id	sid	tid	token	lemma	pos
ejpam-5531	1	1	european	european	PROPN
ejpam-5531	1	2	journal	journal	PROPN
ejpam-5531	1	3	of	of	ADP
ejpam-5531	1	4	pure	pure	ADJ
ejpam-5531	1	5	and	and	CCONJ
ejpam-5531	1	6	applied	apply	VERB
ejpam-5531	1	7	mathematics	mathematic	NOUN
ejpam-5531	1	8	vol	vol	NOUN
ejpam-5531	1	9	.	.	PROPN
ejpam-5531	2	1	17	17	NUM
ejpam-5531	2	2	,	,	PUNCT
ejpam-5531	2	3	no	no	INTJ
ejpam-5531	2	4	.	.	NOUN
ejpam-5531	2	5	4	4	NUM
ejpam-5531	2	6	,	,	PUNCT
ejpam-5531	2	7	2024	2024	NUM
ejpam-5531	2	8	,	,	PUNCT
ejpam-5531	2	9	3677	3677	NUM
ejpam-5531	2	10	-	-	SYM
ejpam-5531	2	11	3686	3686	NUM
ejpam-5531	2	12	issn	issn	PROPN
ejpam-5531	2	13	1307	1307	NUM
ejpam-5531	2	14	-	-	SYM
ejpam-5531	2	15	5543	5543	NUM
ejpam-5531	2	16	–	–	PUNCT
ejpam-5531	3	1	ejpam.com	ejpam.com	X
ejpam-5531	3	2	published	publish	VERB
ejpam-5531	3	3	by	by	ADP
ejpam-5531	3	4	new	new	PROPN
ejpam-5531	3	5	york	york	PROPN
ejpam-5531	3	6	business	business	PROPN
ejpam-5531	3	7	global	global	PROPN
ejpam-5531	3	8	upper	upper	ADJ
ejpam-5531	3	9	and	and	CCONJ
ejpam-5531	3	10	lower	low	ADJ
ejpam-5531	3	11	rarely	rarely	ADV
ejpam-5531	3	12	m	m	VERB
ejpam-5531	3	13	-	-	ADJ
ejpam-5531	3	14	i	i	ADV
ejpam-5531	3	15	-	-	PUNCT
ejpam-5531	3	16	continuous	continuous	ADJ
ejpam-5531	3	17	multifunctions	multifunction	NOUN
ejpam-5531	3	18	takashi	takashi	PROPN
ejpam-5531	3	19	noiri1	noiri1	PROPN
ejpam-5531	3	20	,	,	PUNCT
ejpam-5531	3	21	valeriu	valeriu	PROPN
ejpam-5531	3	22	popa2	popa2	NOUN
ejpam-5531	3	23	1	1	NUM
ejpam-5531	3	24	2949	2949	NUM
ejpam-5531	3	25	-	-	SYM
ejpam-5531	3	26	1	1	NUM
ejpam-5531	3	27	shiokita	shiokita	NOUN
ejpam-5531	3	28	-	-	PUNCT
ejpam-5531	3	29	cho	cho	ADJ
ejpam-5531	3	30	,	,	PUNCT
ejpam-5531	3	31	hinagu	hinagu	ADJ
ejpam-5531	3	32	,	,	PUNCT
ejpam-5531	3	33	yatsushiro	yatsushiro	PROPN
ejpam-5531	3	34	-	-	PUNCT
ejpam-5531	3	35	shi	shi	PROPN
ejpam-5531	3	36	,	,	PUNCT
ejpam-5531	3	37	kumamoto	kumamoto	PROPN
ejpam-5531	3	38	-	-	PUNCT
ejpam-5531	3	39	ken	ken	PROPN
ejpam-5531	3	40	,	,	PUNCT
ejpam-5531	3	41	869	869	NUM
ejpam-5531	3	42	-	-	SYM
ejpam-5531	3	43	5142	5142	NUM
ejpam-5531	3	44	japan	japan	PROPN
ejpam-5531	3	45	2	2	NUM
ejpam-5531	3	46	department	department	NOUN
ejpam-5531	3	47	of	of	ADP
ejpam-5531	3	48	mathematics	mathematic	NOUN
ejpam-5531	3	49	and	and	CCONJ
ejpam-5531	3	50	informatics	informatic	NOUN
ejpam-5531	3	51	,	,	PUNCT
ejpam-5531	3	52	“	"	PUNCT
ejpam-5531	3	53	vasile	vasile	NOUN
ejpam-5531	3	54	alecsandri	alecsandri	NOUN
ejpam-5531	3	55	”	"	PUNCT
ejpam-5531	3	56	university	university	NOUN
ejpam-5531	3	57	of	of	ADP
ejpam-5531	3	58	bacǎu	bacǎu	PROPN
ejpam-5531	3	59	,	,	PUNCT
ejpam-5531	3	60	calea	calea	PROPN
ejpam-5531	3	61	marasesti	marasesti	NOUN
ejpam-5531	3	62	157	157	NUM
ejpam-5531	3	63	,	,	PUNCT
ejpam-5531	3	64	bacǎu	bacǎu	PROPN
ejpam-5531	3	65	,	,	PUNCT
ejpam-5531	3	66	600115	600115	NUM
ejpam-5531	3	67	,	,	PUNCT
ejpam-5531	3	68	romania	romania	PROPN
ejpam-5531	3	69	abstract	abstract	NOUN
ejpam-5531	3	70	.	.	PUNCT
ejpam-5531	4	1	in	in	ADP
ejpam-5531	4	2	1979	1979	NUM
ejpam-5531	4	3	,	,	PUNCT
ejpam-5531	4	4	popa	popa	NOUN
ejpam-5531	4	5	[	[	X
ejpam-5531	4	6	24	24	NUM
ejpam-5531	4	7	]	]	PUNCT
ejpam-5531	4	8	first	first	ADV
ejpam-5531	4	9	introduced	introduce	VERB
ejpam-5531	4	10	rarely	rarely	ADV
ejpam-5531	4	11	continuous	continuous	ADJ
ejpam-5531	4	12	functions	function	NOUN
ejpam-5531	4	13	.	.	PUNCT
ejpam-5531	5	1	in	in	ADP
ejpam-5531	5	2	this	this	DET
ejpam-5531	5	3	paper	paper	NOUN
ejpam-5531	5	4	,	,	PUNCT
ejpam-5531	5	5	we	we	PRON
ejpam-5531	5	6	introduce	introduce	VERB
ejpam-5531	5	7	upper	upper	ADJ
ejpam-5531	5	8	and	and	CCONJ
ejpam-5531	5	9	lower	low	ADJ
ejpam-5531	5	10	rarely	rarely	ADV
ejpam-5531	5	11	m	m	ADJ
ejpam-5531	5	12	-	-	ADJ
ejpam-5531	5	13	continuous	continuous	ADJ
ejpam-5531	5	14	multifunctions	multifunction	NOUN
ejpam-5531	5	15	.	.	PUNCT
ejpam-5531	6	1	moreover	moreover	ADV
ejpam-5531	6	2	,	,	PUNCT
ejpam-5531	6	3	we	we	PRON
ejpam-5531	6	4	extend	extend	VERB
ejpam-5531	6	5	this	this	DET
ejpam-5531	6	6	concept	concept	NOUN
ejpam-5531	6	7	to	to	ADP
ejpam-5531	6	8	a	a	DET
ejpam-5531	6	9	multifunction	multifunction	NOUN
ejpam-5531	6	10	f	f	NOUN
ejpam-5531	6	11	:	:	PUNCT
ejpam-5531	6	12	(	(	PUNCT
ejpam-5531	6	13	x	x	X
ejpam-5531	6	14	,	,	PUNCT
ejpam-5531	6	15	τ	τ	PROPN
ejpam-5531	6	16	,	,	PUNCT
ejpam-5531	6	17	i	i	NOUN
ejpam-5531	6	18	)	)	PUNCT
ejpam-5531	6	19	→	→	SYM
ejpam-5531	6	20	(	(	PUNCT
ejpam-5531	6	21	y	y	PROPN
ejpam-5531	6	22	,	,	PUNCT
ejpam-5531	6	23	σ	σ	PROPN
ejpam-5531	6	24	)	)	PUNCT
ejpam-5531	6	25	,	,	PUNCT
ejpam-5531	6	26	where	where	SCONJ
ejpam-5531	6	27	(	(	PUNCT
ejpam-5531	6	28	x	x	X
ejpam-5531	6	29	,	,	PUNCT
ejpam-5531	6	30	τ	τ	PROPN
ejpam-5531	6	31	,	,	PUNCT
ejpam-5531	6	32	i	i	PROPN
ejpam-5531	6	33	)	)	PUNCT
ejpam-5531	6	34	is	be	AUX
ejpam-5531	6	35	an	an	DET
ejpam-5531	6	36	ideal	ideal	ADJ
ejpam-5531	6	37	topologiccal	topologiccal	ADJ
ejpam-5531	6	38	space	space	NOUN
ejpam-5531	6	39	.	.	PUNCT
ejpam-5531	7	1	2020	2020	NUM
ejpam-5531	7	2	mathematics	mathematic	NOUN
ejpam-5531	7	3	subject	subject	NOUN
ejpam-5531	7	4	classifications	classification	NOUN
ejpam-5531	7	5	:	:	PUNCT
ejpam-5531	7	6	54c08	54c08	NUM
ejpam-5531	7	7	,	,	PUNCT
ejpam-5531	7	8	54c60	54c60	NUM
ejpam-5531	7	9	key	key	ADJ
ejpam-5531	7	10	words	word	NOUN
ejpam-5531	7	11	and	and	CCONJ
ejpam-5531	7	12	phrases	phrase	NOUN
ejpam-5531	7	13	:	:	PUNCT
ejpam-5531	7	14	rare	rare	ADJ
ejpam-5531	7	15	set	set	NOUN
ejpam-5531	7	16	,	,	PUNCT
ejpam-5531	7	17	m	m	NOUN
ejpam-5531	7	18	-	-	ADJ
ejpam-5531	7	19	open	open	ADJ
ejpam-5531	7	20	,	,	PUNCT
ejpam-5531	7	21	m	m	NOUN
ejpam-5531	7	22	-	-	NOUN
ejpam-5531	7	23	structure	structure	NOUN
ejpam-5531	7	24	,	,	PUNCT
ejpam-5531	7	25	mio(x	mio(x	PROPN
ejpam-5531	7	26	)	)	PUNCT
ejpam-5531	7	27	,	,	PUNCT
ejpam-5531	7	28	ideal	ideal	ADJ
ejpam-5531	7	29	topological	topological	ADJ
ejpam-5531	7	30	space	space	NOUN
ejpam-5531	7	31	,	,	PUNCT
ejpam-5531	7	32	rarely	rarely	ADV
ejpam-5531	7	33	continuous	continuous	ADJ
ejpam-5531	7	34	function	function	NOUN
ejpam-5531	7	35	,	,	PUNCT
ejpam-5531	7	36	upper	upper	ADJ
ejpam-5531	7	37	/	/	SYM
ejpam-5531	7	38	lower	low	ADJ
ejpam-5531	7	39	rarely	rarely	ADV
ejpam-5531	7	40	m	m	VERB
ejpam-5531	7	41	-	-	PUNCT
ejpam-5531	7	42	i	i	ADV
ejpam-5531	7	43	-	-	PUNCT
ejpam-5531	7	44	continuous	continuous	ADJ
ejpam-5531	7	45	,	,	PUNCT
ejpam-5531	7	46	multifunction	multifunction	NOUN
ejpam-5531	7	47	1	1	NUM
ejpam-5531	7	48	.	.	PUNCT
ejpam-5531	8	1	introduction	introduction	NOUN
ejpam-5531	8	2	semi	semi	ADJ
ejpam-5531	8	3	-	-	ADJ
ejpam-5531	8	4	open	open	ADJ
ejpam-5531	8	5	sets	set	NOUN
ejpam-5531	8	6	,	,	PUNCT
ejpam-5531	8	7	preopen	preopen	ADJ
ejpam-5531	8	8	sets	set	NOUN
ejpam-5531	8	9	,	,	PUNCT
ejpam-5531	8	10	α	α	NOUN
ejpam-5531	8	11	-	-	ADJ
ejpam-5531	8	12	open	open	ADJ
ejpam-5531	8	13	sets	set	NOUN
ejpam-5531	8	14	,	,	PUNCT
ejpam-5531	8	15	β	β	X
ejpam-5531	8	16	-	-	ADJ
ejpam-5531	8	17	open	open	ADJ
ejpam-5531	8	18	set	set	NOUN
ejpam-5531	8	19	and	and	CCONJ
ejpam-5531	8	20	b	b	NOUN
ejpam-5531	8	21	-	-	PUNCT
ejpam-5531	8	22	open	open	ADJ
ejpam-5531	8	23	sets	set	NOUN
ejpam-5531	8	24	play	play	VERB
ejpam-5531	8	25	an	an	DET
ejpam-5531	8	26	important	important	ADJ
ejpam-5531	8	27	part	part	NOUN
ejpam-5531	8	28	in	in	ADP
ejpam-5531	8	29	the	the	DET
ejpam-5531	8	30	research	research	NOUN
ejpam-5531	8	31	of	of	ADP
ejpam-5531	8	32	generalizations	generalization	NOUN
ejpam-5531	8	33	of	of	ADP
ejpam-5531	8	34	continuous	continuous	ADJ
ejpam-5531	8	35	functions	function	NOUN
ejpam-5531	8	36	.	.	PUNCT
ejpam-5531	9	1	by	by	ADP
ejpam-5531	9	2	using	use	VERB
ejpam-5531	9	3	these	these	DET
ejpam-5531	9	4	notions	notion	NOUN
ejpam-5531	9	5	,	,	PUNCT
ejpam-5531	9	6	various	various	ADJ
ejpam-5531	9	7	types	type	NOUN
ejpam-5531	9	8	of	of	ADP
ejpam-5531	9	9	continuous	continuous	ADJ
ejpam-5531	9	10	multifunctions	multifunction	NOUN
ejpam-5531	9	11	are	be	AUX
ejpam-5531	9	12	introduced	introduce	VERB
ejpam-5531	9	13	and	and	CCONJ
ejpam-5531	9	14	studied	study	VERB
ejpam-5531	9	15	.	.	PUNCT
ejpam-5531	10	1	as	as	ADP
ejpam-5531	10	2	an	an	DET
ejpam-5531	10	3	unified	unified	ADJ
ejpam-5531	10	4	form	form	NOUN
ejpam-5531	10	5	of	of	ADP
ejpam-5531	10	6	the	the	DET
ejpam-5531	10	7	above	above	ADJ
ejpam-5531	10	8	generalizations	generalization	NOUN
ejpam-5531	10	9	of	of	ADP
ejpam-5531	10	10	open	open	ADJ
ejpam-5531	10	11	sets	set	NOUN
ejpam-5531	10	12	,	,	PUNCT
ejpam-5531	10	13	in	in	ADP
ejpam-5531	10	14	[	[	X
ejpam-5531	10	15	27	27	NUM
ejpam-5531	10	16	]	]	PUNCT
ejpam-5531	10	17	and	and	CCONJ
ejpam-5531	10	18	[	[	X
ejpam-5531	10	19	28	28	NUM
ejpam-5531	10	20	]	]	X
ejpam-5531	10	21	the	the	DET
ejpam-5531	10	22	present	present	ADJ
ejpam-5531	10	23	authors	author	NOUN
ejpam-5531	10	24	introduced	introduce	VERB
ejpam-5531	10	25	minimal	minimal	ADJ
ejpam-5531	10	26	structures	structure	NOUN
ejpam-5531	10	27	and	and	CCONJ
ejpam-5531	10	28	m	m	NOUN
ejpam-5531	10	29	-	-	NOUN
ejpam-5531	10	30	spaces	space	NOUN
ejpam-5531	10	31	.	.	PUNCT
ejpam-5531	11	1	we	we	PRON
ejpam-5531	11	2	recall	recall	VERB
ejpam-5531	11	3	the	the	DET
ejpam-5531	11	4	notions	notion	NOUN
ejpam-5531	11	5	in	in	ADP
ejpam-5531	11	6	the	the	DET
ejpam-5531	11	7	section	section	NOUN
ejpam-5531	11	8	2	2	NUM
ejpam-5531	11	9	.	.	PUNCT
ejpam-5531	12	1	in	in	ADP
ejpam-5531	12	2	1979	1979	NUM
ejpam-5531	12	3	,	,	PUNCT
ejpam-5531	12	4	popa	popa	NOUN
ejpam-5531	12	5	[	[	X
ejpam-5531	12	6	24	24	NUM
ejpam-5531	12	7	]	]	PUNCT
ejpam-5531	12	8	first	first	ADV
ejpam-5531	12	9	introduced	introduce	VERB
ejpam-5531	12	10	the	the	DET
ejpam-5531	12	11	concept	concept	NOUN
ejpam-5531	12	12	of	of	ADP
ejpam-5531	12	13	rare	rare	ADJ
ejpam-5531	12	14	continuity	continuity	NOUN
ejpam-5531	12	15	which	which	PRON
ejpam-5531	12	16	was	be	AUX
ejpam-5531	12	17	further	far	ADV
ejpam-5531	12	18	studied	study	VERB
ejpam-5531	12	19	by	by	ADP
ejpam-5531	12	20	long	long	ADV
ejpam-5531	12	21	and	and	CCONJ
ejpam-5531	12	22	herrington	herrington	PROPN
ejpam-5531	13	1	[	[	X
ejpam-5531	13	2	19	19	NUM
ejpam-5531	13	3	]	]	PUNCT
ejpam-5531	13	4	and	and	CCONJ
ejpam-5531	13	5	jafari	jafari	ADJ
ejpam-5531	14	1	[	[	X
ejpam-5531	14	2	10	10	NUM
ejpam-5531	14	3	]	]	PUNCT
ejpam-5531	14	4	,	,	PUNCT
ejpam-5531	15	1	[	[	X
ejpam-5531	15	2	11	11	NUM
ejpam-5531	15	3	]	]	PUNCT
ejpam-5531	15	4	.	.	PUNCT
ejpam-5531	16	1	several	several	ADJ
ejpam-5531	16	2	weak	weak	ADJ
ejpam-5531	16	3	forms	form	NOUN
ejpam-5531	16	4	of	of	ADP
ejpam-5531	16	5	rarely	rarely	ADV
ejpam-5531	16	6	continuous	continuous	ADJ
ejpam-5531	16	7	functions	function	NOUN
ejpam-5531	16	8	,	,	PUNCT
ejpam-5531	16	9	for	for	ADP
ejpam-5531	16	10	example	example	NOUN
ejpam-5531	16	11	,	,	PUNCT
ejpam-5531	16	12	rare	rare	ADJ
ejpam-5531	16	13	quasi	quasi	NOUN
ejpam-5531	16	14	-	-	NOUN
ejpam-5531	16	15	continuity	continuity	NOUN
ejpam-5531	16	16	[	[	X
ejpam-5531	16	17	26	26	NUM
ejpam-5531	16	18	]	]	PUNCT
ejpam-5531	16	19	,	,	PUNCT
ejpam-5531	16	20	rare	rare	ADJ
ejpam-5531	16	21	α	α	NOUN
ejpam-5531	16	22	-	-	NOUN
ejpam-5531	16	23	continuity	continuity	NOUN
ejpam-5531	16	24	[	[	X
ejpam-5531	16	25	13	13	NUM
ejpam-5531	16	26	]	]	PUNCT
ejpam-5531	16	27	,	,	PUNCT
ejpam-5531	16	28	rare	rare	ADJ
ejpam-5531	16	29	pre	pre	NOUN
ejpam-5531	16	30	-	-	NOUN
ejpam-5531	16	31	continuity	continuity	NOUN
ejpam-5531	16	32	[	[	X
ejpam-5531	16	33	12	12	NUM
ejpam-5531	16	34	]	]	PUNCT
ejpam-5531	16	35	etc	etc	X
ejpam-5531	16	36	have	have	AUX
ejpam-5531	16	37	been	be	AUX
ejpam-5531	16	38	introduced	introduce	VERB
ejpam-5531	16	39	and	and	CCONJ
ejpam-5531	16	40	studied	study	VERB
ejpam-5531	16	41	.	.	PUNCT
ejpam-5531	17	1	moreover	moreover	ADV
ejpam-5531	17	2	these	these	DET
ejpam-5531	17	3	concepts	concept	NOUN
ejpam-5531	17	4	are	be	AUX
ejpam-5531	17	5	extended	extend	VERB
ejpam-5531	17	6	to	to	ADP
ejpam-5531	17	7	multifunctions	multifunction	NOUN
ejpam-5531	17	8	:	:	PUNCT
ejpam-5531	18	1	rare	rare	ADJ
ejpam-5531	18	2	continuity	continuity	NOUN
ejpam-5531	18	3	[	[	X
ejpam-5531	18	4	25	25	NUM
ejpam-5531	18	5	]	]	PUNCT
ejpam-5531	18	6	,	,	PUNCT
ejpam-5531	18	7	rare	rare	ADJ
ejpam-5531	18	8	quasi	quasi	NOUN
ejpam-5531	18	9	-	-	NOUN
ejpam-5531	18	10	continuity	continuity	NOUN
ejpam-5531	18	11	[	[	X
ejpam-5531	18	12	15	15	NUM
ejpam-5531	18	13	]	]	PUNCT
ejpam-5531	18	14	,	,	PUNCT
ejpam-5531	18	15	rare	rare	ADJ
ejpam-5531	18	16	α	α	NOUN
ejpam-5531	18	17	-	-	NOUN
ejpam-5531	18	18	continuity	continuity	NOUN
ejpam-5531	18	19	[	[	X
ejpam-5531	18	20	4	4	NUM
ejpam-5531	18	21	]	]	PUNCT
ejpam-5531	18	22	,	,	PUNCT
ejpam-5531	18	23	rare	rare	ADJ
ejpam-5531	18	24	β	β	NOUN
ejpam-5531	18	25	-	-	NOUN
ejpam-5531	18	26	continuity	continuity	NOUN
ejpam-5531	18	27	[	[	X
ejpam-5531	18	28	14	14	NUM
ejpam-5531	18	29	]	]	PUNCT
ejpam-5531	18	30	.	.	PUNCT
ejpam-5531	19	1	the	the	DET
ejpam-5531	19	2	purpose	purpose	NOUN
ejpam-5531	19	3	of	of	ADP
ejpam-5531	19	4	this	this	DET
ejpam-5531	19	5	paper	paper	NOUN
ejpam-5531	19	6	is	be	AUX
ejpam-5531	19	7	to	to	PART
ejpam-5531	19	8	introduce	introduce	VERB
ejpam-5531	19	9	the	the	DET
ejpam-5531	19	10	concept	concept	NOUN
ejpam-5531	19	11	of	of	ADP
ejpam-5531	19	12	upper	upper	ADJ
ejpam-5531	19	13	and	and	CCONJ
ejpam-5531	19	14	lower	low	ADJ
ejpam-5531	19	15	rarely	rarely	ADV
ejpam-5531	19	16	mcontinuous	mcontinuous	ADJ
ejpam-5531	19	17	multifunctions	multifunction	NOUN
ejpam-5531	19	18	which	which	PRON
ejpam-5531	19	19	unifies	unify	VERB
ejpam-5531	19	20	the	the	DET
ejpam-5531	19	21	above	above	ADJ
ejpam-5531	19	22	stated	stated	ADJ
ejpam-5531	19	23	multifunctions	multifunction	NOUN
ejpam-5531	19	24	,	,	PUNCT
ejpam-5531	19	25	that	that	ADV
ejpam-5531	19	26	is	is	ADV
ejpam-5531	19	27	,	,	PUNCT
ejpam-5531	19	28	rare	rare	ADJ
ejpam-5531	19	29	quasi	quasi	NOUN
ejpam-5531	19	30	-	-	NOUN
ejpam-5531	19	31	continuity	continuity	NOUN
ejpam-5531	19	32	,	,	PUNCT
ejpam-5531	19	33	rare	rare	ADJ
ejpam-5531	19	34	pre	pre	NOUN
ejpam-5531	19	35	-	-	NOUN
ejpam-5531	19	36	continuity	continuity	ADJ
ejpam-5531	19	37	,	,	PUNCT
ejpam-5531	19	38	rare	rare	ADJ
ejpam-5531	19	39	α	α	NOUN
ejpam-5531	19	40	-	-	NOUN
ejpam-5531	19	41	continuity	continuity	NOUN
ejpam-5531	19	42	,	,	PUNCT
ejpam-5531	19	43	and	and	CCONJ
ejpam-5531	19	44	rare	rare	ADJ
ejpam-5531	19	45	β	β	NOUN
ejpam-5531	19	46	-	-	NOUN
ejpam-5531	19	47	continuity	continuity	NOUN
ejpam-5531	19	48	.	.	PUNCT
ejpam-5531	20	1	as	as	ADP
ejpam-5531	20	2	generalizations	generalization	NOUN
ejpam-5531	20	3	of	of	ADP
ejpam-5531	20	4	open	open	ADJ
ejpam-5531	20	5	sets	set	NOUN
ejpam-5531	20	6	,	,	PUNCT
ejpam-5531	20	7	the	the	DET
ejpam-5531	20	8	notion	notion	NOUN
ejpam-5531	20	9	of	of	ADP
ejpam-5531	20	10	i	i	NOUN
ejpam-5531	20	11	-	-	PUNCT
ejpam-5531	20	12	open	open	ADJ
ejpam-5531	20	13	sets	set	NOUN
ejpam-5531	20	14	,	,	PUNCT
ejpam-5531	20	15	semi	semi	ADJ
ejpam-5531	20	16	-	-	ADJ
ejpam-5531	20	17	i	i	ADV
ejpam-5531	20	18	-	-	PUNCT
ejpam-5531	20	19	open	open	ADJ
ejpam-5531	20	20	sets	set	NOUN
ejpam-5531	20	21	,	,	PUNCT
ejpam-5531	20	22	pre	pre	ADJ
ejpam-5531	20	23	-	-	ADJ
ejpam-5531	20	24	i	i	PRON
ejpam-5531	20	25	-	-	PUNCT
ejpam-5531	20	26	open	open	ADJ
ejpam-5531	20	27	sets	set	NOUN
ejpam-5531	20	28	,	,	PUNCT
ejpam-5531	20	29	α	α	X
ejpam-5531	20	30	-	-	PUNCT
ejpam-5531	20	31	i	i	NOUN
ejpam-5531	20	32	-	-	PUNCT
ejpam-5531	20	33	open	open	ADJ
ejpam-5531	20	34	sets	set	NOUN
ejpam-5531	20	35	,	,	PUNCT
ejpam-5531	20	36	β	β	X
ejpam-5531	20	37	-	-	ADJ
ejpam-5531	20	38	i	i	NOUN
ejpam-5531	20	39	-	-	PUNCT
ejpam-5531	20	40	open	open	ADJ
ejpam-5531	20	41	sets	set	NOUN
ejpam-5531	20	42	and	and	CCONJ
ejpam-5531	20	43	b	b	X
ejpam-5531	20	44	-	-	PUNCT
ejpam-5531	20	45	i	i	NOUN
ejpam-5531	20	46	-	-	PUNCT
ejpam-5531	20	47	open	open	ADJ
ejpam-5531	20	48	sets	set	NOUN
ejpam-5531	20	49	are	be	AUX
ejpam-5531	20	50	introduced	introduce	VERB
ejpam-5531	20	51	and	and	CCONJ
ejpam-5531	20	52	studied	study	VERB
ejpam-5531	20	53	in	in	ADP
ejpam-5531	20	54	an	an	DET
ejpam-5531	20	55	ideal	ideal	ADJ
ejpam-5531	20	56	topological	topological	ADJ
ejpam-5531	20	57	space	space	NOUN
ejpam-5531	20	58	(	(	PUNCT
ejpam-5531	20	59	x.τ	x.τ	PROPN
ejpam-5531	20	60	,	,	PUNCT
ejpam-5531	20	61	i	i	PROPN
ejpam-5531	20	62	)	)	PUNCT
ejpam-5531	20	63	.	.	PUNCT
ejpam-5531	21	1	in	in	ADP
ejpam-5531	21	2	the	the	DET
ejpam-5531	21	3	last	last	ADJ
ejpam-5531	21	4	section	section	NOUN
ejpam-5531	21	5	,	,	PUNCT
ejpam-5531	21	6	we	we	PRON
ejpam-5531	21	7	extend	extend	VERB
ejpam-5531	21	8	the	the	DET
ejpam-5531	21	9	results	result	NOUN
ejpam-5531	21	10	of	of	ADP
ejpam-5531	21	11	an	an	DET
ejpam-5531	21	12	upper	upper	ADJ
ejpam-5531	21	13	and	and	CCONJ
ejpam-5531	21	14	lower	low	ADJ
ejpam-5531	21	15	rarely	rarely	ADV
ejpam-5531	21	16	doi	doi	ADJ
ejpam-5531	21	17	:	:	PUNCT
ejpam-5531	21	18	https://doi.org/10.29020/nybg.ejpam.v17i4.5531	https://doi.org/10.29020/nybg.ejpam.v17i4.5531	PROPN
ejpam-5531	21	19	email	email	NOUN
ejpam-5531	21	20	addresses	address	VERB
ejpam-5531	21	21	:	:	PUNCT
ejpam-5531	21	22	t.noiri@nifty.com	t.noiri@nifty.com	X
ejpam-5531	21	23	(	(	PUNCT
ejpam-5531	21	24	t.	t.	PROPN
ejpam-5531	21	25	noiri	noiri	PROPN
ejpam-5531	21	26	)	)	PUNCT
ejpam-5531	21	27	,	,	PUNCT
ejpam-5531	21	28	vpopa@ub.ro	vpopa@ub.ro	NOUN
ejpam-5531	21	29	(	(	PUNCT
ejpam-5531	21	30	v.	v.	ADP
ejpam-5531	21	31	popa	popa	NOUN
ejpam-5531	21	32	)	)	PUNCT
ejpam-5531	21	33	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5531	22	1	3677	3677	NUM
ejpam-5531	22	2	copyright	copyright	NOUN
ejpam-5531	22	3	:	:	PUNCT
ejpam-5531	22	4	©	©	PROPN
ejpam-5531	22	5	2024	2024	NUM
ejpam-5531	22	6	the	the	DET
ejpam-5531	22	7	author(s	author(s	NOUN
ejpam-5531	22	8	)	)	PUNCT
ejpam-5531	22	9	.	.	PUNCT
ejpam-5531	23	1	(	(	PUNCT
ejpam-5531	23	2	cc	cc	NOUN
ejpam-5531	23	3	by	by	ADP
ejpam-5531	23	4	-	-	PUNCT
ejpam-5531	23	5	nc	nc	PROPN
ejpam-5531	23	6	4.0	4.0	NUM
ejpam-5531	23	7	)	)	PUNCT
ejpam-5531	23	8	t.	t.	NOUN
ejpam-5531	23	9	noiri	noiri	PROPN
ejpam-5531	23	10	,	,	PUNCT
ejpam-5531	23	11	v.	v.	CCONJ
ejpam-5531	23	12	popa	popa	NOUN
ejpam-5531	23	13	/	/	SYM
ejpam-5531	23	14	eur	eur	PROPN
ejpam-5531	23	15	.	.	PUNCT
ejpam-5531	24	1	j.	j.	PROPN
ejpam-5531	24	2	pure	pure	PROPN
ejpam-5531	24	3	appl	appl	PROPN
ejpam-5531	24	4	.	.	PROPN
ejpam-5531	24	5	math	math	PROPN
ejpam-5531	24	6	,	,	PUNCT
ejpam-5531	24	7	17	17	NUM
ejpam-5531	24	8	(	(	PUNCT
ejpam-5531	24	9	4	4	NUM
ejpam-5531	24	10	)	)	PUNCT
ejpam-5531	24	11	(	(	PUNCT
ejpam-5531	24	12	2024	2024	NUM
ejpam-5531	24	13	)	)	PUNCT
ejpam-5531	24	14	,	,	PUNCT
ejpam-5531	24	15	3677	3677	NUM
ejpam-5531	24	16	-	-	SYM
ejpam-5531	24	17	3686	3686	NUM
ejpam-5531	24	18	3678	3678	NUM
ejpam-5531	24	19	m	m	ADJ
ejpam-5531	24	20	-	-	PUNCT
ejpam-5531	24	21	continuous	continuous	ADJ
ejpam-5531	24	22	multifunction	multifunction	NOUN
ejpam-5531	24	23	f	f	NOUN
ejpam-5531	24	24	:	:	PUNCT
ejpam-5531	24	25	(	(	PUNCT
ejpam-5531	24	26	x	x	X
ejpam-5531	24	27	,	,	PUNCT
ejpam-5531	24	28	m	m	NOUN
ejpam-5531	24	29	)	)	PUNCT
ejpam-5531	24	30	→	→	SYM
ejpam-5531	24	31	(	(	PUNCT
ejpam-5531	24	32	y	y	PROPN
ejpam-5531	24	33	,	,	PUNCT
ejpam-5531	24	34	σ	σ	PROPN
ejpam-5531	24	35	)	)	PUNCT
ejpam-5531	24	36	to	to	ADP
ejpam-5531	24	37	a	a	DET
ejpam-5531	24	38	multifunction	multifunction	NOUN
ejpam-5531	24	39	f	f	NOUN
ejpam-5531	24	40	:	:	PUNCT
ejpam-5531	24	41	(	(	PUNCT
ejpam-5531	24	42	x	x	X
ejpam-5531	24	43	,	,	PUNCT
ejpam-5531	24	44	τ	τ	PROPN
ejpam-5531	24	45	,	,	PUNCT
ejpam-5531	24	46	i	i	NOUN
ejpam-5531	24	47	)	)	PUNCT
ejpam-5531	24	48	→	→	SYM
ejpam-5531	24	49	(	(	PUNCT
ejpam-5531	24	50	y	y	PROPN
ejpam-5531	24	51	,	,	PUNCT
ejpam-5531	24	52	σ	σ	PROPN
ejpam-5531	24	53	)	)	PUNCT
ejpam-5531	24	54	.	.	PUNCT
ejpam-5531	25	1	throughout	throughout	ADP
ejpam-5531	25	2	the	the	DET
ejpam-5531	25	3	present	present	ADJ
ejpam-5531	25	4	paper	paper	NOUN
ejpam-5531	25	5	,	,	PUNCT
ejpam-5531	25	6	(	(	PUNCT
ejpam-5531	25	7	x	x	X
ejpam-5531	25	8	,	,	PUNCT
ejpam-5531	25	9	τ	τ	X
ejpam-5531	25	10	)	)	PUNCT
ejpam-5531	25	11	and	and	CCONJ
ejpam-5531	25	12	(	(	PUNCT
ejpam-5531	25	13	y	y	PROPN
ejpam-5531	25	14	,	,	PUNCT
ejpam-5531	25	15	σ	σ	PROPN
ejpam-5531	25	16	)	)	PUNCT
ejpam-5531	25	17	(	(	PUNCT
ejpam-5531	25	18	briefly	briefly	ADV
ejpam-5531	25	19	x	x	X
ejpam-5531	25	20	and	and	CCONJ
ejpam-5531	25	21	y	y	PROPN
ejpam-5531	25	22	)	)	PUNCT
ejpam-5531	25	23	always	always	ADV
ejpam-5531	25	24	denote	denote	VERB
ejpam-5531	25	25	topological	topological	ADJ
ejpam-5531	25	26	spaces	space	NOUN
ejpam-5531	25	27	and	and	CCONJ
ejpam-5531	25	28	f	f	NOUN
ejpam-5531	25	29	:	:	PUNCT
ejpam-5531	25	30	x	x	X
ejpam-5531	25	31	→	→	SYM
ejpam-5531	25	32	y	y	PROPN
ejpam-5531	25	33	presents	present	VERB
ejpam-5531	25	34	a	a	DET
ejpam-5531	25	35	multivalued	multivalued	ADJ
ejpam-5531	25	36	function	function	NOUN
ejpam-5531	25	37	.	.	PUNCT
ejpam-5531	26	1	for	for	ADP
ejpam-5531	26	2	a	a	DET
ejpam-5531	26	3	multifunction	multifunction	NOUN
ejpam-5531	26	4	f	f	NOUN
ejpam-5531	26	5	:	:	PUNCT
ejpam-5531	26	6	x	x	X
ejpam-5531	26	7	→	→	SYM
ejpam-5531	26	8	y	y	PROPN
ejpam-5531	26	9	,	,	PUNCT
ejpam-5531	26	10	we	we	PRON
ejpam-5531	26	11	shall	shall	AUX
ejpam-5531	26	12	denote	denote	VERB
ejpam-5531	26	13	the	the	DET
ejpam-5531	26	14	upper	upper	ADJ
ejpam-5531	26	15	and	and	CCONJ
ejpam-5531	26	16	lower	low	ADJ
ejpam-5531	26	17	inverse	inverse	NOUN
ejpam-5531	26	18	of	of	ADP
ejpam-5531	26	19	a	a	DET
ejpam-5531	26	20	subset	subset	NOUN
ejpam-5531	26	21	b	b	NOUN
ejpam-5531	26	22	of	of	ADP
ejpam-5531	26	23	a	a	DET
ejpam-5531	26	24	space	space	NOUN
ejpam-5531	26	25	y	y	NOUN
ejpam-5531	26	26	by	by	ADP
ejpam-5531	26	27	f+(b	f+(b	NOUN
ejpam-5531	26	28	)	)	PUNCT
ejpam-5531	26	29	and	and	CCONJ
ejpam-5531	26	30	f−(b	f−(b	NOUN
ejpam-5531	26	31	)	)	PUNCT
ejpam-5531	26	32	,	,	PUNCT
ejpam-5531	26	33	respectively	respectively	ADV
ejpam-5531	26	34	,	,	PUNCT
ejpam-5531	26	35	that	that	PRON
ejpam-5531	26	36	is	be	AUX
ejpam-5531	26	37	f+(b	f+(b	NOUN
ejpam-5531	26	38	)	)	PUNCT
ejpam-5531	26	39	=	=	PRON
ejpam-5531	27	1	{	{	PUNCT
ejpam-5531	27	2	x	x	PUNCT
ejpam-5531	27	3	∈	∈	PROPN
ejpam-5531	27	4	x	x	X
ejpam-5531	27	5	:	:	PUNCT
ejpam-5531	27	6	f	f	X
ejpam-5531	27	7	(	(	PUNCT
ejpam-5531	27	8	x	x	X
ejpam-5531	27	9	)	)	PUNCT
ejpam-5531	27	10	⊂	⊂	PROPN
ejpam-5531	27	11	b	b	X
ejpam-5531	27	12	}	}	PUNCT
ejpam-5531	27	13	and	and	CCONJ
ejpam-5531	27	14	f−(b	f−(b	PROPN
ejpam-5531	27	15	)	)	PUNCT
ejpam-5531	27	16	=	=	PRON
ejpam-5531	27	17	{	{	PUNCT
ejpam-5531	27	18	x	x	PUNCT
ejpam-5531	27	19	∈	∈	PROPN
ejpam-5531	27	20	x	x	X
ejpam-5531	27	21	:	:	PUNCT
ejpam-5531	27	22	f	f	X
ejpam-5531	27	23	(	(	PUNCT
ejpam-5531	27	24	x	x	X
ejpam-5531	27	25	)	)	PUNCT
ejpam-5531	27	26	∩b	∩b	NOUN
ejpam-5531	27	27	̸=	̸=	PROPN
ejpam-5531	27	28	∅	∅	NOUN
ejpam-5531	27	29	}	}	PUNCT
ejpam-5531	27	30	.	.	PUNCT
ejpam-5531	28	1	2	2	X
ejpam-5531	28	2	.	.	X
ejpam-5531	28	3	preliminaries	preliminary	NOUN
ejpam-5531	28	4	let	let	VERB
ejpam-5531	28	5	(	(	PUNCT
ejpam-5531	28	6	x	x	NOUN
ejpam-5531	28	7	,	,	PUNCT
ejpam-5531	28	8	τ	τ	X
ejpam-5531	28	9	)	)	PUNCT
ejpam-5531	28	10	be	be	VERB
ejpam-5531	28	11	a	a	DET
ejpam-5531	28	12	topological	topological	ADJ
ejpam-5531	28	13	space	space	NOUN
ejpam-5531	28	14	and	and	CCONJ
ejpam-5531	28	15	a	a	DET
ejpam-5531	28	16	a	a	DET
ejpam-5531	28	17	subset	subset	NOUN
ejpam-5531	28	18	of	of	ADP
ejpam-5531	28	19	x.	x.	NOUN
ejpam-5531	28	20	the	the	DET
ejpam-5531	28	21	closure	closure	NOUN
ejpam-5531	28	22	of	of	ADP
ejpam-5531	28	23	a	a	PRON
ejpam-5531	28	24	and	and	CCONJ
ejpam-5531	28	25	the	the	DET
ejpam-5531	28	26	interior	interior	NOUN
ejpam-5531	28	27	of	of	ADP
ejpam-5531	28	28	a	a	PRON
ejpam-5531	28	29	are	be	AUX
ejpam-5531	28	30	denoted	denote	VERB
ejpam-5531	28	31	by	by	ADP
ejpam-5531	28	32	cl(a	cl(a	NOUN
ejpam-5531	28	33	)	)	PUNCT
ejpam-5531	28	34	and	and	CCONJ
ejpam-5531	28	35	int(a	int(a	PROPN
ejpam-5531	28	36	)	)	PUNCT
ejpam-5531	28	37	,	,	PUNCT
ejpam-5531	28	38	respectively	respectively	ADV
ejpam-5531	28	39	.	.	PUNCT
ejpam-5531	29	1	a	a	DET
ejpam-5531	29	2	subset	subset	NOUN
ejpam-5531	29	3	a	a	PRON
ejpam-5531	29	4	is	be	AUX
ejpam-5531	29	5	said	say	VERB
ejpam-5531	29	6	to	to	PART
ejpam-5531	29	7	be	be	AUX
ejpam-5531	29	8	regular	regular	ADJ
ejpam-5531	29	9	open	open	ADJ
ejpam-5531	29	10	(	(	PUNCT
ejpam-5531	29	11	resp	resp	NOUN
ejpam-5531	29	12	.	.	PUNCT
ejpam-5531	30	1	regular	regular	ADJ
ejpam-5531	30	2	closed	closed	ADJ
ejpam-5531	30	3	)	)	PUNCT
ejpam-5531	30	4	if	if	SCONJ
ejpam-5531	30	5	int(cl(a	int(cl(a	PROPN
ejpam-5531	30	6	)	)	PUNCT
ejpam-5531	30	7	)	)	PUNCT
ejpam-5531	31	1	=	=	SYM
ejpam-5531	31	2	a	a	PRON
ejpam-5531	31	3	(	(	PUNCT
ejpam-5531	31	4	resp	resp	NOUN
ejpam-5531	31	5	.	.	PUNCT
ejpam-5531	31	6	cl(int(a	cl(int(a	PROPN
ejpam-5531	31	7	)	)	PUNCT
ejpam-5531	31	8	)	)	PUNCT
ejpam-5531	32	1	=	=	PUNCT
ejpam-5531	32	2	a	a	X
ejpam-5531	32	3	)	)	PUNCT
ejpam-5531	32	4	.	.	PUNCT
ejpam-5531	33	1	definition	definition	NOUN
ejpam-5531	33	2	1	1	NUM
ejpam-5531	33	3	.	.	PUNCT
ejpam-5531	34	1	let	let	VERB
ejpam-5531	34	2	(	(	PUNCT
ejpam-5531	34	3	x	x	NOUN
ejpam-5531	34	4	,	,	PUNCT
ejpam-5531	34	5	τ	τ	X
ejpam-5531	34	6	)	)	PUNCT
ejpam-5531	34	7	be	be	VERB
ejpam-5531	34	8	a	a	DET
ejpam-5531	34	9	topological	topological	ADJ
ejpam-5531	34	10	space	space	NOUN
ejpam-5531	34	11	.	.	PUNCT
ejpam-5531	35	1	a	a	DET
ejpam-5531	35	2	subset	subset	NOUN
ejpam-5531	35	3	a	a	PRON
ejpam-5531	35	4	of	of	ADP
ejpam-5531	35	5	x	x	SYM
ejpam-5531	35	6	is	be	AUX
ejpam-5531	35	7	said	say	VERB
ejpam-5531	35	8	to	to	PART
ejpam-5531	35	9	be	be	AUX
ejpam-5531	35	10	(	(	PUNCT
ejpam-5531	35	11	1	1	X
ejpam-5531	35	12	)	)	PUNCT
ejpam-5531	35	13	α	α	NOUN
ejpam-5531	35	14	-	-	NOUN
ejpam-5531	35	15	open	open	ADJ
ejpam-5531	35	16	[	[	X
ejpam-5531	35	17	23	23	NUM
ejpam-5531	35	18	]	]	PUNCT
ejpam-5531	35	19	if	if	SCONJ
ejpam-5531	35	20	a	a	DET
ejpam-5531	35	21	⊂	⊂	X
ejpam-5531	35	22	int(cl(int(a	int(cl(int(a	NOUN
ejpam-5531	35	23	)	)	PUNCT
ejpam-5531	35	24	)	)	PUNCT
ejpam-5531	35	25	)	)	PUNCT
ejpam-5531	35	26	,	,	PUNCT
ejpam-5531	35	27	(	(	PUNCT
ejpam-5531	35	28	2	2	X
ejpam-5531	35	29	)	)	PUNCT
ejpam-5531	35	30	semi	semi	ADJ
ejpam-5531	35	31	-	-	ADJ
ejpam-5531	35	32	open	open	ADJ
ejpam-5531	35	33	[	[	X
ejpam-5531	35	34	18	18	NUM
ejpam-5531	35	35	]	]	PUNCT
ejpam-5531	35	36	if	if	SCONJ
ejpam-5531	35	37	a	a	DET
ejpam-5531	35	38	⊂	⊂	PROPN
ejpam-5531	35	39	cl(int(a	cl(int(a	PROPN
ejpam-5531	35	40	)	)	PUNCT
ejpam-5531	35	41	)	)	PUNCT
ejpam-5531	35	42	,	,	PUNCT
ejpam-5531	35	43	(	(	PUNCT
ejpam-5531	35	44	3	3	X
ejpam-5531	35	45	)	)	PUNCT
ejpam-5531	35	46	preopen	preopen	NOUN
ejpam-5531	36	1	[	[	X
ejpam-5531	36	2	21	21	NUM
ejpam-5531	36	3	]	]	X
ejpam-5531	36	4	if	if	SCONJ
ejpam-5531	36	5	a	a	DET
ejpam-5531	36	6	⊂	⊂	PROPN
ejpam-5531	36	7	int(cl(a	int(cl(a	PROPN
ejpam-5531	36	8	)	)	PUNCT
ejpam-5531	36	9	)	)	PUNCT
ejpam-5531	36	10	,	,	PUNCT
ejpam-5531	36	11	(	(	PUNCT
ejpam-5531	36	12	4	4	X
ejpam-5531	36	13	)	)	PUNCT
ejpam-5531	36	14	β	β	NOUN
ejpam-5531	36	15	-	-	VERB
ejpam-5531	36	16	open	open	ADJ
ejpam-5531	36	17	[	[	X
ejpam-5531	36	18	3	3	NUM
ejpam-5531	36	19	]	]	X
ejpam-5531	36	20	if	if	SCONJ
ejpam-5531	36	21	a	a	DET
ejpam-5531	36	22	⊂	⊂	PROPN
ejpam-5531	36	23	cl(int(cl(a	cl(int(cl(a	NOUN
ejpam-5531	36	24	)	)	PUNCT
ejpam-5531	36	25	)	)	PUNCT
ejpam-5531	36	26	)	)	PUNCT
ejpam-5531	36	27	,	,	PUNCT
ejpam-5531	36	28	(	(	PUNCT
ejpam-5531	36	29	5	5	X
ejpam-5531	36	30	)	)	PUNCT
ejpam-5531	36	31	b	b	NOUN
ejpam-5531	36	32	-	-	PUNCT
ejpam-5531	36	33	open	open	ADJ
ejpam-5531	36	34	[	[	X
ejpam-5531	36	35	1	1	NUM
ejpam-5531	36	36	]	]	X
ejpam-5531	36	37	if	if	SCONJ
ejpam-5531	36	38	a	a	DET
ejpam-5531	36	39	⊂	⊂	PROPN
ejpam-5531	36	40	int(cl(a	int(cl(a	PROPN
ejpam-5531	36	41	)	)	PUNCT
ejpam-5531	36	42	)	)	PUNCT
ejpam-5531	36	43	∪	∪	ADP
ejpam-5531	36	44	cl(int(a	cl(int(a	PROPN
ejpam-5531	36	45	)	)	PUNCT
ejpam-5531	36	46	)	)	PUNCT
ejpam-5531	36	47	.	.	PUNCT
ejpam-5531	37	1	the	the	DET
ejpam-5531	37	2	family	family	NOUN
ejpam-5531	37	3	of	of	ADP
ejpam-5531	37	4	all	all	PRON
ejpam-5531	37	5	semi	semi	ADJ
ejpam-5531	37	6	-	-	ADJ
ejpam-5531	37	7	open	open	ADJ
ejpam-5531	37	8	(	(	PUNCT
ejpam-5531	37	9	resp	resp	NOUN
ejpam-5531	37	10	.	.	PUNCT
ejpam-5531	38	1	preopen	preopen	ADJ
ejpam-5531	38	2	,	,	PUNCT
ejpam-5531	38	3	α	α	NOUN
ejpam-5531	38	4	-	-	ADJ
ejpam-5531	38	5	open	open	ADJ
ejpam-5531	38	6	,	,	PUNCT
ejpam-5531	38	7	β	β	NOUN
ejpam-5531	38	8	-	-	ADJ
ejpam-5531	38	9	open	open	ADJ
ejpam-5531	38	10	,	,	PUNCT
ejpam-5531	38	11	b	b	X
ejpam-5531	38	12	-	-	PUNCT
ejpam-5531	38	13	open	open	ADJ
ejpam-5531	38	14	)	)	PUNCT
ejpam-5531	38	15	sets	set	NOUN
ejpam-5531	38	16	in	in	ADP
ejpam-5531	38	17	x	x	PUNCT
ejpam-5531	38	18	is	be	AUX
ejpam-5531	38	19	denoted	denote	VERB
ejpam-5531	38	20	by	by	ADP
ejpam-5531	38	21	so(x	so(x	NOUN
ejpam-5531	38	22	)	)	PUNCT
ejpam-5531	38	23	(	(	PUNCT
ejpam-5531	38	24	resp	resp	NOUN
ejpam-5531	38	25	.	.	PUNCT
ejpam-5531	39	1	po(x	po(x	NUM
ejpam-5531	39	2	)	)	PUNCT
ejpam-5531	39	3	,	,	PUNCT
ejpam-5531	40	1	α(x	α(x	NOUN
ejpam-5531	40	2	)	)	PUNCT
ejpam-5531	40	3	,	,	PUNCT
ejpam-5531	40	4	β(x	β(x	NOUN
ejpam-5531	40	5	)	)	PUNCT
ejpam-5531	40	6	,	,	PUNCT
ejpam-5531	40	7	bo(x	bo(x	NUM
ejpam-5531	40	8	)	)	PUNCT
ejpam-5531	40	9	)	)	PUNCT
ejpam-5531	40	10	.	.	PUNCT
ejpam-5531	41	1	definition	definition	NOUN
ejpam-5531	41	2	2	2	NUM
ejpam-5531	41	3	.	.	PUNCT
ejpam-5531	42	1	a	a	DET
ejpam-5531	42	2	subfamily	subfamily	ADV
ejpam-5531	42	3	m	m	NOUN
ejpam-5531	42	4	of	of	ADP
ejpam-5531	42	5	the	the	DET
ejpam-5531	42	6	power	power	NOUN
ejpam-5531	42	7	set	set	NOUN
ejpam-5531	42	8	p(x	p(x	NOUN
ejpam-5531	42	9	)	)	PUNCT
ejpam-5531	42	10	of	of	ADP
ejpam-5531	42	11	a	a	DET
ejpam-5531	42	12	nonempty	nonempty	ADV
ejpam-5531	42	13	set	set	VERB
ejpam-5531	42	14	x	x	PUNCT
ejpam-5531	42	15	is	be	AUX
ejpam-5531	42	16	called	call	VERB
ejpam-5531	42	17	a	a	DET
ejpam-5531	42	18	minimal	minimal	ADJ
ejpam-5531	42	19	structure	structure	NOUN
ejpam-5531	42	20	(	(	PUNCT
ejpam-5531	42	21	briefly	briefly	NOUN
ejpam-5531	42	22	m	m	NOUN
ejpam-5531	42	23	-	-	NOUN
ejpam-5531	42	24	structure	structure	NOUN
ejpam-5531	42	25	)	)	PUNCT
ejpam-5531	43	1	[	[	X
ejpam-5531	43	2	27	27	NUM
ejpam-5531	43	3	]	]	PUNCT
ejpam-5531	43	4	,	,	PUNCT
ejpam-5531	43	5	[	[	X
ejpam-5531	43	6	28	28	NUM
ejpam-5531	43	7	]	]	X
ejpam-5531	43	8	on	on	ADP
ejpam-5531	43	9	x	x	SYM
ejpam-5531	43	10	if	if	SCONJ
ejpam-5531	43	11	∅	∅	NOUN
ejpam-5531	43	12	∈	∈	NOUN
ejpam-5531	43	13	m	m	NOUN
ejpam-5531	43	14	and	and	CCONJ
ejpam-5531	43	15	x	x	PROPN
ejpam-5531	43	16	∈	∈	NOUN
ejpam-5531	43	17	m.	m.	NOUN
ejpam-5531	43	18	by	by	ADP
ejpam-5531	43	19	(	(	PUNCT
ejpam-5531	43	20	x	x	X
ejpam-5531	43	21	,	,	PUNCT
ejpam-5531	43	22	m	m	PROPN
ejpam-5531	43	23	)	)	PUNCT
ejpam-5531	43	24	,	,	PUNCT
ejpam-5531	43	25	we	we	PRON
ejpam-5531	43	26	denote	denote	VERB
ejpam-5531	43	27	a	a	DET
ejpam-5531	43	28	nonempty	nonempty	ADV
ejpam-5531	43	29	set	set	VERB
ejpam-5531	43	30	x	x	PUNCT
ejpam-5531	43	31	with	with	ADP
ejpam-5531	43	32	a	a	DET
ejpam-5531	43	33	minimal	minimal	ADJ
ejpam-5531	43	34	structure	structure	NOUN
ejpam-5531	43	35	m	m	VERB
ejpam-5531	43	36	on	on	ADP
ejpam-5531	43	37	x	x	PUNCT
ejpam-5531	43	38	and	and	CCONJ
ejpam-5531	43	39	call	call	VERB
ejpam-5531	43	40	it	it	PRON
ejpam-5531	43	41	an	an	DET
ejpam-5531	43	42	m	m	NOUN
ejpam-5531	43	43	-	-	NOUN
ejpam-5531	43	44	space	space	NOUN
ejpam-5531	43	45	.	.	PUNCT
ejpam-5531	44	1	each	each	DET
ejpam-5531	44	2	member	member	NOUN
ejpam-5531	44	3	of	of	ADP
ejpam-5531	44	4	m	m	PROPN
ejpam-5531	44	5	is	be	AUX
ejpam-5531	44	6	said	say	VERB
ejpam-5531	44	7	to	to	PART
ejpam-5531	44	8	be	be	AUX
ejpam-5531	44	9	m	m	NOUN
ejpam-5531	44	10	-	-	ADJ
ejpam-5531	44	11	open	open	ADJ
ejpam-5531	44	12	and	and	CCONJ
ejpam-5531	44	13	the	the	DET
ejpam-5531	44	14	complement	complement	NOUN
ejpam-5531	44	15	of	of	ADP
ejpam-5531	44	16	an	an	DET
ejpam-5531	44	17	m	m	NOUN
ejpam-5531	44	18	-	-	ADJ
ejpam-5531	44	19	open	open	ADJ
ejpam-5531	44	20	set	set	NOUN
ejpam-5531	44	21	is	be	AUX
ejpam-5531	44	22	said	say	VERB
ejpam-5531	44	23	to	to	PART
ejpam-5531	44	24	be	be	AUX
ejpam-5531	44	25	m	m	NOUN
ejpam-5531	44	26	-	-	PUNCT
ejpam-5531	44	27	closed	closed	ADJ
ejpam-5531	44	28	.	.	PUNCT
ejpam-5531	45	1	by	by	ADP
ejpam-5531	45	2	m(x	m(x	PROPN
ejpam-5531	45	3	)	)	PUNCT
ejpam-5531	45	4	,	,	PUNCT
ejpam-5531	45	5	we	we	PRON
ejpam-5531	45	6	denote	denote	VERB
ejpam-5531	45	7	the	the	DET
ejpam-5531	45	8	family	family	NOUN
ejpam-5531	45	9	{	{	PUNCT
ejpam-5531	45	10	u	u	NOUN
ejpam-5531	45	11	:	:	PUNCT
ejpam-5531	45	12	x	x	SYM
ejpam-5531	45	13	∈	∈	X
ejpam-5531	45	14	u	u	NOUN
ejpam-5531	45	15	∈	∈	PROPN
ejpam-5531	45	16	m	m	PRON
ejpam-5531	45	17	}	}	PUNCT
ejpam-5531	45	18	.	.	PUNCT
ejpam-5531	46	1	definition	definition	NOUN
ejpam-5531	46	2	3	3	X
ejpam-5531	46	3	.	.	PUNCT
ejpam-5531	47	1	let	let	AUX
ejpam-5531	47	2	(	(	PUNCT
ejpam-5531	47	3	x	x	X
ejpam-5531	47	4	,	,	PUNCT
ejpam-5531	47	5	m	m	VERB
ejpam-5531	47	6	)	)	PUNCT
ejpam-5531	47	7	be	be	VERB
ejpam-5531	47	8	an	an	DET
ejpam-5531	47	9	m	m	NOUN
ejpam-5531	47	10	-	-	NOUN
ejpam-5531	47	11	space	space	NOUN
ejpam-5531	47	12	.	.	PUNCT
ejpam-5531	48	1	for	for	ADP
ejpam-5531	48	2	a	a	DET
ejpam-5531	48	3	subset	subset	NOUN
ejpam-5531	48	4	a	a	PRON
ejpam-5531	48	5	of	of	ADP
ejpam-5531	48	6	x	x	PRON
ejpam-5531	48	7	,	,	PUNCT
ejpam-5531	48	8	the	the	DET
ejpam-5531	48	9	m	m	NOUN
ejpam-5531	48	10	-	-	NOUN
ejpam-5531	48	11	closure	closure	NOUN
ejpam-5531	48	12	of	of	ADP
ejpam-5531	48	13	a	a	DET
ejpam-5531	48	14	and	and	CCONJ
ejpam-5531	48	15	the	the	DET
ejpam-5531	48	16	m	m	NOUN
ejpam-5531	48	17	-	-	NOUN
ejpam-5531	48	18	interior	interior	ADJ
ejpam-5531	48	19	of	of	ADP
ejpam-5531	48	20	a	a	PRON
ejpam-5531	48	21	are	be	AUX
ejpam-5531	48	22	defined	define	VERB
ejpam-5531	48	23	in	in	ADP
ejpam-5531	48	24	[	[	X
ejpam-5531	48	25	20	20	NUM
ejpam-5531	48	26	]	]	PUNCT
ejpam-5531	48	27	as	as	SCONJ
ejpam-5531	48	28	follows	follow	VERB
ejpam-5531	48	29	:	:	PUNCT
ejpam-5531	48	30	(	(	PUNCT
ejpam-5531	48	31	1	1	X
ejpam-5531	48	32	)	)	PUNCT
ejpam-5531	48	33	mcl(a	mcl(a	X
ejpam-5531	48	34	)	)	PUNCT
ejpam-5531	49	1	=	=	SYM
ejpam-5531	49	2	∩{f	∩{f	NOUN
ejpam-5531	49	3	:	:	PUNCT
ejpam-5531	49	4	a	a	DET
ejpam-5531	49	5	⊂	⊂	PROPN
ejpam-5531	49	6	f	f	X
ejpam-5531	49	7	,	,	PUNCT
ejpam-5531	49	8	x	x	SYM
ejpam-5531	49	9	\	\	PROPN
ejpam-5531	49	10	f	f	PROPN
ejpam-5531	49	11	∈	∈	PROPN
ejpam-5531	49	12	m	m	PROPN
ejpam-5531	49	13	}	}	PUNCT
ejpam-5531	49	14	,	,	PUNCT
ejpam-5531	49	15	(	(	PUNCT
ejpam-5531	49	16	2	2	X
ejpam-5531	49	17	)	)	PUNCT
ejpam-5531	49	18	mint(a	mint(a	PROPN
ejpam-5531	49	19	)	)	PUNCT
ejpam-5531	49	20	=	=	SYM
ejpam-5531	50	1	∪{u	∪{u	VERB
ejpam-5531	50	2	:	:	PUNCT
ejpam-5531	50	3	u	u	X
ejpam-5531	50	4	⊂	⊂	PROPN
ejpam-5531	50	5	a	a	X
ejpam-5531	50	6	,	,	PUNCT
ejpam-5531	50	7	u	u	PROPN
ejpam-5531	50	8	∈	∈	PROPN
ejpam-5531	50	9	m	m	PRON
ejpam-5531	50	10	}	}	PUNCT
ejpam-5531	50	11	.	.	PUNCT
ejpam-5531	51	1	lemma	lemma	PROPN
ejpam-5531	51	2	1	1	NUM
ejpam-5531	51	3	.	.	PUNCT
ejpam-5531	52	1	(	(	PUNCT
ejpam-5531	52	2	maki	maki	NOUN
ejpam-5531	52	3	et	et	PROPN
ejpam-5531	52	4	al	al	PROPN
ejpam-5531	52	5	.	.	PUNCT
ejpam-5531	53	1	[	[	X
ejpam-5531	53	2	20	20	NUM
ejpam-5531	53	3	]	]	PUNCT
ejpam-5531	53	4	)	)	PUNCT
ejpam-5531	53	5	.	.	PUNCT
ejpam-5531	54	1	let	let	VERB
ejpam-5531	54	2	(	(	PUNCT
ejpam-5531	54	3	x	x	X
ejpam-5531	54	4	,	,	PUNCT
ejpam-5531	54	5	m	m	VERB
ejpam-5531	54	6	)	)	PUNCT
ejpam-5531	54	7	be	be	VERB
ejpam-5531	54	8	an	an	DET
ejpam-5531	54	9	m	m	NOUN
ejpam-5531	54	10	-	-	NOUN
ejpam-5531	54	11	space	space	NOUN
ejpam-5531	54	12	.	.	PUNCT
ejpam-5531	55	1	for	for	ADP
ejpam-5531	55	2	subsets	subset	NOUN
ejpam-5531	55	3	a	a	PRON
ejpam-5531	55	4	and	and	CCONJ
ejpam-5531	55	5	b	b	NOUN
ejpam-5531	55	6	of	of	ADP
ejpam-5531	55	7	x	x	PRON
ejpam-5531	55	8	,	,	PUNCT
ejpam-5531	55	9	the	the	DET
ejpam-5531	55	10	following	follow	VERB
ejpam-5531	55	11	properties	property	NOUN
ejpam-5531	55	12	hold	hold	VERB
ejpam-5531	55	13	:	:	PUNCT
ejpam-5531	55	14	(	(	PUNCT
ejpam-5531	55	15	1	1	X
ejpam-5531	55	16	)	)	PUNCT
ejpam-5531	55	17	mcl(x	mcl(x	NOUN
ejpam-5531	55	18	\a	\a	ADJ
ejpam-5531	55	19	)	)	PUNCT
ejpam-5531	56	1	=	=	SYM
ejpam-5531	56	2	x	x	SYM
ejpam-5531	56	3	\mint(a	\mint(a	NUM
ejpam-5531	56	4	)	)	PUNCT
ejpam-5531	56	5	and	and	CCONJ
ejpam-5531	56	6	mint(x	mint(x	NOUN
ejpam-5531	56	7	\a	\a	PUNCT
ejpam-5531	56	8	)	)	PUNCT
ejpam-5531	57	1	=	=	PUNCT
ejpam-5531	57	2	x	x	SYM
ejpam-5531	57	3	\mcl(a	\mcl(a	PROPN
ejpam-5531	57	4	)	)	PUNCT
ejpam-5531	57	5	,	,	PUNCT
ejpam-5531	57	6	(	(	PUNCT
ejpam-5531	57	7	2	2	X
ejpam-5531	57	8	)	)	PUNCT
ejpam-5531	57	9	if	if	SCONJ
ejpam-5531	57	10	(	(	PUNCT
ejpam-5531	57	11	x	x	NOUN
ejpam-5531	57	12	\a	\a	ADJ
ejpam-5531	57	13	)	)	PUNCT
ejpam-5531	57	14	∈	∈	PROPN
ejpam-5531	57	15	m	m	PROPN
ejpam-5531	57	16	,	,	PUNCT
ejpam-5531	57	17	then	then	ADV
ejpam-5531	57	18	mcl(a	mcl(a	X
ejpam-5531	57	19	)	)	PUNCT
ejpam-5531	57	20	=	=	SYM
ejpam-5531	57	21	a	a	PROPN
ejpam-5531	57	22	and	and	CCONJ
ejpam-5531	57	23	if	if	SCONJ
ejpam-5531	57	24	a	a	DET
ejpam-5531	57	25	∈	∈	PROPN
ejpam-5531	57	26	m	m	NOUN
ejpam-5531	57	27	,	,	PUNCT
ejpam-5531	57	28	then	then	ADV
ejpam-5531	57	29	mint(a	mint(a	PROPN
ejpam-5531	57	30	)	)	PUNCT
ejpam-5531	57	31	=	=	SYM
ejpam-5531	57	32	a	a	PRON
ejpam-5531	57	33	,	,	PUNCT
ejpam-5531	57	34	(	(	PUNCT
ejpam-5531	57	35	3	3	NUM
ejpam-5531	57	36	)	)	PUNCT
ejpam-5531	57	37	mcl(∅	mcl(∅	NOUN
ejpam-5531	57	38	)	)	PUNCT
ejpam-5531	57	39	=	=	SYM
ejpam-5531	57	40	∅	∅	NOUN
ejpam-5531	57	41	,	,	PUNCT
ejpam-5531	57	42	mcl(x	mcl(x	PROPN
ejpam-5531	57	43	)	)	PUNCT
ejpam-5531	57	44	=	=	SYM
ejpam-5531	57	45	x	x	PROPN
ejpam-5531	57	46	,	,	PUNCT
ejpam-5531	57	47	mint(∅	mint(∅	PROPN
ejpam-5531	57	48	)	)	PUNCT
ejpam-5531	57	49	=	=	NOUN
ejpam-5531	57	50	∅	∅	NOUN
ejpam-5531	57	51	and	and	CCONJ
ejpam-5531	57	52	mint(x	mint(x	NOUN
ejpam-5531	57	53	)	)	PUNCT
ejpam-5531	57	54	=	=	SYM
ejpam-5531	58	1	x	x	X
ejpam-5531	58	2	,	,	PUNCT
ejpam-5531	58	3	(	(	PUNCT
ejpam-5531	58	4	4	4	X
ejpam-5531	58	5	)	)	PUNCT
ejpam-5531	58	6	if	if	SCONJ
ejpam-5531	58	7	a	a	PRON
ejpam-5531	58	8	⊂	⊂	PROPN
ejpam-5531	58	9	b	b	PROPN
ejpam-5531	58	10	,	,	PUNCT
ejpam-5531	58	11	then	then	ADV
ejpam-5531	58	12	mcl(a	mcl(a	X
ejpam-5531	58	13	)	)	PUNCT
ejpam-5531	58	14	⊂	⊂	PROPN
ejpam-5531	58	15	mcl(b	mcl(b	PROPN
ejpam-5531	58	16	)	)	PUNCT
ejpam-5531	58	17	and	and	CCONJ
ejpam-5531	58	18	mint(a	mint(a	PROPN
ejpam-5531	58	19	)	)	PUNCT
ejpam-5531	58	20	⊂	⊂	PROPN
ejpam-5531	58	21	mint(b	mint(b	PROPN
ejpam-5531	58	22	)	)	PUNCT
ejpam-5531	58	23	,	,	PUNCT
ejpam-5531	58	24	(	(	PUNCT
ejpam-5531	58	25	5	5	X
ejpam-5531	58	26	)	)	PUNCT
ejpam-5531	58	27	mint(a	mint(a	PROPN
ejpam-5531	58	28	)	)	PUNCT
ejpam-5531	58	29	⊂	⊂	PROPN
ejpam-5531	58	30	a	a	DET
ejpam-5531	58	31	⊂	⊂	PROPN
ejpam-5531	58	32	mcl(a	mcl(a	PROPN
ejpam-5531	58	33	)	)	PUNCT
ejpam-5531	58	34	,	,	PUNCT
ejpam-5531	58	35	(	(	PUNCT
ejpam-5531	58	36	6	6	X
ejpam-5531	58	37	)	)	PUNCT
ejpam-5531	58	38	mcl(mcl(a	mcl(mcl(a	ADJ
ejpam-5531	58	39	)	)	PUNCT
ejpam-5531	58	40	)	)	PUNCT
ejpam-5531	59	1	=	=	SYM
ejpam-5531	59	2	mcl(a	mcl(a	X
ejpam-5531	59	3	)	)	PUNCT
ejpam-5531	59	4	and	and	CCONJ
ejpam-5531	59	5	mint(mint(a	mint(mint(a	NUM
ejpam-5531	59	6	)	)	PUNCT
ejpam-5531	59	7	)	)	PUNCT
ejpam-5531	60	1	=	=	PUNCT
ejpam-5531	60	2	mint(a	mint(a	PROPN
ejpam-5531	60	3	)	)	PUNCT
ejpam-5531	60	4	.	.	PUNCT
ejpam-5531	61	1	t.	t.	PROPN
ejpam-5531	61	2	noiri	noiri	PROPN
ejpam-5531	61	3	,	,	PUNCT
ejpam-5531	61	4	v.	v.	CCONJ
ejpam-5531	61	5	popa	popa	NOUN
ejpam-5531	61	6	/	/	SYM
ejpam-5531	61	7	eur	eur	PROPN
ejpam-5531	61	8	.	.	PUNCT
ejpam-5531	62	1	j.	j.	PROPN
ejpam-5531	62	2	pure	pure	PROPN
ejpam-5531	62	3	appl	appl	PROPN
ejpam-5531	62	4	.	.	PROPN
ejpam-5531	62	5	math	math	PROPN
ejpam-5531	62	6	,	,	PUNCT
ejpam-5531	62	7	17	17	NUM
ejpam-5531	62	8	(	(	PUNCT
ejpam-5531	62	9	4	4	NUM
ejpam-5531	62	10	)	)	PUNCT
ejpam-5531	62	11	(	(	PUNCT
ejpam-5531	62	12	2024	2024	NUM
ejpam-5531	62	13	)	)	PUNCT
ejpam-5531	62	14	,	,	PUNCT
ejpam-5531	62	15	3677	3677	NUM
ejpam-5531	62	16	-	-	SYM
ejpam-5531	62	17	3686	3686	NUM
ejpam-5531	62	18	3679	3679	NUM
ejpam-5531	62	19	lemma	lemma	PROPN
ejpam-5531	62	20	2	2	NUM
ejpam-5531	62	21	.	.	PUNCT
ejpam-5531	62	22	(	(	PUNCT
ejpam-5531	62	23	popa	popa	NOUN
ejpam-5531	62	24	and	and	CCONJ
ejpam-5531	62	25	noiri	noiri	ADV
ejpam-5531	63	1	[	[	X
ejpam-5531	63	2	28	28	NUM
ejpam-5531	63	3	]	]	PUNCT
ejpam-5531	63	4	)	)	PUNCT
ejpam-5531	63	5	.	.	PUNCT
ejpam-5531	64	1	let	let	VERB
ejpam-5531	64	2	(	(	PUNCT
ejpam-5531	64	3	x	x	X
ejpam-5531	64	4	,	,	PUNCT
ejpam-5531	64	5	m	m	VERB
ejpam-5531	64	6	)	)	PUNCT
ejpam-5531	64	7	be	be	VERB
ejpam-5531	64	8	an	an	DET
ejpam-5531	64	9	m	m	NOUN
ejpam-5531	64	10	-	-	NOUN
ejpam-5531	64	11	space	space	NOUN
ejpam-5531	64	12	and	and	CCONJ
ejpam-5531	64	13	a	a	DET
ejpam-5531	64	14	a	a	DET
ejpam-5531	64	15	subset	subset	NOUN
ejpam-5531	64	16	of	of	ADP
ejpam-5531	64	17	x.	x.	NOUN
ejpam-5531	64	18	then	then	ADV
ejpam-5531	64	19	x	x	PROPN
ejpam-5531	64	20	∈	∈	PROPN
ejpam-5531	64	21	mcl(a	mcl(a	PROPN
ejpam-5531	64	22	)	)	PUNCT
ejpam-5531	65	1	if	if	SCONJ
ejpam-5531	65	2	and	and	CCONJ
ejpam-5531	65	3	only	only	ADV
ejpam-5531	66	1	if	if	SCONJ
ejpam-5531	66	2	u	u	PROPN
ejpam-5531	66	3	∩a	∩a	PROPN
ejpam-5531	66	4	̸=	̸=	PROPN
ejpam-5531	66	5	∅	∅	NOUN
ejpam-5531	66	6	for	for	ADP
ejpam-5531	66	7	every	every	PRON
ejpam-5531	66	8	u	u	PROPN
ejpam-5531	66	9	∈	∈	PROPN
ejpam-5531	66	10	m	m	AUX
ejpam-5531	66	11	containing	contain	VERB
ejpam-5531	66	12	x.	x.	NOUN
ejpam-5531	66	13	definition	definition	NOUN
ejpam-5531	66	14	4	4	NUM
ejpam-5531	66	15	.	.	PUNCT
ejpam-5531	67	1	an	an	DET
ejpam-5531	67	2	m	m	NOUN
ejpam-5531	67	3	-	-	NOUN
ejpam-5531	67	4	structure	structure	NOUN
ejpam-5531	67	5	m	m	NOUN
ejpam-5531	67	6	on	on	ADP
ejpam-5531	67	7	a	a	DET
ejpam-5531	67	8	nonempty	nonempty	ADJ
ejpam-5531	67	9	set	set	VERB
ejpam-5531	67	10	x	x	SYM
ejpam-5531	67	11	is	be	AUX
ejpam-5531	67	12	said	say	VERB
ejpam-5531	67	13	to	to	PART
ejpam-5531	67	14	have	have	VERB
ejpam-5531	67	15	property	property	NOUN
ejpam-5531	67	16	b	b	PROPN
ejpam-5531	68	1	[	[	X
ejpam-5531	68	2	20	20	NUM
ejpam-5531	68	3	]	]	PUNCT
ejpam-5531	68	4	if	if	SCONJ
ejpam-5531	68	5	the	the	DET
ejpam-5531	68	6	union	union	NOUN
ejpam-5531	68	7	of	of	ADP
ejpam-5531	68	8	any	any	DET
ejpam-5531	68	9	family	family	NOUN
ejpam-5531	68	10	of	of	ADP
ejpam-5531	68	11	subsets	subset	NOUN
ejpam-5531	68	12	belonging	belong	VERB
ejpam-5531	68	13	to	to	ADP
ejpam-5531	68	14	m	m	PROPN
ejpam-5531	68	15	belongs	belong	VERB
ejpam-5531	68	16	to	to	ADP
ejpam-5531	68	17	m.	m.	NOUN
ejpam-5531	68	18	remark	remark	NOUN
ejpam-5531	68	19	1	1	NUM
ejpam-5531	68	20	.	.	PUNCT
ejpam-5531	69	1	let	let	VERB
ejpam-5531	69	2	(	(	PUNCT
ejpam-5531	69	3	x	x	NOUN
ejpam-5531	69	4	,	,	PUNCT
ejpam-5531	69	5	τ	τ	X
ejpam-5531	69	6	)	)	PUNCT
ejpam-5531	69	7	be	be	VERB
ejpam-5531	69	8	a	a	DET
ejpam-5531	69	9	topological	topological	ADJ
ejpam-5531	69	10	space	space	NOUN
ejpam-5531	69	11	.	.	PUNCT
ejpam-5531	70	1	then	then	ADV
ejpam-5531	70	2	the	the	DET
ejpam-5531	70	3	families	family	NOUN
ejpam-5531	70	4	τ	τ	PROPN
ejpam-5531	70	5	,	,	PUNCT
ejpam-5531	70	6	so(x	so(x	NOUN
ejpam-5531	70	7	)	)	PUNCT
ejpam-5531	70	8	,	,	PUNCT
ejpam-5531	70	9	po(x	po(x	NUM
ejpam-5531	70	10	)	)	PUNCT
ejpam-5531	70	11	,	,	PUNCT
ejpam-5531	70	12	α(x	α(x	NOUN
ejpam-5531	70	13	)	)	PUNCT
ejpam-5531	70	14	,	,	PUNCT
ejpam-5531	70	15	bo(x	bo(x	NUM
ejpam-5531	70	16	)	)	PUNCT
ejpam-5531	70	17	and	and	CCONJ
ejpam-5531	70	18	β(x	β(x	NOUN
ejpam-5531	70	19	)	)	PUNCT
ejpam-5531	70	20	are	be	AUX
ejpam-5531	70	21	m	m	NOUN
ejpam-5531	70	22	-	-	PUNCT
ejpam-5531	70	23	structures	structure	NOUN
ejpam-5531	70	24	and	and	CCONJ
ejpam-5531	70	25	have	have	VERB
ejpam-5531	70	26	property	property	NOUN
ejpam-5531	70	27	b.	b.	PROPN
ejpam-5531	70	28	lemma	lemma	PROPN
ejpam-5531	70	29	3	3	X
ejpam-5531	70	30	.	.	PUNCT
ejpam-5531	70	31	(	(	PUNCT
ejpam-5531	70	32	popa	popa	NOUN
ejpam-5531	70	33	and	and	CCONJ
ejpam-5531	70	34	noiri	noiri	ADV
ejpam-5531	70	35	[	[	X
ejpam-5531	70	36	29	29	NUM
ejpam-5531	70	37	]	]	PUNCT
ejpam-5531	70	38	)	)	PUNCT
ejpam-5531	70	39	.	.	PUNCT
ejpam-5531	71	1	for	for	ADP
ejpam-5531	71	2	an	an	DET
ejpam-5531	71	3	m	m	NOUN
ejpam-5531	71	4	-	-	NOUN
ejpam-5531	71	5	structure	structure	NOUN
ejpam-5531	71	6	m	m	NOUN
ejpam-5531	71	7	on	on	ADP
ejpam-5531	71	8	a	a	DET
ejpam-5531	71	9	nonempty	nonempty	ADV
ejpam-5531	71	10	set	set	VERB
ejpam-5531	71	11	x	x	NOUN
ejpam-5531	71	12	,	,	PUNCT
ejpam-5531	71	13	the	the	DET
ejpam-5531	71	14	following	follow	VERB
ejpam-5531	71	15	properties	property	NOUN
ejpam-5531	71	16	are	be	AUX
ejpam-5531	71	17	equivalent	equivalent	ADJ
ejpam-5531	71	18	:	:	PUNCT
ejpam-5531	71	19	(	(	PUNCT
ejpam-5531	71	20	1	1	X
ejpam-5531	71	21	)	)	PUNCT
ejpam-5531	72	1	m	m	VERB
ejpam-5531	72	2	has	have	VERB
ejpam-5531	72	3	property	property	NOUN
ejpam-5531	72	4	b	b	NOUN
ejpam-5531	72	5	;	;	PUNCT
ejpam-5531	72	6	(	(	PUNCT
ejpam-5531	72	7	2	2	X
ejpam-5531	72	8	)	)	PUNCT
ejpam-5531	72	9	if	if	SCONJ
ejpam-5531	72	10	mint(a	mint(a	PROPN
ejpam-5531	72	11	)	)	PUNCT
ejpam-5531	72	12	=	=	SYM
ejpam-5531	73	1	a	a	PROPN
ejpam-5531	73	2	,	,	PUNCT
ejpam-5531	73	3	then	then	ADV
ejpam-5531	73	4	a	a	DET
ejpam-5531	73	5	∈	∈	NOUN
ejpam-5531	73	6	m	m	NOUN
ejpam-5531	73	7	;	;	PUNCT
ejpam-5531	73	8	(	(	PUNCT
ejpam-5531	73	9	3	3	X
ejpam-5531	73	10	)	)	PUNCT
ejpam-5531	73	11	if	if	SCONJ
ejpam-5531	73	12	mcl(a	mcl(a	X
ejpam-5531	73	13	)	)	PUNCT
ejpam-5531	73	14	=	=	SYM
ejpam-5531	74	1	a	a	PROPN
ejpam-5531	74	2	,	,	PUNCT
ejpam-5531	74	3	then	then	ADV
ejpam-5531	74	4	a	a	PRON
ejpam-5531	74	5	is	be	AUX
ejpam-5531	74	6	m	m	NOUN
ejpam-5531	74	7	-	-	PUNCT
ejpam-5531	74	8	closed	closed	ADJ
ejpam-5531	74	9	.	.	PUNCT
ejpam-5531	75	1	definition	definition	NOUN
ejpam-5531	75	2	5	5	NUM
ejpam-5531	75	3	.	.	PUNCT
ejpam-5531	76	1	a	a	DET
ejpam-5531	76	2	subset	subset	NOUN
ejpam-5531	76	3	a	a	PRON
ejpam-5531	76	4	of	of	ADP
ejpam-5531	76	5	a	a	DET
ejpam-5531	76	6	topological	topological	ADJ
ejpam-5531	76	7	space	space	NOUN
ejpam-5531	76	8	(	(	PUNCT
ejpam-5531	76	9	x	x	X
ejpam-5531	76	10	,	,	PUNCT
ejpam-5531	76	11	τ	τ	X
ejpam-5531	76	12	)	)	PUNCT
ejpam-5531	76	13	is	be	AUX
ejpam-5531	76	14	called	call	VERB
ejpam-5531	76	15	a	a	DET
ejpam-5531	76	16	rare	rare	ADV
ejpam-5531	76	17	-	-	PUNCT
ejpam-5531	76	18	set	set	VERB
ejpam-5531	76	19	if	if	SCONJ
ejpam-5531	76	20	int(a	int(a	PROPN
ejpam-5531	76	21	)	)	PUNCT
ejpam-5531	76	22	=	=	PUNCT
ejpam-5531	76	23	∅.	∅.	PRON
ejpam-5531	76	24	lemma	lemma	PROPN
ejpam-5531	76	25	4	4	NUM
ejpam-5531	76	26	.	.	PUNCT
ejpam-5531	77	1	in	in	ADP
ejpam-5531	77	2	a	a	DET
ejpam-5531	77	3	topological	topological	ADJ
ejpam-5531	77	4	space	space	NOUN
ejpam-5531	77	5	(	(	PUNCT
ejpam-5531	77	6	x	x	X
ejpam-5531	77	7	,	,	PUNCT
ejpam-5531	77	8	τ	τ	PROPN
ejpam-5531	77	9	)	)	PUNCT
ejpam-5531	77	10	,	,	PUNCT
ejpam-5531	77	11	int(f	int(f	NOUN
ejpam-5531	77	12	∪	∪	ADP
ejpam-5531	77	13	r	r	NOUN
ejpam-5531	77	14	)	)	PUNCT
ejpam-5531	77	15	⊂	⊂	PROPN
ejpam-5531	77	16	f	f	PROPN
ejpam-5531	77	17	for	for	ADP
ejpam-5531	77	18	every	every	DET
ejpam-5531	77	19	rare	rare	ADJ
ejpam-5531	77	20	set	set	VERB
ejpam-5531	77	21	r	r	NOUN
ejpam-5531	77	22	and	and	CCONJ
ejpam-5531	77	23	every	every	DET
ejpam-5531	77	24	closet	closet	NOUN
ejpam-5531	77	25	set	set	VERB
ejpam-5531	77	26	f	f	PROPN
ejpam-5531	77	27	.	.	PUNCT
ejpam-5531	78	1	proof	proof	NOUN
ejpam-5531	78	2	.	.	PUNCT
ejpam-5531	79	1	it	it	PRON
ejpam-5531	79	2	is	be	AUX
ejpam-5531	79	3	obvious	obvious	ADJ
ejpam-5531	79	4	that	that	SCONJ
ejpam-5531	79	5	o∩cl(a	o∩cl(a	PROPN
ejpam-5531	79	6	)	)	PUNCT
ejpam-5531	79	7	⊂	⊂	PROPN
ejpam-5531	79	8	cl(o∩a	cl(o∩a	NOUN
ejpam-5531	79	9	)	)	PUNCT
ejpam-5531	79	10	of	of	ADP
ejpam-5531	79	11	every	every	DET
ejpam-5531	79	12	subset	subset	NOUN
ejpam-5531	79	13	a	a	PRON
ejpam-5531	79	14	of	of	ADP
ejpam-5531	79	15	x	x	X
ejpam-5531	79	16	and	and	CCONJ
ejpam-5531	79	17	any	any	DET
ejpam-5531	79	18	open	open	ADJ
ejpam-5531	79	19	set	set	NOUN
ejpam-5531	79	20	o	o	NOUN
ejpam-5531	79	21	of	of	ADP
ejpam-5531	79	22	x.	x.	NOUN
ejpam-5531	79	23	hence	hence	ADV
ejpam-5531	79	24	int(f	int(f	PROPN
ejpam-5531	79	25	∪b	∪b	X
ejpam-5531	79	26	)	)	PUNCT
ejpam-5531	79	27	⊂	⊂	PROPN
ejpam-5531	80	1	(	(	PUNCT
ejpam-5531	80	2	f	f	PROPN
ejpam-5531	80	3	∪	∪	ADP
ejpam-5531	80	4	int(b	int(b	PROPN
ejpam-5531	80	5	)	)	PUNCT
ejpam-5531	80	6	)	)	PUNCT
ejpam-5531	80	7	for	for	ADP
ejpam-5531	80	8	every	every	DET
ejpam-5531	80	9	subset	subset	NOUN
ejpam-5531	80	10	b	b	NOUN
ejpam-5531	80	11	and	and	CCONJ
ejpam-5531	80	12	every	every	PRON
ejpam-5531	80	13	closed	close	VERB
ejpam-5531	80	14	set	set	VERB
ejpam-5531	80	15	f	f	X
ejpam-5531	80	16	.	.	PUNCT
ejpam-5531	81	1	therefore	therefore	ADV
ejpam-5531	81	2	,	,	PUNCT
ejpam-5531	81	3	int(f	int(f	X
ejpam-5531	81	4	∪r	∪r	NUM
ejpam-5531	81	5	)	)	PUNCT
ejpam-5531	81	6	⊂	⊂	PROPN
ejpam-5531	81	7	f	f	PROPN
ejpam-5531	81	8	for	for	ADP
ejpam-5531	81	9	every	every	DET
ejpam-5531	81	10	rare	rare	ADJ
ejpam-5531	81	11	set	set	VERB
ejpam-5531	81	12	r	r	NOUN
ejpam-5531	81	13	and	and	CCONJ
ejpam-5531	81	14	every	every	PRON
ejpam-5531	81	15	closed	close	VERB
ejpam-5531	81	16	set	set	VERB
ejpam-5531	81	17	f	f	PROPN
ejpam-5531	81	18	.	.	PUNCT
ejpam-5531	82	1	definition	definition	NOUN
ejpam-5531	82	2	6	6	NUM
ejpam-5531	82	3	.	.	PUNCT
ejpam-5531	83	1	a	a	DET
ejpam-5531	83	2	function	function	NOUN
ejpam-5531	83	3	f	f	NOUN
ejpam-5531	83	4	:	:	PUNCT
ejpam-5531	83	5	(	(	PUNCT
ejpam-5531	83	6	x	x	X
ejpam-5531	83	7	,	,	PUNCT
ejpam-5531	83	8	τ	τ	X
ejpam-5531	83	9	)	)	PUNCT
ejpam-5531	83	10	→	→	SYM
ejpam-5531	83	11	(	(	PUNCT
ejpam-5531	83	12	y	y	PROPN
ejpam-5531	83	13	,	,	PUNCT
ejpam-5531	83	14	σ	σ	PROPN
ejpam-5531	83	15	)	)	PUNCT
ejpam-5531	83	16	is	be	AUX
ejpam-5531	83	17	said	say	VERB
ejpam-5531	83	18	to	to	PART
ejpam-5531	83	19	be	be	AUX
ejpam-5531	83	20	rarely	rarely	ADV
ejpam-5531	83	21	continuous	continuous	ADJ
ejpam-5531	83	22	[	[	X
ejpam-5531	83	23	24	24	NUM
ejpam-5531	83	24	]	]	X
ejpam-5531	83	25	at	at	ADP
ejpam-5531	83	26	x	x	X
ejpam-5531	83	27	∈	∈	PROPN
ejpam-5531	83	28	x	x	INTJ
ejpam-5531	83	29	if	if	SCONJ
ejpam-5531	83	30	for	for	ADP
ejpam-5531	83	31	any	any	DET
ejpam-5531	83	32	open	open	ADJ
ejpam-5531	83	33	set	set	NOUN
ejpam-5531	83	34	v	v	NOUN
ejpam-5531	83	35	of	of	ADP
ejpam-5531	83	36	y	y	PRON
ejpam-5531	83	37	such	such	ADJ
ejpam-5531	83	38	that	that	SCONJ
ejpam-5531	83	39	f(x	f(x	PROPN
ejpam-5531	83	40	)	)	PUNCT
ejpam-5531	83	41	∈	∈	PROPN
ejpam-5531	83	42	v	v	NOUN
ejpam-5531	83	43	,	,	PUNCT
ejpam-5531	83	44	there	there	PRON
ejpam-5531	83	45	exist	exist	VERB
ejpam-5531	83	46	a	a	DET
ejpam-5531	83	47	rare	rare	ADJ
ejpam-5531	83	48	set	set	NOUN
ejpam-5531	83	49	rv	rv	PROPN
ejpam-5531	83	50	with	with	ADP
ejpam-5531	83	51	rv	rv	PROPN
ejpam-5531	83	52	∩	∩	PROPN
ejpam-5531	83	53	v	v	NOUN
ejpam-5531	83	54	=	=	NOUN
ejpam-5531	83	55	∅	∅	NOUN
ejpam-5531	83	56	and	and	CCONJ
ejpam-5531	83	57	an	an	DET
ejpam-5531	83	58	open	open	ADJ
ejpam-5531	83	59	set	set	NOUN
ejpam-5531	83	60	u	u	NOUN
ejpam-5531	83	61	containing	contain	VERB
ejpam-5531	83	62	x	x	PUNCT
ejpam-5531	83	63	such	such	ADJ
ejpam-5531	83	64	that	that	DET
ejpam-5531	83	65	f(u	f(u	PROPN
ejpam-5531	83	66	)	)	PUNCT
ejpam-5531	84	1	⊂	⊂	PROPN
ejpam-5531	84	2	v	v	ADP
ejpam-5531	84	3	∪rv	∪rv	NOUN
ejpam-5531	84	4	.	.	PUNCT
ejpam-5531	85	1	3	3	X
ejpam-5531	85	2	.	.	X
ejpam-5531	85	3	rarely	rarely	ADV
ejpam-5531	85	4	m	m	ADJ
ejpam-5531	85	5	-	-	ADJ
ejpam-5531	85	6	continuous	continuous	ADJ
ejpam-5531	85	7	multifunctions	multifunction	NOUN
ejpam-5531	85	8	in	in	ADP
ejpam-5531	85	9	this	this	DET
ejpam-5531	85	10	section	section	NOUN
ejpam-5531	85	11	,	,	PUNCT
ejpam-5531	85	12	we	we	PRON
ejpam-5531	85	13	define	define	VERB
ejpam-5531	85	14	upper	upper	ADJ
ejpam-5531	85	15	and	and	CCONJ
ejpam-5531	85	16	lower	low	ADJ
ejpam-5531	85	17	rare	rare	ADJ
ejpam-5531	85	18	m	m	NOUN
ejpam-5531	85	19	-	-	NOUN
ejpam-5531	85	20	continuity	continuity	NOUN
ejpam-5531	85	21	on	on	ADP
ejpam-5531	85	22	a	a	DET
ejpam-5531	85	23	multifunction	multifunction	NOUN
ejpam-5531	85	24	f	f	NOUN
ejpam-5531	85	25	:	:	PUNCT
ejpam-5531	85	26	(	(	PUNCT
ejpam-5531	85	27	x	x	X
ejpam-5531	85	28	,	,	PUNCT
ejpam-5531	85	29	m	m	NOUN
ejpam-5531	85	30	)	)	PUNCT
ejpam-5531	85	31	→	→	SYM
ejpam-5531	85	32	(	(	PUNCT
ejpam-5531	85	33	y	y	PROPN
ejpam-5531	85	34	,	,	PUNCT
ejpam-5531	85	35	σ	σ	PROPN
ejpam-5531	85	36	)	)	PUNCT
ejpam-5531	85	37	and	and	CCONJ
ejpam-5531	85	38	obtain	obtain	VERB
ejpam-5531	85	39	their	their	PRON
ejpam-5531	85	40	characterizations	characterization	NOUN
ejpam-5531	85	41	.	.	PUNCT
ejpam-5531	86	1	definition	definition	NOUN
ejpam-5531	86	2	7	7	NUM
ejpam-5531	86	3	.	.	PUNCT
ejpam-5531	87	1	let	let	AUX
ejpam-5531	87	2	(	(	PUNCT
ejpam-5531	87	3	x	x	X
ejpam-5531	87	4	,	,	PUNCT
ejpam-5531	87	5	m	m	VERB
ejpam-5531	87	6	)	)	PUNCT
ejpam-5531	87	7	be	be	VERB
ejpam-5531	87	8	an	an	DET
ejpam-5531	87	9	m	m	NOUN
ejpam-5531	87	10	-	-	NOUN
ejpam-5531	87	11	space	space	NOUN
ejpam-5531	87	12	and	and	CCONJ
ejpam-5531	87	13	(	(	PUNCT
ejpam-5531	87	14	y	y	PROPN
ejpam-5531	87	15	,	,	PUNCT
ejpam-5531	87	16	σ	σ	PROPN
ejpam-5531	87	17	)	)	PUNCT
ejpam-5531	87	18	a	a	DET
ejpam-5531	87	19	topological	topological	ADJ
ejpam-5531	87	20	space	space	NOUN
ejpam-5531	87	21	.	.	PUNCT
ejpam-5531	88	1	a	a	DET
ejpam-5531	88	2	multifunction	multifunction	NOUN
ejpam-5531	88	3	f	f	NOUN
ejpam-5531	88	4	:	:	PUNCT
ejpam-5531	88	5	(	(	PUNCT
ejpam-5531	88	6	x	x	X
ejpam-5531	88	7	,	,	PUNCT
ejpam-5531	88	8	m	m	NOUN
ejpam-5531	88	9	)	)	PUNCT
ejpam-5531	88	10	→	→	SYM
ejpam-5531	88	11	(	(	PUNCT
ejpam-5531	88	12	y	y	PROPN
ejpam-5531	88	13	,	,	PUNCT
ejpam-5531	88	14	σ	σ	PROPN
ejpam-5531	88	15	)	)	PUNCT
ejpam-5531	88	16	is	be	AUX
ejpam-5531	88	17	said	say	VERB
ejpam-5531	88	18	to	to	PART
ejpam-5531	88	19	be	be	AUX
ejpam-5531	88	20	(	(	PUNCT
ejpam-5531	88	21	1	1	X
ejpam-5531	88	22	)	)	PUNCT
ejpam-5531	88	23	upper	upper	ADJ
ejpam-5531	88	24	rarely	rarely	ADV
ejpam-5531	88	25	m	m	NOUN
ejpam-5531	88	26	-	-	ADJ
ejpam-5531	88	27	continuous	continuous	ADJ
ejpam-5531	88	28	at	at	ADP
ejpam-5531	88	29	a	a	DET
ejpam-5531	88	30	point	point	NOUN
ejpam-5531	88	31	x	x	SYM
ejpam-5531	88	32	∈	∈	NOUN
ejpam-5531	88	33	x	x	INTJ
ejpam-5531	88	34	if	if	SCONJ
ejpam-5531	88	35	for	for	ADP
ejpam-5531	88	36	each	each	DET
ejpam-5531	88	37	open	open	ADJ
ejpam-5531	88	38	set	set	VERB
ejpam-5531	88	39	v	v	NOUN
ejpam-5531	88	40	containing	contain	VERB
ejpam-5531	88	41	f	f	X
ejpam-5531	88	42	(	(	PUNCT
ejpam-5531	88	43	x	x	NOUN
ejpam-5531	88	44	)	)	PUNCT
ejpam-5531	88	45	,	,	PUNCT
ejpam-5531	88	46	there	there	PRON
ejpam-5531	88	47	exist	exist	VERB
ejpam-5531	88	48	a	a	DET
ejpam-5531	88	49	rare	rare	ADJ
ejpam-5531	88	50	set	set	NOUN
ejpam-5531	88	51	rv	rv	PROPN
ejpam-5531	88	52	with	with	ADP
ejpam-5531	88	53	rv	rv	PROPN
ejpam-5531	88	54	∩	∩	PROPN
ejpam-5531	88	55	v	v	NOUN
ejpam-5531	88	56	=	=	NOUN
ejpam-5531	88	57	∅	∅	NOUN
ejpam-5531	88	58	and	and	CCONJ
ejpam-5531	88	59	an	an	DET
ejpam-5531	88	60	m	m	NOUN
ejpam-5531	88	61	-	-	ADJ
ejpam-5531	88	62	open	open	ADJ
ejpam-5531	88	63	set	set	NOUN
ejpam-5531	88	64	u	u	PROPN
ejpam-5531	88	65	∈	∈	PROPN
ejpam-5531	88	66	m(x	m(x	PROPN
ejpam-5531	88	67	)	)	PUNCT
ejpam-5531	88	68	such	such	ADJ
ejpam-5531	88	69	that	that	SCONJ
ejpam-5531	88	70	f	f	PROPN
ejpam-5531	88	71	(	(	PUNCT
ejpam-5531	88	72	u	u	NOUN
ejpam-5531	88	73	)	)	PUNCT
ejpam-5531	88	74	⊂	⊂	PROPN
ejpam-5531	88	75	v	v	ADP
ejpam-5531	88	76	∪rv	∪rv	PROPN
ejpam-5531	88	77	,	,	PUNCT
ejpam-5531	88	78	(	(	PUNCT
ejpam-5531	88	79	2	2	X
ejpam-5531	88	80	)	)	PUNCT
ejpam-5531	88	81	lower	low	ADJ
ejpam-5531	88	82	rarely	rarely	ADV
ejpam-5531	88	83	m	m	NOUN
ejpam-5531	88	84	-	-	ADJ
ejpam-5531	88	85	continuous	continuous	ADJ
ejpam-5531	88	86	at	at	ADP
ejpam-5531	88	87	a	a	DET
ejpam-5531	88	88	point	point	NOUN
ejpam-5531	88	89	x	x	SYM
ejpam-5531	88	90	∈	∈	NOUN
ejpam-5531	88	91	x	x	INTJ
ejpam-5531	88	92	if	if	SCONJ
ejpam-5531	88	93	for	for	ADP
ejpam-5531	88	94	each	each	DET
ejpam-5531	88	95	open	open	ADJ
ejpam-5531	88	96	set	set	VERB
ejpam-5531	88	97	v	v	NUM
ejpam-5531	88	98	meeting	meeting	NOUN
ejpam-5531	88	99	f	f	X
ejpam-5531	88	100	(	(	PUNCT
ejpam-5531	88	101	x	x	NOUN
ejpam-5531	88	102	)	)	PUNCT
ejpam-5531	88	103	,	,	PUNCT
ejpam-5531	88	104	there	there	PRON
ejpam-5531	88	105	exist	exist	VERB
ejpam-5531	88	106	a	a	DET
ejpam-5531	88	107	rare	rare	ADJ
ejpam-5531	88	108	set	set	NOUN
ejpam-5531	88	109	rv	rv	PROPN
ejpam-5531	88	110	with	with	ADP
ejpam-5531	88	111	rv	rv	PROPN
ejpam-5531	88	112	∩	∩	PROPN
ejpam-5531	88	113	v	v	NOUN
ejpam-5531	88	114	=	=	NOUN
ejpam-5531	88	115	∅	∅	NOUN
ejpam-5531	88	116	and	and	CCONJ
ejpam-5531	88	117	an	an	DET
ejpam-5531	88	118	m	m	NOUN
ejpam-5531	88	119	-	-	ADJ
ejpam-5531	88	120	open	open	ADJ
ejpam-5531	88	121	set	set	NOUN
ejpam-5531	88	122	u	u	PROPN
ejpam-5531	88	123	∈	∈	PROPN
ejpam-5531	88	124	m(x	m(x	PROPN
ejpam-5531	88	125	)	)	PUNCT
ejpam-5531	88	126	such	such	ADJ
ejpam-5531	88	127	that	that	SCONJ
ejpam-5531	88	128	f	f	PROPN
ejpam-5531	88	129	(	(	PUNCT
ejpam-5531	88	130	u	u	NOUN
ejpam-5531	88	131	)	)	PUNCT
ejpam-5531	88	132	∩	∩	NOUN
ejpam-5531	88	133	(	(	PUNCT
ejpam-5531	88	134	v	v	NUM
ejpam-5531	88	135	∪rv	∪rv	NOUN
ejpam-5531	88	136	)	)	PUNCT
ejpam-5531	88	137	̸=	̸=	NOUN
ejpam-5531	88	138	∅	∅	NOUN
ejpam-5531	88	139	for	for	ADP
ejpam-5531	88	140	each	each	DET
ejpam-5531	88	141	u	u	PROPN
ejpam-5531	88	142	∈	∈	PROPN
ejpam-5531	88	143	u	u	NOUN
ejpam-5531	88	144	,	,	PUNCT
ejpam-5531	88	145	theorem	theorem	VERB
ejpam-5531	88	146	1	1	NUM
ejpam-5531	88	147	.	.	PUNCT
ejpam-5531	88	148	for	for	ADP
ejpam-5531	88	149	a	a	DET
ejpam-5531	88	150	multifunction	multifunction	NOUN
ejpam-5531	88	151	f	f	NOUN
ejpam-5531	88	152	:	:	PUNCT
ejpam-5531	88	153	(	(	PUNCT
ejpam-5531	88	154	x	x	X
ejpam-5531	88	155	,	,	PUNCT
ejpam-5531	88	156	m	m	NOUN
ejpam-5531	88	157	)	)	PUNCT
ejpam-5531	88	158	→	→	SYM
ejpam-5531	88	159	(	(	PUNCT
ejpam-5531	88	160	y	y	PROPN
ejpam-5531	88	161	,	,	PUNCT
ejpam-5531	88	162	σ	σ	PROPN
ejpam-5531	88	163	)	)	PUNCT
ejpam-5531	88	164	,	,	PUNCT
ejpam-5531	88	165	the	the	DET
ejpam-5531	88	166	following	follow	VERB
ejpam-5531	88	167	properties	property	NOUN
ejpam-5531	88	168	are	be	AUX
ejpam-5531	88	169	equivalent	equivalent	ADJ
ejpam-5531	88	170	:	:	PUNCT
ejpam-5531	88	171	(	(	PUNCT
ejpam-5531	88	172	1	1	X
ejpam-5531	88	173	)	)	PUNCT
ejpam-5531	88	174	f	f	PROPN
ejpam-5531	88	175	is	be	AUX
ejpam-5531	88	176	upper	upper	ADJ
ejpam-5531	88	177	rarely	rarely	ADV
ejpam-5531	88	178	m	m	NOUN
ejpam-5531	88	179	-	-	ADJ
ejpam-5531	88	180	continuous	continuous	ADJ
ejpam-5531	88	181	at	at	ADP
ejpam-5531	88	182	x	x	X
ejpam-5531	88	183	∈	∈	PROPN
ejpam-5531	88	184	x	x	NOUN
ejpam-5531	88	185	;	;	PUNCT
ejpam-5531	88	186	t.	t.	PROPN
ejpam-5531	88	187	noiri	noiri	PROPN
ejpam-5531	88	188	,	,	PUNCT
ejpam-5531	88	189	v.	v.	CCONJ
ejpam-5531	88	190	popa	popa	NOUN
ejpam-5531	88	191	/	/	SYM
ejpam-5531	88	192	eur	eur	PROPN
ejpam-5531	88	193	.	.	PUNCT
ejpam-5531	89	1	j.	j.	PROPN
ejpam-5531	89	2	pure	pure	PROPN
ejpam-5531	89	3	appl	appl	PROPN
ejpam-5531	89	4	.	.	PROPN
ejpam-5531	89	5	math	math	PROPN
ejpam-5531	89	6	,	,	PUNCT
ejpam-5531	89	7	17	17	NUM
ejpam-5531	89	8	(	(	PUNCT
ejpam-5531	89	9	4	4	NUM
ejpam-5531	89	10	)	)	PUNCT
ejpam-5531	89	11	(	(	PUNCT
ejpam-5531	89	12	2024	2024	NUM
ejpam-5531	89	13	)	)	PUNCT
ejpam-5531	89	14	,	,	PUNCT
ejpam-5531	89	15	3677	3677	NUM
ejpam-5531	89	16	-	-	SYM
ejpam-5531	89	17	3686	3686	NUM
ejpam-5531	89	18	3680	3680	NUM
ejpam-5531	89	19	(	(	PUNCT
ejpam-5531	89	20	2	2	NUM
ejpam-5531	89	21	)	)	PUNCT
ejpam-5531	89	22	for	for	ADP
ejpam-5531	89	23	each	each	DET
ejpam-5531	89	24	open	open	ADJ
ejpam-5531	89	25	set	set	VERB
ejpam-5531	89	26	v	v	NOUN
ejpam-5531	89	27	of	of	ADP
ejpam-5531	89	28	y	y	NOUN
ejpam-5531	89	29	containing	contain	VERB
ejpam-5531	89	30	f(x	f(x	PROPN
ejpam-5531	89	31	)	)	PUNCT
ejpam-5531	90	1	,	,	PUNCT
ejpam-5531	90	2	there	there	PRON
ejpam-5531	90	3	exists	exist	VERB
ejpam-5531	90	4	a	a	DET
ejpam-5531	90	5	rare	rare	ADJ
ejpam-5531	90	6	set	set	NOUN
ejpam-5531	90	7	rv	rv	PROPN
ejpam-5531	90	8	with	with	ADP
ejpam-5531	90	9	v	v	NOUN
ejpam-5531	90	10	∩rv	∩rv	NOUN
ejpam-5531	90	11	=	=	VERB
ejpam-5531	90	12	∅	∅	NOUN
ejpam-5531	90	13	such	such	ADJ
ejpam-5531	90	14	that	that	SCONJ
ejpam-5531	90	15	x	x	SYM
ejpam-5531	90	16	∈	∈	PROPN
ejpam-5531	90	17	mint(f+(v	mint(f+(v	X
ejpam-5531	90	18	∪rv	∪rv	PROPN
ejpam-5531	90	19	)	)	PUNCT
ejpam-5531	90	20	)	)	PUNCT
ejpam-5531	90	21	;	;	PUNCT
ejpam-5531	90	22	(	(	PUNCT
ejpam-5531	90	23	3	3	X
ejpam-5531	90	24	)	)	PUNCT
ejpam-5531	90	25	for	for	ADP
ejpam-5531	90	26	each	each	DET
ejpam-5531	90	27	open	open	ADJ
ejpam-5531	90	28	set	set	VERB
ejpam-5531	90	29	v	v	NOUN
ejpam-5531	90	30	of	of	ADP
ejpam-5531	90	31	y	y	NOUN
ejpam-5531	90	32	containing	contain	VERB
ejpam-5531	90	33	f(x	f(x	PROPN
ejpam-5531	90	34	)	)	PUNCT
ejpam-5531	90	35	,	,	PUNCT
ejpam-5531	90	36	there	there	PRON
ejpam-5531	90	37	exists	exist	VERB
ejpam-5531	90	38	a	a	DET
ejpam-5531	90	39	rare	rare	ADJ
ejpam-5531	90	40	set	set	NOUN
ejpam-5531	90	41	rv	rv	PROPN
ejpam-5531	90	42	with	with	ADP
ejpam-5531	90	43	cl(v	cl(v	NOUN
ejpam-5531	90	44	)	)	PUNCT
ejpam-5531	90	45	∩	∩	NOUN
ejpam-5531	90	46	rv	rv	NOUN
ejpam-5531	90	47	=	=	PUNCT
ejpam-5531	90	48	∅	∅	NOUN
ejpam-5531	90	49	such	such	ADJ
ejpam-5531	90	50	that	that	SCONJ
ejpam-5531	90	51	x	x	SYM
ejpam-5531	90	52	∈	∈	PROPN
ejpam-5531	90	53	mint(f+(cl(v	mint(f+(cl(v	PROPN
ejpam-5531	90	54	)	)	PUNCT
ejpam-5531	90	55	∪rv	∪rv	NOUN
ejpam-5531	90	56	)	)	PUNCT
ejpam-5531	90	57	)	)	PUNCT
ejpam-5531	90	58	;	;	PUNCT
ejpam-5531	90	59	(	(	PUNCT
ejpam-5531	90	60	4	4	X
ejpam-5531	90	61	)	)	PUNCT
ejpam-5531	90	62	for	for	ADP
ejpam-5531	90	63	each	each	DET
ejpam-5531	90	64	regular	regular	ADJ
ejpam-5531	90	65	open	open	ADJ
ejpam-5531	90	66	set	set	VERB
ejpam-5531	90	67	v	v	NOUN
ejpam-5531	90	68	of	of	ADP
ejpam-5531	90	69	y	y	NOUN
ejpam-5531	90	70	containing	contain	VERB
ejpam-5531	90	71	f(x	f(x	PROPN
ejpam-5531	90	72	)	)	PUNCT
ejpam-5531	90	73	,	,	PUNCT
ejpam-5531	90	74	there	there	PRON
ejpam-5531	90	75	exists	exist	VERB
ejpam-5531	90	76	a	a	DET
ejpam-5531	90	77	rare	rare	ADJ
ejpam-5531	90	78	set	set	NOUN
ejpam-5531	90	79	rv	rv	PROPN
ejpam-5531	90	80	with	with	ADP
ejpam-5531	90	81	v	v	NOUN
ejpam-5531	90	82	∩rv	∩rv	NOUN
ejpam-5531	90	83	=	=	VERB
ejpam-5531	90	84	∅	∅	NOUN
ejpam-5531	90	85	such	such	ADJ
ejpam-5531	90	86	that	that	SCONJ
ejpam-5531	90	87	x	x	SYM
ejpam-5531	90	88	∈	∈	PROPN
ejpam-5531	90	89	mint(f+(v	mint(f+(v	X
ejpam-5531	90	90	∪rv	∪rv	PROPN
ejpam-5531	90	91	)	)	PUNCT
ejpam-5531	90	92	)	)	PUNCT
ejpam-5531	90	93	;	;	PUNCT
ejpam-5531	90	94	(	(	PUNCT
ejpam-5531	90	95	5	5	X
ejpam-5531	90	96	)	)	PUNCT
ejpam-5531	90	97	for	for	ADP
ejpam-5531	90	98	each	each	DET
ejpam-5531	90	99	open	open	ADJ
ejpam-5531	90	100	set	set	VERB
ejpam-5531	90	101	v	v	NOUN
ejpam-5531	90	102	of	of	ADP
ejpam-5531	90	103	y	y	NOUN
ejpam-5531	90	104	containing	contain	VERB
ejpam-5531	90	105	f(x	f(x	PROPN
ejpam-5531	90	106	)	)	PUNCT
ejpam-5531	90	107	,	,	PUNCT
ejpam-5531	90	108	there	there	PRON
ejpam-5531	90	109	exists	exist	VERB
ejpam-5531	90	110	u	u	PROPN
ejpam-5531	90	111	∈	∈	PROPN
ejpam-5531	90	112	m(x	m(x	PROPN
ejpam-5531	90	113	)	)	PUNCT
ejpam-5531	90	114	such	such	ADJ
ejpam-5531	90	115	that	that	SCONJ
ejpam-5531	90	116	int[f	int[f	X
ejpam-5531	90	117	(	(	PUNCT
ejpam-5531	90	118	u	u	NOUN
ejpam-5531	90	119	)	)	PUNCT
ejpam-5531	90	120	∩	∩	NOUN
ejpam-5531	90	121	(	(	PUNCT
ejpam-5531	90	122	y	y	PROPN
ejpam-5531	90	123	\	\	PROPN
ejpam-5531	90	124	v	v	NOUN
ejpam-5531	90	125	)	)	PUNCT
ejpam-5531	90	126	]	]	PUNCT
ejpam-5531	91	1	=	=	SYM
ejpam-5531	91	2	∅	∅	NOUN
ejpam-5531	91	3	,	,	PUNCT
ejpam-5531	91	4	(	(	PUNCT
ejpam-5531	91	5	6	6	NUM
ejpam-5531	91	6	)	)	PUNCT
ejpam-5531	91	7	for	for	ADP
ejpam-5531	91	8	each	each	DET
ejpam-5531	91	9	open	open	ADJ
ejpam-5531	91	10	set	set	VERB
ejpam-5531	91	11	v	v	NOUN
ejpam-5531	91	12	of	of	ADP
ejpam-5531	91	13	y	y	NOUN
ejpam-5531	91	14	containing	contain	VERB
ejpam-5531	91	15	f(x	f(x	PROPN
ejpam-5531	91	16	)	)	PUNCT
ejpam-5531	91	17	,	,	PUNCT
ejpam-5531	91	18	there	there	PRON
ejpam-5531	91	19	exists	exist	VERB
ejpam-5531	91	20	u	u	PROPN
ejpam-5531	91	21	∈	∈	PROPN
ejpam-5531	91	22	m(x	m(x	PROPN
ejpam-5531	91	23	)	)	PUNCT
ejpam-5531	92	1	such	such	ADJ
ejpam-5531	92	2	that	that	SCONJ
ejpam-5531	92	3	int(f	int(f	PROPN
ejpam-5531	92	4	(	(	PUNCT
ejpam-5531	92	5	u	u	NOUN
ejpam-5531	92	6	)	)	PUNCT
ejpam-5531	92	7	)	)	PUNCT
ejpam-5531	92	8	⊂	⊂	PROPN
ejpam-5531	92	9	cl(v	cl(v	NOUN
ejpam-5531	92	10	)	)	PUNCT
ejpam-5531	92	11	.	.	PUNCT
ejpam-5531	93	1	proof	proof	NOUN
ejpam-5531	93	2	.	.	PUNCT
ejpam-5531	94	1	(	(	PUNCT
ejpam-5531	94	2	1	1	X
ejpam-5531	94	3	)	)	PUNCT
ejpam-5531	94	4	⇒	⇒	NOUN
ejpam-5531	94	5	(	(	PUNCT
ejpam-5531	94	6	2	2	NUM
ejpam-5531	94	7	):	):	PUNCT
ejpam-5531	94	8	let	let	VERB
ejpam-5531	94	9	v	v	PART
ejpam-5531	94	10	be	be	AUX
ejpam-5531	94	11	any	any	DET
ejpam-5531	94	12	open	open	ADJ
ejpam-5531	94	13	set	set	NOUN
ejpam-5531	94	14	of	of	ADP
ejpam-5531	94	15	y	y	PROPN
ejpam-5531	94	16	containing	contain	VERB
ejpam-5531	94	17	f	f	PROPN
ejpam-5531	94	18	(	(	PUNCT
ejpam-5531	94	19	x	x	NOUN
ejpam-5531	94	20	)	)	PUNCT
ejpam-5531	94	21	.	.	PUNCT
ejpam-5531	95	1	by	by	ADP
ejpam-5531	95	2	(	(	PUNCT
ejpam-5531	95	3	1	1	NUM
ejpam-5531	95	4	)	)	PUNCT
ejpam-5531	95	5	,	,	PUNCT
ejpam-5531	95	6	there	there	PRON
ejpam-5531	95	7	exist	exist	VERB
ejpam-5531	95	8	a	a	DET
ejpam-5531	95	9	rare	rare	ADJ
ejpam-5531	95	10	set	set	NOUN
ejpam-5531	95	11	rv	rv	PROPN
ejpam-5531	95	12	with	with	ADP
ejpam-5531	95	13	rv	rv	PROPN
ejpam-5531	95	14	∩	∩	PROPN
ejpam-5531	95	15	v	v	NOUN
ejpam-5531	95	16	=	=	NOUN
ejpam-5531	95	17	∅	∅	NOUN
ejpam-5531	95	18	and	and	CCONJ
ejpam-5531	95	19	an	an	DET
ejpam-5531	95	20	m	m	NOUN
ejpam-5531	95	21	-	-	ADJ
ejpam-5531	95	22	open	open	ADJ
ejpam-5531	95	23	set	set	NOUN
ejpam-5531	95	24	u	u	PROPN
ejpam-5531	95	25	∈	∈	PROPN
ejpam-5531	95	26	m(x	m(x	PROPN
ejpam-5531	95	27	)	)	PUNCT
ejpam-5531	95	28	such	such	ADJ
ejpam-5531	95	29	that	that	SCONJ
ejpam-5531	95	30	f	f	PROPN
ejpam-5531	95	31	(	(	PUNCT
ejpam-5531	95	32	u	u	NOUN
ejpam-5531	95	33	)	)	PUNCT
ejpam-5531	95	34	⊂	⊂	PROPN
ejpam-5531	95	35	v	v	ADP
ejpam-5531	95	36	∪	∪	X
ejpam-5531	95	37	rv	rv	PROPN
ejpam-5531	95	38	.	.	PUNCT
ejpam-5531	96	1	hence	hence	ADV
ejpam-5531	96	2	x	x	X
ejpam-5531	96	3	∈	∈	PROPN
ejpam-5531	96	4	u	u	NOUN
ejpam-5531	96	5	⊂	⊂	PROPN
ejpam-5531	96	6	f+(v	f+(v	NOUN
ejpam-5531	96	7	∪rv	∪rv	PROPN
ejpam-5531	96	8	)	)	PUNCT
ejpam-5531	96	9	.	.	PUNCT
ejpam-5531	97	1	since	since	SCONJ
ejpam-5531	97	2	u	u	PROPN
ejpam-5531	97	3	is	be	AUX
ejpam-5531	97	4	m	m	NOUN
ejpam-5531	97	5	-	-	ADJ
ejpam-5531	97	6	open	open	ADJ
ejpam-5531	97	7	,	,	PUNCT
ejpam-5531	97	8	x	x	SYM
ejpam-5531	97	9	∈	∈	NOUN
ejpam-5531	97	10	mint(f+(v	mint(f+(v	X
ejpam-5531	97	11	∪rv	∪rv	PROPN
ejpam-5531	97	12	)	)	PUNCT
ejpam-5531	97	13	)	)	PUNCT
ejpam-5531	97	14	.	.	PUNCT
ejpam-5531	98	1	(	(	PUNCT
ejpam-5531	98	2	2	2	X
ejpam-5531	98	3	)	)	PUNCT
ejpam-5531	98	4	⇒	⇒	NOUN
ejpam-5531	98	5	(	(	PUNCT
ejpam-5531	98	6	3	3	NUM
ejpam-5531	98	7	):	):	PUNCT
ejpam-5531	98	8	let	let	VERB
ejpam-5531	98	9	v	v	PART
ejpam-5531	98	10	be	be	AUX
ejpam-5531	98	11	any	any	DET
ejpam-5531	98	12	open	open	ADJ
ejpam-5531	98	13	set	set	NOUN
ejpam-5531	98	14	of	of	ADP
ejpam-5531	98	15	y	y	PRON
ejpam-5531	98	16	such	such	ADJ
ejpam-5531	98	17	that	that	SCONJ
ejpam-5531	98	18	f	f	PROPN
ejpam-5531	98	19	(	(	PUNCT
ejpam-5531	98	20	x	x	X
ejpam-5531	98	21	)	)	PUNCT
ejpam-5531	98	22	⊂	⊂	PROPN
ejpam-5531	98	23	v	v	PROPN
ejpam-5531	98	24	.	.	PUNCT
ejpam-5531	99	1	then	then	ADV
ejpam-5531	99	2	by	by	ADP
ejpam-5531	99	3	(	(	PUNCT
ejpam-5531	99	4	2	2	NUM
ejpam-5531	99	5	)	)	PUNCT
ejpam-5531	99	6	,	,	PUNCT
ejpam-5531	99	7	there	there	PRON
ejpam-5531	99	8	exists	exist	VERB
ejpam-5531	99	9	a	a	DET
ejpam-5531	99	10	rare	rare	ADJ
ejpam-5531	99	11	set	set	NOUN
ejpam-5531	99	12	rv	rv	PROPN
ejpam-5531	99	13	with	with	ADP
ejpam-5531	99	14	v	v	NOUN
ejpam-5531	99	15	∩rv	∩rv	NOUN
ejpam-5531	99	16	=	=	VERB
ejpam-5531	99	17	∅	∅	NOUN
ejpam-5531	99	18	such	such	ADJ
ejpam-5531	99	19	that	that	SCONJ
ejpam-5531	99	20	x	x	SYM
ejpam-5531	99	21	∈	∈	PROPN
ejpam-5531	99	22	mint(f+(v	mint(f+(v	X
ejpam-5531	99	23	∪rv	∪rv	PROPN
ejpam-5531	99	24	)	)	PUNCT
ejpam-5531	99	25	)	)	PUNCT
ejpam-5531	99	26	.	.	PUNCT
ejpam-5531	100	1	let	let	VERB
ejpam-5531	100	2	sv	sv	VERB
ejpam-5531	100	3	=	=	SYM
ejpam-5531	100	4	rv	rv	PROPN
ejpam-5531	100	5	∩(y	∩(y	PROPN
ejpam-5531	100	6	\cl(v	\cl(v	NOUN
ejpam-5531	100	7	)	)	PUNCT
ejpam-5531	100	8	)	)	PUNCT
ejpam-5531	100	9	,	,	PUNCT
ejpam-5531	100	10	then	then	ADV
ejpam-5531	100	11	sv	sv	PROPN
ejpam-5531	100	12	∩cl(v	∩cl(v	PROPN
ejpam-5531	100	13	)	)	PUNCT
ejpam-5531	101	1	=	=	NOUN
ejpam-5531	101	2	∅	∅	NOUN
ejpam-5531	101	3	and	and	CCONJ
ejpam-5531	101	4	sv	sv	PROPN
ejpam-5531	101	5	is	be	AUX
ejpam-5531	101	6	a	a	DET
ejpam-5531	101	7	rare	rare	ADJ
ejpam-5531	101	8	set	set	NOUN
ejpam-5531	101	9	.	.	PUNCT
ejpam-5531	102	1	since	since	SCONJ
ejpam-5531	102	2	cl(v	cl(v	NOUN
ejpam-5531	102	3	)	)	PUNCT
ejpam-5531	102	4	∪sv	∪sv	NOUN
ejpam-5531	102	5	=	=	SYM
ejpam-5531	102	6	cl(v	cl(v	NOUN
ejpam-5531	102	7	)	)	PUNCT
ejpam-5531	102	8	∪	∪	VERB
ejpam-5531	102	9	[	[	X
ejpam-5531	102	10	rv	rv	NOUN
ejpam-5531	102	11	∩(y	∩(y	PROPN
ejpam-5531	102	12	\cl(v	\cl(v	NOUN
ejpam-5531	102	13	)	)	PUNCT
ejpam-5531	102	14	)	)	PUNCT
ejpam-5531	102	15	]	]	PUNCT
ejpam-5531	103	1	=	=	SYM
ejpam-5531	103	2	cl(v	cl(v	X
ejpam-5531	103	3	)	)	PUNCT
ejpam-5531	103	4	∪rv	∪rv	VERB
ejpam-5531	103	5	⊃	⊃	PROPN
ejpam-5531	103	6	v	v	ADP
ejpam-5531	103	7	∪rv	∪rv	PROPN
ejpam-5531	103	8	.	.	PUNCT
ejpam-5531	104	1	therefore	therefore	ADV
ejpam-5531	104	2	,	,	PUNCT
ejpam-5531	104	3	x	x	PROPN
ejpam-5531	104	4	∈	∈	NOUN
ejpam-5531	104	5	mint(f+(v	mint(f+(v	X
ejpam-5531	104	6	∪rv	∪rv	PROPN
ejpam-5531	104	7	)	)	PUNCT
ejpam-5531	104	8	)	)	PUNCT
ejpam-5531	105	1	⊂	⊂	PROPN
ejpam-5531	105	2	mint(f+(cl(v	mint(f+(cl(v	PROPN
ejpam-5531	105	3	)	)	PUNCT
ejpam-5531	105	4	∪	∪	ADP
ejpam-5531	105	5	sv	sv	PROPN
ejpam-5531	105	6	)	)	PUNCT
ejpam-5531	105	7	)	)	PUNCT
ejpam-5531	105	8	.	.	PUNCT
ejpam-5531	106	1	(	(	PUNCT
ejpam-5531	106	2	3	3	X
ejpam-5531	106	3	)	)	PUNCT
ejpam-5531	106	4	⇒	⇒	NOUN
ejpam-5531	106	5	(	(	PUNCT
ejpam-5531	106	6	4	4	NUM
ejpam-5531	106	7	):	):	PUNCT
ejpam-5531	106	8	let	let	VERB
ejpam-5531	106	9	v	v	PART
ejpam-5531	106	10	be	be	AUX
ejpam-5531	106	11	any	any	DET
ejpam-5531	106	12	regular	regular	ADJ
ejpam-5531	106	13	open	open	ADJ
ejpam-5531	106	14	set	set	NOUN
ejpam-5531	106	15	of	of	ADP
ejpam-5531	106	16	y	y	PROPN
ejpam-5531	106	17	containing	contain	VERB
ejpam-5531	106	18	f	f	PROPN
ejpam-5531	106	19	(	(	PUNCT
ejpam-5531	106	20	x	x	NOUN
ejpam-5531	106	21	)	)	PUNCT
ejpam-5531	106	22	.	.	PUNCT
ejpam-5531	107	1	by	by	ADP
ejpam-5531	107	2	(	(	PUNCT
ejpam-5531	107	3	3	3	NUM
ejpam-5531	107	4	)	)	PUNCT
ejpam-5531	107	5	,	,	PUNCT
ejpam-5531	107	6	there	there	PRON
ejpam-5531	107	7	exists	exist	VERB
ejpam-5531	107	8	a	a	DET
ejpam-5531	107	9	rare	rare	ADJ
ejpam-5531	107	10	set	set	NOUN
ejpam-5531	107	11	rv	rv	PROPN
ejpam-5531	107	12	with	with	ADP
ejpam-5531	107	13	cl(v	cl(v	NOUN
ejpam-5531	107	14	)	)	PUNCT
ejpam-5531	107	15	∩	∩	NOUN
ejpam-5531	107	16	rv	rv	NOUN
ejpam-5531	107	17	=	=	PUNCT
ejpam-5531	107	18	∅	∅	NOUN
ejpam-5531	107	19	such	such	ADJ
ejpam-5531	107	20	that	that	SCONJ
ejpam-5531	107	21	x	x	SYM
ejpam-5531	107	22	∈	∈	PROPN
ejpam-5531	107	23	mint(f+(cl(v	mint(f+(cl(v	PROPN
ejpam-5531	107	24	)	)	PUNCT
ejpam-5531	107	25	∪	∪	ADP
ejpam-5531	107	26	rv	rv	PROPN
ejpam-5531	107	27	)	)	PUNCT
ejpam-5531	107	28	)	)	PUNCT
ejpam-5531	107	29	.	.	PUNCT
ejpam-5531	108	1	let	let	VERB
ejpam-5531	108	2	sv	sv	VERB
ejpam-5531	108	3	=	=	PROPN
ejpam-5531	108	4	rv	rv	PROPN
ejpam-5531	108	5	∪	∪	X
ejpam-5531	108	6	(	(	PUNCT
ejpam-5531	108	7	cl(v	cl(v	X
ejpam-5531	108	8	)	)	PUNCT
ejpam-5531	108	9	\	\	PROPN
ejpam-5531	108	10	v	v	NOUN
ejpam-5531	108	11	)	)	PUNCT
ejpam-5531	108	12	.	.	PUNCT
ejpam-5531	109	1	then	then	ADV
ejpam-5531	109	2	by	by	ADP
ejpam-5531	109	3	lemma	lemma	PROPN
ejpam-5531	109	4	4	4	NUM
ejpam-5531	109	5	,	,	PUNCT
ejpam-5531	109	6	sv	sv	PROPN
ejpam-5531	109	7	is	be	AUX
ejpam-5531	109	8	a	a	DET
ejpam-5531	109	9	rare	rare	ADJ
ejpam-5531	109	10	set	set	NOUN
ejpam-5531	109	11	and	and	CCONJ
ejpam-5531	109	12	sv	sv	PROPN
ejpam-5531	109	13	∩	∩	PROPN
ejpam-5531	109	14	v	v	X
ejpam-5531	109	15	=	=	PUNCT
ejpam-5531	109	16	∅.	∅.	VERB
ejpam-5531	109	17	therefore	therefore	ADV
ejpam-5531	109	18	,	,	PUNCT
ejpam-5531	109	19	x	x	PROPN
ejpam-5531	109	20	∈	∈	PROPN
ejpam-5531	109	21	mint(f+(v	mint(f+(v	X
ejpam-5531	109	22	∪	∪	X
ejpam-5531	109	23	sv	sv	PROPN
ejpam-5531	109	24	)	)	PUNCT
ejpam-5531	109	25	)	)	PUNCT
ejpam-5531	109	26	.	.	PUNCT
ejpam-5531	110	1	(	(	PUNCT
ejpam-5531	110	2	4	4	X
ejpam-5531	110	3	)	)	PUNCT
ejpam-5531	110	4	⇒	⇒	NOUN
ejpam-5531	110	5	(	(	PUNCT
ejpam-5531	110	6	5	5	NUM
ejpam-5531	110	7	):	):	PUNCT
ejpam-5531	110	8	v	v	NOUN
ejpam-5531	110	9	be	be	AUX
ejpam-5531	110	10	any	any	DET
ejpam-5531	110	11	open	open	ADJ
ejpam-5531	110	12	set	set	NOUN
ejpam-5531	110	13	of	of	ADP
ejpam-5531	110	14	y	y	PROPN
ejpam-5531	110	15	containing	contain	VERB
ejpam-5531	110	16	f	f	PROPN
ejpam-5531	110	17	(	(	PUNCT
ejpam-5531	110	18	x	x	NOUN
ejpam-5531	110	19	)	)	PUNCT
ejpam-5531	110	20	.	.	PUNCT
ejpam-5531	111	1	then	then	ADV
ejpam-5531	111	2	f	f	X
ejpam-5531	111	3	(	(	PUNCT
ejpam-5531	111	4	x	x	X
ejpam-5531	111	5	)	)	PUNCT
ejpam-5531	111	6	⊂	⊂	PROPN
ejpam-5531	111	7	v	v	ADP
ejpam-5531	111	8	⊂	⊂	PROPN
ejpam-5531	111	9	int(cl(v	int(cl(v	NOUN
ejpam-5531	111	10	)	)	PUNCT
ejpam-5531	111	11	)	)	PUNCT
ejpam-5531	111	12	and	and	CCONJ
ejpam-5531	111	13	int(cl(v	int(cl(v	NOUN
ejpam-5531	111	14	)	)	PUNCT
ejpam-5531	111	15	)	)	PUNCT
ejpam-5531	111	16	is	be	AUX
ejpam-5531	111	17	regular	regular	ADJ
ejpam-5531	111	18	open	open	ADJ
ejpam-5531	111	19	.	.	PUNCT
ejpam-5531	112	1	by	by	ADP
ejpam-5531	112	2	(	(	PUNCT
ejpam-5531	112	3	4	4	NUM
ejpam-5531	112	4	)	)	PUNCT
ejpam-5531	112	5	,	,	PUNCT
ejpam-5531	112	6	there	there	PRON
ejpam-5531	112	7	exists	exist	VERB
ejpam-5531	112	8	a	a	DET
ejpam-5531	112	9	rare	rare	ADJ
ejpam-5531	112	10	set	set	NOUN
ejpam-5531	112	11	rv	rv	PROPN
ejpam-5531	112	12	with	with	ADP
ejpam-5531	112	13	rv	rv	PROPN
ejpam-5531	112	14	∩	∩	NOUN
ejpam-5531	112	15	int(cl(v	int(cl(v	NOUN
ejpam-5531	112	16	)	)	PUNCT
ejpam-5531	112	17	)	)	PUNCT
ejpam-5531	113	1	=	=	NOUN
ejpam-5531	113	2	∅	∅	NOUN
ejpam-5531	113	3	and	and	CCONJ
ejpam-5531	113	4	x	x	PUNCT
ejpam-5531	113	5	∈	∈	PROPN
ejpam-5531	113	6	mint(f+(int(cl(v	mint(f+(int(cl(v	NOUN
ejpam-5531	113	7	)	)	PUNCT
ejpam-5531	113	8	)	)	PUNCT
ejpam-5531	113	9	∪	∪	ADP
ejpam-5531	113	10	rv	rv	PROPN
ejpam-5531	113	11	)	)	PUNCT
ejpam-5531	113	12	)	)	PUNCT
ejpam-5531	113	13	.	.	PUNCT
ejpam-5531	114	1	hence	hence	ADV
ejpam-5531	114	2	there	there	PRON
ejpam-5531	114	3	exists	exist	VERB
ejpam-5531	114	4	u	u	PROPN
ejpam-5531	114	5	∈	∈	PROPN
ejpam-5531	114	6	m(x	m(x	PROPN
ejpam-5531	114	7	)	)	PUNCT
ejpam-5531	114	8	such	such	ADJ
ejpam-5531	114	9	that	that	SCONJ
ejpam-5531	114	10	x	x	SYM
ejpam-5531	114	11	∈	∈	PROPN
ejpam-5531	114	12	u	u	NOUN
ejpam-5531	114	13	⊂	⊂	PROPN
ejpam-5531	114	14	f+(int(cl(v	f+(int(cl(v	PRON
ejpam-5531	114	15	)	)	PUNCT
ejpam-5531	114	16	)	)	PUNCT
ejpam-5531	114	17	∪rv	∪rv	PROPN
ejpam-5531	114	18	)	)	PUNCT
ejpam-5531	114	19	.	.	PUNCT
ejpam-5531	115	1	thus	thus	ADV
ejpam-5531	115	2	,	,	PUNCT
ejpam-5531	115	3	f	f	PROPN
ejpam-5531	115	4	(	(	PUNCT
ejpam-5531	115	5	u	u	NOUN
ejpam-5531	115	6	)	)	PUNCT
ejpam-5531	115	7	⊂	⊂	PROPN
ejpam-5531	115	8	int(cl(v	int(cl(v	NOUN
ejpam-5531	115	9	)	)	PUNCT
ejpam-5531	115	10	)	)	PUNCT
ejpam-5531	115	11	∪rv	∪rv	PROPN
ejpam-5531	115	12	.	.	PUNCT
ejpam-5531	116	1	therefore	therefore	ADV
ejpam-5531	116	2	,	,	PUNCT
ejpam-5531	116	3	by	by	ADP
ejpam-5531	116	4	using	use	VERB
ejpam-5531	116	5	lemma	lemma	PROPN
ejpam-5531	116	6	4	4	NUM
ejpam-5531	116	7	,	,	PUNCT
ejpam-5531	116	8	we	we	PRON
ejpam-5531	116	9	have	have	AUX
ejpam-5531	116	10	int[f	int[f	VERB
ejpam-5531	116	11	(	(	PUNCT
ejpam-5531	116	12	u	u	NOUN
ejpam-5531	116	13	)	)	PUNCT
ejpam-5531	116	14	∩	∩	NOUN
ejpam-5531	116	15	(	(	PUNCT
ejpam-5531	116	16	y	y	PROPN
ejpam-5531	116	17	\	\	PROPN
ejpam-5531	116	18	v	v	NOUN
ejpam-5531	116	19	)	)	PUNCT
ejpam-5531	116	20	]	]	PUNCT
ejpam-5531	117	1	=	=	PUNCT
ejpam-5531	117	2	int(f	int(f	PROPN
ejpam-5531	117	3	(	(	PUNCT
ejpam-5531	117	4	u	u	NOUN
ejpam-5531	117	5	)	)	PUNCT
ejpam-5531	117	6	)	)	PUNCT
ejpam-5531	117	7	∩	∩	NOUN
ejpam-5531	117	8	int(y	int(y	PROPN
ejpam-5531	117	9	\	\	PROPN
ejpam-5531	117	10	v	v	NOUN
ejpam-5531	117	11	)	)	PUNCT
ejpam-5531	117	12	⊂	⊂	PROPN
ejpam-5531	117	13	int(cl(v	int(cl(v	NOUN
ejpam-5531	117	14	)	)	PUNCT
ejpam-5531	117	15	∪rv	∪rv	PROPN
ejpam-5531	117	16	)	)	PUNCT
ejpam-5531	117	17	∩	∩	NOUN
ejpam-5531	117	18	(	(	PUNCT
ejpam-5531	117	19	y	y	PROPN
ejpam-5531	117	20	\	\	PROPN
ejpam-5531	117	21	cl(v	cl(v	NOUN
ejpam-5531	117	22	)	)	PUNCT
ejpam-5531	117	23	)	)	PUNCT
ejpam-5531	118	1	⊂	⊂	PROPN
ejpam-5531	118	2	(	(	PUNCT
ejpam-5531	118	3	cl(v	cl(v	X
ejpam-5531	118	4	)	)	PUNCT
ejpam-5531	118	5	∪	∪	ADP
ejpam-5531	118	6	int(rv	int(rv	NOUN
ejpam-5531	118	7	)	)	PUNCT
ejpam-5531	118	8	)	)	PUNCT
ejpam-5531	118	9	∩	∩	NOUN
ejpam-5531	118	10	(	(	PUNCT
ejpam-5531	118	11	y	y	PROPN
ejpam-5531	118	12	\	\	PROPN
ejpam-5531	118	13	cl(v	cl(v	NOUN
ejpam-5531	118	14	)	)	PUNCT
ejpam-5531	118	15	)	)	PUNCT
ejpam-5531	119	1	=	=	SYM
ejpam-5531	119	2	cl(v	cl(v	NOUN
ejpam-5531	119	3	)	)	PUNCT
ejpam-5531	119	4	∩	∩	NOUN
ejpam-5531	119	5	(	(	PUNCT
ejpam-5531	119	6	y	y	PROPN
ejpam-5531	119	7	\	\	PROPN
ejpam-5531	119	8	cl(v	cl(v	NOUN
ejpam-5531	119	9	)	)	PUNCT
ejpam-5531	119	10	)	)	PUNCT
ejpam-5531	120	1	=	=	PUNCT
ejpam-5531	120	2	∅.	∅.	VERB
ejpam-5531	120	3	therefore	therefore	ADV
ejpam-5531	120	4	,	,	PUNCT
ejpam-5531	120	5	we	we	PRON
ejpam-5531	120	6	have	have	AUX
ejpam-5531	120	7	int[f	int[f	VERB
ejpam-5531	120	8	(	(	PUNCT
ejpam-5531	120	9	u	u	NOUN
ejpam-5531	120	10	)	)	PUNCT
ejpam-5531	120	11	∩	∩	NOUN
ejpam-5531	120	12	(	(	PUNCT
ejpam-5531	120	13	y	y	PROPN
ejpam-5531	120	14	\	\	PROPN
ejpam-5531	120	15	v	v	NOUN
ejpam-5531	120	16	)	)	PUNCT
ejpam-5531	120	17	]	]	PUNCT
ejpam-5531	121	1	=	=	PUNCT
ejpam-5531	121	2	∅.	∅.	X
ejpam-5531	121	3	(	(	PUNCT
ejpam-5531	121	4	5	5	NUM
ejpam-5531	121	5	)	)	PUNCT
ejpam-5531	121	6	⇒	⇒	NOUN
ejpam-5531	121	7	(	(	PUNCT
ejpam-5531	121	8	6	6	NUM
ejpam-5531	121	9	):	):	PUNCT
ejpam-5531	121	10	for	for	ADP
ejpam-5531	121	11	each	each	DET
ejpam-5531	121	12	open	open	ADJ
ejpam-5531	121	13	set	set	VERB
ejpam-5531	121	14	v	v	NOUN
ejpam-5531	121	15	of	of	ADP
ejpam-5531	121	16	y	y	PROPN
ejpam-5531	121	17	containing	contain	VERB
ejpam-5531	121	18	f	f	PROPN
ejpam-5531	121	19	(	(	PUNCT
ejpam-5531	121	20	x	x	NOUN
ejpam-5531	121	21	)	)	PUNCT
ejpam-5531	121	22	,	,	PUNCT
ejpam-5531	121	23	there	there	PRON
ejpam-5531	121	24	exists	exist	VERB
ejpam-5531	121	25	u	u	PROPN
ejpam-5531	121	26	∈	∈	PROPN
ejpam-5531	121	27	m(x	m(x	PROPN
ejpam-5531	121	28	)	)	PUNCT
ejpam-5531	121	29	such	such	ADJ
ejpam-5531	121	30	that	that	SCONJ
ejpam-5531	121	31	int[f	int[f	X
ejpam-5531	121	32	(	(	PUNCT
ejpam-5531	121	33	u	u	NOUN
ejpam-5531	121	34	)	)	PUNCT
ejpam-5531	121	35	∩	∩	NOUN
ejpam-5531	121	36	(	(	PUNCT
ejpam-5531	121	37	y	y	PROPN
ejpam-5531	121	38	\	\	PROPN
ejpam-5531	121	39	v	v	NOUN
ejpam-5531	121	40	)	)	PUNCT
ejpam-5531	121	41	]	]	PUNCT
ejpam-5531	122	1	=	=	PUNCT
ejpam-5531	122	2	∅.	∅.	VERB
ejpam-5531	122	3	hence	hence	ADV
ejpam-5531	122	4	int[f	int[f	X
ejpam-5531	122	5	(	(	PUNCT
ejpam-5531	122	6	u	u	NOUN
ejpam-5531	122	7	)	)	PUNCT
ejpam-5531	122	8	)	)	PUNCT
ejpam-5531	122	9	∩	∩	NOUN
ejpam-5531	122	10	(	(	PUNCT
ejpam-5531	122	11	y	y	PROPN
ejpam-5531	122	12	\	\	PROPN
ejpam-5531	122	13	cl(v	cl(v	NOUN
ejpam-5531	122	14	)	)	PUNCT
ejpam-5531	122	15	]	]	PUNCT
ejpam-5531	122	16	=	=	PUNCT
ejpam-5531	122	17	∅	∅	NOUN
ejpam-5531	122	18	and	and	CCONJ
ejpam-5531	122	19	int(f	int(f	PROPN
ejpam-5531	122	20	(	(	PUNCT
ejpam-5531	122	21	u	u	NOUN
ejpam-5531	122	22	)	)	PUNCT
ejpam-5531	122	23	)	)	PUNCT
ejpam-5531	123	1	⊂	⊂	PROPN
ejpam-5531	123	2	cl(v	cl(v	NOUN
ejpam-5531	123	3	)	)	PUNCT
ejpam-5531	123	4	.	.	PUNCT
ejpam-5531	124	1	(	(	PUNCT
ejpam-5531	124	2	6	6	X
ejpam-5531	124	3	)	)	PUNCT
ejpam-5531	124	4	⇒	⇒	NOUN
ejpam-5531	124	5	(	(	PUNCT
ejpam-5531	124	6	1	1	NUM
ejpam-5531	124	7	):	):	PUNCT
ejpam-5531	124	8	let	let	VERB
ejpam-5531	124	9	v	v	PART
ejpam-5531	124	10	be	be	AUX
ejpam-5531	124	11	any	any	DET
ejpam-5531	124	12	open	open	ADJ
ejpam-5531	124	13	set	set	NOUN
ejpam-5531	124	14	of	of	ADP
ejpam-5531	124	15	y	y	PROPN
ejpam-5531	124	16	containing	contain	VERB
ejpam-5531	124	17	f	f	PROPN
ejpam-5531	124	18	(	(	PUNCT
ejpam-5531	124	19	x	x	NOUN
ejpam-5531	124	20	)	)	PUNCT
ejpam-5531	124	21	.	.	PUNCT
ejpam-5531	125	1	by	by	ADP
ejpam-5531	125	2	(	(	PUNCT
ejpam-5531	125	3	6	6	NUM
ejpam-5531	125	4	)	)	PUNCT
ejpam-5531	125	5	,	,	PUNCT
ejpam-5531	125	6	there	there	PRON
ejpam-5531	125	7	exists	exist	VERB
ejpam-5531	125	8	u	u	PROPN
ejpam-5531	125	9	∈	∈	PROPN
ejpam-5531	125	10	m(x	m(x	PROPN
ejpam-5531	125	11	)	)	PUNCT
ejpam-5531	126	1	such	such	ADJ
ejpam-5531	126	2	that	that	SCONJ
ejpam-5531	126	3	int(f	int(f	PROPN
ejpam-5531	126	4	(	(	PUNCT
ejpam-5531	126	5	u	u	NOUN
ejpam-5531	126	6	)	)	PUNCT
ejpam-5531	126	7	)	)	PUNCT
ejpam-5531	126	8	⊂	⊂	PROPN
ejpam-5531	126	9	cl(v	cl(v	NOUN
ejpam-5531	126	10	)	)	PUNCT
ejpam-5531	126	11	.	.	PUNCT
ejpam-5531	127	1	letm	letm	PROPN
ejpam-5531	128	1	=	=	PUNCT
ejpam-5531	128	2	f	f	PROPN
ejpam-5531	128	3	(	(	PUNCT
ejpam-5531	128	4	u)∩(y	u)∩(y	PROPN
ejpam-5531	128	5	\v	\v	PROPN
ejpam-5531	128	6	)	)	PUNCT
ejpam-5531	128	7	.	.	PUNCT
ejpam-5531	129	1	then	then	ADV
ejpam-5531	129	2	int(m	int(m	PROPN
ejpam-5531	129	3	)	)	PUNCT
ejpam-5531	129	4	⊂	⊂	PROPN
ejpam-5531	130	1	int(f	int(f	PROPN
ejpam-5531	130	2	(	(	PUNCT
ejpam-5531	130	3	u))∩int(y	u))∩int(y	PROPN
ejpam-5531	130	4	\	\	PROPN
ejpam-5531	130	5	v	v	NOUN
ejpam-5531	130	6	)	)	PUNCT
ejpam-5531	130	7	=	=	SYM
ejpam-5531	130	8	int(f	int(f	PROPN
ejpam-5531	130	9	(	(	PUNCT
ejpam-5531	130	10	u))∩(y	u))∩(y	NOUN
ejpam-5531	130	11	\cl(v	\cl(v	NOUN
ejpam-5531	130	12	)	)	PUNCT
ejpam-5531	130	13	)	)	PUNCT
ejpam-5531	131	1	=	=	PUNCT
ejpam-5531	131	2	∅.	∅.	NOUN
ejpam-5531	131	3	hencem	hencem	NOUN
ejpam-5531	131	4	is	be	AUX
ejpam-5531	131	5	a	a	DET
ejpam-5531	131	6	rare	rare	ADJ
ejpam-5531	131	7	set	set	NOUN
ejpam-5531	131	8	andm∩v	andm∩v	NOUN
ejpam-5531	131	9	=	=	PUNCT
ejpam-5531	131	10	∅.	∅.	ADP
ejpam-5531	131	11	letn	letn	NOUN
ejpam-5531	131	12	=	=	SYM
ejpam-5531	131	13	cl(v	cl(v	X
ejpam-5531	131	14	)	)	PUNCT
ejpam-5531	131	15	\v	\v	X
ejpam-5531	131	16	.	.	PUNCT
ejpam-5531	132	1	then	then	ADV
ejpam-5531	132	2	n	n	PRON
ejpam-5531	132	3	is	be	AUX
ejpam-5531	132	4	a	a	DET
ejpam-5531	132	5	closed	closed	ADJ
ejpam-5531	132	6	rare	rare	ADJ
ejpam-5531	132	7	set	set	NOUN
ejpam-5531	132	8	such	such	ADJ
ejpam-5531	132	9	that	that	SCONJ
ejpam-5531	132	10	n	n	PRON
ejpam-5531	132	11	∩v	∩v	NOUN
ejpam-5531	132	12	=	=	PUNCT
ejpam-5531	132	13	∅.	∅.	NOUN
ejpam-5531	132	14	therefore	therefore	ADV
ejpam-5531	132	15	,	,	PUNCT
ejpam-5531	132	16	rv	rv	PROPN
ejpam-5531	133	1	=	=	SYM
ejpam-5531	133	2	m	m	VERB
ejpam-5531	133	3	∪n	∪n	NUM
ejpam-5531	133	4	is	be	AUX
ejpam-5531	133	5	a	a	DET
ejpam-5531	133	6	rare	rare	ADJ
ejpam-5531	133	7	set	set	NOUN
ejpam-5531	133	8	and	and	CCONJ
ejpam-5531	133	9	rv	rv	NOUN
ejpam-5531	133	10	∩v	∩v	NOUN
ejpam-5531	134	1	=	=	PUNCT
ejpam-5531	134	2	∅	∅	NOUN
ejpam-5531	134	3	by	by	ADP
ejpam-5531	134	4	using	use	VERB
ejpam-5531	134	5	lemma	lemma	PROPN
ejpam-5531	134	6	4	4	NUM
ejpam-5531	134	7	:	:	PUNCT
ejpam-5531	134	8	int(rv	int(rv	NOUN
ejpam-5531	134	9	)	)	PUNCT
ejpam-5531	134	10	=	=	SYM
ejpam-5531	134	11	int(int(rv	int(int(rv	ADJ
ejpam-5531	134	12	)	)	PUNCT
ejpam-5531	134	13	)	)	PUNCT
ejpam-5531	135	1	=	=	PUNCT
ejpam-5531	135	2	int(int(m	int(int(m	X
ejpam-5531	135	3	∪n	∪n	NUM
ejpam-5531	135	4	)	)	PUNCT
ejpam-5531	135	5	)	)	PUNCT
ejpam-5531	136	1	⊂	⊂	PROPN
ejpam-5531	136	2	int(n	int(n	PROPN
ejpam-5531	136	3	)	)	PUNCT
ejpam-5531	137	1	=	=	NOUN
ejpam-5531	137	2	∅.	∅.	ADP
ejpam-5531	137	3	now	now	ADV
ejpam-5531	137	4	,	,	PUNCT
ejpam-5531	137	5	we	we	PRON
ejpam-5531	137	6	have	have	VERB
ejpam-5531	137	7	the	the	DET
ejpam-5531	137	8	following	following	NOUN
ejpam-5531	137	9	:	:	PUNCT
ejpam-5531	137	10	f	f	PROPN
ejpam-5531	137	11	(	(	PUNCT
ejpam-5531	137	12	u	u	NOUN
ejpam-5531	137	13	)	)	PUNCT
ejpam-5531	137	14	=	=	PUNCT
ejpam-5531	138	1	[	[	X
ejpam-5531	138	2	f	f	X
ejpam-5531	138	3	(	(	PUNCT
ejpam-5531	138	4	u	u	NOUN
ejpam-5531	138	5	)	)	PUNCT
ejpam-5531	138	6	\	\	PUNCT
ejpam-5531	139	1	int(f	int(f	PROPN
ejpam-5531	139	2	(	(	PUNCT
ejpam-5531	139	3	u	u	NOUN
ejpam-5531	139	4	)	)	PUNCT
ejpam-5531	139	5	]	]	PUNCT
ejpam-5531	139	6	∪	∪	ADP
ejpam-5531	139	7	int(f	int(f	PROPN
ejpam-5531	139	8	(	(	PUNCT
ejpam-5531	139	9	u	u	NOUN
ejpam-5531	139	10	)	)	PUNCT
ejpam-5531	139	11	)	)	PUNCT
ejpam-5531	139	12	]	]	PUNCT
ejpam-5531	140	1	⊂	⊂	X
ejpam-5531	141	1	[	[	X
ejpam-5531	141	2	f	f	X
ejpam-5531	141	3	(	(	PUNCT
ejpam-5531	141	4	u	u	NOUN
ejpam-5531	141	5	)	)	PUNCT
ejpam-5531	141	6	\	\	PUNCT
ejpam-5531	141	7	int(f	int(f	PROPN
ejpam-5531	141	8	(	(	PUNCT
ejpam-5531	141	9	u	u	NOUN
ejpam-5531	141	10	)	)	PUNCT
ejpam-5531	141	11	]	]	PUNCT
ejpam-5531	141	12	∪	∪	ADP
ejpam-5531	141	13	cl(v	cl(v	NOUN
ejpam-5531	141	14	)	)	PUNCT
ejpam-5531	141	15	=	=	PUNCT
ejpam-5531	142	1	[	[	X
ejpam-5531	142	2	(	(	PUNCT
ejpam-5531	142	3	f	f	X
ejpam-5531	142	4	(	(	PUNCT
ejpam-5531	142	5	u	u	NOUN
ejpam-5531	142	6	)	)	PUNCT
ejpam-5531	142	7	)	)	PUNCT
ejpam-5531	142	8	∩	∩	NOUN
ejpam-5531	142	9	(	(	PUNCT
ejpam-5531	142	10	v	v	NOUN
ejpam-5531	142	11	∪	∪	X
ejpam-5531	142	12	(	(	PUNCT
ejpam-5531	142	13	y	y	PROPN
ejpam-5531	142	14	\	\	PROPN
ejpam-5531	142	15	v	v	NOUN
ejpam-5531	142	16	)	)	PUNCT
ejpam-5531	142	17	)	)	PUNCT
ejpam-5531	142	18	\	\	PROPN
ejpam-5531	143	1	int(f	int(f	PROPN
ejpam-5531	143	2	(	(	PUNCT
ejpam-5531	143	3	u	u	NOUN
ejpam-5531	143	4	)	)	PUNCT
ejpam-5531	143	5	]	]	PUNCT
ejpam-5531	143	6	∪	∪	ADP
ejpam-5531	143	7	[	[	X
ejpam-5531	143	8	(	(	PUNCT
ejpam-5531	143	9	cl(v	cl(v	X
ejpam-5531	143	10	)	)	PUNCT
ejpam-5531	143	11	\	\	PROPN
ejpam-5531	143	12	v	v	X
ejpam-5531	143	13	)	)	PUNCT
ejpam-5531	143	14	∪	∪	ADP
ejpam-5531	143	15	v	v	NOUN
ejpam-5531	143	16	]	]	PUNCT
ejpam-5531	143	17	=	=	PUNCT
ejpam-5531	143	18	(	(	PUNCT
ejpam-5531	143	19	f	f	X
ejpam-5531	143	20	(	(	PUNCT
ejpam-5531	143	21	u	u	NOUN
ejpam-5531	143	22	)	)	PUNCT
ejpam-5531	143	23	∩	∩	ADJ
ejpam-5531	143	24	v	v	X
ejpam-5531	143	25	)	)	PUNCT
ejpam-5531	143	26	∪	∪	NOUN
ejpam-5531	143	27	(	(	PUNCT
ejpam-5531	143	28	f	f	PROPN
ejpam-5531	143	29	(	(	PUNCT
ejpam-5531	143	30	u	u	NOUN
ejpam-5531	143	31	)	)	PUNCT
ejpam-5531	143	32	∩	∩	NOUN
ejpam-5531	143	33	(	(	PUNCT
ejpam-5531	143	34	y	y	PROPN
ejpam-5531	143	35	\	\	PROPN
ejpam-5531	143	36	v	v	NOUN
ejpam-5531	143	37	)	)	PUNCT
ejpam-5531	143	38	)	)	PUNCT
ejpam-5531	143	39	\	\	PROPN
ejpam-5531	144	1	int(f	int(f	PROPN
ejpam-5531	144	2	(	(	PUNCT
ejpam-5531	144	3	u	u	NOUN
ejpam-5531	144	4	)	)	PUNCT
ejpam-5531	144	5	]	]	PUNCT
ejpam-5531	144	6	∪	∪	ADP
ejpam-5531	144	7	[	[	X
ejpam-5531	144	8	n	n	CCONJ
ejpam-5531	144	9	∪	∪	ADJ
ejpam-5531	144	10	v	v	NOUN
ejpam-5531	144	11	]	]	PUNCT
ejpam-5531	144	12	⊂	⊂	PROPN
ejpam-5531	145	1	[	[	X
ejpam-5531	145	2	v	v	X
ejpam-5531	145	3	∪	∪	X
ejpam-5531	145	4	(	(	PUNCT
ejpam-5531	145	5	f	f	PROPN
ejpam-5531	145	6	(	(	PUNCT
ejpam-5531	145	7	u	u	NOUN
ejpam-5531	145	8	)	)	PUNCT
ejpam-5531	145	9	∩	∩	NOUN
ejpam-5531	145	10	(	(	PUNCT
ejpam-5531	145	11	y	y	PROPN
ejpam-5531	145	12	\	\	PROPN
ejpam-5531	145	13	v	v	NOUN
ejpam-5531	145	14	)	)	PUNCT
ejpam-5531	145	15	)	)	PUNCT
ejpam-5531	145	16	]	]	PUNCT
ejpam-5531	145	17	∪	∪	X
ejpam-5531	145	18	[	[	X
ejpam-5531	145	19	n	n	CCONJ
ejpam-5531	145	20	∪	∪	ADJ
ejpam-5531	145	21	v	v	NOUN
ejpam-5531	145	22	]	]	PUNCT
ejpam-5531	145	23	=	=	SYM
ejpam-5531	145	24	v	v	NOUN
ejpam-5531	145	25	∪	∪	X
ejpam-5531	145	26	(	(	PUNCT
ejpam-5531	145	27	m	m	NOUN
ejpam-5531	145	28	∪n	∪n	NUM
ejpam-5531	145	29	)	)	PUNCT
ejpam-5531	145	30	t.	t.	PROPN
ejpam-5531	145	31	noiri	noiri	PROPN
ejpam-5531	145	32	,	,	PUNCT
ejpam-5531	145	33	v.	v.	CCONJ
ejpam-5531	145	34	popa	popa	NOUN
ejpam-5531	145	35	/	/	SYM
ejpam-5531	145	36	eur	eur	PROPN
ejpam-5531	145	37	.	.	PUNCT
ejpam-5531	146	1	j.	j.	PROPN
ejpam-5531	146	2	pure	pure	PROPN
ejpam-5531	146	3	appl	appl	PROPN
ejpam-5531	146	4	.	.	PROPN
ejpam-5531	146	5	math	math	PROPN
ejpam-5531	146	6	,	,	PUNCT
ejpam-5531	146	7	17	17	NUM
ejpam-5531	146	8	(	(	PUNCT
ejpam-5531	146	9	4	4	NUM
ejpam-5531	146	10	)	)	PUNCT
ejpam-5531	146	11	(	(	PUNCT
ejpam-5531	146	12	2024	2024	NUM
ejpam-5531	146	13	)	)	PUNCT
ejpam-5531	146	14	,	,	PUNCT
ejpam-5531	146	15	3677	3677	NUM
ejpam-5531	146	16	-	-	SYM
ejpam-5531	146	17	3686	3686	NUM
ejpam-5531	146	18	3681	3681	NUM
ejpam-5531	146	19	=	=	SYM
ejpam-5531	146	20	v	v	NOUN
ejpam-5531	146	21	∪rv	∪rv	NOUN
ejpam-5531	146	22	.	.	PUNCT
ejpam-5531	147	1	consequently	consequently	ADV
ejpam-5531	147	2	,	,	PUNCT
ejpam-5531	147	3	there	there	PRON
ejpam-5531	147	4	exists	exist	VERB
ejpam-5531	147	5	a	a	DET
ejpam-5531	147	6	rare	rare	ADJ
ejpam-5531	147	7	set	set	NOUN
ejpam-5531	147	8	rv	rv	PROPN
ejpam-5531	148	1	=	=	PUNCT
ejpam-5531	148	2	m	m	VERB
ejpam-5531	148	3	∪	∪	ADJ
ejpam-5531	148	4	n	n	PRON
ejpam-5531	148	5	such	such	ADJ
ejpam-5531	148	6	that	that	SCONJ
ejpam-5531	148	7	rv	rv	PROPN
ejpam-5531	148	8	∩	∩	PROPN
ejpam-5531	148	9	v	v	NOUN
ejpam-5531	148	10	=	=	NOUN
ejpam-5531	148	11	∅	∅	NOUN
ejpam-5531	148	12	and	and	CCONJ
ejpam-5531	148	13	f	f	PROPN
ejpam-5531	148	14	(	(	PUNCT
ejpam-5531	148	15	u	u	NOUN
ejpam-5531	148	16	)	)	PUNCT
ejpam-5531	148	17	⊂	⊂	PROPN
ejpam-5531	148	18	v	v	ADP
ejpam-5531	148	19	∪rv	∪rv	PROPN
ejpam-5531	148	20	.	.	PUNCT
ejpam-5531	149	1	thus	thus	ADV
ejpam-5531	149	2	,	,	PUNCT
ejpam-5531	149	3	f	f	PROPN
ejpam-5531	149	4	is	be	AUX
ejpam-5531	149	5	upper	upper	ADJ
ejpam-5531	149	6	rarely	rarely	ADV
ejpam-5531	149	7	m	m	NOUN
ejpam-5531	149	8	-	-	ADJ
ejpam-5531	149	9	continuous	continuous	ADJ
ejpam-5531	149	10	at	at	ADP
ejpam-5531	149	11	x	x	SYM
ejpam-5531	149	12	∈	∈	PROPN
ejpam-5531	149	13	x.	x.	NOUN
ejpam-5531	149	14	theorem	theorem	VERB
ejpam-5531	149	15	2	2	NUM
ejpam-5531	149	16	.	.	X
ejpam-5531	149	17	for	for	ADP
ejpam-5531	149	18	a	a	DET
ejpam-5531	149	19	multifunction	multifunction	NOUN
ejpam-5531	149	20	f	f	NOUN
ejpam-5531	149	21	:	:	PUNCT
ejpam-5531	149	22	(	(	PUNCT
ejpam-5531	149	23	x	x	X
ejpam-5531	149	24	,	,	PUNCT
ejpam-5531	149	25	m	m	NOUN
ejpam-5531	149	26	)	)	PUNCT
ejpam-5531	149	27	→	→	SYM
ejpam-5531	149	28	(	(	PUNCT
ejpam-5531	149	29	y	y	PROPN
ejpam-5531	149	30	,	,	PUNCT
ejpam-5531	149	31	σ	σ	PROPN
ejpam-5531	149	32	)	)	PUNCT
ejpam-5531	149	33	,	,	PUNCT
ejpam-5531	149	34	the	the	DET
ejpam-5531	149	35	following	follow	VERB
ejpam-5531	149	36	properties	property	NOUN
ejpam-5531	149	37	are	be	AUX
ejpam-5531	149	38	equivalent	equivalent	ADJ
ejpam-5531	149	39	:	:	PUNCT
ejpam-5531	149	40	(	(	PUNCT
ejpam-5531	149	41	1	1	X
ejpam-5531	149	42	)	)	PUNCT
ejpam-5531	149	43	f	f	PROPN
ejpam-5531	149	44	is	be	AUX
ejpam-5531	149	45	lower	low	ADJ
ejpam-5531	149	46	rarely	rarely	ADV
ejpam-5531	149	47	m	m	ADJ
ejpam-5531	149	48	-	-	ADJ
ejpam-5531	149	49	continuous	continuous	ADJ
ejpam-5531	149	50	at	at	ADP
ejpam-5531	149	51	x	x	X
ejpam-5531	149	52	∈	∈	PROPN
ejpam-5531	149	53	x	x	X
ejpam-5531	149	54	;	;	PUNCT
ejpam-5531	149	55	(	(	PUNCT
ejpam-5531	149	56	2	2	X
ejpam-5531	149	57	)	)	PUNCT
ejpam-5531	149	58	for	for	ADP
ejpam-5531	149	59	each	each	DET
ejpam-5531	149	60	open	open	ADJ
ejpam-5531	149	61	set	set	VERB
ejpam-5531	149	62	v	v	NOUN
ejpam-5531	149	63	of	of	ADP
ejpam-5531	149	64	y	y	PRON
ejpam-5531	149	65	such	such	ADJ
ejpam-5531	149	66	that	that	SCONJ
ejpam-5531	149	67	f	f	PROPN
ejpam-5531	149	68	(	(	PUNCT
ejpam-5531	149	69	x	x	NOUN
ejpam-5531	149	70	)	)	PUNCT
ejpam-5531	149	71	∩	∩	NOUN
ejpam-5531	149	72	v	v	ADP
ejpam-5531	149	73	̸=	̸=	PROPN
ejpam-5531	149	74	∅	∅	NOUN
ejpam-5531	149	75	,	,	PUNCT
ejpam-5531	149	76	there	there	PRON
ejpam-5531	149	77	exists	exist	VERB
ejpam-5531	149	78	a	a	DET
ejpam-5531	149	79	rare	rare	ADJ
ejpam-5531	149	80	set	set	NOUN
ejpam-5531	149	81	rv	rv	PROPN
ejpam-5531	149	82	with	with	ADP
ejpam-5531	149	83	v	v	NOUN
ejpam-5531	149	84	∩rv	∩rv	NOUN
ejpam-5531	149	85	=	=	VERB
ejpam-5531	149	86	∅	∅	NOUN
ejpam-5531	149	87	such	such	ADJ
ejpam-5531	149	88	that	that	SCONJ
ejpam-5531	149	89	x	x	SYM
ejpam-5531	149	90	∈	∈	PROPN
ejpam-5531	149	91	mint(f−(v	mint(f−(v	PROPN
ejpam-5531	149	92	∪rv	∪rv	PROPN
ejpam-5531	149	93	)	)	PUNCT
ejpam-5531	149	94	)	)	PUNCT
ejpam-5531	149	95	;	;	PUNCT
ejpam-5531	149	96	(	(	PUNCT
ejpam-5531	149	97	3	3	X
ejpam-5531	149	98	)	)	PUNCT
ejpam-5531	149	99	for	for	ADP
ejpam-5531	149	100	each	each	DET
ejpam-5531	149	101	open	open	ADJ
ejpam-5531	149	102	set	set	VERB
ejpam-5531	149	103	v	v	NOUN
ejpam-5531	149	104	of	of	ADP
ejpam-5531	149	105	y	y	PRON
ejpam-5531	149	106	such	such	ADJ
ejpam-5531	149	107	that	that	SCONJ
ejpam-5531	149	108	f	f	PROPN
ejpam-5531	149	109	(	(	PUNCT
ejpam-5531	149	110	x	x	NOUN
ejpam-5531	149	111	)	)	PUNCT
ejpam-5531	149	112	∩	∩	NOUN
ejpam-5531	149	113	v	v	ADP
ejpam-5531	149	114	̸=	̸=	PROPN
ejpam-5531	149	115	∅	∅	NOUN
ejpam-5531	149	116	,	,	PUNCT
ejpam-5531	149	117	there	there	PRON
ejpam-5531	149	118	exists	exist	VERB
ejpam-5531	149	119	a	a	DET
ejpam-5531	149	120	rare	rare	ADJ
ejpam-5531	149	121	set	set	NOUN
ejpam-5531	149	122	rv	rv	PROPN
ejpam-5531	149	123	with	with	ADP
ejpam-5531	149	124	cl(v	cl(v	NOUN
ejpam-5531	149	125	)	)	PUNCT
ejpam-5531	149	126	∩rv	∩rv	NOUN
ejpam-5531	149	127	=	=	PUNCT
ejpam-5531	149	128	∅	∅	NOUN
ejpam-5531	149	129	such	such	ADJ
ejpam-5531	149	130	that	that	SCONJ
ejpam-5531	149	131	x	x	SYM
ejpam-5531	149	132	∈	∈	PROPN
ejpam-5531	149	133	mint(f−(cl(v	mint(f−(cl(v	NOUN
ejpam-5531	149	134	)	)	PUNCT
ejpam-5531	149	135	∪rv	∪rv	NOUN
ejpam-5531	149	136	)	)	PUNCT
ejpam-5531	149	137	)	)	PUNCT
ejpam-5531	149	138	;	;	PUNCT
ejpam-5531	149	139	(	(	PUNCT
ejpam-5531	149	140	4	4	X
ejpam-5531	149	141	)	)	PUNCT
ejpam-5531	149	142	for	for	ADP
ejpam-5531	149	143	each	each	DET
ejpam-5531	149	144	regular	regular	ADJ
ejpam-5531	149	145	open	open	ADJ
ejpam-5531	149	146	set	set	VERB
ejpam-5531	149	147	v	v	NOUN
ejpam-5531	149	148	of	of	ADP
ejpam-5531	149	149	y	y	PRON
ejpam-5531	149	150	such	such	ADJ
ejpam-5531	149	151	that	that	SCONJ
ejpam-5531	149	152	f	f	PROPN
ejpam-5531	149	153	(	(	PUNCT
ejpam-5531	149	154	x	x	NOUN
ejpam-5531	149	155	)	)	PUNCT
ejpam-5531	149	156	∩	∩	NOUN
ejpam-5531	149	157	v	v	ADP
ejpam-5531	149	158	̸=	̸=	PROPN
ejpam-5531	149	159	∅	∅	NOUN
ejpam-5531	149	160	,	,	PUNCT
ejpam-5531	149	161	there	there	PRON
ejpam-5531	149	162	exists	exist	VERB
ejpam-5531	149	163	a	a	DET
ejpam-5531	149	164	rare	rare	ADJ
ejpam-5531	149	165	set	set	NOUN
ejpam-5531	149	166	rv	rv	PROPN
ejpam-5531	149	167	with	with	ADP
ejpam-5531	149	168	v	v	NOUN
ejpam-5531	149	169	∩rv	∩rv	NOUN
ejpam-5531	149	170	=	=	VERB
ejpam-5531	149	171	∅	∅	NOUN
ejpam-5531	149	172	such	such	ADJ
ejpam-5531	149	173	that	that	SCONJ
ejpam-5531	149	174	x	x	SYM
ejpam-5531	149	175	∈	∈	PROPN
ejpam-5531	149	176	mint(f−(v	mint(f−(v	PROPN
ejpam-5531	149	177	∪rv	∪rv	PROPN
ejpam-5531	149	178	)	)	PUNCT
ejpam-5531	149	179	)	)	PUNCT
ejpam-5531	149	180	.	.	PUNCT
ejpam-5531	150	1	proof	proof	NOUN
ejpam-5531	150	2	.	.	PUNCT
ejpam-5531	151	1	the	the	DET
ejpam-5531	151	2	proofs	proof	NOUN
ejpam-5531	151	3	of	of	ADP
ejpam-5531	151	4	(	(	PUNCT
ejpam-5531	151	5	1	1	NUM
ejpam-5531	151	6	)	)	PUNCT
ejpam-5531	151	7	⇒	⇒	NOUN
ejpam-5531	151	8	(	(	PUNCT
ejpam-5531	151	9	2	2	NUM
ejpam-5531	151	10	)	)	PUNCT
ejpam-5531	151	11	,	,	PUNCT
ejpam-5531	151	12	(	(	PUNCT
ejpam-5531	151	13	2	2	X
ejpam-5531	151	14	)	)	PUNCT
ejpam-5531	151	15	⇒	⇒	NOUN
ejpam-5531	151	16	(	(	PUNCT
ejpam-5531	151	17	3	3	NUM
ejpam-5531	151	18	)	)	PUNCT
ejpam-5531	151	19	and	and	CCONJ
ejpam-5531	151	20	(	(	PUNCT
ejpam-5531	151	21	3	3	X
ejpam-5531	151	22	)	)	PUNCT
ejpam-5531	151	23	⇒	⇒	NOUN
ejpam-5531	151	24	(	(	PUNCT
ejpam-5531	151	25	4	4	X
ejpam-5531	151	26	)	)	PUNCT
ejpam-5531	151	27	are	be	AUX
ejpam-5531	151	28	similar	similar	ADJ
ejpam-5531	151	29	with	with	ADP
ejpam-5531	151	30	theorem	theorem	NOUN
ejpam-5531	151	31	1	1	NUM
ejpam-5531	151	32	.	.	PUNCT
ejpam-5531	151	33	(	(	PUNCT
ejpam-5531	151	34	4	4	X
ejpam-5531	151	35	)	)	PUNCT
ejpam-5531	151	36	⇒	⇒	NOUN
ejpam-5531	151	37	(	(	PUNCT
ejpam-5531	151	38	1	1	NUM
ejpam-5531	151	39	):	):	PUNCT
ejpam-5531	151	40	let	let	VERB
ejpam-5531	151	41	v	v	PART
ejpam-5531	151	42	be	be	AUX
ejpam-5531	151	43	an	an	DET
ejpam-5531	151	44	open	open	ADJ
ejpam-5531	151	45	set	set	NOUN
ejpam-5531	151	46	in	in	ADP
ejpam-5531	151	47	y	y	PRON
ejpam-5531	151	48	such	such	ADJ
ejpam-5531	151	49	that	that	SCONJ
ejpam-5531	151	50	f	f	PROPN
ejpam-5531	151	51	(	(	PUNCT
ejpam-5531	151	52	x	x	NOUN
ejpam-5531	151	53	)	)	PUNCT
ejpam-5531	151	54	∩	∩	NOUN
ejpam-5531	151	55	v	v	ADP
ejpam-5531	151	56	̸=	̸=	PROPN
ejpam-5531	151	57	∅.	∅.	ADV
ejpam-5531	151	58	then	then	ADV
ejpam-5531	151	59	f	f	PROPN
ejpam-5531	151	60	(	(	PUNCT
ejpam-5531	151	61	x	x	NOUN
ejpam-5531	151	62	)	)	PUNCT
ejpam-5531	151	63	∩	∩	NOUN
ejpam-5531	151	64	int(cl(v	int(cl(v	NOUN
ejpam-5531	151	65	)	)	PUNCT
ejpam-5531	151	66	)	)	PUNCT
ejpam-5531	152	1	̸=	̸=	PROPN
ejpam-5531	152	2	∅.	∅.	PRON
ejpam-5531	152	3	by	by	ADP
ejpam-5531	152	4	(	(	PUNCT
ejpam-5531	152	5	4	4	NUM
ejpam-5531	152	6	)	)	PUNCT
ejpam-5531	152	7	,	,	PUNCT
ejpam-5531	152	8	there	there	PRON
ejpam-5531	152	9	exists	exist	VERB
ejpam-5531	152	10	a	a	DET
ejpam-5531	152	11	rare	rare	ADJ
ejpam-5531	152	12	set	set	NOUN
ejpam-5531	152	13	rv	rv	PROPN
ejpam-5531	152	14	with	with	ADP
ejpam-5531	152	15	int(cl(v	int(cl(v	PROPN
ejpam-5531	152	16	)	)	PUNCT
ejpam-5531	152	17	)	)	PUNCT
ejpam-5531	153	1	∩	∩	PROPN
ejpam-5531	153	2	rv	rv	NOUN
ejpam-5531	154	1	=	=	PUNCT
ejpam-5531	154	2	∅	∅	NOUN
ejpam-5531	154	3	such	such	ADJ
ejpam-5531	154	4	that	that	SCONJ
ejpam-5531	154	5	x	x	SYM
ejpam-5531	154	6	∈	∈	NOUN
ejpam-5531	154	7	mint(f−(int(cl(v	mint(f−(int(cl(v	NOUN
ejpam-5531	154	8	)	)	PUNCT
ejpam-5531	154	9	)	)	PUNCT
ejpam-5531	154	10	∪	∪	ADP
ejpam-5531	154	11	rv	rv	PROPN
ejpam-5531	154	12	)	)	PUNCT
ejpam-5531	154	13	)	)	PUNCT
ejpam-5531	154	14	.	.	PUNCT
ejpam-5531	155	1	since	since	SCONJ
ejpam-5531	155	2	cl(v	cl(v	NOUN
ejpam-5531	155	3	)	)	PUNCT
ejpam-5531	155	4	\	\	PROPN
ejpam-5531	155	5	v	v	NOUN
ejpam-5531	155	6	is	be	AUX
ejpam-5531	155	7	a	a	DET
ejpam-5531	155	8	closed	closed	ADJ
ejpam-5531	155	9	rare	rare	ADJ
ejpam-5531	155	10	set	set	NOUN
ejpam-5531	155	11	,	,	PUNCT
ejpam-5531	155	12	by	by	ADP
ejpam-5531	155	13	lemma	lemma	PROPN
ejpam-5531	155	14	4	4	NUM
ejpam-5531	155	15	,	,	PUNCT
ejpam-5531	155	16	(	(	PUNCT
ejpam-5531	155	17	cl(v	cl(v	X
ejpam-5531	155	18	)	)	PUNCT
ejpam-5531	155	19	\	\	PROPN
ejpam-5531	155	20	v	v	X
ejpam-5531	155	21	)	)	PUNCT
ejpam-5531	155	22	∪rv	∪rv	PROPN
ejpam-5531	155	23	is	be	AUX
ejpam-5531	155	24	a	a	DET
ejpam-5531	155	25	rare	rare	ADJ
ejpam-5531	155	26	set	set	NOUN
ejpam-5531	155	27	.	.	PUNCT
ejpam-5531	156	1	therefore	therefore	ADV
ejpam-5531	156	2	,	,	PUNCT
ejpam-5531	156	3	sv	sv	INTJ
ejpam-5531	156	4	=	=	PUNCT
ejpam-5531	157	1	[	[	X
ejpam-5531	157	2	int(cl(v	int(cl(v	NOUN
ejpam-5531	157	3	)	)	PUNCT
ejpam-5531	157	4	)	)	PUNCT
ejpam-5531	157	5	\	\	PROPN
ejpam-5531	158	1	v	v	NOUN
ejpam-5531	158	2	]	]	PUNCT
ejpam-5531	158	3	∪rv	∪rv	PROPN
ejpam-5531	158	4	is	be	AUX
ejpam-5531	158	5	a	a	DET
ejpam-5531	158	6	rare	rare	ADJ
ejpam-5531	158	7	set	set	NOUN
ejpam-5531	158	8	.	.	PUNCT
ejpam-5531	159	1	and	and	CCONJ
ejpam-5531	159	2	int(cl(v	int(cl(v	NOUN
ejpam-5531	159	3	)	)	PUNCT
ejpam-5531	159	4	)	)	PUNCT
ejpam-5531	160	1	∪rv	∪rv	PROPN
ejpam-5531	160	2	=	=	PUNCT
ejpam-5531	160	3	v	v	X
ejpam-5531	160	4	∪	∪	VERB
ejpam-5531	160	5	[	[	PUNCT
ejpam-5531	160	6	int(cl(v	int(cl(v	NOUN
ejpam-5531	160	7	)	)	PUNCT
ejpam-5531	160	8	)	)	PUNCT
ejpam-5531	160	9	\v	\v	X
ejpam-5531	161	1	]	]	PUNCT
ejpam-5531	161	2	∪rv	∪rv	PROPN
ejpam-5531	161	3	=	=	SYM
ejpam-5531	161	4	v	v	ADP
ejpam-5531	161	5	∪sv	∪sv	NOUN
ejpam-5531	161	6	.	.	PUNCT
ejpam-5531	162	1	therefore	therefore	ADV
ejpam-5531	162	2	,	,	PUNCT
ejpam-5531	162	3	x	x	PROPN
ejpam-5531	162	4	∈	∈	PROPN
ejpam-5531	162	5	mint(f−(v	mint(f−(v	PROPN
ejpam-5531	162	6	∪sv	∪sv	NOUN
ejpam-5531	162	7	)	)	PUNCT
ejpam-5531	162	8	)	)	PUNCT
ejpam-5531	162	9	.	.	PUNCT
ejpam-5531	163	1	hence	hence	ADV
ejpam-5531	163	2	there	there	PRON
ejpam-5531	163	3	exists	exist	VERB
ejpam-5531	163	4	u	u	PROPN
ejpam-5531	163	5	∈	∈	PROPN
ejpam-5531	163	6	m(x	m(x	PROPN
ejpam-5531	163	7	)	)	PUNCT
ejpam-5531	163	8	such	such	ADJ
ejpam-5531	163	9	that	that	SCONJ
ejpam-5531	163	10	u	u	PROPN
ejpam-5531	163	11	⊂	⊂	PROPN
ejpam-5531	163	12	f−(v	f−(v	PROPN
ejpam-5531	163	13	∪	∪	PROPN
ejpam-5531	163	14	sv	sv	PROPN
ejpam-5531	163	15	)	)	PUNCT
ejpam-5531	163	16	and	and	CCONJ
ejpam-5531	163	17	f	f	PROPN
ejpam-5531	163	18	(	(	PUNCT
ejpam-5531	163	19	u	u	NOUN
ejpam-5531	163	20	)	)	PUNCT
ejpam-5531	163	21	∩	∩	NOUN
ejpam-5531	163	22	(	(	PUNCT
ejpam-5531	163	23	v	v	X
ejpam-5531	163	24	∪	∪	X
ejpam-5531	163	25	sv	sv	NOUN
ejpam-5531	163	26	)	)	PUNCT
ejpam-5531	163	27	̸=	̸=	PROPN
ejpam-5531	163	28	∅	∅	NOUN
ejpam-5531	163	29	for	for	ADP
ejpam-5531	163	30	every	every	DET
ejpam-5531	163	31	u	u	PROPN
ejpam-5531	163	32	∈	∈	PROPN
ejpam-5531	163	33	u	u	PROPN
ejpam-5531	163	34	.	.	PUNCT
ejpam-5531	163	35	remark	remark	PROPN
ejpam-5531	163	36	2	2	NUM
ejpam-5531	163	37	.	.	PUNCT
ejpam-5531	164	1	if	if	SCONJ
ejpam-5531	164	2	m	m	PROPN
ejpam-5531	164	3	=	=	SYM
ejpam-5531	164	4	τ	τ	PROPN
ejpam-5531	164	5	(	(	PUNCT
ejpam-5531	164	6	resp	resp	NOUN
ejpam-5531	164	7	.	.	PUNCT
ejpam-5531	165	1	α(x	α(x	PROPN
ejpam-5531	165	2	)	)	PUNCT
ejpam-5531	165	3	,	,	PUNCT
ejpam-5531	165	4	β(x	β(x	NOUN
ejpam-5531	165	5	)	)	PUNCT
ejpam-5531	165	6	,	,	PUNCT
ejpam-5531	165	7	so(x	so(x	NOUN
ejpam-5531	165	8	)	)	PUNCT
ejpam-5531	165	9	)	)	PUNCT
ejpam-5531	166	1	,	,	PUNCT
ejpam-5531	166	2	then	then	ADV
ejpam-5531	166	3	we	we	PRON
ejpam-5531	166	4	have	have	VERB
ejpam-5531	166	5	characterizations	characterization	NOUN
ejpam-5531	166	6	in	in	ADP
ejpam-5531	166	7	[	[	X
ejpam-5531	166	8	25	25	NUM
ejpam-5531	166	9	]	]	PUNCT
ejpam-5531	166	10	(	(	PUNCT
ejpam-5531	166	11	resp	resp	NOUN
ejpam-5531	166	12	.	.	PUNCT
ejpam-5531	167	1	[	[	X
ejpam-5531	167	2	4	4	NUM
ejpam-5531	167	3	]	]	PUNCT
ejpam-5531	167	4	,	,	PUNCT
ejpam-5531	167	5	[	[	X
ejpam-5531	167	6	14	14	NUM
ejpam-5531	167	7	]	]	PUNCT
ejpam-5531	167	8	,	,	PUNCT
ejpam-5531	167	9	[	[	X
ejpam-5531	167	10	15	15	NUM
ejpam-5531	167	11	]	]	PUNCT
ejpam-5531	167	12	)	)	PUNCT
ejpam-5531	167	13	.	.	PUNCT
ejpam-5531	168	1	by	by	ADP
ejpam-5531	168	2	theorem	theorem	NOUN
ejpam-5531	168	3	1	1	NUM
ejpam-5531	168	4	,	,	PUNCT
ejpam-5531	168	5	we	we	PRON
ejpam-5531	168	6	have	have	VERB
ejpam-5531	168	7	the	the	DET
ejpam-5531	168	8	following	follow	VERB
ejpam-5531	168	9	characterizations	characterization	NOUN
ejpam-5531	168	10	of	of	ADP
ejpam-5531	168	11	rare	rare	ADJ
ejpam-5531	168	12	m	m	NOUN
ejpam-5531	168	13	-	-	NOUN
ejpam-5531	168	14	continuity	continuity	NOUN
ejpam-5531	168	15	for	for	ADP
ejpam-5531	168	16	a	a	DET
ejpam-5531	168	17	function	function	NOUN
ejpam-5531	168	18	f	f	NOUN
ejpam-5531	168	19	:	:	PUNCT
ejpam-5531	168	20	(	(	PUNCT
ejpam-5531	168	21	x	x	X
ejpam-5531	168	22	,	,	PUNCT
ejpam-5531	168	23	m	m	NOUN
ejpam-5531	168	24	)	)	PUNCT
ejpam-5531	168	25	→	→	SYM
ejpam-5531	168	26	(	(	PUNCT
ejpam-5531	168	27	y	y	PROPN
ejpam-5531	168	28	,	,	PUNCT
ejpam-5531	168	29	σ	σ	PROPN
ejpam-5531	168	30	)	)	PUNCT
ejpam-5531	168	31	corollary	corollary	ADJ
ejpam-5531	168	32	1	1	NUM
ejpam-5531	168	33	.	.	PUNCT
ejpam-5531	169	1	for	for	ADP
ejpam-5531	169	2	a	a	DET
ejpam-5531	169	3	function	function	NOUN
ejpam-5531	169	4	f	f	NOUN
ejpam-5531	169	5	:	:	PUNCT
ejpam-5531	169	6	(	(	PUNCT
ejpam-5531	169	7	x	x	X
ejpam-5531	169	8	,	,	PUNCT
ejpam-5531	169	9	m	m	NOUN
ejpam-5531	169	10	)	)	PUNCT
ejpam-5531	169	11	→	→	SYM
ejpam-5531	169	12	(	(	PUNCT
ejpam-5531	169	13	y	y	PROPN
ejpam-5531	169	14	,	,	PUNCT
ejpam-5531	169	15	σ	σ	PROPN
ejpam-5531	169	16	)	)	PUNCT
ejpam-5531	169	17	,	,	PUNCT
ejpam-5531	169	18	the	the	DET
ejpam-5531	169	19	following	follow	VERB
ejpam-5531	169	20	properties	property	NOUN
ejpam-5531	169	21	are	be	AUX
ejpam-5531	169	22	equivalent	equivalent	ADJ
ejpam-5531	169	23	:	:	PUNCT
ejpam-5531	169	24	(	(	PUNCT
ejpam-5531	169	25	1	1	X
ejpam-5531	169	26	)	)	PUNCT
ejpam-5531	169	27	f	f	PROPN
ejpam-5531	169	28	is	be	AUX
ejpam-5531	169	29	rarely	rarely	ADV
ejpam-5531	169	30	m	m	ADJ
ejpam-5531	169	31	-	-	ADJ
ejpam-5531	169	32	continuous	continuous	ADJ
ejpam-5531	169	33	at	at	ADP
ejpam-5531	169	34	x	x	X
ejpam-5531	169	35	∈	∈	PROPN
ejpam-5531	169	36	x	x	X
ejpam-5531	169	37	;	;	PUNCT
ejpam-5531	169	38	(	(	PUNCT
ejpam-5531	169	39	2	2	X
ejpam-5531	169	40	)	)	PUNCT
ejpam-5531	169	41	for	for	ADP
ejpam-5531	169	42	each	each	DET
ejpam-5531	169	43	open	open	ADJ
ejpam-5531	169	44	set	set	VERB
ejpam-5531	169	45	v	v	NOUN
ejpam-5531	169	46	of	of	ADP
ejpam-5531	169	47	y	y	NOUN
ejpam-5531	169	48	containing	contain	VERB
ejpam-5531	169	49	f(x	f(x	PROPN
ejpam-5531	169	50	)	)	PUNCT
ejpam-5531	169	51	,	,	PUNCT
ejpam-5531	169	52	there	there	PRON
ejpam-5531	169	53	exists	exist	VERB
ejpam-5531	169	54	a	a	DET
ejpam-5531	169	55	rare	rare	ADJ
ejpam-5531	169	56	set	set	NOUN
ejpam-5531	169	57	rv	rv	PROPN
ejpam-5531	169	58	with	with	ADP
ejpam-5531	169	59	v	v	NOUN
ejpam-5531	169	60	∩rv	∩rv	NOUN
ejpam-5531	169	61	=	=	VERB
ejpam-5531	169	62	∅	∅	NOUN
ejpam-5531	169	63	such	such	ADJ
ejpam-5531	169	64	that	that	SCONJ
ejpam-5531	169	65	x	x	SYM
ejpam-5531	169	66	∈	∈	PROPN
ejpam-5531	169	67	mint(f−1(v	mint(f−1(v	NOUN
ejpam-5531	169	68	∪rv	∪rv	NOUN
ejpam-5531	169	69	)	)	PUNCT
ejpam-5531	169	70	)	)	PUNCT
ejpam-5531	169	71	;	;	PUNCT
ejpam-5531	169	72	(	(	PUNCT
ejpam-5531	169	73	3	3	X
ejpam-5531	169	74	)	)	PUNCT
ejpam-5531	169	75	for	for	ADP
ejpam-5531	169	76	each	each	DET
ejpam-5531	169	77	open	open	ADJ
ejpam-5531	169	78	set	set	VERB
ejpam-5531	169	79	v	v	NOUN
ejpam-5531	169	80	of	of	ADP
ejpam-5531	169	81	y	y	NOUN
ejpam-5531	169	82	containing	contain	VERB
ejpam-5531	169	83	f(x	f(x	PROPN
ejpam-5531	169	84	)	)	PUNCT
ejpam-5531	169	85	,	,	PUNCT
ejpam-5531	169	86	there	there	PRON
ejpam-5531	169	87	exists	exist	VERB
ejpam-5531	169	88	a	a	DET
ejpam-5531	169	89	rare	rare	ADJ
ejpam-5531	169	90	set	set	NOUN
ejpam-5531	169	91	rv	rv	PROPN
ejpam-5531	169	92	with	with	ADP
ejpam-5531	169	93	cl(v	cl(v	NOUN
ejpam-5531	169	94	)	)	PUNCT
ejpam-5531	169	95	∩	∩	NOUN
ejpam-5531	169	96	rv	rv	NOUN
ejpam-5531	169	97	=	=	PUNCT
ejpam-5531	169	98	∅	∅	NOUN
ejpam-5531	169	99	such	such	ADJ
ejpam-5531	169	100	that	that	SCONJ
ejpam-5531	169	101	x	x	SYM
ejpam-5531	169	102	∈	∈	PROPN
ejpam-5531	169	103	mint(f−1(cl(v	mint(f−1(cl(v	PROPN
ejpam-5531	169	104	)	)	PUNCT
ejpam-5531	169	105	∪rv	∪rv	NOUN
ejpam-5531	169	106	)	)	PUNCT
ejpam-5531	169	107	)	)	PUNCT
ejpam-5531	169	108	;	;	PUNCT
ejpam-5531	169	109	(	(	PUNCT
ejpam-5531	169	110	4	4	X
ejpam-5531	169	111	)	)	PUNCT
ejpam-5531	169	112	for	for	ADP
ejpam-5531	169	113	each	each	DET
ejpam-5531	169	114	regular	regular	ADJ
ejpam-5531	169	115	open	open	ADJ
ejpam-5531	169	116	set	set	VERB
ejpam-5531	169	117	v	v	NOUN
ejpam-5531	169	118	of	of	ADP
ejpam-5531	169	119	y	y	NOUN
ejpam-5531	169	120	containing	contain	VERB
ejpam-5531	169	121	f(x	f(x	PROPN
ejpam-5531	169	122	)	)	PUNCT
ejpam-5531	169	123	,	,	PUNCT
ejpam-5531	169	124	there	there	PRON
ejpam-5531	169	125	exists	exist	VERB
ejpam-5531	169	126	a	a	DET
ejpam-5531	169	127	rare	rare	ADJ
ejpam-5531	169	128	set	set	NOUN
ejpam-5531	169	129	rv	rv	PROPN
ejpam-5531	169	130	with	with	ADP
ejpam-5531	169	131	v	v	NOUN
ejpam-5531	169	132	∩rv	∩rv	NOUN
ejpam-5531	169	133	=	=	VERB
ejpam-5531	169	134	∅	∅	NOUN
ejpam-5531	169	135	such	such	ADJ
ejpam-5531	169	136	that	that	SCONJ
ejpam-5531	169	137	x	x	SYM
ejpam-5531	169	138	∈	∈	PROPN
ejpam-5531	169	139	mint(f−1(v	mint(f−1(v	NOUN
ejpam-5531	169	140	∪rv	∪rv	NOUN
ejpam-5531	169	141	)	)	PUNCT
ejpam-5531	169	142	)	)	PUNCT
ejpam-5531	169	143	;	;	PUNCT
ejpam-5531	169	144	(	(	PUNCT
ejpam-5531	169	145	5	5	X
ejpam-5531	169	146	)	)	PUNCT
ejpam-5531	169	147	for	for	ADP
ejpam-5531	169	148	each	each	DET
ejpam-5531	169	149	open	open	ADJ
ejpam-5531	169	150	set	set	VERB
ejpam-5531	169	151	v	v	NOUN
ejpam-5531	169	152	of	of	ADP
ejpam-5531	169	153	y	y	NOUN
ejpam-5531	169	154	containing	contain	VERB
ejpam-5531	169	155	f(x	f(x	PROPN
ejpam-5531	169	156	)	)	PUNCT
ejpam-5531	169	157	,	,	PUNCT
ejpam-5531	169	158	there	there	PRON
ejpam-5531	169	159	exists	exist	VERB
ejpam-5531	169	160	u	u	PROPN
ejpam-5531	169	161	∈	∈	PROPN
ejpam-5531	169	162	m(x	m(x	PROPN
ejpam-5531	169	163	)	)	PUNCT
ejpam-5531	170	1	such	such	ADJ
ejpam-5531	170	2	that	that	SCONJ
ejpam-5531	170	3	int[f(u)∩	int[f(u)∩	PROPN
ejpam-5531	170	4	(	(	PUNCT
ejpam-5531	170	5	y	y	PROPN
ejpam-5531	170	6	\	\	PROPN
ejpam-5531	170	7	v	v	NOUN
ejpam-5531	170	8	)	)	PUNCT
ejpam-5531	170	9	]	]	PUNCT
ejpam-5531	171	1	=	=	SYM
ejpam-5531	171	2	∅	∅	NOUN
ejpam-5531	171	3	,	,	PUNCT
ejpam-5531	171	4	(	(	PUNCT
ejpam-5531	171	5	6	6	NUM
ejpam-5531	171	6	)	)	PUNCT
ejpam-5531	171	7	for	for	ADP
ejpam-5531	171	8	each	each	DET
ejpam-5531	171	9	open	open	ADJ
ejpam-5531	171	10	set	set	VERB
ejpam-5531	171	11	v	v	NOUN
ejpam-5531	171	12	of	of	ADP
ejpam-5531	171	13	y	y	NOUN
ejpam-5531	171	14	containing	contain	VERB
ejpam-5531	171	15	f(x	f(x	PROPN
ejpam-5531	171	16	)	)	PUNCT
ejpam-5531	171	17	,	,	PUNCT
ejpam-5531	171	18	there	there	PRON
ejpam-5531	171	19	exists	exist	VERB
ejpam-5531	171	20	u	u	PROPN
ejpam-5531	171	21	∈	∈	PROPN
ejpam-5531	171	22	m(x	m(x	PROPN
ejpam-5531	171	23	)	)	PUNCT
ejpam-5531	171	24	such	such	ADJ
ejpam-5531	171	25	that	that	DET
ejpam-5531	171	26	int(f(u	int(f(u	NOUN
ejpam-5531	171	27	)	)	PUNCT
ejpam-5531	171	28	)	)	PUNCT
ejpam-5531	172	1	⊂	⊂	PROPN
ejpam-5531	172	2	cl(v	cl(v	NOUN
ejpam-5531	172	3	)	)	PUNCT
ejpam-5531	172	4	.	.	PUNCT
ejpam-5531	172	5	remark	remark	PROPN
ejpam-5531	172	6	3	3	NUM
ejpam-5531	172	7	.	.	PUNCT
ejpam-5531	173	1	if	if	SCONJ
ejpam-5531	173	2	m	m	PROPN
ejpam-5531	173	3	=	=	SYM
ejpam-5531	173	4	τ	τ	PROPN
ejpam-5531	173	5	(	(	PUNCT
ejpam-5531	173	6	resp	resp	NOUN
ejpam-5531	173	7	.	.	PUNCT
ejpam-5531	174	1	α	α	X
ejpam-5531	174	2	,	,	PUNCT
ejpam-5531	174	3	po(x	po(x	NUM
ejpam-5531	174	4	)	)	PUNCT
ejpam-5531	174	5	,	,	PUNCT
ejpam-5531	174	6	so(x	so(x	NOUN
ejpam-5531	174	7	)	)	PUNCT
ejpam-5531	174	8	)	)	PUNCT
ejpam-5531	174	9	,	,	PUNCT
ejpam-5531	174	10	then	then	ADV
ejpam-5531	174	11	by	by	ADP
ejpam-5531	174	12	corollary	corollary	ADJ
ejpam-5531	174	13	1	1	NUM
ejpam-5531	174	14	,	,	PUNCT
ejpam-5531	174	15	we	we	PRON
ejpam-5531	174	16	obtain	obtain	VERB
ejpam-5531	174	17	the	the	DET
ejpam-5531	174	18	characterizations	characterization	NOUN
ejpam-5531	174	19	of	of	ADP
ejpam-5531	174	20	rare	rare	ADJ
ejpam-5531	174	21	continuity	continuity	NOUN
ejpam-5531	174	22	[	[	X
ejpam-5531	174	23	19	19	NUM
ejpam-5531	174	24	]	]	PUNCT
ejpam-5531	174	25	(	(	PUNCT
ejpam-5531	174	26	resp	resp	NOUN
ejpam-5531	174	27	.	.	PUNCT
ejpam-5531	175	1	rare	rare	ADJ
ejpam-5531	175	2	α	α	NOUN
ejpam-5531	175	3	-	-	NOUN
ejpam-5531	175	4	continuity	continuity	NOUN
ejpam-5531	175	5	[	[	X
ejpam-5531	175	6	13	13	NUM
ejpam-5531	175	7	]	]	PUNCT
ejpam-5531	175	8	,	,	PUNCT
ejpam-5531	175	9	rare	rare	ADJ
ejpam-5531	175	10	pre	pre	NOUN
ejpam-5531	175	11	-	-	NOUN
ejpam-5531	175	12	continuity	continuity	NOUN
ejpam-5531	175	13	[	[	X
ejpam-5531	175	14	12	12	NUM
ejpam-5531	175	15	]	]	PUNCT
ejpam-5531	175	16	,	,	PUNCT
ejpam-5531	175	17	rare	rare	ADJ
ejpam-5531	175	18	quasicontinuity	quasicontinuity	NOUN
ejpam-5531	175	19	[	[	X
ejpam-5531	175	20	26	26	NUM
ejpam-5531	175	21	]	]	NUM
ejpam-5531	175	22	)	)	PUNCT
ejpam-5531	175	23	.	.	PUNCT
ejpam-5531	176	1	t.	t.	PROPN
ejpam-5531	176	2	noiri	noiri	PROPN
ejpam-5531	176	3	,	,	PUNCT
ejpam-5531	176	4	v.	v.	CCONJ
ejpam-5531	176	5	popa	popa	NOUN
ejpam-5531	176	6	/	/	SYM
ejpam-5531	176	7	eur	eur	PROPN
ejpam-5531	176	8	.	.	PUNCT
ejpam-5531	177	1	j.	j.	PROPN
ejpam-5531	177	2	pure	pure	PROPN
ejpam-5531	177	3	appl	appl	PROPN
ejpam-5531	177	4	.	.	PROPN
ejpam-5531	177	5	math	math	PROPN
ejpam-5531	177	6	,	,	PUNCT
ejpam-5531	177	7	17	17	NUM
ejpam-5531	177	8	(	(	PUNCT
ejpam-5531	177	9	4	4	NUM
ejpam-5531	177	10	)	)	PUNCT
ejpam-5531	177	11	(	(	PUNCT
ejpam-5531	177	12	2024	2024	NUM
ejpam-5531	177	13	)	)	PUNCT
ejpam-5531	177	14	,	,	PUNCT
ejpam-5531	177	15	3677	3677	NUM
ejpam-5531	177	16	-	-	SYM
ejpam-5531	177	17	3686	3686	NUM
ejpam-5531	177	18	3682	3682	NUM
ejpam-5531	177	19	4	4	NUM
ejpam-5531	177	20	.	.	PUNCT
ejpam-5531	177	21	ideal	ideal	ADJ
ejpam-5531	177	22	topological	topological	ADJ
ejpam-5531	177	23	spaces	space	NOUN
ejpam-5531	177	24	definition	definition	NOUN
ejpam-5531	177	25	8	8	NUM
ejpam-5531	177	26	.	.	PUNCT
ejpam-5531	178	1	a	a	DET
ejpam-5531	178	2	nonempty	nonempty	ADJ
ejpam-5531	178	3	collection	collection	NOUN
ejpam-5531	178	4	i	i	PRON
ejpam-5531	178	5	of	of	ADP
ejpam-5531	178	6	subsets	subset	NOUN
ejpam-5531	178	7	of	of	ADP
ejpam-5531	178	8	a	a	DET
ejpam-5531	178	9	set	set	NOUN
ejpam-5531	178	10	x	x	PUNCT
ejpam-5531	178	11	is	be	AUX
ejpam-5531	178	12	called	call	VERB
ejpam-5531	178	13	an	an	DET
ejpam-5531	178	14	ideal	ideal	NOUN
ejpam-5531	178	15	on	on	ADP
ejpam-5531	178	16	x	x	PUNCT
ejpam-5531	179	1	[	[	X
ejpam-5531	179	2	17	17	NUM
ejpam-5531	179	3	]	]	PUNCT
ejpam-5531	179	4	,	,	PUNCT
ejpam-5531	179	5	[	[	X
ejpam-5531	179	6	30	30	NUM
ejpam-5531	179	7	]	]	X
ejpam-5531	179	8	if	if	SCONJ
ejpam-5531	179	9	it	it	PRON
ejpam-5531	179	10	satisfies	satisfy	VERB
ejpam-5531	179	11	the	the	DET
ejpam-5531	179	12	following	follow	VERB
ejpam-5531	179	13	two	two	NUM
ejpam-5531	179	14	conditions	condition	NOUN
ejpam-5531	179	15	:	:	PUNCT
ejpam-5531	179	16	(	(	PUNCT
ejpam-5531	179	17	1	1	X
ejpam-5531	179	18	)	)	PUNCT
ejpam-5531	179	19	a	a	DET
ejpam-5531	179	20	∈	∈	NOUN
ejpam-5531	180	1	i	i	PRON
ejpam-5531	180	2	and	and	CCONJ
ejpam-5531	180	3	b	b	PROPN
ejpam-5531	180	4	⊂	⊂	PROPN
ejpam-5531	180	5	a	a	PRON
ejpam-5531	180	6	implies	imply	VERB
ejpam-5531	180	7	b	b	X
ejpam-5531	180	8	∈	∈	PROPN
ejpam-5531	180	9	i	i	PRON
ejpam-5531	180	10	,	,	PUNCT
ejpam-5531	180	11	(	(	PUNCT
ejpam-5531	180	12	2	2	X
ejpam-5531	180	13	)	)	PUNCT
ejpam-5531	181	1	a	a	DET
ejpam-5531	181	2	∈	∈	NOUN
ejpam-5531	181	3	i	i	PRON
ejpam-5531	181	4	and	and	CCONJ
ejpam-5531	181	5	b	b	X
ejpam-5531	181	6	∈	∈	PROPN
ejpam-5531	181	7	i	i	PRON
ejpam-5531	181	8	implies	imply	VERB
ejpam-5531	181	9	a	a	DET
ejpam-5531	181	10	∪b	∪b	PUNCT
ejpam-5531	181	11	∈	∈	PROPN
ejpam-5531	181	12	i.	i.	NOUN
ejpam-5531	181	13	a	a	DET
ejpam-5531	181	14	topological	topological	ADJ
ejpam-5531	181	15	space	space	NOUN
ejpam-5531	181	16	(	(	PUNCT
ejpam-5531	181	17	x	x	X
ejpam-5531	181	18	,	,	PUNCT
ejpam-5531	181	19	τ	τ	X
ejpam-5531	181	20	)	)	PUNCT
ejpam-5531	181	21	with	with	ADP
ejpam-5531	181	22	an	an	DET
ejpam-5531	181	23	ideal	ideal	ADJ
ejpam-5531	181	24	i	i	PRON
ejpam-5531	181	25	on	on	ADP
ejpam-5531	181	26	x	x	SYM
ejpam-5531	181	27	is	be	AUX
ejpam-5531	181	28	called	call	VERB
ejpam-5531	181	29	an	an	DET
ejpam-5531	181	30	ideal	ideal	ADJ
ejpam-5531	181	31	topological	topological	ADJ
ejpam-5531	181	32	space	space	NOUN
ejpam-5531	181	33	and	and	CCONJ
ejpam-5531	181	34	is	be	AUX
ejpam-5531	181	35	denoted	denote	VERB
ejpam-5531	181	36	by	by	ADP
ejpam-5531	181	37	(	(	PUNCT
ejpam-5531	181	38	x	x	X
ejpam-5531	181	39	,	,	PUNCT
ejpam-5531	181	40	τ	τ	PROPN
ejpam-5531	181	41	,	,	PUNCT
ejpam-5531	181	42	i	i	PROPN
ejpam-5531	181	43	)	)	PUNCT
ejpam-5531	181	44	.	.	PUNCT
ejpam-5531	182	1	let	let	VERB
ejpam-5531	182	2	(	(	PUNCT
ejpam-5531	182	3	x	x	X
ejpam-5531	182	4	,	,	PUNCT
ejpam-5531	182	5	τ	τ	PROPN
ejpam-5531	182	6	,	,	PUNCT
ejpam-5531	182	7	i	i	PRON
ejpam-5531	182	8	)	)	PUNCT
ejpam-5531	182	9	be	be	VERB
ejpam-5531	182	10	an	an	DET
ejpam-5531	182	11	ideal	ideal	ADJ
ejpam-5531	182	12	topological	topological	ADJ
ejpam-5531	182	13	space	space	NOUN
ejpam-5531	182	14	.	.	PUNCT
ejpam-5531	183	1	for	for	ADP
ejpam-5531	183	2	any	any	DET
ejpam-5531	183	3	subset	subset	NOUN
ejpam-5531	183	4	a	a	PRON
ejpam-5531	183	5	of	of	ADP
ejpam-5531	183	6	x	x	PROPN
ejpam-5531	183	7	,	,	PUNCT
ejpam-5531	183	8	a⋆(i	a⋆(i	PROPN
ejpam-5531	183	9	,	,	PUNCT
ejpam-5531	183	10	τ	τ	X
ejpam-5531	183	11	)	)	PUNCT
ejpam-5531	183	12	=	=	PRON
ejpam-5531	183	13	{	{	PUNCT
ejpam-5531	183	14	x	x	PUNCT
ejpam-5531	183	15	∈	∈	PROPN
ejpam-5531	183	16	x	x	X
ejpam-5531	183	17	:	:	PUNCT
ejpam-5531	183	18	u	u	NOUN
ejpam-5531	183	19	∩	∩	NOUN
ejpam-5531	183	20	a	a	X
ejpam-5531	183	21	/∈	/∈	PUNCT
ejpam-5531	183	22	i	i	PRON
ejpam-5531	183	23	for	for	ADP
ejpam-5531	183	24	every	every	DET
ejpam-5531	183	25	u	u	PROPN
ejpam-5531	183	26	∈	∈	PROPN
ejpam-5531	183	27	τ(x	τ(x	NOUN
ejpam-5531	183	28	)	)	PUNCT
ejpam-5531	183	29	}	}	PUNCT
ejpam-5531	183	30	,	,	PUNCT
ejpam-5531	183	31	where	where	SCONJ
ejpam-5531	183	32	τ(x	τ(x	NOUN
ejpam-5531	183	33	)	)	PUNCT
ejpam-5531	183	34	=	=	PRON
ejpam-5531	183	35	{	{	PUNCT
ejpam-5531	183	36	u	u	X
ejpam-5531	183	37	∈	∈	PROPN
ejpam-5531	183	38	τ	τ	X
ejpam-5531	183	39	:	:	PUNCT
ejpam-5531	183	40	x	x	SYM
ejpam-5531	183	41	∈	∈	PROPN
ejpam-5531	183	42	u	u	NOUN
ejpam-5531	183	43	}	}	PUNCT
ejpam-5531	183	44	,	,	PUNCT
ejpam-5531	183	45	is	be	AUX
ejpam-5531	183	46	called	call	VERB
ejpam-5531	183	47	the	the	DET
ejpam-5531	183	48	local	local	ADJ
ejpam-5531	183	49	function	function	NOUN
ejpam-5531	183	50	of	of	ADP
ejpam-5531	183	51	a	a	PRON
ejpam-5531	183	52	with	with	ADP
ejpam-5531	183	53	respect	respect	NOUN
ejpam-5531	183	54	to	to	ADP
ejpam-5531	183	55	τ	τ	PROPN
ejpam-5531	183	56	and	and	CCONJ
ejpam-5531	183	57	i	i	PRON
ejpam-5531	183	58	[	[	X
ejpam-5531	183	59	16	16	NUM
ejpam-5531	183	60	]	]	PUNCT
ejpam-5531	183	61	.	.	PUNCT
ejpam-5531	184	1	hereafter	hereafter	PROPN
ejpam-5531	184	2	a⋆(i	a⋆(i	PROPN
ejpam-5531	184	3	,	,	PUNCT
ejpam-5531	184	4	τ	τ	X
ejpam-5531	184	5	)	)	PUNCT
ejpam-5531	184	6	is	be	AUX
ejpam-5531	184	7	simply	simply	ADV
ejpam-5531	184	8	denoted	denote	VERB
ejpam-5531	184	9	by	by	ADP
ejpam-5531	184	10	a⋆.	a⋆.	NOUN
ejpam-5531	184	11	it	it	PRON
ejpam-5531	184	12	is	be	AUX
ejpam-5531	184	13	well	well	ADV
ejpam-5531	184	14	known	know	VERB
ejpam-5531	184	15	that	that	SCONJ
ejpam-5531	184	16	cl⋆(a	cl⋆(a	VERB
ejpam-5531	184	17	)	)	PUNCT
ejpam-5531	184	18	=	=	NOUN
ejpam-5531	184	19	a	a	DET
ejpam-5531	184	20	∪	∪	NOUN
ejpam-5531	184	21	a⋆	a⋆	ADP
ejpam-5531	184	22	defines	define	NOUN
ejpam-5531	184	23	a	a	DET
ejpam-5531	184	24	kuratowski	kuratowski	ADJ
ejpam-5531	184	25	closure	closure	NOUN
ejpam-5531	184	26	operator	operator	NOUN
ejpam-5531	184	27	on	on	ADP
ejpam-5531	184	28	x	x	PUNCT
ejpam-5531	184	29	and	and	CCONJ
ejpam-5531	184	30	the	the	DET
ejpam-5531	184	31	topology	topology	NOUN
ejpam-5531	184	32	generated	generate	VERB
ejpam-5531	184	33	by	by	ADP
ejpam-5531	184	34	cl⋆	cl⋆	PROPN
ejpam-5531	184	35	is	be	AUX
ejpam-5531	184	36	denoted	denote	VERB
ejpam-5531	184	37	by	by	ADP
ejpam-5531	184	38	τ⋆.	τ⋆.	PROPN
ejpam-5531	184	39	lemma	lemma	PROPN
ejpam-5531	184	40	5	5	X
ejpam-5531	184	41	.	.	PUNCT
ejpam-5531	185	1	let	let	VERB
ejpam-5531	185	2	(	(	PUNCT
ejpam-5531	185	3	x	x	X
ejpam-5531	185	4	,	,	PUNCT
ejpam-5531	185	5	τ	τ	PROPN
ejpam-5531	185	6	,	,	PUNCT
ejpam-5531	185	7	i	i	PRON
ejpam-5531	185	8	)	)	PUNCT
ejpam-5531	185	9	be	be	VERB
ejpam-5531	185	10	an	an	DET
ejpam-5531	185	11	ideal	ideal	ADJ
ejpam-5531	185	12	topological	topological	ADJ
ejpam-5531	185	13	space	space	NOUN
ejpam-5531	185	14	and	and	CCONJ
ejpam-5531	185	15	a	a	DET
ejpam-5531	185	16	,	,	PUNCT
ejpam-5531	185	17	b	b	PROPN
ejpam-5531	185	18	be	be	AUX
ejpam-5531	185	19	subsets	subset	NOUN
ejpam-5531	185	20	of	of	ADP
ejpam-5531	185	21	x.	x.	NOUN
ejpam-5531	185	22	then	then	ADV
ejpam-5531	185	23	the	the	DET
ejpam-5531	185	24	following	follow	VERB
ejpam-5531	185	25	properties	property	NOUN
ejpam-5531	185	26	hold	hold	VERB
ejpam-5531	185	27	:	:	PUNCT
ejpam-5531	185	28	(	(	PUNCT
ejpam-5531	185	29	1	1	X
ejpam-5531	185	30	)	)	PUNCT
ejpam-5531	185	31	a	a	DET
ejpam-5531	185	32	⊂	⊂	PROPN
ejpam-5531	185	33	b	b	PROPN
ejpam-5531	185	34	implies	imply	VERB
ejpam-5531	185	35	cl⋆(a	cl⋆(a	NOUN
ejpam-5531	185	36	)	)	PUNCT
ejpam-5531	185	37	⊂	⊂	PROPN
ejpam-5531	185	38	cl⋆(b	cl⋆(b	NOUN
ejpam-5531	185	39	)	)	PUNCT
ejpam-5531	185	40	,	,	PUNCT
ejpam-5531	185	41	(	(	PUNCT
ejpam-5531	185	42	2	2	X
ejpam-5531	185	43	)	)	PUNCT
ejpam-5531	185	44	cl⋆(x	cl⋆(x	NOUN
ejpam-5531	185	45	)	)	PUNCT
ejpam-5531	185	46	=	=	SYM
ejpam-5531	185	47	x	x	PROPN
ejpam-5531	185	48	and	and	CCONJ
ejpam-5531	185	49	cl⋆(∅	cl⋆(∅	NOUN
ejpam-5531	185	50	)	)	PUNCT
ejpam-5531	185	51	=	=	SYM
ejpam-5531	185	52	∅	∅	NOUN
ejpam-5531	185	53	,	,	PUNCT
ejpam-5531	185	54	(	(	PUNCT
ejpam-5531	185	55	3	3	X
ejpam-5531	185	56	)	)	PUNCT
ejpam-5531	185	57	cl⋆(a	cl⋆(a	NOUN
ejpam-5531	185	58	)	)	PUNCT
ejpam-5531	185	59	∪	∪	ADP
ejpam-5531	185	60	cl⋆(b	cl⋆(b	NOUN
ejpam-5531	185	61	)	)	PUNCT
ejpam-5531	185	62	⊂	⊂	PROPN
ejpam-5531	185	63	cl⋆(a	cl⋆(a	X
ejpam-5531	185	64	∪b	∪b	NOUN
ejpam-5531	185	65	)	)	PUNCT
ejpam-5531	185	66	.	.	PUNCT
ejpam-5531	186	1	definition	definition	NOUN
ejpam-5531	186	2	9	9	NUM
ejpam-5531	186	3	.	.	PUNCT
ejpam-5531	187	1	let	let	VERB
ejpam-5531	187	2	(	(	PUNCT
ejpam-5531	187	3	x	x	X
ejpam-5531	187	4	,	,	PUNCT
ejpam-5531	187	5	τ	τ	PROPN
ejpam-5531	187	6	,	,	PUNCT
ejpam-5531	187	7	i	i	PRON
ejpam-5531	187	8	)	)	PUNCT
ejpam-5531	187	9	be	be	VERB
ejpam-5531	187	10	an	an	DET
ejpam-5531	187	11	ideal	ideal	ADJ
ejpam-5531	187	12	topological	topological	ADJ
ejpam-5531	187	13	space	space	NOUN
ejpam-5531	187	14	.	.	PUNCT
ejpam-5531	188	1	a	a	DET
ejpam-5531	188	2	subset	subset	NOUN
ejpam-5531	188	3	a	a	PRON
ejpam-5531	188	4	of	of	ADP
ejpam-5531	188	5	x	x	SYM
ejpam-5531	188	6	is	be	AUX
ejpam-5531	188	7	said	say	VERB
ejpam-5531	188	8	to	to	PART
ejpam-5531	188	9	be	be	AUX
ejpam-5531	188	10	(	(	PUNCT
ejpam-5531	188	11	1	1	X
ejpam-5531	188	12	)	)	PUNCT
ejpam-5531	188	13	α	α	PROPN
ejpam-5531	188	14	-	-	PUNCT
ejpam-5531	188	15	i	i	PRON
ejpam-5531	188	16	-	-	PUNCT
ejpam-5531	188	17	open	open	ADJ
ejpam-5531	189	1	[	[	X
ejpam-5531	189	2	8	8	NUM
ejpam-5531	189	3	]	]	X
ejpam-5531	189	4	if	if	SCONJ
ejpam-5531	189	5	a	a	DET
ejpam-5531	189	6	⊂	⊂	PROPN
ejpam-5531	189	7	int(cl⋆(int(a	int(cl⋆(int(a	PROPN
ejpam-5531	189	8	)	)	PUNCT
ejpam-5531	189	9	)	)	PUNCT
ejpam-5531	189	10	)	)	PUNCT
ejpam-5531	189	11	,	,	PUNCT
ejpam-5531	189	12	(	(	PUNCT
ejpam-5531	189	13	2	2	X
ejpam-5531	189	14	)	)	PUNCT
ejpam-5531	189	15	semi	semi	ADJ
ejpam-5531	189	16	-	-	ADJ
ejpam-5531	189	17	i	i	PRON
ejpam-5531	189	18	-	-	PUNCT
ejpam-5531	189	19	open	open	ADJ
ejpam-5531	189	20	[	[	X
ejpam-5531	189	21	8	8	NUM
ejpam-5531	189	22	]	]	X
ejpam-5531	189	23	if	if	SCONJ
ejpam-5531	189	24	a	a	DET
ejpam-5531	189	25	⊂	⊂	X
ejpam-5531	189	26	cl⋆(int(a	cl⋆(int(a	PROPN
ejpam-5531	189	27	)	)	PUNCT
ejpam-5531	189	28	)	)	PUNCT
ejpam-5531	189	29	,	,	PUNCT
ejpam-5531	189	30	(	(	PUNCT
ejpam-5531	189	31	3	3	X
ejpam-5531	189	32	)	)	PUNCT
ejpam-5531	189	33	pre	pre	ADJ
ejpam-5531	189	34	-	-	ADJ
ejpam-5531	189	35	i	i	PRON
ejpam-5531	189	36	-	-	PUNCT
ejpam-5531	189	37	open	open	ADJ
ejpam-5531	189	38	[	[	X
ejpam-5531	189	39	2	2	NUM
ejpam-5531	189	40	]	]	PUNCT
ejpam-5531	189	41	if	if	SCONJ
ejpam-5531	189	42	a	a	DET
ejpam-5531	189	43	⊂	⊂	ADJ
ejpam-5531	189	44	int(cl⋆(a	int(cl⋆(a	NOUN
ejpam-5531	189	45	)	)	PUNCT
ejpam-5531	189	46	)	)	PUNCT
ejpam-5531	189	47	,	,	PUNCT
ejpam-5531	189	48	(	(	PUNCT
ejpam-5531	189	49	4	4	X
ejpam-5531	189	50	)	)	PUNCT
ejpam-5531	189	51	b	b	NOUN
ejpam-5531	189	52	-	-	PUNCT
ejpam-5531	189	53	i	i	PRON
ejpam-5531	189	54	-	-	PUNCT
ejpam-5531	189	55	open	open	ADJ
ejpam-5531	189	56	[	[	X
ejpam-5531	189	57	5	5	NUM
ejpam-5531	189	58	]	]	PUNCT
ejpam-5531	189	59	if	if	SCONJ
ejpam-5531	189	60	a	a	DET
ejpam-5531	189	61	⊂	⊂	PROPN
ejpam-5531	189	62	int(cl⋆(a	int(cl⋆(a	NOUN
ejpam-5531	189	63	)	)	PUNCT
ejpam-5531	189	64	)	)	PUNCT
ejpam-5531	189	65	∪	∪	ADP
ejpam-5531	189	66	cl⋆(int(a	cl⋆(int(a	PROPN
ejpam-5531	189	67	)	)	PUNCT
ejpam-5531	189	68	)	)	PUNCT
ejpam-5531	189	69	,	,	PUNCT
ejpam-5531	189	70	(	(	PUNCT
ejpam-5531	189	71	5	5	X
ejpam-5531	189	72	)	)	PUNCT
ejpam-5531	189	73	β	β	X
ejpam-5531	189	74	-	-	PUNCT
ejpam-5531	189	75	i	i	PRON
ejpam-5531	189	76	-	-	PUNCT
ejpam-5531	189	77	open	open	ADJ
ejpam-5531	189	78	[	[	X
ejpam-5531	189	79	9	9	NUM
ejpam-5531	189	80	]	]	X
ejpam-5531	189	81	if	if	SCONJ
ejpam-5531	189	82	a	a	DET
ejpam-5531	189	83	⊂	⊂	X
ejpam-5531	189	84	cl(int(cl⋆(a	cl(int(cl⋆(a	NOUN
ejpam-5531	189	85	)	)	PUNCT
ejpam-5531	189	86	)	)	PUNCT
ejpam-5531	189	87	)	)	PUNCT
ejpam-5531	190	1	,	,	PUNCT
ejpam-5531	190	2	(	(	PUNCT
ejpam-5531	190	3	6	6	X
ejpam-5531	190	4	)	)	PUNCT
ejpam-5531	190	5	weakly	weakly	ADJ
ejpam-5531	190	6	semi	semi	ADJ
ejpam-5531	190	7	-	-	ADJ
ejpam-5531	190	8	i	i	PRON
ejpam-5531	190	9	-	-	PUNCT
ejpam-5531	190	10	open	open	ADJ
ejpam-5531	190	11	[	[	X
ejpam-5531	190	12	6	6	NUM
ejpam-5531	190	13	]	]	PUNCT
ejpam-5531	190	14	if	if	SCONJ
ejpam-5531	190	15	a	a	PRON
ejpam-5531	190	16	⊂	⊂	PROPN
ejpam-5531	190	17	cl⋆(int(cl(a	cl⋆(int(cl(a	X
ejpam-5531	190	18	)	)	PUNCT
ejpam-5531	190	19	)	)	PUNCT
ejpam-5531	190	20	)	)	PUNCT
ejpam-5531	190	21	,	,	PUNCT
ejpam-5531	190	22	(	(	PUNCT
ejpam-5531	190	23	7	7	X
ejpam-5531	190	24	)	)	PUNCT
ejpam-5531	190	25	weakly	weakly	ADJ
ejpam-5531	190	26	b	b	X
ejpam-5531	190	27	-	-	PUNCT
ejpam-5531	190	28	i	i	PRON
ejpam-5531	190	29	-	-	PUNCT
ejpam-5531	190	30	open	open	ADJ
ejpam-5531	190	31	[	[	X
ejpam-5531	190	32	22	22	NUM
ejpam-5531	190	33	]	]	PUNCT
ejpam-5531	190	34	if	if	SCONJ
ejpam-5531	190	35	a	a	DET
ejpam-5531	190	36	⊂	⊂	X
ejpam-5531	190	37	cl(int(cl⋆(a	cl(int(cl⋆(a	NOUN
ejpam-5531	190	38	)	)	PUNCT
ejpam-5531	190	39	)	)	PUNCT
ejpam-5531	190	40	)	)	PUNCT
ejpam-5531	190	41	∪	∪	ADP
ejpam-5531	190	42	cl⋆(int(cl(a	cl⋆(int(cl(a	PROPN
ejpam-5531	190	43	)	)	PUNCT
ejpam-5531	190	44	)	)	PUNCT
ejpam-5531	190	45	)	)	PUNCT
ejpam-5531	190	46	,	,	PUNCT
ejpam-5531	190	47	(	(	PUNCT
ejpam-5531	190	48	8)	8)	NUM
ejpam-5531	190	49	strongly	strongly	ADV
ejpam-5531	190	50	β	β	AUX
ejpam-5531	190	51	-	-	ADJ
ejpam-5531	190	52	i	i	PRON
ejpam-5531	190	53	-	-	PUNCT
ejpam-5531	190	54	open	open	ADJ
ejpam-5531	190	55	[	[	X
ejpam-5531	190	56	7	7	NUM
ejpam-5531	190	57	]	]	X
ejpam-5531	190	58	if	if	SCONJ
ejpam-5531	190	59	a	a	DET
ejpam-5531	190	60	⊂	⊂	PROPN
ejpam-5531	190	61	cl⋆(int(cl⋆(a	cl⋆(int(cl⋆(a	PROPN
ejpam-5531	190	62	)	)	PUNCT
ejpam-5531	190	63	)	)	PUNCT
ejpam-5531	190	64	)	)	PUNCT
ejpam-5531	190	65	.	.	PUNCT
ejpam-5531	191	1	among	among	ADP
ejpam-5531	191	2	the	the	DET
ejpam-5531	191	3	sets	set	NOUN
ejpam-5531	191	4	in	in	ADP
ejpam-5531	191	5	definition	definition	NOUN
ejpam-5531	191	6	9	9	NUM
ejpam-5531	191	7	,	,	PUNCT
ejpam-5531	191	8	we	we	PRON
ejpam-5531	191	9	have	have	VERB
ejpam-5531	191	10	the	the	DET
ejpam-5531	191	11	following	follow	VERB
ejpam-5531	191	12	relations	relation	NOUN
ejpam-5531	191	13	:	:	PUNCT
ejpam-5531	191	14	diagram	diagram	VERB
ejpam-5531	191	15	open	open	ADJ
ejpam-5531	191	16	⇒	⇒	PROPN
ejpam-5531	191	17	α	α	PROPN
ejpam-5531	191	18	-	-	ADJ
ejpam-5531	191	19	i	i	PRON
ejpam-5531	191	20	-	-	PUNCT
ejpam-5531	191	21	open	open	ADJ
ejpam-5531	191	22	⇒	⇒	NOUN
ejpam-5531	191	23	semi	semi	ADJ
ejpam-5531	191	24	-	-	ADJ
ejpam-5531	191	25	i	i	PRON
ejpam-5531	191	26	-	-	PUNCT
ejpam-5531	191	27	open	open	ADJ
ejpam-5531	191	28	⇒	⇒	NOUN
ejpam-5531	191	29	weakly	weakly	ADJ
ejpam-5531	191	30	semi	semi	ADJ
ejpam-5531	191	31	-	-	ADJ
ejpam-5531	191	32	i	i	PRON
ejpam-5531	191	33	-	-	PUNCT
ejpam-5531	191	34	open	open	ADJ
ejpam-5531	191	35	⇓	⇓	PROPN
ejpam-5531	191	36	⇓	⇓	PROPN
ejpam-5531	191	37	⇓	⇓	PROPN
ejpam-5531	191	38	pre	pre	ADJ
ejpam-5531	191	39	-	-	ADJ
ejpam-5531	191	40	i	i	PRON
ejpam-5531	191	41	-	-	PUNCT
ejpam-5531	191	42	open	open	ADJ
ejpam-5531	191	43	⇒	⇒	NOUN
ejpam-5531	191	44	b	b	X
ejpam-5531	191	45	-	-	PUNCT
ejpam-5531	191	46	i	i	NOUN
ejpam-5531	191	47	-	-	PUNCT
ejpam-5531	191	48	open	open	ADJ
ejpam-5531	191	49	⇒	⇒	NOUN
ejpam-5531	191	50	weakly	weakly	ADJ
ejpam-5531	191	51	b	b	X
ejpam-5531	191	52	-	-	PUNCT
ejpam-5531	191	53	i	i	NOUN
ejpam-5531	191	54	-	-	PUNCT
ejpam-5531	191	55	open	open	ADJ
ejpam-5531	191	56	⇓	⇓	PROPN
ejpam-5531	191	57	⇑	⇑	PROPN
ejpam-5531	191	58	strongly	strongly	ADV
ejpam-5531	191	59	β	β	AUX
ejpam-5531	191	60	-	-	ADJ
ejpam-5531	191	61	i	i	NOUN
ejpam-5531	191	62	-	-	PUNCT
ejpam-5531	191	63	open	open	ADJ
ejpam-5531	191	64	⇒	⇒	NOUN
ejpam-5531	191	65	β	β	X
ejpam-5531	191	66	-	-	PUNCT
ejpam-5531	191	67	i	i	PRON
ejpam-5531	191	68	-	-	PUNCT
ejpam-5531	191	69	open	open	VERB
ejpam-5531	191	70	the	the	DET
ejpam-5531	191	71	family	family	NOUN
ejpam-5531	191	72	of	of	ADP
ejpam-5531	191	73	all	all	DET
ejpam-5531	191	74	α	α	PROPN
ejpam-5531	191	75	-	-	ADJ
ejpam-5531	191	76	i	i	PRON
ejpam-5531	191	77	-	-	PUNCT
ejpam-5531	191	78	open	open	ADJ
ejpam-5531	191	79	(	(	PUNCT
ejpam-5531	191	80	resp	resp	NOUN
ejpam-5531	191	81	.	.	PUNCT
ejpam-5531	192	1	semi	semi	ADJ
ejpam-5531	192	2	-	-	ADJ
ejpam-5531	192	3	i	i	PRON
ejpam-5531	192	4	-	-	PUNCT
ejpam-5531	192	5	open	open	ADJ
ejpam-5531	192	6	,	,	PUNCT
ejpam-5531	192	7	pre	pre	ADJ
ejpam-5531	192	8	-	-	ADJ
ejpam-5531	192	9	i	i	PRON
ejpam-5531	192	10	-	-	PUNCT
ejpam-5531	192	11	open	open	ADJ
ejpam-5531	192	12	,	,	PUNCT
ejpam-5531	192	13	b	b	X
ejpam-5531	192	14	-	-	PUNCT
ejpam-5531	192	15	i	i	PRON
ejpam-5531	192	16	-	-	PUNCT
ejpam-5531	192	17	open	open	ADJ
ejpam-5531	192	18	,	,	PUNCT
ejpam-5531	192	19	β	β	X
ejpam-5531	192	20	-	-	ADJ
ejpam-5531	192	21	i	i	PRON
ejpam-5531	192	22	-	-	PUNCT
ejpam-5531	192	23	open	open	ADJ
ejpam-5531	192	24	,	,	PUNCT
ejpam-5531	192	25	weakly	weakly	ADJ
ejpam-5531	192	26	semi	semi	ADJ
ejpam-5531	192	27	-	-	ADJ
ejpam-5531	192	28	i	i	PRON
ejpam-5531	192	29	-	-	PUNCT
ejpam-5531	192	30	open	open	ADJ
ejpam-5531	192	31	,	,	PUNCT
ejpam-5531	192	32	weakly	weakly	ADJ
ejpam-5531	192	33	b	b	X
ejpam-5531	192	34	-	-	PUNCT
ejpam-5531	192	35	i	i	NOUN
ejpam-5531	192	36	-	-	PUNCT
ejpam-5531	192	37	open	open	ADJ
ejpam-5531	192	38	,	,	PUNCT
ejpam-5531	192	39	strongly	strongly	ADV
ejpam-5531	192	40	β	β	X
ejpam-5531	192	41	-	-	ADJ
ejpam-5531	192	42	i	i	PRON
ejpam-5531	192	43	-	-	PUNCT
ejpam-5531	192	44	open	open	ADJ
ejpam-5531	192	45	)	)	PUNCT
ejpam-5531	192	46	sets	set	NOUN
ejpam-5531	192	47	in	in	ADP
ejpam-5531	192	48	an	an	DET
ejpam-5531	192	49	ideal	ideal	ADJ
ejpam-5531	192	50	topological	topological	ADJ
ejpam-5531	192	51	space	space	NOUN
ejpam-5531	192	52	(	(	PUNCT
ejpam-5531	192	53	x	x	X
ejpam-5531	192	54	,	,	PUNCT
ejpam-5531	192	55	τ	τ	PROPN
ejpam-5531	192	56	,	,	PUNCT
ejpam-5531	192	57	i	i	PROPN
ejpam-5531	192	58	)	)	PUNCT
ejpam-5531	192	59	is	be	AUX
ejpam-5531	192	60	denoted	denote	VERB
ejpam-5531	192	61	by	by	ADP
ejpam-5531	192	62	αio(x	αio(x	PROPN
ejpam-5531	192	63	)	)	PUNCT
ejpam-5531	192	64	(	(	PUNCT
ejpam-5531	192	65	resp	resp	NOUN
ejpam-5531	192	66	.	.	PUNCT
ejpam-5531	193	1	sio(x	sio(x	VERB
ejpam-5531	193	2	)	)	PUNCT
ejpam-5531	193	3	,	,	PUNCT
ejpam-5531	193	4	pio(x	pio(x	PROPN
ejpam-5531	193	5	)	)	PUNCT
ejpam-5531	193	6	,	,	PUNCT
ejpam-5531	193	7	bio(x	bio(x	PROPN
ejpam-5531	193	8	)	)	PUNCT
ejpam-5531	193	9	,	,	PUNCT
ejpam-5531	193	10	βio(x	βio(x	NUM
ejpam-5531	193	11	)	)	PUNCT
ejpam-5531	193	12	,	,	PUNCT
ejpam-5531	193	13	wsio(x	wsio(x	NOUN
ejpam-5531	193	14	)	)	PUNCT
ejpam-5531	193	15	,	,	PUNCT
ejpam-5531	193	16	wbio(x	wbio(x	PROPN
ejpam-5531	193	17	)	)	PUNCT
ejpam-5531	193	18	,	,	PUNCT
ejpam-5531	193	19	sβio(x	sβio(x	NOUN
ejpam-5531	193	20	)	)	PUNCT
ejpam-5531	193	21	)	)	PUNCT
ejpam-5531	193	22	.	.	PUNCT
ejpam-5531	194	1	t.	t.	PROPN
ejpam-5531	194	2	noiri	noiri	PROPN
ejpam-5531	194	3	,	,	PUNCT
ejpam-5531	194	4	v.	v.	CCONJ
ejpam-5531	194	5	popa	popa	NOUN
ejpam-5531	194	6	/	/	SYM
ejpam-5531	194	7	eur	eur	PROPN
ejpam-5531	194	8	.	.	PUNCT
ejpam-5531	195	1	j.	j.	PROPN
ejpam-5531	195	2	pure	pure	PROPN
ejpam-5531	195	3	appl	appl	PROPN
ejpam-5531	195	4	.	.	PROPN
ejpam-5531	195	5	math	math	PROPN
ejpam-5531	195	6	,	,	PUNCT
ejpam-5531	195	7	17	17	NUM
ejpam-5531	195	8	(	(	PUNCT
ejpam-5531	195	9	4	4	NUM
ejpam-5531	195	10	)	)	PUNCT
ejpam-5531	195	11	(	(	PUNCT
ejpam-5531	195	12	2024	2024	NUM
ejpam-5531	195	13	)	)	PUNCT
ejpam-5531	195	14	,	,	PUNCT
ejpam-5531	195	15	3677	3677	NUM
ejpam-5531	195	16	-	-	SYM
ejpam-5531	195	17	3686	3686	NUM
ejpam-5531	195	18	3683	3683	NUM
ejpam-5531	195	19	remark	remark	NOUN
ejpam-5531	195	20	4	4	NUM
ejpam-5531	195	21	.	.	PUNCT
ejpam-5531	196	1	if	if	SCONJ
ejpam-5531	196	2	i	i	PRON
ejpam-5531	196	3	=	=	SYM
ejpam-5531	196	4	{	{	PUNCT
ejpam-5531	196	5	∅	∅	NOUN
ejpam-5531	196	6	}	}	PUNCT
ejpam-5531	196	7	,	,	PUNCT
ejpam-5531	196	8	then	then	ADV
ejpam-5531	196	9	a⋆	a⋆	ADV
ejpam-5531	196	10	=	=	NOUN
ejpam-5531	196	11	cl(a	cl(a	X
ejpam-5531	196	12	)	)	PUNCT
ejpam-5531	196	13	and	and	CCONJ
ejpam-5531	196	14	cl⋆(a	cl⋆(a	NOUN
ejpam-5531	196	15	)	)	PUNCT
ejpam-5531	196	16	=	=	PUNCT
ejpam-5531	196	17	a⋆	a⋆	NOUN
ejpam-5531	196	18	∪a	∪a	NUM
ejpam-5531	196	19	=	=	SYM
ejpam-5531	196	20	cl(a	cl(a	X
ejpam-5531	196	21	)	)	PUNCT
ejpam-5531	196	22	.	.	PUNCT
ejpam-5531	197	1	therefore	therefore	ADV
ejpam-5531	197	2	,	,	PUNCT
ejpam-5531	197	3	(	(	PUNCT
ejpam-5531	197	4	1	1	X
ejpam-5531	197	5	)	)	PUNCT
ejpam-5531	197	6	τ⋆	τ⋆	NOUN
ejpam-5531	197	7	=	=	SYM
ejpam-5531	198	1	τ	τ	PROPN
ejpam-5531	198	2	,	,	PUNCT
ejpam-5531	198	3	αio(x	αio(x	PROPN
ejpam-5531	198	4	)	)	PUNCT
ejpam-5531	198	5	=	=	SYM
ejpam-5531	198	6	α(x	α(x	NOUN
ejpam-5531	198	7	)	)	PUNCT
ejpam-5531	198	8	,	,	PUNCT
ejpam-5531	198	9	sio(x	sio(x	NOUN
ejpam-5531	198	10	)	)	PUNCT
ejpam-5531	198	11	=	=	SYM
ejpam-5531	198	12	so(x	so(x	NUM
ejpam-5531	198	13	)	)	PUNCT
ejpam-5531	198	14	,	,	PUNCT
ejpam-5531	198	15	pio(x	pio(x	PROPN
ejpam-5531	198	16	)	)	PUNCT
ejpam-5531	198	17	=	=	NOUN
ejpam-5531	198	18	po(x	po(x	NUM
ejpam-5531	198	19	)	)	PUNCT
ejpam-5531	198	20	,	,	PUNCT
ejpam-5531	198	21	bio(x	bio(x	PROPN
ejpam-5531	198	22	)	)	PUNCT
ejpam-5531	198	23	=	=	PUNCT
ejpam-5531	198	24	bo(x	bo(x	X
ejpam-5531	198	25	)	)	PUNCT
ejpam-5531	198	26	and	and	CCONJ
ejpam-5531	198	27	βio(x	βio(x	X
ejpam-5531	198	28	)	)	PUNCT
ejpam-5531	198	29	=	=	SYM
ejpam-5531	198	30	β(x	β(x	NOUN
ejpam-5531	198	31	)	)	PUNCT
ejpam-5531	198	32	.	.	PUNCT
ejpam-5531	199	1	(	(	PUNCT
ejpam-5531	199	2	2	2	X
ejpam-5531	199	3	)	)	PUNCT
ejpam-5531	199	4	wsio(x	wsio(x	NOUN
ejpam-5531	199	5	)	)	PUNCT
ejpam-5531	199	6	,	,	PUNCT
ejpam-5531	199	7	wbio(x	wbio(x	PROPN
ejpam-5531	199	8	)	)	PUNCT
ejpam-5531	199	9	,	,	PUNCT
ejpam-5531	199	10	sβio(x	sβio(x	NOUN
ejpam-5531	199	11	)	)	PUNCT
ejpam-5531	199	12	and	and	CCONJ
ejpam-5531	199	13	βio(x	βio(x	X
ejpam-5531	199	14	)	)	PUNCT
ejpam-5531	199	15	are	be	AUX
ejpam-5531	199	16	coincide	coincide	ADJ
ejpam-5531	199	17	with	with	ADP
ejpam-5531	199	18	β(x	β(x	NOUN
ejpam-5531	199	19	)	)	PUNCT
ejpam-5531	199	20	.	.	PUNCT
ejpam-5531	200	1	definition	definition	NOUN
ejpam-5531	200	2	10	10	NUM
ejpam-5531	200	3	.	.	PUNCT
ejpam-5531	201	1	by	by	ADP
ejpam-5531	201	2	mio(x	mio(x	PROPN
ejpam-5531	201	3	)	)	PUNCT
ejpam-5531	201	4	,	,	PUNCT
ejpam-5531	201	5	we	we	PRON
ejpam-5531	201	6	denote	denote	VERB
ejpam-5531	201	7	each	each	DET
ejpam-5531	201	8	one	one	NUM
ejpam-5531	201	9	of	of	ADP
ejpam-5531	201	10	the	the	DET
ejpam-5531	201	11	families	family	NOUN
ejpam-5531	201	12	τ⋆	τ⋆	SYM
ejpam-5531	201	13	,	,	PUNCT
ejpam-5531	201	14	αio(x	αio(x	PROPN
ejpam-5531	201	15	)	)	PUNCT
ejpam-5531	201	16	,	,	PUNCT
ejpam-5531	201	17	sio(x	sio(x	NOUN
ejpam-5531	201	18	)	)	PUNCT
ejpam-5531	201	19	,	,	PUNCT
ejpam-5531	201	20	pio(x	pio(x	PROPN
ejpam-5531	201	21	)	)	PUNCT
ejpam-5531	201	22	,	,	PUNCT
ejpam-5531	201	23	bio(x	bio(x	PROPN
ejpam-5531	201	24	)	)	PUNCT
ejpam-5531	201	25	,	,	PUNCT
ejpam-5531	201	26	βio(x	βio(x	NUM
ejpam-5531	201	27	)	)	PUNCT
ejpam-5531	201	28	,	,	PUNCT
ejpam-5531	201	29	wsio(x	wsio(x	NOUN
ejpam-5531	201	30	)	)	PUNCT
ejpam-5531	201	31	,	,	PUNCT
ejpam-5531	201	32	wbio(x	wbio(x	PROPN
ejpam-5531	201	33	)	)	PUNCT
ejpam-5531	201	34	,	,	PUNCT
ejpam-5531	201	35	sβio(x	sβio(x	NOUN
ejpam-5531	201	36	)	)	PUNCT
ejpam-5531	201	37	.	.	PUNCT
ejpam-5531	202	1	lemma	lemma	PROPN
ejpam-5531	202	2	6	6	NUM
ejpam-5531	202	3	.	.	PUNCT
ejpam-5531	203	1	let	let	VERB
ejpam-5531	203	2	(	(	PUNCT
ejpam-5531	203	3	x	x	X
ejpam-5531	203	4	,	,	PUNCT
ejpam-5531	203	5	τ	τ	PROPN
ejpam-5531	203	6	,	,	PUNCT
ejpam-5531	203	7	i	i	PRON
ejpam-5531	203	8	)	)	PUNCT
ejpam-5531	203	9	be	be	VERB
ejpam-5531	203	10	an	an	DET
ejpam-5531	203	11	ideal	ideal	ADJ
ejpam-5531	203	12	topological	topological	ADJ
ejpam-5531	203	13	space	space	NOUN
ejpam-5531	203	14	.	.	PUNCT
ejpam-5531	204	1	then	then	ADV
ejpam-5531	204	2	mio(x	mio(x	PROPN
ejpam-5531	204	3	)	)	PUNCT
ejpam-5531	204	4	is	be	AUX
ejpam-5531	204	5	an	an	DET
ejpam-5531	204	6	m	m	NOUN
ejpam-5531	204	7	-	-	NOUN
ejpam-5531	204	8	structure	structure	NOUN
ejpam-5531	204	9	and	and	CCONJ
ejpam-5531	204	10	has	have	VERB
ejpam-5531	204	11	property	property	NOUN
ejpam-5531	204	12	b.	b.	PROPN
ejpam-5531	204	13	proof	proof	NOUN
ejpam-5531	204	14	.	.	PUNCT
ejpam-5531	205	1	the	the	DET
ejpam-5531	205	2	proof	proof	NOUN
ejpam-5531	205	3	follows	follow	VERB
ejpam-5531	205	4	from	from	ADP
ejpam-5531	205	5	lemma	lemma	PROPN
ejpam-5531	205	6	5(1)(2	5(1)(2	PROPN
ejpam-5531	205	7	)	)	PUNCT
ejpam-5531	205	8	.	.	PUNCT
ejpam-5531	206	1	as	as	ADP
ejpam-5531	206	2	an	an	DET
ejpam-5531	206	3	example	example	NOUN
ejpam-5531	206	4	,	,	PUNCT
ejpam-5531	206	5	we	we	PRON
ejpam-5531	206	6	shall	shall	AUX
ejpam-5531	206	7	show	show	VERB
ejpam-5531	206	8	that	that	SCONJ
ejpam-5531	206	9	αio(x	αio(x	PROPN
ejpam-5531	206	10	)	)	PUNCT
ejpam-5531	206	11	has	have	VERB
ejpam-5531	206	12	property	property	NOUN
ejpam-5531	206	13	b.	b.	PROPN
ejpam-5531	206	14	let	let	VERB
ejpam-5531	206	15	aα	aα	NOUN
ejpam-5531	206	16	be	be	AUX
ejpam-5531	206	17	an	an	DET
ejpam-5531	206	18	α	α	NOUN
ejpam-5531	206	19	-	-	PUNCT
ejpam-5531	206	20	i	i	PRON
ejpam-5531	206	21	-	-	PUNCT
ejpam-5531	206	22	open	open	ADJ
ejpam-5531	206	23	set	set	NOUN
ejpam-5531	206	24	for	for	ADP
ejpam-5531	206	25	each	each	DET
ejpam-5531	206	26	α	α	NOUN
ejpam-5531	206	27	∈	∈	PROPN
ejpam-5531	206	28	λ	λ	PROPN
ejpam-5531	206	29	.	.	PUNCT
ejpam-5531	207	1	then	then	ADV
ejpam-5531	207	2	aα	aα	PROPN
ejpam-5531	207	3	⊂	⊂	X
ejpam-5531	207	4	int(cl⋆(int(aα	int(cl⋆(int(aα	PROPN
ejpam-5531	207	5	)	)	PUNCT
ejpam-5531	207	6	)	)	PUNCT
ejpam-5531	207	7	)	)	PUNCT
ejpam-5531	208	1	⊂	⊂	PROPN
ejpam-5531	208	2	int(cl⋆(int(∪α∈λaα	int(cl⋆(int(∪α∈λaα	NOUN
ejpam-5531	208	3	)	)	PUNCT
ejpam-5531	208	4	)	)	PUNCT
ejpam-5531	208	5	)	)	PUNCT
ejpam-5531	209	1	for	for	ADP
ejpam-5531	209	2	each	each	DET
ejpam-5531	209	3	α	α	NOUN
ejpam-5531	209	4	∈	∈	PROPN
ejpam-5531	209	5	λ	λ	NOUN
ejpam-5531	209	6	and	and	CCONJ
ejpam-5531	209	7	hence	hence	ADV
ejpam-5531	209	8	∪α∈λaα	∪α∈λaα	PROPN
ejpam-5531	209	9	⊂	⊂	PROPN
ejpam-5531	209	10	int(cl⋆(int(∪α∈λaα	int(cl⋆(int(∪α∈λaα	NOUN
ejpam-5531	209	11	)	)	PUNCT
ejpam-5531	209	12	)	)	PUNCT
ejpam-5531	209	13	)	)	PUNCT
ejpam-5531	209	14	.	.	PUNCT
ejpam-5531	210	1	therefore	therefore	ADV
ejpam-5531	210	2	,	,	PUNCT
ejpam-5531	210	3	∪α∈λaα	∪α∈λaα	PROPN
ejpam-5531	210	4	is	be	AUX
ejpam-5531	210	5	α	α	PROPN
ejpam-5531	210	6	-	-	PUNCT
ejpam-5531	210	7	i	i	PRON
ejpam-5531	210	8	-	-	PUNCT
ejpam-5531	210	9	open	open	ADJ
ejpam-5531	210	10	.	.	PUNCT
ejpam-5531	211	1	remark	remark	NOUN
ejpam-5531	211	2	5	5	NUM
ejpam-5531	211	3	.	.	PUNCT
ejpam-5531	212	1	it	it	PRON
ejpam-5531	212	2	is	be	AUX
ejpam-5531	212	3	shown	show	VERB
ejpam-5531	212	4	in	in	ADP
ejpam-5531	212	5	theorem	theorem	ADJ
ejpam-5531	212	6	3.4	3.4	NUM
ejpam-5531	212	7	of	of	ADP
ejpam-5531	212	8	[	[	X
ejpam-5531	212	9	8	8	NUM
ejpam-5531	212	10	]	]	PUNCT
ejpam-5531	212	11	(	(	PUNCT
ejpam-5531	212	12	resp	resp	NOUN
ejpam-5531	212	13	.	.	PUNCT
ejpam-5531	213	1	theorem	theorem	VERB
ejpam-5531	213	2	2.10	2.10	NUM
ejpam-5531	213	3	of	of	ADP
ejpam-5531	213	4	[	[	X
ejpam-5531	213	5	2	2	NUM
ejpam-5531	213	6	]	]	PUNCT
ejpam-5531	213	7	,	,	PUNCT
ejpam-5531	213	8	theorem	theorem	VERB
ejpam-5531	213	9	2.1	2.1	NUM
ejpam-5531	213	10	of	of	ADP
ejpam-5531	213	11	[	[	X
ejpam-5531	213	12	6	6	NUM
ejpam-5531	213	13	]	]	PUNCT
ejpam-5531	213	14	,	,	PUNCT
ejpam-5531	213	15	theorem	theorem	VERB
ejpam-5531	213	16	2.7	2.7	NUM
ejpam-5531	213	17	of	of	ADP
ejpam-5531	213	18	[	[	X
ejpam-5531	213	19	22	22	NUM
ejpam-5531	213	20	]	]	PUNCT
ejpam-5531	213	21	,	,	PUNCT
ejpam-5531	213	22	proposition	proposition	NOUN
ejpam-5531	213	23	3	3	NUM
ejpam-5531	213	24	of	of	ADP
ejpam-5531	213	25	[	[	X
ejpam-5531	213	26	7	7	NUM
ejpam-5531	213	27	]	]	PUNCT
ejpam-5531	213	28	)	)	PUNCT
ejpam-5531	213	29	that	that	SCONJ
ejpam-5531	213	30	sio(x	sio(x	VERB
ejpam-5531	213	31	)	)	PUNCT
ejpam-5531	213	32	(	(	PUNCT
ejpam-5531	213	33	resp	resp	NOUN
ejpam-5531	213	34	.	.	PUNCT
ejpam-5531	214	1	pio(x	pio(x	PROPN
ejpam-5531	214	2	)	)	PUNCT
ejpam-5531	214	3	,	,	PUNCT
ejpam-5531	215	1	wsio(x	wsio(x	NOUN
ejpam-5531	215	2	)	)	PUNCT
ejpam-5531	215	3	,	,	PUNCT
ejpam-5531	215	4	wbio(x	wbio(x	PROPN
ejpam-5531	215	5	)	)	PUNCT
ejpam-5531	215	6	,	,	PUNCT
ejpam-5531	215	7	sβio(x	sβio(x	NOUN
ejpam-5531	215	8	)	)	PUNCT
ejpam-5531	215	9	)	)	PUNCT
ejpam-5531	215	10	has	have	VERB
ejpam-5531	215	11	property	property	NOUN
ejpam-5531	215	12	b.	b.	PROPN
ejpam-5531	215	13	definition	definition	NOUN
ejpam-5531	215	14	11	11	NUM
ejpam-5531	215	15	.	.	PUNCT
ejpam-5531	216	1	let	let	VERB
ejpam-5531	216	2	(	(	PUNCT
ejpam-5531	216	3	x	x	X
ejpam-5531	216	4	,	,	PUNCT
ejpam-5531	216	5	τ	τ	PROPN
ejpam-5531	216	6	,	,	PUNCT
ejpam-5531	216	7	i	i	PRON
ejpam-5531	216	8	)	)	PUNCT
ejpam-5531	216	9	be	be	VERB
ejpam-5531	216	10	an	an	DET
ejpam-5531	216	11	ideal	ideal	ADJ
ejpam-5531	216	12	topological	topological	ADJ
ejpam-5531	216	13	space	space	NOUN
ejpam-5531	216	14	.	.	PUNCT
ejpam-5531	217	1	for	for	ADP
ejpam-5531	217	2	a	a	DET
ejpam-5531	217	3	subset	subset	NOUN
ejpam-5531	217	4	a	a	PRON
ejpam-5531	217	5	of	of	ADP
ejpam-5531	217	6	x	x	PRON
ejpam-5531	217	7	,	,	PUNCT
ejpam-5531	217	8	the	the	DET
ejpam-5531	217	9	mio(x)-closure	mio(x)-closure	NOUN
ejpam-5531	217	10	mcli(a	mcli(a	PROPN
ejpam-5531	217	11	)	)	PUNCT
ejpam-5531	217	12	and	and	CCONJ
ejpam-5531	217	13	the	the	DET
ejpam-5531	217	14	mio(x)-interior	mio(x)-interior	PROPN
ejpam-5531	217	15	minti(a	minti(a	PROPN
ejpam-5531	217	16	)	)	PUNCT
ejpam-5531	217	17	are	be	AUX
ejpam-5531	217	18	defined	define	VERB
ejpam-5531	217	19	as	as	SCONJ
ejpam-5531	217	20	follows	follow	VERB
ejpam-5531	217	21	:	:	PUNCT
ejpam-5531	217	22	(	(	PUNCT
ejpam-5531	217	23	1	1	X
ejpam-5531	217	24	)	)	PUNCT
ejpam-5531	217	25	mcli(a	mcli(a	NOUN
ejpam-5531	217	26	)	)	PUNCT
ejpam-5531	218	1	=	=	PUNCT
ejpam-5531	218	2	∩{f	∩{f	NOUN
ejpam-5531	218	3	:	:	PUNCT
ejpam-5531	218	4	a	a	DET
ejpam-5531	218	5	⊂	⊂	PROPN
ejpam-5531	218	6	f	f	X
ejpam-5531	218	7	,	,	PUNCT
ejpam-5531	218	8	x	x	SYM
ejpam-5531	218	9	\	\	PROPN
ejpam-5531	218	10	f	f	PROPN
ejpam-5531	218	11	∈	∈	PROPN
ejpam-5531	218	12	mio(x	mio(x	PROPN
ejpam-5531	218	13	)	)	PUNCT
ejpam-5531	218	14	}	}	PUNCT
ejpam-5531	218	15	,	,	PUNCT
ejpam-5531	218	16	(	(	PUNCT
ejpam-5531	218	17	2	2	X
ejpam-5531	218	18	)	)	PUNCT
ejpam-5531	218	19	minti(a	minti(a	PROPN
ejpam-5531	218	20	)	)	PUNCT
ejpam-5531	218	21	=	=	PUNCT
ejpam-5531	219	1	∪{u	∪{u	VERB
ejpam-5531	219	2	:	:	PUNCT
ejpam-5531	219	3	u	u	X
ejpam-5531	219	4	⊂	⊂	PROPN
ejpam-5531	219	5	a	a	X
ejpam-5531	219	6	,	,	PUNCT
ejpam-5531	219	7	u	u	PROPN
ejpam-5531	219	8	∈	∈	PROPN
ejpam-5531	219	9	mio(x	mio(x	PROPN
ejpam-5531	219	10	)	)	PUNCT
ejpam-5531	219	11	}	}	PUNCT
ejpam-5531	219	12	.	.	PUNCT
ejpam-5531	220	1	let	let	VERB
ejpam-5531	220	2	(	(	PUNCT
ejpam-5531	220	3	x	x	X
ejpam-5531	220	4	,	,	PUNCT
ejpam-5531	220	5	τ	τ	PROPN
ejpam-5531	220	6	,	,	PUNCT
ejpam-5531	220	7	i	i	PRON
ejpam-5531	220	8	)	)	PUNCT
ejpam-5531	220	9	be	be	VERB
ejpam-5531	220	10	an	an	DET
ejpam-5531	220	11	ideal	ideal	ADJ
ejpam-5531	220	12	topological	topological	ADJ
ejpam-5531	220	13	space	space	NOUN
ejpam-5531	220	14	and	and	CCONJ
ejpam-5531	220	15	mio(x	mio(x	NOUN
ejpam-5531	220	16	)	)	PUNCT
ejpam-5531	220	17	the	the	DET
ejpam-5531	220	18	m	m	NOUN
ejpam-5531	220	19	-	-	NOUN
ejpam-5531	220	20	structure	structure	NOUN
ejpam-5531	220	21	on	on	ADP
ejpam-5531	220	22	x.	x.	NOUN
ejpam-5531	220	23	if	if	SCONJ
ejpam-5531	220	24	mio(x	mio(x	PROPN
ejpam-5531	220	25	)	)	PUNCT
ejpam-5531	220	26	=	=	SYM
ejpam-5531	220	27	αio(x	αio(x	PROPN
ejpam-5531	220	28	)	)	PUNCT
ejpam-5531	220	29	(	(	PUNCT
ejpam-5531	220	30	resp	resp	NOUN
ejpam-5531	220	31	.	.	PUNCT
ejpam-5531	221	1	sio(x	sio(x	VERB
ejpam-5531	221	2	)	)	PUNCT
ejpam-5531	221	3	,	,	PUNCT
ejpam-5531	221	4	pio(x	pio(x	PROPN
ejpam-5531	221	5	)	)	PUNCT
ejpam-5531	221	6	,	,	PUNCT
ejpam-5531	221	7	bio(x	bio(x	PROPN
ejpam-5531	221	8	)	)	PUNCT
ejpam-5531	221	9	,	,	PUNCT
ejpam-5531	221	10	βio(x	βio(x	NUM
ejpam-5531	221	11	)	)	PUNCT
ejpam-5531	221	12	,	,	PUNCT
ejpam-5531	221	13	wsio(x	wsio(x	NOUN
ejpam-5531	221	14	)	)	PUNCT
ejpam-5531	221	15	,	,	PUNCT
ejpam-5531	221	16	wbio(x	wbio(x	PROPN
ejpam-5531	221	17	)	)	PUNCT
ejpam-5531	221	18	,	,	PUNCT
ejpam-5531	221	19	sβio(x	sβio(x	NOUN
ejpam-5531	221	20	)	)	PUNCT
ejpam-5531	221	21	)	)	PUNCT
ejpam-5531	221	22	,	,	PUNCT
ejpam-5531	221	23	then	then	ADV
ejpam-5531	221	24	we	we	PRON
ejpam-5531	221	25	have	have	VERB
ejpam-5531	221	26	(	(	PUNCT
ejpam-5531	221	27	1	1	X
ejpam-5531	221	28	)	)	PUNCT
ejpam-5531	221	29	mcli(a	mcli(a	NOUN
ejpam-5531	221	30	)	)	PUNCT
ejpam-5531	222	1	=	=	SYM
ejpam-5531	222	2	αcli(a	αcli(a	PROPN
ejpam-5531	222	3	)	)	PUNCT
ejpam-5531	222	4	(	(	PUNCT
ejpam-5531	222	5	resp	resp	NOUN
ejpam-5531	222	6	.	.	PUNCT
ejpam-5531	223	1	scli(a	scli(a	X
ejpam-5531	223	2	)	)	PUNCT
ejpam-5531	223	3	,	,	PUNCT
ejpam-5531	223	4	pcli(a	pcli(a	NOUN
ejpam-5531	223	5	)	)	PUNCT
ejpam-5531	223	6	,	,	PUNCT
ejpam-5531	223	7	bcli(a	bcli(a	NOUN
ejpam-5531	223	8	)	)	PUNCT
ejpam-5531	223	9	,	,	PUNCT
ejpam-5531	223	10	βcli(a	βcli(a	PROPN
ejpam-5531	223	11	)	)	PUNCT
ejpam-5531	223	12	,	,	PUNCT
ejpam-5531	223	13	wscli(a	wscli(a	PROPN
ejpam-5531	223	14	)	)	PUNCT
ejpam-5531	223	15	,	,	PUNCT
ejpam-5531	223	16	wbcli(a	wbcli(a	PROPN
ejpam-5531	223	17	)	)	PUNCT
ejpam-5531	223	18	,	,	PUNCT
ejpam-5531	223	19	sβcli(a	sβcli(a	NOUN
ejpam-5531	223	20	)	)	PUNCT
ejpam-5531	223	21	)	)	PUNCT
ejpam-5531	223	22	,	,	PUNCT
ejpam-5531	223	23	(	(	PUNCT
ejpam-5531	223	24	2	2	X
ejpam-5531	223	25	)	)	PUNCT
ejpam-5531	223	26	minti(a	minti(a	PROPN
ejpam-5531	223	27	)	)	PUNCT
ejpam-5531	224	1	=	=	SYM
ejpam-5531	224	2	αinti(a	αinti(a	X
ejpam-5531	224	3	)	)	PUNCT
ejpam-5531	224	4	(	(	PUNCT
ejpam-5531	224	5	resp	resp	NOUN
ejpam-5531	224	6	.	.	PUNCT
ejpam-5531	225	1	sinti(a	sinti(a	PROPN
ejpam-5531	225	2	)	)	PUNCT
ejpam-5531	225	3	,	,	PUNCT
ejpam-5531	225	4	pinti(a	pinti(a	NOUN
ejpam-5531	225	5	)	)	PUNCT
ejpam-5531	225	6	,	,	PUNCT
ejpam-5531	225	7	binti(a	binti(a	ADP
ejpam-5531	225	8	)	)	PUNCT
ejpam-5531	225	9	,	,	PUNCT
ejpam-5531	225	10	βinti(a	βinti(a	NOUN
ejpam-5531	225	11	)	)	PUNCT
ejpam-5531	225	12	,	,	PUNCT
ejpam-5531	225	13	wsinti(a	wsinti(a	PROPN
ejpam-5531	225	14	)	)	PUNCT
ejpam-5531	225	15	,	,	PUNCT
ejpam-5531	225	16	wbinti(a	wbinti(a	PROPN
ejpam-5531	225	17	)	)	PUNCT
ejpam-5531	225	18	,	,	PUNCT
ejpam-5531	225	19	sβinti(a	sβinti(a	NOUN
ejpam-5531	225	20	)	)	PUNCT
ejpam-5531	225	21	)	)	PUNCT
ejpam-5531	225	22	.	.	PUNCT
ejpam-5531	226	1	5	5	X
ejpam-5531	226	2	.	.	X
ejpam-5531	226	3	rarely	rarely	ADV
ejpam-5531	226	4	m	m	PROPN
ejpam-5531	226	5	-	-	PUNCT
ejpam-5531	226	6	i	i	ADV
ejpam-5531	226	7	-	-	PUNCT
ejpam-5531	226	8	continuous	continuous	ADJ
ejpam-5531	226	9	multifunctions	multifunction	NOUN
ejpam-5531	226	10	in	in	ADP
ejpam-5531	226	11	this	this	DET
ejpam-5531	226	12	section	section	NOUN
ejpam-5531	226	13	,	,	PUNCT
ejpam-5531	226	14	by	by	ADP
ejpam-5531	226	15	using	use	VERB
ejpam-5531	226	16	the	the	DET
ejpam-5531	226	17	results	result	NOUN
ejpam-5531	226	18	in	in	ADP
ejpam-5531	226	19	section	section	NOUN
ejpam-5531	226	20	3	3	NUM
ejpam-5531	226	21	,	,	PUNCT
ejpam-5531	226	22	we	we	PRON
ejpam-5531	226	23	obtain	obtain	VERB
ejpam-5531	226	24	properties	property	NOUN
ejpam-5531	226	25	of	of	ADP
ejpam-5531	226	26	upper	upper	ADJ
ejpam-5531	226	27	/	/	SYM
ejpam-5531	226	28	lower	low	ADJ
ejpam-5531	226	29	rarely	rarely	ADV
ejpam-5531	226	30	m	m	VERB
ejpam-5531	226	31	-	-	ADJ
ejpam-5531	226	32	i	i	ADV
ejpam-5531	226	33	-	-	PUNCT
ejpam-5531	226	34	continuous	continuous	ADJ
ejpam-5531	226	35	multifunction	multifunction	NOUN
ejpam-5531	226	36	f	f	NOUN
ejpam-5531	226	37	:	:	PUNCT
ejpam-5531	226	38	(	(	PUNCT
ejpam-5531	226	39	x	x	X
ejpam-5531	226	40	,	,	PUNCT
ejpam-5531	226	41	τ	τ	PROPN
ejpam-5531	226	42	,	,	PUNCT
ejpam-5531	226	43	i	i	NOUN
ejpam-5531	226	44	)	)	PUNCT
ejpam-5531	226	45	→	→	SYM
ejpam-5531	226	46	(	(	PUNCT
ejpam-5531	226	47	y	y	PROPN
ejpam-5531	226	48	,	,	PUNCT
ejpam-5531	226	49	σ	σ	PROPN
ejpam-5531	226	50	)	)	PUNCT
ejpam-5531	226	51	.	.	PUNCT
ejpam-5531	227	1	definition	definition	NOUN
ejpam-5531	227	2	12	12	NUM
ejpam-5531	227	3	.	.	PUNCT
ejpam-5531	228	1	let	let	VERB
ejpam-5531	228	2	(	(	PUNCT
ejpam-5531	228	3	x	x	X
ejpam-5531	228	4	,	,	PUNCT
ejpam-5531	228	5	τ	τ	PROPN
ejpam-5531	228	6	,	,	PUNCT
ejpam-5531	228	7	i	i	PRON
ejpam-5531	228	8	)	)	PUNCT
ejpam-5531	228	9	be	be	VERB
ejpam-5531	228	10	an	an	DET
ejpam-5531	228	11	ideal	ideal	ADJ
ejpam-5531	228	12	topological	topological	ADJ
ejpam-5531	228	13	space	space	NOUN
ejpam-5531	228	14	and	and	CCONJ
ejpam-5531	228	15	(	(	PUNCT
ejpam-5531	228	16	y	y	PROPN
ejpam-5531	228	17	,	,	PUNCT
ejpam-5531	228	18	σ	σ	PROPN
ejpam-5531	228	19	)	)	PUNCT
ejpam-5531	228	20	a	a	DET
ejpam-5531	228	21	topological	topological	ADJ
ejpam-5531	228	22	space	space	NOUN
ejpam-5531	228	23	.	.	PUNCT
ejpam-5531	229	1	a	a	DET
ejpam-5531	229	2	multifunction	multifunction	NOUN
ejpam-5531	229	3	f	f	NOUN
ejpam-5531	229	4	:	:	PUNCT
ejpam-5531	229	5	(	(	PUNCT
ejpam-5531	229	6	x	x	X
ejpam-5531	229	7	,	,	PUNCT
ejpam-5531	229	8	τ	τ	PROPN
ejpam-5531	229	9	,	,	PUNCT
ejpam-5531	229	10	i	i	NOUN
ejpam-5531	229	11	)	)	PUNCT
ejpam-5531	229	12	→	→	SYM
ejpam-5531	229	13	(	(	PUNCT
ejpam-5531	229	14	y	y	PROPN
ejpam-5531	229	15	,	,	PUNCT
ejpam-5531	229	16	σ	σ	PROPN
ejpam-5531	229	17	)	)	PUNCT
ejpam-5531	229	18	is	be	AUX
ejpam-5531	229	19	said	say	VERB
ejpam-5531	229	20	to	to	PART
ejpam-5531	229	21	be	be	AUX
ejpam-5531	229	22	(	(	PUNCT
ejpam-5531	229	23	1	1	X
ejpam-5531	229	24	)	)	PUNCT
ejpam-5531	229	25	upper	upper	ADJ
ejpam-5531	229	26	rarely	rarely	ADV
ejpam-5531	229	27	m	m	PROPN
ejpam-5531	229	28	-	-	ADJ
ejpam-5531	229	29	i	i	PRON
ejpam-5531	229	30	-	-	NOUN
ejpam-5531	229	31	continuous	continuous	ADJ
ejpam-5531	229	32	at	at	ADP
ejpam-5531	229	33	a	a	DET
ejpam-5531	229	34	point	point	NOUN
ejpam-5531	229	35	x	x	SYM
ejpam-5531	229	36	∈	∈	NOUN
ejpam-5531	229	37	x	x	INTJ
ejpam-5531	229	38	if	if	SCONJ
ejpam-5531	229	39	for	for	ADP
ejpam-5531	229	40	each	each	DET
ejpam-5531	229	41	open	open	ADJ
ejpam-5531	229	42	set	set	VERB
ejpam-5531	229	43	v	v	NOUN
ejpam-5531	229	44	containing	contain	VERB
ejpam-5531	229	45	f	f	X
ejpam-5531	229	46	(	(	PUNCT
ejpam-5531	229	47	x	x	NOUN
ejpam-5531	229	48	)	)	PUNCT
ejpam-5531	229	49	,	,	PUNCT
ejpam-5531	229	50	there	there	PRON
ejpam-5531	229	51	exist	exist	VERB
ejpam-5531	229	52	a	a	DET
ejpam-5531	229	53	rare	rare	ADJ
ejpam-5531	229	54	set	set	NOUN
ejpam-5531	229	55	rv	rv	PROPN
ejpam-5531	229	56	with	with	ADP
ejpam-5531	229	57	rv	rv	PROPN
ejpam-5531	229	58	∩	∩	PROPN
ejpam-5531	229	59	v	v	NOUN
ejpam-5531	229	60	=	=	NOUN
ejpam-5531	229	61	∅	∅	NOUN
ejpam-5531	229	62	and	and	CCONJ
ejpam-5531	229	63	an	an	DET
ejpam-5531	229	64	mi	mi	NOUN
ejpam-5531	229	65	-	-	ADJ
ejpam-5531	229	66	open	open	ADJ
ejpam-5531	229	67	set	set	NOUN
ejpam-5531	229	68	u	u	PROPN
ejpam-5531	229	69	∈	∈	PROPN
ejpam-5531	229	70	mio(x	mio(x	NOUN
ejpam-5531	229	71	)	)	PUNCT
ejpam-5531	229	72	containing	contain	VERB
ejpam-5531	229	73	x	x	PUNCT
ejpam-5531	229	74	such	such	ADJ
ejpam-5531	229	75	that	that	SCONJ
ejpam-5531	229	76	f	f	PROPN
ejpam-5531	229	77	(	(	PUNCT
ejpam-5531	229	78	u	u	NOUN
ejpam-5531	229	79	)	)	PUNCT
ejpam-5531	229	80	⊂	⊂	PROPN
ejpam-5531	229	81	v	v	ADP
ejpam-5531	229	82	∪rv	∪rv	PROPN
ejpam-5531	229	83	,	,	PUNCT
ejpam-5531	229	84	(	(	PUNCT
ejpam-5531	229	85	2	2	X
ejpam-5531	229	86	)	)	PUNCT
ejpam-5531	229	87	lower	low	ADJ
ejpam-5531	229	88	rarely	rarely	ADV
ejpam-5531	229	89	m	m	VERB
ejpam-5531	229	90	-	-	ADJ
ejpam-5531	229	91	i	i	PRON
ejpam-5531	229	92	-	-	NOUN
ejpam-5531	229	93	continuous	continuous	ADJ
ejpam-5531	229	94	at	at	ADP
ejpam-5531	229	95	a	a	DET
ejpam-5531	229	96	point	point	NOUN
ejpam-5531	229	97	x	x	SYM
ejpam-5531	229	98	∈	∈	NOUN
ejpam-5531	229	99	x	x	INTJ
ejpam-5531	229	100	if	if	SCONJ
ejpam-5531	229	101	for	for	ADP
ejpam-5531	229	102	each	each	DET
ejpam-5531	229	103	open	open	ADJ
ejpam-5531	229	104	set	set	VERB
ejpam-5531	229	105	v	v	NUM
ejpam-5531	229	106	meeting	meeting	NOUN
ejpam-5531	229	107	f	f	X
ejpam-5531	229	108	(	(	PUNCT
ejpam-5531	229	109	x	x	NOUN
ejpam-5531	229	110	)	)	PUNCT
ejpam-5531	229	111	,	,	PUNCT
ejpam-5531	229	112	there	there	PRON
ejpam-5531	229	113	exist	exist	VERB
ejpam-5531	229	114	a	a	DET
ejpam-5531	229	115	rare	rare	ADJ
ejpam-5531	229	116	set	set	NOUN
ejpam-5531	229	117	rv	rv	PROPN
ejpam-5531	229	118	with	with	ADP
ejpam-5531	229	119	rv	rv	PROPN
ejpam-5531	229	120	∩	∩	PROPN
ejpam-5531	229	121	v	v	NOUN
ejpam-5531	229	122	=	=	NOUN
ejpam-5531	229	123	∅	∅	NOUN
ejpam-5531	229	124	and	and	CCONJ
ejpam-5531	229	125	an	an	DET
ejpam-5531	229	126	m	m	NOUN
ejpam-5531	229	127	-	-	ADJ
ejpam-5531	229	128	open	open	ADJ
ejpam-5531	229	129	set	set	VERB
ejpam-5531	229	130	u	u	PROPN
ejpam-5531	229	131	∈	∈	PROPN
ejpam-5531	229	132	mio(x	mio(x	NOUN
ejpam-5531	229	133	)	)	PUNCT
ejpam-5531	229	134	containing	contain	VERB
ejpam-5531	229	135	x	x	PUNCT
ejpam-5531	229	136	t.	t.	PROPN
ejpam-5531	229	137	noiri	noiri	PROPN
ejpam-5531	229	138	,	,	PUNCT
ejpam-5531	229	139	v.	v.	CCONJ
ejpam-5531	229	140	popa	popa	NOUN
ejpam-5531	229	141	/	/	SYM
ejpam-5531	229	142	eur	eur	PROPN
ejpam-5531	229	143	.	.	PUNCT
ejpam-5531	230	1	j.	j.	PROPN
ejpam-5531	230	2	pure	pure	PROPN
ejpam-5531	230	3	appl	appl	PROPN
ejpam-5531	230	4	.	.	PROPN
ejpam-5531	230	5	math	math	PROPN
ejpam-5531	230	6	,	,	PUNCT
ejpam-5531	230	7	17	17	NUM
ejpam-5531	230	8	(	(	PUNCT
ejpam-5531	230	9	4	4	NUM
ejpam-5531	230	10	)	)	PUNCT
ejpam-5531	230	11	(	(	PUNCT
ejpam-5531	230	12	2024	2024	NUM
ejpam-5531	230	13	)	)	PUNCT
ejpam-5531	230	14	,	,	PUNCT
ejpam-5531	230	15	3677	3677	NUM
ejpam-5531	230	16	-	-	SYM
ejpam-5531	230	17	3686	3686	NUM
ejpam-5531	230	18	3684	3684	NUM
ejpam-5531	230	19	such	such	ADJ
ejpam-5531	230	20	that	that	SCONJ
ejpam-5531	230	21	f	f	PROPN
ejpam-5531	230	22	(	(	PUNCT
ejpam-5531	230	23	u	u	NOUN
ejpam-5531	230	24	)	)	PUNCT
ejpam-5531	230	25	∩	∩	NOUN
ejpam-5531	230	26	(	(	PUNCT
ejpam-5531	230	27	v	v	NUM
ejpam-5531	230	28	∪rv	∪rv	NOUN
ejpam-5531	230	29	)	)	PUNCT
ejpam-5531	230	30	̸=	̸=	NOUN
ejpam-5531	230	31	∅	∅	NOUN
ejpam-5531	230	32	for	for	ADP
ejpam-5531	230	33	each	each	DET
ejpam-5531	230	34	u	u	PROPN
ejpam-5531	230	35	∈	∈	PROPN
ejpam-5531	230	36	u	u	NOUN
ejpam-5531	230	37	,	,	PUNCT
ejpam-5531	230	38	lemma	lemma	PROPN
ejpam-5531	230	39	7	7	NUM
ejpam-5531	230	40	.	.	PUNCT
ejpam-5531	230	41	a	a	DET
ejpam-5531	230	42	multifunction	multifunction	NOUN
ejpam-5531	230	43	f	f	NOUN
ejpam-5531	230	44	:	:	PUNCT
ejpam-5531	230	45	(	(	PUNCT
ejpam-5531	230	46	x	x	X
ejpam-5531	230	47	,	,	PUNCT
ejpam-5531	230	48	τ	τ	PROPN
ejpam-5531	230	49	,	,	PUNCT
ejpam-5531	230	50	i	i	NOUN
ejpam-5531	230	51	)	)	PUNCT
ejpam-5531	230	52	→	→	SYM
ejpam-5531	230	53	(	(	PUNCT
ejpam-5531	230	54	y	y	PROPN
ejpam-5531	230	55	,	,	PUNCT
ejpam-5531	230	56	σ	σ	PROPN
ejpam-5531	230	57	)	)	PUNCT
ejpam-5531	230	58	is	be	AUX
ejpam-5531	230	59	upper	upper	ADJ
ejpam-5531	230	60	/	/	SYM
ejpam-5531	230	61	lower	low	ADJ
ejpam-5531	230	62	rarely	rarely	ADV
ejpam-5531	230	63	m	m	VERB
ejpam-5531	230	64	-	-	PUNCT
ejpam-5531	230	65	i	i	PRON
ejpam-5531	230	66	-	-	NOUN
ejpam-5531	230	67	continuous	continuous	ADJ
ejpam-5531	230	68	at	at	ADP
ejpam-5531	230	69	x	x	X
ejpam-5531	230	70	∈	∈	PROPN
ejpam-5531	230	71	x	x	SYM
ejpam-5531	230	72	if	if	SCONJ
ejpam-5531	231	1	and	and	CCONJ
ejpam-5531	231	2	only	only	ADV
ejpam-5531	231	3	if	if	SCONJ
ejpam-5531	231	4	a	a	DET
ejpam-5531	231	5	multifunction	multifunction	NOUN
ejpam-5531	231	6	f	f	NOUN
ejpam-5531	231	7	:	:	PUNCT
ejpam-5531	231	8	(	(	PUNCT
ejpam-5531	231	9	x	x	NOUN
ejpam-5531	231	10	,	,	PUNCT
ejpam-5531	231	11	mio(x	mio(x	NOUN
ejpam-5531	231	12	)	)	PUNCT
ejpam-5531	231	13	)	)	PUNCT
ejpam-5531	232	1	→	→	SYM
ejpam-5531	232	2	(	(	PUNCT
ejpam-5531	232	3	y	y	PROPN
ejpam-5531	232	4	,	,	PUNCT
ejpam-5531	232	5	σ	σ	PROPN
ejpam-5531	232	6	)	)	PUNCT
ejpam-5531	232	7	is	be	AUX
ejpam-5531	232	8	upper	upper	ADJ
ejpam-5531	232	9	/	/	SYM
ejpam-5531	232	10	lower	low	ADJ
ejpam-5531	232	11	rarely	rarely	ADV
ejpam-5531	232	12	m	m	ADJ
ejpam-5531	232	13	-	-	ADJ
ejpam-5531	232	14	continuous	continuous	ADJ
ejpam-5531	232	15	at	at	ADP
ejpam-5531	232	16	x	x	SYM
ejpam-5531	232	17	∈	∈	NOUN
ejpam-5531	232	18	x.	x.	NOUN
ejpam-5531	232	19	proof	proof	NOUN
ejpam-5531	232	20	.	.	PUNCT
ejpam-5531	233	1	this	this	PRON
ejpam-5531	233	2	is	be	AUX
ejpam-5531	233	3	obvious	obvious	ADJ
ejpam-5531	233	4	from	from	ADP
ejpam-5531	233	5	definitions	definition	NOUN
ejpam-5531	233	6	7	7	NUM
ejpam-5531	233	7	and	and	CCONJ
ejpam-5531	233	8	12	12	NUM
ejpam-5531	233	9	theorem	theorem	NOUN
ejpam-5531	233	10	3	3	NUM
ejpam-5531	233	11	.	.	X
ejpam-5531	233	12	for	for	ADP
ejpam-5531	233	13	a	a	DET
ejpam-5531	233	14	multifunction	multifunction	NOUN
ejpam-5531	233	15	f	f	NOUN
ejpam-5531	233	16	:	:	PUNCT
ejpam-5531	233	17	(	(	PUNCT
ejpam-5531	233	18	x	x	X
ejpam-5531	233	19	,	,	PUNCT
ejpam-5531	233	20	τ	τ	PROPN
ejpam-5531	233	21	,	,	PUNCT
ejpam-5531	233	22	i	i	NOUN
ejpam-5531	233	23	)	)	PUNCT
ejpam-5531	233	24	→	→	SYM
ejpam-5531	233	25	(	(	PUNCT
ejpam-5531	233	26	y	y	PROPN
ejpam-5531	233	27	,	,	PUNCT
ejpam-5531	233	28	σ	σ	PROPN
ejpam-5531	233	29	)	)	PUNCT
ejpam-5531	233	30	,	,	PUNCT
ejpam-5531	233	31	the	the	DET
ejpam-5531	233	32	following	follow	VERB
ejpam-5531	233	33	properties	property	NOUN
ejpam-5531	233	34	are	be	AUX
ejpam-5531	233	35	equivalent	equivalent	ADJ
ejpam-5531	233	36	:	:	PUNCT
ejpam-5531	233	37	(	(	PUNCT
ejpam-5531	233	38	1	1	X
ejpam-5531	233	39	)	)	PUNCT
ejpam-5531	233	40	f	f	PROPN
ejpam-5531	233	41	is	be	AUX
ejpam-5531	233	42	upper	upper	ADJ
ejpam-5531	233	43	rarely	rarely	ADV
ejpam-5531	233	44	m	m	NOUN
ejpam-5531	233	45	-	-	ADJ
ejpam-5531	233	46	i	i	PRON
ejpam-5531	233	47	-	-	NOUN
ejpam-5531	233	48	continuous	continuous	ADJ
ejpam-5531	233	49	at	at	ADP
ejpam-5531	233	50	x	x	X
ejpam-5531	233	51	∈	∈	PROPN
ejpam-5531	233	52	x	x	X
ejpam-5531	233	53	;	;	PUNCT
ejpam-5531	233	54	(	(	PUNCT
ejpam-5531	233	55	2	2	X
ejpam-5531	233	56	)	)	PUNCT
ejpam-5531	233	57	for	for	ADP
ejpam-5531	233	58	each	each	DET
ejpam-5531	233	59	open	open	ADJ
ejpam-5531	233	60	set	set	VERB
ejpam-5531	233	61	v	v	NOUN
ejpam-5531	233	62	of	of	ADP
ejpam-5531	233	63	y	y	NOUN
ejpam-5531	233	64	containing	contain	VERB
ejpam-5531	233	65	f(x	f(x	PROPN
ejpam-5531	233	66	)	)	PUNCT
ejpam-5531	233	67	,	,	PUNCT
ejpam-5531	233	68	there	there	PRON
ejpam-5531	233	69	exists	exist	VERB
ejpam-5531	233	70	a	a	DET
ejpam-5531	233	71	rare	rare	ADJ
ejpam-5531	233	72	set	set	NOUN
ejpam-5531	233	73	rv	rv	PROPN
ejpam-5531	233	74	with	with	ADP
ejpam-5531	233	75	v	v	NOUN
ejpam-5531	233	76	∩rv	∩rv	NOUN
ejpam-5531	233	77	=	=	VERB
ejpam-5531	233	78	∅	∅	NOUN
ejpam-5531	233	79	such	such	ADJ
ejpam-5531	233	80	that	that	SCONJ
ejpam-5531	233	81	x	x	SYM
ejpam-5531	233	82	∈	∈	NOUN
ejpam-5531	233	83	minti(f	minti(f	PRON
ejpam-5531	233	84	+	+	ADJ
ejpam-5531	233	85	(	(	PUNCT
ejpam-5531	233	86	v	v	NOUN
ejpam-5531	233	87	∪rv	∪rv	NOUN
ejpam-5531	233	88	)	)	PUNCT
ejpam-5531	233	89	)	)	PUNCT
ejpam-5531	233	90	;	;	PUNCT
ejpam-5531	233	91	(	(	PUNCT
ejpam-5531	233	92	3	3	X
ejpam-5531	233	93	)	)	PUNCT
ejpam-5531	233	94	for	for	ADP
ejpam-5531	233	95	each	each	DET
ejpam-5531	233	96	open	open	ADJ
ejpam-5531	233	97	set	set	VERB
ejpam-5531	233	98	v	v	NOUN
ejpam-5531	233	99	of	of	ADP
ejpam-5531	233	100	y	y	NOUN
ejpam-5531	233	101	containing	contain	VERB
ejpam-5531	233	102	f(x	f(x	PROPN
ejpam-5531	233	103	)	)	PUNCT
ejpam-5531	233	104	,	,	PUNCT
ejpam-5531	233	105	there	there	PRON
ejpam-5531	233	106	exists	exist	VERB
ejpam-5531	233	107	a	a	DET
ejpam-5531	233	108	rare	rare	ADJ
ejpam-5531	233	109	set	set	NOUN
ejpam-5531	233	110	rv	rv	PROPN
ejpam-5531	233	111	with	with	ADP
ejpam-5531	233	112	cl(v	cl(v	NOUN
ejpam-5531	233	113	)	)	PUNCT
ejpam-5531	233	114	∩	∩	NOUN
ejpam-5531	233	115	rv	rv	NOUN
ejpam-5531	233	116	=	=	PUNCT
ejpam-5531	233	117	∅	∅	NOUN
ejpam-5531	233	118	such	such	ADJ
ejpam-5531	233	119	that	that	SCONJ
ejpam-5531	233	120	x	x	SYM
ejpam-5531	233	121	∈	∈	NOUN
ejpam-5531	233	122	minti(f	minti(f	NOUN
ejpam-5531	233	123	+	+	NOUN
ejpam-5531	233	124	(	(	PUNCT
ejpam-5531	233	125	cl(v	cl(v	X
ejpam-5531	233	126	)	)	PUNCT
ejpam-5531	233	127	∪rv	∪rv	NOUN
ejpam-5531	233	128	)	)	PUNCT
ejpam-5531	233	129	)	)	PUNCT
ejpam-5531	233	130	;	;	PUNCT
ejpam-5531	233	131	(	(	PUNCT
ejpam-5531	233	132	4	4	X
ejpam-5531	233	133	)	)	PUNCT
ejpam-5531	233	134	for	for	ADP
ejpam-5531	233	135	each	each	DET
ejpam-5531	233	136	regular	regular	ADJ
ejpam-5531	233	137	open	open	ADJ
ejpam-5531	233	138	set	set	VERB
ejpam-5531	233	139	v	v	NOUN
ejpam-5531	233	140	of	of	ADP
ejpam-5531	233	141	y	y	NOUN
ejpam-5531	233	142	containing	contain	VERB
ejpam-5531	233	143	f(x	f(x	PROPN
ejpam-5531	233	144	)	)	PUNCT
ejpam-5531	233	145	,	,	PUNCT
ejpam-5531	233	146	there	there	PRON
ejpam-5531	233	147	exists	exist	VERB
ejpam-5531	233	148	a	a	DET
ejpam-5531	233	149	rare	rare	ADJ
ejpam-5531	233	150	set	set	NOUN
ejpam-5531	233	151	rv	rv	PROPN
ejpam-5531	233	152	with	with	ADP
ejpam-5531	233	153	v	v	NOUN
ejpam-5531	233	154	∩rv	∩rv	NOUN
ejpam-5531	233	155	=	=	VERB
ejpam-5531	233	156	∅	∅	NOUN
ejpam-5531	233	157	such	such	ADJ
ejpam-5531	233	158	that	that	SCONJ
ejpam-5531	233	159	x	x	SYM
ejpam-5531	233	160	∈	∈	NOUN
ejpam-5531	233	161	minti(f	minti(f	PRON
ejpam-5531	233	162	+	+	ADJ
ejpam-5531	233	163	(	(	PUNCT
ejpam-5531	233	164	v	v	NOUN
ejpam-5531	233	165	∪rv	∪rv	NOUN
ejpam-5531	233	166	)	)	PUNCT
ejpam-5531	233	167	)	)	PUNCT
ejpam-5531	233	168	;	;	PUNCT
ejpam-5531	233	169	(	(	PUNCT
ejpam-5531	233	170	5	5	X
ejpam-5531	233	171	)	)	PUNCT
ejpam-5531	233	172	for	for	ADP
ejpam-5531	233	173	each	each	DET
ejpam-5531	233	174	open	open	ADJ
ejpam-5531	233	175	set	set	VERB
ejpam-5531	233	176	v	v	NOUN
ejpam-5531	233	177	of	of	ADP
ejpam-5531	233	178	y	y	NOUN
ejpam-5531	233	179	containing	contain	VERB
ejpam-5531	233	180	f(x	f(x	PROPN
ejpam-5531	233	181	)	)	PUNCT
ejpam-5531	233	182	,	,	PUNCT
ejpam-5531	233	183	there	there	PRON
ejpam-5531	233	184	exists	exist	VERB
ejpam-5531	233	185	u	u	PROPN
ejpam-5531	233	186	∈	∈	PROPN
ejpam-5531	233	187	mio(x	mio(x	PROPN
ejpam-5531	233	188	)	)	PUNCT
ejpam-5531	233	189	containing	contain	VERB
ejpam-5531	233	190	x	x	PUNCT
ejpam-5531	233	191	such	such	ADJ
ejpam-5531	233	192	that	that	SCONJ
ejpam-5531	233	193	int[f	int[f	X
ejpam-5531	233	194	(	(	PUNCT
ejpam-5531	233	195	u	u	NOUN
ejpam-5531	233	196	)	)	PUNCT
ejpam-5531	233	197	∩	∩	NOUN
ejpam-5531	233	198	(	(	PUNCT
ejpam-5531	233	199	y	y	PROPN
ejpam-5531	233	200	\	\	PROPN
ejpam-5531	233	201	v	v	NOUN
ejpam-5531	233	202	)	)	PUNCT
ejpam-5531	233	203	]	]	PUNCT
ejpam-5531	234	1	=	=	SYM
ejpam-5531	234	2	∅	∅	NOUN
ejpam-5531	234	3	,	,	PUNCT
ejpam-5531	234	4	(	(	PUNCT
ejpam-5531	234	5	6	6	NUM
ejpam-5531	234	6	)	)	PUNCT
ejpam-5531	234	7	for	for	ADP
ejpam-5531	234	8	each	each	DET
ejpam-5531	234	9	open	open	ADJ
ejpam-5531	234	10	set	set	VERB
ejpam-5531	234	11	v	v	NOUN
ejpam-5531	234	12	of	of	ADP
ejpam-5531	234	13	y	y	NOUN
ejpam-5531	234	14	containing	contain	VERB
ejpam-5531	234	15	f(x	f(x	PROPN
ejpam-5531	234	16	)	)	PUNCT
ejpam-5531	234	17	,	,	PUNCT
ejpam-5531	234	18	there	there	PRON
ejpam-5531	234	19	exists	exist	VERB
ejpam-5531	234	20	u	u	PROPN
ejpam-5531	234	21	∈	∈	PROPN
ejpam-5531	234	22	mio(x	mio(x	PROPN
ejpam-5531	234	23	)	)	PUNCT
ejpam-5531	234	24	containing	contain	VERB
ejpam-5531	234	25	x	x	PUNCT
ejpam-5531	234	26	such	such	ADJ
ejpam-5531	234	27	that	that	SCONJ
ejpam-5531	234	28	int(f	int(f	PROPN
ejpam-5531	234	29	(	(	PUNCT
ejpam-5531	234	30	u	u	NOUN
ejpam-5531	234	31	)	)	PUNCT
ejpam-5531	234	32	)	)	PUNCT
ejpam-5531	235	1	⊂	⊂	PROPN
ejpam-5531	235	2	cl(v	cl(v	NOUN
ejpam-5531	235	3	)	)	PUNCT
ejpam-5531	235	4	.	.	PUNCT
ejpam-5531	236	1	theorem	theorem	ADJ
ejpam-5531	236	2	4	4	NUM
ejpam-5531	236	3	.	.	X
ejpam-5531	236	4	for	for	ADP
ejpam-5531	236	5	a	a	DET
ejpam-5531	236	6	multifunction	multifunction	NOUN
ejpam-5531	237	1	f	f	NOUN
ejpam-5531	237	2	:	:	PUNCT
ejpam-5531	237	3	(	(	PUNCT
ejpam-5531	237	4	x	x	X
ejpam-5531	237	5	,	,	PUNCT
ejpam-5531	237	6	τ	τ	PROPN
ejpam-5531	237	7	,	,	PUNCT
ejpam-5531	237	8	i	i	NOUN
ejpam-5531	237	9	)	)	PUNCT
ejpam-5531	237	10	→	→	SYM
ejpam-5531	237	11	(	(	PUNCT
ejpam-5531	237	12	y	y	PROPN
ejpam-5531	237	13	,	,	PUNCT
ejpam-5531	237	14	σ	σ	PROPN
ejpam-5531	237	15	)	)	PUNCT
ejpam-5531	237	16	,	,	PUNCT
ejpam-5531	237	17	the	the	DET
ejpam-5531	237	18	following	follow	VERB
ejpam-5531	237	19	properties	property	NOUN
ejpam-5531	237	20	are	be	AUX
ejpam-5531	237	21	equivalent	equivalent	ADJ
ejpam-5531	237	22	:	:	PUNCT
ejpam-5531	237	23	(	(	PUNCT
ejpam-5531	237	24	1	1	X
ejpam-5531	237	25	)	)	PUNCT
ejpam-5531	237	26	f	f	PROPN
ejpam-5531	237	27	is	be	AUX
ejpam-5531	237	28	lower	low	ADJ
ejpam-5531	237	29	rarely	rarely	ADV
ejpam-5531	237	30	m	m	NOUN
ejpam-5531	237	31	-	-	PUNCT
ejpam-5531	237	32	i	i	PRON
ejpam-5531	237	33	-	-	NOUN
ejpam-5531	237	34	continuous	continuous	ADJ
ejpam-5531	237	35	at	at	ADP
ejpam-5531	237	36	x	x	X
ejpam-5531	237	37	∈	∈	PROPN
ejpam-5531	237	38	x	x	X
ejpam-5531	237	39	;	;	PUNCT
ejpam-5531	237	40	(	(	PUNCT
ejpam-5531	237	41	2	2	X
ejpam-5531	237	42	)	)	PUNCT
ejpam-5531	237	43	for	for	ADP
ejpam-5531	237	44	each	each	DET
ejpam-5531	237	45	open	open	ADJ
ejpam-5531	237	46	set	set	VERB
ejpam-5531	237	47	v	v	NOUN
ejpam-5531	237	48	of	of	ADP
ejpam-5531	237	49	y	y	PRON
ejpam-5531	237	50	such	such	ADJ
ejpam-5531	237	51	that	that	SCONJ
ejpam-5531	237	52	f	f	PROPN
ejpam-5531	237	53	(	(	PUNCT
ejpam-5531	237	54	x	x	NOUN
ejpam-5531	237	55	)	)	PUNCT
ejpam-5531	237	56	∩	∩	NOUN
ejpam-5531	237	57	v	v	ADP
ejpam-5531	237	58	̸=	̸=	PROPN
ejpam-5531	237	59	∅	∅	NOUN
ejpam-5531	237	60	,	,	PUNCT
ejpam-5531	237	61	there	there	PRON
ejpam-5531	237	62	exists	exist	VERB
ejpam-5531	237	63	a	a	DET
ejpam-5531	237	64	rare	rare	ADJ
ejpam-5531	237	65	set	set	NOUN
ejpam-5531	237	66	rv	rv	PROPN
ejpam-5531	237	67	with	with	ADP
ejpam-5531	237	68	v	v	NOUN
ejpam-5531	237	69	∩rv	∩rv	NOUN
ejpam-5531	237	70	=	=	VERB
ejpam-5531	237	71	∅	∅	NOUN
ejpam-5531	237	72	such	such	ADJ
ejpam-5531	237	73	that	that	SCONJ
ejpam-5531	237	74	x	x	SYM
ejpam-5531	237	75	∈	∈	NOUN
ejpam-5531	237	76	minti(f	minti(f	PRON
ejpam-5531	237	77	−(v	−(v	NOUN
ejpam-5531	237	78	∪rv	∪rv	NOUN
ejpam-5531	237	79	)	)	PUNCT
ejpam-5531	237	80	)	)	PUNCT
ejpam-5531	237	81	;	;	PUNCT
ejpam-5531	237	82	(	(	PUNCT
ejpam-5531	237	83	3	3	X
ejpam-5531	237	84	)	)	PUNCT
ejpam-5531	237	85	for	for	ADP
ejpam-5531	237	86	each	each	DET
ejpam-5531	237	87	open	open	ADJ
ejpam-5531	237	88	set	set	VERB
ejpam-5531	237	89	v	v	NOUN
ejpam-5531	237	90	of	of	ADP
ejpam-5531	237	91	y	y	PRON
ejpam-5531	237	92	such	such	ADJ
ejpam-5531	237	93	that	that	SCONJ
ejpam-5531	237	94	f	f	PROPN
ejpam-5531	237	95	(	(	PUNCT
ejpam-5531	237	96	x	x	NOUN
ejpam-5531	237	97	)	)	PUNCT
ejpam-5531	237	98	∩	∩	NOUN
ejpam-5531	237	99	v	v	ADP
ejpam-5531	237	100	̸=	̸=	PROPN
ejpam-5531	237	101	∅	∅	NOUN
ejpam-5531	237	102	,	,	PUNCT
ejpam-5531	237	103	there	there	PRON
ejpam-5531	237	104	exists	exist	VERB
ejpam-5531	237	105	a	a	DET
ejpam-5531	237	106	rare	rare	ADJ
ejpam-5531	237	107	set	set	NOUN
ejpam-5531	237	108	rv	rv	PROPN
ejpam-5531	237	109	with	with	ADP
ejpam-5531	237	110	cl(v	cl(v	NOUN
ejpam-5531	237	111	)	)	PUNCT
ejpam-5531	237	112	∩rv	∩rv	NOUN
ejpam-5531	237	113	=	=	PUNCT
ejpam-5531	237	114	∅	∅	NOUN
ejpam-5531	237	115	such	such	ADJ
ejpam-5531	237	116	that	that	SCONJ
ejpam-5531	237	117	x	x	SYM
ejpam-5531	237	118	∈	∈	NOUN
ejpam-5531	237	119	minti(f	minti(f	NOUN
ejpam-5531	237	120	−(cl(v	−(cl(v	PROPN
ejpam-5531	237	121	)	)	PUNCT
ejpam-5531	237	122	∪rv	∪rv	NOUN
ejpam-5531	237	123	)	)	PUNCT
ejpam-5531	237	124	)	)	PUNCT
ejpam-5531	237	125	;	;	PUNCT
ejpam-5531	237	126	(	(	PUNCT
ejpam-5531	237	127	4	4	X
ejpam-5531	237	128	)	)	PUNCT
ejpam-5531	237	129	for	for	ADP
ejpam-5531	237	130	each	each	DET
ejpam-5531	237	131	regular	regular	ADJ
ejpam-5531	237	132	open	open	ADJ
ejpam-5531	237	133	set	set	VERB
ejpam-5531	237	134	v	v	NOUN
ejpam-5531	237	135	of	of	ADP
ejpam-5531	237	136	y	y	PRON
ejpam-5531	237	137	such	such	ADJ
ejpam-5531	237	138	that	that	SCONJ
ejpam-5531	237	139	f	f	PROPN
ejpam-5531	237	140	(	(	PUNCT
ejpam-5531	237	141	x	x	NOUN
ejpam-5531	237	142	)	)	PUNCT
ejpam-5531	237	143	∩	∩	NOUN
ejpam-5531	237	144	v	v	ADP
ejpam-5531	237	145	̸=	̸=	PROPN
ejpam-5531	237	146	∅	∅	NOUN
ejpam-5531	237	147	,	,	PUNCT
ejpam-5531	237	148	there	there	PRON
ejpam-5531	237	149	exists	exist	VERB
ejpam-5531	237	150	a	a	DET
ejpam-5531	237	151	rare	rare	ADJ
ejpam-5531	237	152	set	set	NOUN
ejpam-5531	237	153	rv	rv	PROPN
ejpam-5531	237	154	with	with	ADP
ejpam-5531	237	155	v	v	NOUN
ejpam-5531	237	156	∩rv	∩rv	NOUN
ejpam-5531	237	157	=	=	VERB
ejpam-5531	237	158	∅	∅	NOUN
ejpam-5531	237	159	such	such	ADJ
ejpam-5531	237	160	that	that	SCONJ
ejpam-5531	237	161	x	x	SYM
ejpam-5531	237	162	∈	∈	NOUN
ejpam-5531	237	163	minti(f	minti(f	PRON
ejpam-5531	237	164	−(v	−(v	NOUN
ejpam-5531	237	165	∪rv	∪rv	NOUN
ejpam-5531	237	166	)	)	PUNCT
ejpam-5531	237	167	)	)	PUNCT
ejpam-5531	237	168	.	.	PUNCT
ejpam-5531	238	1	by	by	ADP
ejpam-5531	238	2	theorem	theorem	NOUN
ejpam-5531	238	3	3	3	NUM
ejpam-5531	238	4	,	,	PUNCT
ejpam-5531	238	5	we	we	PRON
ejpam-5531	238	6	have	have	VERB
ejpam-5531	238	7	the	the	DET
ejpam-5531	238	8	following	follow	VERB
ejpam-5531	238	9	characterizations	characterization	NOUN
ejpam-5531	238	10	of	of	ADP
ejpam-5531	238	11	rare	rare	ADJ
ejpam-5531	238	12	m	m	PROPN
ejpam-5531	238	13	-	-	ADJ
ejpam-5531	238	14	i	i	NOUN
ejpam-5531	238	15	-	-	PUNCT
ejpam-5531	238	16	continuity	continuity	NOUN
ejpam-5531	238	17	of	of	ADP
ejpam-5531	238	18	function	function	NOUN
ejpam-5531	238	19	f	f	NOUN
ejpam-5531	238	20	:	:	PUNCT
ejpam-5531	238	21	(	(	PUNCT
ejpam-5531	238	22	x	x	X
ejpam-5531	238	23	,	,	PUNCT
ejpam-5531	238	24	τ	τ	PROPN
ejpam-5531	238	25	,	,	PUNCT
ejpam-5531	238	26	i	i	NOUN
ejpam-5531	238	27	)	)	PUNCT
ejpam-5531	238	28	→	→	SYM
ejpam-5531	238	29	(	(	PUNCT
ejpam-5531	238	30	y	y	PROPN
ejpam-5531	238	31	,	,	PUNCT
ejpam-5531	238	32	σ	σ	PROPN
ejpam-5531	238	33	)	)	PUNCT
ejpam-5531	238	34	corollary	corollary	ADJ
ejpam-5531	238	35	2	2	NUM
ejpam-5531	238	36	.	.	PUNCT
ejpam-5531	238	37	for	for	ADP
ejpam-5531	238	38	a	a	DET
ejpam-5531	238	39	function	function	NOUN
ejpam-5531	238	40	f	f	NOUN
ejpam-5531	238	41	:	:	PUNCT
ejpam-5531	238	42	(	(	PUNCT
ejpam-5531	238	43	x	x	X
ejpam-5531	238	44	,	,	PUNCT
ejpam-5531	238	45	τ	τ	PROPN
ejpam-5531	238	46	,	,	PUNCT
ejpam-5531	238	47	i	i	NOUN
ejpam-5531	238	48	)	)	PUNCT
ejpam-5531	238	49	→	→	SYM
ejpam-5531	238	50	(	(	PUNCT
ejpam-5531	238	51	y	y	PROPN
ejpam-5531	238	52	,	,	PUNCT
ejpam-5531	238	53	σ	σ	PROPN
ejpam-5531	238	54	)	)	PUNCT
ejpam-5531	238	55	,	,	PUNCT
ejpam-5531	238	56	the	the	DET
ejpam-5531	238	57	following	follow	VERB
ejpam-5531	238	58	properties	property	NOUN
ejpam-5531	238	59	are	be	AUX
ejpam-5531	238	60	equivalent	equivalent	ADJ
ejpam-5531	238	61	:	:	PUNCT
ejpam-5531	238	62	(	(	PUNCT
ejpam-5531	238	63	1	1	X
ejpam-5531	238	64	)	)	PUNCT
ejpam-5531	238	65	f	f	PROPN
ejpam-5531	238	66	is	be	AUX
ejpam-5531	238	67	rarely	rarely	ADV
ejpam-5531	238	68	m	m	NOUN
ejpam-5531	238	69	-	-	ADJ
ejpam-5531	238	70	i	i	PRON
ejpam-5531	238	71	-	-	NOUN
ejpam-5531	238	72	continuous	continuous	ADJ
ejpam-5531	238	73	at	at	ADP
ejpam-5531	238	74	x	x	X
ejpam-5531	238	75	∈	∈	PROPN
ejpam-5531	238	76	x	x	X
ejpam-5531	238	77	;	;	PUNCT
ejpam-5531	238	78	(	(	PUNCT
ejpam-5531	238	79	2	2	X
ejpam-5531	238	80	)	)	PUNCT
ejpam-5531	238	81	for	for	ADP
ejpam-5531	238	82	each	each	DET
ejpam-5531	238	83	open	open	ADJ
ejpam-5531	238	84	set	set	VERB
ejpam-5531	238	85	v	v	NOUN
ejpam-5531	238	86	of	of	ADP
ejpam-5531	238	87	y	y	NOUN
ejpam-5531	238	88	containing	contain	VERB
ejpam-5531	238	89	f(x	f(x	PROPN
ejpam-5531	238	90	)	)	PUNCT
ejpam-5531	238	91	,	,	PUNCT
ejpam-5531	238	92	there	there	PRON
ejpam-5531	238	93	exists	exist	VERB
ejpam-5531	238	94	a	a	DET
ejpam-5531	238	95	rare	rare	ADJ
ejpam-5531	238	96	set	set	NOUN
ejpam-5531	238	97	rv	rv	PROPN
ejpam-5531	238	98	with	with	ADP
ejpam-5531	238	99	v	v	NOUN
ejpam-5531	238	100	∩rv	∩rv	NOUN
ejpam-5531	238	101	=	=	VERB
ejpam-5531	238	102	∅	∅	NOUN
ejpam-5531	238	103	such	such	ADJ
ejpam-5531	238	104	that	that	SCONJ
ejpam-5531	238	105	x	x	SYM
ejpam-5531	238	106	∈	∈	NOUN
ejpam-5531	238	107	minti(f	minti(f	PRON
ejpam-5531	238	108	−1(v	−1(v	PRON
ejpam-5531	238	109	∪rv	∪rv	NOUN
ejpam-5531	238	110	)	)	PUNCT
ejpam-5531	238	111	)	)	PUNCT
ejpam-5531	238	112	;	;	PUNCT
ejpam-5531	238	113	(	(	PUNCT
ejpam-5531	238	114	3	3	X
ejpam-5531	238	115	)	)	PUNCT
ejpam-5531	238	116	for	for	ADP
ejpam-5531	238	117	each	each	DET
ejpam-5531	238	118	open	open	ADJ
ejpam-5531	238	119	set	set	VERB
ejpam-5531	238	120	v	v	NOUN
ejpam-5531	238	121	of	of	ADP
ejpam-5531	238	122	y	y	NOUN
ejpam-5531	238	123	containing	contain	VERB
ejpam-5531	238	124	f(x	f(x	PROPN
ejpam-5531	238	125	)	)	PUNCT
ejpam-5531	238	126	,	,	PUNCT
ejpam-5531	238	127	there	there	PRON
ejpam-5531	238	128	exists	exist	VERB
ejpam-5531	238	129	a	a	DET
ejpam-5531	238	130	rare	rare	ADJ
ejpam-5531	238	131	set	set	NOUN
ejpam-5531	238	132	rv	rv	PROPN
ejpam-5531	238	133	with	with	ADP
ejpam-5531	238	134	cl(v	cl(v	NOUN
ejpam-5531	238	135	)	)	PUNCT
ejpam-5531	238	136	∩	∩	NOUN
ejpam-5531	238	137	rv	rv	NOUN
ejpam-5531	238	138	=	=	PUNCT
ejpam-5531	238	139	∅	∅	NOUN
ejpam-5531	238	140	such	such	ADJ
ejpam-5531	238	141	that	that	SCONJ
ejpam-5531	238	142	x	x	SYM
ejpam-5531	238	143	∈	∈	NOUN
ejpam-5531	238	144	minti(f	minti(f	PRON
ejpam-5531	238	145	−1(cl(v	−1(cl(v	NOUN
ejpam-5531	238	146	)	)	PUNCT
ejpam-5531	238	147	∪rv	∪rv	NOUN
ejpam-5531	238	148	)	)	PUNCT
ejpam-5531	238	149	)	)	PUNCT
ejpam-5531	238	150	;	;	PUNCT
ejpam-5531	238	151	(	(	PUNCT
ejpam-5531	238	152	4	4	X
ejpam-5531	238	153	)	)	PUNCT
ejpam-5531	238	154	for	for	ADP
ejpam-5531	238	155	each	each	DET
ejpam-5531	238	156	regular	regular	ADJ
ejpam-5531	238	157	open	open	ADJ
ejpam-5531	238	158	set	set	VERB
ejpam-5531	238	159	v	v	NOUN
ejpam-5531	238	160	of	of	ADP
ejpam-5531	238	161	y	y	NOUN
ejpam-5531	238	162	containing	contain	VERB
ejpam-5531	238	163	f(x	f(x	PROPN
ejpam-5531	238	164	)	)	PUNCT
ejpam-5531	238	165	,	,	PUNCT
ejpam-5531	238	166	there	there	PRON
ejpam-5531	238	167	exists	exist	VERB
ejpam-5531	238	168	a	a	DET
ejpam-5531	238	169	rare	rare	ADJ
ejpam-5531	238	170	set	set	NOUN
ejpam-5531	238	171	rv	rv	PROPN
ejpam-5531	238	172	with	with	ADP
ejpam-5531	238	173	v	v	NOUN
ejpam-5531	238	174	∩rv	∩rv	NOUN
ejpam-5531	238	175	=	=	VERB
ejpam-5531	238	176	∅	∅	NOUN
ejpam-5531	238	177	such	such	ADJ
ejpam-5531	238	178	that	that	SCONJ
ejpam-5531	238	179	x	x	SYM
ejpam-5531	238	180	∈	∈	NOUN
ejpam-5531	238	181	minti(f	minti(f	PRON
ejpam-5531	238	182	−1(v	−1(v	PRON
ejpam-5531	238	183	∪rv	∪rv	NOUN
ejpam-5531	238	184	)	)	PUNCT
ejpam-5531	238	185	)	)	PUNCT
ejpam-5531	238	186	;	;	PUNCT
ejpam-5531	238	187	(	(	PUNCT
ejpam-5531	238	188	5	5	X
ejpam-5531	238	189	)	)	PUNCT
ejpam-5531	238	190	for	for	ADP
ejpam-5531	238	191	each	each	DET
ejpam-5531	238	192	open	open	ADJ
ejpam-5531	238	193	set	set	VERB
ejpam-5531	238	194	v	v	NOUN
ejpam-5531	238	195	of	of	ADP
ejpam-5531	238	196	y	y	NOUN
ejpam-5531	238	197	containing	contain	VERB
ejpam-5531	238	198	f(x	f(x	PROPN
ejpam-5531	238	199	)	)	PUNCT
ejpam-5531	238	200	,	,	PUNCT
ejpam-5531	238	201	there	there	PRON
ejpam-5531	238	202	exists	exist	VERB
ejpam-5531	238	203	u	u	PROPN
ejpam-5531	238	204	∈	∈	PROPN
ejpam-5531	238	205	mio(x	mio(x	PROPN
ejpam-5531	238	206	)	)	PUNCT
ejpam-5531	238	207	containing	contain	VERB
ejpam-5531	238	208	x	x	SYM
ejpam-5531	238	209	references	reference	NOUN
ejpam-5531	238	210	3685	3685	NUM
ejpam-5531	238	211	such	such	ADJ
ejpam-5531	238	212	that	that	DET
ejpam-5531	238	213	int[f(u	int[f(u	NOUN
ejpam-5531	238	214	)	)	PUNCT
ejpam-5531	238	215	∩	∩	NOUN
ejpam-5531	238	216	(	(	PUNCT
ejpam-5531	238	217	y	y	PROPN
ejpam-5531	238	218	\	\	PROPN
ejpam-5531	238	219	v	v	NOUN
ejpam-5531	238	220	)	)	PUNCT
ejpam-5531	238	221	]	]	PUNCT
ejpam-5531	239	1	=	=	SYM
ejpam-5531	239	2	∅	∅	NOUN
ejpam-5531	239	3	,	,	PUNCT
ejpam-5531	239	4	(	(	PUNCT
ejpam-5531	239	5	6	6	NUM
ejpam-5531	239	6	)	)	PUNCT
ejpam-5531	239	7	for	for	ADP
ejpam-5531	239	8	each	each	DET
ejpam-5531	239	9	open	open	ADJ
ejpam-5531	239	10	set	set	VERB
ejpam-5531	239	11	v	v	NOUN
ejpam-5531	239	12	of	of	ADP
ejpam-5531	239	13	y	y	NOUN
ejpam-5531	239	14	containing	contain	VERB
ejpam-5531	239	15	f(x	f(x	PROPN
ejpam-5531	239	16	)	)	PUNCT
ejpam-5531	239	17	,	,	PUNCT
ejpam-5531	239	18	there	there	PRON
ejpam-5531	239	19	exists	exist	VERB
ejpam-5531	239	20	u	u	PROPN
ejpam-5531	239	21	∈	∈	PROPN
ejpam-5531	239	22	mio(x	mio(x	PROPN
ejpam-5531	239	23	)	)	PUNCT
ejpam-5531	239	24	containing	contain	VERB
ejpam-5531	239	25	x	x	PUNCT
ejpam-5531	239	26	such	such	ADJ
ejpam-5531	239	27	that	that	DET
ejpam-5531	239	28	int(f(u	int(f(u	NOUN
ejpam-5531	239	29	)	)	PUNCT
ejpam-5531	239	30	)	)	PUNCT
ejpam-5531	240	1	⊂	⊂	PROPN
ejpam-5531	240	2	cl(v	cl(v	NOUN
ejpam-5531	240	3	)	)	PUNCT
ejpam-5531	240	4	.	.	PUNCT
ejpam-5531	241	1	references	reference	NOUN
ejpam-5531	241	2	[	[	X
ejpam-5531	241	3	1	1	NUM
ejpam-5531	241	4	]	]	PUNCT
ejpam-5531	241	5	d.	d.	PROPN
ejpam-5531	241	6	andrijević.	andrijević.	PROPN
ejpam-5531	241	7	on	on	ADP
ejpam-5531	241	8	b	b	X
ejpam-5531	241	9	-	-	PUNCT
ejpam-5531	241	10	open	open	ADJ
ejpam-5531	241	11	sets	set	NOUN
ejpam-5531	241	12	.	.	PUNCT
ejpam-5531	242	1	mat	mat	X
ejpam-5531	242	2	.	.	PROPN
ejpam-5531	242	3	vesnik	vesnik	PROPN
ejpam-5531	242	4	,	,	PUNCT
ejpam-5531	242	5	48:59–64	48:59–64	PROPN
ejpam-5531	242	6	,	,	PUNCT
ejpam-5531	242	7	1996	1996	NUM
ejpam-5531	242	8	.	.	PUNCT
ejpam-5531	243	1	[	[	X
ejpam-5531	243	2	2	2	X
ejpam-5531	243	3	]	]	PUNCT
ejpam-5531	243	4	j.	j.	PROPN
ejpam-5531	243	5	dontchev	dontchev	PROPN
ejpam-5531	243	6	.	.	PUNCT
ejpam-5531	244	1	on	on	ADP
ejpam-5531	244	2	pre	pre	ADJ
ejpam-5531	244	3	-	-	ADJ
ejpam-5531	244	4	i	i	PRON
ejpam-5531	244	5	-	-	PUNCT
ejpam-5531	244	6	open	open	ADJ
ejpam-5531	244	7	sets	set	NOUN
ejpam-5531	244	8	and	and	CCONJ
ejpam-5531	244	9	a	a	DET
ejpam-5531	244	10	decomposition	decomposition	NOUN
ejpam-5531	244	11	of	of	ADP
ejpam-5531	244	12	i	i	NOUN
ejpam-5531	244	13	-	-	PUNCT
ejpam-5531	244	14	continuity	continuity	NOUN
ejpam-5531	244	15	.	.	PUNCT
ejpam-5531	245	1	banyan	banyan	ADJ
ejpam-5531	245	2	math	math	NOUN
ejpam-5531	245	3	.	.	PUNCT
ejpam-5531	246	1	j.	j.	PROPN
ejpam-5531	246	2	,	,	PUNCT
ejpam-5531	246	3	2	2	NUM
ejpam-5531	246	4	,	,	PUNCT
ejpam-5531	246	5	1996	1996	NUM
ejpam-5531	246	6	.	.	PUNCT
ejpam-5531	247	1	[	[	X
ejpam-5531	247	2	3	3	X
ejpam-5531	247	3	]	]	PUNCT
ejpam-5531	247	4	m.	m.	NOUN
ejpam-5531	247	5	e.	e.	PROPN
ejpam-5531	247	6	abd	abd	PROPN
ejpam-5531	248	1	el	el	PROPN
ejpam-5531	248	2	-	-	PROPN
ejpam-5531	248	3	monsef	monsef	PROPN
ejpam-5531	248	4	,	,	PUNCT
ejpam-5531	248	5	s.	s.	PROPN
ejpam-5531	248	6	n.	n.	PROPN
ejpam-5531	248	7	el	el	PROPN
ejpam-5531	248	8	-	-	PROPN
ejpam-5531	248	9	deeb	deeb	PROPN
ejpam-5531	248	10	,	,	PUNCT
ejpam-5531	248	11	and	and	CCONJ
ejpam-5531	248	12	r.	r.	PROPN
ejpam-5531	248	13	a.	a.	PROPN
ejpam-5531	248	14	mahmoud	mahmoud	PROPN
ejpam-5531	248	15	.	.	PUNCT
ejpam-5531	249	1	β	β	X
ejpam-5531	249	2	-	-	ADJ
ejpam-5531	249	3	open	open	ADJ
ejpam-5531	249	4	sets	set	NOUN
ejpam-5531	249	5	and	and	CCONJ
ejpam-5531	249	6	βcontinuous	βcontinuous	ADJ
ejpam-5531	249	7	mappings	mapping	NOUN
ejpam-5531	249	8	.	.	PUNCT
ejpam-5531	250	1	bull	bull	NOUN
ejpam-5531	250	2	.	.	PUNCT
ejpam-5531	251	1	fac	fac	PROPN
ejpam-5531	251	2	.	.	PUNCT
ejpam-5531	252	1	sci	sci	PROPN
ejpam-5531	252	2	.	.	PUNCT
ejpam-5531	252	3	assiut	assiut	PROPN
ejpam-5531	252	4	univ	univ	PROPN
ejpam-5531	252	5	.	.	PROPN
ejpam-5531	252	6	,	,	PUNCT
ejpam-5531	252	7	12:77–90	12:77–90	NUM
ejpam-5531	252	8	,	,	PUNCT
ejpam-5531	252	9	1983	1983	NUM
ejpam-5531	252	10	.	.	PUNCT
ejpam-5531	253	1	[	[	X
ejpam-5531	253	2	4	4	NUM
ejpam-5531	253	3	]	]	X
ejpam-5531	253	4	m.	m.	NOUN
ejpam-5531	253	5	ganster	ganster	NOUN
ejpam-5531	253	6	and	and	CCONJ
ejpam-5531	253	7	s.	s.	PROPN
ejpam-5531	253	8	jafari	jafari	PROPN
ejpam-5531	253	9	.	.	PUNCT
ejpam-5531	254	1	upper	upper	ADJ
ejpam-5531	254	2	and	and	CCONJ
ejpam-5531	254	3	lower	low	ADJ
ejpam-5531	254	4	rarely	rarely	ADV
ejpam-5531	254	5	α	α	NUM
ejpam-5531	254	6	-	-	ADJ
ejpam-5531	254	7	continuous	continuous	ADJ
ejpam-5531	254	8	multifunctions	multifunction	NOUN
ejpam-5531	254	9	.	.	PUNCT
ejpam-5531	255	1	far	far	PROPN
ejpam-5531	255	2	east	east	PROPN
ejpam-5531	255	3	j.	j.	PROPN
ejpam-5531	255	4	special	special	PROPN
ejpam-5531	255	5	volume	volume	NOUN
ejpam-5531	255	6	,	,	PUNCT
ejpam-5531	255	7	6:25–31	6:25–31	PROPN
ejpam-5531	255	8	,	,	PUNCT
ejpam-5531	255	9	2001	2001	NUM
ejpam-5531	255	10	.	.	PUNCT
ejpam-5531	256	1	[	[	X
ejpam-5531	256	2	5	5	NUM
ejpam-5531	256	3	]	]	PUNCT
ejpam-5531	256	4	a.	a.	NOUN
ejpam-5531	256	5	caksu	caksu	NOUN
ejpam-5531	256	6	guler	guler	NOUN
ejpam-5531	256	7	and	and	CCONJ
ejpam-5531	256	8	g.	g.	PROPN
ejpam-5531	256	9	aslim	aslim	PROPN
ejpam-5531	256	10	.	.	PUNCT
ejpam-5531	257	1	b	b	X
ejpam-5531	257	2	-	-	PUNCT
ejpam-5531	257	3	i	i	NOUN
ejpam-5531	257	4	-	-	PUNCT
ejpam-5531	257	5	open	open	ADJ
ejpam-5531	257	6	sets	set	NOUN
ejpam-5531	257	7	and	and	CCONJ
ejpam-5531	257	8	decompositions	decomposition	NOUN
ejpam-5531	257	9	of	of	ADP
ejpam-5531	257	10	continuity	continuity	NOUN
ejpam-5531	257	11	via	via	ADP
ejpam-5531	257	12	idealization	idealization	NOUN
ejpam-5531	257	13	.	.	PUNCT
ejpam-5531	258	1	proc	proc	PROPN
ejpam-5531	258	2	.	.	PUNCT
ejpam-5531	259	1	inst	inst	PROPN
ejpam-5531	259	2	.	.	PUNCT
ejpam-5531	260	1	math	math	PROPN
ejpam-5531	260	2	.	.	PUNCT
ejpam-5531	261	1	mech	mech	PROPN
ejpam-5531	261	2	.	.	PUNCT
ejpam-5531	262	1	nat	nat	PROPN
ejpam-5531	262	2	.	.	PUNCT
ejpam-5531	263	1	acad	acad	PROPN
ejpam-5531	263	2	.	.	PUNCT
ejpam-5531	264	1	sci	sci	PROPN
ejpam-5531	264	2	.	.	PROPN
ejpam-5531	264	3	azerbaijan	azerbaijan	PROPN
ejpam-5531	264	4	,	,	PUNCT
ejpam-5531	264	5	22:27–32	22:27–32	NUM
ejpam-5531	264	6	,	,	PUNCT
ejpam-5531	264	7	2003	2003	NUM
ejpam-5531	264	8	.	.	PUNCT
ejpam-5531	265	1	[	[	X
ejpam-5531	265	2	6	6	X
ejpam-5531	265	3	]	]	PUNCT
ejpam-5531	265	4	e.	e.	PROPN
ejpam-5531	265	5	hatir	hatir	PROPN
ejpam-5531	265	6	and	and	CCONJ
ejpam-5531	265	7	s.	s.	PROPN
ejpam-5531	265	8	jafari	jafari	PROPN
ejpam-5531	265	9	.	.	PUNCT
ejpam-5531	266	1	on	on	ADP
ejpam-5531	266	2	weakly	weakly	ADJ
ejpam-5531	266	3	semi	semi	ADJ
ejpam-5531	266	4	-	-	ADJ
ejpam-5531	266	5	i	i	PRON
ejpam-5531	266	6	-	-	PUNCT
ejpam-5531	266	7	open	open	ADJ
ejpam-5531	266	8	sets	set	NOUN
ejpam-5531	266	9	and	and	CCONJ
ejpam-5531	266	10	other	other	ADJ
ejpam-5531	266	11	decomposition	decomposition	NOUN
ejpam-5531	266	12	of	of	ADP
ejpam-5531	266	13	continuity	continuity	NOUN
ejpam-5531	266	14	via	via	ADP
ejpam-5531	266	15	ideals	ideal	NOUN
ejpam-5531	266	16	.	.	PUNCT
ejpam-5531	267	1	sarajevo	sarajevo	PROPN
ejpam-5531	267	2	j.	j.	PROPN
ejpam-5531	267	3	math	math	PROPN
ejpam-5531	267	4	.	.	PUNCT
ejpam-5531	267	5	,	,	PUNCT
ejpam-5531	267	6	14:107–114	14:107–114	PROPN
ejpam-5531	267	7	,	,	PUNCT
ejpam-5531	267	8	2006	2006	NUM
ejpam-5531	267	9	.	.	PUNCT
ejpam-5531	268	1	[	[	X
ejpam-5531	268	2	7	7	X
ejpam-5531	268	3	]	]	X
ejpam-5531	268	4	e.	e.	PROPN
ejpam-5531	268	5	hatir	hatir	PROPN
ejpam-5531	268	6	,	,	PUNCT
ejpam-5531	268	7	a.	a.	PROPN
ejpam-5531	268	8	keskin	keskin	PROPN
ejpam-5531	268	9	,	,	PUNCT
ejpam-5531	268	10	and	and	CCONJ
ejpam-5531	268	11	t.	t.	PROPN
ejpam-5531	268	12	noiri	noiri	PROPN
ejpam-5531	268	13	.	.	PUNCT
ejpam-5531	269	1	on	on	ADP
ejpam-5531	269	2	a	a	DET
ejpam-5531	269	3	new	new	ADJ
ejpam-5531	269	4	decomposition	decomposition	NOUN
ejpam-5531	269	5	of	of	ADP
ejpam-5531	269	6	continuity	continuity	NOUN
ejpam-5531	269	7	via	via	ADP
ejpam-5531	269	8	idealization	idealization	NOUN
ejpam-5531	269	9	.	.	PUNCT
ejpam-5531	270	1	jp	jp	PROPN
ejpam-5531	270	2	j.	j.	PROPN
ejpam-5531	270	3	geometry	geometry	PROPN
ejpam-5531	270	4	toplogy	toplogy	NOUN
ejpam-5531	270	5	,	,	PUNCT
ejpam-5531	270	6	3(1):53–64	3(1):53–64	NUM
ejpam-5531	270	7	,	,	PUNCT
ejpam-5531	270	8	2003	2003	NUM
ejpam-5531	270	9	.	.	PUNCT
ejpam-5531	271	1	[	[	X
ejpam-5531	271	2	8	8	X
ejpam-5531	271	3	]	]	X
ejpam-5531	271	4	e.	e.	PROPN
ejpam-5531	271	5	hatir	hatir	PROPN
ejpam-5531	271	6	and	and	CCONJ
ejpam-5531	271	7	t.	t.	PROPN
ejpam-5531	271	8	noiri	noiri	PROPN
ejpam-5531	271	9	.	.	PUNCT
ejpam-5531	272	1	on	on	ADP
ejpam-5531	272	2	decompositions	decomposition	NOUN
ejpam-5531	272	3	of	of	ADP
ejpam-5531	272	4	continuity	continuity	NOUN
ejpam-5531	272	5	via	via	ADP
ejpam-5531	272	6	idealization	idealization	NOUN
ejpam-5531	272	7	.	.	PUNCT
ejpam-5531	273	1	acta	acta	PROPN
ejpam-5531	273	2	math	math	PROPN
ejpam-5531	273	3	.	.	PUNCT
ejpam-5531	274	1	hungar	hungar	PROPN
ejpam-5531	274	2	.	.	PUNCT
ejpam-5531	274	3	,	,	PUNCT
ejpam-5531	274	4	96(4):341–349	96(4):341–349	NUM
ejpam-5531	274	5	,	,	PUNCT
ejpam-5531	274	6	2002	2002	NUM
ejpam-5531	274	7	.	.	PUNCT
ejpam-5531	275	1	[	[	X
ejpam-5531	275	2	9	9	X
ejpam-5531	275	3	]	]	X
ejpam-5531	275	4	e.	e.	PROPN
ejpam-5531	275	5	hatir	hatir	PROPN
ejpam-5531	275	6	and	and	CCONJ
ejpam-5531	275	7	t.	t.	PROPN
ejpam-5531	275	8	noiri	noiri	PROPN
ejpam-5531	275	9	.	.	PUNCT
ejpam-5531	276	1	on	on	ADP
ejpam-5531	276	2	β	β	X
ejpam-5531	276	3	-	-	ADJ
ejpam-5531	276	4	i	i	NOUN
ejpam-5531	276	5	-	-	PUNCT
ejpam-5531	276	6	open	open	ADJ
ejpam-5531	276	7	sets	set	NOUN
ejpam-5531	276	8	and	and	CCONJ
ejpam-5531	276	9	a	a	DET
ejpam-5531	276	10	decomposition	decomposition	NOUN
ejpam-5531	276	11	of	of	ADP
ejpam-5531	276	12	almost	almost	ADV
ejpam-5531	276	13	-	-	PUNCT
ejpam-5531	276	14	i	i	NOUN
ejpam-5531	276	15	-	-	PUNCT
ejpam-5531	276	16	continuity	continuity	NOUN
ejpam-5531	276	17	.	.	PUNCT
ejpam-5531	277	1	bull	bull	NOUN
ejpam-5531	277	2	.	.	PUNCT
ejpam-5531	278	1	malays	malays	PROPN
ejpam-5531	278	2	.	.	PUNCT
ejpam-5531	279	1	math	math	NOUN
ejpam-5531	279	2	.	.	PUNCT
ejpam-5531	280	1	sci	sci	PROPN
ejpam-5531	280	2	.	.	PROPN
ejpam-5531	280	3	soc	soc	PROPN
ejpam-5531	280	4	.	.	PUNCT
ejpam-5531	281	1	(	(	PUNCT
ejpam-5531	281	2	2	2	NUM
ejpam-5531	281	3	)	)	PUNCT
ejpam-5531	281	4	,	,	PUNCT
ejpam-5531	281	5	29(1):119–124	29(1):119–124	NOUN
ejpam-5531	281	6	,	,	PUNCT
ejpam-5531	281	7	2006	2006	NUM
ejpam-5531	281	8	.	.	PUNCT
ejpam-5531	282	1	[	[	X
ejpam-5531	282	2	10	10	NUM
ejpam-5531	282	3	]	]	PUNCT
ejpam-5531	282	4	s.	s.	PROPN
ejpam-5531	282	5	jafari	jafari	PROPN
ejpam-5531	282	6	.	.	PUNCT
ejpam-5531	283	1	a	a	DET
ejpam-5531	283	2	note	note	NOUN
ejpam-5531	283	3	on	on	ADP
ejpam-5531	283	4	rarely	rarely	ADV
ejpam-5531	283	5	continuous	continuous	ADJ
ejpam-5531	283	6	functions	function	NOUN
ejpam-5531	283	7	.	.	PUNCT
ejpam-5531	284	1	univ	univ	PROPN
ejpam-5531	284	2	.	.	PUNCT
ejpam-5531	285	1	bacǎu	bacǎu	NOUN
ejpam-5531	285	2	stud	stud	NOUN
ejpam-5531	285	3	.	.	PUNCT
ejpam-5531	286	1	cerc	cerc	PROPN
ejpam-5531	286	2	.	.	PUNCT
ejpam-5531	287	1	st	st	PROPN
ejpam-5531	287	2	.	.	PROPN
ejpam-5531	287	3	ser	ser	PROPN
ejpam-5531	287	4	.	.	PROPN
ejpam-5531	288	1	mat	mat	PROPN
ejpam-5531	288	2	.	.	PROPN
ejpam-5531	288	3	,	,	PUNCT
ejpam-5531	288	4	5:29–34	5:29–34	NUM
ejpam-5531	288	5	,	,	PUNCT
ejpam-5531	288	6	1995	1995	NUM
ejpam-5531	288	7	.	.	PUNCT
ejpam-5531	289	1	[	[	X
ejpam-5531	289	2	11	11	NUM
ejpam-5531	289	3	]	]	PUNCT
ejpam-5531	289	4	s.	s.	PROPN
ejpam-5531	289	5	jafari	jafari	PROPN
ejpam-5531	289	6	.	.	PUNCT
ejpam-5531	290	1	on	on	ADP
ejpam-5531	290	2	some	some	DET
ejpam-5531	290	3	properties	property	NOUN
ejpam-5531	290	4	of	of	ADP
ejpam-5531	290	5	rarely	rarely	ADV
ejpam-5531	290	6	continuous	continuous	ADJ
ejpam-5531	290	7	functions	function	NOUN
ejpam-5531	290	8	.	.	PUNCT
ejpam-5531	291	1	univ	univ	PROPN
ejpam-5531	291	2	.	.	PUNCT
ejpam-5531	292	1	bacǎu	bacǎu	NOUN
ejpam-5531	292	2	stud	stud	NOUN
ejpam-5531	292	3	.	.	PUNCT
ejpam-5531	293	1	cerc	cerc	PROPN
ejpam-5531	293	2	.	.	PUNCT
ejpam-5531	294	1	st	st	PROPN
ejpam-5531	294	2	.	.	PROPN
ejpam-5531	294	3	ser	ser	PROPN
ejpam-5531	294	4	.	.	PROPN
ejpam-5531	295	1	mat	mat	PROPN
ejpam-5531	295	2	.	.	PROPN
ejpam-5531	295	3	,	,	PUNCT
ejpam-5531	295	4	7:65–73	7:65–73	PROPN
ejpam-5531	295	5	,	,	PUNCT
ejpam-5531	295	6	1997	1997	NUM
ejpam-5531	295	7	.	.	PUNCT
ejpam-5531	296	1	[	[	X
ejpam-5531	296	2	12	12	NUM
ejpam-5531	296	3	]	]	PUNCT
ejpam-5531	296	4	s.	s.	PROPN
ejpam-5531	296	5	jafari	jafari	PROPN
ejpam-5531	296	6	.	.	PUNCT
ejpam-5531	297	1	on	on	ADP
ejpam-5531	297	2	rarely	rarely	ADV
ejpam-5531	297	3	pre	pre	ADJ
ejpam-5531	297	4	-	-	ADJ
ejpam-5531	297	5	continuous	continuous	ADJ
ejpam-5531	297	6	functions	function	NOUN
ejpam-5531	297	7	.	.	PUNCT
ejpam-5531	298	1	far	far	PROPN
ejpam-5531	298	2	east	east	PROPN
ejpam-5531	298	3	j.	j.	PROPN
ejpam-5531	298	4	math	math	PROPN
ejpam-5531	298	5	.	.	PUNCT
ejpam-5531	299	1	sci	sci	PROPN
ejpam-5531	299	2	.	.	PROPN
ejpam-5531	299	3	,	,	PUNCT
ejpam-5531	299	4	special	special	ADJ
ejpam-5531	299	5	volume	volume	NOUN
ejpam-5531	299	6	part	part	NOUN
ejpam-5531	299	7	iii:305–314	iii:305–314	PROPN
ejpam-5531	299	8	,	,	PUNCT
ejpam-5531	299	9	2000	2000	NUM
ejpam-5531	299	10	.	.	PUNCT
ejpam-5531	300	1	[	[	X
ejpam-5531	300	2	13	13	NUM
ejpam-5531	300	3	]	]	PUNCT
ejpam-5531	300	4	s.	s.	PROPN
ejpam-5531	300	5	jafari	jafari	PROPN
ejpam-5531	300	6	.	.	PUNCT
ejpam-5531	301	1	rare	rare	ADJ
ejpam-5531	301	2	α	α	NOUN
ejpam-5531	301	3	-	-	NOUN
ejpam-5531	301	4	continuity	continuity	NOUN
ejpam-5531	301	5	.	.	PUNCT
ejpam-5531	302	1	bull	bull	NOUN
ejpam-5531	302	2	.	.	PUNCT
ejpam-5531	303	1	malays	malays	PROPN
ejpam-5531	303	2	.	.	PUNCT
ejpam-5531	304	1	math	math	NOUN
ejpam-5531	304	2	.	.	PUNCT
ejpam-5531	305	1	sci	sci	PROPN
ejpam-5531	305	2	.	.	PROPN
ejpam-5531	305	3	soc	soc	PROPN
ejpam-5531	305	4	.	.	PROPN
ejpam-5531	305	5	,	,	PUNCT
ejpam-5531	305	6	28(2):157–161	28(2):157–161	PROPN
ejpam-5531	305	7	,	,	PUNCT
ejpam-5531	305	8	2005	2005	NUM
ejpam-5531	305	9	.	.	PUNCT
ejpam-5531	306	1	[	[	X
ejpam-5531	306	2	14	14	NUM
ejpam-5531	306	3	]	]	X
ejpam-5531	306	4	s.	s.	PROPN
ejpam-5531	306	5	jafari	jafari	PROPN
ejpam-5531	306	6	and	and	CCONJ
ejpam-5531	306	7	t.	t.	PROPN
ejpam-5531	306	8	noiri	noiri	PROPN
ejpam-5531	306	9	.	.	PUNCT
ejpam-5531	307	1	on	on	ADP
ejpam-5531	307	2	rarely	rarely	ADV
ejpam-5531	307	3	β	β	ADJ
ejpam-5531	307	4	-	-	ADJ
ejpam-5531	307	5	continuous	continuous	ADJ
ejpam-5531	307	6	multifunctions	multifunction	NOUN
ejpam-5531	307	7	.	.	PUNCT
ejpam-5531	308	1	far	far	PROPN
ejpam-5531	308	2	east	east	PROPN
ejpam-5531	308	3	j.	j.	PROPN
ejpam-5531	308	4	math	math	PROPN
ejpam-5531	308	5	.	.	PUNCT
ejpam-5531	309	1	sci	sci	PROPN
ejpam-5531	309	2	.	.	PROPN
ejpam-5531	309	3	,	,	PUNCT
ejpam-5531	309	4	6(2):283–289	6(2):283–289	NUM
ejpam-5531	309	5	,	,	PUNCT
ejpam-5531	309	6	1998	1998	NUM
ejpam-5531	309	7	.	.	PUNCT
ejpam-5531	310	1	[	[	X
ejpam-5531	310	2	15	15	NUM
ejpam-5531	310	3	]	]	X
ejpam-5531	310	4	s.	s.	PROPN
ejpam-5531	310	5	jafari	jafari	PROPN
ejpam-5531	310	6	and	and	CCONJ
ejpam-5531	310	7	v.	v.	ADP
ejpam-5531	310	8	popa	popa	NOUN
ejpam-5531	310	9	.	.	PUNCT
ejpam-5531	311	1	rarely	rarely	ADV
ejpam-5531	311	2	quasi	quasi	ADJ
ejpam-5531	311	3	-	-	ADJ
ejpam-5531	311	4	continuous	continuous	ADJ
ejpam-5531	311	5	multifunctions	multifunction	NOUN
ejpam-5531	311	6	.	.	PUNCT
ejpam-5531	312	1	an	an	DET
ejpam-5531	312	2	.	.	PROPN
ejpam-5531	312	3	univ	univ	PROPN
ejpam-5531	312	4	.	.	PUNCT
ejpam-5531	313	1	timişoara	timişoara	NOUN
ejpam-5531	313	2	,	,	PUNCT
ejpam-5531	313	3	37(2):83–90	37(2):83–90	NUM
ejpam-5531	313	4	,	,	PUNCT
ejpam-5531	313	5	1999	1999	NUM
ejpam-5531	313	6	.	.	PUNCT
ejpam-5531	314	1	references	reference	NOUN
ejpam-5531	314	2	3686	3686	NUM
ejpam-5531	314	3	[	[	X
ejpam-5531	314	4	16	16	NUM
ejpam-5531	314	5	]	]	X
ejpam-5531	314	6	d.	d.	PROPN
ejpam-5531	314	7	jankovič	jankovič	NOUN
ejpam-5531	314	8	and	and	CCONJ
ejpam-5531	314	9	t.	t.	PROPN
ejpam-5531	314	10	r.	r.	PROPN
ejpam-5531	314	11	hamlett	hamlett	PROPN
ejpam-5531	314	12	.	.	PUNCT
ejpam-5531	315	1	new	new	ADJ
ejpam-5531	315	2	topologies	topology	NOUN
ejpam-5531	315	3	from	from	ADP
ejpam-5531	315	4	old	old	ADJ
ejpam-5531	315	5	via	via	ADP
ejpam-5531	315	6	ideals	ideal	NOUN
ejpam-5531	315	7	.	.	PUNCT
ejpam-5531	316	1	amer	amer	PROPN
ejpam-5531	316	2	.	.	PUNCT
ejpam-5531	316	3	math	math	PROPN
ejpam-5531	316	4	.	.	PUNCT
ejpam-5531	317	1	monthly	monthly	ADJ
ejpam-5531	317	2	,	,	PUNCT
ejpam-5531	317	3	97:295–310	97:295–310	PROPN
ejpam-5531	317	4	,	,	PUNCT
ejpam-5531	317	5	1990	1990	NUM
ejpam-5531	317	6	.	.	PUNCT
ejpam-5531	318	1	[	[	X
ejpam-5531	318	2	17	17	NUM
ejpam-5531	318	3	]	]	PUNCT
ejpam-5531	318	4	k.	k.	PROPN
ejpam-5531	318	5	kuratowski	kuratowski	PROPN
ejpam-5531	318	6	.	.	PUNCT
ejpam-5531	319	1	topology	topology	PROPN
ejpam-5531	319	2	,	,	PUNCT
ejpam-5531	319	3	vol	vol	NOUN
ejpam-5531	319	4	.	.	PUNCT
ejpam-5531	319	5	i.	i.	PROPN
ejpam-5531	319	6	academic	academic	PROPN
ejpam-5531	319	7	press	press	PROPN
ejpam-5531	319	8	,	,	PUNCT
ejpam-5531	319	9	new	new	PROPN
ejpam-5531	319	10	york	york	PROPN
ejpam-5531	319	11	,	,	PUNCT
ejpam-5531	319	12	1966	1966	NUM
ejpam-5531	319	13	.	.	PUNCT
ejpam-5531	320	1	[	[	X
ejpam-5531	320	2	18	18	NUM
ejpam-5531	320	3	]	]	X
ejpam-5531	320	4	n.	n.	PROPN
ejpam-5531	320	5	levine	levine	PROPN
ejpam-5531	320	6	.	.	PUNCT
ejpam-5531	321	1	semi	semi	ADJ
ejpam-5531	321	2	-	-	ADJ
ejpam-5531	321	3	open	open	ADJ
ejpam-5531	321	4	sets	set	NOUN
ejpam-5531	321	5	and	and	CCONJ
ejpam-5531	321	6	semi	semi	ADJ
ejpam-5531	321	7	-	-	NOUN
ejpam-5531	321	8	continuity	continuity	NOUN
ejpam-5531	321	9	in	in	ADP
ejpam-5531	321	10	topological	topological	ADJ
ejpam-5531	321	11	spaces	space	NOUN
ejpam-5531	321	12	.	.	PUNCT
ejpam-5531	322	1	amer	amer	PROPN
ejpam-5531	322	2	.	.	PUNCT
ejpam-5531	322	3	math	math	PROPN
ejpam-5531	322	4	.	.	PUNCT
ejpam-5531	323	1	monthly	monthly	ADJ
ejpam-5531	323	2	,	,	PUNCT
ejpam-5531	323	3	70:36–41	70:36–41	NUM
ejpam-5531	323	4	,	,	PUNCT
ejpam-5531	323	5	1963	1963	NUM
ejpam-5531	323	6	.	.	PUNCT
ejpam-5531	324	1	[	[	X
ejpam-5531	324	2	19	19	NUM
ejpam-5531	324	3	]	]	PUNCT
ejpam-5531	324	4	p.	p.	NOUN
ejpam-5531	324	5	e.	e.	PROPN
ejpam-5531	325	1	long	long	PROPN
ejpam-5531	325	2	and	and	CCONJ
ejpam-5531	325	3	l.	l.	PROPN
ejpam-5531	325	4	l.	l.	PROPN
ejpam-5531	325	5	herrington	herrington	PROPN
ejpam-5531	325	6	.	.	PUNCT
ejpam-5531	326	1	properties	property	NOUN
ejpam-5531	326	2	of	of	ADP
ejpam-5531	326	3	rarely	rarely	ADV
ejpam-5531	326	4	continuous	continuous	ADJ
ejpam-5531	326	5	functions	function	NOUN
ejpam-5531	326	6	.	.	PUNCT
ejpam-5531	327	1	glasnik	glasnik	PROPN
ejpam-5531	327	2	mat	mat	PROPN
ejpam-5531	327	3	.	.	PROPN
ejpam-5531	327	4	,	,	PUNCT
ejpam-5531	327	5	17(37):147–153	17(37):147–153	NUM
ejpam-5531	327	6	,	,	PUNCT
ejpam-5531	327	7	1982	1982	NUM
ejpam-5531	327	8	.	.	PUNCT
ejpam-5531	328	1	[	[	X
ejpam-5531	328	2	20	20	NUM
ejpam-5531	328	3	]	]	PUNCT
ejpam-5531	328	4	h.	h.	NOUN
ejpam-5531	328	5	maki	maki	PROPN
ejpam-5531	328	6	,	,	PUNCT
ejpam-5531	328	7	c.	c.	PROPN
ejpam-5531	328	8	k.	k.	PROPN
ejpam-5531	328	9	rao	rao	PROPN
ejpam-5531	328	10	,	,	PUNCT
ejpam-5531	328	11	and	and	CCONJ
ejpam-5531	328	12	a.	a.	NOUN
ejpam-5531	328	13	nagoor	nagoor	PROPN
ejpam-5531	328	14	gani	gani	PROPN
ejpam-5531	328	15	.	.	PUNCT
ejpam-5531	329	1	on	on	ADP
ejpam-5531	329	2	generalizing	generalize	VERB
ejpam-5531	329	3	semi	semi	ADJ
ejpam-5531	329	4	-	-	ADJ
ejpam-5531	329	5	open	open	ADJ
ejpam-5531	329	6	and	and	CCONJ
ejpam-5531	329	7	preopen	preopen	ADJ
ejpam-5531	329	8	sets	set	NOUN
ejpam-5531	329	9	.	.	PUNCT
ejpam-5531	330	1	pure	pure	ADJ
ejpam-5531	330	2	appl	appl	PROPN
ejpam-5531	330	3	.	.	PUNCT
ejpam-5531	330	4	math	math	PROPN
ejpam-5531	330	5	.	.	PUNCT
ejpam-5531	331	1	sci	sci	PROPN
ejpam-5531	331	2	.	.	PROPN
ejpam-5531	331	3	,	,	PUNCT
ejpam-5531	331	4	49:17–29	49:17–29	PROPN
ejpam-5531	331	5	,	,	PUNCT
ejpam-5531	331	6	1999	1999	NUM
ejpam-5531	331	7	.	.	PUNCT
ejpam-5531	332	1	[	[	X
ejpam-5531	332	2	21	21	NUM
ejpam-5531	332	3	]	]	PUNCT
ejpam-5531	332	4	a.	a.	NOUN
ejpam-5531	332	5	s.	s.	PROPN
ejpam-5531	332	6	mashhour	mashhour	PROPN
ejpam-5531	332	7	,	,	PUNCT
ejpam-5531	332	8	m.	m.	PROPN
ejpam-5531	332	9	e.	e.	PROPN
ejpam-5531	332	10	abd	abd	PROPN
ejpam-5531	332	11	el	el	PROPN
ejpam-5531	332	12	-	-	PROPN
ejpam-5531	332	13	monsef	monsef	ADJ
ejpam-5531	332	14	,	,	PUNCT
ejpam-5531	332	15	and	and	CCONJ
ejpam-5531	332	16	s.	s.	PROPN
ejpam-5531	332	17	n.	n.	PROPN
ejpam-5531	332	18	el	el	PROPN
ejpam-5531	332	19	-	-	PUNCT
ejpam-5531	332	20	deep	deep	ADJ
ejpam-5531	332	21	.	.	PUNCT
ejpam-5531	333	1	on	on	ADP
ejpam-5531	333	2	precontinuous	precontinuous	ADJ
ejpam-5531	333	3	and	and	CCONJ
ejpam-5531	333	4	weak	weak	ADJ
ejpam-5531	333	5	precontinuous	precontinuous	ADJ
ejpam-5531	333	6	mappings	mapping	NOUN
ejpam-5531	333	7	.	.	PUNCT
ejpam-5531	334	1	proc	proc	NOUN
ejpam-5531	334	2	.	.	PUNCT
ejpam-5531	335	1	math	math	NOUN
ejpam-5531	335	2	.	.	PUNCT
ejpam-5531	336	1	phys	phy	NOUN
ejpam-5531	336	2	.	.	PUNCT
ejpam-5531	337	1	soc	soc	PROPN
ejpam-5531	337	2	.	.	PUNCT
ejpam-5531	338	1	egypt	egypt	PROPN
ejpam-5531	338	2	,	,	PUNCT
ejpam-5531	338	3	53:47–53	53:47–53	NUM
ejpam-5531	338	4	,	,	PUNCT
ejpam-5531	338	5	1982	1982	NUM
ejpam-5531	338	6	.	.	PUNCT
ejpam-5531	339	1	[	[	X
ejpam-5531	339	2	22	22	NUM
ejpam-5531	339	3	]	]	X
ejpam-5531	339	4	j.	j.	PROPN
ejpam-5531	339	5	m.	m.	PROPN
ejpam-5531	339	6	mustafa	mustafa	PROPN
ejpam-5531	339	7	,	,	PUNCT
ejpam-5531	339	8	s.	s.	PROPN
ejpam-5531	339	9	al	al	PROPN
ejpam-5531	339	10	ghour	ghour	PROPN
ejpam-5531	339	11	,	,	PUNCT
ejpam-5531	339	12	and	and	CCONJ
ejpam-5531	339	13	k.	k.	PROPN
ejpam-5531	339	14	al	al	PROPN
ejpam-5531	339	15	zoubi	zoubi	PROPN
ejpam-5531	339	16	.	.	PUNCT
ejpam-5531	340	1	weakly	weakly	ADJ
ejpam-5531	340	2	b	b	X
ejpam-5531	340	3	-	-	PUNCT
ejpam-5531	340	4	i	i	NOUN
ejpam-5531	340	5	-	-	PUNCT
ejpam-5531	340	6	open	open	ADJ
ejpam-5531	340	7	sets	set	NOUN
ejpam-5531	340	8	and	and	CCONJ
ejpam-5531	340	9	weakly	weakly	ADJ
ejpam-5531	340	10	b	b	NOUN
ejpam-5531	340	11	-	-	PUNCT
ejpam-5531	340	12	i	i	NOUN
ejpam-5531	340	13	-	-	PUNCT
ejpam-5531	340	14	continuous	continuous	ADJ
ejpam-5531	340	15	functions	function	NOUN
ejpam-5531	340	16	.	.	PUNCT
ejpam-5531	341	1	ital	ital	PROPN
ejpam-5531	341	2	.	.	PUNCT
ejpam-5531	342	1	j.	j.	PROPN
ejpam-5531	342	2	pure	pure	PROPN
ejpam-5531	342	3	appl	appl	PROPN
ejpam-5531	342	4	.	.	PUNCT
ejpam-5531	342	5	math	math	PROPN
ejpam-5531	342	6	.	.	PUNCT
ejpam-5531	342	7	,	,	PUNCT
ejpam-5531	342	8	30:23–32	30:23–32	NUM
ejpam-5531	342	9	,	,	PUNCT
ejpam-5531	342	10	2013	2013	NUM
ejpam-5531	342	11	.	.	PUNCT
ejpam-5531	343	1	[	[	X
ejpam-5531	343	2	23	23	NUM
ejpam-5531	343	3	]	]	PUNCT
ejpam-5531	343	4	o.	o.	PROPN
ejpam-5531	343	5	njǎstad	njǎstad	PROPN
ejpam-5531	343	6	.	.	PUNCT
ejpam-5531	344	1	on	on	ADP
ejpam-5531	344	2	some	some	DET
ejpam-5531	344	3	classes	class	NOUN
ejpam-5531	344	4	of	of	ADP
ejpam-5531	344	5	nearly	nearly	ADV
ejpam-5531	344	6	open	open	ADJ
ejpam-5531	344	7	sets	set	NOUN
ejpam-5531	344	8	.	.	PUNCT
ejpam-5531	345	1	pacific	pacific	PROPN
ejpam-5531	345	2	j.	j.	PROPN
ejpam-5531	345	3	math	math	PROPN
ejpam-5531	345	4	.	.	PUNCT
ejpam-5531	345	5	,	,	PUNCT
ejpam-5531	345	6	15:961–970	15:961–970	PROPN
ejpam-5531	345	7	,	,	PUNCT
ejpam-5531	345	8	1965	1965	NUM
ejpam-5531	345	9	.	.	PUNCT
ejpam-5531	346	1	[	[	X
ejpam-5531	346	2	24	24	NUM
ejpam-5531	346	3	]	]	PUNCT
ejpam-5531	346	4	v.	v.	CCONJ
ejpam-5531	346	5	popa	popa	NOUN
ejpam-5531	346	6	.	.	PUNCT
ejpam-5531	347	1	sur	sur	PROPN
ejpam-5531	347	2	certaine	certaine	PROPN
ejpam-5531	347	3	decomposition	decomposition	NOUN
ejpam-5531	347	4	de	de	X
ejpam-5531	347	5	la	la	X
ejpam-5531	347	6	continuite	continuite	PROPN
ejpam-5531	347	7	dans	dans	PROPN
ejpam-5531	347	8	les	les	PROPN
ejpam-5531	347	9	espaces	espaces	PROPN
ejpam-5531	347	10	topologiques	topologique	NOUN
ejpam-5531	347	11	.	.	PUNCT
ejpam-5531	348	1	glasnik	glasnik	PROPN
ejpam-5531	348	2	mat	mat	PROPN
ejpam-5531	348	3	.	.	PROPN
ejpam-5531	348	4	,	,	PUNCT
ejpam-5531	348	5	14(34):359–362	14(34):359–362	NUM
ejpam-5531	348	6	,	,	PUNCT
ejpam-5531	348	7	1979	1979	NUM
ejpam-5531	348	8	.	.	PUNCT
ejpam-5531	349	1	[	[	X
ejpam-5531	349	2	25	25	NUM
ejpam-5531	349	3	]	]	PUNCT
ejpam-5531	349	4	v.	v.	CCONJ
ejpam-5531	349	5	popa	popa	NOUN
ejpam-5531	349	6	.	.	PUNCT
ejpam-5531	350	1	some	some	DET
ejpam-5531	350	2	properties	property	NOUN
ejpam-5531	350	3	of	of	ADP
ejpam-5531	350	4	rarely	rarely	ADV
ejpam-5531	350	5	continuous	continuous	ADJ
ejpam-5531	350	6	multifunctions	multifunction	NOUN
ejpam-5531	350	7	.	.	PUNCT
ejpam-5531	350	8	conf	conf	PROPN
ejpam-5531	350	9	.	.	PUNCT
ejpam-5531	351	1	nat	nat	PROPN
ejpam-5531	351	2	.	.	PUNCT
ejpam-5531	352	1	geometrytopology	geometrytopology	NOUN
ejpam-5531	352	2	,	,	PUNCT
ejpam-5531	352	3	1988	1988	NUM
ejpam-5531	352	4	.	.	PUNCT
ejpam-5531	353	1	univ	univ	PROPN
ejpam-5531	353	2	.	.	PUNCT
ejpam-5531	354	1	al	al	PROPN
ejpam-5531	354	2	.	.	PROPN
ejpam-5531	354	3	i.	i.	PROPN
ejpam-5531	354	4	cuza	cuza	PROPN
ejpam-5531	354	5	.	.	PUNCT
ejpam-5531	354	6	iasi	iasi	PROPN
ejpam-5531	354	7	,	,	PUNCT
ejpam-5531	354	8	269	269	NUM
ejpam-5531	354	9	-	-	SYM
ejpam-5531	354	10	274	274	NUM
ejpam-5531	354	11	,	,	PUNCT
ejpam-5531	354	12	1989	1989	NUM
ejpam-5531	354	13	.	.	PUNCT
ejpam-5531	355	1	[	[	X
ejpam-5531	355	2	26	26	NUM
ejpam-5531	355	3	]	]	PUNCT
ejpam-5531	355	4	v.	v.	CCONJ
ejpam-5531	355	5	popa	popa	NOUN
ejpam-5531	355	6	and	and	CCONJ
ejpam-5531	355	7	t.	t.	PROPN
ejpam-5531	355	8	noiri	noiri	PROPN
ejpam-5531	355	9	.	.	PUNCT
ejpam-5531	356	1	some	some	DET
ejpam-5531	356	2	properties	property	NOUN
ejpam-5531	356	3	of	of	ADP
ejpam-5531	356	4	rarely	rarely	ADV
ejpam-5531	356	5	quasicontinuous	quasicontinuous	ADJ
ejpam-5531	356	6	functions	function	NOUN
ejpam-5531	356	7	.	.	PUNCT
ejpam-5531	357	1	an	an	DET
ejpam-5531	357	2	.	.	PROPN
ejpam-5531	357	3	univ	univ	PROPN
ejpam-5531	357	4	.	.	PUNCT
ejpam-5531	358	1	timişoara	timişoara	NOUN
ejpam-5531	358	2	,	,	PUNCT
ejpam-5531	358	3	29(1):65–71	29(1):65–71	NUM
ejpam-5531	358	4	,	,	PUNCT
ejpam-5531	358	5	1991	1991	NUM
ejpam-5531	358	6	.	.	PUNCT
ejpam-5531	359	1	[	[	X
ejpam-5531	359	2	27	27	NUM
ejpam-5531	359	3	]	]	X
ejpam-5531	359	4	v.	v.	CCONJ
ejpam-5531	359	5	popa	popa	NOUN
ejpam-5531	359	6	and	and	CCONJ
ejpam-5531	359	7	t.	t.	PROPN
ejpam-5531	359	8	noiri	noiri	PROPN
ejpam-5531	359	9	.	.	PUNCT
ejpam-5531	360	1	on	on	ADP
ejpam-5531	360	2	m	m	PROPN
ejpam-5531	360	3	-continuous	-continuous	ADJ
ejpam-5531	360	4	functions	function	NOUN
ejpam-5531	360	5	.	.	PUNCT
ejpam-5531	361	1	anal	anal	PROPN
ejpam-5531	361	2	.	.	PUNCT
ejpam-5531	361	3	univ	univ	PROPN
ejpam-5531	361	4	.	.	PUNCT
ejpam-5531	361	5	”	"	PUNCT
ejpam-5531	361	6	dunǎrea	dunǎrea	PROPN
ejpam-5531	361	7	de	de	X
ejpam-5531	361	8	jos	jos	PROPN
ejpam-5531	361	9	”	"	PUNCT
ejpam-5531	361	10	gala̧ti	gala̧ti	PROPN
ejpam-5531	361	11	,	,	PUNCT
ejpam-5531	361	12	ser	ser	PROPN
ejpam-5531	361	13	.	.	PROPN
ejpam-5531	362	1	mat	mat	PROPN
ejpam-5531	362	2	.	.	PUNCT
ejpam-5531	362	3	fiz	fiz	PROPN
ejpam-5531	362	4	.	.	PUNCT
ejpam-5531	363	1	mec	mec	PROPN
ejpam-5531	363	2	.	.	PROPN
ejpam-5531	363	3	teor	teor	PROPN
ejpam-5531	363	4	.	.	PROPN
ejpam-5531	363	5	,	,	PUNCT
ejpam-5531	363	6	fasc	fasc	PROPN
ejpam-5531	363	7	.	.	PROPN
ejpam-5531	363	8	ii	ii	PROPN
ejpam-5531	363	9	,	,	PUNCT
ejpam-5531	363	10	18(23):31–41	18(23):31–41	NUM
ejpam-5531	363	11	,	,	PUNCT
ejpam-5531	363	12	2000	2000	NUM
ejpam-5531	363	13	.	.	PUNCT
ejpam-5531	364	1	[	[	X
ejpam-5531	364	2	28	28	NUM
ejpam-5531	364	3	]	]	X
ejpam-5531	364	4	v.	v.	CCONJ
ejpam-5531	364	5	popa	popa	NOUN
ejpam-5531	364	6	and	and	CCONJ
ejpam-5531	364	7	t.	t.	PROPN
ejpam-5531	364	8	noiri	noiri	PROPN
ejpam-5531	364	9	.	.	PUNCT
ejpam-5531	365	1	on	on	ADP
ejpam-5531	365	2	the	the	DET
ejpam-5531	365	3	definitions	definition	NOUN
ejpam-5531	365	4	of	of	ADP
ejpam-5531	365	5	some	some	DET
ejpam-5531	365	6	generalized	generalized	ADJ
ejpam-5531	365	7	forms	form	NOUN
ejpam-5531	365	8	of	of	ADP
ejpam-5531	365	9	continuity	continuity	NOUN
ejpam-5531	365	10	under	under	ADP
ejpam-5531	365	11	minimal	minimal	ADJ
ejpam-5531	365	12	conditions	condition	NOUN
ejpam-5531	365	13	.	.	PUNCT
ejpam-5531	366	1	mem	mem	PROPN
ejpam-5531	366	2	.	.	PUNCT
ejpam-5531	366	3	fac	fac	PROPN
ejpam-5531	366	4	.	.	PUNCT
ejpam-5531	367	1	sci	sci	PROPN
ejpam-5531	367	2	.	.	PROPN
ejpam-5531	367	3	kochi	kochi	PROPN
ejpam-5531	367	4	univ	univ	PROPN
ejpam-5531	367	5	.	.	PUNCT
ejpam-5531	368	1	ser	ser	PROPN
ejpam-5531	368	2	.	.	PUNCT
ejpam-5531	368	3	math	math	PROPN
ejpam-5531	368	4	.	.	PUNCT
ejpam-5531	368	5	,	,	PUNCT
ejpam-5531	368	6	22:9–18	22:9–18	NUM
ejpam-5531	368	7	,	,	PUNCT
ejpam-5531	368	8	2001	2001	NUM
ejpam-5531	368	9	.	.	PUNCT
ejpam-5531	369	1	[	[	X
ejpam-5531	369	2	29	29	NUM
ejpam-5531	369	3	]	]	PUNCT
ejpam-5531	369	4	v.	v.	CCONJ
ejpam-5531	369	5	popa	popa	NOUN
ejpam-5531	369	6	and	and	CCONJ
ejpam-5531	369	7	t.	t.	PROPN
ejpam-5531	369	8	noiri	noiri	PROPN
ejpam-5531	369	9	.	.	PUNCT
ejpam-5531	370	1	a	a	DET
ejpam-5531	370	2	unified	unified	ADJ
ejpam-5531	370	3	theory	theory	NOUN
ejpam-5531	370	4	of	of	ADP
ejpam-5531	370	5	weak	weak	ADJ
ejpam-5531	370	6	continuity	continuity	NOUN
ejpam-5531	370	7	for	for	ADP
ejpam-5531	370	8	functions	function	NOUN
ejpam-5531	370	9	.	.	PUNCT
ejpam-5531	371	1	rend	rend	VERB
ejpam-5531	371	2	.	.	PUNCT
ejpam-5531	372	1	circ	circ	PROPN
ejpam-5531	372	2	.	.	PUNCT
ejpam-5531	373	1	mat	mat	PROPN
ejpam-5531	373	2	.	.	PUNCT
ejpam-5531	373	3	palermo	palermo	PROPN
ejpam-5531	373	4	(	(	PUNCT
ejpam-5531	373	5	2	2	NUM
ejpam-5531	373	6	)	)	PUNCT
ejpam-5531	373	7	,	,	PUNCT
ejpam-5531	373	8	51:439–464	51:439–464	PROPN
ejpam-5531	373	9	,	,	PUNCT
ejpam-5531	373	10	2002	2002	NUM
ejpam-5531	373	11	.	.	PUNCT
ejpam-5531	374	1	[	[	X
ejpam-5531	374	2	30	30	NUM
ejpam-5531	374	3	]	]	X
ejpam-5531	374	4	r.	r.	PROPN
ejpam-5531	374	5	vaidyanathaswani	vaidyanathaswani	PROPN
ejpam-5531	374	6	.	.	PUNCT
ejpam-5531	375	1	the	the	DET
ejpam-5531	375	2	localization	localization	NOUN
ejpam-5531	375	3	theory	theory	NOUN
ejpam-5531	375	4	in	in	ADP
ejpam-5531	375	5	set	set	NOUN
ejpam-5531	375	6	-	-	PUNCT
ejpam-5531	375	7	topology	topology	NOUN
ejpam-5531	375	8	.	.	PUNCT
ejpam-5531	376	1	proc	proc	PROPN
ejpam-5531	376	2	.	.	PUNCT
ejpam-5531	377	1	indian	indian	PROPN
ejpam-5531	377	2	acad	acad	PROPN
ejpam-5531	377	3	.	.	PUNCT
ejpam-5531	378	1	sci	sci	PROPN
ejpam-5531	378	2	.	.	PROPN
ejpam-5531	378	3	,	,	PUNCT
ejpam-5531	378	4	20:51–62	20:51–62	NUM
ejpam-5531	378	5	,	,	PUNCT
ejpam-5531	378	6	1945	1945	NUM
ejpam-5531	378	7	.	.	PUNCT