id	sid	tid	token	lemma	pos
ejpam-4691	1	1	european	european	PROPN
ejpam-4691	1	2	journal	journal	PROPN
ejpam-4691	1	3	of	of	ADP
ejpam-4691	1	4	pure	pure	ADJ
ejpam-4691	1	5	and	and	CCONJ
ejpam-4691	1	6	applied	apply	VERB
ejpam-4691	1	7	mathematics	mathematic	NOUN
ejpam-4691	1	8	vol	vol	NOUN
ejpam-4691	1	9	.	.	PUNCT
ejpam-4691	2	1	16	16	NUM
ejpam-4691	2	2	,	,	PUNCT
ejpam-4691	2	3	no	no	INTJ
ejpam-4691	2	4	.	.	NOUN
ejpam-4691	2	5	1	1	NUM
ejpam-4691	2	6	,	,	PUNCT
ejpam-4691	2	7	2023	2023	NUM
ejpam-4691	2	8	,	,	PUNCT
ejpam-4691	2	9	430	430	NUM
ejpam-4691	2	10	-	-	SYM
ejpam-4691	2	11	439	439	NUM
ejpam-4691	2	12	issn	issn	PROPN
ejpam-4691	2	13	1307	1307	NUM
ejpam-4691	2	14	-	-	SYM
ejpam-4691	2	15	5543	5543	NUM
ejpam-4691	2	16	–	–	PUNCT
ejpam-4691	3	1	ejpam.com	ejpam.com	X
ejpam-4691	3	2	published	publish	VERB
ejpam-4691	3	3	by	by	ADP
ejpam-4691	3	4	new	new	PROPN
ejpam-4691	3	5	york	york	PROPN
ejpam-4691	3	6	business	business	PROPN
ejpam-4691	3	7	global	global	ADJ
ejpam-4691	3	8	some	some	DET
ejpam-4691	3	9	forms	form	NOUN
ejpam-4691	3	10	of	of	ADP
ejpam-4691	3	11	open	open	ADJ
ejpam-4691	3	12	multifunctions	multifunction	NOUN
ejpam-4691	3	13	in	in	ADP
ejpam-4691	3	14	ideal	ideal	ADJ
ejpam-4691	3	15	topological	topological	ADJ
ejpam-4691	3	16	spaces	space	NOUN
ejpam-4691	3	17	takashi	takashi	PROPN
ejpam-4691	3	18	noiri	noiri	PROPN
ejpam-4691	3	19	1,∗	1,∗	PROPN
ejpam-4691	3	20	,	,	PUNCT
ejpam-4691	3	21	valeriu	valeriu	PROPN
ejpam-4691	3	22	popa2	popa2	NOUN
ejpam-4691	3	23	1	1	NUM
ejpam-4691	3	24	shiokita	shiokita	NOUN
ejpam-4691	3	25	-	-	PUNCT
ejpam-4691	3	26	cho	cho	ADJ
ejpam-4691	3	27	,	,	PUNCT
ejpam-4691	3	28	hinagu	hinagu	ADJ
ejpam-4691	3	29	,	,	PUNCT
ejpam-4691	3	30	yatsushiro	yatsushiro	PROPN
ejpam-4691	3	31	-	-	PUNCT
ejpam-4691	3	32	shi	shi	PROPN
ejpam-4691	3	33	,	,	PUNCT
ejpam-4691	3	34	kumamoto	kumamoto	PROPN
ejpam-4691	3	35	-	-	PUNCT
ejpam-4691	3	36	ken	ken	PROPN
ejpam-4691	3	37	,	,	PUNCT
ejpam-4691	3	38	869	869	NUM
ejpam-4691	3	39	-	-	SYM
ejpam-4691	3	40	5142	5142	NUM
ejpam-4691	3	41	japan	japan	PROPN
ejpam-4691	3	42	2	2	NUM
ejpam-4691	3	43	department	department	NOUN
ejpam-4691	3	44	of	of	ADP
ejpam-4691	3	45	mathematics	mathematic	NOUN
ejpam-4691	3	46	,	,	PUNCT
ejpam-4691	3	47	university	university	NOUN
ejpam-4691	3	48	of	of	ADP
ejpam-4691	3	49	vasile	vasile	PROPN
ejpam-4691	3	50	alecsandri	alecsandri	NOUN
ejpam-4691	3	51	of	of	ADP
ejpam-4691	3	52	bacǎu	bacǎu	PROPN
ejpam-4691	3	53	,	,	PUNCT
ejpam-4691	3	54	600115	600115	NUM
ejpam-4691	3	55	bacǎu	bacǎu	PROPN
ejpam-4691	3	56	,	,	PUNCT
ejpam-4691	3	57	romania	romania	PROPN
ejpam-4691	3	58	abstract	abstract	NOUN
ejpam-4691	3	59	.	.	PUNCT
ejpam-4691	4	1	by	by	ADP
ejpam-4691	4	2	using	use	VERB
ejpam-4691	4	3	m	m	PROPN
ejpam-4691	4	4	-	-	ADJ
ejpam-4691	4	5	open	open	ADJ
ejpam-4691	4	6	multifunctions	multifunction	NOUN
ejpam-4691	4	7	from	from	ADP
ejpam-4691	4	8	an	an	DET
ejpam-4691	4	9	m	m	NOUN
ejpam-4691	4	10	-	-	NOUN
ejpam-4691	4	11	space	space	NOUN
ejpam-4691	4	12	into	into	ADP
ejpam-4691	4	13	an	an	DET
ejpam-4691	4	14	m	m	NOUN
ejpam-4691	4	15	-	-	NOUN
ejpam-4691	4	16	space	space	NOUN
ejpam-4691	4	17	,	,	PUNCT
ejpam-4691	4	18	we	we	PRON
ejpam-4691	4	19	establish	establish	VERB
ejpam-4691	4	20	the	the	DET
ejpam-4691	4	21	unified	unified	ADJ
ejpam-4691	4	22	theory	theory	NOUN
ejpam-4691	4	23	for	for	ADP
ejpam-4691	4	24	several	several	ADJ
ejpam-4691	4	25	weak	weak	ADJ
ejpam-4691	4	26	forms	form	NOUN
ejpam-4691	4	27	of	of	ADP
ejpam-4691	4	28	open	open	ADJ
ejpam-4691	4	29	multifunctions	multifunction	NOUN
ejpam-4691	4	30	between	between	ADP
ejpam-4691	4	31	topological	topological	ADJ
ejpam-4691	4	32	spaces	space	NOUN
ejpam-4691	4	33	.	.	PUNCT
ejpam-4691	5	1	2020	2020	NUM
ejpam-4691	5	2	mathematics	mathematic	NOUN
ejpam-4691	5	3	subject	subject	NOUN
ejpam-4691	5	4	classifications	classification	NOUN
ejpam-4691	5	5	:	:	PUNCT
ejpam-4691	5	6	54a05	54a05	NUM
ejpam-4691	5	7	,	,	PUNCT
ejpam-4691	5	8	54c10	54c10	NUM
ejpam-4691	5	9	,	,	PUNCT
ejpam-4691	5	10	54c60	54c60	NUM
ejpam-4691	5	11	key	key	ADJ
ejpam-4691	5	12	words	word	NOUN
ejpam-4691	5	13	and	and	CCONJ
ejpam-4691	5	14	phrases	phrase	NOUN
ejpam-4691	5	15	:	:	PUNCT
ejpam-4691	5	16	m	m	NOUN
ejpam-4691	5	17	-	-	NOUN
ejpam-4691	5	18	structure	structure	NOUN
ejpam-4691	5	19	,	,	PUNCT
ejpam-4691	5	20	m	m	NOUN
ejpam-4691	5	21	-	-	NOUN
ejpam-4691	5	22	space	space	NOUN
ejpam-4691	5	23	,	,	PUNCT
ejpam-4691	5	24	m	m	NOUN
ejpam-4691	5	25	-	-	ADJ
ejpam-4691	5	26	open	open	ADJ
ejpam-4691	5	27	multifunction	multifunction	NOUN
ejpam-4691	5	28	,	,	PUNCT
ejpam-4691	5	29	ideal	ideal	ADJ
ejpam-4691	5	30	1	1	NUM
ejpam-4691	5	31	.	.	PUNCT
ejpam-4691	5	32	introduction	introduction	NOUN
ejpam-4691	5	33	the	the	DET
ejpam-4691	5	34	notion	notion	NOUN
ejpam-4691	5	35	of	of	ADP
ejpam-4691	5	36	ideal	ideal	ADJ
ejpam-4691	5	37	topological	topological	ADJ
ejpam-4691	5	38	spaces	space	NOUN
ejpam-4691	5	39	is	be	AUX
ejpam-4691	5	40	introduced	introduce	VERB
ejpam-4691	5	41	in	in	ADP
ejpam-4691	5	42	[	[	X
ejpam-4691	5	43	15	15	NUM
ejpam-4691	5	44	]	]	PUNCT
ejpam-4691	5	45	and	and	CCONJ
ejpam-4691	5	46	[	[	X
ejpam-4691	5	47	27	27	NUM
ejpam-4691	5	48	]	]	PUNCT
ejpam-4691	5	49	.	.	PUNCT
ejpam-4691	6	1	in	in	ADP
ejpam-4691	6	2	[	[	X
ejpam-4691	6	3	14	14	NUM
ejpam-4691	6	4	]	]	PUNCT
ejpam-4691	6	5	,	,	PUNCT
ejpam-4691	6	6	the	the	DET
ejpam-4691	6	7	authors	author	NOUN
ejpam-4691	6	8	introduced	introduce	VERB
ejpam-4691	6	9	the	the	DET
ejpam-4691	6	10	notion	notion	NOUN
ejpam-4691	6	11	of	of	ADP
ejpam-4691	6	12	i	i	NOUN
ejpam-4691	6	13	-	-	PUNCT
ejpam-4691	6	14	open	open	ADJ
ejpam-4691	6	15	sets	set	NOUN
ejpam-4691	6	16	in	in	ADP
ejpam-4691	6	17	an	an	DET
ejpam-4691	6	18	ideal	ideal	ADJ
ejpam-4691	6	19	topological	topological	ADJ
ejpam-4691	6	20	space	space	NOUN
ejpam-4691	6	21	.	.	PUNCT
ejpam-4691	7	1	as	as	SCONJ
ejpam-4691	7	2	generalizations	generalization	NOUN
ejpam-4691	7	3	of	of	ADP
ejpam-4691	7	4	open	open	ADJ
ejpam-4691	7	5	sets	set	NOUN
ejpam-4691	7	6	and	and	CCONJ
ejpam-4691	7	7	i	i	PRON
ejpam-4691	7	8	-	-	PUNCT
ejpam-4691	7	9	open	open	ADJ
ejpam-4691	7	10	sets	set	NOUN
ejpam-4691	7	11	,	,	PUNCT
ejpam-4691	7	12	semi	semi	ADJ
ejpam-4691	7	13	-	-	ADJ
ejpam-4691	7	14	i	i	ADV
ejpam-4691	7	15	-	-	PUNCT
ejpam-4691	7	16	open	open	ADJ
ejpam-4691	7	17	sets	set	NOUN
ejpam-4691	7	18	,	,	PUNCT
ejpam-4691	7	19	pre	pre	ADJ
ejpam-4691	7	20	-	-	ADJ
ejpam-4691	7	21	i	i	PRON
ejpam-4691	7	22	-	-	PUNCT
ejpam-4691	7	23	open	open	ADJ
ejpam-4691	7	24	sets	set	NOUN
ejpam-4691	7	25	,	,	PUNCT
ejpam-4691	7	26	α	α	X
ejpam-4691	7	27	-	-	PUNCT
ejpam-4691	7	28	i	i	NOUN
ejpam-4691	7	29	-	-	PUNCT
ejpam-4691	7	30	open	open	ADJ
ejpam-4691	7	31	sets	set	NOUN
ejpam-4691	7	32	,	,	PUNCT
ejpam-4691	7	33	β	β	X
ejpam-4691	7	34	-	-	ADJ
ejpam-4691	7	35	i	i	NOUN
ejpam-4691	7	36	-	-	PUNCT
ejpam-4691	7	37	open	open	ADJ
ejpam-4691	7	38	sets	set	NOUN
ejpam-4691	7	39	and	and	CCONJ
ejpam-4691	7	40	b	b	X
ejpam-4691	7	41	-	-	PUNCT
ejpam-4691	7	42	i	i	NOUN
ejpam-4691	7	43	-	-	PUNCT
ejpam-4691	7	44	open	open	ADJ
ejpam-4691	7	45	sets	set	NOUN
ejpam-4691	7	46	are	be	AUX
ejpam-4691	7	47	introduced	introduce	VERB
ejpam-4691	7	48	and	and	CCONJ
ejpam-4691	7	49	used	use	VERB
ejpam-4691	7	50	to	to	PART
ejpam-4691	7	51	obtain	obtain	VERB
ejpam-4691	7	52	decompositions	decomposition	NOUN
ejpam-4691	7	53	of	of	ADP
ejpam-4691	7	54	continuity	continuity	NOUN
ejpam-4691	7	55	.	.	PUNCT
ejpam-4691	8	1	recently	recently	ADV
ejpam-4691	8	2	,	,	PUNCT
ejpam-4691	8	3	in	in	ADP
ejpam-4691	8	4	[	[	X
ejpam-4691	8	5	24	24	NUM
ejpam-4691	8	6	]	]	PUNCT
ejpam-4691	8	7	and	and	CCONJ
ejpam-4691	8	8	[	[	X
ejpam-4691	8	9	25	25	NUM
ejpam-4691	8	10	]	]	PUNCT
ejpam-4691	8	11	the	the	DET
ejpam-4691	8	12	present	present	ADJ
ejpam-4691	8	13	authors	author	NOUN
ejpam-4691	8	14	introduced	introduce	VERB
ejpam-4691	8	15	the	the	DET
ejpam-4691	8	16	notions	notion	NOUN
ejpam-4691	8	17	of	of	ADP
ejpam-4691	8	18	minimal	minimal	ADJ
ejpam-4691	8	19	structures	structure	NOUN
ejpam-4691	8	20	and	and	CCONJ
ejpam-4691	8	21	m	m	NOUN
ejpam-4691	8	22	-	-	NOUN
ejpam-4691	8	23	spaces	space	NOUN
ejpam-4691	8	24	as	as	ADP
ejpam-4691	8	25	a	a	DET
ejpam-4691	8	26	generalization	generalization	NOUN
ejpam-4691	8	27	of	of	ADP
ejpam-4691	8	28	topological	topological	ADJ
ejpam-4691	8	29	spaces	space	NOUN
ejpam-4691	8	30	.	.	PUNCT
ejpam-4691	9	1	the	the	DET
ejpam-4691	9	2	notion	notion	NOUN
ejpam-4691	9	3	of	of	ADP
ejpam-4691	9	4	m	m	NOUN
ejpam-4691	9	5	-	-	ADJ
ejpam-4691	9	6	open	open	ADJ
ejpam-4691	9	7	multifunctions	multifunction	NOUN
ejpam-4691	9	8	is	be	AUX
ejpam-4691	9	9	introduced	introduce	VERB
ejpam-4691	9	10	in	in	ADP
ejpam-4691	9	11	[	[	X
ejpam-4691	9	12	21	21	NUM
ejpam-4691	9	13	]	]	PUNCT
ejpam-4691	9	14	.	.	PUNCT
ejpam-4691	10	1	the	the	DET
ejpam-4691	10	2	notion	notion	NOUN
ejpam-4691	10	3	of	of	ADP
ejpam-4691	10	4	m	m	PROPN
ejpam-4691	10	5	-	-	PUNCT
ejpam-4691	10	6	i	i	PRON
ejpam-4691	10	7	-	-	PUNCT
ejpam-4691	10	8	open	open	ADJ
ejpam-4691	10	9	functions	function	NOUN
ejpam-4691	10	10	is	be	AUX
ejpam-4691	10	11	introduced	introduce	VERB
ejpam-4691	10	12	in	in	ADP
ejpam-4691	10	13	[	[	X
ejpam-4691	10	14	22	22	NUM
ejpam-4691	10	15	]	]	PUNCT
ejpam-4691	10	16	.	.	PUNCT
ejpam-4691	11	1	in	in	ADP
ejpam-4691	11	2	this	this	DET
ejpam-4691	11	3	paper	paper	NOUN
ejpam-4691	11	4	,	,	PUNCT
ejpam-4691	11	5	the	the	DET
ejpam-4691	11	6	authors	author	NOUN
ejpam-4691	11	7	introduce	introduce	VERB
ejpam-4691	11	8	a	a	DET
ejpam-4691	11	9	minimal	minimal	ADJ
ejpam-4691	11	10	structure	structure	NOUN
ejpam-4691	11	11	mio(x	mio(x	NOUN
ejpam-4691	11	12	)	)	PUNCT
ejpam-4691	11	13	determined	determine	VERB
ejpam-4691	11	14	by	by	ADP
ejpam-4691	11	15	operations	operation	NOUN
ejpam-4691	11	16	int	int	NOUN
ejpam-4691	11	17	,	,	PUNCT
ejpam-4691	11	18	cl	cl	NOUN
ejpam-4691	11	19	,	,	PUNCT
ejpam-4691	11	20	cl⋆	cl⋆	PROPN
ejpam-4691	11	21	in	in	ADP
ejpam-4691	11	22	an	an	DET
ejpam-4691	11	23	ideal	ideal	ADJ
ejpam-4691	11	24	topological	topological	ADJ
ejpam-4691	11	25	space	space	NOUN
ejpam-4691	11	26	(	(	PUNCT
ejpam-4691	11	27	x	x	X
ejpam-4691	11	28	,	,	PUNCT
ejpam-4691	11	29	τ	τ	PROPN
ejpam-4691	11	30	,	,	PUNCT
ejpam-4691	11	31	i	i	PROPN
ejpam-4691	11	32	)	)	PUNCT
ejpam-4691	11	33	.	.	PUNCT
ejpam-4691	12	1	by	by	ADP
ejpam-4691	12	2	using	use	VERB
ejpam-4691	12	3	mio(x	mio(x	PROPN
ejpam-4691	12	4	)	)	PUNCT
ejpam-4691	12	5	,	,	PUNCT
ejpam-4691	12	6	the	the	DET
ejpam-4691	12	7	authors	author	NOUN
ejpam-4691	12	8	introduce	introduce	VERB
ejpam-4691	12	9	and	and	CCONJ
ejpam-4691	12	10	study	study	VERB
ejpam-4691	12	11	the	the	DET
ejpam-4691	12	12	notion	notion	NOUN
ejpam-4691	12	13	of	of	ADP
ejpam-4691	12	14	mi	mi	ADJ
ejpam-4691	12	15	-	-	ADJ
ejpam-4691	12	16	open	open	ADJ
ejpam-4691	12	17	multifunctions	multifunction	NOUN
ejpam-4691	12	18	.	.	PUNCT
ejpam-4691	13	1	as	as	ADP
ejpam-4691	13	2	special	special	ADJ
ejpam-4691	13	3	case	case	NOUN
ejpam-4691	13	4	of	of	ADP
ejpam-4691	13	5	mi	mi	ADJ
ejpam-4691	13	6	-	-	ADJ
ejpam-4691	13	7	open	open	ADJ
ejpam-4691	13	8	multifunctions	multifunction	NOUN
ejpam-4691	13	9	,	,	PUNCT
ejpam-4691	13	10	we	we	PRON
ejpam-4691	13	11	obtain	obtain	VERB
ejpam-4691	13	12	semi	semi	ADJ
ejpam-4691	13	13	-	-	ADJ
ejpam-4691	13	14	i	i	PRON
ejpam-4691	13	15	-	-	PUNCT
ejpam-4691	13	16	open	open	ADJ
ejpam-4691	13	17	functions	function	NOUN
ejpam-4691	13	18	[	[	X
ejpam-4691	13	19	12	12	NUM
ejpam-4691	13	20	]	]	PUNCT
ejpam-4691	13	21	,	,	PUNCT
ejpam-4691	13	22	pre	pre	ADJ
ejpam-4691	13	23	-	-	ADJ
ejpam-4691	13	24	i	i	PRON
ejpam-4691	13	25	-	-	PUNCT
ejpam-4691	13	26	open	open	ADJ
ejpam-4691	13	27	functions	function	NOUN
ejpam-4691	13	28	[	[	X
ejpam-4691	13	29	2	2	NUM
ejpam-4691	13	30	]	]	PUNCT
ejpam-4691	13	31	,	,	PUNCT
ejpam-4691	13	32	α	α	PROPN
ejpam-4691	13	33	-	-	ADJ
ejpam-4691	13	34	i	i	NOUN
ejpam-4691	13	35	-	-	PUNCT
ejpam-4691	13	36	open	open	ADJ
ejpam-4691	13	37	functions	function	NOUN
ejpam-4691	13	38	[	[	X
ejpam-4691	13	39	2	2	NUM
ejpam-4691	13	40	]	]	PUNCT
ejpam-4691	13	41	,	,	PUNCT
ejpam-4691	13	42	b	b	X
ejpam-4691	13	43	-	-	PUNCT
ejpam-4691	13	44	i	i	NOUN
ejpam-4691	13	45	-	-	PUNCT
ejpam-4691	13	46	open	open	ADJ
ejpam-4691	13	47	functions	function	NOUN
ejpam-4691	13	48	[	[	X
ejpam-4691	13	49	3	3	NUM
ejpam-4691	13	50	]	]	PUNCT
ejpam-4691	13	51	,	,	PUNCT
ejpam-4691	13	52	weakly	weakly	ADJ
ejpam-4691	13	53	semi	semi	ADJ
ejpam-4691	13	54	-	-	ADJ
ejpam-4691	13	55	i	i	PRON
ejpam-4691	13	56	-	-	PUNCT
ejpam-4691	13	57	open	open	ADJ
ejpam-4691	13	58	functions	function	NOUN
ejpam-4691	13	59	[	[	X
ejpam-4691	13	60	9	9	NUM
ejpam-4691	13	61	]	]	PUNCT
ejpam-4691	13	62	and	and	CCONJ
ejpam-4691	13	63	weakly	weakly	ADJ
ejpam-4691	13	64	b	b	PROPN
ejpam-4691	13	65	−	−	NOUN
ejpam-4691	13	66	iopen	iopen	NOUN
ejpam-4691	13	67	functions	function	NOUN
ejpam-4691	13	68	[	[	X
ejpam-4691	13	69	19	19	NUM
ejpam-4691	13	70	]	]	PUNCT
ejpam-4691	13	71	.	.	PUNCT
ejpam-4691	14	1	in	in	ADP
ejpam-4691	14	2	section	section	NOUN
ejpam-4691	14	3	3	3	NUM
ejpam-4691	14	4	,	,	PUNCT
ejpam-4691	14	5	we	we	PRON
ejpam-4691	14	6	introduce	introduce	VERB
ejpam-4691	14	7	the	the	DET
ejpam-4691	14	8	notion	notion	NOUN
ejpam-4691	14	9	of	of	ADP
ejpam-4691	14	10	an	an	DET
ejpam-4691	14	11	m	m	NOUN
ejpam-4691	14	12	-	-	ADJ
ejpam-4691	14	13	open	open	ADJ
ejpam-4691	14	14	multifunction	multifunction	NOUN
ejpam-4691	14	15	from	from	ADP
ejpam-4691	14	16	an	an	DET
ejpam-4691	14	17	m	m	NOUN
ejpam-4691	14	18	-	-	NOUN
ejpam-4691	14	19	space	space	NOUN
ejpam-4691	14	20	into	into	ADP
ejpam-4691	14	21	an	an	DET
ejpam-4691	14	22	m	m	NOUN
ejpam-4691	14	23	-	-	NOUN
ejpam-4691	14	24	space	space	NOUN
ejpam-4691	14	25	.	.	PUNCT
ejpam-4691	15	1	we	we	PRON
ejpam-4691	15	2	obtain	obtain	VERB
ejpam-4691	15	3	the	the	DET
ejpam-4691	15	4	characterizations	characterization	NOUN
ejpam-4691	15	5	of	of	ADP
ejpam-4691	15	6	m	m	NOUN
ejpam-4691	15	7	-	-	ADJ
ejpam-4691	15	8	open	open	ADJ
ejpam-4691	15	9	multifunctions	multifunction	NOUN
ejpam-4691	15	10	and	and	CCONJ
ejpam-4691	15	11	characterize	characterize	VERB
ejpam-4691	15	12	the	the	DET
ejpam-4691	15	13	set	set	NOUN
ejpam-4691	15	14	of	of	ADP
ejpam-4691	15	15	all	all	DET
ejpam-4691	15	16	points	point	NOUN
ejpam-4691	15	17	at	at	ADP
ejpam-4691	15	18	which	which	PRON
ejpam-4691	15	19	a	a	DET
ejpam-4691	15	20	multifunction	multifunction	NOUN
ejpam-4691	15	21	is	be	AUX
ejpam-4691	15	22	not	not	PART
ejpam-4691	15	23	m	m	NOUN
ejpam-4691	15	24	-	-	ADJ
ejpam-4691	15	25	open	open	ADJ
ejpam-4691	15	26	.	.	PUNCT
ejpam-4691	16	1	in	in	ADP
ejpam-4691	16	2	the	the	DET
ejpam-4691	16	3	last	last	ADJ
ejpam-4691	16	4	part	part	NOUN
ejpam-4691	16	5	,	,	PUNCT
ejpam-4691	16	6	a	a	DET
ejpam-4691	16	7	new	new	ADJ
ejpam-4691	16	8	modification	modification	NOUN
ejpam-4691	16	9	of	of	ADP
ejpam-4691	16	10	m	m	NOUN
ejpam-4691	16	11	-	-	ADJ
ejpam-4691	16	12	open	open	ADJ
ejpam-4691	16	13	multifunctions	multifunction	NOUN
ejpam-4691	16	14	,	,	PUNCT
ejpam-4691	16	15	called	call	VERB
ejpam-4691	16	16	mi	mi	ADJ
ejpam-4691	16	17	-	-	ADJ
ejpam-4691	16	18	open	open	ADJ
ejpam-4691	16	19	multifunctions	multifunction	NOUN
ejpam-4691	16	20	,	,	PUNCT
ejpam-4691	16	21	is	be	AUX
ejpam-4691	16	22	introduced	introduce	VERB
ejpam-4691	16	23	and	and	CCONJ
ejpam-4691	16	24	investigated	investigate	VERB
ejpam-4691	16	25	.	.	PUNCT
ejpam-4691	17	1	∗corresponding	∗corresponde	VERB
ejpam-4691	17	2	author	author	NOUN
ejpam-4691	17	3	.	.	PUNCT
ejpam-4691	18	1	doi	doi	NOUN
ejpam-4691	18	2	:	:	PUNCT
ejpam-4691	18	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4691	https://doi.org/10.29020/nybg.ejpam.v16i1.4691	PROPN
ejpam-4691	18	4	email	email	NOUN
ejpam-4691	18	5	addresses	address	NOUN
ejpam-4691	18	6	:	:	PUNCT
ejpam-4691	18	7	t.noiri@nifty.com	t.noiri@nifty.com	X
ejpam-4691	18	8	(	(	PUNCT
ejpam-4691	18	9	t.	t.	PROPN
ejpam-4691	18	10	noiri	noiri	PROPN
ejpam-4691	18	11	)	)	PUNCT
ejpam-4691	18	12	,	,	PUNCT
ejpam-4691	18	13	vpopa@ub.ro	vpopa@ub.ro	NOUN
ejpam-4691	18	14	(	(	PUNCT
ejpam-4691	18	15	v.	v.	ADP
ejpam-4691	18	16	popa	popa	NOUN
ejpam-4691	18	17	)	)	PUNCT
ejpam-4691	18	18	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4691	18	19	430	430	NUM
ejpam-4691	19	1	©	©	PROPN
ejpam-4691	19	2	2023	2023	NUM
ejpam-4691	19	3	ejpam	ejpam	NOUN
ejpam-4691	19	4	all	all	DET
ejpam-4691	19	5	rights	right	NOUN
ejpam-4691	19	6	reserved	reserve	VERB
ejpam-4691	19	7	.	.	PUNCT
ejpam-4691	20	1	t.	t.	PROPN
ejpam-4691	20	2	noiri	noiri	PROPN
ejpam-4691	20	3	,	,	PUNCT
ejpam-4691	20	4	v.	v.	CCONJ
ejpam-4691	20	5	popa	popa	NOUN
ejpam-4691	20	6	/	/	SYM
ejpam-4691	20	7	eur	eur	PROPN
ejpam-4691	20	8	.	.	PUNCT
ejpam-4691	21	1	j.	j.	PROPN
ejpam-4691	21	2	pure	pure	PROPN
ejpam-4691	21	3	appl	appl	PROPN
ejpam-4691	21	4	.	.	PROPN
ejpam-4691	21	5	math	math	PROPN
ejpam-4691	21	6	,	,	PUNCT
ejpam-4691	21	7	16	16	NUM
ejpam-4691	21	8	(	(	PUNCT
ejpam-4691	21	9	1	1	NUM
ejpam-4691	21	10	)	)	PUNCT
ejpam-4691	21	11	(	(	PUNCT
ejpam-4691	21	12	2023	2023	NUM
ejpam-4691	21	13	)	)	PUNCT
ejpam-4691	21	14	,	,	PUNCT
ejpam-4691	21	15	430	430	NUM
ejpam-4691	21	16	-	-	SYM
ejpam-4691	21	17	439	439	NUM
ejpam-4691	21	18	431	431	NUM
ejpam-4691	21	19	2	2	NUM
ejpam-4691	21	20	.	.	PUNCT
ejpam-4691	22	1	preliminaries	preliminary	NOUN
ejpam-4691	22	2	let	let	VERB
ejpam-4691	22	3	(	(	PUNCT
ejpam-4691	22	4	x	x	NOUN
ejpam-4691	22	5	,	,	PUNCT
ejpam-4691	22	6	τ	τ	X
ejpam-4691	22	7	)	)	PUNCT
ejpam-4691	22	8	be	be	VERB
ejpam-4691	22	9	a	a	DET
ejpam-4691	22	10	topological	topological	ADJ
ejpam-4691	22	11	space	space	NOUN
ejpam-4691	22	12	and	and	CCONJ
ejpam-4691	22	13	a	a	DET
ejpam-4691	22	14	a	a	DET
ejpam-4691	22	15	subset	subset	NOUN
ejpam-4691	22	16	of	of	ADP
ejpam-4691	22	17	x.	x.	NOUN
ejpam-4691	22	18	the	the	DET
ejpam-4691	22	19	closure	closure	NOUN
ejpam-4691	22	20	and	and	CCONJ
ejpam-4691	22	21	the	the	DET
ejpam-4691	22	22	interior	interior	NOUN
ejpam-4691	22	23	of	of	ADP
ejpam-4691	22	24	a	a	PRON
ejpam-4691	22	25	are	be	AUX
ejpam-4691	22	26	denoted	denote	VERB
ejpam-4691	22	27	by	by	ADP
ejpam-4691	22	28	cl(a	cl(a	NOUN
ejpam-4691	22	29	)	)	PUNCT
ejpam-4691	22	30	and	and	CCONJ
ejpam-4691	22	31	int(a	int(a	PROPN
ejpam-4691	22	32	)	)	PUNCT
ejpam-4691	22	33	,	,	PUNCT
ejpam-4691	22	34	respectively	respectively	ADV
ejpam-4691	22	35	.	.	PUNCT
ejpam-4691	23	1	definition	definition	NOUN
ejpam-4691	23	2	1	1	NUM
ejpam-4691	23	3	.	.	PUNCT
ejpam-4691	24	1	let	let	VERB
ejpam-4691	24	2	(	(	PUNCT
ejpam-4691	24	3	x	x	NOUN
ejpam-4691	24	4	,	,	PUNCT
ejpam-4691	24	5	τ	τ	X
ejpam-4691	24	6	)	)	PUNCT
ejpam-4691	24	7	be	be	VERB
ejpam-4691	24	8	a	a	DET
ejpam-4691	24	9	topological	topological	ADJ
ejpam-4691	24	10	space	space	NOUN
ejpam-4691	24	11	.	.	PUNCT
ejpam-4691	25	1	a	a	DET
ejpam-4691	25	2	subset	subset	NOUN
ejpam-4691	25	3	a	a	PRON
ejpam-4691	25	4	of	of	ADP
ejpam-4691	25	5	x	x	SYM
ejpam-4691	25	6	is	be	AUX
ejpam-4691	25	7	said	say	VERB
ejpam-4691	25	8	to	to	PART
ejpam-4691	25	9	be	be	AUX
ejpam-4691	25	10	α	α	X
ejpam-4691	25	11	-	-	ADJ
ejpam-4691	25	12	open	open	ADJ
ejpam-4691	25	13	[	[	X
ejpam-4691	25	14	20	20	NUM
ejpam-4691	25	15	]	]	PUNCT
ejpam-4691	25	16	(	(	PUNCT
ejpam-4691	25	17	resp	resp	NOUN
ejpam-4691	25	18	.	.	PUNCT
ejpam-4691	26	1	semi	semi	ADJ
ejpam-4691	26	2	-	-	ADJ
ejpam-4691	26	3	open	open	ADJ
ejpam-4691	26	4	[	[	X
ejpam-4691	26	5	16	16	NUM
ejpam-4691	26	6	]	]	PUNCT
ejpam-4691	26	7	,	,	PUNCT
ejpam-4691	26	8	preopen	preopen	ADJ
ejpam-4691	26	9	[	[	X
ejpam-4691	26	10	18	18	NUM
ejpam-4691	26	11	]	]	PUNCT
ejpam-4691	26	12	,	,	PUNCT
ejpam-4691	26	13	β	β	X
ejpam-4691	26	14	-	-	VERB
ejpam-4691	26	15	open	open	ADJ
ejpam-4691	26	16	[	[	X
ejpam-4691	26	17	1	1	NUM
ejpam-4691	26	18	]	]	PUNCT
ejpam-4691	26	19	,	,	PUNCT
ejpam-4691	26	20	b	b	X
ejpam-4691	26	21	-	-	PUNCT
ejpam-4691	26	22	open	open	ADJ
ejpam-4691	26	23	[	[	X
ejpam-4691	26	24	4	4	NUM
ejpam-4691	26	25	]	]	PUNCT
ejpam-4691	26	26	)	)	PUNCT
ejpam-4691	26	27	if	if	SCONJ
ejpam-4691	26	28	a	a	DET
ejpam-4691	26	29	⊂	⊂	X
ejpam-4691	26	30	int(cl(int(a	int(cl(int(a	NOUN
ejpam-4691	26	31	)	)	PUNCT
ejpam-4691	26	32	)	)	PUNCT
ejpam-4691	26	33	)	)	PUNCT
ejpam-4691	27	1	(	(	PUNCT
ejpam-4691	27	2	resp	resp	NOUN
ejpam-4691	27	3	.	.	PUNCT
ejpam-4691	28	1	a	a	DET
ejpam-4691	28	2	⊂	⊂	PROPN
ejpam-4691	28	3	cl(int(a	cl(int(a	PROPN
ejpam-4691	28	4	)	)	PUNCT
ejpam-4691	28	5	)	)	PUNCT
ejpam-4691	28	6	,	,	PUNCT
ejpam-4691	28	7	a	a	DET
ejpam-4691	28	8	⊂	⊂	PROPN
ejpam-4691	28	9	int(cl(a	int(cl(a	PROPN
ejpam-4691	28	10	)	)	PUNCT
ejpam-4691	28	11	)	)	PUNCT
ejpam-4691	28	12	,	,	PUNCT
ejpam-4691	28	13	a	a	DET
ejpam-4691	28	14	⊂	⊂	PROPN
ejpam-4691	28	15	cl(int(cl(a	cl(int(cl(a	NOUN
ejpam-4691	28	16	)	)	PUNCT
ejpam-4691	28	17	)	)	PUNCT
ejpam-4691	28	18	)	)	PUNCT
ejpam-4691	28	19	,	,	PUNCT
ejpam-4691	28	20	a	a	DET
ejpam-4691	28	21	⊂	⊂	PROPN
ejpam-4691	28	22	int(cl(a	int(cl(a	PROPN
ejpam-4691	28	23	)	)	PUNCT
ejpam-4691	28	24	)	)	PUNCT
ejpam-4691	28	25	∪	∪	ADP
ejpam-4691	28	26	cl(int(a	cl(int(a	PROPN
ejpam-4691	28	27	)	)	PUNCT
ejpam-4691	28	28	)	)	PUNCT
ejpam-4691	28	29	)	)	PUNCT
ejpam-4691	28	30	.	.	PUNCT
ejpam-4691	29	1	the	the	DET
ejpam-4691	29	2	family	family	NOUN
ejpam-4691	29	3	of	of	ADP
ejpam-4691	29	4	all	all	PRON
ejpam-4691	29	5	semi	semi	ADJ
ejpam-4691	29	6	-	-	ADJ
ejpam-4691	29	7	open	open	ADJ
ejpam-4691	29	8	(	(	PUNCT
ejpam-4691	29	9	resp	resp	NOUN
ejpam-4691	29	10	.	.	PUNCT
ejpam-4691	30	1	preopen	preopen	ADJ
ejpam-4691	30	2	,	,	PUNCT
ejpam-4691	30	3	α	α	NOUN
ejpam-4691	30	4	-	-	ADJ
ejpam-4691	30	5	open	open	ADJ
ejpam-4691	30	6	,	,	PUNCT
ejpam-4691	30	7	β	β	NOUN
ejpam-4691	30	8	-	-	ADJ
ejpam-4691	30	9	open	open	ADJ
ejpam-4691	30	10	,	,	PUNCT
ejpam-4691	30	11	b	b	X
ejpam-4691	30	12	-	-	PUNCT
ejpam-4691	30	13	open	open	ADJ
ejpam-4691	30	14	)	)	PUNCT
ejpam-4691	30	15	sets	set	NOUN
ejpam-4691	30	16	in	in	ADP
ejpam-4691	30	17	x	x	PUNCT
ejpam-4691	30	18	is	be	AUX
ejpam-4691	30	19	denoted	denote	VERB
ejpam-4691	30	20	by	by	ADP
ejpam-4691	30	21	so(x	so(x	NOUN
ejpam-4691	30	22	)	)	PUNCT
ejpam-4691	30	23	(	(	PUNCT
ejpam-4691	30	24	resp	resp	NOUN
ejpam-4691	30	25	.	.	PUNCT
ejpam-4691	31	1	po(x	po(x	NUM
ejpam-4691	31	2	)	)	PUNCT
ejpam-4691	31	3	,	,	PUNCT
ejpam-4691	32	1	α(x	α(x	NOUN
ejpam-4691	32	2	)	)	PUNCT
ejpam-4691	32	3	,	,	PUNCT
ejpam-4691	32	4	β(x	β(x	NOUN
ejpam-4691	32	5	)	)	PUNCT
ejpam-4691	32	6	,	,	PUNCT
ejpam-4691	32	7	bo(x	bo(x	NUM
ejpam-4691	32	8	)	)	PUNCT
ejpam-4691	32	9	)	)	PUNCT
ejpam-4691	32	10	.	.	PUNCT
ejpam-4691	33	1	throughout	throughout	ADP
ejpam-4691	33	2	the	the	DET
ejpam-4691	33	3	present	present	ADJ
ejpam-4691	33	4	paper	paper	NOUN
ejpam-4691	33	5	,	,	PUNCT
ejpam-4691	33	6	(	(	PUNCT
ejpam-4691	33	7	x	x	X
ejpam-4691	33	8	,	,	PUNCT
ejpam-4691	33	9	τ	τ	X
ejpam-4691	33	10	)	)	PUNCT
ejpam-4691	33	11	and	and	CCONJ
ejpam-4691	33	12	(	(	PUNCT
ejpam-4691	33	13	y	y	PROPN
ejpam-4691	33	14	,	,	PUNCT
ejpam-4691	33	15	σ	σ	PROPN
ejpam-4691	33	16	)	)	PUNCT
ejpam-4691	33	17	always	always	ADV
ejpam-4691	33	18	denote	denote	VERB
ejpam-4691	33	19	topological	topological	ADJ
ejpam-4691	33	20	spaces	space	NOUN
ejpam-4691	33	21	and	and	CCONJ
ejpam-4691	33	22	f	f	NOUN
ejpam-4691	33	23	:	:	PUNCT
ejpam-4691	33	24	x	x	X
ejpam-4691	33	25	→	→	SYM
ejpam-4691	33	26	y	y	PROPN
ejpam-4691	33	27	presents	present	VERB
ejpam-4691	33	28	a	a	DET
ejpam-4691	33	29	multivalued	multivalued	ADJ
ejpam-4691	33	30	function	function	NOUN
ejpam-4691	33	31	.	.	PUNCT
ejpam-4691	34	1	for	for	ADP
ejpam-4691	34	2	a	a	DET
ejpam-4691	34	3	multifunction	multifunction	NOUN
ejpam-4691	34	4	f	f	NOUN
ejpam-4691	34	5	:	:	PUNCT
ejpam-4691	34	6	x	x	X
ejpam-4691	34	7	→	→	SYM
ejpam-4691	34	8	y	y	PROPN
ejpam-4691	34	9	,	,	PUNCT
ejpam-4691	34	10	we	we	PRON
ejpam-4691	34	11	shall	shall	AUX
ejpam-4691	34	12	denote	denote	VERB
ejpam-4691	34	13	the	the	DET
ejpam-4691	34	14	upper	upper	ADJ
ejpam-4691	34	15	and	and	CCONJ
ejpam-4691	34	16	lower	low	ADJ
ejpam-4691	34	17	inverse	inverse	NOUN
ejpam-4691	34	18	of	of	ADP
ejpam-4691	34	19	a	a	DET
ejpam-4691	34	20	subset	subset	NOUN
ejpam-4691	34	21	b	b	NOUN
ejpam-4691	34	22	of	of	ADP
ejpam-4691	34	23	a	a	DET
ejpam-4691	34	24	space	space	NOUN
ejpam-4691	34	25	y	y	NOUN
ejpam-4691	34	26	by	by	ADP
ejpam-4691	34	27	f+(b	f+(b	NOUN
ejpam-4691	34	28	)	)	PUNCT
ejpam-4691	34	29	and	and	CCONJ
ejpam-4691	34	30	f−(b	f−(b	NOUN
ejpam-4691	34	31	)	)	PUNCT
ejpam-4691	34	32	,	,	PUNCT
ejpam-4691	34	33	respectively	respectively	ADV
ejpam-4691	34	34	,	,	PUNCT
ejpam-4691	34	35	that	that	PRON
ejpam-4691	34	36	is	be	AUX
ejpam-4691	34	37	f+(b	f+(b	NOUN
ejpam-4691	34	38	)	)	PUNCT
ejpam-4691	34	39	=	=	PRON
ejpam-4691	35	1	{	{	PUNCT
ejpam-4691	35	2	x	x	PUNCT
ejpam-4691	35	3	∈	∈	PROPN
ejpam-4691	35	4	x	x	X
ejpam-4691	35	5	:	:	PUNCT
ejpam-4691	35	6	f	f	X
ejpam-4691	35	7	(	(	PUNCT
ejpam-4691	35	8	x	x	X
ejpam-4691	35	9	)	)	PUNCT
ejpam-4691	35	10	⊂	⊂	PROPN
ejpam-4691	35	11	b	b	X
ejpam-4691	35	12	}	}	PUNCT
ejpam-4691	35	13	and	and	CCONJ
ejpam-4691	35	14	f−(b	f−(b	PROPN
ejpam-4691	35	15	)	)	PUNCT
ejpam-4691	35	16	=	=	PRON
ejpam-4691	35	17	{	{	PUNCT
ejpam-4691	35	18	x	x	PUNCT
ejpam-4691	35	19	∈	∈	PROPN
ejpam-4691	35	20	x	x	X
ejpam-4691	35	21	:	:	PUNCT
ejpam-4691	35	22	f	f	X
ejpam-4691	35	23	(	(	PUNCT
ejpam-4691	35	24	x	x	X
ejpam-4691	35	25	)	)	PUNCT
ejpam-4691	35	26	∩b	∩b	NOUN
ejpam-4691	35	27	̸=	̸=	PROPN
ejpam-4691	35	28	∅	∅	NOUN
ejpam-4691	35	29	}	}	PUNCT
ejpam-4691	35	30	.	.	PUNCT
ejpam-4691	36	1	definition	definition	NOUN
ejpam-4691	36	2	2	2	NUM
ejpam-4691	36	3	.	.	PUNCT
ejpam-4691	36	4	a	a	DET
ejpam-4691	36	5	multifunction	multifunction	NOUN
ejpam-4691	36	6	f	f	NOUN
ejpam-4691	36	7	:	:	PUNCT
ejpam-4691	36	8	(	(	PUNCT
ejpam-4691	36	9	x	x	X
ejpam-4691	36	10	,	,	PUNCT
ejpam-4691	36	11	τ	τ	X
ejpam-4691	36	12	)	)	PUNCT
ejpam-4691	36	13	→	→	SYM
ejpam-4691	36	14	(	(	PUNCT
ejpam-4691	36	15	y	y	PROPN
ejpam-4691	36	16	,	,	PUNCT
ejpam-4691	36	17	σ	σ	PROPN
ejpam-4691	36	18	)	)	PUNCT
ejpam-4691	36	19	is	be	AUX
ejpam-4691	36	20	said	say	VERB
ejpam-4691	36	21	to	to	PART
ejpam-4691	36	22	be	be	AUX
ejpam-4691	36	23	open	open	ADJ
ejpam-4691	36	24	[	[	X
ejpam-4691	36	25	5	5	NUM
ejpam-4691	36	26	]	]	PUNCT
ejpam-4691	36	27	(	(	PUNCT
ejpam-4691	36	28	resp	resp	NOUN
ejpam-4691	36	29	.	.	PUNCT
ejpam-4691	37	1	semiopen	semiopen	VERB
ejpam-4691	38	1	[	[	X
ejpam-4691	38	2	23	23	NUM
ejpam-4691	38	3	]	]	PUNCT
ejpam-4691	38	4	,	,	PUNCT
ejpam-4691	38	5	preopen	preopen	ADJ
ejpam-4691	38	6	[	[	X
ejpam-4691	38	7	7	7	NUM
ejpam-4691	38	8	]	]	PUNCT
ejpam-4691	38	9	,	,	PUNCT
ejpam-4691	38	10	α	α	X
ejpam-4691	38	11	-	-	ADJ
ejpam-4691	38	12	open	open	ADJ
ejpam-4691	38	13	[	[	X
ejpam-4691	38	14	6	6	NUM
ejpam-4691	38	15	]	]	PUNCT
ejpam-4691	38	16	,	,	PUNCT
ejpam-4691	38	17	β	β	X
ejpam-4691	38	18	-	-	VERB
ejpam-4691	38	19	open	open	ADJ
ejpam-4691	38	20	[	[	X
ejpam-4691	38	21	21	21	NUM
ejpam-4691	38	22	]	]	PUNCT
ejpam-4691	38	23	)	)	PUNCT
ejpam-4691	38	24	if	if	SCONJ
ejpam-4691	38	25	f	f	PROPN
ejpam-4691	38	26	(	(	PUNCT
ejpam-4691	38	27	u	u	NOUN
ejpam-4691	38	28	)	)	PUNCT
ejpam-4691	38	29	is	be	AUX
ejpam-4691	38	30	open	open	ADJ
ejpam-4691	38	31	(	(	PUNCT
ejpam-4691	38	32	resp	resp	NOUN
ejpam-4691	38	33	.	.	PUNCT
ejpam-4691	39	1	semi	semi	ADJ
ejpam-4691	39	2	-	-	ADJ
ejpam-4691	39	3	open	open	ADJ
ejpam-4691	39	4	,	,	PUNCT
ejpam-4691	39	5	preopen	preopen	ADJ
ejpam-4691	39	6	,	,	PUNCT
ejpam-4691	39	7	α	α	NOUN
ejpam-4691	39	8	-	-	ADJ
ejpam-4691	39	9	open	open	ADJ
ejpam-4691	39	10	,	,	PUNCT
ejpam-4691	39	11	β	β	NOUN
ejpam-4691	39	12	-	-	ADJ
ejpam-4691	39	13	open	open	ADJ
ejpam-4691	39	14	)	)	PUNCT
ejpam-4691	39	15	for	for	ADP
ejpam-4691	39	16	each	each	DET
ejpam-4691	39	17	open	open	ADJ
ejpam-4691	39	18	set	set	NOUN
ejpam-4691	39	19	u	u	NOUN
ejpam-4691	39	20	of	of	ADP
ejpam-4691	39	21	x.	x.	NOUN
ejpam-4691	39	22	definition	definition	NOUN
ejpam-4691	39	23	3	3	NUM
ejpam-4691	39	24	.	.	PUNCT
ejpam-4691	40	1	a	a	DET
ejpam-4691	40	2	subfamily	subfamily	ADV
ejpam-4691	40	3	mx	mx	NOUN
ejpam-4691	40	4	of	of	ADP
ejpam-4691	40	5	the	the	DET
ejpam-4691	40	6	power	power	NOUN
ejpam-4691	40	7	set	set	NOUN
ejpam-4691	40	8	p(x	p(x	NOUN
ejpam-4691	40	9	)	)	PUNCT
ejpam-4691	40	10	of	of	ADP
ejpam-4691	40	11	a	a	DET
ejpam-4691	40	12	nonempty	nonempty	ADV
ejpam-4691	40	13	set	set	VERB
ejpam-4691	40	14	x	x	PUNCT
ejpam-4691	40	15	is	be	AUX
ejpam-4691	40	16	called	call	VERB
ejpam-4691	40	17	a	a	DET
ejpam-4691	40	18	minimal	minimal	ADJ
ejpam-4691	40	19	structure	structure	NOUN
ejpam-4691	40	20	(	(	PUNCT
ejpam-4691	40	21	or	or	CCONJ
ejpam-4691	40	22	briefly	briefly	NOUN
ejpam-4691	40	23	m	m	NOUN
ejpam-4691	40	24	-	-	NOUN
ejpam-4691	40	25	structure	structure	NOUN
ejpam-4691	40	26	)	)	PUNCT
ejpam-4691	41	1	[	[	X
ejpam-4691	41	2	24	24	NUM
ejpam-4691	41	3	]	]	PUNCT
ejpam-4691	41	4	,	,	PUNCT
ejpam-4691	41	5	[	[	X
ejpam-4691	41	6	25	25	NUM
ejpam-4691	41	7	]	]	PUNCT
ejpam-4691	41	8	on	on	ADP
ejpam-4691	41	9	x	x	SYM
ejpam-4691	41	10	if	if	SCONJ
ejpam-4691	41	11	∅	∅	NOUN
ejpam-4691	41	12	∈	∈	PROPN
ejpam-4691	41	13	mx	mx	PROPN
ejpam-4691	41	14	and	and	CCONJ
ejpam-4691	41	15	x	x	PROPN
ejpam-4691	41	16	∈	∈	PROPN
ejpam-4691	41	17	mx	mx	PROPN
ejpam-4691	41	18	.	.	PUNCT
ejpam-4691	42	1	by	by	ADP
ejpam-4691	42	2	(	(	PUNCT
ejpam-4691	42	3	x	x	NOUN
ejpam-4691	42	4	,	,	PUNCT
ejpam-4691	42	5	mx	mx	NOUN
ejpam-4691	42	6	)	)	PUNCT
ejpam-4691	42	7	(	(	PUNCT
ejpam-4691	42	8	or	or	CCONJ
ejpam-4691	42	9	briefly	briefly	ADV
ejpam-4691	42	10	(	(	PUNCT
ejpam-4691	42	11	x	x	X
ejpam-4691	42	12	,	,	PUNCT
ejpam-4691	42	13	m	m	NOUN
ejpam-4691	42	14	)	)	PUNCT
ejpam-4691	42	15	)	)	PUNCT
ejpam-4691	42	16	,	,	PUNCT
ejpam-4691	42	17	we	we	PRON
ejpam-4691	42	18	denote	denote	VERB
ejpam-4691	42	19	a	a	DET
ejpam-4691	42	20	nonempty	nonempty	ADV
ejpam-4691	42	21	set	set	VERB
ejpam-4691	42	22	x	x	PUNCT
ejpam-4691	42	23	with	with	ADP
ejpam-4691	42	24	a	a	DET
ejpam-4691	42	25	minimal	minimal	ADJ
ejpam-4691	42	26	structure	structure	NOUN
ejpam-4691	42	27	mx	mx	NOUN
ejpam-4691	42	28	on	on	ADP
ejpam-4691	42	29	x	x	PUNCT
ejpam-4691	42	30	and	and	CCONJ
ejpam-4691	42	31	call	call	VERB
ejpam-4691	42	32	it	it	PRON
ejpam-4691	42	33	an	an	DET
ejpam-4691	42	34	m	m	NOUN
ejpam-4691	42	35	-	-	NOUN
ejpam-4691	42	36	space	space	NOUN
ejpam-4691	42	37	.	.	PUNCT
ejpam-4691	43	1	each	each	DET
ejpam-4691	43	2	member	member	NOUN
ejpam-4691	43	3	of	of	ADP
ejpam-4691	43	4	mx	mx	PROPN
ejpam-4691	43	5	is	be	AUX
ejpam-4691	43	6	said	say	VERB
ejpam-4691	43	7	to	to	PART
ejpam-4691	43	8	be	be	AUX
ejpam-4691	43	9	mx	mx	PROPN
ejpam-4691	43	10	-open	-open	ADJ
ejpam-4691	43	11	(	(	PUNCT
ejpam-4691	43	12	or	or	CCONJ
ejpam-4691	43	13	briefly	briefly	NOUN
ejpam-4691	43	14	m	m	NOUN
ejpam-4691	43	15	-	-	VERB
ejpam-4691	43	16	open	open	ADJ
ejpam-4691	43	17	)	)	PUNCT
ejpam-4691	43	18	and	and	CCONJ
ejpam-4691	43	19	the	the	DET
ejpam-4691	43	20	complement	complement	NOUN
ejpam-4691	43	21	of	of	ADP
ejpam-4691	43	22	an	an	DET
ejpam-4691	43	23	mx	mx	PROPN
ejpam-4691	43	24	-open	-open	NOUN
ejpam-4691	43	25	set	set	NOUN
ejpam-4691	43	26	is	be	AUX
ejpam-4691	43	27	said	say	VERB
ejpam-4691	43	28	to	to	PART
ejpam-4691	43	29	be	be	AUX
ejpam-4691	43	30	mx	mx	NOUN
ejpam-4691	43	31	-	-	ADJ
ejpam-4691	43	32	closed	closed	ADJ
ejpam-4691	43	33	(	(	PUNCT
ejpam-4691	43	34	or	or	CCONJ
ejpam-4691	43	35	briefly	briefly	ADV
ejpam-4691	43	36	mclosed	mclose	VERB
ejpam-4691	43	37	)	)	PUNCT
ejpam-4691	43	38	.	.	PUNCT
ejpam-4691	44	1	definition	definition	NOUN
ejpam-4691	44	2	4	4	X
ejpam-4691	44	3	.	.	PUNCT
ejpam-4691	45	1	let	let	VERB
ejpam-4691	45	2	x	x	PRON
ejpam-4691	45	3	be	be	AUX
ejpam-4691	45	4	a	a	DET
ejpam-4691	45	5	nonempty	nonempty	ADV
ejpam-4691	45	6	set	set	VERB
ejpam-4691	45	7	and	and	CCONJ
ejpam-4691	45	8	mx	mx	X
ejpam-4691	45	9	an	an	DET
ejpam-4691	45	10	m	m	NOUN
ejpam-4691	45	11	-	-	NOUN
ejpam-4691	45	12	structure	structure	NOUN
ejpam-4691	45	13	on	on	ADP
ejpam-4691	45	14	x.	x.	NOUN
ejpam-4691	45	15	for	for	ADP
ejpam-4691	45	16	a	a	DET
ejpam-4691	45	17	subset	subset	NOUN
ejpam-4691	45	18	a	a	DET
ejpam-4691	45	19	of	of	ADP
ejpam-4691	45	20	x	x	PRON
ejpam-4691	45	21	,	,	PUNCT
ejpam-4691	45	22	the	the	DET
ejpam-4691	45	23	mx	mx	NOUN
ejpam-4691	45	24	-	-	NOUN
ejpam-4691	45	25	closure	closure	NOUN
ejpam-4691	45	26	and	and	CCONJ
ejpam-4691	45	27	the	the	DET
ejpam-4691	45	28	mx	mx	NOUN
ejpam-4691	45	29	-	-	NOUN
ejpam-4691	45	30	interior	interior	NOUN
ejpam-4691	45	31	of	of	ADP
ejpam-4691	45	32	a	a	PRON
ejpam-4691	45	33	are	be	AUX
ejpam-4691	45	34	defined	define	VERB
ejpam-4691	45	35	in	in	ADP
ejpam-4691	45	36	[	[	X
ejpam-4691	45	37	17	17	NUM
ejpam-4691	45	38	]	]	PUNCT
ejpam-4691	45	39	as	as	SCONJ
ejpam-4691	45	40	follows	follow	VERB
ejpam-4691	45	41	:	:	PUNCT
ejpam-4691	45	42	(	(	PUNCT
ejpam-4691	45	43	1	1	X
ejpam-4691	45	44	)	)	PUNCT
ejpam-4691	45	45	mxcl(a	mxcl(a	NOUN
ejpam-4691	45	46	)	)	PUNCT
ejpam-4691	46	1	=	=	PUNCT
ejpam-4691	46	2	∩{f	∩{f	NOUN
ejpam-4691	46	3	:	:	PUNCT
ejpam-4691	46	4	a	a	DET
ejpam-4691	46	5	⊂	⊂	PROPN
ejpam-4691	46	6	f	f	X
ejpam-4691	46	7	,	,	PUNCT
ejpam-4691	46	8	x	x	PROPN
ejpam-4691	46	9	−	−	PROPN
ejpam-4691	46	10	f	f	PROPN
ejpam-4691	46	11	∈	∈	PROPN
ejpam-4691	46	12	mx	mx	PROPN
ejpam-4691	46	13	}	}	PUNCT
ejpam-4691	46	14	,	,	PUNCT
ejpam-4691	46	15	(	(	PUNCT
ejpam-4691	46	16	2	2	X
ejpam-4691	46	17	)	)	PUNCT
ejpam-4691	46	18	mxint(a	mxint(a	NOUN
ejpam-4691	46	19	)	)	PUNCT
ejpam-4691	46	20	=	=	SYM
ejpam-4691	47	1	∪{u	∪{u	VERB
ejpam-4691	47	2	:	:	PUNCT
ejpam-4691	47	3	u	u	X
ejpam-4691	47	4	⊂	⊂	PROPN
ejpam-4691	47	5	a	a	X
ejpam-4691	47	6	,	,	PUNCT
ejpam-4691	47	7	u	u	PROPN
ejpam-4691	47	8	∈	∈	PROPN
ejpam-4691	47	9	mx	mx	PROPN
ejpam-4691	47	10	}	}	PUNCT
ejpam-4691	47	11	.	.	PUNCT
ejpam-4691	48	1	lemma	lemma	PROPN
ejpam-4691	48	2	1	1	NUM
ejpam-4691	48	3	.	.	PUNCT
ejpam-4691	49	1	(	(	PUNCT
ejpam-4691	49	2	maki	maki	NOUN
ejpam-4691	49	3	et	et	PROPN
ejpam-4691	49	4	al	al	PROPN
ejpam-4691	49	5	.	.	PUNCT
ejpam-4691	50	1	[	[	X
ejpam-4691	50	2	17	17	NUM
ejpam-4691	50	3	]	]	PUNCT
ejpam-4691	50	4	)	)	PUNCT
ejpam-4691	50	5	let	let	VERB
ejpam-4691	50	6	(	(	PUNCT
ejpam-4691	50	7	x	x	NOUN
ejpam-4691	50	8	,	,	PUNCT
ejpam-4691	50	9	mx	mx	NOUN
ejpam-4691	50	10	)	)	PUNCT
ejpam-4691	50	11	be	be	AUX
ejpam-4691	50	12	an	an	DET
ejpam-4691	50	13	m	m	NOUN
ejpam-4691	50	14	-	-	NOUN
ejpam-4691	50	15	space	space	NOUN
ejpam-4691	50	16	.	.	PUNCT
ejpam-4691	51	1	for	for	ADP
ejpam-4691	51	2	subsets	subset	NOUN
ejpam-4691	51	3	a	a	PRON
ejpam-4691	51	4	and	and	CCONJ
ejpam-4691	51	5	b	b	NOUN
ejpam-4691	51	6	of	of	ADP
ejpam-4691	51	7	x	x	PRON
ejpam-4691	51	8	,	,	PUNCT
ejpam-4691	51	9	the	the	DET
ejpam-4691	51	10	following	follow	VERB
ejpam-4691	51	11	properties	property	NOUN
ejpam-4691	51	12	hold	hold	VERB
ejpam-4691	51	13	:	:	PUNCT
ejpam-4691	51	14	(	(	PUNCT
ejpam-4691	51	15	1	1	X
ejpam-4691	51	16	)	)	PUNCT
ejpam-4691	51	17	mxcl(x	mxcl(x	PROPN
ejpam-4691	51	18	−a	−a	NOUN
ejpam-4691	51	19	)	)	PUNCT
ejpam-4691	52	1	=	=	PUNCT
ejpam-4691	52	2	x	x	SYM
ejpam-4691	52	3	−mxint(a	−mxint(a	NOUN
ejpam-4691	52	4	)	)	PUNCT
ejpam-4691	52	5	and	and	CCONJ
ejpam-4691	52	6	mxint(x	mxint(x	NOUN
ejpam-4691	52	7	−a	−a	NOUN
ejpam-4691	52	8	)	)	PUNCT
ejpam-4691	52	9	=	=	PUNCT
ejpam-4691	53	1	x	x	SYM
ejpam-4691	53	2	−mxcl(a	−mxcl(a	NUM
ejpam-4691	53	3	)	)	PUNCT
ejpam-4691	53	4	,	,	PUNCT
ejpam-4691	53	5	(	(	PUNCT
ejpam-4691	53	6	2	2	X
ejpam-4691	53	7	)	)	PUNCT
ejpam-4691	53	8	if	if	SCONJ
ejpam-4691	53	9	(	(	PUNCT
ejpam-4691	53	10	x	x	NOUN
ejpam-4691	53	11	−a	−a	ADJ
ejpam-4691	53	12	)	)	PUNCT
ejpam-4691	53	13	∈	∈	PROPN
ejpam-4691	53	14	mx	mx	PROPN
ejpam-4691	53	15	,	,	PUNCT
ejpam-4691	53	16	then	then	ADV
ejpam-4691	53	17	mxcl(a	mxcl(a	NUM
ejpam-4691	53	18	)	)	PUNCT
ejpam-4691	53	19	=	=	NOUN
ejpam-4691	53	20	a	a	PROPN
ejpam-4691	54	1	and	and	CCONJ
ejpam-4691	54	2	if	if	SCONJ
ejpam-4691	54	3	a	a	DET
ejpam-4691	54	4	∈	∈	PROPN
ejpam-4691	54	5	mx	mx	NOUN
ejpam-4691	54	6	,	,	PUNCT
ejpam-4691	54	7	then	then	ADV
ejpam-4691	54	8	mxint(a	mxint(a	PROPN
ejpam-4691	54	9	)	)	PUNCT
ejpam-4691	54	10	=	=	SYM
ejpam-4691	55	1	a	a	PRON
ejpam-4691	55	2	,	,	PUNCT
ejpam-4691	55	3	(	(	PUNCT
ejpam-4691	55	4	3	3	NUM
ejpam-4691	55	5	)	)	PUNCT
ejpam-4691	55	6	mxcl(∅	mxcl(∅	ADJ
ejpam-4691	55	7	)	)	PUNCT
ejpam-4691	55	8	=	=	SYM
ejpam-4691	55	9	∅,mxcl(x	∅,mxcl(x	PROPN
ejpam-4691	55	10	)	)	PUNCT
ejpam-4691	55	11	=	=	SYM
ejpam-4691	56	1	x	x	NOUN
ejpam-4691	56	2	,	,	PUNCT
ejpam-4691	56	3	mxint(∅	mxint(∅	NOUN
ejpam-4691	56	4	)	)	PUNCT
ejpam-4691	56	5	=	=	NOUN
ejpam-4691	56	6	∅	∅	NOUN
ejpam-4691	56	7	and	and	CCONJ
ejpam-4691	56	8	mxint(x	mxint(x	NUM
ejpam-4691	56	9	)	)	PUNCT
ejpam-4691	57	1	=	=	SYM
ejpam-4691	57	2	x	x	X
ejpam-4691	57	3	,	,	PUNCT
ejpam-4691	57	4	(	(	PUNCT
ejpam-4691	57	5	4	4	X
ejpam-4691	57	6	)	)	PUNCT
ejpam-4691	57	7	if	if	SCONJ
ejpam-4691	57	8	a	a	DET
ejpam-4691	57	9	⊂	⊂	PROPN
ejpam-4691	57	10	b	b	PROPN
ejpam-4691	57	11	,	,	PUNCT
ejpam-4691	57	12	then	then	ADV
ejpam-4691	57	13	mxcl(a	mxcl(a	NUM
ejpam-4691	57	14	)	)	PUNCT
ejpam-4691	57	15	⊂	⊂	PROPN
ejpam-4691	57	16	mxcl(b	mxcl(b	PROPN
ejpam-4691	57	17	)	)	PUNCT
ejpam-4691	57	18	and	and	CCONJ
ejpam-4691	57	19	mxint(a	mxint(a	PROPN
ejpam-4691	57	20	)	)	PUNCT
ejpam-4691	57	21	⊂	⊂	PROPN
ejpam-4691	57	22	mxint(b	mxint(b	PROPN
ejpam-4691	57	23	)	)	PUNCT
ejpam-4691	57	24	,	,	PUNCT
ejpam-4691	57	25	(	(	PUNCT
ejpam-4691	57	26	5	5	X
ejpam-4691	57	27	)	)	PUNCT
ejpam-4691	57	28	a	a	DET
ejpam-4691	57	29	⊂	⊂	PROPN
ejpam-4691	57	30	mxcl(a	mxcl(a	NOUN
ejpam-4691	57	31	)	)	PUNCT
ejpam-4691	57	32	and	and	CCONJ
ejpam-4691	57	33	mxint(a	mxint(a	PROPN
ejpam-4691	57	34	)	)	PUNCT
ejpam-4691	57	35	⊂	⊂	PROPN
ejpam-4691	57	36	a	a	X
ejpam-4691	57	37	,	,	PUNCT
ejpam-4691	57	38	(	(	PUNCT
ejpam-4691	57	39	6	6	NUM
ejpam-4691	57	40	)	)	PUNCT
ejpam-4691	57	41	mxcl(mxcl(a	mxcl(mxcl(a	NUM
ejpam-4691	57	42	)	)	PUNCT
ejpam-4691	57	43	)	)	PUNCT
ejpam-4691	58	1	=	=	SYM
ejpam-4691	58	2	mxcl(a	mxcl(a	NOUN
ejpam-4691	58	3	)	)	PUNCT
ejpam-4691	58	4	and	and	CCONJ
ejpam-4691	58	5	mxint(mxint(a	mxint(mxint(a	NOUN
ejpam-4691	58	6	)	)	PUNCT
ejpam-4691	58	7	)	)	PUNCT
ejpam-4691	59	1	=	=	PUNCT
ejpam-4691	59	2	mxint(a	mxint(a	NOUN
ejpam-4691	59	3	)	)	PUNCT
ejpam-4691	59	4	.	.	PUNCT
ejpam-4691	60	1	definition	definition	NOUN
ejpam-4691	60	2	5	5	NUM
ejpam-4691	60	3	.	.	PUNCT
ejpam-4691	61	1	an	an	DET
ejpam-4691	61	2	m	m	NOUN
ejpam-4691	61	3	-	-	PUNCT
ejpam-4691	61	4	structure	structure	ADJ
ejpam-4691	61	5	mx	mx	NOUN
ejpam-4691	61	6	on	on	ADP
ejpam-4691	61	7	a	a	DET
ejpam-4691	61	8	nonempty	nonempty	ADJ
ejpam-4691	61	9	set	set	VERB
ejpam-4691	61	10	x	x	SYM
ejpam-4691	61	11	is	be	AUX
ejpam-4691	61	12	said	say	VERB
ejpam-4691	61	13	to	to	PART
ejpam-4691	61	14	have	have	VERB
ejpam-4691	61	15	property	property	NOUN
ejpam-4691	61	16	b	b	PROPN
ejpam-4691	62	1	[	[	X
ejpam-4691	62	2	17	17	NUM
ejpam-4691	62	3	]	]	PUNCT
ejpam-4691	62	4	if	if	SCONJ
ejpam-4691	62	5	the	the	DET
ejpam-4691	62	6	union	union	NOUN
ejpam-4691	62	7	of	of	ADP
ejpam-4691	62	8	any	any	DET
ejpam-4691	62	9	family	family	NOUN
ejpam-4691	62	10	of	of	ADP
ejpam-4691	62	11	subsets	subset	NOUN
ejpam-4691	62	12	belonging	belong	VERB
ejpam-4691	62	13	to	to	ADP
ejpam-4691	62	14	mx	mx	PROPN
ejpam-4691	62	15	belongs	belong	VERB
ejpam-4691	62	16	to	to	ADP
ejpam-4691	62	17	mx	mx	PROPN
ejpam-4691	62	18	.	.	PUNCT
ejpam-4691	63	1	t.	t.	PROPN
ejpam-4691	63	2	noiri	noiri	PROPN
ejpam-4691	63	3	,	,	PUNCT
ejpam-4691	63	4	v.	v.	CCONJ
ejpam-4691	63	5	popa	popa	NOUN
ejpam-4691	63	6	/	/	SYM
ejpam-4691	63	7	eur	eur	PROPN
ejpam-4691	63	8	.	.	PUNCT
ejpam-4691	64	1	j.	j.	PROPN
ejpam-4691	64	2	pure	pure	PROPN
ejpam-4691	64	3	appl	appl	PROPN
ejpam-4691	64	4	.	.	PROPN
ejpam-4691	64	5	math	math	PROPN
ejpam-4691	64	6	,	,	PUNCT
ejpam-4691	64	7	16	16	NUM
ejpam-4691	64	8	(	(	PUNCT
ejpam-4691	64	9	1	1	NUM
ejpam-4691	64	10	)	)	PUNCT
ejpam-4691	64	11	(	(	PUNCT
ejpam-4691	64	12	2023	2023	NUM
ejpam-4691	64	13	)	)	PUNCT
ejpam-4691	64	14	,	,	PUNCT
ejpam-4691	64	15	430	430	NUM
ejpam-4691	64	16	-	-	SYM
ejpam-4691	64	17	439	439	NUM
ejpam-4691	64	18	432	432	NUM
ejpam-4691	64	19	remark	remark	NOUN
ejpam-4691	64	20	1	1	NUM
ejpam-4691	64	21	.	.	PUNCT
ejpam-4691	65	1	let	let	VERB
ejpam-4691	65	2	(	(	PUNCT
ejpam-4691	65	3	x	x	NOUN
ejpam-4691	65	4	,	,	PUNCT
ejpam-4691	65	5	τ	τ	X
ejpam-4691	65	6	)	)	PUNCT
ejpam-4691	65	7	be	be	VERB
ejpam-4691	65	8	a	a	DET
ejpam-4691	65	9	topological	topological	ADJ
ejpam-4691	65	10	space	space	NOUN
ejpam-4691	65	11	and	and	CCONJ
ejpam-4691	65	12	mx	mx	NOUN
ejpam-4691	65	13	=	=	SYM
ejpam-4691	65	14	so(x	so(x	X
ejpam-4691	65	15	)	)	PUNCT
ejpam-4691	65	16	(	(	PUNCT
ejpam-4691	65	17	resp	resp	NOUN
ejpam-4691	65	18	.	.	PUNCT
ejpam-4691	66	1	po(x	po(x	NUM
ejpam-4691	66	2	)	)	PUNCT
ejpam-4691	66	3	,	,	PUNCT
ejpam-4691	67	1	α(x	α(x	NOUN
ejpam-4691	67	2	)	)	PUNCT
ejpam-4691	67	3	,	,	PUNCT
ejpam-4691	67	4	β(x	β(x	NOUN
ejpam-4691	67	5	)	)	PUNCT
ejpam-4691	67	6	,	,	PUNCT
ejpam-4691	67	7	bo(x	bo(x	NUM
ejpam-4691	67	8	)	)	PUNCT
ejpam-4691	67	9	)	)	PUNCT
ejpam-4691	67	10	,	,	PUNCT
ejpam-4691	67	11	then	then	ADV
ejpam-4691	67	12	mx	mx	PROPN
ejpam-4691	67	13	is	be	AUX
ejpam-4691	67	14	an	an	DET
ejpam-4691	67	15	m	m	NOUN
ejpam-4691	67	16	-	-	NOUN
ejpam-4691	67	17	structure	structure	NOUN
ejpam-4691	67	18	having	have	VERB
ejpam-4691	67	19	property	property	NOUN
ejpam-4691	67	20	b.	b.	PROPN
ejpam-4691	67	21	lemma	lemma	PROPN
ejpam-4691	68	1	2	2	X
ejpam-4691	68	2	.	.	PUNCT
ejpam-4691	68	3	(	(	PUNCT
ejpam-4691	68	4	popa	popa	NOUN
ejpam-4691	68	5	and	and	CCONJ
ejpam-4691	68	6	noiri	noiri	ADV
ejpam-4691	69	1	[	[	X
ejpam-4691	69	2	26	26	NUM
ejpam-4691	69	3	]	]	PUNCT
ejpam-4691	69	4	)	)	PUNCT
ejpam-4691	69	5	let	let	AUX
ejpam-4691	69	6	(	(	PUNCT
ejpam-4691	69	7	x	x	NOUN
ejpam-4691	69	8	,	,	PUNCT
ejpam-4691	69	9	mx	mx	NOUN
ejpam-4691	69	10	)	)	PUNCT
ejpam-4691	69	11	be	be	AUX
ejpam-4691	69	12	an	an	DET
ejpam-4691	69	13	m	m	NOUN
ejpam-4691	69	14	-	-	NOUN
ejpam-4691	69	15	space	space	NOUN
ejpam-4691	69	16	and	and	CCONJ
ejpam-4691	69	17	mx	mx	PROPN
ejpam-4691	69	18	have	have	VERB
ejpam-4691	69	19	property	property	NOUN
ejpam-4691	69	20	b.	b.	PROPN
ejpam-4691	70	1	then	then	ADV
ejpam-4691	70	2	for	for	ADP
ejpam-4691	70	3	a	a	DET
ejpam-4691	70	4	subset	subset	NOUN
ejpam-4691	70	5	a	a	PRON
ejpam-4691	70	6	of	of	ADP
ejpam-4691	70	7	x	x	PRON
ejpam-4691	70	8	,	,	PUNCT
ejpam-4691	70	9	the	the	DET
ejpam-4691	70	10	following	follow	VERB
ejpam-4691	70	11	properties	property	NOUN
ejpam-4691	70	12	hold	hold	VERB
ejpam-4691	70	13	:	:	PUNCT
ejpam-4691	70	14	(	(	PUNCT
ejpam-4691	70	15	1	1	X
ejpam-4691	70	16	)	)	PUNCT
ejpam-4691	70	17	a	a	DET
ejpam-4691	70	18	∈	∈	PROPN
ejpam-4691	70	19	mx	mx	NOUN
ejpam-4691	71	1	if	if	SCONJ
ejpam-4691	71	2	and	and	CCONJ
ejpam-4691	71	3	only	only	ADV
ejpam-4691	71	4	if	if	SCONJ
ejpam-4691	71	5	mxint(a	mxint(a	PROPN
ejpam-4691	71	6	)	)	PUNCT
ejpam-4691	71	7	=	=	SYM
ejpam-4691	71	8	a	a	PRON
ejpam-4691	71	9	,	,	PUNCT
ejpam-4691	71	10	(	(	PUNCT
ejpam-4691	71	11	2	2	X
ejpam-4691	71	12	)	)	PUNCT
ejpam-4691	71	13	a	a	PRON
ejpam-4691	71	14	is	be	AUX
ejpam-4691	71	15	m	m	NOUN
ejpam-4691	71	16	-	-	PUNCT
ejpam-4691	71	17	closed	closed	ADJ
ejpam-4691	71	18	if	if	SCONJ
ejpam-4691	71	19	and	and	CCONJ
ejpam-4691	71	20	only	only	ADV
ejpam-4691	71	21	if	if	SCONJ
ejpam-4691	71	22	mxcl(a	mxcl(a	NUM
ejpam-4691	71	23	)	)	PUNCT
ejpam-4691	71	24	=	=	SYM
ejpam-4691	71	25	a	a	DET
ejpam-4691	71	26	,	,	PUNCT
ejpam-4691	71	27	(	(	PUNCT
ejpam-4691	71	28	3	3	X
ejpam-4691	71	29	)	)	PUNCT
ejpam-4691	71	30	mxint(a	mxint(a	NOUN
ejpam-4691	71	31	)	)	PUNCT
ejpam-4691	71	32	∈	∈	PROPN
ejpam-4691	71	33	mx	mx	PROPN
ejpam-4691	71	34	and	and	CCONJ
ejpam-4691	71	35	mxcl(a	mxcl(a	NUM
ejpam-4691	71	36	)	)	PUNCT
ejpam-4691	71	37	is	be	AUX
ejpam-4691	71	38	mx	mx	NOUN
ejpam-4691	71	39	-	-	ADJ
ejpam-4691	71	40	closed	closed	ADJ
ejpam-4691	71	41	.	.	PUNCT
ejpam-4691	72	1	3	3	X
ejpam-4691	72	2	.	.	X
ejpam-4691	72	3	m	m	ADJ
ejpam-4691	72	4	-	-	ADJ
ejpam-4691	72	5	open	open	ADJ
ejpam-4691	72	6	multifunctions	multifunction	NOUN
ejpam-4691	72	7	definition	definition	NOUN
ejpam-4691	72	8	6	6	NUM
ejpam-4691	72	9	.	.	PUNCT
ejpam-4691	73	1	let	let	VERB
ejpam-4691	73	2	(	(	PUNCT
ejpam-4691	73	3	x	x	NOUN
ejpam-4691	73	4	,	,	PUNCT
ejpam-4691	73	5	mx	mx	PROPN
ejpam-4691	73	6	)	)	PUNCT
ejpam-4691	73	7	and	and	CCONJ
ejpam-4691	73	8	(	(	PUNCT
ejpam-4691	73	9	y	y	PROPN
ejpam-4691	73	10	,	,	PUNCT
ejpam-4691	73	11	my	my	PRON
ejpam-4691	73	12	)	)	PUNCT
ejpam-4691	73	13	be	be	AUX
ejpam-4691	73	14	twom	twom	NOUN
ejpam-4691	73	15	-	-	PUNCT
ejpam-4691	73	16	spaces	space	NOUN
ejpam-4691	73	17	.	.	PUNCT
ejpam-4691	74	1	a	a	DET
ejpam-4691	74	2	multifunction	multifunction	NOUN
ejpam-4691	74	3	f	f	NOUN
ejpam-4691	74	4	:	:	PUNCT
ejpam-4691	74	5	(	(	PUNCT
ejpam-4691	74	6	x	x	NOUN
ejpam-4691	74	7	,	,	PUNCT
ejpam-4691	74	8	mx	mx	NOUN
ejpam-4691	74	9	)	)	PUNCT
ejpam-4691	74	10	→	→	SYM
ejpam-4691	74	11	(	(	PUNCT
ejpam-4691	74	12	y	y	PROPN
ejpam-4691	74	13	,	,	PUNCT
ejpam-4691	74	14	my	my	INTJ
ejpam-4691	74	15	)	)	PUNCT
ejpam-4691	74	16	is	be	AUX
ejpam-4691	74	17	said	say	VERB
ejpam-4691	74	18	to	to	PART
ejpam-4691	74	19	be	be	AUX
ejpam-4691	74	20	m	m	NOUN
ejpam-4691	74	21	-	-	ADJ
ejpam-4691	74	22	open	open	ADJ
ejpam-4691	74	23	at	at	ADP
ejpam-4691	74	24	x	x	X
ejpam-4691	74	25	∈	∈	PROPN
ejpam-4691	74	26	x	x	SYM
ejpam-4691	74	27	if	if	SCONJ
ejpam-4691	74	28	for	for	ADP
ejpam-4691	74	29	each	each	DET
ejpam-4691	74	30	mx	mx	PROPN
ejpam-4691	74	31	-open	-open	PROPN
ejpam-4691	74	32	set	set	VERB
ejpam-4691	74	33	u	u	NOUN
ejpam-4691	74	34	containing	contain	VERB
ejpam-4691	74	35	x	x	PRON
ejpam-4691	74	36	,	,	PUNCT
ejpam-4691	74	37	there	there	PRON
ejpam-4691	74	38	exists	exist	VERB
ejpam-4691	74	39	v	v	ADP
ejpam-4691	74	40	∈	∈	PRON
ejpam-4691	74	41	my	my	PRON
ejpam-4691	74	42	containing	contain	VERB
ejpam-4691	74	43	f	f	X
ejpam-4691	74	44	(	(	PUNCT
ejpam-4691	74	45	x	x	X
ejpam-4691	74	46	)	)	PUNCT
ejpam-4691	74	47	such	such	ADJ
ejpam-4691	74	48	that	that	DET
ejpam-4691	74	49	v	v	X
ejpam-4691	74	50	⊂	⊂	PROPN
ejpam-4691	74	51	f	f	X
ejpam-4691	74	52	(	(	PUNCT
ejpam-4691	74	53	u	u	NOUN
ejpam-4691	74	54	)	)	PUNCT
ejpam-4691	74	55	.	.	PUNCT
ejpam-4691	75	1	if	if	SCONJ
ejpam-4691	75	2	f	f	PROPN
ejpam-4691	75	3	is	be	AUX
ejpam-4691	75	4	m	m	NOUN
ejpam-4691	75	5	-	-	ADJ
ejpam-4691	75	6	open	open	ADJ
ejpam-4691	75	7	at	at	ADP
ejpam-4691	75	8	each	each	DET
ejpam-4691	75	9	point	point	NOUN
ejpam-4691	75	10	x	x	X
ejpam-4691	75	11	∈	∈	NOUN
ejpam-4691	75	12	x	x	NOUN
ejpam-4691	75	13	,	,	PUNCT
ejpam-4691	75	14	then	then	ADV
ejpam-4691	75	15	f	f	PROPN
ejpam-4691	75	16	is	be	AUX
ejpam-4691	75	17	said	say	VERB
ejpam-4691	75	18	to	to	PART
ejpam-4691	75	19	be	be	AUX
ejpam-4691	75	20	m	m	NOUN
ejpam-4691	75	21	-	-	ADJ
ejpam-4691	75	22	open	open	ADJ
ejpam-4691	75	23	.	.	PUNCT
ejpam-4691	76	1	theorem	theorem	NOUN
ejpam-4691	76	2	1	1	NUM
ejpam-4691	76	3	.	.	PUNCT
ejpam-4691	76	4	a	a	DET
ejpam-4691	76	5	multifunction	multifunction	NOUN
ejpam-4691	77	1	f	f	NOUN
ejpam-4691	77	2	:	:	PUNCT
ejpam-4691	77	3	(	(	PUNCT
ejpam-4691	77	4	x	x	NOUN
ejpam-4691	77	5	,	,	PUNCT
ejpam-4691	77	6	mx	mx	NOUN
ejpam-4691	77	7	)	)	PUNCT
ejpam-4691	77	8	→	→	SYM
ejpam-4691	77	9	(	(	PUNCT
ejpam-4691	77	10	y	y	PROPN
ejpam-4691	77	11	,	,	PUNCT
ejpam-4691	77	12	my	my	PRON
ejpam-4691	77	13	)	)	PUNCT
ejpam-4691	77	14	is	be	AUX
ejpam-4691	77	15	m	m	NOUN
ejpam-4691	77	16	-	-	ADJ
ejpam-4691	77	17	open	open	ADJ
ejpam-4691	77	18	at	at	ADP
ejpam-4691	77	19	x	x	X
ejpam-4691	77	20	∈	∈	PROPN
ejpam-4691	77	21	x	x	NOUN
ejpam-4691	77	22	,	,	PUNCT
ejpam-4691	77	23	where	where	SCONJ
ejpam-4691	77	24	my	my	PRON
ejpam-4691	77	25	has	have	VERB
ejpam-4691	77	26	property	property	NOUN
ejpam-4691	77	27	b	b	PROPN
ejpam-4691	77	28	,	,	PUNCT
ejpam-4691	77	29	if	if	SCONJ
ejpam-4691	77	30	and	and	CCONJ
ejpam-4691	77	31	only	only	ADV
ejpam-4691	77	32	if	if	SCONJ
ejpam-4691	77	33	for	for	SCONJ
ejpam-4691	77	34	each	each	DET
ejpam-4691	77	35	mx	mx	NOUN
ejpam-4691	77	36	-	-	ADJ
ejpam-4691	77	37	open	open	ADJ
ejpam-4691	77	38	set	set	NOUN
ejpam-4691	77	39	u	u	NOUN
ejpam-4691	77	40	containing	contain	VERB
ejpam-4691	77	41	x	x	PRON
ejpam-4691	77	42	,	,	PUNCT
ejpam-4691	77	43	x	x	SYM
ejpam-4691	77	44	∈	∈	NOUN
ejpam-4691	77	45	f+(my	f+(my	NOUN
ejpam-4691	77	46	int(f	int(f	NOUN
ejpam-4691	77	47	(	(	PUNCT
ejpam-4691	77	48	u	u	NOUN
ejpam-4691	77	49	)	)	PUNCT
ejpam-4691	77	50	)	)	PUNCT
ejpam-4691	77	51	)	)	PUNCT
ejpam-4691	77	52	.	.	PUNCT
ejpam-4691	78	1	proof	proof	NOUN
ejpam-4691	78	2	.	.	PUNCT
ejpam-4691	79	1	necessity	necessity	NOUN
ejpam-4691	79	2	.	.	PUNCT
ejpam-4691	80	1	let	let	VERB
ejpam-4691	80	2	u	u	PRON
ejpam-4691	80	3	be	be	AUX
ejpam-4691	80	4	any	any	DET
ejpam-4691	80	5	mx	mx	PROPN
ejpam-4691	80	6	-open	-open	NOUN
ejpam-4691	80	7	set	set	NOUN
ejpam-4691	80	8	containing	contain	VERB
ejpam-4691	80	9	x.	x.	NOUN
ejpam-4691	80	10	then	then	ADV
ejpam-4691	80	11	,	,	PUNCT
ejpam-4691	80	12	there	there	PRON
ejpam-4691	80	13	exists	exist	VERB
ejpam-4691	80	14	v	v	ADP
ejpam-4691	80	15	∈	∈	PRON
ejpam-4691	80	16	my	my	PRON
ejpam-4691	80	17	such	such	ADJ
ejpam-4691	80	18	that	that	SCONJ
ejpam-4691	80	19	f	f	PROPN
ejpam-4691	80	20	(	(	PUNCT
ejpam-4691	80	21	x	x	X
ejpam-4691	80	22	)	)	PUNCT
ejpam-4691	80	23	⊂	⊂	PROPN
ejpam-4691	80	24	v	v	ADP
ejpam-4691	80	25	⊂	⊂	PROPN
ejpam-4691	80	26	f	f	X
ejpam-4691	80	27	(	(	PUNCT
ejpam-4691	80	28	u	u	NOUN
ejpam-4691	80	29	)	)	PUNCT
ejpam-4691	80	30	and	and	CCONJ
ejpam-4691	80	31	hence	hence	ADV
ejpam-4691	80	32	f	f	PROPN
ejpam-4691	80	33	(	(	PUNCT
ejpam-4691	80	34	x	x	X
ejpam-4691	80	35	)	)	PUNCT
ejpam-4691	80	36	⊂	⊂	PRON
ejpam-4691	80	37	my	my	PRON
ejpam-4691	80	38	int(f	int(f	PROPN
ejpam-4691	80	39	(	(	PUNCT
ejpam-4691	80	40	u	u	NOUN
ejpam-4691	80	41	)	)	PUNCT
ejpam-4691	80	42	)	)	PUNCT
ejpam-4691	80	43	.	.	PUNCT
ejpam-4691	81	1	therefore	therefore	ADV
ejpam-4691	81	2	,	,	PUNCT
ejpam-4691	81	3	we	we	PRON
ejpam-4691	81	4	obtain	obtain	VERB
ejpam-4691	81	5	that	that	SCONJ
ejpam-4691	81	6	x	x	SYM
ejpam-4691	81	7	∈	∈	NOUN
ejpam-4691	81	8	f+(my	f+(my	NOUN
ejpam-4691	81	9	int(f	int(f	NOUN
ejpam-4691	81	10	(	(	PUNCT
ejpam-4691	81	11	u	u	NOUN
ejpam-4691	81	12	)	)	PUNCT
ejpam-4691	81	13	)	)	PUNCT
ejpam-4691	81	14	)	)	PUNCT
ejpam-4691	81	15	.	.	PUNCT
ejpam-4691	82	1	sufficiency	sufficiency	PROPN
ejpam-4691	82	2	.	.	PUNCT
ejpam-4691	83	1	suppose	suppose	VERB
ejpam-4691	83	2	that	that	SCONJ
ejpam-4691	83	3	x	x	PUNCT
ejpam-4691	83	4	∈	∈	PROPN
ejpam-4691	83	5	f+(my	f+(my	NOUN
ejpam-4691	83	6	int(f	int(f	NOUN
ejpam-4691	83	7	(	(	PUNCT
ejpam-4691	83	8	u	u	NOUN
ejpam-4691	83	9	)	)	PUNCT
ejpam-4691	83	10	)	)	PUNCT
ejpam-4691	83	11	)	)	PUNCT
ejpam-4691	83	12	for	for	ADP
ejpam-4691	83	13	each	each	DET
ejpam-4691	83	14	mx	mx	PROPN
ejpam-4691	83	15	-open	-open	PROPN
ejpam-4691	83	16	set	set	VERB
ejpam-4691	83	17	u	u	NOUN
ejpam-4691	83	18	containing	contain	VERB
ejpam-4691	83	19	x.	x.	NOUN
ejpam-4691	83	20	then	then	ADV
ejpam-4691	83	21	f	f	PROPN
ejpam-4691	83	22	(	(	PUNCT
ejpam-4691	83	23	x	x	X
ejpam-4691	83	24	)	)	PUNCT
ejpam-4691	83	25	⊂	⊂	PRON
ejpam-4691	83	26	my	my	PRON
ejpam-4691	83	27	int(f	int(f	PROPN
ejpam-4691	83	28	(	(	PUNCT
ejpam-4691	83	29	u	u	NOUN
ejpam-4691	83	30	)	)	PUNCT
ejpam-4691	83	31	)	)	PUNCT
ejpam-4691	83	32	.	.	PUNCT
ejpam-4691	84	1	set	set	VERB
ejpam-4691	84	2	v	v	NOUN
ejpam-4691	84	3	=	=	PRON
ejpam-4691	84	4	my	my	PRON
ejpam-4691	84	5	int(f	int(f	PROPN
ejpam-4691	84	6	(	(	PUNCT
ejpam-4691	84	7	u	u	NOUN
ejpam-4691	84	8	)	)	PUNCT
ejpam-4691	84	9	)	)	PUNCT
ejpam-4691	84	10	,	,	PUNCT
ejpam-4691	84	11	then	then	ADV
ejpam-4691	84	12	by	by	ADP
ejpam-4691	84	13	lemma	lemma	PROPN
ejpam-4691	84	14	2	2	NUM
ejpam-4691	84	15	v	v	NOUN
ejpam-4691	84	16	∈	∈	PRON
ejpam-4691	84	17	my	my	PRON
ejpam-4691	84	18	and	and	CCONJ
ejpam-4691	84	19	f	f	PROPN
ejpam-4691	84	20	(	(	PUNCT
ejpam-4691	84	21	x	x	X
ejpam-4691	84	22	)	)	PUNCT
ejpam-4691	84	23	⊂	⊂	PROPN
ejpam-4691	84	24	v	v	ADP
ejpam-4691	84	25	⊂	⊂	PROPN
ejpam-4691	84	26	f	f	X
ejpam-4691	84	27	(	(	PUNCT
ejpam-4691	84	28	u	u	NOUN
ejpam-4691	84	29	)	)	PUNCT
ejpam-4691	84	30	.	.	PUNCT
ejpam-4691	85	1	therefore	therefore	ADV
ejpam-4691	85	2	,	,	PUNCT
ejpam-4691	85	3	f	f	PROPN
ejpam-4691	85	4	is	be	AUX
ejpam-4691	85	5	m	m	NOUN
ejpam-4691	85	6	-	-	ADJ
ejpam-4691	85	7	open	open	ADJ
ejpam-4691	85	8	at	at	ADP
ejpam-4691	85	9	x.	x.	NOUN
ejpam-4691	85	10	theorem	theorem	NOUN
ejpam-4691	85	11	2	2	NUM
ejpam-4691	85	12	.	.	PUNCT
ejpam-4691	85	13	a	a	DET
ejpam-4691	85	14	multifunction	multifunction	NOUN
ejpam-4691	85	15	f	f	NOUN
ejpam-4691	85	16	:	:	PUNCT
ejpam-4691	85	17	(	(	PUNCT
ejpam-4691	85	18	x	x	NOUN
ejpam-4691	85	19	,	,	PUNCT
ejpam-4691	85	20	mx	mx	NOUN
ejpam-4691	85	21	)	)	PUNCT
ejpam-4691	85	22	→	→	SYM
ejpam-4691	85	23	(	(	PUNCT
ejpam-4691	85	24	y	y	PROPN
ejpam-4691	85	25	,	,	PUNCT
ejpam-4691	85	26	my	my	PRON
ejpam-4691	85	27	)	)	PUNCT
ejpam-4691	85	28	is	be	AUX
ejpam-4691	85	29	m	m	NOUN
ejpam-4691	85	30	-	-	ADJ
ejpam-4691	85	31	open	open	ADJ
ejpam-4691	85	32	,	,	PUNCT
ejpam-4691	85	33	where	where	SCONJ
ejpam-4691	85	34	(	(	PUNCT
ejpam-4691	85	35	y	y	NOUN
ejpam-4691	85	36	,	,	PUNCT
ejpam-4691	85	37	my	my	INTJ
ejpam-4691	85	38	)	)	PUNCT
ejpam-4691	85	39	has	have	VERB
ejpam-4691	85	40	property	property	NOUN
ejpam-4691	85	41	b	b	NOUN
ejpam-4691	85	42	,	,	PUNCT
ejpam-4691	85	43	if	if	SCONJ
ejpam-4691	85	44	and	and	CCONJ
ejpam-4691	85	45	only	only	ADV
ejpam-4691	85	46	if	if	SCONJ
ejpam-4691	85	47	f	f	PROPN
ejpam-4691	85	48	(	(	PUNCT
ejpam-4691	85	49	u	u	NOUN
ejpam-4691	85	50	)	)	PUNCT
ejpam-4691	85	51	is	be	AUX
ejpam-4691	85	52	my	my	PRON
ejpam-4691	85	53	-open	-open	NOUN
ejpam-4691	85	54	for	for	ADP
ejpam-4691	85	55	each	each	DET
ejpam-4691	85	56	mx	mx	NOUN
ejpam-4691	85	57	-	-	ADJ
ejpam-4691	85	58	open	open	ADJ
ejpam-4691	85	59	set	set	NOUN
ejpam-4691	85	60	u	u	NOUN
ejpam-4691	85	61	of	of	ADP
ejpam-4691	85	62	x.	x.	NOUN
ejpam-4691	85	63	proof	proof	NOUN
ejpam-4691	85	64	.	.	PUNCT
ejpam-4691	86	1	necessity	necessity	NOUN
ejpam-4691	86	2	.	.	PUNCT
ejpam-4691	87	1	let	let	VERB
ejpam-4691	87	2	u	u	PRON
ejpam-4691	87	3	be	be	AUX
ejpam-4691	87	4	any	any	DET
ejpam-4691	87	5	mx	mx	PROPN
ejpam-4691	87	6	-open	-open	NOUN
ejpam-4691	87	7	set	set	NOUN
ejpam-4691	87	8	of	of	ADP
ejpam-4691	87	9	x	x	PUNCT
ejpam-4691	87	10	and	and	CCONJ
ejpam-4691	87	11	x	x	SYM
ejpam-4691	87	12	∈	∈	PROPN
ejpam-4691	87	13	u	u	NOUN
ejpam-4691	87	14	.	.	PUNCT
ejpam-4691	88	1	since	since	SCONJ
ejpam-4691	88	2	f	f	PROPN
ejpam-4691	88	3	is	be	AUX
ejpam-4691	88	4	m	m	NOUN
ejpam-4691	88	5	-	-	ADJ
ejpam-4691	88	6	open	open	ADJ
ejpam-4691	88	7	at	at	ADP
ejpam-4691	88	8	x	x	X
ejpam-4691	88	9	∈	∈	PROPN
ejpam-4691	88	10	x	x	NOUN
ejpam-4691	88	11	,	,	PUNCT
ejpam-4691	88	12	by	by	ADP
ejpam-4691	88	13	theorem	theorem	NOUN
ejpam-4691	88	14	1	1	NUM
ejpam-4691	88	15	we	we	PRON
ejpam-4691	88	16	have	have	VERB
ejpam-4691	88	17	f	f	PROPN
ejpam-4691	88	18	(	(	PUNCT
ejpam-4691	88	19	x	x	X
ejpam-4691	88	20	)	)	PUNCT
ejpam-4691	88	21	⊂	⊂	PRON
ejpam-4691	88	22	my	my	PRON
ejpam-4691	88	23	int(f	int(f	PROPN
ejpam-4691	88	24	(	(	PUNCT
ejpam-4691	88	25	u	u	NOUN
ejpam-4691	88	26	)	)	PUNCT
ejpam-4691	88	27	)	)	PUNCT
ejpam-4691	89	1	and	and	CCONJ
ejpam-4691	89	2	f	f	PROPN
ejpam-4691	89	3	(	(	PUNCT
ejpam-4691	89	4	u	u	NOUN
ejpam-4691	89	5	)	)	PUNCT
ejpam-4691	89	6	=	=	VERB
ejpam-4691	89	7	my	my	PRON
ejpam-4691	89	8	int(f	int(f	PROPN
ejpam-4691	89	9	(	(	PUNCT
ejpam-4691	89	10	u	u	NOUN
ejpam-4691	89	11	)	)	PUNCT
ejpam-4691	89	12	)	)	PUNCT
ejpam-4691	89	13	.	.	PUNCT
ejpam-4691	90	1	by	by	ADP
ejpam-4691	90	2	lemma	lemma	PROPN
ejpam-4691	90	3	2	2	NUM
ejpam-4691	90	4	,	,	PUNCT
ejpam-4691	90	5	f	f	PROPN
ejpam-4691	90	6	(	(	PUNCT
ejpam-4691	90	7	u	u	NOUN
ejpam-4691	90	8	)	)	PUNCT
ejpam-4691	90	9	is	be	AUX
ejpam-4691	90	10	my	my	PRON
ejpam-4691	90	11	-open	-open	NOUN
ejpam-4691	90	12	.	.	PUNCT
ejpam-4691	91	1	sufficiency	sufficiency	PROPN
ejpam-4691	91	2	.	.	PUNCT
ejpam-4691	92	1	let	let	VERB
ejpam-4691	92	2	x	x	PRON
ejpam-4691	92	3	be	be	AUX
ejpam-4691	92	4	an	an	DET
ejpam-4691	92	5	arbitrary	arbitrary	ADJ
ejpam-4691	92	6	point	point	NOUN
ejpam-4691	92	7	of	of	ADP
ejpam-4691	92	8	x	x	PUNCT
ejpam-4691	92	9	and	and	CCONJ
ejpam-4691	92	10	u	u	PRON
ejpam-4691	92	11	any	any	DET
ejpam-4691	92	12	mx	mx	PROPN
ejpam-4691	92	13	-open	-open	NOUN
ejpam-4691	92	14	set	set	NOUN
ejpam-4691	92	15	of	of	ADP
ejpam-4691	92	16	x	x	PUNCT
ejpam-4691	92	17	containing	contain	VERB
ejpam-4691	92	18	x.	x.	NOUN
ejpam-4691	92	19	then	then	ADV
ejpam-4691	92	20	,	,	PUNCT
ejpam-4691	92	21	we	we	PRON
ejpam-4691	92	22	have	have	VERB
ejpam-4691	92	23	f	f	PROPN
ejpam-4691	92	24	(	(	PUNCT
ejpam-4691	92	25	x	x	X
ejpam-4691	92	26	)	)	PUNCT
ejpam-4691	93	1	⊂	⊂	PROPN
ejpam-4691	93	2	f	f	X
ejpam-4691	93	3	(	(	PUNCT
ejpam-4691	93	4	u	u	NOUN
ejpam-4691	93	5	)	)	PUNCT
ejpam-4691	93	6	=	=	VERB
ejpam-4691	93	7	my	my	PRON
ejpam-4691	93	8	int(f	int(f	PROPN
ejpam-4691	93	9	(	(	PUNCT
ejpam-4691	93	10	u	u	NOUN
ejpam-4691	93	11	)	)	PUNCT
ejpam-4691	93	12	)	)	PUNCT
ejpam-4691	93	13	.	.	PUNCT
ejpam-4691	94	1	therefore	therefore	ADV
ejpam-4691	94	2	,	,	PUNCT
ejpam-4691	94	3	x	x	PUNCT
ejpam-4691	94	4	∈	∈	NOUN
ejpam-4691	94	5	f+(my	f+(my	NOUN
ejpam-4691	94	6	int(f	int(f	NOUN
ejpam-4691	94	7	(	(	PUNCT
ejpam-4691	94	8	u	u	NOUN
ejpam-4691	94	9	)	)	PUNCT
ejpam-4691	94	10	)	)	PUNCT
ejpam-4691	94	11	.	.	PUNCT
ejpam-4691	95	1	by	by	ADP
ejpam-4691	95	2	theorem	theorem	NOUN
ejpam-4691	95	3	1	1	NUM
ejpam-4691	95	4	,	,	PUNCT
ejpam-4691	95	5	f	f	PROPN
ejpam-4691	95	6	is	be	AUX
ejpam-4691	95	7	m	m	NOUN
ejpam-4691	95	8	-	-	ADJ
ejpam-4691	95	9	open	open	ADJ
ejpam-4691	95	10	at	at	ADP
ejpam-4691	95	11	an	an	DET
ejpam-4691	95	12	arbitrary	arbitrary	ADJ
ejpam-4691	95	13	point	point	NOUN
ejpam-4691	95	14	x	x	X
ejpam-4691	95	15	∈	∈	NOUN
ejpam-4691	95	16	x.	x.	NOUN
ejpam-4691	95	17	remark	remark	NOUN
ejpam-4691	95	18	2	2	NUM
ejpam-4691	95	19	.	.	PUNCT
ejpam-4691	95	20	for	for	ADP
ejpam-4691	95	21	a	a	DET
ejpam-4691	95	22	multifunction	multifunction	NOUN
ejpam-4691	96	1	f	f	NOUN
ejpam-4691	96	2	:	:	PUNCT
ejpam-4691	96	3	(	(	PUNCT
ejpam-4691	96	4	x	x	NOUN
ejpam-4691	96	5	,	,	PUNCT
ejpam-4691	96	6	mx	mx	NOUN
ejpam-4691	96	7	)	)	PUNCT
ejpam-4691	96	8	→	→	SYM
ejpam-4691	96	9	(	(	PUNCT
ejpam-4691	96	10	y	y	PROPN
ejpam-4691	96	11	,	,	PUNCT
ejpam-4691	96	12	my	my	INTJ
ejpam-4691	96	13	)	)	PUNCT
ejpam-4691	96	14	,	,	PUNCT
ejpam-4691	96	15	let	let	VERB
ejpam-4691	96	16	mx	mx	VERB
ejpam-4691	96	17	=	=	SYM
ejpam-4691	96	18	τ	τ	PROPN
ejpam-4691	96	19	and	and	CCONJ
ejpam-4691	96	20	my	my	PRON
ejpam-4691	96	21	=	=	PROPN
ejpam-4691	96	22	σ	σ	PROPN
ejpam-4691	96	23	(	(	PUNCT
ejpam-4691	96	24	resp	resp	PROPN
ejpam-4691	96	25	.	.	PUNCT
ejpam-4691	97	1	so(y	so(y	PROPN
ejpam-4691	97	2	)	)	PUNCT
ejpam-4691	97	3	,	,	PUNCT
ejpam-4691	97	4	po(y	po(y	X
ejpam-4691	97	5	)	)	PUNCT
ejpam-4691	97	6	,	,	PUNCT
ejpam-4691	97	7	α(y	α(y	NOUN
ejpam-4691	97	8	)	)	PUNCT
ejpam-4691	97	9	,	,	PUNCT
ejpam-4691	97	10	β(y	β(y	PROPN
ejpam-4691	97	11	)	)	PUNCT
ejpam-4691	97	12	)	)	PUNCT
ejpam-4691	98	1	,	,	PUNCT
ejpam-4691	98	2	then	then	ADV
ejpam-4691	98	3	we	we	PRON
ejpam-4691	98	4	obtain	obtain	VERB
ejpam-4691	98	5	definition	definition	NOUN
ejpam-4691	98	6	2	2	NUM
ejpam-4691	98	7	,	,	PUNCT
ejpam-4691	98	8	that	that	ADV
ejpam-4691	98	9	is	is	ADV
ejpam-4691	98	10	,	,	PUNCT
ejpam-4691	98	11	the	the	DET
ejpam-4691	98	12	definition	definition	NOUN
ejpam-4691	98	13	of	of	ADP
ejpam-4691	98	14	an	an	DET
ejpam-4691	98	15	open	open	ADJ
ejpam-4691	98	16	(	(	PUNCT
ejpam-4691	98	17	resp	resp	NOUN
ejpam-4691	98	18	.	.	PUNCT
ejpam-4691	99	1	semi	semi	ADJ
ejpam-4691	99	2	-	-	ADJ
ejpam-4691	99	3	open	open	ADJ
ejpam-4691	99	4	,	,	PUNCT
ejpam-4691	99	5	preopen	preopen	ADJ
ejpam-4691	99	6	,	,	PUNCT
ejpam-4691	99	7	α	α	NOUN
ejpam-4691	99	8	-	-	ADJ
ejpam-4691	99	9	open	open	ADJ
ejpam-4691	99	10	,	,	PUNCT
ejpam-4691	99	11	β	β	ADJ
ejpam-4691	99	12	-	-	ADJ
ejpam-4691	99	13	open	open	ADJ
ejpam-4691	99	14	)	)	PUNCT
ejpam-4691	99	15	multifunction	multifunction	NOUN
ejpam-4691	99	16	.	.	PUNCT
ejpam-4691	100	1	theorem	theorem	VERB
ejpam-4691	100	2	3	3	NUM
ejpam-4691	100	3	.	.	X
ejpam-4691	100	4	for	for	ADP
ejpam-4691	100	5	a	a	DET
ejpam-4691	100	6	multifunction	multifunction	NOUN
ejpam-4691	101	1	f	f	NOUN
ejpam-4691	101	2	:	:	PUNCT
ejpam-4691	101	3	(	(	PUNCT
ejpam-4691	101	4	x	x	NOUN
ejpam-4691	101	5	,	,	PUNCT
ejpam-4691	101	6	mx	mx	NOUN
ejpam-4691	101	7	)	)	PUNCT
ejpam-4691	101	8	→	→	SYM
ejpam-4691	101	9	(	(	PUNCT
ejpam-4691	101	10	y	y	PROPN
ejpam-4691	101	11	,	,	PUNCT
ejpam-4691	101	12	my	my	INTJ
ejpam-4691	101	13	)	)	PUNCT
ejpam-4691	101	14	,	,	PUNCT
ejpam-4691	101	15	where	where	SCONJ
ejpam-4691	101	16	my	my	PRON
ejpam-4691	101	17	has	have	VERB
ejpam-4691	101	18	property	property	NOUN
ejpam-4691	101	19	b	b	PROPN
ejpam-4691	101	20	,	,	PUNCT
ejpam-4691	101	21	the	the	DET
ejpam-4691	101	22	following	follow	VERB
ejpam-4691	101	23	properties	property	NOUN
ejpam-4691	101	24	are	be	AUX
ejpam-4691	101	25	equivalent	equivalent	ADJ
ejpam-4691	101	26	:	:	PUNCT
ejpam-4691	101	27	(	(	PUNCT
ejpam-4691	101	28	1	1	X
ejpam-4691	101	29	)	)	PUNCT
ejpam-4691	101	30	f	f	PROPN
ejpam-4691	101	31	is	be	AUX
ejpam-4691	101	32	m	m	NOUN
ejpam-4691	101	33	-	-	ADJ
ejpam-4691	101	34	open	open	ADJ
ejpam-4691	101	35	at	at	ADP
ejpam-4691	101	36	x	x	PRON
ejpam-4691	101	37	;	;	PUNCT
ejpam-4691	101	38	(	(	PUNCT
ejpam-4691	101	39	2	2	X
ejpam-4691	101	40	)	)	PUNCT
ejpam-4691	102	1	if	if	SCONJ
ejpam-4691	102	2	x	x	SYM
ejpam-4691	102	3	∈	∈	PROPN
ejpam-4691	102	4	mxint(a	mxint(a	NOUN
ejpam-4691	102	5	)	)	PUNCT
ejpam-4691	102	6	for	for	ADP
ejpam-4691	102	7	any	any	DET
ejpam-4691	102	8	a	a	DET
ejpam-4691	102	9	∈	∈	PROPN
ejpam-4691	102	10	p(x	p(x	NOUN
ejpam-4691	102	11	)	)	PUNCT
ejpam-4691	102	12	,	,	PUNCT
ejpam-4691	102	13	then	then	ADV
ejpam-4691	102	14	x	x	X
ejpam-4691	102	15	∈	∈	NOUN
ejpam-4691	102	16	f+(my	f+(my	NOUN
ejpam-4691	102	17	int(f	int(f	NOUN
ejpam-4691	102	18	(	(	PUNCT
ejpam-4691	102	19	a	a	NOUN
ejpam-4691	102	20	)	)	PUNCT
ejpam-4691	102	21	)	)	PUNCT
ejpam-4691	102	22	)	)	PUNCT
ejpam-4691	102	23	;	;	PUNCT
ejpam-4691	102	24	(	(	PUNCT
ejpam-4691	102	25	3	3	X
ejpam-4691	102	26	)	)	PUNCT
ejpam-4691	102	27	if	if	SCONJ
ejpam-4691	102	28	x	x	X
ejpam-4691	102	29	∈	∈	NOUN
ejpam-4691	102	30	mxint(f+(b	mxint(f+(b	NOUN
ejpam-4691	102	31	)	)	PUNCT
ejpam-4691	102	32	)	)	PUNCT
ejpam-4691	102	33	for	for	ADP
ejpam-4691	102	34	any	any	DET
ejpam-4691	102	35	b	b	PROPN
ejpam-4691	102	36	∈	∈	PROPN
ejpam-4691	102	37	p(y	p(y	PROPN
ejpam-4691	102	38	)	)	PUNCT
ejpam-4691	102	39	,	,	PUNCT
ejpam-4691	102	40	then	then	ADV
ejpam-4691	102	41	x	x	X
ejpam-4691	102	42	∈	∈	PROPN
ejpam-4691	102	43	f+(my	f+(my	VERB
ejpam-4691	102	44	int(b	int(b	NOUN
ejpam-4691	102	45	)	)	PUNCT
ejpam-4691	102	46	)	)	PUNCT
ejpam-4691	102	47	;	;	PUNCT
ejpam-4691	102	48	(	(	PUNCT
ejpam-4691	102	49	4	4	X
ejpam-4691	102	50	)	)	PUNCT
ejpam-4691	102	51	if	if	SCONJ
ejpam-4691	102	52	x	x	SYM
ejpam-4691	102	53	∈	∈	PROPN
ejpam-4691	102	54	f−(my	f−(my	NOUN
ejpam-4691	102	55	cl(b	cl(b	NOUN
ejpam-4691	102	56	)	)	PUNCT
ejpam-4691	102	57	)	)	PUNCT
ejpam-4691	102	58	for	for	ADP
ejpam-4691	102	59	any	any	DET
ejpam-4691	102	60	b	b	PROPN
ejpam-4691	102	61	∈	∈	PROPN
ejpam-4691	102	62	p(y	p(y	PROPN
ejpam-4691	102	63	)	)	PUNCT
ejpam-4691	102	64	,	,	PUNCT
ejpam-4691	102	65	then	then	ADV
ejpam-4691	102	66	x	x	X
ejpam-4691	102	67	∈	∈	PROPN
ejpam-4691	102	68	mxcl(f−(b	mxcl(f−(b	PROPN
ejpam-4691	102	69	)	)	PUNCT
ejpam-4691	102	70	)	)	PUNCT
ejpam-4691	102	71	.	.	PUNCT
ejpam-4691	103	1	t.	t.	PROPN
ejpam-4691	103	2	noiri	noiri	PROPN
ejpam-4691	103	3	,	,	PUNCT
ejpam-4691	103	4	v.	v.	CCONJ
ejpam-4691	103	5	popa	popa	NOUN
ejpam-4691	103	6	/	/	SYM
ejpam-4691	103	7	eur	eur	PROPN
ejpam-4691	103	8	.	.	PUNCT
ejpam-4691	104	1	j.	j.	PROPN
ejpam-4691	104	2	pure	pure	PROPN
ejpam-4691	104	3	appl	appl	PROPN
ejpam-4691	104	4	.	.	PROPN
ejpam-4691	104	5	math	math	PROPN
ejpam-4691	104	6	,	,	PUNCT
ejpam-4691	104	7	16	16	NUM
ejpam-4691	104	8	(	(	PUNCT
ejpam-4691	104	9	1	1	NUM
ejpam-4691	104	10	)	)	PUNCT
ejpam-4691	104	11	(	(	PUNCT
ejpam-4691	104	12	2023	2023	NUM
ejpam-4691	104	13	)	)	PUNCT
ejpam-4691	104	14	,	,	PUNCT
ejpam-4691	104	15	430	430	NUM
ejpam-4691	104	16	-	-	SYM
ejpam-4691	104	17	439	439	NUM
ejpam-4691	104	18	433	433	NUM
ejpam-4691	104	19	proof	proof	NOUN
ejpam-4691	104	20	.	.	PUNCT
ejpam-4691	105	1	(	(	PUNCT
ejpam-4691	105	2	1	1	X
ejpam-4691	105	3	)	)	PUNCT
ejpam-4691	105	4	⇒	⇒	NOUN
ejpam-4691	105	5	(	(	PUNCT
ejpam-4691	105	6	2	2	NUM
ejpam-4691	105	7	):	):	PUNCT
ejpam-4691	105	8	let	let	VERB
ejpam-4691	105	9	a	a	DET
ejpam-4691	105	10	∈	∈	PROPN
ejpam-4691	105	11	p(x	p(x	NOUN
ejpam-4691	105	12	)	)	PUNCT
ejpam-4691	105	13	and	and	CCONJ
ejpam-4691	105	14	x	x	PUNCT
ejpam-4691	105	15	∈	∈	PROPN
ejpam-4691	105	16	mxint(a	mxint(a	PROPN
ejpam-4691	105	17	)	)	PUNCT
ejpam-4691	105	18	.	.	PUNCT
ejpam-4691	106	1	then	then	ADV
ejpam-4691	106	2	,	,	PUNCT
ejpam-4691	106	3	there	there	PRON
ejpam-4691	106	4	exists	exist	VERB
ejpam-4691	106	5	an	an	DET
ejpam-4691	106	6	mx	mx	PROPN
ejpam-4691	106	7	open	open	NOUN
ejpam-4691	106	8	set	set	VERB
ejpam-4691	106	9	u	u	PRON
ejpam-4691	106	10	such	such	ADJ
ejpam-4691	106	11	that	that	SCONJ
ejpam-4691	106	12	x	x	SYM
ejpam-4691	106	13	∈	∈	PROPN
ejpam-4691	106	14	u	u	X
ejpam-4691	106	15	⊂	⊂	PROPN
ejpam-4691	106	16	a	a	PROPN
ejpam-4691	106	17	and	and	CCONJ
ejpam-4691	106	18	hence	hence	ADV
ejpam-4691	106	19	f	f	PROPN
ejpam-4691	106	20	(	(	PUNCT
ejpam-4691	106	21	x	x	X
ejpam-4691	106	22	)	)	PUNCT
ejpam-4691	107	1	⊂	⊂	PROPN
ejpam-4691	107	2	f	f	X
ejpam-4691	107	3	(	(	PUNCT
ejpam-4691	107	4	u	u	NOUN
ejpam-4691	107	5	)	)	PUNCT
ejpam-4691	107	6	⊂	⊂	PROPN
ejpam-4691	108	1	f	f	X
ejpam-4691	108	2	(	(	PUNCT
ejpam-4691	108	3	a	a	NOUN
ejpam-4691	108	4	)	)	PUNCT
ejpam-4691	108	5	.	.	PUNCT
ejpam-4691	109	1	since	since	SCONJ
ejpam-4691	109	2	f	f	PROPN
ejpam-4691	109	3	is	be	AUX
ejpam-4691	109	4	m	m	NOUN
ejpam-4691	109	5	-	-	ADJ
ejpam-4691	109	6	open	open	ADJ
ejpam-4691	109	7	at	at	ADP
ejpam-4691	109	8	x	x	X
ejpam-4691	109	9	,	,	PUNCT
ejpam-4691	109	10	by	by	ADP
ejpam-4691	109	11	theorem	theorem	NOUN
ejpam-4691	109	12	1	1	NUM
ejpam-4691	109	13	and	and	CCONJ
ejpam-4691	109	14	lemma	lemma	PROPN
ejpam-4691	109	15	1	1	NUM
ejpam-4691	109	16	,	,	PUNCT
ejpam-4691	109	17	we	we	PRON
ejpam-4691	109	18	obtain	obtain	VERB
ejpam-4691	109	19	x	x	PUNCT
ejpam-4691	109	20	∈	∈	NOUN
ejpam-4691	109	21	f+(my	f+(my	NOUN
ejpam-4691	109	22	int(f	int(f	NOUN
ejpam-4691	109	23	(	(	PUNCT
ejpam-4691	109	24	u	u	NOUN
ejpam-4691	109	25	)	)	PUNCT
ejpam-4691	109	26	)	)	PUNCT
ejpam-4691	109	27	)	)	PUNCT
ejpam-4691	110	1	⊂	⊂	PRON
ejpam-4691	110	2	f+(my	f+(my	VERB
ejpam-4691	110	3	int(f	int(f	NOUN
ejpam-4691	110	4	(	(	PUNCT
ejpam-4691	110	5	a	a	NOUN
ejpam-4691	110	6	)	)	PUNCT
ejpam-4691	110	7	)	)	PUNCT
ejpam-4691	110	8	)	)	PUNCT
ejpam-4691	110	9	.	.	PUNCT
ejpam-4691	111	1	(	(	PUNCT
ejpam-4691	111	2	2)⇒	2)⇒	NUM
ejpam-4691	111	3	(	(	PUNCT
ejpam-4691	111	4	3	3	NUM
ejpam-4691	111	5	):	):	PUNCT
ejpam-4691	111	6	letb	letb	NOUN
ejpam-4691	111	7	∈	∈	PROPN
ejpam-4691	111	8	p(y	p(y	PROPN
ejpam-4691	111	9	)	)	PUNCT
ejpam-4691	111	10	and	and	CCONJ
ejpam-4691	111	11	x	x	PUNCT
ejpam-4691	111	12	∈	∈	NOUN
ejpam-4691	111	13	mxint(f+(b	mxint(f+(b	NOUN
ejpam-4691	111	14	)	)	PUNCT
ejpam-4691	111	15	)	)	PUNCT
ejpam-4691	111	16	.	.	PUNCT
ejpam-4691	112	1	then	then	ADV
ejpam-4691	112	2	,	,	PUNCT
ejpam-4691	112	3	x	x	PUNCT
ejpam-4691	112	4	∈	∈	NOUN
ejpam-4691	112	5	f+(my	f+(my	NOUN
ejpam-4691	112	6	int(f	int(f	NOUN
ejpam-4691	112	7	(	(	PUNCT
ejpam-4691	112	8	f+(b	f+(b	NOUN
ejpam-4691	112	9	)	)	PUNCT
ejpam-4691	112	10	)	)	PUNCT
ejpam-4691	112	11	)	)	PUNCT
ejpam-4691	112	12	)	)	PUNCT
ejpam-4691	113	1	⊂	⊂	PROPN
ejpam-4691	113	2	f+(my	f+(my	VERB
ejpam-4691	113	3	int(b	int(b	NOUN
ejpam-4691	113	4	)	)	PUNCT
ejpam-4691	113	5	)	)	PUNCT
ejpam-4691	113	6	.	.	PUNCT
ejpam-4691	114	1	(	(	PUNCT
ejpam-4691	114	2	3	3	X
ejpam-4691	114	3	)	)	PUNCT
ejpam-4691	114	4	⇒	⇒	NOUN
ejpam-4691	114	5	(	(	PUNCT
ejpam-4691	114	6	4	4	NUM
ejpam-4691	114	7	):	):	PUNCT
ejpam-4691	114	8	let	let	VERB
ejpam-4691	114	9	b	b	NOUN
ejpam-4691	114	10	∈	∈	PROPN
ejpam-4691	114	11	p(y	p(y	PROPN
ejpam-4691	114	12	)	)	PUNCT
ejpam-4691	114	13	and	and	CCONJ
ejpam-4691	114	14	x	x	X
ejpam-4691	114	15	/∈	/∈	PUNCT
ejpam-4691	114	16	mxcl(f−(b	mxcl(f−(b	PROPN
ejpam-4691	114	17	)	)	PUNCT
ejpam-4691	114	18	)	)	PUNCT
ejpam-4691	114	19	.	.	PUNCT
ejpam-4691	115	1	then	then	ADV
ejpam-4691	115	2	x	x	SYM
ejpam-4691	115	3	∈	∈	PROPN
ejpam-4691	115	4	x	x	X
ejpam-4691	115	5	−	−	PROPN
ejpam-4691	115	6	mxcl(f−(b	mxcl(f−(b	PROPN
ejpam-4691	115	7	)	)	PUNCT
ejpam-4691	115	8	)	)	PUNCT
ejpam-4691	116	1	=	=	PUNCT
ejpam-4691	116	2	mxint(x	mxint(x	NOUN
ejpam-4691	116	3	−	−	PROPN
ejpam-4691	116	4	f−(b	f−(b	PROPN
ejpam-4691	116	5	)	)	PUNCT
ejpam-4691	116	6	)	)	PUNCT
ejpam-4691	117	1	=	=	PUNCT
ejpam-4691	117	2	mxint(f+(y	mxint(f+(y	NOUN
ejpam-4691	117	3	−	−	PROPN
ejpam-4691	117	4	b	b	NOUN
ejpam-4691	117	5	)	)	PUNCT
ejpam-4691	117	6	)	)	PUNCT
ejpam-4691	117	7	.	.	PUNCT
ejpam-4691	118	1	by	by	ADP
ejpam-4691	118	2	(	(	PUNCT
ejpam-4691	118	3	3	3	X
ejpam-4691	118	4	)	)	PUNCT
ejpam-4691	118	5	we	we	PRON
ejpam-4691	118	6	have	have	VERB
ejpam-4691	118	7	x	x	PART
ejpam-4691	118	8	∈	∈	PROPN
ejpam-4691	118	9	f+(my	f+(my	VERB
ejpam-4691	118	10	int(y	int(y	ADJ
ejpam-4691	118	11	−	−	PROPN
ejpam-4691	118	12	b	b	NOUN
ejpam-4691	118	13	)	)	PUNCT
ejpam-4691	118	14	)	)	PUNCT
ejpam-4691	119	1	=	=	PUNCT
ejpam-4691	119	2	x	x	PUNCT
ejpam-4691	120	1	−	−	NOUN
ejpam-4691	120	2	f−(my	f−(my	NOUN
ejpam-4691	120	3	cl(b	cl(b	NOUN
ejpam-4691	120	4	)	)	PUNCT
ejpam-4691	120	5	)	)	PUNCT
ejpam-4691	120	6	.	.	PUNCT
ejpam-4691	121	1	hence	hence	ADV
ejpam-4691	121	2	,	,	PUNCT
ejpam-4691	121	3	x	x	X
ejpam-4691	121	4	/∈	/∈	PUNCT
ejpam-4691	121	5	f−(my	f−(my	NOUN
ejpam-4691	121	6	cl(b	cl(b	NOUN
ejpam-4691	121	7	)	)	PUNCT
ejpam-4691	121	8	)	)	PUNCT
ejpam-4691	121	9	.	.	PUNCT
ejpam-4691	122	1	therefore	therefore	ADV
ejpam-4691	122	2	,	,	PUNCT
ejpam-4691	122	3	if	if	SCONJ
ejpam-4691	122	4	x	x	SYM
ejpam-4691	122	5	∈	∈	PROPN
ejpam-4691	122	6	f−(my	f−(my	NOUN
ejpam-4691	122	7	cl(b	cl(b	NOUN
ejpam-4691	122	8	)	)	PUNCT
ejpam-4691	122	9	)	)	PUNCT
ejpam-4691	122	10	,	,	PUNCT
ejpam-4691	122	11	then	then	ADV
ejpam-4691	122	12	x	x	X
ejpam-4691	122	13	∈	∈	PROPN
ejpam-4691	122	14	mxcl(f−(b	mxcl(f−(b	PROPN
ejpam-4691	122	15	)	)	PUNCT
ejpam-4691	122	16	)	)	PUNCT
ejpam-4691	122	17	.	.	PUNCT
ejpam-4691	123	1	(	(	PUNCT
ejpam-4691	123	2	4	4	X
ejpam-4691	123	3	)	)	PUNCT
ejpam-4691	123	4	⇒	⇒	NOUN
ejpam-4691	123	5	(	(	PUNCT
ejpam-4691	123	6	1	1	NUM
ejpam-4691	123	7	):	):	PUNCT
ejpam-4691	123	8	let	let	VERB
ejpam-4691	123	9	u	u	PRON
ejpam-4691	123	10	be	be	AUX
ejpam-4691	123	11	any	any	DET
ejpam-4691	123	12	mx	mx	PROPN
ejpam-4691	123	13	-open	-open	NOUN
ejpam-4691	123	14	set	set	NOUN
ejpam-4691	123	15	of	of	ADP
ejpam-4691	123	16	x	x	PUNCT
ejpam-4691	123	17	containing	contain	VERB
ejpam-4691	123	18	x	x	PROPN
ejpam-4691	123	19	and	and	CCONJ
ejpam-4691	123	20	b	b	X
ejpam-4691	124	1	=	=	SYM
ejpam-4691	124	2	y	y	PROPN
ejpam-4691	124	3	−	−	PROPN
ejpam-4691	125	1	f	f	PROPN
ejpam-4691	125	2	(	(	PUNCT
ejpam-4691	125	3	u	u	NOUN
ejpam-4691	125	4	)	)	PUNCT
ejpam-4691	125	5	.	.	PUNCT
ejpam-4691	126	1	since	since	SCONJ
ejpam-4691	126	2	mxcl(f−(b	mxcl(f−(b	PRON
ejpam-4691	126	3	)	)	PUNCT
ejpam-4691	126	4	)	)	PUNCT
ejpam-4691	127	1	=	=	NOUN
ejpam-4691	127	2	mxcl(f−(y	mxcl(f−(y	NOUN
ejpam-4691	127	3	−	−	PROPN
ejpam-4691	127	4	f	f	PROPN
ejpam-4691	127	5	(	(	PUNCT
ejpam-4691	127	6	u	u	NOUN
ejpam-4691	127	7	)	)	PUNCT
ejpam-4691	127	8	)	)	PUNCT
ejpam-4691	127	9	)	)	PUNCT
ejpam-4691	128	1	=	=	PUNCT
ejpam-4691	128	2	mxcl(x	mxcl(x	NUM
ejpam-4691	128	3	−	−	PROPN
ejpam-4691	128	4	f+(f	f+(f	PROPN
ejpam-4691	128	5	(	(	PUNCT
ejpam-4691	128	6	u	u	NOUN
ejpam-4691	128	7	)	)	PUNCT
ejpam-4691	128	8	)	)	PUNCT
ejpam-4691	128	9	)	)	PUNCT
ejpam-4691	129	1	⊂	⊂	PUNCT
ejpam-4691	129	2	x	x	PUNCT
ejpam-4691	130	1	−	−	ADP
ejpam-4691	130	2	mxint(u	mxint(u	NUM
ejpam-4691	130	3	)	)	PUNCT
ejpam-4691	130	4	=	=	PUNCT
ejpam-4691	130	5	x−u	x−u	X
ejpam-4691	130	6	and	and	CCONJ
ejpam-4691	130	7	x	x	SYM
ejpam-4691	130	8	∈	∈	PROPN
ejpam-4691	130	9	u	u	NOUN
ejpam-4691	130	10	,	,	PUNCT
ejpam-4691	130	11	we	we	PRON
ejpam-4691	130	12	obtain	obtain	VERB
ejpam-4691	130	13	that	that	PRON
ejpam-4691	130	14	x	x	PUNCT
ejpam-4691	130	15	/∈	/∈	PUNCT
ejpam-4691	130	16	mxcl(f−(b	mxcl(f−(b	PROPN
ejpam-4691	130	17	)	)	PUNCT
ejpam-4691	130	18	)	)	PUNCT
ejpam-4691	130	19	.	.	PUNCT
ejpam-4691	131	1	by	by	ADP
ejpam-4691	131	2	(	(	PUNCT
ejpam-4691	131	3	4	4	NUM
ejpam-4691	131	4	)	)	PUNCT
ejpam-4691	131	5	,	,	PUNCT
ejpam-4691	131	6	we	we	PRON
ejpam-4691	131	7	have	have	VERB
ejpam-4691	131	8	x	x	X
ejpam-4691	131	9	/∈	/∈	PUNCT
ejpam-4691	131	10	f−(my	f−(my	NOUN
ejpam-4691	131	11	cl(b	cl(b	NOUN
ejpam-4691	131	12	)	)	PUNCT
ejpam-4691	131	13	)	)	PUNCT
ejpam-4691	132	1	=	=	PUNCT
ejpam-4691	132	2	f−(my	f−(my	NOUN
ejpam-4691	132	3	cl(y	cl(y	X
ejpam-4691	132	4	−	−	PROPN
ejpam-4691	132	5	f	f	X
ejpam-4691	132	6	(	(	PUNCT
ejpam-4691	132	7	u	u	NOUN
ejpam-4691	132	8	)	)	PUNCT
ejpam-4691	132	9	)	)	PUNCT
ejpam-4691	132	10	)	)	PUNCT
ejpam-4691	133	1	=	=	PUNCT
ejpam-4691	134	1	x	x	PUNCT
ejpam-4691	134	2	−	−	NOUN
ejpam-4691	134	3	f+(my	f+(my	ADJ
ejpam-4691	134	4	int(f	int(f	NOUN
ejpam-4691	134	5	(	(	PUNCT
ejpam-4691	134	6	u	u	NOUN
ejpam-4691	134	7	)	)	PUNCT
ejpam-4691	134	8	)	)	PUNCT
ejpam-4691	134	9	)	)	PUNCT
ejpam-4691	134	10	.	.	PUNCT
ejpam-4691	135	1	therefore	therefore	ADV
ejpam-4691	135	2	,	,	PUNCT
ejpam-4691	135	3	x	x	PUNCT
ejpam-4691	135	4	∈	∈	NOUN
ejpam-4691	135	5	f+(my	f+(my	NOUN
ejpam-4691	135	6	int(f	int(f	NOUN
ejpam-4691	135	7	(	(	PUNCT
ejpam-4691	135	8	u	u	NOUN
ejpam-4691	135	9	)	)	PUNCT
ejpam-4691	135	10	)	)	PUNCT
ejpam-4691	135	11	)	)	PUNCT
ejpam-4691	135	12	.	.	PUNCT
ejpam-4691	136	1	by	by	ADP
ejpam-4691	136	2	theorem	theorem	NOUN
ejpam-4691	136	3	1	1	NUM
ejpam-4691	136	4	,	,	PUNCT
ejpam-4691	136	5	f	f	PROPN
ejpam-4691	136	6	is	be	AUX
ejpam-4691	136	7	m	m	NOUN
ejpam-4691	136	8	-	-	ADJ
ejpam-4691	136	9	open	open	ADJ
ejpam-4691	136	10	at	at	ADP
ejpam-4691	136	11	x.	x.	NOUN
ejpam-4691	136	12	theorem	theorem	VERB
ejpam-4691	136	13	4	4	NUM
ejpam-4691	136	14	.	.	X
ejpam-4691	136	15	for	for	ADP
ejpam-4691	136	16	a	a	DET
ejpam-4691	136	17	multifunction	multifunction	NOUN
ejpam-4691	136	18	f	f	NOUN
ejpam-4691	136	19	:	:	PUNCT
ejpam-4691	136	20	(	(	PUNCT
ejpam-4691	136	21	x	x	NOUN
ejpam-4691	136	22	,	,	PUNCT
ejpam-4691	136	23	mx	mx	NOUN
ejpam-4691	136	24	)	)	PUNCT
ejpam-4691	136	25	→	→	SYM
ejpam-4691	136	26	(	(	PUNCT
ejpam-4691	136	27	y	y	PROPN
ejpam-4691	136	28	,	,	PUNCT
ejpam-4691	136	29	my	my	INTJ
ejpam-4691	136	30	)	)	PUNCT
ejpam-4691	136	31	,	,	PUNCT
ejpam-4691	136	32	where	where	SCONJ
ejpam-4691	136	33	my	my	PRON
ejpam-4691	136	34	has	have	VERB
ejpam-4691	136	35	property	property	NOUN
ejpam-4691	136	36	b	b	PROPN
ejpam-4691	136	37	,	,	PUNCT
ejpam-4691	136	38	the	the	DET
ejpam-4691	136	39	following	follow	VERB
ejpam-4691	136	40	properties	property	NOUN
ejpam-4691	136	41	are	be	AUX
ejpam-4691	136	42	equivalent	equivalent	ADJ
ejpam-4691	136	43	:	:	PUNCT
ejpam-4691	136	44	(	(	PUNCT
ejpam-4691	136	45	1	1	X
ejpam-4691	136	46	)	)	PUNCT
ejpam-4691	136	47	f	f	PROPN
ejpam-4691	136	48	is	be	AUX
ejpam-4691	136	49	m	m	NOUN
ejpam-4691	136	50	-	-	ADJ
ejpam-4691	136	51	open	open	ADJ
ejpam-4691	136	52	;	;	PUNCT
ejpam-4691	136	53	(	(	PUNCT
ejpam-4691	136	54	2	2	X
ejpam-4691	136	55	)	)	PUNCT
ejpam-4691	136	56	f	f	NOUN
ejpam-4691	136	57	(	(	PUNCT
ejpam-4691	136	58	mxint(a	mxint(a	NOUN
ejpam-4691	136	59	)	)	PUNCT
ejpam-4691	136	60	)	)	PUNCT
ejpam-4691	137	1	⊂	⊂	PRON
ejpam-4691	137	2	my	my	PRON
ejpam-4691	137	3	int(f	int(f	PROPN
ejpam-4691	137	4	(	(	PUNCT
ejpam-4691	137	5	a	a	NOUN
ejpam-4691	137	6	)	)	PUNCT
ejpam-4691	137	7	)	)	PUNCT
ejpam-4691	137	8	for	for	ADP
ejpam-4691	137	9	any	any	DET
ejpam-4691	137	10	subset	subset	NOUN
ejpam-4691	137	11	a	a	PRON
ejpam-4691	137	12	of	of	ADP
ejpam-4691	137	13	x	x	PRON
ejpam-4691	137	14	;	;	PUNCT
ejpam-4691	137	15	(	(	PUNCT
ejpam-4691	137	16	3	3	X
ejpam-4691	137	17	)	)	PUNCT
ejpam-4691	137	18	mxint(f+(b	mxint(f+(b	NOUN
ejpam-4691	137	19	)	)	PUNCT
ejpam-4691	137	20	)	)	PUNCT
ejpam-4691	138	1	⊂	⊂	PROPN
ejpam-4691	138	2	f+(my	f+(my	VERB
ejpam-4691	138	3	int(b	int(b	NOUN
ejpam-4691	138	4	)	)	PUNCT
ejpam-4691	138	5	)	)	PUNCT
ejpam-4691	138	6	for	for	ADP
ejpam-4691	138	7	any	any	DET
ejpam-4691	138	8	subset	subset	NOUN
ejpam-4691	138	9	b	b	PROPN
ejpam-4691	138	10	of	of	ADP
ejpam-4691	138	11	y	y	PROPN
ejpam-4691	138	12	;	;	PUNCT
ejpam-4691	138	13	(	(	PUNCT
ejpam-4691	138	14	4	4	X
ejpam-4691	138	15	)	)	PUNCT
ejpam-4691	138	16	f−(my	f−(my	NOUN
ejpam-4691	138	17	cl(b	cl(b	NOUN
ejpam-4691	138	18	)	)	PUNCT
ejpam-4691	138	19	)	)	PUNCT
ejpam-4691	139	1	⊂	⊂	PROPN
ejpam-4691	139	2	mxcl(f−(b	mxcl(f−(b	PROPN
ejpam-4691	139	3	)	)	PUNCT
ejpam-4691	139	4	)	)	PUNCT
ejpam-4691	140	1	for	for	ADP
ejpam-4691	140	2	any	any	DET
ejpam-4691	140	3	subset	subset	NOUN
ejpam-4691	140	4	b	b	PROPN
ejpam-4691	140	5	of	of	ADP
ejpam-4691	140	6	y.	y.	PROPN
ejpam-4691	140	7	proof	proof	NOUN
ejpam-4691	140	8	.	.	PUNCT
ejpam-4691	141	1	(	(	PUNCT
ejpam-4691	141	2	1	1	X
ejpam-4691	141	3	)	)	PUNCT
ejpam-4691	141	4	⇒	⇒	NOUN
ejpam-4691	141	5	(	(	PUNCT
ejpam-4691	141	6	2	2	NUM
ejpam-4691	141	7	):	):	PUNCT
ejpam-4691	141	8	let	let	VERB
ejpam-4691	141	9	a	a	PRON
ejpam-4691	141	10	be	be	AUX
ejpam-4691	141	11	any	any	DET
ejpam-4691	141	12	subset	subset	NOUN
ejpam-4691	141	13	of	of	ADP
ejpam-4691	141	14	x	x	PUNCT
ejpam-4691	141	15	and	and	CCONJ
ejpam-4691	141	16	x	x	SYM
ejpam-4691	141	17	∈	∈	PROPN
ejpam-4691	141	18	mxint(a	mxint(a	PROPN
ejpam-4691	141	19	)	)	PUNCT
ejpam-4691	141	20	.	.	PUNCT
ejpam-4691	142	1	since	since	SCONJ
ejpam-4691	142	2	f	f	PROPN
ejpam-4691	142	3	is	be	AUX
ejpam-4691	142	4	m	m	NOUN
ejpam-4691	142	5	-	-	ADJ
ejpam-4691	142	6	open	open	ADJ
ejpam-4691	142	7	at	at	ADP
ejpam-4691	142	8	each	each	DET
ejpam-4691	142	9	x	x	SYM
ejpam-4691	142	10	∈	∈	PROPN
ejpam-4691	142	11	a	a	PRON
ejpam-4691	142	12	,	,	PUNCT
ejpam-4691	142	13	by	by	ADP
ejpam-4691	142	14	theorem	theorem	NOUN
ejpam-4691	142	15	3	3	NUM
ejpam-4691	142	16	f	f	PROPN
ejpam-4691	142	17	(	(	PUNCT
ejpam-4691	142	18	x	x	X
ejpam-4691	142	19	)	)	PUNCT
ejpam-4691	142	20	⊂	⊂	PRON
ejpam-4691	142	21	my	my	PRON
ejpam-4691	142	22	int(f	int(f	PROPN
ejpam-4691	142	23	(	(	PUNCT
ejpam-4691	142	24	a	a	NOUN
ejpam-4691	142	25	)	)	PUNCT
ejpam-4691	142	26	)	)	PUNCT
ejpam-4691	142	27	.	.	PUNCT
ejpam-4691	143	1	hence	hence	ADV
ejpam-4691	143	2	f	f	PROPN
ejpam-4691	143	3	(	(	PUNCT
ejpam-4691	143	4	mxint(a	mxint(a	NOUN
ejpam-4691	143	5	)	)	PUNCT
ejpam-4691	143	6	)	)	PUNCT
ejpam-4691	144	1	⊂	⊂	PRON
ejpam-4691	144	2	my	my	PRON
ejpam-4691	144	3	int(f	int(f	PROPN
ejpam-4691	144	4	(	(	PUNCT
ejpam-4691	144	5	a	a	NOUN
ejpam-4691	144	6	)	)	PUNCT
ejpam-4691	144	7	)	)	PUNCT
ejpam-4691	144	8	.	.	PUNCT
ejpam-4691	145	1	(	(	PUNCT
ejpam-4691	145	2	2)⇒	2)⇒	NUM
ejpam-4691	145	3	(	(	PUNCT
ejpam-4691	145	4	3	3	NUM
ejpam-4691	145	5	):	):	PUNCT
ejpam-4691	145	6	letb	letb	ADV
ejpam-4691	145	7	be	be	AUX
ejpam-4691	145	8	any	any	DET
ejpam-4691	145	9	subset	subset	NOUN
ejpam-4691	145	10	of	of	ADP
ejpam-4691	145	11	y	y	PROPN
ejpam-4691	145	12	.	.	PUNCT
ejpam-4691	146	1	by	by	ADP
ejpam-4691	146	2	(	(	PUNCT
ejpam-4691	146	3	2	2	NUM
ejpam-4691	146	4	)	)	PUNCT
ejpam-4691	146	5	,	,	PUNCT
ejpam-4691	146	6	we	we	PRON
ejpam-4691	146	7	have	have	VERB
ejpam-4691	146	8	f	f	X
ejpam-4691	146	9	(	(	PUNCT
ejpam-4691	146	10	mxint(f+(b	mxint(f+(b	NOUN
ejpam-4691	146	11	)	)	PUNCT
ejpam-4691	146	12	)	)	PUNCT
ejpam-4691	146	13	)	)	PUNCT
ejpam-4691	147	1	⊂	⊂	PRON
ejpam-4691	147	2	my	my	PRON
ejpam-4691	147	3	int(f	int(f	PROPN
ejpam-4691	147	4	(	(	PUNCT
ejpam-4691	147	5	f+(b	f+(b	NOUN
ejpam-4691	147	6	)	)	PUNCT
ejpam-4691	147	7	)	)	PUNCT
ejpam-4691	147	8	)	)	PUNCT
ejpam-4691	148	1	⊂	⊂	PRON
ejpam-4691	148	2	my	my	PRON
ejpam-4691	148	3	int(b	int(b	NOUN
ejpam-4691	148	4	)	)	PUNCT
ejpam-4691	148	5	.	.	PUNCT
ejpam-4691	149	1	hence	hence	ADV
ejpam-4691	149	2	,	,	PUNCT
ejpam-4691	149	3	we	we	PRON
ejpam-4691	149	4	have	have	VERB
ejpam-4691	149	5	mxint(f+(b	mxint(f+(b	NOUN
ejpam-4691	149	6	)	)	PUNCT
ejpam-4691	149	7	)	)	PUNCT
ejpam-4691	150	1	⊂	⊂	PROPN
ejpam-4691	150	2	f+(my	f+(my	VERB
ejpam-4691	150	3	int(b	int(b	NOUN
ejpam-4691	150	4	)	)	PUNCT
ejpam-4691	150	5	)	)	PUNCT
ejpam-4691	150	6	.	.	PUNCT
ejpam-4691	151	1	(	(	PUNCT
ejpam-4691	151	2	3	3	X
ejpam-4691	151	3	)	)	PUNCT
ejpam-4691	151	4	⇒	⇒	NOUN
ejpam-4691	151	5	(	(	PUNCT
ejpam-4691	151	6	4	4	NUM
ejpam-4691	151	7	):	):	PUNCT
ejpam-4691	151	8	let	let	VERB
ejpam-4691	151	9	b	b	X
ejpam-4691	151	10	be	be	AUX
ejpam-4691	151	11	any	any	DET
ejpam-4691	151	12	subset	subset	NOUN
ejpam-4691	151	13	of	of	ADP
ejpam-4691	151	14	y	y	PROPN
ejpam-4691	151	15	.	.	PUNCT
ejpam-4691	152	1	by	by	ADP
ejpam-4691	152	2	(	(	PUNCT
ejpam-4691	152	3	3	3	NUM
ejpam-4691	152	4	)	)	PUNCT
ejpam-4691	152	5	,	,	PUNCT
ejpam-4691	152	6	we	we	PRON
ejpam-4691	152	7	have	have	VERB
ejpam-4691	152	8	x	x	X
ejpam-4691	152	9	−	−	PROPN
ejpam-4691	152	10	mxcl(f−(b	mxcl(f−(b	PROPN
ejpam-4691	152	11	)	)	PUNCT
ejpam-4691	152	12	)	)	PUNCT
ejpam-4691	153	1	=	=	PUNCT
ejpam-4691	153	2	mxint(x	mxint(x	NOUN
ejpam-4691	153	3	−	−	PROPN
ejpam-4691	153	4	f−(b	f−(b	PROPN
ejpam-4691	153	5	)	)	PUNCT
ejpam-4691	153	6	)	)	PUNCT
ejpam-4691	154	1	=	=	SYM
ejpam-4691	154	2	mxint(f+(y	mxint(f+(y	NOUN
ejpam-4691	154	3	−b	−b	ADJ
ejpam-4691	154	4	)	)	PUNCT
ejpam-4691	154	5	)	)	PUNCT
ejpam-4691	155	1	⊂	⊂	PRON
ejpam-4691	155	2	f+(my	f+(my	VERB
ejpam-4691	156	1	int(y	int(y	ADJ
ejpam-4691	156	2	−b	−b	NOUN
ejpam-4691	156	3	)	)	PUNCT
ejpam-4691	156	4	)	)	PUNCT
ejpam-4691	157	1	=	=	PUNCT
ejpam-4691	157	2	x	x	PUNCT
ejpam-4691	158	1	−	−	NOUN
ejpam-4691	158	2	f−(my	f−(my	NOUN
ejpam-4691	158	3	cl(b	cl(b	NOUN
ejpam-4691	158	4	)	)	PUNCT
ejpam-4691	158	5	)	)	PUNCT
ejpam-4691	158	6	.	.	PUNCT
ejpam-4691	159	1	hence	hence	ADV
ejpam-4691	159	2	,	,	PUNCT
ejpam-4691	159	3	f−(my	f−(my	NOUN
ejpam-4691	159	4	cl(b	cl(b	NOUN
ejpam-4691	159	5	)	)	PUNCT
ejpam-4691	159	6	)	)	PUNCT
ejpam-4691	160	1	⊂	⊂	PROPN
ejpam-4691	160	2	mxcl(f−(b	mxcl(f−(b	PROPN
ejpam-4691	160	3	)	)	PUNCT
ejpam-4691	160	4	)	)	PUNCT
ejpam-4691	160	5	.	.	PUNCT
ejpam-4691	161	1	(	(	PUNCT
ejpam-4691	161	2	4	4	X
ejpam-4691	161	3	)	)	PUNCT
ejpam-4691	161	4	⇒	⇒	NOUN
ejpam-4691	161	5	(	(	PUNCT
ejpam-4691	161	6	1	1	NUM
ejpam-4691	161	7	):	):	PUNCT
ejpam-4691	161	8	let	let	VERB
ejpam-4691	161	9	u	u	PRON
ejpam-4691	161	10	be	be	AUX
ejpam-4691	161	11	any	any	DET
ejpam-4691	161	12	mx	mx	PROPN
ejpam-4691	161	13	-open	-open	NOUN
ejpam-4691	161	14	set	set	NOUN
ejpam-4691	161	15	of	of	ADP
ejpam-4691	161	16	x	x	PROPN
ejpam-4691	161	17	and	and	CCONJ
ejpam-4691	162	1	b	b	X
ejpam-4691	162	2	=	=	SYM
ejpam-4691	162	3	y	y	PROPN
ejpam-4691	162	4	−	−	PROPN
ejpam-4691	163	1	f	f	PROPN
ejpam-4691	163	2	(	(	PUNCT
ejpam-4691	163	3	u	u	NOUN
ejpam-4691	163	4	)	)	PUNCT
ejpam-4691	163	5	.	.	PUNCT
ejpam-4691	164	1	by	by	ADP
ejpam-4691	164	2	(	(	PUNCT
ejpam-4691	164	3	4	4	NUM
ejpam-4691	164	4	)	)	PUNCT
ejpam-4691	164	5	,	,	PUNCT
ejpam-4691	164	6	we	we	PRON
ejpam-4691	164	7	have	have	VERB
ejpam-4691	164	8	f−(my	f−(my	NOUN
ejpam-4691	164	9	cl(y	cl(y	NOUN
ejpam-4691	165	1	−	−	PROPN
ejpam-4691	166	1	f	f	X
ejpam-4691	166	2	(	(	PUNCT
ejpam-4691	166	3	u	u	NOUN
ejpam-4691	166	4	)	)	PUNCT
ejpam-4691	166	5	)	)	PUNCT
ejpam-4691	166	6	)	)	PUNCT
ejpam-4691	167	1	⊂	⊂	PROPN
ejpam-4691	167	2	mxcl(f−(y	mxcl(f−(y	VERB
ejpam-4691	167	3	−	−	PROPN
ejpam-4691	167	4	f	f	PROPN
ejpam-4691	167	5	(	(	PUNCT
ejpam-4691	167	6	u	u	NOUN
ejpam-4691	167	7	)	)	PUNCT
ejpam-4691	167	8	)	)	PUNCT
ejpam-4691	167	9	)	)	PUNCT
ejpam-4691	167	10	.	.	PUNCT
ejpam-4691	168	1	now	now	ADV
ejpam-4691	168	2	,	,	PUNCT
ejpam-4691	168	3	f−(my	f−(my	NOUN
ejpam-4691	168	4	cl(y	cl(y	PUNCT
ejpam-4691	168	5	−	−	PROPN
ejpam-4691	168	6	f	f	X
ejpam-4691	168	7	(	(	PUNCT
ejpam-4691	168	8	u	u	NOUN
ejpam-4691	168	9	)	)	PUNCT
ejpam-4691	168	10	)	)	PUNCT
ejpam-4691	168	11	)	)	PUNCT
ejpam-4691	169	1	=	=	PUNCT
ejpam-4691	169	2	f−(y	f−(y	NOUN
ejpam-4691	169	3	−	−	ADP
ejpam-4691	169	4	my	my	PRON
ejpam-4691	169	5	int(f	int(f	PROPN
ejpam-4691	169	6	(	(	PUNCT
ejpam-4691	169	7	u	u	NOUN
ejpam-4691	169	8	)	)	PUNCT
ejpam-4691	169	9	)	)	PUNCT
ejpam-4691	169	10	)	)	PUNCT
ejpam-4691	170	1	=	=	PUNCT
ejpam-4691	171	1	x	x	PUNCT
ejpam-4691	171	2	−	−	NOUN
ejpam-4691	171	3	f+(my	f+(my	ADJ
ejpam-4691	171	4	int(f	int(f	NOUN
ejpam-4691	171	5	(	(	PUNCT
ejpam-4691	171	6	u	u	NOUN
ejpam-4691	171	7	)	)	PUNCT
ejpam-4691	171	8	)	)	PUNCT
ejpam-4691	171	9	)	)	PUNCT
ejpam-4691	171	10	.	.	PUNCT
ejpam-4691	172	1	and	and	CCONJ
ejpam-4691	172	2	also	also	ADV
ejpam-4691	172	3	we	we	PRON
ejpam-4691	172	4	have	have	VERB
ejpam-4691	172	5	mxcl(f−(y	mxcl(f−(y	NOUN
ejpam-4691	172	6	−	−	PROPN
ejpam-4691	172	7	f	f	PROPN
ejpam-4691	172	8	(	(	PUNCT
ejpam-4691	172	9	u	u	NOUN
ejpam-4691	172	10	)	)	PUNCT
ejpam-4691	172	11	)	)	PUNCT
ejpam-4691	172	12	)	)	PUNCT
ejpam-4691	173	1	=	=	PUNCT
ejpam-4691	173	2	mxcl(x	mxcl(x	NUM
ejpam-4691	173	3	−	−	PROPN
ejpam-4691	173	4	f+(f	f+(f	PROPN
ejpam-4691	173	5	(	(	PUNCT
ejpam-4691	173	6	u	u	NOUN
ejpam-4691	173	7	)	)	PUNCT
ejpam-4691	173	8	)	)	PUNCT
ejpam-4691	173	9	)	)	PUNCT
ejpam-4691	174	1	⊂	⊂	PUNCT
ejpam-4691	174	2	x	x	PUNCT
ejpam-4691	175	1	−	−	ADP
ejpam-4691	175	2	mxint(u	mxint(u	NUM
ejpam-4691	175	3	)	)	PUNCT
ejpam-4691	175	4	=	=	PUNCT
ejpam-4691	176	1	x	x	PUNCT
ejpam-4691	176	2	−	−	PROPN
ejpam-4691	176	3	u	u	NOUN
ejpam-4691	176	4	.	.	PUNCT
ejpam-4691	177	1	therefore	therefore	ADV
ejpam-4691	177	2	,	,	PUNCT
ejpam-4691	177	3	we	we	PRON
ejpam-4691	177	4	obtain	obtain	VERB
ejpam-4691	177	5	u	u	NOUN
ejpam-4691	177	6	⊂	⊂	NOUN
ejpam-4691	177	7	f+(my	f+(my	ADJ
ejpam-4691	178	1	int(f	int(f	PROPN
ejpam-4691	178	2	(	(	PUNCT
ejpam-4691	178	3	u	u	NOUN
ejpam-4691	178	4	)	)	PUNCT
ejpam-4691	178	5	)	)	PUNCT
ejpam-4691	178	6	)	)	PUNCT
ejpam-4691	178	7	and	and	CCONJ
ejpam-4691	178	8	hence	hence	ADV
ejpam-4691	178	9	f	f	PROPN
ejpam-4691	178	10	(	(	PUNCT
ejpam-4691	178	11	u	u	NOUN
ejpam-4691	178	12	)	)	PUNCT
ejpam-4691	178	13	⊂	⊂	PRON
ejpam-4691	178	14	my	my	PRON
ejpam-4691	178	15	int(f	int(f	PROPN
ejpam-4691	178	16	(	(	PUNCT
ejpam-4691	178	17	u	u	NOUN
ejpam-4691	178	18	)	)	PUNCT
ejpam-4691	178	19	)	)	PUNCT
ejpam-4691	178	20	.	.	PUNCT
ejpam-4691	179	1	consequently	consequently	ADV
ejpam-4691	179	2	,	,	PUNCT
ejpam-4691	179	3	we	we	PRON
ejpam-4691	179	4	obtain	obtain	VERB
ejpam-4691	179	5	f	f	PROPN
ejpam-4691	179	6	(	(	PUNCT
ejpam-4691	179	7	u	u	NOUN
ejpam-4691	179	8	)	)	PUNCT
ejpam-4691	179	9	=	=	VERB
ejpam-4691	179	10	my	my	PRON
ejpam-4691	179	11	int(f	int(f	PROPN
ejpam-4691	179	12	(	(	PUNCT
ejpam-4691	179	13	u	u	NOUN
ejpam-4691	179	14	)	)	PUNCT
ejpam-4691	179	15	)	)	PUNCT
ejpam-4691	179	16	and	and	CCONJ
ejpam-4691	179	17	f	f	PROPN
ejpam-4691	179	18	(	(	PUNCT
ejpam-4691	179	19	u	u	NOUN
ejpam-4691	179	20	)	)	PUNCT
ejpam-4691	179	21	is	be	AUX
ejpam-4691	179	22	my	my	PRON
ejpam-4691	179	23	-open	-open	NOUN
ejpam-4691	179	24	.	.	PUNCT
ejpam-4691	180	1	therefore	therefore	ADV
ejpam-4691	180	2	,	,	PUNCT
ejpam-4691	180	3	by	by	ADP
ejpam-4691	180	4	theorem	theorem	NOUN
ejpam-4691	180	5	2	2	NUM
ejpam-4691	180	6	f	f	NOUN
ejpam-4691	180	7	is	be	AUX
ejpam-4691	180	8	m	m	NOUN
ejpam-4691	180	9	-	-	ADJ
ejpam-4691	180	10	open	open	ADJ
ejpam-4691	180	11	.	.	PUNCT
ejpam-4691	181	1	for	for	ADP
ejpam-4691	181	2	a	a	DET
ejpam-4691	181	3	multifunction	multifunction	NOUN
ejpam-4691	181	4	f	f	NOUN
ejpam-4691	181	5	:	:	PUNCT
ejpam-4691	181	6	(	(	PUNCT
ejpam-4691	181	7	x	x	NOUN
ejpam-4691	181	8	,	,	PUNCT
ejpam-4691	181	9	mx	mx	NOUN
ejpam-4691	181	10	)	)	PUNCT
ejpam-4691	181	11	→	→	SYM
ejpam-4691	181	12	(	(	PUNCT
ejpam-4691	181	13	y	y	PROPN
ejpam-4691	181	14	,	,	PUNCT
ejpam-4691	181	15	my	my	INTJ
ejpam-4691	181	16	)	)	PUNCT
ejpam-4691	181	17	,	,	PUNCT
ejpam-4691	181	18	we	we	PRON
ejpam-4691	181	19	denote	denote	VERB
ejpam-4691	181	20	d0(f	d0(f	PROPN
ejpam-4691	181	21	)	)	PUNCT
ejpam-4691	182	1	=	=	PRON
ejpam-4691	182	2	{	{	PUNCT
ejpam-4691	182	3	x	x	PUNCT
ejpam-4691	182	4	∈	∈	PROPN
ejpam-4691	182	5	x	x	NOUN
ejpam-4691	182	6	:	:	PUNCT
ejpam-4691	182	7	f	f	X
ejpam-4691	182	8	is	be	AUX
ejpam-4691	182	9	not	not	PART
ejpam-4691	182	10	m	m	NOUN
ejpam-4691	182	11	-	-	ADJ
ejpam-4691	182	12	open	open	ADJ
ejpam-4691	182	13	at	at	ADP
ejpam-4691	182	14	x	x	X
ejpam-4691	182	15	}	}	PUNCT
ejpam-4691	182	16	.	.	PUNCT
ejpam-4691	183	1	theorem	theorem	NOUN
ejpam-4691	183	2	5	5	NUM
ejpam-4691	183	3	.	.	X
ejpam-4691	183	4	for	for	ADP
ejpam-4691	183	5	a	a	DET
ejpam-4691	183	6	multifunction	multifunction	NOUN
ejpam-4691	184	1	f	f	NOUN
ejpam-4691	184	2	:	:	PUNCT
ejpam-4691	184	3	(	(	PUNCT
ejpam-4691	184	4	x	x	NOUN
ejpam-4691	184	5	,	,	PUNCT
ejpam-4691	184	6	mx	mx	NOUN
ejpam-4691	184	7	)	)	PUNCT
ejpam-4691	184	8	→	→	SYM
ejpam-4691	184	9	(	(	PUNCT
ejpam-4691	184	10	y	y	PROPN
ejpam-4691	184	11	,	,	PUNCT
ejpam-4691	184	12	my	my	INTJ
ejpam-4691	184	13	)	)	PUNCT
ejpam-4691	184	14	,	,	PUNCT
ejpam-4691	184	15	where	where	SCONJ
ejpam-4691	184	16	my	my	PRON
ejpam-4691	184	17	has	have	VERB
ejpam-4691	184	18	property	property	NOUN
ejpam-4691	184	19	b	b	PROPN
ejpam-4691	184	20	,	,	PUNCT
ejpam-4691	184	21	the	the	DET
ejpam-4691	184	22	following	follow	VERB
ejpam-4691	184	23	properties	property	NOUN
ejpam-4691	184	24	hold	hold	VERB
ejpam-4691	184	25	:	:	PUNCT
ejpam-4691	184	26	d0(f	d0(f	NUM
ejpam-4691	184	27	)	)	PUNCT
ejpam-4691	184	28	=	=	SYM
ejpam-4691	184	29	∪u∈mx	∪u∈mx	NOUN
ejpam-4691	184	30	{	{	PUNCT
ejpam-4691	184	31	u	u	NOUN
ejpam-4691	184	32	−	−	NOUN
ejpam-4691	184	33	f+(my	f+(my	NOUN
ejpam-4691	184	34	int(f	int(f	PROPN
ejpam-4691	184	35	(	(	PUNCT
ejpam-4691	184	36	u	u	NOUN
ejpam-4691	184	37	)	)	PUNCT
ejpam-4691	184	38	)	)	PUNCT
ejpam-4691	184	39	)	)	PUNCT
ejpam-4691	184	40	}	}	PUNCT
ejpam-4691	185	1	=	=	PUNCT
ejpam-4691	185	2	∪a∈p	∪a∈p	X
ejpam-4691	185	3	(	(	PUNCT
ejpam-4691	185	4	x){mxint(a)−	x){mxint(a)−	SYM
ejpam-4691	185	5	f+(my	f+(my	PROPN
ejpam-4691	185	6	int(f	int(f	PROPN
ejpam-4691	185	7	(	(	PUNCT
ejpam-4691	185	8	a	a	NOUN
ejpam-4691	185	9	)	)	PUNCT
ejpam-4691	185	10	)	)	PUNCT
ejpam-4691	185	11	)	)	PUNCT
ejpam-4691	185	12	}	}	PUNCT
ejpam-4691	185	13	t.	t.	NOUN
ejpam-4691	185	14	noiri	noiri	PROPN
ejpam-4691	185	15	,	,	PUNCT
ejpam-4691	185	16	v.	v.	CCONJ
ejpam-4691	185	17	popa	popa	NOUN
ejpam-4691	185	18	/	/	SYM
ejpam-4691	185	19	eur	eur	PROPN
ejpam-4691	185	20	.	.	PUNCT
ejpam-4691	186	1	j.	j.	PROPN
ejpam-4691	186	2	pure	pure	PROPN
ejpam-4691	186	3	appl	appl	PROPN
ejpam-4691	186	4	.	.	PROPN
ejpam-4691	186	5	math	math	PROPN
ejpam-4691	186	6	,	,	PUNCT
ejpam-4691	186	7	16	16	NUM
ejpam-4691	186	8	(	(	PUNCT
ejpam-4691	186	9	1	1	NUM
ejpam-4691	186	10	)	)	PUNCT
ejpam-4691	186	11	(	(	PUNCT
ejpam-4691	186	12	2023	2023	NUM
ejpam-4691	186	13	)	)	PUNCT
ejpam-4691	186	14	,	,	PUNCT
ejpam-4691	186	15	430	430	NUM
ejpam-4691	186	16	-	-	SYM
ejpam-4691	186	17	439	439	NUM
ejpam-4691	186	18	434	434	NUM
ejpam-4691	186	19	=	=	SYM
ejpam-4691	186	20	∪b∈p	∪b∈p	PROPN
ejpam-4691	186	21	(	(	PUNCT
ejpam-4691	186	22	y	y	PROPN
ejpam-4691	186	23	)	)	PUNCT
ejpam-4691	186	24	{	{	PUNCT
ejpam-4691	186	25	mxint(f+(b))−	mxint(f+(b))−	NOUN
ejpam-4691	186	26	f+(my	f+(my	NOUN
ejpam-4691	186	27	int(b	int(b	NOUN
ejpam-4691	186	28	)	)	PUNCT
ejpam-4691	186	29	)	)	PUNCT
ejpam-4691	186	30	}	}	PUNCT
ejpam-4691	187	1	=	=	SYM
ejpam-4691	187	2	∪b∈p	∪b∈p	PROPN
ejpam-4691	187	3	(	(	PUNCT
ejpam-4691	187	4	y	y	PROPN
ejpam-4691	187	5	)	)	PUNCT
ejpam-4691	187	6	{	{	PUNCT
ejpam-4691	187	7	f−(my	f−(my	PROPN
ejpam-4691	187	8	cl(b))−mxcl(f−(b	cl(b))−mxcl(f−(b	PROPN
ejpam-4691	187	9	)	)	PUNCT
ejpam-4691	187	10	)	)	PUNCT
ejpam-4691	187	11	}	}	PUNCT
ejpam-4691	187	12	.	.	PUNCT
ejpam-4691	188	1	proof	proof	NOUN
ejpam-4691	188	2	.	.	PUNCT
ejpam-4691	189	1	let	let	VERB
ejpam-4691	189	2	x	x	SYM
ejpam-4691	189	3	∈	∈	PROPN
ejpam-4691	189	4	d0(f	d0(f	PROPN
ejpam-4691	189	5	)	)	PUNCT
ejpam-4691	189	6	.	.	PUNCT
ejpam-4691	190	1	then	then	ADV
ejpam-4691	190	2	,	,	PUNCT
ejpam-4691	190	3	by	by	ADP
ejpam-4691	190	4	theorem	theorem	NOUN
ejpam-4691	190	5	1	1	NUM
ejpam-4691	190	6	,	,	PUNCT
ejpam-4691	190	7	there	there	PRON
ejpam-4691	190	8	exists	exist	VERB
ejpam-4691	190	9	anmx	anmx	PROPN
ejpam-4691	190	10	-open	-open	PROPN
ejpam-4691	190	11	set	set	VERB
ejpam-4691	190	12	u0	u0	NOUN
ejpam-4691	190	13	containing	contain	VERB
ejpam-4691	190	14	x	x	PUNCT
ejpam-4691	190	15	such	such	ADJ
ejpam-4691	190	16	that	that	SCONJ
ejpam-4691	190	17	x	x	SYM
ejpam-4691	190	18	/∈	/∈	PRON
ejpam-4691	190	19	f+(my	f+(my	NOUN
ejpam-4691	190	20	int(f	int(f	NOUN
ejpam-4691	190	21	(	(	PUNCT
ejpam-4691	190	22	u0	u0	ADJ
ejpam-4691	190	23	)	)	PUNCT
ejpam-4691	190	24	)	)	PUNCT
ejpam-4691	190	25	)	)	PUNCT
ejpam-4691	190	26	.	.	PUNCT
ejpam-4691	191	1	hence	hence	ADV
ejpam-4691	191	2	,	,	PUNCT
ejpam-4691	191	3	x	x	PUNCT
ejpam-4691	191	4	∈	∈	NOUN
ejpam-4691	191	5	u0	u0	ADJ
ejpam-4691	191	6	∩	∩	NOUN
ejpam-4691	191	7	(	(	PUNCT
ejpam-4691	191	8	x	x	SYM
ejpam-4691	191	9	−	−	NOUN
ejpam-4691	191	10	f+(my	f+(my	ADJ
ejpam-4691	191	11	int(f	int(f	NOUN
ejpam-4691	191	12	(	(	PUNCT
ejpam-4691	191	13	u0	u0	ADJ
ejpam-4691	191	14	)	)	PUNCT
ejpam-4691	191	15	)	)	PUNCT
ejpam-4691	191	16	)	)	PUNCT
ejpam-4691	191	17	)	)	PUNCT
ejpam-4691	191	18	=	=	PUNCT
ejpam-4691	191	19	u0	u0	ADJ
ejpam-4691	191	20	−	−	NOUN
ejpam-4691	191	21	f+(my	f+(my	NOUN
ejpam-4691	191	22	int(f	int(f	NOUN
ejpam-4691	191	23	(	(	PUNCT
ejpam-4691	191	24	u0	u0	ADJ
ejpam-4691	191	25	)	)	PUNCT
ejpam-4691	191	26	)	)	PUNCT
ejpam-4691	191	27	)	)	PUNCT
ejpam-4691	192	1	⊂	⊂	PROPN
ejpam-4691	192	2	∪u∈mx	∪u∈mx	NOUN
ejpam-4691	192	3	{	{	PUNCT
ejpam-4691	192	4	u	u	NOUN
ejpam-4691	192	5	−	−	NOUN
ejpam-4691	192	6	f+(my	f+(my	NOUN
ejpam-4691	192	7	int(f	int(f	PROPN
ejpam-4691	192	8	(	(	PUNCT
ejpam-4691	192	9	u	u	NOUN
ejpam-4691	192	10	)	)	PUNCT
ejpam-4691	192	11	)	)	PUNCT
ejpam-4691	192	12	)	)	PUNCT
ejpam-4691	192	13	}	}	PUNCT
ejpam-4691	192	14	.	.	PUNCT
ejpam-4691	193	1	conversely	conversely	ADV
ejpam-4691	193	2	,	,	PUNCT
ejpam-4691	193	3	let	let	VERB
ejpam-4691	193	4	x	x	PART
ejpam-4691	193	5	∈	∈	PROPN
ejpam-4691	193	6	∪u∈mx	∪u∈mx	NOUN
ejpam-4691	193	7	{	{	PUNCT
ejpam-4691	193	8	u−f+(my	u−f+(my	X
ejpam-4691	193	9	int(f	int(f	PROPN
ejpam-4691	193	10	(	(	PUNCT
ejpam-4691	193	11	u	u	NOUN
ejpam-4691	193	12	)	)	PUNCT
ejpam-4691	193	13	)	)	PUNCT
ejpam-4691	193	14	)	)	PUNCT
ejpam-4691	193	15	}	}	PUNCT
ejpam-4691	193	16	.	.	PUNCT
ejpam-4691	194	1	then	then	ADV
ejpam-4691	194	2	,	,	PUNCT
ejpam-4691	194	3	there	there	PRON
ejpam-4691	194	4	exists	exist	VERB
ejpam-4691	194	5	u0	u0	PROPN
ejpam-4691	194	6	∈	∈	PROPN
ejpam-4691	194	7	mx	mx	PROPN
ejpam-4691	194	8	such	such	ADJ
ejpam-4691	194	9	that	that	SCONJ
ejpam-4691	194	10	x	x	SYM
ejpam-4691	194	11	∈	∈	PROPN
ejpam-4691	194	12	u0	u0	NOUN
ejpam-4691	194	13	−	−	PROPN
ejpam-4691	194	14	f+(my	f+(my	NOUN
ejpam-4691	194	15	int(f	int(f	NOUN
ejpam-4691	194	16	(	(	PUNCT
ejpam-4691	194	17	u0	u0	ADJ
ejpam-4691	194	18	)	)	PUNCT
ejpam-4691	194	19	)	)	PUNCT
ejpam-4691	194	20	)	)	PUNCT
ejpam-4691	194	21	.	.	PUNCT
ejpam-4691	195	1	therefore	therefore	ADV
ejpam-4691	195	2	,	,	PUNCT
ejpam-4691	195	3	by	by	ADP
ejpam-4691	195	4	theorem	theorem	NOUN
ejpam-4691	195	5	1	1	NUM
ejpam-4691	195	6	x	x	SYM
ejpam-4691	195	7	∈	∈	PROPN
ejpam-4691	195	8	d0(f	d0(f	PROPN
ejpam-4691	195	9	)	)	PUNCT
ejpam-4691	195	10	.	.	PUNCT
ejpam-4691	196	1	for	for	ADP
ejpam-4691	196	2	the	the	DET
ejpam-4691	196	3	second	second	ADJ
ejpam-4691	196	4	equation	equation	NOUN
ejpam-4691	196	5	,	,	PUNCT
ejpam-4691	196	6	let	let	VERB
ejpam-4691	196	7	x	x	SYM
ejpam-4691	196	8	∈	∈	PROPN
ejpam-4691	196	9	d0(f	d0(f	PROPN
ejpam-4691	196	10	)	)	PUNCT
ejpam-4691	196	11	.	.	PUNCT
ejpam-4691	197	1	then	then	ADV
ejpam-4691	197	2	,	,	PUNCT
ejpam-4691	197	3	by	by	ADP
ejpam-4691	197	4	theorem	theorem	NOUN
ejpam-4691	197	5	3	3	NUM
ejpam-4691	197	6	,	,	PUNCT
ejpam-4691	197	7	there	there	PRON
ejpam-4691	197	8	exists	exist	VERB
ejpam-4691	197	9	a1	a1	NOUN
ejpam-4691	197	10	∈	∈	PROPN
ejpam-4691	197	11	p	p	X
ejpam-4691	197	12	(	(	PUNCT
ejpam-4691	197	13	x	x	X
ejpam-4691	197	14	)	)	PUNCT
ejpam-4691	197	15	such	such	ADJ
ejpam-4691	197	16	that	that	SCONJ
ejpam-4691	197	17	x	x	SYM
ejpam-4691	197	18	∈	∈	PROPN
ejpam-4691	197	19	mxint(a1	mxint(a1	VERB
ejpam-4691	197	20	)	)	PUNCT
ejpam-4691	197	21	and	and	CCONJ
ejpam-4691	197	22	x	x	X
ejpam-4691	197	23	/∈	/∈	PRON
ejpam-4691	197	24	f+(my	f+(my	NOUN
ejpam-4691	197	25	int(f	int(f	NOUN
ejpam-4691	197	26	(	(	PUNCT
ejpam-4691	197	27	a1	a1	NOUN
ejpam-4691	197	28	)	)	PUNCT
ejpam-4691	197	29	)	)	PUNCT
ejpam-4691	197	30	)	)	PUNCT
ejpam-4691	197	31	.	.	PUNCT
ejpam-4691	198	1	therefore	therefore	ADV
ejpam-4691	198	2	,	,	PUNCT
ejpam-4691	198	3	x	x	PUNCT
ejpam-4691	198	4	∈	∈	NOUN
ejpam-4691	198	5	mxint(a1)−	mxint(a1)−	NOUN
ejpam-4691	198	6	f+(my	f+(my	NOUN
ejpam-4691	198	7	int(f	int(f	PROPN
ejpam-4691	198	8	(	(	PUNCT
ejpam-4691	198	9	a1	a1	NOUN
ejpam-4691	198	10	)	)	PUNCT
ejpam-4691	198	11	)	)	PUNCT
ejpam-4691	198	12	)	)	PUNCT
ejpam-4691	199	1	⊂	⊂	PROPN
ejpam-4691	199	2	∪a∈p	∪a∈p	X
ejpam-4691	199	3	(	(	PUNCT
ejpam-4691	199	4	x){mxint(a)−	x){mxint(a)−	SYM
ejpam-4691	199	5	f+(my	f+(my	PROPN
ejpam-4691	199	6	int(f	int(f	PROPN
ejpam-4691	199	7	(	(	PUNCT
ejpam-4691	199	8	a	a	NOUN
ejpam-4691	199	9	)	)	PUNCT
ejpam-4691	199	10	)	)	PUNCT
ejpam-4691	199	11	)	)	PUNCT
ejpam-4691	199	12	}	}	PUNCT
ejpam-4691	199	13	.	.	PUNCT
ejpam-4691	200	1	conversely	conversely	ADV
ejpam-4691	200	2	,	,	PUNCT
ejpam-4691	200	3	x	x	SYM
ejpam-4691	200	4	∈	∈	PROPN
ejpam-4691	200	5	∪a∈p	∪a∈p	X
ejpam-4691	200	6	(	(	PUNCT
ejpam-4691	200	7	x){mxint(a	x){mxint(a	PROPN
ejpam-4691	200	8	)	)	PUNCT
ejpam-4691	200	9	−	−	PRON
ejpam-4691	200	10	f+(my	f+(my	NOUN
ejpam-4691	200	11	int(f	int(f	NOUN
ejpam-4691	200	12	(	(	PUNCT
ejpam-4691	200	13	a	a	NOUN
ejpam-4691	200	14	)	)	PUNCT
ejpam-4691	200	15	)	)	PUNCT
ejpam-4691	200	16	)	)	PUNCT
ejpam-4691	200	17	}	}	PUNCT
ejpam-4691	200	18	.	.	PUNCT
ejpam-4691	201	1	then	then	ADV
ejpam-4691	201	2	,	,	PUNCT
ejpam-4691	201	3	there	there	PRON
ejpam-4691	201	4	exists	exist	VERB
ejpam-4691	201	5	a1	a1	PROPN
ejpam-4691	201	6	∈	∈	PROPN
ejpam-4691	201	7	p(x	p(x	NOUN
ejpam-4691	201	8	)	)	PUNCT
ejpam-4691	201	9	such	such	ADJ
ejpam-4691	201	10	that	that	SCONJ
ejpam-4691	201	11	x	x	SYM
ejpam-4691	201	12	∈	∈	NOUN
ejpam-4691	201	13	mxint(a1)−	mxint(a1)−	NOUN
ejpam-4691	201	14	f+(my	f+(my	NOUN
ejpam-4691	201	15	int(f	int(f	PROPN
ejpam-4691	201	16	(	(	PUNCT
ejpam-4691	201	17	a1	a1	NOUN
ejpam-4691	201	18	)	)	PUNCT
ejpam-4691	201	19	)	)	PUNCT
ejpam-4691	201	20	)	)	PUNCT
ejpam-4691	201	21	.	.	PUNCT
ejpam-4691	202	1	by	by	ADP
ejpam-4691	202	2	theorem	theorem	NOUN
ejpam-4691	202	3	3	3	NUM
ejpam-4691	202	4	,	,	PUNCT
ejpam-4691	202	5	x	x	SYM
ejpam-4691	202	6	∈	∈	PROPN
ejpam-4691	202	7	d0(f	d0(f	PROPN
ejpam-4691	202	8	)	)	PUNCT
ejpam-4691	202	9	.	.	PUNCT
ejpam-4691	203	1	the	the	DET
ejpam-4691	203	2	other	other	ADJ
ejpam-4691	203	3	equations	equation	NOUN
ejpam-4691	203	4	are	be	AUX
ejpam-4691	203	5	similarly	similarly	ADV
ejpam-4691	203	6	proved	prove	VERB
ejpam-4691	203	7	.	.	PUNCT
ejpam-4691	204	1	4	4	X
ejpam-4691	204	2	.	.	X
ejpam-4691	204	3	ideal	ideal	ADJ
ejpam-4691	204	4	topological	topological	ADJ
ejpam-4691	204	5	spaces	space	NOUN
ejpam-4691	204	6	let	let	VERB
ejpam-4691	204	7	(	(	PUNCT
ejpam-4691	204	8	x	x	NOUN
ejpam-4691	204	9	,	,	PUNCT
ejpam-4691	204	10	τ	τ	X
ejpam-4691	204	11	)	)	PUNCT
ejpam-4691	204	12	be	be	VERB
ejpam-4691	204	13	a	a	DET
ejpam-4691	204	14	topological	topological	ADJ
ejpam-4691	204	15	space	space	NOUN
ejpam-4691	204	16	.	.	PUNCT
ejpam-4691	205	1	the	the	DET
ejpam-4691	205	2	notion	notion	NOUN
ejpam-4691	205	3	of	of	ADP
ejpam-4691	205	4	ideals	ideal	NOUN
ejpam-4691	205	5	has	have	AUX
ejpam-4691	205	6	been	be	AUX
ejpam-4691	205	7	introduced	introduce	VERB
ejpam-4691	205	8	in	in	ADP
ejpam-4691	205	9	[	[	X
ejpam-4691	205	10	15	15	NUM
ejpam-4691	205	11	]	]	PUNCT
ejpam-4691	205	12	and	and	CCONJ
ejpam-4691	205	13	[	[	X
ejpam-4691	205	14	27	27	NUM
ejpam-4691	205	15	]	]	PUNCT
ejpam-4691	205	16	and	and	CCONJ
ejpam-4691	205	17	further	far	ADV
ejpam-4691	205	18	investigated	investigate	VERB
ejpam-4691	205	19	in	in	ADP
ejpam-4691	205	20	[	[	PUNCT
ejpam-4691	205	21	13	13	NUM
ejpam-4691	205	22	]	]	PUNCT
ejpam-4691	205	23	definition	definition	NOUN
ejpam-4691	205	24	7	7	NUM
ejpam-4691	205	25	.	.	PUNCT
ejpam-4691	206	1	a	a	DET
ejpam-4691	206	2	nonempty	nonempty	ADJ
ejpam-4691	206	3	collection	collection	NOUN
ejpam-4691	206	4	i	i	PRON
ejpam-4691	206	5	of	of	ADP
ejpam-4691	206	6	subsets	subset	NOUN
ejpam-4691	206	7	of	of	ADP
ejpam-4691	206	8	a	a	DET
ejpam-4691	206	9	set	set	NOUN
ejpam-4691	206	10	x	x	PUNCT
ejpam-4691	206	11	is	be	AUX
ejpam-4691	206	12	called	call	VERB
ejpam-4691	206	13	an	an	DET
ejpam-4691	206	14	ideal	ideal	NOUN
ejpam-4691	206	15	on	on	ADP
ejpam-4691	206	16	x	x	SYM
ejpam-4691	206	17	if	if	SCONJ
ejpam-4691	206	18	it	it	PRON
ejpam-4691	206	19	satisfies	satisfy	VERB
ejpam-4691	206	20	the	the	DET
ejpam-4691	206	21	following	follow	VERB
ejpam-4691	206	22	two	two	NUM
ejpam-4691	206	23	conditions	condition	NOUN
ejpam-4691	206	24	:	:	PUNCT
ejpam-4691	206	25	(	(	PUNCT
ejpam-4691	206	26	1	1	X
ejpam-4691	206	27	)	)	PUNCT
ejpam-4691	207	1	a	a	DET
ejpam-4691	207	2	∈	∈	NOUN
ejpam-4691	207	3	i	i	PRON
ejpam-4691	207	4	and	and	CCONJ
ejpam-4691	207	5	b	b	PROPN
ejpam-4691	207	6	⊂	⊂	PROPN
ejpam-4691	207	7	a	a	PRON
ejpam-4691	207	8	implies	imply	VERB
ejpam-4691	207	9	b	b	X
ejpam-4691	207	10	∈	∈	PROPN
ejpam-4691	207	11	i	i	PRON
ejpam-4691	207	12	,	,	PUNCT
ejpam-4691	207	13	(	(	PUNCT
ejpam-4691	207	14	2	2	X
ejpam-4691	207	15	)	)	PUNCT
ejpam-4691	208	1	a	a	DET
ejpam-4691	208	2	∈	∈	NOUN
ejpam-4691	208	3	i	i	PRON
ejpam-4691	208	4	and	and	CCONJ
ejpam-4691	208	5	b	b	X
ejpam-4691	208	6	∈	∈	PROPN
ejpam-4691	208	7	i	i	PRON
ejpam-4691	208	8	implies	imply	VERB
ejpam-4691	208	9	a	a	DET
ejpam-4691	208	10	∪b	∪b	PUNCT
ejpam-4691	208	11	∈	∈	PROPN
ejpam-4691	208	12	i.	i.	NOUN
ejpam-4691	208	13	a	a	DET
ejpam-4691	208	14	topological	topological	ADJ
ejpam-4691	208	15	space	space	NOUN
ejpam-4691	208	16	(	(	PUNCT
ejpam-4691	208	17	x	x	X
ejpam-4691	208	18	,	,	PUNCT
ejpam-4691	208	19	τ	τ	X
ejpam-4691	208	20	)	)	PUNCT
ejpam-4691	208	21	with	with	ADP
ejpam-4691	208	22	an	an	DET
ejpam-4691	208	23	ideal	ideal	ADJ
ejpam-4691	208	24	i	i	PRON
ejpam-4691	208	25	on	on	ADP
ejpam-4691	208	26	x	x	SYM
ejpam-4691	208	27	is	be	AUX
ejpam-4691	208	28	called	call	VERB
ejpam-4691	208	29	an	an	DET
ejpam-4691	208	30	ideal	ideal	ADJ
ejpam-4691	208	31	topological	topological	ADJ
ejpam-4691	208	32	space	space	NOUN
ejpam-4691	208	33	and	and	CCONJ
ejpam-4691	208	34	is	be	AUX
ejpam-4691	208	35	denoted	denote	VERB
ejpam-4691	208	36	by	by	ADP
ejpam-4691	208	37	(	(	PUNCT
ejpam-4691	208	38	x	x	X
ejpam-4691	208	39	,	,	PUNCT
ejpam-4691	208	40	τ	τ	PROPN
ejpam-4691	208	41	,	,	PUNCT
ejpam-4691	208	42	i	i	PROPN
ejpam-4691	208	43	)	)	PUNCT
ejpam-4691	208	44	.	.	PUNCT
ejpam-4691	209	1	let	let	VERB
ejpam-4691	209	2	(	(	PUNCT
ejpam-4691	209	3	x	x	X
ejpam-4691	209	4	,	,	PUNCT
ejpam-4691	209	5	τ	τ	PROPN
ejpam-4691	209	6	,	,	PUNCT
ejpam-4691	209	7	i	i	PRON
ejpam-4691	209	8	)	)	PUNCT
ejpam-4691	209	9	be	be	VERB
ejpam-4691	209	10	an	an	DET
ejpam-4691	209	11	ideal	ideal	ADJ
ejpam-4691	209	12	topological	topological	ADJ
ejpam-4691	209	13	space	space	NOUN
ejpam-4691	209	14	.	.	PUNCT
ejpam-4691	210	1	for	for	ADP
ejpam-4691	210	2	any	any	DET
ejpam-4691	210	3	subset	subset	NOUN
ejpam-4691	210	4	a	a	PRON
ejpam-4691	210	5	of	of	ADP
ejpam-4691	210	6	x	x	PROPN
ejpam-4691	210	7	,	,	PUNCT
ejpam-4691	210	8	a⋆(i	a⋆(i	PROPN
ejpam-4691	210	9	,	,	PUNCT
ejpam-4691	210	10	τ	τ	X
ejpam-4691	210	11	)	)	PUNCT
ejpam-4691	210	12	=	=	PRON
ejpam-4691	210	13	{	{	PUNCT
ejpam-4691	210	14	x	x	PUNCT
ejpam-4691	210	15	∈	∈	PROPN
ejpam-4691	210	16	x	x	X
ejpam-4691	210	17	:	:	PUNCT
ejpam-4691	210	18	u	u	NOUN
ejpam-4691	210	19	∩	∩	NOUN
ejpam-4691	210	20	a	a	X
ejpam-4691	210	21	/∈	/∈	PUNCT
ejpam-4691	210	22	i	i	PRON
ejpam-4691	210	23	for	for	ADP
ejpam-4691	210	24	every	every	DET
ejpam-4691	210	25	u	u	PROPN
ejpam-4691	210	26	∈	∈	PROPN
ejpam-4691	210	27	τ(x	τ(x	NOUN
ejpam-4691	210	28	)	)	PUNCT
ejpam-4691	210	29	}	}	PUNCT
ejpam-4691	210	30	,	,	PUNCT
ejpam-4691	210	31	where	where	SCONJ
ejpam-4691	210	32	τ(x	τ(x	NOUN
ejpam-4691	210	33	)	)	PUNCT
ejpam-4691	210	34	=	=	PRON
ejpam-4691	210	35	{	{	PUNCT
ejpam-4691	210	36	u	u	X
ejpam-4691	210	37	∈	∈	PROPN
ejpam-4691	210	38	τ	τ	X
ejpam-4691	210	39	:	:	PUNCT
ejpam-4691	210	40	x	x	SYM
ejpam-4691	210	41	∈	∈	PROPN
ejpam-4691	210	42	u	u	NOUN
ejpam-4691	210	43	}	}	PUNCT
ejpam-4691	210	44	,	,	PUNCT
ejpam-4691	210	45	is	be	AUX
ejpam-4691	210	46	called	call	VERB
ejpam-4691	210	47	the	the	DET
ejpam-4691	210	48	local	local	ADJ
ejpam-4691	210	49	function	function	NOUN
ejpam-4691	210	50	of	of	ADP
ejpam-4691	210	51	a	a	PRON
ejpam-4691	210	52	with	with	ADP
ejpam-4691	210	53	respect	respect	NOUN
ejpam-4691	210	54	to	to	ADP
ejpam-4691	210	55	τ	τ	PROPN
ejpam-4691	210	56	and	and	CCONJ
ejpam-4691	210	57	i	i	PRON
ejpam-4691	210	58	[	[	X
ejpam-4691	210	59	13	13	NUM
ejpam-4691	210	60	]	]	PUNCT
ejpam-4691	210	61	.	.	PUNCT
ejpam-4691	211	1	hereafter	hereafter	ADV
ejpam-4691	211	2	,	,	PUNCT
ejpam-4691	211	3	a⋆(i	a⋆(i	PROPN
ejpam-4691	211	4	,	,	PUNCT
ejpam-4691	211	5	τ	τ	X
ejpam-4691	211	6	)	)	PUNCT
ejpam-4691	211	7	is	be	AUX
ejpam-4691	211	8	simply	simply	ADV
ejpam-4691	211	9	denoted	denote	VERB
ejpam-4691	211	10	by	by	ADP
ejpam-4691	211	11	a⋆.	a⋆.	NOUN
ejpam-4691	211	12	it	it	PRON
ejpam-4691	211	13	is	be	AUX
ejpam-4691	211	14	well	well	ADV
ejpam-4691	211	15	known	know	VERB
ejpam-4691	211	16	that	that	SCONJ
ejpam-4691	211	17	cl⋆(a	cl⋆(a	VERB
ejpam-4691	211	18	)	)	PUNCT
ejpam-4691	211	19	=	=	NOUN
ejpam-4691	211	20	a	a	DET
ejpam-4691	211	21	∪	∪	NOUN
ejpam-4691	211	22	a⋆	a⋆	ADP
ejpam-4691	211	23	defines	define	NOUN
ejpam-4691	211	24	a	a	DET
ejpam-4691	211	25	kuratowski	kuratowski	ADJ
ejpam-4691	211	26	closure	closure	NOUN
ejpam-4691	211	27	operator	operator	NOUN
ejpam-4691	211	28	on	on	ADP
ejpam-4691	211	29	x	x	PUNCT
ejpam-4691	211	30	and	and	CCONJ
ejpam-4691	211	31	the	the	DET
ejpam-4691	211	32	topology	topology	NOUN
ejpam-4691	211	33	generated	generate	VERB
ejpam-4691	211	34	by	by	ADP
ejpam-4691	211	35	cl⋆	cl⋆	PROPN
ejpam-4691	211	36	is	be	AUX
ejpam-4691	211	37	denoted	denote	VERB
ejpam-4691	211	38	by	by	ADP
ejpam-4691	211	39	τ⋆.	τ⋆.	PROPN
ejpam-4691	211	40	lemma	lemma	PROPN
ejpam-4691	211	41	3	3	PROPN
ejpam-4691	211	42	.	.	PUNCT
ejpam-4691	211	43	(	(	PUNCT
ejpam-4691	211	44	janković	janković	ADJ
ejpam-4691	211	45	and	and	CCONJ
ejpam-4691	211	46	hamlett	hamlett	PROPN
ejpam-4691	212	1	[	[	X
ejpam-4691	212	2	13	13	NUM
ejpam-4691	212	3	]	]	PUNCT
ejpam-4691	212	4	)	)	PUNCT
ejpam-4691	212	5	let	let	VERB
ejpam-4691	212	6	(	(	PUNCT
ejpam-4691	212	7	x	x	NOUN
ejpam-4691	212	8	,	,	PUNCT
ejpam-4691	212	9	τ	τ	PROPN
ejpam-4691	212	10	,	,	PUNCT
ejpam-4691	212	11	i	i	PRON
ejpam-4691	212	12	)	)	PUNCT
ejpam-4691	212	13	be	be	VERB
ejpam-4691	212	14	an	an	DET
ejpam-4691	212	15	ideal	ideal	ADJ
ejpam-4691	212	16	topological	topological	ADJ
ejpam-4691	212	17	space	space	NOUN
ejpam-4691	212	18	and	and	CCONJ
ejpam-4691	212	19	a	a	DET
ejpam-4691	212	20	,	,	PUNCT
ejpam-4691	212	21	b	b	PROPN
ejpam-4691	212	22	be	be	AUX
ejpam-4691	212	23	two	two	NUM
ejpam-4691	212	24	subsets	subset	NOUN
ejpam-4691	212	25	of	of	ADP
ejpam-4691	212	26	x.	x.	NOUN
ejpam-4691	212	27	then	then	ADV
ejpam-4691	212	28	,	,	PUNCT
ejpam-4691	212	29	the	the	DET
ejpam-4691	212	30	following	follow	VERB
ejpam-4691	212	31	properties	property	NOUN
ejpam-4691	212	32	hold	hold	VERB
ejpam-4691	212	33	:	:	PUNCT
ejpam-4691	212	34	(	(	PUNCT
ejpam-4691	212	35	1	1	X
ejpam-4691	212	36	)	)	PUNCT
ejpam-4691	212	37	a	a	DET
ejpam-4691	212	38	⊂	⊂	PROPN
ejpam-4691	212	39	b	b	PROPN
ejpam-4691	212	40	implies	imply	VERB
ejpam-4691	212	41	cl⋆(a	cl⋆(a	NOUN
ejpam-4691	212	42	)	)	PUNCT
ejpam-4691	212	43	⊂	⊂	PROPN
ejpam-4691	212	44	cl⋆(b	cl⋆(b	NOUN
ejpam-4691	212	45	)	)	PUNCT
ejpam-4691	212	46	,	,	PUNCT
ejpam-4691	212	47	(	(	PUNCT
ejpam-4691	212	48	2	2	X
ejpam-4691	212	49	)	)	PUNCT
ejpam-4691	212	50	cl⋆(x	cl⋆(x	NOUN
ejpam-4691	212	51	)	)	PUNCT
ejpam-4691	212	52	=	=	SYM
ejpam-4691	212	53	x	x	PROPN
ejpam-4691	212	54	and	and	CCONJ
ejpam-4691	212	55	cl⋆(∅	cl⋆(∅	NOUN
ejpam-4691	212	56	)	)	PUNCT
ejpam-4691	212	57	=	=	SYM
ejpam-4691	212	58	∅	∅	NOUN
ejpam-4691	212	59	,	,	PUNCT
ejpam-4691	212	60	(	(	PUNCT
ejpam-4691	212	61	3	3	X
ejpam-4691	212	62	)	)	PUNCT
ejpam-4691	212	63	cl⋆(a	cl⋆(a	NOUN
ejpam-4691	212	64	)	)	PUNCT
ejpam-4691	212	65	∪	∪	ADP
ejpam-4691	212	66	cl⋆(b	cl⋆(b	NOUN
ejpam-4691	212	67	)	)	PUNCT
ejpam-4691	212	68	⊂	⊂	PROPN
ejpam-4691	212	69	cl⋆(a	cl⋆(a	X
ejpam-4691	212	70	∪b	∪b	NOUN
ejpam-4691	212	71	)	)	PUNCT
ejpam-4691	212	72	.	.	PUNCT
ejpam-4691	213	1	a	a	DET
ejpam-4691	213	2	subset	subset	NOUN
ejpam-4691	213	3	a	a	PRON
ejpam-4691	213	4	is	be	AUX
ejpam-4691	213	5	said	say	VERB
ejpam-4691	213	6	to	to	PART
ejpam-4691	213	7	be	be	AUX
ejpam-4691	213	8	i	i	NOUN
ejpam-4691	213	9	-	-	NOUN
ejpam-4691	213	10	open	open	ADJ
ejpam-4691	213	11	[	[	X
ejpam-4691	213	12	14	14	NUM
ejpam-4691	213	13	]	]	X
ejpam-4691	213	14	if	if	SCONJ
ejpam-4691	213	15	a	a	DET
ejpam-4691	213	16	⊂	⊂	PROPN
ejpam-4691	213	17	int(a⋆	int(a⋆	NOUN
ejpam-4691	213	18	)	)	PUNCT
ejpam-4691	213	19	.	.	PUNCT
ejpam-4691	214	1	as	as	ADP
ejpam-4691	214	2	generalizations	generalization	NOUN
ejpam-4691	214	3	of	of	ADP
ejpam-4691	214	4	open	open	ADJ
ejpam-4691	214	5	sets	set	NOUN
ejpam-4691	214	6	and	and	CCONJ
ejpam-4691	214	7	i	i	PRON
ejpam-4691	214	8	-	-	PUNCT
ejpam-4691	214	9	open	open	ADJ
ejpam-4691	214	10	sets	set	NOUN
ejpam-4691	214	11	,	,	PUNCT
ejpam-4691	214	12	the	the	DET
ejpam-4691	214	13	following	follow	VERB
ejpam-4691	214	14	subsets	subset	NOUN
ejpam-4691	214	15	are	be	AUX
ejpam-4691	214	16	introduced	introduce	VERB
ejpam-4691	214	17	and	and	CCONJ
ejpam-4691	214	18	investigated	investigate	VERB
ejpam-4691	214	19	.	.	PUNCT
ejpam-4691	215	1	definition	definition	NOUN
ejpam-4691	215	2	8	8	NUM
ejpam-4691	215	3	.	.	PUNCT
ejpam-4691	216	1	let	let	VERB
ejpam-4691	216	2	(	(	PUNCT
ejpam-4691	216	3	x	x	X
ejpam-4691	216	4	,	,	PUNCT
ejpam-4691	216	5	τ	τ	PROPN
ejpam-4691	216	6	,	,	PUNCT
ejpam-4691	216	7	i	i	PRON
ejpam-4691	216	8	)	)	PUNCT
ejpam-4691	216	9	be	be	VERB
ejpam-4691	216	10	an	an	DET
ejpam-4691	216	11	ideal	ideal	ADJ
ejpam-4691	216	12	topological	topological	ADJ
ejpam-4691	216	13	space	space	NOUN
ejpam-4691	216	14	.	.	PUNCT
ejpam-4691	217	1	a	a	DET
ejpam-4691	217	2	subset	subset	NOUN
ejpam-4691	217	3	a	a	PRON
ejpam-4691	217	4	of	of	ADP
ejpam-4691	217	5	x	x	SYM
ejpam-4691	217	6	is	be	AUX
ejpam-4691	217	7	said	say	VERB
ejpam-4691	217	8	to	to	PART
ejpam-4691	217	9	be	be	AUX
ejpam-4691	217	10	(	(	PUNCT
ejpam-4691	217	11	1	1	X
ejpam-4691	217	12	)	)	PUNCT
ejpam-4691	217	13	α	α	PROPN
ejpam-4691	217	14	-	-	PUNCT
ejpam-4691	217	15	i	i	PRON
ejpam-4691	217	16	-	-	PUNCT
ejpam-4691	217	17	open	open	ADJ
ejpam-4691	218	1	[	[	X
ejpam-4691	218	2	11	11	NUM
ejpam-4691	218	3	]	]	X
ejpam-4691	218	4	if	if	SCONJ
ejpam-4691	218	5	a	a	DET
ejpam-4691	218	6	⊂	⊂	PROPN
ejpam-4691	218	7	int(cl⋆(int(a	int(cl⋆(int(a	PROPN
ejpam-4691	218	8	)	)	PUNCT
ejpam-4691	218	9	)	)	PUNCT
ejpam-4691	218	10	)	)	PUNCT
ejpam-4691	219	1	,	,	PUNCT
ejpam-4691	219	2	(	(	PUNCT
ejpam-4691	219	3	2	2	X
ejpam-4691	219	4	)	)	PUNCT
ejpam-4691	219	5	semi	semi	ADJ
ejpam-4691	219	6	-	-	ADJ
ejpam-4691	219	7	i	i	PRON
ejpam-4691	219	8	-	-	PUNCT
ejpam-4691	219	9	open	open	ADJ
ejpam-4691	219	10	[	[	X
ejpam-4691	219	11	12	12	NUM
ejpam-4691	219	12	]	]	X
ejpam-4691	219	13	if	if	SCONJ
ejpam-4691	219	14	a	a	DET
ejpam-4691	219	15	⊂	⊂	X
ejpam-4691	219	16	cl⋆(int(a	cl⋆(int(a	PROPN
ejpam-4691	219	17	)	)	PUNCT
ejpam-4691	219	18	)	)	PUNCT
ejpam-4691	219	19	,	,	PUNCT
ejpam-4691	219	20	(	(	PUNCT
ejpam-4691	219	21	3	3	X
ejpam-4691	219	22	)	)	PUNCT
ejpam-4691	219	23	pre	pre	ADJ
ejpam-4691	219	24	-	-	ADJ
ejpam-4691	219	25	i	i	PRON
ejpam-4691	219	26	-	-	PUNCT
ejpam-4691	219	27	open	open	ADJ
ejpam-4691	220	1	[	[	X
ejpam-4691	220	2	8	8	NUM
ejpam-4691	220	3	]	]	X
ejpam-4691	220	4	if	if	SCONJ
ejpam-4691	220	5	a	a	DET
ejpam-4691	220	6	⊂	⊂	ADJ
ejpam-4691	220	7	int(cl⋆(a	int(cl⋆(a	NOUN
ejpam-4691	220	8	)	)	PUNCT
ejpam-4691	220	9	)	)	PUNCT
ejpam-4691	220	10	,	,	PUNCT
ejpam-4691	220	11	t.	t.	PROPN
ejpam-4691	220	12	noiri	noiri	PROPN
ejpam-4691	220	13	,	,	PUNCT
ejpam-4691	220	14	v.	v.	CCONJ
ejpam-4691	220	15	popa	popa	NOUN
ejpam-4691	220	16	/	/	SYM
ejpam-4691	220	17	eur	eur	PROPN
ejpam-4691	220	18	.	.	PUNCT
ejpam-4691	221	1	j.	j.	PROPN
ejpam-4691	221	2	pure	pure	PROPN
ejpam-4691	221	3	appl	appl	PROPN
ejpam-4691	221	4	.	.	PROPN
ejpam-4691	221	5	math	math	PROPN
ejpam-4691	221	6	,	,	PUNCT
ejpam-4691	221	7	16	16	NUM
ejpam-4691	221	8	(	(	PUNCT
ejpam-4691	221	9	1	1	NUM
ejpam-4691	221	10	)	)	PUNCT
ejpam-4691	221	11	(	(	PUNCT
ejpam-4691	221	12	2023	2023	NUM
ejpam-4691	221	13	)	)	PUNCT
ejpam-4691	221	14	,	,	PUNCT
ejpam-4691	221	15	430	430	NUM
ejpam-4691	221	16	-	-	SYM
ejpam-4691	221	17	439	439	NUM
ejpam-4691	221	18	435	435	NUM
ejpam-4691	221	19	(	(	PUNCT
ejpam-4691	221	20	4	4	NUM
ejpam-4691	221	21	)	)	PUNCT
ejpam-4691	221	22	b	b	NOUN
ejpam-4691	221	23	-	-	PUNCT
ejpam-4691	221	24	i	i	PRON
ejpam-4691	221	25	-	-	PUNCT
ejpam-4691	221	26	open	open	ADJ
ejpam-4691	221	27	[	[	X
ejpam-4691	221	28	3	3	NUM
ejpam-4691	221	29	]	]	PUNCT
ejpam-4691	221	30	if	if	SCONJ
ejpam-4691	221	31	a	a	PRON
ejpam-4691	221	32	⊂	⊂	PROPN
ejpam-4691	221	33	int(cl⋆(a	int(cl⋆(a	NOUN
ejpam-4691	221	34	)	)	PUNCT
ejpam-4691	221	35	)	)	PUNCT
ejpam-4691	221	36	∪	∪	ADP
ejpam-4691	221	37	cl⋆(int(a	cl⋆(int(a	PROPN
ejpam-4691	221	38	)	)	PUNCT
ejpam-4691	221	39	)	)	PUNCT
ejpam-4691	221	40	,	,	PUNCT
ejpam-4691	221	41	(	(	PUNCT
ejpam-4691	221	42	5	5	X
ejpam-4691	221	43	)	)	PUNCT
ejpam-4691	221	44	β	β	X
ejpam-4691	221	45	-	-	PUNCT
ejpam-4691	221	46	i	i	PRON
ejpam-4691	221	47	-	-	PUNCT
ejpam-4691	221	48	open	open	ADJ
ejpam-4691	221	49	[	[	X
ejpam-4691	221	50	11	11	NUM
ejpam-4691	221	51	]	]	X
ejpam-4691	221	52	if	if	SCONJ
ejpam-4691	221	53	a	a	DET
ejpam-4691	221	54	⊂	⊂	X
ejpam-4691	221	55	cl(int(cl⋆(a	cl(int(cl⋆(a	NOUN
ejpam-4691	221	56	)	)	PUNCT
ejpam-4691	221	57	)	)	PUNCT
ejpam-4691	221	58	)	)	PUNCT
ejpam-4691	221	59	,	,	PUNCT
ejpam-4691	221	60	(	(	PUNCT
ejpam-4691	221	61	6	6	X
ejpam-4691	221	62	)	)	PUNCT
ejpam-4691	221	63	weakly	weakly	ADJ
ejpam-4691	221	64	semi	semi	ADJ
ejpam-4691	221	65	-	-	ADJ
ejpam-4691	221	66	i	i	PRON
ejpam-4691	221	67	-	-	PUNCT
ejpam-4691	221	68	open	open	ADJ
ejpam-4691	222	1	[	[	X
ejpam-4691	222	2	9	9	NUM
ejpam-4691	222	3	]	]	X
ejpam-4691	222	4	if	if	SCONJ
ejpam-4691	222	5	a	a	PRON
ejpam-4691	222	6	⊂	⊂	PROPN
ejpam-4691	222	7	cl⋆(int(cl(a	cl⋆(int(cl(a	X
ejpam-4691	222	8	)	)	PUNCT
ejpam-4691	222	9	)	)	PUNCT
ejpam-4691	222	10	)	)	PUNCT
ejpam-4691	222	11	,	,	PUNCT
ejpam-4691	222	12	(	(	PUNCT
ejpam-4691	222	13	7	7	X
ejpam-4691	222	14	)	)	PUNCT
ejpam-4691	222	15	weakly	weakly	ADJ
ejpam-4691	222	16	b	b	X
ejpam-4691	222	17	-	-	PUNCT
ejpam-4691	222	18	i	i	PRON
ejpam-4691	222	19	-	-	PUNCT
ejpam-4691	222	20	open	open	ADJ
ejpam-4691	222	21	[	[	X
ejpam-4691	222	22	19	19	NUM
ejpam-4691	222	23	]	]	X
ejpam-4691	222	24	if	if	SCONJ
ejpam-4691	222	25	a	a	DET
ejpam-4691	222	26	⊂	⊂	X
ejpam-4691	222	27	cl(int(cl⋆(a	cl(int(cl⋆(a	NOUN
ejpam-4691	222	28	)	)	PUNCT
ejpam-4691	222	29	)	)	PUNCT
ejpam-4691	222	30	)	)	PUNCT
ejpam-4691	222	31	∪	∪	ADP
ejpam-4691	222	32	cl⋆(int(cl(a	cl⋆(int(cl(a	PROPN
ejpam-4691	222	33	)	)	PUNCT
ejpam-4691	222	34	)	)	PUNCT
ejpam-4691	222	35	)	)	PUNCT
ejpam-4691	222	36	,	,	PUNCT
ejpam-4691	222	37	(	(	PUNCT
ejpam-4691	222	38	8)	8)	NUM
ejpam-4691	222	39	strongly	strongly	ADV
ejpam-4691	222	40	β	β	AUX
ejpam-4691	222	41	-	-	ADJ
ejpam-4691	222	42	i	i	PRON
ejpam-4691	222	43	-	-	PUNCT
ejpam-4691	222	44	open	open	ADJ
ejpam-4691	223	1	[	[	X
ejpam-4691	223	2	10	10	NUM
ejpam-4691	223	3	]	]	X
ejpam-4691	223	4	if	if	SCONJ
ejpam-4691	223	5	a	a	DET
ejpam-4691	223	6	⊂	⊂	PROPN
ejpam-4691	223	7	cl⋆(int(cl⋆(a	cl⋆(int(cl⋆(a	PROPN
ejpam-4691	223	8	)	)	PUNCT
ejpam-4691	223	9	)	)	PUNCT
ejpam-4691	223	10	)	)	PUNCT
ejpam-4691	223	11	.	.	PUNCT
ejpam-4691	224	1	between	between	ADP
ejpam-4691	224	2	the	the	DET
ejpam-4691	224	3	sets	set	NOUN
ejpam-4691	224	4	in	in	ADP
ejpam-4691	224	5	definition	definition	NOUN
ejpam-4691	224	6	8	8	NUM
ejpam-4691	224	7	,	,	PUNCT
ejpam-4691	224	8	we	we	PRON
ejpam-4691	224	9	have	have	VERB
ejpam-4691	224	10	the	the	DET
ejpam-4691	224	11	following	follow	VERB
ejpam-4691	224	12	relations	relation	NOUN
ejpam-4691	224	13	:	:	PUNCT
ejpam-4691	224	14	diagram	diagram	NOUN
ejpam-4691	224	15	1	1	NUM
ejpam-4691	224	16	open	open	ADJ
ejpam-4691	224	17	⇒	⇒	NOUN
ejpam-4691	224	18	α	α	PROPN
ejpam-4691	224	19	-	-	ADJ
ejpam-4691	224	20	i	i	PRON
ejpam-4691	224	21	-	-	PUNCT
ejpam-4691	224	22	open	open	ADJ
ejpam-4691	224	23	⇒	⇒	NOUN
ejpam-4691	224	24	semi	semi	ADJ
ejpam-4691	224	25	-	-	ADJ
ejpam-4691	224	26	i	i	PRON
ejpam-4691	224	27	-	-	PUNCT
ejpam-4691	224	28	open	open	ADJ
ejpam-4691	224	29	⇒	⇒	NOUN
ejpam-4691	224	30	weakly	weakly	ADJ
ejpam-4691	224	31	semi	semi	ADJ
ejpam-4691	224	32	-	-	ADJ
ejpam-4691	224	33	i	i	PRON
ejpam-4691	224	34	-	-	PUNCT
ejpam-4691	224	35	open	open	ADJ
ejpam-4691	224	36	⇓	⇓	PROPN
ejpam-4691	224	37	⇓	⇓	PROPN
ejpam-4691	224	38	⇓	⇓	PROPN
ejpam-4691	224	39	i	i	PROPN
ejpam-4691	224	40	-	-	PUNCT
ejpam-4691	224	41	open	open	ADJ
ejpam-4691	224	42	⇒	⇒	NOUN
ejpam-4691	224	43	pre	pre	ADJ
ejpam-4691	224	44	-	-	ADJ
ejpam-4691	224	45	i	i	PRON
ejpam-4691	224	46	-	-	PUNCT
ejpam-4691	224	47	open	open	ADJ
ejpam-4691	224	48	⇒	⇒	NOUN
ejpam-4691	224	49	b	b	X
ejpam-4691	224	50	-	-	PUNCT
ejpam-4691	224	51	i	i	NOUN
ejpam-4691	224	52	-	-	PUNCT
ejpam-4691	224	53	open	open	ADJ
ejpam-4691	224	54	⇒	⇒	NOUN
ejpam-4691	224	55	weakly	weakly	ADJ
ejpam-4691	224	56	b	b	X
ejpam-4691	224	57	-	-	PUNCT
ejpam-4691	224	58	i	i	NOUN
ejpam-4691	224	59	-	-	PUNCT
ejpam-4691	224	60	open	open	ADJ
ejpam-4691	224	61	⇓	⇓	PROPN
ejpam-4691	224	62	⇑	⇑	PROPN
ejpam-4691	224	63	strongly	strongly	ADV
ejpam-4691	224	64	β	β	AUX
ejpam-4691	224	65	-	-	ADJ
ejpam-4691	224	66	i	i	NOUN
ejpam-4691	224	67	-	-	PUNCT
ejpam-4691	224	68	open	open	ADJ
ejpam-4691	224	69	⇒	⇒	NOUN
ejpam-4691	224	70	β	β	X
ejpam-4691	224	71	-	-	PUNCT
ejpam-4691	224	72	i	i	PRON
ejpam-4691	224	73	-	-	PUNCT
ejpam-4691	224	74	open	open	VERB
ejpam-4691	224	75	the	the	DET
ejpam-4691	224	76	family	family	NOUN
ejpam-4691	224	77	of	of	ADP
ejpam-4691	224	78	all	all	DET
ejpam-4691	224	79	α	α	PROPN
ejpam-4691	224	80	-	-	ADJ
ejpam-4691	224	81	i	i	PRON
ejpam-4691	224	82	-	-	PUNCT
ejpam-4691	224	83	open	open	ADJ
ejpam-4691	224	84	(	(	PUNCT
ejpam-4691	224	85	resp	resp	NOUN
ejpam-4691	224	86	.	.	PUNCT
ejpam-4691	225	1	semi	semi	ADJ
ejpam-4691	225	2	-	-	ADJ
ejpam-4691	225	3	i	i	PRON
ejpam-4691	225	4	-	-	PUNCT
ejpam-4691	225	5	open	open	ADJ
ejpam-4691	225	6	,	,	PUNCT
ejpam-4691	225	7	pre	pre	ADJ
ejpam-4691	225	8	-	-	ADJ
ejpam-4691	225	9	i	i	PRON
ejpam-4691	225	10	-	-	PUNCT
ejpam-4691	225	11	open	open	ADJ
ejpam-4691	225	12	,	,	PUNCT
ejpam-4691	225	13	b	b	X
ejpam-4691	225	14	-	-	PUNCT
ejpam-4691	225	15	i	i	PRON
ejpam-4691	225	16	-	-	PUNCT
ejpam-4691	225	17	open	open	ADJ
ejpam-4691	225	18	,	,	PUNCT
ejpam-4691	225	19	β	β	X
ejpam-4691	225	20	-	-	ADJ
ejpam-4691	225	21	i	i	PRON
ejpam-4691	225	22	-	-	PUNCT
ejpam-4691	225	23	open	open	ADJ
ejpam-4691	225	24	,	,	PUNCT
ejpam-4691	225	25	weakly	weakly	ADJ
ejpam-4691	225	26	semi	semi	ADJ
ejpam-4691	225	27	-	-	ADJ
ejpam-4691	225	28	i	i	PRON
ejpam-4691	225	29	-	-	PUNCT
ejpam-4691	225	30	open	open	ADJ
ejpam-4691	225	31	,	,	PUNCT
ejpam-4691	225	32	weakly	weakly	ADJ
ejpam-4691	225	33	b	b	X
ejpam-4691	225	34	-	-	PUNCT
ejpam-4691	225	35	i	i	NOUN
ejpam-4691	225	36	-	-	PUNCT
ejpam-4691	225	37	open	open	ADJ
ejpam-4691	225	38	,	,	PUNCT
ejpam-4691	225	39	strongly	strongly	ADV
ejpam-4691	225	40	β	β	X
ejpam-4691	225	41	-	-	ADJ
ejpam-4691	225	42	i	i	PRON
ejpam-4691	225	43	-	-	PUNCT
ejpam-4691	225	44	open	open	ADJ
ejpam-4691	225	45	)	)	PUNCT
ejpam-4691	225	46	sets	set	NOUN
ejpam-4691	225	47	in	in	ADP
ejpam-4691	225	48	an	an	DET
ejpam-4691	225	49	ideal	ideal	ADJ
ejpam-4691	225	50	topological	topological	ADJ
ejpam-4691	225	51	space	space	NOUN
ejpam-4691	225	52	(	(	PUNCT
ejpam-4691	225	53	x	x	X
ejpam-4691	225	54	,	,	PUNCT
ejpam-4691	225	55	τ	τ	PROPN
ejpam-4691	225	56	,	,	PUNCT
ejpam-4691	225	57	i	i	PROPN
ejpam-4691	225	58	)	)	PUNCT
ejpam-4691	225	59	is	be	AUX
ejpam-4691	225	60	denoted	denote	VERB
ejpam-4691	225	61	by	by	ADP
ejpam-4691	225	62	αio(x	αio(x	PROPN
ejpam-4691	225	63	)	)	PUNCT
ejpam-4691	225	64	(	(	PUNCT
ejpam-4691	225	65	resp	resp	NOUN
ejpam-4691	225	66	.	.	PUNCT
ejpam-4691	226	1	sio(x	sio(x	VERB
ejpam-4691	226	2	)	)	PUNCT
ejpam-4691	226	3	,	,	PUNCT
ejpam-4691	226	4	pio(x	pio(x	PROPN
ejpam-4691	226	5	)	)	PUNCT
ejpam-4691	226	6	,	,	PUNCT
ejpam-4691	226	7	bio(x	bio(x	PROPN
ejpam-4691	226	8	)	)	PUNCT
ejpam-4691	226	9	,	,	PUNCT
ejpam-4691	226	10	βio(x	βio(x	NUM
ejpam-4691	226	11	)	)	PUNCT
ejpam-4691	226	12	,	,	PUNCT
ejpam-4691	226	13	wsio(x	wsio(x	NOUN
ejpam-4691	226	14	)	)	PUNCT
ejpam-4691	226	15	,	,	PUNCT
ejpam-4691	226	16	wbio(x	wbio(x	PROPN
ejpam-4691	226	17	)	)	PUNCT
ejpam-4691	226	18	,	,	PUNCT
ejpam-4691	226	19	sβio(x	sβio(x	NOUN
ejpam-4691	226	20	)	)	PUNCT
ejpam-4691	226	21	)	)	PUNCT
ejpam-4691	226	22	.	.	PUNCT
ejpam-4691	227	1	definition	definition	NOUN
ejpam-4691	227	2	9	9	NUM
ejpam-4691	227	3	.	.	PUNCT
ejpam-4691	227	4	by	by	ADP
ejpam-4691	227	5	mio(x	mio(x	PROPN
ejpam-4691	227	6	)	)	PUNCT
ejpam-4691	228	1	,	,	PUNCT
ejpam-4691	228	2	we	we	PRON
ejpam-4691	228	3	denote	denote	VERB
ejpam-4691	228	4	each	each	DET
ejpam-4691	228	5	one	one	NUM
ejpam-4691	228	6	of	of	ADP
ejpam-4691	228	7	the	the	DET
ejpam-4691	228	8	families	family	NOUN
ejpam-4691	228	9	τ⋆	τ⋆	SYM
ejpam-4691	228	10	,	,	PUNCT
ejpam-4691	228	11	αio(x	αio(x	PROPN
ejpam-4691	228	12	)	)	PUNCT
ejpam-4691	228	13	,	,	PUNCT
ejpam-4691	228	14	sio(x	sio(x	NOUN
ejpam-4691	228	15	)	)	PUNCT
ejpam-4691	228	16	,	,	PUNCT
ejpam-4691	228	17	pio(x	pio(x	PROPN
ejpam-4691	228	18	)	)	PUNCT
ejpam-4691	228	19	,	,	PUNCT
ejpam-4691	228	20	bio(x	bio(x	PROPN
ejpam-4691	228	21	)	)	PUNCT
ejpam-4691	228	22	,	,	PUNCT
ejpam-4691	228	23	βio(x	βio(x	NUM
ejpam-4691	228	24	)	)	PUNCT
ejpam-4691	228	25	,	,	PUNCT
ejpam-4691	228	26	wsio(x	wsio(x	NOUN
ejpam-4691	228	27	)	)	PUNCT
ejpam-4691	228	28	,	,	PUNCT
ejpam-4691	228	29	wbio(x	wbio(x	PROPN
ejpam-4691	228	30	)	)	PUNCT
ejpam-4691	228	31	,	,	PUNCT
ejpam-4691	228	32	sβio(x	sβio(x	NOUN
ejpam-4691	228	33	)	)	PUNCT
ejpam-4691	228	34	.	.	PUNCT
ejpam-4691	229	1	lemma	lemma	PROPN
ejpam-4691	229	2	4	4	X
ejpam-4691	229	3	.	.	PUNCT
ejpam-4691	230	1	let	let	VERB
ejpam-4691	230	2	(	(	PUNCT
ejpam-4691	230	3	x	x	X
ejpam-4691	230	4	,	,	PUNCT
ejpam-4691	230	5	τ	τ	PROPN
ejpam-4691	230	6	,	,	PUNCT
ejpam-4691	230	7	i	i	PRON
ejpam-4691	230	8	)	)	PUNCT
ejpam-4691	230	9	be	be	VERB
ejpam-4691	230	10	an	an	DET
ejpam-4691	230	11	ideal	ideal	ADJ
ejpam-4691	230	12	topological	topological	ADJ
ejpam-4691	230	13	space	space	NOUN
ejpam-4691	230	14	.	.	PUNCT
ejpam-4691	231	1	then	then	ADV
ejpam-4691	231	2	,	,	PUNCT
ejpam-4691	231	3	mio(x	mio(x	PROPN
ejpam-4691	231	4	)	)	PUNCT
ejpam-4691	231	5	is	be	AUX
ejpam-4691	231	6	an	an	DET
ejpam-4691	231	7	m	m	NOUN
ejpam-4691	231	8	-	-	NOUN
ejpam-4691	231	9	structure	structure	NOUN
ejpam-4691	231	10	on	on	ADP
ejpam-4691	231	11	x	x	PUNCT
ejpam-4691	231	12	and	and	CCONJ
ejpam-4691	231	13	has	have	VERB
ejpam-4691	231	14	property	property	NOUN
ejpam-4691	231	15	b.	b.	NOUN
ejpam-4691	231	16	proof	proof	NOUN
ejpam-4691	231	17	.	.	PUNCT
ejpam-4691	232	1	we	we	PRON
ejpam-4691	232	2	shall	shall	AUX
ejpam-4691	232	3	show	show	VERB
ejpam-4691	232	4	that	that	SCONJ
ejpam-4691	232	5	sio(x	sio(x	NOUN
ejpam-4691	232	6	)	)	PUNCT
ejpam-4691	232	7	is	be	AUX
ejpam-4691	232	8	an	an	DET
ejpam-4691	232	9	m	m	NOUN
ejpam-4691	232	10	-	-	NOUN
ejpam-4691	232	11	structure	structure	NOUN
ejpam-4691	232	12	with	with	ADP
ejpam-4691	232	13	property	property	NOUN
ejpam-4691	232	14	b.	b.	PROPN
ejpam-4691	232	15	(	(	PUNCT
ejpam-4691	232	16	1	1	X
ejpam-4691	232	17	)	)	PUNCT
ejpam-4691	232	18	it	it	PRON
ejpam-4691	232	19	is	be	AUX
ejpam-4691	232	20	obvious	obvious	ADJ
ejpam-4691	232	21	that	that	SCONJ
ejpam-4691	232	22	by	by	ADP
ejpam-4691	232	23	lemma	lemma	PROPN
ejpam-4691	232	24	3	3	NUM
ejpam-4691	232	25	cl⋆(int(∅	cl⋆(int(∅	NOUN
ejpam-4691	232	26	)	)	PUNCT
ejpam-4691	232	27	)	)	PUNCT
ejpam-4691	233	1	=	=	SYM
ejpam-4691	233	2	cl⋆(∅	cl⋆(∅	X
ejpam-4691	233	3	)	)	PUNCT
ejpam-4691	233	4	=	=	SYM
ejpam-4691	233	5	∅	∅	NOUN
ejpam-4691	233	6	and	and	CCONJ
ejpam-4691	233	7	cl⋆(int(x	cl⋆(int(x	PROPN
ejpam-4691	233	8	)	)	PUNCT
ejpam-4691	233	9	)	)	PUNCT
ejpam-4691	234	1	=	=	SYM
ejpam-4691	234	2	cl⋆(x	cl⋆(x	NOUN
ejpam-4691	234	3	)	)	PUNCT
ejpam-4691	234	4	=	=	SYM
ejpam-4691	235	1	x.	x.	NOUN
ejpam-4691	235	2	hence	hence	ADV
ejpam-4691	235	3	,	,	PUNCT
ejpam-4691	235	4	sio(x	sio(x	PROPN
ejpam-4691	235	5	)	)	PUNCT
ejpam-4691	235	6	is	be	AUX
ejpam-4691	235	7	an	an	DET
ejpam-4691	235	8	m	m	NOUN
ejpam-4691	235	9	-	-	NOUN
ejpam-4691	235	10	structure	structure	NOUN
ejpam-4691	235	11	.	.	PUNCT
ejpam-4691	236	1	(	(	PUNCT
ejpam-4691	236	2	2	2	X
ejpam-4691	236	3	)	)	PUNCT
ejpam-4691	236	4	let	let	VERB
ejpam-4691	236	5	{	{	PUNCT
ejpam-4691	236	6	aα	aα	NOUN
ejpam-4691	236	7	:	:	PUNCT
ejpam-4691	236	8	α	α	PROPN
ejpam-4691	236	9	∈	∈	PROPN
ejpam-4691	236	10	∆	∆	PROPN
ejpam-4691	236	11	}	}	PUNCT
ejpam-4691	236	12	be	be	AUX
ejpam-4691	236	13	any	any	DET
ejpam-4691	236	14	family	family	NOUN
ejpam-4691	236	15	of	of	ADP
ejpam-4691	236	16	semi	semi	ADJ
ejpam-4691	236	17	-	-	ADJ
ejpam-4691	236	18	i	i	ADV
ejpam-4691	236	19	-	-	PUNCT
ejpam-4691	236	20	open	open	ADJ
ejpam-4691	236	21	sets	set	NOUN
ejpam-4691	236	22	.	.	PUNCT
ejpam-4691	237	1	then	then	ADV
ejpam-4691	237	2	,	,	PUNCT
ejpam-4691	237	3	for	for	ADP
ejpam-4691	237	4	each	each	DET
ejpam-4691	237	5	α	α	NOUN
ejpam-4691	237	6	∈	∈	NOUN
ejpam-4691	237	7	∆	∆	PROPN
ejpam-4691	237	8	,	,	PUNCT
ejpam-4691	237	9	by	by	ADP
ejpam-4691	237	10	lemma	lemma	PROPN
ejpam-4691	237	11	3	3	NUM
ejpam-4691	237	12	we	we	PRON
ejpam-4691	237	13	have	have	VERB
ejpam-4691	237	14	aα	aα	PROPN
ejpam-4691	237	15	⊂	⊂	ADJ
ejpam-4691	237	16	cl⋆(int(aα	cl⋆(int(aα	PROPN
ejpam-4691	237	17	)	)	PUNCT
ejpam-4691	237	18	)	)	PUNCT
ejpam-4691	238	1	⊂	⊂	PROPN
ejpam-4691	238	2	cl⋆(int(∪{aα	cl⋆(int(∪{aα	NOUN
ejpam-4691	238	3	:	:	PUNCT
ejpam-4691	238	4	α	α	X
ejpam-4691	238	5	∈	∈	NOUN
ejpam-4691	238	6	∆	∆	X
ejpam-4691	238	7	}	}	PUNCT
ejpam-4691	238	8	)	)	PUNCT
ejpam-4691	238	9	)	)	PUNCT
ejpam-4691	238	10	.	.	PUNCT
ejpam-4691	239	1	therefore	therefore	ADV
ejpam-4691	239	2	,	,	PUNCT
ejpam-4691	239	3	∪{aα	∪{aα	PROPN
ejpam-4691	239	4	:	:	PUNCT
ejpam-4691	239	5	α	α	PROPN
ejpam-4691	239	6	∈	∈	NOUN
ejpam-4691	239	7	∆	∆	X
ejpam-4691	239	8	}	}	PUNCT
ejpam-4691	239	9	⊂	⊂	PROPN
ejpam-4691	239	10	cl⋆(int(∪{aα	cl⋆(int(∪{aα	NOUN
ejpam-4691	239	11	:	:	PUNCT
ejpam-4691	239	12	α	α	X
ejpam-4691	239	13	∈	∈	NOUN
ejpam-4691	239	14	∆	∆	X
ejpam-4691	239	15	}	}	PUNCT
ejpam-4691	239	16	)	)	PUNCT
ejpam-4691	239	17	)	)	PUNCT
ejpam-4691	239	18	and	and	CCONJ
ejpam-4691	239	19	hence	hence	ADV
ejpam-4691	239	20	∪{aα	∪{aα	NUM
ejpam-4691	239	21	:	:	PUNCT
ejpam-4691	239	22	α	α	NUM
ejpam-4691	239	23	∈	∈	NOUN
ejpam-4691	239	24	∆	∆	X
ejpam-4691	239	25	}	}	PUNCT
ejpam-4691	239	26	∈	∈	PROPN
ejpam-4691	239	27	sio(x	sio(x	NOUN
ejpam-4691	239	28	)	)	PUNCT
ejpam-4691	239	29	.	.	PUNCT
ejpam-4691	240	1	hence	hence	ADV
ejpam-4691	240	2	sio(x	sio(x	VERB
ejpam-4691	240	3	)	)	PUNCT
ejpam-4691	240	4	has	have	VERB
ejpam-4691	240	5	property	property	NOUN
ejpam-4691	240	6	b.	b.	PROPN
ejpam-4691	240	7	for	for	ADP
ejpam-4691	240	8	other	other	ADJ
ejpam-4691	240	9	families	family	NOUN
ejpam-4691	240	10	,	,	PUNCT
ejpam-4691	240	11	the	the	DET
ejpam-4691	240	12	proofs	proof	NOUN
ejpam-4691	240	13	are	be	AUX
ejpam-4691	240	14	similar	similar	ADJ
ejpam-4691	240	15	.	.	PUNCT
ejpam-4691	241	1	definition	definition	NOUN
ejpam-4691	241	2	10	10	NUM
ejpam-4691	241	3	.	.	PUNCT
ejpam-4691	242	1	let	let	VERB
ejpam-4691	242	2	(	(	PUNCT
ejpam-4691	242	3	x	x	X
ejpam-4691	242	4	,	,	PUNCT
ejpam-4691	242	5	τ	τ	PROPN
ejpam-4691	242	6	,	,	PUNCT
ejpam-4691	242	7	i	i	PRON
ejpam-4691	242	8	)	)	PUNCT
ejpam-4691	242	9	be	be	VERB
ejpam-4691	242	10	an	an	DET
ejpam-4691	242	11	ideal	ideal	ADJ
ejpam-4691	242	12	topological	topological	ADJ
ejpam-4691	242	13	space	space	NOUN
ejpam-4691	242	14	.	.	PUNCT
ejpam-4691	243	1	for	for	ADP
ejpam-4691	243	2	a	a	DET
ejpam-4691	243	3	subset	subset	NOUN
ejpam-4691	243	4	a	a	PRON
ejpam-4691	243	5	of	of	ADP
ejpam-4691	243	6	x	x	SYM
ejpam-4691	243	7	,	,	PUNCT
ejpam-4691	243	8	mcli(a	mcli(a	PROPN
ejpam-4691	243	9	)	)	PUNCT
ejpam-4691	243	10	and	and	CCONJ
ejpam-4691	243	11	minti(a	minti(a	PROPN
ejpam-4691	243	12	)	)	PUNCT
ejpam-4691	243	13	are	be	AUX
ejpam-4691	243	14	defined	define	VERB
ejpam-4691	243	15	as	as	SCONJ
ejpam-4691	243	16	follows	follow	VERB
ejpam-4691	243	17	:	:	PUNCT
ejpam-4691	243	18	(	(	PUNCT
ejpam-4691	243	19	1	1	X
ejpam-4691	243	20	)	)	PUNCT
ejpam-4691	243	21	mcli(a	mcli(a	NOUN
ejpam-4691	243	22	)	)	PUNCT
ejpam-4691	244	1	=	=	PUNCT
ejpam-4691	244	2	∩{f	∩{f	NOUN
ejpam-4691	244	3	:	:	PUNCT
ejpam-4691	244	4	a	a	DET
ejpam-4691	244	5	⊂	⊂	PROPN
ejpam-4691	244	6	f	f	X
ejpam-4691	244	7	,	,	PUNCT
ejpam-4691	244	8	x	x	SYM
ejpam-4691	244	9	\	\	PROPN
ejpam-4691	244	10	f	f	PROPN
ejpam-4691	244	11	∈	∈	PROPN
ejpam-4691	244	12	mio(x	mio(x	PROPN
ejpam-4691	244	13	)	)	PUNCT
ejpam-4691	244	14	}	}	PUNCT
ejpam-4691	244	15	,	,	PUNCT
ejpam-4691	244	16	(	(	PUNCT
ejpam-4691	244	17	2	2	X
ejpam-4691	244	18	)	)	PUNCT
ejpam-4691	244	19	minti(a	minti(a	PROPN
ejpam-4691	244	20	)	)	PUNCT
ejpam-4691	244	21	=	=	PUNCT
ejpam-4691	245	1	∪{u	∪{u	VERB
ejpam-4691	245	2	:	:	PUNCT
ejpam-4691	245	3	u	u	X
ejpam-4691	245	4	⊂	⊂	PROPN
ejpam-4691	245	5	a	a	X
ejpam-4691	245	6	,	,	PUNCT
ejpam-4691	245	7	u	u	PROPN
ejpam-4691	245	8	∈	∈	PROPN
ejpam-4691	245	9	mio(x	mio(x	PROPN
ejpam-4691	245	10	)	)	PUNCT
ejpam-4691	245	11	}	}	PUNCT
ejpam-4691	245	12	.	.	PUNCT
ejpam-4691	246	1	let	let	VERB
ejpam-4691	246	2	(	(	PUNCT
ejpam-4691	246	3	x	x	X
ejpam-4691	246	4	,	,	PUNCT
ejpam-4691	246	5	τ	τ	PROPN
ejpam-4691	246	6	,	,	PUNCT
ejpam-4691	246	7	i	i	PRON
ejpam-4691	246	8	)	)	PUNCT
ejpam-4691	246	9	be	be	VERB
ejpam-4691	246	10	an	an	DET
ejpam-4691	246	11	ideal	ideal	ADJ
ejpam-4691	246	12	topological	topological	ADJ
ejpam-4691	246	13	space	space	NOUN
ejpam-4691	246	14	and	and	CCONJ
ejpam-4691	246	15	mio(x	mio(x	NOUN
ejpam-4691	246	16	)	)	PUNCT
ejpam-4691	246	17	the	the	DET
ejpam-4691	246	18	m	m	NOUN
ejpam-4691	246	19	-	-	NOUN
ejpam-4691	246	20	structure	structure	NOUN
ejpam-4691	246	21	on	on	ADP
ejpam-4691	246	22	x.	x.	NOUN
ejpam-4691	246	23	if	if	SCONJ
ejpam-4691	246	24	mio(x	mio(x	PROPN
ejpam-4691	246	25	)	)	PUNCT
ejpam-4691	246	26	=	=	PUNCT
ejpam-4691	246	27	τ⋆	τ⋆	PRON
ejpam-4691	246	28	(	(	PUNCT
ejpam-4691	246	29	resp	resp	NOUN
ejpam-4691	246	30	.	.	PUNCT
ejpam-4691	247	1	αio(x	αio(x	NUM
ejpam-4691	247	2	)	)	PUNCT
ejpam-4691	247	3	,	,	PUNCT
ejpam-4691	248	1	sio(x	sio(x	NOUN
ejpam-4691	248	2	)	)	PUNCT
ejpam-4691	248	3	,	,	PUNCT
ejpam-4691	248	4	pio(x	pio(x	PROPN
ejpam-4691	248	5	)	)	PUNCT
ejpam-4691	248	6	,	,	PUNCT
ejpam-4691	248	7	bio(x	bio(x	PROPN
ejpam-4691	248	8	)	)	PUNCT
ejpam-4691	248	9	,	,	PUNCT
ejpam-4691	248	10	βio(x	βio(x	NUM
ejpam-4691	248	11	)	)	PUNCT
ejpam-4691	248	12	,	,	PUNCT
ejpam-4691	248	13	wsio(x	wsio(x	NOUN
ejpam-4691	248	14	)	)	PUNCT
ejpam-4691	248	15	,	,	PUNCT
ejpam-4691	248	16	wbio(x	wbio(x	PROPN
ejpam-4691	248	17	)	)	PUNCT
ejpam-4691	248	18	,	,	PUNCT
ejpam-4691	248	19	sβio(x	sβio(x	NOUN
ejpam-4691	248	20	)	)	PUNCT
ejpam-4691	248	21	)	)	PUNCT
ejpam-4691	248	22	,	,	PUNCT
ejpam-4691	248	23	then	then	ADV
ejpam-4691	248	24	we	we	PRON
ejpam-4691	248	25	have	have	VERB
ejpam-4691	248	26	the	the	DET
ejpam-4691	248	27	following	following	NOUN
ejpam-4691	248	28	:	:	PUNCT
ejpam-4691	248	29	(	(	PUNCT
ejpam-4691	248	30	1	1	X
ejpam-4691	248	31	)	)	PUNCT
ejpam-4691	248	32	mcli(a	mcli(a	NOUN
ejpam-4691	248	33	)	)	PUNCT
ejpam-4691	248	34	=	=	SYM
ejpam-4691	248	35	cl⋆(a	cl⋆(a	PROPN
ejpam-4691	248	36	)	)	PUNCT
ejpam-4691	248	37	(	(	PUNCT
ejpam-4691	248	38	resp	resp	NOUN
ejpam-4691	248	39	.	.	PUNCT
ejpam-4691	249	1	αcli(a	αcli(a	NUM
ejpam-4691	249	2	)	)	PUNCT
ejpam-4691	249	3	,	,	PUNCT
ejpam-4691	249	4	scli(a	scli(a	ADP
ejpam-4691	249	5	)	)	PUNCT
ejpam-4691	249	6	,	,	PUNCT
ejpam-4691	249	7	pcli(a	pcli(a	NOUN
ejpam-4691	249	8	)	)	PUNCT
ejpam-4691	249	9	,	,	PUNCT
ejpam-4691	249	10	bcli(a	bcli(a	NOUN
ejpam-4691	249	11	)	)	PUNCT
ejpam-4691	249	12	,	,	PUNCT
ejpam-4691	249	13	βcli(a	βcli(a	PROPN
ejpam-4691	249	14	)	)	PUNCT
ejpam-4691	249	15	,	,	PUNCT
ejpam-4691	249	16	wscli(a	wscli(a	PROPN
ejpam-4691	249	17	)	)	PUNCT
ejpam-4691	249	18	,	,	PUNCT
ejpam-4691	249	19	wbcli(a	wbcli(a	PROPN
ejpam-4691	249	20	)	)	PUNCT
ejpam-4691	249	21	,	,	PUNCT
ejpam-4691	249	22	sβcli(a	sβcli(a	NOUN
ejpam-4691	249	23	)	)	PUNCT
ejpam-4691	249	24	)	)	PUNCT
ejpam-4691	249	25	.	.	PUNCT
ejpam-4691	250	1	(	(	PUNCT
ejpam-4691	250	2	2	2	X
ejpam-4691	250	3	)	)	PUNCT
ejpam-4691	250	4	minti(a	minti(a	PROPN
ejpam-4691	250	5	)	)	PUNCT
ejpam-4691	250	6	=	=	SYM
ejpam-4691	250	7	int⋆(a	int⋆(a	NOUN
ejpam-4691	250	8	)	)	PUNCT
ejpam-4691	250	9	(	(	PUNCT
ejpam-4691	250	10	resp	resp	NOUN
ejpam-4691	250	11	.	.	PUNCT
ejpam-4691	251	1	αinti(a	αinti(a	X
ejpam-4691	251	2	)	)	PUNCT
ejpam-4691	251	3	,	,	PUNCT
ejpam-4691	251	4	sinti(a	sinti(a	PROPN
ejpam-4691	251	5	)	)	PUNCT
ejpam-4691	251	6	,	,	PUNCT
ejpam-4691	251	7	pinti(a	pinti(a	NOUN
ejpam-4691	251	8	)	)	PUNCT
ejpam-4691	251	9	,	,	PUNCT
ejpam-4691	251	10	binti(a	binti(a	ADP
ejpam-4691	251	11	)	)	PUNCT
ejpam-4691	251	12	,	,	PUNCT
ejpam-4691	251	13	βinti(a	βinti(a	NOUN
ejpam-4691	251	14	)	)	PUNCT
ejpam-4691	251	15	,	,	PUNCT
ejpam-4691	251	16	wsinti(a	wsinti(a	PROPN
ejpam-4691	251	17	)	)	PUNCT
ejpam-4691	251	18	,	,	PUNCT
ejpam-4691	251	19	wbinti(a	wbinti(a	PROPN
ejpam-4691	251	20	)	)	PUNCT
ejpam-4691	251	21	,	,	PUNCT
ejpam-4691	251	22	sβinti(a	sβinti(a	NOUN
ejpam-4691	251	23	)	)	PUNCT
ejpam-4691	251	24	)	)	PUNCT
ejpam-4691	251	25	.	.	PUNCT
ejpam-4691	252	1	t.	t.	PROPN
ejpam-4691	252	2	noiri	noiri	PROPN
ejpam-4691	252	3	,	,	PUNCT
ejpam-4691	252	4	v.	v.	CCONJ
ejpam-4691	252	5	popa	popa	NOUN
ejpam-4691	252	6	/	/	SYM
ejpam-4691	252	7	eur	eur	PROPN
ejpam-4691	252	8	.	.	PUNCT
ejpam-4691	253	1	j.	j.	PROPN
ejpam-4691	253	2	pure	pure	PROPN
ejpam-4691	253	3	appl	appl	PROPN
ejpam-4691	253	4	.	.	PROPN
ejpam-4691	253	5	math	math	PROPN
ejpam-4691	253	6	,	,	PUNCT
ejpam-4691	253	7	16	16	NUM
ejpam-4691	253	8	(	(	PUNCT
ejpam-4691	253	9	1	1	NUM
ejpam-4691	253	10	)	)	PUNCT
ejpam-4691	253	11	(	(	PUNCT
ejpam-4691	253	12	2023	2023	NUM
ejpam-4691	253	13	)	)	PUNCT
ejpam-4691	253	14	,	,	PUNCT
ejpam-4691	253	15	430	430	NUM
ejpam-4691	253	16	-	-	SYM
ejpam-4691	253	17	439	439	NUM
ejpam-4691	253	18	436	436	NUM
ejpam-4691	253	19	5	5	NUM
ejpam-4691	253	20	.	.	PUNCT
ejpam-4691	253	21	mi	mi	ADJ
ejpam-4691	253	22	-	-	ADJ
ejpam-4691	253	23	open	open	ADJ
ejpam-4691	253	24	multifunctions	multifunction	NOUN
ejpam-4691	253	25	definition	definition	NOUN
ejpam-4691	253	26	11	11	NUM
ejpam-4691	253	27	.	.	PUNCT
ejpam-4691	254	1	let	let	AUX
ejpam-4691	254	2	(	(	PUNCT
ejpam-4691	254	3	x	x	NOUN
ejpam-4691	254	4	,	,	PUNCT
ejpam-4691	254	5	mx	mx	NOUN
ejpam-4691	254	6	)	)	PUNCT
ejpam-4691	254	7	be	be	AUX
ejpam-4691	254	8	an	an	DET
ejpam-4691	254	9	m	m	NOUN
ejpam-4691	254	10	-	-	NOUN
ejpam-4691	254	11	space	space	NOUN
ejpam-4691	254	12	and	and	CCONJ
ejpam-4691	254	13	(	(	PUNCT
ejpam-4691	254	14	y	y	PROPN
ejpam-4691	254	15	,	,	PUNCT
ejpam-4691	254	16	τ	τ	PROPN
ejpam-4691	254	17	,	,	PUNCT
ejpam-4691	254	18	i	i	PRON
ejpam-4691	254	19	)	)	PUNCT
ejpam-4691	254	20	be	be	VERB
ejpam-4691	254	21	an	an	DET
ejpam-4691	254	22	ideal	ideal	ADJ
ejpam-4691	254	23	topological	topological	ADJ
ejpam-4691	254	24	space	space	NOUN
ejpam-4691	254	25	.	.	PUNCT
ejpam-4691	255	1	a	a	DET
ejpam-4691	255	2	multifunction	multifunction	NOUN
ejpam-4691	255	3	f	f	NOUN
ejpam-4691	255	4	:	:	PUNCT
ejpam-4691	255	5	(	(	PUNCT
ejpam-4691	255	6	x	x	NOUN
ejpam-4691	255	7	,	,	PUNCT
ejpam-4691	255	8	mx	mx	NOUN
ejpam-4691	255	9	)	)	PUNCT
ejpam-4691	255	10	→	→	SYM
ejpam-4691	255	11	(	(	PUNCT
ejpam-4691	255	12	y	y	PROPN
ejpam-4691	255	13	,	,	PUNCT
ejpam-4691	255	14	τ	τ	PROPN
ejpam-4691	255	15	,	,	PUNCT
ejpam-4691	255	16	i	i	PROPN
ejpam-4691	255	17	)	)	PUNCT
ejpam-4691	255	18	is	be	AUX
ejpam-4691	255	19	said	say	VERB
ejpam-4691	255	20	to	to	PART
ejpam-4691	255	21	be	be	AUX
ejpam-4691	255	22	mi	mi	NOUN
ejpam-4691	255	23	-	-	ADJ
ejpam-4691	255	24	open	open	ADJ
ejpam-4691	255	25	at	at	ADP
ejpam-4691	255	26	x	x	X
ejpam-4691	255	27	∈	∈	PROPN
ejpam-4691	255	28	x	x	SYM
ejpam-4691	255	29	if	if	SCONJ
ejpam-4691	255	30	for	for	ADP
ejpam-4691	255	31	each	each	DET
ejpam-4691	255	32	mx	mx	PROPN
ejpam-4691	255	33	-open	-open	PROPN
ejpam-4691	255	34	set	set	VERB
ejpam-4691	255	35	u	u	NOUN
ejpam-4691	255	36	containing	contain	VERB
ejpam-4691	255	37	x	x	PRON
ejpam-4691	255	38	,	,	PUNCT
ejpam-4691	255	39	there	there	PRON
ejpam-4691	255	40	exists	exist	VERB
ejpam-4691	255	41	v	v	ADP
ejpam-4691	255	42	∈	∈	PROPN
ejpam-4691	255	43	mio(y	mio(y	NOUN
ejpam-4691	255	44	)	)	PUNCT
ejpam-4691	255	45	containing	contain	VERB
ejpam-4691	255	46	f	f	PROPN
ejpam-4691	255	47	(	(	PUNCT
ejpam-4691	255	48	x	x	X
ejpam-4691	255	49	)	)	PUNCT
ejpam-4691	255	50	such	such	ADJ
ejpam-4691	255	51	that	that	DET
ejpam-4691	255	52	v	v	X
ejpam-4691	255	53	⊂	⊂	PROPN
ejpam-4691	255	54	f	f	X
ejpam-4691	255	55	(	(	PUNCT
ejpam-4691	255	56	u	u	NOUN
ejpam-4691	255	57	)	)	PUNCT
ejpam-4691	255	58	.	.	PUNCT
ejpam-4691	256	1	if	if	SCONJ
ejpam-4691	256	2	f	f	PROPN
ejpam-4691	256	3	is	be	AUX
ejpam-4691	256	4	mi	mi	NOUN
ejpam-4691	256	5	-	-	ADJ
ejpam-4691	256	6	open	open	ADJ
ejpam-4691	256	7	at	at	ADP
ejpam-4691	256	8	each	each	DET
ejpam-4691	256	9	point	point	NOUN
ejpam-4691	256	10	x	x	X
ejpam-4691	256	11	∈	∈	NOUN
ejpam-4691	256	12	x	x	NOUN
ejpam-4691	256	13	,	,	PUNCT
ejpam-4691	256	14	then	then	ADV
ejpam-4691	256	15	f	f	PROPN
ejpam-4691	256	16	is	be	AUX
ejpam-4691	256	17	said	say	VERB
ejpam-4691	256	18	to	to	PART
ejpam-4691	256	19	be	be	AUX
ejpam-4691	256	20	mi	mi	NOUN
ejpam-4691	256	21	-	-	ADJ
ejpam-4691	256	22	open	open	ADJ
ejpam-4691	256	23	.	.	PUNCT
ejpam-4691	257	1	then	then	ADV
ejpam-4691	257	2	f	f	X
ejpam-4691	257	3	:	:	PUNCT
ejpam-4691	257	4	(	(	PUNCT
ejpam-4691	257	5	x	x	NOUN
ejpam-4691	257	6	,	,	PUNCT
ejpam-4691	257	7	mx	mx	NOUN
ejpam-4691	257	8	)	)	PUNCT
ejpam-4691	257	9	→	→	SYM
ejpam-4691	257	10	(	(	PUNCT
ejpam-4691	257	11	y	y	PROPN
ejpam-4691	257	12	,	,	PUNCT
ejpam-4691	257	13	τ	τ	PROPN
ejpam-4691	257	14	,	,	PUNCT
ejpam-4691	257	15	i	i	PROPN
ejpam-4691	257	16	)	)	PUNCT
ejpam-4691	257	17	is	be	AUX
ejpam-4691	257	18	mi	mi	NOUN
ejpam-4691	257	19	-	-	ADJ
ejpam-4691	257	20	open	open	ADJ
ejpam-4691	257	21	at	at	ADP
ejpam-4691	257	22	x	x	X
ejpam-4691	257	23	∈	∈	PROPN
ejpam-4691	257	24	x	x	INTJ
ejpam-4691	257	25	(	(	PUNCT
ejpam-4691	257	26	resp	resp	NOUN
ejpam-4691	257	27	.	.	PUNCT
ejpam-4691	258	1	on	on	ADP
ejpam-4691	258	2	x	x	SYM
ejpam-4691	258	3	)	)	PUNCT
ejpam-4691	258	4	if	if	SCONJ
ejpam-4691	258	5	and	and	CCONJ
ejpam-4691	258	6	only	only	ADV
ejpam-4691	258	7	if	if	SCONJ
ejpam-4691	258	8	f	f	X
ejpam-4691	258	9	:	:	PUNCT
ejpam-4691	258	10	(	(	PUNCT
ejpam-4691	258	11	x	x	NOUN
ejpam-4691	258	12	,	,	PUNCT
ejpam-4691	258	13	mx	mx	NOUN
ejpam-4691	258	14	)	)	PUNCT
ejpam-4691	258	15	→	→	SYM
ejpam-4691	258	16	(	(	PUNCT
ejpam-4691	258	17	y	y	NOUN
ejpam-4691	258	18	,	,	PUNCT
ejpam-4691	258	19	mio(x	mio(x	NOUN
ejpam-4691	258	20	)	)	PUNCT
ejpam-4691	258	21	)	)	PUNCT
ejpam-4691	258	22	is	be	AUX
ejpam-4691	258	23	m	m	NOUN
ejpam-4691	258	24	-	-	ADJ
ejpam-4691	258	25	open	open	ADJ
ejpam-4691	258	26	at	at	ADP
ejpam-4691	258	27	x	x	X
ejpam-4691	258	28	∈	∈	PROPN
ejpam-4691	258	29	x	x	INTJ
ejpam-4691	258	30	(	(	PUNCT
ejpam-4691	258	31	resp	resp	NOUN
ejpam-4691	258	32	.	.	PUNCT
ejpam-4691	259	1	on	on	ADP
ejpam-4691	259	2	x	x	NOUN
ejpam-4691	259	3	)	)	PUNCT
ejpam-4691	259	4	.	.	PUNCT
ejpam-4691	260	1	therefore	therefore	ADV
ejpam-4691	260	2	,	,	PUNCT
ejpam-4691	260	3	by	by	ADP
ejpam-4691	260	4	the	the	DET
ejpam-4691	260	5	results	result	NOUN
ejpam-4691	260	6	of	of	ADP
ejpam-4691	260	7	section	section	NOUN
ejpam-4691	260	8	3	3	NUM
ejpam-4691	260	9	,	,	PUNCT
ejpam-4691	260	10	we	we	PRON
ejpam-4691	260	11	obtain	obtain	VERB
ejpam-4691	260	12	the	the	DET
ejpam-4691	260	13	following	follow	VERB
ejpam-4691	260	14	properties	property	NOUN
ejpam-4691	260	15	of	of	ADP
ejpam-4691	260	16	mi	mi	ADJ
ejpam-4691	260	17	-	-	ADJ
ejpam-4691	260	18	open	open	ADJ
ejpam-4691	260	19	multifunctions	multifunction	NOUN
ejpam-4691	260	20	.	.	PUNCT
ejpam-4691	261	1	theorem	theorem	VERB
ejpam-4691	261	2	6	6	NUM
ejpam-4691	261	3	.	.	PUNCT
ejpam-4691	262	1	a	a	DET
ejpam-4691	262	2	multifunction	multifunction	NOUN
ejpam-4691	262	3	f	f	NOUN
ejpam-4691	262	4	:	:	PUNCT
ejpam-4691	262	5	(	(	PUNCT
ejpam-4691	262	6	x	x	NOUN
ejpam-4691	262	7	,	,	PUNCT
ejpam-4691	262	8	mx	mx	NOUN
ejpam-4691	262	9	)	)	PUNCT
ejpam-4691	262	10	→	→	SYM
ejpam-4691	262	11	(	(	PUNCT
ejpam-4691	262	12	y	y	PROPN
ejpam-4691	262	13	,	,	PUNCT
ejpam-4691	262	14	τ	τ	PROPN
ejpam-4691	262	15	,	,	PUNCT
ejpam-4691	262	16	i	i	PROPN
ejpam-4691	262	17	)	)	PUNCT
ejpam-4691	262	18	is	be	AUX
ejpam-4691	262	19	mi	mi	NOUN
ejpam-4691	262	20	-	-	ADJ
ejpam-4691	262	21	open	open	ADJ
ejpam-4691	262	22	at	at	ADP
ejpam-4691	262	23	x	x	X
ejpam-4691	262	24	∈	∈	PROPN
ejpam-4691	262	25	x	x	SYM
ejpam-4691	263	1	if	if	SCONJ
ejpam-4691	263	2	and	and	CCONJ
ejpam-4691	263	3	only	only	ADV
ejpam-4691	263	4	if	if	SCONJ
ejpam-4691	263	5	for	for	ADP
ejpam-4691	263	6	each	each	DET
ejpam-4691	263	7	mx	mx	NOUN
ejpam-4691	263	8	-	-	ADJ
ejpam-4691	263	9	open	open	ADJ
ejpam-4691	263	10	set	set	NOUN
ejpam-4691	263	11	u	u	NOUN
ejpam-4691	263	12	containing	contain	VERB
ejpam-4691	263	13	x	x	PRON
ejpam-4691	263	14	,	,	PUNCT
ejpam-4691	263	15	x	x	SYM
ejpam-4691	263	16	∈	∈	NOUN
ejpam-4691	263	17	f+(minti(f	f+(minti(f	NOUN
ejpam-4691	263	18	(	(	PUNCT
ejpam-4691	263	19	u	u	NOUN
ejpam-4691	263	20	)	)	PUNCT
ejpam-4691	263	21	)	)	PUNCT
ejpam-4691	263	22	)	)	PUNCT
ejpam-4691	263	23	.	.	PUNCT
ejpam-4691	264	1	proof	proof	NOUN
ejpam-4691	264	2	.	.	PUNCT
ejpam-4691	265	1	the	the	DET
ejpam-4691	265	2	proof	proof	NOUN
ejpam-4691	265	3	follows	follow	VERB
ejpam-4691	265	4	from	from	ADP
ejpam-4691	265	5	theorem	theorem	ADJ
ejpam-4691	265	6	1	1	NUM
ejpam-4691	265	7	and	and	CCONJ
ejpam-4691	265	8	lemma	lemma	PROPN
ejpam-4691	265	9	4	4	NUM
ejpam-4691	265	10	.	.	PUNCT
ejpam-4691	265	11	theorem	theorem	VERB
ejpam-4691	265	12	7	7	NUM
ejpam-4691	265	13	.	.	PUNCT
ejpam-4691	265	14	a	a	DET
ejpam-4691	265	15	multifunction	multifunction	NOUN
ejpam-4691	265	16	f	f	NOUN
ejpam-4691	265	17	:	:	PUNCT
ejpam-4691	265	18	(	(	PUNCT
ejpam-4691	265	19	x	x	NOUN
ejpam-4691	265	20	,	,	PUNCT
ejpam-4691	265	21	mx	mx	NOUN
ejpam-4691	265	22	)	)	PUNCT
ejpam-4691	265	23	→	→	SYM
ejpam-4691	265	24	(	(	PUNCT
ejpam-4691	265	25	y	y	PROPN
ejpam-4691	265	26	,	,	PUNCT
ejpam-4691	265	27	τ	τ	PROPN
ejpam-4691	265	28	,	,	PUNCT
ejpam-4691	265	29	i	i	PROPN
ejpam-4691	265	30	)	)	PUNCT
ejpam-4691	265	31	is	be	AUX
ejpam-4691	265	32	mi	mi	NOUN
ejpam-4691	265	33	-	-	ADJ
ejpam-4691	265	34	open	open	ADJ
ejpam-4691	265	35	if	if	SCONJ
ejpam-4691	265	36	and	and	CCONJ
ejpam-4691	265	37	only	only	ADV
ejpam-4691	265	38	if	if	SCONJ
ejpam-4691	265	39	f	f	PROPN
ejpam-4691	265	40	(	(	PUNCT
ejpam-4691	265	41	u	u	NOUN
ejpam-4691	265	42	)	)	PUNCT
ejpam-4691	265	43	is	be	AUX
ejpam-4691	265	44	mi	mi	NOUN
ejpam-4691	265	45	-	-	ADJ
ejpam-4691	265	46	open	open	ADJ
ejpam-4691	265	47	for	for	ADP
ejpam-4691	265	48	each	each	DET
ejpam-4691	265	49	mx	mx	NOUN
ejpam-4691	265	50	-	-	ADJ
ejpam-4691	265	51	open	open	ADJ
ejpam-4691	265	52	set	set	NOUN
ejpam-4691	265	53	u	u	NOUN
ejpam-4691	265	54	of	of	ADP
ejpam-4691	265	55	x.	x.	NOUN
ejpam-4691	265	56	proof	proof	NOUN
ejpam-4691	265	57	.	.	PUNCT
ejpam-4691	266	1	the	the	DET
ejpam-4691	266	2	proof	proof	NOUN
ejpam-4691	266	3	follows	follow	VERB
ejpam-4691	266	4	from	from	ADP
ejpam-4691	266	5	theorem	theorem	ADJ
ejpam-4691	266	6	2	2	NUM
ejpam-4691	266	7	and	and	CCONJ
ejpam-4691	266	8	lemma	lemma	PROPN
ejpam-4691	266	9	4	4	NUM
ejpam-4691	266	10	.	.	PUNCT
ejpam-4691	266	11	theorem	theorem	VERB
ejpam-4691	266	12	8	8	NUM
ejpam-4691	266	13	.	.	PUNCT
ejpam-4691	266	14	for	for	ADP
ejpam-4691	266	15	a	a	DET
ejpam-4691	266	16	multifunction	multifunction	NOUN
ejpam-4691	266	17	f	f	NOUN
ejpam-4691	266	18	:	:	PUNCT
ejpam-4691	266	19	(	(	PUNCT
ejpam-4691	266	20	x	x	NOUN
ejpam-4691	266	21	,	,	PUNCT
ejpam-4691	266	22	mx	mx	NOUN
ejpam-4691	266	23	)	)	PUNCT
ejpam-4691	266	24	→	→	SYM
ejpam-4691	266	25	(	(	PUNCT
ejpam-4691	266	26	y	y	PROPN
ejpam-4691	266	27	,	,	PUNCT
ejpam-4691	266	28	τ	τ	PROPN
ejpam-4691	266	29	,	,	PUNCT
ejpam-4691	266	30	i	i	PROPN
ejpam-4691	266	31	)	)	PUNCT
ejpam-4691	266	32	,	,	PUNCT
ejpam-4691	266	33	the	the	DET
ejpam-4691	266	34	following	follow	VERB
ejpam-4691	266	35	properties	property	NOUN
ejpam-4691	266	36	are	be	AUX
ejpam-4691	266	37	equivalent	equivalent	ADJ
ejpam-4691	266	38	:	:	PUNCT
ejpam-4691	266	39	(	(	PUNCT
ejpam-4691	266	40	1	1	X
ejpam-4691	266	41	)	)	PUNCT
ejpam-4691	266	42	f	f	PROPN
ejpam-4691	266	43	is	be	AUX
ejpam-4691	266	44	mi	mi	NOUN
ejpam-4691	266	45	-	-	ADJ
ejpam-4691	266	46	open	open	ADJ
ejpam-4691	266	47	at	at	ADP
ejpam-4691	266	48	x	x	X
ejpam-4691	266	49	;	;	PUNCT
ejpam-4691	266	50	(	(	PUNCT
ejpam-4691	266	51	2	2	X
ejpam-4691	266	52	)	)	PUNCT
ejpam-4691	266	53	if	if	SCONJ
ejpam-4691	266	54	x	x	SYM
ejpam-4691	266	55	∈	∈	PROPN
ejpam-4691	266	56	mxint(a	mxint(a	NOUN
ejpam-4691	266	57	)	)	PUNCT
ejpam-4691	266	58	for	for	ADP
ejpam-4691	266	59	a	a	DET
ejpam-4691	266	60	∈	∈	PROPN
ejpam-4691	266	61	p(x	p(x	NOUN
ejpam-4691	266	62	)	)	PUNCT
ejpam-4691	266	63	,	,	PUNCT
ejpam-4691	266	64	then	then	ADV
ejpam-4691	266	65	x	x	SYM
ejpam-4691	266	66	∈	∈	NOUN
ejpam-4691	266	67	f+(minti(f	f+(minti(f	NOUN
ejpam-4691	266	68	(	(	PUNCT
ejpam-4691	266	69	a	a	NOUN
ejpam-4691	266	70	)	)	PUNCT
ejpam-4691	266	71	)	)	PUNCT
ejpam-4691	266	72	)	)	PUNCT
ejpam-4691	266	73	;	;	PUNCT
ejpam-4691	266	74	(	(	PUNCT
ejpam-4691	266	75	3	3	X
ejpam-4691	266	76	)	)	PUNCT
ejpam-4691	266	77	x	x	SYM
ejpam-4691	266	78	∈	∈	NOUN
ejpam-4691	266	79	mxint(f+(b	mxint(f+(b	NOUN
ejpam-4691	266	80	)	)	PUNCT
ejpam-4691	266	81	)	)	PUNCT
ejpam-4691	266	82	for	for	ADP
ejpam-4691	266	83	b	b	PROPN
ejpam-4691	266	84	∈	∈	PROPN
ejpam-4691	266	85	p(y	p(y	PROPN
ejpam-4691	266	86	)	)	PUNCT
ejpam-4691	266	87	,	,	PUNCT
ejpam-4691	266	88	then	then	ADV
ejpam-4691	266	89	x	x	X
ejpam-4691	266	90	∈	∈	PROPN
ejpam-4691	266	91	f+(minti(b	f+(minti(b	NUM
ejpam-4691	266	92	)	)	PUNCT
ejpam-4691	266	93	)	)	PUNCT
ejpam-4691	266	94	;	;	PUNCT
ejpam-4691	266	95	(	(	PUNCT
ejpam-4691	266	96	4	4	X
ejpam-4691	266	97	)	)	PUNCT
ejpam-4691	266	98	if	if	SCONJ
ejpam-4691	266	99	x	x	PROPN
ejpam-4691	266	100	∈	∈	PROPN
ejpam-4691	266	101	f−(mcli(b	f−(mcli(b	PROPN
ejpam-4691	266	102	)	)	PUNCT
ejpam-4691	266	103	)	)	PUNCT
ejpam-4691	266	104	for	for	ADP
ejpam-4691	266	105	b	b	PROPN
ejpam-4691	266	106	∈	∈	PROPN
ejpam-4691	266	107	p(y	p(y	PROPN
ejpam-4691	266	108	)	)	PUNCT
ejpam-4691	266	109	,	,	PUNCT
ejpam-4691	266	110	then	then	ADV
ejpam-4691	266	111	x	x	X
ejpam-4691	266	112	∈	∈	PROPN
ejpam-4691	266	113	mxcl(f−(b	mxcl(f−(b	PROPN
ejpam-4691	266	114	)	)	PUNCT
ejpam-4691	266	115	)	)	PUNCT
ejpam-4691	266	116	.	.	PUNCT
ejpam-4691	267	1	proof	proof	NOUN
ejpam-4691	267	2	.	.	PUNCT
ejpam-4691	268	1	the	the	DET
ejpam-4691	268	2	proof	proof	NOUN
ejpam-4691	268	3	follows	follow	VERB
ejpam-4691	268	4	from	from	ADP
ejpam-4691	268	5	theorem	theorem	ADJ
ejpam-4691	268	6	3	3	NUM
ejpam-4691	268	7	and	and	CCONJ
ejpam-4691	268	8	lemma	lemma	PROPN
ejpam-4691	268	9	4	4	NUM
ejpam-4691	268	10	.	.	PUNCT
ejpam-4691	268	11	theorem	theorem	VERB
ejpam-4691	268	12	9	9	NUM
ejpam-4691	268	13	.	.	X
ejpam-4691	268	14	for	for	ADP
ejpam-4691	268	15	a	a	DET
ejpam-4691	268	16	multifunction	multifunction	NOUN
ejpam-4691	268	17	f	f	NOUN
ejpam-4691	268	18	:	:	PUNCT
ejpam-4691	268	19	(	(	PUNCT
ejpam-4691	268	20	x	x	NOUN
ejpam-4691	268	21	,	,	PUNCT
ejpam-4691	268	22	mx	mx	NOUN
ejpam-4691	268	23	)	)	PUNCT
ejpam-4691	268	24	→	→	SYM
ejpam-4691	268	25	(	(	PUNCT
ejpam-4691	268	26	y	y	PROPN
ejpam-4691	268	27	,	,	PUNCT
ejpam-4691	268	28	τ	τ	PROPN
ejpam-4691	268	29	,	,	PUNCT
ejpam-4691	268	30	i	i	PROPN
ejpam-4691	268	31	)	)	PUNCT
ejpam-4691	268	32	,	,	PUNCT
ejpam-4691	268	33	the	the	DET
ejpam-4691	268	34	following	follow	VERB
ejpam-4691	268	35	properties	property	NOUN
ejpam-4691	268	36	are	be	AUX
ejpam-4691	268	37	equivalent	equivalent	ADJ
ejpam-4691	268	38	:	:	PUNCT
ejpam-4691	268	39	(	(	PUNCT
ejpam-4691	268	40	1	1	X
ejpam-4691	268	41	)	)	PUNCT
ejpam-4691	268	42	f	f	PROPN
ejpam-4691	268	43	is	be	AUX
ejpam-4691	268	44	mi	mi	NOUN
ejpam-4691	268	45	-	-	ADJ
ejpam-4691	268	46	open	open	ADJ
ejpam-4691	268	47	;	;	PUNCT
ejpam-4691	268	48	(	(	PUNCT
ejpam-4691	268	49	2	2	X
ejpam-4691	268	50	)	)	PUNCT
ejpam-4691	268	51	f	f	NOUN
ejpam-4691	268	52	(	(	PUNCT
ejpam-4691	268	53	mxint(a	mxint(a	NOUN
ejpam-4691	268	54	)	)	PUNCT
ejpam-4691	268	55	)	)	PUNCT
ejpam-4691	269	1	⊂	⊂	PROPN
ejpam-4691	269	2	minti(f	minti(f	X
ejpam-4691	269	3	(	(	PUNCT
ejpam-4691	269	4	a	a	NOUN
ejpam-4691	269	5	)	)	PUNCT
ejpam-4691	269	6	)	)	PUNCT
ejpam-4691	269	7	for	for	ADP
ejpam-4691	269	8	any	any	DET
ejpam-4691	269	9	subset	subset	NOUN
ejpam-4691	269	10	a	a	PRON
ejpam-4691	269	11	of	of	ADP
ejpam-4691	269	12	x	x	PRON
ejpam-4691	269	13	;	;	PUNCT
ejpam-4691	269	14	(	(	PUNCT
ejpam-4691	269	15	3	3	X
ejpam-4691	269	16	)	)	PUNCT
ejpam-4691	269	17	mxint(f+(b	mxint(f+(b	NOUN
ejpam-4691	269	18	)	)	PUNCT
ejpam-4691	269	19	)	)	PUNCT
ejpam-4691	270	1	⊂	⊂	PROPN
ejpam-4691	270	2	f+(minti(b	f+(minti(b	NUM
ejpam-4691	270	3	)	)	PUNCT
ejpam-4691	270	4	)	)	PUNCT
ejpam-4691	271	1	for	for	ADP
ejpam-4691	271	2	any	any	DET
ejpam-4691	271	3	subset	subset	NOUN
ejpam-4691	271	4	b	b	PROPN
ejpam-4691	271	5	of	of	ADP
ejpam-4691	271	6	y	y	PROPN
ejpam-4691	271	7	;	;	PUNCT
ejpam-4691	271	8	(	(	PUNCT
ejpam-4691	271	9	4	4	X
ejpam-4691	271	10	)	)	PUNCT
ejpam-4691	271	11	f−(mcli(b	f−(mcli(b	PROPN
ejpam-4691	271	12	)	)	PUNCT
ejpam-4691	271	13	)	)	PUNCT
ejpam-4691	272	1	⊂	⊂	PROPN
ejpam-4691	272	2	mxcl(f−(b	mxcl(f−(b	PROPN
ejpam-4691	272	3	)	)	PUNCT
ejpam-4691	272	4	)	)	PUNCT
ejpam-4691	273	1	for	for	ADP
ejpam-4691	273	2	any	any	DET
ejpam-4691	273	3	subset	subset	NOUN
ejpam-4691	273	4	b	b	PROPN
ejpam-4691	273	5	of	of	ADP
ejpam-4691	273	6	y.	y.	PROPN
ejpam-4691	273	7	proof	proof	PROPN
ejpam-4691	273	8	.	.	PUNCT
ejpam-4691	274	1	the	the	DET
ejpam-4691	274	2	proof	proof	NOUN
ejpam-4691	274	3	follows	follow	VERB
ejpam-4691	274	4	from	from	ADP
ejpam-4691	274	5	theorem	theorem	ADJ
ejpam-4691	274	6	4	4	NUM
ejpam-4691	274	7	and	and	CCONJ
ejpam-4691	274	8	lemma	lemma	PROPN
ejpam-4691	274	9	4	4	NUM
ejpam-4691	274	10	.	.	PUNCT
ejpam-4691	274	11	for	for	ADP
ejpam-4691	274	12	a	a	DET
ejpam-4691	274	13	multifunction	multifunction	NOUN
ejpam-4691	274	14	f	f	NOUN
ejpam-4691	274	15	:	:	PUNCT
ejpam-4691	274	16	(	(	PUNCT
ejpam-4691	274	17	x	x	NOUN
ejpam-4691	274	18	,	,	PUNCT
ejpam-4691	274	19	mx	mx	NOUN
ejpam-4691	274	20	)	)	PUNCT
ejpam-4691	274	21	→	→	SYM
ejpam-4691	274	22	(	(	PUNCT
ejpam-4691	274	23	y	y	PROPN
ejpam-4691	274	24	,	,	PUNCT
ejpam-4691	274	25	τ	τ	PROPN
ejpam-4691	274	26	,	,	PUNCT
ejpam-4691	274	27	i	i	PROPN
ejpam-4691	274	28	)	)	PUNCT
ejpam-4691	274	29	,	,	PUNCT
ejpam-4691	274	30	we	we	PRON
ejpam-4691	274	31	denote	denote	VERB
ejpam-4691	274	32	d0	d0	PROPN
ejpam-4691	274	33	i	i	PRON
ejpam-4691	274	34	(	(	PUNCT
ejpam-4691	274	35	f	f	PROPN
ejpam-4691	274	36	)	)	PUNCT
ejpam-4691	274	37	=	=	PRON
ejpam-4691	275	1	{	{	PUNCT
ejpam-4691	275	2	x	x	PUNCT
ejpam-4691	275	3	∈	∈	PROPN
ejpam-4691	275	4	x	x	NOUN
ejpam-4691	275	5	:	:	PUNCT
ejpam-4691	275	6	f	f	X
ejpam-4691	275	7	is	be	AUX
ejpam-4691	275	8	not	not	PART
ejpam-4691	275	9	mi	mi	NOUN
ejpam-4691	275	10	-	-	NOUN
ejpam-4691	275	11	open	open	ADJ
ejpam-4691	275	12	at	at	ADP
ejpam-4691	275	13	x	x	X
ejpam-4691	275	14	}	}	PUNCT
ejpam-4691	275	15	.	.	PUNCT
ejpam-4691	276	1	theorem	theorem	ADJ
ejpam-4691	276	2	10	10	NUM
ejpam-4691	276	3	.	.	PUNCT
ejpam-4691	277	1	for	for	ADP
ejpam-4691	277	2	a	a	DET
ejpam-4691	277	3	multifunction	multifunction	NOUN
ejpam-4691	277	4	f	f	NOUN
ejpam-4691	277	5	:	:	PUNCT
ejpam-4691	277	6	(	(	PUNCT
ejpam-4691	277	7	x	x	NOUN
ejpam-4691	277	8	,	,	PUNCT
ejpam-4691	277	9	mx	mx	NOUN
ejpam-4691	277	10	)	)	PUNCT
ejpam-4691	277	11	→	→	SYM
ejpam-4691	277	12	(	(	PUNCT
ejpam-4691	277	13	y	y	PROPN
ejpam-4691	277	14	,	,	PUNCT
ejpam-4691	277	15	τ	τ	PROPN
ejpam-4691	277	16	,	,	PUNCT
ejpam-4691	277	17	i	i	PROPN
ejpam-4691	277	18	)	)	PUNCT
ejpam-4691	277	19	,	,	PUNCT
ejpam-4691	277	20	the	the	DET
ejpam-4691	277	21	following	follow	VERB
ejpam-4691	277	22	properties	property	NOUN
ejpam-4691	277	23	hold	hold	VERB
ejpam-4691	277	24	:	:	PUNCT
ejpam-4691	277	25	d0	d0	PROPN
ejpam-4691	277	26	i	i	PRON
ejpam-4691	277	27	(	(	PUNCT
ejpam-4691	277	28	f	f	X
ejpam-4691	277	29	)	)	PUNCT
ejpam-4691	278	1	=	=	SYM
ejpam-4691	278	2	∪u∈mx	∪u∈mx	NOUN
ejpam-4691	278	3	{	{	PUNCT
ejpam-4691	278	4	u	u	NOUN
ejpam-4691	278	5	−	−	PROPN
ejpam-4691	278	6	f−(minti(f	f−(minti(f	PROPN
ejpam-4691	278	7	(	(	PUNCT
ejpam-4691	278	8	u	u	NOUN
ejpam-4691	278	9	)	)	PUNCT
ejpam-4691	278	10	)	)	PUNCT
ejpam-4691	278	11	)	)	PUNCT
ejpam-4691	278	12	}	}	PUNCT
ejpam-4691	279	1	=	=	PUNCT
ejpam-4691	279	2	∪a∈p	∪a∈p	X
ejpam-4691	279	3	(	(	PUNCT
ejpam-4691	279	4	x){mxint(a)−	x){mxint(a)−	SYM
ejpam-4691	279	5	f+(minti(f	f+(minti(f	X
ejpam-4691	279	6	(	(	PUNCT
ejpam-4691	279	7	a	a	NOUN
ejpam-4691	279	8	)	)	PUNCT
ejpam-4691	279	9	)	)	PUNCT
ejpam-4691	279	10	)	)	PUNCT
ejpam-4691	279	11	}	}	PUNCT
ejpam-4691	280	1	=	=	SYM
ejpam-4691	280	2	∪b∈p	∪b∈p	PROPN
ejpam-4691	280	3	(	(	PUNCT
ejpam-4691	280	4	y	y	PROPN
ejpam-4691	280	5	)	)	PUNCT
ejpam-4691	280	6	{	{	PUNCT
ejpam-4691	280	7	mxint(f+(b))−	mxint(f+(b))−	NOUN
ejpam-4691	280	8	f+(minti(b	f+(minti(b	NOUN
ejpam-4691	280	9	)	)	PUNCT
ejpam-4691	280	10	)	)	PUNCT
ejpam-4691	280	11	}	}	PUNCT
ejpam-4691	281	1	=	=	SYM
ejpam-4691	281	2	∪b∈p	∪b∈p	PROPN
ejpam-4691	281	3	(	(	PUNCT
ejpam-4691	281	4	y	y	PROPN
ejpam-4691	281	5	)	)	PUNCT
ejpam-4691	281	6	{	{	PUNCT
ejpam-4691	281	7	f−(mcli(b))−mxcl(f−(b	f−(mcli(b))−mxcl(f−(b	NOUN
ejpam-4691	281	8	)	)	PUNCT
ejpam-4691	281	9	)	)	PUNCT
ejpam-4691	281	10	}	}	PUNCT
ejpam-4691	281	11	.	.	PUNCT
ejpam-4691	282	1	references	reference	NOUN
ejpam-4691	282	2	437	437	NUM
ejpam-4691	282	3	proof	proof	NOUN
ejpam-4691	282	4	.	.	PUNCT
ejpam-4691	283	1	the	the	DET
ejpam-4691	283	2	proof	proof	NOUN
ejpam-4691	283	3	follows	follow	VERB
ejpam-4691	283	4	from	from	ADP
ejpam-4691	283	5	theorem	theorem	ADJ
ejpam-4691	283	6	5	5	NUM
ejpam-4691	283	7	and	and	CCONJ
ejpam-4691	283	8	lemma	lemma	PROPN
ejpam-4691	283	9	4	4	PROPN
ejpam-4691	283	10	.	.	NOUN
ejpam-4691	283	11	remark	remark	NOUN
ejpam-4691	283	12	3	3	NUM
ejpam-4691	283	13	.	.	NOUN
ejpam-4691	283	14	1	1	NUM
ejpam-4691	283	15	)	)	PUNCT
ejpam-4691	283	16	let	let	VERB
ejpam-4691	283	17	f	f	NOUN
ejpam-4691	283	18	:	:	PUNCT
ejpam-4691	283	19	(	(	PUNCT
ejpam-4691	283	20	x	x	X
ejpam-4691	283	21	,	,	PUNCT
ejpam-4691	283	22	τ	τ	X
ejpam-4691	283	23	)	)	PUNCT
ejpam-4691	283	24	→	→	SYM
ejpam-4691	283	25	(	(	PUNCT
ejpam-4691	283	26	y	y	PROPN
ejpam-4691	283	27	,	,	PUNCT
ejpam-4691	283	28	σ	σ	PROPN
ejpam-4691	283	29	,	,	PUNCT
ejpam-4691	283	30	j	j	PROPN
ejpam-4691	283	31	)	)	PUNCT
ejpam-4691	283	32	be	be	VERB
ejpam-4691	283	33	a	a	DET
ejpam-4691	283	34	multifunction	multifunction	NOUN
ejpam-4691	283	35	,	,	PUNCT
ejpam-4691	283	36	where	where	SCONJ
ejpam-4691	283	37	(	(	PUNCT
ejpam-4691	283	38	x	x	X
ejpam-4691	283	39	,	,	PUNCT
ejpam-4691	283	40	τ	τ	X
ejpam-4691	283	41	)	)	PUNCT
ejpam-4691	283	42	is	be	AUX
ejpam-4691	283	43	a	a	DET
ejpam-4691	283	44	topological	topological	ADJ
ejpam-4691	283	45	space	space	NOUN
ejpam-4691	283	46	.	.	PUNCT
ejpam-4691	284	1	since	since	SCONJ
ejpam-4691	284	2	mx	mx	PROPN
ejpam-4691	284	3	=	=	SYM
ejpam-4691	284	4	so(x	so(x	X
ejpam-4691	284	5	)	)	PUNCT
ejpam-4691	284	6	(	(	PUNCT
ejpam-4691	284	7	resp	resp	NOUN
ejpam-4691	284	8	.	.	PUNCT
ejpam-4691	285	1	po(x	po(x	NUM
ejpam-4691	285	2	)	)	PUNCT
ejpam-4691	285	3	,	,	PUNCT
ejpam-4691	286	1	α(x	α(x	NOUN
ejpam-4691	286	2	)	)	PUNCT
ejpam-4691	286	3	,	,	PUNCT
ejpam-4691	286	4	β(x	β(x	NOUN
ejpam-4691	286	5	)	)	PUNCT
ejpam-4691	286	6	,	,	PUNCT
ejpam-4691	286	7	bo(x	bo(x	NUM
ejpam-4691	286	8	)	)	PUNCT
ejpam-4691	286	9	)	)	PUNCT
ejpam-4691	286	10	is	be	AUX
ejpam-4691	286	11	an	an	DET
ejpam-4691	286	12	m	m	NOUN
ejpam-4691	286	13	-	-	NOUN
ejpam-4691	286	14	structure	structure	NOUN
ejpam-4691	286	15	having	have	VERB
ejpam-4691	286	16	property	property	NOUN
ejpam-4691	286	17	b	b	PROPN
ejpam-4691	286	18	,	,	PUNCT
ejpam-4691	286	19	an	an	DET
ejpam-4691	286	20	mj	mj	NOUN
ejpam-4691	286	21	-	-	PUNCT
ejpam-4691	286	22	open	open	NOUN
ejpam-4691	286	23	multifunction	multifunction	NOUN
ejpam-4691	286	24	f	f	NOUN
ejpam-4691	286	25	:	:	PUNCT
ejpam-4691	286	26	(	(	PUNCT
ejpam-4691	286	27	x	x	NOUN
ejpam-4691	286	28	,	,	PUNCT
ejpam-4691	286	29	mx	mx	NOUN
ejpam-4691	286	30	)	)	PUNCT
ejpam-4691	286	31	→	→	SYM
ejpam-4691	286	32	(	(	PUNCT
ejpam-4691	286	33	y	y	PROPN
ejpam-4691	286	34	,	,	PUNCT
ejpam-4691	286	35	σ	σ	PROPN
ejpam-4691	286	36	,	,	PUNCT
ejpam-4691	286	37	j	j	PROPN
ejpam-4691	286	38	)	)	PUNCT
ejpam-4691	286	39	is	be	AUX
ejpam-4691	286	40	defined	define	VERB
ejpam-4691	286	41	and	and	CCONJ
ejpam-4691	286	42	it	it	PRON
ejpam-4691	286	43	is	be	AUX
ejpam-4691	286	44	equivalent	equivalent	ADJ
ejpam-4691	286	45	to	to	ADP
ejpam-4691	286	46	an	an	DET
ejpam-4691	286	47	m	m	ADJ
ejpam-4691	286	48	-	-	ADJ
ejpam-4691	286	49	open	open	ADJ
ejpam-4691	286	50	multifunction	multifunction	NOUN
ejpam-4691	286	51	f	f	NOUN
ejpam-4691	286	52	:	:	PUNCT
ejpam-4691	286	53	(	(	PUNCT
ejpam-4691	286	54	x	x	NOUN
ejpam-4691	286	55	,	,	PUNCT
ejpam-4691	286	56	mx	mx	NOUN
ejpam-4691	286	57	)	)	PUNCT
ejpam-4691	286	58	→	→	SYM
ejpam-4691	286	59	(	(	PUNCT
ejpam-4691	286	60	y	y	NOUN
ejpam-4691	286	61	,	,	PUNCT
ejpam-4691	286	62	mjo(y	mjo(y	NOUN
ejpam-4691	286	63	)	)	PUNCT
ejpam-4691	286	64	)	)	PUNCT
ejpam-4691	286	65	.	.	PUNCT
ejpam-4691	287	1	for	for	ADP
ejpam-4691	287	2	example	example	NOUN
ejpam-4691	287	3	,	,	PUNCT
ejpam-4691	287	4	let	let	VERB
ejpam-4691	287	5	mx	mx	NOUN
ejpam-4691	287	6	=	=	SYM
ejpam-4691	287	7	so(x	so(x	X
ejpam-4691	287	8	)	)	PUNCT
ejpam-4691	287	9	and	and	CCONJ
ejpam-4691	287	10	mjo(y	mjo(y	NOUN
ejpam-4691	287	11	)	)	PUNCT
ejpam-4691	288	1	=	=	SYM
ejpam-4691	288	2	sjo(y	sjo(y	PROPN
ejpam-4691	288	3	)	)	PUNCT
ejpam-4691	288	4	,	,	PUNCT
ejpam-4691	288	5	then	then	ADV
ejpam-4691	288	6	an	an	DET
ejpam-4691	288	7	m	m	ADJ
ejpam-4691	288	8	-	-	ADJ
ejpam-4691	288	9	open	open	ADJ
ejpam-4691	288	10	multifunction	multifunction	NOUN
ejpam-4691	288	11	f	f	NOUN
ejpam-4691	288	12	:	:	PUNCT
ejpam-4691	288	13	(	(	PUNCT
ejpam-4691	288	14	x	x	NOUN
ejpam-4691	288	15	,	,	PUNCT
ejpam-4691	288	16	so(x	so(x	NOUN
ejpam-4691	288	17	)	)	PUNCT
ejpam-4691	288	18	)	)	PUNCT
ejpam-4691	289	1	→	→	PUNCT
ejpam-4691	289	2	(	(	PUNCT
ejpam-4691	289	3	y	y	PROPN
ejpam-4691	289	4	,	,	PUNCT
ejpam-4691	289	5	sjo(y	sjo(y	PROPN
ejpam-4691	289	6	)	)	PUNCT
ejpam-4691	289	7	)	)	PUNCT
ejpam-4691	289	8	is	be	AUX
ejpam-4691	289	9	defined	define	VERB
ejpam-4691	289	10	and	and	CCONJ
ejpam-4691	289	11	we	we	PRON
ejpam-4691	289	12	obtain	obtain	VERB
ejpam-4691	289	13	the	the	DET
ejpam-4691	289	14	properties	property	NOUN
ejpam-4691	289	15	from	from	ADP
ejpam-4691	289	16	the	the	DET
ejpam-4691	289	17	results	result	NOUN
ejpam-4691	289	18	of	of	ADP
ejpam-4691	289	19	sections	section	NOUN
ejpam-4691	289	20	3	3	NUM
ejpam-4691	289	21	and	and	CCONJ
ejpam-4691	289	22	5	5	NUM
ejpam-4691	289	23	.	.	NOUN
ejpam-4691	289	24	2	2	NUM
ejpam-4691	289	25	)	)	PUNCT
ejpam-4691	289	26	an	an	DET
ejpam-4691	289	27	mij	mij	ADJ
ejpam-4691	289	28	-	-	ADJ
ejpam-4691	289	29	open	open	ADJ
ejpam-4691	289	30	multifunction	multifunction	NOUN
ejpam-4691	289	31	f	f	NOUN
ejpam-4691	289	32	:	:	PUNCT
ejpam-4691	289	33	(	(	PUNCT
ejpam-4691	289	34	x	x	X
ejpam-4691	289	35	,	,	PUNCT
ejpam-4691	289	36	τ	τ	PROPN
ejpam-4691	289	37	,	,	PUNCT
ejpam-4691	289	38	i	i	NOUN
ejpam-4691	289	39	)	)	PUNCT
ejpam-4691	289	40	→	→	SYM
ejpam-4691	289	41	(	(	PUNCT
ejpam-4691	289	42	y	y	PROPN
ejpam-4691	289	43	,	,	PUNCT
ejpam-4691	289	44	σ	σ	PROPN
ejpam-4691	289	45	,	,	PUNCT
ejpam-4691	289	46	j	j	PROPN
ejpam-4691	289	47	)	)	PUNCT
ejpam-4691	289	48	is	be	AUX
ejpam-4691	289	49	defined	define	VERB
ejpam-4691	289	50	by	by	ADP
ejpam-4691	289	51	(	(	PUNCT
ejpam-4691	289	52	i	i	NOUN
ejpam-4691	289	53	)	)	PUNCT
ejpam-4691	289	54	an	an	DET
ejpam-4691	289	55	mjopen	mjopen	PROPN
ejpam-4691	289	56	multifunction	multifunction	NOUN
ejpam-4691	290	1	f	f	NOUN
ejpam-4691	290	2	:	:	PUNCT
ejpam-4691	290	3	(	(	PUNCT
ejpam-4691	290	4	x	x	NOUN
ejpam-4691	290	5	,	,	PUNCT
ejpam-4691	290	6	mio(x	mio(x	NOUN
ejpam-4691	290	7	)	)	PUNCT
ejpam-4691	290	8	)	)	PUNCT
ejpam-4691	291	1	→	→	SYM
ejpam-4691	291	2	(	(	PUNCT
ejpam-4691	291	3	y	y	PROPN
ejpam-4691	291	4	,	,	PUNCT
ejpam-4691	291	5	σ	σ	PROPN
ejpam-4691	291	6	,	,	PUNCT
ejpam-4691	291	7	j	j	PROPN
ejpam-4691	291	8	)	)	PUNCT
ejpam-4691	291	9	or	or	CCONJ
ejpam-4691	291	10	(	(	PUNCT
ejpam-4691	291	11	ii	ii	NOUN
ejpam-4691	291	12	)	)	PUNCT
ejpam-4691	291	13	an	an	DET
ejpam-4691	291	14	m	m	ADJ
ejpam-4691	291	15	-	-	ADJ
ejpam-4691	291	16	open	open	ADJ
ejpam-4691	291	17	multifunction	multifunction	NOUN
ejpam-4691	291	18	f	f	NOUN
ejpam-4691	291	19	:	:	PUNCT
ejpam-4691	291	20	(	(	PUNCT
ejpam-4691	291	21	x	x	NOUN
ejpam-4691	291	22	,	,	PUNCT
ejpam-4691	291	23	mio(x	mio(x	NOUN
ejpam-4691	291	24	)	)	PUNCT
ejpam-4691	291	25	)	)	PUNCT
ejpam-4691	291	26	→	→	SYM
ejpam-4691	291	27	(	(	PUNCT
ejpam-4691	291	28	y	y	NOUN
ejpam-4691	291	29	,	,	PUNCT
ejpam-4691	291	30	mjo(y	mjo(y	NOUN
ejpam-4691	291	31	)	)	PUNCT
ejpam-4691	291	32	)	)	PUNCT
ejpam-4691	291	33	.	.	PUNCT
ejpam-4691	292	1	for	for	ADP
ejpam-4691	292	2	example	example	NOUN
ejpam-4691	292	3	,	,	PUNCT
ejpam-4691	292	4	let	let	VERB
ejpam-4691	292	5	mio(x	mio(x	NOUN
ejpam-4691	292	6	)	)	PUNCT
ejpam-4691	292	7	=	=	SYM
ejpam-4691	292	8	sio(x	sio(x	VERB
ejpam-4691	292	9	)	)	PUNCT
ejpam-4691	292	10	and	and	CCONJ
ejpam-4691	292	11	mjo(y	mjo(y	NOUN
ejpam-4691	292	12	)	)	PUNCT
ejpam-4691	293	1	=	=	SYM
ejpam-4691	293	2	sjo(y	sjo(y	PROPN
ejpam-4691	293	3	)	)	PUNCT
ejpam-4691	293	4	,	,	PUNCT
ejpam-4691	293	5	then	then	ADV
ejpam-4691	293	6	an	an	DET
ejpam-4691	293	7	m	m	ADJ
ejpam-4691	293	8	-	-	ADJ
ejpam-4691	293	9	open	open	ADJ
ejpam-4691	293	10	multifunction	multifunction	NOUN
ejpam-4691	293	11	f	f	NOUN
ejpam-4691	293	12	:	:	PUNCT
ejpam-4691	293	13	(	(	PUNCT
ejpam-4691	293	14	x	x	NOUN
ejpam-4691	293	15	,	,	PUNCT
ejpam-4691	293	16	sio(x	sio(x	NOUN
ejpam-4691	293	17	)	)	PUNCT
ejpam-4691	293	18	)	)	PUNCT
ejpam-4691	293	19	→	→	SYM
ejpam-4691	293	20	(	(	PUNCT
ejpam-4691	293	21	y	y	PROPN
ejpam-4691	293	22	,	,	PUNCT
ejpam-4691	293	23	sjo(y	sjo(y	PROPN
ejpam-4691	293	24	)	)	PUNCT
ejpam-4691	293	25	)	)	PUNCT
ejpam-4691	293	26	is	be	AUX
ejpam-4691	293	27	defined	define	VERB
ejpam-4691	293	28	and	and	CCONJ
ejpam-4691	293	29	we	we	PRON
ejpam-4691	293	30	obtain	obtain	VERB
ejpam-4691	293	31	the	the	DET
ejpam-4691	293	32	properties	property	NOUN
ejpam-4691	293	33	from	from	ADP
ejpam-4691	293	34	the	the	DET
ejpam-4691	293	35	results	result	NOUN
ejpam-4691	293	36	of	of	ADP
ejpam-4691	293	37	sections	section	NOUN
ejpam-4691	293	38	3	3	NUM
ejpam-4691	293	39	and	and	CCONJ
ejpam-4691	293	40	5	5	NUM
ejpam-4691	293	41	.	.	PUNCT
ejpam-4691	293	42	corollary	corollary	ADJ
ejpam-4691	293	43	1	1	NUM
ejpam-4691	293	44	.	.	PUNCT
ejpam-4691	293	45	for	for	ADP
ejpam-4691	293	46	a	a	DET
ejpam-4691	293	47	multifunction	multifunction	NOUN
ejpam-4691	293	48	f	f	NOUN
ejpam-4691	293	49	:	:	PUNCT
ejpam-4691	293	50	(	(	PUNCT
ejpam-4691	293	51	x	x	X
ejpam-4691	293	52	,	,	PUNCT
ejpam-4691	293	53	τ	τ	PROPN
ejpam-4691	293	54	,	,	PUNCT
ejpam-4691	293	55	i	i	NOUN
ejpam-4691	293	56	)	)	PUNCT
ejpam-4691	293	57	→	→	SYM
ejpam-4691	293	58	(	(	PUNCT
ejpam-4691	293	59	y	y	PROPN
ejpam-4691	293	60	,	,	PUNCT
ejpam-4691	293	61	σ	σ	PROPN
ejpam-4691	293	62	,	,	PUNCT
ejpam-4691	293	63	j	j	PROPN
ejpam-4691	293	64	)	)	PUNCT
ejpam-4691	293	65	,	,	PUNCT
ejpam-4691	293	66	the	the	DET
ejpam-4691	293	67	following	follow	VERB
ejpam-4691	293	68	properties	property	NOUN
ejpam-4691	293	69	are	be	AUX
ejpam-4691	293	70	equivalent	equivalent	ADJ
ejpam-4691	293	71	:	:	PUNCT
ejpam-4691	293	72	(	(	PUNCT
ejpam-4691	293	73	1	1	X
ejpam-4691	293	74	)	)	PUNCT
ejpam-4691	293	75	f	f	NOUN
ejpam-4691	293	76	:	:	PUNCT
ejpam-4691	293	77	(	(	PUNCT
ejpam-4691	293	78	x	x	X
ejpam-4691	293	79	,	,	PUNCT
ejpam-4691	293	80	τ	τ	PROPN
ejpam-4691	293	81	,	,	PUNCT
ejpam-4691	293	82	i	i	NOUN
ejpam-4691	293	83	)	)	PUNCT
ejpam-4691	293	84	→	→	SYM
ejpam-4691	293	85	(	(	PUNCT
ejpam-4691	293	86	y	y	PROPN
ejpam-4691	293	87	,	,	PUNCT
ejpam-4691	293	88	σ	σ	PROPN
ejpam-4691	293	89	,	,	PUNCT
ejpam-4691	293	90	j	j	PROPN
ejpam-4691	293	91	)	)	PUNCT
ejpam-4691	293	92	is	be	AUX
ejpam-4691	293	93	mij	mij	ADJ
ejpam-4691	293	94	-	-	ADJ
ejpam-4691	293	95	open	open	ADJ
ejpam-4691	293	96	;	;	PUNCT
ejpam-4691	293	97	(	(	PUNCT
ejpam-4691	293	98	2	2	X
ejpam-4691	293	99	)	)	PUNCT
ejpam-4691	293	100	f	f	NOUN
ejpam-4691	293	101	:	:	PUNCT
ejpam-4691	293	102	(	(	PUNCT
ejpam-4691	293	103	x	x	NOUN
ejpam-4691	293	104	,	,	PUNCT
ejpam-4691	293	105	sio(x	sio(x	NOUN
ejpam-4691	293	106	)	)	PUNCT
ejpam-4691	293	107	)	)	PUNCT
ejpam-4691	294	1	→	→	SYM
ejpam-4691	294	2	(	(	PUNCT
ejpam-4691	294	3	y	y	PROPN
ejpam-4691	294	4	,	,	PUNCT
ejpam-4691	294	5	σ	σ	PROPN
ejpam-4691	294	6	,	,	PUNCT
ejpam-4691	294	7	j	j	PROPN
ejpam-4691	294	8	)	)	PUNCT
ejpam-4691	294	9	is	be	AUX
ejpam-4691	294	10	mj	mj	NOUN
ejpam-4691	294	11	-	-	PUNCT
ejpam-4691	294	12	open	open	ADJ
ejpam-4691	294	13	;	;	PUNCT
ejpam-4691	294	14	(	(	PUNCT
ejpam-4691	294	15	3	3	X
ejpam-4691	294	16	)	)	PUNCT
ejpam-4691	294	17	f	f	NOUN
ejpam-4691	294	18	:	:	PUNCT
ejpam-4691	294	19	(	(	PUNCT
ejpam-4691	294	20	x	x	NOUN
ejpam-4691	294	21	,	,	PUNCT
ejpam-4691	294	22	sio(x	sio(x	NOUN
ejpam-4691	294	23	)	)	PUNCT
ejpam-4691	294	24	)	)	PUNCT
ejpam-4691	295	1	→	→	SYM
ejpam-4691	295	2	(	(	PUNCT
ejpam-4691	295	3	y	y	PROPN
ejpam-4691	295	4	,	,	PUNCT
ejpam-4691	295	5	sjo(y	sjo(y	PROPN
ejpam-4691	295	6	)	)	PUNCT
ejpam-4691	295	7	)	)	PUNCT
ejpam-4691	295	8	is	be	AUX
ejpam-4691	295	9	m	m	NOUN
ejpam-4691	295	10	-	-	ADJ
ejpam-4691	295	11	open	open	ADJ
ejpam-4691	295	12	;	;	PUNCT
ejpam-4691	295	13	(	(	PUNCT
ejpam-4691	295	14	4	4	X
ejpam-4691	295	15	)	)	PUNCT
ejpam-4691	295	16	f	f	NOUN
ejpam-4691	295	17	(	(	PUNCT
ejpam-4691	295	18	sinti(a	sinti(a	PROPN
ejpam-4691	295	19	)	)	PUNCT
ejpam-4691	295	20	)	)	PUNCT
ejpam-4691	296	1	⊂	⊂	PROPN
ejpam-4691	296	2	sintj(f	sintj(f	NOUN
ejpam-4691	296	3	(	(	PUNCT
ejpam-4691	296	4	a	a	NOUN
ejpam-4691	296	5	)	)	PUNCT
ejpam-4691	296	6	)	)	PUNCT
ejpam-4691	296	7	for	for	ADP
ejpam-4691	296	8	any	any	DET
ejpam-4691	296	9	subset	subset	NOUN
ejpam-4691	296	10	a	a	PRON
ejpam-4691	296	11	of	of	ADP
ejpam-4691	296	12	x	x	PRON
ejpam-4691	296	13	;	;	PUNCT
ejpam-4691	296	14	(	(	PUNCT
ejpam-4691	296	15	5	5	X
ejpam-4691	296	16	)	)	PUNCT
ejpam-4691	296	17	sinti(f	sinti(f	NOUN
ejpam-4691	296	18	+	+	PROPN
ejpam-4691	296	19	(	(	PUNCT
ejpam-4691	296	20	b	b	NOUN
ejpam-4691	296	21	)	)	PUNCT
ejpam-4691	296	22	)	)	PUNCT
ejpam-4691	297	1	⊂	⊂	PROPN
ejpam-4691	297	2	f+(sintj(b	f+(sintj(b	NOUN
ejpam-4691	297	3	)	)	PUNCT
ejpam-4691	297	4	)	)	PUNCT
ejpam-4691	298	1	for	for	ADP
ejpam-4691	298	2	any	any	DET
ejpam-4691	298	3	subset	subset	NOUN
ejpam-4691	298	4	b	b	PROPN
ejpam-4691	298	5	of	of	ADP
ejpam-4691	298	6	y	y	PROPN
ejpam-4691	298	7	;	;	PUNCT
ejpam-4691	298	8	(	(	PUNCT
ejpam-4691	298	9	6	6	NUM
ejpam-4691	298	10	)	)	PUNCT
ejpam-4691	298	11	f−(sclj(b	f−(sclj(b	NOUN
ejpam-4691	298	12	)	)	PUNCT
ejpam-4691	298	13	)	)	PUNCT
ejpam-4691	299	1	⊂	⊂	PROPN
ejpam-4691	299	2	scli(f	scli(f	AUX
ejpam-4691	299	3	−(b	−(b	NOUN
ejpam-4691	299	4	)	)	PUNCT
ejpam-4691	299	5	)	)	PUNCT
ejpam-4691	299	6	for	for	ADP
ejpam-4691	299	7	any	any	DET
ejpam-4691	299	8	subset	subset	NOUN
ejpam-4691	299	9	b	b	PROPN
ejpam-4691	299	10	of	of	ADP
ejpam-4691	299	11	y.	y.	PROPN
ejpam-4691	299	12	proof	proof	PROPN
ejpam-4691	299	13	.	.	PUNCT
ejpam-4691	300	1	the	the	DET
ejpam-4691	300	2	proof	proof	NOUN
ejpam-4691	300	3	easily	easily	ADV
ejpam-4691	300	4	follows	follow	VERB
ejpam-4691	300	5	from	from	ADP
ejpam-4691	300	6	theorem	theorem	ADJ
ejpam-4691	300	7	9	9	NUM
ejpam-4691	300	8	.	.	PUNCT
ejpam-4691	300	9	references	reference	NOUN
ejpam-4691	301	1	[	[	X
ejpam-4691	301	2	1	1	NUM
ejpam-4691	301	3	]	]	X
ejpam-4691	301	4	m.e	m.e	PROPN
ejpam-4691	301	5	.	.	PROPN
ejpam-4691	301	6	abd	abd	PROPN
ejpam-4691	301	7	el	el	PROPN
ejpam-4691	301	8	-	-	PROPN
ejpam-4691	301	9	monsef	monsef	ADJ
ejpam-4691	301	10	,	,	PUNCT
ejpam-4691	301	11	s.n	s.n	PROPN
ejpam-4691	301	12	.	.	PROPN
ejpam-4691	301	13	el	el	PROPN
ejpam-4691	301	14	-	-	PUNCT
ejpam-4691	301	15	deeb	deeb	PROPN
ejpam-4691	301	16	,	,	PUNCT
ejpam-4691	301	17	and	and	CCONJ
ejpam-4691	301	18	r.a	r.a	PROPN
ejpam-4691	301	19	.	.	PROPN
ejpam-4691	301	20	mahmoud	mahmoud	PROPN
ejpam-4691	301	21	.	.	PUNCT
ejpam-4691	302	1	β	β	X
ejpam-4691	302	2	-	-	ADJ
ejpam-4691	302	3	open	open	ADJ
ejpam-4691	302	4	sets	set	NOUN
ejpam-4691	302	5	and	and	CCONJ
ejpam-4691	302	6	βcontinuous	βcontinuous	ADJ
ejpam-4691	302	7	mappings	mapping	NOUN
ejpam-4691	302	8	.	.	PUNCT
ejpam-4691	303	1	bull	bull	NOUN
ejpam-4691	303	2	.	.	PUNCT
ejpam-4691	304	1	fac	fac	PROPN
ejpam-4691	304	2	.	.	PUNCT
ejpam-4691	305	1	sci	sci	PROPN
ejpam-4691	305	2	.	.	PUNCT
ejpam-4691	305	3	assiut	assiut	PROPN
ejpam-4691	305	4	univ	univ	PROPN
ejpam-4691	305	5	.	.	PROPN
ejpam-4691	305	6	,	,	PUNCT
ejpam-4691	305	7	12:77–90	12:77–90	NUM
ejpam-4691	305	8	,	,	PUNCT
ejpam-4691	305	9	1983	1983	NUM
ejpam-4691	305	10	.	.	PUNCT
ejpam-4691	306	1	[	[	X
ejpam-4691	306	2	2	2	NUM
ejpam-4691	306	3	]	]	PUNCT
ejpam-4691	306	4	a.	a.	NOUN
ejpam-4691	306	5	açıkgöz	açıkgöz	NOUN
ejpam-4691	306	6	,	,	PUNCT
ejpam-4691	306	7	t.	t.	PROPN
ejpam-4691	306	8	noiri	noiri	PROPN
ejpam-4691	306	9	,	,	PUNCT
ejpam-4691	306	10	and	and	CCONJ
ejpam-4691	306	11	s.	s.	PROPN
ejpam-4691	306	12	yüksel	yüksel	PROPN
ejpam-4691	306	13	.	.	PUNCT
ejpam-4691	307	1	on	on	ADP
ejpam-4691	307	2	α	α	PROPN
ejpam-4691	307	3	-	-	PUNCT
ejpam-4691	307	4	i	i	PRON
ejpam-4691	307	5	-	-	PUNCT
ejpam-4691	307	6	continuous	continuous	ADJ
ejpam-4691	307	7	functions	function	NOUN
ejpam-4691	307	8	and	and	CCONJ
ejpam-4691	307	9	α	α	X
ejpam-4691	307	10	-	-	ADJ
ejpam-4691	307	11	i	i	NOUN
ejpam-4691	307	12	-	-	PUNCT
ejpam-4691	307	13	open	open	ADJ
ejpam-4691	307	14	functions	function	NOUN
ejpam-4691	307	15	.	.	PUNCT
ejpam-4691	308	1	acta	acta	PROPN
ejpam-4691	308	2	math	math	PROPN
ejpam-4691	308	3	.	.	PUNCT
ejpam-4691	309	1	hungar	hungar	PROPN
ejpam-4691	309	2	.	.	PUNCT
ejpam-4691	310	1	,	,	PUNCT
ejpam-4691	310	2	105	105	NUM
ejpam-4691	310	3	(	(	PUNCT
ejpam-4691	310	4	1	1	NUM
ejpam-4691	310	5	-	-	PUNCT
ejpam-4691	310	6	2):27–37	2):27–37	NUM
ejpam-4691	310	7	,	,	PUNCT
ejpam-4691	310	8	2004	2004	NUM
ejpam-4691	310	9	.	.	PUNCT
ejpam-4691	311	1	[	[	X
ejpam-4691	311	2	3	3	X
ejpam-4691	311	3	]	]	PUNCT
ejpam-4691	311	4	m.	m.	NOUN
ejpam-4691	311	5	akdağ.	akdağ.	PROPN
ejpam-4691	311	6	on	on	ADP
ejpam-4691	311	7	b	b	X
ejpam-4691	311	8	-	-	PUNCT
ejpam-4691	311	9	i	i	NOUN
ejpam-4691	311	10	-	-	PUNCT
ejpam-4691	311	11	open	open	ADJ
ejpam-4691	311	12	sets	set	NOUN
ejpam-4691	311	13	and	and	CCONJ
ejpam-4691	311	14	b	b	X
ejpam-4691	311	15	-	-	PUNCT
ejpam-4691	311	16	i	i	NOUN
ejpam-4691	311	17	-	-	PUNCT
ejpam-4691	311	18	continuous	continuous	ADJ
ejpam-4691	311	19	functions	function	NOUN
ejpam-4691	311	20	.	.	PUNCT
ejpam-4691	312	1	int	int	NOUN
ejpam-4691	312	2	.	.	PUNCT
ejpam-4691	313	1	j.	j.	PROPN
ejpam-4691	313	2	math	math	PROPN
ejpam-4691	313	3	.	.	PUNCT
ejpam-4691	314	1	math	math	NOUN
ejpam-4691	314	2	.	.	PUNCT
ejpam-4691	315	1	sci	sci	PROPN
ejpam-4691	315	2	.	.	PROPN
ejpam-4691	315	3	,	,	PUNCT
ejpam-4691	315	4	2007	2007	NUM
ejpam-4691	315	5	:	:	PUNCT
ejpam-4691	315	6	article	article	NOUN
ejpam-4691	315	7	i	i	PROPN
ejpam-4691	315	8	d	d	PROPN
ejpam-4691	315	9	75721	75721	NUM
ejpam-4691	315	10	,	,	PUNCT
ejpam-4691	315	11	2007	2007	NUM
ejpam-4691	315	12	.	.	PUNCT
ejpam-4691	316	1	[	[	X
ejpam-4691	316	2	4	4	X
ejpam-4691	316	3	]	]	X
ejpam-4691	316	4	d.	d.	PROPN
ejpam-4691	316	5	andrijević.	andrijević.	PROPN
ejpam-4691	316	6	on	on	ADP
ejpam-4691	316	7	b	b	X
ejpam-4691	316	8	-	-	PUNCT
ejpam-4691	316	9	open	open	ADJ
ejpam-4691	316	10	sets	set	NOUN
ejpam-4691	316	11	.	.	PUNCT
ejpam-4691	317	1	mat	mat	X
ejpam-4691	317	2	.	.	PROPN
ejpam-4691	317	3	vesnik	vesnik	PROPN
ejpam-4691	317	4	,	,	PUNCT
ejpam-4691	317	5	48:59–64	48:59–64	PROPN
ejpam-4691	317	6	,	,	PUNCT
ejpam-4691	317	7	1996	1996	NUM
ejpam-4691	317	8	.	.	PUNCT
ejpam-4691	318	1	[	[	X
ejpam-4691	318	2	5	5	X
ejpam-4691	318	3	]	]	PUNCT
ejpam-4691	318	4	t.	t.	NOUN
ejpam-4691	318	5	bânzaru	bânzaru	PROPN
ejpam-4691	318	6	.	.	PUNCT
ejpam-4691	319	1	topologies	topology	NOUN
ejpam-4691	319	2	on	on	ADP
ejpam-4691	319	3	spaces	space	NOUN
ejpam-4691	319	4	of	of	ADP
ejpam-4691	319	5	subsets	subset	NOUN
ejpam-4691	319	6	and	and	CCONJ
ejpam-4691	319	7	multivalued	multivalued	ADJ
ejpam-4691	319	8	mappings	mapping	NOUN
ejpam-4691	319	9	.	.	PUNCT
ejpam-4691	320	1	mathematical	mathematical	ADJ
ejpam-4691	320	2	monographs	monograph	NOUN
ejpam-4691	320	3	,	,	PUNCT
ejpam-4691	320	4	university	university	NOUN
ejpam-4691	320	5	of	of	ADP
ejpam-4691	320	6	timişoara	timişoara	NOUN
ejpam-4691	320	7	,	,	PUNCT
ejpam-4691	320	8	1997	1997	NUM
ejpam-4691	320	9	.	.	PUNCT
ejpam-4691	321	1	[	[	X
ejpam-4691	321	2	6	6	X
ejpam-4691	321	3	]	]	PUNCT
ejpam-4691	321	4	j.	j.	PROPN
ejpam-4691	321	5	cao	cao	PROPN
ejpam-4691	321	6	and	and	CCONJ
ejpam-4691	321	7	i.	i.	PROPN
ejpam-4691	321	8	l.	l.	PROPN
ejpam-4691	321	9	reilly	reilly	PROPN
ejpam-4691	321	10	.	.	PUNCT
ejpam-4691	322	1	α	α	X
ejpam-4691	322	2	-	-	ADJ
ejpam-4691	322	3	continuous	continuous	ADJ
ejpam-4691	322	4	and	and	CCONJ
ejpam-4691	322	5	α	α	NOUN
ejpam-4691	322	6	-	-	PUNCT
ejpam-4691	322	7	irresolute	irresolute	ADJ
ejpam-4691	322	8	multifunctions	multifunction	NOUN
ejpam-4691	322	9	.	.	PUNCT
ejpam-4691	323	1	math	math	NOUN
ejpam-4691	323	2	.	.	PUNCT
ejpam-4691	324	1	bohemica	bohemica	PROPN
ejpam-4691	324	2	,	,	PUNCT
ejpam-4691	324	3	121:415–424	121:415–424	NUM
ejpam-4691	324	4	,	,	PUNCT
ejpam-4691	324	5	1996	1996	NUM
ejpam-4691	324	6	.	.	PUNCT
ejpam-4691	325	1	references	reference	NOUN
ejpam-4691	325	2	438	438	NUM
ejpam-4691	326	1	[	[	X
ejpam-4691	326	2	7	7	X
ejpam-4691	326	3	]	]	PUNCT
ejpam-4691	326	4	j.	j.	PROPN
ejpam-4691	326	5	cao	cao	PROPN
ejpam-4691	326	6	and	and	CCONJ
ejpam-4691	326	7	i.	i.	PROPN
ejpam-4691	326	8	l.	l.	PROPN
ejpam-4691	326	9	reilly	reilly	PROPN
ejpam-4691	326	10	.	.	PUNCT
ejpam-4691	327	1	on	on	ADP
ejpam-4691	327	2	pairwise	pairwise	NOUN
ejpam-4691	327	3	almost	almost	ADV
ejpam-4691	327	4	continuous	continuous	ADJ
ejpam-4691	327	5	multifunctions	multifunction	NOUN
ejpam-4691	327	6	and	and	CCONJ
ejpam-4691	327	7	closed	closed	ADJ
ejpam-4691	327	8	graph	graph	NOUN
ejpam-4691	327	9	.	.	PUNCT
ejpam-4691	328	1	indian	indian	PROPN
ejpam-4691	328	2	j.	j.	PROPN
ejpam-4691	328	3	math	math	PROPN
ejpam-4691	328	4	.	.	PUNCT
ejpam-4691	328	5	,	,	PUNCT
ejpam-4691	328	6	38:1–17	38:1–17	NUM
ejpam-4691	328	7	,	,	PUNCT
ejpam-4691	328	8	1996	1996	NUM
ejpam-4691	328	9	.	.	PUNCT
ejpam-4691	329	1	[	[	X
ejpam-4691	329	2	8	8	X
ejpam-4691	329	3	]	]	PUNCT
ejpam-4691	329	4	j.	j.	PROPN
ejpam-4691	329	5	dontchev	dontchev	PROPN
ejpam-4691	329	6	.	.	PUNCT
ejpam-4691	330	1	on	on	ADP
ejpam-4691	330	2	pre	pre	ADJ
ejpam-4691	330	3	-	-	ADJ
ejpam-4691	330	4	i	i	PRON
ejpam-4691	330	5	-	-	PUNCT
ejpam-4691	330	6	open	open	ADJ
ejpam-4691	330	7	sets	set	NOUN
ejpam-4691	330	8	and	and	CCONJ
ejpam-4691	330	9	a	a	DET
ejpam-4691	330	10	decomposition	decomposition	NOUN
ejpam-4691	330	11	of	of	ADP
ejpam-4691	330	12	i	i	NOUN
ejpam-4691	330	13	-	-	PUNCT
ejpam-4691	330	14	continuity	continuity	NOUN
ejpam-4691	330	15	.	.	PUNCT
ejpam-4691	331	1	banyan	banyan	ADJ
ejpam-4691	331	2	math	math	NOUN
ejpam-4691	331	3	.	.	PUNCT
ejpam-4691	332	1	j.	j.	PROPN
ejpam-4691	332	2	,	,	PUNCT
ejpam-4691	332	3	2	2	NUM
ejpam-4691	332	4	,	,	PUNCT
ejpam-4691	332	5	1996	1996	NUM
ejpam-4691	332	6	.	.	PUNCT
ejpam-4691	333	1	[	[	X
ejpam-4691	333	2	9	9	NUM
ejpam-4691	333	3	]	]	X
ejpam-4691	333	4	e.	e.	PROPN
ejpam-4691	333	5	hatır	hatır	PROPN
ejpam-4691	333	6	and	and	CCONJ
ejpam-4691	333	7	s.	s.	PROPN
ejpam-4691	333	8	jafari	jafari	PROPN
ejpam-4691	333	9	.	.	PUNCT
ejpam-4691	334	1	on	on	ADP
ejpam-4691	334	2	weakly	weakly	ADJ
ejpam-4691	334	3	semi	semi	ADJ
ejpam-4691	334	4	-	-	ADJ
ejpam-4691	334	5	i	i	PRON
ejpam-4691	334	6	-	-	PUNCT
ejpam-4691	334	7	open	open	ADJ
ejpam-4691	334	8	sets	set	NOUN
ejpam-4691	334	9	and	and	CCONJ
ejpam-4691	334	10	other	other	ADJ
ejpam-4691	334	11	decomposition	decomposition	NOUN
ejpam-4691	334	12	of	of	ADP
ejpam-4691	334	13	continuity	continuity	NOUN
ejpam-4691	334	14	via	via	ADP
ejpam-4691	334	15	ideals	ideal	NOUN
ejpam-4691	334	16	.	.	PUNCT
ejpam-4691	335	1	sarajevo	sarajevo	PROPN
ejpam-4691	335	2	j.	j.	PROPN
ejpam-4691	335	3	math	math	PROPN
ejpam-4691	335	4	.	.	PUNCT
ejpam-4691	335	5	,	,	PUNCT
ejpam-4691	335	6	14:107–114	14:107–114	PROPN
ejpam-4691	335	7	,	,	PUNCT
ejpam-4691	335	8	2006	2006	NUM
ejpam-4691	335	9	.	.	PUNCT
ejpam-4691	336	1	[	[	X
ejpam-4691	336	2	10	10	NUM
ejpam-4691	336	3	]	]	X
ejpam-4691	336	4	e.	e.	PROPN
ejpam-4691	336	5	hatır	hatır	PROPN
ejpam-4691	336	6	,	,	PUNCT
ejpam-4691	336	7	a.	a.	PROPN
ejpam-4691	336	8	keskin	keskin	PROPN
ejpam-4691	336	9	,	,	PUNCT
ejpam-4691	336	10	and	and	CCONJ
ejpam-4691	336	11	t.	t.	PROPN
ejpam-4691	336	12	noiri	noiri	PROPN
ejpam-4691	336	13	.	.	PUNCT
ejpam-4691	337	1	on	on	ADP
ejpam-4691	337	2	a	a	DET
ejpam-4691	337	3	new	new	ADJ
ejpam-4691	337	4	decomposition	decomposition	NOUN
ejpam-4691	337	5	of	of	ADP
ejpam-4691	337	6	continuity	continuity	NOUN
ejpam-4691	337	7	via	via	ADP
ejpam-4691	337	8	idealization	idealization	NOUN
ejpam-4691	337	9	.	.	PUNCT
ejpam-4691	338	1	jp	jp	PROPN
ejpam-4691	338	2	j.	j.	PROPN
ejpam-4691	338	3	geometry	geometry	PROPN
ejpam-4691	338	4	topology	topology	NOUN
ejpam-4691	338	5	,	,	PUNCT
ejpam-4691	338	6	3	3	NUM
ejpam-4691	338	7	(	(	PUNCT
ejpam-4691	338	8	1):53–64	1):53–64	NUM
ejpam-4691	338	9	,	,	PUNCT
ejpam-4691	338	10	2003	2003	NUM
ejpam-4691	338	11	.	.	PUNCT
ejpam-4691	339	1	[	[	X
ejpam-4691	339	2	11	11	NUM
ejpam-4691	339	3	]	]	X
ejpam-4691	339	4	e.	e.	PROPN
ejpam-4691	339	5	hatır	hatır	PROPN
ejpam-4691	339	6	and	and	CCONJ
ejpam-4691	339	7	t.	t.	PROPN
ejpam-4691	339	8	noiri	noiri	PROPN
ejpam-4691	339	9	.	.	PUNCT
ejpam-4691	340	1	on	on	ADP
ejpam-4691	340	2	decompositions	decomposition	NOUN
ejpam-4691	340	3	of	of	ADP
ejpam-4691	340	4	continuity	continuity	NOUN
ejpam-4691	340	5	via	via	ADP
ejpam-4691	340	6	idealization	idealization	NOUN
ejpam-4691	340	7	.	.	PUNCT
ejpam-4691	341	1	acta	acta	PROPN
ejpam-4691	341	2	math	math	PROPN
ejpam-4691	341	3	.	.	PUNCT
ejpam-4691	342	1	hungar	hungar	PROPN
ejpam-4691	342	2	.	.	PUNCT
ejpam-4691	343	1	,	,	PUNCT
ejpam-4691	343	2	96	96	NUM
ejpam-4691	343	3	(	(	PUNCT
ejpam-4691	343	4	4):341–349	4):341–349	NUM
ejpam-4691	343	5	,	,	PUNCT
ejpam-4691	343	6	2002	2002	NUM
ejpam-4691	343	7	.	.	PUNCT
ejpam-4691	344	1	[	[	X
ejpam-4691	344	2	12	12	NUM
ejpam-4691	344	3	]	]	X
ejpam-4691	344	4	e.	e.	PROPN
ejpam-4691	344	5	hatır	hatır	PROPN
ejpam-4691	344	6	and	and	CCONJ
ejpam-4691	344	7	t.	t.	PROPN
ejpam-4691	344	8	noiri	noiri	PROPN
ejpam-4691	344	9	.	.	PUNCT
ejpam-4691	345	1	on	on	ADP
ejpam-4691	345	2	semi	semi	ADJ
ejpam-4691	345	3	-	-	ADJ
ejpam-4691	345	4	i	i	PRON
ejpam-4691	345	5	-	-	PUNCT
ejpam-4691	345	6	open	open	ADJ
ejpam-4691	345	7	sets	set	NOUN
ejpam-4691	345	8	and	and	CCONJ
ejpam-4691	345	9	semi	semi	ADJ
ejpam-4691	345	10	-	-	ADJ
ejpam-4691	345	11	i	i	ADV
ejpam-4691	345	12	-	-	PUNCT
ejpam-4691	345	13	continuous	continuous	ADJ
ejpam-4691	345	14	functions	function	NOUN
ejpam-4691	345	15	.	.	PUNCT
ejpam-4691	346	1	acta	acta	PROPN
ejpam-4691	346	2	math	math	PROPN
ejpam-4691	346	3	.	.	PUNCT
ejpam-4691	347	1	hungar	hungar	PROPN
ejpam-4691	347	2	.	.	PUNCT
ejpam-4691	348	1	,	,	PUNCT
ejpam-4691	348	2	107	107	NUM
ejpam-4691	348	3	(	(	PUNCT
ejpam-4691	348	4	4):345–353	4):345–353	NOUN
ejpam-4691	348	5	,	,	PUNCT
ejpam-4691	348	6	2005	2005	NUM
ejpam-4691	348	7	.	.	PUNCT
ejpam-4691	349	1	[	[	X
ejpam-4691	349	2	13	13	NUM
ejpam-4691	349	3	]	]	X
ejpam-4691	349	4	d.	d.	PROPN
ejpam-4691	349	5	janković	janković	PROPN
ejpam-4691	349	6	and	and	CCONJ
ejpam-4691	349	7	t.	t.	PROPN
ejpam-4691	349	8	r.	r.	PROPN
ejpam-4691	349	9	hamlett	hamlett	PROPN
ejpam-4691	349	10	.	.	PUNCT
ejpam-4691	350	1	new	new	ADJ
ejpam-4691	350	2	topologies	topology	NOUN
ejpam-4691	350	3	from	from	ADP
ejpam-4691	350	4	old	old	ADJ
ejpam-4691	350	5	via	via	ADP
ejpam-4691	350	6	ideals	ideal	NOUN
ejpam-4691	350	7	.	.	PUNCT
ejpam-4691	351	1	amer	amer	PROPN
ejpam-4691	351	2	.	.	PUNCT
ejpam-4691	351	3	math	math	PROPN
ejpam-4691	351	4	.	.	PUNCT
ejpam-4691	352	1	monthly	monthly	ADJ
ejpam-4691	352	2	,	,	PUNCT
ejpam-4691	352	3	97:295–310	97:295–310	PROPN
ejpam-4691	352	4	,	,	PUNCT
ejpam-4691	352	5	1990	1990	NUM
ejpam-4691	352	6	.	.	PUNCT
ejpam-4691	353	1	[	[	X
ejpam-4691	353	2	14	14	NUM
ejpam-4691	353	3	]	]	X
ejpam-4691	353	4	d.	d.	PROPN
ejpam-4691	353	5	janković	janković	PROPN
ejpam-4691	353	6	and	and	CCONJ
ejpam-4691	353	7	t.	t.	PROPN
ejpam-4691	353	8	r.	r.	PROPN
ejpam-4691	353	9	hamlett	hamlett	PROPN
ejpam-4691	353	10	.	.	PUNCT
ejpam-4691	354	1	compatible	compatible	ADJ
ejpam-4691	354	2	extensions	extension	NOUN
ejpam-4691	354	3	of	of	ADP
ejpam-4691	354	4	ideals	ideal	NOUN
ejpam-4691	354	5	.	.	PUNCT
ejpam-4691	355	1	boll	boll	NOUN
ejpam-4691	355	2	.	.	PUNCT
ejpam-4691	356	1	un	un	PROPN
ejpam-4691	356	2	.	.	PROPN
ejpam-4691	356	3	mat	mat	PROPN
ejpam-4691	356	4	.	.	PUNCT
ejpam-4691	356	5	ital	ital	PROPN
ejpam-4691	356	6	.	.	PROPN
ejpam-4691	356	7	,	,	PUNCT
ejpam-4691	356	8	(	(	PUNCT
ejpam-4691	356	9	7	7	X
ejpam-4691	356	10	)	)	SYM
ejpam-4691	356	11	6	6	NUM
ejpam-4691	356	12	-	-	PUNCT
ejpam-4691	356	13	b:453–465	b:453–465	NOUN
ejpam-4691	356	14	,	,	PUNCT
ejpam-4691	356	15	1992	1992	NUM
ejpam-4691	356	16	.	.	PUNCT
ejpam-4691	357	1	[	[	X
ejpam-4691	357	2	15	15	NUM
ejpam-4691	357	3	]	]	PUNCT
ejpam-4691	357	4	k.	k.	PROPN
ejpam-4691	357	5	kuratowski	kuratowski	PROPN
ejpam-4691	357	6	.	.	PUNCT
ejpam-4691	358	1	topology	topology	PROPN
ejpam-4691	358	2	.	.	PUNCT
ejpam-4691	359	1	academic	academic	ADJ
ejpam-4691	359	2	press	press	NOUN
ejpam-4691	359	3	,	,	PUNCT
ejpam-4691	359	4	new	new	PROPN
ejpam-4691	359	5	york	york	PROPN
ejpam-4691	359	6	,	,	PUNCT
ejpam-4691	359	7	1966	1966	NUM
ejpam-4691	359	8	.	.	PUNCT
ejpam-4691	360	1	[	[	X
ejpam-4691	360	2	16	16	NUM
ejpam-4691	360	3	]	]	X
ejpam-4691	360	4	n.	n.	PROPN
ejpam-4691	360	5	levine	levine	PROPN
ejpam-4691	360	6	.	.	PUNCT
ejpam-4691	361	1	semi	semi	ADJ
ejpam-4691	361	2	-	-	ADJ
ejpam-4691	361	3	open	open	ADJ
ejpam-4691	361	4	sets	set	NOUN
ejpam-4691	361	5	and	and	CCONJ
ejpam-4691	361	6	semi	semi	ADJ
ejpam-4691	361	7	-	-	NOUN
ejpam-4691	361	8	continuity	continuity	NOUN
ejpam-4691	361	9	in	in	ADP
ejpam-4691	361	10	topological	topological	ADJ
ejpam-4691	361	11	spaces	space	NOUN
ejpam-4691	361	12	.	.	PUNCT
ejpam-4691	362	1	amer	amer	PROPN
ejpam-4691	362	2	.	.	PUNCT
ejpam-4691	362	3	math	math	PROPN
ejpam-4691	362	4	.	.	PUNCT
ejpam-4691	363	1	monthly	monthly	ADJ
ejpam-4691	363	2	,	,	PUNCT
ejpam-4691	363	3	70:36–41	70:36–41	NUM
ejpam-4691	363	4	,	,	PUNCT
ejpam-4691	363	5	1963	1963	NUM
ejpam-4691	363	6	.	.	PUNCT
ejpam-4691	364	1	[	[	X
ejpam-4691	364	2	17	17	NUM
ejpam-4691	364	3	]	]	X
ejpam-4691	364	4	h.	h.	PROPN
ejpam-4691	364	5	maki	maki	PROPN
ejpam-4691	364	6	,	,	PUNCT
ejpam-4691	364	7	k.	k.	PROPN
ejpam-4691	364	8	c.	c.	PROPN
ejpam-4691	364	9	rao	rao	PROPN
ejpam-4691	364	10	,	,	PUNCT
ejpam-4691	364	11	and	and	CCONJ
ejpam-4691	364	12	a.	a.	NOUN
ejpam-4691	364	13	nagoor	nagoor	PROPN
ejpam-4691	364	14	gani	gani	PROPN
ejpam-4691	364	15	.	.	PUNCT
ejpam-4691	365	1	on	on	ADP
ejpam-4691	365	2	generalizing	generalize	VERB
ejpam-4691	365	3	semi	semi	ADJ
ejpam-4691	365	4	-	-	ADJ
ejpam-4691	365	5	open	open	ADJ
ejpam-4691	365	6	and	and	CCONJ
ejpam-4691	365	7	preopen	preopen	ADJ
ejpam-4691	365	8	sets	set	NOUN
ejpam-4691	365	9	.	.	PUNCT
ejpam-4691	366	1	pure	pure	ADJ
ejpam-4691	366	2	appl	appl	PROPN
ejpam-4691	366	3	.	.	PUNCT
ejpam-4691	366	4	math	math	PROPN
ejpam-4691	366	5	.	.	PUNCT
ejpam-4691	367	1	sci	sci	PROPN
ejpam-4691	367	2	.	.	PROPN
ejpam-4691	367	3	,	,	PUNCT
ejpam-4691	367	4	49:17–29	49:17–29	PROPN
ejpam-4691	367	5	,	,	PUNCT
ejpam-4691	367	6	1999	1999	NUM
ejpam-4691	367	7	.	.	PUNCT
ejpam-4691	368	1	[	[	X
ejpam-4691	368	2	18	18	NUM
ejpam-4691	368	3	]	]	PUNCT
ejpam-4691	368	4	a.	a.	NOUN
ejpam-4691	368	5	s.	s.	PROPN
ejpam-4691	368	6	mashhour	mashhour	PROPN
ejpam-4691	368	7	,	,	PUNCT
ejpam-4691	368	8	m.	m.	PROPN
ejpam-4691	368	9	e.	e.	PROPN
ejpam-4691	368	10	abd	abd	PROPN
ejpam-4691	368	11	el	el	PROPN
ejpam-4691	368	12	-	-	PROPN
ejpam-4691	368	13	monsef	monsef	ADJ
ejpam-4691	368	14	,	,	PUNCT
ejpam-4691	368	15	and	and	CCONJ
ejpam-4691	368	16	s.	s.	PROPN
ejpam-4691	368	17	n.	n.	PROPN
ejpam-4691	368	18	el	el	PROPN
ejpam-4691	368	19	-	-	PUNCT
ejpam-4691	368	20	deep	deep	ADJ
ejpam-4691	368	21	.	.	PUNCT
ejpam-4691	369	1	on	on	ADP
ejpam-4691	369	2	precontinuous	precontinuous	ADJ
ejpam-4691	369	3	and	and	CCONJ
ejpam-4691	369	4	weak	weak	ADJ
ejpam-4691	369	5	precontinuous	precontinuous	ADJ
ejpam-4691	369	6	mappings	mapping	NOUN
ejpam-4691	369	7	.	.	PUNCT
ejpam-4691	370	1	proc	proc	NOUN
ejpam-4691	370	2	.	.	PUNCT
ejpam-4691	371	1	math	math	NOUN
ejpam-4691	371	2	.	.	PUNCT
ejpam-4691	372	1	phys	phy	NOUN
ejpam-4691	372	2	.	.	PUNCT
ejpam-4691	373	1	soc	soc	PROPN
ejpam-4691	373	2	.	.	PUNCT
ejpam-4691	374	1	egypt	egypt	PROPN
ejpam-4691	374	2	.	.	PROPN
ejpam-4691	374	3	,	,	PUNCT
ejpam-4691	374	4	53:47–53	53:47–53	NUM
ejpam-4691	374	5	,	,	PUNCT
ejpam-4691	374	6	1982	1982	NUM
ejpam-4691	374	7	.	.	PUNCT
ejpam-4691	375	1	[	[	X
ejpam-4691	375	2	19	19	NUM
ejpam-4691	375	3	]	]	X
ejpam-4691	375	4	j.	j.	PROPN
ejpam-4691	375	5	m.	m.	PROPN
ejpam-4691	375	6	mustafa	mustafa	PROPN
ejpam-4691	375	7	,	,	PUNCT
ejpam-4691	375	8	s.	s.	PROPN
ejpam-4691	375	9	al	al	PROPN
ejpam-4691	375	10	ghour	ghour	PROPN
ejpam-4691	375	11	,	,	PUNCT
ejpam-4691	375	12	and	and	CCONJ
ejpam-4691	375	13	k.al	k.al	PROPN
ejpam-4691	375	14	zoubi	zoubi	NOUN
ejpam-4691	375	15	.	.	PUNCT
ejpam-4691	376	1	weakly	weakly	ADJ
ejpam-4691	376	2	b	b	X
ejpam-4691	376	3	-	-	PUNCT
ejpam-4691	376	4	i	i	NOUN
ejpam-4691	376	5	-	-	PUNCT
ejpam-4691	376	6	open	open	ADJ
ejpam-4691	376	7	sets	set	NOUN
ejpam-4691	376	8	and	and	CCONJ
ejpam-4691	376	9	weakly	weakly	ADJ
ejpam-4691	376	10	b	b	NOUN
ejpam-4691	376	11	-	-	PUNCT
ejpam-4691	376	12	i	i	NOUN
ejpam-4691	376	13	-	-	PUNCT
ejpam-4691	376	14	continuous	continuous	ADJ
ejpam-4691	376	15	functions	function	NOUN
ejpam-4691	376	16	.	.	PUNCT
ejpam-4691	377	1	ital	ital	PROPN
ejpam-4691	377	2	.	.	PUNCT
ejpam-4691	378	1	j.	j.	PROPN
ejpam-4691	378	2	pure	pure	PROPN
ejpam-4691	378	3	appl	appl	PROPN
ejpam-4691	378	4	.	.	PUNCT
ejpam-4691	378	5	math	math	PROPN
ejpam-4691	378	6	.	.	PUNCT
ejpam-4691	378	7	,	,	PUNCT
ejpam-4691	378	8	30:23–32	30:23–32	NUM
ejpam-4691	378	9	,	,	PUNCT
ejpam-4691	378	10	2013	2013	NUM
ejpam-4691	378	11	.	.	PUNCT
ejpam-4691	379	1	[	[	X
ejpam-4691	379	2	20	20	NUM
ejpam-4691	379	3	]	]	X
ejpam-4691	379	4	o.	o.	NOUN
ejpam-4691	379	5	nj̊astad	nj̊astad	NOUN
ejpam-4691	379	6	.	.	PUNCT
ejpam-4691	380	1	on	on	ADP
ejpam-4691	380	2	some	some	DET
ejpam-4691	380	3	classes	class	NOUN
ejpam-4691	380	4	of	of	ADP
ejpam-4691	380	5	nearly	nearly	ADV
ejpam-4691	380	6	open	open	ADJ
ejpam-4691	380	7	sets	set	NOUN
ejpam-4691	380	8	.	.	PUNCT
ejpam-4691	381	1	pacific	pacific	PROPN
ejpam-4691	381	2	j.	j.	PROPN
ejpam-4691	381	3	math	math	PROPN
ejpam-4691	381	4	.	.	PUNCT
ejpam-4691	381	5	,	,	PUNCT
ejpam-4691	381	6	15:961–970	15:961–970	PROPN
ejpam-4691	381	7	,	,	PUNCT
ejpam-4691	381	8	1965	1965	NUM
ejpam-4691	381	9	.	.	PUNCT
ejpam-4691	382	1	[	[	X
ejpam-4691	382	2	21	21	NUM
ejpam-4691	382	3	]	]	X
ejpam-4691	382	4	t.	t.	PROPN
ejpam-4691	382	5	noiri	noiri	PROPN
ejpam-4691	382	6	and	and	CCONJ
ejpam-4691	382	7	v.	v.	ADP
ejpam-4691	382	8	popa	popa	NOUN
ejpam-4691	382	9	.	.	PUNCT
ejpam-4691	383	1	minimal	minimal	ADJ
ejpam-4691	383	2	structures	structure	NOUN
ejpam-4691	383	3	,	,	PUNCT
ejpam-4691	383	4	m	m	NOUN
ejpam-4691	383	5	-	-	ADJ
ejpam-4691	383	6	open	open	ADJ
ejpam-4691	383	7	multifunctions	multifunction	NOUN
ejpam-4691	383	8	and	and	CCONJ
ejpam-4691	383	9	bitopological	bitopological	ADJ
ejpam-4691	383	10	spaces	space	NOUN
ejpam-4691	383	11	.	.	PUNCT
ejpam-4691	384	1	j.	j.	PROPN
ejpam-4691	384	2	pure	pure	PROPN
ejpam-4691	384	3	math	math	PROPN
ejpam-4691	384	4	.	.	PUNCT
ejpam-4691	384	5	,	,	PUNCT
ejpam-4691	384	6	24:1–12	24:1–12	NUM
ejpam-4691	384	7	,	,	PUNCT
ejpam-4691	384	8	2007	2007	NUM
ejpam-4691	384	9	.	.	PUNCT
ejpam-4691	385	1	[	[	X
ejpam-4691	385	2	22	22	NUM
ejpam-4691	385	3	]	]	PUNCT
ejpam-4691	385	4	t.	t.	PROPN
ejpam-4691	385	5	noiri	noiri	PROPN
ejpam-4691	385	6	and	and	CCONJ
ejpam-4691	385	7	v.	v.	ADP
ejpam-4691	385	8	popa	popa	NOUN
ejpam-4691	385	9	.	.	PUNCT
ejpam-4691	386	1	on	on	ADP
ejpam-4691	386	2	some	some	DET
ejpam-4691	386	3	forms	form	NOUN
ejpam-4691	386	4	of	of	ADP
ejpam-4691	386	5	open	open	ADJ
ejpam-4691	386	6	functions	function	NOUN
ejpam-4691	386	7	in	in	ADP
ejpam-4691	386	8	ideal	ideal	ADJ
ejpam-4691	386	9	topological	topological	ADJ
ejpam-4691	386	10	spaces	space	NOUN
ejpam-4691	386	11	.	.	PUNCT
ejpam-4691	387	1	sci	sci	PROPN
ejpam-4691	387	2	.	.	PROPN
ejpam-4691	387	3	stud	stud	PROPN
ejpam-4691	387	4	.	.	PUNCT
ejpam-4691	388	1	res	re	NOUN
ejpam-4691	388	2	.	.	PUNCT
ejpam-4691	388	3	ser	ser	PROPN
ejpam-4691	388	4	.	.	PROPN
ejpam-4691	388	5	math	math	PROPN
ejpam-4691	388	6	.	.	PUNCT
ejpam-4691	389	1	inform	inform	NOUN
ejpam-4691	389	2	.	.	PUNCT
ejpam-4691	389	3	,	,	PUNCT
ejpam-4691	389	4	29(1):103–112	29(1):103–112	PROPN
ejpam-4691	389	5	,	,	PUNCT
ejpam-4691	389	6	2019	2019	NUM
ejpam-4691	389	7	.	.	PUNCT
ejpam-4691	390	1	[	[	X
ejpam-4691	390	2	23	23	NUM
ejpam-4691	390	3	]	]	PUNCT
ejpam-4691	390	4	v.	v.	CCONJ
ejpam-4691	390	5	popa	popa	NOUN
ejpam-4691	390	6	,	,	PUNCT
ejpam-4691	390	7	y.	y.	PROPN
ejpam-4691	390	8	küçük	küçük	PROPN
ejpam-4691	390	9	,	,	PUNCT
ejpam-4691	390	10	and	and	CCONJ
ejpam-4691	390	11	t.	t.	PROPN
ejpam-4691	390	12	noiri	noiri	PROPN
ejpam-4691	390	13	.	.	PUNCT
ejpam-4691	391	1	on	on	ADP
ejpam-4691	391	2	upper	upper	ADJ
ejpam-4691	391	3	and	and	CCONJ
ejpam-4691	391	4	lower	low	ADJ
ejpam-4691	391	5	preirresolute	preirresolute	PROPN
ejpam-4691	391	6	multifunctions	multifunction	NOUN
ejpam-4691	391	7	.	.	PUNCT
ejpam-4691	392	1	pure	pure	ADJ
ejpam-4691	392	2	appl	appl	PROPN
ejpam-4691	392	3	.	.	PUNCT
ejpam-4691	392	4	math	math	PROPN
ejpam-4691	392	5	.	.	PUNCT
ejpam-4691	393	1	sci	sci	PROPN
ejpam-4691	393	2	.	.	PROPN
ejpam-4691	393	3	,	,	PUNCT
ejpam-4691	393	4	44:5–16	44:5–16	PROPN
ejpam-4691	393	5	,	,	PUNCT
ejpam-4691	393	6	1997	1997	NUM
ejpam-4691	393	7	.	.	PUNCT
ejpam-4691	394	1	references	reference	NOUN
ejpam-4691	394	2	439	439	NUM
ejpam-4691	395	1	[	[	X
ejpam-4691	395	2	24	24	NUM
ejpam-4691	395	3	]	]	PUNCT
ejpam-4691	395	4	v.	v.	CCONJ
ejpam-4691	395	5	popa	popa	NOUN
ejpam-4691	395	6	and	and	CCONJ
ejpam-4691	395	7	t.	t.	PROPN
ejpam-4691	395	8	noiri	noiri	PROPN
ejpam-4691	395	9	.	.	PUNCT
ejpam-4691	396	1	on	on	ADP
ejpam-4691	396	2	m	m	PROPN
ejpam-4691	396	3	-continuous	-continuous	ADJ
ejpam-4691	396	4	functions	function	NOUN
ejpam-4691	396	5	.	.	PUNCT
ejpam-4691	397	1	anal	anal	PROPN
ejpam-4691	397	2	.	.	PUNCT
ejpam-4691	397	3	univ	univ	PROPN
ejpam-4691	397	4	.	.	PUNCT
ejpam-4691	397	5	”	"	PUNCT
ejpam-4691	397	6	dunǎrea	dunǎrea	PROPN
ejpam-4691	397	7	de	de	X
ejpam-4691	397	8	jos	jos	PROPN
ejpam-4691	397	9	”	"	PUNCT
ejpam-4691	397	10	,	,	PUNCT
ejpam-4691	397	11	galaţi	galaţi	ADJ
ejpam-4691	397	12	,	,	PUNCT
ejpam-4691	397	13	ser	ser	NOUN
ejpam-4691	397	14	.	.	PROPN
ejpam-4691	398	1	mat	mat	PROPN
ejpam-4691	398	2	.	.	PUNCT
ejpam-4691	398	3	fiz	fiz	PROPN
ejpam-4691	398	4	.	.	PUNCT
ejpam-4691	399	1	mec	mec	PROPN
ejpam-4691	399	2	.	.	PROPN
ejpam-4691	399	3	teor	teor	PROPN
ejpam-4691	399	4	.	.	PROPN
ejpam-4691	399	5	,	,	PUNCT
ejpam-4691	399	6	18	18	NUM
ejpam-4691	399	7	(	(	PUNCT
ejpam-4691	399	8	23):31–41	23):31–41	NUM
ejpam-4691	399	9	,	,	PUNCT
ejpam-4691	399	10	2000	2000	NUM
ejpam-4691	399	11	.	.	PUNCT
ejpam-4691	400	1	[	[	X
ejpam-4691	400	2	25	25	NUM
ejpam-4691	400	3	]	]	PUNCT
ejpam-4691	400	4	v.	v.	CCONJ
ejpam-4691	400	5	popa	popa	NOUN
ejpam-4691	400	6	and	and	CCONJ
ejpam-4691	400	7	t.	t.	PROPN
ejpam-4691	400	8	noiri	noiri	PROPN
ejpam-4691	400	9	.	.	PUNCT
ejpam-4691	401	1	on	on	ADP
ejpam-4691	401	2	the	the	DET
ejpam-4691	401	3	definitions	definition	NOUN
ejpam-4691	401	4	of	of	ADP
ejpam-4691	401	5	some	some	DET
ejpam-4691	401	6	generalized	generalized	ADJ
ejpam-4691	401	7	forms	form	NOUN
ejpam-4691	401	8	of	of	ADP
ejpam-4691	401	9	continuity	continuity	NOUN
ejpam-4691	401	10	under	under	ADP
ejpam-4691	401	11	minimal	minimal	ADJ
ejpam-4691	401	12	conditions	condition	NOUN
ejpam-4691	401	13	.	.	PUNCT
ejpam-4691	402	1	mem	mem	PROPN
ejpam-4691	402	2	.	.	PUNCT
ejpam-4691	402	3	fac	fac	PROPN
ejpam-4691	402	4	.	.	PUNCT
ejpam-4691	403	1	sci	sci	PROPN
ejpam-4691	403	2	.	.	PROPN
ejpam-4691	403	3	kochi	kochi	PROPN
ejpam-4691	403	4	univ	univ	PROPN
ejpam-4691	403	5	.	.	PUNCT
ejpam-4691	404	1	ser	ser	PROPN
ejpam-4691	404	2	.	.	PUNCT
ejpam-4691	405	1	a	a	DET
ejpam-4691	405	2	math	math	NOUN
ejpam-4691	405	3	.	.	PUNCT
ejpam-4691	405	4	,	,	PUNCT
ejpam-4691	405	5	22:9–18	22:9–18	NUM
ejpam-4691	405	6	,	,	PUNCT
ejpam-4691	405	7	2001	2001	NUM
ejpam-4691	405	8	.	.	PUNCT
ejpam-4691	406	1	[	[	X
ejpam-4691	406	2	26	26	NUM
ejpam-4691	406	3	]	]	PUNCT
ejpam-4691	406	4	v.	v.	CCONJ
ejpam-4691	406	5	popa	popa	NOUN
ejpam-4691	406	6	and	and	CCONJ
ejpam-4691	406	7	t.	t.	PROPN
ejpam-4691	406	8	noiri	noiri	PROPN
ejpam-4691	406	9	.	.	PUNCT
ejpam-4691	407	1	a	a	DET
ejpam-4691	407	2	unified	unified	ADJ
ejpam-4691	407	3	theory	theory	NOUN
ejpam-4691	407	4	of	of	ADP
ejpam-4691	407	5	weak	weak	ADJ
ejpam-4691	407	6	continuity	continuity	NOUN
ejpam-4691	407	7	for	for	ADP
ejpam-4691	407	8	functions	function	NOUN
ejpam-4691	407	9	.	.	PUNCT
ejpam-4691	408	1	rend	rend	VERB
ejpam-4691	408	2	.	.	PUNCT
ejpam-4691	409	1	circ	circ	PROPN
ejpam-4691	409	2	.	.	PUNCT
ejpam-4691	410	1	mat	mat	PROPN
ejpam-4691	410	2	.	.	PUNCT
ejpam-4691	410	3	palermo	palermo	PROPN
ejpam-4691	410	4	(	(	PUNCT
ejpam-4691	410	5	2	2	NUM
ejpam-4691	410	6	)	)	PUNCT
ejpam-4691	410	7	,	,	PUNCT
ejpam-4691	410	8	51:439–464	51:439–464	PROPN
ejpam-4691	410	9	,	,	PUNCT
ejpam-4691	410	10	2002	2002	NUM
ejpam-4691	410	11	.	.	PUNCT
ejpam-4691	411	1	[	[	X
ejpam-4691	411	2	27	27	NUM
ejpam-4691	411	3	]	]	X
ejpam-4691	411	4	r.	r.	PROPN
ejpam-4691	411	5	vaidyanathaswani	vaidyanathaswani	PROPN
ejpam-4691	411	6	.	.	PUNCT
ejpam-4691	412	1	the	the	DET
ejpam-4691	412	2	localization	localization	NOUN
ejpam-4691	412	3	theory	theory	NOUN
ejpam-4691	412	4	in	in	ADP
ejpam-4691	412	5	set	set	NOUN
ejpam-4691	412	6	-	-	PUNCT
ejpam-4691	412	7	topology	topology	NOUN
ejpam-4691	412	8	.	.	PUNCT
ejpam-4691	413	1	proc	proc	PROPN
ejpam-4691	413	2	.	.	PUNCT
ejpam-4691	414	1	indian	indian	PROPN
ejpam-4691	414	2	acad	acad	PROPN
ejpam-4691	414	3	.	.	PUNCT
ejpam-4691	415	1	sci	sci	PROPN
ejpam-4691	415	2	.	.	PROPN
ejpam-4691	415	3	,	,	PUNCT
ejpam-4691	415	4	20:51–61	20:51–61	NUM
ejpam-4691	415	5	,	,	PUNCT
ejpam-4691	415	6	1945	1945	NUM
ejpam-4691	415	7	.	.	PUNCT