id	sid	tid	token	lemma	pos
ejpam-21	1	1	european	european	PROPN
ejpam-21	1	2	journal	journal	PROPN
ejpam-21	1	3	of	of	ADP
ejpam-21	1	4	pure	pure	ADJ
ejpam-21	1	5	and	and	CCONJ
ejpam-21	1	6	applied	apply	VERB
ejpam-21	1	7	mathematics	mathematic	NOUN
ejpam-21	1	8	vol	vol	NOUN
ejpam-21	1	9	.	.	PROPN
ejpam-21	2	1	1	1	NUM
ejpam-21	2	2	,	,	PUNCT
ejpam-21	2	3	no	no	INTJ
ejpam-21	2	4	.	.	NOUN
ejpam-21	2	5	1	1	NUM
ejpam-21	2	6	,	,	PUNCT
ejpam-21	2	7	2008	2008	NUM
ejpam-21	2	8	,	,	PUNCT
ejpam-21	2	9	(	(	PUNCT
ejpam-21	2	10	82	82	NUM
ejpam-21	2	11	-	-	SYM
ejpam-21	2	12	98	98	NUM
ejpam-21	2	13	)	)	PUNCT
ejpam-21	2	14	issn	issn	PROPN
ejpam-21	2	15	1307	1307	NUM
ejpam-21	2	16	-	-	SYM
ejpam-21	2	17	5543	5543	NUM
ejpam-21	2	18	–	–	PUNCT
ejpam-21	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-21	2	20	honorary	honorary	PROPN
ejpam-21	2	21	invited	invite	VERB
ejpam-21	2	22	paper	paper	NOUN
ejpam-21	2	23	some	some	DET
ejpam-21	2	24	forms	form	NOUN
ejpam-21	2	25	of	of	ADP
ejpam-21	2	26	c	c	NOUN
ejpam-21	2	27	-	-	PUNCT
ejpam-21	2	28	continuity	continuity	NOUN
ejpam-21	2	29	for	for	ADP
ejpam-21	2	30	multifunctions	multifunction	NOUN
ejpam-21	2	31	takashi	takashi	PROPN
ejpam-21	2	32	noiri1,∗	noiri1,∗	PROPN
ejpam-21	2	33	,	,	PUNCT
ejpam-21	2	34	valeriu	valeriu	PROPN
ejpam-21	2	35	popa2	popa2	PROPN
ejpam-21	2	36	1	1	NUM
ejpam-21	2	37	department	department	NOUN
ejpam-21	2	38	of	of	ADP
ejpam-21	2	39	mathematics	mathematic	NOUN
ejpam-21	2	40	,	,	PUNCT
ejpam-21	2	41	yatsushiro	yatsushiro	PROPN
ejpam-21	2	42	college	college	PROPN
ejpam-21	2	43	of	of	ADP
ejpam-21	2	44	technology	technology	NOUN
ejpam-21	2	45	,	,	PUNCT
ejpam-21	2	46	yatsushiro	yatsushiro	PROPN
ejpam-21	2	47	,	,	PUNCT
ejpam-21	2	48	kumamoto,866	kumamoto,866	PROPN
ejpam-21	2	49	-	-	PUNCT
ejpam-21	2	50	8501	8501	NUM
ejpam-21	2	51	japan	japan	PROPN
ejpam-21	2	52	2	2	NUM
ejpam-21	2	53	department	department	NOUN
ejpam-21	2	54	of	of	ADP
ejpam-21	2	55	mathematics	mathematic	NOUN
ejpam-21	2	56	,	,	PUNCT
ejpam-21	2	57	university	university	NOUN
ejpam-21	2	58	of	of	ADP
ejpam-21	2	59	bacǎu	bacǎu	PROPN
ejpam-21	2	60	,	,	PUNCT
ejpam-21	2	61	5500	5500	NUM
ejpam-21	2	62	bacǎu	bacǎu	PROPN
ejpam-21	2	63	,	,	PUNCT
ejpam-21	2	64	romania	romania	PROPN
ejpam-21	2	65	abstract	abstract	NOUN
ejpam-21	2	66	.	.	PUNCT
ejpam-21	3	1	lipski	lipski	ADJ
ejpam-21	4	1	[	[	X
ejpam-21	4	2	14	14	NUM
ejpam-21	4	3	]	]	PUNCT
ejpam-21	4	4	introduced	introduce	VERB
ejpam-21	4	5	the	the	DET
ejpam-21	4	6	notion	notion	NOUN
ejpam-21	4	7	of	of	ADP
ejpam-21	4	8	c	c	NOUN
ejpam-21	4	9	-	-	PUNCT
ejpam-21	4	10	quasi	quasi	ADJ
ejpam-21	4	11	-	-	ADJ
ejpam-21	4	12	continuous	continuous	ADJ
ejpam-21	4	13	multifunctions	multifunction	NOUN
ejpam-21	4	14	as	as	ADP
ejpam-21	4	15	a	a	DET
ejpam-21	4	16	generalization	generalization	NOUN
ejpam-21	4	17	of	of	ADP
ejpam-21	4	18	c	c	NOUN
ejpam-21	4	19	-	-	PUNCT
ejpam-21	4	20	continuous	continuous	ADJ
ejpam-21	4	21	multifunctions	multifunction	NOUN
ejpam-21	4	22	[	[	X
ejpam-21	4	23	20	20	NUM
ejpam-21	4	24	]	]	PUNCT
ejpam-21	4	25	and	and	CCONJ
ejpam-21	4	26	quasi	quasi	ADJ
ejpam-21	4	27	-	-	ADJ
ejpam-21	4	28	continuous	continuous	ADJ
ejpam-21	4	29	multifunctions	multifunction	NOUN
ejpam-21	4	30	[	[	X
ejpam-21	4	31	26	26	NUM
ejpam-21	4	32	]	]	PUNCT
ejpam-21	4	33	.	.	PUNCT
ejpam-21	5	1	in	in	ADP
ejpam-21	5	2	this	this	DET
ejpam-21	5	3	paper	paper	NOUN
ejpam-21	5	4	we	we	PRON
ejpam-21	5	5	obtain	obtain	VERB
ejpam-21	5	6	the	the	DET
ejpam-21	5	7	unified	unified	ADJ
ejpam-21	5	8	theory	theory	NOUN
ejpam-21	5	9	of	of	ADP
ejpam-21	5	10	multifunctions	multifunction	NOUN
ejpam-21	5	11	containing	contain	VERB
ejpam-21	5	12	upper	upper	ADJ
ejpam-21	5	13	/	/	SYM
ejpam-21	5	14	lower	low	ADJ
ejpam-21	5	15	c	c	NOUN
ejpam-21	5	16	-	-	PUNCT
ejpam-21	5	17	quasi	quasi	ADJ
ejpam-21	5	18	-	-	ADJ
ejpam-21	5	19	continuous	continuous	ADJ
ejpam-21	5	20	multifunctions	multifunction	NOUN
ejpam-21	5	21	and	and	CCONJ
ejpam-21	5	22	upper	upper	ADJ
ejpam-21	5	23	/	/	SYM
ejpam-21	5	24	lower	low	ADJ
ejpam-21	5	25	c	c	NOUN
ejpam-21	5	26	-	-	ADJ
ejpam-21	5	27	continuous	continuous	ADJ
ejpam-21	5	28	multifunctions	multifunction	NOUN
ejpam-21	5	29	.	.	PUNCT
ejpam-21	6	1	ams	am	NOUN
ejpam-21	6	2	subject	subject	ADJ
ejpam-21	6	3	classifications	classification	NOUN
ejpam-21	6	4	:	:	PUNCT
ejpam-21	6	5	54c08	54c08	NUM
ejpam-21	6	6	,	,	PUNCT
ejpam-21	6	7	54c60	54c60	NUM
ejpam-21	6	8	.	.	PUNCT
ejpam-21	7	1	key	key	ADJ
ejpam-21	7	2	words	word	NOUN
ejpam-21	7	3	:	:	PUNCT
ejpam-21	7	4	c	c	X
ejpam-21	7	5	-	-	PUNCT
ejpam-21	7	6	continuous	continuous	ADJ
ejpam-21	7	7	,	,	PUNCT
ejpam-21	7	8	c	c	NOUN
ejpam-21	7	9	-	-	PUNCT
ejpam-21	7	10	quasi	quasi	ADJ
ejpam-21	7	11	-	-	ADJ
ejpam-21	7	12	continuous	continuous	ADJ
ejpam-21	7	13	,	,	PUNCT
ejpam-21	7	14	upper	upper	ADJ
ejpam-21	7	15	/	/	SYM
ejpam-21	7	16	lower	low	ADJ
ejpam-21	7	17	c	c	NOUN
ejpam-21	7	18	-	-	PUNCT
ejpam-21	7	19	m	m	NOUN
ejpam-21	7	20	-continuous	-continuous	ADJ
ejpam-21	7	21	,	,	PUNCT
ejpam-21	7	22	multifunction	multifunction	NOUN
ejpam-21	7	23	.	.	PUNCT
ejpam-21	8	1	1	1	X
ejpam-21	8	2	.	.	X
ejpam-21	8	3	introduction	introduction	NOUN
ejpam-21	8	4	semi	semi	ADJ
ejpam-21	8	5	-	-	ADJ
ejpam-21	8	6	open	open	ADJ
ejpam-21	8	7	sets	set	NOUN
ejpam-21	8	8	,	,	PUNCT
ejpam-21	8	9	preopen	preopen	ADJ
ejpam-21	8	10	sets	set	NOUN
ejpam-21	8	11	,	,	PUNCT
ejpam-21	8	12	α	α	NOUN
ejpam-21	8	13	-	-	ADJ
ejpam-21	8	14	open	open	ADJ
ejpam-21	8	15	sets	set	NOUN
ejpam-21	8	16	,	,	PUNCT
ejpam-21	8	17	β	β	ADJ
ejpam-21	8	18	-	-	ADJ
ejpam-21	8	19	open	open	ADJ
ejpam-21	8	20	sets	set	NOUN
ejpam-21	8	21	and	and	CCONJ
ejpam-21	8	22	δ	δ	NOUN
ejpam-21	8	23	-	-	PUNCT
ejpam-21	8	24	open	open	ADJ
ejpam-21	8	25	sets	set	NOUN
ejpam-21	8	26	play	play	VERB
ejpam-21	8	27	an	an	DET
ejpam-21	8	28	important	important	ADJ
ejpam-21	8	29	role	role	NOUN
ejpam-21	8	30	in	in	ADP
ejpam-21	8	31	researching	researching	NOUN
ejpam-21	8	32	of	of	ADP
ejpam-21	8	33	generalizations	generalization	NOUN
ejpam-21	8	34	of	of	ADP
ejpam-21	8	35	continuity	continuity	NOUN
ejpam-21	8	36	in	in	ADP
ejpam-21	8	37	topological	topological	ADJ
ejpam-21	8	38	spaces	space	NOUN
ejpam-21	8	39	.	.	PUNCT
ejpam-21	9	1	by	by	ADP
ejpam-21	9	2	using	use	VERB
ejpam-21	9	3	these	these	DET
ejpam-21	9	4	sets	set	NOUN
ejpam-21	9	5	many	many	ADJ
ejpam-21	9	6	authors	author	NOUN
ejpam-21	9	7	introduced	introduce	VERB
ejpam-21	9	8	and	and	CCONJ
ejpam-21	9	9	investigated	investigate	VERB
ejpam-21	9	10	various	various	ADJ
ejpam-21	9	11	types	type	NOUN
ejpam-21	9	12	of	of	ADP
ejpam-21	9	13	noncontinuous	noncontinuous	ADJ
ejpam-21	9	14	functions	function	NOUN
ejpam-21	9	15	and	and	CCONJ
ejpam-21	9	16	multifunctions	multifunction	NOUN
ejpam-21	9	17	.	.	PUNCT
ejpam-21	10	1	in	in	ADP
ejpam-21	10	2	1970	1970	NUM
ejpam-21	10	3	,	,	PUNCT
ejpam-21	10	4	gentry	gentry	NOUN
ejpam-21	10	5	and	and	CCONJ
ejpam-21	10	6	hoyle	hoyle	PROPN
ejpam-21	10	7	iii	iii	PROPN
ejpam-21	10	8	[	[	X
ejpam-21	10	9	9	9	NUM
ejpam-21	10	10	]	]	PUNCT
ejpam-21	10	11	defined	define	VERB
ejpam-21	10	12	a	a	DET
ejpam-21	10	13	function	function	NOUN
ejpam-21	10	14	f	f	NOUN
ejpam-21	10	15	:	:	PUNCT
ejpam-21	10	16	x	x	X
ejpam-21	10	17	→	→	SYM
ejpam-21	10	18	y	y	PROPN
ejpam-21	10	19	to	to	PART
ejpam-21	10	20	be	be	AUX
ejpam-21	10	21	c	c	NOUN
ejpam-21	10	22	-	-	ADJ
ejpam-21	10	23	continuous	continuous	ADJ
ejpam-21	10	24	at	at	ADP
ejpam-21	10	25	a	a	DET
ejpam-21	10	26	point	point	NOUN
ejpam-21	10	27	x	x	SYM
ejpam-21	10	28	∈	∈	NOUN
ejpam-21	10	29	x	x	INTJ
ejpam-21	10	30	if	if	SCONJ
ejpam-21	10	31	for	for	ADP
ejpam-21	10	32	each	each	DET
ejpam-21	10	33	open	open	ADJ
ejpam-21	10	34	set	set	VERB
ejpam-21	10	35	v	v	NOUN
ejpam-21	10	36	of	of	ADP
ejpam-21	10	37	y	y	NOUN
ejpam-21	10	38	containing	contain	VERB
ejpam-21	10	39	f(x	f(x	PROPN
ejpam-21	10	40	)	)	PUNCT
ejpam-21	10	41	and	and	CCONJ
ejpam-21	10	42	having	have	VERB
ejpam-21	10	43	compact	compact	ADJ
ejpam-21	10	44	complement	complement	NOUN
ejpam-21	10	45	,	,	PUNCT
ejpam-21	10	46	there	there	PRON
ejpam-21	10	47	exists	exist	VERB
ejpam-21	10	48	an	an	DET
ejpam-21	10	49	open	open	ADJ
ejpam-21	10	50	set	set	NOUN
ejpam-21	10	51	u	u	NOUN
ejpam-21	10	52	of	of	ADP
ejpam-21	10	53	x	x	PUNCT
ejpam-21	10	54	containing	contain	VERB
ejpam-21	10	55	x	x	PUNCT
ejpam-21	10	56	such	such	ADJ
ejpam-21	10	57	that	that	DET
ejpam-21	10	58	f(u	f(u	PROPN
ejpam-21	10	59	)	)	PUNCT
ejpam-21	11	1	⊂	⊂	PROPN
ejpam-21	11	2	v	v	NOUN
ejpam-21	11	3	.	.	PUNCT
ejpam-21	12	1	some	some	DET
ejpam-21	12	2	properties	property	NOUN
ejpam-21	12	3	of	of	ADP
ejpam-21	12	4	c	c	NOUN
ejpam-21	12	5	-	-	PUNCT
ejpam-21	12	6	continuous	continuous	ADJ
ejpam-21	12	7	functions	function	NOUN
ejpam-21	12	8	are	be	AUX
ejpam-21	12	9	studied	study	VERB
ejpam-21	12	10	in	in	ADP
ejpam-21	12	11	[	[	X
ejpam-21	12	12	15	15	NUM
ejpam-21	12	13	]	]	PUNCT
ejpam-21	12	14	,	,	PUNCT
ejpam-21	12	15	[	[	X
ejpam-21	12	16	16	16	NUM
ejpam-21	12	17	]	]	PUNCT
ejpam-21	12	18	,	,	PUNCT
ejpam-21	12	19	[	[	X
ejpam-21	12	20	24	24	NUM
ejpam-21	12	21	]	]	PUNCT
ejpam-21	12	22	and	and	CCONJ
ejpam-21	12	23	other	other	ADJ
ejpam-21	12	24	papers	paper	NOUN
ejpam-21	12	25	.	.	PUNCT
ejpam-21	13	1	neubrunn	neubrunn	NOUN
ejpam-21	14	1	[	[	X
ejpam-21	14	2	20	20	NUM
ejpam-21	14	3	]	]	PUNCT
ejpam-21	14	4	and	and	CCONJ
ejpam-21	14	5	holá	holá	NOUN
ejpam-21	14	6	et	et	PROPN
ejpam-21	14	7	al	al	PROPN
ejpam-21	14	8	.	.	PUNCT
ejpam-21	15	1	[	[	X
ejpam-21	15	2	11	11	NUM
ejpam-21	15	3	]	]	PUNCT
ejpam-21	15	4	extended	extend	VERB
ejpam-21	15	5	this	this	DET
ejpam-21	15	6	notion	notion	NOUN
ejpam-21	15	7	to	to	ADP
ejpam-21	15	8	the	the	DET
ejpam-21	15	9	setting	setting	NOUN
ejpam-21	15	10	of	of	ADP
ejpam-21	15	11	multifunctions	multifunction	NOUN
ejpam-21	15	12	.	.	PUNCT
ejpam-21	16	1	in	in	ADP
ejpam-21	16	2	[	[	X
ejpam-21	16	3	14	14	NUM
ejpam-21	16	4	]	]	PUNCT
ejpam-21	16	5	,	,	PUNCT
ejpam-21	16	6	lipski	lipski	PROPN
ejpam-21	16	7	introduced	introduce	VERB
ejpam-21	16	8	the	the	DET
ejpam-21	16	9	notion	notion	NOUN
ejpam-21	16	10	of	of	ADP
ejpam-21	16	11	c	c	PROPN
ejpam-21	16	12	-quasicontinuous	-quasicontinuous	ADJ
ejpam-21	16	13	multifunctions	multifunction	NOUN
ejpam-21	16	14	as	as	ADP
ejpam-21	16	15	a	a	DET
ejpam-21	16	16	generalization	generalization	NOUN
ejpam-21	16	17	of	of	ADP
ejpam-21	16	18	c	c	NOUN
ejpam-21	16	19	-	-	PUNCT
ejpam-21	16	20	continuous	continuous	ADJ
ejpam-21	16	21	multifunctions	multifunction	NOUN
ejpam-21	16	22	and	and	CCONJ
ejpam-21	16	23	quasi	quasi	ADJ
ejpam-21	16	24	-	-	ADJ
ejpam-21	16	25	continuous	continuous	ADJ
ejpam-21	16	26	multifunctions	multifunction	NOUN
ejpam-21	17	1	[	[	X
ejpam-21	17	2	26	26	NUM
ejpam-21	17	3	]	]	PUNCT
ejpam-21	17	4	.	.	PUNCT
ejpam-21	18	1	some	some	DET
ejpam-21	18	2	properties	property	NOUN
ejpam-21	18	3	of	of	ADP
ejpam-21	18	4	c	c	NOUN
ejpam-21	18	5	-	-	PUNCT
ejpam-21	18	6	quasi	quasi	ADJ
ejpam-21	18	7	-	-	ADJ
ejpam-21	18	8	continuous	continuous	ADJ
ejpam-21	18	9	multifunctions	multifunction	NOUN
ejpam-21	18	10	are	be	AUX
ejpam-21	18	11	studied	study	VERB
ejpam-21	18	12	in	in	ADP
ejpam-21	18	13	[	[	X
ejpam-21	18	14	36	36	NUM
ejpam-21	18	15	]	]	PUNCT
ejpam-21	18	16	.	.	PUNCT
ejpam-21	19	1	in	in	ADP
ejpam-21	19	2	this	this	DET
ejpam-21	19	3	paper	paper	NOUN
ejpam-21	19	4	we	we	PRON
ejpam-21	19	5	introduce	introduce	VERB
ejpam-21	19	6	upper	upper	ADV
ejpam-21	19	7	/	/	SYM
ejpam-21	19	8	lower	low	ADJ
ejpam-21	19	9	c	c	NOUN
ejpam-21	19	10	-	-	PUNCT
ejpam-21	19	11	m	m	NOUN
ejpam-21	19	12	-	-	ADJ
ejpam-21	19	13	continuous	continuous	ADJ
ejpam-21	19	14	multifunctions	multifunction	NOUN
ejpam-21	19	15	as	as	ADP
ejpam-21	19	16	multifunctions	multifunction	NOUN
ejpam-21	19	17	defined	define	VERB
ejpam-21	19	18	on	on	ADP
ejpam-21	19	19	a	a	DET
ejpam-21	19	20	set	set	NOUN
ejpam-21	19	21	satisfying	satisfy	VERB
ejpam-21	19	22	some	some	DET
ejpam-21	19	23	minimal	minimal	ADJ
ejpam-21	19	24	conditions	condition	NOUN
ejpam-21	19	25	.	.	PUNCT
ejpam-21	20	1	we	we	PRON
ejpam-21	20	2	obtain	obtain	VERB
ejpam-21	20	3	some	some	DET
ejpam-21	20	4	characterizations	characterization	NOUN
ejpam-21	20	5	and	and	CCONJ
ejpam-21	20	6	several	several	ADJ
ejpam-21	20	7	properties	property	NOUN
ejpam-21	20	8	of	of	ADP
ejpam-21	20	9	such	such	ADJ
ejpam-21	20	10	multifunctions	multifunction	NOUN
ejpam-21	20	11	which	which	PRON
ejpam-21	20	12	turn	turn	VERB
ejpam-21	20	13	out	out	ADP
ejpam-21	20	14	unify	unify	VERB
ejpam-21	20	15	some	some	DET
ejpam-21	20	16	results	result	NOUN
ejpam-21	20	17	established	establish	VERB
ejpam-21	20	18	in	in	ADP
ejpam-21	20	19	[	[	X
ejpam-21	20	20	11	11	NUM
ejpam-21	20	21	]	]	PUNCT
ejpam-21	20	22	,	,	PUNCT
ejpam-21	20	23	[	[	X
ejpam-21	20	24	14	14	NUM
ejpam-21	20	25	]	]	PUNCT
ejpam-21	20	26	and	and	CCONJ
ejpam-21	20	27	[	[	X
ejpam-21	20	28	36	36	NUM
ejpam-21	20	29	]	]	PUNCT
ejpam-21	20	30	.	.	PUNCT
ejpam-21	21	1	in	in	ADP
ejpam-21	21	2	the	the	DET
ejpam-21	21	3	last	last	ADJ
ejpam-21	21	4	section	section	NOUN
ejpam-21	21	5	,	,	PUNCT
ejpam-21	21	6	we	we	PRON
ejpam-21	21	7	recall	recall	VERB
ejpam-21	21	8	some	some	DET
ejpam-21	21	9	types	type	NOUN
ejpam-21	21	10	of	of	ADP
ejpam-21	21	11	modifications	modification	NOUN
ejpam-21	21	12	of	of	ADP
ejpam-21	21	13	open	open	ADJ
ejpam-21	21	14	sets	set	NOUN
ejpam-21	21	15	and	and	CCONJ
ejpam-21	21	16	point	point	VERB
ejpam-21	21	17	out	out	ADP
ejpam-21	21	18	the	the	DET
ejpam-21	21	19	possibility	possibility	NOUN
ejpam-21	21	20	for	for	ADP
ejpam-21	21	21	new	new	ADJ
ejpam-21	21	22	forms	form	NOUN
ejpam-21	21	23	of	of	ADP
ejpam-21	21	24	c	c	NOUN
ejpam-21	21	25	-continuous	-continuous	ADJ
ejpam-21	21	26	multifunctions	multifunction	NOUN
ejpam-21	21	27	.	.	PUNCT
ejpam-21	22	1	∗corresponding	∗corresponde	VERB
ejpam-21	22	2	author	author	NOUN
ejpam-21	22	3	.	.	PUNCT
ejpam-21	23	1	email	email	NOUN
ejpam-21	23	2	addresses	address	NOUN
ejpam-21	23	3	:	:	PUNCT
ejpam-21	23	4	noiri@as.yatsushiro-nct.ac.jp	noiri@as.yatsushiro-nct.ac.jp	PROPN
ejpam-21	23	5	(	(	PUNCT
ejpam-21	23	6	t.noiri	t.noiri	NOUN
ejpam-21	23	7	)	)	PUNCT
ejpam-21	23	8	vpopa@ub.ro	vpopa@ub.ro	NOUN
ejpam-21	23	9	(	(	PUNCT
ejpam-21	23	10	v.popa	v.popa	NOUN
ejpam-21	23	11	)	)	PUNCT
ejpam-21	23	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-21	24	1	82	82	NUM
ejpam-21	25	1	c	c	X
ejpam-21	25	2	©	©	PROPN
ejpam-21	25	3	2007	2007	NUM
ejpam-21	25	4	ejpam	ejpam	NOUN
ejpam-21	25	5	all	all	DET
ejpam-21	25	6	rights	right	NOUN
ejpam-21	25	7	reserved	reserve	VERB
ejpam-21	25	8	.	.	PUNCT
ejpam-21	26	1	t.noiri	t.noiri	ADV
ejpam-21	26	2	,	,	PUNCT
ejpam-21	26	3	v.popa	v.popa	NOUN
ejpam-21	26	4	/	/	SYM
ejpam-21	26	5	eur	eur	PROPN
ejpam-21	26	6	.	.	PUNCT
ejpam-21	27	1	j.	j.	PROPN
ejpam-21	27	2	pure	pure	PROPN
ejpam-21	27	3	appl	appl	PROPN
ejpam-21	27	4	.	.	PROPN
ejpam-21	27	5	math	math	PROPN
ejpam-21	27	6	,	,	PUNCT
ejpam-21	27	7	1	1	NUM
ejpam-21	27	8	(	(	PUNCT
ejpam-21	27	9	2008	2008	NUM
ejpam-21	27	10	)	)	PUNCT
ejpam-21	27	11	,	,	PUNCT
ejpam-21	27	12	(	(	PUNCT
ejpam-21	27	13	82	82	NUM
ejpam-21	27	14	-	-	SYM
ejpam-21	27	15	98	98	NUM
ejpam-21	27	16	)	)	PUNCT
ejpam-21	27	17	83	83	NUM
ejpam-21	27	18	2	2	NUM
ejpam-21	27	19	.	.	PUNCT
ejpam-21	28	1	preliminaries	preliminary	NOUN
ejpam-21	28	2	let	let	VERB
ejpam-21	28	3	(	(	PUNCT
ejpam-21	28	4	x	x	NOUN
ejpam-21	28	5	,	,	PUNCT
ejpam-21	28	6	τ	τ	X
ejpam-21	28	7	)	)	PUNCT
ejpam-21	28	8	be	be	VERB
ejpam-21	28	9	a	a	DET
ejpam-21	28	10	topological	topological	ADJ
ejpam-21	28	11	space	space	NOUN
ejpam-21	28	12	and	and	CCONJ
ejpam-21	28	13	a	a	DET
ejpam-21	28	14	a	a	DET
ejpam-21	28	15	subset	subset	NOUN
ejpam-21	28	16	of	of	ADP
ejpam-21	28	17	x	x	PRON
ejpam-21	28	18	.	.	PUNCT
ejpam-21	29	1	the	the	DET
ejpam-21	29	2	closure	closure	NOUN
ejpam-21	29	3	of	of	ADP
ejpam-21	29	4	a	a	PRON
ejpam-21	29	5	and	and	CCONJ
ejpam-21	29	6	the	the	DET
ejpam-21	29	7	interior	interior	NOUN
ejpam-21	29	8	of	of	ADP
ejpam-21	29	9	a	a	PRON
ejpam-21	29	10	are	be	AUX
ejpam-21	29	11	denoted	denote	VERB
ejpam-21	29	12	by	by	ADP
ejpam-21	29	13	cl(a	cl(a	NOUN
ejpam-21	29	14	)	)	PUNCT
ejpam-21	29	15	and	and	CCONJ
ejpam-21	29	16	int(a	int(a	PROPN
ejpam-21	29	17	)	)	PUNCT
ejpam-21	29	18	,	,	PUNCT
ejpam-21	29	19	respectively	respectively	ADV
ejpam-21	29	20	.	.	PUNCT
ejpam-21	30	1	definition	definition	NOUN
ejpam-21	30	2	2.1	2.1	NUM
ejpam-21	30	3	.	.	PUNCT
ejpam-21	31	1	let	let	VERB
ejpam-21	31	2	(	(	PUNCT
ejpam-21	31	3	x	x	NOUN
ejpam-21	31	4	,	,	PUNCT
ejpam-21	31	5	τ	τ	X
ejpam-21	31	6	)	)	PUNCT
ejpam-21	31	7	be	be	VERB
ejpam-21	31	8	a	a	DET
ejpam-21	31	9	topological	topological	ADJ
ejpam-21	31	10	space	space	NOUN
ejpam-21	31	11	.	.	PUNCT
ejpam-21	32	1	a	a	DET
ejpam-21	32	2	subset	subset	NOUN
ejpam-21	32	3	a	a	PRON
ejpam-21	32	4	of	of	ADP
ejpam-21	32	5	x	x	SYM
ejpam-21	32	6	is	be	AUX
ejpam-21	32	7	said	say	VERB
ejpam-21	32	8	to	to	PART
ejpam-21	32	9	be	be	AUX
ejpam-21	32	10	α	α	X
ejpam-21	32	11	-	-	ADJ
ejpam-21	32	12	open	open	ADJ
ejpam-21	32	13	[	[	X
ejpam-21	32	14	22	22	NUM
ejpam-21	32	15	]	]	PUNCT
ejpam-21	32	16	(	(	PUNCT
ejpam-21	32	17	resp	resp	NOUN
ejpam-21	32	18	.	.	PUNCT
ejpam-21	33	1	semi	semi	ADJ
ejpam-21	33	2	-	-	ADJ
ejpam-21	33	3	open	open	ADJ
ejpam-21	33	4	[	[	PUNCT
ejpam-21	33	5	13	13	NUM
ejpam-21	33	6	]	]	PUNCT
ejpam-21	33	7	,	,	PUNCT
ejpam-21	33	8	preopen	preopen	ADJ
ejpam-21	33	9	[	[	X
ejpam-21	33	10	18	18	NUM
ejpam-21	33	11	]	]	PUNCT
ejpam-21	33	12	,	,	PUNCT
ejpam-21	33	13	β	β	X
ejpam-21	33	14	-	-	VERB
ejpam-21	33	15	open	open	ADJ
ejpam-21	33	16	[	[	X
ejpam-21	33	17	1	1	NUM
ejpam-21	33	18	]	]	PUNCT
ejpam-21	33	19	or	or	CCONJ
ejpam-21	33	20	semi	semi	ADJ
ejpam-21	33	21	-	-	ADJ
ejpam-21	33	22	preopen	preopen	ADJ
ejpam-21	33	23	[	[	X
ejpam-21	33	24	4	4	NUM
ejpam-21	33	25	]	]	PUNCT
ejpam-21	33	26	,	,	PUNCT
ejpam-21	33	27	b	b	X
ejpam-21	33	28	-	-	PUNCT
ejpam-21	33	29	open	open	ADJ
ejpam-21	33	30	[	[	X
ejpam-21	33	31	5	5	NUM
ejpam-21	33	32	]	]	PUNCT
ejpam-21	33	33	)	)	PUNCT
ejpam-21	33	34	if	if	SCONJ
ejpam-21	33	35	a	a	DET
ejpam-21	33	36	⊂	⊂	X
ejpam-21	33	37	int(cl(int(a	int(cl(int(a	NOUN
ejpam-21	33	38	)	)	PUNCT
ejpam-21	33	39	)	)	PUNCT
ejpam-21	33	40	)	)	PUNCT
ejpam-21	34	1	(	(	PUNCT
ejpam-21	34	2	resp	resp	NOUN
ejpam-21	34	3	.	.	PUNCT
ejpam-21	35	1	a	a	DET
ejpam-21	35	2	⊂	⊂	PROPN
ejpam-21	35	3	cl(int(a	cl(int(a	PROPN
ejpam-21	35	4	)	)	PUNCT
ejpam-21	35	5	)	)	PUNCT
ejpam-21	35	6	,	,	PUNCT
ejpam-21	35	7	a	a	DET
ejpam-21	35	8	⊂	⊂	PROPN
ejpam-21	35	9	int(cl(a	int(cl(a	PROPN
ejpam-21	35	10	)	)	PUNCT
ejpam-21	35	11	)	)	PUNCT
ejpam-21	35	12	,	,	PUNCT
ejpam-21	35	13	a	a	DET
ejpam-21	35	14	⊂	⊂	PROPN
ejpam-21	35	15	cl(int(cl(a	cl(int(cl(a	NOUN
ejpam-21	35	16	)	)	PUNCT
ejpam-21	35	17	)	)	PUNCT
ejpam-21	35	18	)	)	PUNCT
ejpam-21	35	19	,	,	PUNCT
ejpam-21	35	20	a	a	DET
ejpam-21	35	21	⊂	⊂	PROPN
ejpam-21	35	22	int(cl(a	int(cl(a	PROPN
ejpam-21	35	23	)	)	PUNCT
ejpam-21	35	24	)	)	PUNCT
ejpam-21	35	25	∪	∪	ADP
ejpam-21	35	26	cl(int(a	cl(int(a	PROPN
ejpam-21	35	27	)	)	PUNCT
ejpam-21	35	28	)	)	PUNCT
ejpam-21	35	29	)	)	PUNCT
ejpam-21	35	30	.	.	PUNCT
ejpam-21	36	1	the	the	DET
ejpam-21	36	2	family	family	NOUN
ejpam-21	36	3	of	of	ADP
ejpam-21	36	4	all	all	PRON
ejpam-21	36	5	semi	semi	ADJ
ejpam-21	36	6	-	-	ADJ
ejpam-21	36	7	open	open	ADJ
ejpam-21	36	8	(	(	PUNCT
ejpam-21	36	9	resp	resp	NOUN
ejpam-21	36	10	.	.	PUNCT
ejpam-21	37	1	preopen	preopen	ADJ
ejpam-21	37	2	,	,	PUNCT
ejpam-21	37	3	α	α	NOUN
ejpam-21	37	4	-	-	ADJ
ejpam-21	37	5	open	open	ADJ
ejpam-21	37	6	,	,	PUNCT
ejpam-21	37	7	β	β	NOUN
ejpam-21	37	8	-	-	ADJ
ejpam-21	37	9	open	open	ADJ
ejpam-21	37	10	,	,	PUNCT
ejpam-21	37	11	semi	semi	ADJ
ejpam-21	37	12	-	-	ADJ
ejpam-21	37	13	preopen	preopen	ADJ
ejpam-21	37	14	,	,	PUNCT
ejpam-21	37	15	b	b	X
ejpam-21	37	16	-	-	PUNCT
ejpam-21	37	17	open	open	ADJ
ejpam-21	37	18	)	)	PUNCT
ejpam-21	37	19	sets	set	NOUN
ejpam-21	37	20	in	in	ADP
ejpam-21	37	21	x	x	PUNCT
ejpam-21	37	22	is	be	AUX
ejpam-21	37	23	denoted	denote	VERB
ejpam-21	37	24	by	by	ADP
ejpam-21	37	25	so(x	so(x	NOUN
ejpam-21	37	26	)	)	PUNCT
ejpam-21	37	27	(	(	PUNCT
ejpam-21	37	28	resp	resp	NOUN
ejpam-21	37	29	.	.	PUNCT
ejpam-21	38	1	po(x	po(x	NUM
ejpam-21	38	2	)	)	PUNCT
ejpam-21	38	3	,	,	PUNCT
ejpam-21	39	1	α(x	α(x	NOUN
ejpam-21	39	2	)	)	PUNCT
ejpam-21	39	3	,	,	PUNCT
ejpam-21	39	4	β(x	β(x	NOUN
ejpam-21	39	5	)	)	PUNCT
ejpam-21	39	6	,	,	PUNCT
ejpam-21	39	7	spo(x	spo(x	PROPN
ejpam-21	39	8	)	)	PUNCT
ejpam-21	39	9	,	,	PUNCT
ejpam-21	39	10	bo(x	bo(x	NUM
ejpam-21	39	11	)	)	PUNCT
ejpam-21	39	12	)	)	PUNCT
ejpam-21	39	13	.	.	PUNCT
ejpam-21	40	1	definition	definition	NOUN
ejpam-21	40	2	2.2	2.2	NUM
ejpam-21	40	3	.	.	PUNCT
ejpam-21	41	1	the	the	DET
ejpam-21	41	2	complement	complement	NOUN
ejpam-21	41	3	of	of	ADP
ejpam-21	41	4	a	a	DET
ejpam-21	41	5	semi	semi	ADJ
ejpam-21	41	6	-	-	ADJ
ejpam-21	41	7	open	open	ADJ
ejpam-21	41	8	(	(	PUNCT
ejpam-21	41	9	resp	resp	NOUN
ejpam-21	41	10	.	.	PUNCT
ejpam-21	42	1	preopen	preopen	ADJ
ejpam-21	42	2	,	,	PUNCT
ejpam-21	42	3	α	α	NOUN
ejpam-21	42	4	-	-	ADJ
ejpam-21	42	5	open	open	ADJ
ejpam-21	42	6	,	,	PUNCT
ejpam-21	42	7	β	β	NOUN
ejpam-21	42	8	-	-	ADJ
ejpam-21	42	9	open	open	ADJ
ejpam-21	42	10	,	,	PUNCT
ejpam-21	42	11	semi	semi	ADJ
ejpam-21	42	12	-	-	ADJ
ejpam-21	42	13	preopen	preopen	ADJ
ejpam-21	42	14	,	,	PUNCT
ejpam-21	42	15	b	b	X
ejpam-21	42	16	-	-	PUNCT
ejpam-21	42	17	open	open	ADJ
ejpam-21	42	18	)	)	PUNCT
ejpam-21	42	19	set	set	NOUN
ejpam-21	42	20	is	be	AUX
ejpam-21	42	21	said	say	VERB
ejpam-21	42	22	to	to	PART
ejpam-21	42	23	be	be	AUX
ejpam-21	42	24	semi	semi	ADJ
ejpam-21	42	25	-	-	ADJ
ejpam-21	42	26	closed	closed	ADJ
ejpam-21	42	27	[	[	X
ejpam-21	42	28	7	7	NUM
ejpam-21	42	29	]	]	X
ejpam-21	42	30	(	(	PUNCT
ejpam-21	42	31	resp	resp	NOUN
ejpam-21	42	32	.	.	PUNCT
ejpam-21	43	1	preclosed	preclose	VERB
ejpam-21	43	2	[	[	X
ejpam-21	43	3	8	8	NUM
ejpam-21	43	4	]	]	PUNCT
ejpam-21	43	5	,	,	PUNCT
ejpam-21	43	6	α	α	X
ejpam-21	43	7	-	-	PUNCT
ejpam-21	43	8	closed	closed	ADJ
ejpam-21	43	9	[	[	X
ejpam-21	43	10	19	19	NUM
ejpam-21	43	11	]	]	PUNCT
ejpam-21	43	12	,	,	PUNCT
ejpam-21	43	13	β	β	X
ejpam-21	43	14	-	-	PUNCT
ejpam-21	43	15	closed	closed	ADJ
ejpam-21	43	16	[	[	X
ejpam-21	43	17	1	1	NUM
ejpam-21	43	18	]	]	PUNCT
ejpam-21	43	19	,	,	PUNCT
ejpam-21	43	20	semi	semi	ADJ
ejpam-21	43	21	-	-	ADJ
ejpam-21	43	22	preclosed	preclosed	ADJ
ejpam-21	43	23	[	[	X
ejpam-21	43	24	4	4	NUM
ejpam-21	43	25	]	]	PUNCT
ejpam-21	43	26	,	,	PUNCT
ejpam-21	43	27	b	b	X
ejpam-21	43	28	-	-	PUNCT
ejpam-21	43	29	closed	closed	ADJ
ejpam-21	43	30	[	[	X
ejpam-21	43	31	5	5	NUM
ejpam-21	43	32	]	]	NUM
ejpam-21	43	33	)	)	PUNCT
ejpam-21	43	34	.	.	PUNCT
ejpam-21	44	1	definition	definition	NOUN
ejpam-21	44	2	2.3	2.3	NUM
ejpam-21	44	3	.	.	PUNCT
ejpam-21	45	1	the	the	DET
ejpam-21	45	2	intersection	intersection	NOUN
ejpam-21	45	3	of	of	ADP
ejpam-21	45	4	all	all	PRON
ejpam-21	45	5	semi	semi	ADJ
ejpam-21	45	6	-	-	ADJ
ejpam-21	45	7	closed	closed	ADJ
ejpam-21	45	8	(	(	PUNCT
ejpam-21	45	9	resp	resp	NOUN
ejpam-21	45	10	.	.	PUNCT
ejpam-21	45	11	preclosed	preclose	VERB
ejpam-21	45	12	,	,	PUNCT
ejpam-21	45	13	α	α	NOUN
ejpam-21	45	14	-	-	PUNCT
ejpam-21	45	15	closed	closed	ADJ
ejpam-21	45	16	,	,	PUNCT
ejpam-21	45	17	β	β	NOUN
ejpam-21	45	18	-	-	VERB
ejpam-21	45	19	closed	closed	ADJ
ejpam-21	45	20	,	,	PUNCT
ejpam-21	45	21	semipreclosed	semipreclose	VERB
ejpam-21	45	22	,	,	PUNCT
ejpam-21	45	23	b	b	X
ejpam-21	45	24	-	-	PUNCT
ejpam-21	45	25	closed	closed	ADJ
ejpam-21	45	26	)	)	PUNCT
ejpam-21	45	27	sets	set	NOUN
ejpam-21	45	28	of	of	ADP
ejpam-21	45	29	x	x	PUNCT
ejpam-21	45	30	containing	contain	VERB
ejpam-21	45	31	a	a	PRON
ejpam-21	45	32	is	be	AUX
ejpam-21	45	33	called	call	VERB
ejpam-21	45	34	the	the	DET
ejpam-21	45	35	semi	semi	NOUN
ejpam-21	45	36	-	-	NOUN
ejpam-21	45	37	closure	closure	ADJ
ejpam-21	45	38	[	[	X
ejpam-21	45	39	7	7	NUM
ejpam-21	45	40	]	]	X
ejpam-21	45	41	(	(	PUNCT
ejpam-21	45	42	resp	resp	NOUN
ejpam-21	45	43	.	.	PUNCT
ejpam-21	46	1	preclosure	preclosure	ADJ
ejpam-21	47	1	[	[	X
ejpam-21	47	2	8	8	NUM
ejpam-21	47	3	]	]	PUNCT
ejpam-21	47	4	,	,	PUNCT
ejpam-21	47	5	α	α	X
ejpam-21	47	6	-	-	NOUN
ejpam-21	47	7	closure	closure	NOUN
ejpam-21	47	8	[	[	X
ejpam-21	47	9	19	19	NUM
ejpam-21	47	10	]	]	PUNCT
ejpam-21	47	11	,	,	PUNCT
ejpam-21	47	12	β	β	NOUN
ejpam-21	47	13	-	-	NOUN
ejpam-21	47	14	closure	closure	NOUN
ejpam-21	47	15	[	[	X
ejpam-21	47	16	2	2	NUM
ejpam-21	47	17	]	]	PUNCT
ejpam-21	47	18	,	,	PUNCT
ejpam-21	47	19	semi	semi	ADJ
ejpam-21	47	20	-	-	ADJ
ejpam-21	47	21	preclosure	preclosure	ADJ
ejpam-21	47	22	[	[	X
ejpam-21	47	23	4	4	NUM
ejpam-21	47	24	]	]	PUNCT
ejpam-21	47	25	,	,	PUNCT
ejpam-21	47	26	b	b	X
ejpam-21	47	27	-	-	PUNCT
ejpam-21	47	28	closure	closure	NOUN
ejpam-21	47	29	[	[	X
ejpam-21	47	30	5	5	NUM
ejpam-21	47	31	]	]	PUNCT
ejpam-21	47	32	)	)	PUNCT
ejpam-21	47	33	of	of	ADP
ejpam-21	47	34	a	a	PRON
ejpam-21	47	35	and	and	CCONJ
ejpam-21	47	36	is	be	AUX
ejpam-21	47	37	denoted	denote	VERB
ejpam-21	47	38	by	by	ADP
ejpam-21	47	39	scl(a	scl(a	PROPN
ejpam-21	47	40	)	)	PUNCT
ejpam-21	47	41	(	(	PUNCT
ejpam-21	47	42	resp	resp	NOUN
ejpam-21	47	43	.	.	PUNCT
ejpam-21	48	1	pcl(a	pcl(a	NUM
ejpam-21	48	2	)	)	PUNCT
ejpam-21	48	3	,	,	PUNCT
ejpam-21	48	4	αcl(a	αcl(a	PROPN
ejpam-21	48	5	)	)	PUNCT
ejpam-21	48	6	,	,	PUNCT
ejpam-21	48	7	βcl(a	βcl(a	PROPN
ejpam-21	48	8	)	)	PUNCT
ejpam-21	48	9	,	,	PUNCT
ejpam-21	48	10	spcl(a	spcl(a	NUM
ejpam-21	48	11	)	)	PUNCT
ejpam-21	48	12	,	,	PUNCT
ejpam-21	48	13	bcl(a	bcl(a	PROPN
ejpam-21	48	14	)	)	PUNCT
ejpam-21	48	15	.	.	PUNCT
ejpam-21	49	1	definition	definition	NOUN
ejpam-21	49	2	2.4	2.4	NUM
ejpam-21	49	3	.	.	PUNCT
ejpam-21	50	1	the	the	DET
ejpam-21	50	2	union	union	NOUN
ejpam-21	50	3	of	of	ADP
ejpam-21	50	4	all	all	PRON
ejpam-21	50	5	semi	semi	ADJ
ejpam-21	50	6	-	-	ADJ
ejpam-21	50	7	open	open	ADJ
ejpam-21	50	8	(	(	PUNCT
ejpam-21	50	9	resp	resp	NOUN
ejpam-21	50	10	.	.	PUNCT
ejpam-21	51	1	preopen	preopen	ADJ
ejpam-21	51	2	,	,	PUNCT
ejpam-21	51	3	α	α	NOUN
ejpam-21	51	4	-	-	ADJ
ejpam-21	51	5	open	open	ADJ
ejpam-21	51	6	,	,	PUNCT
ejpam-21	51	7	β	β	NOUN
ejpam-21	51	8	-	-	ADJ
ejpam-21	51	9	open	open	ADJ
ejpam-21	51	10	,	,	PUNCT
ejpam-21	51	11	semi	semi	ADJ
ejpam-21	51	12	-	-	ADJ
ejpam-21	51	13	preopen	preopen	ADJ
ejpam-21	51	14	,	,	PUNCT
ejpam-21	51	15	b	b	X
ejpam-21	51	16	-	-	PUNCT
ejpam-21	51	17	open	open	ADJ
ejpam-21	51	18	)	)	PUNCT
ejpam-21	51	19	sets	set	NOUN
ejpam-21	51	20	of	of	ADP
ejpam-21	51	21	x	x	PUNCT
ejpam-21	51	22	contained	contain	VERB
ejpam-21	51	23	in	in	ADP
ejpam-21	51	24	a	a	PRON
ejpam-21	51	25	is	be	AUX
ejpam-21	51	26	called	call	VERB
ejpam-21	51	27	the	the	DET
ejpam-21	51	28	semi	semi	ADJ
ejpam-21	51	29	-	-	ADJ
ejpam-21	51	30	interior	interior	ADJ
ejpam-21	51	31	(	(	PUNCT
ejpam-21	51	32	resp	resp	NOUN
ejpam-21	51	33	.	.	PUNCT
ejpam-21	52	1	preinterior	preinterior	PROPN
ejpam-21	52	2	,	,	PUNCT
ejpam-21	52	3	α	α	NOUN
ejpam-21	52	4	-	-	NOUN
ejpam-21	52	5	interior	interior	ADJ
ejpam-21	52	6	,	,	PUNCT
ejpam-21	52	7	β	β	NOUN
ejpam-21	52	8	-	-	ADJ
ejpam-21	52	9	interior	interior	ADJ
ejpam-21	52	10	,	,	PUNCT
ejpam-21	52	11	semipreinterior	semipreinterior	NOUN
ejpam-21	52	12	,	,	PUNCT
ejpam-21	52	13	b	b	NOUN
ejpam-21	52	14	-	-	PUNCT
ejpam-21	52	15	interior	interior	NOUN
ejpam-21	52	16	)	)	PUNCT
ejpam-21	52	17	of	of	ADP
ejpam-21	52	18	a	a	PRON
ejpam-21	52	19	and	and	CCONJ
ejpam-21	52	20	is	be	AUX
ejpam-21	52	21	denoted	denote	VERB
ejpam-21	52	22	by	by	ADP
ejpam-21	52	23	sint(a	sint(a	PROPN
ejpam-21	52	24	)	)	PUNCT
ejpam-21	52	25	(	(	PUNCT
ejpam-21	52	26	resp	resp	NOUN
ejpam-21	52	27	.	.	PUNCT
ejpam-21	53	1	pint(a	pint(a	NOUN
ejpam-21	53	2	)	)	PUNCT
ejpam-21	53	3	,	,	PUNCT
ejpam-21	53	4	αint(a	αint(a	NOUN
ejpam-21	53	5	)	)	PUNCT
ejpam-21	53	6	,	,	PUNCT
ejpam-21	53	7	βint(a	βint(a	NOUN
ejpam-21	53	8	)	)	PUNCT
ejpam-21	53	9	,	,	PUNCT
ejpam-21	53	10	spint(a	spint(a	NOUN
ejpam-21	53	11	)	)	PUNCT
ejpam-21	53	12	,	,	PUNCT
ejpam-21	53	13	bint(a	bint(a	NOUN
ejpam-21	53	14	)	)	PUNCT
ejpam-21	53	15	)	)	PUNCT
ejpam-21	53	16	.	.	PUNCT
ejpam-21	54	1	throughout	throughout	ADP
ejpam-21	54	2	the	the	DET
ejpam-21	54	3	present	present	ADJ
ejpam-21	54	4	paper	paper	NOUN
ejpam-21	54	5	,	,	PUNCT
ejpam-21	54	6	(	(	PUNCT
ejpam-21	54	7	x	x	X
ejpam-21	54	8	,	,	PUNCT
ejpam-21	54	9	τ	τ	X
ejpam-21	54	10	)	)	PUNCT
ejpam-21	54	11	and	and	CCONJ
ejpam-21	54	12	(	(	PUNCT
ejpam-21	54	13	y	y	PROPN
ejpam-21	54	14	,	,	PUNCT
ejpam-21	54	15	σ	σ	PROPN
ejpam-21	54	16	)	)	PUNCT
ejpam-21	54	17	(	(	PUNCT
ejpam-21	54	18	briefly	briefly	ADV
ejpam-21	54	19	x	x	X
ejpam-21	54	20	and	and	CCONJ
ejpam-21	54	21	y	y	PROPN
ejpam-21	54	22	)	)	PUNCT
ejpam-21	54	23	always	always	ADV
ejpam-21	54	24	denote	denote	VERB
ejpam-21	54	25	topological	topological	ADJ
ejpam-21	54	26	spaces	space	NOUN
ejpam-21	54	27	and	and	CCONJ
ejpam-21	54	28	f	f	NOUN
ejpam-21	54	29	:	:	PUNCT
ejpam-21	54	30	x	x	X
ejpam-21	54	31	→	→	SYM
ejpam-21	54	32	y	y	PROPN
ejpam-21	54	33	(	(	PUNCT
ejpam-21	54	34	resp	resp	PROPN
ejpam-21	54	35	.	.	PUNCT
ejpam-21	55	1	f	f	X
ejpam-21	55	2	:	:	PUNCT
ejpam-21	55	3	x	x	X
ejpam-21	55	4	→	→	SYM
ejpam-21	55	5	y	y	PROPN
ejpam-21	55	6	)	)	PUNCT
ejpam-21	55	7	presents	present	VERB
ejpam-21	55	8	a	a	DET
ejpam-21	55	9	multivalued	multivalue	VERB
ejpam-21	55	10	(	(	PUNCT
ejpam-21	55	11	resp	resp	NOUN
ejpam-21	55	12	.	.	PUNCT
ejpam-21	56	1	single	single	ADJ
ejpam-21	56	2	valued	value	VERB
ejpam-21	56	3	)	)	PUNCT
ejpam-21	56	4	function	function	NOUN
ejpam-21	56	5	.	.	PUNCT
ejpam-21	57	1	for	for	ADP
ejpam-21	57	2	a	a	DET
ejpam-21	57	3	multifunction	multifunction	NOUN
ejpam-21	57	4	f	f	NOUN
ejpam-21	57	5	:	:	PUNCT
ejpam-21	57	6	x	x	X
ejpam-21	57	7	→	→	SYM
ejpam-21	57	8	y	y	PROPN
ejpam-21	57	9	,	,	PUNCT
ejpam-21	57	10	we	we	PRON
ejpam-21	57	11	shall	shall	AUX
ejpam-21	57	12	denote	denote	VERB
ejpam-21	57	13	the	the	DET
ejpam-21	57	14	upper	upper	ADJ
ejpam-21	57	15	and	and	CCONJ
ejpam-21	57	16	lower	low	ADJ
ejpam-21	57	17	inverse	inverse	NOUN
ejpam-21	57	18	of	of	ADP
ejpam-21	57	19	a	a	DET
ejpam-21	57	20	subset	subset	NOUN
ejpam-21	57	21	b	b	NOUN
ejpam-21	57	22	of	of	ADP
ejpam-21	57	23	a	a	DET
ejpam-21	57	24	space	space	NOUN
ejpam-21	57	25	y	y	NOUN
ejpam-21	57	26	by	by	ADP
ejpam-21	57	27	f+(b	f+(b	NOUN
ejpam-21	57	28	)	)	PUNCT
ejpam-21	57	29	and	and	CCONJ
ejpam-21	57	30	f−(b	f−(b	NOUN
ejpam-21	57	31	)	)	PUNCT
ejpam-21	57	32	,	,	PUNCT
ejpam-21	57	33	respectively	respectively	ADV
ejpam-21	57	34	,	,	PUNCT
ejpam-21	57	35	that	that	PRON
ejpam-21	57	36	is	be	AUX
ejpam-21	57	37	f+(b	f+(b	NOUN
ejpam-21	57	38	)	)	PUNCT
ejpam-21	57	39	=	=	PRON
ejpam-21	58	1	{	{	PUNCT
ejpam-21	58	2	x	x	PUNCT
ejpam-21	58	3	∈	∈	PROPN
ejpam-21	58	4	x	x	X
ejpam-21	58	5	:	:	PUNCT
ejpam-21	58	6	f	f	X
ejpam-21	58	7	(	(	PUNCT
ejpam-21	58	8	x	x	X
ejpam-21	58	9	)	)	PUNCT
ejpam-21	58	10	⊂	⊂	PROPN
ejpam-21	58	11	b	b	X
ejpam-21	58	12	}	}	PUNCT
ejpam-21	58	13	and	and	CCONJ
ejpam-21	58	14	f−(b	f−(b	PROPN
ejpam-21	58	15	)	)	PUNCT
ejpam-21	58	16	=	=	PRON
ejpam-21	58	17	{	{	PUNCT
ejpam-21	58	18	x	x	PUNCT
ejpam-21	58	19	∈	∈	PROPN
ejpam-21	58	20	x	x	X
ejpam-21	58	21	:	:	PUNCT
ejpam-21	58	22	f	f	X
ejpam-21	58	23	(	(	PUNCT
ejpam-21	58	24	x	x	NOUN
ejpam-21	58	25	)	)	PUNCT
ejpam-21	58	26	∩b	∩b	NOUN
ejpam-21	58	27	6=	6=	NOUN
ejpam-21	58	28	∅	∅	NOUN
ejpam-21	58	29	}	}	PUNCT
ejpam-21	58	30	.	.	PUNCT
ejpam-21	59	1	definition	definition	NOUN
ejpam-21	59	2	2.5	2.5	NUM
ejpam-21	59	3	.	.	PUNCT
ejpam-21	60	1	a	a	DET
ejpam-21	60	2	multifunction	multifunction	NOUN
ejpam-21	60	3	f	f	NOUN
ejpam-21	60	4	:	:	PUNCT
ejpam-21	60	5	(	(	PUNCT
ejpam-21	60	6	x	x	X
ejpam-21	60	7	,	,	PUNCT
ejpam-21	60	8	τ	τ	X
ejpam-21	60	9	)	)	PUNCT
ejpam-21	60	10	→	→	SYM
ejpam-21	60	11	(	(	PUNCT
ejpam-21	60	12	y	y	PROPN
ejpam-21	60	13	,	,	PUNCT
ejpam-21	60	14	σ	σ	PROPN
ejpam-21	60	15	)	)	PUNCT
ejpam-21	60	16	is	be	AUX
ejpam-21	60	17	said	say	VERB
ejpam-21	60	18	to	to	PART
ejpam-21	60	19	be	be	AUX
ejpam-21	60	20	(	(	PUNCT
ejpam-21	60	21	1	1	X
ejpam-21	60	22	)	)	PUNCT
ejpam-21	60	23	upper	upper	ADJ
ejpam-21	60	24	semi	semi	ADJ
ejpam-21	60	25	-	-	ADJ
ejpam-21	60	26	continuous	continuous	ADJ
ejpam-21	60	27	(	(	PUNCT
ejpam-21	60	28	briefly	briefly	ADV
ejpam-21	60	29	u.s.c	u.s.c	ADJ
ejpam-21	60	30	.	.	PUNCT
ejpam-21	60	31	)	)	PUNCT
ejpam-21	61	1	at	at	ADP
ejpam-21	61	2	a	a	DET
ejpam-21	61	3	point	point	NOUN
ejpam-21	61	4	x	x	SYM
ejpam-21	61	5	∈	∈	NOUN
ejpam-21	61	6	x	x	INTJ
ejpam-21	61	7	if	if	SCONJ
ejpam-21	61	8	for	for	ADP
ejpam-21	61	9	each	each	DET
ejpam-21	61	10	open	open	ADJ
ejpam-21	61	11	set	set	VERB
ejpam-21	61	12	v	v	NOUN
ejpam-21	61	13	containing	contain	VERB
ejpam-21	61	14	f	f	X
ejpam-21	61	15	(	(	PUNCT
ejpam-21	61	16	x	x	NOUN
ejpam-21	61	17	)	)	PUNCT
ejpam-21	61	18	,	,	PUNCT
ejpam-21	61	19	there	there	PRON
ejpam-21	61	20	exists	exist	VERB
ejpam-21	61	21	an	an	DET
ejpam-21	61	22	open	open	ADJ
ejpam-21	61	23	set	set	NOUN
ejpam-21	61	24	u	u	NOUN
ejpam-21	61	25	of	of	ADP
ejpam-21	61	26	x	x	PUNCT
ejpam-21	61	27	containing	contain	VERB
ejpam-21	61	28	x	x	PUNCT
ejpam-21	61	29	such	such	ADJ
ejpam-21	61	30	that	that	SCONJ
ejpam-21	61	31	f	f	PROPN
ejpam-21	61	32	(	(	PUNCT
ejpam-21	61	33	u	u	NOUN
ejpam-21	61	34	)	)	PUNCT
ejpam-21	61	35	⊂	⊂	PROPN
ejpam-21	61	36	v	v	PROPN
ejpam-21	61	37	,	,	PUNCT
ejpam-21	61	38	(	(	PUNCT
ejpam-21	61	39	2	2	NUM
ejpam-21	61	40	)	)	PUNCT
ejpam-21	61	41	lower	low	ADJ
ejpam-21	61	42	semi	semi	ADJ
ejpam-21	61	43	-	-	ADJ
ejpam-21	61	44	continuous	continuous	ADJ
ejpam-21	61	45	(	(	PUNCT
ejpam-21	61	46	briefly	briefly	ADV
ejpam-21	61	47	l.s.c	l.s.c	NOUN
ejpam-21	61	48	.	.	PUNCT
ejpam-21	61	49	)	)	PUNCT
ejpam-21	62	1	at	at	ADP
ejpam-21	62	2	a	a	DET
ejpam-21	62	3	point	point	NOUN
ejpam-21	62	4	x	x	SYM
ejpam-21	62	5	∈	∈	NOUN
ejpam-21	62	6	x	x	INTJ
ejpam-21	62	7	if	if	SCONJ
ejpam-21	62	8	for	for	ADP
ejpam-21	62	9	each	each	DET
ejpam-21	62	10	open	open	ADJ
ejpam-21	62	11	set	set	VERB
ejpam-21	62	12	v	v	NUM
ejpam-21	62	13	meeting	meeting	NOUN
ejpam-21	62	14	f	f	X
ejpam-21	62	15	(	(	PUNCT
ejpam-21	62	16	x	x	NOUN
ejpam-21	62	17	)	)	PUNCT
ejpam-21	62	18	,	,	PUNCT
ejpam-21	62	19	there	there	PRON
ejpam-21	62	20	exists	exist	VERB
ejpam-21	62	21	an	an	DET
ejpam-21	62	22	open	open	ADJ
ejpam-21	62	23	set	set	NOUN
ejpam-21	62	24	u	u	NOUN
ejpam-21	62	25	of	of	ADP
ejpam-21	62	26	x	x	PUNCT
ejpam-21	62	27	containing	contain	VERB
ejpam-21	62	28	x	x	PUNCT
ejpam-21	62	29	such	such	ADJ
ejpam-21	62	30	that	that	SCONJ
ejpam-21	62	31	f	f	PROPN
ejpam-21	62	32	(	(	PUNCT
ejpam-21	62	33	u	u	NOUN
ejpam-21	62	34	)	)	PUNCT
ejpam-21	62	35	∩	∩	NOUN
ejpam-21	62	36	v	v	ADP
ejpam-21	62	37	6=	6=	NOUN
ejpam-21	62	38	∅	∅	NOUN
ejpam-21	62	39	for	for	ADP
ejpam-21	62	40	each	each	DET
ejpam-21	62	41	u	u	PROPN
ejpam-21	62	42	∈	∈	PROPN
ejpam-21	62	43	u	u	NOUN
ejpam-21	62	44	,	,	PUNCT
ejpam-21	62	45	(	(	PUNCT
ejpam-21	62	46	3	3	X
ejpam-21	62	47	)	)	PUNCT
ejpam-21	62	48	upper	upper	ADJ
ejpam-21	62	49	/	/	SYM
ejpam-21	62	50	lower	low	ADJ
ejpam-21	62	51	semi	semi	ADJ
ejpam-21	62	52	-	-	ADJ
ejpam-21	62	53	continuous	continuous	ADJ
ejpam-21	62	54	on	on	ADP
ejpam-21	62	55	x	x	SYM
ejpam-21	62	56	if	if	SCONJ
ejpam-21	62	57	it	it	PRON
ejpam-21	62	58	has	have	VERB
ejpam-21	62	59	this	this	DET
ejpam-21	62	60	property	property	NOUN
ejpam-21	62	61	at	at	ADP
ejpam-21	62	62	each	each	DET
ejpam-21	62	63	point	point	NOUN
ejpam-21	62	64	of	of	ADP
ejpam-21	62	65	x	x	X
ejpam-21	62	66	.	.	PUNCT
ejpam-21	63	1	t.noiri	t.noiri	ADV
ejpam-21	63	2	,	,	PUNCT
ejpam-21	63	3	v.popa	v.popa	NOUN
ejpam-21	63	4	/	/	SYM
ejpam-21	63	5	eur	eur	PROPN
ejpam-21	63	6	.	.	PUNCT
ejpam-21	64	1	j.	j.	PROPN
ejpam-21	64	2	pure	pure	PROPN
ejpam-21	64	3	appl	appl	PROPN
ejpam-21	64	4	.	.	PROPN
ejpam-21	64	5	math	math	PROPN
ejpam-21	64	6	,	,	PUNCT
ejpam-21	64	7	1	1	NUM
ejpam-21	64	8	(	(	PUNCT
ejpam-21	64	9	2008	2008	NUM
ejpam-21	64	10	)	)	PUNCT
ejpam-21	64	11	,	,	PUNCT
ejpam-21	64	12	(	(	PUNCT
ejpam-21	64	13	82	82	NUM
ejpam-21	64	14	-	-	SYM
ejpam-21	64	15	98	98	NUM
ejpam-21	64	16	)	)	PUNCT
ejpam-21	64	17	84	84	NUM
ejpam-21	64	18	definition	definition	NOUN
ejpam-21	64	19	2.6	2.6	NUM
ejpam-21	64	20	.	.	PUNCT
ejpam-21	65	1	a	a	DET
ejpam-21	65	2	multifunction	multifunction	NOUN
ejpam-21	65	3	f	f	NOUN
ejpam-21	65	4	:	:	PUNCT
ejpam-21	65	5	(	(	PUNCT
ejpam-21	65	6	x	x	X
ejpam-21	65	7	,	,	PUNCT
ejpam-21	65	8	τ	τ	X
ejpam-21	65	9	)	)	PUNCT
ejpam-21	65	10	→	→	SYM
ejpam-21	65	11	(	(	PUNCT
ejpam-21	65	12	y	y	PROPN
ejpam-21	65	13	,	,	PUNCT
ejpam-21	65	14	σ	σ	PROPN
ejpam-21	65	15	)	)	PUNCT
ejpam-21	65	16	is	be	AUX
ejpam-21	65	17	said	say	VERB
ejpam-21	65	18	to	to	PART
ejpam-21	65	19	be	be	AUX
ejpam-21	65	20	(	(	PUNCT
ejpam-21	65	21	a	a	X
ejpam-21	65	22	)	)	PUNCT
ejpam-21	65	23	upper	upper	ADJ
ejpam-21	65	24	c	c	NOUN
ejpam-21	65	25	-	-	ADJ
ejpam-21	65	26	continuous	continuous	ADJ
ejpam-21	65	27	(	(	PUNCT
ejpam-21	65	28	briefly	briefly	ADV
ejpam-21	65	29	u.c.c	u.c.c	ADP
ejpam-21	65	30	.	.	PUNCT
ejpam-21	65	31	)	)	PUNCT
ejpam-21	66	1	[	[	X
ejpam-21	66	2	20	20	NUM
ejpam-21	66	3	]	]	PUNCT
ejpam-21	66	4	(	(	PUNCT
ejpam-21	66	5	resp	resp	NOUN
ejpam-21	66	6	.	.	PUNCT
ejpam-21	67	1	upper	upper	ADJ
ejpam-21	67	2	c	c	NOUN
ejpam-21	67	3	-	-	PUNCT
ejpam-21	67	4	quasi	quasi	NOUN
ejpam-21	67	5	-	-	ADJ
ejpam-21	67	6	continuous	continuous	ADJ
ejpam-21	67	7	(	(	PUNCT
ejpam-21	67	8	briefly	briefly	NOUN
ejpam-21	67	9	u.c.q.c	u.c.q.c	PROPN
ejpam-21	67	10	.	.	PUNCT
ejpam-21	67	11	)	)	PUNCT
ejpam-21	68	1	[	[	X
ejpam-21	68	2	14	14	NUM
ejpam-21	68	3	]	]	PUNCT
ejpam-21	68	4	,	,	PUNCT
ejpam-21	68	5	[	[	X
ejpam-21	68	6	36	36	NUM
ejpam-21	68	7	]	]	SYM
ejpam-21	68	8	)	)	PUNCT
ejpam-21	68	9	if	if	SCONJ
ejpam-21	68	10	for	for	ADP
ejpam-21	68	11	each	each	DET
ejpam-21	68	12	open	open	ADJ
ejpam-21	68	13	set	set	VERB
ejpam-21	68	14	v	v	NOUN
ejpam-21	68	15	containing	contain	VERB
ejpam-21	68	16	f	f	X
ejpam-21	68	17	(	(	PUNCT
ejpam-21	68	18	x	x	NOUN
ejpam-21	68	19	)	)	PUNCT
ejpam-21	68	20	and	and	CCONJ
ejpam-21	68	21	having	have	VERB
ejpam-21	68	22	compact	compact	ADJ
ejpam-21	68	23	complement	complement	NOUN
ejpam-21	68	24	,	,	PUNCT
ejpam-21	68	25	there	there	PRON
ejpam-21	68	26	exists	exist	VERB
ejpam-21	68	27	an	an	DET
ejpam-21	68	28	open	open	ADJ
ejpam-21	68	29	(	(	PUNCT
ejpam-21	68	30	resp	resp	NOUN
ejpam-21	68	31	.	.	PUNCT
ejpam-21	69	1	semi	semi	ADJ
ejpam-21	69	2	-	-	ADJ
ejpam-21	69	3	open	open	ADJ
ejpam-21	69	4	)	)	PUNCT
ejpam-21	69	5	set	set	VERB
ejpam-21	69	6	u	u	NOUN
ejpam-21	69	7	of	of	ADP
ejpam-21	69	8	x	x	PUNCT
ejpam-21	69	9	containing	contain	VERB
ejpam-21	69	10	x	x	PUNCT
ejpam-21	69	11	such	such	ADJ
ejpam-21	69	12	that	that	SCONJ
ejpam-21	69	13	f	f	PROPN
ejpam-21	69	14	(	(	PUNCT
ejpam-21	69	15	u	u	NOUN
ejpam-21	69	16	)	)	PUNCT
ejpam-21	69	17	⊂	⊂	PROPN
ejpam-21	69	18	v	v	PROPN
ejpam-21	69	19	,	,	PUNCT
ejpam-21	69	20	(	(	PUNCT
ejpam-21	69	21	2	2	X
ejpam-21	69	22	)	)	PUNCT
ejpam-21	69	23	lower	low	ADJ
ejpam-21	69	24	c	c	NOUN
ejpam-21	69	25	-	-	ADJ
ejpam-21	69	26	continuous	continuous	ADJ
ejpam-21	69	27	(	(	PUNCT
ejpam-21	69	28	briefly	briefly	NOUN
ejpam-21	69	29	l.c.c	l.c.c	NOUN
ejpam-21	69	30	.	.	PUNCT
ejpam-21	69	31	)	)	PUNCT
ejpam-21	70	1	[	[	X
ejpam-21	70	2	20	20	NUM
ejpam-21	70	3	]	]	PUNCT
ejpam-21	70	4	(	(	PUNCT
ejpam-21	70	5	resp	resp	NOUN
ejpam-21	70	6	.	.	PUNCT
ejpam-21	71	1	lower	low	ADJ
ejpam-21	71	2	c	c	NOUN
ejpam-21	71	3	-	-	PUNCT
ejpam-21	71	4	quasi	quasi	NOUN
ejpam-21	71	5	-	-	ADJ
ejpam-21	71	6	continuous	continuous	ADJ
ejpam-21	71	7	(	(	PUNCT
ejpam-21	71	8	briefly	briefly	NOUN
ejpam-21	71	9	l.c.q.c	l.c.q.c	PROPN
ejpam-21	71	10	.	.	PUNCT
ejpam-21	71	11	)	)	PUNCT
ejpam-21	72	1	[	[	X
ejpam-21	72	2	14	14	NUM
ejpam-21	72	3	]	]	PUNCT
ejpam-21	72	4	,	,	PUNCT
ejpam-21	72	5	[	[	X
ejpam-21	72	6	36	36	NUM
ejpam-21	72	7	]	]	PUNCT
ejpam-21	72	8	)	)	PUNCT
ejpam-21	72	9	at	at	ADP
ejpam-21	72	10	a	a	DET
ejpam-21	72	11	point	point	NOUN
ejpam-21	72	12	x	x	SYM
ejpam-21	72	13	∈	∈	NOUN
ejpam-21	72	14	x	x	INTJ
ejpam-21	72	15	if	if	SCONJ
ejpam-21	72	16	for	for	ADP
ejpam-21	72	17	each	each	DET
ejpam-21	72	18	open	open	ADJ
ejpam-21	72	19	set	set	VERB
ejpam-21	72	20	v	v	NUM
ejpam-21	72	21	meeting	meeting	NOUN
ejpam-21	72	22	f	f	X
ejpam-21	72	23	(	(	PUNCT
ejpam-21	72	24	x	x	NOUN
ejpam-21	72	25	)	)	PUNCT
ejpam-21	72	26	and	and	CCONJ
ejpam-21	72	27	having	have	VERB
ejpam-21	72	28	compact	compact	ADJ
ejpam-21	72	29	complement	complement	NOUN
ejpam-21	72	30	,	,	PUNCT
ejpam-21	72	31	there	there	PRON
ejpam-21	72	32	exists	exist	VERB
ejpam-21	72	33	an	an	DET
ejpam-21	72	34	open	open	ADJ
ejpam-21	72	35	(	(	PUNCT
ejpam-21	72	36	resp	resp	NOUN
ejpam-21	72	37	.	.	PUNCT
ejpam-21	73	1	semi	semi	ADJ
ejpam-21	73	2	-	-	ADJ
ejpam-21	73	3	open	open	ADJ
ejpam-21	73	4	)	)	PUNCT
ejpam-21	73	5	set	set	VERB
ejpam-21	73	6	u	u	NOUN
ejpam-21	73	7	of	of	ADP
ejpam-21	73	8	x	x	PUNCT
ejpam-21	73	9	containing	contain	VERB
ejpam-21	73	10	x	x	PUNCT
ejpam-21	73	11	such	such	ADJ
ejpam-21	73	12	that	that	SCONJ
ejpam-21	73	13	f	f	PROPN
ejpam-21	73	14	(	(	PUNCT
ejpam-21	73	15	u	u	NOUN
ejpam-21	73	16	)	)	PUNCT
ejpam-21	73	17	∩	∩	NOUN
ejpam-21	73	18	v	v	ADP
ejpam-21	73	19	6=	6=	NOUN
ejpam-21	73	20	∅	∅	NOUN
ejpam-21	73	21	for	for	ADP
ejpam-21	73	22	each	each	DET
ejpam-21	73	23	u	u	PROPN
ejpam-21	73	24	∈	∈	PROPN
ejpam-21	73	25	u	u	NOUN
ejpam-21	73	26	,	,	PUNCT
ejpam-21	73	27	(	(	PUNCT
ejpam-21	73	28	3	3	X
ejpam-21	73	29	)	)	PUNCT
ejpam-21	73	30	upper	upper	ADJ
ejpam-21	73	31	/	/	SYM
ejpam-21	73	32	lower	low	ADJ
ejpam-21	73	33	c	c	NOUN
ejpam-21	73	34	-	-	ADJ
ejpam-21	73	35	continuous	continuous	ADJ
ejpam-21	73	36	(	(	PUNCT
ejpam-21	73	37	resp	resp	NOUN
ejpam-21	73	38	.	.	PUNCT
ejpam-21	74	1	upper	upper	ADJ
ejpam-21	74	2	/	/	SYM
ejpam-21	74	3	lower	low	ADJ
ejpam-21	74	4	c	c	NOUN
ejpam-21	74	5	-	-	PUNCT
ejpam-21	74	6	quasi	quasi	ADJ
ejpam-21	74	7	-	-	ADJ
ejpam-21	74	8	continuous	continuous	ADJ
ejpam-21	74	9	)	)	PUNCT
ejpam-21	74	10	on	on	ADP
ejpam-21	74	11	x	x	SYM
ejpam-21	74	12	if	if	SCONJ
ejpam-21	74	13	it	it	PRON
ejpam-21	74	14	has	have	VERB
ejpam-21	74	15	this	this	DET
ejpam-21	74	16	property	property	NOUN
ejpam-21	74	17	at	at	ADP
ejpam-21	74	18	each	each	DET
ejpam-21	74	19	point	point	NOUN
ejpam-21	74	20	of	of	ADP
ejpam-21	74	21	x	x	X
ejpam-21	74	22	.	.	PUNCT
ejpam-21	75	1	remark	remark	PROPN
ejpam-21	75	2	2.1	2.1	NUM
ejpam-21	75	3	.	.	PUNCT
ejpam-21	76	1	for	for	ADP
ejpam-21	76	2	the	the	DET
ejpam-21	76	3	multifunctions	multifunction	NOUN
ejpam-21	76	4	defined	define	VERB
ejpam-21	76	5	above	above	ADV
ejpam-21	76	6	,	,	PUNCT
ejpam-21	76	7	the	the	DET
ejpam-21	76	8	following	follow	VERB
ejpam-21	76	9	implications	implication	NOUN
ejpam-21	76	10	hold	hold	VERB
ejpam-21	76	11	:	:	PUNCT
ejpam-21	76	12	u.s.c	u.s.c	ADJ
ejpam-21	76	13	.	.	PUNCT
ejpam-21	77	1	⇒	⇒	PROPN
ejpam-21	77	2	u.c.c	u.c.c	ADP
ejpam-21	77	3	.	.	PUNCT
ejpam-21	78	1	⇒	⇒	PROPN
ejpam-21	78	2	u.c.q.c	u.c.q.c	PROPN
ejpam-21	78	3	.	.	PUNCT
ejpam-21	78	4	;	;	PUNCT
ejpam-21	78	5	l.s.c	l.s.c	X
ejpam-21	78	6	.	.	PUNCT
ejpam-21	78	7	⇒	⇒	PROPN
ejpam-21	78	8	l.c.c	l.c.c	PROPN
ejpam-21	78	9	.	.	PUNCT
ejpam-21	79	1	⇒	⇒	PROPN
ejpam-21	79	2	l.c.q.c	l.c.q.c	PROPN
ejpam-21	79	3	.	.	PROPN
ejpam-21	80	1	3	3	NUM
ejpam-21	80	2	.	.	X
ejpam-21	80	3	c	c	X
ejpam-21	80	4	-	-	PUNCT
ejpam-21	80	5	m	m	NOUN
ejpam-21	80	6	-	-	ADJ
ejpam-21	80	7	continuous	continuous	ADJ
ejpam-21	80	8	multifunctions	multifunction	NOUN
ejpam-21	80	9	definition	definition	NOUN
ejpam-21	80	10	3.1	3.1	NUM
ejpam-21	80	11	.	.	PUNCT
ejpam-21	81	1	a	a	DET
ejpam-21	81	2	subfamily	subfamily	ADV
ejpam-21	81	3	mx	mx	NOUN
ejpam-21	81	4	of	of	ADP
ejpam-21	81	5	the	the	DET
ejpam-21	81	6	power	power	NOUN
ejpam-21	81	7	set	set	NOUN
ejpam-21	81	8	p(x	p(x	NOUN
ejpam-21	81	9	)	)	PUNCT
ejpam-21	81	10	of	of	ADP
ejpam-21	81	11	a	a	DET
ejpam-21	81	12	nonempty	nonempty	ADV
ejpam-21	81	13	set	set	VERB
ejpam-21	81	14	x	x	PUNCT
ejpam-21	81	15	is	be	AUX
ejpam-21	81	16	called	call	VERB
ejpam-21	81	17	a	a	DET
ejpam-21	81	18	minimal	minimal	ADJ
ejpam-21	81	19	structure	structure	NOUN
ejpam-21	81	20	(	(	PUNCT
ejpam-21	81	21	briefly	briefly	NOUN
ejpam-21	81	22	m	m	NOUN
ejpam-21	81	23	-	-	NOUN
ejpam-21	81	24	structure	structure	NOUN
ejpam-21	81	25	)	)	PUNCT
ejpam-21	82	1	[	[	X
ejpam-21	82	2	31	31	NUM
ejpam-21	82	3	]	]	PUNCT
ejpam-21	82	4	,	,	PUNCT
ejpam-21	82	5	[	[	X
ejpam-21	82	6	33	33	NUM
ejpam-21	82	7	]	]	PUNCT
ejpam-21	82	8	on	on	ADP
ejpam-21	82	9	x	x	SYM
ejpam-21	82	10	if	if	SCONJ
ejpam-21	82	11	∅	∅	NOUN
ejpam-21	82	12	∈	∈	PROPN
ejpam-21	82	13	mx	mx	PROPN
ejpam-21	82	14	and	and	CCONJ
ejpam-21	82	15	x	x	PROPN
ejpam-21	82	16	∈	∈	PROPN
ejpam-21	82	17	mx	mx	PROPN
ejpam-21	82	18	.	.	PUNCT
ejpam-21	83	1	by	by	ADP
ejpam-21	83	2	(	(	PUNCT
ejpam-21	83	3	x	x	NOUN
ejpam-21	83	4	,	,	PUNCT
ejpam-21	83	5	mx	mx	NOUN
ejpam-21	83	6	)	)	PUNCT
ejpam-21	83	7	(	(	PUNCT
ejpam-21	83	8	briefly	briefly	ADV
ejpam-21	83	9	(	(	PUNCT
ejpam-21	83	10	x	x	X
ejpam-21	83	11	,	,	PUNCT
ejpam-21	83	12	m	m	NOUN
ejpam-21	83	13	)	)	PUNCT
ejpam-21	83	14	)	)	PUNCT
ejpam-21	83	15	,	,	PUNCT
ejpam-21	83	16	we	we	PRON
ejpam-21	83	17	denote	denote	VERB
ejpam-21	83	18	a	a	DET
ejpam-21	83	19	nonempty	nonempty	ADV
ejpam-21	83	20	set	set	VERB
ejpam-21	83	21	x	x	PUNCT
ejpam-21	83	22	with	with	ADP
ejpam-21	83	23	a	a	DET
ejpam-21	83	24	minimal	minimal	ADJ
ejpam-21	83	25	structure	structure	NOUN
ejpam-21	83	26	mx	mx	NOUN
ejpam-21	83	27	on	on	ADP
ejpam-21	83	28	x	x	PUNCT
ejpam-21	83	29	and	and	CCONJ
ejpam-21	83	30	call	call	VERB
ejpam-21	83	31	it	it	PRON
ejpam-21	83	32	an	an	DET
ejpam-21	83	33	m	m	NOUN
ejpam-21	83	34	-	-	NOUN
ejpam-21	83	35	space	space	NOUN
ejpam-21	83	36	.	.	PUNCT
ejpam-21	84	1	each	each	DET
ejpam-21	84	2	member	member	NOUN
ejpam-21	84	3	of	of	ADP
ejpam-21	84	4	mx	mx	PROPN
ejpam-21	84	5	is	be	AUX
ejpam-21	84	6	said	say	VERB
ejpam-21	84	7	to	to	PART
ejpam-21	84	8	be	be	AUX
ejpam-21	84	9	mx	mx	PROPN
ejpam-21	84	10	-open	-open	NOUN
ejpam-21	84	11	(	(	PUNCT
ejpam-21	84	12	briefly	briefly	NOUN
ejpam-21	84	13	m	m	NOUN
ejpam-21	84	14	-	-	ADJ
ejpam-21	84	15	open	open	ADJ
ejpam-21	84	16	)	)	PUNCT
ejpam-21	84	17	and	and	CCONJ
ejpam-21	84	18	the	the	DET
ejpam-21	84	19	complement	complement	NOUN
ejpam-21	84	20	of	of	ADP
ejpam-21	84	21	an	an	DET
ejpam-21	84	22	mx	mx	PROPN
ejpam-21	84	23	-open	-open	NOUN
ejpam-21	84	24	set	set	NOUN
ejpam-21	84	25	is	be	AUX
ejpam-21	84	26	said	say	VERB
ejpam-21	84	27	to	to	PART
ejpam-21	84	28	be	be	AUX
ejpam-21	84	29	mx	mx	NOUN
ejpam-21	84	30	-closed	-closed	ADJ
ejpam-21	84	31	(	(	PUNCT
ejpam-21	84	32	briefly	briefly	NOUN
ejpam-21	84	33	m	m	NOUN
ejpam-21	84	34	-	-	PUNCT
ejpam-21	84	35	closed	closed	ADJ
ejpam-21	84	36	)	)	PUNCT
ejpam-21	84	37	.	.	PUNCT
ejpam-21	85	1	remark	remark	PROPN
ejpam-21	85	2	3.1	3.1	NUM
ejpam-21	85	3	.	.	PUNCT
ejpam-21	86	1	let	let	VERB
ejpam-21	86	2	(	(	PUNCT
ejpam-21	86	3	x	x	NOUN
ejpam-21	86	4	,	,	PUNCT
ejpam-21	86	5	τ	τ	X
ejpam-21	86	6	)	)	PUNCT
ejpam-21	86	7	be	be	VERB
ejpam-21	86	8	a	a	DET
ejpam-21	86	9	topological	topological	ADJ
ejpam-21	86	10	space	space	NOUN
ejpam-21	86	11	.	.	PUNCT
ejpam-21	87	1	then	then	ADV
ejpam-21	87	2	the	the	DET
ejpam-21	87	3	families	family	NOUN
ejpam-21	87	4	τ	τ	PROPN
ejpam-21	87	5	,	,	PUNCT
ejpam-21	87	6	so(x	so(x	NOUN
ejpam-21	87	7	)	)	PUNCT
ejpam-21	87	8	,	,	PUNCT
ejpam-21	87	9	po(x	po(x	NUM
ejpam-21	87	10	)	)	PUNCT
ejpam-21	87	11	,	,	PUNCT
ejpam-21	87	12	α(x	α(x	NOUN
ejpam-21	87	13	)	)	PUNCT
ejpam-21	87	14	,	,	PUNCT
ejpam-21	87	15	bo(x	bo(x	NUM
ejpam-21	87	16	)	)	PUNCT
ejpam-21	87	17	and	and	CCONJ
ejpam-21	87	18	spo(x	spo(x	X
ejpam-21	87	19	)	)	PUNCT
ejpam-21	87	20	are	be	AUX
ejpam-21	87	21	all	all	PRON
ejpam-21	87	22	m	m	NOUN
ejpam-21	87	23	-	-	NOUN
ejpam-21	87	24	structures	structure	NOUN
ejpam-21	87	25	on	on	ADP
ejpam-21	87	26	x	x	X
ejpam-21	87	27	.	.	PUNCT
ejpam-21	87	28	definition	definition	NOUN
ejpam-21	87	29	3.2	3.2	NUM
ejpam-21	87	30	.	.	PUNCT
ejpam-21	88	1	let	let	AUX
ejpam-21	88	2	(	(	PUNCT
ejpam-21	88	3	x	x	NOUN
ejpam-21	88	4	,	,	PUNCT
ejpam-21	88	5	mx	mx	NOUN
ejpam-21	88	6	)	)	PUNCT
ejpam-21	88	7	be	be	AUX
ejpam-21	88	8	an	an	DET
ejpam-21	88	9	m	m	NOUN
ejpam-21	88	10	-	-	NOUN
ejpam-21	88	11	space	space	NOUN
ejpam-21	88	12	.	.	PUNCT
ejpam-21	89	1	for	for	ADP
ejpam-21	89	2	a	a	DET
ejpam-21	89	3	subset	subset	NOUN
ejpam-21	89	4	a	a	PRON
ejpam-21	89	5	of	of	ADP
ejpam-21	89	6	x	x	PRON
ejpam-21	89	7	,	,	PUNCT
ejpam-21	89	8	the	the	DET
ejpam-21	89	9	mx	mx	PROPN
ejpam-21	89	10	-closure	-closure	NOUN
ejpam-21	89	11	of	of	ADP
ejpam-21	89	12	a	a	PRON
ejpam-21	89	13	and	and	CCONJ
ejpam-21	89	14	the	the	DET
ejpam-21	89	15	mx	mx	PROPN
ejpam-21	89	16	-interior	-interior	NOUN
ejpam-21	89	17	of	of	ADP
ejpam-21	89	18	a	a	PRON
ejpam-21	89	19	are	be	AUX
ejpam-21	89	20	defined	define	VERB
ejpam-21	89	21	in	in	ADP
ejpam-21	89	22	[	[	X
ejpam-21	89	23	17	17	NUM
ejpam-21	89	24	]	]	PUNCT
ejpam-21	89	25	as	as	SCONJ
ejpam-21	89	26	follows	follow	VERB
ejpam-21	89	27	:	:	PUNCT
ejpam-21	89	28	(	(	PUNCT
ejpam-21	89	29	1	1	X
ejpam-21	89	30	)	)	PUNCT
ejpam-21	89	31	mx	mx	NOUN
ejpam-21	89	32	-cl(a	-cl(a	PROPN
ejpam-21	89	33	)	)	PUNCT
ejpam-21	90	1	=	=	PUNCT
ejpam-21	90	2	∩{f	∩{f	NOUN
ejpam-21	90	3	:	:	PUNCT
ejpam-21	90	4	a	a	DET
ejpam-21	90	5	⊂	⊂	PROPN
ejpam-21	90	6	f	f	X
ejpam-21	90	7	,	,	PUNCT
ejpam-21	90	8	x	x	PROPN
ejpam-21	90	9	−	−	PROPN
ejpam-21	90	10	f	f	PROPN
ejpam-21	90	11	∈	∈	PROPN
ejpam-21	90	12	mx	mx	PROPN
ejpam-21	90	13	}	}	PUNCT
ejpam-21	90	14	,	,	PUNCT
ejpam-21	90	15	(	(	PUNCT
ejpam-21	90	16	2	2	X
ejpam-21	90	17	)	)	PUNCT
ejpam-21	90	18	mx	mx	NOUN
ejpam-21	90	19	-int(a	-int(a	PROPN
ejpam-21	90	20	)	)	PUNCT
ejpam-21	91	1	=	=	SYM
ejpam-21	91	2	∪{u	∪{u	VERB
ejpam-21	91	3	:	:	PUNCT
ejpam-21	91	4	u	u	X
ejpam-21	91	5	⊂	⊂	PROPN
ejpam-21	91	6	a	a	X
ejpam-21	91	7	,	,	PUNCT
ejpam-21	91	8	u	u	PROPN
ejpam-21	91	9	∈	∈	PROPN
ejpam-21	91	10	mx	mx	PROPN
ejpam-21	91	11	}	}	PUNCT
ejpam-21	91	12	.	.	PUNCT
ejpam-21	92	1	remark	remark	PROPN
ejpam-21	92	2	3.2	3.2	NUM
ejpam-21	92	3	.	.	PUNCT
ejpam-21	93	1	let	let	VERB
ejpam-21	93	2	(	(	PUNCT
ejpam-21	93	3	x	x	NOUN
ejpam-21	93	4	,	,	PUNCT
ejpam-21	93	5	τ	τ	X
ejpam-21	93	6	)	)	PUNCT
ejpam-21	93	7	be	be	VERB
ejpam-21	93	8	a	a	DET
ejpam-21	93	9	topological	topological	ADJ
ejpam-21	93	10	space	space	NOUN
ejpam-21	93	11	and	and	CCONJ
ejpam-21	93	12	a	a	DET
ejpam-21	93	13	be	be	AUX
ejpam-21	93	14	a	a	DET
ejpam-21	93	15	subset	subset	NOUN
ejpam-21	93	16	of	of	ADP
ejpam-21	93	17	x	x	X
ejpam-21	93	18	.	.	PUNCT
ejpam-21	94	1	if	if	SCONJ
ejpam-21	94	2	mx	mx	PROPN
ejpam-21	94	3	=	=	SYM
ejpam-21	94	4	τ	τ	PROPN
ejpam-21	94	5	(	(	PUNCT
ejpam-21	94	6	resp	resp	NOUN
ejpam-21	94	7	.	.	PUNCT
ejpam-21	94	8	so(x	so(x	NUM
ejpam-21	94	9	)	)	PUNCT
ejpam-21	94	10	,	,	PUNCT
ejpam-21	94	11	po(x	po(x	NUM
ejpam-21	94	12	)	)	PUNCT
ejpam-21	94	13	,	,	PUNCT
ejpam-21	94	14	α(x	α(x	NOUN
ejpam-21	94	15	)	)	PUNCT
ejpam-21	94	16	,	,	PUNCT
ejpam-21	94	17	bo(x	bo(x	NUM
ejpam-21	94	18	)	)	PUNCT
ejpam-21	94	19	,	,	PUNCT
ejpam-21	94	20	spo(x	spo(x	PROPN
ejpam-21	94	21	)	)	PUNCT
ejpam-21	94	22	)	)	PUNCT
ejpam-21	94	23	,	,	PUNCT
ejpam-21	94	24	then	then	ADV
ejpam-21	94	25	we	we	PRON
ejpam-21	94	26	have	have	VERB
ejpam-21	94	27	(	(	PUNCT
ejpam-21	94	28	a	a	X
ejpam-21	94	29	)	)	PUNCT
ejpam-21	94	30	mx	mx	NOUN
ejpam-21	94	31	-cl(a	-cl(a	PROPN
ejpam-21	94	32	)	)	PUNCT
ejpam-21	94	33	=	=	SYM
ejpam-21	94	34	cl(a	cl(a	X
ejpam-21	94	35	)	)	PUNCT
ejpam-21	94	36	(	(	PUNCT
ejpam-21	94	37	resp	resp	NOUN
ejpam-21	94	38	.	.	PUNCT
ejpam-21	95	1	scl(a	scl(a	PROPN
ejpam-21	95	2	)	)	PUNCT
ejpam-21	95	3	,	,	PUNCT
ejpam-21	95	4	pcl(a	pcl(a	PROPN
ejpam-21	95	5	)	)	PUNCT
ejpam-21	95	6	,	,	PUNCT
ejpam-21	95	7	αcl(a	αcl(a	PROPN
ejpam-21	95	8	)	)	PUNCT
ejpam-21	95	9	,	,	PUNCT
ejpam-21	95	10	bcl(a	bcl(a	PROPN
ejpam-21	95	11	)	)	PUNCT
ejpam-21	95	12	,	,	PUNCT
ejpam-21	95	13	spcl(a	spcl(a	NUM
ejpam-21	95	14	)	)	PUNCT
ejpam-21	95	15	)	)	PUNCT
ejpam-21	95	16	,	,	PUNCT
ejpam-21	95	17	(	(	PUNCT
ejpam-21	95	18	b	b	X
ejpam-21	95	19	)	)	PUNCT
ejpam-21	95	20	mx	mx	NOUN
ejpam-21	95	21	-int(a	-int(a	PROPN
ejpam-21	95	22	)	)	PUNCT
ejpam-21	96	1	=	=	PUNCT
ejpam-21	96	2	int(a	int(a	NOUN
ejpam-21	96	3	)	)	PUNCT
ejpam-21	96	4	(	(	PUNCT
ejpam-21	96	5	resp	resp	NOUN
ejpam-21	96	6	.	.	PUNCT
ejpam-21	97	1	sint(a	sint(a	NOUN
ejpam-21	97	2	)	)	PUNCT
ejpam-21	97	3	,	,	PUNCT
ejpam-21	97	4	pint(a	pint(a	NOUN
ejpam-21	97	5	)	)	PUNCT
ejpam-21	97	6	,	,	PUNCT
ejpam-21	97	7	αint(a	αint(a	NOUN
ejpam-21	97	8	)	)	PUNCT
ejpam-21	97	9	,	,	PUNCT
ejpam-21	97	10	bint(a	bint(a	NOUN
ejpam-21	97	11	)	)	PUNCT
ejpam-21	97	12	,	,	PUNCT
ejpam-21	97	13	spint(a	spint(a	NOUN
ejpam-21	97	14	)	)	PUNCT
ejpam-21	97	15	)	)	PUNCT
ejpam-21	97	16	.	.	PUNCT
ejpam-21	98	1	lemma	lemma	PROPN
ejpam-21	98	2	3.1	3.1	NUM
ejpam-21	98	3	.	.	PUNCT
ejpam-21	99	1	(	(	PUNCT
ejpam-21	99	2	maki	maki	NOUN
ejpam-21	99	3	et	et	PROPN
ejpam-21	99	4	al	al	PROPN
ejpam-21	99	5	.	.	PUNCT
ejpam-21	100	1	[	[	X
ejpam-21	100	2	17	17	NUM
ejpam-21	100	3	]	]	PUNCT
ejpam-21	100	4	)	)	PUNCT
ejpam-21	100	5	.	.	PUNCT
ejpam-21	101	1	let	let	AUX
ejpam-21	101	2	(	(	PUNCT
ejpam-21	101	3	x	x	NOUN
ejpam-21	101	4	,	,	PUNCT
ejpam-21	101	5	mx	mx	NOUN
ejpam-21	101	6	)	)	PUNCT
ejpam-21	101	7	be	be	AUX
ejpam-21	101	8	an	an	DET
ejpam-21	101	9	m	m	NOUN
ejpam-21	101	10	-	-	NOUN
ejpam-21	101	11	space	space	NOUN
ejpam-21	101	12	.	.	PUNCT
ejpam-21	102	1	for	for	ADP
ejpam-21	102	2	subsets	subset	NOUN
ejpam-21	102	3	a	a	PRON
ejpam-21	102	4	and	and	CCONJ
ejpam-21	102	5	b	b	NOUN
ejpam-21	102	6	of	of	ADP
ejpam-21	102	7	x	x	PRON
ejpam-21	102	8	,	,	PUNCT
ejpam-21	102	9	the	the	DET
ejpam-21	102	10	following	follow	VERB
ejpam-21	102	11	properties	property	NOUN
ejpam-21	102	12	hold	hold	VERB
ejpam-21	102	13	:	:	PUNCT
ejpam-21	102	14	t.noiri	t.noiri	ADV
ejpam-21	102	15	,	,	PUNCT
ejpam-21	102	16	v.popa	v.popa	NOUN
ejpam-21	102	17	/	/	SYM
ejpam-21	102	18	eur	eur	PROPN
ejpam-21	102	19	.	.	PUNCT
ejpam-21	103	1	j.	j.	PROPN
ejpam-21	103	2	pure	pure	PROPN
ejpam-21	103	3	appl	appl	PROPN
ejpam-21	103	4	.	.	PROPN
ejpam-21	103	5	math	math	PROPN
ejpam-21	103	6	,	,	PUNCT
ejpam-21	103	7	1	1	NUM
ejpam-21	103	8	(	(	PUNCT
ejpam-21	103	9	2008	2008	NUM
ejpam-21	103	10	)	)	PUNCT
ejpam-21	103	11	,	,	PUNCT
ejpam-21	103	12	(	(	PUNCT
ejpam-21	103	13	82	82	NUM
ejpam-21	103	14	-	-	SYM
ejpam-21	103	15	98	98	NUM
ejpam-21	103	16	)	)	PUNCT
ejpam-21	103	17	85	85	NUM
ejpam-21	103	18	(	(	PUNCT
ejpam-21	103	19	1	1	NUM
ejpam-21	103	20	)	)	PUNCT
ejpam-21	103	21	mx	mx	NOUN
ejpam-21	103	22	-cl(x	-cl(x	PROPN
ejpam-21	103	23	−a	−a	NOUN
ejpam-21	103	24	)	)	PUNCT
ejpam-21	103	25	=	=	PUNCT
ejpam-21	104	1	x	x	PUNCT
ejpam-21	104	2	−mx	−mx	NUM
ejpam-21	104	3	-int(a	-int(a	PROPN
ejpam-21	104	4	)	)	PUNCT
ejpam-21	104	5	and	and	CCONJ
ejpam-21	104	6	mx	mx	PROPN
ejpam-21	104	7	-int(x	-int(x	PROPN
ejpam-21	104	8	−a	−a	ADV
ejpam-21	104	9	)	)	PUNCT
ejpam-21	104	10	=	=	PUNCT
ejpam-21	105	1	x	x	PUNCT
ejpam-21	105	2	−mx	−mx	NOUN
ejpam-21	105	3	-cl(a	-cl(a	NUM
ejpam-21	105	4	)	)	PUNCT
ejpam-21	105	5	,	,	PUNCT
ejpam-21	105	6	(	(	PUNCT
ejpam-21	105	7	2	2	X
ejpam-21	105	8	)	)	PUNCT
ejpam-21	105	9	if	if	SCONJ
ejpam-21	105	10	(	(	PUNCT
ejpam-21	105	11	x	x	NOUN
ejpam-21	105	12	−a	−a	ADJ
ejpam-21	105	13	)	)	PUNCT
ejpam-21	105	14	∈	∈	PROPN
ejpam-21	105	15	mx	mx	PROPN
ejpam-21	105	16	,	,	PUNCT
ejpam-21	105	17	then	then	ADV
ejpam-21	105	18	mx	mx	PROPN
ejpam-21	105	19	-cl(a	-cl(a	PROPN
ejpam-21	105	20	)	)	PUNCT
ejpam-21	105	21	=	=	SYM
ejpam-21	106	1	a	a	PROPN
ejpam-21	107	1	and	and	CCONJ
ejpam-21	107	2	if	if	SCONJ
ejpam-21	107	3	a	a	DET
ejpam-21	107	4	∈	∈	PROPN
ejpam-21	107	5	mx	mx	NOUN
ejpam-21	107	6	,	,	PUNCT
ejpam-21	107	7	then	then	ADV
ejpam-21	107	8	mx	mx	PROPN
ejpam-21	107	9	-int(a	-int(a	PROPN
ejpam-21	107	10	)	)	PUNCT
ejpam-21	107	11	=	=	SYM
ejpam-21	108	1	a	a	DET
ejpam-21	108	2	,	,	PUNCT
ejpam-21	108	3	(	(	PUNCT
ejpam-21	108	4	3	3	X
ejpam-21	108	5	)	)	PUNCT
ejpam-21	108	6	mx	mx	NOUN
ejpam-21	108	7	-cl(∅	-cl(∅	PROPN
ejpam-21	108	8	)	)	PUNCT
ejpam-21	109	1	=	=	PUNCT
ejpam-21	109	2	∅,mx	∅,mx	NOUN
ejpam-21	109	3	-cl(x	-cl(x	NOUN
ejpam-21	109	4	)	)	PUNCT
ejpam-21	109	5	=	=	SYM
ejpam-21	110	1	x	x	X
ejpam-21	110	2	,	,	PUNCT
ejpam-21	110	3	mx	mx	PROPN
ejpam-21	110	4	-int(∅	-int(∅	NOUN
ejpam-21	110	5	)	)	PUNCT
ejpam-21	111	1	=	=	NOUN
ejpam-21	111	2	∅	∅	NOUN
ejpam-21	111	3	and	and	CCONJ
ejpam-21	111	4	mx	mx	PROPN
ejpam-21	111	5	-int(x	-int(x	PUNCT
ejpam-21	111	6	)	)	PUNCT
ejpam-21	112	1	=	=	PUNCT
ejpam-21	113	1	x	x	X
ejpam-21	113	2	,	,	PUNCT
ejpam-21	113	3	(	(	PUNCT
ejpam-21	113	4	4	4	X
ejpam-21	113	5	)	)	PUNCT
ejpam-21	113	6	if	if	SCONJ
ejpam-21	113	7	a	a	DET
ejpam-21	113	8	⊂	⊂	PROPN
ejpam-21	113	9	b	b	PROPN
ejpam-21	113	10	,	,	PUNCT
ejpam-21	113	11	then	then	ADV
ejpam-21	113	12	mx	mx	PROPN
ejpam-21	113	13	-cl(a	-cl(a	PROPN
ejpam-21	113	14	)	)	PUNCT
ejpam-21	113	15	⊂	⊂	PROPN
ejpam-21	113	16	mx	mx	PROPN
ejpam-21	113	17	-cl(b	-cl(b	PROPN
ejpam-21	113	18	)	)	PUNCT
ejpam-21	113	19	and	and	CCONJ
ejpam-21	113	20	mx	mx	PROPN
ejpam-21	113	21	-int(a	-int(a	PROPN
ejpam-21	113	22	)	)	PUNCT
ejpam-21	113	23	⊂	⊂	PROPN
ejpam-21	113	24	mx	mx	PROPN
ejpam-21	113	25	-int(b	-int(b	PROPN
ejpam-21	113	26	)	)	PUNCT
ejpam-21	113	27	,	,	PUNCT
ejpam-21	113	28	(	(	PUNCT
ejpam-21	113	29	5	5	X
ejpam-21	113	30	)	)	PUNCT
ejpam-21	113	31	a	a	DET
ejpam-21	113	32	⊂	⊂	PROPN
ejpam-21	113	33	mx	mx	PROPN
ejpam-21	113	34	-cl(a	-cl(a	PROPN
ejpam-21	113	35	)	)	PUNCT
ejpam-21	113	36	and	and	CCONJ
ejpam-21	113	37	mx	mx	PROPN
ejpam-21	113	38	-int(a	-int(a	PROPN
ejpam-21	113	39	)	)	PUNCT
ejpam-21	114	1	⊂	⊂	PROPN
ejpam-21	114	2	a	a	X
ejpam-21	114	3	,	,	PUNCT
ejpam-21	114	4	(	(	PUNCT
ejpam-21	114	5	6	6	NUM
ejpam-21	114	6	)	)	PUNCT
ejpam-21	114	7	mx	mx	PROPN
ejpam-21	114	8	-cl(mx	-cl(mx	PROPN
ejpam-21	114	9	-cl(a	-cl(a	NUM
ejpam-21	114	10	)	)	PUNCT
ejpam-21	114	11	)	)	PUNCT
ejpam-21	115	1	=	=	SYM
ejpam-21	115	2	mx	mx	PROPN
ejpam-21	115	3	-cl(a	-cl(a	PROPN
ejpam-21	115	4	)	)	PUNCT
ejpam-21	115	5	and	and	CCONJ
ejpam-21	115	6	mx	mx	PROPN
ejpam-21	115	7	-int(mx	-int(mx	PUNCT
ejpam-21	115	8	-int(a	-int(a	PROPN
ejpam-21	115	9	)	)	PUNCT
ejpam-21	115	10	)	)	PUNCT
ejpam-21	116	1	=	=	PUNCT
ejpam-21	116	2	mx	mx	PROPN
ejpam-21	116	3	-int(a	-int(a	PROPN
ejpam-21	116	4	)	)	PUNCT
ejpam-21	116	5	.	.	PUNCT
ejpam-21	117	1	lemma	lemma	PROPN
ejpam-21	117	2	3.2	3.2	NUM
ejpam-21	117	3	.	.	PUNCT
ejpam-21	118	1	(	(	PUNCT
ejpam-21	118	2	popa	popa	NOUN
ejpam-21	118	3	and	and	CCONJ
ejpam-21	118	4	noiri	noiri	ADV
ejpam-21	119	1	[	[	X
ejpam-21	119	2	31	31	NUM
ejpam-21	119	3	]	]	PUNCT
ejpam-21	119	4	)	)	PUNCT
ejpam-21	119	5	.	.	PUNCT
ejpam-21	120	1	let	let	AUX
ejpam-21	120	2	(	(	PUNCT
ejpam-21	120	3	x	x	NOUN
ejpam-21	120	4	,	,	PUNCT
ejpam-21	120	5	mx	mx	NOUN
ejpam-21	120	6	)	)	PUNCT
ejpam-21	120	7	be	be	AUX
ejpam-21	120	8	an	an	DET
ejpam-21	120	9	m	m	NOUN
ejpam-21	120	10	-	-	NOUN
ejpam-21	120	11	space	space	NOUN
ejpam-21	120	12	and	and	CCONJ
ejpam-21	120	13	a	a	DET
ejpam-21	120	14	a	a	DET
ejpam-21	120	15	subset	subset	NOUN
ejpam-21	120	16	of	of	ADP
ejpam-21	120	17	x.	x.	NOUN
ejpam-21	120	18	then	then	ADV
ejpam-21	120	19	x	x	PROPN
ejpam-21	120	20	∈	∈	PROPN
ejpam-21	120	21	mx	mx	PROPN
ejpam-21	120	22	-cl(a	-cl(a	PROPN
ejpam-21	120	23	)	)	PUNCT
ejpam-21	120	24	if	if	SCONJ
ejpam-21	120	25	and	and	CCONJ
ejpam-21	120	26	only	only	ADV
ejpam-21	120	27	if	if	SCONJ
ejpam-21	120	28	u∩a	u∩a	PROPN
ejpam-21	120	29	6=	6=	SYM
ejpam-21	120	30	∅	∅	NOUN
ejpam-21	120	31	for	for	ADP
ejpam-21	120	32	every	every	DET
ejpam-21	120	33	u	u	PROPN
ejpam-21	120	34	∈	∈	PROPN
ejpam-21	120	35	mx	mx	NOUN
ejpam-21	120	36	containing	contain	VERB
ejpam-21	120	37	x.	x.	NOUN
ejpam-21	120	38	definition	definition	NOUN
ejpam-21	120	39	3.3	3.3	NUM
ejpam-21	120	40	.	.	PUNCT
ejpam-21	121	1	a	a	DET
ejpam-21	121	2	minimal	minimal	ADJ
ejpam-21	121	3	structure	structure	NOUN
ejpam-21	121	4	mx	mx	NOUN
ejpam-21	121	5	on	on	ADP
ejpam-21	121	6	a	a	DET
ejpam-21	121	7	nonempty	nonempty	ADJ
ejpam-21	121	8	set	set	VERB
ejpam-21	121	9	x	x	SYM
ejpam-21	121	10	is	be	AUX
ejpam-21	121	11	said	say	VERB
ejpam-21	121	12	to	to	PART
ejpam-21	121	13	have	have	VERB
ejpam-21	121	14	property	property	NOUN
ejpam-21	121	15	b	b	PROPN
ejpam-21	122	1	[	[	X
ejpam-21	122	2	17	17	NUM
ejpam-21	122	3	]	]	PUNCT
ejpam-21	122	4	if	if	SCONJ
ejpam-21	122	5	the	the	DET
ejpam-21	122	6	union	union	NOUN
ejpam-21	122	7	of	of	ADP
ejpam-21	122	8	any	any	DET
ejpam-21	122	9	family	family	NOUN
ejpam-21	122	10	of	of	ADP
ejpam-21	122	11	subsets	subset	NOUN
ejpam-21	122	12	belonging	belong	VERB
ejpam-21	122	13	to	to	ADP
ejpam-21	122	14	mx	mx	PROPN
ejpam-21	122	15	belongs	belong	VERB
ejpam-21	122	16	to	to	ADP
ejpam-21	122	17	mx	mx	PROPN
ejpam-21	122	18	.	.	PUNCT
ejpam-21	123	1	lemma	lemma	PROPN
ejpam-21	123	2	3.3	3.3	NUM
ejpam-21	123	3	.	.	PUNCT
ejpam-21	124	1	(	(	PUNCT
ejpam-21	124	2	popa	popa	NOUN
ejpam-21	124	3	and	and	CCONJ
ejpam-21	124	4	noiri	noiri	ADV
ejpam-21	125	1	[	[	X
ejpam-21	125	2	33	33	NUM
ejpam-21	125	3	]	]	PUNCT
ejpam-21	125	4	)	)	PUNCT
ejpam-21	125	5	.	.	PUNCT
ejpam-21	126	1	for	for	ADP
ejpam-21	126	2	an	an	DET
ejpam-21	126	3	m	m	NOUN
ejpam-21	126	4	-	-	PUNCT
ejpam-21	126	5	structure	structure	ADJ
ejpam-21	126	6	mx	mx	NOUN
ejpam-21	126	7	on	on	ADP
ejpam-21	126	8	a	a	DET
ejpam-21	126	9	nonempty	nonempty	ADV
ejpam-21	126	10	set	set	VERB
ejpam-21	126	11	x	x	SYM
ejpam-21	126	12	,	,	PUNCT
ejpam-21	126	13	the	the	DET
ejpam-21	126	14	following	follow	VERB
ejpam-21	126	15	properties	property	NOUN
ejpam-21	126	16	are	be	AUX
ejpam-21	126	17	equivalent	equivalent	ADJ
ejpam-21	126	18	:	:	PUNCT
ejpam-21	126	19	(	(	PUNCT
ejpam-21	126	20	1	1	X
ejpam-21	126	21	)	)	PUNCT
ejpam-21	126	22	mx	mx	NOUN
ejpam-21	126	23	has	have	VERB
ejpam-21	126	24	property	property	NOUN
ejpam-21	126	25	b	b	NOUN
ejpam-21	126	26	;	;	PUNCT
ejpam-21	126	27	(	(	PUNCT
ejpam-21	126	28	2	2	X
ejpam-21	126	29	)	)	PUNCT
ejpam-21	126	30	if	if	SCONJ
ejpam-21	126	31	mx	mx	PROPN
ejpam-21	126	32	-int(a	-int(a	PROPN
ejpam-21	126	33	)	)	PUNCT
ejpam-21	126	34	=	=	SYM
ejpam-21	127	1	a	a	PRON
ejpam-21	127	2	,	,	PUNCT
ejpam-21	127	3	then	then	ADV
ejpam-21	127	4	a	a	DET
ejpam-21	127	5	∈	∈	PROPN
ejpam-21	127	6	mx	mx	NOUN
ejpam-21	127	7	;	;	PUNCT
ejpam-21	127	8	(	(	PUNCT
ejpam-21	127	9	3	3	X
ejpam-21	127	10	)	)	PUNCT
ejpam-21	127	11	if	if	SCONJ
ejpam-21	127	12	mx	mx	PROPN
ejpam-21	127	13	-cl(a	-cl(a	PROPN
ejpam-21	127	14	)	)	PUNCT
ejpam-21	127	15	=	=	SYM
ejpam-21	128	1	a	a	PROPN
ejpam-21	128	2	,	,	PUNCT
ejpam-21	128	3	then	then	ADV
ejpam-21	128	4	a	a	PRON
ejpam-21	128	5	is	be	AUX
ejpam-21	128	6	mx	mx	NOUN
ejpam-21	128	7	-closed	-closed	ADJ
ejpam-21	128	8	.	.	PUNCT
ejpam-21	129	1	definition	definition	NOUN
ejpam-21	129	2	3.4	3.4	NUM
ejpam-21	129	3	.	.	PUNCT
ejpam-21	130	1	let	let	AUX
ejpam-21	130	2	(	(	PUNCT
ejpam-21	130	3	x	x	NOUN
ejpam-21	130	4	,	,	PUNCT
ejpam-21	130	5	mx	mx	NOUN
ejpam-21	130	6	)	)	PUNCT
ejpam-21	130	7	be	be	AUX
ejpam-21	130	8	an	an	DET
ejpam-21	130	9	m	m	NOUN
ejpam-21	130	10	-	-	NOUN
ejpam-21	130	11	space	space	NOUN
ejpam-21	130	12	and	and	CCONJ
ejpam-21	130	13	(	(	PUNCT
ejpam-21	130	14	y	y	PROPN
ejpam-21	130	15	,	,	PUNCT
ejpam-21	130	16	σ	σ	PROPN
ejpam-21	130	17	)	)	PUNCT
ejpam-21	130	18	a	a	DET
ejpam-21	130	19	topological	topological	ADJ
ejpam-21	130	20	space	space	NOUN
ejpam-21	130	21	.	.	PUNCT
ejpam-21	131	1	a	a	DET
ejpam-21	131	2	multifunction	multifunction	NOUN
ejpam-21	131	3	f	f	NOUN
ejpam-21	131	4	:	:	PUNCT
ejpam-21	131	5	(	(	PUNCT
ejpam-21	131	6	x	x	NOUN
ejpam-21	131	7	,	,	PUNCT
ejpam-21	131	8	mx	mx	NOUN
ejpam-21	131	9	)	)	PUNCT
ejpam-21	131	10	→	→	SYM
ejpam-21	131	11	(	(	PUNCT
ejpam-21	131	12	y	y	PROPN
ejpam-21	131	13	,	,	PUNCT
ejpam-21	131	14	σ	σ	PROPN
ejpam-21	131	15	)	)	PUNCT
ejpam-21	131	16	is	be	AUX
ejpam-21	131	17	said	say	VERB
ejpam-21	131	18	to	to	PART
ejpam-21	131	19	be	be	AUX
ejpam-21	131	20	(	(	PUNCT
ejpam-21	131	21	1	1	X
ejpam-21	131	22	)	)	PUNCT
ejpam-21	131	23	upper	upper	ADJ
ejpam-21	131	24	c	c	NOUN
ejpam-21	131	25	-	-	PUNCT
ejpam-21	131	26	m	m	NOUN
ejpam-21	131	27	-	-	ADJ
ejpam-21	131	28	continuous	continuous	ADJ
ejpam-21	131	29	(	(	PUNCT
ejpam-21	131	30	briefly	briefly	NOUN
ejpam-21	131	31	u.c.m.c	u.c.m.c	PROPN
ejpam-21	131	32	.	.	PUNCT
ejpam-21	131	33	)	)	PUNCT
ejpam-21	131	34	at	at	ADP
ejpam-21	131	35	a	a	DET
ejpam-21	131	36	point	point	NOUN
ejpam-21	132	1	x	x	SYM
ejpam-21	132	2	∈	∈	NOUN
ejpam-21	132	3	x	x	INTJ
ejpam-21	132	4	if	if	SCONJ
ejpam-21	132	5	for	for	ADP
ejpam-21	132	6	each	each	DET
ejpam-21	132	7	open	open	ADJ
ejpam-21	132	8	set	set	VERB
ejpam-21	132	9	v	v	NOUN
ejpam-21	132	10	containing	contain	VERB
ejpam-21	132	11	f	f	X
ejpam-21	132	12	(	(	PUNCT
ejpam-21	132	13	x	x	NOUN
ejpam-21	132	14	)	)	PUNCT
ejpam-21	132	15	and	and	CCONJ
ejpam-21	132	16	having	have	VERB
ejpam-21	132	17	compact	compact	ADJ
ejpam-21	132	18	complement	complement	NOUN
ejpam-21	132	19	,	,	PUNCT
ejpam-21	132	20	there	there	PRON
ejpam-21	132	21	exists	exist	VERB
ejpam-21	132	22	an	an	DET
ejpam-21	132	23	mx	mx	PROPN
ejpam-21	132	24	-open	-open	NOUN
ejpam-21	132	25	set	set	NOUN
ejpam-21	132	26	u	u	NOUN
ejpam-21	132	27	containing	contain	VERB
ejpam-21	132	28	x	x	PUNCT
ejpam-21	132	29	such	such	ADJ
ejpam-21	132	30	that	that	SCONJ
ejpam-21	132	31	f	f	PROPN
ejpam-21	132	32	(	(	PUNCT
ejpam-21	132	33	u	u	NOUN
ejpam-21	132	34	)	)	PUNCT
ejpam-21	132	35	⊂	⊂	PROPN
ejpam-21	132	36	v	v	PROPN
ejpam-21	132	37	,	,	PUNCT
ejpam-21	132	38	(	(	PUNCT
ejpam-21	132	39	2	2	X
ejpam-21	132	40	)	)	PUNCT
ejpam-21	132	41	lower	low	ADJ
ejpam-21	132	42	c	c	NOUN
ejpam-21	132	43	-	-	PUNCT
ejpam-21	132	44	m	m	NOUN
ejpam-21	132	45	-	-	ADJ
ejpam-21	132	46	continuous	continuous	ADJ
ejpam-21	132	47	(	(	PUNCT
ejpam-21	132	48	briefly	briefly	ADV
ejpam-21	132	49	l.c.m.c	l.c.m.c	PROPN
ejpam-21	132	50	.	.	PUNCT
ejpam-21	132	51	)	)	PUNCT
ejpam-21	132	52	at	at	ADP
ejpam-21	132	53	a	a	DET
ejpam-21	132	54	point	point	NOUN
ejpam-21	132	55	x	x	SYM
ejpam-21	132	56	∈	∈	NOUN
ejpam-21	132	57	x	x	INTJ
ejpam-21	132	58	if	if	SCONJ
ejpam-21	132	59	for	for	ADP
ejpam-21	132	60	each	each	DET
ejpam-21	132	61	open	open	ADJ
ejpam-21	132	62	set	set	VERB
ejpam-21	132	63	v	v	NUM
ejpam-21	132	64	meeting	meeting	NOUN
ejpam-21	132	65	f	f	X
ejpam-21	132	66	(	(	PUNCT
ejpam-21	132	67	x	x	NOUN
ejpam-21	132	68	)	)	PUNCT
ejpam-21	132	69	and	and	CCONJ
ejpam-21	132	70	having	have	VERB
ejpam-21	132	71	compact	compact	ADJ
ejpam-21	132	72	complement	complement	NOUN
ejpam-21	132	73	,	,	PUNCT
ejpam-21	132	74	there	there	PRON
ejpam-21	132	75	exists	exist	VERB
ejpam-21	132	76	an	an	DET
ejpam-21	132	77	mx	mx	PROPN
ejpam-21	132	78	-open	-open	NOUN
ejpam-21	132	79	set	set	NOUN
ejpam-21	132	80	u	u	NOUN
ejpam-21	132	81	containing	contain	VERB
ejpam-21	132	82	x	x	PUNCT
ejpam-21	132	83	such	such	ADJ
ejpam-21	132	84	that	that	SCONJ
ejpam-21	132	85	f	f	PROPN
ejpam-21	132	86	(	(	PUNCT
ejpam-21	132	87	u	u	NOUN
ejpam-21	132	88	)	)	PUNCT
ejpam-21	132	89	∩	∩	NOUN
ejpam-21	132	90	v	v	ADP
ejpam-21	132	91	6=	6=	NOUN
ejpam-21	132	92	∅	∅	NOUN
ejpam-21	132	93	for	for	ADP
ejpam-21	132	94	each	each	DET
ejpam-21	132	95	u	u	PROPN
ejpam-21	132	96	∈	∈	PROPN
ejpam-21	132	97	u	u	NOUN
ejpam-21	132	98	,	,	PUNCT
ejpam-21	132	99	(	(	PUNCT
ejpam-21	132	100	3	3	X
ejpam-21	132	101	)	)	PUNCT
ejpam-21	132	102	upper	upper	ADJ
ejpam-21	132	103	/	/	SYM
ejpam-21	132	104	lower	low	ADJ
ejpam-21	132	105	c	c	NOUN
ejpam-21	132	106	-	-	PUNCT
ejpam-21	132	107	m	m	NOUN
ejpam-21	132	108	-	-	ADJ
ejpam-21	132	109	continuous	continuous	ADJ
ejpam-21	132	110	on	on	ADP
ejpam-21	132	111	x	x	SYM
ejpam-21	132	112	if	if	SCONJ
ejpam-21	132	113	it	it	PRON
ejpam-21	132	114	has	have	VERB
ejpam-21	132	115	this	this	DET
ejpam-21	132	116	property	property	NOUN
ejpam-21	132	117	at	at	ADP
ejpam-21	132	118	every	every	DET
ejpam-21	132	119	point	point	NOUN
ejpam-21	132	120	of	of	ADP
ejpam-21	132	121	x	x	X
ejpam-21	132	122	.	.	PUNCT
ejpam-21	133	1	t.noiri	t.noiri	ADV
ejpam-21	133	2	,	,	PUNCT
ejpam-21	133	3	v.popa	v.popa	NOUN
ejpam-21	133	4	/	/	SYM
ejpam-21	133	5	eur	eur	PROPN
ejpam-21	133	6	.	.	PUNCT
ejpam-21	134	1	j.	j.	PROPN
ejpam-21	134	2	pure	pure	PROPN
ejpam-21	134	3	appl	appl	PROPN
ejpam-21	134	4	.	.	PROPN
ejpam-21	134	5	math	math	PROPN
ejpam-21	134	6	,	,	PUNCT
ejpam-21	134	7	1	1	NUM
ejpam-21	134	8	(	(	PUNCT
ejpam-21	134	9	2008	2008	NUM
ejpam-21	134	10	)	)	PUNCT
ejpam-21	134	11	,	,	PUNCT
ejpam-21	134	12	(	(	PUNCT
ejpam-21	134	13	82	82	NUM
ejpam-21	134	14	-	-	SYM
ejpam-21	134	15	98	98	NUM
ejpam-21	134	16	)	)	PUNCT
ejpam-21	134	17	86	86	NUM
ejpam-21	134	18	remark	remark	NOUN
ejpam-21	134	19	3.3	3.3	NUM
ejpam-21	134	20	.	.	PUNCT
ejpam-21	135	1	let	let	AUX
ejpam-21	135	2	(	(	PUNCT
ejpam-21	135	3	x	x	NOUN
ejpam-21	135	4	,	,	PUNCT
ejpam-21	135	5	τ	τ	X
ejpam-21	135	6	)	)	PUNCT
ejpam-21	135	7	and	and	CCONJ
ejpam-21	135	8	(	(	PUNCT
ejpam-21	135	9	y	y	PROPN
ejpam-21	135	10	,	,	PUNCT
ejpam-21	135	11	σ	σ	PROPN
ejpam-21	135	12	)	)	PUNCT
ejpam-21	135	13	be	be	VERB
ejpam-21	135	14	topological	topological	ADJ
ejpam-21	135	15	spaces	space	NOUN
ejpam-21	135	16	.	.	PUNCT
ejpam-21	136	1	(	(	PUNCT
ejpam-21	136	2	1	1	X
ejpam-21	136	3	)	)	PUNCT
ejpam-21	136	4	if	if	SCONJ
ejpam-21	136	5	mx	mx	PROPN
ejpam-21	136	6	=	=	SYM
ejpam-21	136	7	τ	τ	PROPN
ejpam-21	136	8	(	(	PUNCT
ejpam-21	136	9	resp	resp	NOUN
ejpam-21	136	10	.	.	PUNCT
ejpam-21	136	11	so(x	so(x	NOUN
ejpam-21	136	12	)	)	PUNCT
ejpam-21	136	13	)	)	PUNCT
ejpam-21	136	14	and	and	CCONJ
ejpam-21	136	15	is	be	AUX
ejpam-21	136	16	upper	upper	ADJ
ejpam-21	136	17	/	/	SYM
ejpam-21	136	18	lower	low	ADJ
ejpam-21	136	19	c	c	NOUN
ejpam-21	136	20	-	-	PUNCT
ejpam-21	136	21	m	m	NOUN
ejpam-21	136	22	-	-	ADJ
ejpam-21	136	23	continuous	continuous	ADJ
ejpam-21	136	24	,	,	PUNCT
ejpam-21	136	25	then	then	ADV
ejpam-21	136	26	f	f	PROPN
ejpam-21	136	27	is	be	AUX
ejpam-21	136	28	upper	upper	ADJ
ejpam-21	136	29	/	/	SYM
ejpam-21	136	30	lower	low	ADJ
ejpam-21	136	31	c	c	NOUN
ejpam-21	136	32	-	-	ADJ
ejpam-21	136	33	continuous	continuous	ADJ
ejpam-21	136	34	(	(	PUNCT
ejpam-21	136	35	resp	resp	NOUN
ejpam-21	136	36	.	.	PUNCT
ejpam-21	137	1	upper	upper	ADJ
ejpam-21	137	2	/	/	SYM
ejpam-21	137	3	lower	low	ADJ
ejpam-21	137	4	c	c	NOUN
ejpam-21	137	5	-	-	PUNCT
ejpam-21	137	6	quasi	quasi	ADJ
ejpam-21	137	7	-	-	ADJ
ejpam-21	137	8	continuous	continuous	ADJ
ejpam-21	137	9	)	)	PUNCT
ejpam-21	137	10	.	.	PUNCT
ejpam-21	138	1	(	(	PUNCT
ejpam-21	138	2	2	2	X
ejpam-21	138	3	)	)	PUNCT
ejpam-21	138	4	for	for	ADP
ejpam-21	138	5	mx	mx	NOUN
ejpam-21	138	6	=	=	SYM
ejpam-21	138	7	α(x	α(x	PROPN
ejpam-21	138	8	)	)	PUNCT
ejpam-21	138	9	,	,	PUNCT
ejpam-21	138	10	po(x	po(x	NUM
ejpam-21	138	11	)	)	PUNCT
ejpam-21	138	12	,	,	PUNCT
ejpam-21	138	13	spo(x	spo(x	PROPN
ejpam-21	138	14	)	)	PUNCT
ejpam-21	138	15	or	or	CCONJ
ejpam-21	138	16	bo(x	bo(x	NUM
ejpam-21	138	17	)	)	PUNCT
ejpam-21	138	18	,	,	PUNCT
ejpam-21	138	19	we	we	PRON
ejpam-21	138	20	can	can	AUX
ejpam-21	138	21	define	define	VERB
ejpam-21	138	22	new	new	ADJ
ejpam-21	138	23	types	type	NOUN
ejpam-21	138	24	of	of	ADP
ejpam-21	138	25	modifications	modification	NOUN
ejpam-21	138	26	of	of	ADP
ejpam-21	138	27	upper	upper	ADJ
ejpam-21	138	28	/	/	SYM
ejpam-21	138	29	lower	low	ADJ
ejpam-21	138	30	c	c	NOUN
ejpam-21	138	31	-	-	ADJ
ejpam-21	138	32	continuous	continuous	ADJ
ejpam-21	138	33	multifunctions	multifunction	NOUN
ejpam-21	138	34	.	.	PUNCT
ejpam-21	139	1	the	the	DET
ejpam-21	139	2	definitions	definition	NOUN
ejpam-21	139	3	will	will	AUX
ejpam-21	139	4	be	be	AUX
ejpam-21	139	5	given	give	VERB
ejpam-21	139	6	in	in	ADP
ejpam-21	139	7	the	the	DET
ejpam-21	139	8	last	last	ADJ
ejpam-21	139	9	section	section	NOUN
ejpam-21	139	10	.	.	PUNCT
ejpam-21	140	1	theorem	theorem	VERB
ejpam-21	140	2	3.1	3.1	NUM
ejpam-21	140	3	.	.	PUNCT
ejpam-21	141	1	for	for	ADP
ejpam-21	141	2	a	a	DET
ejpam-21	141	3	multifunction	multifunction	NOUN
ejpam-21	141	4	f	f	NOUN
ejpam-21	141	5	:	:	PUNCT
ejpam-21	141	6	(	(	PUNCT
ejpam-21	141	7	x	x	NOUN
ejpam-21	141	8	,	,	PUNCT
ejpam-21	141	9	mx	mx	NOUN
ejpam-21	141	10	)	)	PUNCT
ejpam-21	141	11	→	→	SYM
ejpam-21	141	12	(	(	PUNCT
ejpam-21	141	13	y	y	PROPN
ejpam-21	141	14	,	,	PUNCT
ejpam-21	141	15	σ	σ	PROPN
ejpam-21	141	16	)	)	PUNCT
ejpam-21	141	17	,	,	PUNCT
ejpam-21	141	18	the	the	DET
ejpam-21	141	19	following	follow	VERB
ejpam-21	141	20	properties	property	NOUN
ejpam-21	141	21	are	be	AUX
ejpam-21	141	22	equivalent	equivalent	ADJ
ejpam-21	141	23	:	:	PUNCT
ejpam-21	141	24	(	(	PUNCT
ejpam-21	141	25	1	1	X
ejpam-21	141	26	)	)	PUNCT
ejpam-21	141	27	f	f	PROPN
ejpam-21	141	28	is	be	AUX
ejpam-21	141	29	u.c.m.c	u.c.m.c	PROPN
ejpam-21	141	30	.	.	PUNCT
ejpam-21	142	1	at	at	ADP
ejpam-21	142	2	x	x	X
ejpam-21	142	3	∈	∈	PROPN
ejpam-21	142	4	x	x	X
ejpam-21	142	5	;	;	PUNCT
ejpam-21	142	6	(	(	PUNCT
ejpam-21	142	7	2	2	X
ejpam-21	142	8	)	)	PUNCT
ejpam-21	142	9	x	x	SYM
ejpam-21	142	10	∈	∈	PROPN
ejpam-21	142	11	mx	mx	PROPN
ejpam-21	142	12	-int(f+(v	-int(f+(v	PROPN
ejpam-21	142	13	)	)	PUNCT
ejpam-21	142	14	)	)	PUNCT
ejpam-21	142	15	for	for	ADP
ejpam-21	142	16	each	each	DET
ejpam-21	142	17	open	open	ADJ
ejpam-21	142	18	set	set	VERB
ejpam-21	142	19	v	v	NOUN
ejpam-21	142	20	containing	contain	VERB
ejpam-21	142	21	f(x	f(x	PROPN
ejpam-21	142	22	)	)	PUNCT
ejpam-21	142	23	and	and	CCONJ
ejpam-21	142	24	having	have	VERB
ejpam-21	142	25	compact	compact	ADJ
ejpam-21	142	26	complement	complement	NOUN
ejpam-21	142	27	;	;	PUNCT
ejpam-21	142	28	(	(	PUNCT
ejpam-21	142	29	3	3	X
ejpam-21	142	30	)	)	PUNCT
ejpam-21	142	31	x	x	SYM
ejpam-21	142	32	∈	∈	PROPN
ejpam-21	142	33	f−(cl(b	f−(cl(b	PROPN
ejpam-21	142	34	)	)	PUNCT
ejpam-21	142	35	)	)	PUNCT
ejpam-21	143	1	for	for	ADP
ejpam-21	143	2	each	each	DET
ejpam-21	143	3	subset	subset	NOUN
ejpam-21	143	4	b	b	PROPN
ejpam-21	143	5	of	of	ADP
ejpam-21	143	6	y	y	PROPN
ejpam-21	143	7	having	have	VERB
ejpam-21	143	8	the	the	DET
ejpam-21	143	9	compact	compact	ADJ
ejpam-21	143	10	closure	closure	NOUN
ejpam-21	143	11	such	such	ADJ
ejpam-21	143	12	that	that	SCONJ
ejpam-21	143	13	x	x	SYM
ejpam-21	143	14	∈	∈	PROPN
ejpam-21	143	15	mx	mx	PROPN
ejpam-21	143	16	cl(f−(b	cl(f−(b	PROPN
ejpam-21	143	17	)	)	PUNCT
ejpam-21	143	18	)	)	PUNCT
ejpam-21	143	19	;	;	PUNCT
ejpam-21	143	20	(	(	PUNCT
ejpam-21	143	21	4	4	X
ejpam-21	143	22	)	)	PUNCT
ejpam-21	143	23	x	x	SYM
ejpam-21	143	24	∈	∈	PROPN
ejpam-21	143	25	mx	mx	NOUN
ejpam-21	143	26	-int(f+(b	-int(f+(b	NOUN
ejpam-21	143	27	)	)	PUNCT
ejpam-21	143	28	)	)	PUNCT
ejpam-21	143	29	for	for	ADP
ejpam-21	143	30	each	each	DET
ejpam-21	143	31	subset	subset	NOUN
ejpam-21	143	32	b	b	PROPN
ejpam-21	143	33	of	of	ADP
ejpam-21	143	34	y	y	PRON
ejpam-21	143	35	such	such	ADJ
ejpam-21	143	36	that	that	SCONJ
ejpam-21	143	37	y	y	PROPN
ejpam-21	143	38	−	−	PROPN
ejpam-21	143	39	int(b	int(b	PROPN
ejpam-21	143	40	)	)	PUNCT
ejpam-21	143	41	is	be	AUX
ejpam-21	143	42	compact	compact	ADJ
ejpam-21	143	43	and	and	CCONJ
ejpam-21	143	44	x	x	PUNCT
ejpam-21	143	45	∈	∈	PROPN
ejpam-21	143	46	f+(int(b	f+(int(b	NOUN
ejpam-21	143	47	)	)	PUNCT
ejpam-21	143	48	)	)	PUNCT
ejpam-21	143	49	.	.	PUNCT
ejpam-21	144	1	proof	proof	NOUN
ejpam-21	144	2	.	.	PUNCT
ejpam-21	145	1	(	(	PUNCT
ejpam-21	145	2	1	1	X
ejpam-21	145	3	)	)	PUNCT
ejpam-21	145	4	⇒	⇒	NOUN
ejpam-21	145	5	(	(	PUNCT
ejpam-21	145	6	2	2	NUM
ejpam-21	145	7	):	):	PUNCT
ejpam-21	145	8	let	let	VERB
ejpam-21	145	9	v	v	PART
ejpam-21	145	10	be	be	AUX
ejpam-21	145	11	any	any	DET
ejpam-21	145	12	open	open	ADJ
ejpam-21	145	13	set	set	NOUN
ejpam-21	145	14	of	of	ADP
ejpam-21	145	15	y	y	PROPN
ejpam-21	145	16	containing	contain	VERB
ejpam-21	145	17	f	f	PROPN
ejpam-21	145	18	(	(	PUNCT
ejpam-21	145	19	x	x	NOUN
ejpam-21	145	20	)	)	PUNCT
ejpam-21	145	21	and	and	CCONJ
ejpam-21	145	22	having	have	VERB
ejpam-21	145	23	compact	compact	ADJ
ejpam-21	145	24	complement	complement	NOUN
ejpam-21	145	25	.	.	PUNCT
ejpam-21	146	1	there	there	PRON
ejpam-21	146	2	exists	exist	VERB
ejpam-21	146	3	an	an	DET
ejpam-21	146	4	mx	mx	PROPN
ejpam-21	146	5	-open	-open	NOUN
ejpam-21	146	6	set	set	NOUN
ejpam-21	146	7	u	u	NOUN
ejpam-21	146	8	containing	contain	VERB
ejpam-21	146	9	x	x	PUNCT
ejpam-21	146	10	such	such	ADJ
ejpam-21	146	11	that	that	SCONJ
ejpam-21	146	12	f	f	PROPN
ejpam-21	146	13	(	(	PUNCT
ejpam-21	146	14	u	u	NOUN
ejpam-21	146	15	)	)	PUNCT
ejpam-21	146	16	⊂	⊂	PROPN
ejpam-21	146	17	v	v	NOUN
ejpam-21	146	18	.	.	PUNCT
ejpam-21	147	1	thus	thus	ADV
ejpam-21	147	2	x	x	SYM
ejpam-21	147	3	∈	∈	X
ejpam-21	147	4	u	u	NOUN
ejpam-21	147	5	⊂	⊂	PROPN
ejpam-21	147	6	f+(v	f+(v	PROPN
ejpam-21	147	7	)	)	PUNCT
ejpam-21	147	8	.	.	PUNCT
ejpam-21	148	1	since	since	SCONJ
ejpam-21	148	2	u	u	PROPN
ejpam-21	148	3	∈	∈	PROPN
ejpam-21	148	4	mx	mx	PROPN
ejpam-21	148	5	,	,	PUNCT
ejpam-21	148	6	we	we	PRON
ejpam-21	148	7	have	have	VERB
ejpam-21	148	8	x	x	X
ejpam-21	148	9	∈	∈	PROPN
ejpam-21	148	10	mx	mx	PROPN
ejpam-21	148	11	-int(f+(v	-int(f+(v	PROPN
ejpam-21	148	12	)	)	PUNCT
ejpam-21	148	13	)	)	PUNCT
ejpam-21	148	14	.	.	PUNCT
ejpam-21	149	1	(	(	PUNCT
ejpam-21	149	2	2	2	X
ejpam-21	149	3	)	)	PUNCT
ejpam-21	149	4	⇒	⇒	NOUN
ejpam-21	149	5	(	(	PUNCT
ejpam-21	149	6	3	3	NUM
ejpam-21	149	7	):	):	PUNCT
ejpam-21	149	8	suppose	suppose	VERB
ejpam-21	149	9	that	that	SCONJ
ejpam-21	149	10	b	b	PROPN
ejpam-21	149	11	is	be	AUX
ejpam-21	149	12	any	any	DET
ejpam-21	149	13	subset	subset	NOUN
ejpam-21	149	14	of	of	ADP
ejpam-21	149	15	y	y	PROPN
ejpam-21	149	16	having	have	VERB
ejpam-21	149	17	the	the	DET
ejpam-21	149	18	compact	compact	ADJ
ejpam-21	149	19	closure	closure	NOUN
ejpam-21	149	20	.	.	PUNCT
ejpam-21	150	1	then	then	ADV
ejpam-21	150	2	cl(b	cl(b	NOUN
ejpam-21	150	3	)	)	PUNCT
ejpam-21	150	4	is	be	AUX
ejpam-21	150	5	closed	closed	ADJ
ejpam-21	150	6	and	and	CCONJ
ejpam-21	150	7	y	y	PROPN
ejpam-21	150	8	-cl(b	-cl(b	PROPN
ejpam-21	150	9	)	)	PUNCT
ejpam-21	150	10	is	be	AUX
ejpam-21	150	11	an	an	DET
ejpam-21	150	12	open	open	ADJ
ejpam-21	150	13	set	set	NOUN
ejpam-21	150	14	having	have	VERB
ejpam-21	150	15	compact	compact	ADJ
ejpam-21	150	16	complement	complement	NOUN
ejpam-21	150	17	.	.	PUNCT
ejpam-21	151	1	let	let	VERB
ejpam-21	151	2	x	x	PRON
ejpam-21	151	3	/∈	/∈	PUNCT
ejpam-21	151	4	f−(cl(b	f−(cl(b	NOUN
ejpam-21	151	5	)	)	PUNCT
ejpam-21	151	6	)	)	PUNCT
ejpam-21	151	7	.	.	PUNCT
ejpam-21	152	1	then	then	ADV
ejpam-21	152	2	x	x	SYM
ejpam-21	152	3	∈	∈	PROPN
ejpam-21	152	4	x	x	PUNCT
ejpam-21	152	5	−f−(cl(b	−f−(cl(b	NOUN
ejpam-21	152	6	)	)	PUNCT
ejpam-21	152	7	)	)	PUNCT
ejpam-21	153	1	=	=	PUNCT
ejpam-21	153	2	f+(y	f+(y	NOUN
ejpam-21	153	3	−cl(b	−cl(b	NOUN
ejpam-21	153	4	)	)	PUNCT
ejpam-21	153	5	)	)	PUNCT
ejpam-21	153	6	.	.	PUNCT
ejpam-21	154	1	this	this	PRON
ejpam-21	154	2	implies	imply	VERB
ejpam-21	154	3	f	f	PROPN
ejpam-21	154	4	(	(	PUNCT
ejpam-21	154	5	x	x	X
ejpam-21	154	6	)	)	PUNCT
ejpam-21	154	7	⊂	⊂	PROPN
ejpam-21	154	8	y	y	PROPN
ejpam-21	154	9	−cl(b	−cl(b	PROPN
ejpam-21	154	10	)	)	PUNCT
ejpam-21	154	11	.	.	PUNCT
ejpam-21	155	1	since	since	SCONJ
ejpam-21	155	2	y	y	PROPN
ejpam-21	155	3	−cl(b	−cl(b	PROPN
ejpam-21	155	4	)	)	PUNCT
ejpam-21	155	5	is	be	AUX
ejpam-21	155	6	an	an	DET
ejpam-21	155	7	open	open	ADJ
ejpam-21	155	8	set	set	NOUN
ejpam-21	155	9	having	have	VERB
ejpam-21	155	10	compact	compact	ADJ
ejpam-21	155	11	complement	complement	NOUN
ejpam-21	155	12	,	,	PUNCT
ejpam-21	155	13	by	by	ADP
ejpam-21	155	14	(	(	PUNCT
ejpam-21	155	15	2	2	X
ejpam-21	155	16	)	)	PUNCT
ejpam-21	155	17	we	we	PRON
ejpam-21	155	18	have	have	AUX
ejpam-21	155	19	x	x	X
ejpam-21	155	20	∈	∈	PROPN
ejpam-21	155	21	mx	mx	PROPN
ejpam-21	155	22	-int(f+(y	-int(f+(y	NOUN
ejpam-21	155	23	−	−	PROPN
ejpam-21	155	24	cl(b	cl(b	NOUN
ejpam-21	155	25	)	)	PUNCT
ejpam-21	155	26	)	)	PUNCT
ejpam-21	155	27	)	)	PUNCT
ejpam-21	156	1	=	=	PUNCT
ejpam-21	156	2	mx	mx	PROPN
ejpam-21	156	3	-int(x	-int(x	PROPN
ejpam-21	156	4	−	−	PROPN
ejpam-21	156	5	f−(cl(b	f−(cl(b	NOUN
ejpam-21	156	6	)	)	PUNCT
ejpam-21	156	7	)	)	PUNCT
ejpam-21	157	1	=	=	PUNCT
ejpam-21	157	2	x	x	PUNCT
ejpam-21	157	3	−mx	−mx	NUM
ejpam-21	157	4	-cl(f−(cl(b	-cl(f−(cl(b	NOUN
ejpam-21	157	5	)	)	PUNCT
ejpam-21	157	6	)	)	PUNCT
ejpam-21	157	7	)	)	PUNCT
ejpam-21	158	1	⊂	⊂	PUNCT
ejpam-21	158	2	x	x	PUNCT
ejpam-21	158	3	−mx	−mx	VERB
ejpam-21	158	4	-cl(f−(b	-cl(f−(b	NOUN
ejpam-21	158	5	)	)	PUNCT
ejpam-21	158	6	)	)	PUNCT
ejpam-21	158	7	.	.	PUNCT
ejpam-21	159	1	hence	hence	ADV
ejpam-21	159	2	x	x	X
ejpam-21	159	3	/∈	/∈	PROPN
ejpam-21	159	4	mx	mx	PROPN
ejpam-21	159	5	-cl(f−(b	-cl(f−(b	PROPN
ejpam-21	159	6	)	)	PUNCT
ejpam-21	159	7	)	)	PUNCT
ejpam-21	159	8	.	.	PUNCT
ejpam-21	160	1	(	(	PUNCT
ejpam-21	160	2	3	3	X
ejpam-21	160	3	)	)	PUNCT
ejpam-21	160	4	⇒	⇒	NOUN
ejpam-21	160	5	(	(	PUNCT
ejpam-21	160	6	4	4	NUM
ejpam-21	160	7	):	):	PUNCT
ejpam-21	160	8	let	let	VERB
ejpam-21	160	9	b	b	X
ejpam-21	160	10	be	be	AUX
ejpam-21	160	11	any	any	DET
ejpam-21	160	12	subset	subset	NOUN
ejpam-21	160	13	of	of	ADP
ejpam-21	160	14	y	y	PRON
ejpam-21	160	15	such	such	ADJ
ejpam-21	160	16	that	that	SCONJ
ejpam-21	160	17	y	y	PROPN
ejpam-21	160	18	-int(b	-int(b	PROPN
ejpam-21	160	19	)	)	PUNCT
ejpam-21	160	20	is	be	AUX
ejpam-21	160	21	compact	compact	ADJ
ejpam-21	160	22	and	and	CCONJ
ejpam-21	160	23	let	let	VERB
ejpam-21	160	24	x	x	PRON
ejpam-21	160	25	/∈	/∈	PROPN
ejpam-21	160	26	mx	mx	PROPN
ejpam-21	160	27	int(f+(b	int(f+(b	NOUN
ejpam-21	160	28	)	)	PUNCT
ejpam-21	160	29	)	)	PUNCT
ejpam-21	160	30	.	.	PUNCT
ejpam-21	161	1	then	then	ADV
ejpam-21	161	2	we	we	PRON
ejpam-21	161	3	have	have	VERB
ejpam-21	161	4	x	x	X
ejpam-21	161	5	∈	∈	NOUN
ejpam-21	161	6	x	x	PUNCT
ejpam-21	161	7	−	−	PROPN
ejpam-21	161	8	mx	mx	PROPN
ejpam-21	161	9	-int(f+(b	-int(f+(b	NOUN
ejpam-21	161	10	)	)	PUNCT
ejpam-21	161	11	)	)	PUNCT
ejpam-21	162	1	=	=	SYM
ejpam-21	162	2	mx	mx	PROPN
ejpam-21	162	3	-cl(x	-cl(x	PRON
ejpam-21	162	4	−	−	PROPN
ejpam-21	162	5	f+(b	f+(b	NOUN
ejpam-21	162	6	)	)	PUNCT
ejpam-21	162	7	)	)	PUNCT
ejpam-21	163	1	=	=	SYM
ejpam-21	163	2	mx	mx	PROPN
ejpam-21	163	3	cl(f−(y	cl(f−(y	NOUN
ejpam-21	163	4	−b	−b	NOUN
ejpam-21	163	5	)	)	PUNCT
ejpam-21	163	6	)	)	PUNCT
ejpam-21	163	7	.	.	PUNCT
ejpam-21	164	1	by	by	ADP
ejpam-21	164	2	(	(	PUNCT
ejpam-21	164	3	3	3	NUM
ejpam-21	164	4	)	)	PUNCT
ejpam-21	164	5	,	,	PUNCT
ejpam-21	164	6	we	we	PRON
ejpam-21	164	7	have	have	VERB
ejpam-21	164	8	x	x	X
ejpam-21	164	9	∈	∈	PROPN
ejpam-21	164	10	f−(cl(y	f−(cl(y	PROPN
ejpam-21	164	11	−b	−b	NOUN
ejpam-21	164	12	)	)	PUNCT
ejpam-21	164	13	)	)	PUNCT
ejpam-21	165	1	=	=	PUNCT
ejpam-21	165	2	f−(y	f−(y	NOUN
ejpam-21	165	3	−	−	NOUN
ejpam-21	165	4	int(b	int(b	NOUN
ejpam-21	165	5	)	)	PUNCT
ejpam-21	165	6	)	)	PUNCT
ejpam-21	166	1	=	=	SYM
ejpam-21	166	2	x−f+(int(b	x−f+(int(b	NOUN
ejpam-21	166	3	)	)	PUNCT
ejpam-21	166	4	)	)	PUNCT
ejpam-21	166	5	.	.	PUNCT
ejpam-21	167	1	hence	hence	ADV
ejpam-21	167	2	x	x	SYM
ejpam-21	167	3	/∈	/∈	PUNCT
ejpam-21	167	4	f+(int(b	f+(int(b	NOUN
ejpam-21	167	5	)	)	PUNCT
ejpam-21	167	6	)	)	PUNCT
ejpam-21	167	7	.	.	PUNCT
ejpam-21	168	1	(	(	PUNCT
ejpam-21	168	2	4	4	X
ejpam-21	168	3	)	)	PUNCT
ejpam-21	168	4	⇒	⇒	NOUN
ejpam-21	168	5	(	(	PUNCT
ejpam-21	168	6	1	1	NUM
ejpam-21	168	7	):	):	PUNCT
ejpam-21	168	8	let	let	VERB
ejpam-21	168	9	v	v	PART
ejpam-21	168	10	be	be	AUX
ejpam-21	168	11	any	any	DET
ejpam-21	168	12	open	open	ADJ
ejpam-21	168	13	set	set	NOUN
ejpam-21	168	14	of	of	ADP
ejpam-21	168	15	y	y	PROPN
ejpam-21	168	16	containing	contain	VERB
ejpam-21	168	17	f	f	PROPN
ejpam-21	168	18	(	(	PUNCT
ejpam-21	168	19	x	x	NOUN
ejpam-21	168	20	)	)	PUNCT
ejpam-21	168	21	and	and	CCONJ
ejpam-21	168	22	having	have	VERB
ejpam-21	168	23	compact	compact	ADJ
ejpam-21	168	24	complement	complement	NOUN
ejpam-21	168	25	.	.	PUNCT
ejpam-21	169	1	we	we	PRON
ejpam-21	169	2	have	have	VERB
ejpam-21	169	3	f+(v	f+(v	NOUN
ejpam-21	169	4	)	)	PUNCT
ejpam-21	170	1	=	=	SYM
ejpam-21	170	2	f+(int(v	f+(int(v	NOUN
ejpam-21	170	3	)	)	PUNCT
ejpam-21	170	4	)	)	PUNCT
ejpam-21	170	5	.	.	PUNCT
ejpam-21	171	1	then	then	ADV
ejpam-21	171	2	y	y	PROPN
ejpam-21	172	1	−	−	PROPN
ejpam-21	172	2	int(v	int(v	PROPN
ejpam-21	172	3	)	)	PUNCT
ejpam-21	172	4	=	=	PUNCT
ejpam-21	173	1	y	y	PROPN
ejpam-21	173	2	−	−	PROPN
ejpam-21	173	3	v	v	NUM
ejpam-21	173	4	which	which	PRON
ejpam-21	173	5	is	be	AUX
ejpam-21	173	6	compact	compact	ADJ
ejpam-21	173	7	and	and	CCONJ
ejpam-21	173	8	by	by	ADP
ejpam-21	173	9	(	(	PUNCT
ejpam-21	173	10	4	4	NUM
ejpam-21	173	11	)	)	PUNCT
ejpam-21	173	12	x	x	SYM
ejpam-21	173	13	∈	∈	PROPN
ejpam-21	173	14	mx	mx	PROPN
ejpam-21	173	15	int	int	PROPN
ejpam-21	173	16	(	(	PUNCT
ejpam-21	173	17	f+(v	f+(v	PROPN
ejpam-21	173	18	)	)	PUNCT
ejpam-21	173	19	)	)	PUNCT
ejpam-21	173	20	.	.	PUNCT
ejpam-21	174	1	therefore	therefore	ADV
ejpam-21	174	2	,	,	PUNCT
ejpam-21	174	3	there	there	PRON
ejpam-21	174	4	exists	exist	VERB
ejpam-21	174	5	an	an	DET
ejpam-21	174	6	mx	mx	PROPN
ejpam-21	174	7	-open	-open	NOUN
ejpam-21	174	8	set	set	NOUN
ejpam-21	174	9	u	u	NOUN
ejpam-21	174	10	containing	contain	VERB
ejpam-21	174	11	x	x	PUNCT
ejpam-21	174	12	such	such	ADJ
ejpam-21	174	13	that	that	SCONJ
ejpam-21	174	14	x	x	SYM
ejpam-21	174	15	∈	∈	PROPN
ejpam-21	174	16	u	u	NOUN
ejpam-21	174	17	⊂	⊂	PROPN
ejpam-21	174	18	f+(v	f+(v	PROPN
ejpam-21	174	19	)	)	PUNCT
ejpam-21	174	20	.	.	PUNCT
ejpam-21	175	1	thus	thus	ADV
ejpam-21	175	2	f	f	X
ejpam-21	175	3	(	(	PUNCT
ejpam-21	175	4	u	u	NOUN
ejpam-21	175	5	)	)	PUNCT
ejpam-21	175	6	⊂	⊂	PROPN
ejpam-21	175	7	v	v	NOUN
ejpam-21	175	8	.	.	PUNCT
ejpam-21	176	1	this	this	PRON
ejpam-21	176	2	shows	show	VERB
ejpam-21	176	3	that	that	SCONJ
ejpam-21	176	4	f	f	PROPN
ejpam-21	176	5	is	be	AUX
ejpam-21	176	6	u.c.m.c	u.c.m.c	PROPN
ejpam-21	176	7	.	.	PUNCT
ejpam-21	177	1	at	at	ADP
ejpam-21	177	2	x.	x.	NOUN
ejpam-21	177	3	t.noiri	t.noiri	ADV
ejpam-21	177	4	,	,	PUNCT
ejpam-21	177	5	v.popa	v.popa	NOUN
ejpam-21	177	6	/	/	SYM
ejpam-21	177	7	eur	eur	PROPN
ejpam-21	177	8	.	.	PUNCT
ejpam-21	178	1	j.	j.	PROPN
ejpam-21	178	2	pure	pure	PROPN
ejpam-21	178	3	appl	appl	PROPN
ejpam-21	178	4	.	.	PROPN
ejpam-21	178	5	math	math	PROPN
ejpam-21	178	6	,	,	PUNCT
ejpam-21	178	7	1	1	NUM
ejpam-21	178	8	(	(	PUNCT
ejpam-21	178	9	2008	2008	NUM
ejpam-21	178	10	)	)	PUNCT
ejpam-21	178	11	,	,	PUNCT
ejpam-21	178	12	(	(	PUNCT
ejpam-21	178	13	82	82	NUM
ejpam-21	178	14	-	-	SYM
ejpam-21	178	15	98	98	NUM
ejpam-21	178	16	)	)	PUNCT
ejpam-21	178	17	87	87	NUM
ejpam-21	178	18	theorem	theorem	VERB
ejpam-21	178	19	3.2	3.2	NUM
ejpam-21	178	20	.	.	PUNCT
ejpam-21	179	1	for	for	ADP
ejpam-21	179	2	a	a	DET
ejpam-21	179	3	multifunction	multifunction	NOUN
ejpam-21	179	4	f	f	NOUN
ejpam-21	179	5	:	:	PUNCT
ejpam-21	179	6	(	(	PUNCT
ejpam-21	179	7	x	x	NOUN
ejpam-21	179	8	,	,	PUNCT
ejpam-21	179	9	mx	mx	NOUN
ejpam-21	179	10	)	)	PUNCT
ejpam-21	179	11	→	→	SYM
ejpam-21	179	12	(	(	PUNCT
ejpam-21	179	13	y	y	PROPN
ejpam-21	179	14	,	,	PUNCT
ejpam-21	179	15	σ	σ	PROPN
ejpam-21	179	16	)	)	PUNCT
ejpam-21	179	17	,	,	PUNCT
ejpam-21	179	18	the	the	DET
ejpam-21	179	19	following	follow	VERB
ejpam-21	179	20	properties	property	NOUN
ejpam-21	179	21	are	be	AUX
ejpam-21	179	22	equivalent	equivalent	ADJ
ejpam-21	179	23	:	:	PUNCT
ejpam-21	179	24	(	(	PUNCT
ejpam-21	179	25	1	1	X
ejpam-21	179	26	)	)	PUNCT
ejpam-21	179	27	f	f	PROPN
ejpam-21	179	28	is	be	AUX
ejpam-21	179	29	l.c.m.c	l.c.m.c	PROPN
ejpam-21	179	30	.	.	PUNCT
ejpam-21	180	1	at	at	ADP
ejpam-21	180	2	x	x	X
ejpam-21	180	3	∈	∈	PROPN
ejpam-21	180	4	x	x	X
ejpam-21	180	5	;	;	PUNCT
ejpam-21	180	6	(	(	PUNCT
ejpam-21	180	7	2	2	X
ejpam-21	180	8	)	)	PUNCT
ejpam-21	180	9	x	x	SYM
ejpam-21	180	10	∈	∈	PROPN
ejpam-21	180	11	mx	mx	PROPN
ejpam-21	180	12	-int(f−(v	-int(f−(v	PROPN
ejpam-21	180	13	)	)	PUNCT
ejpam-21	180	14	)	)	PUNCT
ejpam-21	181	1	for	for	ADP
ejpam-21	181	2	each	each	DET
ejpam-21	181	3	open	open	ADJ
ejpam-21	181	4	set	set	VERB
ejpam-21	181	5	v	v	NOUN
ejpam-21	181	6	containing	contain	VERB
ejpam-21	181	7	f(x	f(x	PROPN
ejpam-21	181	8	)	)	PUNCT
ejpam-21	181	9	and	and	CCONJ
ejpam-21	181	10	having	have	VERB
ejpam-21	181	11	compact	compact	ADJ
ejpam-21	181	12	complement	complement	NOUN
ejpam-21	181	13	;	;	PUNCT
ejpam-21	181	14	(	(	PUNCT
ejpam-21	181	15	3	3	X
ejpam-21	181	16	)	)	PUNCT
ejpam-21	181	17	x	x	SYM
ejpam-21	181	18	∈	∈	PROPN
ejpam-21	181	19	f+(cl(b	f+(cl(b	PROPN
ejpam-21	181	20	)	)	PUNCT
ejpam-21	181	21	)	)	PUNCT
ejpam-21	181	22	for	for	ADP
ejpam-21	181	23	each	each	DET
ejpam-21	181	24	subset	subset	NOUN
ejpam-21	181	25	b	b	PROPN
ejpam-21	181	26	of	of	ADP
ejpam-21	181	27	y	y	PROPN
ejpam-21	181	28	having	have	VERB
ejpam-21	181	29	the	the	DET
ejpam-21	181	30	compact	compact	ADJ
ejpam-21	181	31	closure	closure	NOUN
ejpam-21	181	32	such	such	ADJ
ejpam-21	181	33	that	that	SCONJ
ejpam-21	181	34	x	x	SYM
ejpam-21	181	35	∈	∈	PROPN
ejpam-21	181	36	mx	mx	NOUN
ejpam-21	181	37	cl(f+(b	cl(f+(b	PROPN
ejpam-21	181	38	)	)	PUNCT
ejpam-21	181	39	)	)	PUNCT
ejpam-21	181	40	;	;	PUNCT
ejpam-21	181	41	(	(	PUNCT
ejpam-21	181	42	4	4	X
ejpam-21	181	43	)	)	PUNCT
ejpam-21	181	44	x	x	SYM
ejpam-21	181	45	∈	∈	PROPN
ejpam-21	181	46	mx	mx	PROPN
ejpam-21	181	47	-int(f−(b	-int(f−(b	PROPN
ejpam-21	181	48	)	)	PUNCT
ejpam-21	181	49	)	)	PUNCT
ejpam-21	181	50	for	for	ADP
ejpam-21	181	51	each	each	DET
ejpam-21	181	52	b	b	PROPN
ejpam-21	181	53	of	of	ADP
ejpam-21	181	54	y	y	PRON
ejpam-21	181	55	such	such	ADJ
ejpam-21	181	56	that	that	SCONJ
ejpam-21	181	57	y−int(b	y−int(b	NUM
ejpam-21	181	58	)	)	PUNCT
ejpam-21	181	59	is	be	AUX
ejpam-21	181	60	compact	compact	ADJ
ejpam-21	181	61	and	and	CCONJ
ejpam-21	181	62	x	x	SYM
ejpam-21	181	63	∈	∈	NOUN
ejpam-21	181	64	f−(int(b	f−(int(b	NUM
ejpam-21	181	65	)	)	PUNCT
ejpam-21	181	66	)	)	PUNCT
ejpam-21	181	67	.	.	PUNCT
ejpam-21	182	1	proof	proof	NOUN
ejpam-21	182	2	.	.	PUNCT
ejpam-21	183	1	the	the	DET
ejpam-21	183	2	proof	proof	NOUN
ejpam-21	183	3	is	be	AUX
ejpam-21	183	4	similar	similar	ADJ
ejpam-21	183	5	to	to	ADP
ejpam-21	183	6	that	that	PRON
ejpam-21	183	7	of	of	ADP
ejpam-21	183	8	theorem	theorem	ADJ
ejpam-21	183	9	3.1	3.1	NUM
ejpam-21	183	10	theorem	theorem	NOUN
ejpam-21	183	11	3.3	3.3	NUM
ejpam-21	183	12	.	.	PUNCT
ejpam-21	184	1	for	for	ADP
ejpam-21	184	2	a	a	DET
ejpam-21	184	3	multifunction	multifunction	NOUN
ejpam-21	184	4	f	f	NOUN
ejpam-21	184	5	:	:	PUNCT
ejpam-21	184	6	(	(	PUNCT
ejpam-21	184	7	x	x	NOUN
ejpam-21	184	8	,	,	PUNCT
ejpam-21	184	9	mx	mx	NOUN
ejpam-21	184	10	)	)	PUNCT
ejpam-21	184	11	→	→	SYM
ejpam-21	184	12	(	(	PUNCT
ejpam-21	184	13	y	y	PROPN
ejpam-21	184	14	,	,	PUNCT
ejpam-21	184	15	σ	σ	PROPN
ejpam-21	184	16	)	)	PUNCT
ejpam-21	184	17	,	,	PUNCT
ejpam-21	184	18	the	the	DET
ejpam-21	184	19	following	follow	VERB
ejpam-21	184	20	properties	property	NOUN
ejpam-21	184	21	are	be	AUX
ejpam-21	184	22	equivalent	equivalent	ADJ
ejpam-21	184	23	:	:	PUNCT
ejpam-21	184	24	(	(	PUNCT
ejpam-21	184	25	1	1	X
ejpam-21	184	26	)	)	PUNCT
ejpam-21	184	27	f	f	PROPN
ejpam-21	184	28	is	be	AUX
ejpam-21	184	29	u.c.m.c	u.c.m.c	PROPN
ejpam-21	184	30	.	.	PROPN
ejpam-21	184	31	;	;	PUNCT
ejpam-21	184	32	(	(	PUNCT
ejpam-21	184	33	2	2	X
ejpam-21	184	34	)	)	PUNCT
ejpam-21	184	35	f+(v	f+(v	NOUN
ejpam-21	184	36	)	)	PUNCT
ejpam-21	185	1	=	=	PUNCT
ejpam-21	185	2	mx	mx	PROPN
ejpam-21	185	3	-int(f+(v	-int(f+(v	PROPN
ejpam-21	185	4	)	)	PUNCT
ejpam-21	185	5	)	)	PUNCT
ejpam-21	185	6	for	for	ADP
ejpam-21	185	7	each	each	DET
ejpam-21	185	8	open	open	ADJ
ejpam-21	185	9	set	set	VERB
ejpam-21	185	10	v	v	NOUN
ejpam-21	185	11	of	of	ADP
ejpam-21	185	12	y	y	PROPN
ejpam-21	185	13	having	have	VERB
ejpam-21	185	14	compact	compact	ADJ
ejpam-21	185	15	complement	complement	NOUN
ejpam-21	185	16	;	;	PUNCT
ejpam-21	185	17	(	(	PUNCT
ejpam-21	185	18	3	3	X
ejpam-21	185	19	)	)	PUNCT
ejpam-21	185	20	f−(k	f−(k	PROPN
ejpam-21	185	21	)	)	PUNCT
ejpam-21	185	22	=	=	SYM
ejpam-21	185	23	mx	mx	NOUN
ejpam-21	185	24	-cl(f−(k	-cl(f−(k	PROPN
ejpam-21	185	25	)	)	PUNCT
ejpam-21	185	26	)	)	PUNCT
ejpam-21	185	27	for	for	SCONJ
ejpam-21	185	28	every	every	DET
ejpam-21	185	29	compact	compact	ADJ
ejpam-21	185	30	closed	close	VERB
ejpam-21	185	31	set	set	VERB
ejpam-21	185	32	k	k	PROPN
ejpam-21	185	33	of	of	ADP
ejpam-21	185	34	y	y	PROPN
ejpam-21	185	35	;	;	PUNCT
ejpam-21	185	36	(	(	PUNCT
ejpam-21	185	37	4	4	X
ejpam-21	185	38	)	)	PUNCT
ejpam-21	185	39	mx	mx	NOUN
ejpam-21	185	40	-cl(f−(b	-cl(f−(b	PROPN
ejpam-21	185	41	)	)	PUNCT
ejpam-21	185	42	)	)	PUNCT
ejpam-21	186	1	⊂	⊂	PROPN
ejpam-21	186	2	f−(cl(b	f−(cl(b	NOUN
ejpam-21	186	3	)	)	PUNCT
ejpam-21	186	4	)	)	PUNCT
ejpam-21	186	5	for	for	ADP
ejpam-21	186	6	every	every	DET
ejpam-21	186	7	subset	subset	NOUN
ejpam-21	186	8	b	b	PROPN
ejpam-21	186	9	of	of	ADP
ejpam-21	186	10	y	y	PROPN
ejpam-21	186	11	having	have	VERB
ejpam-21	186	12	the	the	DET
ejpam-21	186	13	compact	compact	ADJ
ejpam-21	186	14	closure	closure	NOUN
ejpam-21	186	15	;	;	PUNCT
ejpam-21	186	16	(	(	PUNCT
ejpam-21	186	17	5	5	X
ejpam-21	186	18	)	)	PUNCT
ejpam-21	186	19	f+(int(b	f+(int(b	NOUN
ejpam-21	186	20	)	)	PUNCT
ejpam-21	186	21	)	)	PUNCT
ejpam-21	187	1	⊂	⊂	PROPN
ejpam-21	187	2	mx	mx	PROPN
ejpam-21	187	3	-int(f+(b	-int(f+(b	PROPN
ejpam-21	187	4	)	)	PUNCT
ejpam-21	187	5	)	)	PUNCT
ejpam-21	187	6	for	for	ADP
ejpam-21	187	7	every	every	DET
ejpam-21	187	8	subset	subset	NOUN
ejpam-21	187	9	b	b	PROPN
ejpam-21	187	10	of	of	ADP
ejpam-21	187	11	y	y	PRON
ejpam-21	187	12	such	such	ADJ
ejpam-21	187	13	that	that	SCONJ
ejpam-21	187	14	y	y	PROPN
ejpam-21	187	15	−	−	PROPN
ejpam-21	187	16	int(b	int(b	PROPN
ejpam-21	187	17	)	)	PUNCT
ejpam-21	187	18	is	be	AUX
ejpam-21	187	19	compact	compact	ADJ
ejpam-21	187	20	.	.	PUNCT
ejpam-21	188	1	proof	proof	NOUN
ejpam-21	188	2	.	.	PUNCT
ejpam-21	189	1	(	(	PUNCT
ejpam-21	189	2	1	1	X
ejpam-21	189	3	)	)	PUNCT
ejpam-21	189	4	⇒	⇒	NOUN
ejpam-21	189	5	(	(	PUNCT
ejpam-21	189	6	2	2	NUM
ejpam-21	189	7	):	):	PUNCT
ejpam-21	189	8	let	let	VERB
ejpam-21	189	9	v	v	PART
ejpam-21	189	10	be	be	AUX
ejpam-21	189	11	any	any	DET
ejpam-21	189	12	open	open	ADJ
ejpam-21	189	13	set	set	NOUN
ejpam-21	189	14	of	of	ADP
ejpam-21	189	15	y	y	PROPN
ejpam-21	189	16	having	have	VERB
ejpam-21	189	17	compact	compact	ADJ
ejpam-21	189	18	complement	complement	NOUN
ejpam-21	189	19	and	and	CCONJ
ejpam-21	189	20	x	x	PUNCT
ejpam-21	189	21	∈	∈	PROPN
ejpam-21	189	22	f+(v	f+(v	NOUN
ejpam-21	189	23	)	)	PUNCT
ejpam-21	189	24	.	.	PUNCT
ejpam-21	190	1	then	then	ADV
ejpam-21	190	2	f	f	X
ejpam-21	190	3	(	(	PUNCT
ejpam-21	190	4	x	x	X
ejpam-21	190	5	)	)	PUNCT
ejpam-21	190	6	⊂	⊂	PROPN
ejpam-21	190	7	v	v	NOUN
ejpam-21	190	8	and	and	CCONJ
ejpam-21	190	9	by	by	ADP
ejpam-21	190	10	theorem	theorem	ADJ
ejpam-21	190	11	3.1	3.1	NUM
ejpam-21	190	12	,	,	PUNCT
ejpam-21	190	13	x	x	SYM
ejpam-21	190	14	∈	∈	PROPN
ejpam-21	190	15	mx	mx	PROPN
ejpam-21	190	16	-int(f+(v	-int(f+(v	PROPN
ejpam-21	190	17	)	)	PUNCT
ejpam-21	190	18	)	)	PUNCT
ejpam-21	190	19	.	.	PUNCT
ejpam-21	191	1	by	by	ADP
ejpam-21	191	2	lemma	lemma	PROPN
ejpam-21	191	3	3.1	3.1	NUM
ejpam-21	191	4	,	,	PUNCT
ejpam-21	191	5	we	we	PRON
ejpam-21	191	6	have	have	VERB
ejpam-21	191	7	mx	mx	NOUN
ejpam-21	191	8	int(f+(v	int(f+(v	PROPN
ejpam-21	191	9	)	)	PUNCT
ejpam-21	191	10	)	)	PUNCT
ejpam-21	192	1	⊂	⊂	PROPN
ejpam-21	192	2	f+(v	f+(v	PROPN
ejpam-21	192	3	)	)	PUNCT
ejpam-21	192	4	.	.	PUNCT
ejpam-21	193	1	therefore	therefore	ADV
ejpam-21	193	2	,	,	PUNCT
ejpam-21	193	3	we	we	PRON
ejpam-21	193	4	obtain	obtain	VERB
ejpam-21	193	5	f+(v	f+(v	NOUN
ejpam-21	193	6	)	)	PUNCT
ejpam-21	194	1	=	=	PUNCT
ejpam-21	194	2	mx	mx	PROPN
ejpam-21	194	3	-int(f+(v	-int(f+(v	PROPN
ejpam-21	194	4	)	)	PUNCT
ejpam-21	194	5	)	)	PUNCT
ejpam-21	194	6	.	.	PUNCT
ejpam-21	195	1	(	(	PUNCT
ejpam-21	195	2	2)⇒	2)⇒	NUM
ejpam-21	195	3	(	(	PUNCT
ejpam-21	195	4	3	3	NUM
ejpam-21	195	5	):	):	PUNCT
ejpam-21	195	6	let	let	VERB
ejpam-21	195	7	k	k	PRON
ejpam-21	195	8	be	be	AUX
ejpam-21	195	9	any	any	DET
ejpam-21	195	10	compact	compact	ADJ
ejpam-21	195	11	closed	close	VERB
ejpam-21	195	12	set	set	NOUN
ejpam-21	195	13	of	of	ADP
ejpam-21	195	14	y	y	PROPN
ejpam-21	195	15	.	.	PUNCT
ejpam-21	196	1	then	then	ADV
ejpam-21	196	2	,	,	PUNCT
ejpam-21	196	3	by	by	ADP
ejpam-21	196	4	lemma	lemma	PROPN
ejpam-21	196	5	3.1	3.1	NUM
ejpam-21	196	6	we	we	PRON
ejpam-21	196	7	have	have	VERB
ejpam-21	196	8	x−f−(k	x−f−(k	NUM
ejpam-21	196	9	)	)	PUNCT
ejpam-21	197	1	=	=	PUNCT
ejpam-21	197	2	f+(y	f+(y	NOUN
ejpam-21	197	3	−k	−k	PROPN
ejpam-21	197	4	)	)	PUNCT
ejpam-21	197	5	=	=	SYM
ejpam-21	197	6	mx	mx	NOUN
ejpam-21	197	7	-int(f+(y	-int(f+(y	PUNCT
ejpam-21	197	8	−k	−k	ADJ
ejpam-21	197	9	)	)	PUNCT
ejpam-21	197	10	)	)	PUNCT
ejpam-21	198	1	=	=	SYM
ejpam-21	198	2	mx	mx	PROPN
ejpam-21	198	3	-int(x	-int(x	PROPN
ejpam-21	198	4	−f−(k	−f−(k	PROPN
ejpam-21	198	5	)	)	PUNCT
ejpam-21	198	6	)	)	PUNCT
ejpam-21	199	1	=	=	PUNCT
ejpam-21	199	2	x	x	PUNCT
ejpam-21	199	3	−mx	−mx	NOUN
ejpam-21	199	4	-cl(f−(k	-cl(f−(k	NOUN
ejpam-21	199	5	)	)	PUNCT
ejpam-21	199	6	)	)	PUNCT
ejpam-21	199	7	.	.	PUNCT
ejpam-21	200	1	therefore	therefore	ADV
ejpam-21	200	2	,	,	PUNCT
ejpam-21	200	3	we	we	PRON
ejpam-21	200	4	obtain	obtain	VERB
ejpam-21	200	5	f−(k	f−(k	PROPN
ejpam-21	200	6	)	)	PUNCT
ejpam-21	200	7	=	=	SYM
ejpam-21	200	8	mx	mx	NOUN
ejpam-21	200	9	-cl(f−(k	-cl(f−(k	PROPN
ejpam-21	200	10	)	)	PUNCT
ejpam-21	200	11	)	)	PUNCT
ejpam-21	200	12	.	.	PUNCT
ejpam-21	201	1	(	(	PUNCT
ejpam-21	201	2	3	3	X
ejpam-21	201	3	)	)	PUNCT
ejpam-21	201	4	⇒	⇒	NOUN
ejpam-21	201	5	(	(	PUNCT
ejpam-21	201	6	4	4	NUM
ejpam-21	201	7	):	):	PUNCT
ejpam-21	201	8	let	let	VERB
ejpam-21	201	9	b	b	X
ejpam-21	201	10	be	be	AUX
ejpam-21	201	11	any	any	DET
ejpam-21	201	12	subset	subset	NOUN
ejpam-21	201	13	of	of	ADP
ejpam-21	201	14	y	y	PROPN
ejpam-21	201	15	having	have	VERB
ejpam-21	201	16	the	the	DET
ejpam-21	201	17	compact	compact	ADJ
ejpam-21	201	18	closure	closure	NOUN
ejpam-21	201	19	.	.	PUNCT
ejpam-21	202	1	by	by	ADP
ejpam-21	202	2	lemma	lemma	PROPN
ejpam-21	202	3	3.1	3.1	NUM
ejpam-21	202	4	,	,	PUNCT
ejpam-21	202	5	we	we	PRON
ejpam-21	202	6	have	have	VERB
ejpam-21	202	7	f−(b	f−(b	PROPN
ejpam-21	202	8	)	)	PUNCT
ejpam-21	202	9	⊂	⊂	PROPN
ejpam-21	202	10	f−(cl(b	f−(cl(b	PROPN
ejpam-21	202	11	)	)	PUNCT
ejpam-21	202	12	)	)	PUNCT
ejpam-21	203	1	=	=	PUNCT
ejpam-21	203	2	mx	mx	PROPN
ejpam-21	203	3	-cl(f−(cl(b	-cl(f−(cl(b	PROPN
ejpam-21	203	4	)	)	PUNCT
ejpam-21	203	5	)	)	PUNCT
ejpam-21	203	6	)	)	PUNCT
ejpam-21	203	7	.	.	PUNCT
ejpam-21	204	1	hence	hence	ADV
ejpam-21	204	2	mx	mx	PROPN
ejpam-21	204	3	-cl(f−(b	-cl(f−(b	PROPN
ejpam-21	204	4	)	)	PUNCT
ejpam-21	204	5	)	)	PUNCT
ejpam-21	205	1	⊂	⊂	PROPN
ejpam-21	205	2	mx	mx	PROPN
ejpam-21	205	3	-cl(f−(cl(b	-cl(f−(cl(b	PROPN
ejpam-21	205	4	)	)	PUNCT
ejpam-21	205	5	)	)	PUNCT
ejpam-21	205	6	)	)	PUNCT
ejpam-21	206	1	=	=	SYM
ejpam-21	206	2	f−(cl(b	f−(cl(b	NOUN
ejpam-21	206	3	)	)	PUNCT
ejpam-21	206	4	)	)	PUNCT
ejpam-21	206	5	.	.	PUNCT
ejpam-21	207	1	(	(	PUNCT
ejpam-21	207	2	4	4	X
ejpam-21	207	3	)	)	PUNCT
ejpam-21	207	4	⇒	⇒	NOUN
ejpam-21	207	5	(	(	PUNCT
ejpam-21	207	6	5	5	NUM
ejpam-21	207	7	):	):	PUNCT
ejpam-21	207	8	let	let	VERB
ejpam-21	207	9	b	b	X
ejpam-21	207	10	be	be	AUX
ejpam-21	207	11	a	a	DET
ejpam-21	207	12	subset	subset	NOUN
ejpam-21	207	13	of	of	ADP
ejpam-21	207	14	y	y	PRON
ejpam-21	207	15	such	such	ADJ
ejpam-21	207	16	that	that	SCONJ
ejpam-21	207	17	y	y	PROPN
ejpam-21	207	18	−	−	PROPN
ejpam-21	207	19	int(b	int(b	PROPN
ejpam-21	207	20	)	)	PUNCT
ejpam-21	207	21	is	be	AUX
ejpam-21	207	22	compact	compact	ADJ
ejpam-21	207	23	.	.	PUNCT
ejpam-21	208	1	then	then	ADV
ejpam-21	208	2	by	by	ADP
ejpam-21	208	3	lemma	lemma	PROPN
ejpam-21	208	4	3.1	3.1	NUM
ejpam-21	208	5	we	we	PRON
ejpam-21	208	6	have	have	VERB
ejpam-21	208	7	x	x	X
ejpam-21	208	8	−mx	−mx	VERB
ejpam-21	208	9	-int(f+(b	-int(f+(b	NOUN
ejpam-21	208	10	)	)	PUNCT
ejpam-21	208	11	)	)	PUNCT
ejpam-21	209	1	=	=	SYM
ejpam-21	209	2	mx	mx	PROPN
ejpam-21	209	3	-cl(x	-cl(x	PRON
ejpam-21	209	4	−	−	PROPN
ejpam-21	209	5	f+(b	f+(b	NOUN
ejpam-21	209	6	)	)	PUNCT
ejpam-21	209	7	)	)	PUNCT
ejpam-21	210	1	=	=	SYM
ejpam-21	210	2	mx	mx	PROPN
ejpam-21	210	3	-cl(f−(y	-cl(f−(y	VERB
ejpam-21	210	4	−b	−b	ADJ
ejpam-21	210	5	)	)	PUNCT
ejpam-21	210	6	)	)	PUNCT
ejpam-21	211	1	⊂	⊂	PROPN
ejpam-21	211	2	⊂	⊂	PROPN
ejpam-21	211	3	mx	mx	PROPN
ejpam-21	211	4	-cl(f−(y	-cl(f−(y	VERB
ejpam-21	211	5	−	−	PROPN
ejpam-21	211	6	int(b	int(b	NOUN
ejpam-21	211	7	)	)	PUNCT
ejpam-21	211	8	)	)	PUNCT
ejpam-21	211	9	)	)	PUNCT
ejpam-21	212	1	⊂	⊂	PROPN
ejpam-21	212	2	f−(y	f−(y	VERB
ejpam-21	212	3	−	−	NOUN
ejpam-21	212	4	int(b	int(b	NOUN
ejpam-21	212	5	)	)	PUNCT
ejpam-21	212	6	)	)	PUNCT
ejpam-21	213	1	=	=	PUNCT
ejpam-21	213	2	x	x	X
ejpam-21	214	1	−	−	NOUN
ejpam-21	214	2	f+(int(b	f+(int(b	NOUN
ejpam-21	214	3	)	)	PUNCT
ejpam-21	214	4	)	)	PUNCT
ejpam-21	214	5	.	.	PUNCT
ejpam-21	215	1	therefore	therefore	ADV
ejpam-21	215	2	,	,	PUNCT
ejpam-21	215	3	we	we	PRON
ejpam-21	215	4	obtain	obtain	VERB
ejpam-21	215	5	f+(int(b	f+(int(b	NOUN
ejpam-21	215	6	)	)	PUNCT
ejpam-21	215	7	)	)	PUNCT
ejpam-21	216	1	⊂	⊂	PROPN
ejpam-21	216	2	mx	mx	PROPN
ejpam-21	216	3	-int(f+(b	-int(f+(b	PROPN
ejpam-21	216	4	)	)	PUNCT
ejpam-21	216	5	)	)	PUNCT
ejpam-21	216	6	.	.	PUNCT
ejpam-21	217	1	t.noiri	t.noiri	ADV
ejpam-21	217	2	,	,	PUNCT
ejpam-21	217	3	v.popa	v.popa	NOUN
ejpam-21	217	4	/	/	SYM
ejpam-21	217	5	eur	eur	PROPN
ejpam-21	217	6	.	.	PUNCT
ejpam-21	218	1	j.	j.	PROPN
ejpam-21	218	2	pure	pure	PROPN
ejpam-21	218	3	appl	appl	PROPN
ejpam-21	218	4	.	.	PROPN
ejpam-21	218	5	math	math	PROPN
ejpam-21	218	6	,	,	PUNCT
ejpam-21	218	7	1	1	NUM
ejpam-21	218	8	(	(	PUNCT
ejpam-21	218	9	2008	2008	NUM
ejpam-21	218	10	)	)	PUNCT
ejpam-21	218	11	,	,	PUNCT
ejpam-21	218	12	(	(	PUNCT
ejpam-21	218	13	82	82	NUM
ejpam-21	218	14	-	-	SYM
ejpam-21	218	15	98	98	NUM
ejpam-21	218	16	)	)	PUNCT
ejpam-21	218	17	88	88	NUM
ejpam-21	218	18	(	(	PUNCT
ejpam-21	218	19	5	5	NUM
ejpam-21	218	20	)	)	PUNCT
ejpam-21	218	21	⇒	⇒	NOUN
ejpam-21	218	22	(	(	PUNCT
ejpam-21	218	23	1	1	NUM
ejpam-21	218	24	):	):	PUNCT
ejpam-21	218	25	let	let	VERB
ejpam-21	218	26	x	x	PUNCT
ejpam-21	218	27	∈	∈	PROPN
ejpam-21	218	28	x	x	X
ejpam-21	218	29	and	and	CCONJ
ejpam-21	218	30	v	v	X
ejpam-21	218	31	be	be	AUX
ejpam-21	218	32	any	any	DET
ejpam-21	218	33	open	open	ADJ
ejpam-21	218	34	set	set	NOUN
ejpam-21	218	35	of	of	ADP
ejpam-21	218	36	y	y	PROPN
ejpam-21	218	37	containing	contain	VERB
ejpam-21	218	38	f	f	PROPN
ejpam-21	218	39	(	(	PUNCT
ejpam-21	218	40	x	x	NOUN
ejpam-21	218	41	)	)	PUNCT
ejpam-21	218	42	and	and	CCONJ
ejpam-21	218	43	having	have	VERB
ejpam-21	218	44	compact	compact	ADJ
ejpam-21	218	45	complement	complement	NOUN
ejpam-21	218	46	.	.	PUNCT
ejpam-21	219	1	then	then	ADV
ejpam-21	219	2	x	x	SYM
ejpam-21	219	3	∈	∈	PROPN
ejpam-21	219	4	f+(v	f+(v	NOUN
ejpam-21	219	5	)	)	PUNCT
ejpam-21	220	1	=	=	SYM
ejpam-21	220	2	f+(int(v	f+(int(v	NOUN
ejpam-21	220	3	)	)	PUNCT
ejpam-21	220	4	)	)	PUNCT
ejpam-21	221	1	⊂	⊂	PROPN
ejpam-21	221	2	mx	mx	PROPN
ejpam-21	221	3	-int(f+(v	-int(f+(v	PROPN
ejpam-21	221	4	)	)	PUNCT
ejpam-21	221	5	)	)	PUNCT
ejpam-21	221	6	.	.	PUNCT
ejpam-21	222	1	by	by	ADP
ejpam-21	222	2	theorem	theorem	NOUN
ejpam-21	222	3	3.1	3.1	NUM
ejpam-21	222	4	,	,	PUNCT
ejpam-21	222	5	f	f	PROPN
ejpam-21	222	6	is	be	AUX
ejpam-21	222	7	u.c.m.c	u.c.m.c	PROPN
ejpam-21	222	8	.	.	PUNCT
ejpam-21	223	1	at	at	ADP
ejpam-21	223	2	x.	x.	PROPN
ejpam-21	223	3	theorem	theorem	VERB
ejpam-21	223	4	3.4	3.4	NUM
ejpam-21	223	5	.	.	PUNCT
ejpam-21	224	1	for	for	ADP
ejpam-21	224	2	a	a	DET
ejpam-21	224	3	multifunction	multifunction	NOUN
ejpam-21	224	4	,	,	PUNCT
ejpam-21	224	5	the	the	DET
ejpam-21	224	6	following	follow	VERB
ejpam-21	224	7	properties	property	NOUN
ejpam-21	224	8	are	be	AUX
ejpam-21	224	9	equivalent	equivalent	ADJ
ejpam-21	224	10	:	:	PUNCT
ejpam-21	224	11	(	(	PUNCT
ejpam-21	224	12	1	1	X
ejpam-21	224	13	)	)	PUNCT
ejpam-21	224	14	f	f	PROPN
ejpam-21	224	15	is	be	AUX
ejpam-21	224	16	l.c.m.c	l.c.m.c	PROPN
ejpam-21	224	17	.	.	PUNCT
ejpam-21	224	18	;	;	PUNCT
ejpam-21	224	19	(	(	PUNCT
ejpam-21	224	20	2	2	X
ejpam-21	224	21	)	)	PUNCT
ejpam-21	224	22	f−(v	f−(v	NOUN
ejpam-21	224	23	)	)	PUNCT
ejpam-21	225	1	=	=	SYM
ejpam-21	225	2	mx	mx	PROPN
ejpam-21	225	3	-int(f−v	-int(f−v	PROPN
ejpam-21	225	4	)	)	PUNCT
ejpam-21	225	5	)	)	PUNCT
ejpam-21	225	6	for	for	ADP
ejpam-21	225	7	each	each	DET
ejpam-21	225	8	open	open	ADJ
ejpam-21	225	9	set	set	VERB
ejpam-21	225	10	v	v	NOUN
ejpam-21	225	11	of	of	ADP
ejpam-21	225	12	y	y	PROPN
ejpam-21	225	13	having	have	VERB
ejpam-21	225	14	compact	compact	ADJ
ejpam-21	225	15	complement	complement	NOUN
ejpam-21	225	16	;	;	PUNCT
ejpam-21	225	17	(	(	PUNCT
ejpam-21	225	18	3	3	X
ejpam-21	225	19	)	)	PUNCT
ejpam-21	225	20	f+(k	f+(k	NOUN
ejpam-21	225	21	)	)	PUNCT
ejpam-21	225	22	=	=	SYM
ejpam-21	225	23	mx	mx	PROPN
ejpam-21	225	24	-cl(f+(k	-cl(f+(k	PROPN
ejpam-21	225	25	)	)	PUNCT
ejpam-21	225	26	)	)	PUNCT
ejpam-21	225	27	is	be	AUX
ejpam-21	225	28	for	for	SCONJ
ejpam-21	225	29	every	every	DET
ejpam-21	225	30	compact	compact	ADJ
ejpam-21	225	31	closed	close	VERB
ejpam-21	225	32	set	set	VERB
ejpam-21	225	33	k	k	PROPN
ejpam-21	225	34	of	of	ADP
ejpam-21	225	35	y	y	PROPN
ejpam-21	225	36	;	;	PUNCT
ejpam-21	225	37	(	(	PUNCT
ejpam-21	225	38	4	4	X
ejpam-21	225	39	)	)	PUNCT
ejpam-21	225	40	mx	mx	NOUN
ejpam-21	225	41	-cl(f+(b	-cl(f+(b	PROPN
ejpam-21	225	42	)	)	PUNCT
ejpam-21	225	43	)	)	PUNCT
ejpam-21	226	1	⊂	⊂	PROPN
ejpam-21	226	2	f+(cl(b	f+(cl(b	PROPN
ejpam-21	226	3	)	)	PUNCT
ejpam-21	226	4	)	)	PUNCT
ejpam-21	226	5	for	for	ADP
ejpam-21	226	6	every	every	DET
ejpam-21	226	7	subset	subset	NOUN
ejpam-21	226	8	b	b	PROPN
ejpam-21	226	9	of	of	ADP
ejpam-21	226	10	y	y	PROPN
ejpam-21	226	11	having	have	VERB
ejpam-21	226	12	the	the	DET
ejpam-21	226	13	compact	compact	ADJ
ejpam-21	226	14	closure	closure	NOUN
ejpam-21	226	15	;	;	PUNCT
ejpam-21	226	16	(	(	PUNCT
ejpam-21	226	17	5	5	NUM
ejpam-21	226	18	)	)	PUNCT
ejpam-21	226	19	f−(int(b	f−(int(b	NUM
ejpam-21	226	20	)	)	PUNCT
ejpam-21	226	21	)	)	PUNCT
ejpam-21	227	1	⊂	⊂	PROPN
ejpam-21	227	2	mx	mx	PROPN
ejpam-21	227	3	-int(f−(b	-int(f−(b	PROPN
ejpam-21	227	4	)	)	PUNCT
ejpam-21	227	5	)	)	PUNCT
ejpam-21	227	6	for	for	ADP
ejpam-21	227	7	every	every	DET
ejpam-21	227	8	subset	subset	NOUN
ejpam-21	227	9	b	b	PROPN
ejpam-21	227	10	of	of	ADP
ejpam-21	227	11	y	y	PRON
ejpam-21	227	12	such	such	ADJ
ejpam-21	227	13	that	that	SCONJ
ejpam-21	227	14	y	y	PROPN
ejpam-21	227	15	−	−	PROPN
ejpam-21	227	16	int(b	int(b	PROPN
ejpam-21	227	17	)	)	PUNCT
ejpam-21	227	18	is	be	AUX
ejpam-21	227	19	compact	compact	ADJ
ejpam-21	227	20	.	.	PUNCT
ejpam-21	228	1	proof	proof	NOUN
ejpam-21	228	2	.	.	PUNCT
ejpam-21	229	1	the	the	DET
ejpam-21	229	2	proof	proof	NOUN
ejpam-21	229	3	is	be	AUX
ejpam-21	229	4	similar	similar	ADJ
ejpam-21	229	5	to	to	ADP
ejpam-21	229	6	that	that	PRON
ejpam-21	229	7	of	of	ADP
ejpam-21	229	8	theorem	theorem	ADJ
ejpam-21	229	9	3.3	3.3	NUM
ejpam-21	229	10	.	.	PUNCT
ejpam-21	230	1	corollary	corollary	ADJ
ejpam-21	230	2	3.1	3.1	NUM
ejpam-21	230	3	.	.	PUNCT
ejpam-21	231	1	let	let	AUX
ejpam-21	231	2	(	(	PUNCT
ejpam-21	231	3	x	x	NOUN
ejpam-21	231	4	,	,	PUNCT
ejpam-21	231	5	mx	mx	NOUN
ejpam-21	231	6	)	)	PUNCT
ejpam-21	231	7	be	be	AUX
ejpam-21	231	8	an	an	DET
ejpam-21	231	9	m	m	NOUN
ejpam-21	231	10	-	-	NOUN
ejpam-21	231	11	space	space	NOUN
ejpam-21	231	12	and	and	CCONJ
ejpam-21	231	13	mx	mx	PROPN
ejpam-21	231	14	have	have	VERB
ejpam-21	231	15	property	property	NOUN
ejpam-21	231	16	b.	b.	PROPN
ejpam-21	231	17	for	for	ADP
ejpam-21	231	18	a	a	DET
ejpam-21	231	19	multifunction	multifunction	NOUN
ejpam-21	231	20	f	f	NOUN
ejpam-21	231	21	:	:	PUNCT
ejpam-21	231	22	(	(	PUNCT
ejpam-21	231	23	x	x	NOUN
ejpam-21	231	24	,	,	PUNCT
ejpam-21	231	25	mx	mx	NOUN
ejpam-21	231	26	)	)	PUNCT
ejpam-21	231	27	→	→	SYM
ejpam-21	231	28	(	(	PUNCT
ejpam-21	231	29	y	y	PROPN
ejpam-21	231	30	,	,	PUNCT
ejpam-21	231	31	σ	σ	PROPN
ejpam-21	231	32	)	)	PUNCT
ejpam-21	231	33	,	,	PUNCT
ejpam-21	231	34	the	the	DET
ejpam-21	231	35	following	follow	VERB
ejpam-21	231	36	properties	property	NOUN
ejpam-21	231	37	are	be	AUX
ejpam-21	231	38	equivalent	equivalent	ADJ
ejpam-21	231	39	:	:	PUNCT
ejpam-21	231	40	(	(	PUNCT
ejpam-21	231	41	1	1	X
ejpam-21	231	42	)	)	PUNCT
ejpam-21	231	43	f	f	PROPN
ejpam-21	231	44	is	be	AUX
ejpam-21	231	45	u.c.m.c	u.c.m.c	PROPN
ejpam-21	231	46	.	.	PUNCT
ejpam-21	232	1	(	(	PUNCT
ejpam-21	232	2	resp	resp	NOUN
ejpam-21	232	3	.	.	PUNCT
ejpam-21	233	1	l.c.m.c	l.c.m.c	PROPN
ejpam-21	233	2	.	.	PROPN
ejpam-21	233	3	)	)	PUNCT
ejpam-21	233	4	;	;	PUNCT
ejpam-21	233	5	(	(	PUNCT
ejpam-21	233	6	2	2	X
ejpam-21	233	7	)	)	PUNCT
ejpam-21	233	8	f+(v	f+(v	NOUN
ejpam-21	233	9	)	)	PUNCT
ejpam-21	234	1	(	(	PUNCT
ejpam-21	234	2	resp	resp	NOUN
ejpam-21	234	3	.	.	PUNCT
ejpam-21	235	1	f−(v	f−(v	NOUN
ejpam-21	235	2	)	)	PUNCT
ejpam-21	235	3	)	)	PUNCT
ejpam-21	235	4	is	be	AUX
ejpam-21	235	5	mx	mx	NOUN
ejpam-21	235	6	-open	-open	NOUN
ejpam-21	235	7	for	for	ADP
ejpam-21	235	8	each	each	DET
ejpam-21	235	9	open	open	ADJ
ejpam-21	235	10	set	set	VERB
ejpam-21	235	11	v	v	NOUN
ejpam-21	235	12	of	of	ADP
ejpam-21	235	13	y	y	PROPN
ejpam-21	235	14	having	have	VERB
ejpam-21	235	15	compact	compact	ADJ
ejpam-21	235	16	complement	complement	NOUN
ejpam-21	235	17	;	;	PUNCT
ejpam-21	235	18	(	(	PUNCT
ejpam-21	235	19	3	3	X
ejpam-21	235	20	)	)	PUNCT
ejpam-21	235	21	f−(k	f−(k	PROPN
ejpam-21	235	22	)	)	PUNCT
ejpam-21	235	23	(	(	PUNCT
ejpam-21	235	24	resp	resp	NOUN
ejpam-21	235	25	.	.	PUNCT
ejpam-21	236	1	f+(k	f+(k	NUM
ejpam-21	236	2	)	)	PUNCT
ejpam-21	236	3	)	)	PUNCT
ejpam-21	236	4	is	be	AUX
ejpam-21	236	5	mx	mx	PROPN
ejpam-21	236	6	-closed	-close	VERB
ejpam-21	236	7	for	for	ADP
ejpam-21	236	8	every	every	DET
ejpam-21	236	9	compact	compact	ADJ
ejpam-21	236	10	closed	close	VERB
ejpam-21	236	11	set	set	VERB
ejpam-21	236	12	k	k	PROPN
ejpam-21	236	13	of	of	ADP
ejpam-21	236	14	y.	y.	PROPN
ejpam-21	236	15	proof	proof	PROPN
ejpam-21	236	16	.	.	PUNCT
ejpam-21	237	1	this	this	PRON
ejpam-21	237	2	is	be	AUX
ejpam-21	237	3	an	an	DET
ejpam-21	237	4	immediate	immediate	ADJ
ejpam-21	237	5	consequence	consequence	NOUN
ejpam-21	237	6	of	of	ADP
ejpam-21	237	7	theorems	theorem	NOUN
ejpam-21	237	8	3.3	3.3	NUM
ejpam-21	237	9	and	and	CCONJ
ejpam-21	237	10	3.4	3.4	NUM
ejpam-21	237	11	and	and	CCONJ
ejpam-21	237	12	lemma	lemma	PROPN
ejpam-21	237	13	3.3	3.3	NUM
ejpam-21	237	14	.	.	PUNCT
ejpam-21	238	1	remark	remark	VERB
ejpam-21	238	2	3.4	3.4	NUM
ejpam-21	238	3	.	.	PUNCT
ejpam-21	239	1	let	let	AUX
ejpam-21	239	2	(	(	PUNCT
ejpam-21	239	3	x	x	NOUN
ejpam-21	239	4	,	,	PUNCT
ejpam-21	239	5	τ	τ	X
ejpam-21	239	6	)	)	PUNCT
ejpam-21	239	7	and	and	CCONJ
ejpam-21	239	8	(	(	PUNCT
ejpam-21	239	9	y	y	PROPN
ejpam-21	239	10	,	,	PUNCT
ejpam-21	239	11	σ	σ	PROPN
ejpam-21	239	12	)	)	PUNCT
ejpam-21	239	13	be	be	VERB
ejpam-21	239	14	topological	topological	ADJ
ejpam-21	239	15	spaces	space	NOUN
ejpam-21	239	16	.	.	PUNCT
ejpam-21	240	1	if	if	SCONJ
ejpam-21	240	2	mx	mx	PROPN
ejpam-21	240	3	=	=	SYM
ejpam-21	240	4	τ	τ	PROPN
ejpam-21	240	5	(	(	PUNCT
ejpam-21	240	6	resp	resp	NOUN
ejpam-21	240	7	.	.	PUNCT
ejpam-21	240	8	so(x	so(x	NOUN
ejpam-21	240	9	)	)	PUNCT
ejpam-21	240	10	)	)	PUNCT
ejpam-21	240	11	and	and	CCONJ
ejpam-21	240	12	is	be	AUX
ejpam-21	240	13	upper	upper	ADJ
ejpam-21	240	14	/	/	SYM
ejpam-21	240	15	lower	low	ADJ
ejpam-21	240	16	c	c	NOUN
ejpam-21	240	17	-	-	PUNCT
ejpam-21	240	18	m	m	NOUN
ejpam-21	240	19	-	-	ADJ
ejpam-21	240	20	continuous	continuous	ADJ
ejpam-21	240	21	,	,	PUNCT
ejpam-21	240	22	then	then	ADV
ejpam-21	240	23	by	by	ADP
ejpam-21	240	24	theorems	theorem	NOUN
ejpam-21	240	25	3.3	3.3	NUM
ejpam-21	240	26	and	and	CCONJ
ejpam-21	240	27	3.4	3.4	NUM
ejpam-21	240	28	and	and	CCONJ
ejpam-21	240	29	corollary	corollary	ADJ
ejpam-21	240	30	3.1	3.1	NUM
ejpam-21	240	31	we	we	PRON
ejpam-21	240	32	obtain	obtain	VERB
ejpam-21	240	33	the	the	DET
ejpam-21	240	34	results	result	NOUN
ejpam-21	240	35	established	establish	VERB
ejpam-21	240	36	in	in	ADP
ejpam-21	240	37	proposition	proposition	NOUN
ejpam-21	240	38	1	1	NUM
ejpam-21	240	39	of	of	ADP
ejpam-21	240	40	[	[	X
ejpam-21	240	41	11	11	NUM
ejpam-21	240	42	]	]	PUNCT
ejpam-21	240	43	(	(	PUNCT
ejpam-21	240	44	resp	resp	NOUN
ejpam-21	240	45	.	.	PUNCT
ejpam-21	241	1	theorem	theorem	NOUN
ejpam-21	241	2	1	1	NUM
ejpam-21	241	3	of	of	ADP
ejpam-21	241	4	[	[	X
ejpam-21	241	5	14	14	NUM
ejpam-21	241	6	]	]	PUNCT
ejpam-21	241	7	,	,	PUNCT
ejpam-21	241	8	theorems	theorem	VERB
ejpam-21	241	9	3.3	3.3	NUM
ejpam-21	241	10	and	and	CCONJ
ejpam-21	241	11	3.4	3.4	NUM
ejpam-21	241	12	of	of	ADP
ejpam-21	241	13	[	[	X
ejpam-21	241	14	36	36	NUM
ejpam-21	241	15	]	]	NUM
ejpam-21	241	16	)	)	PUNCT
ejpam-21	241	17	.	.	PUNCT
ejpam-21	242	1	definition	definition	NOUN
ejpam-21	242	2	3.5	3.5	NUM
ejpam-21	242	3	.	.	PUNCT
ejpam-21	243	1	a	a	DET
ejpam-21	243	2	function	function	NOUN
ejpam-21	243	3	f	f	NOUN
ejpam-21	243	4	:	:	PUNCT
ejpam-21	243	5	(	(	PUNCT
ejpam-21	243	6	x	x	NOUN
ejpam-21	243	7	,	,	PUNCT
ejpam-21	243	8	mx	mx	NOUN
ejpam-21	243	9	)	)	PUNCT
ejpam-21	243	10	→	→	SYM
ejpam-21	243	11	(	(	PUNCT
ejpam-21	243	12	y	y	PROPN
ejpam-21	243	13	,	,	PUNCT
ejpam-21	243	14	σ	σ	PROPN
ejpam-21	243	15	)	)	PUNCT
ejpam-21	243	16	is	be	AUX
ejpam-21	243	17	said	say	VERB
ejpam-21	243	18	to	to	PART
ejpam-21	243	19	be	be	AUX
ejpam-21	243	20	c	c	NOUN
ejpam-21	243	21	-	-	PUNCT
ejpam-21	243	22	m	m	NOUN
ejpam-21	243	23	-	-	ADJ
ejpam-21	243	24	continuous	continuous	ADJ
ejpam-21	243	25	if	if	SCONJ
ejpam-21	243	26	for	for	ADP
ejpam-21	243	27	each	each	DET
ejpam-21	243	28	point	point	NOUN
ejpam-21	243	29	x	x	X
ejpam-21	243	30	∈	∈	NOUN
ejpam-21	243	31	x	x	X
ejpam-21	243	32	and	and	CCONJ
ejpam-21	243	33	each	each	DET
ejpam-21	243	34	open	open	ADJ
ejpam-21	243	35	set	set	VERB
ejpam-21	243	36	v	v	NOUN
ejpam-21	243	37	containing	contain	VERB
ejpam-21	243	38	f(x	f(x	PROPN
ejpam-21	243	39	)	)	PUNCT
ejpam-21	243	40	and	and	CCONJ
ejpam-21	243	41	having	have	VERB
ejpam-21	243	42	compact	compact	ADJ
ejpam-21	243	43	complement	complement	NOUN
ejpam-21	243	44	,	,	PUNCT
ejpam-21	243	45	there	there	PRON
ejpam-21	243	46	exists	exist	VERB
ejpam-21	243	47	an	an	DET
ejpam-21	243	48	mx	mx	PROPN
ejpam-21	243	49	-open	-open	NOUN
ejpam-21	243	50	set	set	NOUN
ejpam-21	243	51	u	u	NOUN
ejpam-21	243	52	containing	contain	VERB
ejpam-21	243	53	x	x	PUNCT
ejpam-21	243	54	such	such	ADJ
ejpam-21	243	55	that	that	DET
ejpam-21	243	56	f(u	f(u	PROPN
ejpam-21	243	57	)	)	PUNCT
ejpam-21	243	58	⊂	⊂	PROPN
ejpam-21	243	59	v	v	X
ejpam-21	243	60	.	.	PUNCT
ejpam-21	244	1	corollary	corollary	ADJ
ejpam-21	244	2	3.2	3.2	NUM
ejpam-21	244	3	.	.	PUNCT
ejpam-21	245	1	for	for	ADP
ejpam-21	245	2	a	a	DET
ejpam-21	245	3	function	function	NOUN
ejpam-21	245	4	f	f	NOUN
ejpam-21	245	5	:	:	PUNCT
ejpam-21	245	6	(	(	PUNCT
ejpam-21	245	7	x	x	NOUN
ejpam-21	245	8	,	,	PUNCT
ejpam-21	245	9	mx	mx	NOUN
ejpam-21	245	10	)	)	PUNCT
ejpam-21	245	11	→	→	SYM
ejpam-21	245	12	(	(	PUNCT
ejpam-21	245	13	y	y	PROPN
ejpam-21	245	14	,	,	PUNCT
ejpam-21	245	15	σ	σ	PROPN
ejpam-21	245	16	)	)	PUNCT
ejpam-21	245	17	,	,	PUNCT
ejpam-21	245	18	the	the	DET
ejpam-21	245	19	following	follow	VERB
ejpam-21	245	20	properties	property	NOUN
ejpam-21	245	21	are	be	AUX
ejpam-21	245	22	equivalent	equivalent	ADJ
ejpam-21	245	23	:	:	PUNCT
ejpam-21	245	24	(	(	PUNCT
ejpam-21	245	25	1	1	X
ejpam-21	245	26	)	)	PUNCT
ejpam-21	245	27	f	f	PROPN
ejpam-21	245	28	is	be	AUX
ejpam-21	245	29	c	c	NOUN
ejpam-21	245	30	-	-	PUNCT
ejpam-21	245	31	m	m	NOUN
ejpam-21	245	32	-	-	ADJ
ejpam-21	245	33	continuous	continuous	ADJ
ejpam-21	245	34	;	;	PUNCT
ejpam-21	245	35	(	(	PUNCT
ejpam-21	245	36	2	2	X
ejpam-21	245	37	)	)	PUNCT
ejpam-21	245	38	f−1(v	f−1(v	NOUN
ejpam-21	245	39	)	)	PUNCT
ejpam-21	246	1	=	=	PUNCT
ejpam-21	246	2	mx	mx	PROPN
ejpam-21	246	3	-int(f−1(v	-int(f−1(v	PROPN
ejpam-21	246	4	)	)	PUNCT
ejpam-21	246	5	)	)	PUNCT
ejpam-21	247	1	for	for	ADP
ejpam-21	247	2	each	each	DET
ejpam-21	247	3	open	open	ADJ
ejpam-21	247	4	set	set	VERB
ejpam-21	247	5	v	v	NOUN
ejpam-21	247	6	of	of	ADP
ejpam-21	247	7	y	y	PROPN
ejpam-21	247	8	having	have	VERB
ejpam-21	247	9	compact	compact	ADJ
ejpam-21	247	10	complement	complement	NOUN
ejpam-21	247	11	;	;	PUNCT
ejpam-21	247	12	(	(	PUNCT
ejpam-21	247	13	3	3	X
ejpam-21	247	14	)	)	PUNCT
ejpam-21	247	15	f−1(k	f−1(k	PROPN
ejpam-21	247	16	)	)	PUNCT
ejpam-21	247	17	=	=	SYM
ejpam-21	247	18	mx	mx	NOUN
ejpam-21	247	19	-cl(f−1(k	-cl(f−1(k	PROPN
ejpam-21	247	20	)	)	PUNCT
ejpam-21	247	21	)	)	PUNCT
ejpam-21	247	22	for	for	SCONJ
ejpam-21	247	23	every	every	DET
ejpam-21	247	24	compact	compact	ADJ
ejpam-21	247	25	closed	close	VERB
ejpam-21	247	26	set	set	VERB
ejpam-21	247	27	k	k	PROPN
ejpam-21	247	28	of	of	ADP
ejpam-21	247	29	y	y	PROPN
ejpam-21	247	30	;	;	PUNCT
ejpam-21	247	31	t.noiri	t.noiri	ADV
ejpam-21	247	32	,	,	PUNCT
ejpam-21	247	33	v.popa	v.popa	NOUN
ejpam-21	247	34	/	/	SYM
ejpam-21	247	35	eur	eur	PROPN
ejpam-21	247	36	.	.	PUNCT
ejpam-21	248	1	j.	j.	PROPN
ejpam-21	248	2	pure	pure	PROPN
ejpam-21	248	3	appl	appl	PROPN
ejpam-21	248	4	.	.	PROPN
ejpam-21	248	5	math	math	PROPN
ejpam-21	248	6	,	,	PUNCT
ejpam-21	248	7	1	1	NUM
ejpam-21	248	8	(	(	PUNCT
ejpam-21	248	9	2008	2008	NUM
ejpam-21	248	10	)	)	PUNCT
ejpam-21	248	11	,	,	PUNCT
ejpam-21	248	12	(	(	PUNCT
ejpam-21	248	13	82	82	NUM
ejpam-21	248	14	-	-	SYM
ejpam-21	248	15	98	98	NUM
ejpam-21	248	16	)	)	PUNCT
ejpam-21	248	17	89	89	NUM
ejpam-21	248	18	(	(	PUNCT
ejpam-21	248	19	4	4	NUM
ejpam-21	248	20	)	)	PUNCT
ejpam-21	248	21	mx	mx	PROPN
ejpam-21	248	22	-cl(f−1(b	-cl(f−1(b	PROPN
ejpam-21	248	23	)	)	PUNCT
ejpam-21	248	24	)	)	PUNCT
ejpam-21	249	1	⊂	⊂	PROPN
ejpam-21	249	2	f−1(cl(b	f−1(cl(b	NOUN
ejpam-21	249	3	)	)	PUNCT
ejpam-21	249	4	)	)	PUNCT
ejpam-21	249	5	for	for	ADP
ejpam-21	249	6	every	every	DET
ejpam-21	249	7	subset	subset	NOUN
ejpam-21	249	8	b	b	PROPN
ejpam-21	249	9	of	of	ADP
ejpam-21	249	10	y	y	PROPN
ejpam-21	249	11	having	have	VERB
ejpam-21	249	12	the	the	DET
ejpam-21	249	13	compact	compact	ADJ
ejpam-21	249	14	closure	closure	NOUN
ejpam-21	249	15	;	;	PUNCT
ejpam-21	249	16	(	(	PUNCT
ejpam-21	249	17	5	5	X
ejpam-21	249	18	)	)	PUNCT
ejpam-21	249	19	f−1(int(b	f−1(int(b	NOUN
ejpam-21	249	20	)	)	PUNCT
ejpam-21	249	21	)	)	PUNCT
ejpam-21	250	1	⊂	⊂	PROPN
ejpam-21	250	2	mx	mx	PROPN
ejpam-21	250	3	-int(f−1(b	-int(f−1(b	PROPN
ejpam-21	250	4	)	)	PUNCT
ejpam-21	250	5	)	)	PUNCT
ejpam-21	251	1	for	for	ADP
ejpam-21	251	2	every	every	DET
ejpam-21	251	3	subset	subset	NOUN
ejpam-21	251	4	b	b	PROPN
ejpam-21	251	5	of	of	ADP
ejpam-21	251	6	y	y	PRON
ejpam-21	251	7	such	such	ADJ
ejpam-21	251	8	that	that	SCONJ
ejpam-21	251	9	y	y	PROPN
ejpam-21	251	10	−int(b	−int(b	PROPN
ejpam-21	251	11	)	)	PUNCT
ejpam-21	251	12	is	be	AUX
ejpam-21	251	13	compact	compact	ADJ
ejpam-21	251	14	.	.	PUNCT
ejpam-21	252	1	remark	remark	NOUN
ejpam-21	252	2	3.5	3.5	NUM
ejpam-21	252	3	.	.	PUNCT
ejpam-21	253	1	let	let	AUX
ejpam-21	253	2	(	(	PUNCT
ejpam-21	253	3	x	x	NOUN
ejpam-21	253	4	,	,	PUNCT
ejpam-21	253	5	τ	τ	X
ejpam-21	253	6	)	)	PUNCT
ejpam-21	253	7	and	and	CCONJ
ejpam-21	253	8	(	(	PUNCT
ejpam-21	253	9	y	y	PROPN
ejpam-21	253	10	,	,	PUNCT
ejpam-21	253	11	σ	σ	PROPN
ejpam-21	253	12	)	)	PUNCT
ejpam-21	253	13	be	be	VERB
ejpam-21	253	14	topological	topological	ADJ
ejpam-21	253	15	spaces	space	NOUN
ejpam-21	253	16	.	.	PUNCT
ejpam-21	254	1	if	if	SCONJ
ejpam-21	254	2	mx	mx	PROPN
ejpam-21	254	3	=	=	SYM
ejpam-21	254	4	τ	τ	PROPN
ejpam-21	254	5	and	and	CCONJ
ejpam-21	254	6	f	f	PROPN
ejpam-21	254	7	:	:	PUNCT
ejpam-21	254	8	(	(	PUNCT
ejpam-21	254	9	x	x	NOUN
ejpam-21	254	10	,	,	PUNCT
ejpam-21	254	11	mx	mx	NOUN
ejpam-21	254	12	)	)	PUNCT
ejpam-21	254	13	→	→	SYM
ejpam-21	254	14	(	(	PUNCT
ejpam-21	254	15	y	y	PROPN
ejpam-21	254	16	,	,	PUNCT
ejpam-21	254	17	σ	σ	PROPN
ejpam-21	254	18	)	)	PUNCT
ejpam-21	254	19	is	be	AUX
ejpam-21	254	20	c	c	NOUN
ejpam-21	254	21	-	-	PUNCT
ejpam-21	254	22	m	m	NOUN
ejpam-21	254	23	-	-	ADJ
ejpam-21	254	24	continuous	continuous	ADJ
ejpam-21	254	25	,	,	PUNCT
ejpam-21	254	26	then	then	ADV
ejpam-21	254	27	by	by	ADP
ejpam-21	254	28	corollary	corollary	ADJ
ejpam-21	254	29	3.2	3.2	NUM
ejpam-21	254	30	we	we	PRON
ejpam-21	254	31	obtain	obtain	VERB
ejpam-21	254	32	the	the	DET
ejpam-21	254	33	results	result	NOUN
ejpam-21	254	34	established	establish	VERB
ejpam-21	254	35	in	in	ADP
ejpam-21	254	36	theorem	theorem	NOUN
ejpam-21	254	37	1	1	NUM
ejpam-21	254	38	of	of	ADP
ejpam-21	254	39	[	[	X
ejpam-21	254	40	9	9	NUM
ejpam-21	254	41	]	]	PUNCT
ejpam-21	254	42	and	and	CCONJ
ejpam-21	254	43	theorems	theorem	NOUN
ejpam-21	254	44	2	2	NUM
ejpam-21	254	45	of	of	ADP
ejpam-21	254	46	[	[	X
ejpam-21	254	47	15	15	NUM
ejpam-21	254	48	]	]	PUNCT
ejpam-21	254	49	.	.	PUNCT
ejpam-21	255	1	corollary	corollary	ADJ
ejpam-21	255	2	3.3	3.3	NUM
ejpam-21	255	3	.	.	PUNCT
ejpam-21	256	1	a	a	DET
ejpam-21	256	2	multifunction	multifunction	NOUN
ejpam-21	256	3	is	be	AUX
ejpam-21	256	4	u.c.m.c	u.c.m.c	PROPN
ejpam-21	256	5	.	.	PUNCT
ejpam-21	257	1	(	(	PUNCT
ejpam-21	257	2	resp	resp	NOUN
ejpam-21	257	3	.	.	PUNCT
ejpam-21	258	1	l.c.m.c	l.c.m.c	PROPN
ejpam-21	258	2	.	.	PUNCT
ejpam-21	258	3	)	)	PUNCT
ejpam-21	259	1	if	if	SCONJ
ejpam-21	259	2	f−(k	f−(k	PROPN
ejpam-21	259	3	)	)	PUNCT
ejpam-21	259	4	=	=	SYM
ejpam-21	259	5	mx	mx	NOUN
ejpam-21	259	6	-cl(f−(k	-cl(f−(k	PROPN
ejpam-21	259	7	)	)	PUNCT
ejpam-21	259	8	)	)	PUNCT
ejpam-21	259	9	(	(	PUNCT
ejpam-21	259	10	resp	resp	NOUN
ejpam-21	259	11	.	.	PUNCT
ejpam-21	259	12	f+(k	f+(k	PUNCT
ejpam-21	259	13	)	)	PUNCT
ejpam-21	260	1	=	=	SYM
ejpam-21	260	2	mx	mx	PROPN
ejpam-21	260	3	-cl(f+(k	-cl(f+(k	PROPN
ejpam-21	260	4	)	)	PUNCT
ejpam-21	260	5	)	)	PUNCT
ejpam-21	260	6	)	)	PUNCT
ejpam-21	260	7	for	for	SCONJ
ejpam-21	260	8	every	every	DET
ejpam-21	260	9	compact	compact	ADJ
ejpam-21	260	10	set	set	NOUN
ejpam-21	260	11	k	k	PROPN
ejpam-21	260	12	of	of	ADP
ejpam-21	260	13	y.	y.	PROPN
ejpam-21	260	14	proof	proof	PROPN
ejpam-21	260	15	.	.	PUNCT
ejpam-21	261	1	let	let	VERB
ejpam-21	261	2	g	g	NOUN
ejpam-21	261	3	be	be	AUX
ejpam-21	261	4	any	any	DET
ejpam-21	261	5	open	open	ADJ
ejpam-21	261	6	set	set	NOUN
ejpam-21	261	7	of	of	ADP
ejpam-21	261	8	y	y	PROPN
ejpam-21	261	9	having	have	VERB
ejpam-21	261	10	compact	compact	ADJ
ejpam-21	261	11	complement	complement	NOUN
ejpam-21	261	12	.	.	PUNCT
ejpam-21	262	1	then	then	ADV
ejpam-21	262	2	y	y	PROPN
ejpam-21	262	3	−	−	PROPN
ejpam-21	262	4	g	g	PROPN
ejpam-21	262	5	is	be	AUX
ejpam-21	262	6	a	a	DET
ejpam-21	262	7	compact	compact	ADJ
ejpam-21	262	8	closed	close	VERB
ejpam-21	262	9	set	set	NOUN
ejpam-21	262	10	.	.	PUNCT
ejpam-21	263	1	by	by	ADP
ejpam-21	263	2	the	the	DET
ejpam-21	263	3	hypothesis	hypothesis	NOUN
ejpam-21	263	4	,	,	PUNCT
ejpam-21	263	5	x	x	PRON
ejpam-21	263	6	−	−	PUNCT
ejpam-21	263	7	f+(g	f+(g	NOUN
ejpam-21	263	8	)	)	PUNCT
ejpam-21	263	9	=	=	SYM
ejpam-21	263	10	f−(y	f−(y	NOUN
ejpam-21	263	11	−	−	NOUN
ejpam-21	263	12	g	g	NOUN
ejpam-21	263	13	)	)	PUNCT
ejpam-21	263	14	=	=	SYM
ejpam-21	263	15	mx	mx	PROPN
ejpam-21	263	16	-cl(f−(y	-cl(f−(y	VERB
ejpam-21	263	17	−	−	PROPN
ejpam-21	263	18	g	g	NOUN
ejpam-21	263	19	)	)	PUNCT
ejpam-21	263	20	)	)	PUNCT
ejpam-21	264	1	=	=	SYM
ejpam-21	264	2	mx	mx	PROPN
ejpam-21	264	3	cl(x	cl(x	X
ejpam-21	264	4	−	−	PROPN
ejpam-21	264	5	f+(g	f+(g	NOUN
ejpam-21	264	6	)	)	PUNCT
ejpam-21	264	7	)	)	PUNCT
ejpam-21	265	1	=	=	PUNCT
ejpam-21	265	2	x	x	PUNCT
ejpam-21	266	1	−	−	PROPN
ejpam-21	266	2	mx	mx	PROPN
ejpam-21	266	3	-int(f+(g	-int(f+(g	PROPN
ejpam-21	266	4	)	)	PUNCT
ejpam-21	266	5	)	)	PUNCT
ejpam-21	266	6	and	and	CCONJ
ejpam-21	266	7	hence	hence	ADV
ejpam-21	266	8	,	,	PUNCT
ejpam-21	266	9	f+(g	f+(g	PROPN
ejpam-21	266	10	)	)	PUNCT
ejpam-21	266	11	=	=	SYM
ejpam-21	266	12	mx	mx	NOUN
ejpam-21	266	13	-int(f+(g	-int(f+(g	PROPN
ejpam-21	266	14	)	)	PUNCT
ejpam-21	266	15	)	)	PUNCT
ejpam-21	266	16	.	.	PUNCT
ejpam-21	267	1	it	it	PRON
ejpam-21	267	2	follows	follow	VERB
ejpam-21	267	3	from	from	ADP
ejpam-21	267	4	theorem	theorem	ADJ
ejpam-21	267	5	3.3	3.3	NUM
ejpam-21	267	6	that	that	PRON
ejpam-21	267	7	f	f	PROPN
ejpam-21	267	8	is	be	AUX
ejpam-21	267	9	u.c.m.c	u.c.m.c	PROPN
ejpam-21	267	10	.	.	PUNCT
ejpam-21	268	1	the	the	DET
ejpam-21	268	2	proof	proof	NOUN
ejpam-21	268	3	of	of	ADP
ejpam-21	268	4	lower	low	ADJ
ejpam-21	268	5	c	c	NOUN
ejpam-21	268	6	-	-	PUNCT
ejpam-21	268	7	m	m	NOUN
ejpam-21	268	8	-	-	PUNCT
ejpam-21	268	9	continuity	continuity	NOUN
ejpam-21	268	10	is	be	AUX
ejpam-21	268	11	entirely	entirely	ADV
ejpam-21	268	12	similar	similar	ADJ
ejpam-21	268	13	.	.	PUNCT
ejpam-21	269	1	remark	remark	NOUN
ejpam-21	269	2	3.6	3.6	NUM
ejpam-21	269	3	.	.	PUNCT
ejpam-21	270	1	(	(	PUNCT
ejpam-21	270	2	1	1	X
ejpam-21	270	3	)	)	PUNCT
ejpam-21	270	4	let	let	VERB
ejpam-21	270	5	mx	mx	PROPN
ejpam-21	270	6	=	=	SYM
ejpam-21	270	7	τ	τ	PROPN
ejpam-21	270	8	(	(	PUNCT
ejpam-21	270	9	resp	resp	NOUN
ejpam-21	270	10	.	.	PUNCT
ejpam-21	270	11	so(x	so(x	NOUN
ejpam-21	270	12	)	)	PUNCT
ejpam-21	270	13	)	)	PUNCT
ejpam-21	270	14	,	,	PUNCT
ejpam-21	270	15	then	then	ADV
ejpam-21	270	16	by	by	ADP
ejpam-21	270	17	corollary	corollary	ADJ
ejpam-21	270	18	3.3	3.3	NUM
ejpam-21	270	19	we	we	PRON
ejpam-21	270	20	obtain	obtain	VERB
ejpam-21	270	21	the	the	DET
ejpam-21	270	22	results	result	NOUN
ejpam-21	270	23	established	establish	VERB
ejpam-21	270	24	in	in	ADP
ejpam-21	270	25	proposition	proposition	NOUN
ejpam-21	270	26	2	2	NUM
ejpam-21	270	27	of	of	ADP
ejpam-21	270	28	[	[	X
ejpam-21	270	29	20	20	NUM
ejpam-21	270	30	]	]	PUNCT
ejpam-21	270	31	(	(	PUNCT
ejpam-21	270	32	resp	resp	NOUN
ejpam-21	270	33	.	.	PUNCT
ejpam-21	271	1	corollary	corollary	ADJ
ejpam-21	271	2	3.3	3.3	NUM
ejpam-21	271	3	of	of	ADP
ejpam-21	271	4	[	[	X
ejpam-21	271	5	36	36	NUM
ejpam-21	271	6	]	]	NUM
ejpam-21	271	7	)	)	PUNCT
ejpam-21	271	8	.	.	PUNCT
ejpam-21	272	1	(	(	PUNCT
ejpam-21	272	2	2	2	X
ejpam-21	272	3	)	)	PUNCT
ejpam-21	272	4	it	it	PRON
ejpam-21	272	5	is	be	AUX
ejpam-21	272	6	shown	show	VERB
ejpam-21	272	7	in	in	ADP
ejpam-21	272	8	remark	remark	NOUN
ejpam-21	272	9	4	4	NUM
ejpam-21	272	10	of	of	ADP
ejpam-21	272	11	[	[	X
ejpam-21	272	12	11	11	NUM
ejpam-21	272	13	]	]	PUNCT
ejpam-21	272	14	that	that	SCONJ
ejpam-21	272	15	the	the	DET
ejpam-21	272	16	converse	converse	NOUN
ejpam-21	272	17	of	of	ADP
ejpam-21	272	18	corollary	corollary	ADJ
ejpam-21	272	19	3.3	3.3	NUM
ejpam-21	272	20	is	be	AUX
ejpam-21	272	21	not	not	PART
ejpam-21	272	22	true	true	ADJ
ejpam-21	272	23	.	.	PUNCT
ejpam-21	273	1	definition	definition	NOUN
ejpam-21	273	2	3.6	3.6	NUM
ejpam-21	273	3	.	.	PUNCT
ejpam-21	274	1	a	a	DET
ejpam-21	274	2	subset	subset	NOUN
ejpam-21	274	3	a	a	PRON
ejpam-21	274	4	of	of	ADP
ejpam-21	274	5	a	a	DET
ejpam-21	274	6	topological	topological	ADJ
ejpam-21	274	7	space	space	NOUN
ejpam-21	274	8	(	(	PUNCT
ejpam-21	274	9	x	x	X
ejpam-21	274	10	,	,	PUNCT
ejpam-21	274	11	τ	τ	X
ejpam-21	274	12	)	)	PUNCT
ejpam-21	274	13	is	be	AUX
ejpam-21	274	14	said	say	VERB
ejpam-21	274	15	to	to	PART
ejpam-21	274	16	be	be	AUX
ejpam-21	274	17	(	(	PUNCT
ejpam-21	274	18	1	1	X
ejpam-21	274	19	)	)	PUNCT
ejpam-21	274	20	α	α	NOUN
ejpam-21	274	21	-	-	NOUN
ejpam-21	274	22	paracompact	paracompact	NOUN
ejpam-21	275	1	[	[	X
ejpam-21	275	2	40	40	NUM
ejpam-21	275	3	]	]	PUNCT
ejpam-21	275	4	if	if	SCONJ
ejpam-21	275	5	every	every	DET
ejpam-21	275	6	cover	cover	NOUN
ejpam-21	275	7	of	of	ADP
ejpam-21	275	8	a	a	PRON
ejpam-21	275	9	by	by	ADP
ejpam-21	275	10	open	open	ADJ
ejpam-21	275	11	sets	set	NOUN
ejpam-21	275	12	of	of	ADP
ejpam-21	275	13	x	x	VERB
ejpam-21	275	14	is	be	AUX
ejpam-21	275	15	refined	refine	VERB
ejpam-21	275	16	by	by	ADP
ejpam-21	275	17	a	a	DET
ejpam-21	275	18	cover	cover	NOUN
ejpam-21	275	19	of	of	ADP
ejpam-21	275	20	a	a	PRON
ejpam-21	275	21	which	which	PRON
ejpam-21	275	22	consists	consist	VERB
ejpam-21	275	23	of	of	ADP
ejpam-21	275	24	open	open	ADJ
ejpam-21	275	25	sets	set	NOUN
ejpam-21	275	26	of	of	ADP
ejpam-21	275	27	x	x	PUNCT
ejpam-21	275	28	and	and	CCONJ
ejpam-21	275	29	is	be	AUX
ejpam-21	275	30	locally	locally	ADV
ejpam-21	275	31	finite	finite	ADJ
ejpam-21	275	32	in	in	ADP
ejpam-21	275	33	x	x	X
ejpam-21	275	34	,	,	PUNCT
ejpam-21	275	35	(	(	PUNCT
ejpam-21	275	36	2	2	X
ejpam-21	275	37	)	)	PUNCT
ejpam-21	275	38	α	α	NOUN
ejpam-21	275	39	-	-	NOUN
ejpam-21	275	40	regular	regular	ADJ
ejpam-21	275	41	[	[	X
ejpam-21	275	42	12	12	NUM
ejpam-21	275	43	]	]	X
ejpam-21	275	44	if	if	SCONJ
ejpam-21	275	45	for	for	ADP
ejpam-21	275	46	each	each	DET
ejpam-21	275	47	a	a	DET
ejpam-21	275	48	∈	∈	PROPN
ejpam-21	275	49	a	a	PRON
ejpam-21	275	50	and	and	CCONJ
ejpam-21	275	51	each	each	DET
ejpam-21	275	52	open	open	ADJ
ejpam-21	275	53	set	set	VERB
ejpam-21	275	54	u	u	NOUN
ejpam-21	275	55	of	of	ADP
ejpam-21	275	56	x	x	SYM
ejpam-21	275	57	containing	contain	VERB
ejpam-21	275	58	a	a	PRON
ejpam-21	275	59	,	,	PUNCT
ejpam-21	275	60	there	there	PRON
ejpam-21	275	61	exists	exist	VERB
ejpam-21	275	62	an	an	DET
ejpam-21	275	63	open	open	ADJ
ejpam-21	275	64	set	set	NOUN
ejpam-21	275	65	g	g	NOUN
ejpam-21	275	66	of	of	ADP
ejpam-21	275	67	x	x	SYM
ejpam-21	275	68	such	such	ADJ
ejpam-21	275	69	that	that	SCONJ
ejpam-21	275	70	a	a	DET
ejpam-21	275	71	∈	∈	PROPN
ejpam-21	275	72	g	g	PROPN
ejpam-21	275	73	⊂	⊂	PROPN
ejpam-21	275	74	cl(g	cl(g	X
ejpam-21	275	75	)	)	PUNCT
ejpam-21	275	76	⊂	⊂	PROPN
ejpam-21	275	77	u	u	PROPN
ejpam-21	275	78	.	.	PUNCT
ejpam-21	276	1	lemma	lemma	PROPN
ejpam-21	276	2	3.4	3.4	NUM
ejpam-21	276	3	.	.	PUNCT
ejpam-21	277	1	(	(	PUNCT
ejpam-21	277	2	kovačević	kovačević	PROPN
ejpam-21	278	1	[	[	X
ejpam-21	278	2	12	12	NUM
ejpam-21	278	3	]	]	PUNCT
ejpam-21	278	4	)	)	PUNCT
ejpam-21	278	5	if	if	SCONJ
ejpam-21	278	6	a	a	PRON
ejpam-21	278	7	is	be	AUX
ejpam-21	278	8	an	an	DET
ejpam-21	278	9	α	α	NOUN
ejpam-21	278	10	-	-	ADJ
ejpam-21	278	11	regular	regular	ADJ
ejpam-21	278	12	α	α	NOUN
ejpam-21	278	13	-	-	PUNCT
ejpam-21	278	14	paracompact	paracompact	ADJ
ejpam-21	278	15	set	set	NOUN
ejpam-21	278	16	of	of	ADP
ejpam-21	278	17	a	a	DET
ejpam-21	278	18	topological	topological	ADJ
ejpam-21	278	19	space	space	NOUN
ejpam-21	278	20	x	x	PUNCT
ejpam-21	278	21	and	and	CCONJ
ejpam-21	278	22	u	u	NOUN
ejpam-21	278	23	is	be	AUX
ejpam-21	278	24	an	an	DET
ejpam-21	278	25	open	open	ADJ
ejpam-21	278	26	neighborhood	neighborhood	NOUN
ejpam-21	278	27	of	of	ADP
ejpam-21	278	28	a	a	PRON
ejpam-21	278	29	,	,	PUNCT
ejpam-21	278	30	then	then	ADV
ejpam-21	278	31	there	there	PRON
ejpam-21	278	32	exists	exist	VERB
ejpam-21	278	33	an	an	DET
ejpam-21	278	34	open	open	ADJ
ejpam-21	278	35	set	set	NOUN
ejpam-21	278	36	g	g	NOUN
ejpam-21	278	37	of	of	ADP
ejpam-21	278	38	x	x	SYM
ejpam-21	278	39	such	such	ADJ
ejpam-21	278	40	that	that	SCONJ
ejpam-21	278	41	a	a	DET
ejpam-21	278	42	⊂	⊂	X
ejpam-21	278	43	g	g	PROPN
ejpam-21	278	44	⊂	⊂	PROPN
ejpam-21	278	45	cl(g	cl(g	X
ejpam-21	278	46	)	)	PUNCT
ejpam-21	278	47	⊂	⊂	PROPN
ejpam-21	278	48	u	u	PROPN
ejpam-21	278	49	.	.	PUNCT
ejpam-21	279	1	for	for	ADP
ejpam-21	279	2	a	a	DET
ejpam-21	279	3	multifunction	multifunction	NOUN
ejpam-21	279	4	f	f	NOUN
ejpam-21	279	5	:	:	PUNCT
ejpam-21	279	6	(	(	PUNCT
ejpam-21	279	7	x	x	NOUN
ejpam-21	279	8	,	,	PUNCT
ejpam-21	279	9	mx	mx	NOUN
ejpam-21	279	10	)	)	PUNCT
ejpam-21	279	11	→	→	SYM
ejpam-21	279	12	(	(	PUNCT
ejpam-21	279	13	y	y	PROPN
ejpam-21	279	14	,	,	PUNCT
ejpam-21	279	15	σ	σ	PROPN
ejpam-21	279	16	)	)	PUNCT
ejpam-21	279	17	,	,	PUNCT
ejpam-21	279	18	by	by	ADP
ejpam-21	279	19	clf	clf	PROPN
ejpam-21	279	20	:	:	PUNCT
ejpam-21	279	21	(	(	PUNCT
ejpam-21	279	22	x	x	NOUN
ejpam-21	279	23	,	,	PUNCT
ejpam-21	279	24	mx	mx	NOUN
ejpam-21	279	25	)	)	PUNCT
ejpam-21	279	26	→	→	SYM
ejpam-21	279	27	(	(	PUNCT
ejpam-21	279	28	y	y	PROPN
ejpam-21	279	29	,	,	PUNCT
ejpam-21	279	30	σ	σ	PROPN
ejpam-21	279	31	)	)	PUNCT
ejpam-21	279	32	we	we	PRON
ejpam-21	279	33	denote	denote	VERB
ejpam-21	279	34	a	a	DET
ejpam-21	279	35	multifunction	multifunction	NOUN
ejpam-21	279	36	defined	define	VERB
ejpam-21	279	37	as	as	SCONJ
ejpam-21	279	38	follows	follow	VERB
ejpam-21	279	39	:	:	PUNCT
ejpam-21	279	40	(	(	PUNCT
ejpam-21	279	41	clf	clf	PROPN
ejpam-21	279	42	)	)	PUNCT
ejpam-21	279	43	(	(	PUNCT
ejpam-21	279	44	x	x	X
ejpam-21	279	45	)	)	PUNCT
ejpam-21	279	46	=	=	SYM
ejpam-21	279	47	cl(f	cl(f	PROPN
ejpam-21	279	48	(	(	PUNCT
ejpam-21	279	49	x	x	NOUN
ejpam-21	279	50	)	)	PUNCT
ejpam-21	279	51	)	)	PUNCT
ejpam-21	279	52	for	for	ADP
ejpam-21	279	53	each	each	DET
ejpam-21	279	54	point	point	NOUN
ejpam-21	279	55	x	x	X
ejpam-21	279	56	∈	∈	NOUN
ejpam-21	279	57	x	x	X
ejpam-21	279	58	.	.	PUNCT
ejpam-21	280	1	similarly	similarly	ADV
ejpam-21	280	2	,	,	PUNCT
ejpam-21	280	3	we	we	PRON
ejpam-21	280	4	can	can	AUX
ejpam-21	280	5	define	define	VERB
ejpam-21	280	6	αclf	αclf	PROPN
ejpam-21	280	7	,	,	PUNCT
ejpam-21	280	8	sclf	sclf	ADJ
ejpam-21	280	9	,	,	PUNCT
ejpam-21	280	10	pclf	pclf	ADV
ejpam-21	280	11	,	,	PUNCT
ejpam-21	280	12	spclf	spclf	ADJ
ejpam-21	280	13	,	,	PUNCT
ejpam-21	280	14	bclf	bclf	NOUN
ejpam-21	280	15	.	.	PUNCT
ejpam-21	281	1	lemma	lemma	PROPN
ejpam-21	281	2	3.5	3.5	NUM
ejpam-21	281	3	.	.	PUNCT
ejpam-21	282	1	if	if	SCONJ
ejpam-21	282	2	is	be	AUX
ejpam-21	282	3	a	a	DET
ejpam-21	282	4	multifunction	multifunction	NOUN
ejpam-21	282	5	such	such	ADJ
ejpam-21	282	6	that	that	SCONJ
ejpam-21	282	7	f	f	PROPN
ejpam-21	282	8	(	(	PUNCT
ejpam-21	282	9	x	x	X
ejpam-21	282	10	)	)	PUNCT
ejpam-21	282	11	is	be	AUX
ejpam-21	282	12	α	α	DET
ejpam-21	282	13	-	-	NOUN
ejpam-21	282	14	paracompact	paracompact	ADJ
ejpam-21	282	15	and	and	CCONJ
ejpam-21	282	16	α	α	NOUN
ejpam-21	282	17	-	-	ADJ
ejpam-21	282	18	regular	regular	ADJ
ejpam-21	282	19	for	for	ADP
ejpam-21	282	20	each	each	DET
ejpam-21	282	21	x	x	SYM
ejpam-21	282	22	∈	∈	PROPN
ejpam-21	282	23	x	x	X
ejpam-21	282	24	,	,	PUNCT
ejpam-21	282	25	then	then	ADV
ejpam-21	282	26	for	for	SCONJ
ejpam-21	282	27	each	each	DET
ejpam-21	282	28	open	open	ADJ
ejpam-21	282	29	set	set	VERB
ejpam-21	282	30	v	v	NOUN
ejpam-21	282	31	of	of	ADP
ejpam-21	282	32	y	y	PROPN
ejpam-21	282	33	f+(v	f+(v	PROPN
ejpam-21	282	34	)	)	PUNCT
ejpam-21	283	1	=	=	PUNCT
ejpam-21	283	2	g+(v	g+(v	PROPN
ejpam-21	283	3	)	)	PUNCT
ejpam-21	283	4	,	,	PUNCT
ejpam-21	283	5	where	where	SCONJ
ejpam-21	283	6	g	g	PROPN
ejpam-21	283	7	denotes	denotes	PROPN
ejpam-21	283	8	clf	clf	PROPN
ejpam-21	283	9	,	,	PUNCT
ejpam-21	283	10	αclf	αclf	VERB
ejpam-21	283	11	,	,	PUNCT
ejpam-21	283	12	sclf	sclf	ADJ
ejpam-21	283	13	,	,	PUNCT
ejpam-21	283	14	pclf	pclf	PROPN
ejpam-21	283	15	,	,	PUNCT
ejpam-21	283	16	bclf	bclf	NOUN
ejpam-21	283	17	or	or	CCONJ
ejpam-21	283	18	spclf	spclf	ADJ
ejpam-21	283	19	.	.	PUNCT
ejpam-21	284	1	proof	proof	NOUN
ejpam-21	284	2	.	.	PUNCT
ejpam-21	285	1	the	the	DET
ejpam-21	285	2	proof	proof	NOUN
ejpam-21	285	3	is	be	AUX
ejpam-21	285	4	similar	similar	ADJ
ejpam-21	285	5	to	to	ADP
ejpam-21	285	6	that	that	PRON
ejpam-21	285	7	of	of	ADP
ejpam-21	285	8	lemma	lemma	PROPN
ejpam-21	285	9	3.3	3.3	NUM
ejpam-21	285	10	of	of	ADP
ejpam-21	285	11	[	[	X
ejpam-21	285	12	30	30	NUM
ejpam-21	285	13	]	]	PUNCT
ejpam-21	285	14	.	.	PUNCT
ejpam-21	286	1	theorem	theorem	NOUN
ejpam-21	286	2	3.5	3.5	NUM
ejpam-21	286	3	.	.	PUNCT
ejpam-21	287	1	let	let	AUX
ejpam-21	287	2	be	be	AUX
ejpam-21	287	3	a	a	DET
ejpam-21	287	4	multifunction	multifunction	NOUN
ejpam-21	287	5	such	such	ADJ
ejpam-21	287	6	that	that	SCONJ
ejpam-21	287	7	f	f	PROPN
ejpam-21	287	8	(	(	PUNCT
ejpam-21	287	9	x	x	X
ejpam-21	287	10	)	)	PUNCT
ejpam-21	287	11	is	be	AUX
ejpam-21	287	12	α	α	X
ejpam-21	287	13	-	-	ADJ
ejpam-21	287	14	regular	regular	ADJ
ejpam-21	287	15	and	and	CCONJ
ejpam-21	287	16	α	α	NOUN
ejpam-21	287	17	-	-	NOUN
ejpam-21	287	18	paracompact	paracompact	NOUN
ejpam-21	287	19	for	for	ADP
ejpam-21	287	20	each	each	DET
ejpam-21	287	21	x	x	SYM
ejpam-21	287	22	∈	∈	PROPN
ejpam-21	287	23	x	x	X
ejpam-21	287	24	.	.	PUNCT
ejpam-21	288	1	then	then	ADV
ejpam-21	288	2	the	the	DET
ejpam-21	288	3	following	follow	VERB
ejpam-21	288	4	properties	property	NOUN
ejpam-21	288	5	are	be	AUX
ejpam-21	288	6	equivalent	equivalent	ADJ
ejpam-21	288	7	:	:	PUNCT
ejpam-21	288	8	(	(	PUNCT
ejpam-21	288	9	1	1	X
ejpam-21	288	10	)	)	PUNCT
ejpam-21	288	11	f	f	PROPN
ejpam-21	288	12	is	be	AUX
ejpam-21	288	13	u.c.m.c	u.c.m.c	PROPN
ejpam-21	288	14	.	.	PROPN
ejpam-21	288	15	;	;	PUNCT
ejpam-21	288	16	(	(	PUNCT
ejpam-21	288	17	2	2	X
ejpam-21	288	18	)	)	PUNCT
ejpam-21	288	19	clf	clf	PROPN
ejpam-21	288	20	is	be	AUX
ejpam-21	288	21	u.c.m.c	u.c.m.c	PROPN
ejpam-21	288	22	.	.	PROPN
ejpam-21	288	23	;	;	PUNCT
ejpam-21	288	24	(	(	PUNCT
ejpam-21	288	25	3	3	X
ejpam-21	288	26	)	)	PUNCT
ejpam-21	288	27	αclf	αclf	X
ejpam-21	288	28	is	be	AUX
ejpam-21	288	29	u.c.m.c	u.c.m.c	PROPN
ejpam-21	288	30	.	.	PROPN
ejpam-21	288	31	;	;	PUNCT
ejpam-21	288	32	(	(	PUNCT
ejpam-21	288	33	4	4	X
ejpam-21	288	34	)	)	PUNCT
ejpam-21	288	35	sclf	sclf	NOUN
ejpam-21	288	36	is	be	AUX
ejpam-21	288	37	u.c.m.c	u.c.m.c	PROPN
ejpam-21	288	38	.	.	PROPN
ejpam-21	288	39	;	;	PUNCT
ejpam-21	288	40	(	(	PUNCT
ejpam-21	288	41	5	5	X
ejpam-21	288	42	)	)	PUNCT
ejpam-21	288	43	pclf	pclf	NOUN
ejpam-21	288	44	is	be	AUX
ejpam-21	288	45	u.c.m.c	u.c.m.c	PROPN
ejpam-21	288	46	.	.	PROPN
ejpam-21	288	47	;	;	PUNCT
ejpam-21	288	48	(	(	PUNCT
ejpam-21	288	49	6	6	X
ejpam-21	288	50	)	)	PUNCT
ejpam-21	288	51	bclf	bclf	NOUN
ejpam-21	288	52	is	be	AUX
ejpam-21	288	53	u.c.m.c	u.c.m.c	PROPN
ejpam-21	288	54	.	.	PROPN
ejpam-21	288	55	;	;	PUNCT
ejpam-21	288	56	(	(	PUNCT
ejpam-21	288	57	7	7	X
ejpam-21	288	58	)	)	PUNCT
ejpam-21	288	59	spclf	spclf	NOUN
ejpam-21	288	60	is	be	AUX
ejpam-21	288	61	u.c.m.c	u.c.m.c	PROPN
ejpam-21	288	62	.	.	PUNCT
ejpam-21	288	63	t.noiri	t.noiri	NOUN
ejpam-21	288	64	,	,	PUNCT
ejpam-21	288	65	v.popa	v.popa	NOUN
ejpam-21	288	66	/	/	SYM
ejpam-21	288	67	eur	eur	PROPN
ejpam-21	288	68	.	.	PUNCT
ejpam-21	289	1	j.	j.	PROPN
ejpam-21	289	2	pure	pure	PROPN
ejpam-21	289	3	appl	appl	PROPN
ejpam-21	289	4	.	.	PROPN
ejpam-21	289	5	math	math	PROPN
ejpam-21	289	6	,	,	PUNCT
ejpam-21	289	7	1	1	NUM
ejpam-21	289	8	(	(	PUNCT
ejpam-21	289	9	2008	2008	NUM
ejpam-21	289	10	)	)	PUNCT
ejpam-21	289	11	,	,	PUNCT
ejpam-21	289	12	(	(	PUNCT
ejpam-21	289	13	82	82	NUM
ejpam-21	289	14	-	-	SYM
ejpam-21	289	15	98	98	NUM
ejpam-21	289	16	)	)	PUNCT
ejpam-21	289	17	90	90	NUM
ejpam-21	289	18	proof	proof	NOUN
ejpam-21	289	19	.	.	PUNCT
ejpam-21	290	1	we	we	PRON
ejpam-21	290	2	set	set	VERB
ejpam-21	290	3	g	g	PROPN
ejpam-21	290	4	=	=	PROPN
ejpam-21	290	5	clf	clf	PROPN
ejpam-21	290	6	,	,	PUNCT
ejpam-21	290	7	αclf	αclf	INTJ
ejpam-21	290	8	,	,	PUNCT
ejpam-21	290	9	sclf	sclf	ADJ
ejpam-21	290	10	,	,	PUNCT
ejpam-21	290	11	pclf	pclf	ADV
ejpam-21	290	12	,	,	PUNCT
ejpam-21	290	13	bclf	bclf	NOUN
ejpam-21	290	14	or	or	CCONJ
ejpam-21	290	15	spclf	spclf	ADJ
ejpam-21	290	16	.	.	PUNCT
ejpam-21	291	1	suppose	suppose	VERB
ejpam-21	291	2	that	that	SCONJ
ejpam-21	291	3	f	f	PROPN
ejpam-21	291	4	is	be	AUX
ejpam-21	291	5	u.c.m.c	u.c.m.c	PROPN
ejpam-21	291	6	.	.	PROPN
ejpam-21	291	7	let	let	VERB
ejpam-21	291	8	v	v	PART
ejpam-21	291	9	be	be	AUX
ejpam-21	291	10	any	any	DET
ejpam-21	291	11	open	open	ADJ
ejpam-21	291	12	set	set	NOUN
ejpam-21	291	13	of	of	ADP
ejpam-21	291	14	y	y	NOUN
ejpam-21	291	15	containing	contain	VERB
ejpam-21	291	16	g(x	g(x	NOUN
ejpam-21	291	17	)	)	PUNCT
ejpam-21	291	18	and	and	CCONJ
ejpam-21	291	19	having	have	VERB
ejpam-21	291	20	compact	compact	ADJ
ejpam-21	291	21	complement	complement	NOUN
ejpam-21	291	22	.	.	PUNCT
ejpam-21	292	1	by	by	ADP
ejpam-21	292	2	lemma	lemma	PROPN
ejpam-21	292	3	3.5	3.5	NUM
ejpam-21	292	4	,	,	PUNCT
ejpam-21	292	5	we	we	PRON
ejpam-21	292	6	have	have	VERB
ejpam-21	292	7	x	x	X
ejpam-21	292	8	∈	∈	PROPN
ejpam-21	292	9	g+(v	g+(v	PROPN
ejpam-21	292	10	)	)	PUNCT
ejpam-21	292	11	=	=	PUNCT
ejpam-21	293	1	f+(v	f+(v	NOUN
ejpam-21	293	2	)	)	PUNCT
ejpam-21	294	1	and	and	CCONJ
ejpam-21	294	2	by	by	ADP
ejpam-21	294	3	theorem	theorem	NOUN
ejpam-21	294	4	3.1	3.1	NUM
ejpam-21	294	5	there	there	PRON
ejpam-21	294	6	exists	exist	VERB
ejpam-21	294	7	u	u	PROPN
ejpam-21	294	8	∈	∈	PROPN
ejpam-21	294	9	mx	mx	NOUN
ejpam-21	294	10	containing	contain	VERB
ejpam-21	294	11	x	x	PUNCT
ejpam-21	294	12	such	such	ADJ
ejpam-21	294	13	that	that	SCONJ
ejpam-21	294	14	f	f	PROPN
ejpam-21	294	15	(	(	PUNCT
ejpam-21	294	16	u	u	NOUN
ejpam-21	294	17	)	)	PUNCT
ejpam-21	294	18	⊂	⊂	PROPN
ejpam-21	294	19	v	v	NOUN
ejpam-21	294	20	.	.	PUNCT
ejpam-21	295	1	since	since	SCONJ
ejpam-21	295	2	f	f	PROPN
ejpam-21	295	3	(	(	PUNCT
ejpam-21	295	4	u	u	NOUN
ejpam-21	295	5	)	)	PUNCT
ejpam-21	295	6	is	be	AUX
ejpam-21	295	7	α	α	DET
ejpam-21	295	8	-	-	NOUN
ejpam-21	295	9	paracompact	paracompact	ADJ
ejpam-21	295	10	and	and	CCONJ
ejpam-21	295	11	α	α	NOUN
ejpam-21	295	12	-	-	ADJ
ejpam-21	295	13	regular	regular	ADJ
ejpam-21	295	14	for	for	ADP
ejpam-21	295	15	each	each	DET
ejpam-21	295	16	u	u	PROPN
ejpam-21	295	17	∈	∈	PROPN
ejpam-21	295	18	u	u	NOUN
ejpam-21	295	19	,	,	PUNCT
ejpam-21	295	20	by	by	ADP
ejpam-21	295	21	lemma	lemma	PROPN
ejpam-21	295	22	3.4	3.4	NUM
ejpam-21	295	23	there	there	ADV
ejpam-21	295	24	exists	exist	VERB
ejpam-21	295	25	an	an	DET
ejpam-21	295	26	open	open	ADJ
ejpam-21	295	27	set	set	NOUN
ejpam-21	295	28	h	h	NOUN
ejpam-21	295	29	such	such	ADJ
ejpam-21	295	30	that	that	SCONJ
ejpam-21	295	31	f	f	PROPN
ejpam-21	295	32	(	(	PUNCT
ejpam-21	295	33	u	u	NOUN
ejpam-21	295	34	)	)	PUNCT
ejpam-21	296	1	⊂	⊂	PROPN
ejpam-21	296	2	h	h	PROPN
ejpam-21	297	1	⊂	⊂	PROPN
ejpam-21	297	2	cl(h	cl(h	X
ejpam-21	297	3	)	)	PUNCT
ejpam-21	298	1	⊂	⊂	PROPN
ejpam-21	298	2	v	v	X
ejpam-21	298	3	;	;	PUNCT
ejpam-21	298	4	hence	hence	ADV
ejpam-21	298	5	g(u	g(u	PROPN
ejpam-21	298	6	)	)	PUNCT
ejpam-21	299	1	⊂	⊂	PROPN
ejpam-21	299	2	cl(h	cl(h	X
ejpam-21	299	3	)	)	PUNCT
ejpam-21	300	1	⊂	⊂	PROPN
ejpam-21	300	2	v	v	NOUN
ejpam-21	300	3	for	for	ADP
ejpam-21	300	4	every	every	DET
ejpam-21	300	5	u	u	PROPN
ejpam-21	300	6	∈	∈	PROPN
ejpam-21	300	7	u	u	NOUN
ejpam-21	300	8	.	.	PUNCT
ejpam-21	301	1	therefore	therefore	ADV
ejpam-21	301	2	,	,	PUNCT
ejpam-21	301	3	we	we	PRON
ejpam-21	301	4	obtain	obtain	VERB
ejpam-21	301	5	g(u	g(u	NOUN
ejpam-21	301	6	)	)	PUNCT
ejpam-21	301	7	⊂	⊂	PROPN
ejpam-21	301	8	v	v	NOUN
ejpam-21	301	9	.	.	PUNCT
ejpam-21	302	1	this	this	PRON
ejpam-21	302	2	shows	show	VERB
ejpam-21	302	3	that	that	SCONJ
ejpam-21	302	4	g	g	PROPN
ejpam-21	302	5	is	be	AUX
ejpam-21	302	6	u.c.m.c	u.c.m.c	PROPN
ejpam-21	302	7	.	.	PUNCT
ejpam-21	302	8	conversely	conversely	ADV
ejpam-21	302	9	,	,	PUNCT
ejpam-21	302	10	suppose	suppose	VERB
ejpam-21	302	11	that	that	SCONJ
ejpam-21	302	12	g	g	PROPN
ejpam-21	302	13	is	be	AUX
ejpam-21	302	14	u.c.m.c	u.c.m.c	PROPN
ejpam-21	302	15	.	.	PUNCT
ejpam-21	303	1	let	let	VERB
ejpam-21	303	2	x	x	SYM
ejpam-21	303	3	∈	∈	PROPN
ejpam-21	303	4	x	x	X
ejpam-21	303	5	and	and	CCONJ
ejpam-21	303	6	v	v	X
ejpam-21	303	7	be	be	AUX
ejpam-21	303	8	any	any	DET
ejpam-21	303	9	open	open	ADJ
ejpam-21	303	10	set	set	NOUN
ejpam-21	303	11	of	of	ADP
ejpam-21	303	12	y	y	PROPN
ejpam-21	303	13	containing	contain	VERB
ejpam-21	303	14	f	f	PROPN
ejpam-21	303	15	(	(	PUNCT
ejpam-21	303	16	x	x	NOUN
ejpam-21	303	17	)	)	PUNCT
ejpam-21	303	18	and	and	CCONJ
ejpam-21	303	19	having	have	VERB
ejpam-21	303	20	compact	compact	ADJ
ejpam-21	303	21	complement	complement	NOUN
ejpam-21	303	22	.	.	PUNCT
ejpam-21	304	1	by	by	ADP
ejpam-21	304	2	lemma	lemma	PROPN
ejpam-21	304	3	3.5	3.5	NUM
ejpam-21	304	4	,	,	PUNCT
ejpam-21	304	5	we	we	PRON
ejpam-21	304	6	have	have	VERB
ejpam-21	304	7	x	x	X
ejpam-21	304	8	∈	∈	NOUN
ejpam-21	304	9	f+(v	f+(v	NOUN
ejpam-21	304	10	)	)	PUNCT
ejpam-21	305	1	=	=	PUNCT
ejpam-21	305	2	g+(v	g+(v	PROPN
ejpam-21	305	3	)	)	PUNCT
ejpam-21	305	4	and	and	CCONJ
ejpam-21	305	5	hence	hence	ADV
ejpam-21	305	6	g(x	g(x	NOUN
ejpam-21	305	7	)	)	PUNCT
ejpam-21	306	1	⊂	⊂	PROPN
ejpam-21	306	2	v	v	X
ejpam-21	306	3	.	.	PUNCT
ejpam-21	307	1	by	by	ADP
ejpam-21	307	2	theorem	theorem	NOUN
ejpam-21	307	3	3.1	3.1	NUM
ejpam-21	307	4	,	,	PUNCT
ejpam-21	307	5	there	there	PRON
ejpam-21	307	6	exists	exist	VERB
ejpam-21	307	7	u	u	PROPN
ejpam-21	307	8	∈	∈	PROPN
ejpam-21	307	9	mx	mx	NOUN
ejpam-21	307	10	containing	contain	VERB
ejpam-21	307	11	x	x	PUNCT
ejpam-21	307	12	such	such	ADJ
ejpam-21	307	13	that	that	SCONJ
ejpam-21	307	14	g(u	g(u	PROPN
ejpam-21	307	15	)	)	PUNCT
ejpam-21	307	16	⊂	⊂	PROPN
ejpam-21	307	17	v	v	NOUN
ejpam-21	307	18	.	.	PUNCT
ejpam-21	308	1	therefore	therefore	ADV
ejpam-21	308	2	,	,	PUNCT
ejpam-21	308	3	we	we	PRON
ejpam-21	308	4	obtain	obtain	VERB
ejpam-21	308	5	u	u	NOUN
ejpam-21	308	6	⊂	⊂	NOUN
ejpam-21	308	7	g+(v	g+(v	PROPN
ejpam-21	308	8	)	)	PUNCT
ejpam-21	308	9	=	=	PUNCT
ejpam-21	309	1	f+(v	f+(v	NOUN
ejpam-21	309	2	)	)	PUNCT
ejpam-21	310	1	and	and	CCONJ
ejpam-21	310	2	hence	hence	ADV
ejpam-21	310	3	f	f	PROPN
ejpam-21	310	4	(	(	PUNCT
ejpam-21	310	5	u	u	NOUN
ejpam-21	310	6	)	)	PUNCT
ejpam-21	310	7	⊂	⊂	PROPN
ejpam-21	310	8	v	v	NOUN
ejpam-21	310	9	.	.	PUNCT
ejpam-21	311	1	this	this	PRON
ejpam-21	311	2	shows	show	VERB
ejpam-21	311	3	that	that	SCONJ
ejpam-21	311	4	f	f	PROPN
ejpam-21	311	5	is	be	AUX
ejpam-21	311	6	u.c.m.c	u.c.m.c	PROPN
ejpam-21	311	7	.	.	PUNCT
ejpam-21	311	8	lemma	lemma	PROPN
ejpam-21	311	9	3.6	3.6	NUM
ejpam-21	311	10	.	.	PUNCT
ejpam-21	312	1	if	if	SCONJ
ejpam-21	312	2	is	be	AUX
ejpam-21	312	3	a	a	DET
ejpam-21	312	4	multifunction	multifunction	NOUN
ejpam-21	312	5	,	,	PUNCT
ejpam-21	312	6	then	then	ADV
ejpam-21	312	7	for	for	SCONJ
ejpam-21	312	8	each	each	DET
ejpam-21	312	9	open	open	ADJ
ejpam-21	312	10	set	set	VERB
ejpam-21	312	11	v	v	NOUN
ejpam-21	312	12	of	of	ADP
ejpam-21	312	13	y	y	PROPN
ejpam-21	312	14	g−(v	g−(v	PROPN
ejpam-21	312	15	)	)	PUNCT
ejpam-21	313	1	=	=	SYM
ejpam-21	313	2	f−(v	f−(v	ADJ
ejpam-21	313	3	)	)	PUNCT
ejpam-21	313	4	,	,	PUNCT
ejpam-21	313	5	where	where	SCONJ
ejpam-21	313	6	g	g	PROPN
ejpam-21	313	7	=	=	SYM
ejpam-21	313	8	clf	clf	PROPN
ejpam-21	313	9	,	,	PUNCT
ejpam-21	313	10	αclf	αclf	VERB
ejpam-21	313	11	,	,	PUNCT
ejpam-21	313	12	sclf	sclf	ADJ
ejpam-21	313	13	,	,	PUNCT
ejpam-21	313	14	pclf	pclf	PROPN
ejpam-21	313	15	,	,	PUNCT
ejpam-21	313	16	bclf	bclf	NOUN
ejpam-21	313	17	or	or	CCONJ
ejpam-21	313	18	spclf	spclf	ADJ
ejpam-21	313	19	.	.	PUNCT
ejpam-21	314	1	proof	proof	NOUN
ejpam-21	314	2	.	.	PUNCT
ejpam-21	315	1	the	the	DET
ejpam-21	315	2	proof	proof	NOUN
ejpam-21	315	3	is	be	AUX
ejpam-21	315	4	similar	similar	ADJ
ejpam-21	315	5	to	to	ADP
ejpam-21	315	6	that	that	PRON
ejpam-21	315	7	of	of	ADP
ejpam-21	315	8	lemma	lemma	PROPN
ejpam-21	315	9	3.4	3.4	NUM
ejpam-21	315	10	of	of	ADP
ejpam-21	315	11	[	[	X
ejpam-21	315	12	30	30	NUM
ejpam-21	315	13	]	]	PUNCT
ejpam-21	315	14	.	.	PUNCT
ejpam-21	316	1	theorem	theorem	VERB
ejpam-21	316	2	3.6	3.6	NUM
ejpam-21	316	3	.	.	PUNCT
ejpam-21	317	1	for	for	ADP
ejpam-21	317	2	a	a	DET
ejpam-21	317	3	multifunction	multifunction	NOUN
ejpam-21	317	4	,	,	PUNCT
ejpam-21	317	5	the	the	DET
ejpam-21	317	6	following	follow	VERB
ejpam-21	317	7	properties	property	NOUN
ejpam-21	317	8	are	be	AUX
ejpam-21	317	9	equivalent	equivalent	ADJ
ejpam-21	317	10	:	:	PUNCT
ejpam-21	317	11	(	(	PUNCT
ejpam-21	317	12	1	1	X
ejpam-21	317	13	)	)	PUNCT
ejpam-21	317	14	f	f	PROPN
ejpam-21	317	15	is	be	AUX
ejpam-21	317	16	l.c.m.c	l.c.m.c	PROPN
ejpam-21	317	17	.	.	PUNCT
ejpam-21	317	18	;	;	PUNCT
ejpam-21	317	19	(	(	PUNCT
ejpam-21	317	20	2	2	X
ejpam-21	317	21	)	)	PUNCT
ejpam-21	317	22	clf	clf	PROPN
ejpam-21	317	23	is	be	AUX
ejpam-21	317	24	l.c.m.c	l.c.m.c	PROPN
ejpam-21	317	25	.	.	PUNCT
ejpam-21	317	26	;	;	PUNCT
ejpam-21	317	27	(	(	PUNCT
ejpam-21	317	28	3	3	X
ejpam-21	317	29	)	)	PUNCT
ejpam-21	317	30	αclf	αclf	PROPN
ejpam-21	317	31	is	be	AUX
ejpam-21	317	32	l.c.m.c	l.c.m.c	PROPN
ejpam-21	317	33	.	.	PUNCT
ejpam-21	317	34	;	;	PUNCT
ejpam-21	317	35	(	(	PUNCT
ejpam-21	317	36	4	4	X
ejpam-21	317	37	)	)	PUNCT
ejpam-21	317	38	sclf	sclf	NOUN
ejpam-21	317	39	is	be	AUX
ejpam-21	317	40	l.c.m.c	l.c.m.c	PROPN
ejpam-21	317	41	.	.	PUNCT
ejpam-21	317	42	;	;	PUNCT
ejpam-21	317	43	(	(	PUNCT
ejpam-21	317	44	5	5	X
ejpam-21	317	45	)	)	PUNCT
ejpam-21	317	46	pclf	pclf	NOUN
ejpam-21	317	47	is	be	AUX
ejpam-21	317	48	l.c.m.c	l.c.m.c	PROPN
ejpam-21	317	49	.	.	PUNCT
ejpam-21	317	50	;	;	PUNCT
ejpam-21	317	51	(	(	PUNCT
ejpam-21	317	52	6	6	X
ejpam-21	317	53	)	)	PUNCT
ejpam-21	317	54	bclf	bclf	NOUN
ejpam-21	317	55	is	be	AUX
ejpam-21	317	56	l.c.m.c	l.c.m.c	PROPN
ejpam-21	317	57	.	.	PUNCT
ejpam-21	317	58	;	;	PUNCT
ejpam-21	317	59	(	(	PUNCT
ejpam-21	317	60	7	7	X
ejpam-21	317	61	)	)	PUNCT
ejpam-21	317	62	spclf	spclf	NOUN
ejpam-21	317	63	is	be	AUX
ejpam-21	317	64	l.c.m.c	l.c.m.c	PROPN
ejpam-21	317	65	.	.	PUNCT
ejpam-21	317	66	proof	proof	NOUN
ejpam-21	317	67	.	.	PUNCT
ejpam-21	318	1	by	by	ADP
ejpam-21	318	2	using	use	VERB
ejpam-21	318	3	lemma	lemma	PROPN
ejpam-21	318	4	3.6	3.6	NUM
ejpam-21	318	5	this	this	PRON
ejpam-21	318	6	is	be	AUX
ejpam-21	318	7	shown	show	VERB
ejpam-21	318	8	similarly	similarly	ADV
ejpam-21	318	9	as	as	ADP
ejpam-21	318	10	in	in	ADP
ejpam-21	318	11	theorem	theorem	ADJ
ejpam-21	318	12	3.5	3.5	NUM
ejpam-21	318	13	.	.	PUNCT
ejpam-21	319	1	remark	remark	PROPN
ejpam-21	319	2	3.7	3.7	NUM
ejpam-21	319	3	.	.	PUNCT
ejpam-21	320	1	let	let	AUX
ejpam-21	320	2	(	(	PUNCT
ejpam-21	320	3	x	x	NOUN
ejpam-21	320	4	,	,	PUNCT
ejpam-21	320	5	τ	τ	X
ejpam-21	320	6	)	)	PUNCT
ejpam-21	320	7	and	and	CCONJ
ejpam-21	320	8	(	(	PUNCT
ejpam-21	320	9	y	y	PROPN
ejpam-21	320	10	,	,	PUNCT
ejpam-21	320	11	σ	σ	PROPN
ejpam-21	320	12	)	)	PUNCT
ejpam-21	320	13	be	be	VERB
ejpam-21	320	14	topological	topological	ADJ
ejpam-21	320	15	spaces	space	NOUN
ejpam-21	320	16	and	and	CCONJ
ejpam-21	320	17	mx	mx	NOUN
ejpam-21	320	18	=	=	SYM
ejpam-21	320	19	so(x	so(x	NOUN
ejpam-21	320	20	)	)	PUNCT
ejpam-21	320	21	.	.	PUNCT
ejpam-21	321	1	by	by	ADP
ejpam-21	321	2	theorems	theorem	NOUN
ejpam-21	321	3	3.5	3.5	NUM
ejpam-21	321	4	and	and	CCONJ
ejpam-21	321	5	3.6	3.6	NUM
ejpam-21	321	6	,	,	PUNCT
ejpam-21	321	7	we	we	PRON
ejpam-21	321	8	obtain	obtain	VERB
ejpam-21	321	9	the	the	DET
ejpam-21	321	10	results	result	NOUN
ejpam-21	321	11	established	establish	VERB
ejpam-21	321	12	in	in	ADP
ejpam-21	321	13	theorems	theorem	NOUN
ejpam-21	321	14	3.5	3.5	NUM
ejpam-21	321	15	and	and	CCONJ
ejpam-21	321	16	3.6	3.6	NUM
ejpam-21	321	17	of	of	ADP
ejpam-21	321	18	[	[	X
ejpam-21	321	19	36	36	NUM
ejpam-21	321	20	]	]	PUNCT
ejpam-21	321	21	.	.	PUNCT
ejpam-21	322	1	4	4	X
ejpam-21	322	2	.	.	X
ejpam-21	322	3	the	the	DET
ejpam-21	322	4	set	set	NOUN
ejpam-21	322	5	of	of	ADP
ejpam-21	322	6	points	point	NOUN
ejpam-21	322	7	of	of	ADP
ejpam-21	322	8	m	m	PROPN
ejpam-21	322	9	-	-	PUNCT
ejpam-21	322	10	c	c	NOUN
ejpam-21	322	11	-	-	PUNCT
ejpam-21	322	12	discontinuity	discontinuity	NOUN
ejpam-21	322	13	for	for	ADP
ejpam-21	322	14	a	a	DET
ejpam-21	322	15	multifunction	multifunction	NOUN
ejpam-21	322	16	f	f	NOUN
ejpam-21	322	17	:	:	PUNCT
ejpam-21	322	18	(	(	PUNCT
ejpam-21	322	19	x	x	NOUN
ejpam-21	322	20	,	,	PUNCT
ejpam-21	322	21	mx	mx	NOUN
ejpam-21	322	22	)	)	PUNCT
ejpam-21	322	23	→	→	SYM
ejpam-21	322	24	(	(	PUNCT
ejpam-21	322	25	y	y	PROPN
ejpam-21	322	26	,	,	PUNCT
ejpam-21	322	27	σ	σ	PROPN
ejpam-21	322	28	)	)	PUNCT
ejpam-21	322	29	,	,	PUNCT
ejpam-21	322	30	the	the	DET
ejpam-21	322	31	sets	set	NOUN
ejpam-21	322	32	d+	d+	PUNCT
ejpam-21	322	33	mc(f	mc(f	PUNCT
ejpam-21	322	34	)	)	PUNCT
ejpam-21	322	35	and	and	CCONJ
ejpam-21	322	36	d−	d−	PROPN
ejpam-21	322	37	mc(f	mc(f	PUNCT
ejpam-21	322	38	)	)	PUNCT
ejpam-21	322	39	are	be	AUX
ejpam-21	322	40	defined	define	VERB
ejpam-21	322	41	as	as	SCONJ
ejpam-21	322	42	follows	follow	VERB
ejpam-21	322	43	:	:	PUNCT
ejpam-21	322	44	d+	d+	NOUN
ejpam-21	322	45	mc(f	mc(f	PUNCT
ejpam-21	322	46	)	)	PUNCT
ejpam-21	323	1	=	=	PRON
ejpam-21	323	2	{	{	PUNCT
ejpam-21	323	3	x	x	PUNCT
ejpam-21	323	4	∈	∈	PROPN
ejpam-21	323	5	x	x	X
ejpam-21	323	6	:	:	PUNCT
ejpam-21	323	7	f	f	X
ejpam-21	323	8	is	be	AUX
ejpam-21	323	9	not	not	PART
ejpam-21	323	10	upper	upper	ADJ
ejpam-21	323	11	c	c	NOUN
ejpam-21	323	12	-	-	PUNCT
ejpam-21	323	13	m	m	NOUN
ejpam-21	323	14	-	-	NOUN
ejpam-21	323	15	continuous	continuous	ADJ
ejpam-21	323	16	at	at	ADP
ejpam-21	323	17	x	x	X
ejpam-21	323	18	}	}	PUNCT
ejpam-21	323	19	,	,	PUNCT
ejpam-21	323	20	d−	d−	PROPN
ejpam-21	323	21	mc(f	mc(f	PUNCT
ejpam-21	323	22	)	)	PUNCT
ejpam-21	323	23	=	=	SYM
ejpam-21	324	1	{	{	PUNCT
ejpam-21	324	2	x	x	PUNCT
ejpam-21	324	3	∈	∈	PROPN
ejpam-21	324	4	x	x	X
ejpam-21	324	5	:	:	PUNCT
ejpam-21	324	6	f	f	X
ejpam-21	324	7	is	be	AUX
ejpam-21	324	8	not	not	PART
ejpam-21	324	9	lower	low	ADJ
ejpam-21	324	10	c	c	NOUN
ejpam-21	324	11	-	-	PUNCT
ejpam-21	324	12	m	m	NOUN
ejpam-21	324	13	-	-	NOUN
ejpam-21	324	14	continuous	continuous	ADJ
ejpam-21	324	15	at	at	ADP
ejpam-21	324	16	x	x	X
ejpam-21	324	17	}	}	PUNCT
ejpam-21	324	18	.	.	PUNCT
ejpam-21	325	1	theorem	theorem	VERB
ejpam-21	325	2	4.1	4.1	NUM
ejpam-21	325	3	.	.	PUNCT
ejpam-21	326	1	for	for	ADP
ejpam-21	326	2	a	a	DET
ejpam-21	326	3	multifunction	multifunction	NOUN
ejpam-21	326	4	,	,	PUNCT
ejpam-21	326	5	the	the	DET
ejpam-21	326	6	following	follow	VERB
ejpam-21	326	7	properties	property	NOUN
ejpam-21	326	8	hold	hold	VERB
ejpam-21	326	9	:	:	PUNCT
ejpam-21	326	10	d+	d+	NOUN
ejpam-21	326	11	mc(f	mc(f	PUNCT
ejpam-21	326	12	)	)	PUNCT
ejpam-21	327	1	=	=	PUNCT
ejpam-21	327	2	⋃	⋃	NOUN
ejpam-21	327	3	g∈cσ{f+(g)−	g∈cσ{f+(g)−	PROPN
ejpam-21	327	4	[	[	X
ejpam-21	327	5	mx	mx	NOUN
ejpam-21	327	6	-int(f+(g	-int(f+(g	PROPN
ejpam-21	327	7	)	)	PUNCT
ejpam-21	327	8	)	)	PUNCT
ejpam-21	327	9	]	]	PUNCT
ejpam-21	327	10	}	}	PUNCT
ejpam-21	327	11	=	=	SYM
ejpam-21	327	12	⋃	⋃	PROPN
ejpam-21	327	13	b∈	b∈	NOUN
ejpam-21	327	14	ip	ip	NOUN
ejpam-21	327	15	(	(	PUNCT
ejpam-21	327	16	y	y	PROPN
ejpam-21	327	17	)	)	PUNCT
ejpam-21	327	18	{	{	PUNCT
ejpam-21	327	19	f+(int(b))−	f+(int(b))−	NOUN
ejpam-21	327	20	[	[	X
ejpam-21	327	21	mx	mx	NOUN
ejpam-21	327	22	-int(f+(b	-int(f+(b	NOUN
ejpam-21	327	23	)	)	PUNCT
ejpam-21	327	24	)	)	PUNCT
ejpam-21	327	25	]	]	PUNCT
ejpam-21	327	26	}	}	PUNCT
ejpam-21	327	27	=	=	SYM
ejpam-21	327	28	⋃	⋃	PROPN
ejpam-21	327	29	b∈	b∈	NOUN
ejpam-21	327	30	cp	cp	PROPN
ejpam-21	327	31	(	(	PUNCT
ejpam-21	327	32	y	y	PROPN
ejpam-21	327	33	)	)	PUNCT
ejpam-21	327	34	{	{	PUNCT
ejpam-21	327	35	mx	mx	NOUN
ejpam-21	327	36	-cl(f−(b))−	-cl(f−(b))−	PROPN
ejpam-21	327	37	f−(cl(b	f−(cl(b	NOUN
ejpam-21	327	38	)	)	PUNCT
ejpam-21	327	39	)	)	PUNCT
ejpam-21	327	40	}	}	PUNCT
ejpam-21	328	1	=	=	SYM
ejpam-21	328	2	⋃	⋃	ADP
ejpam-21	328	3	h∈	h∈	ADJ
ejpam-21	328	4	cf	cf	NOUN
ejpam-21	328	5	{	{	PUNCT
ejpam-21	328	6	mx	mx	PROPN
ejpam-21	328	7	-cl(f−(h))−	-cl(f−(h))−	ADJ
ejpam-21	328	8	f−(h	f−(h	PROPN
ejpam-21	328	9	)	)	PUNCT
ejpam-21	328	10	}	}	PUNCT
ejpam-21	328	11	,	,	PUNCT
ejpam-21	328	12	where	where	SCONJ
ejpam-21	328	13	cσ	cσ	ADV
ejpam-21	328	14	is	be	AUX
ejpam-21	328	15	the	the	DET
ejpam-21	328	16	family	family	NOUN
ejpam-21	328	17	of	of	ADP
ejpam-21	328	18	open	open	ADJ
ejpam-21	328	19	set	set	NOUN
ejpam-21	328	20	g	g	NOUN
ejpam-21	328	21	having	have	VERB
ejpam-21	328	22	compact	compact	ADJ
ejpam-21	328	23	complement	complement	NOUN
ejpam-21	328	24	,	,	PUNCT
ejpam-21	328	25	ip(y	ip(y	PUNCT
ejpam-21	328	26	)	)	PUNCT
ejpam-21	328	27	is	be	AUX
ejpam-21	328	28	the	the	DET
ejpam-21	328	29	family	family	NOUN
ejpam-21	328	30	of	of	ADP
ejpam-21	328	31	subset	subset	PROPN
ejpam-21	328	32	b	b	PROPN
ejpam-21	328	33	of	of	ADP
ejpam-21	328	34	y	y	PRON
ejpam-21	328	35	such	such	ADJ
ejpam-21	328	36	that	that	SCONJ
ejpam-21	328	37	y	y	PROPN
ejpam-21	328	38	−	−	PROPN
ejpam-21	328	39	int(b	int(b	PROPN
ejpam-21	328	40	)	)	PUNCT
ejpam-21	328	41	is	be	AUX
ejpam-21	328	42	compact	compact	ADJ
ejpam-21	328	43	,	,	PUNCT
ejpam-21	328	44	cp(y	cp(y	X
ejpam-21	328	45	)	)	PUNCT
ejpam-21	328	46	is	be	AUX
ejpam-21	328	47	the	the	DET
ejpam-21	328	48	family	family	NOUN
ejpam-21	328	49	of	of	ADP
ejpam-21	328	50	subset	subset	PROPN
ejpam-21	328	51	b	b	PROPN
ejpam-21	328	52	of	of	ADP
ejpam-21	328	53	y	y	PROPN
ejpam-21	328	54	with	with	ADP
ejpam-21	328	55	the	the	DET
ejpam-21	328	56	compact	compact	ADJ
ejpam-21	328	57	closure	closure	NOUN
ejpam-21	328	58	and	and	CCONJ
ejpam-21	328	59	cf	cf	NOUN
ejpam-21	328	60	is	be	AUX
ejpam-21	328	61	the	the	DET
ejpam-21	328	62	family	family	NOUN
ejpam-21	328	63	of	of	ADP
ejpam-21	328	64	closed	closed	ADJ
ejpam-21	328	65	compact	compact	ADJ
ejpam-21	328	66	subsets	subset	NOUN
ejpam-21	328	67	of	of	ADP
ejpam-21	328	68	y.	y.	PROPN
ejpam-21	328	69	t.noiri	t.noiri	PROPN
ejpam-21	328	70	,	,	PUNCT
ejpam-21	328	71	v.popa	v.popa	NOUN
ejpam-21	328	72	/	/	SYM
ejpam-21	328	73	eur	eur	PROPN
ejpam-21	328	74	.	.	PUNCT
ejpam-21	329	1	j.	j.	PROPN
ejpam-21	329	2	pure	pure	PROPN
ejpam-21	329	3	appl	appl	PROPN
ejpam-21	329	4	.	.	PROPN
ejpam-21	329	5	math	math	PROPN
ejpam-21	329	6	,	,	PUNCT
ejpam-21	329	7	1	1	NUM
ejpam-21	329	8	(	(	PUNCT
ejpam-21	329	9	2008	2008	NUM
ejpam-21	329	10	)	)	PUNCT
ejpam-21	329	11	,	,	PUNCT
ejpam-21	329	12	(	(	PUNCT
ejpam-21	329	13	82	82	NUM
ejpam-21	329	14	-	-	SYM
ejpam-21	329	15	98	98	NUM
ejpam-21	329	16	)	)	PUNCT
ejpam-21	329	17	91	91	NUM
ejpam-21	329	18	proof	proof	NOUN
ejpam-21	329	19	.	.	PUNCT
ejpam-21	330	1	we	we	PRON
ejpam-21	330	2	shall	shall	AUX
ejpam-21	330	3	show	show	VERB
ejpam-21	330	4	only	only	ADV
ejpam-21	330	5	the	the	DET
ejpam-21	330	6	first	first	ADJ
ejpam-21	330	7	equality	equality	NOUN
ejpam-21	330	8	and	and	CCONJ
ejpam-21	330	9	the	the	DET
ejpam-21	330	10	last	last	ADJ
ejpam-21	330	11	since	since	SCONJ
ejpam-21	330	12	the	the	DET
ejpam-21	330	13	proof	proof	NOUN
ejpam-21	330	14	of	of	ADP
ejpam-21	330	15	any	any	DET
ejpam-21	330	16	other	other	ADJ
ejpam-21	330	17	equality	equality	NOUN
ejpam-21	330	18	is	be	AUX
ejpam-21	330	19	similar	similar	ADJ
ejpam-21	330	20	to	to	ADP
ejpam-21	330	21	the	the	DET
ejpam-21	330	22	first	first	ADJ
ejpam-21	330	23	.	.	PUNCT
ejpam-21	331	1	let	let	VERB
ejpam-21	331	2	x	x	PUNCT
ejpam-21	331	3	∈	∈	NOUN
ejpam-21	331	4	d+	d+	NOUN
ejpam-21	331	5	mc(f	mc(f	NUM
ejpam-21	331	6	)	)	PUNCT
ejpam-21	331	7	.	.	PUNCT
ejpam-21	332	1	by	by	ADP
ejpam-21	332	2	theorem	theorem	NOUN
ejpam-21	332	3	3.1	3.1	NUM
ejpam-21	332	4	,	,	PUNCT
ejpam-21	332	5	there	there	PRON
ejpam-21	332	6	exists	exist	VERB
ejpam-21	332	7	an	an	DET
ejpam-21	332	8	open	open	ADJ
ejpam-21	332	9	set	set	NOUN
ejpam-21	332	10	v	v	NOUN
ejpam-21	332	11	of	of	ADP
ejpam-21	332	12	y	y	PROPN
ejpam-21	332	13	having	have	VERB
ejpam-21	332	14	compact	compact	ADJ
ejpam-21	332	15	complement	complement	VERB
ejpam-21	332	16	such	such	ADJ
ejpam-21	332	17	that	that	SCONJ
ejpam-21	332	18	x	x	SYM
ejpam-21	332	19	∈	∈	PROPN
ejpam-21	332	20	f+(v	f+(v	NOUN
ejpam-21	332	21	)	)	PUNCT
ejpam-21	333	1	and	and	CCONJ
ejpam-21	333	2	x	x	X
ejpam-21	333	3	/∈	/∈	PROPN
ejpam-21	333	4	mx	mx	PROPN
ejpam-21	333	5	int(f+(v	int(f+(v	PROPN
ejpam-21	333	6	)	)	PUNCT
ejpam-21	333	7	)	)	PUNCT
ejpam-21	333	8	.	.	PUNCT
ejpam-21	334	1	therefore	therefore	ADV
ejpam-21	334	2	,	,	PUNCT
ejpam-21	334	3	we	we	PRON
ejpam-21	334	4	obtain	obtain	VERB
ejpam-21	334	5	x	x	SYM
ejpam-21	334	6	∈	∈	NOUN
ejpam-21	334	7	f+(v	f+(v	NOUN
ejpam-21	334	8	)	)	PUNCT
ejpam-21	334	9	−	−	PROPN
ejpam-21	335	1	[	[	X
ejpam-21	335	2	mx	mx	X
ejpam-21	335	3	int(f+(v	int(f+(v	ADJ
ejpam-21	335	4	)	)	PUNCT
ejpam-21	335	5	)	)	PUNCT
ejpam-21	335	6	]	]	PUNCT
ejpam-21	336	1	⊂	⊂	X
ejpam-21	336	2	⋃	⋃	PUNCT
ejpam-21	336	3	g∈cσ{f+(g	g∈cσ{f+(g	NOUN
ejpam-21	336	4	)	)	PUNCT
ejpam-21	336	5	−	−	PROPN
ejpam-21	337	1	[	[	X
ejpam-21	337	2	mx	mx	NOUN
ejpam-21	337	3	-int(f+(g	-int(f+(g	PROPN
ejpam-21	337	4	)	)	PUNCT
ejpam-21	337	5	)	)	PUNCT
ejpam-21	338	1	]	]	PUNCT
ejpam-21	338	2	}	}	PUNCT
ejpam-21	338	3	.	.	PUNCT
ejpam-21	339	1	conversely	conversely	ADV
ejpam-21	339	2	,	,	PUNCT
ejpam-21	339	3	let	let	VERB
ejpam-21	339	4	x	x	X
ejpam-21	339	5	∈	∈	VERB
ejpam-21	339	6	⋃	⋃	NOUN
ejpam-21	339	7	g∈cσ{f+(g	g∈cσ{f+(g	NOUN
ejpam-21	339	8	)	)	PUNCT
ejpam-21	339	9	−	−	PROPN
ejpam-21	340	1	[	[	X
ejpam-21	340	2	mx	mx	NOUN
ejpam-21	340	3	-int(f+(g	-int(f+(g	PROPN
ejpam-21	340	4	)	)	PUNCT
ejpam-21	340	5	)	)	PUNCT
ejpam-21	341	1	]	]	PUNCT
ejpam-21	341	2	}	}	PUNCT
ejpam-21	341	3	.	.	PUNCT
ejpam-21	342	1	there	there	PRON
ejpam-21	342	2	exists	exist	VERB
ejpam-21	342	3	v	v	ADP
ejpam-21	342	4	∈	∈	NOUN
ejpam-21	342	5	cσ	cσ	ADP
ejpam-21	342	6	such	such	ADJ
ejpam-21	342	7	that	that	SCONJ
ejpam-21	342	8	x	x	SYM
ejpam-21	342	9	∈	∈	PROPN
ejpam-21	342	10	f+(v	f+(v	NOUN
ejpam-21	342	11	)	)	PUNCT
ejpam-21	342	12	−	−	PROPN
ejpam-21	343	1	[	[	X
ejpam-21	343	2	mx	mx	X
ejpam-21	343	3	-int(f+(v	-int(f+(v	PROPN
ejpam-21	343	4	)	)	PUNCT
ejpam-21	343	5	)	)	PUNCT
ejpam-21	343	6	]	]	PUNCT
ejpam-21	343	7	.	.	PUNCT
ejpam-21	344	1	by	by	ADP
ejpam-21	344	2	theorem	theorem	NOUN
ejpam-21	344	3	3.1	3.1	NUM
ejpam-21	344	4	,	,	PUNCT
ejpam-21	344	5	we	we	PRON
ejpam-21	344	6	obtain	obtain	VERB
ejpam-21	344	7	x	x	SYM
ejpam-21	344	8	∈	∈	NOUN
ejpam-21	344	9	d+	d+	NOUN
ejpam-21	344	10	mc(f	mc(f	NUM
ejpam-21	344	11	)	)	PUNCT
ejpam-21	344	12	.	.	PUNCT
ejpam-21	345	1	we	we	PRON
ejpam-21	345	2	prove	prove	VERB
ejpam-21	345	3	the	the	DET
ejpam-21	345	4	last	last	ADJ
ejpam-21	345	5	equality.⋃	equality.⋃	NOUN
ejpam-21	345	6	h∈	h∈	ADJ
ejpam-21	345	7	cf	cf	INTJ
ejpam-21	345	8	{	{	PUNCT
ejpam-21	345	9	mx	mx	PROPN
ejpam-21	345	10	-cl(f−(h))−f−(h)}⊂	-cl(f−(h))−f−(h)}⊂	PUNCT
ejpam-21	345	11	⋃	⋃	PROPN
ejpam-21	345	12	b∈	b∈	PROPN
ejpam-21	345	13	cp	cp	PROPN
ejpam-21	345	14	(	(	PUNCT
ejpam-21	345	15	y	y	PROPN
ejpam-21	345	16	)	)	PUNCT
ejpam-21	345	17	{	{	PUNCT
ejpam-21	345	18	mx	mx	PROPN
ejpam-21	345	19	-cl(f−(b))−f−(cl(b	-cl(f−(b))−f−(cl(b	PROPN
ejpam-21	345	20	)	)	PUNCT
ejpam-21	345	21	)	)	PUNCT
ejpam-21	345	22	}	}	PUNCT
ejpam-21	345	23	=	=	PUNCT
ejpam-21	345	24	d+	d+	NOUN
ejpam-21	345	25	mc(f	mc(f	NUM
ejpam-21	345	26	)	)	PUNCT
ejpam-21	345	27	.	.	PUNCT
ejpam-21	346	1	conversely	conversely	ADV
ejpam-21	346	2	,	,	PUNCT
ejpam-21	346	3	by	by	ADP
ejpam-21	346	4	lemma	lemma	PROPN
ejpam-21	346	5	3.1	3.1	NUM
ejpam-21	346	6	we	we	PRON
ejpam-21	346	7	have	have	VERB
ejpam-21	346	8	d+	d+	NOUN
ejpam-21	346	9	mc(f	mc(f	PUNCT
ejpam-21	346	10	)	)	PUNCT
ejpam-21	346	11	=	=	SYM
ejpam-21	346	12	⋃	⋃	NOUN
ejpam-21	346	13	b∈	b∈	NOUN
ejpam-21	346	14	cp	cp	PROPN
ejpam-21	346	15	(	(	PUNCT
ejpam-21	346	16	y	y	PROPN
ejpam-21	346	17	)	)	PUNCT
ejpam-21	346	18	{	{	PUNCT
ejpam-21	346	19	mx	mx	NOUN
ejpam-21	346	20	cl(f−(b))−	cl(f−(b))−	PROPN
ejpam-21	346	21	f−(cl(b	f−(cl(b	PROPN
ejpam-21	346	22	)	)	PUNCT
ejpam-21	346	23	)	)	PUNCT
ejpam-21	346	24	}	}	PUNCT
ejpam-21	346	25	⊂	⊂	PRON
ejpam-21	346	26	⋃	⋃	ADV
ejpam-21	346	27	h∈	h∈	ADJ
ejpam-21	346	28	cf	cf	NOUN
ejpam-21	346	29	{	{	PUNCT
ejpam-21	346	30	mx	mx	PROPN
ejpam-21	346	31	-cl(f−(h))−	-cl(f−(h))−	ADJ
ejpam-21	346	32	f−(h	f−(h	PROPN
ejpam-21	346	33	)	)	PUNCT
ejpam-21	346	34	}	}	PUNCT
ejpam-21	346	35	.	.	PUNCT
ejpam-21	347	1	theorem	theorem	VERB
ejpam-21	347	2	4.2	4.2	NUM
ejpam-21	347	3	.	.	PUNCT
ejpam-21	348	1	for	for	ADP
ejpam-21	348	2	a	a	DET
ejpam-21	348	3	multifunction	multifunction	NOUN
ejpam-21	348	4	,	,	PUNCT
ejpam-21	348	5	the	the	DET
ejpam-21	348	6	following	follow	VERB
ejpam-21	348	7	properties	property	NOUN
ejpam-21	348	8	hold	hold	VERB
ejpam-21	348	9	:	:	PUNCT
ejpam-21	348	10	d−	d−	PROPN
ejpam-21	348	11	mc(f	mc(f	PUNCT
ejpam-21	348	12	)	)	PUNCT
ejpam-21	349	1	=	=	SYM
ejpam-21	349	2	⋃	⋃	ADP
ejpam-21	349	3	g∈cσ{f−(g)−	g∈cσ{f−(g)−	NOUN
ejpam-21	349	4	[	[	X
ejpam-21	349	5	mx	mx	NOUN
ejpam-21	349	6	-int(f−(g	-int(f−(g	NOUN
ejpam-21	349	7	)	)	PUNCT
ejpam-21	349	8	)	)	PUNCT
ejpam-21	349	9	]	]	PUNCT
ejpam-21	349	10	}	}	PUNCT
ejpam-21	349	11	=	=	SYM
ejpam-21	349	12	⋃	⋃	PROPN
ejpam-21	349	13	b∈	b∈	NOUN
ejpam-21	349	14	ip	ip	NOUN
ejpam-21	349	15	(	(	PUNCT
ejpam-21	349	16	y	y	PROPN
ejpam-21	349	17	)	)	PUNCT
ejpam-21	349	18	{	{	PUNCT
ejpam-21	349	19	f−(int(b))−	f−(int(b))−	VERB
ejpam-21	349	20	[	[	X
ejpam-21	349	21	mx	mx	PROPN
ejpam-21	349	22	-int(f−(b	-int(f−(b	PROPN
ejpam-21	349	23	)	)	PUNCT
ejpam-21	349	24	)	)	PUNCT
ejpam-21	349	25	]	]	PUNCT
ejpam-21	349	26	}	}	PUNCT
ejpam-21	349	27	=	=	SYM
ejpam-21	349	28	⋃	⋃	PROPN
ejpam-21	349	29	b∈	b∈	NOUN
ejpam-21	349	30	cp	cp	PROPN
ejpam-21	349	31	(	(	PUNCT
ejpam-21	349	32	y	y	PROPN
ejpam-21	349	33	)	)	PUNCT
ejpam-21	349	34	{	{	PUNCT
ejpam-21	349	35	mx	mx	PROPN
ejpam-21	349	36	-cl(f+(b))−	-cl(f+(b))−	PROPN
ejpam-21	349	37	f+(cl(b	f+(cl(b	PROPN
ejpam-21	349	38	)	)	PUNCT
ejpam-21	349	39	)	)	PUNCT
ejpam-21	349	40	}	}	PUNCT
ejpam-21	350	1	=	=	SYM
ejpam-21	350	2	⋃	⋃	ADP
ejpam-21	350	3	h∈	h∈	ADJ
ejpam-21	350	4	cf	cf	NOUN
ejpam-21	350	5	{	{	PUNCT
ejpam-21	350	6	mx	mx	PROPN
ejpam-21	350	7	-cl(f+(h))−	-cl(f+(h))−	NOUN
ejpam-21	350	8	f+(h	f+(h	PROPN
ejpam-21	350	9	)	)	PUNCT
ejpam-21	350	10	}	}	PUNCT
ejpam-21	350	11	.	.	PUNCT
ejpam-21	351	1	proof	proof	NOUN
ejpam-21	351	2	.	.	PUNCT
ejpam-21	352	1	the	the	DET
ejpam-21	352	2	proof	proof	NOUN
ejpam-21	352	3	is	be	AUX
ejpam-21	352	4	similar	similar	ADJ
ejpam-21	352	5	to	to	ADP
ejpam-21	352	6	that	that	PRON
ejpam-21	352	7	of	of	ADP
ejpam-21	352	8	theorem	theorem	ADJ
ejpam-21	352	9	4.1	4.1	NUM
ejpam-21	352	10	remark	remark	NOUN
ejpam-21	352	11	4.1	4.1	NUM
ejpam-21	352	12	.	.	PUNCT
ejpam-21	353	1	if	if	SCONJ
ejpam-21	353	2	is	be	AUX
ejpam-21	353	3	a	a	DET
ejpam-21	353	4	multifunction	multifunction	NOUN
ejpam-21	353	5	and	and	CCONJ
ejpam-21	353	6	mx	mx	PROPN
ejpam-21	353	7	=	=	SYM
ejpam-21	353	8	τ	τ	PROPN
ejpam-21	353	9	(	(	PUNCT
ejpam-21	353	10	resp	resp	NOUN
ejpam-21	353	11	.	.	PUNCT
ejpam-21	353	12	so(x	so(x	NOUN
ejpam-21	353	13	)	)	PUNCT
ejpam-21	353	14	)	)	PUNCT
ejpam-21	353	15	,	,	PUNCT
ejpam-21	353	16	then	then	ADV
ejpam-21	353	17	the	the	DET
ejpam-21	353	18	set	set	NOUN
ejpam-21	353	19	of	of	ADP
ejpam-21	353	20	points	point	NOUN
ejpam-21	353	21	of	of	ADP
ejpam-21	353	22	upper	upper	ADJ
ejpam-21	353	23	/	/	SYM
ejpam-21	353	24	lower	low	ADJ
ejpam-21	353	25	c	c	NOUN
ejpam-21	353	26	-	-	PUNCT
ejpam-21	353	27	discontinuity	discontinuity	NOUN
ejpam-21	353	28	(	(	PUNCT
ejpam-21	353	29	resp	resp	NOUN
ejpam-21	353	30	.	.	PUNCT
ejpam-21	354	1	c	c	X
ejpam-21	354	2	-	-	PUNCT
ejpam-21	354	3	quasi	quasi	NOUN
ejpam-21	354	4	-	-	NOUN
ejpam-21	354	5	discontinuity	discontinuity	NOUN
ejpam-21	354	6	)	)	PUNCT
ejpam-21	354	7	is	be	AUX
ejpam-21	354	8	obtained	obtain	VERB
ejpam-21	354	9	.	.	PUNCT
ejpam-21	355	1	definition	definition	NOUN
ejpam-21	355	2	4.1	4.1	NUM
ejpam-21	355	3	.	.	PUNCT
ejpam-21	356	1	let	let	AUX
ejpam-21	356	2	(	(	PUNCT
ejpam-21	356	3	x	x	NOUN
ejpam-21	356	4	,	,	PUNCT
ejpam-21	356	5	mx	mx	NOUN
ejpam-21	356	6	)	)	PUNCT
ejpam-21	356	7	be	be	AUX
ejpam-21	356	8	an	an	DET
ejpam-21	356	9	m	m	NOUN
ejpam-21	356	10	-	-	NOUN
ejpam-21	356	11	space	space	NOUN
ejpam-21	356	12	and	and	CCONJ
ejpam-21	356	13	a	a	DET
ejpam-21	356	14	a	a	DET
ejpam-21	356	15	subset	subset	NOUN
ejpam-21	356	16	of	of	ADP
ejpam-21	356	17	x	x	X
ejpam-21	356	18	.	.	PUNCT
ejpam-21	357	1	the	the	DET
ejpam-21	357	2	mx	mx	PROPN
ejpam-21	357	3	-frontier	-frontier	NOUN
ejpam-21	357	4	of	of	ADP
ejpam-21	357	5	a	a	PRON
ejpam-21	357	6	[	[	X
ejpam-21	357	7	35	35	NUM
ejpam-21	357	8	]	]	PUNCT
ejpam-21	357	9	,	,	PUNCT
ejpam-21	357	10	denoted	denote	VERB
ejpam-21	357	11	by	by	ADP
ejpam-21	357	12	mx	mx	PROPN
ejpam-21	357	13	-fr(a	-fr(a	PROPN
ejpam-21	357	14	)	)	PUNCT
ejpam-21	357	15	,	,	PUNCT
ejpam-21	357	16	is	be	AUX
ejpam-21	357	17	defined	define	VERB
ejpam-21	357	18	as	as	SCONJ
ejpam-21	357	19	follows	follow	VERB
ejpam-21	357	20	:	:	PUNCT
ejpam-21	357	21	mx	mx	PROPN
ejpam-21	357	22	-fr(a	-fr(a	PROPN
ejpam-21	357	23	)	)	PUNCT
ejpam-21	358	1	=	=	SYM
ejpam-21	358	2	mx	mx	PROPN
ejpam-21	358	3	-cl(a	-cl(a	PROPN
ejpam-21	358	4	)	)	PUNCT
ejpam-21	358	5	∩mx	∩mx	PROPN
ejpam-21	358	6	-cl(x	-cl(x	PROPN
ejpam-21	358	7	−a	−a	NOUN
ejpam-21	358	8	)	)	PUNCT
ejpam-21	359	1	=	=	SYM
ejpam-21	359	2	mx	mx	PROPN
ejpam-21	359	3	-cl(a)−mx	-cl(a)−mx	PROPN
ejpam-21	359	4	-int(a	-int(a	PROPN
ejpam-21	359	5	)	)	PUNCT
ejpam-21	359	6	.	.	PUNCT
ejpam-21	360	1	theorem	theorem	VERB
ejpam-21	360	2	4.3	4.3	NUM
ejpam-21	360	3	.	.	PUNCT
ejpam-21	361	1	the	the	DET
ejpam-21	361	2	set	set	NOUN
ejpam-21	361	3	of	of	ADP
ejpam-21	361	4	all	all	DET
ejpam-21	361	5	points	point	NOUN
ejpam-21	361	6	x	x	X
ejpam-21	361	7	∈	∈	NOUN
ejpam-21	361	8	x	x	PUNCT
ejpam-21	361	9	at	at	ADP
ejpam-21	361	10	which	which	PRON
ejpam-21	361	11	a	a	DET
ejpam-21	361	12	function	function	NOUN
ejpam-21	361	13	is	be	AUX
ejpam-21	361	14	not	not	PART
ejpam-21	361	15	u.c.m.c	u.c.m.c	PROPN
ejpam-21	361	16	.	.	PUNCT
ejpam-21	361	17	(	(	PUNCT
ejpam-21	361	18	resp	resp	NOUN
ejpam-21	361	19	.	.	PUNCT
ejpam-21	362	1	l.c.m.c	l.c.m.c	PROPN
ejpam-21	362	2	.	.	PUNCT
ejpam-21	362	3	)	)	PUNCT
ejpam-21	362	4	is	be	AUX
ejpam-21	362	5	identical	identical	ADJ
ejpam-21	362	6	with	with	ADP
ejpam-21	362	7	the	the	DET
ejpam-21	362	8	union	union	NOUN
ejpam-21	362	9	of	of	ADP
ejpam-21	362	10	the	the	DET
ejpam-21	362	11	mx	mx	PROPN
ejpam-21	362	12	-frontiers	-frontier	NOUN
ejpam-21	362	13	of	of	ADP
ejpam-21	362	14	the	the	DET
ejpam-21	362	15	u.c.m.c	u.c.m.c	PROPN
ejpam-21	362	16	.	.	PUNCT
ejpam-21	363	1	(	(	PUNCT
ejpam-21	363	2	resp	resp	NOUN
ejpam-21	363	3	.	.	PUNCT
ejpam-21	364	1	l.c.m.c	l.c.m.c	PROPN
ejpam-21	364	2	.	.	PUNCT
ejpam-21	364	3	)	)	PUNCT
ejpam-21	365	1	inverse	inverse	NOUN
ejpam-21	365	2	images	image	NOUN
ejpam-21	365	3	of	of	ADP
ejpam-21	365	4	open	open	ADJ
ejpam-21	365	5	sets	set	NOUN
ejpam-21	365	6	containing	contain	VERB
ejpam-21	365	7	(	(	PUNCT
ejpam-21	365	8	resp	resp	NOUN
ejpam-21	365	9	.	.	PUNCT
ejpam-21	366	1	meeting	meeting	NOUN
ejpam-21	366	2	)	)	PUNCT
ejpam-21	367	1	f(x	f(x	PROPN
ejpam-21	367	2	)	)	PUNCT
ejpam-21	367	3	and	and	CCONJ
ejpam-21	367	4	having	have	VERB
ejpam-21	367	5	compact	compact	ADJ
ejpam-21	367	6	complement	complement	NOUN
ejpam-21	367	7	.	.	PUNCT
ejpam-21	368	1	proof	proof	NOUN
ejpam-21	368	2	.	.	PUNCT
ejpam-21	369	1	suppose	suppose	VERB
ejpam-21	369	2	that	that	SCONJ
ejpam-21	369	3	f	f	PROPN
ejpam-21	369	4	is	be	AUX
ejpam-21	369	5	not	not	PART
ejpam-21	369	6	u.c.m.c	u.c.m.c	PROPN
ejpam-21	369	7	.	.	PUNCT
ejpam-21	370	1	at	at	ADP
ejpam-21	370	2	x	x	X
ejpam-21	370	3	∈	∈	PROPN
ejpam-21	370	4	x	x	X
ejpam-21	370	5	.	.	PUNCT
ejpam-21	371	1	then	then	ADV
ejpam-21	371	2	,	,	PUNCT
ejpam-21	371	3	there	there	PRON
ejpam-21	371	4	exists	exist	VERB
ejpam-21	371	5	an	an	DET
ejpam-21	371	6	open	open	ADJ
ejpam-21	371	7	set	set	NOUN
ejpam-21	371	8	v	v	NOUN
ejpam-21	371	9	of	of	ADP
ejpam-21	371	10	y	y	PROPN
ejpam-21	371	11	containing	contain	VERB
ejpam-21	371	12	f	f	PROPN
ejpam-21	371	13	(	(	PUNCT
ejpam-21	371	14	x	x	NOUN
ejpam-21	371	15	)	)	PUNCT
ejpam-21	371	16	and	and	CCONJ
ejpam-21	371	17	having	have	VERB
ejpam-21	371	18	compact	compact	ADJ
ejpam-21	371	19	complement	complement	VERB
ejpam-21	371	20	such	such	ADJ
ejpam-21	371	21	that	that	SCONJ
ejpam-21	371	22	u	u	PROPN
ejpam-21	371	23	∩	∩	NOUN
ejpam-21	371	24	(	(	PUNCT
ejpam-21	371	25	x	x	NOUN
ejpam-21	371	26	−	−	PROPN
ejpam-21	371	27	f+(v	f+(v	NOUN
ejpam-21	371	28	)	)	PUNCT
ejpam-21	371	29	)	)	PUNCT
ejpam-21	372	1	6=	6=	ADP
ejpam-21	372	2	∅	∅	NOUN
ejpam-21	372	3	for	for	ADP
ejpam-21	372	4	every	every	DET
ejpam-21	372	5	mx	mx	PROPN
ejpam-21	372	6	-open	-open	PROPN
ejpam-21	372	7	set	set	NOUN
ejpam-21	372	8	u	u	NOUN
ejpam-21	372	9	containing	contain	VERB
ejpam-21	372	10	x.	x.	NOUN
ejpam-21	372	11	hence	hence	ADV
ejpam-21	372	12	,	,	PUNCT
ejpam-21	372	13	by	by	ADP
ejpam-21	372	14	lemma	lemma	PROPN
ejpam-21	372	15	3.2	3.2	NUM
ejpam-21	372	16	we	we	PRON
ejpam-21	372	17	have	have	VERB
ejpam-21	372	18	x	x	X
ejpam-21	372	19	∈	∈	PROPN
ejpam-21	372	20	mx	mx	PROPN
ejpam-21	372	21	-cl(x	-cl(x	PROPN
ejpam-21	372	22	−	−	PROPN
ejpam-21	372	23	f+(v	f+(v	NOUN
ejpam-21	372	24	)	)	PUNCT
ejpam-21	372	25	)	)	PUNCT
ejpam-21	372	26	.	.	PUNCT
ejpam-21	373	1	on	on	ADP
ejpam-21	373	2	the	the	DET
ejpam-21	373	3	other	other	ADJ
ejpam-21	373	4	hand	hand	NOUN
ejpam-21	373	5	,	,	PUNCT
ejpam-21	373	6	we	we	PRON
ejpam-21	373	7	have	have	VERB
ejpam-21	373	8	x	x	X
ejpam-21	373	9	∈	∈	PROPN
ejpam-21	373	10	f+(v	f+(v	NOUN
ejpam-21	373	11	)	)	PUNCT
ejpam-21	374	1	⊂	⊂	PROPN
ejpam-21	374	2	mx	mx	PROPN
ejpam-21	374	3	-cl(f+(v	-cl(f+(v	PUNCT
ejpam-21	374	4	)	)	PUNCT
ejpam-21	374	5	)	)	PUNCT
ejpam-21	374	6	and	and	CCONJ
ejpam-21	374	7	hence	hence	ADV
ejpam-21	374	8	x	x	X
ejpam-21	374	9	∈	∈	PROPN
ejpam-21	374	10	mx	mx	PROPN
ejpam-21	374	11	-fr(f+(v	-fr(f+(v	PROPN
ejpam-21	374	12	)	)	PUNCT
ejpam-21	374	13	)	)	PUNCT
ejpam-21	374	14	.	.	PUNCT
ejpam-21	375	1	conversely	conversely	ADV
ejpam-21	375	2	,	,	PUNCT
ejpam-21	375	3	suppose	suppose	VERB
ejpam-21	375	4	that	that	SCONJ
ejpam-21	375	5	v	v	NOUN
ejpam-21	375	6	is	be	AUX
ejpam-21	375	7	an	an	DET
ejpam-21	375	8	open	open	ADJ
ejpam-21	375	9	set	set	NOUN
ejpam-21	375	10	of	of	ADP
ejpam-21	375	11	y	y	PROPN
ejpam-21	375	12	containing	contain	VERB
ejpam-21	375	13	f	f	PROPN
ejpam-21	375	14	(	(	PUNCT
ejpam-21	375	15	x	x	NOUN
ejpam-21	375	16	)	)	PUNCT
ejpam-21	375	17	and	and	CCONJ
ejpam-21	375	18	having	have	VERB
ejpam-21	375	19	compact	compact	ADJ
ejpam-21	375	20	complement	complement	VERB
ejpam-21	375	21	such	such	ADJ
ejpam-21	375	22	that	that	SCONJ
ejpam-21	375	23	x	x	SYM
ejpam-21	375	24	∈	∈	PROPN
ejpam-21	375	25	mx	mx	PROPN
ejpam-21	375	26	-fr(f+(v	-fr(f+(v	PROPN
ejpam-21	375	27	)	)	PUNCT
ejpam-21	375	28	)	)	PUNCT
ejpam-21	375	29	.	.	PUNCT
ejpam-21	376	1	if	if	SCONJ
ejpam-21	376	2	f	f	PROPN
ejpam-21	376	3	is	be	AUX
ejpam-21	376	4	u.c.m.c	u.c.m.c	PROPN
ejpam-21	376	5	.	.	PUNCT
ejpam-21	377	1	at	at	ADP
ejpam-21	377	2	x	x	PROPN
ejpam-21	377	3	∈	∈	PROPN
ejpam-21	377	4	x	x	X
ejpam-21	377	5	,	,	PUNCT
ejpam-21	377	6	then	then	ADV
ejpam-21	377	7	there	there	PRON
ejpam-21	377	8	exists	exist	VERB
ejpam-21	377	9	u	u	PROPN
ejpam-21	377	10	∈	∈	PROPN
ejpam-21	377	11	mx	mx	NOUN
ejpam-21	377	12	containing	contain	VERB
ejpam-21	377	13	x	x	PUNCT
ejpam-21	377	14	such	such	ADJ
ejpam-21	377	15	that	that	SCONJ
ejpam-21	377	16	u	u	PROPN
ejpam-21	377	17	⊂	⊂	PROPN
ejpam-21	377	18	f+(v	f+(v	PROPN
ejpam-21	377	19	)	)	PUNCT
ejpam-21	377	20	and	and	CCONJ
ejpam-21	377	21	hence	hence	ADV
ejpam-21	377	22	,	,	PUNCT
ejpam-21	377	23	x	x	PROPN
ejpam-21	377	24	∈	∈	PROPN
ejpam-21	377	25	mx	mx	PROPN
ejpam-21	377	26	-int(f+(v	-int(f+(v	PROPN
ejpam-21	377	27	)	)	PUNCT
ejpam-21	377	28	)	)	PUNCT
ejpam-21	377	29	.	.	PUNCT
ejpam-21	378	1	this	this	PRON
ejpam-21	378	2	is	be	AUX
ejpam-21	378	3	a	a	DET
ejpam-21	378	4	contradiction	contradiction	NOUN
ejpam-21	378	5	and	and	CCONJ
ejpam-21	378	6	hence	hence	ADV
ejpam-21	378	7	,	,	PUNCT
ejpam-21	378	8	f	f	PROPN
ejpam-21	378	9	is	be	AUX
ejpam-21	378	10	not	not	PART
ejpam-21	378	11	u.c.m.c	u.c.m.c	PROPN
ejpam-21	378	12	.	.	PUNCT
ejpam-21	379	1	the	the	DET
ejpam-21	379	2	proof	proof	NOUN
ejpam-21	379	3	for	for	ADP
ejpam-21	379	4	l.c.m.c	l.c.m.c	PROPN
ejpam-21	379	5	.	.	PROPN
ejpam-21	379	6	is	be	AUX
ejpam-21	379	7	similar	similar	ADJ
ejpam-21	379	8	.	.	PUNCT
ejpam-21	380	1	t.noiri	t.noiri	ADV
ejpam-21	380	2	,	,	PUNCT
ejpam-21	380	3	v.popa	v.popa	NOUN
ejpam-21	380	4	/	/	SYM
ejpam-21	380	5	eur	eur	PROPN
ejpam-21	380	6	.	.	PUNCT
ejpam-21	381	1	j.	j.	PROPN
ejpam-21	381	2	pure	pure	PROPN
ejpam-21	381	3	appl	appl	PROPN
ejpam-21	381	4	.	.	PROPN
ejpam-21	381	5	math	math	PROPN
ejpam-21	381	6	,	,	PUNCT
ejpam-21	381	7	1	1	NUM
ejpam-21	381	8	(	(	PUNCT
ejpam-21	381	9	2008	2008	NUM
ejpam-21	381	10	)	)	PUNCT
ejpam-21	381	11	,	,	PUNCT
ejpam-21	381	12	(	(	PUNCT
ejpam-21	381	13	82	82	NUM
ejpam-21	381	14	-	-	SYM
ejpam-21	381	15	98	98	NUM
ejpam-21	381	16	)	)	PUNCT
ejpam-21	381	17	92	92	NUM
ejpam-21	381	18	5	5	NUM
ejpam-21	381	19	.	.	PUNCT
ejpam-21	382	1	m	m	NOUN
ejpam-21	382	2	-	-	NOUN
ejpam-21	382	3	continuity	continuity	NOUN
ejpam-21	382	4	and	and	CCONJ
ejpam-21	382	5	c	c	NOUN
ejpam-21	382	6	-	-	PUNCT
ejpam-21	382	7	m	m	NOUN
ejpam-21	382	8	-	-	PUNCT
ejpam-21	382	9	continuity	continuity	NOUN
ejpam-21	382	10	definition	definition	NOUN
ejpam-21	382	11	5.1	5.1	NUM
ejpam-21	382	12	.	.	PUNCT
ejpam-21	383	1	a	a	DET
ejpam-21	383	2	multifunction	multifunction	NOUN
ejpam-21	383	3	is	be	AUX
ejpam-21	383	4	said	say	VERB
ejpam-21	383	5	to	to	PART
ejpam-21	383	6	be	be	AUX
ejpam-21	383	7	(	(	PUNCT
ejpam-21	383	8	1	1	NUM
ejpam-21	383	9	)	)	PUNCT
ejpam-21	383	10	upper	upper	ADJ
ejpam-21	383	11	m	m	NOUN
ejpam-21	383	12	-	-	ADJ
ejpam-21	383	13	continuous	continuous	ADJ
ejpam-21	383	14	(	(	PUNCT
ejpam-21	383	15	briefly	briefly	ADV
ejpam-21	383	16	u.m.c	u.m.c	ADJ
ejpam-21	383	17	.	.	PUNCT
ejpam-21	383	18	)	)	PUNCT
ejpam-21	384	1	at	at	ADP
ejpam-21	384	2	x	x	X
ejpam-21	384	3	∈	∈	NOUN
ejpam-21	384	4	x	x	PUNCT
ejpam-21	385	1	[	[	X
ejpam-21	385	2	34	34	NUM
ejpam-21	385	3	]	]	X
ejpam-21	385	4	if	if	SCONJ
ejpam-21	385	5	for	for	ADP
ejpam-21	385	6	each	each	DET
ejpam-21	385	7	open	open	ADJ
ejpam-21	385	8	set	set	VERB
ejpam-21	385	9	v	v	NOUN
ejpam-21	385	10	containing	contain	VERB
ejpam-21	385	11	f	f	X
ejpam-21	385	12	(	(	PUNCT
ejpam-21	385	13	x	x	NOUN
ejpam-21	385	14	)	)	PUNCT
ejpam-21	385	15	,	,	PUNCT
ejpam-21	385	16	there	there	PRON
ejpam-21	385	17	exists	exist	VERB
ejpam-21	385	18	u	u	PROPN
ejpam-21	385	19	∈	∈	PROPN
ejpam-21	385	20	mx	mx	NOUN
ejpam-21	385	21	containing	contain	VERB
ejpam-21	385	22	x	x	PUNCT
ejpam-21	385	23	such	such	ADJ
ejpam-21	385	24	that	that	SCONJ
ejpam-21	385	25	f	f	PROPN
ejpam-21	385	26	(	(	PUNCT
ejpam-21	385	27	u	u	NOUN
ejpam-21	385	28	)	)	PUNCT
ejpam-21	385	29	⊂	⊂	PROPN
ejpam-21	385	30	v	v	PROPN
ejpam-21	385	31	,	,	PUNCT
ejpam-21	385	32	(	(	PUNCT
ejpam-21	385	33	2	2	NUM
ejpam-21	385	34	)	)	PUNCT
ejpam-21	385	35	lower	low	ADJ
ejpam-21	385	36	m	m	NOUN
ejpam-21	385	37	-	-	ADJ
ejpam-21	385	38	continuous	continuous	ADJ
ejpam-21	385	39	(	(	PUNCT
ejpam-21	385	40	briefly	briefly	ADV
ejpam-21	385	41	l.m.c	l.m.c	NOUN
ejpam-21	385	42	.	.	PUNCT
ejpam-21	385	43	)	)	PUNCT
ejpam-21	386	1	at	at	ADP
ejpam-21	386	2	x	x	X
ejpam-21	386	3	∈	∈	NOUN
ejpam-21	386	4	x	x	PUNCT
ejpam-21	387	1	[	[	X
ejpam-21	387	2	34	34	NUM
ejpam-21	387	3	]	]	X
ejpam-21	387	4	if	if	SCONJ
ejpam-21	387	5	for	for	SCONJ
ejpam-21	387	6	each	each	DET
ejpam-21	387	7	open	open	ADJ
ejpam-21	387	8	set	set	VERB
ejpam-21	387	9	v	v	ADP
ejpam-21	387	10	such	such	ADJ
ejpam-21	387	11	that	that	SCONJ
ejpam-21	387	12	f	f	PROPN
ejpam-21	387	13	(	(	PUNCT
ejpam-21	387	14	x	x	NOUN
ejpam-21	387	15	)	)	PUNCT
ejpam-21	387	16	∩	∩	ADJ
ejpam-21	387	17	v	v	ADP
ejpam-21	387	18	6=	6=	NOUN
ejpam-21	387	19	∅	∅	NOUN
ejpam-21	387	20	,	,	PUNCT
ejpam-21	387	21	there	there	PRON
ejpam-21	387	22	exists	exist	VERB
ejpam-21	387	23	u	u	PROPN
ejpam-21	387	24	∈	∈	PROPN
ejpam-21	387	25	mx	mx	NOUN
ejpam-21	387	26	containing	contain	VERB
ejpam-21	387	27	x	x	PUNCT
ejpam-21	387	28	such	such	ADJ
ejpam-21	387	29	that	that	SCONJ
ejpam-21	387	30	f	f	PROPN
ejpam-21	387	31	(	(	PUNCT
ejpam-21	387	32	u	u	NOUN
ejpam-21	387	33	)	)	PUNCT
ejpam-21	387	34	∩	∩	NOUN
ejpam-21	387	35	v	v	ADP
ejpam-21	387	36	6=	6=	NOUN
ejpam-21	387	37	∅	∅	NOUN
ejpam-21	387	38	for	for	ADP
ejpam-21	387	39	every	every	DET
ejpam-21	387	40	u	u	PROPN
ejpam-21	387	41	∈	∈	PROPN
ejpam-21	387	42	u	u	NOUN
ejpam-21	387	43	,	,	PUNCT
ejpam-21	387	44	(	(	PUNCT
ejpam-21	387	45	3	3	X
ejpam-21	387	46	)	)	PUNCT
ejpam-21	387	47	upper	upper	ADJ
ejpam-21	387	48	/	/	SYM
ejpam-21	387	49	lower	low	ADJ
ejpam-21	387	50	m	m	NOUN
ejpam-21	387	51	-	-	ADJ
ejpam-21	387	52	continuous	continuous	ADJ
ejpam-21	387	53	on	on	ADP
ejpam-21	387	54	x	x	SYM
ejpam-21	387	55	if	if	SCONJ
ejpam-21	387	56	it	it	PRON
ejpam-21	387	57	has	have	AUX
ejpam-21	387	58	the	the	DET
ejpam-21	387	59	properties	property	NOUN
ejpam-21	387	60	at	at	ADP
ejpam-21	387	61	each	each	DET
ejpam-21	387	62	point	point	NOUN
ejpam-21	387	63	of	of	ADP
ejpam-21	387	64	x	x	X
ejpam-21	387	65	.	.	PUNCT
ejpam-21	388	1	remark	remark	PROPN
ejpam-21	388	2	5.1	5.1	NUM
ejpam-21	388	3	.	.	PUNCT
ejpam-21	389	1	let	let	VERB
ejpam-21	389	2	(	(	PUNCT
ejpam-21	389	3	x	x	NOUN
ejpam-21	389	4	,	,	PUNCT
ejpam-21	389	5	τ	τ	X
ejpam-21	389	6	)	)	PUNCT
ejpam-21	389	7	be	be	VERB
ejpam-21	389	8	a	a	DET
ejpam-21	389	9	topological	topological	ADJ
ejpam-21	389	10	space	space	NOUN
ejpam-21	389	11	and	and	CCONJ
ejpam-21	389	12	mx	mx	NOUN
ejpam-21	389	13	=	=	SYM
ejpam-21	389	14	τ	τ	PROPN
ejpam-21	389	15	(	(	PUNCT
ejpam-21	389	16	resp	resp	NOUN
ejpam-21	389	17	.	.	PUNCT
ejpam-21	389	18	so(x	so(x	NUM
ejpam-21	389	19	)	)	PUNCT
ejpam-21	389	20	,	,	PUNCT
ejpam-21	389	21	po(x	po(x	NUM
ejpam-21	389	22	)	)	PUNCT
ejpam-21	389	23	,	,	PUNCT
ejpam-21	389	24	α(x	α(x	NOUN
ejpam-21	389	25	)	)	PUNCT
ejpam-21	389	26	,	,	PUNCT
ejpam-21	389	27	spo(x	spo(x	PROPN
ejpam-21	389	28	)	)	PUNCT
ejpam-21	389	29	,	,	PUNCT
ejpam-21	389	30	bo(x	bo(x	NUM
ejpam-21	389	31	)	)	PUNCT
ejpam-21	389	32	)	)	PUNCT
ejpam-21	389	33	.	.	PUNCT
ejpam-21	390	1	if	if	SCONJ
ejpam-21	390	2	a	a	DET
ejpam-21	390	3	multifunction	multifunction	NOUN
ejpam-21	390	4	is	be	AUX
ejpam-21	390	5	upper	upper	ADJ
ejpam-21	390	6	/	/	SYM
ejpam-21	390	7	lower	low	ADJ
ejpam-21	390	8	m	m	NOUN
ejpam-21	390	9	-	-	ADJ
ejpam-21	390	10	continuous	continuous	ADJ
ejpam-21	390	11	,	,	PUNCT
ejpam-21	390	12	then	then	ADV
ejpam-21	390	13	f	f	PROPN
ejpam-21	390	14	is	be	AUX
ejpam-21	390	15	upper	upper	ADJ
ejpam-21	390	16	/	/	SYM
ejpam-21	390	17	lower	low	ADJ
ejpam-21	390	18	continuous	continuous	ADJ
ejpam-21	390	19	(	(	PUNCT
ejpam-21	390	20	resp	resp	NOUN
ejpam-21	390	21	.	.	PUNCT
ejpam-21	391	1	upper	upper	ADJ
ejpam-21	391	2	/	/	SYM
ejpam-21	391	3	lower	low	ADJ
ejpam-21	391	4	semi	semi	ADJ
ejpam-21	391	5	-	-	ADJ
ejpam-21	391	6	continuous	continuous	ADJ
ejpam-21	392	1	[	[	X
ejpam-21	392	2	27	27	NUM
ejpam-21	392	3	]	]	PUNCT
ejpam-21	392	4	or	or	CCONJ
ejpam-21	392	5	upper	upper	ADJ
ejpam-21	392	6	/	/	SYM
ejpam-21	392	7	lower	low	ADJ
ejpam-21	392	8	quasi	quasi	ADJ
ejpam-21	392	9	-	-	ADJ
ejpam-21	392	10	continuous	continuous	ADJ
ejpam-21	392	11	[	[	X
ejpam-21	392	12	28	28	NUM
ejpam-21	392	13	]	]	X
ejpam-21	392	14	,	,	PUNCT
ejpam-21	392	15	upper	upper	ADJ
ejpam-21	392	16	/	/	SYM
ejpam-21	392	17	lower	low	ADJ
ejpam-21	392	18	precontinuous	precontinuous	ADJ
ejpam-21	393	1	[	[	X
ejpam-21	393	2	29	29	NUM
ejpam-21	393	3	]	]	X
ejpam-21	393	4	,	,	PUNCT
ejpam-21	393	5	upper	upper	ADJ
ejpam-21	393	6	/	/	SYM
ejpam-21	393	7	lower	low	ADJ
ejpam-21	393	8	α	α	NOUN
ejpam-21	393	9	-	-	ADJ
ejpam-21	393	10	continuous	continuous	ADJ
ejpam-21	393	11	[	[	X
ejpam-21	393	12	21	21	NUM
ejpam-21	393	13	]	]	X
ejpam-21	393	14	,	,	PUNCT
ejpam-21	393	15	upper	upper	ADJ
ejpam-21	393	16	/	/	SYM
ejpam-21	393	17	lower	low	ADJ
ejpam-21	393	18	β	β	NOUN
ejpam-21	393	19	-	-	ADJ
ejpam-21	393	20	continuous	continuous	ADJ
ejpam-21	393	21	[	[	X
ejpam-21	393	22	30	30	NUM
ejpam-21	393	23	]	]	PUNCT
ejpam-21	393	24	,	,	PUNCT
ejpam-21	393	25	upper	upper	ADJ
ejpam-21	393	26	/	/	SYM
ejpam-21	393	27	lower	low	ADJ
ejpam-21	393	28	b	b	NOUN
ejpam-21	393	29	-	-	ADJ
ejpam-21	393	30	continuous	continuous	ADJ
ejpam-21	393	31	or	or	CCONJ
ejpam-21	393	32	upper	upper	ADJ
ejpam-21	393	33	/	/	SYM
ejpam-21	393	34	lowerγ	lowerγ	NOUN
ejpam-21	393	35	-	-	PUNCT
ejpam-21	393	36	continuous	continuous	ADJ
ejpam-21	393	37	[	[	X
ejpam-21	393	38	3	3	NUM
ejpam-21	393	39	]	]	NUM
ejpam-21	393	40	)	)	PUNCT
ejpam-21	393	41	.	.	PUNCT
ejpam-21	394	1	a	a	DET
ejpam-21	394	2	topological	topological	ADJ
ejpam-21	394	3	space	space	NOUN
ejpam-21	394	4	(	(	PUNCT
ejpam-21	394	5	y	y	PROPN
ejpam-21	394	6	,	,	PUNCT
ejpam-21	394	7	σ	σ	PROPN
ejpam-21	394	8	)	)	PUNCT
ejpam-21	394	9	is	be	AUX
ejpam-21	394	10	called	call	VERB
ejpam-21	394	11	a	a	DET
ejpam-21	394	12	kc	kc	NOUN
ejpam-21	394	13	-	-	PUNCT
ejpam-21	394	14	space	space	NOUN
ejpam-21	394	15	[	[	X
ejpam-21	394	16	39	39	NUM
ejpam-21	394	17	]	]	PUNCT
ejpam-21	394	18	if	if	SCONJ
ejpam-21	394	19	every	every	DET
ejpam-21	394	20	compact	compact	ADJ
ejpam-21	394	21	set	set	NOUN
ejpam-21	394	22	of	of	ADP
ejpam-21	394	23	y	y	PROPN
ejpam-21	394	24	is	be	AUX
ejpam-21	394	25	closed	closed	ADJ
ejpam-21	394	26	.	.	PUNCT
ejpam-21	395	1	definition	definition	NOUN
ejpam-21	395	2	5.2	5.2	NUM
ejpam-21	395	3	.	.	PUNCT
ejpam-21	396	1	a	a	DET
ejpam-21	396	2	multifunction	multifunction	NOUN
ejpam-21	396	3	is	be	AUX
ejpam-21	396	4	said	say	VERB
ejpam-21	396	5	to	to	PART
ejpam-21	396	6	be	be	AUX
ejpam-21	396	7	m	m	NOUN
ejpam-21	396	8	-	-	PUNCT
ejpam-21	396	9	bounded	bound	VERB
ejpam-21	396	10	at	at	ADP
ejpam-21	396	11	the	the	DET
ejpam-21	396	12	point	point	NOUN
ejpam-21	396	13	p	p	X
ejpam-21	396	14	∈	∈	PROPN
ejpam-21	396	15	x	x	INTJ
ejpam-21	396	16	if	if	SCONJ
ejpam-21	396	17	there	there	PRON
ejpam-21	396	18	exists	exist	VERB
ejpam-21	396	19	u	u	PROPN
ejpam-21	396	20	∈	∈	PROPN
ejpam-21	396	21	mx	mx	NOUN
ejpam-21	396	22	containing	contain	VERB
ejpam-21	396	23	p	p	NOUN
ejpam-21	396	24	and	and	CCONJ
ejpam-21	396	25	a	a	DET
ejpam-21	396	26	compact	compact	ADJ
ejpam-21	396	27	set	set	NOUN
ejpam-21	396	28	c	c	PROPN
ejpam-21	396	29	of	of	ADP
ejpam-21	396	30	y	y	PRON
ejpam-21	396	31	such	such	ADJ
ejpam-21	397	1	that	that	SCONJ
ejpam-21	397	2	f	f	PROPN
ejpam-21	397	3	(	(	PUNCT
ejpam-21	397	4	x	x	X
ejpam-21	397	5	)	)	PUNCT
ejpam-21	397	6	⊂	⊂	PROPN
ejpam-21	397	7	c	c	PROPN
ejpam-21	397	8	for	for	ADP
ejpam-21	397	9	each	each	DET
ejpam-21	397	10	x	x	SYM
ejpam-21	397	11	∈	∈	PROPN
ejpam-21	397	12	u	u	PROPN
ejpam-21	397	13	.	.	PUNCT
ejpam-21	398	1	theorem	theorem	VERB
ejpam-21	398	2	5.1	5.1	NUM
ejpam-21	398	3	.	.	PUNCT
ejpam-21	399	1	let	let	AUX
ejpam-21	399	2	(	(	PUNCT
ejpam-21	399	3	y	y	PROPN
ejpam-21	399	4	,	,	PUNCT
ejpam-21	399	5	σ	σ	PROPN
ejpam-21	399	6	)	)	PUNCT
ejpam-21	399	7	be	be	VERB
ejpam-21	399	8	a	a	DET
ejpam-21	399	9	kc	kc	PROPN
ejpam-21	399	10	space	space	NOUN
ejpam-21	399	11	and	and	CCONJ
ejpam-21	399	12	x	x	ADP
ejpam-21	399	13	a	a	DET
ejpam-21	399	14	nonempty	nonempty	ADV
ejpam-21	399	15	set	set	VERB
ejpam-21	399	16	with	with	ADP
ejpam-21	399	17	two	two	NUM
ejpam-21	399	18	minimal	minimal	ADJ
ejpam-21	399	19	structures	structure	NOUN
ejpam-21	399	20	m1	m1	NOUN
ejpam-21	399	21	x	x	X
ejpam-21	399	22	and	and	CCONJ
ejpam-21	399	23	m2	m2	PROPN
ejpam-21	399	24	x	x	PROPN
ejpam-21	399	25	such	such	ADJ
ejpam-21	399	26	that	that	SCONJ
ejpam-21	399	27	u	u	PROPN
ejpam-21	399	28	∩	∩	NOUN
ejpam-21	399	29	v	v	ADP
ejpam-21	399	30	∈	∈	PROPN
ejpam-21	399	31	m2	m2	PROPN
ejpam-21	399	32	x	x	PUNCT
ejpam-21	399	33	for	for	ADP
ejpam-21	399	34	every	every	DET
ejpam-21	399	35	u	u	PROPN
ejpam-21	399	36	∈	∈	PROPN
ejpam-21	399	37	m1	m1	NOUN
ejpam-21	399	38	x	x	X
ejpam-21	399	39	and	and	CCONJ
ejpam-21	399	40	v	v	ADP
ejpam-21	399	41	∈	∈	NOUN
ejpam-21	399	42	m2	m2	PROPN
ejpam-21	400	1	x	x	INTJ
ejpam-21	400	2	.	.	PUNCT
ejpam-21	401	1	then	then	ADV
ejpam-21	401	2	f	f	X
ejpam-21	401	3	:	:	PUNCT
ejpam-21	401	4	(	(	PUNCT
ejpam-21	401	5	x	x	NOUN
ejpam-21	401	6	,	,	PUNCT
ejpam-21	401	7	m2	m2	PROPN
ejpam-21	401	8	x	x	PROPN
ejpam-21	401	9	)	)	PUNCT
ejpam-21	401	10	→	→	SYM
ejpam-21	401	11	(	(	PUNCT
ejpam-21	401	12	y	y	PROPN
ejpam-21	401	13	,	,	PUNCT
ejpam-21	401	14	σ	σ	PROPN
ejpam-21	401	15	)	)	PUNCT
ejpam-21	401	16	is	be	AUX
ejpam-21	401	17	u.m.c	u.m.c	ADJ
ejpam-21	401	18	.	.	PUNCT
ejpam-21	402	1	(	(	PUNCT
ejpam-21	402	2	resp	resp	NOUN
ejpam-21	402	3	.	.	PUNCT
ejpam-21	403	1	l.m.c	l.m.c	PROPN
ejpam-21	403	2	.	.	PUNCT
ejpam-21	403	3	)	)	PUNCT
ejpam-21	404	1	at	at	ADP
ejpam-21	404	2	p	p	PROPN
ejpam-21	404	3	∈	∈	PROPN
ejpam-21	404	4	x	x	SYM
ejpam-21	404	5	if	if	SCONJ
ejpam-21	404	6	the	the	DET
ejpam-21	404	7	following	follow	VERB
ejpam-21	404	8	conditions	condition	NOUN
ejpam-21	404	9	satisfy	satisfy	VERB
ejpam-21	404	10	:	:	PUNCT
ejpam-21	404	11	(	(	PUNCT
ejpam-21	404	12	1	1	X
ejpam-21	404	13	)	)	PUNCT
ejpam-21	404	14	f	f	NOUN
ejpam-21	404	15	:	:	PUNCT
ejpam-21	404	16	(	(	PUNCT
ejpam-21	404	17	x	x	X
ejpam-21	404	18	,	,	PUNCT
ejpam-21	404	19	m1	m1	PROPN
ejpam-21	404	20	x	x	SYM
ejpam-21	404	21	)	)	PUNCT
ejpam-21	404	22	→	→	SYM
ejpam-21	404	23	(	(	PUNCT
ejpam-21	404	24	y	y	PROPN
ejpam-21	404	25	,	,	PUNCT
ejpam-21	404	26	σ	σ	PROPN
ejpam-21	404	27	)	)	PUNCT
ejpam-21	404	28	is	be	AUX
ejpam-21	404	29	m	m	NOUN
ejpam-21	404	30	-	-	PUNCT
ejpam-21	404	31	bounded	bound	VERB
ejpam-21	404	32	at	at	ADP
ejpam-21	404	33	p	p	PROPN
ejpam-21	404	34	∈	∈	PROPN
ejpam-21	404	35	x	x	X
ejpam-21	404	36	,	,	PUNCT
ejpam-21	404	37	(	(	PUNCT
ejpam-21	404	38	2	2	X
ejpam-21	404	39	)	)	PUNCT
ejpam-21	404	40	f	f	NOUN
ejpam-21	404	41	:	:	PUNCT
ejpam-21	404	42	(	(	PUNCT
ejpam-21	404	43	x	x	X
ejpam-21	404	44	,	,	PUNCT
ejpam-21	404	45	m2	m2	PROPN
ejpam-21	404	46	x	x	PROPN
ejpam-21	404	47	)	)	PUNCT
ejpam-21	404	48	→	→	SYM
ejpam-21	404	49	(	(	PUNCT
ejpam-21	404	50	y	y	PROPN
ejpam-21	404	51	,	,	PUNCT
ejpam-21	404	52	σ	σ	PROPN
ejpam-21	404	53	)	)	PUNCT
ejpam-21	404	54	is	be	AUX
ejpam-21	404	55	u.c.m.c	u.c.m.c	PROPN
ejpam-21	404	56	.	.	PUNCT
ejpam-21	405	1	(	(	PUNCT
ejpam-21	405	2	resp	resp	NOUN
ejpam-21	405	3	.	.	PUNCT
ejpam-21	406	1	l.c.m.c	l.c.m.c	PROPN
ejpam-21	406	2	.	.	PUNCT
ejpam-21	406	3	)	)	PUNCT
ejpam-21	407	1	at	at	ADP
ejpam-21	407	2	p	p	PROPN
ejpam-21	407	3	∈	∈	PROPN
ejpam-21	407	4	x	x	X
ejpam-21	407	5	.	.	PUNCT
ejpam-21	408	1	proof	proof	NOUN
ejpam-21	408	2	.	.	PUNCT
ejpam-21	409	1	we	we	PRON
ejpam-21	409	2	prove	prove	VERB
ejpam-21	409	3	only	only	ADV
ejpam-21	409	4	the	the	DET
ejpam-21	409	5	first	first	ADJ
ejpam-21	409	6	case	case	NOUN
ejpam-21	409	7	,	,	PUNCT
ejpam-21	409	8	the	the	DET
ejpam-21	409	9	proof	proof	NOUN
ejpam-21	409	10	of	of	ADP
ejpam-21	409	11	the	the	DET
ejpam-21	409	12	second	second	ADJ
ejpam-21	409	13	being	be	AUX
ejpam-21	409	14	entirely	entirely	ADV
ejpam-21	409	15	analogous	analogous	ADJ
ejpam-21	409	16	.	.	PUNCT
ejpam-21	410	1	let	let	VERB
ejpam-21	410	2	u	u	PRON
ejpam-21	410	3	∈	∈	PROPN
ejpam-21	410	4	m1	m1	PROPN
ejpam-21	410	5	x	x	PUNCT
ejpam-21	410	6	containing	contain	VERB
ejpam-21	410	7	p	p	NOUN
ejpam-21	410	8	and	and	CCONJ
ejpam-21	410	9	c	c	PROPN
ejpam-21	410	10	be	be	AUX
ejpam-21	410	11	a	a	DET
ejpam-21	410	12	compact	compact	ADJ
ejpam-21	410	13	set	set	NOUN
ejpam-21	410	14	of	of	ADP
ejpam-21	410	15	y	y	PRON
ejpam-21	410	16	such	such	ADJ
ejpam-21	410	17	that	that	SCONJ
ejpam-21	410	18	f	f	PROPN
ejpam-21	410	19	(	(	PUNCT
ejpam-21	410	20	x	x	X
ejpam-21	410	21	)	)	PUNCT
ejpam-21	410	22	⊂	⊂	PROPN
ejpam-21	410	23	c	c	PROPN
ejpam-21	410	24	for	for	ADP
ejpam-21	410	25	each	each	DET
ejpam-21	410	26	x	x	SYM
ejpam-21	410	27	∈	∈	PROPN
ejpam-21	410	28	u	u	NOUN
ejpam-21	410	29	.	.	PUNCT
ejpam-21	411	1	let	let	VERB
ejpam-21	411	2	v	v	PART
ejpam-21	411	3	be	be	AUX
ejpam-21	411	4	any	any	DET
ejpam-21	411	5	open	open	ADJ
ejpam-21	411	6	set	set	NOUN
ejpam-21	411	7	of	of	ADP
ejpam-21	411	8	y	y	PRON
ejpam-21	411	9	such	such	ADJ
ejpam-21	411	10	that	that	SCONJ
ejpam-21	411	11	f	f	PROPN
ejpam-21	411	12	(	(	PUNCT
ejpam-21	411	13	p	p	X
ejpam-21	411	14	)	)	PUNCT
ejpam-21	411	15	⊂	⊂	PROPN
ejpam-21	411	16	v	v	X
ejpam-21	411	17	.	.	PUNCT
ejpam-21	412	1	put	put	VERB
ejpam-21	412	2	g	g	NOUN
ejpam-21	412	3	=	=	NOUN
ejpam-21	412	4	v	v	NOUN
ejpam-21	412	5	∪	∪	X
ejpam-21	412	6	(	(	PUNCT
ejpam-21	412	7	y	y	PROPN
ejpam-21	412	8	−	−	PROPN
ejpam-21	412	9	c	c	NOUN
ejpam-21	412	10	)	)	PUNCT
ejpam-21	412	11	.	.	PUNCT
ejpam-21	413	1	then	then	ADV
ejpam-21	413	2	g	g	PROPN
ejpam-21	413	3	is	be	AUX
ejpam-21	413	4	open	open	ADJ
ejpam-21	413	5	and	and	CCONJ
ejpam-21	413	6	y	y	PROPN
ejpam-21	413	7	−g	−g	NOUN
ejpam-21	413	8	is	be	AUX
ejpam-21	413	9	compact	compact	ADJ
ejpam-21	413	10	.	.	PUNCT
ejpam-21	414	1	by	by	ADP
ejpam-21	414	2	the	the	DET
ejpam-21	414	3	condition	condition	NOUN
ejpam-21	414	4	(	(	PUNCT
ejpam-21	414	5	2	2	NUM
ejpam-21	414	6	)	)	PUNCT
ejpam-21	414	7	,	,	PUNCT
ejpam-21	414	8	there	there	PRON
ejpam-21	414	9	exists	exist	VERB
ejpam-21	414	10	w	w	PROPN
ejpam-21	414	11	∈	∈	PROPN
ejpam-21	414	12	m2	m2	PROPN
ejpam-21	414	13	x	x	X
ejpam-21	414	14	containing	contain	VERB
ejpam-21	414	15	p	p	NOUN
ejpam-21	414	16	such	such	ADJ
ejpam-21	414	17	that	that	SCONJ
ejpam-21	414	18	f	f	PROPN
ejpam-21	414	19	(	(	PUNCT
ejpam-21	414	20	x	x	X
ejpam-21	414	21	)	)	PUNCT
ejpam-21	414	22	⊂	⊂	PROPN
ejpam-21	414	23	g	g	PROPN
ejpam-21	414	24	for	for	ADP
ejpam-21	414	25	every	every	DET
ejpam-21	414	26	x	x	SYM
ejpam-21	414	27	∈	∈	PROPN
ejpam-21	414	28	w	w	PROPN
ejpam-21	414	29	.	.	PUNCT
ejpam-21	415	1	put	put	VERB
ejpam-21	415	2	h	h	NOUN
ejpam-21	416	1	=	=	SYM
ejpam-21	416	2	w	w	PROPN
ejpam-21	416	3	∩	∩	ADJ
ejpam-21	416	4	u	u	NOUN
ejpam-21	416	5	,	,	PUNCT
ejpam-21	416	6	then	then	ADV
ejpam-21	416	7	h	h	PROPN
ejpam-21	416	8	∈	∈	PROPN
ejpam-21	416	9	m2	m2	PROPN
ejpam-21	416	10	x	x	X
ejpam-21	416	11	containing	contain	VERB
ejpam-21	416	12	p	p	NOUN
ejpam-21	416	13	and	and	CCONJ
ejpam-21	416	14	f	f	PROPN
ejpam-21	416	15	(	(	PUNCT
ejpam-21	416	16	x	x	X
ejpam-21	416	17	)	)	PUNCT
ejpam-21	416	18	⊂	⊂	PROPN
ejpam-21	416	19	g	g	PROPN
ejpam-21	416	20	∩	∩	PROPN
ejpam-21	416	21	c	c	PROPN
ejpam-21	416	22	for	for	ADP
ejpam-21	416	23	any	any	DET
ejpam-21	416	24	x	x	SYM
ejpam-21	416	25	∈	∈	PROPN
ejpam-21	416	26	h	h	NOUN
ejpam-21	416	27	.	.	PUNCT
ejpam-21	417	1	then	then	ADV
ejpam-21	417	2	f	f	X
ejpam-21	417	3	(	(	PUNCT
ejpam-21	417	4	x	x	X
ejpam-21	417	5	)	)	PUNCT
ejpam-21	417	6	⊂	⊂	PROPN
ejpam-21	417	7	v	v	NOUN
ejpam-21	417	8	for	for	ADP
ejpam-21	417	9	any	any	DET
ejpam-21	417	10	x	x	SYM
ejpam-21	417	11	∈	∈	PROPN
ejpam-21	417	12	h	h	NOUN
ejpam-21	417	13	.	.	PUNCT
ejpam-21	418	1	therefore	therefore	ADV
ejpam-21	418	2	,	,	PUNCT
ejpam-21	418	3	f	f	X
ejpam-21	418	4	:	:	PUNCT
ejpam-21	418	5	(	(	PUNCT
ejpam-21	418	6	x	x	NOUN
ejpam-21	418	7	,	,	PUNCT
ejpam-21	418	8	m2	m2	PROPN
ejpam-21	418	9	x	x	PROPN
ejpam-21	418	10	)	)	PUNCT
ejpam-21	418	11	→	→	SYM
ejpam-21	418	12	(	(	PUNCT
ejpam-21	418	13	y	y	PROPN
ejpam-21	418	14	,	,	PUNCT
ejpam-21	418	15	σ	σ	PROPN
ejpam-21	418	16	)	)	PUNCT
ejpam-21	418	17	is	be	AUX
ejpam-21	418	18	u.m.c	u.m.c	ADJ
ejpam-21	418	19	.	.	PUNCT
ejpam-21	419	1	at	at	ADP
ejpam-21	419	2	p	p	PROPN
ejpam-21	419	3	∈	∈	PROPN
ejpam-21	419	4	x	x	X
ejpam-21	419	5	.	.	PUNCT
ejpam-21	420	1	remark	remark	PROPN
ejpam-21	420	2	5.2	5.2	NUM
ejpam-21	420	3	.	.	PUNCT
ejpam-21	421	1	if	if	SCONJ
ejpam-21	421	2	m1	m1	PROPN
ejpam-21	421	3	x	x	PUNCT
ejpam-21	421	4	=	=	SYM
ejpam-21	421	5	m2	m2	PROPN
ejpam-21	421	6	x	x	PROPN
ejpam-21	421	7	=	=	SYM
ejpam-21	421	8	τ	τ	PROPN
ejpam-21	421	9	,	,	PUNCT
ejpam-21	421	10	then	then	ADV
ejpam-21	421	11	by	by	ADP
ejpam-21	421	12	theorem	theorem	NOUN
ejpam-21	421	13	5.1	5.1	NUM
ejpam-21	421	14	we	we	PRON
ejpam-21	421	15	obtain	obtain	VERB
ejpam-21	421	16	the	the	DET
ejpam-21	421	17	result	result	NOUN
ejpam-21	421	18	established	establish	VERB
ejpam-21	421	19	in	in	ADP
ejpam-21	421	20	proposition	proposition	NOUN
ejpam-21	421	21	5	5	NUM
ejpam-21	421	22	of	of	ADP
ejpam-21	421	23	[	[	X
ejpam-21	421	24	11	11	NUM
ejpam-21	421	25	]	]	PUNCT
ejpam-21	421	26	.	.	PUNCT
ejpam-21	422	1	definition	definition	NOUN
ejpam-21	422	2	5.3	5.3	NUM
ejpam-21	422	3	.	.	PUNCT
ejpam-21	423	1	an	an	DET
ejpam-21	423	2	m	m	NOUN
ejpam-21	423	3	-	-	NOUN
ejpam-21	423	4	space	space	NOUN
ejpam-21	423	5	(	(	PUNCT
ejpam-21	423	6	x	x	NOUN
ejpam-21	423	7	,	,	PUNCT
ejpam-21	423	8	mx	mx	NOUN
ejpam-21	423	9	)	)	PUNCT
ejpam-21	423	10	is	be	AUX
ejpam-21	423	11	said	say	VERB
ejpam-21	423	12	to	to	PART
ejpam-21	423	13	be	be	AUX
ejpam-21	423	14	m	m	ADJ
ejpam-21	423	15	-	-	ADJ
ejpam-21	423	16	saturated	saturate	VERB
ejpam-21	423	17	if	if	SCONJ
ejpam-21	423	18	for	for	SCONJ
ejpam-21	423	19	any	any	DET
ejpam-21	423	20	x	x	SYM
ejpam-21	423	21	∈	∈	PROPN
ejpam-21	423	22	x	x	X
ejpam-21	423	23	the	the	DET
ejpam-21	423	24	intersection	intersection	NOUN
ejpam-21	423	25	of	of	ADP
ejpam-21	423	26	all	all	DET
ejpam-21	423	27	mx	mx	PROPN
ejpam-21	423	28	-open	-open	PROPN
ejpam-21	423	29	sets	set	NOUN
ejpam-21	423	30	containing	contain	VERB
ejpam-21	423	31	x	x	VERB
ejpam-21	423	32	is	be	AUX
ejpam-21	423	33	mx	mx	PROPN
ejpam-21	423	34	-open	-open	NOUN
ejpam-21	423	35	.	.	PUNCT
ejpam-21	424	1	theorem	theorem	VERB
ejpam-21	424	2	5.2	5.2	NUM
ejpam-21	424	3	.	.	PUNCT
ejpam-21	425	1	let	let	AUX
ejpam-21	425	2	(	(	PUNCT
ejpam-21	425	3	x	x	NOUN
ejpam-21	425	4	,	,	PUNCT
ejpam-21	425	5	mx	mx	NOUN
ejpam-21	425	6	)	)	PUNCT
ejpam-21	425	7	be	be	AUX
ejpam-21	425	8	an	an	DET
ejpam-21	425	9	m	m	ADV
ejpam-21	425	10	-	-	PUNCT
ejpam-21	425	11	saturated	saturate	VERB
ejpam-21	425	12	m	m	NOUN
ejpam-21	425	13	-	-	NOUN
ejpam-21	425	14	space	space	NOUN
ejpam-21	425	15	and	and	CCONJ
ejpam-21	425	16	(	(	PUNCT
ejpam-21	425	17	y	y	PROPN
ejpam-21	425	18	,	,	PUNCT
ejpam-21	425	19	σ	σ	PROPN
ejpam-21	425	20	)	)	PUNCT
ejpam-21	425	21	a	a	DET
ejpam-21	425	22	t1	t1	NOUN
ejpam-21	425	23	-	-	PUNCT
ejpam-21	425	24	space	space	NOUN
ejpam-21	425	25	.	.	PUNCT
ejpam-21	426	1	if	if	SCONJ
ejpam-21	426	2	is	be	AUX
ejpam-21	426	3	u.c.m.c	u.c.m.c	PROPN
ejpam-21	426	4	.	.	PROPN
ejpam-21	426	5	,	,	PUNCT
ejpam-21	426	6	then	then	ADV
ejpam-21	426	7	f	f	PROPN
ejpam-21	426	8	is	be	AUX
ejpam-21	426	9	u.m.c	u.m.c	ADJ
ejpam-21	426	10	.	.	PUNCT
ejpam-21	427	1	t.noiri	t.noiri	ADV
ejpam-21	427	2	,	,	PUNCT
ejpam-21	427	3	v.popa	v.popa	NOUN
ejpam-21	427	4	/	/	SYM
ejpam-21	427	5	eur	eur	PROPN
ejpam-21	427	6	.	.	PUNCT
ejpam-21	428	1	j.	j.	PROPN
ejpam-21	428	2	pure	pure	PROPN
ejpam-21	428	3	appl	appl	PROPN
ejpam-21	428	4	.	.	PROPN
ejpam-21	428	5	math	math	PROPN
ejpam-21	428	6	,	,	PUNCT
ejpam-21	428	7	1	1	NUM
ejpam-21	428	8	(	(	PUNCT
ejpam-21	428	9	2008	2008	NUM
ejpam-21	428	10	)	)	PUNCT
ejpam-21	428	11	,	,	PUNCT
ejpam-21	428	12	(	(	PUNCT
ejpam-21	428	13	82	82	NUM
ejpam-21	428	14	-	-	SYM
ejpam-21	428	15	98	98	NUM
ejpam-21	428	16	)	)	PUNCT
ejpam-21	428	17	93	93	NUM
ejpam-21	428	18	proof	proof	NOUN
ejpam-21	428	19	.	.	PUNCT
ejpam-21	428	20	suppose	suppose	VERB
ejpam-21	428	21	that	that	SCONJ
ejpam-21	428	22	f	f	PROPN
ejpam-21	428	23	is	be	AUX
ejpam-21	428	24	not	not	PART
ejpam-21	428	25	u.m.c	u.m.c	ADJ
ejpam-21	428	26	.	.	PUNCT
ejpam-21	429	1	at	at	ADP
ejpam-21	429	2	some	some	DET
ejpam-21	429	3	point	point	NOUN
ejpam-21	429	4	x0	x0	PROPN
ejpam-21	429	5	∈	∈	PROPN
ejpam-21	429	6	x	x	X
ejpam-21	429	7	.	.	PUNCT
ejpam-21	430	1	there	there	PRON
ejpam-21	430	2	exists	exist	VERB
ejpam-21	430	3	an	an	DET
ejpam-21	430	4	open	open	ADJ
ejpam-21	430	5	set	set	NOUN
ejpam-21	430	6	v	v	NOUN
ejpam-21	430	7	of	of	ADP
ejpam-21	430	8	y	y	PRON
ejpam-21	430	9	such	such	ADJ
ejpam-21	430	10	that	that	SCONJ
ejpam-21	430	11	f	f	PROPN
ejpam-21	430	12	(	(	PUNCT
ejpam-21	430	13	x0	x0	PROPN
ejpam-21	430	14	)	)	PUNCT
ejpam-21	430	15	⊂	⊂	PROPN
ejpam-21	430	16	v	v	PROPN
ejpam-21	430	17	and	and	CCONJ
ejpam-21	430	18	f	f	PROPN
ejpam-21	430	19	(	(	PUNCT
ejpam-21	430	20	u	u	NOUN
ejpam-21	430	21	)	)	PUNCT
ejpam-21	430	22	∩	∩	NOUN
ejpam-21	430	23	(	(	PUNCT
ejpam-21	430	24	y	y	PROPN
ejpam-21	430	25	−	−	PROPN
ejpam-21	430	26	v	v	NOUN
ejpam-21	430	27	)	)	PUNCT
ejpam-21	430	28	6=	6=	ADP
ejpam-21	430	29	∅	∅	NOUN
ejpam-21	430	30	for	for	ADP
ejpam-21	430	31	every	every	DET
ejpam-21	430	32	u	u	PROPN
ejpam-21	430	33	∈	∈	PROPN
ejpam-21	430	34	mx	mx	NOUN
ejpam-21	430	35	containing	contain	VERB
ejpam-21	430	36	x0	x0	PROPN
ejpam-21	430	37	.	.	PUNCT
ejpam-21	431	1	let	let	VERB
ejpam-21	431	2	u0	u0	ADJ
ejpam-21	431	3	be	be	AUX
ejpam-21	431	4	the	the	DET
ejpam-21	431	5	intersection	intersection	NOUN
ejpam-21	431	6	of	of	ADP
ejpam-21	431	7	all	all	DET
ejpam-21	431	8	mx	mx	PROPN
ejpam-21	431	9	-open	-open	PROPN
ejpam-21	431	10	sets	set	NOUN
ejpam-21	431	11	containing	contain	VERB
ejpam-21	431	12	x0	x0	PROPN
ejpam-21	431	13	.	.	PUNCT
ejpam-21	432	1	then	then	ADV
ejpam-21	432	2	u0	u0	PROPN
ejpam-21	432	3	∈	∈	PROPN
ejpam-21	432	4	mx	mx	PROPN
ejpam-21	432	5	and	and	CCONJ
ejpam-21	432	6	there	there	PRON
ejpam-21	432	7	exists	exist	VERB
ejpam-21	432	8	z1	z1	PROPN
ejpam-21	432	9	∈	∈	PROPN
ejpam-21	432	10	u0	u0	NOUN
ejpam-21	432	11	such	such	ADJ
ejpam-21	432	12	that	that	SCONJ
ejpam-21	432	13	f	f	PROPN
ejpam-21	432	14	(	(	PUNCT
ejpam-21	432	15	z1	z1	PROPN
ejpam-21	432	16	)	)	PUNCT
ejpam-21	432	17	∩	∩	NOUN
ejpam-21	432	18	(	(	PUNCT
ejpam-21	432	19	y	y	PROPN
ejpam-21	432	20	−	−	PROPN
ejpam-21	432	21	v	v	NOUN
ejpam-21	432	22	)	)	PUNCT
ejpam-21	432	23	6=	6=	ADP
ejpam-21	432	24	∅.	∅.	VERB
ejpam-21	432	25	hence	hence	ADV
ejpam-21	432	26	there	there	PRON
ejpam-21	432	27	exists	exist	VERB
ejpam-21	432	28	y	y	PROPN
ejpam-21	432	29	∈	∈	PROPN
ejpam-21	432	30	f	f	PROPN
ejpam-21	432	31	(	(	PUNCT
ejpam-21	432	32	z1	z1	PROPN
ejpam-21	432	33	)	)	PUNCT
ejpam-21	432	34	∩	∩	NOUN
ejpam-21	432	35	(	(	PUNCT
ejpam-21	432	36	y	y	PROPN
ejpam-21	432	37	−	−	PROPN
ejpam-21	432	38	v	v	NOUN
ejpam-21	432	39	)	)	PUNCT
ejpam-21	432	40	.	.	PUNCT
ejpam-21	433	1	the	the	DET
ejpam-21	433	2	set	set	NOUN
ejpam-21	433	3	y	y	PROPN
ejpam-21	433	4	−	−	PROPN
ejpam-21	433	5	{	{	PUNCT
ejpam-21	433	6	y	y	NOUN
ejpam-21	433	7	}	}	PUNCT
ejpam-21	433	8	is	be	AUX
ejpam-21	433	9	an	an	DET
ejpam-21	433	10	open	open	ADJ
ejpam-21	433	11	set	set	NOUN
ejpam-21	433	12	with	with	ADP
ejpam-21	433	13	compact	compact	ADJ
ejpam-21	433	14	complement	complement	NOUN
ejpam-21	433	15	.	.	PUNCT
ejpam-21	434	1	since	since	SCONJ
ejpam-21	434	2	f	f	PROPN
ejpam-21	434	3	(	(	PUNCT
ejpam-21	434	4	x0	x0	PROPN
ejpam-21	434	5	)	)	PUNCT
ejpam-21	435	1	⊂	⊂	PROPN
ejpam-21	435	2	y	y	PROPN
ejpam-21	435	3	−{y	−{y	PROPN
ejpam-21	435	4	}	}	PUNCT
ejpam-21	435	5	and	and	CCONJ
ejpam-21	435	6	f	f	PROPN
ejpam-21	435	7	is	be	AUX
ejpam-21	435	8	u.c.m.c	u.c.m.c	PROPN
ejpam-21	435	9	.	.	PUNCT
ejpam-21	436	1	at	at	ADP
ejpam-21	436	2	x0	x0	PROPN
ejpam-21	436	3	,	,	PUNCT
ejpam-21	436	4	there	there	PRON
ejpam-21	436	5	exists	exist	VERB
ejpam-21	436	6	g	g	PROPN
ejpam-21	436	7	∈	∈	PROPN
ejpam-21	436	8	mx	mx	NOUN
ejpam-21	436	9	containing	contain	VERB
ejpam-21	436	10	x0	x0	PROPN
ejpam-21	436	11	such	such	ADJ
ejpam-21	436	12	that	that	SCONJ
ejpam-21	436	13	for	for	ADP
ejpam-21	436	14	any	any	DET
ejpam-21	436	15	x	x	SYM
ejpam-21	436	16	∈	∈	PROPN
ejpam-21	436	17	g	g	NOUN
ejpam-21	436	18	we	we	PRON
ejpam-21	436	19	have	have	VERB
ejpam-21	436	20	f	f	PROPN
ejpam-21	436	21	(	(	PUNCT
ejpam-21	436	22	x	x	X
ejpam-21	436	23	)	)	PUNCT
ejpam-21	436	24	⊂	⊂	PROPN
ejpam-21	437	1	y	y	PROPN
ejpam-21	437	2	−	−	PROPN
ejpam-21	437	3	{	{	PUNCT
ejpam-21	437	4	y	y	NOUN
ejpam-21	437	5	}	}	PUNCT
ejpam-21	437	6	.	.	PUNCT
ejpam-21	438	1	this	this	PRON
ejpam-21	438	2	is	be	AUX
ejpam-21	438	3	a	a	DET
ejpam-21	438	4	contradiction	contradiction	NOUN
ejpam-21	438	5	.	.	PUNCT
ejpam-21	439	1	since	since	SCONJ
ejpam-21	439	2	u0	u0	PROPN
ejpam-21	439	3	⊂	⊂	PROPN
ejpam-21	439	4	g	g	NOUN
ejpam-21	439	5	,	,	PUNCT
ejpam-21	439	6	z1	z1	PROPN
ejpam-21	439	7	∈	∈	PROPN
ejpam-21	439	8	g	g	PROPN
ejpam-21	439	9	and	and	CCONJ
ejpam-21	439	10	f	f	PROPN
ejpam-21	439	11	(	(	PUNCT
ejpam-21	439	12	z1	z1	PROPN
ejpam-21	439	13	)	)	PUNCT
ejpam-21	439	14	⊂	⊂	PROPN
ejpam-21	439	15	y	y	PROPN
ejpam-21	439	16	−	−	PROPN
ejpam-21	439	17	{	{	PUNCT
ejpam-21	439	18	y	y	NOUN
ejpam-21	439	19	}	}	PUNCT
ejpam-21	439	20	.	.	PUNCT
ejpam-21	440	1	this	this	PRON
ejpam-21	440	2	contradicts	contradict	VERB
ejpam-21	440	3	that	that	SCONJ
ejpam-21	440	4	y	y	PROPN
ejpam-21	440	5	∈	∈	PROPN
ejpam-21	440	6	f	f	PROPN
ejpam-21	440	7	(	(	PUNCT
ejpam-21	440	8	z1	z1	PROPN
ejpam-21	440	9	)	)	PUNCT
ejpam-21	440	10	.	.	PUNCT
ejpam-21	441	1	remark	remark	VERB
ejpam-21	441	2	5.3	5.3	NUM
ejpam-21	441	3	.	.	PUNCT
ejpam-21	442	1	if	if	SCONJ
ejpam-21	442	2	mx	mx	PROPN
ejpam-21	442	3	=	=	SYM
ejpam-21	442	4	τ	τ	PROPN
ejpam-21	442	5	,	,	PUNCT
ejpam-21	442	6	then	then	ADV
ejpam-21	442	7	by	by	ADP
ejpam-21	442	8	theorem	theorem	NOUN
ejpam-21	442	9	5.2	5.2	NUM
ejpam-21	442	10	we	we	PRON
ejpam-21	442	11	obtain	obtain	VERB
ejpam-21	442	12	the	the	DET
ejpam-21	442	13	result	result	NOUN
ejpam-21	442	14	established	establish	VERB
ejpam-21	442	15	in	in	ADP
ejpam-21	442	16	proposition	proposition	NOUN
ejpam-21	442	17	8	8	NUM
ejpam-21	442	18	of	of	ADP
ejpam-21	442	19	[	[	X
ejpam-21	442	20	11	11	NUM
ejpam-21	442	21	]	]	PUNCT
ejpam-21	442	22	.	.	PUNCT
ejpam-21	443	1	theorem	theorem	VERB
ejpam-21	443	2	5.3	5.3	NUM
ejpam-21	443	3	.	.	PUNCT
ejpam-21	444	1	let	let	AUX
ejpam-21	444	2	(	(	PUNCT
ejpam-21	444	3	x	x	NOUN
ejpam-21	444	4	,	,	PUNCT
ejpam-21	444	5	mx	mx	NOUN
ejpam-21	444	6	)	)	PUNCT
ejpam-21	444	7	be	be	AUX
ejpam-21	444	8	an	an	DET
ejpam-21	444	9	m	m	ADV
ejpam-21	444	10	-	-	PUNCT
ejpam-21	444	11	saturated	saturate	VERB
ejpam-21	444	12	m	m	NOUN
ejpam-21	444	13	-	-	NOUN
ejpam-21	444	14	space	space	NOUN
ejpam-21	444	15	and	and	CCONJ
ejpam-21	444	16	(	(	PUNCT
ejpam-21	444	17	y	y	PROPN
ejpam-21	444	18	,	,	PUNCT
ejpam-21	444	19	σ	σ	PROPN
ejpam-21	444	20	)	)	PUNCT
ejpam-21	444	21	a	a	DET
ejpam-21	444	22	locally	locally	ADV
ejpam-21	444	23	compact	compact	ADJ
ejpam-21	444	24	hausdorff	hausdorff	NOUN
ejpam-21	444	25	space	space	NOUN
ejpam-21	444	26	.	.	PUNCT
ejpam-21	445	1	if	if	SCONJ
ejpam-21	445	2	is	be	AUX
ejpam-21	445	3	an	an	DET
ejpam-21	445	4	u.c.m.c	u.c.m.c	PROPN
ejpam-21	445	5	.	.	PROPN
ejpam-21	445	6	and	and	CCONJ
ejpam-21	445	7	closed	close	VERB
ejpam-21	445	8	valued	value	VERB
ejpam-21	445	9	multifunction	multifunction	NOUN
ejpam-21	445	10	,	,	PUNCT
ejpam-21	445	11	then	then	ADV
ejpam-21	445	12	f	f	PROPN
ejpam-21	445	13	is	be	AUX
ejpam-21	445	14	u.m.c	u.m.c	ADJ
ejpam-21	445	15	.	.	PUNCT
ejpam-21	446	1	proof	proof	NOUN
ejpam-21	446	2	.	.	PUNCT
ejpam-21	447	1	suppose	suppose	VERB
ejpam-21	447	2	that	that	SCONJ
ejpam-21	447	3	f	f	PROPN
ejpam-21	447	4	is	be	AUX
ejpam-21	447	5	not	not	PART
ejpam-21	447	6	u.m.c	u.m.c	ADJ
ejpam-21	447	7	.	.	PUNCT
ejpam-21	448	1	at	at	ADP
ejpam-21	448	2	x0	x0	PROPN
ejpam-21	448	3	∈	∈	PROPN
ejpam-21	448	4	x	x	X
ejpam-21	448	5	.	.	PUNCT
ejpam-21	449	1	then	then	ADV
ejpam-21	449	2	,	,	PUNCT
ejpam-21	449	3	there	there	PRON
ejpam-21	449	4	exists	exist	VERB
ejpam-21	449	5	an	an	DET
ejpam-21	449	6	open	open	ADJ
ejpam-21	449	7	set	set	NOUN
ejpam-21	449	8	v	v	NOUN
ejpam-21	449	9	of	of	ADP
ejpam-21	449	10	y	y	PRON
ejpam-21	449	11	such	such	ADJ
ejpam-21	449	12	that	that	SCONJ
ejpam-21	449	13	f	f	PROPN
ejpam-21	449	14	(	(	PUNCT
ejpam-21	449	15	x0	x0	PROPN
ejpam-21	449	16	)	)	PUNCT
ejpam-21	449	17	⊂	⊂	PROPN
ejpam-21	449	18	v	v	PROPN
ejpam-21	449	19	and	and	CCONJ
ejpam-21	449	20	f	f	PROPN
ejpam-21	449	21	(	(	PUNCT
ejpam-21	449	22	u	u	NOUN
ejpam-21	449	23	)	)	PUNCT
ejpam-21	449	24	∩	∩	NOUN
ejpam-21	449	25	(	(	PUNCT
ejpam-21	449	26	y	y	PROPN
ejpam-21	449	27	−	−	PROPN
ejpam-21	449	28	v	v	NOUN
ejpam-21	449	29	)	)	PUNCT
ejpam-21	449	30	6=	6=	ADP
ejpam-21	449	31	∅	∅	NOUN
ejpam-21	449	32	for	for	ADP
ejpam-21	449	33	every	every	DET
ejpam-21	449	34	u	u	PROPN
ejpam-21	449	35	∈	∈	PROPN
ejpam-21	449	36	mx	mx	NOUN
ejpam-21	449	37	containing	contain	VERB
ejpam-21	449	38	x0	x0	PROPN
ejpam-21	449	39	.	.	PUNCT
ejpam-21	450	1	let	let	VERB
ejpam-21	450	2	u0	u0	ADJ
ejpam-21	450	3	be	be	AUX
ejpam-21	450	4	the	the	DET
ejpam-21	450	5	intersection	intersection	NOUN
ejpam-21	450	6	of	of	ADP
ejpam-21	450	7	all	all	DET
ejpam-21	450	8	mx	mx	PROPN
ejpam-21	450	9	-open	-open	PROPN
ejpam-21	450	10	sets	set	NOUN
ejpam-21	450	11	containing	contain	VERB
ejpam-21	450	12	x0	x0	PROPN
ejpam-21	450	13	.	.	PUNCT
ejpam-21	451	1	then	then	ADV
ejpam-21	451	2	u0	u0	PROPN
ejpam-21	451	3	∈	∈	PROPN
ejpam-21	451	4	mx	mx	PROPN
ejpam-21	451	5	and	and	CCONJ
ejpam-21	451	6	there	there	PRON
ejpam-21	451	7	exists	exist	VERB
ejpam-21	451	8	z1	z1	PROPN
ejpam-21	451	9	∈	∈	PROPN
ejpam-21	451	10	u0	u0	NOUN
ejpam-21	451	11	such	such	ADJ
ejpam-21	451	12	that	that	SCONJ
ejpam-21	451	13	f	f	PROPN
ejpam-21	451	14	(	(	PUNCT
ejpam-21	451	15	z1	z1	PROPN
ejpam-21	451	16	)	)	PUNCT
ejpam-21	451	17	∩	∩	NOUN
ejpam-21	451	18	(	(	PUNCT
ejpam-21	451	19	y	y	PROPN
ejpam-21	451	20	−	−	PROPN
ejpam-21	451	21	v	v	NOUN
ejpam-21	451	22	)	)	PUNCT
ejpam-21	451	23	6=	6=	ADP
ejpam-21	451	24	∅.	∅.	VERB
ejpam-21	451	25	hence	hence	ADV
ejpam-21	451	26	there	there	PRON
ejpam-21	451	27	exists	exist	VERB
ejpam-21	451	28	y	y	PROPN
ejpam-21	451	29	∈	∈	PROPN
ejpam-21	451	30	f	f	PROPN
ejpam-21	451	31	(	(	PUNCT
ejpam-21	451	32	z1	z1	PROPN
ejpam-21	451	33	)	)	PUNCT
ejpam-21	451	34	∩	∩	NOUN
ejpam-21	451	35	(	(	PUNCT
ejpam-21	451	36	y	y	PROPN
ejpam-21	451	37	−	−	PROPN
ejpam-21	451	38	v	v	NOUN
ejpam-21	451	39	)	)	PUNCT
ejpam-21	451	40	.	.	PUNCT
ejpam-21	452	1	since	since	SCONJ
ejpam-21	452	2	(	(	PUNCT
ejpam-21	452	3	y	y	PROPN
ejpam-21	452	4	,	,	PUNCT
ejpam-21	452	5	σ	σ	PROPN
ejpam-21	452	6	)	)	PUNCT
ejpam-21	452	7	is	be	AUX
ejpam-21	452	8	locally	locally	ADV
ejpam-21	452	9	compact	compact	ADJ
ejpam-21	452	10	hausdorff	hausdorff	NOUN
ejpam-21	452	11	,	,	PUNCT
ejpam-21	452	12	(	(	PUNCT
ejpam-21	452	13	y	y	PROPN
ejpam-21	452	14	,	,	PUNCT
ejpam-21	452	15	σ	σ	PROPN
ejpam-21	452	16	)	)	PUNCT
ejpam-21	452	17	is	be	AUX
ejpam-21	452	18	regular	regular	ADJ
ejpam-21	452	19	.	.	PUNCT
ejpam-21	453	1	since	since	SCONJ
ejpam-21	453	2	f	f	PROPN
ejpam-21	453	3	(	(	PUNCT
ejpam-21	453	4	x0	x0	PROPN
ejpam-21	453	5	)	)	PUNCT
ejpam-21	453	6	is	be	AUX
ejpam-21	453	7	a	a	DET
ejpam-21	453	8	closed	closed	ADJ
ejpam-21	453	9	set	set	NOUN
ejpam-21	453	10	and	and	CCONJ
ejpam-21	453	11	y	y	PROPN
ejpam-21	453	12	/∈	/∈	PUNCT
ejpam-21	454	1	f	f	PROPN
ejpam-21	454	2	(	(	PUNCT
ejpam-21	454	3	x0	x0	PROPN
ejpam-21	454	4	)	)	PUNCT
ejpam-21	454	5	,	,	PUNCT
ejpam-21	454	6	there	there	PRON
ejpam-21	454	7	exists	exist	VERB
ejpam-21	454	8	an	an	DET
ejpam-21	454	9	open	open	ADJ
ejpam-21	454	10	set	set	NOUN
ejpam-21	454	11	w	w	NOUN
ejpam-21	454	12	containing	contain	VERB
ejpam-21	454	13	y	y	PROPN
ejpam-21	454	14	such	such	ADJ
ejpam-21	454	15	that	that	SCONJ
ejpam-21	454	16	cl(w	cl(w	NOUN
ejpam-21	454	17	)	)	PUNCT
ejpam-21	454	18	is	be	AUX
ejpam-21	454	19	a	a	DET
ejpam-21	454	20	compact	compact	ADJ
ejpam-21	454	21	set	set	NOUN
ejpam-21	454	22	and	and	CCONJ
ejpam-21	454	23	cl(w	cl(w	NOUN
ejpam-21	454	24	)	)	PUNCT
ejpam-21	455	1	⊂	⊂	PROPN
ejpam-21	456	1	y	y	PROPN
ejpam-21	456	2	−	−	PROPN
ejpam-21	456	3	f	f	PROPN
ejpam-21	456	4	(	(	PUNCT
ejpam-21	456	5	x0	x0	PROPN
ejpam-21	456	6	)	)	PUNCT
ejpam-21	456	7	.	.	PUNCT
ejpam-21	457	1	since	since	SCONJ
ejpam-21	457	2	f	f	PROPN
ejpam-21	457	3	(	(	PUNCT
ejpam-21	457	4	x0	x0	PROPN
ejpam-21	457	5	)	)	PUNCT
ejpam-21	457	6	⊂	⊂	PROPN
ejpam-21	457	7	y	y	PROPN
ejpam-21	457	8	−	−	PROPN
ejpam-21	457	9	cl(w	cl(w	NOUN
ejpam-21	457	10	)	)	PUNCT
ejpam-21	457	11	and	and	CCONJ
ejpam-21	457	12	f	f	PROPN
ejpam-21	457	13	is	be	AUX
ejpam-21	457	14	u.c.m.c	u.c.m.c	PROPN
ejpam-21	457	15	.	.	PUNCT
ejpam-21	458	1	at	at	ADP
ejpam-21	458	2	x0	x0	PROPN
ejpam-21	458	3	,	,	PUNCT
ejpam-21	458	4	there	there	PRON
ejpam-21	458	5	exists	exist	VERB
ejpam-21	458	6	an	an	DET
ejpam-21	458	7	mx	mx	PROPN
ejpam-21	458	8	-open	-open	NOUN
ejpam-21	458	9	set	set	VERB
ejpam-21	458	10	g	g	NOUN
ejpam-21	458	11	containing	contain	VERB
ejpam-21	458	12	x0	x0	PROPN
ejpam-21	458	13	and	and	CCONJ
ejpam-21	458	14	f	f	PROPN
ejpam-21	458	15	(	(	PUNCT
ejpam-21	458	16	x	x	X
ejpam-21	458	17	)	)	PUNCT
ejpam-21	458	18	⊂	⊂	PROPN
ejpam-21	459	1	y	y	PROPN
ejpam-21	459	2	−	−	PROPN
ejpam-21	459	3	cl(w	cl(w	NOUN
ejpam-21	459	4	)	)	PUNCT
ejpam-21	459	5	for	for	ADP
ejpam-21	459	6	each	each	DET
ejpam-21	459	7	x	x	SYM
ejpam-21	459	8	∈	∈	PROPN
ejpam-21	459	9	g.	g.	NOUN
ejpam-21	459	10	this	this	PRON
ejpam-21	459	11	is	be	AUX
ejpam-21	459	12	a	a	DET
ejpam-21	459	13	contradiction	contradiction	NOUN
ejpam-21	459	14	.	.	PUNCT
ejpam-21	460	1	since	since	SCONJ
ejpam-21	460	2	z1	z1	PROPN
ejpam-21	460	3	∈	∈	PROPN
ejpam-21	460	4	u0	u0	NOUN
ejpam-21	460	5	⊂	⊂	PROPN
ejpam-21	460	6	g	g	PROPN
ejpam-21	460	7	,	,	PUNCT
ejpam-21	460	8	f	f	PROPN
ejpam-21	460	9	(	(	PUNCT
ejpam-21	460	10	z1	z1	PROPN
ejpam-21	460	11	)	)	PUNCT
ejpam-21	460	12	⊂	⊂	PROPN
ejpam-21	460	13	y	y	PROPN
ejpam-21	460	14	−	−	PROPN
ejpam-21	460	15	cl(w	cl(w	NOUN
ejpam-21	460	16	)	)	PUNCT
ejpam-21	460	17	.	.	PUNCT
ejpam-21	461	1	this	this	PRON
ejpam-21	461	2	contradicts	contradict	VERB
ejpam-21	461	3	that	that	SCONJ
ejpam-21	461	4	f	f	PROPN
ejpam-21	461	5	(	(	PUNCT
ejpam-21	461	6	z1	z1	PROPN
ejpam-21	461	7	)	)	PUNCT
ejpam-21	461	8	∩	∩	NOUN
ejpam-21	461	9	cl(w	cl(w	NOUN
ejpam-21	461	10	)	)	PUNCT
ejpam-21	461	11	6=	6=	ADP
ejpam-21	461	12	∅.	∅.	PRON
ejpam-21	461	13	remark	remark	NOUN
ejpam-21	461	14	5.4	5.4	NUM
ejpam-21	461	15	.	.	PUNCT
ejpam-21	462	1	if	if	SCONJ
ejpam-21	462	2	mx	mx	PROPN
ejpam-21	462	3	=	=	SYM
ejpam-21	462	4	τ	τ	PROPN
ejpam-21	462	5	,	,	PUNCT
ejpam-21	462	6	then	then	ADV
ejpam-21	462	7	by	by	ADP
ejpam-21	462	8	theorem	theorem	NOUN
ejpam-21	462	9	5.3	5.3	NUM
ejpam-21	462	10	we	we	PRON
ejpam-21	462	11	obtain	obtain	VERB
ejpam-21	462	12	the	the	DET
ejpam-21	462	13	result	result	NOUN
ejpam-21	462	14	established	establish	VERB
ejpam-21	462	15	in	in	ADP
ejpam-21	462	16	proposition	proposition	NOUN
ejpam-21	462	17	10	10	NUM
ejpam-21	462	18	of	of	ADP
ejpam-21	462	19	[	[	X
ejpam-21	462	20	11	11	NUM
ejpam-21	462	21	]	]	PUNCT
ejpam-21	462	22	.	.	PUNCT
ejpam-21	463	1	theorem	theorem	NOUN
ejpam-21	463	2	5.4	5.4	NUM
ejpam-21	463	3	.	.	PUNCT
ejpam-21	464	1	let	let	AUX
ejpam-21	464	2	(	(	PUNCT
ejpam-21	464	3	x	x	NOUN
ejpam-21	464	4	,	,	PUNCT
ejpam-21	464	5	mx	mx	NOUN
ejpam-21	464	6	)	)	PUNCT
ejpam-21	464	7	be	be	AUX
ejpam-21	464	8	an	an	DET
ejpam-21	464	9	m	m	ADV
ejpam-21	464	10	-	-	PUNCT
ejpam-21	464	11	saturated	saturate	VERB
ejpam-21	464	12	m	m	NOUN
ejpam-21	464	13	-	-	NOUN
ejpam-21	464	14	space	space	NOUN
ejpam-21	464	15	and	and	CCONJ
ejpam-21	464	16	(	(	PUNCT
ejpam-21	464	17	y	y	PROPN
ejpam-21	464	18	,	,	PUNCT
ejpam-21	464	19	σ	σ	PROPN
ejpam-21	464	20	)	)	PUNCT
ejpam-21	464	21	a	a	DET
ejpam-21	464	22	kc	kc	PROPN
ejpam-21	464	23	space	space	NOUN
ejpam-21	464	24	.	.	PUNCT
ejpam-21	465	1	if	if	SCONJ
ejpam-21	465	2	is	be	AUX
ejpam-21	465	3	l.c.m.c	l.c.m.c	PROPN
ejpam-21	465	4	.	.	PUNCT
ejpam-21	466	1	and	and	CCONJ
ejpam-21	466	2	for	for	ADP
ejpam-21	466	3	each	each	DET
ejpam-21	466	4	x	x	SYM
ejpam-21	466	5	∈	∈	PROPN
ejpam-21	466	6	x	x	PUNCT
ejpam-21	466	7	there	there	PRON
ejpam-21	466	8	exists	exist	VERB
ejpam-21	466	9	a	a	DET
ejpam-21	466	10	compact	compact	ADJ
ejpam-21	466	11	set	set	NOUN
ejpam-21	466	12	cx	cx	PROPN
ejpam-21	467	1	such	such	ADJ
ejpam-21	467	2	that	that	SCONJ
ejpam-21	467	3	f	f	PROPN
ejpam-21	467	4	(	(	PUNCT
ejpam-21	467	5	x	x	X
ejpam-21	467	6	)	)	PUNCT
ejpam-21	467	7	⊂	⊂	PROPN
ejpam-21	467	8	cx	cx	PROPN
ejpam-21	467	9	,	,	PUNCT
ejpam-21	467	10	then	then	ADV
ejpam-21	467	11	f	f	PROPN
ejpam-21	467	12	is	be	AUX
ejpam-21	467	13	l.m.c	l.m.c	ADJ
ejpam-21	467	14	.	.	PUNCT
ejpam-21	468	1	proof	proof	NOUN
ejpam-21	468	2	.	.	PUNCT
ejpam-21	469	1	suppose	suppose	VERB
ejpam-21	469	2	that	that	SCONJ
ejpam-21	469	3	f	f	PROPN
ejpam-21	469	4	is	be	AUX
ejpam-21	469	5	not	not	PART
ejpam-21	469	6	l.m.c	l.m.c	ADJ
ejpam-21	469	7	.	.	PUNCT
ejpam-21	470	1	at	at	ADP
ejpam-21	470	2	x0	x0	PROPN
ejpam-21	470	3	∈	∈	PROPN
ejpam-21	470	4	x	x	X
ejpam-21	470	5	.	.	PUNCT
ejpam-21	471	1	then	then	ADV
ejpam-21	471	2	,	,	PUNCT
ejpam-21	471	3	there	there	PRON
ejpam-21	471	4	exists	exist	VERB
ejpam-21	471	5	an	an	DET
ejpam-21	471	6	open	open	ADJ
ejpam-21	471	7	set	set	NOUN
ejpam-21	471	8	v	v	NOUN
ejpam-21	471	9	of	of	ADP
ejpam-21	471	10	y	y	PRON
ejpam-21	471	11	such	such	ADJ
ejpam-21	471	12	that	that	SCONJ
ejpam-21	471	13	f	f	PROPN
ejpam-21	471	14	(	(	PUNCT
ejpam-21	471	15	x0	x0	PROPN
ejpam-21	471	16	)	)	PUNCT
ejpam-21	471	17	∩	∩	NOUN
ejpam-21	471	18	v	v	ADP
ejpam-21	471	19	6=	6=	NOUN
ejpam-21	471	20	∅	∅	NOUN
ejpam-21	471	21	and	and	CCONJ
ejpam-21	471	22	for	for	ADP
ejpam-21	471	23	each	each	DET
ejpam-21	471	24	u	u	PROPN
ejpam-21	471	25	∈	∈	PROPN
ejpam-21	471	26	mx	mx	NOUN
ejpam-21	471	27	containing	contain	VERB
ejpam-21	471	28	x0	x0	PROPN
ejpam-21	471	29	there	there	PRON
ejpam-21	471	30	exists	exist	VERB
ejpam-21	471	31	u	u	PROPN
ejpam-21	471	32	∈	∈	PROPN
ejpam-21	471	33	u	u	NOUN
ejpam-21	471	34	such	such	ADJ
ejpam-21	471	35	that	that	SCONJ
ejpam-21	471	36	f	f	PROPN
ejpam-21	471	37	(	(	PUNCT
ejpam-21	471	38	u	u	NOUN
ejpam-21	471	39	)	)	PUNCT
ejpam-21	471	40	∩	∩	ADJ
ejpam-21	471	41	v	v	AUX
ejpam-21	471	42	=	=	PUNCT
ejpam-21	471	43	∅.	∅.	AUX
ejpam-21	471	44	let	let	VERB
ejpam-21	471	45	u0	u0	ADJ
ejpam-21	471	46	be	be	AUX
ejpam-21	471	47	the	the	DET
ejpam-21	471	48	intersection	intersection	NOUN
ejpam-21	471	49	of	of	ADP
ejpam-21	471	50	all	all	DET
ejpam-21	471	51	mx	mx	PROPN
ejpam-21	471	52	-open	-open	PROPN
ejpam-21	471	53	sets	set	NOUN
ejpam-21	471	54	containing	contain	VERB
ejpam-21	471	55	x0	x0	PROPN
ejpam-21	471	56	.	.	PUNCT
ejpam-21	472	1	then	then	ADV
ejpam-21	472	2	u0	u0	PROPN
ejpam-21	472	3	∈	∈	PROPN
ejpam-21	472	4	mx	mx	PROPN
ejpam-21	472	5	and	and	CCONJ
ejpam-21	472	6	there	there	PRON
ejpam-21	472	7	exists	exist	VERB
ejpam-21	472	8	x	x	X
ejpam-21	472	9	∈	∈	PROPN
ejpam-21	472	10	u0	u0	NOUN
ejpam-21	472	11	such	such	ADJ
ejpam-21	472	12	that	that	SCONJ
ejpam-21	472	13	f	f	PROPN
ejpam-21	472	14	(	(	PUNCT
ejpam-21	472	15	x)∩	x)∩	PROPN
ejpam-21	472	16	v	v	X
ejpam-21	472	17	=	=	PUNCT
ejpam-21	472	18	∅.	∅.	NOUN
ejpam-21	472	19	by	by	ADP
ejpam-21	472	20	the	the	DET
ejpam-21	472	21	hypothesis	hypothesis	NOUN
ejpam-21	472	22	,	,	PUNCT
ejpam-21	472	23	there	there	PRON
ejpam-21	472	24	exists	exist	VERB
ejpam-21	472	25	a	a	DET
ejpam-21	472	26	compact	compact	ADJ
ejpam-21	472	27	set	set	NOUN
ejpam-21	472	28	cx	cx	PROPN
ejpam-21	473	1	such	such	ADJ
ejpam-21	473	2	that	that	SCONJ
ejpam-21	473	3	f	f	PROPN
ejpam-21	473	4	(	(	PUNCT
ejpam-21	473	5	x	x	X
ejpam-21	473	6	)	)	PUNCT
ejpam-21	473	7	⊂	⊂	PROPN
ejpam-21	473	8	cx	cx	PROPN
ejpam-21	473	9	.	.	PUNCT
ejpam-21	474	1	therefore	therefore	ADV
ejpam-21	474	2	,	,	PUNCT
ejpam-21	474	3	we	we	PRON
ejpam-21	474	4	have	have	VERB
ejpam-21	474	5	f	f	PROPN
ejpam-21	474	6	(	(	PUNCT
ejpam-21	474	7	x	x	X
ejpam-21	474	8	)	)	PUNCT
ejpam-21	474	9	⊂	⊂	PROPN
ejpam-21	474	10	cx	cx	PROPN
ejpam-21	475	1	−	−	PROPN
ejpam-21	475	2	v	v	PROPN
ejpam-21	475	3	and	and	CCONJ
ejpam-21	475	4	cx	cx	PROPN
ejpam-21	476	1	−	−	PROPN
ejpam-21	476	2	v	v	NOUN
ejpam-21	476	3	is	be	AUX
ejpam-21	476	4	a	a	DET
ejpam-21	476	5	compact	compact	ADJ
ejpam-21	476	6	set.the	set.the	PRON
ejpam-21	476	7	set	set	NOUN
ejpam-21	476	8	y	y	PROPN
ejpam-21	476	9	−	−	PROPN
ejpam-21	477	1	(	(	PUNCT
ejpam-21	477	2	cx	cx	PROPN
ejpam-21	477	3	−	−	PROPN
ejpam-21	477	4	v	v	NOUN
ejpam-21	477	5	)	)	PUNCT
ejpam-21	477	6	is	be	AUX
ejpam-21	477	7	open	open	ADJ
ejpam-21	477	8	and	and	CCONJ
ejpam-21	477	9	f	f	PROPN
ejpam-21	477	10	(	(	PUNCT
ejpam-21	477	11	x0	x0	PROPN
ejpam-21	477	12	)	)	PUNCT
ejpam-21	477	13	∩	∩	NOUN
ejpam-21	477	14	(	(	PUNCT
ejpam-21	477	15	y	y	PROPN
ejpam-21	477	16	−	−	PROPN
ejpam-21	477	17	(	(	PUNCT
ejpam-21	477	18	cx	cx	PROPN
ejpam-21	477	19	−	−	PROPN
ejpam-21	477	20	v	v	NOUN
ejpam-21	477	21	)	)	PUNCT
ejpam-21	477	22	)	)	PUNCT
ejpam-21	477	23	6=	6=	ADP
ejpam-21	477	24	∅.	∅.	ADP
ejpam-21	477	25	since	since	SCONJ
ejpam-21	477	26	f	f	PROPN
ejpam-21	477	27	is	be	AUX
ejpam-21	477	28	l.c.m.c	l.c.m.c	PROPN
ejpam-21	477	29	.	.	PUNCT
ejpam-21	478	1	at	at	ADP
ejpam-21	478	2	x0	x0	PROPN
ejpam-21	478	3	,	,	PUNCT
ejpam-21	478	4	there	there	PRON
ejpam-21	478	5	exists	exist	VERB
ejpam-21	478	6	an	an	DET
ejpam-21	478	7	mx	mx	PROPN
ejpam-21	478	8	-open	-open	NOUN
ejpam-21	478	9	set	set	VERB
ejpam-21	478	10	g	g	NOUN
ejpam-21	478	11	containing	contain	VERB
ejpam-21	478	12	x0	x0	PROPN
ejpam-21	478	13	such	such	ADJ
ejpam-21	478	14	that	that	SCONJ
ejpam-21	478	15	for	for	ADP
ejpam-21	478	16	any	any	DET
ejpam-21	478	17	z	z	NOUN
ejpam-21	478	18	∈	∈	PROPN
ejpam-21	478	19	g	g	NOUN
ejpam-21	479	1	we	we	PRON
ejpam-21	479	2	have	have	VERB
ejpam-21	479	3	f	f	PROPN
ejpam-21	479	4	(	(	PUNCT
ejpam-21	479	5	z	z	NOUN
ejpam-21	479	6	)	)	PUNCT
ejpam-21	479	7	∩	∩	NOUN
ejpam-21	479	8	(	(	PUNCT
ejpam-21	479	9	y	y	PROPN
ejpam-21	479	10	−	−	PROPN
ejpam-21	479	11	(	(	PUNCT
ejpam-21	479	12	cx	cx	PROPN
ejpam-21	479	13	−	−	PROPN
ejpam-21	479	14	v	v	NOUN
ejpam-21	479	15	)	)	PUNCT
ejpam-21	479	16	)	)	PUNCT
ejpam-21	480	1	6=	6=	ADP
ejpam-21	480	2	∅.	∅.	VERB
ejpam-21	480	3	this	this	PRON
ejpam-21	480	4	is	be	AUX
ejpam-21	480	5	a	a	DET
ejpam-21	480	6	contradiction	contradiction	NOUN
ejpam-21	480	7	because	because	SCONJ
ejpam-21	480	8	x	x	PROPN
ejpam-21	480	9	∈	∈	PROPN
ejpam-21	480	10	u0	u0	PROPN
ejpam-21	480	11	⊂	⊂	PROPN
ejpam-21	480	12	g	g	PROPN
ejpam-21	480	13	and	and	CCONJ
ejpam-21	480	14	f	f	PROPN
ejpam-21	480	15	(	(	PUNCT
ejpam-21	480	16	x	x	X
ejpam-21	480	17	)	)	PUNCT
ejpam-21	480	18	⊂	⊂	PROPN
ejpam-21	480	19	cx	cx	PROPN
ejpam-21	481	1	−	−	PROPN
ejpam-21	481	2	v	v	NOUN
ejpam-21	481	3	.	.	PUNCT
ejpam-21	482	1	remark	remark	VERB
ejpam-21	482	2	5.5	5.5	NUM
ejpam-21	482	3	.	.	PUNCT
ejpam-21	483	1	if	if	SCONJ
ejpam-21	483	2	mx	mx	PROPN
ejpam-21	483	3	=	=	SYM
ejpam-21	483	4	τ	τ	PROPN
ejpam-21	483	5	,	,	PUNCT
ejpam-21	483	6	then	then	ADV
ejpam-21	483	7	by	by	ADP
ejpam-21	483	8	theorem	theorem	NOUN
ejpam-21	483	9	5.4	5.4	NUM
ejpam-21	483	10	we	we	PRON
ejpam-21	483	11	obtain	obtain	VERB
ejpam-21	483	12	the	the	DET
ejpam-21	483	13	result	result	NOUN
ejpam-21	483	14	established	establish	VERB
ejpam-21	483	15	in	in	ADP
ejpam-21	483	16	proposition	proposition	NOUN
ejpam-21	483	17	11	11	NUM
ejpam-21	483	18	of	of	ADP
ejpam-21	483	19	[	[	X
ejpam-21	483	20	11	11	NUM
ejpam-21	483	21	]	]	PUNCT
ejpam-21	483	22	.	.	PUNCT
ejpam-21	484	1	6	6	X
ejpam-21	484	2	.	.	X
ejpam-21	485	1	some	some	DET
ejpam-21	485	2	properties	property	NOUN
ejpam-21	485	3	definition	definition	NOUN
ejpam-21	485	4	6.1	6.1	NUM
ejpam-21	485	5	.	.	PUNCT
ejpam-21	486	1	a	a	DET
ejpam-21	486	2	multifunction	multifunction	NOUN
ejpam-21	486	3	is	be	AUX
ejpam-21	486	4	said	say	VERB
ejpam-21	486	5	to	to	PART
ejpam-21	486	6	be	be	AUX
ejpam-21	486	7	upper	upper	ADJ
ejpam-21	486	8	c	c	NOUN
ejpam-21	486	9	-	-	PUNCT
ejpam-21	486	10	m	m	VERB
ejpam-21	486	11	-	-	PUNCT
ejpam-21	486	12	rarely	rarely	ADV
ejpam-21	486	13	continuous	continuous	ADJ
ejpam-21	486	14	at	at	ADP
ejpam-21	486	15	a	a	DET
ejpam-21	486	16	point	point	NOUN
ejpam-21	486	17	x	x	SYM
ejpam-21	486	18	∈	∈	NOUN
ejpam-21	486	19	x	x	INTJ
ejpam-21	486	20	if	if	SCONJ
ejpam-21	486	21	for	for	SCONJ
ejpam-21	486	22	each	each	DET
ejpam-21	486	23	open	open	ADJ
ejpam-21	486	24	set	set	VERB
ejpam-21	486	25	g	g	NOUN
ejpam-21	486	26	of	of	ADP
ejpam-21	486	27	y	y	PROPN
ejpam-21	486	28	containing	contain	VERB
ejpam-21	486	29	f	f	PROPN
ejpam-21	486	30	(	(	PUNCT
ejpam-21	486	31	x	x	NOUN
ejpam-21	486	32	)	)	PUNCT
ejpam-21	486	33	and	and	CCONJ
ejpam-21	486	34	having	have	VERB
ejpam-21	486	35	compact	compact	ADJ
ejpam-21	486	36	complement	complement	NOUN
ejpam-21	486	37	,	,	PUNCT
ejpam-21	486	38	there	there	PRON
ejpam-21	486	39	exists	exist	VERB
ejpam-21	486	40	a	a	DET
ejpam-21	486	41	rare	rare	ADJ
ejpam-21	486	42	t.noiri	t.noiri	NOUN
ejpam-21	486	43	,	,	PUNCT
ejpam-21	486	44	v.popa	v.popa	NOUN
ejpam-21	486	45	/	/	SYM
ejpam-21	486	46	eur	eur	PROPN
ejpam-21	486	47	.	.	PUNCT
ejpam-21	487	1	j.	j.	PROPN
ejpam-21	487	2	pure	pure	PROPN
ejpam-21	487	3	appl	appl	PROPN
ejpam-21	487	4	.	.	PROPN
ejpam-21	487	5	math	math	PROPN
ejpam-21	487	6	,	,	PUNCT
ejpam-21	487	7	1	1	NUM
ejpam-21	487	8	(	(	PUNCT
ejpam-21	487	9	2008	2008	NUM
ejpam-21	487	10	)	)	PUNCT
ejpam-21	487	11	,	,	PUNCT
ejpam-21	487	12	(	(	PUNCT
ejpam-21	487	13	82	82	NUM
ejpam-21	487	14	-	-	SYM
ejpam-21	487	15	98	98	NUM
ejpam-21	487	16	)	)	PUNCT
ejpam-21	487	17	94	94	NUM
ejpam-21	487	18	set	set	VERB
ejpam-21	487	19	rg	rg	NOUN
ejpam-21	487	20	with	with	ADP
ejpam-21	487	21	cl(rg	cl(rg	PROPN
ejpam-21	487	22	)	)	PUNCT
ejpam-21	487	23	∩	∩	PROPN
ejpam-21	487	24	g	g	NOUN
ejpam-21	487	25	=	=	SYM
ejpam-21	487	26	∅	∅	NOUN
ejpam-21	487	27	and	and	CCONJ
ejpam-21	487	28	an	an	DET
ejpam-21	487	29	mx	mx	PROPN
ejpam-21	487	30	-open	-open	NOUN
ejpam-21	487	31	set	set	NOUN
ejpam-21	487	32	u	u	NOUN
ejpam-21	487	33	containing	contain	VERB
ejpam-21	487	34	x	x	PUNCT
ejpam-21	487	35	such	such	ADJ
ejpam-21	487	36	that	that	SCONJ
ejpam-21	487	37	f	f	PROPN
ejpam-21	487	38	(	(	PUNCT
ejpam-21	487	39	u	u	NOUN
ejpam-21	487	40	)	)	PUNCT
ejpam-21	487	41	⊂	⊂	PROPN
ejpam-21	487	42	g	g	PROPN
ejpam-21	487	43	∪	∪	PROPN
ejpam-21	487	44	rg	rg	PROPN
ejpam-21	487	45	.	.	PUNCT
ejpam-21	488	1	a	a	DET
ejpam-21	488	2	multifunction	multifunction	NOUN
ejpam-21	488	3	is	be	AUX
ejpam-21	488	4	said	say	VERB
ejpam-21	488	5	to	to	PART
ejpam-21	488	6	be	be	AUX
ejpam-21	488	7	upper	upper	ADJ
ejpam-21	488	8	c	c	NOUN
ejpam-21	488	9	-	-	PUNCT
ejpam-21	488	10	m	m	VERB
ejpam-21	488	11	-	-	PUNCT
ejpam-21	488	12	rarely	rarely	ADV
ejpam-21	488	13	continuous	continuous	ADJ
ejpam-21	488	14	if	if	SCONJ
ejpam-21	488	15	it	it	PRON
ejpam-21	488	16	has	have	VERB
ejpam-21	488	17	this	this	DET
ejpam-21	488	18	property	property	NOUN
ejpam-21	488	19	at	at	ADP
ejpam-21	488	20	each	each	DET
ejpam-21	488	21	point	point	NOUN
ejpam-21	488	22	x	x	X
ejpam-21	488	23	∈	∈	PROPN
ejpam-21	488	24	x	x	X
ejpam-21	488	25	.	.	PUNCT
ejpam-21	489	1	theorem	theorem	NOUN
ejpam-21	489	2	6.1	6.1	NUM
ejpam-21	489	3	.	.	PUNCT
ejpam-21	490	1	let	let	VERB
ejpam-21	490	2	x	x	PRON
ejpam-21	490	3	be	be	AUX
ejpam-21	490	4	a	a	DET
ejpam-21	490	5	nonempty	nonempty	NOUN
ejpam-21	490	6	set	set	VERB
ejpam-21	490	7	with	with	ADP
ejpam-21	490	8	two	two	NUM
ejpam-21	490	9	minimal	minimal	ADJ
ejpam-21	490	10	structures	structure	NOUN
ejpam-21	490	11	m1	m1	NOUN
ejpam-21	490	12	x	x	X
ejpam-21	490	13	and	and	CCONJ
ejpam-21	490	14	m2	m2	PROPN
ejpam-21	490	15	x	x	PROPN
ejpam-21	490	16	such	such	ADJ
ejpam-21	490	17	that	that	SCONJ
ejpam-21	490	18	u	u	PROPN
ejpam-21	490	19	∩	∩	NOUN
ejpam-21	490	20	v	v	ADP
ejpam-21	490	21	∈	∈	PROPN
ejpam-21	490	22	m2	m2	PROPN
ejpam-21	490	23	x	x	PUNCT
ejpam-21	490	24	for	for	ADP
ejpam-21	490	25	every	every	DET
ejpam-21	490	26	u	u	PROPN
ejpam-21	490	27	∈	∈	PROPN
ejpam-21	490	28	m1	m1	NOUN
ejpam-21	490	29	x	x	X
ejpam-21	490	30	and	and	CCONJ
ejpam-21	490	31	v	v	ADP
ejpam-21	490	32	∈	∈	NOUN
ejpam-21	490	33	m2	m2	PROPN
ejpam-21	490	34	x	x	INTJ
ejpam-21	490	35	.	.	PUNCT
ejpam-21	491	1	then	then	ADV
ejpam-21	491	2	f	f	X
ejpam-21	491	3	:	:	PUNCT
ejpam-21	491	4	(	(	PUNCT
ejpam-21	491	5	x	x	NOUN
ejpam-21	491	6	,	,	PUNCT
ejpam-21	491	7	m2	m2	PROPN
ejpam-21	491	8	x	x	PROPN
ejpam-21	491	9	)	)	PUNCT
ejpam-21	491	10	→	→	SYM
ejpam-21	491	11	(	(	PUNCT
ejpam-21	491	12	y	y	PROPN
ejpam-21	491	13	,	,	PUNCT
ejpam-21	491	14	σ	σ	PROPN
ejpam-21	491	15	)	)	PUNCT
ejpam-21	491	16	is	be	AUX
ejpam-21	491	17	u.c.m.c	u.c.m.c	PROPN
ejpam-21	491	18	.	.	PUNCT
ejpam-21	492	1	if	if	SCONJ
ejpam-21	492	2	the	the	DET
ejpam-21	492	3	following	follow	VERB
ejpam-21	492	4	conditions	condition	NOUN
ejpam-21	492	5	satisfy	satisfy	VERB
ejpam-21	492	6	:	:	PUNCT
ejpam-21	492	7	(	(	PUNCT
ejpam-21	492	8	1	1	X
ejpam-21	492	9	)	)	PUNCT
ejpam-21	492	10	f	f	NOUN
ejpam-21	492	11	:	:	PUNCT
ejpam-21	492	12	(	(	PUNCT
ejpam-21	492	13	x	x	X
ejpam-21	492	14	,	,	PUNCT
ejpam-21	492	15	m1	m1	PROPN
ejpam-21	492	16	x	x	SYM
ejpam-21	492	17	)	)	PUNCT
ejpam-21	492	18	→	→	SYM
ejpam-21	492	19	(	(	PUNCT
ejpam-21	492	20	y	y	PROPN
ejpam-21	492	21	,	,	PUNCT
ejpam-21	492	22	σ	σ	PROPN
ejpam-21	492	23	)	)	PUNCT
ejpam-21	492	24	is	be	AUX
ejpam-21	492	25	upper	upper	ADJ
ejpam-21	492	26	c	c	NOUN
ejpam-21	492	27	-	-	PUNCT
ejpam-21	492	28	m	m	VERB
ejpam-21	492	29	-	-	PUNCT
ejpam-21	492	30	rarely	rarely	ADV
ejpam-21	492	31	continuous	continuous	ADJ
ejpam-21	492	32	and	and	CCONJ
ejpam-21	492	33	(	(	PUNCT
ejpam-21	492	34	2	2	NUM
ejpam-21	492	35	)	)	PUNCT
ejpam-21	492	36	for	for	ADP
ejpam-21	492	37	each	each	DET
ejpam-21	492	38	open	open	ADJ
ejpam-21	492	39	set	set	VERB
ejpam-21	492	40	g	g	NOUN
ejpam-21	492	41	containing	contain	VERB
ejpam-21	492	42	f(x	f(x	PROPN
ejpam-21	492	43	)	)	PUNCT
ejpam-21	492	44	and	and	CCONJ
ejpam-21	492	45	having	have	VERB
ejpam-21	492	46	compact	compact	ADJ
ejpam-21	492	47	complement	complement	NOUN
ejpam-21	492	48	,	,	PUNCT
ejpam-21	492	49	f−(cl(rg	f−(cl(rg	NOUN
ejpam-21	492	50	)	)	PUNCT
ejpam-21	492	51	)	)	PUNCT
ejpam-21	493	1	is	be	AUX
ejpam-21	493	2	an	an	DET
ejpam-21	493	3	m2	m2	PROPN
ejpam-21	493	4	x	x	SYM
ejpam-21	493	5	-closed	-closed	ADJ
ejpam-21	493	6	set	set	NOUN
ejpam-21	493	7	of	of	ADP
ejpam-21	493	8	x	x	NOUN
ejpam-21	493	9	,	,	PUNCT
ejpam-21	493	10	where	where	SCONJ
ejpam-21	493	11	rg	rg	PROPN
ejpam-21	493	12	is	be	AUX
ejpam-21	493	13	the	the	DET
ejpam-21	493	14	rare	rare	ADJ
ejpam-21	493	15	set	set	NOUN
ejpam-21	493	16	of	of	ADP
ejpam-21	493	17	definition	definition	NOUN
ejpam-21	493	18	6.1	6.1	NUM
ejpam-21	493	19	.	.	PUNCT
ejpam-21	494	1	proof	proof	NOUN
ejpam-21	494	2	.	.	PUNCT
ejpam-21	495	1	let	let	VERB
ejpam-21	495	2	x	x	PUNCT
ejpam-21	495	3	∈	∈	PROPN
ejpam-21	495	4	x	x	X
ejpam-21	495	5	and	and	CCONJ
ejpam-21	495	6	g	g	PROPN
ejpam-21	495	7	be	be	VERB
ejpam-21	495	8	any	any	DET
ejpam-21	495	9	open	open	ADJ
ejpam-21	495	10	set	set	NOUN
ejpam-21	495	11	of	of	ADP
ejpam-21	495	12	y	y	PROPN
ejpam-21	495	13	containing	contain	VERB
ejpam-21	495	14	f	f	PROPN
ejpam-21	495	15	(	(	PUNCT
ejpam-21	495	16	x	x	NOUN
ejpam-21	495	17	)	)	PUNCT
ejpam-21	495	18	and	and	CCONJ
ejpam-21	495	19	having	have	VERB
ejpam-21	495	20	compact	compact	ADJ
ejpam-21	495	21	complement	complement	NOUN
ejpam-21	495	22	.	.	PUNCT
ejpam-21	496	1	by	by	ADP
ejpam-21	496	2	the	the	DET
ejpam-21	496	3	condition	condition	NOUN
ejpam-21	496	4	(	(	PUNCT
ejpam-21	496	5	1	1	NUM
ejpam-21	496	6	)	)	PUNCT
ejpam-21	496	7	,	,	PUNCT
ejpam-21	496	8	there	there	PRON
ejpam-21	496	9	exists	exist	VERB
ejpam-21	496	10	v	v	ADP
ejpam-21	496	11	∈	∈	PROPN
ejpam-21	496	12	m1	m1	NOUN
ejpam-21	496	13	x	x	PUNCT
ejpam-21	496	14	containing	contain	VERB
ejpam-21	496	15	x	x	PROPN
ejpam-21	496	16	and	and	CCONJ
ejpam-21	496	17	a	a	DET
ejpam-21	496	18	rare	rare	ADJ
ejpam-21	496	19	set	set	NOUN
ejpam-21	496	20	rg	rg	NOUN
ejpam-21	496	21	with	with	ADP
ejpam-21	496	22	cl(rg	cl(rg	PROPN
ejpam-21	496	23	)	)	PUNCT
ejpam-21	497	1	∩	∩	PROPN
ejpam-21	497	2	g	g	NOUN
ejpam-21	497	3	=	=	PUNCT
ejpam-21	497	4	∅	∅	NOUN
ejpam-21	497	5	such	such	ADJ
ejpam-21	497	6	that	that	SCONJ
ejpam-21	497	7	f	f	PROPN
ejpam-21	497	8	(	(	PUNCT
ejpam-21	497	9	v	v	NOUN
ejpam-21	497	10	)	)	PUNCT
ejpam-21	498	1	⊂	⊂	PROPN
ejpam-21	498	2	g	g	PROPN
ejpam-21	498	3	∪	∪	PROPN
ejpam-21	498	4	rg	rg	PROPN
ejpam-21	498	5	.	.	PUNCT
ejpam-21	499	1	if	if	SCONJ
ejpam-21	499	2	we	we	PRON
ejpam-21	499	3	suppose	suppose	VERB
ejpam-21	499	4	that	that	SCONJ
ejpam-21	499	5	x	x	PROPN
ejpam-21	499	6	∈	∈	PROPN
ejpam-21	499	7	f−(cl(rg	f−(cl(rg	NOUN
ejpam-21	499	8	)	)	PUNCT
ejpam-21	499	9	)	)	PUNCT
ejpam-21	499	10	,	,	PUNCT
ejpam-21	499	11	then	then	ADV
ejpam-21	499	12	cl(rg	cl(rg	PROPN
ejpam-21	499	13	)	)	PUNCT
ejpam-21	499	14	∩g	∩g	PROPN
ejpam-21	499	15	6=	6=	ADP
ejpam-21	499	16	∅.	∅.	VERB
ejpam-21	499	17	this	this	PRON
ejpam-21	499	18	is	be	AUX
ejpam-21	499	19	a	a	DET
ejpam-21	499	20	contradiction	contradiction	NOUN
ejpam-21	499	21	.	.	PUNCT
ejpam-21	500	1	thus	thus	ADV
ejpam-21	500	2	x	x	X
ejpam-21	500	3	/∈	/∈	PUNCT
ejpam-21	500	4	f−(cl(rg	f−(cl(rg	ADJ
ejpam-21	500	5	)	)	PUNCT
ejpam-21	500	6	)	)	PUNCT
ejpam-21	500	7	.	.	PUNCT
ejpam-21	501	1	put	put	VERB
ejpam-21	501	2	u	u	NOUN
ejpam-21	501	3	=	=	SYM
ejpam-21	501	4	v	v	NOUN
ejpam-21	501	5	∩	∩	NOUN
ejpam-21	501	6	(	(	PUNCT
ejpam-21	501	7	x	x	SYM
ejpam-21	501	8	−	−	NOUN
ejpam-21	501	9	f−(cl(rg	f−(cl(rg	NOUN
ejpam-21	501	10	)	)	PUNCT
ejpam-21	501	11	)	)	PUNCT
ejpam-21	501	12	)	)	PUNCT
ejpam-21	501	13	.	.	PUNCT
ejpam-21	502	1	then	then	ADV
ejpam-21	502	2	u	u	PROPN
ejpam-21	502	3	∈	∈	PROPN
ejpam-21	502	4	m2	m2	PROPN
ejpam-21	502	5	x	x	PROPN
ejpam-21	502	6	and	and	CCONJ
ejpam-21	502	7	x	x	SYM
ejpam-21	502	8	∈	∈	PROPN
ejpam-21	502	9	u	u	NOUN
ejpam-21	502	10	since	since	SCONJ
ejpam-21	502	11	x	x	PROPN
ejpam-21	502	12	∈	∈	PROPN
ejpam-21	502	13	v	v	NOUN
ejpam-21	502	14	and	and	CCONJ
ejpam-21	502	15	x	x	NOUN
ejpam-21	502	16	∈	∈	PROPN
ejpam-21	502	17	x	x	PUNCT
ejpam-21	502	18	−	−	NOUN
ejpam-21	502	19	f−(cl(rg	f−(cl(rg	NOUN
ejpam-21	502	20	)	)	PUNCT
ejpam-21	502	21	)	)	PUNCT
ejpam-21	502	22	.	.	PUNCT
ejpam-21	503	1	let	let	VERB
ejpam-21	503	2	u	u	PRON
ejpam-21	503	3	∈	∈	PROPN
ejpam-21	503	4	u	u	NOUN
ejpam-21	503	5	,	,	PUNCT
ejpam-21	503	6	then	then	ADV
ejpam-21	503	7	f	f	PROPN
ejpam-21	503	8	(	(	PUNCT
ejpam-21	503	9	u	u	NOUN
ejpam-21	503	10	)	)	PUNCT
ejpam-21	503	11	⊂	⊂	PROPN
ejpam-21	503	12	g	g	PROPN
ejpam-21	503	13	∪	∪	ADP
ejpam-21	503	14	rg	rg	PROPN
ejpam-21	503	15	and	and	CCONJ
ejpam-21	503	16	f	f	PROPN
ejpam-21	503	17	(	(	PUNCT
ejpam-21	503	18	u	u	NOUN
ejpam-21	503	19	)	)	PUNCT
ejpam-21	503	20	∩	∩	ADJ
ejpam-21	503	21	cl(rg	cl(rg	NOUN
ejpam-21	503	22	)	)	PUNCT
ejpam-21	504	1	=	=	PUNCT
ejpam-21	504	2	∅.	∅.	VERB
ejpam-21	504	3	therefore	therefore	ADV
ejpam-21	504	4	,	,	PUNCT
ejpam-21	504	5	we	we	PRON
ejpam-21	504	6	have	have	VERB
ejpam-21	504	7	f	f	PROPN
ejpam-21	504	8	(	(	PUNCT
ejpam-21	504	9	u	u	NOUN
ejpam-21	504	10	)	)	PUNCT
ejpam-21	504	11	∩	∩	NOUN
ejpam-21	504	12	rg	rg	NOUN
ejpam-21	504	13	=	=	PUNCT
ejpam-21	504	14	∅	∅	NOUN
ejpam-21	504	15	and	and	CCONJ
ejpam-21	504	16	hence	hence	ADV
ejpam-21	504	17	,	,	PUNCT
ejpam-21	504	18	f	f	PROPN
ejpam-21	504	19	(	(	PUNCT
ejpam-21	504	20	u	u	NOUN
ejpam-21	504	21	)	)	PUNCT
ejpam-21	504	22	⊂	⊂	PROPN
ejpam-21	504	23	g	g	PROPN
ejpam-21	504	24	for	for	ADP
ejpam-21	504	25	each	each	DET
ejpam-21	504	26	u	u	PROPN
ejpam-21	504	27	∈	∈	PROPN
ejpam-21	504	28	u	u	NOUN
ejpam-21	504	29	.	.	PUNCT
ejpam-21	505	1	since	since	SCONJ
ejpam-21	505	2	u	u	PROPN
ejpam-21	505	3	∈	∈	PROPN
ejpam-21	505	4	m2	m2	PROPN
ejpam-21	505	5	x	x	PUNCT
ejpam-21	505	6	containing	contain	VERB
ejpam-21	505	7	x	x	PRON
ejpam-21	505	8	,	,	PUNCT
ejpam-21	505	9	it	it	PRON
ejpam-21	505	10	follows	follow	VERB
ejpam-21	505	11	that	that	SCONJ
ejpam-21	505	12	f	f	X
ejpam-21	505	13	:	:	PUNCT
ejpam-21	505	14	(	(	PUNCT
ejpam-21	505	15	x	x	NOUN
ejpam-21	505	16	,	,	PUNCT
ejpam-21	505	17	m2	m2	PROPN
ejpam-21	505	18	x	x	PROPN
ejpam-21	505	19	)	)	PUNCT
ejpam-21	505	20	→	→	SYM
ejpam-21	505	21	(	(	PUNCT
ejpam-21	505	22	y	y	PROPN
ejpam-21	505	23	,	,	PUNCT
ejpam-21	505	24	σ	σ	PROPN
ejpam-21	505	25	)	)	PUNCT
ejpam-21	505	26	is	be	AUX
ejpam-21	505	27	u.c.m.c	u.c.m.c	PROPN
ejpam-21	505	28	.	.	NOUN
ejpam-21	505	29	definition	definition	NOUN
ejpam-21	505	30	6.2	6.2	NUM
ejpam-21	505	31	.	.	PUNCT
ejpam-21	506	1	for	for	ADP
ejpam-21	506	2	a	a	DET
ejpam-21	506	3	multifunction	multifunction	NOUN
ejpam-21	506	4	,	,	PUNCT
ejpam-21	506	5	the	the	DET
ejpam-21	506	6	graph	graph	NOUN
ejpam-21	506	7	g(f	g(f	PROPN
ejpam-21	506	8	)	)	PUNCT
ejpam-21	507	1	=	=	PUNCT
ejpam-21	507	2	{	{	PUNCT
ejpam-21	507	3	(	(	PUNCT
ejpam-21	507	4	x	x	X
ejpam-21	507	5	,	,	PUNCT
ejpam-21	507	6	f	f	PROPN
ejpam-21	507	7	(	(	PUNCT
ejpam-21	507	8	x	x	NOUN
ejpam-21	507	9	)	)	PUNCT
ejpam-21	507	10	)	)	PUNCT
ejpam-21	507	11	:	:	PUNCT
ejpam-21	508	1	x	x	X
ejpam-21	508	2	∈	∈	NOUN
ejpam-21	508	3	x	x	PRON
ejpam-21	508	4	}	}	PUNCT
ejpam-21	508	5	is	be	AUX
ejpam-21	508	6	said	say	VERB
ejpam-21	508	7	to	to	PART
ejpam-21	508	8	be	be	AUX
ejpam-21	508	9	strongly	strongly	ADV
ejpam-21	508	10	m	m	ADJ
ejpam-21	508	11	-	-	PUNCT
ejpam-21	508	12	closed	closed	ADJ
ejpam-21	508	13	[	[	X
ejpam-21	508	14	32	32	NUM
ejpam-21	508	15	]	]	X
ejpam-21	508	16	if	if	SCONJ
ejpam-21	508	17	for	for	ADP
ejpam-21	508	18	each	each	DET
ejpam-21	508	19	(	(	PUNCT
ejpam-21	508	20	x	x	NOUN
ejpam-21	508	21	,	,	PUNCT
ejpam-21	508	22	y	y	NOUN
ejpam-21	508	23	)	)	PUNCT
ejpam-21	508	24	∈	∈	PROPN
ejpam-21	508	25	(	(	PUNCT
ejpam-21	508	26	x	x	SYM
ejpam-21	508	27	×	×	PROPN
ejpam-21	508	28	y	y	PROPN
ejpam-21	508	29	)	)	PUNCT
ejpam-21	508	30	−g(f	−g(f	NOUN
ejpam-21	508	31	)	)	PUNCT
ejpam-21	508	32	,	,	PUNCT
ejpam-21	508	33	there	there	PRON
ejpam-21	508	34	exist	exist	VERB
ejpam-21	508	35	an	an	DET
ejpam-21	508	36	mx	mx	NOUN
ejpam-21	508	37	-open	-open	NOUN
ejpam-21	508	38	set	set	NOUN
ejpam-21	508	39	u	u	NOUN
ejpam-21	508	40	containing	contain	VERB
ejpam-21	508	41	x	x	PUNCT
ejpam-21	508	42	and	and	CCONJ
ejpam-21	508	43	an	an	DET
ejpam-21	508	44	open	open	ADJ
ejpam-21	508	45	set	set	NOUN
ejpam-21	508	46	v	v	NOUN
ejpam-21	508	47	of	of	ADP
ejpam-21	508	48	y	y	PROPN
ejpam-21	508	49	containing	contain	VERB
ejpam-21	508	50	y	y	PRON
ejpam-21	508	51	such	such	ADJ
ejpam-21	508	52	that	that	SCONJ
ejpam-21	509	1	[	[	X
ejpam-21	509	2	u	u	X
ejpam-21	509	3	×	×	NOUN
ejpam-21	509	4	cl(v	cl(v	NOUN
ejpam-21	509	5	)	)	PUNCT
ejpam-21	509	6	]	]	PUNCT
ejpam-21	509	7	∩g(f	∩g(f	PROPN
ejpam-21	509	8	)	)	PUNCT
ejpam-21	510	1	=	=	PUNCT
ejpam-21	510	2	∅.	∅.	PRON
ejpam-21	510	3	lemma	lemma	PROPN
ejpam-21	510	4	6.1	6.1	NUM
ejpam-21	510	5	.	.	PUNCT
ejpam-21	511	1	a	a	DET
ejpam-21	511	2	multifunction	multifunction	NOUN
ejpam-21	511	3	has	have	VERB
ejpam-21	511	4	a	a	DET
ejpam-21	511	5	strongly	strongly	ADV
ejpam-21	511	6	m	m	ADJ
ejpam-21	511	7	-	-	PUNCT
ejpam-21	511	8	closed	closed	ADJ
ejpam-21	511	9	graph	graph	NOUN
ejpam-21	511	10	if	if	SCONJ
ejpam-21	511	11	and	and	CCONJ
ejpam-21	511	12	only	only	ADV
ejpam-21	511	13	if	if	SCONJ
ejpam-21	511	14	for	for	ADP
ejpam-21	511	15	each	each	DET
ejpam-21	511	16	(	(	PUNCT
ejpam-21	511	17	x	x	NOUN
ejpam-21	511	18	,	,	PUNCT
ejpam-21	511	19	y	y	NOUN
ejpam-21	511	20	)	)	PUNCT
ejpam-21	511	21	∈	∈	PROPN
ejpam-21	511	22	(	(	PUNCT
ejpam-21	511	23	x	x	SYM
ejpam-21	511	24	×	×	PROPN
ejpam-21	511	25	y	y	PROPN
ejpam-21	511	26	)	)	PUNCT
ejpam-21	511	27	−g(f	−g(f	PROPN
ejpam-21	511	28	)	)	PUNCT
ejpam-21	511	29	,	,	PUNCT
ejpam-21	511	30	there	there	PRON
ejpam-21	511	31	exist	exist	VERB
ejpam-21	511	32	an	an	DET
ejpam-21	511	33	mx	mx	NOUN
ejpam-21	511	34	-open	-open	NOUN
ejpam-21	511	35	set	set	NOUN
ejpam-21	511	36	u	u	NOUN
ejpam-21	511	37	containing	contain	VERB
ejpam-21	511	38	x	x	PUNCT
ejpam-21	511	39	and	and	CCONJ
ejpam-21	511	40	an	an	DET
ejpam-21	511	41	open	open	ADJ
ejpam-21	511	42	set	set	NOUN
ejpam-21	511	43	v	v	NOUN
ejpam-21	511	44	of	of	ADP
ejpam-21	511	45	y	y	PROPN
ejpam-21	511	46	containing	contain	VERB
ejpam-21	511	47	y	y	PRON
ejpam-21	511	48	such	such	ADJ
ejpam-21	511	49	that	that	SCONJ
ejpam-21	511	50	f	f	PROPN
ejpam-21	511	51	(	(	PUNCT
ejpam-21	511	52	u	u	NOUN
ejpam-21	511	53	)	)	PUNCT
ejpam-21	511	54	∩	∩	NOUN
ejpam-21	511	55	cl(v	cl(v	NOUN
ejpam-21	511	56	)	)	PUNCT
ejpam-21	511	57	=	=	PUNCT
ejpam-21	511	58	∅.	∅.	NOUN
ejpam-21	511	59	theorem	theorem	VERB
ejpam-21	511	60	6.2	6.2	NUM
ejpam-21	511	61	.	.	PUNCT
ejpam-21	512	1	let	let	AUX
ejpam-21	512	2	(	(	PUNCT
ejpam-21	512	3	y	y	PROPN
ejpam-21	512	4	,	,	PUNCT
ejpam-21	512	5	σ	σ	PROPN
ejpam-21	512	6	)	)	PUNCT
ejpam-21	512	7	be	be	AUX
ejpam-21	512	8	a	a	DET
ejpam-21	512	9	locally	locally	ADV
ejpam-21	512	10	compact	compact	ADJ
ejpam-21	512	11	hausdorff	hausdorff	NOUN
ejpam-21	512	12	space	space	NOUN
ejpam-21	512	13	.	.	PUNCT
ejpam-21	513	1	if	if	SCONJ
ejpam-21	513	2	a	a	DET
ejpam-21	513	3	multifunction	multifunction	NOUN
ejpam-21	513	4	is	be	AUX
ejpam-21	513	5	u.c.m.c	u.c.m.c	PROPN
ejpam-21	513	6	.	.	PROPN
ejpam-21	514	1	and	and	CCONJ
ejpam-21	514	2	f	f	PROPN
ejpam-21	514	3	(	(	PUNCT
ejpam-21	514	4	x	x	X
ejpam-21	514	5	)	)	PUNCT
ejpam-21	514	6	is	be	AUX
ejpam-21	514	7	closed	close	VERB
ejpam-21	514	8	for	for	SCONJ
ejpam-21	514	9	each	each	DET
ejpam-21	514	10	x	x	SYM
ejpam-21	514	11	∈	∈	PROPN
ejpam-21	514	12	x	x	X
ejpam-21	514	13	,	,	PUNCT
ejpam-21	514	14	then	then	ADV
ejpam-21	514	15	g(f	g(f	PROPN
ejpam-21	514	16	)	)	PUNCT
ejpam-21	514	17	is	be	AUX
ejpam-21	514	18	strongly	strongly	ADV
ejpam-21	514	19	m	m	NOUN
ejpam-21	514	20	-	-	PUNCT
ejpam-21	514	21	closed	closed	ADJ
ejpam-21	514	22	.	.	PUNCT
ejpam-21	515	1	proof	proof	NOUN
ejpam-21	515	2	.	.	PUNCT
ejpam-21	516	1	let	let	VERB
ejpam-21	516	2	(	(	PUNCT
ejpam-21	516	3	x	x	NOUN
ejpam-21	516	4	,	,	PUNCT
ejpam-21	516	5	y	y	NOUN
ejpam-21	516	6	)	)	PUNCT
ejpam-21	516	7	∈	∈	PROPN
ejpam-21	516	8	(	(	PUNCT
ejpam-21	516	9	x×y	x×y	PROPN
ejpam-21	516	10	)	)	PUNCT
ejpam-21	516	11	−g(f	−g(f	NOUN
ejpam-21	516	12	)	)	PUNCT
ejpam-21	516	13	.	.	PUNCT
ejpam-21	517	1	then	then	ADV
ejpam-21	517	2	y	y	PROPN
ejpam-21	517	3	/∈	/∈	PUNCT
ejpam-21	518	1	f	f	PROPN
ejpam-21	518	2	(	(	PUNCT
ejpam-21	518	3	x	x	NOUN
ejpam-21	518	4	)	)	PUNCT
ejpam-21	518	5	.	.	PUNCT
ejpam-21	519	1	since	since	SCONJ
ejpam-21	519	2	y	y	PROPN
ejpam-21	519	3	is	be	AUX
ejpam-21	519	4	locally	locally	ADV
ejpam-21	519	5	compact	compact	ADJ
ejpam-21	519	6	hausdorff	hausdorff	NOUN
ejpam-21	519	7	,	,	PUNCT
ejpam-21	519	8	y	y	PROPN
ejpam-21	519	9	is	be	AUX
ejpam-21	519	10	regular	regular	ADJ
ejpam-21	519	11	.	.	PUNCT
ejpam-21	520	1	since	since	SCONJ
ejpam-21	520	2	f	f	PROPN
ejpam-21	520	3	(	(	PUNCT
ejpam-21	520	4	x	x	X
ejpam-21	520	5	)	)	PUNCT
ejpam-21	520	6	is	be	AUX
ejpam-21	520	7	a	a	DET
ejpam-21	520	8	closed	closed	ADJ
ejpam-21	520	9	set	set	NOUN
ejpam-21	520	10	and	and	CCONJ
ejpam-21	520	11	y	y	PROPN
ejpam-21	520	12	/∈	/∈	PUNCT
ejpam-21	521	1	f	f	PROPN
ejpam-21	521	2	(	(	PUNCT
ejpam-21	521	3	x	x	X
ejpam-21	521	4	)	)	PUNCT
ejpam-21	521	5	,	,	PUNCT
ejpam-21	521	6	there	there	PRON
ejpam-21	521	7	exists	exist	VERB
ejpam-21	521	8	an	an	DET
ejpam-21	521	9	open	open	ADJ
ejpam-21	521	10	set	set	NOUN
ejpam-21	521	11	v	v	NOUN
ejpam-21	521	12	in	in	ADP
ejpam-21	521	13	y	y	NOUN
ejpam-21	521	14	containing	contain	VERB
ejpam-21	521	15	y	y	PRON
ejpam-21	521	16	such	such	ADJ
ejpam-21	521	17	that	that	SCONJ
ejpam-21	521	18	cl(v	cl(v	NOUN
ejpam-21	521	19	)	)	PUNCT
ejpam-21	521	20	is	be	AUX
ejpam-21	521	21	a	a	DET
ejpam-21	521	22	compact	compact	ADJ
ejpam-21	521	23	set	set	NOUN
ejpam-21	521	24	and	and	CCONJ
ejpam-21	521	25	cl(v	cl(v	NOUN
ejpam-21	521	26	)	)	PUNCT
ejpam-21	522	1	⊂	⊂	PROPN
ejpam-21	522	2	x−f	x−f	X
ejpam-21	522	3	(	(	PUNCT
ejpam-21	522	4	x	x	X
ejpam-21	522	5	)	)	PUNCT
ejpam-21	522	6	and	and	CCONJ
ejpam-21	522	7	hence	hence	ADV
ejpam-21	522	8	,	,	PUNCT
ejpam-21	522	9	f	f	PROPN
ejpam-21	522	10	(	(	PUNCT
ejpam-21	522	11	x	x	X
ejpam-21	522	12	)	)	PUNCT
ejpam-21	522	13	⊂	⊂	PROPN
ejpam-21	522	14	y	y	PROPN
ejpam-21	522	15	−cl(v	−cl(v	PROPN
ejpam-21	522	16	)	)	PUNCT
ejpam-21	522	17	.	.	PUNCT
ejpam-21	523	1	since	since	SCONJ
ejpam-21	523	2	f	f	PROPN
ejpam-21	523	3	is	be	AUX
ejpam-21	523	4	u.c.m.c	u.c.m.c	PROPN
ejpam-21	523	5	.	.	PUNCT
ejpam-21	524	1	at	at	ADP
ejpam-21	524	2	x	x	X
ejpam-21	524	3	and	and	CCONJ
ejpam-21	524	4	y	y	PROPN
ejpam-21	524	5	−	−	PROPN
ejpam-21	524	6	cl(v	cl(v	NOUN
ejpam-21	524	7	)	)	PUNCT
ejpam-21	524	8	is	be	AUX
ejpam-21	524	9	an	an	DET
ejpam-21	524	10	open	open	ADJ
ejpam-21	524	11	set	set	NOUN
ejpam-21	524	12	having	have	VERB
ejpam-21	524	13	compact	compact	ADJ
ejpam-21	524	14	complement	complement	NOUN
ejpam-21	524	15	,	,	PUNCT
ejpam-21	524	16	there	there	PRON
ejpam-21	524	17	exists	exist	VERB
ejpam-21	524	18	u	u	PROPN
ejpam-21	524	19	∈	∈	PROPN
ejpam-21	524	20	mx	mx	NOUN
ejpam-21	524	21	containing	contain	VERB
ejpam-21	524	22	x	x	PUNCT
ejpam-21	524	23	such	such	ADJ
ejpam-21	524	24	that	that	SCONJ
ejpam-21	524	25	f	f	PROPN
ejpam-21	524	26	(	(	PUNCT
ejpam-21	524	27	u	u	NOUN
ejpam-21	524	28	)	)	PUNCT
ejpam-21	524	29	⊂	⊂	PROPN
ejpam-21	524	30	y	y	PROPN
ejpam-21	524	31	−cl(v	−cl(v	PROPN
ejpam-21	524	32	)	)	PUNCT
ejpam-21	524	33	.	.	PUNCT
ejpam-21	525	1	this	this	PRON
ejpam-21	525	2	implies	imply	VERB
ejpam-21	525	3	that	that	SCONJ
ejpam-21	525	4	f	f	PROPN
ejpam-21	525	5	(	(	PUNCT
ejpam-21	525	6	u	u	NOUN
ejpam-21	525	7	)	)	PUNCT
ejpam-21	525	8	∩cl(v	∩cl(v	PROPN
ejpam-21	525	9	)	)	PUNCT
ejpam-21	526	1	=	=	NOUN
ejpam-21	526	2	∅	∅	NOUN
ejpam-21	526	3	and	and	CCONJ
ejpam-21	526	4	by	by	ADP
ejpam-21	526	5	lemma	lemma	PROPN
ejpam-21	526	6	6.1	6.1	NUM
ejpam-21	526	7	g(f	g(f	NOUN
ejpam-21	526	8	)	)	PUNCT
ejpam-21	526	9	is	be	AUX
ejpam-21	526	10	strongly	strongly	ADV
ejpam-21	526	11	m	m	NOUN
ejpam-21	526	12	-	-	PUNCT
ejpam-21	526	13	closed	closed	ADJ
ejpam-21	526	14	.	.	PUNCT
ejpam-21	527	1	7	7	X
ejpam-21	527	2	.	.	X
ejpam-21	527	3	new	new	ADJ
ejpam-21	527	4	modifications	modification	NOUN
ejpam-21	527	5	of	of	ADP
ejpam-21	527	6	c	c	NOUN
ejpam-21	527	7	-	-	PUNCT
ejpam-21	527	8	continuous	continuous	ADJ
ejpam-21	527	9	multifunctions	multifunction	NOUN
ejpam-21	527	10	for	for	ADP
ejpam-21	527	11	modifications	modification	NOUN
ejpam-21	527	12	of	of	ADP
ejpam-21	527	13	open	open	ADJ
ejpam-21	527	14	sets	set	NOUN
ejpam-21	527	15	defined	define	VERB
ejpam-21	527	16	in	in	ADP
ejpam-21	527	17	definition	definition	NOUN
ejpam-21	527	18	2.1	2.1	NUM
ejpam-21	527	19	,	,	PUNCT
ejpam-21	527	20	the	the	DET
ejpam-21	527	21	following	follow	VERB
ejpam-21	527	22	relationships	relationship	NOUN
ejpam-21	527	23	are	be	AUX
ejpam-21	527	24	known	know	VERB
ejpam-21	527	25	:	:	PUNCT
ejpam-21	527	26	open	open	ADJ
ejpam-21	527	27	⇒	⇒	NOUN
ejpam-21	527	28	α	α	X
ejpam-21	527	29	-	-	ADJ
ejpam-21	527	30	open	open	ADJ
ejpam-21	527	31	⇒	⇒	NOUN
ejpam-21	527	32	preopen	preopen	VERB
ejpam-21	527	33	⇓	⇓	PROPN
ejpam-21	527	34	⇓	⇓	PROPN
ejpam-21	527	35	semi	semi	ADJ
ejpam-21	527	36	-	-	ADJ
ejpam-21	527	37	open	open	ADJ
ejpam-21	527	38	⇒	⇒	NOUN
ejpam-21	527	39	b	b	X
ejpam-21	527	40	-	-	PUNCT
ejpam-21	527	41	open	open	ADJ
ejpam-21	527	42	⇒	⇒	NOUN
ejpam-21	527	43	semi	semi	ADV
ejpam-21	527	44	-	-	ADJ
ejpam-21	527	45	preopen	preopen	ADJ
ejpam-21	527	46	t.noiri	t.noiri	ADV
ejpam-21	527	47	,	,	PUNCT
ejpam-21	527	48	v.popa	v.popa	NOUN
ejpam-21	527	49	/	/	SYM
ejpam-21	527	50	eur	eur	PROPN
ejpam-21	527	51	.	.	PUNCT
ejpam-21	528	1	j.	j.	PROPN
ejpam-21	528	2	pure	pure	PROPN
ejpam-21	528	3	appl	appl	PROPN
ejpam-21	528	4	.	.	PROPN
ejpam-21	528	5	math	math	PROPN
ejpam-21	528	6	,	,	PUNCT
ejpam-21	528	7	1	1	NUM
ejpam-21	528	8	(	(	PUNCT
ejpam-21	528	9	2008	2008	NUM
ejpam-21	528	10	)	)	PUNCT
ejpam-21	528	11	,	,	PUNCT
ejpam-21	528	12	(	(	PUNCT
ejpam-21	528	13	82	82	NUM
ejpam-21	528	14	-	-	SYM
ejpam-21	528	15	98	98	NUM
ejpam-21	528	16	)	)	PUNCT
ejpam-21	528	17	95	95	NUM
ejpam-21	528	18	first	first	ADV
ejpam-21	528	19	,	,	PUNCT
ejpam-21	528	20	we	we	PRON
ejpam-21	528	21	can	can	AUX
ejpam-21	528	22	define	define	VERB
ejpam-21	528	23	the	the	DET
ejpam-21	528	24	following	follow	VERB
ejpam-21	528	25	modifications	modification	NOUN
ejpam-21	528	26	of	of	ADP
ejpam-21	528	27	upper	upper	ADJ
ejpam-21	528	28	/	/	SYM
ejpam-21	528	29	lower	low	ADJ
ejpam-21	528	30	c	c	NOUN
ejpam-21	528	31	-continuous	-continuous	ADJ
ejpam-21	528	32	multifunctions	multifunction	NOUN
ejpam-21	528	33	.	.	PUNCT
ejpam-21	529	1	definition	definition	NOUN
ejpam-21	529	2	7.1	7.1	NUM
ejpam-21	529	3	.	.	PUNCT
ejpam-21	530	1	a	a	DET
ejpam-21	530	2	multifunction	multifunction	NOUN
ejpam-21	530	3	f	f	NOUN
ejpam-21	530	4	:	:	PUNCT
ejpam-21	530	5	(	(	PUNCT
ejpam-21	530	6	x	x	X
ejpam-21	530	7	,	,	PUNCT
ejpam-21	530	8	τ	τ	X
ejpam-21	530	9	)	)	PUNCT
ejpam-21	530	10	→	→	SYM
ejpam-21	530	11	(	(	PUNCT
ejpam-21	530	12	y	y	PROPN
ejpam-21	530	13	,	,	PUNCT
ejpam-21	530	14	σ	σ	PROPN
ejpam-21	530	15	)	)	PUNCT
ejpam-21	530	16	is	be	AUX
ejpam-21	530	17	said	say	VERB
ejpam-21	530	18	to	to	PART
ejpam-21	530	19	be	be	AUX
ejpam-21	530	20	(	(	PUNCT
ejpam-21	530	21	1	1	X
ejpam-21	530	22	)	)	PUNCT
ejpam-21	530	23	upper	upper	ADJ
ejpam-21	530	24	c	c	NOUN
ejpam-21	530	25	-	-	PUNCT
ejpam-21	530	26	α	α	NOUN
ejpam-21	530	27	-	-	ADJ
ejpam-21	530	28	continuous	continuous	ADJ
ejpam-21	530	29	(	(	PUNCT
ejpam-21	530	30	resp	resp	NOUN
ejpam-21	530	31	.	.	PUNCT
ejpam-21	531	1	upper	upper	ADJ
ejpam-21	531	2	c	c	NOUN
ejpam-21	531	3	-	-	NOUN
ejpam-21	531	4	precontinuous	precontinuous	ADJ
ejpam-21	531	5	,	,	PUNCT
ejpam-21	531	6	upper	upper	ADJ
ejpam-21	531	7	c	c	NOUN
ejpam-21	531	8	-	-	PUNCT
ejpam-21	531	9	b	b	NOUN
ejpam-21	531	10	-	-	PUNCT
ejpam-21	531	11	continuous	continuous	ADJ
ejpam-21	531	12	,	,	PUNCT
ejpam-21	531	13	upper	upper	ADJ
ejpam-21	531	14	csp	csp	PROPN
ejpam-21	531	15	-	-	PUNCT
ejpam-21	531	16	continuous	continuous	ADJ
ejpam-21	531	17	)	)	PUNCT
ejpam-21	531	18	at	at	ADP
ejpam-21	531	19	a	a	DET
ejpam-21	531	20	point	point	NOUN
ejpam-21	531	21	x	x	SYM
ejpam-21	531	22	∈	∈	NOUN
ejpam-21	531	23	x	x	INTJ
ejpam-21	531	24	if	if	SCONJ
ejpam-21	531	25	for	for	ADP
ejpam-21	531	26	each	each	DET
ejpam-21	531	27	open	open	ADJ
ejpam-21	531	28	set	set	VERB
ejpam-21	531	29	v	v	NOUN
ejpam-21	531	30	containing	contain	VERB
ejpam-21	531	31	f	f	X
ejpam-21	531	32	(	(	PUNCT
ejpam-21	531	33	x	x	NOUN
ejpam-21	531	34	)	)	PUNCT
ejpam-21	531	35	and	and	CCONJ
ejpam-21	531	36	having	have	VERB
ejpam-21	531	37	compact	compact	ADJ
ejpam-21	531	38	complement	complement	NOUN
ejpam-21	531	39	,	,	PUNCT
ejpam-21	531	40	there	there	PRON
ejpam-21	531	41	exists	exist	VERB
ejpam-21	531	42	an	an	DET
ejpam-21	531	43	α	α	NOUN
ejpam-21	531	44	-	-	ADJ
ejpam-21	531	45	open	open	ADJ
ejpam-21	531	46	(	(	PUNCT
ejpam-21	531	47	resp	resp	NOUN
ejpam-21	531	48	.	.	PUNCT
ejpam-21	532	1	preopen	preopen	ADJ
ejpam-21	532	2	,	,	PUNCT
ejpam-21	532	3	b	b	X
ejpam-21	532	4	-	-	PUNCT
ejpam-21	532	5	open	open	ADJ
ejpam-21	532	6	,	,	PUNCT
ejpam-21	532	7	semi	semi	ADJ
ejpam-21	532	8	-	-	ADJ
ejpam-21	532	9	preopen	preopen	ADJ
ejpam-21	532	10	)	)	PUNCT
ejpam-21	532	11	set	set	VERB
ejpam-21	532	12	u	u	NOUN
ejpam-21	532	13	containing	contain	VERB
ejpam-21	532	14	x	x	PUNCT
ejpam-21	532	15	such	such	ADJ
ejpam-21	532	16	that	that	SCONJ
ejpam-21	532	17	f	f	PROPN
ejpam-21	532	18	(	(	PUNCT
ejpam-21	532	19	u	u	NOUN
ejpam-21	532	20	)	)	PUNCT
ejpam-21	532	21	⊂	⊂	PROPN
ejpam-21	532	22	v	v	PROPN
ejpam-21	532	23	,	,	PUNCT
ejpam-21	532	24	(	(	PUNCT
ejpam-21	532	25	2	2	X
ejpam-21	532	26	)	)	PUNCT
ejpam-21	532	27	lower	low	ADJ
ejpam-21	532	28	c	c	NOUN
ejpam-21	532	29	-	-	PUNCT
ejpam-21	532	30	α	α	NOUN
ejpam-21	532	31	-	-	ADJ
ejpam-21	532	32	continuous	continuous	ADJ
ejpam-21	532	33	(	(	PUNCT
ejpam-21	532	34	resp	resp	NOUN
ejpam-21	532	35	.	.	PUNCT
ejpam-21	533	1	lower	low	ADJ
ejpam-21	533	2	c	c	NOUN
ejpam-21	533	3	-	-	NOUN
ejpam-21	533	4	precontinuous	precontinuous	ADJ
ejpam-21	533	5	,	,	PUNCT
ejpam-21	533	6	lower	low	ADJ
ejpam-21	533	7	c	c	NOUN
ejpam-21	533	8	-	-	PUNCT
ejpam-21	533	9	b	b	NOUN
ejpam-21	533	10	-	-	PUNCT
ejpam-21	533	11	continuous	continuous	ADJ
ejpam-21	533	12	,	,	PUNCT
ejpam-21	533	13	lower	low	ADJ
ejpam-21	533	14	c	c	NOUN
ejpam-21	533	15	-	-	ADJ
ejpam-21	533	16	spcontinuous	spcontinuous	ADJ
ejpam-21	533	17	)	)	PUNCT
ejpam-21	533	18	at	at	ADP
ejpam-21	533	19	a	a	DET
ejpam-21	533	20	point	point	NOUN
ejpam-21	533	21	x	x	SYM
ejpam-21	533	22	∈	∈	NOUN
ejpam-21	533	23	x	x	INTJ
ejpam-21	533	24	if	if	SCONJ
ejpam-21	533	25	for	for	ADP
ejpam-21	533	26	each	each	DET
ejpam-21	533	27	open	open	ADJ
ejpam-21	533	28	set	set	VERB
ejpam-21	533	29	v	v	NUM
ejpam-21	533	30	meeting	meeting	NOUN
ejpam-21	533	31	f	f	X
ejpam-21	533	32	(	(	PUNCT
ejpam-21	533	33	x	x	NOUN
ejpam-21	533	34	)	)	PUNCT
ejpam-21	533	35	and	and	CCONJ
ejpam-21	533	36	having	have	VERB
ejpam-21	533	37	compact	compact	ADJ
ejpam-21	533	38	complement	complement	NOUN
ejpam-21	533	39	,	,	PUNCT
ejpam-21	533	40	there	there	PRON
ejpam-21	533	41	exists	exist	VERB
ejpam-21	533	42	an	an	DET
ejpam-21	533	43	α	α	NOUN
ejpam-21	533	44	-	-	ADJ
ejpam-21	533	45	open	open	ADJ
ejpam-21	533	46	(	(	PUNCT
ejpam-21	533	47	resp	resp	NOUN
ejpam-21	533	48	.	.	PUNCT
ejpam-21	534	1	preopen	preopen	ADJ
ejpam-21	534	2	,	,	PUNCT
ejpam-21	534	3	b	b	X
ejpam-21	534	4	-	-	PUNCT
ejpam-21	534	5	open	open	ADJ
ejpam-21	534	6	,	,	PUNCT
ejpam-21	534	7	semi	semi	ADJ
ejpam-21	534	8	-	-	ADJ
ejpam-21	534	9	preopen	preopen	ADJ
ejpam-21	534	10	)	)	PUNCT
ejpam-21	534	11	set	set	VERB
ejpam-21	534	12	u	u	NOUN
ejpam-21	534	13	containing	contain	VERB
ejpam-21	534	14	x	x	PUNCT
ejpam-21	534	15	such	such	ADJ
ejpam-21	534	16	that	that	SCONJ
ejpam-21	534	17	f	f	PROPN
ejpam-21	534	18	(	(	PUNCT
ejpam-21	534	19	u	u	NOUN
ejpam-21	534	20	)	)	PUNCT
ejpam-21	534	21	∩	∩	NOUN
ejpam-21	534	22	v	v	ADP
ejpam-21	534	23	6=	6=	NOUN
ejpam-21	534	24	∅	∅	NOUN
ejpam-21	534	25	for	for	ADP
ejpam-21	534	26	each	each	DET
ejpam-21	534	27	u	u	PROPN
ejpam-21	534	28	∈	∈	PROPN
ejpam-21	534	29	u	u	NOUN
ejpam-21	534	30	,	,	PUNCT
ejpam-21	534	31	(	(	PUNCT
ejpam-21	534	32	3	3	X
ejpam-21	534	33	)	)	PUNCT
ejpam-21	534	34	upper	upper	ADJ
ejpam-21	534	35	/	/	SYM
ejpam-21	534	36	lower	low	ADJ
ejpam-21	534	37	c	c	NOUN
ejpam-21	534	38	-	-	PUNCT
ejpam-21	534	39	α	α	NOUN
ejpam-21	534	40	-	-	ADJ
ejpam-21	534	41	continuous	continuous	ADJ
ejpam-21	534	42	(	(	PUNCT
ejpam-21	534	43	resp	resp	NOUN
ejpam-21	534	44	.	.	PUNCT
ejpam-21	535	1	upper	upper	ADJ
ejpam-21	535	2	/	/	SYM
ejpam-21	535	3	lower	low	ADJ
ejpam-21	535	4	c	c	NOUN
ejpam-21	535	5	-	-	ADJ
ejpam-21	535	6	precontinuous	precontinuous	ADJ
ejpam-21	535	7	,	,	PUNCT
ejpam-21	535	8	upper	upper	ADJ
ejpam-21	535	9	/	/	SYM
ejpam-21	535	10	lower	low	ADJ
ejpam-21	535	11	c	c	NOUN
ejpam-21	535	12	-	-	PUNCT
ejpam-21	535	13	b	b	NOUN
ejpam-21	535	14	-	-	PUNCT
ejpam-21	535	15	continuous	continuous	ADJ
ejpam-21	535	16	,	,	PUNCT
ejpam-21	535	17	upper	upper	ADJ
ejpam-21	535	18	/	/	SYM
ejpam-21	535	19	lower	low	ADJ
ejpam-21	535	20	c	c	NOUN
ejpam-21	535	21	-	-	PUNCT
ejpam-21	535	22	sp	sp	NOUN
ejpam-21	535	23	-	-	PUNCT
ejpam-21	535	24	continuous	continuous	ADJ
ejpam-21	535	25	)	)	PUNCT
ejpam-21	536	1	on	on	ADP
ejpam-21	536	2	x	x	SYM
ejpam-21	536	3	if	if	SCONJ
ejpam-21	536	4	it	it	PRON
ejpam-21	536	5	has	have	AUX
ejpam-21	536	6	this	this	DET
ejpam-21	536	7	property	property	NOUN
ejpam-21	536	8	at	at	ADP
ejpam-21	536	9	each	each	DET
ejpam-21	536	10	x	x	SYM
ejpam-21	536	11	∈	∈	PROPN
ejpam-21	536	12	x	x	X
ejpam-21	536	13	.	.	PUNCT
ejpam-21	537	1	for	for	ADP
ejpam-21	537	2	multifunctions	multifunction	NOUN
ejpam-21	537	3	defined	define	VERB
ejpam-21	537	4	in	in	ADP
ejpam-21	537	5	definition	definition	NOUN
ejpam-21	537	6	7.1	7.1	NUM
ejpam-21	537	7	,	,	PUNCT
ejpam-21	537	8	the	the	DET
ejpam-21	537	9	following	follow	VERB
ejpam-21	537	10	relationships	relationship	NOUN
ejpam-21	537	11	hold	hold	VERB
ejpam-21	537	12	:	:	PUNCT
ejpam-21	537	13	upper	upper	ADJ
ejpam-21	537	14	c	c	NOUN
ejpam-21	537	15	-	-	NOUN
ejpam-21	537	16	con	con	NOUN
ejpam-21	537	17	.	.	PUNCT
ejpam-21	538	1	⇒	⇒	PROPN
ejpam-21	538	2	upper	upper	ADJ
ejpam-21	538	3	c	c	NOUN
ejpam-21	538	4	-	-	PUNCT
ejpam-21	538	5	α	α	NOUN
ejpam-21	538	6	-	-	NOUN
ejpam-21	538	7	con	con	NOUN
ejpam-21	538	8	.	.	PUNCT
ejpam-21	539	1	⇒	⇒	PROPN
ejpam-21	539	2	upper	upper	ADJ
ejpam-21	539	3	c	c	NOUN
ejpam-21	539	4	-	-	PUNCT
ejpam-21	539	5	precon	precon	NOUN
ejpam-21	539	6	.	.	PUNCT
ejpam-21	540	1	⇓	⇓	PROPN
ejpam-21	540	2	⇓	⇓	PROPN
ejpam-21	540	3	upper	upper	ADJ
ejpam-21	540	4	c	c	NOUN
ejpam-21	540	5	-	-	PUNCT
ejpam-21	540	6	quasi	quasi	NOUN
ejpam-21	540	7	-	-	NOUN
ejpam-21	540	8	con	con	NOUN
ejpam-21	540	9	.	.	PUNCT
ejpam-21	541	1	⇒	⇒	PROPN
ejpam-21	541	2	upper	upper	ADJ
ejpam-21	541	3	c	c	PROPN
ejpam-21	541	4	-	-	PUNCT
ejpam-21	541	5	b	b	NOUN
ejpam-21	541	6	-	-	PUNCT
ejpam-21	541	7	con	con	NOUN
ejpam-21	541	8	.	.	PUNCT
ejpam-21	542	1	⇒	⇒	PROPN
ejpam-21	542	2	upper	upper	ADJ
ejpam-21	542	3	c	c	NOUN
ejpam-21	542	4	-	-	PUNCT
ejpam-21	542	5	sp	sp	NOUN
ejpam-21	542	6	-	-	PUNCT
ejpam-21	542	7	con	con	NOUN
ejpam-21	542	8	.	.	PUNCT
ejpam-21	543	1	remark	remark	PROPN
ejpam-21	543	2	7.1	7.1	NUM
ejpam-21	543	3	.	.	PUNCT
ejpam-21	544	1	in	in	ADP
ejpam-21	544	2	the	the	DET
ejpam-21	544	3	diagram	diagram	NOUN
ejpam-21	544	4	above	above	ADV
ejpam-21	544	5	,	,	PUNCT
ejpam-21	544	6	”	"	PUNCT
ejpam-21	544	7	con	con	X
ejpam-21	544	8	.	.	PUNCT
ejpam-21	544	9	”	"	PUNCT
ejpam-21	544	10	means	mean	VERB
ejpam-21	544	11	continuity	continuity	NOUN
ejpam-21	544	12	and	and	CCONJ
ejpam-21	544	13	the	the	DET
ejpam-21	544	14	analogous	analogous	ADJ
ejpam-21	544	15	diagram	diagram	NOUN
ejpam-21	544	16	holds	hold	VERB
ejpam-21	544	17	for	for	ADP
ejpam-21	544	18	the	the	DET
ejpam-21	544	19	case	case	NOUN
ejpam-21	544	20	”	"	PUNCT
ejpam-21	544	21	lower	low	ADJ
ejpam-21	544	22	”	"	PUNCT
ejpam-21	544	23	.	.	PUNCT
ejpam-21	545	1	let	let	VERB
ejpam-21	545	2	define	define	VERB
ejpam-21	545	3	the	the	DET
ejpam-21	545	4	further	further	ADJ
ejpam-21	545	5	modifications	modification	NOUN
ejpam-21	545	6	of	of	ADP
ejpam-21	545	7	upper	upper	ADJ
ejpam-21	545	8	/	/	SYM
ejpam-21	545	9	lower	low	ADJ
ejpam-21	545	10	c	c	NOUN
ejpam-21	545	11	-	-	ADJ
ejpam-21	545	12	continuous	continuous	ADJ
ejpam-21	545	13	multifunctions	multifunction	NOUN
ejpam-21	545	14	.	.	PUNCT
ejpam-21	546	1	for	for	ADP
ejpam-21	546	2	the	the	DET
ejpam-21	546	3	purpose	purpose	NOUN
ejpam-21	546	4	,	,	PUNCT
ejpam-21	546	5	we	we	PRON
ejpam-21	546	6	recall	recall	VERB
ejpam-21	546	7	the	the	DET
ejpam-21	546	8	definitions	definition	NOUN
ejpam-21	546	9	of	of	ADP
ejpam-21	546	10	the	the	DET
ejpam-21	546	11	θ	θ	PROPN
ejpam-21	546	12	-closure	-closure	NOUN
ejpam-21	546	13	and	and	CCONJ
ejpam-21	546	14	the	the	DET
ejpam-21	546	15	δ	δ	PROPN
ejpam-21	546	16	-	-	NOUN
ejpam-21	546	17	closure	closure	NOUN
ejpam-21	546	18	due	due	ADP
ejpam-21	546	19	to	to	ADP
ejpam-21	546	20	veličko	veličko	PROPN
ejpam-21	546	21	[	[	X
ejpam-21	546	22	38	38	NUM
ejpam-21	546	23	]	]	PUNCT
ejpam-21	546	24	.	.	PUNCT
ejpam-21	547	1	let	let	VERB
ejpam-21	547	2	(	(	PUNCT
ejpam-21	547	3	x	x	NOUN
ejpam-21	547	4	,	,	PUNCT
ejpam-21	547	5	τ	τ	X
ejpam-21	547	6	)	)	PUNCT
ejpam-21	547	7	be	be	VERB
ejpam-21	547	8	a	a	DET
ejpam-21	547	9	topological	topological	ADJ
ejpam-21	547	10	space	space	NOUN
ejpam-21	547	11	and	and	CCONJ
ejpam-21	547	12	a	a	DET
ejpam-21	547	13	a	a	DET
ejpam-21	547	14	subset	subset	NOUN
ejpam-21	547	15	of	of	ADP
ejpam-21	547	16	x	x	X
ejpam-21	547	17	.	.	PUNCT
ejpam-21	548	1	a	a	DET
ejpam-21	548	2	point	point	NOUN
ejpam-21	548	3	x	x	X
ejpam-21	548	4	∈	∈	NOUN
ejpam-21	548	5	x	x	PUNCT
ejpam-21	548	6	is	be	AUX
ejpam-21	548	7	called	call	VERB
ejpam-21	548	8	a	a	DET
ejpam-21	548	9	θ	θ	NOUN
ejpam-21	548	10	-	-	NOUN
ejpam-21	548	11	cluster	cluster	NOUN
ejpam-21	548	12	(	(	PUNCT
ejpam-21	548	13	resp	resp	NOUN
ejpam-21	548	14	.	.	PUNCT
ejpam-21	549	1	δ	δ	NOUN
ejpam-21	549	2	-	-	PUNCT
ejpam-21	549	3	cluster	cluster	NOUN
ejpam-21	549	4	)	)	PUNCT
ejpam-21	549	5	point	point	NOUN
ejpam-21	549	6	of	of	ADP
ejpam-21	549	7	a	a	DET
ejpam-21	549	8	if	if	SCONJ
ejpam-21	549	9	cl(v	cl(v	NOUN
ejpam-21	549	10	)	)	PUNCT
ejpam-21	550	1	∩a	∩a	PROPN
ejpam-21	550	2	6=	6=	NUM
ejpam-21	550	3	∅	∅	NOUN
ejpam-21	550	4	(	(	PUNCT
ejpam-21	550	5	resp	resp	NOUN
ejpam-21	550	6	.	.	PUNCT
ejpam-21	550	7	int(cl(v	int(cl(v	NOUN
ejpam-21	550	8	)	)	PUNCT
ejpam-21	550	9	)	)	PUNCT
ejpam-21	551	1	∩a	∩a	PROPN
ejpam-21	551	2	6=	6=	NUM
ejpam-21	551	3	∅	∅	NOUN
ejpam-21	551	4	)	)	PUNCT
ejpam-21	551	5	for	for	ADP
ejpam-21	551	6	every	every	DET
ejpam-21	551	7	open	open	ADJ
ejpam-21	551	8	set	set	VERB
ejpam-21	551	9	v	v	NOUN
ejpam-21	551	10	containing	contain	VERB
ejpam-21	551	11	x.	x.	NOUN
ejpam-21	551	12	the	the	DET
ejpam-21	551	13	set	set	NOUN
ejpam-21	551	14	of	of	ADP
ejpam-21	551	15	all	all	DET
ejpam-21	551	16	θ	θ	NOUN
ejpam-21	551	17	-	-	NOUN
ejpam-21	551	18	cluster	cluster	NOUN
ejpam-21	551	19	(	(	PUNCT
ejpam-21	551	20	resp	resp	NOUN
ejpam-21	551	21	.	.	PUNCT
ejpam-21	552	1	δ	δ	NOUN
ejpam-21	552	2	-	-	PUNCT
ejpam-21	552	3	cluster	cluster	NOUN
ejpam-21	552	4	)	)	PUNCT
ejpam-21	552	5	points	point	NOUN
ejpam-21	552	6	of	of	ADP
ejpam-21	552	7	a	a	PRON
ejpam-21	552	8	is	be	AUX
ejpam-21	552	9	called	call	VERB
ejpam-21	552	10	the	the	DET
ejpam-21	552	11	θ	θ	NOUN
ejpam-21	552	12	-	-	NOUN
ejpam-21	552	13	closure	closure	NOUN
ejpam-21	552	14	(	(	PUNCT
ejpam-21	552	15	resp	resp	NOUN
ejpam-21	552	16	.	.	PUNCT
ejpam-21	553	1	δ	δ	NOUN
ejpam-21	553	2	-	-	PUNCT
ejpam-21	553	3	closure	closure	NOUN
ejpam-21	553	4	)	)	PUNCT
ejpam-21	553	5	of	of	ADP
ejpam-21	553	6	a	a	PRON
ejpam-21	553	7	and	and	CCONJ
ejpam-21	553	8	is	be	AUX
ejpam-21	553	9	denoted	denote	VERB
ejpam-21	553	10	by	by	ADP
ejpam-21	553	11	clθ(a	clθ(a	PROPN
ejpam-21	553	12	)	)	PUNCT
ejpam-21	553	13	(	(	PUNCT
ejpam-21	553	14	resp	resp	NOUN
ejpam-21	553	15	.	.	PUNCT
ejpam-21	554	1	clδ(a	clδ(a	X
ejpam-21	554	2	)	)	PUNCT
ejpam-21	554	3	)	)	PUNCT
ejpam-21	555	1	[	[	X
ejpam-21	555	2	38	38	NUM
ejpam-21	555	3	]	]	PUNCT
ejpam-21	555	4	.	.	PUNCT
ejpam-21	556	1	a	a	DET
ejpam-21	556	2	subset	subset	NOUN
ejpam-21	556	3	a	a	PRON
ejpam-21	556	4	is	be	AUX
ejpam-21	556	5	said	say	VERB
ejpam-21	556	6	to	to	PART
ejpam-21	556	7	be	be	AUX
ejpam-21	556	8	θ	θ	NOUN
ejpam-21	556	9	-	-	ADJ
ejpam-21	556	10	closed	closed	ADJ
ejpam-21	556	11	(	(	PUNCT
ejpam-21	556	12	resp	resp	NOUN
ejpam-21	556	13	.	.	PUNCT
ejpam-21	557	1	δ	δ	NOUN
ejpam-21	557	2	-	-	PUNCT
ejpam-21	557	3	closed	closed	ADJ
ejpam-21	557	4	)	)	PUNCT
ejpam-21	557	5	if	if	SCONJ
ejpam-21	557	6	clθ(a	clθ(a	PROPN
ejpam-21	557	7	)	)	PUNCT
ejpam-21	557	8	=	=	SYM
ejpam-21	558	1	a	a	DET
ejpam-21	558	2	(	(	PUNCT
ejpam-21	558	3	resp	resp	NOUN
ejpam-21	558	4	.	.	PUNCT
ejpam-21	559	1	clδ(a	clδ(a	X
ejpam-21	559	2	)	)	PUNCT
ejpam-21	560	1	=	=	SYM
ejpam-21	560	2	a	a	NOUN
ejpam-21	560	3	)	)	PUNCT
ejpam-21	560	4	.	.	PUNCT
ejpam-21	561	1	the	the	DET
ejpam-21	561	2	complement	complement	NOUN
ejpam-21	561	3	of	of	ADP
ejpam-21	561	4	a	a	DET
ejpam-21	561	5	θ	θ	NOUN
ejpam-21	561	6	-	-	ADJ
ejpam-21	561	7	closed	closed	ADJ
ejpam-21	561	8	(	(	PUNCT
ejpam-21	561	9	resp	resp	NOUN
ejpam-21	561	10	.	.	PUNCT
ejpam-21	562	1	δ	δ	NOUN
ejpam-21	562	2	-	-	PUNCT
ejpam-21	562	3	closed	closed	ADJ
ejpam-21	562	4	)	)	PUNCT
ejpam-21	562	5	set	set	NOUN
ejpam-21	562	6	is	be	AUX
ejpam-21	562	7	said	say	VERB
ejpam-21	562	8	to	to	PART
ejpam-21	562	9	be	be	AUX
ejpam-21	562	10	θ	θ	NOUN
ejpam-21	562	11	-	-	ADJ
ejpam-21	562	12	open	open	ADJ
ejpam-21	562	13	(	(	PUNCT
ejpam-21	562	14	resp	resp	NOUN
ejpam-21	562	15	.	.	PUNCT
ejpam-21	563	1	δ	δ	NOUN
ejpam-21	563	2	-	-	NOUN
ejpam-21	563	3	open	open	ADJ
ejpam-21	563	4	)	)	PUNCT
ejpam-21	563	5	.	.	PUNCT
ejpam-21	564	1	the	the	DET
ejpam-21	564	2	union	union	NOUN
ejpam-21	564	3	of	of	ADP
ejpam-21	564	4	all	all	DET
ejpam-21	564	5	θ	θ	NOUN
ejpam-21	564	6	-	-	ADJ
ejpam-21	564	7	open	open	ADJ
ejpam-21	564	8	(	(	PUNCT
ejpam-21	564	9	resp	resp	NOUN
ejpam-21	564	10	.	.	PUNCT
ejpam-21	565	1	δ	δ	NOUN
ejpam-21	565	2	-	-	ADJ
ejpam-21	565	3	open	open	ADJ
ejpam-21	565	4	)	)	PUNCT
ejpam-21	565	5	sets	set	NOUN
ejpam-21	565	6	contained	contain	VERB
ejpam-21	565	7	in	in	ADP
ejpam-21	565	8	the	the	DET
ejpam-21	565	9	subset	subset	NOUN
ejpam-21	565	10	a	a	PRON
ejpam-21	565	11	is	be	AUX
ejpam-21	565	12	called	call	VERB
ejpam-21	565	13	the	the	DET
ejpam-21	565	14	θ	θ	NOUN
ejpam-21	565	15	-	-	NOUN
ejpam-21	565	16	interior	interior	ADJ
ejpam-21	565	17	(	(	PUNCT
ejpam-21	565	18	resp	resp	NOUN
ejpam-21	565	19	.	.	PUNCT
ejpam-21	566	1	δ	δ	PROPN
ejpam-21	566	2	-	-	NOUN
ejpam-21	566	3	interior	interior	NOUN
ejpam-21	566	4	)	)	PUNCT
ejpam-21	566	5	of	of	ADP
ejpam-21	566	6	a	a	PRON
ejpam-21	566	7	and	and	CCONJ
ejpam-21	566	8	is	be	AUX
ejpam-21	566	9	denoted	denote	VERB
ejpam-21	566	10	by	by	ADP
ejpam-21	566	11	intθ(a	intθ(a	PROPN
ejpam-21	566	12	)	)	PUNCT
ejpam-21	566	13	(	(	PUNCT
ejpam-21	566	14	resp	resp	NOUN
ejpam-21	566	15	.	.	PUNCT
ejpam-21	567	1	intδ(a	intδ(a	NOUN
ejpam-21	567	2	)	)	PUNCT
ejpam-21	567	3	)	)	PUNCT
ejpam-21	567	4	.	.	PUNCT
ejpam-21	568	1	definition	definition	NOUN
ejpam-21	568	2	7.2	7.2	NUM
ejpam-21	568	3	.	.	PUNCT
ejpam-21	569	1	a	a	DET
ejpam-21	569	2	subset	subset	NOUN
ejpam-21	569	3	a	a	PRON
ejpam-21	569	4	of	of	ADP
ejpam-21	569	5	a	a	DET
ejpam-21	569	6	topological	topological	ADJ
ejpam-21	569	7	space	space	NOUN
ejpam-21	569	8	(	(	PUNCT
ejpam-21	569	9	x	x	X
ejpam-21	569	10	,	,	PUNCT
ejpam-21	569	11	τ	τ	X
ejpam-21	569	12	)	)	PUNCT
ejpam-21	569	13	is	be	AUX
ejpam-21	569	14	said	say	VERB
ejpam-21	569	15	to	to	PART
ejpam-21	569	16	be	be	AUX
ejpam-21	569	17	(	(	PUNCT
ejpam-21	569	18	1	1	X
ejpam-21	569	19	)	)	PUNCT
ejpam-21	569	20	δ	δ	NOUN
ejpam-21	569	21	-	-	PUNCT
ejpam-21	569	22	semiopen	semiopen	PROPN
ejpam-21	570	1	[	[	X
ejpam-21	570	2	25	25	NUM
ejpam-21	570	3	]	]	PUNCT
ejpam-21	570	4	(	(	PUNCT
ejpam-21	570	5	resp	resp	NOUN
ejpam-21	570	6	.	.	PUNCT
ejpam-21	571	1	θ	θ	X
ejpam-21	571	2	-	-	PUNCT
ejpam-21	571	3	semiopen	semiopen	ADJ
ejpam-21	572	1	[	[	X
ejpam-21	572	2	6	6	NUM
ejpam-21	572	3	]	]	SYM
ejpam-21	572	4	)	)	PUNCT
ejpam-21	572	5	if	if	SCONJ
ejpam-21	572	6	a	a	DET
ejpam-21	572	7	⊂	⊂	PROPN
ejpam-21	572	8	cl(intδ(a	cl(intδ(a	PROPN
ejpam-21	572	9	)	)	PUNCT
ejpam-21	572	10	)	)	PUNCT
ejpam-21	572	11	(	(	PUNCT
ejpam-21	572	12	resp	resp	NOUN
ejpam-21	572	13	.	.	PUNCT
ejpam-21	573	1	a	a	DET
ejpam-21	573	2	⊂	⊂	PROPN
ejpam-21	573	3	cl(intθ(a	cl(intθ(a	NOUN
ejpam-21	573	4	)	)	PUNCT
ejpam-21	573	5	)	)	PUNCT
ejpam-21	573	6	)	)	PUNCT
ejpam-21	573	7	,	,	PUNCT
ejpam-21	573	8	(	(	PUNCT
ejpam-21	573	9	2	2	X
ejpam-21	573	10	)	)	PUNCT
ejpam-21	573	11	δ	δ	NOUN
ejpam-21	573	12	-	-	NOUN
ejpam-21	573	13	preopen	preopen	ADJ
ejpam-21	573	14	[	[	X
ejpam-21	573	15	37	37	NUM
ejpam-21	573	16	]	]	PUNCT
ejpam-21	573	17	(	(	PUNCT
ejpam-21	573	18	resp	resp	NOUN
ejpam-21	573	19	.	.	PUNCT
ejpam-21	574	1	θ	θ	X
ejpam-21	574	2	-	-	PUNCT
ejpam-21	574	3	preopen	preopen	ADJ
ejpam-21	574	4	[	[	X
ejpam-21	574	5	23	23	NUM
ejpam-21	574	6	]	]	SYM
ejpam-21	574	7	)	)	PUNCT
ejpam-21	574	8	if	if	SCONJ
ejpam-21	574	9	a	a	DET
ejpam-21	574	10	⊂	⊂	PROPN
ejpam-21	574	11	int(clδ(a	int(clδ(a	PROPN
ejpam-21	574	12	)	)	PUNCT
ejpam-21	574	13	)	)	PUNCT
ejpam-21	574	14	(	(	PUNCT
ejpam-21	574	15	resp	resp	NOUN
ejpam-21	574	16	.	.	PUNCT
ejpam-21	575	1	a	a	DET
ejpam-21	575	2	⊂	⊂	PROPN
ejpam-21	575	3	int(clθ(a	int(clθ(a	PROPN
ejpam-21	575	4	)	)	PUNCT
ejpam-21	575	5	)	)	PUNCT
ejpam-21	575	6	)	)	PUNCT
ejpam-21	575	7	,	,	PUNCT
ejpam-21	575	8	(	(	PUNCT
ejpam-21	575	9	3	3	X
ejpam-21	575	10	)	)	PUNCT
ejpam-21	575	11	δ	δ	PROPN
ejpam-21	575	12	-	-	PUNCT
ejpam-21	575	13	sp	sp	NOUN
ejpam-21	575	14	-	-	PUNCT
ejpam-21	575	15	open	open	NOUN
ejpam-21	575	16	[	[	X
ejpam-21	575	17	10	10	NUM
ejpam-21	575	18	]	]	PUNCT
ejpam-21	575	19	(	(	PUNCT
ejpam-21	575	20	resp	resp	NOUN
ejpam-21	575	21	.	.	PUNCT
ejpam-21	576	1	θ	θ	X
ejpam-21	576	2	-	-	PUNCT
ejpam-21	576	3	sp	sp	NOUN
ejpam-21	576	4	-	-	PUNCT
ejpam-21	576	5	open	open	NOUN
ejpam-21	576	6	[	[	X
ejpam-21	576	7	23	23	NUM
ejpam-21	576	8	]	]	SYM
ejpam-21	576	9	)	)	PUNCT
ejpam-21	576	10	if	if	SCONJ
ejpam-21	576	11	a	a	DET
ejpam-21	576	12	⊂	⊂	NOUN
ejpam-21	576	13	cl(int(clδ(a	cl(int(clδ(a	NOUN
ejpam-21	576	14	)	)	PUNCT
ejpam-21	576	15	)	)	PUNCT
ejpam-21	576	16	)	)	PUNCT
ejpam-21	576	17	(	(	PUNCT
ejpam-21	576	18	resp	resp	NOUN
ejpam-21	576	19	.	.	PUNCT
ejpam-21	577	1	a	a	DET
ejpam-21	577	2	⊂	⊂	PROPN
ejpam-21	577	3	cl(int(clθ(a	cl(int(clθ(a	NOUN
ejpam-21	577	4	)	)	PUNCT
ejpam-21	577	5	)	)	PUNCT
ejpam-21	577	6	)	)	PUNCT
ejpam-21	577	7	)	)	PUNCT
ejpam-21	577	8	.	.	PUNCT
ejpam-21	578	1	by	by	ADP
ejpam-21	578	2	δso(x	δso(x	NUM
ejpam-21	578	3	)	)	PUNCT
ejpam-21	578	4	(	(	PUNCT
ejpam-21	578	5	resp	resp	NOUN
ejpam-21	578	6	.	.	PUNCT
ejpam-21	578	7	δpo(x	δpo(x	PROPN
ejpam-21	578	8	)	)	PUNCT
ejpam-21	578	9	,	,	PUNCT
ejpam-21	578	10	δspo(x	δspo(x	PROPN
ejpam-21	578	11	)	)	PUNCT
ejpam-21	578	12	,	,	PUNCT
ejpam-21	578	13	θ	θ	PROPN
ejpam-21	578	14	so(x	so(x	NUM
ejpam-21	578	15	)	)	PUNCT
ejpam-21	578	16	,	,	PUNCT
ejpam-21	578	17	θpo(x	θpo(x	PROPN
ejpam-21	578	18	)	)	PUNCT
ejpam-21	578	19	,	,	PUNCT
ejpam-21	578	20	θspo(x	θspo(x	NOUN
ejpam-21	578	21	)	)	PUNCT
ejpam-21	578	22	)	)	PUNCT
ejpam-21	578	23	,	,	PUNCT
ejpam-21	578	24	we	we	PRON
ejpam-21	578	25	denote	denote	VERB
ejpam-21	578	26	the	the	DET
ejpam-21	578	27	collection	collection	NOUN
ejpam-21	578	28	of	of	ADP
ejpam-21	578	29	all	all	DET
ejpam-21	578	30	δ	δ	PROPN
ejpam-21	578	31	-	-	PUNCT
ejpam-21	578	32	semiopen	semiopen	ADJ
ejpam-21	578	33	(	(	PUNCT
ejpam-21	578	34	resp	resp	NOUN
ejpam-21	578	35	.	.	PUNCT
ejpam-21	579	1	δ	δ	PROPN
ejpam-21	579	2	-	-	PUNCT
ejpam-21	579	3	preopen	preopen	ADJ
ejpam-21	579	4	,	,	PUNCT
ejpam-21	579	5	δ	δ	PROPN
ejpam-21	579	6	-	-	PUNCT
ejpam-21	579	7	sp	sp	NOUN
ejpam-21	579	8	-	-	PUNCT
ejpam-21	579	9	open	open	ADJ
ejpam-21	579	10	,	,	PUNCT
ejpam-21	579	11	θ	θ	NOUN
ejpam-21	579	12	-semiopen	-semiopen	NOUN
ejpam-21	579	13	,	,	PUNCT
ejpam-21	579	14	θ	θ	NOUN
ejpam-21	579	15	-	-	NOUN
ejpam-21	579	16	preopen	preopen	ADJ
ejpam-21	579	17	,	,	PUNCT
ejpam-21	579	18	θ	θ	NOUN
ejpam-21	579	19	-	-	PUNCT
ejpam-21	579	20	sp	sp	NOUN
ejpam-21	579	21	-	-	PUNCT
ejpam-21	579	22	open	open	ADJ
ejpam-21	579	23	)	)	PUNCT
ejpam-21	579	24	sets	set	NOUN
ejpam-21	579	25	of	of	ADP
ejpam-21	579	26	a	a	DET
ejpam-21	579	27	topological	topological	ADJ
ejpam-21	579	28	space	space	NOUN
ejpam-21	579	29	(	(	PUNCT
ejpam-21	579	30	x	x	X
ejpam-21	579	31	,	,	PUNCT
ejpam-21	579	32	τ	τ	PROPN
ejpam-21	579	33	)	)	PUNCT
ejpam-21	579	34	.	.	PUNCT
ejpam-21	580	1	these	these	DET
ejpam-21	580	2	six	six	NUM
ejpam-21	580	3	collections	collection	NOUN
ejpam-21	580	4	are	be	AUX
ejpam-21	580	5	all	all	PRON
ejpam-21	580	6	m	m	NOUN
ejpam-21	580	7	-	-	NOUN
ejpam-21	580	8	structures	structure	NOUN
ejpam-21	580	9	with	with	ADP
ejpam-21	580	10	property	property	NOUN
ejpam-21	580	11	b.	b.	NOUN
ejpam-21	581	1	it	it	PRON
ejpam-21	581	2	is	be	AUX
ejpam-21	581	3	known	know	VERB
ejpam-21	581	4	that	that	SCONJ
ejpam-21	581	5	the	the	DET
ejpam-21	581	6	families	family	NOUN
ejpam-21	581	7	of	of	ADP
ejpam-21	581	8	all	all	DET
ejpam-21	581	9	θ	θ	ADJ
ejpam-21	581	10	-	-	ADJ
ejpam-21	581	11	open	open	ADJ
ejpam-21	581	12	sets	set	NOUN
ejpam-21	581	13	and	and	CCONJ
ejpam-21	581	14	δ	δ	NOUN
ejpam-21	581	15	-	-	ADJ
ejpam-21	581	16	open	open	ADJ
ejpam-21	581	17	sets	set	NOUN
ejpam-21	581	18	of	of	ADP
ejpam-21	581	19	(	(	PUNCT
ejpam-21	581	20	x	x	NOUN
ejpam-21	581	21	,	,	PUNCT
ejpam-21	581	22	τ	τ	X
ejpam-21	581	23	)	)	PUNCT
ejpam-21	581	24	are	be	AUX
ejpam-21	581	25	topologies	topology	NOUN
ejpam-21	581	26	for	for	ADP
ejpam-21	581	27	x	x	X
ejpam-21	581	28	,	,	PUNCT
ejpam-21	581	29	respectively	respectively	ADV
ejpam-21	581	30	.	.	PUNCT
ejpam-21	582	1	in	in	ADP
ejpam-21	582	2	[	[	X
ejpam-21	582	3	23	23	NUM
ejpam-21	582	4	]	]	PUNCT
ejpam-21	582	5	and	and	CCONJ
ejpam-21	582	6	[	[	X
ejpam-21	582	7	6	6	NUM
ejpam-21	582	8	]	]	PUNCT
ejpam-21	582	9	,	,	PUNCT
ejpam-21	582	10	the	the	DET
ejpam-21	582	11	following	follow	VERB
ejpam-21	582	12	relationships	relationship	NOUN
ejpam-21	582	13	are	be	AUX
ejpam-21	582	14	known	know	VERB
ejpam-21	582	15	:	:	PUNCT
ejpam-21	582	16	references	reference	NOUN
ejpam-21	582	17	96	96	NUM
ejpam-21	582	18	θ	θ	ADJ
ejpam-21	582	19	-	-	ADJ
ejpam-21	582	20	open	open	ADJ
ejpam-21	582	21	⇒	⇒	NOUN
ejpam-21	582	22	δ	δ	PROPN
ejpam-21	582	23	-open	-open	PROPN
ejpam-21	582	24	⇒	⇒	NOUN
ejpam-21	582	25	open	open	ADJ
ejpam-21	582	26	⇒	⇒	NOUN
ejpam-21	583	1	preopen	preopen	ADJ
ejpam-21	583	2	⇒	⇒	PROPN
ejpam-21	583	3	δ	δ	PROPN
ejpam-21	583	4	-preopen	-preopen	PROPN
ejpam-21	583	5	⇒	⇒	PROPN
ejpam-21	583	6	θ	θ	PROPN
ejpam-21	583	7	-	-	PUNCT
ejpam-21	583	8	preopen	preopen	ADJ
ejpam-21	583	9	⇓	⇓	PROPN
ejpam-21	583	10	⇓	⇓	PROPN
ejpam-21	583	11	⇓	⇓	PROPN
ejpam-21	583	12	⇓	⇓	PROPN
ejpam-21	583	13	⇓	⇓	PROPN
ejpam-21	583	14	⇓	⇓	PROPN
ejpam-21	583	15	θ	θ	PROPN
ejpam-21	583	16	-	-	PUNCT
ejpam-21	583	17	semiopen	semiopen	ADJ
ejpam-21	583	18	⇒	⇒	PROPN
ejpam-21	583	19	δ	δ	PROPN
ejpam-21	583	20	-	-	PUNCT
ejpam-21	583	21	semiopen	semiopen	ADJ
ejpam-21	583	22	⇒	⇒	NOUN
ejpam-21	583	23	semi	semi	ADJ
ejpam-21	583	24	-	-	ADJ
ejpam-21	583	25	open	open	ADJ
ejpam-21	583	26	⇒	⇒	NOUN
ejpam-21	583	27	sp	sp	NOUN
ejpam-21	583	28	-	-	PUNCT
ejpam-21	583	29	open	open	ADJ
ejpam-21	583	30	⇒	⇒	NOUN
ejpam-21	583	31	δ	δ	PROPN
ejpam-21	583	32	-	-	PUNCT
ejpam-21	583	33	sp	sp	NOUN
ejpam-21	583	34	-	-	PUNCT
ejpam-21	583	35	open	open	ADJ
ejpam-21	583	36	⇒	⇒	NOUN
ejpam-21	583	37	θ	θ	PROPN
ejpam-21	583	38	-	-	PUNCT
ejpam-21	583	39	sp	sp	NOUN
ejpam-21	583	40	-	-	PUNCT
ejpam-21	583	41	open	open	ADJ
ejpam-21	583	42	definition	definition	NOUN
ejpam-21	583	43	7.3	7.3	NUM
ejpam-21	583	44	.	.	PUNCT
ejpam-21	584	1	a	a	DET
ejpam-21	584	2	multifunction	multifunction	NOUN
ejpam-21	584	3	f	f	NOUN
ejpam-21	584	4	:	:	PUNCT
ejpam-21	584	5	(	(	PUNCT
ejpam-21	584	6	x	x	X
ejpam-21	584	7	,	,	PUNCT
ejpam-21	584	8	τ	τ	X
ejpam-21	584	9	)	)	PUNCT
ejpam-21	584	10	→	→	SYM
ejpam-21	584	11	(	(	PUNCT
ejpam-21	584	12	y	y	PROPN
ejpam-21	584	13	,	,	PUNCT
ejpam-21	584	14	σ	σ	PROPN
ejpam-21	584	15	)	)	PUNCT
ejpam-21	584	16	is	be	AUX
ejpam-21	584	17	said	say	VERB
ejpam-21	584	18	to	to	PART
ejpam-21	584	19	be	be	AUX
ejpam-21	584	20	(	(	PUNCT
ejpam-21	584	21	1	1	X
ejpam-21	584	22	)	)	PUNCT
ejpam-21	584	23	upper	upper	ADJ
ejpam-21	584	24	c	c	NOUN
ejpam-21	584	25	-	-	PUNCT
ejpam-21	584	26	θ	θ	NOUN
ejpam-21	584	27	-	-	ADJ
ejpam-21	584	28	continuous	continuous	ADJ
ejpam-21	584	29	(	(	PUNCT
ejpam-21	584	30	resp	resp	NOUN
ejpam-21	584	31	.	.	PUNCT
ejpam-21	585	1	upper	upper	ADJ
ejpam-21	585	2	c	c	NOUN
ejpam-21	585	3	-	-	PUNCT
ejpam-21	585	4	θ	θ	NOUN
ejpam-21	585	5	-	-	NOUN
ejpam-21	585	6	precontinuous	precontinuous	ADJ
ejpam-21	585	7	,	,	PUNCT
ejpam-21	585	8	upper	upper	ADJ
ejpam-21	585	9	c	c	NOUN
ejpam-21	585	10	-	-	PUNCT
ejpam-21	585	11	θ	θ	NOUN
ejpam-21	585	12	-	-	PUNCT
ejpam-21	585	13	semi	semi	ADJ
ejpam-21	585	14	-	-	ADJ
ejpam-21	585	15	continuous	continuous	ADJ
ejpam-21	585	16	,	,	PUNCT
ejpam-21	585	17	upper	upper	ADJ
ejpam-21	585	18	c	c	NOUN
ejpam-21	585	19	-	-	PUNCT
ejpam-21	585	20	θ	θ	NOUN
ejpam-21	585	21	-	-	PUNCT
ejpam-21	585	22	sp	sp	NOUN
ejpam-21	585	23	-	-	PUNCT
ejpam-21	585	24	continuous	continuous	ADJ
ejpam-21	585	25	)	)	PUNCT
ejpam-21	585	26	at	at	ADP
ejpam-21	585	27	a	a	DET
ejpam-21	585	28	point	point	NOUN
ejpam-21	585	29	x	x	SYM
ejpam-21	585	30	∈	∈	NOUN
ejpam-21	585	31	x	x	INTJ
ejpam-21	585	32	if	if	SCONJ
ejpam-21	585	33	for	for	ADP
ejpam-21	585	34	each	each	DET
ejpam-21	585	35	open	open	ADJ
ejpam-21	585	36	set	set	VERB
ejpam-21	585	37	v	v	NOUN
ejpam-21	585	38	containing	contain	VERB
ejpam-21	585	39	f	f	X
ejpam-21	585	40	(	(	PUNCT
ejpam-21	585	41	x	x	NOUN
ejpam-21	585	42	)	)	PUNCT
ejpam-21	585	43	and	and	CCONJ
ejpam-21	585	44	having	have	VERB
ejpam-21	585	45	compact	compact	ADJ
ejpam-21	585	46	complement	complement	NOUN
ejpam-21	585	47	,	,	PUNCT
ejpam-21	585	48	there	there	PRON
ejpam-21	585	49	exists	exist	VERB
ejpam-21	585	50	a	a	DET
ejpam-21	585	51	θ	θ	NOUN
ejpam-21	585	52	-	-	ADJ
ejpam-21	585	53	open	open	ADJ
ejpam-21	585	54	(	(	PUNCT
ejpam-21	585	55	resp	resp	NOUN
ejpam-21	585	56	.	.	PUNCT
ejpam-21	586	1	θ	θ	X
ejpam-21	586	2	-	-	PUNCT
ejpam-21	586	3	preopen	preopen	ADJ
ejpam-21	586	4	,	,	PUNCT
ejpam-21	586	5	θ	θ	NOUN
ejpam-21	586	6	-	-	PUNCT
ejpam-21	586	7	semiopen	semiopen	ADJ
ejpam-21	586	8	,	,	PUNCT
ejpam-21	586	9	θ	θ	PROPN
ejpam-21	586	10	-	-	PUNCT
ejpam-21	586	11	sp	sp	NOUN
ejpam-21	586	12	-	-	PUNCT
ejpam-21	586	13	open	open	ADJ
ejpam-21	586	14	)	)	PUNCT
ejpam-21	586	15	set	set	VERB
ejpam-21	586	16	u	u	NOUN
ejpam-21	586	17	containing	contain	VERB
ejpam-21	586	18	x	x	PUNCT
ejpam-21	586	19	such	such	ADJ
ejpam-21	586	20	that	that	SCONJ
ejpam-21	586	21	f	f	PROPN
ejpam-21	586	22	(	(	PUNCT
ejpam-21	586	23	u	u	NOUN
ejpam-21	586	24	)	)	PUNCT
ejpam-21	586	25	⊂	⊂	PROPN
ejpam-21	586	26	v	v	PROPN
ejpam-21	586	27	,	,	PUNCT
ejpam-21	586	28	(	(	PUNCT
ejpam-21	586	29	2	2	X
ejpam-21	586	30	)	)	PUNCT
ejpam-21	586	31	lower	low	ADJ
ejpam-21	586	32	c	c	NOUN
ejpam-21	586	33	-	-	PUNCT
ejpam-21	586	34	θ	θ	NOUN
ejpam-21	586	35	-	-	ADJ
ejpam-21	586	36	continuous	continuous	ADJ
ejpam-21	586	37	(	(	PUNCT
ejpam-21	586	38	resp	resp	NOUN
ejpam-21	586	39	.	.	PUNCT
ejpam-21	587	1	lower	low	ADJ
ejpam-21	587	2	c	c	X
ejpam-21	587	3	-	-	PUNCT
ejpam-21	587	4	θ	θ	NOUN
ejpam-21	587	5	-	-	NOUN
ejpam-21	587	6	precontinuous	precontinuous	ADJ
ejpam-21	587	7	,	,	PUNCT
ejpam-21	587	8	lower	low	ADJ
ejpam-21	587	9	c	c	NOUN
ejpam-21	587	10	-	-	PUNCT
ejpam-21	587	11	θ	θ	NOUN
ejpam-21	587	12	-	-	PUNCT
ejpam-21	587	13	semi	semi	ADJ
ejpam-21	587	14	-	-	ADJ
ejpam-21	587	15	continuous	continuous	ADJ
ejpam-21	587	16	,	,	PUNCT
ejpam-21	587	17	lower	low	ADJ
ejpam-21	587	18	c	c	NOUN
ejpam-21	587	19	-	-	PUNCT
ejpam-21	587	20	θ	θ	NOUN
ejpam-21	587	21	-	-	PUNCT
ejpam-21	587	22	sp	sp	NOUN
ejpam-21	587	23	-	-	PUNCT
ejpam-21	587	24	continuous	continuous	ADJ
ejpam-21	587	25	)	)	PUNCT
ejpam-21	587	26	at	at	ADP
ejpam-21	587	27	a	a	DET
ejpam-21	587	28	point	point	NOUN
ejpam-21	587	29	x	x	SYM
ejpam-21	587	30	∈	∈	NOUN
ejpam-21	587	31	x	x	INTJ
ejpam-21	587	32	if	if	SCONJ
ejpam-21	587	33	for	for	ADP
ejpam-21	587	34	each	each	DET
ejpam-21	587	35	open	open	ADJ
ejpam-21	587	36	set	set	VERB
ejpam-21	587	37	v	v	NUM
ejpam-21	587	38	meeting	meeting	NOUN
ejpam-21	587	39	f	f	X
ejpam-21	587	40	(	(	PUNCT
ejpam-21	587	41	x	x	NOUN
ejpam-21	587	42	)	)	PUNCT
ejpam-21	587	43	and	and	CCONJ
ejpam-21	587	44	having	have	VERB
ejpam-21	587	45	compact	compact	ADJ
ejpam-21	587	46	complement	complement	NOUN
ejpam-21	587	47	,	,	PUNCT
ejpam-21	587	48	there	there	PRON
ejpam-21	587	49	exists	exist	VERB
ejpam-21	587	50	a	a	DET
ejpam-21	587	51	θ	θ	NOUN
ejpam-21	587	52	-	-	ADJ
ejpam-21	587	53	open	open	ADJ
ejpam-21	587	54	(	(	PUNCT
ejpam-21	587	55	resp	resp	NOUN
ejpam-21	587	56	.	.	PUNCT
ejpam-21	588	1	θ	θ	X
ejpam-21	588	2	-	-	PUNCT
ejpam-21	588	3	preopen	preopen	ADJ
ejpam-21	588	4	,	,	PUNCT
ejpam-21	588	5	θ	θ	NOUN
ejpam-21	588	6	-	-	PUNCT
ejpam-21	588	7	semiopen	semiopen	ADJ
ejpam-21	588	8	,	,	PUNCT
ejpam-21	588	9	θ	θ	PROPN
ejpam-21	588	10	-	-	PUNCT
ejpam-21	588	11	sp	sp	NOUN
ejpam-21	588	12	-	-	PUNCT
ejpam-21	588	13	open	open	ADJ
ejpam-21	588	14	)	)	PUNCT
ejpam-21	588	15	set	set	VERB
ejpam-21	588	16	u	u	NOUN
ejpam-21	588	17	containing	contain	VERB
ejpam-21	588	18	x	x	PUNCT
ejpam-21	588	19	such	such	ADJ
ejpam-21	588	20	that	that	SCONJ
ejpam-21	588	21	f	f	PROPN
ejpam-21	588	22	(	(	PUNCT
ejpam-21	588	23	u	u	NOUN
ejpam-21	588	24	)	)	PUNCT
ejpam-21	588	25	∩	∩	NOUN
ejpam-21	588	26	v	v	ADP
ejpam-21	588	27	6=	6=	NOUN
ejpam-21	588	28	∅	∅	NOUN
ejpam-21	588	29	for	for	ADP
ejpam-21	588	30	each	each	DET
ejpam-21	588	31	u	u	PROPN
ejpam-21	588	32	∈	∈	PROPN
ejpam-21	588	33	u	u	NOUN
ejpam-21	588	34	,	,	PUNCT
ejpam-21	588	35	(	(	PUNCT
ejpam-21	588	36	3	3	X
ejpam-21	588	37	)	)	PUNCT
ejpam-21	588	38	upper	upper	ADJ
ejpam-21	588	39	/	/	SYM
ejpam-21	588	40	lower	low	ADJ
ejpam-21	588	41	c	c	NOUN
ejpam-21	588	42	-	-	PUNCT
ejpam-21	588	43	θ	θ	NOUN
ejpam-21	588	44	-	-	ADJ
ejpam-21	588	45	continuous	continuous	ADJ
ejpam-21	588	46	(	(	PUNCT
ejpam-21	588	47	resp	resp	NOUN
ejpam-21	588	48	.	.	PUNCT
ejpam-21	589	1	upper	upper	ADJ
ejpam-21	589	2	/	/	SYM
ejpam-21	589	3	lower	low	ADJ
ejpam-21	589	4	c	c	NOUN
ejpam-21	589	5	-	-	PUNCT
ejpam-21	589	6	θ	θ	NOUN
ejpam-21	589	7	-	-	NOUN
ejpam-21	589	8	precontinuous	precontinuous	ADJ
ejpam-21	589	9	,	,	PUNCT
ejpam-21	589	10	upper	upper	ADJ
ejpam-21	589	11	/	/	SYM
ejpam-21	589	12	lower	low	ADJ
ejpam-21	589	13	c	c	NOUN
ejpam-21	589	14	-	-	PUNCT
ejpam-21	589	15	θsemi	θsemi	ADJ
ejpam-21	589	16	-	-	ADJ
ejpam-21	589	17	continuous	continuous	ADJ
ejpam-21	589	18	,	,	PUNCT
ejpam-21	589	19	upper	upper	ADJ
ejpam-21	589	20	/	/	SYM
ejpam-21	589	21	lower	low	ADJ
ejpam-21	589	22	c	c	NOUN
ejpam-21	589	23	-	-	PUNCT
ejpam-21	589	24	θ	θ	NOUN
ejpam-21	589	25	-	-	PUNCT
ejpam-21	589	26	sp	sp	NOUN
ejpam-21	589	27	-	-	PUNCT
ejpam-21	589	28	continuous	continuous	ADJ
ejpam-21	589	29	)	)	PUNCT
ejpam-21	589	30	on	on	ADP
ejpam-21	589	31	x	x	SYM
ejpam-21	589	32	if	if	SCONJ
ejpam-21	589	33	it	it	PRON
ejpam-21	589	34	has	have	VERB
ejpam-21	589	35	this	this	DET
ejpam-21	589	36	property	property	NOUN
ejpam-21	589	37	at	at	ADP
ejpam-21	589	38	each	each	DET
ejpam-21	589	39	x	x	SYM
ejpam-21	589	40	∈	∈	PROPN
ejpam-21	589	41	x	x	X
ejpam-21	589	42	.	.	PUNCT
ejpam-21	590	1	definition	definition	NOUN
ejpam-21	590	2	7.4	7.4	NUM
ejpam-21	590	3	.	.	PUNCT
ejpam-21	591	1	a	a	DET
ejpam-21	591	2	multifunction	multifunction	NOUN
ejpam-21	591	3	f	f	NOUN
ejpam-21	591	4	:	:	PUNCT
ejpam-21	591	5	(	(	PUNCT
ejpam-21	591	6	x	x	X
ejpam-21	591	7	,	,	PUNCT
ejpam-21	591	8	τ	τ	X
ejpam-21	591	9	)	)	PUNCT
ejpam-21	591	10	→	→	SYM
ejpam-21	591	11	(	(	PUNCT
ejpam-21	591	12	y	y	PROPN
ejpam-21	591	13	,	,	PUNCT
ejpam-21	591	14	σ	σ	PROPN
ejpam-21	591	15	)	)	PUNCT
ejpam-21	591	16	is	be	AUX
ejpam-21	591	17	said	say	VERB
ejpam-21	591	18	to	to	PART
ejpam-21	591	19	be	be	AUX
ejpam-21	591	20	(	(	PUNCT
ejpam-21	591	21	1	1	X
ejpam-21	591	22	)	)	PUNCT
ejpam-21	591	23	upper	upper	ADJ
ejpam-21	591	24	c	c	NOUN
ejpam-21	591	25	-	-	PUNCT
ejpam-21	591	26	δ	δ	NOUN
ejpam-21	591	27	-	-	ADJ
ejpam-21	591	28	continuous	continuous	ADJ
ejpam-21	591	29	(	(	PUNCT
ejpam-21	591	30	resp	resp	NOUN
ejpam-21	591	31	.	.	PUNCT
ejpam-21	592	1	upper	upper	ADJ
ejpam-21	592	2	c	c	PROPN
ejpam-21	592	3	-	-	PUNCT
ejpam-21	592	4	δ	δ	NOUN
ejpam-21	592	5	-	-	NOUN
ejpam-21	592	6	precontinuous	precontinuous	ADJ
ejpam-21	592	7	,	,	PUNCT
ejpam-21	592	8	upper	upper	ADJ
ejpam-21	592	9	c	c	NOUN
ejpam-21	592	10	-	-	PUNCT
ejpam-21	592	11	δ	δ	NOUN
ejpam-21	592	12	-	-	PUNCT
ejpam-21	592	13	semi	semi	ADV
ejpam-21	592	14	-	-	ADJ
ejpam-21	592	15	continuous	continuous	ADJ
ejpam-21	592	16	,	,	PUNCT
ejpam-21	592	17	upper	upper	ADJ
ejpam-21	592	18	c	c	NOUN
ejpam-21	592	19	-	-	PUNCT
ejpam-21	592	20	δ	δ	NOUN
ejpam-21	592	21	-	-	PUNCT
ejpam-21	592	22	sp	sp	NOUN
ejpam-21	592	23	-	-	PUNCT
ejpam-21	592	24	continuous	continuous	ADJ
ejpam-21	592	25	)	)	PUNCT
ejpam-21	592	26	at	at	ADP
ejpam-21	592	27	a	a	DET
ejpam-21	592	28	point	point	NOUN
ejpam-21	592	29	x	x	SYM
ejpam-21	592	30	∈	∈	NOUN
ejpam-21	592	31	x	x	INTJ
ejpam-21	592	32	if	if	SCONJ
ejpam-21	592	33	for	for	ADP
ejpam-21	592	34	each	each	DET
ejpam-21	592	35	open	open	ADJ
ejpam-21	592	36	set	set	VERB
ejpam-21	592	37	v	v	NOUN
ejpam-21	592	38	containing	contain	VERB
ejpam-21	592	39	f	f	X
ejpam-21	592	40	(	(	PUNCT
ejpam-21	592	41	x	x	NOUN
ejpam-21	592	42	)	)	PUNCT
ejpam-21	592	43	and	and	CCONJ
ejpam-21	592	44	having	have	VERB
ejpam-21	592	45	compact	compact	ADJ
ejpam-21	592	46	complement	complement	NOUN
ejpam-21	592	47	,	,	PUNCT
ejpam-21	592	48	there	there	PRON
ejpam-21	592	49	exists	exist	VERB
ejpam-21	592	50	a	a	DET
ejpam-21	592	51	δ	δ	NOUN
ejpam-21	592	52	-	-	ADJ
ejpam-21	592	53	open	open	ADJ
ejpam-21	592	54	(	(	PUNCT
ejpam-21	592	55	resp	resp	NOUN
ejpam-21	592	56	.	.	PUNCT
ejpam-21	593	1	δ	δ	PROPN
ejpam-21	593	2	-	-	PUNCT
ejpam-21	593	3	preopen	preopen	ADJ
ejpam-21	593	4	,	,	PUNCT
ejpam-21	593	5	δ	δ	PROPN
ejpam-21	593	6	-	-	PUNCT
ejpam-21	593	7	semiopen	semiopen	ADJ
ejpam-21	593	8	,	,	PUNCT
ejpam-21	593	9	δ	δ	PROPN
ejpam-21	593	10	-	-	PUNCT
ejpam-21	593	11	sp	sp	NOUN
ejpam-21	593	12	-	-	PUNCT
ejpam-21	593	13	open	open	ADJ
ejpam-21	593	14	)	)	PUNCT
ejpam-21	593	15	set	set	VERB
ejpam-21	593	16	u	u	NOUN
ejpam-21	593	17	containing	contain	VERB
ejpam-21	593	18	x	x	PUNCT
ejpam-21	593	19	such	such	ADJ
ejpam-21	593	20	that	that	SCONJ
ejpam-21	593	21	f	f	PROPN
ejpam-21	593	22	(	(	PUNCT
ejpam-21	593	23	u	u	NOUN
ejpam-21	593	24	)	)	PUNCT
ejpam-21	593	25	⊂	⊂	PROPN
ejpam-21	593	26	v	v	PROPN
ejpam-21	593	27	,	,	PUNCT
ejpam-21	593	28	(	(	PUNCT
ejpam-21	593	29	2	2	X
ejpam-21	593	30	)	)	PUNCT
ejpam-21	593	31	lower	low	ADJ
ejpam-21	593	32	c	c	X
ejpam-21	593	33	-	-	PUNCT
ejpam-21	593	34	δ	δ	NOUN
ejpam-21	593	35	-	-	ADJ
ejpam-21	593	36	continuous	continuous	ADJ
ejpam-21	593	37	(	(	PUNCT
ejpam-21	593	38	resp	resp	NOUN
ejpam-21	593	39	.	.	PUNCT
ejpam-21	594	1	lower	low	ADJ
ejpam-21	594	2	c	c	X
ejpam-21	594	3	-	-	PUNCT
ejpam-21	594	4	δ	δ	NOUN
ejpam-21	594	5	-	-	NOUN
ejpam-21	594	6	precontinuous	precontinuous	ADJ
ejpam-21	594	7	,	,	PUNCT
ejpam-21	594	8	lower	low	ADJ
ejpam-21	594	9	c	c	NOUN
ejpam-21	594	10	-	-	PUNCT
ejpam-21	594	11	δ	δ	NOUN
ejpam-21	594	12	-	-	PUNCT
ejpam-21	594	13	semi	semi	ADV
ejpam-21	594	14	-	-	ADJ
ejpam-21	594	15	continuous	continuous	ADJ
ejpam-21	594	16	,	,	PUNCT
ejpam-21	594	17	lower	low	ADJ
ejpam-21	594	18	c	c	NOUN
ejpam-21	594	19	-	-	PUNCT
ejpam-21	594	20	δ	δ	NOUN
ejpam-21	594	21	-	-	PUNCT
ejpam-21	594	22	sp	sp	NOUN
ejpam-21	594	23	-	-	PUNCT
ejpam-21	594	24	continuous	continuous	ADJ
ejpam-21	594	25	)	)	PUNCT
ejpam-21	594	26	at	at	ADP
ejpam-21	594	27	a	a	DET
ejpam-21	594	28	point	point	NOUN
ejpam-21	594	29	x	x	SYM
ejpam-21	594	30	∈	∈	NOUN
ejpam-21	594	31	x	x	INTJ
ejpam-21	594	32	if	if	SCONJ
ejpam-21	594	33	for	for	ADP
ejpam-21	594	34	each	each	DET
ejpam-21	594	35	open	open	ADJ
ejpam-21	594	36	set	set	VERB
ejpam-21	594	37	v	v	NUM
ejpam-21	594	38	meeting	meeting	NOUN
ejpam-21	594	39	f	f	X
ejpam-21	594	40	(	(	PUNCT
ejpam-21	594	41	x	x	NOUN
ejpam-21	594	42	)	)	PUNCT
ejpam-21	594	43	and	and	CCONJ
ejpam-21	594	44	having	have	VERB
ejpam-21	594	45	compact	compact	ADJ
ejpam-21	594	46	complement	complement	NOUN
ejpam-21	594	47	,	,	PUNCT
ejpam-21	594	48	there	there	PRON
ejpam-21	594	49	exists	exist	VERB
ejpam-21	594	50	a	a	DET
ejpam-21	594	51	δ	δ	NOUN
ejpam-21	594	52	-	-	ADJ
ejpam-21	594	53	open	open	ADJ
ejpam-21	594	54	(	(	PUNCT
ejpam-21	594	55	resp	resp	NOUN
ejpam-21	594	56	.	.	PUNCT
ejpam-21	595	1	δ	δ	PROPN
ejpam-21	595	2	-	-	PUNCT
ejpam-21	595	3	preopen	preopen	ADJ
ejpam-21	595	4	,	,	PUNCT
ejpam-21	595	5	δ	δ	PROPN
ejpam-21	595	6	-	-	PUNCT
ejpam-21	595	7	semiopen	semiopen	ADJ
ejpam-21	595	8	,	,	PUNCT
ejpam-21	595	9	δ	δ	PROPN
ejpam-21	595	10	-	-	PUNCT
ejpam-21	595	11	sp	sp	NOUN
ejpam-21	595	12	-	-	PUNCT
ejpam-21	595	13	open	open	ADJ
ejpam-21	595	14	)	)	PUNCT
ejpam-21	595	15	set	set	VERB
ejpam-21	595	16	u	u	NOUN
ejpam-21	595	17	containing	contain	VERB
ejpam-21	595	18	x	x	PUNCT
ejpam-21	595	19	such	such	ADJ
ejpam-21	595	20	that	that	SCONJ
ejpam-21	595	21	f	f	PROPN
ejpam-21	595	22	(	(	PUNCT
ejpam-21	595	23	u	u	NOUN
ejpam-21	595	24	)	)	PUNCT
ejpam-21	595	25	∩	∩	NOUN
ejpam-21	595	26	v	v	ADP
ejpam-21	595	27	6=	6=	NOUN
ejpam-21	595	28	∅	∅	NOUN
ejpam-21	595	29	for	for	ADP
ejpam-21	595	30	each	each	DET
ejpam-21	595	31	u	u	PROPN
ejpam-21	595	32	∈	∈	PROPN
ejpam-21	595	33	u	u	NOUN
ejpam-21	595	34	,	,	PUNCT
ejpam-21	595	35	(	(	PUNCT
ejpam-21	595	36	3	3	X
ejpam-21	595	37	)	)	PUNCT
ejpam-21	595	38	upper	upper	ADJ
ejpam-21	595	39	/	/	SYM
ejpam-21	595	40	lower	low	ADJ
ejpam-21	595	41	c	c	NOUN
ejpam-21	595	42	-	-	PUNCT
ejpam-21	595	43	δ	δ	NOUN
ejpam-21	595	44	-	-	ADJ
ejpam-21	595	45	continuous	continuous	ADJ
ejpam-21	595	46	(	(	PUNCT
ejpam-21	595	47	resp	resp	NOUN
ejpam-21	595	48	.	.	PUNCT
ejpam-21	596	1	upper	upper	ADJ
ejpam-21	596	2	/	/	SYM
ejpam-21	596	3	lower	low	ADJ
ejpam-21	596	4	c	c	NOUN
ejpam-21	596	5	-	-	PUNCT
ejpam-21	596	6	δ	δ	NOUN
ejpam-21	596	7	-	-	NOUN
ejpam-21	596	8	precontinuous	precontinuous	ADJ
ejpam-21	596	9	,	,	PUNCT
ejpam-21	596	10	upper	upper	ADJ
ejpam-21	596	11	/	/	SYM
ejpam-21	596	12	lower	low	ADJ
ejpam-21	596	13	c	c	NOUN
ejpam-21	596	14	-	-	PUNCT
ejpam-21	596	15	δ	δ	NOUN
ejpam-21	596	16	-	-	PUNCT
ejpam-21	596	17	semicontinuous	semicontinuous	ADJ
ejpam-21	596	18	,	,	PUNCT
ejpam-21	596	19	upper	upper	ADJ
ejpam-21	596	20	/	/	SYM
ejpam-21	596	21	lower	low	ADJ
ejpam-21	596	22	c	c	NOUN
ejpam-21	596	23	-	-	PUNCT
ejpam-21	596	24	δ	δ	NOUN
ejpam-21	596	25	-	-	PUNCT
ejpam-21	596	26	sp	sp	NOUN
ejpam-21	596	27	-	-	PUNCT
ejpam-21	596	28	continuous	continuous	ADJ
ejpam-21	596	29	)	)	PUNCT
ejpam-21	597	1	on	on	ADP
ejpam-21	597	2	x	x	SYM
ejpam-21	597	3	if	if	SCONJ
ejpam-21	597	4	it	it	PRON
ejpam-21	597	5	has	have	AUX
ejpam-21	597	6	this	this	DET
ejpam-21	597	7	property	property	NOUN
ejpam-21	597	8	at	at	ADP
ejpam-21	597	9	each	each	DET
ejpam-21	597	10	x	x	SYM
ejpam-21	597	11	∈	∈	PROPN
ejpam-21	597	12	x	x	X
ejpam-21	597	13	.	.	PUNCT
ejpam-21	598	1	for	for	ADP
ejpam-21	598	2	the	the	DET
ejpam-21	598	3	multifunctions	multifunction	NOUN
ejpam-21	598	4	defined	define	VERB
ejpam-21	598	5	above	above	ADV
ejpam-21	598	6	,	,	PUNCT
ejpam-21	598	7	the	the	DET
ejpam-21	598	8	following	follow	VERB
ejpam-21	598	9	diagram	diagram	NOUN
ejpam-21	598	10	hold	hold	NOUN
ejpam-21	598	11	,	,	PUNCT
ejpam-21	598	12	where	where	SCONJ
ejpam-21	598	13	c.	c.	PROPN
ejpam-21	598	14	means	mean	VERB
ejpam-21	598	15	continuity	continuity	NOUN
ejpam-21	598	16	.	.	PUNCT
ejpam-21	599	1	u	u	NOUN
ejpam-21	599	2	/	/	SYM
ejpam-21	599	3	l	l	PROPN
ejpam-21	599	4	c.θ	c.θ	PROPN
ejpam-21	599	5	-	-	PUNCT
ejpam-21	599	6	c.	c.	PROPN
ejpam-21	599	7	⇒	⇒	PROPN
ejpam-21	599	8	u	u	PROPN
ejpam-21	599	9	/	/	SYM
ejpam-21	599	10	l	l	PROPN
ejpam-21	599	11	c.	c.	PROPN
ejpam-21	599	12	δ	δ	PROPN
ejpam-21	599	13	-	-	PROPN
ejpam-21	599	14	c.	c.	PROPN
ejpam-21	599	15	⇒	⇒	PROPN
ejpam-21	599	16	u	u	PROPN
ejpam-21	599	17	/	/	PROPN
ejpam-21	599	18	l	l	PROPN
ejpam-21	599	19	c.c	c.c	PROPN
ejpam-21	599	20	.	.	PROPN
ejpam-21	599	21	⇒	⇒	PROPN
ejpam-21	599	22	u	u	PROPN
ejpam-21	599	23	/	/	SYM
ejpam-21	599	24	l	l	NOUN
ejpam-21	599	25	c.p.c	c.p.c	NOUN
ejpam-21	599	26	.	.	PUNCT
ejpam-21	600	1	⇒	⇒	PROPN
ejpam-21	600	2	u	u	PROPN
ejpam-21	600	3	/	/	PROPN
ejpam-21	600	4	l	l	PROPN
ejpam-21	600	5	c.δ	c.δ	PROPN
ejpam-21	600	6	-	-	PUNCT
ejpam-21	600	7	p.c	p.c	PROPN
ejpam-21	600	8	.	.	PROPN
ejpam-21	600	9	⇒	⇒	PROPN
ejpam-21	600	10	u	u	PROPN
ejpam-21	600	11	/	/	PROPN
ejpam-21	600	12	l	l	PROPN
ejpam-21	600	13	c.θ	c.θ	NOUN
ejpam-21	600	14	-p.c	-p.c	PUNCT
ejpam-21	600	15	.	.	PUNCT
ejpam-21	601	1	⇓	⇓	PROPN
ejpam-21	601	2	⇓	⇓	PROPN
ejpam-21	601	3	⇓	⇓	PROPN
ejpam-21	601	4	⇓	⇓	PROPN
ejpam-21	601	5	⇓	⇓	PROPN
ejpam-21	601	6	⇓	⇓	PROPN
ejpam-21	601	7	u	u	PROPN
ejpam-21	601	8	/	/	SYM
ejpam-21	601	9	l	l	PROPN
ejpam-21	601	10	c.θ	c.θ	PROPN
ejpam-21	601	11	-	-	PUNCT
ejpam-21	601	12	s.c	s.c	PROPN
ejpam-21	601	13	.	.	PROPN
ejpam-21	601	14	⇒	⇒	PROPN
ejpam-21	601	15	u	u	PROPN
ejpam-21	601	16	/	/	PROPN
ejpam-21	601	17	l	l	PROPN
ejpam-21	601	18	c.δ	c.δ	PROPN
ejpam-21	601	19	-	-	PUNCT
ejpam-21	601	20	s.c	s.c	PROPN
ejpam-21	601	21	.	.	PROPN
ejpam-21	601	22	⇒	⇒	PROPN
ejpam-21	601	23	u	u	PROPN
ejpam-21	601	24	/	/	SYM
ejpam-21	601	25	l	l	NOUN
ejpam-21	601	26	c.q.c	c.q.c	NOUN
ejpam-21	601	27	.	.	PUNCT
ejpam-21	602	1	⇒	⇒	PROPN
ejpam-21	602	2	u	u	PROPN
ejpam-21	602	3	/	/	SYM
ejpam-21	602	4	l	l	NOUN
ejpam-21	602	5	c.sp.c	c.sp.c	PROPN
ejpam-21	602	6	.	.	PUNCT
ejpam-21	603	1	⇒	⇒	PROPN
ejpam-21	603	2	u	u	PROPN
ejpam-21	603	3	/	/	PROPN
ejpam-21	603	4	l	l	PRON
ejpam-21	603	5	c.δ	c.δ	PROPN
ejpam-21	603	6	-	-	PUNCT
ejpam-21	603	7	sp.c	sp.c	NOUN
ejpam-21	603	8	.	.	PUNCT
ejpam-21	604	1	⇒	⇒	PROPN
ejpam-21	604	2	u	u	PROPN
ejpam-21	604	3	/	/	PROPN
ejpam-21	604	4	l	l	PROPN
ejpam-21	604	5	c.θ	c.θ	NOUN
ejpam-21	604	6	-	-	PUNCT
ejpam-21	604	7	sp.c	sp.c	NOUN
ejpam-21	604	8	.	.	PUNCT
ejpam-21	604	9	conclusion	conclusion	NOUN
ejpam-21	604	10	.	.	PUNCT
ejpam-21	605	1	we	we	PRON
ejpam-21	605	2	can	can	AUX
ejpam-21	605	3	apply	apply	VERB
ejpam-21	605	4	the	the	DET
ejpam-21	605	5	results	result	NOUN
ejpam-21	605	6	established	establish	VERB
ejpam-21	605	7	in	in	ADP
ejpam-21	605	8	sections	section	NOUN
ejpam-21	605	9	3	3	NUM
ejpam-21	605	10	6	6	NUM
ejpam-21	605	11	to	to	ADP
ejpam-21	605	12	all	all	DET
ejpam-21	605	13	multifunctions	multifunction	NOUN
ejpam-21	605	14	defined	define	VERB
ejpam-21	605	15	in	in	ADP
ejpam-21	605	16	definitions	definition	NOUN
ejpam-21	605	17	7.1	7.1	NUM
ejpam-21	605	18	,	,	PUNCT
ejpam-21	605	19	7.2	7.2	NUM
ejpam-21	605	20	and	and	CCONJ
ejpam-21	605	21	7.3	7.3	NUM
ejpam-21	605	22	.	.	PUNCT
ejpam-21	606	1	references	reference	NOUN
ejpam-21	606	2	[	[	X
ejpam-21	606	3	1	1	NUM
ejpam-21	606	4	]	]	PUNCT
ejpam-21	606	5	m.	m.	NOUN
ejpam-21	606	6	e.	e.	PROPN
ejpam-21	606	7	abd	abd	PROPN
ejpam-21	606	8	el	el	PROPN
ejpam-21	606	9	-	-	PROPN
ejpam-21	606	10	monsef	monsef	PROPN
ejpam-21	606	11	,	,	PUNCT
ejpam-21	606	12	s.	s.	PROPN
ejpam-21	606	13	n.	n.	PROPN
ejpam-21	606	14	el	el	PROPN
ejpam-21	606	15	-	-	PUNCT
ejpam-21	606	16	deeb	deeb	PROPN
ejpam-21	606	17	and	and	CCONJ
ejpam-21	606	18	r.	r.	PROPN
ejpam-21	606	19	a.	a.	PROPN
ejpam-21	606	20	mahmoud	mahmoud	PROPN
ejpam-21	606	21	,	,	PUNCT
ejpam-21	606	22	β	β	ADJ
ejpam-21	606	23	-	-	ADJ
ejpam-21	606	24	open	open	ADJ
ejpam-21	606	25	sets	set	NOUN
ejpam-21	606	26	and	and	CCONJ
ejpam-21	606	27	β	β	ADJ
ejpam-21	606	28	-	-	ADJ
ejpam-21	606	29	continuous	continuous	ADJ
ejpam-21	606	30	mappings	mapping	NOUN
ejpam-21	606	31	,	,	PUNCT
ejpam-21	606	32	bull	bull	NOUN
ejpam-21	606	33	.	.	PUNCT
ejpam-21	607	1	fac	fac	PROPN
ejpam-21	607	2	.	.	PUNCT
ejpam-21	608	1	sci	sci	PROPN
ejpam-21	608	2	.	.	PUNCT
ejpam-21	608	3	assiut	assiut	PROPN
ejpam-21	608	4	univ	univ	PROPN
ejpam-21	608	5	.	.	PROPN
ejpam-21	609	1	12	12	NUM
ejpam-21	609	2	(	(	PUNCT
ejpam-21	609	3	1983	1983	NUM
ejpam-21	609	4	)	)	PUNCT
ejpam-21	609	5	,	,	PUNCT
ejpam-21	609	6	77–90	77–90	NUM
ejpam-21	609	7	.	.	PUNCT
ejpam-21	610	1	[	[	X
ejpam-21	610	2	2	2	NUM
ejpam-21	610	3	]	]	PUNCT
ejpam-21	610	4	m.	m.	NOUN
ejpam-21	610	5	e.	e.	PROPN
ejpam-21	610	6	abd	abd	PROPN
ejpam-21	611	1	el	el	PROPN
ejpam-21	611	2	-	-	PROPN
ejpam-21	611	3	monsef	monsef	PROPN
ejpam-21	611	4	,	,	PUNCT
ejpam-21	611	5	r.	r.	PROPN
ejpam-21	611	6	a.	a.	PROPN
ejpam-21	611	7	mahmoud	mahmoud	PROPN
ejpam-21	611	8	and	and	CCONJ
ejpam-21	611	9	e.	e.	PROPN
ejpam-21	611	10	r.	r.	PROPN
ejpam-21	611	11	lashin	lashin	PROPN
ejpam-21	611	12	,	,	PUNCT
ejpam-21	611	13	β	β	NOUN
ejpam-21	611	14	-	-	PUNCT
ejpam-21	611	15	closure	closure	NOUN
ejpam-21	611	16	and	and	CCONJ
ejpam-21	611	17	β	β	NOUN
ejpam-21	611	18	-	-	NOUN
ejpam-21	611	19	interior	interior	ADJ
ejpam-21	611	20	,	,	PUNCT
ejpam-21	611	21	j.	j.	PROPN
ejpam-21	611	22	fac	fac	PROPN
ejpam-21	611	23	.	.	PUNCT
ejpam-21	612	1	ed	ed	PROPN
ejpam-21	612	2	.	.	PUNCT
ejpam-21	612	3	ain	ain	PROPN
ejpam-21	612	4	shans	shans	PROPN
ejpam-21	612	5	univ	univ	PROPN
ejpam-21	612	6	.	.	PUNCT
ejpam-21	613	1	10	10	NUM
ejpam-21	613	2	(	(	PUNCT
ejpam-21	613	3	1986	1986	NUM
ejpam-21	613	4	)	)	PUNCT
ejpam-21	613	5	,	,	PUNCT
ejpam-21	613	6	235–245	235–245	NUM
ejpam-21	613	7	.	.	PUNCT
ejpam-21	614	1	[	[	X
ejpam-21	614	2	3	3	NUM
ejpam-21	614	3	]	]	PUNCT
ejpam-21	614	4	m.	m.	NOUN
ejpam-21	614	5	e.	e.	PROPN
ejpam-21	614	6	abd	abd	PROPN
ejpam-21	614	7	el	el	PROPN
ejpam-21	614	8	-	-	PROPN
ejpam-21	614	9	monsef	monsef	PROPN
ejpam-21	614	10	and	and	CCONJ
ejpam-21	614	11	a.	a.	NOUN
ejpam-21	614	12	a.	a.	NOUN
ejpam-21	614	13	nasef	nasef	PROPN
ejpam-21	614	14	,	,	PUNCT
ejpam-21	614	15	on	on	ADP
ejpam-21	614	16	multifunctions	multifunction	NOUN
ejpam-21	614	17	,	,	PUNCT
ejpam-21	614	18	chaos	chaos	NOUN
ejpam-21	614	19	,	,	PUNCT
ejpam-21	614	20	solitons	soliton	NOUN
ejpam-21	614	21	and	and	CCONJ
ejpam-21	614	22	fractals	fractal	NOUN
ejpam-21	614	23	12	12	NUM
ejpam-21	614	24	(	(	PUNCT
ejpam-21	614	25	2001	2001	NUM
ejpam-21	614	26	)	)	PUNCT
ejpam-21	614	27	,	,	PUNCT
ejpam-21	614	28	2387–2394	2387–2394	NUM
ejpam-21	614	29	.	.	PUNCT
ejpam-21	614	30	references	reference	NOUN
ejpam-21	614	31	97	97	NUM
ejpam-21	615	1	[	[	X
ejpam-21	615	2	4	4	NUM
ejpam-21	615	3	]	]	X
ejpam-21	615	4	d.	d.	PROPN
ejpam-21	615	5	andrijević	andrijević	PROPN
ejpam-21	615	6	,	,	PUNCT
ejpam-21	615	7	semi	semi	ADJ
ejpam-21	615	8	-	-	ADJ
ejpam-21	615	9	preopen	preopen	ADJ
ejpam-21	615	10	sets	set	NOUN
ejpam-21	615	11	,	,	PUNCT
ejpam-21	615	12	mat	mat	PROPN
ejpam-21	615	13	.	.	PROPN
ejpam-21	615	14	vesnik	vesnik	PROPN
ejpam-21	615	15	38	38	NUM
ejpam-21	615	16	(	(	PUNCT
ejpam-21	615	17	1986	1986	NUM
ejpam-21	615	18	)	)	PUNCT
ejpam-21	615	19	,	,	PUNCT
ejpam-21	615	20	24–32	24–32	NUM
ejpam-21	615	21	.	.	PUNCT
ejpam-21	616	1	[	[	X
ejpam-21	616	2	5	5	X
ejpam-21	616	3	]	]	X
ejpam-21	616	4	d.	d.	PROPN
ejpam-21	616	5	andrijević	andrijević	PROPN
ejpam-21	616	6	,	,	PUNCT
ejpam-21	616	7	on	on	ADP
ejpam-21	616	8	b	b	X
ejpam-21	616	9	-	-	PUNCT
ejpam-21	616	10	open	open	ADJ
ejpam-21	616	11	sets	set	NOUN
ejpam-21	616	12	,	,	PUNCT
ejpam-21	616	13	mat	mat	PROPN
ejpam-21	616	14	.	.	PROPN
ejpam-21	616	15	vesnik	vesnik	PROPN
ejpam-21	616	16	48	48	NUM
ejpam-21	616	17	(	(	PUNCT
ejpam-21	616	18	1996	1996	NUM
ejpam-21	616	19	)	)	PUNCT
ejpam-21	616	20	,	,	PUNCT
ejpam-21	616	21	59–64	59–64	NUM
ejpam-21	616	22	.	.	PUNCT
ejpam-21	617	1	[	[	X
ejpam-21	617	2	6	6	NUM
ejpam-21	617	3	]	]	PUNCT
ejpam-21	617	4	m.	m.	NOUN
ejpam-21	617	5	caldas	caldas	PROPN
ejpam-21	617	6	,	,	PUNCT
ejpam-21	617	7	m.	m.	NOUN
ejpam-21	617	8	ganster	ganster	NOUN
ejpam-21	617	9	,	,	PUNCT
ejpam-21	617	10	d.	d.	PROPN
ejpam-21	617	11	n.	n.	PROPN
ejpam-21	617	12	georgiou	georgiou	PROPN
ejpam-21	617	13	,	,	PUNCT
ejpam-21	617	14	s.	s.	PROPN
ejpam-21	617	15	jafari	jafari	PROPN
ejpam-21	617	16	and	and	CCONJ
ejpam-21	617	17	t.	t.	PROPN
ejpam-21	617	18	noiri	noiri	PROPN
ejpam-21	617	19	,	,	PUNCT
ejpam-21	617	20	on	on	ADP
ejpam-21	617	21	θ	θ	ADJ
ejpam-21	617	22	-	-	PUNCT
ejpam-21	617	23	semiopen	semiopen	ADJ
ejpam-21	617	24	sets	set	NOUN
ejpam-21	617	25	and	and	CCONJ
ejpam-21	617	26	separation	separation	NOUN
ejpam-21	617	27	axioms	axiom	NOUN
ejpam-21	617	28	in	in	ADP
ejpam-21	617	29	topological	topological	ADJ
ejpam-21	617	30	spaces	space	NOUN
ejpam-21	617	31	(	(	PUNCT
ejpam-21	617	32	submitted	submit	VERB
ejpam-21	617	33	)	)	PUNCT
ejpam-21	617	34	.	.	PUNCT
ejpam-21	618	1	[	[	X
ejpam-21	618	2	7	7	X
ejpam-21	618	3	]	]	X
ejpam-21	618	4	s.	s.	PROPN
ejpam-21	618	5	g.	g.	PROPN
ejpam-21	618	6	crossley	crossley	PROPN
ejpam-21	618	7	and	and	CCONJ
ejpam-21	618	8	s.	s.	PROPN
ejpam-21	618	9	k.	k.	PROPN
ejpam-21	618	10	hildeband	hildeband	PROPN
ejpam-21	618	11	,	,	PUNCT
ejpam-21	618	12	semi	semi	ADJ
ejpam-21	618	13	-	-	ADJ
ejpam-21	618	14	closure	closure	ADJ
ejpam-21	618	15	,	,	PUNCT
ejpam-21	618	16	texas	texas	PROPN
ejpam-21	618	17	j.	j.	PROPN
ejpam-21	618	18	sci	sci	PROPN
ejpam-21	618	19	.	.	PROPN
ejpam-21	619	1	22	22	NUM
ejpam-21	619	2	(	(	PUNCT
ejpam-21	619	3	1971	1971	NUM
ejpam-21	619	4	)	)	PUNCT
ejpam-21	619	5	,	,	PUNCT
ejpam-21	620	1	99–112	99–112	NUM
ejpam-21	620	2	.	.	PUNCT
ejpam-21	621	1	[	[	X
ejpam-21	621	2	8	8	NUM
ejpam-21	621	3	]	]	X
ejpam-21	621	4	n.	n.	PROPN
ejpam-21	621	5	el	el	PROPN
ejpam-21	621	6	-	-	PUNCT
ejpam-21	621	7	deeb	deeb	PROPN
ejpam-21	621	8	,	,	PUNCT
ejpam-21	621	9	i.	i.	PROPN
ejpam-21	621	10	a.	a.	PROPN
ejpam-21	621	11	hasanein	hasanein	PROPN
ejpam-21	621	12	,	,	PUNCT
ejpam-21	621	13	a.	a.	PROPN
ejpam-21	621	14	s.	s.	PROPN
ejpam-21	621	15	mashhour	mashhour	PROPN
ejpam-21	621	16	and	and	CCONJ
ejpam-21	621	17	t.	t.	PROPN
ejpam-21	621	18	noiri	noiri	PROPN
ejpam-21	621	19	,	,	PUNCT
ejpam-21	621	20	on	on	ADP
ejpam-21	621	21	p	p	NOUN
ejpam-21	621	22	-	-	PUNCT
ejpam-21	621	23	regular	regular	ADJ
ejpam-21	621	24	spaces	space	NOUN
ejpam-21	621	25	,	,	PUNCT
ejpam-21	621	26	bull	bull	NOUN
ejpam-21	621	27	.	.	PUNCT
ejpam-21	621	28	math	math	NOUN
ejpam-21	621	29	.	.	PUNCT
ejpam-21	622	1	soc	soc	PROPN
ejpam-21	622	2	.	.	PUNCT
ejpam-21	623	1	sci	sci	PROPN
ejpam-21	623	2	.	.	PROPN
ejpam-21	623	3	math	math	PROPN
ejpam-21	623	4	.	.	PUNCT
ejpam-21	624	1	r.	r.	PROPN
ejpam-21	624	2	s.	s.	PROPN
ejpam-21	624	3	roumanie	roumanie	PROPN
ejpam-21	624	4	27(75	27(75	PROPN
ejpam-21	624	5	)	)	PUNCT
ejpam-21	624	6	(	(	PUNCT
ejpam-21	624	7	1983	1983	NUM
ejpam-21	624	8	)	)	PUNCT
ejpam-21	624	9	,	,	PUNCT
ejpam-21	624	10	311–315	311–315	NUM
ejpam-21	624	11	.	.	PUNCT
ejpam-21	625	1	[	[	X
ejpam-21	625	2	9	9	NUM
ejpam-21	625	3	]	]	PUNCT
ejpam-21	625	4	k.	k.	PROPN
ejpam-21	625	5	r.	r.	PROPN
ejpam-21	625	6	gentry	gentry	PROPN
ejpam-21	625	7	and	and	CCONJ
ejpam-21	625	8	h.	h.	PROPN
ejpam-21	625	9	b.	b.	PROPN
ejpam-21	625	10	hoyle	hoyle	PROPN
ejpam-21	625	11	iii	iii	PROPN
ejpam-21	625	12	,	,	PUNCT
ejpam-21	625	13	c	c	NOUN
ejpam-21	625	14	-	-	PUNCT
ejpam-21	625	15	continuous	continuous	ADJ
ejpam-21	625	16	functions	function	NOUN
ejpam-21	625	17	,	,	PUNCT
ejpam-21	625	18	yokohama	yokohama	PROPN
ejpam-21	625	19	math	math	PROPN
ejpam-21	625	20	.	.	PUNCT
ejpam-21	626	1	j.	j.	PROPN
ejpam-21	626	2	18	18	NUM
ejpam-21	626	3	(	(	PUNCT
ejpam-21	626	4	1970	1970	NUM
ejpam-21	626	5	)	)	PUNCT
ejpam-21	626	6	,	,	PUNCT
ejpam-21	626	7	71–76	71–76	NUM
ejpam-21	626	8	.	.	PUNCT
ejpam-21	627	1	[	[	X
ejpam-21	627	2	10	10	NUM
ejpam-21	627	3	]	]	X
ejpam-21	627	4	e.	e.	PROPN
ejpam-21	627	5	hatir	hatir	PROPN
ejpam-21	627	6	and	and	CCONJ
ejpam-21	627	7	t.	t.	PROPN
ejpam-21	627	8	noiri	noiri	PROPN
ejpam-21	627	9	,	,	PUNCT
ejpam-21	627	10	decompositions	decomposition	NOUN
ejpam-21	627	11	of	of	ADP
ejpam-21	627	12	continuity	continuity	NOUN
ejpam-21	627	13	and	and	CCONJ
ejpam-21	627	14	complete	complete	ADJ
ejpam-21	627	15	continuity	continuity	NOUN
ejpam-21	627	16	,	,	PUNCT
ejpam-21	627	17	acta	acta	PROPN
ejpam-21	627	18	math	math	PROPN
ejpam-21	627	19	.	.	PUNCT
ejpam-21	628	1	hungar	hungar	NOUN
ejpam-21	628	2	.	.	PUNCT
ejpam-21	629	1	113	113	NUM
ejpam-21	629	2	(	(	PUNCT
ejpam-21	629	3	2006	2006	NUM
ejpam-21	629	4	)	)	PUNCT
ejpam-21	629	5	,	,	PUNCT
ejpam-21	629	6	281–287	281–287	NUM
ejpam-21	629	7	.	.	PUNCT
ejpam-21	630	1	[	[	X
ejpam-21	630	2	11	11	NUM
ejpam-21	630	3	]	]	X
ejpam-21	630	4	l.	l.	PROPN
ejpam-21	630	5	holá	holá	PROPN
ejpam-21	630	6	,	,	PUNCT
ejpam-21	630	7	v.	v.	ADP
ejpam-21	630	8	baláz	baláz	NOUN
ejpam-21	630	9	and	and	CCONJ
ejpam-21	630	10	t.	t.	PROPN
ejpam-21	630	11	neubrunn	neubrunn	PROPN
ejpam-21	630	12	,	,	PUNCT
ejpam-21	630	13	remarks	remark	VERB
ejpam-21	630	14	on	on	ADP
ejpam-21	630	15	c	c	NOUN
ejpam-21	630	16	-	-	PUNCT
ejpam-21	630	17	continuous	continuous	ADJ
ejpam-21	630	18	multifunctions	multifunction	NOUN
ejpam-21	630	19	,	,	PUNCT
ejpam-21	630	20	acta	acta	PROPN
ejpam-21	630	21	math	math	PROPN
ejpam-21	630	22	.	.	PUNCT
ejpam-21	631	1	univ	univ	PROPN
ejpam-21	631	2	.	.	PROPN
ejpam-21	632	1	comenianae	comenianae	PROPN
ejpam-21	632	2	50/51	50/51	NUM
ejpam-21	632	3	(	(	PUNCT
ejpam-21	632	4	1987	1987	NUM
ejpam-21	632	5	)	)	PUNCT
ejpam-21	632	6	,	,	PUNCT
ejpam-21	632	7	51–59	51–59	NUM
ejpam-21	632	8	.	.	PUNCT
ejpam-21	633	1	[	[	X
ejpam-21	633	2	12	12	NUM
ejpam-21	633	3	]	]	PUNCT
ejpam-21	633	4	i.	i.	PROPN
ejpam-21	633	5	kovačević	kovačević	PROPN
ejpam-21	633	6	,	,	PUNCT
ejpam-21	633	7	subsets	subset	NOUN
ejpam-21	633	8	and	and	CCONJ
ejpam-21	633	9	paracompactness	paracompactness	NOUN
ejpam-21	633	10	,	,	PUNCT
ejpam-21	633	11	univ	univ	PROPN
ejpam-21	633	12	.	.	PUNCT
ejpam-21	634	1	u	u	PROPN
ejpam-21	634	2	novom	novom	ADJ
ejpam-21	634	3	sadu	sadu	PROPN
ejpam-21	634	4	zb	zb	PROPN
ejpam-21	634	5	.	.	PUNCT
ejpam-21	635	1	rad	rad	PROPN
ejpam-21	635	2	.	.	PROPN
ejpam-21	635	3	priod.-mat	priod.-mat	NOUN
ejpam-21	635	4	.	.	PUNCT
ejpam-21	636	1	fak	fak	PROPN
ejpam-21	636	2	.	.	PUNCT
ejpam-21	636	3	ser	ser	PROPN
ejpam-21	636	4	.	.	PROPN
ejpam-21	637	1	mat	mat	PROPN
ejpam-21	637	2	.	.	PROPN
ejpam-21	637	3	14	14	NUM
ejpam-21	637	4	(	(	PUNCT
ejpam-21	637	5	1984	1984	NUM
ejpam-21	637	6	)	)	PUNCT
ejpam-21	637	7	,	,	PUNCT
ejpam-21	637	8	79–87	79–87	NUM
ejpam-21	637	9	.	.	PUNCT
ejpam-21	638	1	[	[	X
ejpam-21	638	2	13	13	NUM
ejpam-21	638	3	]	]	X
ejpam-21	638	4	n.	n.	PROPN
ejpam-21	638	5	levine	levine	PROPN
ejpam-21	638	6	,	,	PUNCT
ejpam-21	638	7	semi	semi	ADJ
ejpam-21	638	8	-	-	ADJ
ejpam-21	638	9	open	open	ADJ
ejpam-21	638	10	sets	set	NOUN
ejpam-21	638	11	and	and	CCONJ
ejpam-21	638	12	semi	semi	ADJ
ejpam-21	638	13	-	-	NOUN
ejpam-21	638	14	continuity	continuity	NOUN
ejpam-21	638	15	in	in	ADP
ejpam-21	638	16	topological	topological	ADJ
ejpam-21	638	17	spaces	space	NOUN
ejpam-21	638	18	,	,	PUNCT
ejpam-21	638	19	amer	amer	PROPN
ejpam-21	638	20	.	.	PROPN
ejpam-21	638	21	math	math	PROPN
ejpam-21	638	22	.	.	PUNCT
ejpam-21	639	1	monthly	monthly	ADJ
ejpam-21	639	2	70	70	NUM
ejpam-21	639	3	(	(	PUNCT
ejpam-21	639	4	1963	1963	NUM
ejpam-21	639	5	)	)	PUNCT
ejpam-21	639	6	,	,	PUNCT
ejpam-21	639	7	36–41	36–41	NUM
ejpam-21	639	8	.	.	PUNCT
ejpam-21	640	1	[	[	X
ejpam-21	640	2	14	14	NUM
ejpam-21	640	3	]	]	PUNCT
ejpam-21	640	4	t.	t.	NOUN
ejpam-21	640	5	lipski	lipski	PROPN
ejpam-21	640	6	,	,	PUNCT
ejpam-21	640	7	remarks	remark	NOUN
ejpam-21	640	8	on	on	ADP
ejpam-21	640	9	limits	limit	NOUN
ejpam-21	640	10	of	of	ADP
ejpam-21	640	11	sequences	sequence	NOUN
ejpam-21	640	12	of	of	ADP
ejpam-21	640	13	c	c	NOUN
ejpam-21	640	14	-	-	PUNCT
ejpam-21	640	15	quasicontinuous	quasicontinuous	ADJ
ejpam-21	640	16	multivalued	multivalued	ADJ
ejpam-21	640	17	maps	map	NOUN
ejpam-21	640	18	,	,	PUNCT
ejpam-21	640	19	radovi	radovi	PROPN
ejpam-21	640	20	mat	mat	NOUN
ejpam-21	640	21	.	.	PROPN
ejpam-21	640	22	7	7	NUM
ejpam-21	640	23	(	(	PUNCT
ejpam-21	640	24	1991	1991	NUM
ejpam-21	640	25	)	)	PUNCT
ejpam-21	640	26	,	,	PUNCT
ejpam-21	640	27	17–27	17–27	NUM
ejpam-21	640	28	.	.	PUNCT
ejpam-21	641	1	[	[	X
ejpam-21	641	2	15	15	NUM
ejpam-21	641	3	]	]	X
ejpam-21	642	1	p.	p.	NOUN
ejpam-21	642	2	e.	e.	PROPN
ejpam-21	643	1	long	long	PROPN
ejpam-21	643	2	and	and	CCONJ
ejpam-21	643	3	michael	michael	PROPN
ejpam-21	643	4	d.	d.	PROPN
ejpam-21	643	5	hendrix	hendrix	PROPN
ejpam-21	643	6	,	,	PUNCT
ejpam-21	643	7	properties	property	NOUN
ejpam-21	643	8	of	of	ADP
ejpam-21	643	9	c	c	NOUN
ejpam-21	643	10	-	-	PUNCT
ejpam-21	643	11	continuous	continuous	ADJ
ejpam-21	643	12	functions	function	NOUN
ejpam-21	643	13	,	,	PUNCT
ejpam-21	643	14	yokohama	yokohama	PROPN
ejpam-21	643	15	math	math	PROPN
ejpam-21	643	16	.	.	PUNCT
ejpam-21	644	1	j.	j.	PROPN
ejpam-21	644	2	22	22	NUM
ejpam-21	644	3	(	(	PUNCT
ejpam-21	644	4	1974	1974	NUM
ejpam-21	644	5	)	)	PUNCT
ejpam-21	644	6	,	,	PUNCT
ejpam-21	644	7	117–123	117–123	NUM
ejpam-21	644	8	.	.	PUNCT
ejpam-21	645	1	[	[	X
ejpam-21	645	2	16	16	NUM
ejpam-21	645	3	]	]	PUNCT
ejpam-21	645	4	p.	p.	PROPN
ejpam-21	645	5	e.	e.	PROPN
ejpam-21	646	1	long	long	PROPN
ejpam-21	646	2	and	and	CCONJ
ejpam-21	646	3	l.	l.	PROPN
ejpam-21	646	4	l.	l.	PROPN
ejpam-21	646	5	herrington	herrington	PROPN
ejpam-21	646	6	,	,	PUNCT
ejpam-21	646	7	properties	property	NOUN
ejpam-21	646	8	of	of	ADP
ejpam-21	646	9	c	c	NOUN
ejpam-21	646	10	-	-	PUNCT
ejpam-21	646	11	continuous	continuous	ADJ
ejpam-21	646	12	and	and	CCONJ
ejpam-21	646	13	c∗-continuous	c∗-continuous	ADJ
ejpam-21	646	14	functions	function	NOUN
ejpam-21	646	15	,	,	PUNCT
ejpam-21	646	16	kyungpook	kyungpook	NOUN
ejpam-21	646	17	math	math	NOUN
ejpam-21	646	18	.	.	PUNCT
ejpam-21	647	1	j.	j.	PROPN
ejpam-21	647	2	15	15	NUM
ejpam-21	647	3	(	(	PUNCT
ejpam-21	647	4	1975	1975	NUM
ejpam-21	647	5	)	)	PUNCT
ejpam-21	647	6	,	,	PUNCT
ejpam-21	647	7	213–221	213–221	NUM
ejpam-21	647	8	.	.	PUNCT
ejpam-21	648	1	[	[	X
ejpam-21	648	2	17	17	NUM
ejpam-21	648	3	]	]	X
ejpam-21	648	4	h.	h.	PROPN
ejpam-21	648	5	maki	maki	PROPN
ejpam-21	648	6	,	,	PUNCT
ejpam-21	648	7	k.	k.	PROPN
ejpam-21	648	8	c.	c.	PROPN
ejpam-21	648	9	rao	rao	PROPN
ejpam-21	648	10	and	and	CCONJ
ejpam-21	648	11	a.	a.	PROPN
ejpam-21	648	12	nagoor	nagoor	PROPN
ejpam-21	648	13	gani	gani	PROPN
ejpam-21	648	14	,	,	PUNCT
ejpam-21	648	15	on	on	ADP
ejpam-21	648	16	generalizing	generalize	VERB
ejpam-21	648	17	semi	semi	ADJ
ejpam-21	648	18	-	-	ADJ
ejpam-21	648	19	open	open	ADJ
ejpam-21	648	20	and	and	CCONJ
ejpam-21	648	21	preopen	preopen	ADJ
ejpam-21	648	22	sets	set	NOUN
ejpam-21	648	23	,	,	PUNCT
ejpam-21	648	24	pure	pure	ADJ
ejpam-21	648	25	appl	appl	NOUN
ejpam-21	648	26	.	.	PUNCT
ejpam-21	648	27	math	math	PROPN
ejpam-21	648	28	.	.	PUNCT
ejpam-21	649	1	sci	sci	PROPN
ejpam-21	649	2	.	.	PROPN
ejpam-21	650	1	49	49	NUM
ejpam-21	650	2	(	(	PUNCT
ejpam-21	650	3	1999	1999	NUM
ejpam-21	650	4	)	)	PUNCT
ejpam-21	650	5	,	,	PUNCT
ejpam-21	650	6	17–29	17–29	NUM
ejpam-21	650	7	.	.	PUNCT
ejpam-21	651	1	[	[	X
ejpam-21	651	2	18	18	NUM
ejpam-21	651	3	]	]	PUNCT
ejpam-21	651	4	a.	a.	NOUN
ejpam-21	651	5	s.	s.	PROPN
ejpam-21	651	6	mashhour	mashhour	PROPN
ejpam-21	651	7	,	,	PUNCT
ejpam-21	651	8	m.	m.	PROPN
ejpam-21	651	9	e.	e.	PROPN
ejpam-21	651	10	abd	abd	PROPN
ejpam-21	651	11	el	el	PROPN
ejpam-21	651	12	-	-	PROPN
ejpam-21	651	13	monsef	monsef	PROPN
ejpam-21	651	14	and	and	CCONJ
ejpam-21	651	15	s.	s.	PROPN
ejpam-21	651	16	n.	n.	PROPN
ejpam-21	651	17	el	el	PROPN
ejpam-21	651	18	-	-	PUNCT
ejpam-21	651	19	deep	deep	ADJ
ejpam-21	651	20	,	,	PUNCT
ejpam-21	651	21	on	on	ADP
ejpam-21	651	22	precontinuous	precontinuous	ADJ
ejpam-21	651	23	and	and	CCONJ
ejpam-21	651	24	weak	weak	ADJ
ejpam-21	651	25	precontinuous	precontinuous	ADJ
ejpam-21	651	26	mappings	mapping	NOUN
ejpam-21	651	27	,	,	PUNCT
ejpam-21	651	28	proc	proc	NOUN
ejpam-21	651	29	.	.	PUNCT
ejpam-21	652	1	math	math	NOUN
ejpam-21	652	2	.	.	PUNCT
ejpam-21	653	1	phys	phy	NOUN
ejpam-21	653	2	.	.	PUNCT
ejpam-21	654	1	soc	soc	PROPN
ejpam-21	654	2	.	.	PUNCT
ejpam-21	655	1	egypt	egypt	PROPN
ejpam-21	655	2	.	.	PUNCT
ejpam-21	656	1	53	53	NUM
ejpam-21	656	2	(	(	PUNCT
ejpam-21	656	3	1982	1982	NUM
ejpam-21	656	4	)	)	PUNCT
ejpam-21	656	5	,	,	PUNCT
ejpam-21	656	6	47–53	47–53	NUM
ejpam-21	656	7	.	.	PUNCT
ejpam-21	657	1	[	[	X
ejpam-21	657	2	19	19	NUM
ejpam-21	657	3	]	]	PUNCT
ejpam-21	657	4	a.	a.	NOUN
ejpam-21	657	5	s.	s.	PROPN
ejpam-21	657	6	mashhour	mashhour	PROPN
ejpam-21	657	7	,	,	PUNCT
ejpam-21	657	8	i.	i.	PROPN
ejpam-21	657	9	a.	a.	PROPN
ejpam-21	657	10	hasanein	hasanein	PROPN
ejpam-21	657	11	and	and	CCONJ
ejpam-21	657	12	s.	s.	PROPN
ejpam-21	657	13	n.	n.	PROPN
ejpam-21	657	14	el	el	PROPN
ejpam-21	657	15	-	-	PROPN
ejpam-21	657	16	deeb	deeb	PROPN
ejpam-21	657	17	,	,	PUNCT
ejpam-21	657	18	α	α	NOUN
ejpam-21	657	19	-	-	ADJ
ejpam-21	657	20	continuous	continuous	ADJ
ejpam-21	657	21	and	and	CCONJ
ejpam-21	657	22	α	α	NOUN
ejpam-21	657	23	-	-	ADJ
ejpam-21	657	24	open	open	ADJ
ejpam-21	657	25	mappings	mapping	NOUN
ejpam-21	657	26	,	,	PUNCT
ejpam-21	657	27	acta	acta	PROPN
ejpam-21	657	28	math	math	PROPN
ejpam-21	657	29	.	.	PUNCT
ejpam-21	658	1	hungar	hungar	NOUN
ejpam-21	658	2	.	.	PUNCT
ejpam-21	659	1	41	41	NUM
ejpam-21	659	2	(	(	PUNCT
ejpam-21	659	3	1983	1983	NUM
ejpam-21	659	4	)	)	PUNCT
ejpam-21	659	5	,	,	PUNCT
ejpam-21	659	6	213–218	213–218	NUM
ejpam-21	659	7	.	.	PUNCT
ejpam-21	660	1	[	[	X
ejpam-21	660	2	20	20	NUM
ejpam-21	660	3	]	]	PUNCT
ejpam-21	660	4	t.	t.	NOUN
ejpam-21	660	5	neubrunn	neubrunn	PROPN
ejpam-21	660	6	,	,	PUNCT
ejpam-21	660	7	c	c	NOUN
ejpam-21	660	8	-	-	PUNCT
ejpam-21	660	9	continuity	continuity	NOUN
ejpam-21	660	10	and	and	CCONJ
ejpam-21	660	11	closed	closed	ADJ
ejpam-21	660	12	graphs	graph	NOUN
ejpam-21	660	13	,	,	PUNCT
ejpam-21	660	14	časopis	časopis	X
ejpam-21	660	15	pěst	pěst	ADJ
ejpam-21	660	16	.	.	PUNCT
ejpam-21	660	17	mat	mat	NOUN
ejpam-21	660	18	.	.	NOUN
ejpam-21	660	19	110	110	NUM
ejpam-21	660	20	(	(	PUNCT
ejpam-21	660	21	1985	1985	NUM
ejpam-21	660	22	)	)	PUNCT
ejpam-21	660	23	,	,	PUNCT
ejpam-21	660	24	172–178	172–178	NUM
ejpam-21	660	25	.	.	PUNCT
ejpam-21	661	1	[	[	X
ejpam-21	661	2	21	21	NUM
ejpam-21	661	3	]	]	X
ejpam-21	661	4	t.	t.	NOUN
ejpam-21	661	5	neubrunn	neubrunn	PROPN
ejpam-21	661	6	,	,	PUNCT
ejpam-21	661	7	strongly	strongly	ADV
ejpam-21	661	8	quasi	quasi	ADJ
ejpam-21	661	9	-	-	ADJ
ejpam-21	661	10	continuous	continuous	ADJ
ejpam-21	661	11	multivalued	multivalued	ADJ
ejpam-21	661	12	mappings	mapping	NOUN
ejpam-21	661	13	,	,	PUNCT
ejpam-21	661	14	general	general	ADJ
ejpam-21	661	15	topology	topology	NOUN
ejpam-21	661	16	and	and	CCONJ
ejpam-21	661	17	its	its	PRON
ejpam-21	661	18	relations	relation	NOUN
ejpam-21	661	19	to	to	ADP
ejpam-21	661	20	modern	modern	ADJ
ejpam-21	661	21	analysis	analysis	NOUN
ejpam-21	661	22	and	and	CCONJ
ejpam-21	661	23	algebra	algebra	NOUN
ejpam-21	661	24	vi	vi	PROPN
ejpam-21	661	25	,	,	PUNCT
ejpam-21	661	26	proc	proc	NOUN
ejpam-21	661	27	.	.	PUNCT
ejpam-21	662	1	praque	praque	ADJ
ejpam-21	662	2	topological	topological	ADJ
ejpam-21	662	3	symposium	symposium	NOUN
ejpam-21	662	4	1986	1986	NUM
ejpam-21	662	5	,	,	PUNCT
ejpam-21	662	6	heldermann	heldermann	PROPN
ejpam-21	662	7	verlag	verlag	PROPN
ejpam-21	662	8	,	,	PUNCT
ejpam-21	662	9	berlin	berlin	PROPN
ejpam-21	662	10	,	,	PUNCT
ejpam-21	662	11	1988	1988	NUM
ejpam-21	662	12	,	,	PUNCT
ejpam-21	662	13	351–360	351–360	NUM
ejpam-21	662	14	.	.	PUNCT
ejpam-21	663	1	[	[	X
ejpam-21	663	2	22	22	NUM
ejpam-21	663	3	]	]	X
ejpam-21	663	4	o.	o.	PROPN
ejpam-21	663	5	njåstad	njåstad	PROPN
ejpam-21	663	6	,	,	PUNCT
ejpam-21	663	7	on	on	ADP
ejpam-21	663	8	some	some	DET
ejpam-21	663	9	classes	class	NOUN
ejpam-21	663	10	of	of	ADP
ejpam-21	663	11	nearly	nearly	ADV
ejpam-21	663	12	open	open	ADJ
ejpam-21	663	13	sets	set	NOUN
ejpam-21	663	14	,	,	PUNCT
ejpam-21	663	15	pacific	pacific	PROPN
ejpam-21	663	16	j.	j.	PROPN
ejpam-21	663	17	math	math	PROPN
ejpam-21	663	18	.	.	PUNCT
ejpam-21	664	1	15	15	NUM
ejpam-21	664	2	(	(	PUNCT
ejpam-21	664	3	1965	1965	NUM
ejpam-21	664	4	)	)	PUNCT
ejpam-21	664	5	,	,	PUNCT
ejpam-21	664	6	961–970	961–970	NUM
ejpam-21	664	7	.	.	PUNCT
ejpam-21	665	1	[	[	X
ejpam-21	665	2	23	23	NUM
ejpam-21	665	3	]	]	PUNCT
ejpam-21	665	4	t.	t.	PROPN
ejpam-21	665	5	noiri	noiri	PROPN
ejpam-21	665	6	and	and	CCONJ
ejpam-21	665	7	v.	v.	ADP
ejpam-21	665	8	popa	popa	NOUN
ejpam-21	665	9	,	,	PUNCT
ejpam-21	665	10	on	on	ADP
ejpam-21	665	11	upper	upper	ADJ
ejpam-21	665	12	and	and	CCONJ
ejpam-21	665	13	lower	low	ADJ
ejpam-21	665	14	m	m	VERB
ejpam-21	665	15	-continuous	-continuous	ADJ
ejpam-21	665	16	multifunctions	multifunction	NOUN
ejpam-21	665	17	,	,	PUNCT
ejpam-21	665	18	filomat	filomat	NOUN
ejpam-21	665	19	(	(	PUNCT
ejpam-21	665	20	nis	nis	NOUN
ejpam-21	665	21	)	)	PUNCT
ejpam-21	665	22	14	14	NUM
ejpam-21	665	23	(	(	PUNCT
ejpam-21	665	24	2000	2000	NUM
ejpam-21	665	25	)	)	PUNCT
ejpam-21	665	26	,	,	PUNCT
ejpam-21	665	27	73–86	73–86	NUM
ejpam-21	665	28	.	.	PUNCT
ejpam-21	666	1	[	[	X
ejpam-21	666	2	24	24	NUM
ejpam-21	666	3	]	]	X
ejpam-21	666	4	ö.	ö.	PROPN
ejpam-21	666	5	orhan	orhan	PROPN
ejpam-21	666	6	,	,	PUNCT
ejpam-21	666	7	properties	property	NOUN
ejpam-21	666	8	of	of	ADP
ejpam-21	666	9	c	c	NOUN
ejpam-21	666	10	-	-	PUNCT
ejpam-21	666	11	continuous	continuous	ADJ
ejpam-21	666	12	functions	function	NOUN
ejpam-21	666	13	,	,	PUNCT
ejpam-21	666	14	hacettepe	hacettepe	NOUN
ejpam-21	666	15	bull	bull	NOUN
ejpam-21	666	16	.	.	PUNCT
ejpam-21	667	1	natur	natur	PROPN
ejpam-21	667	2	.	.	PUNCT
ejpam-21	668	1	sci	sci	PROPN
ejpam-21	668	2	.	.	PUNCT
ejpam-21	669	1	eng	eng	PROPN
ejpam-21	669	2	.	.	PROPN
ejpam-21	670	1	7	7	NUM
ejpam-21	670	2	-	-	SYM
ejpam-21	670	3	8	8	NUM
ejpam-21	670	4	(	(	PUNCT
ejpam-21	670	5	1978/79	1978/79	NUM
ejpam-21	670	6	)	)	PUNCT
ejpam-21	670	7	,	,	PUNCT
ejpam-21	670	8	77–83	77–83	NUM
ejpam-21	670	9	.	.	PUNCT
ejpam-21	671	1	[	[	X
ejpam-21	671	2	25	25	NUM
ejpam-21	671	3	]	]	PUNCT
ejpam-21	671	4	j.	j.	PROPN
ejpam-21	671	5	h.	h.	PROPN
ejpam-21	671	6	park	park	PROPN
ejpam-21	671	7	,	,	PUNCT
ejpam-21	671	8	b.	b.	PROPN
ejpam-21	671	9	y.	y.	PROPN
ejpam-21	671	10	lee	lee	PROPN
ejpam-21	671	11	and	and	CCONJ
ejpam-21	671	12	m.	m.	PROPN
ejpam-21	671	13	j.	j.	PROPN
ejpam-21	671	14	son	son	PROPN
ejpam-21	671	15	,	,	PUNCT
ejpam-21	671	16	on	on	ADP
ejpam-21	671	17	δ	δ	PROPN
ejpam-21	671	18	-	-	PUNCT
ejpam-21	671	19	semi	semi	ADJ
ejpam-21	671	20	-	-	ADJ
ejpam-21	671	21	open	open	ADJ
ejpam-21	671	22	sets	set	NOUN
ejpam-21	671	23	in	in	ADP
ejpam-21	671	24	topological	topological	ADJ
ejpam-21	671	25	spaces	space	NOUN
ejpam-21	671	26	,	,	PUNCT
ejpam-21	671	27	j.	j.	PROPN
ejpam-21	671	28	indian	indian	PROPN
ejpam-21	671	29	acad	acad	PROPN
ejpam-21	671	30	.	.	PUNCT
ejpam-21	672	1	math	math	NOUN
ejpam-21	672	2	.	.	PUNCT
ejpam-21	673	1	19	19	NUM
ejpam-21	673	2	(	(	PUNCT
ejpam-21	673	3	1997	1997	NUM
ejpam-21	673	4	)	)	PUNCT
ejpam-21	673	5	,	,	PUNCT
ejpam-21	673	6	59–67	59–67	NUM
ejpam-21	673	7	.	.	PUNCT
ejpam-21	674	1	[	[	X
ejpam-21	674	2	26	26	NUM
ejpam-21	674	3	]	]	PUNCT
ejpam-21	674	4	v.	v.	CCONJ
ejpam-21	674	5	popa	popa	NOUN
ejpam-21	674	6	,	,	PUNCT
ejpam-21	674	7	on	on	ADP
ejpam-21	674	8	some	some	DET
ejpam-21	674	9	decomposition	decomposition	NOUN
ejpam-21	674	10	of	of	ADP
ejpam-21	674	11	quasicontinuity	quasicontinuity	NOUN
ejpam-21	674	12	of	of	ADP
ejpam-21	674	13	multifunctions	multifunction	NOUN
ejpam-21	674	14	(	(	PUNCT
ejpam-21	674	15	romanian	romanian	NOUN
ejpam-21	674	16	)	)	PUNCT
ejpam-21	674	17	,	,	PUNCT
ejpam-21	674	18	stud	stud	NOUN
ejpam-21	674	19	.	.	PUNCT
ejpam-21	675	1	cerc	cerc	PROPN
ejpam-21	675	2	.	.	PUNCT
ejpam-21	676	1	mat	mat	NOUN
ejpam-21	676	2	.	.	PROPN
ejpam-21	676	3	27	27	NUM
ejpam-21	676	4	(	(	PUNCT
ejpam-21	676	5	1975	1975	NUM
ejpam-21	676	6	)	)	PUNCT
ejpam-21	676	7	,	,	PUNCT
ejpam-21	676	8	322–328	322–328	NUM
ejpam-21	676	9	.	.	PUNCT
ejpam-21	677	1	[	[	X
ejpam-21	677	2	27	27	NUM
ejpam-21	677	3	]	]	X
ejpam-21	677	4	v.	v.	CCONJ
ejpam-21	677	5	popa	popa	NOUN
ejpam-21	677	6	,	,	PUNCT
ejpam-21	677	7	multifonctions	multifonction	NOUN
ejpam-21	677	8	semi	semi	NOUN
ejpam-21	677	9	-	-	NOUN
ejpam-21	677	10	continues	continue	NOUN
ejpam-21	677	11	,	,	PUNCT
ejpam-21	677	12	rev	rev	PROPN
ejpam-21	677	13	.	.	PROPN
ejpam-21	677	14	roumaine	roumaine	PROPN
ejpam-21	677	15	math	math	NOUN
ejpam-21	677	16	.	.	PUNCT
ejpam-21	678	1	pures	pure	NOUN
ejpam-21	678	2	appl	appl	PROPN
ejpam-21	678	3	.	.	PROPN
ejpam-21	679	1	27	27	NUM
ejpam-21	679	2	(	(	PUNCT
ejpam-21	679	3	1982	1982	NUM
ejpam-21	679	4	)	)	PUNCT
ejpam-21	679	5	,	,	PUNCT
ejpam-21	679	6	807–815	807–815	NUM
ejpam-21	679	7	.	.	PUNCT
ejpam-21	680	1	[	[	X
ejpam-21	680	2	28	28	NUM
ejpam-21	680	3	]	]	X
ejpam-21	680	4	v.	v.	CCONJ
ejpam-21	680	5	popa	popa	NOUN
ejpam-21	680	6	,	,	PUNCT
ejpam-21	680	7	some	some	DET
ejpam-21	680	8	characterizations	characterization	NOUN
ejpam-21	680	9	of	of	ADP
ejpam-21	680	10	quasicontinuous	quasicontinuous	ADJ
ejpam-21	680	11	and	and	CCONJ
ejpam-21	680	12	weakly	weakly	ADJ
ejpam-21	680	13	continuous	continuous	ADJ
ejpam-21	680	14	multifunctions	multifunction	NOUN
ejpam-21	680	15	(	(	PUNCT
ejpam-21	680	16	romanian	romanian	NOUN
ejpam-21	680	17	)	)	PUNCT
ejpam-21	680	18	,	,	PUNCT
ejpam-21	680	19	stud	stud	NOUN
ejpam-21	680	20	.	.	PUNCT
ejpam-21	681	1	cerc	cerc	PROPN
ejpam-21	681	2	.	.	PUNCT
ejpam-21	682	1	mat	mat	NOUN
ejpam-21	682	2	.	.	PROPN
ejpam-21	682	3	37	37	NUM
ejpam-21	682	4	(	(	PUNCT
ejpam-21	682	5	1985	1985	NUM
ejpam-21	682	6	)	)	PUNCT
ejpam-21	682	7	,	,	PUNCT
ejpam-21	682	8	77–82	77–82	X
ejpam-21	682	9	.	.	PUNCT
ejpam-21	683	1	[	[	X
ejpam-21	683	2	29	29	NUM
ejpam-21	683	3	]	]	PUNCT
ejpam-21	683	4	v.	v.	CCONJ
ejpam-21	683	5	popa	popa	NOUN
ejpam-21	683	6	,	,	PUNCT
ejpam-21	683	7	some	some	DET
ejpam-21	683	8	properties	property	NOUN
ejpam-21	683	9	of	of	ADP
ejpam-21	683	10	h	h	NOUN
ejpam-21	683	11	-	-	PUNCT
ejpam-21	683	12	almost	almost	ADV
ejpam-21	683	13	continuous	continuous	ADJ
ejpam-21	683	14	multifunctions	multifunction	NOUN
ejpam-21	683	15	,	,	PUNCT
ejpam-21	683	16	problemy	problemy	PROPN
ejpam-21	683	17	mat	mat	NOUN
ejpam-21	683	18	.	.	PROPN
ejpam-21	683	19	10	10	NUM
ejpam-21	683	20	(	(	PUNCT
ejpam-21	683	21	1988	1988	NUM
ejpam-21	683	22	)	)	PUNCT
ejpam-21	683	23	,	,	PUNCT
ejpam-21	683	24	9–26	9–26	NOUN
ejpam-21	683	25	.	.	PUNCT
ejpam-21	684	1	[	[	X
ejpam-21	684	2	30	30	NUM
ejpam-21	684	3	]	]	X
ejpam-21	684	4	v.	v.	CCONJ
ejpam-21	684	5	popa	popa	NOUN
ejpam-21	684	6	and	and	CCONJ
ejpam-21	684	7	t.	t.	PROPN
ejpam-21	684	8	noiri	noiri	PROPN
ejpam-21	684	9	,	,	PUNCT
ejpam-21	684	10	on	on	ADP
ejpam-21	684	11	upper	upper	ADJ
ejpam-21	684	12	and	and	CCONJ
ejpam-21	684	13	lower	low	ADJ
ejpam-21	684	14	β	β	ADJ
ejpam-21	684	15	-	-	ADJ
ejpam-21	684	16	continuous	continuous	ADJ
ejpam-21	684	17	multifunctions	multifunction	NOUN
ejpam-21	684	18	,	,	PUNCT
ejpam-21	684	19	real	real	ADJ
ejpam-21	684	20	anal	anal	NOUN
ejpam-21	684	21	.	.	PUNCT
ejpam-21	685	1	exchange	exchange	NOUN
ejpam-21	685	2	22	22	NUM
ejpam-21	685	3	(	(	PUNCT
ejpam-21	685	4	1996/97	1996/97	NUM
ejpam-21	685	5	)	)	PUNCT
ejpam-21	685	6	,	,	PUNCT
ejpam-21	685	7	362–376	362–376	NUM
ejpam-21	685	8	.	.	PUNCT
ejpam-21	686	1	[	[	X
ejpam-21	686	2	31	31	NUM
ejpam-21	686	3	]	]	PUNCT
ejpam-21	686	4	v.	v.	CCONJ
ejpam-21	686	5	popa	popa	NOUN
ejpam-21	686	6	and	and	CCONJ
ejpam-21	686	7	t.	t.	PROPN
ejpam-21	686	8	noiri	noiri	PROPN
ejpam-21	686	9	,	,	PUNCT
ejpam-21	686	10	on	on	ADP
ejpam-21	686	11	m	m	ADJ
ejpam-21	686	12	-	-	ADJ
ejpam-21	686	13	continuous	continuous	ADJ
ejpam-21	686	14	functions	function	NOUN
ejpam-21	686	15	,	,	PUNCT
ejpam-21	686	16	anal	anal	NOUN
ejpam-21	686	17	.	.	PUNCT
ejpam-21	686	18	univ	univ	PROPN
ejpam-21	686	19	.	.	PUNCT
ejpam-21	686	20	”	"	PUNCT
ejpam-21	686	21	dunǎrea	dunǎrea	PROPN
ejpam-21	686	22	de	de	X
ejpam-21	686	23	jos	jos	PROPN
ejpam-21	686	24	”	"	PUNCT
ejpam-21	686	25	galaţi	galaţi	ADJ
ejpam-21	686	26	,	,	PUNCT
ejpam-21	686	27	ser	ser	NOUN
ejpam-21	686	28	.	.	PROPN
ejpam-21	687	1	mat	mat	PROPN
ejpam-21	687	2	.	.	PUNCT
ejpam-21	687	3	fiz	fiz	PROPN
ejpam-21	687	4	.	.	PUNCT
ejpam-21	688	1	references	reference	NOUN
ejpam-21	688	2	98	98	NUM
ejpam-21	688	3	mec	mec	PROPN
ejpam-21	688	4	.	.	PUNCT
ejpam-21	688	5	teor	teor	PROPN
ejpam-21	688	6	.	.	PUNCT
ejpam-21	689	1	(	(	PUNCT
ejpam-21	689	2	2	2	X
ejpam-21	689	3	)	)	PUNCT
ejpam-21	689	4	18(23	18(23	NOUN
ejpam-21	689	5	)	)	PUNCT
ejpam-21	689	6	(	(	PUNCT
ejpam-21	689	7	2000	2000	NUM
ejpam-21	689	8	)	)	PUNCT
ejpam-21	689	9	,	,	PUNCT
ejpam-21	689	10	31–41	31–41	NUM
ejpam-21	689	11	.	.	PUNCT
ejpam-21	690	1	[	[	X
ejpam-21	690	2	32	32	NUM
ejpam-21	690	3	]	]	PUNCT
ejpam-21	690	4	v.	v.	CCONJ
ejpam-21	690	5	popa	popa	NOUN
ejpam-21	690	6	and	and	CCONJ
ejpam-21	690	7	t.	t.	PROPN
ejpam-21	690	8	noiri	noiri	PROPN
ejpam-21	690	9	,	,	PUNCT
ejpam-21	690	10	a	a	DET
ejpam-21	690	11	unified	unified	ADJ
ejpam-21	690	12	theorey	theorey	NOUN
ejpam-21	690	13	for	for	ADP
ejpam-21	690	14	s	s	NOUN
ejpam-21	690	15	-	-	NOUN
ejpam-21	690	16	continuity	continuity	NOUN
ejpam-21	690	17	of	of	ADP
ejpam-21	690	18	multifunctions	multifunction	NOUN
ejpam-21	690	19	,	,	PUNCT
ejpam-21	690	20	j.	j.	PROPN
ejpam-21	690	21	math	math	PROPN
ejpam-21	690	22	.	.	PUNCT
ejpam-21	691	1	fac	fac	PROPN
ejpam-21	691	2	.	.	PUNCT
ejpam-21	692	1	sci	sci	PROPN
ejpam-21	692	2	.	.	PROPN
ejpam-21	692	3	univ	univ	PROPN
ejpam-21	692	4	.	.	PUNCT
ejpam-21	693	1	istanbul	istanbul	PROPN
ejpam-21	693	2	59	59	NUM
ejpam-21	693	3	(	(	PUNCT
ejpam-21	693	4	2000	2000	NUM
ejpam-21	693	5	)	)	PUNCT
ejpam-21	693	6	,	,	PUNCT
ejpam-21	693	7	1–15	1–15	NUM
ejpam-21	693	8	.	.	PUNCT
ejpam-21	694	1	[	[	X
ejpam-21	694	2	33	33	NUM
ejpam-21	694	3	]	]	PUNCT
ejpam-21	694	4	v.	v.	CCONJ
ejpam-21	694	5	popa	popa	NOUN
ejpam-21	694	6	and	and	CCONJ
ejpam-21	694	7	t.	t.	PROPN
ejpam-21	694	8	noiri	noiri	PROPN
ejpam-21	694	9	,	,	PUNCT
ejpam-21	694	10	on	on	ADP
ejpam-21	694	11	the	the	DET
ejpam-21	694	12	definitions	definition	NOUN
ejpam-21	694	13	of	of	ADP
ejpam-21	694	14	some	some	DET
ejpam-21	694	15	generalized	generalized	ADJ
ejpam-21	694	16	forms	form	NOUN
ejpam-21	694	17	of	of	ADP
ejpam-21	694	18	continuity	continuity	NOUN
ejpam-21	694	19	under	under	ADP
ejpam-21	694	20	minimal	minimal	ADJ
ejpam-21	694	21	conditions	condition	NOUN
ejpam-21	694	22	,	,	PUNCT
ejpam-21	694	23	mem	mem	PROPN
ejpam-21	694	24	.	.	PUNCT
ejpam-21	694	25	fac	fac	PROPN
ejpam-21	694	26	.	.	PUNCT
ejpam-21	694	27	sci	sci	PROPN
ejpam-21	694	28	.	.	PROPN
ejpam-21	694	29	kochi	kochi	PROPN
ejpam-21	694	30	univ	univ	PROPN
ejpam-21	694	31	.	.	PUNCT
ejpam-21	694	32	ser	ser	PROPN
ejpam-21	694	33	.	.	PUNCT
ejpam-21	694	34	math	math	NOUN
ejpam-21	694	35	.	.	PUNCT
ejpam-21	695	1	22	22	NUM
ejpam-21	695	2	(	(	PUNCT
ejpam-21	695	3	2001	2001	NUM
ejpam-21	695	4	)	)	PUNCT
ejpam-21	695	5	,	,	PUNCT
ejpam-21	695	6	9–19	9–19	NOUN
ejpam-21	695	7	.	.	PUNCT
ejpam-21	696	1	[	[	X
ejpam-21	696	2	34	34	NUM
ejpam-21	696	3	]	]	PUNCT
ejpam-21	696	4	v.	v.	CCONJ
ejpam-21	696	5	popa	popa	NOUN
ejpam-21	696	6	and	and	CCONJ
ejpam-21	696	7	t.	t.	PROPN
ejpam-21	696	8	noiri	noiri	PROPN
ejpam-21	696	9	,	,	PUNCT
ejpam-21	696	10	on	on	ADP
ejpam-21	696	11	m	m	ADJ
ejpam-21	696	12	-	-	ADJ
ejpam-21	696	13	continuous	continuous	ADJ
ejpam-21	696	14	multifunctions	multifunction	NOUN
ejpam-21	696	15	,	,	PUNCT
ejpam-21	696	16	bull	bull	NOUN
ejpam-21	696	17	.	.	PUNCT
ejpam-21	697	1	st	st	PROPN
ejpam-21	697	2	.	.	PROPN
ejpam-21	697	3	univ	univ	PROPN
ejpam-21	697	4	.	.	PUNCT
ejpam-21	698	1	politeh	politeh	NOUN
ejpam-21	698	2	.	.	PUNCT
ejpam-21	699	1	timişoara	timişoara	NOUN
ejpam-21	699	2	,	,	PUNCT
ejpam-21	699	3	ser	ser	NOUN
ejpam-21	699	4	.	.	PROPN
ejpam-21	699	5	mat	mat	PROPN
ejpam-21	699	6	.	.	PUNCT
ejpam-21	700	1	fiz	fiz	PROPN
ejpam-21	700	2	.	.	PUNCT
ejpam-21	701	1	46(50	46(50	NOUN
ejpam-21	701	2	)	)	PUNCT
ejpam-21	701	3	(	(	PUNCT
ejpam-21	701	4	2001	2001	NUM
ejpam-21	701	5	)	)	PUNCT
ejpam-21	701	6	,	,	PUNCT
ejpam-21	701	7	1–12	1–12	NOUN
ejpam-21	701	8	.	.	PUNCT
ejpam-21	702	1	[	[	X
ejpam-21	702	2	35	35	NUM
ejpam-21	702	3	]	]	PUNCT
ejpam-21	702	4	v.	v.	CCONJ
ejpam-21	702	5	popa	popa	NOUN
ejpam-21	702	6	and	and	CCONJ
ejpam-21	702	7	t.	t.	PROPN
ejpam-21	702	8	noiri	noiri	PROPN
ejpam-21	702	9	,	,	PUNCT
ejpam-21	702	10	a	a	DET
ejpam-21	702	11	unified	unified	ADJ
ejpam-21	702	12	theory	theory	NOUN
ejpam-21	702	13	of	of	ADP
ejpam-21	702	14	weak	weak	ADJ
ejpam-21	702	15	continuity	continuity	NOUN
ejpam-21	702	16	for	for	ADP
ejpam-21	702	17	functions	function	NOUN
ejpam-21	702	18	,	,	PUNCT
ejpam-21	702	19	rend	rend	VERB
ejpam-21	702	20	.	.	PUNCT
ejpam-21	703	1	circ	circ	PROPN
ejpam-21	703	2	.	.	PUNCT
ejpam-21	704	1	mat	mat	PROPN
ejpam-21	704	2	.	.	PUNCT
ejpam-21	704	3	palermo	palermo	PROPN
ejpam-21	704	4	(	(	PUNCT
ejpam-21	704	5	2	2	NUM
ejpam-21	704	6	)	)	PUNCT
ejpam-21	704	7	51	51	NUM
ejpam-21	704	8	(	(	PUNCT
ejpam-21	704	9	2002	2002	NUM
ejpam-21	704	10	)	)	PUNCT
ejpam-21	704	11	,	,	PUNCT
ejpam-21	704	12	439–464	439–464	NUM
ejpam-21	704	13	.	.	PUNCT
ejpam-21	705	1	[	[	X
ejpam-21	705	2	36	36	NUM
ejpam-21	705	3	]	]	X
ejpam-21	705	4	v.	v.	CCONJ
ejpam-21	705	5	popa	popa	NOUN
ejpam-21	705	6	and	and	CCONJ
ejpam-21	705	7	t.	t.	PROPN
ejpam-21	705	8	noiri	noiri	PROPN
ejpam-21	705	9	,	,	PUNCT
ejpam-21	705	10	characterizations	characterization	NOUN
ejpam-21	705	11	of	of	ADP
ejpam-21	705	12	c	c	NOUN
ejpam-21	705	13	-	-	PUNCT
ejpam-21	705	14	quasicontinuous	quasicontinuous	ADJ
ejpam-21	705	15	multifunctions	multifunction	NOUN
ejpam-21	705	16	,	,	PUNCT
ejpam-21	705	17	math	math	NOUN
ejpam-21	705	18	.	.	PUNCT
ejpam-21	706	1	balkanica	balkanica	PROPN
ejpam-21	706	2	(	(	PUNCT
ejpam-21	706	3	n.	n.	PROPN
ejpam-21	706	4	s.	s.	PROPN
ejpam-21	706	5	)	)	PUNCT
ejpam-21	706	6	20	20	NUM
ejpam-21	706	7	(	(	PUNCT
ejpam-21	706	8	2006	2006	NUM
ejpam-21	706	9	)	)	PUNCT
ejpam-21	706	10	,	,	PUNCT
ejpam-21	706	11	265–274	265–274	NUM
ejpam-21	706	12	.	.	PUNCT
ejpam-21	707	1	[	[	X
ejpam-21	707	2	37	37	NUM
ejpam-21	707	3	]	]	PUNCT
ejpam-21	707	4	s.	s.	PROPN
ejpam-21	707	5	raychaudhuri	raychaudhuri	PROPN
ejpam-21	707	6	and	and	CCONJ
ejpam-21	707	7	m.	m.	PROPN
ejpam-21	707	8	n.	n.	PROPN
ejpam-21	707	9	mukherjee	mukherjee	PROPN
ejpam-21	707	10	,	,	PUNCT
ejpam-21	707	11	on	on	ADP
ejpam-21	707	12	δ	δ	PROPN
ejpam-21	707	13	-	-	PUNCT
ejpam-21	707	14	almost	almost	ADV
ejpam-21	707	15	continuity	continuity	NOUN
ejpam-21	707	16	and	and	CCONJ
ejpam-21	707	17	δ	δ	NOUN
ejpam-21	707	18	-	-	PUNCT
ejpam-21	707	19	preopen	preopen	ADJ
ejpam-21	707	20	sets	set	NOUN
ejpam-21	707	21	,	,	PUNCT
ejpam-21	707	22	bull	bull	NOUN
ejpam-21	707	23	.	.	PUNCT
ejpam-21	707	24	inst	inst	PROPN
ejpam-21	707	25	.	.	PUNCT
ejpam-21	707	26	math	math	NOUN
ejpam-21	707	27	.	.	PUNCT
ejpam-21	708	1	acad	acad	PROPN
ejpam-21	708	2	.	.	PUNCT
ejpam-21	709	1	sinica	sinica	PROPN
ejpam-21	709	2	21	21	NUM
ejpam-21	709	3	(	(	PUNCT
ejpam-21	709	4	1993	1993	NUM
ejpam-21	709	5	)	)	PUNCT
ejpam-21	709	6	,	,	PUNCT
ejpam-21	709	7	357–366	357–366	NUM
ejpam-21	709	8	.	.	PUNCT
ejpam-21	710	1	[	[	X
ejpam-21	710	2	38	38	NUM
ejpam-21	710	3	]	]	PUNCT
ejpam-21	710	4	n.	n.	NOUN
ejpam-21	710	5	v.	v.	PROPN
ejpam-21	710	6	veličko	veličko	PROPN
ejpam-21	710	7	,	,	PUNCT
ejpam-21	710	8	h	h	NOUN
ejpam-21	710	9	-	-	PUNCT
ejpam-21	710	10	closed	closed	ADJ
ejpam-21	710	11	topological	topological	ADJ
ejpam-21	710	12	spaces	space	NOUN
ejpam-21	710	13	,	,	PUNCT
ejpam-21	710	14	amer	amer	PROPN
ejpam-21	710	15	.	.	PROPN
ejpam-21	710	16	math	math	PROPN
ejpam-21	710	17	.	.	PUNCT
ejpam-21	711	1	soc	soc	PROPN
ejpam-21	711	2	.	.	PUNCT
ejpam-21	712	1	transl	transl	PROPN
ejpam-21	712	2	.	.	PUNCT
ejpam-21	713	1	78	78	NUM
ejpam-21	713	2	(	(	PUNCT
ejpam-21	713	3	1968	1968	NUM
ejpam-21	713	4	)	)	PUNCT
ejpam-21	713	5	,	,	PUNCT
ejpam-21	713	6	103–118	103–118	NUM
ejpam-21	713	7	.	.	PUNCT
ejpam-21	714	1	[	[	X
ejpam-21	714	2	39	39	NUM
ejpam-21	714	3	]	]	PUNCT
ejpam-21	714	4	a.	a.	NOUN
ejpam-21	714	5	wilanski	wilanski	PROPN
ejpam-21	714	6	,	,	PUNCT
ejpam-21	714	7	between	between	ADP
ejpam-21	714	8	t1	t1	NOUN
ejpam-21	714	9	and	and	CCONJ
ejpam-21	714	10	t2	t2	PROPN
ejpam-21	714	11	,	,	PUNCT
ejpam-21	714	12	amer	amer	PROPN
ejpam-21	714	13	.	.	PROPN
ejpam-21	714	14	math	math	PROPN
ejpam-21	714	15	.	.	PUNCT
ejpam-21	715	1	monthly	monthly	ADJ
ejpam-21	715	2	74	74	NUM
ejpam-21	715	3	(	(	PUNCT
ejpam-21	715	4	1967	1967	NUM
ejpam-21	715	5	)	)	PUNCT
ejpam-21	715	6	,	,	PUNCT
ejpam-21	715	7	261–266	261–266	NUM
ejpam-21	715	8	.	.	PUNCT
ejpam-21	716	1	[	[	X
ejpam-21	716	2	40	40	NUM
ejpam-21	716	3	]	]	PUNCT
ejpam-21	716	4	j.	j.	PROPN
ejpam-21	716	5	d.	d.	PROPN
ejpam-21	716	6	wine	wine	PROPN
ejpam-21	716	7	,	,	PUNCT
ejpam-21	716	8	locally	locally	ADV
ejpam-21	716	9	paracompact	paracompact	ADJ
ejpam-21	716	10	spaces	space	NOUN
ejpam-21	716	11	,	,	PUNCT
ejpam-21	716	12	glasnik	glasnik	PROPN
ejpam-21	716	13	mat	mat	PROPN
ejpam-21	716	14	.	.	PUNCT
ejpam-21	716	15	10(30	10(30	NUM
ejpam-21	716	16	)	)	PUNCT
ejpam-21	716	17	(	(	PUNCT
ejpam-21	716	18	1975	1975	NUM
ejpam-21	716	19	)	)	PUNCT
ejpam-21	716	20	,	,	PUNCT
ejpam-21	716	21	351–357	351–357	NUM
ejpam-21	716	22	.	.	PUNCT