCT
ejpam-4944	199	5	s	s	PROPN
ejpam-4944	199	6	,	,	PUNCT
ejpam-4944	199	7	v)⋆	v)⋆	PROPN
ejpam-4944	199	8	−d(x	−d(x	NOUN
ejpam-4944	199	9	)	)	PUNCT
ejpam-4944	199	10	.	.	PUNCT
ejpam-4944	200	1	take	take	VERB
ejpam-4944	200	2	s	s	NOUN
ejpam-4944	200	3	=	=	SYM
ejpam-4944	200	4	1	1	NUM
ejpam-4944	200	5	;	;	PUNCT
ejpam-4944	200	6	v	v	NOUN
ejpam-4944	200	7	=	=	SYM
ejpam-4944	200	8	2	2	NUM
ejpam-4944	200	9	.	.	PUNCT
ejpam-4944	201	1	then	then	ADV
ejpam-4944	201	2	q	q	PROPN
ejpam-4944	201	3	∈	∈	PROPN
ejpam-4944	201	4	(	(	PUNCT
ejpam-4944	201	5	1	1	NUM
ejpam-4944	201	6	,	,	PUNCT
ejpam-4944	201	7	2)⋆	2)⋆	NOUN
ejpam-4944	201	8	−	−	NOUN
ejpam-4944	201	9	d(x	d(x	NOUN
ejpam-4944	201	10	)	)	PUNCT
ejpam-4944	201	11	so	so	SCONJ
ejpam-4944	201	12	that	that	SCONJ
ejpam-4944	201	13	c2(q	c2(q	PROPN
ejpam-4944	201	14	)	)	PUNCT
ejpam-4944	201	15	∩	∩	NOUN
ejpam-4944	201	16	m	m	VERB
ejpam-4944	201	17	̸=	̸=	NOUN
ejpam-4944	201	18	∅	∅	NOUN
ejpam-4944	201	19	for	for	ADP
ejpam-4944	201	20	every	every	DET
ejpam-4944	201	21	m	m	NOUN
ejpam-4944	201	22	∈	∈	ADJ
ejpam-4944	201	23	σ̃1	σ̃1	PROPN
ejpam-4944	201	24	.	.	PROPN
ejpam-4944	202	1	since	since	SCONJ
ejpam-4944	202	2	µ1	µ1	PROPN
ejpam-4944	202	3	⊂	⊂	PROPN
ejpam-4944	202	4	σ1	σ1	PROPN
ejpam-4944	202	5	,	,	PUNCT
ejpam-4944	202	6	c2(q	c2(q	PROPN
ejpam-4944	202	7	)	)	PUNCT
ejpam-4944	202	8	∩k	∩k	PROPN
ejpam-4944	202	9	̸=	̸=	PROPN
ejpam-4944	202	10	∅	∅	NOUN
ejpam-4944	202	11	for	for	ADP
ejpam-4944	202	12	every	every	DET
ejpam-4944	202	13	k	k	PROPN
ejpam-4944	202	14	∈	∈	PROPN
ejpam-4944	202	15	µ̃1	µ̃1	PROPN
ejpam-4944	202	16	.	.	PUNCT
ejpam-4944	203	1	therefore	therefore	ADV
ejpam-4944	203	2	,	,	PUNCT
ejpam-4944	203	3	q	q	PROPN
ejpam-4944	203	4	∈	∈	PROPN
ejpam-4944	203	5	(	(	PUNCT
ejpam-4944	203	6	1	1	NUM
ejpam-4944	203	7	,	,	PUNCT
ejpam-4944	203	8	2)−d(x	2)−d(x	NUM
ejpam-4944	203	9	)	)	PUNCT
ejpam-4944	203	10	.	.	PUNCT
ejpam-4944	204	1	fix	fix	NOUN
ejpam-4944	204	2	s	s	PART
ejpam-4944	204	3	=	=	NOUN
ejpam-4944	204	4	2	2	NUM
ejpam-4944	204	5	;	;	PUNCT
ejpam-4944	204	6	v	v	NOUN
ejpam-4944	204	7	=	=	SYM
ejpam-4944	204	8	1	1	X
ejpam-4944	204	9	.	.	PUNCT
ejpam-4944	205	1	we	we	PRON
ejpam-4944	205	2	get	get	VERB
ejpam-4944	205	3	q	q	X
ejpam-4944	205	4	∈	∈	NOUN
ejpam-4944	205	5	(	(	PUNCT
ejpam-4944	205	6	2	2	NUM
ejpam-4944	205	7	,	,	PUNCT
ejpam-4944	205	8	1)⋆	1)⋆	PROPN
ejpam-4944	205	9	−	−	PROPN
ejpam-4944	205	10	d(x	d(x	PROPN
ejpam-4944	205	11	)	)	PUNCT
ejpam-4944	205	12	for	for	ADP
ejpam-4944	205	13	that	that	DET
ejpam-4944	205	14	c1(q	c1(q	NOUN
ejpam-4944	205	15	)	)	PUNCT
ejpam-4944	205	16	∩	∩	NOUN
ejpam-4944	205	17	l	l	PROPN
ejpam-4944	205	18	̸=	̸=	PROPN
ejpam-4944	205	19	∅	∅	NOUN
ejpam-4944	205	20	for	for	ADP
ejpam-4944	205	21	every	every	DET
ejpam-4944	205	22	l	l	NOUN
ejpam-4944	205	23	∈	∈	PROPN
ejpam-4944	205	24	σ̃2	σ̃2	PROPN
ejpam-4944	205	25	.	.	PUNCT
ejpam-4944	206	1	since	since	SCONJ
ejpam-4944	206	2	µ2	µ2	PROPN
ejpam-4944	206	3	⊂	⊂	PROPN
ejpam-4944	206	4	σ2	σ2	PROPN
ejpam-4944	206	5	,	,	PUNCT
ejpam-4944	206	6	c1(q	c1(q	ADJ
ejpam-4944	206	7	)	)	PUNCT
ejpam-4944	206	8	∩g	∩g	NOUN
ejpam-4944	206	9	̸=	̸=	NOUN
ejpam-4944	206	10	∅	∅	NOUN
ejpam-4944	206	11	for	for	ADP
ejpam-4944	206	12	every	every	DET
ejpam-4944	206	13	g	g	PROPN
ejpam-4944	206	14	∈	∈	PROPN
ejpam-4944	206	15	µ̃2	µ̃2	PROPN
ejpam-4944	206	16	.	.	PUNCT
ejpam-4944	206	17	therefore	therefore	ADV
ejpam-4944	206	18	,	,	PUNCT
ejpam-4944	206	19	q	q	PROPN
ejpam-4944	206	20	∈	∈	PROPN
ejpam-4944	206	21	(	(	PUNCT
ejpam-4944	206	22	2	2	NUM
ejpam-4944	206	23	,	,	PUNCT
ejpam-4944	206	24	1)−d(x	1)−d(x	NUM
ejpam-4944	206	25	)	)	PUNCT
ejpam-4944	206	26	.	.	PUNCT
ejpam-4944	207	1	the	the	DET
ejpam-4944	207	2	below	below	ADJ
ejpam-4944	207	3	example	example	NOUN
ejpam-4944	207	4	16	16	NUM
ejpam-4944	207	5	shows	show	VERB
ejpam-4944	207	6	that	that	SCONJ
ejpam-4944	207	7	in	in	ADP
ejpam-4944	207	8	a	a	DET
ejpam-4944	207	9	bigeneralized	bigeneralize	VERB
ejpam-4944	207	10	topological	topological	ADJ
ejpam-4944	207	11	space	space	NOUN
ejpam-4944	207	12	,	,	PUNCT
ejpam-4944	207	13	the	the	DET
ejpam-4944	207	14	reverse	reverse	ADJ
ejpam-4944	207	15	implication	implication	NOUN
ejpam-4944	207	16	of	of	ADP
ejpam-4944	207	17	the	the	DET
ejpam-4944	207	18	above	above	ADJ
ejpam-4944	207	19	theorem	theorem	NOUN
ejpam-4944	207	20	15	15	NUM
ejpam-4944	207	21	need	need	AUX
ejpam-4944	207	22	not	not	PART
ejpam-4944	207	23	be	be	AUX
ejpam-4944	207	24	true	true	ADJ
ejpam-4944	207	25	in	in	ADP
ejpam-4944	207	26	general	general	ADJ
ejpam-4944	207	27	.	.	PUNCT
ejpam-4944	208	1	example	example	NOUN
ejpam-4944	208	2	16	16	NUM
ejpam-4944	208	3	.	.	PUNCT
ejpam-4944	209	1	consider	consider	VERB
ejpam-4944	209	2	the	the	DET
ejpam-4944	209	3	bigeneralized	bigeneralized	ADJ
ejpam-4944	209	4	topological	topological	ADJ
ejpam-4944	209	5	space	space	NOUN
ejpam-4944	209	6	(	(	PUNCT
ejpam-4944	209	7	x,µ1	x,µ1	PROPN
ejpam-4944	209	8	,	,	PUNCT
ejpam-4944	209	9	µ2	µ2	PROPN
ejpam-4944	209	10	)	)	PUNCT
ejpam-4944	209	11	where	where	SCONJ
ejpam-4944	209	12	x	x	X
ejpam-4944	209	13	=	=	PRON
ejpam-4944	209	14	{	{	PUNCT
ejpam-4944	209	15	p	p	X
ejpam-4944	209	16	,	,	PUNCT
ejpam-4944	209	17	q	q	ADJ
ejpam-4944	209	18	,	,	PUNCT
ejpam-4944	209	19	r	r	NOUN
ejpam-4944	209	20	,	,	PUNCT
ejpam-4944	209	21	s	s	PART
ejpam-4944	209	22	}	}	PUNCT
ejpam-4944	209	23	;	;	PUNCT
ejpam-4944	209	24	µ1	µ1	PROPN
ejpam-4944	209	25	=	=	SYM
ejpam-4944	209	26	{	{	PUNCT
ejpam-4944	209	27	∅	∅	NOUN
ejpam-4944	209	28	,	,	PUNCT
ejpam-4944	209	29	{	{	PUNCT
ejpam-4944	209	30	p	p	X
ejpam-4944	209	31	,	,	PUNCT
ejpam-4944	209	32	r	r	NOUN
ejpam-4944	209	33	}	}	PUNCT
ejpam-4944	209	34	,	,	PUNCT
ejpam-4944	209	35	{	{	PUNCT
ejpam-4944	209	36	r	r	NOUN
ejpam-4944	209	37	,	,	PUNCT
ejpam-4944	209	38	s	s	PART
ejpam-4944	209	39	}	}	PUNCT
ejpam-4944	209	40	,	,	PUNCT
ejpam-4944	209	41	{	{	PUNCT
ejpam-4944	209	42	p	p	X
ejpam-4944	209	43	,	,	PUNCT
ejpam-4944	209	44	r	r	NOUN
ejpam-4944	209	45	,	,	PUNCT
ejpam-4944	209	46	s	s	PART
ejpam-4944	209	47	}	}	PUNCT
ejpam-4944	209	48	}	}	PUNCT
ejpam-4944	209	49	and	and	CCONJ
ejpam-4944	209	50	µ2	µ2	PROPN
ejpam-4944	209	51	=	=	PUNCT
ejpam-4944	209	52	{	{	PUNCT
ejpam-4944	209	53	∅	∅	NOUN
ejpam-4944	209	54	,	,	PUNCT
ejpam-4944	209	55	{	{	PUNCT
ejpam-4944	209	56	p	p	X
ejpam-4944	209	57	,	,	PUNCT
ejpam-4944	209	58	q	q	NOUN
ejpam-4944	209	59	}	}	PUNCT
ejpam-4944	209	60	,	,	PUNCT
ejpam-4944	209	61	{	{	PUNCT
ejpam-4944	209	62	p	p	X
ejpam-4944	209	63	,	,	PUNCT
ejpam-4944	209	64	r	r	NOUN
ejpam-4944	209	65	}	}	PUNCT
ejpam-4944	209	66	,	,	PUNCT
ejpam-4944	209	67	{	{	PUNCT
ejpam-4944	209	68	q	q	X
ejpam-4944	209	69	,	,	PUNCT
ejpam-4944	209	70	r	r	NOUN
ejpam-4944	209	71	}	}	PUNCT
ejpam-4944	209	72	,	,	PUNCT
ejpam-4944	209	73	{	{	PUNCT
ejpam-4944	209	74	p	p	X
ejpam-4944	209	75	,	,	PUNCT
ejpam-4944	209	76	q	q	ADJ
ejpam-4944	209	77	,	,	PUNCT
ejpam-4944	209	78	r	r	NOUN
ejpam-4944	209	79	}	}	PUNCT
ejpam-4944	209	80	}	}	PUNCT
ejpam-4944	209	81	.	.	PUNCT
ejpam-4944	210	1	then	then	ADV
ejpam-4944	210	2	σ1	σ1	PROPN
ejpam-4944	210	3	=	=	PUNCT
ejpam-4944	210	4	{	{	PUNCT
ejpam-4944	210	5	∅	∅	NOUN
ejpam-4944	210	6	,	,	PUNCT
ejpam-4944	210	7	{	{	PUNCT
ejpam-4944	210	8	q	q	X
ejpam-4944	210	9	}	}	PUNCT
ejpam-4944	210	10	,	,	PUNCT
ejpam-4944	210	11	{	{	PUNCT
ejpam-4944	210	12	p	p	X
ejpam-4944	210	13	,	,	PUNCT
ejpam-4944	210	14	r	r	NOUN
ejpam-4944	210	15	}	}	PUNCT
ejpam-4944	210	16	,	,	PUNCT
ejpam-4944	210	17	{	{	PUNCT
ejpam-4944	210	18	r	r	NOUN
ejpam-4944	210	19	,	,	PUNCT
ejpam-4944	210	20	s	s	PART
ejpam-4944	210	21	}	}	PUNCT
ejpam-4944	210	22	,	,	PUNCT
ejpam-4944	210	23	{	{	PUNCT
ejpam-4944	210	24	p	p	X
ejpam-4944	210	25	,	,	PUNCT
ejpam-4944	210	26	q	q	ADJ
ejpam-4944	210	27	,	,	PUNCT
ejpam-4944	210	28	r	r	NOUN
ejpam-4944	210	29	}	}	PUNCT
ejpam-4944	210	30	,	,	PUNCT
ejpam-4944	210	31	{	{	PUNCT
ejpam-4944	210	32	p	p	X
ejpam-4944	210	33	,	,	PUNCT
ejpam-4944	210	34	r	r	NOUN
ejpam-4944	210	35	,	,	PUNCT
ejpam-4944	210	36	s	s	PART
ejpam-4944	210	37	}	}	PUNCT
ejpam-4944	210	38	,	,	PUNCT
ejpam-4944	210	39	{	{	PUNCT
ejpam-4944	210	40	q	q	X
ejpam-4944	210	41	,	,	PUNCT
ejpam-4944	210	42	r	r	NOUN
ejpam-4944	210	43	,	,	PUNCT
ejpam-4944	210	44	s	s	PART
ejpam-4944	210	45	}	}	PUNCT
ejpam-4944	210	46	,	,	PUNCT
ejpam-4944	210	47	x	x	X
ejpam-4944	210	48	}	}	PUNCT
ejpam-4944	210	49	and	and	CCONJ
ejpam-4944	210	50	d.	d.	PROPN
ejpam-4944	210	51	elgezouli	elgezouli	PROPN
ejpam-4944	210	52	et	et	PROPN
ejpam-4944	210	53	al	al	PROPN
ejpam-4944	210	54	.	.	PUNCT
ejpam-4944	210	55	/	/	SYM
ejpam-4944	210	56	eur	eur	PROPN
ejpam-4944	210	57	.	.	PUNCT
ejpam-4944	211	1	j.	j.	PROPN
ejpam-4944	211	2	pure	pure	PROPN
ejpam-4944	211	3	appl	appl	PROPN
ejpam-4944	211	4	.	.	PROPN
ejpam-4944	211	5	math	math	PROPN
ejpam-4944	211	6	,	,	PUNCT
ejpam-4944	211	7	16	16	NUM
ejpam-4944	211	8	(	(	PUNCT
ejpam-4944	211	9	4	4	NUM
ejpam-4944	211	10	)	)	PUNCT
ejpam-4944	211	11	(	(	PUNCT
ejpam-4944	211	12	2023	2023	NUM
ejpam-4944	211	13	)	)	PUNCT
ejpam-4944	211	14	,	,	PUNCT
ejpam-4944	211	15	2286	2286	NUM
ejpam-4944	211	16	-	-	SYM
ejpam-4944	211	17	2305	2305	NUM
ejpam-4944	211	18	2293	2293	NUM
ejpam-4944	211	19	σ2	σ2	NOUN
ejpam-4944	211	20	=	=	SYM
ejpam-4944	211	21	{	{	PUNCT
ejpam-4944	211	22	∅	∅	NOUN
ejpam-4944	211	23	,	,	PUNCT
ejpam-4944	211	24	{	{	PUNCT
ejpam-4944	211	25	s	s	X
ejpam-4944	211	26	}	}	PUNCT
ejpam-4944	211	27	,	,	PUNCT
ejpam-4944	211	28	{	{	PUNCT
ejpam-4944	211	29	p	p	X
ejpam-4944	211	30	,	,	PUNCT
ejpam-4944	211	31	q	q	NOUN
ejpam-4944	211	32	}	}	PUNCT
ejpam-4944	211	33	,	,	PUNCT
ejpam-4944	211	34	{	{	PUNCT
ejpam-4944	211	35	p	p	X
ejpam-4944	211	36	,	,	PUNCT
ejpam-4944	211	37	r	r	NOUN
ejpam-4944	211	38	}	}	PUNCT
ejpam-4944	211	39	,	,	PUNCT
ejpam-4944	211	40	{	{	PUNCT
ejpam-4944	211	41	q	q	X
ejpam-4944	211	42	,	,	PUNCT
ejpam-4944	211	43	r	r	NOUN
ejpam-4944	211	44	}	}	PUNCT
ejpam-4944	211	45	,	,	PUNCT
ejpam-4944	211	46	{	{	PUNCT
ejpam-4944	211	47	p	p	X
ejpam-4944	211	48	,	,	PUNCT
ejpam-4944	211	49	q	q	ADJ
ejpam-4944	211	50	,	,	PUNCT
ejpam-4944	211	51	r	r	NOUN
ejpam-4944	211	52	}	}	PUNCT
ejpam-4944	211	53	,	,	PUNCT
ejpam-4944	211	54	{	{	PUNCT
ejpam-4944	211	55	p	p	X
ejpam-4944	211	56	,	,	PUNCT
ejpam-4944	211	57	q	q	X
ejpam-4944	211	58	,	,	PUNCT
ejpam-4944	211	59	s	s	PART
ejpam-4944	211	60	}	}	PUNCT
ejpam-4944	211	61	,	,	PUNCT
ejpam-4944	211	62	{	{	PUNCT
ejpam-4944	211	63	p	p	X
ejpam-4944	211	64	,	,	PUNCT
ejpam-4944	211	65	r	r	NOUN
ejpam-4944	211	66	,	,	PUNCT
ejpam-4944	211	67	s	s	PART
ejpam-4944	211	68	}	}	PUNCT
ejpam-4944	211	69	,	,	PUNCT
ejpam-4944	211	70	{	{	PUNCT
ejpam-4944	211	71	q	q	X
ejpam-4944	211	72	,	,	PUNCT
ejpam-4944	211	73	r	r	NOUN
ejpam-4944	211	74	,	,	PUNCT
ejpam-4944	211	75	s	s	PART
ejpam-4944	211	76	}	}	PUNCT
ejpam-4944	211	77	,	,	PUNCT
ejpam-4944	211	78	x	x	NOUN
ejpam-4944	211	79	}	}	PUNCT
ejpam-4944	211	80	.	.	PUNCT
ejpam-4944	212	1	•	•	NUM
ejpam-4944	212	2	fix	fix	NOUN
ejpam-4944	212	3	s	s	PART
ejpam-4944	212	4	=	=	SYM
ejpam-4944	212	5	1	1	NUM
ejpam-4944	212	6	and	and	CCONJ
ejpam-4944	212	7	v	v	NOUN
ejpam-4944	212	8	=	=	SYM
ejpam-4944	212	9	2	2	X
ejpam-4944	212	10	.	.	PUNCT
ejpam-4944	213	1	choose	choose	VERB
ejpam-4944	213	2	k	k	X
ejpam-4944	213	3	=	=	PRON
ejpam-4944	213	4	{	{	PUNCT
ejpam-4944	213	5	p	p	X
ejpam-4944	213	6	,	,	PUNCT
ejpam-4944	213	7	s	s	X
ejpam-4944	213	8	}	}	PUNCT
ejpam-4944	213	9	we	we	PRON
ejpam-4944	213	10	get	get	VERB
ejpam-4944	213	11	k	k	PROPN
ejpam-4944	213	12	is	be	AUX
ejpam-4944	213	13	(	(	PUNCT
ejpam-4944	213	14	1	1	NUM
ejpam-4944	213	15	,	,	PUNCT
ejpam-4944	213	16	2)-dense	2)-dense	NOUN
ejpam-4944	213	17	.	.	PUNCT
ejpam-4944	214	1	but	but	CCONJ
ejpam-4944	214	2	k	k	PROPN
ejpam-4944	214	3	/∈	/∈	PUNCT
ejpam-4944	215	1	(	(	PUNCT
ejpam-4944	215	2	1	1	NUM
ejpam-4944	215	3	,	,	PUNCT
ejpam-4944	215	4	2)⋆−d(x	2)⋆−d(x	NUM
ejpam-4944	215	5	)	)	PUNCT
ejpam-4944	215	6	.	.	PUNCT
ejpam-4944	216	1	for	for	ADP
ejpam-4944	216	2	,	,	PUNCT
ejpam-4944	216	3	if	if	SCONJ
ejpam-4944	216	4	we	we	PRON
ejpam-4944	216	5	choose	choose	VERB
ejpam-4944	216	6	d	d	X
ejpam-4944	216	7	=	=	PRON
ejpam-4944	216	8	{	{	PUNCT
ejpam-4944	216	9	q	q	NOUN
ejpam-4944	216	10	}	}	PUNCT
ejpam-4944	216	11	,	,	PUNCT
ejpam-4944	216	12	then	then	ADV
ejpam-4944	216	13	d	d	PROPN
ejpam-4944	216	14	∈	∈	PROPN
ejpam-4944	216	15	σ̃1	σ̃1	PROPN
ejpam-4944	216	16	.	.	PUNCT
ejpam-4944	217	1	but	but	CCONJ
ejpam-4944	217	2	d	d	PROPN
ejpam-4944	217	3	∩	∩	X
ejpam-4944	217	4	c2(k	c2(k	PROPN
ejpam-4944	217	5	)	)	PUNCT
ejpam-4944	217	6	=	=	NOUN
ejpam-4944	217	7	∅.	∅.	ADP
ejpam-4944	217	8	thus	thus	ADV
ejpam-4944	217	9	,	,	PUNCT
ejpam-4944	217	10	there	there	PRON
ejpam-4944	217	11	is	be	VERB
ejpam-4944	217	12	d	d	PROPN
ejpam-4944	217	13	∈	∈	PROPN
ejpam-4944	217	14	σ̃1	σ̃1	PROPN
ejpam-4944	217	15	such	such	ADJ
ejpam-4944	217	16	that	that	SCONJ
ejpam-4944	217	17	d	d	NOUN
ejpam-4944	217	18	∩	∩	X
ejpam-4944	217	19	c2(k	c2(k	NOUN
ejpam-4944	217	20	)	)	PUNCT
ejpam-4944	217	21	=	=	PUNCT
ejpam-4944	217	22	∅.	∅.	PRON
ejpam-4944	217	23	•	•	NUM
ejpam-4944	217	24	fix	fix	NOUN
ejpam-4944	217	25	s	s	PART
ejpam-4944	217	26	=	=	SYM
ejpam-4944	217	27	2	2	NUM
ejpam-4944	217	28	and	and	CCONJ
ejpam-4944	217	29	v	v	NOUN
ejpam-4944	217	30	=	=	SYM
ejpam-4944	217	31	1	1	X
ejpam-4944	217	32	.	.	PUNCT
ejpam-4944	218	1	take	take	VERB
ejpam-4944	218	2	l	l	NOUN
ejpam-4944	218	3	=	=	PUNCT
ejpam-4944	218	4	{	{	PUNCT
ejpam-4944	218	5	p	p	X
ejpam-4944	218	6	,	,	PUNCT
ejpam-4944	218	7	q	q	NOUN
ejpam-4944	218	8	}	}	PUNCT
ejpam-4944	218	9	,	,	PUNCT
ejpam-4944	218	10	then	then	ADV
ejpam-4944	218	11	we	we	PRON
ejpam-4944	218	12	get	get	VERB
ejpam-4944	218	13	l	l	NOUN
ejpam-4944	218	14	∈	∈	NOUN
ejpam-4944	218	15	(	(	PUNCT
ejpam-4944	218	16	1	1	NUM
ejpam-4944	218	17	,	,	PUNCT
ejpam-4944	218	18	2	2	NUM
ejpam-4944	218	19	)	)	PUNCT
ejpam-4944	218	20	−	−	PROPN
ejpam-4944	218	21	d(x	d(x	NOUN
ejpam-4944	218	22	)	)	PUNCT
ejpam-4944	218	23	.	.	PUNCT
ejpam-4944	219	1	here	here	ADV
ejpam-4944	219	2	,	,	PUNCT
ejpam-4944	219	3	we	we	PRON
ejpam-4944	219	4	take	take	VERB
ejpam-4944	219	5	h	h	NOUN
ejpam-4944	219	6	=	=	PUNCT
ejpam-4944	219	7	{	{	PUNCT
ejpam-4944	219	8	s	s	NOUN
ejpam-4944	219	9	}	}	PUNCT
ejpam-4944	219	10	so	so	SCONJ
ejpam-4944	219	11	that	that	SCONJ
ejpam-4944	219	12	h	h	NOUN
ejpam-4944	219	13	∈	∈	PROPN
ejpam-4944	219	14	σ̃2	σ̃2	PROPN
ejpam-4944	219	15	but	but	CCONJ
ejpam-4944	219	16	h	h	NOUN
ejpam-4944	219	17	∩	∩	NOUN
ejpam-4944	219	18	c1(l	c1(l	X
ejpam-4944	219	19	)	)	PUNCT
ejpam-4944	219	20	=	=	NOUN
ejpam-4944	219	21	∅.	∅.	ADP
ejpam-4944	219	22	thus	thus	ADV
ejpam-4944	219	23	,	,	PUNCT
ejpam-4944	219	24	l	l	PROPN
ejpam-4944	219	25	/∈	/∈	PUNCT
ejpam-4944	220	1	(	(	PUNCT
ejpam-4944	220	2	1	1	NUM
ejpam-4944	220	3	,	,	PUNCT
ejpam-4944	220	4	2)⋆	2)⋆	PROPN
ejpam-4944	220	5	−d(x	−d(x	NOUN
ejpam-4944	220	6	)	)	PUNCT
ejpam-4944	220	7	.	.	PUNCT
ejpam-4944	221	1	theorem	theorem	NOUN
ejpam-4944	221	2	17	17	NUM
ejpam-4944	221	3	.	.	PUNCT
ejpam-4944	222	1	let	let	AUX
ejpam-4944	222	2	(	(	PUNCT
ejpam-4944	222	3	x,µ1	x,µ1	NOUN
ejpam-4944	222	4	,	,	PUNCT
ejpam-4944	222	5	µ2	µ2	PROPN
ejpam-4944	222	6	)	)	PUNCT
ejpam-4944	222	7	be	be	AUX
ejpam-4944	222	8	a	a	DET
ejpam-4944	222	9	bgts	bgts	NOUN
ejpam-4944	222	10	.	.	PUNCT
ejpam-4944	223	1	if	if	SCONJ
ejpam-4944	223	2	µs	µs	NOUN
ejpam-4944	223	3	is	be	AUX
ejpam-4944	223	4	a	a	DET
ejpam-4944	223	5	sgt	sgt	NOUN
ejpam-4944	223	6	,	,	PUNCT
ejpam-4944	223	7	then	then	ADV
ejpam-4944	223	8	(	(	PUNCT
ejpam-4944	223	9	s	s	X
ejpam-4944	223	10	,	,	PUNCT
ejpam-4944	223	11	v)−d(x	v)−d(x	NUM
ejpam-4944	223	12	)	)	PUNCT
ejpam-4944	223	13	⊂	⊂	PROPN
ejpam-4944	223	14	(	(	PUNCT
ejpam-4944	223	15	s	s	PROPN
ejpam-4944	223	16	,	,	PUNCT
ejpam-4944	223	17	v)⋆	v)⋆	PROPN
ejpam-4944	223	18	−	−	PROPN
ejpam-4944	223	19	d(x	d(x	PROPN
ejpam-4944	223	20	)	)	PUNCT
ejpam-4944	223	21	where	where	SCONJ
ejpam-4944	223	22	s	s	X
ejpam-4944	223	23	,	,	PUNCT
ejpam-4944	223	24	v	v	NOUN
ejpam-4944	223	25	=	=	SYM
ejpam-4944	223	26	1	1	NUM
ejpam-4944	223	27	,	,	PUNCT
ejpam-4944	223	28	2	2	NUM
ejpam-4944	223	29	;	;	PUNCT
ejpam-4944	223	30	s	s	VERB
ejpam-4944	223	31	̸=	̸=	PROPN
ejpam-4944	223	32	v.	v.	ADP
ejpam-4944	223	33	proof	proof	NOUN
ejpam-4944	223	34	.	.	PUNCT
ejpam-4944	224	1	assume	assume	VERB
ejpam-4944	224	2	that	that	SCONJ
ejpam-4944	224	3	,	,	PUNCT
ejpam-4944	224	4	µs	µs	NOUN
ejpam-4944	224	5	is	be	AUX
ejpam-4944	224	6	sgt	sgt	PROPN
ejpam-4944	224	7	and	and	CCONJ
ejpam-4944	224	8	q	q	ADJ
ejpam-4944	224	9	∈	∈	PROPN
ejpam-4944	224	10	(	(	PUNCT
ejpam-4944	224	11	s	s	NOUN
ejpam-4944	224	12	,	,	PUNCT
ejpam-4944	224	13	v)−d(x	v)−d(x	NUM
ejpam-4944	224	14	)	)	PUNCT
ejpam-4944	224	15	.	.	PUNCT
ejpam-4944	225	1	take	take	VERB
ejpam-4944	225	2	s	s	NOUN
ejpam-4944	225	3	=	=	SYM
ejpam-4944	225	4	1	1	NUM
ejpam-4944	225	5	;	;	PUNCT
ejpam-4944	225	6	v	v	NOUN
ejpam-4944	225	7	=	=	SYM
ejpam-4944	225	8	2	2	NUM
ejpam-4944	225	9	.	.	PUNCT
ejpam-4944	226	1	then	then	ADV
ejpam-4944	226	2	q	q	PROPN
ejpam-4944	226	3	∈	∈	PROPN
ejpam-4944	226	4	(	(	PUNCT
ejpam-4944	226	5	1	1	NUM
ejpam-4944	226	6	,	,	PUNCT
ejpam-4944	226	7	2)−d(x	2)−d(x	NUM
ejpam-4944	226	8	)	)	PUNCT
ejpam-4944	226	9	so	so	SCONJ
ejpam-4944	226	10	that	that	PRON
ejpam-4944	226	11	c1(c2(q	c1(c2(q	PROPN
ejpam-4944	226	12	)	)	PUNCT
ejpam-4944	226	13	)	)	PUNCT
ejpam-4944	227	1	=	=	PUNCT
ejpam-4944	227	2	x.	x.	NOUN
ejpam-4944	227	3	thus	thus	ADV
ejpam-4944	227	4	,	,	PUNCT
ejpam-4944	227	5	c2(q	c2(q	PROPN
ejpam-4944	227	6	)	)	PUNCT
ejpam-4944	227	7	∩m	∩m	PROPN
ejpam-4944	227	8	̸=	̸=	PROPN
ejpam-4944	227	9	∅	∅	NOUN
ejpam-4944	227	10	for	for	ADP
ejpam-4944	227	11	all	all	DET
ejpam-4944	227	12	m	m	NOUN
ejpam-4944	227	13	∈	∈	ADJ
ejpam-4944	227	14	µ̃1	µ̃1	NOUN
ejpam-4944	227	15	.	.	PUNCT
ejpam-4944	228	1	let	let	AUX
ejpam-4944	228	2	h	h	PRON
ejpam-4944	228	3	∈	∈	PROPN
ejpam-4944	228	4	σ̃1	σ̃1	PROPN
ejpam-4944	228	5	.	.	PROPN
ejpam-4944	228	6	suppose	suppose	VERB
ejpam-4944	228	7	h	h	PROPN
ejpam-4944	228	8	∈	∈	PROPN
ejpam-4944	228	9	µ̃1	µ̃1	PROPN
ejpam-4944	228	10	.	.	PUNCT
ejpam-4944	229	1	then	then	ADV
ejpam-4944	229	2	there	there	PRON
ejpam-4944	229	3	is	be	VERB
ejpam-4944	229	4	nothing	nothing	PRON
ejpam-4944	229	5	to	to	PART
ejpam-4944	229	6	prove	prove	VERB
ejpam-4944	229	7	.	.	PUNCT
ejpam-4944	230	1	suppose	suppose	VERB
ejpam-4944	230	2	h	h	NOUN
ejpam-4944	230	3	/∈	/∈	PUNCT
ejpam-4944	231	1	µ̃1	µ̃1	NOUN
ejpam-4944	231	2	.	.	PUNCT
ejpam-4944	231	3	here	here	ADV
ejpam-4944	231	4	h	h	PROPN
ejpam-4944	231	5	⊂	⊂	PROPN
ejpam-4944	231	6	c1(i1(h	c1(i1(h	PROPN
ejpam-4944	231	7	)	)	PUNCT
ejpam-4944	231	8	)	)	PUNCT
ejpam-4944	231	9	.	.	PUNCT
ejpam-4944	232	1	this	this	PRON
ejpam-4944	232	2	implies	imply	VERB
ejpam-4944	232	3	c1(i1(h	c1(i1(h	NOUN
ejpam-4944	232	4	)	)	PUNCT
ejpam-4944	232	5	)	)	PUNCT
ejpam-4944	233	1	̸=	̸=	PROPN
ejpam-4944	233	2	∅	∅	NOUN
ejpam-4944	233	3	which	which	PRON
ejpam-4944	233	4	implies	imply	VERB
ejpam-4944	233	5	that	that	SCONJ
ejpam-4944	233	6	i1(h	i1(h	PROPN
ejpam-4944	233	7	)	)	PUNCT
ejpam-4944	233	8	̸=	̸=	NOUN
ejpam-4944	233	9	∅	∅	NOUN
ejpam-4944	233	10	,	,	PUNCT
ejpam-4944	233	11	by	by	ADP
ejpam-4944	233	12	hypothesis	hypothesis	NOUN
ejpam-4944	233	13	.	.	PUNCT
ejpam-4944	234	1	thus	thus	ADV
ejpam-4944	234	2	,	,	PUNCT
ejpam-4944	234	3	i1(h	i1(h	PROPN
ejpam-4944	234	4	)	)	PUNCT
ejpam-4944	234	5	∈	∈	PROPN
ejpam-4944	234	6	µ̃1	µ̃1	NOUN
ejpam-4944	234	7	so	so	SCONJ
ejpam-4944	234	8	that	that	PRON
ejpam-4944	234	9	c2(q)∩h	c2(q)∩h	VERB
ejpam-4944	234	10	̸=	̸=	PROPN
ejpam-4944	234	11	∅.	∅.	ADV
ejpam-4944	234	12	thus	thus	ADV
ejpam-4944	234	13	,	,	PUNCT
ejpam-4944	234	14	c2(q)∩h	c2(q)∩h	VERB
ejpam-4944	234	15	̸=	̸=	PROPN
ejpam-4944	234	16	∅	∅	NOUN
ejpam-4944	234	17	for	for	ADP
ejpam-4944	234	18	all	all	DET
ejpam-4944	234	19	h	h	NOUN
ejpam-4944	234	20	∈	∈	PROPN
ejpam-4944	234	21	σ̃1	σ̃1	PROPN
ejpam-4944	234	22	.	.	PROPN
ejpam-4944	235	1	hence	hence	ADV
ejpam-4944	235	2	q	q	X
ejpam-4944	235	3	∈	∈	PROPN
ejpam-4944	235	4	(	(	PUNCT
ejpam-4944	235	5	1	1	NUM
ejpam-4944	235	6	,	,	PUNCT
ejpam-4944	235	7	2)⋆	2)⋆	PROPN
ejpam-4944	235	8	−d(x	−d(x	NOUN
ejpam-4944	235	9	)	)	PUNCT
ejpam-4944	235	10	.	.	PUNCT
ejpam-4944	236	1	fix	fix	NOUN
ejpam-4944	236	2	s	s	PART
ejpam-4944	236	3	=	=	NOUN
ejpam-4944	236	4	2	2	NUM
ejpam-4944	236	5	;	;	PUNCT
ejpam-4944	236	6	v	v	NOUN
ejpam-4944	236	7	=	=	SYM
ejpam-4944	236	8	1	1	X
ejpam-4944	236	9	.	.	PUNCT
ejpam-4944	237	1	we	we	PRON
ejpam-4944	237	2	get	get	VERB
ejpam-4944	237	3	q	q	X
ejpam-4944	237	4	∈	∈	NOUN
ejpam-4944	237	5	(	(	PUNCT
ejpam-4944	237	6	2	2	NUM
ejpam-4944	237	7	,	,	PUNCT
ejpam-4944	237	8	1	1	NUM
ejpam-4944	237	9	)	)	PUNCT
ejpam-4944	237	10	−	−	PROPN
ejpam-4944	237	11	d(x	d(x	NOUN
ejpam-4944	237	12	)	)	PUNCT
ejpam-4944	237	13	such	such	ADJ
ejpam-4944	237	14	that	that	DET
ejpam-4944	237	15	c2(c1(q	c2(c1(q	NOUN
ejpam-4944	237	16	)	)	PUNCT
ejpam-4944	237	17	)	)	PUNCT
ejpam-4944	238	1	=	=	PUNCT
ejpam-4944	238	2	x	x	X
ejpam-4944	238	3	which	which	PRON
ejpam-4944	238	4	implies	imply	VERB
ejpam-4944	238	5	c1(q	c1(q	ADJ
ejpam-4944	238	6	)	)	PUNCT
ejpam-4944	238	7	∩	∩	NOUN
ejpam-4944	238	8	l	l	PROPN
ejpam-4944	238	9	̸=	̸=	PROPN
ejpam-4944	238	10	∅	∅	NOUN
ejpam-4944	238	11	for	for	ADP
ejpam-4944	238	12	all	all	DET
ejpam-4944	238	13	l	l	NOUN
ejpam-4944	238	14	∈	∈	PROPN
ejpam-4944	238	15	µ̃2	µ̃2	PROPN
ejpam-4944	238	16	.	.	PUNCT
ejpam-4944	239	1	let	let	VERB
ejpam-4944	239	2	k	k	PROPN
ejpam-4944	239	3	∈	∈	PROPN
ejpam-4944	239	4	σ̃2	σ̃2	PROPN
ejpam-4944	239	5	.	.	PUNCT
ejpam-4944	239	6	suppose	suppose	VERB
ejpam-4944	239	7	k	k	PROPN
ejpam-4944	239	8	∈	∈	PROPN
ejpam-4944	239	9	µ̃2	µ̃2	PROPN
ejpam-4944	239	10	.	.	PUNCT
ejpam-4944	240	1	then	then	ADV
ejpam-4944	240	2	there	there	PRON
ejpam-4944	240	3	is	be	VERB
ejpam-4944	240	4	nothing	nothing	PRON
ejpam-4944	240	5	to	to	PART
ejpam-4944	240	6	prove	prove	VERB
ejpam-4944	240	7	.	.	PUNCT
ejpam-4944	241	1	if	if	SCONJ
ejpam-4944	241	2	k	k	PROPN
ejpam-4944	241	3	/∈	/∈	PUNCT
ejpam-4944	242	1	µ̃2	µ̃2	PROPN
ejpam-4944	242	2	,	,	PUNCT
ejpam-4944	242	3	then	then	ADV
ejpam-4944	242	4	from	from	ADP
ejpam-4944	242	5	the	the	DET
ejpam-4944	242	6	definition	definition	NOUN
ejpam-4944	242	7	of	of	ADP
ejpam-4944	242	8	k	k	PROPN
ejpam-4944	242	9	such	such	ADJ
ejpam-4944	242	10	that	that	SCONJ
ejpam-4944	242	11	k	k	PROPN
ejpam-4944	242	12	⊂	⊂	PROPN
ejpam-4944	242	13	c2(i2(k	c2(i2(k	PROPN
ejpam-4944	242	14	)	)	PUNCT
ejpam-4944	242	15	)	)	PUNCT
ejpam-4944	242	16	.	.	PUNCT
ejpam-4944	243	1	this	this	PRON
ejpam-4944	243	2	implies	imply	VERB
ejpam-4944	243	3	c2(i2(k	c2(i2(k	NOUN
ejpam-4944	243	4	)	)	PUNCT
ejpam-4944	243	5	)	)	PUNCT
ejpam-4944	244	1	̸=	̸=	PROPN
ejpam-4944	244	2	∅	∅	NOUN
ejpam-4944	244	3	which	which	PRON
ejpam-4944	244	4	implies	imply	VERB
ejpam-4944	244	5	that	that	SCONJ
ejpam-4944	244	6	i2(k	i2(k	NOUN
ejpam-4944	244	7	)	)	PUNCT
ejpam-4944	244	8	̸=	̸=	PROPN
ejpam-4944	244	9	∅	∅	NOUN
ejpam-4944	244	10	since	since	SCONJ
ejpam-4944	244	11	µ2	µ2	PROPN
ejpam-4944	244	12	is	be	AUX
ejpam-4944	244	13	a	a	DET
ejpam-4944	244	14	sgt	sgt	PROPN
ejpam-4944	244	15	.	.	PUNCT
ejpam-4944	245	1	thus	thus	ADV
ejpam-4944	245	2	,	,	PUNCT
ejpam-4944	245	3	i2(k	i2(k	NOUN
ejpam-4944	245	4	)	)	PUNCT
ejpam-4944	245	5	∈	∈	PROPN
ejpam-4944	245	6	µ̃2	µ̃2	PROPN
ejpam-4944	245	7	so	so	SCONJ
ejpam-4944	245	8	that	that	SCONJ
ejpam-4944	245	9	c1(q	c1(q	ADJ
ejpam-4944	245	10	)	)	PUNCT
ejpam-4944	245	11	∩k	∩k	NOUN
ejpam-4944	245	12	̸=	̸=	PROPN
ejpam-4944	245	13	∅.	∅.	ADP
ejpam-4944	245	14	thus	thus	ADV
ejpam-4944	245	15	,	,	PUNCT
ejpam-4944	245	16	c1(q	c1(q	ADJ
ejpam-4944	245	17	)	)	PUNCT
ejpam-4944	245	18	∩k	∩k	NOUN
ejpam-4944	245	19	̸=	̸=	PROPN
ejpam-4944	245	20	∅	∅	NOUN
ejpam-4944	245	21	for	for	ADP
ejpam-4944	245	22	all	all	DET
ejpam-4944	245	23	k	k	PROPN
ejpam-4944	245	24	∈	∈	PROPN
ejpam-4944	245	25	σ̃2	σ̃2	PROPN
ejpam-4944	245	26	.	.	PUNCT
ejpam-4944	246	1	hence	hence	ADV
ejpam-4944	246	2	q	q	PROPN
ejpam-4944	246	3	∈	∈	PROPN
ejpam-4944	246	4	(	(	PUNCT
ejpam-4944	246	5	2	2	NUM
ejpam-4944	246	6	,	,	PUNCT
ejpam-4944	246	7	1)⋆	1)⋆	PROPN
ejpam-4944	246	8	−d(x	−d(x	NOUN
ejpam-4944	246	9	)	)	PUNCT
ejpam-4944	246	10	.	.	PUNCT
ejpam-4944	247	1	the	the	DET
ejpam-4944	247	2	above	above	ADJ
ejpam-4944	247	3	example	example	NOUN
ejpam-4944	247	4	16	16	NUM
ejpam-4944	247	5	also	also	ADV
ejpam-4944	247	6	proves	prove	VERB
ejpam-4944	247	7	that	that	SCONJ
ejpam-4944	247	8	the	the	DET
ejpam-4944	247	9	hypothesis	hypothesis	NOUN
ejpam-4944	247	10	of	of	ADP
ejpam-4944	247	11	theorem	theorem	NOUN
ejpam-4944	247	12	17	17	NUM
ejpam-4944	247	13	can	can	AUX
ejpam-4944	247	14	not	not	PART
ejpam-4944	247	15	be	be	AUX
ejpam-4944	247	16	dropped	drop	VERB
ejpam-4944	247	17	.	.	PUNCT
ejpam-4944	248	1	theorem	theorem	NOUN
ejpam-4944	248	2	18	18	NUM
ejpam-4944	248	3	.	.	PUNCT
ejpam-4944	249	1	let	let	AUX
ejpam-4944	249	2	(	(	PUNCT
ejpam-4944	249	3	x,µ1	x,µ1	NOUN
ejpam-4944	249	4	,	,	PUNCT
ejpam-4944	249	5	µ2	µ2	PROPN
ejpam-4944	249	6	)	)	PUNCT
ejpam-4944	249	7	be	be	VERB
ejpam-4944	249	8	a	a	DET
ejpam-4944	249	9	bgts	bgts	NOUN
ejpam-4944	249	10	and	and	CCONJ
ejpam-4944	249	11	µ1	µ1	PROPN
ejpam-4944	249	12	⊂	⊂	PROPN
ejpam-4944	249	13	µ2	µ2	PROPN
ejpam-4944	249	14	.	.	PUNCT
ejpam-4944	250	1	if	if	SCONJ
ejpam-4944	250	2	µ1	µ1	PROPN
ejpam-4944	250	3	⊂	⊂	PROPN
ejpam-4944	250	4	(	(	PUNCT
ejpam-4944	250	5	s	s	PROPN
ejpam-4944	250	6	,	,	PUNCT
ejpam-4944	250	7	v)⋆	v)⋆	PROPN
ejpam-4944	250	8	−	−	PROPN
ejpam-4944	250	9	d(x	d(x	PROPN
ejpam-4944	250	10	)	)	PUNCT
ejpam-4944	250	11	,	,	PUNCT
ejpam-4944	250	12	then	then	ADV
ejpam-4944	250	13	(	(	PUNCT
ejpam-4944	250	14	x,µ1	x,µ1	NOUN
ejpam-4944	250	15	)	)	PUNCT
ejpam-4944	250	16	is	be	AUX
ejpam-4944	250	17	hyperconnected	hyperconnecte	VERB
ejpam-4944	250	18	for	for	ADP
ejpam-4944	250	19	s	s	PROPN
ejpam-4944	250	20	,	,	PUNCT
ejpam-4944	250	21	v	v	NOUN
ejpam-4944	250	22	=	=	SYM
ejpam-4944	250	23	1	1	NUM
ejpam-4944	250	24	,	,	PUNCT
ejpam-4944	250	25	2	2	NUM
ejpam-4944	250	26	;	;	PUNCT
ejpam-4944	250	27	s	s	VERB
ejpam-4944	250	28	̸=	̸=	PROPN
ejpam-4944	250	29	v.	v.	ADP
ejpam-4944	250	30	proof	proof	NOUN
ejpam-4944	250	31	.	.	PUNCT
ejpam-4944	251	1	let	let	VERB
ejpam-4944	251	2	q	q	PROPN
ejpam-4944	251	3	∈	∈	PROPN
ejpam-4944	251	4	µ̃1	µ̃1	PROPN
ejpam-4944	251	5	.	.	PUNCT
ejpam-4944	251	6	choose	choose	PROPN
ejpam-4944	251	7	s	s	NOUN
ejpam-4944	251	8	=	=	SYM
ejpam-4944	251	9	1	1	NUM
ejpam-4944	251	10	and	and	CCONJ
ejpam-4944	251	11	v	v	NOUN
ejpam-4944	251	12	=	=	SYM
ejpam-4944	251	13	2	2	NUM
ejpam-4944	251	14	.	.	PUNCT
ejpam-4944	251	15	then	then	ADV
ejpam-4944	251	16	q	q	PROPN
ejpam-4944	251	17	∈	∈	PROPN
ejpam-4944	251	18	(	(	PUNCT
ejpam-4944	251	19	1	1	NUM
ejpam-4944	251	20	,	,	PUNCT
ejpam-4944	251	21	2)⋆	2)⋆	NOUN
ejpam-4944	251	22	−	−	NOUN
ejpam-4944	251	23	d(x	d(x	NOUN
ejpam-4944	251	24	)	)	PUNCT
ejpam-4944	251	25	.	.	PUNCT
ejpam-4944	252	1	by	by	ADP
ejpam-4944	252	2	hypothesis	hypothesis	NOUN
ejpam-4944	252	3	and	and	CCONJ
ejpam-4944	252	4	theorem	theorem	VERB
ejpam-4944	252	5	13	13	NUM
ejpam-4944	252	6	,	,	PUNCT
ejpam-4944	252	7	q	q	PROPN
ejpam-4944	252	8	is	be	AUX
ejpam-4944	252	9	µ1	µ1	NOUN
ejpam-4944	252	10	-	-	PUNCT
ejpam-4944	252	11	dense	dense	ADJ
ejpam-4944	252	12	so	so	SCONJ
ejpam-4944	252	13	that	that	SCONJ
ejpam-4944	252	14	(	(	PUNCT
ejpam-4944	252	15	x,µ1	x,µ1	NOUN
ejpam-4944	252	16	)	)	PUNCT
ejpam-4944	252	17	is	be	AUX
ejpam-4944	252	18	a	a	DET
ejpam-4944	252	19	hyperconnected	hyperconnected	ADJ
ejpam-4944	252	20	space	space	NOUN
ejpam-4944	252	21	.	.	PUNCT
ejpam-4944	253	1	fix	fix	NOUN
ejpam-4944	253	2	s	s	PART
ejpam-4944	253	3	=	=	NOUN
ejpam-4944	253	4	2	2	NUM
ejpam-4944	253	5	;	;	PUNCT
ejpam-4944	253	6	v	v	NOUN
ejpam-4944	253	7	=	=	SYM
ejpam-4944	253	8	1	1	X
ejpam-4944	253	9	.	.	PUNCT
ejpam-4944	254	1	then	then	ADV
ejpam-4944	254	2	q	q	PROPN
ejpam-4944	254	3	∈	∈	PROPN
ejpam-4944	254	4	(	(	PUNCT
ejpam-4944	254	5	2	2	NUM
ejpam-4944	254	6	,	,	PUNCT
ejpam-4944	254	7	1)⋆	1)⋆	PROPN
ejpam-4944	254	8	−d(x	−d(x	NOUN
ejpam-4944	254	9	)	)	PUNCT
ejpam-4944	254	10	so	so	SCONJ
ejpam-4944	254	11	that	that	SCONJ
ejpam-4944	254	12	c1(q	c1(q	ADJ
ejpam-4944	254	13	)	)	PUNCT
ejpam-4944	254	14	∩m	∩m	PROPN
ejpam-4944	254	15	̸=	̸=	PROPN
ejpam-4944	254	16	∅	∅	NOUN
ejpam-4944	254	17	for	for	ADP
ejpam-4944	254	18	every	every	DET
ejpam-4944	254	19	m	m	PROPN
ejpam-4944	254	20	∈	∈	PROPN
ejpam-4944	254	21	σ̃2	σ̃2	PROPN
ejpam-4944	254	22	.	.	PUNCT
ejpam-4944	255	1	let	let	VERB
ejpam-4944	255	2	k	k	PROPN
ejpam-4944	255	3	∈	∈	PROPN
ejpam-4944	255	4	µ̃1	µ̃1	PROPN
ejpam-4944	255	5	.	.	PUNCT
ejpam-4944	255	6	by	by	ADP
ejpam-4944	255	7	hypothesis	hypothesis	NOUN
ejpam-4944	255	8	,	,	PUNCT
ejpam-4944	255	9	k	k	PROPN
ejpam-4944	255	10	∈	∈	PROPN
ejpam-4944	255	11	µ̃2	µ̃2	PROPN
ejpam-4944	255	12	which	which	PRON
ejpam-4944	255	13	implies	imply	VERB
ejpam-4944	255	14	k	k	PROPN
ejpam-4944	255	15	∈	∈	PROPN
ejpam-4944	255	16	σ̃2	σ̃2	PROPN
ejpam-4944	255	17	,	,	PUNCT
ejpam-4944	255	18	since	since	SCONJ
ejpam-4944	255	19	µ2	µ2	PROPN
ejpam-4944	255	20	⊂	⊂	PROPN
ejpam-4944	255	21	σ2	σ2	PROPN
ejpam-4944	255	22	which	which	DET
ejpam-4944	255	23	turn	turn	NOUN
ejpam-4944	255	24	implies	imply	VERB
ejpam-4944	255	25	that	that	SCONJ
ejpam-4944	255	26	c1(q)∩k	c1(q)∩k	PROPN
ejpam-4944	255	27	̸=	̸=	PROPN
ejpam-4944	255	28	∅.	∅.	ADV
ejpam-4944	255	29	thus	thus	ADV
ejpam-4944	255	30	,	,	PUNCT
ejpam-4944	255	31	q∩k	q∩k	PROPN
ejpam-4944	255	32	̸=	̸=	PROPN
ejpam-4944	255	33	∅.	∅.	ADV
ejpam-4944	255	34	since	since	SCONJ
ejpam-4944	255	35	k	k	PROPN
ejpam-4944	255	36	is	be	AUX
ejpam-4944	255	37	an	an	DET
ejpam-4944	255	38	arbitrary	arbitrary	ADJ
ejpam-4944	255	39	non	non	ADJ
ejpam-4944	255	40	-	-	ADJ
ejpam-4944	255	41	null	null	ADJ
ejpam-4944	255	42	µ1	µ1	NOUN
ejpam-4944	255	43	-	-	PUNCT
ejpam-4944	255	44	open	open	NOUN
ejpam-4944	255	45	set	set	NOUN
ejpam-4944	255	46	,	,	PUNCT
ejpam-4944	255	47	q	q	PROPN
ejpam-4944	255	48	is	be	AUX
ejpam-4944	255	49	µ1	µ1	NOUN
ejpam-4944	255	50	-	-	PUNCT
ejpam-4944	255	51	dense	dense	ADJ
ejpam-4944	255	52	.	.	PUNCT
ejpam-4944	256	1	therefore	therefore	ADV
ejpam-4944	256	2	,	,	PUNCT
ejpam-4944	256	3	(	(	PUNCT
ejpam-4944	256	4	x,µ1	x,µ1	NOUN
ejpam-4944	256	5	)	)	PUNCT
ejpam-4944	256	6	is	be	AUX
ejpam-4944	256	7	a	a	DET
ejpam-4944	256	8	hyperconnected	hyperconnected	ADJ
ejpam-4944	256	9	space	space	NOUN
ejpam-4944	256	10	.	.	PUNCT
ejpam-4944	257	1	theorem	theorem	NOUN
ejpam-4944	257	2	19	19	NUM
ejpam-4944	257	3	.	.	PUNCT
ejpam-4944	258	1	let	let	AUX
ejpam-4944	258	2	(	(	PUNCT
ejpam-4944	258	3	x,µ1	x,µ1	NOUN
ejpam-4944	258	4	,	,	PUNCT
ejpam-4944	258	5	µ2	µ2	PROPN
ejpam-4944	258	6	)	)	PUNCT
ejpam-4944	258	7	be	be	AUX
ejpam-4944	258	8	a	a	DET
ejpam-4944	258	9	bgts	bgts	NOUN
ejpam-4944	258	10	.	.	PUNCT
ejpam-4944	259	1	if	if	SCONJ
ejpam-4944	259	2	µ2	µ2	PROPN
ejpam-4944	259	3	⊂	⊂	PROPN
ejpam-4944	259	4	µ1	µ1	PROPN
ejpam-4944	259	5	and	and	CCONJ
ejpam-4944	259	6	if	if	SCONJ
ejpam-4944	259	7	µ2	µ2	PROPN
ejpam-4944	259	8	⊂	⊂	PROPN
ejpam-4944	259	9	(	(	PUNCT
ejpam-4944	259	10	s	s	PROPN
ejpam-4944	259	11	,	,	PUNCT
ejpam-4944	259	12	v)⋆	v)⋆	PROPN
ejpam-4944	259	13	−	−	PROPN
ejpam-4944	259	14	d(x	d(x	PROPN
ejpam-4944	259	15	)	)	PUNCT
ejpam-4944	259	16	where	where	SCONJ
ejpam-4944	259	17	s	s	X
ejpam-4944	259	18	,	,	PUNCT
ejpam-4944	259	19	v	v	NOUN
ejpam-4944	259	20	=	=	SYM
ejpam-4944	259	21	1	1	NUM
ejpam-4944	259	22	,	,	PUNCT
ejpam-4944	259	23	2	2	NUM
ejpam-4944	259	24	;	;	PUNCT
ejpam-4944	259	25	s	s	VERB
ejpam-4944	259	26	̸=	̸=	PROPN
ejpam-4944	259	27	v	v	NOUN
ejpam-4944	259	28	,	,	PUNCT
ejpam-4944	259	29	then	then	ADV
ejpam-4944	259	30	(	(	PUNCT
ejpam-4944	259	31	x,µ2	x,µ2	PROPN
ejpam-4944	259	32	)	)	PUNCT
ejpam-4944	259	33	is	be	AUX
ejpam-4944	259	34	hyperconnected	hyperconnecte	VERB
ejpam-4944	259	35	.	.	PUNCT
ejpam-4944	260	1	d.	d.	PROPN
ejpam-4944	260	2	elgezouli	elgezouli	PROPN
ejpam-4944	260	3	et	et	PROPN
ejpam-4944	260	4	al	al	PROPN
ejpam-4944	260	5	.	.	PUNCT
ejpam-4944	260	6	/	/	SYM
ejpam-4944	260	7	eur	eur	PROPN
ejpam-4944	260	8	.	.	PUNCT
ejpam-4944	261	1	j.	j.	PROPN
ejpam-4944	261	2	pure	pure	PROPN
ejpam-4944	261	3	appl	appl	PROPN
ejpam-4944	261	4	.	.	PROPN
ejpam-4944	261	5	math	math	PROPN
ejpam-4944	261	6	,	,	PUNCT
ejpam-4944	261	7	16	16	NUM
ejpam-4944	261	8	(	(	PUNCT
ejpam-4944	261	9	4	4	NUM
ejpam-4944	261	10	)	)	PUNCT
ejpam-4944	261	11	(	(	PUNCT
ejpam-4944	261	12	2023	2023	NUM
ejpam-4944	261	13	)	)	PUNCT
ejpam-4944	261	14	,	,	PUNCT
ejpam-4944	261	15	2286	2286	NUM
ejpam-4944	261	16	-	-	SYM
ejpam-4944	261	17	2305	2305	NUM
ejpam-4944	261	18	2294	2294	NUM
ejpam-4944	261	19	proof	proof	NOUN
ejpam-4944	261	20	.	.	PUNCT
ejpam-4944	262	1	let	let	VERB
ejpam-4944	262	2	p	p	PRON
ejpam-4944	262	3	∈	∈	PROPN
ejpam-4944	262	4	µ̃2	µ̃2	PROPN
ejpam-4944	262	5	.	.	PUNCT
ejpam-4944	263	1	take	take	NOUN
ejpam-4944	263	2	s	s	NOUN
ejpam-4944	263	3	=	=	SYM
ejpam-4944	263	4	1	1	NUM
ejpam-4944	263	5	and	and	CCONJ
ejpam-4944	263	6	v	v	NOUN
ejpam-4944	263	7	=	=	SYM
ejpam-4944	263	8	2	2	NUM
ejpam-4944	263	9	.	.	PUNCT
ejpam-4944	264	1	then	then	ADV
ejpam-4944	264	2	p	p	PROPN
ejpam-4944	264	3	∈	∈	PROPN
ejpam-4944	264	4	(	(	PUNCT
ejpam-4944	264	5	1	1	NUM
ejpam-4944	264	6	,	,	PUNCT
ejpam-4944	264	7	2)⋆	2)⋆	PROPN
ejpam-4944	264	8	−d(x	−d(x	NOUN
ejpam-4944	264	9	)	)	PUNCT
ejpam-4944	264	10	so	so	SCONJ
ejpam-4944	264	11	that	that	PRON
ejpam-4944	264	12	c2(p	c2(p	X
ejpam-4944	264	13	)	)	PUNCT
ejpam-4944	264	14	∩m	∩m	PROPN
ejpam-4944	264	15	̸=	̸=	PROPN
ejpam-4944	264	16	∅	∅	NOUN
ejpam-4944	264	17	for	for	ADP
ejpam-4944	264	18	every	every	DET
ejpam-4944	264	19	m	m	NOUN
ejpam-4944	264	20	∈	∈	ADJ
ejpam-4944	264	21	σ̃1	σ̃1	PROPN
ejpam-4944	264	22	.	.	PUNCT
ejpam-4944	264	23	let	let	VERB
ejpam-4944	264	24	k	k	PROPN
ejpam-4944	264	25	∈	∈	PROPN
ejpam-4944	264	26	µ̃2	µ̃2	PROPN
ejpam-4944	264	27	.	.	PUNCT
ejpam-4944	265	1	by	by	ADP
ejpam-4944	265	2	hypothesis	hypothesis	NOUN
ejpam-4944	265	3	,	,	PUNCT
ejpam-4944	265	4	k	k	PROPN
ejpam-4944	265	5	∈	∈	PROPN
ejpam-4944	265	6	µ̃1	µ̃1	PROPN
ejpam-4944	265	7	which	which	PRON
ejpam-4944	265	8	implies	imply	VERB
ejpam-4944	265	9	k	k	PROPN
ejpam-4944	265	10	∈	∈	PROPN
ejpam-4944	265	11	σ̃1	σ̃1	PROPN
ejpam-4944	265	12	,	,	PUNCT
ejpam-4944	265	13	since	since	SCONJ
ejpam-4944	265	14	µ1	µ1	PROPN
ejpam-4944	265	15	⊂	⊂	PROPN
ejpam-4944	265	16	σ1	σ1	PROPN
ejpam-4944	265	17	which	which	PRON
ejpam-4944	265	18	turn	turn	VERB
ejpam-4944	265	19	implies	imply	VERB
ejpam-4944	265	20	that	that	SCONJ
ejpam-4944	265	21	c2(p	c2(p	NUM
ejpam-4944	265	22	)	)	PUNCT
ejpam-4944	265	23	∩k	∩k	NOUN
ejpam-4944	265	24	̸=	̸=	PROPN
ejpam-4944	265	25	∅.	∅.	ADP
ejpam-4944	265	26	thus	thus	ADV
ejpam-4944	265	27	,	,	PUNCT
ejpam-4944	265	28	p	p	NOUN
ejpam-4944	265	29	∩k	∩k	NOUN
ejpam-4944	265	30	̸=	̸=	PROPN
ejpam-4944	265	31	∅.	∅.	ADV
ejpam-4944	265	32	since	since	SCONJ
ejpam-4944	265	33	k	k	PROPN
ejpam-4944	265	34	is	be	AUX
ejpam-4944	265	35	an	an	DET
ejpam-4944	265	36	arbitrary	arbitrary	ADJ
ejpam-4944	265	37	non	non	ADJ
ejpam-4944	265	38	-	-	ADJ
ejpam-4944	265	39	null	null	ADJ
ejpam-4944	265	40	µ2	µ2	ADJ
ejpam-4944	265	41	-	-	PUNCT
ejpam-4944	265	42	open	open	NOUN
ejpam-4944	265	43	set	set	NOUN
ejpam-4944	265	44	,	,	PUNCT
ejpam-4944	265	45	p	p	PROPN
ejpam-4944	265	46	is	be	AUX
ejpam-4944	265	47	µ2	µ2	ADJ
ejpam-4944	265	48	-	-	PUNCT
ejpam-4944	265	49	dense	dense	ADJ
ejpam-4944	265	50	.	.	PUNCT
ejpam-4944	266	1	hence	hence	ADV
ejpam-4944	266	2	(	(	PUNCT
ejpam-4944	266	3	x,µ2	x,µ2	PROPN
ejpam-4944	266	4	)	)	PUNCT
ejpam-4944	266	5	is	be	AUX
ejpam-4944	266	6	hyperconnected	hyperconnecte	VERB
ejpam-4944	266	7	.	.	PUNCT
ejpam-4944	267	1	now	now	ADV
ejpam-4944	267	2	we	we	PRON
ejpam-4944	267	3	choose	choose	VERB
ejpam-4944	267	4	s	s	NOUN
ejpam-4944	267	5	=	=	SYM
ejpam-4944	267	6	2	2	NUM
ejpam-4944	267	7	;	;	PUNCT
ejpam-4944	267	8	v	v	NOUN
ejpam-4944	267	9	=	=	SYM
ejpam-4944	267	10	1	1	X
ejpam-4944	267	11	.	.	PUNCT
ejpam-4944	268	1	we	we	PRON
ejpam-4944	268	2	get	get	VERB
ejpam-4944	268	3	p	p	X
ejpam-4944	268	4	∈	∈	NOUN
ejpam-4944	268	5	(	(	PUNCT
ejpam-4944	268	6	2	2	NUM
ejpam-4944	268	7	,	,	PUNCT
ejpam-4944	268	8	1)⋆−d(x	1)⋆−d(x	NUM
ejpam-4944	268	9	)	)	PUNCT
ejpam-4944	268	10	.	.	PUNCT
ejpam-4944	269	1	by	by	ADP
ejpam-4944	269	2	theorem	theorem	ADJ
ejpam-4944	269	3	13	13	NUM
ejpam-4944	269	4	and	and	CCONJ
ejpam-4944	269	5	hypothesis	hypothesis	NOUN
ejpam-4944	269	6	,	,	PUNCT
ejpam-4944	269	7	we	we	PRON
ejpam-4944	269	8	get	get	VERB
ejpam-4944	269	9	q	q	PROPN
ejpam-4944	269	10	is	be	AUX
ejpam-4944	269	11	µ2	µ2	ADJ
ejpam-4944	269	12	-	-	PUNCT
ejpam-4944	269	13	dense	dense	ADJ
ejpam-4944	269	14	.	.	PUNCT
ejpam-4944	270	1	therefore	therefore	ADV
ejpam-4944	270	2	,	,	PUNCT
ejpam-4944	270	3	(	(	PUNCT
ejpam-4944	270	4	x,µ2	x,µ2	PROPN
ejpam-4944	270	5	)	)	PUNCT
ejpam-4944	270	6	is	be	AUX
ejpam-4944	270	7	a	a	DET
ejpam-4944	270	8	hyperconnected	hyperconnected	ADJ
ejpam-4944	270	9	space	space	NOUN
ejpam-4944	270	10	.	.	PUNCT
ejpam-4944	271	1	theorem	theorem	ADJ
ejpam-4944	271	2	20	20	NUM
ejpam-4944	271	3	.	.	PUNCT
ejpam-4944	272	1	let	let	AUX
ejpam-4944	272	2	(	(	PUNCT
ejpam-4944	272	3	x,µ1	x,µ1	NOUN
ejpam-4944	272	4	,	,	PUNCT
ejpam-4944	272	5	µ2	µ2	PROPN
ejpam-4944	272	6	)	)	PUNCT
ejpam-4944	272	7	be	be	VERB
ejpam-4944	272	8	a	a	DET
ejpam-4944	272	9	bgts	bgts	NOUN
ejpam-4944	272	10	and	and	CCONJ
ejpam-4944	272	11	q	q	NOUN
ejpam-4944	272	12	∈	∈	PROPN
ejpam-4944	272	13	(	(	PUNCT
ejpam-4944	272	14	s	s	PROPN
ejpam-4944	272	15	,	,	PUNCT
ejpam-4944	272	16	v	v	NOUN
ejpam-4944	272	17	)	)	PUNCT
ejpam-4944	272	18	−	−	PROPN
ejpam-4944	272	19	d(x	d(x	NOUN
ejpam-4944	272	20	)	)	PUNCT
ejpam-4944	272	21	;	;	PUNCT
ejpam-4944	272	22	q	q	PROPN
ejpam-4944	272	23	∈	∈	PROPN
ejpam-4944	272	24	µv	µv	PROPN
ejpam-4944	272	25	;	;	PUNCT
ejpam-4944	272	26	j	j	PROPN
ejpam-4944	272	27	∈	∈	PROPN
ejpam-4944	272	28	(	(	PUNCT
ejpam-4944	272	29	v	v	NOUN
ejpam-4944	272	30	,	,	PUNCT
ejpam-4944	272	31	s)⋆	s)⋆	PROPN
ejpam-4944	272	32	−	−	PROPN
ejpam-4944	272	33	d(x	d(x	NOUN
ejpam-4944	272	34	)	)	PUNCT
ejpam-4944	272	35	.	.	PUNCT
ejpam-4944	273	1	if	if	SCONJ
ejpam-4944	273	2	µv	µv	PRON
ejpam-4944	273	3	⊂	⊂	PART
ejpam-4944	273	4	µs	µs	X
ejpam-4944	273	5	and	and	CCONJ
ejpam-4944	273	6	if	if	SCONJ
ejpam-4944	273	7	µv	µv	PRON
ejpam-4944	273	8	has	have	VERB
ejpam-4944	273	9	the	the	DET
ejpam-4944	273	10	i	i	NOUN
ejpam-4944	273	11	-	-	PUNCT
ejpam-4944	273	12	property	property	NOUN
ejpam-4944	273	13	,	,	PUNCT
ejpam-4944	273	14	then	then	ADV
ejpam-4944	273	15	q∩j	q∩j	PROPN
ejpam-4944	273	16	∈	∈	PROPN
ejpam-4944	273	17	(	(	PUNCT
ejpam-4944	273	18	v	v	NOUN
ejpam-4944	273	19	,	,	PUNCT
ejpam-4944	273	20	s)−d(x	s)−d(x	NOUN
ejpam-4944	273	21	)	)	PUNCT
ejpam-4944	273	22	where	where	SCONJ
ejpam-4944	273	23	s	s	X
ejpam-4944	273	24	,	,	PUNCT
ejpam-4944	273	25	v	v	NOUN
ejpam-4944	273	26	=	=	SYM
ejpam-4944	273	27	1	1	NUM
ejpam-4944	273	28	,	,	PUNCT
ejpam-4944	273	29	2	2	NUM
ejpam-4944	273	30	;	;	PUNCT
ejpam-4944	273	31	s	s	VERB
ejpam-4944	273	32	̸=	̸=	PROPN
ejpam-4944	273	33	v.	v.	ADP
ejpam-4944	273	34	proof	proof	NOUN
ejpam-4944	273	35	.	.	PUNCT
ejpam-4944	274	1	fix	fix	NOUN
ejpam-4944	274	2	s	s	PART
ejpam-4944	274	3	=	=	SYM
ejpam-4944	274	4	1	1	NUM
ejpam-4944	274	5	,	,	PUNCT
ejpam-4944	274	6	v	v	NOUN
ejpam-4944	274	7	=	=	SYM
ejpam-4944	274	8	2	2	X
ejpam-4944	274	9	.	.	X
ejpam-4944	274	10	assume	assume	VERB
ejpam-4944	274	11	that	that	SCONJ
ejpam-4944	274	12	,	,	PUNCT
ejpam-4944	274	13	q	q	PROPN
ejpam-4944	274	14	∈	∈	PROPN
ejpam-4944	274	15	(	(	PUNCT
ejpam-4944	274	16	1	1	NUM
ejpam-4944	274	17	,	,	PUNCT
ejpam-4944	274	18	2	2	NUM
ejpam-4944	274	19	)	)	PUNCT
ejpam-4944	274	20	−	−	PROPN
ejpam-4944	274	21	d(x	d(x	NOUN
ejpam-4944	274	22	)	)	PUNCT
ejpam-4944	274	23	;	;	PUNCT
ejpam-4944	274	24	q	q	PROPN
ejpam-4944	274	25	∈	∈	PROPN
ejpam-4944	274	26	µ2	µ2	PROPN
ejpam-4944	274	27	and	and	CCONJ
ejpam-4944	274	28	j	j	PROPN
ejpam-4944	274	29	∈	∈	PROPN
ejpam-4944	274	30	(	(	PUNCT
ejpam-4944	274	31	2	2	NUM
ejpam-4944	274	32	,	,	PUNCT
ejpam-4944	274	33	1)⋆	1)⋆	PROPN
ejpam-4944	274	34	−	−	PROPN
ejpam-4944	274	35	d(x	d(x	PROPN
ejpam-4944	274	36	)	)	PUNCT
ejpam-4944	274	37	.	.	PUNCT
ejpam-4944	275	1	then	then	ADV
ejpam-4944	275	2	(	(	PUNCT
ejpam-4944	275	3	a	a	X
ejpam-4944	275	4	)	)	PUNCT
ejpam-4944	275	5	c1(c2(q	c1(c2(q	PROPN
ejpam-4944	275	6	)	)	PUNCT
ejpam-4944	275	7	)	)	PUNCT
ejpam-4944	276	1	=	=	PUNCT
ejpam-4944	276	2	x.	x.	NOUN
ejpam-4944	276	3	(	(	PUNCT
ejpam-4944	276	4	b	b	NOUN
ejpam-4944	276	5	)	)	PUNCT
ejpam-4944	276	6	c1j	c1j	VERB
ejpam-4944	276	7	∩m	∩m	PROPN
ejpam-4944	276	8	̸=	̸=	PROPN
ejpam-4944	276	9	∅	∅	NOUN
ejpam-4944	276	10	for	for	ADP
ejpam-4944	276	11	all	all	DET
ejpam-4944	276	12	m	m	PROPN
ejpam-4944	276	13	∈	∈	PROPN
ejpam-4944	276	14	σ̃2	σ̃2	PROPN
ejpam-4944	276	15	.	.	PUNCT
ejpam-4944	276	16	suppose	suppose	VERB
ejpam-4944	276	17	µ2	µ2	PROPN
ejpam-4944	276	18	has	have	VERB
ejpam-4944	276	19	the	the	DET
ejpam-4944	276	20	i	i	NOUN
ejpam-4944	276	21	-	-	PUNCT
ejpam-4944	276	22	property	property	NOUN
ejpam-4944	276	23	and	and	CCONJ
ejpam-4944	276	24	µ2	µ2	PROPN
ejpam-4944	276	25	⊂	⊂	PROPN
ejpam-4944	276	26	µ1	µ1	PROPN
ejpam-4944	276	27	.	.	PUNCT
ejpam-4944	277	1	let	let	VERB
ejpam-4944	277	2	k	k	PROPN
ejpam-4944	277	3	∈	∈	PROPN
ejpam-4944	277	4	µ̃2	µ̃2	PROPN
ejpam-4944	277	5	.	.	PUNCT
ejpam-4944	278	1	by	by	ADP
ejpam-4944	278	2	hypothesis	hypothesis	NOUN
ejpam-4944	278	3	,	,	PUNCT
ejpam-4944	278	4	k	k	PROPN
ejpam-4944	278	5	∈	∈	PROPN
ejpam-4944	278	6	µ̃1	µ̃1	NOUN
ejpam-4944	278	7	so	so	SCONJ
ejpam-4944	278	8	that	that	SCONJ
ejpam-4944	278	9	k	k	PROPN
ejpam-4944	278	10	∩	∩	ADJ
ejpam-4944	278	11	c2(q	c2(q	PROPN
ejpam-4944	278	12	)	)	PUNCT
ejpam-4944	278	13	̸=	̸=	NOUN
ejpam-4944	278	14	∅	∅	NOUN
ejpam-4944	278	15	,	,	PUNCT
ejpam-4944	278	16	by	by	ADP
ejpam-4944	278	17	(	(	PUNCT
ejpam-4944	278	18	a	a	X
ejpam-4944	278	19	)	)	PUNCT
ejpam-4944	278	20	which	which	PRON
ejpam-4944	278	21	implies	imply	VERB
ejpam-4944	278	22	that	that	SCONJ
ejpam-4944	278	23	k	k	PROPN
ejpam-4944	278	24	∩	∩	PROPN
ejpam-4944	278	25	q	q	PROPN
ejpam-4944	278	26	̸=	̸=	PROPN
ejpam-4944	278	27	∅	∅	NOUN
ejpam-4944	278	28	,	,	PUNCT
ejpam-4944	278	29	by	by	ADP
ejpam-4944	278	30	lemma	lemma	PROPN
ejpam-4944	278	31	3	3	NUM
ejpam-4944	278	32	.	.	PUNCT
ejpam-4944	278	33	by	by	ADP
ejpam-4944	278	34	our	our	PRON
ejpam-4944	278	35	assumption	assumption	NOUN
ejpam-4944	278	36	,	,	PUNCT
ejpam-4944	278	37	i2(k∩q	i2(k∩q	PROPN
ejpam-4944	278	38	)	)	PUNCT
ejpam-4944	278	39	̸=	̸=	PROPN
ejpam-4944	278	40	∅.	∅.	PRON
ejpam-4944	278	41	by	by	ADP
ejpam-4944	278	42	(	(	PUNCT
ejpam-4944	278	43	b	b	NOUN
ejpam-4944	278	44	)	)	PUNCT
ejpam-4944	278	45	,	,	PUNCT
ejpam-4944	278	46	c1j∩i2(k∩q	c1j∩i2(k∩q	NOUN
ejpam-4944	278	47	)	)	PUNCT
ejpam-4944	278	48	̸=	̸=	PROPN
ejpam-4944	278	49	∅	∅	NOUN
ejpam-4944	278	50	which	which	PRON
ejpam-4944	278	51	implies	imply	VERB
ejpam-4944	278	52	c2j∩i2(k∩q	c2j∩i2(k∩q	NUM
ejpam-4944	278	53	)	)	PUNCT
ejpam-4944	278	54	̸=	̸=	PROPN
ejpam-4944	278	55	∅	∅	NOUN
ejpam-4944	278	56	by	by	ADP
ejpam-4944	278	57	hypothesis	hypothesis	NOUN
ejpam-4944	278	58	which	which	PRON
ejpam-4944	278	59	turn	turn	VERB
ejpam-4944	278	60	implies	imply	VERB
ejpam-4944	278	61	that	that	SCONJ
ejpam-4944	278	62	j	j	PROPN
ejpam-4944	278	63	∩	∩	PROPN
ejpam-4944	278	64	i2(k	i2(k	PROPN
ejpam-4944	278	65	∩q	∩q	PROPN
ejpam-4944	278	66	)	)	PUNCT
ejpam-4944	278	67	̸=	̸=	NOUN
ejpam-4944	278	68	∅	∅	NOUN
ejpam-4944	278	69	,	,	PUNCT
ejpam-4944	278	70	by	by	ADP
ejpam-4944	278	71	lemma	lemma	PROPN
ejpam-4944	278	72	3	3	NUM
ejpam-4944	278	73	.	.	PUNCT
ejpam-4944	279	1	thus	thus	ADV
ejpam-4944	279	2	,	,	PUNCT
ejpam-4944	279	3	j	j	PROPN
ejpam-4944	279	4	∩	∩	NOUN
ejpam-4944	279	5	(	(	PUNCT
ejpam-4944	279	6	k	k	X
ejpam-4944	279	7	∩q	∩q	PROPN
ejpam-4944	279	8	)	)	PUNCT
ejpam-4944	280	1	̸=	̸=	NOUN
ejpam-4944	280	2	∅	∅	NOUN
ejpam-4944	280	3	so	so	SCONJ
ejpam-4944	280	4	that	that	SCONJ
ejpam-4944	280	5	(	(	PUNCT
ejpam-4944	280	6	j	j	PROPN
ejpam-4944	280	7	∩q	∩q	PROPN
ejpam-4944	280	8	)	)	PUNCT
ejpam-4944	281	1	∩k	∩k	PROPN
ejpam-4944	281	2	̸=	̸=	PROPN
ejpam-4944	281	3	∅.	∅.	VERB
ejpam-4944	281	4	therefore	therefore	ADV
ejpam-4944	281	5	,	,	PUNCT
ejpam-4944	281	6	c1(j	c1(j	X
ejpam-4944	281	7	∩q	∩q	NOUN
ejpam-4944	281	8	)	)	PUNCT
ejpam-4944	282	1	∩k	∩k	PROPN
ejpam-4944	282	2	̸=	̸=	PROPN
ejpam-4944	282	3	∅.	∅.	PRON
ejpam-4944	282	4	hence	hence	ADV
ejpam-4944	282	5	q	q	NOUN
ejpam-4944	282	6	∩	∩	ADJ
ejpam-4944	282	7	j	j	PROPN
ejpam-4944	282	8	∈	∈	PROPN
ejpam-4944	282	9	(	(	PUNCT
ejpam-4944	282	10	2	2	NUM
ejpam-4944	282	11	,	,	PUNCT
ejpam-4944	282	12	1)−d(x	1)−d(x	NUM
ejpam-4944	282	13	)	)	PUNCT
ejpam-4944	282	14	.	.	PUNCT
ejpam-4944	283	1	take	take	VERB
ejpam-4944	283	2	s	s	NOUN
ejpam-4944	283	3	=	=	SYM
ejpam-4944	283	4	2	2	NUM
ejpam-4944	283	5	,	,	PUNCT
ejpam-4944	283	6	v	v	NOUN
ejpam-4944	283	7	=	=	SYM
ejpam-4944	283	8	1	1	X
ejpam-4944	283	9	.	.	PUNCT
ejpam-4944	283	10	assume	assume	VERB
ejpam-4944	283	11	that	that	SCONJ
ejpam-4944	283	12	,	,	PUNCT
ejpam-4944	283	13	q	q	PROPN
ejpam-4944	283	14	∈	∈	PROPN
ejpam-4944	283	15	(	(	PUNCT
ejpam-4944	283	16	2	2	NUM
ejpam-4944	283	17	,	,	PUNCT
ejpam-4944	283	18	1	1	NUM
ejpam-4944	283	19	)	)	PUNCT
ejpam-4944	283	20	−	−	PROPN
ejpam-4944	283	21	d(x	d(x	NOUN
ejpam-4944	283	22	)	)	PUNCT
ejpam-4944	283	23	;	;	PUNCT
ejpam-4944	283	24	q	q	PROPN
ejpam-4944	283	25	∈	∈	PROPN
ejpam-4944	283	26	µ1	µ1	PROPN
ejpam-4944	283	27	and	and	CCONJ
ejpam-4944	283	28	j	j	PROPN
ejpam-4944	283	29	∈	∈	PROPN
ejpam-4944	283	30	(	(	PUNCT
ejpam-4944	283	31	1	1	NUM
ejpam-4944	283	32	,	,	PUNCT
ejpam-4944	283	33	2)⋆	2)⋆	NOUN
ejpam-4944	283	34	−	−	NOUN
ejpam-4944	283	35	d(x	d(x	NOUN
ejpam-4944	283	36	)	)	PUNCT
ejpam-4944	283	37	.	.	PUNCT
ejpam-4944	284	1	we	we	PRON
ejpam-4944	284	2	get	get	VERB
ejpam-4944	284	3	(	(	PUNCT
ejpam-4944	284	4	c	c	NOUN
ejpam-4944	284	5	)	)	PUNCT
ejpam-4944	284	6	c2(c1(q	c2(c1(q	NOUN
ejpam-4944	284	7	)	)	PUNCT
ejpam-4944	284	8	)	)	PUNCT
ejpam-4944	285	1	=	=	PUNCT
ejpam-4944	285	2	x.	x.	NOUN
ejpam-4944	286	1	(	(	PUNCT
ejpam-4944	286	2	d	d	X
ejpam-4944	286	3	)	)	PUNCT
ejpam-4944	286	4	c2j	c2j	NOUN
ejpam-4944	286	5	∩h	∩h	NOUN
ejpam-4944	286	6	̸=	̸=	PROPN
ejpam-4944	286	7	∅	∅	NOUN
ejpam-4944	286	8	for	for	ADP
ejpam-4944	286	9	all	all	DET
ejpam-4944	286	10	h	h	NOUN
ejpam-4944	286	11	∈	∈	PROPN
ejpam-4944	286	12	σ̃1	σ̃1	PROPN
ejpam-4944	286	13	.	.	PROPN
ejpam-4944	286	14	suppose	suppose	VERB
ejpam-4944	286	15	µ1	µ1	PROPN
ejpam-4944	286	16	has	have	VERB
ejpam-4944	286	17	the	the	DET
ejpam-4944	286	18	i	i	NOUN
ejpam-4944	286	19	-	-	PUNCT
ejpam-4944	286	20	property	property	NOUN
ejpam-4944	286	21	and	and	CCONJ
ejpam-4944	286	22	µ1	µ1	PROPN
ejpam-4944	286	23	⊂	⊂	PROPN
ejpam-4944	286	24	µ2	µ2	PROPN
ejpam-4944	286	25	.	.	PUNCT
ejpam-4944	287	1	let	let	VERB
ejpam-4944	287	2	l	l	NOUN
ejpam-4944	287	3	∈	∈	PROPN
ejpam-4944	287	4	µ̃1	µ̃1	PROPN
ejpam-4944	287	5	.	.	PUNCT
ejpam-4944	287	6	by	by	ADP
ejpam-4944	287	7	hypothesis	hypothesis	NOUN
ejpam-4944	287	8	,	,	PUNCT
ejpam-4944	287	9	l	l	PROPN
ejpam-4944	287	10	∈	∈	PROPN
ejpam-4944	287	11	µ̃2	µ̃2	VERB
ejpam-4944	287	12	so	so	SCONJ
ejpam-4944	287	13	that	that	SCONJ
ejpam-4944	287	14	l	l	NOUN
ejpam-4944	287	15	∩	∩	X
ejpam-4944	287	16	c1(q	c1(q	ADJ
ejpam-4944	287	17	)	)	PUNCT
ejpam-4944	287	18	̸=	̸=	NOUN
ejpam-4944	287	19	∅	∅	NOUN
ejpam-4944	287	20	,	,	PUNCT
ejpam-4944	287	21	by	by	ADP
ejpam-4944	287	22	(	(	PUNCT
ejpam-4944	287	23	c	c	NOUN
ejpam-4944	287	24	)	)	PUNCT
ejpam-4944	287	25	which	which	PRON
ejpam-4944	287	26	implies	imply	VERB
ejpam-4944	287	27	that	that	SCONJ
ejpam-4944	287	28	l	l	NOUN
ejpam-4944	287	29	∩	∩	X
ejpam-4944	287	30	q	q	PROPN
ejpam-4944	287	31	̸=	̸=	PROPN
ejpam-4944	287	32	∅	∅	NOUN
ejpam-4944	287	33	,	,	PUNCT
ejpam-4944	287	34	by	by	ADP
ejpam-4944	287	35	lemma	lemma	PROPN
ejpam-4944	287	36	3	3	NUM
ejpam-4944	287	37	.	.	PUNCT
ejpam-4944	287	38	by	by	ADP
ejpam-4944	287	39	our	our	PRON
ejpam-4944	287	40	assumption	assumption	NOUN
ejpam-4944	287	41	,	,	PUNCT
ejpam-4944	287	42	i1(l∩q	i1(l∩q	PROPN
ejpam-4944	287	43	)	)	PUNCT
ejpam-4944	287	44	̸=	̸=	PROPN
ejpam-4944	287	45	∅.	∅.	ADV
ejpam-4944	287	46	by	by	ADP
ejpam-4944	287	47	(	(	PUNCT
ejpam-4944	287	48	d	d	NOUN
ejpam-4944	287	49	)	)	PUNCT
ejpam-4944	287	50	,	,	PUNCT
ejpam-4944	287	51	c2j	c2j	PROPN
ejpam-4944	287	52	∩	∩	NOUN
ejpam-4944	287	53	i1(l∩q	i1(l∩q	PROPN
ejpam-4944	287	54	)	)	PUNCT
ejpam-4944	287	55	̸=	̸=	PROPN
ejpam-4944	287	56	∅.	∅.	ADP
ejpam-4944	287	57	this	this	DET
ejpam-4944	287	58	implies	imply	VERB
ejpam-4944	287	59	c1j	c1j	NOUN
ejpam-4944	287	60	∩	∩	ADJ
ejpam-4944	287	61	i1(l∩q	i1(l∩q	PROPN
ejpam-4944	287	62	)	)	PUNCT
ejpam-4944	287	63	̸=	̸=	PROPN
ejpam-4944	287	64	∅	∅	NOUN
ejpam-4944	287	65	by	by	ADP
ejpam-4944	287	66	hypothesis	hypothesis	NOUN
ejpam-4944	287	67	which	which	PRON
ejpam-4944	287	68	implies	imply	VERB
ejpam-4944	287	69	that	that	SCONJ
ejpam-4944	287	70	j	j	PROPN
ejpam-4944	287	71	∩	∩	NOUN
ejpam-4944	287	72	i1(l	i1(l	PRON
ejpam-4944	287	73	∩	∩	ADJ
ejpam-4944	287	74	q	q	X
ejpam-4944	287	75	)	)	PUNCT
ejpam-4944	287	76	̸=	̸=	NOUN
ejpam-4944	287	77	∅	∅	NOUN
ejpam-4944	287	78	,	,	PUNCT
ejpam-4944	287	79	by	by	ADP
ejpam-4944	287	80	lemma	lemma	PROPN
ejpam-4944	287	81	3	3	NUM
ejpam-4944	287	82	.	.	PUNCT
ejpam-4944	288	1	thus	thus	ADV
ejpam-4944	288	2	,	,	PUNCT
ejpam-4944	288	3	j	j	PROPN
ejpam-4944	288	4	∩	∩	X
ejpam-4944	288	5	(	(	PUNCT
ejpam-4944	288	6	l	l	NOUN
ejpam-4944	288	7	∩	∩	ADJ
ejpam-4944	288	8	q	q	X
ejpam-4944	288	9	)	)	PUNCT
ejpam-4944	288	10	̸=	̸=	NOUN
ejpam-4944	288	11	∅	∅	NOUN
ejpam-4944	288	12	so	so	SCONJ
ejpam-4944	288	13	that	that	SCONJ
ejpam-4944	288	14	(	(	PUNCT
ejpam-4944	288	15	j	j	PROPN
ejpam-4944	288	16	∩q	∩q	PROPN
ejpam-4944	288	17	)	)	PUNCT
ejpam-4944	288	18	∩	∩	NOUN
ejpam-4944	288	19	l	l	PROPN
ejpam-4944	288	20	̸=	̸=	PROPN
ejpam-4944	288	21	∅.	∅.	VERB
ejpam-4944	288	22	therefore	therefore	ADV
ejpam-4944	288	23	,	,	PUNCT
ejpam-4944	288	24	c2(j	c2(j	PROPN
ejpam-4944	288	25	∩q	∩q	NOUN
ejpam-4944	288	26	)	)	PUNCT
ejpam-4944	288	27	∩	∩	NOUN
ejpam-4944	288	28	l	l	PROPN
ejpam-4944	288	29	̸=	̸=	PROPN
ejpam-4944	288	30	∅.	∅.	PRON
ejpam-4944	288	31	hence	hence	ADV
ejpam-4944	288	32	q	q	PROPN
ejpam-4944	288	33	∩	∩	ADJ
ejpam-4944	288	34	j	j	PROPN
ejpam-4944	288	35	∈	∈	PROPN
ejpam-4944	288	36	(	(	PUNCT
ejpam-4944	288	37	1	1	NUM
ejpam-4944	288	38	,	,	PUNCT
ejpam-4944	288	39	2)−d(x	2)−d(x	NUM
ejpam-4944	288	40	)	)	PUNCT
ejpam-4944	288	41	.	.	PUNCT
ejpam-4944	289	1	moreover	moreover	ADV
ejpam-4944	289	2	,	,	PUNCT
ejpam-4944	289	3	in	in	ADP
ejpam-4944	289	4	a	a	DET
ejpam-4944	289	5	bgts	bgts	NOUN
ejpam-4944	289	6	every	every	DET
ejpam-4944	289	7	µv	µv	NOUN
ejpam-4944	289	8	-	-	PUNCT
ejpam-4944	289	9	dense	dense	ADJ
ejpam-4944	289	10	set	set	NOUN
ejpam-4944	289	11	is	be	AUX
ejpam-4944	289	12	(	(	PUNCT
ejpam-4944	289	13	s	s	X
ejpam-4944	289	14	,	,	PUNCT
ejpam-4944	289	15	v)-preopen	v)-preopen	VERB
ejpam-4944	289	16	where	where	SCONJ
ejpam-4944	289	17	s	s	X
ejpam-4944	289	18	,	,	PUNCT
ejpam-4944	289	19	v	v	NOUN
ejpam-4944	289	20	=	=	SYM
ejpam-4944	289	21	1	1	NUM
ejpam-4944	289	22	,	,	PUNCT
ejpam-4944	289	23	2	2	NUM
ejpam-4944	289	24	;	;	PUNCT
ejpam-4944	289	25	s	s	VERB
ejpam-4944	289	26	̸=	̸=	PROPN
ejpam-4944	289	27	v.	v.	ADP
ejpam-4944	289	28	theorem	theorem	PROPN
ejpam-4944	289	29	21	21	NUM
ejpam-4944	289	30	.	.	PUNCT
ejpam-4944	290	1	let	let	AUX
ejpam-4944	290	2	(	(	PUNCT
ejpam-4944	290	3	x,µ1	x,µ1	NOUN
ejpam-4944	290	4	,	,	PUNCT
ejpam-4944	290	5	µ2	µ2	PROPN
ejpam-4944	290	6	)	)	PUNCT
ejpam-4944	290	7	be	be	VERB
ejpam-4944	290	8	a	a	DET
ejpam-4944	290	9	bgts	bgts	NOUN
ejpam-4944	290	10	and	and	CCONJ
ejpam-4944	290	11	η1	η1	NOUN
ejpam-4944	290	12	=	=	PUNCT
ejpam-4944	290	13	{	{	PUNCT
ejpam-4944	290	14	q	q	X
ejpam-4944	290	15	⊂	⊂	X
ejpam-4944	291	1	x	x	PROPN
ejpam-4944	292	1	|	|	ADV
ejpam-4944	292	2	q	q	NOUN
ejpam-4944	292	3	∈	∈	PROPN
ejpam-4944	292	4	(	(	PUNCT
ejpam-4944	292	5	1	1	NUM
ejpam-4944	292	6	,	,	PUNCT
ejpam-4944	292	7	2)⋆	2)⋆	NOUN
ejpam-4944	292	8	−	−	NOUN
ejpam-4944	292	9	d(x	d(x	PROPN
ejpam-4944	292	10	)	)	PUNCT
ejpam-4944	292	11	;	;	PUNCT
ejpam-4944	292	12	η2	η2	PROPN
ejpam-4944	292	13	=	=	PUNCT
ejpam-4944	292	14	{	{	PUNCT
ejpam-4944	292	15	p	p	X
ejpam-4944	292	16	⊂	⊂	X
ejpam-4944	292	17	x	x	PROPN
ejpam-4944	293	1	|	|	ADV
ejpam-4944	293	2	p	p	X
ejpam-4944	293	3	∈	∈	PROPN
ejpam-4944	293	4	(	(	PUNCT
ejpam-4944	293	5	2	2	NUM
ejpam-4944	293	6	,	,	PUNCT
ejpam-4944	293	7	1)⋆	1)⋆	PROPN
ejpam-4944	293	8	−d(x	−d(x	NOUN
ejpam-4944	293	9	)	)	PUNCT
ejpam-4944	293	10	}	}	PUNCT
ejpam-4944	293	11	.	.	PUNCT
ejpam-4944	294	1	then	then	ADV
ejpam-4944	294	2	(	(	PUNCT
ejpam-4944	294	3	a	a	X
ejpam-4944	294	4	)	)	PUNCT
ejpam-4944	294	5	if	if	SCONJ
ejpam-4944	294	6	ζ	ζ	NOUN
ejpam-4944	294	7	=	=	SYM
ejpam-4944	294	8	η1	η1	NOUN
ejpam-4944	294	9	∪	∪	X
ejpam-4944	294	10	{	{	PUNCT
ejpam-4944	294	11	∅	∅	NOUN
ejpam-4944	294	12	}	}	PUNCT
ejpam-4944	294	13	and	and	CCONJ
ejpam-4944	294	14	if	if	SCONJ
ejpam-4944	294	15	∅	∅	NOUN
ejpam-4944	294	16	=	=	NOUN
ejpam-4944	294	17	̸	̸	NUM
ejpam-4944	294	18	ζ	ζ	NOUN
ejpam-4944	294	19	⊂	⊂	PROPN
ejpam-4944	294	20	µ1	µ1	PROPN
ejpam-4944	294	21	∩	∩	ADJ
ejpam-4944	294	22	µ2	µ2	NOUN
ejpam-4944	294	23	,	,	PUNCT
ejpam-4944	294	24	then	then	ADV
ejpam-4944	294	25	(	(	PUNCT
ejpam-4944	294	26	x	x	NOUN
ejpam-4944	294	27	,	,	PUNCT
ejpam-4944	294	28	ζ	ζ	NOUN
ejpam-4944	294	29	)	)	PUNCT
ejpam-4944	294	30	is	be	AUX
ejpam-4944	294	31	a	a	DET
ejpam-4944	294	32	hyperconnected	hyperconnected	ADJ
ejpam-4944	294	33	space	space	NOUN
ejpam-4944	294	34	.	.	PUNCT
ejpam-4944	295	1	(	(	PUNCT
ejpam-4944	295	2	b	b	X
ejpam-4944	295	3	)	)	PUNCT
ejpam-4944	295	4	if	if	SCONJ
ejpam-4944	295	5	ζ	ζ	NOUN
ejpam-4944	295	6	=	=	SYM
ejpam-4944	295	7	η2	η2	X
ejpam-4944	295	8	∪	∪	VERB
ejpam-4944	295	9	{	{	PUNCT
ejpam-4944	295	10	∅	∅	NOUN
ejpam-4944	295	11	}	}	PUNCT
ejpam-4944	295	12	and	and	CCONJ
ejpam-4944	296	1	if	if	SCONJ
ejpam-4944	296	2	∅	∅	NOUN
ejpam-4944	296	3	=	=	NOUN
ejpam-4944	296	4	̸	̸	NUM
ejpam-4944	296	5	ζ	ζ	NOUN
ejpam-4944	296	6	⊂	⊂	PROPN
ejpam-4944	296	7	µ1	µ1	PROPN
ejpam-4944	296	8	∩	∩	ADJ
ejpam-4944	296	9	µ2	µ2	NOUN
ejpam-4944	296	10	,	,	PUNCT
ejpam-4944	296	11	then	then	ADV
ejpam-4944	296	12	(	(	PUNCT
ejpam-4944	296	13	x	x	NOUN
ejpam-4944	296	14	,	,	PUNCT
ejpam-4944	296	15	ζ	ζ	NOUN
ejpam-4944	296	16	)	)	PUNCT
ejpam-4944	296	17	is	be	AUX
ejpam-4944	296	18	a	a	DET
ejpam-4944	296	19	hyperconnected	hyperconnected	ADJ
ejpam-4944	296	20	space	space	NOUN
ejpam-4944	296	21	.	.	PUNCT
ejpam-4944	297	1	d.	d.	PROPN
ejpam-4944	297	2	elgezouli	elgezouli	PROPN
ejpam-4944	297	3	et	et	PROPN
ejpam-4944	297	4	al	al	PROPN
ejpam-4944	297	5	.	.	PUNCT
ejpam-4944	297	6	/	/	SYM
ejpam-4944	297	7	eur	eur	PROPN
ejpam-4944	297	8	.	.	PUNCT
ejpam-4944	298	1	j.	j.	PROPN
ejpam-4944	298	2	pure	pure	PROPN
ejpam-4944	298	3	appl	appl	PROPN
ejpam-4944	298	4	.	.	PROPN
ejpam-4944	298	5	math	math	PROPN
ejpam-4944	298	6	,	,	PUNCT
ejpam-4944	298	7	16	16	NUM
ejpam-4944	298	8	(	(	PUNCT
ejpam-4944	298	9	4	4	NUM
ejpam-4944	298	10	)	)	PUNCT
ejpam-4944	298	11	(	(	PUNCT
ejpam-4944	298	12	2023	2023	NUM
ejpam-4944	298	13	)	)	PUNCT
ejpam-4944	298	14	,	,	PUNCT
ejpam-4944	298	15	2286	2286	NUM
ejpam-4944	298	16	-	-	SYM
ejpam-4944	298	17	2305	2305	NUM
ejpam-4944	298	18	2295	2295	NUM
ejpam-4944	298	19	proof	proof	NOUN
ejpam-4944	298	20	.	.	PUNCT
ejpam-4944	299	1	(	(	PUNCT
ejpam-4944	299	2	a	a	X
ejpam-4944	299	3	)	)	PUNCT
ejpam-4944	299	4	assume	assume	VERB
ejpam-4944	299	5	that	that	SCONJ
ejpam-4944	299	6	,	,	PUNCT
ejpam-4944	299	7	ζ	ζ	NOUN
ejpam-4944	299	8	=	=	SYM
ejpam-4944	299	9	η1	η1	NOUN
ejpam-4944	299	10	∪	∪	X
ejpam-4944	299	11	{	{	PUNCT
ejpam-4944	299	12	∅	∅	NOUN
ejpam-4944	299	13	}	}	PUNCT
ejpam-4944	299	14	and	and	CCONJ
ejpam-4944	299	15	∅	∅	NOUN
ejpam-4944	299	16	̸=	̸=	PROPN
ejpam-4944	299	17	ζ	ζ	PROPN
ejpam-4944	299	18	⊂	⊂	PROPN
ejpam-4944	299	19	µ1	µ1	PROPN
ejpam-4944	299	20	∩	∩	PROPN
ejpam-4944	299	21	µ2	µ2	NOUN
ejpam-4944	299	22	.	.	PUNCT
ejpam-4944	300	1	let	let	VERB
ejpam-4944	300	2	k	k	PROPN
ejpam-4944	300	3	∈	∈	PROPN
ejpam-4944	300	4	ζ̃.	ζ̃.	PROPN
ejpam-4944	300	5	then	then	ADV
ejpam-4944	300	6	k	k	PROPN
ejpam-4944	300	7	∈	∈	PROPN
ejpam-4944	300	8	(	(	PUNCT
ejpam-4944	300	9	1	1	NUM
ejpam-4944	300	10	,	,	PUNCT
ejpam-4944	300	11	2)⋆	2)⋆	PROPN
ejpam-4944	300	12	−d(x	−d(x	NOUN
ejpam-4944	300	13	)	)	PUNCT
ejpam-4944	300	14	and	and	CCONJ
ejpam-4944	300	15	so	so	ADV
ejpam-4944	300	16	c2k	c2k	ADJ
ejpam-4944	300	17	∩	∩	ADJ
ejpam-4944	300	18	j	j	PROPN
ejpam-4944	300	19	̸=	̸=	PROPN
ejpam-4944	300	20	∅	∅	NOUN
ejpam-4944	300	21	for	for	ADP
ejpam-4944	300	22	all	all	DET
ejpam-4944	300	23	j	j	PROPN
ejpam-4944	300	24	∈	∈	PROPN
ejpam-4944	300	25	σ̃1	σ̃1	PROPN
ejpam-4944	300	26	.	.	PUNCT
ejpam-4944	300	27	let	let	VERB
ejpam-4944	300	28	d	d	X
ejpam-4944	300	29	∈	∈	PROPN
ejpam-4944	300	30	ζ̃.	ζ̃.	ADJ
ejpam-4944	300	31	by	by	ADP
ejpam-4944	300	32	hypothesis	hypothesis	NOUN
ejpam-4944	300	33	,	,	PUNCT
ejpam-4944	300	34	d	d	PROPN
ejpam-4944	300	35	∈	∈	PROPN
ejpam-4944	300	36	µ1	µ1	NOUN
ejpam-4944	300	37	so	so	SCONJ
ejpam-4944	300	38	that	that	SCONJ
ejpam-4944	300	39	d	d	PROPN
ejpam-4944	300	40	∈	∈	PROPN
ejpam-4944	300	41	σ̃1	σ̃1	PROPN
ejpam-4944	300	42	.	.	PUNCT
ejpam-4944	301	1	thus	thus	ADV
ejpam-4944	301	2	,	,	PUNCT
ejpam-4944	301	3	c2k	c2k	X
ejpam-4944	301	4	∩	∩	NOUN
ejpam-4944	301	5	d	d	X
ejpam-4944	301	6	̸=	̸=	PROPN
ejpam-4944	301	7	∅.	∅.	ADV
ejpam-4944	301	8	since	since	SCONJ
ejpam-4944	301	9	d	d	PROPN
ejpam-4944	301	10	∈	∈	PROPN
ejpam-4944	301	11	µ2	µ2	NOUN
ejpam-4944	301	12	we	we	PRON
ejpam-4944	301	13	have	have	VERB
ejpam-4944	301	14	k	k	NOUN
ejpam-4944	301	15	∩	∩	ADJ
ejpam-4944	301	16	d	d	PROPN
ejpam-4944	301	17	̸=	̸=	PROPN
ejpam-4944	301	18	∅	∅	NOUN
ejpam-4944	301	19	,	,	PUNCT
ejpam-4944	301	20	by	by	ADP
ejpam-4944	301	21	lemma	lemma	PROPN
ejpam-4944	301	22	3	3	NUM
ejpam-4944	301	23	.	.	PUNCT
ejpam-4944	302	1	hence	hence	ADV
ejpam-4944	302	2	k	k	PROPN
ejpam-4944	302	3	is	be	AUX
ejpam-4944	302	4	ζ	ζ	NOUN
ejpam-4944	302	5	-	-	PUNCT
ejpam-4944	302	6	dense	dense	ADJ
ejpam-4944	302	7	.	.	PUNCT
ejpam-4944	303	1	therefore	therefore	ADV
ejpam-4944	303	2	,	,	PUNCT
ejpam-4944	303	3	(	(	PUNCT
ejpam-4944	303	4	x	x	NOUN
ejpam-4944	303	5	,	,	PUNCT
ejpam-4944	303	6	ζ	ζ	NOUN
ejpam-4944	303	7	)	)	PUNCT
ejpam-4944	303	8	is	be	AUX
ejpam-4944	303	9	a	a	DET
ejpam-4944	303	10	hyperconnected	hyperconnected	ADJ
ejpam-4944	303	11	space	space	NOUN
ejpam-4944	303	12	.	.	PUNCT
ejpam-4944	304	1	(	(	PUNCT
ejpam-4944	304	2	b	b	X
ejpam-4944	304	3	)	)	PUNCT
ejpam-4944	304	4	suppose	suppose	VERB
ejpam-4944	304	5	that	that	SCONJ
ejpam-4944	304	6	,	,	PUNCT
ejpam-4944	304	7	ζ	ζ	NOUN
ejpam-4944	304	8	=	=	SYM
ejpam-4944	304	9	η2	η2	X
ejpam-4944	304	10	∪	∪	VERB
ejpam-4944	304	11	{	{	PUNCT
ejpam-4944	304	12	∅	∅	NOUN
ejpam-4944	304	13	}	}	PUNCT
ejpam-4944	304	14	and	and	CCONJ
ejpam-4944	304	15	∅	∅	NOUN
ejpam-4944	304	16	=	=	NOUN
ejpam-4944	304	17	̸	̸	NUM
ejpam-4944	304	18	ζ	ζ	NOUN
ejpam-4944	304	19	⊂	⊂	PROPN
ejpam-4944	304	20	µ1	µ1	PROPN
ejpam-4944	304	21	∩	∩	PROPN
ejpam-4944	304	22	µ2	µ2	NOUN
ejpam-4944	304	23	.	.	PUNCT
ejpam-4944	305	1	let	let	VERB
ejpam-4944	305	2	p	p	PRON
ejpam-4944	305	3	∈	∈	PROPN
ejpam-4944	305	4	ζ̃.	ζ̃.	VERB
ejpam-4944	305	5	then	then	ADV
ejpam-4944	305	6	p	p	PROPN
ejpam-4944	305	7	∈	∈	PROPN
ejpam-4944	305	8	(	(	PUNCT
ejpam-4944	305	9	2	2	NUM
ejpam-4944	305	10	,	,	PUNCT
ejpam-4944	305	11	1)⋆	1)⋆	PROPN
ejpam-4944	305	12	−d(x	−d(x	NOUN
ejpam-4944	305	13	)	)	PUNCT
ejpam-4944	305	14	and	and	CCONJ
ejpam-4944	305	15	so	so	ADV
ejpam-4944	305	16	c1p	c1p	NOUN
ejpam-4944	305	17	∩	∩	PROPN
ejpam-4944	305	18	j	j	PROPN
ejpam-4944	305	19	̸=	̸=	PROPN
ejpam-4944	305	20	∅	∅	NOUN
ejpam-4944	305	21	for	for	ADP
ejpam-4944	305	22	all	all	DET
ejpam-4944	305	23	j	j	PROPN
ejpam-4944	305	24	∈	∈	PROPN
ejpam-4944	305	25	σ̃2	σ̃2	PROPN
ejpam-4944	305	26	.	.	PUNCT
ejpam-4944	306	1	let	let	VERB
ejpam-4944	306	2	m	m	PRON
ejpam-4944	306	3	∈	∈	NOUN
ejpam-4944	306	4	ζ̃.	ζ̃.	ADJ
ejpam-4944	306	5	by	by	ADP
ejpam-4944	306	6	hypothesis	hypothesis	NOUN
ejpam-4944	306	7	,	,	PUNCT
ejpam-4944	306	8	m	m	PROPN
ejpam-4944	306	9	∈	∈	NOUN
ejpam-4944	306	10	µ2	µ2	NOUN
ejpam-4944	306	11	so	so	SCONJ
ejpam-4944	306	12	that	that	SCONJ
ejpam-4944	306	13	m	m	PROPN
ejpam-4944	306	14	∈	∈	PROPN
ejpam-4944	306	15	σ̃2	σ̃2	PROPN
ejpam-4944	306	16	.	.	PUNCT
ejpam-4944	307	1	thus	thus	ADV
ejpam-4944	307	2	,	,	PUNCT
ejpam-4944	307	3	c1p	c1p	NOUN
ejpam-4944	307	4	∩m	∩m	PROPN
ejpam-4944	307	5	̸=	̸=	PROPN
ejpam-4944	307	6	∅.	∅.	ADV
ejpam-4944	307	7	since	since	SCONJ
ejpam-4944	307	8	m	m	PROPN
ejpam-4944	307	9	∈	∈	PROPN
ejpam-4944	307	10	µ1	µ1	PROPN
ejpam-4944	307	11	we	we	PRON
ejpam-4944	307	12	have	have	VERB
ejpam-4944	307	13	p	p	NOUN
ejpam-4944	307	14	∩m	∩m	PROPN
ejpam-4944	307	15	̸=	̸=	PROPN
ejpam-4944	307	16	∅	∅	NOUN
ejpam-4944	307	17	,	,	PUNCT
ejpam-4944	307	18	by	by	ADP
ejpam-4944	307	19	lemma	lemma	PROPN
ejpam-4944	307	20	3	3	NUM
ejpam-4944	307	21	.	.	PUNCT
ejpam-4944	308	1	hence	hence	ADV
ejpam-4944	308	2	p	p	PROPN
ejpam-4944	308	3	is	be	AUX
ejpam-4944	308	4	ζ	ζ	NOUN
ejpam-4944	308	5	-	-	PUNCT
ejpam-4944	308	6	dense	dense	ADJ
ejpam-4944	308	7	.	.	PUNCT
ejpam-4944	309	1	therefore	therefore	ADV
ejpam-4944	309	2	,	,	PUNCT
ejpam-4944	309	3	(	(	PUNCT
ejpam-4944	309	4	x	x	NOUN
ejpam-4944	309	5	,	,	PUNCT
ejpam-4944	309	6	ζ	ζ	NOUN
ejpam-4944	309	7	)	)	PUNCT
ejpam-4944	309	8	is	be	AUX
ejpam-4944	309	9	a	a	DET
ejpam-4944	309	10	hyperconnected	hyperconnected	ADJ
ejpam-4944	309	11	space	space	NOUN
ejpam-4944	309	12	.	.	PUNCT
ejpam-4944	310	1	definition	definition	NOUN
ejpam-4944	310	2	22	22	NUM
ejpam-4944	310	3	.	.	PUNCT
ejpam-4944	311	1	let	let	VERB
ejpam-4944	311	2	(	(	PUNCT
ejpam-4944	311	3	x,µ	x,µ	NOUN
ejpam-4944	311	4	)	)	PUNCT
ejpam-4944	311	5	be	be	AUX
ejpam-4944	311	6	a	a	DET
ejpam-4944	311	7	gts	gts	NOUN
ejpam-4944	311	8	.	.	PUNCT
ejpam-4944	312	1	a	a	DET
ejpam-4944	312	2	gt	gt	PROPN
ejpam-4944	312	3	µ	µ	PROPN
ejpam-4944	312	4	is	be	AUX
ejpam-4944	312	5	said	say	VERB
ejpam-4944	312	6	to	to	PART
ejpam-4944	312	7	satisfy	satisfy	VERB
ejpam-4944	312	8	the	the	DET
ejpam-4944	312	9	id	id	NOUN
ejpam-4944	312	10	-	-	PUNCT
ejpam-4944	312	11	property	property	NOUN
ejpam-4944	312	12	if	if	SCONJ
ejpam-4944	312	13	p	p	PROPN
ejpam-4944	312	14	∈	∈	PROPN
ejpam-4944	312	15	µ̃	µ̃	PROPN
ejpam-4944	312	16	and	and	CCONJ
ejpam-4944	312	17	cµq	cµq	ADJ
ejpam-4944	312	18	=	=	SYM
ejpam-4944	312	19	x	x	NOUN
ejpam-4944	312	20	,	,	PUNCT
ejpam-4944	312	21	then	then	ADV
ejpam-4944	312	22	iµ(p	iµ(p	ADV
ejpam-4944	312	23	∩q	∩q	NOUN
ejpam-4944	312	24	)	)	PUNCT
ejpam-4944	313	1	̸=	̸=	PROPN
ejpam-4944	313	2	∅.	∅.	ADV
ejpam-4944	313	3	theorem	theorem	VERB
ejpam-4944	313	4	23	23	NUM
ejpam-4944	313	5	.	.	PUNCT
ejpam-4944	314	1	let	let	AUX
ejpam-4944	314	2	(	(	PUNCT
ejpam-4944	314	3	x,µ1	x,µ1	NOUN
ejpam-4944	314	4	,	,	PUNCT
ejpam-4944	314	5	µ2	µ2	PROPN
ejpam-4944	314	6	)	)	PUNCT
ejpam-4944	314	7	be	be	VERB
ejpam-4944	314	8	a	a	DET
ejpam-4944	314	9	bigeneralized	bigeneralized	ADJ
ejpam-4944	314	10	topological	topological	ADJ
ejpam-4944	314	11	space	space	NOUN
ejpam-4944	314	12	and	and	CCONJ
ejpam-4944	314	13	η1	η1	NOUN
ejpam-4944	314	14	=	=	PUNCT
ejpam-4944	314	15	{	{	PUNCT
ejpam-4944	314	16	p	p	X
ejpam-4944	314	17	⊂	⊂	X
ejpam-4944	314	18	x	x	PROPN
ejpam-4944	314	19	|	|	ADV
ejpam-4944	314	20	cµ1p	cµ1p	NOUN
ejpam-4944	314	21	=	=	SYM
ejpam-4944	314	22	x	x	X
ejpam-4944	314	23	}	}	PUNCT
ejpam-4944	314	24	;	;	PUNCT
ejpam-4944	314	25	η2	η2	PROPN
ejpam-4944	314	26	=	=	PUNCT
ejpam-4944	314	27	{	{	PUNCT
ejpam-4944	314	28	q	q	X
ejpam-4944	314	29	⊂	⊂	X
ejpam-4944	314	30	x	x	PUNCT
ejpam-4944	314	31	|	|	ADV
ejpam-4944	314	32	cµ2q	cµ2q	VERB
ejpam-4944	314	33	=	=	PUNCT
ejpam-4944	314	34	x	x	NOUN
ejpam-4944	314	35	}	}	PUNCT
ejpam-4944	314	36	.	.	PUNCT
ejpam-4944	315	1	then	then	ADV
ejpam-4944	315	2	(	(	PUNCT
ejpam-4944	315	3	a	a	X
ejpam-4944	315	4	)	)	PUNCT
ejpam-4944	315	5	if	if	SCONJ
ejpam-4944	315	6	∅	∅	NOUN
ejpam-4944	315	7	=	=	NOUN
ejpam-4944	315	8	̸	̸	NOUN
ejpam-4944	315	9	ζ	ζ	NOUN
ejpam-4944	315	10	=	=	SYM
ejpam-4944	315	11	η1	η1	NOUN
ejpam-4944	315	12	∪	∪	X
ejpam-4944	315	13	{	{	PUNCT
ejpam-4944	315	14	∅	∅	NOUN
ejpam-4944	315	15	}	}	PUNCT
ejpam-4944	315	16	and	and	CCONJ
ejpam-4944	315	17	if	if	SCONJ
ejpam-4944	315	18	µ1	µ1	PROPN
ejpam-4944	315	19	has	have	VERB
ejpam-4944	315	20	id	id	NOUN
ejpam-4944	315	21	-	-	PUNCT
ejpam-4944	315	22	property	property	NOUN
ejpam-4944	315	23	,	,	PUNCT
ejpam-4944	315	24	then	then	ADV
ejpam-4944	315	25	(	(	PUNCT
ejpam-4944	315	26	x	x	NOUN
ejpam-4944	315	27	,	,	PUNCT
ejpam-4944	315	28	ζ	ζ	NOUN
ejpam-4944	315	29	)	)	PUNCT
ejpam-4944	315	30	is	be	AUX
ejpam-4944	315	31	a	a	DET
ejpam-4944	315	32	hyperconnected	hyperconnected	ADJ
ejpam-4944	315	33	space	space	NOUN
ejpam-4944	315	34	.	.	PUNCT
ejpam-4944	316	1	(	(	PUNCT
ejpam-4944	316	2	b	b	X
ejpam-4944	316	3	)	)	PUNCT
ejpam-4944	316	4	if	if	SCONJ
ejpam-4944	316	5	∅	∅	NOUN
ejpam-4944	316	6	=	=	NOUN
ejpam-4944	316	7	̸	̸	ADV
ejpam-4944	316	8	ζ	ζ	NOUN
ejpam-4944	316	9	=	=	SYM
ejpam-4944	316	10	η2	η2	ADJ
ejpam-4944	316	11	∪	∪	VERB
ejpam-4944	316	12	{	{	PUNCT
ejpam-4944	316	13	∅	∅	NOUN
ejpam-4944	316	14	}	}	PUNCT
ejpam-4944	316	15	and	and	CCONJ
ejpam-4944	316	16	if	if	SCONJ
ejpam-4944	316	17	µ2	µ2	PROPN
ejpam-4944	316	18	has	have	VERB
ejpam-4944	316	19	id	id	NOUN
ejpam-4944	316	20	-	-	PUNCT
ejpam-4944	316	21	property	property	NOUN
ejpam-4944	316	22	,	,	PUNCT
ejpam-4944	316	23	then	then	ADV
ejpam-4944	316	24	(	(	PUNCT
ejpam-4944	316	25	x	x	NOUN
ejpam-4944	316	26	,	,	PUNCT
ejpam-4944	316	27	ζ	ζ	NOUN
ejpam-4944	316	28	)	)	PUNCT
ejpam-4944	316	29	is	be	AUX
ejpam-4944	316	30	a	a	DET
ejpam-4944	316	31	hyperconnected	hyperconnected	ADJ
ejpam-4944	316	32	space	space	NOUN
ejpam-4944	316	33	.	.	PUNCT
ejpam-4944	317	1	proof	proof	NOUN
ejpam-4944	317	2	.	.	PUNCT
ejpam-4944	318	1	(	(	PUNCT
ejpam-4944	318	2	a	a	X
ejpam-4944	318	3	)	)	PUNCT
ejpam-4944	318	4	suppose	suppose	VERB
ejpam-4944	318	5	∅	∅	NOUN
ejpam-4944	318	6	=	=	NOUN
ejpam-4944	318	7	̸	̸	NOUN
ejpam-4944	318	8	ζ	ζ	NOUN
ejpam-4944	318	9	=	=	SYM
ejpam-4944	318	10	η1	η1	NOUN
ejpam-4944	318	11	∪	∪	X
ejpam-4944	318	12	{	{	PUNCT
ejpam-4944	318	13	∅	∅	NOUN
ejpam-4944	318	14	}	}	PUNCT
ejpam-4944	318	15	and	and	CCONJ
ejpam-4944	318	16	if	if	SCONJ
ejpam-4944	318	17	µ1	µ1	PROPN
ejpam-4944	318	18	has	have	VERB
ejpam-4944	318	19	id	id	NOUN
ejpam-4944	318	20	-	-	PUNCT
ejpam-4944	318	21	property	property	NOUN
ejpam-4944	318	22	.	.	PUNCT
ejpam-4944	319	1	let	let	VERB
ejpam-4944	319	2	k	k	PROPN
ejpam-4944	319	3	∈	∈	PROPN
ejpam-4944	319	4	ζ̃.	ζ̃.	ADJ
ejpam-4944	319	5	then	then	ADV
ejpam-4944	319	6	cµ1k	cµ1k	VERB
ejpam-4944	319	7	=	=	PUNCT
ejpam-4944	319	8	x	x	X
ejpam-4944	320	1	and	and	CCONJ
ejpam-4944	320	2	so	so	ADV
ejpam-4944	320	3	k	k	PROPN
ejpam-4944	320	4	∩	∩	PROPN
ejpam-4944	320	5	j	j	PROPN
ejpam-4944	320	6	̸=	̸=	PROPN
ejpam-4944	320	7	∅	∅	NOUN
ejpam-4944	320	8	for	for	ADP
ejpam-4944	320	9	every	every	PRON
ejpam-4944	320	10	j	j	PROPN
ejpam-4944	320	11	∈	∈	PROPN
ejpam-4944	320	12	µ̃1	µ̃1	PROPN
ejpam-4944	320	13	.	.	PUNCT
ejpam-4944	320	14	take	take	VERB
ejpam-4944	320	15	h	h	NOUN
ejpam-4944	320	16	∈	∈	PROPN
ejpam-4944	320	17	ζ̃	ζ̃	PROPN
ejpam-4944	320	18	which	which	PRON
ejpam-4944	320	19	implies	imply	VERB
ejpam-4944	320	20	that	that	SCONJ
ejpam-4944	320	21	h	h	NOUN
ejpam-4944	320	22	∩m	∩m	PROPN
ejpam-4944	320	23	̸=	̸=	PROPN
ejpam-4944	320	24	∅	∅	NOUN
ejpam-4944	320	25	for	for	ADP
ejpam-4944	320	26	all	all	DET
ejpam-4944	320	27	m	m	NOUN
ejpam-4944	320	28	∈	∈	ADJ
ejpam-4944	320	29	µ̃1	µ̃1	NOUN
ejpam-4944	320	30	.	.	PUNCT
ejpam-4944	321	1	thus	thus	ADV
ejpam-4944	321	2	,	,	PUNCT
ejpam-4944	321	3	there	there	PRON
ejpam-4944	321	4	is	be	VERB
ejpam-4944	321	5	d	d	PRON
ejpam-4944	321	6	∈	∈	PROPN
ejpam-4944	321	7	µ̃1	µ̃1	NOUN
ejpam-4944	321	8	such	such	ADJ
ejpam-4944	321	9	that	that	DET
ejpam-4944	321	10	k∩d	k∩d	NOUN
ejpam-4944	321	11	̸=	̸=	PROPN
ejpam-4944	321	12	∅	∅	NOUN
ejpam-4944	321	13	and	and	CCONJ
ejpam-4944	321	14	h∩d	h∩d	PROPN
ejpam-4944	321	15	̸=	̸=	PROPN
ejpam-4944	321	16	∅.	∅.	ADV
ejpam-4944	321	17	since	since	SCONJ
ejpam-4944	321	18	cµ1h	cµ1h	PROPN
ejpam-4944	321	19	=	=	PUNCT
ejpam-4944	322	1	x	x	X
ejpam-4944	322	2	and	and	CCONJ
ejpam-4944	322	3	d	d	PROPN
ejpam-4944	322	4	∈	∈	PROPN
ejpam-4944	322	5	µ̃1	µ̃1	NOUN
ejpam-4944	322	6	we	we	PRON
ejpam-4944	322	7	have	have	VERB
ejpam-4944	322	8	iµ1(h	iµ1(h	PROPN
ejpam-4944	322	9	∩d	∩d	NOUN
ejpam-4944	322	10	)	)	PUNCT
ejpam-4944	322	11	̸=	̸=	NOUN
ejpam-4944	322	12	∅	∅	NOUN
ejpam-4944	322	13	,	,	PUNCT
ejpam-4944	322	14	by	by	ADP
ejpam-4944	322	15	hypothesis	hypothesis	NOUN
ejpam-4944	322	16	.	.	PUNCT
ejpam-4944	323	1	thus	thus	ADV
ejpam-4944	323	2	,	,	PUNCT
ejpam-4944	323	3	iµ1(h	iµ1(h	PROPN
ejpam-4944	323	4	∩d	∩d	NOUN
ejpam-4944	323	5	)	)	PUNCT
ejpam-4944	323	6	∈	∈	PROPN
ejpam-4944	323	7	µ̃1	µ̃1	NOUN
ejpam-4944	323	8	which	which	PRON
ejpam-4944	323	9	implies	imply	VERB
ejpam-4944	323	10	that	that	SCONJ
ejpam-4944	323	11	k	k	PROPN
ejpam-4944	323	12	∩	∩	PROPN
ejpam-4944	323	13	iµ1(h	iµ1(h	PROPN
ejpam-4944	323	14	∩	∩	ADJ
ejpam-4944	323	15	d	d	NOUN
ejpam-4944	323	16	)	)	PUNCT
ejpam-4944	323	17	̸=	̸=	PROPN
ejpam-4944	323	18	∅	∅	NOUN
ejpam-4944	323	19	which	which	PRON
ejpam-4944	323	20	turn	turn	VERB
ejpam-4944	323	21	implies	imply	VERB
ejpam-4944	323	22	that	that	SCONJ
ejpam-4944	323	23	k	k	PROPN
ejpam-4944	323	24	∩	∩	PROPN
ejpam-4944	323	25	h	h	PROPN
ejpam-4944	323	26	̸=	̸=	PROPN
ejpam-4944	323	27	∅.	∅.	VERB
ejpam-4944	323	28	therefore	therefore	ADV
ejpam-4944	323	29	,	,	PUNCT
ejpam-4944	323	30	k	k	PROPN
ejpam-4944	323	31	is	be	AUX
ejpam-4944	323	32	ζ	ζ	NOUN
ejpam-4944	323	33	-	-	PUNCT
ejpam-4944	323	34	dense	dense	ADJ
ejpam-4944	323	35	.	.	PUNCT
ejpam-4944	324	1	hence	hence	ADV
ejpam-4944	324	2	(	(	PUNCT
ejpam-4944	324	3	x	x	NOUN
ejpam-4944	324	4	,	,	PUNCT
ejpam-4944	324	5	ζ	ζ	NOUN
ejpam-4944	324	6	)	)	PUNCT
ejpam-4944	324	7	is	be	AUX
ejpam-4944	324	8	a	a	DET
ejpam-4944	324	9	hyperconnected	hyperconnected	ADJ
ejpam-4944	324	10	space	space	NOUN
ejpam-4944	324	11	.	.	PUNCT
ejpam-4944	325	1	(	(	PUNCT
ejpam-4944	325	2	b	b	X
ejpam-4944	325	3	)	)	PUNCT
ejpam-4944	325	4	assume	assume	VERB
ejpam-4944	325	5	that	that	SCONJ
ejpam-4944	325	6	,	,	PUNCT
ejpam-4944	325	7	∅	∅	NOUN
ejpam-4944	325	8	=	=	NOUN
ejpam-4944	325	9	̸	̸	ADV
ejpam-4944	325	10	ζ	ζ	NOUN
ejpam-4944	325	11	=	=	SYM
ejpam-4944	325	12	η2	η2	ADJ
ejpam-4944	325	13	∪	∪	VERB
ejpam-4944	325	14	{	{	PUNCT
ejpam-4944	325	15	∅	∅	NOUN
ejpam-4944	325	16	}	}	PUNCT
ejpam-4944	325	17	and	and	CCONJ
ejpam-4944	325	18	if	if	SCONJ
ejpam-4944	325	19	µ2	µ2	PROPN
ejpam-4944	325	20	has	have	VERB
ejpam-4944	325	21	id	id	NOUN
ejpam-4944	325	22	-	-	PUNCT
ejpam-4944	325	23	property	property	NOUN
ejpam-4944	325	24	.	.	PUNCT
ejpam-4944	326	1	let	let	VERB
ejpam-4944	326	2	l	l	NOUN
ejpam-4944	326	3	∈	∈	PROPN
ejpam-4944	326	4	ζ̃.	ζ̃.	ADJ
ejpam-4944	326	5	then	then	ADV
ejpam-4944	326	6	cµ2l	cµ2l	X
ejpam-4944	326	7	=	=	SYM
ejpam-4944	327	1	x	x	PUNCT
ejpam-4944	327	2	and	and	CCONJ
ejpam-4944	327	3	so	so	ADV
ejpam-4944	327	4	l	l	NOUN
ejpam-4944	327	5	∩	∩	PROPN
ejpam-4944	327	6	j	j	PROPN
ejpam-4944	327	7	̸=	̸=	PROPN
ejpam-4944	327	8	∅	∅	NOUN
ejpam-4944	327	9	for	for	ADP
ejpam-4944	327	10	every	every	DET
ejpam-4944	327	11	j	j	PROPN
ejpam-4944	327	12	∈	∈	PROPN
ejpam-4944	327	13	µ̃2	µ̃2	PROPN
ejpam-4944	327	14	.	.	PUNCT
ejpam-4944	328	1	take	take	VERB
ejpam-4944	328	2	h	h	NOUN
ejpam-4944	328	3	∈	∈	PROPN
ejpam-4944	328	4	ζ̃	ζ̃	PROPN
ejpam-4944	328	5	which	which	PRON
ejpam-4944	328	6	implies	imply	VERB
ejpam-4944	328	7	that	that	SCONJ
ejpam-4944	328	8	h	h	NOUN
ejpam-4944	328	9	∩	∩	NOUN
ejpam-4944	328	10	k	k	PROPN
ejpam-4944	328	11	̸=	̸=	PROPN
ejpam-4944	328	12	∅	∅	NOUN
ejpam-4944	328	13	for	for	ADP
ejpam-4944	328	14	all	all	DET
ejpam-4944	328	15	k	k	PROPN
ejpam-4944	328	16	∈	∈	PROPN
ejpam-4944	328	17	µ̃2	µ̃2	PROPN
ejpam-4944	328	18	.	.	PUNCT
ejpam-4944	329	1	thus	thus	ADV
ejpam-4944	329	2	,	,	PUNCT
ejpam-4944	329	3	there	there	PRON
ejpam-4944	329	4	is	be	VERB
ejpam-4944	329	5	d	d	PRON
ejpam-4944	329	6	∈	∈	PROPN
ejpam-4944	329	7	µ̃2	µ̃2	PROPN
ejpam-4944	329	8	such	such	ADJ
ejpam-4944	329	9	that	that	SCONJ
ejpam-4944	329	10	l	l	NOUN
ejpam-4944	329	11	∩d	∩d	X
ejpam-4944	329	12	̸=	̸=	NOUN
ejpam-4944	329	13	∅	∅	NOUN
ejpam-4944	329	14	and	and	CCONJ
ejpam-4944	329	15	h	h	NOUN
ejpam-4944	329	16	∩d	∩d	VERB
ejpam-4944	329	17	̸=	̸=	PROPN
ejpam-4944	329	18	∅.	∅.	ADV
ejpam-4944	329	19	since	since	SCONJ
ejpam-4944	329	20	cµ2h	cµ2h	PROPN
ejpam-4944	329	21	=	=	PUNCT
ejpam-4944	330	1	x	x	X
ejpam-4944	330	2	and	and	CCONJ
ejpam-4944	330	3	d	d	X
ejpam-4944	330	4	∈	∈	PROPN
ejpam-4944	331	1	µ̃2	µ̃2	PROPN
ejpam-4944	331	2	we	we	PRON
ejpam-4944	331	3	have	have	VERB
ejpam-4944	331	4	iµ2(h	iµ2(h	VERB
ejpam-4944	331	5	∩d	∩d	NOUN
ejpam-4944	331	6	)	)	PUNCT
ejpam-4944	332	1	̸=	̸=	NOUN
ejpam-4944	332	2	∅	∅	NOUN
ejpam-4944	332	3	,	,	PUNCT
ejpam-4944	332	4	by	by	ADP
ejpam-4944	332	5	hypothesis	hypothesis	NOUN
ejpam-4944	332	6	.	.	PUNCT
ejpam-4944	333	1	thus	thus	ADV
ejpam-4944	333	2	,	,	PUNCT
ejpam-4944	333	3	iµ2(h	iµ2(h	PROPN
ejpam-4944	333	4	∩d	∩d	NOUN
ejpam-4944	333	5	)	)	PUNCT
ejpam-4944	333	6	∈	∈	PROPN
ejpam-4944	333	7	µ̃2	µ̃2	PROPN
ejpam-4944	333	8	which	which	PRON
ejpam-4944	333	9	implies	imply	VERB
ejpam-4944	333	10	that	that	SCONJ
ejpam-4944	333	11	l	l	NOUN
ejpam-4944	333	12	∩	∩	X
ejpam-4944	333	13	iµ2(h	iµ2(h	ADP
ejpam-4944	333	14	∩d	∩d	NOUN
ejpam-4944	333	15	)	)	PUNCT
ejpam-4944	333	16	̸=	̸=	PROPN
ejpam-4944	333	17	∅	∅	NOUN
ejpam-4944	333	18	which	which	PRON
ejpam-4944	333	19	turn	turn	VERB
ejpam-4944	333	20	implies	imply	VERB
ejpam-4944	333	21	that	that	SCONJ
ejpam-4944	333	22	l	l	NOUN
ejpam-4944	333	23	∩h	∩h	NOUN
ejpam-4944	333	24	̸=	̸=	PROPN
ejpam-4944	333	25	∅.	∅.	VERB
ejpam-4944	333	26	therefore	therefore	ADV
ejpam-4944	333	27	,	,	PUNCT
ejpam-4944	333	28	l	l	NOUN
ejpam-4944	333	29	is	be	AUX
ejpam-4944	333	30	ζ	ζ	NOUN
ejpam-4944	333	31	-	-	PUNCT
ejpam-4944	333	32	dense	dense	ADJ
ejpam-4944	333	33	.	.	PUNCT
ejpam-4944	334	1	hence	hence	ADV
ejpam-4944	334	2	(	(	PUNCT
ejpam-4944	334	3	x	x	NOUN
ejpam-4944	334	4	,	,	PUNCT
ejpam-4944	334	5	ζ	ζ	NOUN
ejpam-4944	334	6	)	)	PUNCT
ejpam-4944	334	7	is	be	AUX
ejpam-4944	334	8	a	a	DET
ejpam-4944	334	9	hyperconnected	hyperconnected	ADJ
ejpam-4944	334	10	space	space	NOUN
ejpam-4944	334	11	.	.	PUNCT
ejpam-4944	335	1	theorem	theorem	NOUN
ejpam-4944	335	2	24	24	NUM
ejpam-4944	335	3	.	.	PUNCT
ejpam-4944	336	1	let	let	AUX
ejpam-4944	336	2	(	(	PUNCT
ejpam-4944	336	3	x,µ1	x,µ1	NOUN
ejpam-4944	336	4	,	,	PUNCT
ejpam-4944	336	5	µ2	µ2	PROPN
ejpam-4944	336	6	)	)	PUNCT
ejpam-4944	336	7	be	be	VERB
ejpam-4944	336	8	a	a	DET
ejpam-4944	336	9	bigeneralized	bigeneralized	ADJ
ejpam-4944	336	10	topological	topological	ADJ
ejpam-4944	336	11	space	space	NOUN
ejpam-4944	336	12	where	where	SCONJ
ejpam-4944	336	13	µ1	µ1	PROPN
ejpam-4944	336	14	=	=	SYM
ejpam-4944	336	15	µ	µ	X
ejpam-4944	336	16	and	and	CCONJ
ejpam-4944	336	17	µ2	µ2	PROPN
ejpam-4944	336	18	=	=	PUNCT
ejpam-4944	336	19	µ⋆⋆	µ⋆⋆	ADJ
ejpam-4944	336	20	̸=	̸=	PROPN
ejpam-4944	336	21	∅	∅	NOUN
ejpam-4944	336	22	,	,	PUNCT
ejpam-4944	336	23	µ	µ	X
ejpam-4944	336	24	is	be	AUX
ejpam-4944	336	25	a	a	DET
ejpam-4944	336	26	generalized	generalized	ADJ
ejpam-4944	336	27	topology	topology	NOUN
ejpam-4944	336	28	on	on	ADP
ejpam-4944	336	29	x.	x.	NOUN
ejpam-4944	336	30	then	then	ADV
ejpam-4944	336	31	every	every	DET
ejpam-4944	336	32	µ⋆⋆-dense	µ⋆⋆-dense	PROPN
ejpam-4944	336	33	set	set	NOUN
ejpam-4944	336	34	is	be	AUX
ejpam-4944	336	35	(	(	PUNCT
ejpam-4944	336	36	2	2	NUM
ejpam-4944	336	37	,	,	PUNCT
ejpam-4944	336	38	1)⋆dense	1)⋆dense	NUM
ejpam-4944	336	39	set	set	NOUN
ejpam-4944	336	40	in	in	ADP
ejpam-4944	336	41	x.	x.	NOUN
ejpam-4944	336	42	proof	proof	NOUN
ejpam-4944	336	43	.	.	PUNCT
ejpam-4944	337	1	let	let	VERB
ejpam-4944	337	2	k	k	PRON
ejpam-4944	337	3	be	be	AUX
ejpam-4944	337	4	a	a	DET
ejpam-4944	337	5	µ⋆⋆-dense	µ⋆⋆-dense	PROPN
ejpam-4944	337	6	set	set	NOUN
ejpam-4944	337	7	.	.	PUNCT
ejpam-4944	338	1	then	then	ADV
ejpam-4944	338	2	c2(k	c2(k	PROPN
ejpam-4944	338	3	)	)	PUNCT
ejpam-4944	338	4	=	=	PUNCT
ejpam-4944	338	5	x.	x.	NOUN
ejpam-4944	338	6	by	by	ADP
ejpam-4944	338	7	hypothesis	hypothesis	NOUN
ejpam-4944	338	8	,	,	PUNCT
ejpam-4944	338	9	µ2	µ2	PROPN
ejpam-4944	338	10	is	be	AUX
ejpam-4944	338	11	a	a	DET
ejpam-4944	338	12	sgt	sgt	PROPN
ejpam-4944	338	13	.	.	PUNCT
ejpam-4944	339	1	by	by	ADP
ejpam-4944	339	2	theorem	theorem	NOUN
ejpam-4944	339	3	11	11	NUM
ejpam-4944	339	4	,	,	PUNCT
ejpam-4944	339	5	k	k	PROPN
ejpam-4944	339	6	is	be	AUX
ejpam-4944	339	7	a	a	DET
ejpam-4944	339	8	(	(	PUNCT
ejpam-4944	339	9	2	2	NUM
ejpam-4944	339	10	,	,	PUNCT
ejpam-4944	339	11	1)⋆-dense	1)⋆-dense	NUM
ejpam-4944	339	12	set	set	VERB
ejpam-4944	339	13	in	in	ADP
ejpam-4944	339	14	x.	x.	PROPN
ejpam-4944	339	15	theorem	theorem	VERB
ejpam-4944	339	16	25	25	NUM
ejpam-4944	339	17	.	.	PUNCT
ejpam-4944	340	1	let	let	AUX
ejpam-4944	340	2	(	(	PUNCT
ejpam-4944	340	3	x,µ1	x,µ1	NOUN
ejpam-4944	340	4	,	,	PUNCT
ejpam-4944	340	5	µ2	µ2	PROPN
ejpam-4944	340	6	)	)	PUNCT
ejpam-4944	340	7	satisfy	satisfy	VERB
ejpam-4944	340	8	the	the	DET
ejpam-4944	340	9	condition	condition	NOUN
ejpam-4944	340	10	;	;	PUNCT
ejpam-4944	340	11	if	if	SCONJ
ejpam-4944	340	12	p	p	PROPN
ejpam-4944	340	13	∈	∈	PROPN
ejpam-4944	340	14	µ̃1;q	µ̃1;q	PROPN
ejpam-4944	340	15	∈	∈	PROPN
ejpam-4944	340	16	µ̃2	µ̃2	PROPN
ejpam-4944	340	17	and	and	CCONJ
ejpam-4944	340	18	p	p	NOUN
ejpam-4944	340	19	∩	∩	ADJ
ejpam-4944	340	20	q	q	PROPN
ejpam-4944	340	21	̸=	̸=	PROPN
ejpam-4944	340	22	∅	∅	NOUN
ejpam-4944	340	23	,	,	PUNCT
ejpam-4944	340	24	then	then	ADV
ejpam-4944	340	25	iµ1(p	iµ1(p	PROPN
ejpam-4944	340	26	∩	∩	ADJ
ejpam-4944	340	27	q	q	X
ejpam-4944	340	28	)	)	PUNCT
ejpam-4944	340	29	̸=	̸=	PROPN
ejpam-4944	340	30	∅	∅	NOUN
ejpam-4944	340	31	here	here	ADV
ejpam-4944	340	32	µ1	µ1	PROPN
ejpam-4944	340	33	=	=	SYM
ejpam-4944	340	34	µ	µ	X
ejpam-4944	340	35	and	and	CCONJ
ejpam-4944	340	36	µ2	µ2	PROPN
ejpam-4944	340	37	=	=	PUNCT
ejpam-4944	340	38	µ⋆⋆	µ⋆⋆	ADJ
ejpam-4944	340	39	̸=	̸=	PROPN
ejpam-4944	340	40	∅	∅	NOUN
ejpam-4944	340	41	where	where	SCONJ
ejpam-4944	340	42	µ	µ	NOUN
ejpam-4944	340	43	is	be	AUX
ejpam-4944	340	44	a	a	DET
ejpam-4944	340	45	gt	gt	PROPN
ejpam-4944	340	46	on	on	ADP
ejpam-4944	340	47	x.	x.	NOUN
ejpam-4944	340	48	then	then	ADV
ejpam-4944	340	49	every	every	DET
ejpam-4944	340	50	(	(	PUNCT
ejpam-4944	340	51	1	1	NUM
ejpam-4944	340	52	,	,	PUNCT
ejpam-4944	340	53	2)⋆-dense	2)⋆-dense	NUM
ejpam-4944	340	54	set	set	NOUN
ejpam-4944	340	55	is	be	AUX
ejpam-4944	340	56	µ2	µ2	ADJ
ejpam-4944	340	57	-	-	PUNCT
ejpam-4944	340	58	dense	dense	ADJ
ejpam-4944	340	59	set	set	NOUN
ejpam-4944	340	60	in	in	ADP
ejpam-4944	340	61	x.	x.	PROPN
ejpam-4944	340	62	d.	d.	PROPN
ejpam-4944	340	63	elgezouli	elgezouli	PROPN
ejpam-4944	340	64	et	et	PROPN
ejpam-4944	341	1	al	al	PROPN
ejpam-4944	341	2	.	.	PUNCT
ejpam-4944	341	3	/	/	SYM
ejpam-4944	341	4	eur	eur	PROPN
ejpam-4944	341	5	.	.	PUNCT
ejpam-4944	342	1	j.	j.	PROPN
ejpam-4944	342	2	pure	pure	PROPN
ejpam-4944	342	3	appl	appl	PROPN
ejpam-4944	342	4	.	.	PROPN
ejpam-4944	342	5	math	math	PROPN
ejpam-4944	342	6	,	,	PUNCT
ejpam-4944	342	7	16	16	NUM
ejpam-4944	342	8	(	(	PUNCT
ejpam-4944	342	9	4	4	NUM
ejpam-4944	342	10	)	)	PUNCT
ejpam-4944	342	11	(	(	PUNCT
ejpam-4944	342	12	2023	2023	NUM
ejpam-4944	342	13	)	)	PUNCT
ejpam-4944	342	14	,	,	PUNCT
ejpam-4944	342	15	2286	2286	NUM
ejpam-4944	342	16	-	-	SYM
ejpam-4944	342	17	2305	2305	NUM
ejpam-4944	342	18	2296	2296	NUM
ejpam-4944	342	19	proof	proof	NOUN
ejpam-4944	342	20	.	.	PUNCT
ejpam-4944	343	1	let	let	VERB
ejpam-4944	343	2	p	p	X
ejpam-4944	343	3	∈	∈	PROPN
ejpam-4944	343	4	(	(	PUNCT
ejpam-4944	343	5	1	1	NUM
ejpam-4944	343	6	,	,	PUNCT
ejpam-4944	343	7	2)⋆	2)⋆	NOUN
ejpam-4944	343	8	−	−	NOUN
ejpam-4944	343	9	d(x	d(x	NOUN
ejpam-4944	343	10	)	)	PUNCT
ejpam-4944	343	11	.	.	PUNCT
ejpam-4944	344	1	then	then	ADV
ejpam-4944	344	2	c2p	c2p	NOUN
ejpam-4944	344	3	∩k	∩k	NOUN
ejpam-4944	344	4	̸=	̸=	PROPN
ejpam-4944	344	5	∅	∅	NOUN
ejpam-4944	344	6	for	for	ADP
ejpam-4944	344	7	all	all	DET
ejpam-4944	344	8	k	k	PROPN
ejpam-4944	344	9	∈	∈	PROPN
ejpam-4944	344	10	σ̃1	σ̃1	PROPN
ejpam-4944	344	11	.	.	PUNCT
ejpam-4944	345	1	let	let	VERB
ejpam-4944	345	2	l	l	NOUN
ejpam-4944	345	3	∈	∈	PROPN
ejpam-4944	345	4	µ̃2	µ̃2	PROPN
ejpam-4944	345	5	.	.	PUNCT
ejpam-4944	346	1	then	then	ADV
ejpam-4944	346	2	l	l	PROPN
ejpam-4944	346	3	is	be	AUX
ejpam-4944	346	4	of	of	ADP
ejpam-4944	346	5	µ-second	µ-second	NOUN
ejpam-4944	346	6	category	category	NOUN
ejpam-4944	346	7	and	and	CCONJ
ejpam-4944	346	8	so	so	ADV
ejpam-4944	346	9	l	l	NOUN
ejpam-4944	346	10	is	be	AUX
ejpam-4944	346	11	not	not	PART
ejpam-4944	346	12	a	a	DET
ejpam-4944	346	13	µ-meager	µ-meager	NOUN
ejpam-4944	346	14	set	set	NOUN
ejpam-4944	346	15	which	which	PRON
ejpam-4944	346	16	implies	imply	VERB
ejpam-4944	346	17	i1(c1(l	i1(c1(l	ADV
ejpam-4944	346	18	)	)	PUNCT
ejpam-4944	346	19	)	)	PUNCT
ejpam-4944	347	1	̸=	̸=	PROPN
ejpam-4944	347	2	∅.	∅.	ADV
ejpam-4944	347	3	take	take	VERB
ejpam-4944	347	4	d	d	NOUN
ejpam-4944	347	5	=	=	PUNCT
ejpam-4944	347	6	i1(c1(l	i1(c1(l	ADJ
ejpam-4944	347	7	)	)	PUNCT
ejpam-4944	347	8	)	)	PUNCT
ejpam-4944	347	9	.	.	PUNCT
ejpam-4944	348	1	then	then	ADV
ejpam-4944	348	2	d	d	X
ejpam-4944	348	3	∈	∈	PROPN
ejpam-4944	348	4	µ̃1	µ̃1	NOUN
ejpam-4944	348	5	so	so	SCONJ
ejpam-4944	348	6	that	that	SCONJ
ejpam-4944	348	7	d	d	ADP
ejpam-4944	348	8	∩	∩	ADJ
ejpam-4944	348	9	c2p	c2p	PROPN
ejpam-4944	348	10	̸=	̸=	PROPN
ejpam-4944	348	11	∅.	∅.	ADV
ejpam-4944	348	12	thus	thus	ADV
ejpam-4944	348	13	,	,	PUNCT
ejpam-4944	348	14	c1l	c1l	PROPN
ejpam-4944	348	15	∩	∩	ADJ
ejpam-4944	348	16	c2p	c2p	PROPN
ejpam-4944	348	17	̸=	̸=	PROPN
ejpam-4944	348	18	∅.	∅.	ADV
ejpam-4944	348	19	choose	choose	VERB
ejpam-4944	348	20	t	t	PROPN
ejpam-4944	348	21	∈	∈	PROPN
ejpam-4944	348	22	(	(	PUNCT
ejpam-4944	348	23	c1l	c1l	PROPN
ejpam-4944	348	24	∩	∩	ADJ
ejpam-4944	348	25	c2p	c2p	NOUN
ejpam-4944	348	26	)	)	PUNCT
ejpam-4944	348	27	.	.	PUNCT
ejpam-4944	349	1	then	then	ADV
ejpam-4944	349	2	t	t	PROPN
ejpam-4944	349	3	∈	∈	PROPN
ejpam-4944	349	4	c1l	c1l	X
ejpam-4944	349	5	which	which	PRON
ejpam-4944	349	6	implies	imply	VERB
ejpam-4944	349	7	h	h	NOUN
ejpam-4944	349	8	∩	∩	ADJ
ejpam-4944	349	9	l	l	PROPN
ejpam-4944	349	10	̸=	̸=	PROPN
ejpam-4944	349	11	∅	∅	NOUN
ejpam-4944	349	12	for	for	ADP
ejpam-4944	349	13	every	every	DET
ejpam-4944	349	14	h	h	NOUN
ejpam-4944	349	15	∈	∈	PROPN
ejpam-4944	349	16	µ1(t	µ1(t	PROPN
ejpam-4944	349	17	)	)	PUNCT
ejpam-4944	349	18	,	,	PUNCT
ejpam-4944	349	19	by	by	ADP
ejpam-4944	349	20	lemma	lemma	PROPN
ejpam-4944	349	21	2	2	NUM
ejpam-4944	349	22	.	.	PUNCT
ejpam-4944	349	23	by	by	ADP
ejpam-4944	349	24	hypothesis	hypothesis	NOUN
ejpam-4944	349	25	,	,	PUNCT
ejpam-4944	349	26	iµ1(h	iµ1(h	PROPN
ejpam-4944	349	27	∩	∩	ADJ
ejpam-4944	349	28	l	l	NOUN
ejpam-4944	349	29	)	)	PUNCT
ejpam-4944	349	30	̸=	̸=	PROPN
ejpam-4944	349	31	∅.	∅.	ADP
ejpam-4944	349	32	this	this	PRON
ejpam-4944	349	33	implies	imply	VERB
ejpam-4944	349	34	c2p	c2p	PROPN
ejpam-4944	349	35	∩	∩	NOUN
ejpam-4944	349	36	iµ1(h	iµ1(h	PROPN
ejpam-4944	349	37	∩	∩	ADJ
ejpam-4944	349	38	l	l	NOUN
ejpam-4944	349	39	)	)	PUNCT
ejpam-4944	349	40	̸=	̸=	PROPN
ejpam-4944	349	41	∅	∅	NOUN
ejpam-4944	349	42	which	which	PRON
ejpam-4944	349	43	implies	imply	VERB
ejpam-4944	349	44	c2p	c2p	NOUN
ejpam-4944	349	45	∩	∩	NOUN
ejpam-4944	349	46	(	(	PUNCT
ejpam-4944	349	47	h	h	NOUN
ejpam-4944	349	48	∩l	∩l	ADJ
ejpam-4944	349	49	)	)	PUNCT
ejpam-4944	349	50	̸=	̸=	PROPN
ejpam-4944	349	51	∅	∅	NOUN
ejpam-4944	349	52	which	which	PRON
ejpam-4944	349	53	turn	turn	VERB
ejpam-4944	349	54	implies	imply	VERB
ejpam-4944	349	55	that	that	SCONJ
ejpam-4944	349	56	c2p	c2p	NOUN
ejpam-4944	349	57	∩l	∩l	VERB
ejpam-4944	349	58	̸=	̸=	PROPN
ejpam-4944	349	59	∅.	∅.	ADV
ejpam-4944	349	60	since	since	SCONJ
ejpam-4944	349	61	l	l	NOUN
ejpam-4944	349	62	∈	∈	PROPN
ejpam-4944	349	63	µ̃2	µ̃2	PROPN
ejpam-4944	349	64	we	we	PRON
ejpam-4944	349	65	have	have	VERB
ejpam-4944	349	66	p	p	NOUN
ejpam-4944	349	67	∩l	∩l	ADP
ejpam-4944	349	68	̸=	̸=	PROPN
ejpam-4944	349	69	∅	∅	NOUN
ejpam-4944	349	70	,	,	PUNCT
ejpam-4944	349	71	by	by	ADP
ejpam-4944	349	72	lemma	lemma	PROPN
ejpam-4944	349	73	3	3	NUM
ejpam-4944	349	74	.	.	PUNCT
ejpam-4944	350	1	hence	hence	ADV
ejpam-4944	350	2	p	p	PROPN
ejpam-4944	350	3	is	be	AUX
ejpam-4944	350	4	µ2	µ2	ADJ
ejpam-4944	350	5	-	-	PUNCT
ejpam-4944	350	6	dense	dense	ADJ
ejpam-4944	350	7	.	.	PUNCT
ejpam-4944	351	1	theorem	theorem	NOUN
ejpam-4944	351	2	26	26	NUM
ejpam-4944	351	3	.	.	PUNCT
ejpam-4944	352	1	let	let	AUX
ejpam-4944	352	2	(	(	PUNCT
ejpam-4944	352	3	x,µ1	x,µ1	NOUN
ejpam-4944	352	4	,	,	PUNCT
ejpam-4944	352	5	µ2	µ2	PROPN
ejpam-4944	352	6	)	)	PUNCT
ejpam-4944	352	7	be	be	VERB
ejpam-4944	352	8	a	a	DET
ejpam-4944	352	9	bgts	bgts	NOUN
ejpam-4944	352	10	here	here	ADV
ejpam-4944	352	11	µ1	µ1	PROPN
ejpam-4944	352	12	=	=	SYM
ejpam-4944	352	13	µ	µ	X
ejpam-4944	352	14	and	and	CCONJ
ejpam-4944	352	15	µ2	µ2	PROPN
ejpam-4944	352	16	=	=	PUNCT
ejpam-4944	352	17	µ⋆	µ⋆	X
ejpam-4944	352	18	where	where	SCONJ
ejpam-4944	352	19	µ	µ	NOUN
ejpam-4944	352	20	is	be	AUX
ejpam-4944	352	21	a	a	DET
ejpam-4944	352	22	gt	gt	PROPN
ejpam-4944	352	23	on	on	ADP
ejpam-4944	352	24	x.	x.	NOUN
ejpam-4944	352	25	if	if	SCONJ
ejpam-4944	352	26	µ1	µ1	PROPN
ejpam-4944	352	27	has	have	VERB
ejpam-4944	352	28	the	the	DET
ejpam-4944	352	29	i	i	NOUN
ejpam-4944	352	30	-	-	PUNCT
ejpam-4944	352	31	property	property	NOUN
ejpam-4944	352	32	,	,	PUNCT
ejpam-4944	352	33	then	then	ADV
ejpam-4944	352	34	every	every	DET
ejpam-4944	352	35	(	(	PUNCT
ejpam-4944	352	36	1	1	NUM
ejpam-4944	352	37	,	,	PUNCT
ejpam-4944	352	38	2)⋆-dense	2)⋆-dense	NUM
ejpam-4944	352	39	set	set	NOUN
ejpam-4944	352	40	is	be	AUX
ejpam-4944	352	41	µ2	µ2	ADJ
ejpam-4944	352	42	-	-	PUNCT
ejpam-4944	352	43	dense	dense	ADJ
ejpam-4944	352	44	in	in	ADP
ejpam-4944	352	45	x.	x.	NOUN
ejpam-4944	352	46	proof	proof	NOUN
ejpam-4944	352	47	.	.	PUNCT
ejpam-4944	353	1	let	let	VERB
ejpam-4944	353	2	q	q	PROPN
ejpam-4944	353	3	∈	∈	PROPN
ejpam-4944	353	4	(	(	PUNCT
ejpam-4944	353	5	1	1	NUM
ejpam-4944	353	6	,	,	PUNCT
ejpam-4944	353	7	2)⋆−d(x	2)⋆−d(x	NUM
ejpam-4944	353	8	)	)	PUNCT
ejpam-4944	353	9	.	.	PUNCT
ejpam-4944	354	1	then	then	ADV
ejpam-4944	354	2	c2q∩k	c2q∩k	PROPN
ejpam-4944	354	3	̸=	̸=	PROPN
ejpam-4944	354	4	∅	∅	NOUN
ejpam-4944	354	5	for	for	ADP
ejpam-4944	354	6	every	every	DET
ejpam-4944	354	7	k	k	PROPN
ejpam-4944	354	8	∈	∈	PROPN
ejpam-4944	354	9	σ̃1	σ̃1	PROPN
ejpam-4944	354	10	.	.	PUNCT
ejpam-4944	355	1	let	let	VERB
ejpam-4944	355	2	l	l	NOUN
ejpam-4944	355	3	∈	∈	PROPN
ejpam-4944	355	4	µ̃2	µ̃2	PROPN
ejpam-4944	355	5	.	.	PUNCT
ejpam-4944	356	1	then	then	ADV
ejpam-4944	356	2	l	l	NOUN
ejpam-4944	356	3	=	=	PUNCT
ejpam-4944	356	4	⋃	⋃	PROPN
ejpam-4944	356	5	t(l	t(l	PROPN
ejpam-4944	356	6	t	t	PROPN
ejpam-4944	356	7	1∩lt	1∩lt	NUM
ejpam-4944	356	8	2∩	2∩	NUM
ejpam-4944	356	9	·	·	PUNCT
ejpam-4944	356	10	·	·	PUNCT
ejpam-4944	356	11	·	·	PUNCT
ejpam-4944	356	12	∩lt	∩lt	PROPN
ejpam-4944	356	13	nt	not	PART
ejpam-4944	356	14	)	)	PUNCT
ejpam-4944	356	15	where	where	SCONJ
ejpam-4944	356	16	each	each	PRON
ejpam-4944	356	17	lt	lt	VERB
ejpam-4944	356	18	i	i	NOUN
ejpam-4944	356	19	∈	∈	PROPN
ejpam-4944	357	1	µ̃1	µ̃1	NOUN
ejpam-4944	357	2	for	for	ADP
ejpam-4944	357	3	i	i	PRON
ejpam-4944	357	4	=	=	NOUN
ejpam-4944	357	5	1	1	NUM
ejpam-4944	357	6	to	to	PART
ejpam-4944	357	7	nt	not	PART
ejpam-4944	357	8	.	.	PUNCT
ejpam-4944	358	1	choose	choose	VERB
ejpam-4944	358	2	d	d	NOUN
ejpam-4944	358	3	=	=	SYM
ejpam-4944	358	4	lk	lk	PROPN
ejpam-4944	358	5	1∩lk	1∩lk	NUM
ejpam-4944	358	6	2∩	2∩	NUM
ejpam-4944	358	7	·	·	PUNCT
ejpam-4944	358	8	·	·	PUNCT
ejpam-4944	359	1	·	·	PUNCT
ejpam-4944	359	2	∩lk	∩lk	PROPN
ejpam-4944	359	3	nk	nk	PROPN
ejpam-4944	359	4	for	for	ADP
ejpam-4944	359	5	some	some	DET
ejpam-4944	359	6	k	k	NOUN
ejpam-4944	359	7	;	;	PUNCT
ejpam-4944	359	8	each	each	DET
ejpam-4944	359	9	lk	lk	PROPN
ejpam-4944	359	10	m	m	PROPN
ejpam-4944	359	11	∈	∈	PROPN
ejpam-4944	359	12	µ̃1	µ̃1	NOUN
ejpam-4944	359	13	for	for	ADP
ejpam-4944	359	14	m	m	NOUN
ejpam-4944	359	15	=	=	SYM
ejpam-4944	359	16	1	1	NUM
ejpam-4944	359	17	to	to	PART
ejpam-4944	359	18	nk	nk	PROPN
ejpam-4944	359	19	with	with	ADP
ejpam-4944	359	20	d	d	PROPN
ejpam-4944	359	21	̸=	̸=	PROPN
ejpam-4944	359	22	∅.	∅.	ADV
ejpam-4944	359	23	by	by	ADP
ejpam-4944	359	24	hypothesis	hypothesis	NOUN
ejpam-4944	359	25	,	,	PUNCT
ejpam-4944	359	26	iµ1d	iµ1d	PROPN
ejpam-4944	359	27	̸=	̸=	PROPN
ejpam-4944	359	28	∅	∅	NOUN
ejpam-4944	359	29	which	which	PRON
ejpam-4944	359	30	implies	imply	VERB
ejpam-4944	359	31	that	that	SCONJ
ejpam-4944	359	32	iµ1d	iµ1d	PROPN
ejpam-4944	359	33	∈	∈	PROPN
ejpam-4944	359	34	µ̃1	µ̃1	NOUN
ejpam-4944	359	35	which	which	DET
ejpam-4944	359	36	turn	turn	VERB
ejpam-4944	359	37	implies	imply	VERB
ejpam-4944	359	38	that	that	SCONJ
ejpam-4944	359	39	iµ1d∩	iµ1d∩	NOUN
ejpam-4944	359	40	c2q	c2q	NOUN
ejpam-4944	359	41	̸=	̸=	PROPN
ejpam-4944	359	42	∅.	∅.	ADV
ejpam-4944	359	43	thus	thus	ADV
ejpam-4944	359	44	,	,	PUNCT
ejpam-4944	359	45	c2q∩d	c2q∩d	PUNCT
ejpam-4944	359	46	̸=	̸=	PROPN
ejpam-4944	359	47	∅	∅	NOUN
ejpam-4944	359	48	so	so	SCONJ
ejpam-4944	359	49	that	that	SCONJ
ejpam-4944	359	50	c2q	c2q	NOUN
ejpam-4944	359	51	∩	∩	NOUN
ejpam-4944	359	52	l	l	PROPN
ejpam-4944	359	53	̸=	̸=	PROPN
ejpam-4944	359	54	∅.	∅.	ADV
ejpam-4944	359	55	since	since	SCONJ
ejpam-4944	359	56	l	l	NOUN
ejpam-4944	359	57	∈	∈	PROPN
ejpam-4944	359	58	µ̃2	µ̃2	PROPN
ejpam-4944	359	59	we	we	PRON
ejpam-4944	359	60	have	have	VERB
ejpam-4944	359	61	q	q	NOUN
ejpam-4944	359	62	∩	∩	ADJ
ejpam-4944	359	63	l	l	NOUN
ejpam-4944	359	64	̸=	̸=	PROPN
ejpam-4944	359	65	∅	∅	NOUN
ejpam-4944	359	66	,	,	PUNCT
ejpam-4944	359	67	by	by	ADP
ejpam-4944	359	68	lemma	lemma	PROPN
ejpam-4944	359	69	3	3	NUM
ejpam-4944	359	70	.	.	PUNCT
ejpam-4944	360	1	therefore	therefore	ADV
ejpam-4944	360	2	,	,	PUNCT
ejpam-4944	360	3	q	q	PROPN
ejpam-4944	360	4	is	be	AUX
ejpam-4944	360	5	µ2	µ2	ADJ
ejpam-4944	360	6	-	-	PUNCT
ejpam-4944	360	7	dense	dense	ADJ
ejpam-4944	360	8	.	.	PUNCT
ejpam-4944	361	1	theorem	theorem	ADJ
ejpam-4944	361	2	27	27	NUM
ejpam-4944	361	3	.	.	PUNCT
ejpam-4944	362	1	let	let	AUX
ejpam-4944	362	2	(	(	PUNCT
ejpam-4944	362	3	x,µ1	x,µ1	NOUN
ejpam-4944	362	4	,	,	PUNCT
ejpam-4944	362	5	µ2	µ2	PROPN
ejpam-4944	362	6	)	)	PUNCT
ejpam-4944	362	7	be	be	VERB
ejpam-4944	362	8	a	a	DET
ejpam-4944	362	9	bgts	bgts	NOUN
ejpam-4944	362	10	here	here	ADV
ejpam-4944	362	11	µ1	µ1	PROPN
ejpam-4944	362	12	=	=	SYM
ejpam-4944	362	13	µ	µ	X
ejpam-4944	362	14	and	and	CCONJ
ejpam-4944	362	15	µ2	µ2	PROPN
ejpam-4944	362	16	=	=	PUNCT
ejpam-4944	362	17	µ⋆⋆	µ⋆⋆	ADJ
ejpam-4944	362	18	where	where	SCONJ
ejpam-4944	362	19	µ	µ	NOUN
ejpam-4944	362	20	is	be	AUX
ejpam-4944	362	21	a	a	DET
ejpam-4944	362	22	generalized	generalized	ADJ
ejpam-4944	362	23	topology	topology	NOUN
ejpam-4944	362	24	on	on	ADP
ejpam-4944	362	25	x.	x.	NOUN
ejpam-4944	362	26	if	if	SCONJ
ejpam-4944	362	27	(	(	PUNCT
ejpam-4944	362	28	x,µ1	x,µ1	NOUN
ejpam-4944	362	29	)	)	PUNCT
ejpam-4944	362	30	is	be	AUX
ejpam-4944	362	31	a	a	DET
ejpam-4944	362	32	hyperconnected	hyperconnecte	VERB
ejpam-4944	362	33	space	space	NOUN
ejpam-4944	362	34	and	and	CCONJ
ejpam-4944	362	35	if	if	SCONJ
ejpam-4944	362	36	µ1	µ1	PROPN
ejpam-4944	362	37	is	be	AUX
ejpam-4944	362	38	a	a	DET
ejpam-4944	362	39	sgt	sgt	NOUN
ejpam-4944	362	40	,	,	PUNCT
ejpam-4944	362	41	then	then	ADV
ejpam-4944	362	42	every	every	DET
ejpam-4944	362	43	non	non	ADJ
ejpam-4944	362	44	-	-	ADJ
ejpam-4944	362	45	null	null	ADJ
ejpam-4944	362	46	µ2	µ2	ADJ
ejpam-4944	362	47	-	-	PUNCT
ejpam-4944	362	48	open	open	ADJ
ejpam-4944	362	49	set	set	NOUN
ejpam-4944	362	50	is	be	AUX
ejpam-4944	362	51	(	(	PUNCT
ejpam-4944	362	52	1	1	NUM
ejpam-4944	362	53	,	,	PUNCT
ejpam-4944	362	54	2)⋆-dense	2)⋆-dense	NUM
ejpam-4944	362	55	in	in	ADP
ejpam-4944	362	56	x.	x.	NOUN
ejpam-4944	362	57	proof	proof	NOUN
ejpam-4944	362	58	.	.	PUNCT
ejpam-4944	363	1	let	let	VERB
ejpam-4944	363	2	p	p	PRON
ejpam-4944	363	3	∈	∈	PROPN
ejpam-4944	363	4	µ̃2	µ̃2	PROPN
ejpam-4944	363	5	.	.	PUNCT
ejpam-4944	364	1	then	then	ADV
ejpam-4944	364	2	p	p	X
ejpam-4944	364	3	is	be	AUX
ejpam-4944	364	4	of	of	ADP
ejpam-4944	364	5	µ1	µ1	NOUN
ejpam-4944	364	6	-	-	PUNCT
ejpam-4944	364	7	second	second	NOUN
ejpam-4944	364	8	category	category	NOUN
ejpam-4944	364	9	so	so	SCONJ
ejpam-4944	364	10	that	that	SCONJ
ejpam-4944	364	11	p	p	NOUN
ejpam-4944	364	12	is	be	AUX
ejpam-4944	364	13	not	not	PART
ejpam-4944	364	14	a	a	DET
ejpam-4944	364	15	µ1	µ1	NOUN
ejpam-4944	364	16	-	-	PUNCT
ejpam-4944	364	17	meager	meager	ADJ
ejpam-4944	364	18	set	set	NOUN
ejpam-4944	364	19	which	which	PRON
ejpam-4944	364	20	implies	imply	VERB
ejpam-4944	364	21	iµ1(cµ1(p	iµ1(cµ1(p	NOUN
ejpam-4944	364	22	)	)	PUNCT
ejpam-4944	364	23	)	)	PUNCT
ejpam-4944	365	1	̸=	̸=	PROPN
ejpam-4944	365	2	∅.	∅.	ADV
ejpam-4944	365	3	thus	thus	ADV
ejpam-4944	365	4	,	,	PUNCT
ejpam-4944	365	5	iµ1(cµ1(p	iµ1(cµ1(p	NOUN
ejpam-4944	365	6	)	)	PUNCT
ejpam-4944	365	7	)	)	PUNCT
ejpam-4944	366	1	∈	∈	PROPN
ejpam-4944	366	2	µ̃1	µ̃1	PROPN
ejpam-4944	366	3	.	.	PUNCT
ejpam-4944	366	4	let	let	VERB
ejpam-4944	366	5	k	k	PROPN
ejpam-4944	366	6	∈	∈	PROPN
ejpam-4944	366	7	σ̃1	σ̃1	PROPN
ejpam-4944	366	8	.	.	PUNCT
ejpam-4944	366	9	by	by	ADP
ejpam-4944	366	10	hypothesis	hypothesis	NOUN
ejpam-4944	366	11	,	,	PUNCT
ejpam-4944	366	12	iµ1k	iµ1k	PROPN
ejpam-4944	366	13	∈	∈	PROPN
ejpam-4944	366	14	µ̃1	µ̃1	PROPN
ejpam-4944	366	15	.	.	PUNCT
ejpam-4944	367	1	since	since	SCONJ
ejpam-4944	367	2	(	(	PUNCT
ejpam-4944	367	3	x,µ1	x,µ1	NOUN
ejpam-4944	367	4	)	)	PUNCT
ejpam-4944	367	5	is	be	AUX
ejpam-4944	367	6	a	a	DET
ejpam-4944	367	7	hyperconnected	hyperconnecte	VERB
ejpam-4944	367	8	space	space	NOUN
ejpam-4944	367	9	we	we	PRON
ejpam-4944	367	10	have	have	VERB
ejpam-4944	367	11	iµ1k	iµ1k	PROPN
ejpam-4944	367	12	is	be	AUX
ejpam-4944	367	13	µ1	µ1	NOUN
ejpam-4944	367	14	-	-	PUNCT
ejpam-4944	367	15	dense	dense	ADJ
ejpam-4944	367	16	.	.	PUNCT
ejpam-4944	368	1	therefore	therefore	ADV
ejpam-4944	368	2	,	,	PUNCT
ejpam-4944	368	3	iµ1(cµ1(p	iµ1(cµ1(p	NOUN
ejpam-4944	368	4	)	)	PUNCT
ejpam-4944	368	5	)	)	PUNCT
ejpam-4944	368	6	∩	∩	PROPN
ejpam-4944	368	7	iµ1k	iµ1k	PROPN
ejpam-4944	368	8	̸=	̸=	PROPN
ejpam-4944	368	9	∅.	∅.	ADP
ejpam-4944	368	10	this	this	PRON
ejpam-4944	368	11	implies	imply	VERB
ejpam-4944	368	12	cµ1p	cµ1p	NOUN
ejpam-4944	368	13	∩	∩	ADJ
ejpam-4944	368	14	iµ1k	iµ1k	PROPN
ejpam-4944	368	15	̸=	̸=	PROPN
ejpam-4944	368	16	∅	∅	NOUN
ejpam-4944	368	17	which	which	PRON
ejpam-4944	368	18	implies	imply	VERB
ejpam-4944	368	19	that	that	SCONJ
ejpam-4944	368	20	iµ1k	iµ1k	PROPN
ejpam-4944	368	21	∩	∩	NOUN
ejpam-4944	368	22	p	p	X
ejpam-4944	368	23	̸=	̸=	PROPN
ejpam-4944	368	24	∅	∅	NOUN
ejpam-4944	368	25	,	,	PUNCT
ejpam-4944	368	26	by	by	ADP
ejpam-4944	368	27	lemma	lemma	PROPN
ejpam-4944	368	28	3	3	NUM
ejpam-4944	368	29	.	.	PUNCT
ejpam-4944	369	1	thus	thus	ADV
ejpam-4944	369	2	,	,	PUNCT
ejpam-4944	369	3	p	p	NOUN
ejpam-4944	369	4	∩k	∩k	NOUN
ejpam-4944	369	5	̸=	̸=	PROPN
ejpam-4944	369	6	∅.	∅.	VERB
ejpam-4944	369	7	therefore	therefore	ADV
ejpam-4944	369	8	,	,	PUNCT
ejpam-4944	369	9	p	p	PROPN
ejpam-4944	369	10	∈	∈	PROPN
ejpam-4944	369	11	(	(	PUNCT
ejpam-4944	369	12	1	1	NUM
ejpam-4944	369	13	,	,	PUNCT
ejpam-4944	369	14	2)⋆	2)⋆	PROPN
ejpam-4944	369	15	−d(x	−d(x	NOUN
ejpam-4944	369	16	)	)	PUNCT
ejpam-4944	369	17	.	.	PUNCT
ejpam-4944	370	1	theorem	theorem	PROPN
ejpam-4944	370	2	28	28	NUM
ejpam-4944	370	3	.	.	PUNCT
ejpam-4944	371	1	let	let	AUX
ejpam-4944	371	2	(	(	PUNCT
ejpam-4944	371	3	x,µ1	x,µ1	NOUN
ejpam-4944	371	4	,	,	PUNCT
ejpam-4944	371	5	µ2	µ2	PROPN
ejpam-4944	371	6	)	)	PUNCT
ejpam-4944	371	7	be	be	VERB
ejpam-4944	371	8	a	a	DET
ejpam-4944	371	9	bgts	bgts	NOUN
ejpam-4944	371	10	here	here	ADV
ejpam-4944	371	11	µ1	µ1	PROPN
ejpam-4944	371	12	=	=	SYM
ejpam-4944	371	13	µ	µ	X
ejpam-4944	371	14	and	and	CCONJ
ejpam-4944	371	15	µ2	µ2	PROPN
ejpam-4944	371	16	=	=	PUNCT
ejpam-4944	371	17	µ⋆	µ⋆	X
ejpam-4944	371	18	where	where	SCONJ
ejpam-4944	371	19	µ	µ	NOUN
ejpam-4944	371	20	is	be	AUX
ejpam-4944	371	21	a	a	DET
ejpam-4944	371	22	sgt	sgt	PROPN
ejpam-4944	371	23	on	on	ADP
ejpam-4944	371	24	x.	x.	NOUN
ejpam-4944	371	25	if	if	SCONJ
ejpam-4944	371	26	(	(	PUNCT
ejpam-4944	371	27	x,µ1	x,µ1	NOUN
ejpam-4944	371	28	)	)	PUNCT
ejpam-4944	371	29	is	be	AUX
ejpam-4944	371	30	a	a	DET
ejpam-4944	371	31	hyperconnected	hyperconnecte	VERB
ejpam-4944	371	32	space	space	NOUN
ejpam-4944	371	33	and	and	CCONJ
ejpam-4944	371	34	if	if	SCONJ
ejpam-4944	371	35	µ1	µ1	PROPN
ejpam-4944	371	36	has	have	VERB
ejpam-4944	371	37	i	i	NOUN
ejpam-4944	371	38	-	-	PUNCT
ejpam-4944	371	39	property	property	NOUN
ejpam-4944	371	40	,	,	PUNCT
ejpam-4944	371	41	then	then	ADV
ejpam-4944	371	42	every	every	DET
ejpam-4944	371	43	non	non	ADJ
ejpam-4944	371	44	-	-	ADJ
ejpam-4944	371	45	null	null	ADJ
ejpam-4944	371	46	µ2	µ2	ADJ
ejpam-4944	371	47	-	-	PUNCT
ejpam-4944	371	48	open	open	ADJ
ejpam-4944	371	49	set	set	NOUN
ejpam-4944	371	50	is	be	AUX
ejpam-4944	371	51	a	a	DET
ejpam-4944	371	52	(	(	PUNCT
ejpam-4944	371	53	1	1	NUM
ejpam-4944	371	54	,	,	PUNCT
ejpam-4944	371	55	2)⋆-dense	2)⋆-dense	NUM
ejpam-4944	371	56	set	set	VERB
ejpam-4944	371	57	in	in	ADP
ejpam-4944	371	58	x.	x.	NOUN
ejpam-4944	371	59	proof	proof	NOUN
ejpam-4944	371	60	.	.	PUNCT
ejpam-4944	372	1	let	let	VERB
ejpam-4944	372	2	p	p	X
ejpam-4944	372	3	∈	∈	PROPN
ejpam-4944	372	4	µ̃⋆.	µ̃⋆.	PUNCT
ejpam-4944	372	5	then	then	ADV
ejpam-4944	372	6	p	p	NOUN
ejpam-4944	372	7	=	=	PUNCT
ejpam-4944	372	8	⋃	⋃	PROPN
ejpam-4944	372	9	t(p	t(p	PROPN
ejpam-4944	372	10	t	t	PROPN
ejpam-4944	372	11	1	1	NUM
ejpam-4944	372	12	∩	∩	PROPN
ejpam-4944	372	13	p	p	PROPN
ejpam-4944	372	14	t	t	PROPN
ejpam-4944	372	15	2	2	NUM
ejpam-4944	372	16	∩	∩	X
ejpam-4944	372	17	·	·	PUNCT
ejpam-4944	372	18	·	·	PUNCT
ejpam-4944	372	19	·	·	PUNCT
ejpam-4944	373	1	∩	∩	NOUN
ejpam-4944	373	2	p	p	PROPN
ejpam-4944	373	3	t	t	PROPN
ejpam-4944	373	4	nt	not	PART
ejpam-4944	373	5	)	)	PUNCT
ejpam-4944	374	1	where	where	SCONJ
ejpam-4944	374	2	each	each	DET
ejpam-4944	374	3	p	p	NOUN
ejpam-4944	374	4	t	t	X
ejpam-4944	375	1	i	i	PRON
ejpam-4944	375	2	∈	∈	PROPN
ejpam-4944	375	3	µ̃1	µ̃1	NOUN
ejpam-4944	375	4	for	for	ADP
ejpam-4944	375	5	i	i	PRON
ejpam-4944	375	6	=	=	NOUN
ejpam-4944	375	7	1	1	NUM
ejpam-4944	375	8	to	to	PART
ejpam-4944	375	9	nt	not	PART
ejpam-4944	375	10	.	.	PUNCT
ejpam-4944	376	1	choose	choose	VERB
ejpam-4944	376	2	d	d	X
ejpam-4944	376	3	=	=	SYM
ejpam-4944	376	4	p	p	X
ejpam-4944	376	5	k	k	PROPN
ejpam-4944	376	6	1	1	NUM
ejpam-4944	376	7	∩p	∩p	NOUN
ejpam-4944	376	8	k	k	X
ejpam-4944	376	9	2	2	NUM
ejpam-4944	376	10	∩	∩	X
ejpam-4944	376	11	·	·	PUNCT
ejpam-4944	376	12	·	·	PUNCT
ejpam-4944	376	13	·	·	PUNCT
ejpam-4944	376	14	∩p	∩p	X
ejpam-4944	376	15	k	k	PROPN
ejpam-4944	376	16	nk	nk	PROPN
ejpam-4944	376	17	for	for	ADP
ejpam-4944	376	18	some	some	DET
ejpam-4944	376	19	k	k	NOUN
ejpam-4944	376	20	;	;	PUNCT
ejpam-4944	376	21	each	each	PRON
ejpam-4944	376	22	p	p	X
ejpam-4944	376	23	k	k	NOUN
ejpam-4944	376	24	m	m	VERB
ejpam-4944	376	25	∈	∈	PROPN
ejpam-4944	376	26	µ̃1	µ̃1	NOUN
ejpam-4944	376	27	for	for	ADP
ejpam-4944	376	28	m	m	NOUN
ejpam-4944	376	29	=	=	SYM
ejpam-4944	376	30	1	1	NUM
ejpam-4944	376	31	to	to	PART
ejpam-4944	376	32	nk	nk	PROPN
ejpam-4944	376	33	with	with	ADP
ejpam-4944	376	34	d	d	PROPN
ejpam-4944	376	35	̸=	̸=	PROPN
ejpam-4944	376	36	∅.	∅.	ADV
ejpam-4944	376	37	by	by	ADP
ejpam-4944	376	38	hypothesis	hypothesis	NOUN
ejpam-4944	376	39	,	,	PUNCT
ejpam-4944	376	40	iµ1d	iµ1d	PROPN
ejpam-4944	376	41	̸=	̸=	PROPN
ejpam-4944	376	42	∅	∅	NOUN
ejpam-4944	376	43	which	which	PRON
ejpam-4944	376	44	implies	imply	VERB
ejpam-4944	376	45	that	that	SCONJ
ejpam-4944	376	46	iµ1d	iµ1d	PROPN
ejpam-4944	376	47	∈	∈	PROPN
ejpam-4944	376	48	µ̃1	µ̃1	PROPN
ejpam-4944	376	49	.	.	PUNCT
ejpam-4944	377	1	since	since	SCONJ
ejpam-4944	377	2	(	(	PUNCT
ejpam-4944	377	3	x,µ1	x,µ1	NOUN
ejpam-4944	377	4	)	)	PUNCT
ejpam-4944	377	5	is	be	AUX
ejpam-4944	377	6	a	a	DET
ejpam-4944	377	7	hyperconnected	hyperconnected	ADJ
ejpam-4944	377	8	space	space	NOUN
ejpam-4944	377	9	,	,	PUNCT
ejpam-4944	377	10	iµ1d	iµ1d	PROPN
ejpam-4944	377	11	is	be	AUX
ejpam-4944	377	12	µ1	µ1	NOUN
ejpam-4944	377	13	-	-	PUNCT
ejpam-4944	377	14	dense	dense	ADJ
ejpam-4944	377	15	which	which	PRON
ejpam-4944	377	16	implies	imply	VERB
ejpam-4944	377	17	p	p	NOUN
ejpam-4944	377	18	is	be	AUX
ejpam-4944	377	19	µ1	µ1	NOUN
ejpam-4944	377	20	-	-	PUNCT
ejpam-4944	377	21	dense	dense	ADJ
ejpam-4944	377	22	.	.	PUNCT
ejpam-4944	378	1	by	by	ADP
ejpam-4944	378	2	hypothesis	hypothesis	NOUN
ejpam-4944	378	3	and	and	CCONJ
ejpam-4944	378	4	theorem	theorem	VERB
ejpam-4944	378	5	11	11	NUM
ejpam-4944	378	6	,	,	PUNCT
ejpam-4944	378	7	p	p	NOUN
ejpam-4944	378	8	is	be	AUX
ejpam-4944	378	9	(	(	PUNCT
ejpam-4944	378	10	1	1	NUM
ejpam-4944	378	11	,	,	PUNCT
ejpam-4944	378	12	2)⋆-dense	2)⋆-dense	NUM
ejpam-4944	378	13	.	.	PUNCT
ejpam-4944	379	1	theorem	theorem	NOUN
ejpam-4944	379	2	29	29	NUM
ejpam-4944	379	3	.	.	PUNCT
ejpam-4944	380	1	let	let	AUX
ejpam-4944	380	2	(	(	PUNCT
ejpam-4944	380	3	x,µ1	x,µ1	NOUN
ejpam-4944	380	4	,	,	PUNCT
ejpam-4944	380	5	µ2	µ2	PROPN
ejpam-4944	380	6	)	)	PUNCT
ejpam-4944	380	7	be	be	VERB
ejpam-4944	380	8	a	a	DET
ejpam-4944	380	9	bigeneralized	bigeneralized	ADJ
ejpam-4944	380	10	topological	topological	ADJ
ejpam-4944	380	11	space	space	NOUN
ejpam-4944	380	12	.	.	PUNCT
ejpam-4944	381	1	if	if	SCONJ
ejpam-4944	381	2	(	(	PUNCT
ejpam-4944	381	3	x,µs	x,µs	NUM
ejpam-4944	381	4	)	)	PUNCT
ejpam-4944	381	5	is	be	AUX
ejpam-4944	381	6	a	a	DET
ejpam-4944	381	7	hyperconnected	hyperconnecte	VERB
ejpam-4944	381	8	space	space	NOUN
ejpam-4944	381	9	and	and	CCONJ
ejpam-4944	381	10	if	if	SCONJ
ejpam-4944	381	11	µs	µs	NOUN
ejpam-4944	381	12	is	be	AUX
ejpam-4944	381	13	a	a	DET
ejpam-4944	381	14	sgt	sgt	NOUN
ejpam-4944	381	15	for	for	ADP
ejpam-4944	381	16	s	s	NOUN
ejpam-4944	381	17	=	=	SYM
ejpam-4944	381	18	1	1	NUM
ejpam-4944	381	19	,	,	PUNCT
ejpam-4944	381	20	2	2	NUM
ejpam-4944	381	21	,	,	PUNCT
ejpam-4944	381	22	then	then	ADV
ejpam-4944	381	23	(	(	PUNCT
ejpam-4944	381	24	a	a	X
ejpam-4944	381	25	)	)	PUNCT
ejpam-4944	381	26	every	every	DET
ejpam-4944	381	27	non	non	ADJ
ejpam-4944	381	28	-	-	ADJ
ejpam-4944	381	29	null	null	ADJ
ejpam-4944	381	30	µs	µs	NOUN
ejpam-4944	381	31	-	-	PUNCT
ejpam-4944	381	32	semi	semi	ADJ
ejpam-4944	381	33	-	-	ADJ
ejpam-4944	381	34	open	open	ADJ
ejpam-4944	381	35	set	set	NOUN
ejpam-4944	381	36	is	be	AUX
ejpam-4944	381	37	(	(	PUNCT
ejpam-4944	381	38	s	s	X
ejpam-4944	381	39	,	,	PUNCT
ejpam-4944	381	40	v)⋆-dense	v)⋆-dense	PROPN
ejpam-4944	381	41	.	.	PUNCT
ejpam-4944	382	1	(	(	PUNCT
ejpam-4944	382	2	b	b	X
ejpam-4944	382	3	)	)	PUNCT
ejpam-4944	382	4	every	every	DET
ejpam-4944	382	5	non	non	ADJ
ejpam-4944	382	6	-	-	ADJ
ejpam-4944	382	7	null	null	ADJ
ejpam-4944	382	8	µs	µs	NOUN
ejpam-4944	382	9	-	-	PUNCT
ejpam-4944	382	10	pre	pre	ADJ
ejpam-4944	382	11	-	-	ADJ
ejpam-4944	382	12	open	open	ADJ
ejpam-4944	382	13	set	set	NOUN
ejpam-4944	382	14	is	be	AUX
ejpam-4944	382	15	(	(	PUNCT
ejpam-4944	382	16	s	s	X
ejpam-4944	382	17	,	,	PUNCT
ejpam-4944	382	18	v)⋆-dense	v)⋆-dense	PROPN
ejpam-4944	382	19	.	.	PUNCT
ejpam-4944	383	1	(	(	PUNCT
ejpam-4944	383	2	c	c	X
ejpam-4944	383	3	)	)	PUNCT
ejpam-4944	383	4	every	every	DET
ejpam-4944	383	5	non	non	ADJ
ejpam-4944	383	6	-	-	ADJ
ejpam-4944	383	7	null	null	ADJ
ejpam-4944	383	8	µs	µs	NOUN
ejpam-4944	383	9	-	-	PUNCT
ejpam-4944	383	10	α	α	PRON
ejpam-4944	383	11	-	-	ADJ
ejpam-4944	383	12	open	open	ADJ
ejpam-4944	383	13	set	set	NOUN
ejpam-4944	383	14	is	be	AUX
ejpam-4944	383	15	(	(	PUNCT
ejpam-4944	383	16	s	s	X
ejpam-4944	383	17	,	,	PUNCT
ejpam-4944	383	18	v)⋆-dense	v)⋆-dense	PROPN
ejpam-4944	383	19	.	.	PUNCT
ejpam-4944	384	1	(	(	PUNCT
ejpam-4944	384	2	d	d	X
ejpam-4944	384	3	)	)	PUNCT
ejpam-4944	384	4	every	every	DET
ejpam-4944	384	5	non	non	ADJ
ejpam-4944	384	6	-	-	ADJ
ejpam-4944	384	7	null	null	ADJ
ejpam-4944	384	8	µs	µs	NOUN
ejpam-4944	384	9	-	-	PUNCT
ejpam-4944	384	10	β	β	NOUN
ejpam-4944	384	11	-	-	ADJ
ejpam-4944	384	12	open	open	ADJ
ejpam-4944	384	13	set	set	NOUN
ejpam-4944	384	14	is	be	AUX
ejpam-4944	384	15	(	(	PUNCT
ejpam-4944	384	16	s	s	X
ejpam-4944	384	17	,	,	PUNCT
ejpam-4944	384	18	v)⋆-dense	v)⋆-dense	PROPN
ejpam-4944	384	19	.	.	PUNCT
ejpam-4944	385	1	d.	d.	PROPN
ejpam-4944	385	2	elgezouli	elgezouli	PROPN
ejpam-4944	385	3	et	et	PROPN
ejpam-4944	385	4	al	al	PROPN
ejpam-4944	385	5	.	.	PUNCT
ejpam-4944	385	6	/	/	SYM
ejpam-4944	385	7	eur	eur	PROPN
ejpam-4944	385	8	.	.	PUNCT
ejpam-4944	386	1	j.	j.	PROPN
ejpam-4944	386	2	pure	pure	PROPN
ejpam-4944	386	3	appl	appl	PROPN
ejpam-4944	386	4	.	.	PROPN
ejpam-4944	386	5	math	math	PROPN
ejpam-4944	386	6	,	,	PUNCT
ejpam-4944	386	7	16	16	NUM
ejpam-4944	386	8	(	(	PUNCT
ejpam-4944	386	9	4	4	NUM
ejpam-4944	386	10	)	)	PUNCT
ejpam-4944	386	11	(	(	PUNCT
ejpam-4944	386	12	2023	2023	NUM
ejpam-4944	386	13	)	)	PUNCT
ejpam-4944	386	14	,	,	PUNCT
ejpam-4944	386	15	2286	2286	NUM
ejpam-4944	386	16	-	-	SYM
ejpam-4944	386	17	2305	2305	NUM
ejpam-4944	386	18	2297	2297	NUM
ejpam-4944	386	19	(	(	PUNCT
ejpam-4944	386	20	e	e	NOUN
ejpam-4944	386	21	)	)	PUNCT
ejpam-4944	386	22	every	every	DET
ejpam-4944	386	23	non	non	ADJ
ejpam-4944	386	24	-	-	ADJ
ejpam-4944	386	25	null	null	ADJ
ejpam-4944	386	26	µs	µs	NOUN
ejpam-4944	386	27	-	-	PUNCT
ejpam-4944	386	28	b	b	NOUN
ejpam-4944	386	29	-	-	PUNCT
ejpam-4944	386	30	open	open	ADJ
ejpam-4944	386	31	set	set	NOUN
ejpam-4944	386	32	is	be	AUX
ejpam-4944	386	33	(	(	PUNCT
ejpam-4944	386	34	s	s	X
ejpam-4944	386	35	,	,	PUNCT
ejpam-4944	386	36	v)⋆-dense	v)⋆-dense	PROPN
ejpam-4944	386	37	where	where	SCONJ
ejpam-4944	386	38	s	s	X
ejpam-4944	386	39	,	,	PUNCT
ejpam-4944	386	40	v	v	NOUN
ejpam-4944	386	41	=	=	SYM
ejpam-4944	386	42	1	1	NUM
ejpam-4944	386	43	,	,	PUNCT
ejpam-4944	386	44	2	2	NUM
ejpam-4944	386	45	;	;	PUNCT
ejpam-4944	386	46	s	s	VERB
ejpam-4944	386	47	̸=	̸=	PROPN
ejpam-4944	386	48	v.	v.	ADP
ejpam-4944	386	49	proof	proof	NOUN
ejpam-4944	386	50	.	.	PUNCT
ejpam-4944	387	1	assume	assume	VERB
ejpam-4944	387	2	that	that	SCONJ
ejpam-4944	387	3	,	,	PUNCT
ejpam-4944	387	4	(	(	PUNCT
ejpam-4944	387	5	x,µs	x,µs	NUM
ejpam-4944	387	6	)	)	PUNCT
ejpam-4944	387	7	is	be	AUX
ejpam-4944	387	8	a	a	DET
ejpam-4944	387	9	hyperconnected	hyperconnecte	VERB
ejpam-4944	387	10	space	space	NOUN
ejpam-4944	387	11	and	and	CCONJ
ejpam-4944	387	12	µs	µs	NOUN
ejpam-4944	387	13	is	be	AUX
ejpam-4944	387	14	a	a	DET
ejpam-4944	387	15	sgt	sgt	NOUN
ejpam-4944	387	16	for	for	ADP
ejpam-4944	387	17	s	s	NOUN
ejpam-4944	387	18	=	=	SYM
ejpam-4944	387	19	1	1	NUM
ejpam-4944	387	20	,	,	PUNCT
ejpam-4944	387	21	2	2	NUM
ejpam-4944	387	22	..	..	PUNCT
ejpam-4944	387	23	choose	choose	VERB
ejpam-4944	387	24	s	s	NOUN
ejpam-4944	387	25	=	=	SYM
ejpam-4944	387	26	2	2	NUM
ejpam-4944	387	27	and	and	CCONJ
ejpam-4944	387	28	v	v	NOUN
ejpam-4944	387	29	=	=	SYM
ejpam-4944	387	30	1	1	NUM
ejpam-4944	387	31	.	.	PUNCT
ejpam-4944	388	1	then	then	ADV
ejpam-4944	388	2	(	(	PUNCT
ejpam-4944	388	3	x,µ2	x,µ2	PROPN
ejpam-4944	388	4	)	)	PUNCT
ejpam-4944	388	5	is	be	AUX
ejpam-4944	388	6	a	a	DET
ejpam-4944	388	7	hyperconnected	hyperconnected	ADJ
ejpam-4944	388	8	space	space	NOUN
ejpam-4944	388	9	,	,	PUNCT
ejpam-4944	388	10	µ2	µ2	PROPN
ejpam-4944	388	11	is	be	AUX
ejpam-4944	388	12	a	a	DET
ejpam-4944	388	13	strong	strong	ADJ
ejpam-4944	388	14	generalized	generalized	ADJ
ejpam-4944	388	15	topology	topology	NOUN
ejpam-4944	388	16	.	.	PUNCT
ejpam-4944	389	1	(	(	PUNCT
ejpam-4944	389	2	a	a	X
ejpam-4944	389	3	)	)	PUNCT
ejpam-4944	389	4	.	.	PUNCT
ejpam-4944	390	1	let	let	VERB
ejpam-4944	390	2	q	q	PRON
ejpam-4944	390	3	be	be	AUX
ejpam-4944	390	4	a	a	DET
ejpam-4944	390	5	non	non	ADJ
ejpam-4944	390	6	-	-	ADJ
ejpam-4944	390	7	null	null	ADJ
ejpam-4944	390	8	µs	µs	NOUN
ejpam-4944	390	9	-	-	PUNCT
ejpam-4944	390	10	semi	semi	ADJ
ejpam-4944	390	11	-	-	ADJ
ejpam-4944	390	12	open	open	ADJ
ejpam-4944	390	13	set	set	NOUN
ejpam-4944	390	14	.	.	PUNCT
ejpam-4944	391	1	then	then	ADV
ejpam-4944	391	2	q	q	PROPN
ejpam-4944	391	3	is	be	AUX
ejpam-4944	391	4	µ2	µ2	ADJ
ejpam-4944	391	5	-	-	PUNCT
ejpam-4944	391	6	semi	semi	ADV
ejpam-4944	391	7	-	-	ADJ
ejpam-4944	391	8	open	open	ADJ
ejpam-4944	391	9	set	set	NOUN
ejpam-4944	391	10	in	in	ADP
ejpam-4944	391	11	x.	x.	NOUN
ejpam-4944	391	12	let	let	VERB
ejpam-4944	391	13	h	h	PROPN
ejpam-4944	391	14	∈	∈	PROPN
ejpam-4944	391	15	σ̃2	σ̃2	PROPN
ejpam-4944	391	16	.	.	PUNCT
ejpam-4944	391	17	suppose	suppose	VERB
ejpam-4944	391	18	h	h	PROPN
ejpam-4944	391	19	∈	∈	PROPN
ejpam-4944	391	20	µ̃2	µ̃2	PROPN
ejpam-4944	391	21	.	.	PUNCT
ejpam-4944	392	1	then	then	ADV
ejpam-4944	392	2	there	there	PRON
ejpam-4944	392	3	is	be	VERB
ejpam-4944	392	4	nothing	nothing	PRON
ejpam-4944	392	5	to	to	PART
ejpam-4944	392	6	prove	prove	VERB
ejpam-4944	392	7	.	.	PUNCT
ejpam-4944	393	1	suppose	suppose	VERB
ejpam-4944	393	2	that	that	SCONJ
ejpam-4944	393	3	,	,	PUNCT
ejpam-4944	393	4	h	h	NOUN
ejpam-4944	393	5	/∈	/∈	PUNCT
ejpam-4944	394	1	µ̃2	µ̃2	PROPN
ejpam-4944	394	2	.	.	PUNCT
ejpam-4944	395	1	here	here	ADV
ejpam-4944	395	2	h	h	PROPN
ejpam-4944	395	3	⊂	⊂	PROPN
ejpam-4944	395	4	c2(i2(h	c2(i2(h	PROPN
ejpam-4944	395	5	)	)	PUNCT
ejpam-4944	395	6	)	)	PUNCT
ejpam-4944	396	1	which	which	PRON
ejpam-4944	396	2	implies	imply	VERB
ejpam-4944	396	3	i2(h	i2(h	NOUN
ejpam-4944	396	4	)	)	PUNCT
ejpam-4944	396	5	∈	∈	PROPN
ejpam-4944	396	6	µ̃2	µ̃2	PROPN
ejpam-4944	396	7	,	,	PUNCT
ejpam-4944	396	8	by	by	ADP
ejpam-4944	396	9	our	our	PRON
ejpam-4944	396	10	assumption	assumption	NOUN
ejpam-4944	396	11	.	.	PUNCT
ejpam-4944	397	1	since	since	SCONJ
ejpam-4944	397	2	(	(	PUNCT
ejpam-4944	397	3	x,µ2	x,µ2	PROPN
ejpam-4944	397	4	)	)	PUNCT
ejpam-4944	397	5	is	be	AUX
ejpam-4944	397	6	a	a	DET
ejpam-4944	397	7	hyperconnected	hyperconnecte	VERB
ejpam-4944	397	8	space	space	NOUN
ejpam-4944	397	9	we	we	PRON
ejpam-4944	397	10	have	have	VERB
ejpam-4944	397	11	i2h	i2h	PROPN
ejpam-4944	397	12	is	be	AUX
ejpam-4944	397	13	a	a	DET
ejpam-4944	397	14	µ2	µ2	ADJ
ejpam-4944	397	15	-	-	PUNCT
ejpam-4944	397	16	dense	dense	ADJ
ejpam-4944	397	17	set	set	NOUN
ejpam-4944	397	18	in	in	ADP
ejpam-4944	397	19	x.	x.	NOUN
ejpam-4944	397	20	also	also	ADV
ejpam-4944	397	21	,	,	PUNCT
ejpam-4944	397	22	q	q	PROPN
ejpam-4944	397	23	⊂	⊂	X
ejpam-4944	397	24	c2(i2(q	c2(i2(q	PROPN
ejpam-4944	397	25	)	)	PUNCT
ejpam-4944	397	26	)	)	PUNCT
ejpam-4944	397	27	which	which	PRON
ejpam-4944	397	28	implies	imply	VERB
ejpam-4944	397	29	i2(q	i2(q	PROPN
ejpam-4944	397	30	)	)	PUNCT
ejpam-4944	397	31	∈	∈	PROPN
ejpam-4944	397	32	µ̃2	µ̃2	PROPN
ejpam-4944	397	33	which	which	DET
ejpam-4944	397	34	turn	turn	VERB
ejpam-4944	397	35	implies	imply	VERB
ejpam-4944	397	36	that	that	SCONJ
ejpam-4944	397	37	i2(q)∩	i2(q)∩	VERB
ejpam-4944	398	1	i2h	i2h	VERB
ejpam-4944	398	2	̸=	̸=	PROPN
ejpam-4944	398	3	∅.	∅.	ADV
ejpam-4944	398	4	thus	thus	ADV
ejpam-4944	398	5	,	,	PUNCT
ejpam-4944	398	6	q∩	q∩	PROPN
ejpam-4944	398	7	i2h	i2h	X
ejpam-4944	398	8	̸=	̸=	PROPN
ejpam-4944	398	9	∅.	∅.	VERB
ejpam-4944	398	10	therefore	therefore	ADV
ejpam-4944	398	11	,	,	PUNCT
ejpam-4944	398	12	c1q	c1q	ADP
ejpam-4944	398	13	∩h	∩h	PROPN
ejpam-4944	398	14	̸=	̸=	PROPN
ejpam-4944	398	15	∅.	∅.	PRON
ejpam-4944	398	16	hence	hence	ADV
ejpam-4944	398	17	q	q	NOUN
ejpam-4944	398	18	∈	∈	PROPN
ejpam-4944	398	19	(	(	PUNCT
ejpam-4944	398	20	2	2	NUM
ejpam-4944	398	21	,	,	PUNCT
ejpam-4944	398	22	1)⋆	1)⋆	PROPN
ejpam-4944	398	23	−d(x	−d(x	NOUN
ejpam-4944	398	24	)	)	PUNCT
ejpam-4944	398	25	.	.	PUNCT
ejpam-4944	399	1	(	(	PUNCT
ejpam-4944	399	2	b	b	NOUN
ejpam-4944	399	3	)	)	PUNCT
ejpam-4944	399	4	.	.	PUNCT
ejpam-4944	400	1	let	let	VERB
ejpam-4944	400	2	p	p	PRON
ejpam-4944	400	3	be	be	AUX
ejpam-4944	400	4	a	a	DET
ejpam-4944	400	5	non	non	ADJ
ejpam-4944	400	6	-	-	ADJ
ejpam-4944	400	7	null	null	ADJ
ejpam-4944	400	8	µs	µs	NOUN
ejpam-4944	400	9	-	-	PUNCT
ejpam-4944	400	10	preopen	preopen	ADJ
ejpam-4944	400	11	set	set	NOUN
ejpam-4944	400	12	.	.	PUNCT
ejpam-4944	401	1	then	then	ADV
ejpam-4944	401	2	p	p	PROPN
ejpam-4944	401	3	is	be	AUX
ejpam-4944	401	4	µ2	µ2	ADJ
ejpam-4944	401	5	-	-	PUNCT
ejpam-4944	401	6	preopen	preopen	NOUN
ejpam-4944	401	7	set	set	NOUN
ejpam-4944	401	8	in	in	ADP
ejpam-4944	401	9	x.	x.	NOUN
ejpam-4944	401	10	let	let	VERB
ejpam-4944	401	11	g	g	PROPN
ejpam-4944	401	12	∈	∈	PROPN
ejpam-4944	401	13	σ̃2	σ̃2	PROPN
ejpam-4944	401	14	.	.	PUNCT
ejpam-4944	402	1	if	if	SCONJ
ejpam-4944	402	2	g	g	PROPN
ejpam-4944	402	3	∈	∈	PROPN
ejpam-4944	402	4	µ̃2	µ̃2	PROPN
ejpam-4944	402	5	,	,	PUNCT
ejpam-4944	402	6	then	then	ADV
ejpam-4944	402	7	the	the	DET
ejpam-4944	402	8	proof	proof	NOUN
ejpam-4944	402	9	is	be	AUX
ejpam-4944	402	10	trivial	trivial	ADJ
ejpam-4944	402	11	.	.	PUNCT
ejpam-4944	403	1	assume	assume	VERB
ejpam-4944	403	2	that	that	SCONJ
ejpam-4944	403	3	,	,	PUNCT
ejpam-4944	403	4	g	g	NOUN
ejpam-4944	403	5	/∈	/∈	PUNCT
ejpam-4944	404	1	µ̃2	µ̃2	PROPN
ejpam-4944	404	2	.	.	PUNCT
ejpam-4944	405	1	here	here	ADV
ejpam-4944	405	2	g	g	PROPN
ejpam-4944	405	3	⊂	⊂	PROPN
ejpam-4944	405	4	c2(i2(g	c2(i2(g	PUNCT
ejpam-4944	405	5	)	)	PUNCT
ejpam-4944	405	6	)	)	PUNCT
ejpam-4944	405	7	which	which	PRON
ejpam-4944	405	8	implies	imply	VERB
ejpam-4944	405	9	i2(g	i2(g	NUM
ejpam-4944	405	10	)	)	PUNCT
ejpam-4944	405	11	∈	∈	PROPN
ejpam-4944	405	12	µ̃2	µ̃2	PROPN
ejpam-4944	405	13	,	,	PUNCT
ejpam-4944	405	14	by	by	ADP
ejpam-4944	405	15	our	our	PRON
ejpam-4944	405	16	assumption	assumption	NOUN
ejpam-4944	405	17	which	which	DET
ejpam-4944	405	18	turn	turn	VERB
ejpam-4944	405	19	implies	imply	VERB
ejpam-4944	405	20	that	that	SCONJ
ejpam-4944	405	21	i2	i2	PROPN
ejpam-4944	405	22	g	g	PROPN
ejpam-4944	405	23	is	be	AUX
ejpam-4944	405	24	a	a	DET
ejpam-4944	405	25	µ2	µ2	ADJ
ejpam-4944	405	26	-	-	PUNCT
ejpam-4944	405	27	dense	dense	ADJ
ejpam-4944	405	28	set	set	NOUN
ejpam-4944	405	29	in	in	ADP
ejpam-4944	405	30	x.	x.	NOUN
ejpam-4944	405	31	also	also	ADV
ejpam-4944	405	32	,	,	PUNCT
ejpam-4944	405	33	p	p	PROPN
ejpam-4944	405	34	⊂	⊂	X
ejpam-4944	405	35	i2(c2(p	i2(c2(p	PROPN
ejpam-4944	405	36	)	)	PUNCT
ejpam-4944	405	37	)	)	PUNCT
ejpam-4944	406	1	so	so	SCONJ
ejpam-4944	406	2	that	that	SCONJ
ejpam-4944	406	3	i2(c2(p	i2(c2(p	NUM
ejpam-4944	406	4	)	)	PUNCT
ejpam-4944	406	5	)	)	PUNCT
ejpam-4944	407	1	∈	∈	PROPN
ejpam-4944	407	2	µ̃2	µ̃2	PROPN
ejpam-4944	407	3	for	for	ADP
ejpam-4944	407	4	that	that	DET
ejpam-4944	407	5	i2(c2(p	i2(c2(p	PROPN
ejpam-4944	407	6	)	)	PUNCT
ejpam-4944	407	7	)	)	PUNCT
ejpam-4944	407	8	∩	∩	NOUN
ejpam-4944	407	9	i2	i2	PROPN
ejpam-4944	407	10	g	g	PROPN
ejpam-4944	407	11	̸=	̸=	PROPN
ejpam-4944	407	12	∅.	∅.	ADP
ejpam-4944	407	13	thus	thus	ADV
ejpam-4944	407	14	,	,	PUNCT
ejpam-4944	407	15	c2p	c2p	NOUN
ejpam-4944	407	16	∩	∩	NOUN
ejpam-4944	407	17	i2	i2	PROPN
ejpam-4944	407	18	g	g	PROPN
ejpam-4944	407	19	̸=	̸=	PROPN
ejpam-4944	407	20	∅	∅	NOUN
ejpam-4944	407	21	so	so	SCONJ
ejpam-4944	407	22	that	that	SCONJ
ejpam-4944	407	23	p	p	PROPN
ejpam-4944	407	24	∩	∩	ADJ
ejpam-4944	407	25	i2	i2	PROPN
ejpam-4944	407	26	g	g	PROPN
ejpam-4944	407	27	̸=	̸=	PROPN
ejpam-4944	407	28	∅	∅	NOUN
ejpam-4944	407	29	,	,	PUNCT
ejpam-4944	407	30	by	by	ADP
ejpam-4944	407	31	lemma	lemma	PROPN
ejpam-4944	407	32	3	3	NUM
ejpam-4944	407	33	.	.	PUNCT
ejpam-4944	407	34	therefore	therefore	ADV
ejpam-4944	407	35	,	,	PUNCT
ejpam-4944	407	36	c1p	c1p	NOUN
ejpam-4944	407	37	∩g	∩g	PUNCT
ejpam-4944	407	38	̸=	̸=	PROPN
ejpam-4944	407	39	∅.	∅.	PRON
ejpam-4944	407	40	hence	hence	ADV
ejpam-4944	407	41	p	p	NOUN
ejpam-4944	407	42	∈	∈	PROPN
ejpam-4944	407	43	(	(	PUNCT
ejpam-4944	407	44	2	2	NUM
ejpam-4944	407	45	,	,	PUNCT
ejpam-4944	407	46	1)⋆	1)⋆	PROPN
ejpam-4944	407	47	−d(x	−d(x	NOUN
ejpam-4944	407	48	)	)	PUNCT
ejpam-4944	407	49	.	.	PUNCT
ejpam-4944	408	1	(	(	PUNCT
ejpam-4944	408	2	c	c	NOUN
ejpam-4944	408	3	)	)	PUNCT
ejpam-4944	408	4	.	.	PUNCT
ejpam-4944	409	1	let	let	VERB
ejpam-4944	409	2	k	k	PRON
ejpam-4944	409	3	be	be	AUX
ejpam-4944	409	4	a	a	DET
ejpam-4944	409	5	non	non	ADJ
ejpam-4944	409	6	-	-	ADJ
ejpam-4944	409	7	null	null	ADJ
ejpam-4944	409	8	µs	µs	NOUN
ejpam-4944	409	9	-	-	PUNCT
ejpam-4944	409	10	α	α	PRON
ejpam-4944	409	11	-	-	ADJ
ejpam-4944	409	12	open	open	ADJ
ejpam-4944	409	13	set	set	NOUN
ejpam-4944	409	14	.	.	PUNCT
ejpam-4944	410	1	then	then	ADV
ejpam-4944	410	2	k	k	PROPN
ejpam-4944	410	3	is	be	AUX
ejpam-4944	410	4	µ2	µ2	PROPN
ejpam-4944	410	5	-	-	PUNCT
ejpam-4944	410	6	α	α	NOUN
ejpam-4944	410	7	-	-	ADJ
ejpam-4944	410	8	open	open	ADJ
ejpam-4944	410	9	set	set	NOUN
ejpam-4944	410	10	in	in	ADP
ejpam-4944	410	11	x	x	ADP
ejpam-4944	410	12	which	which	PRON
ejpam-4944	410	13	implies	imply	VERB
ejpam-4944	410	14	k	k	PROPN
ejpam-4944	410	15	is	be	AUX
ejpam-4944	410	16	µ2	µ2	ADJ
ejpam-4944	410	17	-	-	PUNCT
ejpam-4944	410	18	semi	semi	ADV
ejpam-4944	410	19	-	-	ADJ
ejpam-4944	410	20	open	open	ADJ
ejpam-4944	410	21	set	set	NOUN
ejpam-4944	410	22	.	.	PUNCT
ejpam-4944	411	1	hence	hence	ADV
ejpam-4944	411	2	k	k	PROPN
ejpam-4944	411	3	∈	∈	PROPN
ejpam-4944	411	4	(	(	PUNCT
ejpam-4944	411	5	2	2	NUM
ejpam-4944	411	6	,	,	PUNCT
ejpam-4944	411	7	1)⋆	1)⋆	PROPN
ejpam-4944	411	8	−d(x	−d(x	NOUN
ejpam-4944	411	9	)	)	PUNCT
ejpam-4944	411	10	,	,	PUNCT
ejpam-4944	411	11	by	by	ADP
ejpam-4944	411	12	(	(	PUNCT
ejpam-4944	411	13	a	a	NOUN
ejpam-4944	411	14	)	)	PUNCT
ejpam-4944	411	15	.	.	PUNCT
ejpam-4944	412	1	(	(	PUNCT
ejpam-4944	412	2	d	d	NOUN
ejpam-4944	412	3	)	)	PUNCT
ejpam-4944	412	4	.	.	PUNCT
ejpam-4944	413	1	choose	choose	VERB
ejpam-4944	413	2	l	l	NOUN
ejpam-4944	413	3	be	be	AUX
ejpam-4944	413	4	a	a	DET
ejpam-4944	413	5	non	non	ADJ
ejpam-4944	413	6	-	-	ADJ
ejpam-4944	413	7	null	null	ADJ
ejpam-4944	413	8	µs	µs	NOUN
ejpam-4944	413	9	-	-	PUNCT
ejpam-4944	413	10	β	β	NOUN
ejpam-4944	413	11	-	-	ADJ
ejpam-4944	413	12	open	open	ADJ
ejpam-4944	413	13	set	set	NOUN
ejpam-4944	413	14	.	.	PUNCT
ejpam-4944	414	1	then	then	ADV
ejpam-4944	414	2	l	l	PROPN
ejpam-4944	414	3	is	be	AUX
ejpam-4944	414	4	µ2	µ2	ADJ
ejpam-4944	414	5	-	-	PUNCT
ejpam-4944	414	6	β	β	NOUN
ejpam-4944	414	7	-	-	ADJ
ejpam-4944	414	8	open	open	ADJ
ejpam-4944	414	9	set	set	NOUN
ejpam-4944	414	10	in	in	ADP
ejpam-4944	414	11	x.	x.	NOUN
ejpam-4944	414	12	let	let	VERB
ejpam-4944	414	13	m	m	PROPN
ejpam-4944	414	14	∈	∈	PROPN
ejpam-4944	414	15	σ̃2	σ̃2	PROPN
ejpam-4944	414	16	.	.	PUNCT
ejpam-4944	415	1	if	if	SCONJ
ejpam-4944	415	2	m	m	VERB
ejpam-4944	415	3	∈	∈	PROPN
ejpam-4944	415	4	µ̃2	µ̃2	PROPN
ejpam-4944	415	5	,	,	PUNCT
ejpam-4944	415	6	then	then	ADV
ejpam-4944	415	7	there	there	PRON
ejpam-4944	415	8	is	be	VERB
ejpam-4944	415	9	nothing	nothing	PRON
ejpam-4944	415	10	to	to	PART
ejpam-4944	415	11	prove	prove	VERB
ejpam-4944	415	12	.	.	PUNCT
ejpam-4944	416	1	suppose	suppose	VERB
ejpam-4944	416	2	m	m	VERB
ejpam-4944	416	3	/∈	/∈	PUNCT
ejpam-4944	417	1	µ̃2	µ̃2	PROPN
ejpam-4944	417	2	.	.	PUNCT
ejpam-4944	418	1	since	since	SCONJ
ejpam-4944	418	2	m	m	PROPN
ejpam-4944	418	3	⊂	⊂	PROPN
ejpam-4944	418	4	c2(i2(m	c2(i2(m	NOUN
ejpam-4944	418	5	)	)	PUNCT
ejpam-4944	418	6	)	)	PUNCT
ejpam-4944	418	7	we	we	PRON
ejpam-4944	418	8	have	have	VERB
ejpam-4944	418	9	i2(m	i2(m	NOUN
ejpam-4944	418	10	)	)	PUNCT
ejpam-4944	418	11	∈	∈	PROPN
ejpam-4944	418	12	µ̃2	µ̃2	PROPN
ejpam-4944	418	13	,	,	PUNCT
ejpam-4944	418	14	by	by	ADP
ejpam-4944	418	15	our	our	PRON
ejpam-4944	418	16	assumption	assumption	NOUN
ejpam-4944	418	17	.	.	PUNCT
ejpam-4944	419	1	by	by	ADP
ejpam-4944	419	2	our	our	PRON
ejpam-4944	419	3	assumption	assumption	NOUN
ejpam-4944	419	4	,	,	PUNCT
ejpam-4944	419	5	i2	i2	PROPN
ejpam-4944	419	6	m	m	PROPN
ejpam-4944	419	7	is	be	AUX
ejpam-4944	419	8	a	a	DET
ejpam-4944	419	9	µ2	µ2	ADJ
ejpam-4944	419	10	-	-	PUNCT
ejpam-4944	419	11	dense	dense	ADJ
ejpam-4944	419	12	set	set	NOUN
ejpam-4944	419	13	in	in	ADP
ejpam-4944	419	14	x.	x.	NOUN
ejpam-4944	419	15	also	also	ADV
ejpam-4944	419	16	,	,	PUNCT
ejpam-4944	419	17	l	l	PROPN
ejpam-4944	419	18	⊂	⊂	PROPN
ejpam-4944	419	19	c2(i2(c2(l	c2(i2(c2(l	NOUN
ejpam-4944	419	20	)	)	PUNCT
ejpam-4944	419	21	)	)	PUNCT
ejpam-4944	419	22	)	)	PUNCT
ejpam-4944	419	23	for	for	ADP
ejpam-4944	419	24	that	that	DET
ejpam-4944	419	25	i2(c2(l	i2(c2(l	NOUN
ejpam-4944	419	26	)	)	PUNCT
ejpam-4944	419	27	)	)	PUNCT
ejpam-4944	420	1	∈	∈	PROPN
ejpam-4944	420	2	µ̃2	µ̃2	PROPN
ejpam-4944	420	3	which	which	DET
ejpam-4944	420	4	turn	turn	VERB
ejpam-4944	420	5	implies	imply	VERB
ejpam-4944	420	6	that	that	SCONJ
ejpam-4944	420	7	i2(c2(l	i2(c2(l	NOUN
ejpam-4944	420	8	)	)	PUNCT
ejpam-4944	420	9	)	)	PUNCT
ejpam-4944	420	10	∩	∩	PROPN
ejpam-4944	420	11	i2	i2	PROPN
ejpam-4944	420	12	m	m	PROPN
ejpam-4944	420	13	̸=	̸=	PROPN
ejpam-4944	420	14	∅.	∅.	ADV
ejpam-4944	420	15	thus	thus	ADV
ejpam-4944	420	16	,	,	PUNCT
ejpam-4944	420	17	c2l	c2l	PROPN
ejpam-4944	420	18	∩	∩	PROPN
ejpam-4944	420	19	i2	i2	PROPN
ejpam-4944	420	20	m	m	PROPN
ejpam-4944	420	21	̸=	̸=	PROPN
ejpam-4944	420	22	∅	∅	NOUN
ejpam-4944	420	23	so	so	SCONJ
ejpam-4944	420	24	that	that	SCONJ
ejpam-4944	420	25	l	l	NOUN
ejpam-4944	420	26	∩	∩	PROPN
ejpam-4944	420	27	i2	i2	PROPN
ejpam-4944	420	28	m	m	PROPN
ejpam-4944	420	29	̸=	̸=	PROPN
ejpam-4944	420	30	∅	∅	NOUN
ejpam-4944	420	31	,	,	PUNCT
ejpam-4944	420	32	by	by	ADP
ejpam-4944	420	33	lemma	lemma	PROPN
ejpam-4944	420	34	3	3	NUM
ejpam-4944	420	35	.	.	PUNCT
ejpam-4944	421	1	therefore	therefore	ADV
ejpam-4944	421	2	,	,	PUNCT
ejpam-4944	421	3	c1l	c1l	PROPN
ejpam-4944	421	4	∩m	∩m	PROPN
ejpam-4944	421	5	̸=	̸=	PROPN
ejpam-4944	421	6	∅.	∅.	PRON
ejpam-4944	421	7	hence	hence	ADV
ejpam-4944	421	8	l	l	NOUN
ejpam-4944	421	9	∈	∈	PROPN
ejpam-4944	421	10	(	(	PUNCT
ejpam-4944	421	11	2	2	NUM
ejpam-4944	421	12	,	,	PUNCT
ejpam-4944	421	13	1)⋆	1)⋆	PROPN
ejpam-4944	421	14	−d(x	−d(x	NOUN
ejpam-4944	421	15	)	)	PUNCT
ejpam-4944	421	16	.	.	PUNCT
ejpam-4944	422	1	(	(	PUNCT
ejpam-4944	422	2	e	e	NOUN
ejpam-4944	422	3	)	)	PUNCT
ejpam-4944	422	4	.	.	PUNCT
ejpam-4944	423	1	take	take	VERB
ejpam-4944	423	2	f	f	PRON
ejpam-4944	423	3	be	be	AUX
ejpam-4944	423	4	a	a	DET
ejpam-4944	423	5	non	non	ADJ
ejpam-4944	423	6	-	-	ADJ
ejpam-4944	423	7	null	null	ADJ
ejpam-4944	423	8	µs	µs	NOUN
ejpam-4944	423	9	-	-	PUNCT
ejpam-4944	423	10	b	b	NOUN
ejpam-4944	423	11	-	-	PUNCT
ejpam-4944	423	12	open	open	ADJ
ejpam-4944	423	13	set	set	NOUN
ejpam-4944	423	14	.	.	PUNCT
ejpam-4944	424	1	we	we	PRON
ejpam-4944	424	2	get	get	VERB
ejpam-4944	424	3	f	f	PROPN
ejpam-4944	424	4	is	be	AUX
ejpam-4944	424	5	µ2	µ2	PROPN
ejpam-4944	424	6	-	-	PUNCT
ejpam-4944	424	7	b	b	NOUN
ejpam-4944	424	8	-	-	PUNCT
ejpam-4944	424	9	open	open	ADJ
ejpam-4944	424	10	set	set	NOUN
ejpam-4944	424	11	inx	inx	PROPN
ejpam-4944	424	12	.	.	PUNCT
ejpam-4944	425	1	let	let	VERB
ejpam-4944	425	2	v	v	NUM
ejpam-4944	425	3	∈	∈	PROPN
ejpam-4944	425	4	σ̃2	σ̃2	PROPN
ejpam-4944	425	5	.	.	PUNCT
ejpam-4944	426	1	if	if	SCONJ
ejpam-4944	426	2	v	v	NUM
ejpam-4944	426	3	∈	∈	PROPN
ejpam-4944	427	1	µ̃2	µ̃2	PROPN
ejpam-4944	427	2	,	,	PUNCT
ejpam-4944	427	3	then	then	ADV
ejpam-4944	427	4	the	the	DET
ejpam-4944	427	5	proof	proof	NOUN
ejpam-4944	427	6	is	be	AUX
ejpam-4944	427	7	obvious	obvious	ADJ
ejpam-4944	427	8	.	.	PUNCT
ejpam-4944	428	1	assume	assume	VERB
ejpam-4944	428	2	that	that	SCONJ
ejpam-4944	428	3	,	,	PUNCT
ejpam-4944	428	4	v	v	NOUN
ejpam-4944	428	5	/∈	/∈	PUNCT
ejpam-4944	429	1	µ̃2	µ̃2	PROPN
ejpam-4944	429	2	then	then	ADV
ejpam-4944	429	3	v	v	ADP
ejpam-4944	429	4	⊂	⊂	PROPN
ejpam-4944	429	5	c2(i2(v	c2(i2(v	NOUN
ejpam-4944	429	6	)	)	PUNCT
ejpam-4944	429	7	)	)	PUNCT
ejpam-4944	430	1	so	so	SCONJ
ejpam-4944	430	2	that	that	SCONJ
ejpam-4944	430	3	i2(v	i2(v	PRON
ejpam-4944	430	4	)	)	PUNCT
ejpam-4944	430	5	∈	∈	PROPN
ejpam-4944	430	6	µ̃2	µ̃2	PROPN
ejpam-4944	430	7	,	,	PUNCT
ejpam-4944	430	8	by	by	ADP
ejpam-4944	430	9	our	our	PRON
ejpam-4944	430	10	assumption	assumption	NOUN
ejpam-4944	430	11	.	.	PUNCT
ejpam-4944	431	1	thus	thus	ADV
ejpam-4944	431	2	,	,	PUNCT
ejpam-4944	431	3	i2v	i2v	PRON
ejpam-4944	431	4	is	be	AUX
ejpam-4944	431	5	a	a	DET
ejpam-4944	431	6	µ2	µ2	ADJ
ejpam-4944	431	7	-	-	PUNCT
ejpam-4944	431	8	dense	dense	ADJ
ejpam-4944	431	9	set	set	NOUN
ejpam-4944	431	10	in	in	ADP
ejpam-4944	431	11	x.	x.	NOUN
ejpam-4944	431	12	here	here	ADV
ejpam-4944	431	13	,	,	PUNCT
ejpam-4944	431	14	f	f	PROPN
ejpam-4944	431	15	⊂	⊂	PROPN
ejpam-4944	431	16	c2(i2(f	c2(i2(f	PROPN
ejpam-4944	431	17	)	)	PUNCT
ejpam-4944	431	18	)	)	PUNCT
ejpam-4944	431	19	∪	∪	ADP
ejpam-4944	431	20	i2(c2(f	i2(c2(f	PROPN
ejpam-4944	431	21	)	)	PUNCT
ejpam-4944	431	22	)	)	PUNCT
ejpam-4944	432	1	which	which	PRON
ejpam-4944	432	2	implies	imply	VERB
ejpam-4944	432	3	(	(	PUNCT
ejpam-4944	432	4	1	1	NUM
ejpam-4944	432	5	)	)	PUNCT
ejpam-4944	432	6	i2(c2(f	i2(c2(f	PROPN
ejpam-4944	432	7	)	)	PUNCT
ejpam-4944	432	8	)	)	PUNCT
ejpam-4944	433	1	∈	∈	PROPN
ejpam-4944	433	2	µ̃2	µ̃2	PROPN
ejpam-4944	433	3	or	or	CCONJ
ejpam-4944	433	4	(	(	PUNCT
ejpam-4944	433	5	2	2	NUM
ejpam-4944	433	6	)	)	PUNCT
ejpam-4944	433	7	i2(f	i2(f	X
ejpam-4944	433	8	)	)	PUNCT
ejpam-4944	433	9	∈	∈	PROPN
ejpam-4944	433	10	µ̃2	µ̃2	PROPN
ejpam-4944	433	11	or	or	CCONJ
ejpam-4944	433	12	(	(	PUNCT
ejpam-4944	433	13	3	3	NUM
ejpam-4944	433	14	)	)	PUNCT
ejpam-4944	433	15	i2(c2(f	i2(c2(f	NUM
ejpam-4944	433	16	)	)	PUNCT
ejpam-4944	433	17	)	)	PUNCT
ejpam-4944	434	1	∈	∈	PROPN
ejpam-4944	434	2	µ̃2	µ̃2	PROPN
ejpam-4944	434	3	and	and	CCONJ
ejpam-4944	434	4	i2(f	i2(f	PROPN
ejpam-4944	434	5	)	)	PUNCT
ejpam-4944	434	6	∈	∈	PROPN
ejpam-4944	434	7	µ̃2	µ̃2	PROPN
ejpam-4944	434	8	from	from	ADP
ejpam-4944	434	9	the	the	DET
ejpam-4944	434	10	above	above	ADJ
ejpam-4944	434	11	three	three	NUM
ejpam-4944	434	12	cases	case	NOUN
ejpam-4944	434	13	,	,	PUNCT
ejpam-4944	434	14	we	we	PRON
ejpam-4944	434	15	get	get	VERB
ejpam-4944	434	16	f	f	NOUN
ejpam-4944	434	17	∩	∩	NOUN
ejpam-4944	434	18	i2v	i2v	PRON
ejpam-4944	434	19	̸=	̸=	PROPN
ejpam-4944	434	20	∅.	∅.	VERB
ejpam-4944	434	21	therefore	therefore	ADV
ejpam-4944	434	22	,	,	PUNCT
ejpam-4944	434	23	c1f	c1f	PROPN
ejpam-4944	434	24	∩	∩	NOUN
ejpam-4944	434	25	v	v	ADP
ejpam-4944	434	26	̸=	̸=	PROPN
ejpam-4944	434	27	∅.	∅.	PRON
ejpam-4944	434	28	hence	hence	ADV
ejpam-4944	434	29	f	f	PROPN
ejpam-4944	434	30	∈	∈	PROPN
ejpam-4944	434	31	(	(	PUNCT
ejpam-4944	434	32	2	2	NUM
ejpam-4944	434	33	,	,	PUNCT
ejpam-4944	434	34	1)⋆	1)⋆	PROPN
ejpam-4944	434	35	−d(x	−d(x	NOUN
ejpam-4944	434	36	)	)	PUNCT
ejpam-4944	434	37	.	.	PUNCT
ejpam-4944	435	1	by	by	ADP
ejpam-4944	435	2	similar	similar	ADJ
ejpam-4944	435	3	considerations	consideration	NOUN
ejpam-4944	435	4	,	,	PUNCT
ejpam-4944	435	5	we	we	PRON
ejpam-4944	435	6	can	can	AUX
ejpam-4944	435	7	prove	prove	VERB
ejpam-4944	435	8	this	this	DET
ejpam-4944	435	9	theorem	theorem	NOUN
ejpam-4944	435	10	for	for	ADP
ejpam-4944	435	11	the	the	DET
ejpam-4944	435	12	case	case	NOUN
ejpam-4944	435	13	s	s	PART
ejpam-4944	435	14	=	=	SYM
ejpam-4944	435	15	1	1	NUM
ejpam-4944	435	16	and	and	CCONJ
ejpam-4944	435	17	v	v	NOUN
ejpam-4944	435	18	=	=	SYM
ejpam-4944	435	19	2	2	X
ejpam-4944	435	20	.	.	X
ejpam-4944	435	21	d.	d.	PROPN
ejpam-4944	435	22	elgezouli	elgezouli	PROPN
ejpam-4944	435	23	et	et	PROPN
ejpam-4944	435	24	al	al	PROPN
ejpam-4944	435	25	.	.	PUNCT
ejpam-4944	435	26	/	/	SYM
ejpam-4944	435	27	eur	eur	PROPN
ejpam-4944	435	28	.	.	PUNCT
ejpam-4944	436	1	j.	j.	PROPN
ejpam-4944	436	2	pure	pure	PROPN
ejpam-4944	436	3	appl	appl	PROPN
ejpam-4944	436	4	.	.	PROPN
ejpam-4944	436	5	math	math	PROPN
ejpam-4944	436	6	,	,	PUNCT
ejpam-4944	436	7	16	16	NUM
ejpam-4944	436	8	(	(	PUNCT
ejpam-4944	436	9	4	4	NUM
ejpam-4944	436	10	)	)	PUNCT
ejpam-4944	436	11	(	(	PUNCT
ejpam-4944	436	12	2023	2023	NUM
ejpam-4944	436	13	)	)	PUNCT
ejpam-4944	436	14	,	,	PUNCT
ejpam-4944	436	15	2286	2286	NUM
ejpam-4944	436	16	-	-	SYM
ejpam-4944	436	17	2305	2305	NUM
ejpam-4944	436	18	2298	2298	NUM
ejpam-4944	436	19	theorem	theorem	VERB
ejpam-4944	436	20	30	30	NUM
ejpam-4944	436	21	.	.	PUNCT
ejpam-4944	437	1	let	let	AUX
ejpam-4944	437	2	(	(	PUNCT
ejpam-4944	437	3	x,µ1	x,µ1	NOUN
ejpam-4944	437	4	,	,	PUNCT
ejpam-4944	437	5	µ2	µ2	PROPN
ejpam-4944	437	6	)	)	PUNCT
ejpam-4944	437	7	be	be	AUX
ejpam-4944	437	8	a	a	DET
ejpam-4944	437	9	bgts	bgts	NOUN
ejpam-4944	437	10	.	.	PUNCT
ejpam-4944	438	1	if	if	SCONJ
ejpam-4944	438	2	(	(	PUNCT
ejpam-4944	438	3	x,µs	x,µs	NUM
ejpam-4944	438	4	)	)	PUNCT
ejpam-4944	438	5	is	be	AUX
ejpam-4944	438	6	a	a	DET
ejpam-4944	438	7	hyperconnected	hyperconnecte	VERB
ejpam-4944	438	8	space	space	NOUN
ejpam-4944	438	9	and	and	CCONJ
ejpam-4944	438	10	if	if	SCONJ
ejpam-4944	438	11	µs	µs	NOUN
ejpam-4944	438	12	is	be	AUX
ejpam-4944	438	13	a	a	DET
ejpam-4944	438	14	sgt	sgt	NOUN
ejpam-4944	438	15	for	for	ADP
ejpam-4944	438	16	s	s	NOUN
ejpam-4944	438	17	=	=	SYM
ejpam-4944	438	18	1	1	NUM
ejpam-4944	438	19	,	,	PUNCT
ejpam-4944	438	20	2	2	NUM
ejpam-4944	438	21	,	,	PUNCT
ejpam-4944	438	22	then	then	ADV
ejpam-4944	438	23	(	(	PUNCT
ejpam-4944	438	24	a	a	X
ejpam-4944	438	25	)	)	PUNCT
ejpam-4944	438	26	every	every	DET
ejpam-4944	438	27	non	non	ADJ
ejpam-4944	438	28	-	-	ADJ
ejpam-4944	438	29	null	null	ADJ
ejpam-4944	438	30	(	(	PUNCT
ejpam-4944	438	31	s	s	PROPN
ejpam-4944	438	32	,	,	PUNCT
ejpam-4944	438	33	v)-µ-pre	v)-µ-pre	ADJ
ejpam-4944	438	34	-	-	ADJ
ejpam-4944	438	35	open	open	ADJ
ejpam-4944	438	36	set	set	NOUN
ejpam-4944	438	37	is	be	AUX
ejpam-4944	438	38	(	(	PUNCT
ejpam-4944	438	39	s	s	X
ejpam-4944	438	40	,	,	PUNCT
ejpam-4944	438	41	v)⋆-dense	v)⋆-dense	PROPN
ejpam-4944	438	42	.	.	PUNCT
ejpam-4944	439	1	(	(	PUNCT
ejpam-4944	439	2	b	b	X
ejpam-4944	439	3	)	)	PUNCT
ejpam-4944	439	4	every	every	DET
ejpam-4944	439	5	non	non	ADJ
ejpam-4944	439	6	-	-	ADJ
ejpam-4944	439	7	null	null	ADJ
ejpam-4944	439	8	(	(	PUNCT
ejpam-4944	439	9	s	s	NOUN
ejpam-4944	439	10	,	,	PUNCT
ejpam-4944	439	11	v)-µ-α	v)-µ-α	NOUN
ejpam-4944	439	12	-	-	PUNCT
ejpam-4944	439	13	open	open	ADJ
ejpam-4944	439	14	set	set	NOUN
ejpam-4944	439	15	is	be	AUX
ejpam-4944	439	16	(	(	PUNCT
ejpam-4944	439	17	s	s	X
ejpam-4944	439	18	,	,	PUNCT
ejpam-4944	439	19	v)⋆-dense	v)⋆-dense	PROPN
ejpam-4944	439	20	where	where	SCONJ
ejpam-4944	439	21	s	s	X
ejpam-4944	439	22	,	,	PUNCT
ejpam-4944	439	23	v	v	NOUN
ejpam-4944	439	24	=	=	SYM
ejpam-4944	439	25	1	1	NUM
ejpam-4944	439	26	,	,	PUNCT
ejpam-4944	439	27	2	2	NUM
ejpam-4944	439	28	;	;	PUNCT
ejpam-4944	439	29	s	s	VERB
ejpam-4944	439	30	̸=	̸=	PROPN
ejpam-4944	439	31	v.	v.	ADP
ejpam-4944	439	32	proof	proof	NOUN
ejpam-4944	439	33	.	.	PUNCT
ejpam-4944	440	1	assume	assume	VERB
ejpam-4944	440	2	that	that	SCONJ
ejpam-4944	440	3	,	,	PUNCT
ejpam-4944	440	4	(	(	PUNCT
ejpam-4944	440	5	x,µs	x,µs	NUM
ejpam-4944	440	6	)	)	PUNCT
ejpam-4944	440	7	is	be	AUX
ejpam-4944	440	8	a	a	DET
ejpam-4944	440	9	hyperconnected	hyperconnecte	VERB
ejpam-4944	440	10	space	space	NOUN
ejpam-4944	440	11	and	and	CCONJ
ejpam-4944	440	12	µs	µs	NOUN
ejpam-4944	440	13	is	be	AUX
ejpam-4944	440	14	a	a	DET
ejpam-4944	440	15	strong	strong	ADJ
ejpam-4944	440	16	generalized	generalized	ADJ
ejpam-4944	440	17	topological	topological	ADJ
ejpam-4944	440	18	space	space	NOUN
ejpam-4944	440	19	for	for	ADP
ejpam-4944	440	20	s	s	NOUN
ejpam-4944	440	21	=	=	SYM
ejpam-4944	440	22	1	1	NUM
ejpam-4944	440	23	,	,	PUNCT
ejpam-4944	440	24	2	2	NUM
ejpam-4944	440	25	.	.	X
ejpam-4944	440	26	take	take	VERB
ejpam-4944	440	27	s	s	NOUN
ejpam-4944	440	28	=	=	SYM
ejpam-4944	440	29	2	2	NUM
ejpam-4944	440	30	and	and	CCONJ
ejpam-4944	440	31	v	v	NOUN
ejpam-4944	440	32	=	=	SYM
ejpam-4944	440	33	1	1	NUM
ejpam-4944	440	34	.	.	PUNCT
ejpam-4944	441	1	then	then	ADV
ejpam-4944	441	2	(	(	PUNCT
ejpam-4944	441	3	x,µ2	x,µ2	PROPN
ejpam-4944	441	4	)	)	PUNCT
ejpam-4944	441	5	is	be	AUX
ejpam-4944	441	6	a	a	DET
ejpam-4944	441	7	hyperconnected	hyperconnected	ADJ
ejpam-4944	441	8	space	space	NOUN
ejpam-4944	441	9	,	,	PUNCT
ejpam-4944	441	10	µ2	µ2	PROPN
ejpam-4944	441	11	is	be	AUX
ejpam-4944	441	12	a	a	DET
ejpam-4944	441	13	sgt	sgt	PROPN
ejpam-4944	441	14	.	.	PUNCT
ejpam-4944	442	1	(	(	PUNCT
ejpam-4944	442	2	a	a	X
ejpam-4944	442	3	)	)	PUNCT
ejpam-4944	442	4	.	.	PUNCT
ejpam-4944	443	1	let	let	VERB
ejpam-4944	443	2	q	q	PRON
ejpam-4944	443	3	be	be	AUX
ejpam-4944	443	4	a	a	DET
ejpam-4944	443	5	non	non	ADJ
ejpam-4944	443	6	-	-	ADJ
ejpam-4944	443	7	null	null	ADJ
ejpam-4944	443	8	(	(	PUNCT
ejpam-4944	443	9	s	s	PROPN
ejpam-4944	443	10	,	,	PUNCT
ejpam-4944	443	11	v)-µ-pre	v)-µ-pre	ADJ
ejpam-4944	443	12	-	-	ADJ
ejpam-4944	443	13	open	open	ADJ
ejpam-4944	443	14	set	set	NOUN
ejpam-4944	443	15	where	where	SCONJ
ejpam-4944	443	16	s	s	X
ejpam-4944	443	17	,	,	PUNCT
ejpam-4944	443	18	v	v	NOUN
ejpam-4944	443	19	=	=	SYM
ejpam-4944	443	20	1	1	NUM
ejpam-4944	443	21	,	,	PUNCT
ejpam-4944	443	22	2	2	NUM
ejpam-4944	443	23	;	;	PUNCT
ejpam-4944	443	24	s	s	VERB
ejpam-4944	443	25	̸=	̸=	PROPN
ejpam-4944	443	26	v.	v.	ADV
ejpam-4944	443	27	then	then	ADV
ejpam-4944	443	28	q	q	X
ejpam-4944	443	29	is	be	AUX
ejpam-4944	443	30	(	(	PUNCT
ejpam-4944	443	31	2	2	NUM
ejpam-4944	443	32	,	,	PUNCT
ejpam-4944	443	33	1)µ-pre	1)µ-pre	NUM
ejpam-4944	443	34	-	-	NOUN
ejpam-4944	443	35	open	open	ADJ
ejpam-4944	443	36	.	.	PUNCT
ejpam-4944	444	1	let	let	VERB
ejpam-4944	444	2	k	k	PROPN
ejpam-4944	444	3	∈	∈	PROPN
ejpam-4944	444	4	σ̃2	σ̃2	PROPN
ejpam-4944	444	5	.	.	PUNCT
ejpam-4944	445	1	if	if	SCONJ
ejpam-4944	445	2	k	k	PROPN
ejpam-4944	445	3	∈	∈	PROPN
ejpam-4944	445	4	µ̃2	µ̃2	PROPN
ejpam-4944	445	5	,	,	PUNCT
ejpam-4944	445	6	then	then	ADV
ejpam-4944	445	7	there	there	PRON
ejpam-4944	445	8	is	be	VERB
ejpam-4944	445	9	nothing	nothing	PRON
ejpam-4944	445	10	to	to	PART
ejpam-4944	445	11	prove	prove	VERB
ejpam-4944	445	12	.	.	PUNCT
ejpam-4944	446	1	assume	assume	VERB
ejpam-4944	446	2	that	that	SCONJ
ejpam-4944	446	3	,	,	PUNCT
ejpam-4944	446	4	k	k	PROPN
ejpam-4944	446	5	/∈	/∈	PUNCT
ejpam-4944	447	1	µ̃2	µ̃2	PROPN
ejpam-4944	447	2	.	.	PUNCT
ejpam-4944	448	1	here	here	ADV
ejpam-4944	448	2	k	k	PROPN
ejpam-4944	448	3	⊂	⊂	PROPN
ejpam-4944	448	4	c2(i2(k	c2(i2(k	PROPN
ejpam-4944	448	5	)	)	PUNCT
ejpam-4944	448	6	)	)	PUNCT
ejpam-4944	448	7	.	.	PUNCT
ejpam-4944	449	1	by	by	ADP
ejpam-4944	449	2	our	our	PRON
ejpam-4944	449	3	assumption	assumption	NOUN
ejpam-4944	449	4	,	,	PUNCT
ejpam-4944	449	5	i2k	i2k	PRON
ejpam-4944	449	6	is	be	AUX
ejpam-4944	449	7	µ2	µ2	ADJ
ejpam-4944	449	8	-	-	PUNCT
ejpam-4944	449	9	dense	dense	ADJ
ejpam-4944	449	10	.	.	PUNCT
ejpam-4944	450	1	since	since	SCONJ
ejpam-4944	450	2	q	q	PROPN
ejpam-4944	450	3	⊂	⊂	PROPN
ejpam-4944	450	4	i2(c1(q	i2(c1(q	ADJ
ejpam-4944	450	5	)	)	PUNCT
ejpam-4944	450	6	)	)	PUNCT
ejpam-4944	450	7	we	we	PRON
ejpam-4944	450	8	have	have	VERB
ejpam-4944	450	9	i2(c1(q	i2(c1(q	ADJ
ejpam-4944	450	10	)	)	PUNCT
ejpam-4944	450	11	)	)	PUNCT
ejpam-4944	451	1	∈	∈	PROPN
ejpam-4944	451	2	µ̃2	µ̃2	PROPN
ejpam-4944	451	3	.	.	PUNCT
ejpam-4944	452	1	this	this	PRON
ejpam-4944	452	2	implies	imply	VERB
ejpam-4944	452	3	i2(c1(q	i2(c1(q	ADJ
ejpam-4944	452	4	)	)	PUNCT
ejpam-4944	452	5	)	)	PUNCT
ejpam-4944	453	1	∩	∩	NOUN
ejpam-4944	453	2	i2k	i2k	PRON
ejpam-4944	453	3	̸=	̸=	PROPN
ejpam-4944	453	4	∅	∅	NOUN
ejpam-4944	453	5	which	which	PRON
ejpam-4944	453	6	implies	imply	VERB
ejpam-4944	453	7	c1(q	c1(q	ADJ
ejpam-4944	453	8	)	)	PUNCT
ejpam-4944	453	9	∩	∩	NOUN
ejpam-4944	453	10	i2k	i2k	PRON
ejpam-4944	453	11	̸=	̸=	PROPN
ejpam-4944	453	12	∅	∅	NOUN
ejpam-4944	453	13	which	which	PRON
ejpam-4944	453	14	turn	turn	VERB
ejpam-4944	453	15	implies	imply	VERB
ejpam-4944	453	16	that	that	SCONJ
ejpam-4944	453	17	c1q	c1q	ADP
ejpam-4944	453	18	∩k	∩k	PRON
ejpam-4944	453	19	̸=	̸=	PROPN
ejpam-4944	453	20	∅.	∅.	PRON
ejpam-4944	453	21	hence	hence	ADV
ejpam-4944	453	22	q	q	NOUN
ejpam-4944	453	23	∈	∈	PROPN
ejpam-4944	453	24	(	(	PUNCT
ejpam-4944	453	25	2	2	NUM
ejpam-4944	453	26	,	,	PUNCT
ejpam-4944	453	27	1)⋆	1)⋆	PROPN
ejpam-4944	453	28	−d(x	−d(x	NOUN
ejpam-4944	453	29	)	)	PUNCT
ejpam-4944	453	30	.	.	PUNCT
ejpam-4944	454	1	(	(	PUNCT
ejpam-4944	454	2	b	b	NOUN
ejpam-4944	454	3	)	)	PUNCT
ejpam-4944	454	4	.	.	PUNCT
ejpam-4944	455	1	take	take	VERB
ejpam-4944	455	2	p	p	NOUN
ejpam-4944	455	3	be	be	AUX
ejpam-4944	455	4	a	a	DET
ejpam-4944	455	5	non	non	ADJ
ejpam-4944	455	6	-	-	ADJ
ejpam-4944	455	7	null	null	ADJ
ejpam-4944	455	8	(	(	PUNCT
ejpam-4944	455	9	s	s	NOUN
ejpam-4944	455	10	,	,	PUNCT
ejpam-4944	455	11	v)-µ-α	v)-µ-α	NOUN
ejpam-4944	455	12	-	-	PUNCT
ejpam-4944	455	13	open	open	ADJ
ejpam-4944	455	14	set	set	NOUN
ejpam-4944	455	15	where	where	SCONJ
ejpam-4944	455	16	s	s	X
ejpam-4944	455	17	,	,	PUNCT
ejpam-4944	455	18	v	v	NOUN
ejpam-4944	455	19	=	=	SYM
ejpam-4944	455	20	1	1	NUM
ejpam-4944	455	21	,	,	PUNCT
ejpam-4944	455	22	2	2	NUM
ejpam-4944	455	23	;	;	PUNCT
ejpam-4944	455	24	s	s	AUX
ejpam-4944	455	25	̸=	̸=	PROPN
ejpam-4944	455	26	v.	v.	CCONJ
ejpam-4944	455	27	we	we	PRON
ejpam-4944	455	28	get	get	VERB
ejpam-4944	455	29	p	p	NOUN
ejpam-4944	455	30	is	be	AUX
ejpam-4944	455	31	(	(	PUNCT
ejpam-4944	455	32	2	2	NUM
ejpam-4944	455	33	,	,	PUNCT
ejpam-4944	455	34	1)-µ-α	1)-µ-α	NUM
ejpam-4944	455	35	-	-	PUNCT
ejpam-4944	455	36	open	open	ADJ
ejpam-4944	455	37	.	.	PUNCT
ejpam-4944	456	1	let	let	VERB
ejpam-4944	456	2	g	g	PROPN
ejpam-4944	456	3	∈	∈	PROPN
ejpam-4944	456	4	σ̃2	σ̃2	PROPN
ejpam-4944	456	5	.	.	PUNCT
ejpam-4944	457	1	if	if	SCONJ
ejpam-4944	457	2	g	g	PROPN
ejpam-4944	457	3	∈	∈	PROPN
ejpam-4944	457	4	µ̃2	µ̃2	PROPN
ejpam-4944	457	5	,	,	PUNCT
ejpam-4944	457	6	then	then	ADV
ejpam-4944	457	7	the	the	DET
ejpam-4944	457	8	proof	proof	NOUN
ejpam-4944	457	9	is	be	AUX
ejpam-4944	457	10	trivial	trivial	ADJ
ejpam-4944	457	11	.	.	PUNCT
ejpam-4944	458	1	suppose	suppose	VERB
ejpam-4944	458	2	g	g	NOUN
ejpam-4944	458	3	/∈	/∈	PUNCT
ejpam-4944	459	1	µ̃2	µ̃2	PROPN
ejpam-4944	459	2	.	.	PUNCT
ejpam-4944	460	1	by	by	ADP
ejpam-4944	460	2	our	our	PRON
ejpam-4944	460	3	assumption	assumption	NOUN
ejpam-4944	460	4	,	,	PUNCT
ejpam-4944	460	5	i2	i2	PROPN
ejpam-4944	460	6	g	g	PROPN
ejpam-4944	460	7	is	be	AUX
ejpam-4944	460	8	µ2	µ2	ADJ
ejpam-4944	460	9	-	-	PUNCT
ejpam-4944	460	10	dense	dense	ADJ
ejpam-4944	460	11	.	.	PUNCT
ejpam-4944	461	1	since	since	SCONJ
ejpam-4944	461	2	p	p	PROPN
ejpam-4944	461	3	⊂	⊂	PROPN
ejpam-4944	461	4	i2(c1(i2(p	i2(c1(i2(p	PROPN
ejpam-4944	461	5	)	)	PUNCT
ejpam-4944	461	6	)	)	PUNCT
ejpam-4944	461	7	)	)	PUNCT
ejpam-4944	461	8	we	we	PRON
ejpam-4944	461	9	have	have	VERB
ejpam-4944	461	10	i2(c1(i2(p	i2(c1(i2(p	NOUN
ejpam-4944	461	11	)	)	PUNCT
ejpam-4944	461	12	)	)	PUNCT
ejpam-4944	461	13	)	)	PUNCT
ejpam-4944	462	1	∈	∈	PROPN
ejpam-4944	463	1	µ̃2	µ̃2	PROPN
ejpam-4944	463	2	.	.	PUNCT
ejpam-4944	464	1	this	this	PRON
ejpam-4944	464	2	implies	imply	VERB
ejpam-4944	464	3	i2(c1(i2(p	i2(c1(i2(p	NOUN
ejpam-4944	464	4	)	)	PUNCT
ejpam-4944	464	5	)	)	PUNCT
ejpam-4944	464	6	)	)	PUNCT
ejpam-4944	464	7	∩	∩	NOUN
ejpam-4944	464	8	i2	i2	PROPN
ejpam-4944	464	9	g	g	PROPN
ejpam-4944	464	10	̸=	̸=	PROPN
ejpam-4944	464	11	∅	∅	NOUN
ejpam-4944	464	12	which	which	PRON
ejpam-4944	464	13	implies	imply	VERB
ejpam-4944	464	14	c1(i2(p	c1(i2(p	PUNCT
ejpam-4944	464	15	)	)	PUNCT
ejpam-4944	464	16	)	)	PUNCT
ejpam-4944	464	17	∩	∩	NOUN
ejpam-4944	464	18	i2	i2	PROPN
ejpam-4944	464	19	g	g	PROPN
ejpam-4944	464	20	̸=	̸=	PROPN
ejpam-4944	464	21	∅	∅	NOUN
ejpam-4944	464	22	which	which	PRON
ejpam-4944	464	23	turn	turn	VERB
ejpam-4944	464	24	implies	imply	VERB
ejpam-4944	464	25	that	that	SCONJ
ejpam-4944	464	26	c1p	c1p	NOUN
ejpam-4944	464	27	∩	∩	ADJ
ejpam-4944	464	28	i2	i2	PROPN
ejpam-4944	464	29	g	g	PROPN
ejpam-4944	464	30	̸=	̸=	PROPN
ejpam-4944	464	31	∅.	∅.	ADV
ejpam-4944	464	32	thus	thus	ADV
ejpam-4944	464	33	,	,	PUNCT
ejpam-4944	464	34	c1p	c1p	NOUN
ejpam-4944	464	35	∩g	∩g	PUNCT
ejpam-4944	464	36	̸=	̸=	PROPN
ejpam-4944	464	37	∅.	∅.	PRON
ejpam-4944	464	38	hence	hence	ADV
ejpam-4944	464	39	p	p	NOUN
ejpam-4944	464	40	∈	∈	PROPN
ejpam-4944	464	41	(	(	PUNCT
ejpam-4944	464	42	2	2	NUM
ejpam-4944	464	43	,	,	PUNCT
ejpam-4944	464	44	1)⋆	1)⋆	PROPN
ejpam-4944	464	45	−d(x	−d(x	NOUN
ejpam-4944	464	46	)	)	PUNCT
ejpam-4944	464	47	.	.	PUNCT
ejpam-4944	465	1	similarly	similarly	ADV
ejpam-4944	465	2	we	we	PRON
ejpam-4944	465	3	can	can	AUX
ejpam-4944	465	4	prove	prove	VERB
ejpam-4944	465	5	this	this	DET
ejpam-4944	465	6	theorem	theorem	NOUN
ejpam-4944	465	7	for	for	ADP
ejpam-4944	465	8	the	the	DET
ejpam-4944	465	9	case	case	NOUN
ejpam-4944	465	10	s	s	PART
ejpam-4944	465	11	=	=	SYM
ejpam-4944	465	12	1	1	NUM
ejpam-4944	465	13	and	and	CCONJ
ejpam-4944	465	14	v	v	NOUN
ejpam-4944	465	15	=	=	SYM
ejpam-4944	465	16	2	2	NUM
ejpam-4944	465	17	.	.	PUNCT
ejpam-4944	465	18	theorem	theorem	NOUN
ejpam-4944	465	19	31	31	NUM
ejpam-4944	465	20	.	.	PUNCT
ejpam-4944	466	1	let	let	AUX
ejpam-4944	466	2	(	(	PUNCT
ejpam-4944	466	3	x,µ1	x,µ1	NOUN
ejpam-4944	466	4	,	,	PUNCT
ejpam-4944	466	5	µ2	µ2	PROPN
ejpam-4944	466	6	)	)	PUNCT
ejpam-4944	466	7	be	be	AUX
ejpam-4944	466	8	a	a	DET
ejpam-4944	466	9	bgts	bgts	NOUN
ejpam-4944	466	10	.	.	PUNCT
ejpam-4944	467	1	if	if	SCONJ
ejpam-4944	467	2	(	(	PUNCT
ejpam-4944	467	3	x,µs	x,µs	NUM
ejpam-4944	467	4	)	)	PUNCT
ejpam-4944	467	5	is	be	AUX
ejpam-4944	467	6	a	a	DET
ejpam-4944	467	7	hyperconnected	hyperconnected	ADJ
ejpam-4944	467	8	space	space	NOUN
ejpam-4944	467	9	,	,	PUNCT
ejpam-4944	467	10	µs	µs	X
ejpam-4944	467	11	⊂	⊂	PROPN
ejpam-4944	467	12	µv	µv	PROPN
ejpam-4944	467	13	and	and	CCONJ
ejpam-4944	467	14	if	if	SCONJ
ejpam-4944	467	15	µs	µs	NOUN
ejpam-4944	467	16	is	be	AUX
ejpam-4944	467	17	a	a	DET
ejpam-4944	467	18	strong	strong	ADJ
ejpam-4944	467	19	generalized	generalized	ADJ
ejpam-4944	467	20	topology	topology	NOUN
ejpam-4944	467	21	,	,	PUNCT
ejpam-4944	467	22	then	then	ADV
ejpam-4944	467	23	every	every	DET
ejpam-4944	467	24	non	non	ADJ
ejpam-4944	467	25	-	-	ADJ
ejpam-4944	467	26	null	null	ADJ
ejpam-4944	467	27	(	(	PUNCT
ejpam-4944	467	28	s	s	PROPN
ejpam-4944	467	29	,	,	PUNCT
ejpam-4944	467	30	v)-µ-semi	v)-µ-semi	ADJ
ejpam-4944	467	31	-	-	PUNCT
ejpam-4944	467	32	open	open	ADJ
ejpam-4944	467	33	set	set	NOUN
ejpam-4944	467	34	is	be	AUX
ejpam-4944	467	35	(	(	PUNCT
ejpam-4944	467	36	s	s	X
ejpam-4944	467	37	,	,	PUNCT
ejpam-4944	467	38	v)⋆-dense	v)⋆-dense	PROPN
ejpam-4944	467	39	where	where	SCONJ
ejpam-4944	467	40	s	s	X
ejpam-4944	467	41	,	,	PUNCT
ejpam-4944	467	42	v	v	NOUN
ejpam-4944	467	43	=	=	SYM
ejpam-4944	467	44	1	1	NUM
ejpam-4944	467	45	,	,	PUNCT
ejpam-4944	467	46	2	2	NUM
ejpam-4944	467	47	;	;	PUNCT
ejpam-4944	467	48	s	s	VERB
ejpam-4944	467	49	̸=	̸=	PROPN
ejpam-4944	467	50	v.	v.	ADP
ejpam-4944	467	51	proof	proof	NOUN
ejpam-4944	467	52	.	.	PUNCT
ejpam-4944	468	1	assume	assume	VERB
ejpam-4944	468	2	that	that	SCONJ
ejpam-4944	468	3	,	,	PUNCT
ejpam-4944	468	4	(	(	PUNCT
ejpam-4944	468	5	x,µs	x,µs	NUM
ejpam-4944	468	6	)	)	PUNCT
ejpam-4944	468	7	is	be	AUX
ejpam-4944	468	8	a	a	DET
ejpam-4944	468	9	hyperconnected	hyperconnecte	VERB
ejpam-4944	468	10	space	space	NOUN
ejpam-4944	468	11	;	;	PUNCT
ejpam-4944	468	12	µs	µs	X
ejpam-4944	468	13	⊂	⊂	PROPN
ejpam-4944	468	14	µv	µv	PROPN
ejpam-4944	468	15	and	and	CCONJ
ejpam-4944	468	16	µs	µs	NOUN
ejpam-4944	468	17	is	be	AUX
ejpam-4944	468	18	a	a	DET
ejpam-4944	468	19	strong	strong	ADJ
ejpam-4944	468	20	generalized	generalized	ADJ
ejpam-4944	468	21	topological	topological	ADJ
ejpam-4944	468	22	space	space	NOUN
ejpam-4944	468	23	for	for	ADP
ejpam-4944	468	24	s	s	NOUN
ejpam-4944	468	25	=	=	SYM
ejpam-4944	468	26	1	1	NUM
ejpam-4944	468	27	,	,	PUNCT
ejpam-4944	468	28	2	2	NUM
ejpam-4944	468	29	.	.	X
ejpam-4944	468	30	take	take	VERB
ejpam-4944	468	31	s	s	NOUN
ejpam-4944	468	32	=	=	SYM
ejpam-4944	468	33	1	1	NUM
ejpam-4944	468	34	and	and	CCONJ
ejpam-4944	468	35	v	v	NOUN
ejpam-4944	468	36	=	=	SYM
ejpam-4944	468	37	2	2	NUM
ejpam-4944	468	38	.	.	PUNCT
ejpam-4944	469	1	then	then	ADV
ejpam-4944	469	2	(	(	PUNCT
ejpam-4944	469	3	x,µ1	x,µ1	NOUN
ejpam-4944	469	4	)	)	PUNCT
ejpam-4944	469	5	is	be	AUX
ejpam-4944	469	6	a	a	DET
ejpam-4944	469	7	hyperconnected	hyperconnecte	VERB
ejpam-4944	469	8	space	space	NOUN
ejpam-4944	469	9	;	;	PUNCT
ejpam-4944	469	10	µ1	µ1	PROPN
ejpam-4944	469	11	⊂	⊂	PROPN
ejpam-4944	469	12	µ2	µ2	PROPN
ejpam-4944	469	13	and	and	CCONJ
ejpam-4944	469	14	µ1	µ1	PROPN
ejpam-4944	469	15	is	be	AUX
ejpam-4944	469	16	a	a	DET
ejpam-4944	469	17	sgt	sgt	PROPN
ejpam-4944	469	18	.	.	PUNCT
ejpam-4944	470	1	let	let	VERB
ejpam-4944	470	2	q	q	PART
ejpam-4944	470	3	be	be	AUX
ejpam-4944	470	4	a	a	DET
ejpam-4944	470	5	non	non	ADJ
ejpam-4944	470	6	-	-	ADJ
ejpam-4944	470	7	null	null	ADJ
ejpam-4944	470	8	(	(	PUNCT
ejpam-4944	470	9	s	s	PROPN
ejpam-4944	470	10	,	,	PUNCT
ejpam-4944	470	11	v)-µ-semi	v)-µ-semi	NOUN
ejpam-4944	470	12	-	-	PUNCT
ejpam-4944	470	13	open	open	ADJ
ejpam-4944	470	14	set	set	NOUN
ejpam-4944	470	15	where	where	SCONJ
ejpam-4944	470	16	s	s	X
ejpam-4944	470	17	,	,	PUNCT
ejpam-4944	470	18	v	v	NOUN
ejpam-4944	470	19	=	=	SYM
ejpam-4944	470	20	1	1	NUM
ejpam-4944	470	21	,	,	PUNCT
ejpam-4944	470	22	2	2	NUM
ejpam-4944	470	23	;	;	PUNCT
ejpam-4944	470	24	s	s	VERB
ejpam-4944	470	25	̸=	̸=	PROPN
ejpam-4944	470	26	v.	v.	ADV
ejpam-4944	470	27	then	then	ADV
ejpam-4944	470	28	q	q	X
ejpam-4944	470	29	is	be	AUX
ejpam-4944	470	30	(	(	PUNCT
ejpam-4944	470	31	1	1	NUM
ejpam-4944	470	32	,	,	PUNCT
ejpam-4944	470	33	2)-µsemi	2)-µsemi	NOUN
ejpam-4944	470	34	-	-	PUNCT
ejpam-4944	470	35	open	open	ADJ
ejpam-4944	470	36	.	.	PUNCT
ejpam-4944	471	1	let	let	VERB
ejpam-4944	471	2	h	h	PRON
ejpam-4944	471	3	∈	∈	PROPN
ejpam-4944	471	4	σ̃1	σ̃1	PROPN
ejpam-4944	471	5	.	.	PROPN
ejpam-4944	471	6	suppose	suppose	VERB
ejpam-4944	471	7	h	h	PROPN
ejpam-4944	471	8	∈	∈	PROPN
ejpam-4944	471	9	µ̃1	µ̃1	PROPN
ejpam-4944	471	10	,	,	PUNCT
ejpam-4944	471	11	then	then	ADV
ejpam-4944	471	12	there	there	PRON
ejpam-4944	471	13	is	be	VERB
ejpam-4944	471	14	nothing	nothing	PRON
ejpam-4944	471	15	to	to	PART
ejpam-4944	471	16	prove	prove	VERB
ejpam-4944	471	17	.	.	PUNCT
ejpam-4944	472	1	assume	assume	VERB
ejpam-4944	472	2	that	that	SCONJ
ejpam-4944	472	3	,	,	PUNCT
ejpam-4944	472	4	h	h	NOUN
ejpam-4944	472	5	/∈	/∈	PUNCT
ejpam-4944	473	1	µ̃1	µ̃1	NOUN
ejpam-4944	473	2	.	.	PUNCT
ejpam-4944	473	3	here	here	ADV
ejpam-4944	473	4	h	h	PROPN
ejpam-4944	473	5	⊂	⊂	PROPN
ejpam-4944	473	6	c1(i1(h	c1(i1(h	PROPN
ejpam-4944	473	7	)	)	PUNCT
ejpam-4944	473	8	)	)	PUNCT
ejpam-4944	473	9	.	.	PUNCT
ejpam-4944	474	1	by	by	ADP
ejpam-4944	474	2	our	our	PRON
ejpam-4944	474	3	assumption	assumption	NOUN
ejpam-4944	474	4	,	,	PUNCT
ejpam-4944	474	5	i1h	i1h	PROPN
ejpam-4944	474	6	is	be	AUX
ejpam-4944	474	7	µ1	µ1	NOUN
ejpam-4944	474	8	-	-	PUNCT
ejpam-4944	474	9	dense	dense	ADJ
ejpam-4944	474	10	.	.	PUNCT
ejpam-4944	475	1	since	since	SCONJ
ejpam-4944	475	2	q	q	PROPN
ejpam-4944	475	3	⊂	⊂	PROPN
ejpam-4944	475	4	c2(i1(q	c2(i1(q	PROPN
ejpam-4944	475	5	)	)	PUNCT
ejpam-4944	475	6	)	)	PUNCT
ejpam-4944	475	7	)	)	PUNCT
ejpam-4944	475	8	we	we	PRON
ejpam-4944	475	9	have	have	VERB
ejpam-4944	475	10	i1(q	i1(q	X
ejpam-4944	475	11	)	)	PUNCT
ejpam-4944	475	12	∈	∈	PROPN
ejpam-4944	475	13	µ̃1	µ̃1	PROPN
ejpam-4944	475	14	,	,	PUNCT
ejpam-4944	475	15	µ1	µ1	PROPN
ejpam-4944	475	16	⊂	⊂	PROPN
ejpam-4944	475	17	µ2	µ2	PROPN
ejpam-4944	475	18	and	and	CCONJ
ejpam-4944	475	19	µ1	µ1	PROPN
ejpam-4944	475	20	is	be	AUX
ejpam-4944	475	21	a	a	DET
ejpam-4944	475	22	sgt	sgt	PROPN
ejpam-4944	475	23	.	.	PUNCT
ejpam-4944	476	1	this	this	PRON
ejpam-4944	476	2	implies	imply	VERB
ejpam-4944	476	3	i1(q)∩	i1(q)∩	VERB
ejpam-4944	476	4	i1h	i1h	DET
ejpam-4944	476	5	̸=	̸=	PROPN
ejpam-4944	476	6	∅	∅	NOUN
ejpam-4944	476	7	which	which	PRON
ejpam-4944	476	8	implies	imply	VERB
ejpam-4944	476	9	c2q	c2q	NOUN
ejpam-4944	476	10	∩h	∩h	PROPN
ejpam-4944	476	11	̸=	̸=	PROPN
ejpam-4944	476	12	∅.	∅.	PRON
ejpam-4944	476	13	hence	hence	ADV
ejpam-4944	476	14	q	q	NOUN
ejpam-4944	476	15	∈	∈	PROPN
ejpam-4944	476	16	(	(	PUNCT
ejpam-4944	476	17	1	1	NUM
ejpam-4944	476	18	,	,	PUNCT
ejpam-4944	476	19	2)⋆	2)⋆	PROPN
ejpam-4944	476	20	−d(x	−d(x	NOUN
ejpam-4944	476	21	)	)	PUNCT
ejpam-4944	476	22	.	.	PUNCT
ejpam-4944	477	1	choose	choose	VERB
ejpam-4944	477	2	s	s	NOUN
ejpam-4944	477	3	=	=	SYM
ejpam-4944	477	4	2	2	NUM
ejpam-4944	477	5	and	and	CCONJ
ejpam-4944	477	6	v	v	NOUN
ejpam-4944	477	7	=	=	SYM
ejpam-4944	477	8	1	1	X
ejpam-4944	477	9	.	.	PUNCT
ejpam-4944	478	1	we	we	PRON
ejpam-4944	478	2	get	get	VERB
ejpam-4944	478	3	(	(	PUNCT
ejpam-4944	478	4	x,µ2	x,µ2	PROPN
ejpam-4944	478	5	)	)	PUNCT
ejpam-4944	478	6	is	be	AUX
ejpam-4944	478	7	a	a	DET
ejpam-4944	478	8	hyperconnected	hyperconnecte	VERB
ejpam-4944	478	9	space	space	NOUN
ejpam-4944	478	10	;	;	PUNCT
ejpam-4944	478	11	µ2	µ2	PROPN
ejpam-4944	478	12	⊂	⊂	PROPN
ejpam-4944	478	13	µ1	µ1	PROPN
ejpam-4944	478	14	and	and	CCONJ
ejpam-4944	478	15	µ2	µ2	PROPN
ejpam-4944	478	16	is	be	AUX
ejpam-4944	478	17	a	a	DET
ejpam-4944	478	18	sgt	sgt	PROPN
ejpam-4944	478	19	.	.	PUNCT
ejpam-4944	479	1	consider	consider	VERB
ejpam-4944	479	2	p	p	NOUN
ejpam-4944	479	3	is	be	AUX
ejpam-4944	479	4	a	a	DET
ejpam-4944	479	5	non	non	ADJ
ejpam-4944	479	6	-	-	ADJ
ejpam-4944	479	7	null	null	ADJ
ejpam-4944	479	8	(	(	PUNCT
ejpam-4944	479	9	s	s	PROPN
ejpam-4944	479	10	,	,	PUNCT
ejpam-4944	479	11	v)-µ-semi	v)-µ-semi	NOUN
ejpam-4944	479	12	-	-	PUNCT
ejpam-4944	479	13	open	open	ADJ
ejpam-4944	479	14	set	set	NOUN
ejpam-4944	479	15	where	where	SCONJ
ejpam-4944	479	16	s	s	X
ejpam-4944	479	17	,	,	PUNCT
ejpam-4944	479	18	v	v	NOUN
ejpam-4944	479	19	=	=	SYM
ejpam-4944	479	20	1	1	NUM
ejpam-4944	479	21	,	,	PUNCT
ejpam-4944	479	22	2	2	NUM
ejpam-4944	479	23	;	;	PUNCT
ejpam-4944	479	24	s	s	VERB
ejpam-4944	479	25	̸=	̸=	PROPN
ejpam-4944	480	1	v.	v.	ADP
ejpam-4944	480	2	then	then	ADV
ejpam-4944	480	3	p	p	X
ejpam-4944	480	4	is	be	AUX
ejpam-4944	480	5	(	(	PUNCT
ejpam-4944	480	6	2	2	NUM
ejpam-4944	480	7	,	,	PUNCT
ejpam-4944	480	8	1)-µ-semi	1)-µ-semi	NUM
ejpam-4944	480	9	-	-	NOUN
ejpam-4944	480	10	open	open	ADJ
ejpam-4944	480	11	.	.	PUNCT
ejpam-4944	481	1	let	let	VERB
ejpam-4944	481	2	g	g	PROPN
ejpam-4944	481	3	∈	∈	PROPN
ejpam-4944	481	4	σ̃2	σ̃2	PROPN
ejpam-4944	481	5	.	.	PUNCT
ejpam-4944	482	1	if	if	SCONJ
ejpam-4944	482	2	g	g	PROPN
ejpam-4944	482	3	∈	∈	PROPN
ejpam-4944	482	4	µ̃2	µ̃2	PROPN
ejpam-4944	482	5	,	,	PUNCT
ejpam-4944	482	6	then	then	ADV
ejpam-4944	482	7	the	the	DET
ejpam-4944	482	8	proof	proof	NOUN
ejpam-4944	482	9	is	be	AUX
ejpam-4944	482	10	obvious	obvious	ADJ
ejpam-4944	482	11	.	.	PUNCT
ejpam-4944	483	1	suppose	suppose	VERB
ejpam-4944	483	2	g	g	NOUN
ejpam-4944	483	3	/∈	/∈	PUNCT
ejpam-4944	484	1	µ̃2	µ̃2	PROPN
ejpam-4944	484	2	.	.	PUNCT
ejpam-4944	485	1	d.	d.	PROPN
ejpam-4944	485	2	elgezouli	elgezouli	PROPN
ejpam-4944	485	3	et	et	PROPN
ejpam-4944	485	4	al	al	PROPN
ejpam-4944	485	5	.	.	PUNCT
ejpam-4944	485	6	/	/	SYM
ejpam-4944	485	7	eur	eur	PROPN
ejpam-4944	485	8	.	.	PUNCT
ejpam-4944	486	1	j.	j.	PROPN
ejpam-4944	486	2	pure	pure	PROPN
ejpam-4944	486	3	appl	appl	PROPN
ejpam-4944	486	4	.	.	PROPN
ejpam-4944	486	5	math	math	PROPN
ejpam-4944	486	6	,	,	PUNCT
ejpam-4944	486	7	16	16	NUM
ejpam-4944	486	8	(	(	PUNCT
ejpam-4944	486	9	4	4	NUM
ejpam-4944	486	10	)	)	PUNCT
ejpam-4944	486	11	(	(	PUNCT
ejpam-4944	486	12	2023	2023	NUM
ejpam-4944	486	13	)	)	PUNCT
ejpam-4944	486	14	,	,	PUNCT
ejpam-4944	486	15	2286	2286	NUM
ejpam-4944	486	16	-	-	SYM
ejpam-4944	486	17	2305	2305	NUM
ejpam-4944	486	18	2299	2299	NUM
ejpam-4944	486	19	here	here	ADV
ejpam-4944	486	20	g	g	PROPN
ejpam-4944	486	21	⊂	⊂	PROPN
ejpam-4944	486	22	c2(i2(g	c2(i2(g	PUNCT
ejpam-4944	486	23	)	)	PUNCT
ejpam-4944	486	24	)	)	PUNCT
ejpam-4944	486	25	.	.	PUNCT
ejpam-4944	487	1	by	by	ADP
ejpam-4944	487	2	hypothesis	hypothesis	NOUN
ejpam-4944	487	3	,	,	PUNCT
ejpam-4944	487	4	i2	i2	PROPN
ejpam-4944	487	5	g	g	PROPN
ejpam-4944	487	6	is	be	AUX
ejpam-4944	487	7	µ2	µ2	ADJ
ejpam-4944	487	8	-	-	PUNCT
ejpam-4944	487	9	dense	dense	ADJ
ejpam-4944	487	10	.	.	PUNCT
ejpam-4944	488	1	since	since	SCONJ
ejpam-4944	488	2	p	p	PROPN
ejpam-4944	488	3	⊂	⊂	PROPN
ejpam-4944	488	4	c1(i2(p	c1(i2(p	NOUN
ejpam-4944	488	5	)	)	PUNCT
ejpam-4944	488	6	)	)	PUNCT
ejpam-4944	488	7	)	)	PUNCT
ejpam-4944	488	8	we	we	PRON
ejpam-4944	488	9	have	have	VERB
ejpam-4944	488	10	i2(p	i2(p	X
ejpam-4944	488	11	)	)	PUNCT
ejpam-4944	488	12	∈	∈	PROPN
ejpam-4944	488	13	µ̃2	µ̃2	PROPN
ejpam-4944	488	14	,	,	PUNCT
ejpam-4944	488	15	by	by	ADP
ejpam-4944	488	16	hypothesis	hypothesis	NOUN
ejpam-4944	488	17	so	so	SCONJ
ejpam-4944	488	18	that	that	SCONJ
ejpam-4944	488	19	i2(p	i2(p	PROPN
ejpam-4944	488	20	)	)	PUNCT
ejpam-4944	488	21	∩	∩	PROPN
ejpam-4944	488	22	i2	i2	PROPN
ejpam-4944	488	23	g	g	PROPN
ejpam-4944	488	24	̸=	̸=	PROPN
ejpam-4944	488	25	∅	∅	NOUN
ejpam-4944	488	26	which	which	PRON
ejpam-4944	488	27	implies	imply	VERB
ejpam-4944	488	28	that	that	SCONJ
ejpam-4944	488	29	c1p	c1p	NOUN
ejpam-4944	488	30	∩g	∩g	ADJ
ejpam-4944	488	31	̸=	̸=	PROPN
ejpam-4944	488	32	∅.	∅.	PRON
ejpam-4944	488	33	hence	hence	ADV
ejpam-4944	488	34	p	p	NOUN
ejpam-4944	488	35	∈	∈	PROPN
ejpam-4944	488	36	(	(	PUNCT
ejpam-4944	488	37	2	2	NUM
ejpam-4944	488	38	,	,	PUNCT
ejpam-4944	488	39	1)⋆	1)⋆	PROPN
ejpam-4944	488	40	−d(x	−d(x	NOUN
ejpam-4944	488	41	)	)	PUNCT
ejpam-4944	488	42	.	.	PUNCT
ejpam-4944	489	1	in	in	ADP
ejpam-4944	489	2	the	the	DET
ejpam-4944	489	3	rest	rest	NOUN
ejpam-4944	489	4	of	of	ADP
ejpam-4944	489	5	this	this	DET
ejpam-4944	489	6	section	section	NOUN
ejpam-4944	489	7	,	,	PUNCT
ejpam-4944	489	8	we	we	PRON
ejpam-4944	489	9	analyze	analyze	VERB
ejpam-4944	489	10	the	the	DET
ejpam-4944	489	11	nature	nature	NOUN
ejpam-4944	489	12	of	of	ADP
ejpam-4944	489	13	(	(	PUNCT
ejpam-4944	489	14	s	s	X
ejpam-4944	489	15	,	,	PUNCT
ejpam-4944	489	16	v)⋆-dense	v)⋆-dense	ADJ
ejpam-4944	489	17	sets	set	NOUN
ejpam-4944	489	18	in	in	ADP
ejpam-4944	489	19	a	a	DET
ejpam-4944	489	20	subspace	subspace	NOUN
ejpam-4944	489	21	.	.	PUNCT
ejpam-4944	490	1	let	let	VERB
ejpam-4944	490	2	(	(	PUNCT
ejpam-4944	490	3	x,µ	x,µ	NOUN
ejpam-4944	490	4	)	)	PUNCT
ejpam-4944	490	5	be	be	VERB
ejpam-4944	490	6	a	a	DET
ejpam-4944	490	7	gts	gts	NOUN
ejpam-4944	490	8	,	,	PUNCT
ejpam-4944	490	9	q	q	X
ejpam-4944	490	10	⊂	⊂	PROPN
ejpam-4944	490	11	x	x	X
ejpam-4944	490	12	and	and	CCONJ
ejpam-4944	490	13	µq	µq	PROPN
ejpam-4944	490	14	=	=	PUNCT
ejpam-4944	490	15	{	{	PUNCT
ejpam-4944	490	16	p	p	NOUN
ejpam-4944	490	17	∩	∩	PROPN
ejpam-4944	490	18	q	q	PROPN
ejpam-4944	491	1	|	|	ADV
ejpam-4944	491	2	p	p	X
ejpam-4944	491	3	∈	∈	PROPN
ejpam-4944	491	4	µ	µ	X
ejpam-4944	491	5	}	}	PUNCT
ejpam-4944	491	6	.	.	PUNCT
ejpam-4944	492	1	then	then	ADV
ejpam-4944	492	2	µq	µq	PROPN
ejpam-4944	492	3	is	be	AUX
ejpam-4944	492	4	called	call	VERB
ejpam-4944	492	5	relative	relative	ADJ
ejpam-4944	492	6	generalized	generalized	ADJ
ejpam-4944	492	7	topology	topology	NOUN
ejpam-4944	492	8	on	on	ADP
ejpam-4944	492	9	q	q	NOUN
ejpam-4944	493	1	[	[	X
ejpam-4944	493	2	7	7	NUM
ejpam-4944	493	3	]	]	PUNCT
ejpam-4944	493	4	.	.	PUNCT
ejpam-4944	494	1	theorem	theorem	ADJ
ejpam-4944	494	2	32	32	NUM
ejpam-4944	494	3	.	.	PUNCT
ejpam-4944	495	1	let	let	AUX
ejpam-4944	495	2	(	(	PUNCT
ejpam-4944	495	3	x,µ1	x,µ1	NOUN
ejpam-4944	495	4	,	,	PUNCT
ejpam-4944	495	5	µ2	µ2	PROPN
ejpam-4944	495	6	)	)	PUNCT
ejpam-4944	495	7	be	be	VERB
ejpam-4944	495	8	a	a	DET
ejpam-4944	495	9	bigeneralized	bigeneralized	ADJ
ejpam-4944	495	10	topological	topological	ADJ
ejpam-4944	495	11	space	space	NOUN
ejpam-4944	495	12	,	,	PUNCT
ejpam-4944	495	13	q	q	PUNCT
ejpam-4944	495	14	be	be	AUX
ejpam-4944	495	15	a	a	DET
ejpam-4944	495	16	µs	µs	NOUN
ejpam-4944	495	17	-	-	PUNCT
ejpam-4944	495	18	dense	dense	ADJ
ejpam-4944	495	19	subspace	subspace	NOUN
ejpam-4944	495	20	of	of	ADP
ejpam-4944	495	21	x	x	PUNCT
ejpam-4944	495	22	for	for	ADP
ejpam-4944	495	23	s	s	NOUN
ejpam-4944	495	24	=	=	SYM
ejpam-4944	495	25	1	1	NUM
ejpam-4944	495	26	,	,	PUNCT
ejpam-4944	495	27	2	2	NUM
ejpam-4944	495	28	.	.	PUNCT
ejpam-4944	496	1	if	if	SCONJ
ejpam-4944	496	2	p	p	NOUN
ejpam-4944	496	3	is	be	AUX
ejpam-4944	496	4	a	a	DET
ejpam-4944	496	5	µsq	µsq	VERB
ejpam-4944	496	6	-	-	PUNCT
ejpam-4944	496	7	dense	dense	ADJ
ejpam-4944	496	8	and	and	CCONJ
ejpam-4944	496	9	µs	µs	NOUN
ejpam-4944	496	10	is	be	AUX
ejpam-4944	496	11	a	a	DET
ejpam-4944	496	12	sgt	sgt	PROPN
ejpam-4944	496	13	,	,	PUNCT
ejpam-4944	496	14	then	then	ADV
ejpam-4944	496	15	p	p	PROPN
ejpam-4944	496	16	∈	∈	PROPN
ejpam-4944	496	17	(	(	PUNCT
ejpam-4944	496	18	s	s	PROPN
ejpam-4944	496	19	,	,	PUNCT
ejpam-4944	496	20	v)⋆	v)⋆	PROPN
ejpam-4944	496	21	−	−	PROPN
ejpam-4944	496	22	d(x	d(x	PROPN
ejpam-4944	496	23	)	)	PUNCT
ejpam-4944	496	24	where	where	SCONJ
ejpam-4944	496	25	s	s	X
ejpam-4944	496	26	,	,	PUNCT
ejpam-4944	496	27	v	v	NOUN
ejpam-4944	496	28	=	=	SYM
ejpam-4944	496	29	1	1	NUM
ejpam-4944	496	30	,	,	PUNCT
ejpam-4944	496	31	2	2	NUM
ejpam-4944	496	32	;	;	PUNCT
ejpam-4944	496	33	s	s	VERB
ejpam-4944	496	34	̸=	̸=	PROPN
ejpam-4944	496	35	v.	v.	ADP
ejpam-4944	496	36	proof	proof	NOUN
ejpam-4944	496	37	.	.	PUNCT
ejpam-4944	497	1	assume	assume	VERB
ejpam-4944	497	2	that	that	SCONJ
ejpam-4944	497	3	,	,	PUNCT
ejpam-4944	497	4	q	q	X
ejpam-4944	497	5	is	be	AUX
ejpam-4944	497	6	µs	µs	NOUN
ejpam-4944	497	7	-	-	PUNCT
ejpam-4944	497	8	dense	dense	ADJ
ejpam-4944	497	9	in	in	ADP
ejpam-4944	497	10	x	x	PUNCT
ejpam-4944	497	11	and	and	CCONJ
ejpam-4944	497	12	µs	µs	NOUN
ejpam-4944	497	13	is	be	AUX
ejpam-4944	497	14	a	a	DET
ejpam-4944	497	15	strong	strong	ADJ
ejpam-4944	497	16	generalized	generalized	ADJ
ejpam-4944	497	17	topology	topology	NOUN
ejpam-4944	497	18	for	for	ADP
ejpam-4944	497	19	s	s	NOUN
ejpam-4944	497	20	=	=	SYM
ejpam-4944	497	21	1	1	NUM
ejpam-4944	497	22	,	,	PUNCT
ejpam-4944	497	23	2	2	NUM
ejpam-4944	497	24	.	.	X
ejpam-4944	498	1	let	let	VERB
ejpam-4944	498	2	p	p	PRON
ejpam-4944	498	3	be	be	AUX
ejpam-4944	498	4	a	a	DET
ejpam-4944	498	5	µsq	µsq	VERB
ejpam-4944	498	6	-	-	PUNCT
ejpam-4944	498	7	dense	dense	ADJ
ejpam-4944	498	8	set	set	NOUN
ejpam-4944	498	9	in	in	ADP
ejpam-4944	498	10	q	q	PROPN
ejpam-4944	498	11	where	where	SCONJ
ejpam-4944	498	12	s	s	VERB
ejpam-4944	498	13	=	=	SYM
ejpam-4944	498	14	1	1	NUM
ejpam-4944	498	15	,	,	PUNCT
ejpam-4944	498	16	2	2	NUM
ejpam-4944	498	17	.	.	X
ejpam-4944	499	1	take	take	VERB
ejpam-4944	499	2	s	s	NOUN
ejpam-4944	499	3	=	=	SYM
ejpam-4944	499	4	1	1	NUM
ejpam-4944	499	5	and	and	CCONJ
ejpam-4944	499	6	v	v	NOUN
ejpam-4944	499	7	=	=	SYM
ejpam-4944	499	8	2	2	NUM
ejpam-4944	499	9	.	.	PUNCT
ejpam-4944	500	1	then	then	ADV
ejpam-4944	500	2	q	q	PROPN
ejpam-4944	500	3	is	be	AUX
ejpam-4944	500	4	µ1	µ1	NOUN
ejpam-4944	500	5	-	-	PUNCT
ejpam-4944	500	6	dense	dense	ADJ
ejpam-4944	500	7	,	,	PUNCT
ejpam-4944	500	8	µ1	µ1	PROPN
ejpam-4944	500	9	is	be	AUX
ejpam-4944	500	10	a	a	DET
ejpam-4944	500	11	sgt	sgt	NOUN
ejpam-4944	500	12	and	and	CCONJ
ejpam-4944	500	13	p	p	NOUN
ejpam-4944	500	14	is	be	AUX
ejpam-4944	500	15	µ1q	µ1q	NOUN
ejpam-4944	500	16	-	-	PUNCT
ejpam-4944	500	17	dense	dense	ADJ
ejpam-4944	500	18	in	in	ADP
ejpam-4944	500	19	q.	q.	PROPN
ejpam-4944	500	20	let	let	VERB
ejpam-4944	500	21	k	k	PROPN
ejpam-4944	500	22	∈	∈	PROPN
ejpam-4944	500	23	σ̃1	σ̃1	PROPN
ejpam-4944	500	24	.	.	PUNCT
ejpam-4944	501	1	if	if	SCONJ
ejpam-4944	501	2	k	k	PROPN
ejpam-4944	501	3	∈	∈	PROPN
ejpam-4944	501	4	µ̃1	µ̃1	PROPN
ejpam-4944	501	5	,	,	PUNCT
ejpam-4944	501	6	then	then	ADV
ejpam-4944	501	7	further	further	ADJ
ejpam-4944	501	8	proof	proof	NOUN
ejpam-4944	501	9	investigation	investigation	NOUN
ejpam-4944	501	10	no	no	ADV
ejpam-4944	501	11	longer	long	ADV
ejpam-4944	501	12	required	require	VERB
ejpam-4944	501	13	.	.	PUNCT
ejpam-4944	502	1	suppose	suppose	VERB
ejpam-4944	502	2	k	k	X
ejpam-4944	502	3	/∈	/∈	PUNCT
ejpam-4944	502	4	µ̃1	µ̃1	NOUN
ejpam-4944	502	5	.	.	PUNCT
ejpam-4944	502	6	by	by	ADP
ejpam-4944	502	7	hypothesis	hypothesis	NOUN
ejpam-4944	502	8	,	,	PUNCT
ejpam-4944	502	9	iµ1k	iµ1k	PROPN
ejpam-4944	502	10	∈	∈	PROPN
ejpam-4944	502	11	µ̃1	µ̃1	NOUN
ejpam-4944	502	12	which	which	PRON
ejpam-4944	502	13	implies	imply	VERB
ejpam-4944	502	14	iµ1k	iµ1k	PROPN
ejpam-4944	502	15	∩	∩	NOUN
ejpam-4944	502	16	q	q	X
ejpam-4944	502	17	∈	∈	PROPN
ejpam-4944	502	18	˜µ1q	˜µ1q	PROPN
ejpam-4944	502	19	.	.	PUNCT
ejpam-4944	503	1	take	take	VERB
ejpam-4944	503	2	l	l	NOUN
ejpam-4944	503	3	=	=	SYM
ejpam-4944	503	4	iµ1k	iµ1k	PROPN
ejpam-4944	503	5	∩	∩	NOUN
ejpam-4944	503	6	q.	q.	NOUN
ejpam-4944	503	7	then	then	ADV
ejpam-4944	503	8	l	l	PROPN
ejpam-4944	503	9	∩	∩	PROPN
ejpam-4944	503	10	p	p	PROPN
ejpam-4944	503	11	̸=	̸=	PROPN
ejpam-4944	503	12	∅	∅	NOUN
ejpam-4944	503	13	so	so	SCONJ
ejpam-4944	503	14	that	that	SCONJ
ejpam-4944	503	15	iµ1k	iµ1k	PROPN
ejpam-4944	503	16	∩	∩	NOUN
ejpam-4944	503	17	p	p	X
ejpam-4944	503	18	̸=	̸=	PROPN
ejpam-4944	503	19	∅.	∅.	ADP
ejpam-4944	503	20	this	this	PRON
ejpam-4944	503	21	implies	imply	VERB
ejpam-4944	503	22	k	k	PROPN
ejpam-4944	503	23	∩	∩	PROPN
ejpam-4944	503	24	p	p	PROPN
ejpam-4944	503	25	̸=	̸=	PROPN
ejpam-4944	503	26	∅	∅	NOUN
ejpam-4944	503	27	which	which	PRON
ejpam-4944	503	28	implies	imply	VERB
ejpam-4944	503	29	k	k	PROPN
ejpam-4944	503	30	∩	∩	ADJ
ejpam-4944	503	31	c2p	c2p	PROPN
ejpam-4944	503	32	̸=	̸=	PROPN
ejpam-4944	503	33	∅.	∅.	VERB
ejpam-4944	503	34	therefore	therefore	ADV
ejpam-4944	503	35	,	,	PUNCT
ejpam-4944	503	36	p	p	PROPN
ejpam-4944	503	37	∈	∈	PROPN
ejpam-4944	503	38	(	(	PUNCT
ejpam-4944	503	39	1	1	NUM
ejpam-4944	503	40	,	,	PUNCT
ejpam-4944	503	41	2)⋆	2)⋆	PROPN
ejpam-4944	503	42	−d(x	−d(x	NOUN
ejpam-4944	503	43	)	)	PUNCT
ejpam-4944	503	44	.	.	PUNCT
ejpam-4944	504	1	fix	fix	NOUN
ejpam-4944	504	2	s	s	PART
ejpam-4944	504	3	=	=	SYM
ejpam-4944	504	4	2	2	NUM
ejpam-4944	504	5	,	,	PUNCT
ejpam-4944	504	6	v	v	NOUN
ejpam-4944	504	7	=	=	SYM
ejpam-4944	504	8	1	1	NUM
ejpam-4944	504	9	.	.	PUNCT
ejpam-4944	505	1	then	then	ADV
ejpam-4944	505	2	q	q	PROPN
ejpam-4944	505	3	is	be	AUX
ejpam-4944	505	4	µ2	µ2	ADJ
ejpam-4944	505	5	-	-	PUNCT
ejpam-4944	505	6	dense	dense	ADJ
ejpam-4944	505	7	,	,	PUNCT
ejpam-4944	505	8	µ2	µ2	PROPN
ejpam-4944	505	9	is	be	AUX
ejpam-4944	505	10	a	a	DET
ejpam-4944	505	11	sgt	sgt	NOUN
ejpam-4944	505	12	and	and	CCONJ
ejpam-4944	505	13	p	p	NOUN
ejpam-4944	505	14	is	be	AUX
ejpam-4944	505	15	µ2q	µ2q	NOUN
ejpam-4944	505	16	-	-	ADJ
ejpam-4944	505	17	dense	dense	ADJ
ejpam-4944	505	18	in	in	ADP
ejpam-4944	505	19	q.	q.	PROPN
ejpam-4944	505	20	let	let	VERB
ejpam-4944	505	21	m	m	PROPN
ejpam-4944	505	22	∈	∈	PROPN
ejpam-4944	505	23	σ̃2	σ̃2	PROPN
ejpam-4944	505	24	.	.	PUNCT
ejpam-4944	506	1	if	if	SCONJ
ejpam-4944	506	2	m	m	VERB
ejpam-4944	506	3	∈	∈	PROPN
ejpam-4944	506	4	µ̃2	µ̃2	PROPN
ejpam-4944	506	5	,	,	PUNCT
ejpam-4944	506	6	then	then	ADV
ejpam-4944	506	7	the	the	DET
ejpam-4944	506	8	proof	proof	NOUN
ejpam-4944	506	9	is	be	AUX
ejpam-4944	506	10	directly	directly	ADV
ejpam-4944	506	11	follows	follow	VERB
ejpam-4944	506	12	.	.	PUNCT
ejpam-4944	507	1	assume	assume	VERB
ejpam-4944	507	2	that	that	SCONJ
ejpam-4944	507	3	,	,	PUNCT
ejpam-4944	507	4	m	m	VERB
ejpam-4944	507	5	/∈	/∈	PUNCT
ejpam-4944	508	1	µ̃2	µ̃2	PROPN
ejpam-4944	508	2	.	.	PUNCT
ejpam-4944	509	1	by	by	ADP
ejpam-4944	509	2	hypothesis	hypothesis	NOUN
ejpam-4944	509	3	,	,	PUNCT
ejpam-4944	509	4	iµ2	iµ2	PROPN
ejpam-4944	509	5	m	m	NOUN
ejpam-4944	509	6	∈	∈	NOUN
ejpam-4944	509	7	µ̃2	µ̃2	PROPN
ejpam-4944	509	8	which	which	PRON
ejpam-4944	509	9	implies	imply	VERB
ejpam-4944	509	10	iµ2	iµ2	PROPN
ejpam-4944	509	11	m	m	NOUN
ejpam-4944	509	12	∩q	∩q	PROPN
ejpam-4944	509	13	∈	∈	PROPN
ejpam-4944	509	14	˜µ2q	˜µ2q	PROPN
ejpam-4944	509	15	.	.	PUNCT
ejpam-4944	510	1	take	take	VERB
ejpam-4944	510	2	v	v	NOUN
ejpam-4944	510	3	=	=	PUNCT
ejpam-4944	510	4	iµ2	iµ2	PROPN
ejpam-4944	510	5	m	m	ADJ
ejpam-4944	510	6	∩q	∩q	NOUN
ejpam-4944	510	7	.	.	PUNCT
ejpam-4944	511	1	then	then	ADV
ejpam-4944	511	2	v	v	ADP
ejpam-4944	511	3	∩	∩	NOUN
ejpam-4944	511	4	p	p	X
ejpam-4944	511	5	̸=	̸=	PROPN
ejpam-4944	511	6	∅	∅	NOUN
ejpam-4944	511	7	so	so	SCONJ
ejpam-4944	511	8	that	that	DET
ejpam-4944	511	9	iµ2	iµ2	PROPN
ejpam-4944	511	10	m	m	PROPN
ejpam-4944	511	11	∩	∩	NOUN
ejpam-4944	511	12	p	p	X
ejpam-4944	511	13	̸=	̸=	PROPN
ejpam-4944	511	14	∅	∅	NOUN
ejpam-4944	511	15	which	which	PRON
ejpam-4944	511	16	implies	imply	VERB
ejpam-4944	511	17	m	m	NOUN
ejpam-4944	511	18	∩	∩	NOUN
ejpam-4944	511	19	p	p	PROPN
ejpam-4944	511	20	̸=	̸=	PROPN
ejpam-4944	511	21	∅	∅	NOUN
ejpam-4944	511	22	which	which	PRON
ejpam-4944	511	23	turn	turn	VERB
ejpam-4944	511	24	implies	imply	VERB
ejpam-4944	511	25	that	that	SCONJ
ejpam-4944	511	26	m	m	PROPN
ejpam-4944	511	27	∩	∩	ADJ
ejpam-4944	511	28	c2p	c2p	PROPN
ejpam-4944	511	29	̸=	̸=	PROPN
ejpam-4944	511	30	∅.	∅.	PRON
ejpam-4944	511	31	hence	hence	ADV
ejpam-4944	511	32	,	,	PUNCT
ejpam-4944	511	33	p	p	PROPN
ejpam-4944	511	34	∈	∈	PROPN
ejpam-4944	511	35	(	(	PUNCT
ejpam-4944	511	36	2	2	NUM
ejpam-4944	511	37	,	,	PUNCT
ejpam-4944	511	38	1)⋆	1)⋆	PROPN
ejpam-4944	511	39	−d(x	−d(x	NOUN
ejpam-4944	511	40	)	)	PUNCT
ejpam-4944	511	41	.	.	PUNCT
ejpam-4944	512	1	theorem	theorem	NOUN
ejpam-4944	512	2	33	33	NUM
ejpam-4944	512	3	.	.	PUNCT
ejpam-4944	513	1	let	let	AUX
ejpam-4944	513	2	(	(	PUNCT
ejpam-4944	513	3	x,µ1	x,µ1	NOUN
ejpam-4944	513	4	,	,	PUNCT
ejpam-4944	513	5	µ2	µ2	PROPN
ejpam-4944	513	6	)	)	PUNCT
ejpam-4944	513	7	be	be	VERB
ejpam-4944	513	8	a	a	DET
ejpam-4944	513	9	bgts	bgts	NOUN
ejpam-4944	513	10	,	,	PUNCT
ejpam-4944	513	11	µs	µs	X
ejpam-4944	513	12	satisfy	satisfy	VERB
ejpam-4944	513	13	the	the	DET
ejpam-4944	513	14	i	i	NOUN
ejpam-4944	513	15	-	-	PUNCT
ejpam-4944	513	16	property	property	NOUN
ejpam-4944	513	17	and	and	CCONJ
ejpam-4944	513	18	q	q	AUX
ejpam-4944	513	19	be	be	AUX
ejpam-4944	513	20	a	a	DET
ejpam-4944	513	21	µs	µs	NOUN
ejpam-4944	513	22	-	-	ADJ
ejpam-4944	513	23	open	open	ADJ
ejpam-4944	513	24	subset	subset	NOUN
ejpam-4944	513	25	of	of	ADP
ejpam-4944	513	26	x	x	PUNCT
ejpam-4944	513	27	for	for	ADP
ejpam-4944	513	28	s	s	NOUN
ejpam-4944	513	29	=	=	SYM
ejpam-4944	513	30	1	1	NUM
ejpam-4944	513	31	,	,	PUNCT
ejpam-4944	513	32	2	2	NUM
ejpam-4944	513	33	.	.	PUNCT
ejpam-4944	514	1	if	if	SCONJ
ejpam-4944	514	2	µs	µs	X
ejpam-4944	514	3	⊂	⊂	PROPN
ejpam-4944	514	4	µv	µv	PROPN
ejpam-4944	514	5	and	and	CCONJ
ejpam-4944	514	6	if	if	SCONJ
ejpam-4944	514	7	p	p	X
ejpam-4944	514	8	∈	∈	PROPN
ejpam-4944	514	9	(	(	PUNCT
ejpam-4944	514	10	s	s	PROPN
ejpam-4944	514	11	,	,	PUNCT
ejpam-4944	514	12	v)⋆	v)⋆	PROPN
ejpam-4944	514	13	−d(x	−d(x	NOUN
ejpam-4944	514	14	)	)	PUNCT
ejpam-4944	514	15	,	,	PUNCT
ejpam-4944	514	16	then	then	ADV
ejpam-4944	514	17	p	p	NOUN
ejpam-4944	514	18	is	be	AUX
ejpam-4944	514	19	µsq	µsq	VERB
ejpam-4944	514	20	-	-	PUNCT
ejpam-4944	514	21	dense	dense	ADJ
ejpam-4944	514	22	set	set	NOUN
ejpam-4944	514	23	in	in	ADP
ejpam-4944	514	24	q	q	PROPN
ejpam-4944	514	25	where	where	SCONJ
ejpam-4944	514	26	p	p	X
ejpam-4944	514	27	⊂	⊂	PROPN
ejpam-4944	514	28	q	q	X
ejpam-4944	514	29	;	;	PUNCT
ejpam-4944	514	30	s	s	X
ejpam-4944	514	31	,	,	PUNCT
ejpam-4944	514	32	v	v	NOUN
ejpam-4944	514	33	=	=	SYM
ejpam-4944	514	34	1	1	NUM
ejpam-4944	514	35	,	,	PUNCT
ejpam-4944	514	36	2	2	NUM
ejpam-4944	514	37	;	;	PUNCT
ejpam-4944	514	38	s	s	VERB
ejpam-4944	514	39	̸=	̸=	PROPN
ejpam-4944	514	40	v.	v.	ADP
ejpam-4944	514	41	proof	proof	NOUN
ejpam-4944	514	42	.	.	PUNCT
ejpam-4944	515	1	assume	assume	VERB
ejpam-4944	515	2	that	that	SCONJ
ejpam-4944	515	3	,	,	PUNCT
ejpam-4944	515	4	q	q	X
ejpam-4944	515	5	is	be	AUX
ejpam-4944	515	6	µs	µs	NOUN
ejpam-4944	515	7	-	-	ADJ
ejpam-4944	515	8	open	open	ADJ
ejpam-4944	515	9	subset	subset	NOUN
ejpam-4944	515	10	of	of	ADP
ejpam-4944	515	11	x;µs	x;µs	PROPN
ejpam-4944	515	12	⊂	⊂	PROPN
ejpam-4944	515	13	µv	µv	PROPN
ejpam-4944	515	14	and	and	CCONJ
ejpam-4944	515	15	p	p	PROPN
ejpam-4944	515	16	∈	∈	PROPN
ejpam-4944	515	17	(	(	PUNCT
ejpam-4944	515	18	s	s	PROPN
ejpam-4944	515	19	,	,	PUNCT
ejpam-4944	515	20	v)⋆	v)⋆	PROPN
ejpam-4944	515	21	−	−	PROPN
ejpam-4944	515	22	d(x	d(x	PROPN
ejpam-4944	515	23	)	)	PUNCT
ejpam-4944	515	24	for	for	ADP
ejpam-4944	515	25	s	s	PROPN
ejpam-4944	515	26	,	,	PUNCT
ejpam-4944	515	27	v	v	NOUN
ejpam-4944	515	28	=	=	SYM
ejpam-4944	515	29	1	1	NUM
ejpam-4944	515	30	,	,	PUNCT
ejpam-4944	515	31	2	2	NUM
ejpam-4944	515	32	;	;	PUNCT
ejpam-4944	515	33	s	s	AUX
ejpam-4944	515	34	̸=	̸=	PROPN
ejpam-4944	515	35	v.	v.	ADP
ejpam-4944	515	36	choose	choose	VERB
ejpam-4944	515	37	s	s	PART
ejpam-4944	515	38	=	=	SYM
ejpam-4944	515	39	1	1	NUM
ejpam-4944	515	40	and	and	CCONJ
ejpam-4944	515	41	v	v	NOUN
ejpam-4944	515	42	=	=	SYM
ejpam-4944	515	43	2	2	NUM
ejpam-4944	515	44	.	.	PUNCT
ejpam-4944	516	1	then	then	ADV
ejpam-4944	516	2	q	q	X
ejpam-4944	516	3	∈	∈	PROPN
ejpam-4944	516	4	µ̃1	µ̃1	NOUN
ejpam-4944	516	5	;	;	PUNCT
ejpam-4944	516	6	µ1	µ1	PROPN
ejpam-4944	516	7	⊂	⊂	ADJ
ejpam-4944	516	8	µ2	µ2	PROPN
ejpam-4944	516	9	and	and	CCONJ
ejpam-4944	516	10	p	p	NOUN
ejpam-4944	516	11	∈	∈	PROPN
ejpam-4944	516	12	(	(	PUNCT
ejpam-4944	516	13	1	1	NUM
ejpam-4944	516	14	,	,	PUNCT
ejpam-4944	516	15	2)⋆	2)⋆	NOUN
ejpam-4944	516	16	−	−	NOUN
ejpam-4944	516	17	d(x	d(x	NOUN
ejpam-4944	516	18	)	)	PUNCT
ejpam-4944	516	19	.	.	PUNCT
ejpam-4944	517	1	let	let	VERB
ejpam-4944	517	2	l	l	PROPN
ejpam-4944	517	3	∈	∈	PROPN
ejpam-4944	517	4	˜µ1q	˜µ1q	PROPN
ejpam-4944	517	5	.	.	PUNCT
ejpam-4944	518	1	then	then	ADV
ejpam-4944	518	2	l	l	X
ejpam-4944	519	1	=	=	PUNCT
ejpam-4944	519	2	k	k	X
ejpam-4944	519	3	∩q	∩q	PROPN
ejpam-4944	519	4	where	where	SCONJ
ejpam-4944	519	5	k	k	PROPN
ejpam-4944	519	6	∈	∈	PROPN
ejpam-4944	519	7	µ̃1	µ̃1	PROPN
ejpam-4944	519	8	.	.	PUNCT
ejpam-4944	519	9	by	by	ADP
ejpam-4944	519	10	hypothesis	hypothesis	NOUN
ejpam-4944	519	11	,	,	PUNCT
ejpam-4944	519	12	iµ1l	iµ1l	PROPN
ejpam-4944	519	13	∈	∈	PROPN
ejpam-4944	519	14	µ̃1	µ̃1	PROPN
ejpam-4944	519	15	.	.	PUNCT
ejpam-4944	520	1	this	this	PRON
ejpam-4944	520	2	implies	imply	VERB
ejpam-4944	520	3	l∩	l∩	VERB
ejpam-4944	520	4	c2p	c2p	NOUN
ejpam-4944	520	5	̸=	̸=	PROPN
ejpam-4944	520	6	∅	∅	NOUN
ejpam-4944	520	7	which	which	PRON
ejpam-4944	520	8	implies	imply	VERB
ejpam-4944	520	9	that	that	SCONJ
ejpam-4944	520	10	l	l	NOUN
ejpam-4944	520	11	∩	∩	NOUN
ejpam-4944	520	12	p	p	PROPN
ejpam-4944	520	13	̸=	̸=	PROPN
ejpam-4944	520	14	∅	∅	NOUN
ejpam-4944	520	15	,	,	PUNCT
ejpam-4944	520	16	by	by	ADP
ejpam-4944	520	17	lemma	lemma	PROPN
ejpam-4944	520	18	3	3	NUM
ejpam-4944	520	19	.	.	PUNCT
ejpam-4944	521	1	hence	hence	ADV
ejpam-4944	521	2	p	p	PROPN
ejpam-4944	521	3	is	be	AUX
ejpam-4944	521	4	a	a	DET
ejpam-4944	521	5	µ1q	µ1q	ADJ
ejpam-4944	521	6	-	-	PUNCT
ejpam-4944	521	7	dense	dense	ADJ
ejpam-4944	521	8	set	set	NOUN
ejpam-4944	521	9	in	in	ADP
ejpam-4944	521	10	q.	q.	PROPN
ejpam-4944	521	11	fix	fix	PROPN
ejpam-4944	521	12	s	s	PART
ejpam-4944	521	13	=	=	SYM
ejpam-4944	521	14	2	2	NUM
ejpam-4944	521	15	and	and	CCONJ
ejpam-4944	521	16	v	v	NOUN
ejpam-4944	521	17	=	=	SYM
ejpam-4944	521	18	1	1	X
ejpam-4944	521	19	.	.	PUNCT
ejpam-4944	522	1	we	we	PRON
ejpam-4944	522	2	get	get	VERB
ejpam-4944	522	3	q	q	PUNCT
ejpam-4944	522	4	∈	∈	PROPN
ejpam-4944	522	5	µ̃2	µ̃2	PROPN
ejpam-4944	522	6	;	;	PUNCT
ejpam-4944	522	7	µ2	µ2	PROPN
ejpam-4944	522	8	⊂	⊂	PROPN
ejpam-4944	522	9	µ1	µ1	PROPN
ejpam-4944	522	10	and	and	CCONJ
ejpam-4944	522	11	p	p	NOUN
ejpam-4944	522	12	∈	∈	PROPN
ejpam-4944	522	13	(	(	PUNCT
ejpam-4944	522	14	2	2	NUM
ejpam-4944	522	15	,	,	PUNCT
ejpam-4944	522	16	1)⋆	1)⋆	PROPN
ejpam-4944	522	17	−	−	PROPN
ejpam-4944	522	18	d(x	d(x	PROPN
ejpam-4944	522	19	)	)	PUNCT
ejpam-4944	522	20	.	.	PUNCT
ejpam-4944	523	1	let	let	VERB
ejpam-4944	523	2	v	v	NUM
ejpam-4944	523	3	∈	∈	PROPN
ejpam-4944	523	4	˜µ2q	˜µ2q	PROPN
ejpam-4944	523	5	.	.	PUNCT
ejpam-4944	524	1	then	then	ADV
ejpam-4944	524	2	v	v	X
ejpam-4944	524	3	=	=	SYM
ejpam-4944	524	4	m	m	NOUN
ejpam-4944	524	5	∩	∩	NOUN
ejpam-4944	524	6	q	q	X
ejpam-4944	524	7	where	where	SCONJ
ejpam-4944	524	8	m	m	VERB
ejpam-4944	524	9	∈	∈	NOUN
ejpam-4944	524	10	µ̃2	µ̃2	PROPN
ejpam-4944	524	11	.	.	PUNCT
ejpam-4944	524	12	by	by	ADP
ejpam-4944	524	13	assumption	assumption	NOUN
ejpam-4944	524	14	,	,	PUNCT
ejpam-4944	524	15	iµ2v	iµ2v	PROPN
ejpam-4944	524	16	∈	∈	PROPN
ejpam-4944	524	17	µ̃2	µ̃2	PROPN
ejpam-4944	524	18	so	so	SCONJ
ejpam-4944	525	1	that	that	SCONJ
ejpam-4944	525	2	v	v	ADP
ejpam-4944	525	3	∩	∩	NOUN
ejpam-4944	525	4	c1p	c1p	NOUN
ejpam-4944	525	5	̸=	̸=	PROPN
ejpam-4944	525	6	∅	∅	NOUN
ejpam-4944	525	7	which	which	PRON
ejpam-4944	525	8	implies	imply	VERB
ejpam-4944	525	9	that	that	SCONJ
ejpam-4944	525	10	v	v	ADP
ejpam-4944	525	11	∩	∩	NOUN
ejpam-4944	525	12	p	p	X
ejpam-4944	525	13	̸=	̸=	PROPN
ejpam-4944	525	14	∅	∅	NOUN
ejpam-4944	525	15	,	,	PUNCT
ejpam-4944	525	16	by	by	ADP
ejpam-4944	525	17	lemma	lemma	PROPN
ejpam-4944	525	18	3	3	NUM
ejpam-4944	525	19	.	.	PUNCT
ejpam-4944	526	1	therefore	therefore	ADV
ejpam-4944	526	2	,	,	PUNCT
ejpam-4944	526	3	p	p	PRON
ejpam-4944	526	4	is	be	AUX
ejpam-4944	526	5	a	a	DET
ejpam-4944	526	6	µ2q	µ2q	NOUN
ejpam-4944	526	7	-	-	PUNCT
ejpam-4944	526	8	dense	dense	ADJ
ejpam-4944	526	9	set	set	NOUN
ejpam-4944	526	10	in	in	ADP
ejpam-4944	526	11	q.	q.	PROPN
ejpam-4944	526	12	d.	d.	PROPN
ejpam-4944	526	13	elgezouli	elgezouli	PROPN
ejpam-4944	526	14	et	et	PROPN
ejpam-4944	526	15	al	al	PROPN
ejpam-4944	526	16	.	.	PUNCT
ejpam-4944	526	17	/	/	SYM
ejpam-4944	526	18	eur	eur	PROPN
ejpam-4944	526	19	.	.	PUNCT
ejpam-4944	527	1	j.	j.	PROPN
ejpam-4944	527	2	pure	pure	PROPN
ejpam-4944	527	3	appl	appl	PROPN
ejpam-4944	527	4	.	.	PROPN
ejpam-4944	527	5	math	math	PROPN
ejpam-4944	527	6	,	,	PUNCT
ejpam-4944	527	7	16	16	NUM
ejpam-4944	527	8	(	(	PUNCT
ejpam-4944	527	9	4	4	NUM
ejpam-4944	527	10	)	)	PUNCT
ejpam-4944	527	11	(	(	PUNCT
ejpam-4944	527	12	2023	2023	NUM
ejpam-4944	527	13	)	)	PUNCT
ejpam-4944	527	14	,	,	PUNCT
ejpam-4944	527	15	2286	2286	NUM
ejpam-4944	527	16	-	-	SYM
ejpam-4944	527	17	2305	2305	NUM
ejpam-4944	527	18	2300	2300	NUM
ejpam-4944	527	19	theorem	theorem	VERB
ejpam-4944	527	20	34	34	NUM
ejpam-4944	527	21	.	.	PUNCT
ejpam-4944	528	1	let	let	AUX
ejpam-4944	528	2	(	(	PUNCT
ejpam-4944	528	3	x,µ1	x,µ1	NOUN
ejpam-4944	528	4	,	,	PUNCT
ejpam-4944	528	5	µ2	µ2	PROPN
ejpam-4944	528	6	)	)	PUNCT
ejpam-4944	528	7	be	be	VERB
ejpam-4944	528	8	a	a	DET
ejpam-4944	528	9	bigeneralized	bigeneralized	ADJ
ejpam-4944	528	10	topological	topological	ADJ
ejpam-4944	528	11	space	space	NOUN
ejpam-4944	528	12	,	,	PUNCT
ejpam-4944	528	13	q	q	PUNCT
ejpam-4944	528	14	be	be	AUX
ejpam-4944	528	15	a	a	DET
ejpam-4944	528	16	µs	µs	NOUN
ejpam-4944	528	17	-	-	ADJ
ejpam-4944	528	18	open	open	ADJ
ejpam-4944	528	19	subset	subset	NOUN
ejpam-4944	528	20	of	of	ADP
ejpam-4944	528	21	x	x	X
ejpam-4944	528	22	and	and	CCONJ
ejpam-4944	528	23	µs	µs	NOUN
ejpam-4944	528	24	satisfy	satisfy	VERB
ejpam-4944	528	25	the	the	DET
ejpam-4944	528	26	i	i	NOUN
ejpam-4944	528	27	-	-	PUNCT
ejpam-4944	528	28	property	property	NOUN
ejpam-4944	528	29	for	for	ADP
ejpam-4944	528	30	s	s	NOUN
ejpam-4944	528	31	=	=	SYM
ejpam-4944	528	32	1	1	NUM
ejpam-4944	528	33	,	,	PUNCT
ejpam-4944	528	34	2	2	NUM
ejpam-4944	528	35	.	.	X
ejpam-4944	529	1	if	if	SCONJ
ejpam-4944	529	2	µsq	µsq	VERB
ejpam-4944	529	3	is	be	AUX
ejpam-4944	529	4	a	a	DET
ejpam-4944	529	5	sgt	sgt	PROPN
ejpam-4944	529	6	and	and	CCONJ
ejpam-4944	529	7	p	p	NOUN
ejpam-4944	529	8	∈	∈	PROPN
ejpam-4944	529	9	(	(	PUNCT
ejpam-4944	529	10	s	s	PROPN
ejpam-4944	529	11	,	,	PUNCT
ejpam-4944	529	12	v)⋆	v)⋆	PROPN
ejpam-4944	529	13	−d(x	−d(x	NOUN
ejpam-4944	529	14	)	)	PUNCT
ejpam-4944	529	15	,	,	PUNCT
ejpam-4944	529	16	then	then	ADV
ejpam-4944	529	17	p	p	PROPN
ejpam-4944	529	18	∈	∈	PROPN
ejpam-4944	529	19	(	(	PUNCT
ejpam-4944	529	20	µsq	µsq	VERB
ejpam-4944	529	21	,	,	PUNCT
ejpam-4944	529	22	µv)−d(q	µv)−d(q	NOUN
ejpam-4944	529	23	)	)	PUNCT
ejpam-4944	529	24	where	where	SCONJ
ejpam-4944	529	25	p	p	PROPN
ejpam-4944	529	26	⊂	⊂	PROPN
ejpam-4944	529	27	q	q	X
ejpam-4944	529	28	;	;	PUNCT
ejpam-4944	529	29	s	s	X
ejpam-4944	529	30	,	,	PUNCT
ejpam-4944	529	31	v	v	NOUN
ejpam-4944	529	32	=	=	SYM
ejpam-4944	529	33	1	1	NUM
ejpam-4944	529	34	,	,	PUNCT
ejpam-4944	529	35	2	2	NUM
ejpam-4944	529	36	;	;	PUNCT
ejpam-4944	529	37	s	s	VERB
ejpam-4944	529	38	̸=	̸=	PROPN
ejpam-4944	529	39	v.	v.	ADP
ejpam-4944	529	40	proof	proof	NOUN
ejpam-4944	529	41	.	.	PUNCT
ejpam-4944	530	1	suppose	suppose	VERB
ejpam-4944	530	2	that	that	SCONJ
ejpam-4944	530	3	,	,	PUNCT
ejpam-4944	530	4	q	q	PROPN
ejpam-4944	530	5	∈	∈	PROPN
ejpam-4944	530	6	µ̃s	µ̃s	NOUN
ejpam-4944	530	7	,	,	PUNCT
ejpam-4944	530	8	µs	µs	X
ejpam-4944	530	9	satisfy	satisfy	VERB
ejpam-4944	530	10	the	the	DET
ejpam-4944	530	11	i	i	NOUN
ejpam-4944	530	12	-	-	PUNCT
ejpam-4944	530	13	property	property	NOUN
ejpam-4944	530	14	and	and	CCONJ
ejpam-4944	530	15	µsq	µsq	VERB
ejpam-4944	530	16	is	be	AUX
ejpam-4944	530	17	a	a	DET
ejpam-4944	530	18	strong	strong	ADJ
ejpam-4944	530	19	generalized	generalized	ADJ
ejpam-4944	530	20	topology	topology	NOUN
ejpam-4944	530	21	for	for	ADP
ejpam-4944	530	22	s	s	NOUN
ejpam-4944	530	23	=	=	SYM
ejpam-4944	530	24	1	1	NUM
ejpam-4944	530	25	,	,	PUNCT
ejpam-4944	530	26	2	2	NUM
ejpam-4944	530	27	.	.	PUNCT
ejpam-4944	531	1	let	let	VERB
ejpam-4944	531	2	p	p	X
ejpam-4944	531	3	∈	∈	PROPN
ejpam-4944	531	4	(	(	PUNCT
ejpam-4944	531	5	s	s	PROPN
ejpam-4944	531	6	,	,	PUNCT
ejpam-4944	531	7	v)⋆	v)⋆	PROPN
ejpam-4944	531	8	−d(x	−d(x	NOUN
ejpam-4944	531	9	)	)	PUNCT
ejpam-4944	531	10	where	where	SCONJ
ejpam-4944	531	11	s	s	X
ejpam-4944	531	12	,	,	PUNCT
ejpam-4944	531	13	v	v	NOUN
ejpam-4944	531	14	=	=	SYM
ejpam-4944	531	15	1	1	NUM
ejpam-4944	531	16	,	,	PUNCT
ejpam-4944	531	17	2	2	NUM
ejpam-4944	531	18	;	;	PUNCT
ejpam-4944	531	19	s	s	AUX
ejpam-4944	531	20	̸=	̸=	PROPN
ejpam-4944	531	21	v.	v.	ADP
ejpam-4944	531	22	choose	choose	VERB
ejpam-4944	531	23	s	s	PART
ejpam-4944	531	24	=	=	SYM
ejpam-4944	531	25	1	1	NUM
ejpam-4944	531	26	and	and	CCONJ
ejpam-4944	531	27	v	v	NOUN
ejpam-4944	531	28	=	=	SYM
ejpam-4944	531	29	2	2	NUM
ejpam-4944	531	30	.	.	PUNCT
ejpam-4944	531	31	then	then	ADV
ejpam-4944	531	32	q	q	PROPN
ejpam-4944	531	33	∈	∈	PROPN
ejpam-4944	531	34	µ̃1	µ̃1	PROPN
ejpam-4944	531	35	,	,	PUNCT
ejpam-4944	531	36	µ1	µ1	NOUN
ejpam-4944	531	37	satisfy	satisfy	VERB
ejpam-4944	531	38	the	the	DET
ejpam-4944	531	39	i	i	NOUN
ejpam-4944	531	40	-	-	PUNCT
ejpam-4944	531	41	property	property	NOUN
ejpam-4944	531	42	,	,	PUNCT
ejpam-4944	531	43	µ1q	µ1q	SCONJ
ejpam-4944	531	44	is	be	AUX
ejpam-4944	531	45	a	a	DET
ejpam-4944	531	46	sgt	sgt	PROPN
ejpam-4944	531	47	and	and	CCONJ
ejpam-4944	531	48	p	p	NOUN
ejpam-4944	531	49	∈	∈	PROPN
ejpam-4944	531	50	(	(	PUNCT
ejpam-4944	531	51	1	1	NUM
ejpam-4944	531	52	,	,	PUNCT
ejpam-4944	531	53	2)⋆	2)⋆	NOUN
ejpam-4944	531	54	−	−	NOUN
ejpam-4944	531	55	d(x	d(x	NOUN
ejpam-4944	531	56	)	)	PUNCT
ejpam-4944	531	57	.	.	PUNCT
ejpam-4944	532	1	let	let	VERB
ejpam-4944	532	2	j	j	PROPN
ejpam-4944	532	3	∈	∈	PROPN
ejpam-4944	532	4	σ̃1q	σ̃1q	NOUN
ejpam-4944	532	5	.	.	PUNCT
ejpam-4944	533	1	if	if	SCONJ
ejpam-4944	533	2	j	j	PROPN
ejpam-4944	533	3	∈	∈	PROPN
ejpam-4944	533	4	µ̃1q	µ̃1q	X
ejpam-4944	533	5	,	,	PUNCT
ejpam-4944	533	6	then	then	ADV
ejpam-4944	533	7	there	there	PRON
ejpam-4944	533	8	is	be	VERB
ejpam-4944	533	9	nothing	nothing	PRON
ejpam-4944	533	10	to	to	PART
ejpam-4944	533	11	prove	prove	VERB
ejpam-4944	533	12	.	.	PUNCT
ejpam-4944	534	1	suppose	suppose	VERB
ejpam-4944	534	2	j	j	PROPN
ejpam-4944	534	3	/∈	/∈	PROPN
ejpam-4944	534	4	µ̃1q	µ̃1q	PROPN
ejpam-4944	534	5	.	.	PUNCT
ejpam-4944	535	1	since	since	SCONJ
ejpam-4944	535	2	j	j	PROPN
ejpam-4944	535	3	∈	∈	PROPN
ejpam-4944	535	4	σ̃1q	σ̃1q	NOUN
ejpam-4944	535	5	and	and	CCONJ
ejpam-4944	535	6	µ1q	µ1q	ADP
ejpam-4944	535	7	is	be	AUX
ejpam-4944	535	8	a	a	DET
ejpam-4944	535	9	strong	strong	ADJ
ejpam-4944	535	10	subspace	subspace	NOUN
ejpam-4944	535	11	generalized	generalize	VERB
ejpam-4944	535	12	topology	topology	NOUN
ejpam-4944	535	13	we	we	PRON
ejpam-4944	535	14	have	have	VERB
ejpam-4944	535	15	i1qj	i1qj	X
ejpam-4944	535	16	∈	∈	PROPN
ejpam-4944	535	17	µ̃1q	µ̃1q	X
ejpam-4944	535	18	.	.	PUNCT
ejpam-4944	536	1	take	take	VERB
ejpam-4944	536	2	k	k	NOUN
ejpam-4944	536	3	=	=	PUNCT
ejpam-4944	536	4	i1qj	i1qj	PROPN
ejpam-4944	536	5	.	.	PUNCT
ejpam-4944	537	1	then	then	ADV
ejpam-4944	537	2	k	k	PROPN
ejpam-4944	537	3	̸=	̸=	PROPN
ejpam-4944	537	4	∅	∅	NOUN
ejpam-4944	537	5	and	and	CCONJ
ejpam-4944	537	6	k	k	NOUN
ejpam-4944	537	7	=	=	PUNCT
ejpam-4944	538	1	l	l	X
ejpam-4944	538	2	∩q	∩q	PROPN
ejpam-4944	538	3	where	where	SCONJ
ejpam-4944	538	4	l	l	PROPN
ejpam-4944	538	5	∈	∈	PROPN
ejpam-4944	538	6	µ̃1	µ̃1	PROPN
ejpam-4944	538	7	.	.	PUNCT
ejpam-4944	538	8	since	since	SCONJ
ejpam-4944	538	9	l	l	NOUN
ejpam-4944	538	10	,	,	PUNCT
ejpam-4944	538	11	q	q	NOUN
ejpam-4944	538	12	∈	∈	PROPN
ejpam-4944	538	13	µ̃1	µ̃1	NOUN
ejpam-4944	538	14	and	and	CCONJ
ejpam-4944	538	15	µ1	µ1	NOUN
ejpam-4944	538	16	satisfy	satisfy	NOUN
ejpam-4944	538	17	the	the	DET
ejpam-4944	538	18	i	i	NOUN
ejpam-4944	538	19	-	-	PUNCT
ejpam-4944	538	20	property	property	NOUN
ejpam-4944	538	21	,	,	PUNCT
ejpam-4944	538	22	iµ1(k	iµ1(k	PROPN
ejpam-4944	538	23	)	)	PUNCT
ejpam-4944	538	24	∈	∈	PROPN
ejpam-4944	539	1	µ̃1	µ̃1	PROPN
ejpam-4944	539	2	.	.	PUNCT
ejpam-4944	540	1	this	this	PRON
ejpam-4944	540	2	implies	imply	VERB
ejpam-4944	540	3	iµ1k	iµ1k	PROPN
ejpam-4944	540	4	∩	∩	ADJ
ejpam-4944	540	5	c2p	c2p	NOUN
ejpam-4944	540	6	̸=	̸=	PROPN
ejpam-4944	540	7	∅	∅	NOUN
ejpam-4944	540	8	which	which	PRON
ejpam-4944	540	9	implies	imply	VERB
ejpam-4944	540	10	k	k	PROPN
ejpam-4944	540	11	∩	∩	ADJ
ejpam-4944	540	12	c2p	c2p	PROPN
ejpam-4944	540	13	̸=	̸=	PROPN
ejpam-4944	540	14	∅	∅	NOUN
ejpam-4944	540	15	which	which	PRON
ejpam-4944	540	16	turn	turn	VERB
ejpam-4944	540	17	implies	imply	VERB
ejpam-4944	540	18	that	that	SCONJ
ejpam-4944	540	19	j	j	PROPN
ejpam-4944	540	20	∩	∩	NOUN
ejpam-4944	540	21	c2p	c2p	PROPN
ejpam-4944	540	22	̸=	̸=	PROPN
ejpam-4944	540	23	∅.	∅.	VERB
ejpam-4944	540	24	hence	hence	ADV
ejpam-4944	540	25	p	p	NOUN
ejpam-4944	540	26	∈	∈	PROPN
ejpam-4944	540	27	(	(	PUNCT
ejpam-4944	540	28	µ1q	µ1q	ADP
ejpam-4944	540	29	,	,	PUNCT
ejpam-4944	540	30	µ2	µ2	PROPN
ejpam-4944	540	31	)	)	PUNCT
ejpam-4944	540	32	⋆	⋆	VERB
ejpam-4944	540	33	−d(q	−d(q	NOUN
ejpam-4944	540	34	)	)	PUNCT
ejpam-4944	540	35	.	.	PUNCT
ejpam-4944	541	1	take	take	VERB
ejpam-4944	541	2	s	s	NOUN
ejpam-4944	541	3	=	=	SYM
ejpam-4944	541	4	2	2	NUM
ejpam-4944	541	5	and	and	CCONJ
ejpam-4944	541	6	v	v	NOUN
ejpam-4944	541	7	=	=	SYM
ejpam-4944	541	8	1	1	X
ejpam-4944	541	9	.	.	PUNCT
ejpam-4944	542	1	we	we	PRON
ejpam-4944	542	2	get	get	VERB
ejpam-4944	542	3	q	q	X
ejpam-4944	542	4	∈	∈	PROPN
ejpam-4944	542	5	µ̃2	µ̃2	PROPN
ejpam-4944	542	6	,	,	PUNCT
ejpam-4944	542	7	µ2	µ2	PROPN
ejpam-4944	542	8	satisfy	satisfy	VERB
ejpam-4944	542	9	the	the	DET
ejpam-4944	542	10	i	i	NOUN
ejpam-4944	542	11	-	-	PUNCT
ejpam-4944	542	12	property	property	NOUN
ejpam-4944	542	13	,	,	PUNCT
ejpam-4944	542	14	µ2q	µ2q	PUNCT
ejpam-4944	542	15	is	be	AUX
ejpam-4944	542	16	a	a	DET
ejpam-4944	542	17	sgt	sgt	PROPN
ejpam-4944	542	18	and	and	CCONJ
ejpam-4944	542	19	p	p	NOUN
ejpam-4944	542	20	∈	∈	PROPN
ejpam-4944	542	21	(	(	PUNCT
ejpam-4944	542	22	2	2	NUM
ejpam-4944	542	23	,	,	PUNCT
ejpam-4944	542	24	1)⋆	1)⋆	PROPN
ejpam-4944	542	25	−d(x	−d(x	NOUN
ejpam-4944	542	26	)	)	PUNCT
ejpam-4944	542	27	.	.	PUNCT
ejpam-4944	543	1	let	let	VERB
ejpam-4944	543	2	v	v	X
ejpam-4944	543	3	∈	∈	PROPN
ejpam-4944	543	4	σ̃2q	σ̃2q	VERB
ejpam-4944	543	5	.	.	PUNCT
ejpam-4944	544	1	if	if	SCONJ
ejpam-4944	544	2	v	v	PRON
ejpam-4944	544	3	∈	∈	PROPN
ejpam-4944	544	4	µ̃2q	µ̃2q	NUM
ejpam-4944	544	5	,	,	PUNCT
ejpam-4944	544	6	then	then	ADV
ejpam-4944	544	7	the	the	DET
ejpam-4944	544	8	proof	proof	NOUN
ejpam-4944	544	9	is	be	AUX
ejpam-4944	544	10	obvious	obvious	ADJ
ejpam-4944	544	11	.	.	PUNCT
ejpam-4944	545	1	assume	assume	VERB
ejpam-4944	545	2	v	v	X
ejpam-4944	545	3	/∈	/∈	PUNCT
ejpam-4944	545	4	µ̃2q	µ̃2q	NUM
ejpam-4944	545	5	.	.	PUNCT
ejpam-4944	546	1	by	by	ADP
ejpam-4944	546	2	the	the	DET
ejpam-4944	546	3	definition	definition	NOUN
ejpam-4944	546	4	of	of	ADP
ejpam-4944	546	5	v	v	NOUN
ejpam-4944	546	6	and	and	CCONJ
ejpam-4944	546	7	µ2q	µ2q	PROPN
ejpam-4944	546	8	is	be	AUX
ejpam-4944	546	9	a	a	DET
ejpam-4944	546	10	strong	strong	ADJ
ejpam-4944	546	11	subspace	subspace	NOUN
ejpam-4944	546	12	generalized	generalize	VERB
ejpam-4944	546	13	topology	topology	NOUN
ejpam-4944	546	14	we	we	PRON
ejpam-4944	546	15	have	have	VERB
ejpam-4944	546	16	i2qv	i2qv	NOUN
ejpam-4944	546	17	∈	∈	PROPN
ejpam-4944	546	18	µ̃2q	µ̃2q	NUM
ejpam-4944	546	19	.	.	PUNCT
ejpam-4944	547	1	take	take	VERB
ejpam-4944	547	2	l	l	NOUN
ejpam-4944	547	3	=	=	PUNCT
ejpam-4944	547	4	i2qv	i2qv	PROPN
ejpam-4944	547	5	.	.	PUNCT
ejpam-4944	548	1	then	then	ADV
ejpam-4944	548	2	l	l	NOUN
ejpam-4944	548	3	̸=	̸=	PROPN
ejpam-4944	548	4	∅	∅	NOUN
ejpam-4944	548	5	and	and	CCONJ
ejpam-4944	548	6	l	l	NOUN
ejpam-4944	548	7	=	=	PUNCT
ejpam-4944	548	8	m	m	PROPN
ejpam-4944	548	9	∩	∩	NOUN
ejpam-4944	548	10	q	q	X
ejpam-4944	548	11	where	where	SCONJ
ejpam-4944	548	12	m	m	VERB
ejpam-4944	548	13	∈	∈	PROPN
ejpam-4944	548	14	µ̃2	µ̃2	PROPN
ejpam-4944	548	15	.	.	PUNCT
ejpam-4944	549	1	here	here	ADV
ejpam-4944	549	2	,	,	PUNCT
ejpam-4944	549	3	m	m	PROPN
ejpam-4944	549	4	,	,	PUNCT
ejpam-4944	549	5	q	q	PROPN
ejpam-4944	549	6	∈	∈	PROPN
ejpam-4944	549	7	µ̃2	µ̃2	PROPN
ejpam-4944	549	8	and	and	CCONJ
ejpam-4944	549	9	µ2	µ2	PROPN
ejpam-4944	549	10	satisfy	satisfy	VERB
ejpam-4944	549	11	the	the	DET
ejpam-4944	549	12	i	i	NOUN
ejpam-4944	549	13	-	-	PUNCT
ejpam-4944	549	14	property	property	NOUN
ejpam-4944	549	15	,	,	PUNCT
ejpam-4944	549	16	iµ2(l	iµ2(l	PROPN
ejpam-4944	549	17	)	)	PUNCT
ejpam-4944	549	18	∈	∈	PROPN
ejpam-4944	549	19	µ̃2	µ̃2	PROPN
ejpam-4944	549	20	so	so	SCONJ
ejpam-4944	549	21	that	that	SCONJ
ejpam-4944	549	22	iµ2l∩c1p	iµ2l∩c1p	NOUN
ejpam-4944	549	23	̸=	̸=	PROPN
ejpam-4944	549	24	∅	∅	NOUN
ejpam-4944	549	25	which	which	PRON
ejpam-4944	549	26	implies	imply	VERB
ejpam-4944	549	27	l∩c1p	l∩c1p	NUM
ejpam-4944	549	28	̸=	̸=	PROPN
ejpam-4944	549	29	∅	∅	NOUN
ejpam-4944	549	30	which	which	PRON
ejpam-4944	549	31	turn	turn	VERB
ejpam-4944	549	32	implies	imply	VERB
ejpam-4944	549	33	that	that	SCONJ
ejpam-4944	549	34	v	v	ADP
ejpam-4944	549	35	∩	∩	NOUN
ejpam-4944	549	36	c1p	c1p	NOUN
ejpam-4944	549	37	̸=	̸=	PROPN
ejpam-4944	549	38	∅.	∅.	VERB
ejpam-4944	549	39	therefore	therefore	ADV
ejpam-4944	549	40	,	,	PUNCT
ejpam-4944	549	41	p	p	PROPN
ejpam-4944	549	42	∈	∈	PROPN
ejpam-4944	549	43	(	(	PUNCT
ejpam-4944	549	44	µ2q	µ2q	NOUN
ejpam-4944	549	45	,	,	PUNCT
ejpam-4944	549	46	µ1	µ1	PROPN
ejpam-4944	549	47	)	)	PUNCT
ejpam-4944	549	48	⋆	⋆	VERB
ejpam-4944	549	49	−d(q	−d(q	NOUN
ejpam-4944	549	50	)	)	PUNCT
ejpam-4944	549	51	.	.	PUNCT
ejpam-4944	550	1	theorem	theorem	VERB
ejpam-4944	550	2	35	35	NUM
ejpam-4944	550	3	.	.	PUNCT
ejpam-4944	551	1	let	let	AUX
ejpam-4944	551	2	(	(	PUNCT
ejpam-4944	551	3	x,µ1	x,µ1	NOUN
ejpam-4944	551	4	,	,	PUNCT
ejpam-4944	551	5	µ2	µ2	PROPN
ejpam-4944	551	6	)	)	PUNCT
ejpam-4944	551	7	be	be	VERB
ejpam-4944	551	8	a	a	DET
ejpam-4944	551	9	bgts	bgts	NOUN
ejpam-4944	551	10	and	and	CCONJ
ejpam-4944	551	11	q	q	AUX
ejpam-4944	551	12	be	be	AUX
ejpam-4944	551	13	a	a	DET
ejpam-4944	551	14	µs	µs	NOUN
ejpam-4944	551	15	-	-	PUNCT
ejpam-4944	551	16	dense	dense	ADJ
ejpam-4944	551	17	subset	subset	NOUN
ejpam-4944	551	18	of	of	ADP
ejpam-4944	551	19	x	x	PUNCT
ejpam-4944	551	20	for	for	ADP
ejpam-4944	551	21	s	s	NOUN
ejpam-4944	551	22	=	=	SYM
ejpam-4944	551	23	1	1	NUM
ejpam-4944	551	24	,	,	PUNCT
ejpam-4944	551	25	2	2	NUM
ejpam-4944	551	26	.	.	X
ejpam-4944	552	1	if	if	SCONJ
ejpam-4944	552	2	µs	µs	NOUN
ejpam-4944	552	3	is	be	AUX
ejpam-4944	552	4	a	a	DET
ejpam-4944	552	5	strong	strong	ADJ
ejpam-4944	552	6	generalized	generalized	ADJ
ejpam-4944	552	7	topology	topology	NOUN
ejpam-4944	552	8	and	and	CCONJ
ejpam-4944	552	9	if	if	SCONJ
ejpam-4944	552	10	p	p	X
ejpam-4944	552	11	∈	∈	PROPN
ejpam-4944	552	12	(	(	PUNCT
ejpam-4944	552	13	µsq	µsq	VERB
ejpam-4944	552	14	,	,	PUNCT
ejpam-4944	552	15	µvq	µvq	ADJ
ejpam-4944	552	16	)	)	PUNCT
ejpam-4944	552	17	⋆−d(q	⋆−d(q	PROPN
ejpam-4944	552	18	)	)	PUNCT
ejpam-4944	552	19	,	,	PUNCT
ejpam-4944	552	20	then	then	ADV
ejpam-4944	552	21	p	p	PROPN
ejpam-4944	552	22	∈	∈	PROPN
ejpam-4944	552	23	(	(	PUNCT
ejpam-4944	552	24	s	s	NOUN
ejpam-4944	552	25	,	,	PUNCT
ejpam-4944	552	26	v)⋆−d(x	v)⋆−d(x	PROPN
ejpam-4944	552	27	)	)	PUNCT
ejpam-4944	552	28	for	for	ADP
ejpam-4944	552	29	s	s	PROPN
ejpam-4944	552	30	,	,	PUNCT
ejpam-4944	552	31	v	v	NOUN
ejpam-4944	552	32	=	=	SYM
ejpam-4944	552	33	1	1	NUM
ejpam-4944	552	34	,	,	PUNCT
ejpam-4944	552	35	2	2	NUM
ejpam-4944	552	36	;	;	PUNCT
ejpam-4944	552	37	s	s	VERB
ejpam-4944	552	38	̸=	̸=	PROPN
ejpam-4944	552	39	v.	v.	ADP
ejpam-4944	552	40	proof	proof	NOUN
ejpam-4944	552	41	.	.	PUNCT
ejpam-4944	553	1	assume	assume	VERB
ejpam-4944	553	2	that	that	SCONJ
ejpam-4944	553	3	,	,	PUNCT
ejpam-4944	553	4	p	p	PROPN
ejpam-4944	553	5	∈	∈	PROPN
ejpam-4944	553	6	(	(	PUNCT
ejpam-4944	553	7	µsq	µsq	VERB
ejpam-4944	553	8	,	,	PUNCT
ejpam-4944	553	9	µvq	µvq	ADJ
ejpam-4944	553	10	)	)	PUNCT
ejpam-4944	553	11	⋆	⋆	VERB
ejpam-4944	553	12	−d(q	−d(q	NOUN
ejpam-4944	553	13	)	)	PUNCT
ejpam-4944	553	14	where	where	SCONJ
ejpam-4944	553	15	s	s	X
ejpam-4944	553	16	,	,	PUNCT
ejpam-4944	553	17	v	v	NOUN
ejpam-4944	553	18	=	=	SYM
ejpam-4944	553	19	1	1	NUM
ejpam-4944	553	20	,	,	PUNCT
ejpam-4944	553	21	2	2	NUM
ejpam-4944	553	22	;	;	PUNCT
ejpam-4944	553	23	s	s	AUX
ejpam-4944	553	24	̸=	̸=	PROPN
ejpam-4944	553	25	v.	v.	ADP
ejpam-4944	553	26	choose	choose	VERB
ejpam-4944	553	27	s	s	PART
ejpam-4944	553	28	=	=	SYM
ejpam-4944	553	29	1	1	NUM
ejpam-4944	553	30	and	and	CCONJ
ejpam-4944	553	31	v	v	NOUN
ejpam-4944	553	32	=	=	SYM
ejpam-4944	553	33	2	2	NUM
ejpam-4944	553	34	.	.	PUNCT
ejpam-4944	554	1	then	then	ADV
ejpam-4944	554	2	p	p	PROPN
ejpam-4944	554	3	∈	∈	PROPN
ejpam-4944	554	4	(	(	PUNCT
ejpam-4944	554	5	µ1q	µ1q	ADP
ejpam-4944	554	6	,	,	PUNCT
ejpam-4944	554	7	µ2q	µ2q	PROPN
ejpam-4944	554	8	)	)	PUNCT
ejpam-4944	554	9	⋆	⋆	VERB
ejpam-4944	554	10	−	−	PROPN
ejpam-4944	554	11	d(q	d(q	NOUN
ejpam-4944	554	12	)	)	PUNCT
ejpam-4944	554	13	.	.	PUNCT
ejpam-4944	555	1	let	let	VERB
ejpam-4944	555	2	h	h	PRON
ejpam-4944	555	3	∈	∈	PROPN
ejpam-4944	555	4	σ̃1	σ̃1	PROPN
ejpam-4944	555	5	.	.	PROPN
ejpam-4944	555	6	suppose	suppose	VERB
ejpam-4944	555	7	h	h	PROPN
ejpam-4944	555	8	∈	∈	PROPN
ejpam-4944	555	9	µ̃1	µ̃1	PROPN
ejpam-4944	555	10	.	.	PUNCT
ejpam-4944	556	1	then	then	ADV
ejpam-4944	556	2	h	h	PROPN
ejpam-4944	556	3	∩	∩	PROPN
ejpam-4944	556	4	q	q	PROPN
ejpam-4944	556	5	∈	∈	PROPN
ejpam-4944	556	6	µ̃1q	µ̃1q	X
ejpam-4944	556	7	.	.	PUNCT
ejpam-4944	557	1	take	take	VERB
ejpam-4944	557	2	k	k	NOUN
ejpam-4944	557	3	=	=	PUNCT
ejpam-4944	557	4	h	h	PROPN
ejpam-4944	557	5	∩	∩	PROPN
ejpam-4944	557	6	q.	q.	PROPN
ejpam-4944	557	7	then	then	ADV
ejpam-4944	557	8	k	k	PROPN
ejpam-4944	557	9	∩	∩	PROPN
ejpam-4944	557	10	c2qp	c2qp	PROPN
ejpam-4944	557	11	̸=	̸=	PROPN
ejpam-4944	557	12	∅	∅	NOUN
ejpam-4944	557	13	so	so	SCONJ
ejpam-4944	557	14	that	that	SCONJ
ejpam-4944	557	15	k	k	PROPN
ejpam-4944	557	16	∩	∩	ADJ
ejpam-4944	557	17	c2p	c2p	PROPN
ejpam-4944	557	18	̸=	̸=	PROPN
ejpam-4944	557	19	∅.	∅.	ADP
ejpam-4944	557	20	this	this	PRON
ejpam-4944	557	21	implies	imply	VERB
ejpam-4944	557	22	h	h	NOUN
ejpam-4944	557	23	∩	∩	ADJ
ejpam-4944	557	24	c2(p	c2(p	X
ejpam-4944	557	25	)	)	PUNCT
ejpam-4944	557	26	̸=	̸=	PROPN
ejpam-4944	557	27	∅	∅	NOUN
ejpam-4944	557	28	which	which	PRON
ejpam-4944	557	29	implies	imply	VERB
ejpam-4944	557	30	that	that	SCONJ
ejpam-4944	557	31	p	p	PROPN
ejpam-4944	557	32	∈	∈	PROPN
ejpam-4944	557	33	(	(	PUNCT
ejpam-4944	557	34	1	1	NUM
ejpam-4944	557	35	,	,	PUNCT
ejpam-4944	557	36	2)⋆	2)⋆	PROPN
ejpam-4944	557	37	−d(x	−d(x	NOUN
ejpam-4944	557	38	)	)	PUNCT
ejpam-4944	557	39	.	.	PUNCT
ejpam-4944	558	1	if	if	SCONJ
ejpam-4944	558	2	h	h	NOUN
ejpam-4944	558	3	/∈	/∈	PUNCT
ejpam-4944	559	1	µ̃1	µ̃1	NOUN
ejpam-4944	559	2	,	,	PUNCT
ejpam-4944	559	3	then	then	ADV
ejpam-4944	559	4	i1h	i1h	PROPN
ejpam-4944	559	5	∈	∈	PROPN
ejpam-4944	559	6	µ̃1	µ̃1	PROPN
ejpam-4944	559	7	.	.	PUNCT
ejpam-4944	560	1	take	take	VERB
ejpam-4944	560	2	l	l	NOUN
ejpam-4944	560	3	=	=	SYM
ejpam-4944	560	4	i1h	i1h	PROPN
ejpam-4944	560	5	.	.	PUNCT
ejpam-4944	561	1	then	then	ADV
ejpam-4944	561	2	by	by	ADP
ejpam-4944	561	3	similar	similar	ADJ
ejpam-4944	561	4	arguments	argument	NOUN
ejpam-4944	561	5	in	in	ADP
ejpam-4944	561	6	the	the	DET
ejpam-4944	561	7	above	above	ADJ
ejpam-4944	561	8	case	case	NOUN
ejpam-4944	561	9	,	,	PUNCT
ejpam-4944	561	10	we	we	PRON
ejpam-4944	561	11	get	get	VERB
ejpam-4944	561	12	p	p	X
ejpam-4944	561	13	∈	∈	NOUN
ejpam-4944	561	14	(	(	PUNCT
ejpam-4944	561	15	1	1	NUM
ejpam-4944	561	16	,	,	PUNCT
ejpam-4944	561	17	2)⋆	2)⋆	PROPN
ejpam-4944	561	18	−d(x	−d(x	NOUN
ejpam-4944	561	19	)	)	PUNCT
ejpam-4944	561	20	.	.	PUNCT
ejpam-4944	562	1	fix	fix	NOUN
ejpam-4944	562	2	s	s	NOUN
ejpam-4944	562	3	=	=	SYM
ejpam-4944	562	4	2	2	NUM
ejpam-4944	562	5	and	and	CCONJ
ejpam-4944	562	6	v	v	NOUN
ejpam-4944	562	7	=	=	SYM
ejpam-4944	562	8	1	1	X
ejpam-4944	562	9	.	.	PUNCT
ejpam-4944	563	1	we	we	PRON
ejpam-4944	563	2	get	get	VERB
ejpam-4944	563	3	p	p	X
ejpam-4944	563	4	∈	∈	PROPN
ejpam-4944	563	5	(	(	PUNCT
ejpam-4944	563	6	µ2q	µ2q	X
ejpam-4944	563	7	,	,	PUNCT
ejpam-4944	563	8	µ1q	µ1q	ADP
ejpam-4944	563	9	)	)	PUNCT
ejpam-4944	563	10	⋆	⋆	VERB
ejpam-4944	563	11	−d(q	−d(q	NOUN
ejpam-4944	563	12	)	)	PUNCT
ejpam-4944	563	13	.	.	PUNCT
ejpam-4944	564	1	let	let	VERB
ejpam-4944	564	2	g	g	PROPN
ejpam-4944	564	3	∈	∈	PROPN
ejpam-4944	564	4	σ̃2	σ̃2	PROPN
ejpam-4944	564	5	.	.	PUNCT
ejpam-4944	564	6	suppose	suppose	VERB
ejpam-4944	564	7	g	g	PROPN
ejpam-4944	564	8	∈	∈	PROPN
ejpam-4944	564	9	µ̃2	µ̃2	PROPN
ejpam-4944	564	10	we	we	PRON
ejpam-4944	564	11	get	get	VERB
ejpam-4944	564	12	g	g	ADP
ejpam-4944	564	13	∩q	∩q	PROPN
ejpam-4944	564	14	∈	∈	PROPN
ejpam-4944	564	15	µ̃2q	µ̃2q	NUM
ejpam-4944	564	16	.	.	PUNCT
ejpam-4944	565	1	choose	choose	VERB
ejpam-4944	565	2	k	k	X
ejpam-4944	565	3	=	=	PUNCT
ejpam-4944	566	1	g	g	PROPN
ejpam-4944	566	2	∩q	∩q	PROPN
ejpam-4944	567	1	so	so	SCONJ
ejpam-4944	567	2	that	that	SCONJ
ejpam-4944	567	3	k	k	PROPN
ejpam-4944	567	4	∩	∩	PROPN
ejpam-4944	567	5	c1qp	c1qp	NOUN
ejpam-4944	567	6	̸=	̸=	PROPN
ejpam-4944	567	7	∅	∅	NOUN
ejpam-4944	567	8	which	which	PRON
ejpam-4944	567	9	implies	imply	VERB
ejpam-4944	567	10	that	that	SCONJ
ejpam-4944	567	11	k	k	PROPN
ejpam-4944	567	12	∩	∩	NOUN
ejpam-4944	567	13	c1p	c1p	NOUN
ejpam-4944	567	14	̸=	̸=	PROPN
ejpam-4944	567	15	∅.	∅.	ADP
ejpam-4944	567	16	thus	thus	ADV
ejpam-4944	567	17	,	,	PUNCT
ejpam-4944	567	18	g	g	PROPN
ejpam-4944	567	19	∩	∩	NOUN
ejpam-4944	567	20	c1(p	c1(p	X
ejpam-4944	567	21	)	)	PUNCT
ejpam-4944	567	22	̸=	̸=	NOUN
ejpam-4944	567	23	∅	∅	NOUN
ejpam-4944	567	24	so	so	SCONJ
ejpam-4944	567	25	that	that	SCONJ
ejpam-4944	567	26	p	p	PROPN
ejpam-4944	567	27	∈	∈	PROPN
ejpam-4944	567	28	(	(	PUNCT
ejpam-4944	567	29	2	2	NUM
ejpam-4944	567	30	,	,	PUNCT
ejpam-4944	567	31	1)⋆	1)⋆	PROPN
ejpam-4944	567	32	−	−	PROPN
ejpam-4944	567	33	d(x	d(x	PROPN
ejpam-4944	567	34	)	)	PUNCT
ejpam-4944	567	35	.	.	PUNCT
ejpam-4944	568	1	assume	assume	VERB
ejpam-4944	568	2	that	that	SCONJ
ejpam-4944	568	3	,	,	PUNCT
ejpam-4944	568	4	g	g	NOUN
ejpam-4944	568	5	/∈	/∈	PUNCT
ejpam-4944	568	6	µ̃2	µ̃2	PROPN
ejpam-4944	568	7	,	,	PUNCT
ejpam-4944	568	8	then	then	ADV
ejpam-4944	568	9	i2	i2	PROPN
ejpam-4944	568	10	g	g	PROPN
ejpam-4944	568	11	∈	∈	PROPN
ejpam-4944	568	12	µ̃2	µ̃2	PROPN
ejpam-4944	568	13	.	.	PUNCT
ejpam-4944	569	1	take	take	VERB
ejpam-4944	569	2	l	l	NOUN
ejpam-4944	569	3	=	=	SYM
ejpam-4944	569	4	i2	i2	PROPN
ejpam-4944	569	5	g.	g.	PROPN
ejpam-4944	569	6	by	by	ADP
ejpam-4944	569	7	similar	similar	ADJ
ejpam-4944	569	8	considerations	consideration	NOUN
ejpam-4944	569	9	,	,	PUNCT
ejpam-4944	569	10	we	we	PRON
ejpam-4944	569	11	get	get	VERB
ejpam-4944	569	12	p	p	X
ejpam-4944	569	13	∈	∈	NOUN
ejpam-4944	569	14	(	(	PUNCT
ejpam-4944	569	15	2	2	NUM
ejpam-4944	569	16	,	,	PUNCT
ejpam-4944	569	17	1)⋆	1)⋆	PROPN
ejpam-4944	569	18	−d(x	−d(x	NOUN
ejpam-4944	569	19	)	)	PUNCT
ejpam-4944	569	20	.	.	PUNCT
ejpam-4944	570	1	4	4	X
ejpam-4944	570	2	.	.	NUM
ejpam-4944	570	3	images	image	NOUN
ejpam-4944	570	4	of	of	ADP
ejpam-4944	570	5	(	(	PUNCT
ejpam-4944	570	6	s	s	X
ejpam-4944	570	7	,	,	PUNCT
ejpam-4944	570	8	v)⋆-dense	v)⋆-dense	PROPN
ejpam-4944	570	9	sets	set	VERB
ejpam-4944	570	10	a	a	DET
ejpam-4944	570	11	function	function	NOUN
ejpam-4944	570	12	f	f	NOUN
ejpam-4944	570	13	:	:	PUNCT
ejpam-4944	570	14	(	(	PUNCT
ejpam-4944	570	15	x,µ	x,µ	NOUN
ejpam-4944	570	16	)	)	PUNCT
ejpam-4944	570	17	→	→	SYM
ejpam-4944	570	18	(	(	PUNCT
ejpam-4944	570	19	y	y	PROPN
ejpam-4944	570	20	,	,	PUNCT
ejpam-4944	570	21	η	η	NOUN
ejpam-4944	570	22	)	)	PUNCT
ejpam-4944	570	23	is	be	AUX
ejpam-4944	570	24	said	say	VERB
ejpam-4944	570	25	to	to	PART
ejpam-4944	570	26	be	be	AUX
ejpam-4944	570	27	(	(	PUNCT
ejpam-4944	570	28	µ	µ	NUM
ejpam-4944	570	29	,	,	PUNCT
ejpam-4944	570	30	η)-continuous	η)-continuous	ADJ
ejpam-4944	570	31	[	[	X
ejpam-4944	570	32	4	4	NUM
ejpam-4944	570	33	]	]	X
ejpam-4944	570	34	(	(	PUNCT
ejpam-4944	570	35	resp	resp	NOUN
ejpam-4944	570	36	.	.	PUNCT
ejpam-4944	571	1	(	(	PUNCT
ejpam-4944	571	2	µ	µ	NOUN
ejpam-4944	571	3	,	,	PUNCT
ejpam-4944	571	4	η)-open	η)-open	PUNCT
ejpam-4944	571	5	)	)	PUNCT
ejpam-4944	572	1	[	[	X
ejpam-4944	572	2	18	18	NUM
ejpam-4944	572	3	]	]	PUNCT
ejpam-4944	572	4	if	if	SCONJ
ejpam-4944	572	5	f−1(q	f−1(q	NUM
ejpam-4944	572	6	)	)	PUNCT
ejpam-4944	572	7	∈	∈	PROPN
ejpam-4944	572	8	µ	µ	X
ejpam-4944	572	9	whenever	whenever	SCONJ
ejpam-4944	572	10	q	q	PROPN
ejpam-4944	572	11	∈	∈	PROPN
ejpam-4944	572	12	η	η	PROPN
ejpam-4944	572	13	(	(	PUNCT
ejpam-4944	572	14	resp	resp	NOUN
ejpam-4944	572	15	.	.	PUNCT
ejpam-4944	573	1	f(p	f(p	NOUN
ejpam-4944	573	2	)	)	PUNCT
ejpam-4944	574	1	∈	∈	PROPN
ejpam-4944	574	2	η	η	PROPN
ejpam-4944	574	3	whenever	whenever	SCONJ
ejpam-4944	574	4	p	p	PROPN
ejpam-4944	574	5	∈	∈	PROPN
ejpam-4944	574	6	µ	µ	NUM
ejpam-4944	574	7	)	)	PUNCT
ejpam-4944	574	8	.	.	PUNCT
ejpam-4944	575	1	d.	d.	PROPN
ejpam-4944	575	2	elgezouli	elgezouli	PROPN
ejpam-4944	575	3	et	et	PROPN
ejpam-4944	575	4	al	al	PROPN
ejpam-4944	575	5	.	.	PUNCT
ejpam-4944	575	6	/	/	SYM
ejpam-4944	575	7	eur	eur	PROPN
ejpam-4944	575	8	.	.	PUNCT
ejpam-4944	576	1	j.	j.	PROPN
ejpam-4944	576	2	pure	pure	PROPN
ejpam-4944	576	3	appl	appl	PROPN
ejpam-4944	576	4	.	.	PROPN
ejpam-4944	576	5	math	math	PROPN
ejpam-4944	576	6	,	,	PUNCT
ejpam-4944	576	7	16	16	NUM
ejpam-4944	576	8	(	(	PUNCT
ejpam-4944	576	9	4	4	NUM
ejpam-4944	576	10	)	)	PUNCT
ejpam-4944	576	11	(	(	PUNCT
ejpam-4944	576	12	2023	2023	NUM
ejpam-4944	576	13	)	)	PUNCT
ejpam-4944	576	14	,	,	PUNCT
ejpam-4944	576	15	2286	2286	NUM
ejpam-4944	576	16	-	-	SYM
ejpam-4944	576	17	2305	2305	NUM
ejpam-4944	576	18	2301	2301	NUM
ejpam-4944	576	19	lemma	lemma	PROPN
ejpam-4944	576	20	5	5	NUM
ejpam-4944	576	21	.	.	PUNCT
ejpam-4944	577	1	[	[	X
ejpam-4944	577	2	12	12	NUM
ejpam-4944	577	3	,	,	PUNCT
ejpam-4944	577	4	lemma	lemma	PROPN
ejpam-4944	577	5	7.3	7.3	NUM
ejpam-4944	577	6	]	]	PUNCT
ejpam-4944	577	7	a	a	DET
ejpam-4944	577	8	map	map	NOUN
ejpam-4944	577	9	f	f	X
ejpam-4944	577	10	:	:	PUNCT
ejpam-4944	577	11	(	(	PUNCT
ejpam-4944	577	12	x,µ	x,µ	NOUN
ejpam-4944	577	13	)	)	PUNCT
ejpam-4944	577	14	→	→	SYM
ejpam-4944	577	15	(	(	PUNCT
ejpam-4944	577	16	y	y	PROPN
ejpam-4944	577	17	,	,	PUNCT
ejpam-4944	577	18	η	η	PROPN
ejpam-4944	577	19	)	)	PUNCT
ejpam-4944	577	20	is	be	AUX
ejpam-4944	577	21	(	(	PUNCT
ejpam-4944	577	22	µ	µ	NOUN
ejpam-4944	577	23	,	,	PUNCT
ejpam-4944	577	24	η)-open	η)-open	VERB
ejpam-4944	577	25	if	if	SCONJ
ejpam-4944	577	26	and	and	CCONJ
ejpam-4944	577	27	only	only	ADV
ejpam-4944	577	28	if	if	SCONJ
ejpam-4944	577	29	f−1(cp	f−1(cp	NOUN
ejpam-4944	577	30	)	)	PUNCT
ejpam-4944	578	1	⊂	⊂	PROPN
ejpam-4944	578	2	c(f−1(p	c(f−1(p	PROPN
ejpam-4944	578	3	)	)	PUNCT
ejpam-4944	578	4	)	)	PUNCT
ejpam-4944	579	1	for	for	ADP
ejpam-4944	579	2	any	any	PRON
ejpam-4944	579	3	p	p	PROPN
ejpam-4944	579	4	⊂	⊂	PROPN
ejpam-4944	579	5	y.	y.	PROPN
ejpam-4944	579	6	theorem	theorem	VERB
ejpam-4944	579	7	36	36	NUM
ejpam-4944	579	8	.	.	PUNCT
ejpam-4944	580	1	let	let	VERB
ejpam-4944	580	2	(	(	PUNCT
ejpam-4944	580	3	x,µ1	x,µ1	NOUN
ejpam-4944	580	4	,	,	PUNCT
ejpam-4944	580	5	µ2	µ2	PROPN
ejpam-4944	580	6	)	)	PUNCT
ejpam-4944	580	7	and	and	CCONJ
ejpam-4944	580	8	(	(	PUNCT
ejpam-4944	580	9	y	y	PROPN
ejpam-4944	580	10	,	,	PUNCT
ejpam-4944	580	11	η1	η1	NOUN
ejpam-4944	580	12	,	,	PUNCT
ejpam-4944	580	13	η2	η2	PROPN
ejpam-4944	580	14	)	)	PUNCT
ejpam-4944	580	15	be	be	VERB
ejpam-4944	580	16	two	two	NUM
ejpam-4944	580	17	bgtss	bgtss	NOUN
ejpam-4944	580	18	.	.	PUNCT
ejpam-4944	581	1	if	if	SCONJ
ejpam-4944	581	2	f	f	PROPN
ejpam-4944	581	3	:	:	PUNCT
ejpam-4944	581	4	x	x	X
ejpam-4944	581	5	→	→	SYM
ejpam-4944	581	6	y	y	PROPN
ejpam-4944	581	7	is	be	AUX
ejpam-4944	581	8	(	(	PUNCT
ejpam-4944	581	9	µt	µt	ADJ
ejpam-4944	581	10	,	,	PUNCT
ejpam-4944	581	11	ηt)continuous	ηt)continuous	ADJ
ejpam-4944	581	12	for	for	ADP
ejpam-4944	581	13	t	t	NOUN
ejpam-4944	581	14	=	=	SYM
ejpam-4944	581	15	1	1	NUM
ejpam-4944	581	16	,	,	PUNCT
ejpam-4944	581	17	2	2	NUM
ejpam-4944	581	18	and	and	CCONJ
ejpam-4944	581	19	ηs	ηs	PROPN
ejpam-4944	581	20	is	be	AUX
ejpam-4944	581	21	sgt	sgt	PROPN
ejpam-4944	581	22	for	for	ADP
ejpam-4944	581	23	s	s	NOUN
ejpam-4944	581	24	=	=	SYM
ejpam-4944	581	25	1	1	NUM
ejpam-4944	581	26	,	,	PUNCT
ejpam-4944	581	27	2	2	NUM
ejpam-4944	581	28	,	,	PUNCT
ejpam-4944	581	29	then	then	ADV
ejpam-4944	581	30	image	image	NOUN
ejpam-4944	581	31	of	of	ADP
ejpam-4944	581	32	a	a	DET
ejpam-4944	581	33	(	(	PUNCT
ejpam-4944	581	34	s	s	PROPN
ejpam-4944	581	35	,	,	PUNCT
ejpam-4944	581	36	v)⋆-dense	v)⋆-dense	PROPN
ejpam-4944	581	37	set	set	NOUN
ejpam-4944	581	38	is	be	AUX
ejpam-4944	581	39	(	(	PUNCT
ejpam-4944	581	40	s	s	X
ejpam-4944	581	41	,	,	PUNCT
ejpam-4944	581	42	v)⋆-dense	v)⋆-dense	PROPN
ejpam-4944	581	43	where	where	SCONJ
ejpam-4944	581	44	s	s	X
ejpam-4944	581	45	,	,	PUNCT
ejpam-4944	581	46	v	v	NOUN
ejpam-4944	581	47	=	=	SYM
ejpam-4944	581	48	1	1	NUM
ejpam-4944	581	49	,	,	PUNCT
ejpam-4944	581	50	2	2	NUM
ejpam-4944	581	51	;	;	PUNCT
ejpam-4944	581	52	s	s	VERB
ejpam-4944	581	53	̸=	̸=	PROPN
ejpam-4944	581	54	v.	v.	ADP
ejpam-4944	581	55	proof	proof	NOUN
ejpam-4944	581	56	.	.	PUNCT
ejpam-4944	582	1	assume	assume	VERB
ejpam-4944	582	2	that	that	SCONJ
ejpam-4944	582	3	,	,	PUNCT
ejpam-4944	582	4	f	f	PROPN
ejpam-4944	582	5	is	be	AUX
ejpam-4944	582	6	(	(	PUNCT
ejpam-4944	582	7	µt	µt	ADJ
ejpam-4944	582	8	,	,	PUNCT
ejpam-4944	582	9	ηt)-continuous	ηt)-continuous	ADJ
ejpam-4944	582	10	for	for	ADP
ejpam-4944	582	11	t	t	NOUN
ejpam-4944	582	12	=	=	SYM
ejpam-4944	582	13	1	1	NUM
ejpam-4944	582	14	,	,	PUNCT
ejpam-4944	582	15	2	2	NUM
ejpam-4944	582	16	.	.	X
ejpam-4944	583	1	let	let	VERB
ejpam-4944	583	2	q	q	PROPN
ejpam-4944	583	3	∈	∈	PROPN
ejpam-4944	583	4	(	(	PUNCT
ejpam-4944	583	5	s	s	NOUN
ejpam-4944	583	6	,	,	PUNCT
ejpam-4944	583	7	v)⋆−d(x	v)⋆−d(x	PROPN
ejpam-4944	583	8	)	)	PUNCT
ejpam-4944	583	9	where	where	SCONJ
ejpam-4944	583	10	s	s	X
ejpam-4944	583	11	,	,	PUNCT
ejpam-4944	583	12	v	v	NOUN
ejpam-4944	583	13	=	=	SYM
ejpam-4944	583	14	1	1	NUM
ejpam-4944	583	15	,	,	PUNCT
ejpam-4944	583	16	2	2	NUM
ejpam-4944	583	17	;	;	PUNCT
ejpam-4944	583	18	s	s	VERB
ejpam-4944	583	19	̸=	̸=	PROPN
ejpam-4944	583	20	v.	v.	ADP
ejpam-4944	583	21	fix	fix	NOUN
ejpam-4944	583	22	s	s	PART
ejpam-4944	583	23	=	=	SYM
ejpam-4944	583	24	1	1	NUM
ejpam-4944	583	25	and	and	CCONJ
ejpam-4944	583	26	v	v	NOUN
ejpam-4944	583	27	=	=	SYM
ejpam-4944	583	28	2	2	X
ejpam-4944	583	29	.	.	X
ejpam-4944	584	1	we	we	PRON
ejpam-4944	584	2	get	get	VERB
ejpam-4944	584	3	q	q	X
ejpam-4944	584	4	∈	∈	NOUN
ejpam-4944	584	5	(	(	PUNCT
ejpam-4944	584	6	1	1	NUM
ejpam-4944	584	7	,	,	PUNCT
ejpam-4944	584	8	2)⋆	2)⋆	NOUN
ejpam-4944	584	9	−	−	NOUN
ejpam-4944	584	10	d(x	d(x	NOUN
ejpam-4944	584	11	)	)	PUNCT
ejpam-4944	584	12	so	so	SCONJ
ejpam-4944	584	13	that	that	SCONJ
ejpam-4944	584	14	cµ2q	cµ2q	PROPN
ejpam-4944	584	15	∩h	∩h	ADJ
ejpam-4944	584	16	̸=	̸=	PROPN
ejpam-4944	584	17	∅	∅	NOUN
ejpam-4944	584	18	for	for	ADP
ejpam-4944	584	19	h	h	PROPN
ejpam-4944	584	20	∈	∈	PROPN
ejpam-4944	584	21	σ̃µ1	σ̃µ1	PROPN
ejpam-4944	584	22	.	.	PUNCT
ejpam-4944	585	1	let	let	VERB
ejpam-4944	585	2	k	k	PROPN
ejpam-4944	585	3	∈	∈	PROPN
ejpam-4944	585	4	σ̃η1	σ̃η1	PROPN
ejpam-4944	585	5	.	.	PUNCT
ejpam-4944	586	1	by	by	ADP
ejpam-4944	586	2	assumption	assumption	NOUN
ejpam-4944	586	3	,	,	PUNCT
ejpam-4944	586	4	η1	η1	NOUN
ejpam-4944	586	5	is	be	AUX
ejpam-4944	586	6	a	a	DET
ejpam-4944	586	7	sgt	sgt	NOUN
ejpam-4944	586	8	so	so	SCONJ
ejpam-4944	586	9	that	that	SCONJ
ejpam-4944	586	10	iη1k	iη1k	PROPN
ejpam-4944	586	11	∈	∈	PROPN
ejpam-4944	586	12	η̃1	η̃1	PROPN
ejpam-4944	586	13	.	.	PUNCT
ejpam-4944	587	1	this	this	PRON
ejpam-4944	587	2	implies	imply	VERB
ejpam-4944	587	3	f−1(iη1k	f−1(iη1k	X
ejpam-4944	587	4	)	)	PUNCT
ejpam-4944	587	5	∈	∈	PROPN
ejpam-4944	587	6	µ̃1	µ̃1	NOUN
ejpam-4944	587	7	,	,	PUNCT
ejpam-4944	587	8	by	by	ADP
ejpam-4944	587	9	hypothesis	hypothesis	NOUN
ejpam-4944	587	10	which	which	PRON
ejpam-4944	587	11	implies	imply	VERB
ejpam-4944	587	12	that	that	SCONJ
ejpam-4944	587	13	cµ2q	cµ2q	PROPN
ejpam-4944	587	14	∩	∩	ADJ
ejpam-4944	587	15	f−1(iη1k	f−1(iη1k	NOUN
ejpam-4944	587	16	)	)	PUNCT
ejpam-4944	587	17	̸=	̸=	PROPN
ejpam-4944	587	18	∅.	∅.	ADV
ejpam-4944	587	19	thus	thus	ADV
ejpam-4944	587	20	,	,	PUNCT
ejpam-4944	587	21	f(cµ2q	f(cµ2q	X
ejpam-4944	587	22	∩	∩	ADJ
ejpam-4944	587	23	f−1(iη1k	f−1(iη1k	X
ejpam-4944	587	24	)	)	PUNCT
ejpam-4944	587	25	)	)	PUNCT
ejpam-4944	588	1	̸=	̸=	NOUN
ejpam-4944	588	2	∅	∅	NOUN
ejpam-4944	588	3	so	so	SCONJ
ejpam-4944	588	4	that	that	DET
ejpam-4944	588	5	f(cµ2q	f(cµ2q	NOUN
ejpam-4944	588	6	)	)	PUNCT
ejpam-4944	588	7	∩	∩	NOUN
ejpam-4944	588	8	iη1k	iη1k	PRON
ejpam-4944	588	9	̸=	̸=	PROPN
ejpam-4944	588	10	∅.	∅.	NOUN
ejpam-4944	588	11	since	since	SCONJ
ejpam-4944	588	12	f	f	PROPN
ejpam-4944	588	13	is	be	AUX
ejpam-4944	588	14	(	(	PUNCT
ejpam-4944	588	15	µ1	µ1	ADJ
ejpam-4944	588	16	,	,	PUNCT
ejpam-4944	588	17	η1)-continuous	η1)-continuous	ADJ
ejpam-4944	588	18	we	we	PRON
ejpam-4944	588	19	have	have	VERB
ejpam-4944	588	20	cη2(f(q	cη2(f(q	PUNCT
ejpam-4944	588	21	)	)	PUNCT
ejpam-4944	588	22	)	)	PUNCT
ejpam-4944	588	23	∩	∩	NOUN
ejpam-4944	588	24	iη1k	iη1k	PROPN
ejpam-4944	588	25	̸=	̸=	PROPN
ejpam-4944	588	26	∅.	∅.	VERB
ejpam-4944	588	27	therefore	therefore	ADV
ejpam-4944	588	28	,	,	PUNCT
ejpam-4944	588	29	f(q	f(q	PROPN
ejpam-4944	588	30	)	)	PUNCT
ejpam-4944	588	31	∈	∈	PROPN
ejpam-4944	588	32	(	(	PUNCT
ejpam-4944	588	33	1	1	NUM
ejpam-4944	588	34	,	,	PUNCT
ejpam-4944	588	35	2)⋆	2)⋆	PROPN
ejpam-4944	588	36	−d(y	−d(y	NOUN
ejpam-4944	588	37	)	)	PUNCT
ejpam-4944	588	38	.	.	PUNCT
ejpam-4944	589	1	take	take	VERB
ejpam-4944	589	2	s	s	NOUN
ejpam-4944	589	3	=	=	SYM
ejpam-4944	589	4	2	2	NUM
ejpam-4944	589	5	and	and	CCONJ
ejpam-4944	589	6	v	v	NOUN
ejpam-4944	589	7	=	=	SYM
ejpam-4944	589	8	1	1	NUM
ejpam-4944	589	9	.	.	PUNCT
ejpam-4944	590	1	then	then	ADV
ejpam-4944	590	2	q	q	PROPN
ejpam-4944	590	3	∈	∈	PROPN
ejpam-4944	590	4	(	(	PUNCT
ejpam-4944	590	5	2	2	NUM
ejpam-4944	590	6	,	,	PUNCT
ejpam-4944	590	7	1)⋆−d(x	1)⋆−d(x	NUM
ejpam-4944	590	8	)	)	PUNCT
ejpam-4944	590	9	and	and	CCONJ
ejpam-4944	590	10	so	so	ADV
ejpam-4944	590	11	cµ1q∩m	cµ1q∩m	PROPN
ejpam-4944	590	12	̸=	̸=	PROPN
ejpam-4944	590	13	∅	∅	NOUN
ejpam-4944	590	14	for	for	ADP
ejpam-4944	590	15	m	m	PROPN
ejpam-4944	590	16	∈	∈	PROPN
ejpam-4944	590	17	σ̃µ2	σ̃µ2	NOUN
ejpam-4944	590	18	.	.	PUNCT
ejpam-4944	591	1	choose	choose	VERB
ejpam-4944	591	2	l	l	PROPN
ejpam-4944	591	3	∈	∈	PROPN
ejpam-4944	591	4	σ̃η2	σ̃η2	PROPN
ejpam-4944	591	5	.	.	PUNCT
ejpam-4944	592	1	by	by	ADP
ejpam-4944	592	2	hypothesis	hypothesis	NOUN
ejpam-4944	592	3	,	,	PUNCT
ejpam-4944	592	4	η2	η2	PROPN
ejpam-4944	592	5	is	be	AUX
ejpam-4944	592	6	a	a	DET
ejpam-4944	592	7	sgt	sgt	NOUN
ejpam-4944	592	8	so	so	SCONJ
ejpam-4944	592	9	that	that	SCONJ
ejpam-4944	592	10	iη2l	iη2l	PROPN
ejpam-4944	592	11	∈	∈	PROPN
ejpam-4944	592	12	η̃2	η̃2	PROPN
ejpam-4944	592	13	which	which	PRON
ejpam-4944	592	14	implies	imply	VERB
ejpam-4944	592	15	f−1(iη2l	f−1(iη2l	PROPN
ejpam-4944	592	16	)	)	PUNCT
ejpam-4944	592	17	∈	∈	PROPN
ejpam-4944	592	18	µ̃2	µ̃2	PROPN
ejpam-4944	592	19	,	,	PUNCT
ejpam-4944	592	20	by	by	ADP
ejpam-4944	592	21	assumption	assumption	NOUN
ejpam-4944	592	22	which	which	DET
ejpam-4944	592	23	turn	turn	VERB
ejpam-4944	592	24	implies	imply	VERB
ejpam-4944	592	25	that	that	SCONJ
ejpam-4944	592	26	cµ1q∩	cµ1q∩	ADJ
ejpam-4944	592	27	f−1(iη2l	f−1(iη2l	NOUN
ejpam-4944	592	28	)	)	PUNCT
ejpam-4944	592	29	̸=	̸=	PROPN
ejpam-4944	592	30	∅.	∅.	ADP
ejpam-4944	592	31	thus	thus	ADV
ejpam-4944	592	32	,	,	PUNCT
ejpam-4944	592	33	f(cµ1q∩	f(cµ1q∩	PROPN
ejpam-4944	592	34	f−1(iη2l	f−1(iη2l	PROPN
ejpam-4944	592	35	)	)	PUNCT
ejpam-4944	592	36	)	)	PUNCT
ejpam-4944	592	37	̸=	̸=	NOUN
ejpam-4944	592	38	∅	∅	NOUN
ejpam-4944	592	39	for	for	ADP
ejpam-4944	592	40	that	that	DET
ejpam-4944	592	41	f(cµ1q	f(cµ1q	VERB
ejpam-4944	592	42	)	)	PUNCT
ejpam-4944	592	43	∩	∩	NOUN
ejpam-4944	592	44	iη2l	iη2l	PROPN
ejpam-4944	592	45	̸=	̸=	PROPN
ejpam-4944	592	46	∅.	∅.	VERB
ejpam-4944	592	47	by	by	ADP
ejpam-4944	592	48	hypothesis	hypothesis	NOUN
ejpam-4944	592	49	,	,	PUNCT
ejpam-4944	592	50	cη1(f(q	cη1(f(q	PROPN
ejpam-4944	592	51	)	)	PUNCT
ejpam-4944	592	52	)	)	PUNCT
ejpam-4944	593	1	∩	∩	PROPN
ejpam-4944	593	2	iη2l	iη2l	PROPN
ejpam-4944	593	3	̸=	̸=	PROPN
ejpam-4944	593	4	∅.	∅.	PRON
ejpam-4944	593	5	hence	hence	ADV
ejpam-4944	593	6	f(q	f(q	NOUN
ejpam-4944	593	7	)	)	PUNCT
ejpam-4944	593	8	∈	∈	PROPN
ejpam-4944	593	9	(	(	PUNCT
ejpam-4944	593	10	2	2	NUM
ejpam-4944	593	11	,	,	PUNCT
ejpam-4944	593	12	1)⋆	1)⋆	PROPN
ejpam-4944	593	13	−	−	NOUN
ejpam-4944	593	14	d(y	d(y	PROPN
ejpam-4944	593	15	)	)	PUNCT
ejpam-4944	593	16	.	.	PUNCT
ejpam-4944	594	1	theorem	theorem	VERB
ejpam-4944	594	2	37	37	NUM
ejpam-4944	594	3	.	.	PUNCT
ejpam-4944	595	1	let	let	VERB
ejpam-4944	595	2	(	(	PUNCT
ejpam-4944	595	3	x,µ1	x,µ1	NOUN
ejpam-4944	595	4	,	,	PUNCT
ejpam-4944	595	5	µ2	µ2	PROPN
ejpam-4944	595	6	)	)	PUNCT
ejpam-4944	595	7	and	and	CCONJ
ejpam-4944	595	8	(	(	PUNCT
ejpam-4944	595	9	y	y	PROPN
ejpam-4944	595	10	,	,	PUNCT
ejpam-4944	595	11	η1	η1	NOUN
ejpam-4944	595	12	,	,	PUNCT
ejpam-4944	595	13	η2	η2	PROPN
ejpam-4944	595	14	)	)	PUNCT
ejpam-4944	595	15	be	be	VERB
ejpam-4944	595	16	two	two	NUM
ejpam-4944	595	17	bigeneralized	bigeneralize	VERB
ejpam-4944	595	18	topological	topological	ADJ
ejpam-4944	595	19	spaces	space	NOUN
ejpam-4944	595	20	.	.	PUNCT
ejpam-4944	596	1	if	if	SCONJ
ejpam-4944	596	2	f	f	PROPN
ejpam-4944	596	3	:	:	PUNCT
ejpam-4944	596	4	x	x	X
ejpam-4944	596	5	→	→	SYM
ejpam-4944	596	6	y	y	PROPN
ejpam-4944	596	7	is	be	AUX
ejpam-4944	596	8	(	(	PUNCT
ejpam-4944	596	9	µt	µt	ADJ
ejpam-4944	596	10	,	,	PUNCT
ejpam-4944	596	11	ηt)-open	ηt)-open	VERB
ejpam-4944	596	12	for	for	ADP
ejpam-4944	596	13	t	t	NOUN
ejpam-4944	596	14	=	=	SYM
ejpam-4944	596	15	1	1	NUM
ejpam-4944	596	16	,	,	PUNCT
ejpam-4944	596	17	2	2	NUM
ejpam-4944	596	18	;	;	PUNCT
ejpam-4944	596	19	one	one	NUM
ejpam-4944	596	20	-	-	PUNCT
ejpam-4944	596	21	one	one	NUM
ejpam-4944	596	22	map	map	NOUN
ejpam-4944	596	23	and	and	CCONJ
ejpam-4944	596	24	µs	µs	NOUN
ejpam-4944	596	25	is	be	AUX
ejpam-4944	596	26	sgt	sgt	PROPN
ejpam-4944	596	27	for	for	ADP
ejpam-4944	596	28	s	s	NOUN
ejpam-4944	596	29	=	=	SYM
ejpam-4944	596	30	1	1	NUM
ejpam-4944	596	31	,	,	PUNCT
ejpam-4944	596	32	2	2	NUM
ejpam-4944	596	33	,	,	PUNCT
ejpam-4944	596	34	then	then	ADV
ejpam-4944	596	35	inverse	inverse	NOUN
ejpam-4944	596	36	image	image	NOUN
ejpam-4944	596	37	of	of	ADP
ejpam-4944	596	38	a	a	DET
ejpam-4944	596	39	(	(	PUNCT
ejpam-4944	596	40	s	s	PROPN
ejpam-4944	596	41	,	,	PUNCT
ejpam-4944	596	42	v)⋆-dense	v)⋆-dense	PROPN
ejpam-4944	596	43	set	set	NOUN
ejpam-4944	596	44	is	be	AUX
ejpam-4944	596	45	(	(	PUNCT
ejpam-4944	596	46	s	s	X
ejpam-4944	596	47	,	,	PUNCT
ejpam-4944	596	48	v)⋆-dense	v)⋆-dense	PROPN
ejpam-4944	596	49	.	.	PUNCT
ejpam-4944	597	1	proof	proof	NOUN
ejpam-4944	597	2	.	.	PUNCT
ejpam-4944	598	1	let	let	VERB
ejpam-4944	598	2	p	p	X
ejpam-4944	598	3	∈	∈	PROPN
ejpam-4944	598	4	(	(	PUNCT
ejpam-4944	598	5	s	s	PROPN
ejpam-4944	598	6	,	,	PUNCT
ejpam-4944	598	7	v)⋆	v)⋆	PROPN
ejpam-4944	598	8	−d(y	−d(y	NOUN
ejpam-4944	598	9	)	)	PUNCT
ejpam-4944	598	10	for	for	ADP
ejpam-4944	598	11	s	s	PROPN
ejpam-4944	598	12	,	,	PUNCT
ejpam-4944	598	13	v	v	NOUN
ejpam-4944	598	14	=	=	SYM
ejpam-4944	598	15	1	1	NUM
ejpam-4944	598	16	,	,	PUNCT
ejpam-4944	598	17	2	2	NUM
ejpam-4944	598	18	;	;	PUNCT
ejpam-4944	598	19	s	s	VERB
ejpam-4944	598	20	̸=	̸=	PROPN
ejpam-4944	598	21	v.	v.	ADP
ejpam-4944	598	22	fix	fix	NOUN
ejpam-4944	598	23	s	s	PART
ejpam-4944	599	1	=	=	SYM
ejpam-4944	599	2	1	1	NUM
ejpam-4944	599	3	and	and	CCONJ
ejpam-4944	599	4	v	v	NOUN
ejpam-4944	599	5	=	=	SYM
ejpam-4944	599	6	2	2	NUM
ejpam-4944	599	7	.	.	PUNCT
ejpam-4944	600	1	then	then	ADV
ejpam-4944	600	2	p	p	PROPN
ejpam-4944	600	3	∈	∈	PROPN
ejpam-4944	600	4	(	(	PUNCT
ejpam-4944	600	5	1	1	NUM
ejpam-4944	600	6	,	,	PUNCT
ejpam-4944	600	7	2)⋆	2)⋆	NOUN
ejpam-4944	600	8	−	−	NOUN
ejpam-4944	600	9	d(y	d(y	NOUN
ejpam-4944	600	10	)	)	PUNCT
ejpam-4944	601	1	so	so	SCONJ
ejpam-4944	601	2	that	that	SCONJ
ejpam-4944	601	3	cη2p	cη2p	PRON
ejpam-4944	601	4	∩	∩	VERB
ejpam-4944	601	5	l	l	PROPN
ejpam-4944	601	6	̸=	̸=	PROPN
ejpam-4944	601	7	∅	∅	NOUN
ejpam-4944	601	8	for	for	ADP
ejpam-4944	601	9	all	all	DET
ejpam-4944	601	10	l	l	NOUN
ejpam-4944	601	11	∈	∈	PROPN
ejpam-4944	601	12	σ̃η1	σ̃η1	PROPN
ejpam-4944	601	13	.	.	PUNCT
ejpam-4944	602	1	let	let	VERB
ejpam-4944	602	2	d	d	X
ejpam-4944	602	3	∈	∈	PROPN
ejpam-4944	602	4	σ̃µ1	σ̃µ1	PROPN
ejpam-4944	602	5	so	so	SCONJ
ejpam-4944	602	6	that	that	SCONJ
ejpam-4944	602	7	iµ1d	iµ1d	PROPN
ejpam-4944	602	8	∈	∈	PROPN
ejpam-4944	602	9	µ̃1	µ̃1	PROPN
ejpam-4944	602	10	,	,	PUNCT
ejpam-4944	602	11	by	by	ADP
ejpam-4944	602	12	assumption	assumption	NOUN
ejpam-4944	602	13	.	.	PUNCT
ejpam-4944	603	1	since	since	SCONJ
ejpam-4944	603	2	f	f	PROPN
ejpam-4944	603	3	is	be	AUX
ejpam-4944	603	4	(	(	PUNCT
ejpam-4944	603	5	µ1	µ1	PROPN
ejpam-4944	603	6	,	,	PUNCT
ejpam-4944	603	7	η1)-open	η1)-open	VERB
ejpam-4944	603	8	we	we	PRON
ejpam-4944	603	9	have	have	VERB
ejpam-4944	603	10	f(iµ1d	f(iµ1d	NOUN
ejpam-4944	603	11	)	)	PUNCT
ejpam-4944	603	12	∈	∈	PROPN
ejpam-4944	603	13	η̃1	η̃1	PROPN
ejpam-4944	603	14	.	.	PUNCT
ejpam-4944	604	1	this	this	PRON
ejpam-4944	604	2	implies	imply	VERB
ejpam-4944	604	3	cη2p	cη2p	PRON
ejpam-4944	604	4	∩f(iµ1d	∩f(iµ1d	NOUN
ejpam-4944	604	5	)	)	PUNCT
ejpam-4944	604	6	̸=	̸=	PROPN
ejpam-4944	604	7	∅	∅	NOUN
ejpam-4944	604	8	which	which	PRON
ejpam-4944	604	9	implies	imply	VERB
ejpam-4944	604	10	that	that	SCONJ
ejpam-4944	604	11	f−1(cη2p	f−1(cη2p	ADP
ejpam-4944	604	12	)	)	PUNCT
ejpam-4944	604	13	∩f−1(f(iµ1d	∩f−1(f(iµ1d	PUNCT
ejpam-4944	604	14	)	)	PUNCT
ejpam-4944	604	15	)	)	PUNCT
ejpam-4944	605	1	̸=	̸=	PROPN
ejpam-4944	605	2	∅.	∅.	ADP
ejpam-4944	605	3	here	here	ADV
ejpam-4944	605	4	f	f	PROPN
ejpam-4944	605	5	is	be	AUX
ejpam-4944	605	6	an	an	DET
ejpam-4944	605	7	injective	injective	ADJ
ejpam-4944	605	8	map	map	NOUN
ejpam-4944	605	9	,	,	PUNCT
ejpam-4944	605	10	f−1(cη2p	f−1(cη2p	ADV
ejpam-4944	605	11	)	)	PUNCT
ejpam-4944	605	12	∩	∩	PROPN
ejpam-4944	605	13	iµ1d	iµ1d	PROPN
ejpam-4944	605	14	̸=	̸=	PROPN
ejpam-4944	605	15	∅.	∅.	ADV
ejpam-4944	605	16	by	by	ADP
ejpam-4944	605	17	lemma	lemma	PROPN
ejpam-4944	605	18	5	5	NUM
ejpam-4944	605	19	,	,	PUNCT
ejpam-4944	605	20	cµ2(f	cµ2(f	ADJ
ejpam-4944	605	21	−1(p	−1(p	NOUN
ejpam-4944	605	22	)	)	PUNCT
ejpam-4944	605	23	)	)	PUNCT
ejpam-4944	605	24	∩	∩	NOUN
ejpam-4944	605	25	ıµ1d	ıµ1d	PROPN
ejpam-4944	605	26	̸=	̸=	PROPN
ejpam-4944	605	27	∅.	∅.	PRON
ejpam-4944	605	28	hence	hence	ADV
ejpam-4944	605	29	f−1(p	f−1(p	NOUN
ejpam-4944	605	30	)	)	PUNCT
ejpam-4944	605	31	∈	∈	PROPN
ejpam-4944	605	32	(	(	PUNCT
ejpam-4944	605	33	1	1	NUM
ejpam-4944	605	34	,	,	PUNCT
ejpam-4944	605	35	2)⋆d(x	2)⋆d(x	NUM
ejpam-4944	605	36	)	)	PUNCT
ejpam-4944	605	37	.	.	PUNCT
ejpam-4944	606	1	choose	choose	VERB
ejpam-4944	606	2	s	s	NOUN
ejpam-4944	606	3	=	=	SYM
ejpam-4944	606	4	2	2	NUM
ejpam-4944	606	5	and	and	CCONJ
ejpam-4944	606	6	v	v	NOUN
ejpam-4944	606	7	=	=	SYM
ejpam-4944	606	8	1	1	X
ejpam-4944	606	9	.	.	PUNCT
ejpam-4944	607	1	we	we	PRON
ejpam-4944	607	2	get	get	VERB
ejpam-4944	607	3	p	p	X
ejpam-4944	607	4	∈	∈	NOUN
ejpam-4944	607	5	(	(	PUNCT
ejpam-4944	607	6	2	2	NUM
ejpam-4944	607	7	,	,	PUNCT
ejpam-4944	607	8	1)⋆	1)⋆	PROPN
ejpam-4944	607	9	−	−	PROPN
ejpam-4944	607	10	d(y	d(y	PROPN
ejpam-4944	607	11	)	)	PUNCT
ejpam-4944	607	12	implies	imply	VERB
ejpam-4944	607	13	that	that	SCONJ
ejpam-4944	607	14	cη1p	cη1p	PROPN
ejpam-4944	607	15	∩	∩	NOUN
ejpam-4944	607	16	m	m	VERB
ejpam-4944	607	17	̸=	̸=	NOUN
ejpam-4944	607	18	∅	∅	NOUN
ejpam-4944	607	19	for	for	ADP
ejpam-4944	607	20	all	all	DET
ejpam-4944	607	21	m	m	NOUN
ejpam-4944	607	22	∈	∈	PROPN
ejpam-4944	607	23	σ̃η2	σ̃η2	PROPN
ejpam-4944	607	24	.	.	PUNCT
ejpam-4944	608	1	choose	choose	VERB
ejpam-4944	608	2	v	v	NUM
ejpam-4944	608	3	∈	∈	NOUN
ejpam-4944	608	4	σ̃µ2	σ̃µ2	NOUN
ejpam-4944	608	5	so	so	SCONJ
ejpam-4944	608	6	that	that	SCONJ
ejpam-4944	608	7	iµ2v	iµ2v	PROPN
ejpam-4944	608	8	∈	∈	PROPN
ejpam-4944	608	9	µ̃2	µ̃2	PROPN
ejpam-4944	608	10	,	,	PUNCT
ejpam-4944	608	11	by	by	ADP
ejpam-4944	608	12	hypothesis	hypothesis	NOUN
ejpam-4944	608	13	which	which	PRON
ejpam-4944	608	14	implies	imply	VERB
ejpam-4944	608	15	f(iµ2v	f(iµ2v	X
ejpam-4944	608	16	)	)	PUNCT
ejpam-4944	608	17	∈	∈	PROPN
ejpam-4944	608	18	η̃2	η̃2	PROPN
ejpam-4944	608	19	.	.	PUNCT
ejpam-4944	609	1	thus	thus	ADV
ejpam-4944	609	2	,	,	PUNCT
ejpam-4944	609	3	cη1p	cη1p	PROPN
ejpam-4944	609	4	∩	∩	ADJ
ejpam-4944	609	5	f(iµ2v	f(iµ2v	X
ejpam-4944	609	6	)	)	PUNCT
ejpam-4944	609	7	̸=	̸=	NOUN
ejpam-4944	609	8	∅	∅	NOUN
ejpam-4944	609	9	so	so	SCONJ
ejpam-4944	609	10	that	that	SCONJ
ejpam-4944	609	11	f−1(cη1p	f−1(cη1p	ADJ
ejpam-4944	609	12	)	)	PUNCT
ejpam-4944	609	13	∩	∩	ADJ
ejpam-4944	609	14	f−1(f(iµ2v	f−1(f(iµ2v	PROPN
ejpam-4944	609	15	)	)	PUNCT
ejpam-4944	609	16	)	)	PUNCT
ejpam-4944	610	1	̸=	̸=	PROPN
ejpam-4944	610	2	∅.	∅.	ADV
ejpam-4944	610	3	since	since	SCONJ
ejpam-4944	610	4	f	f	PROPN
ejpam-4944	610	5	is	be	AUX
ejpam-4944	610	6	an	an	DET
ejpam-4944	610	7	injective	injective	ADJ
ejpam-4944	610	8	map	map	NOUN
ejpam-4944	610	9	,	,	PUNCT
ejpam-4944	610	10	f−1(cη1p	f−1(cη1p	ADJ
ejpam-4944	610	11	)	)	PUNCT
ejpam-4944	610	12	∩	∩	PROPN
ejpam-4944	610	13	iµ2v	iµ2v	PROPN
ejpam-4944	610	14	̸=	̸=	PROPN
ejpam-4944	610	15	∅.	∅.	PRON
ejpam-4944	610	16	by	by	ADP
ejpam-4944	610	17	lemma	lemma	PROPN
ejpam-4944	610	18	5	5	NUM
ejpam-4944	610	19	,	,	PUNCT
ejpam-4944	610	20	cµ1(f	cµ1(f	NOUN
ejpam-4944	610	21	−1(p	−1(p	NOUN
ejpam-4944	610	22	)	)	PUNCT
ejpam-4944	610	23	)	)	PUNCT
ejpam-4944	610	24	∩	∩	NOUN
ejpam-4944	610	25	ıµ2v	ıµ2v	PROPN
ejpam-4944	610	26	̸=	̸=	PROPN
ejpam-4944	610	27	∅.	∅.	VERB
ejpam-4944	610	28	therefore	therefore	ADV
ejpam-4944	610	29	,	,	PUNCT
ejpam-4944	610	30	f−1(p	f−1(p	PROPN
ejpam-4944	610	31	)	)	PUNCT
ejpam-4944	610	32	∈	∈	PROPN
ejpam-4944	610	33	(	(	PUNCT
ejpam-4944	610	34	2	2	NUM
ejpam-4944	610	35	,	,	PUNCT
ejpam-4944	610	36	1)⋆	1)⋆	PROPN
ejpam-4944	610	37	−d(x	−d(x	NOUN
ejpam-4944	610	38	)	)	PUNCT
ejpam-4944	610	39	.	.	PUNCT
ejpam-4944	611	1	5	5	X
ejpam-4944	611	2	.	.	X
ejpam-4944	611	3	applications	application	NOUN
ejpam-4944	611	4	for	for	ADP
ejpam-4944	611	5	(	(	PUNCT
ejpam-4944	611	6	s	s	X
ejpam-4944	611	7	,	,	PUNCT
ejpam-4944	611	8	v)⋆-dense	v)⋆-dense	ADJ
ejpam-4944	611	9	sets	set	NOUN
ejpam-4944	611	10	in	in	ADP
ejpam-4944	611	11	1999	1999	NUM
ejpam-4944	611	12	,	,	PUNCT
ejpam-4944	611	13	molodstov	molodstov	PROPN
ejpam-4944	611	14	introduced	introduce	VERB
ejpam-4944	611	15	a	a	DET
ejpam-4944	611	16	new	new	ADJ
ejpam-4944	611	17	mathematical	mathematical	ADJ
ejpam-4944	611	18	tool	tool	NOUN
ejpam-4944	611	19	namely	namely	ADV
ejpam-4944	611	20	,	,	PUNCT
ejpam-4944	611	21	soft	soft	ADJ
ejpam-4944	611	22	set	set	NOUN
ejpam-4944	611	23	theory	theory	NOUN
ejpam-4944	611	24	[	[	X
ejpam-4944	611	25	14	14	NUM
ejpam-4944	611	26	]	]	PUNCT
ejpam-4944	611	27	.	.	PUNCT
ejpam-4944	612	1	it	it	PRON
ejpam-4944	612	2	has	have	AUX
ejpam-4944	612	3	been	be	AUX
ejpam-4944	612	4	used	use	VERB
ejpam-4944	612	5	for	for	ADP
ejpam-4944	612	6	dealing	deal	VERB
ejpam-4944	612	7	with	with	ADP
ejpam-4944	612	8	uncertainty	uncertainty	NOUN
ejpam-4944	612	9	.	.	PUNCT
ejpam-4944	613	1	most	most	ADJ
ejpam-4944	613	2	of	of	ADP
ejpam-4944	613	3	the	the	DET
ejpam-4944	613	4	researchers	researcher	NOUN
ejpam-4944	613	5	presented	present	VERB
ejpam-4944	613	6	an	an	DET
ejpam-4944	613	7	applid	applid	NOUN
ejpam-4944	613	8	.	.	PUNCT
ejpam-4944	614	1	elgezouli	elgezouli	PROPN
ejpam-4944	614	2	et	et	PROPN
ejpam-4944	615	1	al	al	PROPN
ejpam-4944	615	2	.	.	PUNCT
ejpam-4944	615	3	/	/	SYM
ejpam-4944	615	4	eur	eur	PROPN
ejpam-4944	615	5	.	.	PUNCT
ejpam-4944	616	1	j.	j.	PROPN
ejpam-4944	616	2	pure	pure	PROPN
ejpam-4944	616	3	appl	appl	PROPN
ejpam-4944	616	4	.	.	PROPN
ejpam-4944	616	5	math	math	PROPN
ejpam-4944	616	6	,	,	PUNCT
ejpam-4944	616	7	16	16	NUM
ejpam-4944	616	8	(	(	PUNCT
ejpam-4944	616	9	4	4	NUM
ejpam-4944	616	10	)	)	PUNCT
ejpam-4944	616	11	(	(	PUNCT
ejpam-4944	616	12	2023	2023	NUM
ejpam-4944	616	13	)	)	PUNCT
ejpam-4944	616	14	,	,	PUNCT
ejpam-4944	616	15	2286	2286	NUM
ejpam-4944	616	16	-	-	SYM
ejpam-4944	616	17	2305	2305	NUM
ejpam-4944	616	18	2302	2302	NUM
ejpam-4944	616	19	cation	cation	NOUN
ejpam-4944	616	20	of	of	ADP
ejpam-4944	616	21	soft	soft	ADJ
ejpam-4944	616	22	sets	set	NOUN
ejpam-4944	616	23	in	in	ADP
ejpam-4944	616	24	decision	decision	NOUN
ejpam-4944	616	25	-	-	PUNCT
ejpam-4944	616	26	making	make	VERB
ejpam-4944	616	27	problems	problem	NOUN
ejpam-4944	616	28	.	.	PUNCT
ejpam-4944	617	1	motivated	motivate	VERB
ejpam-4944	617	2	,	,	PUNCT
ejpam-4944	617	3	by	by	ADP
ejpam-4944	617	4	this	this	PRON
ejpam-4944	617	5	we	we	PRON
ejpam-4944	617	6	try	try	VERB
ejpam-4944	617	7	to	to	PART
ejpam-4944	617	8	give	give	VERB
ejpam-4944	617	9	an	an	DET
ejpam-4944	617	10	example	example	NOUN
ejpam-4944	617	11	of	of	ADP
ejpam-4944	617	12	the	the	DET
ejpam-4944	617	13	soft	soft	ADJ
ejpam-4944	617	14	set	set	NOUN
ejpam-4944	617	15	using	use	VERB
ejpam-4944	617	16	(	(	PUNCT
ejpam-4944	617	17	s	s	NOUN
ejpam-4944	617	18	,	,	PUNCT
ejpam-4944	617	19	v)⋆-dense	v)⋆-dense	PROPN
ejpam-4944	617	20	and	and	CCONJ
ejpam-4944	617	21	some	some	DET
ejpam-4944	617	22	subsets	subset	NOUN
ejpam-4944	617	23	defined	define	VERB
ejpam-4944	617	24	in	in	ADP
ejpam-4944	617	25	a	a	DET
ejpam-4944	617	26	bigeneralized	bigeneralize	VERB
ejpam-4944	617	27	topological	topological	ADJ
ejpam-4944	617	28	space	space	NOUN
ejpam-4944	617	29	and	and	CCONJ
ejpam-4944	617	30	also	also	ADV
ejpam-4944	617	31	in	in	ADP
ejpam-4944	617	32	generalized	generalized	ADJ
ejpam-4944	617	33	topological	topological	ADJ
ejpam-4944	617	34	space	space	NOUN
ejpam-4944	617	35	.	.	PUNCT
ejpam-4944	618	1	example	example	NOUN
ejpam-4944	618	2	38	38	NUM
ejpam-4944	618	3	.	.	PUNCT
ejpam-4944	619	1	consider	consider	VERB
ejpam-4944	619	2	the	the	DET
ejpam-4944	619	3	bgts	bgts	NOUN
ejpam-4944	619	4	(	(	PUNCT
ejpam-4944	619	5	x,µ1	x,µ1	PROPN
ejpam-4944	619	6	,	,	PUNCT
ejpam-4944	619	7	µ2	µ2	PROPN
ejpam-4944	619	8	)	)	PUNCT
ejpam-4944	619	9	where	where	SCONJ
ejpam-4944	619	10	x	x	X
ejpam-4944	619	11	=	=	PRON
ejpam-4944	619	12	{	{	PUNCT
ejpam-4944	619	13	a	a	PRON
ejpam-4944	619	14	,	,	PUNCT
ejpam-4944	619	15	b	b	NOUN
ejpam-4944	619	16	,	,	PUNCT
ejpam-4944	619	17	c	c	NOUN
ejpam-4944	619	18	,	,	PUNCT
ejpam-4944	619	19	d	d	NOUN
ejpam-4944	619	20	}	}	PUNCT
ejpam-4944	619	21	;	;	PUNCT
ejpam-4944	619	22	µ1	µ1	PROPN
ejpam-4944	619	23	=	=	SYM
ejpam-4944	619	24	{	{	PUNCT
ejpam-4944	619	25	∅	∅	NOUN
ejpam-4944	619	26	,	,	PUNCT
ejpam-4944	619	27	{	{	PUNCT
ejpam-4944	619	28	b	b	NOUN
ejpam-4944	619	29	}	}	PUNCT
ejpam-4944	619	30	,	,	PUNCT
ejpam-4944	619	31	{	{	PUNCT
ejpam-4944	619	32	a	a	PRON
ejpam-4944	619	33	,	,	PUNCT
ejpam-4944	619	34	d	d	NOUN
ejpam-4944	619	35	}	}	PUNCT
ejpam-4944	619	36	,	,	PUNCT
ejpam-4944	619	37	{	{	PUNCT
ejpam-4944	619	38	b	b	X
ejpam-4944	619	39	,	,	PUNCT
ejpam-4944	619	40	d	d	NOUN
ejpam-4944	619	41	}	}	PUNCT
ejpam-4944	619	42	,	,	PUNCT
ejpam-4944	619	43	{	{	PUNCT
ejpam-4944	619	44	a	a	PRON
ejpam-4944	619	45	,	,	PUNCT
ejpam-4944	619	46	b	b	NOUN
ejpam-4944	619	47	,	,	PUNCT
ejpam-4944	619	48	d	d	NOUN
ejpam-4944	619	49	}	}	PUNCT
ejpam-4944	619	50	}	}	PUNCT
ejpam-4944	619	51	;	;	PUNCT
ejpam-4944	619	52	and	and	CCONJ
ejpam-4944	619	53	µ2	µ2	PROPN
ejpam-4944	619	54	=	=	PUNCT
ejpam-4944	619	55	{	{	PUNCT
ejpam-4944	619	56	∅	∅	NOUN
ejpam-4944	619	57	,	,	PUNCT
ejpam-4944	619	58	{	{	PUNCT
ejpam-4944	619	59	c	c	NOUN
ejpam-4944	619	60	}	}	PUNCT
ejpam-4944	619	61	,	,	PUNCT
ejpam-4944	619	62	{	{	PUNCT
ejpam-4944	619	63	a	a	PRON
ejpam-4944	619	64	,	,	PUNCT
ejpam-4944	619	65	b	b	NOUN
ejpam-4944	619	66	}	}	PUNCT
ejpam-4944	619	67	,	,	PUNCT
ejpam-4944	619	68	{	{	PUNCT
ejpam-4944	619	69	a	a	X
ejpam-4944	619	70	,	,	PUNCT
ejpam-4944	619	71	c	c	NOUN
ejpam-4944	619	72	}	}	PUNCT
ejpam-4944	619	73	,	,	PUNCT
ejpam-4944	619	74	{	{	PUNCT
ejpam-4944	619	75	a	a	PRON
ejpam-4944	619	76	,	,	PUNCT
ejpam-4944	619	77	b	b	NOUN
ejpam-4944	619	78	,	,	PUNCT
ejpam-4944	619	79	c	c	NOUN
ejpam-4944	619	80	}	}	PUNCT
ejpam-4944	619	81	}	}	PUNCT
ejpam-4944	619	82	.	.	PUNCT
ejpam-4944	620	1	here	here	ADV
ejpam-4944	620	2	,	,	PUNCT
ejpam-4944	620	3	•	•	NUM
ejpam-4944	620	4	σ1	σ1	NOUN
ejpam-4944	620	5	=	=	SYM
ejpam-4944	620	6	{	{	PUNCT
ejpam-4944	620	7	∅	∅	NOUN
ejpam-4944	620	8	,	,	PUNCT
ejpam-4944	620	9	{	{	PUNCT
ejpam-4944	620	10	b	b	NOUN
ejpam-4944	620	11	}	}	PUNCT
ejpam-4944	620	12	,	,	PUNCT
ejpam-4944	620	13	{	{	PUNCT
ejpam-4944	620	14	c	c	X
ejpam-4944	620	15	}	}	PUNCT
ejpam-4944	620	16	,	,	PUNCT
ejpam-4944	620	17	{	{	PUNCT
ejpam-4944	620	18	a	a	DET
ejpam-4944	620	19	,	,	PUNCT
ejpam-4944	620	20	d	d	NOUN
ejpam-4944	620	21	}	}	PUNCT
ejpam-4944	620	22	,	,	PUNCT
ejpam-4944	620	23	{	{	PUNCT
ejpam-4944	620	24	b	b	X
ejpam-4944	620	25	,	,	PUNCT
ejpam-4944	620	26	c	c	NOUN
ejpam-4944	620	27	}	}	PUNCT
ejpam-4944	620	28	,	,	PUNCT
ejpam-4944	620	29	{	{	PUNCT
ejpam-4944	620	30	b	b	X
ejpam-4944	620	31	,	,	PUNCT
ejpam-4944	620	32	d	d	NOUN
ejpam-4944	620	33	}	}	PUNCT
ejpam-4944	620	34	,	,	PUNCT
ejpam-4944	620	35	{	{	PUNCT
ejpam-4944	620	36	a	a	DET
ejpam-4944	620	37	,	,	PUNCT
ejpam-4944	620	38	b	b	NOUN
ejpam-4944	620	39	,	,	PUNCT
ejpam-4944	620	40	d	d	NOUN
ejpam-4944	620	41	}	}	PUNCT
ejpam-4944	620	42	,	,	PUNCT
ejpam-4944	620	43	{	{	PUNCT
ejpam-4944	620	44	a	a	PRON
ejpam-4944	620	45	,	,	PUNCT
ejpam-4944	620	46	c	c	NOUN
ejpam-4944	620	47	,	,	PUNCT
ejpam-4944	620	48	d	d	NOUN
ejpam-4944	620	49	}	}	PUNCT
ejpam-4944	620	50	,	,	PUNCT
ejpam-4944	620	51	{	{	PUNCT
ejpam-4944	620	52	b	b	X
ejpam-4944	620	53	,	,	PUNCT
ejpam-4944	620	54	c	c	NOUN
ejpam-4944	620	55	,	,	PUNCT
ejpam-4944	620	56	d	d	NOUN
ejpam-4944	620	57	}	}	PUNCT
ejpam-4944	620	58	,	,	PUNCT
ejpam-4944	620	59	x	x	NOUN
ejpam-4944	620	60	}	}	PUNCT
ejpam-4944	620	61	.	.	PUNCT
ejpam-4944	620	62	•	•	NUM
ejpam-4944	620	63	σ2	σ2	PROPN
ejpam-4944	620	64	=	=	SYM
ejpam-4944	620	65	{	{	PUNCT
ejpam-4944	620	66	∅	∅	NOUN
ejpam-4944	620	67	,	,	PUNCT
ejpam-4944	620	68	{	{	PUNCT
ejpam-4944	620	69	c	c	NOUN
ejpam-4944	620	70	}	}	PUNCT
ejpam-4944	620	71	,	,	PUNCT
ejpam-4944	620	72	{	{	PUNCT
ejpam-4944	620	73	d	d	X
ejpam-4944	620	74	}	}	PUNCT
ejpam-4944	620	75	,	,	PUNCT
ejpam-4944	620	76	{	{	PUNCT
ejpam-4944	620	77	a	a	DET
ejpam-4944	620	78	,	,	PUNCT
ejpam-4944	620	79	b	b	NOUN
ejpam-4944	620	80	}	}	PUNCT
ejpam-4944	620	81	,	,	PUNCT
ejpam-4944	620	82	{	{	PUNCT
ejpam-4944	620	83	a	a	X
ejpam-4944	620	84	,	,	PUNCT
ejpam-4944	620	85	c	c	NOUN
ejpam-4944	620	86	}	}	PUNCT
ejpam-4944	620	87	,	,	PUNCT
ejpam-4944	620	88	{	{	PUNCT
ejpam-4944	620	89	c	c	X
ejpam-4944	620	90	,	,	PUNCT
ejpam-4944	620	91	d	d	NOUN
ejpam-4944	620	92	}	}	PUNCT
ejpam-4944	620	93	,	,	PUNCT
ejpam-4944	620	94	{	{	PUNCT
ejpam-4944	620	95	a	a	DET
ejpam-4944	620	96	,	,	PUNCT
ejpam-4944	620	97	b	b	NOUN
ejpam-4944	620	98	,	,	PUNCT
ejpam-4944	620	99	c	c	NOUN
ejpam-4944	620	100	}	}	PUNCT
ejpam-4944	620	101	,	,	PUNCT
ejpam-4944	620	102	{	{	PUNCT
ejpam-4944	620	103	a	a	DET
ejpam-4944	620	104	,	,	PUNCT
ejpam-4944	620	105	b	b	NOUN
ejpam-4944	620	106	,	,	PUNCT
ejpam-4944	620	107	d	d	NOUN
ejpam-4944	620	108	}	}	PUNCT
ejpam-4944	620	109	,	,	PUNCT
ejpam-4944	620	110	{	{	PUNCT
ejpam-4944	620	111	a	a	PRON
ejpam-4944	620	112	,	,	PUNCT
ejpam-4944	620	113	c	c	NOUN
ejpam-4944	620	114	,	,	PUNCT
ejpam-4944	620	115	d	d	NOUN
ejpam-4944	620	116	}	}	PUNCT
ejpam-4944	620	117	,	,	PUNCT
ejpam-4944	620	118	x	x	NOUN
ejpam-4944	620	119	}	}	PUNCT
ejpam-4944	620	120	.	.	PUNCT
ejpam-4944	621	1	then	then	ADV
ejpam-4944	621	2	we	we	PRON
ejpam-4944	621	3	get	get	VERB
ejpam-4944	621	4	,	,	PUNCT
ejpam-4944	621	5	•	•	X
ejpam-4944	621	6	(	(	PUNCT
ejpam-4944	621	7	1	1	NUM
ejpam-4944	621	8	,	,	PUNCT
ejpam-4944	621	9	2)⋆	2)⋆	PROPN
ejpam-4944	621	10	−d(x	−d(x	NOUN
ejpam-4944	621	11	)	)	PUNCT
ejpam-4944	621	12	=	=	SYM
ejpam-4944	621	13	{	{	PUNCT
ejpam-4944	621	14	{	{	PUNCT
ejpam-4944	621	15	a	a	X
ejpam-4944	621	16	,	,	PUNCT
ejpam-4944	621	17	c	c	NOUN
ejpam-4944	621	18	}	}	PUNCT
ejpam-4944	621	19	,	,	PUNCT
ejpam-4944	621	20	{	{	PUNCT
ejpam-4944	621	21	b	b	X
ejpam-4944	621	22	,	,	PUNCT
ejpam-4944	621	23	c	c	NOUN
ejpam-4944	621	24	}	}	PUNCT
ejpam-4944	621	25	,	,	PUNCT
ejpam-4944	621	26	{	{	PUNCT
ejpam-4944	621	27	a	a	DET
ejpam-4944	621	28	,	,	PUNCT
ejpam-4944	621	29	b	b	NOUN
ejpam-4944	621	30	,	,	PUNCT
ejpam-4944	621	31	c	c	NOUN
ejpam-4944	621	32	}	}	PUNCT
ejpam-4944	621	33	,	,	PUNCT
ejpam-4944	621	34	{	{	PUNCT
ejpam-4944	621	35	a	a	PRON
ejpam-4944	621	36	,	,	PUNCT
ejpam-4944	621	37	c	c	NOUN
ejpam-4944	621	38	,	,	PUNCT
ejpam-4944	621	39	d	d	NOUN
ejpam-4944	621	40	}	}	PUNCT
ejpam-4944	621	41	,	,	PUNCT
ejpam-4944	621	42	{	{	PUNCT
ejpam-4944	621	43	b	b	X
ejpam-4944	621	44	,	,	PUNCT
ejpam-4944	621	45	c	c	NOUN
ejpam-4944	621	46	,	,	PUNCT
ejpam-4944	621	47	d	d	NOUN
ejpam-4944	621	48	}	}	PUNCT
ejpam-4944	621	49	,	,	PUNCT
ejpam-4944	621	50	x	x	NOUN
ejpam-4944	621	51	}	}	PUNCT
ejpam-4944	621	52	.	.	PUNCT
ejpam-4944	622	1	•	•	NOUN
ejpam-4944	622	2	(	(	PUNCT
ejpam-4944	622	3	2	2	NUM
ejpam-4944	622	4	,	,	PUNCT
ejpam-4944	622	5	1)⋆−d(x	1)⋆−d(x	NUM
ejpam-4944	622	6	)	)	PUNCT
ejpam-4944	622	7	=	=	PRON
ejpam-4944	622	8	{	{	PUNCT
ejpam-4944	622	9	{	{	PUNCT
ejpam-4944	622	10	d	d	NOUN
ejpam-4944	622	11	}	}	PUNCT
ejpam-4944	622	12	,	,	PUNCT
ejpam-4944	622	13	{	{	PUNCT
ejpam-4944	622	14	a	a	DET
ejpam-4944	622	15	,	,	PUNCT
ejpam-4944	622	16	b	b	NOUN
ejpam-4944	622	17	}	}	PUNCT
ejpam-4944	622	18	,	,	PUNCT
ejpam-4944	622	19	{	{	PUNCT
ejpam-4944	622	20	a	a	DET
ejpam-4944	622	21	,	,	PUNCT
ejpam-4944	622	22	d	d	NOUN
ejpam-4944	622	23	}	}	PUNCT
ejpam-4944	622	24	,	,	PUNCT
ejpam-4944	622	25	{	{	PUNCT
ejpam-4944	622	26	b	b	X
ejpam-4944	622	27	,	,	PUNCT
ejpam-4944	622	28	d	d	NOUN
ejpam-4944	622	29	}	}	PUNCT
ejpam-4944	622	30	,	,	PUNCT
ejpam-4944	622	31	{	{	PUNCT
ejpam-4944	622	32	c	c	X
ejpam-4944	622	33	,	,	PUNCT
ejpam-4944	622	34	d	d	NOUN
ejpam-4944	622	35	}	}	PUNCT
ejpam-4944	622	36	,	,	PUNCT
ejpam-4944	622	37	{	{	PUNCT
ejpam-4944	622	38	a	a	DET
ejpam-4944	622	39	,	,	PUNCT
ejpam-4944	622	40	b	b	NOUN
ejpam-4944	622	41	,	,	PUNCT
ejpam-4944	622	42	c	c	NOUN
ejpam-4944	622	43	}	}	PUNCT
ejpam-4944	622	44	,	,	PUNCT
ejpam-4944	622	45	{	{	PUNCT
ejpam-4944	622	46	a	a	DET
ejpam-4944	622	47	,	,	PUNCT
ejpam-4944	622	48	b	b	NOUN
ejpam-4944	622	49	,	,	PUNCT
ejpam-4944	622	50	d	d	NOUN
ejpam-4944	622	51	}	}	PUNCT
ejpam-4944	622	52	,	,	PUNCT
ejpam-4944	622	53	{	{	PUNCT
ejpam-4944	622	54	a	a	PRON
ejpam-4944	622	55	,	,	PUNCT
ejpam-4944	622	56	c	c	NOUN
ejpam-4944	622	57	,	,	PUNCT
ejpam-4944	622	58	d	d	NOUN
ejpam-4944	622	59	}	}	PUNCT
ejpam-4944	622	60	,	,	PUNCT
ejpam-4944	622	61	{	{	PUNCT
ejpam-4944	622	62	b	b	X
ejpam-4944	622	63	,	,	PUNCT
ejpam-4944	622	64	c	c	NOUN
ejpam-4944	622	65	,	,	PUNCT
ejpam-4944	622	66	d	d	NOUN
ejpam-4944	622	67	}	}	PUNCT
ejpam-4944	622	68	,	,	PUNCT
ejpam-4944	622	69	x	x	NOUN
ejpam-4944	622	70	}	}	PUNCT
ejpam-4944	622	71	.	.	PUNCT
ejpam-4944	623	1	let	let	VERB
ejpam-4944	623	2	u	u	PRON
ejpam-4944	623	3	=	=	X
ejpam-4944	623	4	{	{	PUNCT
ejpam-4944	623	5	a	a	X
ejpam-4944	623	6	,	,	PUNCT
ejpam-4944	623	7	c	c	NOUN
ejpam-4944	623	8	,	,	PUNCT
ejpam-4944	623	9	d	d	AUX
ejpam-4944	623	10	}	}	PUNCT
ejpam-4944	623	11	be	be	AUX
ejpam-4944	623	12	a	a	DET
ejpam-4944	623	13	subset	subset	NOUN
ejpam-4944	623	14	of	of	ADP
ejpam-4944	623	15	x	x	PUNCT
ejpam-4944	623	16	and	and	CCONJ
ejpam-4944	623	17	e	e	X
ejpam-4944	623	18	=	=	PRON
ejpam-4944	623	19	{	{	PUNCT
ejpam-4944	623	20	(	(	PUNCT
ejpam-4944	623	21	1	1	NUM
ejpam-4944	623	22	,	,	PUNCT
ejpam-4944	623	23	2)⋆-dense	2)⋆-dense	NUM
ejpam-4944	623	24	set	set	NOUN
ejpam-4944	623	25	,	,	PUNCT
ejpam-4944	623	26	(	(	PUNCT
ejpam-4944	623	27	2	2	NUM
ejpam-4944	623	28	,	,	PUNCT
ejpam-4944	623	29	1)⋆-dense	1)⋆-dense	NUM
ejpam-4944	623	30	set	set	NOUN
ejpam-4944	623	31	,	,	PUNCT
ejpam-4944	623	32	(	(	PUNCT
ejpam-4944	623	33	1	1	NUM
ejpam-4944	623	34	,	,	PUNCT
ejpam-4944	623	35	2)⋆dense	2)⋆dense	NUM
ejpam-4944	623	36	but	but	CCONJ
ejpam-4944	623	37	not	not	PART
ejpam-4944	623	38	(	(	PUNCT
ejpam-4944	623	39	2	2	NUM
ejpam-4944	623	40	,	,	PUNCT
ejpam-4944	623	41	1)⋆-dense	1)⋆-dense	NUM
ejpam-4944	623	42	,	,	PUNCT
ejpam-4944	623	43	(	(	PUNCT
ejpam-4944	623	44	2	2	NUM
ejpam-4944	623	45	,	,	PUNCT
ejpam-4944	623	46	1)⋆-dense	1)⋆-dense	NUM
ejpam-4944	623	47	but	but	CCONJ
ejpam-4944	623	48	not	not	PART
ejpam-4944	623	49	(	(	PUNCT
ejpam-4944	623	50	1	1	NUM
ejpam-4944	623	51	,	,	PUNCT
ejpam-4944	623	52	2)⋆-dense	2)⋆-dense	NUM
ejpam-4944	623	53	,	,	PUNCT
ejpam-4944	623	54	(	(	PUNCT
ejpam-4944	623	55	1	1	NUM
ejpam-4944	623	56	,	,	PUNCT
ejpam-4944	623	57	2)⋆-dense	2)⋆-dense	NUM
ejpam-4944	623	58	and	and	CCONJ
ejpam-4944	623	59	(	(	PUNCT
ejpam-4944	623	60	2	2	NUM
ejpam-4944	623	61	,	,	PUNCT
ejpam-4944	623	62	1)⋆dense	1)⋆dense	NUM
ejpam-4944	623	63	}	}	PUNCT
ejpam-4944	623	64	=	=	SYM
ejpam-4944	623	65	{	{	PUNCT
ejpam-4944	623	66	e1	e1	PROPN
ejpam-4944	623	67	,	,	PUNCT
ejpam-4944	623	68	e2	e2	PROPN
ejpam-4944	623	69	,	,	PUNCT
ejpam-4944	623	70	e3	e3	NOUN
ejpam-4944	623	71	,	,	PUNCT
ejpam-4944	623	72	e4	e4	PROPN
ejpam-4944	623	73	,	,	PUNCT
ejpam-4944	623	74	e5	e5	PROPN
ejpam-4944	623	75	}	}	PUNCT
ejpam-4944	623	76	is	be	AUX
ejpam-4944	623	77	the	the	DET
ejpam-4944	623	78	set	set	NOUN
ejpam-4944	623	79	of	of	ADP
ejpam-4944	623	80	parameters	parameter	NOUN
ejpam-4944	623	81	.	.	PUNCT
ejpam-4944	624	1	define	define	VERB
ejpam-4944	624	2	a	a	DET
ejpam-4944	624	3	map	map	NOUN
ejpam-4944	624	4	f	f	NOUN
ejpam-4944	624	5	from	from	ADP
ejpam-4944	624	6	e	e	PROPN
ejpam-4944	624	7	to	to	ADP
ejpam-4944	624	8	exp(u	exp(u	PROPN
ejpam-4944	624	9	)	)	PUNCT
ejpam-4944	624	10	by	by	ADP
ejpam-4944	624	11	,	,	PUNCT
ejpam-4944	624	12	f	f	PROPN
ejpam-4944	624	13	(	(	PUNCT
ejpam-4944	624	14	e1	e1	PROPN
ejpam-4944	624	15	)	)	PUNCT
ejpam-4944	624	16	=	=	PRON
ejpam-4944	624	17	{	{	PUNCT
ejpam-4944	624	18	a	a	X
ejpam-4944	624	19	,	,	PUNCT
ejpam-4944	624	20	c};f	c};f	PUNCT
ejpam-4944	624	21	(	(	PUNCT
ejpam-4944	624	22	e2	e2	PROPN
ejpam-4944	624	23	)	)	PUNCT
ejpam-4944	624	24	=	=	PRON
ejpam-4944	624	25	{	{	PUNCT
ejpam-4944	624	26	d};f	d};f	X
ejpam-4944	624	27	(	(	PUNCT
ejpam-4944	624	28	e3	e3	NOUN
ejpam-4944	624	29	)	)	PUNCT
ejpam-4944	624	30	=	=	PRON
ejpam-4944	624	31	{	{	PUNCT
ejpam-4944	624	32	a	a	X
ejpam-4944	624	33	,	,	PUNCT
ejpam-4944	624	34	c};f	c};f	PUNCT
ejpam-4944	624	35	(	(	PUNCT
ejpam-4944	624	36	e4	e4	PROPN
ejpam-4944	624	37	)	)	PUNCT
ejpam-4944	624	38	=	=	PUNCT
ejpam-4944	624	39	{	{	PUNCT
ejpam-4944	624	40	c	c	NOUN
ejpam-4944	624	41	,	,	PUNCT
ejpam-4944	624	42	d	d	NOUN
ejpam-4944	624	43	}	}	PUNCT
ejpam-4944	624	44	,	,	PUNCT
ejpam-4944	624	45	f	f	PROPN
ejpam-4944	624	46	(	(	PUNCT
ejpam-4944	624	47	e5	e5	PROPN
ejpam-4944	624	48	)	)	PUNCT
ejpam-4944	624	49	=	=	PRON
ejpam-4944	624	50	{	{	PUNCT
ejpam-4944	624	51	a	a	X
ejpam-4944	624	52	,	,	PUNCT
ejpam-4944	624	53	c	c	NOUN
ejpam-4944	624	54	,	,	PUNCT
ejpam-4944	624	55	d	d	NOUN
ejpam-4944	624	56	}	}	PUNCT
ejpam-4944	624	57	.	.	PUNCT
ejpam-4944	625	1	then	then	ADV
ejpam-4944	625	2	the	the	DET
ejpam-4944	625	3	pair	pair	NOUN
ejpam-4944	625	4	(	(	PUNCT
ejpam-4944	625	5	f	f	X
ejpam-4944	625	6	,	,	PUNCT
ejpam-4944	625	7	e	e	NOUN
ejpam-4944	625	8	)	)	PUNCT
ejpam-4944	625	9	is	be	AUX
ejpam-4944	625	10	a	a	DET
ejpam-4944	625	11	soft	soft	ADJ
ejpam-4944	625	12	set	set	NOUN
ejpam-4944	625	13	over	over	ADP
ejpam-4944	625	14	u.	u.	NOUN
ejpam-4944	625	15	example	example	NOUN
ejpam-4944	625	16	39	39	NUM
ejpam-4944	625	17	.	.	PUNCT
ejpam-4944	626	1	consider	consider	VERB
ejpam-4944	626	2	the	the	DET
ejpam-4944	626	3	bgts	bgts	NOUN
ejpam-4944	626	4	(	(	PUNCT
ejpam-4944	626	5	x,µ1	x,µ1	PROPN
ejpam-4944	626	6	,	,	PUNCT
ejpam-4944	626	7	µ2	µ2	PROPN
ejpam-4944	626	8	)	)	PUNCT
ejpam-4944	626	9	where	where	SCONJ
ejpam-4944	626	10	x	x	X
ejpam-4944	626	11	=	=	PRON
ejpam-4944	626	12	{	{	PUNCT
ejpam-4944	626	13	p	p	X
ejpam-4944	626	14	,	,	PUNCT
ejpam-4944	626	15	q	q	ADJ
ejpam-4944	626	16	,	,	PUNCT
ejpam-4944	626	17	r	r	NOUN
ejpam-4944	626	18	,	,	PUNCT
ejpam-4944	626	19	s	s	PART
ejpam-4944	626	20	}	}	PUNCT
ejpam-4944	626	21	;	;	PUNCT
ejpam-4944	626	22	µ1	µ1	PROPN
ejpam-4944	626	23	=	=	SYM
ejpam-4944	626	24	{	{	PUNCT
ejpam-4944	626	25	∅	∅	NOUN
ejpam-4944	626	26	,	,	PUNCT
ejpam-4944	626	27	{	{	PUNCT
ejpam-4944	626	28	p	p	X
ejpam-4944	626	29	}	}	PUNCT
ejpam-4944	626	30	,	,	PUNCT
ejpam-4944	626	31	{	{	PUNCT
ejpam-4944	626	32	p	p	X
ejpam-4944	626	33	,	,	PUNCT
ejpam-4944	626	34	s	s	PART
ejpam-4944	626	35	}	}	PUNCT
ejpam-4944	626	36	,	,	PUNCT
ejpam-4944	626	37	{	{	PUNCT
ejpam-4944	626	38	q	q	X
ejpam-4944	626	39	,	,	PUNCT
ejpam-4944	626	40	s	s	PART
ejpam-4944	626	41	}	}	PUNCT
ejpam-4944	626	42	,	,	PUNCT
ejpam-4944	626	43	{	{	PUNCT
ejpam-4944	626	44	p	p	X
ejpam-4944	626	45	,	,	PUNCT
ejpam-4944	626	46	q	q	ADJ
ejpam-4944	626	47	,	,	PUNCT
ejpam-4944	626	48	s	s	PART
ejpam-4944	626	49	}	}	PUNCT
ejpam-4944	626	50	}	}	PUNCT
ejpam-4944	626	51	and	and	CCONJ
ejpam-4944	626	52	µ2	µ2	PROPN
ejpam-4944	626	53	=	=	PUNCT
ejpam-4944	626	54	{	{	PUNCT
ejpam-4944	626	55	∅	∅	NOUN
ejpam-4944	626	56	,	,	PUNCT
ejpam-4944	626	57	{	{	PUNCT
ejpam-4944	626	58	q	q	X
ejpam-4944	626	59	}	}	PUNCT
ejpam-4944	626	60	,	,	PUNCT
ejpam-4944	626	61	{	{	PUNCT
ejpam-4944	626	62	p	p	X
ejpam-4944	626	63	,	,	PUNCT
ejpam-4944	626	64	r	r	NOUN
ejpam-4944	626	65	}	}	PUNCT
ejpam-4944	626	66	,	,	PUNCT
ejpam-4944	626	67	{	{	PUNCT
ejpam-4944	626	68	q	q	X
ejpam-4944	626	69	,	,	PUNCT
ejpam-4944	626	70	r	r	NOUN
ejpam-4944	626	71	}	}	PUNCT
ejpam-4944	626	72	,	,	PUNCT
ejpam-4944	626	73	{	{	PUNCT
ejpam-4944	626	74	p	p	X
ejpam-4944	626	75	,	,	PUNCT
ejpam-4944	626	76	q	q	ADJ
ejpam-4944	626	77	,	,	PUNCT
ejpam-4944	626	78	r	r	NOUN
ejpam-4944	626	79	}	}	PUNCT
ejpam-4944	626	80	}	}	PUNCT
ejpam-4944	626	81	.	.	PUNCT
ejpam-4944	627	1	here	here	ADV
ejpam-4944	627	2	,	,	PUNCT
ejpam-4944	627	3	•	•	NUM
ejpam-4944	627	4	µ1	µ1	NOUN
ejpam-4944	627	5	-	-	PUNCT
ejpam-4944	627	6	semi	semi	ADJ
ejpam-4944	627	7	-	-	ADJ
ejpam-4944	627	8	open	open	ADJ
ejpam-4944	627	9	sets	set	NOUN
ejpam-4944	627	10	=	=	SYM
ejpam-4944	627	11	{	{	PUNCT
ejpam-4944	627	12	∅	∅	NOUN
ejpam-4944	627	13	,	,	PUNCT
ejpam-4944	627	14	{	{	PUNCT
ejpam-4944	627	15	p	p	X
ejpam-4944	627	16	}	}	PUNCT
ejpam-4944	627	17	,	,	PUNCT
ejpam-4944	627	18	{	{	PUNCT
ejpam-4944	627	19	r	r	NOUN
ejpam-4944	627	20	}	}	PUNCT
ejpam-4944	627	21	,	,	PUNCT
ejpam-4944	627	22	{	{	PUNCT
ejpam-4944	627	23	p	p	X
ejpam-4944	627	24	,	,	PUNCT
ejpam-4944	627	25	r	r	NOUN
ejpam-4944	627	26	}	}	PUNCT
ejpam-4944	627	27	,	,	PUNCT
ejpam-4944	627	28	{	{	PUNCT
ejpam-4944	627	29	p	p	X
ejpam-4944	627	30	,	,	PUNCT
ejpam-4944	627	31	s	s	PART
ejpam-4944	627	32	}	}	PUNCT
ejpam-4944	627	33	,	,	PUNCT
ejpam-4944	627	34	{	{	PUNCT
ejpam-4944	627	35	q	q	X
ejpam-4944	627	36	,	,	PUNCT
ejpam-4944	627	37	s	s	PART
ejpam-4944	627	38	}	}	PUNCT
ejpam-4944	627	39	,	,	PUNCT
ejpam-4944	627	40	{	{	PUNCT
ejpam-4944	627	41	p	p	X
ejpam-4944	627	42	,	,	PUNCT
ejpam-4944	627	43	q	q	X
ejpam-4944	627	44	,	,	PUNCT
ejpam-4944	627	45	s	s	PART
ejpam-4944	627	46	}	}	PUNCT
ejpam-4944	627	47	,	,	PUNCT
ejpam-4944	627	48	{	{	PUNCT
ejpam-4944	627	49	p	p	X
ejpam-4944	627	50	,	,	PUNCT
ejpam-4944	627	51	r	r	NOUN
ejpam-4944	627	52	,	,	PUNCT
ejpam-4944	627	53	s	s	PART
ejpam-4944	627	54	}	}	PUNCT
ejpam-4944	627	55	,	,	PUNCT
ejpam-4944	627	56	{	{	PUNCT
ejpam-4944	627	57	q	q	X
ejpam-4944	627	58	,	,	PUNCT
ejpam-4944	627	59	r	r	NOUN
ejpam-4944	627	60	,	,	PUNCT
ejpam-4944	627	61	s	s	PART
ejpam-4944	627	62	}	}	PUNCT
ejpam-4944	627	63	,	,	PUNCT
ejpam-4944	627	64	x	x	NOUN
ejpam-4944	627	65	}	}	PUNCT
ejpam-4944	627	66	.	.	PUNCT
ejpam-4944	628	1	•	•	NUM
ejpam-4944	628	2	µ1	µ1	NOUN
ejpam-4944	628	3	-	-	PUNCT
ejpam-4944	628	4	pre	pre	ADJ
ejpam-4944	628	5	-	-	ADJ
ejpam-4944	628	6	open	open	ADJ
ejpam-4944	628	7	sets	set	NOUN
ejpam-4944	628	8	=	=	SYM
ejpam-4944	628	9	{	{	PUNCT
ejpam-4944	628	10	∅	∅	NOUN
ejpam-4944	628	11	,	,	PUNCT
ejpam-4944	628	12	{	{	PUNCT
ejpam-4944	628	13	p	p	X
ejpam-4944	628	14	}	}	PUNCT
ejpam-4944	628	15	,	,	PUNCT
ejpam-4944	628	16	{	{	PUNCT
ejpam-4944	628	17	s	s	X
ejpam-4944	628	18	}	}	PUNCT
ejpam-4944	628	19	,	,	PUNCT
ejpam-4944	628	20	{	{	PUNCT
ejpam-4944	628	21	p	p	X
ejpam-4944	628	22	,	,	PUNCT
ejpam-4944	628	23	q	q	NOUN
ejpam-4944	628	24	}	}	PUNCT
ejpam-4944	628	25	,	,	PUNCT
ejpam-4944	628	26	{	{	PUNCT
ejpam-4944	628	27	p	p	X
ejpam-4944	628	28	,	,	PUNCT
ejpam-4944	628	29	s	s	PART
ejpam-4944	628	30	}	}	PUNCT
ejpam-4944	628	31	,	,	PUNCT
ejpam-4944	628	32	{	{	PUNCT
ejpam-4944	628	33	q	q	X
ejpam-4944	628	34	,	,	PUNCT
ejpam-4944	628	35	s	s	PART
ejpam-4944	628	36	}	}	PUNCT
ejpam-4944	628	37	,	,	PUNCT
ejpam-4944	628	38	{	{	PUNCT
ejpam-4944	628	39	p	p	X
ejpam-4944	628	40	,	,	PUNCT
ejpam-4944	628	41	q	q	ADJ
ejpam-4944	628	42	,	,	PUNCT
ejpam-4944	628	43	s	s	PART
ejpam-4944	628	44	}	}	PUNCT
ejpam-4944	628	45	}	}	PUNCT
ejpam-4944	628	46	.	.	PUNCT
ejpam-4944	629	1	•	•	NUM
ejpam-4944	629	2	µ1	µ1	NOUN
ejpam-4944	629	3	−	−	NOUN
ejpam-4944	629	4	α	α	NOUN
ejpam-4944	629	5	-	-	ADJ
ejpam-4944	629	6	open	open	ADJ
ejpam-4944	629	7	sets	set	NOUN
ejpam-4944	629	8	=	=	SYM
ejpam-4944	629	9	{	{	PUNCT
ejpam-4944	629	10	∅	∅	NOUN
ejpam-4944	629	11	,	,	PUNCT
ejpam-4944	629	12	{	{	PUNCT
ejpam-4944	629	13	p	p	X
ejpam-4944	629	14	}	}	PUNCT
ejpam-4944	629	15	,	,	PUNCT
ejpam-4944	629	16	{	{	PUNCT
ejpam-4944	629	17	p	p	X
ejpam-4944	629	18	,	,	PUNCT
ejpam-4944	629	19	s	s	PART
ejpam-4944	629	20	}	}	PUNCT
ejpam-4944	629	21	,	,	PUNCT
ejpam-4944	629	22	{	{	PUNCT
ejpam-4944	629	23	q	q	X
ejpam-4944	629	24	,	,	PUNCT
ejpam-4944	629	25	s	s	PART
ejpam-4944	629	26	}	}	PUNCT
ejpam-4944	629	27	,	,	PUNCT
ejpam-4944	629	28	{	{	PUNCT
ejpam-4944	629	29	p	p	X
ejpam-4944	629	30	,	,	PUNCT
ejpam-4944	629	31	q	q	ADJ
ejpam-4944	629	32	,	,	PUNCT
ejpam-4944	629	33	s	s	PART
ejpam-4944	629	34	}	}	PUNCT
ejpam-4944	629	35	}	}	PUNCT
ejpam-4944	629	36	.	.	PUNCT
ejpam-4944	630	1	•	•	NUM
ejpam-4944	630	2	µ1	µ1	NOUN
ejpam-4944	630	3	−	−	NOUN
ejpam-4944	630	4	β	β	NOUN
ejpam-4944	630	5	-	-	ADJ
ejpam-4944	630	6	open	open	ADJ
ejpam-4944	630	7	sets	set	NOUN
ejpam-4944	630	8	=	=	SYM
ejpam-4944	630	9	exp(x)−	exp(x)−	PROPN
ejpam-4944	630	10	{	{	PUNCT
ejpam-4944	630	11	{	{	PUNCT
ejpam-4944	630	12	q	q	NOUN
ejpam-4944	630	13	}	}	PUNCT
ejpam-4944	630	14	,	,	PUNCT
ejpam-4944	630	15	{	{	PUNCT
ejpam-4944	630	16	q	q	X
ejpam-4944	630	17	,	,	PUNCT
ejpam-4944	630	18	r	r	NOUN
ejpam-4944	630	19	}	}	PUNCT
ejpam-4944	630	20	}	}	PUNCT
ejpam-4944	630	21	.	.	PUNCT
ejpam-4944	631	1	•	•	NUM
ejpam-4944	631	2	µ1	µ1	NOUN
ejpam-4944	631	3	−	−	PROPN
ejpam-4944	631	4	b	b	NOUN
ejpam-4944	631	5	-	-	PUNCT
ejpam-4944	631	6	open	open	ADJ
ejpam-4944	631	7	sets	set	NOUN
ejpam-4944	631	8	=	=	SYM
ejpam-4944	631	9	exp(x)−	exp(x)−	PROPN
ejpam-4944	631	10	{	{	PUNCT
ejpam-4944	631	11	q	q	NOUN
ejpam-4944	631	12	}	}	PUNCT
ejpam-4944	631	13	.	.	PUNCT
ejpam-4944	632	1	let	let	VERB
ejpam-4944	632	2	u	u	PRON
ejpam-4944	632	3	=	=	PUNCT
ejpam-4944	632	4	{	{	PUNCT
ejpam-4944	632	5	q	q	NOUN
ejpam-4944	632	6	,	,	PUNCT
ejpam-4944	632	7	r	r	NOUN
ejpam-4944	632	8	,	,	PUNCT
ejpam-4944	632	9	s	s	AUX
ejpam-4944	632	10	}	}	PUNCT
ejpam-4944	632	11	be	be	AUX
ejpam-4944	632	12	a	a	DET
ejpam-4944	632	13	subset	subset	NOUN
ejpam-4944	632	14	ofx	ofx	NOUN
ejpam-4944	632	15	and	and	CCONJ
ejpam-4944	632	16	e	e	NOUN
ejpam-4944	632	17	=	=	NOUN
ejpam-4944	632	18	{	{	PUNCT
ejpam-4944	632	19	µ1	µ1	NOUN
ejpam-4944	632	20	-	-	PUNCT
ejpam-4944	632	21	semi	semi	ADJ
ejpam-4944	632	22	-	-	ADJ
ejpam-4944	632	23	open	open	ADJ
ejpam-4944	632	24	set	set	NOUN
ejpam-4944	632	25	,	,	PUNCT
ejpam-4944	632	26	µ1	µ1	NOUN
ejpam-4944	632	27	-	-	PUNCT
ejpam-4944	632	28	pre	pre	ADJ
ejpam-4944	632	29	-	-	ADJ
ejpam-4944	632	30	open	open	ADJ
ejpam-4944	632	31	set	set	NOUN
ejpam-4944	632	32	,	,	PUNCT
ejpam-4944	632	33	µ1−α	µ1−α	PROPN
ejpam-4944	632	34	-	-	PUNCT
ejpam-4944	632	35	open	open	ADJ
ejpam-4944	632	36	set	set	NOUN
ejpam-4944	632	37	,	,	PUNCT
ejpam-4944	632	38	µ1−β	µ1−β	NOUN
ejpam-4944	632	39	-	-	PUNCT
ejpam-4944	632	40	open	open	ADJ
ejpam-4944	632	41	set	set	NOUN
ejpam-4944	632	42	,	,	PUNCT
ejpam-4944	632	43	µ1−	µ1−	PROPN
ejpam-4944	632	44	b	b	X
ejpam-4944	632	45	-	-	PUNCT
ejpam-4944	632	46	open	open	ADJ
ejpam-4944	632	47	set	set	NOUN
ejpam-4944	632	48	}	}	PUNCT
ejpam-4944	632	49	=	=	SYM
ejpam-4944	632	50	{	{	PUNCT
ejpam-4944	632	51	e1	e1	PROPN
ejpam-4944	632	52	,	,	PUNCT
ejpam-4944	632	53	e2	e2	PROPN
ejpam-4944	632	54	,	,	PUNCT
ejpam-4944	632	55	e3	e3	NOUN
ejpam-4944	632	56	,	,	PUNCT
ejpam-4944	632	57	e4	e4	PROPN
ejpam-4944	632	58	,	,	PUNCT
ejpam-4944	632	59	e5	e5	PROPN
ejpam-4944	632	60	}	}	PUNCT
ejpam-4944	632	61	is	be	AUX
ejpam-4944	632	62	the	the	DET
ejpam-4944	632	63	set	set	NOUN
ejpam-4944	632	64	of	of	ADP
ejpam-4944	632	65	parameters	parameter	NOUN
ejpam-4944	632	66	.	.	PUNCT
ejpam-4944	633	1	define	define	VERB
ejpam-4944	633	2	a	a	DET
ejpam-4944	633	3	function	function	NOUN
ejpam-4944	633	4	f	f	NOUN
ejpam-4944	633	5	from	from	ADP
ejpam-4944	633	6	a	a	DET
ejpam-4944	633	7	set	set	NOUN
ejpam-4944	633	8	e	e	NOUN
ejpam-4944	633	9	to	to	ADP
ejpam-4944	633	10	exp(u	exp(u	PROPN
ejpam-4944	633	11	)	)	PUNCT
ejpam-4944	633	12	by	by	ADP
ejpam-4944	633	13	,	,	PUNCT
ejpam-4944	633	14	f	f	PROPN
ejpam-4944	633	15	(	(	PUNCT
ejpam-4944	633	16	e1	e1	PROPN
ejpam-4944	633	17	)	)	PUNCT
ejpam-4944	633	18	=	=	PRON
ejpam-4944	633	19	{	{	PUNCT
ejpam-4944	633	20	r};f	r};f	NOUN
ejpam-4944	633	21	(	(	PUNCT
ejpam-4944	633	22	e2	e2	PROPN
ejpam-4944	633	23	)	)	PUNCT
ejpam-4944	633	24	=	=	PRON
ejpam-4944	633	25	{	{	PUNCT
ejpam-4944	633	26	s};f	s};f	X
ejpam-4944	633	27	(	(	PUNCT
ejpam-4944	633	28	e3	e3	NOUN
ejpam-4944	633	29	)	)	PUNCT
ejpam-4944	633	30	=	=	PRON
ejpam-4944	633	31	{	{	PUNCT
ejpam-4944	633	32	q	q	X
ejpam-4944	633	33	,	,	PUNCT
ejpam-4944	633	34	s};f	s};f	PROPN
ejpam-4944	633	35	(	(	PUNCT
ejpam-4944	633	36	e4	e4	PROPN
ejpam-4944	633	37	)	)	PUNCT
ejpam-4944	633	38	=	=	PUNCT
ejpam-4944	634	1	d.	d.	PROPN
ejpam-4944	634	2	elgezouli	elgezouli	PROPN
ejpam-4944	634	3	et	et	PROPN
ejpam-4944	634	4	al	al	PROPN
ejpam-4944	634	5	.	.	PUNCT
ejpam-4944	634	6	/	/	SYM
ejpam-4944	634	7	eur	eur	PROPN
ejpam-4944	634	8	.	.	PUNCT
ejpam-4944	635	1	j.	j.	PROPN
ejpam-4944	635	2	pure	pure	PROPN
ejpam-4944	635	3	appl	appl	PROPN
ejpam-4944	635	4	.	.	PROPN
ejpam-4944	635	5	math	math	PROPN
ejpam-4944	635	6	,	,	PUNCT
ejpam-4944	635	7	16	16	NUM
ejpam-4944	635	8	(	(	PUNCT
ejpam-4944	635	9	4	4	NUM
ejpam-4944	635	10	)	)	PUNCT
ejpam-4944	635	11	(	(	PUNCT
ejpam-4944	635	12	2023	2023	NUM
ejpam-4944	635	13	)	)	PUNCT
ejpam-4944	635	14	,	,	PUNCT
ejpam-4944	635	15	2286	2286	NUM
ejpam-4944	635	16	-	-	SYM
ejpam-4944	635	17	2305	2305	NUM
ejpam-4944	635	18	2303	2303	NUM
ejpam-4944	635	19	{	{	PUNCT
ejpam-4944	635	20	r	r	NOUN
ejpam-4944	635	21	,	,	PUNCT
ejpam-4944	635	22	s};f	s};f	PROPN
ejpam-4944	635	23	(	(	PUNCT
ejpam-4944	635	24	e5	e5	PROPN
ejpam-4944	635	25	)	)	PUNCT
ejpam-4944	635	26	=	=	PRON
ejpam-4944	636	1	{	{	PUNCT
ejpam-4944	636	2	q	q	NOUN
ejpam-4944	636	3	,	,	PUNCT
ejpam-4944	636	4	r	r	NOUN
ejpam-4944	636	5	}	}	PUNCT
ejpam-4944	636	6	.	.	PUNCT
ejpam-4944	637	1	then	then	ADV
ejpam-4944	637	2	the	the	DET
ejpam-4944	637	3	pair	pair	NOUN
ejpam-4944	637	4	(	(	PUNCT
ejpam-4944	637	5	f	f	X
ejpam-4944	637	6	,	,	PUNCT
ejpam-4944	637	7	e	e	NOUN
ejpam-4944	637	8	)	)	PUNCT
ejpam-4944	637	9	is	be	AUX
ejpam-4944	637	10	a	a	DET
ejpam-4944	637	11	soft	soft	ADJ
ejpam-4944	637	12	set	set	NOUN
ejpam-4944	637	13	over	over	ADP
ejpam-4944	637	14	u.	u.	NOUN
ejpam-4944	637	15	here	here	ADV
ejpam-4944	637	16	,	,	PUNCT
ejpam-4944	637	17	•	•	NUM
ejpam-4944	637	18	µ2	µ2	ADJ
ejpam-4944	637	19	-	-	PUNCT
ejpam-4944	637	20	semi	semi	ADJ
ejpam-4944	637	21	-	-	ADJ
ejpam-4944	637	22	open	open	ADJ
ejpam-4944	637	23	sets	set	NOUN
ejpam-4944	637	24	=	=	SYM
ejpam-4944	637	25	{	{	PUNCT
ejpam-4944	637	26	∅	∅	NOUN
ejpam-4944	637	27	,	,	PUNCT
ejpam-4944	637	28	{	{	PUNCT
ejpam-4944	637	29	q	q	X
ejpam-4944	637	30	}	}	PUNCT
ejpam-4944	637	31	,	,	PUNCT
ejpam-4944	637	32	{	{	PUNCT
ejpam-4944	637	33	s	s	X
ejpam-4944	637	34	}	}	PUNCT
ejpam-4944	637	35	,	,	PUNCT
ejpam-4944	637	36	{	{	PUNCT
ejpam-4944	637	37	p	p	X
ejpam-4944	637	38	,	,	PUNCT
ejpam-4944	637	39	r	r	NOUN
ejpam-4944	637	40	}	}	PUNCT
ejpam-4944	637	41	,	,	PUNCT
ejpam-4944	637	42	{	{	PUNCT
ejpam-4944	637	43	q	q	X
ejpam-4944	637	44	,	,	PUNCT
ejpam-4944	637	45	r	r	NOUN
ejpam-4944	637	46	}	}	PUNCT
ejpam-4944	637	47	,	,	PUNCT
ejpam-4944	637	48	{	{	PUNCT
ejpam-4944	637	49	q	q	X
ejpam-4944	637	50	,	,	PUNCT
ejpam-4944	637	51	s	s	PART
ejpam-4944	637	52	}	}	PUNCT
ejpam-4944	637	53	,	,	PUNCT
ejpam-4944	637	54	{	{	PUNCT
ejpam-4944	637	55	p	p	X
ejpam-4944	637	56	,	,	PUNCT
ejpam-4944	637	57	q	q	ADJ
ejpam-4944	637	58	,	,	PUNCT
ejpam-4944	637	59	r	r	NOUN
ejpam-4944	637	60	}	}	PUNCT
ejpam-4944	637	61	,	,	PUNCT
ejpam-4944	637	62	{	{	PUNCT
ejpam-4944	637	63	p	p	X
ejpam-4944	637	64	,	,	PUNCT
ejpam-4944	637	65	r	r	NOUN
ejpam-4944	637	66	,	,	PUNCT
ejpam-4944	637	67	s	s	PART
ejpam-4944	637	68	}	}	PUNCT
ejpam-4944	637	69	,	,	PUNCT
ejpam-4944	637	70	{	{	PUNCT
ejpam-4944	637	71	q	q	X
ejpam-4944	637	72	,	,	PUNCT
ejpam-4944	637	73	r	r	NOUN
ejpam-4944	637	74	,	,	PUNCT
ejpam-4944	637	75	s	s	PART
ejpam-4944	637	76	}	}	PUNCT
ejpam-4944	637	77	,	,	PUNCT
ejpam-4944	637	78	x	x	NOUN
ejpam-4944	637	79	}	}	PUNCT
ejpam-4944	637	80	.	.	PUNCT
ejpam-4944	638	1	•	•	NUM
ejpam-4944	638	2	µ2	µ2	PROPN
ejpam-4944	638	3	-	-	PUNCT
ejpam-4944	638	4	pre	pre	ADJ
ejpam-4944	638	5	-	-	ADJ
ejpam-4944	638	6	open	open	ADJ
ejpam-4944	638	7	sets	set	NOUN
ejpam-4944	638	8	=	=	SYM
ejpam-4944	638	9	{	{	PUNCT
ejpam-4944	638	10	∅	∅	NOUN
ejpam-4944	638	11	,	,	PUNCT
ejpam-4944	638	12	{	{	PUNCT
ejpam-4944	638	13	q	q	X
ejpam-4944	638	14	}	}	PUNCT
ejpam-4944	638	15	,	,	PUNCT
ejpam-4944	638	16	{	{	PUNCT
ejpam-4944	638	17	r	r	NOUN
ejpam-4944	638	18	}	}	PUNCT
ejpam-4944	638	19	,	,	PUNCT
ejpam-4944	638	20	{	{	PUNCT
ejpam-4944	638	21	p	p	X
ejpam-4944	638	22	,	,	PUNCT
ejpam-4944	638	23	q	q	NOUN
ejpam-4944	638	24	}	}	PUNCT
ejpam-4944	638	25	,	,	PUNCT
ejpam-4944	638	26	{	{	PUNCT
ejpam-4944	638	27	p	p	X
ejpam-4944	638	28	,	,	PUNCT
ejpam-4944	638	29	r	r	NOUN
ejpam-4944	638	30	}	}	PUNCT
ejpam-4944	638	31	,	,	PUNCT
ejpam-4944	638	32	{	{	PUNCT
ejpam-4944	638	33	q	q	X
ejpam-4944	638	34	,	,	PUNCT
ejpam-4944	638	35	r	r	NOUN
ejpam-4944	638	36	}	}	PUNCT
ejpam-4944	638	37	,	,	PUNCT
ejpam-4944	638	38	{	{	PUNCT
ejpam-4944	638	39	p	p	X
ejpam-4944	638	40	,	,	PUNCT
ejpam-4944	638	41	q	q	ADJ
ejpam-4944	638	42	,	,	PUNCT
ejpam-4944	638	43	r	r	NOUN
ejpam-4944	638	44	}	}	PUNCT
ejpam-4944	638	45	}	}	PUNCT
ejpam-4944	638	46	.	.	PUNCT
ejpam-4944	639	1	•	•	NUM
ejpam-4944	639	2	µ2	µ2	NOUN
ejpam-4944	639	3	−	−	PROPN
ejpam-4944	639	4	α	α	NOUN
ejpam-4944	639	5	-	-	ADJ
ejpam-4944	639	6	open	open	ADJ
ejpam-4944	639	7	sets	set	NOUN
ejpam-4944	639	8	=	=	SYM
ejpam-4944	639	9	{	{	PUNCT
ejpam-4944	639	10	∅	∅	NOUN
ejpam-4944	639	11	,	,	PUNCT
ejpam-4944	639	12	{	{	PUNCT
ejpam-4944	639	13	q	q	X
ejpam-4944	639	14	}	}	PUNCT
ejpam-4944	639	15	,	,	PUNCT
ejpam-4944	639	16	{	{	PUNCT
ejpam-4944	639	17	p	p	X
ejpam-4944	639	18	,	,	PUNCT
ejpam-4944	639	19	r	r	NOUN
ejpam-4944	639	20	}	}	PUNCT
ejpam-4944	639	21	,	,	PUNCT
ejpam-4944	639	22	{	{	PUNCT
ejpam-4944	639	23	q	q	X
ejpam-4944	639	24	,	,	PUNCT
ejpam-4944	639	25	r	r	NOUN
ejpam-4944	639	26	}	}	PUNCT
ejpam-4944	639	27	,	,	PUNCT
ejpam-4944	639	28	{	{	PUNCT
ejpam-4944	639	29	p	p	X
ejpam-4944	639	30	,	,	PUNCT
ejpam-4944	639	31	q	q	ADJ
ejpam-4944	639	32	,	,	PUNCT
ejpam-4944	639	33	r	r	NOUN
ejpam-4944	639	34	}	}	PUNCT
ejpam-4944	639	35	}	}	PUNCT
ejpam-4944	639	36	.	.	PUNCT
ejpam-4944	640	1	•	•	NUM
ejpam-4944	640	2	µ2	µ2	NOUN
ejpam-4944	640	3	−	−	PROPN
ejpam-4944	640	4	β	β	NOUN
ejpam-4944	640	5	-	-	ADJ
ejpam-4944	640	6	open	open	ADJ
ejpam-4944	640	7	sets	set	NOUN
ejpam-4944	640	8	=	=	SYM
ejpam-4944	640	9	exp(x)−	exp(x)−	PROPN
ejpam-4944	640	10	{	{	PUNCT
ejpam-4944	640	11	{	{	PUNCT
ejpam-4944	640	12	p	p	X
ejpam-4944	640	13	}	}	PUNCT
ejpam-4944	640	14	,	,	PUNCT
ejpam-4944	640	15	{	{	PUNCT
ejpam-4944	640	16	p	p	X
ejpam-4944	640	17	,	,	PUNCT
ejpam-4944	640	18	s	s	PART
ejpam-4944	640	19	}	}	PUNCT
ejpam-4944	640	20	}	}	PUNCT
ejpam-4944	640	21	.	.	PUNCT
ejpam-4944	641	1	•	•	NUM
ejpam-4944	641	2	µ2	µ2	NOUN
ejpam-4944	641	3	−	−	PROPN
ejpam-4944	641	4	b	b	X
ejpam-4944	641	5	-	-	PUNCT
ejpam-4944	641	6	open	open	ADJ
ejpam-4944	641	7	sets	set	NOUN
ejpam-4944	641	8	=	=	SYM
ejpam-4944	641	9	exp(x)−	exp(x)−	PROPN
ejpam-4944	641	10	{	{	PUNCT
ejpam-4944	641	11	{	{	PUNCT
ejpam-4944	641	12	p	p	X
ejpam-4944	641	13	}	}	PUNCT
ejpam-4944	641	14	,	,	PUNCT
ejpam-4944	641	15	{	{	PUNCT
ejpam-4944	641	16	p	p	X
ejpam-4944	641	17	,	,	PUNCT
ejpam-4944	641	18	s	s	PART
ejpam-4944	641	19	}	}	PUNCT
ejpam-4944	641	20	}	}	PUNCT
ejpam-4944	641	21	.	.	PUNCT
ejpam-4944	642	1	let	let	VERB
ejpam-4944	642	2	u	u	PRON
ejpam-4944	642	3	=	=	PUNCT
ejpam-4944	642	4	{	{	PUNCT
ejpam-4944	642	5	p	p	X
ejpam-4944	642	6	,	,	PUNCT
ejpam-4944	642	7	r	r	NOUN
ejpam-4944	642	8	,	,	PUNCT
ejpam-4944	642	9	s	s	AUX
ejpam-4944	642	10	}	}	PUNCT
ejpam-4944	642	11	be	be	AUX
ejpam-4944	642	12	a	a	DET
ejpam-4944	642	13	subset	subset	NOUN
ejpam-4944	642	14	ofx	ofx	NOUN
ejpam-4944	642	15	and	and	CCONJ
ejpam-4944	642	16	e	e	NOUN
ejpam-4944	642	17	=	=	PROPN
ejpam-4944	642	18	{	{	PUNCT
ejpam-4944	642	19	µ2	µ2	PROPN
ejpam-4944	642	20	-	-	PUNCT
ejpam-4944	642	21	semi	semi	ADV
ejpam-4944	642	22	-	-	ADJ
ejpam-4944	642	23	open	open	ADJ
ejpam-4944	642	24	set	set	NOUN
ejpam-4944	642	25	,	,	PUNCT
ejpam-4944	642	26	µ2	µ2	PROPN
ejpam-4944	642	27	-	-	PUNCT
ejpam-4944	642	28	pre	pre	ADJ
ejpam-4944	642	29	-	-	ADJ
ejpam-4944	642	30	open	open	ADJ
ejpam-4944	642	31	set	set	NOUN
ejpam-4944	642	32	,	,	PUNCT
ejpam-4944	642	33	µ2−α	µ2−α	PROPN
ejpam-4944	642	34	-	-	PUNCT
ejpam-4944	642	35	open	open	ADJ
ejpam-4944	642	36	set	set	NOUN
ejpam-4944	642	37	,	,	PUNCT
ejpam-4944	642	38	µ2−β	µ2−β	NOUN
ejpam-4944	642	39	-	-	PUNCT
ejpam-4944	642	40	open	open	ADJ
ejpam-4944	642	41	set	set	NOUN
ejpam-4944	642	42	,	,	PUNCT
ejpam-4944	642	43	µ2−	µ2−	PROPN
ejpam-4944	642	44	b	b	X
ejpam-4944	642	45	-	-	PUNCT
ejpam-4944	642	46	open	open	ADJ
ejpam-4944	642	47	set	set	NOUN
ejpam-4944	642	48	}	}	PUNCT
ejpam-4944	642	49	=	=	SYM
ejpam-4944	642	50	{	{	PUNCT
ejpam-4944	642	51	e1	e1	PROPN
ejpam-4944	642	52	,	,	PUNCT
ejpam-4944	642	53	e2	e2	PROPN
ejpam-4944	642	54	,	,	PUNCT
ejpam-4944	642	55	e3	e3	NOUN
ejpam-4944	642	56	,	,	PUNCT
ejpam-4944	642	57	e4	e4	PROPN
ejpam-4944	642	58	,	,	PUNCT
ejpam-4944	642	59	e5	e5	PROPN
ejpam-4944	642	60	}	}	PUNCT
ejpam-4944	642	61	is	be	AUX
ejpam-4944	642	62	the	the	DET
ejpam-4944	642	63	set	set	NOUN
ejpam-4944	642	64	of	of	ADP
ejpam-4944	642	65	parameters	parameter	NOUN
ejpam-4944	642	66	.	.	PUNCT
ejpam-4944	643	1	define	define	VERB
ejpam-4944	643	2	a	a	DET
ejpam-4944	643	3	function	function	NOUN
ejpam-4944	643	4	f	f	NOUN
ejpam-4944	643	5	from	from	ADP
ejpam-4944	643	6	a	a	DET
ejpam-4944	643	7	set	set	NOUN
ejpam-4944	643	8	e	e	NOUN
ejpam-4944	643	9	to	to	ADP
ejpam-4944	643	10	exp(u	exp(u	PROPN
ejpam-4944	643	11	)	)	PUNCT
ejpam-4944	643	12	by	by	ADP
ejpam-4944	643	13	,	,	PUNCT
ejpam-4944	643	14	f	f	PROPN
ejpam-4944	643	15	(	(	PUNCT
ejpam-4944	643	16	e1	e1	PROPN
ejpam-4944	643	17	)	)	PUNCT
ejpam-4944	643	18	=	=	PRON
ejpam-4944	643	19	{	{	PUNCT
ejpam-4944	643	20	s};f	s};f	PROPN
ejpam-4944	643	21	(	(	PUNCT
ejpam-4944	643	22	e2	e2	PROPN
ejpam-4944	643	23	)	)	PUNCT
ejpam-4944	643	24	=	=	PRON
ejpam-4944	643	25	{	{	PUNCT
ejpam-4944	643	26	r};f	r};f	NOUN
ejpam-4944	643	27	(	(	PUNCT
ejpam-4944	643	28	e3	e3	NOUN
ejpam-4944	643	29	)	)	PUNCT
ejpam-4944	643	30	=	=	PRON
ejpam-4944	643	31	{	{	PUNCT
ejpam-4944	643	32	q};f	q};f	PROPN
ejpam-4944	643	33	(	(	PUNCT
ejpam-4944	643	34	e4	e4	PROPN
ejpam-4944	643	35	)	)	PUNCT
ejpam-4944	643	36	=	=	PRON
ejpam-4944	643	37	{	{	PUNCT
ejpam-4944	643	38	r	r	NOUN
ejpam-4944	643	39	,	,	PUNCT
ejpam-4944	643	40	s};f	s};f	PROPN
ejpam-4944	643	41	(	(	PUNCT
ejpam-4944	643	42	e5	e5	PROPN
ejpam-4944	643	43	)	)	PUNCT
ejpam-4944	644	1	=	=	PRON
ejpam-4944	644	2	{	{	PUNCT
ejpam-4944	644	3	p	p	X
ejpam-4944	644	4	,	,	PUNCT
ejpam-4944	644	5	r	r	NOUN
ejpam-4944	644	6	}	}	PUNCT
ejpam-4944	644	7	.	.	PUNCT
ejpam-4944	645	1	then	then	ADV
ejpam-4944	645	2	the	the	DET
ejpam-4944	645	3	pair	pair	NOUN
ejpam-4944	645	4	(	(	PUNCT
ejpam-4944	645	5	f	f	X
ejpam-4944	645	6	,	,	PUNCT
ejpam-4944	645	7	e	e	NOUN
ejpam-4944	645	8	)	)	PUNCT
ejpam-4944	645	9	is	be	AUX
ejpam-4944	645	10	a	a	DET
ejpam-4944	645	11	soft	soft	ADJ
ejpam-4944	645	12	set	set	NOUN
ejpam-4944	645	13	over	over	ADP
ejpam-4944	645	14	u.	u.	NOUN
ejpam-4944	645	15	example	example	NOUN
ejpam-4944	645	16	40	40	NUM
ejpam-4944	645	17	.	.	PUNCT
ejpam-4944	646	1	consider	consider	VERB
ejpam-4944	646	2	the	the	DET
ejpam-4944	646	3	bgts	bgts	NOUN
ejpam-4944	646	4	(	(	PUNCT
ejpam-4944	646	5	x,µ1	x,µ1	PROPN
ejpam-4944	646	6	,	,	PUNCT
ejpam-4944	646	7	µ2	µ2	PROPN
ejpam-4944	646	8	)	)	PUNCT
ejpam-4944	646	9	where	where	SCONJ
ejpam-4944	646	10	x	x	X
ejpam-4944	646	11	=	=	PRON
ejpam-4944	646	12	{	{	PUNCT
ejpam-4944	646	13	p	p	X
ejpam-4944	646	14	,	,	PUNCT
ejpam-4944	646	15	q	q	ADJ
ejpam-4944	646	16	,	,	PUNCT
ejpam-4944	646	17	r	r	NOUN
ejpam-4944	646	18	,	,	PUNCT
ejpam-4944	646	19	s	s	PART
ejpam-4944	646	20	}	}	PUNCT
ejpam-4944	646	21	;	;	PUNCT
ejpam-4944	646	22	µ1	µ1	PROPN
ejpam-4944	646	23	=	=	SYM
ejpam-4944	646	24	{	{	PUNCT
ejpam-4944	646	25	∅	∅	NOUN
ejpam-4944	646	26	,	,	PUNCT
ejpam-4944	646	27	{	{	PUNCT
ejpam-4944	646	28	r	r	NOUN
ejpam-4944	646	29	}	}	PUNCT
ejpam-4944	646	30	,	,	PUNCT
ejpam-4944	646	31	{	{	PUNCT
ejpam-4944	646	32	p	p	X
ejpam-4944	646	33	,	,	PUNCT
ejpam-4944	646	34	s	s	PART
ejpam-4944	646	35	}	}	PUNCT
ejpam-4944	646	36	,	,	PUNCT
ejpam-4944	646	37	{	{	PUNCT
ejpam-4944	646	38	r	r	NOUN
ejpam-4944	646	39	,	,	PUNCT
ejpam-4944	646	40	s	s	PART
ejpam-4944	646	41	}	}	PUNCT
ejpam-4944	646	42	,	,	PUNCT
ejpam-4944	646	43	{	{	PUNCT
ejpam-4944	646	44	p	p	X
ejpam-4944	646	45	,	,	PUNCT
ejpam-4944	646	46	r	r	NOUN
ejpam-4944	646	47	,	,	PUNCT
ejpam-4944	646	48	s	s	PART
ejpam-4944	646	49	}	}	PUNCT
ejpam-4944	646	50	}	}	PUNCT
ejpam-4944	646	51	and	and	CCONJ
ejpam-4944	646	52	µ2	µ2	PROPN
ejpam-4944	646	53	=	=	PUNCT
ejpam-4944	646	54	{	{	PUNCT
ejpam-4944	646	55	∅	∅	NOUN
ejpam-4944	646	56	,	,	PUNCT
ejpam-4944	646	57	{	{	PUNCT
ejpam-4944	646	58	q	q	X
ejpam-4944	646	59	}	}	PUNCT
ejpam-4944	646	60	,	,	PUNCT
ejpam-4944	646	61	{	{	PUNCT
ejpam-4944	646	62	q	q	X
ejpam-4944	646	63	,	,	PUNCT
ejpam-4944	646	64	s	s	PART
ejpam-4944	646	65	}	}	PUNCT
ejpam-4944	646	66	,	,	PUNCT
ejpam-4944	646	67	{	{	PUNCT
ejpam-4944	646	68	r	r	NOUN
ejpam-4944	646	69	,	,	PUNCT
ejpam-4944	646	70	s	s	PART
ejpam-4944	646	71	}	}	PUNCT
ejpam-4944	646	72	,	,	PUNCT
ejpam-4944	646	73	{	{	PUNCT
ejpam-4944	646	74	q	q	X
ejpam-4944	646	75	,	,	PUNCT
ejpam-4944	646	76	r	r	NOUN
ejpam-4944	646	77	,	,	PUNCT
ejpam-4944	646	78	s	s	PART
ejpam-4944	646	79	}	}	PUNCT
ejpam-4944	646	80	}	}	PUNCT
ejpam-4944	646	81	.	.	PUNCT
ejpam-4944	647	1	here	here	ADV
ejpam-4944	647	2	,	,	PUNCT
ejpam-4944	647	3	•	•	X
ejpam-4944	647	4	(	(	PUNCT
ejpam-4944	647	5	s	s	NOUN
ejpam-4944	647	6	,	,	PUNCT
ejpam-4944	647	7	v)-µ1	v)-µ1	NOUN
ejpam-4944	647	8	-	-	PUNCT
ejpam-4944	647	9	regular	regular	ADJ
ejpam-4944	647	10	open	open	ADJ
ejpam-4944	647	11	sets	set	NOUN
ejpam-4944	647	12	=	=	SYM
ejpam-4944	647	13	{	{	PUNCT
ejpam-4944	647	14	∅	∅	NOUN
ejpam-4944	647	15	,	,	PUNCT
ejpam-4944	647	16	{	{	PUNCT
ejpam-4944	647	17	r	r	NOUN
ejpam-4944	647	18	}	}	PUNCT
ejpam-4944	647	19	,	,	PUNCT
ejpam-4944	647	20	{	{	PUNCT
ejpam-4944	647	21	p	p	X
ejpam-4944	647	22	,	,	PUNCT
ejpam-4944	647	23	r	r	NOUN
ejpam-4944	647	24	,	,	PUNCT
ejpam-4944	647	25	s	s	PART
ejpam-4944	647	26	}	}	PUNCT
ejpam-4944	647	27	}	}	PUNCT
ejpam-4944	647	28	.	.	PUNCT
ejpam-4944	648	1	•	•	X
ejpam-4944	648	2	(	(	PUNCT
ejpam-4944	648	3	s	s	NOUN
ejpam-4944	648	4	,	,	PUNCT
ejpam-4944	648	5	v)-µ1	v)-µ1	NOUN
ejpam-4944	648	6	-	-	PUNCT
ejpam-4944	648	7	semi	semi	ADJ
ejpam-4944	648	8	-	-	ADJ
ejpam-4944	648	9	open	open	ADJ
ejpam-4944	648	10	sets	set	NOUN
ejpam-4944	648	11	=	=	SYM
ejpam-4944	648	12	{	{	PUNCT
ejpam-4944	648	13	∅	∅	NOUN
ejpam-4944	648	14	,	,	PUNCT
ejpam-4944	648	15	{	{	PUNCT
ejpam-4944	648	16	p	p	X
ejpam-4944	648	17	}	}	PUNCT
ejpam-4944	648	18	,	,	PUNCT
ejpam-4944	648	19	{	{	PUNCT
ejpam-4944	648	20	r	r	NOUN
ejpam-4944	648	21	}	}	PUNCT
ejpam-4944	648	22	,	,	PUNCT
ejpam-4944	648	23	{	{	PUNCT
ejpam-4944	648	24	p	p	X
ejpam-4944	648	25	,	,	PUNCT
ejpam-4944	648	26	r	r	NOUN
ejpam-4944	648	27	}	}	PUNCT
ejpam-4944	648	28	,	,	PUNCT
ejpam-4944	648	29	{	{	PUNCT
ejpam-4944	648	30	p	p	X
ejpam-4944	648	31	,	,	PUNCT
ejpam-4944	648	32	s	s	PART
ejpam-4944	648	33	}	}	PUNCT
ejpam-4944	648	34	,	,	PUNCT
ejpam-4944	648	35	{	{	PUNCT
ejpam-4944	648	36	r	r	NOUN
ejpam-4944	648	37	,	,	PUNCT
ejpam-4944	648	38	s	s	PART
ejpam-4944	648	39	}	}	PUNCT
ejpam-4944	648	40	,	,	PUNCT
ejpam-4944	648	41	{	{	PUNCT
ejpam-4944	648	42	p	p	X
ejpam-4944	648	43	,	,	PUNCT
ejpam-4944	648	44	r	r	NOUN
ejpam-4944	648	45	,	,	PUNCT
ejpam-4944	648	46	s	s	PART
ejpam-4944	648	47	}	}	PUNCT
ejpam-4944	648	48	}	}	PUNCT
ejpam-4944	648	49	.	.	PUNCT
ejpam-4944	649	1	•	•	X
ejpam-4944	649	2	(	(	PUNCT
ejpam-4944	649	3	s	s	NOUN
ejpam-4944	649	4	,	,	PUNCT
ejpam-4944	649	5	v)-µ1	v)-µ1	NOUN
ejpam-4944	649	6	-	-	PUNCT
ejpam-4944	649	7	pre	pre	ADJ
ejpam-4944	649	8	-	-	ADJ
ejpam-4944	649	9	open	open	ADJ
ejpam-4944	649	10	sets	set	NOUN
ejpam-4944	649	11	=	=	SYM
ejpam-4944	649	12	{	{	PUNCT
ejpam-4944	649	13	∅	∅	NOUN
ejpam-4944	649	14	,	,	PUNCT
ejpam-4944	649	15	{	{	PUNCT
ejpam-4944	649	16	r	r	NOUN
ejpam-4944	649	17	}	}	PUNCT
ejpam-4944	649	18	,	,	PUNCT
ejpam-4944	649	19	{	{	PUNCT
ejpam-4944	649	20	s	s	X
ejpam-4944	649	21	}	}	PUNCT
ejpam-4944	649	22	,	,	PUNCT
ejpam-4944	649	23	{	{	PUNCT
ejpam-4944	649	24	p	p	X
ejpam-4944	649	25	,	,	PUNCT
ejpam-4944	649	26	s	s	PART
ejpam-4944	649	27	}	}	PUNCT
ejpam-4944	649	28	,	,	PUNCT
ejpam-4944	649	29	{	{	PUNCT
ejpam-4944	649	30	r	r	NOUN
ejpam-4944	649	31	,	,	PUNCT
ejpam-4944	649	32	s	s	PART
ejpam-4944	649	33	}	}	PUNCT
ejpam-4944	649	34	,	,	PUNCT
ejpam-4944	649	35	{	{	PUNCT
ejpam-4944	649	36	p	p	X
ejpam-4944	649	37	,	,	PUNCT
ejpam-4944	649	38	r	r	NOUN
ejpam-4944	649	39	,	,	PUNCT
ejpam-4944	649	40	s	s	PART
ejpam-4944	649	41	}	}	PUNCT
ejpam-4944	649	42	,	,	PUNCT
ejpam-4944	649	43	}	}	PUNCT
ejpam-4944	649	44	.	.	PUNCT
ejpam-4944	650	1	•	•	NUM
ejpam-4944	650	2	(	(	PUNCT
ejpam-4944	650	3	s	s	NOUN
ejpam-4944	650	4	,	,	PUNCT
ejpam-4944	650	5	v)-µ1	v)-µ1	NOUN
ejpam-4944	650	6	-	-	PUNCT
ejpam-4944	650	7	α	α	PRON
ejpam-4944	650	8	-	-	ADJ
ejpam-4944	650	9	open	open	ADJ
ejpam-4944	650	10	sets	set	NOUN
ejpam-4944	650	11	=	=	SYM
ejpam-4944	650	12	{	{	PUNCT
ejpam-4944	650	13	∅	∅	NOUN
ejpam-4944	650	14	,	,	PUNCT
ejpam-4944	650	15	{	{	PUNCT
ejpam-4944	650	16	r	r	NOUN
ejpam-4944	650	17	}	}	PUNCT
ejpam-4944	650	18	,	,	PUNCT
ejpam-4944	650	19	{	{	PUNCT
ejpam-4944	650	20	p	p	X
ejpam-4944	650	21	,	,	PUNCT
ejpam-4944	650	22	s	s	PART
ejpam-4944	650	23	}	}	PUNCT
ejpam-4944	650	24	,	,	PUNCT
ejpam-4944	650	25	{	{	PUNCT
ejpam-4944	650	26	r	r	NOUN
ejpam-4944	650	27	,	,	PUNCT
ejpam-4944	650	28	s	s	PART
ejpam-4944	650	29	}	}	PUNCT
ejpam-4944	650	30	,	,	PUNCT
ejpam-4944	650	31	{	{	PUNCT
ejpam-4944	650	32	p	p	X
ejpam-4944	650	33	,	,	PUNCT
ejpam-4944	650	34	r	r	NOUN
ejpam-4944	650	35	,	,	PUNCT
ejpam-4944	650	36	s	s	PART
ejpam-4944	650	37	}	}	PUNCT
ejpam-4944	650	38	}	}	PUNCT
ejpam-4944	650	39	.	.	PUNCT
ejpam-4944	651	1	let	let	VERB
ejpam-4944	651	2	u	u	PRON
ejpam-4944	651	3	=	=	PUNCT
ejpam-4944	651	4	{	{	PUNCT
ejpam-4944	651	5	p	p	X
ejpam-4944	651	6	,	,	PUNCT
ejpam-4944	651	7	r	r	NOUN
ejpam-4944	651	8	,	,	PUNCT
ejpam-4944	651	9	s	s	AUX
ejpam-4944	651	10	}	}	PUNCT
ejpam-4944	651	11	be	be	AUX
ejpam-4944	651	12	a	a	DET
ejpam-4944	651	13	subset	subset	NOUN
ejpam-4944	651	14	of	of	ADP
ejpam-4944	651	15	x	x	PUNCT
ejpam-4944	651	16	and	and	CCONJ
ejpam-4944	651	17	e	e	X
ejpam-4944	651	18	=	=	PUNCT
ejpam-4944	651	19	{	{	PUNCT
ejpam-4944	651	20	(	(	PUNCT
ejpam-4944	651	21	s	s	NOUN
ejpam-4944	651	22	,	,	PUNCT
ejpam-4944	651	23	v)-µ1	v)-µ1	NOUN
ejpam-4944	651	24	-	-	PUNCT
ejpam-4944	651	25	regular	regular	ADJ
ejpam-4944	651	26	open	open	NOUN
ejpam-4944	651	27	,	,	PUNCT
ejpam-4944	651	28	(	(	PUNCT
ejpam-4944	651	29	s	s	X
ejpam-4944	651	30	,	,	PUNCT
ejpam-4944	651	31	v)-µ1	v)-µ1	NOUN
ejpam-4944	651	32	-	-	PUNCT
ejpam-4944	651	33	semi	semi	ADJ
ejpam-4944	651	34	-	-	ADJ
ejpam-4944	651	35	open	open	ADJ
ejpam-4944	651	36	set	set	NOUN
ejpam-4944	651	37	,	,	PUNCT
ejpam-4944	651	38	(	(	PUNCT
ejpam-4944	651	39	s	s	X
ejpam-4944	651	40	,	,	PUNCT
ejpam-4944	651	41	v)-µ1	v)-µ1	NOUN
ejpam-4944	651	42	-	-	PUNCT
ejpam-4944	651	43	pre	pre	ADJ
ejpam-4944	651	44	-	-	ADJ
ejpam-4944	651	45	open	open	ADJ
ejpam-4944	651	46	set	set	NOUN
ejpam-4944	651	47	,	,	PUNCT
ejpam-4944	651	48	(	(	PUNCT
ejpam-4944	651	49	s	s	X
ejpam-4944	651	50	,	,	PUNCT
ejpam-4944	651	51	v)-µ1	v)-µ1	NOUN
ejpam-4944	651	52	−	−	ADP
ejpam-4944	652	1	α	α	X
ejpam-4944	652	2	-	-	ADJ
ejpam-4944	652	3	open	open	ADJ
ejpam-4944	652	4	set	set	NOUN
ejpam-4944	652	5	}	}	PUNCT
ejpam-4944	652	6	=	=	SYM
ejpam-4944	652	7	{	{	PUNCT
ejpam-4944	652	8	e1	e1	PROPN
ejpam-4944	652	9	,	,	PUNCT
ejpam-4944	652	10	e2	e2	PROPN
ejpam-4944	652	11	,	,	PUNCT
ejpam-4944	652	12	e3	e3	NOUN
ejpam-4944	652	13	,	,	PUNCT
ejpam-4944	652	14	e4	e4	PROPN
ejpam-4944	652	15	,	,	PUNCT
ejpam-4944	652	16	}	}	PUNCT
ejpam-4944	652	17	is	be	AUX
ejpam-4944	652	18	the	the	DET
ejpam-4944	652	19	set	set	NOUN
ejpam-4944	652	20	of	of	ADP
ejpam-4944	652	21	parameters	parameter	NOUN
ejpam-4944	652	22	.	.	PUNCT
ejpam-4944	653	1	define	define	VERB
ejpam-4944	653	2	a	a	DET
ejpam-4944	653	3	map	map	NOUN
ejpam-4944	653	4	f	f	NOUN
ejpam-4944	653	5	from	from	ADP
ejpam-4944	653	6	a	a	DET
ejpam-4944	653	7	non	non	ADJ
ejpam-4944	653	8	-	-	ADJ
ejpam-4944	653	9	null	null	ADJ
ejpam-4944	653	10	set	set	ADJ
ejpam-4944	653	11	e	e	NOUN
ejpam-4944	653	12	to	to	ADP
ejpam-4944	653	13	exp(u	exp(u	PROPN
ejpam-4944	653	14	)	)	PUNCT
ejpam-4944	653	15	by	by	ADP
ejpam-4944	653	16	,	,	PUNCT
ejpam-4944	653	17	f	f	PROPN
ejpam-4944	653	18	(	(	PUNCT
ejpam-4944	653	19	e1	e1	PROPN
ejpam-4944	653	20	)	)	PUNCT
ejpam-4944	653	21	=	=	PRON
ejpam-4944	653	22	{	{	PUNCT
ejpam-4944	653	23	r};f	r};f	NOUN
ejpam-4944	653	24	(	(	PUNCT
ejpam-4944	653	25	e2	e2	PROPN
ejpam-4944	653	26	)	)	PUNCT
ejpam-4944	653	27	=	=	PRON
ejpam-4944	653	28	{	{	PUNCT
ejpam-4944	653	29	p};f	p};f	NOUN
ejpam-4944	653	30	(	(	PUNCT
ejpam-4944	653	31	e3	e3	NOUN
ejpam-4944	653	32	)	)	PUNCT
ejpam-4944	654	1	=	=	PRON
ejpam-4944	654	2	{	{	PUNCT
ejpam-4944	654	3	s};f	s};f	PROPN
ejpam-4944	654	4	(	(	PUNCT
ejpam-4944	654	5	e4	e4	PROPN
ejpam-4944	654	6	)	)	PUNCT
ejpam-4944	654	7	=	=	PRON
ejpam-4944	654	8	{	{	PUNCT
ejpam-4944	654	9	r	r	NOUN
ejpam-4944	654	10	,	,	PUNCT
ejpam-4944	654	11	s	s	PART
ejpam-4944	654	12	}	}	PUNCT
ejpam-4944	654	13	.	.	PUNCT
ejpam-4944	655	1	then	then	ADV
ejpam-4944	655	2	the	the	DET
ejpam-4944	655	3	pair	pair	NOUN
ejpam-4944	655	4	(	(	PUNCT
ejpam-4944	655	5	f	f	X
ejpam-4944	655	6	,	,	PUNCT
ejpam-4944	655	7	e	e	NOUN
ejpam-4944	655	8	)	)	PUNCT
ejpam-4944	655	9	is	be	AUX
ejpam-4944	655	10	a	a	DET
ejpam-4944	655	11	soft	soft	ADJ
ejpam-4944	655	12	set	set	NOUN
ejpam-4944	655	13	over	over	ADP
ejpam-4944	655	14	u.	u.	NOUN
ejpam-4944	655	15	now	now	ADV
ejpam-4944	655	16	,	,	PUNCT
ejpam-4944	655	17	•	•	X
ejpam-4944	655	18	(	(	PUNCT
ejpam-4944	655	19	s	s	NOUN
ejpam-4944	655	20	,	,	PUNCT
ejpam-4944	655	21	v)-µ2	v)-µ2	NOUN
ejpam-4944	655	22	-	-	PUNCT
ejpam-4944	655	23	regular	regular	ADJ
ejpam-4944	655	24	open	open	ADJ
ejpam-4944	655	25	sets	set	NOUN
ejpam-4944	655	26	=	=	SYM
ejpam-4944	655	27	{	{	PUNCT
ejpam-4944	655	28	{	{	PUNCT
ejpam-4944	655	29	q	q	NOUN
ejpam-4944	655	30	}	}	PUNCT
ejpam-4944	655	31	,	,	PUNCT
ejpam-4944	655	32	{	{	PUNCT
ejpam-4944	655	33	q	q	X
ejpam-4944	655	34	,	,	PUNCT
ejpam-4944	655	35	s	s	PART
ejpam-4944	655	36	}	}	PUNCT
ejpam-4944	655	37	,	,	PUNCT
ejpam-4944	655	38	{	{	PUNCT
ejpam-4944	655	39	q	q	X
ejpam-4944	655	40	,	,	PUNCT
ejpam-4944	655	41	r	r	NOUN
ejpam-4944	655	42	,	,	PUNCT
ejpam-4944	655	43	s	s	PART
ejpam-4944	655	44	}	}	PUNCT
ejpam-4944	655	45	}	}	PUNCT
ejpam-4944	655	46	.	.	PUNCT
ejpam-4944	656	1	•	•	X
ejpam-4944	656	2	(	(	PUNCT
ejpam-4944	656	3	s	s	NOUN
ejpam-4944	656	4	,	,	PUNCT
ejpam-4944	656	5	v)-µ2	v)-µ2	NOUN
ejpam-4944	656	6	-	-	PUNCT
ejpam-4944	656	7	semi	semi	ADJ
ejpam-4944	656	8	-	-	ADJ
ejpam-4944	656	9	open	open	ADJ
ejpam-4944	656	10	sets	set	NOUN
ejpam-4944	656	11	=	=	SYM
ejpam-4944	656	12	{	{	PUNCT
ejpam-4944	656	13	∅	∅	NOUN
ejpam-4944	656	14	,	,	PUNCT
ejpam-4944	656	15	{	{	PUNCT
ejpam-4944	656	16	q	q	X
ejpam-4944	656	17	}	}	PUNCT
ejpam-4944	656	18	,	,	PUNCT
ejpam-4944	656	19	{	{	PUNCT
ejpam-4944	656	20	q	q	X
ejpam-4944	656	21	,	,	PUNCT
ejpam-4944	656	22	s	s	PART
ejpam-4944	656	23	}	}	PUNCT
ejpam-4944	656	24	,	,	PUNCT
ejpam-4944	656	25	{	{	PUNCT
ejpam-4944	656	26	r	r	NOUN
ejpam-4944	656	27	,	,	PUNCT
ejpam-4944	656	28	s	s	PART
ejpam-4944	656	29	}	}	PUNCT
ejpam-4944	656	30	,	,	PUNCT
ejpam-4944	656	31	{	{	PUNCT
ejpam-4944	656	32	p	p	X
ejpam-4944	656	33	,	,	PUNCT
ejpam-4944	656	34	q	q	X
ejpam-4944	656	35	,	,	PUNCT
ejpam-4944	656	36	s	s	PART
ejpam-4944	656	37	}	}	PUNCT
ejpam-4944	656	38	,	,	PUNCT
ejpam-4944	656	39	{	{	PUNCT
ejpam-4944	656	40	p	p	X
ejpam-4944	656	41	,	,	PUNCT
ejpam-4944	656	42	r	r	NOUN
ejpam-4944	656	43	,	,	PUNCT
ejpam-4944	656	44	s	s	PART
ejpam-4944	656	45	}	}	PUNCT
ejpam-4944	656	46	,	,	PUNCT
ejpam-4944	656	47	{	{	PUNCT
ejpam-4944	656	48	q	q	X
ejpam-4944	656	49	,	,	PUNCT
ejpam-4944	656	50	r	r	NOUN
ejpam-4944	656	51	,	,	PUNCT
ejpam-4944	656	52	s	s	PART
ejpam-4944	656	53	}	}	PUNCT
ejpam-4944	656	54	,	,	PUNCT
ejpam-4944	656	55	x	x	NOUN
ejpam-4944	656	56	}	}	PUNCT
ejpam-4944	656	57	.	.	PUNCT
ejpam-4944	657	1	•	•	NUM
ejpam-4944	657	2	(	(	PUNCT
ejpam-4944	657	3	s	s	NOUN
ejpam-4944	657	4	,	,	PUNCT
ejpam-4944	657	5	v)-µ2	v)-µ2	NOUN
ejpam-4944	657	6	-	-	PUNCT
ejpam-4944	657	7	pre	pre	ADJ
ejpam-4944	657	8	-	-	ADJ
ejpam-4944	657	9	open	open	ADJ
ejpam-4944	657	10	sets	set	NOUN
ejpam-4944	657	11	=	=	SYM
ejpam-4944	657	12	{	{	PUNCT
ejpam-4944	657	13	∅	∅	NOUN
ejpam-4944	657	14	,	,	PUNCT
ejpam-4944	657	15	{	{	PUNCT
ejpam-4944	657	16	q	q	X
ejpam-4944	657	17	}	}	PUNCT
ejpam-4944	657	18	,	,	PUNCT
ejpam-4944	657	19	{	{	PUNCT
ejpam-4944	657	20	s	s	X
ejpam-4944	657	21	}	}	PUNCT
ejpam-4944	657	22	,	,	PUNCT
ejpam-4944	657	23	{	{	PUNCT
ejpam-4944	657	24	q	q	X
ejpam-4944	657	25	,	,	PUNCT
ejpam-4944	657	26	s	s	PART
ejpam-4944	657	27	}	}	PUNCT
ejpam-4944	657	28	,	,	PUNCT
ejpam-4944	657	29	{	{	PUNCT
ejpam-4944	657	30	r	r	NOUN
ejpam-4944	657	31	,	,	PUNCT
ejpam-4944	657	32	s	s	PART
ejpam-4944	657	33	}	}	PUNCT
ejpam-4944	657	34	,	,	PUNCT
ejpam-4944	657	35	{	{	PUNCT
ejpam-4944	657	36	q	q	X
ejpam-4944	657	37	,	,	PUNCT
ejpam-4944	657	38	r	r	NOUN
ejpam-4944	657	39	,	,	PUNCT
ejpam-4944	657	40	s	s	PART
ejpam-4944	657	41	}	}	PUNCT
ejpam-4944	657	42	,	,	PUNCT
ejpam-4944	657	43	}	}	PUNCT
ejpam-4944	657	44	.	.	PUNCT
ejpam-4944	658	1	•	•	NUM
ejpam-4944	658	2	(	(	PUNCT
ejpam-4944	658	3	s	s	NOUN
ejpam-4944	658	4	,	,	PUNCT
ejpam-4944	658	5	v)-µ2	v)-µ2	NOUN
ejpam-4944	658	6	-	-	PUNCT
ejpam-4944	658	7	α	α	PRON
ejpam-4944	658	8	-	-	ADJ
ejpam-4944	658	9	open	open	ADJ
ejpam-4944	658	10	sets	set	NOUN
ejpam-4944	658	11	=	=	SYM
ejpam-4944	658	12	{	{	PUNCT
ejpam-4944	658	13	∅	∅	NOUN
ejpam-4944	658	14	,	,	PUNCT
ejpam-4944	658	15	{	{	PUNCT
ejpam-4944	658	16	q	q	X
ejpam-4944	658	17	}	}	PUNCT
ejpam-4944	658	18	,	,	PUNCT
ejpam-4944	658	19	{	{	PUNCT
ejpam-4944	658	20	q	q	X
ejpam-4944	658	21	,	,	PUNCT
ejpam-4944	658	22	s	s	PART
ejpam-4944	658	23	}	}	PUNCT
ejpam-4944	658	24	,	,	PUNCT
ejpam-4944	658	25	{	{	PUNCT
ejpam-4944	658	26	r	r	NOUN
ejpam-4944	658	27	,	,	PUNCT
ejpam-4944	658	28	s	s	PART
ejpam-4944	658	29	}	}	PUNCT
ejpam-4944	658	30	,	,	PUNCT
ejpam-4944	658	31	{	{	PUNCT
ejpam-4944	658	32	q	q	X
ejpam-4944	658	33	,	,	PUNCT
ejpam-4944	658	34	r	r	NOUN
ejpam-4944	658	35	,	,	PUNCT
ejpam-4944	658	36	s	s	PART
ejpam-4944	658	37	}	}	PUNCT
ejpam-4944	658	38	}	}	PUNCT
ejpam-4944	658	39	.	.	PUNCT
ejpam-4944	659	1	let	let	VERB
ejpam-4944	659	2	u	u	PRON
ejpam-4944	659	3	=	=	PUNCT
ejpam-4944	659	4	{	{	PUNCT
ejpam-4944	659	5	q	q	NOUN
ejpam-4944	659	6	,	,	PUNCT
ejpam-4944	659	7	r	r	NOUN
ejpam-4944	659	8	,	,	PUNCT
ejpam-4944	659	9	s	s	AUX
ejpam-4944	659	10	}	}	PUNCT
ejpam-4944	659	11	be	be	AUX
ejpam-4944	659	12	a	a	DET
ejpam-4944	659	13	subset	subset	NOUN
ejpam-4944	659	14	of	of	ADP
ejpam-4944	659	15	x	x	PUNCT
ejpam-4944	659	16	and	and	CCONJ
ejpam-4944	659	17	e	e	X
ejpam-4944	659	18	=	=	PUNCT
ejpam-4944	659	19	{	{	PUNCT
ejpam-4944	659	20	(	(	PUNCT
ejpam-4944	659	21	s	s	PROPN
ejpam-4944	659	22	,	,	PUNCT
ejpam-4944	659	23	v)-µ2	v)-µ2	NOUN
ejpam-4944	659	24	-	-	PUNCT
ejpam-4944	659	25	regular	regular	ADJ
ejpam-4944	659	26	open	open	NOUN
ejpam-4944	659	27	,	,	PUNCT
ejpam-4944	659	28	(	(	PUNCT
ejpam-4944	659	29	s	s	X
ejpam-4944	659	30	,	,	PUNCT
ejpam-4944	659	31	v)-µ2	v)-µ2	NOUN
ejpam-4944	659	32	-	-	PUNCT
ejpam-4944	659	33	semi	semi	ADV
ejpam-4944	659	34	-	-	ADJ
ejpam-4944	659	35	open	open	ADJ
ejpam-4944	659	36	set	set	NOUN
ejpam-4944	659	37	,	,	PUNCT
ejpam-4944	659	38	(	(	PUNCT
ejpam-4944	659	39	s	s	X
ejpam-4944	659	40	,	,	PUNCT
ejpam-4944	659	41	v)-µ2	v)-µ2	NOUN
ejpam-4944	659	42	-	-	PUNCT
ejpam-4944	659	43	pre	pre	ADJ
ejpam-4944	659	44	-	-	ADJ
ejpam-4944	659	45	open	open	ADJ
ejpam-4944	659	46	set	set	NOUN
ejpam-4944	659	47	,	,	PUNCT
ejpam-4944	659	48	(	(	PUNCT
ejpam-4944	659	49	s	s	X
ejpam-4944	659	50	,	,	PUNCT
ejpam-4944	659	51	v)-µ2	v)-µ2	NUM
ejpam-4944	659	52	−	−	PROPN
ejpam-4944	660	1	α	α	X
ejpam-4944	660	2	-	-	ADJ
ejpam-4944	660	3	open	open	ADJ
ejpam-4944	660	4	set	set	NOUN
ejpam-4944	660	5	}	}	PUNCT
ejpam-4944	660	6	=	=	SYM
ejpam-4944	660	7	{	{	PUNCT
ejpam-4944	660	8	e1	e1	PROPN
ejpam-4944	660	9	,	,	PUNCT
ejpam-4944	660	10	e2	e2	PROPN
ejpam-4944	660	11	,	,	PUNCT
ejpam-4944	660	12	e3	e3	NOUN
ejpam-4944	660	13	,	,	PUNCT
ejpam-4944	660	14	e4	e4	PROPN
ejpam-4944	660	15	,	,	PUNCT
ejpam-4944	660	16	}	}	PUNCT
ejpam-4944	660	17	is	be	AUX
ejpam-4944	660	18	the	the	DET
ejpam-4944	660	19	set	set	NOUN
ejpam-4944	660	20	of	of	ADP
ejpam-4944	660	21	parameters	parameter	NOUN
ejpam-4944	660	22	.	.	PUNCT
ejpam-4944	661	1	define	define	VERB
ejpam-4944	661	2	a	a	DET
ejpam-4944	661	3	map	map	NOUN
ejpam-4944	661	4	f	f	NOUN
ejpam-4944	661	5	from	from	ADP
ejpam-4944	661	6	a	a	DET
ejpam-4944	661	7	set	set	NOUN
ejpam-4944	661	8	e	e	NOUN
ejpam-4944	661	9	to	to	ADP
ejpam-4944	661	10	exp(u	exp(u	PROPN
ejpam-4944	661	11	)	)	PUNCT
ejpam-4944	661	12	by	by	ADP
ejpam-4944	661	13	,	,	PUNCT
ejpam-4944	661	14	f	f	PROPN
ejpam-4944	661	15	(	(	PUNCT
ejpam-4944	661	16	e1	e1	PROPN
ejpam-4944	661	17	)	)	PUNCT
ejpam-4944	661	18	=	=	PRON
ejpam-4944	661	19	{	{	PUNCT
ejpam-4944	661	20	q};f	q};f	PROPN
ejpam-4944	661	21	(	(	PUNCT
ejpam-4944	661	22	e2	e2	PROPN
ejpam-4944	661	23	)	)	PUNCT
ejpam-4944	661	24	=	=	PRON
ejpam-4944	661	25	{	{	PUNCT
ejpam-4944	661	26	q	q	X
ejpam-4944	661	27	,	,	PUNCT
ejpam-4944	661	28	s};f	s};f	PROPN
ejpam-4944	661	29	(	(	PUNCT
ejpam-4944	661	30	e3	e3	NOUN
ejpam-4944	661	31	)	)	PUNCT
ejpam-4944	661	32	=	=	PRON
ejpam-4944	661	33	{	{	PUNCT
ejpam-4944	661	34	s};f	s};f	PROPN
ejpam-4944	661	35	(	(	PUNCT
ejpam-4944	661	36	e4	e4	PROPN
ejpam-4944	661	37	)	)	PUNCT
ejpam-4944	661	38	=	=	PRON
ejpam-4944	661	39	{	{	PUNCT
ejpam-4944	661	40	r	r	NOUN
ejpam-4944	661	41	,	,	PUNCT
ejpam-4944	661	42	s	s	PART
ejpam-4944	661	43	}	}	PUNCT
ejpam-4944	661	44	.	.	PUNCT
ejpam-4944	662	1	then	then	ADV
ejpam-4944	662	2	the	the	DET
ejpam-4944	662	3	pair	pair	NOUN
ejpam-4944	662	4	(	(	PUNCT
ejpam-4944	662	5	f	f	X
ejpam-4944	662	6	,	,	PUNCT
ejpam-4944	662	7	e	e	NOUN
ejpam-4944	662	8	)	)	PUNCT
ejpam-4944	662	9	is	be	AUX
ejpam-4944	662	10	a	a	DET
ejpam-4944	662	11	soft	soft	ADJ
ejpam-4944	662	12	set	set	NOUN
ejpam-4944	662	13	over	over	ADP
ejpam-4944	662	14	u.	u.	NOUN
ejpam-4944	662	15	references	reference	NOUN
ejpam-4944	662	16	2304	2304	NUM
ejpam-4944	662	17	6	6	NUM
ejpam-4944	662	18	.	.	PUNCT
ejpam-4944	662	19	conclusion	conclusion	NOUN
ejpam-4944	662	20	in	in	ADP
ejpam-4944	662	21	this	this	DET
ejpam-4944	662	22	article	article	NOUN
ejpam-4944	662	23	,	,	PUNCT
ejpam-4944	662	24	we	we	PRON
ejpam-4944	662	25	are	be	AUX
ejpam-4944	662	26	given	give	VERB
ejpam-4944	662	27	additional	additional	ADJ
ejpam-4944	662	28	tricks	trick	NOUN
ejpam-4944	662	29	for	for	ADP
ejpam-4944	662	30	finding	find	VERB
ejpam-4944	662	31	the	the	DET
ejpam-4944	662	32	significance	significance	NOUN
ejpam-4944	662	33	of	of	ADP
ejpam-4944	662	34	a	a	DET
ejpam-4944	662	35	given	give	VERB
ejpam-4944	662	36	set	set	NOUN
ejpam-4944	662	37	in	in	ADP
ejpam-4944	662	38	a	a	DET
ejpam-4944	662	39	bigeneralized	bigeneralize	VERB
ejpam-4944	662	40	topological	topological	ADJ
ejpam-4944	662	41	space	space	NOUN
ejpam-4944	662	42	.	.	PUNCT
ejpam-4944	663	1	also	also	ADV
ejpam-4944	663	2	,	,	PUNCT
ejpam-4944	663	3	we	we	PRON
ejpam-4944	663	4	have	have	AUX
ejpam-4944	663	5	proven	prove	VERB
ejpam-4944	663	6	some	some	DET
ejpam-4944	663	7	results	result	NOUN
ejpam-4944	663	8	for	for	ADP
ejpam-4944	663	9	checking	check	VERB
ejpam-4944	663	10	whether	whether	SCONJ
ejpam-4944	663	11	the	the	DET
ejpam-4944	663	12	given	give	VERB
ejpam-4944	663	13	set	set	NOUN
ejpam-4944	663	14	is	be	AUX
ejpam-4944	663	15	(	(	PUNCT
ejpam-4944	663	16	s	s	X
ejpam-4944	663	17	,	,	PUNCT
ejpam-4944	663	18	v)⋆-dense	v)⋆-dense	NOUN
ejpam-4944	663	19	or	or	CCONJ
ejpam-4944	663	20	not	not	PART
ejpam-4944	663	21	.	.	PUNCT
ejpam-4944	664	1	finally	finally	ADV
ejpam-4944	664	2	,	,	PUNCT
ejpam-4944	664	3	we	we	PRON
ejpam-4944	664	4	defined	define	VERB
ejpam-4944	664	5	soft	soft	ADJ
ejpam-4944	664	6	sets	set	NOUN
ejpam-4944	664	7	using	use	VERB
ejpam-4944	664	8	various	various	ADJ
ejpam-4944	664	9	open	open	ADJ
ejpam-4944	664	10	sets	set	NOUN
ejpam-4944	664	11	and	and	CCONJ
ejpam-4944	664	12	(	(	PUNCT
ejpam-4944	664	13	s	s	X
ejpam-4944	664	14	,	,	PUNCT
ejpam-4944	664	15	v)⋆-dense	v)⋆-dense	PROPN
ejpam-4944	664	16	sets	set	NOUN
ejpam-4944	664	17	.	.	PUNCT
ejpam-4944	665	1	references	reference	NOUN
ejpam-4944	665	2	[	[	X
ejpam-4944	665	3	1	1	NUM
ejpam-4944	665	4	]	]	PUNCT
ejpam-4944	665	5	d.	d.	PROPN
ejpam-4944	665	6	andrijević.	andrijević.	PROPN
ejpam-4944	665	7	on	on	ADP
ejpam-4944	665	8	b	b	X
ejpam-4944	665	9	-	-	PUNCT
ejpam-4944	665	10	open	open	ADJ
ejpam-4944	665	11	sets	set	NOUN
ejpam-4944	665	12	.	.	PUNCT
ejpam-4944	666	1	mat	mat	X
ejpam-4944	666	2	.	.	PROPN
ejpam-4944	666	3	vesnik	vesnik	PROPN
ejpam-4944	666	4	,	,	PUNCT
ejpam-4944	666	5	48:59–64	48:59–64	PROPN
ejpam-4944	666	6	,	,	PUNCT
ejpam-4944	666	7	1996	1996	NUM
ejpam-4944	666	8	.	.	PUNCT
ejpam-4944	667	1	[	[	X
ejpam-4944	667	2	2	2	NUM
ejpam-4944	667	3	]	]	PUNCT
ejpam-4944	667	4	chawalit	chawalit	VERB
ejpam-4944	667	5	boonpok	boonpok	NOUN
ejpam-4944	667	6	.	.	PUNCT
ejpam-4944	668	1	weakly	weakly	ADJ
ejpam-4944	668	2	open	open	ADJ
ejpam-4944	668	3	functions	function	NOUN
ejpam-4944	668	4	on	on	ADP
ejpam-4944	668	5	bigeneralized	bigeneralize	VERB
ejpam-4944	668	6	topological	topological	ADJ
ejpam-4944	668	7	spaces	space	NOUN
ejpam-4944	668	8	.	.	PUNCT
ejpam-4944	669	1	int	int	NOUN
ejpam-4944	669	2	.	.	PUNCT
ejpam-4944	670	1	journal	journal	PROPN
ejpam-4944	670	2	of	of	ADP
ejpam-4944	670	3	math	math	NOUN
ejpam-4944	670	4	.	.	PUNCT
ejpam-4944	671	1	analysis	analysis	NOUN
ejpam-4944	671	2	,	,	PUNCT
ejpam-4944	671	3	4(18):891–897	4(18):891–897	NUM
ejpam-4944	671	4	,	,	PUNCT
ejpam-4944	671	5	2010	2010	NUM
ejpam-4944	671	6	.	.	PUNCT
ejpam-4944	672	1	[	[	X
ejpam-4944	672	2	3	3	X
ejpam-4944	672	3	]	]	X
ejpam-4944	672	4	akos	akos	NOUN
ejpam-4944	672	5	császár	császár	PROPN
ejpam-4944	672	6	.	.	PUNCT
ejpam-4944	673	1	generalized	generalize	VERB
ejpam-4944	673	2	open	open	ADJ
ejpam-4944	673	3	sets	set	NOUN
ejpam-4944	673	4	.	.	PUNCT
ejpam-4944	674	1	acta	acta	PROPN
ejpam-4944	674	2	mathematica	mathematica	PROPN
ejpam-4944	674	3	hungarica	hungarica	PROPN
ejpam-4944	674	4	,	,	PUNCT
ejpam-4944	674	5	75	75	NUM
ejpam-4944	674	6	,	,	PUNCT
ejpam-4944	674	7	1997	1997	NUM
ejpam-4944	674	8	.	.	PUNCT
ejpam-4944	675	1	[	[	X
ejpam-4944	675	2	4	4	X
ejpam-4944	675	3	]	]	X
ejpam-4944	675	4	akos	akos	NOUN
ejpam-4944	675	5	császár	császár	PROPN
ejpam-4944	675	6	.	.	PUNCT
ejpam-4944	676	1	generalized	generalized	ADJ
ejpam-4944	676	2	topology	topology	NOUN
ejpam-4944	676	3	,	,	PUNCT
ejpam-4944	676	4	generalized	generalize	VERB
ejpam-4944	676	5	continuity	continuity	NOUN
ejpam-4944	676	6	.	.	PUNCT
ejpam-4944	677	1	acta	acta	PROPN
ejpam-4944	677	2	math	math	PROPN
ejpam-4944	677	3	.	.	PUNCT
ejpam-4944	678	1	hungar	hungar	PROPN
ejpam-4944	678	2	.	.	PUNCT
ejpam-4944	678	3	,	,	PUNCT
ejpam-4944	679	1	96:351–357	96:351–357	PROPN
ejpam-4944	679	2	,	,	PUNCT
ejpam-4944	679	3	2002	2002	NUM
ejpam-4944	679	4	.	.	PUNCT
ejpam-4944	680	1	[	[	X
ejpam-4944	680	2	5	5	X
ejpam-4944	680	3	]	]	PUNCT
ejpam-4944	680	4	akos	akos	NOUN
ejpam-4944	680	5	császár	császár	PROPN
ejpam-4944	680	6	.	.	PUNCT
ejpam-4944	681	1	extremally	extremally	ADV
ejpam-4944	681	2	disconnected	disconnect	VERB
ejpam-4944	681	3	generalized	generalized	ADJ
ejpam-4944	681	4	topologies	topology	NOUN
ejpam-4944	681	5	.	.	PUNCT
ejpam-4944	682	1	annales	annales	PROPN
ejpam-4944	682	2	univ	univ	PROPN
ejpam-4944	682	3	.	.	PUNCT
ejpam-4944	683	1	sci	sci	PROPN
ejpam-4944	683	2	.	.	PUNCT
ejpam-4944	683	3	budapest	budapest	PROPN
ejpam-4944	683	4	.	.	PUNCT
ejpam-4944	683	5	,	,	PUNCT
ejpam-4944	683	6	47:151–161	47:151–161	VERB
ejpam-4944	683	7	,	,	PUNCT
ejpam-4944	683	8	2004	2004	NUM
ejpam-4944	683	9	.	.	PUNCT
ejpam-4944	684	1	[	[	X
ejpam-4944	684	2	6	6	NUM
ejpam-4944	684	3	]	]	PUNCT
ejpam-4944	684	4	akos	akos	NOUN
ejpam-4944	684	5	császár	császár	PROPN
ejpam-4944	684	6	.	.	PUNCT
ejpam-4944	685	1	generalized	generalize	VERB
ejpam-4944	685	2	open	open	ADJ
ejpam-4944	685	3	sets	set	NOUN
ejpam-4944	685	4	in	in	ADP
ejpam-4944	685	5	generalized	generalized	ADJ
ejpam-4944	685	6	topologies	topology	NOUN
ejpam-4944	685	7	.	.	PUNCT
ejpam-4944	686	1	acta	acta	PROPN
ejpam-4944	686	2	mathematica	mathematica	PROPN
ejpam-4944	686	3	hungarica	hungarica	PROPN
ejpam-4944	686	4	,	,	PUNCT
ejpam-4944	686	5	106	106	NUM
ejpam-4944	686	6	,	,	PUNCT
ejpam-4944	686	7	2005	2005	NUM
ejpam-4944	686	8	.	.	PUNCT
ejpam-4944	687	1	[	[	X
ejpam-4944	687	2	7	7	X
ejpam-4944	687	3	]	]	X
ejpam-4944	687	4	e.	e.	PROPN
ejpam-4944	687	5	ekici	ekici	PROPN
ejpam-4944	687	6	.	.	PUNCT
ejpam-4944	688	1	generalized	generalize	VERB
ejpam-4944	688	2	submaximal	submaximal	ADJ
ejpam-4944	688	3	spaces	space	NOUN
ejpam-4944	688	4	.	.	PUNCT
ejpam-4944	689	1	acta	acta	PROPN
ejpam-4944	689	2	math	math	PROPN
ejpam-4944	689	3	.	.	PUNCT
ejpam-4944	690	1	hungar	hungar	PROPN
ejpam-4944	690	2	.	.	PUNCT
ejpam-4944	691	1	,	,	PUNCT
ejpam-4944	691	2	134:132	134:132	PROPN
ejpam-4944	691	3	–	–	PUNCT
ejpam-4944	691	4	138	138	NUM
ejpam-4944	691	5	,	,	PUNCT
ejpam-4944	691	6	2012	2012	NUM
ejpam-4944	691	7	.	.	PUNCT
ejpam-4944	692	1	[	[	X
ejpam-4944	692	2	8	8	NUM
ejpam-4944	692	3	]	]	PUNCT
ejpam-4944	692	4	erdal	erdal	PROPN
ejpam-4944	692	5	ekici	ekici	PROPN
ejpam-4944	692	6	.	.	PUNCT
ejpam-4944	693	1	generalized	generalized	ADJ
ejpam-4944	693	2	hyperconnectedness	hyperconnectedness	NOUN
ejpam-4944	693	3	.	.	PUNCT
ejpam-4944	694	1	acta	acta	PROPN
ejpam-4944	694	2	mathematica	mathematica	PROPN
ejpam-4944	694	3	hungarica	hungarica	PROPN
ejpam-4944	694	4	,	,	PUNCT
ejpam-4944	694	5	133	133	NUM
ejpam-4944	694	6	,	,	PUNCT
ejpam-4944	694	7	2011	2011	NUM
ejpam-4944	694	8	.	.	PUNCT
ejpam-4944	695	1	[	[	X
ejpam-4944	695	2	9	9	NUM
ejpam-4944	695	3	]	]	X
ejpam-4944	695	4	yasser	yasser	PROPN
ejpam-4944	695	5	farhat	farhat	PROPN
ejpam-4944	695	6	and	and	CCONJ
ejpam-4944	695	7	vadakasi	vadakasi	PROPN
ejpam-4944	695	8	subramanian	subramanian	PROPN
ejpam-4944	695	9	.	.	PUNCT
ejpam-4944	696	1	generalized	generalize	VERB
ejpam-4944	696	2	dense	dense	ADJ
ejpam-4944	696	3	sets	set	NOUN
ejpam-4944	696	4	in	in	ADP
ejpam-4944	696	5	bigeneralized	bigeneralize	VERB
ejpam-4944	696	6	topological	topological	ADJ
ejpam-4944	696	7	spaces	space	NOUN
ejpam-4944	696	8	.	.	PUNCT
ejpam-4944	697	1	european	european	ADJ
ejpam-4944	697	2	journal	journal	PROPN
ejpam-4944	697	3	of	of	ADP
ejpam-4944	697	4	pure	pure	ADJ
ejpam-4944	697	5	and	and	CCONJ
ejpam-4944	697	6	applied	applied	ADJ
ejpam-4944	697	7	mathematics	mathematic	NOUN
ejpam-4944	697	8	,	,	PUNCT
ejpam-4944	697	9	16(4):2049	16(4):2049	NUM
ejpam-4944	697	10	–	–	PUNCT
ejpam-4944	697	11	2065	2065	NUM
ejpam-4944	697	12	,	,	PUNCT
ejpam-4944	697	13	2023	2023	NUM
ejpam-4944	697	14	.	.	PUNCT
ejpam-4944	698	1	[	[	X
ejpam-4944	698	2	10	10	NUM
ejpam-4944	698	3	]	]	X
ejpam-4944	698	4	j.c	j.c	PROPN
ejpam-4944	698	5	.	.	PROPN
ejpam-4944	698	6	kelly	kelly	PROPN
ejpam-4944	698	7	.	.	PUNCT
ejpam-4944	699	1	bitopological	bitopological	ADJ
ejpam-4944	699	2	spaces	space	NOUN
ejpam-4944	699	3	.	.	PUNCT
ejpam-4944	700	1	pro	pro	ADJ
ejpam-4944	700	2	.	.	PUNCT
ejpam-4944	700	3	london	london	PROPN
ejpam-4944	700	4	math	math	PROPN
ejpam-4944	700	5	.	.	PUNCT
ejpam-4944	701	1	soc	soc	PROPN
ejpam-4944	701	2	.	.	PUNCT
ejpam-4944	701	3	,	,	PUNCT
ejpam-4944	701	4	3(13):71	3(13):71	NUM
ejpam-4944	701	5	–	–	PUNCT
ejpam-4944	701	6	79	79	NUM
ejpam-4944	701	7	,	,	PUNCT
ejpam-4944	701	8	1969	1969	NUM
ejpam-4944	701	9	.	.	PUNCT
ejpam-4944	702	1	[	[	X
ejpam-4944	702	2	11	11	NUM
ejpam-4944	702	3	]	]	X
ejpam-4944	702	4	ewa	ewa	PROPN
ejpam-4944	702	5	korczak	korczak	PROPN
ejpam-4944	702	6	-	-	PUNCT
ejpam-4944	702	7	kubiak	kubiak	PROPN
ejpam-4944	702	8	,	,	PUNCT
ejpam-4944	702	9	anna	anna	PROPN
ejpam-4944	702	10	loranty	loranty	PROPN
ejpam-4944	702	11	,	,	PUNCT
ejpam-4944	702	12	and	and	CCONJ
ejpam-4944	702	13	ryszard	ryszard	PROPN
ejpam-4944	702	14	j	j	PROPN
ejpam-4944	702	15	pawlak	pawlak	PROPN
ejpam-4944	702	16	.	.	PUNCT
ejpam-4944	703	1	baire	baire	NOUN
ejpam-4944	703	2	generalized	generalize	VERB
ejpam-4944	703	3	topological	topological	ADJ
ejpam-4944	703	4	spaces	space	NOUN
ejpam-4944	703	5	,	,	PUNCT
ejpam-4944	703	6	generalized	generalize	VERB
ejpam-4944	703	7	metric	metric	ADJ
ejpam-4944	703	8	spaces	space	NOUN
ejpam-4944	703	9	and	and	CCONJ
ejpam-4944	703	10	infinite	infinite	ADJ
ejpam-4944	703	11	games	game	NOUN
ejpam-4944	703	12	.	.	PUNCT
ejpam-4944	704	1	acta	acta	PROPN
ejpam-4944	704	2	mathematica	mathematica	PROPN
ejpam-4944	704	3	hungarica	hungarica	PROPN
ejpam-4944	704	4	,	,	PUNCT
ejpam-4944	704	5	140(3):203–231	140(3):203–231	NUM
ejpam-4944	704	6	,	,	PUNCT
ejpam-4944	704	7	2013	2013	NUM
ejpam-4944	704	8	.	.	PUNCT
ejpam-4944	705	1	[	[	X
ejpam-4944	705	2	12	12	NUM
ejpam-4944	705	3	]	]	PUNCT
ejpam-4944	705	4	zhaowen	zhaowen	PROPN
ejpam-4944	705	5	li	li	PROPN
ejpam-4944	705	6	and	and	CCONJ
ejpam-4944	705	7	funing	fune	VERB
ejpam-4944	705	8	lin	lin	PROPN
ejpam-4944	705	9	.	.	PUNCT
ejpam-4944	706	1	baireness	baireness	PROPN
ejpam-4944	706	2	on	on	ADP
ejpam-4944	706	3	generalized	generalized	ADJ
ejpam-4944	706	4	topological	topological	ADJ
ejpam-4944	706	5	spaces	space	NOUN
ejpam-4944	706	6	.	.	PUNCT
ejpam-4944	707	1	acta	acta	PROPN
ejpam-4944	707	2	mathematica	mathematica	PROPN
ejpam-4944	707	3	hungarica	hungarica	PROPN
ejpam-4944	707	4	,	,	PUNCT
ejpam-4944	707	5	139(4	139(4	NUM
ejpam-4944	707	6	)	)	PUNCT
ejpam-4944	707	7	,	,	PUNCT
ejpam-4944	707	8	2013	2013	NUM
ejpam-4944	707	9	.	.	PUNCT
ejpam-4944	708	1	[	[	X
ejpam-4944	708	2	13	13	NUM
ejpam-4944	708	3	]	]	PUNCT
ejpam-4944	708	4	w.	w.	PROPN
ejpam-4944	708	5	k.	k.	PROPN
ejpam-4944	708	6	min	min	PROPN
ejpam-4944	708	7	.	.	PROPN
ejpam-4944	708	8	almost	almost	ADV
ejpam-4944	708	9	continuity	continuity	NOUN
ejpam-4944	708	10	on	on	ADP
ejpam-4944	708	11	generalized	generalized	ADJ
ejpam-4944	708	12	topological	topological	ADJ
ejpam-4944	708	13	spaces	space	NOUN
ejpam-4944	708	14	.	.	PUNCT
ejpam-4944	709	1	acta	acta	PROPN
ejpam-4944	709	2	math	math	PROPN
ejpam-4944	709	3	.	.	PUNCT
ejpam-4944	710	1	hungar	hungar	PROPN
ejpam-4944	710	2	.	.	PUNCT
ejpam-4944	710	3	,	,	PUNCT
ejpam-4944	710	4	125:121	125:121	INTJ
ejpam-4944	710	5	–	–	PUNCT
ejpam-4944	710	6	125	125	NUM
ejpam-4944	710	7	,	,	PUNCT
ejpam-4944	710	8	2009	2009	NUM
ejpam-4944	710	9	.	.	PUNCT
ejpam-4944	711	1	[	[	X
ejpam-4944	711	2	14	14	NUM
ejpam-4944	711	3	]	]	X
ejpam-4944	711	4	d.	d.	PROPN
ejpam-4944	711	5	molodtsov	molodtsov	PROPN
ejpam-4944	711	6	.	.	PUNCT
ejpam-4944	712	1	soft	soft	ADJ
ejpam-4944	712	2	set	set	NOUN
ejpam-4944	712	3	theory	theory	NOUN
ejpam-4944	712	4	-	-	PUNCT
ejpam-4944	712	5	first	first	ADJ
ejpam-4944	712	6	results	result	NOUN
ejpam-4944	712	7	.	.	PUNCT
ejpam-4944	713	1	comput	comput	NOUN
ejpam-4944	713	2	.	.	PUNCT
ejpam-4944	714	1	math	math	NOUN
ejpam-4944	714	2	.	.	PUNCT
ejpam-4944	715	1	appl	appl	PROPN
ejpam-4944	715	2	.	.	PROPN
ejpam-4944	715	3	,	,	PUNCT
ejpam-4944	715	4	37:19	37:19	NUM
ejpam-4944	715	5	–	–	PUNCT
ejpam-4944	715	6	31	31	NUM
ejpam-4944	715	7	,	,	PUNCT
ejpam-4944	715	8	1999	1999	NUM
ejpam-4944	715	9	.	.	PUNCT
ejpam-4944	716	1	references	reference	NOUN
ejpam-4944	716	2	2305	2305	NUM
ejpam-4944	717	1	[	[	X
ejpam-4944	717	2	15	15	NUM
ejpam-4944	717	3	]	]	SYM
ejpam-4944	717	4	v	v	ADP
ejpam-4944	717	5	renukadevi	renukadevi	NOUN
ejpam-4944	717	6	and	and	CCONJ
ejpam-4944	717	7	s	s	NOUN
ejpam-4944	717	8	vadakasi	vadakasi	NOUN
ejpam-4944	717	9	.	.	PUNCT
ejpam-4944	718	1	modifications	modification	NOUN
ejpam-4944	718	2	of	of	ADP
ejpam-4944	718	3	strongly	strongly	ADV
ejpam-4944	718	4	nodec	nodec	ADJ
ejpam-4944	718	5	spaces	space	NOUN
ejpam-4944	718	6	.	.	PUNCT
ejpam-4944	719	1	communications	communication	NOUN
ejpam-4944	719	2	in	in	ADP
ejpam-4944	719	3	advanced	advanced	ADJ
ejpam-4944	719	4	mathematical	mathematical	ADJ
ejpam-4944	719	5	sciences	science	NOUN
ejpam-4944	719	6	,	,	PUNCT
ejpam-4944	719	7	2:99–112	2:99–112	NUM
ejpam-4944	719	8	,	,	PUNCT
ejpam-4944	719	9	2018	2018	NUM
ejpam-4944	719	10	.	.	PUNCT
ejpam-4944	720	1	[	[	X
ejpam-4944	720	2	16	16	X
ejpam-4944	720	3	]	]	X
ejpam-4944	720	4	v.	v.	ADP
ejpam-4944	720	5	renukadevi	renukadevi	PROPN
ejpam-4944	720	6	and	and	CCONJ
ejpam-4944	720	7	s.	s.	PROPN
ejpam-4944	720	8	vadakasi	vadakasi	PROPN
ejpam-4944	720	9	.	.	PUNCT
ejpam-4944	721	1	on	on	ADP
ejpam-4944	721	2	lower	low	ADJ
ejpam-4944	721	3	and	and	CCONJ
ejpam-4944	721	4	upper	upper	ADJ
ejpam-4944	721	5	semi	semi	ADJ
ejpam-4944	721	6	-	-	ADJ
ejpam-4944	721	7	continuous	continuous	ADJ
ejpam-4944	721	8	functions	function	NOUN
ejpam-4944	721	9	.	.	PUNCT
ejpam-4944	722	1	acta	acta	PROPN
ejpam-4944	722	2	math	math	PROPN
ejpam-4944	722	3	.	.	PUNCT
ejpam-4944	723	1	hungar	hungar	PROPN
ejpam-4944	723	2	.	.	PUNCT
ejpam-4944	723	3	,	,	PUNCT
ejpam-4944	723	4	160:1–12	160:1–12	NUM
ejpam-4944	723	5	,	,	PUNCT
ejpam-4944	723	6	2020	2020	NUM
ejpam-4944	723	7	.	.	PUNCT
ejpam-4944	724	1	[	[	X
ejpam-4944	724	2	17	17	NUM
ejpam-4944	724	3	]	]	X
ejpam-4944	724	4	preecha	preecha	NOUN
ejpam-4944	724	5	yupapin	yupapin	PROPN
ejpam-4944	724	6	vadakasi	vadakasi	PROPN
ejpam-4944	724	7	subramanian	subramanian	PROPN
ejpam-4944	724	8	,	,	PUNCT
ejpam-4944	724	9	yasser	yasser	PROPN
ejpam-4944	724	10	farhat	farhat	PROPN
ejpam-4944	724	11	.	.	PUNCT
ejpam-4944	725	1	on	on	ADP
ejpam-4944	725	2	nowhere	nowhere	PRON
ejpam-4944	725	3	dense	dense	ADJ
ejpam-4944	725	4	sets	set	NOUN
ejpam-4944	725	5	.	.	PUNCT
ejpam-4944	726	1	european	european	ADJ
ejpam-4944	726	2	journal	journal	PROPN
ejpam-4944	726	3	of	of	ADP
ejpam-4944	726	4	pure	pure	ADJ
ejpam-4944	726	5	and	and	CCONJ
ejpam-4944	726	6	applied	applied	ADJ
ejpam-4944	726	7	mathematics	mathematic	NOUN
ejpam-4944	726	8	,	,	PUNCT
ejpam-4944	726	9	15(2):403–414	15(2):403–414	NUM
ejpam-4944	726	10	,	,	PUNCT
ejpam-4944	726	11	2022	2022	NUM
ejpam-4944	726	12	.	.	PUNCT
ejpam-4944	727	1	[	[	X
ejpam-4944	727	2	18	18	NUM
ejpam-4944	727	3	]	]	X
ejpam-4944	727	4	w.k.min	w.k.min	PROPN
ejpam-4944	727	5	.	.	PUNCT
ejpam-4944	728	1	some	some	DET
ejpam-4944	728	2	results	result	NOUN
ejpam-4944	728	3	on	on	ADP
ejpam-4944	728	4	generalized	generalized	ADJ
ejpam-4944	728	5	topological	topological	ADJ
ejpam-4944	728	6	spaces	space	NOUN
ejpam-4944	728	7	,	,	PUNCT
ejpam-4944	728	8	and	and	CCONJ
ejpam-4944	728	9	generalized	generalized	ADJ
ejpam-4944	728	10	systems	system	NOUN
ejpam-4944	728	11	.	.	PUNCT
ejpam-4944	729	1	acta	acta	PROPN
ejpam-4944	729	2	math	math	PROPN
ejpam-4944	729	3	.	.	PUNCT
ejpam-4944	730	1	hungar	hungar	PROPN
ejpam-4944	730	2	.	.	PUNCT
ejpam-4944	731	1	,	,	PUNCT
ejpam-4944	731	2	pages	page	NOUN
ejpam-4944	731	3	171–181	171–181	NUM
ejpam-4944	731	4	,	,	PUNCT
ejpam-4944	731	5	2005	2005	NUM
ejpam-4944	731	6	.	.	PUNCT
ejpam-4944	732	1	[	[	X
ejpam-4944	732	2	19	19	NUM
ejpam-4944	732	3	]	]	PUNCT
ejpam-4944	732	4	m.	m.	PROPN
ejpam-4944	732	5	r.	r.	PROPN
ejpam-4944	732	6	ahmadi	ahmadi	PROPN
ejpam-4944	732	7	zand	zand	PROPN
ejpam-4944	732	8	and	and	CCONJ
ejpam-4944	732	9	r.	r.	PROPN
ejpam-4944	732	10	khayyeri	khayyeri	PROPN
ejpam-4944	732	11	.	.	PUNCT
ejpam-4944	733	1	generalized	generalize	VERB
ejpam-4944	733	2	gδ	gδ	NOUN
ejpam-4944	733	3	-	-	PUNCT
ejpam-4944	733	4	submaximal	submaximal	ADJ
ejpam-4944	733	5	spaces	space	NOUN
ejpam-4944	733	6	.	.	PUNCT
ejpam-4944	734	1	acta	acta	PROPN
ejpam-4944	734	2	math	math	PROPN
ejpam-4944	734	3	.	.	PUNCT
ejpam-4944	735	1	hungar	hungar	PROPN
ejpam-4944	735	2	.	.	PUNCT
ejpam-4944	736	1	,	,	PUNCT
ejpam-4944	736	2	pages	page	NOUN
ejpam-4944	736	3	274–285	274–285	NUM
ejpam-4944	736	4	,	,	PUNCT
ejpam-4944	736	5	2016	2016	NUM
ejpam-4944	736	6	.	.	PUNCT