id	sid	tid	token	lemma	pos
ejpam-4655	1	1	european	european	PROPN
ejpam-4655	1	2	journal	journal	PROPN
ejpam-4655	1	3	of	of	ADP
ejpam-4655	1	4	pure	pure	ADJ
ejpam-4655	1	5	and	and	CCONJ
ejpam-4655	1	6	applied	apply	VERB
ejpam-4655	1	7	mathematics	mathematic	NOUN
ejpam-4655	1	8	vol	vol	NOUN
ejpam-4655	1	9	.	.	PUNCT
ejpam-4655	2	1	16	16	NUM
ejpam-4655	2	2	,	,	PUNCT
ejpam-4655	2	3	no	no	INTJ
ejpam-4655	2	4	.	.	NOUN
ejpam-4655	2	5	1	1	NUM
ejpam-4655	2	6	,	,	PUNCT
ejpam-4655	2	7	2023	2023	NUM
ejpam-4655	2	8	,	,	PUNCT
ejpam-4655	2	9	386	386	NUM
ejpam-4655	2	10	-	-	SYM
ejpam-4655	2	11	403	403	NUM
ejpam-4655	2	12	issn	issn	PROPN
ejpam-4655	2	13	1307	1307	NUM
ejpam-4655	2	14	-	-	SYM
ejpam-4655	2	15	5543	5543	NUM
ejpam-4655	2	16	–	–	PUNCT
ejpam-4655	2	17	ejpam.com	ejpam.com	X
ejpam-4655	2	18	published	publish	VERB
ejpam-4655	2	19	by	by	ADP
ejpam-4655	2	20	new	new	PROPN
ejpam-4655	2	21	york	york	PROPN
ejpam-4655	2	22	business	business	PROPN
ejpam-4655	2	23	global	global	ADJ
ejpam-4655	2	24	submaximality	submaximality	PROPN
ejpam-4655	2	25	on	on	ADP
ejpam-4655	2	26	bigeneralized	bigeneralize	VERB
ejpam-4655	2	27	topological	topological	ADJ
ejpam-4655	2	28	spaces	space	NOUN
ejpam-4655	2	29	yasser	yasser	PROPN
ejpam-4655	2	30	farhat1	farhat1	PROPN
ejpam-4655	2	31	,	,	PUNCT
ejpam-4655	2	32	muthumari	muthumari	PROPN
ejpam-4655	2	33	krishnan2,∗	krishnan2,∗	PROPN
ejpam-4655	2	34	,	,	PUNCT
ejpam-4655	2	35	vadakasi	vadakasi	NOUN
ejpam-4655	2	36	subramanian2	subramanian2	NOUN
ejpam-4655	2	37	,	,	PUNCT
ejpam-4655	2	38	m.	m.	PROPN
ejpam-4655	2	39	r.	r.	PROPN
ejpam-4655	2	40	ahmadi	ahmadi	PROPN
ejpam-4655	2	41	zand3	zand3	PROPN
ejpam-4655	2	42	1	1	NUM
ejpam-4655	2	43	academic	academic	ADJ
ejpam-4655	2	44	support	support	NOUN
ejpam-4655	2	45	department	department	NOUN
ejpam-4655	2	46	,	,	PUNCT
ejpam-4655	3	1	abu	abu	PROPN
ejpam-4655	3	2	dhabi	dhabi	PROPN
ejpam-4655	3	3	polytechnic	polytechnic	PROPN
ejpam-4655	3	4	,	,	PUNCT
ejpam-4655	3	5	p.	p.	PROPN
ejpam-4655	3	6	o.	o.	PROPN
ejpam-4655	3	7	box	box	PROPN
ejpam-4655	3	8	111499	111499	NUM
ejpam-4655	3	9	,	,	PUNCT
ejpam-4655	3	10	abu	abu	PROPN
ejpam-4655	3	11	dhabi	dhabi	PROPN
ejpam-4655	3	12	,	,	PUNCT
ejpam-4655	3	13	uae	uae	PROPN
ejpam-4655	3	14	2	2	NUM
ejpam-4655	3	15	department	department	NOUN
ejpam-4655	3	16	of	of	ADP
ejpam-4655	3	17	mathematics	mathematic	NOUN
ejpam-4655	3	18	,	,	PUNCT
ejpam-4655	3	19	a.k.d.dharma	a.k.d.dharma	PROPN
ejpam-4655	3	20	raja	raja	PROPN
ejpam-4655	3	21	women	woman	NOUN
ejpam-4655	3	22	’s	’s	PART
ejpam-4655	3	23	college	college	NOUN
ejpam-4655	3	24	,	,	PUNCT
ejpam-4655	3	25	rajapalayam	rajapalayam	PROPN
ejpam-4655	3	26	3	3	NUM
ejpam-4655	3	27	department	department	NOUN
ejpam-4655	3	28	of	of	ADP
ejpam-4655	3	29	mathematics	mathematics	PROPN
ejpam-4655	3	30	,	,	PUNCT
ejpam-4655	3	31	yazd	yazd	PROPN
ejpam-4655	3	32	university	university	PROPN
ejpam-4655	3	33	,	,	PUNCT
ejpam-4655	3	34	yazd	yazd	PROPN
ejpam-4655	3	35	,	,	PUNCT
ejpam-4655	3	36	iran	iran	PROPN
ejpam-4655	3	37	abstract	abstract	NOUN
ejpam-4655	3	38	.	.	PUNCT
ejpam-4655	4	1	in	in	ADP
ejpam-4655	4	2	this	this	DET
ejpam-4655	4	3	article	article	NOUN
ejpam-4655	4	4	,	,	PUNCT
ejpam-4655	4	5	in	in	ADP
ejpam-4655	4	6	a	a	DET
ejpam-4655	4	7	bigeneralized	bigeneralize	VERB
ejpam-4655	4	8	topological	topological	ADJ
ejpam-4655	4	9	space	space	NOUN
ejpam-4655	4	10	,	,	PUNCT
ejpam-4655	4	11	we	we	PRON
ejpam-4655	4	12	introduce	introduce	VERB
ejpam-4655	4	13	a	a	DET
ejpam-4655	4	14	new	new	ADJ
ejpam-4655	4	15	space	space	NOUN
ejpam-4655	4	16	namely	namely	ADV
ejpam-4655	4	17	,	,	PUNCT
ejpam-4655	4	18	(	(	PUNCT
ejpam-4655	4	19	s	s	X
ejpam-4655	4	20	,	,	PUNCT
ejpam-4655	4	21	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	4	22	submaximal	submaximal	ADJ
ejpam-4655	4	23	space	space	NOUN
ejpam-4655	4	24	,	,	PUNCT
ejpam-4655	4	25	and	and	CCONJ
ejpam-4655	4	26	analyze	analyze	VERB
ejpam-4655	4	27	its	its	PRON
ejpam-4655	4	28	nature	nature	NOUN
ejpam-4655	4	29	.	.	PUNCT
ejpam-4655	5	1	also	also	ADV
ejpam-4655	5	2	,	,	PUNCT
ejpam-4655	5	3	the	the	DET
ejpam-4655	5	4	characterization	characterization	NOUN
ejpam-4655	5	5	theorem	theorem	VERB
ejpam-4655	5	6	for	for	ADP
ejpam-4655	5	7	a	a	DET
ejpam-4655	5	8	(	(	PUNCT
ejpam-4655	5	9	s	s	PROPN
ejpam-4655	5	10	,	,	PUNCT
ejpam-4655	5	11	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	5	12	submaximal	submaximal	ADJ
ejpam-4655	5	13	space	space	NOUN
ejpam-4655	5	14	,	,	PUNCT
ejpam-4655	5	15	image	image	NOUN
ejpam-4655	5	16	and	and	CCONJ
ejpam-4655	5	17	preimage	preimage	NOUN
ejpam-4655	5	18	of	of	ADP
ejpam-4655	5	19	(	(	PUNCT
ejpam-4655	5	20	s	s	PROPN
ejpam-4655	5	21	,	,	PUNCT
ejpam-4655	5	22	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	5	23	submaximal	submaximal	ADJ
ejpam-4655	5	24	is	be	AUX
ejpam-4655	5	25	a	a	DET
ejpam-4655	5	26	(	(	PUNCT
ejpam-4655	5	27	s	s	PROPN
ejpam-4655	5	28	,	,	PUNCT
ejpam-4655	5	29	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	5	30	submaximal	submaximal	ADJ
ejpam-4655	5	31	space	space	NOUN
ejpam-4655	5	32	under	under	ADP
ejpam-4655	5	33	(	(	PUNCT
ejpam-4655	5	34	µ	µ	NOUN
ejpam-4655	5	35	,	,	PUNCT
ejpam-4655	5	36	η)-open	η)-open	ADJ
ejpam-4655	5	37	,	,	PUNCT
ejpam-4655	5	38	(	(	PUNCT
ejpam-4655	5	39	µ	µ	NUM
ejpam-4655	5	40	,	,	PUNCT
ejpam-4655	5	41	η)-continuous	η)-continuous	ADJ
ejpam-4655	5	42	map	map	NOUN
ejpam-4655	5	43	,	,	PUNCT
ejpam-4655	5	44	respectively	respectively	ADV
ejpam-4655	5	45	are	be	AUX
ejpam-4655	5	46	proved	prove	VERB
ejpam-4655	5	47	.	.	PUNCT
ejpam-4655	6	1	further	far	ADV
ejpam-4655	6	2	,	,	PUNCT
ejpam-4655	6	3	the	the	DET
ejpam-4655	6	4	relationship	relationship	NOUN
ejpam-4655	6	5	between	between	ADP
ejpam-4655	6	6	hyperconnected	hyperconnecte	VERB
ejpam-4655	6	7	space	space	NOUN
ejpam-4655	6	8	and	and	CCONJ
ejpam-4655	6	9	submaximal	submaximal	ADJ
ejpam-4655	6	10	space	space	NOUN
ejpam-4655	6	11	in	in	ADP
ejpam-4655	6	12	a	a	DET
ejpam-4655	6	13	pairwise	pairwise	NOUN
ejpam-4655	6	14	bigeneralized	bigeneralize	VERB
ejpam-4655	6	15	submaximal	submaximal	ADJ
ejpam-4655	6	16	space	space	NOUN
ejpam-4655	6	17	is	be	AUX
ejpam-4655	6	18	given	give	VERB
ejpam-4655	6	19	.	.	PUNCT
ejpam-4655	7	1	2020	2020	NUM
ejpam-4655	7	2	mathematics	mathematic	NOUN
ejpam-4655	7	3	subject	subject	NOUN
ejpam-4655	7	4	classifications	classification	NOUN
ejpam-4655	7	5	:	:	PUNCT
ejpam-4655	7	6	54a05	54a05	NUM
ejpam-4655	7	7	,	,	PUNCT
ejpam-4655	7	8	54a10	54a10	NUM
ejpam-4655	7	9	key	key	ADJ
ejpam-4655	7	10	words	word	NOUN
ejpam-4655	7	11	and	and	CCONJ
ejpam-4655	7	12	phrases	phrase	NOUN
ejpam-4655	7	13	:	:	PUNCT
ejpam-4655	7	14	bigeneralized	bigeneralize	VERB
ejpam-4655	7	15	topological	topological	ADJ
ejpam-4655	7	16	spaces	space	NOUN
ejpam-4655	7	17	,	,	PUNCT
ejpam-4655	7	18	(	(	PUNCT
ejpam-4655	7	19	s	s	X
ejpam-4655	7	20	,	,	PUNCT
ejpam-4655	7	21	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	7	22	submaximal	submaximal	ADJ
ejpam-4655	7	23	space	space	NOUN
ejpam-4655	7	24	,	,	PUNCT
ejpam-4655	7	25	(	(	PUNCT
ejpam-4655	7	26	s	s	X
ejpam-4655	7	27	,	,	PUNCT
ejpam-4655	7	28	v)⋆-bigeneralized	v)⋆-bigeneralize	VERB
ejpam-4655	7	29	submaximal	submaximal	ADJ
ejpam-4655	7	30	space	space	NOUN
ejpam-4655	7	31	,	,	PUNCT
ejpam-4655	7	32	(	(	PUNCT
ejpam-4655	7	33	s	s	X
ejpam-4655	7	34	,	,	PUNCT
ejpam-4655	7	35	v)-open	v)-open	ADJ
ejpam-4655	7	36	,	,	PUNCT
ejpam-4655	7	37	(	(	PUNCT
ejpam-4655	7	38	s	s	X
ejpam-4655	7	39	,	,	PUNCT
ejpam-4655	7	40	v)-dense	v)-dense	NOUN
ejpam-4655	7	41	.	.	PUNCT
ejpam-4655	8	1	1	1	X
ejpam-4655	8	2	.	.	X
ejpam-4655	8	3	introduction	introduction	NOUN
ejpam-4655	8	4	the	the	DET
ejpam-4655	8	5	new	new	ADJ
ejpam-4655	8	6	most	most	ADV
ejpam-4655	8	7	interesting	interesting	ADJ
ejpam-4655	8	8	tool	tool	NOUN
ejpam-4655	8	9	namely	namely	ADV
ejpam-4655	8	10	,	,	PUNCT
ejpam-4655	8	11	generalized	generalized	ADJ
ejpam-4655	8	12	topological	topological	ADJ
ejpam-4655	8	13	space	space	NOUN
ejpam-4655	8	14	was	be	AUX
ejpam-4655	8	15	founded	found	VERB
ejpam-4655	8	16	by	by	ADP
ejpam-4655	8	17	császár	császár	NOUN
ejpam-4655	8	18	in	in	ADP
ejpam-4655	8	19	[	[	X
ejpam-4655	8	20	2	2	NUM
ejpam-4655	8	21	]	]	PUNCT
ejpam-4655	8	22	.	.	PUNCT
ejpam-4655	9	1	most	most	ADJ
ejpam-4655	9	2	of	of	ADP
ejpam-4655	9	3	them	they	PRON
ejpam-4655	9	4	studied	study	VERB
ejpam-4655	9	5	the	the	DET
ejpam-4655	9	6	nature	nature	NOUN
ejpam-4655	9	7	of	of	ADP
ejpam-4655	9	8	this	this	DET
ejpam-4655	9	9	space	space	NOUN
ejpam-4655	9	10	and	and	CCONJ
ejpam-4655	9	11	some	some	PRON
ejpam-4655	9	12	,	,	PUNCT
ejpam-4655	9	13	researchers	researcher	NOUN
ejpam-4655	9	14	have	have	AUX
ejpam-4655	9	15	defined	define	VERB
ejpam-4655	9	16	some	some	DET
ejpam-4655	9	17	new	new	ADJ
ejpam-4655	9	18	tools	tool	NOUN
ejpam-4655	9	19	in	in	ADP
ejpam-4655	9	20	this	this	DET
ejpam-4655	9	21	space	space	NOUN
ejpam-4655	9	22	and	and	CCONJ
ejpam-4655	9	23	examined	examine	VERB
ejpam-4655	9	24	their	their	PRON
ejpam-4655	9	25	significance	significance	NOUN
ejpam-4655	9	26	in	in	ADP
ejpam-4655	9	27	generalized	generalized	ADJ
ejpam-4655	9	28	topological	topological	ADJ
ejpam-4655	9	29	space	space	NOUN
ejpam-4655	9	30	.	.	PUNCT
ejpam-4655	10	1	particularly	particularly	ADV
ejpam-4655	10	2	,	,	PUNCT
ejpam-4655	10	3	submaximal	submaximal	ADJ
ejpam-4655	10	4	space	space	NOUN
ejpam-4655	10	5	was	be	AUX
ejpam-4655	10	6	introduced	introduce	VERB
ejpam-4655	10	7	by	by	ADP
ejpam-4655	10	8	ekici	ekici	NOUN
ejpam-4655	10	9	in	in	ADP
ejpam-4655	10	10	a	a	DET
ejpam-4655	10	11	generalized	generalized	ADJ
ejpam-4655	10	12	topological	topological	ADJ
ejpam-4655	10	13	space	space	NOUN
ejpam-4655	10	14	.	.	PUNCT
ejpam-4655	11	1	in	in	ADP
ejpam-4655	11	2	generalized	generalized	ADJ
ejpam-4655	11	3	topological	topological	ADJ
ejpam-4655	11	4	space	space	NOUN
ejpam-4655	11	5	,	,	PUNCT
ejpam-4655	11	6	he	he	PRON
ejpam-4655	11	7	launched	launch	VERB
ejpam-4655	11	8	some	some	DET
ejpam-4655	11	9	characterization	characterization	NOUN
ejpam-4655	11	10	theorems	theorem	NOUN
ejpam-4655	11	11	for	for	ADP
ejpam-4655	11	12	submaximal	submaximal	ADJ
ejpam-4655	11	13	space	space	NOUN
ejpam-4655	11	14	.	.	PUNCT
ejpam-4655	12	1	based	base	VERB
ejpam-4655	12	2	on	on	ADP
ejpam-4655	12	3	this	this	PRON
ejpam-4655	12	4	,	,	PUNCT
ejpam-4655	12	5	some	some	DET
ejpam-4655	12	6	mathematicians	mathematician	NOUN
ejpam-4655	12	7	established	establish	VERB
ejpam-4655	12	8	some	some	DET
ejpam-4655	12	9	new	new	ADJ
ejpam-4655	12	10	results	result	NOUN
ejpam-4655	12	11	for	for	ADP
ejpam-4655	12	12	generalized	generalized	ADJ
ejpam-4655	12	13	submaximal	submaximal	ADJ
ejpam-4655	12	14	space	space	NOUN
ejpam-4655	12	15	e.g.	e.g.	ADV
ejpam-4655	12	16	[	[	X
ejpam-4655	12	17	9	9	NUM
ejpam-4655	12	18	,	,	PUNCT
ejpam-4655	12	19	19	19	NUM
ejpam-4655	12	20	]	]	PUNCT
ejpam-4655	12	21	.	.	PUNCT
ejpam-4655	13	1	in	in	ADP
ejpam-4655	13	2	2016	2016	NUM
ejpam-4655	13	3	,	,	PUNCT
ejpam-4655	13	4	ahmadi	ahmadi	PROPN
ejpam-4655	13	5	zand	zand	PROPN
ejpam-4655	13	6	et.al	et.al	PROPN
ejpam-4655	13	7	gave	give	VERB
ejpam-4655	13	8	few	few	ADJ
ejpam-4655	13	9	results	result	NOUN
ejpam-4655	13	10	for	for	ADP
ejpam-4655	13	11	submaximal	submaximal	ADJ
ejpam-4655	13	12	space	space	NOUN
ejpam-4655	13	13	and	and	CCONJ
ejpam-4655	13	14	defined	define	VERB
ejpam-4655	13	15	a	a	DET
ejpam-4655	13	16	space	space	NOUN
ejpam-4655	13	17	namely	namely	ADV
ejpam-4655	13	18	,	,	PUNCT
ejpam-4655	13	19	generalized	generalized	ADJ
ejpam-4655	13	20	gδ	gδ	NOUN
ejpam-4655	13	21	-	-	PUNCT
ejpam-4655	13	22	submaximal	submaximal	ADJ
ejpam-4655	13	23	space	space	NOUN
ejpam-4655	13	24	,	,	PUNCT
ejpam-4655	13	25	and	and	CCONJ
ejpam-4655	13	26	studied	study	VERB
ejpam-4655	13	27	the	the	DET
ejpam-4655	13	28	nature	nature	NOUN
ejpam-4655	13	29	of	of	ADP
ejpam-4655	13	30	this	this	DET
ejpam-4655	13	31	space	space	NOUN
ejpam-4655	13	32	[	[	X
ejpam-4655	13	33	19	19	NUM
ejpam-4655	13	34	]	]	PUNCT
ejpam-4655	13	35	.	.	PUNCT
ejpam-4655	14	1	in	in	ADP
ejpam-4655	14	2	[	[	X
ejpam-4655	14	3	11	11	NUM
ejpam-4655	14	4	]	]	PUNCT
ejpam-4655	14	5	,	,	PUNCT
ejpam-4655	14	6	j.c	j.c	PROPN
ejpam-4655	14	7	.	.	PROPN
ejpam-4655	14	8	kelly	kelly	PROPN
ejpam-4655	14	9	introduced	introduce	VERB
ejpam-4655	14	10	the	the	DET
ejpam-4655	14	11	notion	notion	NOUN
ejpam-4655	14	12	of	of	ADP
ejpam-4655	14	13	bitopological	bitopological	ADJ
ejpam-4655	14	14	space	space	NOUN
ejpam-4655	14	15	.	.	PUNCT
ejpam-4655	15	1	motivated	motivate	VERB
ejpam-4655	15	2	by	by	ADP
ejpam-4655	15	3	this	this	PRON
ejpam-4655	15	4	,	,	PUNCT
ejpam-4655	15	5	boonpok	boonpok	PROPN
ejpam-4655	15	6	defined	define	VERB
ejpam-4655	15	7	the	the	DET
ejpam-4655	15	8	concept	concept	NOUN
ejpam-4655	15	9	of	of	ADP
ejpam-4655	15	10	bigeneralized	bigeneralize	VERB
ejpam-4655	15	11	topological	topological	ADJ
ejpam-4655	15	12	space	space	NOUN
ejpam-4655	15	13	in	in	ADP
ejpam-4655	15	14	2010	2010	NUM
ejpam-4655	15	15	[	[	X
ejpam-4655	15	16	5	5	NUM
ejpam-4655	15	17	]	]	PUNCT
ejpam-4655	15	18	.	.	PUNCT
ejpam-4655	16	1	in	in	ADP
ejpam-4655	16	2	bigeneralized	bigeneralize	VERB
ejpam-4655	16	3	topological	topological	ADJ
ejpam-4655	16	4	space	space	NOUN
ejpam-4655	16	5	,	,	PUNCT
ejpam-4655	16	6	he	he	PRON
ejpam-4655	16	7	proved	prove	VERB
ejpam-4655	16	8	some	some	DET
ejpam-4655	16	9	results	result	NOUN
ejpam-4655	16	10	for	for	ADP
ejpam-4655	16	11	(	(	PUNCT
ejpam-4655	16	12	m	m	PROPN
ejpam-4655	16	13	,	,	PUNCT
ejpam-4655	16	14	n)-closed	n)-close	VERB
ejpam-4655	16	15	sets	set	NOUN
ejpam-4655	16	16	.	.	PUNCT
ejpam-4655	17	1	in	in	ADP
ejpam-4655	17	2	[	[	X
ejpam-4655	17	3	13	13	NUM
ejpam-4655	17	4	,	,	PUNCT
ejpam-4655	17	5	14	14	NUM
ejpam-4655	17	6	,	,	PUNCT
ejpam-4655	17	7	17	17	NUM
ejpam-4655	17	8	,	,	PUNCT
ejpam-4655	17	9	18	18	NUM
ejpam-4655	17	10	]	]	PUNCT
ejpam-4655	17	11	,	,	PUNCT
ejpam-4655	17	12	some	some	DET
ejpam-4655	17	13	∗corresponding	∗corresponde	VERB
ejpam-4655	17	14	author	author	NOUN
ejpam-4655	17	15	.	.	PUNCT
ejpam-4655	18	1	doi	doi	NOUN
ejpam-4655	18	2	:	:	PUNCT
ejpam-4655	18	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4655	https://doi.org/10.29020/nybg.ejpam.v16i1.4655	ADJ
ejpam-4655	18	4	email	email	NOUN
ejpam-4655	18	5	addresses	address	NOUN
ejpam-4655	18	6	:	:	PUNCT
ejpam-4655	18	7	farhat.yasser.1@gmail.com	farhat.yasser.1@gmail.com	X
ejpam-4655	18	8	(	(	PUNCT
ejpam-4655	18	9	y.	y.	PROPN
ejpam-4655	18	10	farhat	farhat	PROPN
ejpam-4655	18	11	)	)	PUNCT
ejpam-4655	18	12	,	,	PUNCT
ejpam-4655	18	13	muthumarikrishnan060196@gmail.com	muthumarikrishnan060196@gmail.com	X
ejpam-4655	18	14	(	(	PUNCT
ejpam-4655	18	15	k.muthumari	k.muthumari	X
ejpam-4655	18	16	)	)	PUNCT
ejpam-4655	18	17	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4655	19	1	386	386	NUM
ejpam-4655	19	2	©	©	PROPN
ejpam-4655	19	3	2023	2023	NUM
ejpam-4655	19	4	ejpam	ejpam	NOUN
ejpam-4655	19	5	all	all	DET
ejpam-4655	19	6	rights	right	NOUN
ejpam-4655	19	7	reserved	reserve	VERB
ejpam-4655	19	8	.	.	PUNCT
ejpam-4655	20	1	y.	y.	PROPN
ejpam-4655	20	2	farhat	farhat	PROPN
ejpam-4655	20	3	et	et	PROPN
ejpam-4655	20	4	al	al	PROPN
ejpam-4655	20	5	.	.	PUNCT
ejpam-4655	20	6	/	/	SYM
ejpam-4655	20	7	eur	eur	PROPN
ejpam-4655	20	8	.	.	PUNCT
ejpam-4655	21	1	j.	j.	PROPN
ejpam-4655	21	2	pure	pure	PROPN
ejpam-4655	21	3	appl	appl	PROPN
ejpam-4655	21	4	.	.	PROPN
ejpam-4655	21	5	math	math	PROPN
ejpam-4655	21	6	,	,	PUNCT
ejpam-4655	21	7	16	16	NUM
ejpam-4655	21	8	(	(	PUNCT
ejpam-4655	21	9	1	1	NUM
ejpam-4655	21	10	)	)	PUNCT
ejpam-4655	21	11	(	(	PUNCT
ejpam-4655	21	12	2023	2023	NUM
ejpam-4655	21	13	)	)	PUNCT
ejpam-4655	21	14	,	,	PUNCT
ejpam-4655	21	15	386	386	NUM
ejpam-4655	21	16	-	-	SYM
ejpam-4655	21	17	403	403	NUM
ejpam-4655	21	18	387	387	NUM
ejpam-4655	21	19	new	new	ADJ
ejpam-4655	21	20	properties	property	NOUN
ejpam-4655	21	21	of	of	ADP
ejpam-4655	21	22	different	different	ADJ
ejpam-4655	21	23	types	type	NOUN
ejpam-4655	21	24	of	of	ADP
ejpam-4655	21	25	sets	set	NOUN
ejpam-4655	21	26	are	be	AUX
ejpam-4655	21	27	proved	prove	VERB
ejpam-4655	21	28	.	.	PUNCT
ejpam-4655	22	1	based	base	VERB
ejpam-4655	22	2	on	on	ADP
ejpam-4655	22	3	this	this	PRON
ejpam-4655	22	4	,	,	PUNCT
ejpam-4655	22	5	here	here	ADV
ejpam-4655	22	6	we	we	PRON
ejpam-4655	22	7	prove	prove	VERB
ejpam-4655	22	8	some	some	DET
ejpam-4655	22	9	interesting	interesting	ADJ
ejpam-4655	22	10	results	result	NOUN
ejpam-4655	22	11	for	for	ADP
ejpam-4655	22	12	nowhere	nowhere	ADV
ejpam-4655	22	13	-	-	PUNCT
ejpam-4655	22	14	dense	dense	ADJ
ejpam-4655	22	15	sets	set	NOUN
ejpam-4655	22	16	in	in	ADP
ejpam-4655	22	17	bigeneralized	bigeneralize	VERB
ejpam-4655	22	18	topological	topological	ADJ
ejpam-4655	22	19	space	space	NOUN
ejpam-4655	22	20	.	.	PUNCT
ejpam-4655	23	1	from	from	ADP
ejpam-4655	23	2	the	the	DET
ejpam-4655	23	3	previous	previous	ADJ
ejpam-4655	23	4	observations	observation	NOUN
ejpam-4655	23	5	,	,	PUNCT
ejpam-4655	23	6	it	it	PRON
ejpam-4655	23	7	has	have	AUX
ejpam-4655	23	8	been	be	AUX
ejpam-4655	23	9	motivated	motivate	VERB
ejpam-4655	23	10	,	,	PUNCT
ejpam-4655	23	11	in	in	ADP
ejpam-4655	23	12	section	section	NOUN
ejpam-4655	23	13	3	3	NUM
ejpam-4655	23	14	,	,	PUNCT
ejpam-4655	23	15	(	(	PUNCT
ejpam-4655	23	16	s	s	X
ejpam-4655	23	17	,	,	PUNCT
ejpam-4655	23	18	v)-bigenralized	v)-bigenralize	VERB
ejpam-4655	23	19	submaximal	submaximal	ADJ
ejpam-4655	23	20	space	space	NOUN
ejpam-4655	23	21	is	be	AUX
ejpam-4655	23	22	defined	define	VERB
ejpam-4655	23	23	and	and	CCONJ
ejpam-4655	23	24	the	the	DET
ejpam-4655	23	25	equivalent	equivalent	ADJ
ejpam-4655	23	26	conditions	condition	NOUN
ejpam-4655	23	27	for	for	ADP
ejpam-4655	23	28	this	this	DET
ejpam-4655	23	29	space	space	NOUN
ejpam-4655	23	30	are	be	AUX
ejpam-4655	23	31	given	give	VERB
ejpam-4655	23	32	and	and	CCONJ
ejpam-4655	23	33	some	some	DET
ejpam-4655	23	34	properties	property	NOUN
ejpam-4655	23	35	for	for	ADP
ejpam-4655	23	36	nowhere	nowhere	ADV
ejpam-4655	23	37	dense	dense	ADJ
ejpam-4655	23	38	sets	set	NOUN
ejpam-4655	23	39	are	be	AUX
ejpam-4655	23	40	proved	prove	VERB
ejpam-4655	23	41	,	,	PUNCT
ejpam-4655	23	42	also	also	ADV
ejpam-4655	23	43	,	,	PUNCT
ejpam-4655	23	44	the	the	DET
ejpam-4655	23	45	significance	significance	NOUN
ejpam-4655	23	46	of	of	ADP
ejpam-4655	23	47	an	an	DET
ejpam-4655	23	48	image	image	NOUN
ejpam-4655	23	49	and	and	CCONJ
ejpam-4655	23	50	preimage	preimage	NOUN
ejpam-4655	23	51	of	of	ADP
ejpam-4655	23	52	(	(	PUNCT
ejpam-4655	23	53	s	s	PROPN
ejpam-4655	23	54	,	,	PUNCT
ejpam-4655	23	55	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	23	56	submaximal	submaximal	ADJ
ejpam-4655	23	57	space	space	NOUN
ejpam-4655	23	58	are	be	AUX
ejpam-4655	23	59	analyzed	analyze	VERB
ejpam-4655	23	60	.	.	PUNCT
ejpam-4655	24	1	in	in	ADP
ejpam-4655	24	2	a	a	DET
ejpam-4655	24	3	pairwise	pairwise	NOUN
ejpam-4655	24	4	bigeneralized	bigeneralize	VERB
ejpam-4655	24	5	submaximal	submaximal	ADJ
ejpam-4655	24	6	space	space	NOUN
ejpam-4655	24	7	,	,	PUNCT
ejpam-4655	24	8	the	the	DET
ejpam-4655	24	9	relationship	relationship	NOUN
ejpam-4655	24	10	between	between	ADP
ejpam-4655	24	11	generalized	generalized	ADJ
ejpam-4655	24	12	submaximal	submaximal	ADJ
ejpam-4655	24	13	space	space	NOUN
ejpam-4655	24	14	and	and	CCONJ
ejpam-4655	24	15	generalized	generalize	VERB
ejpam-4655	24	16	hyperconnected	hyperconnecte	VERB
ejpam-4655	24	17	space	space	NOUN
ejpam-4655	24	18	is	be	AUX
ejpam-4655	24	19	discussed	discuss	VERB
ejpam-4655	24	20	.	.	PUNCT
ejpam-4655	25	1	in	in	ADP
ejpam-4655	25	2	section	section	NOUN
ejpam-4655	25	3	4	4	NUM
ejpam-4655	25	4	,	,	PUNCT
ejpam-4655	25	5	we	we	PRON
ejpam-4655	25	6	define	define	VERB
ejpam-4655	25	7	the	the	DET
ejpam-4655	25	8	notion	notion	NOUN
ejpam-4655	25	9	(	(	PUNCT
ejpam-4655	25	10	s	s	X
ejpam-4655	25	11	,	,	PUNCT
ejpam-4655	25	12	v)⋆-bigeneralized	v)⋆-bigeneralize	VERB
ejpam-4655	25	13	submaximal	submaximal	ADJ
ejpam-4655	25	14	space	space	NOUN
ejpam-4655	25	15	and	and	CCONJ
ejpam-4655	25	16	the	the	DET
ejpam-4655	25	17	relationship	relationship	NOUN
ejpam-4655	25	18	between	between	ADP
ejpam-4655	25	19	(	(	PUNCT
ejpam-4655	25	20	s	s	PROPN
ejpam-4655	25	21	,	,	PUNCT
ejpam-4655	25	22	v	v	NOUN
ejpam-4655	25	23	)	)	PUNCT
ejpam-4655	25	24	and	and	CCONJ
ejpam-4655	25	25	(	(	PUNCT
ejpam-4655	25	26	s	s	X
ejpam-4655	25	27	,	,	PUNCT
ejpam-4655	25	28	v)⋆	v)⋆	PROPN
ejpam-4655	25	29	bigeneralized	bigeneralize	VERB
ejpam-4655	25	30	submaximal	submaximal	ADJ
ejpam-4655	25	31	space	space	NOUN
ejpam-4655	25	32	is	be	AUX
ejpam-4655	25	33	proven	prove	VERB
ejpam-4655	25	34	.	.	PUNCT
ejpam-4655	26	1	in	in	ADP
ejpam-4655	26	2	the	the	DET
ejpam-4655	26	3	last	last	ADJ
ejpam-4655	26	4	section	section	NOUN
ejpam-4655	26	5	,	,	PUNCT
ejpam-4655	26	6	the	the	DET
ejpam-4655	26	7	necessary	necessary	ADJ
ejpam-4655	26	8	conditions	condition	NOUN
ejpam-4655	26	9	for	for	ADP
ejpam-4655	26	10	a	a	DET
ejpam-4655	26	11	bigeneralized	bigeneralize	VERB
ejpam-4655	26	12	topological	topological	ADJ
ejpam-4655	26	13	space	space	NOUN
ejpam-4655	26	14	is	be	AUX
ejpam-4655	26	15	a	a	DET
ejpam-4655	26	16	(	(	PUNCT
ejpam-4655	26	17	s	s	PROPN
ejpam-4655	26	18	,	,	PUNCT
ejpam-4655	26	19	v)⋆⋆bigeneralized	v)⋆⋆bigeneralize	VERB
ejpam-4655	26	20	topological	topological	ADJ
ejpam-4655	26	21	space	space	NOUN
ejpam-4655	26	22	are	be	AUX
ejpam-4655	26	23	given	give	VERB
ejpam-4655	26	24	.	.	PUNCT
ejpam-4655	27	1	in	in	ADP
ejpam-4655	27	2	this	this	DET
ejpam-4655	27	3	space	space	NOUN
ejpam-4655	27	4	,	,	PUNCT
ejpam-4655	27	5	few	few	ADJ
ejpam-4655	27	6	results	result	NOUN
ejpam-4655	27	7	for	for	ADP
ejpam-4655	27	8	closed	closed	ADJ
ejpam-4655	27	9	sets	set	NOUN
ejpam-4655	27	10	are	be	AUX
ejpam-4655	27	11	proven	prove	VERB
ejpam-4655	27	12	.	.	PUNCT
ejpam-4655	28	1	with	with	ADP
ejpam-4655	28	2	the	the	DET
ejpam-4655	28	3	results	result	NOUN
ejpam-4655	28	4	given	give	VERB
ejpam-4655	28	5	in	in	ADP
ejpam-4655	28	6	the	the	DET
ejpam-4655	28	7	mentioned	mention	VERB
ejpam-4655	28	8	sections	section	NOUN
ejpam-4655	28	9	,	,	PUNCT
ejpam-4655	28	10	it	it	PRON
ejpam-4655	28	11	is	be	AUX
ejpam-4655	28	12	possible	possible	ADJ
ejpam-4655	28	13	to	to	PART
ejpam-4655	28	14	easily	easily	ADV
ejpam-4655	28	15	check	check	VERB
ejpam-4655	28	16	whether	whether	SCONJ
ejpam-4655	28	17	a	a	DET
ejpam-4655	28	18	given	give	VERB
ejpam-4655	28	19	space	space	NOUN
ejpam-4655	28	20	is	be	AUX
ejpam-4655	28	21	(	(	PUNCT
ejpam-4655	28	22	s	s	X
ejpam-4655	28	23	,	,	PUNCT
ejpam-4655	28	24	v	v	NOUN
ejpam-4655	28	25	)	)	PUNCT
ejpam-4655	28	26	or	or	CCONJ
ejpam-4655	28	27	(	(	PUNCT
ejpam-4655	28	28	s	s	X
ejpam-4655	28	29	,	,	PUNCT
ejpam-4655	28	30	v)⋆	v)⋆	PROPN
ejpam-4655	28	31	or	or	CCONJ
ejpam-4655	28	32	(	(	PUNCT
ejpam-4655	28	33	s	s	X
ejpam-4655	28	34	,	,	PUNCT
ejpam-4655	28	35	v)⋆⋆	v)⋆⋆	NOUN
ejpam-4655	28	36	bigeneralized	bigeneralize	VERB
ejpam-4655	28	37	submaximal	submaximal	ADJ
ejpam-4655	28	38	space	space	NOUN
ejpam-4655	28	39	or	or	CCONJ
ejpam-4655	28	40	not	not	PART
ejpam-4655	28	41	,	,	PUNCT
ejpam-4655	28	42	is	be	AUX
ejpam-4655	28	43	obtain	obtain	VERB
ejpam-4655	28	44	some	some	DET
ejpam-4655	28	45	tricks	trick	NOUN
ejpam-4655	28	46	to	to	PART
ejpam-4655	28	47	check	check	VERB
ejpam-4655	28	48	in	in	ADP
ejpam-4655	28	49	a	a	DET
ejpam-4655	28	50	(	(	PUNCT
ejpam-4655	28	51	s	s	PROPN
ejpam-4655	28	52	,	,	PUNCT
ejpam-4655	28	53	v	v	NOUN
ejpam-4655	28	54	)	)	PUNCT
ejpam-4655	28	55	(	(	PUNCT
ejpam-4655	28	56	(	(	PUNCT
ejpam-4655	28	57	s	s	X
ejpam-4655	28	58	,	,	PUNCT
ejpam-4655	28	59	v)⋆	v)⋆	PROPN
ejpam-4655	28	60	and	and	CCONJ
ejpam-4655	28	61	(	(	PUNCT
ejpam-4655	28	62	s	s	X
ejpam-4655	28	63	,	,	PUNCT
ejpam-4655	28	64	v)⋆⋆	v)⋆⋆	NOUN
ejpam-4655	28	65	)	)	PUNCT
ejpam-4655	28	66	bigeneralized	bigeneralize	VERB
ejpam-4655	28	67	submaximal	submaximal	ADJ
ejpam-4655	28	68	space	space	NOUN
ejpam-4655	28	69	,	,	PUNCT
ejpam-4655	28	70	a	a	DET
ejpam-4655	28	71	given	give	VERB
ejpam-4655	28	72	set	set	NOUN
ejpam-4655	28	73	is	be	AUX
ejpam-4655	28	74	(	(	PUNCT
ejpam-4655	28	75	v	v	NOUN
ejpam-4655	28	76	,	,	PUNCT
ejpam-4655	28	77	s)-nowhere	s)-nowhere	X
ejpam-4655	28	78	dense	dense	ADJ
ejpam-4655	28	79	or	or	CCONJ
ejpam-4655	28	80	not	not	PART
ejpam-4655	28	81	,	,	PUNCT
ejpam-4655	28	82	are	be	AUX
ejpam-4655	28	83	given	give	VERB
ejpam-4655	28	84	the	the	DET
ejpam-4655	28	85	necessary	necessary	ADJ
ejpam-4655	28	86	conditions	condition	NOUN
ejpam-4655	28	87	for	for	ADP
ejpam-4655	28	88	check	check	VERB
ejpam-4655	28	89	whether	whether	SCONJ
ejpam-4655	28	90	a	a	DET
ejpam-4655	28	91	given	give	VERB
ejpam-4655	28	92	space	space	NOUN
ejpam-4655	28	93	is	be	AUX
ejpam-4655	28	94	submaximal	submaximal	ADJ
ejpam-4655	28	95	space	space	NOUN
ejpam-4655	28	96	or	or	CCONJ
ejpam-4655	28	97	not	not	PART
ejpam-4655	28	98	.	.	PUNCT
ejpam-4655	29	1	2	2	X
ejpam-4655	29	2	.	.	X
ejpam-4655	29	3	preliminaries	preliminary	NOUN
ejpam-4655	29	4	let	let	VERB
ejpam-4655	29	5	x	x	PRON
ejpam-4655	29	6	be	be	AUX
ejpam-4655	29	7	any	any	DET
ejpam-4655	29	8	non	non	ADJ
ejpam-4655	29	9	-	-	ADJ
ejpam-4655	29	10	null	null	ADJ
ejpam-4655	29	11	set	set	NOUN
ejpam-4655	29	12	.	.	PUNCT
ejpam-4655	30	1	a	a	DET
ejpam-4655	30	2	collection	collection	NOUN
ejpam-4655	30	3	µ	µ	X
ejpam-4655	30	4	of	of	ADP
ejpam-4655	30	5	subsets	subset	NOUN
ejpam-4655	30	6	of	of	ADP
ejpam-4655	30	7	x	x	X
ejpam-4655	30	8	is	be	AUX
ejpam-4655	30	9	a	a	DET
ejpam-4655	30	10	generalized	generalized	ADJ
ejpam-4655	30	11	topology	topology	NOUN
ejpam-4655	31	1	[	[	X
ejpam-4655	31	2	2	2	X
ejpam-4655	31	3	]	]	PUNCT
ejpam-4655	31	4	in	in	ADP
ejpam-4655	31	5	x	x	SYM
ejpam-4655	31	6	if	if	SCONJ
ejpam-4655	31	7	it	it	PRON
ejpam-4655	31	8	contains	contain	VERB
ejpam-4655	31	9	the	the	DET
ejpam-4655	31	10	empty	empty	ADJ
ejpam-4655	31	11	set	set	NOUN
ejpam-4655	31	12	and	and	CCONJ
ejpam-4655	31	13	is	be	AUX
ejpam-4655	31	14	closed	close	VERB
ejpam-4655	31	15	under	under	ADP
ejpam-4655	31	16	arbitrary	arbitrary	ADJ
ejpam-4655	31	17	union	union	NOUN
ejpam-4655	31	18	.	.	PUNCT
ejpam-4655	32	1	the	the	DET
ejpam-4655	32	2	pair	pair	NOUN
ejpam-4655	32	3	(	(	PUNCT
ejpam-4655	32	4	x,µ	x,µ	NOUN
ejpam-4655	32	5	)	)	PUNCT
ejpam-4655	32	6	is	be	AUX
ejpam-4655	32	7	called	call	VERB
ejpam-4655	32	8	a	a	DET
ejpam-4655	32	9	generalized	generalized	ADJ
ejpam-4655	32	10	topological	topological	ADJ
ejpam-4655	32	11	space	space	NOUN
ejpam-4655	32	12	(	(	PUNCT
ejpam-4655	32	13	gts	gts	NOUN
ejpam-4655	32	14	)	)	PUNCT
ejpam-4655	32	15	.	.	PUNCT
ejpam-4655	33	1	the	the	DET
ejpam-4655	33	2	pair	pair	NOUN
ejpam-4655	33	3	(	(	PUNCT
ejpam-4655	33	4	x,µ	x,µ	NOUN
ejpam-4655	33	5	)	)	PUNCT
ejpam-4655	33	6	is	be	AUX
ejpam-4655	33	7	called	call	VERB
ejpam-4655	33	8	a	a	DET
ejpam-4655	33	9	strong	strong	ADJ
ejpam-4655	33	10	generalized	generalized	ADJ
ejpam-4655	33	11	topological	topological	ADJ
ejpam-4655	33	12	space	space	NOUN
ejpam-4655	33	13	(	(	PUNCT
ejpam-4655	33	14	sgts	sgts	NOUN
ejpam-4655	33	15	)	)	PUNCT
ejpam-4655	34	1	[	[	X
ejpam-4655	34	2	20	20	NUM
ejpam-4655	34	3	]	]	PUNCT
ejpam-4655	34	4	if	if	SCONJ
ejpam-4655	34	5	x	x	PROPN
ejpam-4655	34	6	∈	∈	PROPN
ejpam-4655	34	7	µ.	µ.	NOUN
ejpam-4655	34	8	in	in	ADP
ejpam-4655	34	9	[	[	X
ejpam-4655	34	10	3	3	NUM
ejpam-4655	34	11	]	]	PUNCT
ejpam-4655	34	12	,	,	PUNCT
ejpam-4655	34	13	if	if	SCONJ
ejpam-4655	34	14	q	q	X
ejpam-4655	34	15	∈	∈	PROPN
ejpam-4655	34	16	µ	µ	NOUN
ejpam-4655	34	17	,	,	PUNCT
ejpam-4655	34	18	then	then	ADV
ejpam-4655	34	19	q	q	X
ejpam-4655	34	20	is	be	AUX
ejpam-4655	34	21	called	call	VERB
ejpam-4655	34	22	a	a	DET
ejpam-4655	34	23	µ-open	µ-open	NOUN
ejpam-4655	34	24	set	set	VERB
ejpam-4655	34	25	;	;	PUNCT
ejpam-4655	34	26	if	if	SCONJ
ejpam-4655	34	27	x	x	X
ejpam-4655	34	28	−	−	X
ejpam-4655	34	29	q	q	PROPN
ejpam-4655	34	30	∈	∈	PROPN
ejpam-4655	34	31	µ	µ	NOUN
ejpam-4655	34	32	,	,	PUNCT
ejpam-4655	34	33	then	then	ADV
ejpam-4655	34	34	q	q	X
ejpam-4655	34	35	is	be	AUX
ejpam-4655	34	36	said	say	VERB
ejpam-4655	34	37	to	to	PART
ejpam-4655	34	38	be	be	AUX
ejpam-4655	34	39	a	a	DET
ejpam-4655	34	40	µ-closed	µ-close	VERB
ejpam-4655	34	41	set	set	NOUN
ejpam-4655	34	42	.	.	PUNCT
ejpam-4655	35	1	let	let	VERB
ejpam-4655	35	2	d	d	PRON
ejpam-4655	35	3	be	be	AUX
ejpam-4655	35	4	a	a	DET
ejpam-4655	35	5	subset	subset	NOUN
ejpam-4655	35	6	of	of	ADP
ejpam-4655	35	7	a	a	DET
ejpam-4655	35	8	gts	gts	NOUN
ejpam-4655	35	9	(	(	PUNCT
ejpam-4655	35	10	x,µ	x,µ	NOUN
ejpam-4655	35	11	)	)	PUNCT
ejpam-4655	35	12	.	.	PUNCT
ejpam-4655	36	1	the	the	DET
ejpam-4655	36	2	interior	interior	NOUN
ejpam-4655	36	3	of	of	ADP
ejpam-4655	36	4	d	d	PROPN
ejpam-4655	36	5	[	[	X
ejpam-4655	36	6	20	20	NUM
ejpam-4655	36	7	]	]	PUNCT
ejpam-4655	36	8	denoted	denote	VERB
ejpam-4655	36	9	by	by	ADP
ejpam-4655	36	10	i	i	PROPN
ejpam-4655	36	11	d	d	PROPN
ejpam-4655	36	12	,	,	PUNCT
ejpam-4655	36	13	is	be	AUX
ejpam-4655	36	14	the	the	DET
ejpam-4655	36	15	union	union	NOUN
ejpam-4655	36	16	of	of	ADP
ejpam-4655	36	17	all	all	DET
ejpam-4655	36	18	µ-open	µ-open	NOUN
ejpam-4655	36	19	sets	set	NOUN
ejpam-4655	36	20	contained	contain	VERB
ejpam-4655	36	21	in	in	ADP
ejpam-4655	36	22	d	d	PROPN
ejpam-4655	36	23	and	and	CCONJ
ejpam-4655	36	24	the	the	DET
ejpam-4655	36	25	closure	closure	NOUN
ejpam-4655	36	26	of	of	ADP
ejpam-4655	36	27	d	d	PROPN
ejpam-4655	36	28	[	[	X
ejpam-4655	36	29	20	20	NUM
ejpam-4655	36	30	]	]	PUNCT
ejpam-4655	36	31	denoted	denote	VERB
ejpam-4655	36	32	by	by	ADP
ejpam-4655	36	33	cd	cd	PROPN
ejpam-4655	36	34	,	,	PUNCT
ejpam-4655	36	35	is	be	AUX
ejpam-4655	36	36	the	the	DET
ejpam-4655	36	37	intersection	intersection	NOUN
ejpam-4655	36	38	of	of	ADP
ejpam-4655	36	39	all	all	DET
ejpam-4655	36	40	µ-closed	µ-close	VERB
ejpam-4655	36	41	sets	set	NOUN
ejpam-4655	36	42	containing	contain	VERB
ejpam-4655	36	43	d.	d.	NOUN
ejpam-4655	36	44	for	for	ADP
ejpam-4655	36	45	simplicity	simplicity	NOUN
ejpam-4655	36	46	of	of	ADP
ejpam-4655	36	47	notation	notation	NOUN
ejpam-4655	36	48	,	,	PUNCT
ejpam-4655	36	49	we	we	PRON
ejpam-4655	36	50	will	will	AUX
ejpam-4655	36	51	write	write	VERB
ejpam-4655	36	52	i(d	i(d	NOUN
ejpam-4655	36	53	)	)	PUNCT
ejpam-4655	36	54	and	and	CCONJ
ejpam-4655	36	55	c(d	c(d	PROPN
ejpam-4655	36	56	)	)	PUNCT
ejpam-4655	36	57	when	when	SCONJ
ejpam-4655	36	58	no	no	DET
ejpam-4655	36	59	confusion	confusion	NOUN
ejpam-4655	36	60	can	can	AUX
ejpam-4655	36	61	arise	arise	VERB
ejpam-4655	36	62	.	.	PUNCT
ejpam-4655	37	1	next	next	ADV
ejpam-4655	37	2	,	,	PUNCT
ejpam-4655	37	3	we	we	PRON
ejpam-4655	37	4	present	present	VERB
ejpam-4655	37	5	some	some	DET
ejpam-4655	37	6	definitions	definition	NOUN
ejpam-4655	37	7	and	and	CCONJ
ejpam-4655	37	8	lemmas	lemma	NOUN
ejpam-4655	37	9	that	that	PRON
ejpam-4655	37	10	are	be	AUX
ejpam-4655	37	11	useful	useful	ADJ
ejpam-4655	37	12	for	for	ADP
ejpam-4655	37	13	the	the	DET
ejpam-4655	37	14	development	development	NOUN
ejpam-4655	37	15	of	of	ADP
ejpam-4655	37	16	the	the	DET
ejpam-4655	37	17	following	follow	VERB
ejpam-4655	37	18	sections	section	NOUN
ejpam-4655	37	19	.	.	PUNCT
ejpam-4655	38	1	in	in	ADP
ejpam-4655	38	2	[	[	X
ejpam-4655	38	3	10	10	NUM
ejpam-4655	38	4	]	]	PUNCT
ejpam-4655	38	5	,	,	PUNCT
ejpam-4655	38	6	notated	notate	VERB
ejpam-4655	38	7	by	by	ADP
ejpam-4655	38	8	;	;	PUNCT
ejpam-4655	38	9	µ̃	µ̃	PROPN
ejpam-4655	38	10	=	=	SYM
ejpam-4655	38	11	{	{	PUNCT
ejpam-4655	38	12	d	d	X
ejpam-4655	38	13	∈	∈	PROPN
ejpam-4655	38	14	µ	µ	PRON
ejpam-4655	38	15	|	|	NOUN
ejpam-4655	38	16	d	d	PROPN
ejpam-4655	38	17	̸=	̸=	PROPN
ejpam-4655	38	18	∅	∅	NOUN
ejpam-4655	38	19	}	}	PUNCT
ejpam-4655	38	20	,	,	PUNCT
ejpam-4655	38	21	µ(x	µ(x	X
ejpam-4655	38	22	)	)	PUNCT
ejpam-4655	38	23	=	=	SYM
ejpam-4655	38	24	{	{	PUNCT
ejpam-4655	38	25	d	d	X
ejpam-4655	38	26	∈	∈	PROPN
ejpam-4655	38	27	µ	µ	NOUN
ejpam-4655	38	28	|	|	NOUN
ejpam-4655	38	29	x	x	SYM
ejpam-4655	38	30	∈	∈	PROPN
ejpam-4655	38	31	d	d	NOUN
ejpam-4655	38	32	}	}	PUNCT
ejpam-4655	38	33	.	.	PUNCT
ejpam-4655	39	1	a	a	DET
ejpam-4655	39	2	subset	subset	NOUN
ejpam-4655	39	3	q	q	NOUN
ejpam-4655	39	4	of	of	ADP
ejpam-4655	39	5	a	a	DET
ejpam-4655	39	6	gts	gts	NOUN
ejpam-4655	39	7	(	(	PUNCT
ejpam-4655	39	8	x,µ	x,µ	NOUN
ejpam-4655	39	9	)	)	PUNCT
ejpam-4655	39	10	is	be	AUX
ejpam-4655	39	11	said	say	VERB
ejpam-4655	39	12	to	to	PART
ejpam-4655	39	13	be	be	AUX
ejpam-4655	39	14	;	;	PUNCT
ejpam-4655	39	15	•	•	ADP
ejpam-4655	39	16	µ-nowhere	µ-nowhere	VERB
ejpam-4655	39	17	dense	dense	ADJ
ejpam-4655	39	18	[	[	X
ejpam-4655	39	19	8	8	NUM
ejpam-4655	39	20	]	]	X
ejpam-4655	39	21	if	if	SCONJ
ejpam-4655	39	22	icq	icq	NOUN
ejpam-4655	39	23	=	=	PUNCT
ejpam-4655	39	24	∅.	∅.	NUM
ejpam-4655	39	25	•	•	NUM
ejpam-4655	39	26	µ-dense	µ-dense	NOUN
ejpam-4655	40	1	[	[	X
ejpam-4655	40	2	8	8	NUM
ejpam-4655	40	3	]	]	X
ejpam-4655	40	4	if	if	SCONJ
ejpam-4655	40	5	cq	cq	NOUN
ejpam-4655	40	6	=	=	PUNCT
ejpam-4655	40	7	x.	x.	NOUN
ejpam-4655	40	8	•	•	NOUN
ejpam-4655	40	9	µ-codense	µ-codense	NOUN
ejpam-4655	41	1	[	[	X
ejpam-4655	41	2	9	9	NUM
ejpam-4655	41	3	]	]	X
ejpam-4655	41	4	if	if	SCONJ
ejpam-4655	41	5	c(x	c(x	NOUN
ejpam-4655	41	6	−q	−q	NOUN
ejpam-4655	41	7	)	)	PUNCT
ejpam-4655	41	8	=	=	PUNCT
ejpam-4655	42	1	x.	x.	NOUN
ejpam-4655	42	2	a	a	DET
ejpam-4655	42	3	gts	gts	NOUN
ejpam-4655	42	4	(	(	PUNCT
ejpam-4655	42	5	x,µ	x,µ	NOUN
ejpam-4655	42	6	)	)	PUNCT
ejpam-4655	42	7	is	be	AUX
ejpam-4655	42	8	called	call	VERB
ejpam-4655	42	9	as	as	ADP
ejpam-4655	42	10	a	a	PRON
ejpam-4655	42	11	;	;	PUNCT
ejpam-4655	42	12	•	•	NUM
ejpam-4655	42	13	hyperconnected	hyperconnecte	VERB
ejpam-4655	42	14	space	space	NOUN
ejpam-4655	43	1	[	[	X
ejpam-4655	43	2	8	8	X
ejpam-4655	43	3	]	]	X
ejpam-4655	43	4	if	if	SCONJ
ejpam-4655	43	5	cµ(q	cµ(q	NOUN
ejpam-4655	43	6	)	)	PUNCT
ejpam-4655	43	7	=	=	PUNCT
ejpam-4655	44	1	x	x	X
ejpam-4655	44	2	whenever	whenever	SCONJ
ejpam-4655	44	3	q	q	PROPN
ejpam-4655	44	4	∈	∈	PROPN
ejpam-4655	44	5	µ.	µ.	NOUN
ejpam-4655	44	6	•	•	NOUN
ejpam-4655	44	7	generalized	generalize	VERB
ejpam-4655	44	8	submaximal	submaximal	ADJ
ejpam-4655	44	9	[	[	X
ejpam-4655	44	10	9	9	NUM
ejpam-4655	44	11	]	]	X
ejpam-4655	44	12	if	if	SCONJ
ejpam-4655	44	13	q	q	PROPN
ejpam-4655	44	14	∈	∈	PROPN
ejpam-4655	44	15	µ̃	µ̃	PROPN
ejpam-4655	44	16	whenever	whenever	SCONJ
ejpam-4655	44	17	cµ(q	cµ(q	X
ejpam-4655	44	18	)	)	PUNCT
ejpam-4655	44	19	=	=	PUNCT
ejpam-4655	44	20	x.	x.	NOUN
ejpam-4655	44	21	y.	y.	PROPN
ejpam-4655	44	22	farhat	farhat	PROPN
ejpam-4655	44	23	et	et	PROPN
ejpam-4655	44	24	al	al	PROPN
ejpam-4655	44	25	.	.	PUNCT
ejpam-4655	44	26	/	/	SYM
ejpam-4655	44	27	eur	eur	PROPN
ejpam-4655	44	28	.	.	PUNCT
ejpam-4655	45	1	j.	j.	PROPN
ejpam-4655	45	2	pure	pure	PROPN
ejpam-4655	45	3	appl	appl	PROPN
ejpam-4655	45	4	.	.	PROPN
ejpam-4655	45	5	math	math	PROPN
ejpam-4655	45	6	,	,	PUNCT
ejpam-4655	45	7	16	16	NUM
ejpam-4655	45	8	(	(	PUNCT
ejpam-4655	45	9	1	1	NUM
ejpam-4655	45	10	)	)	PUNCT
ejpam-4655	45	11	(	(	PUNCT
ejpam-4655	45	12	2023	2023	NUM
ejpam-4655	45	13	)	)	PUNCT
ejpam-4655	45	14	,	,	PUNCT
ejpam-4655	45	15	386	386	NUM
ejpam-4655	45	16	-	-	SYM
ejpam-4655	45	17	403	403	NUM
ejpam-4655	45	18	388	388	NUM
ejpam-4655	45	19	let	let	VERB
ejpam-4655	45	20	µ1	µ1	PROPN
ejpam-4655	45	21	and	and	CCONJ
ejpam-4655	45	22	µ2	µ2	PROPN
ejpam-4655	45	23	be	be	AUX
ejpam-4655	45	24	two	two	NUM
ejpam-4655	45	25	generalized	generalized	ADJ
ejpam-4655	45	26	topologies	topology	NOUN
ejpam-4655	45	27	defined	define	VERB
ejpam-4655	45	28	on	on	ADP
ejpam-4655	45	29	a	a	DET
ejpam-4655	45	30	non	non	ADJ
ejpam-4655	45	31	-	-	ADJ
ejpam-4655	45	32	null	null	ADJ
ejpam-4655	45	33	set	set	NOUN
ejpam-4655	45	34	x.	x.	NOUN
ejpam-4655	45	35	then	then	ADV
ejpam-4655	45	36	the	the	DET
ejpam-4655	45	37	triple	triple	ADJ
ejpam-4655	45	38	(	(	PUNCT
ejpam-4655	45	39	x,µ1	x,µ1	NOUN
ejpam-4655	45	40	,	,	PUNCT
ejpam-4655	45	41	µ2	µ2	PROPN
ejpam-4655	45	42	)	)	PUNCT
ejpam-4655	45	43	is	be	AUX
ejpam-4655	45	44	called	call	VERB
ejpam-4655	45	45	as	as	ADP
ejpam-4655	45	46	bigeneralized	bigeneralize	VERB
ejpam-4655	45	47	topological	topological	ADJ
ejpam-4655	45	48	space	space	NOUN
ejpam-4655	45	49	(	(	PUNCT
ejpam-4655	45	50	briefly	briefly	ADV
ejpam-4655	45	51	,	,	PUNCT
ejpam-4655	45	52	bgts	bgts	PROPN
ejpam-4655	45	53	)	)	PUNCT
ejpam-4655	46	1	[	[	X
ejpam-4655	46	2	5	5	NUM
ejpam-4655	46	3	]	]	PUNCT
ejpam-4655	46	4	.	.	PUNCT
ejpam-4655	47	1	let	let	VERB
ejpam-4655	47	2	q	q	PART
ejpam-4655	47	3	be	be	AUX
ejpam-4655	47	4	a	a	DET
ejpam-4655	47	5	subset	subset	NOUN
ejpam-4655	47	6	of	of	ADP
ejpam-4655	47	7	a	a	DET
ejpam-4655	47	8	bgts	bgts	NOUN
ejpam-4655	47	9	(	(	PUNCT
ejpam-4655	47	10	x,µ1	x,µ1	PROPN
ejpam-4655	47	11	,	,	PUNCT
ejpam-4655	47	12	µ2	µ2	PROPN
ejpam-4655	47	13	)	)	PUNCT
ejpam-4655	47	14	.	.	PUNCT
ejpam-4655	48	1	then	then	ADV
ejpam-4655	48	2	the	the	DET
ejpam-4655	48	3	closure	closure	NOUN
ejpam-4655	48	4	of	of	ADP
ejpam-4655	48	5	d	d	PROPN
ejpam-4655	48	6	and	and	CCONJ
ejpam-4655	48	7	the	the	DET
ejpam-4655	48	8	interior	interior	NOUN
ejpam-4655	48	9	of	of	ADP
ejpam-4655	48	10	d	d	PROPN
ejpam-4655	48	11	with	with	ADP
ejpam-4655	48	12	respect	respect	NOUN
ejpam-4655	48	13	to	to	ADP
ejpam-4655	48	14	µs	µs	NOUN
ejpam-4655	48	15	are	be	AUX
ejpam-4655	48	16	denoted	denote	VERB
ejpam-4655	48	17	by	by	ADP
ejpam-4655	48	18	cs(d	cs(d	PUNCT
ejpam-4655	48	19	)	)	PUNCT
ejpam-4655	48	20	and	and	CCONJ
ejpam-4655	48	21	is(d	is(d	PROPN
ejpam-4655	48	22	)	)	PUNCT
ejpam-4655	48	23	,	,	PUNCT
ejpam-4655	48	24	respectively	respectively	ADV
ejpam-4655	48	25	,	,	PUNCT
ejpam-4655	48	26	for	for	ADP
ejpam-4655	48	27	s	s	NOUN
ejpam-4655	48	28	=	=	SYM
ejpam-4655	48	29	1	1	NUM
ejpam-4655	48	30	,	,	PUNCT
ejpam-4655	48	31	2	2	NUM
ejpam-4655	48	32	[	[	X
ejpam-4655	48	33	5	5	NUM
ejpam-4655	48	34	]	]	PUNCT
ejpam-4655	48	35	.	.	PUNCT
ejpam-4655	49	1	a	a	DET
ejpam-4655	49	2	subset	subset	NOUN
ejpam-4655	49	3	q	q	NOUN
ejpam-4655	49	4	of	of	ADP
ejpam-4655	49	5	a	a	DET
ejpam-4655	49	6	bgts	bgts	NOUN
ejpam-4655	49	7	(	(	PUNCT
ejpam-4655	49	8	x,µ1	x,µ1	PROPN
ejpam-4655	49	9	,	,	PUNCT
ejpam-4655	49	10	µ2	µ2	PROPN
ejpam-4655	49	11	)	)	PUNCT
ejpam-4655	49	12	is	be	AUX
ejpam-4655	49	13	called	call	VERB
ejpam-4655	49	14	(	(	PUNCT
ejpam-4655	49	15	s	s	PROPN
ejpam-4655	49	16	,	,	PUNCT
ejpam-4655	49	17	v)-closed	v)-close	VERB
ejpam-4655	49	18	if	if	SCONJ
ejpam-4655	49	19	cs(cv(q	cs(cv(q	NOUN
ejpam-4655	49	20	)	)	PUNCT
ejpam-4655	49	21	)	)	PUNCT
ejpam-4655	50	1	=	=	PUNCT
ejpam-4655	51	1	q	q	X
ejpam-4655	51	2	,	,	PUNCT
ejpam-4655	51	3	where	where	SCONJ
ejpam-4655	51	4	s	s	X
ejpam-4655	51	5	,	,	PUNCT
ejpam-4655	51	6	v	v	NOUN
ejpam-4655	51	7	=	=	SYM
ejpam-4655	51	8	1	1	NUM
ejpam-4655	51	9	or	or	CCONJ
ejpam-4655	51	10	2	2	NUM
ejpam-4655	51	11	;	;	PUNCT
ejpam-4655	51	12	s	s	VERB
ejpam-4655	51	13	̸=	̸=	PROPN
ejpam-4655	51	14	v.	v.	ADP
ejpam-4655	51	15	if	if	SCONJ
ejpam-4655	51	16	x	x	PRON
ejpam-4655	51	17	−	−	PROPN
ejpam-4655	51	18	j	j	PROPN
ejpam-4655	51	19	is	be	AUX
ejpam-4655	51	20	(	(	PUNCT
ejpam-4655	51	21	s	s	X
ejpam-4655	51	22	,	,	PUNCT
ejpam-4655	51	23	v)-closed	v)-close	VERB
ejpam-4655	51	24	,	,	PUNCT
ejpam-4655	51	25	then	then	ADV
ejpam-4655	51	26	j	j	PROPN
ejpam-4655	51	27	is	be	AUX
ejpam-4655	51	28	called	call	VERB
ejpam-4655	51	29	as	as	ADP
ejpam-4655	51	30	(	(	PUNCT
ejpam-4655	51	31	s	s	X
ejpam-4655	51	32	,	,	PUNCT
ejpam-4655	51	33	v)-open	v)-open	VERB
ejpam-4655	51	34	where	where	SCONJ
ejpam-4655	51	35	s	s	X
ejpam-4655	51	36	,	,	PUNCT
ejpam-4655	51	37	v	v	NOUN
ejpam-4655	51	38	=	=	SYM
ejpam-4655	51	39	1	1	NUM
ejpam-4655	51	40	or	or	CCONJ
ejpam-4655	51	41	2	2	NUM
ejpam-4655	51	42	;	;	PUNCT
ejpam-4655	51	43	s	s	VERB
ejpam-4655	51	44	̸=	̸=	PROPN
ejpam-4655	51	45	v	v	NOUN
ejpam-4655	51	46	[	[	X
ejpam-4655	51	47	5	5	NUM
ejpam-4655	51	48	]	]	PUNCT
ejpam-4655	51	49	.	.	PUNCT
ejpam-4655	52	1	let	let	VERB
ejpam-4655	52	2	(	(	PUNCT
ejpam-4655	52	3	x,µ	x,µ	NOUN
ejpam-4655	52	4	)	)	PUNCT
ejpam-4655	52	5	and	and	CCONJ
ejpam-4655	52	6	(	(	PUNCT
ejpam-4655	52	7	y	y	PROPN
ejpam-4655	52	8	,	,	PUNCT
ejpam-4655	52	9	η	η	NOUN
ejpam-4655	52	10	)	)	PUNCT
ejpam-4655	52	11	be	be	VERB
ejpam-4655	52	12	two	two	NUM
ejpam-4655	52	13	gtss	gtss	NOUN
ejpam-4655	52	14	.	.	PUNCT
ejpam-4655	53	1	a	a	DET
ejpam-4655	53	2	function	function	NOUN
ejpam-4655	53	3	h	h	NOUN
ejpam-4655	53	4	:	:	PUNCT
ejpam-4655	53	5	(	(	PUNCT
ejpam-4655	53	6	x,µ	x,µ	NOUN
ejpam-4655	53	7	)	)	PUNCT
ejpam-4655	53	8	→	→	SYM
ejpam-4655	53	9	(	(	PUNCT
ejpam-4655	53	10	y	y	PROPN
ejpam-4655	53	11	,	,	PUNCT
ejpam-4655	53	12	η	η	NOUN
ejpam-4655	53	13	)	)	PUNCT
ejpam-4655	53	14	is	be	AUX
ejpam-4655	53	15	called	call	VERB
ejpam-4655	53	16	as	as	ADP
ejpam-4655	53	17	;	;	PUNCT
ejpam-4655	53	18	•	•	X
ejpam-4655	53	19	(	(	PUNCT
ejpam-4655	53	20	µ	µ	NOUN
ejpam-4655	53	21	,	,	PUNCT
ejpam-4655	53	22	η)-continuous	η)-continuous	ADJ
ejpam-4655	53	23	[	[	X
ejpam-4655	53	24	6	6	NUM
ejpam-4655	53	25	]	]	PUNCT
ejpam-4655	53	26	if	if	SCONJ
ejpam-4655	53	27	h−1(q	h−1(q	PROPN
ejpam-4655	53	28	)	)	PUNCT
ejpam-4655	53	29	∈	∈	PROPN
ejpam-4655	53	30	µ	µ	PROPN
ejpam-4655	53	31	for	for	ADP
ejpam-4655	53	32	each	each	DET
ejpam-4655	53	33	q	q	PROPN
ejpam-4655	53	34	∈	∈	PROPN
ejpam-4655	53	35	η	η	PROPN
ejpam-4655	53	36	.	.	PROPN
ejpam-4655	53	37	•	•	PROPN
ejpam-4655	53	38	(	(	PUNCT
ejpam-4655	53	39	µ	µ	NOUN
ejpam-4655	53	40	,	,	PUNCT
ejpam-4655	53	41	η)-open	η)-open	VERB
ejpam-4655	53	42	[	[	X
ejpam-4655	53	43	12	12	NUM
ejpam-4655	53	44	]	]	X
ejpam-4655	53	45	if	if	SCONJ
ejpam-4655	53	46	h(q	h(q	ADV
ejpam-4655	53	47	)	)	PUNCT
ejpam-4655	53	48	∈	∈	PROPN
ejpam-4655	53	49	η	η	PROPN
ejpam-4655	53	50	for	for	ADP
ejpam-4655	53	51	each	each	DET
ejpam-4655	53	52	q	q	PROPN
ejpam-4655	53	53	∈	∈	PROPN
ejpam-4655	53	54	µ.	µ.	NOUN
ejpam-4655	53	55	lemma	lemma	PROPN
ejpam-4655	53	56	1	1	NUM
ejpam-4655	53	57	.	.	PUNCT
ejpam-4655	54	1	[	[	X
ejpam-4655	54	2	19	19	NUM
ejpam-4655	54	3	,	,	PUNCT
ejpam-4655	54	4	lemma	lemma	PROPN
ejpam-4655	54	5	2.6	2.6	NUM
ejpam-4655	54	6	]	]	PUNCT
ejpam-4655	54	7	let	let	VERB
ejpam-4655	54	8	(	(	PUNCT
ejpam-4655	54	9	x,µ	x,µ	NOUN
ejpam-4655	54	10	)	)	PUNCT
ejpam-4655	54	11	be	be	VERB
ejpam-4655	54	12	a	a	DET
ejpam-4655	54	13	gts	gts	NOUN
ejpam-4655	54	14	and	and	CCONJ
ejpam-4655	54	15	q	q	NOUN
ejpam-4655	54	16	⊂	⊂	PROPN
ejpam-4655	54	17	x.	x.	NOUN
ejpam-4655	55	1	then	then	ADV
ejpam-4655	55	2	iµ(cµ(q))−q	iµ(cµ(q))−q	NUM
ejpam-4655	55	3	=	=	PUNCT
ejpam-4655	55	4	∅.	∅.	PRON
ejpam-4655	55	5	lemma	lemma	PROPN
ejpam-4655	55	6	2	2	NUM
ejpam-4655	55	7	.	.	PUNCT
ejpam-4655	56	1	[	[	X
ejpam-4655	56	2	7	7	X
ejpam-4655	56	3	]	]	PUNCT
ejpam-4655	56	4	a	a	DET
ejpam-4655	56	5	mapping	mapping	NOUN
ejpam-4655	56	6	h	h	NOUN
ejpam-4655	56	7	:	:	PUNCT
ejpam-4655	56	8	(	(	PUNCT
ejpam-4655	56	9	x,µ	x,µ	NOUN
ejpam-4655	56	10	)	)	PUNCT
ejpam-4655	56	11	→	→	SYM
ejpam-4655	56	12	(	(	PUNCT
ejpam-4655	56	13	y	y	PROPN
ejpam-4655	56	14	,	,	PUNCT
ejpam-4655	56	15	η	η	PROPN
ejpam-4655	56	16	)	)	PUNCT
ejpam-4655	56	17	is	be	AUX
ejpam-4655	56	18	(	(	PUNCT
ejpam-4655	56	19	µ	µ	NUM
ejpam-4655	56	20	,	,	PUNCT
ejpam-4655	56	21	η)-continuous	η)-continuous	ADJ
ejpam-4655	56	22	if	if	SCONJ
ejpam-4655	56	23	and	and	CCONJ
ejpam-4655	56	24	only	only	ADV
ejpam-4655	56	25	if	if	SCONJ
ejpam-4655	56	26	c(h−1(q	c(h−1(q	PROPN
ejpam-4655	56	27	)	)	PUNCT
ejpam-4655	56	28	)	)	PUNCT
ejpam-4655	57	1	⊂	⊂	PROPN
ejpam-4655	57	2	h−1(cq	h−1(cq	PROPN
ejpam-4655	57	3	)	)	PUNCT
ejpam-4655	57	4	for	for	ADP
ejpam-4655	57	5	any	any	DET
ejpam-4655	57	6	q	q	X
ejpam-4655	57	7	⊂	⊂	PROPN
ejpam-4655	57	8	y.	y.	PROPN
ejpam-4655	57	9	lemma	lemma	PROPN
ejpam-4655	58	1	3	3	X
ejpam-4655	58	2	.	.	PUNCT
ejpam-4655	59	1	[	[	X
ejpam-4655	59	2	20	20	NUM
ejpam-4655	59	3	,	,	PUNCT
ejpam-4655	59	4	lemma	lemma	PROPN
ejpam-4655	59	5	7.3	7.3	NUM
ejpam-4655	59	6	]	]	PUNCT
ejpam-4655	59	7	a	a	DET
ejpam-4655	59	8	mapping	mapping	NOUN
ejpam-4655	59	9	h	h	NOUN
ejpam-4655	59	10	:	:	PUNCT
ejpam-4655	59	11	(	(	PUNCT
ejpam-4655	59	12	x,µ	x,µ	NOUN
ejpam-4655	59	13	)	)	PUNCT
ejpam-4655	59	14	→	→	SYM
ejpam-4655	59	15	(	(	PUNCT
ejpam-4655	59	16	y	y	PROPN
ejpam-4655	59	17	,	,	PUNCT
ejpam-4655	59	18	η	η	PROPN
ejpam-4655	59	19	)	)	PUNCT
ejpam-4655	59	20	is	be	AUX
ejpam-4655	59	21	(	(	PUNCT
ejpam-4655	59	22	µ	µ	NOUN
ejpam-4655	59	23	,	,	PUNCT
ejpam-4655	59	24	η)-open	η)-open	VERB
ejpam-4655	59	25	if	if	SCONJ
ejpam-4655	59	26	and	and	CCONJ
ejpam-4655	59	27	only	only	ADV
ejpam-4655	59	28	if	if	SCONJ
ejpam-4655	59	29	h−1(cq	h−1(cq	NOUN
ejpam-4655	59	30	)	)	PUNCT
ejpam-4655	59	31	⊂	⊂	PROPN
ejpam-4655	59	32	ch−1(q	ch−1(q	PROPN
ejpam-4655	59	33	)	)	PUNCT
ejpam-4655	59	34	for	for	ADP
ejpam-4655	59	35	any	any	DET
ejpam-4655	59	36	q	q	X
ejpam-4655	59	37	⊂	⊂	PROPN
ejpam-4655	59	38	y.	y.	NOUN
ejpam-4655	59	39	3	3	NUM
ejpam-4655	59	40	.	.	PUNCT
ejpam-4655	60	1	(	(	PUNCT
ejpam-4655	60	2	s	s	PROPN
ejpam-4655	60	3	,	,	PUNCT
ejpam-4655	60	4	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	60	5	submaximal	submaximal	ADJ
ejpam-4655	60	6	space	space	NOUN
ejpam-4655	60	7	previously	previously	ADV
ejpam-4655	60	8	,	,	PUNCT
ejpam-4655	60	9	few	few	ADJ
ejpam-4655	60	10	debilitated	debilitate	VERB
ejpam-4655	60	11	forms	form	NOUN
ejpam-4655	60	12	of	of	ADP
ejpam-4655	60	13	open	open	ADJ
ejpam-4655	60	14	sets	set	NOUN
ejpam-4655	60	15	are	be	AUX
ejpam-4655	60	16	studied	study	VERB
ejpam-4655	60	17	.	.	PUNCT
ejpam-4655	61	1	császár	császár	PROPN
ejpam-4655	61	2	was	be	AUX
ejpam-4655	61	3	introduced	introduce	VERB
ejpam-4655	61	4	and	and	CCONJ
ejpam-4655	61	5	studied	study	VERB
ejpam-4655	61	6	some	some	DET
ejpam-4655	61	7	new	new	ADJ
ejpam-4655	61	8	open	open	ADJ
ejpam-4655	61	9	sets	set	NOUN
ejpam-4655	61	10	,	,	PUNCT
ejpam-4655	61	11	namely	namely	ADV
ejpam-4655	61	12	,	,	PUNCT
ejpam-4655	61	13	semi	semi	ADJ
ejpam-4655	61	14	-	-	ADJ
ejpam-4655	61	15	open	open	ADJ
ejpam-4655	61	16	,	,	PUNCT
ejpam-4655	61	17	pre	pre	ADJ
ejpam-4655	61	18	-	-	ADJ
ejpam-4655	61	19	open	open	ADJ
ejpam-4655	61	20	,	,	PUNCT
ejpam-4655	61	21	etc	etc	X
ejpam-4655	61	22	....	....	X
ejpam-4655	61	23	in	in	ADP
ejpam-4655	61	24	[	[	X
ejpam-4655	61	25	2	2	NUM
ejpam-4655	61	26	,	,	PUNCT
ejpam-4655	61	27	3	3	NUM
ejpam-4655	61	28	,	,	PUNCT
ejpam-4655	61	29	6	6	NUM
ejpam-4655	61	30	]	]	PUNCT
ejpam-4655	61	31	.	.	PUNCT
ejpam-4655	62	1	using	use	VERB
ejpam-4655	62	2	these	these	DET
ejpam-4655	62	3	tools	tool	NOUN
ejpam-4655	62	4	,	,	PUNCT
ejpam-4655	62	5	the	the	DET
ejpam-4655	62	6	necessary	necessary	ADJ
ejpam-4655	62	7	condition	condition	NOUN
ejpam-4655	62	8	for	for	ADP
ejpam-4655	62	9	a	a	DET
ejpam-4655	62	10	bgts	bgts	NOUN
ejpam-4655	62	11	is	be	AUX
ejpam-4655	62	12	a	a	DET
ejpam-4655	62	13	(	(	PUNCT
ejpam-4655	62	14	s	s	PROPN
ejpam-4655	62	15	,	,	PUNCT
ejpam-4655	62	16	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	62	17	submaximal	submaximal	ADJ
ejpam-4655	62	18	space	space	NOUN
ejpam-4655	62	19	is	be	AUX
ejpam-4655	62	20	proved	prove	VERB
ejpam-4655	62	21	.	.	PUNCT
ejpam-4655	63	1	in	in	ADP
ejpam-4655	63	2	this	this	DET
ejpam-4655	63	3	section	section	NOUN
ejpam-4655	63	4	,	,	PUNCT
ejpam-4655	63	5	some	some	DET
ejpam-4655	63	6	shortcuts	shortcut	NOUN
ejpam-4655	63	7	for	for	ADP
ejpam-4655	63	8	examining	examine	VERB
ejpam-4655	63	9	whether	whether	SCONJ
ejpam-4655	63	10	a	a	DET
ejpam-4655	63	11	bigeneralized	bigeneralize	VERB
ejpam-4655	63	12	topological	topological	ADJ
ejpam-4655	63	13	space	space	NOUN
ejpam-4655	63	14	is	be	AUX
ejpam-4655	63	15	(	(	PUNCT
ejpam-4655	63	16	s	s	PROPN
ejpam-4655	63	17	,	,	PUNCT
ejpam-4655	63	18	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	63	19	submaximal	submaximal	ADJ
ejpam-4655	63	20	space	space	NOUN
ejpam-4655	63	21	or	or	CCONJ
ejpam-4655	63	22	not	not	PART
ejpam-4655	63	23	are	be	AUX
ejpam-4655	63	24	given	give	VERB
ejpam-4655	63	25	.	.	PUNCT
ejpam-4655	64	1	in	in	ADP
ejpam-4655	64	2	a	a	DET
ejpam-4655	64	3	(	(	PUNCT
ejpam-4655	64	4	s	s	PROPN
ejpam-4655	64	5	,	,	PUNCT
ejpam-4655	64	6	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	64	7	submaximal	submaximal	ADJ
ejpam-4655	64	8	space	space	NOUN
ejpam-4655	64	9	,	,	PUNCT
ejpam-4655	64	10	we	we	PRON
ejpam-4655	64	11	prove	prove	VERB
ejpam-4655	64	12	some	some	DET
ejpam-4655	64	13	easier	easy	ADJ
ejpam-4655	64	14	way	way	NOUN
ejpam-4655	64	15	to	to	PART
ejpam-4655	64	16	check	check	VERB
ejpam-4655	64	17	whether	whether	SCONJ
ejpam-4655	64	18	the	the	DET
ejpam-4655	64	19	given	give	VERB
ejpam-4655	64	20	set	set	NOUN
ejpam-4655	64	21	is	be	AUX
ejpam-4655	64	22	nowhere	nowhere	ADV
ejpam-4655	64	23	dense	dense	ADJ
ejpam-4655	64	24	or	or	CCONJ
ejpam-4655	64	25	not	not	PART
ejpam-4655	64	26	.	.	PUNCT
ejpam-4655	65	1	we	we	PRON
ejpam-4655	65	2	begin	begin	VERB
ejpam-4655	65	3	by	by	ADP
ejpam-4655	65	4	remembering	remember	VERB
ejpam-4655	65	5	some	some	DET
ejpam-4655	65	6	needed	needed	ADJ
ejpam-4655	65	7	definitions	definition	NOUN
ejpam-4655	65	8	.	.	PUNCT
ejpam-4655	66	1	in	in	ADP
ejpam-4655	66	2	[	[	X
ejpam-4655	66	3	3	3	NUM
ejpam-4655	66	4	]	]	PUNCT
ejpam-4655	66	5	,	,	PUNCT
ejpam-4655	66	6	let	let	VERB
ejpam-4655	66	7	(	(	PUNCT
ejpam-4655	66	8	x,µ	x,µ	NOUN
ejpam-4655	66	9	)	)	PUNCT
ejpam-4655	66	10	be	be	VERB
ejpam-4655	66	11	a	a	DET
ejpam-4655	66	12	gts	gts	NOUN
ejpam-4655	66	13	and	and	CCONJ
ejpam-4655	66	14	q	q	NOUN
ejpam-4655	66	15	⊂	⊂	PROPN
ejpam-4655	66	16	x	x	X
ejpam-4655	66	17	is	be	AUX
ejpam-4655	66	18	called	call	VERB
ejpam-4655	66	19	as	as	ADP
ejpam-4655	66	20	;	;	PUNCT
ejpam-4655	66	21	i	i	PROPN
ejpam-4655	66	22	)	)	PUNCT
ejpam-4655	66	23	.	.	PUNCT
ejpam-4655	67	1	µ-semi	µ-semi	NOUN
ejpam-4655	67	2	-	-	ADJ
ejpam-4655	67	3	open	open	ADJ
ejpam-4655	67	4	if	if	SCONJ
ejpam-4655	67	5	q	q	X
ejpam-4655	67	6	⊂	⊂	PROPN
ejpam-4655	67	7	cµ(iµ(q	cµ(iµ(q	PROPN
ejpam-4655	67	8	)	)	PUNCT
ejpam-4655	67	9	)	)	PUNCT
ejpam-4655	67	10	.	.	PUNCT
ejpam-4655	68	1	ii	ii	PROPN
ejpam-4655	68	2	)	)	PUNCT
ejpam-4655	68	3	.	.	PUNCT
ejpam-4655	69	1	µ-pre	µ-pre	X
ejpam-4655	69	2	-	-	PUNCT
ejpam-4655	69	3	open	open	ADJ
ejpam-4655	69	4	if	if	SCONJ
ejpam-4655	69	5	q	q	X
ejpam-4655	69	6	⊂	⊂	PROPN
ejpam-4655	69	7	iµ(cµ(q	iµ(cµ(q	NUM
ejpam-4655	69	8	)	)	PUNCT
ejpam-4655	69	9	)	)	PUNCT
ejpam-4655	69	10	.	.	PUNCT
ejpam-4655	70	1	iii	iii	X
ejpam-4655	70	2	)	)	PUNCT
ejpam-4655	70	3	.	.	PUNCT
ejpam-4655	71	1	µ-α	µ-α	X
ejpam-4655	71	2	-	-	PUNCT
ejpam-4655	71	3	open	open	ADJ
ejpam-4655	71	4	if	if	SCONJ
ejpam-4655	71	5	q	q	X
ejpam-4655	71	6	⊂	⊂	PROPN
ejpam-4655	71	7	iµ(cµ(iµ(q	iµ(cµ(iµ(q	NOUN
ejpam-4655	71	8	)	)	PUNCT
ejpam-4655	71	9	)	)	PUNCT
ejpam-4655	71	10	)	)	PUNCT
ejpam-4655	71	11	.	.	PUNCT
ejpam-4655	72	1	iv	iv	X
ejpam-4655	72	2	)	)	PUNCT
ejpam-4655	72	3	.	.	PUNCT
ejpam-4655	73	1	µ-β	µ-β	ADV
ejpam-4655	73	2	-	-	PUNCT
ejpam-4655	73	3	open	open	ADJ
ejpam-4655	73	4	if	if	SCONJ
ejpam-4655	73	5	q	q	X
ejpam-4655	73	6	⊂	⊂	X
ejpam-4655	73	7	cµ(iµ(cµ(q	cµ(iµ(cµ(q	ADJ
ejpam-4655	73	8	)	)	PUNCT
ejpam-4655	73	9	)	)	PUNCT
ejpam-4655	73	10	)	)	PUNCT
ejpam-4655	73	11	.	.	PUNCT
ejpam-4655	74	1	v	v	X
ejpam-4655	74	2	)	)	PUNCT
ejpam-4655	74	3	.	.	PUNCT
ejpam-4655	75	1	µ-b	µ-b	VERB
ejpam-4655	75	2	-	-	PUNCT
ejpam-4655	75	3	open	open	ADJ
ejpam-4655	75	4	[	[	X
ejpam-4655	75	5	4	4	NUM
ejpam-4655	75	6	]	]	X
ejpam-4655	75	7	if	if	SCONJ
ejpam-4655	75	8	q	q	PROPN
ejpam-4655	75	9	⊂	⊂	PROPN
ejpam-4655	75	10	cµ(iµ(q	cµ(iµ(q	PROPN
ejpam-4655	75	11	)	)	PUNCT
ejpam-4655	75	12	)	)	PUNCT
ejpam-4655	75	13	∪	∪	ADP
ejpam-4655	75	14	iµ(cµ(q	iµ(cµ(q	NOUN
ejpam-4655	75	15	)	)	PUNCT
ejpam-4655	75	16	)	)	PUNCT
ejpam-4655	75	17	.	.	PUNCT
ejpam-4655	76	1	let	let	VERB
ejpam-4655	76	2	q	q	PRON
ejpam-4655	76	3	be	be	AUX
ejpam-4655	76	4	a	a	DET
ejpam-4655	76	5	subset	subset	NOUN
ejpam-4655	76	6	of	of	ADP
ejpam-4655	76	7	a	a	DET
ejpam-4655	76	8	gts	gts	NOUN
ejpam-4655	76	9	(	(	PUNCT
ejpam-4655	76	10	x,µ	x,µ	NOUN
ejpam-4655	76	11	)	)	PUNCT
ejpam-4655	76	12	.	.	PUNCT
ejpam-4655	77	1	then	then	ADV
ejpam-4655	77	2	frontier	frontier	NOUN
ejpam-4655	77	3	of	of	ADP
ejpam-4655	77	4	q	q	NOUN
ejpam-4655	78	1	[	[	X
ejpam-4655	78	2	15	15	NUM
ejpam-4655	78	3	]	]	PUNCT
ejpam-4655	78	4	is	be	AUX
ejpam-4655	78	5	denoted	denote	VERB
ejpam-4655	78	6	by	by	ADP
ejpam-4655	78	7	frµ(q	frµ(q	PROPN
ejpam-4655	78	8	)	)	PUNCT
ejpam-4655	78	9	and	and	CCONJ
ejpam-4655	78	10	defined	define	VERB
ejpam-4655	78	11	by	by	ADP
ejpam-4655	78	12	frµ(q	frµ(q	PROPN
ejpam-4655	78	13	)	)	PUNCT
ejpam-4655	78	14	=	=	NOUN
ejpam-4655	78	15	cµq	cµq	NOUN
ejpam-4655	78	16	∩	∩	NOUN
ejpam-4655	78	17	cµ(x	cµ(x	NOUN
ejpam-4655	78	18	−q	−q	NOUN
ejpam-4655	78	19	)	)	PUNCT
ejpam-4655	78	20	.	.	PUNCT
ejpam-4655	79	1	a	a	DET
ejpam-4655	79	2	subset	subset	NOUN
ejpam-4655	79	3	q	q	NOUN
ejpam-4655	79	4	of	of	ADP
ejpam-4655	79	5	a	a	DET
ejpam-4655	79	6	bgts	bgts	NOUN
ejpam-4655	79	7	(	(	PUNCT
ejpam-4655	79	8	x,µ1	x,µ1	PROPN
ejpam-4655	79	9	,	,	PUNCT
ejpam-4655	79	10	µ2	µ2	PROPN
ejpam-4655	79	11	)	)	PUNCT
ejpam-4655	79	12	is	be	AUX
ejpam-4655	79	13	said	say	VERB
ejpam-4655	79	14	to	to	PART
ejpam-4655	79	15	be	be	AUX
ejpam-4655	79	16	(	(	PUNCT
ejpam-4655	79	17	s	s	X
ejpam-4655	79	18	,	,	PUNCT
ejpam-4655	79	19	v)-nowhere	v)-nowhere	PUNCT
ejpam-4655	79	20	dense	dense	ADJ
ejpam-4655	79	21	[	[	X
ejpam-4655	79	22	1	1	NUM
ejpam-4655	79	23	]	]	X
ejpam-4655	79	24	set	set	VERB
ejpam-4655	79	25	in	in	ADP
ejpam-4655	79	26	x	x	PUNCT
ejpam-4655	79	27	if	if	SCONJ
ejpam-4655	79	28	is(cv(q	is(cv(q	NOUN
ejpam-4655	79	29	)	)	PUNCT
ejpam-4655	79	30	)	)	PUNCT
ejpam-4655	80	1	=	=	NOUN
ejpam-4655	80	2	∅	∅	NOUN
ejpam-4655	80	3	where	where	SCONJ
ejpam-4655	80	4	s	s	X
ejpam-4655	80	5	,	,	PUNCT
ejpam-4655	80	6	v	v	NOUN
ejpam-4655	80	7	=	=	SYM
ejpam-4655	80	8	1	1	NUM
ejpam-4655	80	9	,	,	PUNCT
ejpam-4655	80	10	2	2	NUM
ejpam-4655	80	11	and	and	CCONJ
ejpam-4655	80	12	s	s	VERB
ejpam-4655	80	13	̸=	̸=	PROPN
ejpam-4655	80	14	v.	v.	CCONJ
ejpam-4655	80	15	we	we	PRON
ejpam-4655	80	16	denoted	denote	VERB
ejpam-4655	80	17	by	by	ADP
ejpam-4655	80	18	,	,	PUNCT
ejpam-4655	80	19	(	(	PUNCT
ejpam-4655	80	20	s	s	X
ejpam-4655	80	21	,	,	PUNCT
ejpam-4655	80	22	v)−n	v)−n	X
ejpam-4655	80	23	(	(	PUNCT
ejpam-4655	80	24	x	x	X
ejpam-4655	80	25	)	)	PUNCT
ejpam-4655	80	26	=	=	PRON
ejpam-4655	80	27	{	{	PUNCT
ejpam-4655	80	28	q	q	X
ejpam-4655	80	29	⊂	⊂	X
ejpam-4655	80	30	x	x	PUNCT
ejpam-4655	81	1	|	|	ADV
ejpam-4655	81	2	q	q	NOUN
ejpam-4655	81	3	is	be	AUX
ejpam-4655	81	4	a	a	DET
ejpam-4655	81	5	(	(	PUNCT
ejpam-4655	81	6	s	s	X
ejpam-4655	81	7	,	,	PUNCT
ejpam-4655	81	8	v)-nowhere	v)-nowhere	PUNCT
ejpam-4655	81	9	dense	dense	ADJ
ejpam-4655	81	10	set	set	NOUN
ejpam-4655	81	11	in	in	ADP
ejpam-4655	81	12	x	x	NOUN
ejpam-4655	81	13	}	}	PUNCT
ejpam-4655	81	14	where	where	SCONJ
ejpam-4655	81	15	s	s	X
ejpam-4655	81	16	,	,	PUNCT
ejpam-4655	81	17	v	v	NOUN
ejpam-4655	81	18	=	=	SYM
ejpam-4655	81	19	1	1	NUM
ejpam-4655	81	20	,	,	PUNCT
ejpam-4655	81	21	2	2	NUM
ejpam-4655	81	22	;	;	PUNCT
ejpam-4655	81	23	s	s	VERB
ejpam-4655	81	24	̸=	̸=	PROPN
ejpam-4655	81	25	v	v	NOUN
ejpam-4655	81	26	[	[	X
ejpam-4655	81	27	16	16	NUM
ejpam-4655	81	28	]	]	PUNCT
ejpam-4655	81	29	.	.	PUNCT
ejpam-4655	82	1	y.	y.	PROPN
ejpam-4655	82	2	farhat	farhat	PROPN
ejpam-4655	82	3	et	et	PROPN
ejpam-4655	82	4	al	al	PROPN
ejpam-4655	82	5	.	.	PUNCT
ejpam-4655	82	6	/	/	SYM
ejpam-4655	82	7	eur	eur	PROPN
ejpam-4655	82	8	.	.	PUNCT
ejpam-4655	83	1	j.	j.	PROPN
ejpam-4655	83	2	pure	pure	PROPN
ejpam-4655	83	3	appl	appl	PROPN
ejpam-4655	83	4	.	.	PROPN
ejpam-4655	83	5	math	math	PROPN
ejpam-4655	83	6	,	,	PUNCT
ejpam-4655	83	7	16	16	NUM
ejpam-4655	83	8	(	(	PUNCT
ejpam-4655	83	9	1	1	NUM
ejpam-4655	83	10	)	)	PUNCT
ejpam-4655	83	11	(	(	PUNCT
ejpam-4655	83	12	2023	2023	NUM
ejpam-4655	83	13	)	)	PUNCT
ejpam-4655	83	14	,	,	PUNCT
ejpam-4655	83	15	386	386	NUM
ejpam-4655	83	16	-	-	SYM
ejpam-4655	83	17	403	403	NUM
ejpam-4655	83	18	389	389	NUM
ejpam-4655	83	19	a	a	DET
ejpam-4655	83	20	subset	subset	NOUN
ejpam-4655	83	21	q	q	NOUN
ejpam-4655	83	22	of	of	ADP
ejpam-4655	83	23	a	a	DET
ejpam-4655	83	24	bgts	bgts	NOUN
ejpam-4655	83	25	(	(	PUNCT
ejpam-4655	83	26	x,µ1	x,µ1	PROPN
ejpam-4655	83	27	,	,	PUNCT
ejpam-4655	83	28	µ2	µ2	PROPN
ejpam-4655	83	29	)	)	PUNCT
ejpam-4655	83	30	is	be	AUX
ejpam-4655	83	31	called	call	VERB
ejpam-4655	83	32	(	(	PUNCT
ejpam-4655	83	33	s	s	NOUN
ejpam-4655	83	34	,	,	PUNCT
ejpam-4655	83	35	v)-dense	v)-dense	PUNCT
ejpam-4655	83	36	[	[	X
ejpam-4655	83	37	16	16	NUM
ejpam-4655	83	38	]	]	PUNCT
ejpam-4655	83	39	if	if	SCONJ
ejpam-4655	83	40	cs(cv(q	cs(cv(q	NOUN
ejpam-4655	83	41	)	)	PUNCT
ejpam-4655	83	42	)	)	PUNCT
ejpam-4655	84	1	=	=	PUNCT
ejpam-4655	84	2	x	x	X
ejpam-4655	84	3	,	,	PUNCT
ejpam-4655	84	4	where	where	SCONJ
ejpam-4655	84	5	s	s	X
ejpam-4655	84	6	,	,	PUNCT
ejpam-4655	84	7	v	v	NOUN
ejpam-4655	84	8	=	=	SYM
ejpam-4655	84	9	1	1	NUM
ejpam-4655	84	10	,	,	PUNCT
ejpam-4655	84	11	2	2	NUM
ejpam-4655	84	12	;	;	PUNCT
ejpam-4655	84	13	s	s	AUX
ejpam-4655	84	14	̸=	̸=	PROPN
ejpam-4655	84	15	v.	v.	ADP
ejpam-4655	84	16	notated	notate	VERB
ejpam-4655	84	17	by	by	ADP
ejpam-4655	84	18	,	,	PUNCT
ejpam-4655	84	19	(	(	PUNCT
ejpam-4655	84	20	s	s	X
ejpam-4655	84	21	,	,	PUNCT
ejpam-4655	84	22	v	v	NOUN
ejpam-4655	84	23	)	)	PUNCT
ejpam-4655	84	24	−	−	PROPN
ejpam-4655	84	25	d(x	d(x	NOUN
ejpam-4655	84	26	)	)	PUNCT
ejpam-4655	84	27	=	=	PRON
ejpam-4655	84	28	{	{	PUNCT
ejpam-4655	84	29	q	q	X
ejpam-4655	84	30	⊂	⊂	X
ejpam-4655	84	31	x	x	PUNCT
ejpam-4655	84	32	|	|	ADV
ejpam-4655	84	33	q	q	NOUN
ejpam-4655	84	34	is	be	AUX
ejpam-4655	84	35	a	a	DET
ejpam-4655	84	36	(	(	PUNCT
ejpam-4655	84	37	s	s	NOUN
ejpam-4655	84	38	,	,	PUNCT
ejpam-4655	84	39	v)-dense	v)-dense	NOUN
ejpam-4655	84	40	set	set	VERB
ejpam-4655	84	41	in	in	ADP
ejpam-4655	84	42	x	x	NOUN
ejpam-4655	84	43	}	}	PUNCT
ejpam-4655	84	44	where	where	SCONJ
ejpam-4655	84	45	s	s	X
ejpam-4655	84	46	,	,	PUNCT
ejpam-4655	84	47	v	v	NOUN
ejpam-4655	84	48	=	=	SYM
ejpam-4655	84	49	1	1	NUM
ejpam-4655	84	50	,	,	PUNCT
ejpam-4655	84	51	2	2	NUM
ejpam-4655	84	52	;	;	PUNCT
ejpam-4655	84	53	s	s	VERB
ejpam-4655	84	54	̸=	̸=	PROPN
ejpam-4655	84	55	v	v	NOUN
ejpam-4655	84	56	[	[	X
ejpam-4655	84	57	16	16	NUM
ejpam-4655	84	58	]	]	PUNCT
ejpam-4655	84	59	.	.	PUNCT
ejpam-4655	85	1	definition	definition	NOUN
ejpam-4655	85	2	1	1	NUM
ejpam-4655	85	3	.	.	PUNCT
ejpam-4655	86	1	let	let	AUX
ejpam-4655	86	2	(	(	PUNCT
ejpam-4655	86	3	x,µ1	x,µ1	NOUN
ejpam-4655	86	4	,	,	PUNCT
ejpam-4655	86	5	µ2	µ2	PROPN
ejpam-4655	86	6	)	)	PUNCT
ejpam-4655	86	7	be	be	VERB
ejpam-4655	86	8	a	a	DET
ejpam-4655	86	9	bigeneralized	bigeneralized	ADJ
ejpam-4655	86	10	topological	topological	ADJ
ejpam-4655	86	11	space	space	NOUN
ejpam-4655	86	12	.	.	PUNCT
ejpam-4655	87	1	a	a	DET
ejpam-4655	87	2	space	space	NOUN
ejpam-4655	87	3	x	x	PUNCT
ejpam-4655	87	4	is	be	AUX
ejpam-4655	87	5	called	call	VERB
ejpam-4655	87	6	(	(	PUNCT
ejpam-4655	87	7	µs	µs	X
ejpam-4655	87	8	,	,	PUNCT
ejpam-4655	87	9	µv)-bigeneralized	µv)-bigeneralize	VERB
ejpam-4655	87	10	submaximal	submaximal	ADJ
ejpam-4655	87	11	(	(	PUNCT
ejpam-4655	87	12	briefly	briefly	ADV
ejpam-4655	87	13	,	,	PUNCT
ejpam-4655	87	14	(	(	PUNCT
ejpam-4655	87	15	s	s	X
ejpam-4655	87	16	,	,	PUNCT
ejpam-4655	87	17	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	87	18	submaximal	submaximal	ADJ
ejpam-4655	87	19	)	)	PUNCT
ejpam-4655	87	20	if	if	SCONJ
ejpam-4655	87	21	q	q	X
ejpam-4655	87	22	∈	∈	PROPN
ejpam-4655	87	23	µs	µs	VERB
ejpam-4655	87	24	whenever	whenever	SCONJ
ejpam-4655	87	25	cµv(q	cµv(q	PROPN
ejpam-4655	87	26	)	)	PUNCT
ejpam-4655	87	27	=	=	PUNCT
ejpam-4655	88	1	x	x	X
ejpam-4655	88	2	where	where	SCONJ
ejpam-4655	88	3	s	s	X
ejpam-4655	88	4	,	,	PUNCT
ejpam-4655	88	5	v	v	NOUN
ejpam-4655	88	6	=	=	SYM
ejpam-4655	88	7	1	1	NUM
ejpam-4655	88	8	,	,	PUNCT
ejpam-4655	88	9	2	2	NUM
ejpam-4655	88	10	;	;	PUNCT
ejpam-4655	88	11	s	s	VERB
ejpam-4655	88	12	̸=	̸=	PROPN
ejpam-4655	88	13	v.	v.	ADP
ejpam-4655	88	14	example	example	NOUN
ejpam-4655	88	15	2	2	NUM
ejpam-4655	88	16	.	.	PUNCT
ejpam-4655	88	17	(	(	PUNCT
ejpam-4655	88	18	a	a	X
ejpam-4655	88	19	)	)	PUNCT
ejpam-4655	88	20	.	.	PUNCT
ejpam-4655	89	1	consider	consider	VERB
ejpam-4655	89	2	the	the	DET
ejpam-4655	89	3	bigeneralized	bigeneralized	ADJ
ejpam-4655	89	4	topological	topological	ADJ
ejpam-4655	89	5	space	space	NOUN
ejpam-4655	89	6	(	(	PUNCT
ejpam-4655	89	7	x,µ1	x,µ1	PROPN
ejpam-4655	89	8	,	,	PUNCT
ejpam-4655	89	9	µ2	µ2	PROPN
ejpam-4655	89	10	)	)	PUNCT
ejpam-4655	90	1	where	where	SCONJ
ejpam-4655	90	2	x	x	X
ejpam-4655	90	3	=	=	PRON
ejpam-4655	90	4	{	{	PUNCT
ejpam-4655	90	5	p	p	X
ejpam-4655	90	6	,	,	PUNCT
ejpam-4655	90	7	q	q	ADJ
ejpam-4655	90	8	,	,	PUNCT
ejpam-4655	90	9	r	r	NOUN
ejpam-4655	90	10	,	,	PUNCT
ejpam-4655	90	11	s};µ1	s};µ1	PROPN
ejpam-4655	90	12	=	=	SYM
ejpam-4655	90	13	{	{	PUNCT
ejpam-4655	90	14	∅	∅	NOUN
ejpam-4655	90	15	,	,	PUNCT
ejpam-4655	90	16	{	{	PUNCT
ejpam-4655	90	17	p	p	X
ejpam-4655	90	18	,	,	PUNCT
ejpam-4655	90	19	q	q	NOUN
ejpam-4655	90	20	}	}	PUNCT
ejpam-4655	90	21	,	,	PUNCT
ejpam-4655	90	22	{	{	PUNCT
ejpam-4655	90	23	p	p	X
ejpam-4655	90	24	,	,	PUNCT
ejpam-4655	90	25	s	s	PART
ejpam-4655	90	26	}	}	PUNCT
ejpam-4655	90	27	,	,	PUNCT
ejpam-4655	90	28	{	{	PUNCT
ejpam-4655	90	29	q	q	X
ejpam-4655	90	30	,	,	PUNCT
ejpam-4655	90	31	r	r	NOUN
ejpam-4655	90	32	}	}	PUNCT
ejpam-4655	90	33	,	,	PUNCT
ejpam-4655	90	34	{	{	PUNCT
ejpam-4655	90	35	r	r	NOUN
ejpam-4655	90	36	,	,	PUNCT
ejpam-4655	90	37	s	s	PART
ejpam-4655	90	38	}	}	PUNCT
ejpam-4655	90	39	,	,	PUNCT
ejpam-4655	90	40	{	{	PUNCT
ejpam-4655	90	41	p	p	X
ejpam-4655	90	42	,	,	PUNCT
ejpam-4655	90	43	q	q	ADJ
ejpam-4655	90	44	,	,	PUNCT
ejpam-4655	90	45	r	r	NOUN
ejpam-4655	90	46	}	}	PUNCT
ejpam-4655	90	47	,	,	PUNCT
ejpam-4655	90	48	{	{	PUNCT
ejpam-4655	90	49	p	p	X
ejpam-4655	90	50	,	,	PUNCT
ejpam-4655	90	51	q	q	X
ejpam-4655	90	52	,	,	PUNCT
ejpam-4655	90	53	s	s	PART
ejpam-4655	90	54	}	}	PUNCT
ejpam-4655	90	55	,	,	PUNCT
ejpam-4655	90	56	{	{	PUNCT
ejpam-4655	90	57	p	p	X
ejpam-4655	90	58	,	,	PUNCT
ejpam-4655	90	59	r	r	NOUN
ejpam-4655	90	60	,	,	PUNCT
ejpam-4655	90	61	s	s	PART
ejpam-4655	90	62	}	}	PUNCT
ejpam-4655	90	63	,	,	PUNCT
ejpam-4655	90	64	{	{	PUNCT
ejpam-4655	90	65	q	q	X
ejpam-4655	90	66	,	,	PUNCT
ejpam-4655	90	67	r	r	NOUN
ejpam-4655	90	68	,	,	PUNCT
ejpam-4655	90	69	s	s	PART
ejpam-4655	90	70	}	}	PUNCT
ejpam-4655	90	71	,	,	PUNCT
ejpam-4655	90	72	x	x	NOUN
ejpam-4655	90	73	}	}	PUNCT
ejpam-4655	90	74	and	and	CCONJ
ejpam-4655	90	75	µ2	µ2	PROPN
ejpam-4655	90	76	=	=	PUNCT
ejpam-4655	90	77	{	{	PUNCT
ejpam-4655	90	78	∅	∅	NOUN
ejpam-4655	90	79	,	,	PUNCT
ejpam-4655	90	80	{	{	PUNCT
ejpam-4655	90	81	p	p	X
ejpam-4655	90	82	,	,	PUNCT
ejpam-4655	90	83	r	r	NOUN
ejpam-4655	90	84	}	}	PUNCT
ejpam-4655	90	85	,	,	PUNCT
ejpam-4655	90	86	{	{	PUNCT
ejpam-4655	90	87	q	q	X
ejpam-4655	90	88	,	,	PUNCT
ejpam-4655	90	89	s	s	PART
ejpam-4655	90	90	}	}	PUNCT
ejpam-4655	90	91	,	,	PUNCT
ejpam-4655	90	92	{	{	PUNCT
ejpam-4655	90	93	p	p	X
ejpam-4655	90	94	,	,	PUNCT
ejpam-4655	90	95	r	r	NOUN
ejpam-4655	90	96	,	,	PUNCT
ejpam-4655	90	97	s	s	PART
ejpam-4655	90	98	}	}	PUNCT
ejpam-4655	90	99	,	,	PUNCT
ejpam-4655	90	100	x	x	NOUN
ejpam-4655	90	101	}	}	PUNCT
ejpam-4655	90	102	.	.	PUNCT
ejpam-4655	91	1	then	then	ADV
ejpam-4655	91	2	{	{	PUNCT
ejpam-4655	91	3	p	p	X
ejpam-4655	91	4	,	,	PUNCT
ejpam-4655	91	5	q	q	NOUN
ejpam-4655	91	6	}	}	PUNCT
ejpam-4655	91	7	,	,	PUNCT
ejpam-4655	91	8	{	{	PUNCT
ejpam-4655	91	9	p	p	X
ejpam-4655	91	10	,	,	PUNCT
ejpam-4655	91	11	s	s	PART
ejpam-4655	91	12	}	}	PUNCT
ejpam-4655	91	13	,	,	PUNCT
ejpam-4655	91	14	{	{	PUNCT
ejpam-4655	91	15	q	q	X
ejpam-4655	91	16	,	,	PUNCT
ejpam-4655	91	17	r	r	NOUN
ejpam-4655	91	18	}	}	PUNCT
ejpam-4655	91	19	,	,	PUNCT
ejpam-4655	91	20	{	{	PUNCT
ejpam-4655	91	21	r	r	NOUN
ejpam-4655	91	22	,	,	PUNCT
ejpam-4655	91	23	s	s	PART
ejpam-4655	91	24	}	}	PUNCT
ejpam-4655	91	25	,	,	PUNCT
ejpam-4655	91	26	{	{	PUNCT
ejpam-4655	91	27	p	p	X
ejpam-4655	91	28	,	,	PUNCT
ejpam-4655	91	29	q	q	ADJ
ejpam-4655	91	30	,	,	PUNCT
ejpam-4655	91	31	r	r	NOUN
ejpam-4655	91	32	}	}	PUNCT
ejpam-4655	91	33	,	,	PUNCT
ejpam-4655	91	34	{	{	PUNCT
ejpam-4655	91	35	p	p	X
ejpam-4655	91	36	,	,	PUNCT
ejpam-4655	91	37	q	q	X
ejpam-4655	91	38	,	,	PUNCT
ejpam-4655	91	39	s	s	PART
ejpam-4655	91	40	}	}	PUNCT
ejpam-4655	91	41	,	,	PUNCT
ejpam-4655	91	42	{	{	PUNCT
ejpam-4655	91	43	p	p	X
ejpam-4655	91	44	,	,	PUNCT
ejpam-4655	91	45	r	r	NOUN
ejpam-4655	91	46	,	,	PUNCT
ejpam-4655	91	47	s	s	PART
ejpam-4655	91	48	}	}	PUNCT
ejpam-4655	91	49	,	,	PUNCT
ejpam-4655	91	50	{	{	PUNCT
ejpam-4655	91	51	q	q	X
ejpam-4655	91	52	,	,	PUNCT
ejpam-4655	91	53	r	r	NOUN
ejpam-4655	91	54	,	,	PUNCT
ejpam-4655	91	55	s	s	PART
ejpam-4655	91	56	}	}	PUNCT
ejpam-4655	91	57	and	and	CCONJ
ejpam-4655	91	58	x	x	X
ejpam-4655	91	59	are	be	AUX
ejpam-4655	91	60	µ2	µ2	ADJ
ejpam-4655	91	61	-	-	PUNCT
ejpam-4655	91	62	dense	dense	ADJ
ejpam-4655	91	63	subsets	subset	NOUN
ejpam-4655	91	64	of	of	ADP
ejpam-4655	91	65	x.	x.	NOUN
ejpam-4655	91	66	also	also	ADV
ejpam-4655	91	67	,	,	PUNCT
ejpam-4655	91	68	every	every	DET
ejpam-4655	91	69	µ2	µ2	ADJ
ejpam-4655	91	70	-	-	PUNCT
ejpam-4655	91	71	dense	dense	ADJ
ejpam-4655	91	72	subset	subset	NOUN
ejpam-4655	91	73	of	of	ADP
ejpam-4655	91	74	x	x	PUNCT
ejpam-4655	91	75	is	be	AUX
ejpam-4655	91	76	a	a	DET
ejpam-4655	91	77	µ1	µ1	ADV
ejpam-4655	91	78	-	-	PUNCT
ejpam-4655	91	79	open	open	NOUN
ejpam-4655	91	80	set	set	NOUN
ejpam-4655	91	81	in	in	ADP
ejpam-4655	91	82	x	x	PUNCT
ejpam-4655	91	83	so	so	SCONJ
ejpam-4655	91	84	that	that	SCONJ
ejpam-4655	91	85	x	x	PRON
ejpam-4655	91	86	is	be	AUX
ejpam-4655	91	87	a	a	DET
ejpam-4655	91	88	(	(	PUNCT
ejpam-4655	91	89	1	1	NUM
ejpam-4655	91	90	,	,	PUNCT
ejpam-4655	91	91	2)-bigeneralized	2)-bigeneralized	NUM
ejpam-4655	91	92	submaximal	submaximal	ADJ
ejpam-4655	91	93	space	space	NOUN
ejpam-4655	91	94	.	.	PUNCT
ejpam-4655	92	1	(	(	PUNCT
ejpam-4655	92	2	b	b	X
ejpam-4655	92	3	)	)	PUNCT
ejpam-4655	92	4	.	.	PUNCT
ejpam-4655	93	1	consider	consider	VERB
ejpam-4655	93	2	the	the	DET
ejpam-4655	93	3	bigeneralized	bigeneralized	ADJ
ejpam-4655	93	4	topological	topological	ADJ
ejpam-4655	93	5	space	space	NOUN
ejpam-4655	93	6	(	(	PUNCT
ejpam-4655	93	7	x,µ1	x,µ1	PROPN
ejpam-4655	93	8	,	,	PUNCT
ejpam-4655	93	9	µ2	µ2	PROPN
ejpam-4655	93	10	)	)	PUNCT
ejpam-4655	94	1	where	where	SCONJ
ejpam-4655	94	2	x	x	X
ejpam-4655	94	3	=	=	PRON
ejpam-4655	94	4	{	{	PUNCT
ejpam-4655	94	5	p	p	X
ejpam-4655	94	6	,	,	PUNCT
ejpam-4655	94	7	q	q	ADJ
ejpam-4655	94	8	,	,	PUNCT
ejpam-4655	94	9	r	r	NOUN
ejpam-4655	94	10	,	,	PUNCT
ejpam-4655	94	11	s};µ1	s};µ1	PROPN
ejpam-4655	94	12	=	=	SYM
ejpam-4655	94	13	{	{	PUNCT
ejpam-4655	94	14	∅	∅	NOUN
ejpam-4655	94	15	,	,	PUNCT
ejpam-4655	94	16	{	{	PUNCT
ejpam-4655	94	17	p	p	X
ejpam-4655	94	18	,	,	PUNCT
ejpam-4655	94	19	s	s	PART
ejpam-4655	94	20	}	}	PUNCT
ejpam-4655	94	21	,	,	PUNCT
ejpam-4655	94	22	{	{	PUNCT
ejpam-4655	94	23	q	q	X
ejpam-4655	94	24	,	,	PUNCT
ejpam-4655	94	25	r	r	NOUN
ejpam-4655	94	26	}	}	PUNCT
ejpam-4655	94	27	,	,	PUNCT
ejpam-4655	94	28	{	{	PUNCT
ejpam-4655	94	29	q	q	X
ejpam-4655	94	30	,	,	PUNCT
ejpam-4655	94	31	r	r	NOUN
ejpam-4655	94	32	,	,	PUNCT
ejpam-4655	94	33	s	s	PART
ejpam-4655	94	34	}	}	PUNCT
ejpam-4655	94	35	,	,	PUNCT
ejpam-4655	94	36	x	x	NOUN
ejpam-4655	94	37	}	}	PUNCT
ejpam-4655	94	38	and	and	CCONJ
ejpam-4655	94	39	µ2	µ2	PROPN
ejpam-4655	94	40	=	=	PUNCT
ejpam-4655	94	41	{	{	PUNCT
ejpam-4655	94	42	∅	∅	NOUN
ejpam-4655	94	43	,	,	PUNCT
ejpam-4655	94	44	{	{	PUNCT
ejpam-4655	94	45	p	p	X
ejpam-4655	94	46	,	,	PUNCT
ejpam-4655	94	47	q	q	NOUN
ejpam-4655	94	48	}	}	PUNCT
ejpam-4655	94	49	,	,	PUNCT
ejpam-4655	94	50	{	{	PUNCT
ejpam-4655	94	51	p	p	X
ejpam-4655	94	52	,	,	PUNCT
ejpam-4655	94	53	r	r	NOUN
ejpam-4655	94	54	}	}	PUNCT
ejpam-4655	94	55	,	,	PUNCT
ejpam-4655	94	56	{	{	PUNCT
ejpam-4655	94	57	p	p	X
ejpam-4655	94	58	,	,	PUNCT
ejpam-4655	94	59	s	s	PART
ejpam-4655	94	60	}	}	PUNCT
ejpam-4655	94	61	,	,	PUNCT
ejpam-4655	94	62	{	{	PUNCT
ejpam-4655	94	63	q	q	X
ejpam-4655	94	64	,	,	PUNCT
ejpam-4655	94	65	s	s	PART
ejpam-4655	94	66	}	}	PUNCT
ejpam-4655	94	67	,	,	PUNCT
ejpam-4655	94	68	{	{	PUNCT
ejpam-4655	94	69	r	r	NOUN
ejpam-4655	94	70	,	,	PUNCT
ejpam-4655	94	71	s	s	PART
ejpam-4655	94	72	}	}	PUNCT
ejpam-4655	94	73	,	,	PUNCT
ejpam-4655	94	74	{	{	PUNCT
ejpam-4655	94	75	p	p	X
ejpam-4655	94	76	,	,	PUNCT
ejpam-4655	94	77	q	q	ADJ
ejpam-4655	94	78	,	,	PUNCT
ejpam-4655	94	79	r	r	NOUN
ejpam-4655	94	80	}	}	PUNCT
ejpam-4655	94	81	,	,	PUNCT
ejpam-4655	94	82	{	{	PUNCT
ejpam-4655	94	83	p	p	X
ejpam-4655	94	84	,	,	PUNCT
ejpam-4655	94	85	q	q	X
ejpam-4655	94	86	,	,	PUNCT
ejpam-4655	94	87	s	s	PART
ejpam-4655	94	88	}	}	PUNCT
ejpam-4655	94	89	,	,	PUNCT
ejpam-4655	94	90	{	{	PUNCT
ejpam-4655	94	91	p	p	X
ejpam-4655	94	92	,	,	PUNCT
ejpam-4655	94	93	r	r	NOUN
ejpam-4655	94	94	,	,	PUNCT
ejpam-4655	94	95	s	s	PART
ejpam-4655	94	96	}	}	PUNCT
ejpam-4655	94	97	,	,	PUNCT
ejpam-4655	94	98	{	{	PUNCT
ejpam-4655	94	99	q	q	X
ejpam-4655	94	100	,	,	PUNCT
ejpam-4655	94	101	r	r	NOUN
ejpam-4655	94	102	,	,	PUNCT
ejpam-4655	94	103	s	s	PART
ejpam-4655	94	104	}	}	PUNCT
ejpam-4655	94	105	,	,	PUNCT
ejpam-4655	94	106	x	x	NOUN
ejpam-4655	94	107	}	}	PUNCT
ejpam-4655	94	108	.	.	PUNCT
ejpam-4655	95	1	for	for	ADP
ejpam-4655	95	2	that	that	PRON
ejpam-4655	95	3	,	,	PUNCT
ejpam-4655	95	4	{	{	PUNCT
ejpam-4655	95	5	p	p	X
ejpam-4655	95	6	,	,	PUNCT
ejpam-4655	95	7	q	q	NOUN
ejpam-4655	95	8	}	}	PUNCT
ejpam-4655	95	9	,	,	PUNCT
ejpam-4655	95	10	{	{	PUNCT
ejpam-4655	95	11	p	p	X
ejpam-4655	95	12	,	,	PUNCT
ejpam-4655	95	13	r	r	NOUN
ejpam-4655	95	14	}	}	PUNCT
ejpam-4655	95	15	,	,	PUNCT
ejpam-4655	95	16	{	{	PUNCT
ejpam-4655	95	17	q	q	X
ejpam-4655	95	18	,	,	PUNCT
ejpam-4655	95	19	s	s	PART
ejpam-4655	95	20	}	}	PUNCT
ejpam-4655	95	21	,	,	PUNCT
ejpam-4655	95	22	{	{	PUNCT
ejpam-4655	95	23	r	r	NOUN
ejpam-4655	95	24	,	,	PUNCT
ejpam-4655	95	25	s	s	PART
ejpam-4655	95	26	}	}	PUNCT
ejpam-4655	95	27	,	,	PUNCT
ejpam-4655	95	28	{	{	PUNCT
ejpam-4655	95	29	p	p	X
ejpam-4655	95	30	,	,	PUNCT
ejpam-4655	95	31	q	q	ADJ
ejpam-4655	95	32	,	,	PUNCT
ejpam-4655	95	33	r	r	NOUN
ejpam-4655	95	34	}	}	PUNCT
ejpam-4655	95	35	,	,	PUNCT
ejpam-4655	95	36	{	{	PUNCT
ejpam-4655	95	37	p	p	X
ejpam-4655	95	38	,	,	PUNCT
ejpam-4655	95	39	q	q	X
ejpam-4655	95	40	,	,	PUNCT
ejpam-4655	95	41	s	s	PART
ejpam-4655	95	42	}	}	PUNCT
ejpam-4655	95	43	,	,	PUNCT
ejpam-4655	95	44	{	{	PUNCT
ejpam-4655	95	45	p	p	X
ejpam-4655	95	46	,	,	PUNCT
ejpam-4655	95	47	r	r	NOUN
ejpam-4655	95	48	,	,	PUNCT
ejpam-4655	95	49	s	s	PART
ejpam-4655	95	50	}	}	PUNCT
ejpam-4655	95	51	,	,	PUNCT
ejpam-4655	95	52	{	{	PUNCT
ejpam-4655	95	53	q	q	X
ejpam-4655	95	54	,	,	PUNCT
ejpam-4655	95	55	r	r	NOUN
ejpam-4655	95	56	,	,	PUNCT
ejpam-4655	95	57	s	s	PART
ejpam-4655	95	58	}	}	PUNCT
ejpam-4655	95	59	and	and	CCONJ
ejpam-4655	95	60	x	x	PRON
ejpam-4655	95	61	are	be	AUX
ejpam-4655	95	62	µ1	µ1	NOUN
ejpam-4655	95	63	-	-	PUNCT
ejpam-4655	95	64	dense	dense	ADJ
ejpam-4655	95	65	subsets	subset	NOUN
ejpam-4655	95	66	of	of	ADP
ejpam-4655	95	67	x.	x.	NOUN
ejpam-4655	95	68	also	also	ADV
ejpam-4655	95	69	,	,	PUNCT
ejpam-4655	95	70	every	every	DET
ejpam-4655	95	71	µ1	µ1	NOUN
ejpam-4655	95	72	-	-	PUNCT
ejpam-4655	95	73	dense	dense	ADJ
ejpam-4655	95	74	subset	subset	NOUN
ejpam-4655	95	75	of	of	ADP
ejpam-4655	95	76	x	x	PUNCT
ejpam-4655	95	77	is	be	AUX
ejpam-4655	95	78	a	a	DET
ejpam-4655	95	79	µ2	µ2	ADJ
ejpam-4655	95	80	-	-	PUNCT
ejpam-4655	95	81	open	open	NOUN
ejpam-4655	95	82	set	set	NOUN
ejpam-4655	95	83	in	in	ADP
ejpam-4655	95	84	x.	x.	NOUN
ejpam-4655	95	85	thus	thus	ADV
ejpam-4655	95	86	,	,	PUNCT
ejpam-4655	95	87	x	x	PRON
ejpam-4655	95	88	is	be	AUX
ejpam-4655	95	89	a	a	DET
ejpam-4655	95	90	(	(	PUNCT
ejpam-4655	95	91	2	2	NUM
ejpam-4655	95	92	,	,	PUNCT
ejpam-4655	95	93	1)-bigeneralized	1)-bigeneralized	NUM
ejpam-4655	95	94	submaximal	submaximal	ADJ
ejpam-4655	95	95	space	space	NOUN
ejpam-4655	95	96	.	.	PUNCT
ejpam-4655	96	1	definition	definition	NOUN
ejpam-4655	96	2	3	3	X
ejpam-4655	96	3	.	.	PUNCT
ejpam-4655	97	1	let	let	AUX
ejpam-4655	97	2	(	(	PUNCT
ejpam-4655	97	3	x,µ1	x,µ1	NOUN
ejpam-4655	97	4	,	,	PUNCT
ejpam-4655	97	5	µ2	µ2	PROPN
ejpam-4655	97	6	)	)	PUNCT
ejpam-4655	97	7	be	be	VERB
ejpam-4655	97	8	a	a	DET
ejpam-4655	97	9	bigeneralized	bigeneralized	ADJ
ejpam-4655	97	10	topological	topological	ADJ
ejpam-4655	97	11	space	space	NOUN
ejpam-4655	97	12	.	.	PUNCT
ejpam-4655	98	1	ifx	ifx	PROPN
ejpam-4655	98	2	is	be	AUX
ejpam-4655	98	3	(	(	PUNCT
ejpam-4655	98	4	1	1	NUM
ejpam-4655	98	5	,	,	PUNCT
ejpam-4655	98	6	2)-bigeneralized	2)-bigeneralized	NUM
ejpam-4655	98	7	submaximal	submaximal	ADJ
ejpam-4655	98	8	and	and	CCONJ
ejpam-4655	98	9	(	(	PUNCT
ejpam-4655	98	10	2	2	NUM
ejpam-4655	98	11	,	,	PUNCT
ejpam-4655	98	12	1)-bigeneralized	1)-bigeneralized	NUM
ejpam-4655	98	13	submaximal	submaximal	ADJ
ejpam-4655	98	14	,	,	PUNCT
ejpam-4655	98	15	then	then	ADV
ejpam-4655	98	16	x	x	PUNCT
ejpam-4655	98	17	is	be	AUX
ejpam-4655	98	18	called	call	VERB
ejpam-4655	98	19	pairwise	pairwise	NOUN
ejpam-4655	98	20	bigeneralized	bigeneralize	VERB
ejpam-4655	98	21	submaximal	submaximal	ADJ
ejpam-4655	98	22	space	space	NOUN
ejpam-4655	98	23	.	.	PUNCT
ejpam-4655	99	1	example	example	NOUN
ejpam-4655	100	1	4	4	NUM
ejpam-4655	100	2	.	.	PUNCT
ejpam-4655	100	3	consider	consider	VERB
ejpam-4655	100	4	the	the	DET
ejpam-4655	100	5	bigeneralized	bigeneralized	ADJ
ejpam-4655	100	6	topological	topological	ADJ
ejpam-4655	100	7	space	space	NOUN
ejpam-4655	100	8	(	(	PUNCT
ejpam-4655	100	9	x,µ1	x,µ1	PROPN
ejpam-4655	100	10	,	,	PUNCT
ejpam-4655	100	11	µ2	µ2	ADJ
ejpam-4655	100	12	)	)	PUNCT
ejpam-4655	100	13	wherex	wherex	PROPN
ejpam-4655	100	14	=	=	PUNCT
ejpam-4655	100	15	{	{	PUNCT
ejpam-4655	100	16	p	p	X
ejpam-4655	100	17	,	,	PUNCT
ejpam-4655	100	18	q	q	ADJ
ejpam-4655	100	19	,	,	PUNCT
ejpam-4655	100	20	r	r	NOUN
ejpam-4655	100	21	,	,	PUNCT
ejpam-4655	100	22	s	s	PART
ejpam-4655	100	23	}	}	PUNCT
ejpam-4655	100	24	;	;	PUNCT
ejpam-4655	100	25	µ1	µ1	PROPN
ejpam-4655	100	26	=	=	SYM
ejpam-4655	100	27	{	{	PUNCT
ejpam-4655	100	28	∅	∅	NOUN
ejpam-4655	100	29	,	,	PUNCT
ejpam-4655	100	30	{	{	PUNCT
ejpam-4655	100	31	p	p	X
ejpam-4655	100	32	,	,	PUNCT
ejpam-4655	100	33	q	q	NOUN
ejpam-4655	100	34	}	}	PUNCT
ejpam-4655	100	35	,	,	PUNCT
ejpam-4655	100	36	{	{	PUNCT
ejpam-4655	100	37	p	p	X
ejpam-4655	100	38	,	,	PUNCT
ejpam-4655	100	39	r	r	NOUN
ejpam-4655	100	40	}	}	PUNCT
ejpam-4655	100	41	,	,	PUNCT
ejpam-4655	100	42	{	{	PUNCT
ejpam-4655	100	43	p	p	X
ejpam-4655	100	44	,	,	PUNCT
ejpam-4655	100	45	s	s	PART
ejpam-4655	100	46	}	}	PUNCT
ejpam-4655	100	47	,	,	PUNCT
ejpam-4655	100	48	{	{	PUNCT
ejpam-4655	100	49	p	p	X
ejpam-4655	100	50	,	,	PUNCT
ejpam-4655	100	51	q	q	ADJ
ejpam-4655	100	52	,	,	PUNCT
ejpam-4655	100	53	r	r	NOUN
ejpam-4655	100	54	}	}	PUNCT
ejpam-4655	100	55	,	,	PUNCT
ejpam-4655	100	56	{	{	PUNCT
ejpam-4655	100	57	p	p	X
ejpam-4655	100	58	,	,	PUNCT
ejpam-4655	100	59	q	q	X
ejpam-4655	100	60	,	,	PUNCT
ejpam-4655	100	61	s	s	PART
ejpam-4655	100	62	}	}	PUNCT
ejpam-4655	100	63	,	,	PUNCT
ejpam-4655	100	64	{	{	PUNCT
ejpam-4655	100	65	p	p	X
ejpam-4655	100	66	,	,	PUNCT
ejpam-4655	100	67	r	r	NOUN
ejpam-4655	100	68	,	,	PUNCT
ejpam-4655	100	69	s	s	PART
ejpam-4655	100	70	}	}	PUNCT
ejpam-4655	100	71	,	,	PUNCT
ejpam-4655	100	72	x	x	NOUN
ejpam-4655	100	73	}	}	PUNCT
ejpam-4655	100	74	and	and	CCONJ
ejpam-4655	100	75	µ2	µ2	PROPN
ejpam-4655	100	76	=	=	PUNCT
ejpam-4655	100	77	{	{	PUNCT
ejpam-4655	100	78	∅	∅	NOUN
ejpam-4655	100	79	,	,	PUNCT
ejpam-4655	100	80	{	{	PUNCT
ejpam-4655	100	81	p	p	X
ejpam-4655	100	82	}	}	PUNCT
ejpam-4655	100	83	,	,	PUNCT
ejpam-4655	100	84	{	{	PUNCT
ejpam-4655	100	85	p	p	X
ejpam-4655	100	86	,	,	PUNCT
ejpam-4655	100	87	q	q	NOUN
ejpam-4655	100	88	}	}	PUNCT
ejpam-4655	100	89	,	,	PUNCT
ejpam-4655	100	90	{	{	PUNCT
ejpam-4655	100	91	p	p	X
ejpam-4655	100	92	,	,	PUNCT
ejpam-4655	100	93	r	r	NOUN
ejpam-4655	100	94	}	}	PUNCT
ejpam-4655	100	95	,	,	PUNCT
ejpam-4655	100	96	{	{	PUNCT
ejpam-4655	100	97	p	p	X
ejpam-4655	100	98	,	,	PUNCT
ejpam-4655	100	99	s	s	PART
ejpam-4655	100	100	}	}	PUNCT
ejpam-4655	100	101	,	,	PUNCT
ejpam-4655	100	102	{	{	PUNCT
ejpam-4655	100	103	q	q	X
ejpam-4655	100	104	,	,	PUNCT
ejpam-4655	100	105	r	r	NOUN
ejpam-4655	100	106	}	}	PUNCT
ejpam-4655	100	107	,	,	PUNCT
ejpam-4655	100	108	{	{	PUNCT
ejpam-4655	100	109	q	q	X
ejpam-4655	100	110	,	,	PUNCT
ejpam-4655	100	111	s	s	PART
ejpam-4655	100	112	}	}	PUNCT
ejpam-4655	100	113	,	,	PUNCT
ejpam-4655	100	114	{	{	PUNCT
ejpam-4655	100	115	r	r	NOUN
ejpam-4655	100	116	,	,	PUNCT
ejpam-4655	100	117	s	s	PART
ejpam-4655	100	118	}	}	PUNCT
ejpam-4655	100	119	,	,	PUNCT
ejpam-4655	100	120	{	{	PUNCT
ejpam-4655	100	121	p	p	X
ejpam-4655	100	122	,	,	PUNCT
ejpam-4655	100	123	q	q	ADJ
ejpam-4655	100	124	,	,	PUNCT
ejpam-4655	100	125	r	r	NOUN
ejpam-4655	100	126	}	}	PUNCT
ejpam-4655	100	127	,	,	PUNCT
ejpam-4655	100	128	{	{	PUNCT
ejpam-4655	100	129	p	p	X
ejpam-4655	100	130	,	,	PUNCT
ejpam-4655	100	131	q	q	X
ejpam-4655	100	132	,	,	PUNCT
ejpam-4655	100	133	s	s	PART
ejpam-4655	100	134	}	}	PUNCT
ejpam-4655	100	135	,	,	PUNCT
ejpam-4655	100	136	{	{	PUNCT
ejpam-4655	100	137	p	p	X
ejpam-4655	100	138	,	,	PUNCT
ejpam-4655	100	139	r	r	NOUN
ejpam-4655	100	140	,	,	PUNCT
ejpam-4655	100	141	s	s	PART
ejpam-4655	100	142	}	}	PUNCT
ejpam-4655	100	143	,	,	PUNCT
ejpam-4655	100	144	{	{	PUNCT
ejpam-4655	100	145	q	q	X
ejpam-4655	100	146	,	,	PUNCT
ejpam-4655	100	147	r	r	NOUN
ejpam-4655	100	148	,	,	PUNCT
ejpam-4655	100	149	s	s	PART
ejpam-4655	100	150	}	}	PUNCT
ejpam-4655	100	151	,	,	PUNCT
ejpam-4655	100	152	x	x	NOUN
ejpam-4655	100	153	}	}	PUNCT
ejpam-4655	100	154	.	.	PUNCT
ejpam-4655	101	1	(	(	PUNCT
ejpam-4655	101	2	a	a	NOUN
ejpam-4655	101	3	)	)	PUNCT
ejpam-4655	101	4	.	.	PUNCT
ejpam-4655	102	1	so	so	ADV
ejpam-4655	102	2	that	that	SCONJ
ejpam-4655	102	3	{	{	PUNCT
ejpam-4655	102	4	p	p	X
ejpam-4655	102	5	,	,	PUNCT
ejpam-4655	102	6	q	q	ADJ
ejpam-4655	102	7	,	,	PUNCT
ejpam-4655	102	8	r	r	NOUN
ejpam-4655	102	9	}	}	PUNCT
ejpam-4655	102	10	,	,	PUNCT
ejpam-4655	102	11	{	{	PUNCT
ejpam-4655	102	12	p	p	X
ejpam-4655	102	13	,	,	PUNCT
ejpam-4655	102	14	q	q	X
ejpam-4655	102	15	,	,	PUNCT
ejpam-4655	102	16	s	s	PART
ejpam-4655	102	17	}	}	PUNCT
ejpam-4655	102	18	,	,	PUNCT
ejpam-4655	102	19	{	{	PUNCT
ejpam-4655	102	20	p	p	X
ejpam-4655	102	21	,	,	PUNCT
ejpam-4655	102	22	r	r	NOUN
ejpam-4655	102	23	,	,	PUNCT
ejpam-4655	102	24	s	s	PART
ejpam-4655	102	25	}	}	PUNCT
ejpam-4655	102	26	and	and	CCONJ
ejpam-4655	102	27	x	x	X
ejpam-4655	102	28	are	be	AUX
ejpam-4655	102	29	µ2	µ2	ADJ
ejpam-4655	102	30	-	-	PUNCT
ejpam-4655	102	31	dense	dense	ADJ
ejpam-4655	102	32	subsets	subset	NOUN
ejpam-4655	102	33	of	of	ADP
ejpam-4655	102	34	x	x	PRON
ejpam-4655	102	35	,	,	PUNCT
ejpam-4655	102	36	also	also	ADV
ejpam-4655	102	37	,	,	PUNCT
ejpam-4655	102	38	every	every	DET
ejpam-4655	102	39	µ2dense	µ2dense	NOUN
ejpam-4655	102	40	subset	subset	NOUN
ejpam-4655	102	41	of	of	ADP
ejpam-4655	102	42	x	x	PUNCT
ejpam-4655	102	43	is	be	AUX
ejpam-4655	102	44	a	a	DET
ejpam-4655	102	45	µ1	µ1	ADV
ejpam-4655	102	46	-	-	PUNCT
ejpam-4655	102	47	open	open	ADJ
ejpam-4655	102	48	set	set	NOUN
ejpam-4655	102	49	of	of	ADP
ejpam-4655	102	50	x	x	PUNCT
ejpam-4655	102	51	for	for	ADP
ejpam-4655	102	52	that	that	PRON
ejpam-4655	102	53	x	x	PRON
ejpam-4655	102	54	is	be	AUX
ejpam-4655	102	55	(	(	PUNCT
ejpam-4655	102	56	1	1	NUM
ejpam-4655	102	57	,	,	PUNCT
ejpam-4655	102	58	2)-bigeneralized	2)-bigeneralized	NUM
ejpam-4655	102	59	submaximal	submaximal	ADJ
ejpam-4655	102	60	.	.	PUNCT
ejpam-4655	103	1	(	(	PUNCT
ejpam-4655	103	2	b	b	NOUN
ejpam-4655	103	3	)	)	PUNCT
ejpam-4655	103	4	.	.	PUNCT
ejpam-4655	104	1	since	since	SCONJ
ejpam-4655	104	2	{	{	PUNCT
ejpam-4655	104	3	p	p	X
ejpam-4655	104	4	}	}	PUNCT
ejpam-4655	104	5	,	,	PUNCT
ejpam-4655	104	6	{	{	PUNCT
ejpam-4655	104	7	p	p	X
ejpam-4655	104	8	,	,	PUNCT
ejpam-4655	104	9	q	q	NOUN
ejpam-4655	104	10	}	}	PUNCT
ejpam-4655	104	11	,	,	PUNCT
ejpam-4655	104	12	{	{	PUNCT
ejpam-4655	104	13	p	p	X
ejpam-4655	104	14	,	,	PUNCT
ejpam-4655	104	15	r	r	NOUN
ejpam-4655	104	16	}	}	PUNCT
ejpam-4655	104	17	,	,	PUNCT
ejpam-4655	104	18	{	{	PUNCT
ejpam-4655	104	19	p	p	X
ejpam-4655	104	20	,	,	PUNCT
ejpam-4655	104	21	s	s	PART
ejpam-4655	104	22	}	}	PUNCT
ejpam-4655	104	23	,	,	PUNCT
ejpam-4655	104	24	{	{	PUNCT
ejpam-4655	104	25	p	p	X
ejpam-4655	104	26	,	,	PUNCT
ejpam-4655	104	27	q	q	ADJ
ejpam-4655	104	28	,	,	PUNCT
ejpam-4655	104	29	r	r	NOUN
ejpam-4655	104	30	}	}	PUNCT
ejpam-4655	104	31	,	,	PUNCT
ejpam-4655	104	32	{	{	PUNCT
ejpam-4655	104	33	p	p	X
ejpam-4655	104	34	,	,	PUNCT
ejpam-4655	104	35	q	q	X
ejpam-4655	104	36	,	,	PUNCT
ejpam-4655	104	37	s	s	PART
ejpam-4655	104	38	}	}	PUNCT
ejpam-4655	104	39	,	,	PUNCT
ejpam-4655	104	40	{	{	PUNCT
ejpam-4655	104	41	p	p	X
ejpam-4655	104	42	,	,	PUNCT
ejpam-4655	104	43	r	r	NOUN
ejpam-4655	104	44	,	,	PUNCT
ejpam-4655	104	45	s	s	PART
ejpam-4655	104	46	}	}	PUNCT
ejpam-4655	104	47	,	,	PUNCT
ejpam-4655	104	48	{	{	PUNCT
ejpam-4655	104	49	q	q	X
ejpam-4655	104	50	,	,	PUNCT
ejpam-4655	104	51	r	r	NOUN
ejpam-4655	104	52	,	,	PUNCT
ejpam-4655	104	53	s	s	PART
ejpam-4655	104	54	}	}	PUNCT
ejpam-4655	104	55	and	and	CCONJ
ejpam-4655	104	56	x	x	PRON
ejpam-4655	104	57	are	be	AUX
ejpam-4655	104	58	µ1	µ1	NOUN
ejpam-4655	104	59	-	-	PUNCT
ejpam-4655	104	60	dense	dense	ADJ
ejpam-4655	104	61	subset	subset	NOUN
ejpam-4655	104	62	of	of	ADP
ejpam-4655	104	63	x	x	X
ejpam-4655	104	64	and	and	CCONJ
ejpam-4655	104	65	also	also	ADV
ejpam-4655	104	66	,	,	PUNCT
ejpam-4655	104	67	every	every	DET
ejpam-4655	104	68	µ1	µ1	NOUN
ejpam-4655	104	69	-	-	PUNCT
ejpam-4655	104	70	dense	dense	ADJ
ejpam-4655	104	71	subset	subset	NOUN
ejpam-4655	104	72	of	of	ADP
ejpam-4655	104	73	x	x	PUNCT
ejpam-4655	104	74	is	be	AUX
ejpam-4655	104	75	a	a	DET
ejpam-4655	104	76	µ2	µ2	ADJ
ejpam-4655	104	77	-	-	PUNCT
ejpam-4655	104	78	open	open	NOUN
ejpam-4655	104	79	set	set	NOUN
ejpam-4655	104	80	in	in	ADP
ejpam-4655	104	81	x	x	PUNCT
ejpam-4655	104	82	we	we	PRON
ejpam-4655	104	83	have	have	AUX
ejpam-4655	104	84	x	x	INTJ
ejpam-4655	104	85	is	be	AUX
ejpam-4655	104	86	(	(	PUNCT
ejpam-4655	104	87	2	2	NUM
ejpam-4655	104	88	,	,	PUNCT
ejpam-4655	104	89	1)-bigeneralized	1)-bigeneralized	NUM
ejpam-4655	104	90	submaximal	submaximal	NOUN
ejpam-4655	104	91	.	.	PUNCT
ejpam-4655	105	1	therefore	therefore	ADV
ejpam-4655	105	2	,	,	PUNCT
ejpam-4655	105	3	x	x	X
ejpam-4655	105	4	is	be	AUX
ejpam-4655	105	5	pairwise	pairwise	NOUN
ejpam-4655	105	6	bigeneralized	bigeneralize	VERB
ejpam-4655	105	7	submaximal	submaximal	ADJ
ejpam-4655	105	8	.	.	PUNCT
ejpam-4655	106	1	the	the	DET
ejpam-4655	106	2	following	follow	VERB
ejpam-4655	106	3	theorem	theorem	NOUN
ejpam-4655	106	4	5	5	NUM
ejpam-4655	106	5	is	be	AUX
ejpam-4655	106	6	the	the	DET
ejpam-4655	106	7	characterization	characterization	NOUN
ejpam-4655	106	8	of	of	ADP
ejpam-4655	106	9	(	(	PUNCT
ejpam-4655	106	10	s	s	PROPN
ejpam-4655	106	11	,	,	PUNCT
ejpam-4655	106	12	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	106	13	submaximality	submaximality	NOUN
ejpam-4655	106	14	for	for	ADP
ejpam-4655	106	15	a	a	DET
ejpam-4655	106	16	bgts	bgts	PROPN
ejpam-4655	106	17	.	.	PUNCT
ejpam-4655	107	1	theorem	theorem	NOUN
ejpam-4655	107	2	5	5	NUM
ejpam-4655	107	3	.	.	PUNCT
ejpam-4655	108	1	let	let	AUX
ejpam-4655	108	2	(	(	PUNCT
ejpam-4655	108	3	x,µ1	x,µ1	NOUN
ejpam-4655	108	4	,	,	PUNCT
ejpam-4655	108	5	µ2	µ2	PROPN
ejpam-4655	108	6	)	)	PUNCT
ejpam-4655	108	7	be	be	AUX
ejpam-4655	108	8	a	a	DET
ejpam-4655	108	9	bgts	bgts	NOUN
ejpam-4655	108	10	.	.	PUNCT
ejpam-4655	109	1	then	then	ADV
ejpam-4655	109	2	the	the	DET
ejpam-4655	109	3	following	following	NOUN
ejpam-4655	109	4	are	be	AUX
ejpam-4655	109	5	equivalent	equivalent	ADJ
ejpam-4655	109	6	.	.	PUNCT
ejpam-4655	110	1	(	(	PUNCT
ejpam-4655	110	2	a	a	X
ejpam-4655	110	3	)	)	PUNCT
ejpam-4655	110	4	(	(	PUNCT
ejpam-4655	110	5	s	s	PROPN
ejpam-4655	110	6	,	,	PUNCT
ejpam-4655	110	7	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	110	8	submaximal	submaximal	ADJ
ejpam-4655	110	9	space	space	NOUN
ejpam-4655	110	10	(	(	PUNCT
ejpam-4655	110	11	b	b	NOUN
ejpam-4655	110	12	)	)	PUNCT
ejpam-4655	110	13	every	every	PRON
ejpam-4655	110	14	q	q	X
ejpam-4655	111	1	⊂	⊂	X
ejpam-4655	111	2	x	x	PUNCT
ejpam-4655	111	3	with	with	ADP
ejpam-4655	111	4	iv(q	iv(q	NOUN
ejpam-4655	111	5	)	)	PUNCT
ejpam-4655	111	6	=	=	NOUN
ejpam-4655	111	7	∅	∅	NOUN
ejpam-4655	111	8	,	,	PUNCT
ejpam-4655	111	9	is	be	AUX
ejpam-4655	111	10	a	a	DET
ejpam-4655	111	11	µs	µs	NOUN
ejpam-4655	111	12	-	-	PUNCT
ejpam-4655	111	13	closed	closed	ADJ
ejpam-4655	111	14	set	set	NOUN
ejpam-4655	111	15	.	.	PUNCT
ejpam-4655	112	1	(	(	PUNCT
ejpam-4655	112	2	c	c	X
ejpam-4655	112	3	)	)	PUNCT
ejpam-4655	112	4	q	q	NOUN
ejpam-4655	113	1	⊂	⊂	PROPN
ejpam-4655	113	2	x	x	NOUN
ejpam-4655	113	3	,	,	PUNCT
ejpam-4655	113	4	cv(q)−q	cv(q)−q	PROPN
ejpam-4655	113	5	is	be	AUX
ejpam-4655	113	6	a	a	DET
ejpam-4655	113	7	µs	µs	NOUN
ejpam-4655	113	8	-	-	PUNCT
ejpam-4655	113	9	closed	closed	ADJ
ejpam-4655	113	10	set	set	NOUN
ejpam-4655	113	11	where	where	SCONJ
ejpam-4655	113	12	s	s	X
ejpam-4655	113	13	,	,	PUNCT
ejpam-4655	113	14	v	v	NOUN
ejpam-4655	113	15	=	=	SYM
ejpam-4655	113	16	1	1	NUM
ejpam-4655	113	17	,	,	PUNCT
ejpam-4655	113	18	2	2	NUM
ejpam-4655	113	19	and	and	CCONJ
ejpam-4655	113	20	s	s	VERB
ejpam-4655	113	21	̸=	̸=	PROPN
ejpam-4655	113	22	v.	v.	ADP
ejpam-4655	113	23	proof	proof	NOUN
ejpam-4655	113	24	.	.	PUNCT
ejpam-4655	114	1	we	we	PRON
ejpam-4655	114	2	give	give	VERB
ejpam-4655	114	3	the	the	DET
ejpam-4655	114	4	detailed	detailed	ADJ
ejpam-4655	114	5	proof	proof	NOUN
ejpam-4655	114	6	only	only	ADV
ejpam-4655	114	7	for	for	ADP
ejpam-4655	114	8	s	s	NOUN
ejpam-4655	114	9	=	=	SYM
ejpam-4655	114	10	1	1	NUM
ejpam-4655	114	11	,	,	PUNCT
ejpam-4655	114	12	v	v	NOUN
ejpam-4655	114	13	=	=	SYM
ejpam-4655	114	14	2	2	NUM
ejpam-4655	114	15	.	.	PUNCT
ejpam-4655	114	16	y.	y.	PROPN
ejpam-4655	114	17	farhat	farhat	PROPN
ejpam-4655	114	18	et	et	PROPN
ejpam-4655	114	19	al	al	PROPN
ejpam-4655	114	20	.	.	PUNCT
ejpam-4655	114	21	/	/	SYM
ejpam-4655	114	22	eur	eur	PROPN
ejpam-4655	114	23	.	.	PUNCT
ejpam-4655	115	1	j.	j.	PROPN
ejpam-4655	115	2	pure	pure	PROPN
ejpam-4655	115	3	appl	appl	PROPN
ejpam-4655	115	4	.	.	PROPN
ejpam-4655	115	5	math	math	PROPN
ejpam-4655	115	6	,	,	PUNCT
ejpam-4655	115	7	16	16	NUM
ejpam-4655	115	8	(	(	PUNCT
ejpam-4655	115	9	1	1	NUM
ejpam-4655	115	10	)	)	PUNCT
ejpam-4655	115	11	(	(	PUNCT
ejpam-4655	115	12	2023	2023	NUM
ejpam-4655	115	13	)	)	PUNCT
ejpam-4655	115	14	,	,	PUNCT
ejpam-4655	115	15	386	386	NUM
ejpam-4655	115	16	-	-	SYM
ejpam-4655	115	17	403	403	NUM
ejpam-4655	115	18	390	390	NUM
ejpam-4655	115	19	(	(	PUNCT
ejpam-4655	115	20	a	a	NOUN
ejpam-4655	115	21	)	)	PUNCT
ejpam-4655	115	22	⇒	⇒	NOUN
ejpam-4655	115	23	(	(	PUNCT
ejpam-4655	115	24	b	b	X
ejpam-4655	115	25	)	)	PUNCT
ejpam-4655	115	26	assume	assume	VERB
ejpam-4655	115	27	that	that	SCONJ
ejpam-4655	115	28	,	,	PUNCT
ejpam-4655	115	29	x	x	PRON
ejpam-4655	115	30	is	be	AUX
ejpam-4655	115	31	a	a	DET
ejpam-4655	115	32	(	(	PUNCT
ejpam-4655	115	33	1	1	NUM
ejpam-4655	115	34	,	,	PUNCT
ejpam-4655	115	35	2)-bigeneralized	2)-bigeneralized	NUM
ejpam-4655	115	36	submaximal	submaximal	ADJ
ejpam-4655	115	37	space	space	NOUN
ejpam-4655	115	38	and	and	CCONJ
ejpam-4655	115	39	take	take	VERB
ejpam-4655	115	40	q	q	PROPN
ejpam-4655	115	41	⊂	⊂	X
ejpam-4655	115	42	x	x	PUNCT
ejpam-4655	115	43	with	with	ADP
ejpam-4655	115	44	i2(q	i2(q	NOUN
ejpam-4655	115	45	)	)	PUNCT
ejpam-4655	115	46	=	=	NOUN
ejpam-4655	115	47	∅	∅	NOUN
ejpam-4655	115	48	so	so	SCONJ
ejpam-4655	115	49	that	that	PRON
ejpam-4655	115	50	cµ2(x	cµ2(x	NOUN
ejpam-4655	115	51	−q	−q	NOUN
ejpam-4655	115	52	)	)	PUNCT
ejpam-4655	116	1	=	=	PUNCT
ejpam-4655	116	2	x	x	X
ejpam-4655	116	3	which	which	PRON
ejpam-4655	116	4	implies	imply	VERB
ejpam-4655	116	5	x	x	NOUN
ejpam-4655	116	6	−q	−q	NOUN
ejpam-4655	116	7	∈	∈	NOUN
ejpam-4655	116	8	µ1	µ1	NOUN
ejpam-4655	116	9	,	,	PUNCT
ejpam-4655	116	10	by	by	ADP
ejpam-4655	116	11	hypothesis	hypothesis	NOUN
ejpam-4655	116	12	.	.	PUNCT
ejpam-4655	117	1	therefore	therefore	ADV
ejpam-4655	117	2	,	,	PUNCT
ejpam-4655	117	3	q	q	X
ejpam-4655	117	4	is	be	AUX
ejpam-4655	117	5	a	a	DET
ejpam-4655	117	6	µ1	µ1	NOUN
ejpam-4655	117	7	-	-	PUNCT
ejpam-4655	117	8	closed	closed	ADJ
ejpam-4655	117	9	set	set	NOUN
ejpam-4655	117	10	.	.	PUNCT
ejpam-4655	118	1	(	(	PUNCT
ejpam-4655	118	2	b	b	X
ejpam-4655	118	3	)	)	PUNCT
ejpam-4655	118	4	⇒	⇒	NOUN
ejpam-4655	118	5	(	(	PUNCT
ejpam-4655	118	6	c	c	X
ejpam-4655	118	7	)	)	PUNCT
ejpam-4655	118	8	by	by	ADP
ejpam-4655	118	9	lemma	lemma	PROPN
ejpam-4655	118	10	1	1	NUM
ejpam-4655	118	11	,	,	PUNCT
ejpam-4655	118	12	i2(c2(q)−q	i2(c2(q)−q	PROPN
ejpam-4655	118	13	)	)	PUNCT
ejpam-4655	118	14	=	=	PUNCT
ejpam-4655	118	15	∅	∅	NOUN
ejpam-4655	118	16	whereby	whereby	ADV
ejpam-4655	118	17	by	by	ADP
ejpam-4655	118	18	(	(	PUNCT
ejpam-4655	118	19	b	b	NOUN
ejpam-4655	118	20	)	)	PUNCT
ejpam-4655	118	21	c2(q)−q	c2(q)−q	PROPN
ejpam-4655	118	22	is	be	AUX
ejpam-4655	118	23	a	a	DET
ejpam-4655	118	24	µ1	µ1	NOUN
ejpam-4655	118	25	-	-	PUNCT
ejpam-4655	118	26	closed	closed	ADJ
ejpam-4655	118	27	set	set	NOUN
ejpam-4655	118	28	.	.	PUNCT
ejpam-4655	119	1	(	(	PUNCT
ejpam-4655	119	2	c	c	X
ejpam-4655	119	3	)	)	PUNCT
ejpam-4655	119	4	⇒	⇒	NOUN
ejpam-4655	119	5	(	(	PUNCT
ejpam-4655	119	6	a	a	X
ejpam-4655	119	7	)	)	PUNCT
ejpam-4655	119	8	consider	consider	NOUN
ejpam-4655	119	9	,	,	PUNCT
ejpam-4655	119	10	cµ2(q	cµ2(q	PROPN
ejpam-4655	119	11	)	)	PUNCT
ejpam-4655	120	1	=	=	PUNCT
ejpam-4655	120	2	x	x	PUNCT
ejpam-4655	120	3	for	for	ADP
ejpam-4655	120	4	that	that	DET
ejpam-4655	120	5	c2(q	c2(q	PROPN
ejpam-4655	120	6	)	)	PUNCT
ejpam-4655	121	1	−	−	PROPN
ejpam-4655	121	2	q	q	NOUN
ejpam-4655	122	1	=	=	PUNCT
ejpam-4655	122	2	x	x	X
ejpam-4655	122	3	−	−	NOUN
ejpam-4655	122	4	q	q	NOUN
ejpam-4655	123	1	so	so	SCONJ
ejpam-4655	123	2	that	that	SCONJ
ejpam-4655	123	3	x	x	PUNCT
ejpam-4655	123	4	−	−	NOUN
ejpam-4655	123	5	q	q	NOUN
ejpam-4655	123	6	is	be	AUX
ejpam-4655	123	7	a	a	DET
ejpam-4655	123	8	µ1closed	µ1close	VERB
ejpam-4655	123	9	set	set	NOUN
ejpam-4655	123	10	,	,	PUNCT
ejpam-4655	123	11	by	by	ADP
ejpam-4655	123	12	assumption	assumption	NOUN
ejpam-4655	123	13	which	which	PRON
ejpam-4655	123	14	implies	imply	VERB
ejpam-4655	123	15	q	q	PROPN
ejpam-4655	123	16	∈	∈	PROPN
ejpam-4655	123	17	µ1	µ1	PROPN
ejpam-4655	123	18	.	.	PUNCT
ejpam-4655	124	1	therefore	therefore	ADV
ejpam-4655	124	2	,	,	PUNCT
ejpam-4655	124	3	x	x	X
ejpam-4655	124	4	is	be	AUX
ejpam-4655	124	5	a	a	DET
ejpam-4655	124	6	(	(	PUNCT
ejpam-4655	124	7	1	1	NUM
ejpam-4655	124	8	,	,	PUNCT
ejpam-4655	124	9	2)-bigeneralized	2)-bigeneralized	NUM
ejpam-4655	124	10	submaximal	submaximal	ADJ
ejpam-4655	124	11	space	space	NOUN
ejpam-4655	124	12	.	.	PUNCT
ejpam-4655	125	1	proposition	proposition	NOUN
ejpam-4655	125	2	6	6	NUM
ejpam-4655	125	3	.	.	PUNCT
ejpam-4655	126	1	let	let	AUX
ejpam-4655	126	2	(	(	PUNCT
ejpam-4655	126	3	x,µ1	x,µ1	NOUN
ejpam-4655	126	4	,	,	PUNCT
ejpam-4655	126	5	µ2	µ2	PROPN
ejpam-4655	126	6	)	)	PUNCT
ejpam-4655	126	7	be	be	AUX
ejpam-4655	126	8	a	a	DET
ejpam-4655	126	9	bgts	bgts	NOUN
ejpam-4655	126	10	.	.	PUNCT
ejpam-4655	127	1	if	if	SCONJ
ejpam-4655	127	2	x	x	PRON
ejpam-4655	127	3	is	be	AUX
ejpam-4655	127	4	a	a	DET
ejpam-4655	127	5	(	(	PUNCT
ejpam-4655	127	6	s	s	PROPN
ejpam-4655	127	7	,	,	PUNCT
ejpam-4655	127	8	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	127	9	submaximal	submaximal	ADJ
ejpam-4655	127	10	space	space	NOUN
ejpam-4655	127	11	,	,	PUNCT
ejpam-4655	127	12	then	then	ADV
ejpam-4655	127	13	(	(	PUNCT
ejpam-4655	127	14	x,µs	x,µs	NUM
ejpam-4655	127	15	)	)	PUNCT
ejpam-4655	127	16	is	be	AUX
ejpam-4655	127	17	a	a	DET
ejpam-4655	127	18	sgts	sgts	NOUN
ejpam-4655	127	19	where	where	SCONJ
ejpam-4655	127	20	s	s	X
ejpam-4655	127	21	,	,	PUNCT
ejpam-4655	127	22	v	v	NOUN
ejpam-4655	127	23	=	=	SYM
ejpam-4655	127	24	1	1	NUM
ejpam-4655	127	25	,	,	PUNCT
ejpam-4655	127	26	2	2	NUM
ejpam-4655	127	27	;	;	PUNCT
ejpam-4655	127	28	s	s	VERB
ejpam-4655	127	29	̸=	̸=	PROPN
ejpam-4655	127	30	v.	v.	ADP
ejpam-4655	127	31	proof	proof	NOUN
ejpam-4655	127	32	.	.	PUNCT
ejpam-4655	128	1	if	if	SCONJ
ejpam-4655	128	2	s	s	NOUN
ejpam-4655	128	3	=	=	SYM
ejpam-4655	128	4	1	1	NUM
ejpam-4655	128	5	,	,	PUNCT
ejpam-4655	128	6	v	v	NOUN
ejpam-4655	128	7	=	=	SYM
ejpam-4655	128	8	2	2	NUM
ejpam-4655	128	9	and	and	CCONJ
ejpam-4655	128	10	x	x	PRON
ejpam-4655	128	11	is	be	AUX
ejpam-4655	128	12	a	a	DET
ejpam-4655	128	13	(	(	PUNCT
ejpam-4655	128	14	1	1	NUM
ejpam-4655	128	15	,	,	PUNCT
ejpam-4655	128	16	2)-bigeneralized	2)-bigeneralized	NUM
ejpam-4655	128	17	submaximal	submaximal	ADJ
ejpam-4655	128	18	space	space	NOUN
ejpam-4655	128	19	,	,	PUNCT
ejpam-4655	128	20	then	then	ADV
ejpam-4655	128	21	every	every	DET
ejpam-4655	128	22	µ2dense	µ2dense	NOUN
ejpam-4655	128	23	subset	subset	NOUN
ejpam-4655	128	24	of	of	ADP
ejpam-4655	128	25	x	x	PUNCT
ejpam-4655	128	26	is	be	AUX
ejpam-4655	128	27	µ1	µ1	NOUN
ejpam-4655	128	28	-	-	PUNCT
ejpam-4655	128	29	open	open	ADJ
ejpam-4655	128	30	and	and	CCONJ
ejpam-4655	128	31	so	so	ADV
ejpam-4655	128	32	x	x	PUNCT
ejpam-4655	128	33	is	be	AUX
ejpam-4655	128	34	µ1	µ1	ADV
ejpam-4655	128	35	-	-	PUNCT
ejpam-4655	128	36	open	open	ADJ
ejpam-4655	128	37	whereby	whereby	SCONJ
ejpam-4655	128	38	(	(	PUNCT
ejpam-4655	128	39	x,µ1	x,µ1	NOUN
ejpam-4655	128	40	)	)	PUNCT
ejpam-4655	128	41	is	be	AUX
ejpam-4655	128	42	a	a	DET
ejpam-4655	128	43	sgts	sgts	NOUN
ejpam-4655	128	44	.	.	PUNCT
ejpam-4655	129	1	similarly	similarly	ADV
ejpam-4655	129	2	,	,	PUNCT
ejpam-4655	129	3	we	we	PRON
ejpam-4655	129	4	can	can	AUX
ejpam-4655	129	5	prove	prove	VERB
ejpam-4655	129	6	the	the	DET
ejpam-4655	129	7	result	result	NOUN
ejpam-4655	129	8	for	for	ADP
ejpam-4655	129	9	s	s	NOUN
ejpam-4655	129	10	=	=	SYM
ejpam-4655	129	11	2	2	NUM
ejpam-4655	129	12	;	;	PUNCT
ejpam-4655	129	13	v	v	NOUN
ejpam-4655	129	14	=	=	SYM
ejpam-4655	129	15	1	1	X
ejpam-4655	129	16	.	.	PUNCT
ejpam-4655	129	17	proposition	proposition	NOUN
ejpam-4655	129	18	7	7	NUM
ejpam-4655	129	19	.	.	PUNCT
ejpam-4655	130	1	let	let	AUX
ejpam-4655	130	2	(	(	PUNCT
ejpam-4655	130	3	x,µ1	x,µ1	NOUN
ejpam-4655	130	4	,	,	PUNCT
ejpam-4655	130	5	µ2	µ2	PROPN
ejpam-4655	130	6	)	)	PUNCT
ejpam-4655	130	7	be	be	VERB
ejpam-4655	130	8	a	a	DET
ejpam-4655	130	9	(	(	PUNCT
ejpam-4655	130	10	s	s	PROPN
ejpam-4655	130	11	,	,	PUNCT
ejpam-4655	130	12	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	130	13	submaximal	submaximal	ADJ
ejpam-4655	130	14	space	space	NOUN
ejpam-4655	130	15	.	.	PUNCT
ejpam-4655	131	1	if	if	SCONJ
ejpam-4655	131	2	q	q	X
ejpam-4655	131	3	∈	∈	PROPN
ejpam-4655	131	4	(	(	PUNCT
ejpam-4655	131	5	v	v	NOUN
ejpam-4655	131	6	,	,	PUNCT
ejpam-4655	131	7	s)−	s)−	PROPN
ejpam-4655	131	8	n	n	PART
ejpam-4655	131	9	(	(	PUNCT
ejpam-4655	131	10	x	x	X
ejpam-4655	131	11	)	)	PUNCT
ejpam-4655	131	12	,	,	PUNCT
ejpam-4655	131	13	then	then	ADV
ejpam-4655	131	14	it	it	PRON
ejpam-4655	131	15	is	be	AUX
ejpam-4655	131	16	a	a	DET
ejpam-4655	131	17	µs	µs	NOUN
ejpam-4655	131	18	-	-	PUNCT
ejpam-4655	131	19	closed	closed	ADJ
ejpam-4655	131	20	set	set	NOUN
ejpam-4655	131	21	where	where	SCONJ
ejpam-4655	131	22	s	s	X
ejpam-4655	131	23	,	,	PUNCT
ejpam-4655	131	24	v	v	NOUN
ejpam-4655	131	25	=	=	SYM
ejpam-4655	131	26	1	1	NUM
ejpam-4655	131	27	,	,	PUNCT
ejpam-4655	131	28	2	2	NUM
ejpam-4655	131	29	and	and	CCONJ
ejpam-4655	131	30	s	s	VERB
ejpam-4655	131	31	̸=	̸=	PROPN
ejpam-4655	131	32	v.	v.	ADP
ejpam-4655	131	33	proof	proof	NOUN
ejpam-4655	131	34	.	.	PUNCT
ejpam-4655	132	1	fix	fix	NOUN
ejpam-4655	132	2	s	s	PART
ejpam-4655	132	3	=	=	SYM
ejpam-4655	132	4	2	2	NUM
ejpam-4655	132	5	,	,	PUNCT
ejpam-4655	132	6	v	v	NOUN
ejpam-4655	132	7	=	=	SYM
ejpam-4655	132	8	1	1	NUM
ejpam-4655	132	9	,	,	PUNCT
ejpam-4655	132	10	by	by	ADP
ejpam-4655	132	11	hypothesis	hypothesis	NOUN
ejpam-4655	132	12	,	,	PUNCT
ejpam-4655	132	13	x	x	X
ejpam-4655	132	14	is	be	AUX
ejpam-4655	132	15	a	a	DET
ejpam-4655	132	16	(	(	PUNCT
ejpam-4655	132	17	2	2	NUM
ejpam-4655	132	18	,	,	PUNCT
ejpam-4655	132	19	1)-bigeneralized	1)-bigeneralized	NUM
ejpam-4655	132	20	submaximal	submaximal	ADJ
ejpam-4655	132	21	space	space	NOUN
ejpam-4655	132	22	and	and	CCONJ
ejpam-4655	132	23	let	let	VERB
ejpam-4655	132	24	q	q	PROPN
ejpam-4655	132	25	∈	∈	PROPN
ejpam-4655	132	26	(	(	PUNCT
ejpam-4655	132	27	1	1	NUM
ejpam-4655	132	28	,	,	PUNCT
ejpam-4655	132	29	2)−n	2)−n	NUM
ejpam-4655	132	30	(	(	PUNCT
ejpam-4655	132	31	x	x	X
ejpam-4655	132	32	)	)	PUNCT
ejpam-4655	132	33	so	so	ADV
ejpam-4655	132	34	i1(c2(q	i1(c2(q	NUM
ejpam-4655	132	35	)	)	PUNCT
ejpam-4655	132	36	)	)	PUNCT
ejpam-4655	133	1	=	=	NOUN
ejpam-4655	133	2	∅	∅	NOUN
ejpam-4655	133	3	for	for	ADP
ejpam-4655	133	4	that	that	PRON
ejpam-4655	133	5	i1(q	i1(q	NOUN
ejpam-4655	133	6	)	)	PUNCT
ejpam-4655	133	7	=	=	PUNCT
ejpam-4655	133	8	∅	∅	NOUN
ejpam-4655	133	9	whereby	whereby	ADV
ejpam-4655	133	10	by	by	ADP
ejpam-4655	133	11	theorem	theorem	NOUN
ejpam-4655	133	12	5	5	NUM
ejpam-4655	133	13	,	,	PUNCT
ejpam-4655	133	14	q	q	PUNCT
ejpam-4655	133	15	is	be	AUX
ejpam-4655	133	16	a	a	DET
ejpam-4655	133	17	µ2	µ2	NOUN
ejpam-4655	133	18	-	-	PUNCT
ejpam-4655	133	19	closed	close	VERB
ejpam-4655	133	20	set	set	NOUN
ejpam-4655	133	21	in	in	ADP
ejpam-4655	133	22	x.	x.	NOUN
ejpam-4655	133	23	by	by	ADP
ejpam-4655	133	24	similar	similar	ADJ
ejpam-4655	133	25	considerations	consideration	NOUN
ejpam-4655	133	26	,	,	PUNCT
ejpam-4655	133	27	we	we	PRON
ejpam-4655	133	28	get	get	VERB
ejpam-4655	133	29	the	the	DET
ejpam-4655	133	30	proof	proof	NOUN
ejpam-4655	133	31	for	for	ADP
ejpam-4655	133	32	s	s	NOUN
ejpam-4655	133	33	=	=	SYM
ejpam-4655	133	34	1	1	NUM
ejpam-4655	133	35	;	;	PUNCT
ejpam-4655	133	36	v	v	NOUN
ejpam-4655	133	37	=	=	SYM
ejpam-4655	133	38	2	2	NUM
ejpam-4655	133	39	.	.	PUNCT
ejpam-4655	134	1	the	the	DET
ejpam-4655	134	2	following	follow	VERB
ejpam-4655	134	3	example	example	NOUN
ejpam-4655	134	4	8	8	NUM
ejpam-4655	134	5	shows	show	VERB
ejpam-4655	134	6	that	that	SCONJ
ejpam-4655	134	7	the	the	DET
ejpam-4655	134	8	reverse	reverse	ADJ
ejpam-4655	134	9	implication	implication	NOUN
ejpam-4655	134	10	of	of	ADP
ejpam-4655	134	11	proposition	proposition	NOUN
ejpam-4655	134	12	7	7	NUM
ejpam-4655	134	13	need	need	AUX
ejpam-4655	134	14	not	not	PART
ejpam-4655	134	15	be	be	AUX
ejpam-4655	134	16	true	true	ADJ
ejpam-4655	134	17	.	.	PUNCT
ejpam-4655	135	1	example	example	NOUN
ejpam-4655	135	2	8	8	NUM
ejpam-4655	135	3	.	.	PUNCT
ejpam-4655	136	1	consider	consider	VERB
ejpam-4655	136	2	the	the	DET
ejpam-4655	136	3	bigeneralized	bigeneralized	ADJ
ejpam-4655	136	4	topological	topological	ADJ
ejpam-4655	136	5	space	space	NOUN
ejpam-4655	136	6	(	(	PUNCT
ejpam-4655	136	7	x,µ1	x,µ1	PROPN
ejpam-4655	136	8	,	,	PUNCT
ejpam-4655	136	9	µ2	µ2	ADJ
ejpam-4655	136	10	)	)	PUNCT
ejpam-4655	136	11	wherex	wherex	PROPN
ejpam-4655	136	12	=	=	PUNCT
ejpam-4655	136	13	{	{	PUNCT
ejpam-4655	136	14	p	p	X
ejpam-4655	136	15	,	,	PUNCT
ejpam-4655	136	16	q	q	ADJ
ejpam-4655	136	17	,	,	PUNCT
ejpam-4655	136	18	r	r	NOUN
ejpam-4655	136	19	,	,	PUNCT
ejpam-4655	136	20	s	s	PART
ejpam-4655	136	21	}	}	PUNCT
ejpam-4655	136	22	;	;	PUNCT
ejpam-4655	136	23	µ1	µ1	PROPN
ejpam-4655	136	24	=	=	SYM
ejpam-4655	136	25	{	{	PUNCT
ejpam-4655	136	26	∅	∅	NOUN
ejpam-4655	136	27	,	,	PUNCT
ejpam-4655	136	28	{	{	PUNCT
ejpam-4655	136	29	p	p	X
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ejpam-4655	136	31	q	q	NOUN
ejpam-4655	136	32	}	}	PUNCT
ejpam-4655	136	33	,	,	PUNCT
ejpam-4655	136	34	{	{	PUNCT
ejpam-4655	136	35	p	p	X
ejpam-4655	136	36	,	,	PUNCT
ejpam-4655	136	37	s	s	PART
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ejpam-4655	136	39	,	,	PUNCT
ejpam-4655	136	40	{	{	PUNCT
ejpam-4655	136	41	q	q	X
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ejpam-4655	136	43	r	r	NOUN
ejpam-4655	136	44	}	}	PUNCT
ejpam-4655	136	45	,	,	PUNCT
ejpam-4655	136	46	{	{	PUNCT
ejpam-4655	136	47	q	q	X
ejpam-4655	136	48	,	,	PUNCT
ejpam-4655	136	49	s	s	PART
ejpam-4655	136	50	}	}	PUNCT
ejpam-4655	136	51	,	,	PUNCT
ejpam-4655	136	52	{	{	PUNCT
ejpam-4655	136	53	r	r	NOUN
ejpam-4655	136	54	,	,	PUNCT
ejpam-4655	136	55	s	s	PART
ejpam-4655	136	56	}	}	PUNCT
ejpam-4655	136	57	,	,	PUNCT
ejpam-4655	136	58	{	{	PUNCT
ejpam-4655	136	59	p	p	X
ejpam-4655	136	60	,	,	PUNCT
ejpam-4655	136	61	q	q	ADJ
ejpam-4655	136	62	,	,	PUNCT
ejpam-4655	136	63	r	r	NOUN
ejpam-4655	136	64	}	}	PUNCT
ejpam-4655	136	65	,	,	PUNCT
ejpam-4655	136	66	{	{	PUNCT
ejpam-4655	136	67	p	p	X
ejpam-4655	136	68	,	,	PUNCT
ejpam-4655	136	69	q	q	X
ejpam-4655	136	70	,	,	PUNCT
ejpam-4655	136	71	s	s	PART
ejpam-4655	136	72	}	}	PUNCT
ejpam-4655	136	73	,	,	PUNCT
ejpam-4655	136	74	{	{	PUNCT
ejpam-4655	136	75	p	p	X
ejpam-4655	136	76	,	,	PUNCT
ejpam-4655	136	77	r	r	NOUN
ejpam-4655	136	78	,	,	PUNCT
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ejpam-4655	136	80	}	}	PUNCT
ejpam-4655	136	81	,	,	PUNCT
ejpam-4655	136	82	{	{	PUNCT
ejpam-4655	136	83	q	q	X
ejpam-4655	136	84	,	,	PUNCT
ejpam-4655	136	85	r	r	NOUN
ejpam-4655	136	86	,	,	PUNCT
ejpam-4655	136	87	s	s	PART
ejpam-4655	136	88	}	}	PUNCT
ejpam-4655	136	89	,	,	PUNCT
ejpam-4655	136	90	x	x	NOUN
ejpam-4655	136	91	}	}	PUNCT
ejpam-4655	136	92	and	and	CCONJ
ejpam-4655	136	93	µ2	µ2	PROPN
ejpam-4655	136	94	=	=	PUNCT
ejpam-4655	136	95	{	{	PUNCT
ejpam-4655	136	96	∅	∅	NOUN
ejpam-4655	136	97	,	,	PUNCT
ejpam-4655	136	98	{	{	PUNCT
ejpam-4655	136	99	q	q	NOUN
ejpam-4655	136	100	,	,	PUNCT
ejpam-4655	136	101	r	r	NOUN
ejpam-4655	136	102	}	}	PUNCT
ejpam-4655	136	103	,	,	PUNCT
ejpam-4655	136	104	{	{	PUNCT
ejpam-4655	136	105	q	q	X
ejpam-4655	136	106	,	,	PUNCT
ejpam-4655	136	107	s	s	PART
ejpam-4655	136	108	}	}	PUNCT
ejpam-4655	136	109	,	,	PUNCT
ejpam-4655	136	110	{	{	PUNCT
ejpam-4655	136	111	r	r	NOUN
ejpam-4655	136	112	,	,	PUNCT
ejpam-4655	136	113	s	s	PART
ejpam-4655	136	114	}	}	PUNCT
ejpam-4655	136	115	,	,	PUNCT
ejpam-4655	136	116	{	{	PUNCT
ejpam-4655	136	117	q	q	NOUN
ejpam-4655	136	118	,	,	PUNCT
ejpam-4655	136	119	r	r	NOUN
ejpam-4655	136	120	,	,	PUNCT
ejpam-4655	136	121	s}}.fix	s}}.fix	NOUN
ejpam-4655	136	122	s	s	PART
ejpam-4655	136	123	=	=	SYM
ejpam-4655	136	124	1	1	NUM
ejpam-4655	136	125	and	and	CCONJ
ejpam-4655	136	126	v	v	NOUN
ejpam-4655	136	127	=	=	SYM
ejpam-4655	136	128	2	2	NUM
ejpam-4655	136	129	.	.	PUNCT
ejpam-4655	136	130	here	here	ADV
ejpam-4655	136	131	every	every	DET
ejpam-4655	136	132	µ2	µ2	NOUN
ejpam-4655	136	133	-	-	PUNCT
ejpam-4655	136	134	dense	dense	NOUN
ejpam-4655	136	135	is	be	AUX
ejpam-4655	136	136	µ1	µ1	NOUN
ejpam-4655	136	137	-	-	PUNCT
ejpam-4655	136	138	open	open	ADJ
ejpam-4655	136	139	so	so	SCONJ
ejpam-4655	136	140	that	that	SCONJ
ejpam-4655	136	141	x	x	PRON
ejpam-4655	136	142	is	be	AUX
ejpam-4655	136	143	(	(	PUNCT
ejpam-4655	136	144	1	1	NUM
ejpam-4655	136	145	,	,	PUNCT
ejpam-4655	136	146	2)-bigeneralized	2)-bigeneralized	NUM
ejpam-4655	136	147	submaximal	submaximal	ADJ
ejpam-4655	136	148	space	space	NOUN
ejpam-4655	136	149	.	.	PUNCT
ejpam-4655	137	1	choose	choose	VERB
ejpam-4655	137	2	l	l	NOUN
ejpam-4655	137	3	=	=	SYM
ejpam-4655	137	4	{	{	PUNCT
ejpam-4655	137	5	r	r	NOUN
ejpam-4655	137	6	,	,	PUNCT
ejpam-4655	137	7	s	s	AUX
ejpam-4655	137	8	}	}	PUNCT
ejpam-4655	137	9	we	we	PRON
ejpam-4655	137	10	get	get	VERB
ejpam-4655	137	11	l	l	NOUN
ejpam-4655	137	12	is	be	AUX
ejpam-4655	137	13	µ1	µ1	NOUN
ejpam-4655	137	14	-	-	PUNCT
ejpam-4655	137	15	closed	closed	ADJ
ejpam-4655	137	16	but	but	CCONJ
ejpam-4655	137	17	not	not	PART
ejpam-4655	137	18	in	in	ADP
ejpam-4655	137	19	(	(	PUNCT
ejpam-4655	137	20	2	2	NUM
ejpam-4655	137	21	,	,	PUNCT
ejpam-4655	137	22	1)−n	1)−n	NUM
ejpam-4655	137	23	(	(	PUNCT
ejpam-4655	137	24	x	x	NOUN
ejpam-4655	137	25	)	)	PUNCT
ejpam-4655	137	26	.	.	PUNCT
ejpam-4655	138	1	because	because	SCONJ
ejpam-4655	138	2	,	,	PUNCT
ejpam-4655	138	3	i2(c1(l	i2(c1(l	PROPN
ejpam-4655	138	4	)	)	PUNCT
ejpam-4655	138	5	)	)	PUNCT
ejpam-4655	139	1	=	=	PUNCT
ejpam-4655	139	2	i2(l	i2(l	X
ejpam-4655	139	3	)	)	PUNCT
ejpam-4655	139	4	=	=	PUNCT
ejpam-4655	139	5	l	l	NOUN
ejpam-4655	139	6	̸=	̸=	PROPN
ejpam-4655	139	7	∅.	∅.	ADV
ejpam-4655	139	8	choose	choose	VERB
ejpam-4655	139	9	s	s	PART
ejpam-4655	139	10	=	=	SYM
ejpam-4655	139	11	2	2	NUM
ejpam-4655	139	12	and	and	CCONJ
ejpam-4655	139	13	v	v	NOUN
ejpam-4655	139	14	=	=	SYM
ejpam-4655	139	15	1	1	X
ejpam-4655	139	16	.	.	X
ejpam-4655	139	17	take	take	VERB
ejpam-4655	139	18	µ1	µ1	NOUN
ejpam-4655	139	19	=	=	SYM
ejpam-4655	139	20	{	{	PUNCT
ejpam-4655	139	21	∅	∅	NOUN
ejpam-4655	139	22	,	,	PUNCT
ejpam-4655	139	23	{	{	PUNCT
ejpam-4655	139	24	r	r	NOUN
ejpam-4655	139	25	}	}	PUNCT
ejpam-4655	139	26	,	,	PUNCT
ejpam-4655	139	27	{	{	PUNCT
ejpam-4655	139	28	q	q	X
ejpam-4655	139	29	,	,	PUNCT
ejpam-4655	139	30	r	r	NOUN
ejpam-4655	139	31	}	}	PUNCT
ejpam-4655	139	32	,	,	PUNCT
ejpam-4655	139	33	{	{	PUNCT
ejpam-4655	139	34	q	q	X
ejpam-4655	139	35	,	,	PUNCT
ejpam-4655	139	36	s	s	PART
ejpam-4655	139	37	}	}	PUNCT
ejpam-4655	139	38	,	,	PUNCT
ejpam-4655	139	39	{	{	PUNCT
ejpam-4655	139	40	q	q	X
ejpam-4655	139	41	,	,	PUNCT
ejpam-4655	139	42	r	r	NOUN
ejpam-4655	139	43	,	,	PUNCT
ejpam-4655	139	44	s}};µ2	s}};µ2	VERB
ejpam-4655	139	45	=	=	SYM
ejpam-4655	139	46	{	{	PUNCT
ejpam-4655	139	47	∅	∅	NOUN
ejpam-4655	139	48	,	,	PUNCT
ejpam-4655	139	49	{	{	PUNCT
ejpam-4655	139	50	q	q	NOUN
ejpam-4655	139	51	,	,	PUNCT
ejpam-4655	139	52	r	r	NOUN
ejpam-4655	139	53	}	}	PUNCT
ejpam-4655	139	54	,	,	PUNCT
ejpam-4655	139	55	{	{	PUNCT
ejpam-4655	139	56	q	q	X
ejpam-4655	139	57	,	,	PUNCT
ejpam-4655	139	58	s	s	PART
ejpam-4655	139	59	}	}	PUNCT
ejpam-4655	139	60	,	,	PUNCT
ejpam-4655	139	61	{	{	PUNCT
ejpam-4655	139	62	r	r	NOUN
ejpam-4655	139	63	,	,	PUNCT
ejpam-4655	139	64	s	s	PART
ejpam-4655	139	65	}	}	PUNCT
ejpam-4655	139	66	,	,	PUNCT
ejpam-4655	139	67	{	{	PUNCT
ejpam-4655	139	68	p	p	X
ejpam-4655	139	69	,	,	PUNCT
ejpam-4655	139	70	q	q	ADJ
ejpam-4655	139	71	,	,	PUNCT
ejpam-4655	139	72	r	r	NOUN
ejpam-4655	139	73	}	}	PUNCT
ejpam-4655	139	74	,	,	PUNCT
ejpam-4655	139	75	{	{	PUNCT
ejpam-4655	139	76	p	p	X
ejpam-4655	139	77	,	,	PUNCT
ejpam-4655	139	78	r	r	NOUN
ejpam-4655	139	79	,	,	PUNCT
ejpam-4655	139	80	s	s	PART
ejpam-4655	139	81	}	}	PUNCT
ejpam-4655	139	82	,	,	PUNCT
ejpam-4655	139	83	{	{	PUNCT
ejpam-4655	139	84	q	q	X
ejpam-4655	139	85	,	,	PUNCT
ejpam-4655	139	86	r	r	NOUN
ejpam-4655	139	87	,	,	PUNCT
ejpam-4655	139	88	s	s	PART
ejpam-4655	139	89	}	}	PUNCT
ejpam-4655	139	90	,	,	PUNCT
ejpam-4655	139	91	x	x	NOUN
ejpam-4655	139	92	}	}	PUNCT
ejpam-4655	139	93	.	.	PUNCT
ejpam-4655	140	1	since	since	SCONJ
ejpam-4655	140	2	every	every	DET
ejpam-4655	140	3	µ1	µ1	NOUN
ejpam-4655	140	4	-	-	PUNCT
ejpam-4655	140	5	dense	dense	ADJ
ejpam-4655	140	6	set	set	NOUN
ejpam-4655	140	7	is	be	AUX
ejpam-4655	140	8	µ2	µ2	ADJ
ejpam-4655	140	9	-	-	PUNCT
ejpam-4655	140	10	open	open	ADJ
ejpam-4655	140	11	we	we	PRON
ejpam-4655	140	12	have	have	AUX
ejpam-4655	140	13	x	x	INTJ
ejpam-4655	140	14	is	be	AUX
ejpam-4655	140	15	(	(	PUNCT
ejpam-4655	140	16	2	2	NUM
ejpam-4655	140	17	,	,	PUNCT
ejpam-4655	140	18	1)bigeneralized	1)bigeneralized	NUM
ejpam-4655	140	19	submaximal	submaximal	ADJ
ejpam-4655	140	20	space	space	NOUN
ejpam-4655	140	21	.	.	PUNCT
ejpam-4655	141	1	consider	consider	VERB
ejpam-4655	141	2	k	k	NOUN
ejpam-4655	141	3	=	=	PRON
ejpam-4655	141	4	{	{	PUNCT
ejpam-4655	141	5	p	p	X
ejpam-4655	141	6	,	,	PUNCT
ejpam-4655	141	7	r	r	NOUN
ejpam-4655	141	8	}	}	PUNCT
ejpam-4655	141	9	.	.	PUNCT
ejpam-4655	142	1	then	then	ADV
ejpam-4655	142	2	k	k	PROPN
ejpam-4655	142	3	is	be	AUX
ejpam-4655	142	4	µ2	µ2	ADJ
ejpam-4655	142	5	-	-	PUNCT
ejpam-4655	142	6	closed	closed	ADJ
ejpam-4655	142	7	but	but	CCONJ
ejpam-4655	142	8	not	not	PART
ejpam-4655	142	9	in	in	ADP
ejpam-4655	142	10	(	(	PUNCT
ejpam-4655	142	11	1	1	NUM
ejpam-4655	142	12	,	,	PUNCT
ejpam-4655	142	13	2)−n	2)−n	NUM
ejpam-4655	142	14	(	(	PUNCT
ejpam-4655	142	15	x	x	NOUN
ejpam-4655	142	16	)	)	PUNCT
ejpam-4655	142	17	,	,	PUNCT
ejpam-4655	142	18	because	because	SCONJ
ejpam-4655	142	19	,	,	PUNCT
ejpam-4655	142	20	i1(c2(k	i1(c2(k	PROPN
ejpam-4655	142	21	)	)	PUNCT
ejpam-4655	142	22	)	)	PUNCT
ejpam-4655	143	1	=	=	PUNCT
ejpam-4655	143	2	i1(k	i1(k	X
ejpam-4655	143	3	)	)	PUNCT
ejpam-4655	143	4	=	=	NOUN
ejpam-4655	143	5	{	{	PUNCT
ejpam-4655	143	6	r	r	NOUN
ejpam-4655	143	7	}	}	PUNCT
ejpam-4655	143	8	=	=	NOUN
ejpam-4655	143	9	̸	̸	ADV
ejpam-4655	143	10	∅.	∅.	VERB
ejpam-4655	143	11	proposition	proposition	NOUN
ejpam-4655	143	12	9	9	NUM
ejpam-4655	143	13	.	.	PUNCT
ejpam-4655	144	1	let	let	AUX
ejpam-4655	144	2	(	(	PUNCT
ejpam-4655	144	3	x,µ1	x,µ1	NOUN
ejpam-4655	144	4	,	,	PUNCT
ejpam-4655	144	5	µ2	µ2	PROPN
ejpam-4655	144	6	)	)	PUNCT
ejpam-4655	144	7	be	be	VERB
ejpam-4655	144	8	a	a	DET
ejpam-4655	144	9	(	(	PUNCT
ejpam-4655	144	10	s	s	PROPN
ejpam-4655	144	11	,	,	PUNCT
ejpam-4655	144	12	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	144	13	submaximal	submaximal	ADJ
ejpam-4655	144	14	space	space	NOUN
ejpam-4655	144	15	.	.	PUNCT
ejpam-4655	145	1	if	if	SCONJ
ejpam-4655	145	2	µs	µs	X
ejpam-4655	145	3	⊂	⊂	PROPN
ejpam-4655	145	4	µv	µv	PROPN
ejpam-4655	145	5	,	,	PUNCT
ejpam-4655	145	6	then	then	ADV
ejpam-4655	145	7	(	(	PUNCT
ejpam-4655	145	8	x,µv	x,µv	PROPN
ejpam-4655	145	9	)	)	PUNCT
ejpam-4655	145	10	is	be	AUX
ejpam-4655	145	11	a	a	DET
ejpam-4655	145	12	generalized	generalized	ADJ
ejpam-4655	145	13	submaximal	submaximal	ADJ
ejpam-4655	145	14	space	space	NOUN
ejpam-4655	145	15	where	where	SCONJ
ejpam-4655	145	16	s	s	X
ejpam-4655	145	17	,	,	PUNCT
ejpam-4655	145	18	v	v	NOUN
ejpam-4655	145	19	=	=	SYM
ejpam-4655	145	20	1	1	NUM
ejpam-4655	145	21	,	,	PUNCT
ejpam-4655	145	22	2	2	NUM
ejpam-4655	145	23	;	;	PUNCT
ejpam-4655	145	24	s	s	VERB
ejpam-4655	145	25	̸=	̸=	PROPN
ejpam-4655	145	26	v.	v.	ADP
ejpam-4655	145	27	proof	proof	NOUN
ejpam-4655	145	28	.	.	PUNCT
ejpam-4655	146	1	assume	assume	VERB
ejpam-4655	146	2	that	that	SCONJ
ejpam-4655	146	3	,	,	PUNCT
ejpam-4655	146	4	x	x	PRON
ejpam-4655	146	5	is	be	AUX
ejpam-4655	146	6	a	a	DET
ejpam-4655	146	7	(	(	PUNCT
ejpam-4655	146	8	s	s	PROPN
ejpam-4655	146	9	,	,	PUNCT
ejpam-4655	146	10	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	146	11	submaximal	submaximal	ADJ
ejpam-4655	146	12	space	space	NOUN
ejpam-4655	146	13	.	.	PUNCT
ejpam-4655	147	1	take	take	VERB
ejpam-4655	147	2	s	s	NOUN
ejpam-4655	147	3	=	=	SYM
ejpam-4655	147	4	2	2	NUM
ejpam-4655	147	5	,	,	PUNCT
ejpam-4655	147	6	v	v	NOUN
ejpam-4655	147	7	=	=	SYM
ejpam-4655	147	8	1	1	NUM
ejpam-4655	148	1	then	then	ADV
ejpam-4655	148	2	we	we	PRON
ejpam-4655	148	3	get	get	VERB
ejpam-4655	148	4	x	x	SYM
ejpam-4655	148	5	is	be	AUX
ejpam-4655	148	6	(	(	PUNCT
ejpam-4655	148	7	2	2	NUM
ejpam-4655	148	8	,	,	PUNCT
ejpam-4655	148	9	1)-bigeneralized	1)-bigeneralized	NUM
ejpam-4655	148	10	submaximal	submaximal	ADJ
ejpam-4655	148	11	and	and	CCONJ
ejpam-4655	148	12	µ2	µ2	PROPN
ejpam-4655	148	13	⊂	⊂	PROPN
ejpam-4655	148	14	µ1	µ1	PROPN
ejpam-4655	148	15	.	.	PUNCT
ejpam-4655	149	1	let	let	VERB
ejpam-4655	149	2	k	k	PRON
ejpam-4655	149	3	be	be	AUX
ejpam-4655	149	4	a	a	DET
ejpam-4655	149	5	µ1	µ1	NOUN
ejpam-4655	149	6	-	-	PUNCT
ejpam-4655	149	7	dense	dense	ADJ
ejpam-4655	149	8	set	set	NOUN
ejpam-4655	149	9	in	in	ADP
ejpam-4655	149	10	x	x	PUNCT
ejpam-4655	149	11	we	we	PRON
ejpam-4655	149	12	have	have	VERB
ejpam-4655	149	13	iµ1(x	iµ1(x	PROPN
ejpam-4655	150	1	−	−	PROPN
ejpam-4655	151	1	k	k	NOUN
ejpam-4655	151	2	)	)	PUNCT
ejpam-4655	151	3	=	=	NOUN
ejpam-4655	151	4	∅	∅	NOUN
ejpam-4655	151	5	so	so	SCONJ
ejpam-4655	151	6	that	that	SCONJ
ejpam-4655	151	7	x	x	PUNCT
ejpam-4655	152	1	−	−	X
ejpam-4655	152	2	k	k	PROPN
ejpam-4655	152	3	is	be	AUX
ejpam-4655	152	4	µ2	µ2	ADJ
ejpam-4655	152	5	-	-	PUNCT
ejpam-4655	152	6	closed	closed	ADJ
ejpam-4655	152	7	,	,	PUNCT
ejpam-4655	152	8	by	by	ADP
ejpam-4655	152	9	hypothesis	hypothesis	NOUN
ejpam-4655	152	10	and	and	CCONJ
ejpam-4655	152	11	theorem	theorem	VERB
ejpam-4655	152	12	5	5	NUM
ejpam-4655	152	13	.	.	PUNCT
ejpam-4655	153	1	thus	thus	ADV
ejpam-4655	153	2	,	,	PUNCT
ejpam-4655	153	3	k	k	PROPN
ejpam-4655	153	4	is	be	AUX
ejpam-4655	153	5	µ2	µ2	ADJ
ejpam-4655	153	6	-	-	PUNCT
ejpam-4655	153	7	open	open	ADJ
ejpam-4655	153	8	for	for	ADP
ejpam-4655	153	9	that	that	PRON
ejpam-4655	153	10	k	k	PROPN
ejpam-4655	153	11	is	be	AUX
ejpam-4655	153	12	µ1	µ1	NOUN
ejpam-4655	153	13	-	-	PUNCT
ejpam-4655	153	14	open	open	ADJ
ejpam-4655	153	15	,	,	PUNCT
ejpam-4655	153	16	since	since	SCONJ
ejpam-4655	153	17	µ2	µ2	PROPN
ejpam-4655	153	18	⊂	⊂	PROPN
ejpam-4655	153	19	µ1	µ1	PROPN
ejpam-4655	153	20	.	.	PUNCT
ejpam-4655	154	1	hence	hence	ADV
ejpam-4655	154	2	(	(	PUNCT
ejpam-4655	154	3	x,µ1	x,µ1	NOUN
ejpam-4655	154	4	)	)	PUNCT
ejpam-4655	154	5	is	be	AUX
ejpam-4655	154	6	generalized	generalize	VERB
ejpam-4655	154	7	submaximal	submaximal	ADJ
ejpam-4655	154	8	.	.	PUNCT
ejpam-4655	155	1	by	by	ADP
ejpam-4655	155	2	similar	similar	ADJ
ejpam-4655	155	3	arguments	argument	NOUN
ejpam-4655	155	4	,	,	PUNCT
ejpam-4655	155	5	we	we	PRON
ejpam-4655	155	6	can	can	AUX
ejpam-4655	155	7	prove	prove	VERB
ejpam-4655	155	8	this	this	DET
ejpam-4655	155	9	result	result	NOUN
ejpam-4655	155	10	for	for	ADP
ejpam-4655	155	11	the	the	DET
ejpam-4655	155	12	case	case	NOUN
ejpam-4655	155	13	s	s	PART
ejpam-4655	155	14	=	=	SYM
ejpam-4655	155	15	1	1	NUM
ejpam-4655	155	16	,	,	PUNCT
ejpam-4655	155	17	v	v	NOUN
ejpam-4655	155	18	=	=	SYM
ejpam-4655	155	19	2	2	NUM
ejpam-4655	155	20	.	.	PUNCT
ejpam-4655	155	21	y.	y.	PROPN
ejpam-4655	155	22	farhat	farhat	PROPN
ejpam-4655	155	23	et	et	PROPN
ejpam-4655	155	24	al	al	PROPN
ejpam-4655	155	25	.	.	PUNCT
ejpam-4655	155	26	/	/	SYM
ejpam-4655	155	27	eur	eur	PROPN
ejpam-4655	155	28	.	.	PUNCT
ejpam-4655	156	1	j.	j.	PROPN
ejpam-4655	156	2	pure	pure	PROPN
ejpam-4655	156	3	appl	appl	PROPN
ejpam-4655	156	4	.	.	PROPN
ejpam-4655	156	5	math	math	PROPN
ejpam-4655	156	6	,	,	PUNCT
ejpam-4655	156	7	16	16	NUM
ejpam-4655	156	8	(	(	PUNCT
ejpam-4655	156	9	1	1	NUM
ejpam-4655	156	10	)	)	PUNCT
ejpam-4655	156	11	(	(	PUNCT
ejpam-4655	156	12	2023	2023	NUM
ejpam-4655	156	13	)	)	PUNCT
ejpam-4655	156	14	,	,	PUNCT
ejpam-4655	156	15	386	386	NUM
ejpam-4655	156	16	-	-	SYM
ejpam-4655	156	17	403	403	NUM
ejpam-4655	156	18	391	391	NUM
ejpam-4655	156	19	in	in	ADP
ejpam-4655	156	20	a	a	DET
ejpam-4655	156	21	bgts	bgts	NOUN
ejpam-4655	156	22	(	(	PUNCT
ejpam-4655	156	23	x,µ1	x,µ1	PROPN
ejpam-4655	156	24	,	,	PUNCT
ejpam-4655	156	25	µ2	µ2	PROPN
ejpam-4655	156	26	)	)	PUNCT
ejpam-4655	156	27	,	,	PUNCT
ejpam-4655	156	28	if	if	SCONJ
ejpam-4655	156	29	µ1	µ1	PROPN
ejpam-4655	156	30	=	=	SYM
ejpam-4655	156	31	µ2	µ2	PROPN
ejpam-4655	156	32	=	=	PROPN
ejpam-4655	156	33	µ	µ	NUM
ejpam-4655	156	34	,	,	PUNCT
ejpam-4655	156	35	then	then	ADV
ejpam-4655	156	36	every	every	DET
ejpam-4655	156	37	generalized	generalize	VERB
ejpam-4655	156	38	submaximal	submaximal	ADJ
ejpam-4655	156	39	space	space	NOUN
ejpam-4655	156	40	is	be	AUX
ejpam-4655	156	41	a	a	DET
ejpam-4655	156	42	pairwise	pairwise	NOUN
ejpam-4655	156	43	bigeneralized	bigeneralize	VERB
ejpam-4655	156	44	submaximal	submaximal	ADJ
ejpam-4655	156	45	space	space	NOUN
ejpam-4655	156	46	,	,	PUNCT
ejpam-4655	156	47	and	and	CCONJ
ejpam-4655	156	48	conversely	conversely	ADV
ejpam-4655	156	49	.	.	PUNCT
ejpam-4655	157	1	theorem	theorem	ADJ
ejpam-4655	157	2	10	10	NUM
ejpam-4655	157	3	.	.	PUNCT
ejpam-4655	158	1	let	let	VERB
ejpam-4655	158	2	(	(	PUNCT
ejpam-4655	158	3	x,µ1	x,µ1	NOUN
ejpam-4655	158	4	,	,	PUNCT
ejpam-4655	158	5	µ2	µ2	PROPN
ejpam-4655	158	6	)	)	PUNCT
ejpam-4655	158	7	and	and	CCONJ
ejpam-4655	158	8	(	(	PUNCT
ejpam-4655	158	9	x	x	NOUN
ejpam-4655	158	10	,	,	PUNCT
ejpam-4655	158	11	η1	η1	NOUN
ejpam-4655	158	12	,	,	PUNCT
ejpam-4655	158	13	η2	η2	PROPN
ejpam-4655	158	14	)	)	PUNCT
ejpam-4655	158	15	be	be	VERB
ejpam-4655	158	16	two	two	NUM
ejpam-4655	158	17	bgtss	bgtss	NOUN
ejpam-4655	158	18	.	.	PUNCT
ejpam-4655	159	1	if	if	SCONJ
ejpam-4655	159	2	µi	µi	PROPN
ejpam-4655	159	3	⊂	⊂	PROPN
ejpam-4655	159	4	ηi	ηi	INTJ
ejpam-4655	159	5	where	where	SCONJ
ejpam-4655	159	6	i	i	PRON
ejpam-4655	159	7	=	=	NOUN
ejpam-4655	159	8	1	1	NUM
ejpam-4655	159	9	,	,	PUNCT
ejpam-4655	159	10	2	2	NUM
ejpam-4655	159	11	,	,	PUNCT
ejpam-4655	159	12	and	and	CCONJ
ejpam-4655	159	13	if	if	SCONJ
ejpam-4655	159	14	x	x	PRON
ejpam-4655	159	15	is	be	AUX
ejpam-4655	159	16	a	a	DET
ejpam-4655	159	17	(	(	PUNCT
ejpam-4655	159	18	µs	µs	NOUN
ejpam-4655	159	19	,	,	PUNCT
ejpam-4655	159	20	µv)-bigeneralized	µv)-bigeneralize	VERB
ejpam-4655	159	21	submaximal	submaximal	ADJ
ejpam-4655	159	22	space	space	NOUN
ejpam-4655	159	23	,	,	PUNCT
ejpam-4655	159	24	then	then	ADV
ejpam-4655	159	25	x	x	PUNCT
ejpam-4655	159	26	is	be	AUX
ejpam-4655	159	27	a	a	DET
ejpam-4655	159	28	(	(	PUNCT
ejpam-4655	159	29	ηs	ηs	PROPN
ejpam-4655	159	30	,	,	PUNCT
ejpam-4655	159	31	ηv)-bigeneralized	ηv)-bigeneralize	VERB
ejpam-4655	159	32	submaximal	submaximal	ADJ
ejpam-4655	159	33	space	space	NOUN
ejpam-4655	159	34	for	for	ADP
ejpam-4655	159	35	s	s	PROPN
ejpam-4655	159	36	,	,	PUNCT
ejpam-4655	159	37	v	v	NOUN
ejpam-4655	159	38	=	=	SYM
ejpam-4655	159	39	1	1	NUM
ejpam-4655	159	40	,	,	PUNCT
ejpam-4655	159	41	2	2	NUM
ejpam-4655	159	42	and	and	CCONJ
ejpam-4655	159	43	s	s	PART
ejpam-4655	159	44	̸=	̸=	PROPN
ejpam-4655	159	45	v.	v.	ADP
ejpam-4655	159	46	theorem	theorem	ADJ
ejpam-4655	159	47	11	11	NUM
ejpam-4655	159	48	.	.	PUNCT
ejpam-4655	160	1	let	let	AUX
ejpam-4655	160	2	(	(	PUNCT
ejpam-4655	160	3	x,µ1	x,µ1	NOUN
ejpam-4655	160	4	,	,	PUNCT
ejpam-4655	160	5	µ2	µ2	PROPN
ejpam-4655	160	6	)	)	PUNCT
ejpam-4655	160	7	be	be	VERB
ejpam-4655	160	8	a	a	DET
ejpam-4655	160	9	bgts	bgts	NOUN
ejpam-4655	160	10	and	and	CCONJ
ejpam-4655	160	11	q	q	AUX
ejpam-4655	160	12	be	be	AUX
ejpam-4655	160	13	a	a	DET
ejpam-4655	160	14	non	non	ADJ
ejpam-4655	160	15	-	-	ADJ
ejpam-4655	160	16	null	null	ADJ
ejpam-4655	160	17	subset	subset	NOUN
ejpam-4655	160	18	of	of	ADP
ejpam-4655	160	19	x.	x.	NOUN
ejpam-4655	160	20	if	if	SCONJ
ejpam-4655	160	21	x	x	PRON
ejpam-4655	160	22	is	be	AUX
ejpam-4655	160	23	a	a	DET
ejpam-4655	160	24	(	(	PUNCT
ejpam-4655	160	25	s	s	PROPN
ejpam-4655	160	26	,	,	PUNCT
ejpam-4655	160	27	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	160	28	submaximal	submaximal	ADJ
ejpam-4655	160	29	space	space	NOUN
ejpam-4655	160	30	,	,	PUNCT
ejpam-4655	160	31	then	then	ADV
ejpam-4655	160	32	cv(q)−q	cv(q)−q	VERB
ejpam-4655	160	33	∈	∈	PROPN
ejpam-4655	160	34	(	(	PUNCT
ejpam-4655	160	35	v	v	NOUN
ejpam-4655	160	36	,	,	PUNCT
ejpam-4655	160	37	s)−n	s)−n	X
ejpam-4655	160	38	(	(	PUNCT
ejpam-4655	160	39	x	x	NOUN
ejpam-4655	160	40	)	)	PUNCT
ejpam-4655	160	41	where	where	SCONJ
ejpam-4655	160	42	s	s	X
ejpam-4655	160	43	,	,	PUNCT
ejpam-4655	160	44	v	v	NOUN
ejpam-4655	160	45	=	=	SYM
ejpam-4655	160	46	1	1	NUM
ejpam-4655	160	47	,	,	PUNCT
ejpam-4655	160	48	2	2	NUM
ejpam-4655	160	49	;	;	PUNCT
ejpam-4655	160	50	s	s	VERB
ejpam-4655	160	51	̸=	̸=	PROPN
ejpam-4655	160	52	v.	v.	ADP
ejpam-4655	160	53	proof	proof	NOUN
ejpam-4655	160	54	.	.	PUNCT
ejpam-4655	161	1	it	it	PRON
ejpam-4655	161	2	is	be	AUX
ejpam-4655	161	3	enough	enough	ADJ
ejpam-4655	161	4	to	to	ADP
ejpam-4655	161	5	the	the	DET
ejpam-4655	161	6	case	case	NOUN
ejpam-4655	161	7	only	only	ADV
ejpam-4655	161	8	for	for	ADP
ejpam-4655	161	9	s	s	NOUN
ejpam-4655	161	10	=	=	SYM
ejpam-4655	161	11	1	1	NUM
ejpam-4655	161	12	,	,	PUNCT
ejpam-4655	161	13	v	v	NOUN
ejpam-4655	161	14	=	=	SYM
ejpam-4655	161	15	2	2	X
ejpam-4655	161	16	.	.	X
ejpam-4655	161	17	assume	assume	VERB
ejpam-4655	161	18	that	that	SCONJ
ejpam-4655	161	19	,	,	PUNCT
ejpam-4655	161	20	x	x	PRON
ejpam-4655	161	21	is	be	AUX
ejpam-4655	161	22	a	a	DET
ejpam-4655	161	23	(	(	PUNCT
ejpam-4655	161	24	1	1	NUM
ejpam-4655	161	25	,	,	PUNCT
ejpam-4655	161	26	2)−	2)−	NUM
ejpam-4655	161	27	bigeneralized	bigeneralize	VERB
ejpam-4655	161	28	submaximal	submaximal	ADJ
ejpam-4655	161	29	space	space	NOUN
ejpam-4655	161	30	(	(	PUNCT
ejpam-4655	161	31	1	1	NUM
ejpam-4655	161	32	)	)	PUNCT
ejpam-4655	161	33	and	and	CCONJ
ejpam-4655	161	34	q	q	NOUN
ejpam-4655	161	35	is	be	AUX
ejpam-4655	161	36	a	a	DET
ejpam-4655	161	37	non	non	ADJ
ejpam-4655	161	38	-	-	ADJ
ejpam-4655	161	39	null	null	ADJ
ejpam-4655	161	40	subset	subset	NOUN
ejpam-4655	161	41	of	of	ADP
ejpam-4655	161	42	x	x	PRON
ejpam-4655	161	43	,	,	PUNCT
ejpam-4655	161	44	consider	consider	VERB
ejpam-4655	161	45	,	,	PUNCT
ejpam-4655	161	46	g	g	NOUN
ejpam-4655	161	47	=	=	PUNCT
ejpam-4655	161	48	c2(q)−q	c2(q)−q	PROPN
ejpam-4655	161	49	.	.	PUNCT
ejpam-4655	162	1	by	by	ADP
ejpam-4655	162	2	lemma	lemma	PROPN
ejpam-4655	162	3	1	1	NUM
ejpam-4655	162	4	,	,	PUNCT
ejpam-4655	162	5	i2(g	i2(g	NUM
ejpam-4655	162	6	)	)	PUNCT
ejpam-4655	162	7	=	=	SYM
ejpam-4655	162	8	∅	∅	NOUN
ejpam-4655	163	1	and	and	CCONJ
ejpam-4655	163	2	so	so	ADV
ejpam-4655	163	3	g	g	PROPN
ejpam-4655	163	4	is	be	AUX
ejpam-4655	163	5	a	a	DET
ejpam-4655	163	6	µ1	µ1	NOUN
ejpam-4655	163	7	-	-	PUNCT
ejpam-4655	163	8	closed	closed	ADJ
ejpam-4655	163	9	set	set	NOUN
ejpam-4655	163	10	,	,	PUNCT
ejpam-4655	163	11	by	by	ADP
ejpam-4655	163	12	(	(	PUNCT
ejpam-4655	163	13	1	1	NUM
ejpam-4655	163	14	)	)	PUNCT
ejpam-4655	163	15	.	.	PUNCT
ejpam-4655	164	1	thus	thus	ADV
ejpam-4655	164	2	,	,	PUNCT
ejpam-4655	164	3	i2(c1(g	i2(c1(g	NOUN
ejpam-4655	164	4	)	)	PUNCT
ejpam-4655	164	5	)	)	PUNCT
ejpam-4655	165	1	=	=	PUNCT
ejpam-4655	165	2	∅.	∅.	VERB
ejpam-4655	165	3	therefore	therefore	ADV
ejpam-4655	165	4	,	,	PUNCT
ejpam-4655	165	5	c2(q)−q	c2(q)−q	X
ejpam-4655	165	6	∈	∈	PROPN
ejpam-4655	165	7	(	(	PUNCT
ejpam-4655	165	8	2	2	NUM
ejpam-4655	165	9	,	,	PUNCT
ejpam-4655	165	10	1)−n	1)−n	NUM
ejpam-4655	165	11	(	(	PUNCT
ejpam-4655	165	12	x	x	NOUN
ejpam-4655	165	13	)	)	PUNCT
ejpam-4655	165	14	.	.	PUNCT
ejpam-4655	166	1	the	the	DET
ejpam-4655	166	2	below	below	ADJ
ejpam-4655	166	3	theorem	theorem	NOUN
ejpam-4655	166	4	12	12	NUM
ejpam-4655	166	5	easily	easily	ADV
ejpam-4655	166	6	follows	follow	VERB
ejpam-4655	166	7	from	from	ADP
ejpam-4655	166	8	similar	similar	ADJ
ejpam-4655	166	9	considerations	consideration	NOUN
ejpam-4655	166	10	in	in	ADP
ejpam-4655	166	11	the	the	DET
ejpam-4655	166	12	above	above	ADJ
ejpam-4655	166	13	theorem	theorem	NOUN
ejpam-4655	166	14	11	11	NUM
ejpam-4655	166	15	.	.	PUNCT
ejpam-4655	167	1	theorem	theorem	NOUN
ejpam-4655	167	2	12	12	NUM
ejpam-4655	167	3	.	.	PUNCT
ejpam-4655	168	1	let	let	AUX
ejpam-4655	168	2	(	(	PUNCT
ejpam-4655	168	3	x,µ1	x,µ1	NOUN
ejpam-4655	168	4	,	,	PUNCT
ejpam-4655	168	5	µ2	µ2	PROPN
ejpam-4655	168	6	)	)	PUNCT
ejpam-4655	168	7	be	be	VERB
ejpam-4655	168	8	a	a	DET
ejpam-4655	168	9	bgts	bgts	NOUN
ejpam-4655	168	10	and	and	CCONJ
ejpam-4655	168	11	h	h	NOUN
ejpam-4655	168	12	be	be	AUX
ejpam-4655	168	13	a	a	DET
ejpam-4655	168	14	non	non	ADJ
ejpam-4655	168	15	-	-	ADJ
ejpam-4655	168	16	null	null	ADJ
ejpam-4655	168	17	subset	subset	NOUN
ejpam-4655	168	18	of	of	ADP
ejpam-4655	168	19	x.	x.	NOUN
ejpam-4655	168	20	if	if	SCONJ
ejpam-4655	168	21	x	x	PRON
ejpam-4655	168	22	is	be	AUX
ejpam-4655	168	23	a	a	DET
ejpam-4655	168	24	(	(	PUNCT
ejpam-4655	168	25	v	v	NOUN
ejpam-4655	168	26	,	,	PUNCT
ejpam-4655	168	27	s)-bigeneralized	s)-bigeneralize	VERB
ejpam-4655	168	28	submaximal	submaximal	ADJ
ejpam-4655	168	29	space	space	NOUN
ejpam-4655	168	30	,	,	PUNCT
ejpam-4655	168	31	then	then	ADV
ejpam-4655	169	1	csh	csh	PROPN
ejpam-4655	169	2	−	−	PROPN
ejpam-4655	169	3	h	h	PROPN
ejpam-4655	169	4	∈	∈	PROPN
ejpam-4655	169	5	(	(	PUNCT
ejpam-4655	169	6	s	s	PROPN
ejpam-4655	169	7	,	,	PUNCT
ejpam-4655	169	8	v	v	NOUN
ejpam-4655	169	9	)	)	PUNCT
ejpam-4655	169	10	−	−	PROPN
ejpam-4655	170	1	n	n	CCONJ
ejpam-4655	170	2	(	(	PUNCT
ejpam-4655	170	3	x	x	NOUN
ejpam-4655	170	4	)	)	PUNCT
ejpam-4655	170	5	where	where	SCONJ
ejpam-4655	170	6	s	s	X
ejpam-4655	170	7	,	,	PUNCT
ejpam-4655	170	8	v	v	NOUN
ejpam-4655	170	9	=	=	SYM
ejpam-4655	170	10	1	1	NUM
ejpam-4655	170	11	,	,	PUNCT
ejpam-4655	170	12	2	2	NUM
ejpam-4655	170	13	;	;	PUNCT
ejpam-4655	170	14	s	s	AUX
ejpam-4655	170	15	̸=	̸=	PROPN
ejpam-4655	170	16	v.	v.	ADP
ejpam-4655	170	17	theorem	theorem	ADJ
ejpam-4655	170	18	13	13	NUM
ejpam-4655	170	19	provides	provide	VERB
ejpam-4655	170	20	tricks	trick	NOUN
ejpam-4655	170	21	to	to	PART
ejpam-4655	170	22	effortlessly	effortlessly	ADV
ejpam-4655	170	23	check	check	VERB
ejpam-4655	170	24	,	,	PUNCT
ejpam-4655	170	25	in	in	ADP
ejpam-4655	170	26	a	a	DET
ejpam-4655	170	27	(	(	PUNCT
ejpam-4655	170	28	s	s	PROPN
ejpam-4655	170	29	,	,	PUNCT
ejpam-4655	170	30	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	170	31	submaximal	submaximal	ADJ
ejpam-4655	170	32	space	space	NOUN
ejpam-4655	170	33	,	,	PUNCT
ejpam-4655	170	34	whether	whether	SCONJ
ejpam-4655	170	35	the	the	DET
ejpam-4655	170	36	frontier	frontier	NOUN
ejpam-4655	170	37	of	of	ADP
ejpam-4655	170	38	a	a	DET
ejpam-4655	170	39	given	give	VERB
ejpam-4655	170	40	set	set	NOUN
ejpam-4655	170	41	is	be	AUX
ejpam-4655	170	42	(	(	PUNCT
ejpam-4655	170	43	s	s	X
ejpam-4655	170	44	,	,	PUNCT
ejpam-4655	170	45	v)-nowhere	v)-nowhere	PUNCT
ejpam-4655	170	46	dense	dense	ADJ
ejpam-4655	170	47	or	or	CCONJ
ejpam-4655	170	48	not	not	PART
ejpam-4655	170	49	.	.	PUNCT
ejpam-4655	171	1	theorem	theorem	ADJ
ejpam-4655	171	2	13	13	NUM
ejpam-4655	171	3	.	.	PUNCT
ejpam-4655	172	1	let	let	AUX
ejpam-4655	172	2	(	(	PUNCT
ejpam-4655	172	3	x,µ1	x,µ1	NOUN
ejpam-4655	172	4	,	,	PUNCT
ejpam-4655	172	5	µ2	µ2	PROPN
ejpam-4655	172	6	)	)	PUNCT
ejpam-4655	172	7	be	be	VERB
ejpam-4655	172	8	a	a	DET
ejpam-4655	172	9	(	(	PUNCT
ejpam-4655	172	10	s	s	NOUN
ejpam-4655	172	11	,	,	PUNCT
ejpam-4655	172	12	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	172	13	submaximal	submaximal	ADJ
ejpam-4655	172	14	space	space	NOUN
ejpam-4655	172	15	and	and	CCONJ
ejpam-4655	172	16	q	q	NOUN
ejpam-4655	172	17	∈	∈	PROPN
ejpam-4655	172	18	µ̃v	µ̃v	PROPN
ejpam-4655	172	19	.	.	PUNCT
ejpam-4655	173	1	then	then	ADV
ejpam-4655	173	2	frv(q	frv(q	X
ejpam-4655	173	3	)	)	PUNCT
ejpam-4655	173	4	∈	∈	PROPN
ejpam-4655	173	5	(	(	PUNCT
ejpam-4655	173	6	v	v	NOUN
ejpam-4655	173	7	,	,	PUNCT
ejpam-4655	173	8	s)−n	s)−n	X
ejpam-4655	173	9	(	(	PUNCT
ejpam-4655	173	10	x	x	NOUN
ejpam-4655	173	11	)	)	PUNCT
ejpam-4655	173	12	where	where	SCONJ
ejpam-4655	173	13	s	s	X
ejpam-4655	173	14	,	,	PUNCT
ejpam-4655	173	15	v	v	NOUN
ejpam-4655	173	16	=	=	SYM
ejpam-4655	173	17	1	1	NUM
ejpam-4655	173	18	,	,	PUNCT
ejpam-4655	173	19	2	2	NUM
ejpam-4655	173	20	;	;	PUNCT
ejpam-4655	173	21	s	s	VERB
ejpam-4655	173	22	̸=	̸=	PROPN
ejpam-4655	173	23	v.	v.	ADP
ejpam-4655	173	24	proof	proof	NOUN
ejpam-4655	173	25	.	.	PUNCT
ejpam-4655	174	1	we	we	PRON
ejpam-4655	174	2	give	give	VERB
ejpam-4655	174	3	the	the	DET
ejpam-4655	174	4	detailed	detailed	ADJ
ejpam-4655	174	5	proof	proof	NOUN
ejpam-4655	174	6	only	only	ADV
ejpam-4655	174	7	for	for	ADP
ejpam-4655	174	8	s	s	NOUN
ejpam-4655	174	9	=	=	SYM
ejpam-4655	174	10	1	1	NUM
ejpam-4655	174	11	,	,	PUNCT
ejpam-4655	174	12	v	v	NOUN
ejpam-4655	174	13	=	=	SYM
ejpam-4655	174	14	2	2	X
ejpam-4655	174	15	.	.	X
ejpam-4655	174	16	assume	assume	VERB
ejpam-4655	174	17	that	that	SCONJ
ejpam-4655	174	18	,	,	PUNCT
ejpam-4655	174	19	x	x	PRON
ejpam-4655	174	20	is	be	AUX
ejpam-4655	174	21	a	a	DET
ejpam-4655	174	22	(	(	PUNCT
ejpam-4655	174	23	1	1	NUM
ejpam-4655	174	24	,	,	PUNCT
ejpam-4655	174	25	2)bigeneralized	2)bigeneralized	NUM
ejpam-4655	174	26	submaximal	submaximal	ADJ
ejpam-4655	174	27	space	space	NOUN
ejpam-4655	174	28	and	and	CCONJ
ejpam-4655	174	29	q	q	NOUN
ejpam-4655	174	30	∈	∈	PROPN
ejpam-4655	174	31	µ̃2	µ̃2	PROPN
ejpam-4655	174	32	.	.	PUNCT
ejpam-4655	175	1	(	(	PUNCT
ejpam-4655	175	2	2	2	X
ejpam-4655	175	3	)	)	PUNCT
ejpam-4655	175	4	take	take	VERB
ejpam-4655	175	5	e	e	NOUN
ejpam-4655	175	6	=	=	PUNCT
ejpam-4655	175	7	fr2(q	fr2(q	PROPN
ejpam-4655	175	8	)	)	PUNCT
ejpam-4655	175	9	.	.	PUNCT
ejpam-4655	176	1	then	then	ADV
ejpam-4655	176	2	e	e	PROPN
ejpam-4655	176	3	=	=	NOUN
ejpam-4655	176	4	c2q	c2q	NOUN
ejpam-4655	176	5	∩	∩	NOUN
ejpam-4655	176	6	c2(x	c2(x	PROPN
ejpam-4655	176	7	−	−	PROPN
ejpam-4655	176	8	q	q	NOUN
ejpam-4655	176	9	)	)	PUNCT
ejpam-4655	176	10	.	.	PUNCT
ejpam-4655	177	1	from	from	ADP
ejpam-4655	177	2	(	(	PUNCT
ejpam-4655	177	3	2	2	NUM
ejpam-4655	177	4	)	)	PUNCT
ejpam-4655	177	5	,	,	PUNCT
ejpam-4655	177	6	we	we	PRON
ejpam-4655	177	7	have	have	VERB
ejpam-4655	177	8	e	e	NOUN
ejpam-4655	177	9	=	=	NOUN
ejpam-4655	177	10	c2q	c2q	PROPN
ejpam-4655	177	11	−	−	PROPN
ejpam-4655	177	12	q.	q.	PROPN
ejpam-4655	177	13	by	by	ADP
ejpam-4655	177	14	lemma	lemma	PROPN
ejpam-4655	177	15	1	1	NUM
ejpam-4655	177	16	,	,	PUNCT
ejpam-4655	177	17	i2(e	i2(e	NOUN
ejpam-4655	177	18	)	)	PUNCT
ejpam-4655	177	19	=	=	NOUN
ejpam-4655	177	20	∅	∅	NOUN
ejpam-4655	177	21	and	and	CCONJ
ejpam-4655	177	22	so	so	ADV
ejpam-4655	177	23	e	e	NOUN
ejpam-4655	177	24	is	be	AUX
ejpam-4655	177	25	a	a	DET
ejpam-4655	177	26	µ1	µ1	NOUN
ejpam-4655	177	27	-	-	PUNCT
ejpam-4655	177	28	closed	closed	ADJ
ejpam-4655	177	29	set	set	NOUN
ejpam-4655	177	30	,	,	PUNCT
ejpam-4655	177	31	by	by	ADP
ejpam-4655	177	32	our	our	PRON
ejpam-4655	177	33	assumption	assumption	NOUN
ejpam-4655	177	34	.	.	PUNCT
ejpam-4655	178	1	thus	thus	ADV
ejpam-4655	178	2	,	,	PUNCT
ejpam-4655	178	3	i2(c1(e	i2(c1(e	X
ejpam-4655	178	4	)	)	PUNCT
ejpam-4655	178	5	)	)	PUNCT
ejpam-4655	179	1	=	=	PUNCT
ejpam-4655	179	2	∅.	∅.	VERB
ejpam-4655	179	3	therefore	therefore	ADV
ejpam-4655	179	4	,	,	PUNCT
ejpam-4655	179	5	fr2(q	fr2(q	PROPN
ejpam-4655	179	6	)	)	PUNCT
ejpam-4655	179	7	∈	∈	PROPN
ejpam-4655	179	8	(	(	PUNCT
ejpam-4655	179	9	2	2	NUM
ejpam-4655	179	10	,	,	PUNCT
ejpam-4655	179	11	1)−n	1)−n	NUM
ejpam-4655	179	12	(	(	PUNCT
ejpam-4655	179	13	x	x	NOUN
ejpam-4655	179	14	)	)	PUNCT
ejpam-4655	179	15	.	.	PUNCT
ejpam-4655	180	1	example	example	NOUN
ejpam-4655	180	2	14	14	NUM
ejpam-4655	180	3	shows	show	VERB
ejpam-4655	180	4	that	that	SCONJ
ejpam-4655	180	5	the	the	DET
ejpam-4655	180	6	condition	condition	NOUN
ejpam-4655	180	7	“	"	PUNCT
ejpam-4655	180	8	q	q	PROPN
ejpam-4655	180	9	∈	∈	PROPN
ejpam-4655	180	10	µ̃v	µ̃v	PROPN
ejpam-4655	180	11	”	"	PUNCT
ejpam-4655	180	12	can	can	AUX
ejpam-4655	180	13	not	not	PART
ejpam-4655	180	14	dropped	drop	VERB
ejpam-4655	180	15	in	in	ADP
ejpam-4655	180	16	theorem	theorem	ADJ
ejpam-4655	180	17	13	13	NUM
ejpam-4655	180	18	.	.	PUNCT
ejpam-4655	180	19	example	example	NOUN
ejpam-4655	180	20	15	15	NUM
ejpam-4655	180	21	shows	show	VERB
ejpam-4655	180	22	that	that	SCONJ
ejpam-4655	180	23	the	the	DET
ejpam-4655	180	24	condition	condition	NOUN
ejpam-4655	180	25	“	"	PUNCT
ejpam-4655	180	26	x	x	X
ejpam-4655	180	27	is	be	AUX
ejpam-4655	180	28	a	a	DET
ejpam-4655	180	29	(	(	PUNCT
ejpam-4655	180	30	s	s	PROPN
ejpam-4655	180	31	,	,	PUNCT
ejpam-4655	180	32	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	180	33	submaximal	submaximal	ADJ
ejpam-4655	180	34	space	space	NOUN
ejpam-4655	180	35	”	"	PUNCT
ejpam-4655	180	36	is	be	AUX
ejpam-4655	180	37	necessary	necessary	ADJ
ejpam-4655	180	38	for	for	ADP
ejpam-4655	180	39	theorem	theorem	ADJ
ejpam-4655	180	40	13	13	NUM
ejpam-4655	180	41	.	.	PUNCT
ejpam-4655	180	42	example	example	NOUN
ejpam-4655	181	1	14	14	NUM
ejpam-4655	181	2	.	.	PUNCT
ejpam-4655	182	1	(	(	PUNCT
ejpam-4655	182	2	a	a	X
ejpam-4655	182	3	)	)	PUNCT
ejpam-4655	182	4	consider	consider	VERB
ejpam-4655	182	5	the	the	DET
ejpam-4655	182	6	bigeneralized	bigeneralized	ADJ
ejpam-4655	182	7	topological	topological	ADJ
ejpam-4655	182	8	space	space	NOUN
ejpam-4655	182	9	(	(	PUNCT
ejpam-4655	182	10	x,µ1	x,µ1	PROPN
ejpam-4655	182	11	,	,	PUNCT
ejpam-4655	182	12	µ2	µ2	PROPN
ejpam-4655	182	13	)	)	PUNCT
ejpam-4655	182	14	where	where	SCONJ
ejpam-4655	182	15	x	x	X
ejpam-4655	182	16	=	=	PRON
ejpam-4655	182	17	{	{	PUNCT
ejpam-4655	182	18	p	p	X
ejpam-4655	182	19	,	,	PUNCT
ejpam-4655	182	20	q	q	ADJ
ejpam-4655	182	21	,	,	PUNCT
ejpam-4655	182	22	r	r	NOUN
ejpam-4655	182	23	,	,	PUNCT
ejpam-4655	182	24	s};µ1	s};µ1	PROPN
ejpam-4655	182	25	=	=	SYM
ejpam-4655	182	26	{	{	PUNCT
ejpam-4655	182	27	∅	∅	NOUN
ejpam-4655	182	28	,	,	PUNCT
ejpam-4655	182	29	{	{	PUNCT
ejpam-4655	182	30	s	s	X
ejpam-4655	182	31	}	}	PUNCT
ejpam-4655	182	32	,	,	PUNCT
ejpam-4655	182	33	{	{	PUNCT
ejpam-4655	182	34	p	p	X
ejpam-4655	182	35	,	,	PUNCT
ejpam-4655	182	36	q	q	NOUN
ejpam-4655	182	37	}	}	PUNCT
ejpam-4655	182	38	,	,	PUNCT
ejpam-4655	182	39	{	{	PUNCT
ejpam-4655	182	40	p	p	X
ejpam-4655	182	41	,	,	PUNCT
ejpam-4655	182	42	r	r	NOUN
ejpam-4655	182	43	}	}	PUNCT
ejpam-4655	182	44	,	,	PUNCT
ejpam-4655	182	45	{	{	PUNCT
ejpam-4655	182	46	p	p	X
ejpam-4655	182	47	,	,	PUNCT
ejpam-4655	182	48	s	s	PART
ejpam-4655	182	49	}	}	PUNCT
ejpam-4655	182	50	,	,	PUNCT
ejpam-4655	182	51	{	{	PUNCT
ejpam-4655	182	52	q	q	X
ejpam-4655	182	53	,	,	PUNCT
ejpam-4655	182	54	r	r	NOUN
ejpam-4655	182	55	}	}	PUNCT
ejpam-4655	182	56	,	,	PUNCT
ejpam-4655	182	57	{	{	PUNCT
ejpam-4655	182	58	q	q	X
ejpam-4655	182	59	,	,	PUNCT
ejpam-4655	182	60	s	s	PART
ejpam-4655	182	61	}	}	PUNCT
ejpam-4655	182	62	,	,	PUNCT
ejpam-4655	182	63	{	{	PUNCT
ejpam-4655	182	64	r	r	NOUN
ejpam-4655	182	65	,	,	PUNCT
ejpam-4655	182	66	s	s	PART
ejpam-4655	182	67	}	}	PUNCT
ejpam-4655	182	68	,	,	PUNCT
ejpam-4655	182	69	{	{	PUNCT
ejpam-4655	182	70	p	p	X
ejpam-4655	182	71	,	,	PUNCT
ejpam-4655	182	72	q	q	ADJ
ejpam-4655	182	73	,	,	PUNCT
ejpam-4655	182	74	r	r	NOUN
ejpam-4655	182	75	}	}	PUNCT
ejpam-4655	182	76	,	,	PUNCT
ejpam-4655	182	77	{	{	PUNCT
ejpam-4655	182	78	p	p	X
ejpam-4655	182	79	,	,	PUNCT
ejpam-4655	182	80	q	q	X
ejpam-4655	182	81	,	,	PUNCT
ejpam-4655	182	82	s	s	PART
ejpam-4655	182	83	}	}	PUNCT
ejpam-4655	182	84	,	,	PUNCT
ejpam-4655	182	85	{	{	PUNCT
ejpam-4655	182	86	p	p	X
ejpam-4655	182	87	,	,	PUNCT
ejpam-4655	182	88	r	r	NOUN
ejpam-4655	182	89	,	,	PUNCT
ejpam-4655	182	90	s	s	PART
ejpam-4655	182	91	}	}	PUNCT
ejpam-4655	182	92	,	,	PUNCT
ejpam-4655	182	93	{	{	PUNCT
ejpam-4655	182	94	q	q	X
ejpam-4655	182	95	,	,	PUNCT
ejpam-4655	182	96	r	r	NOUN
ejpam-4655	182	97	,	,	PUNCT
ejpam-4655	182	98	s	s	PART
ejpam-4655	182	99	}	}	PUNCT
ejpam-4655	182	100	,	,	PUNCT
ejpam-4655	182	101	x	x	NOUN
ejpam-4655	182	102	}	}	PUNCT
ejpam-4655	182	103	and	and	CCONJ
ejpam-4655	182	104	µ2	µ2	PROPN
ejpam-4655	182	105	=	=	PUNCT
ejpam-4655	182	106	{	{	PUNCT
ejpam-4655	182	107	∅	∅	NOUN
ejpam-4655	182	108	,	,	PUNCT
ejpam-4655	182	109	{	{	PUNCT
ejpam-4655	182	110	q	q	X
ejpam-4655	182	111	,	,	PUNCT
ejpam-4655	182	112	s	s	PART
ejpam-4655	182	113	}	}	PUNCT
ejpam-4655	182	114	,	,	PUNCT
ejpam-4655	182	115	{	{	PUNCT
ejpam-4655	182	116	r	r	NOUN
ejpam-4655	182	117	,	,	PUNCT
ejpam-4655	182	118	s	s	PART
ejpam-4655	182	119	}	}	PUNCT
ejpam-4655	182	120	,	,	PUNCT
ejpam-4655	182	121	{	{	PUNCT
ejpam-4655	182	122	q	q	X
ejpam-4655	182	123	,	,	PUNCT
ejpam-4655	182	124	r	r	NOUN
ejpam-4655	182	125	,	,	PUNCT
ejpam-4655	182	126	s	s	PART
ejpam-4655	182	127	}	}	PUNCT
ejpam-4655	182	128	}	}	PUNCT
ejpam-4655	182	129	.	.	PUNCT
ejpam-4655	183	1	here	here	ADV
ejpam-4655	183	2	{	{	PUNCT
ejpam-4655	183	3	s	s	X
ejpam-4655	183	4	}	}	PUNCT
ejpam-4655	183	5	,	,	PUNCT
ejpam-4655	183	6	{	{	PUNCT
ejpam-4655	183	7	p	p	X
ejpam-4655	183	8	,	,	PUNCT
ejpam-4655	183	9	s	s	PART
ejpam-4655	183	10	}	}	PUNCT
ejpam-4655	183	11	,	,	PUNCT
ejpam-4655	183	12	{	{	PUNCT
ejpam-4655	183	13	q	q	X
ejpam-4655	183	14	,	,	PUNCT
ejpam-4655	183	15	r	r	NOUN
ejpam-4655	183	16	}	}	PUNCT
ejpam-4655	183	17	,	,	PUNCT
ejpam-4655	183	18	{	{	PUNCT
ejpam-4655	183	19	q	q	X
ejpam-4655	183	20	,	,	PUNCT
ejpam-4655	183	21	s	s	PART
ejpam-4655	183	22	}	}	PUNCT
ejpam-4655	183	23	,	,	PUNCT
ejpam-4655	183	24	{	{	PUNCT
ejpam-4655	183	25	r	r	NOUN
ejpam-4655	183	26	,	,	PUNCT
ejpam-4655	183	27	s	s	PART
ejpam-4655	183	28	}	}	PUNCT
ejpam-4655	183	29	,	,	PUNCT
ejpam-4655	183	30	{	{	PUNCT
ejpam-4655	183	31	p	p	X
ejpam-4655	183	32	,	,	PUNCT
ejpam-4655	183	33	q	q	ADJ
ejpam-4655	183	34	,	,	PUNCT
ejpam-4655	183	35	r	r	NOUN
ejpam-4655	183	36	}	}	PUNCT
ejpam-4655	183	37	,	,	PUNCT
ejpam-4655	183	38	{	{	PUNCT
ejpam-4655	183	39	p	p	X
ejpam-4655	183	40	,	,	PUNCT
ejpam-4655	183	41	q	q	X
ejpam-4655	183	42	,	,	PUNCT
ejpam-4655	183	43	s	s	PART
ejpam-4655	183	44	}	}	PUNCT
ejpam-4655	183	45	,	,	PUNCT
ejpam-4655	183	46	{	{	PUNCT
ejpam-4655	183	47	p	p	X
ejpam-4655	183	48	,	,	PUNCT
ejpam-4655	183	49	r	r	NOUN
ejpam-4655	183	50	,	,	PUNCT
ejpam-4655	183	51	s	s	PART
ejpam-4655	183	52	}	}	PUNCT
ejpam-4655	183	53	,	,	PUNCT
ejpam-4655	183	54	{	{	PUNCT
ejpam-4655	183	55	q	q	X
ejpam-4655	183	56	,	,	PUNCT
ejpam-4655	183	57	r	r	NOUN
ejpam-4655	183	58	,	,	PUNCT
ejpam-4655	183	59	s	s	PART
ejpam-4655	183	60	}	}	PUNCT
ejpam-4655	183	61	and	and	CCONJ
ejpam-4655	183	62	x	x	X
ejpam-4655	183	63	are	be	AUX
ejpam-4655	183	64	µ2	µ2	ADJ
ejpam-4655	183	65	-	-	PUNCT
ejpam-4655	183	66	dense	dense	ADJ
ejpam-4655	183	67	subsets	subset	NOUN
ejpam-4655	183	68	of	of	ADP
ejpam-4655	183	69	x.	x.	NOUN
ejpam-4655	183	70	also	also	ADV
ejpam-4655	183	71	,	,	PUNCT
ejpam-4655	183	72	every	every	DET
ejpam-4655	183	73	µ2	µ2	NOUN
ejpam-4655	183	74	-	-	PUNCT
ejpam-4655	183	75	dense	dense	NOUN
ejpam-4655	183	76	is	be	AUX
ejpam-4655	183	77	µ1	µ1	NOUN
ejpam-4655	183	78	-	-	PUNCT
ejpam-4655	183	79	open	open	ADJ
ejpam-4655	183	80	.	.	PUNCT
ejpam-4655	184	1	therefore	therefore	ADV
ejpam-4655	184	2	,	,	PUNCT
ejpam-4655	184	3	x	x	X
ejpam-4655	184	4	is	be	AUX
ejpam-4655	184	5	a	a	DET
ejpam-4655	184	6	(	(	PUNCT
ejpam-4655	184	7	1	1	NUM
ejpam-4655	184	8	,	,	PUNCT
ejpam-4655	184	9	2)-bigeneralized	2)-bigeneralized	NUM
ejpam-4655	184	10	topological	topological	ADJ
ejpam-4655	184	11	space	space	NOUN
ejpam-4655	184	12	.	.	PUNCT
ejpam-4655	185	1	let	let	VERB
ejpam-4655	185	2	j	j	PROPN
ejpam-4655	185	3	=	=	PUNCT
ejpam-4655	185	4	{	{	PUNCT
ejpam-4655	185	5	q	q	NOUN
ejpam-4655	185	6	,	,	PUNCT
ejpam-4655	185	7	r	r	NOUN
ejpam-4655	185	8	}	}	PUNCT
ejpam-4655	185	9	.	.	PUNCT
ejpam-4655	186	1	then	then	ADV
ejpam-4655	186	2	y.	y.	PROPN
ejpam-4655	186	3	farhat	farhat	PROPN
ejpam-4655	186	4	et	et	PROPN
ejpam-4655	186	5	al	al	PROPN
ejpam-4655	186	6	.	.	PUNCT
ejpam-4655	186	7	/	/	SYM
ejpam-4655	186	8	eur	eur	PROPN
ejpam-4655	186	9	.	.	PUNCT
ejpam-4655	187	1	j.	j.	PROPN
ejpam-4655	187	2	pure	pure	PROPN
ejpam-4655	187	3	appl	appl	PROPN
ejpam-4655	187	4	.	.	PROPN
ejpam-4655	187	5	math	math	PROPN
ejpam-4655	187	6	,	,	PUNCT
ejpam-4655	187	7	16	16	NUM
ejpam-4655	187	8	(	(	PUNCT
ejpam-4655	187	9	1	1	NUM
ejpam-4655	187	10	)	)	PUNCT
ejpam-4655	187	11	(	(	PUNCT
ejpam-4655	187	12	2023	2023	NUM
ejpam-4655	187	13	)	)	PUNCT
ejpam-4655	187	14	,	,	PUNCT
ejpam-4655	187	15	386	386	NUM
ejpam-4655	187	16	-	-	SYM
ejpam-4655	187	17	403	403	NUM
ejpam-4655	187	18	392	392	NUM
ejpam-4655	187	19	j	j	NOUN
ejpam-4655	187	20	/∈	/∈	PUNCT
ejpam-4655	188	1	µ̃2	µ̃2	PROPN
ejpam-4655	188	2	.	.	PUNCT
ejpam-4655	189	1	here	here	ADV
ejpam-4655	189	2	fr2(j	fr2(j	PROPN
ejpam-4655	189	3	)	)	PUNCT
ejpam-4655	190	1	=	=	SYM
ejpam-4655	190	2	c2(j	c2(j	PROPN
ejpam-4655	190	3	)	)	PUNCT
ejpam-4655	190	4	∩	∩	NOUN
ejpam-4655	190	5	c2(x	c2(x	PROPN
ejpam-4655	190	6	−	−	PROPN
ejpam-4655	190	7	j	j	PROPN
ejpam-4655	190	8	)	)	PUNCT
ejpam-4655	190	9	.	.	PUNCT
ejpam-4655	191	1	this	this	PRON
ejpam-4655	191	2	implies	imply	VERB
ejpam-4655	191	3	fr2(j	fr2(j	PROPN
ejpam-4655	191	4	)	)	PUNCT
ejpam-4655	191	5	=	=	PUNCT
ejpam-4655	192	1	x	x	X
ejpam-4655	192	2	which	which	PRON
ejpam-4655	192	3	implies	imply	VERB
ejpam-4655	192	4	that	that	SCONJ
ejpam-4655	192	5	i2(c1(fr2(j	i2(c1(fr2(j	PROPN
ejpam-4655	192	6	)	)	PUNCT
ejpam-4655	192	7	)	)	PUNCT
ejpam-4655	192	8	)	)	PUNCT
ejpam-4655	193	1	=	=	PUNCT
ejpam-4655	193	2	i2(x	i2(x	PROPN
ejpam-4655	193	3	)	)	PUNCT
ejpam-4655	193	4	=	=	NOUN
ejpam-4655	193	5	{	{	PUNCT
ejpam-4655	193	6	q	q	X
ejpam-4655	193	7	,	,	PUNCT
ejpam-4655	193	8	r	r	NOUN
ejpam-4655	193	9	,	,	PUNCT
ejpam-4655	193	10	s	s	PART
ejpam-4655	193	11	}	}	PUNCT
ejpam-4655	193	12	.	.	PUNCT
ejpam-4655	194	1	thus	thus	ADV
ejpam-4655	194	2	,	,	PUNCT
ejpam-4655	194	3	i2(c1(fr2(j	i2(c1(fr2(j	PROPN
ejpam-4655	194	4	)	)	PUNCT
ejpam-4655	194	5	)	)	PUNCT
ejpam-4655	194	6	)	)	PUNCT
ejpam-4655	195	1	̸=	̸=	PROPN
ejpam-4655	195	2	∅.	∅.	ADP
ejpam-4655	195	3	(	(	PUNCT
ejpam-4655	195	4	b	b	NOUN
ejpam-4655	195	5	)	)	PUNCT
ejpam-4655	195	6	consider	consider	VERB
ejpam-4655	195	7	the	the	DET
ejpam-4655	195	8	bigeneralized	bigeneralized	ADJ
ejpam-4655	195	9	topological	topological	ADJ
ejpam-4655	195	10	space	space	NOUN
ejpam-4655	195	11	(	(	PUNCT
ejpam-4655	195	12	x,µ1	x,µ1	PROPN
ejpam-4655	195	13	,	,	PUNCT
ejpam-4655	195	14	µ2	µ2	PROPN
ejpam-4655	195	15	)	)	PUNCT
ejpam-4655	196	1	where	where	SCONJ
ejpam-4655	196	2	x	x	X
ejpam-4655	196	3	=	=	PRON
ejpam-4655	196	4	{	{	PUNCT
ejpam-4655	196	5	p	p	X
ejpam-4655	196	6	,	,	PUNCT
ejpam-4655	196	7	q	q	ADJ
ejpam-4655	196	8	,	,	PUNCT
ejpam-4655	196	9	r	r	NOUN
ejpam-4655	196	10	,	,	PUNCT
ejpam-4655	196	11	s};µ1	s};µ1	PROPN
ejpam-4655	196	12	=	=	SYM
ejpam-4655	196	13	{	{	PUNCT
ejpam-4655	196	14	∅	∅	NOUN
ejpam-4655	196	15	,	,	PUNCT
ejpam-4655	196	16	{	{	PUNCT
ejpam-4655	196	17	p	p	X
ejpam-4655	196	18	,	,	PUNCT
ejpam-4655	196	19	s	s	PART
ejpam-4655	196	20	}	}	PUNCT
ejpam-4655	196	21	,	,	PUNCT
ejpam-4655	196	22	{	{	PUNCT
ejpam-4655	196	23	q	q	X
ejpam-4655	196	24	,	,	PUNCT
ejpam-4655	196	25	s	s	PART
ejpam-4655	196	26	}	}	PUNCT
ejpam-4655	196	27	,	,	PUNCT
ejpam-4655	196	28	{	{	PUNCT
ejpam-4655	196	29	p	p	X
ejpam-4655	196	30	,	,	PUNCT
ejpam-4655	196	31	q	q	ADJ
ejpam-4655	196	32	,	,	PUNCT
ejpam-4655	196	33	s	s	PART
ejpam-4655	196	34	}	}	PUNCT
ejpam-4655	196	35	}	}	PUNCT
ejpam-4655	196	36	and	and	CCONJ
ejpam-4655	196	37	µ2	µ2	PROPN
ejpam-4655	196	38	=	=	PUNCT
ejpam-4655	196	39	{	{	PUNCT
ejpam-4655	196	40	∅	∅	NOUN
ejpam-4655	196	41	,	,	PUNCT
ejpam-4655	196	42	{	{	PUNCT
ejpam-4655	196	43	s	s	X
ejpam-4655	196	44	}	}	PUNCT
ejpam-4655	196	45	,	,	PUNCT
ejpam-4655	196	46	{	{	PUNCT
ejpam-4655	196	47	p	p	X
ejpam-4655	196	48	,	,	PUNCT
ejpam-4655	196	49	q	q	NOUN
ejpam-4655	196	50	}	}	PUNCT
ejpam-4655	196	51	,	,	PUNCT
ejpam-4655	196	52	{	{	PUNCT
ejpam-4655	196	53	p	p	X
ejpam-4655	196	54	,	,	PUNCT
ejpam-4655	196	55	r	r	NOUN
ejpam-4655	196	56	}	}	PUNCT
ejpam-4655	196	57	,	,	PUNCT
ejpam-4655	196	58	{	{	PUNCT
ejpam-4655	196	59	p	p	X
ejpam-4655	196	60	,	,	PUNCT
ejpam-4655	196	61	s	s	PART
ejpam-4655	196	62	}	}	PUNCT
ejpam-4655	196	63	,	,	PUNCT
ejpam-4655	196	64	{	{	PUNCT
ejpam-4655	196	65	q	q	X
ejpam-4655	196	66	,	,	PUNCT
ejpam-4655	196	67	s	s	PART
ejpam-4655	196	68	}	}	PUNCT
ejpam-4655	196	69	,	,	PUNCT
ejpam-4655	196	70	{	{	PUNCT
ejpam-4655	196	71	r	r	NOUN
ejpam-4655	196	72	,	,	PUNCT
ejpam-4655	196	73	s	s	PART
ejpam-4655	196	74	}	}	PUNCT
ejpam-4655	196	75	,	,	PUNCT
ejpam-4655	196	76	{	{	PUNCT
ejpam-4655	196	77	p	p	X
ejpam-4655	196	78	,	,	PUNCT
ejpam-4655	196	79	q	q	ADJ
ejpam-4655	196	80	,	,	PUNCT
ejpam-4655	196	81	r	r	NOUN
ejpam-4655	196	82	}	}	PUNCT
ejpam-4655	196	83	,	,	PUNCT
ejpam-4655	196	84	{	{	PUNCT
ejpam-4655	196	85	p	p	X
ejpam-4655	196	86	,	,	PUNCT
ejpam-4655	196	87	q	q	X
ejpam-4655	196	88	,	,	PUNCT
ejpam-4655	196	89	s	s	PART
ejpam-4655	196	90	}	}	PUNCT
ejpam-4655	196	91	,	,	PUNCT
ejpam-4655	196	92	{	{	PUNCT
ejpam-4655	196	93	p	p	X
ejpam-4655	196	94	,	,	PUNCT
ejpam-4655	196	95	r	r	NOUN
ejpam-4655	196	96	,	,	PUNCT
ejpam-4655	196	97	s	s	PART
ejpam-4655	196	98	}	}	PUNCT
ejpam-4655	196	99	,	,	PUNCT
ejpam-4655	196	100	{	{	PUNCT
ejpam-4655	196	101	q	q	X
ejpam-4655	196	102	,	,	PUNCT
ejpam-4655	196	103	r	r	NOUN
ejpam-4655	196	104	,	,	PUNCT
ejpam-4655	196	105	s	s	PART
ejpam-4655	196	106	}	}	PUNCT
ejpam-4655	196	107	,	,	PUNCT
ejpam-4655	196	108	x}.here	x}.here	X
ejpam-4655	196	109	{	{	PUNCT
ejpam-4655	196	110	s	s	NOUN
ejpam-4655	196	111	}	}	PUNCT
ejpam-4655	196	112	,	,	PUNCT
ejpam-4655	196	113	{	{	PUNCT
ejpam-4655	196	114	p	p	X
ejpam-4655	196	115	,	,	PUNCT
ejpam-4655	196	116	q	q	NOUN
ejpam-4655	196	117	}	}	PUNCT
ejpam-4655	196	118	,	,	PUNCT
ejpam-4655	196	119	{	{	PUNCT
ejpam-4655	196	120	p	p	X
ejpam-4655	196	121	,	,	PUNCT
ejpam-4655	196	122	s	s	PART
ejpam-4655	196	123	}	}	PUNCT
ejpam-4655	196	124	,	,	PUNCT
ejpam-4655	196	125	{	{	PUNCT
ejpam-4655	196	126	q	q	X
ejpam-4655	196	127	,	,	PUNCT
ejpam-4655	196	128	s	s	PART
ejpam-4655	196	129	}	}	PUNCT
ejpam-4655	196	130	,	,	PUNCT
ejpam-4655	196	131	{	{	PUNCT
ejpam-4655	196	132	r	r	NOUN
ejpam-4655	196	133	,	,	PUNCT
ejpam-4655	196	134	s	s	PART
ejpam-4655	196	135	}	}	PUNCT
ejpam-4655	196	136	,	,	PUNCT
ejpam-4655	196	137	{	{	PUNCT
ejpam-4655	196	138	p	p	X
ejpam-4655	196	139	,	,	PUNCT
ejpam-4655	196	140	q	q	ADJ
ejpam-4655	196	141	,	,	PUNCT
ejpam-4655	196	142	r	r	NOUN
ejpam-4655	196	143	}	}	PUNCT
ejpam-4655	196	144	,	,	PUNCT
ejpam-4655	196	145	{	{	PUNCT
ejpam-4655	196	146	p	p	X
ejpam-4655	196	147	,	,	PUNCT
ejpam-4655	196	148	q	q	X
ejpam-4655	196	149	,	,	PUNCT
ejpam-4655	196	150	s	s	PART
ejpam-4655	196	151	}	}	PUNCT
ejpam-4655	196	152	,	,	PUNCT
ejpam-4655	196	153	{	{	PUNCT
ejpam-4655	196	154	p	p	X
ejpam-4655	196	155	,	,	PUNCT
ejpam-4655	196	156	r	r	NOUN
ejpam-4655	196	157	,	,	PUNCT
ejpam-4655	196	158	s	s	PART
ejpam-4655	196	159	}	}	PUNCT
ejpam-4655	196	160	,	,	PUNCT
ejpam-4655	196	161	{	{	PUNCT
ejpam-4655	196	162	q	q	X
ejpam-4655	196	163	,	,	PUNCT
ejpam-4655	196	164	r	r	NOUN
ejpam-4655	196	165	,	,	PUNCT
ejpam-4655	196	166	s	s	PART
ejpam-4655	196	167	}	}	PUNCT
ejpam-4655	196	168	and	and	CCONJ
ejpam-4655	196	169	x	x	PRON
ejpam-4655	196	170	are	be	AUX
ejpam-4655	196	171	µ1	µ1	NOUN
ejpam-4655	196	172	-	-	PUNCT
ejpam-4655	196	173	dense	dense	ADJ
ejpam-4655	196	174	subsets	subset	NOUN
ejpam-4655	196	175	of	of	ADP
ejpam-4655	196	176	x.	x.	NOUN
ejpam-4655	196	177	also	also	ADV
ejpam-4655	196	178	,	,	PUNCT
ejpam-4655	196	179	every	every	DET
ejpam-4655	196	180	µ1	µ1	NOUN
ejpam-4655	196	181	-	-	PUNCT
ejpam-4655	196	182	dense	dense	ADJ
ejpam-4655	196	183	set	set	NOUN
ejpam-4655	196	184	is	be	AUX
ejpam-4655	196	185	µ2	µ2	ADJ
ejpam-4655	196	186	-	-	PUNCT
ejpam-4655	196	187	open	open	ADJ
ejpam-4655	196	188	.	.	PUNCT
ejpam-4655	197	1	therefore	therefore	ADV
ejpam-4655	197	2	,	,	PUNCT
ejpam-4655	197	3	x	x	X
ejpam-4655	197	4	is	be	AUX
ejpam-4655	197	5	a	a	DET
ejpam-4655	197	6	(	(	PUNCT
ejpam-4655	197	7	2	2	NUM
ejpam-4655	197	8	,	,	PUNCT
ejpam-4655	197	9	1)-bigeneralized	1)-bigeneralized	NUM
ejpam-4655	197	10	topological	topological	ADJ
ejpam-4655	197	11	space	space	NOUN
ejpam-4655	197	12	.	.	PUNCT
ejpam-4655	198	1	let	let	VERB
ejpam-4655	198	2	k	k	NOUN
ejpam-4655	198	3	=	=	PUNCT
ejpam-4655	198	4	{	{	PUNCT
ejpam-4655	198	5	p	p	X
ejpam-4655	198	6	,	,	PUNCT
ejpam-4655	198	7	q	q	NOUN
ejpam-4655	198	8	}	}	PUNCT
ejpam-4655	198	9	.	.	PUNCT
ejpam-4655	199	1	then	then	ADV
ejpam-4655	199	2	k	k	PROPN
ejpam-4655	199	3	/∈	/∈	PUNCT
ejpam-4655	200	1	µ̃1	µ̃1	NOUN
ejpam-4655	200	2	.	.	PUNCT
ejpam-4655	200	3	here	here	ADV
ejpam-4655	200	4	fr1(k	fr1(k	NOUN
ejpam-4655	200	5	)	)	PUNCT
ejpam-4655	200	6	=	=	SYM
ejpam-4655	200	7	c1(k	c1(k	NOUN
ejpam-4655	200	8	)	)	PUNCT
ejpam-4655	200	9	∩	∩	NOUN
ejpam-4655	200	10	c1(x	c1(x	NOUN
ejpam-4655	200	11	−	−	NOUN
ejpam-4655	200	12	k	k	NOUN
ejpam-4655	200	13	)	)	PUNCT
ejpam-4655	200	14	.	.	PUNCT
ejpam-4655	201	1	this	this	PRON
ejpam-4655	201	2	implies	imply	VERB
ejpam-4655	201	3	fr1(k	fr1(k	NOUN
ejpam-4655	201	4	)	)	PUNCT
ejpam-4655	201	5	=	=	PUNCT
ejpam-4655	202	1	x	x	X
ejpam-4655	202	2	which	which	PRON
ejpam-4655	202	3	implies	imply	VERB
ejpam-4655	202	4	that	that	SCONJ
ejpam-4655	202	5	i1(c2(fr1(k	i1(c2(fr1(k	NOUN
ejpam-4655	202	6	)	)	PUNCT
ejpam-4655	202	7	)	)	PUNCT
ejpam-4655	202	8	)	)	PUNCT
ejpam-4655	203	1	=	=	PUNCT
ejpam-4655	203	2	i1(x	i1(x	X
ejpam-4655	203	3	)	)	PUNCT
ejpam-4655	203	4	=	=	PRON
ejpam-4655	203	5	{	{	PUNCT
ejpam-4655	203	6	p	p	X
ejpam-4655	203	7	,	,	PUNCT
ejpam-4655	203	8	q	q	X
ejpam-4655	203	9	,	,	PUNCT
ejpam-4655	203	10	s	s	PART
ejpam-4655	203	11	}	}	PUNCT
ejpam-4655	203	12	.	.	PUNCT
ejpam-4655	204	1	thus	thus	ADV
ejpam-4655	204	2	,	,	PUNCT
ejpam-4655	204	3	i1(c2(fr1(k	i1(c2(fr1(k	NOUN
ejpam-4655	204	4	)	)	PUNCT
ejpam-4655	204	5	)	)	PUNCT
ejpam-4655	204	6	)	)	PUNCT
ejpam-4655	205	1	̸=	̸=	PROPN
ejpam-4655	205	2	∅.	∅.	ADP
ejpam-4655	205	3	example	example	NOUN
ejpam-4655	205	4	15	15	NUM
ejpam-4655	205	5	.	.	PUNCT
ejpam-4655	206	1	(	(	PUNCT
ejpam-4655	206	2	a	a	X
ejpam-4655	206	3	)	)	PUNCT
ejpam-4655	206	4	consider	consider	VERB
ejpam-4655	206	5	the	the	DET
ejpam-4655	206	6	bigeneralized	bigeneralized	ADJ
ejpam-4655	206	7	topological	topological	ADJ
ejpam-4655	206	8	space	space	NOUN
ejpam-4655	206	9	(	(	PUNCT
ejpam-4655	206	10	x,µ1	x,µ1	PROPN
ejpam-4655	206	11	,	,	PUNCT
ejpam-4655	206	12	µ2	µ2	PROPN
ejpam-4655	206	13	)	)	PUNCT
ejpam-4655	206	14	where	where	SCONJ
ejpam-4655	206	15	x	x	X
ejpam-4655	206	16	=	=	PRON
ejpam-4655	206	17	{	{	PUNCT
ejpam-4655	206	18	p	p	X
ejpam-4655	206	19	,	,	PUNCT
ejpam-4655	206	20	q	q	ADJ
ejpam-4655	206	21	,	,	PUNCT
ejpam-4655	206	22	r	r	NOUN
ejpam-4655	206	23	,	,	PUNCT
ejpam-4655	206	24	s};µ1	s};µ1	PROPN
ejpam-4655	206	25	=	=	SYM
ejpam-4655	206	26	{	{	PUNCT
ejpam-4655	206	27	∅	∅	NOUN
ejpam-4655	206	28	,	,	PUNCT
ejpam-4655	206	29	{	{	PUNCT
ejpam-4655	206	30	p	p	X
ejpam-4655	206	31	,	,	PUNCT
ejpam-4655	206	32	s	s	PART
ejpam-4655	206	33	}	}	PUNCT
ejpam-4655	206	34	,	,	PUNCT
ejpam-4655	206	35	{	{	PUNCT
ejpam-4655	206	36	r	r	NOUN
ejpam-4655	206	37	,	,	PUNCT
ejpam-4655	206	38	s	s	PART
ejpam-4655	206	39	}	}	PUNCT
ejpam-4655	206	40	,	,	PUNCT
ejpam-4655	206	41	{	{	PUNCT
ejpam-4655	206	42	p	p	X
ejpam-4655	206	43	,	,	PUNCT
ejpam-4655	206	44	r	r	NOUN
ejpam-4655	206	45	,	,	PUNCT
ejpam-4655	206	46	s	s	PART
ejpam-4655	206	47	}	}	PUNCT
ejpam-4655	206	48	}	}	PUNCT
ejpam-4655	206	49	and	and	CCONJ
ejpam-4655	206	50	µ2	µ2	PROPN
ejpam-4655	206	51	=	=	PUNCT
ejpam-4655	206	52	{	{	PUNCT
ejpam-4655	206	53	∅	∅	NOUN
ejpam-4655	206	54	,	,	PUNCT
ejpam-4655	206	55	{	{	PUNCT
ejpam-4655	206	56	q	q	NOUN
ejpam-4655	206	57	,	,	PUNCT
ejpam-4655	206	58	r	r	NOUN
ejpam-4655	206	59	}	}	PUNCT
ejpam-4655	206	60	,	,	PUNCT
ejpam-4655	206	61	{	{	PUNCT
ejpam-4655	206	62	r	r	NOUN
ejpam-4655	206	63	,	,	PUNCT
ejpam-4655	206	64	s	s	PART
ejpam-4655	206	65	}	}	PUNCT
ejpam-4655	206	66	,	,	PUNCT
ejpam-4655	206	67	{	{	PUNCT
ejpam-4655	206	68	q	q	X
ejpam-4655	206	69	,	,	PUNCT
ejpam-4655	206	70	r	r	NOUN
ejpam-4655	206	71	,	,	PUNCT
ejpam-4655	206	72	s	s	PART
ejpam-4655	206	73	}	}	PUNCT
ejpam-4655	206	74	}	}	PUNCT
ejpam-4655	206	75	.	.	PUNCT
ejpam-4655	207	1	take	take	VERB
ejpam-4655	207	2	p	p	NOUN
ejpam-4655	207	3	=	=	X
ejpam-4655	207	4	{	{	PUNCT
ejpam-4655	207	5	q	q	PROPN
ejpam-4655	207	6	,	,	PUNCT
ejpam-4655	207	7	s	s	PART
ejpam-4655	207	8	}	}	PUNCT
ejpam-4655	207	9	.	.	PUNCT
ejpam-4655	208	1	then	then	ADV
ejpam-4655	208	2	cµ2(p	cµ2(p	NOUN
ejpam-4655	208	3	)	)	PUNCT
ejpam-4655	209	1	=	=	PUNCT
ejpam-4655	210	1	x.	x.	NOUN
ejpam-4655	210	2	but	but	CCONJ
ejpam-4655	210	3	p	p	NOUN
ejpam-4655	210	4	/∈	/∈	PUNCT
ejpam-4655	210	5	µ1	µ1	PROPN
ejpam-4655	210	6	.	.	PUNCT
ejpam-4655	211	1	thus	thus	ADV
ejpam-4655	211	2	,	,	PUNCT
ejpam-4655	211	3	x	x	PRON
ejpam-4655	211	4	is	be	AUX
ejpam-4655	211	5	not	not	PART
ejpam-4655	211	6	a	a	DET
ejpam-4655	211	7	(	(	PUNCT
ejpam-4655	211	8	1	1	NUM
ejpam-4655	211	9	,	,	PUNCT
ejpam-4655	211	10	2)-bigeneralized	2)-bigeneralized	NUM
ejpam-4655	211	11	topological	topological	ADJ
ejpam-4655	211	12	space	space	NOUN
ejpam-4655	211	13	.	.	PUNCT
ejpam-4655	212	1	let	let	VERB
ejpam-4655	212	2	k	k	NOUN
ejpam-4655	212	3	=	=	PUNCT
ejpam-4655	212	4	{	{	PUNCT
ejpam-4655	212	5	q	q	NOUN
ejpam-4655	212	6	,	,	PUNCT
ejpam-4655	212	7	r	r	NOUN
ejpam-4655	212	8	}	}	PUNCT
ejpam-4655	212	9	.	.	PUNCT
ejpam-4655	213	1	then	then	ADV
ejpam-4655	213	2	k	k	PROPN
ejpam-4655	213	3	∈	∈	PROPN
ejpam-4655	213	4	µ̃2	µ̃2	PROPN
ejpam-4655	213	5	.	.	PUNCT
ejpam-4655	213	6	here	here	ADV
ejpam-4655	213	7	fr2(k	fr2(k	PROPN
ejpam-4655	213	8	)	)	PUNCT
ejpam-4655	213	9	=	=	SYM
ejpam-4655	213	10	c2(k	c2(k	NOUN
ejpam-4655	213	11	)	)	PUNCT
ejpam-4655	213	12	∩	∩	NOUN
ejpam-4655	213	13	c2(x	c2(x	PROPN
ejpam-4655	213	14	−	−	PROPN
ejpam-4655	213	15	k	k	NOUN
ejpam-4655	213	16	)	)	PUNCT
ejpam-4655	213	17	.	.	PUNCT
ejpam-4655	214	1	this	this	PRON
ejpam-4655	214	2	implies	imply	VERB
ejpam-4655	214	3	fr2(k	fr2(k	NOUN
ejpam-4655	214	4	)	)	PUNCT
ejpam-4655	214	5	=	=	PRON
ejpam-4655	215	1	{	{	PUNCT
ejpam-4655	215	2	p	p	X
ejpam-4655	215	3	,	,	PUNCT
ejpam-4655	215	4	s	s	PART
ejpam-4655	215	5	}	}	PUNCT
ejpam-4655	215	6	which	which	PRON
ejpam-4655	215	7	implies	imply	VERB
ejpam-4655	215	8	that	that	SCONJ
ejpam-4655	215	9	i2(c1(fr2(k	i2(c1(fr2(k	NOUN
ejpam-4655	215	10	)	)	PUNCT
ejpam-4655	215	11	)	)	PUNCT
ejpam-4655	215	12	)	)	PUNCT
ejpam-4655	216	1	=	=	PUNCT
ejpam-4655	216	2	i2(x	i2(x	PROPN
ejpam-4655	216	3	)	)	PUNCT
ejpam-4655	216	4	=	=	NOUN
ejpam-4655	216	5	{	{	PUNCT
ejpam-4655	216	6	q	q	X
ejpam-4655	216	7	,	,	PUNCT
ejpam-4655	216	8	r	r	NOUN
ejpam-4655	216	9	,	,	PUNCT
ejpam-4655	216	10	s	s	PART
ejpam-4655	216	11	}	}	PUNCT
ejpam-4655	216	12	.	.	PUNCT
ejpam-4655	217	1	thus	thus	ADV
ejpam-4655	217	2	,	,	PUNCT
ejpam-4655	217	3	i2(c1(fr2(k	i2(c1(fr2(k	PROPN
ejpam-4655	217	4	)	)	PUNCT
ejpam-4655	217	5	)	)	PUNCT
ejpam-4655	217	6	)	)	PUNCT
ejpam-4655	218	1	̸=	̸=	PROPN
ejpam-4655	218	2	∅.	∅.	ADP
ejpam-4655	218	3	(	(	PUNCT
ejpam-4655	218	4	b	b	NOUN
ejpam-4655	218	5	)	)	PUNCT
ejpam-4655	218	6	consider	consider	VERB
ejpam-4655	218	7	the	the	DET
ejpam-4655	218	8	bigeneralized	bigeneralized	ADJ
ejpam-4655	218	9	topological	topological	ADJ
ejpam-4655	218	10	space	space	NOUN
ejpam-4655	218	11	(	(	PUNCT
ejpam-4655	218	12	x,µ1	x,µ1	PROPN
ejpam-4655	218	13	,	,	PUNCT
ejpam-4655	218	14	µ2	µ2	PROPN
ejpam-4655	218	15	)	)	PUNCT
ejpam-4655	218	16	where	where	SCONJ
ejpam-4655	218	17	x	x	X
ejpam-4655	218	18	=	=	PRON
ejpam-4655	218	19	{	{	PUNCT
ejpam-4655	218	20	p	p	X
ejpam-4655	218	21	,	,	PUNCT
ejpam-4655	218	22	q	q	ADJ
ejpam-4655	218	23	,	,	PUNCT
ejpam-4655	218	24	r	r	NOUN
ejpam-4655	218	25	,	,	PUNCT
ejpam-4655	218	26	s	s	NOUN
ejpam-4655	218	27	,	,	PUNCT
ejpam-4655	218	28	t};µ1	t};µ1	PROPN
ejpam-4655	218	29	=	=	SYM
ejpam-4655	218	30	{	{	PUNCT
ejpam-4655	218	31	∅	∅	NOUN
ejpam-4655	218	32	,	,	PUNCT
ejpam-4655	218	33	{	{	PUNCT
ejpam-4655	218	34	p	p	X
ejpam-4655	218	35	,	,	PUNCT
ejpam-4655	218	36	q	q	X
ejpam-4655	218	37	,	,	PUNCT
ejpam-4655	218	38	s	s	PART
ejpam-4655	218	39	}	}	PUNCT
ejpam-4655	218	40	,	,	PUNCT
ejpam-4655	218	41	{	{	PUNCT
ejpam-4655	218	42	p	p	X
ejpam-4655	218	43	,	,	PUNCT
ejpam-4655	218	44	q	q	X
ejpam-4655	218	45	,	,	PUNCT
ejpam-4655	218	46	t	t	PROPN
ejpam-4655	218	47	}	}	PUNCT
ejpam-4655	218	48	,	,	PUNCT
ejpam-4655	218	49	{	{	PUNCT
ejpam-4655	218	50	q	q	X
ejpam-4655	218	51	,	,	PUNCT
ejpam-4655	218	52	s	s	PROPN
ejpam-4655	218	53	,	,	PUNCT
ejpam-4655	218	54	t	t	PROPN
ejpam-4655	218	55	}	}	PUNCT
ejpam-4655	218	56	,	,	PUNCT
ejpam-4655	218	57	{	{	PUNCT
ejpam-4655	218	58	p	p	X
ejpam-4655	218	59	,	,	PUNCT
ejpam-4655	218	60	q	q	ADJ
ejpam-4655	218	61	,	,	PUNCT
ejpam-4655	218	62	s	s	PROPN
ejpam-4655	218	63	,	,	PUNCT
ejpam-4655	218	64	t	t	PROPN
ejpam-4655	218	65	}	}	PUNCT
ejpam-4655	218	66	}	}	PUNCT
ejpam-4655	218	67	and	and	CCONJ
ejpam-4655	218	68	µ2	µ2	PROPN
ejpam-4655	218	69	=	=	PUNCT
ejpam-4655	218	70	{	{	PUNCT
ejpam-4655	218	71	∅	∅	NOUN
ejpam-4655	218	72	,	,	PUNCT
ejpam-4655	218	73	{	{	PUNCT
ejpam-4655	218	74	q	q	NOUN
ejpam-4655	218	75	,	,	PUNCT
ejpam-4655	218	76	r	r	NOUN
ejpam-4655	218	77	,	,	PUNCT
ejpam-4655	218	78	s	s	PART
ejpam-4655	218	79	}	}	PUNCT
ejpam-4655	218	80	,	,	PUNCT
ejpam-4655	218	81	{	{	PUNCT
ejpam-4655	218	82	q	q	X
ejpam-4655	218	83	,	,	PUNCT
ejpam-4655	218	84	r	r	NOUN
ejpam-4655	218	85	,	,	PUNCT
ejpam-4655	218	86	t	t	PROPN
ejpam-4655	218	87	}	}	PUNCT
ejpam-4655	218	88	,	,	PUNCT
ejpam-4655	218	89	{	{	PUNCT
ejpam-4655	218	90	r	r	NOUN
ejpam-4655	218	91	,	,	PUNCT
ejpam-4655	218	92	s	s	PROPN
ejpam-4655	218	93	,	,	PUNCT
ejpam-4655	218	94	t	t	PROPN
ejpam-4655	218	95	}	}	PUNCT
ejpam-4655	218	96	,	,	PUNCT
ejpam-4655	218	97	{	{	PUNCT
ejpam-4655	218	98	q	q	X
ejpam-4655	218	99	,	,	PUNCT
ejpam-4655	218	100	r	r	NOUN
ejpam-4655	218	101	,	,	PUNCT
ejpam-4655	218	102	s	s	PROPN
ejpam-4655	218	103	,	,	PUNCT
ejpam-4655	218	104	t	t	PROPN
ejpam-4655	218	105	}	}	PUNCT
ejpam-4655	218	106	}	}	PUNCT
ejpam-4655	218	107	.	.	PUNCT
ejpam-4655	219	1	take	take	VERB
ejpam-4655	219	2	m	m	NOUN
ejpam-4655	219	3	=	=	PUNCT
ejpam-4655	219	4	{	{	PUNCT
ejpam-4655	219	5	q	q	NOUN
ejpam-4655	219	6	,	,	PUNCT
ejpam-4655	219	7	r	r	NOUN
ejpam-4655	219	8	}	}	PUNCT
ejpam-4655	219	9	.	.	PUNCT
ejpam-4655	220	1	then	then	ADV
ejpam-4655	220	2	cµ1(m	cµ1(m	X
ejpam-4655	220	3	)	)	PUNCT
ejpam-4655	220	4	=	=	PUNCT
ejpam-4655	221	1	x.	x.	NOUN
ejpam-4655	221	2	but	but	CCONJ
ejpam-4655	221	3	m	m	PROPN
ejpam-4655	221	4	/∈	/∈	PUNCT
ejpam-4655	222	1	µ̃2	µ̃2	PROPN
ejpam-4655	222	2	.	.	PUNCT
ejpam-4655	223	1	thus	thus	ADV
ejpam-4655	223	2	,	,	PUNCT
ejpam-4655	223	3	x	x	PRON
ejpam-4655	223	4	is	be	AUX
ejpam-4655	223	5	not	not	PART
ejpam-4655	223	6	a	a	DET
ejpam-4655	223	7	(	(	PUNCT
ejpam-4655	223	8	2	2	NUM
ejpam-4655	223	9	,	,	PUNCT
ejpam-4655	223	10	1)-bigeneralized	1)-bigeneralized	NUM
ejpam-4655	223	11	topological	topological	ADJ
ejpam-4655	223	12	space	space	NOUN
ejpam-4655	223	13	.	.	PUNCT
ejpam-4655	224	1	let	let	VERB
ejpam-4655	224	2	j	j	NOUN
ejpam-4655	224	3	=	=	PUNCT
ejpam-4655	224	4	{	{	PUNCT
ejpam-4655	224	5	p	p	X
ejpam-4655	224	6	,	,	PUNCT
ejpam-4655	224	7	q	q	X
ejpam-4655	224	8	,	,	PUNCT
ejpam-4655	224	9	t	t	PROPN
ejpam-4655	224	10	}	}	PUNCT
ejpam-4655	224	11	.	.	PUNCT
ejpam-4655	225	1	then	then	ADV
ejpam-4655	225	2	j	j	PROPN
ejpam-4655	225	3	∈	∈	PROPN
ejpam-4655	225	4	µ̃1	µ̃1	PROPN
ejpam-4655	225	5	.	.	PUNCT
ejpam-4655	225	6	here	here	ADV
ejpam-4655	225	7	fr1(j	fr1(j	PROPN
ejpam-4655	225	8	)	)	PUNCT
ejpam-4655	225	9	=	=	SYM
ejpam-4655	225	10	c1(j	c1(j	NOUN
ejpam-4655	225	11	)	)	PUNCT
ejpam-4655	225	12	∩	∩	NOUN
ejpam-4655	225	13	c1(x	c1(x	NUM
ejpam-4655	225	14	−	−	PROPN
ejpam-4655	225	15	j	j	NOUN
ejpam-4655	225	16	)	)	PUNCT
ejpam-4655	225	17	.	.	PUNCT
ejpam-4655	226	1	this	this	PRON
ejpam-4655	226	2	implies	imply	VERB
ejpam-4655	226	3	fr1(j	fr1(j	PROPN
ejpam-4655	226	4	)	)	PUNCT
ejpam-4655	227	1	=	=	PRON
ejpam-4655	227	2	{	{	PUNCT
ejpam-4655	227	3	r	r	NOUN
ejpam-4655	227	4	,	,	PUNCT
ejpam-4655	227	5	s	s	PART
ejpam-4655	227	6	}	}	PUNCT
ejpam-4655	227	7	which	which	PRON
ejpam-4655	227	8	implies	imply	VERB
ejpam-4655	227	9	that	that	SCONJ
ejpam-4655	227	10	i1(c2(fr1(j	i1(c2(fr1(j	ADJ
ejpam-4655	227	11	)	)	PUNCT
ejpam-4655	227	12	)	)	PUNCT
ejpam-4655	227	13	)	)	PUNCT
ejpam-4655	228	1	=	=	PUNCT
ejpam-4655	228	2	i1(x	i1(x	X
ejpam-4655	228	3	)	)	PUNCT
ejpam-4655	228	4	=	=	PRON
ejpam-4655	228	5	{	{	PUNCT
ejpam-4655	228	6	p	p	X
ejpam-4655	228	7	,	,	PUNCT
ejpam-4655	228	8	q	q	ADJ
ejpam-4655	228	9	,	,	PUNCT
ejpam-4655	228	10	s	s	PROPN
ejpam-4655	228	11	,	,	PUNCT
ejpam-4655	228	12	t	t	PROPN
ejpam-4655	228	13	}	}	PUNCT
ejpam-4655	228	14	.	.	PUNCT
ejpam-4655	229	1	thus	thus	ADV
ejpam-4655	229	2	,	,	PUNCT
ejpam-4655	229	3	i1(c2(fr1(j	i1(c2(fr1(j	ADJ
ejpam-4655	229	4	)	)	PUNCT
ejpam-4655	229	5	)	)	PUNCT
ejpam-4655	229	6	)	)	PUNCT
ejpam-4655	230	1	̸=	̸=	PROPN
ejpam-4655	230	2	∅.	∅.	ADP
ejpam-4655	230	3	the	the	DET
ejpam-4655	230	4	below	below	ADP
ejpam-4655	230	5	two	two	NUM
ejpam-4655	230	6	theorems	theorem	NOUN
ejpam-4655	230	7	(	(	PUNCT
ejpam-4655	230	8	theorem	theorem	VERB
ejpam-4655	230	9	16	16	NUM
ejpam-4655	230	10	and	and	CCONJ
ejpam-4655	230	11	theorem	theorem	VERB
ejpam-4655	230	12	17	17	NUM
ejpam-4655	230	13	)	)	PUNCT
ejpam-4655	230	14	reduce	reduce	VERB
ejpam-4655	230	15	the	the	DET
ejpam-4655	230	16	complexity	complexity	NOUN
ejpam-4655	230	17	of	of	ADP
ejpam-4655	230	18	checking	check	VERB
ejpam-4655	230	19	whether	whether	SCONJ
ejpam-4655	230	20	the	the	DET
ejpam-4655	230	21	frontier	frontier	NOUN
ejpam-4655	230	22	of	of	ADP
ejpam-4655	230	23	a	a	DET
ejpam-4655	230	24	given	give	VERB
ejpam-4655	230	25	set	set	NOUN
ejpam-4655	230	26	is	be	AUX
ejpam-4655	230	27	in	in	ADP
ejpam-4655	230	28	(	(	PUNCT
ejpam-4655	230	29	s	s	X
ejpam-4655	230	30	,	,	PUNCT
ejpam-4655	230	31	v)−n	v)−n	X
ejpam-4655	230	32	(	(	PUNCT
ejpam-4655	230	33	x	x	NOUN
ejpam-4655	230	34	)	)	PUNCT
ejpam-4655	230	35	or	or	CCONJ
ejpam-4655	230	36	not	not	PART
ejpam-4655	230	37	.	.	PUNCT
ejpam-4655	231	1	theorem	theorem	NOUN
ejpam-4655	231	2	16	16	NUM
ejpam-4655	231	3	.	.	PUNCT
ejpam-4655	232	1	let	let	AUX
ejpam-4655	232	2	(	(	PUNCT
ejpam-4655	232	3	x,µ1	x,µ1	NOUN
ejpam-4655	232	4	,	,	PUNCT
ejpam-4655	232	5	µ2	µ2	PROPN
ejpam-4655	232	6	)	)	PUNCT
ejpam-4655	232	7	be	be	AUX
ejpam-4655	232	8	a	a	DET
ejpam-4655	232	9	bgts	bgts	NOUN
ejpam-4655	232	10	.	.	PUNCT
ejpam-4655	233	1	if	if	SCONJ
ejpam-4655	233	2	q	q	X
ejpam-4655	233	3	∈	∈	PROPN
ejpam-4655	233	4	(	(	PUNCT
ejpam-4655	233	5	s	s	PROPN
ejpam-4655	233	6	,	,	PUNCT
ejpam-4655	233	7	v)−n	v)−n	X
ejpam-4655	233	8	(	(	PUNCT
ejpam-4655	233	9	x	x	NOUN
ejpam-4655	233	10	)	)	PUNCT
ejpam-4655	233	11	,	,	PUNCT
ejpam-4655	233	12	then	then	ADV
ejpam-4655	233	13	frv(q	frv(q	X
ejpam-4655	233	14	)	)	PUNCT
ejpam-4655	233	15	∈	∈	PROPN
ejpam-4655	233	16	(	(	PUNCT
ejpam-4655	233	17	s	s	PROPN
ejpam-4655	233	18	,	,	PUNCT
ejpam-4655	233	19	v)−	v)−	PROPN
ejpam-4655	233	20	n	n	CCONJ
ejpam-4655	233	21	(	(	PUNCT
ejpam-4655	233	22	x	x	X
ejpam-4655	233	23	)	)	PUNCT
ejpam-4655	233	24	where	where	SCONJ
ejpam-4655	233	25	s	s	X
ejpam-4655	233	26	,	,	PUNCT
ejpam-4655	233	27	v	v	NOUN
ejpam-4655	233	28	=	=	SYM
ejpam-4655	233	29	1	1	NUM
ejpam-4655	233	30	,	,	PUNCT
ejpam-4655	233	31	2	2	NUM
ejpam-4655	233	32	;	;	PUNCT
ejpam-4655	233	33	s	s	VERB
ejpam-4655	233	34	̸=	̸=	PROPN
ejpam-4655	233	35	v.	v.	ADP
ejpam-4655	233	36	proof	proof	NOUN
ejpam-4655	233	37	.	.	PUNCT
ejpam-4655	234	1	fix	fix	NOUN
ejpam-4655	234	2	s	s	PART
ejpam-4655	234	3	=	=	SYM
ejpam-4655	234	4	1	1	NUM
ejpam-4655	234	5	,	,	PUNCT
ejpam-4655	234	6	v	v	NOUN
ejpam-4655	234	7	=	=	SYM
ejpam-4655	234	8	2	2	NUM
ejpam-4655	234	9	and	and	CCONJ
ejpam-4655	234	10	let	let	VERB
ejpam-4655	234	11	q	q	PROPN
ejpam-4655	234	12	∈	∈	PROPN
ejpam-4655	234	13	(	(	PUNCT
ejpam-4655	234	14	1	1	NUM
ejpam-4655	234	15	,	,	PUNCT
ejpam-4655	234	16	2	2	NUM
ejpam-4655	234	17	)	)	PUNCT
ejpam-4655	234	18	−	−	PROPN
ejpam-4655	235	1	n	n	CCONJ
ejpam-4655	235	2	(	(	PUNCT
ejpam-4655	235	3	x	x	X
ejpam-4655	235	4	)	)	PUNCT
ejpam-4655	235	5	for	for	ADP
ejpam-4655	235	6	that	that	PRON
ejpam-4655	235	7	i1(c2(q	i1(c2(q	NOUN
ejpam-4655	235	8	)	)	PUNCT
ejpam-4655	235	9	)	)	PUNCT
ejpam-4655	236	1	=	=	NOUN
ejpam-4655	236	2	∅	∅	NOUN
ejpam-4655	236	3	,	,	PUNCT
ejpam-4655	236	4	also	also	ADV
ejpam-4655	236	5	,	,	PUNCT
ejpam-4655	236	6	fr2(q	fr2(q	PROPN
ejpam-4655	236	7	)	)	PUNCT
ejpam-4655	236	8	⊆	⊆	NUM
ejpam-4655	236	9	c2(q	c2(q	PROPN
ejpam-4655	236	10	)	)	PUNCT
ejpam-4655	236	11	which	which	PRON
ejpam-4655	236	12	implies	imply	VERB
ejpam-4655	236	13	that	that	SCONJ
ejpam-4655	236	14	i1(fr2(q	i1(fr2(q	NOUN
ejpam-4655	236	15	)	)	PUNCT
ejpam-4655	236	16	)	)	PUNCT
ejpam-4655	237	1	=	=	PUNCT
ejpam-4655	237	2	∅	∅	NOUN
ejpam-4655	237	3	which	which	PRON
ejpam-4655	237	4	turn	turn	VERB
ejpam-4655	237	5	implies	imply	VERB
ejpam-4655	237	6	that	that	SCONJ
ejpam-4655	237	7	fr2(q	fr2(q	PROPN
ejpam-4655	237	8	)	)	PUNCT
ejpam-4655	237	9	∈	∈	PROPN
ejpam-4655	237	10	(	(	PUNCT
ejpam-4655	237	11	1	1	NUM
ejpam-4655	237	12	,	,	PUNCT
ejpam-4655	237	13	2)−n	2)−n	NUM
ejpam-4655	237	14	(	(	PUNCT
ejpam-4655	237	15	x	x	NOUN
ejpam-4655	237	16	)	)	PUNCT
ejpam-4655	237	17	,	,	PUNCT
ejpam-4655	237	18	because	because	SCONJ
ejpam-4655	237	19	,	,	PUNCT
ejpam-4655	237	20	fr2(q	fr2(q	PROPN
ejpam-4655	237	21	)	)	PUNCT
ejpam-4655	237	22	is	be	AUX
ejpam-4655	237	23	µ2	µ2	ADJ
ejpam-4655	237	24	-	-	PUNCT
ejpam-4655	237	25	closed	closed	ADJ
ejpam-4655	237	26	.	.	PUNCT
ejpam-4655	238	1	similarly	similarly	ADV
ejpam-4655	238	2	,	,	PUNCT
ejpam-4655	238	3	we	we	PRON
ejpam-4655	238	4	can	can	AUX
ejpam-4655	238	5	prove	prove	VERB
ejpam-4655	238	6	that	that	SCONJ
ejpam-4655	238	7	the	the	DET
ejpam-4655	238	8	result	result	NOUN
ejpam-4655	238	9	is	be	AUX
ejpam-4655	238	10	true	true	ADJ
ejpam-4655	238	11	for	for	ADP
ejpam-4655	238	12	s	s	NOUN
ejpam-4655	238	13	=	=	SYM
ejpam-4655	238	14	2	2	NUM
ejpam-4655	238	15	,	,	PUNCT
ejpam-4655	238	16	v	v	NOUN
ejpam-4655	238	17	=	=	SYM
ejpam-4655	238	18	1	1	X
ejpam-4655	238	19	.	.	PUNCT
ejpam-4655	238	20	theorem	theorem	NOUN
ejpam-4655	238	21	17	17	NUM
ejpam-4655	238	22	.	.	PUNCT
ejpam-4655	239	1	let	let	AUX
ejpam-4655	239	2	(	(	PUNCT
ejpam-4655	239	3	x,µ1	x,µ1	NOUN
ejpam-4655	239	4	,	,	PUNCT
ejpam-4655	239	5	µ2	µ2	PROPN
ejpam-4655	239	6	)	)	PUNCT
ejpam-4655	239	7	be	be	AUX
ejpam-4655	239	8	a	a	DET
ejpam-4655	239	9	bgts	bgts	NOUN
ejpam-4655	239	10	.	.	PUNCT
ejpam-4655	240	1	if	if	SCONJ
ejpam-4655	240	2	cµvq	cµvq	PROPN
ejpam-4655	240	3	=	=	PUNCT
ejpam-4655	240	4	x	x	X
ejpam-4655	241	1	and	and	CCONJ
ejpam-4655	241	2	if	if	SCONJ
ejpam-4655	241	3	q	q	NOUN
ejpam-4655	241	4	is	be	AUX
ejpam-4655	241	5	a	a	DET
ejpam-4655	241	6	(	(	PUNCT
ejpam-4655	241	7	s	s	NOUN
ejpam-4655	241	8	,	,	PUNCT
ejpam-4655	241	9	v)-open	v)-open	ADV
ejpam-4655	241	10	set	set	NOUN
ejpam-4655	241	11	,	,	PUNCT
ejpam-4655	241	12	then	then	ADV
ejpam-4655	241	13	frv(q	frv(q	PROPN
ejpam-4655	241	14	)	)	PUNCT
ejpam-4655	241	15	∈	∈	PROPN
ejpam-4655	241	16	(	(	PUNCT
ejpam-4655	241	17	v	v	NOUN
ejpam-4655	241	18	,	,	PUNCT
ejpam-4655	241	19	s)−n	s)−n	X
ejpam-4655	241	20	(	(	PUNCT
ejpam-4655	241	21	x	x	NOUN
ejpam-4655	241	22	)	)	PUNCT
ejpam-4655	241	23	where	where	SCONJ
ejpam-4655	241	24	s	s	X
ejpam-4655	241	25	,	,	PUNCT
ejpam-4655	241	26	v	v	NOUN
ejpam-4655	241	27	=	=	SYM
ejpam-4655	241	28	1	1	NUM
ejpam-4655	241	29	,	,	PUNCT
ejpam-4655	241	30	2	2	NUM
ejpam-4655	241	31	;	;	PUNCT
ejpam-4655	241	32	s	s	VERB
ejpam-4655	241	33	̸=	̸=	PROPN
ejpam-4655	241	34	v.	v.	ADP
ejpam-4655	241	35	proof	proof	NOUN
ejpam-4655	241	36	.	.	PUNCT
ejpam-4655	242	1	consider	consider	VERB
ejpam-4655	242	2	,	,	PUNCT
ejpam-4655	242	3	s	s	PART
ejpam-4655	242	4	=	=	SYM
ejpam-4655	242	5	1	1	NUM
ejpam-4655	242	6	,	,	PUNCT
ejpam-4655	242	7	v	v	NOUN
ejpam-4655	242	8	=	=	SYM
ejpam-4655	242	9	2	2	NUM
ejpam-4655	242	10	and	and	CCONJ
ejpam-4655	242	11	given	give	VERB
ejpam-4655	242	12	c2(q	c2(q	PROPN
ejpam-4655	242	13	)	)	PUNCT
ejpam-4655	242	14	=	=	PUNCT
ejpam-4655	243	1	x.	x.	NOUN
ejpam-4655	243	2	(	(	PUNCT
ejpam-4655	243	3	3	3	X
ejpam-4655	243	4	)	)	PUNCT
ejpam-4655	243	5	assume	assume	VERB
ejpam-4655	243	6	that	that	SCONJ
ejpam-4655	243	7	,	,	PUNCT
ejpam-4655	243	8	q	q	X
ejpam-4655	243	9	is	be	AUX
ejpam-4655	243	10	a	a	DET
ejpam-4655	243	11	(	(	PUNCT
ejpam-4655	243	12	1	1	NUM
ejpam-4655	243	13	,	,	PUNCT
ejpam-4655	243	14	2)-open	2)-open	NUM
ejpam-4655	243	15	set	set	VERB
ejpam-4655	243	16	for	for	ADP
ejpam-4655	243	17	that	that	PRON
ejpam-4655	243	18	,	,	PUNCT
ejpam-4655	243	19	i1(i2(q	i1(i2(q	PROPN
ejpam-4655	243	20	)	)	PUNCT
ejpam-4655	243	21	)	)	PUNCT
ejpam-4655	244	1	=	=	PUNCT
ejpam-4655	244	2	q	q	ADJ
ejpam-4655	244	3	,	,	PUNCT
ejpam-4655	244	4	also	also	ADV
ejpam-4655	244	5	,	,	PUNCT
ejpam-4655	244	6	fr2(q	fr2(q	PROPN
ejpam-4655	244	7	)	)	PUNCT
ejpam-4655	244	8	=	=	SYM
ejpam-4655	244	9	c2(q	c2(q	ADJ
ejpam-4655	244	10	)	)	PUNCT
ejpam-4655	244	11	∩	∩	NOUN
ejpam-4655	244	12	c2(x	c2(x	PRON
ejpam-4655	244	13	−q	−q	NOUN
ejpam-4655	244	14	)	)	PUNCT
ejpam-4655	244	15	by	by	ADP
ejpam-4655	244	16	which	which	PRON
ejpam-4655	244	17	fr2(q	fr2(q	VERB
ejpam-4655	244	18	)	)	PUNCT
ejpam-4655	244	19	=	=	PUNCT
ejpam-4655	245	1	x	x	X
ejpam-4655	245	2	−	−	PROPN
ejpam-4655	245	3	i2(q	i2(q	PROPN
ejpam-4655	245	4	)	)	PUNCT
ejpam-4655	245	5	which	which	PRON
ejpam-4655	245	6	implies	imply	VERB
ejpam-4655	245	7	that	that	SCONJ
ejpam-4655	245	8	c1(fr2(q	c1(fr2(q	NOUN
ejpam-4655	245	9	)	)	PUNCT
ejpam-4655	245	10	)	)	PUNCT
ejpam-4655	246	1	=	=	PUNCT
ejpam-4655	247	1	c1(x	c1(x	VERB
ejpam-4655	247	2	−	−	NOUN
ejpam-4655	247	3	i2(q	i2(q	PROPN
ejpam-4655	247	4	)	)	PUNCT
ejpam-4655	247	5	)	)	PUNCT
ejpam-4655	248	1	so	so	ADV
ejpam-4655	248	2	c1(fr2(q	c1(fr2(q	PROPN
ejpam-4655	248	3	)	)	PUNCT
ejpam-4655	248	4	)	)	PUNCT
ejpam-4655	249	1	=	=	PUNCT
ejpam-4655	250	1	x	x	X
ejpam-4655	250	2	−	−	NOUN
ejpam-4655	250	3	i1(i2(q	i1(i2(q	NOUN
ejpam-4655	250	4	)	)	PUNCT
ejpam-4655	250	5	)	)	PUNCT
ejpam-4655	250	6	,	,	PUNCT
ejpam-4655	250	7	thus	thus	ADV
ejpam-4655	250	8	,	,	PUNCT
ejpam-4655	250	9	c1(fr2(q	c1(fr2(q	NOUN
ejpam-4655	250	10	)	)	PUNCT
ejpam-4655	250	11	)	)	PUNCT
ejpam-4655	251	1	=	=	PUNCT
ejpam-4655	252	1	x	x	X
ejpam-4655	252	2	−	−	NOUN
ejpam-4655	253	1	q	q	INTJ
ejpam-4655	253	2	,	,	PUNCT
ejpam-4655	253	3	whereby	whereby	ADV
ejpam-4655	253	4	by	by	ADP
ejpam-4655	253	5	(	(	PUNCT
ejpam-4655	253	6	3	3	NUM
ejpam-4655	253	7	)	)	PUNCT
ejpam-4655	253	8	,	,	PUNCT
ejpam-4655	253	9	we	we	PRON
ejpam-4655	253	10	get	get	VERB
ejpam-4655	253	11	i2(c1(fr2(q	i2(c1(fr2(q	PROPN
ejpam-4655	253	12	)	)	PUNCT
ejpam-4655	253	13	)	)	PUNCT
ejpam-4655	253	14	)	)	PUNCT
ejpam-4655	254	1	=	=	NOUN
ejpam-4655	254	2	∅	∅	NOUN
ejpam-4655	254	3	and	and	CCONJ
ejpam-4655	254	4	hence	hence	ADV
ejpam-4655	254	5	fr2(q	fr2(q	PROPN
ejpam-4655	254	6	)	)	PUNCT
ejpam-4655	254	7	∈	∈	PROPN
ejpam-4655	254	8	(	(	PUNCT
ejpam-4655	254	9	2	2	NUM
ejpam-4655	254	10	,	,	PUNCT
ejpam-4655	254	11	1	1	NUM
ejpam-4655	254	12	)	)	PUNCT
ejpam-4655	254	13	−	−	PROPN
ejpam-4655	254	14	n	n	CCONJ
ejpam-4655	254	15	(	(	PUNCT
ejpam-4655	254	16	x	x	NOUN
ejpam-4655	254	17	)	)	PUNCT
ejpam-4655	254	18	.	.	PUNCT
ejpam-4655	255	1	similarly	similarly	ADV
ejpam-4655	255	2	,	,	PUNCT
ejpam-4655	255	3	we	we	PRON
ejpam-4655	255	4	can	can	AUX
ejpam-4655	255	5	prove	prove	VERB
ejpam-4655	255	6	that	that	SCONJ
ejpam-4655	255	7	the	the	DET
ejpam-4655	255	8	result	result	NOUN
ejpam-4655	255	9	is	be	AUX
ejpam-4655	255	10	true	true	ADJ
ejpam-4655	255	11	for	for	ADP
ejpam-4655	255	12	s	s	NOUN
ejpam-4655	255	13	=	=	SYM
ejpam-4655	255	14	2	2	NUM
ejpam-4655	255	15	,	,	PUNCT
ejpam-4655	255	16	v	v	NOUN
ejpam-4655	255	17	=	=	SYM
ejpam-4655	255	18	1	1	NUM
ejpam-4655	255	19	.	.	PUNCT
ejpam-4655	256	1	y.	y.	PROPN
ejpam-4655	256	2	farhat	farhat	PROPN
ejpam-4655	256	3	et	et	PROPN
ejpam-4655	256	4	al	al	PROPN
ejpam-4655	256	5	.	.	PUNCT
ejpam-4655	256	6	/	/	SYM
ejpam-4655	256	7	eur	eur	PROPN
ejpam-4655	256	8	.	.	PUNCT
ejpam-4655	257	1	j.	j.	PROPN
ejpam-4655	257	2	pure	pure	PROPN
ejpam-4655	257	3	appl	appl	PROPN
ejpam-4655	257	4	.	.	PROPN
ejpam-4655	257	5	math	math	PROPN
ejpam-4655	257	6	,	,	PUNCT
ejpam-4655	257	7	16	16	NUM
ejpam-4655	257	8	(	(	PUNCT
ejpam-4655	257	9	1	1	NUM
ejpam-4655	257	10	)	)	PUNCT
ejpam-4655	257	11	(	(	PUNCT
ejpam-4655	257	12	2023	2023	NUM
ejpam-4655	257	13	)	)	PUNCT
ejpam-4655	257	14	,	,	PUNCT
ejpam-4655	257	15	386	386	NUM
ejpam-4655	257	16	-	-	SYM
ejpam-4655	257	17	403	403	NUM
ejpam-4655	257	18	393	393	NUM
ejpam-4655	257	19	the	the	DET
ejpam-4655	257	20	below	below	ADP
ejpam-4655	257	21	corollary	corollary	NOUN
ejpam-4655	257	22	18	18	NUM
ejpam-4655	257	23	directly	directly	ADV
ejpam-4655	257	24	follows	follow	VERB
ejpam-4655	257	25	from	from	ADP
ejpam-4655	257	26	theorem	theorem	ADJ
ejpam-4655	257	27	5	5	NUM
ejpam-4655	257	28	and	and	CCONJ
ejpam-4655	257	29	theorem	theorem	VERB
ejpam-4655	257	30	17	17	NUM
ejpam-4655	257	31	so	so	SCONJ
ejpam-4655	257	32	the	the	DET
ejpam-4655	257	33	trivial	trivial	ADJ
ejpam-4655	257	34	proof	proof	NOUN
ejpam-4655	257	35	is	be	AUX
ejpam-4655	257	36	neglected	neglect	VERB
ejpam-4655	257	37	.	.	PUNCT
ejpam-4655	258	1	corollary	corollary	ADJ
ejpam-4655	258	2	18	18	NUM
ejpam-4655	258	3	.	.	PUNCT
ejpam-4655	259	1	let	let	AUX
ejpam-4655	259	2	(	(	PUNCT
ejpam-4655	259	3	x,µ1	x,µ1	NOUN
ejpam-4655	259	4	,	,	PUNCT
ejpam-4655	259	5	µ2	µ2	PROPN
ejpam-4655	259	6	)	)	PUNCT
ejpam-4655	259	7	be	be	VERB
ejpam-4655	259	8	a	a	DET
ejpam-4655	259	9	(	(	PUNCT
ejpam-4655	259	10	s	s	NOUN
ejpam-4655	259	11	,	,	PUNCT
ejpam-4655	259	12	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	259	13	submaximal	submaximal	ADJ
ejpam-4655	259	14	space	space	NOUN
ejpam-4655	259	15	and	and	CCONJ
ejpam-4655	259	16	cµvq	cµvq	NOUN
ejpam-4655	260	1	=	=	PUNCT
ejpam-4655	260	2	x.	x.	NOUN
ejpam-4655	260	3	if	if	SCONJ
ejpam-4655	260	4	q	q	NOUN
ejpam-4655	260	5	is	be	AUX
ejpam-4655	260	6	a	a	DET
ejpam-4655	260	7	(	(	PUNCT
ejpam-4655	260	8	s	s	NOUN
ejpam-4655	260	9	,	,	PUNCT
ejpam-4655	260	10	v)-open	v)-open	ADV
ejpam-4655	260	11	set	set	NOUN
ejpam-4655	260	12	,	,	PUNCT
ejpam-4655	260	13	then	then	ADV
ejpam-4655	260	14	frv(q	frv(q	PROPN
ejpam-4655	260	15	)	)	PUNCT
ejpam-4655	260	16	is	be	AUX
ejpam-4655	260	17	µs	µs	NOUN
ejpam-4655	260	18	-	-	PUNCT
ejpam-4655	260	19	closed	closed	ADJ
ejpam-4655	260	20	and	and	CCONJ
ejpam-4655	260	21	hence	hence	ADV
ejpam-4655	260	22	frv(q	frv(q	NUM
ejpam-4655	260	23	)	)	PUNCT
ejpam-4655	261	1	is	be	AUX
ejpam-4655	261	2	a	a	DET
ejpam-4655	261	3	(	(	PUNCT
ejpam-4655	261	4	s	s	NOUN
ejpam-4655	261	5	,	,	PUNCT
ejpam-4655	261	6	v)-closed	v)-close	VERB
ejpam-4655	261	7	in	in	ADP
ejpam-4655	261	8	x	x	SYM
ejpam-4655	261	9	where	where	SCONJ
ejpam-4655	261	10	s	s	X
ejpam-4655	261	11	,	,	PUNCT
ejpam-4655	261	12	v	v	NOUN
ejpam-4655	261	13	=	=	SYM
ejpam-4655	261	14	1	1	NUM
ejpam-4655	261	15	,	,	PUNCT
ejpam-4655	261	16	2	2	NUM
ejpam-4655	261	17	;	;	PUNCT
ejpam-4655	261	18	s	s	VERB
ejpam-4655	261	19	̸=	̸=	PROPN
ejpam-4655	261	20	v.	v.	ADP
ejpam-4655	261	21	the	the	DET
ejpam-4655	261	22	following	follow	VERB
ejpam-4655	261	23	two	two	NUM
ejpam-4655	261	24	theorems	theorem	NOUN
ejpam-4655	261	25	(	(	PUNCT
ejpam-4655	261	26	theorem	theorem	ADJ
ejpam-4655	261	27	19	19	NUM
ejpam-4655	261	28	and	and	CCONJ
ejpam-4655	261	29	theorem	theorem	VERB
ejpam-4655	261	30	20	20	NUM
ejpam-4655	261	31	)	)	PUNCT
ejpam-4655	262	1	are	be	AUX
ejpam-4655	262	2	gives	give	VERB
ejpam-4655	262	3	the	the	DET
ejpam-4655	262	4	necessary	necessary	ADJ
ejpam-4655	262	5	condition	condition	NOUN
ejpam-4655	262	6	for	for	ADP
ejpam-4655	262	7	a	a	DET
ejpam-4655	262	8	bgts	bgts	NOUN
ejpam-4655	262	9	is	be	AUX
ejpam-4655	262	10	a	a	DET
ejpam-4655	262	11	(	(	PUNCT
ejpam-4655	262	12	s	s	PROPN
ejpam-4655	262	13	,	,	PUNCT
ejpam-4655	262	14	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	262	15	submaximal	submaximal	ADJ
ejpam-4655	262	16	space	space	NOUN
ejpam-4655	262	17	.	.	PUNCT
ejpam-4655	263	1	theorem	theorem	NOUN
ejpam-4655	263	2	19	19	NUM
ejpam-4655	263	3	.	.	PUNCT
ejpam-4655	264	1	let	let	AUX
ejpam-4655	264	2	(	(	PUNCT
ejpam-4655	264	3	x,µ1	x,µ1	NOUN
ejpam-4655	264	4	,	,	PUNCT
ejpam-4655	264	5	µ2	µ2	PROPN
ejpam-4655	264	6	)	)	PUNCT
ejpam-4655	264	7	be	be	VERB
ejpam-4655	264	8	a	a	DET
ejpam-4655	264	9	bgts	bgts	NOUN
ejpam-4655	264	10	and	and	CCONJ
ejpam-4655	264	11	q	q	NOUN
ejpam-4655	264	12	⊂	⊂	PROPN
ejpam-4655	264	13	x.	x.	NOUN
ejpam-4655	265	1	if	if	SCONJ
ejpam-4655	265	2	cs(x	cs(x	VERB
ejpam-4655	265	3	−q	−q	NOUN
ejpam-4655	265	4	)	)	PUNCT
ejpam-4655	265	5	⊂	⊂	PROPN
ejpam-4655	265	6	cvq	cvq	PROPN
ejpam-4655	265	7	−q	−q	NOUN
ejpam-4655	265	8	,	,	PUNCT
ejpam-4655	265	9	then	then	ADV
ejpam-4655	265	10	x	x	PUNCT
ejpam-4655	265	11	is	be	AUX
ejpam-4655	265	12	a	a	DET
ejpam-4655	265	13	(	(	PUNCT
ejpam-4655	265	14	s	s	PROPN
ejpam-4655	265	15	,	,	PUNCT
ejpam-4655	265	16	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	265	17	submaximal	submaximal	ADJ
ejpam-4655	265	18	space	space	NOUN
ejpam-4655	265	19	for	for	ADP
ejpam-4655	265	20	s	s	PROPN
ejpam-4655	265	21	,	,	PUNCT
ejpam-4655	265	22	v	v	NOUN
ejpam-4655	265	23	=	=	SYM
ejpam-4655	265	24	1	1	NUM
ejpam-4655	265	25	,	,	PUNCT
ejpam-4655	265	26	2	2	NUM
ejpam-4655	265	27	;	;	PUNCT
ejpam-4655	265	28	s	s	VERB
ejpam-4655	265	29	̸=	̸=	PROPN
ejpam-4655	265	30	v.	v.	ADP
ejpam-4655	265	31	(	(	PUNCT
ejpam-4655	265	32	a	a	X
ejpam-4655	265	33	)	)	PUNCT
ejpam-4655	265	34	x	x	X
ejpam-4655	265	35	is	be	AUX
ejpam-4655	265	36	a	a	DET
ejpam-4655	265	37	(	(	PUNCT
ejpam-4655	265	38	s	s	PROPN
ejpam-4655	265	39	,	,	PUNCT
ejpam-4655	265	40	v)−	v)−	PROPN
ejpam-4655	265	41	bigeneralized	bigeneralize	VERB
ejpam-4655	265	42	submaximal	submaximal	ADJ
ejpam-4655	265	43	space	space	NOUN
ejpam-4655	265	44	(	(	PUNCT
ejpam-4655	265	45	b	b	NOUN
ejpam-4655	265	46	)	)	PUNCT
ejpam-4655	265	47	(	(	PUNCT
ejpam-4655	265	48	c	c	NOUN
ejpam-4655	265	49	)	)	PUNCT
ejpam-4655	265	50	where	where	SCONJ
ejpam-4655	265	51	,	,	PUNCT
ejpam-4655	265	52	(	(	PUNCT
ejpam-4655	265	53	a	a	X
ejpam-4655	265	54	)	)	PUNCT
ejpam-4655	265	55	every	every	DET
ejpam-4655	265	56	µv	µv	NOUN
ejpam-4655	265	57	-	-	PUNCT
ejpam-4655	265	58	pre	pre	ADJ
ejpam-4655	265	59	-	-	ADJ
ejpam-4655	265	60	open	open	ADJ
ejpam-4655	265	61	is	be	AUX
ejpam-4655	265	62	µs	µs	NOUN
ejpam-4655	265	63	-	-	ADJ
ejpam-4655	265	64	open	open	ADJ
ejpam-4655	265	65	.	.	PUNCT
ejpam-4655	266	1	(	(	PUNCT
ejpam-4655	266	2	b	b	X
ejpam-4655	266	3	)	)	PUNCT
ejpam-4655	266	4	every	every	DET
ejpam-4655	266	5	µv	µv	NOUN
ejpam-4655	266	6	-	-	PUNCT
ejpam-4655	266	7	β	β	NOUN
ejpam-4655	266	8	-	-	ADJ
ejpam-4655	266	9	open	open	ADJ
ejpam-4655	266	10	is	be	AUX
ejpam-4655	266	11	µs	µs	NOUN
ejpam-4655	266	12	-	-	ADJ
ejpam-4655	266	13	open	open	ADJ
ejpam-4655	266	14	.	.	PUNCT
ejpam-4655	267	1	(	(	PUNCT
ejpam-4655	267	2	c	c	X
ejpam-4655	267	3	)	)	PUNCT
ejpam-4655	267	4	every	every	DET
ejpam-4655	267	5	µv	µv	PROPN
ejpam-4655	267	6	-	-	PUNCT
ejpam-4655	267	7	b	b	NOUN
ejpam-4655	267	8	-	-	PUNCT
ejpam-4655	267	9	open	open	ADJ
ejpam-4655	267	10	is	be	AUX
ejpam-4655	267	11	µs	µs	NOUN
ejpam-4655	267	12	-	-	ADJ
ejpam-4655	267	13	open	open	ADJ
ejpam-4655	267	14	.	.	PUNCT
ejpam-4655	268	1	the	the	DET
ejpam-4655	268	2	following	follow	VERB
ejpam-4655	268	3	theorem	theorem	VERB
ejpam-4655	268	4	20	20	NUM
ejpam-4655	268	5	describes	describe	VERB
ejpam-4655	268	6	the	the	DET
ejpam-4655	268	7	above	above	ADJ
ejpam-4655	268	8	diagram	diagram	NOUN
ejpam-4655	268	9	.	.	PUNCT
ejpam-4655	269	1	theorem	theorem	NOUN
ejpam-4655	269	2	20	20	NUM
ejpam-4655	269	3	.	.	PUNCT
ejpam-4655	270	1	let	let	AUX
ejpam-4655	270	2	(	(	PUNCT
ejpam-4655	270	3	x,µ1	x,µ1	NOUN
ejpam-4655	270	4	,	,	PUNCT
ejpam-4655	270	5	µ2	µ2	PROPN
ejpam-4655	270	6	)	)	PUNCT
ejpam-4655	270	7	be	be	VERB
ejpam-4655	270	8	a	a	DET
ejpam-4655	270	9	bgts	bgts	NOUN
ejpam-4655	270	10	and	and	CCONJ
ejpam-4655	270	11	µv	µv	PROPN
ejpam-4655	270	12	is	be	AUX
ejpam-4655	270	13	a	a	DET
ejpam-4655	270	14	sgt	sgt	PROPN
ejpam-4655	270	15	.	.	PUNCT
ejpam-4655	271	1	then	then	ADV
ejpam-4655	271	2	x	x	X
ejpam-4655	271	3	is	be	AUX
ejpam-4655	271	4	a	a	DET
ejpam-4655	271	5	(	(	PUNCT
ejpam-4655	271	6	s	s	PROPN
ejpam-4655	271	7	,	,	PUNCT
ejpam-4655	271	8	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	271	9	submaximal	submaximal	ADJ
ejpam-4655	271	10	space	space	NOUN
ejpam-4655	271	11	if	if	SCONJ
ejpam-4655	271	12	any	any	DET
ejpam-4655	271	13	one	one	NUM
ejpam-4655	271	14	of	of	ADP
ejpam-4655	271	15	the	the	DET
ejpam-4655	271	16	following	follow	VERB
ejpam-4655	271	17	hold	hold	NOUN
ejpam-4655	271	18	;	;	PUNCT
ejpam-4655	271	19	(	(	PUNCT
ejpam-4655	271	20	a	a	X
ejpam-4655	271	21	)	)	PUNCT
ejpam-4655	271	22	every	every	DET
ejpam-4655	271	23	µv	µv	NOUN
ejpam-4655	271	24	-	-	PUNCT
ejpam-4655	271	25	pre	pre	ADJ
ejpam-4655	271	26	-	-	ADJ
ejpam-4655	271	27	open	open	ADJ
ejpam-4655	271	28	is	be	AUX
ejpam-4655	271	29	µs	µs	NOUN
ejpam-4655	271	30	-	-	ADJ
ejpam-4655	271	31	open	open	ADJ
ejpam-4655	271	32	.	.	PUNCT
ejpam-4655	272	1	(	(	PUNCT
ejpam-4655	272	2	b	b	X
ejpam-4655	272	3	)	)	PUNCT
ejpam-4655	272	4	every	every	DET
ejpam-4655	272	5	µv	µv	NOUN
ejpam-4655	272	6	-	-	PUNCT
ejpam-4655	272	7	β	β	NOUN
ejpam-4655	272	8	-	-	ADJ
ejpam-4655	272	9	open	open	ADJ
ejpam-4655	272	10	is	be	AUX
ejpam-4655	272	11	µs	µs	NOUN
ejpam-4655	272	12	-	-	ADJ
ejpam-4655	272	13	open	open	ADJ
ejpam-4655	272	14	.	.	PUNCT
ejpam-4655	273	1	(	(	PUNCT
ejpam-4655	273	2	c	c	X
ejpam-4655	273	3	)	)	PUNCT
ejpam-4655	273	4	every	every	DET
ejpam-4655	273	5	µv	µv	PROPN
ejpam-4655	273	6	-	-	PUNCT
ejpam-4655	273	7	b	b	NOUN
ejpam-4655	273	8	-	-	PUNCT
ejpam-4655	273	9	open	open	ADJ
ejpam-4655	273	10	is	be	AUX
ejpam-4655	273	11	µs	µs	NOUN
ejpam-4655	273	12	-	-	ADJ
ejpam-4655	273	13	open	open	ADJ
ejpam-4655	273	14	where	where	SCONJ
ejpam-4655	273	15	s	s	X
ejpam-4655	273	16	,	,	PUNCT
ejpam-4655	273	17	v	v	NOUN
ejpam-4655	273	18	=	=	SYM
ejpam-4655	273	19	1	1	NUM
ejpam-4655	273	20	,	,	PUNCT
ejpam-4655	273	21	2	2	NUM
ejpam-4655	273	22	and	and	CCONJ
ejpam-4655	273	23	s	s	VERB
ejpam-4655	273	24	̸=	̸=	PROPN
ejpam-4655	273	25	v.	v.	ADP
ejpam-4655	273	26	proof	proof	NOUN
ejpam-4655	273	27	.	.	PUNCT
ejpam-4655	274	1	we	we	PRON
ejpam-4655	274	2	give	give	VERB
ejpam-4655	274	3	the	the	DET
ejpam-4655	274	4	detailed	detailed	ADJ
ejpam-4655	274	5	proof	proof	NOUN
ejpam-4655	274	6	for	for	ADP
ejpam-4655	274	7	only	only	ADV
ejpam-4655	274	8	s	s	PART
ejpam-4655	274	9	=	=	SYM
ejpam-4655	274	10	1	1	NUM
ejpam-4655	274	11	,	,	PUNCT
ejpam-4655	274	12	v	v	NOUN
ejpam-4655	274	13	=	=	SYM
ejpam-4655	274	14	2	2	NUM
ejpam-4655	274	15	.	.	PUNCT
ejpam-4655	274	16	(	(	PUNCT
ejpam-4655	274	17	a	a	X
ejpam-4655	274	18	)	)	PUNCT
ejpam-4655	274	19	assume	assume	VERB
ejpam-4655	274	20	that	that	SCONJ
ejpam-4655	274	21	,	,	PUNCT
ejpam-4655	274	22	µ2	µ2	PROPN
ejpam-4655	274	23	is	be	AUX
ejpam-4655	274	24	a	a	DET
ejpam-4655	274	25	sgt	sgt	PROPN
ejpam-4655	274	26	,	,	PUNCT
ejpam-4655	274	27	every	every	DET
ejpam-4655	274	28	µ2	µ2	PROPN
ejpam-4655	274	29	-	-	PUNCT
ejpam-4655	274	30	pre	pre	NOUN
ejpam-4655	274	31	-	-	ADJ
ejpam-4655	274	32	open	open	ADJ
ejpam-4655	274	33	is	be	AUX
ejpam-4655	274	34	µ1	µ1	NOUN
ejpam-4655	274	35	-	-	PUNCT
ejpam-4655	274	36	open	open	ADJ
ejpam-4655	274	37	and	and	CCONJ
ejpam-4655	274	38	let	let	VERB
ejpam-4655	274	39	c2(q	c2(q	PROPN
ejpam-4655	274	40	)	)	PUNCT
ejpam-4655	274	41	=	=	PUNCT
ejpam-4655	275	1	x	x	PUNCT
ejpam-4655	275	2	by	by	ADP
ejpam-4655	275	3	which	which	PRON
ejpam-4655	275	4	i2(c2(q	i2(c2(q	NUM
ejpam-4655	275	5	)	)	PUNCT
ejpam-4655	275	6	)	)	PUNCT
ejpam-4655	276	1	=	=	SYM
ejpam-4655	276	2	x	x	X
ejpam-4655	276	3	,	,	PUNCT
ejpam-4655	276	4	thus	thus	ADV
ejpam-4655	276	5	,	,	PUNCT
ejpam-4655	276	6	q	q	X
ejpam-4655	276	7	⊂	⊂	PROPN
ejpam-4655	276	8	i2(c2(q	i2(c2(q	NUM
ejpam-4655	276	9	)	)	PUNCT
ejpam-4655	276	10	)	)	PUNCT
ejpam-4655	277	1	so	so	CCONJ
ejpam-4655	277	2	for	for	ADP
ejpam-4655	277	3	q	q	PROPN
ejpam-4655	277	4	is	be	AUX
ejpam-4655	277	5	µ2	µ2	ADJ
ejpam-4655	277	6	-	-	PUNCT
ejpam-4655	277	7	pre	pre	NOUN
ejpam-4655	277	8	-	-	ADJ
ejpam-4655	277	9	open	open	ADJ
ejpam-4655	277	10	,	,	PUNCT
ejpam-4655	277	11	whereby	whereby	ADV
ejpam-4655	277	12	by	by	ADP
ejpam-4655	277	13	hypothesis	hypothesis	NOUN
ejpam-4655	277	14	,	,	PUNCT
ejpam-4655	277	15	q	q	PUNCT
ejpam-4655	277	16	is	be	AUX
ejpam-4655	277	17	a	a	DET
ejpam-4655	277	18	µ1	µ1	ADV
ejpam-4655	277	19	-	-	PUNCT
ejpam-4655	277	20	open	open	NOUN
ejpam-4655	277	21	set	set	NOUN
ejpam-4655	277	22	and	and	CCONJ
ejpam-4655	277	23	hence	hence	ADV
ejpam-4655	277	24	x	x	PRON
ejpam-4655	277	25	is	be	AUX
ejpam-4655	277	26	a	a	DET
ejpam-4655	277	27	(	(	PUNCT
ejpam-4655	277	28	1	1	NUM
ejpam-4655	277	29	,	,	PUNCT
ejpam-4655	277	30	2)-bigeneralized	2)-bigeneralized	NUM
ejpam-4655	277	31	submaximal	submaximal	ADJ
ejpam-4655	277	32	space	space	NOUN
ejpam-4655	277	33	.	.	PUNCT
ejpam-4655	278	1	(	(	PUNCT
ejpam-4655	278	2	b	b	X
ejpam-4655	278	3	)	)	PUNCT
ejpam-4655	278	4	consider	consider	VERB
ejpam-4655	278	5	,	,	PUNCT
ejpam-4655	278	6	µ2	µ2	PROPN
ejpam-4655	278	7	is	be	AUX
ejpam-4655	278	8	a	a	DET
ejpam-4655	278	9	sgt	sgt	PROPN
ejpam-4655	278	10	,	,	PUNCT
ejpam-4655	278	11	every	every	DET
ejpam-4655	278	12	µ2	µ2	PROPN
ejpam-4655	278	13	-	-	PUNCT
ejpam-4655	278	14	β	β	NOUN
ejpam-4655	278	15	-	-	ADJ
ejpam-4655	278	16	open	open	ADJ
ejpam-4655	278	17	is	be	AUX
ejpam-4655	278	18	µ1	µ1	NOUN
ejpam-4655	278	19	-	-	PUNCT
ejpam-4655	278	20	open	open	ADJ
ejpam-4655	278	21	,	,	PUNCT
ejpam-4655	278	22	we	we	PRON
ejpam-4655	278	23	take	take	VERB
ejpam-4655	278	24	c2(p	c2(p	PRON
ejpam-4655	278	25	)	)	PUNCT
ejpam-4655	279	1	=	=	PUNCT
ejpam-4655	280	1	x	x	PUNCT
ejpam-4655	280	2	so	so	ADV
ejpam-4655	280	3	for	for	ADP
ejpam-4655	280	4	i2(c2(p	i2(c2(p	NOUN
ejpam-4655	280	5	)	)	PUNCT
ejpam-4655	280	6	)	)	PUNCT
ejpam-4655	281	1	=	=	PUNCT
ejpam-4655	281	2	x	x	X
ejpam-4655	281	3	,	,	PUNCT
ejpam-4655	281	4	by	by	ADP
ejpam-4655	281	5	hypothesis	hypothesis	NOUN
ejpam-4655	281	6	,	,	PUNCT
ejpam-4655	281	7	this	this	PRON
ejpam-4655	281	8	implies	imply	VERB
ejpam-4655	281	9	p	p	X
ejpam-4655	281	10	⊂	⊂	PROPN
ejpam-4655	281	11	c2(i2(c2(p	c2(i2(c2(p	NOUN
ejpam-4655	281	12	)	)	PUNCT
ejpam-4655	281	13	)	)	PUNCT
ejpam-4655	281	14	)	)	PUNCT
ejpam-4655	281	15	which	which	PRON
ejpam-4655	281	16	implies	imply	VERB
ejpam-4655	281	17	p	p	NOUN
ejpam-4655	281	18	is	be	AUX
ejpam-4655	281	19	µ2	µ2	ADJ
ejpam-4655	281	20	-	-	PUNCT
ejpam-4655	281	21	βopen	βopen	ADJ
ejpam-4655	281	22	which	which	PRON
ejpam-4655	281	23	turn	turn	VERB
ejpam-4655	281	24	implies	imply	VERB
ejpam-4655	281	25	that	that	SCONJ
ejpam-4655	281	26	p	p	NOUN
ejpam-4655	281	27	is	be	AUX
ejpam-4655	281	28	a	a	DET
ejpam-4655	281	29	µ1	µ1	ADV
ejpam-4655	281	30	-	-	PUNCT
ejpam-4655	281	31	open	open	NOUN
ejpam-4655	281	32	set	set	VERB
ejpam-4655	281	33	by	by	ADP
ejpam-4655	281	34	which	which	PRON
ejpam-4655	281	35	x	x	PRON
ejpam-4655	281	36	is	be	AUX
ejpam-4655	281	37	a	a	DET
ejpam-4655	281	38	(	(	PUNCT
ejpam-4655	281	39	1	1	NUM
ejpam-4655	281	40	,	,	PUNCT
ejpam-4655	281	41	2)-bigeneralized	2)-bigeneralized	NUM
ejpam-4655	281	42	submaximal	submaximal	ADJ
ejpam-4655	281	43	space	space	NOUN
ejpam-4655	281	44	.	.	PUNCT
ejpam-4655	282	1	(	(	PUNCT
ejpam-4655	282	2	c	c	X
ejpam-4655	282	3	)	)	PUNCT
ejpam-4655	282	4	given	give	VERB
ejpam-4655	282	5	µ2	µ2	PROPN
ejpam-4655	282	6	is	be	AUX
ejpam-4655	282	7	a	a	DET
ejpam-4655	282	8	sgt	sgt	PROPN
ejpam-4655	282	9	,	,	PUNCT
ejpam-4655	282	10	every	every	DET
ejpam-4655	282	11	µ2	µ2	PROPN
ejpam-4655	282	12	-	-	PUNCT
ejpam-4655	282	13	b	b	NOUN
ejpam-4655	282	14	-	-	PUNCT
ejpam-4655	282	15	open	open	ADJ
ejpam-4655	282	16	is	be	AUX
ejpam-4655	282	17	µ1	µ1	NOUN
ejpam-4655	282	18	-	-	PUNCT
ejpam-4655	282	19	open	open	ADJ
ejpam-4655	282	20	and	and	CCONJ
ejpam-4655	282	21	consider	consider	VERB
ejpam-4655	282	22	,	,	PUNCT
ejpam-4655	282	23	c2(j	c2(j	PROPN
ejpam-4655	282	24	)	)	PUNCT
ejpam-4655	282	25	=	=	NOUN
ejpam-4655	282	26	x	x	PROPN
ejpam-4655	282	27	implies	imply	VERB
ejpam-4655	282	28	i2(c2(j	i2(c2(j	NOUN
ejpam-4655	282	29	)	)	PUNCT
ejpam-4655	282	30	)	)	PUNCT
ejpam-4655	283	1	=	=	SYM
ejpam-4655	283	2	x	x	X
ejpam-4655	283	3	,	,	PUNCT
ejpam-4655	283	4	by	by	ADP
ejpam-4655	283	5	our	our	PRON
ejpam-4655	283	6	assumption	assumption	NOUN
ejpam-4655	283	7	so	so	SCONJ
ejpam-4655	283	8	for	for	ADP
ejpam-4655	283	9	j	j	PROPN
ejpam-4655	283	10	⊂	⊂	PROPN
ejpam-4655	283	11	c2(i2(j	c2(i2(j	PROPN
ejpam-4655	283	12	)	)	PUNCT
ejpam-4655	283	13	)	)	PUNCT
ejpam-4655	283	14	∪	∪	ADP
ejpam-4655	283	15	i2(c2(j	i2(c2(j	NOUN
ejpam-4655	283	16	)	)	PUNCT
ejpam-4655	283	17	)	)	PUNCT
ejpam-4655	283	18	,	,	PUNCT
ejpam-4655	283	19	this	this	PRON
ejpam-4655	283	20	implies	imply	VERB
ejpam-4655	283	21	j	j	PROPN
ejpam-4655	283	22	is	be	AUX
ejpam-4655	283	23	µ2	µ2	PROPN
ejpam-4655	283	24	-	-	PUNCT
ejpam-4655	283	25	b	b	NOUN
ejpam-4655	283	26	-	-	PUNCT
ejpam-4655	283	27	open	open	ADJ
ejpam-4655	283	28	which	which	PRON
ejpam-4655	283	29	implies	imply	VERB
ejpam-4655	283	30	that	that	SCONJ
ejpam-4655	283	31	j	j	PROPN
ejpam-4655	283	32	is	be	AUX
ejpam-4655	283	33	a	a	DET
ejpam-4655	283	34	µ1	µ1	ADV
ejpam-4655	283	35	-	-	PUNCT
ejpam-4655	283	36	open	open	NOUN
ejpam-4655	283	37	set	set	NOUN
ejpam-4655	283	38	,	,	PUNCT
ejpam-4655	283	39	by	by	ADP
ejpam-4655	283	40	hypothesis	hypothesis	NOUN
ejpam-4655	283	41	.	.	PUNCT
ejpam-4655	284	1	therefore	therefore	ADV
ejpam-4655	284	2	,	,	PUNCT
ejpam-4655	284	3	x	x	X
ejpam-4655	284	4	is	be	AUX
ejpam-4655	284	5	a	a	DET
ejpam-4655	284	6	(	(	PUNCT
ejpam-4655	284	7	1	1	NUM
ejpam-4655	284	8	,	,	PUNCT
ejpam-4655	284	9	2)bigeneralized	2)bigeneralized	NUM
ejpam-4655	284	10	submaximal	submaximal	ADJ
ejpam-4655	284	11	space	space	NOUN
ejpam-4655	284	12	.	.	PUNCT
ejpam-4655	285	1	y.	y.	NOUN
ejpam-4655	285	2	farhat	farhat	PROPN
ejpam-4655	285	3	et	et	PROPN
ejpam-4655	285	4	al	al	PROPN
ejpam-4655	285	5	.	.	PUNCT
ejpam-4655	285	6	/	/	SYM
ejpam-4655	285	7	eur	eur	PROPN
ejpam-4655	285	8	.	.	PUNCT
ejpam-4655	286	1	j.	j.	PROPN
ejpam-4655	286	2	pure	pure	PROPN
ejpam-4655	286	3	appl	appl	PROPN
ejpam-4655	286	4	.	.	PROPN
ejpam-4655	286	5	math	math	PROPN
ejpam-4655	286	6	,	,	PUNCT
ejpam-4655	286	7	16	16	NUM
ejpam-4655	286	8	(	(	PUNCT
ejpam-4655	286	9	1	1	NUM
ejpam-4655	286	10	)	)	PUNCT
ejpam-4655	286	11	(	(	PUNCT
ejpam-4655	286	12	2023	2023	NUM
ejpam-4655	286	13	)	)	PUNCT
ejpam-4655	286	14	,	,	PUNCT
ejpam-4655	286	15	386	386	NUM
ejpam-4655	286	16	-	-	SYM
ejpam-4655	286	17	403	403	NUM
ejpam-4655	286	18	394	394	NUM
ejpam-4655	286	19	next	next	ADV
ejpam-4655	286	20	,	,	PUNCT
ejpam-4655	286	21	in	in	ADP
ejpam-4655	286	22	the	the	DET
ejpam-4655	286	23	rest	rest	NOUN
ejpam-4655	286	24	of	of	ADP
ejpam-4655	286	25	this	this	DET
ejpam-4655	286	26	section	section	NOUN
ejpam-4655	286	27	with	with	ADP
ejpam-4655	286	28	the	the	DET
ejpam-4655	286	29	series	series	NOUN
ejpam-4655	286	30	of	of	ADP
ejpam-4655	286	31	theorems	theorem	NOUN
ejpam-4655	286	32	in	in	ADP
ejpam-4655	286	33	a	a	DET
ejpam-4655	286	34	bgts	bgts	NOUN
ejpam-4655	286	35	,	,	PUNCT
ejpam-4655	286	36	the	the	DET
ejpam-4655	286	37	significance	significance	NOUN
ejpam-4655	286	38	of	of	ADP
ejpam-4655	286	39	(	(	PUNCT
ejpam-4655	286	40	s	s	PROPN
ejpam-4655	286	41	,	,	PUNCT
ejpam-4655	286	42	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	286	43	submaximality	submaximality	NOUN
ejpam-4655	286	44	is	be	AUX
ejpam-4655	286	45	analyzed	analyze	VERB
ejpam-4655	286	46	via	via	ADP
ejpam-4655	286	47	functions	function	NOUN
ejpam-4655	286	48	.	.	PUNCT
ejpam-4655	287	1	theorem	theorem	NOUN
ejpam-4655	287	2	21	21	NUM
ejpam-4655	287	3	.	.	PUNCT
ejpam-4655	288	1	let	let	AUX
ejpam-4655	288	2	(	(	PUNCT
ejpam-4655	288	3	x,µ1	x,µ1	NOUN
ejpam-4655	288	4	,	,	PUNCT
ejpam-4655	288	5	µ2	µ2	PROPN
ejpam-4655	288	6	)	)	PUNCT
ejpam-4655	288	7	and	and	CCONJ
ejpam-4655	288	8	(	(	PUNCT
ejpam-4655	288	9	y	y	PROPN
ejpam-4655	288	10	,	,	PUNCT
ejpam-4655	288	11	η1	η1	NOUN
ejpam-4655	288	12	,	,	PUNCT
ejpam-4655	288	13	η2	η2	PROPN
ejpam-4655	288	14	)	)	PUNCT
ejpam-4655	288	15	be	be	VERB
ejpam-4655	288	16	two	two	NUM
ejpam-4655	288	17	bgts	bgts	NOUN
ejpam-4655	288	18	and	and	CCONJ
ejpam-4655	288	19	h	h	NOUN
ejpam-4655	288	20	:	:	PUNCT
ejpam-4655	288	21	(	(	PUNCT
ejpam-4655	288	22	x,µi	x,µi	NUM
ejpam-4655	288	23	)	)	PUNCT
ejpam-4655	288	24	→	→	PUNCT
ejpam-4655	288	25	(	(	PUNCT
ejpam-4655	288	26	y	y	PROPN
ejpam-4655	288	27	,	,	PUNCT
ejpam-4655	288	28	ηi	ηi	PROPN
ejpam-4655	288	29	)	)	PUNCT
ejpam-4655	288	30	be	be	VERB
ejpam-4655	288	31	a	a	DET
ejpam-4655	288	32	(	(	PUNCT
ejpam-4655	288	33	µi	µi	PROPN
ejpam-4655	288	34	,	,	PUNCT
ejpam-4655	288	35	ηi)-open	ηi)-open	ADJ
ejpam-4655	288	36	map	map	NOUN
ejpam-4655	288	37	for	for	ADP
ejpam-4655	288	38	i	i	PRON
ejpam-4655	288	39	=	=	NOUN
ejpam-4655	288	40	1	1	NUM
ejpam-4655	288	41	,	,	PUNCT
ejpam-4655	288	42	2	2	NUM
ejpam-4655	288	43	.	.	PUNCT
ejpam-4655	289	1	if	if	SCONJ
ejpam-4655	289	2	h	h	NOUN
ejpam-4655	289	3	is	be	AUX
ejpam-4655	289	4	surjective	surjective	ADJ
ejpam-4655	289	5	,	,	PUNCT
ejpam-4655	289	6	then	then	ADV
ejpam-4655	289	7	image	image	NOUN
ejpam-4655	289	8	of	of	ADP
ejpam-4655	289	9	a	a	DET
ejpam-4655	289	10	(	(	PUNCT
ejpam-4655	289	11	s	s	PROPN
ejpam-4655	289	12	,	,	PUNCT
ejpam-4655	289	13	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	289	14	submaximal	submaximal	ADJ
ejpam-4655	289	15	space	space	NOUN
ejpam-4655	289	16	is	be	AUX
ejpam-4655	289	17	(	(	PUNCT
ejpam-4655	289	18	s	s	PROPN
ejpam-4655	289	19	,	,	PUNCT
ejpam-4655	289	20	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	289	21	submaximal	submaximal	ADJ
ejpam-4655	289	22	space	space	NOUN
ejpam-4655	289	23	where	where	SCONJ
ejpam-4655	289	24	s	s	X
ejpam-4655	289	25	,	,	PUNCT
ejpam-4655	289	26	v	v	NOUN
ejpam-4655	289	27	=	=	SYM
ejpam-4655	289	28	1	1	NUM
ejpam-4655	289	29	,	,	PUNCT
ejpam-4655	289	30	2	2	NUM
ejpam-4655	289	31	;	;	PUNCT
ejpam-4655	289	32	s	s	VERB
ejpam-4655	289	33	̸=	̸=	PROPN
ejpam-4655	289	34	v.	v.	ADP
ejpam-4655	289	35	proof	proof	NOUN
ejpam-4655	289	36	.	.	PUNCT
ejpam-4655	290	1	it	it	PRON
ejpam-4655	290	2	is	be	AUX
ejpam-4655	290	3	enough	enough	ADJ
ejpam-4655	290	4	to	to	PART
ejpam-4655	290	5	prove	prove	VERB
ejpam-4655	290	6	the	the	DET
ejpam-4655	290	7	case	case	NOUN
ejpam-4655	290	8	only	only	ADV
ejpam-4655	290	9	for	for	ADP
ejpam-4655	290	10	s	s	NOUN
ejpam-4655	290	11	=	=	SYM
ejpam-4655	290	12	1	1	NUM
ejpam-4655	290	13	,	,	PUNCT
ejpam-4655	290	14	v	v	NOUN
ejpam-4655	290	15	=	=	SYM
ejpam-4655	290	16	2	2	X
ejpam-4655	290	17	.	.	X
ejpam-4655	290	18	assume	assume	VERB
ejpam-4655	290	19	that	that	SCONJ
ejpam-4655	290	20	,	,	PUNCT
ejpam-4655	290	21	x	x	PRON
ejpam-4655	290	22	is	be	AUX
ejpam-4655	290	23	a	a	DET
ejpam-4655	290	24	(	(	PUNCT
ejpam-4655	290	25	1	1	NUM
ejpam-4655	290	26	,	,	PUNCT
ejpam-4655	290	27	2)-bigeneralized	2)-bigeneralized	NUM
ejpam-4655	290	28	submaximal	submaximal	ADJ
ejpam-4655	290	29	space	space	NOUN
ejpam-4655	290	30	.	.	PUNCT
ejpam-4655	291	1	given	give	VERB
ejpam-4655	291	2	h	h	NOUN
ejpam-4655	291	3	:	:	PUNCT
ejpam-4655	291	4	(	(	PUNCT
ejpam-4655	291	5	x,µi	x,µi	NUM
ejpam-4655	291	6	)	)	PUNCT
ejpam-4655	291	7	→	→	PUNCT
ejpam-4655	291	8	(	(	PUNCT
ejpam-4655	291	9	y	y	PROPN
ejpam-4655	291	10	,	,	PUNCT
ejpam-4655	291	11	ηi	ηi	PROPN
ejpam-4655	291	12	)	)	PUNCT
ejpam-4655	291	13	be	be	VERB
ejpam-4655	291	14	a	a	DET
ejpam-4655	291	15	(	(	PUNCT
ejpam-4655	291	16	µi	µi	PROPN
ejpam-4655	291	17	,	,	PUNCT
ejpam-4655	291	18	ηi)-open	ηi)-open	ADJ
ejpam-4655	291	19	map	map	NOUN
ejpam-4655	291	20	for	for	ADP
ejpam-4655	291	21	i	i	PRON
ejpam-4655	291	22	=	=	NOUN
ejpam-4655	291	23	1	1	NUM
ejpam-4655	291	24	,	,	PUNCT
ejpam-4655	291	25	2	2	NUM
ejpam-4655	291	26	.	.	PUNCT
ejpam-4655	292	1	then	then	ADV
ejpam-4655	292	2	h	h	PROPN
ejpam-4655	292	3	is	be	AUX
ejpam-4655	292	4	a	a	DET
ejpam-4655	292	5	(	(	PUNCT
ejpam-4655	292	6	µ1	µ1	PROPN
ejpam-4655	292	7	,	,	PUNCT
ejpam-4655	292	8	η1)−	η1)−	ADJ
ejpam-4655	292	9	open	open	ADJ
ejpam-4655	292	10	map	map	NOUN
ejpam-4655	292	11	(	(	PUNCT
ejpam-4655	292	12	4	4	NUM
ejpam-4655	292	13	)	)	PUNCT
ejpam-4655	292	14	h	h	NOUN
ejpam-4655	292	15	is	be	AUX
ejpam-4655	292	16	a	a	DET
ejpam-4655	292	17	(	(	PUNCT
ejpam-4655	292	18	µ2	µ2	PROPN
ejpam-4655	292	19	,	,	PUNCT
ejpam-4655	292	20	η2)−	η2)−	ADJ
ejpam-4655	292	21	open	open	ADJ
ejpam-4655	292	22	map	map	NOUN
ejpam-4655	292	23	(	(	PUNCT
ejpam-4655	292	24	5	5	X
ejpam-4655	292	25	)	)	PUNCT
ejpam-4655	292	26	let	let	VERB
ejpam-4655	292	27	q	q	NOUN
ejpam-4655	292	28	be	be	AUX
ejpam-4655	292	29	a	a	DET
ejpam-4655	292	30	η2	η2	ADJ
ejpam-4655	292	31	-	-	PUNCT
ejpam-4655	292	32	dense	dense	ADJ
ejpam-4655	292	33	subset	subset	NOUN
ejpam-4655	292	34	of	of	ADP
ejpam-4655	292	35	y.	y.	PROPN
ejpam-4655	292	36	from	from	ADP
ejpam-4655	292	37	(	(	PUNCT
ejpam-4655	292	38	5	5	NUM
ejpam-4655	292	39	)	)	PUNCT
ejpam-4655	292	40	and	and	CCONJ
ejpam-4655	292	41	lemma	lemma	PROPN
ejpam-4655	292	42	3	3	NUM
ejpam-4655	292	43	,	,	PUNCT
ejpam-4655	292	44	cµ2(h	cµ2(h	PROPN
ejpam-4655	292	45	−1(q	−1(q	ADV
ejpam-4655	292	46	)	)	PUNCT
ejpam-4655	292	47	)	)	PUNCT
ejpam-4655	293	1	=	=	PUNCT
ejpam-4655	293	2	x.	x.	NOUN
ejpam-4655	293	3	by	by	ADP
ejpam-4655	293	4	our	our	PRON
ejpam-4655	293	5	assumption	assumption	NOUN
ejpam-4655	293	6	,	,	PUNCT
ejpam-4655	293	7	h−1(q	h−1(q	PROPN
ejpam-4655	293	8	)	)	PUNCT
ejpam-4655	293	9	∈	∈	PROPN
ejpam-4655	293	10	µ1	µ1	PROPN
ejpam-4655	293	11	.	.	PUNCT
ejpam-4655	294	1	by	by	ADP
ejpam-4655	294	2	(	(	PUNCT
ejpam-4655	294	3	4	4	NUM
ejpam-4655	294	4	)	)	PUNCT
ejpam-4655	294	5	,	,	PUNCT
ejpam-4655	294	6	h(h−1(q	h(h−1(q	NOUN
ejpam-4655	294	7	)	)	PUNCT
ejpam-4655	294	8	)	)	PUNCT
ejpam-4655	294	9	∈	∈	PROPN
ejpam-4655	294	10	η1	η1	NOUN
ejpam-4655	294	11	.	.	PUNCT
ejpam-4655	295	1	thus	thus	ADV
ejpam-4655	295	2	,	,	PUNCT
ejpam-4655	295	3	q	q	PROPN
ejpam-4655	295	4	∈	∈	PROPN
ejpam-4655	295	5	η1	η1	NOUN
ejpam-4655	295	6	,	,	PUNCT
ejpam-4655	295	7	by	by	ADP
ejpam-4655	295	8	hypothesis	hypothesis	NOUN
ejpam-4655	295	9	.	.	PUNCT
ejpam-4655	296	1	hence	hence	ADV
ejpam-4655	296	2	y	y	PROPN
ejpam-4655	296	3	is	be	AUX
ejpam-4655	296	4	a	a	DET
ejpam-4655	296	5	(	(	PUNCT
ejpam-4655	296	6	1	1	NUM
ejpam-4655	296	7	,	,	PUNCT
ejpam-4655	296	8	2)-bigeneralized	2)-bigeneralized	NUM
ejpam-4655	296	9	submaximal	submaximal	ADJ
ejpam-4655	296	10	space	space	NOUN
ejpam-4655	296	11	example	example	NOUN
ejpam-4655	296	12	22	22	NUM
ejpam-4655	296	13	shows	show	VERB
ejpam-4655	296	14	that	that	SCONJ
ejpam-4655	296	15	the	the	DET
ejpam-4655	296	16	hypothesis	hypothesis	NOUN
ejpam-4655	296	17	can	can	AUX
ejpam-4655	296	18	not	not	PART
ejpam-4655	296	19	be	be	AUX
ejpam-4655	296	20	dropped	drop	VERB
ejpam-4655	296	21	in	in	ADP
ejpam-4655	296	22	theorem	theorem	ADJ
ejpam-4655	296	23	21	21	NUM
ejpam-4655	296	24	.	.	PUNCT
ejpam-4655	296	25	example	example	NOUN
ejpam-4655	297	1	22	22	NUM
ejpam-4655	297	2	.	.	PUNCT
ejpam-4655	298	1	consider	consider	VERB
ejpam-4655	298	2	the	the	DET
ejpam-4655	298	3	bigeneralized	bigeneralize	VERB
ejpam-4655	298	4	topological	topological	ADJ
ejpam-4655	298	5	spaces	space	NOUN
ejpam-4655	298	6	(	(	PUNCT
ejpam-4655	298	7	x,µ1	x,µ1	NOUN
ejpam-4655	298	8	,	,	PUNCT
ejpam-4655	298	9	µ2	µ2	PROPN
ejpam-4655	298	10	)	)	PUNCT
ejpam-4655	298	11	and	and	CCONJ
ejpam-4655	298	12	(	(	PUNCT
ejpam-4655	298	13	y	y	PROPN
ejpam-4655	298	14	,	,	PUNCT
ejpam-4655	298	15	η1	η1	NOUN
ejpam-4655	298	16	,	,	PUNCT
ejpam-4655	298	17	η2	η2	NOUN
ejpam-4655	298	18	)	)	PUNCT
ejpam-4655	299	1	where	where	SCONJ
ejpam-4655	299	2	x	x	X
ejpam-4655	299	3	=	=	PRON
ejpam-4655	299	4	{	{	PUNCT
ejpam-4655	299	5	p	p	X
ejpam-4655	299	6	,	,	PUNCT
ejpam-4655	299	7	q	q	ADJ
ejpam-4655	299	8	,	,	PUNCT
ejpam-4655	299	9	r	r	NOUN
ejpam-4655	299	10	,	,	PUNCT
ejpam-4655	299	11	s};y	s};y	ADJ
ejpam-4655	299	12	=	=	SYM
ejpam-4655	299	13	{	{	PUNCT
ejpam-4655	299	14	p1	p1	PROPN
ejpam-4655	299	15	,	,	PUNCT
ejpam-4655	299	16	q1	q1	PROPN
ejpam-4655	299	17	,	,	PUNCT
ejpam-4655	299	18	c1	c1	NOUN
ejpam-4655	299	19	,	,	PUNCT
ejpam-4655	299	20	s1	s1	PROPN
ejpam-4655	299	21	}	}	PUNCT
ejpam-4655	299	22	.	.	PUNCT
ejpam-4655	300	1	define	define	VERB
ejpam-4655	300	2	a	a	DET
ejpam-4655	300	3	map	map	NOUN
ejpam-4655	300	4	h	h	NOUN
ejpam-4655	300	5	:	:	PUNCT
ejpam-4655	300	6	(	(	PUNCT
ejpam-4655	300	7	x,µi	x,µi	NUM
ejpam-4655	300	8	)	)	PUNCT
ejpam-4655	300	9	→	→	PUNCT
ejpam-4655	300	10	(	(	PUNCT
ejpam-4655	300	11	y	y	PROPN
ejpam-4655	300	12	,	,	PUNCT
ejpam-4655	300	13	ηi	ηi	PROPN
ejpam-4655	300	14	)	)	PUNCT
ejpam-4655	300	15	for	for	ADP
ejpam-4655	300	16	i	i	PROPN
ejpam-4655	300	17	=	=	SYM
ejpam-4655	300	18	1	1	NUM
ejpam-4655	300	19	,	,	PUNCT
ejpam-4655	300	20	2	2	NUM
ejpam-4655	300	21	as	as	SCONJ
ejpam-4655	300	22	follows	follow	VERB
ejpam-4655	300	23	h(p	h(p	NOUN
ejpam-4655	300	24	)	)	PUNCT
ejpam-4655	300	25	=	=	SYM
ejpam-4655	300	26	q1;h(q	q1;h(q	NOUN
ejpam-4655	300	27	)	)	PUNCT
ejpam-4655	300	28	=	=	SYM
ejpam-4655	300	29	p1;h(r	p1;h(r	NOUN
ejpam-4655	300	30	)	)	PUNCT
ejpam-4655	300	31	=	=	SYM
ejpam-4655	300	32	s1;h(s	s1;h(s	NOUN
ejpam-4655	300	33	)	)	PUNCT
ejpam-4655	301	1	=	=	SYM
ejpam-4655	301	2	r1	r1	PROPN
ejpam-4655	301	3	.	.	PUNCT
ejpam-4655	302	1	clearly	clearly	ADV
ejpam-4655	302	2	,	,	PUNCT
ejpam-4655	302	3	h	h	NOUN
ejpam-4655	302	4	is	be	AUX
ejpam-4655	302	5	a	a	DET
ejpam-4655	302	6	surjective	surjective	ADJ
ejpam-4655	302	7	map	map	NOUN
ejpam-4655	302	8	.	.	PUNCT
ejpam-4655	303	1	(	(	PUNCT
ejpam-4655	303	2	a	a	X
ejpam-4655	303	3	)	)	PUNCT
ejpam-4655	303	4	let	let	AUX
ejpam-4655	303	5	µ1	µ1	NOUN
ejpam-4655	303	6	=	=	SYM
ejpam-4655	303	7	{	{	PUNCT
ejpam-4655	303	8	∅	∅	NOUN
ejpam-4655	303	9	,	,	PUNCT
ejpam-4655	303	10	{	{	PUNCT
ejpam-4655	303	11	p	p	X
ejpam-4655	303	12	,	,	PUNCT
ejpam-4655	303	13	q	q	NOUN
ejpam-4655	303	14	}	}	PUNCT
ejpam-4655	303	15	,	,	PUNCT
ejpam-4655	303	16	{	{	PUNCT
ejpam-4655	303	17	p	p	X
ejpam-4655	303	18	,	,	PUNCT
ejpam-4655	303	19	s	s	PART
ejpam-4655	303	20	}	}	PUNCT
ejpam-4655	303	21	,	,	PUNCT
ejpam-4655	303	22	{	{	PUNCT
ejpam-4655	303	23	q	q	X
ejpam-4655	303	24	,	,	PUNCT
ejpam-4655	303	25	r	r	NOUN
ejpam-4655	303	26	}	}	PUNCT
ejpam-4655	303	27	,	,	PUNCT
ejpam-4655	303	28	{	{	PUNCT
ejpam-4655	303	29	p	p	X
ejpam-4655	303	30	,	,	PUNCT
ejpam-4655	303	31	q	q	ADJ
ejpam-4655	303	32	,	,	PUNCT
ejpam-4655	303	33	r	r	NOUN
ejpam-4655	303	34	}	}	PUNCT
ejpam-4655	303	35	,	,	PUNCT
ejpam-4655	303	36	{	{	PUNCT
ejpam-4655	303	37	p	p	X
ejpam-4655	303	38	,	,	PUNCT
ejpam-4655	303	39	q	q	X
ejpam-4655	303	40	,	,	PUNCT
ejpam-4655	303	41	s	s	PART
ejpam-4655	303	42	}	}	PUNCT
ejpam-4655	303	43	,	,	PUNCT
ejpam-4655	303	44	{	{	PUNCT
ejpam-4655	303	45	p	p	X
ejpam-4655	303	46	,	,	PUNCT
ejpam-4655	303	47	r	r	NOUN
ejpam-4655	303	48	,	,	PUNCT
ejpam-4655	303	49	s	s	PART
ejpam-4655	303	50	}	}	PUNCT
ejpam-4655	303	51	,	,	PUNCT
ejpam-4655	303	52	x};µ2	x};µ2	PROPN
ejpam-4655	304	1	=	=	PRON
ejpam-4655	304	2	{	{	PUNCT
ejpam-4655	304	3	∅	∅	NOUN
ejpam-4655	304	4	,	,	PUNCT
ejpam-4655	304	5	{	{	PUNCT
ejpam-4655	304	6	p	p	X
ejpam-4655	304	7	}	}	PUNCT
ejpam-4655	304	8	,	,	PUNCT
ejpam-4655	304	9	{	{	PUNCT
ejpam-4655	304	10	s	s	X
ejpam-4655	304	11	}	}	PUNCT
ejpam-4655	304	12	,	,	PUNCT
ejpam-4655	304	13	{	{	PUNCT
ejpam-4655	304	14	p	p	X
ejpam-4655	304	15	,	,	PUNCT
ejpam-4655	304	16	s	s	PART
ejpam-4655	304	17	}	}	PUNCT
ejpam-4655	304	18	,	,	PUNCT
ejpam-4655	304	19	{	{	PUNCT
ejpam-4655	304	20	p	p	X
ejpam-4655	304	21	,	,	PUNCT
ejpam-4655	304	22	q	q	ADJ
ejpam-4655	304	23	,	,	PUNCT
ejpam-4655	304	24	r	r	NOUN
ejpam-4655	304	25	}	}	PUNCT
ejpam-4655	304	26	,	,	PUNCT
ejpam-4655	304	27	{	{	PUNCT
ejpam-4655	304	28	q	q	X
ejpam-4655	304	29	,	,	PUNCT
ejpam-4655	304	30	r	r	NOUN
ejpam-4655	304	31	,	,	PUNCT
ejpam-4655	304	32	s	s	PART
ejpam-4655	304	33	}	}	PUNCT
ejpam-4655	304	34	,	,	PUNCT
ejpam-4655	304	35	x	x	X
ejpam-4655	304	36	}	}	PUNCT
ejpam-4655	304	37	;	;	PUNCT
ejpam-4655	304	38	η1	η1	NOUN
ejpam-4655	304	39	=	=	SYM
ejpam-4655	304	40	{	{	PUNCT
ejpam-4655	304	41	∅	∅	NOUN
ejpam-4655	304	42	,	,	PUNCT
ejpam-4655	304	43	{	{	PUNCT
ejpam-4655	304	44	q1	q1	NOUN
ejpam-4655	304	45	}	}	PUNCT
ejpam-4655	304	46	,	,	PUNCT
ejpam-4655	304	47	{	{	PUNCT
ejpam-4655	304	48	p1	p1	NOUN
ejpam-4655	304	49	,	,	PUNCT
ejpam-4655	304	50	q1	q1	PROPN
ejpam-4655	304	51	}	}	PUNCT
ejpam-4655	304	52	,	,	PUNCT
ejpam-4655	304	53	{	{	PUNCT
ejpam-4655	304	54	p1	p1	NOUN
ejpam-4655	304	55	,	,	PUNCT
ejpam-4655	304	56	s1	s1	PROPN
ejpam-4655	304	57	}	}	PUNCT
ejpam-4655	304	58	,	,	PUNCT
ejpam-4655	304	59	{	{	PUNCT
ejpam-4655	304	60	q1	q1	NOUN
ejpam-4655	304	61	,	,	PUNCT
ejpam-4655	304	62	r1	r1	PROPN
ejpam-4655	304	63	}	}	PUNCT
ejpam-4655	304	64	,	,	PUNCT
ejpam-4655	304	65	{	{	PUNCT
ejpam-4655	304	66	p1	p1	PROPN
ejpam-4655	304	67	,	,	PUNCT
ejpam-4655	304	68	q1	q1	PROPN
ejpam-4655	304	69	,	,	PUNCT
ejpam-4655	304	70	r1	r1	PROPN
ejpam-4655	304	71	}	}	PUNCT
ejpam-4655	304	72	,	,	PUNCT
ejpam-4655	304	73	{	{	PUNCT
ejpam-4655	304	74	p1	p1	PROPN
ejpam-4655	304	75	,	,	PUNCT
ejpam-4655	304	76	q1	q1	PROPN
ejpam-4655	304	77	,	,	PUNCT
ejpam-4655	304	78	s1	s1	PROPN
ejpam-4655	304	79	}	}	PUNCT
ejpam-4655	304	80	,	,	PUNCT
ejpam-4655	304	81	{	{	PUNCT
ejpam-4655	304	82	q1	q1	PROPN
ejpam-4655	304	83	,	,	PUNCT
ejpam-4655	304	84	r1	r1	NOUN
ejpam-4655	304	85	,	,	PUNCT
ejpam-4655	304	86	s1	s1	PROPN
ejpam-4655	304	87	}	}	PUNCT
ejpam-4655	304	88	,	,	PUNCT
ejpam-4655	304	89	y	y	PROPN
ejpam-4655	304	90	}	}	PUNCT
ejpam-4655	304	91	and	and	CCONJ
ejpam-4655	304	92	η2	η2	ADJ
ejpam-4655	304	93	=	=	SYM
ejpam-4655	304	94	{	{	PUNCT
ejpam-4655	304	95	∅	∅	NOUN
ejpam-4655	304	96	,	,	PUNCT
ejpam-4655	304	97	{	{	PUNCT
ejpam-4655	304	98	p1	p1	NOUN
ejpam-4655	304	99	,	,	PUNCT
ejpam-4655	304	100	s1	s1	PROPN
ejpam-4655	304	101	}	}	PUNCT
ejpam-4655	304	102	,	,	PUNCT
ejpam-4655	304	103	{	{	PUNCT
ejpam-4655	304	104	q1	q1	NOUN
ejpam-4655	304	105	,	,	PUNCT
ejpam-4655	304	106	s1	s1	PROPN
ejpam-4655	304	107	}	}	PUNCT
ejpam-4655	304	108	,	,	PUNCT
ejpam-4655	304	109	{	{	PUNCT
ejpam-4655	304	110	p1	p1	PROPN
ejpam-4655	304	111	,	,	PUNCT
ejpam-4655	304	112	q1	q1	PROPN
ejpam-4655	304	113	,	,	PUNCT
ejpam-4655	304	114	s1	s1	NOUN
ejpam-4655	304	115	}	}	PUNCT
ejpam-4655	304	116	}	}	PUNCT
ejpam-4655	304	117	.	.	PUNCT
ejpam-4655	305	1	here	here	ADV
ejpam-4655	305	2	h(p	h(p	PROPN
ejpam-4655	305	3	)	)	PUNCT
ejpam-4655	305	4	∈	∈	PROPN
ejpam-4655	305	5	η1	η1	NOUN
ejpam-4655	305	6	whenever	whenever	SCONJ
ejpam-4655	305	7	p	p	PROPN
ejpam-4655	305	8	∈	∈	PROPN
ejpam-4655	305	9	µ1	µ1	PROPN
ejpam-4655	305	10	.	.	PUNCT
ejpam-4655	306	1	therefore	therefore	ADV
ejpam-4655	306	2	,	,	PUNCT
ejpam-4655	306	3	h	h	NOUN
ejpam-4655	306	4	is	be	AUX
ejpam-4655	306	5	a	a	DET
ejpam-4655	306	6	(	(	PUNCT
ejpam-4655	306	7	µ1	µ1	PROPN
ejpam-4655	306	8	,	,	PUNCT
ejpam-4655	306	9	η1)-open	η1)-open	ADJ
ejpam-4655	306	10	map	map	NOUN
ejpam-4655	306	11	.	.	PUNCT
ejpam-4655	307	1	let	let	VERB
ejpam-4655	307	2	j	j	PROPN
ejpam-4655	307	3	=	=	PUNCT
ejpam-4655	307	4	{	{	PUNCT
ejpam-4655	307	5	p	p	X
ejpam-4655	307	6	}	}	PUNCT
ejpam-4655	307	7	.	.	PUNCT
ejpam-4655	308	1	then	then	ADV
ejpam-4655	308	2	j	j	PROPN
ejpam-4655	308	3	∈	∈	PROPN
ejpam-4655	308	4	µ2	µ2	PROPN
ejpam-4655	308	5	.	.	PUNCT
ejpam-4655	309	1	but	but	CCONJ
ejpam-4655	309	2	h(j	h(j	PROPN
ejpam-4655	309	3	)	)	PUNCT
ejpam-4655	309	4	/∈	/∈	PUNCT
ejpam-4655	310	1	η2	η2	PROPN
ejpam-4655	310	2	.	.	PUNCT
ejpam-4655	311	1	thus	thus	ADV
ejpam-4655	311	2	,	,	PUNCT
ejpam-4655	311	3	h	h	NOUN
ejpam-4655	311	4	is	be	AUX
ejpam-4655	311	5	not	not	PART
ejpam-4655	311	6	a	a	DET
ejpam-4655	311	7	(	(	PUNCT
ejpam-4655	311	8	µ2	µ2	ADJ
ejpam-4655	311	9	,	,	PUNCT
ejpam-4655	311	10	η2)-open	η2)-open	VERB
ejpam-4655	311	11	map	map	NOUN
ejpam-4655	311	12	.	.	PUNCT
ejpam-4655	312	1	here	here	ADV
ejpam-4655	312	2	{	{	PUNCT
ejpam-4655	312	3	p	p	X
ejpam-4655	312	4	,	,	PUNCT
ejpam-4655	312	5	s	s	PART
ejpam-4655	312	6	}	}	PUNCT
ejpam-4655	312	7	,	,	PUNCT
ejpam-4655	312	8	{	{	PUNCT
ejpam-4655	312	9	p	p	X
ejpam-4655	312	10	,	,	PUNCT
ejpam-4655	312	11	q	q	X
ejpam-4655	312	12	,	,	PUNCT
ejpam-4655	312	13	s	s	PART
ejpam-4655	312	14	}	}	PUNCT
ejpam-4655	312	15	,	,	PUNCT
ejpam-4655	312	16	{	{	PUNCT
ejpam-4655	312	17	p	p	X
ejpam-4655	312	18	,	,	PUNCT
ejpam-4655	312	19	r	r	NOUN
ejpam-4655	312	20	,	,	PUNCT
ejpam-4655	312	21	s	s	PART
ejpam-4655	312	22	}	}	PUNCT
ejpam-4655	312	23	and	and	CCONJ
ejpam-4655	312	24	x	x	X
ejpam-4655	312	25	are	be	AUX
ejpam-4655	312	26	µ2	µ2	ADJ
ejpam-4655	312	27	-	-	PUNCT
ejpam-4655	312	28	dense	dense	ADJ
ejpam-4655	312	29	subsets	subset	NOUN
ejpam-4655	312	30	of	of	ADP
ejpam-4655	312	31	x.	x.	NOUN
ejpam-4655	312	32	also	also	ADV
ejpam-4655	312	33	,	,	PUNCT
ejpam-4655	312	34	every	every	DET
ejpam-4655	312	35	µ2	µ2	ADJ
ejpam-4655	312	36	-	-	PUNCT
ejpam-4655	312	37	dense	dense	ADJ
ejpam-4655	312	38	set	set	NOUN
ejpam-4655	312	39	is	be	AUX
ejpam-4655	312	40	µ1	µ1	NOUN
ejpam-4655	312	41	-	-	PUNCT
ejpam-4655	312	42	open	open	ADJ
ejpam-4655	312	43	.	.	PUNCT
ejpam-4655	313	1	therefore	therefore	ADV
ejpam-4655	313	2	,	,	PUNCT
ejpam-4655	313	3	x	x	X
ejpam-4655	313	4	is	be	AUX
ejpam-4655	313	5	a	a	DET
ejpam-4655	313	6	(	(	PUNCT
ejpam-4655	313	7	1	1	NUM
ejpam-4655	313	8	,	,	PUNCT
ejpam-4655	313	9	2)-bigeneralized	2)-bigeneralized	NUM
ejpam-4655	313	10	submaximal	submaximal	ADJ
ejpam-4655	313	11	space	space	NOUN
ejpam-4655	313	12	.	.	PUNCT
ejpam-4655	314	1	let	let	VERB
ejpam-4655	314	2	k	k	NOUN
ejpam-4655	314	3	=	=	PRON
ejpam-4655	314	4	{	{	PUNCT
ejpam-4655	314	5	s1	s1	NOUN
ejpam-4655	314	6	}	}	PUNCT
ejpam-4655	314	7	.	.	PUNCT
ejpam-4655	315	1	then	then	ADV
ejpam-4655	315	2	cη2(k	cη2(k	PROPN
ejpam-4655	315	3	)	)	PUNCT
ejpam-4655	316	1	=	=	PUNCT
ejpam-4655	317	1	y.	y.	NOUN
ejpam-4655	317	2	but	but	CCONJ
ejpam-4655	317	3	k	k	PROPN
ejpam-4655	317	4	/∈	/∈	PUNCT
ejpam-4655	317	5	η1	η1	NOUN
ejpam-4655	317	6	.	.	PUNCT
ejpam-4655	318	1	thus	thus	ADV
ejpam-4655	318	2	,	,	PUNCT
ejpam-4655	318	3	y	y	PROPN
ejpam-4655	318	4	is	be	AUX
ejpam-4655	318	5	not	not	PART
ejpam-4655	318	6	a	a	DET
ejpam-4655	318	7	(	(	PUNCT
ejpam-4655	318	8	1	1	NUM
ejpam-4655	318	9	,	,	PUNCT
ejpam-4655	318	10	2)-bigeneralized	2)-bigeneralized	NUM
ejpam-4655	318	11	submaximal	submaximal	ADJ
ejpam-4655	318	12	space	space	NOUN
ejpam-4655	318	13	.	.	PUNCT
ejpam-4655	319	1	(	(	PUNCT
ejpam-4655	319	2	b	b	X
ejpam-4655	319	3	)	)	PUNCT
ejpam-4655	319	4	let	let	VERB
ejpam-4655	319	5	µ1	µ1	NOUN
ejpam-4655	319	6	,	,	PUNCT
ejpam-4655	319	7	η1	η1	NOUN
ejpam-4655	319	8	and	and	CCONJ
ejpam-4655	319	9	η2	η2	PROPN
ejpam-4655	319	10	are	be	AUX
ejpam-4655	319	11	generalized	generalized	ADJ
ejpam-4655	319	12	topologies	topology	NOUN
ejpam-4655	319	13	defined	define	VERB
ejpam-4655	319	14	as	as	ADP
ejpam-4655	319	15	in	in	ADP
ejpam-4655	319	16	(	(	PUNCT
ejpam-4655	319	17	a	a	NOUN
ejpam-4655	319	18	)	)	PUNCT
ejpam-4655	319	19	.	.	PUNCT
ejpam-4655	320	1	take	take	VERB
ejpam-4655	320	2	µ2	µ2	PROPN
ejpam-4655	320	3	=	=	PUNCT
ejpam-4655	320	4	{	{	PUNCT
ejpam-4655	320	5	∅	∅	NOUN
ejpam-4655	320	6	,	,	PUNCT
ejpam-4655	320	7	{	{	PUNCT
ejpam-4655	320	8	p	p	X
ejpam-4655	320	9	}	}	PUNCT
ejpam-4655	320	10	,	,	PUNCT
ejpam-4655	320	11	{	{	PUNCT
ejpam-4655	320	12	s	s	X
ejpam-4655	320	13	}	}	PUNCT
ejpam-4655	320	14	,	,	PUNCT
ejpam-4655	320	15	{	{	PUNCT
ejpam-4655	320	16	p	p	X
ejpam-4655	320	17	,	,	PUNCT
ejpam-4655	320	18	s	s	PART
ejpam-4655	320	19	}	}	PUNCT
ejpam-4655	320	20	,	,	PUNCT
ejpam-4655	320	21	{	{	PUNCT
ejpam-4655	320	22	p	p	X
ejpam-4655	320	23	,	,	PUNCT
ejpam-4655	320	24	q	q	NOUN
ejpam-4655	320	25	}	}	PUNCT
ejpam-4655	320	26	,	,	PUNCT
ejpam-4655	320	27	{	{	PUNCT
ejpam-4655	320	28	p	p	X
ejpam-4655	320	29	,	,	PUNCT
ejpam-4655	320	30	r	r	NOUN
ejpam-4655	320	31	}	}	PUNCT
ejpam-4655	320	32	,	,	PUNCT
ejpam-4655	320	33	{	{	PUNCT
ejpam-4655	320	34	q	q	X
ejpam-4655	320	35	,	,	PUNCT
ejpam-4655	320	36	s	s	PART
ejpam-4655	320	37	}	}	PUNCT
ejpam-4655	320	38	,	,	PUNCT
ejpam-4655	320	39	{	{	PUNCT
ejpam-4655	320	40	p	p	X
ejpam-4655	320	41	,	,	PUNCT
ejpam-4655	320	42	q	q	ADJ
ejpam-4655	320	43	,	,	PUNCT
ejpam-4655	320	44	r	r	NOUN
ejpam-4655	320	45	}	}	PUNCT
ejpam-4655	320	46	,	,	PUNCT
ejpam-4655	320	47	{	{	PUNCT
ejpam-4655	320	48	p	p	X
ejpam-4655	320	49	,	,	PUNCT
ejpam-4655	320	50	q	q	X
ejpam-4655	320	51	,	,	PUNCT
ejpam-4655	320	52	s	s	PART
ejpam-4655	320	53	}	}	PUNCT
ejpam-4655	320	54	,	,	PUNCT
ejpam-4655	320	55	{	{	PUNCT
ejpam-4655	320	56	p	p	X
ejpam-4655	320	57	,	,	PUNCT
ejpam-4655	320	58	r	r	NOUN
ejpam-4655	320	59	,	,	PUNCT
ejpam-4655	320	60	s	s	PART
ejpam-4655	320	61	}	}	PUNCT
ejpam-4655	320	62	,	,	PUNCT
ejpam-4655	320	63	{	{	PUNCT
ejpam-4655	320	64	q	q	X
ejpam-4655	320	65	,	,	PUNCT
ejpam-4655	320	66	r	r	NOUN
ejpam-4655	320	67	,	,	PUNCT
ejpam-4655	320	68	s	s	PART
ejpam-4655	320	69	}	}	PUNCT
ejpam-4655	320	70	,	,	PUNCT
ejpam-4655	320	71	x	x	NOUN
ejpam-4655	320	72	}	}	PUNCT
ejpam-4655	320	73	.	.	PUNCT
ejpam-4655	321	1	here	here	ADV
ejpam-4655	321	2	h(p	h(p	PROPN
ejpam-4655	321	3	)	)	PUNCT
ejpam-4655	321	4	∈	∈	PROPN
ejpam-4655	321	5	η1	η1	NOUN
ejpam-4655	321	6	whenever	whenever	SCONJ
ejpam-4655	321	7	p	p	PROPN
ejpam-4655	321	8	∈	∈	PROPN
ejpam-4655	321	9	µ1	µ1	PROPN
ejpam-4655	321	10	.	.	PUNCT
ejpam-4655	322	1	therefore	therefore	ADV
ejpam-4655	322	2	,	,	PUNCT
ejpam-4655	322	3	h	h	NOUN
ejpam-4655	322	4	is	be	AUX
ejpam-4655	322	5	a	a	DET
ejpam-4655	322	6	(	(	PUNCT
ejpam-4655	322	7	µ1	µ1	PROPN
ejpam-4655	322	8	,	,	PUNCT
ejpam-4655	322	9	η1)-open	η1)-open	ADJ
ejpam-4655	322	10	map	map	NOUN
ejpam-4655	322	11	.	.	PUNCT
ejpam-4655	323	1	let	let	VERB
ejpam-4655	323	2	q	q	NOUN
ejpam-4655	324	1	=	=	PUNCT
ejpam-4655	324	2	{	{	PUNCT
ejpam-4655	324	3	p	p	X
ejpam-4655	324	4	}	}	PUNCT
ejpam-4655	324	5	.	.	PUNCT
ejpam-4655	325	1	then	then	ADV
ejpam-4655	325	2	q	q	PROPN
ejpam-4655	325	3	∈	∈	PROPN
ejpam-4655	325	4	µ2	µ2	PROPN
ejpam-4655	325	5	.	.	PUNCT
ejpam-4655	326	1	but	but	CCONJ
ejpam-4655	326	2	h(q	h(q	ADV
ejpam-4655	326	3	)	)	PUNCT
ejpam-4655	326	4	/∈	/∈	PUNCT
ejpam-4655	327	1	η2	η2	PROPN
ejpam-4655	327	2	.	.	PUNCT
ejpam-4655	328	1	thus	thus	ADV
ejpam-4655	328	2	,	,	PUNCT
ejpam-4655	328	3	h	h	NOUN
ejpam-4655	328	4	is	be	AUX
ejpam-4655	328	5	not	not	PART
ejpam-4655	328	6	a	a	DET
ejpam-4655	328	7	(	(	PUNCT
ejpam-4655	328	8	µ2	µ2	ADJ
ejpam-4655	328	9	,	,	PUNCT
ejpam-4655	328	10	η2)-open	η2)-open	VERB
ejpam-4655	328	11	map	map	NOUN
ejpam-4655	328	12	.	.	PUNCT
ejpam-4655	329	1	here	here	ADV
ejpam-4655	329	2	{	{	PUNCT
ejpam-4655	329	3	p	p	X
ejpam-4655	329	4	,	,	PUNCT
ejpam-4655	329	5	q	q	NOUN
ejpam-4655	329	6	}	}	PUNCT
ejpam-4655	329	7	,	,	PUNCT
ejpam-4655	329	8	{	{	PUNCT
ejpam-4655	329	9	p	p	X
ejpam-4655	329	10	,	,	PUNCT
ejpam-4655	329	11	r	r	NOUN
ejpam-4655	329	12	}	}	PUNCT
ejpam-4655	329	13	,	,	PUNCT
ejpam-4655	329	14	{	{	PUNCT
ejpam-4655	329	15	q	q	X
ejpam-4655	329	16	,	,	PUNCT
ejpam-4655	329	17	s	s	PART
ejpam-4655	329	18	}	}	PUNCT
ejpam-4655	329	19	,	,	PUNCT
ejpam-4655	329	20	{	{	PUNCT
ejpam-4655	329	21	p	p	X
ejpam-4655	329	22	,	,	PUNCT
ejpam-4655	329	23	q	q	ADJ
ejpam-4655	329	24	,	,	PUNCT
ejpam-4655	329	25	r	r	NOUN
ejpam-4655	329	26	}	}	PUNCT
ejpam-4655	329	27	,	,	PUNCT
ejpam-4655	329	28	{	{	PUNCT
ejpam-4655	329	29	p	p	X
ejpam-4655	329	30	,	,	PUNCT
ejpam-4655	329	31	q	q	X
ejpam-4655	329	32	,	,	PUNCT
ejpam-4655	329	33	s	s	PART
ejpam-4655	329	34	}	}	PUNCT
ejpam-4655	329	35	,	,	PUNCT
ejpam-4655	329	36	{	{	PUNCT
ejpam-4655	329	37	p	p	X
ejpam-4655	329	38	,	,	PUNCT
ejpam-4655	329	39	r	r	NOUN
ejpam-4655	329	40	,	,	PUNCT
ejpam-4655	329	41	s	s	PART
ejpam-4655	329	42	}	}	PUNCT
ejpam-4655	329	43	,	,	PUNCT
ejpam-4655	329	44	{	{	PUNCT
ejpam-4655	329	45	q	q	X
ejpam-4655	329	46	,	,	PUNCT
ejpam-4655	329	47	r	r	NOUN
ejpam-4655	329	48	,	,	PUNCT
ejpam-4655	329	49	s	s	PART
ejpam-4655	329	50	}	}	PUNCT
ejpam-4655	329	51	and	and	CCONJ
ejpam-4655	329	52	x	x	PRON
ejpam-4655	329	53	are	be	AUX
ejpam-4655	329	54	µ1	µ1	NOUN
ejpam-4655	329	55	-	-	PUNCT
ejpam-4655	329	56	dense	dense	ADJ
ejpam-4655	329	57	subsets	subset	NOUN
ejpam-4655	329	58	of	of	ADP
ejpam-4655	329	59	x.	x.	NOUN
ejpam-4655	329	60	also	also	ADV
ejpam-4655	329	61	,	,	PUNCT
ejpam-4655	329	62	every	every	DET
ejpam-4655	329	63	µ1	µ1	NOUN
ejpam-4655	329	64	-	-	PUNCT
ejpam-4655	329	65	dense	dense	ADJ
ejpam-4655	329	66	set	set	NOUN
ejpam-4655	329	67	is	be	AUX
ejpam-4655	329	68	µ2	µ2	ADJ
ejpam-4655	329	69	-	-	PUNCT
ejpam-4655	329	70	open	open	ADJ
ejpam-4655	329	71	.	.	PUNCT
ejpam-4655	330	1	therefore	therefore	ADV
ejpam-4655	330	2	,	,	PUNCT
ejpam-4655	330	3	x	x	X
ejpam-4655	330	4	is	be	AUX
ejpam-4655	330	5	a	a	DET
ejpam-4655	330	6	(	(	PUNCT
ejpam-4655	330	7	2	2	NUM
ejpam-4655	330	8	,	,	PUNCT
ejpam-4655	330	9	1)-bigeneralized	1)-bigeneralized	NUM
ejpam-4655	330	10	submaximal	submaximal	ADJ
ejpam-4655	330	11	space	space	NOUN
ejpam-4655	330	12	.	.	PUNCT
ejpam-4655	331	1	let	let	VERB
ejpam-4655	331	2	j	j	PROPN
ejpam-4655	331	3	=	=	PUNCT
ejpam-4655	331	4	{	{	PUNCT
ejpam-4655	331	5	p1	p1	PROPN
ejpam-4655	331	6	,	,	PUNCT
ejpam-4655	331	7	q1	q1	PROPN
ejpam-4655	331	8	}	}	PUNCT
ejpam-4655	331	9	.	.	PUNCT
ejpam-4655	332	1	then	then	ADV
ejpam-4655	332	2	cη1(j	cη1(j	PROPN
ejpam-4655	332	3	)	)	PUNCT
ejpam-4655	333	1	=	=	SYM
ejpam-4655	334	1	y.	y.	PROPN
ejpam-4655	334	2	but	but	CCONJ
ejpam-4655	334	3	j	j	PROPN
ejpam-4655	334	4	/∈	/∈	PUNCT
ejpam-4655	334	5	η2	η2	PROPN
ejpam-4655	334	6	.	.	PUNCT
ejpam-4655	335	1	thus	thus	ADV
ejpam-4655	335	2	,	,	PUNCT
ejpam-4655	335	3	y	y	PROPN
ejpam-4655	335	4	is	be	AUX
ejpam-4655	335	5	not	not	PART
ejpam-4655	335	6	a	a	DET
ejpam-4655	335	7	(	(	PUNCT
ejpam-4655	335	8	2	2	NUM
ejpam-4655	335	9	,	,	PUNCT
ejpam-4655	335	10	1)-bigeneralized	1)-bigeneralized	NUM
ejpam-4655	335	11	submaximal	submaximal	ADJ
ejpam-4655	335	12	space	space	NOUN
ejpam-4655	335	13	.	.	PUNCT
ejpam-4655	336	1	(	(	PUNCT
ejpam-4655	336	2	c	c	X
ejpam-4655	336	3	)	)	PUNCT
ejpam-4655	336	4	let	let	VERB
ejpam-4655	336	5	µ1	µ1	NOUN
ejpam-4655	336	6	=	=	SYM
ejpam-4655	336	7	{	{	PUNCT
ejpam-4655	336	8	∅	∅	NOUN
ejpam-4655	336	9	,	,	PUNCT
ejpam-4655	336	10	{	{	PUNCT
ejpam-4655	336	11	p	p	X
ejpam-4655	336	12	}	}	PUNCT
ejpam-4655	336	13	,	,	PUNCT
ejpam-4655	336	14	{	{	PUNCT
ejpam-4655	336	15	s	s	X
ejpam-4655	336	16	}	}	PUNCT
ejpam-4655	336	17	,	,	PUNCT
ejpam-4655	336	18	{	{	PUNCT
ejpam-4655	336	19	p	p	X
ejpam-4655	336	20	,	,	PUNCT
ejpam-4655	336	21	q	q	NOUN
ejpam-4655	336	22	}	}	PUNCT
ejpam-4655	336	23	,	,	PUNCT
ejpam-4655	336	24	{	{	PUNCT
ejpam-4655	336	25	p	p	X
ejpam-4655	336	26	,	,	PUNCT
ejpam-4655	336	27	s	s	PART
ejpam-4655	336	28	}	}	PUNCT
ejpam-4655	336	29	,	,	PUNCT
ejpam-4655	336	30	{	{	PUNCT
ejpam-4655	336	31	q	q	X
ejpam-4655	336	32	,	,	PUNCT
ejpam-4655	336	33	r	r	NOUN
ejpam-4655	336	34	}	}	PUNCT
ejpam-4655	336	35	,	,	PUNCT
ejpam-4655	336	36	{	{	PUNCT
ejpam-4655	336	37	q	q	X
ejpam-4655	336	38	,	,	PUNCT
ejpam-4655	336	39	s	s	PART
ejpam-4655	336	40	}	}	PUNCT
ejpam-4655	336	41	,	,	PUNCT
ejpam-4655	336	42	{	{	PUNCT
ejpam-4655	336	43	r	r	NOUN
ejpam-4655	336	44	,	,	PUNCT
ejpam-4655	336	45	s	s	PART
ejpam-4655	336	46	}	}	PUNCT
ejpam-4655	336	47	,	,	PUNCT
ejpam-4655	336	48	{	{	PUNCT
ejpam-4655	336	49	p	p	X
ejpam-4655	336	50	,	,	PUNCT
ejpam-4655	336	51	q	q	ADJ
ejpam-4655	336	52	,	,	PUNCT
ejpam-4655	336	53	r	r	NOUN
ejpam-4655	336	54	}	}	PUNCT
ejpam-4655	336	55	,	,	PUNCT
ejpam-4655	336	56	{	{	PUNCT
ejpam-4655	336	57	p	p	X
ejpam-4655	336	58	,	,	PUNCT
ejpam-4655	336	59	q	q	X
ejpam-4655	336	60	,	,	PUNCT
ejpam-4655	336	61	s	s	PART
ejpam-4655	336	62	}	}	PUNCT
ejpam-4655	336	63	,	,	PUNCT
ejpam-4655	336	64	{	{	PUNCT
ejpam-4655	336	65	p	p	X
ejpam-4655	336	66	,	,	PUNCT
ejpam-4655	336	67	r	r	NOUN
ejpam-4655	336	68	,	,	PUNCT
ejpam-4655	336	69	s	s	PART
ejpam-4655	336	70	}	}	PUNCT
ejpam-4655	336	71	,	,	PUNCT
ejpam-4655	336	72	{	{	PUNCT
ejpam-4655	336	73	q	q	X
ejpam-4655	336	74	,	,	PUNCT
ejpam-4655	336	75	r	r	NOUN
ejpam-4655	336	76	,	,	PUNCT
ejpam-4655	336	77	s	s	PART
ejpam-4655	336	78	}	}	PUNCT
ejpam-4655	336	79	,	,	PUNCT
ejpam-4655	336	80	x};µ2	x};µ2	PROPN
ejpam-4655	337	1	=	=	PRON
ejpam-4655	337	2	{	{	PUNCT
ejpam-4655	337	3	∅	∅	NOUN
ejpam-4655	337	4	,	,	PUNCT
ejpam-4655	337	5	{	{	PUNCT
ejpam-4655	337	6	p	p	X
ejpam-4655	337	7	,	,	PUNCT
ejpam-4655	337	8	s	s	PART
ejpam-4655	337	9	}	}	PUNCT
ejpam-4655	337	10	,	,	PUNCT
ejpam-4655	337	11	{	{	PUNCT
ejpam-4655	337	12	q	q	X
ejpam-4655	337	13	,	,	PUNCT
ejpam-4655	337	14	s	s	PART
ejpam-4655	337	15	}	}	PUNCT
ejpam-4655	337	16	,	,	PUNCT
ejpam-4655	337	17	{	{	PUNCT
ejpam-4655	337	18	p	p	X
ejpam-4655	337	19	,	,	PUNCT
ejpam-4655	337	20	q	q	ADJ
ejpam-4655	337	21	,	,	PUNCT
ejpam-4655	337	22	s	s	PART
ejpam-4655	337	23	}	}	PUNCT
ejpam-4655	337	24	}	}	PUNCT
ejpam-4655	337	25	;	;	PUNCT
ejpam-4655	337	26	η1	η1	NOUN
ejpam-4655	337	27	=	=	SYM
ejpam-4655	337	28	{	{	PUNCT
ejpam-4655	337	29	∅	∅	NOUN
ejpam-4655	337	30	,	,	PUNCT
ejpam-4655	337	31	{	{	PUNCT
ejpam-4655	337	32	p1	p1	NOUN
ejpam-4655	337	33	,	,	PUNCT
ejpam-4655	337	34	r1	r1	PROPN
ejpam-4655	337	35	}	}	PUNCT
ejpam-4655	337	36	,	,	PUNCT
ejpam-4655	337	37	{	{	PUNCT
ejpam-4655	337	38	r1	r1	NOUN
ejpam-4655	337	39	,	,	PUNCT
ejpam-4655	337	40	s1	s1	PROPN
ejpam-4655	337	41	}	}	PUNCT
ejpam-4655	337	42	,	,	PUNCT
ejpam-4655	337	43	{	{	PUNCT
ejpam-4655	337	44	p1	p1	NOUN
ejpam-4655	337	45	,	,	PUNCT
ejpam-4655	337	46	r1	r1	NOUN
ejpam-4655	337	47	,	,	PUNCT
ejpam-4655	337	48	s1	s1	NOUN
ejpam-4655	337	49	}	}	PUNCT
ejpam-4655	337	50	}	}	PUNCT
ejpam-4655	337	51	and	and	CCONJ
ejpam-4655	337	52	η2	η2	ADJ
ejpam-4655	337	53	=	=	SYM
ejpam-4655	337	54	{	{	PUNCT
ejpam-4655	337	55	∅	∅	NOUN
ejpam-4655	337	56	,	,	PUNCT
ejpam-4655	337	57	{	{	PUNCT
ejpam-4655	337	58	p1	p1	NOUN
ejpam-4655	337	59	,	,	PUNCT
ejpam-4655	337	60	r1	r1	PROPN
ejpam-4655	337	61	}	}	PUNCT
ejpam-4655	337	62	,	,	PUNCT
ejpam-4655	337	63	{	{	PUNCT
ejpam-4655	337	64	q1	q1	NOUN
ejpam-4655	337	65	,	,	PUNCT
ejpam-4655	337	66	r1	r1	PROPN
ejpam-4655	337	67	}	}	PUNCT
ejpam-4655	337	68	,	,	PUNCT
ejpam-4655	337	69	{	{	PUNCT
ejpam-4655	337	70	p1	p1	PROPN
ejpam-4655	337	71	,	,	PUNCT
ejpam-4655	337	72	q1	q1	PROPN
ejpam-4655	337	73	,	,	PUNCT
ejpam-4655	337	74	r1	r1	PROPN
ejpam-4655	337	75	}	}	PUNCT
ejpam-4655	337	76	}	}	PUNCT
ejpam-4655	337	77	.	.	PUNCT
ejpam-4655	338	1	here	here	ADV
ejpam-4655	338	2	h(p	h(p	PROPN
ejpam-4655	338	3	)	)	PUNCT
ejpam-4655	338	4	∈	∈	PROPN
ejpam-4655	338	5	η2	η2	NOUN
ejpam-4655	338	6	whenever	whenever	SCONJ
ejpam-4655	338	7	p	p	PROPN
ejpam-4655	338	8	∈	∈	PROPN
ejpam-4655	338	9	µ2	µ2	NOUN
ejpam-4655	338	10	.	.	PUNCT
ejpam-4655	339	1	therefore	therefore	ADV
ejpam-4655	339	2	,	,	PUNCT
ejpam-4655	339	3	h	h	NOUN
ejpam-4655	339	4	is	be	AUX
ejpam-4655	339	5	a	a	DET
ejpam-4655	339	6	(	(	PUNCT
ejpam-4655	339	7	µ2	µ2	ADJ
ejpam-4655	339	8	,	,	PUNCT
ejpam-4655	339	9	η2)-open	η2)-open	VERB
ejpam-4655	339	10	map	map	NOUN
ejpam-4655	339	11	.	.	PUNCT
ejpam-4655	340	1	let	let	VERB
ejpam-4655	340	2	j	j	PROPN
ejpam-4655	340	3	=	=	PUNCT
ejpam-4655	340	4	{	{	PUNCT
ejpam-4655	340	5	p	p	X
ejpam-4655	340	6	}	}	PUNCT
ejpam-4655	340	7	.	.	PUNCT
ejpam-4655	341	1	then	then	ADV
ejpam-4655	341	2	j	j	PROPN
ejpam-4655	341	3	∈	∈	PROPN
ejpam-4655	341	4	µ1	µ1	PROPN
ejpam-4655	341	5	.	.	PUNCT
ejpam-4655	342	1	but	but	CCONJ
ejpam-4655	342	2	h(j	h(j	PROPN
ejpam-4655	342	3	)	)	PUNCT
ejpam-4655	342	4	/∈	/∈	PUNCT
ejpam-4655	343	1	η1	η1	NOUN
ejpam-4655	343	2	.	.	PUNCT
ejpam-4655	344	1	thus	thus	ADV
ejpam-4655	344	2	,	,	PUNCT
ejpam-4655	344	3	h	h	NOUN
ejpam-4655	344	4	is	be	AUX
ejpam-4655	344	5	not	not	PART
ejpam-4655	344	6	a	a	DET
ejpam-4655	344	7	(	(	PUNCT
ejpam-4655	344	8	µ1	µ1	PROPN
ejpam-4655	344	9	,	,	PUNCT
ejpam-4655	344	10	η1)open	η1)open	NOUN
ejpam-4655	344	11	map	map	NOUN
ejpam-4655	344	12	.	.	PUNCT
ejpam-4655	345	1	here	here	ADV
ejpam-4655	345	2	{	{	PUNCT
ejpam-4655	345	3	s	s	X
ejpam-4655	345	4	}	}	PUNCT
ejpam-4655	345	5	,	,	PUNCT
ejpam-4655	345	6	{	{	PUNCT
ejpam-4655	345	7	p	p	X
ejpam-4655	345	8	,	,	PUNCT
ejpam-4655	345	9	q	q	NOUN
ejpam-4655	345	10	}	}	PUNCT
ejpam-4655	345	11	,	,	PUNCT
ejpam-4655	345	12	{	{	PUNCT
ejpam-4655	345	13	p	p	X
ejpam-4655	345	14	,	,	PUNCT
ejpam-4655	345	15	s	s	PART
ejpam-4655	345	16	}	}	PUNCT
ejpam-4655	345	17	,	,	PUNCT
ejpam-4655	345	18	{	{	PUNCT
ejpam-4655	345	19	q	q	X
ejpam-4655	345	20	,	,	PUNCT
ejpam-4655	345	21	s	s	PART
ejpam-4655	345	22	}	}	PUNCT
ejpam-4655	345	23	,	,	PUNCT
ejpam-4655	345	24	{	{	PUNCT
ejpam-4655	345	25	r	r	NOUN
ejpam-4655	345	26	,	,	PUNCT
ejpam-4655	345	27	s	s	PART
ejpam-4655	345	28	}	}	PUNCT
ejpam-4655	345	29	,	,	PUNCT
ejpam-4655	345	30	{	{	PUNCT
ejpam-4655	345	31	p	p	X
ejpam-4655	345	32	,	,	PUNCT
ejpam-4655	345	33	q	q	ADJ
ejpam-4655	345	34	,	,	PUNCT
ejpam-4655	345	35	r	r	NOUN
ejpam-4655	345	36	}	}	PUNCT
ejpam-4655	345	37	,	,	PUNCT
ejpam-4655	345	38	{	{	PUNCT
ejpam-4655	345	39	p	p	X
ejpam-4655	345	40	,	,	PUNCT
ejpam-4655	345	41	q	q	X
ejpam-4655	345	42	,	,	PUNCT
ejpam-4655	345	43	s	s	PART
ejpam-4655	345	44	}	}	PUNCT
ejpam-4655	345	45	,	,	PUNCT
ejpam-4655	345	46	{	{	PUNCT
ejpam-4655	345	47	p	p	X
ejpam-4655	345	48	,	,	PUNCT
ejpam-4655	345	49	r	r	NOUN
ejpam-4655	345	50	,	,	PUNCT
ejpam-4655	345	51	s	s	PART
ejpam-4655	345	52	}	}	PUNCT
ejpam-4655	345	53	,	,	PUNCT
ejpam-4655	345	54	{	{	PUNCT
ejpam-4655	345	55	q	q	X
ejpam-4655	345	56	,	,	PUNCT
ejpam-4655	345	57	r	r	NOUN
ejpam-4655	345	58	,	,	PUNCT
ejpam-4655	345	59	s	s	PART
ejpam-4655	345	60	}	}	PUNCT
ejpam-4655	345	61	and	and	CCONJ
ejpam-4655	345	62	x	x	PUNCT
ejpam-4655	345	63	y.	y.	PROPN
ejpam-4655	345	64	farhat	farhat	PROPN
ejpam-4655	345	65	et	et	PROPN
ejpam-4655	345	66	al	al	PROPN
ejpam-4655	345	67	.	.	PUNCT
ejpam-4655	345	68	/	/	SYM
ejpam-4655	345	69	eur	eur	PROPN
ejpam-4655	345	70	.	.	PUNCT
ejpam-4655	346	1	j.	j.	PROPN
ejpam-4655	346	2	pure	pure	PROPN
ejpam-4655	346	3	appl	appl	PROPN
ejpam-4655	346	4	.	.	PROPN
ejpam-4655	346	5	math	math	PROPN
ejpam-4655	346	6	,	,	PUNCT
ejpam-4655	346	7	16	16	NUM
ejpam-4655	346	8	(	(	PUNCT
ejpam-4655	346	9	1	1	NUM
ejpam-4655	346	10	)	)	PUNCT
ejpam-4655	346	11	(	(	PUNCT
ejpam-4655	346	12	2023	2023	NUM
ejpam-4655	346	13	)	)	PUNCT
ejpam-4655	346	14	,	,	PUNCT
ejpam-4655	346	15	386	386	NUM
ejpam-4655	346	16	-	-	SYM
ejpam-4655	346	17	403	403	NUM
ejpam-4655	346	18	395	395	NUM
ejpam-4655	346	19	are	be	AUX
ejpam-4655	346	20	µ2	µ2	ADJ
ejpam-4655	346	21	-	-	PUNCT
ejpam-4655	346	22	dense	dense	ADJ
ejpam-4655	346	23	subsets	subset	NOUN
ejpam-4655	346	24	of	of	ADP
ejpam-4655	346	25	x.	x.	NOUN
ejpam-4655	346	26	also	also	ADV
ejpam-4655	346	27	,	,	PUNCT
ejpam-4655	346	28	every	every	DET
ejpam-4655	346	29	µ2	µ2	ADJ
ejpam-4655	346	30	-	-	PUNCT
ejpam-4655	346	31	dense	dense	ADJ
ejpam-4655	346	32	set	set	NOUN
ejpam-4655	346	33	is	be	AUX
ejpam-4655	346	34	µ1	µ1	NOUN
ejpam-4655	346	35	-	-	PUNCT
ejpam-4655	346	36	open	open	ADJ
ejpam-4655	346	37	.	.	PUNCT
ejpam-4655	347	1	therefore	therefore	ADV
ejpam-4655	347	2	,	,	PUNCT
ejpam-4655	347	3	x	x	X
ejpam-4655	347	4	is	be	AUX
ejpam-4655	347	5	a	a	DET
ejpam-4655	347	6	(	(	PUNCT
ejpam-4655	347	7	1	1	NUM
ejpam-4655	347	8	,	,	PUNCT
ejpam-4655	347	9	2)bigeneralized	2)bigeneralized	NUM
ejpam-4655	347	10	submaximal	submaximal	ADJ
ejpam-4655	347	11	space	space	NOUN
ejpam-4655	347	12	.	.	PUNCT
ejpam-4655	348	1	let	let	VERB
ejpam-4655	348	2	m	m	VERB
ejpam-4655	348	3	=	=	SYM
ejpam-4655	348	4	{	{	PUNCT
ejpam-4655	348	5	p1	p1	PROPN
ejpam-4655	348	6	,	,	PUNCT
ejpam-4655	348	7	q1	q1	PROPN
ejpam-4655	348	8	,	,	PUNCT
ejpam-4655	348	9	r1	r1	PROPN
ejpam-4655	348	10	}	}	PUNCT
ejpam-4655	348	11	.	.	PUNCT
ejpam-4655	349	1	then	then	ADV
ejpam-4655	349	2	cη2(m	cη2(m	X
ejpam-4655	349	3	)	)	PUNCT
ejpam-4655	350	1	=	=	SYM
ejpam-4655	351	1	y.	y.	NOUN
ejpam-4655	351	2	but	but	CCONJ
ejpam-4655	351	3	m	m	NOUN
ejpam-4655	351	4	/∈	/∈	NOUN
ejpam-4655	351	5	η1	η1	NOUN
ejpam-4655	351	6	.	.	PUNCT
ejpam-4655	352	1	thus	thus	ADV
ejpam-4655	352	2	,	,	PUNCT
ejpam-4655	352	3	y	y	PROPN
ejpam-4655	352	4	is	be	AUX
ejpam-4655	352	5	not	not	PART
ejpam-4655	352	6	a	a	DET
ejpam-4655	352	7	(	(	PUNCT
ejpam-4655	352	8	1	1	NUM
ejpam-4655	352	9	,	,	PUNCT
ejpam-4655	352	10	2)-bigeneralized	2)-bigeneralized	NUM
ejpam-4655	352	11	submaximal	submaximal	ADJ
ejpam-4655	352	12	space	space	NOUN
ejpam-4655	352	13	.	.	PUNCT
ejpam-4655	353	1	(	(	PUNCT
ejpam-4655	353	2	d	d	X
ejpam-4655	353	3	)	)	PUNCT
ejpam-4655	353	4	let	let	VERB
ejpam-4655	353	5	µ1	µ1	NOUN
ejpam-4655	353	6	and	and	CCONJ
ejpam-4655	353	7	η1	η1	NOUN
ejpam-4655	353	8	are	be	AUX
ejpam-4655	353	9	generalized	generalized	ADJ
ejpam-4655	353	10	topologies	topology	NOUN
ejpam-4655	353	11	defined	define	VERB
ejpam-4655	353	12	as	as	ADP
ejpam-4655	353	13	in	in	ADP
ejpam-4655	353	14	(	(	PUNCT
ejpam-4655	353	15	c	c	NOUN
ejpam-4655	353	16	)	)	PUNCT
ejpam-4655	353	17	.	.	PUNCT
ejpam-4655	354	1	take	take	VERB
ejpam-4655	354	2	µ2	µ2	PROPN
ejpam-4655	354	3	=	=	PUNCT
ejpam-4655	354	4	{	{	PUNCT
ejpam-4655	354	5	∅	∅	NOUN
ejpam-4655	354	6	,	,	PUNCT
ejpam-4655	354	7	{	{	PUNCT
ejpam-4655	354	8	p	p	X
ejpam-4655	354	9	,	,	PUNCT
ejpam-4655	354	10	r	r	NOUN
ejpam-4655	354	11	}	}	PUNCT
ejpam-4655	354	12	,	,	PUNCT
ejpam-4655	354	13	{	{	PUNCT
ejpam-4655	354	14	p	p	X
ejpam-4655	354	15	,	,	PUNCT
ejpam-4655	354	16	q	q	ADJ
ejpam-4655	354	17	,	,	PUNCT
ejpam-4655	354	18	r	r	NOUN
ejpam-4655	354	19	}	}	PUNCT
ejpam-4655	354	20	,	,	PUNCT
ejpam-4655	354	21	{	{	PUNCT
ejpam-4655	354	22	p	p	X
ejpam-4655	354	23	,	,	PUNCT
ejpam-4655	354	24	q	q	X
ejpam-4655	354	25	,	,	PUNCT
ejpam-4655	354	26	s	s	PART
ejpam-4655	354	27	}	}	PUNCT
ejpam-4655	354	28	,	,	PUNCT
ejpam-4655	354	29	{	{	PUNCT
ejpam-4655	354	30	p	p	X
ejpam-4655	354	31	,	,	PUNCT
ejpam-4655	354	32	r	r	NOUN
ejpam-4655	354	33	,	,	PUNCT
ejpam-4655	354	34	s	s	PART
ejpam-4655	354	35	}	}	PUNCT
ejpam-4655	354	36	,	,	PUNCT
ejpam-4655	354	37	{	{	PUNCT
ejpam-4655	354	38	q	q	X
ejpam-4655	354	39	,	,	PUNCT
ejpam-4655	354	40	r	r	NOUN
ejpam-4655	354	41	,	,	PUNCT
ejpam-4655	354	42	s	s	PART
ejpam-4655	354	43	}	}	PUNCT
ejpam-4655	354	44	,	,	PUNCT
ejpam-4655	354	45	x	x	NOUN
ejpam-4655	354	46	}	}	PUNCT
ejpam-4655	354	47	and	and	CCONJ
ejpam-4655	354	48	η2	η2	ADJ
ejpam-4655	354	49	=	=	SYM
ejpam-4655	354	50	{	{	PUNCT
ejpam-4655	354	51	∅	∅	NOUN
ejpam-4655	354	52	,	,	PUNCT
ejpam-4655	354	53	{	{	PUNCT
ejpam-4655	354	54	q1	q1	NOUN
ejpam-4655	354	55	,	,	PUNCT
ejpam-4655	354	56	s1	s1	PROPN
ejpam-4655	354	57	}	}	PUNCT
ejpam-4655	354	58	,	,	PUNCT
ejpam-4655	354	59	{	{	PUNCT
ejpam-4655	354	60	p1	p1	PROPN
ejpam-4655	354	61	,	,	PUNCT
ejpam-4655	354	62	q1	q1	PROPN
ejpam-4655	354	63	,	,	PUNCT
ejpam-4655	354	64	r1	r1	PROPN
ejpam-4655	354	65	}	}	PUNCT
ejpam-4655	354	66	,	,	PUNCT
ejpam-4655	354	67	{	{	PUNCT
ejpam-4655	354	68	p1	p1	PROPN
ejpam-4655	354	69	,	,	PUNCT
ejpam-4655	354	70	q1	q1	PROPN
ejpam-4655	354	71	,	,	PUNCT
ejpam-4655	354	72	s1	s1	PROPN
ejpam-4655	354	73	}	}	PUNCT
ejpam-4655	354	74	,	,	PUNCT
ejpam-4655	354	75	{	{	PUNCT
ejpam-4655	354	76	p1	p1	NOUN
ejpam-4655	354	77	,	,	PUNCT
ejpam-4655	354	78	r1	r1	NOUN
ejpam-4655	354	79	,	,	PUNCT
ejpam-4655	354	80	s1	s1	PROPN
ejpam-4655	354	81	}	}	PUNCT
ejpam-4655	354	82	,	,	PUNCT
ejpam-4655	354	83	{	{	PUNCT
ejpam-4655	354	84	q1	q1	PROPN
ejpam-4655	354	85	,	,	PUNCT
ejpam-4655	354	86	r1	r1	NOUN
ejpam-4655	354	87	,	,	PUNCT
ejpam-4655	354	88	s1	s1	PROPN
ejpam-4655	354	89	}	}	PUNCT
ejpam-4655	354	90	,	,	PUNCT
ejpam-4655	354	91	y	y	PROPN
ejpam-4655	354	92	}	}	PUNCT
ejpam-4655	354	93	.	.	PUNCT
ejpam-4655	355	1	here	here	ADV
ejpam-4655	355	2	h(p	h(p	PROPN
ejpam-4655	355	3	)	)	PUNCT
ejpam-4655	355	4	∈	∈	PROPN
ejpam-4655	355	5	η2	η2	NOUN
ejpam-4655	355	6	whenever	whenever	SCONJ
ejpam-4655	355	7	p	p	PROPN
ejpam-4655	355	8	∈	∈	PROPN
ejpam-4655	355	9	µ2	µ2	NOUN
ejpam-4655	355	10	.	.	PUNCT
ejpam-4655	356	1	therefore	therefore	ADV
ejpam-4655	356	2	,	,	PUNCT
ejpam-4655	356	3	h	h	NOUN
ejpam-4655	356	4	is	be	AUX
ejpam-4655	356	5	a	a	DET
ejpam-4655	356	6	(	(	PUNCT
ejpam-4655	356	7	µ2	µ2	ADJ
ejpam-4655	356	8	,	,	PUNCT
ejpam-4655	356	9	η2)-open	η2)-open	VERB
ejpam-4655	356	10	map	map	NOUN
ejpam-4655	356	11	.	.	PUNCT
ejpam-4655	357	1	let	let	VERB
ejpam-4655	357	2	k	k	NOUN
ejpam-4655	357	3	=	=	PUNCT
ejpam-4655	357	4	{	{	PUNCT
ejpam-4655	357	5	p	p	X
ejpam-4655	357	6	}	}	PUNCT
ejpam-4655	357	7	.	.	PUNCT
ejpam-4655	358	1	then	then	ADV
ejpam-4655	358	2	k	k	PROPN
ejpam-4655	358	3	∈	∈	PROPN
ejpam-4655	358	4	µ1	µ1	PROPN
ejpam-4655	358	5	.	.	PUNCT
ejpam-4655	359	1	but	but	CCONJ
ejpam-4655	359	2	h(k	h(k	PROPN
ejpam-4655	359	3	)	)	PUNCT
ejpam-4655	359	4	/∈	/∈	PUNCT
ejpam-4655	359	5	η1	η1	NOUN
ejpam-4655	359	6	.	.	PUNCT
ejpam-4655	360	1	thus	thus	ADV
ejpam-4655	360	2	,	,	PUNCT
ejpam-4655	360	3	h	h	NOUN
ejpam-4655	360	4	is	be	AUX
ejpam-4655	360	5	not	not	PART
ejpam-4655	360	6	a	a	DET
ejpam-4655	360	7	(	(	PUNCT
ejpam-4655	360	8	µ1	µ1	PROPN
ejpam-4655	360	9	,	,	PUNCT
ejpam-4655	360	10	η1)-open	η1)-open	ADJ
ejpam-4655	360	11	map	map	NOUN
ejpam-4655	360	12	.	.	PUNCT
ejpam-4655	361	1	here	here	ADV
ejpam-4655	361	2	{	{	PUNCT
ejpam-4655	361	3	p	p	X
ejpam-4655	361	4	,	,	PUNCT
ejpam-4655	361	5	q	q	ADJ
ejpam-4655	361	6	,	,	PUNCT
ejpam-4655	361	7	r	r	NOUN
ejpam-4655	361	8	}	}	PUNCT
ejpam-4655	361	9	,	,	PUNCT
ejpam-4655	361	10	{	{	PUNCT
ejpam-4655	361	11	p	p	X
ejpam-4655	361	12	,	,	PUNCT
ejpam-4655	361	13	q	q	X
ejpam-4655	361	14	,	,	PUNCT
ejpam-4655	361	15	s	s	PART
ejpam-4655	361	16	}	}	PUNCT
ejpam-4655	361	17	,	,	PUNCT
ejpam-4655	361	18	{	{	PUNCT
ejpam-4655	361	19	p	p	X
ejpam-4655	361	20	,	,	PUNCT
ejpam-4655	361	21	r	r	NOUN
ejpam-4655	361	22	,	,	PUNCT
ejpam-4655	361	23	s	s	PART
ejpam-4655	361	24	}	}	PUNCT
ejpam-4655	361	25	,	,	PUNCT
ejpam-4655	361	26	{	{	PUNCT
ejpam-4655	361	27	q	q	X
ejpam-4655	361	28	,	,	PUNCT
ejpam-4655	361	29	r	r	NOUN
ejpam-4655	361	30	,	,	PUNCT
ejpam-4655	361	31	s	s	PART
ejpam-4655	361	32	}	}	PUNCT
ejpam-4655	361	33	and	and	CCONJ
ejpam-4655	361	34	x	x	PRON
ejpam-4655	361	35	are	be	AUX
ejpam-4655	361	36	µ1	µ1	NOUN
ejpam-4655	361	37	-	-	PUNCT
ejpam-4655	361	38	dense	dense	ADJ
ejpam-4655	361	39	subsets	subset	NOUN
ejpam-4655	361	40	of	of	ADP
ejpam-4655	361	41	x.	x.	NOUN
ejpam-4655	361	42	also	also	ADV
ejpam-4655	361	43	,	,	PUNCT
ejpam-4655	361	44	every	every	DET
ejpam-4655	361	45	µ1	µ1	NOUN
ejpam-4655	361	46	-	-	PUNCT
ejpam-4655	361	47	dense	dense	ADJ
ejpam-4655	361	48	set	set	NOUN
ejpam-4655	361	49	is	be	AUX
ejpam-4655	361	50	µ2	µ2	ADJ
ejpam-4655	361	51	-	-	PUNCT
ejpam-4655	361	52	open	open	ADJ
ejpam-4655	361	53	.	.	PUNCT
ejpam-4655	362	1	therefore	therefore	ADV
ejpam-4655	362	2	,	,	PUNCT
ejpam-4655	362	3	x	x	X
ejpam-4655	362	4	is	be	AUX
ejpam-4655	362	5	a	a	DET
ejpam-4655	362	6	(	(	PUNCT
ejpam-4655	362	7	2	2	NUM
ejpam-4655	362	8	,	,	PUNCT
ejpam-4655	362	9	1)-bigeneralized	1)-bigeneralized	NUM
ejpam-4655	362	10	submaximal	submaximal	ADJ
ejpam-4655	362	11	space	space	NOUN
ejpam-4655	362	12	.	.	PUNCT
ejpam-4655	363	1	let	let	VERB
ejpam-4655	363	2	k	k	NOUN
ejpam-4655	363	3	=	=	PRON
ejpam-4655	363	4	{	{	PUNCT
ejpam-4655	363	5	r1	r1	PROPN
ejpam-4655	363	6	}	}	PUNCT
ejpam-4655	363	7	.	.	PUNCT
ejpam-4655	364	1	then	then	ADV
ejpam-4655	364	2	cη1(k	cη1(k	NOUN
ejpam-4655	364	3	)	)	PUNCT
ejpam-4655	364	4	=	=	SYM
ejpam-4655	365	1	y.	y.	NOUN
ejpam-4655	365	2	but	but	CCONJ
ejpam-4655	365	3	k	k	PROPN
ejpam-4655	365	4	/∈	/∈	PUNCT
ejpam-4655	365	5	η2	η2	PROPN
ejpam-4655	365	6	.	.	PUNCT
ejpam-4655	366	1	thus	thus	ADV
ejpam-4655	366	2	,	,	PUNCT
ejpam-4655	366	3	y	y	PROPN
ejpam-4655	366	4	is	be	AUX
ejpam-4655	366	5	not	not	PART
ejpam-4655	366	6	a	a	DET
ejpam-4655	366	7	(	(	PUNCT
ejpam-4655	366	8	2	2	NUM
ejpam-4655	366	9	,	,	PUNCT
ejpam-4655	366	10	1)-bigeneralized	1)-bigeneralized	NUM
ejpam-4655	366	11	submaximal	submaximal	ADJ
ejpam-4655	366	12	space	space	NOUN
ejpam-4655	366	13	.	.	PUNCT
ejpam-4655	367	1	consider	consider	VERB
ejpam-4655	367	2	the	the	DET
ejpam-4655	367	3	bigeneralized	bigeneralize	VERB
ejpam-4655	367	4	topological	topological	ADJ
ejpam-4655	367	5	spaces	space	NOUN
ejpam-4655	367	6	(	(	PUNCT
ejpam-4655	367	7	x,µ1	x,µ1	NOUN
ejpam-4655	367	8	,	,	PUNCT
ejpam-4655	367	9	µ2	µ2	PROPN
ejpam-4655	367	10	)	)	PUNCT
ejpam-4655	367	11	and	and	CCONJ
ejpam-4655	367	12	(	(	PUNCT
ejpam-4655	367	13	y	y	PROPN
ejpam-4655	367	14	,	,	PUNCT
ejpam-4655	367	15	η1	η1	NOUN
ejpam-4655	367	16	,	,	PUNCT
ejpam-4655	367	17	η2	η2	NOUN
ejpam-4655	367	18	)	)	PUNCT
ejpam-4655	368	1	where	where	SCONJ
ejpam-4655	368	2	x	x	X
ejpam-4655	368	3	=	=	PRON
ejpam-4655	368	4	{	{	PUNCT
ejpam-4655	368	5	p	p	X
ejpam-4655	368	6	,	,	PUNCT
ejpam-4655	368	7	q	q	ADJ
ejpam-4655	368	8	,	,	PUNCT
ejpam-4655	368	9	r	r	NOUN
ejpam-4655	368	10	,	,	PUNCT
ejpam-4655	368	11	s};y	s};y	ADJ
ejpam-4655	368	12	=	=	SYM
ejpam-4655	368	13	{	{	PUNCT
ejpam-4655	368	14	p1	p1	PROPN
ejpam-4655	368	15	,	,	PUNCT
ejpam-4655	368	16	q1	q1	PROPN
ejpam-4655	368	17	,	,	PUNCT
ejpam-4655	368	18	r1	r1	PROPN
ejpam-4655	368	19	,	,	PUNCT
ejpam-4655	368	20	s1	s1	NOUN
ejpam-4655	368	21	,	,	PUNCT
ejpam-4655	368	22	t1	t1	NOUN
ejpam-4655	368	23	}	}	PUNCT
ejpam-4655	368	24	.	.	PUNCT
ejpam-4655	369	1	define	define	VERB
ejpam-4655	369	2	a	a	DET
ejpam-4655	369	3	map	map	NOUN
ejpam-4655	369	4	h	h	NOUN
ejpam-4655	369	5	:	:	PUNCT
ejpam-4655	369	6	(	(	PUNCT
ejpam-4655	369	7	x,µi	x,µi	NUM
ejpam-4655	369	8	)	)	PUNCT
ejpam-4655	369	9	→	→	PUNCT
ejpam-4655	369	10	(	(	PUNCT
ejpam-4655	369	11	y	y	PROPN
ejpam-4655	369	12	,	,	PUNCT
ejpam-4655	369	13	ηi	ηi	PROPN
ejpam-4655	369	14	)	)	PUNCT
ejpam-4655	369	15	for	for	ADP
ejpam-4655	369	16	i	i	PROPN
ejpam-4655	369	17	=	=	SYM
ejpam-4655	369	18	1	1	NUM
ejpam-4655	369	19	,	,	PUNCT
ejpam-4655	369	20	2	2	NUM
ejpam-4655	369	21	as	as	SCONJ
ejpam-4655	369	22	follows	follow	VERB
ejpam-4655	369	23	h(p	h(p	NOUN
ejpam-4655	369	24	)	)	PUNCT
ejpam-4655	369	25	=	=	SYM
ejpam-4655	369	26	p1;h(q	p1;h(q	NOUN
ejpam-4655	369	27	)	)	PUNCT
ejpam-4655	369	28	=	=	SYM
ejpam-4655	369	29	q1;h(r	q1;h(r	NOUN
ejpam-4655	369	30	)	)	PUNCT
ejpam-4655	370	1	=	=	SYM
ejpam-4655	370	2	r1;h(s	r1;h(s	NOUN
ejpam-4655	370	3	)	)	PUNCT
ejpam-4655	370	4	=	=	SYM
ejpam-4655	370	5	s1	s1	PROPN
ejpam-4655	370	6	.	.	PUNCT
ejpam-4655	371	1	clearly	clearly	ADV
ejpam-4655	371	2	,	,	PUNCT
ejpam-4655	371	3	h	h	NOUN
ejpam-4655	371	4	is	be	AUX
ejpam-4655	371	5	not	not	PART
ejpam-4655	371	6	a	a	DET
ejpam-4655	371	7	surjective	surjective	ADJ
ejpam-4655	371	8	map	map	NOUN
ejpam-4655	371	9	.	.	PUNCT
ejpam-4655	372	1	(	(	PUNCT
ejpam-4655	372	2	e	e	X
ejpam-4655	372	3	)	)	PUNCT
ejpam-4655	372	4	let	let	VERB
ejpam-4655	372	5	µ1	µ1	NOUN
ejpam-4655	372	6	=	=	SYM
ejpam-4655	372	7	{	{	PUNCT
ejpam-4655	372	8	∅	∅	NOUN
ejpam-4655	372	9	,	,	PUNCT
ejpam-4655	372	10	{	{	PUNCT
ejpam-4655	372	11	q	q	X
ejpam-4655	372	12	}	}	PUNCT
ejpam-4655	372	13	,	,	PUNCT
ejpam-4655	372	14	{	{	PUNCT
ejpam-4655	372	15	p	p	X
ejpam-4655	372	16	,	,	PUNCT
ejpam-4655	372	17	q	q	NOUN
ejpam-4655	372	18	}	}	PUNCT
ejpam-4655	372	19	,	,	PUNCT
ejpam-4655	372	20	{	{	PUNCT
ejpam-4655	372	21	p	p	X
ejpam-4655	372	22	,	,	PUNCT
ejpam-4655	372	23	r	r	NOUN
ejpam-4655	372	24	}	}	PUNCT
ejpam-4655	372	25	,	,	PUNCT
ejpam-4655	372	26	{	{	PUNCT
ejpam-4655	372	27	q	q	X
ejpam-4655	372	28	,	,	PUNCT
ejpam-4655	372	29	r	r	NOUN
ejpam-4655	372	30	}	}	PUNCT
ejpam-4655	372	31	,	,	PUNCT
ejpam-4655	372	32	{	{	PUNCT
ejpam-4655	372	33	q	q	X
ejpam-4655	372	34	,	,	PUNCT
ejpam-4655	372	35	s	s	PART
ejpam-4655	372	36	}	}	PUNCT
ejpam-4655	372	37	,	,	PUNCT
ejpam-4655	372	38	{	{	PUNCT
ejpam-4655	372	39	p	p	X
ejpam-4655	372	40	,	,	PUNCT
ejpam-4655	372	41	q	q	ADJ
ejpam-4655	372	42	,	,	PUNCT
ejpam-4655	372	43	r	r	NOUN
ejpam-4655	372	44	}	}	PUNCT
ejpam-4655	372	45	,	,	PUNCT
ejpam-4655	372	46	{	{	PUNCT
ejpam-4655	372	47	p	p	X
ejpam-4655	372	48	,	,	PUNCT
ejpam-4655	372	49	q	q	X
ejpam-4655	372	50	,	,	PUNCT
ejpam-4655	372	51	s	s	PART
ejpam-4655	372	52	}	}	PUNCT
ejpam-4655	372	53	,	,	PUNCT
ejpam-4655	372	54	{	{	PUNCT
ejpam-4655	372	55	p	p	X
ejpam-4655	372	56	,	,	PUNCT
ejpam-4655	372	57	r	r	NOUN
ejpam-4655	372	58	,	,	PUNCT
ejpam-4655	372	59	s	s	PART
ejpam-4655	372	60	}	}	PUNCT
ejpam-4655	372	61	,	,	PUNCT
ejpam-4655	372	62	{	{	PUNCT
ejpam-4655	372	63	q	q	X
ejpam-4655	372	64	,	,	PUNCT
ejpam-4655	372	65	r	r	NOUN
ejpam-4655	372	66	,	,	PUNCT
ejpam-4655	372	67	s	s	PART
ejpam-4655	372	68	}	}	PUNCT
ejpam-4655	372	69	,	,	PUNCT
ejpam-4655	372	70	x};µ2	x};µ2	PROPN
ejpam-4655	373	1	=	=	PRON
ejpam-4655	373	2	{	{	PUNCT
ejpam-4655	373	3	∅	∅	NOUN
ejpam-4655	373	4	,	,	PUNCT
ejpam-4655	373	5	{	{	PUNCT
ejpam-4655	373	6	p	p	X
ejpam-4655	373	7	,	,	PUNCT
ejpam-4655	373	8	q	q	NOUN
ejpam-4655	373	9	}	}	PUNCT
ejpam-4655	373	10	,	,	PUNCT
ejpam-4655	373	11	{	{	PUNCT
ejpam-4655	373	12	q	q	X
ejpam-4655	373	13	,	,	PUNCT
ejpam-4655	373	14	r	r	NOUN
ejpam-4655	373	15	}	}	PUNCT
ejpam-4655	373	16	,	,	PUNCT
ejpam-4655	373	17	{	{	PUNCT
ejpam-4655	373	18	p	p	X
ejpam-4655	373	19	,	,	PUNCT
ejpam-4655	373	20	q	q	ADJ
ejpam-4655	373	21	,	,	PUNCT
ejpam-4655	373	22	r	r	NOUN
ejpam-4655	373	23	}	}	PUNCT
ejpam-4655	373	24	}	}	PUNCT
ejpam-4655	373	25	;	;	PUNCT
ejpam-4655	373	26	η1	η1	NOUN
ejpam-4655	373	27	=	=	SYM
ejpam-4655	373	28	{	{	PUNCT
ejpam-4655	373	29	∅	∅	NOUN
ejpam-4655	373	30	,	,	PUNCT
ejpam-4655	373	31	{	{	PUNCT
ejpam-4655	373	32	q1	q1	NOUN
ejpam-4655	373	33	}	}	PUNCT
ejpam-4655	373	34	,	,	PUNCT
ejpam-4655	373	35	{	{	PUNCT
ejpam-4655	373	36	p1	p1	NOUN
ejpam-4655	373	37	,	,	PUNCT
ejpam-4655	373	38	q1	q1	PROPN
ejpam-4655	373	39	}	}	PUNCT
ejpam-4655	373	40	,	,	PUNCT
ejpam-4655	373	41	{	{	PUNCT
ejpam-4655	373	42	p1	p1	NOUN
ejpam-4655	373	43	,	,	PUNCT
ejpam-4655	373	44	r1	r1	PROPN
ejpam-4655	373	45	}	}	PUNCT
ejpam-4655	373	46	,	,	PUNCT
ejpam-4655	373	47	{	{	PUNCT
ejpam-4655	373	48	q1	q1	NOUN
ejpam-4655	373	49	,	,	PUNCT
ejpam-4655	373	50	r1	r1	PROPN
ejpam-4655	373	51	}	}	PUNCT
ejpam-4655	373	52	,	,	PUNCT
ejpam-4655	373	53	{	{	PUNCT
ejpam-4655	373	54	q1	q1	NOUN
ejpam-4655	373	55	,	,	PUNCT
ejpam-4655	373	56	s1	s1	PROPN
ejpam-4655	373	57	}	}	PUNCT
ejpam-4655	373	58	,	,	PUNCT
ejpam-4655	373	59	{	{	PUNCT
ejpam-4655	373	60	p1	p1	PROPN
ejpam-4655	373	61	,	,	PUNCT
ejpam-4655	373	62	q1	q1	PROPN
ejpam-4655	373	63	,	,	PUNCT
ejpam-4655	373	64	r1	r1	PROPN
ejpam-4655	373	65	}	}	PUNCT
ejpam-4655	373	66	,	,	PUNCT
ejpam-4655	373	67	{	{	PUNCT
ejpam-4655	373	68	p1	p1	PROPN
ejpam-4655	373	69	,	,	PUNCT
ejpam-4655	373	70	q1	q1	PROPN
ejpam-4655	373	71	,	,	PUNCT
ejpam-4655	373	72	s1	s1	PROPN
ejpam-4655	373	73	}	}	PUNCT
ejpam-4655	373	74	,	,	PUNCT
ejpam-4655	373	75	{	{	PUNCT
ejpam-4655	373	76	p1	p1	NOUN
ejpam-4655	373	77	,	,	PUNCT
ejpam-4655	373	78	r1	r1	NOUN
ejpam-4655	373	79	,	,	PUNCT
ejpam-4655	373	80	s1	s1	PROPN
ejpam-4655	373	81	}	}	PUNCT
ejpam-4655	373	82	,	,	PUNCT
ejpam-4655	373	83	{	{	PUNCT
ejpam-4655	373	84	q1	q1	PROPN
ejpam-4655	373	85	,	,	PUNCT
ejpam-4655	373	86	r1	r1	NOUN
ejpam-4655	373	87	,	,	PUNCT
ejpam-4655	373	88	s1	s1	PROPN
ejpam-4655	373	89	}	}	PUNCT
ejpam-4655	373	90	,	,	PUNCT
ejpam-4655	373	91	{	{	PUNCT
ejpam-4655	373	92	p1	p1	PROPN
ejpam-4655	373	93	,	,	PUNCT
ejpam-4655	373	94	q1	q1	PROPN
ejpam-4655	373	95	,	,	PUNCT
ejpam-4655	373	96	r1	r1	NOUN
ejpam-4655	373	97	,	,	PUNCT
ejpam-4655	373	98	s1	s1	NOUN
ejpam-4655	373	99	}	}	PUNCT
ejpam-4655	373	100	}	}	PUNCT
ejpam-4655	373	101	and	and	CCONJ
ejpam-4655	373	102	η2	η2	ADJ
ejpam-4655	373	103	=	=	SYM
ejpam-4655	373	104	{	{	PUNCT
ejpam-4655	373	105	∅	∅	NOUN
ejpam-4655	373	106	,	,	PUNCT
ejpam-4655	373	107	{	{	PUNCT
ejpam-4655	373	108	p1	p1	NOUN
ejpam-4655	373	109	,	,	PUNCT
ejpam-4655	373	110	q1	q1	PROPN
ejpam-4655	373	111	}	}	PUNCT
ejpam-4655	373	112	,	,	PUNCT
ejpam-4655	373	113	{	{	PUNCT
ejpam-4655	373	114	q1	q1	NOUN
ejpam-4655	373	115	,	,	PUNCT
ejpam-4655	373	116	r1	r1	PROPN
ejpam-4655	373	117	}	}	PUNCT
ejpam-4655	373	118	,	,	PUNCT
ejpam-4655	373	119	{	{	PUNCT
ejpam-4655	373	120	p1	p1	PROPN
ejpam-4655	373	121	,	,	PUNCT
ejpam-4655	373	122	q1	q1	PROPN
ejpam-4655	373	123	,	,	PUNCT
ejpam-4655	373	124	r1	r1	PROPN
ejpam-4655	373	125	}	}	PUNCT
ejpam-4655	373	126	}	}	PUNCT
ejpam-4655	373	127	.	.	PUNCT
ejpam-4655	374	1	here	here	ADV
ejpam-4655	374	2	h(p	h(p	PROPN
ejpam-4655	374	3	)	)	PUNCT
ejpam-4655	374	4	∈	∈	PROPN
ejpam-4655	374	5	η1	η1	NOUN
ejpam-4655	374	6	whenever	whenever	SCONJ
ejpam-4655	374	7	p	p	PROPN
ejpam-4655	374	8	∈	∈	PROPN
ejpam-4655	374	9	µ1	µ1	PROPN
ejpam-4655	374	10	.	.	PUNCT
ejpam-4655	375	1	therefore	therefore	ADV
ejpam-4655	375	2	,	,	PUNCT
ejpam-4655	375	3	f	f	PROPN
ejpam-4655	375	4	is	be	AUX
ejpam-4655	375	5	a	a	DET
ejpam-4655	375	6	(	(	PUNCT
ejpam-4655	375	7	µ1	µ1	PROPN
ejpam-4655	375	8	,	,	PUNCT
ejpam-4655	375	9	η1)-open	η1)-open	ADJ
ejpam-4655	375	10	map	map	NOUN
ejpam-4655	375	11	.	.	PUNCT
ejpam-4655	376	1	also	also	ADV
ejpam-4655	376	2	,	,	PUNCT
ejpam-4655	376	3	h(m	h(m	ADJ
ejpam-4655	376	4	)	)	PUNCT
ejpam-4655	376	5	∈	∈	NOUN
ejpam-4655	376	6	η2	η2	VERB
ejpam-4655	376	7	wheneverm	wheneverm	NOUN
ejpam-4655	376	8	∈	∈	PROPN
ejpam-4655	376	9	µ2	µ2	NOUN
ejpam-4655	376	10	.	.	PUNCT
ejpam-4655	377	1	hence	hence	ADV
ejpam-4655	377	2	h	h	PROPN
ejpam-4655	377	3	is	be	AUX
ejpam-4655	377	4	a	a	DET
ejpam-4655	377	5	(	(	PUNCT
ejpam-4655	377	6	µ2	µ2	ADJ
ejpam-4655	377	7	,	,	PUNCT
ejpam-4655	377	8	η2)-open	η2)-open	VERB
ejpam-4655	377	9	map	map	NOUN
ejpam-4655	377	10	.	.	PUNCT
ejpam-4655	378	1	here	here	ADV
ejpam-4655	378	2	{	{	PUNCT
ejpam-4655	378	3	q	q	X
ejpam-4655	378	4	}	}	PUNCT
ejpam-4655	378	5	,	,	PUNCT
ejpam-4655	378	6	{	{	PUNCT
ejpam-4655	378	7	p	p	X
ejpam-4655	378	8	,	,	PUNCT
ejpam-4655	378	9	q	q	NOUN
ejpam-4655	378	10	}	}	PUNCT
ejpam-4655	378	11	,	,	PUNCT
ejpam-4655	378	12	{	{	PUNCT
ejpam-4655	378	13	p	p	X
ejpam-4655	378	14	,	,	PUNCT
ejpam-4655	378	15	r	r	NOUN
ejpam-4655	378	16	}	}	PUNCT
ejpam-4655	378	17	,	,	PUNCT
ejpam-4655	378	18	{	{	PUNCT
ejpam-4655	378	19	q	q	X
ejpam-4655	378	20	,	,	PUNCT
ejpam-4655	378	21	r	r	NOUN
ejpam-4655	378	22	}	}	PUNCT
ejpam-4655	378	23	,	,	PUNCT
ejpam-4655	378	24	{	{	PUNCT
ejpam-4655	378	25	q	q	X
ejpam-4655	378	26	,	,	PUNCT
ejpam-4655	378	27	s	s	PART
ejpam-4655	378	28	}	}	PUNCT
ejpam-4655	378	29	,	,	PUNCT
ejpam-4655	378	30	{	{	PUNCT
ejpam-4655	378	31	p	p	X
ejpam-4655	378	32	,	,	PUNCT
ejpam-4655	378	33	q	q	ADJ
ejpam-4655	378	34	,	,	PUNCT
ejpam-4655	378	35	r	r	NOUN
ejpam-4655	378	36	}	}	PUNCT
ejpam-4655	378	37	,	,	PUNCT
ejpam-4655	378	38	{	{	PUNCT
ejpam-4655	378	39	p	p	X
ejpam-4655	378	40	,	,	PUNCT
ejpam-4655	378	41	q	q	X
ejpam-4655	378	42	,	,	PUNCT
ejpam-4655	378	43	s	s	PART
ejpam-4655	378	44	}	}	PUNCT
ejpam-4655	378	45	,	,	PUNCT
ejpam-4655	378	46	{	{	PUNCT
ejpam-4655	378	47	p	p	X
ejpam-4655	378	48	,	,	PUNCT
ejpam-4655	378	49	r	r	NOUN
ejpam-4655	378	50	,	,	PUNCT
ejpam-4655	378	51	s	s	PART
ejpam-4655	378	52	}	}	PUNCT
ejpam-4655	378	53	,	,	PUNCT
ejpam-4655	378	54	{	{	PUNCT
ejpam-4655	378	55	q	q	X
ejpam-4655	378	56	,	,	PUNCT
ejpam-4655	378	57	r	r	NOUN
ejpam-4655	378	58	,	,	PUNCT
ejpam-4655	378	59	s	s	PART
ejpam-4655	378	60	}	}	PUNCT
ejpam-4655	378	61	andx	andx	NOUN
ejpam-4655	378	62	are	be	AUX
ejpam-4655	378	63	µ2	µ2	ADJ
ejpam-4655	378	64	-	-	PUNCT
ejpam-4655	378	65	dense	dense	ADJ
ejpam-4655	378	66	subsets	subset	NOUN
ejpam-4655	378	67	ofx	ofx	NOUN
ejpam-4655	378	68	.	.	PUNCT
ejpam-4655	379	1	also	also	ADV
ejpam-4655	379	2	,	,	PUNCT
ejpam-4655	379	3	every	every	DET
ejpam-4655	379	4	µ2	µ2	ADJ
ejpam-4655	379	5	-	-	PUNCT
ejpam-4655	379	6	dense	dense	ADJ
ejpam-4655	379	7	set	set	NOUN
ejpam-4655	379	8	is	be	AUX
ejpam-4655	379	9	µ1	µ1	NOUN
ejpam-4655	379	10	-	-	PUNCT
ejpam-4655	379	11	open	open	ADJ
ejpam-4655	379	12	.	.	PUNCT
ejpam-4655	380	1	therefore	therefore	ADV
ejpam-4655	380	2	,	,	PUNCT
ejpam-4655	380	3	x	x	X
ejpam-4655	380	4	is	be	AUX
ejpam-4655	380	5	a	a	DET
ejpam-4655	380	6	(	(	PUNCT
ejpam-4655	380	7	1	1	NUM
ejpam-4655	380	8	,	,	PUNCT
ejpam-4655	380	9	2)-bigeneralized	2)-bigeneralized	NUM
ejpam-4655	380	10	submaximal	submaximal	ADJ
ejpam-4655	380	11	space	space	NOUN
ejpam-4655	380	12	.	.	PUNCT
ejpam-4655	381	1	let	let	VERB
ejpam-4655	381	2	j	j	PROPN
ejpam-4655	381	3	=	=	PUNCT
ejpam-4655	381	4	{	{	PUNCT
ejpam-4655	381	5	p1	p1	PROPN
ejpam-4655	381	6	,	,	PUNCT
ejpam-4655	381	7	q1	q1	PROPN
ejpam-4655	381	8	,	,	PUNCT
ejpam-4655	381	9	r1	r1	PROPN
ejpam-4655	381	10	,	,	PUNCT
ejpam-4655	381	11	t1	t1	NOUN
ejpam-4655	381	12	}	}	PUNCT
ejpam-4655	381	13	.	.	PUNCT
ejpam-4655	382	1	then	then	ADV
ejpam-4655	382	2	cη2(j	cη2(j	PUNCT
ejpam-4655	382	3	)	)	PUNCT
ejpam-4655	383	1	=	=	PUNCT
ejpam-4655	384	1	y.	y.	PROPN
ejpam-4655	384	2	but	but	CCONJ
ejpam-4655	384	3	j	j	PROPN
ejpam-4655	384	4	/∈	/∈	PUNCT
ejpam-4655	384	5	η1	η1	PROPN
ejpam-4655	384	6	.	.	PUNCT
ejpam-4655	385	1	thus	thus	ADV
ejpam-4655	385	2	,	,	PUNCT
ejpam-4655	385	3	y	y	PROPN
ejpam-4655	385	4	is	be	AUX
ejpam-4655	385	5	not	not	PART
ejpam-4655	385	6	a	a	DET
ejpam-4655	385	7	(	(	PUNCT
ejpam-4655	385	8	1	1	NUM
ejpam-4655	385	9	,	,	PUNCT
ejpam-4655	385	10	2)-bigeneralized	2)-bigeneralized	NUM
ejpam-4655	385	11	submaximal	submaximal	ADJ
ejpam-4655	385	12	space	space	NOUN
ejpam-4655	385	13	.	.	PUNCT
ejpam-4655	386	1	(	(	PUNCT
ejpam-4655	386	2	f	f	X
ejpam-4655	386	3	)	)	PUNCT
ejpam-4655	386	4	let	let	VERB
ejpam-4655	386	5	µ1	µ1	NOUN
ejpam-4655	386	6	and	and	CCONJ
ejpam-4655	386	7	η1	η1	NOUN
ejpam-4655	386	8	are	be	AUX
ejpam-4655	386	9	generalized	generalized	ADJ
ejpam-4655	386	10	topologies	topology	NOUN
ejpam-4655	386	11	defined	define	VERB
ejpam-4655	386	12	as	as	ADP
ejpam-4655	386	13	in	in	ADP
ejpam-4655	386	14	(	(	PUNCT
ejpam-4655	386	15	e	e	NOUN
ejpam-4655	386	16	)	)	PUNCT
ejpam-4655	386	17	.	.	PUNCT
ejpam-4655	387	1	take	take	VERB
ejpam-4655	387	2	µ2	µ2	PROPN
ejpam-4655	387	3	=	=	PUNCT
ejpam-4655	387	4	{	{	PUNCT
ejpam-4655	387	5	∅	∅	NOUN
ejpam-4655	387	6	,	,	PUNCT
ejpam-4655	387	7	{	{	PUNCT
ejpam-4655	387	8	p	p	X
ejpam-4655	387	9	,	,	PUNCT
ejpam-4655	387	10	q	q	NOUN
ejpam-4655	387	11	}	}	PUNCT
ejpam-4655	387	12	,	,	PUNCT
ejpam-4655	387	13	{	{	PUNCT
ejpam-4655	387	14	q	q	X
ejpam-4655	387	15	,	,	PUNCT
ejpam-4655	387	16	r	r	NOUN
ejpam-4655	387	17	}	}	PUNCT
ejpam-4655	387	18	,	,	PUNCT
ejpam-4655	387	19	{	{	PUNCT
ejpam-4655	387	20	p	p	X
ejpam-4655	387	21	,	,	PUNCT
ejpam-4655	387	22	q	q	ADJ
ejpam-4655	387	23	,	,	PUNCT
ejpam-4655	387	24	r	r	NOUN
ejpam-4655	387	25	}	}	PUNCT
ejpam-4655	387	26	,	,	PUNCT
ejpam-4655	387	27	{	{	PUNCT
ejpam-4655	387	28	p	p	X
ejpam-4655	387	29	,	,	PUNCT
ejpam-4655	387	30	q	q	X
ejpam-4655	387	31	,	,	PUNCT
ejpam-4655	387	32	s	s	PART
ejpam-4655	387	33	}	}	PUNCT
ejpam-4655	387	34	,	,	PUNCT
ejpam-4655	387	35	{	{	PUNCT
ejpam-4655	387	36	q	q	X
ejpam-4655	387	37	,	,	PUNCT
ejpam-4655	387	38	r	r	NOUN
ejpam-4655	387	39	,	,	PUNCT
ejpam-4655	387	40	s	s	PART
ejpam-4655	387	41	}	}	PUNCT
ejpam-4655	387	42	,	,	PUNCT
ejpam-4655	387	43	x	x	X
ejpam-4655	387	44	}	}	PUNCT
ejpam-4655	387	45	;	;	PUNCT
ejpam-4655	387	46	η2	η2	PROPN
ejpam-4655	387	47	=	=	SYM
ejpam-4655	387	48	{	{	PUNCT
ejpam-4655	387	49	∅	∅	NOUN
ejpam-4655	387	50	,	,	PUNCT
ejpam-4655	387	51	{	{	PUNCT
ejpam-4655	387	52	p1	p1	NOUN
ejpam-4655	387	53	,	,	PUNCT
ejpam-4655	387	54	q1	q1	PROPN
ejpam-4655	387	55	}	}	PUNCT
ejpam-4655	387	56	,	,	PUNCT
ejpam-4655	387	57	{	{	PUNCT
ejpam-4655	387	58	q1	q1	NOUN
ejpam-4655	387	59	,	,	PUNCT
ejpam-4655	387	60	r1	r1	PROPN
ejpam-4655	387	61	}	}	PUNCT
ejpam-4655	387	62	,	,	PUNCT
ejpam-4655	387	63	{	{	PUNCT
ejpam-4655	387	64	p1	p1	PROPN
ejpam-4655	387	65	,	,	PUNCT
ejpam-4655	387	66	q1	q1	PROPN
ejpam-4655	387	67	,	,	PUNCT
ejpam-4655	387	68	r1	r1	PROPN
ejpam-4655	387	69	}	}	PUNCT
ejpam-4655	387	70	,	,	PUNCT
ejpam-4655	387	71	{	{	PUNCT
ejpam-4655	387	72	p1	p1	PROPN
ejpam-4655	387	73	,	,	PUNCT
ejpam-4655	387	74	q1	q1	PROPN
ejpam-4655	387	75	,	,	PUNCT
ejpam-4655	387	76	s1	s1	PROPN
ejpam-4655	387	77	}	}	PUNCT
ejpam-4655	387	78	,	,	PUNCT
ejpam-4655	387	79	{	{	PUNCT
ejpam-4655	387	80	q1	q1	PROPN
ejpam-4655	387	81	,	,	PUNCT
ejpam-4655	387	82	r1	r1	NOUN
ejpam-4655	387	83	,	,	PUNCT
ejpam-4655	387	84	s1	s1	PROPN
ejpam-4655	387	85	}	}	PUNCT
ejpam-4655	387	86	,	,	PUNCT
ejpam-4655	387	87	{	{	PUNCT
ejpam-4655	387	88	p1	p1	PROPN
ejpam-4655	387	89	,	,	PUNCT
ejpam-4655	387	90	q1	q1	PROPN
ejpam-4655	387	91	,	,	PUNCT
ejpam-4655	387	92	r1	r1	NOUN
ejpam-4655	387	93	,	,	PUNCT
ejpam-4655	387	94	s1	s1	NOUN
ejpam-4655	387	95	}	}	PUNCT
ejpam-4655	387	96	}	}	PUNCT
ejpam-4655	387	97	.	.	PUNCT
ejpam-4655	388	1	here	here	ADV
ejpam-4655	388	2	h(k	h(k	PROPN
ejpam-4655	388	3	)	)	PUNCT
ejpam-4655	388	4	∈	∈	PROPN
ejpam-4655	388	5	η1	η1	NOUN
ejpam-4655	388	6	whenever	whenever	SCONJ
ejpam-4655	388	7	k	k	PROPN
ejpam-4655	388	8	∈	∈	PROPN
ejpam-4655	388	9	µ1	µ1	PROPN
ejpam-4655	388	10	.	.	PUNCT
ejpam-4655	389	1	therefore	therefore	ADV
ejpam-4655	389	2	,	,	PUNCT
ejpam-4655	389	3	h	h	NOUN
ejpam-4655	389	4	is	be	AUX
ejpam-4655	389	5	a	a	DET
ejpam-4655	389	6	(	(	PUNCT
ejpam-4655	389	7	µ1	µ1	PROPN
ejpam-4655	389	8	,	,	PUNCT
ejpam-4655	389	9	η1)-open	η1)-open	ADJ
ejpam-4655	389	10	map	map	NOUN
ejpam-4655	389	11	.	.	PUNCT
ejpam-4655	390	1	also	also	ADV
ejpam-4655	390	2	,	,	PUNCT
ejpam-4655	390	3	h(q	h(q	ADV
ejpam-4655	390	4	)	)	PUNCT
ejpam-4655	390	5	∈	∈	PROPN
ejpam-4655	390	6	η2	η2	VERB
ejpam-4655	390	7	wheneverq	wheneverq	NOUN
ejpam-4655	390	8	∈	∈	PROPN
ejpam-4655	391	1	µ2.hence	µ2.hence	NOUN
ejpam-4655	391	2	h	h	NOUN
ejpam-4655	391	3	is	be	AUX
ejpam-4655	391	4	a	a	DET
ejpam-4655	391	5	(	(	PUNCT
ejpam-4655	391	6	µ2	µ2	ADJ
ejpam-4655	391	7	,	,	PUNCT
ejpam-4655	391	8	η2)-open	η2)-open	VERB
ejpam-4655	391	9	map	map	NOUN
ejpam-4655	391	10	.	.	PUNCT
ejpam-4655	392	1	here	here	ADV
ejpam-4655	392	2	{	{	PUNCT
ejpam-4655	392	3	p	p	X
ejpam-4655	392	4	,	,	PUNCT
ejpam-4655	392	5	q	q	NOUN
ejpam-4655	392	6	}	}	PUNCT
ejpam-4655	392	7	,	,	PUNCT
ejpam-4655	392	8	{	{	PUNCT
ejpam-4655	392	9	q	q	X
ejpam-4655	392	10	,	,	PUNCT
ejpam-4655	392	11	r	r	NOUN
ejpam-4655	392	12	}	}	PUNCT
ejpam-4655	392	13	,	,	PUNCT
ejpam-4655	392	14	{	{	PUNCT
ejpam-4655	392	15	p	p	X
ejpam-4655	392	16	,	,	PUNCT
ejpam-4655	392	17	q	q	ADJ
ejpam-4655	392	18	,	,	PUNCT
ejpam-4655	392	19	r	r	NOUN
ejpam-4655	392	20	}	}	PUNCT
ejpam-4655	392	21	,	,	PUNCT
ejpam-4655	392	22	{	{	PUNCT
ejpam-4655	392	23	p	p	X
ejpam-4655	392	24	,	,	PUNCT
ejpam-4655	392	25	q	q	X
ejpam-4655	392	26	,	,	PUNCT
ejpam-4655	392	27	s	s	PART
ejpam-4655	392	28	}	}	PUNCT
ejpam-4655	392	29	,	,	PUNCT
ejpam-4655	392	30	{	{	PUNCT
ejpam-4655	392	31	q	q	X
ejpam-4655	392	32	,	,	PUNCT
ejpam-4655	392	33	r	r	NOUN
ejpam-4655	392	34	,	,	PUNCT
ejpam-4655	392	35	s	s	PART
ejpam-4655	392	36	}	}	PUNCT
ejpam-4655	392	37	and	and	CCONJ
ejpam-4655	392	38	x	x	PRON
ejpam-4655	392	39	are	be	AUX
ejpam-4655	392	40	µ1	µ1	NOUN
ejpam-4655	392	41	-	-	PUNCT
ejpam-4655	392	42	dense	dense	ADJ
ejpam-4655	392	43	subsets	subset	NOUN
ejpam-4655	392	44	of	of	ADP
ejpam-4655	392	45	x.	x.	NOUN
ejpam-4655	392	46	also	also	ADV
ejpam-4655	392	47	,	,	PUNCT
ejpam-4655	392	48	every	every	DET
ejpam-4655	392	49	µ1	µ1	NOUN
ejpam-4655	392	50	-	-	PUNCT
ejpam-4655	392	51	dense	dense	ADJ
ejpam-4655	392	52	set	set	NOUN
ejpam-4655	392	53	is	be	AUX
ejpam-4655	392	54	µ2	µ2	ADJ
ejpam-4655	392	55	-	-	PUNCT
ejpam-4655	392	56	open	open	ADJ
ejpam-4655	392	57	.	.	PUNCT
ejpam-4655	393	1	therefore	therefore	ADV
ejpam-4655	393	2	,	,	PUNCT
ejpam-4655	393	3	x	x	X
ejpam-4655	393	4	is	be	AUX
ejpam-4655	393	5	a	a	DET
ejpam-4655	393	6	(	(	PUNCT
ejpam-4655	393	7	2	2	NUM
ejpam-4655	393	8	,	,	PUNCT
ejpam-4655	393	9	1)-bigeneralized	1)-bigeneralized	NUM
ejpam-4655	393	10	submaximal	submaximal	ADJ
ejpam-4655	393	11	space	space	NOUN
ejpam-4655	393	12	.	.	PUNCT
ejpam-4655	394	1	let	let	VERB
ejpam-4655	394	2	p	p	NOUN
ejpam-4655	394	3	=	=	SYM
ejpam-4655	394	4	{	{	PUNCT
ejpam-4655	394	5	q1	q1	PROPN
ejpam-4655	394	6	,	,	PUNCT
ejpam-4655	394	7	r1	r1	PROPN
ejpam-4655	394	8	,	,	PUNCT
ejpam-4655	394	9	s1	s1	NOUN
ejpam-4655	394	10	,	,	PUNCT
ejpam-4655	394	11	t1	t1	NOUN
ejpam-4655	394	12	}	}	PUNCT
ejpam-4655	394	13	.	.	PUNCT
ejpam-4655	395	1	then	then	ADV
ejpam-4655	395	2	cη1(p	cη1(p	PROPN
ejpam-4655	395	3	)	)	PUNCT
ejpam-4655	396	1	=	=	PUNCT
ejpam-4655	397	1	y.	y.	NOUN
ejpam-4655	397	2	but	but	CCONJ
ejpam-4655	397	3	p	p	PROPN
ejpam-4655	397	4	/∈	/∈	PUNCT
ejpam-4655	397	5	η2	η2	PROPN
ejpam-4655	397	6	.	.	PUNCT
ejpam-4655	398	1	thus	thus	ADV
ejpam-4655	398	2	,	,	PUNCT
ejpam-4655	398	3	y	y	PROPN
ejpam-4655	398	4	is	be	AUX
ejpam-4655	398	5	not	not	PART
ejpam-4655	398	6	a	a	DET
ejpam-4655	398	7	(	(	PUNCT
ejpam-4655	398	8	2	2	NUM
ejpam-4655	398	9	,	,	PUNCT
ejpam-4655	398	10	1)-bigeneralized	1)-bigeneralized	NUM
ejpam-4655	398	11	submaximal	submaximal	ADJ
ejpam-4655	398	12	space	space	NOUN
ejpam-4655	398	13	.	.	PUNCT
ejpam-4655	399	1	theorem	theorem	NOUN
ejpam-4655	399	2	23	23	NUM
ejpam-4655	399	3	.	.	PUNCT
ejpam-4655	400	1	let	let	AUX
ejpam-4655	400	2	(	(	PUNCT
ejpam-4655	400	3	x,µ1	x,µ1	NOUN
ejpam-4655	400	4	,	,	PUNCT
ejpam-4655	400	5	µ2	µ2	PROPN
ejpam-4655	400	6	)	)	PUNCT
ejpam-4655	400	7	and	and	CCONJ
ejpam-4655	400	8	(	(	PUNCT
ejpam-4655	400	9	y	y	PROPN
ejpam-4655	400	10	,	,	PUNCT
ejpam-4655	400	11	η1	η1	NOUN
ejpam-4655	400	12	,	,	PUNCT
ejpam-4655	400	13	η2	η2	PROPN
ejpam-4655	400	14	)	)	PUNCT
ejpam-4655	400	15	be	be	VERB
ejpam-4655	400	16	two	two	NUM
ejpam-4655	400	17	bgtss	bgtss	NOUN
ejpam-4655	400	18	and	and	CCONJ
ejpam-4655	400	19	h	h	NOUN
ejpam-4655	400	20	:	:	PUNCT
ejpam-4655	400	21	(	(	PUNCT
ejpam-4655	400	22	x,µi	x,µi	NUM
ejpam-4655	400	23	)	)	PUNCT
ejpam-4655	400	24	→	→	PUNCT
ejpam-4655	400	25	(	(	PUNCT
ejpam-4655	400	26	y	y	PROPN
ejpam-4655	400	27	,	,	PUNCT
ejpam-4655	400	28	ηi	ηi	PROPN
ejpam-4655	400	29	)	)	PUNCT
ejpam-4655	400	30	be	be	VERB
ejpam-4655	400	31	a	a	DET
ejpam-4655	400	32	(	(	PUNCT
ejpam-4655	400	33	µi	µi	PROPN
ejpam-4655	400	34	,	,	PUNCT
ejpam-4655	400	35	ηi)-continuous	ηi)-continuous	ADJ
ejpam-4655	400	36	map	map	NOUN
ejpam-4655	400	37	for	for	ADP
ejpam-4655	400	38	i	i	PROPN
ejpam-4655	400	39	=	=	NOUN
ejpam-4655	400	40	1	1	NUM
ejpam-4655	400	41	,	,	PUNCT
ejpam-4655	400	42	2	2	NUM
ejpam-4655	400	43	.	.	PUNCT
ejpam-4655	400	44	then	then	ADV
ejpam-4655	400	45	inverse	inverse	ADJ
ejpam-4655	400	46	image	image	NOUN
ejpam-4655	400	47	of	of	ADP
ejpam-4655	400	48	a	a	DET
ejpam-4655	400	49	(	(	PUNCT
ejpam-4655	400	50	s	s	PROPN
ejpam-4655	400	51	,	,	PUNCT
ejpam-4655	400	52	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	400	53	submaximal	submaximal	ADJ
ejpam-4655	400	54	space	space	NOUN
ejpam-4655	400	55	is	be	AUX
ejpam-4655	400	56	(	(	PUNCT
ejpam-4655	400	57	s	s	PROPN
ejpam-4655	400	58	,	,	PUNCT
ejpam-4655	400	59	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	400	60	submaximal	submaximal	ADJ
ejpam-4655	400	61	space	space	NOUN
ejpam-4655	400	62	,	,	PUNCT
ejpam-4655	400	63	s	s	X
ejpam-4655	400	64	,	,	PUNCT
ejpam-4655	400	65	v	v	NOUN
ejpam-4655	400	66	=	=	SYM
ejpam-4655	400	67	1	1	NUM
ejpam-4655	400	68	,	,	PUNCT
ejpam-4655	400	69	2	2	NUM
ejpam-4655	400	70	;	;	PUNCT
ejpam-4655	400	71	s	s	VERB
ejpam-4655	400	72	̸=	̸=	PROPN
ejpam-4655	400	73	v.	v.	ADP
ejpam-4655	400	74	proof	proof	NOUN
ejpam-4655	400	75	.	.	PUNCT
ejpam-4655	401	1	it	it	PRON
ejpam-4655	401	2	follows	follow	VERB
ejpam-4655	401	3	from	from	ADP
ejpam-4655	401	4	lemma	lemma	PROPN
ejpam-4655	401	5	2	2	NUM
ejpam-4655	401	6	and	and	CCONJ
ejpam-4655	401	7	the	the	DET
ejpam-4655	401	8	similar	similar	ADJ
ejpam-4655	401	9	arguments	argument	NOUN
ejpam-4655	401	10	in	in	ADP
ejpam-4655	401	11	theorem	theorem	NOUN
ejpam-4655	401	12	21	21	NUM
ejpam-4655	401	13	.	.	PUNCT
ejpam-4655	402	1	the	the	DET
ejpam-4655	402	2	hypothesis	hypothesis	NOUN
ejpam-4655	402	3	of	of	ADP
ejpam-4655	402	4	theorem	theorem	NOUN
ejpam-4655	402	5	23	23	NUM
ejpam-4655	402	6	is	be	AUX
ejpam-4655	402	7	necessary	necessary	ADJ
ejpam-4655	402	8	as	as	SCONJ
ejpam-4655	402	9	shown	show	VERB
ejpam-4655	402	10	by	by	ADP
ejpam-4655	402	11	example	example	NOUN
ejpam-4655	402	12	24	24	NUM
ejpam-4655	402	13	.	.	PUNCT
ejpam-4655	402	14	example	example	NOUN
ejpam-4655	403	1	24	24	NUM
ejpam-4655	403	2	.	.	PUNCT
ejpam-4655	404	1	consider	consider	VERB
ejpam-4655	404	2	the	the	DET
ejpam-4655	404	3	bigeneralized	bigeneralize	VERB
ejpam-4655	404	4	topological	topological	ADJ
ejpam-4655	404	5	spaces	space	NOUN
ejpam-4655	404	6	(	(	PUNCT
ejpam-4655	404	7	x,µ1	x,µ1	NOUN
ejpam-4655	404	8	,	,	PUNCT
ejpam-4655	404	9	µ2	µ2	PROPN
ejpam-4655	404	10	)	)	PUNCT
ejpam-4655	404	11	and	and	CCONJ
ejpam-4655	404	12	(	(	PUNCT
ejpam-4655	404	13	y	y	PROPN
ejpam-4655	404	14	,	,	PUNCT
ejpam-4655	404	15	η1	η1	NOUN
ejpam-4655	404	16	,	,	PUNCT
ejpam-4655	404	17	η2	η2	NOUN
ejpam-4655	404	18	)	)	PUNCT
ejpam-4655	405	1	where	where	SCONJ
ejpam-4655	405	2	x	x	X
ejpam-4655	405	3	=	=	PRON
ejpam-4655	405	4	{	{	PUNCT
ejpam-4655	405	5	p	p	X
ejpam-4655	405	6	,	,	PUNCT
ejpam-4655	405	7	q	q	ADJ
ejpam-4655	405	8	,	,	PUNCT
ejpam-4655	405	9	r	r	NOUN
ejpam-4655	405	10	,	,	PUNCT
ejpam-4655	405	11	s};y	s};y	ADJ
ejpam-4655	405	12	=	=	SYM
ejpam-4655	405	13	{	{	PUNCT
ejpam-4655	405	14	p1	p1	PROPN
ejpam-4655	405	15	,	,	PUNCT
ejpam-4655	405	16	q1	q1	PROPN
ejpam-4655	405	17	,	,	PUNCT
ejpam-4655	405	18	r1	r1	NOUN
ejpam-4655	405	19	,	,	PUNCT
ejpam-4655	405	20	s1	s1	NOUN
ejpam-4655	405	21	}	}	PUNCT
ejpam-4655	405	22	.	.	PUNCT
ejpam-4655	406	1	define	define	VERB
ejpam-4655	406	2	a	a	DET
ejpam-4655	406	3	map	map	NOUN
ejpam-4655	406	4	h	h	NOUN
ejpam-4655	406	5	:	:	PUNCT
ejpam-4655	406	6	(	(	PUNCT
ejpam-4655	406	7	x,µi	x,µi	NUM
ejpam-4655	406	8	)	)	PUNCT
ejpam-4655	406	9	→	→	PUNCT
ejpam-4655	406	10	(	(	PUNCT
ejpam-4655	406	11	y	y	PROPN
ejpam-4655	406	12	,	,	PUNCT
ejpam-4655	406	13	ηi	ηi	PROPN
ejpam-4655	406	14	)	)	PUNCT
ejpam-4655	406	15	for	for	ADP
ejpam-4655	406	16	i	i	PROPN
ejpam-4655	406	17	=	=	SYM
ejpam-4655	406	18	1	1	NUM
ejpam-4655	406	19	,	,	PUNCT
ejpam-4655	406	20	2	2	NUM
ejpam-4655	406	21	as	as	SCONJ
ejpam-4655	406	22	follows	follow	VERB
ejpam-4655	406	23	h(p	h(p	NOUN
ejpam-4655	406	24	)	)	PUNCT
ejpam-4655	406	25	=	=	SYM
ejpam-4655	406	26	p1;h(q	p1;h(q	NOUN
ejpam-4655	406	27	)	)	PUNCT
ejpam-4655	406	28	=	=	SYM
ejpam-4655	406	29	q1;h(r	q1;h(r	NOUN
ejpam-4655	406	30	)	)	PUNCT
ejpam-4655	407	1	=	=	SYM
ejpam-4655	407	2	r1;h(s	r1;h(s	NOUN
ejpam-4655	407	3	)	)	PUNCT
ejpam-4655	407	4	=	=	SYM
ejpam-4655	407	5	s1	s1	PROPN
ejpam-4655	407	6	.	.	PUNCT
ejpam-4655	408	1	clearly	clearly	ADV
ejpam-4655	408	2	,	,	PUNCT
ejpam-4655	408	3	h	h	NOUN
ejpam-4655	408	4	is	be	AUX
ejpam-4655	408	5	a	a	DET
ejpam-4655	408	6	surjective	surjective	ADJ
ejpam-4655	408	7	map	map	NOUN
ejpam-4655	408	8	.	.	PUNCT
ejpam-4655	409	1	y.	y.	PROPN
ejpam-4655	409	2	farhat	farhat	PROPN
ejpam-4655	409	3	et	et	PROPN
ejpam-4655	409	4	al	al	PROPN
ejpam-4655	409	5	.	.	PUNCT
ejpam-4655	409	6	/	/	SYM
ejpam-4655	409	7	eur	eur	PROPN
ejpam-4655	409	8	.	.	PUNCT
ejpam-4655	410	1	j.	j.	PROPN
ejpam-4655	410	2	pure	pure	PROPN
ejpam-4655	410	3	appl	appl	PROPN
ejpam-4655	410	4	.	.	PROPN
ejpam-4655	410	5	math	math	PROPN
ejpam-4655	410	6	,	,	PUNCT
ejpam-4655	410	7	16	16	NUM
ejpam-4655	410	8	(	(	PUNCT
ejpam-4655	410	9	1	1	NUM
ejpam-4655	410	10	)	)	PUNCT
ejpam-4655	410	11	(	(	PUNCT
ejpam-4655	410	12	2023	2023	NUM
ejpam-4655	410	13	)	)	PUNCT
ejpam-4655	410	14	,	,	PUNCT
ejpam-4655	410	15	386	386	NUM
ejpam-4655	410	16	-	-	SYM
ejpam-4655	410	17	403	403	NUM
ejpam-4655	410	18	396	396	NUM
ejpam-4655	410	19	(	(	PUNCT
ejpam-4655	410	20	a	a	X
ejpam-4655	410	21	)	)	PUNCT
ejpam-4655	410	22	let	let	VERB
ejpam-4655	410	23	µ1	µ1	NOUN
ejpam-4655	410	24	=	=	SYM
ejpam-4655	410	25	{	{	PUNCT
ejpam-4655	410	26	∅	∅	NOUN
ejpam-4655	410	27	,	,	PUNCT
ejpam-4655	410	28	{	{	PUNCT
ejpam-4655	410	29	p	p	X
ejpam-4655	410	30	}	}	PUNCT
ejpam-4655	410	31	,	,	PUNCT
ejpam-4655	410	32	{	{	PUNCT
ejpam-4655	410	33	r	r	NOUN
ejpam-4655	410	34	}	}	PUNCT
ejpam-4655	410	35	,	,	PUNCT
ejpam-4655	410	36	{	{	PUNCT
ejpam-4655	410	37	p	p	X
ejpam-4655	410	38	,	,	PUNCT
ejpam-4655	410	39	q	q	NOUN
ejpam-4655	410	40	}	}	PUNCT
ejpam-4655	410	41	,	,	PUNCT
ejpam-4655	410	42	{	{	PUNCT
ejpam-4655	410	43	p	p	X
ejpam-4655	410	44	,	,	PUNCT
ejpam-4655	410	45	r	r	NOUN
ejpam-4655	410	46	}	}	PUNCT
ejpam-4655	410	47	,	,	PUNCT
ejpam-4655	410	48	{	{	PUNCT
ejpam-4655	410	49	p	p	X
ejpam-4655	410	50	,	,	PUNCT
ejpam-4655	410	51	s	s	PART
ejpam-4655	410	52	}	}	PUNCT
ejpam-4655	410	53	,	,	PUNCT
ejpam-4655	410	54	{	{	PUNCT
ejpam-4655	410	55	q	q	X
ejpam-4655	410	56	,	,	PUNCT
ejpam-4655	410	57	r	r	NOUN
ejpam-4655	410	58	}	}	PUNCT
ejpam-4655	410	59	,	,	PUNCT
ejpam-4655	410	60	{	{	PUNCT
ejpam-4655	410	61	q	q	X
ejpam-4655	410	62	,	,	PUNCT
ejpam-4655	410	63	s	s	PART
ejpam-4655	410	64	}	}	PUNCT
ejpam-4655	410	65	,	,	PUNCT
ejpam-4655	410	66	{	{	PUNCT
ejpam-4655	410	67	r	r	NOUN
ejpam-4655	410	68	,	,	PUNCT
ejpam-4655	410	69	s	s	PART
ejpam-4655	410	70	}	}	PUNCT
ejpam-4655	410	71	,	,	PUNCT
ejpam-4655	410	72	{	{	PUNCT
ejpam-4655	410	73	p	p	X
ejpam-4655	410	74	,	,	PUNCT
ejpam-4655	410	75	q	q	ADJ
ejpam-4655	410	76	,	,	PUNCT
ejpam-4655	410	77	r	r	NOUN
ejpam-4655	410	78	}	}	PUNCT
ejpam-4655	410	79	,	,	PUNCT
ejpam-4655	410	80	{	{	PUNCT
ejpam-4655	410	81	p	p	X
ejpam-4655	410	82	,	,	PUNCT
ejpam-4655	410	83	q	q	X
ejpam-4655	410	84	,	,	PUNCT
ejpam-4655	410	85	s	s	PART
ejpam-4655	410	86	}	}	PUNCT
ejpam-4655	410	87	,	,	PUNCT
ejpam-4655	410	88	{	{	PUNCT
ejpam-4655	410	89	p	p	X
ejpam-4655	410	90	,	,	PUNCT
ejpam-4655	410	91	r	r	NOUN
ejpam-4655	410	92	,	,	PUNCT
ejpam-4655	410	93	s	s	PART
ejpam-4655	410	94	}	}	PUNCT
ejpam-4655	410	95	,	,	PUNCT
ejpam-4655	410	96	{	{	PUNCT
ejpam-4655	410	97	q	q	X
ejpam-4655	410	98	,	,	PUNCT
ejpam-4655	410	99	r	r	NOUN
ejpam-4655	410	100	,	,	PUNCT
ejpam-4655	410	101	s	s	PART
ejpam-4655	410	102	}	}	PUNCT
ejpam-4655	410	103	,	,	PUNCT
ejpam-4655	410	104	x};µ2	x};µ2	PROPN
ejpam-4655	410	105	=	=	PRON
ejpam-4655	410	106	{	{	PUNCT
ejpam-4655	410	107	∅	∅	NOUN
ejpam-4655	410	108	,	,	PUNCT
ejpam-4655	410	109	{	{	PUNCT
ejpam-4655	410	110	p	p	X
ejpam-4655	410	111	,	,	PUNCT
ejpam-4655	410	112	q	q	NOUN
ejpam-4655	410	113	}	}	PUNCT
ejpam-4655	410	114	,	,	PUNCT
ejpam-4655	410	115	{	{	PUNCT
ejpam-4655	410	116	q	q	X
ejpam-4655	410	117	,	,	PUNCT
ejpam-4655	410	118	r	r	NOUN
ejpam-4655	410	119	}	}	PUNCT
ejpam-4655	410	120	,	,	PUNCT
ejpam-4655	410	121	{	{	PUNCT
ejpam-4655	410	122	p	p	X
ejpam-4655	410	123	,	,	PUNCT
ejpam-4655	410	124	q	q	ADJ
ejpam-4655	410	125	,	,	PUNCT
ejpam-4655	410	126	r	r	NOUN
ejpam-4655	410	127	}	}	PUNCT
ejpam-4655	410	128	}	}	PUNCT
ejpam-4655	410	129	;	;	PUNCT
ejpam-4655	410	130	η1	η1	NOUN
ejpam-4655	410	131	=	=	SYM
ejpam-4655	410	132	{	{	PUNCT
ejpam-4655	410	133	∅	∅	NOUN
ejpam-4655	410	134	,	,	PUNCT
ejpam-4655	410	135	{	{	PUNCT
ejpam-4655	410	136	p1	p1	NOUN
ejpam-4655	410	137	}	}	PUNCT
ejpam-4655	410	138	,	,	PUNCT
ejpam-4655	410	139	{	{	PUNCT
ejpam-4655	410	140	r1	r1	PROPN
ejpam-4655	410	141	}	}	PUNCT
ejpam-4655	410	142	,	,	PUNCT
ejpam-4655	410	143	{	{	PUNCT
ejpam-4655	410	144	p1	p1	NOUN
ejpam-4655	410	145	,	,	PUNCT
ejpam-4655	410	146	q1	q1	PROPN
ejpam-4655	410	147	}	}	PUNCT
ejpam-4655	410	148	,	,	PUNCT
ejpam-4655	410	149	{	{	PUNCT
ejpam-4655	410	150	p1	p1	NOUN
ejpam-4655	410	151	,	,	PUNCT
ejpam-4655	410	152	r1	r1	PROPN
ejpam-4655	410	153	}	}	PUNCT
ejpam-4655	410	154	,	,	PUNCT
ejpam-4655	410	155	{	{	PUNCT
ejpam-4655	410	156	p1	p1	NOUN
ejpam-4655	410	157	,	,	PUNCT
ejpam-4655	410	158	s1	s1	PROPN
ejpam-4655	410	159	}	}	PUNCT
ejpam-4655	410	160	,	,	PUNCT
ejpam-4655	410	161	{	{	PUNCT
ejpam-4655	410	162	q1	q1	NOUN
ejpam-4655	410	163	,	,	PUNCT
ejpam-4655	410	164	r1	r1	PROPN
ejpam-4655	410	165	}	}	PUNCT
ejpam-4655	410	166	,	,	PUNCT
ejpam-4655	410	167	{	{	PUNCT
ejpam-4655	410	168	q1	q1	NOUN
ejpam-4655	410	169	,	,	PUNCT
ejpam-4655	410	170	s1	s1	PROPN
ejpam-4655	410	171	}	}	PUNCT
ejpam-4655	410	172	,	,	PUNCT
ejpam-4655	410	173	{	{	PUNCT
ejpam-4655	410	174	r1	r1	NOUN
ejpam-4655	410	175	,	,	PUNCT
ejpam-4655	410	176	s1	s1	PROPN
ejpam-4655	410	177	}	}	PUNCT
ejpam-4655	410	178	,	,	PUNCT
ejpam-4655	410	179	{	{	PUNCT
ejpam-4655	410	180	p1	p1	PROPN
ejpam-4655	410	181	,	,	PUNCT
ejpam-4655	410	182	q1	q1	PROPN
ejpam-4655	410	183	,	,	PUNCT
ejpam-4655	410	184	r1	r1	PROPN
ejpam-4655	410	185	}	}	PUNCT
ejpam-4655	410	186	,	,	PUNCT
ejpam-4655	410	187	{	{	PUNCT
ejpam-4655	410	188	p1	p1	PROPN
ejpam-4655	410	189	,	,	PUNCT
ejpam-4655	410	190	q1	q1	PROPN
ejpam-4655	410	191	,	,	PUNCT
ejpam-4655	410	192	s1	s1	PROPN
ejpam-4655	410	193	}	}	PUNCT
ejpam-4655	410	194	,	,	PUNCT
ejpam-4655	410	195	{	{	PUNCT
ejpam-4655	410	196	p1	p1	NOUN
ejpam-4655	410	197	,	,	PUNCT
ejpam-4655	410	198	r1	r1	NOUN
ejpam-4655	410	199	,	,	PUNCT
ejpam-4655	410	200	s1	s1	PROPN
ejpam-4655	410	201	}	}	PUNCT
ejpam-4655	410	202	,	,	PUNCT
ejpam-4655	410	203	{	{	PUNCT
ejpam-4655	410	204	q1	q1	PROPN
ejpam-4655	410	205	,	,	PUNCT
ejpam-4655	410	206	r1	r1	NOUN
ejpam-4655	410	207	,	,	PUNCT
ejpam-4655	410	208	s1	s1	PROPN
ejpam-4655	410	209	}	}	PUNCT
ejpam-4655	410	210	,	,	PUNCT
ejpam-4655	410	211	y	y	PROPN
ejpam-4655	410	212	}	}	PUNCT
ejpam-4655	410	213	and	and	CCONJ
ejpam-4655	410	214	η2	η2	ADJ
ejpam-4655	410	215	=	=	SYM
ejpam-4655	410	216	{	{	PUNCT
ejpam-4655	410	217	∅	∅	NOUN
ejpam-4655	410	218	,	,	PUNCT
ejpam-4655	410	219	{	{	PUNCT
ejpam-4655	410	220	p1	p1	PROPN
ejpam-4655	410	221	,	,	PUNCT
ejpam-4655	410	222	q1	q1	PROPN
ejpam-4655	410	223	,	,	PUNCT
ejpam-4655	410	224	r1	r1	PROPN
ejpam-4655	410	225	}	}	PUNCT
ejpam-4655	410	226	,	,	PUNCT
ejpam-4655	410	227	{	{	PUNCT
ejpam-4655	410	228	p1	p1	PROPN
ejpam-4655	410	229	,	,	PUNCT
ejpam-4655	410	230	q1	q1	PROPN
ejpam-4655	410	231	,	,	PUNCT
ejpam-4655	410	232	s1	s1	PROPN
ejpam-4655	410	233	}	}	PUNCT
ejpam-4655	410	234	,	,	PUNCT
ejpam-4655	410	235	{	{	PUNCT
ejpam-4655	410	236	p1	p1	PROPN
ejpam-4655	410	237	,	,	PUNCT
ejpam-4655	410	238	q1	q1	PROPN
ejpam-4655	410	239	,	,	PUNCT
ejpam-4655	410	240	r1	r1	NOUN
ejpam-4655	410	241	,	,	PUNCT
ejpam-4655	410	242	s1	s1	NOUN
ejpam-4655	410	243	}	}	PUNCT
ejpam-4655	410	244	}	}	PUNCT
ejpam-4655	410	245	.	.	PUNCT
ejpam-4655	411	1	here	here	ADV
ejpam-4655	411	2	h−1(p	h−1(p	NOUN
ejpam-4655	411	3	)	)	PUNCT
ejpam-4655	411	4	∈	∈	PROPN
ejpam-4655	411	5	µ1	µ1	NOUN
ejpam-4655	411	6	whenever	whenever	SCONJ
ejpam-4655	411	7	p	p	PRON
ejpam-4655	411	8	∈	∈	PROPN
ejpam-4655	411	9	η1	η1	NOUN
ejpam-4655	411	10	.	.	PUNCT
ejpam-4655	412	1	therefore	therefore	ADV
ejpam-4655	412	2	,	,	PUNCT
ejpam-4655	412	3	h	h	NOUN
ejpam-4655	412	4	is	be	AUX
ejpam-4655	412	5	a	a	DET
ejpam-4655	412	6	(	(	PUNCT
ejpam-4655	412	7	µ1	µ1	ADJ
ejpam-4655	412	8	,	,	PUNCT
ejpam-4655	412	9	η1)-continuous	η1)-continuous	ADJ
ejpam-4655	412	10	map	map	NOUN
ejpam-4655	412	11	.	.	PUNCT
ejpam-4655	413	1	let	let	VERB
ejpam-4655	413	2	j	j	PROPN
ejpam-4655	413	3	=	=	PUNCT
ejpam-4655	413	4	{	{	PUNCT
ejpam-4655	413	5	p1	p1	PROPN
ejpam-4655	413	6	,	,	PUNCT
ejpam-4655	413	7	q1	q1	PROPN
ejpam-4655	413	8	,	,	PUNCT
ejpam-4655	413	9	s1	s1	NOUN
ejpam-4655	413	10	}	}	PUNCT
ejpam-4655	413	11	.	.	PUNCT
ejpam-4655	414	1	then	then	ADV
ejpam-4655	414	2	j	j	PROPN
ejpam-4655	414	3	∈	∈	PROPN
ejpam-4655	414	4	η2	η2	PROPN
ejpam-4655	414	5	.	.	PUNCT
ejpam-4655	415	1	but	but	CCONJ
ejpam-4655	415	2	h	h	NOUN
ejpam-4655	415	3	−1(j	−1(j	NOUN
ejpam-4655	415	4	)	)	PUNCT
ejpam-4655	415	5	/∈	/∈	PUNCT
ejpam-4655	416	1	µ2	µ2	PROPN
ejpam-4655	416	2	.	.	PUNCT
ejpam-4655	417	1	thus	thus	ADV
ejpam-4655	417	2	,	,	PUNCT
ejpam-4655	417	3	h	h	NOUN
ejpam-4655	417	4	is	be	AUX
ejpam-4655	417	5	not	not	PART
ejpam-4655	417	6	a	a	DET
ejpam-4655	417	7	(	(	PUNCT
ejpam-4655	417	8	µ2	µ2	PROPN
ejpam-4655	417	9	,	,	PUNCT
ejpam-4655	417	10	η2)-continuous	η2)-continuous	ADJ
ejpam-4655	417	11	map	map	NOUN
ejpam-4655	417	12	.	.	PUNCT
ejpam-4655	418	1	here	here	ADV
ejpam-4655	418	2	{	{	PUNCT
ejpam-4655	418	3	p1	p1	PROPN
ejpam-4655	418	4	}	}	PUNCT
ejpam-4655	418	5	,	,	PUNCT
ejpam-4655	418	6	{	{	PUNCT
ejpam-4655	418	7	r1	r1	PROPN
ejpam-4655	418	8	}	}	PUNCT
ejpam-4655	418	9	,	,	PUNCT
ejpam-4655	418	10	{	{	PUNCT
ejpam-4655	418	11	p1	p1	NOUN
ejpam-4655	418	12	,	,	PUNCT
ejpam-4655	418	13	q1	q1	PROPN
ejpam-4655	418	14	}	}	PUNCT
ejpam-4655	418	15	,	,	PUNCT
ejpam-4655	418	16	{	{	PUNCT
ejpam-4655	418	17	p1	p1	NOUN
ejpam-4655	418	18	,	,	PUNCT
ejpam-4655	418	19	r1	r1	PROPN
ejpam-4655	418	20	}	}	PUNCT
ejpam-4655	418	21	,	,	PUNCT
ejpam-4655	418	22	{	{	PUNCT
ejpam-4655	418	23	p1	p1	NOUN
ejpam-4655	418	24	,	,	PUNCT
ejpam-4655	418	25	s1	s1	PROPN
ejpam-4655	418	26	}	}	PUNCT
ejpam-4655	418	27	,	,	PUNCT
ejpam-4655	418	28	{	{	PUNCT
ejpam-4655	418	29	q1	q1	NOUN
ejpam-4655	418	30	,	,	PUNCT
ejpam-4655	418	31	r1	r1	PROPN
ejpam-4655	418	32	}	}	PUNCT
ejpam-4655	418	33	,	,	PUNCT
ejpam-4655	418	34	{	{	PUNCT
ejpam-4655	418	35	q1	q1	NOUN
ejpam-4655	418	36	,	,	PUNCT
ejpam-4655	418	37	s1	s1	PROPN
ejpam-4655	418	38	}	}	PUNCT
ejpam-4655	418	39	,	,	PUNCT
ejpam-4655	418	40	{	{	PUNCT
ejpam-4655	418	41	r1	r1	NOUN
ejpam-4655	418	42	,	,	PUNCT
ejpam-4655	418	43	s1	s1	PROPN
ejpam-4655	418	44	}	}	PUNCT
ejpam-4655	418	45	,	,	PUNCT
ejpam-4655	418	46	{	{	PUNCT
ejpam-4655	418	47	p1	p1	PROPN
ejpam-4655	418	48	,	,	PUNCT
ejpam-4655	418	49	q1	q1	PROPN
ejpam-4655	418	50	,	,	PUNCT
ejpam-4655	418	51	r1	r1	PROPN
ejpam-4655	418	52	}	}	PUNCT
ejpam-4655	418	53	,	,	PUNCT
ejpam-4655	418	54	{	{	PUNCT
ejpam-4655	418	55	p1	p1	PROPN
ejpam-4655	418	56	,	,	PUNCT
ejpam-4655	418	57	q1	q1	PROPN
ejpam-4655	418	58	,	,	PUNCT
ejpam-4655	418	59	s1	s1	PROPN
ejpam-4655	418	60	}	}	PUNCT
ejpam-4655	418	61	,	,	PUNCT
ejpam-4655	418	62	{	{	PUNCT
ejpam-4655	418	63	p1	p1	NOUN
ejpam-4655	418	64	,	,	PUNCT
ejpam-4655	418	65	r1	r1	NOUN
ejpam-4655	418	66	,	,	PUNCT
ejpam-4655	418	67	s1	s1	PROPN
ejpam-4655	418	68	}	}	PUNCT
ejpam-4655	418	69	,	,	PUNCT
ejpam-4655	418	70	{	{	PUNCT
ejpam-4655	418	71	q1	q1	PROPN
ejpam-4655	418	72	,	,	PUNCT
ejpam-4655	418	73	r1	r1	NOUN
ejpam-4655	418	74	,	,	PUNCT
ejpam-4655	418	75	s1	s1	NOUN
ejpam-4655	418	76	}	}	PUNCT
ejpam-4655	418	77	and	and	CCONJ
ejpam-4655	418	78	y	y	PROPN
ejpam-4655	418	79	are	be	AUX
ejpam-4655	418	80	η2	η2	ADJ
ejpam-4655	418	81	-	-	PUNCT
ejpam-4655	418	82	dense	dense	ADJ
ejpam-4655	418	83	subsets	subset	NOUN
ejpam-4655	418	84	of	of	ADP
ejpam-4655	418	85	y.	y.	PROPN
ejpam-4655	418	86	also	also	ADV
ejpam-4655	418	87	,	,	PUNCT
ejpam-4655	418	88	every	every	DET
ejpam-4655	418	89	η2	η2	ADJ
ejpam-4655	418	90	-	-	PUNCT
ejpam-4655	418	91	dense	dense	ADJ
ejpam-4655	418	92	set	set	NOUN
ejpam-4655	418	93	is	be	AUX
ejpam-4655	418	94	η1	η1	NOUN
ejpam-4655	418	95	-	-	PUNCT
ejpam-4655	418	96	open	open	ADJ
ejpam-4655	418	97	.	.	PUNCT
ejpam-4655	419	1	therefore	therefore	ADV
ejpam-4655	419	2	,	,	PUNCT
ejpam-4655	419	3	y	y	PROPN
ejpam-4655	419	4	is	be	AUX
ejpam-4655	419	5	a	a	DET
ejpam-4655	419	6	(	(	PUNCT
ejpam-4655	419	7	1	1	NUM
ejpam-4655	419	8	,	,	PUNCT
ejpam-4655	419	9	2)-bigeneralized	2)-bigeneralized	NUM
ejpam-4655	419	10	submaximal	submaximal	ADJ
ejpam-4655	419	11	space	space	NOUN
ejpam-4655	419	12	.	.	PUNCT
ejpam-4655	420	1	let	let	VERB
ejpam-4655	420	2	k	k	NOUN
ejpam-4655	420	3	=	=	PUNCT
ejpam-4655	420	4	{	{	PUNCT
ejpam-4655	420	5	q	q	X
ejpam-4655	420	6	}	}	PUNCT
ejpam-4655	420	7	.	.	PUNCT
ejpam-4655	421	1	then	then	ADV
ejpam-4655	421	2	cµ2(k	cµ2(k	PROPN
ejpam-4655	421	3	)	)	PUNCT
ejpam-4655	421	4	=	=	PUNCT
ejpam-4655	422	1	x.	x.	NOUN
ejpam-4655	422	2	but	but	CCONJ
ejpam-4655	422	3	k	k	PROPN
ejpam-4655	422	4	/∈	/∈	PUNCT
ejpam-4655	422	5	µ1	µ1	PROPN
ejpam-4655	422	6	.	.	PUNCT
ejpam-4655	423	1	thus	thus	ADV
ejpam-4655	423	2	,	,	PUNCT
ejpam-4655	423	3	x	x	PRON
ejpam-4655	423	4	is	be	AUX
ejpam-4655	423	5	not	not	PART
ejpam-4655	423	6	a	a	DET
ejpam-4655	423	7	(	(	PUNCT
ejpam-4655	423	8	1	1	NUM
ejpam-4655	423	9	,	,	PUNCT
ejpam-4655	423	10	2)-bigeneralized	2)-bigeneralized	NUM
ejpam-4655	423	11	submaximal	submaximal	ADJ
ejpam-4655	423	12	space	space	NOUN
ejpam-4655	423	13	.	.	PUNCT
ejpam-4655	424	1	(	(	PUNCT
ejpam-4655	424	2	b	b	X
ejpam-4655	424	3	)	)	PUNCT
ejpam-4655	424	4	let	let	VERB
ejpam-4655	424	5	µ1	µ1	NOUN
ejpam-4655	424	6	,	,	PUNCT
ejpam-4655	424	7	η1	η1	NOUN
ejpam-4655	424	8	and	and	CCONJ
ejpam-4655	424	9	µ2	µ2	PROPN
ejpam-4655	424	10	are	be	AUX
ejpam-4655	424	11	generalized	generalized	ADJ
ejpam-4655	424	12	topologies	topology	NOUN
ejpam-4655	424	13	defined	define	VERB
ejpam-4655	424	14	as	as	ADP
ejpam-4655	424	15	in	in	ADP
ejpam-4655	424	16	(	(	PUNCT
ejpam-4655	424	17	a	a	NOUN
ejpam-4655	424	18	)	)	PUNCT
ejpam-4655	424	19	.	.	PUNCT
ejpam-4655	425	1	take	take	VERB
ejpam-4655	425	2	η2	η2	ADJ
ejpam-4655	425	3	=	=	SYM
ejpam-4655	425	4	{	{	PUNCT
ejpam-4655	425	5	∅	∅	NOUN
ejpam-4655	425	6	,	,	PUNCT
ejpam-4655	425	7	{	{	PUNCT
ejpam-4655	425	8	p1	p1	PROPN
ejpam-4655	425	9	,	,	PUNCT
ejpam-4655	425	10	q1	q1	PROPN
ejpam-4655	425	11	,	,	PUNCT
ejpam-4655	425	12	r1	r1	PROPN
ejpam-4655	425	13	}	}	PUNCT
ejpam-4655	425	14	,	,	PUNCT
ejpam-4655	425	15	{	{	PUNCT
ejpam-4655	425	16	p1	p1	NOUN
ejpam-4655	425	17	,	,	PUNCT
ejpam-4655	425	18	r1	r1	NOUN
ejpam-4655	425	19	,	,	PUNCT
ejpam-4655	425	20	s1	s1	PROPN
ejpam-4655	425	21	}	}	PUNCT
ejpam-4655	425	22	,	,	PUNCT
ejpam-4655	425	23	y	y	PROPN
ejpam-4655	425	24	}	}	PUNCT
ejpam-4655	425	25	.	.	PUNCT
ejpam-4655	426	1	here	here	ADV
ejpam-4655	426	2	h−1(m	h−1(m	PROPN
ejpam-4655	426	3	)	)	PUNCT
ejpam-4655	426	4	∈	∈	PROPN
ejpam-4655	426	5	µ1	µ1	PROPN
ejpam-4655	426	6	whenever	whenever	SCONJ
ejpam-4655	426	7	m	m	VERB
ejpam-4655	426	8	∈	∈	PROPN
ejpam-4655	426	9	η1	η1	NOUN
ejpam-4655	426	10	.	.	PUNCT
ejpam-4655	427	1	therefore	therefore	ADV
ejpam-4655	427	2	,	,	PUNCT
ejpam-4655	427	3	h	h	NOUN
ejpam-4655	427	4	is	be	AUX
ejpam-4655	427	5	a	a	DET
ejpam-4655	427	6	(	(	PUNCT
ejpam-4655	427	7	µ1	µ1	ADJ
ejpam-4655	427	8	,	,	PUNCT
ejpam-4655	427	9	η1)-continuous	η1)-continuous	ADJ
ejpam-4655	427	10	map	map	NOUN
ejpam-4655	427	11	.	.	PUNCT
ejpam-4655	428	1	let	let	VERB
ejpam-4655	428	2	q	q	NOUN
ejpam-4655	428	3	=	=	PUNCT
ejpam-4655	428	4	{	{	PUNCT
ejpam-4655	428	5	p1	p1	PROPN
ejpam-4655	428	6	,	,	PUNCT
ejpam-4655	428	7	r1	r1	NOUN
ejpam-4655	428	8	,	,	PUNCT
ejpam-4655	428	9	s1	s1	NOUN
ejpam-4655	428	10	}	}	PUNCT
ejpam-4655	428	11	.	.	PUNCT
ejpam-4655	429	1	then	then	ADV
ejpam-4655	429	2	q	q	PROPN
ejpam-4655	429	3	∈	∈	PROPN
ejpam-4655	429	4	η2	η2	PROPN
ejpam-4655	429	5	.	.	PUNCT
ejpam-4655	430	1	but	but	CCONJ
ejpam-4655	430	2	h−1(q	h−1(q	PROPN
ejpam-4655	430	3	)	)	PUNCT
ejpam-4655	430	4	/∈	/∈	PUNCT
ejpam-4655	431	1	µ2	µ2	PROPN
ejpam-4655	431	2	.	.	PUNCT
ejpam-4655	432	1	thus	thus	ADV
ejpam-4655	432	2	,	,	PUNCT
ejpam-4655	432	3	h	h	NOUN
ejpam-4655	432	4	is	be	AUX
ejpam-4655	432	5	not	not	PART
ejpam-4655	432	6	a	a	DET
ejpam-4655	432	7	(	(	PUNCT
ejpam-4655	432	8	µ2	µ2	ADJ
ejpam-4655	432	9	,	,	PUNCT
ejpam-4655	432	10	η2)continuous	η2)continuous	ADJ
ejpam-4655	432	11	map	map	NOUN
ejpam-4655	432	12	.	.	PUNCT
ejpam-4655	433	1	here	here	ADV
ejpam-4655	433	2	{	{	PUNCT
ejpam-4655	433	3	p1	p1	PROPN
ejpam-4655	433	4	,	,	PUNCT
ejpam-4655	433	5	q1	q1	PROPN
ejpam-4655	433	6	,	,	PUNCT
ejpam-4655	433	7	r1	r1	PROPN
ejpam-4655	433	8	}	}	PUNCT
ejpam-4655	433	9	,	,	PUNCT
ejpam-4655	433	10	{	{	PUNCT
ejpam-4655	433	11	p1	p1	NOUN
ejpam-4655	433	12	,	,	PUNCT
ejpam-4655	433	13	r1	r1	NOUN
ejpam-4655	433	14	,	,	PUNCT
ejpam-4655	433	15	s1	s1	NOUN
ejpam-4655	433	16	}	}	PUNCT
ejpam-4655	433	17	and	and	CCONJ
ejpam-4655	433	18	y	y	PROPN
ejpam-4655	433	19	are	be	AUX
ejpam-4655	433	20	η1	η1	NOUN
ejpam-4655	433	21	-	-	PUNCT
ejpam-4655	433	22	dense	dense	ADJ
ejpam-4655	433	23	subsets	subset	NOUN
ejpam-4655	433	24	of	of	ADP
ejpam-4655	433	25	y.	y.	PROPN
ejpam-4655	433	26	also	also	ADV
ejpam-4655	433	27	,	,	PUNCT
ejpam-4655	433	28	every	every	DET
ejpam-4655	433	29	η1	η1	NOUN
ejpam-4655	433	30	-	-	PUNCT
ejpam-4655	433	31	dense	dense	ADJ
ejpam-4655	433	32	set	set	NOUN
ejpam-4655	433	33	is	be	AUX
ejpam-4655	433	34	η2	η2	NOUN
ejpam-4655	433	35	-	-	PUNCT
ejpam-4655	433	36	open	open	ADJ
ejpam-4655	433	37	.	.	PUNCT
ejpam-4655	434	1	therefore	therefore	ADV
ejpam-4655	434	2	,	,	PUNCT
ejpam-4655	434	3	y	y	PROPN
ejpam-4655	434	4	is	be	AUX
ejpam-4655	434	5	a	a	DET
ejpam-4655	434	6	(	(	PUNCT
ejpam-4655	434	7	2	2	NUM
ejpam-4655	434	8	,	,	PUNCT
ejpam-4655	434	9	1)-bigeneralized	1)-bigeneralized	NUM
ejpam-4655	434	10	submaximal	submaximal	ADJ
ejpam-4655	434	11	space	space	NOUN
ejpam-4655	434	12	.	.	PUNCT
ejpam-4655	435	1	let	let	VERB
ejpam-4655	435	2	j	j	PROPN
ejpam-4655	435	3	=	=	PUNCT
ejpam-4655	435	4	{	{	PUNCT
ejpam-4655	435	5	p	p	X
ejpam-4655	435	6	,	,	PUNCT
ejpam-4655	435	7	r	r	NOUN
ejpam-4655	435	8	,	,	PUNCT
ejpam-4655	435	9	s	s	PART
ejpam-4655	435	10	}	}	PUNCT
ejpam-4655	435	11	.	.	PUNCT
ejpam-4655	436	1	then	then	ADV
ejpam-4655	436	2	cµ1(j	cµ1(j	VERB
ejpam-4655	436	3	)	)	PUNCT
ejpam-4655	436	4	=	=	PUNCT
ejpam-4655	437	1	x.	x.	NOUN
ejpam-4655	437	2	but	but	CCONJ
ejpam-4655	437	3	j	j	PROPN
ejpam-4655	437	4	/∈	/∈	PROPN
ejpam-4655	438	1	µ2	µ2	PROPN
ejpam-4655	438	2	.	.	PUNCT
ejpam-4655	439	1	thus	thus	ADV
ejpam-4655	439	2	,	,	PUNCT
ejpam-4655	439	3	x	x	PRON
ejpam-4655	439	4	is	be	AUX
ejpam-4655	439	5	not	not	PART
ejpam-4655	439	6	a	a	DET
ejpam-4655	439	7	(	(	PUNCT
ejpam-4655	439	8	2	2	NUM
ejpam-4655	439	9	,	,	PUNCT
ejpam-4655	439	10	1)-bigeneralized	1)-bigeneralized	NUM
ejpam-4655	439	11	submaximal	submaximal	ADJ
ejpam-4655	439	12	space	space	NOUN
ejpam-4655	439	13	.	.	PUNCT
ejpam-4655	440	1	(	(	PUNCT
ejpam-4655	440	2	c	c	X
ejpam-4655	440	3	)	)	PUNCT
ejpam-4655	440	4	let	let	VERB
ejpam-4655	440	5	µ1	µ1	NOUN
ejpam-4655	440	6	=	=	SYM
ejpam-4655	440	7	{	{	PUNCT
ejpam-4655	440	8	∅	∅	NOUN
ejpam-4655	440	9	,	,	PUNCT
ejpam-4655	440	10	{	{	PUNCT
ejpam-4655	440	11	q	q	X
ejpam-4655	440	12	,	,	PUNCT
ejpam-4655	440	13	s	s	PART
ejpam-4655	440	14	}	}	PUNCT
ejpam-4655	440	15	,	,	PUNCT
ejpam-4655	440	16	{	{	PUNCT
ejpam-4655	440	17	r	r	NOUN
ejpam-4655	440	18	,	,	PUNCT
ejpam-4655	440	19	s	s	PART
ejpam-4655	440	20	}	}	PUNCT
ejpam-4655	440	21	,	,	PUNCT
ejpam-4655	440	22	{	{	PUNCT
ejpam-4655	440	23	q	q	X
ejpam-4655	440	24	,	,	PUNCT
ejpam-4655	440	25	r	r	NOUN
ejpam-4655	440	26	,	,	PUNCT
ejpam-4655	440	27	s}};µ2	s}};µ2	VERB
ejpam-4655	440	28	=	=	SYM
ejpam-4655	440	29	{	{	PUNCT
ejpam-4655	440	30	∅	∅	NOUN
ejpam-4655	440	31	,	,	PUNCT
ejpam-4655	440	32	{	{	PUNCT
ejpam-4655	440	33	p	p	X
ejpam-4655	440	34	}	}	PUNCT
ejpam-4655	440	35	,	,	PUNCT
ejpam-4655	440	36	{	{	PUNCT
ejpam-4655	440	37	p	p	X
ejpam-4655	440	38	,	,	PUNCT
ejpam-4655	440	39	s	s	PART
ejpam-4655	440	40	}	}	PUNCT
ejpam-4655	440	41	,	,	PUNCT
ejpam-4655	440	42	{	{	PUNCT
ejpam-4655	440	43	q	q	X
ejpam-4655	440	44	,	,	PUNCT
ejpam-4655	440	45	s	s	PART
ejpam-4655	440	46	}	}	PUNCT
ejpam-4655	440	47	,	,	PUNCT
ejpam-4655	440	48	{	{	PUNCT
ejpam-4655	440	49	p	p	X
ejpam-4655	440	50	,	,	PUNCT
ejpam-4655	440	51	q	q	ADJ
ejpam-4655	440	52	,	,	PUNCT
ejpam-4655	440	53	s	s	PART
ejpam-4655	440	54	}	}	PUNCT
ejpam-4655	440	55	}	}	PUNCT
ejpam-4655	440	56	;	;	PUNCT
ejpam-4655	440	57	η1	η1	NOUN
ejpam-4655	440	58	=	=	SYM
ejpam-4655	440	59	{	{	PUNCT
ejpam-4655	440	60	∅	∅	NOUN
ejpam-4655	440	61	,	,	PUNCT
ejpam-4655	440	62	{	{	PUNCT
ejpam-4655	440	63	p1	p1	NOUN
ejpam-4655	440	64	,	,	PUNCT
ejpam-4655	440	65	q1	q1	PROPN
ejpam-4655	440	66	}	}	PUNCT
ejpam-4655	440	67	,	,	PUNCT
ejpam-4655	440	68	{	{	PUNCT
ejpam-4655	440	69	p1	p1	NOUN
ejpam-4655	440	70	,	,	PUNCT
ejpam-4655	440	71	s1	s1	PROPN
ejpam-4655	440	72	}	}	PUNCT
ejpam-4655	440	73	,	,	PUNCT
ejpam-4655	440	74	{	{	PUNCT
ejpam-4655	440	75	p1	p1	PROPN
ejpam-4655	440	76	,	,	PUNCT
ejpam-4655	440	77	q1	q1	PROPN
ejpam-4655	440	78	,	,	PUNCT
ejpam-4655	440	79	r1	r1	PROPN
ejpam-4655	440	80	}	}	PUNCT
ejpam-4655	440	81	,	,	PUNCT
ejpam-4655	440	82	{	{	PUNCT
ejpam-4655	440	83	p1	p1	PROPN
ejpam-4655	440	84	,	,	PUNCT
ejpam-4655	440	85	q1	q1	PROPN
ejpam-4655	440	86	,	,	PUNCT
ejpam-4655	440	87	s1	s1	PROPN
ejpam-4655	440	88	}	}	PUNCT
ejpam-4655	440	89	,	,	PUNCT
ejpam-4655	440	90	{	{	PUNCT
ejpam-4655	440	91	p1	p1	NOUN
ejpam-4655	440	92	,	,	PUNCT
ejpam-4655	440	93	r1	r1	NOUN
ejpam-4655	440	94	,	,	PUNCT
ejpam-4655	440	95	s1	s1	PROPN
ejpam-4655	440	96	}	}	PUNCT
ejpam-4655	440	97	,	,	PUNCT
ejpam-4655	440	98	y	y	PROPN
ejpam-4655	440	99	}	}	PUNCT
ejpam-4655	440	100	and	and	CCONJ
ejpam-4655	440	101	η2	η2	ADJ
ejpam-4655	440	102	=	=	SYM
ejpam-4655	440	103	{	{	PUNCT
ejpam-4655	440	104	∅	∅	NOUN
ejpam-4655	440	105	,	,	PUNCT
ejpam-4655	440	106	{	{	PUNCT
ejpam-4655	440	107	p1	p1	NOUN
ejpam-4655	440	108	}	}	PUNCT
ejpam-4655	440	109	,	,	PUNCT
ejpam-4655	440	110	{	{	PUNCT
ejpam-4655	440	111	p1	p1	NOUN
ejpam-4655	440	112	,	,	PUNCT
ejpam-4655	440	113	s1	s1	PROPN
ejpam-4655	440	114	}	}	PUNCT
ejpam-4655	440	115	,	,	PUNCT
ejpam-4655	440	116	{	{	PUNCT
ejpam-4655	440	117	q1	q1	NOUN
ejpam-4655	440	118	,	,	PUNCT
ejpam-4655	440	119	s1	s1	PROPN
ejpam-4655	440	120	}	}	PUNCT
ejpam-4655	440	121	,	,	PUNCT
ejpam-4655	440	122	{	{	PUNCT
ejpam-4655	440	123	p1	p1	PROPN
ejpam-4655	440	124	,	,	PUNCT
ejpam-4655	440	125	q1	q1	PROPN
ejpam-4655	440	126	,	,	PUNCT
ejpam-4655	440	127	s1	s1	NOUN
ejpam-4655	440	128	}	}	PUNCT
ejpam-4655	440	129	}	}	PUNCT
ejpam-4655	440	130	.	.	PUNCT
ejpam-4655	441	1	here	here	ADV
ejpam-4655	441	2	h−1(p	h−1(p	NOUN
ejpam-4655	441	3	)	)	PUNCT
ejpam-4655	442	1	∈	∈	PROPN
ejpam-4655	442	2	µ2	µ2	NOUN
ejpam-4655	442	3	whenever	whenever	SCONJ
ejpam-4655	442	4	p	p	PROPN
ejpam-4655	442	5	∈	∈	PROPN
ejpam-4655	442	6	η2	η2	PROPN
ejpam-4655	442	7	.	.	PUNCT
ejpam-4655	443	1	therefore	therefore	ADV
ejpam-4655	443	2	,	,	PUNCT
ejpam-4655	443	3	h	h	NOUN
ejpam-4655	443	4	is	be	AUX
ejpam-4655	443	5	a	a	DET
ejpam-4655	443	6	(	(	PUNCT
ejpam-4655	443	7	µ2	µ2	PROPN
ejpam-4655	443	8	,	,	PUNCT
ejpam-4655	443	9	η2)-continuous	η2)-continuous	ADJ
ejpam-4655	443	10	map	map	NOUN
ejpam-4655	443	11	.	.	PUNCT
ejpam-4655	444	1	let	let	VERB
ejpam-4655	444	2	k	k	NOUN
ejpam-4655	444	3	=	=	PRON
ejpam-4655	444	4	{	{	PUNCT
ejpam-4655	444	5	p1	p1	PROPN
ejpam-4655	444	6	,	,	PUNCT
ejpam-4655	444	7	q1	q1	PROPN
ejpam-4655	444	8	}	}	PUNCT
ejpam-4655	444	9	.	.	PUNCT
ejpam-4655	445	1	then	then	ADV
ejpam-4655	445	2	k	k	PROPN
ejpam-4655	445	3	∈	∈	PROPN
ejpam-4655	445	4	η1	η1	NOUN
ejpam-4655	445	5	.	.	PUNCT
ejpam-4655	446	1	but	but	CCONJ
ejpam-4655	446	2	h	h	NOUN
ejpam-4655	446	3	−1(k	−1(k	NOUN
ejpam-4655	446	4	)	)	PUNCT
ejpam-4655	446	5	/∈	/∈	PUNCT
ejpam-4655	447	1	µ1	µ1	PROPN
ejpam-4655	447	2	.	.	PUNCT
ejpam-4655	448	1	thus	thus	ADV
ejpam-4655	448	2	,	,	PUNCT
ejpam-4655	448	3	h	h	NOUN
ejpam-4655	448	4	is	be	AUX
ejpam-4655	448	5	not	not	PART
ejpam-4655	448	6	a	a	DET
ejpam-4655	448	7	(	(	PUNCT
ejpam-4655	448	8	µ1	µ1	ADJ
ejpam-4655	448	9	,	,	PUNCT
ejpam-4655	448	10	η1)-continuous	η1)-continuous	ADJ
ejpam-4655	448	11	map	map	NOUN
ejpam-4655	448	12	.	.	PUNCT
ejpam-4655	449	1	here	here	ADV
ejpam-4655	449	2	{	{	PUNCT
ejpam-4655	449	3	p1	p1	PROPN
ejpam-4655	449	4	,	,	PUNCT
ejpam-4655	449	5	q1	q1	PROPN
ejpam-4655	449	6	}	}	PUNCT
ejpam-4655	449	7	,	,	PUNCT
ejpam-4655	449	8	{	{	PUNCT
ejpam-4655	449	9	p1	p1	NOUN
ejpam-4655	449	10	,	,	PUNCT
ejpam-4655	449	11	s1	s1	PROPN
ejpam-4655	449	12	}	}	PUNCT
ejpam-4655	449	13	,	,	PUNCT
ejpam-4655	449	14	{	{	PUNCT
ejpam-4655	449	15	p1	p1	PROPN
ejpam-4655	449	16	,	,	PUNCT
ejpam-4655	449	17	q1	q1	PROPN
ejpam-4655	449	18	,	,	PUNCT
ejpam-4655	449	19	r1	r1	PROPN
ejpam-4655	449	20	}	}	PUNCT
ejpam-4655	449	21	,	,	PUNCT
ejpam-4655	449	22	{	{	PUNCT
ejpam-4655	449	23	p1	p1	PROPN
ejpam-4655	449	24	,	,	PUNCT
ejpam-4655	449	25	q1	q1	PROPN
ejpam-4655	449	26	,	,	PUNCT
ejpam-4655	449	27	s1	s1	PROPN
ejpam-4655	449	28	}	}	PUNCT
ejpam-4655	449	29	,	,	PUNCT
ejpam-4655	449	30	{	{	PUNCT
ejpam-4655	449	31	p1	p1	NOUN
ejpam-4655	449	32	,	,	PUNCT
ejpam-4655	449	33	r1	r1	NOUN
ejpam-4655	449	34	,	,	PUNCT
ejpam-4655	449	35	s1	s1	NOUN
ejpam-4655	449	36	}	}	PUNCT
ejpam-4655	449	37	and	and	CCONJ
ejpam-4655	449	38	y	y	PROPN
ejpam-4655	449	39	are	be	AUX
ejpam-4655	449	40	η2	η2	ADJ
ejpam-4655	449	41	-	-	PUNCT
ejpam-4655	449	42	dense	dense	ADJ
ejpam-4655	449	43	subsets	subset	NOUN
ejpam-4655	449	44	of	of	ADP
ejpam-4655	449	45	y.	y.	PROPN
ejpam-4655	449	46	also	also	ADV
ejpam-4655	449	47	,	,	PUNCT
ejpam-4655	449	48	every	every	DET
ejpam-4655	449	49	η2	η2	ADJ
ejpam-4655	449	50	-	-	PUNCT
ejpam-4655	449	51	dense	dense	ADJ
ejpam-4655	449	52	set	set	NOUN
ejpam-4655	449	53	is	be	AUX
ejpam-4655	449	54	η1	η1	NOUN
ejpam-4655	449	55	-	-	PUNCT
ejpam-4655	449	56	open	open	ADJ
ejpam-4655	449	57	.	.	PUNCT
ejpam-4655	450	1	therefore	therefore	ADV
ejpam-4655	450	2	,	,	PUNCT
ejpam-4655	450	3	y	y	PROPN
ejpam-4655	450	4	is	be	AUX
ejpam-4655	450	5	a	a	DET
ejpam-4655	450	6	(	(	PUNCT
ejpam-4655	450	7	1	1	NUM
ejpam-4655	450	8	,	,	PUNCT
ejpam-4655	450	9	2)-bigeneralized	2)-bigeneralized	NUM
ejpam-4655	450	10	submaximal	submaximal	ADJ
ejpam-4655	450	11	space	space	NOUN
ejpam-4655	450	12	.	.	PUNCT
ejpam-4655	451	1	let	let	VERB
ejpam-4655	451	2	m	m	VERB
ejpam-4655	451	3	=	=	PUNCT
ejpam-4655	451	4	{	{	PUNCT
ejpam-4655	451	5	p	p	X
ejpam-4655	451	6	,	,	PUNCT
ejpam-4655	451	7	s	s	PART
ejpam-4655	451	8	}	}	PUNCT
ejpam-4655	451	9	.	.	PUNCT
ejpam-4655	452	1	then	then	ADV
ejpam-4655	452	2	cµ2(m	cµ2(m	NOUN
ejpam-4655	452	3	)	)	PUNCT
ejpam-4655	452	4	=	=	PUNCT
ejpam-4655	453	1	x.	x.	NOUN
ejpam-4655	453	2	but	but	CCONJ
ejpam-4655	453	3	m	m	PROPN
ejpam-4655	453	4	/∈	/∈	PUNCT
ejpam-4655	454	1	µ1	µ1	PROPN
ejpam-4655	454	2	.	.	PUNCT
ejpam-4655	455	1	thus	thus	ADV
ejpam-4655	455	2	,	,	PUNCT
ejpam-4655	455	3	x	x	PRON
ejpam-4655	455	4	is	be	AUX
ejpam-4655	455	5	not	not	PART
ejpam-4655	455	6	a	a	DET
ejpam-4655	455	7	(	(	PUNCT
ejpam-4655	455	8	1	1	NUM
ejpam-4655	455	9	,	,	PUNCT
ejpam-4655	455	10	2)bigeneralized	2)bigeneralized	NUM
ejpam-4655	455	11	submaximal	submaximal	ADJ
ejpam-4655	455	12	space	space	NOUN
ejpam-4655	455	13	.	.	PUNCT
ejpam-4655	456	1	(	(	PUNCT
ejpam-4655	456	2	d	d	X
ejpam-4655	456	3	)	)	PUNCT
ejpam-4655	456	4	let	let	VERB
ejpam-4655	456	5	µ1	µ1	NOUN
ejpam-4655	456	6	and	and	CCONJ
ejpam-4655	456	7	η1	η1	NOUN
ejpam-4655	456	8	are	be	AUX
ejpam-4655	456	9	generalized	generalized	ADJ
ejpam-4655	456	10	topologies	topology	NOUN
ejpam-4655	456	11	defined	define	VERB
ejpam-4655	456	12	as	as	ADP
ejpam-4655	456	13	in	in	ADP
ejpam-4655	456	14	(	(	PUNCT
ejpam-4655	456	15	c	c	NOUN
ejpam-4655	456	16	)	)	PUNCT
ejpam-4655	456	17	.	.	PUNCT
ejpam-4655	457	1	take	take	VERB
ejpam-4655	457	2	µ2	µ2	PROPN
ejpam-4655	457	3	=	=	PUNCT
ejpam-4655	457	4	{	{	PUNCT
ejpam-4655	457	5	∅	∅	NOUN
ejpam-4655	457	6	,	,	PUNCT
ejpam-4655	457	7	{	{	PUNCT
ejpam-4655	457	8	p	p	X
ejpam-4655	457	9	}	}	PUNCT
ejpam-4655	457	10	,	,	PUNCT
ejpam-4655	457	11	{	{	PUNCT
ejpam-4655	457	12	p	p	X
ejpam-4655	457	13	,	,	PUNCT
ejpam-4655	457	14	q	q	NOUN
ejpam-4655	457	15	}	}	PUNCT
ejpam-4655	457	16	,	,	PUNCT
ejpam-4655	457	17	{	{	PUNCT
ejpam-4655	457	18	p	p	X
ejpam-4655	457	19	,	,	PUNCT
ejpam-4655	457	20	r	r	NOUN
ejpam-4655	457	21	}	}	PUNCT
ejpam-4655	457	22	,	,	PUNCT
ejpam-4655	457	23	{	{	PUNCT
ejpam-4655	457	24	p	p	X
ejpam-4655	457	25	,	,	PUNCT
ejpam-4655	457	26	s	s	PART
ejpam-4655	457	27	}	}	PUNCT
ejpam-4655	457	28	,	,	PUNCT
ejpam-4655	457	29	{	{	PUNCT
ejpam-4655	457	30	q	q	X
ejpam-4655	457	31	,	,	PUNCT
ejpam-4655	457	32	s	s	PART
ejpam-4655	457	33	}	}	PUNCT
ejpam-4655	457	34	,	,	PUNCT
ejpam-4655	457	35	{	{	PUNCT
ejpam-4655	457	36	p	p	X
ejpam-4655	457	37	,	,	PUNCT
ejpam-4655	457	38	q	q	ADJ
ejpam-4655	457	39	,	,	PUNCT
ejpam-4655	457	40	r	r	NOUN
ejpam-4655	457	41	}	}	PUNCT
ejpam-4655	457	42	,	,	PUNCT
ejpam-4655	457	43	{	{	PUNCT
ejpam-4655	457	44	p	p	X
ejpam-4655	457	45	,	,	PUNCT
ejpam-4655	457	46	q	q	X
ejpam-4655	457	47	,	,	PUNCT
ejpam-4655	457	48	s	s	PART
ejpam-4655	457	49	}	}	PUNCT
ejpam-4655	457	50	,	,	PUNCT
ejpam-4655	457	51	{	{	PUNCT
ejpam-4655	457	52	p	p	X
ejpam-4655	457	53	,	,	PUNCT
ejpam-4655	457	54	r	r	NOUN
ejpam-4655	457	55	,	,	PUNCT
ejpam-4655	457	56	s	s	PART
ejpam-4655	457	57	}	}	PUNCT
ejpam-4655	457	58	,	,	PUNCT
ejpam-4655	457	59	{	{	PUNCT
ejpam-4655	457	60	q	q	X
ejpam-4655	457	61	,	,	PUNCT
ejpam-4655	457	62	r	r	NOUN
ejpam-4655	457	63	,	,	PUNCT
ejpam-4655	457	64	s	s	PART
ejpam-4655	457	65	}	}	PUNCT
ejpam-4655	457	66	,	,	PUNCT
ejpam-4655	457	67	x	x	NOUN
ejpam-4655	457	68	}	}	PUNCT
ejpam-4655	457	69	and	and	CCONJ
ejpam-4655	457	70	η2	η2	ADJ
ejpam-4655	457	71	=	=	SYM
ejpam-4655	457	72	{	{	PUNCT
ejpam-4655	457	73	∅	∅	NOUN
ejpam-4655	457	74	,	,	PUNCT
ejpam-4655	457	75	{	{	PUNCT
ejpam-4655	457	76	p1	p1	NOUN
ejpam-4655	457	77	}	}	PUNCT
ejpam-4655	457	78	,	,	PUNCT
ejpam-4655	457	79	{	{	PUNCT
ejpam-4655	457	80	p1	p1	NOUN
ejpam-4655	457	81	,	,	PUNCT
ejpam-4655	457	82	q1	q1	PROPN
ejpam-4655	457	83	}	}	PUNCT
ejpam-4655	457	84	,	,	PUNCT
ejpam-4655	457	85	{	{	PUNCT
ejpam-4655	457	86	p1	p1	NOUN
ejpam-4655	457	87	,	,	PUNCT
ejpam-4655	457	88	r1	r1	PROPN
ejpam-4655	457	89	}	}	PUNCT
ejpam-4655	457	90	,	,	PUNCT
ejpam-4655	457	91	{	{	PUNCT
ejpam-4655	457	92	p1	p1	NOUN
ejpam-4655	457	93	,	,	PUNCT
ejpam-4655	457	94	s1	s1	PROPN
ejpam-4655	457	95	}	}	PUNCT
ejpam-4655	457	96	,	,	PUNCT
ejpam-4655	457	97	{	{	PUNCT
ejpam-4655	457	98	q1	q1	NOUN
ejpam-4655	457	99	,	,	PUNCT
ejpam-4655	457	100	s1	s1	PROPN
ejpam-4655	457	101	}	}	PUNCT
ejpam-4655	457	102	,	,	PUNCT
ejpam-4655	457	103	{	{	PUNCT
ejpam-4655	457	104	p1	p1	PROPN
ejpam-4655	457	105	,	,	PUNCT
ejpam-4655	457	106	q1	q1	PROPN
ejpam-4655	457	107	,	,	PUNCT
ejpam-4655	457	108	r1	r1	PROPN
ejpam-4655	457	109	}	}	PUNCT
ejpam-4655	457	110	,	,	PUNCT
ejpam-4655	457	111	{	{	PUNCT
ejpam-4655	457	112	p1	p1	PROPN
ejpam-4655	457	113	,	,	PUNCT
ejpam-4655	457	114	q1	q1	PROPN
ejpam-4655	457	115	,	,	PUNCT
ejpam-4655	457	116	s1	s1	PROPN
ejpam-4655	457	117	}	}	PUNCT
ejpam-4655	457	118	,	,	PUNCT
ejpam-4655	457	119	{	{	PUNCT
ejpam-4655	457	120	p1	p1	NOUN
ejpam-4655	457	121	,	,	PUNCT
ejpam-4655	457	122	r1	r1	NOUN
ejpam-4655	457	123	,	,	PUNCT
ejpam-4655	457	124	s1	s1	PROPN
ejpam-4655	457	125	}	}	PUNCT
ejpam-4655	457	126	,	,	PUNCT
ejpam-4655	457	127	{	{	PUNCT
ejpam-4655	457	128	q1	q1	PROPN
ejpam-4655	457	129	,	,	PUNCT
ejpam-4655	457	130	r1	r1	NOUN
ejpam-4655	457	131	,	,	PUNCT
ejpam-4655	457	132	s1	s1	PROPN
ejpam-4655	457	133	}	}	PUNCT
ejpam-4655	457	134	,	,	PUNCT
ejpam-4655	457	135	y	y	PROPN
ejpam-4655	457	136	}	}	PUNCT
ejpam-4655	457	137	here	here	ADV
ejpam-4655	457	138	h−1(p	h−1(p	PROPN
ejpam-4655	457	139	)	)	PUNCT
ejpam-4655	458	1	∈	∈	PROPN
ejpam-4655	458	2	µ2	µ2	NOUN
ejpam-4655	458	3	whenever	whenever	SCONJ
ejpam-4655	458	4	p	p	PROPN
ejpam-4655	458	5	∈	∈	PROPN
ejpam-4655	458	6	η2	η2	PROPN
ejpam-4655	458	7	.	.	PUNCT
ejpam-4655	459	1	therefore	therefore	ADV
ejpam-4655	459	2	,	,	PUNCT
ejpam-4655	459	3	h	h	NOUN
ejpam-4655	459	4	is	be	AUX
ejpam-4655	459	5	a	a	DET
ejpam-4655	459	6	(	(	PUNCT
ejpam-4655	459	7	µ2	µ2	PROPN
ejpam-4655	459	8	,	,	PUNCT
ejpam-4655	459	9	η2)-continuous	η2)-continuous	ADJ
ejpam-4655	459	10	map	map	NOUN
ejpam-4655	459	11	.	.	PUNCT
ejpam-4655	460	1	let	let	VERB
ejpam-4655	460	2	j	j	PROPN
ejpam-4655	460	3	=	=	PUNCT
ejpam-4655	460	4	{	{	PUNCT
ejpam-4655	460	5	p1	p1	PROPN
ejpam-4655	460	6	,	,	PUNCT
ejpam-4655	460	7	s1	s1	NOUN
ejpam-4655	460	8	}	}	PUNCT
ejpam-4655	460	9	.	.	PUNCT
ejpam-4655	461	1	then	then	ADV
ejpam-4655	461	2	j	j	PROPN
ejpam-4655	461	3	∈	∈	PROPN
ejpam-4655	461	4	η1	η1	NOUN
ejpam-4655	461	5	.	.	PUNCT
ejpam-4655	462	1	but	but	CCONJ
ejpam-4655	462	2	h−1(j	h−1(j	NOUN
ejpam-4655	462	3	)	)	PUNCT
ejpam-4655	462	4	/∈	/∈	PUNCT
ejpam-4655	463	1	µ1	µ1	PROPN
ejpam-4655	463	2	.	.	PUNCT
ejpam-4655	464	1	thus	thus	ADV
ejpam-4655	464	2	,	,	PUNCT
ejpam-4655	464	3	h	h	NOUN
ejpam-4655	464	4	is	be	AUX
ejpam-4655	464	5	not	not	PART
ejpam-4655	464	6	a	a	DET
ejpam-4655	464	7	(	(	PUNCT
ejpam-4655	464	8	µ1	µ1	ADJ
ejpam-4655	464	9	,	,	PUNCT
ejpam-4655	464	10	η1)-continuous	η1)-continuous	ADJ
ejpam-4655	464	11	map	map	NOUN
ejpam-4655	464	12	.	.	PUNCT
ejpam-4655	465	1	here	here	ADV
ejpam-4655	465	2	{	{	PUNCT
ejpam-4655	465	3	p1	p1	PROPN
ejpam-4655	465	4	}	}	PUNCT
ejpam-4655	465	5	,	,	PUNCT
ejpam-4655	465	6	{	{	PUNCT
ejpam-4655	465	7	p1	p1	NOUN
ejpam-4655	465	8	,	,	PUNCT
ejpam-4655	465	9	q1	q1	PROPN
ejpam-4655	465	10	}	}	PUNCT
ejpam-4655	465	11	,	,	PUNCT
ejpam-4655	465	12	{	{	PUNCT
ejpam-4655	465	13	p1	p1	NOUN
ejpam-4655	465	14	,	,	PUNCT
ejpam-4655	465	15	r1	r1	PROPN
ejpam-4655	465	16	}	}	PUNCT
ejpam-4655	465	17	,	,	PUNCT
ejpam-4655	465	18	{	{	PUNCT
ejpam-4655	465	19	p1	p1	NOUN
ejpam-4655	465	20	,	,	PUNCT
ejpam-4655	465	21	s1	s1	PROPN
ejpam-4655	465	22	}	}	PUNCT
ejpam-4655	465	23	,	,	PUNCT
ejpam-4655	465	24	{	{	PUNCT
ejpam-4655	465	25	q1	q1	NOUN
ejpam-4655	465	26	,	,	PUNCT
ejpam-4655	465	27	s1	s1	PROPN
ejpam-4655	465	28	}	}	PUNCT
ejpam-4655	465	29	,	,	PUNCT
ejpam-4655	465	30	{	{	PUNCT
ejpam-4655	465	31	p1	p1	PROPN
ejpam-4655	465	32	,	,	PUNCT
ejpam-4655	465	33	q1	q1	PROPN
ejpam-4655	465	34	,	,	PUNCT
ejpam-4655	465	35	r1	r1	PROPN
ejpam-4655	465	36	}	}	PUNCT
ejpam-4655	465	37	,	,	PUNCT
ejpam-4655	465	38	{	{	PUNCT
ejpam-4655	465	39	p1	p1	PROPN
ejpam-4655	465	40	,	,	PUNCT
ejpam-4655	465	41	q1	q1	PROPN
ejpam-4655	465	42	,	,	PUNCT
ejpam-4655	465	43	s1	s1	PROPN
ejpam-4655	465	44	}	}	PUNCT
ejpam-4655	465	45	,	,	PUNCT
ejpam-4655	465	46	{	{	PUNCT
ejpam-4655	465	47	p1	p1	NOUN
ejpam-4655	465	48	,	,	PUNCT
ejpam-4655	465	49	r1	r1	NOUN
ejpam-4655	465	50	,	,	PUNCT
ejpam-4655	465	51	s1	s1	PROPN
ejpam-4655	465	52	}	}	PUNCT
ejpam-4655	465	53	,	,	PUNCT
ejpam-4655	465	54	{	{	PUNCT
ejpam-4655	465	55	q1	q1	PROPN
ejpam-4655	465	56	,	,	PUNCT
ejpam-4655	465	57	r1	r1	NOUN
ejpam-4655	465	58	,	,	PUNCT
ejpam-4655	465	59	s1	s1	NOUN
ejpam-4655	465	60	}	}	PUNCT
ejpam-4655	465	61	and	and	CCONJ
ejpam-4655	465	62	y	y	PROPN
ejpam-4655	465	63	are	be	AUX
ejpam-4655	465	64	η1	η1	NOUN
ejpam-4655	465	65	-	-	PUNCT
ejpam-4655	465	66	dense	dense	ADJ
ejpam-4655	465	67	subsets	subset	NOUN
ejpam-4655	465	68	of	of	ADP
ejpam-4655	465	69	x.	x.	NOUN
ejpam-4655	465	70	also	also	ADV
ejpam-4655	465	71	,	,	PUNCT
ejpam-4655	465	72	every	every	DET
ejpam-4655	465	73	η1	η1	NOUN
ejpam-4655	465	74	-	-	PUNCT
ejpam-4655	465	75	dense	dense	ADJ
ejpam-4655	465	76	set	set	NOUN
ejpam-4655	465	77	is	be	AUX
ejpam-4655	465	78	η2	η2	NOUN
ejpam-4655	465	79	-	-	PUNCT
ejpam-4655	465	80	open	open	ADJ
ejpam-4655	465	81	.	.	PUNCT
ejpam-4655	466	1	therefore	therefore	ADV
ejpam-4655	466	2	,	,	PUNCT
ejpam-4655	466	3	y	y	PROPN
ejpam-4655	466	4	is	be	AUX
ejpam-4655	466	5	a	a	DET
ejpam-4655	466	6	(	(	PUNCT
ejpam-4655	466	7	2	2	NUM
ejpam-4655	466	8	,	,	PUNCT
ejpam-4655	466	9	1)-bigeneralized	1)-bigeneralized	NUM
ejpam-4655	466	10	submaximal	submaximal	ADJ
ejpam-4655	466	11	space	space	NOUN
ejpam-4655	466	12	.	.	PUNCT
ejpam-4655	467	1	let	let	VERB
ejpam-4655	467	2	k	k	NOUN
ejpam-4655	467	3	=	=	PUNCT
ejpam-4655	467	4	{	{	PUNCT
ejpam-4655	467	5	q	q	NOUN
ejpam-4655	467	6	,	,	PUNCT
ejpam-4655	467	7	r	r	NOUN
ejpam-4655	467	8	,	,	PUNCT
ejpam-4655	467	9	s	s	PART
ejpam-4655	467	10	}	}	PUNCT
ejpam-4655	467	11	.	.	PUNCT
ejpam-4655	468	1	then	then	ADV
ejpam-4655	468	2	cµ1k	cµ1k	PROPN
ejpam-4655	468	3	=	=	PUNCT
ejpam-4655	468	4	x.	x.	NOUN
ejpam-4655	468	5	but	but	CCONJ
ejpam-4655	468	6	k	k	PROPN
ejpam-4655	468	7	/∈	/∈	PROPN
ejpam-4655	468	8	µ2	µ2	PROPN
ejpam-4655	468	9	.	.	PUNCT
ejpam-4655	469	1	thus	thus	ADV
ejpam-4655	469	2	,	,	PUNCT
ejpam-4655	469	3	x	x	PRON
ejpam-4655	469	4	is	be	AUX
ejpam-4655	469	5	not	not	PART
ejpam-4655	469	6	a	a	DET
ejpam-4655	469	7	(	(	PUNCT
ejpam-4655	469	8	2	2	NUM
ejpam-4655	469	9	,	,	PUNCT
ejpam-4655	469	10	1)bigeneralized	1)bigeneralized	NUM
ejpam-4655	469	11	submaximal	submaximal	ADJ
ejpam-4655	469	12	space	space	NOUN
ejpam-4655	469	13	.	.	PUNCT
ejpam-4655	470	1	an	an	DET
ejpam-4655	470	2	interesting	interesting	ADJ
ejpam-4655	470	3	result	result	NOUN
ejpam-4655	470	4	has	have	AUX
ejpam-4655	470	5	been	be	AUX
ejpam-4655	470	6	proved	prove	VERB
ejpam-4655	470	7	that	that	SCONJ
ejpam-4655	470	8	,	,	PUNCT
ejpam-4655	470	9	in	in	ADP
ejpam-4655	470	10	a	a	DET
ejpam-4655	470	11	pairwise	pairwise	NOUN
ejpam-4655	470	12	bigeneralized	bigeneralize	VERB
ejpam-4655	470	13	submaximal	submaximal	ADJ
ejpam-4655	470	14	space	space	NOUN
ejpam-4655	470	15	,	,	PUNCT
ejpam-4655	470	16	every	every	DET
ejpam-4655	470	17	hyperconnected	hyperconnecte	VERB
ejpam-4655	470	18	space	space	NOUN
ejpam-4655	470	19	is	be	AUX
ejpam-4655	470	20	submaximal	submaximal	ADJ
ejpam-4655	470	21	.	.	PUNCT
ejpam-4655	471	1	the	the	DET
ejpam-4655	471	2	proof	proof	NOUN
ejpam-4655	471	3	is	be	AUX
ejpam-4655	471	4	a	a	DET
ejpam-4655	471	5	direct	direct	ADJ
ejpam-4655	471	6	consequence	consequence	NOUN
ejpam-4655	471	7	of	of	ADP
ejpam-4655	471	8	the	the	DET
ejpam-4655	471	9	definitions	definition	NOUN
ejpam-4655	471	10	so	so	SCONJ
ejpam-4655	471	11	the	the	DET
ejpam-4655	471	12	proof	proof	NOUN
ejpam-4655	471	13	is	be	AUX
ejpam-4655	471	14	neglected	neglect	VERB
ejpam-4655	471	15	.	.	PUNCT
ejpam-4655	472	1	theorem	theorem	VERB
ejpam-4655	472	2	25	25	NUM
ejpam-4655	472	3	.	.	PUNCT
ejpam-4655	473	1	let	let	AUX
ejpam-4655	473	2	(	(	PUNCT
ejpam-4655	473	3	x,µ1	x,µ1	NOUN
ejpam-4655	473	4	,	,	PUNCT
ejpam-4655	473	5	µ2	µ2	PROPN
ejpam-4655	473	6	)	)	PUNCT
ejpam-4655	473	7	be	be	AUX
ejpam-4655	473	8	a	a	DET
ejpam-4655	473	9	bgts	bgts	NOUN
ejpam-4655	473	10	.	.	PUNCT
ejpam-4655	474	1	if	if	SCONJ
ejpam-4655	474	2	x	x	PRON
ejpam-4655	474	3	is	be	AUX
ejpam-4655	474	4	pairwise	pairwise	NOUN
ejpam-4655	474	5	bigeneralized	bigeneralize	VERB
ejpam-4655	474	6	submaximal	submaximal	ADJ
ejpam-4655	474	7	space	space	NOUN
ejpam-4655	474	8	,	,	PUNCT
ejpam-4655	474	9	then	then	ADV
ejpam-4655	474	10	the	the	DET
ejpam-4655	474	11	followings	following	NOUN
ejpam-4655	474	12	are	be	AUX
ejpam-4655	474	13	true	true	ADJ
ejpam-4655	474	14	.	.	PUNCT
ejpam-4655	475	1	y.	y.	PROPN
ejpam-4655	475	2	farhat	farhat	PROPN
ejpam-4655	475	3	et	et	PROPN
ejpam-4655	475	4	al	al	PROPN
ejpam-4655	475	5	.	.	PUNCT
ejpam-4655	475	6	/	/	SYM
ejpam-4655	475	7	eur	eur	PROPN
ejpam-4655	475	8	.	.	PUNCT
ejpam-4655	476	1	j.	j.	PROPN
ejpam-4655	476	2	pure	pure	PROPN
ejpam-4655	476	3	appl	appl	PROPN
ejpam-4655	476	4	.	.	PROPN
ejpam-4655	476	5	math	math	PROPN
ejpam-4655	476	6	,	,	PUNCT
ejpam-4655	476	7	16	16	NUM
ejpam-4655	476	8	(	(	PUNCT
ejpam-4655	476	9	1	1	NUM
ejpam-4655	476	10	)	)	PUNCT
ejpam-4655	476	11	(	(	PUNCT
ejpam-4655	476	12	2023	2023	NUM
ejpam-4655	476	13	)	)	PUNCT
ejpam-4655	476	14	,	,	PUNCT
ejpam-4655	476	15	386	386	NUM
ejpam-4655	476	16	-	-	SYM
ejpam-4655	476	17	403	403	NUM
ejpam-4655	476	18	397	397	NUM
ejpam-4655	476	19	(	(	PUNCT
ejpam-4655	476	20	a	a	X
ejpam-4655	476	21	)	)	PUNCT
ejpam-4655	476	22	if	if	SCONJ
ejpam-4655	476	23	(	(	PUNCT
ejpam-4655	476	24	x,µ1	x,µ1	NOUN
ejpam-4655	476	25	)	)	PUNCT
ejpam-4655	476	26	is	be	AUX
ejpam-4655	476	27	hyperconnected	hyperconnecte	VERB
ejpam-4655	476	28	,	,	PUNCT
ejpam-4655	476	29	then	then	ADV
ejpam-4655	476	30	(	(	PUNCT
ejpam-4655	476	31	x,µ2	x,µ2	PROPN
ejpam-4655	476	32	)	)	PUNCT
ejpam-4655	476	33	is	be	AUX
ejpam-4655	476	34	a	a	DET
ejpam-4655	476	35	generalized	generalized	ADJ
ejpam-4655	476	36	submaximal	submaximal	ADJ
ejpam-4655	476	37	space	space	NOUN
ejpam-4655	476	38	.	.	PUNCT
ejpam-4655	477	1	(	(	PUNCT
ejpam-4655	477	2	b	b	X
ejpam-4655	477	3	)	)	PUNCT
ejpam-4655	477	4	if	if	SCONJ
ejpam-4655	477	5	(	(	PUNCT
ejpam-4655	477	6	x,µ2	x,µ2	PROPN
ejpam-4655	477	7	)	)	PUNCT
ejpam-4655	477	8	is	be	AUX
ejpam-4655	477	9	hyperconnected	hyperconnecte	VERB
ejpam-4655	477	10	,	,	PUNCT
ejpam-4655	477	11	then	then	ADV
ejpam-4655	477	12	(	(	PUNCT
ejpam-4655	477	13	x,µ1	x,µ1	NOUN
ejpam-4655	477	14	)	)	PUNCT
ejpam-4655	477	15	is	be	AUX
ejpam-4655	477	16	a	a	DET
ejpam-4655	477	17	generalized	generalized	ADJ
ejpam-4655	477	18	submaximal	submaximal	ADJ
ejpam-4655	477	19	space	space	NOUN
ejpam-4655	477	20	.	.	PUNCT
ejpam-4655	478	1	example	example	NOUN
ejpam-4655	478	2	26	26	NUM
ejpam-4655	478	3	shows	show	VERB
ejpam-4655	478	4	that	that	SCONJ
ejpam-4655	478	5	the	the	DET
ejpam-4655	478	6	condition	condition	NOUN
ejpam-4655	478	7	“	"	PUNCT
ejpam-4655	478	8	(	(	PUNCT
ejpam-4655	478	9	x,µi	x,µi	NUM
ejpam-4655	478	10	)	)	PUNCT
ejpam-4655	478	11	is	be	AUX
ejpam-4655	478	12	hyperconnected	hyperconnecte	VERB
ejpam-4655	478	13	”	"	PUNCT
ejpam-4655	478	14	for	for	ADP
ejpam-4655	478	15	i	i	PROPN
ejpam-4655	478	16	=	=	SYM
ejpam-4655	478	17	1	1	NUM
ejpam-4655	478	18	,	,	PUNCT
ejpam-4655	478	19	2	2	NUM
ejpam-4655	478	20	is	be	AUX
ejpam-4655	478	21	necessary	necessary	ADJ
ejpam-4655	478	22	in	in	ADP
ejpam-4655	478	23	theorem	theorem	NOUN
ejpam-4655	478	24	25	25	NUM
ejpam-4655	478	25	.	.	PUNCT
ejpam-4655	478	26	example	example	NOUN
ejpam-4655	479	1	26	26	NUM
ejpam-4655	479	2	.	.	PUNCT
ejpam-4655	480	1	(	(	PUNCT
ejpam-4655	480	2	a	a	X
ejpam-4655	480	3	)	)	PUNCT
ejpam-4655	480	4	let	let	NOUN
ejpam-4655	480	5	(	(	PUNCT
ejpam-4655	480	6	x,µ1	x,µ1	NOUN
ejpam-4655	480	7	,	,	PUNCT
ejpam-4655	480	8	µ2	µ2	PROPN
ejpam-4655	480	9	)	)	PUNCT
ejpam-4655	480	10	be	be	VERB
ejpam-4655	480	11	a	a	DET
ejpam-4655	480	12	bgts	bgts	NOUN
ejpam-4655	480	13	defined	define	VERB
ejpam-4655	480	14	as	as	ADP
ejpam-4655	480	15	in	in	ADP
ejpam-4655	480	16	4	4	NUM
ejpam-4655	480	17	.	.	PUNCT
ejpam-4655	481	1	then	then	ADV
ejpam-4655	481	2	x	x	PRON
ejpam-4655	481	3	is	be	AUX
ejpam-4655	481	4	a	a	DET
ejpam-4655	481	5	pairwise	pairwise	NOUN
ejpam-4655	481	6	bigeneralized	bigeneralize	VERB
ejpam-4655	481	7	topological	topological	ADJ
ejpam-4655	481	8	space	space	NOUN
ejpam-4655	481	9	.	.	PUNCT
ejpam-4655	482	1	here	here	ADV
ejpam-4655	482	2	{	{	PUNCT
ejpam-4655	482	3	p	p	NOUN
ejpam-4655	482	4	}	}	PUNCT
ejpam-4655	482	5	∈	∈	PROPN
ejpam-4655	482	6	µ2	µ2	NOUN
ejpam-4655	482	7	but	but	CCONJ
ejpam-4655	482	8	cµ2({p	cµ2({p	PROPN
ejpam-4655	482	9	}	}	PUNCT
ejpam-4655	482	10	)	)	PUNCT
ejpam-4655	483	1	̸=	̸=	PROPN
ejpam-4655	483	2	x.	x.	NOUN
ejpam-4655	483	3	therefore	therefore	ADV
ejpam-4655	483	4	,	,	PUNCT
ejpam-4655	483	5	(	(	PUNCT
ejpam-4655	483	6	x,µ2	x,µ2	PROPN
ejpam-4655	483	7	)	)	PUNCT
ejpam-4655	483	8	is	be	AUX
ejpam-4655	483	9	not	not	PART
ejpam-4655	483	10	a	a	DET
ejpam-4655	483	11	hyperconnected	hyperconnecte	VERB
ejpam-4655	483	12	space	space	NOUN
ejpam-4655	483	13	.	.	PUNCT
ejpam-4655	484	1	also	also	ADV
ejpam-4655	484	2	,	,	PUNCT
ejpam-4655	484	3	cµ1({p	cµ1({p	VERB
ejpam-4655	484	4	}	}	PUNCT
ejpam-4655	484	5	)	)	PUNCT
ejpam-4655	485	1	=	=	PUNCT
ejpam-4655	485	2	x	x	PUNCT
ejpam-4655	486	1	but	but	CCONJ
ejpam-4655	486	2	{	{	PUNCT
ejpam-4655	486	3	p	p	X
ejpam-4655	486	4	}	}	PUNCT
ejpam-4655	486	5	/∈	/∈	PUNCT
ejpam-4655	486	6	µ1	µ1	PROPN
ejpam-4655	486	7	.	.	PUNCT
ejpam-4655	487	1	thus	thus	ADV
ejpam-4655	487	2	,	,	PUNCT
ejpam-4655	487	3	(	(	PUNCT
ejpam-4655	487	4	x,µ1	x,µ1	NOUN
ejpam-4655	487	5	)	)	PUNCT
ejpam-4655	487	6	is	be	AUX
ejpam-4655	487	7	not	not	PART
ejpam-4655	487	8	a	a	DET
ejpam-4655	487	9	generalized	generalized	ADJ
ejpam-4655	487	10	submaximal	submaximal	ADJ
ejpam-4655	487	11	space	space	NOUN
ejpam-4655	487	12	.	.	PUNCT
ejpam-4655	488	1	(	(	PUNCT
ejpam-4655	488	2	b	b	X
ejpam-4655	488	3	)	)	PUNCT
ejpam-4655	488	4	let	let	NOUN
ejpam-4655	488	5	(	(	PUNCT
ejpam-4655	488	6	x,µ1	x,µ1	NOUN
ejpam-4655	488	7	,	,	PUNCT
ejpam-4655	488	8	µ2	µ2	PROPN
ejpam-4655	488	9	)	)	PUNCT
ejpam-4655	488	10	be	be	VERB
ejpam-4655	488	11	a	a	DET
ejpam-4655	488	12	bgts	bgts	NOUN
ejpam-4655	488	13	wherex	wherex	NOUN
ejpam-4655	488	14	=	=	PUNCT
ejpam-4655	488	15	{	{	PUNCT
ejpam-4655	488	16	p	p	X
ejpam-4655	488	17	,	,	PUNCT
ejpam-4655	488	18	q	q	ADJ
ejpam-4655	488	19	,	,	PUNCT
ejpam-4655	488	20	r	r	NOUN
ejpam-4655	488	21	,	,	PUNCT
ejpam-4655	488	22	s};µ1	s};µ1	PROPN
ejpam-4655	488	23	=	=	SYM
ejpam-4655	488	24	{	{	PUNCT
ejpam-4655	488	25	∅	∅	NOUN
ejpam-4655	488	26	,	,	PUNCT
ejpam-4655	488	27	{	{	PUNCT
ejpam-4655	488	28	p	p	X
ejpam-4655	488	29	}	}	PUNCT
ejpam-4655	488	30	,	,	PUNCT
ejpam-4655	488	31	{	{	PUNCT
ejpam-4655	488	32	q	q	X
ejpam-4655	488	33	}	}	PUNCT
ejpam-4655	488	34	,	,	PUNCT
ejpam-4655	488	35	{	{	PUNCT
ejpam-4655	488	36	p	p	X
ejpam-4655	488	37	,	,	PUNCT
ejpam-4655	488	38	q	q	NOUN
ejpam-4655	488	39	}	}	PUNCT
ejpam-4655	488	40	,	,	PUNCT
ejpam-4655	488	41	{	{	PUNCT
ejpam-4655	488	42	p	p	X
ejpam-4655	488	43	,	,	PUNCT
ejpam-4655	488	44	r	r	NOUN
ejpam-4655	488	45	}	}	PUNCT
ejpam-4655	488	46	,	,	PUNCT
ejpam-4655	488	47	{	{	PUNCT
ejpam-4655	488	48	p	p	X
ejpam-4655	488	49	,	,	PUNCT
ejpam-4655	488	50	s	s	PART
ejpam-4655	488	51	}	}	PUNCT
ejpam-4655	488	52	,	,	PUNCT
ejpam-4655	488	53	{	{	PUNCT
ejpam-4655	488	54	q	q	X
ejpam-4655	488	55	,	,	PUNCT
ejpam-4655	488	56	r	r	NOUN
ejpam-4655	488	57	}	}	PUNCT
ejpam-4655	488	58	,	,	PUNCT
ejpam-4655	488	59	{	{	PUNCT
ejpam-4655	488	60	q	q	X
ejpam-4655	488	61	,	,	PUNCT
ejpam-4655	488	62	s	s	PART
ejpam-4655	488	63	}	}	PUNCT
ejpam-4655	488	64	,	,	PUNCT
ejpam-4655	488	65	{	{	PUNCT
ejpam-4655	488	66	r	r	NOUN
ejpam-4655	488	67	,	,	PUNCT
ejpam-4655	488	68	s	s	PART
ejpam-4655	488	69	}	}	PUNCT
ejpam-4655	488	70	,	,	PUNCT
ejpam-4655	488	71	{	{	PUNCT
ejpam-4655	488	72	p	p	X
ejpam-4655	488	73	,	,	PUNCT
ejpam-4655	488	74	q	q	ADJ
ejpam-4655	488	75	,	,	PUNCT
ejpam-4655	488	76	r	r	NOUN
ejpam-4655	488	77	}	}	PUNCT
ejpam-4655	488	78	,	,	PUNCT
ejpam-4655	488	79	{	{	PUNCT
ejpam-4655	488	80	p	p	X
ejpam-4655	488	81	,	,	PUNCT
ejpam-4655	488	82	q	q	X
ejpam-4655	488	83	,	,	PUNCT
ejpam-4655	488	84	s	s	PART
ejpam-4655	488	85	}	}	PUNCT
ejpam-4655	488	86	,	,	PUNCT
ejpam-4655	488	87	{	{	PUNCT
ejpam-4655	488	88	p	p	X
ejpam-4655	488	89	,	,	PUNCT
ejpam-4655	488	90	r	r	NOUN
ejpam-4655	488	91	,	,	PUNCT
ejpam-4655	488	92	s	s	PART
ejpam-4655	488	93	}	}	PUNCT
ejpam-4655	488	94	,	,	PUNCT
ejpam-4655	488	95	{	{	PUNCT
ejpam-4655	488	96	q	q	X
ejpam-4655	488	97	,	,	PUNCT
ejpam-4655	488	98	r	r	NOUN
ejpam-4655	488	99	,	,	PUNCT
ejpam-4655	488	100	s	s	PART
ejpam-4655	488	101	}	}	PUNCT
ejpam-4655	488	102	,	,	PUNCT
ejpam-4655	488	103	x	x	NOUN
ejpam-4655	488	104	}	}	PUNCT
ejpam-4655	488	105	and	and	CCONJ
ejpam-4655	488	106	µ2	µ2	PROPN
ejpam-4655	488	107	=	=	PUNCT
ejpam-4655	488	108	{	{	PUNCT
ejpam-4655	488	109	∅	∅	NOUN
ejpam-4655	488	110	,	,	PUNCT
ejpam-4655	488	111	{	{	PUNCT
ejpam-4655	488	112	p	p	X
ejpam-4655	488	113	,	,	PUNCT
ejpam-4655	488	114	q	q	ADJ
ejpam-4655	488	115	,	,	PUNCT
ejpam-4655	488	116	r	r	NOUN
ejpam-4655	488	117	}	}	PUNCT
ejpam-4655	488	118	,	,	PUNCT
ejpam-4655	488	119	{	{	PUNCT
ejpam-4655	488	120	p	p	X
ejpam-4655	488	121	,	,	PUNCT
ejpam-4655	488	122	q	q	X
ejpam-4655	488	123	,	,	PUNCT
ejpam-4655	488	124	s	s	PART
ejpam-4655	488	125	}	}	PUNCT
ejpam-4655	488	126	,	,	PUNCT
ejpam-4655	488	127	{	{	PUNCT
ejpam-4655	488	128	p	p	X
ejpam-4655	488	129	,	,	PUNCT
ejpam-4655	488	130	r	r	NOUN
ejpam-4655	488	131	,	,	PUNCT
ejpam-4655	488	132	s	s	PART
ejpam-4655	488	133	}	}	PUNCT
ejpam-4655	488	134	,	,	PUNCT
ejpam-4655	488	135	{	{	PUNCT
ejpam-4655	488	136	q	q	X
ejpam-4655	488	137	,	,	PUNCT
ejpam-4655	488	138	r	r	NOUN
ejpam-4655	488	139	,	,	PUNCT
ejpam-4655	488	140	s	s	PART
ejpam-4655	488	141	}	}	PUNCT
ejpam-4655	488	142	,	,	PUNCT
ejpam-4655	488	143	x	x	NOUN
ejpam-4655	488	144	}	}	PUNCT
ejpam-4655	488	145	.	.	PUNCT
ejpam-4655	489	1	then	then	ADV
ejpam-4655	489	2	{	{	PUNCT
ejpam-4655	489	3	p	p	X
ejpam-4655	489	4	,	,	PUNCT
ejpam-4655	489	5	q	q	NOUN
ejpam-4655	489	6	}	}	PUNCT
ejpam-4655	489	7	,	,	PUNCT
ejpam-4655	489	8	{	{	PUNCT
ejpam-4655	489	9	p	p	X
ejpam-4655	489	10	,	,	PUNCT
ejpam-4655	489	11	r	r	NOUN
ejpam-4655	489	12	}	}	PUNCT
ejpam-4655	489	13	,	,	PUNCT
ejpam-4655	489	14	{	{	PUNCT
ejpam-4655	489	15	p	p	X
ejpam-4655	489	16	,	,	PUNCT
ejpam-4655	489	17	s	s	PART
ejpam-4655	489	18	}	}	PUNCT
ejpam-4655	489	19	,	,	PUNCT
ejpam-4655	489	20	{	{	PUNCT
ejpam-4655	489	21	q	q	X
ejpam-4655	489	22	,	,	PUNCT
ejpam-4655	489	23	r	r	NOUN
ejpam-4655	489	24	}	}	PUNCT
ejpam-4655	489	25	,	,	PUNCT
ejpam-4655	489	26	{	{	PUNCT
ejpam-4655	489	27	q	q	X
ejpam-4655	489	28	,	,	PUNCT
ejpam-4655	489	29	s	s	PART
ejpam-4655	489	30	}	}	PUNCT
ejpam-4655	489	31	,	,	PUNCT
ejpam-4655	489	32	{	{	PUNCT
ejpam-4655	489	33	r	r	NOUN
ejpam-4655	489	34	,	,	PUNCT
ejpam-4655	489	35	s	s	PART
ejpam-4655	489	36	}	}	PUNCT
ejpam-4655	489	37	,	,	PUNCT
ejpam-4655	489	38	{	{	PUNCT
ejpam-4655	489	39	p	p	X
ejpam-4655	489	40	,	,	PUNCT
ejpam-4655	489	41	q	q	ADJ
ejpam-4655	489	42	,	,	PUNCT
ejpam-4655	489	43	r	r	NOUN
ejpam-4655	489	44	}	}	PUNCT
ejpam-4655	489	45	,	,	PUNCT
ejpam-4655	489	46	{	{	PUNCT
ejpam-4655	489	47	p	p	X
ejpam-4655	489	48	,	,	PUNCT
ejpam-4655	489	49	q	q	X
ejpam-4655	489	50	,	,	PUNCT
ejpam-4655	489	51	s	s	PART
ejpam-4655	489	52	}	}	PUNCT
ejpam-4655	489	53	,	,	PUNCT
ejpam-4655	489	54	{	{	PUNCT
ejpam-4655	489	55	p	p	X
ejpam-4655	489	56	,	,	PUNCT
ejpam-4655	489	57	r	r	NOUN
ejpam-4655	489	58	,	,	PUNCT
ejpam-4655	489	59	s	s	PART
ejpam-4655	489	60	}	}	PUNCT
ejpam-4655	489	61	,	,	PUNCT
ejpam-4655	489	62	{	{	PUNCT
ejpam-4655	489	63	q	q	X
ejpam-4655	489	64	,	,	PUNCT
ejpam-4655	489	65	r	r	NOUN
ejpam-4655	489	66	,	,	PUNCT
ejpam-4655	489	67	s	s	PART
ejpam-4655	489	68	}	}	PUNCT
ejpam-4655	489	69	and	and	CCONJ
ejpam-4655	489	70	x	x	X
ejpam-4655	489	71	are	be	AUX
ejpam-4655	489	72	µ2	µ2	ADJ
ejpam-4655	489	73	-	-	PUNCT
ejpam-4655	489	74	dense	dense	ADJ
ejpam-4655	489	75	subsets	subset	NOUN
ejpam-4655	489	76	of	of	ADP
ejpam-4655	489	77	x.	x.	NOUN
ejpam-4655	489	78	also	also	ADV
ejpam-4655	489	79	,	,	PUNCT
ejpam-4655	489	80	every	every	DET
ejpam-4655	489	81	µ2	µ2	ADJ
ejpam-4655	489	82	-	-	PUNCT
ejpam-4655	489	83	dense	dense	ADJ
ejpam-4655	489	84	set	set	NOUN
ejpam-4655	489	85	is	be	AUX
ejpam-4655	489	86	µ2	µ2	ADJ
ejpam-4655	489	87	-	-	PUNCT
ejpam-4655	489	88	open	open	ADJ
ejpam-4655	489	89	.	.	PUNCT
ejpam-4655	490	1	therefore	therefore	ADV
ejpam-4655	490	2	,	,	PUNCT
ejpam-4655	490	3	x	x	X
ejpam-4655	490	4	is	be	AUX
ejpam-4655	490	5	(	(	PUNCT
ejpam-4655	490	6	1	1	NUM
ejpam-4655	490	7	,	,	PUNCT
ejpam-4655	490	8	2)-bigeneralized	2)-bigeneralized	NUM
ejpam-4655	490	9	submaximal	submaximal	ADJ
ejpam-4655	490	10	space	space	NOUN
ejpam-4655	490	11	.	.	PUNCT
ejpam-4655	491	1	here	here	ADV
ejpam-4655	491	2	{	{	PUNCT
ejpam-4655	491	3	p	p	X
ejpam-4655	491	4	,	,	PUNCT
ejpam-4655	491	5	q	q	ADJ
ejpam-4655	491	6	,	,	PUNCT
ejpam-4655	491	7	r	r	NOUN
ejpam-4655	491	8	}	}	PUNCT
ejpam-4655	491	9	,	,	PUNCT
ejpam-4655	491	10	{	{	PUNCT
ejpam-4655	491	11	p	p	X
ejpam-4655	491	12	,	,	PUNCT
ejpam-4655	491	13	q	q	X
ejpam-4655	491	14	,	,	PUNCT
ejpam-4655	491	15	s	s	PART
ejpam-4655	491	16	}	}	PUNCT
ejpam-4655	491	17	,	,	PUNCT
ejpam-4655	491	18	{	{	PUNCT
ejpam-4655	491	19	p	p	X
ejpam-4655	491	20	,	,	PUNCT
ejpam-4655	491	21	r	r	NOUN
ejpam-4655	491	22	,	,	PUNCT
ejpam-4655	491	23	s	s	PART
ejpam-4655	491	24	}	}	PUNCT
ejpam-4655	491	25	,	,	PUNCT
ejpam-4655	491	26	{	{	PUNCT
ejpam-4655	491	27	q	q	X
ejpam-4655	491	28	,	,	PUNCT
ejpam-4655	491	29	r	r	NOUN
ejpam-4655	491	30	,	,	PUNCT
ejpam-4655	491	31	s	s	PART
ejpam-4655	491	32	}	}	PUNCT
ejpam-4655	491	33	and	and	CCONJ
ejpam-4655	491	34	x	x	PRON
ejpam-4655	491	35	are	be	AUX
ejpam-4655	491	36	µ1	µ1	NOUN
ejpam-4655	491	37	-	-	PUNCT
ejpam-4655	491	38	dense	dense	ADJ
ejpam-4655	491	39	subsets	subset	NOUN
ejpam-4655	491	40	of	of	ADP
ejpam-4655	491	41	x.	x.	NOUN
ejpam-4655	491	42	also	also	ADV
ejpam-4655	491	43	,	,	PUNCT
ejpam-4655	491	44	every	every	DET
ejpam-4655	491	45	µ1	µ1	NOUN
ejpam-4655	491	46	-	-	PUNCT
ejpam-4655	491	47	dense	dense	ADJ
ejpam-4655	491	48	set	set	NOUN
ejpam-4655	491	49	is	be	AUX
ejpam-4655	491	50	µ2	µ2	ADJ
ejpam-4655	491	51	-	-	PUNCT
ejpam-4655	491	52	open	open	ADJ
ejpam-4655	491	53	.	.	PUNCT
ejpam-4655	492	1	therefore	therefore	ADV
ejpam-4655	492	2	,	,	PUNCT
ejpam-4655	492	3	x	x	X
ejpam-4655	492	4	is	be	AUX
ejpam-4655	492	5	(	(	PUNCT
ejpam-4655	492	6	2	2	NUM
ejpam-4655	492	7	,	,	PUNCT
ejpam-4655	492	8	1)-bigeneralized	1)-bigeneralized	NUM
ejpam-4655	492	9	submaximal	submaximal	ADJ
ejpam-4655	492	10	space	space	NOUN
ejpam-4655	492	11	.	.	PUNCT
ejpam-4655	493	1	hence	hence	ADV
ejpam-4655	493	2	x	x	X
ejpam-4655	493	3	is	be	AUX
ejpam-4655	493	4	pairwise	pairwise	NOUN
ejpam-4655	493	5	bigeneralized	bigeneralize	VERB
ejpam-4655	493	6	submaximal	submaximal	ADJ
ejpam-4655	493	7	space	space	NOUN
ejpam-4655	493	8	.	.	PUNCT
ejpam-4655	494	1	let	let	VERB
ejpam-4655	494	2	q	q	NOUN
ejpam-4655	495	1	=	=	PUNCT
ejpam-4655	495	2	{	{	PUNCT
ejpam-4655	495	3	p	p	X
ejpam-4655	495	4	}	}	PUNCT
ejpam-4655	495	5	.	.	PUNCT
ejpam-4655	496	1	then	then	ADV
ejpam-4655	496	2	q	q	PROPN
ejpam-4655	496	3	∈	∈	PROPN
ejpam-4655	496	4	µ̃1	µ̃1	PROPN
ejpam-4655	496	5	.	.	PUNCT
ejpam-4655	496	6	but	but	CCONJ
ejpam-4655	496	7	cµ1(q	cµ1(q	X
ejpam-4655	496	8	)	)	PUNCT
ejpam-4655	496	9	̸=	̸=	PROPN
ejpam-4655	496	10	x.	x.	NOUN
ejpam-4655	496	11	therefore	therefore	ADV
ejpam-4655	496	12	,	,	PUNCT
ejpam-4655	496	13	(	(	PUNCT
ejpam-4655	496	14	x,µ1	x,µ1	NOUN
ejpam-4655	496	15	)	)	PUNCT
ejpam-4655	496	16	is	be	AUX
ejpam-4655	496	17	not	not	PART
ejpam-4655	496	18	a	a	DET
ejpam-4655	496	19	hyperconnected	hyperconnecte	VERB
ejpam-4655	496	20	space	space	NOUN
ejpam-4655	496	21	.	.	PUNCT
ejpam-4655	497	1	also	also	ADV
ejpam-4655	497	2	,	,	PUNCT
ejpam-4655	497	3	cµ2({p	cµ2({p	PROPN
ejpam-4655	497	4	,	,	PUNCT
ejpam-4655	497	5	q	q	NOUN
ejpam-4655	497	6	}	}	PUNCT
ejpam-4655	497	7	)	)	PUNCT
ejpam-4655	498	1	=	=	PUNCT
ejpam-4655	498	2	x	x	PUNCT
ejpam-4655	499	1	but	but	CCONJ
ejpam-4655	499	2	{	{	PUNCT
ejpam-4655	499	3	p	p	X
ejpam-4655	499	4	,	,	PUNCT
ejpam-4655	499	5	q	q	ADJ
ejpam-4655	499	6	}	}	PUNCT
ejpam-4655	499	7	/∈	/∈	PUNCT
ejpam-4655	500	1	µ2	µ2	PROPN
ejpam-4655	500	2	.	.	PUNCT
ejpam-4655	501	1	thus	thus	ADV
ejpam-4655	501	2	,	,	PUNCT
ejpam-4655	501	3	(	(	PUNCT
ejpam-4655	501	4	x,µ2	x,µ2	PROPN
ejpam-4655	501	5	)	)	PUNCT
ejpam-4655	501	6	is	be	AUX
ejpam-4655	501	7	not	not	PART
ejpam-4655	501	8	a	a	DET
ejpam-4655	501	9	generalized	generalized	ADJ
ejpam-4655	501	10	submaximal	submaximal	ADJ
ejpam-4655	501	11	space	space	NOUN
ejpam-4655	501	12	.	.	PUNCT
ejpam-4655	502	1	4	4	X
ejpam-4655	502	2	.	.	X
ejpam-4655	502	3	(	(	PUNCT
ejpam-4655	502	4	s	s	X
ejpam-4655	502	5	,	,	PUNCT
ejpam-4655	502	6	v)⋆-bigeneralized	v)⋆-bigeneralize	VERB
ejpam-4655	502	7	submaximal	submaximal	ADJ
ejpam-4655	502	8	space	space	NOUN
ejpam-4655	502	9	here	here	ADV
ejpam-4655	502	10	,	,	PUNCT
ejpam-4655	502	11	we	we	PRON
ejpam-4655	502	12	define	define	VERB
ejpam-4655	502	13	a	a	DET
ejpam-4655	502	14	space	space	NOUN
ejpam-4655	502	15	namely	namely	ADV
ejpam-4655	502	16	,	,	PUNCT
ejpam-4655	502	17	(	(	PUNCT
ejpam-4655	502	18	s	s	X
ejpam-4655	502	19	,	,	PUNCT
ejpam-4655	502	20	v)⋆-bigeneralized	v)⋆-bigeneralize	VERB
ejpam-4655	502	21	submaximal	submaximal	ADJ
ejpam-4655	502	22	space	space	NOUN
ejpam-4655	502	23	and	and	CCONJ
ejpam-4655	502	24	give	give	VERB
ejpam-4655	502	25	few	few	ADJ
ejpam-4655	502	26	results	result	NOUN
ejpam-4655	502	27	about	about	ADP
ejpam-4655	502	28	this	this	DET
ejpam-4655	502	29	space	space	NOUN
ejpam-4655	502	30	which	which	PRON
ejpam-4655	502	31	is	be	AUX
ejpam-4655	502	32	helpful	helpful	ADJ
ejpam-4655	502	33	to	to	PART
ejpam-4655	502	34	reduce	reduce	VERB
ejpam-4655	502	35	the	the	DET
ejpam-4655	502	36	complexity	complexity	NOUN
ejpam-4655	502	37	to	to	PART
ejpam-4655	502	38	check	check	VERB
ejpam-4655	502	39	whether	whether	SCONJ
ejpam-4655	502	40	the	the	DET
ejpam-4655	502	41	given	give	VERB
ejpam-4655	502	42	bgts	bgts	PROPN
ejpam-4655	502	43	is	be	AUX
ejpam-4655	502	44	(	(	PUNCT
ejpam-4655	502	45	s	s	X
ejpam-4655	502	46	,	,	PUNCT
ejpam-4655	502	47	v)⋆-bigeneralized	v)⋆-bigeneralize	VERB
ejpam-4655	502	48	submaximal	submaximal	ADJ
ejpam-4655	502	49	space	space	NOUN
ejpam-4655	502	50	or	or	CCONJ
ejpam-4655	502	51	not	not	PART
ejpam-4655	502	52	.	.	PUNCT
ejpam-4655	503	1	we	we	PRON
ejpam-4655	503	2	begin	begin	VERB
ejpam-4655	503	3	with	with	ADP
ejpam-4655	503	4	a	a	DET
ejpam-4655	503	5	definition	definition	NOUN
ejpam-4655	503	6	of	of	ADP
ejpam-4655	503	7	(	(	PUNCT
ejpam-4655	503	8	s	s	PROPN
ejpam-4655	503	9	,	,	PUNCT
ejpam-4655	503	10	v)⋆-bigeneralized	v)⋆-bigeneralize	VERB
ejpam-4655	503	11	submaximal	submaximal	ADJ
ejpam-4655	503	12	space	space	NOUN
ejpam-4655	503	13	.	.	PUNCT
ejpam-4655	504	1	definition	definition	NOUN
ejpam-4655	504	2	27	27	NUM
ejpam-4655	504	3	.	.	PUNCT
ejpam-4655	505	1	let	let	AUX
ejpam-4655	505	2	(	(	PUNCT
ejpam-4655	505	3	x,µ1	x,µ1	NOUN
ejpam-4655	505	4	,	,	PUNCT
ejpam-4655	505	5	µ2	µ2	PROPN
ejpam-4655	505	6	)	)	PUNCT
ejpam-4655	505	7	be	be	AUX
ejpam-4655	505	8	a	a	DET
ejpam-4655	505	9	bgts	bgts	NOUN
ejpam-4655	505	10	.	.	PUNCT
ejpam-4655	506	1	a	a	DET
ejpam-4655	506	2	space	space	NOUN
ejpam-4655	506	3	x	x	PUNCT
ejpam-4655	506	4	is	be	AUX
ejpam-4655	506	5	said	say	VERB
ejpam-4655	506	6	to	to	PART
ejpam-4655	506	7	be	be	AUX
ejpam-4655	506	8	(	(	PUNCT
ejpam-4655	506	9	µs	µs	NOUN
ejpam-4655	506	10	,	,	PUNCT
ejpam-4655	506	11	µv	µv	PROPN
ejpam-4655	506	12	)	)	PUNCT
ejpam-4655	506	13	⋆-bigeneralized	⋆-bigeneralize	VERB
ejpam-4655	506	14	submaximal	submaximal	ADJ
ejpam-4655	506	15	(	(	PUNCT
ejpam-4655	506	16	briefly	briefly	ADV
ejpam-4655	506	17	,	,	PUNCT
ejpam-4655	506	18	(	(	PUNCT
ejpam-4655	506	19	s	s	X
ejpam-4655	506	20	,	,	PUNCT
ejpam-4655	506	21	v)⋆-bigeneralized	v)⋆-bigeneralize	VERB
ejpam-4655	506	22	submaximal	submaximal	ADJ
ejpam-4655	506	23	)	)	PUNCT
ejpam-4655	506	24	if	if	SCONJ
ejpam-4655	506	25	q	q	X
ejpam-4655	506	26	∈	∈	PROPN
ejpam-4655	506	27	µs	µs	VERB
ejpam-4655	506	28	whenever	whenever	SCONJ
ejpam-4655	506	29	q	q	PROPN
ejpam-4655	506	30	∈	∈	PROPN
ejpam-4655	506	31	(	(	PUNCT
ejpam-4655	506	32	s	s	PROPN
ejpam-4655	506	33	,	,	PUNCT
ejpam-4655	506	34	v	v	NOUN
ejpam-4655	506	35	)	)	PUNCT
ejpam-4655	506	36	−	−	PROPN
ejpam-4655	506	37	d(x	d(x	NOUN
ejpam-4655	506	38	)	)	PUNCT
ejpam-4655	506	39	where	where	SCONJ
ejpam-4655	506	40	s	s	X
ejpam-4655	506	41	,	,	PUNCT
ejpam-4655	506	42	v	v	NOUN
ejpam-4655	506	43	=	=	SYM
ejpam-4655	506	44	1	1	NUM
ejpam-4655	506	45	,	,	PUNCT
ejpam-4655	506	46	2	2	NUM
ejpam-4655	506	47	;	;	PUNCT
ejpam-4655	506	48	s	s	VERB
ejpam-4655	506	49	̸=	̸=	PROPN
ejpam-4655	506	50	v.	v.	ADP
ejpam-4655	506	51	example	example	NOUN
ejpam-4655	506	52	28	28	NUM
ejpam-4655	506	53	.	.	PUNCT
ejpam-4655	507	1	(	(	PUNCT
ejpam-4655	507	2	a	a	X
ejpam-4655	507	3	)	)	PUNCT
ejpam-4655	507	4	consider	consider	VERB
ejpam-4655	507	5	the	the	DET
ejpam-4655	507	6	bigeneralized	bigeneralized	ADJ
ejpam-4655	507	7	topological	topological	ADJ
ejpam-4655	507	8	space	space	NOUN
ejpam-4655	507	9	(	(	PUNCT
ejpam-4655	507	10	x,µ1	x,µ1	PROPN
ejpam-4655	507	11	,	,	PUNCT
ejpam-4655	507	12	µ2	µ2	PROPN
ejpam-4655	507	13	)	)	PUNCT
ejpam-4655	507	14	where	where	SCONJ
ejpam-4655	507	15	x	x	X
ejpam-4655	507	16	=	=	PRON
ejpam-4655	507	17	{	{	PUNCT
ejpam-4655	507	18	p	p	X
ejpam-4655	507	19	,	,	PUNCT
ejpam-4655	507	20	q	q	ADJ
ejpam-4655	507	21	,	,	PUNCT
ejpam-4655	507	22	r	r	NOUN
ejpam-4655	507	23	,	,	PUNCT
ejpam-4655	507	24	s};µ1	s};µ1	PROPN
ejpam-4655	507	25	=	=	SYM
ejpam-4655	507	26	{	{	PUNCT
ejpam-4655	507	27	∅	∅	NOUN
ejpam-4655	507	28	,	,	PUNCT
ejpam-4655	507	29	{	{	PUNCT
ejpam-4655	507	30	q	q	X
ejpam-4655	507	31	}	}	PUNCT
ejpam-4655	507	32	,	,	PUNCT
ejpam-4655	507	33	{	{	PUNCT
ejpam-4655	507	34	s	s	X
ejpam-4655	507	35	}	}	PUNCT
ejpam-4655	507	36	,	,	PUNCT
ejpam-4655	507	37	{	{	PUNCT
ejpam-4655	507	38	p	p	X
ejpam-4655	507	39	,	,	PUNCT
ejpam-4655	507	40	q	q	NOUN
ejpam-4655	507	41	}	}	PUNCT
ejpam-4655	507	42	,	,	PUNCT
ejpam-4655	507	43	{	{	PUNCT
ejpam-4655	507	44	p	p	X
ejpam-4655	507	45	,	,	PUNCT
ejpam-4655	507	46	s	s	PART
ejpam-4655	507	47	}	}	PUNCT
ejpam-4655	507	48	,	,	PUNCT
ejpam-4655	507	49	{	{	PUNCT
ejpam-4655	507	50	q	q	X
ejpam-4655	507	51	,	,	PUNCT
ejpam-4655	507	52	r	r	NOUN
ejpam-4655	507	53	}	}	PUNCT
ejpam-4655	507	54	,	,	PUNCT
ejpam-4655	507	55	{	{	PUNCT
ejpam-4655	507	56	q	q	X
ejpam-4655	507	57	,	,	PUNCT
ejpam-4655	507	58	s	s	PART
ejpam-4655	507	59	}	}	PUNCT
ejpam-4655	507	60	,	,	PUNCT
ejpam-4655	507	61	{	{	PUNCT
ejpam-4655	507	62	r	r	NOUN
ejpam-4655	507	63	,	,	PUNCT
ejpam-4655	507	64	s	s	PART
ejpam-4655	507	65	}	}	PUNCT
ejpam-4655	507	66	,	,	PUNCT
ejpam-4655	507	67	{	{	PUNCT
ejpam-4655	507	68	p	p	X
ejpam-4655	507	69	,	,	PUNCT
ejpam-4655	507	70	q	q	ADJ
ejpam-4655	507	71	,	,	PUNCT
ejpam-4655	507	72	r	r	NOUN
ejpam-4655	507	73	}	}	PUNCT
ejpam-4655	507	74	,	,	PUNCT
ejpam-4655	507	75	{	{	PUNCT
ejpam-4655	507	76	p	p	X
ejpam-4655	507	77	,	,	PUNCT
ejpam-4655	507	78	q	q	X
ejpam-4655	507	79	,	,	PUNCT
ejpam-4655	507	80	s	s	PART
ejpam-4655	507	81	}	}	PUNCT
ejpam-4655	507	82	,	,	PUNCT
ejpam-4655	507	83	{	{	PUNCT
ejpam-4655	507	84	p	p	X
ejpam-4655	507	85	,	,	PUNCT
ejpam-4655	507	86	r	r	NOUN
ejpam-4655	507	87	,	,	PUNCT
ejpam-4655	507	88	s	s	PART
ejpam-4655	507	89	}	}	PUNCT
ejpam-4655	507	90	,	,	PUNCT
ejpam-4655	507	91	{	{	PUNCT
ejpam-4655	507	92	q	q	X
ejpam-4655	507	93	,	,	PUNCT
ejpam-4655	507	94	r	r	NOUN
ejpam-4655	507	95	,	,	PUNCT
ejpam-4655	507	96	s	s	PART
ejpam-4655	507	97	}	}	PUNCT
ejpam-4655	507	98	,	,	PUNCT
ejpam-4655	507	99	x	x	NOUN
ejpam-4655	507	100	}	}	PUNCT
ejpam-4655	507	101	and	and	CCONJ
ejpam-4655	507	102	µ2	µ2	PROPN
ejpam-4655	507	103	=	=	PUNCT
ejpam-4655	507	104	{	{	PUNCT
ejpam-4655	507	105	∅	∅	NOUN
ejpam-4655	507	106	,	,	PUNCT
ejpam-4655	507	107	{	{	PUNCT
ejpam-4655	507	108	p	p	X
ejpam-4655	507	109	,	,	PUNCT
ejpam-4655	507	110	s	s	PART
ejpam-4655	507	111	}	}	PUNCT
ejpam-4655	507	112	,	,	PUNCT
ejpam-4655	507	113	{	{	PUNCT
ejpam-4655	507	114	q	q	X
ejpam-4655	507	115	,	,	PUNCT
ejpam-4655	507	116	s	s	PART
ejpam-4655	507	117	}	}	PUNCT
ejpam-4655	507	118	,	,	PUNCT
ejpam-4655	507	119	{	{	PUNCT
ejpam-4655	507	120	p	p	X
ejpam-4655	507	121	,	,	PUNCT
ejpam-4655	507	122	q	q	ADJ
ejpam-4655	507	123	,	,	PUNCT
ejpam-4655	507	124	s	s	PART
ejpam-4655	507	125	}	}	PUNCT
ejpam-4655	507	126	}	}	PUNCT
ejpam-4655	507	127	.	.	PUNCT
ejpam-4655	508	1	here	here	ADV
ejpam-4655	508	2	{	{	PUNCT
ejpam-4655	508	3	s	s	X
ejpam-4655	508	4	}	}	PUNCT
ejpam-4655	508	5	,	,	PUNCT
ejpam-4655	508	6	{	{	PUNCT
ejpam-4655	508	7	p	p	X
ejpam-4655	508	8	,	,	PUNCT
ejpam-4655	508	9	q	q	NOUN
ejpam-4655	508	10	}	}	PUNCT
ejpam-4655	508	11	,	,	PUNCT
ejpam-4655	508	12	{	{	PUNCT
ejpam-4655	508	13	p	p	X
ejpam-4655	508	14	,	,	PUNCT
ejpam-4655	508	15	s	s	PART
ejpam-4655	508	16	}	}	PUNCT
ejpam-4655	508	17	,	,	PUNCT
ejpam-4655	508	18	{	{	PUNCT
ejpam-4655	508	19	q	q	X
ejpam-4655	508	20	,	,	PUNCT
ejpam-4655	508	21	s	s	PART
ejpam-4655	508	22	}	}	PUNCT
ejpam-4655	508	23	,	,	PUNCT
ejpam-4655	508	24	{	{	PUNCT
ejpam-4655	508	25	r	r	NOUN
ejpam-4655	508	26	,	,	PUNCT
ejpam-4655	508	27	s	s	PART
ejpam-4655	508	28	}	}	PUNCT
ejpam-4655	508	29	,	,	PUNCT
ejpam-4655	508	30	{	{	PUNCT
ejpam-4655	508	31	p	p	X
ejpam-4655	508	32	,	,	PUNCT
ejpam-4655	508	33	q	q	ADJ
ejpam-4655	508	34	,	,	PUNCT
ejpam-4655	508	35	r	r	NOUN
ejpam-4655	508	36	}	}	PUNCT
ejpam-4655	508	37	,	,	PUNCT
ejpam-4655	508	38	{	{	PUNCT
ejpam-4655	508	39	p	p	X
ejpam-4655	508	40	,	,	PUNCT
ejpam-4655	508	41	q	q	X
ejpam-4655	508	42	,	,	PUNCT
ejpam-4655	508	43	s	s	PART
ejpam-4655	508	44	}	}	PUNCT
ejpam-4655	508	45	,	,	PUNCT
ejpam-4655	508	46	{	{	PUNCT
ejpam-4655	508	47	p	p	X
ejpam-4655	508	48	,	,	PUNCT
ejpam-4655	508	49	r	r	NOUN
ejpam-4655	508	50	,	,	PUNCT
ejpam-4655	508	51	s	s	PART
ejpam-4655	508	52	}	}	PUNCT
ejpam-4655	508	53	,	,	PUNCT
ejpam-4655	508	54	{	{	PUNCT
ejpam-4655	508	55	q	q	X
ejpam-4655	508	56	,	,	PUNCT
ejpam-4655	508	57	r	r	NOUN
ejpam-4655	508	58	,	,	PUNCT
ejpam-4655	508	59	s	s	PART
ejpam-4655	508	60	}	}	PUNCT
ejpam-4655	508	61	and	and	CCONJ
ejpam-4655	508	62	x	x	X
ejpam-4655	508	63	are	be	AUX
ejpam-4655	508	64	(	(	PUNCT
ejpam-4655	508	65	1	1	NUM
ejpam-4655	508	66	,	,	PUNCT
ejpam-4655	508	67	2)-dense	2)-dense	NUM
ejpam-4655	508	68	subsets	subset	NOUN
ejpam-4655	508	69	of	of	ADP
ejpam-4655	508	70	x.	x.	NOUN
ejpam-4655	508	71	thus	thus	ADV
ejpam-4655	508	72	,	,	PUNCT
ejpam-4655	508	73	(	(	PUNCT
ejpam-4655	508	74	1	1	NUM
ejpam-4655	508	75	,	,	PUNCT
ejpam-4655	508	76	2	2	NUM
ejpam-4655	508	77	)	)	PUNCT
ejpam-4655	508	78	−	−	PROPN
ejpam-4655	508	79	d(x	d(x	PROPN
ejpam-4655	508	80	)	)	PUNCT
ejpam-4655	508	81	⊂	⊂	PROPN
ejpam-4655	508	82	µ1	µ1	PROPN
ejpam-4655	508	83	.	.	PUNCT
ejpam-4655	509	1	hence	hence	ADV
ejpam-4655	509	2	x	x	PRON
ejpam-4655	509	3	is	be	AUX
ejpam-4655	509	4	a	a	DET
ejpam-4655	509	5	(	(	PUNCT
ejpam-4655	509	6	1	1	NUM
ejpam-4655	509	7	,	,	PUNCT
ejpam-4655	509	8	2)⋆-bigeneralized	2)⋆-bigeneralized	NUM
ejpam-4655	509	9	submaximal	submaximal	ADJ
ejpam-4655	509	10	space	space	NOUN
ejpam-4655	509	11	.	.	PUNCT
ejpam-4655	510	1	(	(	PUNCT
ejpam-4655	510	2	b	b	X
ejpam-4655	510	3	)	)	PUNCT
ejpam-4655	510	4	consider	consider	VERB
ejpam-4655	510	5	the	the	DET
ejpam-4655	510	6	bigeneralized	bigeneralized	ADJ
ejpam-4655	510	7	topological	topological	ADJ
ejpam-4655	510	8	space	space	NOUN
ejpam-4655	510	9	(	(	PUNCT
ejpam-4655	510	10	x,µ1	x,µ1	PROPN
ejpam-4655	510	11	,	,	PUNCT
ejpam-4655	510	12	µ2	µ2	PROPN
ejpam-4655	510	13	)	)	PUNCT
ejpam-4655	511	1	where	where	SCONJ
ejpam-4655	511	2	x	x	X
ejpam-4655	511	3	=	=	PRON
ejpam-4655	511	4	{	{	PUNCT
ejpam-4655	511	5	p	p	X
ejpam-4655	511	6	,	,	PUNCT
ejpam-4655	511	7	q	q	ADJ
ejpam-4655	511	8	,	,	PUNCT
ejpam-4655	511	9	r	r	NOUN
ejpam-4655	511	10	,	,	PUNCT
ejpam-4655	511	11	s};µ1	s};µ1	PROPN
ejpam-4655	511	12	=	=	SYM
ejpam-4655	511	13	{	{	PUNCT
ejpam-4655	511	14	∅	∅	NOUN
ejpam-4655	511	15	,	,	PUNCT
ejpam-4655	511	16	{	{	PUNCT
ejpam-4655	511	17	p	p	X
ejpam-4655	511	18	,	,	PUNCT
ejpam-4655	511	19	q	q	NOUN
ejpam-4655	511	20	}	}	PUNCT
ejpam-4655	511	21	,	,	PUNCT
ejpam-4655	511	22	{	{	PUNCT
ejpam-4655	511	23	q	q	X
ejpam-4655	511	24	,	,	PUNCT
ejpam-4655	511	25	r	r	NOUN
ejpam-4655	511	26	}	}	PUNCT
ejpam-4655	511	27	,	,	PUNCT
ejpam-4655	511	28	{	{	PUNCT
ejpam-4655	511	29	p	p	X
ejpam-4655	511	30	,	,	PUNCT
ejpam-4655	511	31	q	q	ADJ
ejpam-4655	511	32	,	,	PUNCT
ejpam-4655	511	33	r	r	NOUN
ejpam-4655	511	34	}	}	PUNCT
ejpam-4655	511	35	}	}	PUNCT
ejpam-4655	511	36	and	and	CCONJ
ejpam-4655	511	37	µ2	µ2	PROPN
ejpam-4655	511	38	=	=	PUNCT
ejpam-4655	511	39	{	{	PUNCT
ejpam-4655	511	40	∅	∅	NOUN
ejpam-4655	511	41	,	,	PUNCT
ejpam-4655	511	42	{	{	PUNCT
ejpam-4655	511	43	q	q	X
ejpam-4655	511	44	}	}	PUNCT
ejpam-4655	511	45	,	,	PUNCT
ejpam-4655	511	46	{	{	PUNCT
ejpam-4655	511	47	p	p	X
ejpam-4655	511	48	,	,	PUNCT
ejpam-4655	511	49	q	q	NOUN
ejpam-4655	511	50	}	}	PUNCT
ejpam-4655	511	51	,	,	PUNCT
ejpam-4655	511	52	{	{	PUNCT
ejpam-4655	511	53	p	p	X
ejpam-4655	511	54	,	,	PUNCT
ejpam-4655	511	55	r	r	NOUN
ejpam-4655	511	56	}	}	PUNCT
ejpam-4655	511	57	,	,	PUNCT
ejpam-4655	511	58	{	{	PUNCT
ejpam-4655	511	59	p	p	X
ejpam-4655	511	60	,	,	PUNCT
ejpam-4655	511	61	s	s	PART
ejpam-4655	511	62	}	}	PUNCT
ejpam-4655	511	63	,	,	PUNCT
ejpam-4655	511	64	{	{	PUNCT
ejpam-4655	511	65	q	q	X
ejpam-4655	511	66	,	,	PUNCT
ejpam-4655	511	67	r	r	NOUN
ejpam-4655	511	68	}	}	PUNCT
ejpam-4655	511	69	,	,	PUNCT
ejpam-4655	511	70	{	{	PUNCT
ejpam-4655	511	71	q	q	X
ejpam-4655	511	72	,	,	PUNCT
ejpam-4655	511	73	s	s	PART
ejpam-4655	511	74	}	}	PUNCT
ejpam-4655	511	75	,	,	PUNCT
ejpam-4655	511	76	{	{	PUNCT
ejpam-4655	511	77	r	r	NOUN
ejpam-4655	511	78	,	,	PUNCT
ejpam-4655	511	79	s	s	PART
ejpam-4655	511	80	}	}	PUNCT
ejpam-4655	511	81	,	,	PUNCT
ejpam-4655	511	82	{	{	PUNCT
ejpam-4655	511	83	p	p	X
ejpam-4655	511	84	,	,	PUNCT
ejpam-4655	511	85	q	q	ADJ
ejpam-4655	511	86	,	,	PUNCT
ejpam-4655	511	87	r	r	NOUN
ejpam-4655	511	88	}	}	PUNCT
ejpam-4655	511	89	,	,	PUNCT
ejpam-4655	511	90	{	{	PUNCT
ejpam-4655	511	91	p	p	X
ejpam-4655	511	92	,	,	PUNCT
ejpam-4655	511	93	q	q	X
ejpam-4655	511	94	,	,	PUNCT
ejpam-4655	511	95	s	s	PART
ejpam-4655	511	96	}	}	PUNCT
ejpam-4655	511	97	,	,	PUNCT
ejpam-4655	511	98	{	{	PUNCT
ejpam-4655	511	99	p	p	X
ejpam-4655	511	100	,	,	PUNCT
ejpam-4655	511	101	r	r	NOUN
ejpam-4655	511	102	,	,	PUNCT
ejpam-4655	511	103	s	s	PART
ejpam-4655	511	104	}	}	PUNCT
ejpam-4655	511	105	,	,	PUNCT
ejpam-4655	511	106	{	{	PUNCT
ejpam-4655	511	107	q	q	X
ejpam-4655	511	108	,	,	PUNCT
ejpam-4655	511	109	r	r	NOUN
ejpam-4655	511	110	,	,	PUNCT
ejpam-4655	511	111	s	s	PART
ejpam-4655	511	112	}	}	PUNCT
ejpam-4655	511	113	,	,	PUNCT
ejpam-4655	511	114	x}.here	x}.here	PROPN
ejpam-4655	511	115	{	{	PUNCT
ejpam-4655	511	116	q	q	X
ejpam-4655	511	117	}	}	PUNCT
ejpam-4655	511	118	,	,	PUNCT
ejpam-4655	511	119	{	{	PUNCT
ejpam-4655	511	120	p	p	X
ejpam-4655	511	121	,	,	PUNCT
ejpam-4655	511	122	q	q	NOUN
ejpam-4655	511	123	}	}	PUNCT
ejpam-4655	511	124	,	,	PUNCT
ejpam-4655	511	125	{	{	PUNCT
ejpam-4655	511	126	p	p	X
ejpam-4655	511	127	,	,	PUNCT
ejpam-4655	511	128	r	r	NOUN
ejpam-4655	511	129	}	}	PUNCT
ejpam-4655	511	130	,	,	PUNCT
ejpam-4655	511	131	{	{	PUNCT
ejpam-4655	511	132	q	q	X
ejpam-4655	511	133	,	,	PUNCT
ejpam-4655	511	134	r	r	NOUN
ejpam-4655	511	135	}	}	PUNCT
ejpam-4655	511	136	,	,	PUNCT
ejpam-4655	511	137	{	{	PUNCT
ejpam-4655	511	138	q	q	X
ejpam-4655	511	139	,	,	PUNCT
ejpam-4655	511	140	s	s	PART
ejpam-4655	511	141	}	}	PUNCT
ejpam-4655	511	142	,	,	PUNCT
ejpam-4655	511	143	{	{	PUNCT
ejpam-4655	511	144	p	p	X
ejpam-4655	511	145	,	,	PUNCT
ejpam-4655	511	146	q	q	ADJ
ejpam-4655	511	147	,	,	PUNCT
ejpam-4655	511	148	r	r	NOUN
ejpam-4655	511	149	}	}	PUNCT
ejpam-4655	511	150	,	,	PUNCT
ejpam-4655	511	151	{	{	PUNCT
ejpam-4655	511	152	p	p	X
ejpam-4655	511	153	,	,	PUNCT
ejpam-4655	511	154	q	q	X
ejpam-4655	511	155	,	,	PUNCT
ejpam-4655	511	156	s	s	PART
ejpam-4655	511	157	}	}	PUNCT
ejpam-4655	511	158	,	,	PUNCT
ejpam-4655	511	159	{	{	PUNCT
ejpam-4655	511	160	p	p	X
ejpam-4655	511	161	,	,	PUNCT
ejpam-4655	511	162	r	r	NOUN
ejpam-4655	511	163	,	,	PUNCT
ejpam-4655	511	164	s	s	PART
ejpam-4655	511	165	}	}	PUNCT
ejpam-4655	511	166	,	,	PUNCT
ejpam-4655	511	167	{	{	PUNCT
ejpam-4655	511	168	q	q	X
ejpam-4655	511	169	,	,	PUNCT
ejpam-4655	511	170	r	r	NOUN
ejpam-4655	511	171	,	,	PUNCT
ejpam-4655	511	172	s	s	PART
ejpam-4655	511	173	}	}	PUNCT
ejpam-4655	511	174	and	and	CCONJ
ejpam-4655	511	175	x	x	X
ejpam-4655	511	176	are	be	AUX
ejpam-4655	511	177	(	(	PUNCT
ejpam-4655	511	178	2	2	NUM
ejpam-4655	511	179	,	,	PUNCT
ejpam-4655	511	180	1)-dense	1)-dense	NUM
ejpam-4655	511	181	subsets	subset	NOUN
ejpam-4655	511	182	of	of	ADP
ejpam-4655	511	183	x.	x.	NOUN
ejpam-4655	511	184	thus	thus	ADV
ejpam-4655	511	185	,	,	PUNCT
ejpam-4655	511	186	(	(	PUNCT
ejpam-4655	511	187	2	2	NUM
ejpam-4655	511	188	,	,	PUNCT
ejpam-4655	511	189	1	1	NUM
ejpam-4655	511	190	)	)	PUNCT
ejpam-4655	511	191	−	−	PROPN
ejpam-4655	511	192	d(x	d(x	PROPN
ejpam-4655	511	193	)	)	PUNCT
ejpam-4655	512	1	⊂	⊂	PROPN
ejpam-4655	512	2	µ2	µ2	PROPN
ejpam-4655	512	3	.	.	PUNCT
ejpam-4655	513	1	hence	hence	ADV
ejpam-4655	513	2	x	x	PRON
ejpam-4655	513	3	is	be	AUX
ejpam-4655	513	4	a	a	DET
ejpam-4655	513	5	(	(	PUNCT
ejpam-4655	513	6	2	2	NUM
ejpam-4655	513	7	,	,	PUNCT
ejpam-4655	513	8	1)⋆-bigeneralized	1)⋆-bigeneralized	NUM
ejpam-4655	513	9	submaximal	submaximal	ADJ
ejpam-4655	513	10	space	space	NOUN
ejpam-4655	513	11	.	.	PUNCT
ejpam-4655	514	1	y.	y.	PROPN
ejpam-4655	514	2	farhat	farhat	PROPN
ejpam-4655	514	3	et	et	PROPN
ejpam-4655	514	4	al	al	PROPN
ejpam-4655	514	5	.	.	PUNCT
ejpam-4655	514	6	/	/	SYM
ejpam-4655	514	7	eur	eur	PROPN
ejpam-4655	514	8	.	.	PUNCT
ejpam-4655	515	1	j.	j.	PROPN
ejpam-4655	515	2	pure	pure	PROPN
ejpam-4655	515	3	appl	appl	PROPN
ejpam-4655	515	4	.	.	PROPN
ejpam-4655	515	5	math	math	PROPN
ejpam-4655	515	6	,	,	PUNCT
ejpam-4655	515	7	16	16	NUM
ejpam-4655	515	8	(	(	PUNCT
ejpam-4655	515	9	1	1	NUM
ejpam-4655	515	10	)	)	PUNCT
ejpam-4655	515	11	(	(	PUNCT
ejpam-4655	515	12	2023	2023	NUM
ejpam-4655	515	13	)	)	PUNCT
ejpam-4655	515	14	,	,	PUNCT
ejpam-4655	515	15	386	386	NUM
ejpam-4655	515	16	-	-	SYM
ejpam-4655	515	17	403	403	NUM
ejpam-4655	515	18	398	398	NUM
ejpam-4655	515	19	theorem	theorem	NOUN
ejpam-4655	515	20	29	29	NUM
ejpam-4655	515	21	.	.	PUNCT
ejpam-4655	516	1	let	let	AUX
ejpam-4655	516	2	(	(	PUNCT
ejpam-4655	516	3	x,µ1	x,µ1	NOUN
ejpam-4655	516	4	,	,	PUNCT
ejpam-4655	516	5	µ2	µ2	PROPN
ejpam-4655	516	6	)	)	PUNCT
ejpam-4655	516	7	be	be	AUX
ejpam-4655	516	8	a	a	DET
ejpam-4655	516	9	bgts	bgts	NOUN
ejpam-4655	516	10	.	.	PUNCT
ejpam-4655	517	1	if	if	SCONJ
ejpam-4655	517	2	cµs(frv(j	cµs(frv(j	NOUN
ejpam-4655	517	3	)	)	PUNCT
ejpam-4655	517	4	)	)	PUNCT
ejpam-4655	518	1	=	=	PUNCT
ejpam-4655	519	1	x	x	X
ejpam-4655	519	2	,	,	PUNCT
ejpam-4655	519	3	then	then	ADV
ejpam-4655	519	4	j	j	PROPN
ejpam-4655	519	5	∈	∈	PROPN
ejpam-4655	519	6	(	(	PUNCT
ejpam-4655	519	7	s	s	PROPN
ejpam-4655	519	8	,	,	PUNCT
ejpam-4655	519	9	v	v	NOUN
ejpam-4655	519	10	)	)	PUNCT
ejpam-4655	519	11	−	−	PROPN
ejpam-4655	519	12	d(x	d(x	NOUN
ejpam-4655	519	13	)	)	PUNCT
ejpam-4655	519	14	where	where	SCONJ
ejpam-4655	519	15	s	s	X
ejpam-4655	519	16	,	,	PUNCT
ejpam-4655	519	17	v	v	NOUN
ejpam-4655	519	18	=	=	SYM
ejpam-4655	519	19	1	1	NUM
ejpam-4655	519	20	,	,	PUNCT
ejpam-4655	519	21	2	2	NUM
ejpam-4655	519	22	and	and	CCONJ
ejpam-4655	519	23	s	s	VERB
ejpam-4655	519	24	̸=	̸=	PROPN
ejpam-4655	519	25	v.	v.	ADP
ejpam-4655	519	26	proof	proof	NOUN
ejpam-4655	519	27	.	.	PUNCT
ejpam-4655	520	1	fix	fix	NOUN
ejpam-4655	520	2	s	s	PART
ejpam-4655	520	3	=	=	SYM
ejpam-4655	520	4	1	1	NUM
ejpam-4655	520	5	,	,	PUNCT
ejpam-4655	520	6	v	v	NOUN
ejpam-4655	520	7	=	=	SYM
ejpam-4655	520	8	2	2	NUM
ejpam-4655	520	9	;	;	PUNCT
ejpam-4655	520	10	assume	assume	VERB
ejpam-4655	520	11	that	that	SCONJ
ejpam-4655	520	12	,	,	PUNCT
ejpam-4655	520	13	cµ1(fr2(j	cµ1(fr2(j	NUM
ejpam-4655	520	14	)	)	PUNCT
ejpam-4655	520	15	)	)	PUNCT
ejpam-4655	521	1	=	=	PUNCT
ejpam-4655	521	2	x	x	PUNCT
ejpam-4655	521	3	by	by	ADP
ejpam-4655	521	4	which	which	PRON
ejpam-4655	521	5	c1(c2j	c1(c2j	PROPN
ejpam-4655	521	6	∩c2(x−j	∩c2(x−j	PROPN
ejpam-4655	521	7	)	)	PUNCT
ejpam-4655	521	8	)	)	PUNCT
ejpam-4655	522	1	=	=	PUNCT
ejpam-4655	523	1	x	x	PUNCT
ejpam-4655	523	2	and	and	CCONJ
ejpam-4655	523	3	so	so	ADV
ejpam-4655	523	4	c1(c2(j	c1(c2(j	NOUN
ejpam-4655	523	5	)	)	PUNCT
ejpam-4655	523	6	)	)	PUNCT
ejpam-4655	524	1	=	=	SYM
ejpam-4655	524	2	x	x	X
ejpam-4655	524	3	,	,	PUNCT
ejpam-4655	524	4	thus	thus	ADV
ejpam-4655	524	5	,	,	PUNCT
ejpam-4655	524	6	j	j	PROPN
ejpam-4655	524	7	∈	∈	PROPN
ejpam-4655	524	8	(	(	PUNCT
ejpam-4655	524	9	1	1	NUM
ejpam-4655	524	10	,	,	PUNCT
ejpam-4655	524	11	2)−d(x	2)−d(x	NUM
ejpam-4655	524	12	)	)	PUNCT
ejpam-4655	524	13	.	.	PUNCT
ejpam-4655	525	1	similarly	similarly	ADV
ejpam-4655	525	2	,	,	PUNCT
ejpam-4655	525	3	we	we	PRON
ejpam-4655	525	4	can	can	AUX
ejpam-4655	525	5	prove	prove	VERB
ejpam-4655	525	6	that	that	SCONJ
ejpam-4655	525	7	the	the	DET
ejpam-4655	525	8	result	result	NOUN
ejpam-4655	525	9	is	be	AUX
ejpam-4655	525	10	true	true	ADJ
ejpam-4655	525	11	for	for	ADP
ejpam-4655	525	12	s	s	NOUN
ejpam-4655	525	13	=	=	SYM
ejpam-4655	525	14	2	2	NUM
ejpam-4655	525	15	,	,	PUNCT
ejpam-4655	525	16	v	v	NOUN
ejpam-4655	525	17	=	=	SYM
ejpam-4655	525	18	1	1	NUM
ejpam-4655	525	19	.	.	PUNCT
ejpam-4655	526	1	the	the	DET
ejpam-4655	526	2	below	below	ADJ
ejpam-4655	526	3	corollary	corollary	ADJ
ejpam-4655	526	4	30	30	NUM
ejpam-4655	526	5	is	be	AUX
ejpam-4655	526	6	the	the	DET
ejpam-4655	526	7	direct	direct	ADJ
ejpam-4655	526	8	consequence	consequence	NOUN
ejpam-4655	526	9	of	of	ADP
ejpam-4655	526	10	the	the	DET
ejpam-4655	526	11	above	above	ADJ
ejpam-4655	526	12	theorem	theorem	NOUN
ejpam-4655	526	13	29	29	NUM
ejpam-4655	526	14	and	and	CCONJ
ejpam-4655	526	15	definition	definition	NOUN
ejpam-4655	526	16	27	27	NUM
ejpam-4655	526	17	,	,	PUNCT
ejpam-4655	526	18	so	so	CCONJ
ejpam-4655	526	19	the	the	DET
ejpam-4655	526	20	easy	easy	ADJ
ejpam-4655	526	21	proof	proof	NOUN
ejpam-4655	526	22	is	be	AUX
ejpam-4655	526	23	omitted	omit	VERB
ejpam-4655	526	24	.	.	PUNCT
ejpam-4655	527	1	corollary	corollary	ADJ
ejpam-4655	527	2	30	30	NUM
ejpam-4655	527	3	.	.	PUNCT
ejpam-4655	528	1	let	let	AUX
ejpam-4655	528	2	(	(	PUNCT
ejpam-4655	528	3	x,µ1	x,µ1	NOUN
ejpam-4655	528	4	,	,	PUNCT
ejpam-4655	528	5	µ2	µ2	PROPN
ejpam-4655	528	6	)	)	PUNCT
ejpam-4655	528	7	be	be	VERB
ejpam-4655	528	8	a	a	DET
ejpam-4655	528	9	(	(	PUNCT
ejpam-4655	528	10	s	s	PROPN
ejpam-4655	528	11	,	,	PUNCT
ejpam-4655	528	12	v)⋆-bigeneralized	v)⋆-bigeneralize	VERB
ejpam-4655	528	13	submaximal	submaximal	ADJ
ejpam-4655	528	14	space	space	NOUN
ejpam-4655	528	15	.	.	PUNCT
ejpam-4655	529	1	if	if	SCONJ
ejpam-4655	529	2	cµs(frv(q	cµs(frv(q	PROPN
ejpam-4655	529	3	)	)	PUNCT
ejpam-4655	529	4	)	)	PUNCT
ejpam-4655	530	1	=	=	SYM
ejpam-4655	530	2	x	x	X
ejpam-4655	530	3	,	,	PUNCT
ejpam-4655	530	4	then	then	ADV
ejpam-4655	530	5	q	q	PROPN
ejpam-4655	530	6	∈	∈	PROPN
ejpam-4655	530	7	µs	µs	VERB
ejpam-4655	530	8	where	where	SCONJ
ejpam-4655	530	9	s	s	X
ejpam-4655	530	10	,	,	PUNCT
ejpam-4655	530	11	v	v	NOUN
ejpam-4655	530	12	=	=	SYM
ejpam-4655	530	13	1	1	NUM
ejpam-4655	530	14	,	,	PUNCT
ejpam-4655	530	15	2	2	NUM
ejpam-4655	530	16	;	;	PUNCT
ejpam-4655	530	17	s	s	VERB
ejpam-4655	530	18	̸=	̸=	PROPN
ejpam-4655	530	19	v.	v.	ADP
ejpam-4655	530	20	theorem	theorem	PROPN
ejpam-4655	530	21	31	31	NUM
ejpam-4655	530	22	.	.	PUNCT
ejpam-4655	531	1	let	let	AUX
ejpam-4655	531	2	(	(	PUNCT
ejpam-4655	531	3	x,µ1	x,µ1	NOUN
ejpam-4655	531	4	,	,	PUNCT
ejpam-4655	531	5	µ2	µ2	PROPN
ejpam-4655	531	6	)	)	PUNCT
ejpam-4655	531	7	be	be	AUX
ejpam-4655	531	8	a	a	DET
ejpam-4655	531	9	bgts	bgts	NOUN
ejpam-4655	531	10	.	.	PUNCT
ejpam-4655	532	1	if	if	SCONJ
ejpam-4655	532	2	x	x	PRON
ejpam-4655	532	3	is	be	AUX
ejpam-4655	532	4	a	a	DET
ejpam-4655	532	5	(	(	PUNCT
ejpam-4655	532	6	s	s	PROPN
ejpam-4655	532	7	,	,	PUNCT
ejpam-4655	532	8	v)⋆-bigeneralized	v)⋆-bigeneralize	VERB
ejpam-4655	532	9	submaximal	submaximal	ADJ
ejpam-4655	532	10	space	space	NOUN
ejpam-4655	532	11	,	,	PUNCT
ejpam-4655	532	12	then	then	ADV
ejpam-4655	532	13	x	x	PUNCT
ejpam-4655	532	14	is	be	AUX
ejpam-4655	532	15	a	a	DET
ejpam-4655	532	16	(	(	PUNCT
ejpam-4655	532	17	s	s	PROPN
ejpam-4655	532	18	,	,	PUNCT
ejpam-4655	532	19	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	532	20	submaximal	submaximal	ADJ
ejpam-4655	532	21	space	space	NOUN
ejpam-4655	532	22	where	where	SCONJ
ejpam-4655	532	23	s	s	X
ejpam-4655	532	24	,	,	PUNCT
ejpam-4655	532	25	v	v	NOUN
ejpam-4655	532	26	=	=	SYM
ejpam-4655	532	27	1	1	NUM
ejpam-4655	532	28	,	,	PUNCT
ejpam-4655	532	29	2	2	NUM
ejpam-4655	532	30	;	;	PUNCT
ejpam-4655	532	31	s	s	VERB
ejpam-4655	532	32	̸=	̸=	PROPN
ejpam-4655	532	33	v.	v.	ADP
ejpam-4655	532	34	proof	proof	NOUN
ejpam-4655	532	35	.	.	PUNCT
ejpam-4655	533	1	consider	consider	VERB
ejpam-4655	533	2	,	,	PUNCT
ejpam-4655	533	3	s	s	PART
ejpam-4655	533	4	=	=	SYM
ejpam-4655	533	5	1	1	NUM
ejpam-4655	533	6	,	,	PUNCT
ejpam-4655	533	7	v	v	NOUN
ejpam-4655	533	8	=	=	SYM
ejpam-4655	533	9	2	2	NUM
ejpam-4655	533	10	;	;	PUNCT
ejpam-4655	533	11	assume	assume	VERB
ejpam-4655	533	12	that	that	SCONJ
ejpam-4655	533	13	,	,	PUNCT
ejpam-4655	533	14	x	x	PRON
ejpam-4655	533	15	is	be	AUX
ejpam-4655	533	16	a	a	DET
ejpam-4655	533	17	(	(	PUNCT
ejpam-4655	533	18	1	1	NUM
ejpam-4655	533	19	,	,	PUNCT
ejpam-4655	533	20	2)⋆-bigeneralized	2)⋆-bigeneralized	NUM
ejpam-4655	533	21	submaximal	submaximal	ADJ
ejpam-4655	533	22	space	space	NOUN
ejpam-4655	533	23	and	and	CCONJ
ejpam-4655	533	24	let	let	VERB
ejpam-4655	533	25	c2(j	c2(j	NOUN
ejpam-4655	533	26	)	)	PUNCT
ejpam-4655	533	27	=	=	PUNCT
ejpam-4655	534	1	x	x	X
ejpam-4655	534	2	for	for	ADP
ejpam-4655	534	3	that	that	DET
ejpam-4655	534	4	reason	reason	NOUN
ejpam-4655	534	5	c1(c2(j	c1(c2(j	NOUN
ejpam-4655	534	6	)	)	PUNCT
ejpam-4655	534	7	)	)	PUNCT
ejpam-4655	535	1	=	=	PUNCT
ejpam-4655	535	2	x	x	X
ejpam-4655	535	3	it	it	PRON
ejpam-4655	535	4	turns	turn	VERB
ejpam-4655	535	5	out	out	ADP
ejpam-4655	535	6	j	j	PROPN
ejpam-4655	535	7	∈	∈	PROPN
ejpam-4655	535	8	(	(	PUNCT
ejpam-4655	535	9	1	1	NUM
ejpam-4655	535	10	,	,	PUNCT
ejpam-4655	535	11	2	2	NUM
ejpam-4655	535	12	)	)	PUNCT
ejpam-4655	535	13	−	−	PROPN
ejpam-4655	535	14	d(x	d(x	NOUN
ejpam-4655	535	15	)	)	PUNCT
ejpam-4655	535	16	whereby	whereby	SCONJ
ejpam-4655	535	17	by	by	ADP
ejpam-4655	535	18	our	our	PRON
ejpam-4655	535	19	assumption	assumption	NOUN
ejpam-4655	535	20	,	,	PUNCT
ejpam-4655	535	21	j	j	PROPN
ejpam-4655	535	22	∈	∈	PROPN
ejpam-4655	535	23	µ1	µ1	PROPN
ejpam-4655	535	24	so	so	SCONJ
ejpam-4655	535	25	it	it	PRON
ejpam-4655	535	26	result	result	VERB
ejpam-4655	535	27	that	that	SCONJ
ejpam-4655	535	28	x	x	PRON
ejpam-4655	535	29	is	be	AUX
ejpam-4655	535	30	a	a	DET
ejpam-4655	535	31	(	(	PUNCT
ejpam-4655	535	32	1	1	NUM
ejpam-4655	535	33	,	,	PUNCT
ejpam-4655	535	34	2)-bigeneralized	2)-bigeneralized	NUM
ejpam-4655	535	35	submaximal	submaximal	ADJ
ejpam-4655	535	36	space	space	NOUN
ejpam-4655	535	37	.	.	PUNCT
ejpam-4655	536	1	by	by	ADP
ejpam-4655	536	2	the	the	DET
ejpam-4655	536	3	same	same	ADJ
ejpam-4655	536	4	considerations	consideration	NOUN
ejpam-4655	536	5	in	in	ADP
ejpam-4655	536	6	the	the	DET
ejpam-4655	536	7	above	above	ADJ
ejpam-4655	536	8	case	case	NOUN
ejpam-4655	536	9	,	,	PUNCT
ejpam-4655	536	10	we	we	PRON
ejpam-4655	536	11	can	can	AUX
ejpam-4655	536	12	prove	prove	VERB
ejpam-4655	536	13	that	that	SCONJ
ejpam-4655	536	14	this	this	DET
ejpam-4655	536	15	result	result	NOUN
ejpam-4655	536	16	is	be	AUX
ejpam-4655	536	17	true	true	ADJ
ejpam-4655	536	18	for	for	ADP
ejpam-4655	536	19	s	s	NOUN
ejpam-4655	536	20	=	=	SYM
ejpam-4655	536	21	2	2	NUM
ejpam-4655	536	22	,	,	PUNCT
ejpam-4655	536	23	v	v	NOUN
ejpam-4655	536	24	=	=	SYM
ejpam-4655	536	25	1	1	NUM
ejpam-4655	536	26	.	.	PUNCT
ejpam-4655	536	27	theorem	theorem	VERB
ejpam-4655	536	28	32	32	NUM
ejpam-4655	536	29	describes	describe	VERB
ejpam-4655	536	30	the	the	DET
ejpam-4655	536	31	below	below	ADJ
ejpam-4655	536	32	diagram	diagram	NOUN
ejpam-4655	536	33	.	.	PUNCT
ejpam-4655	537	1	(	(	PUNCT
ejpam-4655	537	2	a	a	X
ejpam-4655	537	3	)	)	PUNCT
ejpam-4655	537	4	x	x	X
ejpam-4655	537	5	is	be	AUX
ejpam-4655	537	6	a	a	DET
ejpam-4655	537	7	(	(	PUNCT
ejpam-4655	537	8	s	s	PROPN
ejpam-4655	537	9	,	,	PUNCT
ejpam-4655	537	10	v)⋆	v)⋆	PROPN
ejpam-4655	537	11	−	−	PROPN
ejpam-4655	537	12	bigeneralized	bigeneralize	VERB
ejpam-4655	537	13	submaximal	submaximal	ADJ
ejpam-4655	537	14	space	space	NOUN
ejpam-4655	537	15	(	(	PUNCT
ejpam-4655	537	16	b	b	NOUN
ejpam-4655	537	17	)	)	PUNCT
ejpam-4655	537	18	(	(	PUNCT
ejpam-4655	537	19	c	c	NOUN
ejpam-4655	537	20	)	)	PUNCT
ejpam-4655	537	21	where	where	SCONJ
ejpam-4655	537	22	,	,	PUNCT
ejpam-4655	537	23	(	(	PUNCT
ejpam-4655	537	24	a	a	X
ejpam-4655	537	25	)	)	PUNCT
ejpam-4655	537	26	every	every	DET
ejpam-4655	537	27	µv	µv	NOUN
ejpam-4655	537	28	-	-	PUNCT
ejpam-4655	537	29	pre	pre	ADJ
ejpam-4655	537	30	-	-	ADJ
ejpam-4655	537	31	open	open	ADJ
ejpam-4655	537	32	is	be	AUX
ejpam-4655	537	33	µs	µs	NOUN
ejpam-4655	537	34	-	-	ADJ
ejpam-4655	537	35	open	open	ADJ
ejpam-4655	537	36	.	.	PUNCT
ejpam-4655	538	1	(	(	PUNCT
ejpam-4655	538	2	b	b	X
ejpam-4655	538	3	)	)	PUNCT
ejpam-4655	538	4	every	every	DET
ejpam-4655	538	5	µv	µv	NOUN
ejpam-4655	538	6	-	-	PUNCT
ejpam-4655	538	7	β	β	NOUN
ejpam-4655	538	8	-	-	ADJ
ejpam-4655	538	9	open	open	ADJ
ejpam-4655	538	10	is	be	AUX
ejpam-4655	538	11	µs	µs	NOUN
ejpam-4655	538	12	-	-	ADJ
ejpam-4655	538	13	open	open	ADJ
ejpam-4655	538	14	.	.	PUNCT
ejpam-4655	539	1	(	(	PUNCT
ejpam-4655	539	2	c	c	X
ejpam-4655	539	3	)	)	PUNCT
ejpam-4655	539	4	every	every	DET
ejpam-4655	539	5	µv	µv	PROPN
ejpam-4655	539	6	-	-	PUNCT
ejpam-4655	539	7	b	b	NOUN
ejpam-4655	539	8	-	-	PUNCT
ejpam-4655	539	9	open	open	ADJ
ejpam-4655	539	10	is	be	AUX
ejpam-4655	539	11	µs	µs	NOUN
ejpam-4655	539	12	-	-	ADJ
ejpam-4655	539	13	open	open	ADJ
ejpam-4655	539	14	.	.	PUNCT
ejpam-4655	540	1	the	the	DET
ejpam-4655	540	2	following	follow	VERB
ejpam-4655	540	3	theorem	theorem	VERB
ejpam-4655	540	4	32	32	NUM
ejpam-4655	540	5	gives	give	VERB
ejpam-4655	540	6	a	a	DET
ejpam-4655	540	7	shortcut	shortcut	NOUN
ejpam-4655	540	8	for	for	ADP
ejpam-4655	540	9	finding	find	VERB
ejpam-4655	540	10	the	the	DET
ejpam-4655	540	11	relationship	relationship	NOUN
ejpam-4655	540	12	between	between	ADP
ejpam-4655	540	13	(	(	PUNCT
ejpam-4655	540	14	v	v	NOUN
ejpam-4655	540	15	,	,	PUNCT
ejpam-4655	540	16	s)bigeneralized	s)bigeneralize	VERB
ejpam-4655	540	17	submaximal	submaximal	ADJ
ejpam-4655	540	18	space	space	NOUN
ejpam-4655	540	19	and	and	CCONJ
ejpam-4655	540	20	(	(	PUNCT
ejpam-4655	540	21	s	s	X
ejpam-4655	540	22	,	,	PUNCT
ejpam-4655	540	23	v)⋆-bigeneralized	v)⋆-bigeneralize	VERB
ejpam-4655	540	24	submaximal	submaximal	ADJ
ejpam-4655	540	25	space	space	NOUN
ejpam-4655	540	26	in	in	ADP
ejpam-4655	540	27	a	a	DET
ejpam-4655	540	28	bigeneralized	bigeneralize	VERB
ejpam-4655	540	29	topological	topological	ADJ
ejpam-4655	540	30	space	space	NOUN
ejpam-4655	540	31	.	.	PUNCT
ejpam-4655	541	1	theorem	theorem	VERB
ejpam-4655	541	2	32	32	NUM
ejpam-4655	541	3	.	.	PUNCT
ejpam-4655	542	1	let	let	AUX
ejpam-4655	542	2	(	(	PUNCT
ejpam-4655	542	3	x,µ1	x,µ1	NOUN
ejpam-4655	542	4	,	,	PUNCT
ejpam-4655	542	5	µ2	µ2	PROPN
ejpam-4655	542	6	)	)	PUNCT
ejpam-4655	542	7	be	be	VERB
ejpam-4655	542	8	a	a	DET
ejpam-4655	542	9	(	(	PUNCT
ejpam-4655	542	10	v	v	NOUN
ejpam-4655	542	11	,	,	PUNCT
ejpam-4655	542	12	s)-bigeneralized	s)-bigeneralize	VERB
ejpam-4655	542	13	submaximal	submaximal	ADJ
ejpam-4655	542	14	space	space	NOUN
ejpam-4655	542	15	.	.	PUNCT
ejpam-4655	543	1	then	then	ADV
ejpam-4655	543	2	x	x	X
ejpam-4655	543	3	is	be	AUX
ejpam-4655	543	4	a	a	DET
ejpam-4655	543	5	(	(	PUNCT
ejpam-4655	543	6	s	s	PROPN
ejpam-4655	543	7	,	,	PUNCT
ejpam-4655	543	8	v)⋆-bigeneralized	v)⋆-bigeneralize	VERB
ejpam-4655	543	9	submaximal	submaximal	ADJ
ejpam-4655	543	10	space	space	NOUN
ejpam-4655	543	11	if	if	SCONJ
ejpam-4655	543	12	any	any	DET
ejpam-4655	543	13	one	one	NUM
ejpam-4655	543	14	of	of	ADP
ejpam-4655	543	15	the	the	DET
ejpam-4655	543	16	following	follow	VERB
ejpam-4655	543	17	is	be	AUX
ejpam-4655	543	18	true	true	ADJ
ejpam-4655	543	19	;	;	PUNCT
ejpam-4655	543	20	(	(	PUNCT
ejpam-4655	543	21	a	a	X
ejpam-4655	543	22	)	)	PUNCT
ejpam-4655	543	23	every	every	DET
ejpam-4655	543	24	µv	µv	NOUN
ejpam-4655	543	25	-	-	PUNCT
ejpam-4655	543	26	pre	pre	ADJ
ejpam-4655	543	27	-	-	ADJ
ejpam-4655	543	28	open	open	ADJ
ejpam-4655	543	29	is	be	AUX
ejpam-4655	543	30	µs	µs	NOUN
ejpam-4655	543	31	-	-	ADJ
ejpam-4655	543	32	open	open	ADJ
ejpam-4655	543	33	.	.	PUNCT
ejpam-4655	544	1	(	(	PUNCT
ejpam-4655	544	2	b	b	X
ejpam-4655	544	3	)	)	PUNCT
ejpam-4655	544	4	every	every	DET
ejpam-4655	544	5	µv	µv	NOUN
ejpam-4655	544	6	-	-	PUNCT
ejpam-4655	544	7	β	β	NOUN
ejpam-4655	544	8	-	-	ADJ
ejpam-4655	544	9	open	open	ADJ
ejpam-4655	544	10	is	be	AUX
ejpam-4655	544	11	µs	µs	NOUN
ejpam-4655	544	12	-	-	ADJ
ejpam-4655	544	13	open	open	ADJ
ejpam-4655	544	14	.	.	PUNCT
ejpam-4655	545	1	(	(	PUNCT
ejpam-4655	545	2	c	c	X
ejpam-4655	545	3	)	)	PUNCT
ejpam-4655	545	4	every	every	DET
ejpam-4655	545	5	µv	µv	PROPN
ejpam-4655	545	6	-	-	PUNCT
ejpam-4655	545	7	b	b	NOUN
ejpam-4655	545	8	-	-	PUNCT
ejpam-4655	545	9	open	open	ADJ
ejpam-4655	545	10	is	be	AUX
ejpam-4655	545	11	µs	µs	NOUN
ejpam-4655	545	12	-	-	ADJ
ejpam-4655	545	13	open	open	ADJ
ejpam-4655	545	14	where	where	SCONJ
ejpam-4655	545	15	s	s	X
ejpam-4655	545	16	,	,	PUNCT
ejpam-4655	545	17	v	v	NOUN
ejpam-4655	545	18	=	=	SYM
ejpam-4655	545	19	1	1	NUM
ejpam-4655	545	20	,	,	PUNCT
ejpam-4655	545	21	2	2	NUM
ejpam-4655	545	22	and	and	CCONJ
ejpam-4655	545	23	s	s	VERB
ejpam-4655	545	24	̸=	̸=	PROPN
ejpam-4655	545	25	v.	v.	ADP
ejpam-4655	545	26	proof	proof	NOUN
ejpam-4655	545	27	.	.	PUNCT
ejpam-4655	546	1	we	we	PRON
ejpam-4655	546	2	give	give	VERB
ejpam-4655	546	3	the	the	DET
ejpam-4655	546	4	detailed	detailed	ADJ
ejpam-4655	546	5	proof	proof	NOUN
ejpam-4655	546	6	for	for	ADP
ejpam-4655	546	7	only	only	ADV
ejpam-4655	546	8	s	s	PART
ejpam-4655	546	9	=	=	SYM
ejpam-4655	546	10	1	1	NUM
ejpam-4655	546	11	,	,	PUNCT
ejpam-4655	546	12	v	v	NOUN
ejpam-4655	546	13	=	=	SYM
ejpam-4655	546	14	2	2	X
ejpam-4655	546	15	.	.	PUNCT
ejpam-4655	546	16	suppose	suppose	VERB
ejpam-4655	546	17	that	that	SCONJ
ejpam-4655	546	18	x	x	PRON
ejpam-4655	546	19	is	be	AUX
ejpam-4655	546	20	(	(	PUNCT
ejpam-4655	546	21	2	2	NUM
ejpam-4655	546	22	,	,	PUNCT
ejpam-4655	546	23	1)bigeneralized	1)bigeneralized	NUM
ejpam-4655	546	24	submaximal	submaximal	ADJ
ejpam-4655	546	25	space	space	NOUN
ejpam-4655	546	26	.	.	PUNCT
ejpam-4655	547	1	(	(	PUNCT
ejpam-4655	547	2	a	a	X
ejpam-4655	547	3	)	)	PUNCT
ejpam-4655	547	4	assume	assume	VERB
ejpam-4655	547	5	that	that	SCONJ
ejpam-4655	547	6	,	,	PUNCT
ejpam-4655	547	7	every	every	DET
ejpam-4655	547	8	µ2	µ2	PROPN
ejpam-4655	547	9	-	-	PUNCT
ejpam-4655	547	10	pre	pre	NOUN
ejpam-4655	547	11	-	-	ADJ
ejpam-4655	547	12	open	open	ADJ
ejpam-4655	547	13	is	be	AUX
ejpam-4655	547	14	µ1	µ1	NOUN
ejpam-4655	547	15	-	-	PUNCT
ejpam-4655	547	16	open	open	ADJ
ejpam-4655	547	17	.	.	PUNCT
ejpam-4655	548	1	letq	letq	ADJ
ejpam-4655	548	2	∈	∈	PROPN
ejpam-4655	548	3	(	(	PUNCT
ejpam-4655	548	4	1	1	NUM
ejpam-4655	548	5	,	,	PUNCT
ejpam-4655	548	6	2)−d(x	2)−d(x	NUM
ejpam-4655	548	7	)	)	PUNCT
ejpam-4655	548	8	.	.	PUNCT
ejpam-4655	549	1	then	then	ADV
ejpam-4655	549	2	c1(c2(q	c1(c2(q	PROPN
ejpam-4655	549	3	)	)	PUNCT
ejpam-4655	549	4	)	)	PUNCT
ejpam-4655	550	1	=	=	PUNCT
ejpam-4655	550	2	x	x	PUNCT
ejpam-4655	551	1	and	and	CCONJ
ejpam-4655	551	2	so	so	ADV
ejpam-4655	551	3	c2(q	c2(q	PROPN
ejpam-4655	551	4	)	)	PUNCT
ejpam-4655	551	5	is	be	AUX
ejpam-4655	551	6	a	a	DET
ejpam-4655	551	7	µ1	µ1	NOUN
ejpam-4655	551	8	-	-	PUNCT
ejpam-4655	551	9	dense	dense	ADJ
ejpam-4655	551	10	set	set	NOUN
ejpam-4655	551	11	in	in	ADP
ejpam-4655	551	12	x.	x.	NOUN
ejpam-4655	551	13	by	by	ADP
ejpam-4655	551	14	our	our	PRON
ejpam-4655	551	15	assumption	assumption	NOUN
ejpam-4655	551	16	,	,	PUNCT
ejpam-4655	551	17	c2(q	c2(q	PROPN
ejpam-4655	551	18	)	)	PUNCT
ejpam-4655	551	19	∈	∈	PROPN
ejpam-4655	551	20	µ2	µ2	PROPN
ejpam-4655	551	21	.	.	PUNCT
ejpam-4655	552	1	thus	thus	ADV
ejpam-4655	552	2	,	,	PUNCT
ejpam-4655	552	3	q	q	X
ejpam-4655	552	4	⊂	⊂	PROPN
ejpam-4655	552	5	i2(c2(q	i2(c2(q	NUM
ejpam-4655	552	6	)	)	PUNCT
ejpam-4655	552	7	)	)	PUNCT
ejpam-4655	552	8	.	.	PUNCT
ejpam-4655	553	1	therefore	therefore	ADV
ejpam-4655	553	2	,	,	PUNCT
ejpam-4655	553	3	q	q	PROPN
ejpam-4655	553	4	is	be	AUX
ejpam-4655	553	5	µ2	µ2	ADJ
ejpam-4655	553	6	-	-	PUNCT
ejpam-4655	553	7	pre	pre	NOUN
ejpam-4655	553	8	-	-	ADJ
ejpam-4655	553	9	open	open	ADJ
ejpam-4655	553	10	.	.	PUNCT
ejpam-4655	554	1	by	by	ADP
ejpam-4655	554	2	hypothesis	hypothesis	NOUN
ejpam-4655	554	3	,	,	PUNCT
ejpam-4655	554	4	q	q	PROPN
ejpam-4655	554	5	∈	∈	PROPN
ejpam-4655	554	6	µ1	µ1	NOUN
ejpam-4655	554	7	.	.	PUNCT
ejpam-4655	555	1	hence	hence	ADV
ejpam-4655	555	2	x	x	PRON
ejpam-4655	555	3	is	be	AUX
ejpam-4655	555	4	a	a	DET
ejpam-4655	555	5	(	(	PUNCT
ejpam-4655	555	6	1	1	NUM
ejpam-4655	555	7	,	,	PUNCT
ejpam-4655	555	8	2)⋆-bigeneralized	2)⋆-bigeneralized	NUM
ejpam-4655	555	9	y.	y.	PROPN
ejpam-4655	555	10	farhat	farhat	PROPN
ejpam-4655	555	11	et	et	PROPN
ejpam-4655	555	12	al	al	PROPN
ejpam-4655	555	13	.	.	PUNCT
ejpam-4655	555	14	/	/	SYM
ejpam-4655	555	15	eur	eur	PROPN
ejpam-4655	555	16	.	.	PUNCT
ejpam-4655	556	1	j.	j.	PROPN
ejpam-4655	556	2	pure	pure	PROPN
ejpam-4655	556	3	appl	appl	PROPN
ejpam-4655	556	4	.	.	PROPN
ejpam-4655	556	5	math	math	PROPN
ejpam-4655	556	6	,	,	PUNCT
ejpam-4655	556	7	16	16	NUM
ejpam-4655	556	8	(	(	PUNCT
ejpam-4655	556	9	1	1	NUM
ejpam-4655	556	10	)	)	PUNCT
ejpam-4655	556	11	(	(	PUNCT
ejpam-4655	556	12	2023	2023	NUM
ejpam-4655	556	13	)	)	PUNCT
ejpam-4655	556	14	,	,	PUNCT
ejpam-4655	556	15	386	386	NUM
ejpam-4655	556	16	-	-	SYM
ejpam-4655	556	17	403	403	NUM
ejpam-4655	556	18	399	399	NUM
ejpam-4655	556	19	submaximal	submaximal	ADJ
ejpam-4655	556	20	space	space	NOUN
ejpam-4655	556	21	.	.	PUNCT
ejpam-4655	557	1	(	(	PUNCT
ejpam-4655	557	2	b	b	X
ejpam-4655	557	3	)	)	PUNCT
ejpam-4655	557	4	suppose	suppose	VERB
ejpam-4655	557	5	every	every	DET
ejpam-4655	557	6	µ2	µ2	PROPN
ejpam-4655	557	7	-	-	PUNCT
ejpam-4655	557	8	β	β	NOUN
ejpam-4655	557	9	-	-	ADJ
ejpam-4655	557	10	open	open	ADJ
ejpam-4655	557	11	is	be	AUX
ejpam-4655	557	12	µ1	µ1	NOUN
ejpam-4655	557	13	-	-	PUNCT
ejpam-4655	557	14	open	open	ADJ
ejpam-4655	557	15	.	.	PUNCT
ejpam-4655	558	1	let	let	VERB
ejpam-4655	558	2	k	k	PROPN
ejpam-4655	558	3	∈	∈	PROPN
ejpam-4655	558	4	(	(	PUNCT
ejpam-4655	558	5	1	1	NUM
ejpam-4655	558	6	,	,	PUNCT
ejpam-4655	558	7	2	2	NUM
ejpam-4655	558	8	)	)	PUNCT
ejpam-4655	558	9	−	−	PROPN
ejpam-4655	558	10	d(x	d(x	NOUN
ejpam-4655	558	11	)	)	PUNCT
ejpam-4655	558	12	.	.	PUNCT
ejpam-4655	559	1	then	then	ADV
ejpam-4655	559	2	c2(k	c2(k	PROPN
ejpam-4655	559	3	)	)	PUNCT
ejpam-4655	559	4	∈	∈	PROPN
ejpam-4655	559	5	µ2	µ2	NOUN
ejpam-4655	559	6	,	,	PUNCT
ejpam-4655	559	7	by	by	ADP
ejpam-4655	559	8	similar	similar	ADJ
ejpam-4655	559	9	arguments	argument	NOUN
ejpam-4655	559	10	in	in	ADP
ejpam-4655	559	11	(	(	PUNCT
ejpam-4655	559	12	a	a	NOUN
ejpam-4655	559	13	)	)	PUNCT
ejpam-4655	559	14	.	.	PUNCT
ejpam-4655	560	1	this	this	PRON
ejpam-4655	560	2	implies	imply	VERB
ejpam-4655	560	3	k	k	PROPN
ejpam-4655	560	4	⊂	⊂	PROPN
ejpam-4655	560	5	c2(i2(c2(k	c2(i2(c2(k	PROPN
ejpam-4655	560	6	)	)	PUNCT
ejpam-4655	560	7	)	)	PUNCT
ejpam-4655	560	8	)	)	PUNCT
ejpam-4655	560	9	which	which	PRON
ejpam-4655	560	10	implies	imply	VERB
ejpam-4655	560	11	that	that	SCONJ
ejpam-4655	560	12	k	k	PROPN
ejpam-4655	560	13	is	be	AUX
ejpam-4655	560	14	µ2	µ2	ADJ
ejpam-4655	560	15	-	-	PUNCT
ejpam-4655	560	16	βopen	βopen	ADJ
ejpam-4655	560	17	.	.	PUNCT
ejpam-4655	561	1	by	by	ADP
ejpam-4655	561	2	our	our	PRON
ejpam-4655	561	3	assumption	assumption	NOUN
ejpam-4655	561	4	,	,	PUNCT
ejpam-4655	561	5	k	k	PROPN
ejpam-4655	561	6	∈	∈	PROPN
ejpam-4655	561	7	µ1	µ1	PROPN
ejpam-4655	561	8	.	.	PUNCT
ejpam-4655	562	1	therefore	therefore	ADV
ejpam-4655	562	2	,	,	PUNCT
ejpam-4655	562	3	x	x	X
ejpam-4655	562	4	is	be	AUX
ejpam-4655	562	5	a	a	DET
ejpam-4655	562	6	(	(	PUNCT
ejpam-4655	562	7	1	1	NUM
ejpam-4655	562	8	,	,	PUNCT
ejpam-4655	562	9	2)⋆-bigeneralized	2)⋆-bigeneralized	NUM
ejpam-4655	562	10	submaximal	submaximal	ADJ
ejpam-4655	562	11	space	space	NOUN
ejpam-4655	562	12	.	.	PUNCT
ejpam-4655	563	1	(	(	PUNCT
ejpam-4655	563	2	c	c	X
ejpam-4655	563	3	)	)	PUNCT
ejpam-4655	563	4	assume	assume	VERB
ejpam-4655	563	5	that	that	SCONJ
ejpam-4655	563	6	,	,	PUNCT
ejpam-4655	563	7	every	every	DET
ejpam-4655	563	8	µ2	µ2	PROPN
ejpam-4655	563	9	-	-	PUNCT
ejpam-4655	563	10	b	b	NOUN
ejpam-4655	563	11	-	-	PUNCT
ejpam-4655	563	12	open	open	ADJ
ejpam-4655	563	13	is	be	AUX
ejpam-4655	563	14	µ1	µ1	NOUN
ejpam-4655	563	15	-	-	PUNCT
ejpam-4655	563	16	open	open	ADJ
ejpam-4655	563	17	.	.	PUNCT
ejpam-4655	564	1	let	let	VERB
ejpam-4655	564	2	p	p	X
ejpam-4655	564	3	∈	∈	PROPN
ejpam-4655	564	4	(	(	PUNCT
ejpam-4655	564	5	1	1	NUM
ejpam-4655	564	6	,	,	PUNCT
ejpam-4655	564	7	2	2	NUM
ejpam-4655	564	8	)	)	PUNCT
ejpam-4655	564	9	−	−	PROPN
ejpam-4655	564	10	d(x	d(x	NOUN
ejpam-4655	564	11	)	)	PUNCT
ejpam-4655	564	12	.	.	PUNCT
ejpam-4655	565	1	then	then	ADV
ejpam-4655	565	2	c2(p	c2(p	NUM
ejpam-4655	565	3	)	)	PUNCT
ejpam-4655	565	4	∈	∈	PROPN
ejpam-4655	565	5	µ2	µ2	PROPN
ejpam-4655	565	6	,	,	PUNCT
ejpam-4655	565	7	by	by	ADP
ejpam-4655	565	8	similar	similar	ADJ
ejpam-4655	565	9	arguments	argument	NOUN
ejpam-4655	565	10	in	in	ADP
ejpam-4655	565	11	(	(	PUNCT
ejpam-4655	565	12	a	a	NOUN
ejpam-4655	565	13	)	)	PUNCT
ejpam-4655	565	14	.	.	PUNCT
ejpam-4655	566	1	thus	thus	ADV
ejpam-4655	566	2	,	,	PUNCT
ejpam-4655	566	3	p	p	X
ejpam-4655	566	4	⊂	⊂	X
ejpam-4655	566	5	c2(i2(p	c2(i2(p	X
ejpam-4655	566	6	)	)	PUNCT
ejpam-4655	566	7	)	)	PUNCT
ejpam-4655	566	8	∪	∪	ADP
ejpam-4655	566	9	i2(c2(p	i2(c2(p	NOUN
ejpam-4655	566	10	)	)	PUNCT
ejpam-4655	566	11	)	)	PUNCT
ejpam-4655	566	12	.	.	PUNCT
ejpam-4655	567	1	this	this	PRON
ejpam-4655	567	2	implies	imply	VERB
ejpam-4655	567	3	p	p	NOUN
ejpam-4655	567	4	is	be	AUX
ejpam-4655	567	5	µ2	µ2	ADJ
ejpam-4655	567	6	-	-	PUNCT
ejpam-4655	567	7	bopen	bopen	NOUN
ejpam-4655	567	8	which	which	PRON
ejpam-4655	567	9	implies	imply	VERB
ejpam-4655	567	10	that	that	SCONJ
ejpam-4655	567	11	p	p	PROPN
ejpam-4655	567	12	∈	∈	PROPN
ejpam-4655	567	13	µ1	µ1	PROPN
ejpam-4655	567	14	,	,	PUNCT
ejpam-4655	567	15	by	by	ADP
ejpam-4655	567	16	hypothesis	hypothesis	NOUN
ejpam-4655	567	17	.	.	PUNCT
ejpam-4655	568	1	therefore	therefore	ADV
ejpam-4655	568	2	,	,	PUNCT
ejpam-4655	568	3	x	x	X
ejpam-4655	568	4	is	be	AUX
ejpam-4655	568	5	a	a	DET
ejpam-4655	568	6	(	(	PUNCT
ejpam-4655	568	7	1	1	NUM
ejpam-4655	568	8	,	,	PUNCT
ejpam-4655	568	9	2)⋆-bigeneralized	2)⋆-bigeneralized	NUM
ejpam-4655	568	10	submaximal	submaximal	ADJ
ejpam-4655	568	11	space	space	NOUN
ejpam-4655	568	12	.	.	PUNCT
ejpam-4655	569	1	the	the	DET
ejpam-4655	569	2	below	below	ADJ
ejpam-4655	569	3	theorem	theorem	NOUN
ejpam-4655	569	4	33	33	NUM
ejpam-4655	569	5	gives	give	VERB
ejpam-4655	569	6	a	a	DET
ejpam-4655	569	7	characterization	characterization	NOUN
ejpam-4655	569	8	of	of	ADP
ejpam-4655	569	9	the	the	DET
ejpam-4655	569	10	(	(	PUNCT
ejpam-4655	569	11	s	s	PROPN
ejpam-4655	569	12	,	,	PUNCT
ejpam-4655	569	13	v)⋆-bigeneralized	v)⋆-bigeneralize	VERB
ejpam-4655	569	14	submaximal	submaximal	ADJ
ejpam-4655	569	15	space	space	NOUN
ejpam-4655	569	16	in	in	ADP
ejpam-4655	569	17	terms	term	NOUN
ejpam-4655	569	18	of	of	ADP
ejpam-4655	569	19	a	a	DET
ejpam-4655	569	20	closed	closed	ADJ
ejpam-4655	569	21	set	set	NOUN
ejpam-4655	569	22	.	.	PUNCT
ejpam-4655	570	1	this	this	DET
ejpam-4655	570	2	theorem	theorem	NOUN
ejpam-4655	570	3	is	be	AUX
ejpam-4655	570	4	a	a	DET
ejpam-4655	570	5	direct	direct	ADJ
ejpam-4655	570	6	implication	implication	NOUN
ejpam-4655	570	7	of	of	ADP
ejpam-4655	570	8	definition	definition	NOUN
ejpam-4655	570	9	27	27	NUM
ejpam-4655	570	10	so	so	SCONJ
ejpam-4655	570	11	the	the	DET
ejpam-4655	570	12	proof	proof	NOUN
ejpam-4655	570	13	is	be	AUX
ejpam-4655	570	14	skipped	skip	VERB
ejpam-4655	570	15	.	.	PUNCT
ejpam-4655	571	1	theorem	theorem	VERB
ejpam-4655	571	2	33	33	NUM
ejpam-4655	571	3	.	.	PUNCT
ejpam-4655	572	1	let	let	AUX
ejpam-4655	572	2	(	(	PUNCT
ejpam-4655	572	3	x,µ1	x,µ1	NOUN
ejpam-4655	572	4	,	,	PUNCT
ejpam-4655	572	5	µ2	µ2	PROPN
ejpam-4655	572	6	)	)	PUNCT
ejpam-4655	572	7	be	be	AUX
ejpam-4655	572	8	a	a	DET
ejpam-4655	572	9	bgts	bgts	NOUN
ejpam-4655	572	10	.	.	PUNCT
ejpam-4655	573	1	then	then	ADV
ejpam-4655	573	2	the	the	DET
ejpam-4655	573	3	following	following	NOUN
ejpam-4655	573	4	are	be	AUX
ejpam-4655	573	5	equivalent	equivalent	ADJ
ejpam-4655	573	6	.	.	PUNCT
ejpam-4655	574	1	(	(	PUNCT
ejpam-4655	574	2	a	a	X
ejpam-4655	574	3	)	)	PUNCT
ejpam-4655	574	4	(	(	PUNCT
ejpam-4655	574	5	s	s	X
ejpam-4655	574	6	,	,	PUNCT
ejpam-4655	574	7	v)⋆-bigeneralized	v)⋆-bigeneralize	VERB
ejpam-4655	574	8	submaximal	submaximal	ADJ
ejpam-4655	574	9	space	space	NOUN
ejpam-4655	574	10	.	.	PUNCT
ejpam-4655	575	1	(	(	PUNCT
ejpam-4655	575	2	b	b	X
ejpam-4655	575	3	)	)	PUNCT
ejpam-4655	575	4	every	every	DET
ejpam-4655	575	5	q	q	X
ejpam-4655	575	6	⊂	⊂	X
ejpam-4655	575	7	x	x	PUNCT
ejpam-4655	575	8	with	with	ADP
ejpam-4655	575	9	is(iv(q	is(iv(q	NOUN
ejpam-4655	575	10	)	)	PUNCT
ejpam-4655	575	11	)	)	PUNCT
ejpam-4655	576	1	=	=	NOUN
ejpam-4655	576	2	∅	∅	NOUN
ejpam-4655	576	3	,	,	PUNCT
ejpam-4655	576	4	is	be	AUX
ejpam-4655	576	5	a	a	DET
ejpam-4655	576	6	µs	µs	NOUN
ejpam-4655	576	7	-	-	PUNCT
ejpam-4655	576	8	closed	closed	ADJ
ejpam-4655	576	9	set	set	NOUN
ejpam-4655	576	10	where	where	SCONJ
ejpam-4655	576	11	s	s	X
ejpam-4655	576	12	,	,	PUNCT
ejpam-4655	576	13	v	v	NOUN
ejpam-4655	576	14	=	=	SYM
ejpam-4655	576	15	1	1	NUM
ejpam-4655	576	16	,	,	PUNCT
ejpam-4655	576	17	2	2	NUM
ejpam-4655	576	18	;	;	PUNCT
ejpam-4655	576	19	s	s	VERB
ejpam-4655	576	20	̸=	̸=	PROPN
ejpam-4655	576	21	v.	v.	ADP
ejpam-4655	576	22	corollary	corollary	ADJ
ejpam-4655	576	23	34	34	NUM
ejpam-4655	576	24	.	.	PUNCT
ejpam-4655	577	1	let	let	AUX
ejpam-4655	577	2	(	(	PUNCT
ejpam-4655	577	3	x,µ1	x,µ1	NOUN
ejpam-4655	577	4	,	,	PUNCT
ejpam-4655	577	5	µ2	µ2	PROPN
ejpam-4655	577	6	)	)	PUNCT
ejpam-4655	577	7	be	be	VERB
ejpam-4655	577	8	a	a	DET
ejpam-4655	577	9	(	(	PUNCT
ejpam-4655	577	10	s	s	PROPN
ejpam-4655	577	11	,	,	PUNCT
ejpam-4655	577	12	v)⋆-bigeneralized	v)⋆-bigeneralize	VERB
ejpam-4655	577	13	submaximal	submaximal	ADJ
ejpam-4655	577	14	space	space	NOUN
ejpam-4655	577	15	.	.	PUNCT
ejpam-4655	578	1	then	then	ADV
ejpam-4655	578	2	cv(q)−q	cv(q)−q	NOUN
ejpam-4655	578	3	is	be	AUX
ejpam-4655	578	4	µs	µs	NOUN
ejpam-4655	578	5	-	-	PUNCT
ejpam-4655	578	6	closed	closed	ADJ
ejpam-4655	578	7	and	and	CCONJ
ejpam-4655	578	8	hence	hence	ADV
ejpam-4655	578	9	(	(	PUNCT
ejpam-4655	578	10	v	v	NOUN
ejpam-4655	578	11	,	,	PUNCT
ejpam-4655	578	12	s)-nowhere	s)-nowhere	PUNCT
ejpam-4655	578	13	dense	dense	ADJ
ejpam-4655	578	14	where	where	SCONJ
ejpam-4655	578	15	q	q	X
ejpam-4655	578	16	⊂	⊂	PROPN
ejpam-4655	578	17	x	x	X
ejpam-4655	578	18	and	and	CCONJ
ejpam-4655	578	19	s	s	PROPN
ejpam-4655	578	20	,	,	PUNCT
ejpam-4655	578	21	v	v	NOUN
ejpam-4655	578	22	=	=	SYM
ejpam-4655	578	23	1	1	NUM
ejpam-4655	578	24	,	,	PUNCT
ejpam-4655	578	25	2	2	NUM
ejpam-4655	578	26	;	;	PUNCT
ejpam-4655	578	27	s	s	VERB
ejpam-4655	578	28	̸=	̸=	PROPN
ejpam-4655	578	29	v.	v.	ADP
ejpam-4655	578	30	proof	proof	NOUN
ejpam-4655	578	31	.	.	PUNCT
ejpam-4655	579	1	this	this	DET
ejpam-4655	579	2	proof	proof	NOUN
ejpam-4655	579	3	is	be	AUX
ejpam-4655	579	4	directly	directly	ADV
ejpam-4655	579	5	follows	follow	VERB
ejpam-4655	579	6	from	from	ADP
ejpam-4655	579	7	above	above	ADP
ejpam-4655	579	8	theorem	theorem	VERB
ejpam-4655	579	9	33	33	NUM
ejpam-4655	579	10	.	.	PUNCT
ejpam-4655	580	1	theorem	theorem	VERB
ejpam-4655	580	2	35	35	NUM
ejpam-4655	580	3	.	.	PUNCT
ejpam-4655	581	1	let	let	AUX
ejpam-4655	581	2	(	(	PUNCT
ejpam-4655	581	3	x,µ1	x,µ1	NOUN
ejpam-4655	581	4	,	,	PUNCT
ejpam-4655	581	5	µ2	µ2	PROPN
ejpam-4655	581	6	)	)	PUNCT
ejpam-4655	581	7	be	be	VERB
ejpam-4655	581	8	a	a	DET
ejpam-4655	581	9	pairwise	pairwise	NOUN
ejpam-4655	581	10	bigeneralized	bigeneralize	VERB
ejpam-4655	581	11	submaximal	submaximal	ADJ
ejpam-4655	581	12	space	space	NOUN
ejpam-4655	581	13	.	.	PUNCT
ejpam-4655	582	1	then	then	ADV
ejpam-4655	582	2	the	the	DET
ejpam-4655	582	3	followings	following	NOUN
ejpam-4655	582	4	are	be	AUX
ejpam-4655	582	5	true	true	ADJ
ejpam-4655	582	6	.	.	PUNCT
ejpam-4655	583	1	(	(	PUNCT
ejpam-4655	583	2	a	a	X
ejpam-4655	583	3	)	)	PUNCT
ejpam-4655	583	4	if	if	SCONJ
ejpam-4655	583	5	(	(	PUNCT
ejpam-4655	583	6	x,µ2	x,µ2	PROPN
ejpam-4655	583	7	)	)	PUNCT
ejpam-4655	583	8	is	be	AUX
ejpam-4655	583	9	hyperconnected	hyperconnecte	VERB
ejpam-4655	583	10	and	and	CCONJ
ejpam-4655	583	11	µ1	µ1	PROPN
ejpam-4655	583	12	is	be	AUX
ejpam-4655	583	13	sgt	sgt	PROPN
ejpam-4655	583	14	,	,	PUNCT
ejpam-4655	583	15	then	then	ADV
ejpam-4655	583	16	x	x	PUNCT
ejpam-4655	583	17	is	be	AUX
ejpam-4655	583	18	a	a	DET
ejpam-4655	583	19	(	(	PUNCT
ejpam-4655	583	20	1	1	NUM
ejpam-4655	583	21	,	,	PUNCT
ejpam-4655	583	22	2)⋆-bigeneralized	2)⋆-bigeneralized	NUM
ejpam-4655	583	23	submaximal	submaximal	ADJ
ejpam-4655	583	24	space	space	NOUN
ejpam-4655	583	25	.	.	PUNCT
ejpam-4655	584	1	(	(	PUNCT
ejpam-4655	584	2	b	b	X
ejpam-4655	584	3	)	)	PUNCT
ejpam-4655	584	4	if	if	SCONJ
ejpam-4655	584	5	(	(	PUNCT
ejpam-4655	584	6	x,µ1	x,µ1	NOUN
ejpam-4655	584	7	)	)	PUNCT
ejpam-4655	584	8	is	be	AUX
ejpam-4655	584	9	hyperconnected	hyperconnecte	VERB
ejpam-4655	584	10	and	and	CCONJ
ejpam-4655	584	11	µ2	µ2	PROPN
ejpam-4655	584	12	is	be	AUX
ejpam-4655	584	13	sgt	sgt	PROPN
ejpam-4655	584	14	,	,	PUNCT
ejpam-4655	584	15	then	then	ADV
ejpam-4655	584	16	x	x	PUNCT
ejpam-4655	584	17	is	be	AUX
ejpam-4655	584	18	a	a	DET
ejpam-4655	584	19	(	(	PUNCT
ejpam-4655	584	20	2	2	NUM
ejpam-4655	584	21	,	,	PUNCT
ejpam-4655	584	22	1)⋆-bigeneralized	1)⋆-bigeneralized	NUM
ejpam-4655	584	23	submaximal	submaximal	ADJ
ejpam-4655	584	24	space	space	NOUN
ejpam-4655	584	25	.	.	PUNCT
ejpam-4655	585	1	proof	proof	NOUN
ejpam-4655	585	2	.	.	PUNCT
ejpam-4655	586	1	we	we	PRON
ejpam-4655	586	2	will	will	AUX
ejpam-4655	586	3	present	present	VERB
ejpam-4655	586	4	the	the	DET
ejpam-4655	586	5	detailed	detailed	ADJ
ejpam-4655	586	6	proof	proof	NOUN
ejpam-4655	586	7	only	only	ADV
ejpam-4655	586	8	for	for	ADP
ejpam-4655	586	9	(	(	PUNCT
ejpam-4655	586	10	a	a	NOUN
ejpam-4655	586	11	)	)	PUNCT
ejpam-4655	586	12	.	.	PUNCT
ejpam-4655	587	1	suppose	suppose	VERB
ejpam-4655	587	2	(	(	PUNCT
ejpam-4655	587	3	x,µ2	x,µ2	PROPN
ejpam-4655	587	4	)	)	PUNCT
ejpam-4655	587	5	is	be	AUX
ejpam-4655	587	6	hyperconnected	hyperconnecte	VERB
ejpam-4655	587	7	and	and	CCONJ
ejpam-4655	587	8	µ1	µ1	PROPN
ejpam-4655	587	9	is	be	AUX
ejpam-4655	587	10	a	a	DET
ejpam-4655	587	11	sgt	sgt	PROPN
ejpam-4655	587	12	.	.	PUNCT
ejpam-4655	588	1	let	let	VERB
ejpam-4655	588	2	p	p	X
ejpam-4655	588	3	∈	∈	PROPN
ejpam-4655	588	4	(	(	PUNCT
ejpam-4655	588	5	1	1	NUM
ejpam-4655	588	6	,	,	PUNCT
ejpam-4655	588	7	2	2	NUM
ejpam-4655	588	8	)	)	PUNCT
ejpam-4655	588	9	−	−	PROPN
ejpam-4655	588	10	d(x	d(x	NOUN
ejpam-4655	588	11	)	)	PUNCT
ejpam-4655	588	12	.	.	PUNCT
ejpam-4655	589	1	then	then	ADV
ejpam-4655	589	2	c2(p	c2(p	NUM
ejpam-4655	589	3	)	)	PUNCT
ejpam-4655	589	4	is	be	AUX
ejpam-4655	589	5	a	a	DET
ejpam-4655	589	6	µ1	µ1	NOUN
ejpam-4655	589	7	-	-	PUNCT
ejpam-4655	589	8	dense	dense	ADJ
ejpam-4655	589	9	set	set	NOUN
ejpam-4655	589	10	in	in	ADP
ejpam-4655	589	11	x	x	PUNCT
ejpam-4655	589	12	and	and	CCONJ
ejpam-4655	589	13	so	so	ADV
ejpam-4655	589	14	c2(p	c2(p	NUM
ejpam-4655	589	15	)	)	PUNCT
ejpam-4655	589	16	∈	∈	PROPN
ejpam-4655	589	17	µ2	µ2	PROPN
ejpam-4655	589	18	,	,	PUNCT
ejpam-4655	589	19	since	since	SCONJ
ejpam-4655	589	20	x	x	PRON
ejpam-4655	589	21	is	be	AUX
ejpam-4655	589	22	(	(	PUNCT
ejpam-4655	589	23	2	2	NUM
ejpam-4655	589	24	,	,	PUNCT
ejpam-4655	589	25	1)-bigeneralized	1)-bigeneralized	NUM
ejpam-4655	589	26	submaximal	submaximal	ADJ
ejpam-4655	589	27	space	space	NOUN
ejpam-4655	589	28	.	.	PUNCT
ejpam-4655	590	1	thus	thus	ADV
ejpam-4655	590	2	,	,	PUNCT
ejpam-4655	590	3	c2(p	c2(p	X
ejpam-4655	590	4	)	)	PUNCT
ejpam-4655	590	5	∈	∈	PROPN
ejpam-4655	591	1	µ̃2	µ̃2	PROPN
ejpam-4655	591	2	.	.	PUNCT
ejpam-4655	592	1	by	by	ADP
ejpam-4655	592	2	our	our	PRON
ejpam-4655	592	3	assumption	assumption	NOUN
ejpam-4655	592	4	,	,	PUNCT
ejpam-4655	592	5	c2(p	c2(p	X
ejpam-4655	592	6	)	)	PUNCT
ejpam-4655	592	7	is	be	AUX
ejpam-4655	592	8	a	a	DET
ejpam-4655	592	9	µ2	µ2	ADJ
ejpam-4655	592	10	-	-	PUNCT
ejpam-4655	592	11	dense	dense	ADJ
ejpam-4655	592	12	set	set	NOUN
ejpam-4655	592	13	.	.	PUNCT
ejpam-4655	593	1	this	this	PRON
ejpam-4655	593	2	implies	imply	VERB
ejpam-4655	593	3	p	p	NOUN
ejpam-4655	593	4	is	be	AUX
ejpam-4655	593	5	a	a	DET
ejpam-4655	593	6	µ2	µ2	ADJ
ejpam-4655	593	7	-	-	PUNCT
ejpam-4655	593	8	dense	dense	ADJ
ejpam-4655	593	9	set	set	NOUN
ejpam-4655	593	10	which	which	PRON
ejpam-4655	593	11	implies	imply	VERB
ejpam-4655	593	12	that	that	SCONJ
ejpam-4655	593	13	p	p	PROPN
ejpam-4655	593	14	∈	∈	PROPN
ejpam-4655	593	15	µ1	µ1	NOUN
ejpam-4655	593	16	,	,	PUNCT
ejpam-4655	593	17	since	since	SCONJ
ejpam-4655	593	18	x	x	PRON
ejpam-4655	593	19	is	be	AUX
ejpam-4655	593	20	a	a	DET
ejpam-4655	593	21	(	(	PUNCT
ejpam-4655	593	22	1	1	NUM
ejpam-4655	593	23	,	,	PUNCT
ejpam-4655	593	24	2)-bigeneralized	2)-bigeneralized	NUM
ejpam-4655	593	25	submaximal	submaximal	ADJ
ejpam-4655	593	26	space	space	NOUN
ejpam-4655	593	27	.	.	PUNCT
ejpam-4655	594	1	therefore	therefore	ADV
ejpam-4655	594	2	,	,	PUNCT
ejpam-4655	594	3	x	x	X
ejpam-4655	594	4	is	be	AUX
ejpam-4655	594	5	a	a	DET
ejpam-4655	594	6	(	(	PUNCT
ejpam-4655	594	7	1	1	NUM
ejpam-4655	594	8	,	,	PUNCT
ejpam-4655	594	9	2)⋆-bigeneralized	2)⋆-bigeneralized	NUM
ejpam-4655	594	10	submaximal	submaximal	ADJ
ejpam-4655	594	11	space	space	NOUN
ejpam-4655	594	12	.	.	PUNCT
ejpam-4655	595	1	5	5	X
ejpam-4655	595	2	.	.	X
ejpam-4655	595	3	(	(	PUNCT
ejpam-4655	595	4	s	s	PROPN
ejpam-4655	595	5	,	,	PUNCT
ejpam-4655	595	6	v)⋆⋆-bigeneralized	v)⋆⋆-bigeneralize	VERB
ejpam-4655	595	7	submaximal	submaximal	ADJ
ejpam-4655	595	8	space	space	NOUN
ejpam-4655	595	9	in	in	ADP
ejpam-4655	595	10	this	this	DET
ejpam-4655	595	11	part	part	NOUN
ejpam-4655	595	12	,	,	PUNCT
ejpam-4655	595	13	we	we	PRON
ejpam-4655	595	14	introduce	introduce	VERB
ejpam-4655	595	15	the	the	DET
ejpam-4655	595	16	notion	notion	NOUN
ejpam-4655	595	17	namely	namely	ADV
ejpam-4655	595	18	,	,	PUNCT
ejpam-4655	595	19	(	(	PUNCT
ejpam-4655	595	20	s	s	X
ejpam-4655	595	21	,	,	PUNCT
ejpam-4655	595	22	v)⋆-bigeneralized	v)⋆-bigeneralize	VERB
ejpam-4655	595	23	submaximal	submaximal	ADJ
ejpam-4655	595	24	space	space	NOUN
ejpam-4655	595	25	.	.	PUNCT
ejpam-4655	596	1	some	some	DET
ejpam-4655	596	2	conditions	condition	NOUN
ejpam-4655	596	3	are	be	AUX
ejpam-4655	596	4	proven	prove	VERB
ejpam-4655	596	5	to	to	PART
ejpam-4655	596	6	examine	examine	VERB
ejpam-4655	596	7	the	the	DET
ejpam-4655	596	8	given	give	VERB
ejpam-4655	596	9	space	space	NOUN
ejpam-4655	596	10	as	as	ADP
ejpam-4655	596	11	either	either	CCONJ
ejpam-4655	596	12	(	(	PUNCT
ejpam-4655	596	13	s	s	X
ejpam-4655	596	14	,	,	PUNCT
ejpam-4655	596	15	v)⋆-bigeneralized	v)⋆-bigeneralize	VERB
ejpam-4655	596	16	submaximal	submaximal	ADJ
ejpam-4655	596	17	or	or	CCONJ
ejpam-4655	596	18	not	not	PART
ejpam-4655	596	19	.	.	PUNCT
ejpam-4655	597	1	y.	y.	PROPN
ejpam-4655	597	2	farhat	farhat	PROPN
ejpam-4655	597	3	et	et	PROPN
ejpam-4655	597	4	al	al	PROPN
ejpam-4655	597	5	.	.	PUNCT
ejpam-4655	597	6	/	/	SYM
ejpam-4655	597	7	eur	eur	PROPN
ejpam-4655	597	8	.	.	PUNCT
ejpam-4655	598	1	j.	j.	PROPN
ejpam-4655	598	2	pure	pure	PROPN
ejpam-4655	598	3	appl	appl	PROPN
ejpam-4655	598	4	.	.	PROPN
ejpam-4655	598	5	math	math	PROPN
ejpam-4655	598	6	,	,	PUNCT
ejpam-4655	598	7	16	16	NUM
ejpam-4655	598	8	(	(	PUNCT
ejpam-4655	598	9	1	1	NUM
ejpam-4655	598	10	)	)	PUNCT
ejpam-4655	598	11	(	(	PUNCT
ejpam-4655	598	12	2023	2023	NUM
ejpam-4655	598	13	)	)	PUNCT
ejpam-4655	598	14	,	,	PUNCT
ejpam-4655	598	15	386	386	NUM
ejpam-4655	598	16	-	-	SYM
ejpam-4655	598	17	403	403	NUM
ejpam-4655	598	18	400	400	NUM
ejpam-4655	598	19	definition	definition	NOUN
ejpam-4655	598	20	36	36	NUM
ejpam-4655	598	21	.	.	PUNCT
ejpam-4655	599	1	let	let	AUX
ejpam-4655	599	2	(	(	PUNCT
ejpam-4655	599	3	x,µ1	x,µ1	NOUN
ejpam-4655	599	4	,	,	PUNCT
ejpam-4655	599	5	µ2	µ2	PROPN
ejpam-4655	599	6	)	)	PUNCT
ejpam-4655	599	7	be	be	VERB
ejpam-4655	599	8	a	a	DET
ejpam-4655	599	9	bigeneralized	bigeneralized	ADJ
ejpam-4655	599	10	topological	topological	ADJ
ejpam-4655	599	11	space	space	NOUN
ejpam-4655	599	12	.	.	PUNCT
ejpam-4655	600	1	a	a	DET
ejpam-4655	600	2	space	space	NOUN
ejpam-4655	600	3	x	x	PUNCT
ejpam-4655	600	4	is	be	AUX
ejpam-4655	600	5	said	say	VERB
ejpam-4655	600	6	to	to	PART
ejpam-4655	600	7	be	be	AUX
ejpam-4655	600	8	(	(	PUNCT
ejpam-4655	600	9	µs	µs	NOUN
ejpam-4655	600	10	,	,	PUNCT
ejpam-4655	600	11	µv	µv	PROPN
ejpam-4655	600	12	)	)	PUNCT
ejpam-4655	600	13	⋆⋆-bigeneralized	⋆⋆-bigeneralize	VERB
ejpam-4655	600	14	submaximal	submaximal	ADJ
ejpam-4655	600	15	(	(	PUNCT
ejpam-4655	600	16	briefly	briefly	ADV
ejpam-4655	600	17	,	,	PUNCT
ejpam-4655	600	18	(	(	PUNCT
ejpam-4655	600	19	s	s	X
ejpam-4655	600	20	,	,	PUNCT
ejpam-4655	600	21	v)⋆⋆-bigeneralized	v)⋆⋆-bigeneralize	VERB
ejpam-4655	600	22	submaximal	submaximal	ADJ
ejpam-4655	600	23	)	)	PUNCT
ejpam-4655	600	24	if	if	SCONJ
ejpam-4655	600	25	q	q	PROPN
ejpam-4655	600	26	∈	∈	PROPN
ejpam-4655	600	27	µv	µv	NOUN
ejpam-4655	600	28	whenever	whenever	SCONJ
ejpam-4655	600	29	q	q	X
ejpam-4655	600	30	∈	∈	PROPN
ejpam-4655	600	31	(	(	PUNCT
ejpam-4655	600	32	s	s	NOUN
ejpam-4655	600	33	,	,	PUNCT
ejpam-4655	600	34	v)−d(x	v)−d(x	NUM
ejpam-4655	600	35	)	)	PUNCT
ejpam-4655	600	36	where	where	SCONJ
ejpam-4655	600	37	s	s	X
ejpam-4655	600	38	,	,	PUNCT
ejpam-4655	600	39	v	v	NOUN
ejpam-4655	600	40	=	=	SYM
ejpam-4655	600	41	1	1	NUM
ejpam-4655	600	42	,	,	PUNCT
ejpam-4655	600	43	2	2	NUM
ejpam-4655	600	44	;	;	PUNCT
ejpam-4655	600	45	s	s	VERB
ejpam-4655	600	46	̸=	̸=	PROPN
ejpam-4655	600	47	v.	v.	ADP
ejpam-4655	600	48	example	example	NOUN
ejpam-4655	600	49	37	37	NUM
ejpam-4655	600	50	.	.	PUNCT
ejpam-4655	601	1	(	(	PUNCT
ejpam-4655	601	2	a	a	X
ejpam-4655	601	3	)	)	PUNCT
ejpam-4655	601	4	consider	consider	VERB
ejpam-4655	601	5	the	the	DET
ejpam-4655	601	6	bigeneralized	bigeneralized	ADJ
ejpam-4655	601	7	topological	topological	ADJ
ejpam-4655	601	8	space	space	NOUN
ejpam-4655	601	9	(	(	PUNCT
ejpam-4655	601	10	x,µ1	x,µ1	PROPN
ejpam-4655	601	11	,	,	PUNCT
ejpam-4655	601	12	µ2	µ2	PROPN
ejpam-4655	601	13	)	)	PUNCT
ejpam-4655	602	1	where	where	SCONJ
ejpam-4655	602	2	x	x	X
ejpam-4655	602	3	=	=	PRON
ejpam-4655	602	4	{	{	PUNCT
ejpam-4655	602	5	p	p	X
ejpam-4655	602	6	,	,	PUNCT
ejpam-4655	602	7	q	q	ADJ
ejpam-4655	602	8	,	,	PUNCT
ejpam-4655	602	9	r	r	NOUN
ejpam-4655	602	10	,	,	PUNCT
ejpam-4655	602	11	s};µ1	s};µ1	PROPN
ejpam-4655	602	12	=	=	SYM
ejpam-4655	602	13	{	{	PUNCT
ejpam-4655	602	14	∅	∅	NOUN
ejpam-4655	602	15	,	,	PUNCT
ejpam-4655	602	16	{	{	PUNCT
ejpam-4655	602	17	p	p	X
ejpam-4655	602	18	,	,	PUNCT
ejpam-4655	602	19	q	q	NOUN
ejpam-4655	602	20	}	}	PUNCT
ejpam-4655	602	21	,	,	PUNCT
ejpam-4655	602	22	{	{	PUNCT
ejpam-4655	602	23	p	p	X
ejpam-4655	602	24	,	,	PUNCT
ejpam-4655	602	25	r	r	NOUN
ejpam-4655	602	26	}	}	PUNCT
ejpam-4655	602	27	,	,	PUNCT
ejpam-4655	602	28	{	{	PUNCT
ejpam-4655	602	29	p	p	X
ejpam-4655	602	30	,	,	PUNCT
ejpam-4655	602	31	q	q	ADJ
ejpam-4655	602	32	,	,	PUNCT
ejpam-4655	602	33	r	r	NOUN
ejpam-4655	602	34	}	}	PUNCT
ejpam-4655	602	35	}	}	PUNCT
ejpam-4655	602	36	and	and	CCONJ
ejpam-4655	602	37	µ2	µ2	PROPN
ejpam-4655	602	38	=	=	PUNCT
ejpam-4655	602	39	{	{	PUNCT
ejpam-4655	602	40	∅	∅	NOUN
ejpam-4655	602	41	,	,	PUNCT
ejpam-4655	602	42	{	{	PUNCT
ejpam-4655	602	43	p	p	X
ejpam-4655	602	44	}	}	PUNCT
ejpam-4655	602	45	,	,	PUNCT
ejpam-4655	602	46	{	{	PUNCT
ejpam-4655	602	47	s	s	X
ejpam-4655	602	48	}	}	PUNCT
ejpam-4655	602	49	,	,	PUNCT
ejpam-4655	602	50	{	{	PUNCT
ejpam-4655	602	51	p	p	X
ejpam-4655	602	52	,	,	PUNCT
ejpam-4655	602	53	q	q	NOUN
ejpam-4655	602	54	}	}	PUNCT
ejpam-4655	602	55	,	,	PUNCT
ejpam-4655	602	56	{	{	PUNCT
ejpam-4655	602	57	p	p	X
ejpam-4655	602	58	,	,	PUNCT
ejpam-4655	602	59	r	r	NOUN
ejpam-4655	602	60	}	}	PUNCT
ejpam-4655	602	61	,	,	PUNCT
ejpam-4655	602	62	{	{	PUNCT
ejpam-4655	602	63	p	p	X
ejpam-4655	602	64	,	,	PUNCT
ejpam-4655	602	65	s	s	PART
ejpam-4655	602	66	}	}	PUNCT
ejpam-4655	602	67	,	,	PUNCT
ejpam-4655	602	68	{	{	PUNCT
ejpam-4655	602	69	q	q	X
ejpam-4655	602	70	,	,	PUNCT
ejpam-4655	602	71	r	r	NOUN
ejpam-4655	602	72	}	}	PUNCT
ejpam-4655	602	73	,	,	PUNCT
ejpam-4655	602	74	{	{	PUNCT
ejpam-4655	602	75	q	q	X
ejpam-4655	602	76	,	,	PUNCT
ejpam-4655	602	77	s	s	PART
ejpam-4655	602	78	}	}	PUNCT
ejpam-4655	602	79	,	,	PUNCT
ejpam-4655	602	80	{	{	PUNCT
ejpam-4655	602	81	p	p	X
ejpam-4655	602	82	,	,	PUNCT
ejpam-4655	602	83	q	q	ADJ
ejpam-4655	602	84	,	,	PUNCT
ejpam-4655	602	85	r	r	NOUN
ejpam-4655	602	86	}	}	PUNCT
ejpam-4655	602	87	,	,	PUNCT
ejpam-4655	602	88	{	{	PUNCT
ejpam-4655	602	89	p	p	X
ejpam-4655	602	90	,	,	PUNCT
ejpam-4655	602	91	q	q	X
ejpam-4655	602	92	,	,	PUNCT
ejpam-4655	602	93	s	s	PART
ejpam-4655	602	94	}	}	PUNCT
ejpam-4655	602	95	,	,	PUNCT
ejpam-4655	602	96	{	{	PUNCT
ejpam-4655	602	97	p	p	X
ejpam-4655	602	98	,	,	PUNCT
ejpam-4655	602	99	r	r	NOUN
ejpam-4655	602	100	,	,	PUNCT
ejpam-4655	602	101	s	s	PART
ejpam-4655	602	102	}	}	PUNCT
ejpam-4655	602	103	,	,	PUNCT
ejpam-4655	602	104	{	{	PUNCT
ejpam-4655	602	105	q	q	X
ejpam-4655	602	106	,	,	PUNCT
ejpam-4655	602	107	r	r	NOUN
ejpam-4655	602	108	,	,	PUNCT
ejpam-4655	602	109	s	s	PART
ejpam-4655	602	110	}	}	PUNCT
ejpam-4655	602	111	,	,	PUNCT
ejpam-4655	602	112	x}.here	x}.here	PROPN
ejpam-4655	602	113	{	{	PUNCT
ejpam-4655	602	114	p	p	X
ejpam-4655	602	115	}	}	PUNCT
ejpam-4655	602	116	,	,	PUNCT
ejpam-4655	602	117	{	{	PUNCT
ejpam-4655	602	118	p	p	X
ejpam-4655	602	119	,	,	PUNCT
ejpam-4655	602	120	q	q	NOUN
ejpam-4655	602	121	}	}	PUNCT
ejpam-4655	602	122	,	,	PUNCT
ejpam-4655	602	123	{	{	PUNCT
ejpam-4655	602	124	p	p	X
ejpam-4655	602	125	,	,	PUNCT
ejpam-4655	602	126	r	r	NOUN
ejpam-4655	602	127	}	}	PUNCT
ejpam-4655	602	128	,	,	PUNCT
ejpam-4655	602	129	{	{	PUNCT
ejpam-4655	602	130	p	p	X
ejpam-4655	602	131	,	,	PUNCT
ejpam-4655	602	132	s	s	PART
ejpam-4655	602	133	}	}	PUNCT
ejpam-4655	602	134	,	,	PUNCT
ejpam-4655	602	135	{	{	PUNCT
ejpam-4655	602	136	q	q	X
ejpam-4655	602	137	,	,	PUNCT
ejpam-4655	602	138	r	r	NOUN
ejpam-4655	602	139	}	}	PUNCT
ejpam-4655	602	140	,	,	PUNCT
ejpam-4655	602	141	{	{	PUNCT
ejpam-4655	602	142	p	p	X
ejpam-4655	602	143	,	,	PUNCT
ejpam-4655	602	144	q	q	ADJ
ejpam-4655	602	145	,	,	PUNCT
ejpam-4655	602	146	r	r	NOUN
ejpam-4655	602	147	}	}	PUNCT
ejpam-4655	602	148	,	,	PUNCT
ejpam-4655	602	149	{	{	PUNCT
ejpam-4655	602	150	p	p	X
ejpam-4655	602	151	,	,	PUNCT
ejpam-4655	602	152	q	q	X
ejpam-4655	602	153	,	,	PUNCT
ejpam-4655	602	154	s	s	PART
ejpam-4655	602	155	}	}	PUNCT
ejpam-4655	602	156	,	,	PUNCT
ejpam-4655	602	157	{	{	PUNCT
ejpam-4655	602	158	p	p	X
ejpam-4655	602	159	,	,	PUNCT
ejpam-4655	602	160	r	r	NOUN
ejpam-4655	602	161	,	,	PUNCT
ejpam-4655	602	162	s	s	PART
ejpam-4655	602	163	}	}	PUNCT
ejpam-4655	602	164	,	,	PUNCT
ejpam-4655	602	165	{	{	PUNCT
ejpam-4655	602	166	q	q	X
ejpam-4655	602	167	,	,	PUNCT
ejpam-4655	602	168	r	r	NOUN
ejpam-4655	602	169	,	,	PUNCT
ejpam-4655	602	170	s	s	PART
ejpam-4655	602	171	}	}	PUNCT
ejpam-4655	602	172	and	and	CCONJ
ejpam-4655	602	173	x	x	X
ejpam-4655	602	174	are	be	AUX
ejpam-4655	602	175	(	(	PUNCT
ejpam-4655	602	176	1	1	NUM
ejpam-4655	602	177	,	,	PUNCT
ejpam-4655	602	178	2)-dense	2)-dense	NUM
ejpam-4655	602	179	subsets	subset	NOUN
ejpam-4655	602	180	of	of	ADP
ejpam-4655	602	181	x.	x.	NOUN
ejpam-4655	602	182	also	also	ADV
ejpam-4655	602	183	,	,	PUNCT
ejpam-4655	602	184	(	(	PUNCT
ejpam-4655	602	185	1	1	NUM
ejpam-4655	602	186	,	,	PUNCT
ejpam-4655	602	187	2	2	NUM
ejpam-4655	602	188	)	)	PUNCT
ejpam-4655	602	189	−	−	PROPN
ejpam-4655	602	190	d(x	d(x	PROPN
ejpam-4655	602	191	)	)	PUNCT
ejpam-4655	603	1	⊂	⊂	PROPN
ejpam-4655	603	2	µ2	µ2	PROPN
ejpam-4655	603	3	.	.	PUNCT
ejpam-4655	604	1	hence	hence	ADV
ejpam-4655	604	2	x	x	PRON
ejpam-4655	604	3	is	be	AUX
ejpam-4655	604	4	a	a	DET
ejpam-4655	604	5	(	(	PUNCT
ejpam-4655	604	6	1	1	NUM
ejpam-4655	604	7	,	,	PUNCT
ejpam-4655	604	8	2)⋆⋆-bigeneralized	2)⋆⋆-bigeneralized	NUM
ejpam-4655	604	9	submaximal	submaximal	ADJ
ejpam-4655	604	10	space	space	NOUN
ejpam-4655	604	11	.	.	PUNCT
ejpam-4655	605	1	(	(	PUNCT
ejpam-4655	605	2	b	b	X
ejpam-4655	605	3	)	)	PUNCT
ejpam-4655	605	4	consider	consider	VERB
ejpam-4655	605	5	the	the	DET
ejpam-4655	605	6	bigeneralized	bigeneralized	ADJ
ejpam-4655	605	7	topological	topological	ADJ
ejpam-4655	605	8	space	space	NOUN
ejpam-4655	605	9	(	(	PUNCT
ejpam-4655	605	10	x,µ1	x,µ1	PROPN
ejpam-4655	605	11	,	,	PUNCT
ejpam-4655	605	12	µ2	µ2	PROPN
ejpam-4655	605	13	)	)	PUNCT
ejpam-4655	606	1	where	where	SCONJ
ejpam-4655	606	2	x	x	X
ejpam-4655	606	3	=	=	PRON
ejpam-4655	606	4	{	{	PUNCT
ejpam-4655	606	5	p	p	X
ejpam-4655	606	6	,	,	PUNCT
ejpam-4655	606	7	q	q	ADJ
ejpam-4655	606	8	,	,	PUNCT
ejpam-4655	606	9	r	r	NOUN
ejpam-4655	606	10	,	,	PUNCT
ejpam-4655	606	11	s};µ1	s};µ1	PROPN
ejpam-4655	606	12	=	=	SYM
ejpam-4655	606	13	{	{	PUNCT
ejpam-4655	606	14	∅	∅	NOUN
ejpam-4655	606	15	,	,	PUNCT
ejpam-4655	606	16	{	{	PUNCT
ejpam-4655	606	17	r	r	NOUN
ejpam-4655	606	18	}	}	PUNCT
ejpam-4655	606	19	,	,	PUNCT
ejpam-4655	606	20	{	{	PUNCT
ejpam-4655	606	21	p	p	X
ejpam-4655	606	22	,	,	PUNCT
ejpam-4655	606	23	q	q	NOUN
ejpam-4655	606	24	}	}	PUNCT
ejpam-4655	606	25	,	,	PUNCT
ejpam-4655	606	26	{	{	PUNCT
ejpam-4655	606	27	p	p	X
ejpam-4655	606	28	,	,	PUNCT
ejpam-4655	606	29	r	r	NOUN
ejpam-4655	606	30	}	}	PUNCT
ejpam-4655	606	31	,	,	PUNCT
ejpam-4655	606	32	{	{	PUNCT
ejpam-4655	606	33	p	p	X
ejpam-4655	606	34	,	,	PUNCT
ejpam-4655	606	35	s	s	PART
ejpam-4655	606	36	}	}	PUNCT
ejpam-4655	606	37	,	,	PUNCT
ejpam-4655	606	38	{	{	PUNCT
ejpam-4655	606	39	q	q	X
ejpam-4655	606	40	,	,	PUNCT
ejpam-4655	606	41	r	r	NOUN
ejpam-4655	606	42	}	}	PUNCT
ejpam-4655	606	43	,	,	PUNCT
ejpam-4655	606	44	{	{	PUNCT
ejpam-4655	606	45	q	q	X
ejpam-4655	606	46	,	,	PUNCT
ejpam-4655	606	47	s	s	PART
ejpam-4655	606	48	}	}	PUNCT
ejpam-4655	606	49	,	,	PUNCT
ejpam-4655	606	50	{	{	PUNCT
ejpam-4655	606	51	r	r	NOUN
ejpam-4655	606	52	,	,	PUNCT
ejpam-4655	606	53	s	s	PART
ejpam-4655	606	54	}	}	PUNCT
ejpam-4655	606	55	,	,	PUNCT
ejpam-4655	606	56	{	{	PUNCT
ejpam-4655	606	57	p	p	X
ejpam-4655	606	58	,	,	PUNCT
ejpam-4655	606	59	q	q	ADJ
ejpam-4655	606	60	,	,	PUNCT
ejpam-4655	606	61	r	r	NOUN
ejpam-4655	606	62	}	}	PUNCT
ejpam-4655	606	63	,	,	PUNCT
ejpam-4655	606	64	{	{	PUNCT
ejpam-4655	606	65	p	p	X
ejpam-4655	606	66	,	,	PUNCT
ejpam-4655	606	67	q	q	X
ejpam-4655	606	68	,	,	PUNCT
ejpam-4655	606	69	s	s	PART
ejpam-4655	606	70	}	}	PUNCT
ejpam-4655	606	71	,	,	PUNCT
ejpam-4655	606	72	{	{	PUNCT
ejpam-4655	606	73	p	p	X
ejpam-4655	606	74	,	,	PUNCT
ejpam-4655	606	75	r	r	NOUN
ejpam-4655	606	76	,	,	PUNCT
ejpam-4655	606	77	s	s	PART
ejpam-4655	606	78	}	}	PUNCT
ejpam-4655	606	79	,	,	PUNCT
ejpam-4655	606	80	{	{	PUNCT
ejpam-4655	606	81	q	q	X
ejpam-4655	606	82	,	,	PUNCT
ejpam-4655	606	83	r	r	NOUN
ejpam-4655	606	84	,	,	PUNCT
ejpam-4655	606	85	s	s	PART
ejpam-4655	606	86	}	}	PUNCT
ejpam-4655	606	87	,	,	PUNCT
ejpam-4655	606	88	x	x	NOUN
ejpam-4655	606	89	}	}	PUNCT
ejpam-4655	606	90	and	and	CCONJ
ejpam-4655	606	91	µ2	µ2	PROPN
ejpam-4655	606	92	=	=	PUNCT
ejpam-4655	606	93	{	{	PUNCT
ejpam-4655	606	94	∅	∅	NOUN
ejpam-4655	606	95	,	,	PUNCT
ejpam-4655	606	96	{	{	PUNCT
ejpam-4655	606	97	p	p	X
ejpam-4655	606	98	,	,	PUNCT
ejpam-4655	606	99	r	r	NOUN
ejpam-4655	606	100	}	}	PUNCT
ejpam-4655	606	101	,	,	PUNCT
ejpam-4655	606	102	{	{	PUNCT
ejpam-4655	606	103	q	q	X
ejpam-4655	606	104	,	,	PUNCT
ejpam-4655	606	105	r	r	NOUN
ejpam-4655	606	106	}	}	PUNCT
ejpam-4655	606	107	,	,	PUNCT
ejpam-4655	606	108	{	{	PUNCT
ejpam-4655	606	109	p	p	X
ejpam-4655	606	110	,	,	PUNCT
ejpam-4655	606	111	q	q	PROPN
ejpam-4655	606	112	,	,	PUNCT
ejpam-4655	606	113	r}}.here	r}}.here	X
ejpam-4655	606	114	{	{	PUNCT
ejpam-4655	606	115	r	r	NOUN
ejpam-4655	606	116	}	}	PUNCT
ejpam-4655	606	117	,	,	PUNCT
ejpam-4655	606	118	{	{	PUNCT
ejpam-4655	606	119	p	p	X
ejpam-4655	606	120	,	,	PUNCT
ejpam-4655	606	121	q	q	NOUN
ejpam-4655	606	122	}	}	PUNCT
ejpam-4655	606	123	,	,	PUNCT
ejpam-4655	606	124	{	{	PUNCT
ejpam-4655	606	125	p	p	X
ejpam-4655	606	126	,	,	PUNCT
ejpam-4655	606	127	r	r	NOUN
ejpam-4655	606	128	}	}	PUNCT
ejpam-4655	606	129	,	,	PUNCT
ejpam-4655	606	130	{	{	PUNCT
ejpam-4655	606	131	q	q	X
ejpam-4655	606	132	,	,	PUNCT
ejpam-4655	606	133	r	r	NOUN
ejpam-4655	606	134	}	}	PUNCT
ejpam-4655	606	135	,	,	PUNCT
ejpam-4655	606	136	{	{	PUNCT
ejpam-4655	606	137	r	r	NOUN
ejpam-4655	606	138	,	,	PUNCT
ejpam-4655	606	139	s	s	PART
ejpam-4655	606	140	}	}	PUNCT
ejpam-4655	606	141	,	,	PUNCT
ejpam-4655	606	142	{	{	PUNCT
ejpam-4655	606	143	p	p	X
ejpam-4655	606	144	,	,	PUNCT
ejpam-4655	606	145	q	q	ADJ
ejpam-4655	606	146	,	,	PUNCT
ejpam-4655	606	147	r	r	NOUN
ejpam-4655	606	148	}	}	PUNCT
ejpam-4655	606	149	,	,	PUNCT
ejpam-4655	606	150	{	{	PUNCT
ejpam-4655	606	151	p	p	X
ejpam-4655	606	152	,	,	PUNCT
ejpam-4655	606	153	q	q	X
ejpam-4655	606	154	,	,	PUNCT
ejpam-4655	606	155	s	s	PART
ejpam-4655	606	156	}	}	PUNCT
ejpam-4655	606	157	,	,	PUNCT
ejpam-4655	606	158	{	{	PUNCT
ejpam-4655	606	159	p	p	X
ejpam-4655	606	160	,	,	PUNCT
ejpam-4655	606	161	r	r	NOUN
ejpam-4655	606	162	,	,	PUNCT
ejpam-4655	606	163	s	s	PART
ejpam-4655	606	164	}	}	PUNCT
ejpam-4655	606	165	,	,	PUNCT
ejpam-4655	606	166	{	{	PUNCT
ejpam-4655	606	167	q	q	X
ejpam-4655	606	168	,	,	PUNCT
ejpam-4655	606	169	r	r	NOUN
ejpam-4655	606	170	,	,	PUNCT
ejpam-4655	606	171	s	s	PART
ejpam-4655	606	172	}	}	PUNCT
ejpam-4655	606	173	and	and	CCONJ
ejpam-4655	606	174	x	x	X
ejpam-4655	606	175	are	be	AUX
ejpam-4655	606	176	(	(	PUNCT
ejpam-4655	606	177	2	2	NUM
ejpam-4655	606	178	,	,	PUNCT
ejpam-4655	606	179	1)-dense	1)-dense	NUM
ejpam-4655	606	180	subsets	subset	NOUN
ejpam-4655	606	181	of	of	ADP
ejpam-4655	606	182	x.	x.	NOUN
ejpam-4655	606	183	also	also	ADV
ejpam-4655	606	184	,	,	PUNCT
ejpam-4655	606	185	(	(	PUNCT
ejpam-4655	606	186	2	2	NUM
ejpam-4655	606	187	,	,	PUNCT
ejpam-4655	606	188	1	1	NUM
ejpam-4655	606	189	)	)	PUNCT
ejpam-4655	606	190	−	−	PROPN
ejpam-4655	606	191	d(x	d(x	PROPN
ejpam-4655	606	192	)	)	PUNCT
ejpam-4655	607	1	⊂	⊂	PROPN
ejpam-4655	607	2	µ1	µ1	PROPN
ejpam-4655	607	3	.	.	PUNCT
ejpam-4655	608	1	hence	hence	ADV
ejpam-4655	608	2	x	x	PRON
ejpam-4655	608	3	is	be	AUX
ejpam-4655	608	4	a	a	DET
ejpam-4655	608	5	(	(	PUNCT
ejpam-4655	608	6	2	2	NUM
ejpam-4655	608	7	,	,	PUNCT
ejpam-4655	608	8	1)⋆⋆-bigeneralized	1)⋆⋆-bigeneralized	NUM
ejpam-4655	608	9	submaximal	submaximal	ADJ
ejpam-4655	608	10	space	space	NOUN
ejpam-4655	608	11	.	.	PUNCT
ejpam-4655	609	1	the	the	DET
ejpam-4655	609	2	following	follow	VERB
ejpam-4655	609	3	theorem	theorem	VERB
ejpam-4655	609	4	38	38	NUM
ejpam-4655	609	5	describes	describe	VERB
ejpam-4655	609	6	the	the	DET
ejpam-4655	609	7	below	below	ADJ
ejpam-4655	609	8	diagram	diagram	NOUN
ejpam-4655	609	9	.	.	PUNCT
ejpam-4655	610	1	(	(	PUNCT
ejpam-4655	610	2	a	a	X
ejpam-4655	610	3	)	)	PUNCT
ejpam-4655	610	4	x	x	X
ejpam-4655	610	5	is	be	AUX
ejpam-4655	610	6	a	a	DET
ejpam-4655	610	7	(	(	PUNCT
ejpam-4655	610	8	s	s	X
ejpam-4655	610	9	,	,	PUNCT
ejpam-4655	610	10	v)⋆⋆	v)⋆⋆	NOUN
ejpam-4655	610	11	−	−	NOUN
ejpam-4655	610	12	bigeneralized	bigeneralize	VERB
ejpam-4655	610	13	submaximal	submaximal	ADJ
ejpam-4655	610	14	space	space	NOUN
ejpam-4655	610	15	(	(	PUNCT
ejpam-4655	610	16	b	b	NOUN
ejpam-4655	610	17	)	)	PUNCT
ejpam-4655	610	18	(	(	PUNCT
ejpam-4655	610	19	c	c	NOUN
ejpam-4655	610	20	)	)	PUNCT
ejpam-4655	610	21	where	where	SCONJ
ejpam-4655	610	22	,	,	PUNCT
ejpam-4655	610	23	(	(	PUNCT
ejpam-4655	610	24	a	a	X
ejpam-4655	610	25	)	)	PUNCT
ejpam-4655	610	26	every	every	DET
ejpam-4655	610	27	µs	µs	NOUN
ejpam-4655	610	28	-	-	PUNCT
ejpam-4655	610	29	pre	pre	ADJ
ejpam-4655	610	30	-	-	ADJ
ejpam-4655	610	31	open	open	ADJ
ejpam-4655	610	32	is	be	AUX
ejpam-4655	610	33	µv	µv	NOUN
ejpam-4655	610	34	-	-	ADV
ejpam-4655	610	35	open	open	ADJ
ejpam-4655	610	36	.	.	PUNCT
ejpam-4655	611	1	(	(	PUNCT
ejpam-4655	611	2	b	b	X
ejpam-4655	611	3	)	)	PUNCT
ejpam-4655	611	4	every	every	DET
ejpam-4655	611	5	µs	µs	NOUN
ejpam-4655	611	6	-	-	PUNCT
ejpam-4655	611	7	β	β	NOUN
ejpam-4655	611	8	-	-	ADJ
ejpam-4655	611	9	open	open	ADJ
ejpam-4655	611	10	is	be	AUX
ejpam-4655	611	11	µv	µv	NOUN
ejpam-4655	611	12	-	-	ADV
ejpam-4655	611	13	open	open	ADJ
ejpam-4655	611	14	.	.	PUNCT
ejpam-4655	612	1	(	(	PUNCT
ejpam-4655	612	2	c	c	X
ejpam-4655	612	3	)	)	PUNCT
ejpam-4655	612	4	every	every	DET
ejpam-4655	612	5	µs	µs	ADP
ejpam-4655	612	6	-	-	PUNCT
ejpam-4655	612	7	b	b	NOUN
ejpam-4655	612	8	-	-	PUNCT
ejpam-4655	612	9	open	open	ADJ
ejpam-4655	612	10	is	be	AUX
ejpam-4655	612	11	µv	µv	NOUN
ejpam-4655	612	12	-	-	ADV
ejpam-4655	612	13	open	open	ADJ
ejpam-4655	612	14	.	.	PUNCT
ejpam-4655	613	1	the	the	DET
ejpam-4655	613	2	following	follow	VERB
ejpam-4655	613	3	theorem	theorem	VERB
ejpam-4655	613	4	38	38	NUM
ejpam-4655	613	5	provides	provide	VERB
ejpam-4655	613	6	an	an	DET
ejpam-4655	613	7	easier	easy	ADJ
ejpam-4655	613	8	way	way	NOUN
ejpam-4655	613	9	to	to	PART
ejpam-4655	613	10	check	check	VERB
ejpam-4655	613	11	the	the	DET
ejpam-4655	613	12	significance	significance	NOUN
ejpam-4655	613	13	of	of	ADP
ejpam-4655	613	14	bigeneralized	bigeneralize	VERB
ejpam-4655	613	15	topological	topological	ADJ
ejpam-4655	613	16	space	space	NOUN
ejpam-4655	613	17	using	use	VERB
ejpam-4655	613	18	different	different	ADJ
ejpam-4655	613	19	types	type	NOUN
ejpam-4655	613	20	of	of	ADP
ejpam-4655	613	21	open	open	ADJ
ejpam-4655	613	22	sets	set	NOUN
ejpam-4655	613	23	.	.	PUNCT
ejpam-4655	614	1	theorem	theorem	VERB
ejpam-4655	614	2	38	38	NUM
ejpam-4655	614	3	.	.	PUNCT
ejpam-4655	615	1	let	let	AUX
ejpam-4655	615	2	(	(	PUNCT
ejpam-4655	615	3	x,µ1	x,µ1	NOUN
ejpam-4655	615	4	,	,	PUNCT
ejpam-4655	615	5	µ2	µ2	PROPN
ejpam-4655	615	6	)	)	PUNCT
ejpam-4655	615	7	be	be	VERB
ejpam-4655	615	8	a	a	DET
ejpam-4655	615	9	bgts	bgts	NOUN
ejpam-4655	615	10	and	and	CCONJ
ejpam-4655	615	11	µs	µs	NOUN
ejpam-4655	615	12	is	be	AUX
ejpam-4655	615	13	sgt	sgt	PROPN
ejpam-4655	615	14	.	.	PUNCT
ejpam-4655	616	1	then	then	ADV
ejpam-4655	616	2	x	x	PRON
ejpam-4655	616	3	is	be	AUX
ejpam-4655	616	4	a	a	DET
ejpam-4655	616	5	(	(	PUNCT
ejpam-4655	616	6	s	s	PROPN
ejpam-4655	616	7	,	,	PUNCT
ejpam-4655	616	8	v)⋆⋆-bigeneralized	v)⋆⋆-bigeneralize	VERB
ejpam-4655	616	9	submaximal	submaximal	ADJ
ejpam-4655	616	10	space	space	NOUN
ejpam-4655	616	11	if	if	SCONJ
ejpam-4655	616	12	any	any	DET
ejpam-4655	616	13	one	one	NUM
ejpam-4655	616	14	of	of	ADP
ejpam-4655	616	15	the	the	DET
ejpam-4655	616	16	following	follow	VERB
ejpam-4655	616	17	is	be	AUX
ejpam-4655	616	18	true	true	ADJ
ejpam-4655	616	19	;	;	PUNCT
ejpam-4655	616	20	(	(	PUNCT
ejpam-4655	616	21	a	a	X
ejpam-4655	616	22	)	)	PUNCT
ejpam-4655	616	23	every	every	DET
ejpam-4655	616	24	µs	µs	NOUN
ejpam-4655	616	25	-	-	PUNCT
ejpam-4655	616	26	pre	pre	ADJ
ejpam-4655	616	27	-	-	ADJ
ejpam-4655	616	28	open	open	ADJ
ejpam-4655	616	29	is	be	AUX
ejpam-4655	616	30	µv	µv	NOUN
ejpam-4655	616	31	-	-	ADV
ejpam-4655	616	32	open	open	ADJ
ejpam-4655	616	33	.	.	PUNCT
ejpam-4655	617	1	(	(	PUNCT
ejpam-4655	617	2	b	b	X
ejpam-4655	617	3	)	)	PUNCT
ejpam-4655	617	4	every	every	DET
ejpam-4655	617	5	µs	µs	NOUN
ejpam-4655	617	6	-	-	PUNCT
ejpam-4655	617	7	β	β	NOUN
ejpam-4655	617	8	-	-	ADJ
ejpam-4655	617	9	open	open	ADJ
ejpam-4655	617	10	is	be	AUX
ejpam-4655	617	11	µv	µv	NOUN
ejpam-4655	617	12	-	-	ADV
ejpam-4655	617	13	open	open	ADJ
ejpam-4655	617	14	.	.	PUNCT
ejpam-4655	618	1	(	(	PUNCT
ejpam-4655	618	2	c	c	X
ejpam-4655	618	3	)	)	PUNCT
ejpam-4655	618	4	every	every	DET
ejpam-4655	618	5	µs	µs	ADP
ejpam-4655	618	6	-	-	PUNCT
ejpam-4655	618	7	b	b	NOUN
ejpam-4655	618	8	-	-	PUNCT
ejpam-4655	618	9	open	open	ADJ
ejpam-4655	618	10	is	be	AUX
ejpam-4655	618	11	µv	µv	NOUN
ejpam-4655	618	12	-	-	PUNCT
ejpam-4655	618	13	open	open	ADJ
ejpam-4655	618	14	where	where	SCONJ
ejpam-4655	618	15	s	s	X
ejpam-4655	618	16	,	,	PUNCT
ejpam-4655	618	17	v	v	NOUN
ejpam-4655	618	18	=	=	SYM
ejpam-4655	618	19	1	1	NUM
ejpam-4655	618	20	,	,	PUNCT
ejpam-4655	618	21	2	2	NUM
ejpam-4655	618	22	and	and	CCONJ
ejpam-4655	618	23	s	s	VERB
ejpam-4655	618	24	̸=	̸=	PROPN
ejpam-4655	618	25	v.	v.	ADP
ejpam-4655	618	26	proof	proof	NOUN
ejpam-4655	618	27	.	.	PUNCT
ejpam-4655	619	1	it	it	PRON
ejpam-4655	619	2	is	be	AUX
ejpam-4655	619	3	enough	enough	ADJ
ejpam-4655	619	4	to	to	PART
ejpam-4655	619	5	prove	prove	VERB
ejpam-4655	619	6	the	the	DET
ejpam-4655	619	7	case	case	NOUN
ejpam-4655	619	8	for	for	ADP
ejpam-4655	619	9	s	s	NOUN
ejpam-4655	619	10	=	=	SYM
ejpam-4655	619	11	1	1	NUM
ejpam-4655	619	12	,	,	PUNCT
ejpam-4655	619	13	v	v	NOUN
ejpam-4655	619	14	=	=	SYM
ejpam-4655	619	15	2	2	NUM
ejpam-4655	619	16	.	.	PUNCT
ejpam-4655	619	17	(	(	PUNCT
ejpam-4655	619	18	a	a	X
ejpam-4655	619	19	)	)	PUNCT
ejpam-4655	619	20	assume	assume	VERB
ejpam-4655	619	21	that	that	SCONJ
ejpam-4655	619	22	,	,	PUNCT
ejpam-4655	619	23	µ1	µ1	PROPN
ejpam-4655	619	24	is	be	AUX
ejpam-4655	619	25	sgt	sgt	PROPN
ejpam-4655	619	26	,	,	PUNCT
ejpam-4655	619	27	every	every	DET
ejpam-4655	619	28	µ1	µ1	PROPN
ejpam-4655	619	29	-	-	PUNCT
ejpam-4655	619	30	pre	pre	NOUN
ejpam-4655	619	31	-	-	ADJ
ejpam-4655	619	32	open	open	ADJ
ejpam-4655	619	33	is	be	AUX
ejpam-4655	619	34	µ2	µ2	ADJ
ejpam-4655	619	35	-	-	PUNCT
ejpam-4655	619	36	open	open	ADJ
ejpam-4655	619	37	and	and	CCONJ
ejpam-4655	619	38	let	let	VERB
ejpam-4655	619	39	q	q	PROPN
ejpam-4655	619	40	∈	∈	PROPN
ejpam-4655	619	41	(	(	PUNCT
ejpam-4655	619	42	1	1	NUM
ejpam-4655	619	43	,	,	PUNCT
ejpam-4655	619	44	2)−d(x	2)−d(x	NUM
ejpam-4655	619	45	)	)	PUNCT
ejpam-4655	619	46	,	,	PUNCT
ejpam-4655	619	47	then	then	ADV
ejpam-4655	619	48	c1(c2(q	c1(c2(q	PROPN
ejpam-4655	619	49	)	)	PUNCT
ejpam-4655	619	50	)	)	PUNCT
ejpam-4655	620	1	=	=	PUNCT
ejpam-4655	620	2	x	x	X
ejpam-4655	620	3	whereby	whereby	ADV
ejpam-4655	620	4	by	by	ADP
ejpam-4655	620	5	hypothesis	hypothesis	NOUN
ejpam-4655	620	6	,	,	PUNCT
ejpam-4655	620	7	c1(q	c1(q	ADJ
ejpam-4655	620	8	)	)	PUNCT
ejpam-4655	620	9	⊃	⊃	PROPN
ejpam-4655	620	10	c2(q	c2(q	PROPN
ejpam-4655	620	11	)	)	PUNCT
ejpam-4655	620	12	,	,	PUNCT
ejpam-4655	620	13	this	this	PRON
ejpam-4655	620	14	implies	imply	VERB
ejpam-4655	620	15	c1(q	c1(q	ADV
ejpam-4655	620	16	)	)	PUNCT
ejpam-4655	620	17	⊃	⊃	PROPN
ejpam-4655	620	18	c1(c2(q	c1(c2(q	PROPN
ejpam-4655	620	19	)	)	PUNCT
ejpam-4655	620	20	)	)	PUNCT
ejpam-4655	620	21	which	which	PRON
ejpam-4655	620	22	implies	imply	VERB
ejpam-4655	620	23	that	that	SCONJ
ejpam-4655	620	24	c1(q	c1(q	ADJ
ejpam-4655	620	25	)	)	PUNCT
ejpam-4655	620	26	=	=	PUNCT
ejpam-4655	620	27	x.	x.	NOUN
ejpam-4655	620	28	also	also	ADV
ejpam-4655	620	29	,	,	PUNCT
ejpam-4655	620	30	i1(c1(q	i1(c1(q	ADP
ejpam-4655	620	31	)	)	PUNCT
ejpam-4655	620	32	)	)	PUNCT
ejpam-4655	621	1	=	=	SYM
ejpam-4655	621	2	x	x	X
ejpam-4655	621	3	,	,	PUNCT
ejpam-4655	621	4	by	by	ADP
ejpam-4655	621	5	our	our	PRON
ejpam-4655	621	6	assumption	assumption	NOUN
ejpam-4655	621	7	.	.	PUNCT
ejpam-4655	622	1	thus	thus	ADV
ejpam-4655	622	2	,	,	PUNCT
ejpam-4655	622	3	q	q	PROPN
ejpam-4655	622	4	⊂	⊂	X
ejpam-4655	622	5	i1(c1(q	i1(c1(q	NOUN
ejpam-4655	622	6	)	)	PUNCT
ejpam-4655	622	7	)	)	PUNCT
ejpam-4655	623	1	so	so	ADV
ejpam-4655	623	2	it	it	PRON
ejpam-4655	623	3	result	result	VERB
ejpam-4655	623	4	that	that	SCONJ
ejpam-4655	623	5	q	q	NOUN
ejpam-4655	623	6	is	be	AUX
ejpam-4655	623	7	µ1	µ1	NOUN
ejpam-4655	623	8	-	-	PUNCT
ejpam-4655	623	9	pre	pre	NOUN
ejpam-4655	623	10	-	-	ADJ
ejpam-4655	623	11	open	open	ADJ
ejpam-4655	623	12	it	it	PRON
ejpam-4655	623	13	turns	turn	VERB
ejpam-4655	623	14	out	out	ADP
ejpam-4655	623	15	q	q	PROPN
ejpam-4655	623	16	∈	∈	PROPN
ejpam-4655	623	17	µ2	µ2	NOUN
ejpam-4655	623	18	and	and	CCONJ
ejpam-4655	623	19	hence	hence	ADV
ejpam-4655	623	20	x	x	PRON
ejpam-4655	623	21	is	be	AUX
ejpam-4655	623	22	a	a	DET
ejpam-4655	623	23	(	(	PUNCT
ejpam-4655	623	24	1	1	NUM
ejpam-4655	623	25	,	,	PUNCT
ejpam-4655	623	26	2)⋆⋆bigeneralized	2)⋆⋆bigeneralized	ADJ
ejpam-4655	623	27	submaximal	submaximal	ADJ
ejpam-4655	623	28	space	space	NOUN
ejpam-4655	623	29	.	.	PUNCT
ejpam-4655	624	1	(	(	PUNCT
ejpam-4655	624	2	b	b	X
ejpam-4655	624	3	)	)	PUNCT
ejpam-4655	624	4	suppose	suppose	VERB
ejpam-4655	624	5	µ1	µ1	PROPN
ejpam-4655	624	6	is	be	AUX
ejpam-4655	624	7	sgt	sgt	PROPN
ejpam-4655	624	8	and	and	CCONJ
ejpam-4655	624	9	every	every	DET
ejpam-4655	624	10	µ1	µ1	PROPN
ejpam-4655	624	11	-	-	PUNCT
ejpam-4655	624	12	β	β	NOUN
ejpam-4655	624	13	-	-	ADJ
ejpam-4655	624	14	open	open	ADJ
ejpam-4655	624	15	is	be	AUX
ejpam-4655	624	16	µ2	µ2	ADJ
ejpam-4655	624	17	-	-	PUNCT
ejpam-4655	624	18	open	open	ADJ
ejpam-4655	624	19	.	.	PUNCT
ejpam-4655	625	1	consider	consider	VERB
ejpam-4655	625	2	,	,	PUNCT
ejpam-4655	625	3	k	k	PROPN
ejpam-4655	625	4	∈	∈	PROPN
ejpam-4655	625	5	(	(	PUNCT
ejpam-4655	625	6	1	1	NUM
ejpam-4655	625	7	,	,	PUNCT
ejpam-4655	625	8	2	2	NUM
ejpam-4655	625	9	)	)	PUNCT
ejpam-4655	625	10	−	−	PROPN
ejpam-4655	625	11	d(x	d(x	NOUN
ejpam-4655	625	12	)	)	PUNCT
ejpam-4655	625	13	so	so	SCONJ
ejpam-4655	625	14	cµ1(k	cµ1(k	NOUN
ejpam-4655	625	15	)	)	PUNCT
ejpam-4655	625	16	=	=	SYM
ejpam-4655	626	1	x	x	X
ejpam-4655	626	2	,	,	PUNCT
ejpam-4655	626	3	by	by	ADP
ejpam-4655	626	4	similar	similar	ADJ
ejpam-4655	626	5	arguments	argument	NOUN
ejpam-4655	626	6	in	in	ADP
ejpam-4655	626	7	(	(	PUNCT
ejpam-4655	626	8	a	a	NOUN
ejpam-4655	626	9	)	)	PUNCT
ejpam-4655	626	10	.	.	PUNCT
ejpam-4655	627	1	thus	thus	ADV
ejpam-4655	627	2	,	,	PUNCT
ejpam-4655	627	3	i1(c1(k	i1(c1(k	NOUN
ejpam-4655	627	4	)	)	PUNCT
ejpam-4655	627	5	)	)	PUNCT
ejpam-4655	628	1	=	=	SYM
ejpam-4655	628	2	x	x	X
ejpam-4655	628	3	,	,	PUNCT
ejpam-4655	628	4	by	by	ADP
ejpam-4655	628	5	hypothesis	hypothesis	NOUN
ejpam-4655	628	6	.	.	PUNCT
ejpam-4655	629	1	by	by	ADP
ejpam-4655	629	2	which	which	PRON
ejpam-4655	629	3	k	k	PROPN
ejpam-4655	629	4	⊂	⊂	X
ejpam-4655	629	5	c1(i1(c1(k	c1(i1(c1(k	NOUN
ejpam-4655	629	6	)	)	PUNCT
ejpam-4655	629	7	)	)	PUNCT
ejpam-4655	629	8	)	)	PUNCT
ejpam-4655	629	9	implies	imply	VERB
ejpam-4655	629	10	that	that	SCONJ
ejpam-4655	629	11	k	k	PROPN
ejpam-4655	629	12	is	be	AUX
ejpam-4655	629	13	µ1	µ1	PROPN
ejpam-4655	629	14	-	-	PUNCT
ejpam-4655	629	15	β	β	NOUN
ejpam-4655	629	16	-	-	ADJ
ejpam-4655	629	17	open	open	ADJ
ejpam-4655	629	18	.	.	PUNCT
ejpam-4655	630	1	by	by	ADP
ejpam-4655	630	2	our	our	PRON
ejpam-4655	630	3	assumption	assumption	NOUN
ejpam-4655	630	4	,	,	PUNCT
ejpam-4655	630	5	k	k	PROPN
ejpam-4655	630	6	∈	∈	PROPN
ejpam-4655	630	7	µ2	µ2	PROPN
ejpam-4655	630	8	.	.	PUNCT
ejpam-4655	631	1	therefore	therefore	ADV
ejpam-4655	631	2	,	,	PUNCT
ejpam-4655	631	3	y.	y.	PROPN
ejpam-4655	631	4	farhat	farhat	PROPN
ejpam-4655	631	5	et	et	PROPN
ejpam-4655	631	6	al	al	PROPN
ejpam-4655	631	7	.	.	PUNCT
ejpam-4655	631	8	/	/	SYM
ejpam-4655	631	9	eur	eur	PROPN
ejpam-4655	631	10	.	.	PUNCT
ejpam-4655	632	1	j.	j.	PROPN
ejpam-4655	632	2	pure	pure	PROPN
ejpam-4655	632	3	appl	appl	PROPN
ejpam-4655	632	4	.	.	PROPN
ejpam-4655	632	5	math	math	PROPN
ejpam-4655	632	6	,	,	PUNCT
ejpam-4655	632	7	16	16	NUM
ejpam-4655	632	8	(	(	PUNCT
ejpam-4655	632	9	1	1	NUM
ejpam-4655	632	10	)	)	PUNCT
ejpam-4655	632	11	(	(	PUNCT
ejpam-4655	632	12	2023	2023	NUM
ejpam-4655	632	13	)	)	PUNCT
ejpam-4655	632	14	,	,	PUNCT
ejpam-4655	632	15	386	386	NUM
ejpam-4655	632	16	-	-	SYM
ejpam-4655	632	17	403	403	NUM
ejpam-4655	632	18	401	401	NUM
ejpam-4655	632	19	x	x	NOUN
ejpam-4655	632	20	is	be	AUX
ejpam-4655	632	21	a	a	DET
ejpam-4655	632	22	(	(	PUNCT
ejpam-4655	632	23	1	1	NUM
ejpam-4655	632	24	,	,	PUNCT
ejpam-4655	632	25	2)⋆⋆-bigeneralized	2)⋆⋆-bigeneralized	NUM
ejpam-4655	632	26	submaximal	submaximal	ADJ
ejpam-4655	632	27	space	space	NOUN
ejpam-4655	632	28	.	.	PUNCT
ejpam-4655	633	1	(	(	PUNCT
ejpam-4655	633	2	c	c	X
ejpam-4655	633	3	)	)	PUNCT
ejpam-4655	633	4	assume	assume	VERB
ejpam-4655	633	5	that	that	SCONJ
ejpam-4655	633	6	,	,	PUNCT
ejpam-4655	633	7	µ1	µ1	PROPN
ejpam-4655	633	8	is	be	AUX
ejpam-4655	633	9	sgt	sgt	PROPN
ejpam-4655	633	10	and	and	CCONJ
ejpam-4655	633	11	every	every	DET
ejpam-4655	633	12	µ1	µ1	PROPN
ejpam-4655	633	13	-	-	PUNCT
ejpam-4655	633	14	b	b	NOUN
ejpam-4655	633	15	-	-	PUNCT
ejpam-4655	633	16	open	open	ADJ
ejpam-4655	633	17	is	be	AUX
ejpam-4655	633	18	µ2	µ2	ADJ
ejpam-4655	633	19	-	-	PUNCT
ejpam-4655	633	20	open	open	ADJ
ejpam-4655	633	21	.	.	PUNCT
ejpam-4655	634	1	take	take	VERB
ejpam-4655	634	2	j	j	PROPN
ejpam-4655	634	3	∈	∈	PROPN
ejpam-4655	634	4	(	(	PUNCT
ejpam-4655	634	5	1	1	NUM
ejpam-4655	634	6	,	,	PUNCT
ejpam-4655	634	7	2	2	NUM
ejpam-4655	634	8	)	)	PUNCT
ejpam-4655	634	9	−	−	PROPN
ejpam-4655	634	10	d(x	d(x	NOUN
ejpam-4655	634	11	)	)	PUNCT
ejpam-4655	634	12	so	so	ADV
ejpam-4655	634	13	for	for	ADP
ejpam-4655	634	14	cµ1(j	cµ1(j	NOUN
ejpam-4655	634	15	)	)	PUNCT
ejpam-4655	634	16	=	=	SYM
ejpam-4655	635	1	x	x	X
ejpam-4655	635	2	,	,	PUNCT
ejpam-4655	635	3	by	by	ADP
ejpam-4655	635	4	similar	similar	ADJ
ejpam-4655	635	5	arguments	argument	NOUN
ejpam-4655	635	6	in	in	ADP
ejpam-4655	635	7	(	(	PUNCT
ejpam-4655	635	8	a	a	NOUN
ejpam-4655	635	9	)	)	PUNCT
ejpam-4655	635	10	.	.	PUNCT
ejpam-4655	636	1	by	by	ADP
ejpam-4655	636	2	our	our	PRON
ejpam-4655	636	3	assumption	assumption	NOUN
ejpam-4655	636	4	,	,	PUNCT
ejpam-4655	636	5	i1(c1(j	i1(c1(j	PROPN
ejpam-4655	636	6	)	)	PUNCT
ejpam-4655	636	7	)	)	PUNCT
ejpam-4655	636	8	=	=	PUNCT
ejpam-4655	636	9	x.	x.	PUNCT
ejpam-4655	636	10	thus	thus	ADV
ejpam-4655	636	11	,	,	PUNCT
ejpam-4655	636	12	j	j	PROPN
ejpam-4655	636	13	⊂	⊂	PROPN
ejpam-4655	636	14	c1(i1(j	c1(i1(j	PROPN
ejpam-4655	636	15	)	)	PUNCT
ejpam-4655	636	16	)	)	PUNCT
ejpam-4655	636	17	∪	∪	ADP
ejpam-4655	636	18	i1(c1(j	i1(c1(j	PROPN
ejpam-4655	636	19	)	)	PUNCT
ejpam-4655	636	20	)	)	PUNCT
ejpam-4655	636	21	.	.	PUNCT
ejpam-4655	637	1	this	this	PRON
ejpam-4655	637	2	implies	imply	VERB
ejpam-4655	637	3	j	j	PROPN
ejpam-4655	637	4	is	be	AUX
ejpam-4655	637	5	µ1	µ1	PROPN
ejpam-4655	637	6	-	-	PUNCT
ejpam-4655	637	7	b	b	NOUN
ejpam-4655	637	8	-	-	PUNCT
ejpam-4655	637	9	open	open	ADJ
ejpam-4655	637	10	which	which	PRON
ejpam-4655	637	11	implies	imply	VERB
ejpam-4655	637	12	that	that	SCONJ
ejpam-4655	637	13	j	j	PROPN
ejpam-4655	637	14	∈	∈	PROPN
ejpam-4655	637	15	µ2	µ2	PROPN
ejpam-4655	637	16	,	,	PUNCT
ejpam-4655	637	17	by	by	ADP
ejpam-4655	637	18	hypothesis	hypothesis	NOUN
ejpam-4655	637	19	.	.	PUNCT
ejpam-4655	638	1	hence	hence	ADV
ejpam-4655	638	2	x	x	PRON
ejpam-4655	638	3	is	be	AUX
ejpam-4655	638	4	a	a	DET
ejpam-4655	638	5	(	(	PUNCT
ejpam-4655	638	6	1	1	NUM
ejpam-4655	638	7	,	,	PUNCT
ejpam-4655	638	8	2)⋆⋆-bigeneralized	2)⋆⋆-bigeneralized	NUM
ejpam-4655	638	9	submaximal	submaximal	ADJ
ejpam-4655	638	10	space	space	NOUN
ejpam-4655	638	11	.	.	PUNCT
ejpam-4655	639	1	the	the	DET
ejpam-4655	639	2	following	following	ADJ
ejpam-4655	639	3	example	example	NOUN
ejpam-4655	639	4	39	39	NUM
ejpam-4655	639	5	shows	show	VERB
ejpam-4655	639	6	that	that	SCONJ
ejpam-4655	639	7	the	the	DET
ejpam-4655	639	8	hypothesis	hypothesis	NOUN
ejpam-4655	639	9	of	of	ADP
ejpam-4655	639	10	theorem	theorem	NOUN
ejpam-4655	639	11	38	38	NUM
ejpam-4655	639	12	can	can	AUX
ejpam-4655	639	13	not	not	PART
ejpam-4655	639	14	be	be	AUX
ejpam-4655	639	15	dropped	drop	VERB
ejpam-4655	639	16	.	.	PUNCT
ejpam-4655	640	1	example	example	NOUN
ejpam-4655	640	2	39	39	NUM
ejpam-4655	640	3	.	.	PUNCT
ejpam-4655	641	1	consider	consider	VERB
ejpam-4655	641	2	the	the	DET
ejpam-4655	641	3	bigeneralized	bigeneralized	ADJ
ejpam-4655	641	4	topological	topological	ADJ
ejpam-4655	641	5	space	space	NOUN
ejpam-4655	641	6	(	(	PUNCT
ejpam-4655	641	7	x,µ1	x,µ1	PROPN
ejpam-4655	641	8	,	,	PUNCT
ejpam-4655	641	9	µ2	µ2	ADJ
ejpam-4655	641	10	)	)	PUNCT
ejpam-4655	641	11	wherex	wherex	PROPN
ejpam-4655	641	12	=	=	PUNCT
ejpam-4655	641	13	{	{	PUNCT
ejpam-4655	641	14	p	p	X
ejpam-4655	641	15	,	,	PUNCT
ejpam-4655	641	16	q	q	ADJ
ejpam-4655	641	17	,	,	PUNCT
ejpam-4655	641	18	r	r	NOUN
ejpam-4655	641	19	,	,	PUNCT
ejpam-4655	641	20	s	s	PART
ejpam-4655	641	21	}	}	PUNCT
ejpam-4655	641	22	;	;	PUNCT
ejpam-4655	641	23	µ1	µ1	PROPN
ejpam-4655	641	24	=	=	SYM
ejpam-4655	641	25	{	{	PUNCT
ejpam-4655	641	26	∅	∅	NOUN
ejpam-4655	641	27	,	,	PUNCT
ejpam-4655	641	28	{	{	PUNCT
ejpam-4655	641	29	p	p	X
ejpam-4655	641	30	,	,	PUNCT
ejpam-4655	641	31	r	r	NOUN
ejpam-4655	641	32	}	}	PUNCT
ejpam-4655	641	33	,	,	PUNCT
ejpam-4655	641	34	{	{	PUNCT
ejpam-4655	641	35	q	q	X
ejpam-4655	641	36	,	,	PUNCT
ejpam-4655	641	37	r	r	NOUN
ejpam-4655	641	38	}	}	PUNCT
ejpam-4655	641	39	,	,	PUNCT
ejpam-4655	641	40	{	{	PUNCT
ejpam-4655	641	41	p	p	X
ejpam-4655	641	42	,	,	PUNCT
ejpam-4655	641	43	q	q	ADJ
ejpam-4655	641	44	,	,	PUNCT
ejpam-4655	641	45	r	r	NOUN
ejpam-4655	641	46	}	}	PUNCT
ejpam-4655	641	47	,	,	PUNCT
ejpam-4655	641	48	x	x	NOUN
ejpam-4655	641	49	}	}	PUNCT
ejpam-4655	641	50	and	and	CCONJ
ejpam-4655	641	51	µ2	µ2	PROPN
ejpam-4655	641	52	=	=	PUNCT
ejpam-4655	641	53	{	{	PUNCT
ejpam-4655	641	54	∅	∅	NOUN
ejpam-4655	641	55	,	,	PUNCT
ejpam-4655	641	56	{	{	PUNCT
ejpam-4655	641	57	p	p	X
ejpam-4655	641	58	,	,	PUNCT
ejpam-4655	641	59	r	r	NOUN
ejpam-4655	641	60	}	}	PUNCT
ejpam-4655	641	61	,	,	PUNCT
ejpam-4655	641	62	{	{	PUNCT
ejpam-4655	641	63	q	q	X
ejpam-4655	641	64	,	,	PUNCT
ejpam-4655	641	65	r	r	NOUN
ejpam-4655	641	66	}	}	PUNCT
ejpam-4655	641	67	,	,	PUNCT
ejpam-4655	641	68	{	{	PUNCT
ejpam-4655	641	69	p	p	X
ejpam-4655	641	70	,	,	PUNCT
ejpam-4655	641	71	s	s	PART
ejpam-4655	641	72	}	}	PUNCT
ejpam-4655	641	73	,	,	PUNCT
ejpam-4655	641	74	{	{	PUNCT
ejpam-4655	641	75	q	q	X
ejpam-4655	641	76	,	,	PUNCT
ejpam-4655	641	77	s	s	PART
ejpam-4655	641	78	}	}	PUNCT
ejpam-4655	641	79	,	,	PUNCT
ejpam-4655	641	80	{	{	PUNCT
ejpam-4655	641	81	p	p	X
ejpam-4655	641	82	,	,	PUNCT
ejpam-4655	641	83	q	q	ADJ
ejpam-4655	641	84	,	,	PUNCT
ejpam-4655	641	85	r	r	NOUN
ejpam-4655	641	86	}	}	PUNCT
ejpam-4655	641	87	,	,	PUNCT
ejpam-4655	641	88	{	{	PUNCT
ejpam-4655	641	89	p	p	X
ejpam-4655	641	90	,	,	PUNCT
ejpam-4655	641	91	q	q	X
ejpam-4655	641	92	,	,	PUNCT
ejpam-4655	641	93	s	s	PART
ejpam-4655	641	94	}	}	PUNCT
ejpam-4655	641	95	,	,	PUNCT
ejpam-4655	641	96	{	{	PUNCT
ejpam-4655	641	97	p	p	X
ejpam-4655	641	98	,	,	PUNCT
ejpam-4655	641	99	r	r	NOUN
ejpam-4655	641	100	,	,	PUNCT
ejpam-4655	641	101	s	s	PART
ejpam-4655	641	102	}	}	PUNCT
ejpam-4655	641	103	,	,	PUNCT
ejpam-4655	641	104	{	{	PUNCT
ejpam-4655	641	105	q	q	X
ejpam-4655	641	106	,	,	PUNCT
ejpam-4655	641	107	r	r	NOUN
ejpam-4655	641	108	,	,	PUNCT
ejpam-4655	641	109	s	s	PART
ejpam-4655	641	110	}	}	PUNCT
ejpam-4655	641	111	,	,	PUNCT
ejpam-4655	641	112	x	x	NOUN
ejpam-4655	641	113	}	}	PUNCT
ejpam-4655	641	114	.	.	PUNCT
ejpam-4655	642	1	here	here	ADV
ejpam-4655	642	2	,	,	PUNCT
ejpam-4655	642	3	µ1	µ1	PROPN
ejpam-4655	642	4	⊂	⊂	PROPN
ejpam-4655	642	5	µ2	µ2	PROPN
ejpam-4655	642	6	and	and	CCONJ
ejpam-4655	642	7	µ1	µ1	PROPN
ejpam-4655	642	8	is	be	AUX
ejpam-4655	642	9	a	a	DET
ejpam-4655	642	10	strong	strong	ADJ
ejpam-4655	642	11	generalized	generalized	ADJ
ejpam-4655	642	12	topology	topology	NOUN
ejpam-4655	642	13	.	.	PUNCT
ejpam-4655	643	1	fix	fix	NOUN
ejpam-4655	643	2	s	s	PART
ejpam-4655	643	3	=	=	SYM
ejpam-4655	643	4	1	1	NUM
ejpam-4655	643	5	and	and	CCONJ
ejpam-4655	643	6	v	v	NOUN
ejpam-4655	643	7	=	=	SYM
ejpam-4655	643	8	2	2	NUM
ejpam-4655	643	9	.	.	NOUN
ejpam-4655	643	10	•	•	NOUN
ejpam-4655	643	11	take	take	VERB
ejpam-4655	643	12	k	k	NOUN
ejpam-4655	643	13	=	=	PRON
ejpam-4655	643	14	{	{	PUNCT
ejpam-4655	643	15	r	r	NOUN
ejpam-4655	643	16	}	}	PUNCT
ejpam-4655	643	17	.	.	PUNCT
ejpam-4655	644	1	then	then	ADV
ejpam-4655	644	2	k	k	PROPN
ejpam-4655	644	3	is	be	AUX
ejpam-4655	644	4	µ1	µ1	NOUN
ejpam-4655	644	5	-	-	PUNCT
ejpam-4655	644	6	pre	pre	NOUN
ejpam-4655	644	7	-	-	ADJ
ejpam-4655	644	8	open	open	ADJ
ejpam-4655	644	9	but	but	CCONJ
ejpam-4655	644	10	not	not	PART
ejpam-4655	644	11	µ2	µ2	ADJ
ejpam-4655	644	12	-	-	PUNCT
ejpam-4655	644	13	open	open	ADJ
ejpam-4655	644	14	.	.	PUNCT
ejpam-4655	645	1	•	•	NUM
ejpam-4655	645	2	choose	choose	VERB
ejpam-4655	645	3	l	l	NOUN
ejpam-4655	645	4	=	=	PUNCT
ejpam-4655	645	5	{	{	PUNCT
ejpam-4655	645	6	p	p	X
ejpam-4655	645	7	,	,	PUNCT
ejpam-4655	645	8	q	q	NOUN
ejpam-4655	645	9	}	}	PUNCT
ejpam-4655	645	10	.	.	PUNCT
ejpam-4655	646	1	we	we	PRON
ejpam-4655	646	2	get	get	VERB
ejpam-4655	646	3	l	l	NOUN
ejpam-4655	646	4	is	be	AUX
ejpam-4655	646	5	µ1	µ1	PROPN
ejpam-4655	646	6	-	-	PUNCT
ejpam-4655	646	7	β	β	NOUN
ejpam-4655	646	8	-	-	ADJ
ejpam-4655	646	9	open	open	ADJ
ejpam-4655	646	10	but	but	CCONJ
ejpam-4655	646	11	l	l	NOUN
ejpam-4655	646	12	/∈	/∈	PUNCT
ejpam-4655	647	1	µ2	µ2	PROPN
ejpam-4655	647	2	.	.	PUNCT
ejpam-4655	648	1	•	•	NUM
ejpam-4655	648	2	let	let	VERB
ejpam-4655	648	3	w	w	NOUN
ejpam-4655	648	4	=	=	PUNCT
ejpam-4655	648	5	{	{	PUNCT
ejpam-4655	648	6	r	r	NOUN
ejpam-4655	648	7	,	,	PUNCT
ejpam-4655	648	8	s	s	PART
ejpam-4655	648	9	}	}	PUNCT
ejpam-4655	648	10	.	.	PUNCT
ejpam-4655	649	1	then	then	ADV
ejpam-4655	649	2	w	w	PROPN
ejpam-4655	649	3	is	be	AUX
ejpam-4655	649	4	µ1	µ1	PROPN
ejpam-4655	649	5	-	-	PUNCT
ejpam-4655	649	6	b	b	NOUN
ejpam-4655	649	7	-	-	PUNCT
ejpam-4655	649	8	open	open	ADJ
ejpam-4655	649	9	but	but	CCONJ
ejpam-4655	649	10	not	not	PART
ejpam-4655	649	11	in	in	ADP
ejpam-4655	649	12	µ2	µ2	PROPN
ejpam-4655	649	13	.	.	PUNCT
ejpam-4655	650	1	since	since	SCONJ
ejpam-4655	650	2	{	{	PUNCT
ejpam-4655	650	3	r	r	NOUN
ejpam-4655	650	4	}	}	PUNCT
ejpam-4655	650	5	is	be	AUX
ejpam-4655	650	6	(	(	PUNCT
ejpam-4655	650	7	1	1	NUM
ejpam-4655	650	8	,	,	PUNCT
ejpam-4655	650	9	2)-dense	2)-dense	NUM
ejpam-4655	650	10	but	but	CCONJ
ejpam-4655	650	11	not	not	PART
ejpam-4655	650	12	in	in	ADP
ejpam-4655	650	13	µ2	µ2	PROPN
ejpam-4655	650	14	we	we	PRON
ejpam-4655	650	15	have	have	VERB
ejpam-4655	650	16	x	x	NOUN
ejpam-4655	650	17	is	be	AUX
ejpam-4655	650	18	not	not	PART
ejpam-4655	650	19	a	a	DET
ejpam-4655	650	20	(	(	PUNCT
ejpam-4655	650	21	1	1	NUM
ejpam-4655	650	22	,	,	PUNCT
ejpam-4655	650	23	2)⋆⋆-bigeneralized	2)⋆⋆-bigeneralized	NUM
ejpam-4655	650	24	submaximal	submaximal	ADJ
ejpam-4655	650	25	space	space	NOUN
ejpam-4655	650	26	.	.	PUNCT
ejpam-4655	651	1	fix	fix	NOUN
ejpam-4655	651	2	s	s	PART
ejpam-4655	651	3	=	=	SYM
ejpam-4655	651	4	2	2	NUM
ejpam-4655	651	5	and	and	CCONJ
ejpam-4655	651	6	v	v	NOUN
ejpam-4655	651	7	=	=	SYM
ejpam-4655	651	8	1	1	X
ejpam-4655	651	9	.	.	X
ejpam-4655	652	1	take	take	VERB
ejpam-4655	652	2	µ1	µ1	NOUN
ejpam-4655	652	3	=	=	SYM
ejpam-4655	652	4	{	{	PUNCT
ejpam-4655	652	5	∅	∅	NOUN
ejpam-4655	652	6	,	,	PUNCT
ejpam-4655	652	7	{	{	PUNCT
ejpam-4655	652	8	p	p	X
ejpam-4655	652	9	,	,	PUNCT
ejpam-4655	652	10	q	q	NOUN
ejpam-4655	652	11	}	}	PUNCT
ejpam-4655	652	12	,	,	PUNCT
ejpam-4655	652	13	{	{	PUNCT
ejpam-4655	652	14	p	p	X
ejpam-4655	652	15	,	,	PUNCT
ejpam-4655	652	16	s	s	PART
ejpam-4655	652	17	}	}	PUNCT
ejpam-4655	652	18	,	,	PUNCT
ejpam-4655	652	19	{	{	PUNCT
ejpam-4655	652	20	r	r	NOUN
ejpam-4655	652	21	,	,	PUNCT
ejpam-4655	652	22	s	s	PART
ejpam-4655	652	23	}	}	PUNCT
ejpam-4655	652	24	,	,	PUNCT
ejpam-4655	652	25	{	{	PUNCT
ejpam-4655	652	26	p	p	X
ejpam-4655	652	27	,	,	PUNCT
ejpam-4655	652	28	q	q	X
ejpam-4655	652	29	,	,	PUNCT
ejpam-4655	652	30	s	s	PART
ejpam-4655	652	31	}	}	PUNCT
ejpam-4655	652	32	,	,	PUNCT
ejpam-4655	652	33	{	{	PUNCT
ejpam-4655	652	34	p	p	X
ejpam-4655	652	35	,	,	PUNCT
ejpam-4655	652	36	r	r	NOUN
ejpam-4655	652	37	,	,	PUNCT
ejpam-4655	652	38	s	s	PART
ejpam-4655	652	39	}	}	PUNCT
ejpam-4655	652	40	,	,	PUNCT
ejpam-4655	652	41	x	x	NOUN
ejpam-4655	652	42	}	}	PUNCT
ejpam-4655	652	43	and	and	CCONJ
ejpam-4655	652	44	µ2	µ2	PROPN
ejpam-4655	652	45	=	=	PUNCT
ejpam-4655	652	46	{	{	PUNCT
ejpam-4655	652	47	∅	∅	NOUN
ejpam-4655	652	48	,	,	PUNCT
ejpam-4655	652	49	{	{	PUNCT
ejpam-4655	652	50	p	p	X
ejpam-4655	652	51	,	,	PUNCT
ejpam-4655	652	52	s	s	PART
ejpam-4655	652	53	}	}	PUNCT
ejpam-4655	652	54	,	,	PUNCT
ejpam-4655	652	55	{	{	PUNCT
ejpam-4655	652	56	r	r	NOUN
ejpam-4655	652	57	,	,	PUNCT
ejpam-4655	652	58	s	s	PART
ejpam-4655	652	59	}	}	PUNCT
ejpam-4655	652	60	,	,	PUNCT
ejpam-4655	652	61	{	{	PUNCT
ejpam-4655	652	62	p	p	X
ejpam-4655	652	63	,	,	PUNCT
ejpam-4655	652	64	r	r	NOUN
ejpam-4655	652	65	,	,	PUNCT
ejpam-4655	652	66	s	s	PART
ejpam-4655	652	67	}	}	PUNCT
ejpam-4655	652	68	,	,	PUNCT
ejpam-4655	652	69	x	x	NOUN
ejpam-4655	652	70	}	}	PUNCT
ejpam-4655	652	71	.	.	PUNCT
ejpam-4655	653	1	thus	thus	ADV
ejpam-4655	653	2	,	,	PUNCT
ejpam-4655	653	3	µ2	µ2	PROPN
ejpam-4655	653	4	⊂	⊂	PROPN
ejpam-4655	653	5	µ1	µ1	PROPN
ejpam-4655	653	6	and	and	CCONJ
ejpam-4655	653	7	µ2	µ2	PROPN
ejpam-4655	653	8	is	be	AUX
ejpam-4655	653	9	a	a	DET
ejpam-4655	653	10	sgt	sgt	PROPN
ejpam-4655	653	11	.	.	PUNCT
ejpam-4655	654	1	here	here	ADV
ejpam-4655	654	2	{	{	PUNCT
ejpam-4655	654	3	s	s	X
ejpam-4655	654	4	}	}	PUNCT
ejpam-4655	654	5	is	be	AUX
ejpam-4655	654	6	µ2	µ2	ADJ
ejpam-4655	654	7	-	-	PUNCT
ejpam-4655	654	8	pre	pre	NOUN
ejpam-4655	654	9	-	-	ADJ
ejpam-4655	654	10	open	open	ADJ
ejpam-4655	654	11	,	,	PUNCT
ejpam-4655	654	12	µ2	µ2	PROPN
ejpam-4655	654	13	-	-	PUNCT
ejpam-4655	654	14	β	β	NOUN
ejpam-4655	654	15	-	-	ADJ
ejpam-4655	654	16	open	open	ADJ
ejpam-4655	654	17	and	and	CCONJ
ejpam-4655	654	18	µ2	µ2	PROPN
ejpam-4655	654	19	-	-	PUNCT
ejpam-4655	654	20	b	b	NOUN
ejpam-4655	654	21	-	-	PUNCT
ejpam-4655	654	22	open	open	ADJ
ejpam-4655	654	23	but	but	CCONJ
ejpam-4655	654	24	not	not	PART
ejpam-4655	654	25	µ1	µ1	NOUN
ejpam-4655	654	26	-	-	PUNCT
ejpam-4655	654	27	open	open	ADJ
ejpam-4655	654	28	.	.	PUNCT
ejpam-4655	655	1	clearly	clearly	ADV
ejpam-4655	655	2	,	,	PUNCT
ejpam-4655	655	3	x	x	PRON
ejpam-4655	655	4	is	be	AUX
ejpam-4655	655	5	not	not	PART
ejpam-4655	655	6	a	a	DET
ejpam-4655	655	7	(	(	PUNCT
ejpam-4655	655	8	2	2	NUM
ejpam-4655	655	9	,	,	PUNCT
ejpam-4655	655	10	1)⋆⋆-bigeneralized	1)⋆⋆-bigeneralized	NUM
ejpam-4655	655	11	submaximal	submaximal	ADJ
ejpam-4655	655	12	space	space	NOUN
ejpam-4655	655	13	.	.	PUNCT
ejpam-4655	656	1	because	because	SCONJ
ejpam-4655	656	2	,	,	PUNCT
ejpam-4655	656	3	choose	choose	VERB
ejpam-4655	656	4	k	k	X
ejpam-4655	656	5	=	=	PRON
ejpam-4655	656	6	{	{	PUNCT
ejpam-4655	656	7	p	p	X
ejpam-4655	656	8	,	,	PUNCT
ejpam-4655	656	9	r	r	NOUN
ejpam-4655	656	10	}	}	PUNCT
ejpam-4655	656	11	.	.	PUNCT
ejpam-4655	657	1	then	then	ADV
ejpam-4655	657	2	k	k	PROPN
ejpam-4655	657	3	is	be	AUX
ejpam-4655	657	4	(	(	PUNCT
ejpam-4655	657	5	2	2	NUM
ejpam-4655	657	6	,	,	PUNCT
ejpam-4655	657	7	1)-dense	1)-dense	NUM
ejpam-4655	657	8	but	but	CCONJ
ejpam-4655	657	9	not	not	PART
ejpam-4655	657	10	µ1	µ1	NOUN
ejpam-4655	657	11	-	-	PUNCT
ejpam-4655	657	12	open	open	ADJ
ejpam-4655	657	13	.	.	PUNCT
ejpam-4655	658	1	theorem	theorem	NOUN
ejpam-4655	658	2	40	40	NUM
ejpam-4655	658	3	.	.	PUNCT
ejpam-4655	659	1	let	let	AUX
ejpam-4655	659	2	(	(	PUNCT
ejpam-4655	659	3	x,µ1	x,µ1	NOUN
ejpam-4655	659	4	,	,	PUNCT
ejpam-4655	659	5	µ2	µ2	PROPN
ejpam-4655	659	6	)	)	PUNCT
ejpam-4655	659	7	be	be	AUX
ejpam-4655	659	8	a	a	DET
ejpam-4655	659	9	bgts	bgts	NOUN
ejpam-4655	659	10	.	.	PUNCT
ejpam-4655	660	1	then	then	ADV
ejpam-4655	660	2	the	the	DET
ejpam-4655	660	3	following	following	NOUN
ejpam-4655	660	4	are	be	AUX
ejpam-4655	660	5	equivalent	equivalent	ADJ
ejpam-4655	660	6	.	.	PUNCT
ejpam-4655	661	1	(	(	PUNCT
ejpam-4655	661	2	a	a	X
ejpam-4655	661	3	)	)	PUNCT
ejpam-4655	661	4	(	(	PUNCT
ejpam-4655	661	5	s	s	PROPN
ejpam-4655	661	6	,	,	PUNCT
ejpam-4655	661	7	v)⋆⋆-bigeneralized	v)⋆⋆-bigeneralize	VERB
ejpam-4655	661	8	submaximal	submaximal	ADJ
ejpam-4655	661	9	space	space	NOUN
ejpam-4655	661	10	.	.	PUNCT
ejpam-4655	662	1	(	(	PUNCT
ejpam-4655	662	2	b	b	X
ejpam-4655	662	3	)	)	PUNCT
ejpam-4655	662	4	every	every	DET
ejpam-4655	662	5	q	q	X
ejpam-4655	662	6	⊂	⊂	X
ejpam-4655	662	7	x	x	PUNCT
ejpam-4655	662	8	with	with	ADP
ejpam-4655	662	9	is(iv(q	is(iv(q	NOUN
ejpam-4655	662	10	)	)	PUNCT
ejpam-4655	662	11	)	)	PUNCT
ejpam-4655	663	1	=	=	NOUN
ejpam-4655	663	2	∅	∅	NOUN
ejpam-4655	663	3	,	,	PUNCT
ejpam-4655	663	4	is	be	AUX
ejpam-4655	663	5	a	a	DET
ejpam-4655	663	6	µv	µv	NOUN
ejpam-4655	663	7	-	-	PUNCT
ejpam-4655	663	8	closed	closed	ADJ
ejpam-4655	663	9	set	set	VERB
ejpam-4655	663	10	where	where	SCONJ
ejpam-4655	663	11	s	s	X
ejpam-4655	663	12	,	,	PUNCT
ejpam-4655	663	13	v	v	NOUN
ejpam-4655	663	14	=	=	SYM
ejpam-4655	663	15	1	1	NUM
ejpam-4655	663	16	,	,	PUNCT
ejpam-4655	663	17	2	2	NUM
ejpam-4655	663	18	;	;	PUNCT
ejpam-4655	663	19	s	s	VERB
ejpam-4655	663	20	̸=	̸=	PROPN
ejpam-4655	663	21	v.	v.	ADP
ejpam-4655	663	22	proof	proof	NOUN
ejpam-4655	663	23	.	.	PUNCT
ejpam-4655	664	1	this	this	DET
ejpam-4655	664	2	proof	proof	NOUN
ejpam-4655	664	3	is	be	AUX
ejpam-4655	664	4	directly	directly	ADV
ejpam-4655	664	5	follows	follow	VERB
ejpam-4655	664	6	from	from	ADP
ejpam-4655	664	7	definition	definition	NOUN
ejpam-4655	664	8	36	36	NUM
ejpam-4655	664	9	so	so	ADV
ejpam-4655	664	10	the	the	DET
ejpam-4655	664	11	easy	easy	ADJ
ejpam-4655	664	12	proof	proof	NOUN
ejpam-4655	664	13	is	be	AUX
ejpam-4655	664	14	neglected	neglect	VERB
ejpam-4655	664	15	.	.	PUNCT
ejpam-4655	665	1	corollary	corollary	ADJ
ejpam-4655	665	2	41	41	NUM
ejpam-4655	665	3	.	.	PUNCT
ejpam-4655	666	1	let	let	AUX
ejpam-4655	666	2	(	(	PUNCT
ejpam-4655	666	3	x,µ1	x,µ1	NOUN
ejpam-4655	666	4	,	,	PUNCT
ejpam-4655	666	5	µ2	µ2	PROPN
ejpam-4655	666	6	)	)	PUNCT
ejpam-4655	666	7	be	be	VERB
ejpam-4655	666	8	a	a	DET
ejpam-4655	666	9	(	(	PUNCT
ejpam-4655	666	10	s	s	PROPN
ejpam-4655	666	11	,	,	PUNCT
ejpam-4655	666	12	v)⋆⋆-bigeneralized	v)⋆⋆-bigeneralize	VERB
ejpam-4655	666	13	submaximal	submaximal	ADJ
ejpam-4655	666	14	space	space	NOUN
ejpam-4655	666	15	.	.	PUNCT
ejpam-4655	667	1	then	then	ADV
ejpam-4655	667	2	cv(q)−	cv(q)−	PROPN
ejpam-4655	667	3	q	q	PUNCT
ejpam-4655	667	4	is	be	AUX
ejpam-4655	667	5	a	a	DET
ejpam-4655	667	6	µv	µv	NOUN
ejpam-4655	667	7	-	-	PUNCT
ejpam-4655	667	8	closed	closed	ADJ
ejpam-4655	667	9	set	set	NOUN
ejpam-4655	667	10	where	where	SCONJ
ejpam-4655	667	11	q	q	PUNCT
ejpam-4655	667	12	⊂	⊂	PROPN
ejpam-4655	667	13	x	x	X
ejpam-4655	667	14	and	and	CCONJ
ejpam-4655	667	15	s	s	PROPN
ejpam-4655	667	16	,	,	PUNCT
ejpam-4655	667	17	v	v	NOUN
ejpam-4655	667	18	=	=	SYM
ejpam-4655	667	19	1	1	NUM
ejpam-4655	667	20	,	,	PUNCT
ejpam-4655	667	21	2	2	NUM
ejpam-4655	667	22	;	;	PUNCT
ejpam-4655	667	23	s	s	AUX
ejpam-4655	667	24	̸=	̸=	PROPN
ejpam-4655	667	25	v.	v.	ADP
ejpam-4655	667	26	theorem	theorem	ADJ
ejpam-4655	667	27	42	42	NUM
ejpam-4655	667	28	.	.	PUNCT
ejpam-4655	668	1	let	let	AUX
ejpam-4655	668	2	(	(	PUNCT
ejpam-4655	668	3	x,µ1	x,µ1	NOUN
ejpam-4655	668	4	,	,	PUNCT
ejpam-4655	668	5	µ2	µ2	PROPN
ejpam-4655	668	6	)	)	PUNCT
ejpam-4655	668	7	be	be	VERB
ejpam-4655	668	8	a	a	DET
ejpam-4655	668	9	(	(	PUNCT
ejpam-4655	668	10	s	s	PROPN
ejpam-4655	668	11	,	,	PUNCT
ejpam-4655	668	12	v)⋆⋆-bigeneralized	v)⋆⋆-bigeneralize	VERB
ejpam-4655	668	13	submaximal	submaximal	ADJ
ejpam-4655	668	14	space	space	NOUN
ejpam-4655	668	15	.	.	PUNCT
ejpam-4655	669	1	if	if	SCONJ
ejpam-4655	669	2	q	q	X
ejpam-4655	669	3	∈	∈	PROPN
ejpam-4655	669	4	(	(	PUNCT
ejpam-4655	669	5	v	v	NOUN
ejpam-4655	669	6	,	,	PUNCT
ejpam-4655	669	7	s)−	s)−	PROPN
ejpam-4655	669	8	n	n	PART
ejpam-4655	669	9	(	(	PUNCT
ejpam-4655	669	10	x	x	X
ejpam-4655	669	11	)	)	PUNCT
ejpam-4655	669	12	,	,	PUNCT
ejpam-4655	669	13	then	then	ADV
ejpam-4655	669	14	csq	csq	PROPN
ejpam-4655	669	15	is	be	AUX
ejpam-4655	669	16	µv	µv	NOUN
ejpam-4655	669	17	-	-	PUNCT
ejpam-4655	669	18	closed	closed	ADJ
ejpam-4655	669	19	,	,	PUNCT
ejpam-4655	669	20	s	s	X
ejpam-4655	669	21	,	,	PUNCT
ejpam-4655	669	22	v	v	NOUN
ejpam-4655	669	23	=	=	SYM
ejpam-4655	669	24	1	1	NUM
ejpam-4655	669	25	,	,	PUNCT
ejpam-4655	669	26	2	2	NUM
ejpam-4655	669	27	;	;	PUNCT
ejpam-4655	669	28	s	s	VERB
ejpam-4655	669	29	̸=	̸=	PROPN
ejpam-4655	669	30	v.	v.	ADP
ejpam-4655	669	31	proof	proof	NOUN
ejpam-4655	669	32	.	.	PUNCT
ejpam-4655	670	1	we	we	PRON
ejpam-4655	670	2	give	give	VERB
ejpam-4655	670	3	the	the	DET
ejpam-4655	670	4	detailed	detailed	ADJ
ejpam-4655	670	5	proof	proof	NOUN
ejpam-4655	670	6	only	only	ADV
ejpam-4655	670	7	for	for	ADP
ejpam-4655	670	8	s	s	NOUN
ejpam-4655	670	9	=	=	SYM
ejpam-4655	670	10	1	1	NUM
ejpam-4655	670	11	,	,	PUNCT
ejpam-4655	670	12	v	v	NOUN
ejpam-4655	670	13	=	=	SYM
ejpam-4655	670	14	2	2	X
ejpam-4655	670	15	.	.	X
ejpam-4655	670	16	assume	assume	VERB
ejpam-4655	670	17	that	that	SCONJ
ejpam-4655	670	18	,	,	PUNCT
ejpam-4655	670	19	x	x	PRON
ejpam-4655	670	20	is	be	AUX
ejpam-4655	670	21	a	a	DET
ejpam-4655	670	22	(	(	PUNCT
ejpam-4655	670	23	1	1	NUM
ejpam-4655	670	24	,	,	PUNCT
ejpam-4655	670	25	2)⋆⋆bigeneralized	2)⋆⋆bigeneralized	ADJ
ejpam-4655	670	26	submaximal	submaximal	ADJ
ejpam-4655	670	27	space	space	NOUN
ejpam-4655	670	28	.	.	PUNCT
ejpam-4655	671	1	let	let	VERB
ejpam-4655	671	2	q	q	PROPN
ejpam-4655	671	3	∈	∈	PROPN
ejpam-4655	671	4	(	(	PUNCT
ejpam-4655	671	5	2	2	NUM
ejpam-4655	671	6	,	,	PUNCT
ejpam-4655	671	7	1	1	NUM
ejpam-4655	671	8	)	)	PUNCT
ejpam-4655	671	9	−	−	PROPN
ejpam-4655	671	10	n	n	CCONJ
ejpam-4655	671	11	(	(	PUNCT
ejpam-4655	671	12	x	x	NOUN
ejpam-4655	671	13	)	)	PUNCT
ejpam-4655	671	14	.	.	PUNCT
ejpam-4655	672	1	then	then	ADV
ejpam-4655	672	2	i2(c1(q	i2(c1(q	X
ejpam-4655	672	3	)	)	PUNCT
ejpam-4655	672	4	)	)	PUNCT
ejpam-4655	673	1	=	=	NOUN
ejpam-4655	673	2	∅	∅	NOUN
ejpam-4655	673	3	and	and	CCONJ
ejpam-4655	673	4	so	so	ADV
ejpam-4655	673	5	i1(i2(c1(q	i1(i2(c1(q	ADJ
ejpam-4655	673	6	)	)	PUNCT
ejpam-4655	673	7	)	)	PUNCT
ejpam-4655	673	8	)	)	PUNCT
ejpam-4655	674	1	=	=	PUNCT
ejpam-4655	674	2	∅.	∅.	X
ejpam-4655	674	3	by	by	ADP
ejpam-4655	674	4	hypothesis	hypothesis	NOUN
ejpam-4655	674	5	,	,	PUNCT
ejpam-4655	674	6	c1(q	c1(q	ADV
ejpam-4655	674	7	)	)	PUNCT
ejpam-4655	674	8	is	be	AUX
ejpam-4655	674	9	a	a	DET
ejpam-4655	674	10	µ2	µ2	NOUN
ejpam-4655	674	11	-	-	PUNCT
ejpam-4655	674	12	closed	close	VERB
ejpam-4655	674	13	set	set	NOUN
ejpam-4655	674	14	in	in	ADP
ejpam-4655	674	15	x.	x.	PROPN
ejpam-4655	674	16	(	(	PUNCT
ejpam-4655	674	17	a	a	X
ejpam-4655	674	18	)	)	PUNCT
ejpam-4655	674	19	x	x	X
ejpam-4655	674	20	is	be	AUX
ejpam-4655	674	21	a	a	DET
ejpam-4655	674	22	(	(	PUNCT
ejpam-4655	674	23	v	v	NOUN
ejpam-4655	674	24	,	,	PUNCT
ejpam-4655	674	25	s)⋆⋆	s)⋆⋆	PROPN
ejpam-4655	674	26	−	−	PROPN
ejpam-4655	674	27	bigeneralized	bigeneralize	VERB
ejpam-4655	674	28	submaximal	submaximal	ADJ
ejpam-4655	674	29	space	space	NOUN
ejpam-4655	674	30	(	(	PUNCT
ejpam-4655	674	31	b	b	NOUN
ejpam-4655	674	32	)	)	PUNCT
ejpam-4655	674	33	(	(	PUNCT
ejpam-4655	674	34	c	c	X
ejpam-4655	674	35	)	)	PUNCT
ejpam-4655	674	36	references	reference	NOUN
ejpam-4655	674	37	402	402	NUM
ejpam-4655	674	38	where	where	SCONJ
ejpam-4655	674	39	,	,	PUNCT
ejpam-4655	674	40	(	(	PUNCT
ejpam-4655	674	41	a	a	X
ejpam-4655	674	42	)	)	PUNCT
ejpam-4655	674	43	every	every	DET
ejpam-4655	674	44	µs	µs	NOUN
ejpam-4655	674	45	-	-	PUNCT
ejpam-4655	674	46	pre	pre	NOUN
ejpam-4655	674	47	-	-	ADJ
ejpam-4655	674	48	open	open	ADJ
ejpam-4655	674	49	is	be	AUX
ejpam-4655	674	50	µs	µs	NOUN
ejpam-4655	674	51	-	-	ADJ
ejpam-4655	674	52	open	open	ADJ
ejpam-4655	674	53	.	.	PUNCT
ejpam-4655	675	1	(	(	PUNCT
ejpam-4655	675	2	b	b	X
ejpam-4655	675	3	)	)	PUNCT
ejpam-4655	675	4	every	every	DET
ejpam-4655	675	5	µs	µs	NOUN
ejpam-4655	675	6	-	-	PUNCT
ejpam-4655	675	7	β	β	NOUN
ejpam-4655	675	8	-	-	ADJ
ejpam-4655	675	9	open	open	ADJ
ejpam-4655	675	10	is	be	AUX
ejpam-4655	675	11	µs	µs	NOUN
ejpam-4655	675	12	-	-	ADJ
ejpam-4655	675	13	open	open	ADJ
ejpam-4655	675	14	.	.	PUNCT
ejpam-4655	676	1	(	(	PUNCT
ejpam-4655	676	2	c	c	X
ejpam-4655	676	3	)	)	PUNCT
ejpam-4655	676	4	every	every	DET
ejpam-4655	676	5	µs	µs	ADP
ejpam-4655	676	6	-	-	PUNCT
ejpam-4655	676	7	b	b	NOUN
ejpam-4655	676	8	-	-	PUNCT
ejpam-4655	676	9	open	open	ADJ
ejpam-4655	676	10	is	be	AUX
ejpam-4655	676	11	µs	µs	NOUN
ejpam-4655	676	12	-	-	ADJ
ejpam-4655	676	13	open	open	ADJ
ejpam-4655	676	14	.	.	PUNCT
ejpam-4655	677	1	the	the	DET
ejpam-4655	677	2	following	follow	VERB
ejpam-4655	677	3	theorem	theorem	VERB
ejpam-4655	677	4	43	43	NUM
ejpam-4655	677	5	describes	describe	VERB
ejpam-4655	677	6	the	the	DET
ejpam-4655	677	7	above	above	ADJ
ejpam-4655	677	8	diagram	diagram	NOUN
ejpam-4655	677	9	.	.	PUNCT
ejpam-4655	678	1	theorem	theorem	PROPN
ejpam-4655	678	2	43	43	NUM
ejpam-4655	678	3	.	.	PUNCT
ejpam-4655	679	1	let	let	AUX
ejpam-4655	679	2	(	(	PUNCT
ejpam-4655	679	3	x,µ1	x,µ1	NOUN
ejpam-4655	679	4	,	,	PUNCT
ejpam-4655	679	5	µ2	µ2	PROPN
ejpam-4655	679	6	)	)	PUNCT
ejpam-4655	679	7	be	be	VERB
ejpam-4655	679	8	a	a	DET
ejpam-4655	679	9	(	(	PUNCT
ejpam-4655	679	10	s	s	PROPN
ejpam-4655	679	11	,	,	PUNCT
ejpam-4655	679	12	v)-bigeneralized	v)-bigeneralize	VERB
ejpam-4655	679	13	submaximal	submaximal	ADJ
ejpam-4655	679	14	space	space	NOUN
ejpam-4655	679	15	.	.	PUNCT
ejpam-4655	680	1	then	then	ADV
ejpam-4655	680	2	x	x	X
ejpam-4655	680	3	is	be	AUX
ejpam-4655	680	4	a	a	DET
ejpam-4655	680	5	(	(	PUNCT
ejpam-4655	680	6	v	v	NOUN
ejpam-4655	680	7	,	,	PUNCT
ejpam-4655	680	8	s)⋆⋆-bigeneralized	s)⋆⋆-bigeneralize	VERB
ejpam-4655	680	9	submaximal	submaximal	ADJ
ejpam-4655	680	10	space	space	NOUN
ejpam-4655	680	11	if	if	SCONJ
ejpam-4655	680	12	any	any	DET
ejpam-4655	680	13	one	one	NUM
ejpam-4655	680	14	of	of	ADP
ejpam-4655	680	15	the	the	DET
ejpam-4655	680	16	following	following	NOUN
ejpam-4655	680	17	is	be	AUX
ejpam-4655	680	18	true	true	ADJ
ejpam-4655	680	19	.	.	PUNCT
ejpam-4655	681	1	(	(	PUNCT
ejpam-4655	681	2	a	a	X
ejpam-4655	681	3	)	)	PUNCT
ejpam-4655	681	4	every	every	DET
ejpam-4655	681	5	µs	µs	NOUN
ejpam-4655	681	6	-	-	PUNCT
ejpam-4655	681	7	pre	pre	ADJ
ejpam-4655	681	8	-	-	ADJ
ejpam-4655	681	9	open	open	ADJ
ejpam-4655	681	10	set	set	NOUN
ejpam-4655	681	11	is	be	AUX
ejpam-4655	681	12	µs	µs	NOUN
ejpam-4655	681	13	-	-	ADJ
ejpam-4655	681	14	open	open	ADJ
ejpam-4655	681	15	.	.	PUNCT
ejpam-4655	682	1	(	(	PUNCT
ejpam-4655	682	2	a	a	X
ejpam-4655	682	3	)	)	PUNCT
ejpam-4655	682	4	every	every	DET
ejpam-4655	682	5	µs	µs	NOUN
ejpam-4655	682	6	-	-	PUNCT
ejpam-4655	682	7	β	β	NOUN
ejpam-4655	682	8	-	-	ADJ
ejpam-4655	682	9	open	open	ADJ
ejpam-4655	682	10	set	set	NOUN
ejpam-4655	682	11	is	be	AUX
ejpam-4655	682	12	µs	µs	NOUN
ejpam-4655	682	13	-	-	ADJ
ejpam-4655	682	14	open	open	ADJ
ejpam-4655	682	15	.	.	PUNCT
ejpam-4655	683	1	(	(	PUNCT
ejpam-4655	683	2	a	a	X
ejpam-4655	683	3	)	)	PUNCT
ejpam-4655	683	4	every	every	DET
ejpam-4655	683	5	µs	µs	PROPN
ejpam-4655	683	6	-	-	PUNCT
ejpam-4655	683	7	b	b	NOUN
ejpam-4655	683	8	-	-	PUNCT
ejpam-4655	683	9	open	open	ADJ
ejpam-4655	683	10	set	set	NOUN
ejpam-4655	683	11	is	be	AUX
ejpam-4655	683	12	µs	µs	NOUN
ejpam-4655	683	13	-	-	ADJ
ejpam-4655	683	14	open	open	ADJ
ejpam-4655	683	15	where	where	SCONJ
ejpam-4655	683	16	s	s	X
ejpam-4655	683	17	,	,	PUNCT
ejpam-4655	683	18	v	v	NOUN
ejpam-4655	683	19	=	=	SYM
ejpam-4655	683	20	1	1	NUM
ejpam-4655	683	21	,	,	PUNCT
ejpam-4655	683	22	2	2	NUM
ejpam-4655	683	23	and	and	CCONJ
ejpam-4655	683	24	s	s	VERB
ejpam-4655	683	25	̸=	̸=	PROPN
ejpam-4655	683	26	v.	v.	ADP
ejpam-4655	683	27	proof	proof	NOUN
ejpam-4655	683	28	.	.	PUNCT
ejpam-4655	684	1	it	it	PRON
ejpam-4655	684	2	is	be	AUX
ejpam-4655	684	3	enough	enough	ADJ
ejpam-4655	684	4	to	to	PART
ejpam-4655	684	5	prove	prove	VERB
ejpam-4655	684	6	(	(	PUNCT
ejpam-4655	684	7	a	a	X
ejpam-4655	684	8	)	)	PUNCT
ejpam-4655	684	9	only	only	ADV
ejpam-4655	684	10	and	and	CCONJ
ejpam-4655	684	11	the	the	DET
ejpam-4655	684	12	case	case	NOUN
ejpam-4655	684	13	s	s	PART
ejpam-4655	684	14	=	=	SYM
ejpam-4655	684	15	1	1	NUM
ejpam-4655	684	16	,	,	PUNCT
ejpam-4655	684	17	v	v	NOUN
ejpam-4655	684	18	=	=	SYM
ejpam-4655	684	19	2	2	X
ejpam-4655	684	20	.	.	X
ejpam-4655	684	21	assume	assume	VERB
ejpam-4655	684	22	that	that	SCONJ
ejpam-4655	684	23	,	,	PUNCT
ejpam-4655	684	24	x	x	PRON
ejpam-4655	684	25	is	be	AUX
ejpam-4655	684	26	a	a	DET
ejpam-4655	684	27	(	(	PUNCT
ejpam-4655	684	28	1	1	NUM
ejpam-4655	684	29	,	,	PUNCT
ejpam-4655	684	30	2)-bigeneralized	2)-bigeneralized	NUM
ejpam-4655	684	31	submaximal	submaximal	ADJ
ejpam-4655	684	32	space	space	NOUN
ejpam-4655	684	33	.	.	PUNCT
ejpam-4655	685	1	let	let	VERB
ejpam-4655	685	2	j	j	PROPN
ejpam-4655	685	3	∈	∈	PROPN
ejpam-4655	685	4	(	(	PUNCT
ejpam-4655	685	5	2	2	NUM
ejpam-4655	685	6	,	,	PUNCT
ejpam-4655	685	7	1	1	NUM
ejpam-4655	685	8	)	)	PUNCT
ejpam-4655	685	9	−	−	PROPN
ejpam-4655	685	10	d(x	d(x	NOUN
ejpam-4655	685	11	)	)	PUNCT
ejpam-4655	685	12	.	.	PUNCT
ejpam-4655	686	1	then	then	ADV
ejpam-4655	686	2	c1(j	c1(j	VERB
ejpam-4655	686	3	)	)	PUNCT
ejpam-4655	686	4	is	be	AUX
ejpam-4655	686	5	µ2	µ2	ADJ
ejpam-4655	686	6	-	-	PUNCT
ejpam-4655	686	7	dense	dense	ADJ
ejpam-4655	686	8	and	and	CCONJ
ejpam-4655	686	9	so	so	ADV
ejpam-4655	686	10	c1(j	c1(j	ADJ
ejpam-4655	686	11	)	)	PUNCT
ejpam-4655	686	12	∈	∈	PROPN
ejpam-4655	686	13	µ1	µ1	PROPN
ejpam-4655	686	14	.	.	PUNCT
ejpam-4655	687	1	this	this	PRON
ejpam-4655	687	2	implies	imply	VERB
ejpam-4655	687	3	j	j	PROPN
ejpam-4655	687	4	is	be	AUX
ejpam-4655	687	5	µ1	µ1	NOUN
ejpam-4655	687	6	-	-	PUNCT
ejpam-4655	687	7	pre	pre	NOUN
ejpam-4655	687	8	-	-	ADJ
ejpam-4655	687	9	open	open	ADJ
ejpam-4655	687	10	which	which	PRON
ejpam-4655	687	11	implies	imply	VERB
ejpam-4655	687	12	that	that	SCONJ
ejpam-4655	687	13	j	j	PROPN
ejpam-4655	687	14	∈	∈	PROPN
ejpam-4655	687	15	µ1	µ1	PROPN
ejpam-4655	687	16	-	-	PUNCT
ejpam-4655	687	17	open	open	ADJ
ejpam-4655	687	18	,	,	PUNCT
ejpam-4655	687	19	by	by	ADP
ejpam-4655	687	20	hypothesis	hypothesis	NOUN
ejpam-4655	687	21	.	.	PUNCT
ejpam-4655	688	1	hence	hence	ADV
ejpam-4655	688	2	x	x	PRON
ejpam-4655	688	3	is	be	AUX
ejpam-4655	688	4	a	a	DET
ejpam-4655	688	5	(	(	PUNCT
ejpam-4655	688	6	2	2	NUM
ejpam-4655	688	7	,	,	PUNCT
ejpam-4655	688	8	1)⋆⋆-bigeneralized	1)⋆⋆-bigeneralized	NUM
ejpam-4655	688	9	submaximal	submaximal	ADJ
ejpam-4655	688	10	space	space	NOUN
ejpam-4655	688	11	.	.	PUNCT
ejpam-4655	689	1	references	reference	NOUN
ejpam-4655	689	2	[	[	X
ejpam-4655	689	3	1	1	X
ejpam-4655	689	4	]	]	PUNCT
ejpam-4655	689	5	s.	s.	PROPN
ejpam-4655	689	6	acharjee	acharjee	PROPN
ejpam-4655	689	7	,	,	PUNCT
ejpam-4655	689	8	binod	binod	PROPN
ejpam-4655	689	9	chandra	chandra	PROPN
ejpam-4655	689	10	tripathy	tripathy	PROPN
ejpam-4655	689	11	,	,	PUNCT
ejpam-4655	689	12	and	and	CCONJ
ejpam-4655	689	13	kyriakos	kyriakos	PROPN
ejpam-4655	689	14	papadopoulos	papadopoulos	PROPN
ejpam-4655	689	15	.	.	PUNCT
ejpam-4655	690	1	two	two	NUM
ejpam-4655	690	2	forms	form	NOUN
ejpam-4655	690	3	of	of	ADP
ejpam-4655	690	4	pairwise	pairwise	NOUN
ejpam-4655	690	5	lindelöfness	lindelöfness	PUNCT
ejpam-4655	690	6	and	and	CCONJ
ejpam-4655	690	7	some	some	DET
ejpam-4655	690	8	results	result	NOUN
ejpam-4655	690	9	related	relate	VERB
ejpam-4655	690	10	to	to	ADP
ejpam-4655	690	11	hereditary	hereditary	ADJ
ejpam-4655	690	12	class	class	NOUN
ejpam-4655	690	13	in	in	ADP
ejpam-4655	690	14	a	a	DET
ejpam-4655	690	15	bigeneralized	bigeneralize	VERB
ejpam-4655	690	16	topological	topological	ADJ
ejpam-4655	690	17	space	space	NOUN
ejpam-4655	690	18	.	.	PUNCT
ejpam-4655	691	1	new	new	ADJ
ejpam-4655	691	2	mathematics	mathematic	NOUN
ejpam-4655	691	3	and	and	CCONJ
ejpam-4655	691	4	natural	natural	ADJ
ejpam-4655	691	5	computation	computation	NOUN
ejpam-4655	691	6	,	,	PUNCT
ejpam-4655	691	7	13(2):181–193	13(2):181–193	NUM
ejpam-4655	691	8	,	,	PUNCT
ejpam-4655	691	9	2017	2017	NUM
ejpam-4655	691	10	.	.	PUNCT
ejpam-4655	692	1	[	[	X
ejpam-4655	692	2	2	2	NUM
ejpam-4655	692	3	]	]	PUNCT
ejpam-4655	692	4	császár	császár	NOUN
ejpam-4655	692	5	akos	akos	NOUN
ejpam-4655	692	6	.	.	PUNCT
ejpam-4655	693	1	generalized	generalize	VERB
ejpam-4655	693	2	open	open	ADJ
ejpam-4655	693	3	sets	set	NOUN
ejpam-4655	693	4	.	.	PUNCT
ejpam-4655	694	1	acta	acta	PROPN
ejpam-4655	694	2	mathematica	mathematica	PROPN
ejpam-4655	694	3	hungarica	hungarica	PROPN
ejpam-4655	694	4	,	,	PUNCT
ejpam-4655	694	5	75	75	NUM
ejpam-4655	694	6	,	,	PUNCT
ejpam-4655	694	7	1997	1997	NUM
ejpam-4655	694	8	.	.	PUNCT
ejpam-4655	695	1	[	[	X
ejpam-4655	695	2	3	3	NUM
ejpam-4655	695	3	]	]	SYM
ejpam-4655	695	4	császár	császár	NOUN
ejpam-4655	695	5	akos	akos	NOUN
ejpam-4655	695	6	.	.	PUNCT
ejpam-4655	696	1	generalized	generalize	VERB
ejpam-4655	696	2	open	open	ADJ
ejpam-4655	696	3	sets	set	NOUN
ejpam-4655	696	4	in	in	ADP
ejpam-4655	696	5	generalized	generalized	ADJ
ejpam-4655	696	6	topologies	topology	NOUN
ejpam-4655	696	7	.	.	PUNCT
ejpam-4655	697	1	acta	acta	PROPN
ejpam-4655	697	2	mathematica	mathematica	PROPN
ejpam-4655	697	3	hungarica	hungarica	PROPN
ejpam-4655	697	4	,	,	PUNCT
ejpam-4655	697	5	106	106	NUM
ejpam-4655	697	6	,	,	PUNCT
ejpam-4655	697	7	2005	2005	NUM
ejpam-4655	697	8	.	.	PUNCT
ejpam-4655	698	1	[	[	X
ejpam-4655	698	2	4	4	X
ejpam-4655	698	3	]	]	X
ejpam-4655	698	4	d.	d.	PROPN
ejpam-4655	698	5	andrijević.	andrijević.	PROPN
ejpam-4655	698	6	on	on	ADP
ejpam-4655	698	7	b	b	X
ejpam-4655	698	8	-	-	PUNCT
ejpam-4655	698	9	open	open	ADJ
ejpam-4655	698	10	sets	set	NOUN
ejpam-4655	698	11	.	.	PUNCT
ejpam-4655	699	1	mat	mat	X
ejpam-4655	699	2	.	.	PROPN
ejpam-4655	699	3	vesnik	vesnik	PROPN
ejpam-4655	699	4	,	,	PUNCT
ejpam-4655	699	5	48:59	48:59	NUM
ejpam-4655	699	6	–	–	PUNCT
ejpam-4655	699	7	64	64	NUM
ejpam-4655	699	8	,	,	PUNCT
ejpam-4655	699	9	1996	1996	NUM
ejpam-4655	699	10	.	.	PUNCT
ejpam-4655	700	1	[	[	X
ejpam-4655	700	2	5	5	NUM
ejpam-4655	700	3	]	]	X
ejpam-4655	700	4	boonpok	boonpok	NOUN
ejpam-4655	700	5	chawalit	chawalit	VERB
ejpam-4655	700	6	.	.	PUNCT
ejpam-4655	701	1	weakly	weakly	ADJ
ejpam-4655	701	2	open	open	ADJ
ejpam-4655	701	3	functions	function	NOUN
ejpam-4655	701	4	on	on	ADP
ejpam-4655	701	5	bigeneralized	bigeneralize	VERB
ejpam-4655	701	6	topological	topological	ADJ
ejpam-4655	701	7	spaces	space	NOUN
ejpam-4655	701	8	.	.	PUNCT
ejpam-4655	702	1	int	int	NOUN
ejpam-4655	702	2	.	.	PUNCT
ejpam-4655	703	1	journal	journal	PROPN
ejpam-4655	703	2	of	of	ADP
ejpam-4655	703	3	math	math	NOUN
ejpam-4655	703	4	.	.	PUNCT
ejpam-4655	704	1	analysis	analysis	NOUN
ejpam-4655	704	2	,	,	PUNCT
ejpam-4655	704	3	4(18):891–897	4(18):891–897	NUM
ejpam-4655	704	4	,	,	PUNCT
ejpam-4655	704	5	2010	2010	NUM
ejpam-4655	704	6	.	.	PUNCT
ejpam-4655	705	1	[	[	X
ejpam-4655	705	2	6	6	NUM
ejpam-4655	705	3	]	]	PUNCT
ejpam-4655	705	4	á.	á.	PROPN
ejpam-4655	705	5	császár	császár	PROPN
ejpam-4655	705	6	.	.	PUNCT
ejpam-4655	706	1	generalized	generalize	VERB
ejpam-4655	706	2	topology	topology	NOUN
ejpam-4655	706	3	,	,	PUNCT
ejpam-4655	706	4	generalized	generalize	VERB
ejpam-4655	706	5	continuity	continuity	NOUN
ejpam-4655	706	6	.	.	PUNCT
ejpam-4655	707	1	acta	acta	PROPN
ejpam-4655	707	2	math	math	PROPN
ejpam-4655	707	3	.	.	PUNCT
ejpam-4655	708	1	hungar	hungar	PROPN
ejpam-4655	708	2	.	.	PUNCT
ejpam-4655	708	3	,	,	PUNCT
ejpam-4655	709	1	96:351–357	96:351–357	PROPN
ejpam-4655	709	2	,	,	PUNCT
ejpam-4655	709	3	2002	2002	NUM
ejpam-4655	709	4	.	.	PUNCT
ejpam-4655	710	1	[	[	X
ejpam-4655	710	2	7	7	X
ejpam-4655	710	3	]	]	PUNCT
ejpam-4655	710	4	á.	á.	PRON
ejpam-4655	710	5	császár	császár	NOUN
ejpam-4655	710	6	.	.	PUNCT
ejpam-4655	711	1	product	product	NOUN
ejpam-4655	711	2	of	of	ADP
ejpam-4655	711	3	generalized	generalized	ADJ
ejpam-4655	711	4	topologies	topology	NOUN
ejpam-4655	711	5	.	.	PUNCT
ejpam-4655	712	1	acta	acta	PROPN
ejpam-4655	712	2	math	math	PROPN
ejpam-4655	712	3	.	.	PUNCT
ejpam-4655	713	1	hungar	hungar	PROPN
ejpam-4655	713	2	.	.	PUNCT
ejpam-4655	714	1	,	,	PUNCT
ejpam-4655	714	2	123:127	123:127	NOUN
ejpam-4655	714	3	–	–	PUNCT
ejpam-4655	714	4	132	132	NUM
ejpam-4655	714	5	,	,	PUNCT
ejpam-4655	714	6	2009	2009	NUM
ejpam-4655	714	7	.	.	PUNCT
ejpam-4655	715	1	[	[	X
ejpam-4655	715	2	8	8	NUM
ejpam-4655	715	3	]	]	PUNCT
ejpam-4655	715	4	erdal	erdal	PROPN
ejpam-4655	715	5	ekici	ekici	PROPN
ejpam-4655	715	6	.	.	PUNCT
ejpam-4655	716	1	generalized	generalized	ADJ
ejpam-4655	716	2	hyperconnectedness	hyperconnectedness	NOUN
ejpam-4655	716	3	.	.	PUNCT
ejpam-4655	717	1	acta	acta	PROPN
ejpam-4655	717	2	mathematica	mathematica	PROPN
ejpam-4655	717	3	hungarica	hungarica	PROPN
ejpam-4655	717	4	,	,	PUNCT
ejpam-4655	717	5	133	133	NUM
ejpam-4655	717	6	,	,	PUNCT
ejpam-4655	717	7	2011	2011	NUM
ejpam-4655	717	8	.	.	PUNCT
ejpam-4655	718	1	[	[	X
ejpam-4655	718	2	9	9	NUM
ejpam-4655	718	3	]	]	PUNCT
ejpam-4655	718	4	erdal	erdal	PROPN
ejpam-4655	718	5	ekici	ekici	PROPN
ejpam-4655	718	6	.	.	PUNCT
ejpam-4655	719	1	generalized	generalize	VERB
ejpam-4655	719	2	submaximal	submaximal	ADJ
ejpam-4655	719	3	spaces	space	NOUN
ejpam-4655	719	4	.	.	PUNCT
ejpam-4655	720	1	acta	acta	PROPN
ejpam-4655	720	2	math	math	PROPN
ejpam-4655	720	3	.	.	PUNCT
ejpam-4655	721	1	hungar	hungar	PROPN
ejpam-4655	721	2	.	.	PUNCT
ejpam-4655	722	1	,	,	PUNCT
ejpam-4655	722	2	134:132	134:132	PROPN
ejpam-4655	722	3	–	–	PUNCT
ejpam-4655	722	4	138	138	NUM
ejpam-4655	722	5	,	,	PUNCT
ejpam-4655	722	6	2012	2012	NUM
ejpam-4655	722	7	.	.	PUNCT
ejpam-4655	723	1	[	[	X
ejpam-4655	723	2	10	10	NUM
ejpam-4655	723	3	]	]	X
ejpam-4655	723	4	korczak	korczak	PROPN
ejpam-4655	723	5	-	-	PUNCT
ejpam-4655	723	6	kubiak	kubiak	PROPN
ejpam-4655	723	7	ewa	ewa	PROPN
ejpam-4655	723	8	,	,	PUNCT
ejpam-4655	723	9	loranty	loranty	PROPN
ejpam-4655	723	10	anna	anna	NOUN
ejpam-4655	723	11	,	,	PUNCT
ejpam-4655	723	12	and	and	CCONJ
ejpam-4655	723	13	pawlak	pawlak	ADJ
ejpam-4655	723	14	ryszard	ryszard	PROPN
ejpam-4655	723	15	j.	j.	PROPN
ejpam-4655	723	16	baire	baire	PROPN
ejpam-4655	723	17	generalized	generalize	VERB
ejpam-4655	723	18	topological	topological	ADJ
ejpam-4655	723	19	spaces	space	NOUN
ejpam-4655	723	20	,	,	PUNCT
ejpam-4655	723	21	generalized	generalize	VERB
ejpam-4655	723	22	metric	metric	ADJ
ejpam-4655	723	23	spaces	space	NOUN
ejpam-4655	723	24	and	and	CCONJ
ejpam-4655	723	25	infinite	infinite	ADJ
ejpam-4655	723	26	games	game	NOUN
ejpam-4655	723	27	.	.	PUNCT
ejpam-4655	724	1	acta	acta	PROPN
ejpam-4655	724	2	mathematica	mathematica	PROPN
ejpam-4655	724	3	hungarica	hungarica	PROPN
ejpam-4655	724	4	,	,	PUNCT
ejpam-4655	724	5	140(3):203–231	140(3):203–231	NUM
ejpam-4655	724	6	,	,	PUNCT
ejpam-4655	724	7	2013	2013	NUM
ejpam-4655	724	8	.	.	PUNCT
ejpam-4655	725	1	references	reference	NOUN
ejpam-4655	725	2	403	403	NUM
ejpam-4655	726	1	[	[	X
ejpam-4655	726	2	11	11	NUM
ejpam-4655	726	3	]	]	X
ejpam-4655	726	4	j.c	j.c	PROPN
ejpam-4655	726	5	.	.	PROPN
ejpam-4655	726	6	kelly	kelly	PROPN
ejpam-4655	726	7	.	.	PUNCT
ejpam-4655	727	1	bitopological	bitopological	ADJ
ejpam-4655	727	2	spaces	space	NOUN
ejpam-4655	727	3	.	.	PUNCT
ejpam-4655	728	1	pro	pro	ADJ
ejpam-4655	728	2	.	.	PUNCT
ejpam-4655	728	3	london	london	PROPN
ejpam-4655	728	4	math	math	PROPN
ejpam-4655	728	5	.	.	PUNCT
ejpam-4655	729	1	soc	soc	PROPN
ejpam-4655	729	2	.	.	PUNCT
ejpam-4655	729	3	,	,	PUNCT
ejpam-4655	729	4	3(13):71	3(13):71	NUM
ejpam-4655	729	5	–	–	PUNCT
ejpam-4655	729	6	79	79	NUM
ejpam-4655	729	7	,	,	PUNCT
ejpam-4655	729	8	1969	1969	NUM
ejpam-4655	729	9	.	.	PUNCT
ejpam-4655	730	1	[	[	X
ejpam-4655	730	2	12	12	NUM
ejpam-4655	730	3	]	]	PUNCT
ejpam-4655	730	4	w.	w.	PROPN
ejpam-4655	730	5	k.	k.	PROPN
ejpam-4655	730	6	min	min	PROPN
ejpam-4655	730	7	.	.	PROPN
ejpam-4655	731	1	some	some	DET
ejpam-4655	731	2	results	result	NOUN
ejpam-4655	731	3	on	on	ADP
ejpam-4655	731	4	generalized	generalized	ADJ
ejpam-4655	731	5	topological	topological	ADJ
ejpam-4655	731	6	spaces	space	NOUN
ejpam-4655	731	7	and	and	CCONJ
ejpam-4655	731	8	generalized	generalized	ADJ
ejpam-4655	731	9	systems	system	NOUN
ejpam-4655	731	10	.	.	PUNCT
ejpam-4655	732	1	acta	acta	PROPN
ejpam-4655	732	2	math	math	PROPN
ejpam-4655	732	3	.	.	PUNCT
ejpam-4655	733	1	hungar	hungar	PROPN
ejpam-4655	733	2	.	.	PUNCT
ejpam-4655	734	1	,	,	PUNCT
ejpam-4655	734	2	108:171	108:171	NOUN
ejpam-4655	734	3	–	–	PUNCT
ejpam-4655	734	4	181	181	NUM
ejpam-4655	734	5	,	,	PUNCT
ejpam-4655	734	6	2005	2005	NUM
ejpam-4655	734	7	.	.	PUNCT
ejpam-4655	735	1	[	[	X
ejpam-4655	735	2	13	13	NUM
ejpam-4655	735	3	]	]	SYM
ejpam-4655	735	4	s.ale	s.ale	NOUN
ejpam-4655	735	5	,	,	PUNCT
ejpam-4655	735	6	s.a.akande	s.a.akande	NOUN
ejpam-4655	735	7	,	,	PUNCT
ejpam-4655	735	8	b.	b.	PROPN
ejpam-4655	735	9	fadipe	fadipe	PROPN
ejpam-4655	735	10	,	,	PUNCT
ejpam-4655	735	11	a.	a.	PROPN
ejpam-4655	735	12	tiamiyu	tiamiyu	PROPN
ejpam-4655	735	13	,	,	PUNCT
ejpam-4655	735	14	and	and	CCONJ
ejpam-4655	735	15	q.	q.	PROPN
ejpam-4655	735	16	rauf	rauf	PROPN
ejpam-4655	735	17	.	.	PUNCT
ejpam-4655	736	1	mathematical	mathematical	ADJ
ejpam-4655	736	2	model	model	NOUN
ejpam-4655	736	3	of	of	ADP
ejpam-4655	736	4	the	the	DET
ejpam-4655	736	5	public	public	ADJ
ejpam-4655	736	6	campaign	campaign	NOUN
ejpam-4655	736	7	on	on	ADP
ejpam-4655	736	8	typhoid	typhoid	NOUN
ejpam-4655	736	9	fever	fever	NOUN
ejpam-4655	736	10	transmission	transmission	NOUN
ejpam-4655	736	11	and	and	CCONJ
ejpam-4655	736	12	control	control	NOUN
ejpam-4655	736	13	.	.	PUNCT
ejpam-4655	737	1	international	international	ADJ
ejpam-4655	737	2	journal	journal	PROPN
ejpam-4655	737	3	on	on	ADP
ejpam-4655	737	4	recent	recent	ADJ
ejpam-4655	737	5	trends	trend	NOUN
ejpam-4655	737	6	in	in	ADP
ejpam-4655	737	7	life	life	NOUN
ejpam-4655	737	8	science	science	NOUN
ejpam-4655	737	9	and	and	CCONJ
ejpam-4655	737	10	mathematics	mathematic	NOUN
ejpam-4655	737	11	,	,	PUNCT
ejpam-4655	737	12	9(3):1–8	9(3):1–8	NUM
ejpam-4655	737	13	,	,	PUNCT
ejpam-4655	737	14	2022	2022	NUM
ejpam-4655	737	15	.	.	PUNCT
ejpam-4655	738	1	[	[	X
ejpam-4655	738	2	14	14	NUM
ejpam-4655	738	3	]	]	X
ejpam-4655	738	4	vadakasi	vadakasi	NOUN
ejpam-4655	738	5	subramanian	subramanian	PROPN
ejpam-4655	738	6	,	,	PUNCT
ejpam-4655	738	7	yasser	yasser	PROPN
ejpam-4655	738	8	farhat	farhat	PROPN
ejpam-4655	738	9	,	,	PUNCT
ejpam-4655	738	10	and	and	CCONJ
ejpam-4655	738	11	preecha	preecha	PROPN
ejpam-4655	738	12	yupapin	yupapin	NOUN
ejpam-4655	738	13	.	.	PUNCT
ejpam-4655	739	1	on	on	ADP
ejpam-4655	739	2	nowhere	nowhere	PRON
ejpam-4655	739	3	dense	dense	ADJ
ejpam-4655	739	4	sets	set	NOUN
ejpam-4655	739	5	.	.	PUNCT
ejpam-4655	740	1	european	european	ADJ
ejpam-4655	740	2	journal	journal	PROPN
ejpam-4655	740	3	of	of	ADP
ejpam-4655	740	4	pure	pure	ADJ
ejpam-4655	740	5	and	and	CCONJ
ejpam-4655	740	6	applied	applied	ADJ
ejpam-4655	740	7	mathematics	mathematic	NOUN
ejpam-4655	740	8	,	,	PUNCT
ejpam-4655	740	9	15(2):403–414	15(2):403–414	NUM
ejpam-4655	740	10	,	,	PUNCT
ejpam-4655	740	11	2022	2022	NUM
ejpam-4655	740	12	.	.	PUNCT
ejpam-4655	741	1	[	[	X
ejpam-4655	741	2	15	15	NUM
ejpam-4655	741	3	]	]	SYM
ejpam-4655	741	4	renukadevi	renukadevi	NOUN
ejpam-4655	741	5	v	v	NOUN
ejpam-4655	741	6	and	and	CCONJ
ejpam-4655	741	7	vadakasi	vadakasi	PROPN
ejpam-4655	741	8	s.	s.	PROPN
ejpam-4655	741	9	modifications	modification	NOUN
ejpam-4655	741	10	of	of	ADP
ejpam-4655	741	11	strongly	strongly	ADV
ejpam-4655	741	12	nodec	nodec	ADJ
ejpam-4655	741	13	spaces	space	NOUN
ejpam-4655	741	14	.	.	PUNCT
ejpam-4655	742	1	communications	communication	NOUN
ejpam-4655	742	2	in	in	ADP
ejpam-4655	742	3	advanced	advanced	ADJ
ejpam-4655	742	4	mathematical	mathematical	ADJ
ejpam-4655	742	5	sciences	science	NOUN
ejpam-4655	742	6	,	,	PUNCT
ejpam-4655	742	7	2:99–112	2:99–112	NUM
ejpam-4655	742	8	,	,	PUNCT
ejpam-4655	742	9	2018	2018	NUM
ejpam-4655	742	10	.	.	PUNCT
ejpam-4655	743	1	[	[	X
ejpam-4655	743	2	16	16	NUM
ejpam-4655	743	3	]	]	PUNCT
ejpam-4655	743	4	s.	s.	PROPN
ejpam-4655	743	5	vadakasi	vadakasi	PROPN
ejpam-4655	743	6	.	.	PUNCT
ejpam-4655	744	1	density	density	NOUN
ejpam-4655	744	2	on	on	ADP
ejpam-4655	744	3	bigeneralized	bigeneralize	VERB
ejpam-4655	744	4	topological	topological	ADJ
ejpam-4655	744	5	space	space	NOUN
ejpam-4655	744	6	.	.	PUNCT
ejpam-4655	744	7	communicated	communicate	VERB
ejpam-4655	744	8	.	.	PUNCT
ejpam-4655	745	1	[	[	X
ejpam-4655	745	2	17	17	NUM
ejpam-4655	745	3	]	]	PUNCT
ejpam-4655	745	4	v.yadav	v.yadav	NOUN
ejpam-4655	745	5	,	,	PUNCT
ejpam-4655	745	6	b.k.chaturvedi	b.k.chaturvedi	ADJ
ejpam-4655	745	7	,	,	PUNCT
ejpam-4655	745	8	and	and	CCONJ
ejpam-4655	745	9	a.k.malik	a.k.malik	PROPN
ejpam-4655	745	10	.	.	PUNCT
ejpam-4655	745	11	advantages	advantage	NOUN
ejpam-4655	745	12	of	of	ADP
ejpam-4655	745	13	fuzzy	fuzzy	ADJ
ejpam-4655	745	14	techniques	technique	NOUN
ejpam-4655	745	15	and	and	CCONJ
ejpam-4655	745	16	applications	application	NOUN
ejpam-4655	745	17	in	in	ADP
ejpam-4655	745	18	inventory	inventory	NOUN
ejpam-4655	745	19	control	control	NOUN
ejpam-4655	745	20	.	.	PUNCT
ejpam-4655	746	1	international	international	ADJ
ejpam-4655	746	2	journal	journal	PROPN
ejpam-4655	746	3	on	on	ADP
ejpam-4655	746	4	recent	recent	ADJ
ejpam-4655	746	5	trends	trend	NOUN
ejpam-4655	746	6	in	in	ADP
ejpam-4655	746	7	life	life	NOUN
ejpam-4655	746	8	science	science	NOUN
ejpam-4655	746	9	and	and	CCONJ
ejpam-4655	746	10	mathematics	mathematic	NOUN
ejpam-4655	746	11	,	,	PUNCT
ejpam-4655	746	12	9(3):9–13	9(3):9–13	NUM
ejpam-4655	746	13	,	,	PUNCT
ejpam-4655	746	14	2022	2022	NUM
ejpam-4655	746	15	.	.	PUNCT
ejpam-4655	747	1	[	[	X
ejpam-4655	747	2	18	18	NUM
ejpam-4655	747	3	]	]	SYM
ejpam-4655	747	4	dungthaisong	dungthaisong	PROPN
ejpam-4655	747	5	wichai	wichai	NOUN
ejpam-4655	747	6	,	,	PUNCT
ejpam-4655	747	7	boonpok	boonpok	NOUN
ejpam-4655	747	8	chawalit	chawalit	VERB
ejpam-4655	747	9	,	,	PUNCT
ejpam-4655	747	10	and	and	CCONJ
ejpam-4655	747	11	viriyapong	viriyapong	PROPN
ejpam-4655	747	12	chokchai	chokchai	PROPN
ejpam-4655	747	13	.	.	PUNCT
ejpam-4655	748	1	generalized	generalize	VERB
ejpam-4655	748	2	closed	close	VERB
ejpam-4655	748	3	sets	set	NOUN
ejpam-4655	748	4	in	in	ADP
ejpam-4655	748	5	bigeneralized	bigeneralize	VERB
ejpam-4655	748	6	topological	topological	ADJ
ejpam-4655	748	7	spaces	space	NOUN
ejpam-4655	748	8	.	.	PUNCT
ejpam-4655	749	1	international	international	ADJ
ejpam-4655	749	2	journal	journal	PROPN
ejpam-4655	749	3	of	of	ADP
ejpam-4655	749	4	mathematical	mathematical	ADJ
ejpam-4655	749	5	analysis	analysis	NOUN
ejpam-4655	749	6	,	,	PUNCT
ejpam-4655	749	7	5(24):1175–1184	5(24):1175–1184	NUM
ejpam-4655	749	8	,	,	PUNCT
ejpam-4655	749	9	2011	2011	NUM
ejpam-4655	749	10	.	.	PUNCT
ejpam-4655	750	1	[	[	X
ejpam-4655	750	2	19	19	NUM
ejpam-4655	750	3	]	]	PUNCT
ejpam-4655	750	4	m.	m.	PROPN
ejpam-4655	750	5	r.	r.	PROPN
ejpam-4655	750	6	ahmadi	ahmadi	PROPN
ejpam-4655	750	7	zand	zand	PROPN
ejpam-4655	750	8	and	and	CCONJ
ejpam-4655	750	9	r.	r.	PROPN
ejpam-4655	750	10	khayyeri	khayyeri	PROPN
ejpam-4655	750	11	.	.	PUNCT
ejpam-4655	751	1	generalized	generalize	VERB
ejpam-4655	751	2	gδ	gδ	NOUN
ejpam-4655	751	3	-	-	PUNCT
ejpam-4655	751	4	submaximal	submaximal	ADJ
ejpam-4655	751	5	spaces	space	NOUN
ejpam-4655	751	6	.	.	PUNCT
ejpam-4655	752	1	acta	acta	PROPN
ejpam-4655	752	2	math	math	PROPN
ejpam-4655	752	3	.	.	PUNCT
ejpam-4655	753	1	hungar	hungar	PROPN
ejpam-4655	753	2	.	.	PUNCT
ejpam-4655	754	1	,	,	PUNCT
ejpam-4655	754	2	149(2):274	149(2):274	NUM
ejpam-4655	754	3	–	–	PUNCT
ejpam-4655	754	4	285	285	NUM
ejpam-4655	754	5	,	,	PUNCT
ejpam-4655	754	6	2016	2016	NUM
ejpam-4655	754	7	.	.	PUNCT
ejpam-4655	755	1	[	[	X
ejpam-4655	755	2	20	20	NUM
ejpam-4655	755	3	]	]	X
ejpam-4655	755	4	li	li	PROPN
ejpam-4655	755	5	zhaowen	zhaowen	PROPN
ejpam-4655	755	6	and	and	CCONJ
ejpam-4655	755	7	lin	lin	PROPN
ejpam-4655	755	8	funing	funing	NOUN
ejpam-4655	755	9	.	.	PUNCT
ejpam-4655	756	1	baireness	baireness	NOUN
ejpam-4655	756	2	on	on	ADP
ejpam-4655	756	3	generalized	generalized	ADJ
ejpam-4655	756	4	topological	topological	ADJ
ejpam-4655	756	5	spaces	space	NOUN
ejpam-4655	756	6	.	.	PUNCT
ejpam-4655	757	1	acta	acta	PROPN
ejpam-4655	757	2	mathematica	mathematica	PROPN
ejpam-4655	757	3	hungarica	hungarica	PROPN
ejpam-4655	757	4	,	,	PUNCT
ejpam-4655	757	5	139(4	139(4	NUM
ejpam-4655	757	6	)	)	PUNCT
ejpam-4655	757	7	,	,	PUNCT
ejpam-4655	757	8	2013	2013	NUM
ejpam-4655	757	9	.	.	PUNCT