id	sid	tid	token	lemma	pos
ejpam-4207	1	1	european	european	PROPN
ejpam-4207	1	2	journal	journal	PROPN
ejpam-4207	1	3	of	of	ADP
ejpam-4207	1	4	pure	pure	ADJ
ejpam-4207	1	5	and	and	CCONJ
ejpam-4207	1	6	applied	apply	VERB
ejpam-4207	1	7	mathematics	mathematic	NOUN
ejpam-4207	1	8	vol	vol	NOUN
ejpam-4207	1	9	.	.	PROPN
ejpam-4207	2	1	15	15	NUM
ejpam-4207	2	2	,	,	PUNCT
ejpam-4207	2	3	no	no	INTJ
ejpam-4207	2	4	.	.	NOUN
ejpam-4207	2	5	1	1	NUM
ejpam-4207	2	6	,	,	PUNCT
ejpam-4207	2	7	2022	2022	NUM
ejpam-4207	2	8	,	,	PUNCT
ejpam-4207	2	9	1	1	NUM
ejpam-4207	2	10	-	-	SYM
ejpam-4207	2	11	14	14	NUM
ejpam-4207	2	12	issn	issn	PROPN
ejpam-4207	2	13	1307	1307	NUM
ejpam-4207	2	14	-	-	SYM
ejpam-4207	2	15	5543	5543	NUM
ejpam-4207	2	16	–	–	PUNCT
ejpam-4207	2	17	ejpam.com	ejpam.com	X
ejpam-4207	2	18	published	publish	VERB
ejpam-4207	2	19	by	by	ADP
ejpam-4207	2	20	new	new	PROPN
ejpam-4207	2	21	york	york	PROPN
ejpam-4207	2	22	business	business	PROPN
ejpam-4207	2	23	global	global	PROPN
ejpam-4207	2	24	on	on	ADP
ejpam-4207	2	25	m	m	PROPN
ejpam-4207	2	26	-	-	ADJ
ejpam-4207	2	27	i	i	PRON
ejpam-4207	2	28	-	-	PUNCT
ejpam-4207	2	29	continuous	continuous	ADJ
ejpam-4207	2	30	multifunctions	multifunction	NOUN
ejpam-4207	2	31	takashi	takashi	PROPN
ejpam-4207	2	32	noiri1,∗	noiri1,∗	PROPN
ejpam-4207	2	33	,	,	PUNCT
ejpam-4207	2	34	valeriu	valeriu	PROPN
ejpam-4207	2	35	popa2	popa2	NOUN
ejpam-4207	2	36	1	1	NUM
ejpam-4207	2	37	2949	2949	NUM
ejpam-4207	2	38	-	-	SYM
ejpam-4207	2	39	1	1	NUM
ejpam-4207	2	40	shiokita	shiokita	NOUN
ejpam-4207	2	41	-	-	PUNCT
ejpam-4207	2	42	cho	cho	ADJ
ejpam-4207	2	43	,	,	PUNCT
ejpam-4207	2	44	hinagu	hinagu	ADJ
ejpam-4207	2	45	,	,	PUNCT
ejpam-4207	2	46	yatsushiro	yatsushiro	PROPN
ejpam-4207	2	47	-	-	PUNCT
ejpam-4207	2	48	shi	shi	PROPN
ejpam-4207	2	49	,	,	PUNCT
ejpam-4207	2	50	kumamoto	kumamoto	PROPN
ejpam-4207	2	51	-	-	PUNCT
ejpam-4207	2	52	ken	ken	PROPN
ejpam-4207	2	53	,	,	PUNCT
ejpam-4207	2	54	869	869	NUM
ejpam-4207	2	55	-	-	SYM
ejpam-4207	2	56	5142	5142	NUM
ejpam-4207	2	57	japan	japan	PROPN
ejpam-4207	2	58	2	2	NUM
ejpam-4207	2	59	department	department	NOUN
ejpam-4207	2	60	of	of	ADP
ejpam-4207	2	61	mathematics	mathematics	PROPN
ejpam-4207	2	62	,	,	PUNCT
ejpam-4207	2	63	university	university	NOUN
ejpam-4207	2	64	vasile	vasile	NOUN
ejpam-4207	2	65	alecsandri	alecsandri	NOUN
ejpam-4207	2	66	of	of	ADP
ejpam-4207	2	67	bacau	bacau	NOUN
ejpam-4207	2	68	,	,	PUNCT
ejpam-4207	2	69	600	600	NUM
ejpam-4207	2	70	115	115	NUM
ejpam-4207	2	71	-	-	PUNCT
ejpam-4207	2	72	bacau	bacau	NOUN
ejpam-4207	2	73	,	,	PUNCT
ejpam-4207	2	74	romania	romania	PROPN
ejpam-4207	2	75	abstract	abstract	NOUN
ejpam-4207	2	76	.	.	PUNCT
ejpam-4207	3	1	let	let	VERB
ejpam-4207	3	2	mio(x	mio(x	NOUN
ejpam-4207	3	3	)	)	PUNCT
ejpam-4207	3	4	be	be	VERB
ejpam-4207	3	5	the	the	DET
ejpam-4207	3	6	family	family	NOUN
ejpam-4207	3	7	of	of	ADP
ejpam-4207	3	8	⋆-open	⋆-open	ADJ
ejpam-4207	3	9	(	(	PUNCT
ejpam-4207	3	10	resp	resp	NOUN
ejpam-4207	3	11	.	.	PUNCT
ejpam-4207	4	1	α	α	X
ejpam-4207	4	2	-	-	PUNCT
ejpam-4207	4	3	i	i	PRON
ejpam-4207	4	4	-	-	PUNCT
ejpam-4207	4	5	open	open	ADJ
ejpam-4207	4	6	,	,	PUNCT
ejpam-4207	4	7	pre	pre	ADJ
ejpam-4207	4	8	-	-	ADJ
ejpam-4207	4	9	i	i	PRON
ejpam-4207	4	10	-	-	PUNCT
ejpam-4207	4	11	open	open	ADJ
ejpam-4207	4	12	,	,	PUNCT
ejpam-4207	4	13	semi	semi	ADJ
ejpam-4207	4	14	-	-	ADJ
ejpam-4207	4	15	i	i	PRON
ejpam-4207	4	16	-	-	PUNCT
ejpam-4207	4	17	open	open	ADJ
ejpam-4207	4	18	,	,	PUNCT
ejpam-4207	4	19	β	β	NOUN
ejpam-4207	4	20	-	-	NOUN
ejpam-4207	4	21	iopen	iopen	VERB
ejpam-4207	4	22	,	,	PUNCT
ejpam-4207	4	23	etc	etc	X
ejpam-4207	4	24	.	.	X
ejpam-4207	4	25	)	)	PUNCT
ejpam-4207	4	26	sets	set	NOUN
ejpam-4207	4	27	in	in	ADP
ejpam-4207	4	28	an	an	DET
ejpam-4207	4	29	ideal	ideal	ADJ
ejpam-4207	4	30	topological	topological	ADJ
ejpam-4207	4	31	space	space	NOUN
ejpam-4207	4	32	(	(	PUNCT
ejpam-4207	4	33	x	x	X
ejpam-4207	4	34	,	,	PUNCT
ejpam-4207	4	35	τ	τ	PROPN
ejpam-4207	4	36	,	,	PUNCT
ejpam-4207	4	37	i	i	PROPN
ejpam-4207	4	38	)	)	PUNCT
ejpam-4207	4	39	.	.	PUNCT
ejpam-4207	5	1	by	by	ADP
ejpam-4207	5	2	using	use	VERB
ejpam-4207	5	3	mio(x	mio(x	PROPN
ejpam-4207	5	4	)	)	PUNCT
ejpam-4207	5	5	,	,	PUNCT
ejpam-4207	5	6	we	we	PRON
ejpam-4207	5	7	introduce	introduce	VERB
ejpam-4207	5	8	and	and	CCONJ
ejpam-4207	5	9	investigate	investigate	VERB
ejpam-4207	5	10	the	the	DET
ejpam-4207	5	11	notions	notion	NOUN
ejpam-4207	5	12	of	of	ADP
ejpam-4207	5	13	an	an	DET
ejpam-4207	5	14	m	m	PROPN
ejpam-4207	5	15	-	-	PUNCT
ejpam-4207	5	16	i	i	NOUN
ejpam-4207	5	17	-	-	PUNCT
ejpam-4207	5	18	continuous	continuous	ADJ
ejpam-4207	5	19	multifunction	multifunction	NOUN
ejpam-4207	5	20	f	f	NOUN
ejpam-4207	5	21	:	:	PUNCT
ejpam-4207	5	22	(	(	PUNCT
ejpam-4207	5	23	x	x	X
ejpam-4207	5	24	,	,	PUNCT
ejpam-4207	5	25	τ	τ	PROPN
ejpam-4207	5	26	,	,	PUNCT
ejpam-4207	5	27	i	i	NOUN
ejpam-4207	5	28	)	)	PUNCT
ejpam-4207	5	29	→	→	SYM
ejpam-4207	5	30	(	(	PUNCT
ejpam-4207	5	31	y	y	PROPN
ejpam-4207	5	32	,	,	PUNCT
ejpam-4207	5	33	σ	σ	PROPN
ejpam-4207	5	34	)	)	PUNCT
ejpam-4207	5	35	and	and	CCONJ
ejpam-4207	5	36	mi⋆-continuous	mi⋆-continuous	ADJ
ejpam-4207	5	37	multifunction	multifunction	NOUN
ejpam-4207	5	38	f	f	NOUN
ejpam-4207	5	39	:	:	PUNCT
ejpam-4207	5	40	(	(	PUNCT
ejpam-4207	5	41	x	x	X
ejpam-4207	5	42	,	,	PUNCT
ejpam-4207	5	43	τ	τ	PROPN
ejpam-4207	5	44	,	,	PUNCT
ejpam-4207	5	45	i	i	NOUN
ejpam-4207	5	46	)	)	PUNCT
ejpam-4207	5	47	→	→	SYM
ejpam-4207	5	48	(	(	PUNCT
ejpam-4207	5	49	y	y	PROPN
ejpam-4207	5	50	,	,	PUNCT
ejpam-4207	5	51	σ	σ	PROPN
ejpam-4207	5	52	,	,	PUNCT
ejpam-4207	5	53	j	j	PROPN
ejpam-4207	5	54	)	)	PUNCT
ejpam-4207	5	55	.	.	PUNCT
ejpam-4207	6	1	the	the	DET
ejpam-4207	6	2	notion	notion	NOUN
ejpam-4207	6	3	of	of	ADP
ejpam-4207	6	4	mi⋆-continuity	mi⋆-continuity	NOUN
ejpam-4207	6	5	is	be	AUX
ejpam-4207	6	6	a	a	DET
ejpam-4207	6	7	generalization	generalization	NOUN
ejpam-4207	6	8	of	of	ADP
ejpam-4207	6	9	m	m	PROPN
ejpam-4207	6	10	-	-	ADJ
ejpam-4207	6	11	icontinuity	icontinuity	NOUN
ejpam-4207	6	12	and	and	CCONJ
ejpam-4207	6	13	i⋆-continuity	i⋆-continuity	NOUN
ejpam-4207	6	14	[	[	X
ejpam-4207	6	15	9	9	NUM
ejpam-4207	6	16	]	]	PUNCT
ejpam-4207	6	17	.	.	PUNCT
ejpam-4207	7	1	2020	2020	NUM
ejpam-4207	7	2	mathematics	mathematic	NOUN
ejpam-4207	7	3	subject	subject	NOUN
ejpam-4207	7	4	classifications	classification	NOUN
ejpam-4207	7	5	:	:	PUNCT
ejpam-4207	7	6	54c08	54c08	NUM
ejpam-4207	7	7	,	,	PUNCT
ejpam-4207	7	8	54c60	54c60	NUM
ejpam-4207	7	9	key	key	ADJ
ejpam-4207	7	10	words	word	NOUN
ejpam-4207	7	11	and	and	CCONJ
ejpam-4207	7	12	phrases	phrase	NOUN
ejpam-4207	7	13	:	:	PUNCT
ejpam-4207	7	14	minimal	minimal	ADJ
ejpam-4207	7	15	structure	structure	NOUN
ejpam-4207	7	16	,	,	PUNCT
ejpam-4207	7	17	ideal	ideal	ADJ
ejpam-4207	7	18	topological	topological	ADJ
ejpam-4207	7	19	space	space	NOUN
ejpam-4207	7	20	,	,	PUNCT
ejpam-4207	7	21	m	m	PROPN
ejpam-4207	7	22	-	-	ADJ
ejpam-4207	7	23	i	i	PRON
ejpam-4207	7	24	-	-	PUNCT
ejpam-4207	7	25	open	open	ADJ
ejpam-4207	7	26	,	,	PUNCT
ejpam-4207	7	27	m	m	PROPN
ejpam-4207	7	28	-	-	ADJ
ejpam-4207	7	29	i	i	NOUN
ejpam-4207	7	30	-	-	PUNCT
ejpam-4207	7	31	continuous	continuous	ADJ
ejpam-4207	7	32	,	,	PUNCT
ejpam-4207	7	33	mi⋆-continuous	mi⋆-continuous	ADJ
ejpam-4207	7	34	,	,	PUNCT
ejpam-4207	7	35	multifunction	multifunction	NOUN
ejpam-4207	7	36	1	1	NUM
ejpam-4207	7	37	.	.	PUNCT
ejpam-4207	8	1	introduction	introduction	NOUN
ejpam-4207	8	2	semi	semi	ADJ
ejpam-4207	8	3	-	-	ADJ
ejpam-4207	8	4	open	open	ADJ
ejpam-4207	8	5	sets	set	NOUN
ejpam-4207	8	6	,	,	PUNCT
ejpam-4207	8	7	pre	pre	ADJ
ejpam-4207	8	8	-	-	ADJ
ejpam-4207	8	9	open	open	ADJ
ejpam-4207	8	10	sets	set	NOUN
ejpam-4207	8	11	,	,	PUNCT
ejpam-4207	8	12	α	α	NOUN
ejpam-4207	8	13	-	-	ADJ
ejpam-4207	8	14	open	open	ADJ
ejpam-4207	8	15	sets	set	NOUN
ejpam-4207	8	16	,	,	PUNCT
ejpam-4207	8	17	b	b	X
ejpam-4207	8	18	-	-	PUNCT
ejpam-4207	8	19	open	open	ADJ
ejpam-4207	8	20	sets	set	NOUN
ejpam-4207	8	21	and	and	CCONJ
ejpam-4207	8	22	β	β	NOUN
ejpam-4207	8	23	-	-	ADJ
ejpam-4207	8	24	open	open	ADJ
ejpam-4207	8	25	sets	set	NOUN
ejpam-4207	8	26	play	play	VERB
ejpam-4207	8	27	an	an	DET
ejpam-4207	8	28	important	important	ADJ
ejpam-4207	8	29	role	role	NOUN
ejpam-4207	8	30	in	in	ADP
ejpam-4207	8	31	the	the	DET
ejpam-4207	8	32	research	research	NOUN
ejpam-4207	8	33	of	of	ADP
ejpam-4207	8	34	generalizations	generalization	NOUN
ejpam-4207	8	35	of	of	ADP
ejpam-4207	8	36	continuity	continuity	NOUN
ejpam-4207	8	37	for	for	ADP
ejpam-4207	8	38	functions	function	NOUN
ejpam-4207	8	39	and	and	CCONJ
ejpam-4207	8	40	multifunctions	multifunction	NOUN
ejpam-4207	8	41	.	.	PUNCT
ejpam-4207	9	1	in	in	ADP
ejpam-4207	9	2	1961	1961	NUM
ejpam-4207	9	3	,	,	PUNCT
ejpam-4207	9	4	marcus	marcus	PROPN
ejpam-4207	10	1	[	[	X
ejpam-4207	10	2	23	23	NUM
ejpam-4207	10	3	]	]	PUNCT
ejpam-4207	10	4	introduced	introduce	VERB
ejpam-4207	10	5	the	the	DET
ejpam-4207	10	6	notion	notion	NOUN
ejpam-4207	10	7	of	of	ADP
ejpam-4207	10	8	quasicontinuity	quasicontinuity	NOUN
ejpam-4207	10	9	in	in	ADP
ejpam-4207	10	10	topological	topological	ADJ
ejpam-4207	10	11	spaces	space	NOUN
ejpam-4207	10	12	.	.	PUNCT
ejpam-4207	11	1	neubrunnova	neubrunnova	ADJ
ejpam-4207	12	1	[	[	X
ejpam-4207	12	2	26	26	NUM
ejpam-4207	12	3	]	]	PUNCT
ejpam-4207	12	4	showed	show	VERB
ejpam-4207	12	5	that	that	DET
ejpam-4207	12	6	quasicontinuity	quasicontinuity	NOUN
ejpam-4207	12	7	is	be	AUX
ejpam-4207	12	8	equivalent	equivalent	ADJ
ejpam-4207	12	9	to	to	ADP
ejpam-4207	12	10	semi	semi	ADJ
ejpam-4207	12	11	-	-	NOUN
ejpam-4207	12	12	continuity	continuity	NOUN
ejpam-4207	12	13	due	due	ADP
ejpam-4207	12	14	to	to	ADP
ejpam-4207	12	15	levine	levine	PROPN
ejpam-4207	12	16	[	[	X
ejpam-4207	12	17	21	21	NUM
ejpam-4207	12	18	]	]	PUNCT
ejpam-4207	12	19	.	.	PUNCT
ejpam-4207	13	1	bânzaru	bânzaru	NOUN
ejpam-4207	14	1	[	[	X
ejpam-4207	14	2	6	6	NUM
ejpam-4207	14	3	]	]	PUNCT
ejpam-4207	14	4	and	and	CCONJ
ejpam-4207	14	5	bânzaru	bânzaru	NOUN
ejpam-4207	14	6	and	and	CCONJ
ejpam-4207	14	7	crivǎţ	crivǎţ	NOUN
ejpam-4207	15	1	[	[	X
ejpam-4207	15	2	7	7	NUM
ejpam-4207	15	3	]	]	PUNCT
ejpam-4207	15	4	extended	extend	VERB
ejpam-4207	15	5	it	it	PRON
ejpam-4207	15	6	to	to	ADP
ejpam-4207	15	7	the	the	DET
ejpam-4207	15	8	notion	notion	NOUN
ejpam-4207	15	9	of	of	ADP
ejpam-4207	15	10	quasicontinuity	quasicontinuity	NOUN
ejpam-4207	15	11	for	for	ADP
ejpam-4207	15	12	multifunctions	multifunction	NOUN
ejpam-4207	15	13	.	.	PUNCT
ejpam-4207	16	1	properties	property	NOUN
ejpam-4207	16	2	of	of	ADP
ejpam-4207	16	3	quasicontinuous	quasicontinuous	ADJ
ejpam-4207	16	4	multifunctions	multifunction	NOUN
ejpam-4207	16	5	are	be	AUX
ejpam-4207	16	6	further	far	ADV
ejpam-4207	16	7	investigated	investigate	VERB
ejpam-4207	16	8	in	in	ADP
ejpam-4207	16	9	[	[	X
ejpam-4207	16	10	13	13	NUM
ejpam-4207	16	11	]	]	PUNCT
ejpam-4207	16	12	,	,	PUNCT
ejpam-4207	16	13	[	[	X
ejpam-4207	16	14	33	33	NUM
ejpam-4207	16	15	]	]	PUNCT
ejpam-4207	16	16	,	,	PUNCT
ejpam-4207	16	17	and	and	CCONJ
ejpam-4207	16	18	[	[	X
ejpam-4207	16	19	39	39	NUM
ejpam-4207	16	20	]	]	PUNCT
ejpam-4207	16	21	.	.	PUNCT
ejpam-4207	17	1	the	the	DET
ejpam-4207	17	2	present	present	ADJ
ejpam-4207	17	3	authors	author	NOUN
ejpam-4207	17	4	introduced	introduce	VERB
ejpam-4207	17	5	and	and	CCONJ
ejpam-4207	17	6	studied	study	VERB
ejpam-4207	17	7	α	α	NUM
ejpam-4207	17	8	-	-	ADJ
ejpam-4207	17	9	continuous	continuous	ADJ
ejpam-4207	17	10	multifunctions	multifunction	NOUN
ejpam-4207	17	11	[	[	X
ejpam-4207	17	12	36	36	NUM
ejpam-4207	17	13	]	]	PUNCT
ejpam-4207	17	14	,	,	PUNCT
ejpam-4207	17	15	precontinuous	precontinuous	ADJ
ejpam-4207	17	16	multifunctions	multifunction	NOUN
ejpam-4207	18	1	[	[	X
ejpam-4207	18	2	39	39	NUM
ejpam-4207	18	3	]	]	PUNCT
ejpam-4207	18	4	,	,	PUNCT
ejpam-4207	18	5	β	β	X
ejpam-4207	18	6	-	-	ADJ
ejpam-4207	18	7	continuous	continuous	ADJ
ejpam-4207	18	8	multifunctions	multifunction	NOUN
ejpam-4207	19	1	[	[	X
ejpam-4207	19	2	37	37	NUM
ejpam-4207	19	3	]	]	PUNCT
ejpam-4207	19	4	.	.	PUNCT
ejpam-4207	20	1	przemski	przemski	PROPN
ejpam-4207	21	1	[	[	X
ejpam-4207	21	2	46	46	NUM
ejpam-4207	21	3	]	]	PUNCT
ejpam-4207	21	4	also	also	ADV
ejpam-4207	21	5	introduced	introduce	VERB
ejpam-4207	21	6	the	the	DET
ejpam-4207	21	7	notions	notion	NOUN
ejpam-4207	21	8	of	of	ADP
ejpam-4207	21	9	α	α	NOUN
ejpam-4207	21	10	-	-	NOUN
ejpam-4207	21	11	continuity	continuity	NOUN
ejpam-4207	21	12	,	,	PUNCT
ejpam-4207	21	13	precontinuity	precontinuity	NOUN
ejpam-4207	21	14	and	and	CCONJ
ejpam-4207	21	15	presemi	presemi	NOUN
ejpam-4207	21	16	-	-	PUNCT
ejpam-4207	21	17	continuity	continuity	NOUN
ejpam-4207	21	18	for	for	ADP
ejpam-4207	21	19	multifunctions	multifunction	NOUN
ejpam-4207	21	20	.	.	PUNCT
ejpam-4207	22	1	it	it	PRON
ejpam-4207	22	2	is	be	AUX
ejpam-4207	22	3	poved	pove	VERB
ejpam-4207	22	4	in	in	ADP
ejpam-4207	22	5	[	[	X
ejpam-4207	22	6	36	36	NUM
ejpam-4207	22	7	]	]	X
ejpam-4207	22	8	(	(	PUNCT
ejpam-4207	22	9	resp	resp	NOUN
ejpam-4207	22	10	.	.	PUNCT
ejpam-4207	23	1	[	[	X
ejpam-4207	23	2	39	39	NUM
ejpam-4207	23	3	]	]	PUNCT
ejpam-4207	23	4	,	,	PUNCT
ejpam-4207	23	5	[	[	X
ejpam-4207	23	6	37	37	NUM
ejpam-4207	23	7	]	]	PUNCT
ejpam-4207	23	8	)	)	PUNCT
ejpam-4207	24	1	that	that	SCONJ
ejpam-4207	24	2	the	the	DET
ejpam-4207	24	3	notion	notion	NOUN
ejpam-4207	24	4	of	of	ADP
ejpam-4207	24	5	α	α	NOUN
ejpam-4207	24	6	-	-	PUNCT
ejpam-4207	24	7	continuity	continuity	NOUN
ejpam-4207	24	8	(	(	PUNCT
ejpam-4207	24	9	resp	resp	NOUN
ejpam-4207	24	10	.	.	PUNCT
ejpam-4207	25	1	precontinuity	precontinuity	NOUN
ejpam-4207	25	2	,	,	PUNCT
ejpam-4207	25	3	β	β	NOUN
ejpam-4207	25	4	-	-	NOUN
ejpam-4207	25	5	continuity	continuity	NOUN
ejpam-4207	25	6	)	)	PUNCT
ejpam-4207	25	7	for	for	ADP
ejpam-4207	25	8	multifunctions	multifunction	NOUN
ejpam-4207	25	9	in	in	ADP
ejpam-4207	25	10	the	the	DET
ejpam-4207	25	11	sense	sense	NOUN
ejpam-4207	25	12	of	of	ADP
ejpam-4207	25	13	popa	popa	NOUN
ejpam-4207	25	14	and	and	CCONJ
ejpam-4207	25	15	noiri	noiri	NOUN
ejpam-4207	25	16	is	be	AUX
ejpam-4207	25	17	equivalent	equivalent	ADJ
ejpam-4207	25	18	to	to	ADP
ejpam-4207	25	19	that	that	PRON
ejpam-4207	25	20	of	of	ADP
ejpam-4207	25	21	α	α	NOUN
ejpam-4207	25	22	-	-	PUNCT
ejpam-4207	25	23	continuity	continuity	NOUN
ejpam-4207	25	24	(	(	PUNCT
ejpam-4207	25	25	resp	resp	NOUN
ejpam-4207	25	26	.	.	PUNCT
ejpam-4207	26	1	precontinuity	precontinuity	NOUN
ejpam-4207	26	2	,	,	PUNCT
ejpam-4207	26	3	presemi	presemi	NOUN
ejpam-4207	26	4	-	-	PUNCT
ejpam-4207	26	5	continuity	continuity	NOUN
ejpam-4207	26	6	)	)	PUNCT
ejpam-4207	26	7	in	in	ADP
ejpam-4207	26	8	the	the	DET
ejpam-4207	26	9	sense	sense	NOUN
ejpam-4207	26	10	of	of	ADP
ejpam-4207	26	11	przemski	przemski	NOUN
ejpam-4207	26	12	.	.	PUNCT
ejpam-4207	27	1	the	the	DET
ejpam-4207	27	2	notions	notion	NOUN
ejpam-4207	27	3	of	of	ADP
ejpam-4207	27	4	minimal	minimal	ADJ
ejpam-4207	27	5	structure	structure	NOUN
ejpam-4207	27	6	,	,	PUNCT
ejpam-4207	27	7	m	m	NOUN
ejpam-4207	27	8	-	-	NOUN
ejpam-4207	27	9	continuity	continuity	NOUN
ejpam-4207	27	10	,	,	PUNCT
ejpam-4207	27	11	m	m	PRON
ejpam-4207	27	12	-continuity	-continuity	ADJ
ejpam-4207	27	13	are	be	AUX
ejpam-4207	27	14	introduced	introduce	VERB
ejpam-4207	27	15	in	in	ADP
ejpam-4207	27	16	[	[	X
ejpam-4207	27	17	40	40	NUM
ejpam-4207	27	18	]	]	PUNCT
ejpam-4207	27	19	and	and	CCONJ
ejpam-4207	27	20	[	[	X
ejpam-4207	27	21	41	41	NUM
ejpam-4207	27	22	]	]	PUNCT
ejpam-4207	27	23	.	.	PUNCT
ejpam-4207	28	1	by	by	ADP
ejpam-4207	28	2	using	use	VERB
ejpam-4207	28	3	these	these	DET
ejpam-4207	28	4	notions	notion	NOUN
ejpam-4207	28	5	,	,	PUNCT
ejpam-4207	28	6	the	the	DET
ejpam-4207	28	7	present	present	ADJ
ejpam-4207	28	8	authors	author	NOUN
ejpam-4207	28	9	unified	unify	VERB
ejpam-4207	28	10	theory	theory	NOUN
ejpam-4207	28	11	of	of	ADP
ejpam-4207	28	12	continuity	continuity	NOUN
ejpam-4207	28	13	in	in	ADP
ejpam-4207	28	14	[	[	X
ejpam-4207	28	15	42	42	NUM
ejpam-4207	28	16	]	]	PUNCT
ejpam-4207	28	17	,	,	PUNCT
ejpam-4207	28	18	∗corresponding	∗corresponde	VERB
ejpam-4207	28	19	author	author	NOUN
ejpam-4207	28	20	.	.	PUNCT
ejpam-4207	29	1	doi	doi	NOUN
ejpam-4207	29	2	:	:	PUNCT
ejpam-4207	29	3	https://doi.org/10.29020/nybg.ejpam.v15i1.4207	https://doi.org/10.29020/nybg.ejpam.v15i1.4207	NOUN
ejpam-4207	29	4	email	email	NOUN
ejpam-4207	29	5	addresses	address	NOUN
ejpam-4207	29	6	:	:	PUNCT
ejpam-4207	29	7	t.noiri@nifty.com	t.noiri@nifty.com	X
ejpam-4207	29	8	(	(	PUNCT
ejpam-4207	29	9	t.	t.	PROPN
ejpam-4207	29	10	noiri	noiri	PROPN
ejpam-4207	29	11	)	)	PUNCT
ejpam-4207	29	12	,	,	PUNCT
ejpam-4207	29	13	vpopa@ub.ro	vpopa@ub.ro	NOUN
ejpam-4207	29	14	(	(	PUNCT
ejpam-4207	29	15	v.	v.	ADP
ejpam-4207	29	16	popa	popa	NOUN
ejpam-4207	29	17	)	)	PUNCT
ejpam-4207	29	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4207	30	1	1	1	NUM
ejpam-4207	30	2	©	©	PROPN
ejpam-4207	30	3	2022	2022	NUM
ejpam-4207	30	4	ejpam	ejpam	VERB
ejpam-4207	30	5	all	all	DET
ejpam-4207	30	6	rights	right	NOUN
ejpam-4207	30	7	reserved	reserve	VERB
ejpam-4207	30	8	.	.	PUNCT
ejpam-4207	31	1	takashi	takashi	PROPN
ejpam-4207	31	2	noiri	noiri	PROPN
ejpam-4207	31	3	,	,	PUNCT
ejpam-4207	31	4	valeriu	valeriu	ADJ
ejpam-4207	31	5	popa	popa	NOUN
ejpam-4207	31	6	/	/	SYM
ejpam-4207	31	7	eur	eur	PROPN
ejpam-4207	31	8	.	.	PUNCT
ejpam-4207	32	1	j.	j.	PROPN
ejpam-4207	32	2	pure	pure	PROPN
ejpam-4207	32	3	appl	appl	PROPN
ejpam-4207	32	4	.	.	PROPN
ejpam-4207	32	5	math	math	PROPN
ejpam-4207	32	6	,	,	PUNCT
ejpam-4207	32	7	15	15	NUM
ejpam-4207	32	8	(	(	PUNCT
ejpam-4207	32	9	1	1	NUM
ejpam-4207	32	10	)	)	PUNCT
ejpam-4207	32	11	(	(	PUNCT
ejpam-4207	32	12	2022	2022	NUM
ejpam-4207	32	13	)	)	PUNCT
ejpam-4207	32	14	,	,	PUNCT
ejpam-4207	32	15	1	1	NUM
ejpam-4207	32	16	-	-	SYM
ejpam-4207	32	17	14	14	NUM
ejpam-4207	32	18	2	2	NUM
ejpam-4207	32	19	[	[	X
ejpam-4207	32	20	44	44	NUM
ejpam-4207	32	21	]	]	PUNCT
ejpam-4207	32	22	,	,	PUNCT
ejpam-4207	32	23	and	and	CCONJ
ejpam-4207	32	24	[	[	X
ejpam-4207	32	25	28	28	NUM
ejpam-4207	32	26	]	]	PUNCT
ejpam-4207	32	27	and	and	CCONJ
ejpam-4207	32	28	other	other	ADJ
ejpam-4207	32	29	papers	paper	NOUN
ejpam-4207	32	30	.	.	PUNCT
ejpam-4207	33	1	the	the	DET
ejpam-4207	33	2	upper	upper	ADJ
ejpam-4207	33	3	/	/	SYM
ejpam-4207	33	4	lower	low	ADJ
ejpam-4207	33	5	m	m	NOUN
ejpam-4207	33	6	-	-	ADJ
ejpam-4207	33	7	continuous	continuous	ADJ
ejpam-4207	33	8	(	(	PUNCT
ejpam-4207	33	9	resp	resp	NOUN
ejpam-4207	33	10	.	.	PUNCT
ejpam-4207	34	1	m	m	VERB
ejpam-4207	34	2	-continuous	-continuous	ADJ
ejpam-4207	34	3	)	)	PUNCT
ejpam-4207	34	4	multifunctions	multifunction	NOUN
ejpam-4207	34	5	are	be	AUX
ejpam-4207	34	6	introduced	introduce	VERB
ejpam-4207	34	7	and	and	CCONJ
ejpam-4207	34	8	investigated	investigate	VERB
ejpam-4207	34	9	in	in	ADP
ejpam-4207	34	10	[	[	X
ejpam-4207	34	11	42	42	NUM
ejpam-4207	34	12	]	]	PUNCT
ejpam-4207	34	13	,	,	PUNCT
ejpam-4207	34	14	[	[	X
ejpam-4207	34	15	44	44	NUM
ejpam-4207	34	16	]	]	PUNCT
ejpam-4207	34	17	(	(	PUNCT
ejpam-4207	34	18	resp	resp	NOUN
ejpam-4207	34	19	.	.	PUNCT
ejpam-4207	35	1	[	[	X
ejpam-4207	35	2	28	28	NUM
ejpam-4207	35	3	]	]	PUNCT
ejpam-4207	35	4	,	,	PUNCT
ejpam-4207	35	5	[	[	X
ejpam-4207	35	6	29	29	NUM
ejpam-4207	35	7	]	]	PUNCT
ejpam-4207	35	8	)	)	PUNCT
ejpam-4207	35	9	and	and	CCONJ
ejpam-4207	35	10	other	other	ADJ
ejpam-4207	35	11	papers	paper	NOUN
ejpam-4207	35	12	.	.	PUNCT
ejpam-4207	36	1	the	the	DET
ejpam-4207	36	2	notion	notion	NOUN
ejpam-4207	36	3	of	of	ADP
ejpam-4207	36	4	ideal	ideal	ADJ
ejpam-4207	36	5	topological	topological	ADJ
ejpam-4207	36	6	spaces	space	NOUN
ejpam-4207	36	7	was	be	AUX
ejpam-4207	36	8	introduced	introduce	VERB
ejpam-4207	36	9	in	in	ADP
ejpam-4207	36	10	[	[	X
ejpam-4207	36	11	20	20	NUM
ejpam-4207	36	12	]	]	PUNCT
ejpam-4207	36	13	,	,	PUNCT
ejpam-4207	36	14	[	[	X
ejpam-4207	36	15	47	47	NUM
ejpam-4207	36	16	]	]	PUNCT
ejpam-4207	36	17	.	.	PUNCT
ejpam-4207	37	1	as	as	ADP
ejpam-4207	37	2	generelarizations	generelarization	NOUN
ejpam-4207	37	3	of	of	ADP
ejpam-4207	37	4	open	open	ADJ
ejpam-4207	37	5	sets	set	NOUN
ejpam-4207	37	6	,	,	PUNCT
ejpam-4207	37	7	the	the	DET
ejpam-4207	37	8	notions	notion	NOUN
ejpam-4207	37	9	of	of	ADP
ejpam-4207	37	10	semi	semi	ADJ
ejpam-4207	37	11	-	-	ADJ
ejpam-4207	37	12	i	i	ADV
ejpam-4207	37	13	-	-	PUNCT
ejpam-4207	37	14	open	open	ADJ
ejpam-4207	37	15	sets	set	NOUN
ejpam-4207	37	16	,	,	PUNCT
ejpam-4207	37	17	pre	pre	ADJ
ejpam-4207	37	18	-	-	ADJ
ejpam-4207	37	19	i	i	PRON
ejpam-4207	37	20	-	-	PUNCT
ejpam-4207	37	21	open	open	ADJ
ejpam-4207	37	22	sets	set	NOUN
ejpam-4207	37	23	,	,	PUNCT
ejpam-4207	37	24	α	α	X
ejpam-4207	37	25	-	-	PUNCT
ejpam-4207	37	26	i	i	NOUN
ejpam-4207	37	27	-	-	PUNCT
ejpam-4207	37	28	open	open	ADJ
ejpam-4207	37	29	sets	set	NOUN
ejpam-4207	37	30	,	,	PUNCT
ejpam-4207	37	31	b	b	X
ejpam-4207	37	32	-	-	PUNCT
ejpam-4207	37	33	i	i	NOUN
ejpam-4207	37	34	-	-	PUNCT
ejpam-4207	37	35	open	open	ADJ
ejpam-4207	37	36	sets	set	NOUN
ejpam-4207	37	37	and	and	CCONJ
ejpam-4207	37	38	β	β	X
ejpam-4207	37	39	-	-	ADJ
ejpam-4207	37	40	i	i	NOUN
ejpam-4207	37	41	-	-	PUNCT
ejpam-4207	37	42	open	open	ADJ
ejpam-4207	37	43	sets	set	NOUN
ejpam-4207	37	44	are	be	AUX
ejpam-4207	37	45	inroduced	inroduce	VERB
ejpam-4207	37	46	and	and	CCONJ
ejpam-4207	37	47	studied	study	VERB
ejpam-4207	37	48	.	.	PUNCT
ejpam-4207	38	1	the	the	DET
ejpam-4207	38	2	notion	notion	NOUN
ejpam-4207	38	3	of	of	ADP
ejpam-4207	38	4	upper	upper	ADJ
ejpam-4207	38	5	/	/	SYM
ejpam-4207	38	6	lower	lower	ADV
ejpam-4207	38	7	-	-	PUNCT
ejpam-4207	38	8	icontinuous	icontinuous	ADJ
ejpam-4207	38	9	multifunctions	multifunction	NOUN
ejpam-4207	38	10	is	be	AUX
ejpam-4207	38	11	introduced	introduce	VERB
ejpam-4207	38	12	in	in	ADP
ejpam-4207	38	13	[	[	X
ejpam-4207	38	14	2	2	NUM
ejpam-4207	38	15	]	]	PUNCT
ejpam-4207	38	16	.	.	PUNCT
ejpam-4207	39	1	quite	quite	ADV
ejpam-4207	39	2	recently	recently	ADV
ejpam-4207	39	3	other	other	ADJ
ejpam-4207	39	4	results	result	NOUN
ejpam-4207	39	5	are	be	AUX
ejpam-4207	39	6	obtained	obtain	VERB
ejpam-4207	39	7	in	in	ADP
ejpam-4207	39	8	[	[	X
ejpam-4207	39	9	8	8	NUM
ejpam-4207	39	10	]	]	PUNCT
ejpam-4207	39	11	,	,	PUNCT
ejpam-4207	40	1	[	[	X
ejpam-4207	40	2	9	9	NUM
ejpam-4207	40	3	]	]	PUNCT
ejpam-4207	40	4	,	,	PUNCT
ejpam-4207	40	5	[	[	X
ejpam-4207	40	6	4	4	NUM
ejpam-4207	40	7	]	]	PUNCT
ejpam-4207	40	8	,	,	PUNCT
ejpam-4207	40	9	[	[	X
ejpam-4207	40	10	31	31	NUM
ejpam-4207	40	11	]	]	PUNCT
ejpam-4207	40	12	and	and	CCONJ
ejpam-4207	40	13	other	other	ADJ
ejpam-4207	40	14	papers	paper	NOUN
ejpam-4207	40	15	.	.	PUNCT
ejpam-4207	41	1	in	in	ADP
ejpam-4207	41	2	this	this	DET
ejpam-4207	41	3	paper	paper	NOUN
ejpam-4207	41	4	,	,	PUNCT
ejpam-4207	41	5	by	by	ADP
ejpam-4207	41	6	mio(x	mio(x	PROPN
ejpam-4207	41	7	)	)	PUNCT
ejpam-4207	41	8	we	we	PRON
ejpam-4207	41	9	denote	denote	VERB
ejpam-4207	41	10	the	the	DET
ejpam-4207	41	11	family	family	NOUN
ejpam-4207	41	12	of	of	ADP
ejpam-4207	41	13	⋆-open	⋆-open	ADJ
ejpam-4207	41	14	(	(	PUNCT
ejpam-4207	41	15	resp	resp	NOUN
ejpam-4207	41	16	.	.	PUNCT
ejpam-4207	42	1	semi	semi	ADJ
ejpam-4207	42	2	-	-	ADJ
ejpam-4207	42	3	i	i	PRON
ejpam-4207	42	4	-	-	PUNCT
ejpam-4207	42	5	open	open	ADJ
ejpam-4207	42	6	,	,	PUNCT
ejpam-4207	42	7	prei	prei	NOUN
ejpam-4207	42	8	-	-	PUNCT
ejpam-4207	42	9	open	open	ADJ
ejpam-4207	42	10	,	,	PUNCT
ejpam-4207	42	11	α	α	PROPN
ejpam-4207	42	12	-	-	ADJ
ejpam-4207	42	13	i	i	PRON
ejpam-4207	42	14	-	-	PUNCT
ejpam-4207	42	15	open	open	ADJ
ejpam-4207	42	16	,	,	PUNCT
ejpam-4207	42	17	b	b	X
ejpam-4207	42	18	-	-	PUNCT
ejpam-4207	42	19	i	i	PRON
ejpam-4207	42	20	-	-	PUNCT
ejpam-4207	42	21	open	open	ADJ
ejpam-4207	42	22	,	,	PUNCT
ejpam-4207	42	23	β	β	X
ejpam-4207	42	24	-	-	ADJ
ejpam-4207	42	25	i	i	PRON
ejpam-4207	42	26	-	-	PUNCT
ejpam-4207	42	27	open	open	ADJ
ejpam-4207	42	28	,	,	PUNCT
ejpam-4207	42	29	etc	etc	X
ejpam-4207	42	30	.	.	X
ejpam-4207	42	31	)	)	PUNCT
ejpam-4207	42	32	sets	set	NOUN
ejpam-4207	42	33	in	in	ADP
ejpam-4207	42	34	an	an	DET
ejpam-4207	42	35	ideal	ideal	ADJ
ejpam-4207	42	36	topological	topological	ADJ
ejpam-4207	42	37	space	space	NOUN
ejpam-4207	42	38	(	(	PUNCT
ejpam-4207	42	39	x	x	X
ejpam-4207	42	40	,	,	PUNCT
ejpam-4207	42	41	τ	τ	PROPN
ejpam-4207	42	42	,	,	PUNCT
ejpam-4207	42	43	i	i	PROPN
ejpam-4207	42	44	)	)	PUNCT
ejpam-4207	42	45	.	.	PUNCT
ejpam-4207	43	1	then	then	ADV
ejpam-4207	43	2	we	we	PRON
ejpam-4207	43	3	introduce	introduce	VERB
ejpam-4207	43	4	and	and	CCONJ
ejpam-4207	43	5	investigate	investigate	VERB
ejpam-4207	43	6	the	the	DET
ejpam-4207	43	7	notion	notion	NOUN
ejpam-4207	43	8	of	of	ADP
ejpam-4207	43	9	an	an	DET
ejpam-4207	43	10	m	m	PROPN
ejpam-4207	43	11	-	-	PUNCT
ejpam-4207	43	12	i	i	NOUN
ejpam-4207	43	13	-	-	PUNCT
ejpam-4207	43	14	continuous	continuous	ADJ
ejpam-4207	43	15	multifunction	multifunction	NOUN
ejpam-4207	43	16	f	f	NOUN
ejpam-4207	43	17	:	:	PUNCT
ejpam-4207	43	18	(	(	PUNCT
ejpam-4207	43	19	x	x	X
ejpam-4207	43	20	,	,	PUNCT
ejpam-4207	43	21	τ	τ	PROPN
ejpam-4207	43	22	,	,	PUNCT
ejpam-4207	43	23	i	i	NOUN
ejpam-4207	43	24	)	)	PUNCT
ejpam-4207	43	25	→	→	SYM
ejpam-4207	43	26	(	(	PUNCT
ejpam-4207	43	27	y	y	PROPN
ejpam-4207	43	28	,	,	PUNCT
ejpam-4207	43	29	σ	σ	PROPN
ejpam-4207	43	30	)	)	PUNCT
ejpam-4207	43	31	which	which	PRON
ejpam-4207	43	32	generalizes	generalize	VERB
ejpam-4207	43	33	the	the	DET
ejpam-4207	43	34	results	result	NOUN
ejpam-4207	43	35	obtained	obtain	VERB
ejpam-4207	43	36	in	in	ADP
ejpam-4207	43	37	[	[	X
ejpam-4207	43	38	36	36	NUM
ejpam-4207	43	39	]	]	PUNCT
ejpam-4207	43	40	,	,	PUNCT
ejpam-4207	43	41	[	[	X
ejpam-4207	43	42	37	37	NUM
ejpam-4207	43	43	]	]	PUNCT
ejpam-4207	43	44	and	and	CCONJ
ejpam-4207	43	45	[	[	X
ejpam-4207	43	46	39	39	NUM
ejpam-4207	43	47	]	]	PUNCT
ejpam-4207	43	48	.	.	PUNCT
ejpam-4207	44	1	furthermore	furthermore	ADV
ejpam-4207	44	2	,	,	PUNCT
ejpam-4207	44	3	we	we	PRON
ejpam-4207	44	4	introduce	introduce	VERB
ejpam-4207	44	5	the	the	DET
ejpam-4207	44	6	notion	notion	NOUN
ejpam-4207	44	7	of	of	ADP
ejpam-4207	44	8	an	an	DET
ejpam-4207	44	9	mi⋆-continuous	mi⋆-continuous	ADJ
ejpam-4207	44	10	multifunction	multifunction	NOUN
ejpam-4207	44	11	f	f	NOUN
ejpam-4207	44	12	:	:	PUNCT
ejpam-4207	44	13	(	(	PUNCT
ejpam-4207	44	14	x	x	X
ejpam-4207	44	15	,	,	PUNCT
ejpam-4207	44	16	τ	τ	PROPN
ejpam-4207	44	17	,	,	PUNCT
ejpam-4207	44	18	i	i	NOUN
ejpam-4207	44	19	)	)	PUNCT
ejpam-4207	44	20	→	→	SYM
ejpam-4207	44	21	(	(	PUNCT
ejpam-4207	44	22	y	y	PROPN
ejpam-4207	44	23	,	,	PUNCT
ejpam-4207	44	24	σ	σ	PROPN
ejpam-4207	44	25	,	,	PUNCT
ejpam-4207	44	26	j	j	PROPN
ejpam-4207	44	27	)	)	PUNCT
ejpam-4207	44	28	which	which	PRON
ejpam-4207	44	29	generalizes	generalize	VERB
ejpam-4207	44	30	the	the	DET
ejpam-4207	44	31	notions	notion	NOUN
ejpam-4207	44	32	of	of	ADP
ejpam-4207	44	33	i⋆-continuous	i⋆-continuous	ADJ
ejpam-4207	44	34	multifunctions	multifunction	NOUN
ejpam-4207	45	1	[	[	X
ejpam-4207	45	2	9	9	NUM
ejpam-4207	45	3	]	]	PUNCT
ejpam-4207	45	4	and	and	CCONJ
ejpam-4207	45	5	m	m	PROPN
ejpam-4207	45	6	-	-	ADJ
ejpam-4207	45	7	i	i	ADV
ejpam-4207	45	8	-	-	PUNCT
ejpam-4207	45	9	continuous	continuous	ADJ
ejpam-4207	45	10	multifunctions	multifunction	NOUN
ejpam-4207	45	11	.	.	PUNCT
ejpam-4207	46	1	2	2	X
ejpam-4207	46	2	.	.	X
ejpam-4207	46	3	preliminaries	preliminary	NOUN
ejpam-4207	46	4	let	let	VERB
ejpam-4207	46	5	(	(	PUNCT
ejpam-4207	46	6	x	x	NOUN
ejpam-4207	46	7	,	,	PUNCT
ejpam-4207	46	8	τ	τ	X
ejpam-4207	46	9	)	)	PUNCT
ejpam-4207	46	10	be	be	VERB
ejpam-4207	46	11	a	a	DET
ejpam-4207	46	12	topological	topological	ADJ
ejpam-4207	46	13	spacce	spacce	NOUN
ejpam-4207	46	14	and	and	CCONJ
ejpam-4207	46	15	a	a	DET
ejpam-4207	46	16	a	a	DET
ejpam-4207	46	17	subset	subset	NOUN
ejpam-4207	46	18	of	of	ADP
ejpam-4207	46	19	x.	x.	NOUN
ejpam-4207	46	20	the	the	DET
ejpam-4207	46	21	closure	closure	NOUN
ejpam-4207	46	22	of	of	ADP
ejpam-4207	46	23	a	a	PRON
ejpam-4207	46	24	and	and	CCONJ
ejpam-4207	46	25	the	the	DET
ejpam-4207	46	26	interior	interior	NOUN
ejpam-4207	46	27	of	of	ADP
ejpam-4207	46	28	a	a	PRON
ejpam-4207	46	29	are	be	AUX
ejpam-4207	46	30	denoted	denote	VERB
ejpam-4207	46	31	by	by	ADP
ejpam-4207	46	32	cl(a	cl(a	NOUN
ejpam-4207	46	33	)	)	PUNCT
ejpam-4207	46	34	and	and	CCONJ
ejpam-4207	46	35	int(a	int(a	PROPN
ejpam-4207	46	36	)	)	PUNCT
ejpam-4207	46	37	,	,	PUNCT
ejpam-4207	46	38	respectively	respectively	ADV
ejpam-4207	46	39	.	.	PUNCT
ejpam-4207	47	1	definition	definition	NOUN
ejpam-4207	47	2	1	1	NUM
ejpam-4207	47	3	.	.	PUNCT
ejpam-4207	48	1	a	a	DET
ejpam-4207	48	2	subset	subset	NOUN
ejpam-4207	48	3	a	a	PRON
ejpam-4207	48	4	of	of	ADP
ejpam-4207	48	5	a	a	DET
ejpam-4207	48	6	topological	topological	ADJ
ejpam-4207	48	7	space	space	NOUN
ejpam-4207	48	8	(	(	PUNCT
ejpam-4207	48	9	x	x	X
ejpam-4207	48	10	,	,	PUNCT
ejpam-4207	48	11	τ	τ	X
ejpam-4207	48	12	)	)	PUNCT
ejpam-4207	48	13	is	be	AUX
ejpam-4207	48	14	said	say	VERB
ejpam-4207	48	15	to	to	PART
ejpam-4207	48	16	be	be	AUX
ejpam-4207	48	17	(	(	PUNCT
ejpam-4207	48	18	1	1	X
ejpam-4207	48	19	)	)	PUNCT
ejpam-4207	48	20	α	α	NOUN
ejpam-4207	48	21	-	-	ADJ
ejpam-4207	48	22	open	open	ADJ
ejpam-4207	48	23	[	[	X
ejpam-4207	48	24	27	27	NUM
ejpam-4207	48	25	]	]	X
ejpam-4207	48	26	if	if	SCONJ
ejpam-4207	48	27	a	a	DET
ejpam-4207	48	28	⊂	⊂	X
ejpam-4207	48	29	int(cl(int(a	int(cl(int(a	NOUN
ejpam-4207	48	30	)	)	PUNCT
ejpam-4207	48	31	)	)	PUNCT
ejpam-4207	48	32	)	)	PUNCT
ejpam-4207	48	33	,	,	PUNCT
ejpam-4207	48	34	(	(	PUNCT
ejpam-4207	48	35	2	2	X
ejpam-4207	48	36	)	)	PUNCT
ejpam-4207	48	37	semi	semi	ADJ
ejpam-4207	48	38	-	-	ADJ
ejpam-4207	48	39	open	open	ADJ
ejpam-4207	48	40	[	[	X
ejpam-4207	48	41	21	21	NUM
ejpam-4207	48	42	]	]	X
ejpam-4207	48	43	if	if	SCONJ
ejpam-4207	48	44	a	a	DET
ejpam-4207	48	45	⊂	⊂	PROPN
ejpam-4207	48	46	cl(int(a	cl(int(a	PROPN
ejpam-4207	48	47	)	)	PUNCT
ejpam-4207	48	48	)	)	PUNCT
ejpam-4207	48	49	,	,	PUNCT
ejpam-4207	48	50	(	(	PUNCT
ejpam-4207	48	51	3	3	X
ejpam-4207	48	52	)	)	PUNCT
ejpam-4207	48	53	preopen	preopen	NOUN
ejpam-4207	48	54	[	[	X
ejpam-4207	48	55	24	24	NUM
ejpam-4207	48	56	]	]	X
ejpam-4207	48	57	if	if	SCONJ
ejpam-4207	48	58	a	a	DET
ejpam-4207	48	59	⊂	⊂	PROPN
ejpam-4207	48	60	int(cl(a	int(cl(a	PROPN
ejpam-4207	48	61	)	)	PUNCT
ejpam-4207	48	62	)	)	PUNCT
ejpam-4207	48	63	,	,	PUNCT
ejpam-4207	48	64	(	(	PUNCT
ejpam-4207	48	65	4	4	X
ejpam-4207	48	66	)	)	PUNCT
ejpam-4207	48	67	b	b	NOUN
ejpam-4207	48	68	-	-	PUNCT
ejpam-4207	48	69	open	open	ADJ
ejpam-4207	48	70	[	[	X
ejpam-4207	48	71	3	3	NUM
ejpam-4207	48	72	]	]	X
ejpam-4207	48	73	if	if	SCONJ
ejpam-4207	48	74	a	a	DET
ejpam-4207	48	75	⊂	⊂	PROPN
ejpam-4207	48	76	cl(int(a	cl(int(a	PROPN
ejpam-4207	48	77	)	)	PUNCT
ejpam-4207	48	78	)	)	PUNCT
ejpam-4207	48	79	∪	∪	ADP
ejpam-4207	48	80	int(cl(a	int(cl(a	PROPN
ejpam-4207	48	81	)	)	PUNCT
ejpam-4207	48	82	)	)	PUNCT
ejpam-4207	48	83	,	,	PUNCT
ejpam-4207	48	84	(	(	PUNCT
ejpam-4207	48	85	5	5	X
ejpam-4207	48	86	)	)	PUNCT
ejpam-4207	48	87	β	β	NOUN
ejpam-4207	48	88	-	-	VERB
ejpam-4207	48	89	open	open	ADJ
ejpam-4207	48	90	[	[	X
ejpam-4207	48	91	1	1	NUM
ejpam-4207	48	92	]	]	X
ejpam-4207	48	93	if	if	SCONJ
ejpam-4207	48	94	a	a	DET
ejpam-4207	48	95	⊂	⊂	PROPN
ejpam-4207	48	96	cl(int(cl(a	cl(int(cl(a	NOUN
ejpam-4207	48	97	)	)	PUNCT
ejpam-4207	48	98	)	)	PUNCT
ejpam-4207	48	99	)	)	PUNCT
ejpam-4207	48	100	.	.	PUNCT
ejpam-4207	49	1	the	the	DET
ejpam-4207	49	2	family	family	NOUN
ejpam-4207	49	3	of	of	ADP
ejpam-4207	49	4	all	all	PRON
ejpam-4207	49	5	semi	semi	ADJ
ejpam-4207	49	6	-	-	ADJ
ejpam-4207	49	7	open	open	ADJ
ejpam-4207	49	8	(	(	PUNCT
ejpam-4207	49	9	resp	resp	NOUN
ejpam-4207	49	10	.	.	PUNCT
ejpam-4207	50	1	preopen	preopen	ADJ
ejpam-4207	50	2	,	,	PUNCT
ejpam-4207	50	3	α	α	NOUN
ejpam-4207	50	4	-	-	ADJ
ejpam-4207	50	5	open	open	ADJ
ejpam-4207	50	6	,	,	PUNCT
ejpam-4207	50	7	b	b	X
ejpam-4207	50	8	-	-	PUNCT
ejpam-4207	50	9	open	open	ADJ
ejpam-4207	50	10	,	,	PUNCT
ejpam-4207	50	11	β	β	ADJ
ejpam-4207	50	12	-	-	ADJ
ejpam-4207	50	13	open	open	ADJ
ejpam-4207	50	14	)	)	PUNCT
ejpam-4207	50	15	sets	set	NOUN
ejpam-4207	50	16	in	in	ADP
ejpam-4207	50	17	(	(	PUNCT
ejpam-4207	50	18	x	x	NOUN
ejpam-4207	50	19	,	,	PUNCT
ejpam-4207	50	20	τ	τ	X
ejpam-4207	50	21	)	)	PUNCT
ejpam-4207	50	22	is	be	AUX
ejpam-4207	50	23	denoted	denote	VERB
ejpam-4207	50	24	by	by	ADP
ejpam-4207	50	25	so(x	so(x	NOUN
ejpam-4207	50	26	)	)	PUNCT
ejpam-4207	50	27	(	(	PUNCT
ejpam-4207	50	28	resp	resp	NOUN
ejpam-4207	50	29	.	.	PUNCT
ejpam-4207	51	1	po(x	po(x	NUM
ejpam-4207	51	2	)	)	PUNCT
ejpam-4207	51	3	,	,	PUNCT
ejpam-4207	52	1	α(x	α(x	NOUN
ejpam-4207	52	2	)	)	PUNCT
ejpam-4207	52	3	,	,	PUNCT
ejpam-4207	52	4	bo(x	bo(x	NUM
ejpam-4207	52	5	)	)	PUNCT
ejpam-4207	52	6	,	,	PUNCT
ejpam-4207	52	7	β(x	β(x	NOUN
ejpam-4207	52	8	)	)	PUNCT
ejpam-4207	52	9	)	)	PUNCT
ejpam-4207	52	10	.	.	PUNCT
ejpam-4207	53	1	throughout	throughout	ADP
ejpam-4207	53	2	the	the	DET
ejpam-4207	53	3	present	present	ADJ
ejpam-4207	53	4	paper	paper	NOUN
ejpam-4207	53	5	,	,	PUNCT
ejpam-4207	53	6	spaces	space	NOUN
ejpam-4207	53	7	(	(	PUNCT
ejpam-4207	53	8	x	x	X
ejpam-4207	53	9	,	,	PUNCT
ejpam-4207	53	10	τ	τ	X
ejpam-4207	53	11	)	)	PUNCT
ejpam-4207	53	12	and	and	CCONJ
ejpam-4207	53	13	(	(	PUNCT
ejpam-4207	53	14	y	y	PROPN
ejpam-4207	53	15	,	,	PUNCT
ejpam-4207	53	16	σ	σ	PROPN
ejpam-4207	53	17	)	)	PUNCT
ejpam-4207	53	18	always	always	ADV
ejpam-4207	53	19	mean	mean	VERB
ejpam-4207	53	20	topological	topological	ADJ
ejpam-4207	53	21	spaces	space	NOUN
ejpam-4207	53	22	and	and	CCONJ
ejpam-4207	53	23	f	f	NOUN
ejpam-4207	53	24	:	:	PUNCT
ejpam-4207	53	25	(	(	PUNCT
ejpam-4207	53	26	x	x	X
ejpam-4207	53	27	,	,	PUNCT
ejpam-4207	53	28	τ	τ	X
ejpam-4207	53	29	)	)	PUNCT
ejpam-4207	53	30	→	→	SYM
ejpam-4207	53	31	(	(	PUNCT
ejpam-4207	53	32	y	y	PROPN
ejpam-4207	53	33	,	,	PUNCT
ejpam-4207	53	34	σ	σ	PROPN
ejpam-4207	53	35	)	)	PUNCT
ejpam-4207	53	36	presents	present	VERB
ejpam-4207	53	37	a	a	DET
ejpam-4207	53	38	multivalued	multivalued	ADJ
ejpam-4207	53	39	function	function	NOUN
ejpam-4207	53	40	.	.	PUNCT
ejpam-4207	54	1	for	for	ADP
ejpam-4207	54	2	a	a	DET
ejpam-4207	54	3	multifunction	multifunction	NOUN
ejpam-4207	54	4	,	,	PUNCT
ejpam-4207	54	5	we	we	PRON
ejpam-4207	54	6	shall	shall	AUX
ejpam-4207	54	7	denote	denote	VERB
ejpam-4207	54	8	the	the	DET
ejpam-4207	54	9	upper	upper	ADJ
ejpam-4207	54	10	and	and	CCONJ
ejpam-4207	54	11	lower	low	ADJ
ejpam-4207	54	12	inverses	inverse	NOUN
ejpam-4207	54	13	of	of	ADP
ejpam-4207	54	14	a	a	DET
ejpam-4207	54	15	subset	subset	NOUN
ejpam-4207	54	16	b	b	NOUN
ejpam-4207	54	17	of	of	ADP
ejpam-4207	54	18	y	y	PROPN
ejpam-4207	54	19	by	by	ADP
ejpam-4207	54	20	f+(b	f+(b	NOUN
ejpam-4207	54	21	)	)	PUNCT
ejpam-4207	54	22	and	and	CCONJ
ejpam-4207	54	23	f−(b	f−(b	NOUN
ejpam-4207	54	24	)	)	PUNCT
ejpam-4207	54	25	,	,	PUNCT
ejpam-4207	54	26	respectively	respectively	ADV
ejpam-4207	54	27	,	,	PUNCT
ejpam-4207	54	28	that	that	ADV
ejpam-4207	54	29	is	is	ADV
ejpam-4207	54	30	,	,	PUNCT
ejpam-4207	54	31	f+(b	f+(b	NOUN
ejpam-4207	54	32	)	)	PUNCT
ejpam-4207	54	33	=	=	PRON
ejpam-4207	55	1	{	{	PUNCT
ejpam-4207	55	2	x	x	PUNCT
ejpam-4207	55	3	∈	∈	PROPN
ejpam-4207	55	4	x	x	X
ejpam-4207	55	5	:	:	PUNCT
ejpam-4207	55	6	f	f	X
ejpam-4207	55	7	(	(	PUNCT
ejpam-4207	55	8	x	x	X
ejpam-4207	55	9	)	)	PUNCT
ejpam-4207	55	10	⊂	⊂	PROPN
ejpam-4207	55	11	b	b	X
ejpam-4207	55	12	}	}	PUNCT
ejpam-4207	55	13	and	and	CCONJ
ejpam-4207	55	14	f−(b	f−(b	PROPN
ejpam-4207	55	15	)	)	PUNCT
ejpam-4207	55	16	=	=	PRON
ejpam-4207	55	17	{	{	PUNCT
ejpam-4207	55	18	x	x	PUNCT
ejpam-4207	55	19	∈	∈	PROPN
ejpam-4207	55	20	x	x	X
ejpam-4207	55	21	:	:	PUNCT
ejpam-4207	55	22	f	f	X
ejpam-4207	55	23	(	(	PUNCT
ejpam-4207	55	24	x	x	X
ejpam-4207	55	25	)	)	PUNCT
ejpam-4207	55	26	∩b	∩b	NOUN
ejpam-4207	55	27	̸=	̸=	PROPN
ejpam-4207	55	28	∅	∅	NOUN
ejpam-4207	55	29	}	}	PUNCT
ejpam-4207	55	30	.	.	PUNCT
ejpam-4207	56	1	let	let	VERB
ejpam-4207	56	2	p(y	p(y	PROPN
ejpam-4207	56	3	)	)	PUNCT
ejpam-4207	56	4	be	be	AUX
ejpam-4207	56	5	the	the	DET
ejpam-4207	56	6	collection	collection	NOUN
ejpam-4207	56	7	of	of	ADP
ejpam-4207	56	8	all	all	DET
ejpam-4207	56	9	nonempty	nonempty	ADJ
ejpam-4207	56	10	subsets	subset	NOUN
ejpam-4207	56	11	of	of	ADP
ejpam-4207	56	12	y	y	PROPN
ejpam-4207	56	13	.	.	PUNCT
ejpam-4207	57	1	for	for	ADP
ejpam-4207	57	2	any	any	DET
ejpam-4207	57	3	open	open	ADJ
ejpam-4207	57	4	set	set	NOUN
ejpam-4207	57	5	v	v	NOUN
ejpam-4207	57	6	of	of	ADP
ejpam-4207	57	7	y	y	PROPN
ejpam-4207	57	8	,	,	PUNCT
ejpam-4207	57	9	we	we	PRON
ejpam-4207	57	10	denote	denote	VERB
ejpam-4207	57	11	v	v	ADP
ejpam-4207	57	12	+	+	NOUN
ejpam-4207	58	1	=	=	SYM
ejpam-4207	58	2	{	{	PUNCT
ejpam-4207	58	3	b	b	NOUN
ejpam-4207	58	4	∈	∈	PROPN
ejpam-4207	58	5	p(y	p(y	PROPN
ejpam-4207	58	6	)	)	PUNCT
ejpam-4207	58	7	:	:	PUNCT
ejpam-4207	59	1	b	b	X
ejpam-4207	59	2	⊂	⊂	X
ejpam-4207	59	3	v	v	NOUN
ejpam-4207	59	4	}	}	PUNCT
ejpam-4207	59	5	and	and	CCONJ
ejpam-4207	59	6	v	v	ADP
ejpam-4207	59	7	−	−	PROPN
ejpam-4207	59	8	=	=	PUNCT
ejpam-4207	59	9	{	{	PUNCT
ejpam-4207	59	10	b	b	NOUN
ejpam-4207	59	11	∈	∈	PROPN
ejpam-4207	59	12	p(y	p(y	PROPN
ejpam-4207	59	13	)	)	PUNCT
ejpam-4207	59	14	:	:	PUNCT
ejpam-4207	59	15	b	b	X
ejpam-4207	59	16	∩	∩	NOUN
ejpam-4207	59	17	v	v	ADP
ejpam-4207	59	18	̸=	̸=	PROPN
ejpam-4207	59	19	∅	∅	NOUN
ejpam-4207	59	20	}	}	PUNCT
ejpam-4207	59	21	[	[	X
ejpam-4207	59	22	46	46	NUM
ejpam-4207	59	23	]	]	PUNCT
ejpam-4207	59	24	.	.	PUNCT
ejpam-4207	60	1	definition	definition	NOUN
ejpam-4207	60	2	2	2	NUM
ejpam-4207	60	3	.	.	PUNCT
ejpam-4207	60	4	a	a	DET
ejpam-4207	60	5	multifunction	multifunction	NOUN
ejpam-4207	60	6	f	f	NOUN
ejpam-4207	60	7	:	:	PUNCT
ejpam-4207	60	8	(	(	PUNCT
ejpam-4207	60	9	x	x	X
ejpam-4207	60	10	,	,	PUNCT
ejpam-4207	60	11	τ	τ	X
ejpam-4207	60	12	)	)	PUNCT
ejpam-4207	60	13	→	→	SYM
ejpam-4207	60	14	(	(	PUNCT
ejpam-4207	60	15	y	y	PROPN
ejpam-4207	60	16	,	,	PUNCT
ejpam-4207	60	17	σ	σ	PROPN
ejpam-4207	60	18	)	)	PUNCT
ejpam-4207	60	19	is	be	AUX
ejpam-4207	60	20	said	say	VERB
ejpam-4207	60	21	to	to	PART
ejpam-4207	60	22	be	be	AUX
ejpam-4207	60	23	quasi	quasi	ADJ
ejpam-4207	60	24	-	-	ADJ
ejpam-4207	60	25	continuous	continuous	ADJ
ejpam-4207	60	26	[	[	X
ejpam-4207	60	27	6	6	NUM
ejpam-4207	60	28	]	]	PUNCT
ejpam-4207	60	29	,	,	PUNCT
ejpam-4207	60	30	[	[	X
ejpam-4207	60	31	7	7	NUM
ejpam-4207	60	32	]	]	PUNCT
ejpam-4207	60	33	,	,	PUNCT
ejpam-4207	60	34	[	[	X
ejpam-4207	60	35	33	33	NUM
ejpam-4207	60	36	]	]	PUNCT
ejpam-4207	60	37	(	(	PUNCT
ejpam-4207	60	38	resp	resp	NOUN
ejpam-4207	60	39	.	.	PUNCT
ejpam-4207	61	1	precontinuous	precontinuous	ADJ
ejpam-4207	62	1	[	[	X
ejpam-4207	62	2	39	39	NUM
ejpam-4207	62	3	]	]	PUNCT
ejpam-4207	62	4	,	,	PUNCT
ejpam-4207	62	5	α	α	X
ejpam-4207	62	6	-	-	ADJ
ejpam-4207	62	7	continuous	continuous	ADJ
ejpam-4207	62	8	[	[	X
ejpam-4207	62	9	36	36	NUM
ejpam-4207	62	10	]	]	PUNCT
ejpam-4207	62	11	,	,	PUNCT
ejpam-4207	62	12	β	β	X
ejpam-4207	62	13	-	-	ADJ
ejpam-4207	62	14	continuous	continuous	ADJ
ejpam-4207	62	15	[	[	X
ejpam-4207	62	16	37	37	NUM
ejpam-4207	62	17	]	]	PUNCT
ejpam-4207	62	18	)	)	PUNCT
ejpam-4207	62	19	at	at	ADP
ejpam-4207	62	20	a	a	DET
ejpam-4207	62	21	point	point	NOUN
ejpam-4207	62	22	x	x	SYM
ejpam-4207	62	23	∈	∈	NOUN
ejpam-4207	62	24	x	x	INTJ
ejpam-4207	62	25	if	if	SCONJ
ejpam-4207	62	26	for	for	ADP
ejpam-4207	62	27	each	each	DET
ejpam-4207	62	28	open	open	ADJ
ejpam-4207	62	29	sets	set	NOUN
ejpam-4207	62	30	g1	g1	NOUN
ejpam-4207	62	31	,	,	PUNCT
ejpam-4207	62	32	g2	g2	PROPN
ejpam-4207	62	33	of	of	ADP
ejpam-4207	62	34	y	y	PRON
ejpam-4207	62	35	such	such	ADJ
ejpam-4207	62	36	that	that	SCONJ
ejpam-4207	62	37	f	f	PROPN
ejpam-4207	62	38	(	(	PUNCT
ejpam-4207	62	39	x	x	X
ejpam-4207	62	40	)	)	PUNCT
ejpam-4207	62	41	∈	∈	NOUN
ejpam-4207	62	42	g+	g+	NOUN
ejpam-4207	62	43	1	1	NUM
ejpam-4207	62	44	∩g−	∩g−	PROPN
ejpam-4207	62	45	2	2	NUM
ejpam-4207	62	46	,	,	PUNCT
ejpam-4207	62	47	there	there	PRON
ejpam-4207	62	48	exists	exist	VERB
ejpam-4207	62	49	a	a	DET
ejpam-4207	62	50	semi	semi	ADJ
ejpam-4207	62	51	-	-	ADJ
ejpam-4207	62	52	open	open	ADJ
ejpam-4207	62	53	(	(	PUNCT
ejpam-4207	62	54	resp	resp	NOUN
ejpam-4207	62	55	.	.	PUNCT
ejpam-4207	63	1	preopen	preopen	ADJ
ejpam-4207	63	2	,	,	PUNCT
ejpam-4207	63	3	α	α	NOUN
ejpam-4207	63	4	-	-	ADJ
ejpam-4207	63	5	open	open	ADJ
ejpam-4207	63	6	,	,	PUNCT
ejpam-4207	63	7	β	β	NOUN
ejpam-4207	63	8	-	-	ADJ
ejpam-4207	63	9	open	open	ADJ
ejpam-4207	63	10	)	)	PUNCT
ejpam-4207	63	11	set	set	VERB
ejpam-4207	63	12	u	u	NOUN
ejpam-4207	63	13	of	of	ADP
ejpam-4207	63	14	x	x	PUNCT
ejpam-4207	63	15	containing	contain	VERB
ejpam-4207	63	16	x	x	PUNCT
ejpam-4207	63	17	such	such	ADJ
ejpam-4207	63	18	that	that	SCONJ
ejpam-4207	63	19	f	f	PROPN
ejpam-4207	63	20	(	(	PUNCT
ejpam-4207	63	21	u	u	NOUN
ejpam-4207	63	22	)	)	PUNCT
ejpam-4207	63	23	∈	∈	PROPN
ejpam-4207	63	24	g+	g+	NOUN
ejpam-4207	63	25	1	1	NUM
ejpam-4207	63	26	∩	∩	X
ejpam-4207	63	27	g−	g−	ADJ
ejpam-4207	63	28	2	2	NUM
ejpam-4207	63	29	for	for	ADP
ejpam-4207	63	30	every	every	DET
ejpam-4207	63	31	u	u	PROPN
ejpam-4207	63	32	∈	∈	PROPN
ejpam-4207	63	33	u	u	NOUN
ejpam-4207	63	34	.	.	PUNCT
ejpam-4207	64	1	a	a	DET
ejpam-4207	64	2	multifunction	multifunction	NOUN
ejpam-4207	64	3	is	be	AUX
ejpam-4207	64	4	said	say	VERB
ejpam-4207	64	5	to	to	PART
ejpam-4207	64	6	be	be	AUX
ejpam-4207	64	7	quasi	quasi	ADJ
ejpam-4207	64	8	-	-	ADJ
ejpam-4207	64	9	continuous	continuous	ADJ
ejpam-4207	64	10	(	(	PUNCT
ejpam-4207	64	11	resp	resp	NOUN
ejpam-4207	64	12	.	.	PUNCT
ejpam-4207	65	1	precontinuous	precontinuous	ADJ
ejpam-4207	65	2	,	,	PUNCT
ejpam-4207	65	3	α	α	NOUN
ejpam-4207	65	4	-	-	ADJ
ejpam-4207	65	5	continuous	continuous	ADJ
ejpam-4207	65	6	,	,	PUNCT
ejpam-4207	65	7	β	β	ADJ
ejpam-4207	65	8	-	-	ADJ
ejpam-4207	65	9	continuous	continuous	ADJ
ejpam-4207	65	10	)	)	PUNCT
ejpam-4207	65	11	if	if	SCONJ
ejpam-4207	65	12	it	it	PRON
ejpam-4207	65	13	has	have	VERB
ejpam-4207	65	14	this	this	DET
ejpam-4207	65	15	property	property	NOUN
ejpam-4207	65	16	at	at	ADP
ejpam-4207	65	17	each	each	DET
ejpam-4207	65	18	point	point	NOUN
ejpam-4207	65	19	of	of	ADP
ejpam-4207	65	20	x	x	SYM
ejpam-4207	65	21	∈	∈	PROPN
ejpam-4207	65	22	x.	x.	NOUN
ejpam-4207	65	23	takashi	takashi	PROPN
ejpam-4207	65	24	noiri	noiri	PROPN
ejpam-4207	65	25	,	,	PUNCT
ejpam-4207	65	26	valeriu	valeriu	ADJ
ejpam-4207	65	27	popa	popa	NOUN
ejpam-4207	65	28	/	/	SYM
ejpam-4207	65	29	eur	eur	PROPN
ejpam-4207	65	30	.	.	PUNCT
ejpam-4207	66	1	j.	j.	PROPN
ejpam-4207	66	2	pure	pure	PROPN
ejpam-4207	66	3	appl	appl	PROPN
ejpam-4207	66	4	.	.	PROPN
ejpam-4207	66	5	math	math	PROPN
ejpam-4207	66	6	,	,	PUNCT
ejpam-4207	66	7	15	15	NUM
ejpam-4207	66	8	(	(	PUNCT
ejpam-4207	66	9	1	1	NUM
ejpam-4207	66	10	)	)	PUNCT
ejpam-4207	66	11	(	(	PUNCT
ejpam-4207	66	12	2022	2022	NUM
ejpam-4207	66	13	)	)	PUNCT
ejpam-4207	66	14	,	,	PUNCT
ejpam-4207	66	15	1	1	NUM
ejpam-4207	66	16	-	-	SYM
ejpam-4207	66	17	14	14	NUM
ejpam-4207	66	18	3	3	NUM
ejpam-4207	66	19	3	3	NUM
ejpam-4207	66	20	.	.	PUNCT
ejpam-4207	67	1	m	m	NOUN
ejpam-4207	67	2	-	-	ADJ
ejpam-4207	67	3	continuous	continuous	ADJ
ejpam-4207	67	4	multifunctions	multifunction	NOUN
ejpam-4207	67	5	definition	definition	NOUN
ejpam-4207	67	6	3	3	X
ejpam-4207	67	7	.	.	PUNCT
ejpam-4207	68	1	a	a	DET
ejpam-4207	68	2	subfamily	subfamily	ADV
ejpam-4207	68	3	mx	mx	NOUN
ejpam-4207	68	4	of	of	ADP
ejpam-4207	68	5	the	the	DET
ejpam-4207	68	6	power	power	NOUN
ejpam-4207	68	7	set	set	NOUN
ejpam-4207	68	8	p(x	p(x	NOUN
ejpam-4207	68	9	)	)	PUNCT
ejpam-4207	68	10	of	of	ADP
ejpam-4207	68	11	a	a	DET
ejpam-4207	68	12	nonempty	nonempty	ADV
ejpam-4207	68	13	set	set	VERB
ejpam-4207	68	14	x	x	PUNCT
ejpam-4207	68	15	is	be	AUX
ejpam-4207	68	16	called	call	VERB
ejpam-4207	68	17	a	a	DET
ejpam-4207	68	18	minimal	minimal	ADJ
ejpam-4207	68	19	structure	structure	NOUN
ejpam-4207	68	20	(	(	PUNCT
ejpam-4207	68	21	briefly	briefly	NOUN
ejpam-4207	68	22	m	m	NOUN
ejpam-4207	68	23	-	-	NOUN
ejpam-4207	68	24	structure	structure	NOUN
ejpam-4207	68	25	)	)	PUNCT
ejpam-4207	68	26	on	on	ADP
ejpam-4207	68	27	x	x	SYM
ejpam-4207	68	28	if	if	SCONJ
ejpam-4207	68	29	∅	∅	NOUN
ejpam-4207	68	30	∈	∈	PROPN
ejpam-4207	68	31	mx	mx	PROPN
ejpam-4207	68	32	and	and	CCONJ
ejpam-4207	68	33	x	x	PROPN
ejpam-4207	68	34	∈	∈	PROPN
ejpam-4207	68	35	mx	mx	PROPN
ejpam-4207	68	36	.	.	PUNCT
ejpam-4207	69	1	each	each	DET
ejpam-4207	69	2	member	member	NOUN
ejpam-4207	69	3	of	of	ADP
ejpam-4207	69	4	mx	mx	PROPN
ejpam-4207	69	5	is	be	AUX
ejpam-4207	69	6	said	say	VERB
ejpam-4207	69	7	to	to	PART
ejpam-4207	69	8	be	be	AUX
ejpam-4207	69	9	mx	mx	NOUN
ejpam-4207	69	10	-	-	ADJ
ejpam-4207	69	11	open	open	ADJ
ejpam-4207	69	12	(	(	PUNCT
ejpam-4207	69	13	briefly	briefly	NOUN
ejpam-4207	69	14	m	m	NOUN
ejpam-4207	69	15	-	-	ADJ
ejpam-4207	69	16	open	open	ADJ
ejpam-4207	69	17	)	)	PUNCT
ejpam-4207	69	18	and	and	CCONJ
ejpam-4207	69	19	the	the	DET
ejpam-4207	69	20	complement	complement	NOUN
ejpam-4207	69	21	of	of	ADP
ejpam-4207	69	22	an	an	DET
ejpam-4207	69	23	mx	mx	PROPN
ejpam-4207	69	24	-open	-open	NOUN
ejpam-4207	69	25	set	set	NOUN
ejpam-4207	69	26	is	be	AUX
ejpam-4207	69	27	said	say	VERB
ejpam-4207	69	28	to	to	PART
ejpam-4207	69	29	be	be	AUX
ejpam-4207	69	30	mx	mx	NOUN
ejpam-4207	69	31	-	-	ADJ
ejpam-4207	69	32	closed	closed	ADJ
ejpam-4207	69	33	.	.	PUNCT
ejpam-4207	70	1	(	(	PUNCT
ejpam-4207	70	2	briefly	briefly	NOUN
ejpam-4207	70	3	m	m	NOUN
ejpam-4207	70	4	-	-	PUNCT
ejpam-4207	70	5	closed	closed	ADJ
ejpam-4207	70	6	)	)	PUNCT
ejpam-4207	70	7	.	.	PUNCT
ejpam-4207	71	1	a	a	DET
ejpam-4207	71	2	set	set	NOUN
ejpam-4207	71	3	x	x	PUNCT
ejpam-4207	71	4	with	with	ADP
ejpam-4207	71	5	an	an	DET
ejpam-4207	71	6	mx	mx	PROPN
ejpam-4207	71	7	-structure	-structure	NOUN
ejpam-4207	71	8	mx	mx	PROPN
ejpam-4207	71	9	is	be	AUX
ejpam-4207	71	10	called	call	VERB
ejpam-4207	71	11	an	an	DET
ejpam-4207	71	12	m	m	NOUN
ejpam-4207	71	13	-	-	NOUN
ejpam-4207	71	14	space	space	NOUN
ejpam-4207	71	15	and	and	CCONJ
ejpam-4207	71	16	is	be	AUX
ejpam-4207	71	17	denoted	denote	VERB
ejpam-4207	71	18	by	by	ADP
ejpam-4207	71	19	(	(	PUNCT
ejpam-4207	71	20	x	x	NOUN
ejpam-4207	71	21	,	,	PUNCT
ejpam-4207	71	22	mx	mx	NOUN
ejpam-4207	71	23	)	)	PUNCT
ejpam-4207	71	24	remark	remark	NOUN
ejpam-4207	71	25	1	1	NUM
ejpam-4207	71	26	.	.	PUNCT
ejpam-4207	72	1	let	let	VERB
ejpam-4207	72	2	(	(	PUNCT
ejpam-4207	72	3	x	x	NOUN
ejpam-4207	72	4	,	,	PUNCT
ejpam-4207	72	5	τ	τ	X
ejpam-4207	72	6	)	)	PUNCT
ejpam-4207	72	7	be	be	VERB
ejpam-4207	72	8	a	a	DET
ejpam-4207	72	9	topological	topological	ADJ
ejpam-4207	72	10	space	space	NOUN
ejpam-4207	72	11	.	.	PUNCT
ejpam-4207	73	1	then	then	ADV
ejpam-4207	73	2	the	the	DET
ejpam-4207	73	3	families	family	NOUN
ejpam-4207	73	4	τ	τ	PROPN
ejpam-4207	73	5	,	,	PUNCT
ejpam-4207	73	6	α(x	α(x	PROPN
ejpam-4207	73	7	)	)	PUNCT
ejpam-4207	73	8	,	,	PUNCT
ejpam-4207	73	9	so(x	so(x	NOUN
ejpam-4207	73	10	)	)	PUNCT
ejpam-4207	73	11	,	,	PUNCT
ejpam-4207	73	12	po(x	po(x	NUM
ejpam-4207	73	13	)	)	PUNCT
ejpam-4207	73	14	,	,	PUNCT
ejpam-4207	73	15	bo(x	bo(x	NUM
ejpam-4207	73	16	)	)	PUNCT
ejpam-4207	73	17	,	,	PUNCT
ejpam-4207	73	18	β(x	β(x	PROPN
ejpam-4207	73	19	)	)	PUNCT
ejpam-4207	73	20	are	be	AUX
ejpam-4207	73	21	all	all	PRON
ejpam-4207	73	22	m	m	NOUN
ejpam-4207	73	23	-	-	NOUN
ejpam-4207	73	24	structures	structure	NOUN
ejpam-4207	73	25	on	on	ADP
ejpam-4207	73	26	x.	x.	NOUN
ejpam-4207	73	27	definition	definition	NOUN
ejpam-4207	73	28	4	4	NUM
ejpam-4207	73	29	.	.	PUNCT
ejpam-4207	74	1	let	let	VERB
ejpam-4207	74	2	x	x	PRON
ejpam-4207	74	3	be	be	AUX
ejpam-4207	74	4	a	a	DET
ejpam-4207	74	5	nonempty	nonempty	ADV
ejpam-4207	74	6	set	set	VERB
ejpam-4207	74	7	and	and	CCONJ
ejpam-4207	74	8	mx	mx	X
ejpam-4207	74	9	an	an	DET
ejpam-4207	74	10	m	m	NOUN
ejpam-4207	74	11	-	-	NOUN
ejpam-4207	74	12	structure	structure	NOUN
ejpam-4207	74	13	on	on	ADP
ejpam-4207	74	14	x.	x.	NOUN
ejpam-4207	74	15	for	for	ADP
ejpam-4207	74	16	a	a	DET
ejpam-4207	74	17	subset	subset	NOUN
ejpam-4207	74	18	a	a	PRON
ejpam-4207	74	19	of	of	ADP
ejpam-4207	74	20	x	x	PRON
ejpam-4207	74	21	,	,	PUNCT
ejpam-4207	74	22	the	the	DET
ejpam-4207	74	23	mx	mx	NOUN
ejpam-4207	74	24	-	-	NOUN
ejpam-4207	74	25	closure	closure	NOUN
ejpam-4207	74	26	of	of	ADP
ejpam-4207	74	27	a	a	PRON
ejpam-4207	74	28	and	and	CCONJ
ejpam-4207	74	29	the	the	DET
ejpam-4207	74	30	mx	mx	NOUN
ejpam-4207	74	31	-	-	NOUN
ejpam-4207	74	32	interior	interior	NOUN
ejpam-4207	74	33	of	of	ADP
ejpam-4207	74	34	a	a	PRON
ejpam-4207	74	35	are	be	AUX
ejpam-4207	74	36	defined	define	VERB
ejpam-4207	74	37	in	in	ADP
ejpam-4207	74	38	[	[	X
ejpam-4207	74	39	22	22	NUM
ejpam-4207	74	40	]	]	PUNCT
ejpam-4207	74	41	as	as	SCONJ
ejpam-4207	74	42	follows	follow	VERB
ejpam-4207	74	43	:	:	PUNCT
ejpam-4207	74	44	(	(	PUNCT
ejpam-4207	74	45	1	1	X
ejpam-4207	74	46	)	)	PUNCT
ejpam-4207	74	47	mcl(a	mcl(a	X
ejpam-4207	74	48	)	)	PUNCT
ejpam-4207	75	1	=	=	SYM
ejpam-4207	75	2	∩{f	∩{f	NOUN
ejpam-4207	75	3	:	:	PUNCT
ejpam-4207	75	4	a	a	DET
ejpam-4207	75	5	⊂	⊂	PROPN
ejpam-4207	75	6	f	f	X
ejpam-4207	75	7	,	,	PUNCT
ejpam-4207	75	8	x	x	PROPN
ejpam-4207	75	9	−	−	PROPN
ejpam-4207	75	10	f	f	PROPN
ejpam-4207	75	11	∈	∈	PROPN
ejpam-4207	75	12	mx	mx	PROPN
ejpam-4207	75	13	}	}	PUNCT
ejpam-4207	75	14	,	,	PUNCT
ejpam-4207	75	15	(	(	PUNCT
ejpam-4207	75	16	2	2	X
ejpam-4207	75	17	)	)	PUNCT
ejpam-4207	75	18	mint(a	mint(a	PROPN
ejpam-4207	75	19	)	)	PUNCT
ejpam-4207	75	20	=	=	SYM
ejpam-4207	76	1	∪{u	∪{u	VERB
ejpam-4207	76	2	:	:	PUNCT
ejpam-4207	76	3	u	u	X
ejpam-4207	76	4	⊂	⊂	PROPN
ejpam-4207	76	5	a	a	X
ejpam-4207	76	6	,	,	PUNCT
ejpam-4207	76	7	u	u	PROPN
ejpam-4207	76	8	∈	∈	PROPN
ejpam-4207	76	9	mx	mx	PROPN
ejpam-4207	76	10	}	}	PUNCT
ejpam-4207	76	11	.	.	PUNCT
ejpam-4207	77	1	remark	remark	NOUN
ejpam-4207	77	2	2	2	NUM
ejpam-4207	77	3	.	.	PUNCT
ejpam-4207	78	1	let	let	VERB
ejpam-4207	78	2	(	(	PUNCT
ejpam-4207	78	3	x	x	NOUN
ejpam-4207	78	4	,	,	PUNCT
ejpam-4207	78	5	τ	τ	X
ejpam-4207	78	6	)	)	PUNCT
ejpam-4207	78	7	be	be	VERB
ejpam-4207	78	8	a	a	DET
ejpam-4207	78	9	topological	topological	ADJ
ejpam-4207	78	10	space	space	NOUN
ejpam-4207	78	11	and	and	CCONJ
ejpam-4207	78	12	a	a	DET
ejpam-4207	78	13	a	a	DET
ejpam-4207	78	14	subset	subset	NOUN
ejpam-4207	78	15	of	of	ADP
ejpam-4207	78	16	x.	x.	NOUN
ejpam-4207	78	17	if	if	SCONJ
ejpam-4207	78	18	mx	mx	PROPN
ejpam-4207	78	19	=	=	SYM
ejpam-4207	78	20	τ	τ	PROPN
ejpam-4207	78	21	(	(	PUNCT
ejpam-4207	78	22	resp	resp	NOUN
ejpam-4207	78	23	.	.	PUNCT
ejpam-4207	78	24	so(x	so(x	NUM
ejpam-4207	78	25	)	)	PUNCT
ejpam-4207	78	26	,	,	PUNCT
ejpam-4207	78	27	po(x	po(x	NUM
ejpam-4207	78	28	)	)	PUNCT
ejpam-4207	78	29	,	,	PUNCT
ejpam-4207	78	30	bo(x	bo(x	NUM
ejpam-4207	78	31	)	)	PUNCT
ejpam-4207	78	32	,	,	PUNCT
ejpam-4207	78	33	α(x	α(x	NOUN
ejpam-4207	78	34	)	)	PUNCT
ejpam-4207	78	35	,	,	PUNCT
ejpam-4207	78	36	β(x	β(x	NOUN
ejpam-4207	78	37	)	)	PUNCT
ejpam-4207	78	38	)	)	PUNCT
ejpam-4207	78	39	,	,	PUNCT
ejpam-4207	78	40	then	then	ADV
ejpam-4207	78	41	we	we	PRON
ejpam-4207	78	42	have	have	VERB
ejpam-4207	78	43	(	(	PUNCT
ejpam-4207	78	44	1	1	X
ejpam-4207	78	45	)	)	PUNCT
ejpam-4207	78	46	mcl(a	mcl(a	NOUN
ejpam-4207	78	47	)	)	PUNCT
ejpam-4207	78	48	=	=	SYM
ejpam-4207	78	49	cl(a	cl(a	X
ejpam-4207	78	50	)	)	PUNCT
ejpam-4207	78	51	(	(	PUNCT
ejpam-4207	78	52	resp	resp	NOUN
ejpam-4207	78	53	.	.	PUNCT
ejpam-4207	79	1	scl(a	scl(a	PROPN
ejpam-4207	79	2	)	)	PUNCT
ejpam-4207	79	3	,	,	PUNCT
ejpam-4207	79	4	pcl(a	pcl(a	PROPN
ejpam-4207	79	5	)	)	PUNCT
ejpam-4207	79	6	,	,	PUNCT
ejpam-4207	79	7	bcl(a	bcl(a	PROPN
ejpam-4207	79	8	)	)	PUNCT
ejpam-4207	79	9	,	,	PUNCT
ejpam-4207	79	10	αcl(a	αcl(a	PROPN
ejpam-4207	79	11	)	)	PUNCT
ejpam-4207	79	12	,	,	PUNCT
ejpam-4207	79	13	βcl(a	βcl(a	PROPN
ejpam-4207	79	14	)	)	PUNCT
ejpam-4207	79	15	)	)	PUNCT
ejpam-4207	80	1	,	,	PUNCT
ejpam-4207	80	2	(	(	PUNCT
ejpam-4207	80	3	2	2	X
ejpam-4207	80	4	)	)	PUNCT
ejpam-4207	80	5	mint(a	mint(a	PROPN
ejpam-4207	80	6	)	)	PUNCT
ejpam-4207	80	7	=	=	SYM
ejpam-4207	80	8	int(a	int(a	NOUN
ejpam-4207	80	9	)	)	PUNCT
ejpam-4207	80	10	(	(	PUNCT
ejpam-4207	80	11	resp	resp	NOUN
ejpam-4207	80	12	.	.	PUNCT
ejpam-4207	81	1	sint(a	sint(a	NOUN
ejpam-4207	81	2	)	)	PUNCT
ejpam-4207	81	3	,	,	PUNCT
ejpam-4207	81	4	pint(a	pint(a	NOUN
ejpam-4207	81	5	)	)	PUNCT
ejpam-4207	81	6	,	,	PUNCT
ejpam-4207	81	7	bint(a	bint(a	PROPN
ejpam-4207	81	8	)	)	PUNCT
ejpam-4207	81	9	,	,	PUNCT
ejpam-4207	81	10	αint(a	αint(a	NOUN
ejpam-4207	81	11	)	)	PUNCT
ejpam-4207	81	12	,	,	PUNCT
ejpam-4207	81	13	βint(a	βint(a	NOUN
ejpam-4207	81	14	)	)	PUNCT
ejpam-4207	81	15	)	)	PUNCT
ejpam-4207	81	16	.	.	PUNCT
ejpam-4207	82	1	lemma	lemma	PROPN
ejpam-4207	82	2	1	1	NUM
ejpam-4207	82	3	.	.	PUNCT
ejpam-4207	83	1	(	(	PUNCT
ejpam-4207	83	2	[	[	X
ejpam-4207	83	3	22	22	NUM
ejpam-4207	83	4	]	]	PUNCT
ejpam-4207	83	5	)	)	PUNCT
ejpam-4207	83	6	.	.	PUNCT
ejpam-4207	84	1	let	let	AUX
ejpam-4207	84	2	(	(	PUNCT
ejpam-4207	84	3	x	x	NOUN
ejpam-4207	84	4	,	,	PUNCT
ejpam-4207	84	5	mx	mx	NOUN
ejpam-4207	84	6	)	)	PUNCT
ejpam-4207	84	7	be	be	AUX
ejpam-4207	84	8	an	an	DET
ejpam-4207	84	9	m	m	NOUN
ejpam-4207	84	10	-	-	NOUN
ejpam-4207	84	11	space	space	NOUN
ejpam-4207	84	12	.	.	PUNCT
ejpam-4207	85	1	for	for	ADP
ejpam-4207	85	2	subsets	subset	NOUN
ejpam-4207	85	3	a	a	PRON
ejpam-4207	85	4	and	and	CCONJ
ejpam-4207	85	5	b	b	NOUN
ejpam-4207	85	6	of	of	ADP
ejpam-4207	85	7	x	x	PRON
ejpam-4207	85	8	,	,	PUNCT
ejpam-4207	85	9	the	the	DET
ejpam-4207	85	10	following	follow	VERB
ejpam-4207	85	11	properties	property	NOUN
ejpam-4207	85	12	hold	hold	VERB
ejpam-4207	85	13	:	:	PUNCT
ejpam-4207	85	14	(	(	PUNCT
ejpam-4207	85	15	1	1	X
ejpam-4207	85	16	)	)	PUNCT
ejpam-4207	85	17	mcl(x	mcl(x	PROPN
ejpam-4207	85	18	−a	−a	NOUN
ejpam-4207	85	19	)	)	PUNCT
ejpam-4207	86	1	=	=	PUNCT
ejpam-4207	87	1	x	x	PUNCT
ejpam-4207	87	2	−mint(a	−mint(a	NOUN
ejpam-4207	87	3	)	)	PUNCT
ejpam-4207	87	4	and	and	CCONJ
ejpam-4207	87	5	mint(x	mint(x	NOUN
ejpam-4207	87	6	−a	−a	NOUN
ejpam-4207	87	7	)	)	PUNCT
ejpam-4207	87	8	=	=	PUNCT
ejpam-4207	87	9	x	x	SYM
ejpam-4207	87	10	−mcl(a	−mcl(a	NOUN
ejpam-4207	87	11	)	)	PUNCT
ejpam-4207	87	12	,	,	PUNCT
ejpam-4207	87	13	(	(	PUNCT
ejpam-4207	87	14	2	2	X
ejpam-4207	87	15	)	)	PUNCT
ejpam-4207	87	16	if	if	SCONJ
ejpam-4207	87	17	(	(	PUNCT
ejpam-4207	87	18	x	x	NOUN
ejpam-4207	87	19	−a	−a	ADJ
ejpam-4207	87	20	)	)	PUNCT
ejpam-4207	87	21	∈	∈	PROPN
ejpam-4207	87	22	mx	mx	PROPN
ejpam-4207	87	23	,	,	PUNCT
ejpam-4207	87	24	then	then	ADV
ejpam-4207	87	25	mcl(a	mcl(a	X
ejpam-4207	87	26	)	)	PUNCT
ejpam-4207	87	27	=	=	SYM
ejpam-4207	87	28	a	a	PROPN
ejpam-4207	87	29	and	and	CCONJ
ejpam-4207	87	30	if	if	SCONJ
ejpam-4207	87	31	a	a	DET
ejpam-4207	87	32	∈	∈	PROPN
ejpam-4207	87	33	mx	mx	NOUN
ejpam-4207	87	34	,	,	PUNCT
ejpam-4207	87	35	then	then	ADV
ejpam-4207	87	36	mint(a	mint(a	PROPN
ejpam-4207	87	37	)	)	PUNCT
ejpam-4207	87	38	=	=	SYM
ejpam-4207	88	1	a	a	PRON
ejpam-4207	88	2	,	,	PUNCT
ejpam-4207	88	3	(	(	PUNCT
ejpam-4207	88	4	3	3	NUM
ejpam-4207	88	5	)	)	PUNCT
ejpam-4207	88	6	mcl(∅	mcl(∅	NOUN
ejpam-4207	88	7	)	)	PUNCT
ejpam-4207	88	8	=	=	SYM
ejpam-4207	88	9	∅	∅	NOUN
ejpam-4207	88	10	,	,	PUNCT
ejpam-4207	88	11	mcl(x	mcl(x	PROPN
ejpam-4207	88	12	)	)	PUNCT
ejpam-4207	88	13	=	=	SYM
ejpam-4207	88	14	x	x	PROPN
ejpam-4207	88	15	,	,	PUNCT
ejpam-4207	88	16	mint(∅	mint(∅	PROPN
ejpam-4207	88	17	)	)	PUNCT
ejpam-4207	88	18	=	=	NOUN
ejpam-4207	88	19	∅	∅	NOUN
ejpam-4207	88	20	and	and	CCONJ
ejpam-4207	88	21	mint(x	mint(x	NOUN
ejpam-4207	88	22	)	)	PUNCT
ejpam-4207	88	23	=	=	SYM
ejpam-4207	89	1	x	x	X
ejpam-4207	89	2	,	,	PUNCT
ejpam-4207	89	3	(	(	PUNCT
ejpam-4207	89	4	4	4	X
ejpam-4207	89	5	)	)	PUNCT
ejpam-4207	89	6	if	if	SCONJ
ejpam-4207	89	7	a	a	PRON
ejpam-4207	89	8	⊂	⊂	PROPN
ejpam-4207	89	9	b	b	PROPN
ejpam-4207	89	10	,	,	PUNCT
ejpam-4207	89	11	then	then	ADV
ejpam-4207	89	12	mcl(a	mcl(a	X
ejpam-4207	89	13	)	)	PUNCT
ejpam-4207	89	14	⊂	⊂	PROPN
ejpam-4207	89	15	mcl(b	mcl(b	PROPN
ejpam-4207	89	16	)	)	PUNCT
ejpam-4207	89	17	and	and	CCONJ
ejpam-4207	89	18	mint(a	mint(a	PROPN
ejpam-4207	89	19	)	)	PUNCT
ejpam-4207	89	20	⊂	⊂	PROPN
ejpam-4207	89	21	mint(b	mint(b	PROPN
ejpam-4207	89	22	)	)	PUNCT
ejpam-4207	89	23	,	,	PUNCT
ejpam-4207	89	24	(	(	PUNCT
ejpam-4207	89	25	5	5	X
ejpam-4207	89	26	)	)	PUNCT
ejpam-4207	89	27	a	a	DET
ejpam-4207	89	28	⊂	⊂	PROPN
ejpam-4207	89	29	mcl(a	mcl(a	X
ejpam-4207	89	30	)	)	PUNCT
ejpam-4207	89	31	and	and	CCONJ
ejpam-4207	89	32	mint(a	mint(a	PROPN
ejpam-4207	89	33	)	)	PUNCT
ejpam-4207	89	34	⊂	⊂	PROPN
ejpam-4207	89	35	a	a	X
ejpam-4207	89	36	,	,	PUNCT
ejpam-4207	89	37	(	(	PUNCT
ejpam-4207	89	38	6	6	NUM
ejpam-4207	89	39	)	)	PUNCT
ejpam-4207	89	40	mcl(mcl(a	mcl(mcl(a	ADJ
ejpam-4207	89	41	)	)	PUNCT
ejpam-4207	89	42	)	)	PUNCT
ejpam-4207	90	1	=	=	SYM
ejpam-4207	90	2	mcl(a	mcl(a	X
ejpam-4207	90	3	)	)	PUNCT
ejpam-4207	90	4	and	and	CCONJ
ejpam-4207	90	5	mint(mint(a	mint(mint(a	NUM
ejpam-4207	90	6	)	)	PUNCT
ejpam-4207	90	7	)	)	PUNCT
ejpam-4207	91	1	=	=	PUNCT
ejpam-4207	91	2	mint(a	mint(a	PROPN
ejpam-4207	91	3	)	)	PUNCT
ejpam-4207	91	4	.	.	PUNCT
ejpam-4207	92	1	definition	definition	NOUN
ejpam-4207	92	2	5	5	NUM
ejpam-4207	92	3	.	.	PUNCT
ejpam-4207	93	1	a	a	DET
ejpam-4207	93	2	minimal	minimal	ADJ
ejpam-4207	93	3	structure	structure	NOUN
ejpam-4207	93	4	mx	mx	NOUN
ejpam-4207	93	5	on	on	ADP
ejpam-4207	93	6	a	a	DET
ejpam-4207	93	7	nonempty	nonempty	ADJ
ejpam-4207	93	8	set	set	VERB
ejpam-4207	93	9	x	x	SYM
ejpam-4207	93	10	is	be	AUX
ejpam-4207	93	11	said	say	VERB
ejpam-4207	93	12	to	to	PART
ejpam-4207	93	13	have	have	VERB
ejpam-4207	93	14	property	property	NOUN
ejpam-4207	93	15	b	b	PROPN
ejpam-4207	94	1	[	[	X
ejpam-4207	94	2	22	22	NUM
ejpam-4207	94	3	]	]	PUNCT
ejpam-4207	94	4	if	if	SCONJ
ejpam-4207	94	5	the	the	DET
ejpam-4207	94	6	union	union	NOUN
ejpam-4207	94	7	of	of	ADP
ejpam-4207	94	8	any	any	DET
ejpam-4207	94	9	family	family	NOUN
ejpam-4207	94	10	of	of	ADP
ejpam-4207	94	11	subsets	subset	NOUN
ejpam-4207	94	12	belonging	belong	VERB
ejpam-4207	94	13	to	to	ADP
ejpam-4207	94	14	mx	mx	PROPN
ejpam-4207	94	15	belongs	belong	VERB
ejpam-4207	94	16	to	to	ADP
ejpam-4207	94	17	mx	mx	PROPN
ejpam-4207	94	18	.	.	PUNCT
ejpam-4207	95	1	remark	remark	PROPN
ejpam-4207	95	2	3	3	NUM
ejpam-4207	95	3	.	.	PUNCT
ejpam-4207	96	1	let	let	AUX
ejpam-4207	96	2	(	(	PUNCT
ejpam-4207	96	3	x	x	NOUN
ejpam-4207	96	4	,	,	PUNCT
ejpam-4207	96	5	τ	τ	X
ejpam-4207	96	6	)	)	PUNCT
ejpam-4207	96	7	be	be	VERB
ejpam-4207	96	8	a	a	DET
ejpam-4207	96	9	topological	topological	ADJ
ejpam-4207	96	10	space	space	NOUN
ejpam-4207	96	11	.	.	PUNCT
ejpam-4207	97	1	then	then	ADV
ejpam-4207	97	2	the	the	DET
ejpam-4207	97	3	families	family	NOUN
ejpam-4207	97	4	τ	τ	PROPN
ejpam-4207	97	5	,	,	PUNCT
ejpam-4207	97	6	so(x	so(x	NOUN
ejpam-4207	97	7	)	)	PUNCT
ejpam-4207	97	8	,	,	PUNCT
ejpam-4207	97	9	po(x	po(x	NUM
ejpam-4207	97	10	)	)	PUNCT
ejpam-4207	97	11	,	,	PUNCT
ejpam-4207	97	12	α(x	α(x	NOUN
ejpam-4207	97	13	)	)	PUNCT
ejpam-4207	97	14	,	,	PUNCT
ejpam-4207	97	15	bo(x	bo(x	NUM
ejpam-4207	97	16	)	)	PUNCT
ejpam-4207	97	17	and	and	CCONJ
ejpam-4207	97	18	β(x	β(x	NOUN
ejpam-4207	97	19	)	)	PUNCT
ejpam-4207	97	20	are	be	AUX
ejpam-4207	97	21	all	all	PRON
ejpam-4207	97	22	minimal	minimal	ADJ
ejpam-4207	97	23	structures	structure	NOUN
ejpam-4207	97	24	having	have	VERB
ejpam-4207	97	25	property	property	NOUN
ejpam-4207	97	26	b.	b.	PROPN
ejpam-4207	97	27	lemma	lemma	PROPN
ejpam-4207	98	1	2	2	X
ejpam-4207	98	2	.	.	PUNCT
ejpam-4207	98	3	let	let	VERB
ejpam-4207	98	4	x	x	PRON
ejpam-4207	98	5	be	be	AUX
ejpam-4207	98	6	a	a	DET
ejpam-4207	98	7	nonempty	nonempty	ADV
ejpam-4207	98	8	set	set	VERB
ejpam-4207	98	9	and	and	CCONJ
ejpam-4207	98	10	mx	mx	X
ejpam-4207	98	11	an	an	DET
ejpam-4207	98	12	m	m	NOUN
ejpam-4207	98	13	-	-	NOUN
ejpam-4207	98	14	structure	structure	NOUN
ejpam-4207	98	15	with	with	ADP
ejpam-4207	98	16	property	property	NOUN
ejpam-4207	98	17	b.	b.	PROPN
ejpam-4207	98	18	then	then	ADV
ejpam-4207	98	19	,	,	PUNCT
ejpam-4207	98	20	the	the	DET
ejpam-4207	98	21	following	follow	VERB
ejpam-4207	98	22	properties	property	NOUN
ejpam-4207	98	23	are	be	AUX
ejpam-4207	98	24	hold	hold	ADJ
ejpam-4207	98	25	:	:	PUNCT
ejpam-4207	98	26	(	(	PUNCT
ejpam-4207	98	27	1	1	X
ejpam-4207	98	28	)	)	PUNCT
ejpam-4207	98	29	mint(a	mint(a	PROPN
ejpam-4207	98	30	)	)	PUNCT
ejpam-4207	98	31	=	=	PUNCT
ejpam-4207	99	1	a	a	DET
ejpam-4207	99	2	if	if	NOUN
ejpam-4207	99	3	and	and	CCONJ
ejpam-4207	99	4	only	only	ADV
ejpam-4207	99	5	if	if	SCONJ
ejpam-4207	99	6	a	a	DET
ejpam-4207	99	7	∈	∈	PROPN
ejpam-4207	99	8	mx	mx	PROPN
ejpam-4207	99	9	,	,	PUNCT
ejpam-4207	99	10	(	(	PUNCT
ejpam-4207	99	11	2	2	X
ejpam-4207	99	12	)	)	PUNCT
ejpam-4207	99	13	mcl(a	mcl(a	NOUN
ejpam-4207	99	14	)	)	PUNCT
ejpam-4207	99	15	=	=	NOUN
ejpam-4207	100	1	a	a	DET
ejpam-4207	100	2	if	if	NOUN
ejpam-4207	100	3	and	and	CCONJ
ejpam-4207	100	4	only	only	ADV
ejpam-4207	100	5	if	if	SCONJ
ejpam-4207	100	6	a	a	PRON
ejpam-4207	100	7	is	be	AUX
ejpam-4207	100	8	m	m	NOUN
ejpam-4207	100	9	-	-	ADJ
ejpam-4207	100	10	closed	closed	ADJ
ejpam-4207	100	11	,	,	PUNCT
ejpam-4207	100	12	(	(	PUNCT
ejpam-4207	100	13	3	3	X
ejpam-4207	100	14	)	)	PUNCT
ejpam-4207	100	15	mint(a	mint(a	PROPN
ejpam-4207	100	16	)	)	PUNCT
ejpam-4207	100	17	∈	∈	PROPN
ejpam-4207	100	18	mx	mx	PROPN
ejpam-4207	100	19	and	and	CCONJ
ejpam-4207	100	20	mcl(a	mcl(a	PROPN
ejpam-4207	100	21	)	)	PUNCT
ejpam-4207	100	22	is	be	AUX
ejpam-4207	100	23	m	m	NOUN
ejpam-4207	100	24	-	-	PUNCT
ejpam-4207	100	25	closed	closed	ADJ
ejpam-4207	100	26	.	.	PUNCT
ejpam-4207	101	1	definition	definition	NOUN
ejpam-4207	101	2	6	6	NUM
ejpam-4207	101	3	.	.	PUNCT
ejpam-4207	102	1	a	a	DET
ejpam-4207	102	2	multifunction	multifunction	NOUN
ejpam-4207	102	3	f	f	NOUN
ejpam-4207	102	4	:	:	PUNCT
ejpam-4207	102	5	(	(	PUNCT
ejpam-4207	102	6	x	x	NOUN
ejpam-4207	102	7	,	,	PUNCT
ejpam-4207	102	8	mx	mx	NOUN
ejpam-4207	102	9	)	)	PUNCT
ejpam-4207	102	10	→	→	SYM
ejpam-4207	102	11	(	(	PUNCT
ejpam-4207	102	12	y	y	PROPN
ejpam-4207	102	13	,	,	PUNCT
ejpam-4207	102	14	σ	σ	PROPN
ejpam-4207	102	15	)	)	PUNCT
ejpam-4207	102	16	is	be	AUX
ejpam-4207	102	17	said	say	VERB
ejpam-4207	102	18	to	to	PART
ejpam-4207	102	19	be	be	AUX
ejpam-4207	102	20	m	m	NOUN
ejpam-4207	102	21	-	-	ADJ
ejpam-4207	102	22	continuous	continuous	ADJ
ejpam-4207	102	23	at	at	ADP
ejpam-4207	102	24	x	x	X
ejpam-4207	102	25	∈	∈	NOUN
ejpam-4207	102	26	x	x	PUNCT
ejpam-4207	103	1	[	[	X
ejpam-4207	103	2	42	42	NUM
ejpam-4207	103	3	]	]	X
ejpam-4207	103	4	if	if	SCONJ
ejpam-4207	103	5	for	for	ADP
ejpam-4207	103	6	each	each	DET
ejpam-4207	103	7	open	open	ADJ
ejpam-4207	103	8	sets	set	NOUN
ejpam-4207	103	9	v1	v1	NOUN
ejpam-4207	103	10	,	,	PUNCT
ejpam-4207	103	11	v2	v2	PROPN
ejpam-4207	103	12	of	of	ADP
ejpam-4207	103	13	y	y	PRON
ejpam-4207	103	14	such	such	ADJ
ejpam-4207	103	15	that	that	SCONJ
ejpam-4207	103	16	f	f	PROPN
ejpam-4207	103	17	(	(	PUNCT
ejpam-4207	103	18	x	x	X
ejpam-4207	103	19	)	)	PUNCT
ejpam-4207	103	20	∈	∈	NOUN
ejpam-4207	103	21	v	v	ADP
ejpam-4207	103	22	+	+	CCONJ
ejpam-4207	103	23	1	1	NUM
ejpam-4207	103	24	∩	∩	NOUN
ejpam-4207	103	25	v	v	ADP
ejpam-4207	103	26	−	−	PROPN
ejpam-4207	103	27	2	2	NUM
ejpam-4207	103	28	,	,	PUNCT
ejpam-4207	103	29	there	there	PRON
ejpam-4207	103	30	exists	exist	VERB
ejpam-4207	103	31	u	u	PROPN
ejpam-4207	103	32	∈	∈	PROPN
ejpam-4207	103	33	mx	mx	NOUN
ejpam-4207	103	34	containing	contain	VERB
ejpam-4207	103	35	x	x	PUNCT
ejpam-4207	103	36	such	such	ADJ
ejpam-4207	103	37	that	that	SCONJ
ejpam-4207	103	38	f	f	PROPN
ejpam-4207	103	39	(	(	PUNCT
ejpam-4207	103	40	u	u	NOUN
ejpam-4207	103	41	)	)	PUNCT
ejpam-4207	103	42	∈	∈	NOUN
ejpam-4207	103	43	v	v	ADP
ejpam-4207	103	44	+	+	CCONJ
ejpam-4207	103	45	1	1	NUM
ejpam-4207	103	46	∩	∩	NOUN
ejpam-4207	103	47	v	v	ADP
ejpam-4207	103	48	−	−	PROPN
ejpam-4207	103	49	2	2	NUM
ejpam-4207	103	50	for	for	ADP
ejpam-4207	103	51	every	every	DET
ejpam-4207	103	52	u	u	PROPN
ejpam-4207	103	53	∈	∈	PROPN
ejpam-4207	103	54	u	u	NOUN
ejpam-4207	103	55	.	.	PUNCT
ejpam-4207	104	1	f	f	PROPN
ejpam-4207	104	2	is	be	AUX
ejpam-4207	104	3	said	say	VERB
ejpam-4207	104	4	to	to	PART
ejpam-4207	104	5	be	be	AUX
ejpam-4207	104	6	m	m	NOUN
ejpam-4207	104	7	-	-	ADJ
ejpam-4207	104	8	continuous	continuous	ADJ
ejpam-4207	104	9	if	if	SCONJ
ejpam-4207	104	10	it	it	PRON
ejpam-4207	104	11	has	have	VERB
ejpam-4207	104	12	the	the	DET
ejpam-4207	104	13	property	property	NOUN
ejpam-4207	104	14	at	at	ADP
ejpam-4207	104	15	each	each	DET
ejpam-4207	104	16	point	point	NOUN
ejpam-4207	104	17	of	of	ADP
ejpam-4207	104	18	x.	x.	PROPN
ejpam-4207	104	19	takashi	takashi	PROPN
ejpam-4207	104	20	noiri	noiri	PROPN
ejpam-4207	104	21	,	,	PUNCT
ejpam-4207	104	22	valeriu	valeriu	ADJ
ejpam-4207	104	23	popa	popa	NOUN
ejpam-4207	104	24	/	/	SYM
ejpam-4207	104	25	eur	eur	PROPN
ejpam-4207	104	26	.	.	PUNCT
ejpam-4207	105	1	j.	j.	PROPN
ejpam-4207	105	2	pure	pure	PROPN
ejpam-4207	105	3	appl	appl	PROPN
ejpam-4207	105	4	.	.	PROPN
ejpam-4207	105	5	math	math	PROPN
ejpam-4207	105	6	,	,	PUNCT
ejpam-4207	105	7	15	15	NUM
ejpam-4207	105	8	(	(	PUNCT
ejpam-4207	105	9	1	1	NUM
ejpam-4207	105	10	)	)	PUNCT
ejpam-4207	105	11	(	(	PUNCT
ejpam-4207	105	12	2022	2022	NUM
ejpam-4207	105	13	)	)	PUNCT
ejpam-4207	105	14	,	,	PUNCT
ejpam-4207	105	15	1	1	NUM
ejpam-4207	105	16	-	-	SYM
ejpam-4207	105	17	14	14	NUM
ejpam-4207	105	18	4	4	NUM
ejpam-4207	105	19	remark	remark	NOUN
ejpam-4207	105	20	4	4	NUM
ejpam-4207	105	21	.	.	PUNCT
ejpam-4207	106	1	let	let	VERB
ejpam-4207	106	2	f	f	NOUN
ejpam-4207	106	3	:	:	PUNCT
ejpam-4207	106	4	(	(	PUNCT
ejpam-4207	106	5	x	x	NOUN
ejpam-4207	106	6	,	,	PUNCT
ejpam-4207	106	7	mx	mx	NOUN
ejpam-4207	106	8	)	)	PUNCT
ejpam-4207	106	9	→	→	SYM
ejpam-4207	106	10	(	(	PUNCT
ejpam-4207	106	11	y	y	PROPN
ejpam-4207	106	12	,	,	PUNCT
ejpam-4207	106	13	σ	σ	PROPN
ejpam-4207	106	14	)	)	PUNCT
ejpam-4207	106	15	be	be	AUX
ejpam-4207	106	16	a	a	DET
ejpam-4207	106	17	multifunction	multifunction	NOUN
ejpam-4207	106	18	.	.	PUNCT
ejpam-4207	107	1	if	if	SCONJ
ejpam-4207	107	2	mx	mx	PROPN
ejpam-4207	107	3	=	=	SYM
ejpam-4207	107	4	so(x	so(x	X
ejpam-4207	107	5	)	)	PUNCT
ejpam-4207	107	6	(	(	PUNCT
ejpam-4207	107	7	resp	resp	NOUN
ejpam-4207	107	8	.	.	PUNCT
ejpam-4207	108	1	po(x	po(x	NUM
ejpam-4207	108	2	)	)	PUNCT
ejpam-4207	108	3	,	,	PUNCT
ejpam-4207	109	1	α(x	α(x	NOUN
ejpam-4207	109	2	)	)	PUNCT
ejpam-4207	109	3	,	,	PUNCT
ejpam-4207	109	4	bo(x	bo(x	NUM
ejpam-4207	109	5	)	)	PUNCT
ejpam-4207	109	6	,	,	PUNCT
ejpam-4207	109	7	β(x	β(x	NOUN
ejpam-4207	109	8	)	)	PUNCT
ejpam-4207	109	9	)	)	PUNCT
ejpam-4207	109	10	,	,	PUNCT
ejpam-4207	109	11	then	then	ADV
ejpam-4207	109	12	f	f	PROPN
ejpam-4207	109	13	is	be	AUX
ejpam-4207	109	14	quasi	quasi	ADJ
ejpam-4207	109	15	-	-	ADJ
ejpam-4207	109	16	continuous	continuous	ADJ
ejpam-4207	109	17	(	(	PUNCT
ejpam-4207	109	18	resp	resp	NOUN
ejpam-4207	109	19	.	.	PUNCT
ejpam-4207	110	1	precontinuous	precontinuous	ADJ
ejpam-4207	110	2	,	,	PUNCT
ejpam-4207	110	3	α	α	NOUN
ejpam-4207	110	4	-	-	ADJ
ejpam-4207	110	5	continuous	continuous	ADJ
ejpam-4207	110	6	,	,	PUNCT
ejpam-4207	110	7	bcontinuous	bcontinuous	ADJ
ejpam-4207	110	8	,	,	PUNCT
ejpam-4207	110	9	β	β	NOUN
ejpam-4207	110	10	-	-	ADJ
ejpam-4207	110	11	continuous	continuous	ADJ
ejpam-4207	110	12	)	)	PUNCT
ejpam-4207	110	13	.	.	PUNCT
ejpam-4207	111	1	theorem	theorem	NOUN
ejpam-4207	111	2	1	1	NUM
ejpam-4207	111	3	.	.	PUNCT
ejpam-4207	112	1	(	(	PUNCT
ejpam-4207	112	2	[	[	X
ejpam-4207	112	3	44	44	NUM
ejpam-4207	112	4	]	]	PUNCT
ejpam-4207	112	5	)	)	PUNCT
ejpam-4207	112	6	.	.	PUNCT
ejpam-4207	113	1	for	for	ADP
ejpam-4207	113	2	a	a	DET
ejpam-4207	113	3	multifunction	multifunction	NOUN
ejpam-4207	113	4	f	f	NOUN
ejpam-4207	113	5	:	:	PUNCT
ejpam-4207	113	6	(	(	PUNCT
ejpam-4207	113	7	x	x	NOUN
ejpam-4207	113	8	,	,	PUNCT
ejpam-4207	113	9	mx	mx	NOUN
ejpam-4207	113	10	)	)	PUNCT
ejpam-4207	113	11	→	→	SYM
ejpam-4207	113	12	(	(	PUNCT
ejpam-4207	113	13	y	y	PROPN
ejpam-4207	113	14	,	,	PUNCT
ejpam-4207	113	15	σ	σ	PROPN
ejpam-4207	113	16	)	)	PUNCT
ejpam-4207	113	17	,	,	PUNCT
ejpam-4207	113	18	the	the	DET
ejpam-4207	113	19	following	follow	VERB
ejpam-4207	113	20	properties	property	NOUN
ejpam-4207	113	21	are	be	AUX
ejpam-4207	113	22	equivalent	equivalent	ADJ
ejpam-4207	113	23	:	:	PUNCT
ejpam-4207	113	24	(	(	PUNCT
ejpam-4207	113	25	1	1	X
ejpam-4207	113	26	)	)	PUNCT
ejpam-4207	113	27	f	f	PROPN
ejpam-4207	113	28	is	be	AUX
ejpam-4207	113	29	m	m	NOUN
ejpam-4207	113	30	-	-	ADJ
ejpam-4207	113	31	continuous	continuous	ADJ
ejpam-4207	113	32	at	at	ADP
ejpam-4207	113	33	x	x	X
ejpam-4207	113	34	∈	∈	PROPN
ejpam-4207	113	35	x	x	X
ejpam-4207	113	36	;	;	PUNCT
ejpam-4207	113	37	(	(	PUNCT
ejpam-4207	113	38	2	2	X
ejpam-4207	113	39	)	)	PUNCT
ejpam-4207	113	40	f	f	NOUN
ejpam-4207	113	41	(	(	PUNCT
ejpam-4207	113	42	x	x	X
ejpam-4207	113	43	)	)	PUNCT
ejpam-4207	113	44	∈	∈	NOUN
ejpam-4207	113	45	v	v	ADP
ejpam-4207	113	46	+	+	CCONJ
ejpam-4207	113	47	1	1	NUM
ejpam-4207	113	48	∩	∩	NOUN
ejpam-4207	113	49	v	v	ADP
ejpam-4207	113	50	−	−	PROPN
ejpam-4207	113	51	2	2	NUM
ejpam-4207	113	52	implies	imply	VERB
ejpam-4207	113	53	x	x	X
ejpam-4207	113	54	∈	∈	PROPN
ejpam-4207	113	55	mint[f+(v1)∩f−(v2	mint[f+(v1)∩f−(v2	PROPN
ejpam-4207	113	56	)	)	PUNCT
ejpam-4207	113	57	]	]	PUNCT
ejpam-4207	113	58	for	for	ADP
ejpam-4207	113	59	every	every	DET
ejpam-4207	113	60	open	open	ADJ
ejpam-4207	113	61	sets	set	NOUN
ejpam-4207	113	62	v1	v1	NOUN
ejpam-4207	113	63	,	,	PUNCT
ejpam-4207	113	64	v2	v2	PROPN
ejpam-4207	113	65	of	of	ADP
ejpam-4207	113	66	y	y	PROPN
ejpam-4207	113	67	;	;	PUNCT
ejpam-4207	113	68	(	(	PUNCT
ejpam-4207	113	69	3	3	X
ejpam-4207	113	70	)	)	PUNCT
ejpam-4207	113	71	x	x	SYM
ejpam-4207	113	72	∈	∈	PROPN
ejpam-4207	113	73	mcl(f−(b1	mcl(f−(b1	NOUN
ejpam-4207	113	74	)	)	PUNCT
ejpam-4207	113	75	∪	∪	ADP
ejpam-4207	113	76	f+(b2	f+(b2	NOUN
ejpam-4207	113	77	)	)	PUNCT
ejpam-4207	113	78	)	)	PUNCT
ejpam-4207	113	79	implies	imply	VERB
ejpam-4207	113	80	x	x	PUNCT
ejpam-4207	113	81	∈	∈	NUM
ejpam-4207	113	82	f−(cl(b1	f−(cl(b1	NOUN
ejpam-4207	113	83	)	)	PUNCT
ejpam-4207	113	84	)	)	PUNCT
ejpam-4207	113	85	∪	∪	ADP
ejpam-4207	113	86	f+(cl(b2	f+(cl(b2	NOUN
ejpam-4207	113	87	)	)	PUNCT
ejpam-4207	113	88	)	)	PUNCT
ejpam-4207	113	89	for	for	ADP
ejpam-4207	113	90	every	every	DET
ejpam-4207	113	91	subsets	subset	NOUN
ejpam-4207	113	92	b1	b1	NOUN
ejpam-4207	113	93	,	,	PUNCT
ejpam-4207	113	94	b2	b2	NOUN
ejpam-4207	113	95	of	of	ADP
ejpam-4207	113	96	y	y	PROPN
ejpam-4207	113	97	;	;	PUNCT
ejpam-4207	113	98	(	(	PUNCT
ejpam-4207	113	99	4	4	X
ejpam-4207	113	100	)	)	PUNCT
ejpam-4207	113	101	x	x	SYM
ejpam-4207	113	102	∈	∈	PROPN
ejpam-4207	113	103	f−(int(b1	f−(int(b1	NOUN
ejpam-4207	113	104	)	)	PUNCT
ejpam-4207	113	105	)	)	PUNCT
ejpam-4207	113	106	∩	∩	PROPN
ejpam-4207	113	107	f+(int(b2	f+(int(b2	PROPN
ejpam-4207	113	108	)	)	PUNCT
ejpam-4207	113	109	)	)	PUNCT
ejpam-4207	113	110	implies	imply	VERB
ejpam-4207	113	111	x	x	PUNCT
ejpam-4207	113	112	∈	∈	PROPN
ejpam-4207	113	113	int(f−(b1	int(f−(b1	NOUN
ejpam-4207	113	114	)	)	PUNCT
ejpam-4207	113	115	∩	∩	PROPN
ejpam-4207	113	116	f+(b2	f+(b2	NOUN
ejpam-4207	113	117	)	)	PUNCT
ejpam-4207	113	118	)	)	PUNCT
ejpam-4207	113	119	for	for	ADP
ejpam-4207	113	120	every	every	DET
ejpam-4207	113	121	subsets	subset	NOUN
ejpam-4207	113	122	b1	b1	NOUN
ejpam-4207	113	123	,	,	PUNCT
ejpam-4207	113	124	b2	b2	NOUN
ejpam-4207	113	125	of	of	ADP
ejpam-4207	113	126	y.	y.	PROPN
ejpam-4207	113	127	theorem	theorem	PROPN
ejpam-4207	113	128	2	2	NUM
ejpam-4207	113	129	.	.	PUNCT
ejpam-4207	114	1	(	(	PUNCT
ejpam-4207	114	2	[	[	X
ejpam-4207	114	3	42	42	NUM
ejpam-4207	114	4	]	]	PUNCT
ejpam-4207	114	5	)	)	PUNCT
ejpam-4207	114	6	.	.	PUNCT
ejpam-4207	115	1	for	for	ADP
ejpam-4207	115	2	a	a	DET
ejpam-4207	115	3	multifunction	multifunction	NOUN
ejpam-4207	115	4	f	f	NOUN
ejpam-4207	115	5	:	:	PUNCT
ejpam-4207	115	6	(	(	PUNCT
ejpam-4207	115	7	x	x	NOUN
ejpam-4207	115	8	,	,	PUNCT
ejpam-4207	115	9	mx	mx	NOUN
ejpam-4207	115	10	)	)	PUNCT
ejpam-4207	115	11	→	→	SYM
ejpam-4207	115	12	(	(	PUNCT
ejpam-4207	115	13	y	y	PROPN
ejpam-4207	115	14	,	,	PUNCT
ejpam-4207	115	15	σ	σ	PROPN
ejpam-4207	115	16	)	)	PUNCT
ejpam-4207	115	17	,	,	PUNCT
ejpam-4207	115	18	the	the	DET
ejpam-4207	115	19	following	follow	VERB
ejpam-4207	115	20	properties	property	NOUN
ejpam-4207	115	21	are	be	AUX
ejpam-4207	115	22	equivalent	equivalent	ADJ
ejpam-4207	115	23	:	:	PUNCT
ejpam-4207	115	24	(	(	PUNCT
ejpam-4207	115	25	1	1	X
ejpam-4207	115	26	)	)	PUNCT
ejpam-4207	115	27	f	f	PROPN
ejpam-4207	115	28	is	be	AUX
ejpam-4207	115	29	m	m	NOUN
ejpam-4207	115	30	-	-	ADJ
ejpam-4207	115	31	continuous	continuous	ADJ
ejpam-4207	115	32	;	;	PUNCT
ejpam-4207	115	33	(	(	PUNCT
ejpam-4207	115	34	2	2	X
ejpam-4207	115	35	)	)	PUNCT
ejpam-4207	115	36	f+(g1	f+(g1	NOUN
ejpam-4207	115	37	)	)	PUNCT
ejpam-4207	115	38	∩	∩	NOUN
ejpam-4207	115	39	f−(g2	f−(g2	NUM
ejpam-4207	115	40	)	)	PUNCT
ejpam-4207	115	41	=	=	SYM
ejpam-4207	115	42	mint(f+(g1	mint(f+(g1	ADJ
ejpam-4207	115	43	)	)	PUNCT
ejpam-4207	115	44	∩	∩	NOUN
ejpam-4207	115	45	f−(g2	f−(g2	PRON
ejpam-4207	115	46	)	)	PUNCT
ejpam-4207	115	47	)	)	PUNCT
ejpam-4207	115	48	for	for	ADP
ejpam-4207	115	49	every	every	DET
ejpam-4207	115	50	open	open	ADJ
ejpam-4207	115	51	sets	set	NOUN
ejpam-4207	115	52	g1	g1	NOUN
ejpam-4207	115	53	,	,	PUNCT
ejpam-4207	115	54	g2	g2	PROPN
ejpam-4207	115	55	of	of	ADP
ejpam-4207	115	56	y	y	PROPN
ejpam-4207	115	57	;	;	PUNCT
ejpam-4207	115	58	(	(	PUNCT
ejpam-4207	115	59	3	3	X
ejpam-4207	115	60	)	)	PUNCT
ejpam-4207	115	61	f−(k1	f−(k1	ADP
ejpam-4207	115	62	)	)	PUNCT
ejpam-4207	115	63	∪	∪	ADP
ejpam-4207	115	64	f+(k2	f+(k2	NOUN
ejpam-4207	115	65	)	)	PUNCT
ejpam-4207	115	66	=	=	SYM
ejpam-4207	115	67	mcl(f−(k1	mcl(f−(k1	NOUN
ejpam-4207	115	68	)	)	PUNCT
ejpam-4207	115	69	∪	∪	ADP
ejpam-4207	115	70	f+(k2	f+(k2	NOUN
ejpam-4207	115	71	)	)	PUNCT
ejpam-4207	115	72	)	)	PUNCT
ejpam-4207	115	73	for	for	ADP
ejpam-4207	115	74	every	every	DET
ejpam-4207	115	75	closed	closed	ADJ
ejpam-4207	115	76	sets	set	NOUN
ejpam-4207	115	77	k1,k2	k1,k2	PROPN
ejpam-4207	115	78	of	of	ADP
ejpam-4207	115	79	y	y	PROPN
ejpam-4207	115	80	;	;	PUNCT
ejpam-4207	115	81	(	(	PUNCT
ejpam-4207	115	82	4	4	X
ejpam-4207	115	83	)	)	PUNCT
ejpam-4207	115	84	mcl(f−(b1	mcl(f−(b1	NOUN
ejpam-4207	115	85	)	)	PUNCT
ejpam-4207	115	86	∪	∪	ADP
ejpam-4207	115	87	f+(b2	f+(b2	PROPN
ejpam-4207	115	88	)	)	PUNCT
ejpam-4207	115	89	)	)	PUNCT
ejpam-4207	116	1	⊂	⊂	PROPN
ejpam-4207	116	2	f−(cl(b1	f−(cl(b1	PROPN
ejpam-4207	116	3	)	)	PUNCT
ejpam-4207	116	4	)	)	PUNCT
ejpam-4207	116	5	∪	∪	ADP
ejpam-4207	116	6	f+(cl(b2	f+(cl(b2	NOUN
ejpam-4207	116	7	)	)	PUNCT
ejpam-4207	116	8	)	)	PUNCT
ejpam-4207	116	9	for	for	ADP
ejpam-4207	116	10	every	every	DET
ejpam-4207	116	11	subsets	subset	NOUN
ejpam-4207	116	12	b1	b1	NOUN
ejpam-4207	116	13	,	,	PUNCT
ejpam-4207	116	14	b2	b2	NOUN
ejpam-4207	116	15	of	of	ADP
ejpam-4207	116	16	y	y	PROPN
ejpam-4207	116	17	;	;	PUNCT
ejpam-4207	116	18	(	(	PUNCT
ejpam-4207	116	19	5	5	X
ejpam-4207	116	20	)	)	PUNCT
ejpam-4207	116	21	f−(int(b1))∩f+(int(b2	f−(int(b1))∩f+(int(b2	NOUN
ejpam-4207	116	22	)	)	PUNCT
ejpam-4207	116	23	)	)	PUNCT
ejpam-4207	117	1	⊂	⊂	PROPN
ejpam-4207	117	2	mint(f−(b1)∩f+(b2	mint(f−(b1)∩f+(b2	PROPN
ejpam-4207	117	3	)	)	PUNCT
ejpam-4207	117	4	)	)	PUNCT
ejpam-4207	117	5	for	for	ADP
ejpam-4207	117	6	every	every	DET
ejpam-4207	117	7	subsets	subset	NOUN
ejpam-4207	117	8	b1	b1	NOUN
ejpam-4207	117	9	,	,	PUNCT
ejpam-4207	117	10	b2	b2	NOUN
ejpam-4207	117	11	of	of	ADP
ejpam-4207	117	12	y	y	PROPN
ejpam-4207	117	13	.	.	PUNCT
ejpam-4207	118	1	for	for	ADP
ejpam-4207	118	2	a	a	DET
ejpam-4207	118	3	multifunction	multifunction	NOUN
ejpam-4207	118	4	f	f	NOUN
ejpam-4207	118	5	:	:	PUNCT
ejpam-4207	118	6	(	(	PUNCT
ejpam-4207	118	7	x	x	NOUN
ejpam-4207	118	8	,	,	PUNCT
ejpam-4207	118	9	mx	mx	NOUN
ejpam-4207	118	10	)	)	PUNCT
ejpam-4207	118	11	→	→	SYM
ejpam-4207	118	12	(	(	PUNCT
ejpam-4207	118	13	y	y	PROPN
ejpam-4207	118	14	,	,	PUNCT
ejpam-4207	118	15	σ	σ	PROPN
ejpam-4207	118	16	)	)	PUNCT
ejpam-4207	118	17	,	,	PUNCT
ejpam-4207	118	18	we	we	PRON
ejpam-4207	118	19	define	define	VERB
ejpam-4207	118	20	dm(f	dm(f	NOUN
ejpam-4207	118	21	)	)	PUNCT
ejpam-4207	118	22	as	as	SCONJ
ejpam-4207	118	23	follows	follow	VERB
ejpam-4207	118	24	:	:	PUNCT
ejpam-4207	118	25	dm(f	dm(f	NOUN
ejpam-4207	118	26	)	)	PUNCT
ejpam-4207	118	27	=	=	PUNCT
ejpam-4207	119	1	{	{	PUNCT
ejpam-4207	119	2	x	x	PUNCT
ejpam-4207	119	3	∈	∈	PROPN
ejpam-4207	119	4	x	x	X
ejpam-4207	119	5	:	:	PUNCT
ejpam-4207	119	6	f	f	X
ejpam-4207	119	7	is	be	AUX
ejpam-4207	119	8	not	not	PART
ejpam-4207	119	9	m	m	NOUN
ejpam-4207	119	10	-	-	ADJ
ejpam-4207	119	11	continuous	continuous	ADJ
ejpam-4207	119	12	at	at	ADP
ejpam-4207	119	13	x	x	X
ejpam-4207	119	14	}	}	PUNCT
ejpam-4207	119	15	.	.	PUNCT
ejpam-4207	120	1	theorem	theorem	NOUN
ejpam-4207	120	2	3	3	NUM
ejpam-4207	120	3	.	.	PUNCT
ejpam-4207	121	1	(	(	PUNCT
ejpam-4207	121	2	[	[	X
ejpam-4207	121	3	44	44	NUM
ejpam-4207	121	4	]	]	PUNCT
ejpam-4207	121	5	)	)	PUNCT
ejpam-4207	121	6	.	.	PUNCT
ejpam-4207	122	1	for	for	ADP
ejpam-4207	122	2	a	a	DET
ejpam-4207	122	3	multifunction	multifunction	NOUN
ejpam-4207	122	4	f	f	NOUN
ejpam-4207	122	5	:	:	PUNCT
ejpam-4207	122	6	(	(	PUNCT
ejpam-4207	122	7	x	x	NOUN
ejpam-4207	122	8	,	,	PUNCT
ejpam-4207	122	9	mx	mx	NOUN
ejpam-4207	122	10	)	)	PUNCT
ejpam-4207	122	11	→	→	SYM
ejpam-4207	122	12	(	(	PUNCT
ejpam-4207	122	13	y	y	PROPN
ejpam-4207	122	14	,	,	PUNCT
ejpam-4207	122	15	σ	σ	PROPN
ejpam-4207	122	16	)	)	PUNCT
ejpam-4207	122	17	,	,	PUNCT
ejpam-4207	122	18	the	the	DET
ejpam-4207	122	19	following	follow	VERB
ejpam-4207	122	20	equalities	equality	NOUN
ejpam-4207	122	21	hold	hold	VERB
ejpam-4207	122	22	:	:	PUNCT
ejpam-4207	122	23	dm(f	dm(f	NOUN
ejpam-4207	122	24	)	)	PUNCT
ejpam-4207	123	1	=	=	SYM
ejpam-4207	123	2	⋃	⋃	ADP
ejpam-4207	123	3	g1,g2∈σ{f	g1,g2∈σ{f	PROPN
ejpam-4207	123	4	+	+	PROPN
ejpam-4207	123	5	(	(	PUNCT
ejpam-4207	123	6	g1	g1	ADJ
ejpam-4207	123	7	)	)	PUNCT
ejpam-4207	123	8	∩	∩	NOUN
ejpam-4207	123	9	f−(g2)−mint(f+(g1	f−(g2)−mint(f+(g1	ADJ
ejpam-4207	123	10	)	)	PUNCT
ejpam-4207	123	11	∩	∩	NOUN
ejpam-4207	123	12	f−(g2	f−(g2	NUM
ejpam-4207	123	13	)	)	PUNCT
ejpam-4207	123	14	)	)	PUNCT
ejpam-4207	123	15	}	}	PUNCT
ejpam-4207	124	1	=	=	SYM
ejpam-4207	124	2	⋃	⋃	ADP
ejpam-4207	124	3	b1,b2∈p	b1,b2∈p	PROPN
ejpam-4207	124	4	(	(	PUNCT
ejpam-4207	124	5	y	y	PROPN
ejpam-4207	124	6	)	)	PUNCT
ejpam-4207	124	7	{	{	PUNCT
ejpam-4207	124	8	f−(int(b1	f−(int(b1	NOUN
ejpam-4207	124	9	)	)	PUNCT
ejpam-4207	124	10	)	)	PUNCT
ejpam-4207	124	11	∩	∩	NOUN
ejpam-4207	124	12	f+(int(b2))−mint(f−(b1	f+(int(b2))−mint(f−(b1	NOUN
ejpam-4207	124	13	)	)	PUNCT
ejpam-4207	124	14	∩	∩	NOUN
ejpam-4207	124	15	f+(b2	f+(b2	NOUN
ejpam-4207	124	16	)	)	PUNCT
ejpam-4207	124	17	)	)	PUNCT
ejpam-4207	124	18	}	}	PUNCT
ejpam-4207	125	1	=	=	SYM
ejpam-4207	125	2	⋃	⋃	ADP
ejpam-4207	125	3	b1,b2∈p	b1,b2∈p	PROPN
ejpam-4207	125	4	(	(	PUNCT
ejpam-4207	125	5	y	y	PROPN
ejpam-4207	125	6	)	)	PUNCT
ejpam-4207	125	7	{	{	PUNCT
ejpam-4207	125	8	mcl(f−(b1	mcl(f−(b1	NOUN
ejpam-4207	125	9	)	)	PUNCT
ejpam-4207	125	10	∪	∪	ADP
ejpam-4207	125	11	f+(b2))−	f+(b2))−	NOUN
ejpam-4207	125	12	[	[	X
ejpam-4207	125	13	f−(cl(b1	f−(cl(b1	NOUN
ejpam-4207	125	14	)	)	PUNCT
ejpam-4207	125	15	)	)	PUNCT
ejpam-4207	125	16	∪	∪	ADP
ejpam-4207	125	17	f+(cl(b2	f+(cl(b2	NOUN
ejpam-4207	125	18	)	)	PUNCT
ejpam-4207	125	19	)	)	PUNCT
ejpam-4207	125	20	]	]	PUNCT
ejpam-4207	125	21	}	}	PUNCT
ejpam-4207	125	22	=	=	SYM
ejpam-4207	125	23	⋃	⋃	PROPN
ejpam-4207	125	24	h1,h2∈f{mcl(f−(h1	h1,h2∈f{mcl(f−(h1	PROPN
ejpam-4207	125	25	)	)	PUNCT
ejpam-4207	125	26	∪	∪	ADP
ejpam-4207	125	27	f+(h2))−	f+(h2))−	PROPN
ejpam-4207	125	28	[	[	NOUN
ejpam-4207	125	29	f−(h1	f−(h1	NUM
ejpam-4207	125	30	)	)	PUNCT
ejpam-4207	125	31	∪	∪	ADP
ejpam-4207	125	32	f+(h2	f+(h2	NOUN
ejpam-4207	125	33	)	)	PUNCT
ejpam-4207	125	34	]	]	PUNCT
ejpam-4207	125	35	}	}	PUNCT
ejpam-4207	125	36	,	,	PUNCT
ejpam-4207	125	37	where	where	SCONJ
ejpam-4207	125	38	f	f	PROPN
ejpam-4207	125	39	is	be	AUX
ejpam-4207	125	40	the	the	DET
ejpam-4207	125	41	family	family	NOUN
ejpam-4207	125	42	of	of	ADP
ejpam-4207	125	43	closed	closed	ADJ
ejpam-4207	125	44	sets	set	NOUN
ejpam-4207	125	45	of	of	ADP
ejpam-4207	125	46	(	(	PUNCT
ejpam-4207	125	47	y	y	PROPN
ejpam-4207	125	48	,	,	PUNCT
ejpam-4207	125	49	σ	σ	PROPN
ejpam-4207	125	50	)	)	PUNCT
ejpam-4207	125	51	.	.	PUNCT
ejpam-4207	126	1	definition	definition	NOUN
ejpam-4207	126	2	7	7	NUM
ejpam-4207	126	3	.	.	PUNCT
ejpam-4207	127	1	(	(	PUNCT
ejpam-4207	127	2	[	[	X
ejpam-4207	127	3	42	42	NUM
ejpam-4207	127	4	]	]	PUNCT
ejpam-4207	127	5	)	)	PUNCT
ejpam-4207	127	6	.	.	PUNCT
ejpam-4207	128	1	let	let	AUX
ejpam-4207	128	2	(	(	PUNCT
ejpam-4207	128	3	x	x	NOUN
ejpam-4207	128	4	,	,	PUNCT
ejpam-4207	128	5	mx	mx	NOUN
ejpam-4207	128	6	)	)	PUNCT
ejpam-4207	128	7	be	be	AUX
ejpam-4207	128	8	an	an	DET
ejpam-4207	128	9	m	m	NOUN
ejpam-4207	128	10	-	-	NOUN
ejpam-4207	128	11	space	space	NOUN
ejpam-4207	128	12	.	.	PUNCT
ejpam-4207	129	1	for	for	ADP
ejpam-4207	129	2	a	a	DET
ejpam-4207	129	3	subset	subset	NOUN
ejpam-4207	129	4	a	a	PRON
ejpam-4207	129	5	of	of	ADP
ejpam-4207	129	6	x	x	PRON
ejpam-4207	129	7	,	,	PUNCT
ejpam-4207	129	8	the	the	DET
ejpam-4207	129	9	mx	mx	NOUN
ejpam-4207	129	10	-	-	NOUN
ejpam-4207	129	11	frontier	frontier	NOUN
ejpam-4207	129	12	mfr(a	mfr(a	NOUN
ejpam-4207	129	13	)	)	PUNCT
ejpam-4207	129	14	of	of	ADP
ejpam-4207	129	15	a	a	PRON
ejpam-4207	129	16	is	be	AUX
ejpam-4207	129	17	defined	define	VERB
ejpam-4207	129	18	as	as	SCONJ
ejpam-4207	129	19	follows	follow	VERB
ejpam-4207	129	20	:	:	PUNCT
ejpam-4207	129	21	mfr(a	mfr(a	NUM
ejpam-4207	129	22	)	)	PUNCT
ejpam-4207	129	23	=	=	SYM
ejpam-4207	129	24	mcl(a	mcl(a	X
ejpam-4207	129	25	)	)	PUNCT
ejpam-4207	129	26	∩mcl(x	∩mcl(x	SYM
ejpam-4207	129	27	−a	−a	NOUN
ejpam-4207	129	28	)	)	PUNCT
ejpam-4207	129	29	.	.	PUNCT
ejpam-4207	130	1	theorem	theorem	ADJ
ejpam-4207	130	2	4	4	NUM
ejpam-4207	130	3	.	.	PUNCT
ejpam-4207	131	1	(	(	PUNCT
ejpam-4207	131	2	[	[	X
ejpam-4207	131	3	42	42	NUM
ejpam-4207	131	4	]	]	PUNCT
ejpam-4207	131	5	)	)	PUNCT
ejpam-4207	131	6	.	.	PUNCT
ejpam-4207	132	1	the	the	DET
ejpam-4207	132	2	set	set	NOUN
ejpam-4207	132	3	of	of	ADP
ejpam-4207	132	4	all	all	DET
ejpam-4207	132	5	points	point	NOUN
ejpam-4207	132	6	x	x	X
ejpam-4207	132	7	∈	∈	NOUN
ejpam-4207	132	8	x	x	PUNCT
ejpam-4207	132	9	at	at	ADP
ejpam-4207	132	10	which	which	PRON
ejpam-4207	132	11	a	a	DET
ejpam-4207	132	12	multifunction	multifunction	NOUN
ejpam-4207	132	13	f	f	NOUN
ejpam-4207	132	14	:	:	PUNCT
ejpam-4207	132	15	(	(	PUNCT
ejpam-4207	132	16	x	x	X
ejpam-4207	132	17	,	,	PUNCT
ejpam-4207	132	18	τ	τ	PROPN
ejpam-4207	132	19	,	,	PUNCT
ejpam-4207	132	20	i	i	NOUN
ejpam-4207	132	21	)	)	PUNCT
ejpam-4207	132	22	→	→	SYM
ejpam-4207	132	23	(	(	PUNCT
ejpam-4207	132	24	y	y	PROPN
ejpam-4207	132	25	,	,	PUNCT
ejpam-4207	132	26	σ	σ	PROPN
ejpam-4207	132	27	)	)	PUNCT
ejpam-4207	132	28	is	be	AUX
ejpam-4207	132	29	not	not	PART
ejpam-4207	132	30	m	m	ADJ
ejpam-4207	132	31	-	-	ADJ
ejpam-4207	132	32	continuous	continuous	ADJ
ejpam-4207	132	33	is	be	AUX
ejpam-4207	132	34	identical	identical	ADJ
ejpam-4207	132	35	with	with	ADP
ejpam-4207	132	36	the	the	DET
ejpam-4207	132	37	union	union	NOUN
ejpam-4207	132	38	of	of	ADP
ejpam-4207	132	39	the	the	DET
ejpam-4207	132	40	mx	mx	NOUN
ejpam-4207	132	41	-	-	NOUN
ejpam-4207	132	42	frontiers	frontier	NOUN
ejpam-4207	132	43	of	of	ADP
ejpam-4207	132	44	the	the	DET
ejpam-4207	132	45	intersections	intersection	NOUN
ejpam-4207	132	46	of	of	ADP
ejpam-4207	132	47	upper	upper	ADJ
ejpam-4207	132	48	/	/	SYM
ejpam-4207	132	49	lower	low	ADJ
ejpam-4207	132	50	inverse	inverse	NOUN
ejpam-4207	132	51	images	image	NOUN
ejpam-4207	132	52	of	of	ADP
ejpam-4207	132	53	open	open	ADJ
ejpam-4207	132	54	sets	set	NOUN
ejpam-4207	132	55	containing	contain	VERB
ejpam-4207	132	56	/	/	SYM
ejpam-4207	132	57	meeting	meeting	NOUN
ejpam-4207	132	58	f	f	X
ejpam-4207	132	59	(	(	PUNCT
ejpam-4207	132	60	x	x	NOUN
ejpam-4207	132	61	)	)	PUNCT
ejpam-4207	132	62	.	.	PUNCT
ejpam-4207	133	1	definition	definition	NOUN
ejpam-4207	133	2	8	8	NUM
ejpam-4207	133	3	.	.	PUNCT
ejpam-4207	134	1	a	a	DET
ejpam-4207	134	2	subset	subset	NOUN
ejpam-4207	134	3	b	b	NOUN
ejpam-4207	134	4	of	of	ADP
ejpam-4207	134	5	a	a	DET
ejpam-4207	134	6	topological	topological	ADJ
ejpam-4207	134	7	space	space	NOUN
ejpam-4207	134	8	(	(	PUNCT
ejpam-4207	134	9	y	y	PROPN
ejpam-4207	134	10	,	,	PUNCT
ejpam-4207	134	11	σ	σ	PROPN
ejpam-4207	134	12	)	)	PUNCT
ejpam-4207	134	13	is	be	AUX
ejpam-4207	134	14	said	say	VERB
ejpam-4207	134	15	to	to	PART
ejpam-4207	134	16	be	be	AUX
ejpam-4207	134	17	(	(	PUNCT
ejpam-4207	134	18	1	1	X
ejpam-4207	134	19	)	)	PUNCT
ejpam-4207	134	20	α	α	NOUN
ejpam-4207	134	21	-	-	ADJ
ejpam-4207	134	22	regular	regular	ADJ
ejpam-4207	134	23	[	[	X
ejpam-4207	134	24	19	19	NUM
ejpam-4207	134	25	]	]	X
ejpam-4207	134	26	if	if	SCONJ
ejpam-4207	134	27	for	for	ADP
ejpam-4207	134	28	each	each	DET
ejpam-4207	134	29	b	b	PROPN
ejpam-4207	134	30	∈	∈	PROPN
ejpam-4207	134	31	b	b	PROPN
ejpam-4207	134	32	and	and	CCONJ
ejpam-4207	134	33	any	any	DET
ejpam-4207	134	34	open	open	ADJ
ejpam-4207	134	35	set	set	NOUN
ejpam-4207	134	36	u	u	NOUN
ejpam-4207	134	37	containing	contain	VERB
ejpam-4207	134	38	b	b	NUM
ejpam-4207	134	39	,	,	PUNCT
ejpam-4207	134	40	there	there	PRON
ejpam-4207	134	41	exists	exist	VERB
ejpam-4207	134	42	an	an	DET
ejpam-4207	134	43	takashi	takashi	PROPN
ejpam-4207	134	44	noiri	noiri	PROPN
ejpam-4207	134	45	,	,	PUNCT
ejpam-4207	134	46	valeriu	valeriu	ADJ
ejpam-4207	134	47	popa	popa	NOUN
ejpam-4207	134	48	/	/	SYM
ejpam-4207	134	49	eur	eur	PROPN
ejpam-4207	134	50	.	.	PUNCT
ejpam-4207	135	1	j.	j.	PROPN
ejpam-4207	135	2	pure	pure	PROPN
ejpam-4207	135	3	appl	appl	PROPN
ejpam-4207	135	4	.	.	PROPN
ejpam-4207	135	5	math	math	PROPN
ejpam-4207	135	6	,	,	PUNCT
ejpam-4207	135	7	15	15	NUM
ejpam-4207	135	8	(	(	PUNCT
ejpam-4207	135	9	1	1	NUM
ejpam-4207	135	10	)	)	PUNCT
ejpam-4207	135	11	(	(	PUNCT
ejpam-4207	135	12	2022	2022	NUM
ejpam-4207	135	13	)	)	PUNCT
ejpam-4207	135	14	,	,	PUNCT
ejpam-4207	135	15	1	1	NUM
ejpam-4207	135	16	-	-	SYM
ejpam-4207	135	17	14	14	NUM
ejpam-4207	135	18	5	5	NUM
ejpam-4207	135	19	open	open	ADJ
ejpam-4207	135	20	set	set	VERB
ejpam-4207	135	21	g	g	NOUN
ejpam-4207	135	22	of	of	ADP
ejpam-4207	135	23	y	y	PRON
ejpam-4207	136	1	such	such	ADJ
ejpam-4207	136	2	that	that	PRON
ejpam-4207	136	3	b	b	X
ejpam-4207	136	4	∈	∈	PROPN
ejpam-4207	136	5	g	g	PROPN
ejpam-4207	136	6	⊂	⊂	PROPN
ejpam-4207	136	7	cl(g	cl(g	X
ejpam-4207	136	8	)	)	PUNCT
ejpam-4207	136	9	⊂	⊂	PROPN
ejpam-4207	136	10	u	u	PROPN
ejpam-4207	136	11	,	,	PUNCT
ejpam-4207	136	12	(	(	PUNCT
ejpam-4207	136	13	2	2	X
ejpam-4207	136	14	)	)	PUNCT
ejpam-4207	136	15	α	α	NOUN
ejpam-4207	136	16	-	-	NOUN
ejpam-4207	136	17	paracompact	paracompact	NOUN
ejpam-4207	136	18	[	[	X
ejpam-4207	136	19	48	48	NUM
ejpam-4207	136	20	]	]	PUNCT
ejpam-4207	136	21	if	if	SCONJ
ejpam-4207	136	22	every	every	DET
ejpam-4207	136	23	σ	σ	NOUN
ejpam-4207	136	24	-	-	PUNCT
ejpam-4207	136	25	open	open	ADJ
ejpam-4207	136	26	cover	cover	NOUN
ejpam-4207	136	27	of	of	ADP
ejpam-4207	136	28	b	b	PROPN
ejpam-4207	136	29	has	have	VERB
ejpam-4207	136	30	a	a	DET
ejpam-4207	136	31	σ	σ	NOUN
ejpam-4207	136	32	-	-	PUNCT
ejpam-4207	136	33	open	open	ADJ
ejpam-4207	136	34	refinement	refinement	NOUN
ejpam-4207	136	35	which	which	PRON
ejpam-4207	136	36	covers	cover	VERB
ejpam-4207	136	37	b	b	NOUN
ejpam-4207	136	38	and	and	CCONJ
ejpam-4207	136	39	is	be	AUX
ejpam-4207	136	40	locally	locally	ADV
ejpam-4207	136	41	finite	finite	ADJ
ejpam-4207	136	42	for	for	ADP
ejpam-4207	136	43	each	each	DET
ejpam-4207	136	44	point	point	NOUN
ejpam-4207	136	45	of	of	ADP
ejpam-4207	136	46	y	y	PROPN
ejpam-4207	136	47	.	.	PUNCT
ejpam-4207	136	48	for	for	ADP
ejpam-4207	136	49	a	a	DET
ejpam-4207	136	50	multifunction	multifunction	NOUN
ejpam-4207	136	51	f	f	NOUN
ejpam-4207	136	52	:	:	PUNCT
ejpam-4207	136	53	(	(	PUNCT
ejpam-4207	136	54	x	x	NOUN
ejpam-4207	136	55	,	,	PUNCT
ejpam-4207	136	56	mx	mx	NOUN
ejpam-4207	136	57	)	)	PUNCT
ejpam-4207	136	58	→	→	SYM
ejpam-4207	136	59	(	(	PUNCT
ejpam-4207	136	60	y	y	PROPN
ejpam-4207	136	61	,	,	PUNCT
ejpam-4207	136	62	σ	σ	PROPN
ejpam-4207	136	63	)	)	PUNCT
ejpam-4207	136	64	,	,	PUNCT
ejpam-4207	136	65	by	by	ADP
ejpam-4207	136	66	cl(f	cl(f	PROPN
ejpam-4207	136	67	)	)	PUNCT
ejpam-4207	136	68	:	:	PUNCT
ejpam-4207	137	1	x	x	X
ejpam-4207	137	2	→	→	SYM
ejpam-4207	137	3	y	y	PROPN
ejpam-4207	138	1	[	[	X
ejpam-4207	138	2	6	6	NUM
ejpam-4207	138	3	]	]	PUNCT
ejpam-4207	138	4	we	we	PRON
ejpam-4207	138	5	denote	denote	VERB
ejpam-4207	138	6	a	a	DET
ejpam-4207	138	7	multifunction	multifunction	NOUN
ejpam-4207	138	8	defined	define	VERB
ejpam-4207	138	9	as	as	SCONJ
ejpam-4207	138	10	follows	follow	VERB
ejpam-4207	138	11	:	:	PUNCT
ejpam-4207	138	12	cl(f	cl(f	NUM
ejpam-4207	138	13	)	)	PUNCT
ejpam-4207	138	14	(	(	PUNCT
ejpam-4207	138	15	x	x	X
ejpam-4207	138	16	)	)	PUNCT
ejpam-4207	138	17	=	=	SYM
ejpam-4207	138	18	cl(f	cl(f	PROPN
ejpam-4207	138	19	(	(	PUNCT
ejpam-4207	138	20	x	x	NOUN
ejpam-4207	138	21	)	)	PUNCT
ejpam-4207	138	22	)	)	PUNCT
ejpam-4207	138	23	for	for	ADP
ejpam-4207	138	24	each	each	DET
ejpam-4207	138	25	x	x	SYM
ejpam-4207	138	26	∈	∈	PROPN
ejpam-4207	138	27	x.	x.	NOUN
ejpam-4207	138	28	similarly	similarly	ADV
ejpam-4207	138	29	,	,	PUNCT
ejpam-4207	138	30	scl(f	scl(f	PROPN
ejpam-4207	138	31	)	)	PUNCT
ejpam-4207	138	32	(	(	PUNCT
ejpam-4207	138	33	resp	resp	NOUN
ejpam-4207	138	34	.	.	PUNCT
ejpam-4207	139	1	pcl(f	pcl(f	PROPN
ejpam-4207	139	2	)	)	PUNCT
ejpam-4207	139	3	,	,	PUNCT
ejpam-4207	139	4	αcl(f	αcl(f	PROPN
ejpam-4207	139	5	)	)	PUNCT
ejpam-4207	139	6	,	,	PUNCT
ejpam-4207	139	7	bcl(f	bcl(f	NOUN
ejpam-4207	139	8	)	)	PUNCT
ejpam-4207	139	9	,	,	PUNCT
ejpam-4207	139	10	βcl(f	βcl(f	PROPN
ejpam-4207	139	11	)	)	PUNCT
ejpam-4207	139	12	)	)	PUNCT
ejpam-4207	139	13	is	be	AUX
ejpam-4207	139	14	defined	define	VERB
ejpam-4207	139	15	in	in	ADP
ejpam-4207	139	16	[	[	X
ejpam-4207	139	17	32	32	NUM
ejpam-4207	139	18	]	]	PUNCT
ejpam-4207	139	19	(	(	PUNCT
ejpam-4207	139	20	resp	resp	NOUN
ejpam-4207	139	21	.	.	PUNCT
ejpam-4207	140	1	[	[	X
ejpam-4207	140	2	34	34	NUM
ejpam-4207	140	3	]	]	PUNCT
ejpam-4207	140	4	,	,	PUNCT
ejpam-4207	140	5	[	[	X
ejpam-4207	140	6	35	35	NUM
ejpam-4207	140	7	]	]	PUNCT
ejpam-4207	140	8	,	,	PUNCT
ejpam-4207	140	9	[	[	X
ejpam-4207	140	10	8	8	NUM
ejpam-4207	140	11	]	]	PUNCT
ejpam-4207	140	12	,	,	PUNCT
ejpam-4207	140	13	[	[	X
ejpam-4207	140	14	38	38	NUM
ejpam-4207	140	15	]	]	PUNCT
ejpam-4207	140	16	)	)	PUNCT
ejpam-4207	140	17	.	.	PUNCT
ejpam-4207	141	1	theorem	theorem	ADJ
ejpam-4207	141	2	5	5	NUM
ejpam-4207	141	3	.	.	PUNCT
ejpam-4207	142	1	(	(	PUNCT
ejpam-4207	142	2	[	[	X
ejpam-4207	142	3	42	42	NUM
ejpam-4207	142	4	]	]	PUNCT
ejpam-4207	142	5	)	)	PUNCT
ejpam-4207	142	6	.	.	PUNCT
ejpam-4207	143	1	let	let	VERB
ejpam-4207	143	2	f	f	NOUN
ejpam-4207	143	3	:	:	PUNCT
ejpam-4207	143	4	(	(	PUNCT
ejpam-4207	143	5	x	x	NOUN
ejpam-4207	143	6	,	,	PUNCT
ejpam-4207	143	7	mx	mx	NOUN
ejpam-4207	143	8	)	)	PUNCT
ejpam-4207	143	9	→	→	SYM
ejpam-4207	143	10	(	(	PUNCT
ejpam-4207	143	11	y	y	PROPN
ejpam-4207	143	12	,	,	PUNCT
ejpam-4207	143	13	σ	σ	PROPN
ejpam-4207	143	14	)	)	PUNCT
ejpam-4207	143	15	be	be	VERB
ejpam-4207	143	16	a	a	DET
ejpam-4207	143	17	multifunction	multifunction	NOUN
ejpam-4207	143	18	such	such	ADJ
ejpam-4207	143	19	that	that	SCONJ
ejpam-4207	143	20	f	f	PROPN
ejpam-4207	143	21	(	(	PUNCT
ejpam-4207	143	22	x	x	X
ejpam-4207	143	23	)	)	PUNCT
ejpam-4207	143	24	is	be	AUX
ejpam-4207	143	25	αregular	αregular	ADJ
ejpam-4207	143	26	and	and	CCONJ
ejpam-4207	143	27	α	α	NOUN
ejpam-4207	143	28	-	-	NOUN
ejpam-4207	143	29	paracompact	paracompact	NOUN
ejpam-4207	143	30	for	for	ADP
ejpam-4207	143	31	each	each	DET
ejpam-4207	143	32	x	x	SYM
ejpam-4207	143	33	∈	∈	PROPN
ejpam-4207	143	34	x.	x.	NOUN
ejpam-4207	143	35	then	then	ADV
ejpam-4207	143	36	the	the	DET
ejpam-4207	143	37	following	follow	VERB
ejpam-4207	143	38	properties	property	NOUN
ejpam-4207	143	39	are	be	AUX
ejpam-4207	143	40	equivalent	equivalent	ADJ
ejpam-4207	143	41	:	:	PUNCT
ejpam-4207	143	42	(	(	PUNCT
ejpam-4207	143	43	1	1	X
ejpam-4207	143	44	)	)	PUNCT
ejpam-4207	143	45	f	f	PROPN
ejpam-4207	143	46	is	be	AUX
ejpam-4207	143	47	m	m	NOUN
ejpam-4207	143	48	-	-	ADJ
ejpam-4207	143	49	continuous	continuous	ADJ
ejpam-4207	143	50	;	;	PUNCT
ejpam-4207	143	51	(	(	PUNCT
ejpam-4207	143	52	2	2	X
ejpam-4207	143	53	)	)	PUNCT
ejpam-4207	143	54	g	g	NOUN
ejpam-4207	143	55	is	be	AUX
ejpam-4207	143	56	m	m	NOUN
ejpam-4207	143	57	-	-	ADJ
ejpam-4207	143	58	continuous	continuous	ADJ
ejpam-4207	143	59	,	,	PUNCT
ejpam-4207	143	60	where	where	SCONJ
ejpam-4207	143	61	g	g	PROPN
ejpam-4207	143	62	=	=	SYM
ejpam-4207	143	63	cl(f	cl(f	PROPN
ejpam-4207	143	64	)	)	PUNCT
ejpam-4207	143	65	,	,	PUNCT
ejpam-4207	143	66	scl(f	scl(f	PROPN
ejpam-4207	143	67	)	)	PUNCT
ejpam-4207	143	68	,	,	PUNCT
ejpam-4207	143	69	pcl(f	pcl(f	PROPN
ejpam-4207	143	70	)	)	PUNCT
ejpam-4207	143	71	,	,	PUNCT
ejpam-4207	143	72	αcl(f	αcl(f	PROPN
ejpam-4207	143	73	)	)	PUNCT
ejpam-4207	143	74	,	,	PUNCT
ejpam-4207	143	75	bcl(f	bcl(f	NOUN
ejpam-4207	143	76	)	)	PUNCT
ejpam-4207	143	77	,	,	PUNCT
ejpam-4207	143	78	and	and	CCONJ
ejpam-4207	143	79	βcl(f	βcl(f	X
ejpam-4207	143	80	)	)	PUNCT
ejpam-4207	143	81	.	.	PUNCT
ejpam-4207	144	1	definition	definition	NOUN
ejpam-4207	144	2	9	9	NUM
ejpam-4207	144	3	.	.	PUNCT
ejpam-4207	145	1	(	(	PUNCT
ejpam-4207	145	2	[	[	X
ejpam-4207	145	3	42	42	NUM
ejpam-4207	145	4	]	]	PUNCT
ejpam-4207	145	5	)	)	PUNCT
ejpam-4207	145	6	.	.	PUNCT
ejpam-4207	146	1	a	a	DET
ejpam-4207	146	2	multifunction	multifunction	NOUN
ejpam-4207	146	3	f	f	NOUN
ejpam-4207	146	4	:	:	PUNCT
ejpam-4207	146	5	(	(	PUNCT
ejpam-4207	146	6	x	x	NOUN
ejpam-4207	146	7	,	,	PUNCT
ejpam-4207	146	8	mx	mx	NOUN
ejpam-4207	146	9	)	)	PUNCT
ejpam-4207	146	10	→	→	SYM
ejpam-4207	146	11	(	(	PUNCT
ejpam-4207	146	12	y	y	PROPN
ejpam-4207	146	13	,	,	PUNCT
ejpam-4207	146	14	σ	σ	PROPN
ejpam-4207	146	15	)	)	PUNCT
ejpam-4207	146	16	is	be	AUX
ejpam-4207	146	17	said	say	VERB
ejpam-4207	146	18	to	to	PART
ejpam-4207	146	19	be	be	AUX
ejpam-4207	146	20	(	(	PUNCT
ejpam-4207	146	21	1	1	NUM
ejpam-4207	146	22	)	)	PUNCT
ejpam-4207	146	23	upper	upper	ADJ
ejpam-4207	146	24	m	m	NOUN
ejpam-4207	146	25	-	-	ADJ
ejpam-4207	146	26	continuous	continuous	ADJ
ejpam-4207	146	27	at	at	ADP
ejpam-4207	146	28	x	x	X
ejpam-4207	146	29	∈	∈	PROPN
ejpam-4207	146	30	x	x	SYM
ejpam-4207	146	31	if	if	SCONJ
ejpam-4207	146	32	for	for	ADP
ejpam-4207	146	33	each	each	DET
ejpam-4207	146	34	open	open	ADJ
ejpam-4207	146	35	set	set	VERB
ejpam-4207	146	36	v	v	NOUN
ejpam-4207	146	37	containing	contain	VERB
ejpam-4207	146	38	f	f	X
ejpam-4207	146	39	(	(	PUNCT
ejpam-4207	146	40	x	x	NOUN
ejpam-4207	146	41	)	)	PUNCT
ejpam-4207	146	42	,	,	PUNCT
ejpam-4207	146	43	there	there	PRON
ejpam-4207	146	44	exists	exist	VERB
ejpam-4207	146	45	u	u	PROPN
ejpam-4207	146	46	∈	∈	PROPN
ejpam-4207	146	47	mx	mx	NOUN
ejpam-4207	146	48	containing	contain	VERB
ejpam-4207	146	49	x	x	PUNCT
ejpam-4207	146	50	such	such	ADJ
ejpam-4207	146	51	that	that	SCONJ
ejpam-4207	146	52	f	f	PROPN
ejpam-4207	146	53	(	(	PUNCT
ejpam-4207	146	54	u	u	NOUN
ejpam-4207	146	55	)	)	PUNCT
ejpam-4207	146	56	⊂	⊂	PROPN
ejpam-4207	146	57	v	v	PROPN
ejpam-4207	146	58	,	,	PUNCT
ejpam-4207	146	59	(	(	PUNCT
ejpam-4207	146	60	2	2	NUM
ejpam-4207	146	61	)	)	PUNCT
ejpam-4207	146	62	lower	low	ADJ
ejpam-4207	146	63	m	m	NOUN
ejpam-4207	146	64	-	-	ADJ
ejpam-4207	146	65	continuous	continuous	ADJ
ejpam-4207	146	66	at	at	ADP
ejpam-4207	146	67	x	x	X
ejpam-4207	146	68	∈	∈	PROPN
ejpam-4207	146	69	x	x	SYM
ejpam-4207	146	70	if	if	SCONJ
ejpam-4207	146	71	for	for	ADP
ejpam-4207	146	72	each	each	DET
ejpam-4207	146	73	open	open	ADJ
ejpam-4207	146	74	set	set	VERB
ejpam-4207	146	75	v	v	NUM
ejpam-4207	146	76	meeting	meeting	NOUN
ejpam-4207	146	77	f	f	X
ejpam-4207	146	78	(	(	PUNCT
ejpam-4207	146	79	x	x	NOUN
ejpam-4207	146	80	)	)	PUNCT
ejpam-4207	146	81	,	,	PUNCT
ejpam-4207	146	82	there	there	PRON
ejpam-4207	146	83	exists	exist	VERB
ejpam-4207	146	84	u	u	PROPN
ejpam-4207	146	85	∈	∈	PROPN
ejpam-4207	146	86	mx	mx	NOUN
ejpam-4207	146	87	containing	contain	VERB
ejpam-4207	146	88	x	x	PUNCT
ejpam-4207	146	89	such	such	ADJ
ejpam-4207	146	90	that	that	SCONJ
ejpam-4207	146	91	f	f	PROPN
ejpam-4207	146	92	(	(	PUNCT
ejpam-4207	146	93	u	u	NOUN
ejpam-4207	146	94	)	)	PUNCT
ejpam-4207	146	95	∩	∩	NOUN
ejpam-4207	146	96	v	v	ADP
ejpam-4207	146	97	̸=	̸=	PROPN
ejpam-4207	146	98	∅	∅	NOUN
ejpam-4207	146	99	for	for	ADP
ejpam-4207	146	100	every	every	DET
ejpam-4207	146	101	u	u	PROPN
ejpam-4207	146	102	∈	∈	PROPN
ejpam-4207	146	103	u	u	NOUN
ejpam-4207	146	104	,	,	PUNCT
ejpam-4207	146	105	(	(	PUNCT
ejpam-4207	146	106	3	3	X
ejpam-4207	146	107	)	)	PUNCT
ejpam-4207	146	108	upper	upper	ADJ
ejpam-4207	146	109	/	/	SYM
ejpam-4207	146	110	lower	low	ADJ
ejpam-4207	146	111	m	m	NOUN
ejpam-4207	146	112	-	-	ADJ
ejpam-4207	146	113	continuous	continuous	ADJ
ejpam-4207	146	114	if	if	SCONJ
ejpam-4207	146	115	it	it	PRON
ejpam-4207	146	116	has	have	VERB
ejpam-4207	146	117	this	this	DET
ejpam-4207	146	118	property	property	NOUN
ejpam-4207	146	119	at	at	ADP
ejpam-4207	146	120	each	each	DET
ejpam-4207	146	121	point	point	NOUN
ejpam-4207	146	122	x	x	X
ejpam-4207	146	123	∈	∈	PROPN
ejpam-4207	146	124	x.	x.	NOUN
ejpam-4207	146	125	theorem	theorem	VERB
ejpam-4207	146	126	6	6	NUM
ejpam-4207	146	127	.	.	PUNCT
ejpam-4207	147	1	(	(	PUNCT
ejpam-4207	147	2	[	[	X
ejpam-4207	147	3	42	42	NUM
ejpam-4207	147	4	]	]	PUNCT
ejpam-4207	147	5	)	)	PUNCT
ejpam-4207	147	6	.	.	PUNCT
ejpam-4207	148	1	let	let	VERB
ejpam-4207	148	2	x	x	PRON
ejpam-4207	148	3	be	be	AUX
ejpam-4207	148	4	a	a	DET
ejpam-4207	148	5	nonempty	nonempty	NOUN
ejpam-4207	148	6	set	set	VERB
ejpam-4207	148	7	with	with	ADP
ejpam-4207	148	8	two	two	NUM
ejpam-4207	148	9	m	m	NOUN
ejpam-4207	148	10	-	-	PUNCT
ejpam-4207	148	11	structures	structure	NOUN
ejpam-4207	148	12	m1	m1	NOUN
ejpam-4207	148	13	x	x	X
ejpam-4207	148	14	and	and	CCONJ
ejpam-4207	148	15	m2	m2	PROPN
ejpam-4207	148	16	x	x	PUNCT
ejpam-4207	148	17	satisfying	satisfy	VERB
ejpam-4207	148	18	property	property	NOUN
ejpam-4207	148	19	b	b	PROPN
ejpam-4207	148	20	such	such	ADJ
ejpam-4207	148	21	that	that	DET
ejpam-4207	148	22	v1	v1	PROPN
ejpam-4207	148	23	∈	∈	PROPN
ejpam-4207	148	24	m1	m1	NOUN
ejpam-4207	148	25	x	x	PUNCT
ejpam-4207	148	26	and	and	CCONJ
ejpam-4207	148	27	v2	v2	PROPN
ejpam-4207	148	28	∈	∈	PROPN
ejpam-4207	148	29	m2	m2	PROPN
ejpam-4207	148	30	x	x	PROPN
ejpam-4207	148	31	implies	imply	VERB
ejpam-4207	148	32	v1	v1	NOUN
ejpam-4207	148	33	∩	∩	ADJ
ejpam-4207	148	34	v2	v2	PROPN
ejpam-4207	148	35	∈	∈	PROPN
ejpam-4207	148	36	m1	m1	NOUN
ejpam-4207	148	37	x	x	PUNCT
ejpam-4207	148	38	.	.	PUNCT
ejpam-4207	149	1	if	if	SCONJ
ejpam-4207	149	2	a	a	DET
ejpam-4207	149	3	multifunction	multifunction	NOUN
ejpam-4207	149	4	f	f	NOUN
ejpam-4207	149	5	:	:	PUNCT
ejpam-4207	149	6	(	(	PUNCT
ejpam-4207	149	7	x	x	X
ejpam-4207	149	8	,	,	PUNCT
ejpam-4207	149	9	m1	m1	PROPN
ejpam-4207	149	10	x	x	SYM
ejpam-4207	149	11	)	)	PUNCT
ejpam-4207	149	12	→	→	SYM
ejpam-4207	149	13	(	(	PUNCT
ejpam-4207	149	14	y	y	PROPN
ejpam-4207	149	15	,	,	PUNCT
ejpam-4207	149	16	σ	σ	PROPN
ejpam-4207	149	17	)	)	PUNCT
ejpam-4207	149	18	is	be	AUX
ejpam-4207	149	19	upper	upper	ADJ
ejpam-4207	149	20	m	m	ADJ
ejpam-4207	149	21	-	-	ADJ
ejpam-4207	149	22	continuous	continuous	ADJ
ejpam-4207	149	23	and	and	CCONJ
ejpam-4207	149	24	f	f	NOUN
ejpam-4207	149	25	:	:	PUNCT
ejpam-4207	149	26	(	(	PUNCT
ejpam-4207	149	27	x	x	X
ejpam-4207	149	28	,	,	PUNCT
ejpam-4207	149	29	m2	m2	PROPN
ejpam-4207	149	30	x	x	PROPN
ejpam-4207	149	31	)	)	PUNCT
ejpam-4207	149	32	→	→	SYM
ejpam-4207	149	33	(	(	PUNCT
ejpam-4207	149	34	y	y	PROPN
ejpam-4207	149	35	,	,	PUNCT
ejpam-4207	149	36	σ	σ	PROPN
ejpam-4207	149	37	)	)	PUNCT
ejpam-4207	149	38	is	be	AUX
ejpam-4207	149	39	lower	low	ADJ
ejpam-4207	149	40	mcontinuous	mcontinuous	ADJ
ejpam-4207	149	41	,	,	PUNCT
ejpam-4207	149	42	then	then	ADV
ejpam-4207	149	43	f	f	X
ejpam-4207	149	44	:	:	PUNCT
ejpam-4207	149	45	(	(	PUNCT
ejpam-4207	149	46	x	x	X
ejpam-4207	149	47	,	,	PUNCT
ejpam-4207	149	48	m1	m1	PROPN
ejpam-4207	149	49	x	x	SYM
ejpam-4207	149	50	)	)	PUNCT
ejpam-4207	149	51	→	→	SYM
ejpam-4207	149	52	(	(	PUNCT
ejpam-4207	149	53	y	y	PROPN
ejpam-4207	149	54	,	,	PUNCT
ejpam-4207	149	55	σ	σ	PROPN
ejpam-4207	149	56	)	)	PUNCT
ejpam-4207	149	57	is	be	AUX
ejpam-4207	149	58	m	m	ADJ
ejpam-4207	149	59	-	-	ADJ
ejpam-4207	149	60	continuous	continuous	ADJ
ejpam-4207	149	61	.	.	PUNCT
ejpam-4207	150	1	theorem	theorem	ADJ
ejpam-4207	150	2	7	7	NUM
ejpam-4207	150	3	.	.	PUNCT
ejpam-4207	151	1	(	(	PUNCT
ejpam-4207	151	2	[	[	X
ejpam-4207	151	3	42	42	NUM
ejpam-4207	151	4	]	]	PUNCT
ejpam-4207	151	5	)	)	PUNCT
ejpam-4207	151	6	.	.	PUNCT
ejpam-4207	152	1	let	let	VERB
ejpam-4207	152	2	x	x	PRON
ejpam-4207	152	3	be	be	AUX
ejpam-4207	152	4	a	a	DET
ejpam-4207	152	5	nonempty	nonempty	NOUN
ejpam-4207	152	6	set	set	VERB
ejpam-4207	152	7	with	with	ADP
ejpam-4207	152	8	two	two	NUM
ejpam-4207	152	9	m	m	NOUN
ejpam-4207	152	10	-	-	PUNCT
ejpam-4207	152	11	structures	structure	NOUN
ejpam-4207	152	12	m1	m1	NOUN
ejpam-4207	152	13	x	x	X
ejpam-4207	152	14	and	and	CCONJ
ejpam-4207	152	15	m2	m2	PROPN
ejpam-4207	152	16	x	x	PUNCT
ejpam-4207	152	17	satisfying	satisfy	VERB
ejpam-4207	152	18	property	property	NOUN
ejpam-4207	152	19	b	b	PROPN
ejpam-4207	152	20	such	such	ADJ
ejpam-4207	152	21	that	that	DET
ejpam-4207	152	22	v1	v1	PROPN
ejpam-4207	152	23	∈	∈	PROPN
ejpam-4207	152	24	m1	m1	NOUN
ejpam-4207	152	25	x	x	PUNCT
ejpam-4207	152	26	and	and	CCONJ
ejpam-4207	152	27	v2	v2	PROPN
ejpam-4207	152	28	∈	∈	PROPN
ejpam-4207	152	29	m2	m2	PROPN
ejpam-4207	152	30	x	x	PROPN
ejpam-4207	152	31	implies	imply	VERB
ejpam-4207	152	32	v1	v1	NOUN
ejpam-4207	152	33	∩	∩	ADJ
ejpam-4207	152	34	v2	v2	PROPN
ejpam-4207	152	35	∈	∈	PROPN
ejpam-4207	152	36	m1	m1	NOUN
ejpam-4207	152	37	x	x	PUNCT
ejpam-4207	152	38	.	.	PUNCT
ejpam-4207	153	1	if	if	SCONJ
ejpam-4207	153	2	a	a	DET
ejpam-4207	153	3	multifunction	multifunction	NOUN
ejpam-4207	153	4	f	f	NOUN
ejpam-4207	153	5	:	:	PUNCT
ejpam-4207	153	6	(	(	PUNCT
ejpam-4207	153	7	x	x	X
ejpam-4207	153	8	,	,	PUNCT
ejpam-4207	153	9	m1	m1	PROPN
ejpam-4207	153	10	x	x	SYM
ejpam-4207	153	11	)	)	PUNCT
ejpam-4207	153	12	→	→	SYM
ejpam-4207	153	13	(	(	PUNCT
ejpam-4207	153	14	y	y	PROPN
ejpam-4207	153	15	,	,	PUNCT
ejpam-4207	153	16	σ	σ	PROPN
ejpam-4207	153	17	)	)	PUNCT
ejpam-4207	153	18	is	be	AUX
ejpam-4207	153	19	lower	low	ADJ
ejpam-4207	153	20	m	m	ADJ
ejpam-4207	153	21	-	-	ADJ
ejpam-4207	153	22	continuous	continuous	ADJ
ejpam-4207	153	23	and	and	CCONJ
ejpam-4207	153	24	f	f	NOUN
ejpam-4207	153	25	:	:	PUNCT
ejpam-4207	153	26	(	(	PUNCT
ejpam-4207	153	27	x	x	X
ejpam-4207	153	28	,	,	PUNCT
ejpam-4207	153	29	m2	m2	PROPN
ejpam-4207	153	30	x	x	PROPN
ejpam-4207	153	31	)	)	PUNCT
ejpam-4207	153	32	→	→	SYM
ejpam-4207	153	33	(	(	PUNCT
ejpam-4207	153	34	y	y	PROPN
ejpam-4207	153	35	,	,	PUNCT
ejpam-4207	153	36	σ	σ	PROPN
ejpam-4207	153	37	)	)	PUNCT
ejpam-4207	153	38	is	be	AUX
ejpam-4207	153	39	upper	upper	ADJ
ejpam-4207	153	40	mcontinuous	mcontinuous	ADJ
ejpam-4207	153	41	,	,	PUNCT
ejpam-4207	153	42	then	then	ADV
ejpam-4207	153	43	f	f	X
ejpam-4207	153	44	:	:	PUNCT
ejpam-4207	153	45	(	(	PUNCT
ejpam-4207	153	46	x	x	X
ejpam-4207	153	47	,	,	PUNCT
ejpam-4207	153	48	m1	m1	PROPN
ejpam-4207	153	49	x	x	SYM
ejpam-4207	153	50	)	)	PUNCT
ejpam-4207	153	51	→	→	SYM
ejpam-4207	153	52	(	(	PUNCT
ejpam-4207	153	53	y	y	PROPN
ejpam-4207	153	54	,	,	PUNCT
ejpam-4207	153	55	σ	σ	PROPN
ejpam-4207	153	56	)	)	PUNCT
ejpam-4207	153	57	is	be	AUX
ejpam-4207	153	58	m	m	NOUN
ejpam-4207	153	59	-	-	ADJ
ejpam-4207	153	60	continuous	continuous	ADJ
ejpam-4207	153	61	.	.	PUNCT
ejpam-4207	154	1	4	4	X
ejpam-4207	154	2	.	.	X
ejpam-4207	154	3	ideal	ideal	ADJ
ejpam-4207	154	4	topological	topological	ADJ
ejpam-4207	154	5	spaces	space	NOUN
ejpam-4207	154	6	let	let	VERB
ejpam-4207	154	7	(	(	PUNCT
ejpam-4207	154	8	x	x	NOUN
ejpam-4207	154	9	,	,	PUNCT
ejpam-4207	154	10	τ	τ	X
ejpam-4207	154	11	)	)	PUNCT
ejpam-4207	154	12	be	be	VERB
ejpam-4207	154	13	a	a	DET
ejpam-4207	154	14	topological	topological	ADJ
ejpam-4207	154	15	space	space	NOUN
ejpam-4207	154	16	.	.	PUNCT
ejpam-4207	155	1	the	the	DET
ejpam-4207	155	2	notion	notion	NOUN
ejpam-4207	155	3	of	of	ADP
ejpam-4207	155	4	ideals	ideal	NOUN
ejpam-4207	155	5	has	have	AUX
ejpam-4207	155	6	been	be	AUX
ejpam-4207	155	7	introduced	introduce	VERB
ejpam-4207	155	8	in	in	ADP
ejpam-4207	155	9	[	[	X
ejpam-4207	155	10	20	20	NUM
ejpam-4207	155	11	]	]	PUNCT
ejpam-4207	155	12	and	and	CCONJ
ejpam-4207	155	13	[	[	X
ejpam-4207	155	14	47	47	NUM
ejpam-4207	155	15	]	]	PUNCT
ejpam-4207	155	16	and	and	CCONJ
ejpam-4207	155	17	further	far	ADV
ejpam-4207	155	18	investigated	investigate	VERB
ejpam-4207	155	19	in	in	ADP
ejpam-4207	155	20	[	[	X
ejpam-4207	155	21	18	18	NUM
ejpam-4207	155	22	]	]	PUNCT
ejpam-4207	155	23	definition	definition	NOUN
ejpam-4207	155	24	10	10	NUM
ejpam-4207	155	25	.	.	PUNCT
ejpam-4207	156	1	a	a	DET
ejpam-4207	156	2	nonempty	nonempty	ADJ
ejpam-4207	156	3	collection	collection	NOUN
ejpam-4207	156	4	i	i	PRON
ejpam-4207	156	5	of	of	ADP
ejpam-4207	156	6	subsets	subset	NOUN
ejpam-4207	156	7	of	of	ADP
ejpam-4207	156	8	a	a	DET
ejpam-4207	156	9	set	set	NOUN
ejpam-4207	156	10	x	x	PUNCT
ejpam-4207	156	11	is	be	AUX
ejpam-4207	156	12	called	call	VERB
ejpam-4207	156	13	an	an	DET
ejpam-4207	156	14	ideal	ideal	NOUN
ejpam-4207	156	15	on	on	ADP
ejpam-4207	156	16	x	x	SYM
ejpam-4207	156	17	if	if	SCONJ
ejpam-4207	156	18	it	it	PRON
ejpam-4207	156	19	satisfies	satisfy	VERB
ejpam-4207	156	20	the	the	DET
ejpam-4207	156	21	following	follow	VERB
ejpam-4207	156	22	two	two	NUM
ejpam-4207	156	23	conditions	condition	NOUN
ejpam-4207	156	24	:	:	PUNCT
ejpam-4207	156	25	(	(	PUNCT
ejpam-4207	156	26	1	1	X
ejpam-4207	156	27	)	)	PUNCT
ejpam-4207	157	1	a	a	DET
ejpam-4207	157	2	∈	∈	NOUN
ejpam-4207	157	3	i	i	PRON
ejpam-4207	157	4	and	and	CCONJ
ejpam-4207	157	5	b	b	PROPN
ejpam-4207	157	6	⊂	⊂	PROPN
ejpam-4207	157	7	a	a	PRON
ejpam-4207	157	8	implies	imply	VERB
ejpam-4207	157	9	b	b	X
ejpam-4207	157	10	∈	∈	PROPN
ejpam-4207	157	11	i	i	PRON
ejpam-4207	157	12	,	,	PUNCT
ejpam-4207	157	13	(	(	PUNCT
ejpam-4207	157	14	2	2	X
ejpam-4207	157	15	)	)	PUNCT
ejpam-4207	158	1	a	a	DET
ejpam-4207	158	2	∈	∈	NOUN
ejpam-4207	158	3	i	i	PRON
ejpam-4207	158	4	and	and	CCONJ
ejpam-4207	158	5	b	b	X
ejpam-4207	158	6	∈	∈	PROPN
ejpam-4207	158	7	i	i	PRON
ejpam-4207	158	8	implies	imply	VERB
ejpam-4207	158	9	a	a	DET
ejpam-4207	158	10	∪b	∪b	PUNCT
ejpam-4207	158	11	∈	∈	PROPN
ejpam-4207	158	12	i.	i.	NOUN
ejpam-4207	158	13	a	a	DET
ejpam-4207	158	14	topological	topological	ADJ
ejpam-4207	158	15	space	space	NOUN
ejpam-4207	158	16	(	(	PUNCT
ejpam-4207	158	17	x	x	X
ejpam-4207	158	18	,	,	PUNCT
ejpam-4207	158	19	τ	τ	X
ejpam-4207	158	20	)	)	PUNCT
ejpam-4207	158	21	with	with	ADP
ejpam-4207	158	22	an	an	DET
ejpam-4207	158	23	ideal	ideal	ADJ
ejpam-4207	158	24	i	i	PRON
ejpam-4207	158	25	on	on	ADP
ejpam-4207	158	26	x	x	SYM
ejpam-4207	158	27	is	be	AUX
ejpam-4207	158	28	called	call	VERB
ejpam-4207	158	29	an	an	DET
ejpam-4207	158	30	ideal	ideal	ADJ
ejpam-4207	158	31	topological	topological	ADJ
ejpam-4207	158	32	space	space	NOUN
ejpam-4207	158	33	and	and	CCONJ
ejpam-4207	158	34	is	be	AUX
ejpam-4207	158	35	denoted	denote	VERB
ejpam-4207	158	36	by	by	ADP
ejpam-4207	158	37	(	(	PUNCT
ejpam-4207	158	38	x	x	X
ejpam-4207	158	39	,	,	PUNCT
ejpam-4207	158	40	τ	τ	PROPN
ejpam-4207	158	41	,	,	PUNCT
ejpam-4207	158	42	i	i	PROPN
ejpam-4207	158	43	)	)	PUNCT
ejpam-4207	158	44	.	.	PUNCT
ejpam-4207	159	1	let	let	VERB
ejpam-4207	159	2	(	(	PUNCT
ejpam-4207	159	3	x	x	X
ejpam-4207	159	4	,	,	PUNCT
ejpam-4207	159	5	τ	τ	PROPN
ejpam-4207	159	6	,	,	PUNCT
ejpam-4207	159	7	i	i	PRON
ejpam-4207	159	8	)	)	PUNCT
ejpam-4207	159	9	be	be	VERB
ejpam-4207	159	10	an	an	DET
ejpam-4207	159	11	ideal	ideal	ADJ
ejpam-4207	159	12	topological	topological	ADJ
ejpam-4207	159	13	space	space	NOUN
ejpam-4207	159	14	.	.	PUNCT
ejpam-4207	160	1	for	for	ADP
ejpam-4207	160	2	any	any	DET
ejpam-4207	160	3	subset	subset	NOUN
ejpam-4207	160	4	a	a	PRON
ejpam-4207	160	5	of	of	ADP
ejpam-4207	160	6	x	x	PROPN
ejpam-4207	160	7	,	,	PUNCT
ejpam-4207	160	8	a⋆(i	a⋆(i	PROPN
ejpam-4207	160	9	,	,	PUNCT
ejpam-4207	160	10	τ	τ	X
ejpam-4207	160	11	)	)	PUNCT
ejpam-4207	160	12	=	=	PRON
ejpam-4207	160	13	{	{	PUNCT
ejpam-4207	160	14	x	x	PUNCT
ejpam-4207	160	15	∈	∈	PROPN
ejpam-4207	160	16	x	x	X
ejpam-4207	160	17	:	:	PUNCT
ejpam-4207	160	18	u	u	NOUN
ejpam-4207	160	19	∩	∩	NOUN
ejpam-4207	160	20	a	a	X
ejpam-4207	160	21	/∈	/∈	PUNCT
ejpam-4207	160	22	i	i	PRON
ejpam-4207	160	23	for	for	ADP
ejpam-4207	160	24	every	every	DET
ejpam-4207	160	25	u	u	PROPN
ejpam-4207	160	26	∈	∈	PROPN
ejpam-4207	160	27	τ(x	τ(x	NOUN
ejpam-4207	160	28	)	)	PUNCT
ejpam-4207	160	29	}	}	PUNCT
ejpam-4207	160	30	,	,	PUNCT
ejpam-4207	160	31	where	where	SCONJ
ejpam-4207	160	32	τ(x	τ(x	NOUN
ejpam-4207	160	33	)	)	PUNCT
ejpam-4207	160	34	=	=	PRON
ejpam-4207	160	35	{	{	PUNCT
ejpam-4207	160	36	u	u	X
ejpam-4207	160	37	∈	∈	PROPN
ejpam-4207	160	38	τ	τ	X
ejpam-4207	160	39	:	:	PUNCT
ejpam-4207	160	40	x	x	SYM
ejpam-4207	160	41	∈	∈	PROPN
ejpam-4207	160	42	u	u	NOUN
ejpam-4207	160	43	}	}	PUNCT
ejpam-4207	160	44	,	,	PUNCT
ejpam-4207	160	45	is	be	AUX
ejpam-4207	160	46	called	call	VERB
ejpam-4207	160	47	the	the	DET
ejpam-4207	160	48	local	local	ADJ
ejpam-4207	160	49	function	function	NOUN
ejpam-4207	160	50	of	of	ADP
ejpam-4207	160	51	a	a	PRON
ejpam-4207	160	52	with	with	ADP
ejpam-4207	160	53	respect	respect	NOUN
ejpam-4207	160	54	to	to	ADP
ejpam-4207	160	55	τ	τ	PROPN
ejpam-4207	160	56	and	and	CCONJ
ejpam-4207	160	57	i	i	PRON
ejpam-4207	160	58	[	[	X
ejpam-4207	160	59	18	18	NUM
ejpam-4207	160	60	]	]	PUNCT
ejpam-4207	160	61	.	.	PUNCT
ejpam-4207	161	1	hereafter	hereafter	PROPN
ejpam-4207	161	2	a⋆(i	a⋆(i	PROPN
ejpam-4207	161	3	,	,	PUNCT
ejpam-4207	161	4	τ	τ	X
ejpam-4207	161	5	)	)	PUNCT
ejpam-4207	161	6	is	be	AUX
ejpam-4207	161	7	simply	simply	ADV
ejpam-4207	161	8	denoted	denote	VERB
ejpam-4207	161	9	by	by	ADP
ejpam-4207	161	10	a⋆.	a⋆.	NOUN
ejpam-4207	161	11	it	it	PRON
ejpam-4207	161	12	is	be	AUX
ejpam-4207	161	13	well	well	ADV
ejpam-4207	161	14	known	know	VERB
ejpam-4207	161	15	that	that	SCONJ
ejpam-4207	161	16	cl⋆(a	cl⋆(a	VERB
ejpam-4207	161	17	)	)	PUNCT
ejpam-4207	161	18	=	=	NOUN
ejpam-4207	161	19	a	a	DET
ejpam-4207	161	20	∪	∪	NOUN
ejpam-4207	161	21	a⋆	a⋆	ADP
ejpam-4207	161	22	defines	define	NOUN
ejpam-4207	161	23	a	a	DET
ejpam-4207	161	24	kuratowski	kuratowski	ADJ
ejpam-4207	161	25	closure	closure	NOUN
ejpam-4207	161	26	operator	operator	NOUN
ejpam-4207	161	27	on	on	ADP
ejpam-4207	161	28	x	x	PUNCT
ejpam-4207	161	29	and	and	CCONJ
ejpam-4207	161	30	the	the	DET
ejpam-4207	161	31	topology	topology	NOUN
ejpam-4207	161	32	generated	generate	VERB
ejpam-4207	161	33	by	by	ADP
ejpam-4207	161	34	cl⋆	cl⋆	PROPN
ejpam-4207	161	35	is	be	AUX
ejpam-4207	161	36	denoted	denote	VERB
ejpam-4207	161	37	by	by	ADP
ejpam-4207	161	38	τ⋆.	τ⋆.	PROPN
ejpam-4207	161	39	takashi	takashi	PROPN
ejpam-4207	161	40	noiri	noiri	PROPN
ejpam-4207	161	41	,	,	PUNCT
ejpam-4207	161	42	valeriu	valeriu	ADJ
ejpam-4207	161	43	popa	popa	NOUN
ejpam-4207	161	44	/	/	SYM
ejpam-4207	161	45	eur	eur	PROPN
ejpam-4207	161	46	.	.	PUNCT
ejpam-4207	162	1	j.	j.	PROPN
ejpam-4207	162	2	pure	pure	PROPN
ejpam-4207	162	3	appl	appl	PROPN
ejpam-4207	162	4	.	.	PROPN
ejpam-4207	162	5	math	math	PROPN
ejpam-4207	162	6	,	,	PUNCT
ejpam-4207	162	7	15	15	NUM
ejpam-4207	162	8	(	(	PUNCT
ejpam-4207	162	9	1	1	NUM
ejpam-4207	162	10	)	)	PUNCT
ejpam-4207	162	11	(	(	PUNCT
ejpam-4207	162	12	2022	2022	NUM
ejpam-4207	162	13	)	)	PUNCT
ejpam-4207	162	14	,	,	PUNCT
ejpam-4207	162	15	1	1	NUM
ejpam-4207	162	16	-	-	SYM
ejpam-4207	162	17	14	14	NUM
ejpam-4207	162	18	6	6	NUM
ejpam-4207	162	19	lemma	lemma	PROPN
ejpam-4207	162	20	3	3	X
ejpam-4207	162	21	.	.	PUNCT
ejpam-4207	163	1	let	let	VERB
ejpam-4207	163	2	(	(	PUNCT
ejpam-4207	163	3	x	x	X
ejpam-4207	163	4	,	,	PUNCT
ejpam-4207	163	5	τ	τ	PROPN
ejpam-4207	163	6	,	,	PUNCT
ejpam-4207	163	7	i	i	PRON
ejpam-4207	163	8	)	)	PUNCT
ejpam-4207	163	9	be	be	VERB
ejpam-4207	163	10	an	an	DET
ejpam-4207	163	11	ideal	ideal	ADJ
ejpam-4207	163	12	topological	topological	ADJ
ejpam-4207	163	13	space	space	NOUN
ejpam-4207	163	14	and	and	CCONJ
ejpam-4207	163	15	a	a	DET
ejpam-4207	163	16	,	,	PUNCT
ejpam-4207	163	17	b	b	PROPN
ejpam-4207	163	18	be	be	AUX
ejpam-4207	163	19	subsets	subset	NOUN
ejpam-4207	163	20	of	of	ADP
ejpam-4207	163	21	x.	x.	NOUN
ejpam-4207	163	22	then	then	ADV
ejpam-4207	163	23	the	the	DET
ejpam-4207	163	24	following	follow	VERB
ejpam-4207	163	25	properties	property	NOUN
ejpam-4207	163	26	hold	hold	VERB
ejpam-4207	163	27	:	:	PUNCT
ejpam-4207	163	28	(	(	PUNCT
ejpam-4207	163	29	1	1	X
ejpam-4207	163	30	)	)	PUNCT
ejpam-4207	163	31	a	a	DET
ejpam-4207	163	32	⊂	⊂	PROPN
ejpam-4207	163	33	b	b	PROPN
ejpam-4207	163	34	implies	imply	VERB
ejpam-4207	163	35	cl⋆(a	cl⋆(a	NOUN
ejpam-4207	163	36	)	)	PUNCT
ejpam-4207	163	37	⊂	⊂	PROPN
ejpam-4207	163	38	cl⋆(b	cl⋆(b	NOUN
ejpam-4207	163	39	)	)	PUNCT
ejpam-4207	163	40	,	,	PUNCT
ejpam-4207	163	41	(	(	PUNCT
ejpam-4207	163	42	2	2	X
ejpam-4207	163	43	)	)	PUNCT
ejpam-4207	163	44	cl⋆(x	cl⋆(x	NOUN
ejpam-4207	163	45	)	)	PUNCT
ejpam-4207	163	46	=	=	SYM
ejpam-4207	163	47	x	x	PROPN
ejpam-4207	163	48	and	and	CCONJ
ejpam-4207	163	49	cl⋆(∅	cl⋆(∅	NOUN
ejpam-4207	163	50	)	)	PUNCT
ejpam-4207	163	51	=	=	SYM
ejpam-4207	163	52	∅	∅	NOUN
ejpam-4207	163	53	,	,	PUNCT
ejpam-4207	163	54	(	(	PUNCT
ejpam-4207	163	55	3	3	X
ejpam-4207	163	56	)	)	PUNCT
ejpam-4207	163	57	cl⋆(a	cl⋆(a	NOUN
ejpam-4207	163	58	)	)	PUNCT
ejpam-4207	163	59	∪	∪	ADP
ejpam-4207	163	60	cl⋆(b	cl⋆(b	NOUN
ejpam-4207	163	61	)	)	PUNCT
ejpam-4207	163	62	⊂	⊂	PROPN
ejpam-4207	163	63	cl⋆(a	cl⋆(a	X
ejpam-4207	163	64	∪b	∪b	NOUN
ejpam-4207	163	65	)	)	PUNCT
ejpam-4207	163	66	.	.	PUNCT
ejpam-4207	164	1	definition	definition	NOUN
ejpam-4207	164	2	11	11	NUM
ejpam-4207	164	3	.	.	PUNCT
ejpam-4207	165	1	let	let	VERB
ejpam-4207	165	2	(	(	PUNCT
ejpam-4207	165	3	x	x	X
ejpam-4207	165	4	,	,	PUNCT
ejpam-4207	165	5	τ	τ	PROPN
ejpam-4207	165	6	,	,	PUNCT
ejpam-4207	165	7	i	i	PRON
ejpam-4207	165	8	)	)	PUNCT
ejpam-4207	165	9	be	be	VERB
ejpam-4207	165	10	an	an	DET
ejpam-4207	165	11	ideal	ideal	ADJ
ejpam-4207	165	12	topological	topological	ADJ
ejpam-4207	165	13	space	space	NOUN
ejpam-4207	165	14	.	.	PUNCT
ejpam-4207	166	1	a	a	DET
ejpam-4207	166	2	subset	subset	NOUN
ejpam-4207	166	3	a	a	PRON
ejpam-4207	166	4	of	of	ADP
ejpam-4207	166	5	x	x	SYM
ejpam-4207	166	6	is	be	AUX
ejpam-4207	166	7	said	say	VERB
ejpam-4207	166	8	to	to	PART
ejpam-4207	166	9	be	be	AUX
ejpam-4207	166	10	(	(	PUNCT
ejpam-4207	166	11	1	1	X
ejpam-4207	166	12	)	)	PUNCT
ejpam-4207	166	13	α	α	PROPN
ejpam-4207	166	14	-	-	PUNCT
ejpam-4207	166	15	i	i	PRON
ejpam-4207	166	16	-	-	PUNCT
ejpam-4207	166	17	open	open	ADJ
ejpam-4207	167	1	[	[	X
ejpam-4207	167	2	16	16	NUM
ejpam-4207	167	3	]	]	X
ejpam-4207	167	4	if	if	SCONJ
ejpam-4207	167	5	a	a	DET
ejpam-4207	167	6	⊂	⊂	PROPN
ejpam-4207	167	7	int(cl⋆(int(a	int(cl⋆(int(a	PROPN
ejpam-4207	167	8	)	)	PUNCT
ejpam-4207	167	9	)	)	PUNCT
ejpam-4207	167	10	)	)	PUNCT
ejpam-4207	167	11	,	,	PUNCT
ejpam-4207	167	12	(	(	PUNCT
ejpam-4207	167	13	2	2	X
ejpam-4207	167	14	)	)	PUNCT
ejpam-4207	167	15	semi	semi	ADJ
ejpam-4207	167	16	-	-	ADJ
ejpam-4207	167	17	i	i	PRON
ejpam-4207	167	18	-	-	PUNCT
ejpam-4207	167	19	open	open	ADJ
ejpam-4207	167	20	[	[	X
ejpam-4207	167	21	16	16	NUM
ejpam-4207	167	22	]	]	X
ejpam-4207	167	23	if	if	SCONJ
ejpam-4207	167	24	a	a	DET
ejpam-4207	167	25	⊂	⊂	X
ejpam-4207	167	26	cl⋆(int(a	cl⋆(int(a	PROPN
ejpam-4207	167	27	)	)	PUNCT
ejpam-4207	167	28	)	)	PUNCT
ejpam-4207	167	29	,	,	PUNCT
ejpam-4207	167	30	(	(	PUNCT
ejpam-4207	167	31	3	3	X
ejpam-4207	167	32	)	)	PUNCT
ejpam-4207	167	33	pre	pre	ADJ
ejpam-4207	167	34	-	-	ADJ
ejpam-4207	167	35	i	i	PRON
ejpam-4207	167	36	-	-	PUNCT
ejpam-4207	167	37	open	open	ADJ
ejpam-4207	168	1	[	[	X
ejpam-4207	168	2	10	10	NUM
ejpam-4207	168	3	]	]	X
ejpam-4207	168	4	if	if	SCONJ
ejpam-4207	168	5	a	a	DET
ejpam-4207	168	6	⊂	⊂	ADJ
ejpam-4207	168	7	int(cl⋆(a	int(cl⋆(a	NOUN
ejpam-4207	168	8	)	)	PUNCT
ejpam-4207	168	9	)	)	PUNCT
ejpam-4207	168	10	,	,	PUNCT
ejpam-4207	168	11	(	(	PUNCT
ejpam-4207	168	12	4	4	X
ejpam-4207	168	13	)	)	PUNCT
ejpam-4207	168	14	b	b	NOUN
ejpam-4207	168	15	-	-	PUNCT
ejpam-4207	168	16	i	i	PRON
ejpam-4207	168	17	-	-	PUNCT
ejpam-4207	168	18	open	open	ADJ
ejpam-4207	169	1	[	[	X
ejpam-4207	169	2	5	5	NUM
ejpam-4207	169	3	]	]	PUNCT
ejpam-4207	169	4	if	if	SCONJ
ejpam-4207	169	5	a	a	DET
ejpam-4207	169	6	⊂	⊂	PROPN
ejpam-4207	169	7	int(cl⋆(a	int(cl⋆(a	NOUN
ejpam-4207	169	8	)	)	PUNCT
ejpam-4207	169	9	)	)	PUNCT
ejpam-4207	169	10	∪	∪	ADP
ejpam-4207	169	11	cl⋆(int(a	cl⋆(int(a	PROPN
ejpam-4207	169	12	)	)	PUNCT
ejpam-4207	169	13	)	)	PUNCT
ejpam-4207	169	14	,	,	PUNCT
ejpam-4207	169	15	(	(	PUNCT
ejpam-4207	169	16	5	5	X
ejpam-4207	169	17	)	)	PUNCT
ejpam-4207	169	18	β	β	X
ejpam-4207	169	19	-	-	PUNCT
ejpam-4207	169	20	i	i	PRON
ejpam-4207	169	21	-	-	PUNCT
ejpam-4207	169	22	open	open	ADJ
ejpam-4207	169	23	[	[	X
ejpam-4207	169	24	17	17	NUM
ejpam-4207	169	25	]	]	PUNCT
ejpam-4207	169	26	if	if	SCONJ
ejpam-4207	169	27	a	a	DET
ejpam-4207	169	28	⊂	⊂	X
ejpam-4207	169	29	cl(int(cl⋆(a	cl(int(cl⋆(a	NOUN
ejpam-4207	169	30	)	)	PUNCT
ejpam-4207	169	31	)	)	PUNCT
ejpam-4207	169	32	)	)	PUNCT
ejpam-4207	169	33	,	,	PUNCT
ejpam-4207	169	34	(	(	PUNCT
ejpam-4207	169	35	6	6	X
ejpam-4207	169	36	)	)	PUNCT
ejpam-4207	169	37	weakly	weakly	ADJ
ejpam-4207	169	38	semi	semi	ADJ
ejpam-4207	169	39	-	-	ADJ
ejpam-4207	169	40	i	i	PRON
ejpam-4207	169	41	-	-	PUNCT
ejpam-4207	169	42	open	open	ADJ
ejpam-4207	169	43	[	[	X
ejpam-4207	169	44	14	14	NUM
ejpam-4207	169	45	]	]	X
ejpam-4207	169	46	if	if	SCONJ
ejpam-4207	169	47	a	a	DET
ejpam-4207	169	48	⊂	⊂	PROPN
ejpam-4207	169	49	cl⋆(int(cl(a	cl⋆(int(cl(a	X
ejpam-4207	169	50	)	)	PUNCT
ejpam-4207	169	51	)	)	PUNCT
ejpam-4207	169	52	)	)	PUNCT
ejpam-4207	169	53	,	,	PUNCT
ejpam-4207	169	54	(	(	PUNCT
ejpam-4207	169	55	7	7	X
ejpam-4207	169	56	)	)	PUNCT
ejpam-4207	169	57	weakly	weakly	ADJ
ejpam-4207	169	58	b	b	X
ejpam-4207	169	59	-	-	PUNCT
ejpam-4207	169	60	i	i	PRON
ejpam-4207	169	61	-	-	PUNCT
ejpam-4207	169	62	open	open	ADJ
ejpam-4207	169	63	[	[	X
ejpam-4207	169	64	25	25	NUM
ejpam-4207	169	65	]	]	PUNCT
ejpam-4207	169	66	if	if	SCONJ
ejpam-4207	169	67	a	a	DET
ejpam-4207	169	68	⊂	⊂	X
ejpam-4207	169	69	cl(int(cl⋆(a	cl(int(cl⋆(a	NOUN
ejpam-4207	169	70	)	)	PUNCT
ejpam-4207	169	71	)	)	PUNCT
ejpam-4207	169	72	)	)	PUNCT
ejpam-4207	169	73	∪	∪	ADP
ejpam-4207	169	74	cl⋆(int(cl(a	cl⋆(int(cl(a	PROPN
ejpam-4207	169	75	)	)	PUNCT
ejpam-4207	169	76	)	)	PUNCT
ejpam-4207	169	77	)	)	PUNCT
ejpam-4207	169	78	,	,	PUNCT
ejpam-4207	169	79	(	(	PUNCT
ejpam-4207	169	80	8)	8)	NUM
ejpam-4207	169	81	strongly	strongly	ADV
ejpam-4207	169	82	β	β	AUX
ejpam-4207	169	83	-	-	ADJ
ejpam-4207	169	84	i	i	PRON
ejpam-4207	169	85	-	-	PUNCT
ejpam-4207	169	86	open	open	ADJ
ejpam-4207	169	87	[	[	X
ejpam-4207	169	88	15	15	NUM
ejpam-4207	169	89	]	]	X
ejpam-4207	169	90	if	if	SCONJ
ejpam-4207	169	91	a	a	DET
ejpam-4207	169	92	⊂	⊂	PROPN
ejpam-4207	169	93	cl⋆(int(cl⋆(a	cl⋆(int(cl⋆(a	PROPN
ejpam-4207	169	94	)	)	PUNCT
ejpam-4207	169	95	)	)	PUNCT
ejpam-4207	169	96	)	)	PUNCT
ejpam-4207	169	97	,	,	PUNCT
ejpam-4207	169	98	(	(	PUNCT
ejpam-4207	169	99	9	9	X
ejpam-4207	169	100	)	)	PUNCT
ejpam-4207	169	101	semi⋆-i	semi⋆-i	NOUN
ejpam-4207	169	102	-	-	ADJ
ejpam-4207	169	103	open	open	ADJ
ejpam-4207	169	104	[	[	X
ejpam-4207	169	105	12	12	NUM
ejpam-4207	169	106	]	]	X
ejpam-4207	169	107	if	if	SCONJ
ejpam-4207	169	108	a	a	DET
ejpam-4207	169	109	⊂	⊂	PROPN
ejpam-4207	169	110	cl(int⋆(a	cl(int⋆(a	PROPN
ejpam-4207	169	111	)	)	PUNCT
ejpam-4207	169	112	)	)	PUNCT
ejpam-4207	169	113	,	,	PUNCT
ejpam-4207	169	114	(	(	PUNCT
ejpam-4207	169	115	10	10	NUM
ejpam-4207	169	116	)	)	PUNCT
ejpam-4207	169	117	pre⋆-i	pre⋆-i	NOUN
ejpam-4207	169	118	-	-	PUNCT
ejpam-4207	169	119	open	open	ADJ
ejpam-4207	169	120	[	[	X
ejpam-4207	169	121	11	11	NUM
ejpam-4207	169	122	]	]	X
ejpam-4207	169	123	if	if	SCONJ
ejpam-4207	169	124	a	a	DET
ejpam-4207	169	125	⊂	⊂	X
ejpam-4207	169	126	int⋆(cl(a	int⋆(cl(a	PROPN
ejpam-4207	169	127	)	)	PUNCT
ejpam-4207	169	128	)	)	PUNCT
ejpam-4207	169	129	,	,	PUNCT
ejpam-4207	169	130	(	(	PUNCT
ejpam-4207	169	131	11	11	NUM
ejpam-4207	169	132	)	)	PUNCT
ejpam-4207	169	133	β⋆	β⋆	PUNCT
ejpam-4207	170	1	i	i	PRON
ejpam-4207	170	2	-open	-open	VERB
ejpam-4207	171	1	[	[	X
ejpam-4207	171	2	11	11	NUM
ejpam-4207	171	3	]	]	PUNCT
ejpam-4207	171	4	if	if	SCONJ
ejpam-4207	171	5	a	a	DET
ejpam-4207	171	6	⊂	⊂	PROPN
ejpam-4207	171	7	cl(int⋆(cl(a	cl(int⋆(cl(a	PROPN
ejpam-4207	171	8	)	)	PUNCT
ejpam-4207	171	9	)	)	PUNCT
ejpam-4207	171	10	)	)	PUNCT
ejpam-4207	171	11	.	.	PUNCT
ejpam-4207	172	1	the	the	DET
ejpam-4207	172	2	family	family	NOUN
ejpam-4207	172	3	of	of	ADP
ejpam-4207	172	4	all	all	DET
ejpam-4207	172	5	α	α	PROPN
ejpam-4207	172	6	-	-	ADJ
ejpam-4207	172	7	i	i	PRON
ejpam-4207	172	8	-	-	PUNCT
ejpam-4207	172	9	open	open	ADJ
ejpam-4207	172	10	(	(	PUNCT
ejpam-4207	172	11	resp	resp	NOUN
ejpam-4207	172	12	.	.	PUNCT
ejpam-4207	173	1	semi	semi	ADJ
ejpam-4207	173	2	-	-	ADJ
ejpam-4207	173	3	i	i	PRON
ejpam-4207	173	4	-	-	PUNCT
ejpam-4207	173	5	open	open	ADJ
ejpam-4207	173	6	,	,	PUNCT
ejpam-4207	173	7	pre	pre	ADJ
ejpam-4207	173	8	-	-	ADJ
ejpam-4207	173	9	i	i	PRON
ejpam-4207	173	10	-	-	PUNCT
ejpam-4207	173	11	open	open	ADJ
ejpam-4207	173	12	,	,	PUNCT
ejpam-4207	173	13	b	b	X
ejpam-4207	173	14	-	-	PUNCT
ejpam-4207	173	15	i	i	PRON
ejpam-4207	173	16	-	-	PUNCT
ejpam-4207	173	17	open	open	ADJ
ejpam-4207	173	18	,	,	PUNCT
ejpam-4207	173	19	β	β	X
ejpam-4207	173	20	-	-	ADJ
ejpam-4207	173	21	i	i	PRON
ejpam-4207	173	22	-	-	PUNCT
ejpam-4207	173	23	open	open	ADJ
ejpam-4207	173	24	,	,	PUNCT
ejpam-4207	173	25	weakly	weakly	ADJ
ejpam-4207	173	26	semi	semi	ADJ
ejpam-4207	173	27	-	-	ADJ
ejpam-4207	173	28	i	i	PRON
ejpam-4207	173	29	-	-	PUNCT
ejpam-4207	173	30	open	open	ADJ
ejpam-4207	173	31	,	,	PUNCT
ejpam-4207	173	32	weakly	weakly	ADJ
ejpam-4207	173	33	b	b	X
ejpam-4207	173	34	-	-	PUNCT
ejpam-4207	173	35	i	i	NOUN
ejpam-4207	173	36	-	-	PUNCT
ejpam-4207	173	37	open	open	ADJ
ejpam-4207	173	38	,	,	PUNCT
ejpam-4207	173	39	strongly	strongly	ADV
ejpam-4207	173	40	β	β	X
ejpam-4207	173	41	-	-	ADJ
ejpam-4207	173	42	i	i	PRON
ejpam-4207	173	43	-	-	PUNCT
ejpam-4207	173	44	open	open	ADJ
ejpam-4207	173	45	,	,	PUNCT
ejpam-4207	173	46	semi⋆-i	semi⋆-i	NOUN
ejpam-4207	173	47	-	-	ADJ
ejpam-4207	173	48	open	open	ADJ
ejpam-4207	173	49	,	,	PUNCT
ejpam-4207	173	50	pre⋆-i	pre⋆-i	NOUN
ejpam-4207	173	51	-	-	PUNCT
ejpam-4207	173	52	open	open	ADJ
ejpam-4207	173	53	,	,	PUNCT
ejpam-4207	173	54	β⋆	β⋆	PUNCT
ejpam-4207	173	55	i	i	PRON
ejpam-4207	173	56	-open	-open	VERB
ejpam-4207	173	57	)	)	PUNCT
ejpam-4207	173	58	sets	set	NOUN
ejpam-4207	173	59	in	in	ADP
ejpam-4207	173	60	an	an	DET
ejpam-4207	173	61	ideal	ideal	ADJ
ejpam-4207	173	62	topological	topological	ADJ
ejpam-4207	173	63	space	space	NOUN
ejpam-4207	173	64	(	(	PUNCT
ejpam-4207	173	65	x	x	X
ejpam-4207	173	66	,	,	PUNCT
ejpam-4207	173	67	τ	τ	PROPN
ejpam-4207	173	68	,	,	PUNCT
ejpam-4207	173	69	i	i	PROPN
ejpam-4207	173	70	)	)	PUNCT
ejpam-4207	173	71	is	be	AUX
ejpam-4207	173	72	denoted	denote	VERB
ejpam-4207	173	73	by	by	ADP
ejpam-4207	173	74	αio(x	αio(x	PROPN
ejpam-4207	173	75	)	)	PUNCT
ejpam-4207	173	76	(	(	PUNCT
ejpam-4207	173	77	resp	resp	NOUN
ejpam-4207	173	78	.	.	PUNCT
ejpam-4207	174	1	sio(x	sio(x	VERB
ejpam-4207	174	2	)	)	PUNCT
ejpam-4207	174	3	,	,	PUNCT
ejpam-4207	174	4	pio(x	pio(x	PROPN
ejpam-4207	174	5	)	)	PUNCT
ejpam-4207	174	6	,	,	PUNCT
ejpam-4207	174	7	bio(x	bio(x	PROPN
ejpam-4207	174	8	)	)	PUNCT
ejpam-4207	174	9	,	,	PUNCT
ejpam-4207	174	10	βio(x	βio(x	NUM
ejpam-4207	174	11	)	)	PUNCT
ejpam-4207	174	12	,	,	PUNCT
ejpam-4207	174	13	wsio(x	wsio(x	NOUN
ejpam-4207	174	14	)	)	PUNCT
ejpam-4207	174	15	,	,	PUNCT
ejpam-4207	174	16	wbio(x	wbio(x	PROPN
ejpam-4207	174	17	)	)	PUNCT
ejpam-4207	174	18	,	,	PUNCT
ejpam-4207	174	19	sβio(x	sβio(x	NOUN
ejpam-4207	174	20	)	)	PUNCT
ejpam-4207	174	21	,	,	PUNCT
ejpam-4207	174	22	s⋆io(x	s⋆io(x	PROPN
ejpam-4207	174	23	)	)	PUNCT
ejpam-4207	174	24	,	,	PUNCT
ejpam-4207	174	25	p⋆io(x	p⋆io(x	PROPN
ejpam-4207	174	26	)	)	PUNCT
ejpam-4207	174	27	,	,	PUNCT
ejpam-4207	174	28	βio(x	βio(x	NUM
ejpam-4207	174	29	)	)	PUNCT
ejpam-4207	174	30	)	)	PUNCT
ejpam-4207	174	31	.	.	PUNCT
ejpam-4207	175	1	definition	definition	NOUN
ejpam-4207	175	2	12	12	NUM
ejpam-4207	175	3	.	.	PUNCT
ejpam-4207	176	1	by	by	ADP
ejpam-4207	176	2	mio(x	mio(x	PROPN
ejpam-4207	176	3	)	)	PUNCT
ejpam-4207	176	4	,	,	PUNCT
ejpam-4207	176	5	we	we	PRON
ejpam-4207	176	6	denote	denote	VERB
ejpam-4207	176	7	each	each	DET
ejpam-4207	176	8	one	one	NUM
ejpam-4207	176	9	of	of	ADP
ejpam-4207	176	10	the	the	DET
ejpam-4207	176	11	families	family	NOUN
ejpam-4207	176	12	τ⋆	τ⋆	SYM
ejpam-4207	176	13	,	,	PUNCT
ejpam-4207	176	14	αio(x	αio(x	PROPN
ejpam-4207	176	15	)	)	PUNCT
ejpam-4207	176	16	,	,	PUNCT
ejpam-4207	176	17	sio(x	sio(x	NOUN
ejpam-4207	176	18	)	)	PUNCT
ejpam-4207	176	19	,	,	PUNCT
ejpam-4207	176	20	pio(x	pio(x	PROPN
ejpam-4207	176	21	)	)	PUNCT
ejpam-4207	176	22	,	,	PUNCT
ejpam-4207	176	23	bio(x	bio(x	PROPN
ejpam-4207	176	24	)	)	PUNCT
ejpam-4207	176	25	,	,	PUNCT
ejpam-4207	176	26	βio(x	βio(x	NUM
ejpam-4207	176	27	)	)	PUNCT
ejpam-4207	176	28	,	,	PUNCT
ejpam-4207	176	29	wsio(x	wsio(x	NOUN
ejpam-4207	176	30	)	)	PUNCT
ejpam-4207	176	31	,	,	PUNCT
ejpam-4207	176	32	wbio(x	wbio(x	PROPN
ejpam-4207	176	33	)	)	PUNCT
ejpam-4207	176	34	,	,	PUNCT
ejpam-4207	176	35	sβio(x	sβio(x	NOUN
ejpam-4207	176	36	)	)	PUNCT
ejpam-4207	176	37	,	,	PUNCT
ejpam-4207	176	38	s⋆io(x	s⋆io(x	PROPN
ejpam-4207	176	39	)	)	PUNCT
ejpam-4207	176	40	,	,	PUNCT
ejpam-4207	176	41	p⋆io(x	p⋆io(x	PROPN
ejpam-4207	176	42	)	)	PUNCT
ejpam-4207	176	43	,	,	PUNCT
ejpam-4207	176	44	β⋆io(x	β⋆io(x	PROPN
ejpam-4207	176	45	)	)	PUNCT
ejpam-4207	176	46	.	.	PUNCT
ejpam-4207	177	1	lemma	lemma	PROPN
ejpam-4207	177	2	4	4	X
ejpam-4207	177	3	.	.	PUNCT
ejpam-4207	178	1	let	let	VERB
ejpam-4207	178	2	(	(	PUNCT
ejpam-4207	178	3	x	x	X
ejpam-4207	178	4	,	,	PUNCT
ejpam-4207	178	5	τ	τ	PROPN
ejpam-4207	178	6	,	,	PUNCT
ejpam-4207	178	7	i	i	PRON
ejpam-4207	178	8	)	)	PUNCT
ejpam-4207	178	9	be	be	VERB
ejpam-4207	178	10	an	an	DET
ejpam-4207	178	11	ideal	ideal	ADJ
ejpam-4207	178	12	topological	topological	ADJ
ejpam-4207	178	13	space	space	NOUN
ejpam-4207	178	14	.	.	PUNCT
ejpam-4207	179	1	then	then	ADV
ejpam-4207	179	2	mio(x	mio(x	PROPN
ejpam-4207	179	3	)	)	PUNCT
ejpam-4207	179	4	is	be	AUX
ejpam-4207	179	5	a	a	DET
ejpam-4207	179	6	minimal	minimal	ADJ
ejpam-4207	179	7	structure	structure	NOUN
ejpam-4207	179	8	and	and	CCONJ
ejpam-4207	179	9	has	have	VERB
ejpam-4207	179	10	property	property	NOUN
ejpam-4207	179	11	b.	b.	PROPN
ejpam-4207	179	12	definition	definition	NOUN
ejpam-4207	179	13	13	13	NUM
ejpam-4207	179	14	.	.	PUNCT
ejpam-4207	180	1	let	let	VERB
ejpam-4207	180	2	(	(	PUNCT
ejpam-4207	180	3	x	x	X
ejpam-4207	180	4	,	,	PUNCT
ejpam-4207	180	5	τ	τ	PROPN
ejpam-4207	180	6	,	,	PUNCT
ejpam-4207	180	7	i	i	PRON
ejpam-4207	180	8	)	)	PUNCT
ejpam-4207	180	9	be	be	VERB
ejpam-4207	180	10	an	an	DET
ejpam-4207	180	11	ideal	ideal	ADJ
ejpam-4207	180	12	topological	topological	ADJ
ejpam-4207	180	13	space	space	NOUN
ejpam-4207	180	14	.	.	PUNCT
ejpam-4207	181	1	for	for	ADP
ejpam-4207	181	2	a	a	DET
ejpam-4207	181	3	subset	subset	NOUN
ejpam-4207	181	4	a	a	PRON
ejpam-4207	181	5	of	of	ADP
ejpam-4207	181	6	x	x	SYM
ejpam-4207	181	7	,	,	PUNCT
ejpam-4207	181	8	mcli(a	mcli(a	PROPN
ejpam-4207	181	9	)	)	PUNCT
ejpam-4207	181	10	and	and	CCONJ
ejpam-4207	181	11	minti(a	minti(a	PROPN
ejpam-4207	181	12	)	)	PUNCT
ejpam-4207	181	13	are	be	AUX
ejpam-4207	181	14	defined	define	VERB
ejpam-4207	181	15	as	as	SCONJ
ejpam-4207	181	16	follows	follow	VERB
ejpam-4207	181	17	:	:	PUNCT
ejpam-4207	181	18	(	(	PUNCT
ejpam-4207	181	19	1	1	X
ejpam-4207	181	20	)	)	PUNCT
ejpam-4207	181	21	mcli(a	mcli(a	NOUN
ejpam-4207	181	22	)	)	PUNCT
ejpam-4207	182	1	=	=	PUNCT
ejpam-4207	182	2	∩{f	∩{f	NOUN
ejpam-4207	182	3	:	:	PUNCT
ejpam-4207	182	4	a	a	DET
ejpam-4207	182	5	⊂	⊂	PROPN
ejpam-4207	182	6	f	f	X
ejpam-4207	182	7	,	,	PUNCT
ejpam-4207	182	8	x	x	SYM
ejpam-4207	182	9	\	\	PROPN
ejpam-4207	182	10	f	f	PROPN
ejpam-4207	182	11	∈	∈	PROPN
ejpam-4207	182	12	mio(x	mio(x	PROPN
ejpam-4207	182	13	)	)	PUNCT
ejpam-4207	182	14	}	}	PUNCT
ejpam-4207	182	15	,	,	PUNCT
ejpam-4207	182	16	(	(	PUNCT
ejpam-4207	182	17	2	2	X
ejpam-4207	182	18	)	)	PUNCT
ejpam-4207	182	19	minti(a	minti(a	PROPN
ejpam-4207	182	20	)	)	PUNCT
ejpam-4207	182	21	=	=	PUNCT
ejpam-4207	183	1	∪{u	∪{u	VERB
ejpam-4207	183	2	:	:	PUNCT
ejpam-4207	183	3	u	u	X
ejpam-4207	183	4	⊂	⊂	PROPN
ejpam-4207	183	5	a	a	X
ejpam-4207	183	6	,	,	PUNCT
ejpam-4207	183	7	u	u	PROPN
ejpam-4207	183	8	∈	∈	PROPN
ejpam-4207	183	9	mio(x	mio(x	PROPN
ejpam-4207	183	10	)	)	PUNCT
ejpam-4207	183	11	}	}	PUNCT
ejpam-4207	183	12	.	.	PUNCT
ejpam-4207	184	1	let	let	VERB
ejpam-4207	184	2	(	(	PUNCT
ejpam-4207	184	3	x	x	X
ejpam-4207	184	4	,	,	PUNCT
ejpam-4207	184	5	τ	τ	PROPN
ejpam-4207	184	6	,	,	PUNCT
ejpam-4207	184	7	i	i	PRON
ejpam-4207	184	8	)	)	PUNCT
ejpam-4207	184	9	be	be	VERB
ejpam-4207	184	10	an	an	DET
ejpam-4207	184	11	ideal	ideal	ADJ
ejpam-4207	184	12	topological	topological	ADJ
ejpam-4207	184	13	space	space	NOUN
ejpam-4207	184	14	and	and	CCONJ
ejpam-4207	184	15	mio(x	mio(x	NOUN
ejpam-4207	184	16	)	)	PUNCT
ejpam-4207	184	17	the	the	DET
ejpam-4207	184	18	mx	mx	PROPN
ejpam-4207	184	19	-structure	-structure	NOUN
ejpam-4207	184	20	on	on	ADP
ejpam-4207	184	21	x.	x.	NOUN
ejpam-4207	184	22	if	if	SCONJ
ejpam-4207	184	23	mio(x	mio(x	PROPN
ejpam-4207	184	24	)	)	PUNCT
ejpam-4207	184	25	=	=	PUNCT
ejpam-4207	184	26	τ⋆	τ⋆	PRON
ejpam-4207	184	27	(	(	PUNCT
ejpam-4207	184	28	resp	resp	NOUN
ejpam-4207	184	29	.	.	PUNCT
ejpam-4207	185	1	αio(x	αio(x	NUM
ejpam-4207	185	2	)	)	PUNCT
ejpam-4207	185	3	,	,	PUNCT
ejpam-4207	185	4	sio(x	sio(x	NOUN
ejpam-4207	185	5	)	)	PUNCT
ejpam-4207	185	6	,	,	PUNCT
ejpam-4207	185	7	pio(x	pio(x	PROPN
ejpam-4207	185	8	)	)	PUNCT
ejpam-4207	185	9	,	,	PUNCT
ejpam-4207	185	10	bio(x	bio(x	PROPN
ejpam-4207	185	11	)	)	PUNCT
ejpam-4207	185	12	,	,	PUNCT
ejpam-4207	185	13	βio(x	βio(x	NUM
ejpam-4207	185	14	)	)	PUNCT
ejpam-4207	185	15	,	,	PUNCT
ejpam-4207	185	16	wsio(x	wsio(x	NOUN
ejpam-4207	185	17	)	)	PUNCT
ejpam-4207	185	18	,	,	PUNCT
ejpam-4207	185	19	wbio(x	wbio(x	PROPN
ejpam-4207	185	20	)	)	PUNCT
ejpam-4207	185	21	,	,	PUNCT
ejpam-4207	185	22	sβio(x	sβio(x	NOUN
ejpam-4207	185	23	)	)	PUNCT
ejpam-4207	185	24	)	)	PUNCT
ejpam-4207	185	25	,	,	PUNCT
ejpam-4207	185	26	s⋆io(x	s⋆io(x	PROPN
ejpam-4207	185	27	)	)	PUNCT
ejpam-4207	185	28	,	,	PUNCT
ejpam-4207	185	29	p⋆io(x	p⋆io(x	PROPN
ejpam-4207	185	30	)	)	PUNCT
ejpam-4207	185	31	,	,	PUNCT
ejpam-4207	185	32	β⋆io(x	β⋆io(x	PROPN
ejpam-4207	185	33	)	)	PUNCT
ejpam-4207	185	34	,	,	PUNCT
ejpam-4207	185	35	then	then	ADV
ejpam-4207	185	36	we	we	PRON
ejpam-4207	185	37	have	have	VERB
ejpam-4207	185	38	the	the	DET
ejpam-4207	185	39	following	following	NOUN
ejpam-4207	185	40	:	:	PUNCT
ejpam-4207	185	41	(	(	PUNCT
ejpam-4207	185	42	1	1	X
ejpam-4207	185	43	)	)	PUNCT
ejpam-4207	185	44	mcli(a	mcli(a	NOUN
ejpam-4207	185	45	)	)	PUNCT
ejpam-4207	185	46	=	=	SYM
ejpam-4207	185	47	cl⋆(a	cl⋆(a	PROPN
ejpam-4207	185	48	)	)	PUNCT
ejpam-4207	185	49	(	(	PUNCT
ejpam-4207	185	50	resp	resp	NOUN
ejpam-4207	185	51	.	.	PUNCT
ejpam-4207	186	1	αcli(a	αcli(a	NUM
ejpam-4207	186	2	)	)	PUNCT
ejpam-4207	186	3	,	,	PUNCT
ejpam-4207	186	4	scli(a	scli(a	ADP
ejpam-4207	186	5	)	)	PUNCT
ejpam-4207	186	6	,	,	PUNCT
ejpam-4207	186	7	pcli(a	pcli(a	NOUN
ejpam-4207	186	8	)	)	PUNCT
ejpam-4207	186	9	,	,	PUNCT
ejpam-4207	186	10	bcli(a	bcli(a	NOUN
ejpam-4207	186	11	)	)	PUNCT
ejpam-4207	186	12	,	,	PUNCT
ejpam-4207	186	13	βcli(a	βcli(a	PROPN
ejpam-4207	186	14	)	)	PUNCT
ejpam-4207	186	15	,	,	PUNCT
ejpam-4207	186	16	wscli(a	wscli(a	PROPN
ejpam-4207	186	17	)	)	PUNCT
ejpam-4207	186	18	,	,	PUNCT
ejpam-4207	186	19	wbcli(a	wbcli(a	PROPN
ejpam-4207	186	20	)	)	PUNCT
ejpam-4207	186	21	,	,	PUNCT
ejpam-4207	186	22	sβcli(a	sβcli(a	NOUN
ejpam-4207	186	23	)	)	PUNCT
ejpam-4207	186	24	,	,	PUNCT
ejpam-4207	186	25	s⋆cli(a	s⋆cli(a	PROPN
ejpam-4207	186	26	)	)	PUNCT
ejpam-4207	186	27	,	,	PUNCT
ejpam-4207	186	28	p⋆cli(a	p⋆cli(a	PROPN
ejpam-4207	186	29	)	)	PUNCT
ejpam-4207	186	30	,	,	PUNCT
ejpam-4207	186	31	β⋆cli(a	β⋆cli(a	PROPN
ejpam-4207	186	32	)	)	PUNCT
ejpam-4207	186	33	)	)	PUNCT
ejpam-4207	186	34	,	,	PUNCT
ejpam-4207	186	35	(	(	PUNCT
ejpam-4207	186	36	2	2	X
ejpam-4207	186	37	)	)	PUNCT
ejpam-4207	186	38	minti(a	minti(a	PROPN
ejpam-4207	186	39	)	)	PUNCT
ejpam-4207	186	40	=	=	SYM
ejpam-4207	186	41	int⋆(a	int⋆(a	NOUN
ejpam-4207	186	42	)	)	PUNCT
ejpam-4207	186	43	(	(	PUNCT
ejpam-4207	186	44	resp	resp	NOUN
ejpam-4207	186	45	.	.	PUNCT
ejpam-4207	187	1	αinti(a	αinti(a	X
ejpam-4207	187	2	)	)	PUNCT
ejpam-4207	187	3	,	,	PUNCT
ejpam-4207	187	4	sinti(a	sinti(a	PROPN
ejpam-4207	187	5	)	)	PUNCT
ejpam-4207	187	6	,	,	PUNCT
ejpam-4207	187	7	pinti(a	pinti(a	NOUN
ejpam-4207	187	8	)	)	PUNCT
ejpam-4207	187	9	,	,	PUNCT
ejpam-4207	187	10	binti(a	binti(a	ADP
ejpam-4207	187	11	)	)	PUNCT
ejpam-4207	187	12	,	,	PUNCT
ejpam-4207	187	13	βinti(a	βinti(a	NOUN
ejpam-4207	187	14	)	)	PUNCT
ejpam-4207	187	15	,	,	PUNCT
ejpam-4207	187	16	wsinti(a	wsinti(a	PROPN
ejpam-4207	187	17	)	)	PUNCT
ejpam-4207	187	18	,	,	PUNCT
ejpam-4207	187	19	wbinti(a	wbinti(a	PROPN
ejpam-4207	187	20	)	)	PUNCT
ejpam-4207	187	21	,	,	PUNCT
ejpam-4207	187	22	sβinti(a	sβinti(a	PROPN
ejpam-4207	187	23	)	)	PUNCT
ejpam-4207	187	24	,	,	PUNCT
ejpam-4207	187	25	s⋆inti(a	s⋆inti(a	PROPN
ejpam-4207	187	26	)	)	PUNCT
ejpam-4207	187	27	,	,	PUNCT
ejpam-4207	187	28	p⋆inti(a	p⋆inti(a	PROPN
ejpam-4207	187	29	)	)	PUNCT
ejpam-4207	187	30	,	,	PUNCT
ejpam-4207	187	31	β⋆inti(a	β⋆inti(a	PROPN
ejpam-4207	187	32	)	)	PUNCT
ejpam-4207	187	33	)	)	PUNCT
ejpam-4207	187	34	.	.	PUNCT
ejpam-4207	188	1	5	5	X
ejpam-4207	188	2	.	.	X
ejpam-4207	188	3	m	m	PROPN
ejpam-4207	188	4	-	-	PUNCT
ejpam-4207	188	5	i	i	PRON
ejpam-4207	188	6	-	-	PUNCT
ejpam-4207	188	7	continuous	continuous	ADJ
ejpam-4207	188	8	multifunctions	multifunction	NOUN
ejpam-4207	188	9	definition	definition	NOUN
ejpam-4207	188	10	14	14	NUM
ejpam-4207	188	11	.	.	PUNCT
ejpam-4207	189	1	a	a	DET
ejpam-4207	189	2	multifunction	multifunction	NOUN
ejpam-4207	189	3	f	f	NOUN
ejpam-4207	189	4	:	:	PUNCT
ejpam-4207	189	5	(	(	PUNCT
ejpam-4207	189	6	x	x	X
ejpam-4207	189	7	,	,	PUNCT
ejpam-4207	189	8	τ	τ	PROPN
ejpam-4207	189	9	,	,	PUNCT
ejpam-4207	189	10	i	i	NOUN
ejpam-4207	189	11	)	)	PUNCT
ejpam-4207	189	12	→	→	SYM
ejpam-4207	189	13	(	(	PUNCT
ejpam-4207	189	14	y	y	PROPN
ejpam-4207	189	15	,	,	PUNCT
ejpam-4207	189	16	σ	σ	PROPN
ejpam-4207	189	17	)	)	PUNCT
ejpam-4207	189	18	is	be	AUX
ejpam-4207	189	19	said	say	VERB
ejpam-4207	189	20	to	to	PART
ejpam-4207	189	21	be	be	AUX
ejpam-4207	189	22	m	m	NOUN
ejpam-4207	189	23	-	-	ADJ
ejpam-4207	189	24	i	i	PRON
ejpam-4207	189	25	-	-	NOUN
ejpam-4207	189	26	continuous	continuous	ADJ
ejpam-4207	189	27	at	at	ADP
ejpam-4207	189	28	x	x	X
ejpam-4207	189	29	∈	∈	PROPN
ejpam-4207	189	30	x	x	SYM
ejpam-4207	189	31	if	if	SCONJ
ejpam-4207	189	32	for	for	ADP
ejpam-4207	189	33	each	each	DET
ejpam-4207	189	34	open	open	ADJ
ejpam-4207	189	35	sets	set	NOUN
ejpam-4207	189	36	v1	v1	NOUN
ejpam-4207	189	37	,	,	PUNCT
ejpam-4207	189	38	v2	v2	PROPN
ejpam-4207	189	39	of	of	ADP
ejpam-4207	189	40	y	y	PRON
ejpam-4207	189	41	such	such	ADJ
ejpam-4207	189	42	that	that	SCONJ
ejpam-4207	189	43	f	f	PROPN
ejpam-4207	189	44	(	(	PUNCT
ejpam-4207	189	45	x	x	X
ejpam-4207	189	46	)	)	PUNCT
ejpam-4207	189	47	∈	∈	NOUN
ejpam-4207	189	48	v	v	ADP
ejpam-4207	189	49	+	+	CCONJ
ejpam-4207	189	50	1	1	NUM
ejpam-4207	189	51	∩v	∩v	NOUN
ejpam-4207	189	52	−	−	PROPN
ejpam-4207	189	53	2	2	NUM
ejpam-4207	189	54	,	,	PUNCT
ejpam-4207	189	55	there	there	PRON
ejpam-4207	189	56	exists	exist	VERB
ejpam-4207	189	57	u	u	PROPN
ejpam-4207	189	58	∈	∈	PROPN
ejpam-4207	189	59	mio(x	mio(x	PROPN
ejpam-4207	189	60	)	)	PUNCT
ejpam-4207	189	61	takashi	takashi	PROPN
ejpam-4207	189	62	noiri	noiri	PROPN
ejpam-4207	189	63	,	,	PUNCT
ejpam-4207	189	64	valeriu	valeriu	ADJ
ejpam-4207	189	65	popa	popa	NOUN
ejpam-4207	189	66	/	/	SYM
ejpam-4207	189	67	eur	eur	PROPN
ejpam-4207	189	68	.	.	PUNCT
ejpam-4207	190	1	j.	j.	PROPN
ejpam-4207	190	2	pure	pure	PROPN
ejpam-4207	190	3	appl	appl	PROPN
ejpam-4207	190	4	.	.	PROPN
ejpam-4207	190	5	math	math	PROPN
ejpam-4207	190	6	,	,	PUNCT
ejpam-4207	190	7	15	15	NUM
ejpam-4207	190	8	(	(	PUNCT
ejpam-4207	190	9	1	1	NUM
ejpam-4207	190	10	)	)	PUNCT
ejpam-4207	190	11	(	(	PUNCT
ejpam-4207	190	12	2022	2022	NUM
ejpam-4207	190	13	)	)	PUNCT
ejpam-4207	190	14	,	,	PUNCT
ejpam-4207	190	15	1	1	NUM
ejpam-4207	190	16	-	-	SYM
ejpam-4207	190	17	14	14	NUM
ejpam-4207	190	18	7	7	NUM
ejpam-4207	190	19	containing	contain	VERB
ejpam-4207	190	20	x	x	PUNCT
ejpam-4207	190	21	such	such	ADJ
ejpam-4207	190	22	that	that	SCONJ
ejpam-4207	190	23	f	f	PROPN
ejpam-4207	190	24	(	(	PUNCT
ejpam-4207	190	25	u	u	NOUN
ejpam-4207	190	26	)	)	PUNCT
ejpam-4207	190	27	∈	∈	NOUN
ejpam-4207	190	28	v	v	ADP
ejpam-4207	190	29	+	+	CCONJ
ejpam-4207	190	30	1	1	NUM
ejpam-4207	190	31	∩	∩	NOUN
ejpam-4207	190	32	v	v	ADP
ejpam-4207	190	33	−	−	PROPN
ejpam-4207	190	34	2	2	NUM
ejpam-4207	190	35	for	for	ADP
ejpam-4207	190	36	every	every	DET
ejpam-4207	190	37	u	u	PROPN
ejpam-4207	190	38	∈	∈	PROPN
ejpam-4207	190	39	u	u	NOUN
ejpam-4207	190	40	.	.	PUNCT
ejpam-4207	191	1	f	f	PROPN
ejpam-4207	191	2	is	be	AUX
ejpam-4207	191	3	said	say	VERB
ejpam-4207	191	4	to	to	PART
ejpam-4207	191	5	be	be	AUX
ejpam-4207	191	6	m	m	NOUN
ejpam-4207	191	7	-	-	ADJ
ejpam-4207	191	8	i	i	PRON
ejpam-4207	191	9	-	-	NOUN
ejpam-4207	191	10	continuous	continuous	ADJ
ejpam-4207	191	11	if	if	SCONJ
ejpam-4207	191	12	it	it	PRON
ejpam-4207	191	13	has	have	VERB
ejpam-4207	191	14	the	the	DET
ejpam-4207	191	15	property	property	NOUN
ejpam-4207	191	16	at	at	ADP
ejpam-4207	191	17	each	each	DET
ejpam-4207	191	18	point	point	NOUN
ejpam-4207	191	19	of	of	ADP
ejpam-4207	191	20	x.	x.	NOUN
ejpam-4207	191	21	by	by	ADP
ejpam-4207	191	22	theorem	theorem	NOUN
ejpam-4207	191	23	1	1	NUM
ejpam-4207	191	24	and	and	CCONJ
ejpam-4207	191	25	definition	definition	NOUN
ejpam-4207	191	26	13	13	NUM
ejpam-4207	191	27	,	,	PUNCT
ejpam-4207	191	28	we	we	PRON
ejpam-4207	191	29	obtain	obtain	VERB
ejpam-4207	191	30	the	the	DET
ejpam-4207	191	31	following	follow	VERB
ejpam-4207	191	32	theorem	theorem	VERB
ejpam-4207	191	33	.	.	PUNCT
ejpam-4207	191	34	theorem	theorem	ADJ
ejpam-4207	191	35	8	8	NUM
ejpam-4207	191	36	.	.	PUNCT
ejpam-4207	191	37	for	for	ADP
ejpam-4207	191	38	a	a	DET
ejpam-4207	191	39	multifunction	multifunction	NOUN
ejpam-4207	191	40	f	f	NOUN
ejpam-4207	191	41	:	:	PUNCT
ejpam-4207	191	42	(	(	PUNCT
ejpam-4207	191	43	x	x	X
ejpam-4207	191	44	,	,	PUNCT
ejpam-4207	191	45	τ	τ	PROPN
ejpam-4207	191	46	,	,	PUNCT
ejpam-4207	191	47	i	i	NOUN
ejpam-4207	191	48	)	)	PUNCT
ejpam-4207	191	49	→	→	SYM
ejpam-4207	191	50	(	(	PUNCT
ejpam-4207	191	51	y	y	PROPN
ejpam-4207	191	52	,	,	PUNCT
ejpam-4207	191	53	σ	σ	PROPN
ejpam-4207	191	54	)	)	PUNCT
ejpam-4207	191	55	,	,	PUNCT
ejpam-4207	191	56	the	the	DET
ejpam-4207	191	57	following	follow	VERB
ejpam-4207	191	58	properties	property	NOUN
ejpam-4207	191	59	are	be	AUX
ejpam-4207	191	60	equivalent	equivalent	ADJ
ejpam-4207	191	61	:	:	PUNCT
ejpam-4207	191	62	(	(	PUNCT
ejpam-4207	191	63	1	1	X
ejpam-4207	191	64	)	)	PUNCT
ejpam-4207	191	65	f	f	PROPN
ejpam-4207	191	66	is	be	AUX
ejpam-4207	191	67	m	m	PROPN
ejpam-4207	191	68	-	-	ADJ
ejpam-4207	191	69	i	i	PRON
ejpam-4207	191	70	-	-	NOUN
ejpam-4207	191	71	continuous	continuous	ADJ
ejpam-4207	191	72	at	at	ADP
ejpam-4207	191	73	x	x	X
ejpam-4207	191	74	∈	∈	PROPN
ejpam-4207	191	75	x	x	X
ejpam-4207	191	76	;	;	PUNCT
ejpam-4207	191	77	(	(	PUNCT
ejpam-4207	191	78	2	2	X
ejpam-4207	191	79	)	)	PUNCT
ejpam-4207	191	80	f	f	NOUN
ejpam-4207	191	81	(	(	PUNCT
ejpam-4207	191	82	x	x	X
ejpam-4207	191	83	)	)	PUNCT
ejpam-4207	191	84	∈	∈	NOUN
ejpam-4207	191	85	v	v	ADP
ejpam-4207	191	86	+	+	CCONJ
ejpam-4207	191	87	1	1	NUM
ejpam-4207	191	88	∩	∩	NOUN
ejpam-4207	191	89	v	v	ADP
ejpam-4207	191	90	−	−	PROPN
ejpam-4207	191	91	2	2	NUM
ejpam-4207	191	92	implies	imply	VERB
ejpam-4207	191	93	x	x	X
ejpam-4207	191	94	∈	∈	NOUN
ejpam-4207	191	95	minti[f	minti[f	NOUN
ejpam-4207	192	1	+	+	NOUN
ejpam-4207	192	2	(	(	PUNCT
ejpam-4207	192	3	v1)∩f−(v2	v1)∩f−(v2	PROPN
ejpam-4207	192	4	)	)	PUNCT
ejpam-4207	192	5	]	]	PUNCT
ejpam-4207	192	6	for	for	ADP
ejpam-4207	192	7	every	every	DET
ejpam-4207	192	8	open	open	ADJ
ejpam-4207	192	9	sets	set	NOUN
ejpam-4207	192	10	v1	v1	NOUN
ejpam-4207	192	11	,	,	PUNCT
ejpam-4207	192	12	v2	v2	PROPN
ejpam-4207	192	13	of	of	ADP
ejpam-4207	192	14	y	y	PROPN
ejpam-4207	192	15	;	;	PUNCT
ejpam-4207	192	16	(	(	PUNCT
ejpam-4207	192	17	3	3	X
ejpam-4207	192	18	)	)	PUNCT
ejpam-4207	192	19	x	x	SYM
ejpam-4207	192	20	∈	∈	PROPN
ejpam-4207	192	21	mcli(f	mcli(f	PRON
ejpam-4207	192	22	−(b1	−(b1	NUM
ejpam-4207	192	23	)	)	PUNCT
ejpam-4207	192	24	∪	∪	NOUN
ejpam-4207	192	25	f+(b2	f+(b2	NOUN
ejpam-4207	192	26	)	)	PUNCT
ejpam-4207	192	27	)	)	PUNCT
ejpam-4207	192	28	implies	imply	VERB
ejpam-4207	192	29	x	x	PUNCT
ejpam-4207	192	30	∈	∈	NUM
ejpam-4207	192	31	f−(cl(b1	f−(cl(b1	NOUN
ejpam-4207	192	32	)	)	PUNCT
ejpam-4207	192	33	)	)	PUNCT
ejpam-4207	192	34	∪	∪	ADP
ejpam-4207	192	35	f+(cl(b2	f+(cl(b2	NOUN
ejpam-4207	192	36	)	)	PUNCT
ejpam-4207	192	37	)	)	PUNCT
ejpam-4207	192	38	for	for	ADP
ejpam-4207	192	39	every	every	DET
ejpam-4207	192	40	subsets	subset	NOUN
ejpam-4207	192	41	b1	b1	NOUN
ejpam-4207	192	42	,	,	PUNCT
ejpam-4207	192	43	b2	b2	NOUN
ejpam-4207	192	44	of	of	ADP
ejpam-4207	192	45	y	y	PROPN
ejpam-4207	192	46	;	;	PUNCT
ejpam-4207	192	47	(	(	PUNCT
ejpam-4207	192	48	4	4	X
ejpam-4207	192	49	)	)	PUNCT
ejpam-4207	192	50	x	x	SYM
ejpam-4207	192	51	∈	∈	PROPN
ejpam-4207	192	52	f−(int(b1	f−(int(b1	NOUN
ejpam-4207	192	53	)	)	PUNCT
ejpam-4207	192	54	)	)	PUNCT
ejpam-4207	192	55	∩	∩	PROPN
ejpam-4207	192	56	f+(int(b2	f+(int(b2	PROPN
ejpam-4207	192	57	)	)	PUNCT
ejpam-4207	192	58	)	)	PUNCT
ejpam-4207	192	59	implies	imply	VERB
ejpam-4207	192	60	x	x	PUNCT
ejpam-4207	192	61	∈	∈	NOUN
ejpam-4207	192	62	minti(f	minti(f	NOUN
ejpam-4207	192	63	−(b1	−(b1	NOUN
ejpam-4207	192	64	)	)	PUNCT
ejpam-4207	192	65	∩	∩	ADJ
ejpam-4207	192	66	f+(b2	f+(b2	NOUN
ejpam-4207	192	67	)	)	PUNCT
ejpam-4207	192	68	)	)	PUNCT
ejpam-4207	192	69	for	for	ADP
ejpam-4207	192	70	every	every	DET
ejpam-4207	192	71	subsets	subset	NOUN
ejpam-4207	192	72	b1	b1	NOUN
ejpam-4207	192	73	,	,	PUNCT
ejpam-4207	192	74	b2	b2	NOUN
ejpam-4207	192	75	of	of	ADP
ejpam-4207	192	76	y.	y.	NOUN
ejpam-4207	192	77	by	by	ADP
ejpam-4207	192	78	theorem	theorem	ADJ
ejpam-4207	192	79	2	2	NUM
ejpam-4207	192	80	and	and	CCONJ
ejpam-4207	192	81	definition	definition	NOUN
ejpam-4207	192	82	13	13	NUM
ejpam-4207	192	83	,	,	PUNCT
ejpam-4207	192	84	we	we	PRON
ejpam-4207	192	85	obtain	obtain	VERB
ejpam-4207	192	86	the	the	DET
ejpam-4207	192	87	following	follow	VERB
ejpam-4207	192	88	theorem	theorem	NOUN
ejpam-4207	192	89	:	:	PUNCT
ejpam-4207	192	90	theorem	theorem	NOUN
ejpam-4207	192	91	9	9	NUM
ejpam-4207	192	92	.	.	X
ejpam-4207	192	93	for	for	ADP
ejpam-4207	192	94	a	a	DET
ejpam-4207	192	95	multifunction	multifunction	NOUN
ejpam-4207	193	1	f	f	NOUN
ejpam-4207	193	2	:	:	PUNCT
ejpam-4207	193	3	(	(	PUNCT
ejpam-4207	193	4	x	x	X
ejpam-4207	193	5	,	,	PUNCT
ejpam-4207	193	6	τ	τ	PROPN
ejpam-4207	193	7	,	,	PUNCT
ejpam-4207	193	8	i	i	NOUN
ejpam-4207	193	9	)	)	PUNCT
ejpam-4207	193	10	→	→	SYM
ejpam-4207	193	11	(	(	PUNCT
ejpam-4207	193	12	y	y	PROPN
ejpam-4207	193	13	,	,	PUNCT
ejpam-4207	193	14	σ	σ	PROPN
ejpam-4207	193	15	)	)	PUNCT
ejpam-4207	193	16	,	,	PUNCT
ejpam-4207	193	17	the	the	DET
ejpam-4207	193	18	following	follow	VERB
ejpam-4207	193	19	properties	property	NOUN
ejpam-4207	193	20	are	be	AUX
ejpam-4207	193	21	equivalent	equivalent	ADJ
ejpam-4207	193	22	:	:	PUNCT
ejpam-4207	193	23	(	(	PUNCT
ejpam-4207	193	24	1	1	X
ejpam-4207	193	25	)	)	PUNCT
ejpam-4207	193	26	f	f	PROPN
ejpam-4207	193	27	is	be	AUX
ejpam-4207	193	28	m	m	NOUN
ejpam-4207	193	29	-	-	ADJ
ejpam-4207	193	30	i	i	NOUN
ejpam-4207	193	31	-	-	PUNCT
ejpam-4207	193	32	continuous	continuous	ADJ
ejpam-4207	193	33	;	;	PUNCT
ejpam-4207	193	34	(	(	PUNCT
ejpam-4207	193	35	2	2	X
ejpam-4207	193	36	)	)	PUNCT
ejpam-4207	193	37	f+(g1	f+(g1	NOUN
ejpam-4207	193	38	)	)	PUNCT
ejpam-4207	193	39	∩	∩	NOUN
ejpam-4207	193	40	f−(g2	f−(g2	PRON
ejpam-4207	193	41	)	)	PUNCT
ejpam-4207	193	42	∈	∈	PROPN
ejpam-4207	193	43	mio(x	mio(x	PROPN
ejpam-4207	193	44	)	)	PUNCT
ejpam-4207	193	45	for	for	ADP
ejpam-4207	193	46	every	every	DET
ejpam-4207	193	47	open	open	ADJ
ejpam-4207	193	48	sets	set	NOUN
ejpam-4207	193	49	g1	g1	NOUN
ejpam-4207	193	50	,	,	PUNCT
ejpam-4207	193	51	g2	g2	PROPN
ejpam-4207	193	52	of	of	ADP
ejpam-4207	193	53	y	y	PROPN
ejpam-4207	193	54	;	;	PUNCT
ejpam-4207	193	55	(	(	PUNCT
ejpam-4207	193	56	3	3	X
ejpam-4207	193	57	)	)	PUNCT
ejpam-4207	193	58	f−(k1	f−(k1	ADP
ejpam-4207	193	59	)	)	PUNCT
ejpam-4207	193	60	∪	∪	ADP
ejpam-4207	193	61	f+(k2	f+(k2	NOUN
ejpam-4207	193	62	)	)	PUNCT
ejpam-4207	193	63	is	be	AUX
ejpam-4207	193	64	m	m	PROPN
ejpam-4207	193	65	-	-	PUNCT
ejpam-4207	193	66	i	i	PRON
ejpam-4207	193	67	-	-	PUNCT
ejpam-4207	193	68	closed	close	VERB
ejpam-4207	193	69	for	for	ADP
ejpam-4207	193	70	every	every	DET
ejpam-4207	193	71	closed	closed	ADJ
ejpam-4207	193	72	sets	set	NOUN
ejpam-4207	193	73	k1,k2	k1,k2	PROPN
ejpam-4207	193	74	of	of	ADP
ejpam-4207	193	75	y	y	PROPN
ejpam-4207	193	76	;	;	PUNCT
ejpam-4207	193	77	(	(	PUNCT
ejpam-4207	193	78	4	4	X
ejpam-4207	193	79	)	)	PUNCT
ejpam-4207	193	80	mcli(f	mcli(f	SYM
ejpam-4207	193	81	−(b1	−(b1	NUM
ejpam-4207	193	82	)	)	PUNCT
ejpam-4207	193	83	∪	∪	NOUN
ejpam-4207	193	84	f+(b2	f+(b2	NOUN
ejpam-4207	193	85	)	)	PUNCT
ejpam-4207	193	86	)	)	PUNCT
ejpam-4207	194	1	⊂	⊂	PROPN
ejpam-4207	194	2	f−(cl(b1	f−(cl(b1	PROPN
ejpam-4207	194	3	)	)	PUNCT
ejpam-4207	194	4	)	)	PUNCT
ejpam-4207	194	5	∪	∪	ADP
ejpam-4207	194	6	f+(cl(b2	f+(cl(b2	NOUN
ejpam-4207	194	7	)	)	PUNCT
ejpam-4207	194	8	)	)	PUNCT
ejpam-4207	194	9	for	for	ADP
ejpam-4207	194	10	every	every	DET
ejpam-4207	194	11	subsets	subset	NOUN
ejpam-4207	194	12	b1	b1	NOUN
ejpam-4207	194	13	,	,	PUNCT
ejpam-4207	194	14	b2	b2	NOUN
ejpam-4207	194	15	of	of	ADP
ejpam-4207	194	16	y	y	PROPN
ejpam-4207	194	17	;	;	PUNCT
ejpam-4207	194	18	(	(	PUNCT
ejpam-4207	194	19	5	5	X
ejpam-4207	194	20	)	)	PUNCT
ejpam-4207	194	21	f−(int(b1	f−(int(b1	NOUN
ejpam-4207	194	22	)	)	PUNCT
ejpam-4207	194	23	)	)	PUNCT
ejpam-4207	194	24	∩	∩	PROPN
ejpam-4207	194	25	f+(int(b2	f+(int(b2	PROPN
ejpam-4207	194	26	)	)	PUNCT
ejpam-4207	194	27	)	)	PUNCT
ejpam-4207	195	1	⊂	⊂	PROPN
ejpam-4207	195	2	minti(f	minti(f	PRON
ejpam-4207	195	3	−(b1	−(b1	NUM
ejpam-4207	195	4	)	)	PUNCT
ejpam-4207	195	5	∩	∩	ADJ
ejpam-4207	195	6	f+(b2	f+(b2	NOUN
ejpam-4207	195	7	)	)	PUNCT
ejpam-4207	195	8	)	)	PUNCT
ejpam-4207	195	9	for	for	ADP
ejpam-4207	195	10	every	every	DET
ejpam-4207	195	11	subsets	subset	NOUN
ejpam-4207	195	12	b1	b1	NOUN
ejpam-4207	195	13	,	,	PUNCT
ejpam-4207	195	14	b2	b2	NOUN
ejpam-4207	195	15	of	of	ADP
ejpam-4207	195	16	y	y	PROPN
ejpam-4207	195	17	.	.	PUNCT
ejpam-4207	196	1	let	let	VERB
ejpam-4207	196	2	mio(x	mio(x	NOUN
ejpam-4207	196	3	)	)	PUNCT
ejpam-4207	196	4	=	=	PUNCT
ejpam-4207	197	1	τ⋆	τ⋆	NOUN
ejpam-4207	197	2	,	,	PUNCT
ejpam-4207	197	3	then	then	ADV
ejpam-4207	197	4	by	by	ADP
ejpam-4207	197	5	theorem	theorem	NOUN
ejpam-4207	197	6	9	9	NUM
ejpam-4207	197	7	,	,	PUNCT
ejpam-4207	197	8	we	we	PRON
ejpam-4207	197	9	obtain	obtain	VERB
ejpam-4207	197	10	the	the	DET
ejpam-4207	197	11	following	follow	VERB
ejpam-4207	197	12	corollary	corollary	ADJ
ejpam-4207	197	13	:	:	PUNCT
ejpam-4207	197	14	corollary	corollary	ADJ
ejpam-4207	197	15	1	1	NUM
ejpam-4207	197	16	.	.	PUNCT
ejpam-4207	197	17	for	for	ADP
ejpam-4207	197	18	a	a	DET
ejpam-4207	197	19	multifunction	multifunction	NOUN
ejpam-4207	197	20	f	f	NOUN
ejpam-4207	197	21	:	:	PUNCT
ejpam-4207	197	22	(	(	PUNCT
ejpam-4207	197	23	x	x	X
ejpam-4207	197	24	,	,	PUNCT
ejpam-4207	197	25	τ	τ	PROPN
ejpam-4207	197	26	,	,	PUNCT
ejpam-4207	197	27	i	i	NOUN
ejpam-4207	197	28	)	)	PUNCT
ejpam-4207	197	29	→	→	SYM
ejpam-4207	197	30	(	(	PUNCT
ejpam-4207	197	31	y	y	PROPN
ejpam-4207	197	32	,	,	PUNCT
ejpam-4207	197	33	σ	σ	PROPN
ejpam-4207	197	34	)	)	PUNCT
ejpam-4207	197	35	,	,	PUNCT
ejpam-4207	197	36	the	the	DET
ejpam-4207	197	37	following	follow	VERB
ejpam-4207	197	38	properties	property	NOUN
ejpam-4207	197	39	are	be	AUX
ejpam-4207	197	40	equivalent	equivalent	ADJ
ejpam-4207	197	41	:	:	PUNCT
ejpam-4207	197	42	(	(	PUNCT
ejpam-4207	197	43	1	1	X
ejpam-4207	197	44	)	)	PUNCT
ejpam-4207	197	45	f	f	PROPN
ejpam-4207	197	46	is	be	AUX
ejpam-4207	197	47	τ⋆-continuous	τ⋆-continuous	ADJ
ejpam-4207	197	48	;	;	PUNCT
ejpam-4207	197	49	(	(	PUNCT
ejpam-4207	197	50	2	2	X
ejpam-4207	197	51	)	)	PUNCT
ejpam-4207	197	52	f+(g1	f+(g1	NOUN
ejpam-4207	197	53	)	)	PUNCT
ejpam-4207	197	54	∩	∩	NOUN
ejpam-4207	197	55	f−(g2	f−(g2	PRON
ejpam-4207	197	56	)	)	PUNCT
ejpam-4207	197	57	∈	∈	NOUN
ejpam-4207	197	58	τ⋆	τ⋆	NOUN
ejpam-4207	197	59	for	for	ADP
ejpam-4207	197	60	every	every	DET
ejpam-4207	197	61	open	open	ADJ
ejpam-4207	197	62	sets	set	NOUN
ejpam-4207	197	63	g1	g1	NOUN
ejpam-4207	197	64	,	,	PUNCT
ejpam-4207	197	65	g2	g2	PROPN
ejpam-4207	197	66	of	of	ADP
ejpam-4207	197	67	y	y	PROPN
ejpam-4207	197	68	;	;	PUNCT
ejpam-4207	197	69	(	(	PUNCT
ejpam-4207	197	70	3	3	X
ejpam-4207	197	71	)	)	PUNCT
ejpam-4207	197	72	f−(k1	f−(k1	ADP
ejpam-4207	197	73	)	)	PUNCT
ejpam-4207	197	74	∪	∪	ADP
ejpam-4207	197	75	f+(k2	f+(k2	NOUN
ejpam-4207	197	76	)	)	PUNCT
ejpam-4207	197	77	is	be	AUX
ejpam-4207	197	78	τ⋆-closed	τ⋆-close	VERB
ejpam-4207	197	79	for	for	ADP
ejpam-4207	197	80	every	every	DET
ejpam-4207	197	81	closed	closed	ADJ
ejpam-4207	197	82	sets	set	NOUN
ejpam-4207	197	83	k1,k2	k1,k2	PROPN
ejpam-4207	197	84	of	of	ADP
ejpam-4207	197	85	y	y	PROPN
ejpam-4207	197	86	;	;	PUNCT
ejpam-4207	197	87	(	(	PUNCT
ejpam-4207	197	88	4	4	X
ejpam-4207	197	89	)	)	PUNCT
ejpam-4207	197	90	cl⋆(f−(b1)∪f+(b2	cl⋆(f−(b1)∪f+(b2	NOUN
ejpam-4207	197	91	)	)	PUNCT
ejpam-4207	197	92	)	)	PUNCT
ejpam-4207	198	1	⊂	⊂	PROPN
ejpam-4207	198	2	f−(cl(b1))∪f+(cl(b2	f−(cl(b1))∪f+(cl(b2	PROPN
ejpam-4207	198	3	)	)	PUNCT
ejpam-4207	198	4	)	)	PUNCT
ejpam-4207	198	5	for	for	ADP
ejpam-4207	198	6	every	every	DET
ejpam-4207	198	7	subsets	subset	NOUN
ejpam-4207	198	8	b1	b1	NOUN
ejpam-4207	198	9	,	,	PUNCT
ejpam-4207	198	10	b2	b2	NOUN
ejpam-4207	198	11	of	of	ADP
ejpam-4207	198	12	y	y	PROPN
ejpam-4207	198	13	;	;	PUNCT
ejpam-4207	198	14	(	(	PUNCT
ejpam-4207	198	15	5	5	X
ejpam-4207	198	16	)	)	PUNCT
ejpam-4207	198	17	f−(int(b1	f−(int(b1	NOUN
ejpam-4207	198	18	)	)	PUNCT
ejpam-4207	198	19	)	)	PUNCT
ejpam-4207	198	20	∩	∩	PROPN
ejpam-4207	198	21	f+(int(b2	f+(int(b2	PROPN
ejpam-4207	198	22	)	)	PUNCT
ejpam-4207	198	23	)	)	PUNCT
ejpam-4207	199	1	⊂	⊂	PROPN
ejpam-4207	199	2	int⋆(f−(b1	int⋆(f−(b1	PROPN
ejpam-4207	199	3	)	)	PUNCT
ejpam-4207	199	4	∩	∩	NOUN
ejpam-4207	199	5	f+(b2	f+(b2	NOUN
ejpam-4207	199	6	)	)	PUNCT
ejpam-4207	199	7	)	)	PUNCT
ejpam-4207	199	8	for	for	ADP
ejpam-4207	199	9	every	every	DET
ejpam-4207	199	10	subsets	subset	NOUN
ejpam-4207	199	11	b1	b1	NOUN
ejpam-4207	199	12	,	,	PUNCT
ejpam-4207	199	13	b2	b2	NOUN
ejpam-4207	199	14	of	of	ADP
ejpam-4207	199	15	y	y	PROPN
ejpam-4207	199	16	.	.	PUNCT
ejpam-4207	200	1	let	let	VERB
ejpam-4207	200	2	mio(x	mio(x	NOUN
ejpam-4207	200	3	)	)	PUNCT
ejpam-4207	200	4	=	=	SYM
ejpam-4207	201	1	sio(x	sio(x	NOUN
ejpam-4207	201	2	)	)	PUNCT
ejpam-4207	201	3	,	,	PUNCT
ejpam-4207	201	4	then	then	ADV
ejpam-4207	201	5	by	by	ADP
ejpam-4207	201	6	theorem	theorem	NOUN
ejpam-4207	201	7	9	9	NUM
ejpam-4207	201	8	,	,	PUNCT
ejpam-4207	201	9	we	we	PRON
ejpam-4207	201	10	obtain	obtain	VERB
ejpam-4207	201	11	the	the	DET
ejpam-4207	201	12	following	follow	VERB
ejpam-4207	201	13	corollary	corollary	ADJ
ejpam-4207	201	14	:	:	PUNCT
ejpam-4207	201	15	corollary	corollary	ADJ
ejpam-4207	201	16	2	2	NUM
ejpam-4207	201	17	.	.	PUNCT
ejpam-4207	201	18	for	for	ADP
ejpam-4207	201	19	a	a	DET
ejpam-4207	201	20	multifunction	multifunction	NOUN
ejpam-4207	201	21	f	f	NOUN
ejpam-4207	201	22	:	:	PUNCT
ejpam-4207	201	23	(	(	PUNCT
ejpam-4207	201	24	x	x	X
ejpam-4207	201	25	,	,	PUNCT
ejpam-4207	201	26	τ	τ	PROPN
ejpam-4207	201	27	,	,	PUNCT
ejpam-4207	201	28	i	i	NOUN
ejpam-4207	201	29	)	)	PUNCT
ejpam-4207	201	30	→	→	SYM
ejpam-4207	201	31	(	(	PUNCT
ejpam-4207	201	32	y	y	PROPN
ejpam-4207	201	33	,	,	PUNCT
ejpam-4207	201	34	σ	σ	PROPN
ejpam-4207	201	35	)	)	PUNCT
ejpam-4207	201	36	,	,	PUNCT
ejpam-4207	201	37	the	the	DET
ejpam-4207	201	38	following	follow	VERB
ejpam-4207	201	39	properties	property	NOUN
ejpam-4207	201	40	are	be	AUX
ejpam-4207	201	41	equivalent	equivalent	ADJ
ejpam-4207	201	42	:	:	PUNCT
ejpam-4207	201	43	(	(	PUNCT
ejpam-4207	201	44	1	1	X
ejpam-4207	201	45	)	)	PUNCT
ejpam-4207	201	46	f	f	PROPN
ejpam-4207	201	47	is	be	AUX
ejpam-4207	201	48	semi	semi	ADJ
ejpam-4207	201	49	-	-	ADJ
ejpam-4207	201	50	i	i	ADV
ejpam-4207	201	51	-	-	PUNCT
ejpam-4207	201	52	continuous	continuous	ADJ
ejpam-4207	201	53	;	;	PUNCT
ejpam-4207	201	54	(	(	PUNCT
ejpam-4207	201	55	2	2	X
ejpam-4207	201	56	)	)	PUNCT
ejpam-4207	201	57	f+(g1	f+(g1	NOUN
ejpam-4207	201	58	)	)	PUNCT
ejpam-4207	201	59	∩	∩	NOUN
ejpam-4207	201	60	f−(g2	f−(g2	PRON
ejpam-4207	201	61	)	)	PUNCT
ejpam-4207	201	62	∈	∈	PROPN
ejpam-4207	201	63	sio(x	sio(x	NOUN
ejpam-4207	201	64	)	)	PUNCT
ejpam-4207	201	65	for	for	ADP
ejpam-4207	201	66	every	every	DET
ejpam-4207	201	67	open	open	ADJ
ejpam-4207	201	68	sets	set	NOUN
ejpam-4207	201	69	g1	g1	NOUN
ejpam-4207	201	70	,	,	PUNCT
ejpam-4207	201	71	g2	g2	PROPN
ejpam-4207	201	72	of	of	ADP
ejpam-4207	201	73	y	y	PROPN
ejpam-4207	201	74	;	;	PUNCT
ejpam-4207	201	75	(	(	PUNCT
ejpam-4207	201	76	3	3	X
ejpam-4207	201	77	)	)	PUNCT
ejpam-4207	201	78	f−(k1	f−(k1	ADP
ejpam-4207	201	79	)	)	PUNCT
ejpam-4207	201	80	∪	∪	ADP
ejpam-4207	201	81	f+(k2	f+(k2	NOUN
ejpam-4207	201	82	)	)	PUNCT
ejpam-4207	201	83	is	be	AUX
ejpam-4207	201	84	semi	semi	ADJ
ejpam-4207	201	85	-	-	ADJ
ejpam-4207	201	86	i	i	PRON
ejpam-4207	201	87	-	-	PUNCT
ejpam-4207	201	88	closed	close	VERB
ejpam-4207	201	89	for	for	ADP
ejpam-4207	201	90	every	every	DET
ejpam-4207	201	91	closed	closed	ADJ
ejpam-4207	201	92	sets	set	NOUN
ejpam-4207	201	93	k1,k2	k1,k2	PROPN
ejpam-4207	201	94	of	of	ADP
ejpam-4207	201	95	y	y	PROPN
ejpam-4207	201	96	;	;	PUNCT
ejpam-4207	201	97	(	(	PUNCT
ejpam-4207	201	98	4	4	X
ejpam-4207	201	99	)	)	PUNCT
ejpam-4207	201	100	scli(f	scli(f	NOUN
ejpam-4207	201	101	−(b1	−(b1	NOUN
ejpam-4207	201	102	)	)	PUNCT
ejpam-4207	201	103	∪	∪	PROPN
ejpam-4207	201	104	f+(b2	f+(b2	NOUN
ejpam-4207	201	105	)	)	PUNCT
ejpam-4207	201	106	)	)	PUNCT
ejpam-4207	202	1	⊂	⊂	PROPN
ejpam-4207	202	2	f−(cl(b1	f−(cl(b1	PROPN
ejpam-4207	202	3	)	)	PUNCT
ejpam-4207	202	4	)	)	PUNCT
ejpam-4207	202	5	∪	∪	ADP
ejpam-4207	202	6	f+(cl(b2	f+(cl(b2	NOUN
ejpam-4207	202	7	)	)	PUNCT
ejpam-4207	202	8	)	)	PUNCT
ejpam-4207	202	9	for	for	ADP
ejpam-4207	202	10	every	every	DET
ejpam-4207	202	11	subsets	subset	NOUN
ejpam-4207	202	12	b1	b1	NOUN
ejpam-4207	202	13	,	,	PUNCT
ejpam-4207	202	14	b2	b2	NOUN
ejpam-4207	202	15	of	of	ADP
ejpam-4207	202	16	takashi	takashi	PROPN
ejpam-4207	202	17	noiri	noiri	PROPN
ejpam-4207	202	18	,	,	PUNCT
ejpam-4207	202	19	valeriu	valeriu	ADJ
ejpam-4207	202	20	popa	popa	NOUN
ejpam-4207	202	21	/	/	SYM
ejpam-4207	202	22	eur	eur	PROPN
ejpam-4207	202	23	.	.	PUNCT
ejpam-4207	203	1	j.	j.	PROPN
ejpam-4207	203	2	pure	pure	PROPN
ejpam-4207	203	3	appl	appl	PROPN
ejpam-4207	203	4	.	.	PROPN
ejpam-4207	203	5	math	math	PROPN
ejpam-4207	203	6	,	,	PUNCT
ejpam-4207	203	7	15	15	NUM
ejpam-4207	203	8	(	(	PUNCT
ejpam-4207	203	9	1	1	NUM
ejpam-4207	203	10	)	)	PUNCT
ejpam-4207	203	11	(	(	PUNCT
ejpam-4207	203	12	2022	2022	NUM
ejpam-4207	203	13	)	)	PUNCT
ejpam-4207	203	14	,	,	PUNCT
ejpam-4207	203	15	1	1	NUM
ejpam-4207	203	16	-	-	SYM
ejpam-4207	203	17	14	14	NUM
ejpam-4207	203	18	8	8	NUM
ejpam-4207	203	19	y	y	NOUN
ejpam-4207	203	20	;	;	PUNCT
ejpam-4207	203	21	(	(	PUNCT
ejpam-4207	203	22	5	5	X
ejpam-4207	203	23	)	)	PUNCT
ejpam-4207	203	24	f−(int(b1))∩f+(int(b2	f−(int(b1))∩f+(int(b2	NOUN
ejpam-4207	203	25	)	)	PUNCT
ejpam-4207	203	26	)	)	PUNCT
ejpam-4207	204	1	⊂	⊂	PROPN
ejpam-4207	204	2	sinti(f	sinti(f	PROPN
ejpam-4207	204	3	−(b1)∩f+(b2	−(b1)∩f+(b2	NOUN
ejpam-4207	204	4	)	)	PUNCT
ejpam-4207	204	5	)	)	PUNCT
ejpam-4207	204	6	for	for	ADP
ejpam-4207	204	7	every	every	DET
ejpam-4207	204	8	subsets	subset	NOUN
ejpam-4207	204	9	b1	b1	NOUN
ejpam-4207	204	10	,	,	PUNCT
ejpam-4207	204	11	b2	b2	NOUN
ejpam-4207	204	12	of	of	ADP
ejpam-4207	204	13	y	y	PROPN
ejpam-4207	204	14	.	.	PUNCT
ejpam-4207	205	1	for	for	ADP
ejpam-4207	205	2	a	a	DET
ejpam-4207	205	3	multifunction	multifunction	NOUN
ejpam-4207	205	4	f	f	NOUN
ejpam-4207	205	5	:	:	PUNCT
ejpam-4207	205	6	(	(	PUNCT
ejpam-4207	205	7	x	x	X
ejpam-4207	205	8	,	,	PUNCT
ejpam-4207	205	9	τ	τ	PROPN
ejpam-4207	205	10	,	,	PUNCT
ejpam-4207	205	11	i	i	NOUN
ejpam-4207	205	12	)	)	PUNCT
ejpam-4207	205	13	→	→	SYM
ejpam-4207	205	14	(	(	PUNCT
ejpam-4207	205	15	y	y	PROPN
ejpam-4207	205	16	,	,	PUNCT
ejpam-4207	205	17	σ	σ	PROPN
ejpam-4207	205	18	)	)	PUNCT
ejpam-4207	205	19	,	,	PUNCT
ejpam-4207	205	20	we	we	PRON
ejpam-4207	205	21	define	define	VERB
ejpam-4207	205	22	dmi(f	dmi(f	PROPN
ejpam-4207	205	23	)	)	PUNCT
ejpam-4207	205	24	as	as	SCONJ
ejpam-4207	205	25	follows	follow	VERB
ejpam-4207	205	26	:	:	PUNCT
ejpam-4207	205	27	dmi(f	dmi(f	INTJ
ejpam-4207	205	28	)	)	PUNCT
ejpam-4207	205	29	=	=	PRON
ejpam-4207	206	1	{	{	PUNCT
ejpam-4207	206	2	x	x	PUNCT
ejpam-4207	206	3	∈	∈	PROPN
ejpam-4207	206	4	x	x	X
ejpam-4207	206	5	:	:	PUNCT
ejpam-4207	206	6	f	f	X
ejpam-4207	206	7	is	be	AUX
ejpam-4207	206	8	not	not	PART
ejpam-4207	206	9	m	m	PROPN
ejpam-4207	206	10	-	-	PUNCT
ejpam-4207	206	11	i	i	PRON
ejpam-4207	206	12	-	-	NOUN
ejpam-4207	206	13	continuous	continuous	ADJ
ejpam-4207	206	14	at	at	ADP
ejpam-4207	206	15	x	x	X
ejpam-4207	206	16	}	}	PUNCT
ejpam-4207	206	17	.	.	PUNCT
ejpam-4207	207	1	theorem	theorem	ADJ
ejpam-4207	207	2	10	10	NUM
ejpam-4207	207	3	.	.	PUNCT
ejpam-4207	208	1	for	for	ADP
ejpam-4207	208	2	a	a	DET
ejpam-4207	208	3	multifunction	multifunction	NOUN
ejpam-4207	208	4	f	f	NOUN
ejpam-4207	208	5	:	:	PUNCT
ejpam-4207	208	6	(	(	PUNCT
ejpam-4207	208	7	x	x	X
ejpam-4207	208	8	,	,	PUNCT
ejpam-4207	208	9	τ	τ	PROPN
ejpam-4207	208	10	,	,	PUNCT
ejpam-4207	208	11	i	i	NOUN
ejpam-4207	208	12	)	)	PUNCT
ejpam-4207	208	13	→	→	SYM
ejpam-4207	208	14	(	(	PUNCT
ejpam-4207	208	15	y	y	PROPN
ejpam-4207	208	16	,	,	PUNCT
ejpam-4207	208	17	σ	σ	PROPN
ejpam-4207	208	18	)	)	PUNCT
ejpam-4207	208	19	,	,	PUNCT
ejpam-4207	208	20	the	the	DET
ejpam-4207	208	21	following	follow	VERB
ejpam-4207	208	22	equalities	equality	NOUN
ejpam-4207	208	23	hold	hold	VERB
ejpam-4207	208	24	:	:	PUNCT
ejpam-4207	208	25	dm(f	dm(f	NOUN
ejpam-4207	208	26	)	)	PUNCT
ejpam-4207	209	1	=	=	SYM
ejpam-4207	209	2	⋃	⋃	ADP
ejpam-4207	209	3	g1,g2∈σ{f	g1,g2∈σ{f	PROPN
ejpam-4207	209	4	+	+	PROPN
ejpam-4207	209	5	(	(	PUNCT
ejpam-4207	209	6	g1	g1	PROPN
ejpam-4207	209	7	)	)	PUNCT
ejpam-4207	209	8	∩	∩	NOUN
ejpam-4207	209	9	f−(g2)−minti(f	f−(g2)−minti(f	PROPN
ejpam-4207	209	10	+	+	PROPN
ejpam-4207	209	11	(	(	PUNCT
ejpam-4207	209	12	g1	g1	PROPN
ejpam-4207	209	13	)	)	PUNCT
ejpam-4207	209	14	∩	∩	NOUN
ejpam-4207	209	15	f−(g2	f−(g2	NUM
ejpam-4207	209	16	)	)	PUNCT
ejpam-4207	209	17	)	)	PUNCT
ejpam-4207	209	18	]	]	PUNCT
ejpam-4207	209	19	}	}	PUNCT
ejpam-4207	209	20	=	=	SYM
ejpam-4207	209	21	⋃	⋃	PROPN
ejpam-4207	209	22	b1,b2∈p	b1,b2∈p	PROPN
ejpam-4207	209	23	(	(	PUNCT
ejpam-4207	209	24	y	y	PROPN
ejpam-4207	209	25	)	)	PUNCT
ejpam-4207	209	26	{	{	PUNCT
ejpam-4207	209	27	f−(int(b1	f−(int(b1	NOUN
ejpam-4207	209	28	)	)	PUNCT
ejpam-4207	209	29	)	)	PUNCT
ejpam-4207	209	30	∩	∩	PROPN
ejpam-4207	209	31	f+(int(b2))−minti(f	f+(int(b2))−minti(f	PROPN
ejpam-4207	209	32	−(b1	−(b1	NUM
ejpam-4207	209	33	)	)	PUNCT
ejpam-4207	209	34	∩	∩	ADJ
ejpam-4207	209	35	f+(b2	f+(b2	NOUN
ejpam-4207	209	36	)	)	PUNCT
ejpam-4207	209	37	)	)	PUNCT
ejpam-4207	209	38	}	}	PUNCT
ejpam-4207	210	1	=	=	SYM
ejpam-4207	210	2	⋃	⋃	ADP
ejpam-4207	210	3	b1,b2∈p	b1,b2∈p	PROPN
ejpam-4207	210	4	(	(	PUNCT
ejpam-4207	210	5	y	y	PROPN
ejpam-4207	210	6	)	)	PUNCT
ejpam-4207	210	7	{	{	PUNCT
ejpam-4207	210	8	mcli(f	mcli(f	PROPN
ejpam-4207	210	9	−(b1	−(b1	NUM
ejpam-4207	210	10	)	)	PUNCT
ejpam-4207	210	11	∪	∪	ADV
ejpam-4207	210	12	f+(b2))−	f+(b2))−	NOUN
ejpam-4207	210	13	[	[	X
ejpam-4207	210	14	f−(cl(b1	f−(cl(b1	NOUN
ejpam-4207	210	15	)	)	PUNCT
ejpam-4207	210	16	)	)	PUNCT
ejpam-4207	210	17	∪	∪	ADP
ejpam-4207	210	18	f+(cl(b2	f+(cl(b2	NOUN
ejpam-4207	210	19	)	)	PUNCT
ejpam-4207	210	20	)	)	PUNCT
ejpam-4207	210	21	]	]	PUNCT
ejpam-4207	210	22	}	}	PUNCT
ejpam-4207	210	23	=	=	SYM
ejpam-4207	210	24	⋃	⋃	NOUN
ejpam-4207	210	25	h1,h2∈f{mcli(f	h1,h2∈f{mcli(f	ADJ
ejpam-4207	210	26	−(h1	−(h1	NOUN
ejpam-4207	210	27	)	)	PUNCT
ejpam-4207	210	28	∪	∪	ADP
ejpam-4207	210	29	f+(h2))−	f+(h2))−	PROPN
ejpam-4207	210	30	[	[	NOUN
ejpam-4207	210	31	f−(h1	f−(h1	NUM
ejpam-4207	210	32	)	)	PUNCT
ejpam-4207	210	33	∪	∪	ADP
ejpam-4207	210	34	f+(h2	f+(h2	NOUN
ejpam-4207	210	35	)	)	PUNCT
ejpam-4207	210	36	]	]	PUNCT
ejpam-4207	210	37	}	}	PUNCT
ejpam-4207	210	38	,	,	PUNCT
ejpam-4207	210	39	where	where	SCONJ
ejpam-4207	210	40	f	f	PROPN
ejpam-4207	210	41	is	be	AUX
ejpam-4207	210	42	the	the	DET
ejpam-4207	210	43	family	family	NOUN
ejpam-4207	210	44	of	of	ADP
ejpam-4207	210	45	closed	closed	ADJ
ejpam-4207	210	46	sets	set	NOUN
ejpam-4207	210	47	of	of	ADP
ejpam-4207	210	48	(	(	PUNCT
ejpam-4207	210	49	y	y	PROPN
ejpam-4207	210	50	,	,	PUNCT
ejpam-4207	210	51	σ	σ	PROPN
ejpam-4207	210	52	)	)	PUNCT
ejpam-4207	210	53	.	.	PUNCT
ejpam-4207	211	1	let	let	VERB
ejpam-4207	211	2	mio(x	mio(x	NOUN
ejpam-4207	211	3	)	)	PUNCT
ejpam-4207	211	4	=	=	SYM
ejpam-4207	212	1	sio(x	sio(x	NOUN
ejpam-4207	212	2	)	)	PUNCT
ejpam-4207	212	3	,	,	PUNCT
ejpam-4207	212	4	then	then	ADV
ejpam-4207	212	5	by	by	ADP
ejpam-4207	212	6	theorem	theorem	NOUN
ejpam-4207	212	7	10	10	NUM
ejpam-4207	212	8	we	we	PRON
ejpam-4207	212	9	obtain	obtain	VERB
ejpam-4207	212	10	the	the	DET
ejpam-4207	212	11	following	follow	VERB
ejpam-4207	212	12	corollary	corollary	NOUN
ejpam-4207	212	13	.	.	PUNCT
ejpam-4207	213	1	corollary	corollary	ADJ
ejpam-4207	213	2	3	3	NUM
ejpam-4207	213	3	.	.	PUNCT
ejpam-4207	214	1	for	for	ADP
ejpam-4207	214	2	a	a	DET
ejpam-4207	214	3	multifunction	multifunction	NOUN
ejpam-4207	214	4	f	f	NOUN
ejpam-4207	214	5	:	:	PUNCT
ejpam-4207	214	6	(	(	PUNCT
ejpam-4207	214	7	x	x	X
ejpam-4207	214	8	,	,	PUNCT
ejpam-4207	214	9	τ	τ	PROPN
ejpam-4207	214	10	,	,	PUNCT
ejpam-4207	214	11	i	i	NOUN
ejpam-4207	214	12	)	)	PUNCT
ejpam-4207	214	13	→	→	SYM
ejpam-4207	214	14	(	(	PUNCT
ejpam-4207	214	15	y	y	PROPN
ejpam-4207	214	16	,	,	PUNCT
ejpam-4207	214	17	σ	σ	PROPN
ejpam-4207	214	18	)	)	PUNCT
ejpam-4207	214	19	,	,	PUNCT
ejpam-4207	214	20	the	the	DET
ejpam-4207	214	21	following	follow	VERB
ejpam-4207	214	22	equalities	equality	NOUN
ejpam-4207	214	23	hold	hold	VERB
ejpam-4207	214	24	:	:	PUNCT
ejpam-4207	214	25	dm(f	dm(f	NOUN
ejpam-4207	214	26	)	)	PUNCT
ejpam-4207	215	1	=	=	SYM
ejpam-4207	215	2	⋃	⋃	ADP
ejpam-4207	215	3	g1,g2∈σ{f	g1,g2∈σ{f	PROPN
ejpam-4207	215	4	+	+	PROPN
ejpam-4207	215	5	(	(	PUNCT
ejpam-4207	215	6	g1	g1	PROPN
ejpam-4207	215	7	)	)	PUNCT
ejpam-4207	215	8	∩	∩	NOUN
ejpam-4207	215	9	f−(g2)−	f−(g2)−	VERB
ejpam-4207	215	10	sinti(f	sinti(f	NOUN
ejpam-4207	215	11	+	+	PROPN
ejpam-4207	215	12	(	(	PUNCT
ejpam-4207	215	13	g1	g1	PROPN
ejpam-4207	215	14	)	)	PUNCT
ejpam-4207	215	15	∩	∩	NOUN
ejpam-4207	215	16	f−(g2	f−(g2	NUM
ejpam-4207	215	17	)	)	PUNCT
ejpam-4207	215	18	)	)	PUNCT
ejpam-4207	215	19	]	]	PUNCT
ejpam-4207	215	20	}	}	PUNCT
ejpam-4207	215	21	=	=	SYM
ejpam-4207	215	22	⋃	⋃	PROPN
ejpam-4207	215	23	b1,b2∈p	b1,b2∈p	PROPN
ejpam-4207	215	24	(	(	PUNCT
ejpam-4207	215	25	y	y	PROPN
ejpam-4207	215	26	)	)	PUNCT
ejpam-4207	215	27	{	{	PUNCT
ejpam-4207	215	28	f−(int(b1	f−(int(b1	NOUN
ejpam-4207	215	29	)	)	PUNCT
ejpam-4207	215	30	)	)	PUNCT
ejpam-4207	215	31	∩	∩	NOUN
ejpam-4207	215	32	f+(int(b2))−	f+(int(b2))−	NUM
ejpam-4207	215	33	sinti(f	sinti(f	DET
ejpam-4207	215	34	−(b1	−(b1	NUM
ejpam-4207	215	35	)	)	PUNCT
ejpam-4207	215	36	∩	∩	ADJ
ejpam-4207	215	37	f+(b2	f+(b2	NOUN
ejpam-4207	215	38	)	)	PUNCT
ejpam-4207	215	39	)	)	PUNCT
ejpam-4207	215	40	}	}	PUNCT
ejpam-4207	215	41	=	=	SYM
ejpam-4207	215	42	⋃	⋃	ADP
ejpam-4207	215	43	b1,b2∈p	b1,b2∈p	PROPN
ejpam-4207	215	44	(	(	PUNCT
ejpam-4207	215	45	y	y	PROPN
ejpam-4207	215	46	)	)	PUNCT
ejpam-4207	215	47	{	{	PUNCT
ejpam-4207	215	48	scli(f−(b1	scli(f−(b1	NOUN
ejpam-4207	215	49	)	)	PUNCT
ejpam-4207	215	50	∪	∪	ADV
ejpam-4207	215	51	f+(b2))−	f+(b2))−	NOUN
ejpam-4207	215	52	[	[	X
ejpam-4207	215	53	f−(cl(b1	f−(cl(b1	NOUN
ejpam-4207	215	54	)	)	PUNCT
ejpam-4207	215	55	)	)	PUNCT
ejpam-4207	215	56	∪	∪	ADP
ejpam-4207	215	57	f+(cl(b2	f+(cl(b2	NOUN
ejpam-4207	215	58	)	)	PUNCT
ejpam-4207	215	59	)	)	PUNCT
ejpam-4207	215	60	]	]	PUNCT
ejpam-4207	215	61	}	}	PUNCT
ejpam-4207	215	62	=	=	SYM
ejpam-4207	215	63	⋃	⋃	NOUN
ejpam-4207	215	64	h1,h2∈f{scli(f−(h1	h1,h2∈f{scli(f−(h1	NOUN
ejpam-4207	215	65	)	)	PUNCT
ejpam-4207	215	66	∪	∪	ADP
ejpam-4207	215	67	f+(h2))−	f+(h2))−	PROPN
ejpam-4207	215	68	[	[	NOUN
ejpam-4207	215	69	f−(h1	f−(h1	NUM
ejpam-4207	215	70	)	)	PUNCT
ejpam-4207	215	71	∪	∪	ADP
ejpam-4207	215	72	f+(h2	f+(h2	NOUN
ejpam-4207	215	73	)	)	PUNCT
ejpam-4207	215	74	]	]	PUNCT
ejpam-4207	215	75	}	}	PUNCT
ejpam-4207	215	76	,	,	PUNCT
ejpam-4207	215	77	where	where	SCONJ
ejpam-4207	215	78	f	f	PROPN
ejpam-4207	215	79	is	be	AUX
ejpam-4207	215	80	the	the	DET
ejpam-4207	215	81	family	family	NOUN
ejpam-4207	215	82	of	of	ADP
ejpam-4207	215	83	closed	closed	ADJ
ejpam-4207	215	84	sets	set	NOUN
ejpam-4207	215	85	of	of	ADP
ejpam-4207	215	86	(	(	PUNCT
ejpam-4207	215	87	y	y	PROPN
ejpam-4207	215	88	,	,	PUNCT
ejpam-4207	215	89	σ	σ	PROPN
ejpam-4207	215	90	)	)	PUNCT
ejpam-4207	215	91	.	.	PUNCT
ejpam-4207	216	1	definition	definition	NOUN
ejpam-4207	216	2	15	15	NUM
ejpam-4207	216	3	.	.	PUNCT
ejpam-4207	217	1	let	let	VERB
ejpam-4207	217	2	(	(	PUNCT
ejpam-4207	217	3	x	x	X
ejpam-4207	217	4	,	,	PUNCT
ejpam-4207	217	5	τ	τ	PROPN
ejpam-4207	217	6	,	,	PUNCT
ejpam-4207	217	7	i	i	PRON
ejpam-4207	217	8	)	)	PUNCT
ejpam-4207	217	9	be	be	VERB
ejpam-4207	217	10	an	an	DET
ejpam-4207	217	11	ideal	ideal	ADJ
ejpam-4207	217	12	topological	topological	ADJ
ejpam-4207	217	13	space	space	NOUN
ejpam-4207	217	14	.	.	PUNCT
ejpam-4207	218	1	for	for	ADP
ejpam-4207	218	2	a	a	DET
ejpam-4207	218	3	subset	subset	NOUN
ejpam-4207	218	4	a	a	PRON
ejpam-4207	218	5	of	of	ADP
ejpam-4207	218	6	x	x	PRON
ejpam-4207	218	7	,	,	PUNCT
ejpam-4207	218	8	the	the	DET
ejpam-4207	218	9	mi	mi	PROPN
ejpam-4207	218	10	-	-	PUNCT
ejpam-4207	218	11	frontier	frontier	NOUN
ejpam-4207	218	12	mifr(a	mifr(a	NOUN
ejpam-4207	218	13	)	)	PUNCT
ejpam-4207	218	14	of	of	ADP
ejpam-4207	218	15	a	a	PRON
ejpam-4207	218	16	is	be	AUX
ejpam-4207	218	17	defined	define	VERB
ejpam-4207	218	18	as	as	SCONJ
ejpam-4207	218	19	follows	follow	VERB
ejpam-4207	218	20	:	:	PUNCT
ejpam-4207	219	1	mifr(a	mifr(a	ADJ
ejpam-4207	219	2	)	)	PUNCT
ejpam-4207	219	3	=	=	SYM
ejpam-4207	219	4	mcli(a	mcli(a	PROPN
ejpam-4207	219	5	)	)	PUNCT
ejpam-4207	219	6	∩mcli(x	∩mcli(x	NOUN
ejpam-4207	219	7	−a	−a	NOUN
ejpam-4207	219	8	)	)	PUNCT
ejpam-4207	219	9	.	.	PUNCT
ejpam-4207	220	1	theorem	theorem	VERB
ejpam-4207	220	2	11	11	NUM
ejpam-4207	220	3	.	.	PUNCT
ejpam-4207	221	1	the	the	DET
ejpam-4207	221	2	set	set	NOUN
ejpam-4207	221	3	of	of	ADP
ejpam-4207	221	4	all	all	DET
ejpam-4207	221	5	points	point	NOUN
ejpam-4207	221	6	x	x	X
ejpam-4207	221	7	∈	∈	NOUN
ejpam-4207	221	8	x	x	PUNCT
ejpam-4207	221	9	at	at	ADP
ejpam-4207	221	10	which	which	PRON
ejpam-4207	221	11	a	a	DET
ejpam-4207	221	12	multifunction	multifunction	NOUN
ejpam-4207	221	13	f	f	NOUN
ejpam-4207	221	14	:	:	PUNCT
ejpam-4207	221	15	(	(	PUNCT
ejpam-4207	221	16	x	x	X
ejpam-4207	221	17	,	,	PUNCT
ejpam-4207	221	18	τ	τ	PROPN
ejpam-4207	221	19	,	,	PUNCT
ejpam-4207	221	20	i	i	NOUN
ejpam-4207	221	21	)	)	PUNCT
ejpam-4207	221	22	→	→	SYM
ejpam-4207	221	23	(	(	PUNCT
ejpam-4207	221	24	y	y	PROPN
ejpam-4207	221	25	,	,	PUNCT
ejpam-4207	221	26	σ	σ	PROPN
ejpam-4207	221	27	)	)	PUNCT
ejpam-4207	221	28	is	be	AUX
ejpam-4207	221	29	not	not	PART
ejpam-4207	221	30	m	m	NOUN
ejpam-4207	221	31	-	-	PUNCT
ejpam-4207	221	32	i	i	PRON
ejpam-4207	221	33	-	-	PUNCT
ejpam-4207	221	34	continuous	continuous	ADJ
ejpam-4207	221	35	is	be	AUX
ejpam-4207	221	36	identical	identical	ADJ
ejpam-4207	221	37	with	with	ADP
ejpam-4207	221	38	the	the	DET
ejpam-4207	221	39	union	union	NOUN
ejpam-4207	221	40	of	of	ADP
ejpam-4207	221	41	the	the	DET
ejpam-4207	221	42	mi	mi	PROPN
ejpam-4207	221	43	-	-	PUNCT
ejpam-4207	221	44	frontiers	frontier	NOUN
ejpam-4207	221	45	of	of	ADP
ejpam-4207	221	46	the	the	DET
ejpam-4207	221	47	intersection	intersection	NOUN
ejpam-4207	221	48	of	of	ADP
ejpam-4207	221	49	upper	upper	ADJ
ejpam-4207	221	50	/	/	SYM
ejpam-4207	221	51	lower	low	ADJ
ejpam-4207	221	52	inverse	inverse	NOUN
ejpam-4207	221	53	images	image	NOUN
ejpam-4207	221	54	of	of	ADP
ejpam-4207	221	55	open	open	ADJ
ejpam-4207	221	56	sets	set	NOUN
ejpam-4207	221	57	containing	contain	VERB
ejpam-4207	221	58	/	/	SYM
ejpam-4207	221	59	meeting	meeting	NOUN
ejpam-4207	221	60	f	f	X
ejpam-4207	221	61	(	(	PUNCT
ejpam-4207	221	62	x	x	NOUN
ejpam-4207	221	63	)	)	PUNCT
ejpam-4207	221	64	.	.	PUNCT
ejpam-4207	222	1	proof	proof	NOUN
ejpam-4207	222	2	.	.	PUNCT
ejpam-4207	223	1	the	the	DET
ejpam-4207	223	2	proof	proof	NOUN
ejpam-4207	223	3	follows	follow	VERB
ejpam-4207	223	4	from	from	ADP
ejpam-4207	223	5	definition	definition	NOUN
ejpam-4207	223	6	13	13	NUM
ejpam-4207	223	7	and	and	CCONJ
ejpam-4207	223	8	theorem	theorem	VERB
ejpam-4207	223	9	4	4	NUM
ejpam-4207	223	10	.	.	PUNCT
ejpam-4207	224	1	if	if	SCONJ
ejpam-4207	224	2	mio(x	mio(x	PROPN
ejpam-4207	224	3	)	)	PUNCT
ejpam-4207	224	4	=	=	PUNCT
ejpam-4207	225	1	τ⋆	τ⋆	NOUN
ejpam-4207	225	2	,	,	PUNCT
ejpam-4207	225	3	then	then	ADV
ejpam-4207	225	4	we	we	PRON
ejpam-4207	225	5	obtain	obtain	VERB
ejpam-4207	225	6	the	the	DET
ejpam-4207	225	7	following	follow	VERB
ejpam-4207	225	8	corollary	corollary	ADJ
ejpam-4207	225	9	:	:	PUNCT
ejpam-4207	225	10	corollary	corollary	ADJ
ejpam-4207	225	11	4	4	NUM
ejpam-4207	225	12	.	.	PUNCT
ejpam-4207	226	1	the	the	DET
ejpam-4207	226	2	set	set	NOUN
ejpam-4207	226	3	of	of	ADP
ejpam-4207	226	4	all	all	DET
ejpam-4207	226	5	points	point	NOUN
ejpam-4207	226	6	x	x	X
ejpam-4207	226	7	∈	∈	NOUN
ejpam-4207	226	8	x	x	PUNCT
ejpam-4207	226	9	at	at	ADP
ejpam-4207	226	10	which	which	PRON
ejpam-4207	226	11	a	a	DET
ejpam-4207	226	12	multifunction	multifunction	NOUN
ejpam-4207	226	13	f	f	NOUN
ejpam-4207	226	14	:	:	PUNCT
ejpam-4207	226	15	(	(	PUNCT
ejpam-4207	226	16	x	x	X
ejpam-4207	226	17	,	,	PUNCT
ejpam-4207	226	18	τ	τ	PROPN
ejpam-4207	226	19	,	,	PUNCT
ejpam-4207	226	20	i	i	NOUN
ejpam-4207	226	21	)	)	PUNCT
ejpam-4207	226	22	→	→	SYM
ejpam-4207	226	23	(	(	PUNCT
ejpam-4207	226	24	y	y	PROPN
ejpam-4207	226	25	,	,	PUNCT
ejpam-4207	226	26	σ	σ	PROPN
ejpam-4207	226	27	)	)	PUNCT
ejpam-4207	226	28	is	be	AUX
ejpam-4207	226	29	not	not	PART
ejpam-4207	226	30	τ⋆-continuous	τ⋆-continuous	ADJ
ejpam-4207	226	31	is	be	AUX
ejpam-4207	226	32	identical	identical	ADJ
ejpam-4207	226	33	with	with	ADP
ejpam-4207	226	34	the	the	DET
ejpam-4207	226	35	union	union	NOUN
ejpam-4207	226	36	of	of	ADP
ejpam-4207	226	37	the	the	DET
ejpam-4207	226	38	τ⋆-frontiers	τ⋆-frontier	NOUN
ejpam-4207	226	39	of	of	ADP
ejpam-4207	226	40	the	the	DET
ejpam-4207	226	41	intersection	intersection	NOUN
ejpam-4207	226	42	of	of	ADP
ejpam-4207	226	43	upper	upper	ADJ
ejpam-4207	226	44	/	/	SYM
ejpam-4207	226	45	lower	low	ADJ
ejpam-4207	226	46	inverse	inverse	NOUN
ejpam-4207	226	47	images	image	NOUN
ejpam-4207	226	48	of	of	ADP
ejpam-4207	226	49	open	open	ADJ
ejpam-4207	226	50	sets	set	NOUN
ejpam-4207	226	51	containing	contain	VERB
ejpam-4207	226	52	/	/	SYM
ejpam-4207	226	53	meeting	meeting	NOUN
ejpam-4207	226	54	f	f	X
ejpam-4207	226	55	(	(	PUNCT
ejpam-4207	226	56	x	x	NOUN
ejpam-4207	226	57	)	)	PUNCT
ejpam-4207	226	58	.	.	PUNCT
ejpam-4207	227	1	if	if	SCONJ
ejpam-4207	227	2	mio(x	mio(x	NOUN
ejpam-4207	227	3	)	)	PUNCT
ejpam-4207	227	4	=	=	SYM
ejpam-4207	228	1	sio(x	sio(x	NOUN
ejpam-4207	228	2	)	)	PUNCT
ejpam-4207	228	3	,	,	PUNCT
ejpam-4207	228	4	then	then	ADV
ejpam-4207	228	5	we	we	PRON
ejpam-4207	228	6	obtain	obtain	VERB
ejpam-4207	228	7	the	the	DET
ejpam-4207	228	8	following	follow	VERB
ejpam-4207	228	9	corollary	corollary	ADJ
ejpam-4207	228	10	:	:	PUNCT
ejpam-4207	228	11	corollary	corollary	ADJ
ejpam-4207	228	12	5	5	NUM
ejpam-4207	228	13	.	.	PUNCT
ejpam-4207	229	1	the	the	DET
ejpam-4207	229	2	set	set	NOUN
ejpam-4207	229	3	of	of	ADP
ejpam-4207	229	4	all	all	DET
ejpam-4207	229	5	points	point	NOUN
ejpam-4207	229	6	x	x	X
ejpam-4207	229	7	∈	∈	NOUN
ejpam-4207	229	8	x	x	PUNCT
ejpam-4207	229	9	at	at	ADP
ejpam-4207	229	10	which	which	PRON
ejpam-4207	229	11	a	a	DET
ejpam-4207	229	12	multifunction	multifunction	NOUN
ejpam-4207	229	13	f	f	NOUN
ejpam-4207	229	14	:	:	PUNCT
ejpam-4207	229	15	(	(	PUNCT
ejpam-4207	229	16	x	x	X
ejpam-4207	229	17	,	,	PUNCT
ejpam-4207	229	18	τ	τ	PROPN
ejpam-4207	229	19	,	,	PUNCT
ejpam-4207	229	20	i	i	NOUN
ejpam-4207	229	21	)	)	PUNCT
ejpam-4207	229	22	→	→	SYM
ejpam-4207	229	23	(	(	PUNCT
ejpam-4207	229	24	y	y	PROPN
ejpam-4207	229	25	,	,	PUNCT
ejpam-4207	229	26	σ	σ	PROPN
ejpam-4207	229	27	)	)	PUNCT
ejpam-4207	229	28	is	be	AUX
ejpam-4207	229	29	not	not	PART
ejpam-4207	229	30	semi	semi	ADJ
ejpam-4207	229	31	-	-	ADJ
ejpam-4207	229	32	i	i	PRON
ejpam-4207	229	33	-	-	PUNCT
ejpam-4207	229	34	continuous	continuous	ADJ
ejpam-4207	229	35	is	be	AUX
ejpam-4207	229	36	identical	identical	ADJ
ejpam-4207	229	37	with	with	ADP
ejpam-4207	229	38	the	the	DET
ejpam-4207	229	39	union	union	NOUN
ejpam-4207	229	40	of	of	ADP
ejpam-4207	229	41	the	the	DET
ejpam-4207	229	42	si	si	NOUN
ejpam-4207	229	43	-	-	PUNCT
ejpam-4207	229	44	frontiers	frontier	NOUN
ejpam-4207	229	45	of	of	ADP
ejpam-4207	229	46	the	the	DET
ejpam-4207	229	47	intersection	intersection	NOUN
ejpam-4207	229	48	of	of	ADP
ejpam-4207	229	49	upper	upper	ADJ
ejpam-4207	229	50	/	/	SYM
ejpam-4207	229	51	lower	low	ADJ
ejpam-4207	229	52	inverse	inverse	NOUN
ejpam-4207	229	53	images	image	NOUN
ejpam-4207	229	54	of	of	ADP
ejpam-4207	229	55	open	open	ADJ
ejpam-4207	229	56	sets	set	NOUN
ejpam-4207	229	57	containing	contain	VERB
ejpam-4207	229	58	/	/	SYM
ejpam-4207	229	59	meeting	meeting	NOUN
ejpam-4207	229	60	f	f	X
ejpam-4207	229	61	(	(	PUNCT
ejpam-4207	229	62	x	x	NOUN
ejpam-4207	229	63	)	)	PUNCT
ejpam-4207	229	64	.	.	PUNCT
ejpam-4207	230	1	takashi	takashi	PROPN
ejpam-4207	230	2	noiri	noiri	PROPN
ejpam-4207	230	3	,	,	PUNCT
ejpam-4207	230	4	valeriu	valeriu	ADJ
ejpam-4207	230	5	popa	popa	NOUN
ejpam-4207	230	6	/	/	SYM
ejpam-4207	230	7	eur	eur	PROPN
ejpam-4207	230	8	.	.	PUNCT
ejpam-4207	231	1	j.	j.	PROPN
ejpam-4207	231	2	pure	pure	PROPN
ejpam-4207	231	3	appl	appl	PROPN
ejpam-4207	231	4	.	.	PROPN
ejpam-4207	231	5	math	math	PROPN
ejpam-4207	231	6	,	,	PUNCT
ejpam-4207	231	7	15	15	NUM
ejpam-4207	231	8	(	(	PUNCT
ejpam-4207	231	9	1	1	NUM
ejpam-4207	231	10	)	)	PUNCT
ejpam-4207	231	11	(	(	PUNCT
ejpam-4207	231	12	2022	2022	NUM
ejpam-4207	231	13	)	)	PUNCT
ejpam-4207	231	14	,	,	PUNCT
ejpam-4207	231	15	1	1	NUM
ejpam-4207	231	16	-	-	SYM
ejpam-4207	231	17	14	14	NUM
ejpam-4207	231	18	9	9	NUM
ejpam-4207	231	19	theorem	theorem	NOUN
ejpam-4207	231	20	12	12	NUM
ejpam-4207	231	21	.	.	PUNCT
ejpam-4207	232	1	let	let	VERB
ejpam-4207	232	2	f	f	NOUN
ejpam-4207	232	3	:	:	PUNCT
ejpam-4207	232	4	(	(	PUNCT
ejpam-4207	232	5	x	x	X
ejpam-4207	232	6	,	,	PUNCT
ejpam-4207	232	7	τ	τ	PROPN
ejpam-4207	232	8	,	,	PUNCT
ejpam-4207	232	9	i	i	NOUN
ejpam-4207	232	10	)	)	PUNCT
ejpam-4207	232	11	→	→	SYM
ejpam-4207	232	12	(	(	PUNCT
ejpam-4207	232	13	y	y	PROPN
ejpam-4207	232	14	,	,	PUNCT
ejpam-4207	232	15	σ	σ	PROPN
ejpam-4207	232	16	)	)	PUNCT
ejpam-4207	232	17	be	be	VERB
ejpam-4207	232	18	a	a	DET
ejpam-4207	232	19	multifunction	multifunction	NOUN
ejpam-4207	232	20	such	such	ADJ
ejpam-4207	232	21	that	that	SCONJ
ejpam-4207	232	22	f	f	PROPN
ejpam-4207	232	23	(	(	PUNCT
ejpam-4207	232	24	x	x	X
ejpam-4207	232	25	)	)	PUNCT
ejpam-4207	232	26	is	be	AUX
ejpam-4207	232	27	α	α	X
ejpam-4207	232	28	-	-	ADJ
ejpam-4207	232	29	regular	regular	ADJ
ejpam-4207	232	30	and	and	CCONJ
ejpam-4207	232	31	α	α	NOUN
ejpam-4207	232	32	-	-	NOUN
ejpam-4207	232	33	paracompact	paracompact	NOUN
ejpam-4207	232	34	for	for	ADP
ejpam-4207	232	35	each	each	DET
ejpam-4207	232	36	x	x	SYM
ejpam-4207	232	37	∈	∈	PROPN
ejpam-4207	232	38	x.	x.	NOUN
ejpam-4207	232	39	then	then	ADV
ejpam-4207	232	40	the	the	DET
ejpam-4207	232	41	following	follow	VERB
ejpam-4207	232	42	properties	property	NOUN
ejpam-4207	232	43	are	be	AUX
ejpam-4207	232	44	equivalent	equivalent	ADJ
ejpam-4207	232	45	:	:	PUNCT
ejpam-4207	232	46	(	(	PUNCT
ejpam-4207	232	47	1	1	X
ejpam-4207	232	48	)	)	PUNCT
ejpam-4207	232	49	f	f	PROPN
ejpam-4207	232	50	is	be	AUX
ejpam-4207	232	51	m	m	NOUN
ejpam-4207	232	52	-	-	ADJ
ejpam-4207	232	53	i	i	NOUN
ejpam-4207	232	54	-	-	PUNCT
ejpam-4207	232	55	continuous	continuous	ADJ
ejpam-4207	232	56	;	;	PUNCT
ejpam-4207	232	57	(	(	PUNCT
ejpam-4207	232	58	2	2	X
ejpam-4207	232	59	)	)	PUNCT
ejpam-4207	232	60	g	g	NOUN
ejpam-4207	232	61	is	be	AUX
ejpam-4207	232	62	m	m	NOUN
ejpam-4207	232	63	-	-	ADJ
ejpam-4207	232	64	i	i	ADV
ejpam-4207	232	65	-	-	PUNCT
ejpam-4207	232	66	continuous	continuous	ADJ
ejpam-4207	232	67	,	,	PUNCT
ejpam-4207	232	68	where	where	SCONJ
ejpam-4207	232	69	g	g	PROPN
ejpam-4207	232	70	=	=	SYM
ejpam-4207	232	71	cl(f	cl(f	PROPN
ejpam-4207	232	72	(	(	PUNCT
ejpam-4207	232	73	x	x	NOUN
ejpam-4207	232	74	)	)	PUNCT
ejpam-4207	232	75	)	)	PUNCT
ejpam-4207	232	76	,	,	PUNCT
ejpam-4207	232	77	scl(f	scl(f	PROPN
ejpam-4207	232	78	)	)	PUNCT
ejpam-4207	232	79	,	,	PUNCT
ejpam-4207	232	80	pcl(f	pcl(f	PROPN
ejpam-4207	232	81	)	)	PUNCT
ejpam-4207	232	82	,	,	PUNCT
ejpam-4207	232	83	αcl(f	αcl(f	PROPN
ejpam-4207	232	84	)	)	PUNCT
ejpam-4207	232	85	,	,	PUNCT
ejpam-4207	232	86	bcl(f	bcl(f	PROPN
ejpam-4207	232	87	)	)	PUNCT
ejpam-4207	232	88	,	,	PUNCT
ejpam-4207	232	89	βcl(f	βcl(f	PROPN
ejpam-4207	232	90	)	)	PUNCT
ejpam-4207	232	91	.	.	PUNCT
ejpam-4207	233	1	proof	proof	NOUN
ejpam-4207	233	2	.	.	PUNCT
ejpam-4207	234	1	the	the	DET
ejpam-4207	234	2	proof	proof	NOUN
ejpam-4207	234	3	follows	follow	VERB
ejpam-4207	234	4	from	from	ADP
ejpam-4207	234	5	theorem	theorem	ADJ
ejpam-4207	234	6	5	5	NUM
ejpam-4207	234	7	.	.	PUNCT
ejpam-4207	234	8	definition	definition	NOUN
ejpam-4207	234	9	16	16	NUM
ejpam-4207	234	10	.	.	PUNCT
ejpam-4207	235	1	a	a	DET
ejpam-4207	235	2	multifunction	multifunction	NOUN
ejpam-4207	235	3	f	f	NOUN
ejpam-4207	235	4	:	:	PUNCT
ejpam-4207	235	5	(	(	PUNCT
ejpam-4207	235	6	x	x	X
ejpam-4207	235	7	,	,	PUNCT
ejpam-4207	235	8	τ	τ	PROPN
ejpam-4207	235	9	,	,	PUNCT
ejpam-4207	235	10	i	i	NOUN
ejpam-4207	235	11	)	)	PUNCT
ejpam-4207	235	12	→	→	SYM
ejpam-4207	235	13	(	(	PUNCT
ejpam-4207	235	14	y	y	PROPN
ejpam-4207	235	15	,	,	PUNCT
ejpam-4207	235	16	σ	σ	PROPN
ejpam-4207	235	17	)	)	PUNCT
ejpam-4207	235	18	is	be	AUX
ejpam-4207	235	19	said	say	VERB
ejpam-4207	235	20	to	to	PART
ejpam-4207	235	21	be	be	AUX
ejpam-4207	235	22	(	(	PUNCT
ejpam-4207	235	23	1	1	NUM
ejpam-4207	235	24	)	)	PUNCT
ejpam-4207	235	25	upper	upper	ADJ
ejpam-4207	235	26	m	m	PROPN
ejpam-4207	235	27	-	-	ADJ
ejpam-4207	235	28	i	i	PRON
ejpam-4207	235	29	-	-	NOUN
ejpam-4207	235	30	continuous	continuous	ADJ
ejpam-4207	235	31	at	at	ADP
ejpam-4207	235	32	x	x	X
ejpam-4207	235	33	∈	∈	PROPN
ejpam-4207	235	34	x	x	SYM
ejpam-4207	235	35	if	if	SCONJ
ejpam-4207	235	36	for	for	ADP
ejpam-4207	235	37	each	each	DET
ejpam-4207	235	38	open	open	ADJ
ejpam-4207	235	39	set	set	VERB
ejpam-4207	235	40	v	v	NOUN
ejpam-4207	235	41	containing	contain	VERB
ejpam-4207	235	42	f	f	X
ejpam-4207	235	43	(	(	PUNCT
ejpam-4207	235	44	x	x	NOUN
ejpam-4207	235	45	)	)	PUNCT
ejpam-4207	235	46	,	,	PUNCT
ejpam-4207	235	47	there	there	PRON
ejpam-4207	235	48	exists	exist	VERB
ejpam-4207	235	49	u	u	PROPN
ejpam-4207	235	50	∈	∈	PROPN
ejpam-4207	235	51	mio(x	mio(x	PROPN
ejpam-4207	235	52	)	)	PUNCT
ejpam-4207	235	53	containing	contain	VERB
ejpam-4207	235	54	x	x	PUNCT
ejpam-4207	235	55	such	such	ADJ
ejpam-4207	235	56	that	that	SCONJ
ejpam-4207	235	57	f	f	PROPN
ejpam-4207	235	58	(	(	PUNCT
ejpam-4207	235	59	u	u	NOUN
ejpam-4207	235	60	)	)	PUNCT
ejpam-4207	235	61	⊂	⊂	PROPN
ejpam-4207	235	62	v	v	PROPN
ejpam-4207	235	63	,	,	PUNCT
ejpam-4207	235	64	(	(	PUNCT
ejpam-4207	235	65	2	2	NUM
ejpam-4207	235	66	)	)	PUNCT
ejpam-4207	235	67	lower	low	ADJ
ejpam-4207	235	68	m	m	PROPN
ejpam-4207	235	69	-	-	ADJ
ejpam-4207	235	70	i	i	PRON
ejpam-4207	235	71	-	-	NOUN
ejpam-4207	235	72	continuous	continuous	ADJ
ejpam-4207	235	73	at	at	ADP
ejpam-4207	235	74	xinx	xinx	PROPN
ejpam-4207	235	75	if	if	SCONJ
ejpam-4207	235	76	for	for	ADP
ejpam-4207	235	77	each	each	DET
ejpam-4207	235	78	open	open	ADJ
ejpam-4207	235	79	set	set	VERB
ejpam-4207	235	80	v	v	NUM
ejpam-4207	235	81	meeting	meeting	NOUN
ejpam-4207	235	82	f	f	X
ejpam-4207	235	83	(	(	PUNCT
ejpam-4207	235	84	x	x	NOUN
ejpam-4207	235	85	)	)	PUNCT
ejpam-4207	235	86	,	,	PUNCT
ejpam-4207	235	87	there	there	PRON
ejpam-4207	235	88	exists	exist	VERB
ejpam-4207	235	89	u	u	PROPN
ejpam-4207	235	90	∈	∈	PROPN
ejpam-4207	235	91	mio(x	mio(x	PROPN
ejpam-4207	235	92	)	)	PUNCT
ejpam-4207	235	93	containing	contain	VERB
ejpam-4207	235	94	x	x	PUNCT
ejpam-4207	235	95	such	such	ADJ
ejpam-4207	235	96	that	that	SCONJ
ejpam-4207	235	97	f	f	PROPN
ejpam-4207	235	98	(	(	PUNCT
ejpam-4207	235	99	u	u	NOUN
ejpam-4207	235	100	)	)	PUNCT
ejpam-4207	235	101	∩	∩	NOUN
ejpam-4207	235	102	v	v	ADP
ejpam-4207	235	103	̸=	̸=	PROPN
ejpam-4207	235	104	∅	∅	NOUN
ejpam-4207	235	105	for	for	ADP
ejpam-4207	235	106	every	every	DET
ejpam-4207	235	107	u	u	PROPN
ejpam-4207	235	108	∈	∈	PROPN
ejpam-4207	235	109	u	u	NOUN
ejpam-4207	235	110	,	,	PUNCT
ejpam-4207	235	111	(	(	PUNCT
ejpam-4207	235	112	3	3	X
ejpam-4207	235	113	)	)	PUNCT
ejpam-4207	235	114	upper	upper	ADJ
ejpam-4207	235	115	/	/	SYM
ejpam-4207	235	116	lower	low	ADJ
ejpam-4207	235	117	m	m	PROPN
ejpam-4207	235	118	-	-	ADJ
ejpam-4207	235	119	i	i	PRON
ejpam-4207	235	120	-	-	NOUN
ejpam-4207	235	121	continuous	continuous	ADJ
ejpam-4207	235	122	if	if	SCONJ
ejpam-4207	235	123	it	it	PRON
ejpam-4207	235	124	has	have	VERB
ejpam-4207	235	125	this	this	DET
ejpam-4207	235	126	property	property	NOUN
ejpam-4207	235	127	at	at	ADP
ejpam-4207	235	128	each	each	DET
ejpam-4207	235	129	point	point	NOUN
ejpam-4207	235	130	x	x	X
ejpam-4207	235	131	∈	∈	PROPN
ejpam-4207	235	132	x.	x.	NOUN
ejpam-4207	235	133	theorem	theorem	VERB
ejpam-4207	235	134	13	13	NUM
ejpam-4207	235	135	.	.	PUNCT
ejpam-4207	236	1	let	let	VERB
ejpam-4207	236	2	x	x	PRON
ejpam-4207	236	3	be	be	AUX
ejpam-4207	236	4	a	a	DET
ejpam-4207	236	5	nonempty	nonempty	NOUN
ejpam-4207	236	6	set	set	VERB
ejpam-4207	236	7	with	with	ADP
ejpam-4207	236	8	two	two	NUM
ejpam-4207	236	9	m	m	NOUN
ejpam-4207	236	10	-	-	PUNCT
ejpam-4207	236	11	structures	structure	NOUN
ejpam-4207	236	12	m1	m1	NOUN
ejpam-4207	236	13	x	x	X
ejpam-4207	236	14	and	and	CCONJ
ejpam-4207	236	15	m2	m2	PROPN
ejpam-4207	236	16	x	x	PUNCT
ejpam-4207	236	17	satisfying	satisfy	VERB
ejpam-4207	236	18	property	property	NOUN
ejpam-4207	236	19	b	b	PROPN
ejpam-4207	236	20	such	such	ADJ
ejpam-4207	236	21	that	that	DET
ejpam-4207	236	22	v1	v1	PROPN
ejpam-4207	236	23	∈	∈	PROPN
ejpam-4207	236	24	m1	m1	NOUN
ejpam-4207	236	25	x	x	PUNCT
ejpam-4207	236	26	and	and	CCONJ
ejpam-4207	236	27	v2	v2	PROPN
ejpam-4207	236	28	∈	∈	PROPN
ejpam-4207	236	29	m2	m2	PROPN
ejpam-4207	236	30	x	x	PROPN
ejpam-4207	236	31	implies	imply	VERB
ejpam-4207	236	32	v1	v1	NOUN
ejpam-4207	236	33	∩	∩	ADJ
ejpam-4207	236	34	v2	v2	PROPN
ejpam-4207	236	35	∈	∈	PROPN
ejpam-4207	236	36	m1	m1	NOUN
ejpam-4207	236	37	x	x	PUNCT
ejpam-4207	236	38	.	.	PUNCT
ejpam-4207	237	1	if	if	SCONJ
ejpam-4207	237	2	a	a	DET
ejpam-4207	237	3	multifunction	multifunction	NOUN
ejpam-4207	237	4	f	f	NOUN
ejpam-4207	237	5	:	:	PUNCT
ejpam-4207	237	6	(	(	PUNCT
ejpam-4207	237	7	x	x	X
ejpam-4207	237	8	,	,	PUNCT
ejpam-4207	237	9	τ	τ	PROPN
ejpam-4207	237	10	,	,	PUNCT
ejpam-4207	237	11	i	i	NOUN
ejpam-4207	237	12	)	)	PUNCT
ejpam-4207	237	13	→	→	SYM
ejpam-4207	237	14	(	(	PUNCT
ejpam-4207	237	15	y	y	PROPN
ejpam-4207	237	16	,	,	PUNCT
ejpam-4207	237	17	σ	σ	PROPN
ejpam-4207	237	18	)	)	PUNCT
ejpam-4207	237	19	is	be	AUX
ejpam-4207	237	20	upper	upper	ADJ
ejpam-4207	237	21	m1	m1	NOUN
ejpam-4207	237	22	x	x	X
ejpam-4207	237	23	-	-	PROPN
ejpam-4207	237	24	i	i	PRON
ejpam-4207	237	25	-	-	PUNCT
ejpam-4207	237	26	continuous	continuous	ADJ
ejpam-4207	237	27	and	and	CCONJ
ejpam-4207	237	28	f	f	NOUN
ejpam-4207	237	29	:	:	PUNCT
ejpam-4207	237	30	(	(	PUNCT
ejpam-4207	237	31	x	x	X
ejpam-4207	237	32	,	,	PUNCT
ejpam-4207	237	33	τ	τ	PROPN
ejpam-4207	237	34	,	,	PUNCT
ejpam-4207	237	35	i	i	NOUN
ejpam-4207	237	36	)	)	PUNCT
ejpam-4207	237	37	→	→	SYM
ejpam-4207	237	38	(	(	PUNCT
ejpam-4207	237	39	y	y	PROPN
ejpam-4207	237	40	,	,	PUNCT
ejpam-4207	237	41	σ	σ	PROPN
ejpam-4207	237	42	)	)	PUNCT
ejpam-4207	237	43	is	be	AUX
ejpam-4207	237	44	lower	low	ADJ
ejpam-4207	237	45	m2	m2	PROPN
ejpam-4207	237	46	x	x	PROPN
ejpam-4207	237	47	-	-	PROPN
ejpam-4207	237	48	i	i	PRON
ejpam-4207	237	49	-	-	PUNCT
ejpam-4207	237	50	continuous	continuous	ADJ
ejpam-4207	237	51	,	,	PUNCT
ejpam-4207	237	52	then	then	ADV
ejpam-4207	237	53	f	f	X
ejpam-4207	237	54	:	:	PUNCT
ejpam-4207	237	55	(	(	PUNCT
ejpam-4207	237	56	x	x	X
ejpam-4207	237	57	,	,	PUNCT
ejpam-4207	237	58	τ	τ	PROPN
ejpam-4207	237	59	,	,	PUNCT
ejpam-4207	237	60	i	i	NOUN
ejpam-4207	237	61	)	)	PUNCT
ejpam-4207	237	62	→	→	SYM
ejpam-4207	237	63	(	(	PUNCT
ejpam-4207	237	64	y	y	PROPN
ejpam-4207	237	65	,	,	PUNCT
ejpam-4207	237	66	σ	σ	PROPN
ejpam-4207	237	67	)	)	PUNCT
ejpam-4207	237	68	is	be	AUX
ejpam-4207	237	69	m1	m1	PROPN
ejpam-4207	237	70	x	x	PROPN
ejpam-4207	237	71	-	-	PROPN
ejpam-4207	237	72	i	i	PRON
ejpam-4207	237	73	-	-	PUNCT
ejpam-4207	237	74	continuous	continuous	ADJ
ejpam-4207	237	75	.	.	PUNCT
ejpam-4207	238	1	theorem	theorem	NOUN
ejpam-4207	238	2	14	14	NUM
ejpam-4207	238	3	.	.	PUNCT
ejpam-4207	239	1	let	let	VERB
ejpam-4207	239	2	x	x	PRON
ejpam-4207	239	3	be	be	AUX
ejpam-4207	239	4	a	a	DET
ejpam-4207	239	5	nonempty	nonempty	NOUN
ejpam-4207	239	6	set	set	VERB
ejpam-4207	239	7	with	with	ADP
ejpam-4207	239	8	two	two	NUM
ejpam-4207	239	9	m	m	NOUN
ejpam-4207	239	10	-	-	PUNCT
ejpam-4207	239	11	structures	structure	NOUN
ejpam-4207	239	12	m1	m1	NOUN
ejpam-4207	239	13	x	x	X
ejpam-4207	239	14	and	and	CCONJ
ejpam-4207	239	15	m2	m2	PROPN
ejpam-4207	239	16	x	x	PUNCT
ejpam-4207	239	17	satisfying	satisfy	VERB
ejpam-4207	239	18	property	property	NOUN
ejpam-4207	239	19	b	b	PROPN
ejpam-4207	239	20	such	such	ADJ
ejpam-4207	239	21	that	that	DET
ejpam-4207	239	22	v1	v1	PROPN
ejpam-4207	239	23	∈	∈	PROPN
ejpam-4207	239	24	m1	m1	NOUN
ejpam-4207	239	25	x	x	PUNCT
ejpam-4207	239	26	and	and	CCONJ
ejpam-4207	239	27	v2	v2	PROPN
ejpam-4207	239	28	∈	∈	PROPN
ejpam-4207	239	29	m2	m2	PROPN
ejpam-4207	239	30	x	x	PROPN
ejpam-4207	239	31	implies	imply	VERB
ejpam-4207	239	32	v1	v1	NOUN
ejpam-4207	239	33	∩	∩	ADJ
ejpam-4207	239	34	v2	v2	PROPN
ejpam-4207	239	35	∈	∈	PROPN
ejpam-4207	239	36	m1	m1	NOUN
ejpam-4207	239	37	x	x	PUNCT
ejpam-4207	239	38	.	.	PUNCT
ejpam-4207	240	1	if	if	SCONJ
ejpam-4207	240	2	a	a	DET
ejpam-4207	240	3	multifunction	multifunction	NOUN
ejpam-4207	240	4	f	f	NOUN
ejpam-4207	240	5	:	:	PUNCT
ejpam-4207	240	6	(	(	PUNCT
ejpam-4207	240	7	x	x	X
ejpam-4207	240	8	,	,	PUNCT
ejpam-4207	240	9	τ	τ	PROPN
ejpam-4207	240	10	,	,	PUNCT
ejpam-4207	240	11	i	i	NOUN
ejpam-4207	240	12	)	)	PUNCT
ejpam-4207	240	13	→	→	SYM
ejpam-4207	240	14	(	(	PUNCT
ejpam-4207	240	15	y	y	PROPN
ejpam-4207	240	16	,	,	PUNCT
ejpam-4207	240	17	σ	σ	PROPN
ejpam-4207	240	18	)	)	PUNCT
ejpam-4207	240	19	is	be	AUX
ejpam-4207	240	20	lower	low	ADJ
ejpam-4207	240	21	m1	m1	NOUN
ejpam-4207	240	22	x	x	SYM
ejpam-4207	240	23	-	-	ADJ
ejpam-4207	240	24	continuous	continuous	ADJ
ejpam-4207	240	25	and	and	CCONJ
ejpam-4207	240	26	f	f	NOUN
ejpam-4207	240	27	:	:	PUNCT
ejpam-4207	240	28	(	(	PUNCT
ejpam-4207	240	29	x	x	X
ejpam-4207	240	30	,	,	PUNCT
ejpam-4207	240	31	τ	τ	PROPN
ejpam-4207	240	32	,	,	PUNCT
ejpam-4207	240	33	i	i	NOUN
ejpam-4207	240	34	)	)	PUNCT
ejpam-4207	240	35	→	→	SYM
ejpam-4207	240	36	(	(	PUNCT
ejpam-4207	240	37	y	y	PROPN
ejpam-4207	240	38	,	,	PUNCT
ejpam-4207	240	39	σ	σ	PROPN
ejpam-4207	240	40	)	)	PUNCT
ejpam-4207	240	41	is	be	AUX
ejpam-4207	240	42	upper	upper	ADJ
ejpam-4207	240	43	m2	m2	PROPN
ejpam-4207	240	44	xcontinuous	xcontinuous	NOUN
ejpam-4207	240	45	,	,	PUNCT
ejpam-4207	240	46	then	then	ADV
ejpam-4207	240	47	f	f	X
ejpam-4207	240	48	:	:	PUNCT
ejpam-4207	240	49	(	(	PUNCT
ejpam-4207	240	50	x	x	X
ejpam-4207	240	51	,	,	PUNCT
ejpam-4207	240	52	τ	τ	PROPN
ejpam-4207	240	53	,	,	PUNCT
ejpam-4207	240	54	i	i	NOUN
ejpam-4207	240	55	)	)	PUNCT
ejpam-4207	240	56	→	→	SYM
ejpam-4207	240	57	(	(	PUNCT
ejpam-4207	240	58	y	y	PROPN
ejpam-4207	240	59	,	,	PUNCT
ejpam-4207	240	60	σ	σ	PROPN
ejpam-4207	240	61	)	)	PUNCT
ejpam-4207	240	62	is	be	AUX
ejpam-4207	240	63	m1	m1	PROPN
ejpam-4207	240	64	x	x	PROPN
ejpam-4207	240	65	-	-	PROPN
ejpam-4207	240	66	i	i	PRON
ejpam-4207	240	67	-	-	PUNCT
ejpam-4207	240	68	continuous	continuous	ADJ
ejpam-4207	240	69	.	.	PUNCT
ejpam-4207	241	1	6	6	NUM
ejpam-4207	241	2	.	.	X
ejpam-4207	241	3	mi⋆-continuous	mi⋆-continuous	ADJ
ejpam-4207	241	4	multifunctions	multifunction	NOUN
ejpam-4207	241	5	a	a	DET
ejpam-4207	241	6	multifunction	multifunction	NOUN
ejpam-4207	241	7	f	f	NOUN
ejpam-4207	241	8	:	:	PUNCT
ejpam-4207	241	9	(	(	PUNCT
ejpam-4207	241	10	x	x	X
ejpam-4207	241	11	,	,	PUNCT
ejpam-4207	241	12	τ	τ	PROPN
ejpam-4207	241	13	,	,	PUNCT
ejpam-4207	241	14	i	i	NOUN
ejpam-4207	241	15	)	)	PUNCT
ejpam-4207	241	16	→	→	SYM
ejpam-4207	241	17	(	(	PUNCT
ejpam-4207	241	18	y	y	PROPN
ejpam-4207	241	19	,	,	PUNCT
ejpam-4207	241	20	σ	σ	PROPN
ejpam-4207	241	21	,	,	PUNCT
ejpam-4207	241	22	j	j	PROPN
ejpam-4207	241	23	)	)	PUNCT
ejpam-4207	241	24	is	be	AUX
ejpam-4207	241	25	said	say	VERB
ejpam-4207	241	26	to	to	PART
ejpam-4207	241	27	be	be	AUX
ejpam-4207	241	28	i⋆-continuous	i⋆-continuous	ADJ
ejpam-4207	241	29	[	[	X
ejpam-4207	241	30	9	9	NUM
ejpam-4207	241	31	]	]	X
ejpam-4207	241	32	if	if	SCONJ
ejpam-4207	241	33	for	for	ADP
ejpam-4207	241	34	each	each	DET
ejpam-4207	241	35	x	x	SYM
ejpam-4207	241	36	∈	∈	PROPN
ejpam-4207	241	37	x	x	X
ejpam-4207	241	38	and	and	CCONJ
ejpam-4207	241	39	each	each	DET
ejpam-4207	241	40	σ⋆-open	σ⋆-open	ADJ
ejpam-4207	241	41	sets	set	NOUN
ejpam-4207	241	42	v1	v1	NOUN
ejpam-4207	241	43	,	,	PUNCT
ejpam-4207	241	44	v2	v2	PROPN
ejpam-4207	241	45	of	of	ADP
ejpam-4207	241	46	y	y	PRON
ejpam-4207	241	47	such	such	ADJ
ejpam-4207	241	48	that	that	SCONJ
ejpam-4207	241	49	f	f	PROPN
ejpam-4207	241	50	(	(	PUNCT
ejpam-4207	241	51	x	x	X
ejpam-4207	241	52	)	)	PUNCT
ejpam-4207	241	53	∈	∈	NOUN
ejpam-4207	241	54	v	v	ADP
ejpam-4207	241	55	+	+	CCONJ
ejpam-4207	241	56	1	1	NUM
ejpam-4207	241	57	∩	∩	NOUN
ejpam-4207	241	58	v	v	ADP
ejpam-4207	241	59	−	−	PROPN
ejpam-4207	241	60	2	2	NUM
ejpam-4207	241	61	,	,	PUNCT
ejpam-4207	241	62	there	there	PRON
ejpam-4207	241	63	exists	exist	VERB
ejpam-4207	241	64	a	a	DET
ejpam-4207	241	65	τ⋆-open	τ⋆-open	NOUN
ejpam-4207	241	66	set	set	NOUN
ejpam-4207	241	67	u	u	NOUN
ejpam-4207	241	68	containing	contain	VERB
ejpam-4207	241	69	x	x	PUNCT
ejpam-4207	241	70	such	such	ADJ
ejpam-4207	241	71	that	that	SCONJ
ejpam-4207	241	72	f	f	PROPN
ejpam-4207	241	73	(	(	PUNCT
ejpam-4207	241	74	u	u	NOUN
ejpam-4207	241	75	)	)	PUNCT
ejpam-4207	241	76	⊂	⊂	PROPN
ejpam-4207	241	77	v	v	ADP
ejpam-4207	241	78	+	+	CCONJ
ejpam-4207	241	79	1	1	NUM
ejpam-4207	241	80	and	and	CCONJ
ejpam-4207	241	81	f	f	PROPN
ejpam-4207	241	82	(	(	PUNCT
ejpam-4207	241	83	u	u	NOUN
ejpam-4207	241	84	)	)	PUNCT
ejpam-4207	241	85	∩	∩	NOUN
ejpam-4207	241	86	v2	v2	PROPN
ejpam-4207	241	87	̸=	̸=	PROPN
ejpam-4207	241	88	∅	∅	NOUN
ejpam-4207	241	89	for	for	ADP
ejpam-4207	241	90	every	every	DET
ejpam-4207	241	91	u	u	PROPN
ejpam-4207	241	92	∈	∈	PROPN
ejpam-4207	241	93	u	u	NOUN
ejpam-4207	241	94	.	.	PUNCT
ejpam-4207	242	1	definition	definition	NOUN
ejpam-4207	242	2	17	17	NUM
ejpam-4207	242	3	.	.	PUNCT
ejpam-4207	243	1	a	a	DET
ejpam-4207	243	2	multifunction	multifunction	NOUN
ejpam-4207	243	3	f	f	NOUN
ejpam-4207	243	4	:	:	PUNCT
ejpam-4207	243	5	(	(	PUNCT
ejpam-4207	243	6	x	x	X
ejpam-4207	243	7	,	,	PUNCT
ejpam-4207	243	8	τ	τ	PROPN
ejpam-4207	243	9	,	,	PUNCT
ejpam-4207	243	10	i	i	NOUN
ejpam-4207	243	11	)	)	PUNCT
ejpam-4207	243	12	→	→	SYM
ejpam-4207	243	13	(	(	PUNCT
ejpam-4207	243	14	y	y	PROPN
ejpam-4207	243	15	,	,	PUNCT
ejpam-4207	243	16	σ	σ	PROPN
ejpam-4207	243	17	,	,	PUNCT
ejpam-4207	243	18	j	j	PROPN
ejpam-4207	243	19	)	)	PUNCT
ejpam-4207	243	20	is	be	AUX
ejpam-4207	243	21	said	say	VERB
ejpam-4207	243	22	to	to	PART
ejpam-4207	243	23	be	be	AUX
ejpam-4207	243	24	mi⋆-continuous	mi⋆-continuous	ADJ
ejpam-4207	243	25	if	if	SCONJ
ejpam-4207	243	26	for	for	ADP
ejpam-4207	243	27	each	each	DET
ejpam-4207	243	28	x	x	SYM
ejpam-4207	243	29	∈	∈	PROPN
ejpam-4207	243	30	x	x	X
ejpam-4207	243	31	and	and	CCONJ
ejpam-4207	243	32	each	each	DET
ejpam-4207	243	33	σ⋆-open	σ⋆-open	ADJ
ejpam-4207	243	34	sets	set	NOUN
ejpam-4207	243	35	v1	v1	NOUN
ejpam-4207	243	36	,	,	PUNCT
ejpam-4207	243	37	v2	v2	PROPN
ejpam-4207	243	38	of	of	ADP
ejpam-4207	243	39	y	y	PRON
ejpam-4207	243	40	such	such	ADJ
ejpam-4207	243	41	that	that	SCONJ
ejpam-4207	243	42	f	f	PROPN
ejpam-4207	243	43	(	(	PUNCT
ejpam-4207	243	44	x	x	X
ejpam-4207	243	45	)	)	PUNCT
ejpam-4207	243	46	∈	∈	NOUN
ejpam-4207	243	47	v	v	ADP
ejpam-4207	243	48	+	+	CCONJ
ejpam-4207	243	49	1	1	NUM
ejpam-4207	243	50	∩	∩	NOUN
ejpam-4207	243	51	v	v	ADP
ejpam-4207	243	52	−	−	PROPN
ejpam-4207	243	53	2	2	NUM
ejpam-4207	243	54	,	,	PUNCT
ejpam-4207	243	55	there	there	PRON
ejpam-4207	243	56	exists	exist	VERB
ejpam-4207	243	57	an	an	DET
ejpam-4207	243	58	mio(x)-open	mio(x)-open	NOUN
ejpam-4207	243	59	set	set	NOUN
ejpam-4207	243	60	u	u	NOUN
ejpam-4207	243	61	containing	contain	VERB
ejpam-4207	243	62	x	x	PUNCT
ejpam-4207	244	1	such	such	ADJ
ejpam-4207	244	2	that	that	SCONJ
ejpam-4207	244	3	f	f	PROPN
ejpam-4207	244	4	(	(	PUNCT
ejpam-4207	244	5	u	u	NOUN
ejpam-4207	244	6	)	)	PUNCT
ejpam-4207	244	7	⊂	⊂	PROPN
ejpam-4207	244	8	v	v	ADP
ejpam-4207	244	9	+	+	CCONJ
ejpam-4207	244	10	1	1	NUM
ejpam-4207	244	11	and	and	CCONJ
ejpam-4207	244	12	f	f	PROPN
ejpam-4207	244	13	(	(	PUNCT
ejpam-4207	244	14	u	u	NOUN
ejpam-4207	244	15	)	)	PUNCT
ejpam-4207	244	16	∩	∩	NOUN
ejpam-4207	244	17	v2	v2	PROPN
ejpam-4207	244	18	̸=	̸=	PROPN
ejpam-4207	244	19	∅	∅	NOUN
ejpam-4207	244	20	for	for	ADP
ejpam-4207	244	21	every	every	DET
ejpam-4207	244	22	u	u	PROPN
ejpam-4207	244	23	∈	∈	PROPN
ejpam-4207	244	24	u	u	PROPN
ejpam-4207	244	25	.	.	PUNCT
ejpam-4207	244	26	remark	remark	PROPN
ejpam-4207	244	27	5	5	NUM
ejpam-4207	244	28	.	.	PUNCT
ejpam-4207	245	1	for	for	ADP
ejpam-4207	245	2	a	a	DET
ejpam-4207	245	3	multifunction	multifunction	NOUN
ejpam-4207	245	4	f	f	NOUN
ejpam-4207	245	5	:	:	PUNCT
ejpam-4207	245	6	(	(	PUNCT
ejpam-4207	245	7	x	x	X
ejpam-4207	245	8	,	,	PUNCT
ejpam-4207	245	9	τ	τ	PROPN
ejpam-4207	245	10	,	,	PUNCT
ejpam-4207	245	11	i	i	NOUN
ejpam-4207	245	12	)	)	PUNCT
ejpam-4207	245	13	→	→	SYM
ejpam-4207	245	14	(	(	PUNCT
ejpam-4207	245	15	y	y	PROPN
ejpam-4207	245	16	,	,	PUNCT
ejpam-4207	245	17	σ	σ	PROPN
ejpam-4207	245	18	,	,	PUNCT
ejpam-4207	245	19	j	j	PROPN
ejpam-4207	245	20	)	)	PUNCT
ejpam-4207	245	21	,	,	PUNCT
ejpam-4207	245	22	we	we	PRON
ejpam-4207	245	23	have	have	VERB
ejpam-4207	245	24	the	the	DET
ejpam-4207	245	25	following	follow	VERB
ejpam-4207	245	26	properties	property	NOUN
ejpam-4207	245	27	:	:	PUNCT
ejpam-4207	245	28	(	(	PUNCT
ejpam-4207	245	29	1	1	X
ejpam-4207	245	30	)	)	PUNCT
ejpam-4207	245	31	if	if	SCONJ
ejpam-4207	245	32	mio(x	mio(x	NOUN
ejpam-4207	245	33	)	)	PUNCT
ejpam-4207	245	34	=	=	PUNCT
ejpam-4207	246	1	τ⋆	τ⋆	NOUN
ejpam-4207	246	2	,	,	PUNCT
ejpam-4207	246	3	then	then	ADV
ejpam-4207	246	4	every	every	DET
ejpam-4207	246	5	mi⋆-continuous	mi⋆-continuous	ADJ
ejpam-4207	246	6	multifunction	multifunction	NOUN
ejpam-4207	246	7	is	be	AUX
ejpam-4207	246	8	i⋆-continuous	i⋆-continuous	ADJ
ejpam-4207	246	9	.	.	PUNCT
ejpam-4207	247	1	therefore	therefore	ADV
ejpam-4207	247	2	,	,	PUNCT
ejpam-4207	247	3	the	the	DET
ejpam-4207	247	4	notion	notion	NOUN
ejpam-4207	247	5	of	of	ADP
ejpam-4207	247	6	mi⋆-continuity	mi⋆-continuity	NOUN
ejpam-4207	247	7	is	be	AUX
ejpam-4207	247	8	a	a	DET
ejpam-4207	247	9	generalization	generalization	NOUN
ejpam-4207	247	10	of	of	ADP
ejpam-4207	247	11	i⋆-continuity	i⋆-continuity	NOUN
ejpam-4207	247	12	.	.	PUNCT
ejpam-4207	248	1	(	(	PUNCT
ejpam-4207	248	2	2	2	X
ejpam-4207	248	3	)	)	PUNCT
ejpam-4207	248	4	if	if	SCONJ
ejpam-4207	248	5	j	j	PROPN
ejpam-4207	248	6	=	=	PUNCT
ejpam-4207	248	7	{	{	PUNCT
ejpam-4207	248	8	∅	∅	NOUN
ejpam-4207	248	9	}	}	PUNCT
ejpam-4207	248	10	,	,	PUNCT
ejpam-4207	248	11	then	then	ADV
ejpam-4207	248	12	σ⋆	σ⋆	X
ejpam-4207	248	13	=	=	SYM
ejpam-4207	248	14	σ	σ	PROPN
ejpam-4207	248	15	.	.	PUNCT
ejpam-4207	249	1	therefore	therefore	ADV
ejpam-4207	249	2	,	,	PUNCT
ejpam-4207	249	3	the	the	DET
ejpam-4207	249	4	notion	notion	NOUN
ejpam-4207	249	5	of	of	ADP
ejpam-4207	249	6	mi⋆-continuity	mi⋆-continuity	NOUN
ejpam-4207	249	7	is	be	AUX
ejpam-4207	249	8	a	a	DET
ejpam-4207	249	9	generalization	generalization	NOUN
ejpam-4207	249	10	of	of	ADP
ejpam-4207	249	11	m	m	PROPN
ejpam-4207	249	12	-	-	PROPN
ejpam-4207	249	13	i	i	NOUN
ejpam-4207	249	14	-	-	PUNCT
ejpam-4207	249	15	continuity	continuity	NOUN
ejpam-4207	249	16	.	.	PUNCT
ejpam-4207	250	1	theorem	theorem	VERB
ejpam-4207	250	2	15	15	NUM
ejpam-4207	250	3	.	.	PUNCT
ejpam-4207	251	1	for	for	ADP
ejpam-4207	251	2	a	a	DET
ejpam-4207	251	3	multifunction	multifunction	NOUN
ejpam-4207	251	4	f	f	NOUN
ejpam-4207	251	5	:	:	PUNCT
ejpam-4207	251	6	(	(	PUNCT
ejpam-4207	251	7	x	x	X
ejpam-4207	251	8	,	,	PUNCT
ejpam-4207	251	9	τ	τ	PROPN
ejpam-4207	251	10	,	,	PUNCT
ejpam-4207	251	11	i	i	NOUN
ejpam-4207	251	12	)	)	PUNCT
ejpam-4207	251	13	→	→	SYM
ejpam-4207	251	14	(	(	PUNCT
ejpam-4207	251	15	y	y	PROPN
ejpam-4207	251	16	,	,	PUNCT
ejpam-4207	251	17	σ	σ	PROPN
ejpam-4207	251	18	,	,	PUNCT
ejpam-4207	251	19	j	j	PROPN
ejpam-4207	251	20	)	)	PUNCT
ejpam-4207	251	21	,	,	PUNCT
ejpam-4207	251	22	the	the	DET
ejpam-4207	251	23	following	follow	VERB
ejpam-4207	251	24	properties	property	NOUN
ejpam-4207	251	25	are	be	AUX
ejpam-4207	251	26	equivalent	equivalent	ADJ
ejpam-4207	251	27	:	:	PUNCT
ejpam-4207	251	28	(	(	PUNCT
ejpam-4207	251	29	1	1	X
ejpam-4207	251	30	)	)	PUNCT
ejpam-4207	251	31	f	f	PROPN
ejpam-4207	251	32	is	be	AUX
ejpam-4207	251	33	mi⋆-continuous	mi⋆-continuous	ADJ
ejpam-4207	251	34	;	;	PUNCT
ejpam-4207	251	35	takashi	takashi	PROPN
ejpam-4207	251	36	noiri	noiri	PROPN
ejpam-4207	251	37	,	,	PUNCT
ejpam-4207	251	38	valeriu	valeriu	ADJ
ejpam-4207	251	39	popa	popa	NOUN
ejpam-4207	251	40	/	/	SYM
ejpam-4207	251	41	eur	eur	PROPN
ejpam-4207	251	42	.	.	PUNCT
ejpam-4207	252	1	j.	j.	PROPN
ejpam-4207	252	2	pure	pure	PROPN
ejpam-4207	252	3	appl	appl	PROPN
ejpam-4207	252	4	.	.	PROPN
ejpam-4207	252	5	math	math	PROPN
ejpam-4207	252	6	,	,	PUNCT
ejpam-4207	252	7	15	15	NUM
ejpam-4207	252	8	(	(	PUNCT
ejpam-4207	252	9	1	1	NUM
ejpam-4207	252	10	)	)	PUNCT
ejpam-4207	252	11	(	(	PUNCT
ejpam-4207	252	12	2022	2022	NUM
ejpam-4207	252	13	)	)	PUNCT
ejpam-4207	252	14	,	,	PUNCT
ejpam-4207	252	15	1	1	NUM
ejpam-4207	252	16	-	-	SYM
ejpam-4207	252	17	14	14	NUM
ejpam-4207	252	18	10	10	NUM
ejpam-4207	252	19	(	(	PUNCT
ejpam-4207	252	20	2	2	NUM
ejpam-4207	252	21	)	)	PUNCT
ejpam-4207	252	22	for	for	ADP
ejpam-4207	252	23	each	each	DET
ejpam-4207	252	24	point	point	NOUN
ejpam-4207	252	25	x	x	X
ejpam-4207	252	26	∈	∈	NOUN
ejpam-4207	252	27	x	x	X
ejpam-4207	252	28	and	and	CCONJ
ejpam-4207	252	29	each	each	DET
ejpam-4207	252	30	σ⋆-open	σ⋆-open	ADJ
ejpam-4207	252	31	sets	set	NOUN
ejpam-4207	252	32	v1	v1	NOUN
ejpam-4207	252	33	,	,	PUNCT
ejpam-4207	252	34	v2	v2	PROPN
ejpam-4207	252	35	of	of	ADP
ejpam-4207	252	36	y	y	PRON
ejpam-4207	252	37	such	such	ADJ
ejpam-4207	252	38	that	that	SCONJ
ejpam-4207	252	39	f	f	PROPN
ejpam-4207	252	40	(	(	PUNCT
ejpam-4207	252	41	x	x	X
ejpam-4207	252	42	)	)	PUNCT
ejpam-4207	252	43	∈	∈	NOUN
ejpam-4207	252	44	v	v	ADP
ejpam-4207	252	45	+	+	CCONJ
ejpam-4207	252	46	1	1	NUM
ejpam-4207	252	47	∩v	∩v	NOUN
ejpam-4207	252	48	−	−	PROPN
ejpam-4207	252	49	2	2	NUM
ejpam-4207	252	50	,	,	PUNCT
ejpam-4207	252	51	x	x	SYM
ejpam-4207	252	52	∈	∈	NOUN
ejpam-4207	252	53	minti(f	minti(f	PRON
ejpam-4207	252	54	+	+	ADJ
ejpam-4207	252	55	(	(	PUNCT
ejpam-4207	252	56	v1	v1	NOUN
ejpam-4207	252	57	)	)	PUNCT
ejpam-4207	252	58	∩	∩	NOUN
ejpam-4207	252	59	f−(v2	f−(v2	NUM
ejpam-4207	252	60	)	)	PUNCT
ejpam-4207	252	61	)	)	PUNCT
ejpam-4207	252	62	;	;	PUNCT
ejpam-4207	252	63	(	(	PUNCT
ejpam-4207	252	64	3	3	X
ejpam-4207	252	65	)	)	PUNCT
ejpam-4207	252	66	f+(v1	f+(v1	NOUN
ejpam-4207	252	67	)	)	PUNCT
ejpam-4207	252	68	∩	∩	NOUN
ejpam-4207	252	69	f−(v2	f−(v2	X
ejpam-4207	252	70	)	)	PUNCT
ejpam-4207	252	71	∈	∈	PROPN
ejpam-4207	252	72	mio(x	mio(x	PROPN
ejpam-4207	252	73	)	)	PUNCT
ejpam-4207	252	74	for	for	ADP
ejpam-4207	252	75	every	every	DET
ejpam-4207	252	76	σ⋆-open	σ⋆-open	ADJ
ejpam-4207	252	77	sets	set	NOUN
ejpam-4207	252	78	v1	v1	NOUN
ejpam-4207	252	79	,	,	PUNCT
ejpam-4207	252	80	v2	v2	PROPN
ejpam-4207	252	81	of	of	ADP
ejpam-4207	252	82	y	y	PROPN
ejpam-4207	252	83	;	;	PUNCT
ejpam-4207	252	84	(	(	PUNCT
ejpam-4207	252	85	4	4	NUM
ejpam-4207	252	86	)	)	PUNCT
ejpam-4207	252	87	f−(k1	f−(k1	ADP
ejpam-4207	252	88	)	)	PUNCT
ejpam-4207	252	89	∪	∪	ADP
ejpam-4207	252	90	f+(k2	f+(k2	NOUN
ejpam-4207	252	91	)	)	PUNCT
ejpam-4207	252	92	is	be	AUX
ejpam-4207	252	93	m	m	PROPN
ejpam-4207	252	94	-	-	PUNCT
ejpam-4207	252	95	i	i	PRON
ejpam-4207	252	96	-	-	PUNCT
ejpam-4207	252	97	closed	close	VERB
ejpam-4207	252	98	for	for	ADP
ejpam-4207	252	99	every	every	DET
ejpam-4207	252	100	σ⋆-closed	σ⋆-closed	NOUN
ejpam-4207	252	101	sets	set	NOUN
ejpam-4207	252	102	k1,k2	k1,k2	PROPN
ejpam-4207	252	103	of	of	ADP
ejpam-4207	252	104	y	y	PROPN
ejpam-4207	252	105	;	;	PUNCT
ejpam-4207	252	106	(	(	PUNCT
ejpam-4207	252	107	5	5	X
ejpam-4207	252	108	)	)	PUNCT
ejpam-4207	252	109	mcli(f	mcli(f	SYM
ejpam-4207	252	110	−(b1	−(b1	NUM
ejpam-4207	252	111	)	)	PUNCT
ejpam-4207	252	112	∪	∪	NOUN
ejpam-4207	252	113	f+(b2	f+(b2	PROPN
ejpam-4207	252	114	)	)	PUNCT
ejpam-4207	252	115	)	)	PUNCT
ejpam-4207	253	1	⊂	⊂	PROPN
ejpam-4207	253	2	f−(cl⋆(b1	f−(cl⋆(b1	PROPN
ejpam-4207	253	3	)	)	PUNCT
ejpam-4207	253	4	)	)	PUNCT
ejpam-4207	253	5	∪	∪	ADP
ejpam-4207	253	6	f+(cl⋆(b2	f+(cl⋆(b2	NOUN
ejpam-4207	253	7	)	)	PUNCT
ejpam-4207	253	8	)	)	PUNCT
ejpam-4207	253	9	for	for	ADP
ejpam-4207	253	10	every	every	DET
ejpam-4207	253	11	subsets	subset	NOUN
ejpam-4207	253	12	b1	b1	NOUN
ejpam-4207	253	13	,	,	PUNCT
ejpam-4207	253	14	b2	b2	NOUN
ejpam-4207	253	15	of	of	ADP
ejpam-4207	253	16	y	y	PROPN
ejpam-4207	253	17	;	;	PUNCT
ejpam-4207	253	18	(	(	PUNCT
ejpam-4207	253	19	6	6	X
ejpam-4207	253	20	)	)	PUNCT
ejpam-4207	253	21	f−(int⋆(b1))∩f+(int⋆(b2	f−(int⋆(b1))∩f+(int⋆(b2	PROPN
ejpam-4207	253	22	)	)	PUNCT
ejpam-4207	253	23	)	)	PUNCT
ejpam-4207	254	1	⊂	⊂	PROPN
ejpam-4207	254	2	minti(f	minti(f	PRON
ejpam-4207	254	3	−(b1)∩f+(b2	−(b1)∩f+(b2	NOUN
ejpam-4207	254	4	)	)	PUNCT
ejpam-4207	254	5	)	)	PUNCT
ejpam-4207	254	6	for	for	ADP
ejpam-4207	254	7	every	every	DET
ejpam-4207	254	8	subsets	subset	NOUN
ejpam-4207	254	9	b1	b1	NOUN
ejpam-4207	254	10	,	,	PUNCT
ejpam-4207	254	11	b2	b2	NOUN
ejpam-4207	254	12	of	of	ADP
ejpam-4207	254	13	y	y	PROPN
ejpam-4207	254	14	.	.	PUNCT
ejpam-4207	255	1	proof	proof	NOUN
ejpam-4207	255	2	.	.	PUNCT
ejpam-4207	256	1	(	(	PUNCT
ejpam-4207	256	2	1	1	X
ejpam-4207	256	3	)	)	PUNCT
ejpam-4207	256	4	=	=	NOUN
ejpam-4207	256	5	>	>	X
ejpam-4207	256	6	(	(	PUNCT
ejpam-4207	256	7	2	2	NUM
ejpam-4207	256	8	):	):	PUNCT
ejpam-4207	256	9	let	let	VERB
ejpam-4207	256	10	x	x	PUNCT
ejpam-4207	256	11	∈	∈	PROPN
ejpam-4207	256	12	x	x	X
ejpam-4207	256	13	and	and	CCONJ
ejpam-4207	256	14	v1	v1	NOUN
ejpam-4207	256	15	,	,	PUNCT
ejpam-4207	256	16	v2	v2	PROPN
ejpam-4207	256	17	be	be	VERB
ejpam-4207	256	18	any	any	DET
ejpam-4207	256	19	σ⋆-open	σ⋆-open	ADJ
ejpam-4207	256	20	sets	set	NOUN
ejpam-4207	256	21	of	of	ADP
ejpam-4207	256	22	y	y	PRON
ejpam-4207	256	23	such	such	ADJ
ejpam-4207	256	24	that	that	SCONJ
ejpam-4207	256	25	f	f	PROPN
ejpam-4207	256	26	(	(	PUNCT
ejpam-4207	256	27	x	x	X
ejpam-4207	256	28	)	)	PUNCT
ejpam-4207	256	29	∈	∈	NOUN
ejpam-4207	256	30	v	v	ADP
ejpam-4207	256	31	+	+	CCONJ
ejpam-4207	256	32	1	1	NUM
ejpam-4207	256	33	∩v	∩v	NOUN
ejpam-4207	256	34	−	−	PROPN
ejpam-4207	256	35	2	2	NUM
ejpam-4207	256	36	.	.	PUNCT
ejpam-4207	257	1	then	then	ADV
ejpam-4207	257	2	there	there	PRON
ejpam-4207	257	3	exists	exist	VERB
ejpam-4207	257	4	u	u	PROPN
ejpam-4207	257	5	∈	∈	PROPN
ejpam-4207	257	6	mio(x	mio(x	PROPN
ejpam-4207	257	7	)	)	PUNCT
ejpam-4207	257	8	containing	contain	VERB
ejpam-4207	257	9	x	x	PUNCT
ejpam-4207	257	10	such	such	ADJ
ejpam-4207	257	11	that	that	SCONJ
ejpam-4207	257	12	f	f	PROPN
ejpam-4207	257	13	(	(	PUNCT
ejpam-4207	257	14	u	u	NOUN
ejpam-4207	257	15	)	)	PUNCT
ejpam-4207	257	16	∈	∈	NOUN
ejpam-4207	257	17	v	v	ADP
ejpam-4207	257	18	+	+	CCONJ
ejpam-4207	257	19	1	1	NUM
ejpam-4207	257	20	∩v	∩v	NOUN
ejpam-4207	257	21	−	−	PROPN
ejpam-4207	257	22	2	2	NUM
ejpam-4207	257	23	.	.	PUNCT
ejpam-4207	258	1	therefore	therefore	ADV
ejpam-4207	258	2	,	,	PUNCT
ejpam-4207	258	3	u	u	PROPN
ejpam-4207	258	4	⊂	⊂	NOUN
ejpam-4207	258	5	f+(v1	f+(v1	X
ejpam-4207	258	6	)	)	PUNCT
ejpam-4207	258	7	∩	∩	NOUN
ejpam-4207	258	8	f−(v2	f−(v2	NUM
ejpam-4207	258	9	)	)	PUNCT
ejpam-4207	258	10	and	and	CCONJ
ejpam-4207	258	11	hence	hence	ADV
ejpam-4207	258	12	x	x	PART
ejpam-4207	258	13	∈	∈	NOUN
ejpam-4207	258	14	minti(f	minti(f	PRON
ejpam-4207	258	15	+	+	ADJ
ejpam-4207	258	16	(	(	PUNCT
ejpam-4207	258	17	v1	v1	NOUN
ejpam-4207	258	18	)	)	PUNCT
ejpam-4207	258	19	∩	∩	NOUN
ejpam-4207	258	20	f−(v2	f−(v2	NUM
ejpam-4207	258	21	)	)	PUNCT
ejpam-4207	258	22	)	)	PUNCT
ejpam-4207	258	23	.	.	PUNCT
ejpam-4207	259	1	(	(	PUNCT
ejpam-4207	259	2	2	2	X
ejpam-4207	259	3	)	)	PUNCT
ejpam-4207	259	4	=	=	NOUN
ejpam-4207	259	5	>	>	X
ejpam-4207	259	6	(	(	PUNCT
ejpam-4207	259	7	3	3	NUM
ejpam-4207	259	8	):	):	PUNCT
ejpam-4207	259	9	let	let	VERB
ejpam-4207	259	10	v1	v1	NOUN
ejpam-4207	259	11	,	,	PUNCT
ejpam-4207	259	12	v2	v2	PROPN
ejpam-4207	259	13	be	be	VERB
ejpam-4207	259	14	any	any	DET
ejpam-4207	259	15	σ⋆-open	σ⋆-open	ADJ
ejpam-4207	259	16	sets	set	NOUN
ejpam-4207	259	17	of	of	ADP
ejpam-4207	259	18	y	y	PROPN
ejpam-4207	259	19	and	and	CCONJ
ejpam-4207	259	20	x	x	PUNCT
ejpam-4207	259	21	∈	∈	NOUN
ejpam-4207	259	22	f+(v1	f+(v1	NOUN
ejpam-4207	259	23	)	)	PUNCT
ejpam-4207	259	24	∩	∩	NOUN
ejpam-4207	259	25	f−(v2	f−(v2	NUM
ejpam-4207	259	26	)	)	PUNCT
ejpam-4207	259	27	.	.	PUNCT
ejpam-4207	260	1	then	then	ADV
ejpam-4207	260	2	f	f	X
ejpam-4207	260	3	(	(	PUNCT
ejpam-4207	260	4	x	x	X
ejpam-4207	260	5	)	)	PUNCT
ejpam-4207	260	6	⊂	⊂	PROPN
ejpam-4207	260	7	v1	v1	PROPN
ejpam-4207	260	8	and	and	CCONJ
ejpam-4207	260	9	f	f	PROPN
ejpam-4207	260	10	(	(	PUNCT
ejpam-4207	260	11	x	x	NOUN
ejpam-4207	260	12	)	)	PUNCT
ejpam-4207	260	13	∩	∩	NOUN
ejpam-4207	260	14	v2	v2	PROPN
ejpam-4207	260	15	̸=	̸=	PROPN
ejpam-4207	260	16	∅.	∅.	VERB
ejpam-4207	260	17	by	by	ADP
ejpam-4207	260	18	(	(	PUNCT
ejpam-4207	260	19	2	2	NUM
ejpam-4207	260	20	)	)	PUNCT
ejpam-4207	260	21	,	,	PUNCT
ejpam-4207	260	22	we	we	PRON
ejpam-4207	260	23	have	have	VERB
ejpam-4207	260	24	x	x	NOUN
ejpam-4207	260	25	∈	∈	NOUN
ejpam-4207	260	26	minti(f	minti(f	PRON
ejpam-4207	260	27	+	+	ADJ
ejpam-4207	260	28	(	(	PUNCT
ejpam-4207	260	29	v1	v1	NOUN
ejpam-4207	260	30	)	)	PUNCT
ejpam-4207	260	31	∩	∩	NOUN
ejpam-4207	260	32	f−(v2	f−(v2	NUM
ejpam-4207	260	33	)	)	PUNCT
ejpam-4207	260	34	)	)	PUNCT
ejpam-4207	260	35	and	and	CCONJ
ejpam-4207	260	36	f+(v1)∩f−(v2	f+(v1)∩f−(v2	NUM
ejpam-4207	260	37	)	)	PUNCT
ejpam-4207	260	38	⊂	⊂	NOUN
ejpam-4207	261	1	minti(f	minti(f	X
ejpam-4207	261	2	+	+	ADJ
ejpam-4207	261	3	(	(	PUNCT
ejpam-4207	261	4	v1)∩f−(v2	v1)∩f−(v2	PROPN
ejpam-4207	261	5	)	)	PUNCT
ejpam-4207	261	6	)	)	PUNCT
ejpam-4207	261	7	.	.	PUNCT
ejpam-4207	262	1	this	this	PRON
ejpam-4207	262	2	shows	show	VERB
ejpam-4207	262	3	that	that	SCONJ
ejpam-4207	262	4	f	f	PROPN
ejpam-4207	262	5	+	+	ADJ
ejpam-4207	262	6	(	(	PUNCT
ejpam-4207	262	7	v1)∩f−(v2	v1)∩f−(v2	PROPN
ejpam-4207	262	8	)	)	PUNCT
ejpam-4207	262	9	∈	∈	PROPN
ejpam-4207	262	10	mio(x	mio(x	PROPN
ejpam-4207	262	11	)	)	PUNCT
ejpam-4207	262	12	.	.	PUNCT
ejpam-4207	263	1	(	(	PUNCT
ejpam-4207	263	2	3	3	X
ejpam-4207	263	3	)	)	PUNCT
ejpam-4207	263	4	=	=	NOUN
ejpam-4207	263	5	>	>	X
ejpam-4207	263	6	(	(	PUNCT
ejpam-4207	263	7	4	4	NUM
ejpam-4207	263	8	):	):	PUNCT
ejpam-4207	263	9	this	this	PRON
ejpam-4207	263	10	easily	easily	ADV
ejpam-4207	263	11	follows	follow	VERB
ejpam-4207	263	12	from	from	ADP
ejpam-4207	263	13	the	the	DET
ejpam-4207	263	14	fact	fact	NOUN
ejpam-4207	263	15	that	that	SCONJ
ejpam-4207	263	16	f−(y	f−(y	NOUN
ejpam-4207	263	17	−	−	NOUN
ejpam-4207	263	18	b	b	NOUN
ejpam-4207	263	19	)	)	PUNCT
ejpam-4207	263	20	=	=	PUNCT
ejpam-4207	263	21	x	x	SYM
ejpam-4207	263	22	−	−	NOUN
ejpam-4207	263	23	f+(b	f+(b	PROPN
ejpam-4207	263	24	)	)	PUNCT
ejpam-4207	263	25	and	and	CCONJ
ejpam-4207	263	26	f+(y	f+(y	X
ejpam-4207	263	27	−b	−b	ADJ
ejpam-4207	263	28	)	)	PUNCT
ejpam-4207	264	1	=	=	PUNCT
ejpam-4207	264	2	x	x	X
ejpam-4207	265	1	−	−	PROPN
ejpam-4207	265	2	f−(b	f−(b	PROPN
ejpam-4207	265	3	)	)	PUNCT
ejpam-4207	265	4	for	for	ADP
ejpam-4207	265	5	every	every	DET
ejpam-4207	265	6	subset	subset	NOUN
ejpam-4207	265	7	b	b	PROPN
ejpam-4207	265	8	of	of	ADP
ejpam-4207	265	9	y	y	PROPN
ejpam-4207	265	10	.	.	PUNCT
ejpam-4207	266	1	(	(	PUNCT
ejpam-4207	266	2	4	4	X
ejpam-4207	266	3	)	)	PUNCT
ejpam-4207	266	4	=	=	NOUN
ejpam-4207	266	5	>	>	X
ejpam-4207	266	6	(	(	PUNCT
ejpam-4207	266	7	5	5	NUM
ejpam-4207	266	8	):	):	PUNCT
ejpam-4207	266	9	b1	b1	NOUN
ejpam-4207	266	10	,	,	PUNCT
ejpam-4207	266	11	b2	b2	NOUN
ejpam-4207	266	12	be	be	VERB
ejpam-4207	266	13	any	any	DET
ejpam-4207	266	14	subsets	subset	NOUN
ejpam-4207	266	15	of	of	ADP
ejpam-4207	266	16	y	y	PROPN
ejpam-4207	266	17	.	.	PUNCT
ejpam-4207	267	1	then	then	ADV
ejpam-4207	267	2	cl⋆(b1	cl⋆(b1	PROPN
ejpam-4207	267	3	)	)	PUNCT
ejpam-4207	267	4	and	and	CCONJ
ejpam-4207	267	5	cl⋆(b2	cl⋆(b2	NOUN
ejpam-4207	267	6	)	)	PUNCT
ejpam-4207	267	7	are	be	AUX
ejpam-4207	267	8	σ⋆-closed	σ⋆-closed	ADJ
ejpam-4207	267	9	.	.	PUNCT
ejpam-4207	268	1	by	by	ADP
ejpam-4207	268	2	(	(	PUNCT
ejpam-4207	268	3	4	4	NUM
ejpam-4207	268	4	)	)	PUNCT
ejpam-4207	268	5	,	,	PUNCT
ejpam-4207	268	6	mcli(f	mcli(f	AUX
ejpam-4207	268	7	−(b1)∪	−(b1)∪	NUM
ejpam-4207	268	8	f+(b2	f+(b2	NOUN
ejpam-4207	268	9	)	)	PUNCT
ejpam-4207	268	10	)	)	PUNCT
ejpam-4207	269	1	⊂	⊂	PROPN
ejpam-4207	269	2	mcli(f	mcli(f	ADP
ejpam-4207	269	3	−(cl⋆(b1))∪	−(cl⋆(b1))∪	NUM
ejpam-4207	269	4	f+(cl⋆(b2	f+(cl⋆(b2	NOUN
ejpam-4207	269	5	)	)	PUNCT
ejpam-4207	269	6	)	)	PUNCT
ejpam-4207	269	7	)	)	PUNCT
ejpam-4207	270	1	=	=	PUNCT
ejpam-4207	271	1	(	(	PUNCT
ejpam-4207	271	2	f−(cl⋆(b1))∪	f−(cl⋆(b1))∪	PROPN
ejpam-4207	271	3	f+(cl⋆(b2	f+(cl⋆(b2	NOUN
ejpam-4207	271	4	)	)	PUNCT
ejpam-4207	271	5	)	)	PUNCT
ejpam-4207	271	6	.	.	PUNCT
ejpam-4207	272	1	(	(	PUNCT
ejpam-4207	272	2	5	5	X
ejpam-4207	272	3	)	)	PUNCT
ejpam-4207	272	4	=	=	NOUN
ejpam-4207	272	5	>	>	X
ejpam-4207	272	6	(	(	PUNCT
ejpam-4207	272	7	6	6	NUM
ejpam-4207	272	8	):	):	PUNCT
ejpam-4207	272	9	b1	b1	NOUN
ejpam-4207	272	10	,	,	PUNCT
ejpam-4207	272	11	b2	b2	NOUN
ejpam-4207	272	12	be	be	VERB
ejpam-4207	272	13	any	any	DET
ejpam-4207	272	14	subsets	subset	NOUN
ejpam-4207	272	15	of	of	ADP
ejpam-4207	272	16	y	y	PROPN
ejpam-4207	272	17	.	.	PUNCT
ejpam-4207	273	1	by	by	ADP
ejpam-4207	273	2	(	(	PUNCT
ejpam-4207	273	3	5	5	NUM
ejpam-4207	273	4	)	)	PUNCT
ejpam-4207	273	5	,	,	PUNCT
ejpam-4207	273	6	we	we	PRON
ejpam-4207	273	7	have	have	VERB
ejpam-4207	273	8	x−minti(f	x−minti(f	PROPN
ejpam-4207	273	9	−(b1)∩f+(b2	−(b1)∩f+(b2	NOUN
ejpam-4207	273	10	)	)	PUNCT
ejpam-4207	273	11	)	)	PUNCT
ejpam-4207	274	1	=	=	SYM
ejpam-4207	274	2	mcli(x−	mcli(x−	NOUN
ejpam-4207	274	3	(	(	PUNCT
ejpam-4207	274	4	f−(b1)∩f+(b2	f−(b1)∩f+(b2	NOUN
ejpam-4207	274	5	)	)	PUNCT
ejpam-4207	274	6	)	)	PUNCT
ejpam-4207	274	7	)	)	PUNCT
ejpam-4207	275	1	=	=	SYM
ejpam-4207	275	2	mcli((x−f−(b1))∪	mcli((x−f−(b1))∪	PROPN
ejpam-4207	275	3	(	(	PUNCT
ejpam-4207	275	4	x−f+(b2	x−f+(b2	NOUN
ejpam-4207	275	5	)	)	PUNCT
ejpam-4207	275	6	)	)	PUNCT
ejpam-4207	275	7	)	)	PUNCT
ejpam-4207	276	1	=	=	PUNCT
ejpam-4207	276	2	mcli(f	mcli(f	NUM
ejpam-4207	276	3	+	+	PROPN
ejpam-4207	276	4	(	(	PUNCT
ejpam-4207	276	5	y	y	PROPN
ejpam-4207	276	6	−b1)∪f−(y	−b1)∪f−(y	PROPN
ejpam-4207	276	7	−b2	−b2	PROPN
ejpam-4207	276	8	)	)	PUNCT
ejpam-4207	276	9	)	)	PUNCT
ejpam-4207	277	1	⊂	⊂	PUNCT
ejpam-4207	277	2	f+(cl⋆(y	f+(cl⋆(y	VERB
ejpam-4207	277	3	−b1))∪f−(cl⋆(y	−b1))∪f−(cl⋆(y	ADJ
ejpam-4207	277	4	−b2	−b2	ADJ
ejpam-4207	277	5	)	)	PUNCT
ejpam-4207	277	6	)	)	PUNCT
ejpam-4207	278	1	=	=	PUNCT
ejpam-4207	278	2	(	(	PUNCT
ejpam-4207	278	3	x	x	NOUN
ejpam-4207	278	4	−	−	NOUN
ejpam-4207	278	5	f−(int⋆(b1	f−(int⋆(b1	NOUN
ejpam-4207	278	6	)	)	PUNCT
ejpam-4207	278	7	)	)	PUNCT
ejpam-4207	278	8	)	)	PUNCT
ejpam-4207	279	1	∪	∪	ADV
ejpam-4207	279	2	(	(	PUNCT
ejpam-4207	279	3	x	x	SYM
ejpam-4207	279	4	−	−	PROPN
ejpam-4207	279	5	f+(int⋆(b2	f+(int⋆(b2	NOUN
ejpam-4207	279	6	)	)	PUNCT
ejpam-4207	279	7	)	)	PUNCT
ejpam-4207	279	8	)	)	PUNCT
ejpam-4207	280	1	=	=	PUNCT
ejpam-4207	280	2	x	x	X
ejpam-4207	280	3	−	−	PROPN
ejpam-4207	280	4	(	(	PUNCT
ejpam-4207	280	5	f−(int⋆(b1	f−(int⋆(b1	NOUN
ejpam-4207	280	6	)	)	PUNCT
ejpam-4207	280	7	)	)	PUNCT
ejpam-4207	280	8	∩	∩	PROPN
ejpam-4207	280	9	f+(int⋆(b2	f+(int⋆(b2	NOUN
ejpam-4207	280	10	)	)	PUNCT
ejpam-4207	280	11	)	)	PUNCT
ejpam-4207	280	12	)	)	PUNCT
ejpam-4207	280	13	.	.	PUNCT
ejpam-4207	281	1	therefore	therefore	ADV
ejpam-4207	281	2	,	,	PUNCT
ejpam-4207	281	3	we	we	PRON
ejpam-4207	281	4	obtain	obtain	VERB
ejpam-4207	281	5	f−(int⋆(b1	f−(int⋆(b1	NOUN
ejpam-4207	281	6	)	)	PUNCT
ejpam-4207	281	7	)	)	PUNCT
ejpam-4207	281	8	∩	∩	PROPN
ejpam-4207	281	9	f+(int⋆(b2	f+(int⋆(b2	PROPN
ejpam-4207	281	10	)	)	PUNCT
ejpam-4207	281	11	)	)	PUNCT
ejpam-4207	282	1	⊂	⊂	PROPN
ejpam-4207	282	2	minti(f	minti(f	PRON
ejpam-4207	282	3	−(b1	−(b1	NUM
ejpam-4207	282	4	)	)	PUNCT
ejpam-4207	282	5	∩	∩	ADJ
ejpam-4207	282	6	f+(b2	f+(b2	NOUN
ejpam-4207	282	7	)	)	PUNCT
ejpam-4207	282	8	)	)	PUNCT
ejpam-4207	282	9	.	.	PUNCT
ejpam-4207	283	1	(	(	PUNCT
ejpam-4207	283	2	6	6	X
ejpam-4207	283	3	)	)	PUNCT
ejpam-4207	283	4	=	=	NOUN
ejpam-4207	283	5	>	>	X
ejpam-4207	283	6	(	(	PUNCT
ejpam-4207	283	7	1	1	NUM
ejpam-4207	283	8	):	):	PUNCT
ejpam-4207	283	9	let	let	VERB
ejpam-4207	283	10	x	x	PUNCT
ejpam-4207	283	11	∈	∈	PROPN
ejpam-4207	283	12	x	x	X
ejpam-4207	283	13	and	and	CCONJ
ejpam-4207	283	14	v1	v1	NOUN
ejpam-4207	283	15	,	,	PUNCT
ejpam-4207	283	16	v2	v2	PROPN
ejpam-4207	283	17	be	be	VERB
ejpam-4207	283	18	any	any	DET
ejpam-4207	283	19	σ⋆-open	σ⋆-open	ADJ
ejpam-4207	283	20	sets	set	NOUN
ejpam-4207	283	21	of	of	ADP
ejpam-4207	283	22	y	y	PRON
ejpam-4207	283	23	such	such	ADJ
ejpam-4207	283	24	that	that	SCONJ
ejpam-4207	283	25	f	f	PROPN
ejpam-4207	283	26	(	(	PUNCT
ejpam-4207	283	27	x	x	X
ejpam-4207	283	28	)	)	PUNCT
ejpam-4207	283	29	∈	∈	NOUN
ejpam-4207	283	30	v	v	ADP
ejpam-4207	283	31	+	+	CCONJ
ejpam-4207	283	32	1	1	NUM
ejpam-4207	283	33	∩v	∩v	NOUN
ejpam-4207	283	34	−	−	PROPN
ejpam-4207	283	35	2	2	NUM
ejpam-4207	283	36	.	.	PUNCT
ejpam-4207	284	1	by	by	ADP
ejpam-4207	284	2	(	(	PUNCT
ejpam-4207	284	3	6	6	NUM
ejpam-4207	284	4	)	)	PUNCT
ejpam-4207	284	5	,	,	PUNCT
ejpam-4207	284	6	f−(v1)∩f+(v2	f−(v1)∩f+(v2	PROPN
ejpam-4207	284	7	)	)	PUNCT
ejpam-4207	284	8	⊂	⊂	PROPN
ejpam-4207	284	9	minti(f	minti(f	X
ejpam-4207	284	10	−(v1)∩f+(v2	−(v1)∩f+(v2	ADV
ejpam-4207	284	11	)	)	PUNCT
ejpam-4207	284	12	)	)	PUNCT
ejpam-4207	284	13	.	.	PUNCT
ejpam-4207	285	1	this	this	PRON
ejpam-4207	285	2	shows	show	VERB
ejpam-4207	285	3	that	that	SCONJ
ejpam-4207	285	4	f	f	PROPN
ejpam-4207	285	5	−(v1)∩f+(v2	−(v1)∩f+(v2	ADV
ejpam-4207	285	6	)	)	PUNCT
ejpam-4207	285	7	∈	∈	PROPN
ejpam-4207	285	8	mio(x	mio(x	PROPN
ejpam-4207	285	9	)	)	PUNCT
ejpam-4207	285	10	.	.	PUNCT
ejpam-4207	286	1	and	and	CCONJ
ejpam-4207	286	2	put	put	VERB
ejpam-4207	286	3	u	u	NOUN
ejpam-4207	286	4	=	=	NOUN
ejpam-4207	286	5	f−(v1	f−(v1	NOUN
ejpam-4207	286	6	)	)	PUNCT
ejpam-4207	286	7	∩	∩	ADJ
ejpam-4207	286	8	f+(v2	f+(v2	NOUN
ejpam-4207	286	9	)	)	PUNCT
ejpam-4207	286	10	.	.	PUNCT
ejpam-4207	287	1	then	then	ADV
ejpam-4207	287	2	u	u	PRON
ejpam-4207	287	3	is	be	AUX
ejpam-4207	287	4	an	an	DET
ejpam-4207	287	5	mio(x)-open	mio(x)-open	ADJ
ejpam-4207	287	6	set	set	NOUN
ejpam-4207	287	7	containing	contain	VERB
ejpam-4207	287	8	x	x	PUNCT
ejpam-4207	287	9	such	such	ADJ
ejpam-4207	287	10	that	that	SCONJ
ejpam-4207	287	11	f	f	PROPN
ejpam-4207	287	12	(	(	PUNCT
ejpam-4207	287	13	u	u	NOUN
ejpam-4207	287	14	)	)	PUNCT
ejpam-4207	287	15	⊂	⊂	PROPN
ejpam-4207	287	16	v	v	ADP
ejpam-4207	287	17	+	+	CCONJ
ejpam-4207	287	18	1	1	NUM
ejpam-4207	287	19	and	and	CCONJ
ejpam-4207	287	20	f	f	PROPN
ejpam-4207	287	21	(	(	PUNCT
ejpam-4207	287	22	u)∩v	u)∩v	NOUN
ejpam-4207	287	23	−	−	PROPN
ejpam-4207	287	24	2	2	NUM
ejpam-4207	287	25	̸=	̸=	PROPN
ejpam-4207	287	26	∅	∅	NOUN
ejpam-4207	287	27	for	for	ADP
ejpam-4207	287	28	every	every	DET
ejpam-4207	287	29	u	u	PROPN
ejpam-4207	287	30	∈	∈	PROPN
ejpam-4207	287	31	u	u	NOUN
ejpam-4207	287	32	.	.	PUNCT
ejpam-4207	288	1	therefore	therefore	ADV
ejpam-4207	288	2	,	,	PUNCT
ejpam-4207	288	3	f	f	PROPN
ejpam-4207	288	4	is	be	AUX
ejpam-4207	288	5	mi⋆-continuous	mi⋆-continuous	ADJ
ejpam-4207	288	6	.	.	PUNCT
ejpam-4207	289	1	if	if	SCONJ
ejpam-4207	289	2	mio(x	mio(x	PROPN
ejpam-4207	289	3	)	)	PUNCT
ejpam-4207	289	4	=	=	SYM
ejpam-4207	289	5	sio(x	sio(x	NOUN
ejpam-4207	289	6	)	)	PUNCT
ejpam-4207	289	7	,	,	PUNCT
ejpam-4207	289	8	by	by	ADP
ejpam-4207	289	9	theorem	theorem	NOUN
ejpam-4207	289	10	15	15	NUM
ejpam-4207	289	11	we	we	PRON
ejpam-4207	289	12	obtain	obtain	VERB
ejpam-4207	289	13	the	the	DET
ejpam-4207	289	14	following	follow	VERB
ejpam-4207	289	15	corollary	corollary	ADJ
ejpam-4207	289	16	:	:	PUNCT
ejpam-4207	289	17	corollary	corollary	ADJ
ejpam-4207	289	18	6	6	NUM
ejpam-4207	289	19	.	.	PUNCT
ejpam-4207	290	1	for	for	ADP
ejpam-4207	290	2	a	a	DET
ejpam-4207	290	3	multifunction	multifunction	NOUN
ejpam-4207	290	4	f	f	NOUN
ejpam-4207	290	5	:	:	PUNCT
ejpam-4207	290	6	(	(	PUNCT
ejpam-4207	290	7	x	x	X
ejpam-4207	290	8	,	,	PUNCT
ejpam-4207	290	9	τ	τ	PROPN
ejpam-4207	290	10	,	,	PUNCT
ejpam-4207	290	11	i	i	NOUN
ejpam-4207	290	12	)	)	PUNCT
ejpam-4207	290	13	→	→	SYM
ejpam-4207	290	14	(	(	PUNCT
ejpam-4207	290	15	y	y	PROPN
ejpam-4207	290	16	,	,	PUNCT
ejpam-4207	290	17	σ	σ	PROPN
ejpam-4207	290	18	,	,	PUNCT
ejpam-4207	290	19	j	j	PROPN
ejpam-4207	290	20	)	)	PUNCT
ejpam-4207	290	21	,	,	PUNCT
ejpam-4207	290	22	the	the	DET
ejpam-4207	290	23	following	follow	VERB
ejpam-4207	290	24	properties	property	NOUN
ejpam-4207	290	25	are	be	AUX
ejpam-4207	290	26	equivalent	equivalent	ADJ
ejpam-4207	290	27	:	:	PUNCT
ejpam-4207	290	28	(	(	PUNCT
ejpam-4207	290	29	1	1	X
ejpam-4207	290	30	)	)	PUNCT
ejpam-4207	290	31	f	f	PROPN
ejpam-4207	290	32	is	be	AUX
ejpam-4207	290	33	si⋆-continuous	si⋆-continuous	ADJ
ejpam-4207	290	34	;	;	PUNCT
ejpam-4207	290	35	(	(	PUNCT
ejpam-4207	290	36	2	2	X
ejpam-4207	290	37	)	)	PUNCT
ejpam-4207	290	38	for	for	ADP
ejpam-4207	290	39	each	each	DET
ejpam-4207	290	40	point	point	NOUN
ejpam-4207	290	41	x	x	X
ejpam-4207	290	42	∈	∈	NOUN
ejpam-4207	290	43	x	x	X
ejpam-4207	290	44	and	and	CCONJ
ejpam-4207	290	45	each	each	DET
ejpam-4207	290	46	σ⋆-open	σ⋆-open	ADJ
ejpam-4207	290	47	sets	set	NOUN
ejpam-4207	290	48	v1	v1	NOUN
ejpam-4207	290	49	,	,	PUNCT
ejpam-4207	290	50	v2	v2	PROPN
ejpam-4207	290	51	of	of	ADP
ejpam-4207	290	52	y	y	PRON
ejpam-4207	290	53	such	such	ADJ
ejpam-4207	290	54	that	that	SCONJ
ejpam-4207	290	55	f	f	PROPN
ejpam-4207	290	56	(	(	PUNCT
ejpam-4207	290	57	x	x	X
ejpam-4207	290	58	)	)	PUNCT
ejpam-4207	290	59	∈	∈	NOUN
ejpam-4207	290	60	v	v	ADP
ejpam-4207	290	61	+	+	CCONJ
ejpam-4207	290	62	1	1	NUM
ejpam-4207	290	63	∩v	∩v	NOUN
ejpam-4207	290	64	−	−	PROPN
ejpam-4207	290	65	2	2	NUM
ejpam-4207	290	66	,	,	PUNCT
ejpam-4207	290	67	x	x	SYM
ejpam-4207	290	68	∈	∈	NOUN
ejpam-4207	290	69	sinti(f	sinti(f	ADP
ejpam-4207	290	70	+	+	PROPN
ejpam-4207	290	71	(	(	PUNCT
ejpam-4207	290	72	v1	v1	NOUN
ejpam-4207	290	73	)	)	PUNCT
ejpam-4207	290	74	∩	∩	NOUN
ejpam-4207	290	75	f−(v2	f−(v2	NUM
ejpam-4207	290	76	)	)	PUNCT
ejpam-4207	290	77	)	)	PUNCT
ejpam-4207	290	78	;	;	PUNCT
ejpam-4207	290	79	(	(	PUNCT
ejpam-4207	290	80	3	3	X
ejpam-4207	290	81	)	)	PUNCT
ejpam-4207	290	82	f+(v1	f+(v1	NOUN
ejpam-4207	290	83	)	)	PUNCT
ejpam-4207	290	84	∩	∩	NOUN
ejpam-4207	290	85	f−(v2	f−(v2	X
ejpam-4207	290	86	)	)	PUNCT
ejpam-4207	290	87	∈	∈	PROPN
ejpam-4207	290	88	sio(x	sio(x	NOUN
ejpam-4207	290	89	)	)	PUNCT
ejpam-4207	290	90	for	for	ADP
ejpam-4207	290	91	every	every	DET
ejpam-4207	290	92	σ⋆-open	σ⋆-open	ADJ
ejpam-4207	290	93	sets	set	NOUN
ejpam-4207	290	94	v1	v1	NOUN
ejpam-4207	290	95	,	,	PUNCT
ejpam-4207	290	96	v2	v2	PROPN
ejpam-4207	290	97	of	of	ADP
ejpam-4207	290	98	y	y	PROPN
ejpam-4207	290	99	;	;	PUNCT
ejpam-4207	290	100	(	(	PUNCT
ejpam-4207	290	101	4	4	NUM
ejpam-4207	290	102	)	)	PUNCT
ejpam-4207	290	103	f−(k1	f−(k1	ADP
ejpam-4207	290	104	)	)	PUNCT
ejpam-4207	290	105	∪	∪	ADP
ejpam-4207	290	106	f+(k2	f+(k2	NOUN
ejpam-4207	290	107	)	)	PUNCT
ejpam-4207	290	108	is	be	AUX
ejpam-4207	290	109	semi	semi	ADJ
ejpam-4207	290	110	-	-	ADJ
ejpam-4207	290	111	i	i	PRON
ejpam-4207	290	112	-	-	PUNCT
ejpam-4207	290	113	closed	close	VERB
ejpam-4207	290	114	for	for	ADP
ejpam-4207	290	115	every	every	DET
ejpam-4207	290	116	σ⋆-closed	σ⋆-closed	NOUN
ejpam-4207	290	117	sets	set	NOUN
ejpam-4207	290	118	k1,k2	k1,k2	PROPN
ejpam-4207	290	119	of	of	ADP
ejpam-4207	290	120	y	y	PROPN
ejpam-4207	290	121	;	;	PUNCT
ejpam-4207	290	122	(	(	PUNCT
ejpam-4207	290	123	5	5	X
ejpam-4207	290	124	)	)	PUNCT
ejpam-4207	290	125	scli(f	scli(f	PROPN
ejpam-4207	290	126	−(b1)∪f+(b2	−(b1)∪f+(b2	PROPN
ejpam-4207	290	127	)	)	PUNCT
ejpam-4207	290	128	)	)	PUNCT
ejpam-4207	291	1	⊂	⊂	PROPN
ejpam-4207	291	2	f−(cl⋆(b1))∪f+(cl⋆(b2	f−(cl⋆(b1))∪f+(cl⋆(b2	PROPN
ejpam-4207	291	3	)	)	PUNCT
ejpam-4207	291	4	)	)	PUNCT
ejpam-4207	291	5	for	for	ADP
ejpam-4207	291	6	every	every	DET
ejpam-4207	291	7	subsets	subset	NOUN
ejpam-4207	291	8	b1	b1	NOUN
ejpam-4207	291	9	,	,	PUNCT
ejpam-4207	291	10	b2	b2	NOUN
ejpam-4207	291	11	of	of	ADP
ejpam-4207	291	12	y	y	PROPN
ejpam-4207	291	13	;	;	PUNCT
ejpam-4207	291	14	(	(	PUNCT
ejpam-4207	291	15	6	6	X
ejpam-4207	291	16	)	)	PUNCT
ejpam-4207	291	17	f−(int⋆(b1	f−(int⋆(b1	PROPN
ejpam-4207	291	18	)	)	PUNCT
ejpam-4207	291	19	)	)	PUNCT
ejpam-4207	291	20	∩	∩	PROPN
ejpam-4207	291	21	f+(int⋆(b2	f+(int⋆(b2	PROPN
ejpam-4207	291	22	)	)	PUNCT
ejpam-4207	291	23	)	)	PUNCT
ejpam-4207	292	1	⊂	⊂	PROPN
ejpam-4207	292	2	sinti(f	sinti(f	ADJ
ejpam-4207	292	3	−(b1	−(b1	NUM
ejpam-4207	292	4	)	)	PUNCT
ejpam-4207	292	5	∩	∩	ADJ
ejpam-4207	292	6	f+(b2	f+(b2	NOUN
ejpam-4207	292	7	)	)	PUNCT
ejpam-4207	292	8	)	)	PUNCT
ejpam-4207	292	9	for	for	ADP
ejpam-4207	292	10	every	every	DET
ejpam-4207	292	11	subsets	subset	NOUN
ejpam-4207	292	12	b1	b1	NOUN
ejpam-4207	292	13	,	,	PUNCT
ejpam-4207	292	14	b2	b2	NOUN
ejpam-4207	292	15	of	of	ADP
ejpam-4207	292	16	y	y	PROPN
ejpam-4207	292	17	.	.	PUNCT
ejpam-4207	293	1	references	reference	NOUN
ejpam-4207	293	2	11	11	NUM
ejpam-4207	293	3	if	if	SCONJ
ejpam-4207	293	4	mio(x	mio(x	NOUN
ejpam-4207	293	5	)	)	PUNCT
ejpam-4207	293	6	=	=	SYM
ejpam-4207	293	7	pio(x	pio(x	PROPN
ejpam-4207	293	8	)	)	PUNCT
ejpam-4207	293	9	,	,	PUNCT
ejpam-4207	293	10	by	by	ADP
ejpam-4207	293	11	theorem	theorem	NOUN
ejpam-4207	293	12	15	15	NUM
ejpam-4207	293	13	we	we	PRON
ejpam-4207	293	14	obtain	obtain	VERB
ejpam-4207	293	15	the	the	DET
ejpam-4207	293	16	following	follow	VERB
ejpam-4207	293	17	corollary	corollary	ADJ
ejpam-4207	293	18	:	:	PUNCT
ejpam-4207	293	19	corollary	corollary	ADJ
ejpam-4207	293	20	7	7	NUM
ejpam-4207	293	21	.	.	PUNCT
ejpam-4207	293	22	for	for	ADP
ejpam-4207	293	23	a	a	DET
ejpam-4207	293	24	multifunction	multifunction	NOUN
ejpam-4207	293	25	f	f	NOUN
ejpam-4207	293	26	:	:	PUNCT
ejpam-4207	293	27	(	(	PUNCT
ejpam-4207	293	28	x	x	X
ejpam-4207	293	29	,	,	PUNCT
ejpam-4207	293	30	τ	τ	PROPN
ejpam-4207	293	31	,	,	PUNCT
ejpam-4207	293	32	i	i	NOUN
ejpam-4207	293	33	)	)	PUNCT
ejpam-4207	293	34	→	→	SYM
ejpam-4207	293	35	(	(	PUNCT
ejpam-4207	293	36	y	y	PROPN
ejpam-4207	293	37	,	,	PUNCT
ejpam-4207	293	38	σ	σ	PROPN
ejpam-4207	293	39	,	,	PUNCT
ejpam-4207	293	40	j	j	PROPN
ejpam-4207	293	41	)	)	PUNCT
ejpam-4207	293	42	,	,	PUNCT
ejpam-4207	293	43	the	the	DET
ejpam-4207	293	44	following	follow	VERB
ejpam-4207	293	45	properties	property	NOUN
ejpam-4207	293	46	are	be	AUX
ejpam-4207	293	47	equivalent	equivalent	ADJ
ejpam-4207	293	48	:	:	PUNCT
ejpam-4207	293	49	(	(	PUNCT
ejpam-4207	293	50	1	1	X
ejpam-4207	293	51	)	)	PUNCT
ejpam-4207	293	52	f	f	PROPN
ejpam-4207	293	53	is	be	AUX
ejpam-4207	293	54	pi⋆-continuous	pi⋆-continuous	ADJ
ejpam-4207	293	55	;	;	PUNCT
ejpam-4207	293	56	(	(	PUNCT
ejpam-4207	293	57	2	2	X
ejpam-4207	293	58	)	)	PUNCT
ejpam-4207	293	59	for	for	ADP
ejpam-4207	293	60	each	each	DET
ejpam-4207	293	61	point	point	NOUN
ejpam-4207	293	62	x	x	X
ejpam-4207	293	63	∈	∈	NOUN
ejpam-4207	293	64	x	x	X
ejpam-4207	293	65	and	and	CCONJ
ejpam-4207	293	66	each	each	DET
ejpam-4207	293	67	σ⋆-open	σ⋆-open	ADJ
ejpam-4207	293	68	sets	set	NOUN
ejpam-4207	293	69	v1	v1	NOUN
ejpam-4207	293	70	,	,	PUNCT
ejpam-4207	293	71	v2	v2	PROPN
ejpam-4207	293	72	of	of	ADP
ejpam-4207	293	73	y	y	PRON
ejpam-4207	293	74	such	such	ADJ
ejpam-4207	293	75	that	that	SCONJ
ejpam-4207	293	76	f	f	PROPN
ejpam-4207	293	77	(	(	PUNCT
ejpam-4207	293	78	x	x	X
ejpam-4207	293	79	)	)	PUNCT
ejpam-4207	293	80	∈	∈	NOUN
ejpam-4207	293	81	v	v	ADP
ejpam-4207	293	82	+	+	CCONJ
ejpam-4207	293	83	1	1	NUM
ejpam-4207	293	84	∩v	∩v	NOUN
ejpam-4207	293	85	−	−	PROPN
ejpam-4207	293	86	2	2	NUM
ejpam-4207	293	87	,	,	PUNCT
ejpam-4207	293	88	x	x	SYM
ejpam-4207	293	89	∈	∈	NOUN
ejpam-4207	293	90	pinti(f	pinti(f	ADP
ejpam-4207	293	91	+	+	PROPN
ejpam-4207	293	92	(	(	PUNCT
ejpam-4207	293	93	v1	v1	NOUN
ejpam-4207	293	94	)	)	PUNCT
ejpam-4207	293	95	∩	∩	NOUN
ejpam-4207	293	96	f−(v2	f−(v2	NUM
ejpam-4207	293	97	)	)	PUNCT
ejpam-4207	293	98	)	)	PUNCT
ejpam-4207	293	99	;	;	PUNCT
ejpam-4207	293	100	(	(	PUNCT
ejpam-4207	293	101	3	3	X
ejpam-4207	293	102	)	)	PUNCT
ejpam-4207	293	103	f+(v1	f+(v1	NOUN
ejpam-4207	293	104	)	)	PUNCT
ejpam-4207	293	105	∩	∩	NOUN
ejpam-4207	293	106	f−(v2	f−(v2	X
ejpam-4207	293	107	)	)	PUNCT
ejpam-4207	293	108	∈	∈	PROPN
ejpam-4207	293	109	pio(x	pio(x	PROPN
ejpam-4207	293	110	)	)	PUNCT
ejpam-4207	293	111	for	for	ADP
ejpam-4207	293	112	every	every	DET
ejpam-4207	293	113	σ⋆-open	σ⋆-open	ADJ
ejpam-4207	293	114	sets	set	NOUN
ejpam-4207	293	115	v1	v1	NOUN
ejpam-4207	293	116	,	,	PUNCT
ejpam-4207	293	117	v2	v2	PROPN
ejpam-4207	293	118	of	of	ADP
ejpam-4207	293	119	y	y	PROPN
ejpam-4207	293	120	;	;	PUNCT
ejpam-4207	293	121	(	(	PUNCT
ejpam-4207	293	122	4	4	NUM
ejpam-4207	293	123	)	)	PUNCT
ejpam-4207	293	124	f−(k1	f−(k1	ADP
ejpam-4207	293	125	)	)	PUNCT
ejpam-4207	293	126	∪	∪	ADP
ejpam-4207	293	127	f+(k2	f+(k2	NOUN
ejpam-4207	293	128	)	)	PUNCT
ejpam-4207	293	129	is	be	AUX
ejpam-4207	293	130	pre	pre	ADJ
ejpam-4207	293	131	-	-	ADJ
ejpam-4207	293	132	i	i	PRON
ejpam-4207	293	133	-	-	PUNCT
ejpam-4207	293	134	closed	close	VERB
ejpam-4207	293	135	for	for	ADP
ejpam-4207	293	136	every	every	DET
ejpam-4207	293	137	σ⋆-closed	σ⋆-closed	NOUN
ejpam-4207	293	138	sets	set	NOUN
ejpam-4207	293	139	k1,k2	k1,k2	PROPN
ejpam-4207	293	140	of	of	ADP
ejpam-4207	293	141	y	y	PROPN
ejpam-4207	293	142	;	;	PUNCT
ejpam-4207	293	143	(	(	PUNCT
ejpam-4207	293	144	5	5	X
ejpam-4207	293	145	)	)	PUNCT
ejpam-4207	293	146	pcli(f	pcli(f	NOUN
ejpam-4207	293	147	−(b1)∪f+(b2	−(b1)∪f+(b2	PROPN
ejpam-4207	293	148	)	)	PUNCT
ejpam-4207	293	149	)	)	PUNCT
ejpam-4207	294	1	⊂	⊂	PROPN
ejpam-4207	294	2	f−(cl⋆(b1))∪f+(cl⋆(b2	f−(cl⋆(b1))∪f+(cl⋆(b2	PROPN
ejpam-4207	294	3	)	)	PUNCT
ejpam-4207	294	4	)	)	PUNCT
ejpam-4207	294	5	for	for	ADP
ejpam-4207	294	6	every	every	DET
ejpam-4207	294	7	subsets	subset	NOUN
ejpam-4207	294	8	b1	b1	NOUN
ejpam-4207	294	9	,	,	PUNCT
ejpam-4207	294	10	b2	b2	NOUN
ejpam-4207	294	11	of	of	ADP
ejpam-4207	294	12	y	y	PROPN
ejpam-4207	294	13	;	;	PUNCT
ejpam-4207	294	14	(	(	PUNCT
ejpam-4207	294	15	6	6	NUM
ejpam-4207	294	16	)	)	PUNCT
ejpam-4207	294	17	f−(int⋆(b1))∩	f−(int⋆(b1))∩	NOUN
ejpam-4207	294	18	f+(int⋆(b2	f+(int⋆(b2	NOUN
ejpam-4207	294	19	)	)	PUNCT
ejpam-4207	294	20	)	)	PUNCT
ejpam-4207	295	1	⊂	⊂	PROPN
ejpam-4207	295	2	pinti(f	pinti(f	X
ejpam-4207	295	3	−(b1)∩	−(b1)∩	PROPN
ejpam-4207	295	4	f+(b2	f+(b2	PROPN
ejpam-4207	295	5	)	)	PUNCT
ejpam-4207	295	6	)	)	PUNCT
ejpam-4207	295	7	for	for	ADP
ejpam-4207	295	8	every	every	DET
ejpam-4207	295	9	subsets	subset	NOUN
ejpam-4207	295	10	b1	b1	NOUN
ejpam-4207	295	11	,	,	PUNCT
ejpam-4207	295	12	b2	b2	NOUN
ejpam-4207	295	13	of	of	ADP
ejpam-4207	295	14	y	y	PROPN
ejpam-4207	295	15	.	.	PUNCT
ejpam-4207	296	1	theorem	theorem	VERB
ejpam-4207	296	2	16	16	NUM
ejpam-4207	296	3	.	.	PUNCT
ejpam-4207	297	1	the	the	DET
ejpam-4207	297	2	set	set	NOUN
ejpam-4207	297	3	of	of	ADP
ejpam-4207	297	4	all	all	DET
ejpam-4207	297	5	points	point	NOUN
ejpam-4207	297	6	x	x	X
ejpam-4207	297	7	∈	∈	NOUN
ejpam-4207	297	8	x	x	PUNCT
ejpam-4207	297	9	at	at	ADP
ejpam-4207	297	10	which	which	PRON
ejpam-4207	297	11	a	a	DET
ejpam-4207	297	12	multifunction	multifunction	NOUN
ejpam-4207	297	13	f	f	NOUN
ejpam-4207	297	14	:	:	PUNCT
ejpam-4207	297	15	(	(	PUNCT
ejpam-4207	297	16	x	x	X
ejpam-4207	297	17	,	,	PUNCT
ejpam-4207	297	18	τ	τ	PROPN
ejpam-4207	297	19	,	,	PUNCT
ejpam-4207	297	20	i	i	NOUN
ejpam-4207	297	21	)	)	PUNCT
ejpam-4207	297	22	→	→	SYM
ejpam-4207	297	23	(	(	PUNCT
ejpam-4207	297	24	y	y	PROPN
ejpam-4207	297	25	,	,	PUNCT
ejpam-4207	297	26	σ	σ	PROPN
ejpam-4207	297	27	,	,	PUNCT
ejpam-4207	297	28	j	j	PROPN
ejpam-4207	297	29	)	)	PUNCT
ejpam-4207	297	30	is	be	AUX
ejpam-4207	297	31	not	not	PART
ejpam-4207	297	32	mi⋆-continuous	mi⋆-continuous	ADJ
ejpam-4207	297	33	is	be	AUX
ejpam-4207	297	34	identical	identical	ADJ
ejpam-4207	297	35	with	with	ADP
ejpam-4207	297	36	the	the	DET
ejpam-4207	297	37	union	union	NOUN
ejpam-4207	297	38	of	of	ADP
ejpam-4207	297	39	the	the	DET
ejpam-4207	297	40	mi	mi	PROPN
ejpam-4207	297	41	-	-	PUNCT
ejpam-4207	297	42	frontiers	frontier	NOUN
ejpam-4207	297	43	of	of	ADP
ejpam-4207	297	44	the	the	DET
ejpam-4207	297	45	intersection	intersection	NOUN
ejpam-4207	297	46	of	of	ADP
ejpam-4207	297	47	upper	upper	ADJ
ejpam-4207	297	48	/	/	SYM
ejpam-4207	297	49	lower	low	ADJ
ejpam-4207	297	50	inverse	inverse	NOUN
ejpam-4207	297	51	images	image	NOUN
ejpam-4207	297	52	of	of	ADP
ejpam-4207	297	53	⋆-open	⋆-open	ADJ
ejpam-4207	297	54	sets	set	NOUN
ejpam-4207	297	55	containing	contain	VERB
ejpam-4207	297	56	/	/	SYM
ejpam-4207	297	57	meeting	meeting	NOUN
ejpam-4207	297	58	f	f	X
ejpam-4207	297	59	(	(	PUNCT
ejpam-4207	297	60	x	x	NOUN
ejpam-4207	297	61	)	)	PUNCT
ejpam-4207	297	62	.	.	PUNCT
ejpam-4207	298	1	proof	proof	NOUN
ejpam-4207	298	2	.	.	PUNCT
ejpam-4207	299	1	the	the	DET
ejpam-4207	299	2	proof	proof	NOUN
ejpam-4207	299	3	follows	follow	VERB
ejpam-4207	299	4	similarly	similarly	ADV
ejpam-4207	299	5	from	from	ADP
ejpam-4207	299	6	theorem	theorem	ADJ
ejpam-4207	299	7	11	11	NUM
ejpam-4207	299	8	.	.	PUNCT
ejpam-4207	300	1	if	if	SCONJ
ejpam-4207	300	2	mio(x	mio(x	NOUN
ejpam-4207	300	3	)	)	PUNCT
ejpam-4207	300	4	=	=	PUNCT
ejpam-4207	301	1	τ⋆	τ⋆	NOUN
ejpam-4207	301	2	,	,	PUNCT
ejpam-4207	301	3	then	then	ADV
ejpam-4207	301	4	we	we	PRON
ejpam-4207	301	5	obtain	obtain	VERB
ejpam-4207	301	6	the	the	DET
ejpam-4207	301	7	following	follow	VERB
ejpam-4207	301	8	corollary	corollary	ADJ
ejpam-4207	301	9	:	:	PUNCT
ejpam-4207	301	10	corollary	corollary	ADJ
ejpam-4207	301	11	8	8	NUM
ejpam-4207	301	12	.	.	PUNCT
ejpam-4207	302	1	the	the	DET
ejpam-4207	302	2	set	set	NOUN
ejpam-4207	302	3	of	of	ADP
ejpam-4207	302	4	all	all	DET
ejpam-4207	302	5	points	point	NOUN
ejpam-4207	302	6	x	x	X
ejpam-4207	302	7	∈	∈	NOUN
ejpam-4207	302	8	x	x	PUNCT
ejpam-4207	302	9	at	at	ADP
ejpam-4207	302	10	which	which	PRON
ejpam-4207	302	11	a	a	DET
ejpam-4207	302	12	multifunction	multifunction	NOUN
ejpam-4207	302	13	f	f	NOUN
ejpam-4207	302	14	:	:	PUNCT
ejpam-4207	302	15	(	(	PUNCT
ejpam-4207	302	16	x	x	X
ejpam-4207	302	17	,	,	PUNCT
ejpam-4207	302	18	τ	τ	PROPN
ejpam-4207	302	19	,	,	PUNCT
ejpam-4207	302	20	i	i	NOUN
ejpam-4207	302	21	)	)	PUNCT
ejpam-4207	302	22	→	→	SYM
ejpam-4207	302	23	(	(	PUNCT
ejpam-4207	302	24	y	y	PROPN
ejpam-4207	302	25	,	,	PUNCT
ejpam-4207	302	26	σ	σ	PROPN
ejpam-4207	302	27	,	,	PUNCT
ejpam-4207	302	28	j	j	PROPN
ejpam-4207	302	29	)	)	PUNCT
ejpam-4207	302	30	is	be	AUX
ejpam-4207	302	31	not	not	PART
ejpam-4207	302	32	τ⋆-continuous	τ⋆-continuous	ADJ
ejpam-4207	302	33	is	be	AUX
ejpam-4207	302	34	identical	identical	ADJ
ejpam-4207	302	35	with	with	ADP
ejpam-4207	302	36	the	the	DET
ejpam-4207	302	37	union	union	NOUN
ejpam-4207	302	38	of	of	ADP
ejpam-4207	302	39	the	the	DET
ejpam-4207	302	40	τ⋆-frontiers	τ⋆-frontier	NOUN
ejpam-4207	302	41	of	of	ADP
ejpam-4207	302	42	the	the	DET
ejpam-4207	302	43	intersection	intersection	NOUN
ejpam-4207	302	44	of	of	ADP
ejpam-4207	302	45	upper	upper	ADJ
ejpam-4207	302	46	/	/	SYM
ejpam-4207	302	47	lower	low	ADJ
ejpam-4207	302	48	inverse	inverse	NOUN
ejpam-4207	302	49	images	image	NOUN
ejpam-4207	302	50	of	of	ADP
ejpam-4207	302	51	⋆-open	⋆-open	ADJ
ejpam-4207	302	52	sets	set	NOUN
ejpam-4207	302	53	containing	contain	VERB
ejpam-4207	302	54	/	/	SYM
ejpam-4207	302	55	meeting	meeting	NOUN
ejpam-4207	302	56	f	f	X
ejpam-4207	302	57	(	(	PUNCT
ejpam-4207	302	58	x	x	NOUN
ejpam-4207	302	59	)	)	PUNCT
ejpam-4207	302	60	.	.	PUNCT
ejpam-4207	303	1	if	if	SCONJ
ejpam-4207	303	2	mio(x	mio(x	NOUN
ejpam-4207	303	3	)	)	PUNCT
ejpam-4207	303	4	=	=	SYM
ejpam-4207	304	1	sio(x	sio(x	NOUN
ejpam-4207	304	2	)	)	PUNCT
ejpam-4207	304	3	,	,	PUNCT
ejpam-4207	304	4	then	then	ADV
ejpam-4207	304	5	we	we	PRON
ejpam-4207	304	6	obtain	obtain	VERB
ejpam-4207	304	7	the	the	DET
ejpam-4207	304	8	following	follow	VERB
ejpam-4207	304	9	corollary	corollary	ADJ
ejpam-4207	304	10	:	:	PUNCT
ejpam-4207	304	11	corollary	corollary	ADJ
ejpam-4207	304	12	9	9	NUM
ejpam-4207	304	13	.	.	PUNCT
ejpam-4207	305	1	the	the	DET
ejpam-4207	305	2	set	set	NOUN
ejpam-4207	305	3	of	of	ADP
ejpam-4207	305	4	all	all	DET
ejpam-4207	305	5	points	point	NOUN
ejpam-4207	305	6	x	x	X
ejpam-4207	305	7	∈	∈	NOUN
ejpam-4207	305	8	x	x	PUNCT
ejpam-4207	305	9	at	at	ADP
ejpam-4207	305	10	which	which	PRON
ejpam-4207	305	11	a	a	DET
ejpam-4207	305	12	multifunction	multifunction	NOUN
ejpam-4207	305	13	f	f	NOUN
ejpam-4207	305	14	:	:	PUNCT
ejpam-4207	305	15	(	(	PUNCT
ejpam-4207	305	16	x	x	X
ejpam-4207	305	17	,	,	PUNCT
ejpam-4207	305	18	τ	τ	PROPN
ejpam-4207	305	19	,	,	PUNCT
ejpam-4207	305	20	i	i	NOUN
ejpam-4207	305	21	)	)	PUNCT
ejpam-4207	305	22	→	→	SYM
ejpam-4207	305	23	(	(	PUNCT
ejpam-4207	305	24	y	y	PROPN
ejpam-4207	305	25	,	,	PUNCT
ejpam-4207	305	26	σ	σ	PROPN
ejpam-4207	305	27	,	,	PUNCT
ejpam-4207	305	28	j	j	PROPN
ejpam-4207	305	29	)	)	PUNCT
ejpam-4207	305	30	is	be	AUX
ejpam-4207	305	31	not	not	PART
ejpam-4207	305	32	si⋆-continuous	si⋆-continuous	ADJ
ejpam-4207	305	33	is	be	AUX
ejpam-4207	305	34	identical	identical	ADJ
ejpam-4207	305	35	with	with	ADP
ejpam-4207	305	36	the	the	DET
ejpam-4207	305	37	union	union	NOUN
ejpam-4207	305	38	of	of	ADP
ejpam-4207	305	39	the	the	DET
ejpam-4207	305	40	si	si	NOUN
ejpam-4207	305	41	-	-	PUNCT
ejpam-4207	305	42	frontiers	frontier	NOUN
ejpam-4207	305	43	of	of	ADP
ejpam-4207	305	44	the	the	DET
ejpam-4207	305	45	intersection	intersection	NOUN
ejpam-4207	305	46	of	of	ADP
ejpam-4207	305	47	upper	upper	ADJ
ejpam-4207	305	48	/	/	SYM
ejpam-4207	305	49	lower	low	ADJ
ejpam-4207	305	50	inverse	inverse	NOUN
ejpam-4207	305	51	images	image	NOUN
ejpam-4207	305	52	of	of	ADP
ejpam-4207	305	53	⋆-open	⋆-open	ADJ
ejpam-4207	305	54	sets	set	NOUN
ejpam-4207	305	55	containing	contain	VERB
ejpam-4207	305	56	/	/	SYM
ejpam-4207	305	57	meeting	meeting	NOUN
ejpam-4207	305	58	f	f	X
ejpam-4207	305	59	(	(	PUNCT
ejpam-4207	305	60	x	x	NOUN
ejpam-4207	305	61	)	)	PUNCT
ejpam-4207	305	62	.	.	PUNCT
ejpam-4207	306	1	references	reference	NOUN
ejpam-4207	306	2	[	[	X
ejpam-4207	306	3	1	1	NUM
ejpam-4207	306	4	]	]	PUNCT
ejpam-4207	306	5	m.	m.	NOUN
ejpam-4207	306	6	e.	e.	PROPN
ejpam-4207	306	7	abd	abd	PROPN
ejpam-4207	306	8	el	el	PROPN
ejpam-4207	306	9	-	-	PROPN
ejpam-4207	306	10	monsef	monsef	PROPN
ejpam-4207	306	11	,	,	PUNCT
ejpam-4207	306	12	s.	s.	PROPN
ejpam-4207	306	13	n.	n.	PROPN
ejpam-4207	306	14	el	el	PROPN
ejpam-4207	306	15	-	-	ADJ
ejpam-4207	306	16	deep	deep	ADJ
ejpam-4207	306	17	and	and	CCONJ
ejpam-4207	306	18	r.	r.	PROPN
ejpam-4207	306	19	a.	a.	PROPN
ejpam-4207	306	20	mahmoud	mahmoud	PROPN
ejpam-4207	306	21	,	,	PUNCT
ejpam-4207	306	22	β	β	ADJ
ejpam-4207	306	23	-	-	ADJ
ejpam-4207	306	24	open	open	ADJ
ejpam-4207	306	25	sets	set	NOUN
ejpam-4207	306	26	and	and	CCONJ
ejpam-4207	306	27	βcontinuous	βcontinuous	ADJ
ejpam-4207	306	28	mappings	mapping	NOUN
ejpam-4207	306	29	,	,	PUNCT
ejpam-4207	306	30	bull	bull	NOUN
ejpam-4207	306	31	.	.	PUNCT
ejpam-4207	307	1	fac	fac	PROPN
ejpam-4207	307	2	.	.	PUNCT
ejpam-4207	308	1	sci	sci	PROPN
ejpam-4207	308	2	.	.	PUNCT
ejpam-4207	308	3	assiut	assiut	PROPN
ejpam-4207	308	4	univ	univ	PROPN
ejpam-4207	308	5	.	.	PROPN
ejpam-4207	309	1	12	12	NUM
ejpam-4207	309	2	(	(	PUNCT
ejpam-4207	309	3	1983	1983	NUM
ejpam-4207	309	4	)	)	PUNCT
ejpam-4207	309	5	,	,	PUNCT
ejpam-4207	309	6	77–90	77–90	NUM
ejpam-4207	309	7	.	.	PUNCT
ejpam-4207	310	1	[	[	X
ejpam-4207	310	2	2	2	NUM
ejpam-4207	310	3	]	]	PUNCT
ejpam-4207	310	4	m.	m.	NOUN
ejpam-4207	310	5	akdag	akdag	PROPN
ejpam-4207	310	6	,	,	PUNCT
ejpam-4207	310	7	on	on	ADP
ejpam-4207	310	8	upper	upper	ADJ
ejpam-4207	310	9	and	and	CCONJ
ejpam-4207	310	10	lower	low	ADJ
ejpam-4207	310	11	i	i	NOUN
ejpam-4207	310	12	-	-	PUNCT
ejpam-4207	310	13	continuous	continuous	ADJ
ejpam-4207	310	14	multifunctions	multifunction	NOUN
ejpam-4207	310	15	,	,	PUNCT
ejpam-4207	310	16	far	far	PROPN
ejpam-4207	310	17	east	east	PROPN
ejpam-4207	310	18	j.	j.	PROPN
ejpam-4207	310	19	math	math	PROPN
ejpam-4207	310	20	.	.	PUNCT
ejpam-4207	311	1	sci	sci	PROPN
ejpam-4207	311	2	.	.	PROPN
ejpam-4207	311	3	25	25	NUM
ejpam-4207	311	4	(	(	PUNCT
ejpam-4207	311	5	2007	2007	NUM
ejpam-4207	311	6	)	)	PUNCT
ejpam-4207	311	7	,	,	PUNCT
ejpam-4207	311	8	48–57	48–57	X
ejpam-4207	311	9	.	.	PUNCT
ejpam-4207	312	1	[	[	X
ejpam-4207	312	2	3	3	X
ejpam-4207	312	3	]	]	X
ejpam-4207	312	4	d.	d.	PROPN
ejpam-4207	312	5	andrijević	andrijević	PROPN
ejpam-4207	312	6	,	,	PUNCT
ejpam-4207	312	7	on	on	ADP
ejpam-4207	312	8	b	b	X
ejpam-4207	312	9	-	-	PUNCT
ejpam-4207	312	10	open	open	ADJ
ejpam-4207	312	11	sets	set	NOUN
ejpam-4207	312	12	,	,	PUNCT
ejpam-4207	312	13	mat	mat	X
ejpam-4207	312	14	.	.	PROPN
ejpam-4207	312	15	vesnik	vesnik	PROPN
ejpam-4207	312	16	48	48	NUM
ejpam-4207	312	17	(	(	PUNCT
ejpam-4207	312	18	1996	1996	NUM
ejpam-4207	312	19	)	)	PUNCT
ejpam-4207	312	20	,	,	PUNCT
ejpam-4207	312	21	59–64	59–64	NUM
ejpam-4207	312	22	.	.	PUNCT
ejpam-4207	313	1	[	[	X
ejpam-4207	313	2	4	4	NUM
ejpam-4207	313	3	]	]	X
ejpam-4207	313	4	c.	c.	PROPN
ejpam-4207	313	5	arivazhagi	arivazhagi	PROPN
ejpam-4207	313	6	and	and	CCONJ
ejpam-4207	313	7	n.	n.	PROPN
ejpam-4207	313	8	rajesh	rajesh	PROPN
ejpam-4207	313	9	,	,	PUNCT
ejpam-4207	313	10	nearly	nearly	ADV
ejpam-4207	313	11	i	i	PRON
ejpam-4207	313	12	-	-	PUNCT
ejpam-4207	313	13	continuous	continuous	ADJ
ejpam-4207	313	14	multifunctions	multifunction	NOUN
ejpam-4207	313	15	,	,	PUNCT
ejpam-4207	313	16	bol	bol	NOUN
ejpam-4207	313	17	.	.	PUNCT
ejpam-4207	314	1	soc	soc	PROPN
ejpam-4207	314	2	.	.	PUNCT
ejpam-4207	315	1	paran	paran	PROPN
ejpam-4207	315	2	.	.	PUNCT
ejpam-4207	316	1	mat	mat	PROPN
ejpam-4207	316	2	.	.	PROPN
ejpam-4207	316	3	37	37	NUM
ejpam-4207	316	4	(	(	PUNCT
ejpam-4207	316	5	2019	2019	NUM
ejpam-4207	316	6	)	)	PUNCT
ejpam-4207	316	7	,	,	PUNCT
ejpam-4207	316	8	33–38	33–38	NUM
ejpam-4207	316	9	.	.	PUNCT
ejpam-4207	317	1	[	[	X
ejpam-4207	317	2	5	5	NUM
ejpam-4207	317	3	]	]	PUNCT
ejpam-4207	317	4	g.	g.	PROPN
ejpam-4207	317	5	aslim	aslim	PROPN
ejpam-4207	317	6	and	and	CCONJ
ejpam-4207	317	7	a.	a.	NOUN
ejpam-4207	317	8	cakusu	cakusu	PROPN
ejpam-4207	317	9	culer	culer	PROPN
ejpam-4207	317	10	,	,	PUNCT
ejpam-4207	317	11	b	b	X
ejpam-4207	317	12	-	-	PUNCT
ejpam-4207	317	13	i	i	NOUN
ejpam-4207	317	14	-	-	PUNCT
ejpam-4207	317	15	open	open	ADJ
ejpam-4207	317	16	sets	set	NOUN
ejpam-4207	317	17	and	and	CCONJ
ejpam-4207	317	18	decompositions	decomposition	NOUN
ejpam-4207	317	19	of	of	ADP
ejpam-4207	317	20	continuity	continuity	NOUN
ejpam-4207	317	21	via	via	ADP
ejpam-4207	317	22	idealizations	idealization	NOUN
ejpam-4207	317	23	proc	proc	NOUN
ejpam-4207	317	24	.	.	PUNCT
ejpam-4207	318	1	inst	inst	PROPN
ejpam-4207	318	2	.	.	PUNCT
ejpam-4207	319	1	math	math	NOUN
ejpam-4207	319	2	.	.	PUNCT
ejpam-4207	320	1	acad	acad	PROPN
ejpam-4207	320	2	.	.	PUNCT
ejpam-4207	321	1	nat	nat	PROPN
ejpam-4207	321	2	.	.	PUNCT
ejpam-4207	322	1	acad	acad	PROPN
ejpam-4207	322	2	.	.	PUNCT
ejpam-4207	323	1	sci	sci	PROPN
ejpam-4207	323	2	.	.	PROPN
ejpam-4207	323	3	azerbaidjan	azerbaidjan	PROPN
ejpam-4207	323	4	22	22	NUM
ejpam-4207	323	5	(	(	PUNCT
ejpam-4207	323	6	2003	2003	NUM
ejpam-4207	323	7	)	)	PUNCT
ejpam-4207	323	8	,	,	PUNCT
ejpam-4207	323	9	27–32	27–32	NUM
ejpam-4207	323	10	.	.	PUNCT
ejpam-4207	324	1	references	reference	NOUN
ejpam-4207	324	2	12	12	NUM
ejpam-4207	324	3	[	[	X
ejpam-4207	324	4	6	6	NUM
ejpam-4207	324	5	]	]	PUNCT
ejpam-4207	324	6	t.	t.	NOUN
ejpam-4207	324	7	bânzaru	bânzaru	PROPN
ejpam-4207	324	8	,	,	PUNCT
ejpam-4207	324	9	multifunctions	multifunction	NOUN
ejpam-4207	324	10	and	and	CCONJ
ejpam-4207	324	11	m	m	PROPN
ejpam-4207	324	12	-product	-product	NOUN
ejpam-4207	324	13	spaces	space	NOUN
ejpam-4207	324	14	(	(	PUNCT
ejpam-4207	324	15	romanian	romanian	NOUN
ejpam-4207	324	16	)	)	PUNCT
ejpam-4207	324	17	,	,	PUNCT
ejpam-4207	324	18	bul	bul	PROPN
ejpam-4207	324	19	.	.	PUNCT
ejpam-4207	324	20	st	st	PROPN
ejpam-4207	324	21	.	.	PROPN
ejpam-4207	324	22	tehn	tehn	PROPN
ejpam-4207	324	23	.	.	PUNCT
ejpam-4207	325	1	inst	inst	PROPN
ejpam-4207	325	2	.	.	PUNCT
ejpam-4207	326	1	politehn	politehn	PROPN
ejpam-4207	326	2	.	.	PUNCT
ejpam-4207	327	1	”	"	PUNCT
ejpam-4207	327	2	traian	traian	PROPN
ejpam-4207	327	3	.	.	PUNCT
ejpam-4207	327	4	vuia	vuia	PROPN
ejpam-4207	327	5	”	"	PUNCT
ejpam-4207	327	6	,	,	PUNCT
ejpam-4207	327	7	timişoara	timişoara	NOUN
ejpam-4207	327	8	,	,	PUNCT
ejpam-4207	327	9	ser	ser	NOUN
ejpam-4207	327	10	.	.	PROPN
ejpam-4207	327	11	mat	mat	PROPN
ejpam-4207	327	12	.	.	PUNCT
ejpam-4207	327	13	fiz	fiz	PROPN
ejpam-4207	327	14	.	.	PUNCT
ejpam-4207	328	1	mec	mec	PROPN
ejpam-4207	328	2	.	.	PROPN
ejpam-4207	328	3	teor	teor	PROPN
ejpam-4207	328	4	.	.	PUNCT
ejpam-4207	328	5	appl	appl	PROPN
ejpam-4207	328	6	.	.	PUNCT
ejpam-4207	329	1	17(31	17(31	NUM
ejpam-4207	329	2	)	)	PUNCT
ejpam-4207	329	3	(	(	PUNCT
ejpam-4207	329	4	1972	1972	NUM
ejpam-4207	329	5	)	)	PUNCT
ejpam-4207	329	6	,	,	PUNCT
ejpam-4207	329	7	17–23	17–23	NUM
ejpam-4207	329	8	.	.	PUNCT
ejpam-4207	330	1	[	[	X
ejpam-4207	330	2	7	7	X
ejpam-4207	330	3	]	]	PUNCT
ejpam-4207	330	4	t.	t.	NOUN
ejpam-4207	330	5	bânzaru	bânzaru	PROPN
ejpam-4207	330	6	et	et	PROPN
ejpam-4207	330	7	n.	n.	PROPN
ejpam-4207	330	8	crivǎţ	crivǎţ	PROPN
ejpam-4207	330	9	,	,	PUNCT
ejpam-4207	330	10	structures	structure	NOUN
ejpam-4207	330	11	uniformes	uniform	VERB
ejpam-4207	330	12	sur	sur	PROPN
ejpam-4207	330	13	l’espace	l’espace	PROPN
ejpam-4207	330	14	des	des	PROPN
ejpam-4207	330	15	parties	party	NOUN
ejpam-4207	330	16	d’un	d’un	PROPN
ejpam-4207	330	17	espace	espace	PROPN
ejpam-4207	330	18	uniform	uniform	PROPN
ejpam-4207	330	19	et	et	PROPN
ejpam-4207	330	20	quasicontinuité	quasicontinuité	PROPN
ejpam-4207	330	21	des	des	PROPN
ejpam-4207	330	22	applications	application	NOUN
ejpam-4207	330	23	multivoques	multivoque	NOUN
ejpam-4207	330	24	,	,	PUNCT
ejpam-4207	330	25	bul	bul	PROPN
ejpam-4207	330	26	.	.	PUNCT
ejpam-4207	330	27	st	st	PROPN
ejpam-4207	330	28	.	.	PROPN
ejpam-4207	330	29	tehn	tehn	PROPN
ejpam-4207	330	30	.	.	PUNCT
ejpam-4207	331	1	inst	inst	PROPN
ejpam-4207	331	2	.	.	PUNCT
ejpam-4207	332	1	politehn	politehn	PROPN
ejpam-4207	332	2	.	.	PUNCT
ejpam-4207	333	1	”	"	PUNCT
ejpam-4207	333	2	traian	traian	PROPN
ejpam-4207	333	3	.	.	PUNCT
ejpam-4207	333	4	vuia	vuia	PROPN
ejpam-4207	333	5	”	"	PUNCT
ejpam-4207	333	6	,	,	PUNCT
ejpam-4207	333	7	timişoara	timişoara	NOUN
ejpam-4207	333	8	,	,	PUNCT
ejpam-4207	333	9	ser	ser	NOUN
ejpam-4207	333	10	.	.	PROPN
ejpam-4207	333	11	mat	mat	PROPN
ejpam-4207	333	12	.	.	PUNCT
ejpam-4207	333	13	fiz	fiz	PROPN
ejpam-4207	333	14	.	.	PUNCT
ejpam-4207	334	1	mec	mec	PROPN
ejpam-4207	334	2	.	.	PROPN
ejpam-4207	334	3	teor	teor	PROPN
ejpam-4207	334	4	.	.	PUNCT
ejpam-4207	334	5	appl	appl	PROPN
ejpam-4207	334	6	.	.	PUNCT
ejpam-4207	335	1	20(34	20(34	NUM
ejpam-4207	335	2	)	)	PUNCT
ejpam-4207	335	3	(	(	PUNCT
ejpam-4207	335	4	1975	1975	NUM
ejpam-4207	335	5	)	)	PUNCT
ejpam-4207	335	6	,	,	PUNCT
ejpam-4207	335	7	135–136	135–136	NUM
ejpam-4207	335	8	.	.	PUNCT
ejpam-4207	336	1	[	[	X
ejpam-4207	336	2	8	8	NUM
ejpam-4207	336	3	]	]	X
ejpam-4207	336	4	c.	c.	PROPN
ejpam-4207	336	5	boonpok	boonpok	PROPN
ejpam-4207	336	6	,	,	PUNCT
ejpam-4207	336	7	on	on	ADP
ejpam-4207	336	8	continuous	continuous	ADJ
ejpam-4207	336	9	multifunctions	multifunction	NOUN
ejpam-4207	336	10	in	in	ADP
ejpam-4207	336	11	ideal	ideal	ADJ
ejpam-4207	336	12	topological	topological	ADJ
ejpam-4207	336	13	spaces	space	NOUN
ejpam-4207	336	14	,	,	PUNCT
ejpam-4207	336	15	lobacewscki	lobacewscki	PROPN
ejpam-4207	336	16	j.	j.	PROPN
ejpam-4207	336	17	math	math	PROPN
ejpam-4207	336	18	.	.	PUNCT
ejpam-4207	337	1	1	1	NUM
ejpam-4207	337	2	(	(	PUNCT
ejpam-4207	337	3	2009	2009	NUM
ejpam-4207	337	4	)	)	PUNCT
ejpam-4207	337	5	,	,	PUNCT
ejpam-4207	337	6	24–35	24–35	NUM
ejpam-4207	337	7	.	.	PUNCT
ejpam-4207	338	1	[	[	X
ejpam-4207	338	2	9	9	NUM
ejpam-4207	338	3	]	]	PUNCT
ejpam-4207	338	4	c.	c.	NOUN
ejpam-4207	338	5	boonpok	boonpok	PROPN
ejpam-4207	338	6	and	and	CCONJ
ejpam-4207	338	7	p.	p.	NOUN
ejpam-4207	338	8	pue	pue	NOUN
ejpam-4207	338	9	-	-	PUNCT
ejpam-4207	338	10	on	on	ADP
ejpam-4207	338	11	continuity	continuity	NOUN
ejpam-4207	338	12	for	for	ADP
ejpam-4207	338	13	multifunctions	multifunction	NOUN
ejpam-4207	338	14	in	in	ADP
ejpam-4207	338	15	ideal	ideal	ADJ
ejpam-4207	338	16	topological	topological	ADJ
ejpam-4207	338	17	spaces	space	NOUN
ejpam-4207	338	18	,	,	PUNCT
ejpam-4207	338	19	wseas	wseas	PROPN
ejpam-4207	338	20	trans	trans	PROPN
ejpam-4207	339	1	.	.	PROPN
ejpam-4207	339	2	math	math	PROPN
ejpam-4207	339	3	.	.	PUNCT
ejpam-4207	340	1	19	19	NUM
ejpam-4207	340	2	(	(	PUNCT
ejpam-4207	340	3	2020	2020	NUM
ejpam-4207	340	4	)	)	PUNCT
ejpam-4207	340	5	,	,	PUNCT
ejpam-4207	341	1	624–631	624–631	NUM
ejpam-4207	341	2	.	.	PUNCT
ejpam-4207	342	1	[	[	X
ejpam-4207	342	2	10	10	NUM
ejpam-4207	342	3	]	]	X
ejpam-4207	342	4	j.	j.	PROPN
ejpam-4207	342	5	dontchev	dontchev	PROPN
ejpam-4207	342	6	,	,	PUNCT
ejpam-4207	342	7	on	on	ADP
ejpam-4207	342	8	pre	pre	ADJ
ejpam-4207	342	9	-	-	ADJ
ejpam-4207	342	10	i	i	PRON
ejpam-4207	342	11	-	-	PUNCT
ejpam-4207	342	12	open	open	ADJ
ejpam-4207	342	13	sets	set	NOUN
ejpam-4207	342	14	and	and	CCONJ
ejpam-4207	342	15	a	a	DET
ejpam-4207	342	16	decomposition	decomposition	NOUN
ejpam-4207	342	17	of	of	ADP
ejpam-4207	342	18	i	i	NOUN
ejpam-4207	342	19	-	-	PUNCT
ejpam-4207	342	20	continuity	continuity	NOUN
ejpam-4207	342	21	,	,	PUNCT
ejpam-4207	342	22	banyan	banyan	ADJ
ejpam-4207	342	23	math	math	NOUN
ejpam-4207	342	24	.	.	PUNCT
ejpam-4207	343	1	j.	j.	PROPN
ejpam-4207	343	2	2	2	PROPN
ejpam-4207	343	3	(	(	PUNCT
ejpam-4207	343	4	1996	1996	NUM
ejpam-4207	343	5	)	)	PUNCT
ejpam-4207	343	6	.	.	PUNCT
ejpam-4207	344	1	[	[	X
ejpam-4207	344	2	11	11	NUM
ejpam-4207	344	3	]	]	X
ejpam-4207	344	4	e.	e.	PROPN
ejpam-4207	344	5	ekici	ekici	PROPN
ejpam-4207	344	6	,	,	PUNCT
ejpam-4207	344	7	on	on	ADP
ejpam-4207	344	8	aci	aci	PROPN
ejpam-4207	344	9	-	-	PUNCT
ejpam-4207	344	10	sets	set	NOUN
ejpam-4207	344	11	,	,	PUNCT
ejpam-4207	344	12	bci	bci	NOUN
ejpam-4207	344	13	-	-	PUNCT
ejpam-4207	344	14	sets	set	NOUN
ejpam-4207	344	15	,	,	PUNCT
ejpam-4207	344	16	β	β	X
ejpam-4207	344	17	⋆	⋆	VERB
ejpam-4207	344	18	i	i	PRON
ejpam-4207	344	19	-open	-open	PROPN
ejpam-4207	344	20	sets	set	NOUN
ejpam-4207	344	21	and	and	CCONJ
ejpam-4207	344	22	decomopositions	decomoposition	NOUN
ejpam-4207	344	23	of	of	ADP
ejpam-4207	344	24	continuity	continuity	NOUN
ejpam-4207	344	25	in	in	ADP
ejpam-4207	344	26	ideal	ideal	ADJ
ejpam-4207	344	27	topological	topological	ADJ
ejpam-4207	344	28	spaces	space	NOUN
ejpam-4207	344	29	creat	creat	PROPN
ejpam-4207	344	30	.	.	PUNCT
ejpam-4207	344	31	math	math	PROPN
ejpam-4207	344	32	.	.	PUNCT
ejpam-4207	345	1	inform	inform	NOUN
ejpam-4207	345	2	.	.	PUNCT
ejpam-4207	346	1	20(1	20(1	NUM
ejpam-4207	346	2	)	)	PUNCT
ejpam-4207	346	3	(	(	PUNCT
ejpam-4207	346	4	2011	2011	NUM
ejpam-4207	346	5	)	)	PUNCT
ejpam-4207	346	6	,	,	PUNCT
ejpam-4207	346	7	47–54	47–54	NUM
ejpam-4207	346	8	.	.	PUNCT
ejpam-4207	347	1	[	[	X
ejpam-4207	347	2	12	12	NUM
ejpam-4207	347	3	]	]	X
ejpam-4207	347	4	e.	e.	PROPN
ejpam-4207	347	5	ekici	ekici	PROPN
ejpam-4207	347	6	and	and	CCONJ
ejpam-4207	347	7	t.	t.	PROPN
ejpam-4207	347	8	noiri	noiri	PROPN
ejpam-4207	347	9	,	,	PUNCT
ejpam-4207	347	10	⋆-hyperconnected	⋆-hyperconnecte	VERB
ejpam-4207	347	11	ideal	ideal	ADJ
ejpam-4207	347	12	topological	topological	ADJ
ejpam-4207	347	13	spaces	space	NOUN
ejpam-4207	347	14	,	,	PUNCT
ejpam-4207	347	15	anal	anal	PROPN
ejpam-4207	347	16	.	.	PUNCT
ejpam-4207	347	17	st	st	PROPN
ejpam-4207	347	18	.	.	PROPN
ejpam-4207	347	19	univ	univ	PROPN
ejpam-4207	347	20	.	.	PUNCT
ejpam-4207	348	1	alexandru	alexandru	PROPN
ejpam-4207	348	2	i.	i.	PROPN
ejpam-4207	348	3	cusi	cusi	PROPN
ejpam-4207	348	4	,	,	PUNCT
ejpam-4207	348	5	iasi	iasi	NOUN
ejpam-4207	348	6	(	(	PUNCT
ejpam-4207	348	7	n.s	n.s	PROPN
ejpam-4207	348	8	.	.	PROPN
ejpam-4207	348	9	)	)	PUNCT
ejpam-4207	348	10	mat	mat	NOUN
ejpam-4207	348	11	.	.	PUNCT
ejpam-4207	348	12	58(1	58(1	X
ejpam-4207	348	13	)	)	PUNCT
ejpam-4207	348	14	(	(	PUNCT
ejpam-4207	348	15	2012	2012	NUM
ejpam-4207	348	16	)	)	PUNCT
ejpam-4207	348	17	,	,	PUNCT
ejpam-4207	348	18	121–129	121–129	NUM
ejpam-4207	348	19	.	.	PUNCT
ejpam-4207	349	1	[	[	X
ejpam-4207	349	2	13	13	NUM
ejpam-4207	349	3	]	]	PUNCT
ejpam-4207	349	4	j.	j.	PROPN
ejpam-4207	349	5	ewert	ewert	PROPN
ejpam-4207	349	6	and	and	CCONJ
ejpam-4207	349	7	t.	t.	PROPN
ejpam-4207	349	8	neubrunn	neubrunn	PROPN
ejpam-4207	349	9	,	,	PUNCT
ejpam-4207	349	10	on	on	ADP
ejpam-4207	349	11	quasicontinuous	quasicontinuous	ADJ
ejpam-4207	349	12	multivalued	multivalue	VERB
ejpam-4207	349	13	maps	map	NOUN
ejpam-4207	349	14	,	,	PUNCT
ejpam-4207	349	15	demonstratio	demonstratio	PROPN
ejpam-4207	349	16	math	math	PROPN
ejpam-4207	349	17	.	.	PUNCT
ejpam-4207	350	1	21	21	NUM
ejpam-4207	350	2	(	(	PUNCT
ejpam-4207	350	3	1988	1988	NUM
ejpam-4207	350	4	)	)	PUNCT
ejpam-4207	350	5	,	,	PUNCT
ejpam-4207	350	6	697–711	697–711	NUM
ejpam-4207	350	7	.	.	PUNCT
ejpam-4207	351	1	[	[	X
ejpam-4207	351	2	14	14	NUM
ejpam-4207	351	3	]	]	X
ejpam-4207	351	4	e.	e.	PROPN
ejpam-4207	351	5	hatir	hatir	PROPN
ejpam-4207	351	6	and	and	CCONJ
ejpam-4207	351	7	s.	s.	PROPN
ejpam-4207	351	8	jafari	jafari	PROPN
ejpam-4207	351	9	,	,	PUNCT
ejpam-4207	351	10	on	on	ADP
ejpam-4207	351	11	weakly	weakly	ADJ
ejpam-4207	351	12	semi	semi	ADJ
ejpam-4207	351	13	-	-	ADJ
ejpam-4207	351	14	i	i	PRON
ejpam-4207	351	15	-	-	PUNCT
ejpam-4207	351	16	open	open	ADJ
ejpam-4207	351	17	sets	set	NOUN
ejpam-4207	351	18	and	and	CCONJ
ejpam-4207	351	19	other	other	ADJ
ejpam-4207	351	20	decomposition	decomposition	NOUN
ejpam-4207	351	21	of	of	ADP
ejpam-4207	351	22	continuity	continuity	NOUN
ejpam-4207	351	23	via	via	ADP
ejpam-4207	351	24	ideals	ideal	NOUN
ejpam-4207	351	25	,	,	PUNCT
ejpam-4207	351	26	sarajevo	sarajevo	PROPN
ejpam-4207	351	27	j.	j.	PROPN
ejpam-4207	351	28	math	math	PROPN
ejpam-4207	351	29	.	.	PUNCT
ejpam-4207	352	1	14	14	NUM
ejpam-4207	352	2	(	(	PUNCT
ejpam-4207	352	3	2006	2006	NUM
ejpam-4207	352	4	)	)	PUNCT
ejpam-4207	352	5	,	,	PUNCT
ejpam-4207	352	6	107–114	107–114	NUM
ejpam-4207	352	7	.	.	PUNCT
ejpam-4207	353	1	[	[	X
ejpam-4207	353	2	15	15	NUM
ejpam-4207	353	3	]	]	X
ejpam-4207	353	4	e.	e.	PROPN
ejpam-4207	353	5	hatir	hatir	PROPN
ejpam-4207	353	6	,	,	PUNCT
ejpam-4207	353	7	a.	a.	NOUN
ejpam-4207	353	8	keskin	keskin	PROPN
ejpam-4207	353	9	and	and	CCONJ
ejpam-4207	353	10	t.	t.	PROPN
ejpam-4207	353	11	noiri	noiri	PROPN
ejpam-4207	353	12	,	,	PUNCT
ejpam-4207	353	13	on	on	ADP
ejpam-4207	353	14	a	a	DET
ejpam-4207	353	15	new	new	ADJ
ejpam-4207	353	16	decomposition	decomposition	NOUN
ejpam-4207	353	17	of	of	ADP
ejpam-4207	353	18	continuity	continuity	NOUN
ejpam-4207	353	19	via	via	ADP
ejpam-4207	353	20	idealization	idealization	NOUN
ejpam-4207	353	21	,	,	PUNCT
ejpam-4207	353	22	jp	jp	NOUN
ejpam-4207	353	23	j.	j.	PROPN
ejpam-4207	353	24	geometry	geometry	PROPN
ejpam-4207	353	25	toplogy	toplogy	NOUN
ejpam-4207	353	26	3(1	3(1	NUM
ejpam-4207	353	27	)	)	PUNCT
ejpam-4207	353	28	(	(	PUNCT
ejpam-4207	353	29	2003	2003	NUM
ejpam-4207	353	30	)	)	PUNCT
ejpam-4207	353	31	,	,	PUNCT
ejpam-4207	353	32	53–64	53–64	NUM
ejpam-4207	353	33	.	.	PUNCT
ejpam-4207	354	1	[	[	X
ejpam-4207	354	2	16	16	NUM
ejpam-4207	354	3	]	]	X
ejpam-4207	354	4	e.	e.	PROPN
ejpam-4207	354	5	hatir	hatir	PROPN
ejpam-4207	354	6	and	and	CCONJ
ejpam-4207	354	7	t.	t.	PROPN
ejpam-4207	354	8	noiri	noiri	PROPN
ejpam-4207	354	9	,	,	PUNCT
ejpam-4207	354	10	on	on	ADP
ejpam-4207	354	11	decompositions	decomposition	NOUN
ejpam-4207	354	12	of	of	ADP
ejpam-4207	354	13	continuity	continuity	NOUN
ejpam-4207	354	14	via	via	ADP
ejpam-4207	354	15	idealization	idealization	NOUN
ejpam-4207	354	16	,	,	PUNCT
ejpam-4207	354	17	acta	acta	PROPN
ejpam-4207	354	18	math	math	PROPN
ejpam-4207	354	19	.	.	PUNCT
ejpam-4207	355	1	hungar	hungar	NOUN
ejpam-4207	355	2	.	.	PUNCT
ejpam-4207	356	1	96(4	96(4	NOUN
ejpam-4207	356	2	)	)	PUNCT
ejpam-4207	356	3	(	(	PUNCT
ejpam-4207	356	4	2002	2002	NUM
ejpam-4207	356	5	)	)	PUNCT
ejpam-4207	356	6	,	,	PUNCT
ejpam-4207	356	7	341–349	341–349	NUM
ejpam-4207	356	8	.	.	PUNCT
ejpam-4207	357	1	[	[	X
ejpam-4207	357	2	17	17	NUM
ejpam-4207	357	3	]	]	X
ejpam-4207	357	4	e.	e.	PROPN
ejpam-4207	357	5	hatir	hatir	PROPN
ejpam-4207	357	6	and	and	CCONJ
ejpam-4207	357	7	t.	t.	PROPN
ejpam-4207	357	8	noiri	noiri	PROPN
ejpam-4207	357	9	,	,	PUNCT
ejpam-4207	357	10	on	on	ADP
ejpam-4207	357	11	β	β	X
ejpam-4207	357	12	-	-	ADJ
ejpam-4207	357	13	i	i	NOUN
ejpam-4207	357	14	-	-	PUNCT
ejpam-4207	357	15	open	open	ADJ
ejpam-4207	357	16	sets	set	NOUN
ejpam-4207	357	17	and	and	CCONJ
ejpam-4207	357	18	decompositions	decomposition	NOUN
ejpam-4207	357	19	of	of	ADP
ejpam-4207	357	20	almost	almost	ADV
ejpam-4207	357	21	-	-	PUNCT
ejpam-4207	357	22	i	i	NOUN
ejpam-4207	357	23	-	-	PUNCT
ejpam-4207	357	24	continuity	continuity	NOUN
ejpam-4207	357	25	,	,	PUNCT
ejpam-4207	357	26	bull	bull	NOUN
ejpam-4207	357	27	.	.	PUNCT
ejpam-4207	358	1	malays	malays	PROPN
ejpam-4207	358	2	.	.	PUNCT
ejpam-4207	359	1	math	math	NOUN
ejpam-4207	359	2	.	.	PUNCT
ejpam-4207	360	1	sci	sci	PROPN
ejpam-4207	360	2	.	.	PROPN
ejpam-4207	360	3	soc	soc	PROPN
ejpam-4207	360	4	.	.	PUNCT
ejpam-4207	361	1	(	(	PUNCT
ejpam-4207	361	2	2	2	X
ejpam-4207	361	3	)	)	PUNCT
ejpam-4207	361	4	29(1	29(1	NUM
ejpam-4207	361	5	)	)	PUNCT
ejpam-4207	361	6	(	(	PUNCT
ejpam-4207	361	7	2006	2006	NUM
ejpam-4207	361	8	)	)	PUNCT
ejpam-4207	361	9	,	,	PUNCT
ejpam-4207	361	10	119–124	119–124	NUM
ejpam-4207	361	11	.	.	PUNCT
ejpam-4207	362	1	[	[	X
ejpam-4207	362	2	18	18	NUM
ejpam-4207	362	3	]	]	X
ejpam-4207	362	4	d.	d.	PROPN
ejpam-4207	362	5	janković	janković	PROPN
ejpam-4207	362	6	and	and	CCONJ
ejpam-4207	362	7	t.	t.	PROPN
ejpam-4207	362	8	r.	r.	PROPN
ejpam-4207	362	9	hamlett	hamlett	PROPN
ejpam-4207	362	10	,	,	PUNCT
ejpam-4207	362	11	new	new	ADJ
ejpam-4207	362	12	topologies	topology	NOUN
ejpam-4207	362	13	from	from	ADP
ejpam-4207	362	14	old	old	ADJ
ejpam-4207	362	15	via	via	ADP
ejpam-4207	362	16	ideals	ideal	NOUN
ejpam-4207	362	17	,	,	PUNCT
ejpam-4207	362	18	amer	amer	PROPN
ejpam-4207	362	19	.	.	PROPN
ejpam-4207	362	20	math	math	PROPN
ejpam-4207	362	21	.	.	PUNCT
ejpam-4207	363	1	monthly	monthly	ADJ
ejpam-4207	363	2	97	97	NUM
ejpam-4207	363	3	(	(	PUNCT
ejpam-4207	363	4	1990	1990	NUM
ejpam-4207	363	5	)	)	PUNCT
ejpam-4207	363	6	,	,	PUNCT
ejpam-4207	363	7	295–310	295–310	NUM
ejpam-4207	363	8	.	.	PUNCT
ejpam-4207	364	1	[	[	X
ejpam-4207	364	2	19	19	NUM
ejpam-4207	364	3	]	]	X
ejpam-4207	364	4	i.	i.	PROPN
ejpam-4207	364	5	kovačević	kovačević	PROPN
ejpam-4207	364	6	,	,	PUNCT
ejpam-4207	364	7	subsets	subset	NOUN
ejpam-4207	364	8	and	and	CCONJ
ejpam-4207	364	9	paracompactness	paracompactness	NOUN
ejpam-4207	364	10	,	,	PUNCT
ejpam-4207	364	11	univ	univ	PROPN
ejpam-4207	364	12	.	.	PUNCT
ejpam-4207	365	1	u	u	PROPN
ejpam-4207	365	2	novom	novom	ADJ
ejpam-4207	365	3	sadu	sadu	NOUN
ejpam-4207	365	4	,	,	PUNCT
ejpam-4207	365	5	zb	zb	PROPN
ejpam-4207	365	6	.	.	PUNCT
ejpam-4207	365	7	rad	rad	PROPN
ejpam-4207	365	8	.	.	PROPN
ejpam-4207	365	9	prirod	prirod	PROPN
ejpam-4207	365	10	.	.	PUNCT
ejpam-4207	366	1	mat	mat	NOUN
ejpam-4207	366	2	.	.	PUNCT
ejpam-4207	366	3	fac	fac	PROPN
ejpam-4207	366	4	.	.	PUNCT
ejpam-4207	366	5	ser	ser	PROPN
ejpam-4207	366	6	.	.	PROPN
ejpam-4207	367	1	mat	mat	PROPN
ejpam-4207	367	2	.	.	PROPN
ejpam-4207	367	3	14	14	NUM
ejpam-4207	367	4	(	(	PUNCT
ejpam-4207	367	5	1984	1984	NUM
ejpam-4207	367	6	)	)	PUNCT
ejpam-4207	367	7	,	,	PUNCT
ejpam-4207	367	8	79–87	79–87	NUM
ejpam-4207	367	9	.	.	PUNCT
ejpam-4207	368	1	[	[	X
ejpam-4207	368	2	20	20	NUM
ejpam-4207	368	3	]	]	PUNCT
ejpam-4207	368	4	k.	k.	PROPN
ejpam-4207	368	5	kuratowski	kuratowski	PROPN
ejpam-4207	368	6	,	,	PUNCT
ejpam-4207	368	7	topology	topology	NOUN
ejpam-4207	368	8	,	,	PUNCT
ejpam-4207	368	9	vol	vol	NOUN
ejpam-4207	368	10	.	.	PUNCT
ejpam-4207	369	1	i	i	PRON
ejpam-4207	369	2	,	,	PUNCT
ejpam-4207	369	3	acadmic	acadmic	ADJ
ejpam-4207	369	4	press	press	PROPN
ejpam-4207	369	5	,	,	PUNCT
ejpam-4207	369	6	new	new	PROPN
ejpam-4207	369	7	york	york	PROPN
ejpam-4207	369	8	,	,	PUNCT
ejpam-4207	369	9	1966	1966	NUM
ejpam-4207	369	10	.	.	PUNCT
ejpam-4207	370	1	[	[	X
ejpam-4207	370	2	21	21	NUM
ejpam-4207	370	3	]	]	X
ejpam-4207	370	4	n.	n.	PROPN
ejpam-4207	370	5	levine	levine	PROPN
ejpam-4207	370	6	,	,	PUNCT
ejpam-4207	370	7	semi	semi	ADJ
ejpam-4207	370	8	-	-	ADJ
ejpam-4207	370	9	open	open	ADJ
ejpam-4207	370	10	sets	set	NOUN
ejpam-4207	370	11	and	and	CCONJ
ejpam-4207	370	12	semi	semi	ADJ
ejpam-4207	370	13	-	-	NOUN
ejpam-4207	370	14	continuity	continuity	NOUN
ejpam-4207	370	15	in	in	ADP
ejpam-4207	370	16	topological	topological	ADJ
ejpam-4207	370	17	spaces	space	NOUN
ejpam-4207	370	18	,	,	PUNCT
ejpam-4207	370	19	amer	amer	PROPN
ejpam-4207	370	20	.	.	PROPN
ejpam-4207	370	21	math	math	PROPN
ejpam-4207	370	22	.	.	PUNCT
ejpam-4207	371	1	monthly	monthly	ADJ
ejpam-4207	371	2	70	70	NUM
ejpam-4207	371	3	(	(	PUNCT
ejpam-4207	371	4	1963	1963	NUM
ejpam-4207	371	5	)	)	PUNCT
ejpam-4207	371	6	,	,	PUNCT
ejpam-4207	371	7	36–41	36–41	NUM
ejpam-4207	371	8	.	.	PUNCT
ejpam-4207	372	1	references	reference	NOUN
ejpam-4207	372	2	13	13	NUM
ejpam-4207	373	1	[	[	X
ejpam-4207	373	2	22	22	NUM
ejpam-4207	373	3	]	]	PUNCT
ejpam-4207	373	4	h.	h.	NOUN
ejpam-4207	373	5	maki	maki	PROPN
ejpam-4207	373	6	,	,	PUNCT
ejpam-4207	373	7	c.	c.	PROPN
ejpam-4207	373	8	k.	k.	PROPN
ejpam-4207	373	9	rao	rao	PROPN
ejpam-4207	373	10	and	and	CCONJ
ejpam-4207	373	11	a.	a.	PROPN
ejpam-4207	373	12	nagoor	nagoor	PROPN
ejpam-4207	373	13	gani	gani	PROPN
ejpam-4207	373	14	,	,	PUNCT
ejpam-4207	373	15	on	on	ADP
ejpam-4207	373	16	generalizing	generalize	VERB
ejpam-4207	373	17	semi	semi	ADJ
ejpam-4207	373	18	-	-	ADJ
ejpam-4207	373	19	open	open	ADJ
ejpam-4207	373	20	and	and	CCONJ
ejpam-4207	373	21	preopen	preopen	ADJ
ejpam-4207	373	22	sets	set	NOUN
ejpam-4207	373	23	,	,	PUNCT
ejpam-4207	373	24	pure	pure	ADJ
ejpam-4207	373	25	appl	appl	NOUN
ejpam-4207	373	26	.	.	PUNCT
ejpam-4207	373	27	math	math	PROPN
ejpam-4207	373	28	.	.	PUNCT
ejpam-4207	374	1	sci	sci	PROPN
ejpam-4207	374	2	.	.	PROPN
ejpam-4207	375	1	49	49	NUM
ejpam-4207	375	2	(	(	PUNCT
ejpam-4207	375	3	1999	1999	NUM
ejpam-4207	375	4	)	)	PUNCT
ejpam-4207	375	5	,	,	PUNCT
ejpam-4207	375	6	17–29	17–29	NUM
ejpam-4207	375	7	.	.	PUNCT
ejpam-4207	376	1	[	[	X
ejpam-4207	376	2	23	23	NUM
ejpam-4207	376	3	]	]	X
ejpam-4207	376	4	s.	s.	PROPN
ejpam-4207	376	5	marcus	marcus	PROPN
ejpam-4207	376	6	,	,	PUNCT
ejpam-4207	376	7	sur	sur	PROPN
ejpam-4207	376	8	les	les	PROPN
ejpam-4207	376	9	fonctions	fonctions	PROPN
ejpam-4207	376	10	quasicontinues	quasicontinue	NOUN
ejpam-4207	376	11	au	au	PROPN
ejpam-4207	376	12	sens	sens	X
ejpam-4207	376	13	de	de	PROPN
ejpam-4207	376	14	s.	s.	PROPN
ejpam-4207	376	15	kempisty	kempisty	PROPN
ejpam-4207	376	16	,	,	PUNCT
ejpam-4207	376	17	colloq	colloq	PROPN
ejpam-4207	376	18	.	.	PUNCT
ejpam-4207	376	19	math	math	PROPN
ejpam-4207	376	20	.	.	PUNCT
ejpam-4207	377	1	8	8	NUM
ejpam-4207	377	2	(	(	PUNCT
ejpam-4207	377	3	1961	1961	NUM
ejpam-4207	377	4	)	)	PUNCT
ejpam-4207	377	5	,	,	PUNCT
ejpam-4207	377	6	47–53	47–53	NUM
ejpam-4207	377	7	.	.	PUNCT
ejpam-4207	378	1	[	[	X
ejpam-4207	378	2	24	24	NUM
ejpam-4207	378	3	]	]	PUNCT
ejpam-4207	378	4	a.	a.	NOUN
ejpam-4207	378	5	s.	s.	PROPN
ejpam-4207	378	6	mashhour	mashhour	PROPN
ejpam-4207	378	7	,	,	PUNCT
ejpam-4207	378	8	m.	m.	PROPN
ejpam-4207	378	9	e.	e.	PROPN
ejpam-4207	378	10	abd	abd	PROPN
ejpam-4207	378	11	el	el	PROPN
ejpam-4207	378	12	-	-	PROPN
ejpam-4207	378	13	monsef	monsef	PROPN
ejpam-4207	378	14	and	and	CCONJ
ejpam-4207	378	15	s.	s.	PROPN
ejpam-4207	378	16	n.	n.	PROPN
ejpam-4207	378	17	el	el	PROPN
ejpam-4207	378	18	-	-	PUNCT
ejpam-4207	378	19	deep	deep	ADJ
ejpam-4207	378	20	,	,	PUNCT
ejpam-4207	378	21	on	on	ADP
ejpam-4207	378	22	precontinuous	precontinuous	ADJ
ejpam-4207	378	23	and	and	CCONJ
ejpam-4207	378	24	weak	weak	ADJ
ejpam-4207	378	25	precontinuous	precontinuous	ADJ
ejpam-4207	378	26	mappings	mapping	NOUN
ejpam-4207	378	27	,	,	PUNCT
ejpam-4207	378	28	proc	proc	NOUN
ejpam-4207	378	29	.	.	PUNCT
ejpam-4207	379	1	math	math	NOUN
ejpam-4207	379	2	.	.	PUNCT
ejpam-4207	380	1	phys	phy	NOUN
ejpam-4207	380	2	.	.	PUNCT
ejpam-4207	381	1	soc	soc	PROPN
ejpam-4207	381	2	.	.	PUNCT
ejpam-4207	382	1	egypt	egypt	PROPN
ejpam-4207	382	2	53	53	NUM
ejpam-4207	382	3	(	(	PUNCT
ejpam-4207	382	4	1982	1982	NUM
ejpam-4207	382	5	)	)	PUNCT
ejpam-4207	382	6	,	,	PUNCT
ejpam-4207	382	7	47–53	47–53	NUM
ejpam-4207	382	8	.	.	PUNCT
ejpam-4207	383	1	[	[	X
ejpam-4207	383	2	25	25	NUM
ejpam-4207	383	3	]	]	PUNCT
ejpam-4207	383	4	j.	j.	PROPN
ejpam-4207	383	5	m.	m.	PROPN
ejpam-4207	383	6	mustafa	mustafa	PROPN
ejpam-4207	383	7	,	,	PUNCT
ejpam-4207	383	8	s.	s.	PROPN
ejpam-4207	383	9	al	al	PROPN
ejpam-4207	383	10	ghour	ghour	PROPN
ejpam-4207	383	11	and	and	CCONJ
ejpam-4207	383	12	k.al	k.al	PROPN
ejpam-4207	383	13	zoubi	zoubi	NOUN
ejpam-4207	383	14	,	,	PUNCT
ejpam-4207	383	15	weakly	weakly	ADJ
ejpam-4207	383	16	b	b	X
ejpam-4207	383	17	-	-	PUNCT
ejpam-4207	383	18	i	i	NOUN
ejpam-4207	383	19	-	-	PUNCT
ejpam-4207	383	20	open	open	ADJ
ejpam-4207	383	21	sets	set	NOUN
ejpam-4207	383	22	and	and	CCONJ
ejpam-4207	383	23	weakly	weakly	ADJ
ejpam-4207	383	24	b	b	X
ejpam-4207	383	25	-	-	PUNCT
ejpam-4207	383	26	icontinuous	icontinuous	ADJ
ejpam-4207	383	27	functiions	functiion	NOUN
ejpam-4207	383	28	,	,	PUNCT
ejpam-4207	383	29	ital	ital	PROPN
ejpam-4207	383	30	.	.	PUNCT
ejpam-4207	384	1	j.	j.	PROPN
ejpam-4207	384	2	pure	pure	PROPN
ejpam-4207	384	3	appl	appl	PROPN
ejpam-4207	384	4	.	.	PUNCT
ejpam-4207	384	5	math	math	PROPN
ejpam-4207	384	6	.	.	PUNCT
ejpam-4207	385	1	n.30	n.30	NOUN
ejpam-4207	385	2	(	(	PUNCT
ejpam-4207	385	3	2013	2013	NUM
ejpam-4207	385	4	)	)	PUNCT
ejpam-4207	385	5	,	,	PUNCT
ejpam-4207	385	6	23–32	23–32	NUM
ejpam-4207	385	7	.	.	PUNCT
ejpam-4207	386	1	[	[	X
ejpam-4207	386	2	26	26	NUM
ejpam-4207	386	3	]	]	PUNCT
ejpam-4207	386	4	t.	t.	PROPN
ejpam-4207	386	5	neubrunnova	neubrunnova	PROPN
ejpam-4207	386	6	,	,	PUNCT
ejpam-4207	386	7	on	on	ADP
ejpam-4207	386	8	certain	certain	ADJ
ejpam-4207	386	9	generalizations	generalization	NOUN
ejpam-4207	386	10	of	of	ADP
ejpam-4207	386	11	the	the	DET
ejpam-4207	386	12	notion	notion	NOUN
ejpam-4207	386	13	of	of	ADP
ejpam-4207	386	14	continuity	continuity	NOUN
ejpam-4207	386	15	,	,	PUNCT
ejpam-4207	386	16	mat	mat	NOUN
ejpam-4207	386	17	.	.	PROPN
ejpam-4207	386	18	casopis	casopis	PROPN
ejpam-4207	386	19	23	23	NUM
ejpam-4207	386	20	(	(	PUNCT
ejpam-4207	386	21	1973	1973	NUM
ejpam-4207	386	22	)	)	PUNCT
ejpam-4207	386	23	,	,	PUNCT
ejpam-4207	387	1	374–380	374–380	NUM
ejpam-4207	387	2	.	.	PUNCT
ejpam-4207	388	1	[	[	X
ejpam-4207	388	2	27	27	NUM
ejpam-4207	388	3	]	]	X
ejpam-4207	388	4	o.	o.	NOUN
ejpam-4207	388	5	nj̊astad	nj̊astad	PROPN
ejpam-4207	388	6	,	,	PUNCT
ejpam-4207	388	7	on	on	ADP
ejpam-4207	388	8	some	some	DET
ejpam-4207	388	9	classes	class	NOUN
ejpam-4207	388	10	of	of	ADP
ejpam-4207	388	11	nearly	nearly	ADV
ejpam-4207	388	12	open	open	ADJ
ejpam-4207	388	13	sets	set	NOUN
ejpam-4207	388	14	,	,	PUNCT
ejpam-4207	388	15	pacific	pacific	PROPN
ejpam-4207	388	16	j.	j.	PROPN
ejpam-4207	388	17	math	math	PROPN
ejpam-4207	388	18	.	.	PUNCT
ejpam-4207	389	1	15	15	NUM
ejpam-4207	389	2	(	(	PUNCT
ejpam-4207	389	3	1965	1965	NUM
ejpam-4207	389	4	)	)	PUNCT
ejpam-4207	389	5	,	,	PUNCT
ejpam-4207	389	6	961–970	961–970	NUM
ejpam-4207	389	7	.	.	PUNCT
ejpam-4207	390	1	[	[	X
ejpam-4207	390	2	28	28	NUM
ejpam-4207	390	3	]	]	X
ejpam-4207	390	4	t.	t.	PROPN
ejpam-4207	390	5	noiri	noiri	PROPN
ejpam-4207	390	6	and	and	CCONJ
ejpam-4207	390	7	v.	v.	ADP
ejpam-4207	390	8	popa	popa	NOUN
ejpam-4207	390	9	,	,	PUNCT
ejpam-4207	390	10	on	on	ADP
ejpam-4207	390	11	upper	upper	ADJ
ejpam-4207	390	12	and	and	CCONJ
ejpam-4207	390	13	lower	low	ADJ
ejpam-4207	390	14	m	m	VERB
ejpam-4207	390	15	-continuous	-continuous	ADJ
ejpam-4207	390	16	multifunctions	multifunction	NOUN
ejpam-4207	390	17	,	,	PUNCT
ejpam-4207	390	18	filomat	filomat	NOUN
ejpam-4207	390	19	14	14	NUM
ejpam-4207	390	20	(	(	PUNCT
ejpam-4207	390	21	2000	2000	NUM
ejpam-4207	390	22	)	)	PUNCT
ejpam-4207	390	23	,	,	PUNCT
ejpam-4207	390	24	73–86	73–86	NUM
ejpam-4207	390	25	.	.	PUNCT
ejpam-4207	391	1	[	[	X
ejpam-4207	391	2	29	29	NUM
ejpam-4207	391	3	]	]	PUNCT
ejpam-4207	391	4	t.	t.	PROPN
ejpam-4207	391	5	noiri	noiri	PROPN
ejpam-4207	391	6	and	and	CCONJ
ejpam-4207	391	7	v.	v.	ADP
ejpam-4207	391	8	popa	popa	NOUN
ejpam-4207	391	9	,	,	PUNCT
ejpam-4207	391	10	a	a	DET
ejpam-4207	391	11	unified	unified	ADJ
ejpam-4207	391	12	theory	theory	NOUN
ejpam-4207	391	13	on	on	ADP
ejpam-4207	391	14	the	the	DET
ejpam-4207	391	15	points	point	NOUN
ejpam-4207	391	16	of	of	ADP
ejpam-4207	391	17	discontinuity	discontinuity	NOUN
ejpam-4207	391	18	for	for	ADP
ejpam-4207	391	19	multifunctions	multifunction	NOUN
ejpam-4207	391	20	,	,	PUNCT
ejpam-4207	391	21	bull	bull	NOUN
ejpam-4207	391	22	.	.	PUNCT
ejpam-4207	391	23	math	math	NOUN
ejpam-4207	391	24	.	.	PUNCT
ejpam-4207	392	1	soc	soc	PROPN
ejpam-4207	392	2	.	.	PUNCT
ejpam-4207	393	1	sci	sci	PROPN
ejpam-4207	393	2	.	.	PROPN
ejpam-4207	393	3	math	math	PROPN
ejpam-4207	393	4	.	.	PUNCT
ejpam-4207	394	1	roumanie	roumanie	PROPN
ejpam-4207	394	2	45(93)(1	45(93)(1	PROPN
ejpam-4207	394	3	-	-	PUNCT
ejpam-4207	394	4	2	2	NUM
ejpam-4207	394	5	)	)	PUNCT
ejpam-4207	394	6	(	(	PUNCT
ejpam-4207	394	7	2002	2002	NUM
ejpam-4207	394	8	)	)	PUNCT
ejpam-4207	394	9	,	,	PUNCT
ejpam-4207	395	1	97–107	97–107	PROPN
ejpam-4207	395	2	.	.	PUNCT
ejpam-4207	396	1	[	[	X
ejpam-4207	396	2	30	30	NUM
ejpam-4207	396	3	]	]	PUNCT
ejpam-4207	396	4	t.	t.	PROPN
ejpam-4207	396	5	noiri	noiri	PROPN
ejpam-4207	396	6	and	and	CCONJ
ejpam-4207	396	7	v.	v.	ADP
ejpam-4207	396	8	popa	popa	NOUN
ejpam-4207	396	9	,	,	PUNCT
ejpam-4207	396	10	a	a	DET
ejpam-4207	396	11	unified	unified	ADJ
ejpam-4207	396	12	theory	theory	NOUN
ejpam-4207	396	13	of	of	ADP
ejpam-4207	396	14	contra	contra	PROPN
ejpam-4207	396	15	-	-	PROPN
ejpam-4207	396	16	i	i	NOUN
ejpam-4207	396	17	-	-	PUNCT
ejpam-4207	396	18	continuous	continuous	ADJ
ejpam-4207	396	19	functions	function	NOUN
ejpam-4207	396	20	in	in	ADP
ejpam-4207	396	21	ideal	ideal	ADJ
ejpam-4207	396	22	topological	topological	ADJ
ejpam-4207	396	23	spaces	space	NOUN
ejpam-4207	396	24	,	,	PUNCT
ejpam-4207	396	25	anal	anal	PROPN
ejpam-4207	396	26	.	.	PUNCT
ejpam-4207	397	1	univ	univ	PROPN
ejpam-4207	397	2	.	.	PUNCT
ejpam-4207	398	1	sci	sci	PROPN
ejpam-4207	398	2	.	.	PUNCT
ejpam-4207	398	3	budapest	budapest	PROPN
ejpam-4207	398	4	.	.	PUNCT
ejpam-4207	399	1	math	math	NOUN
ejpam-4207	399	2	.	.	PUNCT
ejpam-4207	400	1	63	63	NUM
ejpam-4207	400	2	(	(	PUNCT
ejpam-4207	400	3	2020	2020	NUM
ejpam-4207	400	4	)	)	PUNCT
ejpam-4207	400	5	,	,	PUNCT
ejpam-4207	400	6	3–17	3–17	PROPN
ejpam-4207	400	7	.	.	PUNCT
ejpam-4207	401	1	[	[	X
ejpam-4207	401	2	31	31	NUM
ejpam-4207	401	3	]	]	PUNCT
ejpam-4207	401	4	t.	t.	PROPN
ejpam-4207	401	5	noiri	noiri	PROPN
ejpam-4207	401	6	and	and	CCONJ
ejpam-4207	401	7	v.	v.	ADP
ejpam-4207	401	8	popa	popa	NOUN
ejpam-4207	401	9	,	,	PUNCT
ejpam-4207	401	10	faintly	faintly	ADV
ejpam-4207	401	11	m	m	PROPN
ejpam-4207	401	12	-	-	ADJ
ejpam-4207	401	13	i	i	ADV
ejpam-4207	401	14	-	-	PUNCT
ejpam-4207	401	15	continuous	continuous	ADJ
ejpam-4207	401	16	multifunctions	multifunction	NOUN
ejpam-4207	401	17	,	,	PUNCT
ejpam-4207	401	18	eur	eur	PROPN
ejpam-4207	401	19	.	.	PUNCT
ejpam-4207	401	20	bull	bull	PROPN
ejpam-4207	401	21	.	.	PUNCT
ejpam-4207	402	1	math	math	NOUN
ejpam-4207	402	2	.	.	PUNCT
ejpam-4207	403	1	3(2	3(2	NUM
ejpam-4207	403	2	)	)	PUNCT
ejpam-4207	403	3	(	(	PUNCT
ejpam-4207	403	4	2020	2020	NUM
ejpam-4207	403	5	)	)	PUNCT
ejpam-4207	403	6	,	,	PUNCT
ejpam-4207	404	1	103–113	103–113	NUM
ejpam-4207	404	2	.	.	PUNCT
ejpam-4207	405	1	[	[	X
ejpam-4207	405	2	32	32	NUM
ejpam-4207	405	3	]	]	PUNCT
ejpam-4207	405	4	v.	v.	CCONJ
ejpam-4207	405	5	popa	popa	NOUN
ejpam-4207	405	6	,	,	PUNCT
ejpam-4207	405	7	multifonctions	multifonction	NOUN
ejpam-4207	405	8	semi	semi	NOUN
ejpam-4207	405	9	-	-	NOUN
ejpam-4207	405	10	continues	continue	NOUN
ejpam-4207	405	11	,	,	PUNCT
ejpam-4207	405	12	rev	rev	PROPN
ejpam-4207	405	13	.	.	PROPN
ejpam-4207	405	14	roumaine	roumaine	PROPN
ejpam-4207	405	15	math	math	NOUN
ejpam-4207	405	16	.	.	PUNCT
ejpam-4207	406	1	pures	pure	NOUN
ejpam-4207	406	2	appl	appl	PROPN
ejpam-4207	406	3	.	.	PROPN
ejpam-4207	407	1	27	27	NUM
ejpam-4207	407	2	(	(	PUNCT
ejpam-4207	407	3	1982	1982	NUM
ejpam-4207	407	4	)	)	PUNCT
ejpam-4207	407	5	,	,	PUNCT
ejpam-4207	407	6	807–815	807–815	NUM
ejpam-4207	407	7	.	.	PUNCT
ejpam-4207	408	1	[	[	X
ejpam-4207	408	2	33	33	NUM
ejpam-4207	408	3	]	]	PUNCT
ejpam-4207	408	4	v.	v.	CCONJ
ejpam-4207	408	5	popa	popa	NOUN
ejpam-4207	408	6	,	,	PUNCT
ejpam-4207	408	7	some	some	DET
ejpam-4207	408	8	characterizations	characterization	NOUN
ejpam-4207	408	9	of	of	ADP
ejpam-4207	408	10	quasicontinuous	quasicontinuous	ADJ
ejpam-4207	408	11	and	and	CCONJ
ejpam-4207	408	12	weakly	weakly	ADJ
ejpam-4207	408	13	continuous	continuous	ADJ
ejpam-4207	408	14	multifunctions	multifunction	NOUN
ejpam-4207	408	15	(	(	PUNCT
ejpam-4207	408	16	romanian	romanian	NOUN
ejpam-4207	408	17	)	)	PUNCT
ejpam-4207	408	18	,	,	PUNCT
ejpam-4207	408	19	stud	stud	NOUN
ejpam-4207	408	20	.	.	PUNCT
ejpam-4207	409	1	cerc	cerc	PROPN
ejpam-4207	409	2	.	.	PUNCT
ejpam-4207	410	1	mat	mat	NOUN
ejpam-4207	410	2	.	.	PROPN
ejpam-4207	410	3	37	37	NUM
ejpam-4207	410	4	(	(	PUNCT
ejpam-4207	410	5	1985	1985	NUM
ejpam-4207	410	6	)	)	PUNCT
ejpam-4207	410	7	,	,	PUNCT
ejpam-4207	410	8	77–82	77–82	X
ejpam-4207	410	9	.	.	PUNCT
ejpam-4207	411	1	[	[	X
ejpam-4207	411	2	34	34	NUM
ejpam-4207	411	3	]	]	PUNCT
ejpam-4207	411	4	v.	v.	CCONJ
ejpam-4207	411	5	popa	popa	NOUN
ejpam-4207	411	6	,	,	PUNCT
ejpam-4207	411	7	some	some	DET
ejpam-4207	411	8	properties	property	NOUN
ejpam-4207	411	9	of	of	ADP
ejpam-4207	411	10	h	h	NOUN
ejpam-4207	411	11	-	-	PUNCT
ejpam-4207	411	12	almost	almost	ADV
ejpam-4207	411	13	continuous	continuous	ADJ
ejpam-4207	411	14	multifunctions	multifunction	NOUN
ejpam-4207	411	15	,	,	PUNCT
ejpam-4207	411	16	problemy	problemy	PROPN
ejpam-4207	411	17	mat	mat	NOUN
ejpam-4207	411	18	.	.	PROPN
ejpam-4207	411	19	10	10	NUM
ejpam-4207	411	20	(	(	PUNCT
ejpam-4207	411	21	1988	1988	NUM
ejpam-4207	411	22	)	)	PUNCT
ejpam-4207	411	23	,	,	PUNCT
ejpam-4207	411	24	9–26	9–26	NOUN
ejpam-4207	411	25	.	.	PUNCT
ejpam-4207	412	1	[	[	X
ejpam-4207	412	2	35	35	NUM
ejpam-4207	412	3	]	]	PUNCT
ejpam-4207	412	4	v.	v.	CCONJ
ejpam-4207	412	5	popa	popa	NOUN
ejpam-4207	412	6	and	and	CCONJ
ejpam-4207	412	7	t.	t.	PROPN
ejpam-4207	412	8	noiri	noiri	PROPN
ejpam-4207	412	9	,	,	PUNCT
ejpam-4207	412	10	on	on	ADP
ejpam-4207	412	11	upper	upper	ADJ
ejpam-4207	412	12	and	and	CCONJ
ejpam-4207	412	13	lower	low	ADJ
ejpam-4207	412	14	α	α	ADJ
ejpam-4207	412	15	-	-	ADJ
ejpam-4207	412	16	continuous	continuous	ADJ
ejpam-4207	412	17	multifunctions	multifunction	NOUN
ejpam-4207	412	18	,	,	PUNCT
ejpam-4207	412	19	math	math	NOUN
ejpam-4207	412	20	.	.	PUNCT
ejpam-4207	413	1	slovaca	slovaca	NOUN
ejpam-4207	413	2	43	43	NUM
ejpam-4207	413	3	(	(	PUNCT
ejpam-4207	413	4	1993	1993	NUM
ejpam-4207	413	5	)	)	PUNCT
ejpam-4207	413	6	,	,	PUNCT
ejpam-4207	413	7	477–491	477–491	NUM
ejpam-4207	413	8	.	.	PUNCT
ejpam-4207	414	1	[	[	X
ejpam-4207	414	2	36	36	NUM
ejpam-4207	414	3	]	]	X
ejpam-4207	414	4	v.	v.	CCONJ
ejpam-4207	414	5	popa	popa	NOUN
ejpam-4207	414	6	and	and	CCONJ
ejpam-4207	414	7	t.	t.	PROPN
ejpam-4207	414	8	noiri	noiri	PROPN
ejpam-4207	414	9	,	,	PUNCT
ejpam-4207	414	10	characterizations	characterization	NOUN
ejpam-4207	414	11	of	of	ADP
ejpam-4207	414	12	α	α	NOUN
ejpam-4207	414	13	-	-	ADJ
ejpam-4207	414	14	continuous	continuous	ADJ
ejpam-4207	414	15	multifunctions	multifunction	NOUN
ejpam-4207	414	16	,	,	PUNCT
ejpam-4207	414	17	univ	univ	PROPN
ejpam-4207	414	18	.	.	PUNCT
ejpam-4207	415	1	u	u	PROPN
ejpam-4207	415	2	novom	novom	ADJ
ejpam-4207	415	3	sadu	sadu	NOUN
ejpam-4207	415	4	,	,	PUNCT
ejpam-4207	415	5	zb	zb	PROPN
ejpam-4207	415	6	.	.	PUNCT
ejpam-4207	415	7	rad	rad	PROPN
ejpam-4207	415	8	.	.	PROPN
ejpam-4207	415	9	prirod	prirod	PROPN
ejpam-4207	415	10	mat	mat	PROPN
ejpam-4207	415	11	.	.	PUNCT
ejpam-4207	415	12	fac	fac	PROPN
ejpam-4207	415	13	.	.	PUNCT
ejpam-4207	415	14	ser	ser	PROPN
ejpam-4207	415	15	.	.	PROPN
ejpam-4207	415	16	mat	mat	PROPN
ejpam-4207	415	17	.	.	PROPN
ejpam-4207	415	18	23	23	NUM
ejpam-4207	415	19	(	(	PUNCT
ejpam-4207	415	20	1993	1993	NUM
ejpam-4207	415	21	)	)	PUNCT
ejpam-4207	415	22	,	,	PUNCT
ejpam-4207	415	23	29–38	29–38	NUM
ejpam-4207	415	24	.	.	PUNCT
ejpam-4207	416	1	[	[	X
ejpam-4207	416	2	37	37	NUM
ejpam-4207	416	3	]	]	PUNCT
ejpam-4207	416	4	v.	v.	CCONJ
ejpam-4207	416	5	popa	popa	NOUN
ejpam-4207	416	6	and	and	CCONJ
ejpam-4207	416	7	t.	t.	PROPN
ejpam-4207	416	8	noiri	noiri	PROPN
ejpam-4207	416	9	,	,	PUNCT
ejpam-4207	416	10	some	some	DET
ejpam-4207	416	11	properties	property	NOUN
ejpam-4207	416	12	of	of	ADP
ejpam-4207	416	13	β	β	ADJ
ejpam-4207	416	14	-	-	ADJ
ejpam-4207	416	15	continuous	continuous	ADJ
ejpam-4207	416	16	multifunctions	multifunction	NOUN
ejpam-4207	416	17	,	,	PUNCT
ejpam-4207	416	18	anal	anal	PROPN
ejpam-4207	416	19	.	.	PUNCT
ejpam-4207	416	20	st	st	PROPN
ejpam-4207	416	21	.	.	PROPN
ejpam-4207	416	22	univ	univ	PROPN
ejpam-4207	416	23	.	.	PUNCT
ejpam-4207	416	24	”	"	PUNCT
ejpam-4207	416	25	al	al	PROPN
ejpam-4207	416	26	.	.	PROPN
ejpam-4207	416	27	i.	i.	PROPN
ejpam-4207	416	28	cuza	cuza	PROPN
ejpam-4207	416	29	”	"	PUNCT
ejpam-4207	416	30	iaşi	iaşi	VERB
ejpam-4207	416	31	42	42	NUM
ejpam-4207	416	32	,	,	PUNCT
ejpam-4207	416	33	supl	supl	NOUN
ejpam-4207	416	34	.	.	PUNCT
ejpam-4207	417	1	s.i.a	s.i.a	NOUN
ejpam-4207	417	2	,	,	PUNCT
ejpam-4207	417	3	mat	mat	NOUN
ejpam-4207	417	4	.	.	PUNCT
ejpam-4207	417	5	(	(	PUNCT
ejpam-4207	417	6	1996	1996	NUM
ejpam-4207	417	7	)	)	PUNCT
ejpam-4207	417	8	,	,	PUNCT
ejpam-4207	417	9	207–215	207–215	NUM
ejpam-4207	417	10	.	.	PUNCT
ejpam-4207	418	1	[	[	X
ejpam-4207	418	2	38	38	NUM
ejpam-4207	418	3	]	]	PUNCT
ejpam-4207	418	4	v.	v.	CCONJ
ejpam-4207	418	5	popa	popa	NOUN
ejpam-4207	418	6	and	and	CCONJ
ejpam-4207	418	7	t.	t.	PROPN
ejpam-4207	418	8	noiri	noiri	PROPN
ejpam-4207	418	9	,	,	PUNCT
ejpam-4207	418	10	on	on	ADP
ejpam-4207	418	11	upper	upper	ADJ
ejpam-4207	418	12	and	and	CCONJ
ejpam-4207	418	13	lower	low	ADJ
ejpam-4207	418	14	β	β	ADJ
ejpam-4207	418	15	-	-	ADJ
ejpam-4207	418	16	continuous	continuous	ADJ
ejpam-4207	418	17	multifunctions	multifunction	NOUN
ejpam-4207	418	18	,	,	PUNCT
ejpam-4207	418	19	real	real	ADJ
ejpam-4207	418	20	anal	anal	NOUN
ejpam-4207	418	21	.	.	PUNCT
ejpam-4207	419	1	exchange	exchange	NOUN
ejpam-4207	419	2	22	22	NUM
ejpam-4207	419	3	(	(	PUNCT
ejpam-4207	419	4	1996/97	1996/97	NUM
ejpam-4207	419	5	)	)	PUNCT
ejpam-4207	419	6	,	,	PUNCT
ejpam-4207	419	7	362–376	362–376	NUM
ejpam-4207	419	8	.	.	PUNCT
ejpam-4207	420	1	references	reference	NOUN
ejpam-4207	420	2	14	14	NUM
ejpam-4207	421	1	[	[	X
ejpam-4207	421	2	39	39	NUM
ejpam-4207	421	3	]	]	PUNCT
ejpam-4207	421	4	v.	v.	CCONJ
ejpam-4207	421	5	popa	popa	NOUN
ejpam-4207	421	6	and	and	CCONJ
ejpam-4207	421	7	t.	t.	PROPN
ejpam-4207	421	8	noiri	noiri	PROPN
ejpam-4207	421	9	,	,	PUNCT
ejpam-4207	421	10	a	a	DET
ejpam-4207	421	11	note	note	NOUN
ejpam-4207	421	12	on	on	ADP
ejpam-4207	421	13	precontinuity	precontinuity	NOUN
ejpam-4207	421	14	and	and	CCONJ
ejpam-4207	421	15	quasicontinuity	quasicontinuity	NOUN
ejpam-4207	421	16	for	for	ADP
ejpam-4207	421	17	multifunctions	multifunction	NOUN
ejpam-4207	421	18	,	,	PUNCT
ejpam-4207	421	19	demonstratio	demonstratio	PROPN
ejpam-4207	421	20	math	math	PROPN
ejpam-4207	421	21	.	.	PUNCT
ejpam-4207	422	1	30	30	NUM
ejpam-4207	422	2	(	(	PUNCT
ejpam-4207	422	3	1997	1997	NUM
ejpam-4207	422	4	)	)	PUNCT
ejpam-4207	422	5	,	,	PUNCT
ejpam-4207	422	6	271–278	271–278	NUM
ejpam-4207	422	7	.	.	PUNCT
ejpam-4207	423	1	[	[	X
ejpam-4207	423	2	40	40	NUM
ejpam-4207	423	3	]	]	PUNCT
ejpam-4207	423	4	v.	v.	CCONJ
ejpam-4207	423	5	popa	popa	NOUN
ejpam-4207	423	6	and	and	CCONJ
ejpam-4207	423	7	t.	t.	PROPN
ejpam-4207	423	8	noiri	noiri	PROPN
ejpam-4207	423	9	,	,	PUNCT
ejpam-4207	423	10	on	on	ADP
ejpam-4207	423	11	m	m	ADJ
ejpam-4207	423	12	-	-	ADJ
ejpam-4207	423	13	continuous	continuous	ADJ
ejpam-4207	423	14	functions	function	NOUN
ejpam-4207	423	15	,	,	PUNCT
ejpam-4207	423	16	anal	anal	NOUN
ejpam-4207	423	17	.	.	PUNCT
ejpam-4207	423	18	univ	univ	PROPN
ejpam-4207	423	19	.	.	PUNCT
ejpam-4207	423	20	”	"	PUNCT
ejpam-4207	423	21	dunǎrea	dunǎrea	PROPN
ejpam-4207	423	22	de	de	X
ejpam-4207	423	23	jos	jos	PROPN
ejpam-4207	423	24	”	"	PUNCT
ejpam-4207	423	25	gala̧ti	gala̧ti	PROPN
ejpam-4207	423	26	,	,	PUNCT
ejpam-4207	423	27	ser	ser	PROPN
ejpam-4207	423	28	.	.	PROPN
ejpam-4207	423	29	mat	mat	PROPN
ejpam-4207	423	30	.	.	PUNCT
ejpam-4207	423	31	fiz	fiz	PROPN
ejpam-4207	423	32	.	.	PUNCT
ejpam-4207	424	1	mec	mec	PROPN
ejpam-4207	424	2	.	.	PROPN
ejpam-4207	424	3	teor	teor	PROPN
ejpam-4207	424	4	.	.	PROPN
ejpam-4207	424	5	,	,	PUNCT
ejpam-4207	424	6	fasc	fasc	PROPN
ejpam-4207	424	7	.	.	PROPN
ejpam-4207	424	8	ii	ii	PROPN
ejpam-4207	424	9	18	18	NUM
ejpam-4207	424	10	(	(	PUNCT
ejpam-4207	424	11	23	23	NUM
ejpam-4207	424	12	)	)	PUNCT
ejpam-4207	424	13	(	(	PUNCT
ejpam-4207	424	14	2000	2000	NUM
ejpam-4207	424	15	)	)	PUNCT
ejpam-4207	424	16	,	,	PUNCT
ejpam-4207	424	17	31–41	31–41	NUM
ejpam-4207	424	18	.	.	PUNCT
ejpam-4207	425	1	[	[	X
ejpam-4207	425	2	41	41	X
ejpam-4207	425	3	]	]	PUNCT
ejpam-4207	425	4	v.	v.	CCONJ
ejpam-4207	425	5	popa	popa	NOUN
ejpam-4207	425	6	and	and	CCONJ
ejpam-4207	425	7	t.	t.	PROPN
ejpam-4207	425	8	noiri	noiri	PROPN
ejpam-4207	425	9	,	,	PUNCT
ejpam-4207	425	10	on	on	ADP
ejpam-4207	425	11	the	the	DET
ejpam-4207	425	12	definitions	definition	NOUN
ejpam-4207	425	13	of	of	ADP
ejpam-4207	425	14	some	some	DET
ejpam-4207	425	15	generalized	generalized	ADJ
ejpam-4207	425	16	forms	form	NOUN
ejpam-4207	425	17	of	of	ADP
ejpam-4207	425	18	continuity	continuity	NOUN
ejpam-4207	425	19	under	under	ADP
ejpam-4207	425	20	minimal	minimal	ADJ
ejpam-4207	425	21	conditions	condition	NOUN
ejpam-4207	425	22	,	,	PUNCT
ejpam-4207	425	23	mem	mem	PROPN
ejpam-4207	425	24	.	.	PUNCT
ejpam-4207	425	25	fac	fac	PROPN
ejpam-4207	425	26	.	.	PUNCT
ejpam-4207	426	1	sci	sci	PROPN
ejpam-4207	426	2	.	.	PROPN
ejpam-4207	426	3	kochi	kochi	PROPN
ejpam-4207	426	4	univ	univ	PROPN
ejpam-4207	426	5	.	.	PUNCT
ejpam-4207	426	6	math	math	PROPN
ejpam-4207	426	7	.	.	PUNCT
ejpam-4207	427	1	ser	ser	PROPN
ejpam-4207	427	2	.	.	PROPN
ejpam-4207	428	1	22	22	NUM
ejpam-4207	428	2	(	(	PUNCT
ejpam-4207	428	3	2001	2001	NUM
ejpam-4207	428	4	)	)	PUNCT
ejpam-4207	428	5	,	,	PUNCT
ejpam-4207	428	6	9–19	9–19	NOUN
ejpam-4207	428	7	.	.	PUNCT
ejpam-4207	429	1	[	[	X
ejpam-4207	429	2	42	42	NUM
ejpam-4207	429	3	]	]	PUNCT
ejpam-4207	429	4	v.	v.	CCONJ
ejpam-4207	429	5	popa	popa	NOUN
ejpam-4207	429	6	and	and	CCONJ
ejpam-4207	429	7	t.	t.	PROPN
ejpam-4207	429	8	noiri	noiri	PROPN
ejpam-4207	429	9	,	,	PUNCT
ejpam-4207	429	10	on	on	ADP
ejpam-4207	429	11	m	m	ADJ
ejpam-4207	429	12	-	-	ADJ
ejpam-4207	429	13	continuous	continuous	ADJ
ejpam-4207	429	14	multifunctions	multifunction	NOUN
ejpam-4207	429	15	,	,	PUNCT
ejpam-4207	429	16	bul	bul	PROPN
ejpam-4207	429	17	.	.	PUNCT
ejpam-4207	429	18	st	st	PROPN
ejpam-4207	429	19	.	.	PROPN
ejpam-4207	429	20	univ	univ	PROPN
ejpam-4207	429	21	.	.	PUNCT
ejpam-4207	430	1	politeh	politeh	PROPN
ejpam-4207	430	2	.	.	PUNCT
ejpam-4207	431	1	timisoara	timisoara	PROPN
ejpam-4207	431	2	,	,	PUNCT
ejpam-4207	431	3	ser	ser	PROPN
ejpam-4207	431	4	.	.	PROPN
ejpam-4207	431	5	mat	mat	PROPN
ejpam-4207	431	6	.	.	PUNCT
ejpam-4207	432	1	fiz	fiz	PROPN
ejpam-4207	432	2	.	.	PUNCT
ejpam-4207	433	1	46	46	NUM
ejpam-4207	433	2	(	(	PUNCT
ejpam-4207	433	3	60)(2	60)(2	NOUN
ejpam-4207	433	4	)	)	PUNCT
ejpam-4207	433	5	(	(	PUNCT
ejpam-4207	433	6	2001	2001	NUM
ejpam-4207	433	7	)	)	PUNCT
ejpam-4207	433	8	,	,	PUNCT
ejpam-4207	433	9	1–12	1–12	NOUN
ejpam-4207	433	10	.	.	PUNCT
ejpam-4207	434	1	[	[	X
ejpam-4207	434	2	43	43	NUM
ejpam-4207	434	3	]	]	X
ejpam-4207	434	4	v.	v.	CCONJ
ejpam-4207	434	5	popa	popa	NOUN
ejpam-4207	434	6	and	and	CCONJ
ejpam-4207	434	7	t.	t.	PROPN
ejpam-4207	434	8	noiri	noiri	PROPN
ejpam-4207	434	9	,	,	PUNCT
ejpam-4207	434	10	a	a	DET
ejpam-4207	434	11	unified	unified	ADJ
ejpam-4207	434	12	theory	theory	NOUN
ejpam-4207	434	13	of	of	ADP
ejpam-4207	434	14	weak	weak	ADJ
ejpam-4207	434	15	continuity	continuity	NOUN
ejpam-4207	434	16	for	for	ADP
ejpam-4207	434	17	functions	function	NOUN
ejpam-4207	434	18	,	,	PUNCT
ejpam-4207	434	19	rend	rend	VERB
ejpam-4207	434	20	.	.	PUNCT
ejpam-4207	435	1	circ	circ	PROPN
ejpam-4207	435	2	.	.	PUNCT
ejpam-4207	436	1	mat	mat	PROPN
ejpam-4207	436	2	.	.	PUNCT
ejpam-4207	436	3	palermo	palermo	PROPN
ejpam-4207	436	4	(	(	PUNCT
ejpam-4207	436	5	2	2	NUM
ejpam-4207	436	6	)	)	PUNCT
ejpam-4207	436	7	51	51	NUM
ejpam-4207	436	8	(	(	PUNCT
ejpam-4207	436	9	2002	2002	NUM
ejpam-4207	436	10	)	)	PUNCT
ejpam-4207	436	11	,	,	PUNCT
ejpam-4207	436	12	439–464	439–464	NUM
ejpam-4207	436	13	.	.	PUNCT
ejpam-4207	437	1	[	[	X
ejpam-4207	437	2	44	44	NUM
ejpam-4207	437	3	]	]	PUNCT
ejpam-4207	437	4	v.	v.	CCONJ
ejpam-4207	437	5	popa	popa	NOUN
ejpam-4207	437	6	and	and	CCONJ
ejpam-4207	437	7	t.	t.	PROPN
ejpam-4207	437	8	noiri	noiri	PROPN
ejpam-4207	437	9	,	,	PUNCT
ejpam-4207	437	10	a	a	DET
ejpam-4207	437	11	unified	unified	ADJ
ejpam-4207	437	12	theory	theory	NOUN
ejpam-4207	437	13	of	of	ADP
ejpam-4207	437	14	the	the	DET
ejpam-4207	437	15	points	point	NOUN
ejpam-4207	437	16	of	of	ADP
ejpam-4207	437	17	continuity	continuity	NOUN
ejpam-4207	437	18	and	and	CCONJ
ejpam-4207	437	19	discontinuity	discontinuity	NOUN
ejpam-4207	437	20	for	for	ADP
ejpam-4207	437	21	multifunctions	multifunction	NOUN
ejpam-4207	437	22	,	,	PUNCT
ejpam-4207	437	23	annal	annal	PROPN
ejpam-4207	437	24	.	.	PUNCT
ejpam-4207	438	1	univ	univ	PROPN
ejpam-4207	438	2	.	.	PUNCT
ejpam-4207	439	1	de	de	ADP
ejpam-4207	439	2	vest	vest	ADJ
ejpam-4207	439	3	timisoara	timisoara	PROPN
ejpam-4207	439	4	ser	ser	PROPN
ejpam-4207	439	5	.	.	PROPN
ejpam-4207	439	6	math	math	PROPN
ejpam-4207	439	7	.	.	PUNCT
ejpam-4207	440	1	inform	inform	NOUN
ejpam-4207	440	2	.	.	PUNCT
ejpam-4207	441	1	61(1	61(1	X
ejpam-4207	441	2	)	)	PUNCT
ejpam-4207	441	3	(	(	PUNCT
ejpam-4207	441	4	2003	2003	NUM
ejpam-4207	441	5	)	)	PUNCT
ejpam-4207	441	6	,	,	PUNCT
ejpam-4207	441	7	9–19	9–19	NOUN
ejpam-4207	441	8	.	.	PUNCT
ejpam-4207	442	1	[	[	X
ejpam-4207	442	2	45	45	NUM
ejpam-4207	442	3	]	]	PUNCT
ejpam-4207	442	4	v.	v.	CCONJ
ejpam-4207	442	5	popa	popa	NOUN
ejpam-4207	442	6	and	and	CCONJ
ejpam-4207	442	7	t.	t.	PROPN
ejpam-4207	442	8	noiri	noiri	PROPN
ejpam-4207	442	9	,	,	PUNCT
ejpam-4207	442	10	upper	upper	ADJ
ejpam-4207	442	11	and	and	CCONJ
ejpam-4207	442	12	lower	low	ADJ
ejpam-4207	442	13	m	m	PROPN
ejpam-4207	442	14	-	-	ADJ
ejpam-4207	442	15	i	i	ADV
ejpam-4207	442	16	-	-	PUNCT
ejpam-4207	442	17	continuous	continuous	ADJ
ejpam-4207	442	18	multifunctions	multifunction	NOUN
ejpam-4207	442	19	,	,	PUNCT
ejpam-4207	442	20	sci	sci	PROPN
ejpam-4207	442	21	.	.	PROPN
ejpam-4207	442	22	stud	stud	PROPN
ejpam-4207	442	23	.	.	PUNCT
ejpam-4207	443	1	res	re	NOUN
ejpam-4207	443	2	.	.	PROPN
ejpam-4207	443	3	math	math	NOUN
ejpam-4207	443	4	.	.	PUNCT
ejpam-4207	444	1	inform	inform	NOUN
ejpam-4207	444	2	.	.	PUNCT
ejpam-4207	445	1	29(2	29(2	X
ejpam-4207	445	2	)	)	PUNCT
ejpam-4207	445	3	(	(	PUNCT
ejpam-4207	445	4	2019	2019	NUM
ejpam-4207	445	5	)	)	PUNCT
ejpam-4207	445	6	,	,	PUNCT
ejpam-4207	445	7	51–64	51–64	PROPN
ejpam-4207	445	8	.	.	PUNCT
ejpam-4207	446	1	[	[	X
ejpam-4207	446	2	46	46	NUM
ejpam-4207	446	3	]	]	X
ejpam-4207	446	4	m.	m.	NOUN
ejpam-4207	446	5	przemski	przemski	PROPN
ejpam-4207	446	6	,	,	PUNCT
ejpam-4207	446	7	some	some	DET
ejpam-4207	446	8	generalizations	generalization	NOUN
ejpam-4207	446	9	of	of	ADP
ejpam-4207	446	10	continuity	continuity	NOUN
ejpam-4207	446	11	and	and	CCONJ
ejpam-4207	446	12	quasicontinuity	quasicontinuity	NOUN
ejpam-4207	446	13	of	of	ADP
ejpam-4207	446	14	multivalued	multivalued	ADJ
ejpam-4207	446	15	maps	map	NOUN
ejpam-4207	446	16	,	,	PUNCT
ejpam-4207	446	17	demonstratio	demonstratio	PROPN
ejpam-4207	446	18	math	math	PROPN
ejpam-4207	446	19	.	.	PUNCT
ejpam-4207	447	1	26	26	NUM
ejpam-4207	447	2	(	(	PUNCT
ejpam-4207	447	3	1993	1993	NUM
ejpam-4207	447	4	)	)	PUNCT
ejpam-4207	447	5	,	,	PUNCT
ejpam-4207	448	1	381–400	381–400	NUM
ejpam-4207	448	2	.	.	PUNCT
ejpam-4207	449	1	[	[	X
ejpam-4207	449	2	47	47	NUM
ejpam-4207	449	3	]	]	X
ejpam-4207	449	4	r.	r.	PROPN
ejpam-4207	449	5	vaidyanathaswani	vaidyanathaswani	PROPN
ejpam-4207	449	6	,	,	PUNCT
ejpam-4207	449	7	the	the	DET
ejpam-4207	449	8	localization	localization	NOUN
ejpam-4207	449	9	theory	theory	NOUN
ejpam-4207	449	10	in	in	ADP
ejpam-4207	449	11	set	set	NOUN
ejpam-4207	449	12	-	-	PUNCT
ejpam-4207	449	13	topology	topology	NOUN
ejpam-4207	449	14	,	,	PUNCT
ejpam-4207	449	15	proc	proc	NOUN
ejpam-4207	449	16	.	.	PUNCT
ejpam-4207	450	1	indian	indian	PROPN
ejpam-4207	450	2	acad	acad	PROPN
ejpam-4207	450	3	.	.	PUNCT
ejpam-4207	451	1	sci	sci	PROPN
ejpam-4207	451	2	.	.	PROPN
ejpam-4207	451	3	20	20	NUM
ejpam-4207	451	4	(	(	PUNCT
ejpam-4207	451	5	1945	1945	NUM
ejpam-4207	451	6	)	)	PUNCT
ejpam-4207	451	7	,	,	PUNCT
ejpam-4207	451	8	51–61	51–61	NUM
ejpam-4207	451	9	.	.	PUNCT
ejpam-4207	452	1	[	[	X
ejpam-4207	452	2	48	48	NUM
ejpam-4207	452	3	]	]	PUNCT
ejpam-4207	452	4	j.	j.	PROPN
ejpam-4207	452	5	d.	d.	PROPN
ejpam-4207	452	6	wine	wine	PROPN
ejpam-4207	452	7	,	,	PUNCT
ejpam-4207	452	8	locally	locally	ADV
ejpam-4207	452	9	paracompact	paracompact	ADJ
ejpam-4207	452	10	spaces	space	NOUN
ejpam-4207	452	11	,	,	PUNCT
ejpam-4207	452	12	glasnik	glasnik	PROPN
ejpam-4207	452	13	mat	mat	PROPN
ejpam-4207	452	14	.	.	PUNCT
ejpam-4207	452	15	ser	ser	PROPN
ejpam-4207	452	16	.	.	PUNCT
ejpam-4207	453	1	iii	iii	NUM
ejpam-4207	454	1	10(30	10(30	NUM
ejpam-4207	454	2	)	)	PUNCT
ejpam-4207	454	3	(	(	PUNCT
ejpam-4207	454	4	1975	1975	NUM
ejpam-4207	454	5	)	)	PUNCT
ejpam-4207	454	6	,	,	PUNCT
ejpam-4207	454	7	351–357	351–357	NUM
ejpam-4207	454	8	.	.	PUNCT