id	sid	tid	token	lemma	pos
ejpam-4911	1	1	european	european	PROPN
ejpam-4911	1	2	journal	journal	PROPN
ejpam-4911	1	3	of	of	ADP
ejpam-4911	1	4	pure	pure	ADJ
ejpam-4911	1	5	and	and	CCONJ
ejpam-4911	1	6	applied	apply	VERB
ejpam-4911	1	7	mathematics	mathematic	NOUN
ejpam-4911	1	8	vol	vol	NOUN
ejpam-4911	1	9	.	.	PUNCT
ejpam-4911	2	1	16	16	NUM
ejpam-4911	2	2	,	,	PUNCT
ejpam-4911	2	3	no	no	INTJ
ejpam-4911	2	4	.	.	NOUN
ejpam-4911	2	5	4	4	NUM
ejpam-4911	2	6	,	,	PUNCT
ejpam-4911	2	7	2023	2023	NUM
ejpam-4911	2	8	,	,	PUNCT
ejpam-4911	2	9	2049	2049	NUM
ejpam-4911	2	10	-	-	SYM
ejpam-4911	2	11	2065	2065	NUM
ejpam-4911	2	12	issn	issn	PROPN
ejpam-4911	2	13	1307	1307	NUM
ejpam-4911	2	14	-	-	SYM
ejpam-4911	2	15	5543	5543	NUM
ejpam-4911	2	16	–	–	PUNCT
ejpam-4911	3	1	ejpam.com	ejpam.com	X
ejpam-4911	3	2	published	publish	VERB
ejpam-4911	3	3	by	by	ADP
ejpam-4911	3	4	new	new	PROPN
ejpam-4911	3	5	york	york	PROPN
ejpam-4911	3	6	business	business	PROPN
ejpam-4911	3	7	global	global	ADJ
ejpam-4911	3	8	generalized	generalize	VERB
ejpam-4911	3	9	dense	dense	ADJ
ejpam-4911	3	10	sets	set	NOUN
ejpam-4911	3	11	in	in	ADP
ejpam-4911	3	12	bigeneralized	bigeneralize	VERB
ejpam-4911	3	13	topological	topological	ADJ
ejpam-4911	3	14	spaces	space	NOUN
ejpam-4911	3	15	yasser	yasser	PROPN
ejpam-4911	3	16	farhat1	farhat1	PROPN
ejpam-4911	3	17	,	,	PUNCT
ejpam-4911	3	18	vadakasi	vadakasi	NOUN
ejpam-4911	3	19	subramanian2,∗	subramanian2,∗	VERB
ejpam-4911	3	20	1	1	NUM
ejpam-4911	3	21	academic	academic	ADJ
ejpam-4911	3	22	support	support	NOUN
ejpam-4911	3	23	department	department	NOUN
ejpam-4911	3	24	,	,	PUNCT
ejpam-4911	3	25	abu	abu	PROPN
ejpam-4911	3	26	dhabi	dhabi	PROPN
ejpam-4911	3	27	polytechnic	polytechnic	PROPN
ejpam-4911	3	28	,	,	PUNCT
ejpam-4911	3	29	p.	p.	PROPN
ejpam-4911	3	30	o.	o.	PROPN
ejpam-4911	3	31	box	box	PROPN
ejpam-4911	3	32	111499	111499	NUM
ejpam-4911	3	33	,	,	PUNCT
ejpam-4911	3	34	abu	abu	PROPN
ejpam-4911	3	35	dhabi	dhabi	PROPN
ejpam-4911	3	36	,	,	PUNCT
ejpam-4911	3	37	united	united	PROPN
ejpam-4911	3	38	arab	arab	PROPN
ejpam-4911	3	39	emirates	emirates	PROPN
ejpam-4911	3	40	2	2	NUM
ejpam-4911	3	41	department	department	NOUN
ejpam-4911	3	42	of	of	ADP
ejpam-4911	3	43	mathematics	mathematic	NOUN
ejpam-4911	3	44	,	,	PUNCT
ejpam-4911	3	45	a.k.d.dharma	a.k.d.dharma	PROPN
ejpam-4911	3	46	raja	raja	PROPN
ejpam-4911	3	47	women	woman	NOUN
ejpam-4911	3	48	’s	’s	PART
ejpam-4911	3	49	college	college	PROPN
ejpam-4911	3	50	,	,	PUNCT
ejpam-4911	3	51	rajapalayam	rajapalayam	PROPN
ejpam-4911	3	52	,	,	PUNCT
ejpam-4911	3	53	india	india	PROPN
ejpam-4911	3	54	abstract	abstract	NOUN
ejpam-4911	3	55	.	.	PUNCT
ejpam-4911	4	1	in	in	ADP
ejpam-4911	4	2	this	this	DET
ejpam-4911	4	3	article	article	NOUN
ejpam-4911	4	4	,	,	PUNCT
ejpam-4911	4	5	in	in	ADP
ejpam-4911	4	6	a	a	DET
ejpam-4911	4	7	bigeneralized	bigeneralize	VERB
ejpam-4911	4	8	topological	topological	ADJ
ejpam-4911	4	9	space	space	NOUN
ejpam-4911	4	10	,	,	PUNCT
ejpam-4911	4	11	we	we	PRON
ejpam-4911	4	12	introduce	introduce	VERB
ejpam-4911	4	13	an	an	DET
ejpam-4911	4	14	interesting	interesting	ADJ
ejpam-4911	4	15	tool	tool	NOUN
ejpam-4911	4	16	namely	namely	ADV
ejpam-4911	4	17	,	,	PUNCT
ejpam-4911	4	18	(	(	PUNCT
ejpam-4911	4	19	s	s	X
ejpam-4911	4	20	,	,	PUNCT
ejpam-4911	4	21	v)-dense	v)-dense	NOUN
ejpam-4911	4	22	set	set	NOUN
ejpam-4911	4	23	,	,	PUNCT
ejpam-4911	4	24	and	and	CCONJ
ejpam-4911	4	25	examine	examine	VERB
ejpam-4911	4	26	its	its	PRON
ejpam-4911	4	27	significance	significance	NOUN
ejpam-4911	4	28	of	of	ADP
ejpam-4911	4	29	this	this	DET
ejpam-4911	4	30	set	set	NOUN
ejpam-4911	4	31	.	.	PUNCT
ejpam-4911	5	1	also	also	ADV
ejpam-4911	5	2	,	,	PUNCT
ejpam-4911	5	3	we	we	PRON
ejpam-4911	5	4	give	give	VERB
ejpam-4911	5	5	the	the	DET
ejpam-4911	5	6	relationships	relationship	NOUN
ejpam-4911	5	7	among	among	ADP
ejpam-4911	5	8	nowhere	nowhere	ADV
ejpam-4911	5	9	-	-	PUNCT
ejpam-4911	5	10	dense	dense	ADJ
ejpam-4911	5	11	sets	set	NOUN
ejpam-4911	5	12	defined	define	VERB
ejpam-4911	5	13	in	in	ADP
ejpam-4911	5	14	both	both	CCONJ
ejpam-4911	5	15	generalized	generalize	VERB
ejpam-4911	5	16	and	and	CCONJ
ejpam-4911	5	17	bigeneralized	bigeneralize	VERB
ejpam-4911	5	18	topological	topological	ADJ
ejpam-4911	5	19	space	space	NOUN
ejpam-4911	5	20	and	and	CCONJ
ejpam-4911	5	21	give	give	VERB
ejpam-4911	5	22	some	some	PRON
ejpam-4911	5	23	of	of	ADP
ejpam-4911	5	24	their	their	PRON
ejpam-4911	5	25	properties	property	NOUN
ejpam-4911	5	26	by	by	ADP
ejpam-4911	5	27	using	use	VERB
ejpam-4911	5	28	functions	function	NOUN
ejpam-4911	5	29	.	.	PUNCT
ejpam-4911	6	1	finally	finally	ADV
ejpam-4911	6	2	,	,	PUNCT
ejpam-4911	6	3	we	we	PRON
ejpam-4911	6	4	give	give	VERB
ejpam-4911	6	5	some	some	DET
ejpam-4911	6	6	applications	application	NOUN
ejpam-4911	6	7	for	for	ADP
ejpam-4911	6	8	(	(	PUNCT
ejpam-4911	6	9	s	s	X
ejpam-4911	6	10	,	,	PUNCT
ejpam-4911	6	11	v)-dense	v)-dense	PUNCT
ejpam-4911	6	12	and	and	CCONJ
ejpam-4911	6	13	(	(	PUNCT
ejpam-4911	6	14	s	s	X
ejpam-4911	6	15	,	,	PUNCT
ejpam-4911	6	16	v)-nowhere	v)-nowhere	PUNCT
ejpam-4911	6	17	dense	dense	ADJ
ejpam-4911	6	18	sets	set	NOUN
ejpam-4911	6	19	in	in	ADP
ejpam-4911	6	20	a	a	DET
ejpam-4911	6	21	soft	soft	ADJ
ejpam-4911	6	22	set	set	NOUN
ejpam-4911	6	23	theory	theory	NOUN
ejpam-4911	6	24	.	.	PUNCT
ejpam-4911	7	1	2020	2020	NUM
ejpam-4911	7	2	mathematics	mathematic	NOUN
ejpam-4911	7	3	subject	subject	NOUN
ejpam-4911	7	4	classifications	classification	NOUN
ejpam-4911	7	5	:	:	PUNCT
ejpam-4911	7	6	54a05	54a05	NUM
ejpam-4911	7	7	,	,	PUNCT
ejpam-4911	7	8	54a10	54a10	NUM
ejpam-4911	7	9	key	key	ADJ
ejpam-4911	7	10	words	word	NOUN
ejpam-4911	7	11	and	and	CCONJ
ejpam-4911	7	12	phrases	phrase	NOUN
ejpam-4911	7	13	:	:	PUNCT
ejpam-4911	7	14	bigeneralized	bigeneralize	VERB
ejpam-4911	7	15	topological	topological	ADJ
ejpam-4911	7	16	spaces	space	NOUN
ejpam-4911	7	17	,	,	PUNCT
ejpam-4911	7	18	µ(s	µ(	NOUN
ejpam-4911	7	19	,	,	PUNCT
ejpam-4911	7	20	v)-open	v)-open	NOUN
ejpam-4911	7	21	,	,	PUNCT
ejpam-4911	7	22	µ(s	µ(	NOUN
ejpam-4911	7	23	,	,	PUNCT
ejpam-4911	7	24	v)-closed	v)-close	VERB
ejpam-4911	7	25	,	,	PUNCT
ejpam-4911	7	26	µ(s	µ(	NOUN
ejpam-4911	7	27	,	,	PUNCT
ejpam-4911	7	28	v)dense	v)dense	PRON
ejpam-4911	7	29	,	,	PUNCT
ejpam-4911	7	30	g(s	g(s	NOUN
ejpam-4911	7	31	,	,	PUNCT
ejpam-4911	7	32	v)-continuous	v)-continuous	ADJ
ejpam-4911	7	33	function	function	NOUN
ejpam-4911	7	34	.	.	PUNCT
ejpam-4911	8	1	1	1	X
ejpam-4911	8	2	.	.	X
ejpam-4911	8	3	introduction	introduction	NOUN
ejpam-4911	8	4	in	in	ADP
ejpam-4911	8	5	[	[	X
ejpam-4911	8	6	2	2	NUM
ejpam-4911	8	7	]	]	PUNCT
ejpam-4911	8	8	,	,	PUNCT
ejpam-4911	8	9	császár	császár	NOUN
ejpam-4911	8	10	defined	define	VERB
ejpam-4911	8	11	the	the	DET
ejpam-4911	8	12	notion	notion	NOUN
ejpam-4911	8	13	of	of	ADP
ejpam-4911	8	14	generalized	generalized	ADJ
ejpam-4911	8	15	topological	topological	ADJ
ejpam-4911	8	16	space	space	NOUN
ejpam-4911	8	17	.	.	PUNCT
ejpam-4911	9	1	some	some	DET
ejpam-4911	9	2	researchers	researcher	NOUN
ejpam-4911	9	3	have	have	AUX
ejpam-4911	9	4	found	find	VERB
ejpam-4911	9	5	various	various	ADJ
ejpam-4911	9	6	new	new	ADJ
ejpam-4911	9	7	concepts	concept	NOUN
ejpam-4911	9	8	in	in	ADP
ejpam-4911	9	9	this	this	DET
ejpam-4911	9	10	space	space	NOUN
ejpam-4911	9	11	and	and	CCONJ
ejpam-4911	9	12	examined	examine	VERB
ejpam-4911	9	13	their	their	PRON
ejpam-4911	9	14	nature	nature	NOUN
ejpam-4911	9	15	in	in	ADP
ejpam-4911	9	16	a	a	DET
ejpam-4911	9	17	generalized	generalized	ADJ
ejpam-4911	9	18	topological	topological	ADJ
ejpam-4911	9	19	space	space	NOUN
ejpam-4911	9	20	.	.	PUNCT
ejpam-4911	10	1	especially	especially	ADV
ejpam-4911	10	2	,	,	PUNCT
ejpam-4911	10	3	nowhere	nowhere	ADV
ejpam-4911	10	4	dense	dense	ADJ
ejpam-4911	10	5	and	and	CCONJ
ejpam-4911	10	6	dense	dense	ADJ
ejpam-4911	10	7	sets	set	NOUN
ejpam-4911	10	8	were	be	AUX
ejpam-4911	10	9	introduced	introduce	VERB
ejpam-4911	10	10	by	by	ADP
ejpam-4911	10	11	ekici	ekici	NOUN
ejpam-4911	10	12	in	in	ADP
ejpam-4911	10	13	a	a	DET
ejpam-4911	10	14	generalized	generalized	ADJ
ejpam-4911	10	15	topological	topological	ADJ
ejpam-4911	10	16	space	space	NOUN
ejpam-4911	10	17	[	[	X
ejpam-4911	10	18	6	6	NUM
ejpam-4911	10	19	]	]	PUNCT
ejpam-4911	10	20	.	.	PUNCT
ejpam-4911	11	1	he	he	PRON
ejpam-4911	11	2	has	have	AUX
ejpam-4911	11	3	given	give	VERB
ejpam-4911	11	4	few	few	ADJ
ejpam-4911	11	5	results	result	NOUN
ejpam-4911	11	6	for	for	ADP
ejpam-4911	11	7	nowhere	nowhere	ADV
ejpam-4911	11	8	-	-	PUNCT
ejpam-4911	11	9	dense	dense	ADJ
ejpam-4911	11	10	and	and	CCONJ
ejpam-4911	11	11	dense	dense	ADJ
ejpam-4911	11	12	sets	set	NOUN
ejpam-4911	11	13	in	in	ADP
ejpam-4911	11	14	a	a	DET
ejpam-4911	11	15	generalized	generalized	ADJ
ejpam-4911	11	16	topological	topological	ADJ
ejpam-4911	11	17	space	space	NOUN
ejpam-4911	11	18	.	.	PUNCT
ejpam-4911	12	1	some	some	DET
ejpam-4911	12	2	researchers	researcher	NOUN
ejpam-4911	12	3	proved	prove	VERB
ejpam-4911	12	4	various	various	ADJ
ejpam-4911	12	5	properties	property	NOUN
ejpam-4911	12	6	for	for	ADP
ejpam-4911	12	7	nowhere	nowhere	ADV
ejpam-4911	12	8	dense	dense	ADJ
ejpam-4911	12	9	sets	set	NOUN
ejpam-4911	12	10	e.g.	e.g.	ADV
ejpam-4911	12	11	[	[	X
ejpam-4911	12	12	9	9	NUM
ejpam-4911	12	13	,	,	PUNCT
ejpam-4911	12	14	12	12	NUM
ejpam-4911	12	15	,	,	PUNCT
ejpam-4911	12	16	14	14	NUM
ejpam-4911	12	17	]	]	PUNCT
ejpam-4911	12	18	.	.	PUNCT
ejpam-4911	13	1	inspired	inspire	VERB
ejpam-4911	13	2	by	by	ADP
ejpam-4911	13	3	this	this	PRON
ejpam-4911	13	4	,	,	PUNCT
ejpam-4911	13	5	korczak	korczak	NOUN
ejpam-4911	13	6	-	-	PUNCT
ejpam-4911	13	7	kubiak	kubiak	PROPN
ejpam-4911	13	8	,	,	PUNCT
ejpam-4911	13	9	et	et	PROPN
ejpam-4911	13	10	al	al	PROPN
ejpam-4911	13	11	.	.	PROPN
ejpam-4911	13	12	introduced	introduce	VERB
ejpam-4911	13	13	two	two	NUM
ejpam-4911	13	14	new	new	ADJ
ejpam-4911	13	15	generalized	generalized	ADJ
ejpam-4911	13	16	topologies	topology	NOUN
ejpam-4911	13	17	,	,	PUNCT
ejpam-4911	13	18	namely	namely	ADV
ejpam-4911	13	19	,	,	PUNCT
ejpam-4911	13	20	µ⋆	µ⋆	PUNCT
ejpam-4911	13	21	and	and	CCONJ
ejpam-4911	13	22	µ⋆⋆	µ⋆⋆	ADJ
ejpam-4911	13	23	;	;	PUNCT
ejpam-4911	13	24	then	then	ADV
ejpam-4911	13	25	examined	examine	VERB
ejpam-4911	13	26	the	the	DET
ejpam-4911	13	27	nature	nature	NOUN
ejpam-4911	13	28	of	of	ADP
ejpam-4911	13	29	nowhere	nowhere	DET
ejpam-4911	13	30	dense	dense	ADJ
ejpam-4911	13	31	set	set	NOUN
ejpam-4911	13	32	using	use	VERB
ejpam-4911	13	33	µ⋆	µ⋆	PUNCT
ejpam-4911	13	34	and	and	CCONJ
ejpam-4911	13	35	µ⋆⋆	µ⋆⋆	ADJ
ejpam-4911	14	1	[	[	X
ejpam-4911	14	2	8	8	NUM
ejpam-4911	14	3	]	]	PUNCT
ejpam-4911	14	4	.	.	PUNCT
ejpam-4911	15	1	in	in	ADP
ejpam-4911	15	2	[	[	X
ejpam-4911	15	3	7	7	NUM
ejpam-4911	15	4	]	]	PUNCT
ejpam-4911	15	5	,	,	PUNCT
ejpam-4911	15	6	j.c	j.c	PROPN
ejpam-4911	15	7	.	.	PROPN
ejpam-4911	15	8	kelly	kelly	PROPN
ejpam-4911	15	9	introduced	introduce	VERB
ejpam-4911	15	10	the	the	DET
ejpam-4911	15	11	notion	notion	NOUN
ejpam-4911	15	12	of	of	ADP
ejpam-4911	15	13	bitopological	bitopological	ADJ
ejpam-4911	15	14	space	space	NOUN
ejpam-4911	15	15	.	.	PUNCT
ejpam-4911	16	1	motivated	motivate	VERB
ejpam-4911	16	2	by	by	ADP
ejpam-4911	16	3	this	this	PRON
ejpam-4911	16	4	,	,	PUNCT
ejpam-4911	16	5	c.	c.	PROPN
ejpam-4911	16	6	boonpok	boonpok	PROPN
ejpam-4911	16	7	introduced	introduce	VERB
ejpam-4911	16	8	the	the	DET
ejpam-4911	16	9	concept	concept	NOUN
ejpam-4911	16	10	of	of	ADP
ejpam-4911	16	11	bigeneralized	bigeneralize	VERB
ejpam-4911	16	12	topological	topological	ADJ
ejpam-4911	16	13	space	space	NOUN
ejpam-4911	16	14	in	in	ADP
ejpam-4911	16	15	2010	2010	NUM
ejpam-4911	16	16	[	[	X
ejpam-4911	16	17	1	1	NUM
ejpam-4911	16	18	]	]	PUNCT
ejpam-4911	16	19	.	.	PUNCT
ejpam-4911	17	1	he	he	PRON
ejpam-4911	17	2	proved	prove	VERB
ejpam-4911	17	3	some	some	DET
ejpam-4911	17	4	results	result	NOUN
ejpam-4911	17	5	about	about	ADP
ejpam-4911	17	6	(	(	PUNCT
ejpam-4911	17	7	m	m	PROPN
ejpam-4911	17	8	,	,	PUNCT
ejpam-4911	17	9	n)-closed	n)-close	VERB
ejpam-4911	17	10	sets	set	NOUN
ejpam-4911	17	11	in	in	ADP
ejpam-4911	17	12	bigeneralized	bigeneralize	VERB
ejpam-4911	17	13	topological	topological	ADJ
ejpam-4911	17	14	space	space	NOUN
ejpam-4911	17	15	.	.	PUNCT
ejpam-4911	18	1	in	in	ADP
ejpam-4911	18	2	this	this	DET
ejpam-4911	18	3	paper	paper	NOUN
ejpam-4911	18	4	,	,	PUNCT
ejpam-4911	18	5	we	we	PRON
ejpam-4911	18	6	define	define	VERB
ejpam-4911	18	7	the	the	DET
ejpam-4911	18	8	generalization	generalization	NOUN
ejpam-4911	18	9	of	of	ADP
ejpam-4911	18	10	dense	dense	ADJ
ejpam-4911	18	11	sets	set	NOUN
ejpam-4911	18	12	,	,	PUNCT
ejpam-4911	18	13	namely	namely	ADV
ejpam-4911	18	14	,	,	PUNCT
ejpam-4911	18	15	(	(	PUNCT
ejpam-4911	18	16	s	s	X
ejpam-4911	18	17	,	,	PUNCT
ejpam-4911	18	18	v)-dense	v)-dense	NOUN
ejpam-4911	18	19	in	in	ADP
ejpam-4911	18	20	a	a	DET
ejpam-4911	18	21	bigeneralized	bigeneralize	VERB
ejpam-4911	18	22	topological	topological	ADJ
ejpam-4911	18	23	space	space	NOUN
ejpam-4911	18	24	.	.	PUNCT
ejpam-4911	19	1	in	in	ADP
ejpam-4911	19	2	a	a	DET
ejpam-4911	19	3	bigeneralized	bigeneralize	VERB
ejpam-4911	19	4	topological	topological	ADJ
ejpam-4911	19	5	space	space	NOUN
ejpam-4911	19	6	,	,	PUNCT
ejpam-4911	19	7	various	various	ADJ
ejpam-4911	19	8	properties	property	NOUN
ejpam-4911	19	9	for	for	ADP
ejpam-4911	19	10	(	(	PUNCT
ejpam-4911	19	11	s	s	X
ejpam-4911	19	12	,	,	PUNCT
ejpam-4911	19	13	v)-dense	v)-dense	PUNCT
ejpam-4911	19	14	and	and	CCONJ
ejpam-4911	19	15	(	(	PUNCT
ejpam-4911	19	16	s	s	X
ejpam-4911	19	17	,	,	PUNCT
ejpam-4911	19	18	v)-nowhere	v)-nowhere	PUNCT
ejpam-4911	19	19	dense	dense	ADJ
ejpam-4911	19	20	sets	set	NOUN
ejpam-4911	19	21	are	be	AUX
ejpam-4911	19	22	launched	launch	VERB
ejpam-4911	19	23	.	.	PUNCT
ejpam-4911	20	1	∗corresponding	∗corresponde	VERB
ejpam-4911	20	2	author	author	NOUN
ejpam-4911	20	3	.	.	PUNCT
ejpam-4911	21	1	doi	doi	NOUN
ejpam-4911	21	2	:	:	PUNCT
ejpam-4911	21	3	https://doi.org/10.29020/nybg.ejpam.v16i4.4911	https://doi.org/10.29020/nybg.ejpam.v16i4.4911	ADJ
ejpam-4911	21	4	email	email	NOUN
ejpam-4911	21	5	addresses	address	NOUN
ejpam-4911	21	6	:	:	PUNCT
ejpam-4911	21	7	farhat.yasser.1@gmail.com	farhat.yasser.1@gmail.com	X
ejpam-4911	21	8	(	(	PUNCT
ejpam-4911	21	9	y.	y.	PROPN
ejpam-4911	21	10	farhat	farhat	PROPN
ejpam-4911	21	11	)	)	PUNCT
ejpam-4911	21	12	,	,	PUNCT
ejpam-4911	21	13	vadakasivigneswaran@gmail.com	vadakasivigneswaran@gmail.com	X
ejpam-4911	21	14	(	(	PUNCT
ejpam-4911	21	15	s.vadakasi	s.vadakasi	NOUN
ejpam-4911	21	16	)	)	PUNCT
ejpam-4911	21	17	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4911	21	18	2049	2049	NUM
ejpam-4911	22	1	©	©	ADP
ejpam-4911	22	2	2023	2023	NUM
ejpam-4911	22	3	ejpam	ejpam	NOUN
ejpam-4911	22	4	all	all	DET
ejpam-4911	22	5	rights	right	NOUN
ejpam-4911	22	6	reserved	reserve	VERB
ejpam-4911	22	7	.	.	PUNCT
ejpam-4911	23	1	y.	y.	PROPN
ejpam-4911	23	2	farhat	farhat	PROPN
ejpam-4911	23	3	,	,	PUNCT
ejpam-4911	23	4	v.	v.	ADP
ejpam-4911	23	5	subramanian	subramanian	PROPN
ejpam-4911	23	6	/	/	SYM
ejpam-4911	23	7	eur	eur	PROPN
ejpam-4911	23	8	.	.	PUNCT
ejpam-4911	24	1	j.	j.	PROPN
ejpam-4911	24	2	pure	pure	PROPN
ejpam-4911	24	3	appl	appl	PROPN
ejpam-4911	24	4	.	.	PROPN
ejpam-4911	24	5	math	math	PROPN
ejpam-4911	24	6	,	,	PUNCT
ejpam-4911	24	7	16	16	NUM
ejpam-4911	24	8	(	(	PUNCT
ejpam-4911	24	9	4	4	NUM
ejpam-4911	24	10	)	)	PUNCT
ejpam-4911	24	11	(	(	PUNCT
ejpam-4911	24	12	2023	2023	NUM
ejpam-4911	24	13	)	)	PUNCT
ejpam-4911	24	14	,	,	PUNCT
ejpam-4911	24	15	2049	2049	NUM
ejpam-4911	24	16	-	-	SYM
ejpam-4911	24	17	2065	2065	NUM
ejpam-4911	24	18	2050	2050	NUM
ejpam-4911	24	19	the	the	DET
ejpam-4911	24	20	basic	basic	ADJ
ejpam-4911	24	21	definitions	definition	NOUN
ejpam-4911	24	22	and	and	CCONJ
ejpam-4911	24	23	results	result	NOUN
ejpam-4911	24	24	are	be	AUX
ejpam-4911	24	25	presented	present	VERB
ejpam-4911	24	26	in	in	ADP
ejpam-4911	24	27	section	section	NOUN
ejpam-4911	24	28	2	2	NUM
ejpam-4911	24	29	which	which	PRON
ejpam-4911	24	30	is	be	AUX
ejpam-4911	24	31	useful	useful	ADJ
ejpam-4911	24	32	for	for	ADP
ejpam-4911	24	33	the	the	DET
ejpam-4911	24	34	development	development	NOUN
ejpam-4911	24	35	of	of	ADP
ejpam-4911	24	36	the	the	DET
ejpam-4911	24	37	following	follow	VERB
ejpam-4911	24	38	sections	section	NOUN
ejpam-4911	24	39	.	.	PUNCT
ejpam-4911	25	1	in	in	ADP
ejpam-4911	25	2	section	section	NOUN
ejpam-4911	25	3	3	3	NUM
ejpam-4911	25	4	,	,	PUNCT
ejpam-4911	25	5	in	in	ADP
ejpam-4911	25	6	a	a	DET
ejpam-4911	25	7	bigeneralized	bigeneralize	VERB
ejpam-4911	25	8	topological	topological	ADJ
ejpam-4911	25	9	space	space	NOUN
ejpam-4911	25	10	,	,	PUNCT
ejpam-4911	25	11	new	new	ADJ
ejpam-4911	25	12	results	result	NOUN
ejpam-4911	25	13	for	for	ADP
ejpam-4911	25	14	(	(	PUNCT
ejpam-4911	25	15	s	s	X
ejpam-4911	25	16	,	,	PUNCT
ejpam-4911	25	17	v)-dense	v)-dense	ADP
ejpam-4911	25	18	sets	set	NOUN
ejpam-4911	25	19	are	be	AUX
ejpam-4911	25	20	proven	prove	VERB
ejpam-4911	25	21	.	.	PUNCT
ejpam-4911	26	1	the	the	DET
ejpam-4911	26	2	necessary	necessary	ADJ
ejpam-4911	26	3	conditions	condition	NOUN
ejpam-4911	26	4	for	for	ADP
ejpam-4911	26	5	a	a	DET
ejpam-4911	26	6	given	give	VERB
ejpam-4911	26	7	set	set	NOUN
ejpam-4911	26	8	is	be	AUX
ejpam-4911	26	9	(	(	PUNCT
ejpam-4911	26	10	s	s	X
ejpam-4911	26	11	,	,	PUNCT
ejpam-4911	26	12	v)-dense	v)-dense	NOUN
ejpam-4911	26	13	are	be	AUX
ejpam-4911	26	14	given	give	VERB
ejpam-4911	26	15	.	.	PUNCT
ejpam-4911	27	1	section	section	NOUN
ejpam-4911	27	2	4	4	NUM
ejpam-4911	27	3	,	,	PUNCT
ejpam-4911	27	4	some	some	DET
ejpam-4911	27	5	properties	property	NOUN
ejpam-4911	27	6	for	for	ADP
ejpam-4911	27	7	(	(	PUNCT
ejpam-4911	27	8	s	s	X
ejpam-4911	27	9	,	,	PUNCT
ejpam-4911	27	10	v)-nowhere	v)-nowhere	PUNCT
ejpam-4911	27	11	dense	dense	ADJ
ejpam-4911	27	12	sets	set	NOUN
ejpam-4911	27	13	are	be	AUX
ejpam-4911	27	14	proven	prove	VERB
ejpam-4911	27	15	.	.	PUNCT
ejpam-4911	28	1	in	in	ADP
ejpam-4911	28	2	a	a	DET
ejpam-4911	28	3	bigeneralized	bigeneralize	VERB
ejpam-4911	28	4	topological	topological	ADJ
ejpam-4911	28	5	space	space	NOUN
ejpam-4911	28	6	,	,	PUNCT
ejpam-4911	28	7	the	the	DET
ejpam-4911	28	8	relationship	relationship	NOUN
ejpam-4911	28	9	between	between	ADP
ejpam-4911	28	10	µ-nowhere	µ-nowhere	ADP
ejpam-4911	28	11	dense	dense	ADJ
ejpam-4911	28	12	and	and	CCONJ
ejpam-4911	28	13	(	(	PUNCT
ejpam-4911	28	14	s	s	X
ejpam-4911	28	15	,	,	PUNCT
ejpam-4911	28	16	v)nowhere	v)nowhere	X
ejpam-4911	28	17	dense	dense	ADJ
ejpam-4911	28	18	sets	set	NOUN
ejpam-4911	28	19	are	be	AUX
ejpam-4911	28	20	examined	examine	VERB
ejpam-4911	28	21	.	.	PUNCT
ejpam-4911	29	1	finally	finally	ADV
ejpam-4911	29	2	,	,	PUNCT
ejpam-4911	29	3	the	the	DET
ejpam-4911	29	4	set	set	NOUN
ejpam-4911	29	5	(	(	PUNCT
ejpam-4911	29	6	s	s	X
ejpam-4911	29	7	,	,	PUNCT
ejpam-4911	29	8	v)-codense	v)-codense	ADV
ejpam-4911	29	9	is	be	AUX
ejpam-4911	29	10	defined	define	VERB
ejpam-4911	29	11	and	and	CCONJ
ejpam-4911	29	12	find	find	VERB
ejpam-4911	29	13	few	few	ADJ
ejpam-4911	29	14	results	result	NOUN
ejpam-4911	29	15	for	for	ADP
ejpam-4911	29	16	this	this	DET
ejpam-4911	29	17	set	set	NOUN
ejpam-4911	29	18	.	.	PUNCT
ejpam-4911	30	1	in	in	ADP
ejpam-4911	30	2	section	section	NOUN
ejpam-4911	30	3	5	5	NUM
ejpam-4911	30	4	,	,	PUNCT
ejpam-4911	30	5	the	the	DET
ejpam-4911	30	6	nature	nature	NOUN
ejpam-4911	30	7	of	of	ADP
ejpam-4911	30	8	(	(	PUNCT
ejpam-4911	30	9	s	s	X
ejpam-4911	30	10	,	,	PUNCT
ejpam-4911	30	11	v)-dense	v)-dense	PUNCT
ejpam-4911	30	12	and	and	CCONJ
ejpam-4911	30	13	(	(	PUNCT
ejpam-4911	30	14	s	s	X
ejpam-4911	30	15	,	,	PUNCT
ejpam-4911	30	16	v)-codense	v)-codense	ADJ
ejpam-4911	30	17	sets	set	NOUN
ejpam-4911	30	18	are	be	AUX
ejpam-4911	30	19	examined	examine	VERB
ejpam-4911	30	20	by	by	ADP
ejpam-4911	30	21	functions	function	NOUN
ejpam-4911	30	22	in	in	ADP
ejpam-4911	30	23	a	a	DET
ejpam-4911	30	24	bigeneralized	bigeneralize	VERB
ejpam-4911	30	25	topological	topological	ADJ
ejpam-4911	30	26	space	space	NOUN
ejpam-4911	30	27	.	.	PUNCT
ejpam-4911	31	1	in	in	ADP
ejpam-4911	31	2	the	the	DET
ejpam-4911	31	3	last	last	ADJ
ejpam-4911	31	4	section	section	NOUN
ejpam-4911	31	5	,	,	PUNCT
ejpam-4911	31	6	we	we	PRON
ejpam-4911	31	7	define	define	VERB
ejpam-4911	31	8	a	a	DET
ejpam-4911	31	9	soft	soft	ADJ
ejpam-4911	31	10	set	set	NOUN
ejpam-4911	31	11	using	use	VERB
ejpam-4911	31	12	(	(	PUNCT
ejpam-4911	31	13	s	s	NOUN
ejpam-4911	31	14	,	,	PUNCT
ejpam-4911	31	15	v)-dense	v)-dense	NOUN
ejpam-4911	31	16	,	,	PUNCT
ejpam-4911	31	17	(	(	PUNCT
ejpam-4911	31	18	s	s	X
ejpam-4911	31	19	,	,	PUNCT
ejpam-4911	31	20	v)-nowhere	v)-nowhere	PUNCT
ejpam-4911	31	21	dense	dense	ADJ
ejpam-4911	31	22	,	,	PUNCT
ejpam-4911	31	23	and	and	CCONJ
ejpam-4911	31	24	(	(	PUNCT
ejpam-4911	31	25	s	s	X
ejpam-4911	31	26	,	,	PUNCT
ejpam-4911	31	27	v)-codense	v)-codense	ADJ
ejpam-4911	31	28	sets	set	NOUN
ejpam-4911	31	29	are	be	AUX
ejpam-4911	31	30	defined	define	VERB
ejpam-4911	31	31	in	in	ADP
ejpam-4911	31	32	a	a	DET
ejpam-4911	31	33	bigeneralized	bigeneralize	VERB
ejpam-4911	31	34	topological	topological	ADJ
ejpam-4911	31	35	space	space	NOUN
ejpam-4911	31	36	.	.	PUNCT
ejpam-4911	32	1	2	2	X
ejpam-4911	32	2	.	.	X
ejpam-4911	32	3	preliminaries	preliminary	NOUN
ejpam-4911	32	4	let	let	VERB
ejpam-4911	32	5	µ	µ	X
ejpam-4911	32	6	be	be	AUX
ejpam-4911	32	7	the	the	DET
ejpam-4911	32	8	collection	collection	NOUN
ejpam-4911	32	9	of	of	ADP
ejpam-4911	32	10	subsets	subset	NOUN
ejpam-4911	32	11	of	of	ADP
ejpam-4911	32	12	a	a	DET
ejpam-4911	32	13	non	non	ADJ
ejpam-4911	32	14	-	-	ADJ
ejpam-4911	32	15	null	null	ADJ
ejpam-4911	32	16	set	set	VERB
ejpam-4911	32	17	x.	x.	NOUN
ejpam-4911	32	18	µ	µ	X
ejpam-4911	32	19	is	be	AUX
ejpam-4911	32	20	called	call	VERB
ejpam-4911	32	21	generalized	generalized	ADJ
ejpam-4911	32	22	topology	topology	NOUN
ejpam-4911	33	1	[	[	X
ejpam-4911	33	2	2	2	X
ejpam-4911	33	3	]	]	PUNCT
ejpam-4911	33	4	in	in	ADP
ejpam-4911	33	5	x	x	SYM
ejpam-4911	33	6	if	if	SCONJ
ejpam-4911	33	7	it	it	PRON
ejpam-4911	33	8	contains	contain	VERB
ejpam-4911	33	9	the	the	DET
ejpam-4911	33	10	empty	empty	ADJ
ejpam-4911	33	11	set	set	NOUN
ejpam-4911	33	12	and	and	CCONJ
ejpam-4911	33	13	is	be	AUX
ejpam-4911	33	14	closed	close	VERB
ejpam-4911	33	15	under	under	ADP
ejpam-4911	33	16	arbitrary	arbitrary	ADJ
ejpam-4911	33	17	union	union	NOUN
ejpam-4911	33	18	.	.	PUNCT
ejpam-4911	34	1	then	then	ADV
ejpam-4911	34	2	(	(	PUNCT
ejpam-4911	34	3	x,µ	x,µ	NOUN
ejpam-4911	34	4	)	)	PUNCT
ejpam-4911	34	5	is	be	AUX
ejpam-4911	34	6	called	call	VERB
ejpam-4911	34	7	generalized	generalized	ADJ
ejpam-4911	34	8	topological	topological	ADJ
ejpam-4911	34	9	space	space	NOUN
ejpam-4911	34	10	(	(	PUNCT
ejpam-4911	34	11	gts	gts	NOUN
ejpam-4911	34	12	)	)	PUNCT
ejpam-4911	35	1	[	[	X
ejpam-4911	35	2	2	2	NUM
ejpam-4911	35	3	]	]	PUNCT
ejpam-4911	35	4	.	.	PUNCT
ejpam-4911	36	1	if	if	SCONJ
ejpam-4911	36	2	µ	µ	NOUN
ejpam-4911	36	3	contains	contain	VERB
ejpam-4911	36	4	x	x	PRON
ejpam-4911	36	5	,	,	PUNCT
ejpam-4911	36	6	then	then	ADV
ejpam-4911	36	7	(	(	PUNCT
ejpam-4911	36	8	x,µ	x,µ	NOUN
ejpam-4911	36	9	)	)	PUNCT
ejpam-4911	36	10	is	be	AUX
ejpam-4911	36	11	called	call	VERB
ejpam-4911	36	12	as	as	ADP
ejpam-4911	36	13	a	a	DET
ejpam-4911	36	14	strong	strong	ADJ
ejpam-4911	36	15	generalized	generalized	ADJ
ejpam-4911	36	16	topological	topological	ADJ
ejpam-4911	36	17	space	space	NOUN
ejpam-4911	36	18	(	(	PUNCT
ejpam-4911	36	19	sgts	sgts	NOUN
ejpam-4911	36	20	)	)	PUNCT
ejpam-4911	37	1	[	[	X
ejpam-4911	37	2	9	9	NUM
ejpam-4911	37	3	]	]	PUNCT
ejpam-4911	37	4	.	.	PUNCT
ejpam-4911	38	1	in	in	ADP
ejpam-4911	38	2	,	,	PUNCT
ejpam-4911	38	3	[	[	X
ejpam-4911	38	4	3	3	NUM
ejpam-4911	38	5	]	]	PUNCT
ejpam-4911	38	6	,	,	PUNCT
ejpam-4911	38	7	let	let	VERB
ejpam-4911	38	8	q	q	NOUN
ejpam-4911	38	9	be	be	AUX
ejpam-4911	38	10	the	the	DET
ejpam-4911	38	11	subset	subset	NOUN
ejpam-4911	38	12	of	of	ADP
ejpam-4911	38	13	(	(	PUNCT
ejpam-4911	38	14	x,µ	x,µ	NOUN
ejpam-4911	38	15	)	)	PUNCT
ejpam-4911	38	16	,	,	PUNCT
ejpam-4911	38	17	•	•	INTJ
ejpam-4911	38	18	if	if	SCONJ
ejpam-4911	38	19	q	q	X
ejpam-4911	38	20	∈	∈	PROPN
ejpam-4911	38	21	µ	µ	NOUN
ejpam-4911	38	22	,	,	PUNCT
ejpam-4911	38	23	then	then	ADV
ejpam-4911	38	24	q	q	X
ejpam-4911	38	25	is	be	AUX
ejpam-4911	38	26	called	call	VERB
ejpam-4911	38	27	µ-open	µ-open	NOUN
ejpam-4911	38	28	.	.	PUNCT
ejpam-4911	39	1	•	•	INTJ
ejpam-4911	39	2	if	if	SCONJ
ejpam-4911	39	3	x	x	PRON
ejpam-4911	39	4	−q	−q	NOUN
ejpam-4911	39	5	∈	∈	PROPN
ejpam-4911	39	6	µ	µ	NOUN
ejpam-4911	39	7	,	,	PUNCT
ejpam-4911	39	8	then	then	ADV
ejpam-4911	39	9	q	q	X
ejpam-4911	39	10	is	be	AUX
ejpam-4911	39	11	said	say	VERB
ejpam-4911	39	12	to	to	PART
ejpam-4911	39	13	be	be	AUX
ejpam-4911	39	14	µ-closed	µ-close	VERB
ejpam-4911	39	15	.	.	PUNCT
ejpam-4911	40	1	•	•	NUM
ejpam-4911	40	2	the	the	DET
ejpam-4911	40	3	interior	interior	NOUN
ejpam-4911	40	4	of	of	ADP
ejpam-4911	40	5	q	q	PROPN
ejpam-4911	40	6	denoted	denote	VERB
ejpam-4911	40	7	by	by	ADP
ejpam-4911	40	8	iµq	iµq	PROPN
ejpam-4911	40	9	,	,	PUNCT
ejpam-4911	40	10	is	be	AUX
ejpam-4911	40	11	the	the	DET
ejpam-4911	40	12	union	union	NOUN
ejpam-4911	40	13	of	of	ADP
ejpam-4911	40	14	all	all	DET
ejpam-4911	40	15	µ-open	µ-open	NOUN
ejpam-4911	40	16	sets	set	NOUN
ejpam-4911	40	17	contained	contain	VERB
ejpam-4911	40	18	in	in	ADP
ejpam-4911	40	19	q.	q.	PROPN
ejpam-4911	40	20	•	•	ADP
ejpam-4911	40	21	the	the	DET
ejpam-4911	40	22	closure	closure	NOUN
ejpam-4911	40	23	of	of	ADP
ejpam-4911	40	24	q	q	PUNCT
ejpam-4911	40	25	denoted	denote	VERB
ejpam-4911	40	26	by	by	ADP
ejpam-4911	40	27	cµq	cµq	PROPN
ejpam-4911	40	28	,	,	PUNCT
ejpam-4911	40	29	is	be	AUX
ejpam-4911	40	30	the	the	DET
ejpam-4911	40	31	intersection	intersection	NOUN
ejpam-4911	40	32	of	of	ADP
ejpam-4911	40	33	all	all	DET
ejpam-4911	40	34	µ-closed	µ-close	VERB
ejpam-4911	40	35	sets	set	NOUN
ejpam-4911	40	36	containing	contain	VERB
ejpam-4911	40	37	q.	q.	NOUN
ejpam-4911	40	38	for	for	ADP
ejpam-4911	40	39	ease	ease	NOUN
ejpam-4911	40	40	of	of	ADP
ejpam-4911	40	41	notation	notation	NOUN
ejpam-4911	40	42	,	,	PUNCT
ejpam-4911	40	43	we	we	PRON
ejpam-4911	40	44	write	write	VERB
ejpam-4911	40	45	i(q	i(q	NOUN
ejpam-4911	40	46	)	)	PUNCT
ejpam-4911	40	47	and	and	CCONJ
ejpam-4911	40	48	c(q	c(q	PROPN
ejpam-4911	40	49	)	)	PUNCT
ejpam-4911	40	50	when	when	SCONJ
ejpam-4911	40	51	no	no	DET
ejpam-4911	40	52	confusion	confusion	NOUN
ejpam-4911	40	53	can	can	AUX
ejpam-4911	40	54	arise	arise	VERB
ejpam-4911	40	55	.	.	PUNCT
ejpam-4911	41	1	korczak	korczak	PROPN
ejpam-4911	41	2	kubiak	kubiak	PROPN
ejpam-4911	41	3	,	,	PUNCT
ejpam-4911	41	4	et.al	et.al	PROPN
ejpam-4911	41	5	[	[	X
ejpam-4911	41	6	8	8	NUM
ejpam-4911	41	7	]	]	PUNCT
ejpam-4911	41	8	defined	define	VERB
ejpam-4911	41	9	the	the	DET
ejpam-4911	41	10	following	following	ADJ
ejpam-4911	41	11	notations	notation	NOUN
ejpam-4911	41	12	;	;	PUNCT
ejpam-4911	41	13	µ̃	µ̃	PROPN
ejpam-4911	41	14	=	=	SYM
ejpam-4911	41	15	{	{	PUNCT
ejpam-4911	41	16	l	l	NOUN
ejpam-4911	41	17	∈	∈	PROPN
ejpam-4911	41	18	µ	µ	PRON
ejpam-4911	41	19	|	|	NOUN
ejpam-4911	41	20	l	l	NOUN
ejpam-4911	41	21	̸=	̸=	PROPN
ejpam-4911	41	22	∅	∅	NOUN
ejpam-4911	41	23	}	}	PUNCT
ejpam-4911	41	24	.	.	PUNCT
ejpam-4911	42	1	µ(x	µ(x	VERB
ejpam-4911	42	2	)	)	PUNCT
ejpam-4911	42	3	=	=	SYM
ejpam-4911	42	4	{	{	PUNCT
ejpam-4911	42	5	l	l	NOUN
ejpam-4911	42	6	∈	∈	PROPN
ejpam-4911	42	7	µ	µ	X
ejpam-4911	42	8	|	|	NOUN
ejpam-4911	42	9	x	x	SYM
ejpam-4911	42	10	∈	∈	PROPN
ejpam-4911	42	11	l	l	NOUN
ejpam-4911	42	12	}	}	PUNCT
ejpam-4911	42	13	.	.	PUNCT
ejpam-4911	43	1	let	let	VERB
ejpam-4911	43	2	q	q	PART
ejpam-4911	43	3	be	be	AUX
ejpam-4911	43	4	a	a	DET
ejpam-4911	43	5	subset	subset	NOUN
ejpam-4911	43	6	of	of	ADP
ejpam-4911	43	7	a	a	DET
ejpam-4911	43	8	generalized	generalized	ADJ
ejpam-4911	43	9	topological	topological	ADJ
ejpam-4911	43	10	space	space	NOUN
ejpam-4911	43	11	(	(	PUNCT
ejpam-4911	43	12	x,µ	x,µ	NOUN
ejpam-4911	43	13	)	)	PUNCT
ejpam-4911	43	14	.	.	PUNCT
ejpam-4911	44	1	then	then	ADV
ejpam-4911	44	2	q	q	X
ejpam-4911	44	3	is	be	AUX
ejpam-4911	44	4	said	say	VERB
ejpam-4911	44	5	to	to	PART
ejpam-4911	44	6	be	be	AUX
ejpam-4911	44	7	;	;	PUNCT
ejpam-4911	44	8	•	•	ADP
ejpam-4911	44	9	µ-nowhere	µ-nowhere	VERB
ejpam-4911	44	10	dense	dense	ADJ
ejpam-4911	44	11	[	[	X
ejpam-4911	44	12	6	6	NUM
ejpam-4911	44	13	]	]	X
ejpam-4911	44	14	if	if	SCONJ
ejpam-4911	44	15	ic(q	ic(q	VERB
ejpam-4911	44	16	)	)	PUNCT
ejpam-4911	44	17	=	=	SYM
ejpam-4911	44	18	∅	∅	NOUN
ejpam-4911	44	19	;	;	PUNCT
ejpam-4911	44	20	•	•	X
ejpam-4911	44	21	µ-dense	µ-dense	NOUN
ejpam-4911	45	1	[	[	X
ejpam-4911	45	2	6	6	NUM
ejpam-4911	45	3	]	]	PUNCT
ejpam-4911	45	4	if	if	SCONJ
ejpam-4911	45	5	cq	cq	NOUN
ejpam-4911	45	6	=	=	NOUN
ejpam-4911	45	7	x	x	X
ejpam-4911	45	8	;	;	PUNCT
ejpam-4911	45	9	•	•	NUM
ejpam-4911	45	10	µ-codense	µ-codense	NOUN
ejpam-4911	45	11	[	[	X
ejpam-4911	45	12	5	5	NUM
ejpam-4911	45	13	]	]	PUNCT
ejpam-4911	45	14	if	if	SCONJ
ejpam-4911	45	15	c(x	c(x	NOUN
ejpam-4911	45	16	−q	−q	NOUN
ejpam-4911	45	17	)	)	PUNCT
ejpam-4911	45	18	=	=	SYM
ejpam-4911	45	19	x.	x.	NOUN
ejpam-4911	45	20	let	let	VERB
ejpam-4911	45	21	µ1	µ1	PROPN
ejpam-4911	45	22	,	,	PUNCT
ejpam-4911	45	23	µ2	µ2	PROPN
ejpam-4911	45	24	be	be	AUX
ejpam-4911	45	25	two	two	NUM
ejpam-4911	45	26	gt	gt	NOUN
ejpam-4911	45	27	in	in	ADP
ejpam-4911	45	28	a	a	DET
ejpam-4911	45	29	non	non	ADJ
ejpam-4911	45	30	-	-	ADJ
ejpam-4911	45	31	null	null	ADJ
ejpam-4911	45	32	set	set	NOUN
ejpam-4911	45	33	x.	x.	NOUN
ejpam-4911	45	34	then	then	ADV
ejpam-4911	45	35	(	(	PUNCT
ejpam-4911	45	36	x,µ1	x,µ1	PROPN
ejpam-4911	45	37	,	,	PUNCT
ejpam-4911	45	38	µ2	µ2	PROPN
ejpam-4911	45	39	)	)	PUNCT
ejpam-4911	45	40	is	be	AUX
ejpam-4911	45	41	called	call	VERB
ejpam-4911	45	42	as	as	ADP
ejpam-4911	45	43	a	a	DET
ejpam-4911	45	44	bigeneralized	bigeneralized	ADJ
ejpam-4911	45	45	topological	topological	ADJ
ejpam-4911	45	46	space	space	NOUN
ejpam-4911	45	47	(	(	PUNCT
ejpam-4911	45	48	bgts	bgts	PROPN
ejpam-4911	45	49	)	)	PUNCT
ejpam-4911	46	1	[	[	X
ejpam-4911	46	2	1	1	NUM
ejpam-4911	46	3	]	]	PUNCT
ejpam-4911	46	4	.	.	PUNCT
ejpam-4911	47	1	let	let	AUX
ejpam-4911	47	2	(	(	PUNCT
ejpam-4911	47	3	x,µ1	x,µ1	NOUN
ejpam-4911	47	4	,	,	PUNCT
ejpam-4911	47	5	µ2	µ2	PROPN
ejpam-4911	47	6	)	)	PUNCT
ejpam-4911	47	7	be	be	VERB
ejpam-4911	47	8	a	a	DET
ejpam-4911	47	9	bgts	bgts	NOUN
ejpam-4911	47	10	,	,	PUNCT
ejpam-4911	47	11	d	d	PROPN
ejpam-4911	47	12	⊂	⊂	PROPN
ejpam-4911	47	13	x.	x.	PROPN
ejpam-4911	47	14	t	t	PROPN
ejpam-4911	47	15	the	the	DET
ejpam-4911	47	16	closure	closure	NOUN
ejpam-4911	47	17	of	of	ADP
ejpam-4911	47	18	d	d	PROPN
ejpam-4911	47	19	is	be	AUX
ejpam-4911	47	20	notated	notate	VERB
ejpam-4911	47	21	by	by	ADP
ejpam-4911	47	22	cs(d	cs(d	PUNCT
ejpam-4911	47	23	)	)	PUNCT
ejpam-4911	47	24	and	and	CCONJ
ejpam-4911	47	25	is(d	is(d	PRON
ejpam-4911	47	26	)	)	PUNCT
ejpam-4911	47	27	denote	denote	VERB
ejpam-4911	47	28	the	the	DET
ejpam-4911	47	29	interior	interior	NOUN
ejpam-4911	47	30	of	of	ADP
ejpam-4911	47	31	d	d	PROPN
ejpam-4911	47	32	with	with	ADP
ejpam-4911	47	33	respect	respect	NOUN
ejpam-4911	47	34	to	to	ADP
ejpam-4911	47	35	µs	µs	PRON
ejpam-4911	47	36	,	,	PUNCT
ejpam-4911	47	37	respectively	respectively	ADV
ejpam-4911	47	38	,	,	PUNCT
ejpam-4911	47	39	for	for	ADP
ejpam-4911	47	40	s	s	NOUN
ejpam-4911	47	41	=	=	SYM
ejpam-4911	47	42	1	1	NUM
ejpam-4911	47	43	,	,	PUNCT
ejpam-4911	47	44	2	2	NUM
ejpam-4911	47	45	[	[	X
ejpam-4911	47	46	1	1	NUM
ejpam-4911	47	47	]	]	PUNCT
ejpam-4911	47	48	.	.	PUNCT
ejpam-4911	48	1	in	in	ADP
ejpam-4911	48	2	a	a	DET
ejpam-4911	48	3	bgts	bgts	NOUN
ejpam-4911	48	4	(	(	PUNCT
ejpam-4911	48	5	x,µ1	x,µ1	PROPN
ejpam-4911	48	6	,	,	PUNCT
ejpam-4911	48	7	µ2	µ2	PROPN
ejpam-4911	48	8	)	)	PUNCT
ejpam-4911	48	9	,	,	PUNCT
ejpam-4911	48	10	let	let	VERB
ejpam-4911	48	11	q	q	VERB
ejpam-4911	48	12	,	,	PUNCT
ejpam-4911	48	13	p	p	PROPN
ejpam-4911	48	14	⊂	⊂	PROPN
ejpam-4911	48	15	x.	x.	NOUN
ejpam-4911	49	1	then	then	ADV
ejpam-4911	49	2	•	•	PRON
ejpam-4911	49	3	q	q	NOUN
ejpam-4911	49	4	is	be	AUX
ejpam-4911	49	5	called	call	VERB
ejpam-4911	49	6	(	(	PUNCT
ejpam-4911	49	7	s	s	PROPN
ejpam-4911	49	8	,	,	PUNCT
ejpam-4911	49	9	v)-closed	v)-close	VERB
ejpam-4911	49	10	[	[	X
ejpam-4911	49	11	1	1	X
ejpam-4911	49	12	]	]	PUNCT
ejpam-4911	49	13	if	if	SCONJ
ejpam-4911	49	14	cs(cv(q	cs(cv(q	NOUN
ejpam-4911	49	15	)	)	PUNCT
ejpam-4911	49	16	)	)	PUNCT
ejpam-4911	50	1	=	=	PUNCT
ejpam-4911	51	1	q	q	X
ejpam-4911	51	2	,	,	PUNCT
ejpam-4911	51	3	where	where	SCONJ
ejpam-4911	51	4	s	s	X
ejpam-4911	51	5	,	,	PUNCT
ejpam-4911	51	6	v	v	NOUN
ejpam-4911	51	7	=	=	SYM
ejpam-4911	51	8	1	1	NUM
ejpam-4911	51	9	or	or	CCONJ
ejpam-4911	51	10	2	2	NUM
ejpam-4911	51	11	;	;	PUNCT
ejpam-4911	51	12	s	s	VERB
ejpam-4911	51	13	̸=	̸=	PROPN
ejpam-4911	51	14	v.	v.	ADP
ejpam-4911	51	15	y.	y.	PROPN
ejpam-4911	51	16	farhat	farhat	PROPN
ejpam-4911	51	17	,	,	PUNCT
ejpam-4911	51	18	v.	v.	ADP
ejpam-4911	51	19	subramanian	subramanian	PROPN
ejpam-4911	51	20	/	/	SYM
ejpam-4911	51	21	eur	eur	PROPN
ejpam-4911	51	22	.	.	PUNCT
ejpam-4911	52	1	j.	j.	PROPN
ejpam-4911	52	2	pure	pure	PROPN
ejpam-4911	52	3	appl	appl	PROPN
ejpam-4911	52	4	.	.	PROPN
ejpam-4911	52	5	math	math	PROPN
ejpam-4911	52	6	,	,	PUNCT
ejpam-4911	52	7	16	16	NUM
ejpam-4911	52	8	(	(	PUNCT
ejpam-4911	52	9	4	4	NUM
ejpam-4911	52	10	)	)	PUNCT
ejpam-4911	52	11	(	(	PUNCT
ejpam-4911	52	12	2023	2023	NUM
ejpam-4911	52	13	)	)	PUNCT
ejpam-4911	52	14	,	,	PUNCT
ejpam-4911	52	15	2049	2049	NUM
ejpam-4911	52	16	-	-	SYM
ejpam-4911	52	17	2065	2065	NUM
ejpam-4911	52	18	2051	2051	NUM
ejpam-4911	52	19	•	•	NOUN
ejpam-4911	52	20	if	if	SCONJ
ejpam-4911	52	21	x	x	PRON
ejpam-4911	52	22	−q	−q	NOUN
ejpam-4911	52	23	is	be	AUX
ejpam-4911	52	24	(	(	PUNCT
ejpam-4911	52	25	s	s	X
ejpam-4911	52	26	,	,	PUNCT
ejpam-4911	52	27	v)-closed	v)-close	VERB
ejpam-4911	52	28	,	,	PUNCT
ejpam-4911	52	29	then	then	ADV
ejpam-4911	52	30	q	q	X
ejpam-4911	52	31	is	be	AUX
ejpam-4911	52	32	called	call	VERB
ejpam-4911	52	33	(	(	PUNCT
ejpam-4911	52	34	s	s	NOUN
ejpam-4911	52	35	,	,	PUNCT
ejpam-4911	52	36	v)-open	v)-open	VERB
ejpam-4911	53	1	[	[	X
ejpam-4911	53	2	1	1	X
ejpam-4911	53	3	]	]	PUNCT
ejpam-4911	53	4	where	where	SCONJ
ejpam-4911	53	5	s	s	X
ejpam-4911	53	6	,	,	PUNCT
ejpam-4911	53	7	v	v	NOUN
ejpam-4911	53	8	=	=	SYM
ejpam-4911	53	9	1	1	NUM
ejpam-4911	53	10	or	or	CCONJ
ejpam-4911	53	11	2	2	NUM
ejpam-4911	53	12	;	;	PUNCT
ejpam-4911	53	13	s	s	AUX
ejpam-4911	53	14	̸=	̸=	PROPN
ejpam-4911	53	15	v.	v.	ADP
ejpam-4911	53	16	•	•	PROPN
ejpam-4911	53	17	p	p	NOUN
ejpam-4911	53	18	is	be	AUX
ejpam-4911	53	19	called	call	VERB
ejpam-4911	53	20	µ(s	µ(	NOUN
ejpam-4911	53	21	,	,	PUNCT
ejpam-4911	53	22	v)-closed	v)-close	VERB
ejpam-4911	53	23	[	[	X
ejpam-4911	53	24	4	4	X
ejpam-4911	53	25	]	]	PUNCT
ejpam-4911	53	26	if	if	SCONJ
ejpam-4911	53	27	cµv(p	cµv(p	X
ejpam-4911	53	28	)	)	PUNCT
ejpam-4911	54	1	⊂	⊂	PROPN
ejpam-4911	55	1	k	k	PROPN
ejpam-4911	55	2	whenever	whenever	SCONJ
ejpam-4911	55	3	p	p	PROPN
ejpam-4911	55	4	⊂	⊂	PROPN
ejpam-4911	55	5	k	k	PROPN
ejpam-4911	55	6	and	and	CCONJ
ejpam-4911	55	7	k	k	PROPN
ejpam-4911	55	8	is	be	AUX
ejpam-4911	55	9	µs	µs	NOUN
ejpam-4911	55	10	-	-	ADJ
ejpam-4911	55	11	open	open	ADJ
ejpam-4911	55	12	in	in	ADP
ejpam-4911	55	13	x	x	NOUN
ejpam-4911	55	14	,	,	PUNCT
ejpam-4911	55	15	for	for	ADP
ejpam-4911	55	16	s	s	PROPN
ejpam-4911	55	17	,	,	PUNCT
ejpam-4911	55	18	v	v	NOUN
ejpam-4911	55	19	=	=	SYM
ejpam-4911	55	20	1	1	NUM
ejpam-4911	55	21	,	,	PUNCT
ejpam-4911	55	22	2	2	NUM
ejpam-4911	55	23	;	;	PUNCT
ejpam-4911	55	24	s	s	AUX
ejpam-4911	55	25	̸=	̸=	PROPN
ejpam-4911	55	26	v.	v.	ADP
ejpam-4911	55	27	•	•	NOUN
ejpam-4911	55	28	if	if	SCONJ
ejpam-4911	55	29	x	x	PRON
ejpam-4911	55	30	−	−	PROPN
ejpam-4911	55	31	p	p	NOUN
ejpam-4911	55	32	is	be	AUX
ejpam-4911	55	33	µ(s	µ(	NOUN
ejpam-4911	55	34	,	,	PUNCT
ejpam-4911	55	35	v)-closed	v)-close	VERB
ejpam-4911	55	36	,	,	PUNCT
ejpam-4911	55	37	then	then	ADV
ejpam-4911	55	38	p	p	PROPN
ejpam-4911	55	39	is	be	AUX
ejpam-4911	55	40	called	call	VERB
ejpam-4911	55	41	µ(s	µ(	NOUN
ejpam-4911	55	42	,	,	PUNCT
ejpam-4911	55	43	v)-open	v)-open	X
ejpam-4911	55	44	[	[	X
ejpam-4911	55	45	4	4	X
ejpam-4911	55	46	]	]	PUNCT
ejpam-4911	55	47	where	where	SCONJ
ejpam-4911	55	48	s	s	X
ejpam-4911	55	49	,	,	PUNCT
ejpam-4911	55	50	v	v	NOUN
ejpam-4911	55	51	=	=	SYM
ejpam-4911	55	52	1	1	NUM
ejpam-4911	55	53	or	or	CCONJ
ejpam-4911	55	54	2	2	NUM
ejpam-4911	55	55	;	;	PUNCT
ejpam-4911	55	56	s	s	VERB
ejpam-4911	55	57	̸=	̸=	PROPN
ejpam-4911	55	58	v.	v.	ADV
ejpam-4911	55	59	in	in	ADP
ejpam-4911	55	60	[	[	X
ejpam-4911	55	61	1	1	NUM
ejpam-4911	55	62	]	]	PUNCT
ejpam-4911	55	63	,	,	PUNCT
ejpam-4911	55	64	a	a	DET
ejpam-4911	55	65	subset	subset	NOUN
ejpam-4911	55	66	q	q	NOUN
ejpam-4911	55	67	of	of	ADP
ejpam-4911	55	68	a	a	DET
ejpam-4911	55	69	bgts	bgts	NOUN
ejpam-4911	55	70	(	(	PUNCT
ejpam-4911	55	71	x,µ1	x,µ1	PROPN
ejpam-4911	55	72	,	,	PUNCT
ejpam-4911	55	73	µ2	µ2	PROPN
ejpam-4911	55	74	)	)	PUNCT
ejpam-4911	55	75	is	be	AUX
ejpam-4911	55	76	called	call	VERB
ejpam-4911	55	77	•	•	ADP
ejpam-4911	55	78	(	(	PUNCT
ejpam-4911	55	79	s	s	X
ejpam-4911	55	80	,	,	PUNCT
ejpam-4911	55	81	v)-µ-regular	v)-µ-regular	ADV
ejpam-4911	55	82	open	open	ADJ
ejpam-4911	55	83	if	if	SCONJ
ejpam-4911	55	84	q	q	NOUN
ejpam-4911	55	85	=	=	NOUN
ejpam-4911	55	86	is(cv(q	is(cv(q	NOUN
ejpam-4911	55	87	)	)	PUNCT
ejpam-4911	55	88	)	)	PUNCT
ejpam-4911	55	89	for	for	ADP
ejpam-4911	55	90	s	s	PROPN
ejpam-4911	55	91	,	,	PUNCT
ejpam-4911	55	92	v	v	NOUN
ejpam-4911	55	93	=	=	SYM
ejpam-4911	55	94	1	1	NUM
ejpam-4911	55	95	or	or	CCONJ
ejpam-4911	55	96	2	2	NUM
ejpam-4911	55	97	;	;	PUNCT
ejpam-4911	55	98	s	s	VERB
ejpam-4911	55	99	̸=	̸=	PROPN
ejpam-4911	55	100	v.	v.	ADP
ejpam-4911	55	101	•	•	NUM
ejpam-4911	55	102	(	(	PUNCT
ejpam-4911	55	103	s	s	X
ejpam-4911	55	104	,	,	PUNCT
ejpam-4911	55	105	v)-µ-semi	v)-µ-semi	NOUN
ejpam-4911	55	106	-	-	PUNCT
ejpam-4911	55	107	open	open	ADJ
ejpam-4911	55	108	if	if	SCONJ
ejpam-4911	55	109	q	q	NOUN
ejpam-4911	55	110	⊆	⊆	NUM
ejpam-4911	55	111	cv(is(q	cv(is(q	NOUN
ejpam-4911	55	112	)	)	PUNCT
ejpam-4911	55	113	)	)	PUNCT
ejpam-4911	55	114	for	for	ADP
ejpam-4911	55	115	s	s	PROPN
ejpam-4911	55	116	,	,	PUNCT
ejpam-4911	55	117	v	v	NOUN
ejpam-4911	55	118	=	=	SYM
ejpam-4911	55	119	1	1	NUM
ejpam-4911	55	120	or	or	CCONJ
ejpam-4911	55	121	2	2	NUM
ejpam-4911	55	122	;	;	PUNCT
ejpam-4911	55	123	s	s	VERB
ejpam-4911	55	124	̸=	̸=	PROPN
ejpam-4911	55	125	v.	v.	ADP
ejpam-4911	55	126	•	•	NUM
ejpam-4911	55	127	(	(	PUNCT
ejpam-4911	55	128	s	s	X
ejpam-4911	55	129	,	,	PUNCT
ejpam-4911	55	130	v)-µ-preopen	v)-µ-preopen	VERB
ejpam-4911	55	131	if	if	SCONJ
ejpam-4911	55	132	q	q	NOUN
ejpam-4911	55	133	⊆	⊆	NUM
ejpam-4911	55	134	is(cv(q	is(cv(q	NOUN
ejpam-4911	55	135	)	)	PUNCT
ejpam-4911	55	136	)	)	PUNCT
ejpam-4911	55	137	for	for	ADP
ejpam-4911	55	138	s	s	PROPN
ejpam-4911	55	139	,	,	PUNCT
ejpam-4911	55	140	v	v	NOUN
ejpam-4911	55	141	=	=	SYM
ejpam-4911	55	142	1	1	NUM
ejpam-4911	55	143	or	or	CCONJ
ejpam-4911	55	144	2	2	NUM
ejpam-4911	55	145	;	;	PUNCT
ejpam-4911	55	146	s	s	VERB
ejpam-4911	55	147	̸=	̸=	PROPN
ejpam-4911	55	148	v.	v.	ADP
ejpam-4911	55	149	•	•	NUM
ejpam-4911	55	150	(	(	PUNCT
ejpam-4911	55	151	s	s	NOUN
ejpam-4911	55	152	,	,	PUNCT
ejpam-4911	55	153	v)-µ-α	v)-µ-α	NOUN
ejpam-4911	55	154	-	-	PUNCT
ejpam-4911	55	155	open	open	ADJ
ejpam-4911	55	156	if	if	SCONJ
ejpam-4911	55	157	q	q	PROPN
ejpam-4911	55	158	⊆	⊆	NUM
ejpam-4911	55	159	is(cv(is(q	is(cv(is(q	NOUN
ejpam-4911	55	160	)	)	PUNCT
ejpam-4911	55	161	)	)	PUNCT
ejpam-4911	55	162	)	)	PUNCT
ejpam-4911	55	163	for	for	ADP
ejpam-4911	55	164	s	s	SYM
ejpam-4911	55	165	,	,	PUNCT
ejpam-4911	55	166	v	v	NOUN
ejpam-4911	55	167	=	=	SYM
ejpam-4911	55	168	1	1	NUM
ejpam-4911	55	169	or	or	CCONJ
ejpam-4911	55	170	2	2	NUM
ejpam-4911	55	171	;	;	PUNCT
ejpam-4911	55	172	s	s	VERB
ejpam-4911	55	173	̸=	̸=	PROPN
ejpam-4911	55	174	v.	v.	ADP
ejpam-4911	55	175	lemma	lemma	PROPN
ejpam-4911	55	176	1	1	NUM
ejpam-4911	55	177	.	.	PUNCT
ejpam-4911	56	1	[	[	X
ejpam-4911	56	2	proposition	proposition	NOUN
ejpam-4911	56	3	3.4	3.4	NUM
ejpam-4911	56	4	,	,	PUNCT
ejpam-4911	56	5	[	[	X
ejpam-4911	56	6	1	1	NUM
ejpam-4911	56	7	]	]	PUNCT
ejpam-4911	56	8	]	]	X
ejpam-4911	56	9	let	let	VERB
ejpam-4911	56	10	k	k	PRON
ejpam-4911	56	11	be	be	AUX
ejpam-4911	56	12	a	a	DET
ejpam-4911	56	13	subset	subset	NOUN
ejpam-4911	56	14	of	of	ADP
ejpam-4911	56	15	a	a	DET
ejpam-4911	56	16	bgts	bgts	NOUN
ejpam-4911	56	17	(	(	PUNCT
ejpam-4911	56	18	x,µ1	x,µ1	PROPN
ejpam-4911	56	19	,	,	PUNCT
ejpam-4911	56	20	µ2	µ2	PROPN
ejpam-4911	56	21	)	)	PUNCT
ejpam-4911	56	22	.	.	PUNCT
ejpam-4911	57	1	then	then	ADV
ejpam-4911	57	2	k	k	PROPN
ejpam-4911	57	3	is	be	AUX
ejpam-4911	57	4	(	(	PUNCT
ejpam-4911	57	5	s	s	PROPN
ejpam-4911	57	6	,	,	PUNCT
ejpam-4911	57	7	v)-closed	v)-close	VERB
ejpam-4911	57	8	⇔	⇔	PROPN
ejpam-4911	57	9	k	k	PROPN
ejpam-4911	57	10	is	be	AUX
ejpam-4911	57	11	both	both	PRON
ejpam-4911	57	12	µ-closed	µ-close	VERB
ejpam-4911	57	13	in	in	ADP
ejpam-4911	57	14	(	(	PUNCT
ejpam-4911	57	15	x,µs	x,µs	NUM
ejpam-4911	57	16	)	)	PUNCT
ejpam-4911	57	17	and	and	CCONJ
ejpam-4911	57	18	(	(	PUNCT
ejpam-4911	57	19	x,µv	x,µv	PROPN
ejpam-4911	57	20	)	)	PUNCT
ejpam-4911	57	21	where	where	SCONJ
ejpam-4911	57	22	s	s	X
ejpam-4911	57	23	,	,	PUNCT
ejpam-4911	57	24	v	v	NOUN
ejpam-4911	57	25	=	=	SYM
ejpam-4911	57	26	1	1	NUM
ejpam-4911	57	27	or	or	CCONJ
ejpam-4911	57	28	2	2	NUM
ejpam-4911	57	29	;	;	PUNCT
ejpam-4911	57	30	s	s	VERB
ejpam-4911	57	31	̸=	̸=	PROPN
ejpam-4911	57	32	v.	v.	ADP
ejpam-4911	57	33	lemma	lemma	PROPN
ejpam-4911	57	34	2	2	NUM
ejpam-4911	57	35	.	.	PUNCT
ejpam-4911	58	1	[	[	X
ejpam-4911	58	2	proposition	proposition	NOUN
ejpam-4911	58	3	3.3	3.3	NUM
ejpam-4911	58	4	,	,	PUNCT
ejpam-4911	58	5	[	[	X
ejpam-4911	58	6	4	4	NUM
ejpam-4911	58	7	]	]	PUNCT
ejpam-4911	58	8	]	]	X
ejpam-4911	58	9	let	let	VERB
ejpam-4911	58	10	(	(	PUNCT
ejpam-4911	58	11	x,µ1	x,µ1	NOUN
ejpam-4911	58	12	,	,	PUNCT
ejpam-4911	58	13	µ2	µ2	PROPN
ejpam-4911	58	14	)	)	PUNCT
ejpam-4911	58	15	be	be	VERB
ejpam-4911	58	16	a	a	DET
ejpam-4911	58	17	bgts	bgts	NOUN
ejpam-4911	58	18	,	,	PUNCT
ejpam-4911	58	19	k	k	PROPN
ejpam-4911	58	20	⊂	⊂	PROPN
ejpam-4911	58	21	x.	x.	PROPN
ejpam-4911	59	1	then	then	ADV
ejpam-4911	59	2	k	k	PROPN
ejpam-4911	59	3	is	be	AUX
ejpam-4911	59	4	µ(s	µ(	NOUN
ejpam-4911	59	5	,	,	PUNCT
ejpam-4911	59	6	v)closed	v)close	VERB
ejpam-4911	59	7	where	where	SCONJ
ejpam-4911	59	8	s	s	X
ejpam-4911	59	9	,	,	PUNCT
ejpam-4911	59	10	v	v	NOUN
ejpam-4911	59	11	=	=	SYM
ejpam-4911	59	12	1	1	NUM
ejpam-4911	59	13	,	,	PUNCT
ejpam-4911	59	14	2	2	NUM
ejpam-4911	59	15	;	;	PUNCT
ejpam-4911	59	16	s	s	VERB
ejpam-4911	59	17	̸=	̸=	PROPN
ejpam-4911	59	18	v	v	NUM
ejpam-4911	59	19	whenever	whenever	SCONJ
ejpam-4911	59	20	k	k	PROPN
ejpam-4911	59	21	is	be	AUX
ejpam-4911	59	22	µv	µv	NOUN
ejpam-4911	59	23	-	-	PUNCT
ejpam-4911	59	24	closed	closed	ADJ
ejpam-4911	59	25	.	.	PUNCT
ejpam-4911	60	1	lemma	lemma	PROPN
ejpam-4911	60	2	3	3	X
ejpam-4911	60	3	.	.	PUNCT
ejpam-4911	61	1	[	[	X
ejpam-4911	61	2	lemma	lemma	PROPN
ejpam-4911	61	3	3.2	3.2	NUM
ejpam-4911	61	4	,	,	PUNCT
ejpam-4911	61	5	[	[	X
ejpam-4911	61	6	9	9	NUM
ejpam-4911	61	7	]	]	X
ejpam-4911	61	8	]	]	PUNCT
ejpam-4911	61	9	let	let	VERB
ejpam-4911	61	10	d	d	X
ejpam-4911	61	11	,	,	PUNCT
ejpam-4911	61	12	k	k	PROPN
ejpam-4911	61	13	be	be	VERB
ejpam-4911	61	14	two	two	NUM
ejpam-4911	61	15	subsets	subset	NOUN
ejpam-4911	61	16	of	of	ADP
ejpam-4911	61	17	a	a	DET
ejpam-4911	61	18	generalized	generalized	ADJ
ejpam-4911	61	19	topological	topological	ADJ
ejpam-4911	61	20	space	space	NOUN
ejpam-4911	61	21	(	(	PUNCT
ejpam-4911	61	22	x,µ	x,µ	NOUN
ejpam-4911	61	23	)	)	PUNCT
ejpam-4911	61	24	.	.	PUNCT
ejpam-4911	62	1	if	if	SCONJ
ejpam-4911	62	2	k	k	PROPN
ejpam-4911	62	3	∈	∈	PROPN
ejpam-4911	62	4	µ̃	µ̃	PROPN
ejpam-4911	62	5	and	and	CCONJ
ejpam-4911	62	6	k	k	X
ejpam-4911	62	7	∩d	∩d	NOUN
ejpam-4911	62	8	=	=	PUNCT
ejpam-4911	62	9	∅	∅	NOUN
ejpam-4911	62	10	,	,	PUNCT
ejpam-4911	62	11	then	then	ADV
ejpam-4911	62	12	k	k	PROPN
ejpam-4911	62	13	∩	∩	ADJ
ejpam-4911	62	14	cd	cd	PROPN
ejpam-4911	62	15	=	=	PUNCT
ejpam-4911	62	16	∅.	∅.	PRON
ejpam-4911	62	17	lemma	lemma	PROPN
ejpam-4911	62	18	4	4	NUM
ejpam-4911	62	19	.	.	PUNCT
ejpam-4911	63	1	[	[	X
ejpam-4911	63	2	proposition	proposition	NOUN
ejpam-4911	63	3	3.3	3.3	NUM
ejpam-4911	63	4	,	,	PUNCT
ejpam-4911	63	5	[	[	X
ejpam-4911	63	6	9	9	NUM
ejpam-4911	63	7	]	]	X
ejpam-4911	63	8	]	]	PUNCT
ejpam-4911	63	9	in	in	ADP
ejpam-4911	63	10	a	a	DET
ejpam-4911	63	11	gts	gts	NOUN
ejpam-4911	63	12	(	(	PUNCT
ejpam-4911	63	13	x,µ	x,µ	NOUN
ejpam-4911	63	14	)	)	PUNCT
ejpam-4911	63	15	,	,	PUNCT
ejpam-4911	63	16	q	q	PROPN
ejpam-4911	63	17	∈	∈	PROPN
ejpam-4911	63	18	d(µ	d(µ	PROPN
ejpam-4911	63	19	)	)	PUNCT
ejpam-4911	63	20	⇔	⇔	PROPN
ejpam-4911	63	21	h	h	NOUN
ejpam-4911	63	22	∩q	∩q	PROPN
ejpam-4911	63	23	̸=	̸=	PROPN
ejpam-4911	63	24	∅	∅	NOUN
ejpam-4911	63	25	for	for	ADP
ejpam-4911	63	26	any	any	DET
ejpam-4911	63	27	h	h	NOUN
ejpam-4911	63	28	∈	∈	PROPN
ejpam-4911	63	29	µ̃	µ̃	PROPN
ejpam-4911	63	30	where	where	SCONJ
ejpam-4911	63	31	d(µ	d(µ	PROPN
ejpam-4911	63	32	)	)	PUNCT
ejpam-4911	63	33	=	=	PRON
ejpam-4911	64	1	{	{	PUNCT
ejpam-4911	64	2	p	p	X
ejpam-4911	64	3	⊂	⊂	X
ejpam-4911	64	4	x	x	PROPN
ejpam-4911	64	5	|	|	ADV
ejpam-4911	64	6	cµ(p	cµ(p	PUNCT
ejpam-4911	64	7	)	)	PUNCT
ejpam-4911	65	1	=	=	PUNCT
ejpam-4911	66	1	x	x	X
ejpam-4911	66	2	}	}	PUNCT
ejpam-4911	66	3	.	.	PUNCT
ejpam-4911	67	1	lemma	lemma	PROPN
ejpam-4911	67	2	5	5	NUM
ejpam-4911	67	3	.	.	PUNCT
ejpam-4911	68	1	[	[	X
ejpam-4911	68	2	proposition	proposition	NOUN
ejpam-4911	68	3	2.2	2.2	NUM
ejpam-4911	68	4	,	,	PUNCT
ejpam-4911	68	5	[	[	X
ejpam-4911	68	6	10	10	NUM
ejpam-4911	68	7	]	]	X
ejpam-4911	68	8	]	]	X
ejpam-4911	68	9	let	let	VERB
ejpam-4911	68	10	p	p	PRON
ejpam-4911	68	11	,	,	PUNCT
ejpam-4911	68	12	q	q	ADJ
ejpam-4911	68	13	be	be	AUX
ejpam-4911	68	14	two	two	NUM
ejpam-4911	68	15	subsets	subset	NOUN
ejpam-4911	68	16	of	of	ADP
ejpam-4911	68	17	a	a	DET
ejpam-4911	68	18	gts	gts	NOUN
ejpam-4911	68	19	(	(	PUNCT
ejpam-4911	68	20	x,µ	x,µ	NOUN
ejpam-4911	68	21	)	)	PUNCT
ejpam-4911	68	22	.	.	PUNCT
ejpam-4911	69	1	then	then	ADV
ejpam-4911	69	2	the	the	DET
ejpam-4911	69	3	followings	following	NOUN
ejpam-4911	69	4	are	be	AUX
ejpam-4911	69	5	true	true	ADJ
ejpam-4911	69	6	:	:	PUNCT
ejpam-4911	69	7	(	(	PUNCT
ejpam-4911	69	8	a	a	X
ejpam-4911	69	9	)	)	PUNCT
ejpam-4911	69	10	cµ(x	cµ(x	PUNCT
ejpam-4911	69	11	−	−	PROPN
ejpam-4911	69	12	p	p	NOUN
ejpam-4911	69	13	)	)	PUNCT
ejpam-4911	69	14	=	=	PUNCT
ejpam-4911	70	1	x	x	PUNCT
ejpam-4911	70	2	−	−	NOUN
ejpam-4911	70	3	iµ(p	iµ(p	NUM
ejpam-4911	70	4	)	)	PUNCT
ejpam-4911	70	5	;	;	PUNCT
ejpam-4911	70	6	iµ(x	iµ(x	VERB
ejpam-4911	70	7	−	−	PROPN
ejpam-4911	70	8	p	p	NOUN
ejpam-4911	70	9	)	)	PUNCT
ejpam-4911	70	10	=	=	PUNCT
ejpam-4911	71	1	x	x	NOUN
ejpam-4911	71	2	−	−	NOUN
ejpam-4911	71	3	cµ(p	cµ(p	NUM
ejpam-4911	71	4	)	)	PUNCT
ejpam-4911	71	5	.	.	PUNCT
ejpam-4911	72	1	(	(	PUNCT
ejpam-4911	72	2	b	b	X
ejpam-4911	72	3	)	)	PUNCT
ejpam-4911	72	4	if	if	SCONJ
ejpam-4911	72	5	(	(	PUNCT
ejpam-4911	72	6	x	x	SYM
ejpam-4911	72	7	−	−	PROPN
ejpam-4911	72	8	p	p	X
ejpam-4911	72	9	)	)	PUNCT
ejpam-4911	72	10	∈	∈	PROPN
ejpam-4911	72	11	µ	µ	NOUN
ejpam-4911	72	12	,	,	PUNCT
ejpam-4911	72	13	then	then	ADV
ejpam-4911	72	14	cµ(p	cµ(p	PUNCT
ejpam-4911	72	15	)	)	PUNCT
ejpam-4911	73	1	=	=	PUNCT
ejpam-4911	74	1	p	p	NOUN
ejpam-4911	75	1	and	and	CCONJ
ejpam-4911	75	2	if	if	SCONJ
ejpam-4911	75	3	p	p	X
ejpam-4911	75	4	∈	∈	PROPN
ejpam-4911	75	5	µ	µ	NOUN
ejpam-4911	75	6	,	,	PUNCT
ejpam-4911	75	7	then	then	ADV
ejpam-4911	75	8	iµ(p	iµ(p	ADV
ejpam-4911	75	9	)	)	PUNCT
ejpam-4911	76	1	=	=	PUNCT
ejpam-4911	77	1	p.	p.	NOUN
ejpam-4911	77	2	(	(	PUNCT
ejpam-4911	77	3	c	c	X
ejpam-4911	77	4	)	)	PUNCT
ejpam-4911	77	5	if	if	SCONJ
ejpam-4911	77	6	p	p	PRON
ejpam-4911	77	7	⊆	⊆	NUM
ejpam-4911	77	8	q	q	NOUN
ejpam-4911	77	9	,	,	PUNCT
ejpam-4911	77	10	then	then	ADV
ejpam-4911	77	11	cµ(p	cµ(p	PUNCT
ejpam-4911	77	12	)	)	PUNCT
ejpam-4911	77	13	⊆	⊆	NUM
ejpam-4911	77	14	cµ(q	cµ(q	NOUN
ejpam-4911	77	15	)	)	PUNCT
ejpam-4911	77	16	and	and	CCONJ
ejpam-4911	77	17	iµ(p	iµ(p	ADV
ejpam-4911	77	18	)	)	PUNCT
ejpam-4911	77	19	⊆	⊆	NUM
ejpam-4911	77	20	iµ(q	iµ(q	NUM
ejpam-4911	77	21	)	)	PUNCT
ejpam-4911	77	22	.	.	PUNCT
ejpam-4911	78	1	(	(	PUNCT
ejpam-4911	78	2	d	d	X
ejpam-4911	78	3	)	)	PUNCT
ejpam-4911	78	4	p	p	NOUN
ejpam-4911	78	5	⊆	⊆	NUM
ejpam-4911	78	6	cµ(p	cµ(p	NUM
ejpam-4911	78	7	)	)	PUNCT
ejpam-4911	78	8	and	and	CCONJ
ejpam-4911	78	9	iµ(p	iµ(p	ADV
ejpam-4911	78	10	)	)	PUNCT
ejpam-4911	79	1	⊆	⊆	NUM
ejpam-4911	79	2	p.	p.	NOUN
ejpam-4911	79	3	(	(	PUNCT
ejpam-4911	79	4	e	e	NOUN
ejpam-4911	79	5	)	)	PUNCT
ejpam-4911	79	6	cµ(cµ(p	cµ(cµ(p	NOUN
ejpam-4911	79	7	)	)	PUNCT
ejpam-4911	79	8	)	)	PUNCT
ejpam-4911	80	1	=	=	SYM
ejpam-4911	80	2	cµ(p	cµ(p	X
ejpam-4911	80	3	)	)	PUNCT
ejpam-4911	80	4	and	and	CCONJ
ejpam-4911	80	5	iµ(iµ(p	iµ(iµ(p	ADJ
ejpam-4911	80	6	)	)	PUNCT
ejpam-4911	80	7	)	)	PUNCT
ejpam-4911	81	1	=	=	SYM
ejpam-4911	81	2	iµ(p	iµ(p	NUM
ejpam-4911	81	3	)	)	PUNCT
ejpam-4911	81	4	.	.	PUNCT
ejpam-4911	82	1	3	3	X
ejpam-4911	82	2	.	.	X
ejpam-4911	82	3	nature	nature	NOUN
ejpam-4911	82	4	of	of	ADP
ejpam-4911	82	5	(	(	PUNCT
ejpam-4911	82	6	s	s	X
ejpam-4911	82	7	,	,	PUNCT
ejpam-4911	82	8	v)-dense	v)-dense	VERB
ejpam-4911	82	9	sets	set	NOUN
ejpam-4911	82	10	here	here	ADV
ejpam-4911	82	11	,	,	PUNCT
ejpam-4911	82	12	we	we	PRON
ejpam-4911	82	13	define	define	VERB
ejpam-4911	82	14	a	a	DET
ejpam-4911	82	15	generalized	generalized	ADJ
ejpam-4911	82	16	dense	dense	ADJ
ejpam-4911	82	17	set	set	NOUN
ejpam-4911	82	18	using	use	VERB
ejpam-4911	82	19	two	two	NUM
ejpam-4911	82	20	generalized	generalized	ADJ
ejpam-4911	82	21	topologies	topology	NOUN
ejpam-4911	82	22	namely	namely	ADV
ejpam-4911	82	23	,	,	PUNCT
ejpam-4911	82	24	(	(	PUNCT
ejpam-4911	82	25	s	s	X
ejpam-4911	82	26	,	,	PUNCT
ejpam-4911	82	27	v)-dense	v)-dense	NOUN
ejpam-4911	82	28	set	set	NOUN
ejpam-4911	82	29	,	,	PUNCT
ejpam-4911	82	30	and	and	CCONJ
ejpam-4911	82	31	analyze	analyze	VERB
ejpam-4911	82	32	its	its	PRON
ejpam-4911	82	33	nature	nature	NOUN
ejpam-4911	82	34	in	in	ADP
ejpam-4911	82	35	a	a	DET
ejpam-4911	82	36	bgts	bgts	NOUN
ejpam-4911	82	37	(	(	PUNCT
ejpam-4911	82	38	x,µ1	x,µ1	PROPN
ejpam-4911	82	39	,	,	PUNCT
ejpam-4911	82	40	µ2	µ2	PROPN
ejpam-4911	82	41	)	)	PUNCT
ejpam-4911	82	42	.	.	PUNCT
ejpam-4911	83	1	definition	definition	NOUN
ejpam-4911	83	2	1	1	NUM
ejpam-4911	83	3	.	.	PUNCT
ejpam-4911	84	1	let	let	VERB
ejpam-4911	84	2	d	d	PRON
ejpam-4911	84	3	be	be	AUX
ejpam-4911	84	4	a	a	DET
ejpam-4911	84	5	non	non	ADJ
ejpam-4911	84	6	-	-	ADJ
ejpam-4911	84	7	null	null	ADJ
ejpam-4911	84	8	subset	subset	NOUN
ejpam-4911	84	9	of	of	ADP
ejpam-4911	84	10	a	a	DET
ejpam-4911	84	11	bigeneralized	bigeneralize	VERB
ejpam-4911	84	12	topological	topological	ADJ
ejpam-4911	84	13	space	space	NOUN
ejpam-4911	84	14	(	(	PUNCT
ejpam-4911	84	15	x,µ1	x,µ1	PROPN
ejpam-4911	84	16	,	,	PUNCT
ejpam-4911	84	17	µ2	µ2	PROPN
ejpam-4911	84	18	)	)	PUNCT
ejpam-4911	84	19	.	.	PUNCT
ejpam-4911	85	1	then	then	ADV
ejpam-4911	85	2	d	d	PROPN
ejpam-4911	85	3	is	be	AUX
ejpam-4911	85	4	called	call	VERB
ejpam-4911	85	5	(	(	PUNCT
ejpam-4911	85	6	s	s	NOUN
ejpam-4911	85	7	,	,	PUNCT
ejpam-4911	85	8	v)-dense	v)-dense	VERB
ejpam-4911	85	9	if	if	SCONJ
ejpam-4911	85	10	cs(cv(d	cs(cv(d	VERB
ejpam-4911	85	11	)	)	PUNCT
ejpam-4911	85	12	)	)	PUNCT
ejpam-4911	86	1	=	=	PUNCT
ejpam-4911	87	1	x	x	X
ejpam-4911	87	2	where	where	SCONJ
ejpam-4911	87	3	s	s	X
ejpam-4911	87	4	,	,	PUNCT
ejpam-4911	87	5	v	v	NOUN
ejpam-4911	87	6	=	=	SYM
ejpam-4911	87	7	1	1	NUM
ejpam-4911	87	8	,	,	PUNCT
ejpam-4911	87	9	2	2	NUM
ejpam-4911	87	10	and	and	CCONJ
ejpam-4911	87	11	s	s	VERB
ejpam-4911	87	12	̸=	̸=	PROPN
ejpam-4911	87	13	v.	v.	ADP
ejpam-4911	87	14	moreover	moreover	ADV
ejpam-4911	87	15	,	,	PUNCT
ejpam-4911	87	16	(	(	PUNCT
ejpam-4911	87	17	s	s	X
ejpam-4911	87	18	,	,	PUNCT
ejpam-4911	87	19	v)−d(x	v)−d(x	NUM
ejpam-4911	87	20	)	)	PUNCT
ejpam-4911	87	21	=	=	PRON
ejpam-4911	87	22	{	{	PUNCT
ejpam-4911	87	23	q	q	X
ejpam-4911	87	24	⊂	⊂	X
ejpam-4911	87	25	x	x	PUNCT
ejpam-4911	87	26	|	|	ADV
ejpam-4911	87	27	q	q	X
ejpam-4911	87	28	is	be	AUX
ejpam-4911	87	29	(	(	PUNCT
ejpam-4911	87	30	s	s	X
ejpam-4911	87	31	,	,	PUNCT
ejpam-4911	87	32	v)-dense	v)-dense	NOUN
ejpam-4911	87	33	in	in	ADP
ejpam-4911	87	34	x	x	NOUN
ejpam-4911	87	35	}	}	PUNCT
ejpam-4911	87	36	for	for	ADP
ejpam-4911	87	37	s	s	PROPN
ejpam-4911	87	38	,	,	PUNCT
ejpam-4911	87	39	v	v	NOUN
ejpam-4911	87	40	=	=	SYM
ejpam-4911	87	41	1	1	NUM
ejpam-4911	87	42	,	,	PUNCT
ejpam-4911	87	43	2	2	NUM
ejpam-4911	87	44	;	;	PUNCT
ejpam-4911	87	45	s	s	VERB
ejpam-4911	87	46	̸=	̸=	PROPN
ejpam-4911	87	47	v.	v.	ADP
ejpam-4911	87	48	example	example	NOUN
ejpam-4911	88	1	2	2	X
ejpam-4911	88	2	.	.	X
ejpam-4911	88	3	consider	consider	VERB
ejpam-4911	88	4	the	the	DET
ejpam-4911	88	5	bgts	bgts	NOUN
ejpam-4911	88	6	(	(	PUNCT
ejpam-4911	88	7	x,µ1	x,µ1	PROPN
ejpam-4911	88	8	,	,	PUNCT
ejpam-4911	88	9	µ2	µ2	PROPN
ejpam-4911	88	10	)	)	PUNCT
ejpam-4911	88	11	where	where	SCONJ
ejpam-4911	88	12	x	x	X
ejpam-4911	88	13	=	=	PRON
ejpam-4911	88	14	{	{	PUNCT
ejpam-4911	88	15	e	e	NOUN
ejpam-4911	88	16	,	,	PUNCT
ejpam-4911	88	17	f	f	PROPN
ejpam-4911	88	18	,	,	PUNCT
ejpam-4911	88	19	k	k	NOUN
ejpam-4911	88	20	,	,	PUNCT
ejpam-4911	88	21	l	l	NOUN
ejpam-4911	88	22	}	}	PUNCT
ejpam-4911	88	23	;	;	PUNCT
ejpam-4911	88	24	µ1	µ1	PROPN
ejpam-4911	88	25	=	=	SYM
ejpam-4911	88	26	{	{	PUNCT
ejpam-4911	88	27	∅	∅	NOUN
ejpam-4911	88	28	,	,	PUNCT
ejpam-4911	88	29	{	{	PUNCT
ejpam-4911	88	30	e	e	NOUN
ejpam-4911	88	31	}	}	PUNCT
ejpam-4911	88	32	,	,	PUNCT
ejpam-4911	88	33	{	{	PUNCT
ejpam-4911	88	34	e	e	NOUN
ejpam-4911	88	35	,	,	PUNCT
ejpam-4911	88	36	f	f	PROPN
ejpam-4911	88	37	}	}	PUNCT
ejpam-4911	88	38	,	,	PUNCT
ejpam-4911	88	39	{	{	PUNCT
ejpam-4911	88	40	f	f	X
ejpam-4911	88	41	,	,	PUNCT
ejpam-4911	88	42	k	k	NOUN
ejpam-4911	88	43	}	}	PUNCT
ejpam-4911	88	44	,	,	PUNCT
ejpam-4911	88	45	{	{	PUNCT
ejpam-4911	88	46	e	e	NOUN
ejpam-4911	88	47	,	,	PUNCT
ejpam-4911	88	48	f	f	PROPN
ejpam-4911	88	49	,	,	PUNCT
ejpam-4911	88	50	k	k	NOUN
ejpam-4911	88	51	}	}	PUNCT
ejpam-4911	88	52	}	}	PUNCT
ejpam-4911	88	53	and	and	CCONJ
ejpam-4911	88	54	y.	y.	PROPN
ejpam-4911	88	55	farhat	farhat	PROPN
ejpam-4911	88	56	,	,	PUNCT
ejpam-4911	88	57	v.	v.	ADP
ejpam-4911	88	58	subramanian	subramanian	PROPN
ejpam-4911	88	59	/	/	SYM
ejpam-4911	88	60	eur	eur	PROPN
ejpam-4911	88	61	.	.	PUNCT
ejpam-4911	89	1	j.	j.	PROPN
ejpam-4911	89	2	pure	pure	PROPN
ejpam-4911	89	3	appl	appl	PROPN
ejpam-4911	89	4	.	.	PROPN
ejpam-4911	89	5	math	math	PROPN
ejpam-4911	89	6	,	,	PUNCT
ejpam-4911	89	7	16	16	NUM
ejpam-4911	89	8	(	(	PUNCT
ejpam-4911	89	9	4	4	NUM
ejpam-4911	89	10	)	)	PUNCT
ejpam-4911	89	11	(	(	PUNCT
ejpam-4911	89	12	2023	2023	NUM
ejpam-4911	89	13	)	)	PUNCT
ejpam-4911	89	14	,	,	PUNCT
ejpam-4911	89	15	2049	2049	NUM
ejpam-4911	89	16	-	-	SYM
ejpam-4911	89	17	2065	2065	NUM
ejpam-4911	89	18	2052	2052	NUM
ejpam-4911	89	19	µ2	µ2	PROPN
ejpam-4911	89	20	=	=	PUNCT
ejpam-4911	89	21	{	{	PUNCT
ejpam-4911	89	22	∅	∅	NOUN
ejpam-4911	89	23	,	,	PUNCT
ejpam-4911	89	24	{	{	PUNCT
ejpam-4911	89	25	e	e	NOUN
ejpam-4911	89	26	,	,	PUNCT
ejpam-4911	89	27	f	f	PROPN
ejpam-4911	89	28	}	}	PUNCT
ejpam-4911	89	29	,	,	PUNCT
ejpam-4911	89	30	{	{	PUNCT
ejpam-4911	89	31	f	f	X
ejpam-4911	89	32	,	,	PUNCT
ejpam-4911	89	33	l	l	NOUN
ejpam-4911	89	34	}	}	PUNCT
ejpam-4911	89	35	,	,	PUNCT
ejpam-4911	89	36	{	{	PUNCT
ejpam-4911	89	37	e	e	NOUN
ejpam-4911	89	38	,	,	PUNCT
ejpam-4911	89	39	f	f	X
ejpam-4911	89	40	,	,	PUNCT
ejpam-4911	89	41	l	l	NOUN
ejpam-4911	89	42	}	}	PUNCT
ejpam-4911	89	43	}	}	PUNCT
ejpam-4911	89	44	.	.	PUNCT
ejpam-4911	90	1	then	then	ADV
ejpam-4911	90	2	(	(	PUNCT
ejpam-4911	90	3	s	s	X
ejpam-4911	90	4	,	,	PUNCT
ejpam-4911	90	5	v)−d(x	v)−d(x	NUM
ejpam-4911	90	6	)	)	PUNCT
ejpam-4911	90	7	=	=	PRON
ejpam-4911	90	8	{	{	PUNCT
ejpam-4911	90	9	q	q	X
ejpam-4911	90	10	⊂	⊂	X
ejpam-4911	90	11	x	x	PUNCT
ejpam-4911	91	1	|	|	ADV
ejpam-4911	91	2	either	either	CCONJ
ejpam-4911	91	3	e	e	PROPN
ejpam-4911	91	4	∈	∈	PROPN
ejpam-4911	91	5	q	q	NOUN
ejpam-4911	91	6	or	or	CCONJ
ejpam-4911	91	7	f	f	NOUN
ejpam-4911	91	8	∈	∈	PROPN
ejpam-4911	91	9	q	q	NOUN
ejpam-4911	91	10	}	}	PUNCT
ejpam-4911	91	11	where	where	SCONJ
ejpam-4911	91	12	s	s	X
ejpam-4911	91	13	,	,	PUNCT
ejpam-4911	91	14	v	v	NOUN
ejpam-4911	91	15	=	=	SYM
ejpam-4911	91	16	1	1	NUM
ejpam-4911	91	17	,	,	PUNCT
ejpam-4911	91	18	2	2	NUM
ejpam-4911	91	19	;	;	PUNCT
ejpam-4911	91	20	s	s	VERB
ejpam-4911	91	21	̸=	̸=	PROPN
ejpam-4911	91	22	v.	v.	ADV
ejpam-4911	91	23	in	in	ADP
ejpam-4911	91	24	a	a	DET
ejpam-4911	91	25	gts	gts	NOUN
ejpam-4911	91	26	,	,	PUNCT
ejpam-4911	91	27	every	every	DET
ejpam-4911	91	28	superset	superset	NOUN
ejpam-4911	91	29	of	of	ADP
ejpam-4911	91	30	a	a	DET
ejpam-4911	91	31	(	(	PUNCT
ejpam-4911	91	32	s	s	NOUN
ejpam-4911	91	33	,	,	PUNCT
ejpam-4911	91	34	v)-dense	v)-dense	NOUN
ejpam-4911	91	35	set	set	NOUN
ejpam-4911	91	36	is	be	AUX
ejpam-4911	91	37	(	(	PUNCT
ejpam-4911	91	38	s	s	X
ejpam-4911	91	39	,	,	PUNCT
ejpam-4911	91	40	v)-dense	v)-dense	ADP
ejpam-4911	91	41	where	where	SCONJ
ejpam-4911	91	42	s	s	X
ejpam-4911	91	43	,	,	PUNCT
ejpam-4911	91	44	v	v	NOUN
ejpam-4911	91	45	=	=	SYM
ejpam-4911	91	46	1	1	NUM
ejpam-4911	91	47	,	,	PUNCT
ejpam-4911	91	48	2	2	NUM
ejpam-4911	91	49	and	and	CCONJ
ejpam-4911	91	50	s	s	PART
ejpam-4911	91	51	̸=	̸=	PROPN
ejpam-4911	91	52	v.	v.	ADP
ejpam-4911	91	53	theorem	theorem	ADJ
ejpam-4911	91	54	3	3	X
ejpam-4911	91	55	.	.	PUNCT
ejpam-4911	92	1	let	let	AUX
ejpam-4911	92	2	(	(	PUNCT
ejpam-4911	92	3	x,µ1	x,µ1	NOUN
ejpam-4911	92	4	,	,	PUNCT
ejpam-4911	92	5	µ2	µ2	PROPN
ejpam-4911	92	6	)	)	PUNCT
ejpam-4911	92	7	be	be	VERB
ejpam-4911	92	8	a	a	DET
ejpam-4911	92	9	bgts	bgts	NOUN
ejpam-4911	92	10	and	and	CCONJ
ejpam-4911	92	11	q	q	AUX
ejpam-4911	92	12	be	be	AUX
ejpam-4911	92	13	a	a	DET
ejpam-4911	92	14	non	non	ADJ
ejpam-4911	92	15	-	-	ADJ
ejpam-4911	92	16	null	null	ADJ
ejpam-4911	92	17	subset	subset	NOUN
ejpam-4911	92	18	of	of	ADP
ejpam-4911	92	19	x.	x.	NOUN
ejpam-4911	92	20	then	then	ADV
ejpam-4911	92	21	q	q	X
ejpam-4911	92	22	is	be	AUX
ejpam-4911	92	23	(	(	PUNCT
ejpam-4911	92	24	s	s	X
ejpam-4911	92	25	,	,	PUNCT
ejpam-4911	92	26	v)-dense	v)-dense	ADP
ejpam-4911	92	27	⇔	⇔	PROPN
ejpam-4911	92	28	cvq	cvq	PROPN
ejpam-4911	92	29	∩h	∩h	PROPN
ejpam-4911	92	30	̸=	̸=	PROPN
ejpam-4911	92	31	∅	∅	NOUN
ejpam-4911	92	32	for	for	ADP
ejpam-4911	92	33	every	every	DET
ejpam-4911	92	34	h	h	NOUN
ejpam-4911	92	35	is	be	AUX
ejpam-4911	92	36	a	a	DET
ejpam-4911	92	37	non	non	ADJ
ejpam-4911	92	38	-	-	ADJ
ejpam-4911	92	39	null	null	ADJ
ejpam-4911	92	40	µs	µs	NOUN
ejpam-4911	92	41	-	-	ADJ
ejpam-4911	92	42	open	open	ADJ
ejpam-4911	92	43	set	set	NOUN
ejpam-4911	92	44	where	where	SCONJ
ejpam-4911	92	45	s	s	X
ejpam-4911	92	46	,	,	PUNCT
ejpam-4911	92	47	v	v	NOUN
ejpam-4911	92	48	=	=	SYM
ejpam-4911	92	49	1	1	NUM
ejpam-4911	92	50	,	,	PUNCT
ejpam-4911	92	51	2	2	NUM
ejpam-4911	92	52	and	and	CCONJ
ejpam-4911	92	53	s	s	VERB
ejpam-4911	92	54	̸=	̸=	PROPN
ejpam-4911	92	55	v.	v.	ADP
ejpam-4911	92	56	proof	proof	NOUN
ejpam-4911	92	57	.	.	PUNCT
ejpam-4911	93	1	suppose	suppose	VERB
ejpam-4911	93	2	q	q	X
ejpam-4911	93	3	∈	∈	PROPN
ejpam-4911	93	4	(	(	PUNCT
ejpam-4911	93	5	s	s	PROPN
ejpam-4911	93	6	,	,	PUNCT
ejpam-4911	93	7	v	v	NOUN
ejpam-4911	93	8	)	)	PUNCT
ejpam-4911	93	9	−	−	PROPN
ejpam-4911	93	10	d(x	d(x	NOUN
ejpam-4911	93	11	)	)	PUNCT
ejpam-4911	93	12	for	for	ADP
ejpam-4911	93	13	s	s	PROPN
ejpam-4911	93	14	,	,	PUNCT
ejpam-4911	93	15	v	v	NOUN
ejpam-4911	93	16	=	=	SYM
ejpam-4911	93	17	1	1	NUM
ejpam-4911	93	18	,	,	PUNCT
ejpam-4911	93	19	2	2	NUM
ejpam-4911	93	20	;	;	PUNCT
ejpam-4911	93	21	s	s	VERB
ejpam-4911	93	22	̸=	̸=	PROPN
ejpam-4911	93	23	v	v	NOUN
ejpam-4911	93	24	,	,	PUNCT
ejpam-4911	93	25	then	then	ADV
ejpam-4911	93	26	cs(cv(q	cs(cv(q	PROPN
ejpam-4911	93	27	)	)	PUNCT
ejpam-4911	93	28	)	)	PUNCT
ejpam-4911	94	1	=	=	PUNCT
ejpam-4911	94	2	x	x	PUNCT
ejpam-4911	95	1	and	and	CCONJ
ejpam-4911	95	2	so	so	ADV
ejpam-4911	95	3	x	x	X
ejpam-4911	95	4	−	−	PROPN
ejpam-4911	95	5	(	(	PUNCT
ejpam-4911	95	6	cs(cv(q	cs(cv(q	NOUN
ejpam-4911	95	7	)	)	PUNCT
ejpam-4911	95	8	)	)	PUNCT
ejpam-4911	95	9	)	)	PUNCT
ejpam-4911	96	1	=	=	NOUN
ejpam-4911	96	2	∅	∅	NOUN
ejpam-4911	96	3	where	where	SCONJ
ejpam-4911	96	4	s	s	X
ejpam-4911	96	5	,	,	PUNCT
ejpam-4911	96	6	v	v	NOUN
ejpam-4911	96	7	=	=	SYM
ejpam-4911	96	8	1	1	NUM
ejpam-4911	96	9	,	,	PUNCT
ejpam-4911	96	10	2	2	NUM
ejpam-4911	96	11	and	and	CCONJ
ejpam-4911	96	12	s	s	VERB
ejpam-4911	96	13	̸=	̸=	PROPN
ejpam-4911	96	14	v.	v.	ADV
ejpam-4911	96	15	by	by	ADP
ejpam-4911	96	16	lemma	lemma	PROPN
ejpam-4911	96	17	5	5	NUM
ejpam-4911	96	18	,	,	PUNCT
ejpam-4911	96	19	x	x	PRON
ejpam-4911	96	20	−	−	PROPN
ejpam-4911	96	21	(	(	PUNCT
ejpam-4911	96	22	cs(cv(q	cs(cv(q	NOUN
ejpam-4911	96	23	)	)	PUNCT
ejpam-4911	96	24	)	)	PUNCT
ejpam-4911	96	25	)	)	PUNCT
ejpam-4911	97	1	=	=	NOUN
ejpam-4911	97	2	is(x	is(x	PUNCT
ejpam-4911	97	3	−	−	PROPN
ejpam-4911	97	4	(	(	PUNCT
ejpam-4911	97	5	cv(q	cv(q	NOUN
ejpam-4911	97	6	)	)	PUNCT
ejpam-4911	97	7	)	)	PUNCT
ejpam-4911	97	8	)	)	PUNCT
ejpam-4911	97	9	,	,	PUNCT
ejpam-4911	97	10	so	so	SCONJ
ejpam-4911	97	11	that	that	SCONJ
ejpam-4911	97	12	is(x	is(x	PUNCT
ejpam-4911	97	13	−	−	PROPN
ejpam-4911	97	14	(	(	PUNCT
ejpam-4911	97	15	cv(q	cv(q	NOUN
ejpam-4911	97	16	)	)	PUNCT
ejpam-4911	97	17	)	)	PUNCT
ejpam-4911	97	18	)	)	PUNCT
ejpam-4911	98	1	=	=	PUNCT
ejpam-4911	98	2	∅	∅	NOUN
ejpam-4911	98	3	which	which	PRON
ejpam-4911	98	4	implies	imply	VERB
ejpam-4911	98	5	that	that	SCONJ
ejpam-4911	98	6	cv(q	cv(q	NOUN
ejpam-4911	98	7	)	)	PUNCT
ejpam-4911	98	8	∩	∩	PROPN
ejpam-4911	98	9	h	h	PROPN
ejpam-4911	98	10	̸=	̸=	PROPN
ejpam-4911	98	11	∅	∅	NOUN
ejpam-4911	98	12	for	for	ADP
ejpam-4911	98	13	every	every	DET
ejpam-4911	98	14	h	h	NOUN
ejpam-4911	98	15	is	be	AUX
ejpam-4911	98	16	a	a	DET
ejpam-4911	98	17	non	non	ADJ
ejpam-4911	98	18	-	-	ADJ
ejpam-4911	98	19	null	null	ADJ
ejpam-4911	98	20	µs	µs	NOUN
ejpam-4911	98	21	-	-	ADJ
ejpam-4911	98	22	open	open	ADJ
ejpam-4911	98	23	set	set	NOUN
ejpam-4911	98	24	where	where	SCONJ
ejpam-4911	98	25	s	s	X
ejpam-4911	98	26	,	,	PUNCT
ejpam-4911	98	27	v	v	NOUN
ejpam-4911	98	28	=	=	SYM
ejpam-4911	98	29	1	1	NUM
ejpam-4911	98	30	,	,	PUNCT
ejpam-4911	98	31	2	2	NUM
ejpam-4911	98	32	and	and	CCONJ
ejpam-4911	98	33	s	s	VERB
ejpam-4911	98	34	̸=	̸=	PROPN
ejpam-4911	98	35	v.	v.	CCONJ
ejpam-4911	98	36	conversely	conversely	ADV
ejpam-4911	98	37	,	,	PUNCT
ejpam-4911	98	38	assume	assume	VERB
ejpam-4911	98	39	that	that	SCONJ
ejpam-4911	98	40	,	,	PUNCT
ejpam-4911	98	41	cv(q	cv(q	NUM
ejpam-4911	98	42	)	)	PUNCT
ejpam-4911	98	43	∩	∩	PROPN
ejpam-4911	98	44	h	h	PROPN
ejpam-4911	98	45	̸=	̸=	PROPN
ejpam-4911	98	46	∅	∅	NOUN
ejpam-4911	98	47	for	for	ADP
ejpam-4911	98	48	every	every	DET
ejpam-4911	98	49	h	h	NOUN
ejpam-4911	98	50	is	be	AUX
ejpam-4911	98	51	a	a	DET
ejpam-4911	98	52	non	non	ADJ
ejpam-4911	98	53	-	-	ADJ
ejpam-4911	98	54	null	null	ADJ
ejpam-4911	98	55	µs	µs	NOUN
ejpam-4911	98	56	-	-	ADJ
ejpam-4911	98	57	open	open	ADJ
ejpam-4911	98	58	set	set	NOUN
ejpam-4911	98	59	where	where	SCONJ
ejpam-4911	98	60	s	s	X
ejpam-4911	98	61	,	,	PUNCT
ejpam-4911	98	62	v	v	NOUN
ejpam-4911	98	63	=	=	SYM
ejpam-4911	98	64	1	1	NUM
ejpam-4911	98	65	,	,	PUNCT
ejpam-4911	98	66	2	2	NUM
ejpam-4911	98	67	and	and	CCONJ
ejpam-4911	98	68	s	s	VERB
ejpam-4911	98	69	̸=	̸=	PROPN
ejpam-4911	98	70	v.	v.	ADP
ejpam-4911	98	71	then	then	ADV
ejpam-4911	98	72	is(x−(cv(q	is(x−(cv(q	PROPN
ejpam-4911	98	73	)	)	PUNCT
ejpam-4911	98	74	)	)	PUNCT
ejpam-4911	98	75	)	)	PUNCT
ejpam-4911	99	1	=	=	NOUN
ejpam-4911	99	2	∅	∅	NOUN
ejpam-4911	99	3	and	and	CCONJ
ejpam-4911	99	4	so	so	ADV
ejpam-4911	99	5	cs(cv(q	cs(cv(q	PROPN
ejpam-4911	99	6	)	)	PUNCT
ejpam-4911	99	7	)	)	PUNCT
ejpam-4911	100	1	=	=	SYM
ejpam-4911	100	2	x	x	X
ejpam-4911	100	3	,	,	PUNCT
ejpam-4911	100	4	by	by	ADP
ejpam-4911	100	5	lemma	lemma	PROPN
ejpam-4911	100	6	5	5	NUM
ejpam-4911	100	7	where	where	SCONJ
ejpam-4911	100	8	s	s	X
ejpam-4911	100	9	,	,	PUNCT
ejpam-4911	100	10	v	v	NOUN
ejpam-4911	100	11	=	=	SYM
ejpam-4911	100	12	1	1	NUM
ejpam-4911	100	13	,	,	PUNCT
ejpam-4911	100	14	2	2	NUM
ejpam-4911	100	15	and	and	CCONJ
ejpam-4911	100	16	s	s	VERB
ejpam-4911	100	17	̸=	̸=	PROPN
ejpam-4911	100	18	v.	v.	ADP
ejpam-4911	100	19	hence	hence	ADV
ejpam-4911	100	20	q	q	X
ejpam-4911	100	21	is	be	AUX
ejpam-4911	100	22	(	(	PUNCT
ejpam-4911	100	23	s	s	X
ejpam-4911	100	24	,	,	PUNCT
ejpam-4911	100	25	v)-dense	v)-dense	NOUN
ejpam-4911	100	26	for	for	ADP
ejpam-4911	100	27	s	s	PROPN
ejpam-4911	100	28	,	,	PUNCT
ejpam-4911	100	29	v	v	NOUN
ejpam-4911	100	30	=	=	SYM
ejpam-4911	100	31	1	1	NUM
ejpam-4911	100	32	,	,	PUNCT
ejpam-4911	100	33	2	2	NUM
ejpam-4911	100	34	and	and	CCONJ
ejpam-4911	100	35	s	s	AUX
ejpam-4911	100	36	̸=	̸=	PROPN
ejpam-4911	100	37	v.	v.	ADP
ejpam-4911	100	38	theorem	theorem	ADJ
ejpam-4911	100	39	4	4	NUM
ejpam-4911	100	40	and	and	CCONJ
ejpam-4911	100	41	example	example	NOUN
ejpam-4911	100	42	5	5	NUM
ejpam-4911	100	43	are	be	AUX
ejpam-4911	100	44	described	describe	VERB
ejpam-4911	100	45	in	in	ADP
ejpam-4911	100	46	the	the	DET
ejpam-4911	100	47	below	below	ADJ
ejpam-4911	100	48	diagram	diagram	NOUN
ejpam-4911	100	49	.	.	PUNCT
ejpam-4911	101	1	µs	µs	X
ejpam-4911	101	2	−	−	NOUN
ejpam-4911	101	3	dense	dense	ADJ
ejpam-4911	101	4	(	(	PUNCT
ejpam-4911	101	5	s	s	X
ejpam-4911	101	6	,	,	PUNCT
ejpam-4911	101	7	v)−	v)−	PROPN
ejpam-4911	101	8	dense	dense	ADJ
ejpam-4911	101	9	µv	µv	NOUN
ejpam-4911	101	10	−	−	PUNCT
ejpam-4911	101	11	dense	dense	ADJ
ejpam-4911	101	12	/	/	SYM
ejpam-4911	101	13	/	/	SYM
ejpam-4911	101	14	theorem	theorem	NOUN
ejpam-4911	101	15	4	4	NUM
ejpam-4911	101	16	.	.	PUNCT
ejpam-4911	102	1	in	in	ADP
ejpam-4911	102	2	a	a	DET
ejpam-4911	102	3	bgts	bgts	NOUN
ejpam-4911	102	4	(	(	PUNCT
ejpam-4911	102	5	x,µ1	x,µ1	PROPN
ejpam-4911	102	6	,	,	PUNCT
ejpam-4911	102	7	µ2	µ2	PROPN
ejpam-4911	102	8	)	)	PUNCT
ejpam-4911	102	9	,	,	PUNCT
ejpam-4911	102	10	if	if	SCONJ
ejpam-4911	102	11	k	k	PROPN
ejpam-4911	102	12	is	be	AUX
ejpam-4911	102	13	either	either	PRON
ejpam-4911	102	14	µs	µs	NOUN
ejpam-4911	102	15	-	-	PUNCT
ejpam-4911	102	16	dense	dense	ADJ
ejpam-4911	102	17	or	or	CCONJ
ejpam-4911	102	18	µv	µv	NOUN
ejpam-4911	102	19	-	-	PUNCT
ejpam-4911	102	20	dense	dense	ADJ
ejpam-4911	102	21	,	,	PUNCT
ejpam-4911	102	22	then	then	ADV
ejpam-4911	102	23	k	k	PROPN
ejpam-4911	102	24	is	be	AUX
ejpam-4911	102	25	(	(	PUNCT
ejpam-4911	102	26	s	s	X
ejpam-4911	102	27	,	,	PUNCT
ejpam-4911	102	28	v)-dense	v)-dense	ADP
ejpam-4911	102	29	where	where	SCONJ
ejpam-4911	102	30	s	s	X
ejpam-4911	102	31	,	,	PUNCT
ejpam-4911	102	32	v	v	NOUN
ejpam-4911	102	33	=	=	SYM
ejpam-4911	102	34	1	1	NUM
ejpam-4911	102	35	,	,	PUNCT
ejpam-4911	102	36	2	2	NUM
ejpam-4911	102	37	;	;	PUNCT
ejpam-4911	102	38	s	s	VERB
ejpam-4911	102	39	̸=	̸=	PROPN
ejpam-4911	102	40	v.	v.	ADP
ejpam-4911	102	41	proof	proof	NOUN
ejpam-4911	102	42	.	.	PUNCT
ejpam-4911	103	1	assume	assume	VERB
ejpam-4911	103	2	that	that	SCONJ
ejpam-4911	103	3	,	,	PUNCT
ejpam-4911	103	4	k	k	PROPN
ejpam-4911	103	5	is	be	AUX
ejpam-4911	103	6	µs	µs	NOUN
ejpam-4911	103	7	-	-	ADJ
ejpam-4911	103	8	dense	dense	ADJ
ejpam-4911	103	9	where	where	SCONJ
ejpam-4911	103	10	for	for	ADP
ejpam-4911	103	11	s	s	NOUN
ejpam-4911	103	12	=	=	SYM
ejpam-4911	103	13	1	1	NUM
ejpam-4911	103	14	,	,	PUNCT
ejpam-4911	103	15	2	2	NUM
ejpam-4911	103	16	.	.	PUNCT
ejpam-4911	103	17	then	then	ADV
ejpam-4911	103	18	cs(k	cs(k	PUNCT
ejpam-4911	103	19	)	)	PUNCT
ejpam-4911	103	20	=	=	PUNCT
ejpam-4911	104	1	x	x	PUNCT
ejpam-4911	104	2	for	for	ADP
ejpam-4911	104	3	s	s	NOUN
ejpam-4911	104	4	=	=	SYM
ejpam-4911	104	5	1	1	NUM
ejpam-4911	104	6	,	,	PUNCT
ejpam-4911	104	7	2	2	NUM
ejpam-4911	104	8	.	.	X
ejpam-4911	104	9	take	take	VERB
ejpam-4911	104	10	s	s	NOUN
ejpam-4911	104	11	=	=	SYM
ejpam-4911	104	12	2	2	NUM
ejpam-4911	104	13	and	and	CCONJ
ejpam-4911	104	14	v	v	NOUN
ejpam-4911	104	15	=	=	SYM
ejpam-4911	104	16	1	1	NUM
ejpam-4911	104	17	.	.	PUNCT
ejpam-4911	105	1	then	then	ADV
ejpam-4911	105	2	k	k	PROPN
ejpam-4911	105	3	is	be	AUX
ejpam-4911	105	4	µ2	µ2	ADJ
ejpam-4911	105	5	-	-	PUNCT
ejpam-4911	105	6	dense	dense	ADJ
ejpam-4911	105	7	.	.	PUNCT
ejpam-4911	106	1	since	since	SCONJ
ejpam-4911	106	2	k	k	PROPN
ejpam-4911	106	3	⊂	⊂	PROPN
ejpam-4911	106	4	c1(k	c1(k	AUX
ejpam-4911	106	5	)	)	PUNCT
ejpam-4911	106	6	we	we	PRON
ejpam-4911	106	7	have	have	VERB
ejpam-4911	106	8	c2(k	c2(k	NOUN
ejpam-4911	106	9	)	)	PUNCT
ejpam-4911	106	10	⊂	⊂	PROPN
ejpam-4911	106	11	c2(c1(k	c2(c1(k	NOUN
ejpam-4911	106	12	)	)	PUNCT
ejpam-4911	106	13	)	)	PUNCT
ejpam-4911	106	14	.	.	PUNCT
ejpam-4911	107	1	hence	hence	ADV
ejpam-4911	107	2	k	k	PROPN
ejpam-4911	107	3	∈	∈	PROPN
ejpam-4911	107	4	(	(	PUNCT
ejpam-4911	107	5	2	2	NUM
ejpam-4911	107	6	,	,	PUNCT
ejpam-4911	107	7	1)−d(x	1)−d(x	NUM
ejpam-4911	107	8	)	)	PUNCT
ejpam-4911	107	9	(	(	PUNCT
ejpam-4911	107	10	1	1	X
ejpam-4911	107	11	)	)	PUNCT
ejpam-4911	107	12	take	take	VERB
ejpam-4911	107	13	s	s	NOUN
ejpam-4911	107	14	=	=	SYM
ejpam-4911	107	15	1	1	NUM
ejpam-4911	107	16	and	and	CCONJ
ejpam-4911	107	17	v	v	NOUN
ejpam-4911	107	18	=	=	SYM
ejpam-4911	107	19	2	2	NUM
ejpam-4911	107	20	.	.	PUNCT
ejpam-4911	108	1	then	then	ADV
ejpam-4911	108	2	k	k	PROPN
ejpam-4911	108	3	is	be	AUX
ejpam-4911	108	4	µ1	µ1	NOUN
ejpam-4911	108	5	-	-	PUNCT
ejpam-4911	108	6	dense	dense	ADJ
ejpam-4911	108	7	.	.	PUNCT
ejpam-4911	109	1	since	since	SCONJ
ejpam-4911	109	2	k	k	PROPN
ejpam-4911	109	3	⊂	⊂	PROPN
ejpam-4911	109	4	c2(k	c2(k	PROPN
ejpam-4911	109	5	)	)	PUNCT
ejpam-4911	109	6	we	we	PRON
ejpam-4911	109	7	have	have	VERB
ejpam-4911	109	8	c1(k	c1(k	NOUN
ejpam-4911	109	9	)	)	PUNCT
ejpam-4911	109	10	⊂	⊂	NOUN
ejpam-4911	109	11	c1(c2(k	c1(c2(k	NOUN
ejpam-4911	109	12	)	)	PUNCT
ejpam-4911	109	13	)	)	PUNCT
ejpam-4911	109	14	.	.	PUNCT
ejpam-4911	110	1	thus	thus	ADV
ejpam-4911	110	2	,	,	PUNCT
ejpam-4911	110	3	k	k	PROPN
ejpam-4911	110	4	∈	∈	PROPN
ejpam-4911	110	5	(	(	PUNCT
ejpam-4911	110	6	1	1	NUM
ejpam-4911	110	7	,	,	PUNCT
ejpam-4911	110	8	2)−d(x	2)−d(x	NUM
ejpam-4911	110	9	)	)	PUNCT
ejpam-4911	110	10	(	(	PUNCT
ejpam-4911	110	11	2	2	NUM
ejpam-4911	110	12	)	)	PUNCT
ejpam-4911	110	13	from	from	ADP
ejpam-4911	110	14	(	(	PUNCT
ejpam-4911	110	15	1	1	NUM
ejpam-4911	110	16	)	)	PUNCT
ejpam-4911	110	17	&	&	CCONJ
ejpam-4911	110	18	(	(	PUNCT
ejpam-4911	110	19	2	2	NUM
ejpam-4911	110	20	)	)	PUNCT
ejpam-4911	110	21	,	,	PUNCT
ejpam-4911	110	22	k	k	PROPN
ejpam-4911	110	23	is	be	AUX
ejpam-4911	110	24	(	(	PUNCT
ejpam-4911	110	25	s	s	X
ejpam-4911	110	26	,	,	PUNCT
ejpam-4911	110	27	v)-dense	v)-dense	ADP
ejpam-4911	110	28	where	where	SCONJ
ejpam-4911	110	29	s	s	X
ejpam-4911	110	30	,	,	PUNCT
ejpam-4911	110	31	v	v	NOUN
ejpam-4911	110	32	=	=	SYM
ejpam-4911	110	33	1	1	NUM
ejpam-4911	110	34	,	,	PUNCT
ejpam-4911	110	35	2	2	NUM
ejpam-4911	110	36	and	and	CCONJ
ejpam-4911	110	37	s	s	VERB
ejpam-4911	110	38	̸=	̸=	PROPN
ejpam-4911	110	39	v.	v.	CCONJ
ejpam-4911	110	40	similarly	similarly	ADV
ejpam-4911	110	41	,	,	PUNCT
ejpam-4911	110	42	we	we	PRON
ejpam-4911	110	43	can	can	AUX
ejpam-4911	110	44	prove	prove	VERB
ejpam-4911	110	45	that	that	SCONJ
ejpam-4911	110	46	k	k	PROPN
ejpam-4911	110	47	is	be	AUX
ejpam-4911	110	48	(	(	PUNCT
ejpam-4911	110	49	s	s	X
ejpam-4911	110	50	,	,	PUNCT
ejpam-4911	110	51	v)-dense	v)-dense	ADJ
ejpam-4911	110	52	if	if	SCONJ
ejpam-4911	110	53	k	k	PROPN
ejpam-4911	110	54	is	be	AUX
ejpam-4911	110	55	µv	µv	ADV
ejpam-4911	110	56	-	-	PUNCT
ejpam-4911	110	57	dense	dense	ADJ
ejpam-4911	110	58	where	where	SCONJ
ejpam-4911	110	59	s	s	X
ejpam-4911	110	60	,	,	PUNCT
ejpam-4911	110	61	v	v	NOUN
ejpam-4911	110	62	=	=	SYM
ejpam-4911	110	63	1	1	NUM
ejpam-4911	110	64	,	,	PUNCT
ejpam-4911	110	65	2	2	NUM
ejpam-4911	110	66	and	and	CCONJ
ejpam-4911	110	67	s	s	VERB
ejpam-4911	110	68	̸=	̸=	PROPN
ejpam-4911	110	69	v.	v.	ADP
ejpam-4911	110	70	example	example	NOUN
ejpam-4911	110	71	5	5	NUM
ejpam-4911	110	72	describes	describe	VERB
ejpam-4911	110	73	that	that	SCONJ
ejpam-4911	110	74	the	the	DET
ejpam-4911	110	75	theorem	theorem	NOUN
ejpam-4911	110	76	4	4	NUM
ejpam-4911	110	77	is	be	AUX
ejpam-4911	110	78	not	not	PART
ejpam-4911	110	79	reversible	reversible	ADJ
ejpam-4911	110	80	.	.	PUNCT
ejpam-4911	111	1	generally	generally	ADV
ejpam-4911	111	2	,	,	PUNCT
ejpam-4911	111	3	(	(	PUNCT
ejpam-4911	111	4	1	1	NUM
ejpam-4911	111	5	,	,	PUNCT
ejpam-4911	111	6	2)−d(x	2)−d(x	NUM
ejpam-4911	111	7	)	)	PUNCT
ejpam-4911	111	8	̸=	̸=	PROPN
ejpam-4911	111	9	(	(	PUNCT
ejpam-4911	111	10	2	2	NUM
ejpam-4911	111	11	,	,	PUNCT
ejpam-4911	111	12	1)−d(x	1)−d(x	NUM
ejpam-4911	111	13	)	)	PUNCT
ejpam-4911	111	14	in	in	ADP
ejpam-4911	111	15	a	a	DET
ejpam-4911	111	16	bigeneralized	bigeneralize	VERB
ejpam-4911	111	17	topological	topological	ADJ
ejpam-4911	111	18	space	space	NOUN
ejpam-4911	111	19	as	as	SCONJ
ejpam-4911	111	20	given	give	VERB
ejpam-4911	111	21	in	in	ADP
ejpam-4911	111	22	example	example	NOUN
ejpam-4911	111	23	6	6	NUM
ejpam-4911	111	24	.	.	PUNCT
ejpam-4911	111	25	example	example	NOUN
ejpam-4911	111	26	5	5	NUM
ejpam-4911	111	27	.	.	PUNCT
ejpam-4911	111	28	consider	consider	VERB
ejpam-4911	111	29	the	the	DET
ejpam-4911	111	30	bigeneralized	bigeneralized	ADJ
ejpam-4911	111	31	topological	topological	ADJ
ejpam-4911	111	32	space	space	NOUN
ejpam-4911	111	33	(	(	PUNCT
ejpam-4911	111	34	x,µ1	x,µ1	PROPN
ejpam-4911	111	35	,	,	PUNCT
ejpam-4911	111	36	µ2	µ2	PROPN
ejpam-4911	111	37	)	)	PUNCT
ejpam-4911	111	38	,	,	PUNCT
ejpam-4911	111	39	x	x	PUNCT
ejpam-4911	111	40	=	=	PRON
ejpam-4911	111	41	{	{	PUNCT
ejpam-4911	111	42	e	e	NOUN
ejpam-4911	111	43	,	,	PUNCT
ejpam-4911	111	44	f	f	PROPN
ejpam-4911	111	45	,	,	PUNCT
ejpam-4911	111	46	k	k	NOUN
ejpam-4911	111	47	,	,	PUNCT
ejpam-4911	111	48	l	l	NOUN
ejpam-4911	111	49	}	}	PUNCT
ejpam-4911	111	50	;	;	PUNCT
ejpam-4911	111	51	µ1	µ1	PROPN
ejpam-4911	111	52	=	=	SYM
ejpam-4911	111	53	{	{	PUNCT
ejpam-4911	111	54	∅	∅	NOUN
ejpam-4911	111	55	,	,	PUNCT
ejpam-4911	111	56	{	{	PUNCT
ejpam-4911	111	57	e	e	NOUN
ejpam-4911	111	58	,	,	PUNCT
ejpam-4911	111	59	l	l	NOUN
ejpam-4911	111	60	}	}	PUNCT
ejpam-4911	111	61	,	,	PUNCT
ejpam-4911	111	62	{	{	PUNCT
ejpam-4911	111	63	f	f	X
ejpam-4911	111	64	,	,	PUNCT
ejpam-4911	111	65	l	l	NOUN
ejpam-4911	111	66	}	}	PUNCT
ejpam-4911	111	67	,	,	PUNCT
ejpam-4911	111	68	{	{	PUNCT
ejpam-4911	111	69	e	e	NOUN
ejpam-4911	111	70	,	,	PUNCT
ejpam-4911	111	71	f	f	X
ejpam-4911	111	72	,	,	PUNCT
ejpam-4911	111	73	l	l	NOUN
ejpam-4911	111	74	}	}	PUNCT
ejpam-4911	111	75	}	}	PUNCT
ejpam-4911	111	76	and	and	CCONJ
ejpam-4911	111	77	y.	y.	PROPN
ejpam-4911	111	78	farhat	farhat	PROPN
ejpam-4911	111	79	,	,	PUNCT
ejpam-4911	111	80	v.	v.	ADP
ejpam-4911	111	81	subramanian	subramanian	PROPN
ejpam-4911	111	82	/	/	SYM
ejpam-4911	111	83	eur	eur	PROPN
ejpam-4911	111	84	.	.	PUNCT
ejpam-4911	112	1	j.	j.	PROPN
ejpam-4911	112	2	pure	pure	PROPN
ejpam-4911	112	3	appl	appl	PROPN
ejpam-4911	112	4	.	.	PROPN
ejpam-4911	112	5	math	math	PROPN
ejpam-4911	112	6	,	,	PUNCT
ejpam-4911	112	7	16	16	NUM
ejpam-4911	112	8	(	(	PUNCT
ejpam-4911	112	9	4	4	NUM
ejpam-4911	112	10	)	)	PUNCT
ejpam-4911	112	11	(	(	PUNCT
ejpam-4911	112	12	2023	2023	NUM
ejpam-4911	112	13	)	)	PUNCT
ejpam-4911	112	14	,	,	PUNCT
ejpam-4911	112	15	2049	2049	NUM
ejpam-4911	112	16	-	-	SYM
ejpam-4911	112	17	2065	2065	NUM
ejpam-4911	112	18	2053	2053	NUM
ejpam-4911	112	19	µ2	µ2	PROPN
ejpam-4911	112	20	=	=	PUNCT
ejpam-4911	112	21	{	{	PUNCT
ejpam-4911	112	22	∅	∅	NOUN
ejpam-4911	112	23	,	,	PUNCT
ejpam-4911	112	24	{	{	PUNCT
ejpam-4911	112	25	e	e	NOUN
ejpam-4911	112	26	,	,	PUNCT
ejpam-4911	112	27	k	k	NOUN
ejpam-4911	112	28	}	}	PUNCT
ejpam-4911	112	29	,	,	PUNCT
ejpam-4911	112	30	{	{	PUNCT
ejpam-4911	112	31	f	f	X
ejpam-4911	112	32	,	,	PUNCT
ejpam-4911	112	33	k	k	NOUN
ejpam-4911	112	34	}	}	PUNCT
ejpam-4911	112	35	,	,	PUNCT
ejpam-4911	112	36	{	{	PUNCT
ejpam-4911	112	37	e	e	NOUN
ejpam-4911	112	38	,	,	PUNCT
ejpam-4911	112	39	f	f	PROPN
ejpam-4911	112	40	,	,	PUNCT
ejpam-4911	112	41	k	k	NOUN
ejpam-4911	112	42	}	}	PUNCT
ejpam-4911	112	43	}	}	PUNCT
ejpam-4911	112	44	.	.	PUNCT
ejpam-4911	113	1	here	here	ADV
ejpam-4911	113	2	{	{	PUNCT
ejpam-4911	113	3	k	k	NOUN
ejpam-4911	113	4	}	}	PUNCT
ejpam-4911	113	5	is	be	AUX
ejpam-4911	113	6	(	(	PUNCT
ejpam-4911	113	7	2	2	NUM
ejpam-4911	113	8	,	,	PUNCT
ejpam-4911	113	9	1)-dense	1)-dense	NUM
ejpam-4911	113	10	.	.	PUNCT
ejpam-4911	114	1	but	but	CCONJ
ejpam-4911	114	2	{	{	PUNCT
ejpam-4911	114	3	k	k	NOUN
ejpam-4911	114	4	}	}	PUNCT
ejpam-4911	114	5	is	be	AUX
ejpam-4911	114	6	not	not	PART
ejpam-4911	114	7	µ1	µ1	NOUN
ejpam-4911	114	8	-	-	PUNCT
ejpam-4911	114	9	dense	dense	ADJ
ejpam-4911	114	10	.	.	PUNCT
ejpam-4911	115	1	also	also	ADV
ejpam-4911	115	2	,	,	PUNCT
ejpam-4911	115	3	{	{	PUNCT
ejpam-4911	115	4	l	l	NOUN
ejpam-4911	115	5	}	}	PUNCT
ejpam-4911	115	6	is	be	AUX
ejpam-4911	115	7	(	(	PUNCT
ejpam-4911	115	8	1	1	NUM
ejpam-4911	115	9	,	,	PUNCT
ejpam-4911	115	10	2)-dense	2)-dense	NOUN
ejpam-4911	115	11	.	.	PUNCT
ejpam-4911	116	1	but	but	CCONJ
ejpam-4911	116	2	{	{	PUNCT
ejpam-4911	116	3	l	l	NOUN
ejpam-4911	116	4	}	}	PUNCT
ejpam-4911	116	5	is	be	AUX
ejpam-4911	116	6	not	not	PART
ejpam-4911	116	7	µ2	µ2	ADJ
ejpam-4911	116	8	-	-	PUNCT
ejpam-4911	116	9	dense	dense	ADJ
ejpam-4911	116	10	.	.	PUNCT
ejpam-4911	116	11	example	example	NOUN
ejpam-4911	117	1	6	6	NUM
ejpam-4911	117	2	.	.	PUNCT
ejpam-4911	117	3	consider	consider	VERB
ejpam-4911	117	4	the	the	DET
ejpam-4911	117	5	bigeneralized	bigeneralized	ADJ
ejpam-4911	117	6	topological	topological	ADJ
ejpam-4911	117	7	space	space	NOUN
ejpam-4911	117	8	(	(	PUNCT
ejpam-4911	117	9	x,µ1	x,µ1	PROPN
ejpam-4911	117	10	,	,	PUNCT
ejpam-4911	117	11	µ2	µ2	ADJ
ejpam-4911	117	12	)	)	PUNCT
ejpam-4911	117	13	wherex	wherex	PROPN
ejpam-4911	117	14	=	=	SYM
ejpam-4911	117	15	{	{	PUNCT
ejpam-4911	117	16	e	e	PROPN
ejpam-4911	117	17	,	,	PUNCT
ejpam-4911	117	18	f	f	PROPN
ejpam-4911	117	19	,	,	PUNCT
ejpam-4911	117	20	k	k	NOUN
ejpam-4911	117	21	,	,	PUNCT
ejpam-4911	117	22	l	l	NOUN
ejpam-4911	117	23	}	}	PUNCT
ejpam-4911	117	24	;	;	PUNCT
ejpam-4911	117	25	µ1	µ1	PROPN
ejpam-4911	117	26	=	=	SYM
ejpam-4911	117	27	{	{	PUNCT
ejpam-4911	117	28	∅	∅	NOUN
ejpam-4911	117	29	,	,	PUNCT
ejpam-4911	117	30	{	{	PUNCT
ejpam-4911	117	31	e	e	NOUN
ejpam-4911	117	32	,	,	PUNCT
ejpam-4911	117	33	f	f	PROPN
ejpam-4911	117	34	}	}	PUNCT
ejpam-4911	117	35	,	,	PUNCT
ejpam-4911	117	36	{	{	PUNCT
ejpam-4911	117	37	f	f	X
ejpam-4911	117	38	,	,	PUNCT
ejpam-4911	117	39	k	k	NOUN
ejpam-4911	117	40	}	}	PUNCT
ejpam-4911	117	41	,	,	PUNCT
ejpam-4911	117	42	{	{	PUNCT
ejpam-4911	117	43	e	e	NOUN
ejpam-4911	117	44	,	,	PUNCT
ejpam-4911	117	45	f	f	PROPN
ejpam-4911	117	46	,	,	PUNCT
ejpam-4911	117	47	k	k	NOUN
ejpam-4911	117	48	}	}	PUNCT
ejpam-4911	117	49	}	}	PUNCT
ejpam-4911	117	50	and	and	CCONJ
ejpam-4911	117	51	µ2	µ2	PROPN
ejpam-4911	117	52	=	=	PUNCT
ejpam-4911	117	53	{	{	PUNCT
ejpam-4911	117	54	∅	∅	NOUN
ejpam-4911	117	55	,	,	PUNCT
ejpam-4911	117	56	{	{	PUNCT
ejpam-4911	117	57	e	e	NOUN
ejpam-4911	117	58	}	}	PUNCT
ejpam-4911	117	59	,	,	PUNCT
ejpam-4911	117	60	{	{	PUNCT
ejpam-4911	117	61	e	e	NOUN
ejpam-4911	117	62	,	,	PUNCT
ejpam-4911	117	63	l	l	NOUN
ejpam-4911	117	64	}	}	PUNCT
ejpam-4911	117	65	,	,	PUNCT
ejpam-4911	117	66	{	{	PUNCT
ejpam-4911	117	67	k	k	X
ejpam-4911	117	68	,	,	PUNCT
ejpam-4911	117	69	l	l	NOUN
ejpam-4911	117	70	}	}	PUNCT
ejpam-4911	117	71	,	,	PUNCT
ejpam-4911	117	72	{	{	PUNCT
ejpam-4911	117	73	e	e	NOUN
ejpam-4911	117	74	,	,	PUNCT
ejpam-4911	117	75	k	k	NOUN
ejpam-4911	117	76	,	,	PUNCT
ejpam-4911	117	77	l	l	NOUN
ejpam-4911	117	78	}	}	PUNCT
ejpam-4911	117	79	}	}	PUNCT
ejpam-4911	117	80	.	.	PUNCT
ejpam-4911	118	1	then	then	ADV
ejpam-4911	118	2	•	•	X
ejpam-4911	118	3	(	(	PUNCT
ejpam-4911	118	4	1	1	NUM
ejpam-4911	118	5	,	,	PUNCT
ejpam-4911	118	6	2)−d(x	2)−d(x	NUM
ejpam-4911	118	7	)	)	PUNCT
ejpam-4911	118	8	=	=	PRON
ejpam-4911	118	9	{	{	PUNCT
ejpam-4911	118	10	{	{	PUNCT
ejpam-4911	118	11	e	e	NOUN
ejpam-4911	118	12	}	}	PUNCT
ejpam-4911	118	13	,	,	PUNCT
ejpam-4911	118	14	{	{	PUNCT
ejpam-4911	118	15	f	f	X
ejpam-4911	118	16	}	}	PUNCT
ejpam-4911	118	17	,	,	PUNCT
ejpam-4911	118	18	{	{	PUNCT
ejpam-4911	118	19	k	k	X
ejpam-4911	118	20	}	}	PUNCT
ejpam-4911	118	21	,	,	PUNCT
ejpam-4911	118	22	{	{	PUNCT
ejpam-4911	118	23	l	l	NOUN
ejpam-4911	118	24	}	}	PUNCT
ejpam-4911	118	25	,	,	PUNCT
ejpam-4911	118	26	{	{	PUNCT
ejpam-4911	118	27	e	e	NOUN
ejpam-4911	118	28	,	,	PUNCT
ejpam-4911	118	29	f	f	PROPN
ejpam-4911	118	30	}	}	PUNCT
ejpam-4911	118	31	,	,	PUNCT
ejpam-4911	118	32	{	{	PUNCT
ejpam-4911	118	33	e	e	NOUN
ejpam-4911	118	34	,	,	PUNCT
ejpam-4911	118	35	k	k	NOUN
ejpam-4911	118	36	}	}	PUNCT
ejpam-4911	118	37	,	,	PUNCT
ejpam-4911	118	38	{	{	PUNCT
ejpam-4911	118	39	e	e	NOUN
ejpam-4911	118	40	,	,	PUNCT
ejpam-4911	118	41	l	l	NOUN
ejpam-4911	118	42	}	}	PUNCT
ejpam-4911	118	43	,	,	PUNCT
ejpam-4911	118	44	{	{	PUNCT
ejpam-4911	118	45	f	f	X
ejpam-4911	118	46	,	,	PUNCT
ejpam-4911	118	47	k	k	NOUN
ejpam-4911	118	48	}	}	PUNCT
ejpam-4911	118	49	,	,	PUNCT
ejpam-4911	118	50	{	{	PUNCT
ejpam-4911	118	51	f	f	X
ejpam-4911	118	52	,	,	PUNCT
ejpam-4911	118	53	l	l	NOUN
ejpam-4911	118	54	}	}	PUNCT
ejpam-4911	118	55	,	,	PUNCT
ejpam-4911	118	56	{	{	PUNCT
ejpam-4911	118	57	k	k	X
ejpam-4911	118	58	,	,	PUNCT
ejpam-4911	118	59	l	l	NOUN
ejpam-4911	118	60	}	}	PUNCT
ejpam-4911	118	61	,	,	PUNCT
ejpam-4911	118	62	{	{	PUNCT
ejpam-4911	118	63	e	e	NOUN
ejpam-4911	118	64	,	,	PUNCT
ejpam-4911	118	65	f	f	PROPN
ejpam-4911	118	66	,	,	PUNCT
ejpam-4911	118	67	k	k	NOUN
ejpam-4911	118	68	}	}	PUNCT
ejpam-4911	118	69	,	,	PUNCT
ejpam-4911	118	70	{	{	PUNCT
ejpam-4911	118	71	e	e	NOUN
ejpam-4911	118	72	,	,	PUNCT
ejpam-4911	118	73	f	f	X
ejpam-4911	118	74	,	,	PUNCT
ejpam-4911	118	75	l	l	NOUN
ejpam-4911	118	76	}	}	PUNCT
ejpam-4911	118	77	,	,	PUNCT
ejpam-4911	118	78	{	{	PUNCT
ejpam-4911	118	79	e	e	NOUN
ejpam-4911	118	80	,	,	PUNCT
ejpam-4911	118	81	k	k	NOUN
ejpam-4911	118	82	,	,	PUNCT
ejpam-4911	118	83	l	l	NOUN
ejpam-4911	118	84	}	}	PUNCT
ejpam-4911	118	85	,	,	PUNCT
ejpam-4911	118	86	{	{	PUNCT
ejpam-4911	118	87	f	f	X
ejpam-4911	118	88	,	,	PUNCT
ejpam-4911	118	89	k	k	NOUN
ejpam-4911	118	90	,	,	PUNCT
ejpam-4911	118	91	l	l	NOUN
ejpam-4911	118	92	}	}	PUNCT
ejpam-4911	118	93	,	,	PUNCT
ejpam-4911	118	94	x	x	NOUN
ejpam-4911	118	95	}	}	PUNCT
ejpam-4911	118	96	.	.	PUNCT
ejpam-4911	119	1	•	•	NOUN
ejpam-4911	119	2	(	(	PUNCT
ejpam-4911	119	3	2	2	NUM
ejpam-4911	119	4	,	,	PUNCT
ejpam-4911	119	5	1)−d(x	1)−d(x	NUM
ejpam-4911	119	6	)	)	PUNCT
ejpam-4911	119	7	=	=	PRON
ejpam-4911	119	8	{	{	PUNCT
ejpam-4911	119	9	{	{	PUNCT
ejpam-4911	119	10	e	e	NOUN
ejpam-4911	119	11	}	}	PUNCT
ejpam-4911	119	12	,	,	PUNCT
ejpam-4911	119	13	{	{	PUNCT
ejpam-4911	119	14	f	f	X
ejpam-4911	119	15	}	}	PUNCT
ejpam-4911	119	16	,	,	PUNCT
ejpam-4911	119	17	{	{	PUNCT
ejpam-4911	119	18	e	e	NOUN
ejpam-4911	119	19	,	,	PUNCT
ejpam-4911	119	20	f	f	PROPN
ejpam-4911	119	21	}	}	PUNCT
ejpam-4911	119	22	,	,	PUNCT
ejpam-4911	119	23	{	{	PUNCT
ejpam-4911	119	24	e	e	NOUN
ejpam-4911	119	25	,	,	PUNCT
ejpam-4911	119	26	k	k	NOUN
ejpam-4911	119	27	}	}	PUNCT
ejpam-4911	119	28	,	,	PUNCT
ejpam-4911	119	29	{	{	PUNCT
ejpam-4911	119	30	e	e	NOUN
ejpam-4911	119	31	,	,	PUNCT
ejpam-4911	119	32	l	l	NOUN
ejpam-4911	119	33	}	}	PUNCT
ejpam-4911	119	34	,	,	PUNCT
ejpam-4911	119	35	{	{	PUNCT
ejpam-4911	119	36	f	f	X
ejpam-4911	119	37	,	,	PUNCT
ejpam-4911	119	38	k	k	NOUN
ejpam-4911	119	39	}	}	PUNCT
ejpam-4911	119	40	,	,	PUNCT
ejpam-4911	119	41	{	{	PUNCT
ejpam-4911	119	42	f	f	X
ejpam-4911	119	43	,	,	PUNCT
ejpam-4911	119	44	l	l	NOUN
ejpam-4911	119	45	}	}	PUNCT
ejpam-4911	119	46	,	,	PUNCT
ejpam-4911	119	47	{	{	PUNCT
ejpam-4911	119	48	e	e	NOUN
ejpam-4911	119	49	,	,	PUNCT
ejpam-4911	119	50	f	f	PROPN
ejpam-4911	119	51	,	,	PUNCT
ejpam-4911	119	52	k	k	NOUN
ejpam-4911	119	53	}	}	PUNCT
ejpam-4911	119	54	,	,	PUNCT
ejpam-4911	119	55	{	{	PUNCT
ejpam-4911	119	56	e	e	NOUN
ejpam-4911	119	57	,	,	PUNCT
ejpam-4911	119	58	f	f	X
ejpam-4911	119	59	,	,	PUNCT
ejpam-4911	119	60	l	l	NOUN
ejpam-4911	119	61	}	}	PUNCT
ejpam-4911	119	62	,	,	PUNCT
ejpam-4911	119	63	{	{	PUNCT
ejpam-4911	119	64	e	e	NOUN
ejpam-4911	119	65	,	,	PUNCT
ejpam-4911	119	66	k	k	NOUN
ejpam-4911	119	67	,	,	PUNCT
ejpam-4911	119	68	l	l	NOUN
ejpam-4911	119	69	}	}	PUNCT
ejpam-4911	119	70	,	,	PUNCT
ejpam-4911	119	71	{	{	PUNCT
ejpam-4911	119	72	f	f	X
ejpam-4911	119	73	,	,	PUNCT
ejpam-4911	119	74	k	k	NOUN
ejpam-4911	119	75	,	,	PUNCT
ejpam-4911	119	76	l	l	NOUN
ejpam-4911	119	77	}	}	PUNCT
ejpam-4911	119	78	,	,	PUNCT
ejpam-4911	119	79	x	x	NOUN
ejpam-4911	119	80	}	}	PUNCT
ejpam-4911	119	81	.	.	PUNCT
ejpam-4911	120	1	thus	thus	ADV
ejpam-4911	120	2	,	,	PUNCT
ejpam-4911	120	3	(	(	PUNCT
ejpam-4911	120	4	1	1	NUM
ejpam-4911	120	5	,	,	PUNCT
ejpam-4911	120	6	2)−d(x	2)−d(x	NUM
ejpam-4911	120	7	)	)	PUNCT
ejpam-4911	120	8	̸=	̸=	PROPN
ejpam-4911	120	9	(	(	PUNCT
ejpam-4911	120	10	2	2	NUM
ejpam-4911	120	11	,	,	PUNCT
ejpam-4911	120	12	1)−d(x	1)−d(x	NUM
ejpam-4911	120	13	)	)	PUNCT
ejpam-4911	120	14	.	.	PUNCT
ejpam-4911	121	1	theorem	theorem	ADJ
ejpam-4911	121	2	7	7	NUM
ejpam-4911	121	3	.	.	PUNCT
ejpam-4911	122	1	let	let	VERB
ejpam-4911	122	2	µ1	µ1	VERB
ejpam-4911	122	3	and	and	CCONJ
ejpam-4911	122	4	µ2	µ2	PROPN
ejpam-4911	122	5	be	be	AUX
ejpam-4911	122	6	two	two	NUM
ejpam-4911	122	7	generalized	generalized	ADJ
ejpam-4911	122	8	topologies	topology	NOUN
ejpam-4911	122	9	in	in	ADP
ejpam-4911	122	10	x.	x.	NOUN
ejpam-4911	122	11	if	if	SCONJ
ejpam-4911	122	12	µs	µs	ADP
ejpam-4911	122	13	⊆	⊆	NUM
ejpam-4911	122	14	µv	µv	NOUN
ejpam-4911	122	15	,	,	PUNCT
ejpam-4911	122	16	then	then	ADV
ejpam-4911	122	17	(	(	PUNCT
ejpam-4911	122	18	v	v	NOUN
ejpam-4911	122	19	,	,	PUNCT
ejpam-4911	122	20	s	s	NOUN
ejpam-4911	122	21	)	)	PUNCT
ejpam-4911	122	22	−	−	PROPN
ejpam-4911	122	23	d(x	d(x	NOUN
ejpam-4911	122	24	)	)	PUNCT
ejpam-4911	122	25	⊆	⊆	NUM
ejpam-4911	122	26	(	(	PUNCT
ejpam-4911	122	27	s	s	NOUN
ejpam-4911	122	28	,	,	PUNCT
ejpam-4911	122	29	v)−d(x	v)−d(x	NUM
ejpam-4911	122	30	)	)	PUNCT
ejpam-4911	122	31	where	where	SCONJ
ejpam-4911	122	32	s	s	X
ejpam-4911	122	33	,	,	PUNCT
ejpam-4911	122	34	v	v	NOUN
ejpam-4911	122	35	=	=	SYM
ejpam-4911	122	36	1	1	NUM
ejpam-4911	122	37	,	,	PUNCT
ejpam-4911	122	38	2	2	NUM
ejpam-4911	122	39	and	and	CCONJ
ejpam-4911	122	40	s	s	VERB
ejpam-4911	122	41	̸=	̸=	PROPN
ejpam-4911	122	42	v.	v.	ADP
ejpam-4911	122	43	proof	proof	NOUN
ejpam-4911	122	44	.	.	PUNCT
ejpam-4911	123	1	we	we	PRON
ejpam-4911	123	2	give	give	VERB
ejpam-4911	123	3	the	the	DET
ejpam-4911	123	4	detailed	detailed	ADJ
ejpam-4911	123	5	proof	proof	NOUN
ejpam-4911	123	6	only	only	ADV
ejpam-4911	123	7	for	for	ADP
ejpam-4911	123	8	s	s	NOUN
ejpam-4911	123	9	=	=	SYM
ejpam-4911	123	10	1	1	NUM
ejpam-4911	123	11	and	and	CCONJ
ejpam-4911	123	12	v	v	NOUN
ejpam-4911	123	13	=	=	SYM
ejpam-4911	123	14	2	2	X
ejpam-4911	123	15	.	.	PUNCT
ejpam-4911	123	16	suppose	suppose	VERB
ejpam-4911	123	17	that	that	SCONJ
ejpam-4911	123	18	µ1	µ1	PROPN
ejpam-4911	123	19	⊆	⊆	NUM
ejpam-4911	123	20	µ2	µ2	PROPN
ejpam-4911	123	21	and	and	CCONJ
ejpam-4911	123	22	q	q	NOUN
ejpam-4911	123	23	∈	∈	PROPN
ejpam-4911	123	24	(	(	PUNCT
ejpam-4911	123	25	2	2	NUM
ejpam-4911	123	26	,	,	PUNCT
ejpam-4911	123	27	1	1	NUM
ejpam-4911	123	28	)	)	PUNCT
ejpam-4911	123	29	−	−	PROPN
ejpam-4911	123	30	d(x	d(x	NOUN
ejpam-4911	123	31	)	)	PUNCT
ejpam-4911	123	32	,	,	PUNCT
ejpam-4911	123	33	then	then	ADV
ejpam-4911	123	34	c2(c1(q	c2(c1(q	NOUN
ejpam-4911	123	35	)	)	PUNCT
ejpam-4911	123	36	)	)	PUNCT
ejpam-4911	124	1	=	=	PUNCT
ejpam-4911	124	2	x.	x.	NOUN
ejpam-4911	124	3	by	by	ADP
ejpam-4911	124	4	lemma	lemma	PROPN
ejpam-4911	124	5	4	4	NUM
ejpam-4911	124	6	,	,	PUNCT
ejpam-4911	124	7	c1(q	c1(q	NOUN
ejpam-4911	124	8	)	)	PUNCT
ejpam-4911	124	9	∩	∩	ADJ
ejpam-4911	124	10	h	h	PROPN
ejpam-4911	124	11	̸=	̸=	PROPN
ejpam-4911	124	12	∅	∅	NOUN
ejpam-4911	124	13	for	for	ADP
ejpam-4911	124	14	every	every	DET
ejpam-4911	124	15	h	h	NOUN
ejpam-4911	124	16	∈	∈	PROPN
ejpam-4911	124	17	µ̃2	µ̃2	PROPN
ejpam-4911	124	18	.	.	PUNCT
ejpam-4911	125	1	take	take	VERB
ejpam-4911	125	2	g	g	NOUN
ejpam-4911	125	3	∈	∈	NOUN
ejpam-4911	125	4	µ̃1	µ̃1	NOUN
ejpam-4911	125	5	we	we	PRON
ejpam-4911	125	6	get	get	VERB
ejpam-4911	125	7	g	g	NOUN
ejpam-4911	125	8	∈	∈	NOUN
ejpam-4911	125	9	µ̃2	µ̃2	PROPN
ejpam-4911	125	10	for	for	ADP
ejpam-4911	125	11	that	that	DET
ejpam-4911	125	12	c1(q	c1(q	NOUN
ejpam-4911	125	13	)	)	PUNCT
ejpam-4911	125	14	∩	∩	NOUN
ejpam-4911	125	15	g	g	PROPN
ejpam-4911	125	16	̸=	̸=	PROPN
ejpam-4911	125	17	∅.	∅.	ADV
ejpam-4911	125	18	since	since	SCONJ
ejpam-4911	125	19	q	q	PROPN
ejpam-4911	125	20	⊂	⊂	PROPN
ejpam-4911	125	21	c2(q	c2(q	PROPN
ejpam-4911	125	22	)	)	PUNCT
ejpam-4911	125	23	we	we	PRON
ejpam-4911	125	24	have	have	VERB
ejpam-4911	125	25	c1(q	c1(q	ADV
ejpam-4911	125	26	)	)	PUNCT
ejpam-4911	125	27	⊂	⊂	PROPN
ejpam-4911	125	28	c1(c2(q	c1(c2(q	PROPN
ejpam-4911	125	29	)	)	PUNCT
ejpam-4911	125	30	)	)	PUNCT
ejpam-4911	125	31	.	.	PUNCT
ejpam-4911	126	1	thus	thus	ADV
ejpam-4911	126	2	,	,	PUNCT
ejpam-4911	126	3	c1(c2(q	c1(c2(q	PROPN
ejpam-4911	126	4	)	)	PUNCT
ejpam-4911	126	5	)	)	PUNCT
ejpam-4911	127	1	∩	∩	NOUN
ejpam-4911	127	2	g	g	PROPN
ejpam-4911	127	3	̸=	̸=	PROPN
ejpam-4911	127	4	∅.	∅.	ADV
ejpam-4911	127	5	since	since	SCONJ
ejpam-4911	127	6	g	g	PROPN
ejpam-4911	127	7	is	be	AUX
ejpam-4911	127	8	an	an	DET
ejpam-4911	127	9	arbitrary	arbitrary	ADJ
ejpam-4911	127	10	non	non	ADJ
ejpam-4911	127	11	-	-	ADJ
ejpam-4911	127	12	null	null	ADJ
ejpam-4911	127	13	µ1	µ1	NOUN
ejpam-4911	127	14	-	-	PUNCT
ejpam-4911	127	15	open	open	NOUN
ejpam-4911	127	16	set	set	NOUN
ejpam-4911	127	17	we	we	PRON
ejpam-4911	127	18	have	have	VERB
ejpam-4911	127	19	c1(c1(c2(q	c1(c1(c2(q	PROPN
ejpam-4911	127	20	)	)	PUNCT
ejpam-4911	127	21	)	)	PUNCT
ejpam-4911	127	22	)	)	PUNCT
ejpam-4911	128	1	=	=	SYM
ejpam-4911	128	2	x	x	X
ejpam-4911	128	3	,	,	PUNCT
ejpam-4911	128	4	by	by	ADP
ejpam-4911	128	5	lemma	lemma	PROPN
ejpam-4911	128	6	4	4	NUM
ejpam-4911	128	7	.	.	PUNCT
ejpam-4911	128	8	hence	hence	ADV
ejpam-4911	128	9	c1(c2(q	c1(c2(q	PROPN
ejpam-4911	128	10	)	)	PUNCT
ejpam-4911	128	11	)	)	PUNCT
ejpam-4911	129	1	=	=	SYM
ejpam-4911	129	2	x	x	X
ejpam-4911	129	3	,	,	PUNCT
ejpam-4911	129	4	by	by	ADP
ejpam-4911	129	5	lemma	lemma	PROPN
ejpam-4911	129	6	5(e	5(e	NUM
ejpam-4911	129	7	)	)	PUNCT
ejpam-4911	129	8	.	.	PUNCT
ejpam-4911	130	1	therefore	therefore	ADV
ejpam-4911	130	2	,	,	PUNCT
ejpam-4911	130	3	q	q	PROPN
ejpam-4911	130	4	∈	∈	PROPN
ejpam-4911	130	5	(	(	PUNCT
ejpam-4911	130	6	1	1	NUM
ejpam-4911	130	7	,	,	PUNCT
ejpam-4911	130	8	2)−d(x	2)−d(x	NUM
ejpam-4911	130	9	)	)	PUNCT
ejpam-4911	130	10	.	.	PUNCT
ejpam-4911	131	1	theorem	theorem	ADJ
ejpam-4911	131	2	8	8	NUM
ejpam-4911	131	3	.	.	PUNCT
ejpam-4911	132	1	let	let	AUX
ejpam-4911	132	2	(	(	PUNCT
ejpam-4911	132	3	x,µ1	x,µ1	NOUN
ejpam-4911	132	4	,	,	PUNCT
ejpam-4911	132	5	µ2	µ2	PROPN
ejpam-4911	132	6	)	)	PUNCT
ejpam-4911	132	7	be	be	VERB
ejpam-4911	132	8	a	a	DET
ejpam-4911	132	9	bgts	bgts	NOUN
ejpam-4911	132	10	and	and	CCONJ
ejpam-4911	132	11	d	d	AUX
ejpam-4911	132	12	be	be	AUX
ejpam-4911	132	13	a	a	DET
ejpam-4911	132	14	non	non	ADJ
ejpam-4911	132	15	-	-	ADJ
ejpam-4911	132	16	null	null	ADJ
ejpam-4911	132	17	subset	subset	NOUN
ejpam-4911	132	18	of	of	ADP
ejpam-4911	132	19	x.	x.	NOUN
ejpam-4911	132	20	if	if	SCONJ
ejpam-4911	132	21	d	d	PROPN
ejpam-4911	132	22	∈	∈	PROPN
ejpam-4911	132	23	(	(	PUNCT
ejpam-4911	132	24	s	s	PROPN
ejpam-4911	132	25	,	,	PUNCT
ejpam-4911	132	26	v)−	v)−	PROPN
ejpam-4911	132	27	d(x	d(x	PROPN
ejpam-4911	132	28	)	)	PUNCT
ejpam-4911	132	29	,	,	PUNCT
ejpam-4911	132	30	then	then	ADV
ejpam-4911	132	31	d	d	X
ejpam-4911	132	32	∩	∩	ADJ
ejpam-4911	132	33	h	h	PROPN
ejpam-4911	132	34	̸=	̸=	PROPN
ejpam-4911	132	35	∅	∅	NOUN
ejpam-4911	132	36	for	for	ADP
ejpam-4911	132	37	every	every	DET
ejpam-4911	132	38	h	h	NOUN
ejpam-4911	132	39	is	be	AUX
ejpam-4911	132	40	a	a	DET
ejpam-4911	132	41	non	non	ADJ
ejpam-4911	132	42	-	-	ADJ
ejpam-4911	132	43	null	null	ADJ
ejpam-4911	132	44	(	(	PUNCT
ejpam-4911	132	45	s	s	NOUN
ejpam-4911	132	46	,	,	PUNCT
ejpam-4911	132	47	v)-open	v)-open	VERB
ejpam-4911	132	48	set	set	VERB
ejpam-4911	132	49	in	in	ADP
ejpam-4911	132	50	x	x	PUNCT
ejpam-4911	132	51	for	for	ADP
ejpam-4911	132	52	s	s	PROPN
ejpam-4911	132	53	,	,	PUNCT
ejpam-4911	132	54	v	v	NOUN
ejpam-4911	132	55	=	=	SYM
ejpam-4911	132	56	1	1	NUM
ejpam-4911	132	57	,	,	PUNCT
ejpam-4911	132	58	2	2	NUM
ejpam-4911	132	59	;	;	PUNCT
ejpam-4911	132	60	s	s	VERB
ejpam-4911	132	61	̸=	̸=	PROPN
ejpam-4911	132	62	v.	v.	ADP
ejpam-4911	132	63	proof	proof	NOUN
ejpam-4911	132	64	.	.	PUNCT
ejpam-4911	133	1	take	take	VERB
ejpam-4911	133	2	s	s	NOUN
ejpam-4911	133	3	=	=	SYM
ejpam-4911	133	4	1	1	NUM
ejpam-4911	133	5	and	and	CCONJ
ejpam-4911	133	6	v	v	NOUN
ejpam-4911	133	7	=	=	SYM
ejpam-4911	133	8	2	2	X
ejpam-4911	133	9	.	.	X
ejpam-4911	133	10	assume	assume	VERB
ejpam-4911	133	11	that	that	SCONJ
ejpam-4911	133	12	,	,	PUNCT
ejpam-4911	133	13	d	d	X
ejpam-4911	133	14	is	be	AUX
ejpam-4911	133	15	(	(	PUNCT
ejpam-4911	133	16	1	1	NUM
ejpam-4911	133	17	,	,	PUNCT
ejpam-4911	133	18	2)-dense	2)-dense	PROPN
ejpam-4911	133	19	.	.	PUNCT
ejpam-4911	134	1	then	then	ADV
ejpam-4911	134	2	c1(c2(d	c1(c2(d	NUM
ejpam-4911	134	3	)	)	PUNCT
ejpam-4911	134	4	)	)	PUNCT
ejpam-4911	135	1	=	=	PUNCT
ejpam-4911	135	2	x.	x.	NOUN
ejpam-4911	135	3	let	let	VERB
ejpam-4911	135	4	h	h	NOUN
ejpam-4911	135	5	be	be	AUX
ejpam-4911	135	6	a	a	DET
ejpam-4911	135	7	non	non	ADJ
ejpam-4911	135	8	-	-	ADJ
ejpam-4911	135	9	null	null	ADJ
ejpam-4911	135	10	(	(	PUNCT
ejpam-4911	135	11	1	1	NUM
ejpam-4911	135	12	,	,	PUNCT
ejpam-4911	135	13	2)-open	2)-open	NUM
ejpam-4911	135	14	set	set	NOUN
ejpam-4911	135	15	.	.	PUNCT
ejpam-4911	136	1	by	by	ADP
ejpam-4911	136	2	lemma	lemma	PROPN
ejpam-4911	136	3	1	1	NUM
ejpam-4911	136	4	,	,	PUNCT
ejpam-4911	136	5	h	h	NOUN
ejpam-4911	136	6	∈	∈	NOUN
ejpam-4911	136	7	µ̃1	µ̃1	NOUN
ejpam-4911	136	8	(	(	PUNCT
ejpam-4911	136	9	3	3	NUM
ejpam-4911	136	10	)	)	PUNCT
ejpam-4911	136	11	h	h	NOUN
ejpam-4911	136	12	∈	∈	PROPN
ejpam-4911	137	1	µ̃2	µ̃2	PROPN
ejpam-4911	137	2	(	(	PUNCT
ejpam-4911	137	3	4	4	NUM
ejpam-4911	137	4	)	)	PUNCT
ejpam-4911	137	5	then	then	ADV
ejpam-4911	137	6	c2(d)∩h	c2(d)∩h	NOUN
ejpam-4911	137	7	̸=	̸=	PROPN
ejpam-4911	137	8	∅	∅	NOUN
ejpam-4911	137	9	,	,	PUNCT
ejpam-4911	137	10	by	by	ADP
ejpam-4911	137	11	lemma	lemma	PROPN
ejpam-4911	137	12	4	4	NUM
ejpam-4911	137	13	and	and	CCONJ
ejpam-4911	137	14	(	(	PUNCT
ejpam-4911	137	15	3	3	NUM
ejpam-4911	137	16	)	)	PUNCT
ejpam-4911	137	17	.	.	PUNCT
ejpam-4911	138	1	from	from	ADP
ejpam-4911	138	2	(	(	PUNCT
ejpam-4911	138	3	4	4	NUM
ejpam-4911	138	4	)	)	PUNCT
ejpam-4911	138	5	and	and	CCONJ
ejpam-4911	138	6	c2(d)∩h	c2(d)∩h	NOUN
ejpam-4911	138	7	̸=	̸=	PROPN
ejpam-4911	138	8	∅	∅	NOUN
ejpam-4911	138	9	we	we	PRON
ejpam-4911	138	10	have	have	VERB
ejpam-4911	138	11	d∩h	d∩h	NOUN
ejpam-4911	138	12	̸=	̸=	PROPN
ejpam-4911	138	13	∅	∅	NOUN
ejpam-4911	138	14	,	,	PUNCT
ejpam-4911	138	15	by	by	ADP
ejpam-4911	138	16	lemma	lemma	PROPN
ejpam-4911	138	17	3	3	NUM
ejpam-4911	138	18	.	.	PUNCT
ejpam-4911	139	1	thus	thus	ADV
ejpam-4911	139	2	,	,	PUNCT
ejpam-4911	139	3	d	d	ADP
ejpam-4911	139	4	∩h	∩h	PROPN
ejpam-4911	139	5	̸=	̸=	PROPN
ejpam-4911	139	6	∅	∅	NOUN
ejpam-4911	139	7	for	for	ADP
ejpam-4911	139	8	every	every	DET
ejpam-4911	139	9	h	h	NOUN
ejpam-4911	139	10	is	be	AUX
ejpam-4911	139	11	a	a	DET
ejpam-4911	139	12	non	non	ADJ
ejpam-4911	139	13	-	-	ADJ
ejpam-4911	139	14	null	null	ADJ
ejpam-4911	139	15	(	(	PUNCT
ejpam-4911	139	16	1	1	NUM
ejpam-4911	139	17	,	,	PUNCT
ejpam-4911	139	18	2)-open	2)-open	NUM
ejpam-4911	139	19	set	set	NOUN
ejpam-4911	139	20	.	.	PUNCT
ejpam-4911	140	1	take	take	VERB
ejpam-4911	140	2	s	s	NOUN
ejpam-4911	140	3	=	=	SYM
ejpam-4911	140	4	2	2	NUM
ejpam-4911	140	5	and	and	CCONJ
ejpam-4911	140	6	v	v	NOUN
ejpam-4911	140	7	=	=	SYM
ejpam-4911	140	8	1	1	NUM
ejpam-4911	140	9	.	.	PUNCT
ejpam-4911	141	1	by	by	ADP
ejpam-4911	141	2	similar	similar	ADJ
ejpam-4911	141	3	considerations	consideration	NOUN
ejpam-4911	141	4	in	in	ADP
ejpam-4911	141	5	the	the	DET
ejpam-4911	141	6	above	above	ADJ
ejpam-4911	141	7	case	case	NOUN
ejpam-4911	141	8	,	,	PUNCT
ejpam-4911	141	9	we	we	PRON
ejpam-4911	141	10	get	get	VERB
ejpam-4911	141	11	the	the	DET
ejpam-4911	141	12	proof	proof	NOUN
ejpam-4911	141	13	.	.	PUNCT
ejpam-4911	142	1	theorem	theorem	NOUN
ejpam-4911	142	2	9	9	NUM
ejpam-4911	142	3	.	.	PUNCT
ejpam-4911	143	1	let	let	AUX
ejpam-4911	143	2	(	(	PUNCT
ejpam-4911	143	3	x,µ1	x,µ1	NOUN
ejpam-4911	143	4	,	,	PUNCT
ejpam-4911	143	5	µ2	µ2	PROPN
ejpam-4911	143	6	)	)	PUNCT
ejpam-4911	143	7	be	be	VERB
ejpam-4911	143	8	a	a	DET
ejpam-4911	143	9	bgts	bgts	NOUN
ejpam-4911	143	10	,	,	PUNCT
ejpam-4911	144	1	d	d	X
ejpam-4911	144	2	⊂	⊂	PROPN
ejpam-4911	144	3	x.	x.	NOUN
ejpam-4911	144	4	if	if	SCONJ
ejpam-4911	144	5	d	d	PROPN
ejpam-4911	144	6	∩	∩	ADJ
ejpam-4911	144	7	h	h	PROPN
ejpam-4911	144	8	̸=	̸=	PROPN
ejpam-4911	144	9	∅	∅	NOUN
ejpam-4911	144	10	for	for	ADP
ejpam-4911	144	11	every	every	DET
ejpam-4911	144	12	h	h	NOUN
ejpam-4911	144	13	̸=	̸=	PROPN
ejpam-4911	144	14	∅	∅	NOUN
ejpam-4911	144	15	is	be	AUX
ejpam-4911	144	16	µ(s	µ(	NOUN
ejpam-4911	144	17	,	,	PUNCT
ejpam-4911	144	18	v)-open	v)-open	ADJ
ejpam-4911	144	19	,	,	PUNCT
ejpam-4911	144	20	then	then	ADV
ejpam-4911	144	21	d	d	PROPN
ejpam-4911	144	22	∈	∈	PROPN
ejpam-4911	144	23	(	(	PUNCT
ejpam-4911	144	24	s	s	NOUN
ejpam-4911	144	25	,	,	PUNCT
ejpam-4911	144	26	v)−d(x	v)−d(x	NUM
ejpam-4911	144	27	)	)	PUNCT
ejpam-4911	144	28	;	;	PUNCT
ejpam-4911	144	29	s	s	X
ejpam-4911	144	30	,	,	PUNCT
ejpam-4911	144	31	v	v	NOUN
ejpam-4911	144	32	=	=	SYM
ejpam-4911	144	33	1	1	NUM
ejpam-4911	144	34	,	,	PUNCT
ejpam-4911	144	35	2	2	NUM
ejpam-4911	144	36	and	and	CCONJ
ejpam-4911	144	37	s	s	VERB
ejpam-4911	144	38	̸=	̸=	PROPN
ejpam-4911	144	39	v.	v.	ADP
ejpam-4911	144	40	proof	proof	NOUN
ejpam-4911	144	41	.	.	PUNCT
ejpam-4911	145	1	we	we	PRON
ejpam-4911	145	2	give	give	VERB
ejpam-4911	145	3	the	the	DET
ejpam-4911	145	4	detailed	detailed	ADJ
ejpam-4911	145	5	proof	proof	NOUN
ejpam-4911	145	6	for	for	ADP
ejpam-4911	145	7	s	s	NOUN
ejpam-4911	145	8	=	=	SYM
ejpam-4911	145	9	1	1	NUM
ejpam-4911	145	10	and	and	CCONJ
ejpam-4911	145	11	v	v	NOUN
ejpam-4911	145	12	=	=	SYM
ejpam-4911	145	13	2	2	NUM
ejpam-4911	145	14	only	only	ADV
ejpam-4911	145	15	.	.	PUNCT
ejpam-4911	146	1	suppose	suppose	VERB
ejpam-4911	146	2	that	that	SCONJ
ejpam-4911	146	3	d	d	PROPN
ejpam-4911	146	4	∩h	∩h	PROPN
ejpam-4911	146	5	̸=	̸=	PROPN
ejpam-4911	146	6	∅	∅	NOUN
ejpam-4911	146	7	for	for	ADP
ejpam-4911	146	8	every	every	DET
ejpam-4911	146	9	h	h	NOUN
ejpam-4911	146	10	is	be	AUX
ejpam-4911	146	11	non	non	ADJ
ejpam-4911	146	12	-	-	ADJ
ejpam-4911	146	13	null	null	ADJ
ejpam-4911	146	14	µ(1,2)-open	µ(1,2)-open	NOUN
ejpam-4911	146	15	.	.	PUNCT
ejpam-4911	147	1	by	by	ADP
ejpam-4911	147	2	theorem	theorem	NOUN
ejpam-4911	147	3	4	4	NUM
ejpam-4911	147	4	,	,	PUNCT
ejpam-4911	147	5	we	we	PRON
ejpam-4911	147	6	have	have	VERB
ejpam-4911	147	7	to	to	PART
ejpam-4911	147	8	prove	prove	VERB
ejpam-4911	147	9	d	d	NOUN
ejpam-4911	147	10	is	be	AUX
ejpam-4911	147	11	µ2	µ2	ADJ
ejpam-4911	147	12	-	-	PUNCT
ejpam-4911	147	13	dense	dense	ADJ
ejpam-4911	147	14	.	.	PUNCT
ejpam-4911	148	1	let	let	VERB
ejpam-4911	148	2	b	b	X
ejpam-4911	148	3	∈	∈	VERB
ejpam-4911	148	4	µ̃2	µ̃2	PROPN
ejpam-4911	148	5	.	.	PUNCT
ejpam-4911	149	1	then	then	ADV
ejpam-4911	149	2	b	b	PROPN
ejpam-4911	149	3	is	be	AUX
ejpam-4911	149	4	a	a	DET
ejpam-4911	149	5	non	non	ADJ
ejpam-4911	149	6	-	-	ADJ
ejpam-4911	149	7	null	null	ADJ
ejpam-4911	149	8	µ(1,2)-open	µ(1,2)-open	NOUN
ejpam-4911	149	9	set	set	VERB
ejpam-4911	149	10	in	in	ADP
ejpam-4911	149	11	x	x	PROPN
ejpam-4911	149	12	,	,	PUNCT
ejpam-4911	149	13	by	by	ADP
ejpam-4911	149	14	lemma	lemma	PROPN
ejpam-4911	149	15	2	2	NUM
ejpam-4911	149	16	.	.	PUNCT
ejpam-4911	149	17	by	by	ADP
ejpam-4911	149	18	assumption	assumption	NOUN
ejpam-4911	149	19	,	,	PUNCT
ejpam-4911	149	20	d	d	PROPN
ejpam-4911	149	21	∩b	∩b	NOUN
ejpam-4911	149	22	̸=	̸=	PROPN
ejpam-4911	149	23	∅.	∅.	VERB
ejpam-4911	149	24	therefore	therefore	ADV
ejpam-4911	149	25	,	,	PUNCT
ejpam-4911	149	26	d	d	X
ejpam-4911	149	27	is	be	AUX
ejpam-4911	149	28	a	a	DET
ejpam-4911	149	29	µ2	µ2	ADJ
ejpam-4911	149	30	-	-	PUNCT
ejpam-4911	149	31	dense	dense	ADJ
ejpam-4911	149	32	set	set	NOUN
ejpam-4911	149	33	.	.	PUNCT
ejpam-4911	150	1	hence	hence	ADV
ejpam-4911	150	2	d	d	PROPN
ejpam-4911	150	3	is	be	AUX
ejpam-4911	150	4	a	a	DET
ejpam-4911	150	5	(	(	PUNCT
ejpam-4911	150	6	1	1	NUM
ejpam-4911	150	7	,	,	PUNCT
ejpam-4911	150	8	2)-dense	2)-dense	NUM
ejpam-4911	150	9	set	set	NOUN
ejpam-4911	150	10	.	.	PUNCT
ejpam-4911	151	1	y.	y.	PROPN
ejpam-4911	151	2	farhat	farhat	PROPN
ejpam-4911	151	3	,	,	PUNCT
ejpam-4911	151	4	v.	v.	ADP
ejpam-4911	151	5	subramanian	subramanian	PROPN
ejpam-4911	151	6	/	/	SYM
ejpam-4911	151	7	eur	eur	PROPN
ejpam-4911	151	8	.	.	PUNCT
ejpam-4911	152	1	j.	j.	PROPN
ejpam-4911	152	2	pure	pure	PROPN
ejpam-4911	152	3	appl	appl	PROPN
ejpam-4911	152	4	.	.	PROPN
ejpam-4911	152	5	math	math	PROPN
ejpam-4911	152	6	,	,	PUNCT
ejpam-4911	152	7	16	16	NUM
ejpam-4911	152	8	(	(	PUNCT
ejpam-4911	152	9	4	4	NUM
ejpam-4911	152	10	)	)	PUNCT
ejpam-4911	152	11	(	(	PUNCT
ejpam-4911	152	12	2023	2023	NUM
ejpam-4911	152	13	)	)	PUNCT
ejpam-4911	152	14	,	,	PUNCT
ejpam-4911	152	15	2049	2049	NUM
ejpam-4911	152	16	-	-	SYM
ejpam-4911	152	17	2065	2065	NUM
ejpam-4911	152	18	2054	2054	NUM
ejpam-4911	152	19	the	the	DET
ejpam-4911	152	20	below	below	ADJ
ejpam-4911	152	21	example	example	NOUN
ejpam-4911	152	22	10	10	NUM
ejpam-4911	152	23	describes	describe	VERB
ejpam-4911	152	24	that	that	SCONJ
ejpam-4911	152	25	the	the	DET
ejpam-4911	152	26	converse	converse	NOUN
ejpam-4911	152	27	part	part	NOUN
ejpam-4911	152	28	of	of	ADP
ejpam-4911	152	29	theorem	theorem	ADJ
ejpam-4911	152	30	9	9	NUM
ejpam-4911	152	31	is	be	AUX
ejpam-4911	152	32	generally	generally	ADV
ejpam-4911	152	33	not	not	PART
ejpam-4911	152	34	true	true	ADJ
ejpam-4911	152	35	.	.	PUNCT
ejpam-4911	153	1	example	example	NOUN
ejpam-4911	153	2	10	10	NUM
ejpam-4911	153	3	.	.	PUNCT
ejpam-4911	154	1	take	take	VERB
ejpam-4911	154	2	x	x	PUNCT
ejpam-4911	154	3	=	=	PRON
ejpam-4911	154	4	{	{	PUNCT
ejpam-4911	154	5	e	e	PROPN
ejpam-4911	154	6	,	,	PUNCT
ejpam-4911	154	7	f	f	PROPN
ejpam-4911	154	8	,	,	PUNCT
ejpam-4911	154	9	k	k	NOUN
ejpam-4911	154	10	,	,	PUNCT
ejpam-4911	154	11	l	l	NOUN
ejpam-4911	154	12	}	}	PUNCT
ejpam-4911	154	13	;	;	PUNCT
ejpam-4911	154	14	µ1	µ1	PROPN
ejpam-4911	154	15	=	=	SYM
ejpam-4911	154	16	{	{	PUNCT
ejpam-4911	154	17	∅	∅	NOUN
ejpam-4911	154	18	,	,	PUNCT
ejpam-4911	154	19	{	{	PUNCT
ejpam-4911	154	20	e	e	NOUN
ejpam-4911	154	21	,	,	PUNCT
ejpam-4911	154	22	f	f	PROPN
ejpam-4911	154	23	}	}	PUNCT
ejpam-4911	154	24	,	,	PUNCT
ejpam-4911	154	25	{	{	PUNCT
ejpam-4911	154	26	f	f	X
ejpam-4911	154	27	,	,	PUNCT
ejpam-4911	154	28	l	l	NOUN
ejpam-4911	154	29	}	}	PUNCT
ejpam-4911	154	30	,	,	PUNCT
ejpam-4911	154	31	{	{	PUNCT
ejpam-4911	154	32	e	e	NOUN
ejpam-4911	154	33	,	,	PUNCT
ejpam-4911	154	34	f	f	X
ejpam-4911	154	35	,	,	PUNCT
ejpam-4911	154	36	l	l	NOUN
ejpam-4911	154	37	}	}	PUNCT
ejpam-4911	154	38	}	}	PUNCT
ejpam-4911	154	39	and	and	CCONJ
ejpam-4911	154	40	µ2	µ2	PROPN
ejpam-4911	154	41	=	=	PUNCT
ejpam-4911	154	42	{	{	PUNCT
ejpam-4911	154	43	∅	∅	NOUN
ejpam-4911	154	44	,	,	PUNCT
ejpam-4911	154	45	{	{	PUNCT
ejpam-4911	154	46	e	e	NOUN
ejpam-4911	154	47	,	,	PUNCT
ejpam-4911	154	48	k	k	NOUN
ejpam-4911	154	49	}	}	PUNCT
ejpam-4911	154	50	,	,	PUNCT
ejpam-4911	154	51	{	{	PUNCT
ejpam-4911	154	52	f	f	X
ejpam-4911	154	53	,	,	PUNCT
ejpam-4911	154	54	k	k	NOUN
ejpam-4911	154	55	}	}	PUNCT
ejpam-4911	154	56	,	,	PUNCT
ejpam-4911	154	57	{	{	PUNCT
ejpam-4911	154	58	e	e	NOUN
ejpam-4911	154	59	,	,	PUNCT
ejpam-4911	154	60	f	f	PROPN
ejpam-4911	154	61	,	,	PUNCT
ejpam-4911	154	62	k	k	NOUN
ejpam-4911	154	63	}	}	PUNCT
ejpam-4911	154	64	}	}	PUNCT
ejpam-4911	154	65	.	.	PUNCT
ejpam-4911	155	1	then	then	ADV
ejpam-4911	155	2	µ(1,2	µ(1,2	X
ejpam-4911	155	3	)	)	PUNCT
ejpam-4911	155	4	=	=	SYM
ejpam-4911	155	5	{	{	PUNCT
ejpam-4911	155	6	∅	∅	NOUN
ejpam-4911	155	7	,	,	PUNCT
ejpam-4911	155	8	{	{	PUNCT
ejpam-4911	155	9	e	e	NOUN
ejpam-4911	155	10	}	}	PUNCT
ejpam-4911	155	11	,	,	PUNCT
ejpam-4911	155	12	{	{	PUNCT
ejpam-4911	155	13	f	f	X
ejpam-4911	155	14	}	}	PUNCT
ejpam-4911	155	15	,	,	PUNCT
ejpam-4911	155	16	{	{	PUNCT
ejpam-4911	155	17	l	l	NOUN
ejpam-4911	155	18	}	}	PUNCT
ejpam-4911	155	19	,	,	PUNCT
ejpam-4911	155	20	{	{	PUNCT
ejpam-4911	155	21	e	e	NOUN
ejpam-4911	155	22	,	,	PUNCT
ejpam-4911	155	23	f	f	PROPN
ejpam-4911	155	24	}	}	PUNCT
ejpam-4911	155	25	,	,	PUNCT
ejpam-4911	155	26	{	{	PUNCT
ejpam-4911	155	27	e	e	NOUN
ejpam-4911	155	28	,	,	PUNCT
ejpam-4911	155	29	k	k	NOUN
ejpam-4911	155	30	}	}	PUNCT
ejpam-4911	155	31	,	,	PUNCT
ejpam-4911	155	32	{	{	PUNCT
ejpam-4911	155	33	e	e	NOUN
ejpam-4911	155	34	,	,	PUNCT
ejpam-4911	155	35	l	l	NOUN
ejpam-4911	155	36	}	}	PUNCT
ejpam-4911	155	37	,	,	PUNCT
ejpam-4911	155	38	{	{	PUNCT
ejpam-4911	155	39	f	f	X
ejpam-4911	155	40	,	,	PUNCT
ejpam-4911	155	41	k	k	NOUN
ejpam-4911	155	42	}	}	PUNCT
ejpam-4911	155	43	,	,	PUNCT
ejpam-4911	155	44	{	{	PUNCT
ejpam-4911	155	45	f	f	X
ejpam-4911	155	46	,	,	PUNCT
ejpam-4911	155	47	l	l	NOUN
ejpam-4911	155	48	}	}	PUNCT
ejpam-4911	155	49	,	,	PUNCT
ejpam-4911	155	50	{	{	PUNCT
ejpam-4911	155	51	e	e	NOUN
ejpam-4911	155	52	,	,	PUNCT
ejpam-4911	155	53	f	f	PROPN
ejpam-4911	155	54	,	,	PUNCT
ejpam-4911	155	55	k	k	NOUN
ejpam-4911	155	56	}	}	PUNCT
ejpam-4911	155	57	,	,	PUNCT
ejpam-4911	155	58	{	{	PUNCT
ejpam-4911	155	59	e	e	NOUN
ejpam-4911	155	60	,	,	PUNCT
ejpam-4911	155	61	f	f	X
ejpam-4911	155	62	,	,	PUNCT
ejpam-4911	155	63	l	l	NOUN
ejpam-4911	155	64	}	}	PUNCT
ejpam-4911	155	65	}	}	PUNCT
ejpam-4911	155	66	and	and	CCONJ
ejpam-4911	155	67	µ(2,1	µ(2,1	X
ejpam-4911	155	68	)	)	PUNCT
ejpam-4911	155	69	=	=	SYM
ejpam-4911	155	70	{	{	PUNCT
ejpam-4911	155	71	∅	∅	NOUN
ejpam-4911	155	72	,	,	PUNCT
ejpam-4911	155	73	{	{	PUNCT
ejpam-4911	155	74	e	e	NOUN
ejpam-4911	155	75	}	}	PUNCT
ejpam-4911	155	76	,	,	PUNCT
ejpam-4911	155	77	{	{	PUNCT
ejpam-4911	155	78	f	f	X
ejpam-4911	155	79	}	}	PUNCT
ejpam-4911	155	80	,	,	PUNCT
ejpam-4911	155	81	{	{	PUNCT
ejpam-4911	155	82	k	k	X
ejpam-4911	155	83	}	}	PUNCT
ejpam-4911	155	84	,	,	PUNCT
ejpam-4911	155	85	{	{	PUNCT
ejpam-4911	155	86	e	e	NOUN
ejpam-4911	155	87	,	,	PUNCT
ejpam-4911	155	88	f	f	PROPN
ejpam-4911	155	89	}	}	PUNCT
ejpam-4911	155	90	,	,	PUNCT
ejpam-4911	155	91	{	{	PUNCT
ejpam-4911	155	92	e	e	NOUN
ejpam-4911	155	93	,	,	PUNCT
ejpam-4911	155	94	k	k	NOUN
ejpam-4911	155	95	}	}	PUNCT
ejpam-4911	155	96	,	,	PUNCT
ejpam-4911	155	97	{	{	PUNCT
ejpam-4911	155	98	f	f	X
ejpam-4911	155	99	,	,	PUNCT
ejpam-4911	155	100	k	k	NOUN
ejpam-4911	155	101	}	}	PUNCT
ejpam-4911	155	102	,	,	PUNCT
ejpam-4911	155	103	{	{	PUNCT
ejpam-4911	155	104	f	f	X
ejpam-4911	155	105	,	,	PUNCT
ejpam-4911	155	106	l	l	NOUN
ejpam-4911	155	107	}	}	PUNCT
ejpam-4911	155	108	,	,	PUNCT
ejpam-4911	155	109	{	{	PUNCT
ejpam-4911	155	110	e	e	NOUN
ejpam-4911	155	111	,	,	PUNCT
ejpam-4911	155	112	f	f	PROPN
ejpam-4911	155	113	,	,	PUNCT
ejpam-4911	155	114	k	k	NOUN
ejpam-4911	155	115	}	}	PUNCT
ejpam-4911	155	116	,	,	PUNCT
ejpam-4911	155	117	{	{	PUNCT
ejpam-4911	155	118	e	e	NOUN
ejpam-4911	155	119	,	,	PUNCT
ejpam-4911	155	120	f	f	X
ejpam-4911	155	121	,	,	PUNCT
ejpam-4911	155	122	l	l	NOUN
ejpam-4911	155	123	}	}	PUNCT
ejpam-4911	155	124	,	,	PUNCT
ejpam-4911	155	125	{	{	PUNCT
ejpam-4911	155	126	f	f	X
ejpam-4911	155	127	,	,	PUNCT
ejpam-4911	155	128	k	k	NOUN
ejpam-4911	155	129	,	,	PUNCT
ejpam-4911	155	130	l	l	NOUN
ejpam-4911	155	131	}	}	PUNCT
ejpam-4911	155	132	}	}	PUNCT
ejpam-4911	155	133	.	.	PUNCT
ejpam-4911	156	1	take	take	VERB
ejpam-4911	156	2	p	p	NOUN
ejpam-4911	156	3	=	=	PUNCT
ejpam-4911	156	4	{	{	PUNCT
ejpam-4911	156	5	e	e	NOUN
ejpam-4911	156	6	}	}	PUNCT
ejpam-4911	156	7	.	.	PUNCT
ejpam-4911	157	1	then	then	ADV
ejpam-4911	157	2	p	p	PROPN
ejpam-4911	157	3	∈	∈	PROPN
ejpam-4911	157	4	(	(	PUNCT
ejpam-4911	157	5	1	1	NUM
ejpam-4911	157	6	,	,	PUNCT
ejpam-4911	157	7	2	2	NUM
ejpam-4911	157	8	)	)	PUNCT
ejpam-4911	157	9	−	−	PROPN
ejpam-4911	157	10	d(x	d(x	NOUN
ejpam-4911	157	11	)	)	PUNCT
ejpam-4911	157	12	.	.	PUNCT
ejpam-4911	158	1	but	but	CCONJ
ejpam-4911	158	2	p	p	NOUN
ejpam-4911	158	3	∩	∩	ADJ
ejpam-4911	158	4	q	q	NOUN
ejpam-4911	158	5	=	=	NOUN
ejpam-4911	158	6	∅	∅	NOUN
ejpam-4911	158	7	where	where	SCONJ
ejpam-4911	158	8	q	q	NOUN
ejpam-4911	158	9	=	=	PUNCT
ejpam-4911	158	10	{	{	PUNCT
ejpam-4911	158	11	l	l	NOUN
ejpam-4911	158	12	}	}	PUNCT
ejpam-4911	158	13	is	be	AUX
ejpam-4911	158	14	a	a	DET
ejpam-4911	158	15	non	non	ADJ
ejpam-4911	158	16	-	-	ADJ
ejpam-4911	158	17	null	null	ADJ
ejpam-4911	158	18	µ(1,2)-open	µ(1,2)-open	ADJ
ejpam-4911	158	19	set	set	NOUN
ejpam-4911	158	20	.	.	PUNCT
ejpam-4911	159	1	let	let	VERB
ejpam-4911	159	2	m	m	VERB
ejpam-4911	159	3	=	=	PUNCT
ejpam-4911	159	4	{	{	PUNCT
ejpam-4911	159	5	f	f	X
ejpam-4911	159	6	}	}	PUNCT
ejpam-4911	159	7	⊂	⊂	PROPN
ejpam-4911	159	8	x.	x.	NOUN
ejpam-4911	160	1	then	then	ADV
ejpam-4911	160	2	m	m	VERB
ejpam-4911	160	3	∈	∈	NOUN
ejpam-4911	160	4	(	(	PUNCT
ejpam-4911	160	5	2	2	NUM
ejpam-4911	160	6	,	,	PUNCT
ejpam-4911	160	7	1	1	NUM
ejpam-4911	160	8	)	)	PUNCT
ejpam-4911	160	9	−	−	PROPN
ejpam-4911	160	10	d(x	d(x	NOUN
ejpam-4911	160	11	)	)	PUNCT
ejpam-4911	160	12	.	.	PUNCT
ejpam-4911	161	1	but	but	CCONJ
ejpam-4911	161	2	m	m	PROPN
ejpam-4911	161	3	∩	∩	ADJ
ejpam-4911	161	4	l	l	NOUN
ejpam-4911	161	5	=	=	NOUN
ejpam-4911	161	6	∅	∅	NOUN
ejpam-4911	161	7	where	where	SCONJ
ejpam-4911	161	8	l	l	NOUN
ejpam-4911	161	9	=	=	PUNCT
ejpam-4911	161	10	{	{	PUNCT
ejpam-4911	161	11	e	e	NOUN
ejpam-4911	161	12	}	}	PUNCT
ejpam-4911	161	13	is	be	AUX
ejpam-4911	161	14	a	a	DET
ejpam-4911	161	15	non	non	ADJ
ejpam-4911	161	16	-	-	ADJ
ejpam-4911	161	17	null	null	ADJ
ejpam-4911	161	18	µ(2,1)-open	µ(2,1)-open	ADJ
ejpam-4911	161	19	set	set	NOUN
ejpam-4911	161	20	.	.	PUNCT
ejpam-4911	162	1	q	q	PROPN
ejpam-4911	162	2	∈	∈	PROPN
ejpam-4911	162	3	µ̃s	µ̃s	NOUN
ejpam-4911	162	4	q	q	NOUN
ejpam-4911	162	5	is	be	AUX
ejpam-4911	162	6	(	(	PUNCT
ejpam-4911	162	7	s	s	X
ejpam-4911	162	8	,	,	PUNCT
ejpam-4911	162	9	v)−	v)−	PROPN
ejpam-4911	162	10	µ−	µ−	PROPN
ejpam-4911	162	11	semi	semi	ADV
ejpam-4911	162	12	open	open	ADJ
ejpam-4911	162	13	.	.	PUNCT
ejpam-4911	163	1	q	q	PUNCT
ejpam-4911	163	2	is	be	AUX
ejpam-4911	163	3	(	(	PUNCT
ejpam-4911	163	4	s	s	X
ejpam-4911	163	5	,	,	PUNCT
ejpam-4911	163	6	v)−	v)−	PROPN
ejpam-4911	163	7	µ−	µ−	PROPN
ejpam-4911	163	8	preopen	preopen	NOUN
ejpam-4911	163	9	q	q	NOUN
ejpam-4911	163	10	is	be	AUX
ejpam-4911	163	11	(	(	PUNCT
ejpam-4911	163	12	s	s	X
ejpam-4911	163	13	,	,	PUNCT
ejpam-4911	163	14	v)−	v)−	NOUN
ejpam-4911	163	15	µ−	µ−	PROPN
ejpam-4911	163	16	α−	α−	PART
ejpam-4911	163	17	open	open	VERB
ejpam-4911	163	18	the	the	DET
ejpam-4911	163	19	following	follow	VERB
ejpam-4911	163	20	lemma	lemma	PROPN
ejpam-4911	163	21	6	6	NUM
ejpam-4911	163	22	describes	describe	VERB
ejpam-4911	163	23	the	the	DET
ejpam-4911	163	24	above	above	ADJ
ejpam-4911	163	25	diagram	diagram	NOUN
ejpam-4911	163	26	.	.	PUNCT
ejpam-4911	164	1	lemma	lemma	PROPN
ejpam-4911	164	2	6	6	NUM
ejpam-4911	164	3	.	.	PUNCT
ejpam-4911	165	1	let	let	AUX
ejpam-4911	165	2	(	(	PUNCT
ejpam-4911	165	3	x,µ1	x,µ1	NOUN
ejpam-4911	165	4	,	,	PUNCT
ejpam-4911	165	5	µ2	µ2	PROPN
ejpam-4911	165	6	)	)	PUNCT
ejpam-4911	165	7	be	be	AUX
ejpam-4911	165	8	a	a	DET
ejpam-4911	165	9	bgts	bgts	NOUN
ejpam-4911	165	10	.	.	PUNCT
ejpam-4911	166	1	if	if	SCONJ
ejpam-4911	166	2	q	q	PROPN
ejpam-4911	166	3	∈	∈	PROPN
ejpam-4911	166	4	µ̃s	µ̃s	NOUN
ejpam-4911	166	5	,	,	PUNCT
ejpam-4911	166	6	then	then	ADV
ejpam-4911	166	7	the	the	DET
ejpam-4911	166	8	below	below	ADJ
ejpam-4911	166	9	results	result	NOUN
ejpam-4911	166	10	are	be	AUX
ejpam-4911	166	11	true	true	ADJ
ejpam-4911	166	12	.	.	PUNCT
ejpam-4911	167	1	(	(	PUNCT
ejpam-4911	167	2	a	a	X
ejpam-4911	167	3	)	)	PUNCT
ejpam-4911	167	4	q	q	NOUN
ejpam-4911	167	5	is	be	AUX
ejpam-4911	167	6	(	(	PUNCT
ejpam-4911	167	7	s	s	X
ejpam-4911	167	8	,	,	PUNCT
ejpam-4911	167	9	v)-µ-semi	v)-µ-semi	ADV
ejpam-4911	167	10	open	open	ADJ
ejpam-4911	167	11	.	.	PUNCT
ejpam-4911	168	1	(	(	PUNCT
ejpam-4911	168	2	b	b	X
ejpam-4911	168	3	)	)	PUNCT
ejpam-4911	168	4	q	q	NOUN
ejpam-4911	168	5	is	be	AUX
ejpam-4911	168	6	(	(	PUNCT
ejpam-4911	168	7	s	s	X
ejpam-4911	168	8	,	,	PUNCT
ejpam-4911	168	9	v)-µ-preopen	v)-µ-preopen	ADJ
ejpam-4911	168	10	.	.	PUNCT
ejpam-4911	169	1	(	(	PUNCT
ejpam-4911	169	2	c	c	X
ejpam-4911	169	3	)	)	PUNCT
ejpam-4911	169	4	q	q	X
ejpam-4911	169	5	is	be	AUX
ejpam-4911	169	6	(	(	PUNCT
ejpam-4911	169	7	s	s	X
ejpam-4911	169	8	,	,	PUNCT
ejpam-4911	169	9	v)-µ-α	v)-µ-α	NOUN
ejpam-4911	169	10	-	-	PUNCT
ejpam-4911	169	11	open	open	ADJ
ejpam-4911	169	12	where	where	SCONJ
ejpam-4911	169	13	s	s	X
ejpam-4911	169	14	,	,	PUNCT
ejpam-4911	169	15	v	v	NOUN
ejpam-4911	169	16	=	=	SYM
ejpam-4911	169	17	1	1	NUM
ejpam-4911	169	18	,	,	PUNCT
ejpam-4911	169	19	2	2	NUM
ejpam-4911	169	20	and	and	CCONJ
ejpam-4911	169	21	s	s	VERB
ejpam-4911	169	22	̸=	̸=	PROPN
ejpam-4911	169	23	v.	v.	ADP
ejpam-4911	169	24	proof	proof	NOUN
ejpam-4911	169	25	.	.	PUNCT
ejpam-4911	170	1	we	we	PRON
ejpam-4911	170	2	give	give	VERB
ejpam-4911	170	3	the	the	DET
ejpam-4911	170	4	detailed	detailed	ADJ
ejpam-4911	170	5	proof	proof	NOUN
ejpam-4911	170	6	for	for	ADP
ejpam-4911	170	7	(	(	PUNCT
ejpam-4911	170	8	b	b	NOUN
ejpam-4911	170	9	)	)	PUNCT
ejpam-4911	170	10	only	only	ADV
ejpam-4911	170	11	.	.	PUNCT
ejpam-4911	171	1	suppose	suppose	VERB
ejpam-4911	171	2	that	that	SCONJ
ejpam-4911	171	3	,	,	PUNCT
ejpam-4911	171	4	q	q	PROPN
ejpam-4911	171	5	∈	∈	PROPN
ejpam-4911	171	6	µ̃s	µ̃s	NOUN
ejpam-4911	171	7	for	for	ADP
ejpam-4911	171	8	s	s	NOUN
ejpam-4911	171	9	=	=	SYM
ejpam-4911	171	10	1	1	NUM
ejpam-4911	171	11	,	,	PUNCT
ejpam-4911	171	12	2	2	NUM
ejpam-4911	171	13	.	.	PUNCT
ejpam-4911	171	14	then	then	ADV
ejpam-4911	171	15	is(q	is(q	NOUN
ejpam-4911	171	16	)	)	PUNCT
ejpam-4911	171	17	=	=	SYM
ejpam-4911	172	1	q	q	PROPN
ejpam-4911	172	2	for	for	ADP
ejpam-4911	172	3	s	s	NOUN
ejpam-4911	172	4	=	=	SYM
ejpam-4911	172	5	1	1	NUM
ejpam-4911	172	6	,	,	PUNCT
ejpam-4911	172	7	2	2	NUM
ejpam-4911	172	8	.	.	PUNCT
ejpam-4911	173	1	since	since	SCONJ
ejpam-4911	173	2	q	q	PROPN
ejpam-4911	173	3	⊂	⊂	PROPN
ejpam-4911	173	4	cv(q	cv(q	X
ejpam-4911	173	5	)	)	PUNCT
ejpam-4911	173	6	for	for	ADP
ejpam-4911	173	7	v	v	NOUN
ejpam-4911	173	8	=	=	SYM
ejpam-4911	173	9	1	1	NUM
ejpam-4911	173	10	,	,	PUNCT
ejpam-4911	173	11	2	2	NUM
ejpam-4911	173	12	we	we	PRON
ejpam-4911	173	13	have	have	VERB
ejpam-4911	173	14	is(q	is(q	NOUN
ejpam-4911	173	15	)	)	PUNCT
ejpam-4911	173	16	⊂	⊂	PROPN
ejpam-4911	173	17	is(cv(q	is(cv(q	NOUN
ejpam-4911	173	18	)	)	PUNCT
ejpam-4911	173	19	)	)	PUNCT
ejpam-4911	173	20	where	where	SCONJ
ejpam-4911	173	21	s	s	X
ejpam-4911	173	22	,	,	PUNCT
ejpam-4911	173	23	v	v	NOUN
ejpam-4911	173	24	=	=	SYM
ejpam-4911	173	25	1	1	NUM
ejpam-4911	173	26	,	,	PUNCT
ejpam-4911	173	27	2	2	NUM
ejpam-4911	173	28	and	and	CCONJ
ejpam-4911	173	29	s	s	VERB
ejpam-4911	173	30	̸=	̸=	PROPN
ejpam-4911	173	31	v.	v.	ADP
ejpam-4911	173	32	thus	thus	ADV
ejpam-4911	173	33	,	,	PUNCT
ejpam-4911	173	34	q	q	PROPN
ejpam-4911	173	35	⊂	⊂	PROPN
ejpam-4911	173	36	is(cv(q	is(cv(q	NOUN
ejpam-4911	173	37	)	)	PUNCT
ejpam-4911	173	38	)	)	PUNCT
ejpam-4911	173	39	where	where	SCONJ
ejpam-4911	173	40	s	s	X
ejpam-4911	173	41	,	,	PUNCT
ejpam-4911	173	42	v	v	NOUN
ejpam-4911	173	43	=	=	SYM
ejpam-4911	173	44	1	1	NUM
ejpam-4911	173	45	,	,	PUNCT
ejpam-4911	173	46	2	2	NUM
ejpam-4911	173	47	and	and	CCONJ
ejpam-4911	173	48	s	s	VERB
ejpam-4911	173	49	̸=	̸=	PROPN
ejpam-4911	173	50	v.	v.	ADP
ejpam-4911	173	51	hence	hence	ADV
ejpam-4911	173	52	q	q	X
ejpam-4911	173	53	is	be	AUX
ejpam-4911	173	54	a	a	DET
ejpam-4911	173	55	(	(	PUNCT
ejpam-4911	173	56	s	s	X
ejpam-4911	173	57	,	,	PUNCT
ejpam-4911	173	58	v)-µ-preopen	v)-µ-preopen	VERB
ejpam-4911	173	59	set	set	VERB
ejpam-4911	173	60	in	in	ADP
ejpam-4911	173	61	x	x	PUNCT
ejpam-4911	173	62	for	for	ADP
ejpam-4911	173	63	s	s	PROPN
ejpam-4911	173	64	,	,	PUNCT
ejpam-4911	173	65	v	v	NOUN
ejpam-4911	173	66	=	=	SYM
ejpam-4911	173	67	1	1	NUM
ejpam-4911	173	68	,	,	PUNCT
ejpam-4911	173	69	2	2	NUM
ejpam-4911	173	70	;	;	PUNCT
ejpam-4911	173	71	s	s	AUX
ejpam-4911	173	72	̸=	̸=	PROPN
ejpam-4911	173	73	v.	v.	ADP
ejpam-4911	173	74	theorem	theorem	ADJ
ejpam-4911	173	75	11	11	NUM
ejpam-4911	173	76	.	.	PUNCT
ejpam-4911	174	1	let	let	AUX
ejpam-4911	174	2	(	(	PUNCT
ejpam-4911	174	3	x,µ1	x,µ1	NOUN
ejpam-4911	174	4	,	,	PUNCT
ejpam-4911	174	5	µ2	µ2	PROPN
ejpam-4911	174	6	)	)	PUNCT
ejpam-4911	174	7	be	be	AUX
ejpam-4911	174	8	a	a	DET
ejpam-4911	174	9	bgts	bgts	NOUN
ejpam-4911	174	10	.	.	PUNCT
ejpam-4911	175	1	then	then	ADV
ejpam-4911	175	2	d	d	X
ejpam-4911	175	3	∈	∈	PROPN
ejpam-4911	175	4	(	(	PUNCT
ejpam-4911	175	5	s	s	PROPN
ejpam-4911	175	6	,	,	PUNCT
ejpam-4911	175	7	v	v	NOUN
ejpam-4911	175	8	)	)	PUNCT
ejpam-4911	175	9	−	−	PROPN
ejpam-4911	175	10	d(x	d(x	NOUN
ejpam-4911	175	11	)	)	PUNCT
ejpam-4911	175	12	if	if	SCONJ
ejpam-4911	175	13	any	any	DET
ejpam-4911	175	14	one	one	NUM
ejpam-4911	175	15	of	of	ADP
ejpam-4911	175	16	the	the	DET
ejpam-4911	175	17	following	following	NOUN
ejpam-4911	175	18	is	be	AUX
ejpam-4911	175	19	true	true	ADJ
ejpam-4911	175	20	.	.	PUNCT
ejpam-4911	176	1	(	(	PUNCT
ejpam-4911	176	2	a	a	X
ejpam-4911	176	3	)	)	PUNCT
ejpam-4911	176	4	d	d	NOUN
ejpam-4911	176	5	∩m	∩m	PROPN
ejpam-4911	176	6	̸=	̸=	PROPN
ejpam-4911	176	7	∅	∅	NOUN
ejpam-4911	176	8	for	for	ADP
ejpam-4911	176	9	every	every	DET
ejpam-4911	176	10	m	m	NOUN
ejpam-4911	176	11	is	be	AUX
ejpam-4911	176	12	a	a	DET
ejpam-4911	176	13	non	non	ADJ
ejpam-4911	176	14	-	-	ADJ
ejpam-4911	176	15	null	null	ADJ
ejpam-4911	176	16	(	(	PUNCT
ejpam-4911	176	17	s	s	PROPN
ejpam-4911	176	18	,	,	PUNCT
ejpam-4911	176	19	v)-µ-semi	v)-µ-semi	ADV
ejpam-4911	176	20	open	open	ADJ
ejpam-4911	176	21	set	set	VERB
ejpam-4911	176	22	in	in	ADP
ejpam-4911	176	23	x	x	PROPN
ejpam-4911	176	24	(	(	PUNCT
ejpam-4911	176	25	b	b	NOUN
ejpam-4911	176	26	)	)	PUNCT
ejpam-4911	176	27	d	d	NOUN
ejpam-4911	176	28	∩m	∩m	PROPN
ejpam-4911	176	29	̸=	̸=	PROPN
ejpam-4911	176	30	∅	∅	NOUN
ejpam-4911	176	31	for	for	ADP
ejpam-4911	176	32	every	every	DET
ejpam-4911	176	33	m	m	NOUN
ejpam-4911	176	34	is	be	AUX
ejpam-4911	176	35	a	a	DET
ejpam-4911	176	36	non	non	ADJ
ejpam-4911	176	37	-	-	ADJ
ejpam-4911	176	38	null	null	ADJ
ejpam-4911	176	39	(	(	PUNCT
ejpam-4911	176	40	s	s	X
ejpam-4911	176	41	,	,	PUNCT
ejpam-4911	176	42	v)-µ-preopen	v)-µ-preopen	VERB
ejpam-4911	176	43	set	set	VERB
ejpam-4911	176	44	in	in	ADP
ejpam-4911	176	45	x	x	PROPN
ejpam-4911	176	46	(	(	PUNCT
ejpam-4911	176	47	c	c	NOUN
ejpam-4911	176	48	)	)	PUNCT
ejpam-4911	177	1	d	d	X
ejpam-4911	177	2	∩m	∩m	PROPN
ejpam-4911	177	3	̸=	̸=	PROPN
ejpam-4911	177	4	∅	∅	NOUN
ejpam-4911	177	5	for	for	ADP
ejpam-4911	177	6	every	every	DET
ejpam-4911	177	7	m	m	NOUN
ejpam-4911	177	8	is	be	AUX
ejpam-4911	177	9	a	a	DET
ejpam-4911	177	10	non	non	ADJ
ejpam-4911	177	11	-	-	ADJ
ejpam-4911	177	12	null	null	ADJ
ejpam-4911	177	13	(	(	PUNCT
ejpam-4911	177	14	s	s	NOUN
ejpam-4911	177	15	,	,	PUNCT
ejpam-4911	177	16	v)-µ-α	v)-µ-α	NOUN
ejpam-4911	177	17	-	-	PUNCT
ejpam-4911	177	18	open	open	ADJ
ejpam-4911	177	19	set	set	NOUN
ejpam-4911	177	20	in	in	ADP
ejpam-4911	177	21	x	x	PUNCT
ejpam-4911	177	22	where	where	SCONJ
ejpam-4911	177	23	s	s	X
ejpam-4911	177	24	,	,	PUNCT
ejpam-4911	177	25	v	v	NOUN
ejpam-4911	177	26	=	=	SYM
ejpam-4911	177	27	1	1	NUM
ejpam-4911	177	28	,	,	PUNCT
ejpam-4911	177	29	2	2	NUM
ejpam-4911	177	30	;	;	PUNCT
ejpam-4911	177	31	s	s	VERB
ejpam-4911	177	32	̸=	̸=	PROPN
ejpam-4911	177	33	v.	v.	ADP
ejpam-4911	177	34	proof	proof	NOUN
ejpam-4911	177	35	.	.	PUNCT
ejpam-4911	178	1	we	we	PRON
ejpam-4911	178	2	give	give	VERB
ejpam-4911	178	3	the	the	DET
ejpam-4911	178	4	detailed	detailed	ADJ
ejpam-4911	178	5	proof	proof	NOUN
ejpam-4911	178	6	for	for	ADP
ejpam-4911	178	7	(	(	PUNCT
ejpam-4911	178	8	b	b	NOUN
ejpam-4911	178	9	)	)	PUNCT
ejpam-4911	178	10	only	only	ADV
ejpam-4911	178	11	.	.	PUNCT
ejpam-4911	179	1	suppose	suppose	VERB
ejpam-4911	179	2	that	that	SCONJ
ejpam-4911	179	3	d	d	PROPN
ejpam-4911	179	4	∩m	∩m	PROPN
ejpam-4911	179	5	̸=	̸=	PROPN
ejpam-4911	179	6	∅	∅	NOUN
ejpam-4911	179	7	for	for	ADP
ejpam-4911	179	8	every	every	DET
ejpam-4911	179	9	m	m	NOUN
ejpam-4911	179	10	is	be	AUX
ejpam-4911	179	11	a	a	DET
ejpam-4911	179	12	non	non	ADJ
ejpam-4911	179	13	-	-	ADJ
ejpam-4911	179	14	null	null	ADJ
ejpam-4911	179	15	(	(	PUNCT
ejpam-4911	179	16	s	s	X
ejpam-4911	179	17	,	,	PUNCT
ejpam-4911	179	18	v)-µ-preopen	v)-µ-preopen	VERB
ejpam-4911	179	19	set	set	VERB
ejpam-4911	179	20	in	in	ADP
ejpam-4911	179	21	x	x	PUNCT
ejpam-4911	179	22	where	where	SCONJ
ejpam-4911	179	23	s	s	X
ejpam-4911	179	24	,	,	PUNCT
ejpam-4911	179	25	v	v	NOUN
ejpam-4911	179	26	=	=	SYM
ejpam-4911	179	27	1	1	NUM
ejpam-4911	179	28	,	,	PUNCT
ejpam-4911	179	29	2	2	NUM
ejpam-4911	179	30	and	and	CCONJ
ejpam-4911	179	31	s	s	VERB
ejpam-4911	179	32	̸=	̸=	PROPN
ejpam-4911	179	33	v.	v.	ADP
ejpam-4911	179	34	it	it	PRON
ejpam-4911	179	35	is	be	AUX
ejpam-4911	179	36	enough	enough	ADJ
ejpam-4911	179	37	to	to	PART
ejpam-4911	179	38	prove	prove	VERB
ejpam-4911	179	39	,	,	PUNCT
ejpam-4911	179	40	d	d	PRON
ejpam-4911	179	41	is	be	AUX
ejpam-4911	179	42	µs	µs	NOUN
ejpam-4911	179	43	-	-	PUNCT
ejpam-4911	179	44	dense	dense	ADJ
ejpam-4911	179	45	set	set	NOUN
ejpam-4911	179	46	in	in	ADP
ejpam-4911	179	47	x	x	PUNCT
ejpam-4911	179	48	for	for	ADP
ejpam-4911	179	49	s	s	NOUN
ejpam-4911	179	50	=	=	SYM
ejpam-4911	179	51	1	1	NUM
ejpam-4911	179	52	,	,	PUNCT
ejpam-4911	179	53	2	2	NUM
ejpam-4911	179	54	,	,	PUNCT
ejpam-4911	179	55	by	by	ADP
ejpam-4911	179	56	theorem	theorem	NOUN
ejpam-4911	179	57	4	4	NUM
ejpam-4911	179	58	.	.	PUNCT
ejpam-4911	180	1	let	let	VERB
ejpam-4911	180	2	b	b	NOUN
ejpam-4911	180	3	∈	∈	PROPN
ejpam-4911	180	4	µ̃s	µ̃s	NOUN
ejpam-4911	180	5	for	for	ADP
ejpam-4911	180	6	s	s	NOUN
ejpam-4911	180	7	=	=	SYM
ejpam-4911	180	8	1	1	NUM
ejpam-4911	180	9	,	,	PUNCT
ejpam-4911	180	10	2	2	NUM
ejpam-4911	180	11	.	.	PUNCT
ejpam-4911	180	12	by	by	ADP
ejpam-4911	180	13	lemma	lemma	PROPN
ejpam-4911	180	14	6	6	NUM
ejpam-4911	180	15	,	,	PUNCT
ejpam-4911	180	16	b	b	NOUN
ejpam-4911	180	17	is	be	AUX
ejpam-4911	180	18	a	a	DET
ejpam-4911	180	19	non	non	ADJ
ejpam-4911	180	20	-	-	ADJ
ejpam-4911	180	21	null	null	ADJ
ejpam-4911	180	22	(	(	PUNCT
ejpam-4911	180	23	s	s	X
ejpam-4911	180	24	,	,	PUNCT
ejpam-4911	180	25	v)-µ-preopen	v)-µ-preopen	VERB
ejpam-4911	180	26	set	set	VERB
ejpam-4911	180	27	in	in	ADP
ejpam-4911	180	28	x	x	PUNCT
ejpam-4911	180	29	where	where	SCONJ
ejpam-4911	180	30	s	s	X
ejpam-4911	180	31	,	,	PUNCT
ejpam-4911	180	32	v	v	NOUN
ejpam-4911	180	33	=	=	SYM
ejpam-4911	180	34	1	1	NUM
ejpam-4911	180	35	,	,	PUNCT
ejpam-4911	180	36	2	2	NUM
ejpam-4911	180	37	and	and	CCONJ
ejpam-4911	180	38	s	s	VERB
ejpam-4911	180	39	̸=	̸=	PROPN
ejpam-4911	180	40	v.	v.	ADP
ejpam-4911	180	41	by	by	ADP
ejpam-4911	180	42	assumption	assumption	NOUN
ejpam-4911	180	43	,	,	PUNCT
ejpam-4911	181	1	d	d	PROPN
ejpam-4911	181	2	∩	∩	X
ejpam-4911	181	3	b	b	X
ejpam-4911	181	4	̸=	̸=	PROPN
ejpam-4911	181	5	∅.	∅.	VERB
ejpam-4911	181	6	therefore	therefore	ADV
ejpam-4911	181	7	,	,	PUNCT
ejpam-4911	181	8	d	d	PRON
ejpam-4911	181	9	is	be	AUX
ejpam-4911	181	10	a	a	DET
ejpam-4911	181	11	µs	µs	NOUN
ejpam-4911	181	12	-	-	PUNCT
ejpam-4911	181	13	dense	dense	ADJ
ejpam-4911	181	14	set	set	NOUN
ejpam-4911	181	15	for	for	ADP
ejpam-4911	181	16	s	s	NOUN
ejpam-4911	181	17	=	=	SYM
ejpam-4911	181	18	1	1	NUM
ejpam-4911	181	19	,	,	PUNCT
ejpam-4911	181	20	2	2	NUM
ejpam-4911	181	21	.	.	PUNCT
ejpam-4911	182	1	hence	hence	ADV
ejpam-4911	182	2	d	d	X
ejpam-4911	182	3	is	be	AUX
ejpam-4911	182	4	(	(	PUNCT
ejpam-4911	182	5	s	s	X
ejpam-4911	182	6	,	,	PUNCT
ejpam-4911	182	7	v)-dense	v)-dense	ADP
ejpam-4911	182	8	where	where	SCONJ
ejpam-4911	182	9	s	s	X
ejpam-4911	182	10	,	,	PUNCT
ejpam-4911	182	11	v	v	NOUN
ejpam-4911	182	12	=	=	SYM
ejpam-4911	182	13	1	1	NUM
ejpam-4911	182	14	,	,	PUNCT
ejpam-4911	182	15	2	2	NUM
ejpam-4911	182	16	and	and	CCONJ
ejpam-4911	182	17	s	s	VERB
ejpam-4911	182	18	̸=	̸=	PROPN
ejpam-4911	182	19	v.	v.	ADP
ejpam-4911	182	20	y.	y.	PROPN
ejpam-4911	182	21	farhat	farhat	PROPN
ejpam-4911	182	22	,	,	PUNCT
ejpam-4911	182	23	v.	v.	ADP
ejpam-4911	182	24	subramanian	subramanian	PROPN
ejpam-4911	182	25	/	/	SYM
ejpam-4911	182	26	eur	eur	PROPN
ejpam-4911	182	27	.	.	PUNCT
ejpam-4911	183	1	j.	j.	PROPN
ejpam-4911	183	2	pure	pure	PROPN
ejpam-4911	183	3	appl	appl	PROPN
ejpam-4911	183	4	.	.	PROPN
ejpam-4911	183	5	math	math	PROPN
ejpam-4911	183	6	,	,	PUNCT
ejpam-4911	183	7	16	16	NUM
ejpam-4911	183	8	(	(	PUNCT
ejpam-4911	183	9	4	4	NUM
ejpam-4911	183	10	)	)	PUNCT
ejpam-4911	183	11	(	(	PUNCT
ejpam-4911	183	12	2023	2023	NUM
ejpam-4911	183	13	)	)	PUNCT
ejpam-4911	183	14	,	,	PUNCT
ejpam-4911	183	15	2049	2049	NUM
ejpam-4911	183	16	-	-	SYM
ejpam-4911	183	17	2065	2065	NUM
ejpam-4911	183	18	2055	2055	NUM
ejpam-4911	183	19	example	example	NOUN
ejpam-4911	183	20	12	12	NUM
ejpam-4911	183	21	explains	explain	VERB
ejpam-4911	183	22	that	that	SCONJ
ejpam-4911	183	23	the	the	DET
ejpam-4911	183	24	reverse	reverse	ADJ
ejpam-4911	183	25	part	part	NOUN
ejpam-4911	183	26	of	of	ADP
ejpam-4911	183	27	theorem	theorem	ADJ
ejpam-4911	183	28	11	11	NUM
ejpam-4911	183	29	is	be	AUX
ejpam-4911	183	30	generally	generally	ADV
ejpam-4911	183	31	not	not	PART
ejpam-4911	183	32	true	true	ADJ
ejpam-4911	183	33	.	.	PUNCT
ejpam-4911	184	1	example	example	NOUN
ejpam-4911	184	2	12	12	NUM
ejpam-4911	184	3	.	.	PUNCT
ejpam-4911	185	1	(	(	PUNCT
ejpam-4911	185	2	a	a	X
ejpam-4911	185	3	)	)	PUNCT
ejpam-4911	185	4	consider	consider	VERB
ejpam-4911	185	5	the	the	DET
ejpam-4911	185	6	bigeneralized	bigeneralized	ADJ
ejpam-4911	185	7	topological	topological	ADJ
ejpam-4911	185	8	space	space	NOUN
ejpam-4911	185	9	(	(	PUNCT
ejpam-4911	185	10	x,µ1	x,µ1	PROPN
ejpam-4911	185	11	,	,	PUNCT
ejpam-4911	185	12	µ2	µ2	PROPN
ejpam-4911	185	13	)	)	PUNCT
ejpam-4911	185	14	where	where	SCONJ
ejpam-4911	185	15	x	x	X
ejpam-4911	185	16	=	=	PRON
ejpam-4911	185	17	{	{	PUNCT
ejpam-4911	185	18	e	e	NOUN
ejpam-4911	185	19	,	,	PUNCT
ejpam-4911	185	20	f	f	PROPN
ejpam-4911	185	21	,	,	PUNCT
ejpam-4911	185	22	k	k	PROPN
ejpam-4911	185	23	,	,	PUNCT
ejpam-4911	185	24	l	l	NOUN
ejpam-4911	185	25	,	,	PUNCT
ejpam-4911	185	26	r	r	NOUN
ejpam-4911	185	27	}	}	PUNCT
ejpam-4911	185	28	;	;	PUNCT
ejpam-4911	185	29	µ1	µ1	PROPN
ejpam-4911	185	30	=	=	SYM
ejpam-4911	185	31	{	{	PUNCT
ejpam-4911	185	32	∅	∅	NOUN
ejpam-4911	185	33	,	,	PUNCT
ejpam-4911	185	34	{	{	PUNCT
ejpam-4911	185	35	e	e	NOUN
ejpam-4911	185	36	,	,	PUNCT
ejpam-4911	185	37	f	f	PROPN
ejpam-4911	185	38	}	}	PUNCT
ejpam-4911	185	39	,	,	PUNCT
ejpam-4911	185	40	{	{	PUNCT
ejpam-4911	185	41	e	e	NOUN
ejpam-4911	185	42	,	,	PUNCT
ejpam-4911	185	43	l	l	NOUN
ejpam-4911	185	44	}	}	PUNCT
ejpam-4911	185	45	,	,	PUNCT
ejpam-4911	185	46	{	{	PUNCT
ejpam-4911	185	47	f	f	X
ejpam-4911	185	48	,	,	PUNCT
ejpam-4911	185	49	l	l	NOUN
ejpam-4911	185	50	}	}	PUNCT
ejpam-4911	185	51	,	,	PUNCT
ejpam-4911	185	52	{	{	PUNCT
ejpam-4911	185	53	e	e	NOUN
ejpam-4911	185	54	,	,	PUNCT
ejpam-4911	185	55	f	f	X
ejpam-4911	185	56	,	,	PUNCT
ejpam-4911	185	57	l	l	NOUN
ejpam-4911	185	58	}	}	PUNCT
ejpam-4911	185	59	}	}	PUNCT
ejpam-4911	185	60	and	and	CCONJ
ejpam-4911	185	61	µ2	µ2	PROPN
ejpam-4911	185	62	=	=	PUNCT
ejpam-4911	185	63	{	{	PUNCT
ejpam-4911	185	64	∅	∅	NOUN
ejpam-4911	185	65	,	,	PUNCT
ejpam-4911	185	66	{	{	PUNCT
ejpam-4911	185	67	e	e	NOUN
ejpam-4911	185	68	,	,	PUNCT
ejpam-4911	185	69	f	f	PROPN
ejpam-4911	185	70	,	,	PUNCT
ejpam-4911	185	71	k	k	NOUN
ejpam-4911	185	72	}	}	PUNCT
ejpam-4911	185	73	,	,	PUNCT
ejpam-4911	185	74	{	{	PUNCT
ejpam-4911	185	75	e	e	NOUN
ejpam-4911	185	76	,	,	PUNCT
ejpam-4911	185	77	f	f	X
ejpam-4911	185	78	,	,	PUNCT
ejpam-4911	185	79	l	l	NOUN
ejpam-4911	185	80	}	}	PUNCT
ejpam-4911	185	81	,	,	PUNCT
ejpam-4911	185	82	{	{	PUNCT
ejpam-4911	185	83	e	e	NOUN
ejpam-4911	185	84	,	,	PUNCT
ejpam-4911	185	85	k	k	NOUN
ejpam-4911	185	86	,	,	PUNCT
ejpam-4911	185	87	r	r	NOUN
ejpam-4911	185	88	}	}	PUNCT
ejpam-4911	185	89	,	,	PUNCT
ejpam-4911	185	90	{	{	PUNCT
ejpam-4911	185	91	e	e	NOUN
ejpam-4911	185	92	,	,	PUNCT
ejpam-4911	185	93	f	f	PROPN
ejpam-4911	185	94	,	,	PUNCT
ejpam-4911	185	95	k	k	NOUN
ejpam-4911	185	96	,	,	PUNCT
ejpam-4911	185	97	l	l	NOUN
ejpam-4911	185	98	}	}	PUNCT
ejpam-4911	185	99	,	,	PUNCT
ejpam-4911	185	100	{	{	PUNCT
ejpam-4911	185	101	e	e	NOUN
ejpam-4911	185	102	,	,	PUNCT
ejpam-4911	185	103	f	f	PROPN
ejpam-4911	185	104	,	,	PUNCT
ejpam-4911	185	105	k	k	NOUN
ejpam-4911	185	106	,	,	PUNCT
ejpam-4911	185	107	r	r	NOUN
ejpam-4911	185	108	}	}	PUNCT
ejpam-4911	185	109	,	,	PUNCT
ejpam-4911	185	110	x	x	NOUN
ejpam-4911	185	111	}	}	PUNCT
ejpam-4911	185	112	.	.	PUNCT
ejpam-4911	186	1	take	take	VERB
ejpam-4911	186	2	a	a	DET
ejpam-4911	186	3	=	=	SYM
ejpam-4911	186	4	{	{	PUNCT
ejpam-4911	186	5	k	k	NOUN
ejpam-4911	186	6	,	,	PUNCT
ejpam-4911	186	7	l	l	NOUN
ejpam-4911	186	8	,	,	PUNCT
ejpam-4911	186	9	r	r	NOUN
ejpam-4911	186	10	}	}	PUNCT
ejpam-4911	186	11	.	.	PUNCT
ejpam-4911	187	1	then	then	ADV
ejpam-4911	187	2	a	a	PRON
ejpam-4911	187	3	is	be	AUX
ejpam-4911	187	4	(	(	PUNCT
ejpam-4911	187	5	1	1	NUM
ejpam-4911	187	6	,	,	PUNCT
ejpam-4911	187	7	2)-dense	2)-dense	NUM
ejpam-4911	187	8	set	set	NOUN
ejpam-4911	187	9	.	.	PUNCT
ejpam-4911	188	1	but	but	CCONJ
ejpam-4911	188	2	a	a	DET
ejpam-4911	188	3	∩	∩	ADJ
ejpam-4911	188	4	g	g	NOUN
ejpam-4911	188	5	=	=	NOUN
ejpam-4911	188	6	∅	∅	NOUN
ejpam-4911	188	7	where	where	SCONJ
ejpam-4911	188	8	g	g	NOUN
ejpam-4911	188	9	=	=	SYM
ejpam-4911	188	10	{	{	PUNCT
ejpam-4911	188	11	e	e	NOUN
ejpam-4911	188	12	,	,	PUNCT
ejpam-4911	188	13	f	f	X
ejpam-4911	188	14	}	}	PUNCT
ejpam-4911	188	15	is	be	AUX
ejpam-4911	188	16	a	a	DET
ejpam-4911	188	17	non	non	ADJ
ejpam-4911	188	18	-	-	ADJ
ejpam-4911	188	19	null	null	ADJ
ejpam-4911	188	20	µ(1,2)-µ-semi	µ(1,2)-µ-semi	PROPN
ejpam-4911	188	21	open	open	ADJ
ejpam-4911	188	22	set	set	NOUN
ejpam-4911	188	23	.	.	PUNCT
ejpam-4911	189	1	let	let	VERB
ejpam-4911	189	2	b	b	NOUN
ejpam-4911	189	3	=	=	SYM
ejpam-4911	189	4	{	{	PUNCT
ejpam-4911	189	5	l	l	NOUN
ejpam-4911	189	6	,	,	PUNCT
ejpam-4911	189	7	r	r	NOUN
ejpam-4911	189	8	}	}	PUNCT
ejpam-4911	189	9	⊂	⊂	PROPN
ejpam-4911	189	10	x.	x.	NOUN
ejpam-4911	190	1	then	then	ADV
ejpam-4911	190	2	b	b	PROPN
ejpam-4911	190	3	is	be	AUX
ejpam-4911	190	4	(	(	PUNCT
ejpam-4911	190	5	2	2	NUM
ejpam-4911	190	6	,	,	PUNCT
ejpam-4911	190	7	1)-dense	1)-dense	NUM
ejpam-4911	190	8	set	set	NOUN
ejpam-4911	190	9	.	.	PUNCT
ejpam-4911	191	1	but	but	CCONJ
ejpam-4911	191	2	b	b	X
ejpam-4911	191	3	∩h	∩h	NOUN
ejpam-4911	191	4	=	=	PUNCT
ejpam-4911	191	5	∅	∅	NOUN
ejpam-4911	191	6	where	where	SCONJ
ejpam-4911	191	7	h	h	NOUN
ejpam-4911	191	8	=	=	PRON
ejpam-4911	191	9	{	{	PUNCT
ejpam-4911	191	10	e	e	NOUN
ejpam-4911	191	11	,	,	PUNCT
ejpam-4911	191	12	f	f	PROPN
ejpam-4911	191	13	,	,	PUNCT
ejpam-4911	191	14	k	k	NOUN
ejpam-4911	191	15	}	}	PUNCT
ejpam-4911	191	16	is	be	AUX
ejpam-4911	191	17	a	a	DET
ejpam-4911	191	18	non	non	ADJ
ejpam-4911	191	19	-	-	ADJ
ejpam-4911	191	20	null	null	ADJ
ejpam-4911	191	21	µ(2,1)-µ-semi	µ(2,1)-µ-semi	NOUN
ejpam-4911	191	22	-	-	ADJ
ejpam-4911	191	23	open	open	ADJ
ejpam-4911	191	24	set	set	NOUN
ejpam-4911	191	25	.	.	PUNCT
ejpam-4911	192	1	(	(	PUNCT
ejpam-4911	192	2	b	b	X
ejpam-4911	192	3	)	)	PUNCT
ejpam-4911	192	4	consider	consider	VERB
ejpam-4911	192	5	the	the	DET
ejpam-4911	192	6	bgts	bgts	NOUN
ejpam-4911	192	7	(	(	PUNCT
ejpam-4911	192	8	x,µ1	x,µ1	PROPN
ejpam-4911	192	9	,	,	PUNCT
ejpam-4911	192	10	µ2	µ2	PROPN
ejpam-4911	192	11	)	)	PUNCT
ejpam-4911	192	12	,	,	PUNCT
ejpam-4911	192	13	x	x	PUNCT
ejpam-4911	193	1	=	=	PUNCT
ejpam-4911	194	1	[	[	X
ejpam-4911	194	2	0	0	NUM
ejpam-4911	194	3	,	,	PUNCT
ejpam-4911	194	4	3	3	NUM
ejpam-4911	194	5	]	]	PUNCT
ejpam-4911	194	6	;	;	PUNCT
ejpam-4911	194	7	µ1	µ1	PROPN
ejpam-4911	194	8	=	=	SYM
ejpam-4911	194	9	{	{	PUNCT
ejpam-4911	194	10	∅	∅	NOUN
ejpam-4911	194	11	,	,	PUNCT
ejpam-4911	194	12	[	[	X
ejpam-4911	194	13	0	0	NUM
ejpam-4911	194	14	,	,	PUNCT
ejpam-4911	194	15	2	2	NUM
ejpam-4911	194	16	)	)	PUNCT
ejpam-4911	194	17	,	,	PUNCT
ejpam-4911	194	18	(	(	PUNCT
ejpam-4911	194	19	1	1	NUM
ejpam-4911	194	20	,	,	PUNCT
ejpam-4911	194	21	3	3	NUM
ejpam-4911	194	22	]	]	PUNCT
ejpam-4911	194	23	,	,	PUNCT
ejpam-4911	194	24	[	[	X
ejpam-4911	194	25	0	0	NUM
ejpam-4911	194	26	,	,	PUNCT
ejpam-4911	194	27	3	3	NUM
ejpam-4911	194	28	]	]	PUNCT
ejpam-4911	194	29	}	}	PUNCT
ejpam-4911	194	30	and	and	CCONJ
ejpam-4911	194	31	µ2	µ2	PROPN
ejpam-4911	194	32	=	=	PUNCT
ejpam-4911	194	33	{	{	PUNCT
ejpam-4911	194	34	∅	∅	NOUN
ejpam-4911	194	35	,	,	PUNCT
ejpam-4911	194	36	[	[	X
ejpam-4911	194	37	0	0	NUM
ejpam-4911	194	38	,	,	PUNCT
ejpam-4911	194	39	32	32	NUM
ejpam-4911	194	40	]	]	PUNCT
ejpam-4911	194	41	,	,	PUNCT
ejpam-4911	194	42	(	(	PUNCT
ejpam-4911	194	43	1	1	NUM
ejpam-4911	194	44	,	,	PUNCT
ejpam-4911	194	45	2	2	NUM
ejpam-4911	194	46	]	]	PUNCT
ejpam-4911	194	47	,	,	PUNCT
ejpam-4911	194	48	[	[	X
ejpam-4911	194	49	0	0	NUM
ejpam-4911	194	50	,	,	PUNCT
ejpam-4911	194	51	2	2	NUM
ejpam-4911	194	52	]	]	PUNCT
ejpam-4911	194	53	}	}	PUNCT
ejpam-4911	194	54	.	.	PUNCT
ejpam-4911	195	1	let	let	VERB
ejpam-4911	195	2	a	a	PRON
ejpam-4911	195	3	=	=	SYM
ejpam-4911	195	4	(	(	PUNCT
ejpam-4911	195	5	0	0	NUM
ejpam-4911	195	6	,	,	PUNCT
ejpam-4911	195	7	1)∪	1)∪	NUM
ejpam-4911	195	8	(	(	PUNCT
ejpam-4911	195	9	32	32	NUM
ejpam-4911	195	10	,	,	PUNCT
ejpam-4911	195	11	3	3	NUM
ejpam-4911	195	12	]	]	PUNCT
ejpam-4911	195	13	.	.	PUNCT
ejpam-4911	196	1	then	then	ADV
ejpam-4911	196	2	a	a	DET
ejpam-4911	196	3	∈	∈	PROPN
ejpam-4911	196	4	(	(	PUNCT
ejpam-4911	196	5	s	s	NOUN
ejpam-4911	196	6	,	,	PUNCT
ejpam-4911	196	7	v)−d(x	v)−d(x	NUM
ejpam-4911	196	8	)	)	PUNCT
ejpam-4911	196	9	where	where	SCONJ
ejpam-4911	196	10	s	s	X
ejpam-4911	196	11	,	,	PUNCT
ejpam-4911	196	12	v	v	NOUN
ejpam-4911	196	13	=	=	SYM
ejpam-4911	196	14	1	1	NUM
ejpam-4911	196	15	,	,	PUNCT
ejpam-4911	196	16	2	2	NUM
ejpam-4911	196	17	and	and	CCONJ
ejpam-4911	196	18	s	s	VERB
ejpam-4911	196	19	̸=	̸=	PROPN
ejpam-4911	196	20	v.	v.	CCONJ
ejpam-4911	196	21	but	but	CCONJ
ejpam-4911	196	22	a∩b	a∩b	PROPN
ejpam-4911	196	23	=	=	PUNCT
ejpam-4911	196	24	∅	∅	NOUN
ejpam-4911	196	25	where	where	SCONJ
ejpam-4911	196	26	b	b	X
ejpam-4911	196	27	=	=	PRON
ejpam-4911	196	28	{	{	PUNCT
ejpam-4911	196	29	3	3	NUM
ejpam-4911	196	30	2	2	NUM
ejpam-4911	196	31	}	}	PUNCT
ejpam-4911	196	32	is	be	AUX
ejpam-4911	196	33	a	a	DET
ejpam-4911	196	34	non	non	ADJ
ejpam-4911	196	35	-	-	ADJ
ejpam-4911	196	36	null	null	ADJ
ejpam-4911	196	37	(	(	PUNCT
ejpam-4911	196	38	s	s	X
ejpam-4911	196	39	,	,	PUNCT
ejpam-4911	196	40	v)-µ-preopen	v)-µ-preopen	VERB
ejpam-4911	196	41	set	set	VERB
ejpam-4911	196	42	in	in	ADP
ejpam-4911	196	43	x	x	PUNCT
ejpam-4911	196	44	where	where	SCONJ
ejpam-4911	196	45	s	s	X
ejpam-4911	196	46	,	,	PUNCT
ejpam-4911	196	47	v	v	NOUN
ejpam-4911	196	48	=	=	SYM
ejpam-4911	196	49	1	1	NUM
ejpam-4911	196	50	,	,	PUNCT
ejpam-4911	196	51	2	2	NUM
ejpam-4911	196	52	;	;	PUNCT
ejpam-4911	196	53	s	s	AUX
ejpam-4911	196	54	̸=	̸=	PROPN
ejpam-4911	196	55	v.	v.	CCONJ
ejpam-4911	196	56	(	(	PUNCT
ejpam-4911	196	57	c	c	X
ejpam-4911	196	58	)	)	PUNCT
ejpam-4911	196	59	consider	consider	VERB
ejpam-4911	196	60	the	the	DET
ejpam-4911	196	61	bgts	bgts	NOUN
ejpam-4911	196	62	(	(	PUNCT
ejpam-4911	196	63	x,µ1	x,µ1	PROPN
ejpam-4911	196	64	,	,	PUNCT
ejpam-4911	196	65	µ2	µ2	PROPN
ejpam-4911	196	66	)	)	PUNCT
ejpam-4911	196	67	,	,	PUNCT
ejpam-4911	196	68	x	x	PUNCT
ejpam-4911	197	1	=	=	PUNCT
ejpam-4911	198	1	[	[	X
ejpam-4911	198	2	0	0	NUM
ejpam-4911	198	3	,	,	PUNCT
ejpam-4911	198	4	4	4	NUM
ejpam-4911	198	5	]	]	PUNCT
ejpam-4911	198	6	;	;	PUNCT
ejpam-4911	198	7	µ1	µ1	PROPN
ejpam-4911	198	8	=	=	SYM
ejpam-4911	198	9	{	{	PUNCT
ejpam-4911	198	10	∅	∅	NOUN
ejpam-4911	198	11	,	,	PUNCT
ejpam-4911	198	12	[	[	X
ejpam-4911	198	13	0	0	NUM
ejpam-4911	198	14	,	,	PUNCT
ejpam-4911	198	15	2	2	NUM
ejpam-4911	198	16	)	)	PUNCT
ejpam-4911	198	17	,	,	PUNCT
ejpam-4911	198	18	(	(	PUNCT
ejpam-4911	198	19	1	1	NUM
ejpam-4911	198	20	,	,	PUNCT
ejpam-4911	198	21	2	2	NUM
ejpam-4911	198	22	)	)	PUNCT
ejpam-4911	198	23	}	}	PUNCT
ejpam-4911	198	24	and	and	CCONJ
ejpam-4911	198	25	µ2	µ2	PROPN
ejpam-4911	198	26	=	=	PUNCT
ejpam-4911	198	27	{	{	PUNCT
ejpam-4911	198	28	∅	∅	NOUN
ejpam-4911	198	29	,	,	PUNCT
ejpam-4911	198	30	[	[	X
ejpam-4911	198	31	0	0	NUM
ejpam-4911	198	32	,	,	PUNCT
ejpam-4911	198	33	2	2	NUM
ejpam-4911	198	34	)	)	PUNCT
ejpam-4911	198	35	,	,	PUNCT
ejpam-4911	198	36	(	(	PUNCT
ejpam-4911	198	37	1	1	NUM
ejpam-4911	198	38	,	,	PUNCT
ejpam-4911	198	39	2	2	NUM
ejpam-4911	198	40	]	]	PUNCT
ejpam-4911	198	41	,	,	PUNCT
ejpam-4911	198	42	(	(	PUNCT
ejpam-4911	198	43	1	1	NUM
ejpam-4911	198	44	,	,	PUNCT
ejpam-4911	198	45	3	3	NUM
ejpam-4911	198	46	)	)	PUNCT
ejpam-4911	198	47	,	,	PUNCT
ejpam-4911	199	1	[	[	X
ejpam-4911	199	2	0	0	NUM
ejpam-4911	199	3	,	,	PUNCT
ejpam-4911	199	4	2	2	NUM
ejpam-4911	199	5	]	]	PUNCT
ejpam-4911	199	6	,	,	PUNCT
ejpam-4911	199	7	[	[	X
ejpam-4911	199	8	0	0	NUM
ejpam-4911	199	9	,	,	PUNCT
ejpam-4911	199	10	3	3	NUM
ejpam-4911	199	11	)	)	PUNCT
ejpam-4911	199	12	}	}	PUNCT
ejpam-4911	199	13	.	.	PUNCT
ejpam-4911	200	1	let	let	VERB
ejpam-4911	200	2	p	p	NOUN
ejpam-4911	200	3	=	=	X
ejpam-4911	200	4	(	(	PUNCT
ejpam-4911	200	5	0	0	NUM
ejpam-4911	200	6	,	,	PUNCT
ejpam-4911	200	7	1	1	NUM
ejpam-4911	200	8	)	)	PUNCT
ejpam-4911	200	9	∪	∪	ADP
ejpam-4911	200	10	[	[	X
ejpam-4911	200	11	2	2	NUM
ejpam-4911	200	12	,	,	PUNCT
ejpam-4911	200	13	4	4	NUM
ejpam-4911	200	14	]	]	PUNCT
ejpam-4911	200	15	.	.	PUNCT
ejpam-4911	201	1	then	then	ADV
ejpam-4911	201	2	p	p	PROPN
ejpam-4911	201	3	∈	∈	PROPN
ejpam-4911	201	4	(	(	PUNCT
ejpam-4911	201	5	1	1	NUM
ejpam-4911	201	6	,	,	PUNCT
ejpam-4911	201	7	2	2	NUM
ejpam-4911	201	8	)	)	PUNCT
ejpam-4911	201	9	−	−	PROPN
ejpam-4911	201	10	d(x	d(x	NOUN
ejpam-4911	201	11	)	)	PUNCT
ejpam-4911	201	12	.	.	PUNCT
ejpam-4911	202	1	but	but	CCONJ
ejpam-4911	202	2	p	p	NOUN
ejpam-4911	202	3	∩	∩	ADJ
ejpam-4911	202	4	q	q	NOUN
ejpam-4911	202	5	=	=	NOUN
ejpam-4911	202	6	∅	∅	NOUN
ejpam-4911	202	7	where	where	SCONJ
ejpam-4911	202	8	q	q	NOUN
ejpam-4911	203	1	=	=	PUNCT
ejpam-4911	203	2	[	[	X
ejpam-4911	203	3	1	1	NUM
ejpam-4911	203	4	,	,	PUNCT
ejpam-4911	203	5	2	2	NUM
ejpam-4911	203	6	)	)	PUNCT
ejpam-4911	203	7	is	be	AUX
ejpam-4911	203	8	a	a	DET
ejpam-4911	203	9	non	non	ADJ
ejpam-4911	203	10	-	-	ADJ
ejpam-4911	203	11	null	null	ADJ
ejpam-4911	203	12	(	(	PUNCT
ejpam-4911	203	13	s	s	NOUN
ejpam-4911	203	14	,	,	PUNCT
ejpam-4911	203	15	v)-µ-α	v)-µ-α	NOUN
ejpam-4911	203	16	-	-	PUNCT
ejpam-4911	203	17	pen	pen	NOUN
ejpam-4911	203	18	set	set	NOUN
ejpam-4911	203	19	in	in	ADP
ejpam-4911	203	20	x	x	PUNCT
ejpam-4911	203	21	where	where	SCONJ
ejpam-4911	203	22	s	s	X
ejpam-4911	203	23	,	,	PUNCT
ejpam-4911	203	24	v	v	NOUN
ejpam-4911	203	25	=	=	SYM
ejpam-4911	203	26	1	1	NUM
ejpam-4911	203	27	,	,	PUNCT
ejpam-4911	203	28	2	2	NUM
ejpam-4911	203	29	and	and	CCONJ
ejpam-4911	203	30	s	s	VERB
ejpam-4911	203	31	̸=	̸=	PROPN
ejpam-4911	203	32	v.	v.	ADV
ejpam-4911	203	33	let	let	VERB
ejpam-4911	203	34	c	c	NOUN
ejpam-4911	203	35	=	=	SYM
ejpam-4911	203	36	(	(	PUNCT
ejpam-4911	203	37	0	0	NUM
ejpam-4911	203	38	,	,	PUNCT
ejpam-4911	203	39	1	1	NUM
ejpam-4911	203	40	)	)	PUNCT
ejpam-4911	203	41	∪	∪	ADP
ejpam-4911	203	42	[	[	X
ejpam-4911	203	43	3	3	NUM
ejpam-4911	203	44	,	,	PUNCT
ejpam-4911	203	45	4	4	NUM
ejpam-4911	203	46	]	]	PUNCT
ejpam-4911	203	47	.	.	PUNCT
ejpam-4911	204	1	then	then	ADV
ejpam-4911	204	2	c	c	PROPN
ejpam-4911	204	3	is	be	AUX
ejpam-4911	204	4	(	(	PUNCT
ejpam-4911	204	5	2	2	NUM
ejpam-4911	204	6	,	,	PUNCT
ejpam-4911	204	7	1)-dense	1)-dense	NUM
ejpam-4911	204	8	set	set	VERB
ejpam-4911	204	9	in	in	ADP
ejpam-4911	204	10	x.	x.	NOUN
ejpam-4911	204	11	but	but	CCONJ
ejpam-4911	204	12	c	c	NOUN
ejpam-4911	204	13	∩d	∩d	NOUN
ejpam-4911	204	14	=	=	NOUN
ejpam-4911	205	1	∅	∅	NOUN
ejpam-4911	205	2	where	where	SCONJ
ejpam-4911	205	3	d	d	NOUN
ejpam-4911	205	4	=	=	PUNCT
ejpam-4911	206	1	[	[	X
ejpam-4911	206	2	1	1	NUM
ejpam-4911	206	3	,	,	PUNCT
ejpam-4911	206	4	3	3	NUM
ejpam-4911	206	5	)	)	PUNCT
ejpam-4911	206	6	is	be	AUX
ejpam-4911	206	7	a	a	DET
ejpam-4911	206	8	non	non	ADJ
ejpam-4911	206	9	-	-	ADJ
ejpam-4911	206	10	null	null	ADJ
ejpam-4911	206	11	(	(	PUNCT
ejpam-4911	206	12	s	s	NOUN
ejpam-4911	206	13	,	,	PUNCT
ejpam-4911	206	14	v)-µ-α	v)-µ-α	NOUN
ejpam-4911	206	15	-	-	PUNCT
ejpam-4911	206	16	pen	pen	NOUN
ejpam-4911	206	17	set	set	NOUN
ejpam-4911	206	18	in	in	ADP
ejpam-4911	206	19	x	x	PUNCT
ejpam-4911	206	20	where	where	SCONJ
ejpam-4911	206	21	s	s	X
ejpam-4911	206	22	,	,	PUNCT
ejpam-4911	206	23	v	v	NOUN
ejpam-4911	206	24	=	=	SYM
ejpam-4911	206	25	1	1	NUM
ejpam-4911	206	26	,	,	PUNCT
ejpam-4911	206	27	2	2	NUM
ejpam-4911	206	28	and	and	CCONJ
ejpam-4911	206	29	s	s	VERB
ejpam-4911	206	30	̸=	̸=	PROPN
ejpam-4911	206	31	v.	v.	ADP
ejpam-4911	206	32	4	4	NUM
ejpam-4911	206	33	.	.	PUNCT
ejpam-4911	206	34	generalized	generalize	VERB
ejpam-4911	206	35	nowhere	nowhere	ADV
ejpam-4911	206	36	dense	dense	ADJ
ejpam-4911	206	37	sets	set	NOUN
ejpam-4911	206	38	here	here	ADV
ejpam-4911	206	39	,	,	PUNCT
ejpam-4911	206	40	we	we	PRON
ejpam-4911	206	41	find	find	VERB
ejpam-4911	206	42	the	the	DET
ejpam-4911	206	43	new	new	ADJ
ejpam-4911	206	44	results	result	NOUN
ejpam-4911	206	45	for	for	ADP
ejpam-4911	206	46	(	(	PUNCT
ejpam-4911	206	47	s	s	X
ejpam-4911	206	48	,	,	PUNCT
ejpam-4911	206	49	v)-nowhere	v)-nowhere	PUNCT
ejpam-4911	206	50	dense	dense	ADJ
ejpam-4911	206	51	set	set	NOUN
ejpam-4911	206	52	in	in	ADP
ejpam-4911	206	53	a	a	DET
ejpam-4911	206	54	bgts	bgts	NOUN
ejpam-4911	206	55	.	.	PUNCT
ejpam-4911	207	1	definition	definition	NOUN
ejpam-4911	207	2	13	13	NUM
ejpam-4911	207	3	.	.	PUNCT
ejpam-4911	208	1	[	[	X
ejpam-4911	208	2	13	13	NUM
ejpam-4911	208	3	]	]	PUNCT
ejpam-4911	208	4	let	let	VERB
ejpam-4911	208	5	(	(	PUNCT
ejpam-4911	208	6	x,µ1	x,µ1	NOUN
ejpam-4911	208	7	,	,	PUNCT
ejpam-4911	208	8	µ2	µ2	PROPN
ejpam-4911	208	9	)	)	PUNCT
ejpam-4911	208	10	be	be	VERB
ejpam-4911	208	11	a	a	DET
ejpam-4911	208	12	bgts	bgts	NOUN
ejpam-4911	208	13	and	and	CCONJ
ejpam-4911	208	14	d	d	PROPN
ejpam-4911	208	15	⊂	⊂	PROPN
ejpam-4911	208	16	x.	x.	NOUN
ejpam-4911	209	1	then	then	ADV
ejpam-4911	209	2	d	d	PROPN
ejpam-4911	209	3	is	be	AUX
ejpam-4911	209	4	called	call	VERB
ejpam-4911	209	5	(	(	PUNCT
ejpam-4911	209	6	s	s	PROPN
ejpam-4911	209	7	,	,	PUNCT
ejpam-4911	209	8	v)nowhere	v)nowhere	X
ejpam-4911	209	9	dense	dense	ADJ
ejpam-4911	209	10	if	if	SCONJ
ejpam-4911	209	11	is(cv(d	is(cv(d	NOUN
ejpam-4911	209	12	)	)	PUNCT
ejpam-4911	209	13	)	)	PUNCT
ejpam-4911	210	1	=	=	NOUN
ejpam-4911	210	2	∅	∅	NOUN
ejpam-4911	210	3	where	where	SCONJ
ejpam-4911	210	4	s	s	X
ejpam-4911	210	5	,	,	PUNCT
ejpam-4911	210	6	v	v	NOUN
ejpam-4911	210	7	=	=	SYM
ejpam-4911	210	8	1	1	NUM
ejpam-4911	210	9	,	,	PUNCT
ejpam-4911	210	10	2	2	NUM
ejpam-4911	210	11	and	and	CCONJ
ejpam-4911	210	12	s	s	VERB
ejpam-4911	210	13	̸=	̸=	PROPN
ejpam-4911	210	14	v.	v.	CCONJ
ejpam-4911	210	15	we	we	PRON
ejpam-4911	210	16	notated	notate	VERB
ejpam-4911	210	17	,	,	PUNCT
ejpam-4911	210	18	(	(	PUNCT
ejpam-4911	210	19	s	s	X
ejpam-4911	210	20	,	,	PUNCT
ejpam-4911	210	21	v)−n	v)−n	X
ejpam-4911	210	22	(	(	PUNCT
ejpam-4911	210	23	x	x	X
ejpam-4911	210	24	)	)	PUNCT
ejpam-4911	210	25	=	=	PRON
ejpam-4911	210	26	{	{	PUNCT
ejpam-4911	210	27	q	q	X
ejpam-4911	210	28	⊂	⊂	X
ejpam-4911	210	29	x	x	PUNCT
ejpam-4911	211	1	|	|	ADV
ejpam-4911	211	2	q	q	X
ejpam-4911	211	3	is	be	AUX
ejpam-4911	211	4	(	(	PUNCT
ejpam-4911	211	5	s	s	X
ejpam-4911	211	6	,	,	PUNCT
ejpam-4911	211	7	v)-nowhere	v)-nowhere	PUNCT
ejpam-4911	211	8	dense	dense	ADJ
ejpam-4911	211	9	inx	inx	PROPN
ejpam-4911	211	10	}	}	PUNCT
ejpam-4911	211	11	where	where	SCONJ
ejpam-4911	211	12	s	s	X
ejpam-4911	211	13	,	,	PUNCT
ejpam-4911	211	14	v	v	NOUN
ejpam-4911	211	15	=	=	SYM
ejpam-4911	211	16	1	1	NUM
ejpam-4911	211	17	,	,	PUNCT
ejpam-4911	211	18	2	2	NUM
ejpam-4911	211	19	;	;	PUNCT
ejpam-4911	211	20	s	s	VERB
ejpam-4911	211	21	̸=	̸=	PROPN
ejpam-4911	211	22	v.	v.	ADP
ejpam-4911	211	23	y.	y.	PROPN
ejpam-4911	211	24	farhat	farhat	PROPN
ejpam-4911	211	25	,	,	PUNCT
ejpam-4911	211	26	v.	v.	ADP
ejpam-4911	211	27	subramanian	subramanian	PROPN
ejpam-4911	211	28	/	/	SYM
ejpam-4911	211	29	eur	eur	PROPN
ejpam-4911	211	30	.	.	PUNCT
ejpam-4911	212	1	j.	j.	PROPN
ejpam-4911	212	2	pure	pure	PROPN
ejpam-4911	212	3	appl	appl	PROPN
ejpam-4911	212	4	.	.	PROPN
ejpam-4911	212	5	math	math	PROPN
ejpam-4911	212	6	,	,	PUNCT
ejpam-4911	212	7	16	16	NUM
ejpam-4911	212	8	(	(	PUNCT
ejpam-4911	212	9	4	4	NUM
ejpam-4911	212	10	)	)	PUNCT
ejpam-4911	212	11	(	(	PUNCT
ejpam-4911	212	12	2023	2023	NUM
ejpam-4911	212	13	)	)	PUNCT
ejpam-4911	212	14	,	,	PUNCT
ejpam-4911	212	15	2049	2049	NUM
ejpam-4911	212	16	-	-	SYM
ejpam-4911	212	17	2065	2065	NUM
ejpam-4911	212	18	2056	2056	NUM
ejpam-4911	212	19	example	example	NOUN
ejpam-4911	212	20	14	14	NUM
ejpam-4911	212	21	.	.	PUNCT
ejpam-4911	213	1	take	take	VERB
ejpam-4911	213	2	x	x	NOUN
ejpam-4911	213	3	=	=	PRON
ejpam-4911	213	4	{	{	PUNCT
ejpam-4911	213	5	e	e	PROPN
ejpam-4911	213	6	,	,	PUNCT
ejpam-4911	213	7	f	f	PROPN
ejpam-4911	213	8	,	,	PUNCT
ejpam-4911	213	9	k	k	NOUN
ejpam-4911	213	10	,	,	PUNCT
ejpam-4911	213	11	l	l	NOUN
ejpam-4911	213	12	}	}	PUNCT
ejpam-4911	213	13	;	;	PUNCT
ejpam-4911	213	14	µ1	µ1	PROPN
ejpam-4911	213	15	=	=	SYM
ejpam-4911	213	16	{	{	PUNCT
ejpam-4911	213	17	∅	∅	NOUN
ejpam-4911	213	18	,	,	PUNCT
ejpam-4911	213	19	{	{	PUNCT
ejpam-4911	213	20	e	e	NOUN
ejpam-4911	213	21	,	,	PUNCT
ejpam-4911	213	22	f	f	PROPN
ejpam-4911	213	23	}	}	PUNCT
ejpam-4911	213	24	,	,	PUNCT
ejpam-4911	213	25	{	{	PUNCT
ejpam-4911	213	26	e	e	NOUN
ejpam-4911	213	27	,	,	PUNCT
ejpam-4911	213	28	k	k	NOUN
ejpam-4911	213	29	}	}	PUNCT
ejpam-4911	213	30	,	,	PUNCT
ejpam-4911	213	31	{	{	PUNCT
ejpam-4911	213	32	e	e	NOUN
ejpam-4911	213	33	,	,	PUNCT
ejpam-4911	213	34	f	f	PROPN
ejpam-4911	213	35	,	,	PUNCT
ejpam-4911	213	36	k	k	NOUN
ejpam-4911	213	37	}	}	PUNCT
ejpam-4911	213	38	}	}	PUNCT
ejpam-4911	213	39	and	and	CCONJ
ejpam-4911	213	40	µ2	µ2	PROPN
ejpam-4911	213	41	=	=	PUNCT
ejpam-4911	213	42	{	{	PUNCT
ejpam-4911	213	43	∅	∅	NOUN
ejpam-4911	213	44	,	,	PUNCT
ejpam-4911	213	45	{	{	PUNCT
ejpam-4911	213	46	e	e	NOUN
ejpam-4911	213	47	,	,	PUNCT
ejpam-4911	213	48	l	l	NOUN
ejpam-4911	213	49	}	}	PUNCT
ejpam-4911	213	50	,	,	PUNCT
ejpam-4911	213	51	{	{	PUNCT
ejpam-4911	213	52	f	f	X
ejpam-4911	213	53	,	,	PUNCT
ejpam-4911	213	54	l	l	NOUN
ejpam-4911	213	55	}	}	PUNCT
ejpam-4911	213	56	,	,	PUNCT
ejpam-4911	213	57	{	{	PUNCT
ejpam-4911	213	58	e	e	NOUN
ejpam-4911	213	59	,	,	PUNCT
ejpam-4911	213	60	f	f	X
ejpam-4911	213	61	,	,	PUNCT
ejpam-4911	213	62	l	l	NOUN
ejpam-4911	213	63	}	}	PUNCT
ejpam-4911	213	64	}	}	PUNCT
ejpam-4911	213	65	.	.	PUNCT
ejpam-4911	214	1	then	then	ADV
ejpam-4911	214	2	{	{	PUNCT
ejpam-4911	214	3	k	k	NOUN
ejpam-4911	214	4	}	}	PUNCT
ejpam-4911	214	5	is	be	AUX
ejpam-4911	214	6	a	a	DET
ejpam-4911	214	7	non	non	ADJ
ejpam-4911	214	8	-	-	ADJ
ejpam-4911	214	9	null	null	ADJ
ejpam-4911	214	10	(	(	PUNCT
ejpam-4911	214	11	s	s	PROPN
ejpam-4911	214	12	,	,	PUNCT
ejpam-4911	214	13	v)-nowhere	v)-nowhere	PUNCT
ejpam-4911	214	14	dense	dense	ADJ
ejpam-4911	214	15	set	set	NOUN
ejpam-4911	214	16	in	in	ADP
ejpam-4911	214	17	(	(	PUNCT
ejpam-4911	214	18	x,µ1	x,µ1	PROPN
ejpam-4911	214	19	,	,	PUNCT
ejpam-4911	214	20	µ2	µ2	PROPN
ejpam-4911	214	21	)	)	PUNCT
ejpam-4911	214	22	where	where	SCONJ
ejpam-4911	214	23	s	s	X
ejpam-4911	214	24	,	,	PUNCT
ejpam-4911	214	25	v	v	NOUN
ejpam-4911	214	26	=	=	SYM
ejpam-4911	214	27	1	1	NUM
ejpam-4911	214	28	,	,	PUNCT
ejpam-4911	214	29	2	2	NUM
ejpam-4911	214	30	;	;	PUNCT
ejpam-4911	214	31	s	s	VERB
ejpam-4911	214	32	̸=	̸=	PROPN
ejpam-4911	214	33	v.	v.	ADV
ejpam-4911	214	34	in	in	ADP
ejpam-4911	214	35	a	a	DET
ejpam-4911	214	36	bigeneralized	bigeneralize	VERB
ejpam-4911	214	37	topological	topological	ADJ
ejpam-4911	214	38	space	space	NOUN
ejpam-4911	214	39	,	,	PUNCT
ejpam-4911	214	40	if	if	SCONJ
ejpam-4911	214	41	q	q	X
ejpam-4911	214	42	∈	∈	PROPN
ejpam-4911	214	43	(	(	PUNCT
ejpam-4911	214	44	s	s	PROPN
ejpam-4911	214	45	,	,	PUNCT
ejpam-4911	214	46	v	v	NOUN
ejpam-4911	214	47	)	)	PUNCT
ejpam-4911	214	48	−	−	PROPN
ejpam-4911	214	49	n	n	CCONJ
ejpam-4911	214	50	(	(	PUNCT
ejpam-4911	214	51	x	x	X
ejpam-4911	214	52	)	)	PUNCT
ejpam-4911	214	53	and	and	CCONJ
ejpam-4911	214	54	p	p	X
ejpam-4911	214	55	⊂	⊂	PROPN
ejpam-4911	214	56	q	q	X
ejpam-4911	214	57	,	,	PUNCT
ejpam-4911	214	58	then	then	ADV
ejpam-4911	214	59	p	p	PROPN
ejpam-4911	214	60	∈	∈	PROPN
ejpam-4911	214	61	(	(	PUNCT
ejpam-4911	214	62	s	s	PROPN
ejpam-4911	214	63	,	,	PUNCT
ejpam-4911	214	64	v)−n	v)−n	X
ejpam-4911	214	65	(	(	PUNCT
ejpam-4911	214	66	x	x	NOUN
ejpam-4911	214	67	)	)	PUNCT
ejpam-4911	214	68	where	where	SCONJ
ejpam-4911	214	69	s	s	X
ejpam-4911	214	70	,	,	PUNCT
ejpam-4911	214	71	v	v	NOUN
ejpam-4911	214	72	=	=	SYM
ejpam-4911	214	73	1	1	NUM
ejpam-4911	214	74	,	,	PUNCT
ejpam-4911	214	75	2	2	NUM
ejpam-4911	214	76	and	and	CCONJ
ejpam-4911	214	77	s	s	PART
ejpam-4911	214	78	̸=	̸=	PROPN
ejpam-4911	214	79	v.	v.	ADP
ejpam-4911	214	80	theorem	theorem	ADJ
ejpam-4911	214	81	15	15	NUM
ejpam-4911	214	82	.	.	PUNCT
ejpam-4911	215	1	in	in	ADP
ejpam-4911	215	2	a	a	DET
ejpam-4911	215	3	bgts	bgts	NOUN
ejpam-4911	215	4	(	(	PUNCT
ejpam-4911	215	5	x,µ1	x,µ1	PROPN
ejpam-4911	215	6	,	,	PUNCT
ejpam-4911	215	7	µ2	µ2	PROPN
ejpam-4911	215	8	)	)	PUNCT
ejpam-4911	215	9	,	,	PUNCT
ejpam-4911	215	10	d	d	PROPN
ejpam-4911	215	11	∈	∈	PROPN
ejpam-4911	215	12	(	(	PUNCT
ejpam-4911	215	13	s	s	PROPN
ejpam-4911	215	14	,	,	PUNCT
ejpam-4911	215	15	v)−n	v)−n	X
ejpam-4911	215	16	(	(	PUNCT
ejpam-4911	215	17	x	x	X
ejpam-4911	215	18	)	)	PUNCT
ejpam-4911	215	19	if	if	SCONJ
ejpam-4911	215	20	and	and	CCONJ
ejpam-4911	215	21	only	only	ADV
ejpam-4911	215	22	if	if	SCONJ
ejpam-4911	215	23	cv(d	cv(d	VERB
ejpam-4911	215	24	)	)	PUNCT
ejpam-4911	215	25	∈	∈	PROPN
ejpam-4911	215	26	(	(	PUNCT
ejpam-4911	215	27	s	s	PROPN
ejpam-4911	215	28	,	,	PUNCT
ejpam-4911	215	29	v)−	v)−	PROPN
ejpam-4911	215	30	n	n	CCONJ
ejpam-4911	215	31	(	(	PUNCT
ejpam-4911	215	32	x	x	X
ejpam-4911	215	33	)	)	PUNCT
ejpam-4911	215	34	where	where	SCONJ
ejpam-4911	215	35	s	s	X
ejpam-4911	215	36	,	,	PUNCT
ejpam-4911	215	37	v	v	NOUN
ejpam-4911	215	38	=	=	SYM
ejpam-4911	215	39	1	1	NUM
ejpam-4911	215	40	,	,	PUNCT
ejpam-4911	215	41	2	2	NUM
ejpam-4911	215	42	and	and	CCONJ
ejpam-4911	215	43	s	s	VERB
ejpam-4911	215	44	̸=	̸=	PROPN
ejpam-4911	215	45	v.	v.	ADV
ejpam-4911	215	46	in	in	ADP
ejpam-4911	215	47	a	a	DET
ejpam-4911	215	48	bgts	bgts	NOUN
ejpam-4911	215	49	(	(	PUNCT
ejpam-4911	215	50	x,µ1	x,µ1	PROPN
ejpam-4911	215	51	,	,	PUNCT
ejpam-4911	215	52	µ2	µ2	PROPN
ejpam-4911	215	53	)	)	PUNCT
ejpam-4911	215	54	,	,	PUNCT
ejpam-4911	215	55	(	(	PUNCT
ejpam-4911	215	56	1	1	NUM
ejpam-4911	215	57	,	,	PUNCT
ejpam-4911	215	58	2)−n	2)−n	NUM
ejpam-4911	215	59	(	(	PUNCT
ejpam-4911	215	60	x	x	X
ejpam-4911	215	61	)	)	PUNCT
ejpam-4911	215	62	̸=	̸=	PROPN
ejpam-4911	215	63	(	(	PUNCT
ejpam-4911	215	64	2	2	NUM
ejpam-4911	215	65	,	,	PUNCT
ejpam-4911	215	66	1)−n	1)−n	NUM
ejpam-4911	215	67	(	(	PUNCT
ejpam-4911	215	68	x	x	NOUN
ejpam-4911	215	69	)	)	PUNCT
ejpam-4911	215	70	as	as	SCONJ
ejpam-4911	215	71	shown	show	VERB
ejpam-4911	215	72	by	by	ADP
ejpam-4911	215	73	the	the	DET
ejpam-4911	215	74	below	below	ADJ
ejpam-4911	215	75	example	example	NOUN
ejpam-4911	215	76	16	16	NUM
ejpam-4911	215	77	.	.	PUNCT
ejpam-4911	216	1	also	also	ADV
ejpam-4911	216	2	,	,	PUNCT
ejpam-4911	216	3	this	this	DET
ejpam-4911	216	4	example	example	NOUN
ejpam-4911	216	5	shows	show	VERB
ejpam-4911	216	6	that	that	SCONJ
ejpam-4911	216	7	(	(	PUNCT
ejpam-4911	216	8	s	s	X
ejpam-4911	216	9	,	,	PUNCT
ejpam-4911	216	10	v)−n	v)−n	X
ejpam-4911	216	11	(	(	PUNCT
ejpam-4911	216	12	x	x	X
ejpam-4911	216	13	)	)	PUNCT
ejpam-4911	216	14	is	be	AUX
ejpam-4911	216	15	not	not	PART
ejpam-4911	216	16	closed	close	VERB
ejpam-4911	216	17	under	under	ADP
ejpam-4911	216	18	finite	finite	ADJ
ejpam-4911	216	19	union	union	NOUN
ejpam-4911	216	20	in	in	ADP
ejpam-4911	216	21	general	general	PROPN
ejpam-4911	216	22	.	.	PUNCT
ejpam-4911	217	1	example	example	NOUN
ejpam-4911	218	1	16	16	NUM
ejpam-4911	218	2	.	.	PUNCT
ejpam-4911	219	1	let	let	AUX
ejpam-4911	219	2	(	(	PUNCT
ejpam-4911	219	3	x,µ1	x,µ1	NOUN
ejpam-4911	219	4	,	,	PUNCT
ejpam-4911	219	5	µ2	µ2	PROPN
ejpam-4911	219	6	)	)	PUNCT
ejpam-4911	219	7	be	be	AUX
ejpam-4911	219	8	a	a	DET
ejpam-4911	219	9	bgts	bgts	NOUN
ejpam-4911	219	10	where	where	SCONJ
ejpam-4911	219	11	x	x	ADP
ejpam-4911	219	12	=	=	PRON
ejpam-4911	219	13	{	{	PUNCT
ejpam-4911	219	14	e	e	NOUN
ejpam-4911	219	15	,	,	PUNCT
ejpam-4911	219	16	f	f	PROPN
ejpam-4911	219	17	,	,	PUNCT
ejpam-4911	219	18	k	k	NOUN
ejpam-4911	219	19	,	,	PUNCT
ejpam-4911	219	20	l	l	NOUN
ejpam-4911	219	21	}	}	PUNCT
ejpam-4911	219	22	;	;	PUNCT
ejpam-4911	219	23	µ1	µ1	PROPN
ejpam-4911	219	24	=	=	SYM
ejpam-4911	219	25	{	{	PUNCT
ejpam-4911	219	26	∅	∅	NOUN
ejpam-4911	219	27	,	,	PUNCT
ejpam-4911	219	28	{	{	PUNCT
ejpam-4911	219	29	e	e	NOUN
ejpam-4911	219	30	,	,	PUNCT
ejpam-4911	219	31	l	l	NOUN
ejpam-4911	219	32	}	}	PUNCT
ejpam-4911	219	33	,	,	PUNCT
ejpam-4911	219	34	{	{	PUNCT
ejpam-4911	219	35	f	f	X
ejpam-4911	219	36	,	,	PUNCT
ejpam-4911	219	37	l	l	NOUN
ejpam-4911	219	38	}	}	PUNCT
ejpam-4911	219	39	,	,	PUNCT
ejpam-4911	219	40	{	{	PUNCT
ejpam-4911	219	41	e	e	NOUN
ejpam-4911	219	42	,	,	PUNCT
ejpam-4911	219	43	f	f	X
ejpam-4911	219	44	,	,	PUNCT
ejpam-4911	219	45	l	l	NOUN
ejpam-4911	219	46	}	}	PUNCT
ejpam-4911	219	47	}	}	PUNCT
ejpam-4911	219	48	and	and	CCONJ
ejpam-4911	219	49	µ2	µ2	PROPN
ejpam-4911	219	50	=	=	PUNCT
ejpam-4911	219	51	{	{	PUNCT
ejpam-4911	219	52	∅	∅	NOUN
ejpam-4911	219	53	,	,	PUNCT
ejpam-4911	219	54	{	{	PUNCT
ejpam-4911	219	55	e	e	NOUN
ejpam-4911	219	56	,	,	PUNCT
ejpam-4911	219	57	f	f	PROPN
ejpam-4911	219	58	}	}	PUNCT
ejpam-4911	219	59	,	,	PUNCT
ejpam-4911	219	60	{	{	PUNCT
ejpam-4911	219	61	f	f	X
ejpam-4911	219	62	,	,	PUNCT
ejpam-4911	219	63	l	l	NOUN
ejpam-4911	219	64	}	}	PUNCT
ejpam-4911	219	65	,	,	PUNCT
ejpam-4911	219	66	{	{	PUNCT
ejpam-4911	219	67	e	e	NOUN
ejpam-4911	219	68	,	,	PUNCT
ejpam-4911	219	69	f	f	X
ejpam-4911	219	70	,	,	PUNCT
ejpam-4911	219	71	l	l	NOUN
ejpam-4911	219	72	}	}	PUNCT
ejpam-4911	219	73	}	}	PUNCT
ejpam-4911	219	74	.	.	PUNCT
ejpam-4911	220	1	then	then	ADV
ejpam-4911	220	2	•	•	X
ejpam-4911	220	3	(	(	PUNCT
ejpam-4911	220	4	1	1	NUM
ejpam-4911	220	5	,	,	PUNCT
ejpam-4911	220	6	2)−n	2)−n	NUM
ejpam-4911	220	7	(	(	PUNCT
ejpam-4911	220	8	x	x	X
ejpam-4911	220	9	)	)	PUNCT
ejpam-4911	220	10	=	=	SYM
ejpam-4911	220	11	{	{	PUNCT
ejpam-4911	220	12	∅	∅	NOUN
ejpam-4911	220	13	,	,	PUNCT
ejpam-4911	220	14	{	{	PUNCT
ejpam-4911	220	15	e	e	NOUN
ejpam-4911	220	16	}	}	PUNCT
ejpam-4911	220	17	,	,	PUNCT
ejpam-4911	220	18	{	{	PUNCT
ejpam-4911	220	19	k	k	X
ejpam-4911	220	20	}	}	PUNCT
ejpam-4911	220	21	,	,	PUNCT
ejpam-4911	220	22	{	{	PUNCT
ejpam-4911	220	23	l	l	NOUN
ejpam-4911	220	24	}	}	PUNCT
ejpam-4911	220	25	,	,	PUNCT
ejpam-4911	220	26	{	{	PUNCT
ejpam-4911	220	27	e	e	NOUN
ejpam-4911	220	28	,	,	PUNCT
ejpam-4911	220	29	k	k	NOUN
ejpam-4911	220	30	}	}	PUNCT
ejpam-4911	220	31	,	,	PUNCT
ejpam-4911	220	32	{	{	PUNCT
ejpam-4911	220	33	k	k	X
ejpam-4911	220	34	,	,	PUNCT
ejpam-4911	220	35	l	l	NOUN
ejpam-4911	220	36	}	}	PUNCT
ejpam-4911	220	37	}	}	PUNCT
ejpam-4911	220	38	•	•	NOUN
ejpam-4911	220	39	(	(	PUNCT
ejpam-4911	220	40	2	2	NUM
ejpam-4911	220	41	,	,	PUNCT
ejpam-4911	220	42	1)−n	1)−n	NUM
ejpam-4911	220	43	(	(	PUNCT
ejpam-4911	220	44	x	x	X
ejpam-4911	220	45	)	)	PUNCT
ejpam-4911	220	46	=	=	SYM
ejpam-4911	220	47	{	{	PUNCT
ejpam-4911	220	48	∅	∅	NOUN
ejpam-4911	220	49	,	,	PUNCT
ejpam-4911	220	50	{	{	PUNCT
ejpam-4911	220	51	e	e	NOUN
ejpam-4911	220	52	}	}	PUNCT
ejpam-4911	220	53	,	,	PUNCT
ejpam-4911	220	54	{	{	PUNCT
ejpam-4911	220	55	f	f	X
ejpam-4911	220	56	}	}	PUNCT
ejpam-4911	220	57	,	,	PUNCT
ejpam-4911	220	58	{	{	PUNCT
ejpam-4911	220	59	k	k	X
ejpam-4911	220	60	}	}	PUNCT
ejpam-4911	220	61	,	,	PUNCT
ejpam-4911	220	62	{	{	PUNCT
ejpam-4911	220	63	e	e	NOUN
ejpam-4911	220	64	,	,	PUNCT
ejpam-4911	220	65	k	k	NOUN
ejpam-4911	220	66	}	}	PUNCT
ejpam-4911	220	67	,	,	PUNCT
ejpam-4911	220	68	{	{	PUNCT
ejpam-4911	220	69	f	f	X
ejpam-4911	220	70	,	,	PUNCT
ejpam-4911	220	71	k	k	NOUN
ejpam-4911	220	72	}	}	PUNCT
ejpam-4911	220	73	}	}	PUNCT
ejpam-4911	220	74	.	.	PUNCT
ejpam-4911	221	1	thus	thus	ADV
ejpam-4911	221	2	,	,	PUNCT
ejpam-4911	221	3	(	(	PUNCT
ejpam-4911	221	4	2	2	NUM
ejpam-4911	221	5	,	,	PUNCT
ejpam-4911	221	6	1)−n	1)−n	NUM
ejpam-4911	221	7	(	(	PUNCT
ejpam-4911	221	8	x	x	X
ejpam-4911	221	9	)	)	PUNCT
ejpam-4911	221	10	̸=	̸=	PROPN
ejpam-4911	221	11	(	(	PUNCT
ejpam-4911	221	12	1	1	NUM
ejpam-4911	221	13	,	,	PUNCT
ejpam-4911	221	14	2)−n	2)−n	NUM
ejpam-4911	221	15	(	(	PUNCT
ejpam-4911	221	16	x	x	NOUN
ejpam-4911	221	17	)	)	PUNCT
ejpam-4911	221	18	.	.	PUNCT
ejpam-4911	222	1	here	here	ADV
ejpam-4911	222	2	{	{	PUNCT
ejpam-4911	222	3	e	e	NOUN
ejpam-4911	222	4	}	}	PUNCT
ejpam-4911	222	5	and	and	CCONJ
ejpam-4911	222	6	{	{	PUNCT
ejpam-4911	222	7	l	l	NOUN
ejpam-4911	222	8	}	}	PUNCT
ejpam-4911	222	9	are	be	AUX
ejpam-4911	222	10	in	in	ADP
ejpam-4911	222	11	(	(	PUNCT
ejpam-4911	222	12	1	1	NUM
ejpam-4911	222	13	,	,	PUNCT
ejpam-4911	222	14	2)−n	2)−n	NUM
ejpam-4911	222	15	(	(	PUNCT
ejpam-4911	222	16	x	x	NOUN
ejpam-4911	222	17	)	)	PUNCT
ejpam-4911	222	18	.	.	PUNCT
ejpam-4911	223	1	but	but	CCONJ
ejpam-4911	223	2	{	{	PUNCT
ejpam-4911	223	3	e	e	NOUN
ejpam-4911	223	4	,	,	PUNCT
ejpam-4911	223	5	l	l	NOUN
ejpam-4911	223	6	}	}	PUNCT
ejpam-4911	223	7	/∈	/∈	PUNCT
ejpam-4911	224	1	(	(	PUNCT
ejpam-4911	224	2	1	1	NUM
ejpam-4911	224	3	,	,	PUNCT
ejpam-4911	224	4	2)−n	2)−n	NUM
ejpam-4911	224	5	(	(	PUNCT
ejpam-4911	224	6	x	x	NOUN
ejpam-4911	224	7	)	)	PUNCT
ejpam-4911	224	8	.	.	PUNCT
ejpam-4911	225	1	also	also	ADV
ejpam-4911	225	2	,	,	PUNCT
ejpam-4911	225	3	{	{	PUNCT
ejpam-4911	225	4	e	e	NOUN
ejpam-4911	225	5	}	}	PUNCT
ejpam-4911	225	6	and	and	CCONJ
ejpam-4911	225	7	{	{	PUNCT
ejpam-4911	225	8	f	f	X
ejpam-4911	225	9	}	}	PUNCT
ejpam-4911	225	10	are	be	AUX
ejpam-4911	225	11	in	in	ADP
ejpam-4911	225	12	(	(	PUNCT
ejpam-4911	225	13	2	2	NUM
ejpam-4911	225	14	,	,	PUNCT
ejpam-4911	225	15	1)−n	1)−n	NUM
ejpam-4911	225	16	(	(	PUNCT
ejpam-4911	225	17	x	x	NOUN
ejpam-4911	225	18	)	)	PUNCT
ejpam-4911	225	19	.	.	PUNCT
ejpam-4911	226	1	but	but	CCONJ
ejpam-4911	226	2	{	{	PUNCT
ejpam-4911	226	3	e	e	NOUN
ejpam-4911	226	4	,	,	PUNCT
ejpam-4911	226	5	f	f	NOUN
ejpam-4911	226	6	}	}	PUNCT
ejpam-4911	226	7	/∈	/∈	PUNCT
ejpam-4911	227	1	(	(	PUNCT
ejpam-4911	227	2	2	2	NUM
ejpam-4911	227	3	,	,	PUNCT
ejpam-4911	227	4	1)−n	1)−n	NUM
ejpam-4911	227	5	(	(	PUNCT
ejpam-4911	227	6	x	x	NOUN
ejpam-4911	227	7	)	)	PUNCT
ejpam-4911	227	8	.	.	PUNCT
ejpam-4911	228	1	theorem	theorem	NOUN
ejpam-4911	228	2	17	17	NUM
ejpam-4911	228	3	.	.	PUNCT
ejpam-4911	229	1	let	let	VERB
ejpam-4911	229	2	µ1	µ1	VERB
ejpam-4911	229	3	and	and	CCONJ
ejpam-4911	229	4	µ2	µ2	PROPN
ejpam-4911	229	5	be	be	AUX
ejpam-4911	229	6	two	two	NUM
ejpam-4911	229	7	generlized	generlize	VERB
ejpam-4911	229	8	topologies	topology	NOUN
ejpam-4911	229	9	on	on	ADP
ejpam-4911	229	10	a	a	DET
ejpam-4911	229	11	non	non	ADJ
ejpam-4911	229	12	-	-	ADJ
ejpam-4911	229	13	null	null	ADJ
ejpam-4911	229	14	set	set	NOUN
ejpam-4911	229	15	x.	x.	NOUN
ejpam-4911	230	1	if	if	SCONJ
ejpam-4911	230	2	µs	µs	ADP
ejpam-4911	230	3	⊆	⊆	NUM
ejpam-4911	230	4	µv	µv	NOUN
ejpam-4911	230	5	,	,	PUNCT
ejpam-4911	230	6	then	then	ADV
ejpam-4911	230	7	(	(	PUNCT
ejpam-4911	230	8	v	v	NOUN
ejpam-4911	230	9	,	,	PUNCT
ejpam-4911	230	10	s)−n	s)−n	ADP
ejpam-4911	230	11	(	(	PUNCT
ejpam-4911	230	12	x	x	X
ejpam-4911	230	13	)	)	PUNCT
ejpam-4911	230	14	⊆	⊆	NUM
ejpam-4911	230	15	(	(	PUNCT
ejpam-4911	230	16	s	s	X
ejpam-4911	230	17	,	,	PUNCT
ejpam-4911	230	18	v)−n	v)−n	X
ejpam-4911	230	19	(	(	PUNCT
ejpam-4911	230	20	x	x	NOUN
ejpam-4911	230	21	)	)	PUNCT
ejpam-4911	230	22	where	where	SCONJ
ejpam-4911	230	23	s	s	X
ejpam-4911	230	24	,	,	PUNCT
ejpam-4911	230	25	v	v	NOUN
ejpam-4911	230	26	=	=	SYM
ejpam-4911	230	27	1	1	NUM
ejpam-4911	230	28	,	,	PUNCT
ejpam-4911	230	29	2	2	NUM
ejpam-4911	230	30	and	and	CCONJ
ejpam-4911	230	31	s	s	VERB
ejpam-4911	230	32	̸=	̸=	PROPN
ejpam-4911	230	33	v.	v.	ADP
ejpam-4911	230	34	proof	proof	NOUN
ejpam-4911	230	35	.	.	PUNCT
ejpam-4911	231	1	we	we	PRON
ejpam-4911	231	2	give	give	VERB
ejpam-4911	231	3	the	the	DET
ejpam-4911	231	4	detailed	detailed	ADJ
ejpam-4911	231	5	proof	proof	NOUN
ejpam-4911	231	6	only	only	ADV
ejpam-4911	231	7	for	for	ADP
ejpam-4911	231	8	s	s	NOUN
ejpam-4911	231	9	=	=	SYM
ejpam-4911	231	10	1	1	NUM
ejpam-4911	231	11	and	and	CCONJ
ejpam-4911	231	12	v	v	NOUN
ejpam-4911	231	13	=	=	SYM
ejpam-4911	231	14	2	2	X
ejpam-4911	231	15	.	.	X
ejpam-4911	231	16	assume	assume	VERB
ejpam-4911	231	17	that	that	SCONJ
ejpam-4911	231	18	,	,	PUNCT
ejpam-4911	231	19	µ1	µ1	PROPN
ejpam-4911	231	20	⊆	⊆	NUM
ejpam-4911	231	21	µ2	µ2	PROPN
ejpam-4911	231	22	(	(	PUNCT
ejpam-4911	231	23	5	5	NUM
ejpam-4911	231	24	)	)	PUNCT
ejpam-4911	231	25	let	let	VERB
ejpam-4911	231	26	d	d	X
ejpam-4911	231	27	∈	∈	PROPN
ejpam-4911	231	28	(	(	PUNCT
ejpam-4911	231	29	2	2	NUM
ejpam-4911	231	30	,	,	PUNCT
ejpam-4911	231	31	1)−n	1)−n	NUM
ejpam-4911	231	32	(	(	PUNCT
ejpam-4911	231	33	x	x	NOUN
ejpam-4911	231	34	)	)	PUNCT
ejpam-4911	231	35	.	.	PUNCT
ejpam-4911	232	1	then	then	ADV
ejpam-4911	232	2	i2(c1(d	i2(c1(d	NUM
ejpam-4911	232	3	)	)	PUNCT
ejpam-4911	232	4	)	)	PUNCT
ejpam-4911	233	1	=	=	VERB
ejpam-4911	233	2	∅.	∅.	AUX
ejpam-4911	233	3	suppose	suppose	VERB
ejpam-4911	233	4	i1(c2(d	i1(c2(d	ADV
ejpam-4911	233	5	)	)	PUNCT
ejpam-4911	233	6	)	)	PUNCT
ejpam-4911	234	1	̸=	̸=	PROPN
ejpam-4911	234	2	∅.	∅.	NOUN
ejpam-4911	234	3	there	there	ADV
ejpam-4911	234	4	exists	exist	VERB
ejpam-4911	234	5	k	k	PROPN
ejpam-4911	234	6	∈	∈	PROPN
ejpam-4911	234	7	µ̃1	µ̃1	PROPN
ejpam-4911	234	8	such	such	ADJ
ejpam-4911	234	9	that	that	SCONJ
ejpam-4911	234	10	k	k	PROPN
ejpam-4911	234	11	⊂	⊂	PROPN
ejpam-4911	234	12	c2(d	c2(d	PROPN
ejpam-4911	234	13	)	)	PUNCT
ejpam-4911	234	14	.	.	PUNCT
ejpam-4911	235	1	from	from	ADP
ejpam-4911	235	2	(	(	PUNCT
ejpam-4911	235	3	5	5	NUM
ejpam-4911	235	4	)	)	PUNCT
ejpam-4911	235	5	,	,	PUNCT
ejpam-4911	235	6	k	k	PROPN
ejpam-4911	235	7	∈	∈	PROPN
ejpam-4911	235	8	µ̃2	µ̃2	PROPN
ejpam-4911	235	9	.	.	PUNCT
ejpam-4911	235	10	then	then	ADV
ejpam-4911	235	11	i2(c2(d	i2(c2(d	PROPN
ejpam-4911	235	12	)	)	PUNCT
ejpam-4911	235	13	)	)	PUNCT
ejpam-4911	236	1	̸=	̸=	PROPN
ejpam-4911	236	2	∅.	∅.	PRON
ejpam-4911	236	3	by	by	ADP
ejpam-4911	236	4	(	(	PUNCT
ejpam-4911	236	5	5	5	X
ejpam-4911	236	6	)	)	PUNCT
ejpam-4911	236	7	we	we	PRON
ejpam-4911	236	8	get	get	VERB
ejpam-4911	236	9	c2(d	c2(d	ADJ
ejpam-4911	236	10	)	)	PUNCT
ejpam-4911	236	11	⊂	⊂	PROPN
ejpam-4911	236	12	c1(d	c1(d	NUM
ejpam-4911	236	13	)	)	PUNCT
ejpam-4911	236	14	.	.	PUNCT
ejpam-4911	237	1	thus	thus	ADV
ejpam-4911	237	2	,	,	PUNCT
ejpam-4911	237	3	i2(c1(d	i2(c1(d	NOUN
ejpam-4911	237	4	)	)	PUNCT
ejpam-4911	237	5	)	)	PUNCT
ejpam-4911	238	1	̸=	̸=	PROPN
ejpam-4911	238	2	∅	∅	NOUN
ejpam-4911	238	3	which	which	PRON
ejpam-4911	238	4	is	be	AUX
ejpam-4911	238	5	not	not	PART
ejpam-4911	238	6	possible	possible	ADJ
ejpam-4911	238	7	.	.	PUNCT
ejpam-4911	239	1	therefore	therefore	ADV
ejpam-4911	239	2	,	,	PUNCT
ejpam-4911	239	3	i1(c2(d	i1(c2(d	PROPN
ejpam-4911	239	4	)	)	PUNCT
ejpam-4911	239	5	)	)	PUNCT
ejpam-4911	240	1	=	=	PUNCT
ejpam-4911	240	2	∅.	∅.	VERB
ejpam-4911	240	3	hence	hence	ADV
ejpam-4911	240	4	d	d	X
ejpam-4911	240	5	∈	∈	PROPN
ejpam-4911	240	6	(	(	PUNCT
ejpam-4911	240	7	1	1	NUM
ejpam-4911	240	8	,	,	PUNCT
ejpam-4911	240	9	2)−n	2)−n	NUM
ejpam-4911	240	10	(	(	PUNCT
ejpam-4911	240	11	x	x	NOUN
ejpam-4911	240	12	)	)	PUNCT
ejpam-4911	240	13	.	.	PUNCT
ejpam-4911	241	1	the	the	DET
ejpam-4911	241	2	following	follow	VERB
ejpam-4911	241	3	theorem	theorem	VERB
ejpam-4911	241	4	19	19	NUM
ejpam-4911	241	5	describes	describe	VERB
ejpam-4911	241	6	the	the	DET
ejpam-4911	241	7	below	below	ADJ
ejpam-4911	241	8	diagram	diagram	NOUN
ejpam-4911	241	9	.	.	PUNCT
ejpam-4911	242	1	y.	y.	PROPN
ejpam-4911	242	2	farhat	farhat	PROPN
ejpam-4911	242	3	,	,	PUNCT
ejpam-4911	242	4	v.	v.	ADP
ejpam-4911	242	5	subramanian	subramanian	PROPN
ejpam-4911	242	6	/	/	SYM
ejpam-4911	242	7	eur	eur	PROPN
ejpam-4911	242	8	.	.	PUNCT
ejpam-4911	243	1	j.	j.	PROPN
ejpam-4911	243	2	pure	pure	PROPN
ejpam-4911	243	3	appl	appl	PROPN
ejpam-4911	243	4	.	.	PROPN
ejpam-4911	243	5	math	math	PROPN
ejpam-4911	243	6	,	,	PUNCT
ejpam-4911	243	7	16	16	NUM
ejpam-4911	243	8	(	(	PUNCT
ejpam-4911	243	9	4	4	NUM
ejpam-4911	243	10	)	)	PUNCT
ejpam-4911	243	11	(	(	PUNCT
ejpam-4911	243	12	2023	2023	NUM
ejpam-4911	243	13	)	)	PUNCT
ejpam-4911	243	14	,	,	PUNCT
ejpam-4911	243	15	2049	2049	NUM
ejpam-4911	243	16	-	-	SYM
ejpam-4911	243	17	2065	2065	NUM
ejpam-4911	243	18	2057	2057	NUM
ejpam-4911	243	19	µv	µv	NOUN
ejpam-4911	243	20	−	−	PROPN
ejpam-4911	243	21	nowhere	nowhere	ADV
ejpam-4911	243	22	dense	dense	ADJ
ejpam-4911	243	23	(	(	PUNCT
ejpam-4911	243	24	s	s	X
ejpam-4911	243	25	,	,	PUNCT
ejpam-4911	243	26	v)−	v)−	PROPN
ejpam-4911	243	27	nowhere	nowhere	ADV
ejpam-4911	243	28	dense	dense	ADJ
ejpam-4911	243	29	µs	µs	X
ejpam-4911	243	30	−	−	NOUN
ejpam-4911	243	31	nowhere	nowhere	ADV
ejpam-4911	243	32	dense	dense	ADJ
ejpam-4911	243	33	the	the	DET
ejpam-4911	243	34	following	follow	VERB
ejpam-4911	243	35	example	example	NOUN
ejpam-4911	243	36	18	18	NUM
ejpam-4911	243	37	shows	show	VERB
ejpam-4911	243	38	that	that	SCONJ
ejpam-4911	243	39	the	the	DET
ejpam-4911	243	40	existence	existence	NOUN
ejpam-4911	243	41	of	of	ADP
ejpam-4911	243	42	the	the	DET
ejpam-4911	243	43	below	below	NOUN
ejpam-4911	243	44	theorem	theorem	NOUN
ejpam-4911	243	45	19	19	NUM
ejpam-4911	243	46	.	.	PUNCT
ejpam-4911	243	47	example	example	NOUN
ejpam-4911	243	48	18	18	NUM
ejpam-4911	243	49	.	.	PUNCT
ejpam-4911	244	1	(	(	PUNCT
ejpam-4911	244	2	a	a	X
ejpam-4911	244	3	)	)	PUNCT
ejpam-4911	244	4	fix	fix	NOUN
ejpam-4911	244	5	s	s	PART
ejpam-4911	244	6	=	=	SYM
ejpam-4911	244	7	1	1	NUM
ejpam-4911	244	8	,	,	PUNCT
ejpam-4911	244	9	v	v	NOUN
ejpam-4911	244	10	=	=	SYM
ejpam-4911	244	11	2	2	X
ejpam-4911	244	12	.	.	PUNCT
ejpam-4911	244	13	consider	consider	VERB
ejpam-4911	244	14	the	the	DET
ejpam-4911	244	15	bigeneralized	bigeneralized	ADJ
ejpam-4911	244	16	topological	topological	ADJ
ejpam-4911	244	17	space	space	NOUN
ejpam-4911	244	18	(	(	PUNCT
ejpam-4911	244	19	x,µ1	x,µ1	PROPN
ejpam-4911	244	20	,	,	PUNCT
ejpam-4911	244	21	µ2	µ2	PROPN
ejpam-4911	244	22	)	)	PUNCT
ejpam-4911	244	23	where	where	SCONJ
ejpam-4911	244	24	x	x	X
ejpam-4911	244	25	=	=	PRON
ejpam-4911	244	26	{	{	PUNCT
ejpam-4911	244	27	p	p	X
ejpam-4911	244	28	,	,	PUNCT
ejpam-4911	244	29	q	q	ADJ
ejpam-4911	244	30	,	,	PUNCT
ejpam-4911	244	31	r	r	NOUN
ejpam-4911	244	32	,	,	PUNCT
ejpam-4911	244	33	s	s	PART
ejpam-4911	244	34	}	}	PUNCT
ejpam-4911	244	35	;	;	PUNCT
ejpam-4911	244	36	µ1	µ1	PROPN
ejpam-4911	244	37	=	=	SYM
ejpam-4911	244	38	{	{	PUNCT
ejpam-4911	244	39	∅	∅	NOUN
ejpam-4911	244	40	,	,	PUNCT
ejpam-4911	244	41	{	{	PUNCT
ejpam-4911	244	42	p	p	X
ejpam-4911	244	43	,	,	PUNCT
ejpam-4911	244	44	r	r	NOUN
ejpam-4911	244	45	}	}	PUNCT
ejpam-4911	244	46	,	,	PUNCT
ejpam-4911	244	47	{	{	PUNCT
ejpam-4911	244	48	q	q	X
ejpam-4911	244	49	,	,	PUNCT
ejpam-4911	244	50	r	r	NOUN
ejpam-4911	244	51	}	}	PUNCT
ejpam-4911	244	52	,	,	PUNCT
ejpam-4911	244	53	{	{	PUNCT
ejpam-4911	244	54	p	p	X
ejpam-4911	244	55	,	,	PUNCT
ejpam-4911	244	56	q	q	ADJ
ejpam-4911	244	57	,	,	PUNCT
ejpam-4911	244	58	r	r	NOUN
ejpam-4911	244	59	}	}	PUNCT
ejpam-4911	244	60	}	}	PUNCT
ejpam-4911	244	61	and	and	CCONJ
ejpam-4911	244	62	µ2	µ2	PROPN
ejpam-4911	244	63	=	=	PUNCT
ejpam-4911	244	64	{	{	PUNCT
ejpam-4911	244	65	∅	∅	NOUN
ejpam-4911	244	66	,	,	PUNCT
ejpam-4911	244	67	{	{	PUNCT
ejpam-4911	244	68	p	p	X
ejpam-4911	244	69	,	,	PUNCT
ejpam-4911	244	70	r	r	NOUN
ejpam-4911	244	71	}	}	PUNCT
ejpam-4911	244	72	,	,	PUNCT
ejpam-4911	244	73	{	{	PUNCT
ejpam-4911	244	74	q	q	X
ejpam-4911	244	75	,	,	PUNCT
ejpam-4911	244	76	r	r	NOUN
ejpam-4911	244	77	}	}	PUNCT
ejpam-4911	244	78	,	,	PUNCT
ejpam-4911	244	79	{	{	PUNCT
ejpam-4911	244	80	p	p	X
ejpam-4911	244	81	,	,	PUNCT
ejpam-4911	244	82	s}{p	s}{p	NOUN
ejpam-4911	244	83	,	,	PUNCT
ejpam-4911	244	84	q	q	X
ejpam-4911	244	85	,	,	PUNCT
ejpam-4911	244	86	r	r	NOUN
ejpam-4911	244	87	}	}	PUNCT
ejpam-4911	244	88	,	,	PUNCT
ejpam-4911	244	89	{	{	PUNCT
ejpam-4911	244	90	p	p	X
ejpam-4911	244	91	,	,	PUNCT
ejpam-4911	244	92	r	r	NOUN
ejpam-4911	244	93	,	,	PUNCT
ejpam-4911	244	94	s	s	PART
ejpam-4911	244	95	}	}	PUNCT
ejpam-4911	244	96	,	,	PUNCT
ejpam-4911	244	97	x	x	NOUN
ejpam-4911	244	98	}	}	PUNCT
ejpam-4911	244	99	.	.	PUNCT
ejpam-4911	245	1	obviously	obviously	ADV
ejpam-4911	245	2	,	,	PUNCT
ejpam-4911	245	3	µ1	µ1	PROPN
ejpam-4911	245	4	⊂	⊂	PROPN
ejpam-4911	245	5	µ2	µ2	PROPN
ejpam-4911	245	6	.	.	PUNCT
ejpam-4911	246	1	take	take	VERB
ejpam-4911	246	2	k	k	NOUN
ejpam-4911	246	3	=	=	PRON
ejpam-4911	246	4	{	{	PUNCT
ejpam-4911	246	5	p	p	X
ejpam-4911	246	6	,	,	PUNCT
ejpam-4911	246	7	s	s	PART
ejpam-4911	246	8	}	}	PUNCT
ejpam-4911	246	9	and	and	CCONJ
ejpam-4911	246	10	l	l	NOUN
ejpam-4911	246	11	=	=	PUNCT
ejpam-4911	246	12	{	{	PUNCT
ejpam-4911	246	13	q	q	NOUN
ejpam-4911	246	14	}	}	PUNCT
ejpam-4911	246	15	.	.	PUNCT
ejpam-4911	247	1	then	then	ADV
ejpam-4911	247	2	k	k	PROPN
ejpam-4911	247	3	is	be	AUX
ejpam-4911	247	4	a	a	DET
ejpam-4911	247	5	µ1	µ1	NOUN
ejpam-4911	247	6	-	-	PUNCT
ejpam-4911	247	7	nowhere	nowhere	ADV
ejpam-4911	247	8	dense	dense	ADJ
ejpam-4911	247	9	set	set	NOUN
ejpam-4911	247	10	and	and	CCONJ
ejpam-4911	247	11	l	l	NOUN
ejpam-4911	247	12	is	be	AUX
ejpam-4911	247	13	a	a	DET
ejpam-4911	247	14	µ2	µ2	PROPN
ejpam-4911	247	15	-	-	PUNCT
ejpam-4911	247	16	nowhere	nowhere	ADV
ejpam-4911	247	17	dense	dense	ADJ
ejpam-4911	247	18	set	set	NOUN
ejpam-4911	247	19	.	.	PUNCT
ejpam-4911	248	1	here	here	ADV
ejpam-4911	248	2	,	,	PUNCT
ejpam-4911	248	3	both	both	CCONJ
ejpam-4911	248	4	k	k	PROPN
ejpam-4911	248	5	and	and	CCONJ
ejpam-4911	248	6	l	l	NOUN
ejpam-4911	248	7	are	be	AUX
ejpam-4911	248	8	in	in	ADP
ejpam-4911	248	9	(	(	PUNCT
ejpam-4911	248	10	1	1	NUM
ejpam-4911	248	11	,	,	PUNCT
ejpam-4911	248	12	2)−n	2)−n	NUM
ejpam-4911	248	13	(	(	PUNCT
ejpam-4911	248	14	x	x	NOUN
ejpam-4911	248	15	)	)	PUNCT
ejpam-4911	248	16	.	.	PUNCT
ejpam-4911	249	1	(	(	PUNCT
ejpam-4911	249	2	b	b	X
ejpam-4911	249	3	)	)	PUNCT
ejpam-4911	249	4	fix	fix	NOUN
ejpam-4911	249	5	s	s	PART
ejpam-4911	249	6	=	=	SYM
ejpam-4911	249	7	2	2	NUM
ejpam-4911	249	8	,	,	PUNCT
ejpam-4911	249	9	v	v	NOUN
ejpam-4911	249	10	=	=	SYM
ejpam-4911	249	11	1	1	X
ejpam-4911	249	12	.	.	PUNCT
ejpam-4911	249	13	consider	consider	VERB
ejpam-4911	249	14	the	the	DET
ejpam-4911	249	15	bigeneralized	bigeneralized	ADJ
ejpam-4911	249	16	topological	topological	ADJ
ejpam-4911	249	17	space	space	NOUN
ejpam-4911	249	18	(	(	PUNCT
ejpam-4911	249	19	x,µ1	x,µ1	PROPN
ejpam-4911	249	20	,	,	PUNCT
ejpam-4911	249	21	µ2	µ2	PROPN
ejpam-4911	249	22	)	)	PUNCT
ejpam-4911	249	23	where	where	SCONJ
ejpam-4911	249	24	x	x	X
ejpam-4911	249	25	=	=	PRON
ejpam-4911	249	26	{	{	PUNCT
ejpam-4911	249	27	p	p	X
ejpam-4911	249	28	,	,	PUNCT
ejpam-4911	249	29	q	q	ADJ
ejpam-4911	249	30	,	,	PUNCT
ejpam-4911	249	31	r	r	NOUN
ejpam-4911	249	32	,	,	PUNCT
ejpam-4911	249	33	s	s	PART
ejpam-4911	249	34	}	}	PUNCT
ejpam-4911	249	35	;	;	PUNCT
ejpam-4911	249	36	µ1	µ1	PROPN
ejpam-4911	249	37	=	=	SYM
ejpam-4911	249	38	{	{	PUNCT
ejpam-4911	249	39	∅	∅	NOUN
ejpam-4911	249	40	,	,	PUNCT
ejpam-4911	249	41	{	{	PUNCT
ejpam-4911	249	42	p	p	X
ejpam-4911	249	43	,	,	PUNCT
ejpam-4911	249	44	s	s	PART
ejpam-4911	249	45	}	}	PUNCT
ejpam-4911	249	46	,	,	PUNCT
ejpam-4911	249	47	{	{	PUNCT
ejpam-4911	249	48	r	r	NOUN
ejpam-4911	249	49	,	,	PUNCT
ejpam-4911	249	50	s	s	PART
ejpam-4911	249	51	}	}	PUNCT
ejpam-4911	249	52	,	,	PUNCT
ejpam-4911	249	53	{	{	PUNCT
ejpam-4911	249	54	q	q	INTJ
ejpam-4911	249	55	,	,	PUNCT
ejpam-4911	249	56	s}{p	s}{p	NOUN
ejpam-4911	249	57	,	,	PUNCT
ejpam-4911	249	58	q	q	X
ejpam-4911	249	59	,	,	PUNCT
ejpam-4911	249	60	s	s	PART
ejpam-4911	249	61	}	}	PUNCT
ejpam-4911	249	62	,	,	PUNCT
ejpam-4911	249	63	{	{	PUNCT
ejpam-4911	249	64	p	p	X
ejpam-4911	249	65	,	,	PUNCT
ejpam-4911	249	66	r	r	NOUN
ejpam-4911	249	67	,	,	PUNCT
ejpam-4911	249	68	s	s	PART
ejpam-4911	249	69	}	}	PUNCT
ejpam-4911	249	70	,	,	PUNCT
ejpam-4911	249	71	{	{	PUNCT
ejpam-4911	249	72	q	q	X
ejpam-4911	249	73	,	,	PUNCT
ejpam-4911	249	74	r	r	NOUN
ejpam-4911	249	75	,	,	PUNCT
ejpam-4911	249	76	s	s	PART
ejpam-4911	249	77	}	}	PUNCT
ejpam-4911	249	78	,	,	PUNCT
ejpam-4911	249	79	x	x	NOUN
ejpam-4911	249	80	}	}	PUNCT
ejpam-4911	249	81	and	and	CCONJ
ejpam-4911	249	82	µ2	µ2	PROPN
ejpam-4911	249	83	=	=	PUNCT
ejpam-4911	249	84	{	{	PUNCT
ejpam-4911	249	85	∅	∅	NOUN
ejpam-4911	249	86	,	,	PUNCT
ejpam-4911	249	87	{	{	PUNCT
ejpam-4911	249	88	q	q	X
ejpam-4911	249	89	,	,	PUNCT
ejpam-4911	249	90	s	s	PART
ejpam-4911	249	91	}	}	PUNCT
ejpam-4911	249	92	,	,	PUNCT
ejpam-4911	249	93	{	{	PUNCT
ejpam-4911	249	94	r	r	NOUN
ejpam-4911	249	95	,	,	PUNCT
ejpam-4911	249	96	s	s	PART
ejpam-4911	249	97	}	}	PUNCT
ejpam-4911	249	98	,	,	PUNCT
ejpam-4911	249	99	{	{	PUNCT
ejpam-4911	249	100	q	q	X
ejpam-4911	249	101	,	,	PUNCT
ejpam-4911	249	102	r	r	NOUN
ejpam-4911	249	103	,	,	PUNCT
ejpam-4911	249	104	s	s	PART
ejpam-4911	249	105	}	}	PUNCT
ejpam-4911	249	106	}	}	PUNCT
ejpam-4911	249	107	.	.	PUNCT
ejpam-4911	250	1	clearly	clearly	ADV
ejpam-4911	250	2	,	,	PUNCT
ejpam-4911	250	3	µ2	µ2	PROPN
ejpam-4911	250	4	⊂	⊂	PROPN
ejpam-4911	250	5	µ1	µ1	PROPN
ejpam-4911	250	6	.	.	PUNCT
ejpam-4911	251	1	take	take	VERB
ejpam-4911	251	2	h	h	NOUN
ejpam-4911	251	3	=	=	PUNCT
ejpam-4911	251	4	{	{	PUNCT
ejpam-4911	251	5	r	r	NOUN
ejpam-4911	251	6	}	}	PUNCT
ejpam-4911	251	7	and	and	CCONJ
ejpam-4911	251	8	d	d	NOUN
ejpam-4911	251	9	=	=	PUNCT
ejpam-4911	251	10	{	{	PUNCT
ejpam-4911	251	11	p	p	X
ejpam-4911	251	12	,	,	PUNCT
ejpam-4911	251	13	r	r	NOUN
ejpam-4911	251	14	}	}	PUNCT
ejpam-4911	251	15	.	.	PUNCT
ejpam-4911	252	1	then	then	ADV
ejpam-4911	252	2	h	h	PROPN
ejpam-4911	252	3	is	be	AUX
ejpam-4911	252	4	a	a	DET
ejpam-4911	252	5	µ1	µ1	NOUN
ejpam-4911	252	6	-	-	PUNCT
ejpam-4911	252	7	nowhere	nowhere	ADV
ejpam-4911	252	8	dense	dense	ADJ
ejpam-4911	252	9	set	set	NOUN
ejpam-4911	252	10	and	and	CCONJ
ejpam-4911	252	11	d	d	NOUN
ejpam-4911	252	12	is	be	AUX
ejpam-4911	252	13	a	a	DET
ejpam-4911	252	14	µ2	µ2	PROPN
ejpam-4911	252	15	-	-	PUNCT
ejpam-4911	252	16	nowhere	nowhere	ADV
ejpam-4911	252	17	dense	dense	ADJ
ejpam-4911	252	18	set	set	NOUN
ejpam-4911	252	19	.	.	PUNCT
ejpam-4911	253	1	also	also	ADV
ejpam-4911	253	2	,	,	PUNCT
ejpam-4911	253	3	both	both	CCONJ
ejpam-4911	253	4	h	h	NOUN
ejpam-4911	253	5	and	and	CCONJ
ejpam-4911	253	6	d	d	NOUN
ejpam-4911	253	7	are	be	AUX
ejpam-4911	253	8	in	in	ADP
ejpam-4911	253	9	(	(	PUNCT
ejpam-4911	253	10	2	2	NUM
ejpam-4911	253	11	,	,	PUNCT
ejpam-4911	253	12	1)−n	1)−n	NUM
ejpam-4911	253	13	(	(	PUNCT
ejpam-4911	253	14	x	x	NOUN
ejpam-4911	253	15	)	)	PUNCT
ejpam-4911	253	16	.	.	PUNCT
ejpam-4911	254	1	theorem	theorem	NOUN
ejpam-4911	254	2	19	19	NUM
ejpam-4911	254	3	.	.	PUNCT
ejpam-4911	255	1	let	let	VERB
ejpam-4911	255	2	µ1	µ1	PROPN
ejpam-4911	255	3	,	,	PUNCT
ejpam-4911	255	4	µ2	µ2	PROPN
ejpam-4911	255	5	be	be	AUX
ejpam-4911	255	6	two	two	NUM
ejpam-4911	255	7	generlized	generlize	VERB
ejpam-4911	255	8	topologies	topology	NOUN
ejpam-4911	255	9	on	on	ADP
ejpam-4911	255	10	x	x	PUNCT
ejpam-4911	255	11	and	and	CCONJ
ejpam-4911	255	12	µs	µs	ADP
ejpam-4911	255	13	⊆	⊆	NUM
ejpam-4911	255	14	µv	µv	NOUN
ejpam-4911	255	15	where	where	SCONJ
ejpam-4911	255	16	s	s	X
ejpam-4911	255	17	,	,	PUNCT
ejpam-4911	255	18	v	v	NOUN
ejpam-4911	255	19	=	=	SYM
ejpam-4911	255	20	1	1	NUM
ejpam-4911	255	21	,	,	PUNCT
ejpam-4911	255	22	2	2	NUM
ejpam-4911	255	23	and	and	CCONJ
ejpam-4911	255	24	s	s	VERB
ejpam-4911	255	25	̸=	̸=	PROPN
ejpam-4911	255	26	v.	v.	SCONJ
ejpam-4911	255	27	if	if	SCONJ
ejpam-4911	255	28	p	p	X
ejpam-4911	255	29	⊂	⊂	PROPN
ejpam-4911	255	30	x	x	X
ejpam-4911	255	31	is	be	AUX
ejpam-4911	255	32	µv	µv	NOUN
ejpam-4911	255	33	-	-	PUNCT
ejpam-4911	255	34	nowhere	nowhere	ADV
ejpam-4911	255	35	dense	dense	ADJ
ejpam-4911	255	36	set	set	NOUN
ejpam-4911	255	37	or	or	CCONJ
ejpam-4911	255	38	µs	µs	NOUN
ejpam-4911	255	39	-	-	PUNCT
ejpam-4911	255	40	nowhere	nowhere	ADV
ejpam-4911	255	41	dense	dense	ADJ
ejpam-4911	255	42	set	set	NOUN
ejpam-4911	255	43	,	,	PUNCT
ejpam-4911	256	1	then	then	ADV
ejpam-4911	256	2	p	p	PROPN
ejpam-4911	256	3	∈	∈	PROPN
ejpam-4911	256	4	(	(	PUNCT
ejpam-4911	256	5	s	s	PROPN
ejpam-4911	256	6	,	,	PUNCT
ejpam-4911	256	7	v)−	v)−	PROPN
ejpam-4911	256	8	n	n	CCONJ
ejpam-4911	256	9	(	(	PUNCT
ejpam-4911	256	10	x	x	X
ejpam-4911	256	11	)	)	PUNCT
ejpam-4911	256	12	where	where	SCONJ
ejpam-4911	256	13	s	s	X
ejpam-4911	256	14	,	,	PUNCT
ejpam-4911	256	15	v	v	NOUN
ejpam-4911	256	16	=	=	SYM
ejpam-4911	256	17	1	1	NUM
ejpam-4911	256	18	,	,	PUNCT
ejpam-4911	256	19	2	2	NUM
ejpam-4911	256	20	and	and	CCONJ
ejpam-4911	256	21	s	s	VERB
ejpam-4911	256	22	̸=	̸=	PROPN
ejpam-4911	256	23	v.	v.	ADP
ejpam-4911	256	24	proof	proof	NOUN
ejpam-4911	256	25	.	.	PUNCT
ejpam-4911	257	1	we	we	PRON
ejpam-4911	257	2	give	give	VERB
ejpam-4911	257	3	the	the	DET
ejpam-4911	257	4	detailed	detailed	ADJ
ejpam-4911	257	5	proof	proof	NOUN
ejpam-4911	257	6	only	only	ADV
ejpam-4911	257	7	for	for	ADP
ejpam-4911	257	8	s	s	NOUN
ejpam-4911	257	9	=	=	SYM
ejpam-4911	257	10	2	2	NUM
ejpam-4911	257	11	and	and	CCONJ
ejpam-4911	257	12	v	v	NOUN
ejpam-4911	257	13	=	=	SYM
ejpam-4911	257	14	1	1	X
ejpam-4911	257	15	.	.	PUNCT
ejpam-4911	257	16	assume	assume	VERB
ejpam-4911	257	17	that	that	SCONJ
ejpam-4911	257	18	,	,	PUNCT
ejpam-4911	257	19	µ2	µ2	PROPN
ejpam-4911	257	20	⊆	⊆	NUM
ejpam-4911	257	21	µ1	µ1	PROPN
ejpam-4911	257	22	(	(	PUNCT
ejpam-4911	257	23	6	6	NUM
ejpam-4911	257	24	)	)	PUNCT
ejpam-4911	257	25	let	let	VERB
ejpam-4911	257	26	p	p	PRON
ejpam-4911	257	27	be	be	AUX
ejpam-4911	257	28	a	a	DET
ejpam-4911	257	29	µ1	µ1	NOUN
ejpam-4911	257	30	-	-	PUNCT
ejpam-4911	257	31	nowhere	nowhere	ADV
ejpam-4911	257	32	dense	dense	ADJ
ejpam-4911	257	33	set	set	NOUN
ejpam-4911	257	34	.	.	PUNCT
ejpam-4911	258	1	then	then	ADV
ejpam-4911	258	2	i1(c1(p	i1(c1(p	PUNCT
ejpam-4911	258	3	)	)	PUNCT
ejpam-4911	258	4	)	)	PUNCT
ejpam-4911	259	1	=	=	PUNCT
ejpam-4911	259	2	∅.	∅.	AUX
ejpam-4911	259	3	suppose	suppose	VERB
ejpam-4911	259	4	i2(c1(p	i2(c1(p	NOUN
ejpam-4911	259	5	)	)	PUNCT
ejpam-4911	259	6	)	)	PUNCT
ejpam-4911	260	1	̸=	̸=	PROPN
ejpam-4911	260	2	∅.	∅.	ADV
ejpam-4911	260	3	then	then	ADV
ejpam-4911	260	4	there	there	PRON
ejpam-4911	260	5	is	be	VERB
ejpam-4911	260	6	q	q	PROPN
ejpam-4911	260	7	∈	∈	PROPN
ejpam-4911	260	8	µ̃2	µ̃2	PROPN
ejpam-4911	260	9	such	such	ADJ
ejpam-4911	260	10	that	that	SCONJ
ejpam-4911	260	11	q	q	X
ejpam-4911	260	12	⊂	⊂	X
ejpam-4911	260	13	c1(p	c1(p	X
ejpam-4911	260	14	)	)	PUNCT
ejpam-4911	260	15	.	.	PUNCT
ejpam-4911	261	1	from	from	ADP
ejpam-4911	261	2	(	(	PUNCT
ejpam-4911	261	3	6	6	NUM
ejpam-4911	261	4	)	)	PUNCT
ejpam-4911	261	5	,	,	PUNCT
ejpam-4911	261	6	q	q	PROPN
ejpam-4911	261	7	∈	∈	PROPN
ejpam-4911	261	8	µ̃1	µ̃1	PROPN
ejpam-4911	261	9	.	.	PUNCT
ejpam-4911	261	10	then	then	ADV
ejpam-4911	261	11	i1(c1(p	i1(c1(p	NOUN
ejpam-4911	261	12	)	)	PUNCT
ejpam-4911	261	13	)	)	PUNCT
ejpam-4911	262	1	̸=	̸=	NOUN
ejpam-4911	262	2	∅	∅	NOUN
ejpam-4911	262	3	which	which	PRON
ejpam-4911	262	4	is	be	AUX
ejpam-4911	262	5	not	not	PART
ejpam-4911	262	6	possible	possible	ADJ
ejpam-4911	262	7	.	.	PUNCT
ejpam-4911	263	1	therefore	therefore	ADV
ejpam-4911	263	2	,	,	PUNCT
ejpam-4911	263	3	i2(c1(p	i2(c1(p	NOUN
ejpam-4911	263	4	)	)	PUNCT
ejpam-4911	263	5	)	)	PUNCT
ejpam-4911	264	1	=	=	PUNCT
ejpam-4911	264	2	∅.	∅.	VERB
ejpam-4911	264	3	hence	hence	ADV
ejpam-4911	264	4	p	p	NOUN
ejpam-4911	264	5	∈	∈	PROPN
ejpam-4911	264	6	(	(	PUNCT
ejpam-4911	264	7	2	2	NUM
ejpam-4911	264	8	,	,	PUNCT
ejpam-4911	264	9	1)−n	1)−n	NUM
ejpam-4911	264	10	(	(	PUNCT
ejpam-4911	264	11	x	x	NOUN
ejpam-4911	264	12	)	)	PUNCT
ejpam-4911	264	13	.	.	PUNCT
ejpam-4911	265	1	let	let	VERB
ejpam-4911	265	2	p	p	PRON
ejpam-4911	265	3	be	be	AUX
ejpam-4911	265	4	a	a	DET
ejpam-4911	265	5	µ2	µ2	NOUN
ejpam-4911	265	6	-	-	PUNCT
ejpam-4911	265	7	nowhere	nowhere	ADV
ejpam-4911	265	8	dense	dense	ADJ
ejpam-4911	265	9	set	set	NOUN
ejpam-4911	265	10	.	.	PUNCT
ejpam-4911	266	1	then	then	ADV
ejpam-4911	266	2	i2(c2(p	i2(c2(p	NUM
ejpam-4911	266	3	)	)	PUNCT
ejpam-4911	266	4	)	)	PUNCT
ejpam-4911	267	1	=	=	PUNCT
ejpam-4911	267	2	∅.	∅.	AUX
ejpam-4911	267	3	suppose	suppose	VERB
ejpam-4911	267	4	i2(c1(p	i2(c1(p	NOUN
ejpam-4911	267	5	)	)	PUNCT
ejpam-4911	267	6	)	)	PUNCT
ejpam-4911	268	1	̸=	̸=	PROPN
ejpam-4911	268	2	∅.	∅.	ADV
ejpam-4911	268	3	then	then	ADV
ejpam-4911	268	4	there	there	PRON
ejpam-4911	268	5	is	be	VERB
ejpam-4911	268	6	a	a	DET
ejpam-4911	268	7	set	set	NOUN
ejpam-4911	268	8	m	m	NOUN
ejpam-4911	268	9	∈	∈	NOUN
ejpam-4911	268	10	µ̃2	µ̃2	PROPN
ejpam-4911	268	11	such	such	ADJ
ejpam-4911	268	12	that	that	SCONJ
ejpam-4911	268	13	m	m	VERB
ejpam-4911	268	14	⊂	⊂	X
ejpam-4911	268	15	c1(p	c1(p	X
ejpam-4911	268	16	)	)	PUNCT
ejpam-4911	268	17	.	.	PUNCT
ejpam-4911	269	1	by	by	ADP
ejpam-4911	269	2	(	(	PUNCT
ejpam-4911	269	3	6	6	NUM
ejpam-4911	269	4	)	)	PUNCT
ejpam-4911	269	5	,	,	PUNCT
ejpam-4911	269	6	i2(c2(p	i2(c2(p	PROPN
ejpam-4911	269	7	)	)	PUNCT
ejpam-4911	269	8	)	)	PUNCT
ejpam-4911	270	1	̸=	̸=	PROPN
ejpam-4911	270	2	∅	∅	NOUN
ejpam-4911	270	3	which	which	PRON
ejpam-4911	270	4	is	be	AUX
ejpam-4911	270	5	not	not	PART
ejpam-4911	270	6	possible	possible	ADJ
ejpam-4911	270	7	.	.	PUNCT
ejpam-4911	271	1	therefore	therefore	ADV
ejpam-4911	271	2	,	,	PUNCT
ejpam-4911	271	3	i2(c1(p	i2(c1(p	NOUN
ejpam-4911	271	4	)	)	PUNCT
ejpam-4911	271	5	)	)	PUNCT
ejpam-4911	272	1	=	=	PUNCT
ejpam-4911	272	2	∅.	∅.	VERB
ejpam-4911	272	3	hence	hence	ADV
ejpam-4911	272	4	p	p	NOUN
ejpam-4911	272	5	∈	∈	PROPN
ejpam-4911	272	6	(	(	PUNCT
ejpam-4911	272	7	2	2	NUM
ejpam-4911	272	8	,	,	PUNCT
ejpam-4911	272	9	1)−n	1)−n	NUM
ejpam-4911	272	10	(	(	PUNCT
ejpam-4911	272	11	x	x	NOUN
ejpam-4911	272	12	)	)	PUNCT
ejpam-4911	272	13	.	.	PUNCT
ejpam-4911	273	1	in	in	ADP
ejpam-4911	273	2	theorem	theorem	NOUN
ejpam-4911	273	3	19	19	NUM
ejpam-4911	273	4	,	,	PUNCT
ejpam-4911	273	5	the	the	DET
ejpam-4911	273	6	condition	condition	NOUN
ejpam-4911	273	7	“	"	PUNCT
ejpam-4911	273	8	µs	µs	NOUN
ejpam-4911	273	9	⊆	⊆	NUM
ejpam-4911	273	10	µv	µv	NOUN
ejpam-4911	273	11	”	"	PUNCT
ejpam-4911	273	12	where	where	SCONJ
ejpam-4911	273	13	s	s	X
ejpam-4911	273	14	,	,	PUNCT
ejpam-4911	273	15	v	v	NOUN
ejpam-4911	273	16	=	=	SYM
ejpam-4911	273	17	1	1	NUM
ejpam-4911	273	18	,	,	PUNCT
ejpam-4911	273	19	2	2	NUM
ejpam-4911	273	20	;	;	PUNCT
ejpam-4911	273	21	s	s	VERB
ejpam-4911	273	22	̸=	̸=	PROPN
ejpam-4911	273	23	v	v	NOUN
ejpam-4911	273	24	”	"	PUNCT
ejpam-4911	273	25	is	be	AUX
ejpam-4911	273	26	necessary	necessary	ADJ
ejpam-4911	273	27	as	as	SCONJ
ejpam-4911	273	28	shown	show	VERB
ejpam-4911	273	29	in	in	ADP
ejpam-4911	273	30	example	example	NOUN
ejpam-4911	273	31	20	20	NUM
ejpam-4911	273	32	.	.	PUNCT
ejpam-4911	274	1	y.	y.	PROPN
ejpam-4911	274	2	farhat	farhat	PROPN
ejpam-4911	274	3	,	,	PUNCT
ejpam-4911	274	4	v.	v.	ADP
ejpam-4911	274	5	subramanian	subramanian	PROPN
ejpam-4911	274	6	/	/	SYM
ejpam-4911	274	7	eur	eur	PROPN
ejpam-4911	274	8	.	.	PUNCT
ejpam-4911	275	1	j.	j.	PROPN
ejpam-4911	275	2	pure	pure	PROPN
ejpam-4911	275	3	appl	appl	PROPN
ejpam-4911	275	4	.	.	PROPN
ejpam-4911	275	5	math	math	PROPN
ejpam-4911	275	6	,	,	PUNCT
ejpam-4911	275	7	16	16	NUM
ejpam-4911	275	8	(	(	PUNCT
ejpam-4911	275	9	4	4	NUM
ejpam-4911	275	10	)	)	PUNCT
ejpam-4911	275	11	(	(	PUNCT
ejpam-4911	275	12	2023	2023	NUM
ejpam-4911	275	13	)	)	PUNCT
ejpam-4911	275	14	,	,	PUNCT
ejpam-4911	275	15	2049	2049	NUM
ejpam-4911	275	16	-	-	SYM
ejpam-4911	275	17	2065	2065	NUM
ejpam-4911	275	18	2058	2058	NUM
ejpam-4911	275	19	example	example	NOUN
ejpam-4911	275	20	20	20	NUM
ejpam-4911	275	21	.	.	PUNCT
ejpam-4911	276	1	take	take	VERB
ejpam-4911	276	2	x	x	NOUN
ejpam-4911	276	3	=	=	PRON
ejpam-4911	276	4	{	{	PUNCT
ejpam-4911	276	5	e	e	PROPN
ejpam-4911	276	6	,	,	PUNCT
ejpam-4911	276	7	f	f	PROPN
ejpam-4911	276	8	,	,	PUNCT
ejpam-4911	276	9	k	k	NOUN
ejpam-4911	276	10	,	,	PUNCT
ejpam-4911	276	11	l	l	NOUN
ejpam-4911	276	12	}	}	PUNCT
ejpam-4911	276	13	;	;	PUNCT
ejpam-4911	276	14	µ1	µ1	PROPN
ejpam-4911	276	15	=	=	SYM
ejpam-4911	276	16	{	{	PUNCT
ejpam-4911	276	17	∅	∅	NOUN
ejpam-4911	276	18	,	,	PUNCT
ejpam-4911	276	19	{	{	PUNCT
ejpam-4911	276	20	e	e	NOUN
ejpam-4911	276	21	,	,	PUNCT
ejpam-4911	276	22	k	k	NOUN
ejpam-4911	276	23	}	}	PUNCT
ejpam-4911	276	24	,	,	PUNCT
ejpam-4911	276	25	{	{	PUNCT
ejpam-4911	276	26	e	e	NOUN
ejpam-4911	276	27	,	,	PUNCT
ejpam-4911	276	28	l	l	NOUN
ejpam-4911	276	29	}	}	PUNCT
ejpam-4911	276	30	,	,	PUNCT
ejpam-4911	276	31	{	{	PUNCT
ejpam-4911	276	32	f	f	X
ejpam-4911	276	33	,	,	PUNCT
ejpam-4911	276	34	l	l	NOUN
ejpam-4911	276	35	}	}	PUNCT
ejpam-4911	276	36	,	,	PUNCT
ejpam-4911	276	37	{	{	PUNCT
ejpam-4911	276	38	e	e	NOUN
ejpam-4911	276	39	,	,	PUNCT
ejpam-4911	276	40	f	f	X
ejpam-4911	276	41	,	,	PUNCT
ejpam-4911	276	42	l	l	NOUN
ejpam-4911	276	43	}	}	PUNCT
ejpam-4911	276	44	,	,	PUNCT
ejpam-4911	276	45	{	{	PUNCT
ejpam-4911	276	46	e	e	NOUN
ejpam-4911	276	47	,	,	PUNCT
ejpam-4911	276	48	k	k	NOUN
ejpam-4911	276	49	,	,	PUNCT
ejpam-4911	276	50	l	l	NOUN
ejpam-4911	276	51	}	}	PUNCT
ejpam-4911	276	52	,	,	PUNCT
ejpam-4911	276	53	x	x	NOUN
ejpam-4911	276	54	}	}	PUNCT
ejpam-4911	276	55	and	and	CCONJ
ejpam-4911	276	56	µ2	µ2	PROPN
ejpam-4911	276	57	=	=	PUNCT
ejpam-4911	276	58	{	{	PUNCT
ejpam-4911	276	59	∅	∅	NOUN
ejpam-4911	276	60	,	,	PUNCT
ejpam-4911	276	61	{	{	PUNCT
ejpam-4911	276	62	e	e	NOUN
ejpam-4911	276	63	,	,	PUNCT
ejpam-4911	276	64	f	f	PROPN
ejpam-4911	276	65	}	}	PUNCT
ejpam-4911	276	66	,	,	PUNCT
ejpam-4911	276	67	{	{	PUNCT
ejpam-4911	276	68	f	f	X
ejpam-4911	276	69	,	,	PUNCT
ejpam-4911	276	70	k	k	NOUN
ejpam-4911	276	71	}	}	PUNCT
ejpam-4911	276	72	,	,	PUNCT
ejpam-4911	276	73	{	{	PUNCT
ejpam-4911	276	74	e	e	NOUN
ejpam-4911	276	75	,	,	PUNCT
ejpam-4911	276	76	l	l	NOUN
ejpam-4911	276	77	}	}	PUNCT
ejpam-4911	276	78	,	,	PUNCT
ejpam-4911	276	79	{	{	PUNCT
ejpam-4911	276	80	f	f	X
ejpam-4911	276	81	,	,	PUNCT
ejpam-4911	276	82	l	l	NOUN
ejpam-4911	276	83	}	}	PUNCT
ejpam-4911	276	84	,	,	PUNCT
ejpam-4911	276	85	{	{	PUNCT
ejpam-4911	276	86	e	e	NOUN
ejpam-4911	276	87	,	,	PUNCT
ejpam-4911	276	88	f	f	PROPN
ejpam-4911	276	89	,	,	PUNCT
ejpam-4911	276	90	k	k	NOUN
ejpam-4911	276	91	}	}	PUNCT
ejpam-4911	276	92	,	,	PUNCT
ejpam-4911	276	93	{	{	PUNCT
ejpam-4911	276	94	e	e	NOUN
ejpam-4911	276	95	,	,	PUNCT
ejpam-4911	276	96	f	f	X
ejpam-4911	276	97	,	,	PUNCT
ejpam-4911	276	98	l	l	NOUN
ejpam-4911	276	99	}	}	PUNCT
ejpam-4911	276	100	,	,	PUNCT
ejpam-4911	276	101	{	{	PUNCT
ejpam-4911	276	102	e	e	NOUN
ejpam-4911	276	103	,	,	PUNCT
ejpam-4911	276	104	k	k	NOUN
ejpam-4911	276	105	,	,	PUNCT
ejpam-4911	276	106	l	l	NOUN
ejpam-4911	276	107	}	}	PUNCT
ejpam-4911	276	108	,	,	PUNCT
ejpam-4911	276	109	{	{	PUNCT
ejpam-4911	276	110	f	f	X
ejpam-4911	276	111	,	,	PUNCT
ejpam-4911	276	112	k	k	NOUN
ejpam-4911	276	113	,	,	PUNCT
ejpam-4911	276	114	l	l	NOUN
ejpam-4911	276	115	}	}	PUNCT
ejpam-4911	276	116	,	,	PUNCT
ejpam-4911	276	117	x	x	NOUN
ejpam-4911	276	118	}	}	PUNCT
ejpam-4911	276	119	.	.	PUNCT
ejpam-4911	277	1	let	let	VERB
ejpam-4911	277	2	p	p	NOUN
ejpam-4911	277	3	=	=	X
ejpam-4911	277	4	{	{	PUNCT
ejpam-4911	277	5	f	f	PROPN
ejpam-4911	277	6	,	,	PUNCT
ejpam-4911	277	7	k	k	NOUN
ejpam-4911	277	8	}	}	PUNCT
ejpam-4911	277	9	.	.	PUNCT
ejpam-4911	278	1	then	then	ADV
ejpam-4911	278	2	i1(c1(p	i1(c1(p	PUNCT
ejpam-4911	278	3	)	)	PUNCT
ejpam-4911	278	4	)	)	PUNCT
ejpam-4911	279	1	=	=	SYM
ejpam-4911	279	2	i1({f	i1({f	PROPN
ejpam-4911	279	3	,	,	PUNCT
ejpam-4911	279	4	k	k	NOUN
ejpam-4911	279	5	}	}	PUNCT
ejpam-4911	279	6	)	)	PUNCT
ejpam-4911	279	7	=	=	NOUN
ejpam-4911	279	8	∅	∅	NOUN
ejpam-4911	279	9	and	and	CCONJ
ejpam-4911	279	10	so	so	ADV
ejpam-4911	279	11	p	p	PROPN
ejpam-4911	279	12	is	be	AUX
ejpam-4911	279	13	µ1	µ1	NOUN
ejpam-4911	279	14	-	-	PUNCT
ejpam-4911	279	15	nowhere	nowhere	ADV
ejpam-4911	279	16	dense	dense	ADJ
ejpam-4911	279	17	set	set	NOUN
ejpam-4911	279	18	.	.	PUNCT
ejpam-4911	280	1	but	but	CCONJ
ejpam-4911	280	2	p	p	NOUN
ejpam-4911	280	3	/∈	/∈	PUNCT
ejpam-4911	281	1	(	(	PUNCT
ejpam-4911	281	2	2	2	NUM
ejpam-4911	281	3	,	,	PUNCT
ejpam-4911	281	4	1	1	NUM
ejpam-4911	281	5	)	)	PUNCT
ejpam-4911	281	6	−	−	PROPN
ejpam-4911	281	7	n	n	CCONJ
ejpam-4911	281	8	(	(	PUNCT
ejpam-4911	281	9	x	x	NOUN
ejpam-4911	281	10	)	)	PUNCT
ejpam-4911	281	11	.	.	PUNCT
ejpam-4911	282	1	let	let	VERB
ejpam-4911	282	2	m	m	VERB
ejpam-4911	282	3	=	=	PUNCT
ejpam-4911	282	4	{	{	PUNCT
ejpam-4911	282	5	e	e	NOUN
ejpam-4911	282	6	,	,	PUNCT
ejpam-4911	282	7	k	k	NOUN
ejpam-4911	282	8	}	}	PUNCT
ejpam-4911	282	9	.	.	PUNCT
ejpam-4911	283	1	then	then	ADV
ejpam-4911	283	2	i2(c2(m	i2(c2(m	NOUN
ejpam-4911	283	3	)	)	PUNCT
ejpam-4911	283	4	)	)	PUNCT
ejpam-4911	284	1	=	=	PUNCT
ejpam-4911	284	2	i2({e	i2({e	NOUN
ejpam-4911	284	3	,	,	PUNCT
ejpam-4911	284	4	k	k	NOUN
ejpam-4911	284	5	}	}	PUNCT
ejpam-4911	284	6	)	)	PUNCT
ejpam-4911	284	7	=	=	NOUN
ejpam-4911	284	8	∅	∅	NOUN
ejpam-4911	284	9	and	and	CCONJ
ejpam-4911	284	10	so	so	ADV
ejpam-4911	284	11	m	m	VERB
ejpam-4911	284	12	is	be	AUX
ejpam-4911	284	13	a	a	DET
ejpam-4911	284	14	µ2nowhere	µ2nowhere	ADV
ejpam-4911	284	15	dense	dense	ADJ
ejpam-4911	284	16	set	set	NOUN
ejpam-4911	284	17	.	.	PUNCT
ejpam-4911	285	1	butm	butm	ADJ
ejpam-4911	285	2	/∈	/∈	PUNCT
ejpam-4911	286	1	(	(	PUNCT
ejpam-4911	286	2	1	1	NUM
ejpam-4911	286	3	,	,	PUNCT
ejpam-4911	286	4	2)−n	2)−n	NUM
ejpam-4911	286	5	(	(	PUNCT
ejpam-4911	286	6	x	x	NOUN
ejpam-4911	286	7	)	)	PUNCT
ejpam-4911	286	8	.	.	PUNCT
ejpam-4911	287	1	let	let	VERB
ejpam-4911	287	2	c	c	NOUN
ejpam-4911	287	3	=	=	PRON
ejpam-4911	287	4	{	{	PUNCT
ejpam-4911	287	5	k	k	NOUN
ejpam-4911	287	6	,	,	PUNCT
ejpam-4911	287	7	l	l	NOUN
ejpam-4911	287	8	}	}	PUNCT
ejpam-4911	287	9	.	.	PUNCT
ejpam-4911	288	1	then	then	ADV
ejpam-4911	288	2	i2(c2(c	i2(c2(c	PROPN
ejpam-4911	288	3	)	)	PUNCT
ejpam-4911	288	4	)	)	PUNCT
ejpam-4911	289	1	=	=	SYM
ejpam-4911	289	2	i2({k	i2({k	ADJ
ejpam-4911	289	3	,	,	PUNCT
ejpam-4911	289	4	l	l	NOUN
ejpam-4911	289	5	}	}	PUNCT
ejpam-4911	289	6	)	)	PUNCT
ejpam-4911	289	7	=	=	NOUN
ejpam-4911	289	8	∅	∅	NOUN
ejpam-4911	289	9	and	and	CCONJ
ejpam-4911	289	10	so	so	ADV
ejpam-4911	289	11	c	c	PROPN
ejpam-4911	289	12	is	be	AUX
ejpam-4911	289	13	a	a	DET
ejpam-4911	289	14	µ2	µ2	PROPN
ejpam-4911	289	15	-	-	PUNCT
ejpam-4911	289	16	nowhere	nowhere	ADV
ejpam-4911	289	17	dense	dense	ADJ
ejpam-4911	289	18	set	set	NOUN
ejpam-4911	289	19	.	.	PUNCT
ejpam-4911	290	1	but	but	CCONJ
ejpam-4911	290	2	c	c	X
ejpam-4911	290	3	/∈	/∈	PUNCT
ejpam-4911	291	1	(	(	PUNCT
ejpam-4911	291	2	2	2	NUM
ejpam-4911	291	3	,	,	PUNCT
ejpam-4911	291	4	1)−n	1)−n	NUM
ejpam-4911	291	5	(	(	PUNCT
ejpam-4911	291	6	x	x	NOUN
ejpam-4911	291	7	)	)	PUNCT
ejpam-4911	291	8	.	.	PUNCT
ejpam-4911	292	1	consider	consider	VERB
ejpam-4911	292	2	the	the	DET
ejpam-4911	292	3	bgts	bgts	NOUN
ejpam-4911	292	4	(	(	PUNCT
ejpam-4911	292	5	x,µ1	x,µ1	PROPN
ejpam-4911	292	6	,	,	PUNCT
ejpam-4911	292	7	µ2	µ2	PROPN
ejpam-4911	292	8	)	)	PUNCT
ejpam-4911	292	9	,	,	PUNCT
ejpam-4911	292	10	x	x	PUNCT
ejpam-4911	293	1	=	=	PUNCT
ejpam-4911	294	1	[	[	X
ejpam-4911	294	2	0	0	NUM
ejpam-4911	294	3	,	,	PUNCT
ejpam-4911	294	4	3	3	NUM
ejpam-4911	294	5	]	]	PUNCT
ejpam-4911	294	6	;	;	PUNCT
ejpam-4911	294	7	µ1	µ1	PROPN
ejpam-4911	294	8	=	=	SYM
ejpam-4911	294	9	{	{	PUNCT
ejpam-4911	294	10	∅	∅	NOUN
ejpam-4911	294	11	,	,	PUNCT
ejpam-4911	294	12	[	[	X
ejpam-4911	294	13	0	0	NUM
ejpam-4911	294	14	,	,	PUNCT
ejpam-4911	294	15	32	32	NUM
ejpam-4911	294	16	)	)	PUNCT
ejpam-4911	294	17	,	,	PUNCT
ejpam-4911	294	18	(	(	PUNCT
ejpam-4911	294	19	1	1	NUM
ejpam-4911	294	20	,	,	PUNCT
ejpam-4911	294	21	2	2	NUM
ejpam-4911	294	22	]	]	PUNCT
ejpam-4911	294	23	,	,	PUNCT
ejpam-4911	294	24	[	[	X
ejpam-4911	294	25	0	0	NUM
ejpam-4911	294	26	,	,	PUNCT
ejpam-4911	294	27	2	2	NUM
ejpam-4911	294	28	]	]	PUNCT
ejpam-4911	294	29	}	}	PUNCT
ejpam-4911	294	30	and	and	CCONJ
ejpam-4911	294	31	µ2	µ2	PROPN
ejpam-4911	294	32	=	=	PUNCT
ejpam-4911	294	33	{	{	PUNCT
ejpam-4911	294	34	∅	∅	NOUN
ejpam-4911	294	35	,	,	PUNCT
ejpam-4911	294	36	[	[	X
ejpam-4911	294	37	0	0	NUM
ejpam-4911	294	38	,	,	PUNCT
ejpam-4911	294	39	1	1	NUM
ejpam-4911	294	40	)	)	PUNCT
ejpam-4911	294	41	,	,	PUNCT
ejpam-4911	294	42	(	(	PUNCT
ejpam-4911	294	43	1	1	NUM
ejpam-4911	294	44	,	,	PUNCT
ejpam-4911	294	45	2	2	NUM
ejpam-4911	294	46	)	)	PUNCT
ejpam-4911	294	47	,	,	PUNCT
ejpam-4911	295	1	[	[	X
ejpam-4911	295	2	0	0	NUM
ejpam-4911	295	3	,	,	PUNCT
ejpam-4911	295	4	2	2	NUM
ejpam-4911	295	5	)	)	PUNCT
ejpam-4911	295	6	}	}	PUNCT
ejpam-4911	295	7	let	let	VERB
ejpam-4911	295	8	d	d	NOUN
ejpam-4911	295	9	=	=	PUNCT
ejpam-4911	296	1	[	[	X
ejpam-4911	296	2	32	32	NUM
ejpam-4911	296	3	,	,	PUNCT
ejpam-4911	296	4	3	3	NUM
ejpam-4911	296	5	]	]	PUNCT
ejpam-4911	296	6	.	.	PUNCT
ejpam-4911	297	1	then	then	ADV
ejpam-4911	297	2	d	d	PROPN
ejpam-4911	297	3	is	be	AUX
ejpam-4911	297	4	a	a	DET
ejpam-4911	297	5	µ1	µ1	NOUN
ejpam-4911	297	6	-	-	PUNCT
ejpam-4911	297	7	nowhere	nowhere	ADV
ejpam-4911	297	8	dense	dense	ADJ
ejpam-4911	297	9	set	set	NOUN
ejpam-4911	297	10	in	in	ADP
ejpam-4911	297	11	x.	x.	NOUN
ejpam-4911	298	1	but	but	CCONJ
ejpam-4911	298	2	d	d	NOUN
ejpam-4911	298	3	/∈	/∈	PUNCT
ejpam-4911	299	1	(	(	PUNCT
ejpam-4911	299	2	1	1	NUM
ejpam-4911	299	3	,	,	PUNCT
ejpam-4911	299	4	2)−n	2)−n	NUM
ejpam-4911	299	5	(	(	PUNCT
ejpam-4911	299	6	x	x	NOUN
ejpam-4911	299	7	)	)	PUNCT
ejpam-4911	299	8	.	.	PUNCT
ejpam-4911	300	1	µv	µv	AUX
ejpam-4911	300	2	−	−	PROPN
ejpam-4911	300	3	nowhere	nowhere	ADV
ejpam-4911	300	4	dense	dense	ADJ
ejpam-4911	300	5	(	(	PUNCT
ejpam-4911	300	6	s	s	X
ejpam-4911	300	7	,	,	PUNCT
ejpam-4911	300	8	v)−	v)−	PROPN
ejpam-4911	300	9	nowhere	nowhere	ADV
ejpam-4911	300	10	dense	dense	ADJ
ejpam-4911	300	11	µs	µs	X
ejpam-4911	300	12	−	−	NOUN
ejpam-4911	300	13	nowhere	nowhere	ADV
ejpam-4911	300	14	dense	dense	ADJ
ejpam-4911	300	15	the	the	DET
ejpam-4911	300	16	below	below	NOUN
ejpam-4911	300	17	theorem	theorem	NOUN
ejpam-4911	300	18	22	22	NUM
ejpam-4911	300	19	describes	describe	VERB
ejpam-4911	300	20	the	the	DET
ejpam-4911	300	21	above	above	ADJ
ejpam-4911	300	22	diagram	diagram	NOUN
ejpam-4911	300	23	.	.	PUNCT
ejpam-4911	301	1	example	example	NOUN
ejpam-4911	301	2	21	21	NUM
ejpam-4911	301	3	proves	prove	VERB
ejpam-4911	301	4	the	the	DET
ejpam-4911	301	5	existence	existence	NOUN
ejpam-4911	301	6	of	of	ADP
ejpam-4911	301	7	the	the	DET
ejpam-4911	301	8	below	below	NOUN
ejpam-4911	301	9	theorem	theorem	NOUN
ejpam-4911	301	10	22	22	NUM
ejpam-4911	301	11	.	.	PUNCT
ejpam-4911	301	12	example	example	NOUN
ejpam-4911	302	1	21	21	NUM
ejpam-4911	302	2	.	.	PUNCT
ejpam-4911	303	1	(	(	PUNCT
ejpam-4911	303	2	a	a	X
ejpam-4911	303	3	)	)	PUNCT
ejpam-4911	303	4	fix	fix	NOUN
ejpam-4911	303	5	s	s	PART
ejpam-4911	303	6	=	=	SYM
ejpam-4911	303	7	1	1	NUM
ejpam-4911	303	8	,	,	PUNCT
ejpam-4911	303	9	v	v	NOUN
ejpam-4911	303	10	=	=	SYM
ejpam-4911	303	11	2	2	X
ejpam-4911	303	12	.	.	PUNCT
ejpam-4911	303	13	consider	consider	VERB
ejpam-4911	303	14	the	the	DET
ejpam-4911	303	15	bigeneralized	bigeneralized	ADJ
ejpam-4911	303	16	topological	topological	ADJ
ejpam-4911	303	17	space	space	NOUN
ejpam-4911	303	18	(	(	PUNCT
ejpam-4911	303	19	x,µ1	x,µ1	PROPN
ejpam-4911	303	20	,	,	PUNCT
ejpam-4911	303	21	µ2	µ2	PROPN
ejpam-4911	303	22	)	)	PUNCT
ejpam-4911	303	23	where	where	SCONJ
ejpam-4911	303	24	x	x	X
ejpam-4911	303	25	=	=	PRON
ejpam-4911	303	26	{	{	PUNCT
ejpam-4911	303	27	p	p	X
ejpam-4911	303	28	,	,	PUNCT
ejpam-4911	303	29	q	q	ADJ
ejpam-4911	303	30	,	,	PUNCT
ejpam-4911	303	31	r	r	NOUN
ejpam-4911	303	32	,	,	PUNCT
ejpam-4911	303	33	s	s	PART
ejpam-4911	303	34	}	}	PUNCT
ejpam-4911	303	35	;	;	PUNCT
ejpam-4911	303	36	µ1	µ1	PROPN
ejpam-4911	303	37	=	=	SYM
ejpam-4911	303	38	{	{	PUNCT
ejpam-4911	303	39	∅	∅	NOUN
ejpam-4911	303	40	,	,	PUNCT
ejpam-4911	303	41	{	{	PUNCT
ejpam-4911	303	42	p	p	X
ejpam-4911	303	43	,	,	PUNCT
ejpam-4911	303	44	q	q	NOUN
ejpam-4911	303	45	}	}	PUNCT
ejpam-4911	303	46	,	,	PUNCT
ejpam-4911	303	47	{	{	PUNCT
ejpam-4911	303	48	p	p	X
ejpam-4911	303	49	,	,	PUNCT
ejpam-4911	303	50	r	r	NOUN
ejpam-4911	303	51	}	}	PUNCT
ejpam-4911	303	52	,	,	PUNCT
ejpam-4911	303	53	{	{	PUNCT
ejpam-4911	303	54	q	q	X
ejpam-4911	303	55	,	,	PUNCT
ejpam-4911	303	56	r	r	NOUN
ejpam-4911	303	57	}	}	PUNCT
ejpam-4911	303	58	,	,	PUNCT
ejpam-4911	303	59	{	{	PUNCT
ejpam-4911	303	60	p	p	X
ejpam-4911	303	61	,	,	PUNCT
ejpam-4911	303	62	q	q	ADJ
ejpam-4911	303	63	,	,	PUNCT
ejpam-4911	303	64	r	r	NOUN
ejpam-4911	303	65	}	}	PUNCT
ejpam-4911	303	66	}	}	PUNCT
ejpam-4911	303	67	and	and	CCONJ
ejpam-4911	303	68	µ2	µ2	PROPN
ejpam-4911	303	69	=	=	PUNCT
ejpam-4911	303	70	{	{	PUNCT
ejpam-4911	303	71	∅	∅	NOUN
ejpam-4911	303	72	,	,	PUNCT
ejpam-4911	303	73	{	{	PUNCT
ejpam-4911	303	74	p	p	X
ejpam-4911	303	75	,	,	PUNCT
ejpam-4911	303	76	r	r	NOUN
ejpam-4911	303	77	}	}	PUNCT
ejpam-4911	303	78	,	,	PUNCT
ejpam-4911	303	79	{	{	PUNCT
ejpam-4911	303	80	q	q	X
ejpam-4911	303	81	,	,	PUNCT
ejpam-4911	303	82	r	r	NOUN
ejpam-4911	303	83	}	}	PUNCT
ejpam-4911	303	84	,	,	PUNCT
ejpam-4911	303	85	{	{	PUNCT
ejpam-4911	303	86	p	p	X
ejpam-4911	303	87	,	,	PUNCT
ejpam-4911	303	88	q	q	ADJ
ejpam-4911	303	89	,	,	PUNCT
ejpam-4911	303	90	r	r	NOUN
ejpam-4911	303	91	}	}	PUNCT
ejpam-4911	303	92	}	}	PUNCT
ejpam-4911	303	93	.	.	PUNCT
ejpam-4911	304	1	obviously	obviously	ADV
ejpam-4911	304	2	,	,	PUNCT
ejpam-4911	304	3	µ2	µ2	PROPN
ejpam-4911	304	4	⊂	⊂	PROPN
ejpam-4911	304	5	µ1	µ1	PROPN
ejpam-4911	304	6	.	.	PUNCT
ejpam-4911	305	1	consider	consider	VERB
ejpam-4911	305	2	,	,	PUNCT
ejpam-4911	305	3	l	l	NOUN
ejpam-4911	305	4	=	=	PUNCT
ejpam-4911	305	5	{	{	PUNCT
ejpam-4911	305	6	q	q	X
ejpam-4911	305	7	,	,	PUNCT
ejpam-4911	305	8	s	s	PART
ejpam-4911	305	9	}	}	PUNCT
ejpam-4911	305	10	.	.	PUNCT
ejpam-4911	306	1	then	then	ADV
ejpam-4911	306	2	i1(c2(l	i1(c2(l	NOUN
ejpam-4911	306	3	)	)	PUNCT
ejpam-4911	306	4	)	)	PUNCT
ejpam-4911	307	1	=	=	NOUN
ejpam-4911	307	2	∅	∅	NOUN
ejpam-4911	308	1	and	and	CCONJ
ejpam-4911	308	2	so	so	ADV
ejpam-4911	308	3	l	l	NOUN
ejpam-4911	308	4	∈	∈	PROPN
ejpam-4911	308	5	(	(	PUNCT
ejpam-4911	308	6	1	1	NUM
ejpam-4911	308	7	,	,	PUNCT
ejpam-4911	308	8	2	2	NUM
ejpam-4911	308	9	)	)	PUNCT
ejpam-4911	308	10	−n	−n	NOUN
ejpam-4911	308	11	(	(	PUNCT
ejpam-4911	308	12	x	x	NOUN
ejpam-4911	308	13	)	)	PUNCT
ejpam-4911	308	14	.	.	PUNCT
ejpam-4911	309	1	here	here	ADV
ejpam-4911	309	2	,	,	PUNCT
ejpam-4911	309	3	i1(c1(l	i1(c1(l	ADV
ejpam-4911	309	4	)	)	PUNCT
ejpam-4911	309	5	)	)	PUNCT
ejpam-4911	310	1	=	=	PUNCT
ejpam-4911	310	2	∅	∅	NOUN
ejpam-4911	310	3	and	and	CCONJ
ejpam-4911	310	4	i2(c2(l	i2(c2(l	NOUN
ejpam-4911	310	5	)	)	PUNCT
ejpam-4911	310	6	)	)	PUNCT
ejpam-4911	311	1	=	=	PUNCT
ejpam-4911	311	2	∅.	∅.	VERB
ejpam-4911	311	3	thus	thus	ADV
ejpam-4911	311	4	,	,	PUNCT
ejpam-4911	311	5	l	l	NOUN
ejpam-4911	311	6	is	be	AUX
ejpam-4911	311	7	a	a	DET
ejpam-4911	311	8	µ1	µ1	NOUN
ejpam-4911	311	9	-	-	PUNCT
ejpam-4911	311	10	nowhere	nowhere	ADV
ejpam-4911	311	11	dense	dense	ADJ
ejpam-4911	311	12	set	set	NOUN
ejpam-4911	311	13	and	and	CCONJ
ejpam-4911	311	14	also	also	ADV
ejpam-4911	311	15	a	a	DET
ejpam-4911	311	16	µ2	µ2	PROPN
ejpam-4911	311	17	-	-	PUNCT
ejpam-4911	311	18	nowhere	nowhere	ADV
ejpam-4911	311	19	dense	dense	ADJ
ejpam-4911	311	20	set	set	NOUN
ejpam-4911	311	21	.	.	PUNCT
ejpam-4911	312	1	(	(	PUNCT
ejpam-4911	312	2	b	b	X
ejpam-4911	312	3	)	)	PUNCT
ejpam-4911	312	4	fix	fix	NOUN
ejpam-4911	312	5	s	s	PART
ejpam-4911	312	6	=	=	SYM
ejpam-4911	312	7	2	2	NUM
ejpam-4911	312	8	,	,	PUNCT
ejpam-4911	312	9	v	v	NOUN
ejpam-4911	312	10	=	=	SYM
ejpam-4911	312	11	1	1	X
ejpam-4911	312	12	.	.	PUNCT
ejpam-4911	312	13	consider	consider	VERB
ejpam-4911	312	14	the	the	DET
ejpam-4911	312	15	bigeneralized	bigeneralized	ADJ
ejpam-4911	312	16	topological	topological	ADJ
ejpam-4911	312	17	space	space	NOUN
ejpam-4911	312	18	(	(	PUNCT
ejpam-4911	312	19	x,µ1	x,µ1	PROPN
ejpam-4911	312	20	,	,	PUNCT
ejpam-4911	312	21	µ2	µ2	PROPN
ejpam-4911	312	22	)	)	PUNCT
ejpam-4911	313	1	where	where	SCONJ
ejpam-4911	313	2	x	x	X
ejpam-4911	313	3	=	=	PRON
ejpam-4911	313	4	{	{	PUNCT
ejpam-4911	313	5	p	p	X
ejpam-4911	313	6	,	,	PUNCT
ejpam-4911	313	7	q	q	ADJ
ejpam-4911	313	8	,	,	PUNCT
ejpam-4911	313	9	r	r	NOUN
ejpam-4911	313	10	,	,	PUNCT
ejpam-4911	313	11	s	s	PART
ejpam-4911	313	12	}	}	PUNCT
ejpam-4911	313	13	;	;	PUNCT
ejpam-4911	313	14	µ1	µ1	PROPN
ejpam-4911	313	15	=	=	SYM
ejpam-4911	313	16	{	{	PUNCT
ejpam-4911	313	17	∅	∅	NOUN
ejpam-4911	313	18	,	,	PUNCT
ejpam-4911	313	19	{	{	PUNCT
ejpam-4911	313	20	p	p	X
ejpam-4911	313	21	,	,	PUNCT
ejpam-4911	313	22	s	s	PART
ejpam-4911	313	23	}	}	PUNCT
ejpam-4911	313	24	,	,	PUNCT
ejpam-4911	313	25	{	{	PUNCT
ejpam-4911	313	26	q	q	X
ejpam-4911	313	27	,	,	PUNCT
ejpam-4911	313	28	s	s	PART
ejpam-4911	313	29	}	}	PUNCT
ejpam-4911	313	30	,	,	PUNCT
ejpam-4911	313	31	{	{	PUNCT
ejpam-4911	313	32	p	p	X
ejpam-4911	313	33	,	,	PUNCT
ejpam-4911	313	34	q	q	ADJ
ejpam-4911	313	35	,	,	PUNCT
ejpam-4911	313	36	s	s	PART
ejpam-4911	313	37	}	}	PUNCT
ejpam-4911	313	38	}	}	PUNCT
ejpam-4911	313	39	y.	y.	PROPN
ejpam-4911	313	40	farhat	farhat	PROPN
ejpam-4911	313	41	,	,	PUNCT
ejpam-4911	313	42	v.	v.	ADP
ejpam-4911	313	43	subramanian	subramanian	PROPN
ejpam-4911	313	44	/	/	SYM
ejpam-4911	313	45	eur	eur	PROPN
ejpam-4911	313	46	.	.	PUNCT
ejpam-4911	314	1	j.	j.	PROPN
ejpam-4911	314	2	pure	pure	PROPN
ejpam-4911	314	3	appl	appl	PROPN
ejpam-4911	314	4	.	.	PROPN
ejpam-4911	314	5	math	math	PROPN
ejpam-4911	314	6	,	,	PUNCT
ejpam-4911	314	7	16	16	NUM
ejpam-4911	314	8	(	(	PUNCT
ejpam-4911	314	9	4	4	NUM
ejpam-4911	314	10	)	)	PUNCT
ejpam-4911	314	11	(	(	PUNCT
ejpam-4911	314	12	2023	2023	NUM
ejpam-4911	314	13	)	)	PUNCT
ejpam-4911	314	14	,	,	PUNCT
ejpam-4911	314	15	2049	2049	NUM
ejpam-4911	314	16	-	-	SYM
ejpam-4911	314	17	2065	2065	NUM
ejpam-4911	314	18	2059	2059	NUM
ejpam-4911	314	19	and	and	CCONJ
ejpam-4911	314	20	µ2	µ2	PROPN
ejpam-4911	314	21	=	=	PUNCT
ejpam-4911	314	22	{	{	PUNCT
ejpam-4911	314	23	∅	∅	NOUN
ejpam-4911	314	24	,	,	PUNCT
ejpam-4911	314	25	{	{	PUNCT
ejpam-4911	314	26	p	p	X
ejpam-4911	314	27	}	}	PUNCT
ejpam-4911	314	28	,	,	PUNCT
ejpam-4911	314	29	{	{	PUNCT
ejpam-4911	314	30	p	p	X
ejpam-4911	314	31	,	,	PUNCT
ejpam-4911	314	32	s	s	PART
ejpam-4911	314	33	}	}	PUNCT
ejpam-4911	314	34	,	,	PUNCT
ejpam-4911	314	35	{	{	PUNCT
ejpam-4911	314	36	q	q	X
ejpam-4911	314	37	,	,	PUNCT
ejpam-4911	314	38	s	s	PART
ejpam-4911	314	39	}	}	PUNCT
ejpam-4911	314	40	,	,	PUNCT
ejpam-4911	314	41	{	{	PUNCT
ejpam-4911	314	42	p	p	X
ejpam-4911	314	43	,	,	PUNCT
ejpam-4911	314	44	q	q	ADJ
ejpam-4911	314	45	,	,	PUNCT
ejpam-4911	314	46	s	s	PART
ejpam-4911	314	47	}	}	PUNCT
ejpam-4911	314	48	}	}	PUNCT
ejpam-4911	314	49	.	.	PUNCT
ejpam-4911	315	1	clearly	clearly	ADV
ejpam-4911	315	2	,	,	PUNCT
ejpam-4911	315	3	µ1	µ1	PROPN
ejpam-4911	315	4	⊂	⊂	PROPN
ejpam-4911	315	5	µ2	µ2	PROPN
ejpam-4911	315	6	.	.	PUNCT
ejpam-4911	316	1	take	take	VERB
ejpam-4911	316	2	k	k	NOUN
ejpam-4911	316	3	=	=	PRON
ejpam-4911	316	4	{	{	PUNCT
ejpam-4911	316	5	q	q	NOUN
ejpam-4911	316	6	,	,	PUNCT
ejpam-4911	316	7	r	r	NOUN
ejpam-4911	316	8	}	}	PUNCT
ejpam-4911	316	9	then	then	ADV
ejpam-4911	316	10	we	we	PRON
ejpam-4911	316	11	get	get	VERB
ejpam-4911	316	12	i2(c1(k	i2(c1(k	NOUN
ejpam-4911	316	13	)	)	PUNCT
ejpam-4911	316	14	)	)	PUNCT
ejpam-4911	317	1	=	=	NOUN
ejpam-4911	317	2	∅	∅	NOUN
ejpam-4911	317	3	and	and	CCONJ
ejpam-4911	317	4	hence	hence	ADV
ejpam-4911	317	5	k	k	PROPN
ejpam-4911	317	6	∈	∈	PROPN
ejpam-4911	317	7	(	(	PUNCT
ejpam-4911	317	8	2	2	NUM
ejpam-4911	317	9	,	,	PUNCT
ejpam-4911	317	10	1)−n	1)−n	NUM
ejpam-4911	317	11	(	(	PUNCT
ejpam-4911	317	12	x	x	NOUN
ejpam-4911	317	13	)	)	PUNCT
ejpam-4911	317	14	.	.	PUNCT
ejpam-4911	318	1	now	now	ADV
ejpam-4911	318	2	,	,	PUNCT
ejpam-4911	318	3	i1(c1(k	i1(c1(k	NOUN
ejpam-4911	318	4	)	)	PUNCT
ejpam-4911	318	5	)	)	PUNCT
ejpam-4911	319	1	=	=	NOUN
ejpam-4911	319	2	∅	∅	NOUN
ejpam-4911	319	3	and	and	CCONJ
ejpam-4911	319	4	i2(c2(k	i2(c2(k	NOUN
ejpam-4911	319	5	)	)	PUNCT
ejpam-4911	319	6	)	)	PUNCT
ejpam-4911	320	1	=	=	PUNCT
ejpam-4911	320	2	∅	∅	NOUN
ejpam-4911	320	3	which	which	PRON
ejpam-4911	320	4	implies	imply	VERB
ejpam-4911	320	5	that	that	SCONJ
ejpam-4911	320	6	k	k	PROPN
ejpam-4911	320	7	is	be	AUX
ejpam-4911	320	8	a	a	DET
ejpam-4911	320	9	µ1	µ1	NOUN
ejpam-4911	320	10	-	-	PUNCT
ejpam-4911	320	11	nowhere	nowhere	ADV
ejpam-4911	320	12	dense	dense	ADJ
ejpam-4911	320	13	set	set	NOUN
ejpam-4911	320	14	and	and	CCONJ
ejpam-4911	320	15	also	also	ADV
ejpam-4911	320	16	a	a	DET
ejpam-4911	320	17	µ2	µ2	PROPN
ejpam-4911	320	18	-	-	PUNCT
ejpam-4911	320	19	nowhere	nowhere	ADV
ejpam-4911	320	20	dense	dense	ADJ
ejpam-4911	320	21	set	set	NOUN
ejpam-4911	320	22	.	.	PUNCT
ejpam-4911	321	1	theorem	theorem	VERB
ejpam-4911	321	2	22	22	NUM
ejpam-4911	321	3	.	.	PUNCT
ejpam-4911	322	1	let	let	VERB
ejpam-4911	322	2	µ1	µ1	PROPN
ejpam-4911	322	3	,	,	PUNCT
ejpam-4911	322	4	µ2	µ2	PROPN
ejpam-4911	322	5	be	be	AUX
ejpam-4911	322	6	two	two	NUM
ejpam-4911	322	7	generlized	generlize	VERB
ejpam-4911	322	8	topologies	topology	NOUN
ejpam-4911	322	9	on	on	ADP
ejpam-4911	322	10	x	x	PUNCT
ejpam-4911	322	11	and	and	CCONJ
ejpam-4911	322	12	µv	µv	PROPN
ejpam-4911	322	13	⊆	⊆	NUM
ejpam-4911	322	14	µs	µs	ADP
ejpam-4911	322	15	where	where	SCONJ
ejpam-4911	322	16	s	s	X
ejpam-4911	322	17	,	,	PUNCT
ejpam-4911	322	18	v	v	NOUN
ejpam-4911	322	19	=	=	SYM
ejpam-4911	322	20	1	1	NUM
ejpam-4911	322	21	,	,	PUNCT
ejpam-4911	322	22	2	2	NUM
ejpam-4911	322	23	;	;	PUNCT
ejpam-4911	322	24	s	s	VERB
ejpam-4911	322	25	̸=	̸=	PROPN
ejpam-4911	322	26	v.	v.	ADP
ejpam-4911	323	1	if	if	SCONJ
ejpam-4911	323	2	q	q	X
ejpam-4911	323	3	∈	∈	PROPN
ejpam-4911	323	4	(	(	PUNCT
ejpam-4911	323	5	s	s	PROPN
ejpam-4911	323	6	,	,	PUNCT
ejpam-4911	323	7	v	v	NOUN
ejpam-4911	323	8	)	)	PUNCT
ejpam-4911	323	9	−	−	PROPN
ejpam-4911	323	10	n	n	CCONJ
ejpam-4911	323	11	(	(	PUNCT
ejpam-4911	323	12	x	x	NOUN
ejpam-4911	323	13	)	)	PUNCT
ejpam-4911	323	14	,	,	PUNCT
ejpam-4911	323	15	then	then	ADV
ejpam-4911	323	16	q	q	PROPN
ejpam-4911	323	17	is	be	AUX
ejpam-4911	323	18	µv	µv	NOUN
ejpam-4911	323	19	-	-	PUNCT
ejpam-4911	323	20	nowhere	nowhere	ADV
ejpam-4911	323	21	dense	dense	ADJ
ejpam-4911	323	22	and	and	CCONJ
ejpam-4911	323	23	also	also	ADV
ejpam-4911	323	24	µs	µ	NOUN
ejpam-4911	323	25	-	-	PUNCT
ejpam-4911	323	26	nowhere	nowhere	ADV
ejpam-4911	323	27	dense	dense	ADJ
ejpam-4911	323	28	where	where	SCONJ
ejpam-4911	323	29	s	s	X
ejpam-4911	323	30	,	,	PUNCT
ejpam-4911	323	31	v	v	NOUN
ejpam-4911	323	32	=	=	SYM
ejpam-4911	323	33	1	1	NUM
ejpam-4911	323	34	,	,	PUNCT
ejpam-4911	323	35	2	2	NUM
ejpam-4911	323	36	;	;	PUNCT
ejpam-4911	323	37	s	s	VERB
ejpam-4911	323	38	̸=	̸=	PROPN
ejpam-4911	323	39	v.	v.	ADP
ejpam-4911	323	40	proof	proof	NOUN
ejpam-4911	323	41	.	.	PUNCT
ejpam-4911	324	1	we	we	PRON
ejpam-4911	324	2	give	give	VERB
ejpam-4911	324	3	the	the	DET
ejpam-4911	324	4	detailed	detailed	ADJ
ejpam-4911	324	5	proof	proof	NOUN
ejpam-4911	324	6	for	for	ADP
ejpam-4911	324	7	s	s	NOUN
ejpam-4911	324	8	=	=	SYM
ejpam-4911	324	9	1	1	NUM
ejpam-4911	324	10	and	and	CCONJ
ejpam-4911	324	11	v	v	NOUN
ejpam-4911	324	12	=	=	SYM
ejpam-4911	324	13	2	2	NUM
ejpam-4911	324	14	only	only	ADV
ejpam-4911	324	15	.	.	PUNCT
ejpam-4911	325	1	assume	assume	VERB
ejpam-4911	325	2	that	that	SCONJ
ejpam-4911	325	3	,	,	PUNCT
ejpam-4911	325	4	µ2	µ2	PROPN
ejpam-4911	325	5	⊆	⊆	NUM
ejpam-4911	325	6	µ1	µ1	PROPN
ejpam-4911	325	7	.	.	PUNCT
ejpam-4911	326	1	let	let	VERB
ejpam-4911	326	2	q	q	PART
ejpam-4911	326	3	be	be	AUX
ejpam-4911	326	4	a	a	DET
ejpam-4911	326	5	(	(	PUNCT
ejpam-4911	326	6	1	1	NUM
ejpam-4911	326	7	,	,	PUNCT
ejpam-4911	326	8	2)-nowhere	2)-nowhere	NUM
ejpam-4911	326	9	dense	dense	ADJ
ejpam-4911	326	10	set	set	NOUN
ejpam-4911	326	11	.	.	PUNCT
ejpam-4911	327	1	then	then	ADV
ejpam-4911	327	2	i1(c2(q	i1(c2(q	NUM
ejpam-4911	327	3	)	)	PUNCT
ejpam-4911	327	4	)	)	PUNCT
ejpam-4911	328	1	=	=	VERB
ejpam-4911	328	2	∅.	∅.	AUX
ejpam-4911	328	3	suppose	suppose	VERB
ejpam-4911	328	4	i1(c1(q	i1(c1(q	ADP
ejpam-4911	328	5	)	)	PUNCT
ejpam-4911	328	6	)	)	PUNCT
ejpam-4911	329	1	̸=	̸=	PROPN
ejpam-4911	329	2	∅.	∅.	PRON
ejpam-4911	329	3	by	by	ADP
ejpam-4911	329	4	assumption	assumption	NOUN
ejpam-4911	329	5	,	,	PUNCT
ejpam-4911	329	6	i1(c2(q	i1(c2(q	NUM
ejpam-4911	329	7	)	)	PUNCT
ejpam-4911	329	8	)	)	PUNCT
ejpam-4911	330	1	̸=	̸=	PROPN
ejpam-4911	330	2	∅	∅	NOUN
ejpam-4911	330	3	which	which	PRON
ejpam-4911	330	4	is	be	AUX
ejpam-4911	330	5	a	a	DET
ejpam-4911	330	6	contradiction	contradiction	NOUN
ejpam-4911	330	7	.	.	PUNCT
ejpam-4911	331	1	therefore	therefore	ADV
ejpam-4911	331	2	,	,	PUNCT
ejpam-4911	331	3	i1(c1(q	i1(c1(q	ADP
ejpam-4911	331	4	)	)	PUNCT
ejpam-4911	331	5	)	)	PUNCT
ejpam-4911	332	1	=	=	PUNCT
ejpam-4911	332	2	∅.	∅.	VERB
ejpam-4911	332	3	if	if	SCONJ
ejpam-4911	332	4	i2(c2(q	i2(c2(q	NUM
ejpam-4911	332	5	)	)	PUNCT
ejpam-4911	332	6	)	)	PUNCT
ejpam-4911	333	1	̸=	̸=	NOUN
ejpam-4911	333	2	∅	∅	NOUN
ejpam-4911	333	3	,	,	PUNCT
ejpam-4911	333	4	then	then	ADV
ejpam-4911	333	5	there	there	PRON
ejpam-4911	333	6	is	be	VERB
ejpam-4911	333	7	a	a	DET
ejpam-4911	333	8	set	set	NOUN
ejpam-4911	333	9	m	m	NOUN
ejpam-4911	333	10	∈	∈	NOUN
ejpam-4911	333	11	µ̃2	µ̃2	PROPN
ejpam-4911	333	12	such	such	ADJ
ejpam-4911	333	13	that	that	SCONJ
ejpam-4911	333	14	m	m	VERB
ejpam-4911	333	15	⊂	⊂	ADJ
ejpam-4911	333	16	c2(q	c2(q	PROPN
ejpam-4911	333	17	)	)	PUNCT
ejpam-4911	333	18	.	.	PUNCT
ejpam-4911	334	1	by	by	ADP
ejpam-4911	334	2	assumption	assumption	NOUN
ejpam-4911	334	3	,	,	PUNCT
ejpam-4911	334	4	m	m	PROPN
ejpam-4911	334	5	∈	∈	PROPN
ejpam-4911	334	6	µ̃1	µ̃1	NOUN
ejpam-4911	334	7	.	.	PUNCT
ejpam-4911	334	8	thus	thus	ADV
ejpam-4911	334	9	,	,	PUNCT
ejpam-4911	334	10	i1(c2(q	i1(c2(q	NUM
ejpam-4911	334	11	)	)	PUNCT
ejpam-4911	334	12	)	)	PUNCT
ejpam-4911	335	1	̸=	̸=	PROPN
ejpam-4911	335	2	∅	∅	NOUN
ejpam-4911	335	3	which	which	PRON
ejpam-4911	335	4	is	be	AUX
ejpam-4911	335	5	a	a	DET
ejpam-4911	335	6	contradiction	contradiction	NOUN
ejpam-4911	335	7	.	.	PUNCT
ejpam-4911	336	1	therefore	therefore	ADV
ejpam-4911	336	2	,	,	PUNCT
ejpam-4911	336	3	i2(c2(q	i2(c2(q	NUM
ejpam-4911	336	4	)	)	PUNCT
ejpam-4911	336	5	)	)	PUNCT
ejpam-4911	337	1	=	=	PUNCT
ejpam-4911	337	2	∅.	∅.	NOUN
ejpam-4911	337	3	theorem	theorem	VERB
ejpam-4911	337	4	23	23	NUM
ejpam-4911	337	5	.	.	PUNCT
ejpam-4911	338	1	let	let	AUX
ejpam-4911	338	2	(	(	PUNCT
ejpam-4911	338	3	x,µ1	x,µ1	NOUN
ejpam-4911	338	4	,	,	PUNCT
ejpam-4911	338	5	µ2	µ2	PROPN
ejpam-4911	338	6	)	)	PUNCT
ejpam-4911	338	7	be	be	VERB
ejpam-4911	338	8	a	a	DET
ejpam-4911	338	9	bgts	bgts	NOUN
ejpam-4911	338	10	and	and	CCONJ
ejpam-4911	338	11	k	k	PROPN
ejpam-4911	338	12	⊂	⊂	PROPN
ejpam-4911	338	13	x.	x.	NOUN
ejpam-4911	339	1	if	if	SCONJ
ejpam-4911	339	2	k	k	PROPN
ejpam-4911	339	3	∈	∈	PROPN
ejpam-4911	339	4	(	(	PUNCT
ejpam-4911	339	5	s	s	PROPN
ejpam-4911	339	6	,	,	PUNCT
ejpam-4911	339	7	v)−n	v)−n	X
ejpam-4911	339	8	(	(	PUNCT
ejpam-4911	339	9	x	x	X
ejpam-4911	339	10	)	)	PUNCT
ejpam-4911	339	11	then	then	ADV
ejpam-4911	339	12	cv(k)−	cv(k)−	NOUN
ejpam-4911	339	13	k	k	X
ejpam-4911	339	14	∈	∈	PROPN
ejpam-4911	339	15	(	(	PUNCT
ejpam-4911	339	16	s	s	PROPN
ejpam-4911	339	17	,	,	PUNCT
ejpam-4911	339	18	v)−n	v)−n	X
ejpam-4911	339	19	(	(	PUNCT
ejpam-4911	339	20	x	x	NOUN
ejpam-4911	339	21	)	)	PUNCT
ejpam-4911	339	22	where	where	SCONJ
ejpam-4911	339	23	s	s	X
ejpam-4911	339	24	,	,	PUNCT
ejpam-4911	339	25	v	v	NOUN
ejpam-4911	339	26	=	=	SYM
ejpam-4911	339	27	1	1	NUM
ejpam-4911	339	28	,	,	PUNCT
ejpam-4911	339	29	2	2	NUM
ejpam-4911	339	30	and	and	CCONJ
ejpam-4911	339	31	s	s	VERB
ejpam-4911	339	32	̸=	̸=	PROPN
ejpam-4911	339	33	v.	v.	ADP
ejpam-4911	339	34	proof	proof	NOUN
ejpam-4911	339	35	.	.	PUNCT
ejpam-4911	340	1	let	let	VERB
ejpam-4911	340	2	k	k	PROPN
ejpam-4911	340	3	∈	∈	PROPN
ejpam-4911	340	4	(	(	PUNCT
ejpam-4911	340	5	s	s	PROPN
ejpam-4911	340	6	,	,	PUNCT
ejpam-4911	340	7	v	v	NOUN
ejpam-4911	340	8	)	)	PUNCT
ejpam-4911	340	9	−n	−n	NOUN
ejpam-4911	340	10	(	(	PUNCT
ejpam-4911	340	11	x	x	X
ejpam-4911	340	12	)	)	PUNCT
ejpam-4911	340	13	where	where	SCONJ
ejpam-4911	340	14	s	s	X
ejpam-4911	340	15	,	,	PUNCT
ejpam-4911	340	16	v	v	NOUN
ejpam-4911	340	17	=	=	SYM
ejpam-4911	340	18	1	1	NUM
ejpam-4911	340	19	,	,	PUNCT
ejpam-4911	340	20	2	2	NUM
ejpam-4911	340	21	;	;	PUNCT
ejpam-4911	340	22	s	s	VERB
ejpam-4911	340	23	̸=	̸=	PROPN
ejpam-4911	340	24	v.	v.	ADP
ejpam-4911	340	25	take	take	VERB
ejpam-4911	340	26	s	s	PART
ejpam-4911	340	27	=	=	SYM
ejpam-4911	340	28	1	1	NUM
ejpam-4911	340	29	and	and	CCONJ
ejpam-4911	340	30	v	v	NOUN
ejpam-4911	340	31	=	=	SYM
ejpam-4911	340	32	2	2	NUM
ejpam-4911	340	33	.	.	PUNCT
ejpam-4911	341	1	then	then	ADV
ejpam-4911	341	2	k	k	PROPN
ejpam-4911	341	3	is	be	AUX
ejpam-4911	341	4	a	a	DET
ejpam-4911	341	5	(	(	PUNCT
ejpam-4911	341	6	1	1	NUM
ejpam-4911	341	7	,	,	PUNCT
ejpam-4911	341	8	2)-nowhere	2)-nowhere	NUM
ejpam-4911	341	9	dense	dense	ADJ
ejpam-4911	341	10	set	set	NOUN
ejpam-4911	341	11	in	in	ADP
ejpam-4911	341	12	x.	x.	NOUN
ejpam-4911	341	13	since	since	SCONJ
ejpam-4911	341	14	c2(k)−k	c2(k)−k	PROPN
ejpam-4911	341	15	⊂	⊂	X
ejpam-4911	341	16	c2(k	c2(k	PROPN
ejpam-4911	341	17	)	)	PUNCT
ejpam-4911	341	18	we	we	PRON
ejpam-4911	341	19	have	have	AUX
ejpam-4911	341	20	c2(c2(k)−k	c2(c2(k)−k	VERB
ejpam-4911	341	21	)	)	PUNCT
ejpam-4911	341	22	⊂	⊂	PROPN
ejpam-4911	341	23	c2(c2(k	c2(c2(k	PROPN
ejpam-4911	341	24	)	)	PUNCT
ejpam-4911	341	25	)	)	PUNCT
ejpam-4911	341	26	.	.	PUNCT
ejpam-4911	342	1	by	by	ADP
ejpam-4911	342	2	lemma	lemma	PROPN
ejpam-4911	342	3	5	5	NUM
ejpam-4911	342	4	(	(	PUNCT
ejpam-4911	342	5	e	e	NOUN
ejpam-4911	342	6	)	)	PUNCT
ejpam-4911	342	7	,	,	PUNCT
ejpam-4911	342	8	c2(c2(k)−k	c2(c2(k)−k	PROPN
ejpam-4911	342	9	)	)	PUNCT
ejpam-4911	342	10	⊂	⊂	PROPN
ejpam-4911	342	11	c2(k	c2(k	PROPN
ejpam-4911	342	12	)	)	PUNCT
ejpam-4911	342	13	.	.	PUNCT
ejpam-4911	343	1	then	then	ADV
ejpam-4911	343	2	i1(c2(c2(k)−k	i1(c2(c2(k)−k	PRON
ejpam-4911	343	3	)	)	PUNCT
ejpam-4911	343	4	)	)	PUNCT
ejpam-4911	344	1	⊂	⊂	PROPN
ejpam-4911	344	2	i1(c2(k	i1(c2(k	PROPN
ejpam-4911	344	3	)	)	PUNCT
ejpam-4911	344	4	)	)	PUNCT
ejpam-4911	345	1	and	and	CCONJ
ejpam-4911	345	2	so	so	ADV
ejpam-4911	345	3	i1(c2(c2(k)−k	i1(c2(c2(k)−k	NUM
ejpam-4911	345	4	)	)	PUNCT
ejpam-4911	345	5	)	)	PUNCT
ejpam-4911	346	1	=	=	NOUN
ejpam-4911	346	2	∅	∅	NOUN
ejpam-4911	346	3	,	,	PUNCT
ejpam-4911	346	4	by	by	ADP
ejpam-4911	346	5	assumption	assumption	NOUN
ejpam-4911	346	6	.	.	PUNCT
ejpam-4911	347	1	therefore	therefore	ADV
ejpam-4911	347	2	,	,	PUNCT
ejpam-4911	347	3	c2(k)−k	c2(k)−k	PROPN
ejpam-4911	347	4	∈	∈	PROPN
ejpam-4911	347	5	(	(	PUNCT
ejpam-4911	347	6	1	1	NUM
ejpam-4911	347	7	,	,	PUNCT
ejpam-4911	347	8	2)−n	2)−n	NUM
ejpam-4911	347	9	(	(	PUNCT
ejpam-4911	347	10	x	x	NOUN
ejpam-4911	347	11	)	)	PUNCT
ejpam-4911	347	12	.	.	PUNCT
ejpam-4911	348	1	by	by	ADP
ejpam-4911	348	2	similar	similar	ADJ
ejpam-4911	348	3	argument	argument	NOUN
ejpam-4911	348	4	in	in	ADP
ejpam-4911	348	5	the	the	DET
ejpam-4911	348	6	above	above	ADJ
ejpam-4911	348	7	case	case	NOUN
ejpam-4911	348	8	,	,	PUNCT
ejpam-4911	348	9	we	we	PRON
ejpam-4911	348	10	get	get	VERB
ejpam-4911	348	11	c1(k)−k	c1(k)−k	VERB
ejpam-4911	348	12	∈	∈	NOUN
ejpam-4911	348	13	(	(	PUNCT
ejpam-4911	348	14	2	2	NUM
ejpam-4911	348	15	,	,	PUNCT
ejpam-4911	348	16	1)−n	1)−n	NUM
ejpam-4911	348	17	(	(	PUNCT
ejpam-4911	348	18	x	x	NOUN
ejpam-4911	348	19	)	)	PUNCT
ejpam-4911	348	20	.	.	PUNCT
ejpam-4911	349	1	example	example	NOUN
ejpam-4911	350	1	24	24	NUM
ejpam-4911	350	2	.	.	PUNCT
ejpam-4911	351	1	consider	consider	VERB
ejpam-4911	351	2	the	the	DET
ejpam-4911	351	3	bigeneralized	bigeneralized	ADJ
ejpam-4911	351	4	topological	topological	ADJ
ejpam-4911	351	5	space	space	NOUN
ejpam-4911	351	6	(	(	PUNCT
ejpam-4911	351	7	x,µ1	x,µ1	PROPN
ejpam-4911	351	8	,	,	PUNCT
ejpam-4911	351	9	µ2	µ2	PROPN
ejpam-4911	351	10	)	)	PUNCT
ejpam-4911	351	11	,	,	PUNCT
ejpam-4911	351	12	x	x	PUNCT
ejpam-4911	351	13	=	=	PRON
ejpam-4911	351	14	{	{	PUNCT
ejpam-4911	351	15	e	e	NOUN
ejpam-4911	351	16	,	,	PUNCT
ejpam-4911	351	17	f	f	PROPN
ejpam-4911	351	18	,	,	PUNCT
ejpam-4911	351	19	k	k	NOUN
ejpam-4911	351	20	,	,	PUNCT
ejpam-4911	351	21	l	l	NOUN
ejpam-4911	351	22	}	}	PUNCT
ejpam-4911	351	23	;	;	PUNCT
ejpam-4911	351	24	µ1	µ1	PROPN
ejpam-4911	351	25	=	=	SYM
ejpam-4911	351	26	{	{	PUNCT
ejpam-4911	351	27	∅	∅	NOUN
ejpam-4911	351	28	,	,	PUNCT
ejpam-4911	351	29	{	{	PUNCT
ejpam-4911	351	30	e	e	NOUN
ejpam-4911	351	31	,	,	PUNCT
ejpam-4911	351	32	k	k	NOUN
ejpam-4911	351	33	}	}	PUNCT
ejpam-4911	351	34	,	,	PUNCT
ejpam-4911	351	35	{	{	PUNCT
ejpam-4911	351	36	f	f	X
ejpam-4911	351	37	,	,	PUNCT
ejpam-4911	351	38	k	k	NOUN
ejpam-4911	351	39	}	}	PUNCT
ejpam-4911	351	40	,	,	PUNCT
ejpam-4911	351	41	{	{	PUNCT
ejpam-4911	351	42	e	e	NOUN
ejpam-4911	351	43	,	,	PUNCT
ejpam-4911	351	44	f	f	PROPN
ejpam-4911	351	45	,	,	PUNCT
ejpam-4911	351	46	k	k	NOUN
ejpam-4911	351	47	}	}	PUNCT
ejpam-4911	351	48	}	}	PUNCT
ejpam-4911	351	49	and	and	CCONJ
ejpam-4911	351	50	µ2	µ2	PROPN
ejpam-4911	351	51	=	=	PUNCT
ejpam-4911	351	52	{	{	PUNCT
ejpam-4911	351	53	∅	∅	NOUN
ejpam-4911	351	54	,	,	PUNCT
ejpam-4911	351	55	{	{	PUNCT
ejpam-4911	351	56	k	k	NOUN
ejpam-4911	351	57	}	}	PUNCT
ejpam-4911	351	58	,	,	PUNCT
ejpam-4911	351	59	{	{	PUNCT
ejpam-4911	351	60	e	e	NOUN
ejpam-4911	351	61	,	,	PUNCT
ejpam-4911	351	62	k	k	NOUN
ejpam-4911	351	63	}	}	PUNCT
ejpam-4911	351	64	,	,	PUNCT
ejpam-4911	351	65	{	{	PUNCT
ejpam-4911	351	66	f	f	X
ejpam-4911	351	67	,	,	PUNCT
ejpam-4911	351	68	k	k	NOUN
ejpam-4911	351	69	}	}	PUNCT
ejpam-4911	351	70	,	,	PUNCT
ejpam-4911	351	71	{	{	PUNCT
ejpam-4911	351	72	e	e	NOUN
ejpam-4911	351	73	,	,	PUNCT
ejpam-4911	351	74	f	f	PROPN
ejpam-4911	351	75	,	,	PUNCT
ejpam-4911	351	76	k	k	NOUN
ejpam-4911	351	77	}	}	PUNCT
ejpam-4911	351	78	}	}	PUNCT
ejpam-4911	351	79	.	.	PUNCT
ejpam-4911	352	1	take	take	VERB
ejpam-4911	352	2	q	q	NOUN
ejpam-4911	352	3	=	=	PUNCT
ejpam-4911	352	4	{	{	PUNCT
ejpam-4911	352	5	k	k	NOUN
ejpam-4911	352	6	}	}	PUNCT
ejpam-4911	352	7	we	we	PRON
ejpam-4911	352	8	get	get	VERB
ejpam-4911	352	9	c2(q	c2(q	PROPN
ejpam-4911	352	10	)	)	PUNCT
ejpam-4911	352	11	−	−	PROPN
ejpam-4911	352	12	q	q	NOUN
ejpam-4911	353	1	=	=	PUNCT
ejpam-4911	353	2	{	{	PUNCT
ejpam-4911	353	3	e	e	NOUN
ejpam-4911	353	4	,	,	PUNCT
ejpam-4911	353	5	f	f	PROPN
ejpam-4911	353	6	,	,	PUNCT
ejpam-4911	353	7	l	l	NOUN
ejpam-4911	353	8	}	}	PUNCT
ejpam-4911	353	9	and	and	CCONJ
ejpam-4911	353	10	so	so	ADV
ejpam-4911	353	11	i1(c2(c2(q	i1(c2(c2(q	PROPN
ejpam-4911	353	12	)	)	PUNCT
ejpam-4911	353	13	−	−	PROPN
ejpam-4911	353	14	q	q	NOUN
ejpam-4911	353	15	)	)	PUNCT
ejpam-4911	353	16	)	)	PUNCT
ejpam-4911	354	1	=	=	PUNCT
ejpam-4911	354	2	∅.	∅.	VERB
ejpam-4911	354	3	thus	thus	ADV
ejpam-4911	354	4	,	,	PUNCT
ejpam-4911	354	5	c2(q)−q	c2(q)−q	X
ejpam-4911	354	6	∈	∈	PROPN
ejpam-4911	354	7	(	(	PUNCT
ejpam-4911	354	8	1	1	NUM
ejpam-4911	354	9	,	,	PUNCT
ejpam-4911	354	10	2)−n	2)−n	NUM
ejpam-4911	354	11	(	(	PUNCT
ejpam-4911	354	12	x	x	NOUN
ejpam-4911	354	13	)	)	PUNCT
ejpam-4911	354	14	.	.	PUNCT
ejpam-4911	355	1	but	but	CCONJ
ejpam-4911	355	2	q	q	NOUN
ejpam-4911	355	3	/∈	/∈	INTJ
ejpam-4911	356	1	(	(	PUNCT
ejpam-4911	356	2	1	1	NUM
ejpam-4911	356	3	,	,	PUNCT
ejpam-4911	356	4	2)−n	2)−n	NUM
ejpam-4911	356	5	(	(	PUNCT
ejpam-4911	356	6	x	x	NOUN
ejpam-4911	356	7	)	)	PUNCT
ejpam-4911	356	8	.	.	PUNCT
ejpam-4911	357	1	choose	choose	VERB
ejpam-4911	357	2	l	l	NOUN
ejpam-4911	357	3	=	=	PUNCT
ejpam-4911	357	4	{	{	PUNCT
ejpam-4911	357	5	f	f	X
ejpam-4911	357	6	,	,	PUNCT
ejpam-4911	357	7	k	k	NOUN
ejpam-4911	357	8	}	}	PUNCT
ejpam-4911	357	9	so	so	SCONJ
ejpam-4911	357	10	that	that	SCONJ
ejpam-4911	357	11	c1(l	c1(l	NUM
ejpam-4911	357	12	)	)	PUNCT
ejpam-4911	357	13	−	−	NOUN
ejpam-4911	357	14	l	l	NOUN
ejpam-4911	357	15	=	=	SYM
ejpam-4911	357	16	{	{	PUNCT
ejpam-4911	357	17	e	e	NOUN
ejpam-4911	357	18	,	,	PUNCT
ejpam-4911	357	19	l	l	NOUN
ejpam-4911	357	20	}	}	PUNCT
ejpam-4911	357	21	and	and	CCONJ
ejpam-4911	357	22	so	so	ADV
ejpam-4911	357	23	i2(c1(c1(l	i2(c1(c1(l	NOUN
ejpam-4911	357	24	)	)	PUNCT
ejpam-4911	357	25	−	−	PROPN
ejpam-4911	357	26	l	l	NOUN
ejpam-4911	357	27	)	)	PUNCT
ejpam-4911	357	28	)	)	PUNCT
ejpam-4911	358	1	=	=	NOUN
ejpam-4911	358	2	∅	∅	NOUN
ejpam-4911	358	3	implies	imply	VERB
ejpam-4911	358	4	that	that	SCONJ
ejpam-4911	358	5	c1(l)−	c1(l)−	PROPN
ejpam-4911	358	6	l	l	NOUN
ejpam-4911	358	7	∈	∈	PROPN
ejpam-4911	358	8	(	(	PUNCT
ejpam-4911	358	9	2	2	NUM
ejpam-4911	358	10	,	,	PUNCT
ejpam-4911	358	11	1)−n	1)−n	NUM
ejpam-4911	358	12	(	(	PUNCT
ejpam-4911	358	13	x	x	NOUN
ejpam-4911	358	14	)	)	PUNCT
ejpam-4911	358	15	.	.	PUNCT
ejpam-4911	359	1	but	but	CCONJ
ejpam-4911	359	2	l	l	NOUN
ejpam-4911	359	3	/∈	/∈	PUNCT
ejpam-4911	360	1	(	(	PUNCT
ejpam-4911	360	2	2	2	NUM
ejpam-4911	360	3	,	,	PUNCT
ejpam-4911	360	4	1)−n	1)−n	NUM
ejpam-4911	360	5	(	(	PUNCT
ejpam-4911	360	6	x	x	NOUN
ejpam-4911	360	7	)	)	PUNCT
ejpam-4911	360	8	.	.	PUNCT
ejpam-4911	361	1	theorem	theorem	NOUN
ejpam-4911	361	2	25	25	NUM
ejpam-4911	361	3	.	.	PUNCT
ejpam-4911	362	1	let	let	AUX
ejpam-4911	362	2	(	(	PUNCT
ejpam-4911	362	3	x,µ1	x,µ1	NOUN
ejpam-4911	362	4	,	,	PUNCT
ejpam-4911	362	5	µ2	µ2	PROPN
ejpam-4911	362	6	)	)	PUNCT
ejpam-4911	362	7	be	be	AUX
ejpam-4911	362	8	a	a	DET
ejpam-4911	362	9	bgts	bgts	NOUN
ejpam-4911	362	10	.	.	PUNCT
ejpam-4911	363	1	for	for	ADP
ejpam-4911	363	2	s	s	PROPN
ejpam-4911	363	3	,	,	PUNCT
ejpam-4911	363	4	v	v	NOUN
ejpam-4911	363	5	=	=	SYM
ejpam-4911	363	6	1	1	NUM
ejpam-4911	363	7	,	,	PUNCT
ejpam-4911	363	8	2	2	NUM
ejpam-4911	363	9	and	and	CCONJ
ejpam-4911	363	10	s	s	PART
ejpam-4911	363	11	̸=	̸=	PROPN
ejpam-4911	363	12	v	v	NOUN
ejpam-4911	363	13	,	,	PUNCT
ejpam-4911	363	14	if	if	SCONJ
ejpam-4911	363	15	d	d	PROPN
ejpam-4911	363	16	∈	∈	PROPN
ejpam-4911	363	17	(	(	PUNCT
ejpam-4911	363	18	s	s	PROPN
ejpam-4911	363	19	,	,	PUNCT
ejpam-4911	363	20	v)−n	v)−n	X
ejpam-4911	363	21	(	(	PUNCT
ejpam-4911	363	22	x	x	NOUN
ejpam-4911	363	23	)	)	PUNCT
ejpam-4911	363	24	,	,	PUNCT
ejpam-4911	363	25	then	then	ADV
ejpam-4911	363	26	the	the	DET
ejpam-4911	363	27	followings	following	NOUN
ejpam-4911	363	28	are	be	AUX
ejpam-4911	363	29	true	true	ADJ
ejpam-4911	363	30	.	.	PUNCT
ejpam-4911	364	1	(	(	PUNCT
ejpam-4911	364	2	a	a	X
ejpam-4911	364	3	)	)	PUNCT
ejpam-4911	364	4	k	k	NOUN
ejpam-4911	364	5	⊈	⊈	PROPN
ejpam-4911	365	1	d	d	NOUN
ejpam-4911	365	2	for	for	ADP
ejpam-4911	365	3	all	all	PRON
ejpam-4911	365	4	k	k	NOUN
ejpam-4911	365	5	is	be	AUX
ejpam-4911	365	6	a	a	DET
ejpam-4911	365	7	non	non	ADJ
ejpam-4911	365	8	-	-	ADJ
ejpam-4911	365	9	null	null	ADJ
ejpam-4911	365	10	(	(	PUNCT
ejpam-4911	365	11	s	s	X
ejpam-4911	365	12	,	,	PUNCT
ejpam-4911	365	13	v)-µ-preopen	v)-µ-preopen	VERB
ejpam-4911	365	14	set	set	VERB
ejpam-4911	365	15	in	in	ADP
ejpam-4911	365	16	x.	x.	PROPN
ejpam-4911	366	1	(	(	PUNCT
ejpam-4911	366	2	b	b	X
ejpam-4911	366	3	)	)	PUNCT
ejpam-4911	366	4	k	k	NOUN
ejpam-4911	367	1	⊈	⊈	PROPN
ejpam-4911	367	2	d	d	NOUN
ejpam-4911	367	3	for	for	ADP
ejpam-4911	367	4	all	all	PRON
ejpam-4911	367	5	k	k	NOUN
ejpam-4911	367	6	is	be	AUX
ejpam-4911	367	7	a	a	DET
ejpam-4911	367	8	non	non	ADJ
ejpam-4911	367	9	-	-	ADJ
ejpam-4911	367	10	null	null	ADJ
ejpam-4911	367	11	(	(	PUNCT
ejpam-4911	367	12	s	s	PROPN
ejpam-4911	367	13	,	,	PUNCT
ejpam-4911	367	14	v)-µ-regular	v)-µ-regular	ADJ
ejpam-4911	367	15	open	open	ADJ
ejpam-4911	367	16	set	set	VERB
ejpam-4911	367	17	in	in	ADP
ejpam-4911	367	18	x.	x.	PROPN
ejpam-4911	367	19	y.	y.	PROPN
ejpam-4911	367	20	farhat	farhat	PROPN
ejpam-4911	367	21	,	,	PUNCT
ejpam-4911	367	22	v.	v.	ADP
ejpam-4911	367	23	subramanian	subramanian	PROPN
ejpam-4911	367	24	/	/	SYM
ejpam-4911	367	25	eur	eur	PROPN
ejpam-4911	367	26	.	.	PUNCT
ejpam-4911	368	1	j.	j.	PROPN
ejpam-4911	368	2	pure	pure	PROPN
ejpam-4911	368	3	appl	appl	PROPN
ejpam-4911	368	4	.	.	PROPN
ejpam-4911	368	5	math	math	PROPN
ejpam-4911	368	6	,	,	PUNCT
ejpam-4911	368	7	16	16	NUM
ejpam-4911	368	8	(	(	PUNCT
ejpam-4911	368	9	4	4	NUM
ejpam-4911	368	10	)	)	PUNCT
ejpam-4911	368	11	(	(	PUNCT
ejpam-4911	368	12	2023	2023	NUM
ejpam-4911	368	13	)	)	PUNCT
ejpam-4911	368	14	,	,	PUNCT
ejpam-4911	368	15	2049	2049	NUM
ejpam-4911	368	16	-	-	SYM
ejpam-4911	368	17	2065	2065	NUM
ejpam-4911	368	18	2060	2060	NUM
ejpam-4911	368	19	(	(	PUNCT
ejpam-4911	368	20	c	c	X
ejpam-4911	368	21	)	)	PUNCT
ejpam-4911	368	22	k	k	NOUN
ejpam-4911	369	1	⊈	⊈	PROPN
ejpam-4911	369	2	d	d	NOUN
ejpam-4911	369	3	for	for	ADP
ejpam-4911	369	4	all	all	PRON
ejpam-4911	369	5	k	k	NOUN
ejpam-4911	369	6	is	be	AUX
ejpam-4911	369	7	a	a	DET
ejpam-4911	369	8	non	non	ADJ
ejpam-4911	369	9	-	-	ADJ
ejpam-4911	369	10	null	null	ADJ
ejpam-4911	369	11	(	(	PUNCT
ejpam-4911	369	12	s	s	NOUN
ejpam-4911	369	13	,	,	PUNCT
ejpam-4911	369	14	v)-open	v)-open	VERB
ejpam-4911	369	15	set	set	VERB
ejpam-4911	369	16	in	in	ADP
ejpam-4911	369	17	x.	x.	NOUN
ejpam-4911	369	18	(	(	PUNCT
ejpam-4911	369	19	d	d	X
ejpam-4911	369	20	)	)	PUNCT
ejpam-4911	369	21	k	k	NOUN
ejpam-4911	370	1	⊈	⊈	PROPN
ejpam-4911	370	2	d	d	NOUN
ejpam-4911	370	3	for	for	ADP
ejpam-4911	370	4	all	all	PRON
ejpam-4911	370	5	k	k	NOUN
ejpam-4911	370	6	is	be	AUX
ejpam-4911	370	7	a	a	DET
ejpam-4911	370	8	non	non	ADJ
ejpam-4911	370	9	-	-	ADJ
ejpam-4911	370	10	null	null	ADJ
ejpam-4911	370	11	(	(	PUNCT
ejpam-4911	370	12	s	s	NOUN
ejpam-4911	370	13	,	,	PUNCT
ejpam-4911	370	14	v)-µ-α	v)-µ-α	NOUN
ejpam-4911	370	15	-	-	PUNCT
ejpam-4911	370	16	open	open	ADJ
ejpam-4911	370	17	set	set	NOUN
ejpam-4911	370	18	in	in	ADP
ejpam-4911	370	19	x.	x.	NOUN
ejpam-4911	370	20	proof	proof	NOUN
ejpam-4911	370	21	.	.	PUNCT
ejpam-4911	371	1	we	we	PRON
ejpam-4911	371	2	give	give	VERB
ejpam-4911	371	3	the	the	DET
ejpam-4911	371	4	detailed	detailed	ADJ
ejpam-4911	371	5	proof	proof	NOUN
ejpam-4911	371	6	for	for	ADP
ejpam-4911	371	7	(	(	PUNCT
ejpam-4911	371	8	a	a	X
ejpam-4911	371	9	)	)	PUNCT
ejpam-4911	371	10	only	only	ADV
ejpam-4911	371	11	.	.	PUNCT
ejpam-4911	372	1	assume	assume	VERB
ejpam-4911	372	2	that	that	SCONJ
ejpam-4911	372	3	,	,	PUNCT
ejpam-4911	372	4	d	d	X
ejpam-4911	372	5	∈	∈	PROPN
ejpam-4911	372	6	(	(	PUNCT
ejpam-4911	372	7	s	s	PROPN
ejpam-4911	372	8	,	,	PUNCT
ejpam-4911	372	9	v)−n	v)−n	X
ejpam-4911	372	10	(	(	PUNCT
ejpam-4911	372	11	x	x	NOUN
ejpam-4911	372	12	)	)	PUNCT
ejpam-4911	372	13	where	where	SCONJ
ejpam-4911	372	14	s	s	X
ejpam-4911	372	15	,	,	PUNCT
ejpam-4911	372	16	v	v	NOUN
ejpam-4911	372	17	=	=	SYM
ejpam-4911	372	18	1	1	NUM
ejpam-4911	372	19	,	,	PUNCT
ejpam-4911	372	20	2	2	NUM
ejpam-4911	372	21	and	and	CCONJ
ejpam-4911	372	22	s	s	VERB
ejpam-4911	372	23	̸=	̸=	PROPN
ejpam-4911	372	24	v.	v.	ADP
ejpam-4911	372	25	then	then	ADV
ejpam-4911	372	26	is(cv(d	is(cv(d	NOUN
ejpam-4911	372	27	)	)	PUNCT
ejpam-4911	372	28	)	)	PUNCT
ejpam-4911	373	1	=	=	NOUN
ejpam-4911	373	2	∅	∅	NOUN
ejpam-4911	373	3	where	where	SCONJ
ejpam-4911	373	4	s	s	X
ejpam-4911	373	5	,	,	PUNCT
ejpam-4911	373	6	v	v	NOUN
ejpam-4911	373	7	=	=	SYM
ejpam-4911	373	8	1	1	NUM
ejpam-4911	373	9	,	,	PUNCT
ejpam-4911	373	10	2	2	NUM
ejpam-4911	373	11	and	and	CCONJ
ejpam-4911	373	12	s	s	VERB
ejpam-4911	373	13	̸=	̸=	PROPN
ejpam-4911	373	14	v.	v.	ADP
ejpam-4911	373	15	suppose	suppose	VERB
ejpam-4911	373	16	there	there	PRON
ejpam-4911	373	17	is	be	VERB
ejpam-4911	373	18	a	a	DET
ejpam-4911	373	19	non	non	ADJ
ejpam-4911	373	20	-	-	ADJ
ejpam-4911	373	21	null	null	ADJ
ejpam-4911	373	22	(	(	PUNCT
ejpam-4911	373	23	s	s	X
ejpam-4911	373	24	,	,	PUNCT
ejpam-4911	373	25	v)-µ-preopen	v)-µ-preopen	VERB
ejpam-4911	373	26	set	set	VERB
ejpam-4911	373	27	m	m	PROPN
ejpam-4911	373	28	in	in	ADP
ejpam-4911	373	29	x	x	INTJ
ejpam-4911	373	30	such	such	ADJ
ejpam-4911	373	31	that	that	SCONJ
ejpam-4911	373	32	m	m	VERB
ejpam-4911	373	33	⊂	⊂	X
ejpam-4911	373	34	d	d	X
ejpam-4911	373	35	(	(	PUNCT
ejpam-4911	373	36	7	7	NUM
ejpam-4911	373	37	)	)	PUNCT
ejpam-4911	373	38	where	where	SCONJ
ejpam-4911	373	39	s	s	X
ejpam-4911	373	40	,	,	PUNCT
ejpam-4911	373	41	v	v	NOUN
ejpam-4911	373	42	=	=	SYM
ejpam-4911	373	43	1	1	NUM
ejpam-4911	373	44	,	,	PUNCT
ejpam-4911	373	45	2	2	NUM
ejpam-4911	373	46	and	and	CCONJ
ejpam-4911	373	47	s	s	VERB
ejpam-4911	373	48	̸=	̸=	PROPN
ejpam-4911	373	49	v.	v.	ADP
ejpam-4911	373	50	here	here	ADV
ejpam-4911	373	51	,	,	PUNCT
ejpam-4911	373	52	m	m	VERB
ejpam-4911	373	53	⊂	⊂	NOUN
ejpam-4911	373	54	is(cv(m	is(cv(m	NOUN
ejpam-4911	373	55	)	)	PUNCT
ejpam-4911	373	56	)	)	PUNCT
ejpam-4911	374	1	(	(	PUNCT
ejpam-4911	374	2	8)	8)	NUM
ejpam-4911	374	3	where	where	SCONJ
ejpam-4911	374	4	s	s	X
ejpam-4911	374	5	,	,	PUNCT
ejpam-4911	374	6	v	v	NOUN
ejpam-4911	374	7	=	=	SYM
ejpam-4911	374	8	1	1	NUM
ejpam-4911	374	9	,	,	PUNCT
ejpam-4911	374	10	2	2	NUM
ejpam-4911	374	11	and	and	CCONJ
ejpam-4911	374	12	s	s	VERB
ejpam-4911	374	13	̸=	̸=	PROPN
ejpam-4911	374	14	v.	v.	ADP
ejpam-4911	374	15	from	from	ADP
ejpam-4911	374	16	(	(	PUNCT
ejpam-4911	374	17	7	7	NUM
ejpam-4911	374	18	)	)	PUNCT
ejpam-4911	374	19	,	,	PUNCT
ejpam-4911	374	20	we	we	PRON
ejpam-4911	374	21	have	have	VERB
ejpam-4911	374	22	is(cv(m	is(cv(m	NOUN
ejpam-4911	374	23	)	)	PUNCT
ejpam-4911	374	24	)	)	PUNCT
ejpam-4911	375	1	⊂	⊂	PROPN
ejpam-4911	375	2	is(cv(d	is(cv(d	NOUN
ejpam-4911	375	3	)	)	PUNCT
ejpam-4911	375	4	)	)	PUNCT
ejpam-4911	375	5	which	which	PRON
ejpam-4911	375	6	implies	imply	VERB
ejpam-4911	375	7	that	that	SCONJ
ejpam-4911	375	8	m	m	PROPN
ejpam-4911	375	9	⊂	⊂	PROPN
ejpam-4911	375	10	is(cv(d	is(cv(d	NOUN
ejpam-4911	375	11	)	)	PUNCT
ejpam-4911	375	12	)	)	PUNCT
ejpam-4911	376	1	where	where	SCONJ
ejpam-4911	376	2	s	s	X
ejpam-4911	376	3	,	,	PUNCT
ejpam-4911	376	4	v	v	NOUN
ejpam-4911	376	5	=	=	SYM
ejpam-4911	376	6	1	1	NUM
ejpam-4911	376	7	,	,	PUNCT
ejpam-4911	376	8	2	2	NUM
ejpam-4911	376	9	and	and	CCONJ
ejpam-4911	376	10	s	s	PART
ejpam-4911	376	11	̸=	̸=	PROPN
ejpam-4911	376	12	v	v	NOUN
ejpam-4911	376	13	,	,	PUNCT
ejpam-4911	376	14	by	by	ADP
ejpam-4911	376	15	(	(	PUNCT
ejpam-4911	376	16	8)	8)	NUM
ejpam-4911	376	17	.	.	PUNCT
ejpam-4911	376	18	then	then	ADV
ejpam-4911	376	19	is(cv(d	is(cv(d	NOUN
ejpam-4911	376	20	)	)	PUNCT
ejpam-4911	376	21	)	)	PUNCT
ejpam-4911	377	1	̸=	̸=	PROPN
ejpam-4911	377	2	∅	∅	NOUN
ejpam-4911	377	3	which	which	PRON
ejpam-4911	377	4	is	be	AUX
ejpam-4911	377	5	not	not	PART
ejpam-4911	377	6	possible	possible	ADJ
ejpam-4911	377	7	.	.	PUNCT
ejpam-4911	378	1	therefore	therefore	ADV
ejpam-4911	378	2	,	,	PUNCT
ejpam-4911	378	3	there	there	PRON
ejpam-4911	378	4	is	be	VERB
ejpam-4911	378	5	no	no	DET
ejpam-4911	378	6	non	non	ADJ
ejpam-4911	378	7	-	-	ADJ
ejpam-4911	378	8	null	null	ADJ
ejpam-4911	378	9	(	(	PUNCT
ejpam-4911	378	10	s	s	X
ejpam-4911	378	11	,	,	PUNCT
ejpam-4911	378	12	v)-µ-preopen	v)-µ-preopen	VERB
ejpam-4911	378	13	set	set	VERB
ejpam-4911	378	14	m	m	PROPN
ejpam-4911	378	15	in	in	ADP
ejpam-4911	378	16	x	x	INTJ
ejpam-4911	378	17	such	such	ADJ
ejpam-4911	378	18	that	that	SCONJ
ejpam-4911	378	19	m	m	VERB
ejpam-4911	378	20	⊂	⊂	PROPN
ejpam-4911	379	1	d	d	X
ejpam-4911	379	2	where	where	SCONJ
ejpam-4911	379	3	s	s	X
ejpam-4911	379	4	,	,	PUNCT
ejpam-4911	379	5	v	v	NOUN
ejpam-4911	379	6	=	=	SYM
ejpam-4911	379	7	1	1	NUM
ejpam-4911	379	8	,	,	PUNCT
ejpam-4911	379	9	2	2	NUM
ejpam-4911	379	10	and	and	CCONJ
ejpam-4911	379	11	s	s	VERB
ejpam-4911	379	12	̸=	̸=	PROPN
ejpam-4911	379	13	v.	v.	CCONJ
ejpam-4911	379	14	hence	hence	ADV
ejpam-4911	379	15	d	d	NOUN
ejpam-4911	379	16	does	do	AUX
ejpam-4911	379	17	not	not	PART
ejpam-4911	379	18	contain	contain	VERB
ejpam-4911	379	19	any	any	DET
ejpam-4911	379	20	non	non	ADJ
ejpam-4911	379	21	-	-	ADJ
ejpam-4911	379	22	null	null	ADJ
ejpam-4911	379	23	(	(	PUNCT
ejpam-4911	379	24	s	s	X
ejpam-4911	379	25	,	,	PUNCT
ejpam-4911	379	26	v)-µ-preopen	v)-µ-preopen	VERB
ejpam-4911	379	27	set	set	VERB
ejpam-4911	379	28	in	in	ADP
ejpam-4911	379	29	x	x	PUNCT
ejpam-4911	379	30	where	where	SCONJ
ejpam-4911	379	31	s	s	X
ejpam-4911	379	32	,	,	PUNCT
ejpam-4911	379	33	v	v	NOUN
ejpam-4911	379	34	=	=	SYM
ejpam-4911	379	35	1	1	NUM
ejpam-4911	379	36	,	,	PUNCT
ejpam-4911	379	37	2	2	NUM
ejpam-4911	379	38	and	and	CCONJ
ejpam-4911	379	39	s	s	PART
ejpam-4911	379	40	̸=	̸=	PROPN
ejpam-4911	379	41	v.	v.	ADP
ejpam-4911	379	42	theorem	theorem	PROPN
ejpam-4911	379	43	26	26	NUM
ejpam-4911	379	44	.	.	PUNCT
ejpam-4911	380	1	let	let	AUX
ejpam-4911	380	2	(	(	PUNCT
ejpam-4911	380	3	x,µ1	x,µ1	NOUN
ejpam-4911	380	4	,	,	PUNCT
ejpam-4911	380	5	µ2	µ2	PROPN
ejpam-4911	380	6	)	)	PUNCT
ejpam-4911	380	7	be	be	AUX
ejpam-4911	380	8	a	a	DET
ejpam-4911	380	9	bgts	bgts	NOUN
ejpam-4911	380	10	.	.	PUNCT
ejpam-4911	381	1	if	if	SCONJ
ejpam-4911	381	2	d	d	PROPN
ejpam-4911	381	3	∈	∈	PROPN
ejpam-4911	381	4	(	(	PUNCT
ejpam-4911	381	5	s	s	PROPN
ejpam-4911	381	6	,	,	PUNCT
ejpam-4911	381	7	v	v	NOUN
ejpam-4911	381	8	)	)	PUNCT
ejpam-4911	381	9	−	−	PROPN
ejpam-4911	381	10	n	n	CCONJ
ejpam-4911	381	11	(	(	PUNCT
ejpam-4911	381	12	x	x	NOUN
ejpam-4911	381	13	)	)	PUNCT
ejpam-4911	381	14	,	,	PUNCT
ejpam-4911	381	15	then	then	ADV
ejpam-4911	381	16	k	k	PROPN
ejpam-4911	381	17	⊈	⊈	PROPN
ejpam-4911	381	18	d	d	NOUN
ejpam-4911	381	19	for	for	ADP
ejpam-4911	381	20	all	all	DET
ejpam-4911	381	21	k	k	PROPN
ejpam-4911	381	22	∈	∈	PROPN
ejpam-4911	381	23	µ̃s	µ̃s	NOUN
ejpam-4911	381	24	where	where	SCONJ
ejpam-4911	381	25	s	s	X
ejpam-4911	381	26	,	,	PUNCT
ejpam-4911	381	27	v	v	NOUN
ejpam-4911	381	28	=	=	SYM
ejpam-4911	381	29	1	1	NUM
ejpam-4911	381	30	,	,	PUNCT
ejpam-4911	381	31	2	2	NUM
ejpam-4911	381	32	;	;	PUNCT
ejpam-4911	381	33	s	s	VERB
ejpam-4911	381	34	̸=	̸=	PROPN
ejpam-4911	381	35	v.	v.	ADP
ejpam-4911	381	36	proof	proof	NOUN
ejpam-4911	381	37	.	.	PUNCT
ejpam-4911	382	1	assume	assume	VERB
ejpam-4911	382	2	that	that	SCONJ
ejpam-4911	382	3	,	,	PUNCT
ejpam-4911	382	4	d	d	X
ejpam-4911	382	5	∈	∈	PROPN
ejpam-4911	382	6	(	(	PUNCT
ejpam-4911	382	7	s	s	PROPN
ejpam-4911	382	8	,	,	PUNCT
ejpam-4911	382	9	v)−n	v)−n	X
ejpam-4911	382	10	(	(	PUNCT
ejpam-4911	382	11	x	x	NOUN
ejpam-4911	382	12	)	)	PUNCT
ejpam-4911	382	13	where	where	SCONJ
ejpam-4911	382	14	s	s	X
ejpam-4911	382	15	,	,	PUNCT
ejpam-4911	382	16	v	v	NOUN
ejpam-4911	382	17	=	=	SYM
ejpam-4911	382	18	1	1	NUM
ejpam-4911	382	19	,	,	PUNCT
ejpam-4911	382	20	2	2	NUM
ejpam-4911	382	21	;	;	PUNCT
ejpam-4911	382	22	s	s	VERB
ejpam-4911	382	23	̸=	̸=	PROPN
ejpam-4911	382	24	v.	v.	ADP
ejpam-4911	382	25	take	take	VERB
ejpam-4911	382	26	s	s	PART
ejpam-4911	382	27	=	=	SYM
ejpam-4911	382	28	1	1	NUM
ejpam-4911	382	29	and	and	CCONJ
ejpam-4911	382	30	v	v	NOUN
ejpam-4911	382	31	=	=	SYM
ejpam-4911	382	32	2	2	NUM
ejpam-4911	382	33	.	.	PUNCT
ejpam-4911	383	1	then	then	ADV
ejpam-4911	383	2	d	d	PROPN
ejpam-4911	383	3	∈	∈	PROPN
ejpam-4911	383	4	(	(	PUNCT
ejpam-4911	383	5	1	1	NUM
ejpam-4911	383	6	,	,	PUNCT
ejpam-4911	383	7	2	2	NUM
ejpam-4911	383	8	)	)	PUNCT
ejpam-4911	383	9	−	−	PROPN
ejpam-4911	383	10	n	n	CCONJ
ejpam-4911	383	11	(	(	PUNCT
ejpam-4911	383	12	x	x	NOUN
ejpam-4911	383	13	)	)	PUNCT
ejpam-4911	383	14	.	.	PUNCT
ejpam-4911	384	1	if	if	SCONJ
ejpam-4911	384	2	there	there	PRON
ejpam-4911	384	3	is	be	VERB
ejpam-4911	384	4	h	h	PRON
ejpam-4911	384	5	∈	∈	PROPN
ejpam-4911	384	6	µ1	µ1	NOUN
ejpam-4911	384	7	such	such	ADJ
ejpam-4911	384	8	that	that	SCONJ
ejpam-4911	384	9	h	h	NOUN
ejpam-4911	385	1	⊂	⊂	PROPN
ejpam-4911	386	1	d	d	PROPN
ejpam-4911	386	2	,	,	PUNCT
ejpam-4911	386	3	then	then	ADV
ejpam-4911	386	4	i1(h	i1(h	NOUN
ejpam-4911	386	5	)	)	PUNCT
ejpam-4911	386	6	⊂	⊂	PROPN
ejpam-4911	387	1	d	d	PROPN
ejpam-4911	387	2	and	and	CCONJ
ejpam-4911	387	3	so	so	ADV
ejpam-4911	387	4	i1(h	i1(h	NOUN
ejpam-4911	387	5	)	)	PUNCT
ejpam-4911	387	6	⊂	⊂	PROPN
ejpam-4911	387	7	c2(d	c2(d	PROPN
ejpam-4911	387	8	)	)	PUNCT
ejpam-4911	387	9	.	.	PUNCT
ejpam-4911	388	1	this	this	PRON
ejpam-4911	388	2	implies	imply	VERB
ejpam-4911	388	3	i1(i1(h	i1(i1(h	NOUN
ejpam-4911	388	4	)	)	PUNCT
ejpam-4911	388	5	)	)	PUNCT
ejpam-4911	389	1	⊂	⊂	PROPN
ejpam-4911	389	2	i1(c2(d	i1(c2(d	PROPN
ejpam-4911	389	3	)	)	PUNCT
ejpam-4911	389	4	)	)	PUNCT
ejpam-4911	389	5	.	.	PUNCT
ejpam-4911	390	1	by	by	ADP
ejpam-4911	390	2	lemma	lemma	PROPN
ejpam-4911	390	3	5	5	NUM
ejpam-4911	390	4	(	(	PUNCT
ejpam-4911	390	5	e	e	NOUN
ejpam-4911	390	6	)	)	PUNCT
ejpam-4911	390	7	,	,	PUNCT
ejpam-4911	390	8	i1(h	i1(h	PROPN
ejpam-4911	390	9	)	)	PUNCT
ejpam-4911	390	10	⊂	⊂	PRON
ejpam-4911	390	11	i1(c2(d	i1(c2(d	PROPN
ejpam-4911	390	12	)	)	PUNCT
ejpam-4911	390	13	)	)	PUNCT
ejpam-4911	390	14	.	.	PUNCT
ejpam-4911	391	1	by	by	ADP
ejpam-4911	391	2	assumption	assumption	NOUN
ejpam-4911	391	3	,	,	PUNCT
ejpam-4911	391	4	h	h	PROPN
ejpam-4911	391	5	⊂	⊂	X
ejpam-4911	391	6	i1(c2(d	i1(c2(d	PROPN
ejpam-4911	391	7	)	)	PUNCT
ejpam-4911	391	8	)	)	PUNCT
ejpam-4911	391	9	.	.	PUNCT
ejpam-4911	392	1	thus	thus	ADV
ejpam-4911	392	2	,	,	PUNCT
ejpam-4911	392	3	i1(c2(d	i1(c2(d	ADJ
ejpam-4911	392	4	)	)	PUNCT
ejpam-4911	392	5	)	)	PUNCT
ejpam-4911	393	1	̸=	̸=	PROPN
ejpam-4911	393	2	∅	∅	NOUN
ejpam-4911	393	3	which	which	PRON
ejpam-4911	393	4	is	be	AUX
ejpam-4911	393	5	not	not	PART
ejpam-4911	393	6	possible	possible	ADJ
ejpam-4911	393	7	.	.	PUNCT
ejpam-4911	394	1	therefore	therefore	ADV
ejpam-4911	394	2	,	,	PUNCT
ejpam-4911	394	3	d	d	PROPN
ejpam-4911	394	4	does	do	AUX
ejpam-4911	394	5	not	not	PART
ejpam-4911	394	6	contain	contain	VERB
ejpam-4911	394	7	any	any	DET
ejpam-4911	394	8	non	non	ADJ
ejpam-4911	394	9	-	-	ADJ
ejpam-4911	394	10	null	null	ADJ
ejpam-4911	394	11	µ1	µ1	NOUN
ejpam-4911	394	12	-	-	PUNCT
ejpam-4911	394	13	open	open	NOUN
ejpam-4911	394	14	set	set	NOUN
ejpam-4911	394	15	.	.	PUNCT
ejpam-4911	395	1	take	take	VERB
ejpam-4911	395	2	s	s	NOUN
ejpam-4911	395	3	=	=	SYM
ejpam-4911	395	4	2	2	NUM
ejpam-4911	395	5	and	and	CCONJ
ejpam-4911	395	6	v	v	NOUN
ejpam-4911	395	7	=	=	SYM
ejpam-4911	395	8	1	1	NUM
ejpam-4911	395	9	.	.	PUNCT
ejpam-4911	396	1	then	then	ADV
ejpam-4911	396	2	d	d	PROPN
ejpam-4911	396	3	∈	∈	PROPN
ejpam-4911	396	4	(	(	PUNCT
ejpam-4911	396	5	2	2	NUM
ejpam-4911	396	6	,	,	PUNCT
ejpam-4911	396	7	1)−n	1)−n	NUM
ejpam-4911	396	8	(	(	PUNCT
ejpam-4911	396	9	x	x	NOUN
ejpam-4911	396	10	)	)	PUNCT
ejpam-4911	396	11	.	.	PUNCT
ejpam-4911	397	1	by	by	ADP
ejpam-4911	397	2	similar	similar	ADJ
ejpam-4911	397	3	arguments	argument	NOUN
ejpam-4911	397	4	in	in	ADP
ejpam-4911	397	5	the	the	DET
ejpam-4911	397	6	above	above	ADJ
ejpam-4911	397	7	case	case	NOUN
ejpam-4911	397	8	,	,	PUNCT
ejpam-4911	397	9	we	we	PRON
ejpam-4911	397	10	get	get	VERB
ejpam-4911	397	11	the	the	DET
ejpam-4911	397	12	proof	proof	NOUN
ejpam-4911	397	13	.	.	PUNCT
ejpam-4911	398	1	in	in	ADP
ejpam-4911	398	2	the	the	DET
ejpam-4911	398	3	rest	rest	NOUN
ejpam-4911	398	4	of	of	ADP
ejpam-4911	398	5	this	this	DET
ejpam-4911	398	6	section	section	NOUN
ejpam-4911	398	7	,	,	PUNCT
ejpam-4911	398	8	we	we	PRON
ejpam-4911	398	9	introduce	introduce	VERB
ejpam-4911	398	10	a	a	DET
ejpam-4911	398	11	new	new	ADJ
ejpam-4911	398	12	tool	tool	NOUN
ejpam-4911	398	13	namely	namely	ADV
ejpam-4911	398	14	,	,	PUNCT
ejpam-4911	398	15	(	(	PUNCT
ejpam-4911	398	16	s	s	X
ejpam-4911	398	17	,	,	PUNCT
ejpam-4911	398	18	v)-codense	v)-codense	ADJ
ejpam-4911	398	19	,	,	PUNCT
ejpam-4911	398	20	and	and	CCONJ
ejpam-4911	398	21	give	give	VERB
ejpam-4911	398	22	some	some	PRON
ejpam-4911	398	23	of	of	ADP
ejpam-4911	398	24	its	its	PRON
ejpam-4911	398	25	properties	property	NOUN
ejpam-4911	398	26	in	in	ADP
ejpam-4911	398	27	a	a	DET
ejpam-4911	398	28	bgts	bgts	NOUN
ejpam-4911	398	29	(	(	PUNCT
ejpam-4911	398	30	x,µ1	x,µ1	PROPN
ejpam-4911	398	31	,	,	PUNCT
ejpam-4911	398	32	µ2	µ2	PROPN
ejpam-4911	398	33	)	)	PUNCT
ejpam-4911	398	34	.	.	PUNCT
ejpam-4911	399	1	definition	definition	NOUN
ejpam-4911	399	2	27	27	NUM
ejpam-4911	399	3	.	.	PUNCT
ejpam-4911	400	1	let	let	AUX
ejpam-4911	400	2	(	(	PUNCT
ejpam-4911	400	3	x,µ1	x,µ1	NOUN
ejpam-4911	400	4	,	,	PUNCT
ejpam-4911	400	5	µ2	µ2	PROPN
ejpam-4911	400	6	)	)	PUNCT
ejpam-4911	400	7	be	be	VERB
ejpam-4911	400	8	a	a	DET
ejpam-4911	400	9	bgts	bgts	NOUN
ejpam-4911	400	10	and	and	CCONJ
ejpam-4911	400	11	e	e	NOUN
ejpam-4911	400	12	⊂	⊂	PROPN
ejpam-4911	400	13	x.	x.	PROPN
ejpam-4911	401	1	then	then	ADV
ejpam-4911	401	2	e	e	PROPN
ejpam-4911	401	3	is	be	AUX
ejpam-4911	401	4	(	(	PUNCT
ejpam-4911	401	5	s	s	X
ejpam-4911	401	6	,	,	PUNCT
ejpam-4911	401	7	v)-codense	v)-codense	VERB
ejpam-4911	401	8	if	if	SCONJ
ejpam-4911	401	9	cs(cv(x	cs(cv(x	PUNCT
ejpam-4911	401	10	−	−	PROPN
ejpam-4911	401	11	e	e	NOUN
ejpam-4911	401	12	)	)	PUNCT
ejpam-4911	401	13	)	)	PUNCT
ejpam-4911	402	1	=	=	PUNCT
ejpam-4911	403	1	x	x	X
ejpam-4911	403	2	where	where	SCONJ
ejpam-4911	403	3	s	s	X
ejpam-4911	403	4	,	,	PUNCT
ejpam-4911	403	5	v	v	NOUN
ejpam-4911	403	6	=	=	SYM
ejpam-4911	403	7	1	1	NUM
ejpam-4911	403	8	,	,	PUNCT
ejpam-4911	403	9	2	2	NUM
ejpam-4911	403	10	and	and	CCONJ
ejpam-4911	403	11	s	s	VERB
ejpam-4911	403	12	̸=	̸=	PROPN
ejpam-4911	403	13	v.	v.	ADP
ejpam-4911	403	14	example	example	NOUN
ejpam-4911	403	15	28	28	NUM
ejpam-4911	403	16	.	.	PUNCT
ejpam-4911	404	1	consider	consider	VERB
ejpam-4911	404	2	the	the	DET
ejpam-4911	404	3	bigeneralized	bigeneralized	ADJ
ejpam-4911	404	4	topological	topological	ADJ
ejpam-4911	404	5	space	space	NOUN
ejpam-4911	404	6	(	(	PUNCT
ejpam-4911	404	7	x,µ1	x,µ1	PROPN
ejpam-4911	404	8	,	,	PUNCT
ejpam-4911	404	9	µ2	µ2	ADJ
ejpam-4911	404	10	)	)	PUNCT
ejpam-4911	404	11	wherex	wherex	PROPN
ejpam-4911	404	12	=	=	SYM
ejpam-4911	404	13	{	{	PUNCT
ejpam-4911	404	14	e	e	PROPN
ejpam-4911	404	15	,	,	PUNCT
ejpam-4911	404	16	f	f	PROPN
ejpam-4911	404	17	,	,	PUNCT
ejpam-4911	404	18	k	k	NOUN
ejpam-4911	404	19	,	,	PUNCT
ejpam-4911	404	20	l	l	NOUN
ejpam-4911	404	21	}	}	PUNCT
ejpam-4911	404	22	;	;	PUNCT
ejpam-4911	404	23	µ1	µ1	PROPN
ejpam-4911	404	24	=	=	SYM
ejpam-4911	404	25	{	{	PUNCT
ejpam-4911	404	26	∅	∅	NOUN
ejpam-4911	404	27	,	,	PUNCT
ejpam-4911	404	28	{	{	PUNCT
ejpam-4911	404	29	e	e	NOUN
ejpam-4911	404	30	,	,	PUNCT
ejpam-4911	404	31	f	f	PROPN
ejpam-4911	404	32	}	}	PUNCT
ejpam-4911	404	33	,	,	PUNCT
ejpam-4911	404	34	{	{	PUNCT
ejpam-4911	404	35	f	f	X
ejpam-4911	404	36	,	,	PUNCT
ejpam-4911	404	37	l	l	NOUN
ejpam-4911	404	38	}	}	PUNCT
ejpam-4911	404	39	,	,	PUNCT
ejpam-4911	404	40	{	{	PUNCT
ejpam-4911	404	41	e	e	NOUN
ejpam-4911	404	42	,	,	PUNCT
ejpam-4911	404	43	f	f	X
ejpam-4911	404	44	,	,	PUNCT
ejpam-4911	404	45	l	l	NOUN
ejpam-4911	404	46	}	}	PUNCT
ejpam-4911	404	47	}	}	PUNCT
ejpam-4911	404	48	and	and	CCONJ
ejpam-4911	404	49	µ2	µ2	PROPN
ejpam-4911	404	50	=	=	PUNCT
ejpam-4911	404	51	{	{	PUNCT
ejpam-4911	404	52	∅	∅	NOUN
ejpam-4911	404	53	,	,	PUNCT
ejpam-4911	404	54	{	{	PUNCT
ejpam-4911	404	55	e	e	NOUN
ejpam-4911	404	56	,	,	PUNCT
ejpam-4911	404	57	k	k	NOUN
ejpam-4911	404	58	}	}	PUNCT
ejpam-4911	404	59	,	,	PUNCT
ejpam-4911	404	60	{	{	PUNCT
ejpam-4911	404	61	f	f	X
ejpam-4911	404	62	,	,	PUNCT
ejpam-4911	404	63	k	k	NOUN
ejpam-4911	404	64	}	}	PUNCT
ejpam-4911	404	65	,	,	PUNCT
ejpam-4911	404	66	{	{	PUNCT
ejpam-4911	404	67	e	e	NOUN
ejpam-4911	404	68	,	,	PUNCT
ejpam-4911	404	69	f	f	PROPN
ejpam-4911	404	70	,	,	PUNCT
ejpam-4911	404	71	k	k	NOUN
ejpam-4911	404	72	}	}	PUNCT
ejpam-4911	404	73	}	}	PUNCT
ejpam-4911	404	74	.	.	PUNCT
ejpam-4911	405	1	take	take	VERB
ejpam-4911	405	2	a	a	DET
ejpam-4911	405	3	=	=	SYM
ejpam-4911	405	4	{	{	PUNCT
ejpam-4911	405	5	k	k	NOUN
ejpam-4911	405	6	,	,	PUNCT
ejpam-4911	405	7	l	l	NOUN
ejpam-4911	405	8	}	}	PUNCT
ejpam-4911	405	9	we	we	PRON
ejpam-4911	405	10	get	get	VERB
ejpam-4911	405	11	x	x	PUNCT
ejpam-4911	405	12	−	−	PROPN
ejpam-4911	405	13	a	a	PRON
ejpam-4911	405	14	=	=	X
ejpam-4911	405	15	{	{	PUNCT
ejpam-4911	405	16	e	e	NOUN
ejpam-4911	405	17	,	,	PUNCT
ejpam-4911	405	18	f	f	NOUN
ejpam-4911	405	19	}	}	PUNCT
ejpam-4911	405	20	and	and	CCONJ
ejpam-4911	405	21	so	so	ADV
ejpam-4911	405	22	c1(c2({e	c1(c2({e	NOUN
ejpam-4911	405	23	,	,	PUNCT
ejpam-4911	405	24	f	f	NOUN
ejpam-4911	405	25	}	}	PUNCT
ejpam-4911	405	26	)	)	PUNCT
ejpam-4911	405	27	)	)	PUNCT
ejpam-4911	406	1	=	=	PUNCT
ejpam-4911	406	2	x.	x.	PUNCT
ejpam-4911	406	3	thus	thus	ADV
ejpam-4911	406	4	,	,	PUNCT
ejpam-4911	406	5	a	a	PRON
ejpam-4911	406	6	is	be	AUX
ejpam-4911	406	7	a	a	DET
ejpam-4911	406	8	(	(	PUNCT
ejpam-4911	406	9	1	1	NUM
ejpam-4911	406	10	,	,	PUNCT
ejpam-4911	406	11	2)codense	2)codense	NUM
ejpam-4911	406	12	set	set	VERB
ejpam-4911	406	13	in	in	ADP
ejpam-4911	406	14	x.	x.	NOUN
ejpam-4911	406	15	also	also	ADV
ejpam-4911	406	16	,	,	PUNCT
ejpam-4911	406	17	c2(c1({e	c2(c1({e	PROPN
ejpam-4911	406	18	,	,	PUNCT
ejpam-4911	406	19	f	f	NOUN
ejpam-4911	406	20	}	}	PUNCT
ejpam-4911	406	21	)	)	PUNCT
ejpam-4911	406	22	)	)	PUNCT
ejpam-4911	407	1	=	=	PUNCT
ejpam-4911	407	2	x.	x.	NOUN
ejpam-4911	407	3	therefore	therefore	ADV
ejpam-4911	407	4	,	,	PUNCT
ejpam-4911	407	5	a	a	PRON
ejpam-4911	407	6	is	be	AUX
ejpam-4911	407	7	a	a	DET
ejpam-4911	407	8	(	(	PUNCT
ejpam-4911	407	9	2	2	NUM
ejpam-4911	407	10	,	,	PUNCT
ejpam-4911	407	11	1)-codense	1)-codense	NUM
ejpam-4911	407	12	set	set	NOUN
ejpam-4911	407	13	.	.	PUNCT
ejpam-4911	408	1	hence	hence	ADV
ejpam-4911	408	2	a	a	PRON
ejpam-4911	408	3	is	be	AUX
ejpam-4911	408	4	(	(	PUNCT
ejpam-4911	408	5	s	s	X
ejpam-4911	408	6	,	,	PUNCT
ejpam-4911	408	7	v)-codense	v)-codense	ADV
ejpam-4911	408	8	where	where	SCONJ
ejpam-4911	408	9	s	s	X
ejpam-4911	408	10	,	,	PUNCT
ejpam-4911	408	11	v	v	NOUN
ejpam-4911	408	12	=	=	SYM
ejpam-4911	408	13	1	1	NUM
ejpam-4911	408	14	,	,	PUNCT
ejpam-4911	408	15	2	2	NUM
ejpam-4911	408	16	and	and	CCONJ
ejpam-4911	408	17	s	s	VERB
ejpam-4911	408	18	̸=	̸=	PROPN
ejpam-4911	408	19	v.	v.	ADP
ejpam-4911	408	20	y.	y.	PROPN
ejpam-4911	408	21	farhat	farhat	PROPN
ejpam-4911	408	22	,	,	PUNCT
ejpam-4911	408	23	v.	v.	ADP
ejpam-4911	408	24	subramanian	subramanian	PROPN
ejpam-4911	408	25	/	/	SYM
ejpam-4911	408	26	eur	eur	PROPN
ejpam-4911	408	27	.	.	PUNCT
ejpam-4911	409	1	j.	j.	PROPN
ejpam-4911	409	2	pure	pure	PROPN
ejpam-4911	409	3	appl	appl	PROPN
ejpam-4911	409	4	.	.	PROPN
ejpam-4911	409	5	math	math	PROPN
ejpam-4911	409	6	,	,	PUNCT
ejpam-4911	409	7	16	16	NUM
ejpam-4911	409	8	(	(	PUNCT
ejpam-4911	409	9	4	4	NUM
ejpam-4911	409	10	)	)	PUNCT
ejpam-4911	409	11	(	(	PUNCT
ejpam-4911	409	12	2023	2023	NUM
ejpam-4911	409	13	)	)	PUNCT
ejpam-4911	409	14	,	,	PUNCT
ejpam-4911	409	15	2049	2049	NUM
ejpam-4911	409	16	-	-	SYM
ejpam-4911	409	17	2065	2065	NUM
ejpam-4911	409	18	2061	2061	NUM
ejpam-4911	409	19	theorem	theorem	VERB
ejpam-4911	409	20	29	29	NUM
ejpam-4911	409	21	.	.	PUNCT
ejpam-4911	410	1	in	in	ADP
ejpam-4911	410	2	a	a	DET
ejpam-4911	410	3	bgts	bgts	NOUN
ejpam-4911	410	4	(	(	PUNCT
ejpam-4911	410	5	x,µ1	x,µ1	PROPN
ejpam-4911	410	6	,	,	PUNCT
ejpam-4911	410	7	µ2	µ2	PROPN
ejpam-4911	410	8	)	)	PUNCT
ejpam-4911	410	9	,	,	PUNCT
ejpam-4911	410	10	if	if	SCONJ
ejpam-4911	410	11	e	e	PROPN
ejpam-4911	410	12	∈	∈	PROPN
ejpam-4911	410	13	(	(	PUNCT
ejpam-4911	410	14	s	s	PROPN
ejpam-4911	410	15	,	,	PUNCT
ejpam-4911	410	16	v)−n	v)−n	X
ejpam-4911	410	17	(	(	PUNCT
ejpam-4911	410	18	x	x	NOUN
ejpam-4911	410	19	)	)	PUNCT
ejpam-4911	410	20	,	,	PUNCT
ejpam-4911	410	21	then	then	ADV
ejpam-4911	410	22	e	e	PROPN
ejpam-4911	410	23	is	be	AUX
ejpam-4911	410	24	µs	µs	NOUN
ejpam-4911	410	25	-	-	PUNCT
ejpam-4911	410	26	codense	codense	NOUN
ejpam-4911	410	27	where	where	SCONJ
ejpam-4911	410	28	s	s	X
ejpam-4911	410	29	,	,	PUNCT
ejpam-4911	410	30	v	v	NOUN
ejpam-4911	410	31	=	=	SYM
ejpam-4911	410	32	1	1	NUM
ejpam-4911	410	33	,	,	PUNCT
ejpam-4911	410	34	2	2	NUM
ejpam-4911	410	35	and	and	CCONJ
ejpam-4911	410	36	s	s	VERB
ejpam-4911	410	37	̸=	̸=	PROPN
ejpam-4911	410	38	v.	v.	ADP
ejpam-4911	410	39	proof	proof	NOUN
ejpam-4911	410	40	.	.	PUNCT
ejpam-4911	411	1	given	give	VERB
ejpam-4911	411	2	e	e	PROPN
ejpam-4911	411	3	∈	∈	PROPN
ejpam-4911	411	4	(	(	PUNCT
ejpam-4911	411	5	s	s	PROPN
ejpam-4911	411	6	,	,	PUNCT
ejpam-4911	411	7	v	v	NOUN
ejpam-4911	411	8	)	)	PUNCT
ejpam-4911	411	9	−	−	PROPN
ejpam-4911	411	10	n	n	CCONJ
ejpam-4911	411	11	(	(	PUNCT
ejpam-4911	411	12	x	x	X
ejpam-4911	411	13	)	)	PUNCT
ejpam-4911	411	14	for	for	ADP
ejpam-4911	411	15	s	s	PROPN
ejpam-4911	411	16	,	,	PUNCT
ejpam-4911	411	17	v	v	NOUN
ejpam-4911	411	18	=	=	SYM
ejpam-4911	411	19	1	1	NUM
ejpam-4911	411	20	,	,	PUNCT
ejpam-4911	411	21	2	2	NUM
ejpam-4911	411	22	;	;	PUNCT
ejpam-4911	411	23	s	s	VERB
ejpam-4911	411	24	̸=	̸=	PROPN
ejpam-4911	411	25	v.	v.	ADP
ejpam-4911	411	26	then	then	ADV
ejpam-4911	411	27	is(cv(e	is(cv(e	PROPN
ejpam-4911	411	28	)	)	PUNCT
ejpam-4911	411	29	)	)	PUNCT
ejpam-4911	412	1	=	=	NOUN
ejpam-4911	412	2	∅	∅	NOUN
ejpam-4911	413	1	and	and	CCONJ
ejpam-4911	414	1	so	so	ADV
ejpam-4911	414	2	x−	x−	PROPN
ejpam-4911	414	3	(	(	PUNCT
ejpam-4911	414	4	is(cv(e	is(cv(e	PROPN
ejpam-4911	414	5	)	)	PUNCT
ejpam-4911	414	6	)	)	PUNCT
ejpam-4911	414	7	)	)	PUNCT
ejpam-4911	415	1	=	=	PUNCT
ejpam-4911	415	2	x	x	X
ejpam-4911	415	3	where	where	SCONJ
ejpam-4911	415	4	s	s	X
ejpam-4911	415	5	,	,	PUNCT
ejpam-4911	415	6	v	v	NOUN
ejpam-4911	415	7	=	=	SYM
ejpam-4911	415	8	1	1	NUM
ejpam-4911	415	9	,	,	PUNCT
ejpam-4911	415	10	2	2	NUM
ejpam-4911	415	11	and	and	CCONJ
ejpam-4911	415	12	s	s	VERB
ejpam-4911	415	13	̸=	̸=	PROPN
ejpam-4911	415	14	v.	v.	ADP
ejpam-4911	415	15	this	this	PRON
ejpam-4911	415	16	implies	imply	VERB
ejpam-4911	415	17	cs(x−	cs(x−	X
ejpam-4911	415	18	(	(	PUNCT
ejpam-4911	415	19	cv(e	cv(e	NOUN
ejpam-4911	415	20	)	)	PUNCT
ejpam-4911	415	21	)	)	PUNCT
ejpam-4911	415	22	)	)	PUNCT
ejpam-4911	416	1	=	=	PUNCT
ejpam-4911	417	1	x	x	X
ejpam-4911	417	2	where	where	SCONJ
ejpam-4911	417	3	s	s	X
ejpam-4911	417	4	,	,	PUNCT
ejpam-4911	417	5	v	v	NOUN
ejpam-4911	417	6	=	=	SYM
ejpam-4911	417	7	1	1	NUM
ejpam-4911	417	8	,	,	PUNCT
ejpam-4911	417	9	2	2	NUM
ejpam-4911	417	10	and	and	CCONJ
ejpam-4911	417	11	s	s	VERB
ejpam-4911	417	12	̸=	̸=	PROPN
ejpam-4911	417	13	v	v	NUM
ejpam-4911	417	14	which	which	PRON
ejpam-4911	417	15	implies	imply	VERB
ejpam-4911	417	16	that	that	SCONJ
ejpam-4911	417	17	cs(x	cs(x	PUNCT
ejpam-4911	417	18	−	−	X
ejpam-4911	417	19	e	e	X
ejpam-4911	417	20	)	)	PUNCT
ejpam-4911	417	21	=	=	SYM
ejpam-4911	418	1	x	x	X
ejpam-4911	418	2	for	for	ADP
ejpam-4911	418	3	s	s	NOUN
ejpam-4911	418	4	=	=	SYM
ejpam-4911	418	5	1	1	NUM
ejpam-4911	418	6	,	,	PUNCT
ejpam-4911	418	7	2	2	NUM
ejpam-4911	418	8	.	.	X
ejpam-4911	418	9	therefore	therefore	ADV
ejpam-4911	418	10	,	,	PUNCT
ejpam-4911	418	11	e	e	X
ejpam-4911	418	12	is	be	AUX
ejpam-4911	418	13	a	a	DET
ejpam-4911	418	14	µs	µs	NOUN
ejpam-4911	418	15	-	-	PUNCT
ejpam-4911	418	16	codense	codense	NOUN
ejpam-4911	418	17	set	set	VERB
ejpam-4911	418	18	in	in	ADP
ejpam-4911	418	19	x	x	PUNCT
ejpam-4911	418	20	for	for	ADP
ejpam-4911	418	21	s	s	NOUN
ejpam-4911	418	22	=	=	SYM
ejpam-4911	418	23	1	1	NUM
ejpam-4911	418	24	,	,	PUNCT
ejpam-4911	418	25	2	2	NUM
ejpam-4911	418	26	.	.	NOUN
ejpam-4911	418	27	example	example	NOUN
ejpam-4911	418	28	30	30	NUM
ejpam-4911	418	29	explains	explain	VERB
ejpam-4911	418	30	that	that	SCONJ
ejpam-4911	418	31	the	the	DET
ejpam-4911	418	32	reverse	reverse	ADJ
ejpam-4911	418	33	implication	implication	NOUN
ejpam-4911	418	34	of	of	ADP
ejpam-4911	418	35	theorem	theorem	NOUN
ejpam-4911	418	36	29	29	NUM
ejpam-4911	418	37	need	need	AUX
ejpam-4911	418	38	not	not	PART
ejpam-4911	418	39	be	be	AUX
ejpam-4911	418	40	true	true	ADJ
ejpam-4911	418	41	.	.	PUNCT
ejpam-4911	419	1	example	example	NOUN
ejpam-4911	419	2	30	30	NUM
ejpam-4911	419	3	.	.	PUNCT
ejpam-4911	420	1	consider	consider	VERB
ejpam-4911	420	2	the	the	DET
ejpam-4911	420	3	bgts	bgts	NOUN
ejpam-4911	420	4	(	(	PUNCT
ejpam-4911	420	5	x,µ1	x,µ1	PROPN
ejpam-4911	420	6	,	,	PUNCT
ejpam-4911	420	7	µ2	µ2	PROPN
ejpam-4911	420	8	)	)	PUNCT
ejpam-4911	420	9	where	where	SCONJ
ejpam-4911	420	10	x	x	X
ejpam-4911	420	11	=	=	PRON
ejpam-4911	420	12	{	{	PUNCT
ejpam-4911	420	13	e	e	NOUN
ejpam-4911	420	14	,	,	PUNCT
ejpam-4911	420	15	f	f	PROPN
ejpam-4911	420	16	,	,	PUNCT
ejpam-4911	420	17	k	k	PROPN
ejpam-4911	420	18	,	,	PUNCT
ejpam-4911	420	19	l	l	NOUN
ejpam-4911	420	20	,	,	PUNCT
ejpam-4911	420	21	r	r	NOUN
ejpam-4911	420	22	}	}	PUNCT
ejpam-4911	420	23	;	;	PUNCT
ejpam-4911	420	24	µ1	µ1	PROPN
ejpam-4911	420	25	=	=	SYM
ejpam-4911	420	26	{	{	PUNCT
ejpam-4911	420	27	∅	∅	NOUN
ejpam-4911	420	28	,	,	PUNCT
ejpam-4911	420	29	{	{	PUNCT
ejpam-4911	420	30	e	e	NOUN
ejpam-4911	420	31	,	,	PUNCT
ejpam-4911	420	32	f	f	PROPN
ejpam-4911	420	33	}	}	PUNCT
ejpam-4911	420	34	,	,	PUNCT
ejpam-4911	420	35	{	{	PUNCT
ejpam-4911	420	36	e	e	NOUN
ejpam-4911	420	37	,	,	PUNCT
ejpam-4911	420	38	k	k	NOUN
ejpam-4911	420	39	}	}	PUNCT
ejpam-4911	420	40	,	,	PUNCT
ejpam-4911	420	41	{	{	PUNCT
ejpam-4911	420	42	e	e	NOUN
ejpam-4911	420	43	,	,	PUNCT
ejpam-4911	420	44	f	f	PROPN
ejpam-4911	420	45	,	,	PUNCT
ejpam-4911	420	46	k	k	NOUN
ejpam-4911	420	47	}	}	PUNCT
ejpam-4911	420	48	,	,	PUNCT
ejpam-4911	420	49	{	{	PUNCT
ejpam-4911	420	50	e	e	NOUN
ejpam-4911	420	51	,	,	PUNCT
ejpam-4911	420	52	f	f	X
ejpam-4911	420	53	,	,	PUNCT
ejpam-4911	420	54	l	l	NOUN
ejpam-4911	420	55	}	}	PUNCT
ejpam-4911	420	56	,	,	PUNCT
ejpam-4911	420	57	{	{	PUNCT
ejpam-4911	420	58	e	e	NOUN
ejpam-4911	420	59	,	,	PUNCT
ejpam-4911	420	60	f	f	PROPN
ejpam-4911	420	61	,	,	PUNCT
ejpam-4911	420	62	k	k	PROPN
ejpam-4911	420	63	,	,	PUNCT
ejpam-4911	420	64	l	l	NOUN
ejpam-4911	420	65	}	}	PUNCT
ejpam-4911	420	66	}	}	PUNCT
ejpam-4911	420	67	and	and	CCONJ
ejpam-4911	420	68	µ2	µ2	PROPN
ejpam-4911	420	69	=	=	PUNCT
ejpam-4911	420	70	{	{	PUNCT
ejpam-4911	420	71	∅	∅	NOUN
ejpam-4911	420	72	,	,	PUNCT
ejpam-4911	420	73	{	{	PUNCT
ejpam-4911	420	74	e	e	NOUN
ejpam-4911	420	75	,	,	PUNCT
ejpam-4911	420	76	f	f	PROPN
ejpam-4911	420	77	}	}	PUNCT
ejpam-4911	420	78	,	,	PUNCT
ejpam-4911	420	79	{	{	PUNCT
ejpam-4911	420	80	f	f	X
ejpam-4911	420	81	,	,	PUNCT
ejpam-4911	420	82	l	l	NOUN
ejpam-4911	420	83	}	}	PUNCT
ejpam-4911	420	84	,	,	PUNCT
ejpam-4911	420	85	{	{	PUNCT
ejpam-4911	420	86	e	e	NOUN
ejpam-4911	420	87	,	,	PUNCT
ejpam-4911	420	88	r	r	NOUN
ejpam-4911	420	89	}	}	PUNCT
ejpam-4911	420	90	,	,	PUNCT
ejpam-4911	420	91	{	{	PUNCT
ejpam-4911	420	92	e	e	NOUN
ejpam-4911	420	93	,	,	PUNCT
ejpam-4911	420	94	f	f	X
ejpam-4911	420	95	,	,	PUNCT
ejpam-4911	420	96	l	l	NOUN
ejpam-4911	420	97	}	}	PUNCT
ejpam-4911	420	98	,	,	PUNCT
ejpam-4911	420	99	{	{	PUNCT
ejpam-4911	420	100	e	e	NOUN
ejpam-4911	420	101	,	,	PUNCT
ejpam-4911	420	102	f	f	X
ejpam-4911	420	103	,	,	PUNCT
ejpam-4911	420	104	r	r	NOUN
ejpam-4911	420	105	}	}	PUNCT
ejpam-4911	420	106	,	,	PUNCT
ejpam-4911	420	107	{	{	PUNCT
ejpam-4911	420	108	e	e	NOUN
ejpam-4911	420	109	,	,	PUNCT
ejpam-4911	420	110	f	f	PROPN
ejpam-4911	420	111	,	,	PUNCT
ejpam-4911	420	112	l	l	NOUN
ejpam-4911	420	113	,	,	PUNCT
ejpam-4911	420	114	r	r	NOUN
ejpam-4911	420	115	}	}	PUNCT
ejpam-4911	420	116	}	}	PUNCT
ejpam-4911	420	117	.	.	PUNCT
ejpam-4911	421	1	choose	choose	VERB
ejpam-4911	421	2	p	p	NOUN
ejpam-4911	421	3	=	=	X
ejpam-4911	421	4	{	{	PUNCT
ejpam-4911	421	5	f	f	PROPN
ejpam-4911	421	6	,	,	PUNCT
ejpam-4911	421	7	k	k	NOUN
ejpam-4911	421	8	,	,	PUNCT
ejpam-4911	421	9	r	r	NOUN
ejpam-4911	421	10	}	}	PUNCT
ejpam-4911	421	11	,	,	PUNCT
ejpam-4911	421	12	then	then	ADV
ejpam-4911	421	13	c2(x	c2(x	PROPN
ejpam-4911	421	14	−	−	PROPN
ejpam-4911	421	15	p	p	NOUN
ejpam-4911	421	16	)	)	PUNCT
ejpam-4911	421	17	=	=	PUNCT
ejpam-4911	422	1	x.	x.	NOUN
ejpam-4911	422	2	but	but	CCONJ
ejpam-4911	422	3	p	p	NOUN
ejpam-4911	422	4	/∈	/∈	PUNCT
ejpam-4911	423	1	(	(	PUNCT
ejpam-4911	423	2	2	2	NUM
ejpam-4911	423	3	,	,	PUNCT
ejpam-4911	423	4	1	1	NUM
ejpam-4911	423	5	)	)	PUNCT
ejpam-4911	423	6	−	−	PROPN
ejpam-4911	423	7	n	n	CCONJ
ejpam-4911	423	8	(	(	PUNCT
ejpam-4911	423	9	x	x	NOUN
ejpam-4911	423	10	)	)	PUNCT
ejpam-4911	423	11	.	.	PUNCT
ejpam-4911	424	1	for	for	ADP
ejpam-4911	424	2	,	,	PUNCT
ejpam-4911	424	3	i2(c1(p	i2(c1(p	NOUN
ejpam-4911	424	4	)	)	PUNCT
ejpam-4911	424	5	)	)	PUNCT
ejpam-4911	425	1	=	=	PUNCT
ejpam-4911	425	2	i2(x	i2(x	PROPN
ejpam-4911	425	3	)	)	PUNCT
ejpam-4911	425	4	=	=	SYM
ejpam-4911	425	5	{	{	PUNCT
ejpam-4911	425	6	e	e	NOUN
ejpam-4911	425	7	,	,	PUNCT
ejpam-4911	425	8	f	f	PROPN
ejpam-4911	425	9	,	,	PUNCT
ejpam-4911	425	10	l	l	NOUN
ejpam-4911	425	11	,	,	PUNCT
ejpam-4911	425	12	r	r	NOUN
ejpam-4911	425	13	}	}	PUNCT
ejpam-4911	425	14	=	=	NOUN
ejpam-4911	425	15	̸	̸	ADV
ejpam-4911	425	16	∅.	∅.	ADV
ejpam-4911	425	17	consider	consider	VERB
ejpam-4911	425	18	,	,	PUNCT
ejpam-4911	425	19	q	q	PUNCT
ejpam-4911	425	20	=	=	PUNCT
ejpam-4911	425	21	{	{	PUNCT
ejpam-4911	425	22	f	f	PROPN
ejpam-4911	425	23	,	,	PUNCT
ejpam-4911	425	24	l	l	NOUN
ejpam-4911	425	25	,	,	PUNCT
ejpam-4911	425	26	r	r	NOUN
ejpam-4911	425	27	}	}	PUNCT
ejpam-4911	425	28	we	we	PRON
ejpam-4911	425	29	have	have	VERB
ejpam-4911	425	30	c1(x	c1(x	PRON
ejpam-4911	426	1	−q	−q	ADJ
ejpam-4911	426	2	)	)	PUNCT
ejpam-4911	426	3	=	=	SYM
ejpam-4911	426	4	c1({e	c1({e	NOUN
ejpam-4911	426	5	,	,	PUNCT
ejpam-4911	426	6	k	k	NOUN
ejpam-4911	426	7	}	}	PUNCT
ejpam-4911	426	8	)	)	PUNCT
ejpam-4911	426	9	=	=	PUNCT
ejpam-4911	426	10	x.	x.	NOUN
ejpam-4911	426	11	but	but	CCONJ
ejpam-4911	426	12	q	q	NOUN
ejpam-4911	426	13	/∈	/∈	PUNCT
ejpam-4911	427	1	(	(	PUNCT
ejpam-4911	427	2	1	1	NUM
ejpam-4911	427	3	,	,	PUNCT
ejpam-4911	427	4	2)−n	2)−n	NUM
ejpam-4911	427	5	(	(	PUNCT
ejpam-4911	427	6	x	x	NOUN
ejpam-4911	427	7	)	)	PUNCT
ejpam-4911	427	8	.	.	PUNCT
ejpam-4911	428	1	for	for	ADP
ejpam-4911	428	2	,	,	PUNCT
ejpam-4911	428	3	i1(c2(q	i1(c2(q	NUM
ejpam-4911	428	4	)	)	PUNCT
ejpam-4911	428	5	)	)	PUNCT
ejpam-4911	429	1	=	=	PUNCT
ejpam-4911	429	2	i1(x	i1(x	X
ejpam-4911	429	3	)	)	PUNCT
ejpam-4911	429	4	=	=	PRON
ejpam-4911	429	5	{	{	PUNCT
ejpam-4911	429	6	e	e	NOUN
ejpam-4911	429	7	,	,	PUNCT
ejpam-4911	429	8	f	f	PROPN
ejpam-4911	429	9	,	,	PUNCT
ejpam-4911	429	10	k	k	PROPN
ejpam-4911	429	11	,	,	PUNCT
ejpam-4911	429	12	l	l	NOUN
ejpam-4911	429	13	}	}	PUNCT
ejpam-4911	429	14	=	=	NOUN
ejpam-4911	429	15	̸	̸	ADV
ejpam-4911	429	16	∅.	∅.	VERB
ejpam-4911	429	17	proposition	proposition	NOUN
ejpam-4911	429	18	31	31	NUM
ejpam-4911	429	19	.	.	PUNCT
ejpam-4911	430	1	let	let	AUX
ejpam-4911	430	2	(	(	PUNCT
ejpam-4911	430	3	x,µ1	x,µ1	NOUN
ejpam-4911	430	4	,	,	PUNCT
ejpam-4911	430	5	µ2	µ2	PROPN
ejpam-4911	430	6	)	)	PUNCT
ejpam-4911	430	7	be	be	AUX
ejpam-4911	430	8	a	a	DET
ejpam-4911	430	9	bgts	bgts	NOUN
ejpam-4911	430	10	.	.	PUNCT
ejpam-4911	431	1	then	then	ADV
ejpam-4911	431	2	e	e	PROPN
ejpam-4911	431	3	is	be	AUX
ejpam-4911	431	4	a	a	DET
ejpam-4911	431	5	(	(	PUNCT
ejpam-4911	431	6	s	s	X
ejpam-4911	431	7	,	,	PUNCT
ejpam-4911	431	8	v)-codense	v)-codense	ADV
ejpam-4911	431	9	set	set	VERB
ejpam-4911	431	10	in	in	ADP
ejpam-4911	431	11	x	x	PUNCT
ejpam-4911	431	12	if	if	SCONJ
ejpam-4911	432	1	and	and	CCONJ
ejpam-4911	432	2	only	only	ADV
ejpam-4911	432	3	if	if	SCONJ
ejpam-4911	432	4	is(iv(e	is(iv(e	ADJ
ejpam-4911	432	5	)	)	PUNCT
ejpam-4911	432	6	)	)	PUNCT
ejpam-4911	433	1	=	=	NOUN
ejpam-4911	433	2	∅	∅	NOUN
ejpam-4911	433	3	where	where	SCONJ
ejpam-4911	433	4	s	s	X
ejpam-4911	433	5	,	,	PUNCT
ejpam-4911	433	6	v	v	NOUN
ejpam-4911	433	7	=	=	SYM
ejpam-4911	433	8	1	1	NUM
ejpam-4911	433	9	,	,	PUNCT
ejpam-4911	433	10	2	2	NUM
ejpam-4911	433	11	and	and	CCONJ
ejpam-4911	433	12	s	s	VERB
ejpam-4911	433	13	̸=	̸=	PROPN
ejpam-4911	433	14	v.	v.	ADP
ejpam-4911	433	15	proposition	proposition	NOUN
ejpam-4911	433	16	32	32	NUM
ejpam-4911	433	17	.	.	PUNCT
ejpam-4911	434	1	let	let	AUX
ejpam-4911	434	2	(	(	PUNCT
ejpam-4911	434	3	x,µ1	x,µ1	NOUN
ejpam-4911	434	4	,	,	PUNCT
ejpam-4911	434	5	µ2	µ2	PROPN
ejpam-4911	434	6	)	)	PUNCT
ejpam-4911	434	7	be	be	AUX
ejpam-4911	434	8	a	a	DET
ejpam-4911	434	9	bgts	bgts	NOUN
ejpam-4911	434	10	.	.	PUNCT
ejpam-4911	435	1	if	if	SCONJ
ejpam-4911	435	2	e	e	PROPN
ejpam-4911	435	3	∈	∈	PROPN
ejpam-4911	435	4	(	(	PUNCT
ejpam-4911	435	5	s	s	PROPN
ejpam-4911	435	6	,	,	PUNCT
ejpam-4911	435	7	v	v	NOUN
ejpam-4911	435	8	)	)	PUNCT
ejpam-4911	435	9	−	−	PROPN
ejpam-4911	435	10	n	n	CCONJ
ejpam-4911	435	11	(	(	PUNCT
ejpam-4911	435	12	x	x	NOUN
ejpam-4911	435	13	)	)	PUNCT
ejpam-4911	435	14	,	,	PUNCT
ejpam-4911	435	15	then	then	ADV
ejpam-4911	435	16	e	e	PROPN
ejpam-4911	435	17	is	be	AUX
ejpam-4911	435	18	a	a	DET
ejpam-4911	435	19	(	(	PUNCT
ejpam-4911	435	20	s	s	NOUN
ejpam-4911	435	21	,	,	PUNCT
ejpam-4911	435	22	v)codense	v)codense	NOUN
ejpam-4911	435	23	set	set	NOUN
ejpam-4911	435	24	in	in	ADP
ejpam-4911	435	25	x.	x.	NOUN
ejpam-4911	435	26	proposition	proposition	PROPN
ejpam-4911	435	27	33	33	NUM
ejpam-4911	435	28	.	.	PUNCT
ejpam-4911	436	1	let	let	AUX
ejpam-4911	436	2	(	(	PUNCT
ejpam-4911	436	3	x,µ1	x,µ1	NOUN
ejpam-4911	436	4	,	,	PUNCT
ejpam-4911	436	5	µ2	µ2	PROPN
ejpam-4911	436	6	)	)	PUNCT
ejpam-4911	436	7	be	be	AUX
ejpam-4911	436	8	a	a	DET
ejpam-4911	436	9	bgts	bgts	NOUN
ejpam-4911	436	10	.	.	PUNCT
ejpam-4911	437	1	then	then	ADV
ejpam-4911	437	2	e	e	PROPN
ejpam-4911	437	3	∈	∈	PROPN
ejpam-4911	437	4	(	(	PUNCT
ejpam-4911	437	5	s	s	NOUN
ejpam-4911	437	6	,	,	PUNCT
ejpam-4911	437	7	v)−d(x	v)−d(x	NUM
ejpam-4911	437	8	)	)	PUNCT
ejpam-4911	437	9	if	if	SCONJ
ejpam-4911	437	10	and	and	CCONJ
ejpam-4911	437	11	only	only	ADV
ejpam-4911	437	12	if	if	SCONJ
ejpam-4911	437	13	x−e	x−e	ADJ
ejpam-4911	437	14	is	be	AUX
ejpam-4911	437	15	(	(	PUNCT
ejpam-4911	437	16	s	s	X
ejpam-4911	437	17	,	,	PUNCT
ejpam-4911	437	18	v)-codense	v)-codense	ADV
ejpam-4911	437	19	where	where	SCONJ
ejpam-4911	437	20	s	s	X
ejpam-4911	437	21	,	,	PUNCT
ejpam-4911	437	22	v	v	NOUN
ejpam-4911	437	23	=	=	SYM
ejpam-4911	437	24	1	1	NUM
ejpam-4911	437	25	,	,	PUNCT
ejpam-4911	437	26	2	2	NUM
ejpam-4911	437	27	and	and	CCONJ
ejpam-4911	437	28	s	s	VERB
ejpam-4911	437	29	̸=	̸=	PROPN
ejpam-4911	437	30	v.	v.	ADP
ejpam-4911	437	31	proposition	proposition	NOUN
ejpam-4911	437	32	34	34	NUM
ejpam-4911	437	33	.	.	PUNCT
ejpam-4911	438	1	let	let	AUX
ejpam-4911	438	2	(	(	PUNCT
ejpam-4911	438	3	x,µ1	x,µ1	NOUN
ejpam-4911	438	4	,	,	PUNCT
ejpam-4911	438	5	µ2	µ2	PROPN
ejpam-4911	438	6	)	)	PUNCT
ejpam-4911	438	7	be	be	AUX
ejpam-4911	438	8	a	a	DET
ejpam-4911	438	9	bgts	bgts	NOUN
ejpam-4911	438	10	.	.	PUNCT
ejpam-4911	439	1	if	if	SCONJ
ejpam-4911	439	2	e	e	PROPN
ejpam-4911	439	3	is	be	AUX
ejpam-4911	439	4	a	a	DET
ejpam-4911	439	5	(	(	PUNCT
ejpam-4911	439	6	s	s	X
ejpam-4911	439	7	,	,	PUNCT
ejpam-4911	439	8	v)-codense	v)-codense	ADV
ejpam-4911	439	9	set	set	VERB
ejpam-4911	439	10	in	in	ADP
ejpam-4911	439	11	x	x	NOUN
ejpam-4911	439	12	,	,	PUNCT
ejpam-4911	439	13	then	then	ADV
ejpam-4911	439	14	there	there	PRON
ejpam-4911	439	15	is	be	VERB
ejpam-4911	439	16	no	no	DET
ejpam-4911	439	17	non	non	ADJ
ejpam-4911	439	18	-	-	ADJ
ejpam-4911	439	19	null	null	ADJ
ejpam-4911	439	20	(	(	PUNCT
ejpam-4911	439	21	s	s	NOUN
ejpam-4911	439	22	,	,	PUNCT
ejpam-4911	439	23	v)-open	v)-open	VERB
ejpam-4911	439	24	set	set	VERB
ejpam-4911	439	25	h	h	NOUN
ejpam-4911	439	26	such	such	ADJ
ejpam-4911	439	27	that	that	SCONJ
ejpam-4911	439	28	h	h	NOUN
ejpam-4911	439	29	⊂	⊂	PROPN
ejpam-4911	439	30	e	e	X
ejpam-4911	439	31	where	where	SCONJ
ejpam-4911	439	32	s	s	X
ejpam-4911	439	33	,	,	PUNCT
ejpam-4911	439	34	v	v	NOUN
ejpam-4911	439	35	=	=	SYM
ejpam-4911	439	36	1	1	NUM
ejpam-4911	439	37	,	,	PUNCT
ejpam-4911	439	38	2	2	NUM
ejpam-4911	439	39	and	and	CCONJ
ejpam-4911	439	40	s	s	VERB
ejpam-4911	439	41	̸=	̸=	PROPN
ejpam-4911	439	42	v.	v.	ADP
ejpam-4911	439	43	the	the	DET
ejpam-4911	439	44	reverse	reverse	ADJ
ejpam-4911	439	45	implication	implication	NOUN
ejpam-4911	439	46	of	of	ADP
ejpam-4911	439	47	proposition	proposition	NOUN
ejpam-4911	439	48	34	34	NUM
ejpam-4911	439	49	is	be	AUX
ejpam-4911	439	50	generally	generally	ADV
ejpam-4911	439	51	not	not	PART
ejpam-4911	439	52	true	true	ADJ
ejpam-4911	439	53	as	as	SCONJ
ejpam-4911	439	54	given	give	VERB
ejpam-4911	439	55	by	by	ADP
ejpam-4911	439	56	the	the	DET
ejpam-4911	439	57	below	below	ADJ
ejpam-4911	439	58	example	example	NOUN
ejpam-4911	439	59	35	35	NUM
ejpam-4911	439	60	.	.	PUNCT
ejpam-4911	439	61	example	example	NOUN
ejpam-4911	439	62	35	35	NUM
ejpam-4911	439	63	.	.	PUNCT
ejpam-4911	440	1	(	(	PUNCT
ejpam-4911	440	2	a	a	X
ejpam-4911	440	3	)	)	PUNCT
ejpam-4911	440	4	consider	consider	VERB
ejpam-4911	440	5	the	the	DET
ejpam-4911	440	6	bigeneralized	bigeneralized	ADJ
ejpam-4911	440	7	topological	topological	ADJ
ejpam-4911	440	8	space	space	NOUN
ejpam-4911	440	9	(	(	PUNCT
ejpam-4911	440	10	x,µ1	x,µ1	PROPN
ejpam-4911	440	11	,	,	PUNCT
ejpam-4911	440	12	µ2	µ2	PROPN
ejpam-4911	440	13	)	)	PUNCT
ejpam-4911	441	1	where	where	SCONJ
ejpam-4911	441	2	x	x	X
ejpam-4911	441	3	=	=	PUNCT
ejpam-4911	442	1	[	[	X
ejpam-4911	442	2	0	0	NUM
ejpam-4911	442	3	,	,	PUNCT
ejpam-4911	442	4	4	4	NUM
ejpam-4911	442	5	]	]	PUNCT
ejpam-4911	442	6	;	;	PUNCT
ejpam-4911	442	7	µ1	µ1	PROPN
ejpam-4911	442	8	=	=	SYM
ejpam-4911	442	9	{	{	PUNCT
ejpam-4911	442	10	∅	∅	NOUN
ejpam-4911	442	11	,	,	PUNCT
ejpam-4911	442	12	[	[	X
ejpam-4911	442	13	0	0	NUM
ejpam-4911	442	14	,	,	PUNCT
ejpam-4911	442	15	2	2	NUM
ejpam-4911	442	16	)	)	PUNCT
ejpam-4911	442	17	,	,	PUNCT
ejpam-4911	442	18	(	(	PUNCT
ejpam-4911	442	19	1	1	NUM
ejpam-4911	442	20	,	,	PUNCT
ejpam-4911	442	21	3	3	NUM
ejpam-4911	442	22	]	]	PUNCT
ejpam-4911	442	23	,	,	PUNCT
ejpam-4911	442	24	[	[	X
ejpam-4911	442	25	0	0	NUM
ejpam-4911	442	26	,	,	PUNCT
ejpam-4911	442	27	3	3	NUM
ejpam-4911	442	28	]	]	PUNCT
ejpam-4911	442	29	}	}	PUNCT
ejpam-4911	442	30	and	and	CCONJ
ejpam-4911	442	31	µ2	µ2	PROPN
ejpam-4911	442	32	=	=	PUNCT
ejpam-4911	442	33	{	{	PUNCT
ejpam-4911	442	34	∅	∅	NOUN
ejpam-4911	442	35	,	,	PUNCT
ejpam-4911	442	36	[	[	X
ejpam-4911	442	37	0	0	NUM
ejpam-4911	442	38	,	,	PUNCT
ejpam-4911	442	39	32	32	NUM
ejpam-4911	442	40	)	)	PUNCT
ejpam-4911	442	41	,	,	PUNCT
ejpam-4911	442	42	(	(	PUNCT
ejpam-4911	442	43	1	1	NUM
ejpam-4911	442	44	,	,	PUNCT
ejpam-4911	442	45	3	3	NUM
ejpam-4911	442	46	]	]	PUNCT
ejpam-4911	442	47	,	,	PUNCT
ejpam-4911	442	48	[	[	X
ejpam-4911	442	49	0	0	NUM
ejpam-4911	442	50	,	,	PUNCT
ejpam-4911	442	51	3	3	NUM
ejpam-4911	442	52	]	]	PUNCT
ejpam-4911	442	53	}	}	PUNCT
ejpam-4911	442	54	.	.	PUNCT
ejpam-4911	443	1	let	let	VERB
ejpam-4911	443	2	a	a	PRON
ejpam-4911	443	3	=	=	SYM
ejpam-4911	444	1	[	[	X
ejpam-4911	444	2	0	0	NUM
ejpam-4911	444	3	,	,	PUNCT
ejpam-4911	444	4	2	2	NUM
ejpam-4911	444	5	)	)	PUNCT
ejpam-4911	444	6	.	.	PUNCT
ejpam-4911	445	1	here	here	ADV
ejpam-4911	445	2	b	b	X
ejpam-4911	445	3	=	=	SYM
ejpam-4911	445	4	(	(	PUNCT
ejpam-4911	445	5	1	1	NUM
ejpam-4911	445	6	,	,	PUNCT
ejpam-4911	445	7	3	3	NUM
ejpam-4911	445	8	]	]	PUNCT
ejpam-4911	445	9	is	be	AUX
ejpam-4911	445	10	(	(	PUNCT
ejpam-4911	445	11	2	2	NUM
ejpam-4911	445	12	,	,	PUNCT
ejpam-4911	445	13	1)-open	1)-open	NUM
ejpam-4911	445	14	set	set	NOUN
ejpam-4911	445	15	.	.	PUNCT
ejpam-4911	446	1	also	also	ADV
ejpam-4911	446	2	,	,	PUNCT
ejpam-4911	446	3	b	b	X
ejpam-4911	446	4	⊈	⊈	PROPN
ejpam-4911	446	5	a.	a.	NOUN
ejpam-4911	446	6	but	but	CCONJ
ejpam-4911	446	7	i2(i1(a	i2(i1(a	NUM
ejpam-4911	446	8	)	)	PUNCT
ejpam-4911	446	9	)	)	PUNCT
ejpam-4911	447	1	=	=	PUNCT
ejpam-4911	448	1	[	[	X
ejpam-4911	448	2	0	0	NUM
ejpam-4911	448	3	,	,	PUNCT
ejpam-4911	448	4	32	32	NUM
ejpam-4911	448	5	)	)	PUNCT
ejpam-4911	448	6	̸=	̸=	PROPN
ejpam-4911	448	7	∅.	∅.	ADP
ejpam-4911	448	8	(	(	PUNCT
ejpam-4911	448	9	b	b	NOUN
ejpam-4911	448	10	)	)	PUNCT
ejpam-4911	448	11	consider	consider	VERB
ejpam-4911	448	12	the	the	DET
ejpam-4911	448	13	bigeneralized	bigeneralized	ADJ
ejpam-4911	448	14	topological	topological	ADJ
ejpam-4911	448	15	space	space	NOUN
ejpam-4911	448	16	(	(	PUNCT
ejpam-4911	448	17	x,µ1	x,µ1	PROPN
ejpam-4911	448	18	,	,	PUNCT
ejpam-4911	448	19	µ2	µ2	PROPN
ejpam-4911	448	20	)	)	PUNCT
ejpam-4911	449	1	where	where	SCONJ
ejpam-4911	449	2	x	x	X
ejpam-4911	449	3	=	=	PUNCT
ejpam-4911	450	1	[	[	X
ejpam-4911	450	2	0	0	NUM
ejpam-4911	450	3	,	,	PUNCT
ejpam-4911	450	4	3	3	NUM
ejpam-4911	450	5	]	]	PUNCT
ejpam-4911	450	6	;	;	PUNCT
ejpam-4911	450	7	y.	y.	PROPN
ejpam-4911	450	8	farhat	farhat	PROPN
ejpam-4911	450	9	,	,	PUNCT
ejpam-4911	450	10	v.	v.	ADP
ejpam-4911	450	11	subramanian	subramanian	PROPN
ejpam-4911	450	12	/	/	SYM
ejpam-4911	450	13	eur	eur	PROPN
ejpam-4911	450	14	.	.	PUNCT
ejpam-4911	451	1	j.	j.	PROPN
ejpam-4911	451	2	pure	pure	PROPN
ejpam-4911	451	3	appl	appl	PROPN
ejpam-4911	451	4	.	.	PROPN
ejpam-4911	451	5	math	math	PROPN
ejpam-4911	451	6	,	,	PUNCT
ejpam-4911	451	7	16	16	NUM
ejpam-4911	451	8	(	(	PUNCT
ejpam-4911	451	9	4	4	NUM
ejpam-4911	451	10	)	)	PUNCT
ejpam-4911	451	11	(	(	PUNCT
ejpam-4911	451	12	2023	2023	NUM
ejpam-4911	451	13	)	)	PUNCT
ejpam-4911	451	14	,	,	PUNCT
ejpam-4911	451	15	2049	2049	NUM
ejpam-4911	451	16	-	-	SYM
ejpam-4911	451	17	2065	2065	NUM
ejpam-4911	451	18	2062	2062	NUM
ejpam-4911	451	19	µ1	µ1	NOUN
ejpam-4911	451	20	=	=	SYM
ejpam-4911	451	21	{	{	PUNCT
ejpam-4911	451	22	∅	∅	NOUN
ejpam-4911	451	23	,	,	PUNCT
ejpam-4911	451	24	[	[	X
ejpam-4911	451	25	0	0	NUM
ejpam-4911	451	26	,	,	PUNCT
ejpam-4911	451	27	32	32	NUM
ejpam-4911	451	28	)	)	PUNCT
ejpam-4911	451	29	,	,	PUNCT
ejpam-4911	451	30	(	(	PUNCT
ejpam-4911	451	31	1	1	NUM
ejpam-4911	451	32	,	,	PUNCT
ejpam-4911	451	33	2	2	NUM
ejpam-4911	451	34	)	)	PUNCT
ejpam-4911	451	35	,	,	PUNCT
ejpam-4911	451	36	(	(	PUNCT
ejpam-4911	451	37	1	1	NUM
ejpam-4911	451	38	,	,	PUNCT
ejpam-4911	451	39	3	3	NUM
ejpam-4911	451	40	)	)	PUNCT
ejpam-4911	451	41	,	,	PUNCT
ejpam-4911	452	1	[	[	X
ejpam-4911	452	2	0	0	NUM
ejpam-4911	452	3	,	,	PUNCT
ejpam-4911	452	4	3	3	NUM
ejpam-4911	452	5	)	)	PUNCT
ejpam-4911	452	6	}	}	PUNCT
ejpam-4911	452	7	and	and	CCONJ
ejpam-4911	452	8	µ2	µ2	PROPN
ejpam-4911	452	9	=	=	PUNCT
ejpam-4911	452	10	{	{	PUNCT
ejpam-4911	452	11	∅	∅	NOUN
ejpam-4911	452	12	,	,	PUNCT
ejpam-4911	452	13	[	[	X
ejpam-4911	452	14	0	0	NUM
ejpam-4911	452	15	,	,	PUNCT
ejpam-4911	452	16	2	2	NUM
ejpam-4911	452	17	)	)	PUNCT
ejpam-4911	452	18	,	,	PUNCT
ejpam-4911	452	19	(	(	PUNCT
ejpam-4911	452	20	1	1	NUM
ejpam-4911	452	21	,	,	PUNCT
ejpam-4911	452	22	3	3	NUM
ejpam-4911	452	23	)	)	PUNCT
ejpam-4911	452	24	,	,	PUNCT
ejpam-4911	453	1	[	[	X
ejpam-4911	453	2	0	0	NUM
ejpam-4911	453	3	,	,	PUNCT
ejpam-4911	453	4	3	3	NUM
ejpam-4911	453	5	)	)	PUNCT
ejpam-4911	453	6	}	}	PUNCT
ejpam-4911	453	7	.	.	PUNCT
ejpam-4911	454	1	take	take	VERB
ejpam-4911	454	2	a	a	PRON
ejpam-4911	454	3	=	=	PUNCT
ejpam-4911	455	1	[	[	X
ejpam-4911	455	2	0	0	NUM
ejpam-4911	455	3	,	,	PUNCT
ejpam-4911	455	4	2	2	NUM
ejpam-4911	455	5	)	)	PUNCT
ejpam-4911	455	6	.	.	PUNCT
ejpam-4911	456	1	here	here	ADV
ejpam-4911	456	2	b	b	X
ejpam-4911	456	3	=	=	SYM
ejpam-4911	456	4	(	(	PUNCT
ejpam-4911	456	5	1	1	NUM
ejpam-4911	456	6	,	,	PUNCT
ejpam-4911	456	7	3	3	NUM
ejpam-4911	456	8	)	)	PUNCT
ejpam-4911	456	9	is	be	AUX
ejpam-4911	456	10	(	(	PUNCT
ejpam-4911	456	11	1	1	NUM
ejpam-4911	456	12	,	,	PUNCT
ejpam-4911	456	13	2)-open	2)-open	NUM
ejpam-4911	456	14	set	set	NOUN
ejpam-4911	456	15	.	.	PUNCT
ejpam-4911	457	1	also	also	ADV
ejpam-4911	457	2	,	,	PUNCT
ejpam-4911	457	3	b	b	X
ejpam-4911	457	4	⊈	⊈	PROPN
ejpam-4911	457	5	a.	a.	NOUN
ejpam-4911	457	6	but	but	CCONJ
ejpam-4911	457	7	i1(i2(a	i1(i2(a	NOUN
ejpam-4911	457	8	)	)	PUNCT
ejpam-4911	457	9	)	)	PUNCT
ejpam-4911	458	1	=	=	PUNCT
ejpam-4911	459	1	[	[	X
ejpam-4911	459	2	0	0	NUM
ejpam-4911	459	3	,	,	PUNCT
ejpam-4911	459	4	32	32	NUM
ejpam-4911	459	5	)	)	PUNCT
ejpam-4911	459	6	̸=	̸=	PROPN
ejpam-4911	459	7	∅.	∅.	PRON
ejpam-4911	459	8	5	5	NUM
ejpam-4911	459	9	.	.	PUNCT
ejpam-4911	459	10	sets	set	NOUN
ejpam-4911	459	11	via	via	ADP
ejpam-4911	459	12	functions	function	NOUN
ejpam-4911	459	13	in	in	ADP
ejpam-4911	459	14	this	this	DET
ejpam-4911	459	15	section	section	NOUN
ejpam-4911	459	16	,	,	PUNCT
ejpam-4911	459	17	we	we	PRON
ejpam-4911	459	18	give	give	VERB
ejpam-4911	459	19	some	some	DET
ejpam-4911	459	20	properties	property	NOUN
ejpam-4911	459	21	for	for	ADP
ejpam-4911	459	22	(	(	PUNCT
ejpam-4911	459	23	s	s	X
ejpam-4911	459	24	,	,	PUNCT
ejpam-4911	459	25	v)-dense	v)-dense	PUNCT
ejpam-4911	459	26	and	and	CCONJ
ejpam-4911	459	27	(	(	PUNCT
ejpam-4911	459	28	s	s	X
ejpam-4911	459	29	,	,	PUNCT
ejpam-4911	459	30	v)-nowhere	v)-nowhere	PUNCT
ejpam-4911	459	31	dense	dense	ADJ
ejpam-4911	459	32	sets	set	NOUN
ejpam-4911	459	33	under	under	ADP
ejpam-4911	459	34	generalized	generalized	ADJ
ejpam-4911	459	35	continuous	continuous	ADJ
ejpam-4911	459	36	functions	function	NOUN
ejpam-4911	459	37	in	in	ADP
ejpam-4911	459	38	a	a	DET
ejpam-4911	459	39	bigeneralized	bigeneralize	VERB
ejpam-4911	459	40	topological	topological	ADJ
ejpam-4911	459	41	space	space	NOUN
ejpam-4911	459	42	.	.	PUNCT
ejpam-4911	460	1	now	now	ADV
ejpam-4911	460	2	,	,	PUNCT
ejpam-4911	460	3	we	we	PRON
ejpam-4911	460	4	recall	recall	VERB
ejpam-4911	460	5	some	some	DET
ejpam-4911	460	6	basic	basic	ADJ
ejpam-4911	460	7	definitions	definition	NOUN
ejpam-4911	460	8	defined	define	VERB
ejpam-4911	460	9	in	in	ADP
ejpam-4911	460	10	[	[	X
ejpam-4911	460	11	4	4	NUM
ejpam-4911	460	12	]	]	PUNCT
ejpam-4911	460	13	.	.	PUNCT
ejpam-4911	461	1	let	let	VERB
ejpam-4911	461	2	(	(	PUNCT
ejpam-4911	461	3	x,µ1	x,µ1	NOUN
ejpam-4911	461	4	x	x	SYM
ejpam-4911	461	5	,	,	PUNCT
ejpam-4911	461	6	µ2	µ2	PROPN
ejpam-4911	461	7	x	x	X
ejpam-4911	461	8	)	)	PUNCT
ejpam-4911	461	9	and	and	CCONJ
ejpam-4911	461	10	(	(	PUNCT
ejpam-4911	461	11	y	y	PROPN
ejpam-4911	461	12	,	,	PUNCT
ejpam-4911	461	13	µ1	µ1	PROPN
ejpam-4911	461	14	y	y	PROPN
ejpam-4911	461	15	,	,	PUNCT
ejpam-4911	461	16	µ	µ	PROPN
ejpam-4911	461	17	2	2	NUM
ejpam-4911	461	18	y	y	NOUN
ejpam-4911	461	19	)	)	PUNCT
ejpam-4911	461	20	be	be	AUX
ejpam-4911	461	21	two	two	NUM
ejpam-4911	461	22	bgts	bgts	NOUN
ejpam-4911	461	23	and	and	CCONJ
ejpam-4911	461	24	h	h	NOUN
ejpam-4911	461	25	:	:	PUNCT
ejpam-4911	461	26	(	(	PUNCT
ejpam-4911	461	27	x,µ1	x,µ1	NOUN
ejpam-4911	461	28	x	x	SYM
ejpam-4911	461	29	,	,	PUNCT
ejpam-4911	461	30	µ2	µ2	PROPN
ejpam-4911	461	31	x	x	PRON
ejpam-4911	461	32	)	)	PUNCT
ejpam-4911	461	33	→	→	SYM
ejpam-4911	461	34	(	(	PUNCT
ejpam-4911	461	35	y	y	PROPN
ejpam-4911	461	36	,	,	PUNCT
ejpam-4911	461	37	µ1	µ1	PROPN
ejpam-4911	461	38	y	y	PROPN
ejpam-4911	461	39	,	,	PUNCT
ejpam-4911	461	40	µ	µ	PROPN
ejpam-4911	461	41	2	2	NUM
ejpam-4911	461	42	y	y	NOUN
ejpam-4911	461	43	)	)	PUNCT
ejpam-4911	461	44	be	be	AUX
ejpam-4911	461	45	a	a	DET
ejpam-4911	461	46	map	map	NOUN
ejpam-4911	461	47	.	.	PUNCT
ejpam-4911	462	1	then	then	ADV
ejpam-4911	462	2	•	•	NUM
ejpam-4911	462	3	h	h	NOUN
ejpam-4911	462	4	is	be	AUX
ejpam-4911	462	5	called	call	VERB
ejpam-4911	462	6	(	(	PUNCT
ejpam-4911	462	7	s	s	PROPN
ejpam-4911	462	8	,	,	PUNCT
ejpam-4911	462	9	v)-generalized	v)-generalize	VERB
ejpam-4911	462	10	continuous	continuous	ADJ
ejpam-4911	462	11	(	(	PUNCT
ejpam-4911	462	12	µ(s	µ(	NOUN
ejpam-4911	462	13	,	,	PUNCT
ejpam-4911	462	14	v)-continuous	v)-continuous	ADJ
ejpam-4911	462	15	)	)	PUNCT
ejpam-4911	462	16	if	if	SCONJ
ejpam-4911	462	17	h−1(b	h−1(b	PROPN
ejpam-4911	462	18	)	)	PUNCT
ejpam-4911	462	19	is	be	AUX
ejpam-4911	462	20	µ(s	µ(	NOUN
ejpam-4911	462	21	,	,	PUNCT
ejpam-4911	462	22	v)-closed	v)-close	VERB
ejpam-4911	462	23	in	in	ADP
ejpam-4911	462	24	x	x	PUNCT
ejpam-4911	462	25	for	for	ADP
ejpam-4911	462	26	every	every	DET
ejpam-4911	462	27	µv	µv	NOUN
ejpam-4911	462	28	-	-	PUNCT
ejpam-4911	462	29	closed	close	VERB
ejpam-4911	462	30	b	b	PROPN
ejpam-4911	462	31	of	of	ADP
ejpam-4911	462	32	y	y	PROPN
ejpam-4911	462	33	where	where	SCONJ
ejpam-4911	462	34	s	s	X
ejpam-4911	462	35	,	,	PUNCT
ejpam-4911	462	36	v	v	NOUN
ejpam-4911	462	37	=	=	SYM
ejpam-4911	462	38	1	1	NUM
ejpam-4911	462	39	,	,	PUNCT
ejpam-4911	462	40	2	2	NUM
ejpam-4911	462	41	and	and	CCONJ
ejpam-4911	462	42	s	s	VERB
ejpam-4911	462	43	̸=	̸=	PROPN
ejpam-4911	462	44	v.	v.	ADP
ejpam-4911	462	45	•	•	ADJ
ejpam-4911	462	46	h	h	NOUN
ejpam-4911	462	47	is	be	AUX
ejpam-4911	462	48	called	call	VERB
ejpam-4911	462	49	as	as	ADP
ejpam-4911	462	50	µs	µs	NOUN
ejpam-4911	462	51	-	-	ADJ
ejpam-4911	462	52	continuous	continuous	ADJ
ejpam-4911	462	53	if	if	SCONJ
ejpam-4911	462	54	h−1(c	h−1(c	PROPN
ejpam-4911	462	55	)	)	PUNCT
ejpam-4911	462	56	is	be	AUX
ejpam-4911	462	57	µs	µs	NOUN
ejpam-4911	462	58	-	-	PUNCT
ejpam-4911	462	59	closed	closed	ADJ
ejpam-4911	462	60	in	in	ADP
ejpam-4911	462	61	x	x	PUNCT
ejpam-4911	462	62	for	for	ADP
ejpam-4911	462	63	every	every	DET
ejpam-4911	462	64	µs	µs	NOUN
ejpam-4911	462	65	-	-	PUNCT
ejpam-4911	462	66	closed	closed	ADJ
ejpam-4911	462	67	c	c	NOUN
ejpam-4911	462	68	of	of	ADP
ejpam-4911	462	69	y	y	PROPN
ejpam-4911	462	70	for	for	ADP
ejpam-4911	462	71	s	s	NOUN
ejpam-4911	462	72	=	=	SYM
ejpam-4911	462	73	1	1	NUM
ejpam-4911	462	74	,	,	PUNCT
ejpam-4911	462	75	2	2	NUM
ejpam-4911	462	76	.	.	NOUN
ejpam-4911	463	1	•	•	NUM
ejpam-4911	463	2	h	h	NOUN
ejpam-4911	463	3	is	be	AUX
ejpam-4911	463	4	said	say	VERB
ejpam-4911	463	5	to	to	PART
ejpam-4911	463	6	be	be	AUX
ejpam-4911	463	7	µs	µs	NOUN
ejpam-4911	463	8	-	-	ADJ
ejpam-4911	463	9	open	open	ADJ
ejpam-4911	463	10	if	if	SCONJ
ejpam-4911	463	11	h(d	h(d	PROPN
ejpam-4911	463	12	)	)	PUNCT
ejpam-4911	463	13	is	be	AUX
ejpam-4911	463	14	µs	µs	NOUN
ejpam-4911	463	15	-	-	ADJ
ejpam-4911	463	16	open	open	ADJ
ejpam-4911	463	17	of	of	ADP
ejpam-4911	463	18	y	y	PROPN
ejpam-4911	463	19	for	for	ADP
ejpam-4911	463	20	every	every	DET
ejpam-4911	463	21	µs	µs	NOUN
ejpam-4911	463	22	-	-	PUNCT
ejpam-4911	463	23	open	open	ADJ
ejpam-4911	463	24	d	d	NOUN
ejpam-4911	463	25	of	of	ADP
ejpam-4911	463	26	x	x	PUNCT
ejpam-4911	463	27	for	for	ADP
ejpam-4911	463	28	s	s	NOUN
ejpam-4911	463	29	=	=	SYM
ejpam-4911	463	30	1	1	NUM
ejpam-4911	463	31	,	,	PUNCT
ejpam-4911	463	32	2	2	NUM
ejpam-4911	463	33	.	.	X
ejpam-4911	463	34	theorem	theorem	NOUN
ejpam-4911	463	35	36	36	NUM
ejpam-4911	463	36	.	.	PUNCT
ejpam-4911	464	1	let	let	VERB
ejpam-4911	464	2	(	(	PUNCT
ejpam-4911	464	3	x,µ1	x,µ1	NOUN
ejpam-4911	464	4	x	x	SYM
ejpam-4911	464	5	,	,	PUNCT
ejpam-4911	464	6	µ2	µ2	PROPN
ejpam-4911	464	7	x	x	X
ejpam-4911	464	8	)	)	PUNCT
ejpam-4911	464	9	and	and	CCONJ
ejpam-4911	464	10	(	(	PUNCT
ejpam-4911	464	11	y	y	PROPN
ejpam-4911	464	12	,	,	PUNCT
ejpam-4911	464	13	µ1	µ1	PROPN
ejpam-4911	464	14	y	y	PROPN
ejpam-4911	464	15	,	,	PUNCT
ejpam-4911	464	16	µ	µ	PROPN
ejpam-4911	464	17	2	2	NUM
ejpam-4911	464	18	y	y	NOUN
ejpam-4911	464	19	)	)	PUNCT
ejpam-4911	464	20	be	be	AUX
ejpam-4911	464	21	two	two	NUM
ejpam-4911	464	22	bigeneralized	bigeneralize	VERB
ejpam-4911	464	23	topological	topological	ADJ
ejpam-4911	464	24	spaces	space	NOUN
ejpam-4911	464	25	,	,	PUNCT
ejpam-4911	464	26	h	h	NOUN
ejpam-4911	464	27	:	:	PUNCT
ejpam-4911	464	28	(	(	PUNCT
ejpam-4911	464	29	x,µ1	x,µ1	NOUN
ejpam-4911	464	30	x	x	SYM
ejpam-4911	464	31	,	,	PUNCT
ejpam-4911	464	32	µ2	µ2	PROPN
ejpam-4911	464	33	x	x	PRON
ejpam-4911	464	34	)	)	PUNCT
ejpam-4911	464	35	→	→	SYM
ejpam-4911	464	36	(	(	PUNCT
ejpam-4911	464	37	y	y	PROPN
ejpam-4911	464	38	,	,	PUNCT
ejpam-4911	464	39	µ1	µ1	PROPN
ejpam-4911	464	40	y	y	PROPN
ejpam-4911	464	41	,	,	PUNCT
ejpam-4911	464	42	µ	µ	PROPN
ejpam-4911	464	43	2	2	NUM
ejpam-4911	464	44	y	y	NOUN
ejpam-4911	464	45	)	)	PUNCT
ejpam-4911	464	46	be	be	AUX
ejpam-4911	464	47	a	a	DET
ejpam-4911	464	48	µ(s	µ(	NOUN
ejpam-4911	464	49	,	,	PUNCT
ejpam-4911	464	50	v)-continuous	v)-continuous	ADJ
ejpam-4911	464	51	function	function	NOUN
ejpam-4911	464	52	where	where	SCONJ
ejpam-4911	464	53	s	s	X
ejpam-4911	464	54	,	,	PUNCT
ejpam-4911	464	55	v	v	NOUN
ejpam-4911	464	56	=	=	SYM
ejpam-4911	464	57	1	1	NUM
ejpam-4911	464	58	,	,	PUNCT
ejpam-4911	464	59	2	2	NUM
ejpam-4911	464	60	and	and	CCONJ
ejpam-4911	464	61	s	s	VERB
ejpam-4911	464	62	̸=	̸=	PROPN
ejpam-4911	465	1	v.	v.	ADP
ejpam-4911	465	2	if	if	SCONJ
ejpam-4911	465	3	q∩p	q∩p	PROPN
ejpam-4911	465	4	̸=	̸=	PROPN
ejpam-4911	465	5	∅	∅	NOUN
ejpam-4911	465	6	for	for	ADP
ejpam-4911	465	7	every	every	DET
ejpam-4911	465	8	p	p	NOUN
ejpam-4911	465	9	is	be	AUX
ejpam-4911	465	10	non	non	ADJ
ejpam-4911	465	11	-	-	ADJ
ejpam-4911	465	12	null	null	ADJ
ejpam-4911	465	13	µ(s	µ(	NOUN
ejpam-4911	465	14	,	,	PUNCT
ejpam-4911	465	15	v)-open	v)-open	NOUN
ejpam-4911	465	16	,	,	PUNCT
ejpam-4911	466	1	then	then	ADV
ejpam-4911	466	2	h(q	h(q	ADV
ejpam-4911	466	3	)	)	PUNCT
ejpam-4911	466	4	∈	∈	PROPN
ejpam-4911	466	5	(	(	PUNCT
ejpam-4911	466	6	s	s	PROPN
ejpam-4911	466	7	,	,	PUNCT
ejpam-4911	466	8	v)−d(y	v)−d(y	PROPN
ejpam-4911	466	9	)	)	PUNCT
ejpam-4911	466	10	where	where	SCONJ
ejpam-4911	466	11	q	q	X
ejpam-4911	466	12	⊂	⊂	PROPN
ejpam-4911	466	13	x	x	X
ejpam-4911	466	14	;	;	PUNCT
ejpam-4911	466	15	s	s	X
ejpam-4911	466	16	,	,	PUNCT
ejpam-4911	466	17	v	v	NOUN
ejpam-4911	466	18	=	=	SYM
ejpam-4911	466	19	1	1	NUM
ejpam-4911	466	20	,	,	PUNCT
ejpam-4911	466	21	2	2	NUM
ejpam-4911	466	22	and	and	CCONJ
ejpam-4911	466	23	s	s	VERB
ejpam-4911	466	24	̸=	̸=	PROPN
ejpam-4911	466	25	v.	v.	ADP
ejpam-4911	466	26	proof	proof	NOUN
ejpam-4911	466	27	.	.	PUNCT
ejpam-4911	467	1	it	it	PRON
ejpam-4911	467	2	is	be	AUX
ejpam-4911	467	3	enough	enough	ADJ
ejpam-4911	467	4	to	to	PART
ejpam-4911	467	5	prove	prove	VERB
ejpam-4911	467	6	,	,	PUNCT
ejpam-4911	467	7	h(q	h(q	ADV
ejpam-4911	467	8	)	)	PUNCT
ejpam-4911	467	9	∈	∈	PROPN
ejpam-4911	467	10	d(µv	d(µv	PROPN
ejpam-4911	467	11	y	y	PROPN
ejpam-4911	467	12	)	)	PUNCT
ejpam-4911	468	1	where	where	SCONJ
ejpam-4911	468	2	v	v	NOUN
ejpam-4911	468	3	=	=	SYM
ejpam-4911	468	4	1	1	NUM
ejpam-4911	468	5	,	,	PUNCT
ejpam-4911	468	6	2	2	NUM
ejpam-4911	468	7	,	,	PUNCT
ejpam-4911	468	8	by	by	ADP
ejpam-4911	468	9	theorem	theorem	NOUN
ejpam-4911	468	10	4	4	NUM
ejpam-4911	468	11	.	.	X
ejpam-4911	468	12	take	take	VERB
ejpam-4911	468	13	v	v	NOUN
ejpam-4911	468	14	=	=	SYM
ejpam-4911	468	15	2	2	X
ejpam-4911	468	16	.	.	PUNCT
ejpam-4911	468	17	let	let	VERB
ejpam-4911	468	18	p	p	PRON
ejpam-4911	468	19	∈	∈	PROPN
ejpam-4911	468	20	µ̃2	µ̃2	PROPN
ejpam-4911	468	21	y	y	PROPN
ejpam-4911	468	22	.	.	PUNCT
ejpam-4911	469	1	then	then	ADV
ejpam-4911	469	2	y	y	PROPN
ejpam-4911	470	1	−	−	PROPN
ejpam-4911	470	2	p	p	PROPN
ejpam-4911	470	3	is	be	AUX
ejpam-4911	470	4	µ2	µ2	PROPN
ejpam-4911	470	5	y	y	PROPN
ejpam-4911	470	6	-closed	-closed	PROPN
ejpam-4911	470	7	.	.	PUNCT
ejpam-4911	471	1	by	by	ADP
ejpam-4911	471	2	hypothesis	hypothesis	NOUN
ejpam-4911	471	3	,	,	PUNCT
ejpam-4911	471	4	h−1(y	h−1(y	PROPN
ejpam-4911	472	1	−	−	PROPN
ejpam-4911	472	2	p	p	NOUN
ejpam-4911	472	3	)	)	PUNCT
ejpam-4911	472	4	is	be	AUX
ejpam-4911	472	5	µ(1,2)-closed	µ(1,2)-close	VERB
ejpam-4911	472	6	in	in	ADP
ejpam-4911	472	7	x.	x.	NOUN
ejpam-4911	472	8	then	then	ADV
ejpam-4911	472	9	h−1(p	h−1(p	NOUN
ejpam-4911	472	10	)	)	PUNCT
ejpam-4911	472	11	is	be	AUX
ejpam-4911	472	12	non	non	ADJ
ejpam-4911	472	13	-	-	ADJ
ejpam-4911	472	14	null	null	ADJ
ejpam-4911	472	15	µ(1,2)-open	µ(1,2)-open	NOUN
ejpam-4911	472	16	.	.	PUNCT
ejpam-4911	473	1	by	by	ADP
ejpam-4911	473	2	hypothesis	hypothesis	NOUN
ejpam-4911	473	3	,	,	PUNCT
ejpam-4911	473	4	q	q	NOUN
ejpam-4911	473	5	∩	∩	X
ejpam-4911	473	6	h−1(p	h−1(p	NOUN
ejpam-4911	473	7	)	)	PUNCT
ejpam-4911	473	8	̸=	̸=	PROPN
ejpam-4911	473	9	∅.	∅.	ADP
ejpam-4911	473	10	this	this	PRON
ejpam-4911	473	11	implies	imply	VERB
ejpam-4911	473	12	h−1(h(q	h−1(h(q	NOUN
ejpam-4911	473	13	)	)	PUNCT
ejpam-4911	473	14	)	)	PUNCT
ejpam-4911	474	1	∩	∩	PROPN
ejpam-4911	474	2	h−1(p	h−1(p	NOUN
ejpam-4911	474	3	)	)	PUNCT
ejpam-4911	474	4	̸=	̸=	PROPN
ejpam-4911	474	5	∅	∅	NOUN
ejpam-4911	474	6	which	which	PRON
ejpam-4911	474	7	implies	imply	VERB
ejpam-4911	474	8	that	that	SCONJ
ejpam-4911	474	9	h−1(h(q	h−1(h(q	NOUN
ejpam-4911	474	10	)	)	PUNCT
ejpam-4911	474	11	∩	∩	NOUN
ejpam-4911	474	12	p	p	NOUN
ejpam-4911	474	13	)	)	PUNCT
ejpam-4911	474	14	̸=	̸=	PROPN
ejpam-4911	474	15	∅.	∅.	ADP
ejpam-4911	474	16	thus	thus	ADV
ejpam-4911	474	17	,	,	PUNCT
ejpam-4911	474	18	h(q	h(q	ADV
ejpam-4911	474	19	)	)	PUNCT
ejpam-4911	474	20	∩	∩	NOUN
ejpam-4911	474	21	p	p	X
ejpam-4911	474	22	̸=	̸=	PROPN
ejpam-4911	474	23	∅.	∅.	PRON
ejpam-4911	474	24	hence	hence	ADV
ejpam-4911	474	25	h(q	h(q	ADV
ejpam-4911	474	26	)	)	PUNCT
ejpam-4911	474	27	∈	∈	PROPN
ejpam-4911	474	28	d(µ2	d(µ2	NOUN
ejpam-4911	474	29	y	y	PROPN
ejpam-4911	474	30	)	)	PUNCT
ejpam-4911	474	31	.	.	PUNCT
ejpam-4911	475	1	take	take	VERB
ejpam-4911	475	2	v	v	NOUN
ejpam-4911	475	3	=	=	SYM
ejpam-4911	475	4	1	1	NUM
ejpam-4911	475	5	.	.	PUNCT
ejpam-4911	476	1	then	then	ADV
ejpam-4911	476	2	by	by	ADP
ejpam-4911	476	3	the	the	DET
ejpam-4911	476	4	same	same	ADJ
ejpam-4911	476	5	arguments	argument	NOUN
ejpam-4911	476	6	in	in	ADP
ejpam-4911	476	7	the	the	DET
ejpam-4911	476	8	above	above	ADJ
ejpam-4911	476	9	case	case	NOUN
ejpam-4911	476	10	,	,	PUNCT
ejpam-4911	476	11	we	we	PRON
ejpam-4911	476	12	get	get	VERB
ejpam-4911	476	13	h(q	h(q	ADV
ejpam-4911	476	14	)	)	PUNCT
ejpam-4911	477	1	∈	∈	PROPN
ejpam-4911	477	2	d(µ1	d(µ1	NOUN
ejpam-4911	477	3	y	y	PROPN
ejpam-4911	477	4	)	)	PUNCT
ejpam-4911	477	5	.	.	PUNCT
ejpam-4911	478	1	hence	hence	ADV
ejpam-4911	478	2	h(q	h(q	ADV
ejpam-4911	478	3	)	)	PUNCT
ejpam-4911	478	4	∈	∈	PROPN
ejpam-4911	478	5	d(µv	d(µv	PROPN
ejpam-4911	478	6	y	y	PROPN
ejpam-4911	478	7	)	)	PUNCT
ejpam-4911	478	8	where	where	SCONJ
ejpam-4911	478	9	v	v	NOUN
ejpam-4911	478	10	=	=	SYM
ejpam-4911	478	11	1	1	NUM
ejpam-4911	478	12	,	,	PUNCT
ejpam-4911	478	13	2	2	NUM
ejpam-4911	478	14	.	.	X
ejpam-4911	478	15	theorem	theorem	VERB
ejpam-4911	478	16	37	37	NUM
ejpam-4911	478	17	.	.	PUNCT
ejpam-4911	479	1	let	let	VERB
ejpam-4911	479	2	(	(	PUNCT
ejpam-4911	479	3	x,µ1	x,µ1	NOUN
ejpam-4911	479	4	x	x	SYM
ejpam-4911	479	5	,	,	PUNCT
ejpam-4911	479	6	µ2	µ2	PROPN
ejpam-4911	479	7	x	x	X
ejpam-4911	479	8	)	)	PUNCT
ejpam-4911	479	9	and	and	CCONJ
ejpam-4911	479	10	(	(	PUNCT
ejpam-4911	479	11	y	y	PROPN
ejpam-4911	479	12	,	,	PUNCT
ejpam-4911	479	13	µ1	µ1	PROPN
ejpam-4911	479	14	y	y	PROPN
ejpam-4911	479	15	,	,	PUNCT
ejpam-4911	479	16	µ	µ	PROPN
ejpam-4911	479	17	2	2	NUM
ejpam-4911	479	18	y	y	NOUN
ejpam-4911	479	19	)	)	PUNCT
ejpam-4911	479	20	be	be	AUX
ejpam-4911	479	21	two	two	NUM
ejpam-4911	479	22	bigeneralized	bigeneralize	VERB
ejpam-4911	479	23	topological	topological	ADJ
ejpam-4911	479	24	spaces	space	NOUN
ejpam-4911	479	25	,	,	PUNCT
ejpam-4911	479	26	p	p	X
ejpam-4911	479	27	,	,	PUNCT
ejpam-4911	479	28	q	q	X
ejpam-4911	479	29	⊂	⊂	PROPN
ejpam-4911	479	30	x	x	PROPN
ejpam-4911	479	31	,	,	PUNCT
ejpam-4911	479	32	h	h	NOUN
ejpam-4911	479	33	:	:	PUNCT
ejpam-4911	479	34	(	(	PUNCT
ejpam-4911	479	35	x,µ1	x,µ1	NOUN
ejpam-4911	479	36	x	x	SYM
ejpam-4911	479	37	,	,	PUNCT
ejpam-4911	479	38	µ2	µ2	PROPN
ejpam-4911	479	39	x	x	PRON
ejpam-4911	479	40	)	)	PUNCT
ejpam-4911	479	41	→	→	SYM
ejpam-4911	479	42	(	(	PUNCT
ejpam-4911	479	43	y	y	PROPN
ejpam-4911	479	44	,	,	PUNCT
ejpam-4911	479	45	µ1	µ1	PROPN
ejpam-4911	479	46	y	y	PROPN
ejpam-4911	479	47	,	,	PUNCT
ejpam-4911	479	48	µ	µ	PROPN
ejpam-4911	479	49	2	2	NUM
ejpam-4911	479	50	y	y	NOUN
ejpam-4911	479	51	)	)	PUNCT
ejpam-4911	479	52	be	be	AUX
ejpam-4911	479	53	a	a	DET
ejpam-4911	479	54	µs	µs	NOUN
ejpam-4911	479	55	-	-	ADJ
ejpam-4911	479	56	continuous	continuous	ADJ
ejpam-4911	479	57	function	function	NOUN
ejpam-4911	479	58	for	for	ADP
ejpam-4911	479	59	s	s	NOUN
ejpam-4911	479	60	=	=	SYM
ejpam-4911	479	61	1	1	NUM
ejpam-4911	479	62	,	,	PUNCT
ejpam-4911	479	63	2	2	NUM
ejpam-4911	479	64	.	.	PUNCT
ejpam-4911	480	1	then	then	ADV
ejpam-4911	480	2	the	the	DET
ejpam-4911	480	3	followings	following	NOUN
ejpam-4911	480	4	are	be	AUX
ejpam-4911	480	5	true	true	ADJ
ejpam-4911	480	6	.	.	PUNCT
ejpam-4911	481	1	(	(	PUNCT
ejpam-4911	481	2	a	a	X
ejpam-4911	481	3	)	)	PUNCT
ejpam-4911	481	4	if	if	SCONJ
ejpam-4911	481	5	p	p	PROPN
ejpam-4911	481	6	∈	∈	PROPN
ejpam-4911	481	7	d(µv	d(µv	PROPN
ejpam-4911	481	8	)	)	PUNCT
ejpam-4911	481	9	,	,	PUNCT
ejpam-4911	481	10	then	then	ADV
ejpam-4911	481	11	h(p	h(p	PROPN
ejpam-4911	481	12	)	)	PUNCT
ejpam-4911	481	13	∈	∈	PROPN
ejpam-4911	481	14	(	(	PUNCT
ejpam-4911	481	15	s	s	PROPN
ejpam-4911	481	16	,	,	PUNCT
ejpam-4911	481	17	v)−d(y	v)−d(y	PROPN
ejpam-4911	481	18	)	)	PUNCT
ejpam-4911	481	19	where	where	SCONJ
ejpam-4911	481	20	s	s	X
ejpam-4911	481	21	,	,	PUNCT
ejpam-4911	481	22	v	v	NOUN
ejpam-4911	481	23	=	=	SYM
ejpam-4911	481	24	1	1	NUM
ejpam-4911	481	25	,	,	PUNCT
ejpam-4911	481	26	2	2	NUM
ejpam-4911	481	27	and	and	CCONJ
ejpam-4911	481	28	s	s	VERB
ejpam-4911	481	29	̸=	̸=	PROPN
ejpam-4911	481	30	v.	v.	ADP
ejpam-4911	481	31	(	(	PUNCT
ejpam-4911	481	32	b	b	X
ejpam-4911	481	33	)	)	PUNCT
ejpam-4911	481	34	if	if	SCONJ
ejpam-4911	481	35	q	q	NOUN
ejpam-4911	481	36	is	be	AUX
ejpam-4911	481	37	µv	µv	NOUN
ejpam-4911	481	38	-	-	PUNCT
ejpam-4911	481	39	codense	codense	NOUN
ejpam-4911	481	40	and	and	CCONJ
ejpam-4911	481	41	h	h	NOUN
ejpam-4911	481	42	is	be	AUX
ejpam-4911	481	43	one	one	NUM
ejpam-4911	481	44	-	-	PUNCT
ejpam-4911	481	45	one	one	NUM
ejpam-4911	481	46	,	,	PUNCT
ejpam-4911	481	47	then	then	ADV
ejpam-4911	481	48	h(q	h(q	ADV
ejpam-4911	481	49	)	)	PUNCT
ejpam-4911	481	50	is	be	AUX
ejpam-4911	481	51	(	(	PUNCT
ejpam-4911	481	52	s	s	X
ejpam-4911	481	53	,	,	PUNCT
ejpam-4911	481	54	v)-codense	v)-codense	ADJ
ejpam-4911	481	55	in	in	ADP
ejpam-4911	481	56	y	y	PROPN
ejpam-4911	481	57	where	where	SCONJ
ejpam-4911	481	58	s	s	X
ejpam-4911	481	59	,	,	PUNCT
ejpam-4911	481	60	v	v	NOUN
ejpam-4911	481	61	=	=	SYM
ejpam-4911	481	62	1	1	NUM
ejpam-4911	481	63	,	,	PUNCT
ejpam-4911	481	64	2	2	NUM
ejpam-4911	481	65	and	and	CCONJ
ejpam-4911	481	66	s	s	VERB
ejpam-4911	481	67	̸=	̸=	PROPN
ejpam-4911	481	68	v.	v.	ADP
ejpam-4911	481	69	proof	proof	NOUN
ejpam-4911	481	70	.	.	PUNCT
ejpam-4911	482	1	(	(	PUNCT
ejpam-4911	482	2	a	a	X
ejpam-4911	482	3	)	)	PUNCT
ejpam-4911	482	4	.	.	PUNCT
ejpam-4911	483	1	it	it	PRON
ejpam-4911	483	2	is	be	AUX
ejpam-4911	483	3	enough	enough	ADJ
ejpam-4911	483	4	to	to	PART
ejpam-4911	483	5	prove	prove	VERB
ejpam-4911	483	6	,	,	PUNCT
ejpam-4911	483	7	h(p	h(p	PROPN
ejpam-4911	483	8	)	)	PUNCT
ejpam-4911	483	9	∈	∈	PROPN
ejpam-4911	483	10	d(µv	d(µv	PROPN
ejpam-4911	483	11	)	)	PUNCT
ejpam-4911	483	12	in	in	ADP
ejpam-4911	483	13	y	y	PROPN
ejpam-4911	483	14	where	where	SCONJ
ejpam-4911	483	15	v	v	NOUN
ejpam-4911	483	16	=	=	SYM
ejpam-4911	483	17	1	1	NUM
ejpam-4911	483	18	,	,	PUNCT
ejpam-4911	483	19	2	2	NUM
ejpam-4911	483	20	,	,	PUNCT
ejpam-4911	483	21	by	by	ADP
ejpam-4911	483	22	theorem	theorem	NOUN
ejpam-4911	483	23	4	4	NUM
ejpam-4911	483	24	.	.	PUNCT
ejpam-4911	483	25	assume	assume	VERB
ejpam-4911	483	26	that	that	SCONJ
ejpam-4911	483	27	,	,	PUNCT
ejpam-4911	483	28	p	p	PROPN
ejpam-4911	483	29	∈	∈	PROPN
ejpam-4911	483	30	d(µv	d(µv	PROPN
ejpam-4911	483	31	)	)	PUNCT
ejpam-4911	483	32	in	in	ADP
ejpam-4911	483	33	x	x	PUNCT
ejpam-4911	483	34	for	for	ADP
ejpam-4911	483	35	v	v	NOUN
ejpam-4911	483	36	=	=	SYM
ejpam-4911	483	37	1	1	NUM
ejpam-4911	483	38	,	,	PUNCT
ejpam-4911	483	39	2	2	NUM
ejpam-4911	483	40	.	.	X
ejpam-4911	484	1	take	take	VERB
ejpam-4911	484	2	v	v	NOUN
ejpam-4911	484	3	=	=	SYM
ejpam-4911	484	4	1	1	NUM
ejpam-4911	484	5	.	.	PUNCT
ejpam-4911	485	1	then	then	ADV
ejpam-4911	485	2	p	p	X
ejpam-4911	485	3	∈	∈	PROPN
ejpam-4911	485	4	d(µ1	d(µ1	NOUN
ejpam-4911	485	5	)	)	PUNCT
ejpam-4911	485	6	in	in	ADP
ejpam-4911	485	7	x.	x.	NOUN
ejpam-4911	485	8	let	let	VERB
ejpam-4911	485	9	m	m	PRON
ejpam-4911	485	10	∈	∈	PROPN
ejpam-4911	485	11	µ̃1	µ̃1	PROPN
ejpam-4911	485	12	.	.	PUNCT
ejpam-4911	486	1	then	then	ADV
ejpam-4911	486	2	y	y	PROPN
ejpam-4911	486	3	−m	−m	PROPN
ejpam-4911	486	4	is	be	AUX
ejpam-4911	486	5	µ1	µ1	NOUN
ejpam-4911	486	6	-	-	PUNCT
ejpam-4911	486	7	closed	closed	ADJ
ejpam-4911	486	8	in	in	ADP
ejpam-4911	486	9	y.	y.	NOUN
ejpam-4911	486	10	by	by	ADP
ejpam-4911	486	11	hypothesis	hypothesis	NOUN
ejpam-4911	486	12	,	,	PUNCT
ejpam-4911	486	13	h−1(y	h−1(y	PROPN
ejpam-4911	486	14	−m	−m	NOUN
ejpam-4911	486	15	)	)	PUNCT
ejpam-4911	486	16	is	be	AUX
ejpam-4911	486	17	µ1	µ1	ADV
ejpam-4911	486	18	-	-	PUNCT
ejpam-4911	486	19	closed	close	VERB
ejpam-4911	486	20	set	set	NOUN
ejpam-4911	486	21	in	in	ADP
ejpam-4911	486	22	x.	x.	PROPN
ejpam-4911	486	23	then	then	ADV
ejpam-4911	486	24	h−1(m	h−1(m	PROPN
ejpam-4911	486	25	)	)	PUNCT
ejpam-4911	487	1	is	be	AUX
ejpam-4911	487	2	a	a	DET
ejpam-4911	487	3	non	non	ADJ
ejpam-4911	487	4	-	-	ADJ
ejpam-4911	487	5	null	null	ADJ
ejpam-4911	487	6	µ1	µ1	NOUN
ejpam-4911	487	7	-	-	PUNCT
ejpam-4911	487	8	open	open	NOUN
ejpam-4911	487	9	set	set	NOUN
ejpam-4911	487	10	in	in	ADP
ejpam-4911	487	11	x.	x.	NOUN
ejpam-4911	487	12	by	by	ADP
ejpam-4911	487	13	hypothesis	hypothesis	NOUN
ejpam-4911	487	14	,	,	PUNCT
ejpam-4911	487	15	p	p	PROPN
ejpam-4911	487	16	∩h−1(m	∩h−1(m	PROPN
ejpam-4911	487	17	)	)	PUNCT
ejpam-4911	487	18	̸=	̸=	PROPN
ejpam-4911	487	19	∅.	∅.	ADP
ejpam-4911	487	20	this	this	PRON
ejpam-4911	487	21	implies	imply	VERB
ejpam-4911	487	22	y.	y.	PROPN
ejpam-4911	487	23	farhat	farhat	PROPN
ejpam-4911	487	24	,	,	PUNCT
ejpam-4911	487	25	v.	v.	ADP
ejpam-4911	487	26	subramanian	subramanian	PROPN
ejpam-4911	487	27	/	/	SYM
ejpam-4911	487	28	eur	eur	PROPN
ejpam-4911	487	29	.	.	PUNCT
ejpam-4911	488	1	j.	j.	PROPN
ejpam-4911	488	2	pure	pure	PROPN
ejpam-4911	488	3	appl	appl	PROPN
ejpam-4911	488	4	.	.	PROPN
ejpam-4911	488	5	math	math	PROPN
ejpam-4911	488	6	,	,	PUNCT
ejpam-4911	488	7	16	16	NUM
ejpam-4911	488	8	(	(	PUNCT
ejpam-4911	488	9	4	4	NUM
ejpam-4911	488	10	)	)	PUNCT
ejpam-4911	488	11	(	(	PUNCT
ejpam-4911	488	12	2023	2023	NUM
ejpam-4911	488	13	)	)	PUNCT
ejpam-4911	488	14	,	,	PUNCT
ejpam-4911	488	15	2049	2049	NUM
ejpam-4911	488	16	-	-	SYM
ejpam-4911	488	17	2065	2065	NUM
ejpam-4911	488	18	2063	2063	NUM
ejpam-4911	488	19	h−1(h(p	h−1(h(p	NOUN
ejpam-4911	488	20	)	)	PUNCT
ejpam-4911	488	21	)	)	PUNCT
ejpam-4911	489	1	∩	∩	PROPN
ejpam-4911	489	2	h−1(m	h−1(m	PROPN
ejpam-4911	489	3	)	)	PUNCT
ejpam-4911	489	4	̸=	̸=	NOUN
ejpam-4911	489	5	∅	∅	NOUN
ejpam-4911	489	6	,	,	PUNCT
ejpam-4911	489	7	since	since	SCONJ
ejpam-4911	489	8	p	p	PROPN
ejpam-4911	489	9	⊂	⊂	PROPN
ejpam-4911	489	10	h−1(h(p	h−1(h(p	NOUN
ejpam-4911	489	11	)	)	PUNCT
ejpam-4911	489	12	)	)	PUNCT
ejpam-4911	489	13	which	which	PRON
ejpam-4911	489	14	implies	imply	VERB
ejpam-4911	489	15	that	that	PRON
ejpam-4911	489	16	h−1(h(p	h−1(h(p	NOUN
ejpam-4911	489	17	)	)	PUNCT
ejpam-4911	490	1	∩m	∩m	PROPN
ejpam-4911	490	2	)	)	PUNCT
ejpam-4911	490	3	̸=	̸=	PROPN
ejpam-4911	490	4	∅.	∅.	ADP
ejpam-4911	490	5	thus	thus	ADV
ejpam-4911	490	6	,	,	PUNCT
ejpam-4911	490	7	h(p	h(p	PROPN
ejpam-4911	490	8	)	)	PUNCT
ejpam-4911	491	1	∩m	∩m	PROPN
ejpam-4911	491	2	̸=	̸=	PROPN
ejpam-4911	491	3	∅.	∅.	PRON
ejpam-4911	491	4	hence	hence	ADV
ejpam-4911	491	5	h(p	h(p	PROPN
ejpam-4911	491	6	)	)	PUNCT
ejpam-4911	491	7	∈	∈	PROPN
ejpam-4911	491	8	d(µ1	d(µ1	NOUN
ejpam-4911	491	9	)	)	PUNCT
ejpam-4911	491	10	in	in	ADP
ejpam-4911	491	11	y.	y.	PROPN
ejpam-4911	491	12	take	take	VERB
ejpam-4911	491	13	v	v	NOUN
ejpam-4911	491	14	=	=	SYM
ejpam-4911	491	15	2	2	NUM
ejpam-4911	491	16	.	.	PUNCT
ejpam-4911	491	17	then	then	ADV
ejpam-4911	491	18	by	by	ADP
ejpam-4911	491	19	similar	similar	ADJ
ejpam-4911	491	20	arguments	argument	NOUN
ejpam-4911	491	21	in	in	ADP
ejpam-4911	491	22	the	the	DET
ejpam-4911	491	23	above	above	ADJ
ejpam-4911	491	24	case	case	NOUN
ejpam-4911	491	25	,	,	PUNCT
ejpam-4911	491	26	we	we	PRON
ejpam-4911	491	27	get	get	VERB
ejpam-4911	491	28	h(p	h(p	PROPN
ejpam-4911	491	29	)	)	PUNCT
ejpam-4911	491	30	∈	∈	PROPN
ejpam-4911	491	31	d(µ2	d(µ2	NOUN
ejpam-4911	491	32	)	)	PUNCT
ejpam-4911	491	33	in	in	ADP
ejpam-4911	491	34	y.	y.	PROPN
ejpam-4911	491	35	hence	hence	ADV
ejpam-4911	491	36	h(p	h(p	PROPN
ejpam-4911	491	37	)	)	PUNCT
ejpam-4911	491	38	∈	∈	PROPN
ejpam-4911	491	39	d(µv	d(µv	PROPN
ejpam-4911	491	40	)	)	PUNCT
ejpam-4911	491	41	in	in	ADP
ejpam-4911	491	42	y	y	PROPN
ejpam-4911	491	43	where	where	SCONJ
ejpam-4911	491	44	v	v	NOUN
ejpam-4911	491	45	=	=	SYM
ejpam-4911	491	46	1	1	NUM
ejpam-4911	491	47	,	,	PUNCT
ejpam-4911	491	48	2	2	NUM
ejpam-4911	491	49	.	.	PUNCT
ejpam-4911	491	50	(	(	PUNCT
ejpam-4911	491	51	b	b	X
ejpam-4911	491	52	)	)	PUNCT
ejpam-4911	491	53	let	let	VERB
ejpam-4911	491	54	q	q	NOUN
ejpam-4911	491	55	be	be	AUX
ejpam-4911	491	56	a	a	DET
ejpam-4911	491	57	µv	µv	NOUN
ejpam-4911	491	58	-	-	PUNCT
ejpam-4911	491	59	codense	codense	NOUN
ejpam-4911	491	60	set	set	VERB
ejpam-4911	491	61	in	in	ADP
ejpam-4911	491	62	x	x	PUNCT
ejpam-4911	491	63	for	for	ADP
ejpam-4911	491	64	v	v	NOUN
ejpam-4911	491	65	=	=	SYM
ejpam-4911	491	66	1	1	NUM
ejpam-4911	491	67	,	,	PUNCT
ejpam-4911	491	68	2	2	NUM
ejpam-4911	491	69	.	.	PUNCT
ejpam-4911	492	1	then	then	ADV
ejpam-4911	492	2	x	x	PUNCT
ejpam-4911	492	3	−q	−q	PROPN
ejpam-4911	492	4	∈	∈	PROPN
ejpam-4911	492	5	d(µv	d(µv	PROPN
ejpam-4911	492	6	)	)	PUNCT
ejpam-4911	492	7	in	in	ADP
ejpam-4911	492	8	x	x	PUNCT
ejpam-4911	492	9	for	for	ADP
ejpam-4911	492	10	v	v	NOUN
ejpam-4911	492	11	=	=	SYM
ejpam-4911	492	12	1	1	NUM
ejpam-4911	492	13	,	,	PUNCT
ejpam-4911	492	14	2	2	NUM
ejpam-4911	492	15	.	.	PUNCT
ejpam-4911	493	1	by	by	ADP
ejpam-4911	493	2	(	(	PUNCT
ejpam-4911	493	3	a	a	X
ejpam-4911	493	4	)	)	PUNCT
ejpam-4911	493	5	,	,	PUNCT
ejpam-4911	493	6	h(x	h(x	PROPN
ejpam-4911	493	7	−	−	PROPN
ejpam-4911	493	8	q	q	NOUN
ejpam-4911	493	9	)	)	PUNCT
ejpam-4911	493	10	∈	∈	PROPN
ejpam-4911	493	11	(	(	PUNCT
ejpam-4911	493	12	s	s	PROPN
ejpam-4911	493	13	,	,	PUNCT
ejpam-4911	493	14	v	v	NOUN
ejpam-4911	493	15	)	)	PUNCT
ejpam-4911	493	16	−	−	PROPN
ejpam-4911	493	17	d(y	d(y	NOUN
ejpam-4911	493	18	)	)	PUNCT
ejpam-4911	493	19	where	where	SCONJ
ejpam-4911	493	20	s	s	X
ejpam-4911	493	21	,	,	PUNCT
ejpam-4911	493	22	v	v	NOUN
ejpam-4911	493	23	=	=	SYM
ejpam-4911	493	24	1	1	NUM
ejpam-4911	493	25	,	,	PUNCT
ejpam-4911	493	26	2	2	NUM
ejpam-4911	493	27	and	and	CCONJ
ejpam-4911	493	28	s	s	VERB
ejpam-4911	493	29	̸=	̸=	PROPN
ejpam-4911	493	30	v.	v.	ADV
ejpam-4911	493	31	since	since	SCONJ
ejpam-4911	493	32	h	h	PROPN
ejpam-4911	493	33	is	be	AUX
ejpam-4911	493	34	one	one	NUM
ejpam-4911	493	35	-	-	PUNCT
ejpam-4911	493	36	one	one	NUM
ejpam-4911	493	37	,	,	PUNCT
ejpam-4911	493	38	h(x)−h(q	h(x)−h(q	CCONJ
ejpam-4911	493	39	)	)	PUNCT
ejpam-4911	493	40	∈	∈	PROPN
ejpam-4911	493	41	(	(	PUNCT
ejpam-4911	493	42	s	s	PROPN
ejpam-4911	493	43	,	,	PUNCT
ejpam-4911	493	44	v)−d(y	v)−d(y	PROPN
ejpam-4911	493	45	)	)	PUNCT
ejpam-4911	493	46	where	where	SCONJ
ejpam-4911	493	47	s	s	X
ejpam-4911	493	48	,	,	PUNCT
ejpam-4911	493	49	v	v	NOUN
ejpam-4911	493	50	=	=	SYM
ejpam-4911	493	51	1	1	NUM
ejpam-4911	493	52	,	,	PUNCT
ejpam-4911	493	53	2	2	NUM
ejpam-4911	493	54	and	and	CCONJ
ejpam-4911	493	55	s	s	VERB
ejpam-4911	493	56	̸=	̸=	PROPN
ejpam-4911	493	57	v.	v.	CCONJ
ejpam-4911	493	58	therefore	therefore	ADV
ejpam-4911	493	59	,	,	PUNCT
ejpam-4911	493	60	y−h(q	y−h(q	NOUN
ejpam-4911	493	61	)	)	PUNCT
ejpam-4911	493	62	∈	∈	PROPN
ejpam-4911	493	63	(	(	PUNCT
ejpam-4911	493	64	s	s	PROPN
ejpam-4911	493	65	,	,	PUNCT
ejpam-4911	493	66	v)−d(y	v)−d(y	PROPN
ejpam-4911	493	67	)	)	PUNCT
ejpam-4911	493	68	where	where	SCONJ
ejpam-4911	493	69	s	s	X
ejpam-4911	493	70	,	,	PUNCT
ejpam-4911	493	71	v	v	NOUN
ejpam-4911	493	72	=	=	SYM
ejpam-4911	493	73	1	1	NUM
ejpam-4911	493	74	,	,	PUNCT
ejpam-4911	493	75	2	2	NUM
ejpam-4911	493	76	and	and	CCONJ
ejpam-4911	493	77	s	s	VERB
ejpam-4911	493	78	̸=	̸=	PROPN
ejpam-4911	493	79	v.	v.	ADP
ejpam-4911	493	80	hence	hence	ADV
ejpam-4911	493	81	h(q	h(q	ADV
ejpam-4911	493	82	)	)	PUNCT
ejpam-4911	493	83	is	be	AUX
ejpam-4911	493	84	(	(	PUNCT
ejpam-4911	493	85	s	s	X
ejpam-4911	493	86	,	,	PUNCT
ejpam-4911	493	87	v)-codense	v)-codense	ADJ
ejpam-4911	493	88	in	in	ADP
ejpam-4911	493	89	y	y	PROPN
ejpam-4911	493	90	where	where	SCONJ
ejpam-4911	493	91	s	s	X
ejpam-4911	493	92	,	,	PUNCT
ejpam-4911	493	93	v	v	NOUN
ejpam-4911	493	94	=	=	SYM
ejpam-4911	493	95	1	1	NUM
ejpam-4911	493	96	,	,	PUNCT
ejpam-4911	493	97	2	2	NUM
ejpam-4911	493	98	;	;	PUNCT
ejpam-4911	493	99	s	s	AUX
ejpam-4911	493	100	̸=	̸=	PROPN
ejpam-4911	493	101	v.	v.	ADP
ejpam-4911	493	102	theorem	theorem	VERB
ejpam-4911	493	103	38	38	NUM
ejpam-4911	493	104	.	.	PUNCT
ejpam-4911	494	1	let	let	VERB
ejpam-4911	494	2	(	(	PUNCT
ejpam-4911	494	3	x,µ1	x,µ1	NOUN
ejpam-4911	494	4	x	x	SYM
ejpam-4911	494	5	,	,	PUNCT
ejpam-4911	494	6	µ2	µ2	PROPN
ejpam-4911	494	7	x	x	X
ejpam-4911	494	8	)	)	PUNCT
ejpam-4911	494	9	and	and	CCONJ
ejpam-4911	494	10	(	(	PUNCT
ejpam-4911	494	11	y	y	PROPN
ejpam-4911	494	12	,	,	PUNCT
ejpam-4911	494	13	µ1	µ1	PROPN
ejpam-4911	494	14	y	y	PROPN
ejpam-4911	494	15	,	,	PUNCT
ejpam-4911	494	16	µ	µ	PROPN
ejpam-4911	494	17	2	2	NUM
ejpam-4911	494	18	y	y	NOUN
ejpam-4911	494	19	)	)	PUNCT
ejpam-4911	494	20	be	be	AUX
ejpam-4911	494	21	two	two	NUM
ejpam-4911	494	22	bigeneralized	bigeneralize	VERB
ejpam-4911	494	23	topological	topological	ADJ
ejpam-4911	494	24	spaces	space	NOUN
ejpam-4911	494	25	,	,	PUNCT
ejpam-4911	494	26	k	k	X
ejpam-4911	494	27	,	,	PUNCT
ejpam-4911	494	28	l	l	PROPN
ejpam-4911	494	29	⊂	⊂	PROPN
ejpam-4911	494	30	y	y	PROPN
ejpam-4911	494	31	,	,	PUNCT
ejpam-4911	494	32	h	h	NOUN
ejpam-4911	494	33	:	:	PUNCT
ejpam-4911	494	34	(	(	PUNCT
ejpam-4911	494	35	x,µ1	x,µ1	NOUN
ejpam-4911	494	36	x	x	SYM
ejpam-4911	494	37	,	,	PUNCT
ejpam-4911	494	38	µ2	µ2	PROPN
ejpam-4911	494	39	x	x	PRON
ejpam-4911	494	40	)	)	PUNCT
ejpam-4911	494	41	→	→	SYM
ejpam-4911	494	42	(	(	PUNCT
ejpam-4911	494	43	y	y	PROPN
ejpam-4911	494	44	,	,	PUNCT
ejpam-4911	494	45	µ1	µ1	PROPN
ejpam-4911	494	46	y	y	PROPN
ejpam-4911	494	47	,	,	PUNCT
ejpam-4911	494	48	µ	µ	PROPN
ejpam-4911	494	49	2	2	NUM
ejpam-4911	494	50	y	y	NOUN
ejpam-4911	494	51	)	)	PUNCT
ejpam-4911	494	52	be	be	AUX
ejpam-4911	494	53	a	a	DET
ejpam-4911	494	54	µs	µs	NOUN
ejpam-4911	494	55	-	-	ADJ
ejpam-4911	494	56	open	open	ADJ
ejpam-4911	494	57	,	,	PUNCT
ejpam-4911	494	58	one	one	NUM
ejpam-4911	494	59	-	-	PUNCT
ejpam-4911	494	60	one	one	NUM
ejpam-4911	494	61	function	function	NOUN
ejpam-4911	494	62	for	for	ADP
ejpam-4911	494	63	s	s	NOUN
ejpam-4911	494	64	=	=	SYM
ejpam-4911	494	65	1	1	NUM
ejpam-4911	494	66	,	,	PUNCT
ejpam-4911	494	67	2	2	NUM
ejpam-4911	494	68	.	.	PUNCT
ejpam-4911	495	1	then	then	ADV
ejpam-4911	495	2	the	the	DET
ejpam-4911	495	3	followings	following	NOUN
ejpam-4911	495	4	are	be	AUX
ejpam-4911	495	5	true	true	ADJ
ejpam-4911	495	6	.	.	PUNCT
ejpam-4911	496	1	(	(	PUNCT
ejpam-4911	496	2	a	a	X
ejpam-4911	496	3	)	)	PUNCT
ejpam-4911	496	4	if	if	SCONJ
ejpam-4911	496	5	k	k	PROPN
ejpam-4911	496	6	∈	∈	PROPN
ejpam-4911	496	7	d(µv	d(µv	PROPN
ejpam-4911	496	8	)	)	PUNCT
ejpam-4911	496	9	in	in	ADP
ejpam-4911	496	10	y	y	PROPN
ejpam-4911	496	11	,	,	PUNCT
ejpam-4911	496	12	then	then	ADV
ejpam-4911	496	13	h−1(k	h−1(k	PROPN
ejpam-4911	496	14	)	)	PUNCT
ejpam-4911	496	15	∈	∈	PROPN
ejpam-4911	496	16	(	(	PUNCT
ejpam-4911	496	17	s	s	NOUN
ejpam-4911	496	18	,	,	PUNCT
ejpam-4911	496	19	v)−d(x	v)−d(x	NUM
ejpam-4911	496	20	)	)	PUNCT
ejpam-4911	496	21	where	where	SCONJ
ejpam-4911	496	22	s	s	X
ejpam-4911	496	23	,	,	PUNCT
ejpam-4911	496	24	v	v	NOUN
ejpam-4911	496	25	=	=	SYM
ejpam-4911	496	26	1	1	NUM
ejpam-4911	496	27	,	,	PUNCT
ejpam-4911	496	28	2	2	NUM
ejpam-4911	496	29	and	and	CCONJ
ejpam-4911	496	30	s	s	VERB
ejpam-4911	496	31	̸=	̸=	PROPN
ejpam-4911	496	32	v.	v.	ADP
ejpam-4911	496	33	(	(	PUNCT
ejpam-4911	496	34	b	b	NOUN
ejpam-4911	496	35	)	)	PUNCT
ejpam-4911	496	36	if	if	SCONJ
ejpam-4911	496	37	l	l	NOUN
ejpam-4911	496	38	is	be	AUX
ejpam-4911	496	39	µv	µv	NOUN
ejpam-4911	496	40	-	-	PUNCT
ejpam-4911	496	41	codense	codense	NOUN
ejpam-4911	496	42	in	in	ADP
ejpam-4911	496	43	y	y	PROPN
ejpam-4911	496	44	,	,	PUNCT
ejpam-4911	496	45	then	then	ADV
ejpam-4911	496	46	h−1(l	h−1(l	PROPN
ejpam-4911	496	47	)	)	PUNCT
ejpam-4911	496	48	is	be	AUX
ejpam-4911	496	49	(	(	PUNCT
ejpam-4911	496	50	s	s	X
ejpam-4911	496	51	,	,	PUNCT
ejpam-4911	496	52	v)-codense	v)-codense	ADV
ejpam-4911	496	53	where	where	SCONJ
ejpam-4911	496	54	s	s	X
ejpam-4911	496	55	,	,	PUNCT
ejpam-4911	496	56	v	v	NOUN
ejpam-4911	496	57	=	=	SYM
ejpam-4911	496	58	1	1	NUM
ejpam-4911	496	59	,	,	PUNCT
ejpam-4911	496	60	2	2	NUM
ejpam-4911	496	61	and	and	CCONJ
ejpam-4911	496	62	s	s	VERB
ejpam-4911	496	63	̸=	̸=	PROPN
ejpam-4911	496	64	v.	v.	ADP
ejpam-4911	496	65	proof	proof	NOUN
ejpam-4911	496	66	.	.	PUNCT
ejpam-4911	497	1	the	the	DET
ejpam-4911	497	2	trivial	trivial	ADJ
ejpam-4911	497	3	proof	proof	NOUN
ejpam-4911	497	4	is	be	AUX
ejpam-4911	497	5	omitted	omit	VERB
ejpam-4911	497	6	.	.	PUNCT
ejpam-4911	498	1	6	6	X
ejpam-4911	498	2	.	.	PUNCT
ejpam-4911	498	3	(	(	PUNCT
ejpam-4911	498	4	s	s	X
ejpam-4911	498	5	,	,	PUNCT
ejpam-4911	498	6	v)-dense	v)-dense	VERB
ejpam-4911	498	7	sets	set	VERB
ejpam-4911	498	8	applications	application	NOUN
ejpam-4911	498	9	in	in	ADP
ejpam-4911	498	10	1999	1999	NUM
ejpam-4911	498	11	,	,	PUNCT
ejpam-4911	498	12	molodstov	molodstov	PROPN
ejpam-4911	498	13	introduced	introduce	VERB
ejpam-4911	498	14	a	a	DET
ejpam-4911	498	15	new	new	ADJ
ejpam-4911	498	16	mathematical	mathematical	ADJ
ejpam-4911	498	17	tool	tool	NOUN
ejpam-4911	498	18	namely	namely	ADV
ejpam-4911	498	19	,	,	PUNCT
ejpam-4911	498	20	soft	soft	ADJ
ejpam-4911	498	21	set	set	NOUN
ejpam-4911	498	22	theory	theory	NOUN
ejpam-4911	498	23	[	[	X
ejpam-4911	498	24	11	11	NUM
ejpam-4911	498	25	]	]	PUNCT
ejpam-4911	498	26	.	.	PUNCT
ejpam-4911	499	1	it	it	PRON
ejpam-4911	499	2	has	have	AUX
ejpam-4911	499	3	been	be	AUX
ejpam-4911	499	4	used	use	VERB
ejpam-4911	499	5	for	for	ADP
ejpam-4911	499	6	dealing	deal	VERB
ejpam-4911	499	7	with	with	ADP
ejpam-4911	499	8	uncertainty	uncertainty	NOUN
ejpam-4911	499	9	.	.	PUNCT
ejpam-4911	500	1	most	most	ADJ
ejpam-4911	500	2	of	of	ADP
ejpam-4911	500	3	the	the	DET
ejpam-4911	500	4	researchers	researcher	NOUN
ejpam-4911	500	5	presented	present	VERB
ejpam-4911	500	6	an	an	DET
ejpam-4911	500	7	application	application	NOUN
ejpam-4911	500	8	of	of	ADP
ejpam-4911	500	9	soft	soft	ADJ
ejpam-4911	500	10	sets	set	NOUN
ejpam-4911	500	11	in	in	ADP
ejpam-4911	500	12	decision	decision	NOUN
ejpam-4911	500	13	-	-	PUNCT
ejpam-4911	500	14	making	make	VERB
ejpam-4911	500	15	problems	problem	NOUN
ejpam-4911	500	16	.	.	PUNCT
ejpam-4911	501	1	motivated	motivate	VERB
ejpam-4911	501	2	,	,	PUNCT
ejpam-4911	501	3	by	by	ADP
ejpam-4911	501	4	this	this	PRON
ejpam-4911	501	5	we	we	PRON
ejpam-4911	501	6	try	try	VERB
ejpam-4911	501	7	to	to	PART
ejpam-4911	501	8	give	give	VERB
ejpam-4911	501	9	an	an	DET
ejpam-4911	501	10	example	example	NOUN
ejpam-4911	501	11	of	of	ADP
ejpam-4911	501	12	the	the	DET
ejpam-4911	501	13	soft	soft	ADJ
ejpam-4911	501	14	set	set	NOUN
ejpam-4911	501	15	using	use	VERB
ejpam-4911	501	16	(	(	PUNCT
ejpam-4911	501	17	s	s	NOUN
ejpam-4911	501	18	,	,	PUNCT
ejpam-4911	501	19	v)-dense	v)-dense	PUNCT
ejpam-4911	501	20	and	and	CCONJ
ejpam-4911	501	21	(	(	PUNCT
ejpam-4911	501	22	s	s	X
ejpam-4911	501	23	,	,	PUNCT
ejpam-4911	501	24	v)-nowhere	v)-nowhere	PUNCT
ejpam-4911	501	25	dense	dense	ADJ
ejpam-4911	501	26	sets	set	NOUN
ejpam-4911	501	27	in	in	ADP
ejpam-4911	501	28	a	a	DET
ejpam-4911	501	29	bigeneralized	bigeneralize	VERB
ejpam-4911	501	30	topological	topological	ADJ
ejpam-4911	501	31	space	space	NOUN
ejpam-4911	501	32	.	.	PUNCT
ejpam-4911	502	1	example	example	NOUN
ejpam-4911	502	2	39	39	NUM
ejpam-4911	502	3	.	.	PUNCT
ejpam-4911	503	1	consider	consider	VERB
ejpam-4911	503	2	the	the	DET
ejpam-4911	503	3	bgts	bgts	NOUN
ejpam-4911	503	4	(	(	PUNCT
ejpam-4911	503	5	x,µ1	x,µ1	PROPN
ejpam-4911	503	6	,	,	PUNCT
ejpam-4911	503	7	µ2	µ2	PROPN
ejpam-4911	503	8	)	)	PUNCT
ejpam-4911	503	9	where	where	SCONJ
ejpam-4911	503	10	x	x	X
ejpam-4911	503	11	=	=	PRON
ejpam-4911	503	12	{	{	PUNCT
ejpam-4911	503	13	a	a	PRON
ejpam-4911	503	14	,	,	PUNCT
ejpam-4911	503	15	b	b	NOUN
ejpam-4911	503	16	,	,	PUNCT
ejpam-4911	503	17	c	c	NOUN
ejpam-4911	503	18	,	,	PUNCT
ejpam-4911	503	19	d	d	NOUN
ejpam-4911	503	20	}	}	PUNCT
ejpam-4911	503	21	;	;	PUNCT
ejpam-4911	503	22	µ1	µ1	PROPN
ejpam-4911	503	23	=	=	SYM
ejpam-4911	503	24	{	{	PUNCT
ejpam-4911	503	25	∅	∅	NOUN
ejpam-4911	503	26	,	,	PUNCT
ejpam-4911	503	27	{	{	PUNCT
ejpam-4911	503	28	a	a	DET
ejpam-4911	503	29	,	,	PUNCT
ejpam-4911	503	30	b	b	NOUN
ejpam-4911	503	31	}	}	PUNCT
ejpam-4911	503	32	,	,	PUNCT
ejpam-4911	503	33	{	{	PUNCT
ejpam-4911	503	34	a	a	X
ejpam-4911	503	35	,	,	PUNCT
ejpam-4911	503	36	c	c	NOUN
ejpam-4911	503	37	}	}	PUNCT
ejpam-4911	503	38	,	,	PUNCT
ejpam-4911	503	39	{	{	PUNCT
ejpam-4911	503	40	a	a	PRON
ejpam-4911	503	41	,	,	PUNCT
ejpam-4911	503	42	d	d	NOUN
ejpam-4911	503	43	}	}	PUNCT
ejpam-4911	503	44	,	,	PUNCT
ejpam-4911	503	45	{	{	PUNCT
ejpam-4911	503	46	a	a	DET
ejpam-4911	503	47	,	,	PUNCT
ejpam-4911	503	48	b	b	NOUN
ejpam-4911	503	49	,	,	PUNCT
ejpam-4911	503	50	c	c	NOUN
ejpam-4911	503	51	}	}	PUNCT
ejpam-4911	503	52	,	,	PUNCT
ejpam-4911	503	53	{	{	PUNCT
ejpam-4911	503	54	a	a	DET
ejpam-4911	503	55	,	,	PUNCT
ejpam-4911	503	56	b	b	NOUN
ejpam-4911	503	57	,	,	PUNCT
ejpam-4911	503	58	d	d	NOUN
ejpam-4911	503	59	}	}	PUNCT
ejpam-4911	503	60	,	,	PUNCT
ejpam-4911	503	61	{	{	PUNCT
ejpam-4911	503	62	a	a	PRON
ejpam-4911	503	63	,	,	PUNCT
ejpam-4911	503	64	c	c	NOUN
ejpam-4911	503	65	,	,	PUNCT
ejpam-4911	503	66	d	d	NOUN
ejpam-4911	503	67	}	}	PUNCT
ejpam-4911	503	68	,	,	PUNCT
ejpam-4911	503	69	x	x	NOUN
ejpam-4911	503	70	}	}	PUNCT
ejpam-4911	503	71	;	;	PUNCT
ejpam-4911	503	72	and	and	CCONJ
ejpam-4911	503	73	µ2	µ2	PROPN
ejpam-4911	503	74	=	=	PUNCT
ejpam-4911	503	75	{	{	PUNCT
ejpam-4911	503	76	∅	∅	NOUN
ejpam-4911	503	77	,	,	PUNCT
ejpam-4911	503	78	{	{	PUNCT
ejpam-4911	503	79	b	b	NOUN
ejpam-4911	503	80	,	,	PUNCT
ejpam-4911	503	81	c	c	NOUN
ejpam-4911	503	82	}	}	PUNCT
ejpam-4911	503	83	,	,	PUNCT
ejpam-4911	503	84	{	{	PUNCT
ejpam-4911	503	85	b	b	X
ejpam-4911	503	86	,	,	PUNCT
ejpam-4911	503	87	d	d	NOUN
ejpam-4911	503	88	}	}	PUNCT
ejpam-4911	503	89	,	,	PUNCT
ejpam-4911	503	90	{	{	PUNCT
ejpam-4911	503	91	b	b	X
ejpam-4911	503	92	,	,	PUNCT
ejpam-4911	503	93	c	c	NOUN
ejpam-4911	503	94	,	,	PUNCT
ejpam-4911	503	95	d	d	NOUN
ejpam-4911	503	96	}	}	PUNCT
ejpam-4911	503	97	}	}	PUNCT
ejpam-4911	503	98	.	.	PUNCT
ejpam-4911	504	1	here	here	ADV
ejpam-4911	504	2	,	,	PUNCT
ejpam-4911	504	3	•	•	X
ejpam-4911	504	4	(	(	PUNCT
ejpam-4911	504	5	1	1	NUM
ejpam-4911	504	6	,	,	PUNCT
ejpam-4911	504	7	2)−d(x	2)−d(x	NUM
ejpam-4911	504	8	)	)	PUNCT
ejpam-4911	504	9	=	=	SYM
ejpam-4911	504	10	exp(x	exp(x	PROPN
ejpam-4911	504	11	)	)	PUNCT
ejpam-4911	504	12	where	where	SCONJ
ejpam-4911	504	13	exp(x	exp(x	PROPN
ejpam-4911	504	14	)	)	PUNCT
ejpam-4911	504	15	is	be	AUX
ejpam-4911	504	16	the	the	DET
ejpam-4911	504	17	power	power	NOUN
ejpam-4911	504	18	set	set	NOUN
ejpam-4911	504	19	of	of	ADP
ejpam-4911	504	20	x.	x.	PROPN
ejpam-4911	504	21	•	•	PROPN
ejpam-4911	504	22	(	(	PUNCT
ejpam-4911	504	23	2	2	NUM
ejpam-4911	504	24	,	,	PUNCT
ejpam-4911	504	25	1)−d(x	1)−d(x	NUM
ejpam-4911	504	26	)	)	PUNCT
ejpam-4911	504	27	=	=	PRON
ejpam-4911	504	28	{	{	PUNCT
ejpam-4911	504	29	{	{	PUNCT
ejpam-4911	504	30	a	a	NOUN
ejpam-4911	504	31	}	}	PUNCT
ejpam-4911	504	32	,	,	PUNCT
ejpam-4911	504	33	{	{	PUNCT
ejpam-4911	504	34	b	b	NOUN
ejpam-4911	504	35	}	}	PUNCT
ejpam-4911	504	36	,	,	PUNCT
ejpam-4911	504	37	{	{	PUNCT
ejpam-4911	504	38	a	a	DET
ejpam-4911	504	39	,	,	PUNCT
ejpam-4911	504	40	b	b	NOUN
ejpam-4911	504	41	}	}	PUNCT
ejpam-4911	504	42	,	,	PUNCT
ejpam-4911	504	43	{	{	PUNCT
ejpam-4911	504	44	a	a	X
ejpam-4911	504	45	,	,	PUNCT
ejpam-4911	504	46	c	c	NOUN
ejpam-4911	504	47	}	}	PUNCT
ejpam-4911	504	48	,	,	PUNCT
ejpam-4911	504	49	{	{	PUNCT
ejpam-4911	504	50	a	a	DET
ejpam-4911	504	51	,	,	PUNCT
ejpam-4911	504	52	d	d	NOUN
ejpam-4911	504	53	}	}	PUNCT
ejpam-4911	504	54	,	,	PUNCT
ejpam-4911	504	55	{	{	PUNCT
ejpam-4911	504	56	b	b	X
ejpam-4911	504	57	,	,	PUNCT
ejpam-4911	504	58	c	c	NOUN
ejpam-4911	504	59	}	}	PUNCT
ejpam-4911	504	60	,	,	PUNCT
ejpam-4911	504	61	{	{	PUNCT
ejpam-4911	504	62	b	b	X
ejpam-4911	504	63	,	,	PUNCT
ejpam-4911	504	64	d	d	NOUN
ejpam-4911	504	65	}	}	PUNCT
ejpam-4911	504	66	,	,	PUNCT
ejpam-4911	504	67	{	{	PUNCT
ejpam-4911	504	68	a	a	DET
ejpam-4911	504	69	,	,	PUNCT
ejpam-4911	504	70	b	b	NOUN
ejpam-4911	504	71	,	,	PUNCT
ejpam-4911	504	72	c	c	NOUN
ejpam-4911	504	73	}	}	PUNCT
ejpam-4911	504	74	,	,	PUNCT
ejpam-4911	504	75	{	{	PUNCT
ejpam-4911	504	76	a	a	DET
ejpam-4911	504	77	,	,	PUNCT
ejpam-4911	504	78	b	b	NOUN
ejpam-4911	504	79	,	,	PUNCT
ejpam-4911	504	80	d	d	NOUN
ejpam-4911	504	81	}	}	PUNCT
ejpam-4911	504	82	,	,	PUNCT
ejpam-4911	504	83	{	{	PUNCT
ejpam-4911	504	84	a	a	PRON
ejpam-4911	504	85	,	,	PUNCT
ejpam-4911	504	86	c	c	NOUN
ejpam-4911	504	87	,	,	PUNCT
ejpam-4911	504	88	d	d	NOUN
ejpam-4911	504	89	}	}	PUNCT
ejpam-4911	504	90	,	,	PUNCT
ejpam-4911	504	91	{	{	PUNCT
ejpam-4911	504	92	b	b	X
ejpam-4911	504	93	,	,	PUNCT
ejpam-4911	504	94	c	c	NOUN
ejpam-4911	504	95	,	,	PUNCT
ejpam-4911	504	96	d	d	NOUN
ejpam-4911	504	97	}	}	PUNCT
ejpam-4911	504	98	,	,	PUNCT
ejpam-4911	504	99	x	x	NOUN
ejpam-4911	504	100	}	}	PUNCT
ejpam-4911	504	101	.	.	PUNCT
ejpam-4911	505	1	let	let	VERB
ejpam-4911	505	2	u	u	PRON
ejpam-4911	505	3	=	=	X
ejpam-4911	505	4	{	{	PUNCT
ejpam-4911	505	5	a	a	X
ejpam-4911	505	6	,	,	PUNCT
ejpam-4911	505	7	c	c	AUX
ejpam-4911	505	8	}	}	PUNCT
ejpam-4911	505	9	be	be	AUX
ejpam-4911	505	10	a	a	DET
ejpam-4911	505	11	subset	subset	NOUN
ejpam-4911	505	12	of	of	ADP
ejpam-4911	505	13	x	x	PUNCT
ejpam-4911	505	14	and	and	CCONJ
ejpam-4911	505	15	e	e	X
ejpam-4911	505	16	=	=	PRON
ejpam-4911	505	17	{	{	PUNCT
ejpam-4911	505	18	(	(	PUNCT
ejpam-4911	505	19	1	1	NUM
ejpam-4911	505	20	,	,	PUNCT
ejpam-4911	505	21	2)-dense	2)-dense	NUM
ejpam-4911	505	22	set	set	NOUN
ejpam-4911	505	23	,	,	PUNCT
ejpam-4911	505	24	(	(	PUNCT
ejpam-4911	505	25	2	2	NUM
ejpam-4911	505	26	,	,	PUNCT
ejpam-4911	505	27	1)-dense	1)-dense	NUM
ejpam-4911	505	28	set	set	NOUN
ejpam-4911	505	29	,	,	PUNCT
ejpam-4911	505	30	both	both	PRON
ejpam-4911	505	31	}	}	PUNCT
ejpam-4911	505	32	=	=	SYM
ejpam-4911	505	33	{	{	PUNCT
ejpam-4911	505	34	e1	e1	PROPN
ejpam-4911	505	35	,	,	PUNCT
ejpam-4911	505	36	e2	e2	PROPN
ejpam-4911	505	37	,	,	PUNCT
ejpam-4911	505	38	e3	e3	PROPN
ejpam-4911	505	39	}	}	PUNCT
ejpam-4911	505	40	is	be	AUX
ejpam-4911	505	41	the	the	DET
ejpam-4911	505	42	set	set	NOUN
ejpam-4911	505	43	of	of	ADP
ejpam-4911	505	44	parameters	parameter	NOUN
ejpam-4911	505	45	.	.	PUNCT
ejpam-4911	506	1	define	define	VERB
ejpam-4911	506	2	a	a	DET
ejpam-4911	506	3	map	map	NOUN
ejpam-4911	506	4	f	f	NOUN
ejpam-4911	506	5	from	from	ADP
ejpam-4911	506	6	e	e	PROPN
ejpam-4911	506	7	to	to	ADP
ejpam-4911	506	8	exp(u	exp(u	PROPN
ejpam-4911	506	9	)	)	PUNCT
ejpam-4911	506	10	by	by	ADP
ejpam-4911	506	11	,	,	PUNCT
ejpam-4911	506	12	f	f	PROPN
ejpam-4911	506	13	(	(	PUNCT
ejpam-4911	506	14	e1	e1	PROPN
ejpam-4911	506	15	)	)	PUNCT
ejpam-4911	506	16	=	=	PRON
ejpam-4911	506	17	{	{	PUNCT
ejpam-4911	506	18	c};f	c};f	X
ejpam-4911	506	19	(	(	PUNCT
ejpam-4911	506	20	e2	e2	PROPN
ejpam-4911	506	21	)	)	PUNCT
ejpam-4911	506	22	=	=	PRON
ejpam-4911	506	23	{	{	PUNCT
ejpam-4911	506	24	a};f	a};f	VERB
ejpam-4911	506	25	(	(	PUNCT
ejpam-4911	506	26	e3	e3	NOUN
ejpam-4911	506	27	)	)	PUNCT
ejpam-4911	506	28	=	=	PRON
ejpam-4911	506	29	{	{	PUNCT
ejpam-4911	506	30	a	a	X
ejpam-4911	506	31	,	,	PUNCT
ejpam-4911	506	32	c	c	NOUN
ejpam-4911	506	33	}	}	PUNCT
ejpam-4911	506	34	.	.	PUNCT
ejpam-4911	507	1	then	then	ADV
ejpam-4911	507	2	the	the	DET
ejpam-4911	507	3	pair	pair	NOUN
ejpam-4911	507	4	(	(	PUNCT
ejpam-4911	507	5	f	f	X
ejpam-4911	507	6	,	,	PUNCT
ejpam-4911	507	7	e	e	NOUN
ejpam-4911	507	8	)	)	PUNCT
ejpam-4911	507	9	is	be	AUX
ejpam-4911	507	10	a	a	DET
ejpam-4911	507	11	soft	soft	ADJ
ejpam-4911	507	12	set	set	NOUN
ejpam-4911	507	13	over	over	ADP
ejpam-4911	507	14	u.	u.	NOUN
ejpam-4911	507	15	example	example	NOUN
ejpam-4911	507	16	40	40	NUM
ejpam-4911	507	17	.	.	PUNCT
ejpam-4911	508	1	consider	consider	VERB
ejpam-4911	508	2	the	the	DET
ejpam-4911	508	3	bigeneralized	bigeneralized	ADJ
ejpam-4911	508	4	topological	topological	ADJ
ejpam-4911	508	5	space	space	NOUN
ejpam-4911	508	6	(	(	PUNCT
ejpam-4911	508	7	x,µ1	x,µ1	PROPN
ejpam-4911	508	8	,	,	PUNCT
ejpam-4911	508	9	µ2	µ2	ADJ
ejpam-4911	508	10	)	)	PUNCT
ejpam-4911	508	11	wherex	wherex	PROPN
ejpam-4911	508	12	=	=	PUNCT
ejpam-4911	508	13	{	{	PUNCT
ejpam-4911	508	14	a	a	PRON
ejpam-4911	508	15	,	,	PUNCT
ejpam-4911	508	16	b	b	NOUN
ejpam-4911	508	17	,	,	PUNCT
ejpam-4911	508	18	c	c	NOUN
ejpam-4911	508	19	,	,	PUNCT
ejpam-4911	508	20	d	d	NOUN
ejpam-4911	508	21	}	}	PUNCT
ejpam-4911	508	22	;	;	PUNCT
ejpam-4911	508	23	µ1	µ1	PROPN
ejpam-4911	508	24	=	=	SYM
ejpam-4911	508	25	{	{	PUNCT
ejpam-4911	508	26	∅	∅	NOUN
ejpam-4911	508	27	,	,	PUNCT
ejpam-4911	508	28	{	{	PUNCT
ejpam-4911	508	29	b	b	NOUN
ejpam-4911	508	30	}	}	PUNCT
ejpam-4911	508	31	,	,	PUNCT
ejpam-4911	508	32	{	{	PUNCT
ejpam-4911	508	33	a	a	DET
ejpam-4911	508	34	,	,	PUNCT
ejpam-4911	508	35	b	b	NOUN
ejpam-4911	508	36	}	}	PUNCT
ejpam-4911	508	37	,	,	PUNCT
ejpam-4911	508	38	{	{	PUNCT
ejpam-4911	508	39	a	a	X
ejpam-4911	508	40	,	,	PUNCT
ejpam-4911	508	41	c	c	NOUN
ejpam-4911	508	42	}	}	PUNCT
ejpam-4911	508	43	,	,	PUNCT
ejpam-4911	508	44	{	{	PUNCT
ejpam-4911	508	45	a	a	PRON
ejpam-4911	508	46	,	,	PUNCT
ejpam-4911	508	47	b	b	NOUN
ejpam-4911	508	48	,	,	PUNCT
ejpam-4911	508	49	c	c	NOUN
ejpam-4911	508	50	}	}	PUNCT
ejpam-4911	508	51	}	}	PUNCT
ejpam-4911	508	52	y.	y.	PROPN
ejpam-4911	508	53	farhat	farhat	PROPN
ejpam-4911	508	54	,	,	PUNCT
ejpam-4911	508	55	v.	v.	ADP
ejpam-4911	508	56	subramanian	subramanian	PROPN
ejpam-4911	508	57	/	/	SYM
ejpam-4911	508	58	eur	eur	PROPN
ejpam-4911	508	59	.	.	PUNCT
ejpam-4911	509	1	j.	j.	PROPN
ejpam-4911	509	2	pure	pure	PROPN
ejpam-4911	509	3	appl	appl	PROPN
ejpam-4911	509	4	.	.	PROPN
ejpam-4911	509	5	math	math	PROPN
ejpam-4911	509	6	,	,	PUNCT
ejpam-4911	509	7	16	16	NUM
ejpam-4911	509	8	(	(	PUNCT
ejpam-4911	509	9	4	4	NUM
ejpam-4911	509	10	)	)	PUNCT
ejpam-4911	509	11	(	(	PUNCT
ejpam-4911	509	12	2023	2023	NUM
ejpam-4911	509	13	)	)	PUNCT
ejpam-4911	509	14	,	,	PUNCT
ejpam-4911	509	15	2049	2049	NUM
ejpam-4911	509	16	-	-	SYM
ejpam-4911	509	17	2065	2065	NUM
ejpam-4911	509	18	2064	2064	NUM
ejpam-4911	509	19	and	and	CCONJ
ejpam-4911	509	20	µ2	µ2	PROPN
ejpam-4911	509	21	=	=	PUNCT
ejpam-4911	509	22	{	{	PUNCT
ejpam-4911	509	23	∅	∅	NOUN
ejpam-4911	509	24	,	,	PUNCT
ejpam-4911	509	25	{	{	PUNCT
ejpam-4911	509	26	a	a	X
ejpam-4911	509	27	}	}	PUNCT
ejpam-4911	509	28	,	,	PUNCT
ejpam-4911	509	29	{	{	PUNCT
ejpam-4911	509	30	a	a	X
ejpam-4911	509	31	,	,	PUNCT
ejpam-4911	509	32	c	c	NOUN
ejpam-4911	509	33	}	}	PUNCT
ejpam-4911	509	34	,	,	PUNCT
ejpam-4911	509	35	{	{	PUNCT
ejpam-4911	509	36	b	b	X
ejpam-4911	509	37	,	,	PUNCT
ejpam-4911	509	38	c	c	NOUN
ejpam-4911	509	39	}	}	PUNCT
ejpam-4911	509	40	,	,	PUNCT
ejpam-4911	509	41	{	{	PUNCT
ejpam-4911	509	42	a	a	PRON
ejpam-4911	509	43	,	,	PUNCT
ejpam-4911	509	44	b	b	NOUN
ejpam-4911	509	45	,	,	PUNCT
ejpam-4911	509	46	c	c	NOUN
ejpam-4911	509	47	}	}	PUNCT
ejpam-4911	509	48	}	}	PUNCT
ejpam-4911	509	49	.	.	PUNCT
ejpam-4911	510	1	here	here	ADV
ejpam-4911	510	2	,	,	PUNCT
ejpam-4911	510	3	•	•	X
ejpam-4911	510	4	(	(	PUNCT
ejpam-4911	510	5	1	1	NUM
ejpam-4911	510	6	,	,	PUNCT
ejpam-4911	510	7	2)−n	2)−n	NUM
ejpam-4911	510	8	(	(	PUNCT
ejpam-4911	510	9	x	x	X
ejpam-4911	510	10	)	)	PUNCT
ejpam-4911	510	11	=	=	SYM
ejpam-4911	510	12	{	{	PUNCT
ejpam-4911	510	13	∅	∅	NOUN
ejpam-4911	510	14	,	,	PUNCT
ejpam-4911	510	15	{	{	PUNCT
ejpam-4911	510	16	a	a	X
ejpam-4911	510	17	}	}	PUNCT
ejpam-4911	510	18	,	,	PUNCT
ejpam-4911	510	19	{	{	PUNCT
ejpam-4911	510	20	d	d	NOUN
ejpam-4911	510	21	}	}	PUNCT
ejpam-4911	510	22	,	,	PUNCT
ejpam-4911	510	23	{	{	PUNCT
ejpam-4911	510	24	a	a	PRON
ejpam-4911	510	25	,	,	PUNCT
ejpam-4911	510	26	d	d	NOUN
ejpam-4911	510	27	}	}	PUNCT
ejpam-4911	510	28	}	}	PUNCT
ejpam-4911	510	29	;	;	PUNCT
ejpam-4911	510	30	•	•	X
ejpam-4911	510	31	(	(	PUNCT
ejpam-4911	510	32	2	2	NUM
ejpam-4911	510	33	,	,	PUNCT
ejpam-4911	510	34	1)−n	1)−n	NUM
ejpam-4911	510	35	(	(	PUNCT
ejpam-4911	510	36	x	x	X
ejpam-4911	510	37	)	)	PUNCT
ejpam-4911	510	38	=	=	SYM
ejpam-4911	510	39	{	{	PUNCT
ejpam-4911	510	40	∅	∅	NOUN
ejpam-4911	510	41	,	,	PUNCT
ejpam-4911	510	42	{	{	PUNCT
ejpam-4911	510	43	b	b	NOUN
ejpam-4911	510	44	}	}	PUNCT
ejpam-4911	510	45	,	,	PUNCT
ejpam-4911	510	46	{	{	PUNCT
ejpam-4911	510	47	c	c	X
ejpam-4911	510	48	}	}	PUNCT
ejpam-4911	510	49	,	,	PUNCT
ejpam-4911	510	50	{	{	PUNCT
ejpam-4911	510	51	d	d	X
ejpam-4911	510	52	}	}	PUNCT
ejpam-4911	510	53	,	,	PUNCT
ejpam-4911	510	54	{	{	PUNCT
ejpam-4911	510	55	b	b	X
ejpam-4911	510	56	,	,	PUNCT
ejpam-4911	510	57	d	d	NOUN
ejpam-4911	510	58	}	}	PUNCT
ejpam-4911	510	59	,	,	PUNCT
ejpam-4911	510	60	{	{	PUNCT
ejpam-4911	510	61	c	c	X
ejpam-4911	510	62	,	,	PUNCT
ejpam-4911	510	63	d	d	NOUN
ejpam-4911	510	64	}	}	PUNCT
ejpam-4911	510	65	}	}	PUNCT
ejpam-4911	510	66	.	.	PUNCT
ejpam-4911	511	1	let	let	VERB
ejpam-4911	511	2	u	u	PRON
ejpam-4911	511	3	=	=	X
ejpam-4911	511	4	{	{	PUNCT
ejpam-4911	511	5	a	a	X
ejpam-4911	511	6	,	,	PUNCT
ejpam-4911	511	7	c	c	NOUN
ejpam-4911	511	8	,	,	PUNCT
ejpam-4911	511	9	d	d	AUX
ejpam-4911	511	10	}	}	PUNCT
ejpam-4911	511	11	be	be	AUX
ejpam-4911	511	12	a	a	DET
ejpam-4911	511	13	subset	subset	NOUN
ejpam-4911	511	14	of	of	ADP
ejpam-4911	511	15	x	x	PUNCT
ejpam-4911	511	16	and	and	CCONJ
ejpam-4911	511	17	e	e	X
ejpam-4911	511	18	=	=	PRON
ejpam-4911	511	19	{	{	PUNCT
ejpam-4911	511	20	(	(	PUNCT
ejpam-4911	511	21	1	1	NUM
ejpam-4911	511	22	,	,	PUNCT
ejpam-4911	511	23	2)-nowhere	2)-nowhere	NUM
ejpam-4911	511	24	dense	dense	ADJ
ejpam-4911	511	25	set	set	NOUN
ejpam-4911	511	26	,	,	PUNCT
ejpam-4911	511	27	(	(	PUNCT
ejpam-4911	511	28	2	2	NUM
ejpam-4911	511	29	,	,	PUNCT
ejpam-4911	511	30	1)-nowhere	1)-nowhere	NUM
ejpam-4911	511	31	dense	dense	ADJ
ejpam-4911	511	32	set	set	NOUN
ejpam-4911	511	33	,	,	PUNCT
ejpam-4911	511	34	both	both	PRON
ejpam-4911	511	35	}	}	PUNCT
ejpam-4911	511	36	=	=	SYM
ejpam-4911	511	37	{	{	PUNCT
ejpam-4911	511	38	e1	e1	PROPN
ejpam-4911	511	39	,	,	PUNCT
ejpam-4911	511	40	e2	e2	PROPN
ejpam-4911	511	41	,	,	PUNCT
ejpam-4911	511	42	e3	e3	PROPN
ejpam-4911	511	43	}	}	PUNCT
ejpam-4911	511	44	is	be	AUX
ejpam-4911	511	45	the	the	DET
ejpam-4911	511	46	set	set	NOUN
ejpam-4911	511	47	of	of	ADP
ejpam-4911	511	48	parameters	parameter	NOUN
ejpam-4911	511	49	.	.	PUNCT
ejpam-4911	512	1	consider	consider	VERB
ejpam-4911	512	2	the	the	DET
ejpam-4911	512	3	map	map	NOUN
ejpam-4911	512	4	f	f	PROPN
ejpam-4911	512	5	from	from	ADP
ejpam-4911	512	6	e	e	PROPN
ejpam-4911	512	7	into	into	ADP
ejpam-4911	512	8	the	the	DET
ejpam-4911	512	9	power	power	NOUN
ejpam-4911	512	10	set	set	NOUN
ejpam-4911	512	11	of	of	ADP
ejpam-4911	512	12	u.	u.	PROPN
ejpam-4911	512	13	defined	define	VERB
ejpam-4911	512	14	by	by	ADP
ejpam-4911	512	15	f	f	PROPN
ejpam-4911	512	16	(	(	PUNCT
ejpam-4911	512	17	e1	e1	PROPN
ejpam-4911	512	18	)	)	PUNCT
ejpam-4911	512	19	=	=	PRON
ejpam-4911	512	20	{	{	PUNCT
ejpam-4911	512	21	a};f	a};f	VERB
ejpam-4911	512	22	(	(	PUNCT
ejpam-4911	512	23	e2	e2	PROPN
ejpam-4911	512	24	)	)	PUNCT
ejpam-4911	512	25	=	=	PRON
ejpam-4911	512	26	{	{	PUNCT
ejpam-4911	512	27	c};f	c};f	X
ejpam-4911	512	28	(	(	PUNCT
ejpam-4911	512	29	e3	e3	NOUN
ejpam-4911	512	30	)	)	PUNCT
ejpam-4911	512	31	=	=	PRON
ejpam-4911	513	1	{	{	PUNCT
ejpam-4911	513	2	d	d	NOUN
ejpam-4911	513	3	}	}	PUNCT
ejpam-4911	513	4	.	.	PUNCT
ejpam-4911	514	1	then	then	ADV
ejpam-4911	514	2	(	(	PUNCT
ejpam-4911	514	3	f	f	X
ejpam-4911	514	4	,	,	PUNCT
ejpam-4911	514	5	e	e	NOUN
ejpam-4911	514	6	)	)	PUNCT
ejpam-4911	514	7	is	be	AUX
ejpam-4911	514	8	a	a	DET
ejpam-4911	514	9	soft	soft	ADJ
ejpam-4911	514	10	set	set	NOUN
ejpam-4911	514	11	over	over	ADP
ejpam-4911	514	12	u.	u.	PROPN
ejpam-4911	514	13	example	example	NOUN
ejpam-4911	514	14	41	41	NUM
ejpam-4911	514	15	.	.	PUNCT
ejpam-4911	515	1	consider	consider	VERB
ejpam-4911	515	2	the	the	DET
ejpam-4911	515	3	bigeneralized	bigeneralized	ADJ
ejpam-4911	515	4	topological	topological	ADJ
ejpam-4911	515	5	space	space	NOUN
ejpam-4911	515	6	(	(	PUNCT
ejpam-4911	515	7	x,µ1	x,µ1	PROPN
ejpam-4911	515	8	,	,	PUNCT
ejpam-4911	515	9	µ2	µ2	ADJ
ejpam-4911	515	10	)	)	PUNCT
ejpam-4911	515	11	wherex	wherex	PROPN
ejpam-4911	515	12	=	=	PUNCT
ejpam-4911	515	13	{	{	PUNCT
ejpam-4911	515	14	a	a	PRON
ejpam-4911	515	15	,	,	PUNCT
ejpam-4911	515	16	b	b	NOUN
ejpam-4911	515	17	,	,	PUNCT
ejpam-4911	515	18	c	c	NOUN
ejpam-4911	515	19	,	,	PUNCT
ejpam-4911	515	20	d	d	NOUN
ejpam-4911	515	21	}	}	PUNCT
ejpam-4911	515	22	;	;	PUNCT
ejpam-4911	515	23	µ1	µ1	PROPN
ejpam-4911	515	24	=	=	SYM
ejpam-4911	515	25	{	{	PUNCT
ejpam-4911	515	26	∅	∅	NOUN
ejpam-4911	515	27	,	,	PUNCT
ejpam-4911	515	28	{	{	PUNCT
ejpam-4911	515	29	a	a	X
ejpam-4911	515	30	}	}	PUNCT
ejpam-4911	515	31	,	,	PUNCT
ejpam-4911	515	32	{	{	PUNCT
ejpam-4911	515	33	a	a	PRON
ejpam-4911	515	34	,	,	PUNCT
ejpam-4911	515	35	d	d	NOUN
ejpam-4911	515	36	}	}	PUNCT
ejpam-4911	515	37	,	,	PUNCT
ejpam-4911	515	38	{	{	PUNCT
ejpam-4911	515	39	c	c	X
ejpam-4911	515	40	,	,	PUNCT
ejpam-4911	515	41	d	d	NOUN
ejpam-4911	515	42	}	}	PUNCT
ejpam-4911	515	43	,	,	PUNCT
ejpam-4911	515	44	{	{	PUNCT
ejpam-4911	515	45	a	a	PRON
ejpam-4911	515	46	,	,	PUNCT
ejpam-4911	515	47	c	c	NOUN
ejpam-4911	515	48	,	,	PUNCT
ejpam-4911	515	49	d	d	NOUN
ejpam-4911	515	50	}	}	PUNCT
ejpam-4911	515	51	}	}	PUNCT
ejpam-4911	515	52	and	and	CCONJ
ejpam-4911	515	53	µ2	µ2	PROPN
ejpam-4911	515	54	=	=	PUNCT
ejpam-4911	515	55	{	{	PUNCT
ejpam-4911	515	56	∅	∅	NOUN
ejpam-4911	515	57	,	,	PUNCT
ejpam-4911	515	58	{	{	PUNCT
ejpam-4911	515	59	c	c	NOUN
ejpam-4911	515	60	}	}	PUNCT
ejpam-4911	515	61	,	,	PUNCT
ejpam-4911	515	62	{	{	PUNCT
ejpam-4911	515	63	a	a	PRON
ejpam-4911	515	64	,	,	PUNCT
ejpam-4911	515	65	b	b	NOUN
ejpam-4911	515	66	}	}	PUNCT
ejpam-4911	515	67	,	,	PUNCT
ejpam-4911	515	68	{	{	PUNCT
ejpam-4911	515	69	a	a	X
ejpam-4911	515	70	,	,	PUNCT
ejpam-4911	515	71	c	c	NOUN
ejpam-4911	515	72	}	}	PUNCT
ejpam-4911	515	73	,	,	PUNCT
ejpam-4911	515	74	{	{	PUNCT
ejpam-4911	515	75	b	b	X
ejpam-4911	515	76	,	,	PUNCT
ejpam-4911	515	77	c	c	NOUN
ejpam-4911	515	78	}	}	PUNCT
ejpam-4911	515	79	,	,	PUNCT
ejpam-4911	515	80	{	{	PUNCT
ejpam-4911	515	81	a	a	PRON
ejpam-4911	515	82	,	,	PUNCT
ejpam-4911	515	83	b	b	NOUN
ejpam-4911	515	84	,	,	PUNCT
ejpam-4911	515	85	c	c	NOUN
ejpam-4911	515	86	}	}	PUNCT
ejpam-4911	515	87	}	}	PUNCT
ejpam-4911	515	88	.	.	PUNCT
ejpam-4911	516	1	here	here	ADV
ejpam-4911	516	2	,	,	PUNCT
ejpam-4911	516	3	•	•	X
ejpam-4911	516	4	(	(	PUNCT
ejpam-4911	516	5	1	1	NUM
ejpam-4911	516	6	,	,	PUNCT
ejpam-4911	516	7	2)-codense	2)-codense	NUM
ejpam-4911	516	8	sets	set	NOUN
ejpam-4911	516	9	=	=	PRON
ejpam-4911	516	10	{	{	PUNCT
ejpam-4911	516	11	∅	∅	NOUN
ejpam-4911	516	12	,	,	PUNCT
ejpam-4911	516	13	{	{	PUNCT
ejpam-4911	516	14	a	a	X
ejpam-4911	516	15	}	}	PUNCT
ejpam-4911	516	16	,	,	PUNCT
ejpam-4911	516	17	{	{	PUNCT
ejpam-4911	516	18	b	b	NOUN
ejpam-4911	516	19	}	}	PUNCT
ejpam-4911	516	20	,	,	PUNCT
ejpam-4911	516	21	{	{	PUNCT
ejpam-4911	516	22	c	c	X
ejpam-4911	516	23	}	}	PUNCT
ejpam-4911	516	24	,	,	PUNCT
ejpam-4911	516	25	{	{	PUNCT
ejpam-4911	516	26	d	d	X
ejpam-4911	516	27	}	}	PUNCT
ejpam-4911	516	28	,	,	PUNCT
ejpam-4911	516	29	{	{	PUNCT
ejpam-4911	516	30	a	a	DET
ejpam-4911	516	31	,	,	PUNCT
ejpam-4911	516	32	d	d	NOUN
ejpam-4911	516	33	}	}	PUNCT
ejpam-4911	516	34	,	,	PUNCT
ejpam-4911	516	35	{	{	PUNCT
ejpam-4911	516	36	b	b	X
ejpam-4911	516	37	,	,	PUNCT
ejpam-4911	516	38	c	c	NOUN
ejpam-4911	516	39	}	}	PUNCT
ejpam-4911	516	40	,	,	PUNCT
ejpam-4911	516	41	{	{	PUNCT
ejpam-4911	516	42	b	b	X
ejpam-4911	516	43	,	,	PUNCT
ejpam-4911	516	44	d	d	NOUN
ejpam-4911	516	45	}	}	PUNCT
ejpam-4911	516	46	,	,	PUNCT
ejpam-4911	516	47	{	{	PUNCT
ejpam-4911	516	48	c	c	X
ejpam-4911	516	49	,	,	PUNCT
ejpam-4911	516	50	d	d	NOUN
ejpam-4911	516	51	}	}	PUNCT
ejpam-4911	516	52	,	,	PUNCT
ejpam-4911	516	53	{	{	PUNCT
ejpam-4911	516	54	b	b	X
ejpam-4911	516	55	,	,	PUNCT
ejpam-4911	516	56	c	c	NOUN
ejpam-4911	516	57	,	,	PUNCT
ejpam-4911	516	58	d	d	NOUN
ejpam-4911	516	59	}	}	PUNCT
ejpam-4911	516	60	}	}	PUNCT
ejpam-4911	516	61	.	.	PUNCT
ejpam-4911	517	1	•	•	NOUN
ejpam-4911	517	2	(	(	PUNCT
ejpam-4911	517	3	2	2	NUM
ejpam-4911	517	4	,	,	PUNCT
ejpam-4911	517	5	1)-codense	1)-codense	NUM
ejpam-4911	517	6	sets	set	NOUN
ejpam-4911	517	7	=	=	SYM
ejpam-4911	517	8	{	{	PUNCT
ejpam-4911	517	9	∅	∅	NOUN
ejpam-4911	517	10	,	,	PUNCT
ejpam-4911	517	11	{	{	PUNCT
ejpam-4911	517	12	a	a	X
ejpam-4911	517	13	}	}	PUNCT
ejpam-4911	517	14	,	,	PUNCT
ejpam-4911	517	15	{	{	PUNCT
ejpam-4911	517	16	b	b	NOUN
ejpam-4911	517	17	}	}	PUNCT
ejpam-4911	517	18	,	,	PUNCT
ejpam-4911	517	19	{	{	PUNCT
ejpam-4911	517	20	c	c	X
ejpam-4911	517	21	}	}	PUNCT
ejpam-4911	517	22	,	,	PUNCT
ejpam-4911	517	23	{	{	PUNCT
ejpam-4911	517	24	d	d	X
ejpam-4911	517	25	}	}	PUNCT
ejpam-4911	517	26	,	,	PUNCT
ejpam-4911	517	27	{	{	PUNCT
ejpam-4911	517	28	a	a	DET
ejpam-4911	517	29	,	,	PUNCT
ejpam-4911	517	30	b	b	NOUN
ejpam-4911	517	31	}	}	PUNCT
ejpam-4911	517	32	,	,	PUNCT
ejpam-4911	517	33	{	{	PUNCT
ejpam-4911	517	34	a	a	X
ejpam-4911	517	35	,	,	PUNCT
ejpam-4911	517	36	c	c	NOUN
ejpam-4911	517	37	}	}	PUNCT
ejpam-4911	517	38	,	,	PUNCT
ejpam-4911	517	39	{	{	PUNCT
ejpam-4911	517	40	a	a	DET
ejpam-4911	517	41	,	,	PUNCT
ejpam-4911	517	42	d	d	NOUN
ejpam-4911	517	43	}	}	PUNCT
ejpam-4911	517	44	,	,	PUNCT
ejpam-4911	517	45	{	{	PUNCT
ejpam-4911	517	46	b	b	X
ejpam-4911	517	47	,	,	PUNCT
ejpam-4911	517	48	c	c	NOUN
ejpam-4911	517	49	}	}	PUNCT
ejpam-4911	517	50	,	,	PUNCT
ejpam-4911	517	51	{	{	PUNCT
ejpam-4911	517	52	b	b	X
ejpam-4911	517	53	,	,	PUNCT
ejpam-4911	517	54	d	d	NOUN
ejpam-4911	517	55	}	}	PUNCT
ejpam-4911	517	56	,	,	PUNCT
ejpam-4911	517	57	{	{	PUNCT
ejpam-4911	517	58	a	a	DET
ejpam-4911	517	59	,	,	PUNCT
ejpam-4911	517	60	b	b	NOUN
ejpam-4911	517	61	,	,	PUNCT
ejpam-4911	517	62	c	c	NOUN
ejpam-4911	517	63	}	}	PUNCT
ejpam-4911	517	64	,	,	PUNCT
ejpam-4911	517	65	{	{	PUNCT
ejpam-4911	517	66	a	a	DET
ejpam-4911	517	67	,	,	PUNCT
ejpam-4911	517	68	b	b	NOUN
ejpam-4911	517	69	,	,	PUNCT
ejpam-4911	517	70	d	d	NOUN
ejpam-4911	517	71	}	}	PUNCT
ejpam-4911	517	72	}	}	PUNCT
ejpam-4911	517	73	.	.	PUNCT
ejpam-4911	518	1	let	let	VERB
ejpam-4911	518	2	u	u	PRON
ejpam-4911	518	3	=	=	X
ejpam-4911	518	4	{	{	PUNCT
ejpam-4911	518	5	a	a	X
ejpam-4911	518	6	,	,	PUNCT
ejpam-4911	518	7	c	c	NOUN
ejpam-4911	518	8	,	,	PUNCT
ejpam-4911	518	9	d	d	AUX
ejpam-4911	518	10	}	}	PUNCT
ejpam-4911	518	11	be	be	AUX
ejpam-4911	518	12	a	a	DET
ejpam-4911	518	13	subset	subset	NOUN
ejpam-4911	518	14	of	of	ADP
ejpam-4911	518	15	x	x	PUNCT
ejpam-4911	518	16	and	and	CCONJ
ejpam-4911	518	17	e	e	X
ejpam-4911	518	18	=	=	PRON
ejpam-4911	518	19	{	{	PUNCT
ejpam-4911	518	20	(	(	PUNCT
ejpam-4911	518	21	1	1	NUM
ejpam-4911	518	22	,	,	PUNCT
ejpam-4911	518	23	2)-codense	2)-codense	NOUN
ejpam-4911	518	24	set	set	NOUN
ejpam-4911	518	25	,	,	PUNCT
ejpam-4911	518	26	(	(	PUNCT
ejpam-4911	518	27	2	2	NUM
ejpam-4911	518	28	,	,	PUNCT
ejpam-4911	518	29	1)-codense	1)-codense	NUM
ejpam-4911	518	30	set	set	NOUN
ejpam-4911	518	31	,	,	PUNCT
ejpam-4911	518	32	(	(	PUNCT
ejpam-4911	518	33	1	1	NUM
ejpam-4911	518	34	,	,	PUNCT
ejpam-4911	518	35	2)codense	2)codense	NUM
ejpam-4911	518	36	but	but	CCONJ
ejpam-4911	518	37	not	not	PART
ejpam-4911	518	38	(	(	PUNCT
ejpam-4911	518	39	2	2	NUM
ejpam-4911	518	40	,	,	PUNCT
ejpam-4911	518	41	1)-codense	1)-codense	NUM
ejpam-4911	518	42	,	,	PUNCT
ejpam-4911	518	43	(	(	PUNCT
ejpam-4911	518	44	2	2	NUM
ejpam-4911	518	45	,	,	PUNCT
ejpam-4911	518	46	1)-codense	1)-codense	NUM
ejpam-4911	518	47	but	but	CCONJ
ejpam-4911	518	48	not	not	PART
ejpam-4911	518	49	(	(	PUNCT
ejpam-4911	518	50	1	1	NUM
ejpam-4911	518	51	,	,	PUNCT
ejpam-4911	518	52	2)-codense	2)-codense	NUM
ejpam-4911	518	53	,	,	PUNCT
ejpam-4911	518	54	(	(	PUNCT
ejpam-4911	518	55	1	1	NUM
ejpam-4911	518	56	,	,	PUNCT
ejpam-4911	518	57	2)-codense	2)-codense	NUM
ejpam-4911	518	58	and	and	CCONJ
ejpam-4911	518	59	(	(	PUNCT
ejpam-4911	518	60	2	2	NUM
ejpam-4911	518	61	,	,	PUNCT
ejpam-4911	518	62	1)-codense	1)-codense	NUM
ejpam-4911	518	63	}	}	PUNCT
ejpam-4911	518	64	=	=	SYM
ejpam-4911	518	65	{	{	PUNCT
ejpam-4911	518	66	e1	e1	PROPN
ejpam-4911	518	67	,	,	PUNCT
ejpam-4911	518	68	e2	e2	PROPN
ejpam-4911	518	69	,	,	PUNCT
ejpam-4911	518	70	e3	e3	NOUN
ejpam-4911	518	71	,	,	PUNCT
ejpam-4911	518	72	e4	e4	PROPN
ejpam-4911	518	73	,	,	PUNCT
ejpam-4911	518	74	e5	e5	PROPN
ejpam-4911	518	75	}	}	PUNCT
ejpam-4911	518	76	is	be	AUX
ejpam-4911	518	77	the	the	DET
ejpam-4911	518	78	set	set	NOUN
ejpam-4911	518	79	of	of	ADP
ejpam-4911	518	80	parameters	parameter	NOUN
ejpam-4911	518	81	.	.	PUNCT
ejpam-4911	519	1	consider	consider	VERB
ejpam-4911	519	2	the	the	DET
ejpam-4911	519	3	map	map	NOUN
ejpam-4911	519	4	f	f	PROPN
ejpam-4911	519	5	from	from	ADP
ejpam-4911	519	6	e	e	PROPN
ejpam-4911	519	7	into	into	ADP
ejpam-4911	519	8	the	the	DET
ejpam-4911	519	9	power	power	NOUN
ejpam-4911	519	10	set	set	NOUN
ejpam-4911	519	11	of	of	ADP
ejpam-4911	519	12	u.	u.	PROPN
ejpam-4911	519	13	defined	define	VERB
ejpam-4911	519	14	by	by	ADP
ejpam-4911	519	15	f	f	PROPN
ejpam-4911	519	16	(	(	PUNCT
ejpam-4911	519	17	e1	e1	PROPN
ejpam-4911	519	18	)	)	PUNCT
ejpam-4911	519	19	=	=	PRON
ejpam-4911	519	20	{	{	PUNCT
ejpam-4911	519	21	a};f	a};f	VERB
ejpam-4911	519	22	(	(	PUNCT
ejpam-4911	519	23	e2	e2	PROPN
ejpam-4911	519	24	)	)	PUNCT
ejpam-4911	519	25	=	=	PRON
ejpam-4911	519	26	{	{	PUNCT
ejpam-4911	519	27	c};f	c};f	X
ejpam-4911	519	28	(	(	PUNCT
ejpam-4911	519	29	e3	e3	NOUN
ejpam-4911	519	30	)	)	PUNCT
ejpam-4911	519	31	=	=	PRON
ejpam-4911	519	32	{	{	PUNCT
ejpam-4911	519	33	c	c	NOUN
ejpam-4911	519	34	,	,	PUNCT
ejpam-4911	519	35	d};f	d};f	X
ejpam-4911	519	36	(	(	PUNCT
ejpam-4911	519	37	e4	e4	PROPN
ejpam-4911	519	38	)	)	PUNCT
ejpam-4911	519	39	=	=	PRON
ejpam-4911	519	40	{	{	PUNCT
ejpam-4911	519	41	a	a	X
ejpam-4911	519	42	,	,	PUNCT
ejpam-4911	519	43	c};f	c};f	PUNCT
ejpam-4911	519	44	(	(	PUNCT
ejpam-4911	519	45	e5	e5	PROPN
ejpam-4911	519	46	)	)	PUNCT
ejpam-4911	519	47	=	=	PUNCT
ejpam-4911	520	1	{	{	PUNCT
ejpam-4911	520	2	d	d	NOUN
ejpam-4911	520	3	}	}	PUNCT
ejpam-4911	520	4	.	.	PUNCT
ejpam-4911	521	1	then	then	ADV
ejpam-4911	521	2	we	we	PRON
ejpam-4911	521	3	get	get	VERB
ejpam-4911	521	4	the	the	DET
ejpam-4911	521	5	pair	pair	NOUN
ejpam-4911	521	6	(	(	PUNCT
ejpam-4911	521	7	f	f	X
ejpam-4911	521	8	,	,	PUNCT
ejpam-4911	521	9	e	e	NOUN
ejpam-4911	521	10	)	)	PUNCT
ejpam-4911	521	11	is	be	AUX
ejpam-4911	521	12	a	a	DET
ejpam-4911	521	13	soft	soft	ADJ
ejpam-4911	521	14	set	set	NOUN
ejpam-4911	521	15	over	over	ADP
ejpam-4911	521	16	u.	u.	PROPN
ejpam-4911	521	17	example	example	NOUN
ejpam-4911	521	18	42	42	NUM
ejpam-4911	521	19	.	.	PUNCT
ejpam-4911	522	1	consider	consider	VERB
ejpam-4911	522	2	the	the	DET
ejpam-4911	522	3	generalized	generalized	ADJ
ejpam-4911	522	4	topological	topological	ADJ
ejpam-4911	522	5	space	space	NOUN
ejpam-4911	522	6	(	(	PUNCT
ejpam-4911	522	7	x	x	NOUN
ejpam-4911	522	8	,	,	PUNCT
ejpam-4911	522	9	η1	η1	NOUN
ejpam-4911	522	10	,	,	PUNCT
ejpam-4911	522	11	η2	η2	PROPN
ejpam-4911	522	12	)	)	PUNCT
ejpam-4911	522	13	wherex	wherex	NOUN
ejpam-4911	522	14	=	=	PUNCT
ejpam-4911	522	15	{	{	PUNCT
ejpam-4911	522	16	a	a	PRON
ejpam-4911	522	17	,	,	PUNCT
ejpam-4911	522	18	b	b	NOUN
ejpam-4911	522	19	,	,	PUNCT
ejpam-4911	522	20	c	c	NOUN
ejpam-4911	522	21	,	,	PUNCT
ejpam-4911	522	22	d	d	NOUN
ejpam-4911	522	23	}	}	PUNCT
ejpam-4911	522	24	;	;	PUNCT
ejpam-4911	522	25	η1	η1	NOUN
ejpam-4911	522	26	and	and	CCONJ
ejpam-4911	522	27	η2	η2	PROPN
ejpam-4911	522	28	are	be	AUX
ejpam-4911	522	29	defined	define	VERB
ejpam-4911	522	30	in	in	ADP
ejpam-4911	522	31	above	above	ADP
ejpam-4911	522	32	example	example	NOUN
ejpam-4911	522	33	40	40	NUM
ejpam-4911	522	34	,	,	PUNCT
ejpam-4911	522	35	that	that	PRON
ejpam-4911	522	36	is	be	AUX
ejpam-4911	522	37	;	;	PUNCT
ejpam-4911	522	38	we	we	PRON
ejpam-4911	522	39	take	take	VERB
ejpam-4911	522	40	η1	η1	NOUN
ejpam-4911	522	41	=	=	SYM
ejpam-4911	522	42	µ2	µ2	PROPN
ejpam-4911	522	43	and	and	CCONJ
ejpam-4911	522	44	η2	η2	ADJ
ejpam-4911	522	45	=	=	SYM
ejpam-4911	522	46	µ1	µ1	PROPN
ejpam-4911	522	47	.	.	PUNCT
ejpam-4911	523	1	then	then	ADV
ejpam-4911	523	2	we	we	PRON
ejpam-4911	523	3	get	get	VERB
ejpam-4911	523	4	;	;	PUNCT
ejpam-4911	523	5	•	•	NUM
ejpam-4911	523	6	η1	η1	NOUN
ejpam-4911	523	7	-	-	PUNCT
ejpam-4911	523	8	nowhere	nowhere	ADV
ejpam-4911	523	9	dense	dense	ADJ
ejpam-4911	523	10	sets	set	NOUN
ejpam-4911	523	11	=	=	SYM
ejpam-4911	523	12	{	{	PUNCT
ejpam-4911	523	13	∅	∅	NOUN
ejpam-4911	523	14	,	,	PUNCT
ejpam-4911	523	15	{	{	PUNCT
ejpam-4911	523	16	b	b	NOUN
ejpam-4911	523	17	}	}	PUNCT
ejpam-4911	523	18	,	,	PUNCT
ejpam-4911	523	19	{	{	PUNCT
ejpam-4911	523	20	d	d	NOUN
ejpam-4911	523	21	}	}	PUNCT
ejpam-4911	523	22	,	,	PUNCT
ejpam-4911	523	23	{	{	PUNCT
ejpam-4911	523	24	b	b	X
ejpam-4911	523	25	,	,	PUNCT
ejpam-4911	523	26	d	d	NOUN
ejpam-4911	523	27	}	}	PUNCT
ejpam-4911	523	28	}	}	PUNCT
ejpam-4911	523	29	;	;	PUNCT
ejpam-4911	523	30	•	•	NUM
ejpam-4911	523	31	η2	η2	VERB
ejpam-4911	523	32	-	-	PUNCT
ejpam-4911	523	33	nowhere	nowhere	ADV
ejpam-4911	523	34	dense	dense	ADJ
ejpam-4911	523	35	sets	set	NOUN
ejpam-4911	523	36	=	=	SYM
ejpam-4911	523	37	{	{	PUNCT
ejpam-4911	523	38	∅	∅	NOUN
ejpam-4911	523	39	,	,	PUNCT
ejpam-4911	523	40	{	{	PUNCT
ejpam-4911	523	41	c	c	NOUN
ejpam-4911	523	42	}	}	PUNCT
ejpam-4911	523	43	,	,	PUNCT
ejpam-4911	523	44	{	{	PUNCT
ejpam-4911	523	45	d	d	X
ejpam-4911	523	46	}	}	PUNCT
ejpam-4911	523	47	,	,	PUNCT
ejpam-4911	523	48	{	{	PUNCT
ejpam-4911	523	49	c	c	X
ejpam-4911	523	50	,	,	PUNCT
ejpam-4911	523	51	d	d	NOUN
ejpam-4911	523	52	}	}	PUNCT
ejpam-4911	523	53	}	}	PUNCT
ejpam-4911	523	54	;	;	PUNCT
ejpam-4911	523	55	•	•	NUM
ejpam-4911	523	56	η1	η1	NOUN
ejpam-4911	523	57	-	-	PUNCT
ejpam-4911	523	58	dense	dense	ADJ
ejpam-4911	523	59	sets	set	NOUN
ejpam-4911	523	60	=	=	SYM
ejpam-4911	523	61	{	{	PUNCT
ejpam-4911	523	62	{	{	PUNCT
ejpam-4911	523	63	a	a	PROPN
ejpam-4911	523	64	,	,	PUNCT
ejpam-4911	523	65	b	b	NOUN
ejpam-4911	523	66	}	}	PUNCT
ejpam-4911	523	67	,	,	PUNCT
ejpam-4911	523	68	{	{	PUNCT
ejpam-4911	523	69	a	a	X
ejpam-4911	523	70	,	,	PUNCT
ejpam-4911	523	71	c	c	NOUN
ejpam-4911	523	72	}	}	PUNCT
ejpam-4911	523	73	,	,	PUNCT
ejpam-4911	523	74	{	{	PUNCT
ejpam-4911	523	75	a	a	DET
ejpam-4911	523	76	,	,	PUNCT
ejpam-4911	523	77	b	b	NOUN
ejpam-4911	523	78	,	,	PUNCT
ejpam-4911	523	79	c	c	NOUN
ejpam-4911	523	80	}	}	PUNCT
ejpam-4911	523	81	,	,	PUNCT
ejpam-4911	523	82	{	{	PUNCT
ejpam-4911	523	83	a	a	DET
ejpam-4911	523	84	,	,	PUNCT
ejpam-4911	523	85	b	b	NOUN
ejpam-4911	523	86	,	,	PUNCT
ejpam-4911	523	87	d	d	NOUN
ejpam-4911	523	88	}	}	PUNCT
ejpam-4911	523	89	,	,	PUNCT
ejpam-4911	523	90	{	{	PUNCT
ejpam-4911	523	91	a	a	PRON
ejpam-4911	523	92	,	,	PUNCT
ejpam-4911	523	93	c	c	NOUN
ejpam-4911	523	94	,	,	PUNCT
ejpam-4911	523	95	d	d	NOUN
ejpam-4911	523	96	}	}	PUNCT
ejpam-4911	523	97	,	,	PUNCT
ejpam-4911	523	98	x	x	X
ejpam-4911	523	99	}	}	PUNCT
ejpam-4911	523	100	;	;	PUNCT
ejpam-4911	523	101	•	•	NUM
ejpam-4911	523	102	η2	η2	VERB
ejpam-4911	523	103	-	-	PUNCT
ejpam-4911	523	104	dense	dense	ADJ
ejpam-4911	523	105	sets	set	NOUN
ejpam-4911	523	106	=	=	SYM
ejpam-4911	523	107	{	{	PUNCT
ejpam-4911	523	108	{	{	PUNCT
ejpam-4911	523	109	a	a	PROPN
ejpam-4911	523	110	,	,	PUNCT
ejpam-4911	523	111	b	b	NOUN
ejpam-4911	523	112	}	}	PUNCT
ejpam-4911	523	113	,	,	PUNCT
ejpam-4911	523	114	{	{	PUNCT
ejpam-4911	523	115	b	b	X
ejpam-4911	523	116	,	,	PUNCT
ejpam-4911	523	117	c	c	NOUN
ejpam-4911	523	118	}	}	PUNCT
ejpam-4911	523	119	,	,	PUNCT
ejpam-4911	523	120	{	{	PUNCT
ejpam-4911	523	121	a	a	DET
ejpam-4911	523	122	,	,	PUNCT
ejpam-4911	523	123	b	b	NOUN
ejpam-4911	523	124	,	,	PUNCT
ejpam-4911	523	125	c	c	NOUN
ejpam-4911	523	126	}	}	PUNCT
ejpam-4911	523	127	,	,	PUNCT
ejpam-4911	523	128	{	{	PUNCT
ejpam-4911	523	129	a	a	DET
ejpam-4911	523	130	,	,	PUNCT
ejpam-4911	523	131	b	b	NOUN
ejpam-4911	523	132	,	,	PUNCT
ejpam-4911	523	133	d	d	NOUN
ejpam-4911	523	134	}	}	PUNCT
ejpam-4911	523	135	,	,	PUNCT
ejpam-4911	523	136	{	{	PUNCT
ejpam-4911	523	137	b	b	X
ejpam-4911	523	138	,	,	PUNCT
ejpam-4911	523	139	c	c	NOUN
ejpam-4911	523	140	,	,	PUNCT
ejpam-4911	523	141	d	d	NOUN
ejpam-4911	523	142	}	}	PUNCT
ejpam-4911	523	143	,	,	PUNCT
ejpam-4911	523	144	x	x	X
ejpam-4911	523	145	}	}	PUNCT
ejpam-4911	523	146	;	;	PUNCT
ejpam-4911	523	147	•	•	X
ejpam-4911	523	148	(	(	PUNCT
ejpam-4911	523	149	1	1	NUM
ejpam-4911	523	150	,	,	PUNCT
ejpam-4911	523	151	2)−n	2)−n	NUM
ejpam-4911	523	152	(	(	PUNCT
ejpam-4911	523	153	x	x	X
ejpam-4911	523	154	)	)	PUNCT
ejpam-4911	523	155	=	=	SYM
ejpam-4911	523	156	{	{	PUNCT
ejpam-4911	523	157	∅	∅	NOUN
ejpam-4911	523	158	,	,	PUNCT
ejpam-4911	523	159	{	{	PUNCT
ejpam-4911	523	160	b	b	NOUN
ejpam-4911	523	161	}	}	PUNCT
ejpam-4911	523	162	,	,	PUNCT
ejpam-4911	523	163	{	{	PUNCT
ejpam-4911	523	164	c	c	X
ejpam-4911	523	165	}	}	PUNCT
ejpam-4911	523	166	,	,	PUNCT
ejpam-4911	523	167	{	{	PUNCT
ejpam-4911	523	168	d	d	X
ejpam-4911	523	169	}	}	PUNCT
ejpam-4911	523	170	,	,	PUNCT
ejpam-4911	523	171	{	{	PUNCT
ejpam-4911	523	172	b	b	X
ejpam-4911	523	173	,	,	PUNCT
ejpam-4911	523	174	d	d	NOUN
ejpam-4911	523	175	}	}	PUNCT
ejpam-4911	523	176	,	,	PUNCT
ejpam-4911	523	177	{	{	PUNCT
ejpam-4911	523	178	c	c	X
ejpam-4911	523	179	,	,	PUNCT
ejpam-4911	523	180	d	d	NOUN
ejpam-4911	523	181	}	}	PUNCT
ejpam-4911	523	182	}	}	PUNCT
ejpam-4911	523	183	;	;	PUNCT
ejpam-4911	523	184	•	•	X
ejpam-4911	523	185	(	(	PUNCT
ejpam-4911	523	186	2	2	NUM
ejpam-4911	523	187	,	,	PUNCT
ejpam-4911	523	188	1)−n	1)−n	NUM
ejpam-4911	523	189	(	(	PUNCT
ejpam-4911	523	190	x	x	X
ejpam-4911	523	191	)	)	PUNCT
ejpam-4911	523	192	=	=	SYM
ejpam-4911	523	193	{	{	PUNCT
ejpam-4911	523	194	∅	∅	NOUN
ejpam-4911	523	195	,	,	PUNCT
ejpam-4911	523	196	{	{	PUNCT
ejpam-4911	523	197	a	a	X
ejpam-4911	523	198	}	}	PUNCT
ejpam-4911	523	199	,	,	PUNCT
ejpam-4911	523	200	{	{	PUNCT
ejpam-4911	523	201	d	d	NOUN
ejpam-4911	523	202	}	}	PUNCT
ejpam-4911	523	203	,	,	PUNCT
ejpam-4911	523	204	{	{	PUNCT
ejpam-4911	523	205	a	a	PRON
ejpam-4911	523	206	,	,	PUNCT
ejpam-4911	523	207	d	d	NOUN
ejpam-4911	523	208	}	}	PUNCT
ejpam-4911	523	209	}	}	PUNCT
ejpam-4911	523	210	.	.	PUNCT
ejpam-4911	524	1	let	let	VERB
ejpam-4911	524	2	u	u	PRON
ejpam-4911	524	3	=	=	X
ejpam-4911	524	4	{	{	PUNCT
ejpam-4911	524	5	a	a	PRON
ejpam-4911	524	6	,	,	PUNCT
ejpam-4911	524	7	b	b	NOUN
ejpam-4911	524	8	,	,	PUNCT
ejpam-4911	524	9	c	c	AUX
ejpam-4911	524	10	}	}	PUNCT
ejpam-4911	524	11	be	be	AUX
ejpam-4911	524	12	a	a	DET
ejpam-4911	524	13	non	non	ADJ
ejpam-4911	524	14	-	-	ADJ
ejpam-4911	524	15	null	null	ADJ
ejpam-4911	524	16	subset	subset	NOUN
ejpam-4911	524	17	of	of	ADP
ejpam-4911	524	18	x	x	PUNCT
ejpam-4911	524	19	and	and	CCONJ
ejpam-4911	524	20	e	e	NOUN
ejpam-4911	524	21	=	=	SYM
ejpam-4911	524	22	{	{	PUNCT
ejpam-4911	524	23	η1	η1	NOUN
ejpam-4911	524	24	-	-	PUNCT
ejpam-4911	524	25	nowhere	nowhere	ADV
ejpam-4911	524	26	dense	dense	ADJ
ejpam-4911	524	27	set	set	NOUN
ejpam-4911	524	28	,	,	PUNCT
ejpam-4911	524	29	η2	η2	X
ejpam-4911	524	30	-	-	PUNCT
ejpam-4911	524	31	nowhere	nowhere	ADV
ejpam-4911	524	32	dense	dense	ADJ
ejpam-4911	524	33	set	set	NOUN
ejpam-4911	524	34	,	,	PUNCT
ejpam-4911	524	35	η1	η1	NOUN
ejpam-4911	524	36	-	-	PUNCT
ejpam-4911	524	37	dense	dense	ADJ
ejpam-4911	524	38	set	set	NOUN
ejpam-4911	524	39	,	,	PUNCT
ejpam-4911	524	40	η2	η2	ADJ
ejpam-4911	524	41	-	-	PUNCT
ejpam-4911	524	42	dense	dense	ADJ
ejpam-4911	524	43	set	set	NOUN
ejpam-4911	524	44	,	,	PUNCT
ejpam-4911	524	45	(	(	PUNCT
ejpam-4911	524	46	1	1	NUM
ejpam-4911	524	47	,	,	PUNCT
ejpam-4911	524	48	2)-nowhere	2)-nowhere	NUM
ejpam-4911	524	49	dense	dense	ADJ
ejpam-4911	524	50	set	set	NOUN
ejpam-4911	524	51	,	,	PUNCT
ejpam-4911	524	52	(	(	PUNCT
ejpam-4911	524	53	2	2	NUM
ejpam-4911	524	54	,	,	PUNCT
ejpam-4911	524	55	1)-nowhere	1)-nowhere	NUM
ejpam-4911	524	56	dense	dense	ADJ
ejpam-4911	524	57	set	set	NOUN
ejpam-4911	524	58	}	}	PUNCT
ejpam-4911	524	59	=	=	SYM
ejpam-4911	524	60	{	{	PUNCT
ejpam-4911	524	61	e1	e1	PROPN
ejpam-4911	524	62	,	,	PUNCT
ejpam-4911	524	63	e2	e2	PROPN
ejpam-4911	524	64	,	,	PUNCT
ejpam-4911	524	65	e3	e3	NOUN
ejpam-4911	524	66	,	,	PUNCT
ejpam-4911	524	67	e4	e4	PROPN
ejpam-4911	524	68	,	,	PUNCT
ejpam-4911	524	69	e5	e5	PROPN
ejpam-4911	524	70	,	,	PUNCT
ejpam-4911	524	71	e6	e6	PROPN
ejpam-4911	524	72	}	}	PUNCT
ejpam-4911	524	73	is	be	AUX
ejpam-4911	524	74	the	the	DET
ejpam-4911	524	75	set	set	NOUN
ejpam-4911	524	76	of	of	ADP
ejpam-4911	524	77	parameters	parameter	NOUN
ejpam-4911	524	78	.	.	PUNCT
ejpam-4911	525	1	take	take	VERB
ejpam-4911	525	2	f	f	PROPN
ejpam-4911	525	3	be	be	AUX
ejpam-4911	525	4	a	a	DET
ejpam-4911	525	5	function	function	NOUN
ejpam-4911	525	6	defined	define	VERB
ejpam-4911	525	7	from	from	ADP
ejpam-4911	525	8	e	e	PROPN
ejpam-4911	525	9	to	to	ADP
ejpam-4911	525	10	the	the	DET
ejpam-4911	525	11	subsets	subset	NOUN
ejpam-4911	525	12	of	of	ADP
ejpam-4911	525	13	u	u	NOUN
ejpam-4911	525	14	by	by	ADP
ejpam-4911	525	15	;	;	PUNCT
ejpam-4911	525	16	f	f	PROPN
ejpam-4911	525	17	(	(	PUNCT
ejpam-4911	525	18	e1	e1	PROPN
ejpam-4911	525	19	)	)	PUNCT
ejpam-4911	525	20	=	=	PRON
ejpam-4911	525	21	{	{	PUNCT
ejpam-4911	525	22	b};f	b};f	X
ejpam-4911	525	23	(	(	PUNCT
ejpam-4911	525	24	e2	e2	PROPN
ejpam-4911	525	25	)	)	PUNCT
ejpam-4911	525	26	=	=	PRON
ejpam-4911	525	27	{	{	PUNCT
ejpam-4911	525	28	c};f	c};f	X
ejpam-4911	525	29	(	(	PUNCT
ejpam-4911	525	30	e3	e3	NOUN
ejpam-4911	525	31	)	)	PUNCT
ejpam-4911	526	1	=	=	PRON
ejpam-4911	526	2	{	{	PUNCT
ejpam-4911	526	3	a	a	X
ejpam-4911	526	4	,	,	PUNCT
ejpam-4911	526	5	c};f	c};f	PUNCT
ejpam-4911	526	6	(	(	PUNCT
ejpam-4911	526	7	e4	e4	PROPN
ejpam-4911	526	8	)	)	PUNCT
ejpam-4911	526	9	=	=	PUNCT
ejpam-4911	526	10	{	{	PUNCT
ejpam-4911	526	11	b	b	NOUN
ejpam-4911	526	12	,	,	PUNCT
ejpam-4911	526	13	c};f	c};f	PUNCT
ejpam-4911	526	14	(	(	PUNCT
ejpam-4911	526	15	e5	e5	PROPN
ejpam-4911	526	16	)	)	PUNCT
ejpam-4911	526	17	=	=	PRON
ejpam-4911	526	18	{	{	PUNCT
ejpam-4911	526	19	d};f	d};f	X
ejpam-4911	526	20	(	(	PUNCT
ejpam-4911	526	21	e6	e6	PROPN
ejpam-4911	526	22	)	)	PUNCT
ejpam-4911	526	23	=	=	PUNCT
ejpam-4911	526	24	{	{	PUNCT
ejpam-4911	526	25	a	a	X
ejpam-4911	526	26	}	}	PUNCT
ejpam-4911	526	27	.	.	PUNCT
ejpam-4911	527	1	thus	thus	ADV
ejpam-4911	527	2	,	,	PUNCT
ejpam-4911	527	3	(	(	PUNCT
ejpam-4911	527	4	f	f	X
ejpam-4911	527	5	,	,	PUNCT
ejpam-4911	527	6	e	e	NOUN
ejpam-4911	527	7	)	)	PUNCT
ejpam-4911	527	8	is	be	AUX
ejpam-4911	527	9	a	a	DET
ejpam-4911	527	10	soft	soft	ADJ
ejpam-4911	527	11	set	set	NOUN
ejpam-4911	527	12	over	over	ADP
ejpam-4911	527	13	u.	u.	NOUN
ejpam-4911	527	14	references	reference	NOUN
ejpam-4911	527	15	2065	2065	NUM
ejpam-4911	527	16	7	7	NUM
ejpam-4911	527	17	.	.	PUNCT
ejpam-4911	527	18	conclusion	conclusion	NOUN
ejpam-4911	527	19	in	in	ADP
ejpam-4911	527	20	this	this	DET
ejpam-4911	527	21	article	article	NOUN
ejpam-4911	527	22	,	,	PUNCT
ejpam-4911	527	23	various	various	ADJ
ejpam-4911	527	24	properties	property	NOUN
ejpam-4911	527	25	for	for	ADP
ejpam-4911	527	26	(	(	PUNCT
ejpam-4911	527	27	s	s	X
ejpam-4911	527	28	,	,	PUNCT
ejpam-4911	527	29	v)-dense	v)-dense	PUNCT
ejpam-4911	527	30	and	and	CCONJ
ejpam-4911	527	31	(	(	PUNCT
ejpam-4911	527	32	s	s	X
ejpam-4911	527	33	,	,	PUNCT
ejpam-4911	527	34	v)-nowhere	v)-nowhere	PUNCT
ejpam-4911	527	35	dense	dense	ADJ
ejpam-4911	527	36	sets	set	NOUN
ejpam-4911	527	37	are	be	AUX
ejpam-4911	527	38	proved	prove	VERB
ejpam-4911	527	39	,	,	PUNCT
ejpam-4911	527	40	which	which	PRON
ejpam-4911	527	41	are	be	AUX
ejpam-4911	527	42	useful	useful	ADJ
ejpam-4911	527	43	to	to	PART
ejpam-4911	527	44	easily	easily	ADV
ejpam-4911	527	45	check	check	VERB
ejpam-4911	527	46	the	the	DET
ejpam-4911	527	47	characterization	characterization	NOUN
ejpam-4911	527	48	of	of	ADP
ejpam-4911	527	49	a	a	DET
ejpam-4911	527	50	given	give	VERB
ejpam-4911	527	51	set	set	NOUN
ejpam-4911	527	52	in	in	ADP
ejpam-4911	527	53	a	a	DET
ejpam-4911	527	54	bigeneralized	bigeneralize	VERB
ejpam-4911	527	55	topological	topological	ADJ
ejpam-4911	527	56	space	space	NOUN
ejpam-4911	527	57	.	.	PUNCT
ejpam-4911	528	1	references	reference	NOUN
ejpam-4911	528	2	[	[	X
ejpam-4911	528	3	1	1	NUM
ejpam-4911	528	4	]	]	PUNCT
ejpam-4911	528	5	chawalit	chawalit	VERB
ejpam-4911	528	6	boonpok	boonpok	NOUN
ejpam-4911	528	7	.	.	PUNCT
ejpam-4911	529	1	weakly	weakly	ADJ
ejpam-4911	529	2	open	open	ADJ
ejpam-4911	529	3	functions	function	NOUN
ejpam-4911	529	4	on	on	ADP
ejpam-4911	529	5	bigeneralized	bigeneralize	VERB
ejpam-4911	529	6	topological	topological	ADJ
ejpam-4911	529	7	spaces	space	NOUN
ejpam-4911	529	8	.	.	PUNCT
ejpam-4911	530	1	int	int	NOUN
ejpam-4911	530	2	.	.	PUNCT
ejpam-4911	531	1	journal	journal	PROPN
ejpam-4911	531	2	of	of	ADP
ejpam-4911	531	3	math	math	NOUN
ejpam-4911	531	4	.	.	PUNCT
ejpam-4911	532	1	analysis	analysis	NOUN
ejpam-4911	532	2	,	,	PUNCT
ejpam-4911	532	3	4(18):891–897	4(18):891–897	NUM
ejpam-4911	532	4	,	,	PUNCT
ejpam-4911	532	5	2010	2010	NUM
ejpam-4911	532	6	.	.	PUNCT
ejpam-4911	533	1	[	[	X
ejpam-4911	533	2	2	2	X
ejpam-4911	533	3	]	]	PUNCT
ejpam-4911	533	4	akos	akos	NOUN
ejpam-4911	533	5	császár	császár	PROPN
ejpam-4911	533	6	.	.	PUNCT
ejpam-4911	534	1	generalized	generalize	VERB
ejpam-4911	534	2	open	open	ADJ
ejpam-4911	534	3	sets	set	NOUN
ejpam-4911	534	4	.	.	PUNCT
ejpam-4911	535	1	acta	acta	PROPN
ejpam-4911	535	2	mathematica	mathematica	PROPN
ejpam-4911	535	3	hungarica	hungarica	PROPN
ejpam-4911	535	4	,	,	PUNCT
ejpam-4911	535	5	75	75	NUM
ejpam-4911	535	6	,	,	PUNCT
ejpam-4911	535	7	1997	1997	NUM
ejpam-4911	535	8	.	.	PUNCT
ejpam-4911	536	1	[	[	X
ejpam-4911	536	2	3	3	X
ejpam-4911	536	3	]	]	X
ejpam-4911	536	4	akos	akos	NOUN
ejpam-4911	536	5	császár	császár	PROPN
ejpam-4911	536	6	.	.	PUNCT
ejpam-4911	537	1	generalized	generalize	VERB
ejpam-4911	537	2	open	open	ADJ
ejpam-4911	537	3	sets	set	NOUN
ejpam-4911	537	4	in	in	ADP
ejpam-4911	537	5	generalized	generalized	ADJ
ejpam-4911	537	6	topologies	topology	NOUN
ejpam-4911	537	7	.	.	PUNCT
ejpam-4911	538	1	acta	acta	PROPN
ejpam-4911	538	2	mathematica	mathematica	PROPN
ejpam-4911	538	3	hungarica	hungarica	PROPN
ejpam-4911	538	4	,	,	PUNCT
ejpam-4911	538	5	106	106	NUM
ejpam-4911	538	6	,	,	PUNCT
ejpam-4911	538	7	2005	2005	NUM
ejpam-4911	538	8	.	.	PUNCT
ejpam-4911	539	1	[	[	X
ejpam-4911	539	2	4	4	NUM
ejpam-4911	539	3	]	]	X
ejpam-4911	539	4	wichai	wichai	NOUN
ejpam-4911	539	5	dungthaisong	dungthaisong	PROPN
ejpam-4911	539	6	,	,	PUNCT
ejpam-4911	539	7	chawalit	chawalit	VERB
ejpam-4911	539	8	boonpok	boonpok	NOUN
ejpam-4911	539	9	,	,	PUNCT
ejpam-4911	539	10	and	and	CCONJ
ejpam-4911	539	11	chokchai	chokchai	ADJ
ejpam-4911	539	12	viriyapong	viriyapong	PROPN
ejpam-4911	539	13	.	.	PUNCT
ejpam-4911	540	1	generalized	generalize	VERB
ejpam-4911	540	2	closed	close	VERB
ejpam-4911	540	3	sets	set	NOUN
ejpam-4911	540	4	in	in	ADP
ejpam-4911	540	5	bigeneralized	bigeneralize	VERB
ejpam-4911	540	6	topological	topological	ADJ
ejpam-4911	540	7	spaces	space	NOUN
ejpam-4911	540	8	.	.	PUNCT
ejpam-4911	541	1	international	international	ADJ
ejpam-4911	541	2	journal	journal	PROPN
ejpam-4911	541	3	of	of	ADP
ejpam-4911	541	4	mathematical	mathematical	ADJ
ejpam-4911	541	5	analysis	analysis	NOUN
ejpam-4911	541	6	,	,	PUNCT
ejpam-4911	541	7	5(24):1175–1184	5(24):1175–1184	NUM
ejpam-4911	541	8	,	,	PUNCT
ejpam-4911	541	9	2011	2011	NUM
ejpam-4911	541	10	.	.	PUNCT
ejpam-4911	542	1	[	[	X
ejpam-4911	542	2	5	5	X
ejpam-4911	542	3	]	]	PUNCT
ejpam-4911	542	4	e.	e.	PROPN
ejpam-4911	542	5	ekici	ekici	PROPN
ejpam-4911	542	6	.	.	PUNCT
ejpam-4911	543	1	generalized	generalize	VERB
ejpam-4911	543	2	submaximal	submaximal	ADJ
ejpam-4911	543	3	spaces	space	NOUN
ejpam-4911	543	4	.	.	PUNCT
ejpam-4911	544	1	acta	acta	PROPN
ejpam-4911	544	2	math	math	PROPN
ejpam-4911	544	3	.	.	PUNCT
ejpam-4911	545	1	hungar	hungar	PROPN
ejpam-4911	545	2	.	.	PUNCT
ejpam-4911	546	1	,	,	PUNCT
ejpam-4911	546	2	134:132	134:132	PROPN
ejpam-4911	546	3	–	–	PUNCT
ejpam-4911	546	4	138	138	NUM
ejpam-4911	546	5	,	,	PUNCT
ejpam-4911	546	6	2012	2012	NUM
ejpam-4911	546	7	.	.	PUNCT
ejpam-4911	547	1	[	[	X
ejpam-4911	547	2	6	6	NUM
ejpam-4911	547	3	]	]	PUNCT
ejpam-4911	547	4	erdal	erdal	PROPN
ejpam-4911	547	5	ekici	ekici	PROPN
ejpam-4911	547	6	.	.	PUNCT
ejpam-4911	548	1	generalized	generalized	ADJ
ejpam-4911	548	2	hyperconnectedness	hyperconnectedness	NOUN
ejpam-4911	548	3	.	.	PUNCT
ejpam-4911	549	1	acta	acta	PROPN
ejpam-4911	549	2	mathematica	mathematica	PROPN
ejpam-4911	549	3	hungarica	hungarica	PROPN
ejpam-4911	549	4	,	,	PUNCT
ejpam-4911	549	5	133	133	NUM
ejpam-4911	549	6	,	,	PUNCT
ejpam-4911	549	7	2011	2011	NUM
ejpam-4911	549	8	.	.	PUNCT
ejpam-4911	550	1	[	[	X
ejpam-4911	550	2	7	7	X
ejpam-4911	550	3	]	]	X
ejpam-4911	550	4	j.c	j.c	PROPN
ejpam-4911	550	5	.	.	PROPN
ejpam-4911	550	6	kelly	kelly	PROPN
ejpam-4911	550	7	.	.	PUNCT
ejpam-4911	551	1	bitopological	bitopological	ADJ
ejpam-4911	551	2	spaces	space	NOUN
ejpam-4911	551	3	.	.	PUNCT
ejpam-4911	552	1	pro	pro	ADJ
ejpam-4911	552	2	.	.	PUNCT
ejpam-4911	552	3	london	london	PROPN
ejpam-4911	552	4	math	math	PROPN
ejpam-4911	552	5	.	.	PUNCT
ejpam-4911	553	1	soc	soc	PROPN
ejpam-4911	553	2	.	.	PUNCT
ejpam-4911	553	3	,	,	PUNCT
ejpam-4911	553	4	3(13):71	3(13):71	NUM
ejpam-4911	553	5	–	–	PUNCT
ejpam-4911	553	6	79	79	NUM
ejpam-4911	553	7	,	,	PUNCT
ejpam-4911	553	8	1969	1969	NUM
ejpam-4911	553	9	.	.	PUNCT
ejpam-4911	554	1	[	[	X
ejpam-4911	554	2	8	8	NUM
ejpam-4911	554	3	]	]	X
ejpam-4911	554	4	ewa	ewa	PROPN
ejpam-4911	554	5	korczak	korczak	PROPN
ejpam-4911	554	6	-	-	PUNCT
ejpam-4911	554	7	kubiak	kubiak	PROPN
ejpam-4911	554	8	,	,	PUNCT
ejpam-4911	554	9	anna	anna	PROPN
ejpam-4911	554	10	loranty	loranty	PROPN
ejpam-4911	554	11	,	,	PUNCT
ejpam-4911	554	12	and	and	CCONJ
ejpam-4911	554	13	ryszard	ryszard	PROPN
ejpam-4911	554	14	j	j	PROPN
ejpam-4911	554	15	pawlak	pawlak	PROPN
ejpam-4911	554	16	.	.	PUNCT
ejpam-4911	555	1	baire	baire	NOUN
ejpam-4911	555	2	generalized	generalize	VERB
ejpam-4911	555	3	topological	topological	ADJ
ejpam-4911	555	4	spaces	space	NOUN
ejpam-4911	555	5	,	,	PUNCT
ejpam-4911	555	6	generalized	generalize	VERB
ejpam-4911	555	7	metric	metric	ADJ
ejpam-4911	555	8	spaces	space	NOUN
ejpam-4911	555	9	and	and	CCONJ
ejpam-4911	555	10	infinite	infinite	ADJ
ejpam-4911	555	11	games	game	NOUN
ejpam-4911	555	12	.	.	PUNCT
ejpam-4911	556	1	acta	acta	PROPN
ejpam-4911	556	2	mathematica	mathematica	PROPN
ejpam-4911	556	3	hungarica	hungarica	PROPN
ejpam-4911	556	4	,	,	PUNCT
ejpam-4911	556	5	140(3):203–231	140(3):203–231	NUM
ejpam-4911	556	6	,	,	PUNCT
ejpam-4911	556	7	2013	2013	NUM
ejpam-4911	556	8	.	.	PUNCT
ejpam-4911	557	1	[	[	X
ejpam-4911	557	2	9	9	NUM
ejpam-4911	557	3	]	]	PUNCT
ejpam-4911	557	4	zhaowen	zhaowen	NOUN
ejpam-4911	557	5	li	li	PROPN
ejpam-4911	557	6	and	and	CCONJ
ejpam-4911	557	7	funing	fune	VERB
ejpam-4911	557	8	lin	lin	PROPN
ejpam-4911	557	9	.	.	PUNCT
ejpam-4911	557	10	baireness	baireness	PROPN
ejpam-4911	557	11	on	on	ADP
ejpam-4911	557	12	generalized	generalized	ADJ
ejpam-4911	557	13	topological	topological	ADJ
ejpam-4911	557	14	spaces	space	NOUN
ejpam-4911	557	15	.	.	PUNCT
ejpam-4911	558	1	acta	acta	PROPN
ejpam-4911	558	2	mathematica	mathematica	PROPN
ejpam-4911	558	3	hungarica	hungarica	PROPN
ejpam-4911	558	4	,	,	PUNCT
ejpam-4911	558	5	139(4	139(4	NUM
ejpam-4911	558	6	)	)	PUNCT
ejpam-4911	558	7	,	,	PUNCT
ejpam-4911	558	8	2013	2013	NUM
ejpam-4911	558	9	.	.	PUNCT
ejpam-4911	559	1	[	[	X
ejpam-4911	559	2	10	10	NUM
ejpam-4911	559	3	]	]	X
ejpam-4911	559	4	w.	w.	PROPN
ejpam-4911	559	5	k.	k.	PROPN
ejpam-4911	559	6	min	min	PROPN
ejpam-4911	559	7	.	.	PROPN
ejpam-4911	559	8	almost	almost	ADV
ejpam-4911	559	9	continuity	continuity	NOUN
ejpam-4911	559	10	on	on	ADP
ejpam-4911	559	11	generalized	generalized	ADJ
ejpam-4911	559	12	topological	topological	ADJ
ejpam-4911	559	13	spaces	space	NOUN
ejpam-4911	559	14	.	.	PUNCT
ejpam-4911	560	1	acta	acta	PROPN
ejpam-4911	560	2	math	math	PROPN
ejpam-4911	560	3	.	.	PUNCT
ejpam-4911	561	1	hungar	hungar	PROPN
ejpam-4911	561	2	.	.	PUNCT
ejpam-4911	561	3	,	,	PUNCT
ejpam-4911	561	4	125:121	125:121	INTJ
ejpam-4911	561	5	–	–	PUNCT
ejpam-4911	561	6	125	125	NUM
ejpam-4911	561	7	,	,	PUNCT
ejpam-4911	561	8	2009	2009	NUM
ejpam-4911	561	9	.	.	PUNCT
ejpam-4911	562	1	[	[	X
ejpam-4911	562	2	11	11	NUM
ejpam-4911	562	3	]	]	X
ejpam-4911	562	4	d.	d.	PROPN
ejpam-4911	562	5	molodtsov	molodtsov	PROPN
ejpam-4911	562	6	.	.	PUNCT
ejpam-4911	563	1	soft	soft	ADJ
ejpam-4911	563	2	set	set	NOUN
ejpam-4911	563	3	theory	theory	NOUN
ejpam-4911	563	4	-	-	PUNCT
ejpam-4911	563	5	first	first	ADJ
ejpam-4911	563	6	results	result	NOUN
ejpam-4911	563	7	.	.	PUNCT
ejpam-4911	564	1	comput	comput	NOUN
ejpam-4911	564	2	.	.	PUNCT
ejpam-4911	565	1	math	math	NOUN
ejpam-4911	565	2	.	.	PUNCT
ejpam-4911	566	1	appl	appl	PROPN
ejpam-4911	566	2	.	.	PROPN
ejpam-4911	566	3	,	,	PUNCT
ejpam-4911	566	4	37:19	37:19	NUM
ejpam-4911	566	5	–	–	PUNCT
ejpam-4911	566	6	31	31	NUM
ejpam-4911	566	7	,	,	PUNCT
ejpam-4911	566	8	1999	1999	NUM
ejpam-4911	566	9	.	.	PUNCT
ejpam-4911	567	1	[	[	X
ejpam-4911	567	2	12	12	NUM
ejpam-4911	567	3	]	]	SYM
ejpam-4911	567	4	v	v	NOUN
ejpam-4911	567	5	renukadevi	renukadevi	NOUN
ejpam-4911	567	6	and	and	CCONJ
ejpam-4911	567	7	s	s	NOUN
ejpam-4911	567	8	vadakasi	vadakasi	NOUN
ejpam-4911	567	9	.	.	PUNCT
ejpam-4911	568	1	modifications	modification	NOUN
ejpam-4911	568	2	of	of	ADP
ejpam-4911	568	3	strongly	strongly	ADV
ejpam-4911	568	4	nodec	nodec	ADJ
ejpam-4911	568	5	spaces	space	NOUN
ejpam-4911	568	6	.	.	PUNCT
ejpam-4911	569	1	communications	communication	NOUN
ejpam-4911	569	2	in	in	ADP
ejpam-4911	569	3	advanced	advanced	ADJ
ejpam-4911	569	4	mathematical	mathematical	ADJ
ejpam-4911	569	5	sciences	science	NOUN
ejpam-4911	569	6	,	,	PUNCT
ejpam-4911	569	7	2:99–112	2:99–112	NUM
ejpam-4911	569	8	,	,	PUNCT
ejpam-4911	569	9	2018	2018	NUM
ejpam-4911	569	10	.	.	PUNCT
ejpam-4911	570	1	[	[	X
ejpam-4911	570	2	13	13	NUM
ejpam-4911	570	3	]	]	PUNCT
ejpam-4911	570	4	binod	binod	PROPN
ejpam-4911	570	5	chandra	chandra	PROPN
ejpam-4911	570	6	tripathy	tripathy	PROPN
ejpam-4911	570	7	s.	s.	PROPN
ejpam-4911	570	8	acharjee	acharjee	PROPN
ejpam-4911	570	9	and	and	CCONJ
ejpam-4911	570	10	kyriakos	kyriakos	PROPN
ejpam-4911	570	11	papadopoulos	papadopoulos	PROPN
ejpam-4911	570	12	.	.	PUNCT
ejpam-4911	571	1	two	two	NUM
ejpam-4911	571	2	forms	form	NOUN
ejpam-4911	571	3	of	of	ADP
ejpam-4911	571	4	pairwise	pairwise	NOUN
ejpam-4911	571	5	lindelöfness	lindelöfness	PUNCT
ejpam-4911	571	6	and	and	CCONJ
ejpam-4911	571	7	some	some	DET
ejpam-4911	571	8	results	result	NOUN
ejpam-4911	571	9	related	relate	VERB
ejpam-4911	571	10	to	to	ADP
ejpam-4911	571	11	hereditary	hereditary	ADJ
ejpam-4911	571	12	class	class	NOUN
ejpam-4911	571	13	in	in	ADP
ejpam-4911	571	14	a	a	DET
ejpam-4911	571	15	bigeneralized	bigeneralize	VERB
ejpam-4911	571	16	topological	topological	ADJ
ejpam-4911	571	17	space	space	NOUN
ejpam-4911	571	18	.	.	PUNCT
ejpam-4911	572	1	new	new	ADJ
ejpam-4911	572	2	mathematics	mathematic	NOUN
ejpam-4911	572	3	and	and	CCONJ
ejpam-4911	572	4	natural	natural	ADJ
ejpam-4911	572	5	computation	computation	NOUN
ejpam-4911	572	6	,	,	PUNCT
ejpam-4911	572	7	13(2):181–193	13(2):181–193	NUM
ejpam-4911	572	8	,	,	PUNCT
ejpam-4911	572	9	2017	2017	NUM
ejpam-4911	572	10	.	.	PUNCT
ejpam-4911	573	1	[	[	X
ejpam-4911	573	2	14	14	NUM
ejpam-4911	573	3	]	]	X
ejpam-4911	573	4	preecha	preecha	NOUN
ejpam-4911	573	5	yupapin	yupapin	PROPN
ejpam-4911	573	6	vadakasi	vadakasi	PROPN
ejpam-4911	573	7	subramanian	subramanian	PROPN
ejpam-4911	573	8	,	,	PUNCT
ejpam-4911	573	9	yasser	yasser	PROPN
ejpam-4911	573	10	farhat	farhat	PROPN
ejpam-4911	573	11	.	.	PUNCT
ejpam-4911	574	1	on	on	ADP
ejpam-4911	574	2	nowhere	nowhere	PRON
ejpam-4911	574	3	dense	dense	ADJ
ejpam-4911	574	4	sets	set	NOUN
ejpam-4911	574	5	.	.	PUNCT
ejpam-4911	575	1	european	european	ADJ
ejpam-4911	575	2	journal	journal	PROPN
ejpam-4911	575	3	of	of	ADP
ejpam-4911	575	4	pure	pure	ADJ
ejpam-4911	575	5	and	and	CCONJ
ejpam-4911	575	6	applied	applied	ADJ
ejpam-4911	575	7	mathematics	mathematic	NOUN
ejpam-4911	575	8	,	,	PUNCT
ejpam-4911	575	9	15(2):403–414	15(2):403–414	NUM
ejpam-4911	575	10	,	,	PUNCT
ejpam-4911	575	11	2022	2022	NUM
ejpam-4911	575	12	.	.	PUNCT