id	sid	tid	token	lemma	pos
ejpam-4734	1	1	european	european	PROPN
ejpam-4734	1	2	journal	journal	PROPN
ejpam-4734	1	3	of	of	ADP
ejpam-4734	1	4	pure	pure	ADJ
ejpam-4734	1	5	and	and	CCONJ
ejpam-4734	1	6	applied	apply	VERB
ejpam-4734	1	7	mathematics	mathematic	NOUN
ejpam-4734	1	8	vol	vol	NOUN
ejpam-4734	1	9	.	.	PUNCT
ejpam-4734	2	1	16	16	NUM
ejpam-4734	2	2	,	,	PUNCT
ejpam-4734	2	3	no	no	INTJ
ejpam-4734	2	4	.	.	NOUN
ejpam-4734	2	5	4	4	NUM
ejpam-4734	2	6	,	,	PUNCT
ejpam-4734	2	7	2023	2023	NUM
ejpam-4734	2	8	,	,	PUNCT
ejpam-4734	2	9	2544	2544	NUM
ejpam-4734	2	10	-	-	SYM
ejpam-4734	2	11	2556	2556	NUM
ejpam-4734	2	12	issn	issn	PROPN
ejpam-4734	2	13	1307	1307	NUM
ejpam-4734	2	14	-	-	SYM
ejpam-4734	2	15	5543	5543	NUM
ejpam-4734	2	16	–	–	PUNCT
ejpam-4734	2	17	ejpam.com	ejpam.com	X
ejpam-4734	2	18	published	publish	VERB
ejpam-4734	2	19	by	by	ADP
ejpam-4734	2	20	new	new	PROPN
ejpam-4734	2	21	york	york	PROPN
ejpam-4734	2	22	business	business	PROPN
ejpam-4734	2	23	global	global	PROPN
ejpam-4734	2	24	upper	upper	ADJ
ejpam-4734	2	25	and	and	CCONJ
ejpam-4734	2	26	lower	low	ADJ
ejpam-4734	2	27	weak	weak	ADJ
ejpam-4734	2	28	sβ(⋆)-continuity	sβ(⋆)-continuity	NOUN
ejpam-4734	2	29	chawalit	chawalit	VERB
ejpam-4734	2	30	boonpok1	boonpok1	NOUN
ejpam-4734	2	31	,	,	PUNCT
ejpam-4734	2	32	jeeranunt	jeeranunt	PROPN
ejpam-4734	2	33	khampakdee1,∗	khampakdee1,∗	PROPN
ejpam-4734	2	34	1	1	NUM
ejpam-4734	2	35	mathematics	mathematic	NOUN
ejpam-4734	2	36	and	and	CCONJ
ejpam-4734	2	37	applied	apply	VERB
ejpam-4734	2	38	mathematics	mathematics	PROPN
ejpam-4734	2	39	research	research	NOUN
ejpam-4734	2	40	unit	unit	NOUN
ejpam-4734	2	41	,	,	PUNCT
ejpam-4734	2	42	department	department	NOUN
ejpam-4734	2	43	of	of	ADP
ejpam-4734	2	44	mathematics	mathematic	NOUN
ejpam-4734	2	45	,	,	PUNCT
ejpam-4734	2	46	faculty	faculty	NOUN
ejpam-4734	2	47	of	of	ADP
ejpam-4734	2	48	science	science	NOUN
ejpam-4734	2	49	,	,	PUNCT
ejpam-4734	2	50	mahasarakham	mahasarakham	PROPN
ejpam-4734	2	51	university	university	PROPN
ejpam-4734	2	52	,	,	PUNCT
ejpam-4734	2	53	maha	maha	PROPN
ejpam-4734	2	54	sarakham	sarakham	PROPN
ejpam-4734	2	55	,	,	PUNCT
ejpam-4734	2	56	44150	44150	NUM
ejpam-4734	2	57	,	,	PUNCT
ejpam-4734	2	58	thailand	thailand	PROPN
ejpam-4734	2	59	abstract	abstract	PROPN
ejpam-4734	2	60	.	.	PUNCT
ejpam-4734	3	1	this	this	DET
ejpam-4734	3	2	paper	paper	NOUN
ejpam-4734	3	3	is	be	AUX
ejpam-4734	3	4	concerned	concern	VERB
ejpam-4734	3	5	with	with	ADP
ejpam-4734	3	6	the	the	DET
ejpam-4734	3	7	concepts	concept	NOUN
ejpam-4734	3	8	of	of	ADP
ejpam-4734	3	9	upper	upper	ADJ
ejpam-4734	3	10	and	and	CCONJ
ejpam-4734	3	11	lower	low	ADJ
ejpam-4734	3	12	weakly	weakly	ADJ
ejpam-4734	3	13	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	3	14	multifunctions	multifunction	NOUN
ejpam-4734	3	15	.	.	PUNCT
ejpam-4734	4	1	moreover	moreover	ADV
ejpam-4734	4	2	,	,	PUNCT
ejpam-4734	4	3	some	some	DET
ejpam-4734	4	4	characterizations	characterization	NOUN
ejpam-4734	4	5	of	of	ADP
ejpam-4734	4	6	upper	upper	ADJ
ejpam-4734	4	7	and	and	CCONJ
ejpam-4734	4	8	lower	low	ADJ
ejpam-4734	4	9	weakly	weakly	ADJ
ejpam-4734	4	10	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	4	11	multifunctions	multifunction	NOUN
ejpam-4734	4	12	are	be	AUX
ejpam-4734	4	13	investigated	investigate	VERB
ejpam-4734	4	14	.	.	PUNCT
ejpam-4734	5	1	2020	2020	NUM
ejpam-4734	5	2	mathematics	mathematic	NOUN
ejpam-4734	5	3	subject	subject	NOUN
ejpam-4734	5	4	classifications	classification	NOUN
ejpam-4734	5	5	:	:	PUNCT
ejpam-4734	5	6	54c08	54c08	NUM
ejpam-4734	5	7	,	,	PUNCT
ejpam-4734	5	8	54c60	54c60	NUM
ejpam-4734	5	9	key	key	ADJ
ejpam-4734	5	10	words	word	NOUN
ejpam-4734	5	11	and	and	CCONJ
ejpam-4734	5	12	phrases	phrase	NOUN
ejpam-4734	5	13	:	:	PUNCT
ejpam-4734	5	14	upper	upper	ADJ
ejpam-4734	5	15	weakly	weakly	ADJ
ejpam-4734	5	16	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	5	17	multifunction	multifunction	NOUN
ejpam-4734	5	18	,	,	PUNCT
ejpam-4734	5	19	lower	low	ADJ
ejpam-4734	5	20	weakly	weakly	ADJ
ejpam-4734	5	21	sβ(⋆)continuous	sβ(⋆)continuous	ADJ
ejpam-4734	5	22	multifunction	multifunction	NOUN
ejpam-4734	5	23	1	1	NUM
ejpam-4734	5	24	.	.	PUNCT
ejpam-4734	6	1	introduction	introduction	NOUN
ejpam-4734	6	2	in	in	ADP
ejpam-4734	6	3	topology	topology	NOUN
ejpam-4734	6	4	,	,	PUNCT
ejpam-4734	6	5	there	there	PRON
ejpam-4734	6	6	has	have	AUX
ejpam-4734	6	7	been	be	AUX
ejpam-4734	6	8	recently	recently	ADV
ejpam-4734	6	9	significant	significant	ADJ
ejpam-4734	6	10	interest	interest	NOUN
ejpam-4734	6	11	in	in	ADP
ejpam-4734	6	12	characterizing	characterize	VERB
ejpam-4734	6	13	and	and	CCONJ
ejpam-4734	6	14	investigating	investigate	VERB
ejpam-4734	6	15	the	the	DET
ejpam-4734	6	16	characterizations	characterization	NOUN
ejpam-4734	6	17	of	of	ADP
ejpam-4734	6	18	some	some	DET
ejpam-4734	6	19	weak	weak	ADJ
ejpam-4734	6	20	forms	form	NOUN
ejpam-4734	6	21	of	of	ADP
ejpam-4734	6	22	continuity	continuity	NOUN
ejpam-4734	6	23	for	for	ADP
ejpam-4734	6	24	functions	function	NOUN
ejpam-4734	6	25	and	and	CCONJ
ejpam-4734	6	26	multifunctions	multifunction	NOUN
ejpam-4734	6	27	.	.	PUNCT
ejpam-4734	7	1	as	as	ADP
ejpam-4734	7	2	weak	weak	ADJ
ejpam-4734	7	3	forms	form	NOUN
ejpam-4734	7	4	of	of	ADP
ejpam-4734	7	5	continuity	continuity	NOUN
ejpam-4734	7	6	in	in	ADP
ejpam-4734	7	7	topological	topological	ADJ
ejpam-4734	7	8	spaces	space	NOUN
ejpam-4734	7	9	,	,	PUNCT
ejpam-4734	7	10	weak	weak	ADJ
ejpam-4734	7	11	continuity	continuity	NOUN
ejpam-4734	7	12	[	[	X
ejpam-4734	7	13	12	12	NUM
ejpam-4734	7	14	]	]	PUNCT
ejpam-4734	7	15	,	,	PUNCT
ejpam-4734	7	16	quasicontinuity	quasicontinuity	NOUN
ejpam-4734	7	17	[	[	X
ejpam-4734	7	18	14	14	NUM
ejpam-4734	7	19	]	]	X
ejpam-4734	7	20	,	,	PUNCT
ejpam-4734	7	21	semi	semi	ADJ
ejpam-4734	7	22	-	-	NOUN
ejpam-4734	7	23	continuity	continuity	NOUN
ejpam-4734	7	24	[	[	X
ejpam-4734	7	25	13	13	NUM
ejpam-4734	7	26	]	]	PUNCT
ejpam-4734	7	27	and	and	CCONJ
ejpam-4734	7	28	almost	almost	ADV
ejpam-4734	7	29	continuity	continuity	NOUN
ejpam-4734	7	30	in	in	ADP
ejpam-4734	7	31	the	the	DET
ejpam-4734	7	32	sense	sense	NOUN
ejpam-4734	7	33	of	of	ADP
ejpam-4734	7	34	husain	husain	NOUN
ejpam-4734	7	35	[	[	X
ejpam-4734	7	36	9	9	NUM
ejpam-4734	7	37	]	]	PUNCT
ejpam-4734	7	38	are	be	AUX
ejpam-4734	7	39	well	well	ADV
ejpam-4734	7	40	-	-	PUNCT
ejpam-4734	7	41	known	know	VERB
ejpam-4734	7	42	.	.	PUNCT
ejpam-4734	8	1	it	it	PRON
ejpam-4734	8	2	is	be	AUX
ejpam-4734	8	3	shown	show	VERB
ejpam-4734	8	4	in	in	ADP
ejpam-4734	8	5	[	[	X
ejpam-4734	8	6	15	15	NUM
ejpam-4734	8	7	]	]	PUNCT
ejpam-4734	8	8	that	that	DET
ejpam-4734	8	9	quasicontinuity	quasicontinuity	NOUN
ejpam-4734	8	10	is	be	AUX
ejpam-4734	8	11	equivalent	equivalent	ADJ
ejpam-4734	8	12	to	to	ADP
ejpam-4734	8	13	semi	semi	NOUN
ejpam-4734	8	14	-	-	NOUN
ejpam-4734	8	15	continuity	continuity	NOUN
ejpam-4734	8	16	.	.	PUNCT
ejpam-4734	9	1	it	it	PRON
ejpam-4734	9	2	will	will	AUX
ejpam-4734	9	3	be	be	AUX
ejpam-4734	9	4	shown	show	VERB
ejpam-4734	9	5	that	that	SCONJ
ejpam-4734	9	6	weak	weak	ADJ
ejpam-4734	9	7	continuity	continuity	NOUN
ejpam-4734	9	8	,	,	PUNCT
ejpam-4734	9	9	semi	semi	ADJ
ejpam-4734	9	10	-	-	NOUN
ejpam-4734	9	11	continuity	continuity	NOUN
ejpam-4734	9	12	and	and	CCONJ
ejpam-4734	9	13	almost	almost	ADV
ejpam-4734	9	14	continuity	continuity	NOUN
ejpam-4734	9	15	are	be	AUX
ejpam-4734	9	16	respectively	respectively	ADV
ejpam-4734	9	17	independent	independent	ADJ
ejpam-4734	9	18	.	.	PUNCT
ejpam-4734	10	1	popa	popa	NOUN
ejpam-4734	10	2	and	and	CCONJ
ejpam-4734	10	3	stan	stan	PROPN
ejpam-4734	11	1	[	[	X
ejpam-4734	11	2	23	23	NUM
ejpam-4734	11	3	]	]	PUNCT
ejpam-4734	11	4	introduced	introduce	VERB
ejpam-4734	11	5	weak	weak	ADJ
ejpam-4734	11	6	quasi	quasi	NOUN
ejpam-4734	11	7	-	-	NOUN
ejpam-4734	11	8	continuity	continuity	NOUN
ejpam-4734	11	9	which	which	PRON
ejpam-4734	11	10	is	be	AUX
ejpam-4734	11	11	implied	imply	VERB
ejpam-4734	11	12	by	by	ADP
ejpam-4734	11	13	both	both	DET
ejpam-4734	11	14	weak	weak	ADJ
ejpam-4734	11	15	continuity	continuity	NOUN
ejpam-4734	11	16	and	and	CCONJ
ejpam-4734	11	17	quasicontinuity	quasicontinuity	NOUN
ejpam-4734	11	18	.	.	PUNCT
ejpam-4734	11	19	janković	janković	PUNCT
ejpam-4734	12	1	[	[	X
ejpam-4734	12	2	10	10	NUM
ejpam-4734	12	3	]	]	PUNCT
ejpam-4734	12	4	introduced	introduce	VERB
ejpam-4734	12	5	almost	almost	ADV
ejpam-4734	12	6	weak	weak	ADJ
ejpam-4734	12	7	continuity	continuity	NOUN
ejpam-4734	12	8	as	as	ADP
ejpam-4734	12	9	a	a	DET
ejpam-4734	12	10	generalization	generalization	NOUN
ejpam-4734	12	11	of	of	ADP
ejpam-4734	12	12	both	both	DET
ejpam-4734	12	13	weak	weak	ADJ
ejpam-4734	12	14	continuity	continuity	NOUN
ejpam-4734	12	15	and	and	CCONJ
ejpam-4734	12	16	almost	almost	ADV
ejpam-4734	12	17	continuity	continuity	NOUN
ejpam-4734	12	18	.	.	PUNCT
ejpam-4734	13	1	noiri	noiri	ADV
ejpam-4734	14	1	[	[	X
ejpam-4734	14	2	16	16	NUM
ejpam-4734	14	3	]	]	PUNCT
ejpam-4734	14	4	obtained	obtain	VERB
ejpam-4734	14	5	some	some	DET
ejpam-4734	14	6	characterizations	characterization	NOUN
ejpam-4734	14	7	of	of	ADP
ejpam-4734	14	8	almost	almost	ADV
ejpam-4734	14	9	weak	weak	ADJ
ejpam-4734	14	10	continuity	continuity	NOUN
ejpam-4734	14	11	and	and	CCONJ
ejpam-4734	14	12	some	some	DET
ejpam-4734	14	13	relations	relation	NOUN
ejpam-4734	14	14	between	between	ADP
ejpam-4734	14	15	almost	almost	ADV
ejpam-4734	14	16	weak	weak	ADJ
ejpam-4734	14	17	continuity	continuity	NOUN
ejpam-4734	14	18	and	and	CCONJ
ejpam-4734	14	19	weak	weak	ADJ
ejpam-4734	14	20	continuity	continuity	NOUN
ejpam-4734	14	21	.	.	PUNCT
ejpam-4734	15	1	popa	popa	NOUN
ejpam-4734	16	1	[	[	X
ejpam-4734	16	2	20	20	NUM
ejpam-4734	16	3	]	]	PUNCT
ejpam-4734	16	4	and	and	CCONJ
ejpam-4734	16	5	smithson	smithson	PROPN
ejpam-4734	17	1	[	[	X
ejpam-4734	17	2	24	24	NUM
ejpam-4734	17	3	]	]	PUNCT
ejpam-4734	17	4	independently	independently	ADV
ejpam-4734	17	5	introduced	introduce	VERB
ejpam-4734	17	6	the	the	DET
ejpam-4734	17	7	notion	notion	NOUN
ejpam-4734	17	8	of	of	ADP
ejpam-4734	17	9	weakly	weakly	ADJ
ejpam-4734	17	10	continuous	continuous	ADJ
ejpam-4734	17	11	multifunctions	multifunction	NOUN
ejpam-4734	17	12	.	.	PUNCT
ejpam-4734	18	1	the	the	DET
ejpam-4734	18	2	present	present	ADJ
ejpam-4734	18	3	authors	author	NOUN
ejpam-4734	18	4	introduced	introduce	VERB
ejpam-4734	18	5	and	and	CCONJ
ejpam-4734	18	6	studied	study	VERB
ejpam-4734	18	7	other	other	ADJ
ejpam-4734	18	8	weak	weak	ADJ
ejpam-4734	18	9	forms	form	NOUN
ejpam-4734	18	10	of	of	ADP
ejpam-4734	18	11	continuous	continuous	ADJ
ejpam-4734	18	12	multifunctions	multifunction	NOUN
ejpam-4734	18	13	:	:	PUNCT
ejpam-4734	18	14	weakly	weakly	ADJ
ejpam-4734	18	15	quasicontinuous	quasicontinuous	ADJ
ejpam-4734	18	16	multifunctions	multifunction	NOUN
ejpam-4734	19	1	[	[	X
ejpam-4734	19	2	17	17	NUM
ejpam-4734	19	3	]	]	PUNCT
ejpam-4734	19	4	,	,	PUNCT
ejpam-4734	19	5	almost	almost	ADV
ejpam-4734	19	6	weakly	weakly	ADJ
ejpam-4734	19	7	continuous	continuous	ADJ
ejpam-4734	19	8	multifunctions	multifunction	NOUN
ejpam-4734	20	1	[	[	X
ejpam-4734	20	2	18	18	NUM
ejpam-4734	20	3	]	]	PUNCT
ejpam-4734	20	4	,	,	PUNCT
ejpam-4734	20	5	weakly	weakly	ADJ
ejpam-4734	20	6	α	α	X
ejpam-4734	20	7	-	-	ADJ
ejpam-4734	20	8	continuous	continuous	ADJ
ejpam-4734	20	9	multifunctions	multifunction	NOUN
ejpam-4734	21	1	[	[	X
ejpam-4734	21	2	22	22	NUM
ejpam-4734	21	3	]	]	PUNCT
ejpam-4734	21	4	,	,	PUNCT
ejpam-4734	21	5	weakly	weakly	ADJ
ejpam-4734	21	6	β	β	ADJ
ejpam-4734	21	7	-	-	ADJ
ejpam-4734	21	8	continuous	continuous	ADJ
ejpam-4734	21	9	multifunctions	multifunction	NOUN
ejpam-4734	22	1	[	[	X
ejpam-4734	22	2	21	21	NUM
ejpam-4734	22	3	]	]	PUNCT
ejpam-4734	22	4	.	.	PUNCT
ejpam-4734	23	1	these	these	DET
ejpam-4734	23	2	multifunctions	multifunction	NOUN
ejpam-4734	23	3	have	have	VERB
ejpam-4734	23	4	similar	similar	ADJ
ejpam-4734	23	5	characterizations	characterization	NOUN
ejpam-4734	23	6	.	.	PUNCT
ejpam-4734	24	1	the	the	DET
ejpam-4734	24	2	analogy	analogy	NOUN
ejpam-4734	24	3	in	in	ADP
ejpam-4734	24	4	their	their	PRON
ejpam-4734	24	5	definitions	definition	NOUN
ejpam-4734	24	6	and	and	CCONJ
ejpam-4734	24	7	results	result	NOUN
ejpam-4734	24	8	suggests	suggest	VERB
ejpam-4734	24	9	the	the	DET
ejpam-4734	24	10	need	need	NOUN
ejpam-4734	24	11	of	of	ADP
ejpam-4734	24	12	formulating	formulate	VERB
ejpam-4734	24	13	a	a	DET
ejpam-4734	24	14	unified	unified	ADJ
ejpam-4734	24	15	theory	theory	NOUN
ejpam-4734	24	16	.	.	PUNCT
ejpam-4734	25	1	noiri	noiri	PROPN
ejpam-4734	25	2	and	and	CCONJ
ejpam-4734	25	3	popa	popa	NOUN
ejpam-4734	25	4	[	[	X
ejpam-4734	25	5	19	19	NUM
ejpam-4734	25	6	]	]	PUNCT
ejpam-4734	25	7	introduced	introduce	VERB
ejpam-4734	25	8	and	and	CCONJ
ejpam-4734	25	9	studied	study	VERB
ejpam-4734	25	10	the	the	DET
ejpam-4734	25	11	notions	notion	NOUN
ejpam-4734	25	12	of	of	ADP
ejpam-4734	25	13	upper	upper	ADJ
ejpam-4734	25	14	and	and	CCONJ
ejpam-4734	25	15	lower	low	ADJ
ejpam-4734	25	16	weakly	weakly	ADJ
ejpam-4734	25	17	m	m	ADJ
ejpam-4734	25	18	-	-	ADJ
ejpam-4734	25	19	continuous	continuous	ADJ
ejpam-4734	25	20	multifunctions	multifunction	NOUN
ejpam-4734	25	21	as	as	ADP
ejpam-4734	25	22	a	a	DET
ejpam-4734	25	23	multifunction	multifunction	NOUN
ejpam-4734	25	24	from	from	ADP
ejpam-4734	25	25	a	a	DET
ejpam-4734	25	26	set	set	NOUN
ejpam-4734	25	27	satisfying	satisfy	VERB
ejpam-4734	25	28	certain	certain	ADJ
ejpam-4734	25	29	minimal	minimal	ADJ
ejpam-4734	25	30	condition	condition	NOUN
ejpam-4734	25	31	into	into	ADP
ejpam-4734	25	32	a	a	DET
ejpam-4734	25	33	topological	topological	ADJ
ejpam-4734	25	34	space	space	NOUN
ejpam-4734	25	35	.	.	PUNCT
ejpam-4734	26	1	in	in	ADP
ejpam-4734	26	2	[	[	X
ejpam-4734	26	3	2	2	NUM
ejpam-4734	26	4	]	]	PUNCT
ejpam-4734	26	5	,	,	PUNCT
ejpam-4734	26	6	the	the	DET
ejpam-4734	26	7	present	present	ADJ
ejpam-4734	26	8	author	author	NOUN
ejpam-4734	26	9	introduced	introduce	VERB
ejpam-4734	26	10	and	and	CCONJ
ejpam-4734	26	11	studied	study	VERB
ejpam-4734	26	12	∗corresponding	∗corresponde	VERB
ejpam-4734	26	13	author	author	NOUN
ejpam-4734	26	14	.	.	PUNCT
ejpam-4734	27	1	doi	doi	NOUN
ejpam-4734	27	2	:	:	PUNCT
ejpam-4734	27	3	https://doi.org/10.29020/nybg.ejpam.v16i4.4734	https://doi.org/10.29020/nybg.ejpam.v16i4.4734	PRON
ejpam-4734	27	4	email	email	NOUN
ejpam-4734	27	5	addresses	address	NOUN
ejpam-4734	27	6	:	:	PUNCT
ejpam-4734	27	7	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	INTJ
ejpam-4734	27	8	(	(	PUNCT
ejpam-4734	27	9	c.	c.	PROPN
ejpam-4734	27	10	boonpok	boonpok	PROPN
ejpam-4734	27	11	)	)	PUNCT
ejpam-4734	27	12	,	,	PUNCT
ejpam-4734	27	13	jeeranunt.k@msu.ac.th	jeeranunt.k@msu.ac.th	INTJ
ejpam-4734	27	14	(	(	PUNCT
ejpam-4734	27	15	j.	j.	PROPN
ejpam-4734	27	16	khampakdee	khampakdee	PROPN
ejpam-4734	27	17	)	)	PUNCT
ejpam-4734	27	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4734	27	19	2544	2544	NUM
ejpam-4734	27	20	©	©	PROPN
ejpam-4734	27	21	2023	2023	NUM
ejpam-4734	27	22	ejpam	ejpam	NOUN
ejpam-4734	27	23	all	all	DET
ejpam-4734	27	24	rights	right	NOUN
ejpam-4734	27	25	reserved	reserve	VERB
ejpam-4734	27	26	.	.	PUNCT
ejpam-4734	28	1	c.	c.	PROPN
ejpam-4734	28	2	boonpok	boonpok	PROPN
ejpam-4734	28	3	,	,	PUNCT
ejpam-4734	28	4	j.	j.	PROPN
ejpam-4734	28	5	khampakdee	khampakdee	PROPN
ejpam-4734	28	6	/	/	PUNCT
ejpam-4734	28	7	eur	eur	PROPN
ejpam-4734	28	8	.	.	PUNCT
ejpam-4734	29	1	j.	j.	PROPN
ejpam-4734	29	2	pure	pure	PROPN
ejpam-4734	29	3	appl	appl	PROPN
ejpam-4734	29	4	.	.	PROPN
ejpam-4734	29	5	math	math	PROPN
ejpam-4734	29	6	,	,	PUNCT
ejpam-4734	29	7	16	16	NUM
ejpam-4734	29	8	(	(	PUNCT
ejpam-4734	29	9	4	4	NUM
ejpam-4734	29	10	)	)	PUNCT
ejpam-4734	29	11	(	(	PUNCT
ejpam-4734	29	12	2023	2023	NUM
ejpam-4734	29	13	)	)	PUNCT
ejpam-4734	29	14	,	,	PUNCT
ejpam-4734	29	15	2544	2544	NUM
ejpam-4734	29	16	-	-	SYM
ejpam-4734	29	17	2556	2556	NUM
ejpam-4734	29	18	2545	2545	NUM
ejpam-4734	29	19	the	the	DET
ejpam-4734	29	20	concepts	concept	NOUN
ejpam-4734	29	21	of	of	ADP
ejpam-4734	29	22	upper	upper	ADJ
ejpam-4734	29	23	and	and	CCONJ
ejpam-4734	29	24	lower	low	ADJ
ejpam-4734	29	25	⋆-continuous	⋆-continuous	ADJ
ejpam-4734	29	26	multifunctions	multifunction	NOUN
ejpam-4734	29	27	in	in	ADP
ejpam-4734	29	28	ideal	ideal	ADJ
ejpam-4734	29	29	topological	topological	ADJ
ejpam-4734	29	30	spaces	space	NOUN
ejpam-4734	29	31	.	.	PUNCT
ejpam-4734	30	1	moreover	moreover	ADV
ejpam-4734	30	2	,	,	PUNCT
ejpam-4734	30	3	several	several	ADJ
ejpam-4734	30	4	characterizations	characterization	NOUN
ejpam-4734	30	5	of	of	ADP
ejpam-4734	30	6	upper	upper	ADJ
ejpam-4734	30	7	and	and	CCONJ
ejpam-4734	30	8	lower	low	ADJ
ejpam-4734	30	9	⋆-continuous	⋆-continuous	ADJ
ejpam-4734	30	10	multifunctions	multifunction	NOUN
ejpam-4734	30	11	were	be	AUX
ejpam-4734	30	12	investigated	investigate	VERB
ejpam-4734	30	13	in	in	ADP
ejpam-4734	30	14	[	[	X
ejpam-4734	30	15	3	3	NUM
ejpam-4734	30	16	]	]	PUNCT
ejpam-4734	30	17	.	.	PUNCT
ejpam-4734	31	1	the	the	DET
ejpam-4734	31	2	purpose	purpose	NOUN
ejpam-4734	31	3	of	of	ADP
ejpam-4734	31	4	the	the	DET
ejpam-4734	31	5	present	present	ADJ
ejpam-4734	31	6	paper	paper	NOUN
ejpam-4734	31	7	is	be	AUX
ejpam-4734	31	8	to	to	PART
ejpam-4734	31	9	introduce	introduce	VERB
ejpam-4734	31	10	the	the	DET
ejpam-4734	31	11	notions	notion	NOUN
ejpam-4734	31	12	of	of	ADP
ejpam-4734	31	13	upper	upper	ADJ
ejpam-4734	31	14	and	and	CCONJ
ejpam-4734	31	15	lower	low	ADJ
ejpam-4734	31	16	weakly	weakly	ADJ
ejpam-4734	31	17	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	31	18	multifunctions	multifunction	NOUN
ejpam-4734	31	19	.	.	PUNCT
ejpam-4734	32	1	furthermore	furthermore	ADV
ejpam-4734	32	2	,	,	PUNCT
ejpam-4734	32	3	some	some	DET
ejpam-4734	32	4	characterizations	characterization	NOUN
ejpam-4734	32	5	of	of	ADP
ejpam-4734	32	6	upper	upper	ADJ
ejpam-4734	32	7	and	and	CCONJ
ejpam-4734	32	8	lower	low	ADJ
ejpam-4734	32	9	weakly	weakly	ADJ
ejpam-4734	32	10	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	32	11	multifunctions	multifunction	NOUN
ejpam-4734	32	12	are	be	AUX
ejpam-4734	32	13	discussed	discuss	VERB
ejpam-4734	32	14	.	.	PUNCT
ejpam-4734	33	1	2	2	X
ejpam-4734	33	2	.	.	X
ejpam-4734	33	3	preliminaries	preliminary	NOUN
ejpam-4734	33	4	throughout	throughout	ADP
ejpam-4734	33	5	the	the	DET
ejpam-4734	33	6	present	present	ADJ
ejpam-4734	33	7	paper	paper	NOUN
ejpam-4734	33	8	,	,	PUNCT
ejpam-4734	33	9	spaces	space	NOUN
ejpam-4734	33	10	(	(	PUNCT
ejpam-4734	33	11	x	x	X
ejpam-4734	33	12	,	,	PUNCT
ejpam-4734	33	13	τ	τ	X
ejpam-4734	33	14	)	)	PUNCT
ejpam-4734	33	15	and	and	CCONJ
ejpam-4734	33	16	(	(	PUNCT
ejpam-4734	33	17	y	y	PROPN
ejpam-4734	33	18	,	,	PUNCT
ejpam-4734	33	19	σ	σ	PROPN
ejpam-4734	33	20	)	)	PUNCT
ejpam-4734	33	21	(	(	PUNCT
ejpam-4734	33	22	or	or	CCONJ
ejpam-4734	33	23	simply	simply	ADV
ejpam-4734	33	24	x	x	X
ejpam-4734	33	25	and	and	CCONJ
ejpam-4734	33	26	y	y	PROPN
ejpam-4734	33	27	)	)	PUNCT
ejpam-4734	33	28	always	always	ADV
ejpam-4734	33	29	mean	mean	VERB
ejpam-4734	33	30	topological	topological	ADJ
ejpam-4734	33	31	spaces	space	NOUN
ejpam-4734	33	32	on	on	ADP
ejpam-4734	33	33	which	which	PRON
ejpam-4734	33	34	no	no	DET
ejpam-4734	33	35	separation	separation	NOUN
ejpam-4734	33	36	axioms	axiom	NOUN
ejpam-4734	33	37	are	be	AUX
ejpam-4734	33	38	assumed	assume	VERB
ejpam-4734	33	39	unless	unless	SCONJ
ejpam-4734	33	40	explicitly	explicitly	ADV
ejpam-4734	33	41	stated	state	VERB
ejpam-4734	33	42	.	.	PUNCT
ejpam-4734	34	1	let	let	VERB
ejpam-4734	34	2	a	a	DET
ejpam-4734	34	3	be	be	AUX
ejpam-4734	34	4	a	a	DET
ejpam-4734	34	5	subset	subset	NOUN
ejpam-4734	34	6	of	of	ADP
ejpam-4734	34	7	a	a	DET
ejpam-4734	34	8	topological	topological	ADJ
ejpam-4734	34	9	space	space	NOUN
ejpam-4734	34	10	(	(	PUNCT
ejpam-4734	34	11	x	x	X
ejpam-4734	34	12	,	,	PUNCT
ejpam-4734	34	13	τ	τ	PROPN
ejpam-4734	34	14	)	)	PUNCT
ejpam-4734	34	15	.	.	PUNCT
ejpam-4734	35	1	the	the	DET
ejpam-4734	35	2	closure	closure	NOUN
ejpam-4734	35	3	of	of	ADP
ejpam-4734	35	4	a	a	PRON
ejpam-4734	35	5	and	and	CCONJ
ejpam-4734	35	6	the	the	DET
ejpam-4734	35	7	interior	interior	NOUN
ejpam-4734	35	8	of	of	ADP
ejpam-4734	35	9	a	a	PRON
ejpam-4734	35	10	are	be	AUX
ejpam-4734	35	11	denoted	denote	VERB
ejpam-4734	35	12	by	by	ADP
ejpam-4734	35	13	cl(a	cl(a	NOUN
ejpam-4734	35	14	)	)	PUNCT
ejpam-4734	35	15	and	and	CCONJ
ejpam-4734	35	16	int(a	int(a	PROPN
ejpam-4734	35	17	)	)	PUNCT
ejpam-4734	35	18	,	,	PUNCT
ejpam-4734	35	19	respectively	respectively	ADV
ejpam-4734	35	20	.	.	PUNCT
ejpam-4734	36	1	an	an	DET
ejpam-4734	36	2	ideal	ideal	NOUN
ejpam-4734	36	3	i	i	PRON
ejpam-4734	36	4	on	on	ADP
ejpam-4734	36	5	a	a	DET
ejpam-4734	36	6	topological	topological	ADJ
ejpam-4734	36	7	space	space	NOUN
ejpam-4734	36	8	(	(	PUNCT
ejpam-4734	36	9	x	x	X
ejpam-4734	36	10	,	,	PUNCT
ejpam-4734	36	11	τ	τ	X
ejpam-4734	36	12	)	)	PUNCT
ejpam-4734	36	13	is	be	AUX
ejpam-4734	36	14	a	a	DET
ejpam-4734	36	15	nonempty	nonempty	ADJ
ejpam-4734	36	16	collection	collection	NOUN
ejpam-4734	36	17	of	of	ADP
ejpam-4734	36	18	subsets	subset	NOUN
ejpam-4734	36	19	of	of	ADP
ejpam-4734	36	20	x	x	PUNCT
ejpam-4734	36	21	satisfying	satisfy	VERB
ejpam-4734	36	22	the	the	DET
ejpam-4734	36	23	following	follow	VERB
ejpam-4734	36	24	properties	property	NOUN
ejpam-4734	36	25	:	:	PUNCT
ejpam-4734	36	26	(	(	PUNCT
ejpam-4734	36	27	1	1	X
ejpam-4734	36	28	)	)	PUNCT
ejpam-4734	36	29	a	a	DET
ejpam-4734	36	30	∈	∈	NOUN
ejpam-4734	36	31	i	i	PRON
ejpam-4734	36	32	and	and	CCONJ
ejpam-4734	36	33	b	b	X
ejpam-4734	36	34	⊆	⊆	NUM
ejpam-4734	36	35	a	a	DET
ejpam-4734	36	36	imply	imply	NOUN
ejpam-4734	36	37	b	b	X
ejpam-4734	36	38	∈	∈	PROPN
ejpam-4734	36	39	i	i	PRON
ejpam-4734	36	40	;	;	PUNCT
ejpam-4734	36	41	(	(	PUNCT
ejpam-4734	36	42	2	2	X
ejpam-4734	36	43	)	)	PUNCT
ejpam-4734	37	1	a	a	PRON
ejpam-4734	37	2	∈	∈	NOUN
ejpam-4734	38	1	i	i	PRON
ejpam-4734	38	2	and	and	CCONJ
ejpam-4734	38	3	b	b	X
ejpam-4734	38	4	∈	∈	NOUN
ejpam-4734	39	1	i	i	PRON
ejpam-4734	39	2	imply	imply	VERB
ejpam-4734	39	3	a∪b	a∪b	ADJ
ejpam-4734	40	1	∈	∈	INTJ
ejpam-4734	41	1	i	i	PRON
ejpam-4734	41	2	.	.	PUNCT
ejpam-4734	42	1	a	a	DET
ejpam-4734	42	2	topological	topological	ADJ
ejpam-4734	42	3	space	space	NOUN
ejpam-4734	42	4	(	(	PUNCT
ejpam-4734	42	5	x	x	X
ejpam-4734	42	6	,	,	PUNCT
ejpam-4734	42	7	τ	τ	X
ejpam-4734	42	8	)	)	PUNCT
ejpam-4734	42	9	with	with	ADP
ejpam-4734	42	10	an	an	DET
ejpam-4734	42	11	ideal	ideal	ADJ
ejpam-4734	42	12	i	i	PRON
ejpam-4734	42	13	on	on	ADP
ejpam-4734	42	14	x	x	SYM
ejpam-4734	42	15	is	be	AUX
ejpam-4734	42	16	called	call	VERB
ejpam-4734	42	17	an	an	DET
ejpam-4734	42	18	ideal	ideal	ADJ
ejpam-4734	42	19	topological	topological	ADJ
ejpam-4734	42	20	space	space	NOUN
ejpam-4734	42	21	and	and	CCONJ
ejpam-4734	42	22	is	be	AUX
ejpam-4734	42	23	denoted	denote	VERB
ejpam-4734	42	24	by	by	ADP
ejpam-4734	42	25	(	(	PUNCT
ejpam-4734	42	26	x	x	X
ejpam-4734	42	27	,	,	PUNCT
ejpam-4734	42	28	τ	τ	PROPN
ejpam-4734	42	29	,	,	PUNCT
ejpam-4734	42	30	i	i	NOUN
ejpam-4734	42	31	)	)	PUNCT
ejpam-4734	42	32	.	.	PUNCT
ejpam-4734	43	1	for	for	ADP
ejpam-4734	43	2	an	an	DET
ejpam-4734	43	3	ideal	ideal	ADJ
ejpam-4734	43	4	topological	topological	ADJ
ejpam-4734	43	5	space	space	NOUN
ejpam-4734	43	6	(	(	PUNCT
ejpam-4734	43	7	x	x	X
ejpam-4734	43	8	,	,	PUNCT
ejpam-4734	43	9	τ	τ	PROPN
ejpam-4734	43	10	,	,	PUNCT
ejpam-4734	43	11	i	i	PROPN
ejpam-4734	43	12	)	)	PUNCT
ejpam-4734	43	13	and	and	CCONJ
ejpam-4734	43	14	a	a	DET
ejpam-4734	43	15	subset	subset	NOUN
ejpam-4734	43	16	a	a	PRON
ejpam-4734	43	17	of	of	ADP
ejpam-4734	43	18	x	x	PRON
ejpam-4734	43	19	,	,	PUNCT
ejpam-4734	43	20	a⋆(i	a⋆(i	PROPN
ejpam-4734	43	21	)	)	PUNCT
ejpam-4734	43	22	is	be	AUX
ejpam-4734	43	23	defined	define	VERB
ejpam-4734	43	24	as	as	SCONJ
ejpam-4734	43	25	follows	follow	VERB
ejpam-4734	43	26	:	:	PUNCT
ejpam-4734	43	27	a⋆(i	a⋆(i	NOUN
ejpam-4734	43	28	)	)	PUNCT
ejpam-4734	44	1	=	=	PUNCT
ejpam-4734	44	2	{	{	PUNCT
ejpam-4734	44	3	x	x	PUNCT
ejpam-4734	44	4	∈	∈	PROPN
ejpam-4734	44	5	x	x	X
ejpam-4734	44	6	:	:	PUNCT
ejpam-4734	44	7	u	u	X
ejpam-4734	44	8	∩a	∩a	PROPN
ejpam-4734	44	9	̸∈	̸∈	PROPN
ejpam-4734	44	10	i	i	PRON
ejpam-4734	44	11	for	for	ADP
ejpam-4734	44	12	every	every	DET
ejpam-4734	44	13	open	open	ADJ
ejpam-4734	44	14	neighbourhood	neighbourhood	NOUN
ejpam-4734	44	15	u	u	NOUN
ejpam-4734	44	16	of	of	ADP
ejpam-4734	44	17	x	x	NOUN
ejpam-4734	44	18	}	}	PUNCT
ejpam-4734	44	19	.	.	PUNCT
ejpam-4734	45	1	in	in	ADP
ejpam-4734	45	2	case	case	NOUN
ejpam-4734	45	3	there	there	PRON
ejpam-4734	45	4	is	be	VERB
ejpam-4734	45	5	no	no	DET
ejpam-4734	45	6	chance	chance	NOUN
ejpam-4734	45	7	for	for	ADP
ejpam-4734	45	8	confusion	confusion	NOUN
ejpam-4734	45	9	,	,	PUNCT
ejpam-4734	45	10	a⋆(i	a⋆(i	NOUN
ejpam-4734	45	11	)	)	PUNCT
ejpam-4734	45	12	is	be	AUX
ejpam-4734	45	13	simply	simply	ADV
ejpam-4734	45	14	written	write	VERB
ejpam-4734	45	15	as	as	ADP
ejpam-4734	45	16	a⋆.	a⋆.	NOUN
ejpam-4734	45	17	in	in	ADP
ejpam-4734	45	18	[	[	X
ejpam-4734	45	19	11	11	NUM
ejpam-4734	45	20	]	]	PUNCT
ejpam-4734	45	21	,	,	PUNCT
ejpam-4734	45	22	a⋆	a⋆	ADV
ejpam-4734	45	23	is	be	AUX
ejpam-4734	45	24	called	call	VERB
ejpam-4734	45	25	the	the	DET
ejpam-4734	45	26	local	local	ADJ
ejpam-4734	45	27	function	function	NOUN
ejpam-4734	45	28	of	of	ADP
ejpam-4734	45	29	a	a	PRON
ejpam-4734	45	30	with	with	ADP
ejpam-4734	45	31	respect	respect	NOUN
ejpam-4734	45	32	to	to	ADP
ejpam-4734	45	33	i	i	PRON
ejpam-4734	45	34	and	and	CCONJ
ejpam-4734	45	35	τ	τ	PROPN
ejpam-4734	45	36	and	and	CCONJ
ejpam-4734	45	37	cl⋆(a	cl⋆(a	NUM
ejpam-4734	45	38	)	)	PUNCT
ejpam-4734	45	39	=	=	PUNCT
ejpam-4734	45	40	a⋆	a⋆	ADP
ejpam-4734	45	41	∪	∪	ADP
ejpam-4734	45	42	a	a	DET
ejpam-4734	45	43	defines	define	NOUN
ejpam-4734	45	44	a	a	DET
ejpam-4734	45	45	kuratowski	kuratowski	ADJ
ejpam-4734	45	46	closure	closure	NOUN
ejpam-4734	45	47	operator	operator	NOUN
ejpam-4734	45	48	for	for	ADP
ejpam-4734	45	49	a	a	DET
ejpam-4734	45	50	topology	topology	NOUN
ejpam-4734	45	51	τ⋆(i	τ⋆(i	NOUN
ejpam-4734	45	52	)	)	PUNCT
ejpam-4734	45	53	finer	fine	ADJ
ejpam-4734	45	54	than	than	ADP
ejpam-4734	45	55	τ	τ	PROPN
ejpam-4734	45	56	.	.	PUNCT
ejpam-4734	46	1	a	a	DET
ejpam-4734	46	2	subset	subset	NOUN
ejpam-4734	46	3	a	a	PRON
ejpam-4734	46	4	is	be	AUX
ejpam-4734	46	5	said	say	VERB
ejpam-4734	46	6	to	to	PART
ejpam-4734	46	7	be	be	AUX
ejpam-4734	46	8	⋆-closed	⋆-close	VERB
ejpam-4734	46	9	[	[	X
ejpam-4734	46	10	10	10	NUM
ejpam-4734	46	11	]	]	X
ejpam-4734	46	12	if	if	SCONJ
ejpam-4734	46	13	a⋆	a⋆	ADJ
ejpam-4734	46	14	⊆	⊆	NUM
ejpam-4734	46	15	a.	a.	NOUN
ejpam-4734	46	16	the	the	DET
ejpam-4734	46	17	interior	interior	NOUN
ejpam-4734	46	18	of	of	ADP
ejpam-4734	46	19	a	a	DET
ejpam-4734	46	20	subset	subset	NOUN
ejpam-4734	46	21	a	a	DET
ejpam-4734	46	22	in	in	ADP
ejpam-4734	46	23	(	(	PUNCT
ejpam-4734	46	24	x	x	X
ejpam-4734	46	25	,	,	PUNCT
ejpam-4734	46	26	τ⋆(i	τ⋆(i	NOUN
ejpam-4734	46	27	)	)	PUNCT
ejpam-4734	46	28	)	)	PUNCT
ejpam-4734	46	29	is	be	AUX
ejpam-4734	46	30	denoted	denote	VERB
ejpam-4734	46	31	by	by	ADP
ejpam-4734	46	32	int⋆(a	int⋆(a	NOUN
ejpam-4734	46	33	)	)	PUNCT
ejpam-4734	46	34	.	.	PUNCT
ejpam-4734	47	1	lemma	lemma	PROPN
ejpam-4734	47	2	1	1	NUM
ejpam-4734	47	3	.	.	PUNCT
ejpam-4734	48	1	for	for	ADP
ejpam-4734	48	2	a	a	DET
ejpam-4734	48	3	subset	subset	NOUN
ejpam-4734	48	4	a	a	PRON
ejpam-4734	48	5	of	of	ADP
ejpam-4734	48	6	an	an	DET
ejpam-4734	48	7	ideal	ideal	ADJ
ejpam-4734	48	8	topological	topological	ADJ
ejpam-4734	48	9	space	space	NOUN
ejpam-4734	48	10	(	(	PUNCT
ejpam-4734	48	11	x	x	X
ejpam-4734	48	12	,	,	PUNCT
ejpam-4734	48	13	τ	τ	PROPN
ejpam-4734	48	14	,	,	PUNCT
ejpam-4734	48	15	i	i	NOUN
ejpam-4734	48	16	)	)	PUNCT
ejpam-4734	48	17	,	,	PUNCT
ejpam-4734	48	18	the	the	DET
ejpam-4734	48	19	following	follow	VERB
ejpam-4734	48	20	properties	property	NOUN
ejpam-4734	48	21	hold	hold	VERB
ejpam-4734	48	22	:	:	PUNCT
ejpam-4734	48	23	(	(	PUNCT
ejpam-4734	48	24	1	1	X
ejpam-4734	48	25	)	)	PUNCT
ejpam-4734	48	26	if	if	SCONJ
ejpam-4734	48	27	v	v	NOUN
ejpam-4734	48	28	∈	∈	PROPN
ejpam-4734	48	29	τ	τ	X
ejpam-4734	48	30	,	,	PUNCT
ejpam-4734	48	31	then	then	ADV
ejpam-4734	48	32	v	v	ADP
ejpam-4734	48	33	∩	∩	ADJ
ejpam-4734	48	34	cl⋆(a	cl⋆(a	NOUN
ejpam-4734	48	35	)	)	PUNCT
ejpam-4734	48	36	⊆	⊆	NUM
ejpam-4734	48	37	cl⋆(v	cl⋆(v	PROPN
ejpam-4734	48	38	∩a	∩a	PROPN
ejpam-4734	48	39	)	)	PUNCT
ejpam-4734	49	1	[	[	X
ejpam-4734	49	2	8	8	NUM
ejpam-4734	49	3	]	]	PUNCT
ejpam-4734	49	4	.	.	PUNCT
ejpam-4734	50	1	(	(	PUNCT
ejpam-4734	50	2	2	2	X
ejpam-4734	50	3	)	)	PUNCT
ejpam-4734	50	4	if	if	SCONJ
ejpam-4734	50	5	f	f	PROPN
ejpam-4734	50	6	is	be	AUX
ejpam-4734	50	7	closed	close	VERB
ejpam-4734	50	8	in	in	ADP
ejpam-4734	50	9	x	x	NOUN
ejpam-4734	50	10	,	,	PUNCT
ejpam-4734	50	11	then	then	ADV
ejpam-4734	50	12	int⋆(a	int⋆(a	PUNCT
ejpam-4734	50	13	∪	∪	PROPN
ejpam-4734	50	14	f	f	PROPN
ejpam-4734	50	15	)	)	PUNCT
ejpam-4734	50	16	⊆	⊆	NUM
ejpam-4734	50	17	int⋆(a	int⋆(a	NOUN
ejpam-4734	50	18	)	)	PUNCT
ejpam-4734	50	19	∪	∪	ADP
ejpam-4734	50	20	f	f	PROPN
ejpam-4734	50	21	.	.	PUNCT
ejpam-4734	51	1	a	a	DET
ejpam-4734	51	2	subset	subset	NOUN
ejpam-4734	51	3	a	a	PRON
ejpam-4734	51	4	of	of	ADP
ejpam-4734	51	5	an	an	DET
ejpam-4734	51	6	ideal	ideal	ADJ
ejpam-4734	51	7	topological	topological	ADJ
ejpam-4734	51	8	space	space	NOUN
ejpam-4734	51	9	(	(	PUNCT
ejpam-4734	51	10	x	x	X
ejpam-4734	51	11	,	,	PUNCT
ejpam-4734	51	12	τ	τ	PROPN
ejpam-4734	51	13	,	,	PUNCT
ejpam-4734	51	14	i	i	PROPN
ejpam-4734	51	15	)	)	PUNCT
ejpam-4734	51	16	is	be	AUX
ejpam-4734	51	17	called	call	VERB
ejpam-4734	51	18	semi	semi	ADJ
ejpam-4734	51	19	-	-	ADJ
ejpam-4734	51	20	i	i	PRON
ejpam-4734	51	21	-open	-open	NOUN
ejpam-4734	51	22	[	[	X
ejpam-4734	51	23	7	7	NUM
ejpam-4734	51	24	]	]	X
ejpam-4734	51	25	(	(	PUNCT
ejpam-4734	51	26	resp	resp	NOUN
ejpam-4734	51	27	.	.	PUNCT
ejpam-4734	52	1	pre⋆i	pre⋆i	NOUN
ejpam-4734	52	2	-open	-open	NOUN
ejpam-4734	53	1	[	[	X
ejpam-4734	53	2	5	5	NUM
ejpam-4734	53	3	]	]	PUNCT
ejpam-4734	53	4	,	,	PUNCT
ejpam-4734	53	5	strong	strong	ADJ
ejpam-4734	53	6	β	β	X
ejpam-4734	53	7	-	-	VERB
ejpam-4734	53	8	i	i	PRON
ejpam-4734	53	9	-open	-open	NOUN
ejpam-4734	54	1	[	[	X
ejpam-4734	54	2	7	7	NUM
ejpam-4734	54	3	]	]	PUNCT
ejpam-4734	54	4	)	)	PUNCT
ejpam-4734	54	5	if	if	SCONJ
ejpam-4734	54	6	a	a	DET
ejpam-4734	54	7	⊆	⊆	NUM
ejpam-4734	54	8	cl⋆(int(a	cl⋆(int(a	PROPN
ejpam-4734	54	9	)	)	PUNCT
ejpam-4734	54	10	)	)	PUNCT
ejpam-4734	55	1	(	(	PUNCT
ejpam-4734	55	2	resp	resp	NOUN
ejpam-4734	55	3	.	.	PUNCT
ejpam-4734	56	1	a	a	DET
ejpam-4734	56	2	⊆	⊆	NUM
ejpam-4734	56	3	int⋆(cl(a	int⋆(cl(a	NOUN
ejpam-4734	56	4	)	)	PUNCT
ejpam-4734	56	5	)	)	PUNCT
ejpam-4734	56	6	,	,	PUNCT
ejpam-4734	56	7	a	a	DET
ejpam-4734	56	8	⊆	⊆	NUM
ejpam-4734	56	9	cl⋆(int(cl⋆(a	cl⋆(int(cl⋆(a	NOUN
ejpam-4734	56	10	)	)	PUNCT
ejpam-4734	56	11	)	)	PUNCT
ejpam-4734	56	12	)	)	PUNCT
ejpam-4734	56	13	)	)	PUNCT
ejpam-4734	56	14	.	.	PUNCT
ejpam-4734	57	1	the	the	DET
ejpam-4734	57	2	complement	complement	NOUN
ejpam-4734	57	3	of	of	ADP
ejpam-4734	57	4	a	a	DET
ejpam-4734	57	5	semi	semi	ADJ
ejpam-4734	57	6	-	-	ADJ
ejpam-4734	57	7	i	i	PRON
ejpam-4734	57	8	-open	-open	ADJ
ejpam-4734	57	9	(	(	PUNCT
ejpam-4734	57	10	resp	resp	NOUN
ejpam-4734	57	11	.	.	PUNCT
ejpam-4734	58	1	pre⋆i	pre⋆i	PROPN
ejpam-4734	58	2	-open	-open	PROPN
ejpam-4734	58	3	,	,	PUNCT
ejpam-4734	58	4	strong	strong	ADJ
ejpam-4734	58	5	β	β	X
ejpam-4734	58	6	-	-	PUNCT
ejpam-4734	58	7	i	i	PRON
ejpam-4734	58	8	open	open	ADJ
ejpam-4734	58	9	)	)	PUNCT
ejpam-4734	58	10	set	set	NOUN
ejpam-4734	58	11	is	be	AUX
ejpam-4734	58	12	called	call	VERB
ejpam-4734	58	13	semi	semi	ADJ
ejpam-4734	58	14	-	-	ADJ
ejpam-4734	58	15	i	i	PRON
ejpam-4734	58	16	-closed	-close	VERB
ejpam-4734	59	1	[	[	X
ejpam-4734	59	2	7	7	NUM
ejpam-4734	59	3	]	]	X
ejpam-4734	59	4	(	(	PUNCT
ejpam-4734	59	5	resp	resp	NOUN
ejpam-4734	59	6	.	.	PUNCT
ejpam-4734	60	1	pre⋆i	pre⋆i	PROPN
ejpam-4734	60	2	-closed	-close	VERB
ejpam-4734	61	1	[	[	X
ejpam-4734	61	2	5	5	NUM
ejpam-4734	61	3	]	]	PUNCT
ejpam-4734	61	4	,	,	PUNCT
ejpam-4734	61	5	strong	strong	ADJ
ejpam-4734	61	6	β	β	X
ejpam-4734	61	7	-	-	PUNCT
ejpam-4734	61	8	i	i	PRON
ejpam-4734	61	9	-closed	-close	VERB
ejpam-4734	61	10	[	[	X
ejpam-4734	61	11	7	7	NUM
ejpam-4734	61	12	]	]	NUM
ejpam-4734	61	13	)	)	PUNCT
ejpam-4734	61	14	.	.	PUNCT
ejpam-4734	62	1	lemma	lemma	PROPN
ejpam-4734	62	2	2	2	NUM
ejpam-4734	62	3	.	.	X
ejpam-4734	63	1	for	for	ADP
ejpam-4734	63	2	a	a	DET
ejpam-4734	63	3	subset	subset	NOUN
ejpam-4734	63	4	a	a	PRON
ejpam-4734	63	5	of	of	ADP
ejpam-4734	63	6	an	an	DET
ejpam-4734	63	7	ideal	ideal	ADJ
ejpam-4734	63	8	topological	topological	ADJ
ejpam-4734	63	9	space	space	NOUN
ejpam-4734	63	10	(	(	PUNCT
ejpam-4734	63	11	x	x	X
ejpam-4734	63	12	,	,	PUNCT
ejpam-4734	63	13	τ	τ	PROPN
ejpam-4734	63	14	,	,	PUNCT
ejpam-4734	63	15	i	i	NOUN
ejpam-4734	63	16	)	)	PUNCT
ejpam-4734	63	17	,	,	PUNCT
ejpam-4734	63	18	the	the	DET
ejpam-4734	63	19	following	follow	VERB
ejpam-4734	63	20	properties	property	NOUN
ejpam-4734	63	21	hold	hold	VERB
ejpam-4734	63	22	:	:	PUNCT
ejpam-4734	63	23	(	(	PUNCT
ejpam-4734	63	24	1	1	X
ejpam-4734	63	25	)	)	PUNCT
ejpam-4734	63	26	scli	scli	NOUN
ejpam-4734	63	27	(	(	PUNCT
ejpam-4734	63	28	a	a	X
ejpam-4734	63	29	)	)	PUNCT
ejpam-4734	63	30	=	=	NOUN
ejpam-4734	63	31	a	a	DET
ejpam-4734	63	32	∪	∪	ADJ
ejpam-4734	63	33	int⋆(cl(a	int⋆(cl(a	NOUN
ejpam-4734	63	34	)	)	PUNCT
ejpam-4734	63	35	)	)	PUNCT
ejpam-4734	64	1	[	[	X
ejpam-4734	64	2	6	6	NUM
ejpam-4734	64	3	]	]	PUNCT
ejpam-4734	64	4	.	.	PUNCT
ejpam-4734	65	1	(	(	PUNCT
ejpam-4734	65	2	2	2	X
ejpam-4734	65	3	)	)	PUNCT
ejpam-4734	65	4	sβcli	sβcli	NOUN
ejpam-4734	65	5	(	(	PUNCT
ejpam-4734	65	6	a	a	NOUN
ejpam-4734	65	7	)	)	PUNCT
ejpam-4734	65	8	=	=	NOUN
ejpam-4734	65	9	a	a	DET
ejpam-4734	65	10	∪	∪	ADJ
ejpam-4734	65	11	int⋆(cl(int⋆(a	int⋆(cl(int⋆(a	NOUN
ejpam-4734	65	12	)	)	PUNCT
ejpam-4734	65	13	)	)	PUNCT
ejpam-4734	65	14	)	)	PUNCT
ejpam-4734	66	1	[	[	X
ejpam-4734	66	2	6	6	NUM
ejpam-4734	66	3	]	]	PUNCT
ejpam-4734	66	4	.	.	PUNCT
ejpam-4734	67	1	(	(	PUNCT
ejpam-4734	67	2	3	3	X
ejpam-4734	67	3	)	)	PUNCT
ejpam-4734	67	4	sβinti	sβinti	NOUN
ejpam-4734	67	5	(	(	PUNCT
ejpam-4734	67	6	a	a	X
ejpam-4734	67	7	)	)	PUNCT
ejpam-4734	67	8	=	=	SYM
ejpam-4734	67	9	a	a	DET
ejpam-4734	67	10	∩	∩	ADJ
ejpam-4734	67	11	cl⋆(int(cl⋆(a	cl⋆(int(cl⋆(a	NOUN
ejpam-4734	67	12	)	)	PUNCT
ejpam-4734	67	13	)	)	PUNCT
ejpam-4734	67	14	)	)	PUNCT
ejpam-4734	67	15	.	.	PUNCT
ejpam-4734	68	1	lemma	lemma	PROPN
ejpam-4734	68	2	3	3	X
ejpam-4734	68	3	.	.	PUNCT
ejpam-4734	69	1	[	[	X
ejpam-4734	69	2	4	4	X
ejpam-4734	69	3	]	]	X
ejpam-4734	69	4	let	let	VERB
ejpam-4734	69	5	(	(	PUNCT
ejpam-4734	69	6	x	x	NOUN
ejpam-4734	69	7	,	,	PUNCT
ejpam-4734	69	8	τ	τ	PROPN
ejpam-4734	69	9	,	,	PUNCT
ejpam-4734	69	10	i	i	PRON
ejpam-4734	69	11	)	)	PUNCT
ejpam-4734	69	12	be	be	AUX
ejpam-4734	69	13	an	an	DET
ejpam-4734	69	14	ideal	ideal	ADJ
ejpam-4734	69	15	topological	topological	ADJ
ejpam-4734	69	16	space	space	NOUN
ejpam-4734	69	17	.	.	PUNCT
ejpam-4734	70	1	if	if	SCONJ
ejpam-4734	70	2	v	v	NOUN
ejpam-4734	70	3	is	be	AUX
ejpam-4734	70	4	⋆-open	⋆-open	ADJ
ejpam-4734	70	5	,	,	PUNCT
ejpam-4734	70	6	then	then	ADV
ejpam-4734	70	7	scli	scli	PROPN
ejpam-4734	70	8	(	(	PUNCT
ejpam-4734	70	9	v	v	NOUN
ejpam-4734	70	10	)	)	PUNCT
ejpam-4734	70	11	=	=	SYM
ejpam-4734	70	12	int⋆(cl(v	int⋆(cl(v	PROPN
ejpam-4734	70	13	)	)	PUNCT
ejpam-4734	70	14	)	)	PUNCT
ejpam-4734	70	15	.	.	PUNCT
ejpam-4734	71	1	c.	c.	PROPN
ejpam-4734	71	2	boonpok	boonpok	PROPN
ejpam-4734	71	3	,	,	PUNCT
ejpam-4734	71	4	j.	j.	PROPN
ejpam-4734	71	5	khampakdee	khampakdee	PROPN
ejpam-4734	71	6	/	/	PUNCT
ejpam-4734	71	7	eur	eur	PROPN
ejpam-4734	71	8	.	.	PUNCT
ejpam-4734	72	1	j.	j.	PROPN
ejpam-4734	72	2	pure	pure	PROPN
ejpam-4734	72	3	appl	appl	PROPN
ejpam-4734	72	4	.	.	PROPN
ejpam-4734	72	5	math	math	PROPN
ejpam-4734	72	6	,	,	PUNCT
ejpam-4734	72	7	16	16	NUM
ejpam-4734	72	8	(	(	PUNCT
ejpam-4734	72	9	4	4	NUM
ejpam-4734	72	10	)	)	PUNCT
ejpam-4734	72	11	(	(	PUNCT
ejpam-4734	72	12	2023	2023	NUM
ejpam-4734	72	13	)	)	PUNCT
ejpam-4734	72	14	,	,	PUNCT
ejpam-4734	72	15	2544	2544	NUM
ejpam-4734	72	16	-	-	SYM
ejpam-4734	72	17	2556	2556	NUM
ejpam-4734	72	18	2546	2546	NUM
ejpam-4734	72	19	lemma	lemma	PROPN
ejpam-4734	72	20	4	4	NUM
ejpam-4734	72	21	.	.	PUNCT
ejpam-4734	73	1	[	[	X
ejpam-4734	73	2	4	4	X
ejpam-4734	73	3	]	]	PUNCT
ejpam-4734	73	4	for	for	ADP
ejpam-4734	73	5	a	a	DET
ejpam-4734	73	6	subset	subset	NOUN
ejpam-4734	73	7	a	a	PRON
ejpam-4734	73	8	of	of	ADP
ejpam-4734	73	9	an	an	DET
ejpam-4734	73	10	ideal	ideal	ADJ
ejpam-4734	73	11	topological	topological	ADJ
ejpam-4734	73	12	space	space	NOUN
ejpam-4734	73	13	(	(	PUNCT
ejpam-4734	73	14	x	x	X
ejpam-4734	73	15	,	,	PUNCT
ejpam-4734	73	16	τ	τ	PROPN
ejpam-4734	73	17	,	,	PUNCT
ejpam-4734	73	18	i	i	NOUN
ejpam-4734	73	19	)	)	PUNCT
ejpam-4734	73	20	,	,	PUNCT
ejpam-4734	73	21	x	x	PUNCT
ejpam-4734	73	22	∈	∈	NOUN
ejpam-4734	73	23	sβcli	sβcli	NOUN
ejpam-4734	73	24	(	(	PUNCT
ejpam-4734	73	25	a	a	X
ejpam-4734	73	26	)	)	PUNCT
ejpam-4734	73	27	if	if	SCONJ
ejpam-4734	74	1	and	and	CCONJ
ejpam-4734	74	2	only	only	ADV
ejpam-4734	74	3	if	if	SCONJ
ejpam-4734	74	4	u	u	PROPN
ejpam-4734	74	5	∩a	∩a	PROPN
ejpam-4734	74	6	̸=	̸=	PROPN
ejpam-4734	74	7	∅	∅	NOUN
ejpam-4734	74	8	for	for	ADP
ejpam-4734	74	9	every	every	DET
ejpam-4734	74	10	strong	strong	ADJ
ejpam-4734	74	11	β	β	X
ejpam-4734	74	12	-	-	ADJ
ejpam-4734	74	13	i	i	PRON
ejpam-4734	74	14	-open	-open	VERB
ejpam-4734	74	15	set	set	VERB
ejpam-4734	74	16	u	u	NOUN
ejpam-4734	74	17	containing	contain	VERB
ejpam-4734	74	18	x.	x.	NOUN
ejpam-4734	74	19	lemma	lemma	PROPN
ejpam-4734	74	20	5	5	NUM
ejpam-4734	74	21	.	.	PUNCT
ejpam-4734	75	1	[	[	X
ejpam-4734	75	2	4	4	X
ejpam-4734	75	3	]	]	PUNCT
ejpam-4734	75	4	for	for	ADP
ejpam-4734	75	5	a	a	DET
ejpam-4734	75	6	subset	subset	NOUN
ejpam-4734	75	7	a	a	PRON
ejpam-4734	75	8	of	of	ADP
ejpam-4734	75	9	an	an	DET
ejpam-4734	75	10	ideal	ideal	ADJ
ejpam-4734	75	11	topological	topological	ADJ
ejpam-4734	75	12	space	space	NOUN
ejpam-4734	75	13	(	(	PUNCT
ejpam-4734	75	14	x	x	X
ejpam-4734	75	15	,	,	PUNCT
ejpam-4734	75	16	τ	τ	PROPN
ejpam-4734	75	17	,	,	PUNCT
ejpam-4734	75	18	i	i	NOUN
ejpam-4734	75	19	)	)	PUNCT
ejpam-4734	75	20	,	,	PUNCT
ejpam-4734	75	21	the	the	DET
ejpam-4734	75	22	following	follow	VERB
ejpam-4734	75	23	properties	property	NOUN
ejpam-4734	75	24	are	be	AUX
ejpam-4734	75	25	hold	hold	ADJ
ejpam-4734	75	26	:	:	PUNCT
ejpam-4734	75	27	(	(	PUNCT
ejpam-4734	75	28	1	1	X
ejpam-4734	75	29	)	)	PUNCT
ejpam-4734	75	30	x	x	SYM
ejpam-4734	76	1	−	−	NOUN
ejpam-4734	76	2	sβcli	sβcli	NOUN
ejpam-4734	76	3	(	(	PUNCT
ejpam-4734	76	4	a	a	X
ejpam-4734	76	5	)	)	PUNCT
ejpam-4734	76	6	=	=	NOUN
ejpam-4734	76	7	sβinti	sβinti	X
ejpam-4734	76	8	(	(	PUNCT
ejpam-4734	76	9	x	x	NOUN
ejpam-4734	76	10	−a	−a	NOUN
ejpam-4734	76	11	)	)	PUNCT
ejpam-4734	76	12	.	.	PUNCT
ejpam-4734	77	1	(	(	PUNCT
ejpam-4734	77	2	2	2	X
ejpam-4734	77	3	)	)	PUNCT
ejpam-4734	77	4	x	x	SYM
ejpam-4734	77	5	−	−	PROPN
ejpam-4734	77	6	sβinti	sβinti	NOUN
ejpam-4734	77	7	(	(	PUNCT
ejpam-4734	77	8	a	a	X
ejpam-4734	77	9	)	)	PUNCT
ejpam-4734	77	10	=	=	SYM
ejpam-4734	77	11	sβcli	sβcli	NOUN
ejpam-4734	77	12	(	(	PUNCT
ejpam-4734	77	13	x	x	NOUN
ejpam-4734	77	14	−a	−a	NOUN
ejpam-4734	77	15	)	)	PUNCT
ejpam-4734	77	16	.	.	PUNCT
ejpam-4734	78	1	by	by	ADP
ejpam-4734	78	2	a	a	DET
ejpam-4734	78	3	multifunction	multifunction	NOUN
ejpam-4734	78	4	f	f	NOUN
ejpam-4734	78	5	:	:	PUNCT
ejpam-4734	78	6	x	x	X
ejpam-4734	78	7	→	→	SYM
ejpam-4734	78	8	y	y	PROPN
ejpam-4734	78	9	,	,	PUNCT
ejpam-4734	78	10	we	we	PRON
ejpam-4734	78	11	mean	mean	VERB
ejpam-4734	78	12	a	a	DET
ejpam-4734	78	13	point	point	NOUN
ejpam-4734	78	14	-	-	PUNCT
ejpam-4734	78	15	to	to	ADP
ejpam-4734	78	16	-	-	PUNCT
ejpam-4734	78	17	set	set	VERB
ejpam-4734	78	18	correspondence	correspondence	NOUN
ejpam-4734	78	19	from	from	ADP
ejpam-4734	78	20	x	x	PUNCT
ejpam-4734	78	21	into	into	ADP
ejpam-4734	78	22	y	y	PROPN
ejpam-4734	78	23	,	,	PUNCT
ejpam-4734	78	24	and	and	CCONJ
ejpam-4734	78	25	we	we	PRON
ejpam-4734	78	26	always	always	ADV
ejpam-4734	78	27	assume	assume	VERB
ejpam-4734	78	28	that	that	SCONJ
ejpam-4734	78	29	f	f	PROPN
ejpam-4734	78	30	(	(	PUNCT
ejpam-4734	78	31	x	x	X
ejpam-4734	78	32	)	)	PUNCT
ejpam-4734	78	33	̸=	̸=	NOUN
ejpam-4734	78	34	∅	∅	NOUN
ejpam-4734	78	35	for	for	ADP
ejpam-4734	78	36	all	all	PRON
ejpam-4734	78	37	x	x	SYM
ejpam-4734	78	38	∈	∈	ADJ
ejpam-4734	78	39	x.	x.	NOUN
ejpam-4734	78	40	for	for	ADP
ejpam-4734	78	41	a	a	DET
ejpam-4734	78	42	multifunction	multifunction	NOUN
ejpam-4734	78	43	f	f	NOUN
ejpam-4734	79	1	:	:	PUNCT
ejpam-4734	79	2	x	x	X
ejpam-4734	79	3	→	→	SYM
ejpam-4734	79	4	y	y	PROPN
ejpam-4734	79	5	,	,	PUNCT
ejpam-4734	79	6	following	follow	VERB
ejpam-4734	79	7	[	[	X
ejpam-4734	79	8	1	1	X
ejpam-4734	79	9	]	]	PUNCT
ejpam-4734	79	10	we	we	PRON
ejpam-4734	79	11	shall	shall	AUX
ejpam-4734	79	12	denote	denote	VERB
ejpam-4734	79	13	the	the	DET
ejpam-4734	79	14	upper	upper	ADJ
ejpam-4734	79	15	and	and	CCONJ
ejpam-4734	79	16	lower	low	ADJ
ejpam-4734	79	17	inverse	inverse	NOUN
ejpam-4734	79	18	of	of	ADP
ejpam-4734	79	19	a	a	DET
ejpam-4734	79	20	set	set	NOUN
ejpam-4734	79	21	b	b	PROPN
ejpam-4734	79	22	of	of	ADP
ejpam-4734	79	23	y	y	PROPN
ejpam-4734	79	24	by	by	ADP
ejpam-4734	79	25	f+(b	f+(b	NOUN
ejpam-4734	79	26	)	)	PUNCT
ejpam-4734	79	27	and	and	CCONJ
ejpam-4734	79	28	f−(b	f−(b	NOUN
ejpam-4734	79	29	)	)	PUNCT
ejpam-4734	79	30	,	,	PUNCT
ejpam-4734	79	31	respectively	respectively	ADV
ejpam-4734	79	32	,	,	PUNCT
ejpam-4734	79	33	that	that	ADV
ejpam-4734	79	34	is	is	ADV
ejpam-4734	79	35	,	,	PUNCT
ejpam-4734	79	36	f+(b	f+(b	NOUN
ejpam-4734	79	37	)	)	PUNCT
ejpam-4734	79	38	=	=	PRON
ejpam-4734	80	1	{	{	PUNCT
ejpam-4734	80	2	x	x	PUNCT
ejpam-4734	80	3	∈	∈	PROPN
ejpam-4734	80	4	x	x	INTJ
ejpam-4734	81	1	|	|	NOUN
ejpam-4734	81	2	f	f	X
ejpam-4734	81	3	(	(	PUNCT
ejpam-4734	81	4	x	x	NOUN
ejpam-4734	81	5	)	)	PUNCT
ejpam-4734	81	6	⊆	⊆	NUM
ejpam-4734	81	7	b	b	NOUN
ejpam-4734	81	8	}	}	PUNCT
ejpam-4734	81	9	and	and	CCONJ
ejpam-4734	81	10	f−(b	f−(b	PROPN
ejpam-4734	81	11	)	)	PUNCT
ejpam-4734	81	12	=	=	PRON
ejpam-4734	82	1	{	{	PUNCT
ejpam-4734	82	2	x	x	PUNCT
ejpam-4734	82	3	∈	∈	PROPN
ejpam-4734	82	4	x	x	INTJ
ejpam-4734	83	1	|	|	NOUN
ejpam-4734	83	2	f	f	X
ejpam-4734	83	3	(	(	PUNCT
ejpam-4734	83	4	x	x	NOUN
ejpam-4734	83	5	)	)	PUNCT
ejpam-4734	83	6	∩b	∩b	NOUN
ejpam-4734	83	7	̸=	̸=	PROPN
ejpam-4734	83	8	∅	∅	NOUN
ejpam-4734	83	9	}	}	PUNCT
ejpam-4734	83	10	.	.	PUNCT
ejpam-4734	84	1	in	in	ADP
ejpam-4734	84	2	particular	particular	ADJ
ejpam-4734	84	3	,	,	PUNCT
ejpam-4734	84	4	f−(y	f−(y	NOUN
ejpam-4734	84	5	)	)	PUNCT
ejpam-4734	84	6	=	=	SYM
ejpam-4734	85	1	{	{	PUNCT
ejpam-4734	85	2	x	x	PUNCT
ejpam-4734	85	3	∈	∈	PROPN
ejpam-4734	85	4	x	x	INTJ
ejpam-4734	86	1	|	|	ADV
ejpam-4734	86	2	y	y	PROPN
ejpam-4734	86	3	∈	∈	PROPN
ejpam-4734	86	4	f	f	X
ejpam-4734	86	5	(	(	PUNCT
ejpam-4734	86	6	x	x	NOUN
ejpam-4734	86	7	)	)	PUNCT
ejpam-4734	86	8	}	}	PUNCT
ejpam-4734	86	9	for	for	ADP
ejpam-4734	86	10	each	each	DET
ejpam-4734	86	11	point	point	NOUN
ejpam-4734	86	12	y	y	PROPN
ejpam-4734	86	13	∈	∈	PROPN
ejpam-4734	86	14	y	y	PROPN
ejpam-4734	86	15	.	.	PUNCT
ejpam-4734	87	1	for	for	ADP
ejpam-4734	87	2	each	each	PRON
ejpam-4734	87	3	a	a	DET
ejpam-4734	87	4	⊆	⊆	NUM
ejpam-4734	87	5	x	x	SYM
ejpam-4734	87	6	,	,	PUNCT
ejpam-4734	87	7	f	f	PROPN
ejpam-4734	87	8	(	(	PUNCT
ejpam-4734	87	9	a	a	NOUN
ejpam-4734	87	10	)	)	PUNCT
ejpam-4734	87	11	=	=	SYM
ejpam-4734	87	12	∪x∈af	∪x∈af	NOUN
ejpam-4734	87	13	(	(	PUNCT
ejpam-4734	87	14	x	x	NOUN
ejpam-4734	87	15	)	)	PUNCT
ejpam-4734	87	16	.	.	PUNCT
ejpam-4734	88	1	then	then	ADV
ejpam-4734	88	2	f	f	PROPN
ejpam-4734	88	3	is	be	AUX
ejpam-4734	88	4	said	say	VERB
ejpam-4734	88	5	to	to	PART
ejpam-4734	88	6	be	be	AUX
ejpam-4734	88	7	surjection	surjection	NOUN
ejpam-4734	88	8	if	if	SCONJ
ejpam-4734	88	9	f	f	PROPN
ejpam-4734	88	10	(	(	PUNCT
ejpam-4734	88	11	x	x	X
ejpam-4734	88	12	)	)	PUNCT
ejpam-4734	88	13	=	=	SYM
ejpam-4734	88	14	y	y	PROPN
ejpam-4734	88	15	,	,	PUNCT
ejpam-4734	88	16	or	or	CCONJ
ejpam-4734	88	17	equivalent	equivalent	ADJ
ejpam-4734	88	18	,	,	PUNCT
ejpam-4734	88	19	if	if	SCONJ
ejpam-4734	88	20	for	for	ADP
ejpam-4734	88	21	each	each	DET
ejpam-4734	88	22	y	y	PROPN
ejpam-4734	88	23	∈	∈	PROPN
ejpam-4734	88	24	y	y	NOUN
ejpam-4734	88	25	there	there	PRON
ejpam-4734	88	26	exists	exist	VERB
ejpam-4734	88	27	x	x	X
ejpam-4734	88	28	∈	∈	PROPN
ejpam-4734	88	29	x	x	X
ejpam-4734	88	30	such	such	ADJ
ejpam-4734	88	31	that	that	SCONJ
ejpam-4734	88	32	y	y	PROPN
ejpam-4734	88	33	∈	∈	PROPN
ejpam-4734	88	34	f	f	X
ejpam-4734	88	35	(	(	PUNCT
ejpam-4734	88	36	x	x	NOUN
ejpam-4734	88	37	)	)	PUNCT
ejpam-4734	88	38	and	and	CCONJ
ejpam-4734	88	39	f	f	PROPN
ejpam-4734	88	40	is	be	AUX
ejpam-4734	88	41	called	call	VERB
ejpam-4734	88	42	injection	injection	NOUN
ejpam-4734	88	43	if	if	SCONJ
ejpam-4734	88	44	x	x	PROPN
ejpam-4734	88	45	̸=	̸=	PROPN
ejpam-4734	88	46	y	y	PROPN
ejpam-4734	88	47	implies	imply	VERB
ejpam-4734	88	48	f	f	PROPN
ejpam-4734	88	49	(	(	PUNCT
ejpam-4734	88	50	x	x	NOUN
ejpam-4734	88	51	)	)	PUNCT
ejpam-4734	88	52	∩	∩	ADJ
ejpam-4734	88	53	f	f	PROPN
ejpam-4734	88	54	(	(	PUNCT
ejpam-4734	88	55	y	y	NOUN
ejpam-4734	88	56	)	)	PUNCT
ejpam-4734	88	57	=	=	NOUN
ejpam-4734	88	58	∅.	∅.	PRON
ejpam-4734	88	59	3	3	NUM
ejpam-4734	88	60	.	.	PUNCT
ejpam-4734	88	61	upper	upper	ADJ
ejpam-4734	88	62	and	and	CCONJ
ejpam-4734	88	63	lower	low	ADJ
ejpam-4734	88	64	weakly	weakly	ADJ
ejpam-4734	88	65	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	88	66	multifunctions	multifunction	NOUN
ejpam-4734	88	67	in	in	ADP
ejpam-4734	88	68	this	this	DET
ejpam-4734	88	69	section	section	NOUN
ejpam-4734	88	70	,	,	PUNCT
ejpam-4734	88	71	we	we	PRON
ejpam-4734	88	72	introduce	introduce	VERB
ejpam-4734	88	73	the	the	DET
ejpam-4734	88	74	notions	notion	NOUN
ejpam-4734	88	75	of	of	ADP
ejpam-4734	88	76	upper	upper	ADJ
ejpam-4734	88	77	and	and	CCONJ
ejpam-4734	88	78	lower	low	ADJ
ejpam-4734	88	79	weakly	weakly	ADJ
ejpam-4734	88	80	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	88	81	multifunctions	multifunction	NOUN
ejpam-4734	88	82	.	.	PUNCT
ejpam-4734	89	1	moreover	moreover	ADV
ejpam-4734	89	2	,	,	PUNCT
ejpam-4734	89	3	several	several	ADJ
ejpam-4734	89	4	characterizations	characterization	NOUN
ejpam-4734	89	5	of	of	ADP
ejpam-4734	89	6	upper	upper	ADJ
ejpam-4734	89	7	and	and	CCONJ
ejpam-4734	89	8	lower	low	ADJ
ejpam-4734	89	9	weakly	weakly	ADJ
ejpam-4734	89	10	sβ(⋆)continuous	sβ(⋆)continuous	ADJ
ejpam-4734	89	11	multifunctions	multifunction	NOUN
ejpam-4734	89	12	are	be	AUX
ejpam-4734	89	13	discussed	discuss	VERB
ejpam-4734	89	14	.	.	PUNCT
ejpam-4734	90	1	definition	definition	NOUN
ejpam-4734	90	2	1	1	NUM
ejpam-4734	90	3	.	.	PUNCT
ejpam-4734	91	1	a	a	DET
ejpam-4734	91	2	multifunction	multifunction	NOUN
ejpam-4734	91	3	f	f	NOUN
ejpam-4734	91	4	:	:	PUNCT
ejpam-4734	91	5	(	(	PUNCT
ejpam-4734	91	6	x	x	X
ejpam-4734	91	7	,	,	PUNCT
ejpam-4734	91	8	τ	τ	PROPN
ejpam-4734	91	9	,	,	PUNCT
ejpam-4734	91	10	i	i	NOUN
ejpam-4734	91	11	)	)	PUNCT
ejpam-4734	91	12	→	→	PUNCT
ejpam-4734	91	13	(	(	PUNCT
ejpam-4734	91	14	y	y	PROPN
ejpam-4734	91	15	,	,	PUNCT
ejpam-4734	91	16	σ	σ	PROPN
ejpam-4734	91	17	,	,	PUNCT
ejpam-4734	91	18	j	j	PROPN
ejpam-4734	91	19	)	)	PUNCT
ejpam-4734	91	20	is	be	AUX
ejpam-4734	91	21	said	say	VERB
ejpam-4734	91	22	to	to	PART
ejpam-4734	91	23	be	be	AUX
ejpam-4734	91	24	:	:	PUNCT
ejpam-4734	91	25	(	(	PUNCT
ejpam-4734	91	26	1	1	X
ejpam-4734	91	27	)	)	PUNCT
ejpam-4734	91	28	upper	upper	ADJ
ejpam-4734	91	29	weakly	weakly	ADJ
ejpam-4734	91	30	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	91	31	at	at	ADP
ejpam-4734	91	32	a	a	DET
ejpam-4734	91	33	point	point	NOUN
ejpam-4734	91	34	x	x	SYM
ejpam-4734	91	35	∈	∈	NOUN
ejpam-4734	91	36	x	x	INTJ
ejpam-4734	91	37	if	if	SCONJ
ejpam-4734	91	38	for	for	SCONJ
ejpam-4734	91	39	each	each	DET
ejpam-4734	91	40	⋆-open	⋆-open	ADV
ejpam-4734	91	41	set	set	VERB
ejpam-4734	91	42	v	v	NUM
ejpam-4734	91	43	of	of	ADP
ejpam-4734	91	44	y	y	PROPN
ejpam-4734	91	45	containing	contain	VERB
ejpam-4734	91	46	f	f	PROPN
ejpam-4734	91	47	(	(	PUNCT
ejpam-4734	91	48	x	x	NOUN
ejpam-4734	91	49	)	)	PUNCT
ejpam-4734	91	50	,	,	PUNCT
ejpam-4734	91	51	there	there	PRON
ejpam-4734	91	52	exists	exist	VERB
ejpam-4734	91	53	a	a	DET
ejpam-4734	91	54	strong	strong	ADJ
ejpam-4734	91	55	β	β	NOUN
ejpam-4734	91	56	-	-	ADJ
ejpam-4734	91	57	i	i	PRON
ejpam-4734	91	58	-open	-open	VERB
ejpam-4734	91	59	set	set	VERB
ejpam-4734	91	60	u	u	NOUN
ejpam-4734	91	61	of	of	ADP
ejpam-4734	91	62	x	x	PUNCT
ejpam-4734	91	63	containing	contain	VERB
ejpam-4734	91	64	x	x	PUNCT
ejpam-4734	91	65	such	such	ADJ
ejpam-4734	91	66	that	that	SCONJ
ejpam-4734	91	67	f	f	PROPN
ejpam-4734	91	68	(	(	PUNCT
ejpam-4734	91	69	u	u	NOUN
ejpam-4734	91	70	)	)	PUNCT
ejpam-4734	91	71	⊆	⊆	NUM
ejpam-4734	91	72	cl⋆(v	cl⋆(v	NOUN
ejpam-4734	91	73	)	)	PUNCT
ejpam-4734	91	74	;	;	PUNCT
ejpam-4734	91	75	(	(	PUNCT
ejpam-4734	91	76	2	2	X
ejpam-4734	91	77	)	)	PUNCT
ejpam-4734	91	78	lower	low	ADJ
ejpam-4734	91	79	weakly	weakly	ADJ
ejpam-4734	91	80	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	91	81	at	at	ADP
ejpam-4734	91	82	a	a	DET
ejpam-4734	91	83	point	point	NOUN
ejpam-4734	91	84	x	x	SYM
ejpam-4734	91	85	∈	∈	NOUN
ejpam-4734	91	86	x	x	INTJ
ejpam-4734	91	87	if	if	SCONJ
ejpam-4734	91	88	for	for	SCONJ
ejpam-4734	91	89	each	each	DET
ejpam-4734	91	90	⋆-open	⋆-open	ADV
ejpam-4734	91	91	set	set	VERB
ejpam-4734	91	92	v	v	NUM
ejpam-4734	91	93	of	of	ADP
ejpam-4734	91	94	y	y	PRON
ejpam-4734	91	95	such	such	ADJ
ejpam-4734	91	96	that	that	SCONJ
ejpam-4734	91	97	f	f	PROPN
ejpam-4734	91	98	(	(	PUNCT
ejpam-4734	91	99	x	x	NOUN
ejpam-4734	91	100	)	)	PUNCT
ejpam-4734	91	101	∩	∩	NOUN
ejpam-4734	91	102	v	v	ADP
ejpam-4734	91	103	̸=	̸=	PROPN
ejpam-4734	91	104	∅	∅	NOUN
ejpam-4734	91	105	,	,	PUNCT
ejpam-4734	91	106	there	there	PRON
ejpam-4734	91	107	exists	exist	VERB
ejpam-4734	91	108	a	a	DET
ejpam-4734	91	109	strong	strong	ADJ
ejpam-4734	91	110	β	β	NOUN
ejpam-4734	91	111	-	-	ADJ
ejpam-4734	91	112	i	i	PRON
ejpam-4734	91	113	-open	-open	VERB
ejpam-4734	91	114	set	set	VERB
ejpam-4734	91	115	u	u	NOUN
ejpam-4734	91	116	of	of	ADP
ejpam-4734	91	117	x	x	PUNCT
ejpam-4734	91	118	containing	contain	VERB
ejpam-4734	91	119	x	x	PUNCT
ejpam-4734	91	120	such	such	ADJ
ejpam-4734	91	121	that	that	SCONJ
ejpam-4734	91	122	f	f	PROPN
ejpam-4734	91	123	(	(	PUNCT
ejpam-4734	91	124	z	z	NOUN
ejpam-4734	91	125	)	)	PUNCT
ejpam-4734	91	126	∩	∩	NOUN
ejpam-4734	91	127	cl⋆(v	cl⋆(v	NOUN
ejpam-4734	91	128	)	)	PUNCT
ejpam-4734	91	129	̸=	̸=	NOUN
ejpam-4734	91	130	∅	∅	NOUN
ejpam-4734	91	131	for	for	ADP
ejpam-4734	91	132	every	every	DET
ejpam-4734	91	133	z	z	NOUN
ejpam-4734	91	134	∈	∈	PROPN
ejpam-4734	91	135	u	u	NOUN
ejpam-4734	91	136	;	;	PUNCT
ejpam-4734	91	137	(	(	PUNCT
ejpam-4734	91	138	3	3	X
ejpam-4734	91	139	)	)	PUNCT
ejpam-4734	91	140	upper	upper	ADJ
ejpam-4734	91	141	(	(	PUNCT
ejpam-4734	91	142	resp	resp	NOUN
ejpam-4734	91	143	.	.	PUNCT
ejpam-4734	92	1	lower	low	ADJ
ejpam-4734	92	2	)	)	PUNCT
ejpam-4734	92	3	weakly	weakly	ADV
ejpam-4734	92	4	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	92	5	if	if	SCONJ
ejpam-4734	92	6	f	f	PROPN
ejpam-4734	92	7	has	have	VERB
ejpam-4734	92	8	this	this	DET
ejpam-4734	92	9	property	property	NOUN
ejpam-4734	92	10	at	at	ADP
ejpam-4734	92	11	each	each	DET
ejpam-4734	92	12	point	point	NOUN
ejpam-4734	92	13	of	of	ADP
ejpam-4734	92	14	x.	x.	NOUN
ejpam-4734	92	15	theorem	theorem	VERB
ejpam-4734	92	16	1	1	NUM
ejpam-4734	92	17	.	.	X
ejpam-4734	92	18	for	for	ADP
ejpam-4734	92	19	a	a	DET
ejpam-4734	92	20	multifunction	multifunction	NOUN
ejpam-4734	92	21	f	f	NOUN
ejpam-4734	92	22	:	:	PUNCT
ejpam-4734	92	23	(	(	PUNCT
ejpam-4734	92	24	x	x	X
ejpam-4734	92	25	,	,	PUNCT
ejpam-4734	92	26	τ	τ	PROPN
ejpam-4734	92	27	,	,	PUNCT
ejpam-4734	92	28	i	i	NOUN
ejpam-4734	92	29	)	)	PUNCT
ejpam-4734	92	30	→	→	PUNCT
ejpam-4734	92	31	(	(	PUNCT
ejpam-4734	92	32	y	y	PROPN
ejpam-4734	92	33	,	,	PUNCT
ejpam-4734	92	34	σ	σ	PROPN
ejpam-4734	92	35	,	,	PUNCT
ejpam-4734	92	36	j	j	PROPN
ejpam-4734	92	37	)	)	PUNCT
ejpam-4734	92	38	,	,	PUNCT
ejpam-4734	92	39	the	the	DET
ejpam-4734	92	40	following	follow	VERB
ejpam-4734	92	41	properties	property	NOUN
ejpam-4734	92	42	are	be	AUX
ejpam-4734	92	43	equivalent	equivalent	ADJ
ejpam-4734	92	44	:	:	PUNCT
ejpam-4734	92	45	(	(	PUNCT
ejpam-4734	92	46	1	1	X
ejpam-4734	92	47	)	)	PUNCT
ejpam-4734	92	48	f	f	PROPN
ejpam-4734	92	49	is	be	AUX
ejpam-4734	92	50	upper	upper	ADJ
ejpam-4734	92	51	weakly	weakly	ADV
ejpam-4734	92	52	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	92	53	at	at	ADP
ejpam-4734	92	54	a	a	DET
ejpam-4734	92	55	point	point	NOUN
ejpam-4734	92	56	x	x	X
ejpam-4734	92	57	∈	∈	NOUN
ejpam-4734	92	58	x	x	X
ejpam-4734	92	59	;	;	PUNCT
ejpam-4734	92	60	(	(	PUNCT
ejpam-4734	92	61	2	2	X
ejpam-4734	92	62	)	)	PUNCT
ejpam-4734	92	63	x	x	SYM
ejpam-4734	92	64	∈	∈	NOUN
ejpam-4734	92	65	cl⋆(int(cl⋆(f+(cl⋆(v	cl⋆(int(cl⋆(f+(cl⋆(v	NOUN
ejpam-4734	92	66	)	)	PUNCT
ejpam-4734	92	67	)	)	PUNCT
ejpam-4734	92	68	)	)	PUNCT
ejpam-4734	92	69	)	)	PUNCT
ejpam-4734	92	70	)	)	PUNCT
ejpam-4734	93	1	for	for	ADP
ejpam-4734	93	2	every	every	DET
ejpam-4734	93	3	⋆-open	⋆-open	NOUN
ejpam-4734	93	4	set	set	VERB
ejpam-4734	93	5	v	v	NOUN
ejpam-4734	93	6	of	of	ADP
ejpam-4734	93	7	y	y	PROPN
ejpam-4734	93	8	containing	contain	VERB
ejpam-4734	93	9	f	f	PROPN
ejpam-4734	93	10	(	(	PUNCT
ejpam-4734	93	11	x	x	NOUN
ejpam-4734	93	12	)	)	PUNCT
ejpam-4734	93	13	;	;	PUNCT
ejpam-4734	93	14	c.	c.	PROPN
ejpam-4734	93	15	boonpok	boonpok	PROPN
ejpam-4734	93	16	,	,	PUNCT
ejpam-4734	93	17	j.	j.	PROPN
ejpam-4734	93	18	khampakdee	khampakdee	PROPN
ejpam-4734	93	19	/	/	PUNCT
ejpam-4734	93	20	eur	eur	PROPN
ejpam-4734	93	21	.	.	PUNCT
ejpam-4734	94	1	j.	j.	PROPN
ejpam-4734	94	2	pure	pure	PROPN
ejpam-4734	94	3	appl	appl	PROPN
ejpam-4734	94	4	.	.	PROPN
ejpam-4734	94	5	math	math	PROPN
ejpam-4734	94	6	,	,	PUNCT
ejpam-4734	94	7	16	16	NUM
ejpam-4734	94	8	(	(	PUNCT
ejpam-4734	94	9	4	4	NUM
ejpam-4734	94	10	)	)	PUNCT
ejpam-4734	94	11	(	(	PUNCT
ejpam-4734	94	12	2023	2023	NUM
ejpam-4734	94	13	)	)	PUNCT
ejpam-4734	94	14	,	,	PUNCT
ejpam-4734	94	15	2544	2544	NUM
ejpam-4734	94	16	-	-	SYM
ejpam-4734	94	17	2556	2556	NUM
ejpam-4734	94	18	2547	2547	NUM
ejpam-4734	94	19	(	(	PUNCT
ejpam-4734	94	20	3	3	NUM
ejpam-4734	94	21	)	)	PUNCT
ejpam-4734	94	22	x	x	SYM
ejpam-4734	94	23	∈	∈	PROPN
ejpam-4734	94	24	sβinti	sβinti	NOUN
ejpam-4734	94	25	(	(	PUNCT
ejpam-4734	94	26	f+(cl⋆(v	f+(cl⋆(v	PROPN
ejpam-4734	94	27	)	)	PUNCT
ejpam-4734	94	28	)	)	PUNCT
ejpam-4734	94	29	)	)	PUNCT
ejpam-4734	95	1	for	for	ADP
ejpam-4734	95	2	every	every	DET
ejpam-4734	95	3	⋆-open	⋆-open	NOUN
ejpam-4734	95	4	set	set	VERB
ejpam-4734	95	5	v	v	NOUN
ejpam-4734	95	6	of	of	ADP
ejpam-4734	95	7	y	y	PROPN
ejpam-4734	95	8	containing	contain	VERB
ejpam-4734	95	9	f	f	PROPN
ejpam-4734	95	10	(	(	PUNCT
ejpam-4734	95	11	x	x	NOUN
ejpam-4734	95	12	)	)	PUNCT
ejpam-4734	95	13	.	.	PUNCT
ejpam-4734	96	1	proof	proof	NOUN
ejpam-4734	96	2	.	.	PUNCT
ejpam-4734	97	1	(	(	PUNCT
ejpam-4734	97	2	1	1	X
ejpam-4734	97	3	)	)	PUNCT
ejpam-4734	97	4	⇒	⇒	NOUN
ejpam-4734	97	5	(	(	PUNCT
ejpam-4734	97	6	2	2	NUM
ejpam-4734	97	7	):	):	PUNCT
ejpam-4734	97	8	let	let	VERB
ejpam-4734	97	9	v	v	PART
ejpam-4734	97	10	be	be	AUX
ejpam-4734	97	11	any	any	DET
ejpam-4734	97	12	⋆-open	⋆-open	ADJ
ejpam-4734	97	13	set	set	NOUN
ejpam-4734	97	14	of	of	ADP
ejpam-4734	97	15	y	y	PROPN
ejpam-4734	97	16	containing	contain	VERB
ejpam-4734	97	17	f	f	PROPN
ejpam-4734	97	18	(	(	PUNCT
ejpam-4734	97	19	x	x	NOUN
ejpam-4734	97	20	)	)	PUNCT
ejpam-4734	97	21	.	.	PUNCT
ejpam-4734	98	1	by	by	ADP
ejpam-4734	98	2	(	(	PUNCT
ejpam-4734	98	3	1	1	NUM
ejpam-4734	98	4	)	)	PUNCT
ejpam-4734	98	5	,	,	PUNCT
ejpam-4734	98	6	there	there	PRON
ejpam-4734	98	7	exists	exist	VERB
ejpam-4734	98	8	a	a	DET
ejpam-4734	98	9	strong	strong	ADJ
ejpam-4734	98	10	β	β	NOUN
ejpam-4734	98	11	-	-	ADJ
ejpam-4734	98	12	i	i	PRON
ejpam-4734	98	13	-open	-open	VERB
ejpam-4734	98	14	set	set	VERB
ejpam-4734	98	15	u	u	NOUN
ejpam-4734	98	16	of	of	ADP
ejpam-4734	98	17	x	x	PUNCT
ejpam-4734	98	18	containing	contain	VERB
ejpam-4734	98	19	x	x	PUNCT
ejpam-4734	98	20	such	such	ADJ
ejpam-4734	98	21	that	that	SCONJ
ejpam-4734	98	22	f	f	PROPN
ejpam-4734	98	23	(	(	PUNCT
ejpam-4734	98	24	u	u	NOUN
ejpam-4734	98	25	)	)	PUNCT
ejpam-4734	98	26	⊆	⊆	NUM
ejpam-4734	98	27	cl⋆(v	cl⋆(v	NOUN
ejpam-4734	98	28	)	)	PUNCT
ejpam-4734	98	29	.	.	PUNCT
ejpam-4734	99	1	then	then	ADV
ejpam-4734	99	2	,	,	PUNCT
ejpam-4734	99	3	x	x	PUNCT
ejpam-4734	99	4	∈	∈	PROPN
ejpam-4734	99	5	u	u	NOUN
ejpam-4734	99	6	⊆	⊆	NUM
ejpam-4734	99	7	f+(cl⋆(v	f+(cl⋆(v	PROPN
ejpam-4734	99	8	)	)	PUNCT
ejpam-4734	99	9	)	)	PUNCT
ejpam-4734	99	10	.	.	PUNCT
ejpam-4734	100	1	since	since	SCONJ
ejpam-4734	100	2	u	u	NOUN
ejpam-4734	100	3	is	be	AUX
ejpam-4734	100	4	strong	strong	ADJ
ejpam-4734	100	5	β	β	NOUN
ejpam-4734	100	6	-	-	PUNCT
ejpam-4734	100	7	i	i	PRON
ejpam-4734	100	8	-open	-open	ADJ
ejpam-4734	100	9	,	,	PUNCT
ejpam-4734	100	10	we	we	PRON
ejpam-4734	100	11	have	have	VERB
ejpam-4734	100	12	x	x	X
ejpam-4734	100	13	∈	∈	PROPN
ejpam-4734	100	14	u	u	NOUN
ejpam-4734	100	15	⊆	⊆	NUM
ejpam-4734	100	16	cl⋆(int(cl⋆(u	cl⋆(int(cl⋆(u	PROPN
ejpam-4734	100	17	)	)	PUNCT
ejpam-4734	100	18	)	)	PUNCT
ejpam-4734	100	19	)	)	PUNCT
ejpam-4734	101	1	⊆	⊆	NUM
ejpam-4734	101	2	cl⋆(int(cl⋆(f+(cl⋆(v	cl⋆(int(cl⋆(f+(cl⋆(v	NOUN
ejpam-4734	101	3	)	)	PUNCT
ejpam-4734	101	4	)	)	PUNCT
ejpam-4734	101	5	)	)	PUNCT
ejpam-4734	101	6	)	)	PUNCT
ejpam-4734	101	7	)	)	PUNCT
ejpam-4734	101	8	.	.	PUNCT
ejpam-4734	102	1	(	(	PUNCT
ejpam-4734	102	2	2	2	X
ejpam-4734	102	3	)	)	PUNCT
ejpam-4734	102	4	⇒	⇒	NOUN
ejpam-4734	102	5	(	(	PUNCT
ejpam-4734	102	6	3	3	NUM
ejpam-4734	102	7	):	):	PUNCT
ejpam-4734	102	8	let	let	VERB
ejpam-4734	102	9	v	v	PART
ejpam-4734	102	10	be	be	AUX
ejpam-4734	102	11	any	any	DET
ejpam-4734	102	12	⋆-open	⋆-open	ADJ
ejpam-4734	102	13	set	set	NOUN
ejpam-4734	102	14	of	of	ADP
ejpam-4734	102	15	y	y	PROPN
ejpam-4734	102	16	containing	contain	VERB
ejpam-4734	102	17	f	f	PROPN
ejpam-4734	102	18	(	(	PUNCT
ejpam-4734	102	19	x	x	NOUN
ejpam-4734	102	20	)	)	PUNCT
ejpam-4734	102	21	.	.	PUNCT
ejpam-4734	103	1	thus	thus	ADV
ejpam-4734	103	2	,	,	PUNCT
ejpam-4734	103	3	by	by	ADP
ejpam-4734	103	4	(	(	PUNCT
ejpam-4734	103	5	2	2	NUM
ejpam-4734	103	6	)	)	PUNCT
ejpam-4734	103	7	,	,	PUNCT
ejpam-4734	103	8	we	we	PRON
ejpam-4734	103	9	have	have	VERB
ejpam-4734	103	10	x	x	X
ejpam-4734	103	11	∈	∈	PROPN
ejpam-4734	103	12	cl⋆(int(cl⋆(f+(cl⋆(v	cl⋆(int(cl⋆(f+(cl⋆(v	NOUN
ejpam-4734	103	13	)	)	PUNCT
ejpam-4734	103	14	)	)	PUNCT
ejpam-4734	103	15	)	)	PUNCT
ejpam-4734	103	16	)	)	PUNCT
ejpam-4734	103	17	)	)	PUNCT
ejpam-4734	103	18	.	.	PUNCT
ejpam-4734	104	1	since	since	SCONJ
ejpam-4734	104	2	x	x	PROPN
ejpam-4734	104	3	∈	∈	PROPN
ejpam-4734	104	4	f+(cl⋆(v	f+(cl⋆(v	PROPN
ejpam-4734	104	5	)	)	PUNCT
ejpam-4734	104	6	)	)	PUNCT
ejpam-4734	104	7	and	and	CCONJ
ejpam-4734	104	8	by	by	ADP
ejpam-4734	104	9	lemma	lemma	PROPN
ejpam-4734	104	10	2	2	NUM
ejpam-4734	104	11	,	,	PUNCT
ejpam-4734	104	12	we	we	PRON
ejpam-4734	104	13	obtain	obtain	VERB
ejpam-4734	104	14	x	x	PUNCT
ejpam-4734	104	15	∈	∈	PROPN
ejpam-4734	104	16	f+(cl⋆(v	f+(cl⋆(v	PROPN
ejpam-4734	104	17	)	)	PUNCT
ejpam-4734	104	18	)	)	PUNCT
ejpam-4734	104	19	∩	∩	ADJ
ejpam-4734	104	20	cl⋆(int(cl⋆(f+(cl⋆(v	cl⋆(int(cl⋆(f+(cl⋆(v	NOUN
ejpam-4734	104	21	)	)	PUNCT
ejpam-4734	104	22	)	)	PUNCT
ejpam-4734	104	23	)	)	PUNCT
ejpam-4734	104	24	)	)	PUNCT
ejpam-4734	104	25	)	)	PUNCT
ejpam-4734	105	1	=	=	PRON
ejpam-4734	105	2	sβinti	sβinti	X
ejpam-4734	105	3	(	(	PUNCT
ejpam-4734	105	4	f+(cl⋆(v	f+(cl⋆(v	PROPN
ejpam-4734	105	5	)	)	PUNCT
ejpam-4734	105	6	)	)	PUNCT
ejpam-4734	105	7	)	)	PUNCT
ejpam-4734	105	8	.	.	PUNCT
ejpam-4734	106	1	(	(	PUNCT
ejpam-4734	106	2	3	3	X
ejpam-4734	106	3	)	)	PUNCT
ejpam-4734	106	4	⇒	⇒	NOUN
ejpam-4734	106	5	(	(	PUNCT
ejpam-4734	106	6	1	1	NUM
ejpam-4734	106	7	):	):	PUNCT
ejpam-4734	106	8	let	let	VERB
ejpam-4734	106	9	v	v	PART
ejpam-4734	106	10	be	be	AUX
ejpam-4734	106	11	any	any	DET
ejpam-4734	106	12	⋆-open	⋆-open	ADJ
ejpam-4734	106	13	set	set	NOUN
ejpam-4734	106	14	of	of	ADP
ejpam-4734	106	15	y	y	PROPN
ejpam-4734	106	16	containing	contain	VERB
ejpam-4734	106	17	f	f	PROPN
ejpam-4734	106	18	(	(	PUNCT
ejpam-4734	106	19	x	x	NOUN
ejpam-4734	106	20	)	)	PUNCT
ejpam-4734	106	21	.	.	PUNCT
ejpam-4734	107	1	by	by	ADP
ejpam-4734	107	2	(	(	PUNCT
ejpam-4734	107	3	3	3	NUM
ejpam-4734	107	4	)	)	PUNCT
ejpam-4734	107	5	,	,	PUNCT
ejpam-4734	107	6	we	we	PRON
ejpam-4734	107	7	have	have	VERB
ejpam-4734	107	8	x	x	PART
ejpam-4734	107	9	∈	∈	PROPN
ejpam-4734	107	10	sβinti	sβinti	NOUN
ejpam-4734	107	11	(	(	PUNCT
ejpam-4734	107	12	f+(cl⋆(v	f+(cl⋆(v	PROPN
ejpam-4734	107	13	)	)	PUNCT
ejpam-4734	107	14	)	)	PUNCT
ejpam-4734	107	15	)	)	PUNCT
ejpam-4734	108	1	and	and	CCONJ
ejpam-4734	108	2	so	so	ADV
ejpam-4734	108	3	there	there	PRON
ejpam-4734	108	4	exists	exist	VERB
ejpam-4734	108	5	a	a	DET
ejpam-4734	108	6	strong	strong	ADJ
ejpam-4734	108	7	β	β	NOUN
ejpam-4734	108	8	-	-	ADJ
ejpam-4734	108	9	i	i	PRON
ejpam-4734	108	10	-open	-open	VERB
ejpam-4734	108	11	set	set	VERB
ejpam-4734	108	12	u	u	NOUN
ejpam-4734	108	13	of	of	ADP
ejpam-4734	108	14	x	x	PUNCT
ejpam-4734	108	15	containing	contain	VERB
ejpam-4734	108	16	x	x	PUNCT
ejpam-4734	108	17	such	such	ADJ
ejpam-4734	108	18	that	that	SCONJ
ejpam-4734	108	19	u	u	PROPN
ejpam-4734	108	20	⊆	⊆	NUM
ejpam-4734	108	21	f+(cl⋆(v	f+(cl⋆(v	PROPN
ejpam-4734	108	22	)	)	PUNCT
ejpam-4734	108	23	)	)	PUNCT
ejpam-4734	109	1	;	;	PUNCT
ejpam-4734	109	2	hence	hence	ADV
ejpam-4734	109	3	f	f	PROPN
ejpam-4734	109	4	(	(	PUNCT
ejpam-4734	109	5	u	u	NOUN
ejpam-4734	109	6	)	)	PUNCT
ejpam-4734	109	7	⊆	⊆	NUM
ejpam-4734	109	8	cl⋆(v	cl⋆(v	NOUN
ejpam-4734	109	9	)	)	PUNCT
ejpam-4734	109	10	.	.	PUNCT
ejpam-4734	110	1	this	this	PRON
ejpam-4734	110	2	shows	show	VERB
ejpam-4734	110	3	that	that	SCONJ
ejpam-4734	110	4	f	f	PROPN
ejpam-4734	110	5	is	be	AUX
ejpam-4734	110	6	upper	upper	ADJ
ejpam-4734	110	7	weakly	weakly	ADJ
ejpam-4734	110	8	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	110	9	at	at	ADP
ejpam-4734	110	10	x.	x.	NOUN
ejpam-4734	110	11	theorem	theorem	NOUN
ejpam-4734	110	12	2	2	NUM
ejpam-4734	110	13	.	.	X
ejpam-4734	110	14	for	for	ADP
ejpam-4734	110	15	a	a	DET
ejpam-4734	110	16	multifunction	multifunction	NOUN
ejpam-4734	110	17	f	f	NOUN
ejpam-4734	110	18	:	:	PUNCT
ejpam-4734	110	19	(	(	PUNCT
ejpam-4734	110	20	x	x	X
ejpam-4734	110	21	,	,	PUNCT
ejpam-4734	110	22	τ	τ	PROPN
ejpam-4734	110	23	,	,	PUNCT
ejpam-4734	110	24	i	i	NOUN
ejpam-4734	110	25	)	)	PUNCT
ejpam-4734	110	26	→	→	PUNCT
ejpam-4734	110	27	(	(	PUNCT
ejpam-4734	110	28	y	y	PROPN
ejpam-4734	110	29	,	,	PUNCT
ejpam-4734	110	30	σ	σ	PROPN
ejpam-4734	110	31	,	,	PUNCT
ejpam-4734	110	32	j	j	PROPN
ejpam-4734	110	33	)	)	PUNCT
ejpam-4734	110	34	,	,	PUNCT
ejpam-4734	110	35	the	the	DET
ejpam-4734	110	36	following	follow	VERB
ejpam-4734	110	37	properties	property	NOUN
ejpam-4734	110	38	are	be	AUX
ejpam-4734	110	39	equivalent	equivalent	ADJ
ejpam-4734	110	40	:	:	PUNCT
ejpam-4734	110	41	(	(	PUNCT
ejpam-4734	110	42	1	1	X
ejpam-4734	110	43	)	)	PUNCT
ejpam-4734	110	44	f	f	PROPN
ejpam-4734	110	45	is	be	AUX
ejpam-4734	110	46	lower	low	ADJ
ejpam-4734	110	47	weakly	weakly	ADJ
ejpam-4734	110	48	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	110	49	at	at	ADP
ejpam-4734	110	50	a	a	DET
ejpam-4734	110	51	point	point	NOUN
ejpam-4734	110	52	x	x	X
ejpam-4734	110	53	∈	∈	NOUN
ejpam-4734	110	54	x	x	X
ejpam-4734	110	55	;	;	PUNCT
ejpam-4734	110	56	(	(	PUNCT
ejpam-4734	110	57	2	2	X
ejpam-4734	110	58	)	)	PUNCT
ejpam-4734	110	59	x	x	SYM
ejpam-4734	110	60	∈	∈	PROPN
ejpam-4734	110	61	cl⋆(int(cl⋆(f−(cl⋆(v	cl⋆(int(cl⋆(f−(cl⋆(v	PROPN
ejpam-4734	110	62	)	)	PUNCT
ejpam-4734	110	63	)	)	PUNCT
ejpam-4734	110	64	)	)	PUNCT
ejpam-4734	110	65	)	)	PUNCT
ejpam-4734	110	66	)	)	PUNCT
ejpam-4734	110	67	for	for	ADP
ejpam-4734	110	68	every	every	DET
ejpam-4734	110	69	⋆-open	⋆-open	NOUN
ejpam-4734	110	70	set	set	VERB
ejpam-4734	110	71	v	v	NUM
ejpam-4734	110	72	of	of	ADP
ejpam-4734	110	73	y	y	PRON
ejpam-4734	110	74	such	such	ADJ
ejpam-4734	110	75	that	that	SCONJ
ejpam-4734	110	76	f	f	PROPN
ejpam-4734	110	77	(	(	PUNCT
ejpam-4734	110	78	x)∩v	x)∩v	PROPN
ejpam-4734	110	79	̸=	̸=	PROPN
ejpam-4734	110	80	∅	∅	NOUN
ejpam-4734	110	81	;	;	PUNCT
ejpam-4734	110	82	(	(	PUNCT
ejpam-4734	110	83	3	3	X
ejpam-4734	110	84	)	)	PUNCT
ejpam-4734	110	85	x	x	SYM
ejpam-4734	110	86	∈	∈	PROPN
ejpam-4734	110	87	sβinti	sβinti	NOUN
ejpam-4734	110	88	(	(	PUNCT
ejpam-4734	110	89	f−(cl⋆(v	f−(cl⋆(v	PROPN
ejpam-4734	110	90	)	)	PUNCT
ejpam-4734	110	91	)	)	PUNCT
ejpam-4734	110	92	)	)	PUNCT
ejpam-4734	110	93	for	for	SCONJ
ejpam-4734	110	94	every	every	DET
ejpam-4734	110	95	⋆-open	⋆-open	NOUN
ejpam-4734	110	96	set	set	VERB
ejpam-4734	110	97	v	v	NUM
ejpam-4734	110	98	of	of	ADP
ejpam-4734	110	99	y	y	PRON
ejpam-4734	110	100	such	such	ADJ
ejpam-4734	110	101	that	that	SCONJ
ejpam-4734	110	102	f	f	PROPN
ejpam-4734	110	103	(	(	PUNCT
ejpam-4734	110	104	x	x	NOUN
ejpam-4734	110	105	)	)	PUNCT
ejpam-4734	110	106	∩	∩	NOUN
ejpam-4734	110	107	v	v	ADP
ejpam-4734	110	108	̸=	̸=	PROPN
ejpam-4734	110	109	∅.	∅.	ADP
ejpam-4734	110	110	proof	proof	NOUN
ejpam-4734	110	111	.	.	PUNCT
ejpam-4734	111	1	the	the	DET
ejpam-4734	111	2	proof	proof	NOUN
ejpam-4734	111	3	is	be	AUX
ejpam-4734	111	4	similar	similar	ADJ
ejpam-4734	111	5	to	to	ADP
ejpam-4734	111	6	that	that	PRON
ejpam-4734	111	7	of	of	ADP
ejpam-4734	111	8	theorem	theorem	NOUN
ejpam-4734	111	9	1	1	NUM
ejpam-4734	111	10	.	.	PUNCT
ejpam-4734	111	11	definition	definition	NOUN
ejpam-4734	111	12	2	2	NUM
ejpam-4734	111	13	.	.	PUNCT
ejpam-4734	112	1	a	a	DET
ejpam-4734	112	2	function	function	NOUN
ejpam-4734	112	3	f	f	NOUN
ejpam-4734	112	4	:	:	PUNCT
ejpam-4734	112	5	(	(	PUNCT
ejpam-4734	112	6	x	x	X
ejpam-4734	112	7	,	,	PUNCT
ejpam-4734	112	8	τ	τ	PROPN
ejpam-4734	112	9	,	,	PUNCT
ejpam-4734	112	10	i	i	NOUN
ejpam-4734	112	11	)	)	PUNCT
ejpam-4734	112	12	→	→	PUNCT
ejpam-4734	112	13	(	(	PUNCT
ejpam-4734	112	14	y	y	PROPN
ejpam-4734	112	15	,	,	PUNCT
ejpam-4734	112	16	σ	σ	PROPN
ejpam-4734	112	17	,	,	PUNCT
ejpam-4734	112	18	j	j	PROPN
ejpam-4734	112	19	)	)	PUNCT
ejpam-4734	112	20	is	be	AUX
ejpam-4734	112	21	said	say	VERB
ejpam-4734	112	22	to	to	PART
ejpam-4734	112	23	be	be	AUX
ejpam-4734	112	24	weakly	weakly	ADV
ejpam-4734	112	25	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	112	26	at	at	ADP
ejpam-4734	112	27	a	a	DET
ejpam-4734	112	28	point	point	NOUN
ejpam-4734	112	29	x	x	SYM
ejpam-4734	112	30	∈	∈	NOUN
ejpam-4734	112	31	x	x	INTJ
ejpam-4734	112	32	if	if	SCONJ
ejpam-4734	112	33	for	for	SCONJ
ejpam-4734	112	34	each	each	DET
ejpam-4734	112	35	⋆-open	⋆-open	ADV
ejpam-4734	112	36	set	set	VERB
ejpam-4734	112	37	v	v	NUM
ejpam-4734	112	38	of	of	ADP
ejpam-4734	112	39	y	y	NOUN
ejpam-4734	112	40	containing	contain	VERB
ejpam-4734	112	41	f(x	f(x	PROPN
ejpam-4734	112	42	)	)	PUNCT
ejpam-4734	112	43	,	,	PUNCT
ejpam-4734	112	44	there	there	PRON
ejpam-4734	112	45	exists	exist	VERB
ejpam-4734	112	46	a	a	DET
ejpam-4734	112	47	strong	strong	ADJ
ejpam-4734	112	48	β	β	NOUN
ejpam-4734	112	49	-	-	ADJ
ejpam-4734	112	50	i	i	PRON
ejpam-4734	112	51	-open	-open	VERB
ejpam-4734	112	52	set	set	VERB
ejpam-4734	112	53	u	u	NOUN
ejpam-4734	112	54	of	of	ADP
ejpam-4734	112	55	x	x	PUNCT
ejpam-4734	112	56	containing	contain	VERB
ejpam-4734	112	57	x	x	PUNCT
ejpam-4734	112	58	such	such	ADJ
ejpam-4734	112	59	that	that	DET
ejpam-4734	112	60	f(u	f(u	PROPN
ejpam-4734	112	61	)	)	PUNCT
ejpam-4734	112	62	⊆	⊆	NUM
ejpam-4734	112	63	cl⋆(v	cl⋆(v	NOUN
ejpam-4734	112	64	)	)	PUNCT
ejpam-4734	112	65	.	.	PUNCT
ejpam-4734	113	1	a	a	DET
ejpam-4734	113	2	function	function	NOUN
ejpam-4734	113	3	f	f	NOUN
ejpam-4734	113	4	:	:	PUNCT
ejpam-4734	113	5	(	(	PUNCT
ejpam-4734	113	6	x	x	X
ejpam-4734	113	7	,	,	PUNCT
ejpam-4734	113	8	τ	τ	PROPN
ejpam-4734	113	9	,	,	PUNCT
ejpam-4734	113	10	i	i	NOUN
ejpam-4734	113	11	)	)	PUNCT
ejpam-4734	113	12	→	→	PUNCT
ejpam-4734	113	13	(	(	PUNCT
ejpam-4734	113	14	y	y	PROPN
ejpam-4734	113	15	,	,	PUNCT
ejpam-4734	113	16	σ	σ	PROPN
ejpam-4734	113	17	,	,	PUNCT
ejpam-4734	113	18	j	j	PROPN
ejpam-4734	113	19	)	)	PUNCT
ejpam-4734	113	20	is	be	AUX
ejpam-4734	113	21	said	say	VERB
ejpam-4734	113	22	to	to	PART
ejpam-4734	113	23	be	be	AUX
ejpam-4734	113	24	weakly	weakly	ADV
ejpam-4734	113	25	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	113	26	if	if	SCONJ
ejpam-4734	113	27	f	f	PROPN
ejpam-4734	113	28	has	have	VERB
ejpam-4734	113	29	this	this	DET
ejpam-4734	113	30	property	property	NOUN
ejpam-4734	113	31	at	at	ADP
ejpam-4734	113	32	each	each	DET
ejpam-4734	113	33	point	point	NOUN
ejpam-4734	113	34	of	of	ADP
ejpam-4734	113	35	x.	x.	PROPN
ejpam-4734	113	36	corollary	corollary	NOUN
ejpam-4734	113	37	1	1	NUM
ejpam-4734	113	38	.	.	PUNCT
ejpam-4734	114	1	for	for	ADP
ejpam-4734	114	2	a	a	DET
ejpam-4734	114	3	function	function	NOUN
ejpam-4734	114	4	f	f	NOUN
ejpam-4734	114	5	:	:	PUNCT
ejpam-4734	114	6	(	(	PUNCT
ejpam-4734	114	7	x	x	X
ejpam-4734	114	8	,	,	PUNCT
ejpam-4734	114	9	τ	τ	PROPN
ejpam-4734	114	10	,	,	PUNCT
ejpam-4734	114	11	i	i	NOUN
ejpam-4734	114	12	)	)	PUNCT
ejpam-4734	114	13	→	→	PUNCT
ejpam-4734	114	14	(	(	PUNCT
ejpam-4734	114	15	y	y	PROPN
ejpam-4734	114	16	,	,	PUNCT
ejpam-4734	114	17	σ	σ	PROPN
ejpam-4734	114	18	,	,	PUNCT
ejpam-4734	114	19	j	j	PROPN
ejpam-4734	114	20	)	)	PUNCT
ejpam-4734	114	21	,	,	PUNCT
ejpam-4734	114	22	the	the	DET
ejpam-4734	114	23	following	follow	VERB
ejpam-4734	114	24	properties	property	NOUN
ejpam-4734	114	25	are	be	AUX
ejpam-4734	114	26	equivalent	equivalent	ADJ
ejpam-4734	114	27	:	:	PUNCT
ejpam-4734	114	28	(	(	PUNCT
ejpam-4734	114	29	1	1	X
ejpam-4734	114	30	)	)	PUNCT
ejpam-4734	114	31	f	f	PROPN
ejpam-4734	114	32	is	be	AUX
ejpam-4734	114	33	weakly	weakly	ADV
ejpam-4734	114	34	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	114	35	at	at	ADP
ejpam-4734	114	36	a	a	DET
ejpam-4734	114	37	point	point	NOUN
ejpam-4734	114	38	x	x	X
ejpam-4734	114	39	∈	∈	NOUN
ejpam-4734	114	40	x	x	X
ejpam-4734	114	41	;	;	PUNCT
ejpam-4734	114	42	(	(	PUNCT
ejpam-4734	114	43	2	2	X
ejpam-4734	114	44	)	)	PUNCT
ejpam-4734	114	45	x	x	SYM
ejpam-4734	114	46	∈	∈	PROPN
ejpam-4734	114	47	cl⋆(int(cl⋆(f−1(cl⋆(v	cl⋆(int(cl⋆(f−1(cl⋆(v	NOUN
ejpam-4734	114	48	)	)	PUNCT
ejpam-4734	114	49	)	)	PUNCT
ejpam-4734	114	50	)	)	PUNCT
ejpam-4734	114	51	)	)	PUNCT
ejpam-4734	114	52	)	)	PUNCT
ejpam-4734	115	1	for	for	ADP
ejpam-4734	115	2	every	every	DET
ejpam-4734	115	3	⋆-open	⋆-open	NOUN
ejpam-4734	115	4	set	set	VERB
ejpam-4734	115	5	v	v	NOUN
ejpam-4734	115	6	of	of	ADP
ejpam-4734	115	7	y	y	NOUN
ejpam-4734	115	8	containing	contain	VERB
ejpam-4734	115	9	f(x	f(x	PROPN
ejpam-4734	115	10	)	)	PUNCT
ejpam-4734	115	11	;	;	PUNCT
ejpam-4734	115	12	(	(	PUNCT
ejpam-4734	115	13	3	3	X
ejpam-4734	115	14	)	)	PUNCT
ejpam-4734	115	15	x	x	SYM
ejpam-4734	115	16	∈	∈	PROPN
ejpam-4734	115	17	sβinti	sβinti	NOUN
ejpam-4734	115	18	(	(	PUNCT
ejpam-4734	115	19	f−1(cl⋆(v	f−1(cl⋆(v	PROPN
ejpam-4734	115	20	)	)	PUNCT
ejpam-4734	115	21	)	)	PUNCT
ejpam-4734	115	22	)	)	PUNCT
ejpam-4734	115	23	for	for	ADP
ejpam-4734	115	24	every	every	DET
ejpam-4734	115	25	⋆-open	⋆-open	NOUN
ejpam-4734	115	26	set	set	VERB
ejpam-4734	115	27	v	v	NOUN
ejpam-4734	115	28	of	of	ADP
ejpam-4734	115	29	y	y	NOUN
ejpam-4734	115	30	containing	contain	VERB
ejpam-4734	115	31	f(x	f(x	PROPN
ejpam-4734	115	32	)	)	PUNCT
ejpam-4734	115	33	.	.	PUNCT
ejpam-4734	116	1	theorem	theorem	NOUN
ejpam-4734	116	2	3	3	NUM
ejpam-4734	116	3	.	.	X
ejpam-4734	116	4	for	for	ADP
ejpam-4734	116	5	a	a	DET
ejpam-4734	116	6	multifunction	multifunction	NOUN
ejpam-4734	117	1	f	f	NOUN
ejpam-4734	117	2	:	:	PUNCT
ejpam-4734	117	3	(	(	PUNCT
ejpam-4734	117	4	x	x	X
ejpam-4734	117	5	,	,	PUNCT
ejpam-4734	117	6	τ	τ	PROPN
ejpam-4734	117	7	,	,	PUNCT
ejpam-4734	117	8	i	i	NOUN
ejpam-4734	117	9	)	)	PUNCT
ejpam-4734	117	10	→	→	PUNCT
ejpam-4734	117	11	(	(	PUNCT
ejpam-4734	117	12	y	y	PROPN
ejpam-4734	117	13	,	,	PUNCT
ejpam-4734	117	14	σ	σ	PROPN
ejpam-4734	117	15	,	,	PUNCT
ejpam-4734	117	16	j	j	PROPN
ejpam-4734	117	17	)	)	PUNCT
ejpam-4734	117	18	,	,	PUNCT
ejpam-4734	117	19	the	the	DET
ejpam-4734	117	20	following	follow	VERB
ejpam-4734	117	21	properties	property	NOUN
ejpam-4734	117	22	are	be	AUX
ejpam-4734	117	23	equivalent	equivalent	ADJ
ejpam-4734	117	24	:	:	PUNCT
ejpam-4734	117	25	c.	c.	PROPN
ejpam-4734	117	26	boonpok	boonpok	PROPN
ejpam-4734	117	27	,	,	PUNCT
ejpam-4734	117	28	j.	j.	PROPN
ejpam-4734	117	29	khampakdee	khampakdee	PROPN
ejpam-4734	117	30	/	/	PUNCT
ejpam-4734	117	31	eur	eur	PROPN
ejpam-4734	117	32	.	.	PUNCT
ejpam-4734	118	1	j.	j.	PROPN
ejpam-4734	118	2	pure	pure	PROPN
ejpam-4734	118	3	appl	appl	PROPN
ejpam-4734	118	4	.	.	PROPN
ejpam-4734	118	5	math	math	PROPN
ejpam-4734	118	6	,	,	PUNCT
ejpam-4734	118	7	16	16	NUM
ejpam-4734	118	8	(	(	PUNCT
ejpam-4734	118	9	4	4	NUM
ejpam-4734	118	10	)	)	PUNCT
ejpam-4734	118	11	(	(	PUNCT
ejpam-4734	118	12	2023	2023	NUM
ejpam-4734	118	13	)	)	PUNCT
ejpam-4734	118	14	,	,	PUNCT
ejpam-4734	118	15	2544	2544	NUM
ejpam-4734	118	16	-	-	SYM
ejpam-4734	118	17	2556	2556	NUM
ejpam-4734	118	18	2548	2548	NUM
ejpam-4734	118	19	(	(	PUNCT
ejpam-4734	118	20	1	1	NUM
ejpam-4734	118	21	)	)	PUNCT
ejpam-4734	118	22	f	f	PROPN
ejpam-4734	118	23	is	be	AUX
ejpam-4734	118	24	upper	upper	ADJ
ejpam-4734	118	25	weakly	weakly	ADJ
ejpam-4734	118	26	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	118	27	;	;	PUNCT
ejpam-4734	118	28	(	(	PUNCT
ejpam-4734	118	29	2	2	NUM
ejpam-4734	118	30	)	)	PUNCT
ejpam-4734	118	31	f+(v	f+(v	NOUN
ejpam-4734	118	32	)	)	PUNCT
ejpam-4734	119	1	⊆	⊆	NUM
ejpam-4734	119	2	cl⋆(int(cl⋆(f+(cl⋆(v	cl⋆(int(cl⋆(f+(cl⋆(v	NOUN
ejpam-4734	119	3	)	)	PUNCT
ejpam-4734	119	4	)	)	PUNCT
ejpam-4734	119	5	)	)	PUNCT
ejpam-4734	119	6	)	)	PUNCT
ejpam-4734	119	7	)	)	PUNCT
ejpam-4734	119	8	for	for	ADP
ejpam-4734	119	9	every	every	DET
ejpam-4734	119	10	⋆-open	⋆-open	NOUN
ejpam-4734	119	11	set	set	VERB
ejpam-4734	119	12	v	v	NOUN
ejpam-4734	119	13	of	of	ADP
ejpam-4734	119	14	y	y	PROPN
ejpam-4734	119	15	;	;	PUNCT
ejpam-4734	119	16	(	(	PUNCT
ejpam-4734	119	17	3	3	X
ejpam-4734	119	18	)	)	PUNCT
ejpam-4734	119	19	int⋆(cl(int⋆(f−(v	int⋆(cl(int⋆(f−(v	NOUN
ejpam-4734	119	20	)	)	PUNCT
ejpam-4734	119	21	)	)	PUNCT
ejpam-4734	119	22	)	)	PUNCT
ejpam-4734	119	23	)	)	PUNCT
ejpam-4734	120	1	⊆	⊆	NUM
ejpam-4734	120	2	f−(cl⋆(v	f−(cl⋆(v	NOUN
ejpam-4734	120	3	)	)	PUNCT
ejpam-4734	120	4	)	)	PUNCT
ejpam-4734	120	5	for	for	ADP
ejpam-4734	120	6	every	every	DET
ejpam-4734	120	7	⋆-open	⋆-open	NOUN
ejpam-4734	120	8	set	set	VERB
ejpam-4734	120	9	v	v	NOUN
ejpam-4734	120	10	of	of	ADP
ejpam-4734	120	11	y	y	PROPN
ejpam-4734	120	12	;	;	PUNCT
ejpam-4734	120	13	(	(	PUNCT
ejpam-4734	120	14	4	4	X
ejpam-4734	120	15	)	)	PUNCT
ejpam-4734	120	16	int⋆(cl(int⋆(f−(int⋆(k	int⋆(cl(int⋆(f−(int⋆(k	ADJ
ejpam-4734	120	17	)	)	PUNCT
ejpam-4734	120	18	)	)	PUNCT
ejpam-4734	120	19	)	)	PUNCT
ejpam-4734	120	20	)	)	PUNCT
ejpam-4734	120	21	)	)	PUNCT
ejpam-4734	121	1	⊆	⊆	X
ejpam-4734	121	2	f−(k	f−(k	PROPN
ejpam-4734	121	3	)	)	PUNCT
ejpam-4734	121	4	for	for	ADP
ejpam-4734	121	5	every	every	DET
ejpam-4734	121	6	⋆-closed	⋆-close	VERB
ejpam-4734	121	7	set	set	NOUN
ejpam-4734	121	8	k	k	PROPN
ejpam-4734	121	9	of	of	ADP
ejpam-4734	121	10	y	y	PROPN
ejpam-4734	121	11	;	;	PUNCT
ejpam-4734	121	12	(	(	PUNCT
ejpam-4734	121	13	5	5	X
ejpam-4734	121	14	)	)	PUNCT
ejpam-4734	121	15	sβcli	sβcli	NOUN
ejpam-4734	121	16	(	(	PUNCT
ejpam-4734	121	17	f−(int⋆(k	f−(int⋆(k	ADJ
ejpam-4734	121	18	)	)	PUNCT
ejpam-4734	121	19	)	)	PUNCT
ejpam-4734	121	20	)	)	PUNCT
ejpam-4734	122	1	⊆	⊆	X
ejpam-4734	122	2	f−(k	f−(k	PROPN
ejpam-4734	122	3	)	)	PUNCT
ejpam-4734	122	4	for	for	ADP
ejpam-4734	122	5	every	every	DET
ejpam-4734	122	6	⋆-closed	⋆-close	VERB
ejpam-4734	122	7	set	set	NOUN
ejpam-4734	122	8	k	k	PROPN
ejpam-4734	122	9	of	of	ADP
ejpam-4734	122	10	y	y	PROPN
ejpam-4734	122	11	;	;	PUNCT
ejpam-4734	122	12	(	(	PUNCT
ejpam-4734	122	13	6	6	X
ejpam-4734	122	14	)	)	PUNCT
ejpam-4734	122	15	sβcli	sβcli	NOUN
ejpam-4734	122	16	(	(	PUNCT
ejpam-4734	122	17	f−(int⋆(cl⋆(b	f−(int⋆(cl⋆(b	PROPN
ejpam-4734	122	18	)	)	PUNCT
ejpam-4734	122	19	)	)	PUNCT
ejpam-4734	122	20	)	)	PUNCT
ejpam-4734	122	21	)	)	PUNCT
ejpam-4734	122	22	⊆	⊆	NUM
ejpam-4734	122	23	f−(cl⋆(b	f−(cl⋆(b	NOUN
ejpam-4734	122	24	)	)	PUNCT
ejpam-4734	122	25	)	)	PUNCT
ejpam-4734	122	26	for	for	ADP
ejpam-4734	122	27	every	every	DET
ejpam-4734	122	28	subset	subset	NOUN
ejpam-4734	122	29	b	b	PROPN
ejpam-4734	122	30	of	of	ADP
ejpam-4734	122	31	y	y	PROPN
ejpam-4734	122	32	;	;	PUNCT
ejpam-4734	122	33	(	(	PUNCT
ejpam-4734	122	34	7	7	X
ejpam-4734	122	35	)	)	PUNCT
ejpam-4734	122	36	f+(int⋆(b	f+(int⋆(b	NOUN
ejpam-4734	122	37	)	)	PUNCT
ejpam-4734	122	38	)	)	PUNCT
ejpam-4734	123	1	⊆	⊆	NUM
ejpam-4734	123	2	sβinti	sβinti	NOUN
ejpam-4734	123	3	(	(	PUNCT
ejpam-4734	123	4	f+(cl⋆(int⋆(b	f+(cl⋆(int⋆(b	NOUN
ejpam-4734	123	5	)	)	PUNCT
ejpam-4734	123	6	)	)	PUNCT
ejpam-4734	123	7	)	)	PUNCT
ejpam-4734	123	8	)	)	PUNCT
ejpam-4734	123	9	for	for	ADP
ejpam-4734	123	10	every	every	DET
ejpam-4734	123	11	subset	subset	NOUN
ejpam-4734	123	12	b	b	PROPN
ejpam-4734	123	13	of	of	ADP
ejpam-4734	123	14	y	y	PROPN
ejpam-4734	123	15	;	;	PUNCT
ejpam-4734	123	16	(	(	PUNCT
ejpam-4734	123	17	8)	8)	NUM
ejpam-4734	123	18	f+(v	f+(v	NOUN
ejpam-4734	123	19	)	)	PUNCT
ejpam-4734	123	20	⊆	⊆	NUM
ejpam-4734	123	21	sβinti	sβinti	NOUN
ejpam-4734	123	22	(	(	PUNCT
ejpam-4734	123	23	f+(cl⋆(v	f+(cl⋆(v	PROPN
ejpam-4734	123	24	)	)	PUNCT
ejpam-4734	123	25	)	)	PUNCT
ejpam-4734	123	26	)	)	PUNCT
ejpam-4734	123	27	for	for	ADP
ejpam-4734	123	28	every	every	DET
ejpam-4734	123	29	⋆-open	⋆-open	NOUN
ejpam-4734	123	30	set	set	VERB
ejpam-4734	123	31	v	v	NOUN
ejpam-4734	123	32	of	of	ADP
ejpam-4734	123	33	y	y	PROPN
ejpam-4734	123	34	;	;	PUNCT
ejpam-4734	123	35	(	(	PUNCT
ejpam-4734	123	36	9	9	X
ejpam-4734	123	37	)	)	PUNCT
ejpam-4734	123	38	sβcli	sβcli	NOUN
ejpam-4734	123	39	(	(	PUNCT
ejpam-4734	123	40	f−(v	f−(v	NOUN
ejpam-4734	123	41	)	)	PUNCT
ejpam-4734	123	42	)	)	PUNCT
ejpam-4734	124	1	⊆	⊆	NUM
ejpam-4734	124	2	f−(cl⋆(v	f−(cl⋆(v	NOUN
ejpam-4734	124	3	)	)	PUNCT
ejpam-4734	124	4	)	)	PUNCT
ejpam-4734	124	5	for	for	ADP
ejpam-4734	124	6	every	every	DET
ejpam-4734	124	7	⋆-open	⋆-open	NOUN
ejpam-4734	124	8	set	set	VERB
ejpam-4734	124	9	v	v	NOUN
ejpam-4734	124	10	of	of	ADP
ejpam-4734	124	11	y	y	PROPN
ejpam-4734	124	12	.	.	PUNCT
ejpam-4734	125	1	proof	proof	NOUN
ejpam-4734	125	2	.	.	PUNCT
ejpam-4734	126	1	(	(	PUNCT
ejpam-4734	126	2	1	1	X
ejpam-4734	126	3	)	)	PUNCT
ejpam-4734	126	4	⇒	⇒	NOUN
ejpam-4734	126	5	(	(	PUNCT
ejpam-4734	126	6	2	2	NUM
ejpam-4734	126	7	):	):	PUNCT
ejpam-4734	126	8	let	let	VERB
ejpam-4734	126	9	v	v	PART
ejpam-4734	126	10	be	be	AUX
ejpam-4734	126	11	any	any	DET
ejpam-4734	126	12	⋆-open	⋆-open	ADJ
ejpam-4734	126	13	set	set	NOUN
ejpam-4734	126	14	of	of	ADP
ejpam-4734	126	15	y	y	PROPN
ejpam-4734	126	16	and	and	CCONJ
ejpam-4734	126	17	x	x	PROPN
ejpam-4734	126	18	∈	∈	PROPN
ejpam-4734	126	19	f+(v	f+(v	NOUN
ejpam-4734	126	20	)	)	PUNCT
ejpam-4734	126	21	.	.	PUNCT
ejpam-4734	127	1	then	then	ADV
ejpam-4734	127	2	,	,	PUNCT
ejpam-4734	127	3	f	f	PROPN
ejpam-4734	127	4	(	(	PUNCT
ejpam-4734	127	5	x	x	X
ejpam-4734	127	6	)	)	PUNCT
ejpam-4734	127	7	⊆	⊆	NUM
ejpam-4734	127	8	v	v	NOUN
ejpam-4734	127	9	and	and	CCONJ
ejpam-4734	127	10	by	by	ADP
ejpam-4734	127	11	theorem	theorem	NOUN
ejpam-4734	127	12	1	1	NUM
ejpam-4734	127	13	,	,	PUNCT
ejpam-4734	127	14	x	x	SYM
ejpam-4734	127	15	∈	∈	NOUN
ejpam-4734	127	16	sβinti	sβinti	NOUN
ejpam-4734	127	17	(	(	PUNCT
ejpam-4734	127	18	f+(cl⋆(v	f+(cl⋆(v	PROPN
ejpam-4734	127	19	)	)	PUNCT
ejpam-4734	127	20	)	)	PUNCT
ejpam-4734	127	21	)	)	PUNCT
ejpam-4734	127	22	and	and	CCONJ
ejpam-4734	127	23	hence	hence	ADV
ejpam-4734	127	24	f+(v	f+(v	NOUN
ejpam-4734	127	25	)	)	PUNCT
ejpam-4734	128	1	⊆	⊆	NUM
ejpam-4734	128	2	cl⋆(int(cl⋆(f+(cl⋆(v	cl⋆(int(cl⋆(f+(cl⋆(v	NOUN
ejpam-4734	128	3	)	)	PUNCT
ejpam-4734	128	4	)	)	PUNCT
ejpam-4734	128	5	)	)	PUNCT
ejpam-4734	128	6	)	)	PUNCT
ejpam-4734	128	7	)	)	PUNCT
ejpam-4734	128	8	by	by	ADP
ejpam-4734	128	9	lemma	lemma	PROPN
ejpam-4734	128	10	2	2	NUM
ejpam-4734	128	11	.	.	PUNCT
ejpam-4734	128	12	(	(	PUNCT
ejpam-4734	128	13	2	2	X
ejpam-4734	128	14	)	)	PUNCT
ejpam-4734	128	15	⇒	⇒	NOUN
ejpam-4734	128	16	(	(	PUNCT
ejpam-4734	128	17	3	3	NUM
ejpam-4734	128	18	):	):	PUNCT
ejpam-4734	128	19	let	let	VERB
ejpam-4734	128	20	v	v	PART
ejpam-4734	128	21	be	be	AUX
ejpam-4734	128	22	any	any	DET
ejpam-4734	128	23	⋆-open	⋆-open	ADJ
ejpam-4734	128	24	set	set	NOUN
ejpam-4734	128	25	of	of	ADP
ejpam-4734	128	26	y	y	PROPN
ejpam-4734	128	27	.	.	PUNCT
ejpam-4734	129	1	thus	thus	ADV
ejpam-4734	129	2	,	,	PUNCT
ejpam-4734	129	3	by	by	ADP
ejpam-4734	129	4	(	(	PUNCT
ejpam-4734	129	5	2	2	NUM
ejpam-4734	129	6	)	)	PUNCT
ejpam-4734	129	7	,	,	PUNCT
ejpam-4734	129	8	we	we	PRON
ejpam-4734	129	9	have	have	VERB
ejpam-4734	129	10	x	x	X
ejpam-4734	129	11	−	−	PROPN
ejpam-4734	129	12	f−(cl⋆(v	f−(cl⋆(v	NOUN
ejpam-4734	129	13	)	)	PUNCT
ejpam-4734	129	14	)	)	PUNCT
ejpam-4734	130	1	=	=	PUNCT
ejpam-4734	131	1	f+(y	f+(y	NOUN
ejpam-4734	131	2	−	−	PROPN
ejpam-4734	131	3	cl⋆(v	cl⋆(v	PROPN
ejpam-4734	131	4	)	)	PUNCT
ejpam-4734	131	5	)	)	PUNCT
ejpam-4734	132	1	⊆	⊆	X
ejpam-4734	132	2	cl⋆(int(cl⋆(f+(cl⋆(y	cl⋆(int(cl⋆(f+(cl⋆(y	NOUN
ejpam-4734	132	3	−	−	NOUN
ejpam-4734	132	4	cl⋆(v	cl⋆(v	NOUN
ejpam-4734	132	5	)	)	PUNCT
ejpam-4734	132	6	)	)	PUNCT
ejpam-4734	132	7	)	)	PUNCT
ejpam-4734	132	8	)	)	PUNCT
ejpam-4734	132	9	)	)	PUNCT
ejpam-4734	132	10	)	)	PUNCT
ejpam-4734	133	1	=	=	PUNCT
ejpam-4734	133	2	cl⋆(int(cl⋆(f+(y	cl⋆(int(cl⋆(f+(y	NOUN
ejpam-4734	133	3	−	−	NOUN
ejpam-4734	133	4	int⋆(cl⋆(v	int⋆(cl⋆(v	NOUN
ejpam-4734	133	5	)	)	PUNCT
ejpam-4734	133	6	)	)	PUNCT
ejpam-4734	133	7	)	)	PUNCT
ejpam-4734	133	8	)	)	PUNCT
ejpam-4734	133	9	)	)	PUNCT
ejpam-4734	133	10	)	)	PUNCT
ejpam-4734	134	1	⊆	⊆	X
ejpam-4734	134	2	cl⋆(int(cl⋆(f+(y	cl⋆(int(cl⋆(f+(y	NOUN
ejpam-4734	134	3	−	−	NOUN
ejpam-4734	134	4	v	v	NOUN
ejpam-4734	134	5	)	)	PUNCT
ejpam-4734	134	6	)	)	PUNCT
ejpam-4734	134	7	)	)	PUNCT
ejpam-4734	134	8	)	)	PUNCT
ejpam-4734	135	1	=	=	PUNCT
ejpam-4734	135	2	cl⋆(int(cl⋆(x	cl⋆(int(cl⋆(x	PROPN
ejpam-4734	135	3	−	−	PROPN
ejpam-4734	135	4	f−(v	f−(v	NOUN
ejpam-4734	135	5	)	)	PUNCT
ejpam-4734	135	6	)	)	PUNCT
ejpam-4734	135	7	)	)	PUNCT
ejpam-4734	135	8	)	)	PUNCT
ejpam-4734	136	1	=	=	PUNCT
ejpam-4734	136	2	x	x	PUNCT
ejpam-4734	136	3	−	−	PROPN
ejpam-4734	136	4	int⋆(cl(int⋆(f−(v	int⋆(cl(int⋆(f−(v	NOUN
ejpam-4734	136	5	)	)	PUNCT
ejpam-4734	136	6	)	)	PUNCT
ejpam-4734	136	7	)	)	PUNCT
ejpam-4734	136	8	)	)	PUNCT
ejpam-4734	136	9	and	and	CCONJ
ejpam-4734	136	10	hence	hence	ADV
ejpam-4734	136	11	int⋆(cl(int⋆(f−(v	int⋆(cl(int⋆(f−(v	NOUN
ejpam-4734	136	12	)	)	PUNCT
ejpam-4734	136	13	)	)	PUNCT
ejpam-4734	136	14	)	)	PUNCT
ejpam-4734	136	15	)	)	PUNCT
ejpam-4734	137	1	⊆	⊆	NUM
ejpam-4734	137	2	f−(cl⋆(v	f−(cl⋆(v	NOUN
ejpam-4734	137	3	)	)	PUNCT
ejpam-4734	137	4	)	)	PUNCT
ejpam-4734	137	5	.	.	PUNCT
ejpam-4734	138	1	(	(	PUNCT
ejpam-4734	138	2	3	3	X
ejpam-4734	138	3	)	)	PUNCT
ejpam-4734	138	4	⇒	⇒	NOUN
ejpam-4734	138	5	(	(	PUNCT
ejpam-4734	138	6	4	4	NUM
ejpam-4734	138	7	):	):	PUNCT
ejpam-4734	138	8	let	let	VERB
ejpam-4734	138	9	k	k	PRON
ejpam-4734	138	10	be	be	AUX
ejpam-4734	138	11	any	any	DET
ejpam-4734	138	12	⋆-closed	⋆-close	VERB
ejpam-4734	138	13	set	set	NOUN
ejpam-4734	138	14	of	of	ADP
ejpam-4734	138	15	y	y	PROPN
ejpam-4734	138	16	.	.	PUNCT
ejpam-4734	139	1	then	then	ADV
ejpam-4734	139	2	,	,	PUNCT
ejpam-4734	139	3	int⋆(k	int⋆(k	PUNCT
ejpam-4734	139	4	)	)	PUNCT
ejpam-4734	139	5	is	be	AUX
ejpam-4734	139	6	⋆-open	⋆-open	ADJ
ejpam-4734	139	7	in	in	ADP
ejpam-4734	139	8	y	y	PROPN
ejpam-4734	139	9	and	and	CCONJ
ejpam-4734	139	10	so	so	ADV
ejpam-4734	139	11	int⋆(cl(int⋆(f−(int⋆(k	int⋆(cl(int⋆(f−(int⋆(k	ADJ
ejpam-4734	139	12	)	)	PUNCT
ejpam-4734	139	13	)	)	PUNCT
ejpam-4734	139	14	)	)	PUNCT
ejpam-4734	139	15	)	)	PUNCT
ejpam-4734	139	16	)	)	PUNCT
ejpam-4734	140	1	⊆	⊆	X
ejpam-4734	140	2	f−(cl⋆(int⋆(k	f−(cl⋆(int⋆(k	NOUN
ejpam-4734	140	3	)	)	PUNCT
ejpam-4734	140	4	)	)	PUNCT
ejpam-4734	140	5	)	)	PUNCT
ejpam-4734	141	1	⊆	⊆	X
ejpam-4734	141	2	f−(cl⋆(k	f−(cl⋆(k	NOUN
ejpam-4734	141	3	)	)	PUNCT
ejpam-4734	141	4	)	)	PUNCT
ejpam-4734	142	1	=	=	SYM
ejpam-4734	142	2	f−(k	f−(k	PROPN
ejpam-4734	142	3	)	)	PUNCT
ejpam-4734	142	4	.	.	PUNCT
ejpam-4734	143	1	(	(	PUNCT
ejpam-4734	143	2	4	4	X
ejpam-4734	143	3	)	)	PUNCT
ejpam-4734	143	4	⇒	⇒	NOUN
ejpam-4734	143	5	(	(	PUNCT
ejpam-4734	143	6	5	5	NUM
ejpam-4734	143	7	):	):	PUNCT
ejpam-4734	143	8	let	let	VERB
ejpam-4734	143	9	k	k	PRON
ejpam-4734	143	10	be	be	AUX
ejpam-4734	143	11	any	any	DET
ejpam-4734	143	12	⋆-closed	⋆-close	VERB
ejpam-4734	143	13	set	set	NOUN
ejpam-4734	143	14	of	of	ADP
ejpam-4734	143	15	y	y	PROPN
ejpam-4734	143	16	.	.	PUNCT
ejpam-4734	144	1	then	then	ADV
ejpam-4734	144	2	,	,	PUNCT
ejpam-4734	144	3	we	we	PRON
ejpam-4734	144	4	have	have	VERB
ejpam-4734	144	5	int⋆(cl(int⋆(f−(int⋆(k	int⋆(cl(int⋆(f−(int⋆(k	VERB
ejpam-4734	144	6	)	)	PUNCT
ejpam-4734	144	7	)	)	PUNCT
ejpam-4734	144	8	)	)	PUNCT
ejpam-4734	144	9	)	)	PUNCT
ejpam-4734	144	10	)	)	PUNCT
ejpam-4734	145	1	⊆	⊆	X
ejpam-4734	145	2	f−(k	f−(k	NOUN
ejpam-4734	145	3	)	)	PUNCT
ejpam-4734	145	4	and	and	CCONJ
ejpam-4734	145	5	f−(int⋆(k	f−(int⋆(k	ADJ
ejpam-4734	145	6	)	)	PUNCT
ejpam-4734	145	7	)	)	PUNCT
ejpam-4734	146	1	⊆	⊆	NUM
ejpam-4734	146	2	f−(k	f−(k	PROPN
ejpam-4734	146	3	)	)	PUNCT
ejpam-4734	146	4	.	.	PUNCT
ejpam-4734	147	1	thus	thus	ADV
ejpam-4734	147	2	,	,	PUNCT
ejpam-4734	147	3	by	by	ADP
ejpam-4734	147	4	lemma	lemma	PROPN
ejpam-4734	147	5	2	2	NUM
ejpam-4734	147	6	,	,	PUNCT
ejpam-4734	147	7	sβi	sβi	NOUN
ejpam-4734	147	8	cl(f−(int⋆(k	cl(f−(int⋆(k	NUM
ejpam-4734	147	9	)	)	PUNCT
ejpam-4734	147	10	)	)	PUNCT
ejpam-4734	147	11	)	)	PUNCT
ejpam-4734	148	1	⊆	⊆	NUM
ejpam-4734	148	2	f−(k	f−(k	PROPN
ejpam-4734	148	3	)	)	PUNCT
ejpam-4734	148	4	.	.	PUNCT
ejpam-4734	149	1	(	(	PUNCT
ejpam-4734	149	2	5	5	X
ejpam-4734	149	3	)	)	PUNCT
ejpam-4734	149	4	⇒	⇒	NOUN
ejpam-4734	149	5	(	(	PUNCT
ejpam-4734	149	6	6	6	NUM
ejpam-4734	149	7	):	):	PUNCT
ejpam-4734	149	8	let	let	VERB
ejpam-4734	149	9	b	b	X
ejpam-4734	149	10	be	be	AUX
ejpam-4734	149	11	any	any	DET
ejpam-4734	149	12	subset	subset	NOUN
ejpam-4734	149	13	of	of	ADP
ejpam-4734	149	14	y	y	PROPN
ejpam-4734	149	15	.	.	PUNCT
ejpam-4734	150	1	then	then	ADV
ejpam-4734	150	2	,	,	PUNCT
ejpam-4734	150	3	cl⋆(b	cl⋆(b	NOUN
ejpam-4734	150	4	)	)	PUNCT
ejpam-4734	150	5	is	be	AUX
ejpam-4734	150	6	⋆-closed	⋆-close	VERB
ejpam-4734	150	7	in	in	ADP
ejpam-4734	150	8	y	y	PROPN
ejpam-4734	150	9	and	and	CCONJ
ejpam-4734	150	10	by	by	ADP
ejpam-4734	150	11	(	(	PUNCT
ejpam-4734	150	12	5	5	NUM
ejpam-4734	150	13	)	)	PUNCT
ejpam-4734	150	14	,	,	PUNCT
ejpam-4734	150	15	sβcli	sβcli	NOUN
ejpam-4734	150	16	(	(	PUNCT
ejpam-4734	150	17	f−(int⋆(cl⋆(b	f−(int⋆(cl⋆(b	PROPN
ejpam-4734	150	18	)	)	PUNCT
ejpam-4734	150	19	)	)	PUNCT
ejpam-4734	150	20	)	)	PUNCT
ejpam-4734	150	21	)	)	PUNCT
ejpam-4734	151	1	⊆	⊆	NUM
ejpam-4734	151	2	f−(cl⋆(b	f−(cl⋆(b	NOUN
ejpam-4734	151	3	)	)	PUNCT
ejpam-4734	151	4	)	)	PUNCT
ejpam-4734	151	5	.	.	PUNCT
ejpam-4734	152	1	(	(	PUNCT
ejpam-4734	152	2	6	6	X
ejpam-4734	152	3	)	)	PUNCT
ejpam-4734	152	4	⇒	⇒	NOUN
ejpam-4734	152	5	(	(	PUNCT
ejpam-4734	152	6	7	7	NUM
ejpam-4734	152	7	):	):	PUNCT
ejpam-4734	152	8	let	let	VERB
ejpam-4734	152	9	b	b	X
ejpam-4734	152	10	be	be	AUX
ejpam-4734	152	11	any	any	DET
ejpam-4734	152	12	subset	subset	NOUN
ejpam-4734	152	13	of	of	ADP
ejpam-4734	152	14	y	y	PROPN
ejpam-4734	152	15	.	.	PUNCT
ejpam-4734	153	1	by	by	ADP
ejpam-4734	153	2	(	(	PUNCT
ejpam-4734	153	3	6	6	NUM
ejpam-4734	153	4	)	)	PUNCT
ejpam-4734	153	5	,	,	PUNCT
ejpam-4734	153	6	f+(int⋆(b	f+(int⋆(b	NOUN
ejpam-4734	153	7	)	)	PUNCT
ejpam-4734	153	8	)	)	PUNCT
ejpam-4734	154	1	=	=	PUNCT
ejpam-4734	155	1	x	x	PUNCT
ejpam-4734	155	2	−	−	NOUN
ejpam-4734	155	3	f−(cl⋆(y	f−(cl⋆(y	X
ejpam-4734	155	4	−b	−b	NOUN
ejpam-4734	155	5	)	)	PUNCT
ejpam-4734	155	6	)	)	PUNCT
ejpam-4734	156	1	⊆	⊆	NUM
ejpam-4734	156	2	x	x	SYM
ejpam-4734	156	3	−	−	PRON
ejpam-4734	156	4	sβcli	sβcli	NOUN
ejpam-4734	156	5	(	(	PUNCT
ejpam-4734	156	6	f−(int⋆(cl⋆(y	f−(int⋆(cl⋆(y	INTJ
ejpam-4734	156	7	−b	−b	ADJ
ejpam-4734	156	8	)	)	PUNCT
ejpam-4734	156	9	)	)	PUNCT
ejpam-4734	156	10	)	)	PUNCT
ejpam-4734	156	11	)	)	PUNCT
ejpam-4734	156	12	c.	c.	PROPN
ejpam-4734	156	13	boonpok	boonpok	PROPN
ejpam-4734	156	14	,	,	PUNCT
ejpam-4734	156	15	j.	j.	PROPN
ejpam-4734	156	16	khampakdee	khampakdee	PROPN
ejpam-4734	156	17	/	/	PUNCT
ejpam-4734	156	18	eur	eur	PROPN
ejpam-4734	156	19	.	.	PUNCT
ejpam-4734	157	1	j.	j.	PROPN
ejpam-4734	157	2	pure	pure	PROPN
ejpam-4734	157	3	appl	appl	PROPN
ejpam-4734	157	4	.	.	PROPN
ejpam-4734	157	5	math	math	PROPN
ejpam-4734	157	6	,	,	PUNCT
ejpam-4734	157	7	16	16	NUM
ejpam-4734	157	8	(	(	PUNCT
ejpam-4734	157	9	4	4	NUM
ejpam-4734	157	10	)	)	PUNCT
ejpam-4734	157	11	(	(	PUNCT
ejpam-4734	157	12	2023	2023	NUM
ejpam-4734	157	13	)	)	PUNCT
ejpam-4734	157	14	,	,	PUNCT
ejpam-4734	157	15	2544	2544	NUM
ejpam-4734	157	16	-	-	SYM
ejpam-4734	157	17	2556	2556	NUM
ejpam-4734	157	18	2549	2549	NUM
ejpam-4734	157	19	=	=	SYM
ejpam-4734	157	20	sβinti	sβinti	X
ejpam-4734	157	21	(	(	PUNCT
ejpam-4734	157	22	f+(cl⋆(int⋆(b	f+(cl⋆(int⋆(b	NOUN
ejpam-4734	157	23	)	)	PUNCT
ejpam-4734	157	24	)	)	PUNCT
ejpam-4734	157	25	)	)	PUNCT
ejpam-4734	157	26	)	)	PUNCT
ejpam-4734	157	27	.	.	PUNCT
ejpam-4734	158	1	(	(	PUNCT
ejpam-4734	158	2	7	7	X
ejpam-4734	158	3	)	)	PUNCT
ejpam-4734	158	4	⇒	⇒	NOUN
ejpam-4734	158	5	(	(	PUNCT
ejpam-4734	158	6	8)	8)	NUM
ejpam-4734	158	7	:	:	PUNCT
ejpam-4734	158	8	the	the	DET
ejpam-4734	158	9	proof	proof	NOUN
ejpam-4734	158	10	is	be	AUX
ejpam-4734	158	11	obvious	obvious	ADJ
ejpam-4734	158	12	.	.	PUNCT
ejpam-4734	159	1	(	(	PUNCT
ejpam-4734	159	2	8)	8)	NUM
ejpam-4734	159	3	⇒	⇒	NOUN
ejpam-4734	159	4	(	(	PUNCT
ejpam-4734	159	5	9	9	NUM
ejpam-4734	159	6	):	):	PUNCT
ejpam-4734	159	7	let	let	VERB
ejpam-4734	159	8	v	v	PART
ejpam-4734	159	9	be	be	AUX
ejpam-4734	159	10	any	any	DET
ejpam-4734	159	11	⋆-open	⋆-open	ADJ
ejpam-4734	159	12	set	set	NOUN
ejpam-4734	159	13	of	of	ADP
ejpam-4734	159	14	y	y	PROPN
ejpam-4734	159	15	.	.	PUNCT
ejpam-4734	160	1	thus	thus	ADV
ejpam-4734	160	2	,	,	PUNCT
ejpam-4734	160	3	by	by	ADP
ejpam-4734	160	4	(	(	PUNCT
ejpam-4734	160	5	8)	8)	NUM
ejpam-4734	160	6	,	,	PUNCT
ejpam-4734	160	7	we	we	PRON
ejpam-4734	160	8	have	have	VERB
ejpam-4734	160	9	sβcli	sβcli	NOUN
ejpam-4734	160	10	(	(	PUNCT
ejpam-4734	160	11	f−(v	f−(v	NOUN
ejpam-4734	160	12	)	)	PUNCT
ejpam-4734	160	13	)	)	PUNCT
ejpam-4734	161	1	⊆	⊆	X
ejpam-4734	161	2	sβcli	sβcli	NOUN
ejpam-4734	161	3	(	(	PUNCT
ejpam-4734	161	4	f−(int⋆(cl⋆(v	f−(int⋆(cl⋆(v	PROPN
ejpam-4734	161	5	)	)	PUNCT
ejpam-4734	161	6	)	)	PUNCT
ejpam-4734	161	7	)	)	PUNCT
ejpam-4734	161	8	)	)	PUNCT
ejpam-4734	162	1	=	=	SYM
ejpam-4734	162	2	sβcli	sβcli	NOUN
ejpam-4734	162	3	(	(	PUNCT
ejpam-4734	162	4	x	x	SYM
ejpam-4734	162	5	−	−	NOUN
ejpam-4734	162	6	f+(y	f+(y	NOUN
ejpam-4734	162	7	−	−	PROPN
ejpam-4734	162	8	int⋆(cl⋆(v	int⋆(cl⋆(v	PROPN
ejpam-4734	162	9	)	)	PUNCT
ejpam-4734	162	10	)	)	PUNCT
ejpam-4734	162	11	)	)	PUNCT
ejpam-4734	162	12	)	)	PUNCT
ejpam-4734	163	1	=	=	PUNCT
ejpam-4734	163	2	x	x	PUNCT
ejpam-4734	164	1	−	−	NOUN
ejpam-4734	164	2	sβinti	sβinti	NOUN
ejpam-4734	164	3	(	(	PUNCT
ejpam-4734	164	4	f+(y	f+(y	PROPN
ejpam-4734	164	5	−	−	PROPN
ejpam-4734	164	6	int⋆(cl⋆(v	int⋆(cl⋆(v	PROPN
ejpam-4734	164	7	)	)	PUNCT
ejpam-4734	164	8	)	)	PUNCT
ejpam-4734	164	9	)	)	PUNCT
ejpam-4734	164	10	)	)	PUNCT
ejpam-4734	165	1	=	=	PUNCT
ejpam-4734	165	2	x	x	PUNCT
ejpam-4734	166	1	−	−	PROPN
ejpam-4734	166	2	sβinti	sβinti	NOUN
ejpam-4734	166	3	(	(	PUNCT
ejpam-4734	166	4	f+(cl⋆(y	f+(cl⋆(y	NOUN
ejpam-4734	166	5	−	−	NOUN
ejpam-4734	166	6	cl⋆(v	cl⋆(v	NOUN
ejpam-4734	166	7	)	)	PUNCT
ejpam-4734	166	8	)	)	PUNCT
ejpam-4734	166	9	)	)	PUNCT
ejpam-4734	166	10	)	)	PUNCT
ejpam-4734	167	1	⊆	⊆	NUM
ejpam-4734	167	2	x	x	SYM
ejpam-4734	167	3	−	−	NOUN
ejpam-4734	167	4	f+(y	f+(y	NOUN
ejpam-4734	167	5	−	−	PROPN
ejpam-4734	167	6	cl⋆(v	cl⋆(v	NOUN
ejpam-4734	167	7	)	)	PUNCT
ejpam-4734	167	8	)	)	PUNCT
ejpam-4734	168	1	=	=	PUNCT
ejpam-4734	168	2	f−(cl⋆(v	f−(cl⋆(v	NOUN
ejpam-4734	168	3	)	)	PUNCT
ejpam-4734	168	4	)	)	PUNCT
ejpam-4734	168	5	.	.	PUNCT
ejpam-4734	169	1	(	(	PUNCT
ejpam-4734	169	2	9	9	X
ejpam-4734	169	3	)	)	PUNCT
ejpam-4734	169	4	⇒	⇒	NOUN
ejpam-4734	169	5	(	(	PUNCT
ejpam-4734	169	6	1	1	NUM
ejpam-4734	169	7	):	):	PUNCT
ejpam-4734	169	8	let	let	VERB
ejpam-4734	169	9	x	x	PUNCT
ejpam-4734	169	10	∈	∈	PROPN
ejpam-4734	169	11	x	x	X
ejpam-4734	169	12	and	and	CCONJ
ejpam-4734	169	13	v	v	AUX
ejpam-4734	169	14	be	be	AUX
ejpam-4734	169	15	any	any	DET
ejpam-4734	169	16	⋆-open	⋆-open	ADJ
ejpam-4734	169	17	set	set	NOUN
ejpam-4734	169	18	of	of	ADP
ejpam-4734	169	19	y	y	PROPN
ejpam-4734	169	20	containing	contain	VERB
ejpam-4734	169	21	f	f	PROPN
ejpam-4734	169	22	(	(	PUNCT
ejpam-4734	169	23	x	x	NOUN
ejpam-4734	169	24	)	)	PUNCT
ejpam-4734	169	25	.	.	PUNCT
ejpam-4734	170	1	by	by	ADP
ejpam-4734	170	2	(	(	PUNCT
ejpam-4734	170	3	9	9	NUM
ejpam-4734	170	4	)	)	PUNCT
ejpam-4734	170	5	,	,	PUNCT
ejpam-4734	170	6	x	x	PUNCT
ejpam-4734	170	7	∈	∈	PROPN
ejpam-4734	170	8	f+(v	f+(v	NOUN
ejpam-4734	170	9	)	)	PUNCT
ejpam-4734	171	1	⊆	⊆	NUM
ejpam-4734	171	2	f+(int⋆(cl⋆(v	f+(int⋆(cl⋆(v	NOUN
ejpam-4734	171	3	)	)	PUNCT
ejpam-4734	171	4	)	)	PUNCT
ejpam-4734	171	5	)	)	PUNCT
ejpam-4734	172	1	=	=	PUNCT
ejpam-4734	173	1	x	x	X
ejpam-4734	173	2	−	−	NOUN
ejpam-4734	173	3	f−(cl⋆(y	f−(cl⋆(y	DET
ejpam-4734	173	4	−	−	PROPN
ejpam-4734	173	5	cl⋆(v	cl⋆(v	NOUN
ejpam-4734	173	6	)	)	PUNCT
ejpam-4734	173	7	)	)	PUNCT
ejpam-4734	173	8	)	)	PUNCT
ejpam-4734	174	1	⊆	⊆	NUM
ejpam-4734	174	2	x	x	SYM
ejpam-4734	174	3	−	−	X
ejpam-4734	174	4	sβcli	sβcli	NOUN
ejpam-4734	174	5	(	(	PUNCT
ejpam-4734	174	6	f−(y	f−(y	NOUN
ejpam-4734	174	7	−	−	NOUN
ejpam-4734	174	8	cl⋆(v	cl⋆(v	NOUN
ejpam-4734	174	9	)	)	PUNCT
ejpam-4734	174	10	)	)	PUNCT
ejpam-4734	174	11	)	)	PUNCT
ejpam-4734	175	1	=	=	PRON
ejpam-4734	175	2	sβinti	sβinti	X
ejpam-4734	175	3	(	(	PUNCT
ejpam-4734	175	4	f+(cl⋆(v	f+(cl⋆(v	PROPN
ejpam-4734	175	5	)	)	PUNCT
ejpam-4734	175	6	)	)	PUNCT
ejpam-4734	175	7	)	)	PUNCT
ejpam-4734	176	1	and	and	CCONJ
ejpam-4734	176	2	hence	hence	ADV
ejpam-4734	176	3	f	f	PROPN
ejpam-4734	176	4	is	be	AUX
ejpam-4734	176	5	upper	upper	ADJ
ejpam-4734	176	6	weakly	weakly	ADV
ejpam-4734	176	7	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	176	8	by	by	ADP
ejpam-4734	176	9	theorem	theorem	NOUN
ejpam-4734	176	10	1	1	NUM
ejpam-4734	176	11	.	.	PUNCT
ejpam-4734	176	12	theorem	theorem	NOUN
ejpam-4734	176	13	4	4	NUM
ejpam-4734	176	14	.	.	X
ejpam-4734	176	15	for	for	ADP
ejpam-4734	176	16	a	a	DET
ejpam-4734	176	17	multifunction	multifunction	NOUN
ejpam-4734	176	18	f	f	NOUN
ejpam-4734	176	19	:	:	PUNCT
ejpam-4734	176	20	(	(	PUNCT
ejpam-4734	176	21	x	x	X
ejpam-4734	176	22	,	,	PUNCT
ejpam-4734	176	23	τ	τ	PROPN
ejpam-4734	176	24	,	,	PUNCT
ejpam-4734	176	25	i	i	NOUN
ejpam-4734	176	26	)	)	PUNCT
ejpam-4734	176	27	→	→	PUNCT
ejpam-4734	176	28	(	(	PUNCT
ejpam-4734	176	29	y	y	PROPN
ejpam-4734	176	30	,	,	PUNCT
ejpam-4734	176	31	σ	σ	PROPN
ejpam-4734	176	32	,	,	PUNCT
ejpam-4734	176	33	j	j	PROPN
ejpam-4734	176	34	)	)	PUNCT
ejpam-4734	176	35	,	,	PUNCT
ejpam-4734	176	36	the	the	DET
ejpam-4734	176	37	following	follow	VERB
ejpam-4734	176	38	properties	property	NOUN
ejpam-4734	176	39	are	be	AUX
ejpam-4734	176	40	equivalent	equivalent	ADJ
ejpam-4734	176	41	:	:	PUNCT
ejpam-4734	176	42	(	(	PUNCT
ejpam-4734	176	43	1	1	X
ejpam-4734	176	44	)	)	PUNCT
ejpam-4734	176	45	f	f	PROPN
ejpam-4734	176	46	is	be	AUX
ejpam-4734	176	47	lower	low	ADJ
ejpam-4734	176	48	weakly	weakly	ADJ
ejpam-4734	176	49	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	176	50	;	;	PUNCT
ejpam-4734	176	51	(	(	PUNCT
ejpam-4734	176	52	2	2	X
ejpam-4734	176	53	)	)	PUNCT
ejpam-4734	176	54	f−(v	f−(v	NOUN
ejpam-4734	176	55	)	)	PUNCT
ejpam-4734	176	56	⊆	⊆	NUM
ejpam-4734	176	57	cl⋆(int(cl⋆(f−(cl⋆(v	cl⋆(int(cl⋆(f−(cl⋆(v	PROPN
ejpam-4734	176	58	)	)	PUNCT
ejpam-4734	176	59	)	)	PUNCT
ejpam-4734	176	60	)	)	PUNCT
ejpam-4734	176	61	)	)	PUNCT
ejpam-4734	176	62	)	)	PUNCT
ejpam-4734	177	1	for	for	ADP
ejpam-4734	177	2	every	every	DET
ejpam-4734	177	3	⋆-open	⋆-open	NOUN
ejpam-4734	177	4	set	set	VERB
ejpam-4734	177	5	v	v	NOUN
ejpam-4734	177	6	of	of	ADP
ejpam-4734	177	7	y	y	PROPN
ejpam-4734	177	8	;	;	PUNCT
ejpam-4734	177	9	(	(	PUNCT
ejpam-4734	177	10	3	3	X
ejpam-4734	177	11	)	)	PUNCT
ejpam-4734	177	12	int⋆(cl(int⋆(f+(v	int⋆(cl(int⋆(f+(v	NOUN
ejpam-4734	177	13	)	)	PUNCT
ejpam-4734	177	14	)	)	PUNCT
ejpam-4734	177	15	)	)	PUNCT
ejpam-4734	177	16	)	)	PUNCT
ejpam-4734	178	1	⊆	⊆	NUM
ejpam-4734	178	2	f+(cl⋆(v	f+(cl⋆(v	PROPN
ejpam-4734	178	3	)	)	PUNCT
ejpam-4734	178	4	)	)	PUNCT
ejpam-4734	178	5	for	for	ADP
ejpam-4734	178	6	every	every	DET
ejpam-4734	178	7	⋆-open	⋆-open	NOUN
ejpam-4734	178	8	set	set	VERB
ejpam-4734	178	9	v	v	NOUN
ejpam-4734	178	10	of	of	ADP
ejpam-4734	178	11	y	y	PROPN
ejpam-4734	178	12	;	;	PUNCT
ejpam-4734	178	13	(	(	PUNCT
ejpam-4734	178	14	4	4	X
ejpam-4734	178	15	)	)	PUNCT
ejpam-4734	178	16	int⋆(cl(int⋆(f+(int⋆(k	int⋆(cl(int⋆(f+(int⋆(k	NOUN
ejpam-4734	178	17	)	)	PUNCT
ejpam-4734	178	18	)	)	PUNCT
ejpam-4734	178	19	)	)	PUNCT
ejpam-4734	178	20	)	)	PUNCT
ejpam-4734	178	21	)	)	PUNCT
ejpam-4734	179	1	⊆	⊆	NUM
ejpam-4734	179	2	f+(k	f+(k	NOUN
ejpam-4734	179	3	)	)	PUNCT
ejpam-4734	179	4	for	for	ADP
ejpam-4734	179	5	every	every	DET
ejpam-4734	179	6	⋆-closed	⋆-close	VERB
ejpam-4734	179	7	set	set	NOUN
ejpam-4734	179	8	k	k	PROPN
ejpam-4734	179	9	of	of	ADP
ejpam-4734	179	10	y	y	PROPN
ejpam-4734	179	11	;	;	PUNCT
ejpam-4734	179	12	(	(	PUNCT
ejpam-4734	179	13	5	5	X
ejpam-4734	179	14	)	)	PUNCT
ejpam-4734	179	15	sβcli	sβcli	NOUN
ejpam-4734	179	16	(	(	PUNCT
ejpam-4734	179	17	f+(int⋆(k	f+(int⋆(k	NOUN
ejpam-4734	179	18	)	)	PUNCT
ejpam-4734	179	19	)	)	PUNCT
ejpam-4734	179	20	)	)	PUNCT
ejpam-4734	180	1	⊆	⊆	NUM
ejpam-4734	180	2	f+(k	f+(k	NOUN
ejpam-4734	180	3	)	)	PUNCT
ejpam-4734	180	4	for	for	ADP
ejpam-4734	180	5	every	every	DET
ejpam-4734	180	6	⋆-closed	⋆-close	VERB
ejpam-4734	180	7	set	set	NOUN
ejpam-4734	180	8	k	k	PROPN
ejpam-4734	180	9	of	of	ADP
ejpam-4734	180	10	y	y	PROPN
ejpam-4734	180	11	;	;	PUNCT
ejpam-4734	180	12	(	(	PUNCT
ejpam-4734	180	13	6	6	X
ejpam-4734	180	14	)	)	PUNCT
ejpam-4734	180	15	sβcli	sβcli	NOUN
ejpam-4734	180	16	(	(	PUNCT
ejpam-4734	180	17	f+(int⋆(cl⋆(b	f+(int⋆(cl⋆(b	NOUN
ejpam-4734	180	18	)	)	PUNCT
ejpam-4734	180	19	)	)	PUNCT
ejpam-4734	180	20	)	)	PUNCT
ejpam-4734	180	21	)	)	PUNCT
ejpam-4734	181	1	⊆	⊆	NUM
ejpam-4734	181	2	f+(cl⋆(b	f+(cl⋆(b	NOUN
ejpam-4734	181	3	)	)	PUNCT
ejpam-4734	181	4	)	)	PUNCT
ejpam-4734	181	5	for	for	ADP
ejpam-4734	181	6	every	every	DET
ejpam-4734	181	7	subset	subset	NOUN
ejpam-4734	181	8	b	b	PROPN
ejpam-4734	181	9	of	of	ADP
ejpam-4734	181	10	y	y	PROPN
ejpam-4734	181	11	;	;	PUNCT
ejpam-4734	181	12	(	(	PUNCT
ejpam-4734	181	13	7	7	X
ejpam-4734	181	14	)	)	PUNCT
ejpam-4734	181	15	f−(int⋆(b	f−(int⋆(b	NOUN
ejpam-4734	181	16	)	)	PUNCT
ejpam-4734	181	17	)	)	PUNCT
ejpam-4734	182	1	⊆	⊆	NUM
ejpam-4734	182	2	sβinti	sβinti	NOUN
ejpam-4734	182	3	(	(	PUNCT
ejpam-4734	182	4	f−(cl⋆(int⋆(b	f−(cl⋆(int⋆(b	NOUN
ejpam-4734	182	5	)	)	PUNCT
ejpam-4734	182	6	)	)	PUNCT
ejpam-4734	182	7	)	)	PUNCT
ejpam-4734	182	8	)	)	PUNCT
ejpam-4734	182	9	for	for	ADP
ejpam-4734	182	10	every	every	DET
ejpam-4734	182	11	subset	subset	NOUN
ejpam-4734	182	12	b	b	PROPN
ejpam-4734	182	13	of	of	ADP
ejpam-4734	182	14	y	y	PROPN
ejpam-4734	182	15	;	;	PUNCT
ejpam-4734	182	16	(	(	PUNCT
ejpam-4734	182	17	8)	8)	NUM
ejpam-4734	182	18	f−(v	f−(v	NOUN
ejpam-4734	182	19	)	)	PUNCT
ejpam-4734	182	20	⊆	⊆	NUM
ejpam-4734	182	21	sβinti	sβinti	NOUN
ejpam-4734	182	22	(	(	PUNCT
ejpam-4734	182	23	f−(cl⋆(v	f−(cl⋆(v	PROPN
ejpam-4734	182	24	)	)	PUNCT
ejpam-4734	182	25	)	)	PUNCT
ejpam-4734	182	26	)	)	PUNCT
ejpam-4734	182	27	for	for	ADP
ejpam-4734	182	28	every	every	DET
ejpam-4734	182	29	⋆-open	⋆-open	NOUN
ejpam-4734	182	30	set	set	VERB
ejpam-4734	182	31	v	v	NOUN
ejpam-4734	182	32	of	of	ADP
ejpam-4734	182	33	y	y	PROPN
ejpam-4734	182	34	;	;	PUNCT
ejpam-4734	182	35	(	(	PUNCT
ejpam-4734	182	36	9	9	X
ejpam-4734	182	37	)	)	PUNCT
ejpam-4734	182	38	sβcli	sβcli	NOUN
ejpam-4734	182	39	(	(	PUNCT
ejpam-4734	182	40	f+(v	f+(v	PROPN
ejpam-4734	182	41	)	)	PUNCT
ejpam-4734	182	42	)	)	PUNCT
ejpam-4734	183	1	⊆	⊆	NUM
ejpam-4734	183	2	f+(cl⋆(v	f+(cl⋆(v	PROPN
ejpam-4734	183	3	)	)	PUNCT
ejpam-4734	183	4	)	)	PUNCT
ejpam-4734	183	5	for	for	ADP
ejpam-4734	183	6	every	every	DET
ejpam-4734	183	7	⋆-open	⋆-open	NOUN
ejpam-4734	183	8	set	set	VERB
ejpam-4734	183	9	v	v	NOUN
ejpam-4734	183	10	of	of	ADP
ejpam-4734	183	11	y	y	PROPN
ejpam-4734	183	12	.	.	PUNCT
ejpam-4734	184	1	proof	proof	NOUN
ejpam-4734	184	2	.	.	PUNCT
ejpam-4734	185	1	the	the	DET
ejpam-4734	185	2	proof	proof	NOUN
ejpam-4734	185	3	is	be	AUX
ejpam-4734	185	4	similar	similar	ADJ
ejpam-4734	185	5	to	to	ADP
ejpam-4734	185	6	that	that	PRON
ejpam-4734	185	7	of	of	ADP
ejpam-4734	185	8	theorem	theorem	ADJ
ejpam-4734	185	9	3	3	NUM
ejpam-4734	185	10	.	.	PUNCT
ejpam-4734	185	11	corollary	corollary	ADJ
ejpam-4734	185	12	2	2	NUM
ejpam-4734	185	13	.	.	PUNCT
ejpam-4734	185	14	for	for	ADP
ejpam-4734	185	15	a	a	DET
ejpam-4734	185	16	function	function	NOUN
ejpam-4734	185	17	f	f	NOUN
ejpam-4734	185	18	:	:	PUNCT
ejpam-4734	185	19	(	(	PUNCT
ejpam-4734	185	20	x	x	X
ejpam-4734	185	21	,	,	PUNCT
ejpam-4734	185	22	τ	τ	PROPN
ejpam-4734	185	23	,	,	PUNCT
ejpam-4734	185	24	i	i	NOUN
ejpam-4734	185	25	)	)	PUNCT
ejpam-4734	185	26	→	→	PUNCT
ejpam-4734	185	27	(	(	PUNCT
ejpam-4734	185	28	y	y	PROPN
ejpam-4734	185	29	,	,	PUNCT
ejpam-4734	185	30	σ	σ	PROPN
ejpam-4734	185	31	,	,	PUNCT
ejpam-4734	185	32	j	j	PROPN
ejpam-4734	185	33	)	)	PUNCT
ejpam-4734	185	34	,	,	PUNCT
ejpam-4734	185	35	the	the	DET
ejpam-4734	185	36	following	follow	VERB
ejpam-4734	185	37	properties	property	NOUN
ejpam-4734	185	38	are	be	AUX
ejpam-4734	185	39	equivalent	equivalent	ADJ
ejpam-4734	185	40	:	:	PUNCT
ejpam-4734	185	41	c.	c.	PROPN
ejpam-4734	185	42	boonpok	boonpok	PROPN
ejpam-4734	185	43	,	,	PUNCT
ejpam-4734	185	44	j.	j.	PROPN
ejpam-4734	185	45	khampakdee	khampakdee	PROPN
ejpam-4734	185	46	/	/	PUNCT
ejpam-4734	185	47	eur	eur	PROPN
ejpam-4734	185	48	.	.	PUNCT
ejpam-4734	186	1	j.	j.	PROPN
ejpam-4734	186	2	pure	pure	PROPN
ejpam-4734	186	3	appl	appl	PROPN
ejpam-4734	186	4	.	.	PROPN
ejpam-4734	186	5	math	math	PROPN
ejpam-4734	186	6	,	,	PUNCT
ejpam-4734	186	7	16	16	NUM
ejpam-4734	186	8	(	(	PUNCT
ejpam-4734	186	9	4	4	NUM
ejpam-4734	186	10	)	)	PUNCT
ejpam-4734	186	11	(	(	PUNCT
ejpam-4734	186	12	2023	2023	NUM
ejpam-4734	186	13	)	)	PUNCT
ejpam-4734	186	14	,	,	PUNCT
ejpam-4734	186	15	2544	2544	NUM
ejpam-4734	186	16	-	-	SYM
ejpam-4734	186	17	2556	2556	NUM
ejpam-4734	186	18	2550	2550	NUM
ejpam-4734	186	19	(	(	PUNCT
ejpam-4734	186	20	1	1	X
ejpam-4734	186	21	)	)	PUNCT
ejpam-4734	186	22	f	f	PROPN
ejpam-4734	186	23	is	be	AUX
ejpam-4734	186	24	weakly	weakly	ADV
ejpam-4734	186	25	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	186	26	;	;	PUNCT
ejpam-4734	186	27	(	(	PUNCT
ejpam-4734	186	28	2	2	X
ejpam-4734	186	29	)	)	PUNCT
ejpam-4734	186	30	f−1(v	f−1(v	NOUN
ejpam-4734	186	31	)	)	PUNCT
ejpam-4734	187	1	⊆	⊆	NUM
ejpam-4734	187	2	cl⋆(int(cl⋆(f−1(cl⋆(v	cl⋆(int(cl⋆(f−1(cl⋆(v	NOUN
ejpam-4734	187	3	)	)	PUNCT
ejpam-4734	187	4	)	)	PUNCT
ejpam-4734	187	5	)	)	PUNCT
ejpam-4734	187	6	)	)	PUNCT
ejpam-4734	187	7	)	)	PUNCT
ejpam-4734	188	1	for	for	ADP
ejpam-4734	188	2	every	every	DET
ejpam-4734	188	3	⋆-open	⋆-open	NOUN
ejpam-4734	188	4	set	set	VERB
ejpam-4734	188	5	v	v	NOUN
ejpam-4734	188	6	of	of	ADP
ejpam-4734	188	7	y	y	PROPN
ejpam-4734	188	8	;	;	PUNCT
ejpam-4734	188	9	(	(	PUNCT
ejpam-4734	188	10	3	3	X
ejpam-4734	188	11	)	)	PUNCT
ejpam-4734	188	12	int⋆(cl(int⋆(f−1(v	int⋆(cl(int⋆(f−1(v	NOUN
ejpam-4734	188	13	)	)	PUNCT
ejpam-4734	188	14	)	)	PUNCT
ejpam-4734	188	15	)	)	PUNCT
ejpam-4734	188	16	)	)	PUNCT
ejpam-4734	189	1	⊆	⊆	NUM
ejpam-4734	189	2	f−1(cl⋆(v	f−1(cl⋆(v	NOUN
ejpam-4734	189	3	)	)	PUNCT
ejpam-4734	189	4	)	)	PUNCT
ejpam-4734	189	5	for	for	ADP
ejpam-4734	189	6	every	every	DET
ejpam-4734	189	7	⋆-open	⋆-open	NOUN
ejpam-4734	189	8	set	set	VERB
ejpam-4734	189	9	v	v	NOUN
ejpam-4734	189	10	of	of	ADP
ejpam-4734	189	11	y	y	PROPN
ejpam-4734	189	12	;	;	PUNCT
ejpam-4734	189	13	(	(	PUNCT
ejpam-4734	189	14	4	4	X
ejpam-4734	189	15	)	)	PUNCT
ejpam-4734	189	16	int⋆(cl(int⋆(f−1(int⋆(k	int⋆(cl(int⋆(f−1(int⋆(k	VERB
ejpam-4734	189	17	)	)	PUNCT
ejpam-4734	189	18	)	)	PUNCT
ejpam-4734	189	19	)	)	PUNCT
ejpam-4734	189	20	)	)	PUNCT
ejpam-4734	189	21	)	)	PUNCT
ejpam-4734	190	1	⊆	⊆	NUM
ejpam-4734	190	2	f−1(k	f−1(k	PROPN
ejpam-4734	190	3	)	)	PUNCT
ejpam-4734	190	4	for	for	ADP
ejpam-4734	190	5	every	every	DET
ejpam-4734	190	6	⋆-closed	⋆-close	VERB
ejpam-4734	190	7	set	set	NOUN
ejpam-4734	190	8	k	k	PROPN
ejpam-4734	190	9	of	of	ADP
ejpam-4734	190	10	y	y	PROPN
ejpam-4734	190	11	;	;	PUNCT
ejpam-4734	190	12	(	(	PUNCT
ejpam-4734	190	13	5	5	X
ejpam-4734	190	14	)	)	PUNCT
ejpam-4734	190	15	sβcli	sβcli	NOUN
ejpam-4734	190	16	(	(	PUNCT
ejpam-4734	190	17	f−1(int⋆(k	f−1(int⋆(k	NOUN
ejpam-4734	190	18	)	)	PUNCT
ejpam-4734	190	19	)	)	PUNCT
ejpam-4734	190	20	)	)	PUNCT
ejpam-4734	190	21	⊆	⊆	NUM
ejpam-4734	190	22	f−1(k	f−1(k	PROPN
ejpam-4734	190	23	)	)	PUNCT
ejpam-4734	190	24	for	for	ADP
ejpam-4734	190	25	every	every	DET
ejpam-4734	190	26	⋆-closed	⋆-close	VERB
ejpam-4734	190	27	set	set	NOUN
ejpam-4734	190	28	k	k	PROPN
ejpam-4734	190	29	of	of	ADP
ejpam-4734	190	30	y	y	PROPN
ejpam-4734	190	31	;	;	PUNCT
ejpam-4734	190	32	(	(	PUNCT
ejpam-4734	190	33	6	6	X
ejpam-4734	190	34	)	)	PUNCT
ejpam-4734	190	35	sβcli	sβcli	NOUN
ejpam-4734	190	36	(	(	PUNCT
ejpam-4734	190	37	f−1(int⋆(cl⋆(b	f−1(int⋆(cl⋆(b	PROPN
ejpam-4734	190	38	)	)	PUNCT
ejpam-4734	190	39	)	)	PUNCT
ejpam-4734	190	40	)	)	PUNCT
ejpam-4734	190	41	)	)	PUNCT
ejpam-4734	191	1	⊆	⊆	NUM
ejpam-4734	191	2	f−1(cl⋆(b	f−1(cl⋆(b	NOUN
ejpam-4734	191	3	)	)	PUNCT
ejpam-4734	191	4	)	)	PUNCT
ejpam-4734	191	5	for	for	ADP
ejpam-4734	191	6	every	every	DET
ejpam-4734	191	7	subset	subset	NOUN
ejpam-4734	191	8	b	b	PROPN
ejpam-4734	191	9	of	of	ADP
ejpam-4734	191	10	y	y	PROPN
ejpam-4734	191	11	;	;	PUNCT
ejpam-4734	191	12	(	(	PUNCT
ejpam-4734	191	13	7	7	X
ejpam-4734	191	14	)	)	PUNCT
ejpam-4734	191	15	f−1(int⋆(b	f−1(int⋆(b	NOUN
ejpam-4734	191	16	)	)	PUNCT
ejpam-4734	191	17	)	)	PUNCT
ejpam-4734	192	1	⊆	⊆	NUM
ejpam-4734	192	2	sβinti	sβinti	NOUN
ejpam-4734	192	3	(	(	PUNCT
ejpam-4734	192	4	f−1(cl⋆(int⋆(b	f−1(cl⋆(int⋆(b	NOUN
ejpam-4734	192	5	)	)	PUNCT
ejpam-4734	192	6	)	)	PUNCT
ejpam-4734	192	7	)	)	PUNCT
ejpam-4734	192	8	)	)	PUNCT
ejpam-4734	192	9	for	for	ADP
ejpam-4734	192	10	every	every	DET
ejpam-4734	192	11	subset	subset	NOUN
ejpam-4734	192	12	b	b	PROPN
ejpam-4734	192	13	of	of	ADP
ejpam-4734	192	14	y	y	PROPN
ejpam-4734	192	15	;	;	PUNCT
ejpam-4734	192	16	(	(	PUNCT
ejpam-4734	192	17	8)	8)	NUM
ejpam-4734	192	18	f−1(v	f−1(v	NOUN
ejpam-4734	192	19	)	)	PUNCT
ejpam-4734	192	20	⊆	⊆	NUM
ejpam-4734	192	21	sβinti	sβinti	NOUN
ejpam-4734	192	22	(	(	PUNCT
ejpam-4734	192	23	f−1(cl⋆(v	f−1(cl⋆(v	PROPN
ejpam-4734	192	24	)	)	PUNCT
ejpam-4734	192	25	)	)	PUNCT
ejpam-4734	192	26	)	)	PUNCT
ejpam-4734	192	27	for	for	ADP
ejpam-4734	192	28	every	every	DET
ejpam-4734	192	29	⋆-open	⋆-open	NOUN
ejpam-4734	192	30	set	set	VERB
ejpam-4734	192	31	v	v	NOUN
ejpam-4734	192	32	of	of	ADP
ejpam-4734	192	33	y	y	PROPN
ejpam-4734	192	34	;	;	PUNCT
ejpam-4734	192	35	(	(	PUNCT
ejpam-4734	192	36	9	9	X
ejpam-4734	192	37	)	)	PUNCT
ejpam-4734	192	38	sβcli	sβcli	NOUN
ejpam-4734	192	39	(	(	PUNCT
ejpam-4734	192	40	f−1(v	f−1(v	NOUN
ejpam-4734	192	41	)	)	PUNCT
ejpam-4734	192	42	)	)	PUNCT
ejpam-4734	192	43	⊆	⊆	NUM
ejpam-4734	192	44	f−1(cl⋆(v	f−1(cl⋆(v	NOUN
ejpam-4734	192	45	)	)	PUNCT
ejpam-4734	192	46	)	)	PUNCT
ejpam-4734	192	47	for	for	ADP
ejpam-4734	192	48	every	every	PRON
ejpam-4734	192	49	⋆-open	⋆-open	NOUN
ejpam-4734	192	50	set	set	VERB
ejpam-4734	192	51	v	v	NOUN
ejpam-4734	192	52	of	of	ADP
ejpam-4734	192	53	y	y	PROPN
ejpam-4734	192	54	.	.	PUNCT
ejpam-4734	193	1	recall	recall	VERB
ejpam-4734	193	2	that	that	SCONJ
ejpam-4734	193	3	a	a	DET
ejpam-4734	193	4	subset	subset	NOUN
ejpam-4734	193	5	a	a	PRON
ejpam-4734	193	6	of	of	ADP
ejpam-4734	193	7	an	an	DET
ejpam-4734	193	8	ideal	ideal	ADJ
ejpam-4734	193	9	topological	topological	ADJ
ejpam-4734	193	10	space	space	NOUN
ejpam-4734	193	11	(	(	PUNCT
ejpam-4734	193	12	x	x	X
ejpam-4734	193	13	,	,	PUNCT
ejpam-4734	193	14	τ	τ	PROPN
ejpam-4734	193	15	,	,	PUNCT
ejpam-4734	193	16	i	i	PROPN
ejpam-4734	193	17	)	)	PUNCT
ejpam-4734	193	18	is	be	AUX
ejpam-4734	193	19	called	call	VERB
ejpam-4734	193	20	r	r	AUX
ejpam-4734	193	21	-	-	PUNCT
ejpam-4734	193	22	i	i	PRON
ejpam-4734	193	23	⋆-open	⋆-open	VERB
ejpam-4734	194	1	[	[	X
ejpam-4734	194	2	2	2	NUM
ejpam-4734	194	3	]	]	PUNCT
ejpam-4734	194	4	(	(	PUNCT
ejpam-4734	194	5	resp	resp	NOUN
ejpam-4734	194	6	.	.	PUNCT
ejpam-4734	195	1	i	i	PRON
ejpam-4734	195	2	⋆-preopen	⋆-preopen	VERB
ejpam-4734	196	1	[	[	X
ejpam-4734	196	2	2	2	NUM
ejpam-4734	196	3	]	]	PUNCT
ejpam-4734	196	4	,	,	PUNCT
ejpam-4734	196	5	i	i	PRON
ejpam-4734	196	6	⋆-semi	⋆-semi	NOUN
ejpam-4734	196	7	-	-	PUNCT
ejpam-4734	196	8	open	open	ADJ
ejpam-4734	196	9	[	[	X
ejpam-4734	196	10	3	3	NUM
ejpam-4734	196	11	]	]	PUNCT
ejpam-4734	196	12	)	)	PUNCT
ejpam-4734	196	13	if	if	SCONJ
ejpam-4734	196	14	a	a	DET
ejpam-4734	196	15	=	=	PUNCT
ejpam-4734	196	16	int⋆(cl⋆(a	int⋆(cl⋆(a	NOUN
ejpam-4734	196	17	)	)	PUNCT
ejpam-4734	196	18	)	)	PUNCT
ejpam-4734	196	19	(	(	PUNCT
ejpam-4734	196	20	resp	resp	NOUN
ejpam-4734	196	21	.	.	PUNCT
ejpam-4734	197	1	a	a	DET
ejpam-4734	197	2	⊆	⊆	NUM
ejpam-4734	197	3	int⋆(cl⋆(a	int⋆(cl⋆(a	NOUN
ejpam-4734	197	4	)	)	PUNCT
ejpam-4734	197	5	)	)	PUNCT
ejpam-4734	197	6	,	,	PUNCT
ejpam-4734	197	7	a	a	DET
ejpam-4734	197	8	⊆	⊆	NUM
ejpam-4734	197	9	cl⋆(int⋆(a	cl⋆(int⋆(a	NOUN
ejpam-4734	197	10	)	)	PUNCT
ejpam-4734	197	11	)	)	PUNCT
ejpam-4734	197	12	)	)	PUNCT
ejpam-4734	197	13	.	.	PUNCT
ejpam-4734	198	1	the	the	DET
ejpam-4734	198	2	complement	complement	NOUN
ejpam-4734	198	3	of	of	ADP
ejpam-4734	198	4	a	a	DET
ejpam-4734	198	5	r	r	NOUN
ejpam-4734	198	6	-	-	PUNCT
ejpam-4734	198	7	i	i	PRON
ejpam-4734	198	8	⋆-open	⋆-open	VERB
ejpam-4734	198	9	(	(	PUNCT
ejpam-4734	198	10	resp	resp	NOUN
ejpam-4734	198	11	.	.	PUNCT
ejpam-4734	199	1	i	i	PRON
ejpam-4734	199	2	⋆-preopen	⋆-preopen	VERB
ejpam-4734	199	3	,	,	PUNCT
ejpam-4734	199	4	i	i	PRON
ejpam-4734	199	5	⋆-semi	⋆-semi	NOUN
ejpam-4734	199	6	-	-	PUNCT
ejpam-4734	199	7	open	open	ADJ
ejpam-4734	199	8	)	)	PUNCT
ejpam-4734	199	9	set	set	NOUN
ejpam-4734	199	10	is	be	AUX
ejpam-4734	199	11	called	call	VERB
ejpam-4734	199	12	r	r	AUX
ejpam-4734	199	13	-	-	PUNCT
ejpam-4734	199	14	i	i	PRON
ejpam-4734	199	15	⋆-closed	⋆-close	VERB
ejpam-4734	200	1	[	[	X
ejpam-4734	200	2	2	2	NUM
ejpam-4734	200	3	]	]	PUNCT
ejpam-4734	200	4	(	(	PUNCT
ejpam-4734	200	5	resp	resp	NOUN
ejpam-4734	200	6	.	.	PUNCT
ejpam-4734	201	1	i	i	PRON
ejpam-4734	201	2	⋆-preclosed	⋆-preclose	VERB
ejpam-4734	201	3	[	[	X
ejpam-4734	201	4	2	2	NUM
ejpam-4734	201	5	]	]	PUNCT
ejpam-4734	201	6	,	,	PUNCT
ejpam-4734	201	7	i	i	PRON
ejpam-4734	201	8	⋆-semi	⋆-semi	PROPN
ejpam-4734	201	9	-	-	PUNCT
ejpam-4734	201	10	closed	closed	ADJ
ejpam-4734	201	11	[	[	X
ejpam-4734	201	12	3	3	NUM
ejpam-4734	201	13	]	]	NUM
ejpam-4734	201	14	)	)	PUNCT
ejpam-4734	201	15	.	.	PUNCT
ejpam-4734	202	1	let	let	VERB
ejpam-4734	202	2	a	a	DET
ejpam-4734	202	3	be	be	AUX
ejpam-4734	202	4	a	a	DET
ejpam-4734	202	5	subset	subset	NOUN
ejpam-4734	202	6	of	of	ADP
ejpam-4734	202	7	an	an	DET
ejpam-4734	202	8	ideal	ideal	ADJ
ejpam-4734	202	9	topological	topological	ADJ
ejpam-4734	202	10	space	space	NOUN
ejpam-4734	202	11	(	(	PUNCT
ejpam-4734	202	12	x	x	X
ejpam-4734	202	13	,	,	PUNCT
ejpam-4734	202	14	τ	τ	PROPN
ejpam-4734	202	15	,	,	PUNCT
ejpam-4734	202	16	i	i	NOUN
ejpam-4734	202	17	)	)	PUNCT
ejpam-4734	202	18	.	.	PUNCT
ejpam-4734	203	1	a	a	DET
ejpam-4734	203	2	point	point	NOUN
ejpam-4734	203	3	x	x	X
ejpam-4734	203	4	in	in	ADP
ejpam-4734	203	5	an	an	DET
ejpam-4734	203	6	ideal	ideal	ADJ
ejpam-4734	203	7	topological	topological	ADJ
ejpam-4734	203	8	space	space	NOUN
ejpam-4734	203	9	(	(	PUNCT
ejpam-4734	203	10	x	x	X
ejpam-4734	203	11	,	,	PUNCT
ejpam-4734	203	12	τ	τ	PROPN
ejpam-4734	203	13	,	,	PUNCT
ejpam-4734	203	14	i	i	PROPN
ejpam-4734	203	15	)	)	PUNCT
ejpam-4734	203	16	is	be	AUX
ejpam-4734	203	17	called	call	VERB
ejpam-4734	203	18	a	a	DET
ejpam-4734	203	19	⋆θ	⋆θ	ADJ
ejpam-4734	203	20	-	-	PUNCT
ejpam-4734	203	21	cluster	cluster	NOUN
ejpam-4734	203	22	point	point	NOUN
ejpam-4734	203	23	of	of	ADP
ejpam-4734	203	24	a	a	PRON
ejpam-4734	203	25	[	[	X
ejpam-4734	203	26	3	3	X
ejpam-4734	203	27	]	]	PUNCT
ejpam-4734	203	28	if	if	SCONJ
ejpam-4734	203	29	cl⋆(u)∩a	cl⋆(u)∩a	PROPN
ejpam-4734	203	30	̸=	̸=	PROPN
ejpam-4734	203	31	∅	∅	NOUN
ejpam-4734	203	32	for	for	ADP
ejpam-4734	203	33	every	every	DET
ejpam-4734	203	34	⋆-open	⋆-open	ADV
ejpam-4734	203	35	set	set	NOUN
ejpam-4734	203	36	u	u	NOUN
ejpam-4734	203	37	of	of	ADP
ejpam-4734	203	38	x	x	SYM
ejpam-4734	203	39	containing	contain	VERB
ejpam-4734	203	40	x.	x.	NOUN
ejpam-4734	203	41	the	the	DET
ejpam-4734	203	42	set	set	NOUN
ejpam-4734	203	43	of	of	ADP
ejpam-4734	203	44	all	all	DET
ejpam-4734	203	45	⋆θ	⋆θ	ADJ
ejpam-4734	203	46	-	-	PUNCT
ejpam-4734	203	47	cluster	cluster	NOUN
ejpam-4734	203	48	points	point	NOUN
ejpam-4734	203	49	of	of	ADP
ejpam-4734	203	50	a	a	PRON
ejpam-4734	203	51	is	be	AUX
ejpam-4734	203	52	called	call	VERB
ejpam-4734	203	53	the	the	DET
ejpam-4734	203	54	⋆θ	⋆θ	NOUN
ejpam-4734	203	55	-	-	PUNCT
ejpam-4734	203	56	closure	closure	NOUN
ejpam-4734	203	57	[	[	X
ejpam-4734	203	58	3	3	NUM
ejpam-4734	203	59	]	]	PUNCT
ejpam-4734	203	60	of	of	ADP
ejpam-4734	203	61	a	a	PRON
ejpam-4734	203	62	and	and	CCONJ
ejpam-4734	203	63	is	be	AUX
ejpam-4734	203	64	denoted	denote	VERB
ejpam-4734	203	65	by	by	ADP
ejpam-4734	203	66	⋆θcl(a	⋆θcl(a	PROPN
ejpam-4734	203	67	)	)	PUNCT
ejpam-4734	203	68	.	.	PUNCT
ejpam-4734	204	1	a	a	DET
ejpam-4734	204	2	subset	subset	NOUN
ejpam-4734	204	3	b	b	NOUN
ejpam-4734	204	4	of	of	ADP
ejpam-4734	204	5	an	an	DET
ejpam-4734	204	6	ideal	ideal	ADJ
ejpam-4734	204	7	topological	topological	ADJ
ejpam-4734	204	8	space	space	NOUN
ejpam-4734	204	9	(	(	PUNCT
ejpam-4734	204	10	x	x	X
ejpam-4734	204	11	,	,	PUNCT
ejpam-4734	204	12	τ	τ	PROPN
ejpam-4734	204	13	,	,	PUNCT
ejpam-4734	204	14	i	i	PROPN
ejpam-4734	204	15	)	)	PUNCT
ejpam-4734	204	16	is	be	AUX
ejpam-4734	204	17	called	call	VERB
ejpam-4734	204	18	⋆θ	⋆θ	NOUN
ejpam-4734	204	19	-	-	PUNCT
ejpam-4734	204	20	closed	closed	ADJ
ejpam-4734	204	21	[	[	X
ejpam-4734	204	22	3	3	X
ejpam-4734	204	23	]	]	X
ejpam-4734	204	24	if	if	SCONJ
ejpam-4734	204	25	⋆θcl(b	⋆θcl(b	NOUN
ejpam-4734	204	26	)	)	PUNCT
ejpam-4734	204	27	=	=	SYM
ejpam-4734	204	28	b.	b.	PROPN
ejpam-4734	204	29	the	the	DET
ejpam-4734	204	30	complement	complement	NOUN
ejpam-4734	204	31	of	of	ADP
ejpam-4734	204	32	a	a	DET
ejpam-4734	204	33	⋆θ	⋆θ	ADV
ejpam-4734	204	34	-	-	PUNCT
ejpam-4734	204	35	closed	closed	ADJ
ejpam-4734	204	36	set	set	NOUN
ejpam-4734	204	37	is	be	AUX
ejpam-4734	204	38	called	call	VERB
ejpam-4734	204	39	⋆θ	⋆θ	NOUN
ejpam-4734	204	40	-	-	ADJ
ejpam-4734	204	41	open	open	ADJ
ejpam-4734	204	42	[	[	X
ejpam-4734	204	43	3	3	NUM
ejpam-4734	204	44	]	]	PUNCT
ejpam-4734	204	45	.	.	PUNCT
ejpam-4734	205	1	lemma	lemma	PROPN
ejpam-4734	205	2	6	6	NUM
ejpam-4734	205	3	.	.	PUNCT
ejpam-4734	206	1	[	[	X
ejpam-4734	206	2	3	3	X
ejpam-4734	206	3	]	]	PUNCT
ejpam-4734	206	4	for	for	ADP
ejpam-4734	206	5	a	a	DET
ejpam-4734	206	6	subset	subset	NOUN
ejpam-4734	206	7	a	a	PRON
ejpam-4734	206	8	of	of	ADP
ejpam-4734	206	9	an	an	DET
ejpam-4734	206	10	ideal	ideal	ADJ
ejpam-4734	206	11	topological	topological	ADJ
ejpam-4734	206	12	space	space	NOUN
ejpam-4734	206	13	(	(	PUNCT
ejpam-4734	206	14	x	x	X
ejpam-4734	206	15	,	,	PUNCT
ejpam-4734	206	16	τ	τ	PROPN
ejpam-4734	206	17	,	,	PUNCT
ejpam-4734	206	18	i	i	NOUN
ejpam-4734	206	19	)	)	PUNCT
ejpam-4734	206	20	,	,	PUNCT
ejpam-4734	206	21	the	the	DET
ejpam-4734	206	22	following	follow	VERB
ejpam-4734	206	23	properties	property	NOUN
ejpam-4734	206	24	hold	hold	VERB
ejpam-4734	206	25	:	:	PUNCT
ejpam-4734	206	26	(	(	PUNCT
ejpam-4734	206	27	1	1	X
ejpam-4734	206	28	)	)	PUNCT
ejpam-4734	206	29	if	if	SCONJ
ejpam-4734	206	30	a	a	PRON
ejpam-4734	206	31	is	be	AUX
ejpam-4734	206	32	⋆-open	⋆-open	ADJ
ejpam-4734	206	33	in	in	ADP
ejpam-4734	206	34	x	x	PRON
ejpam-4734	206	35	,	,	PUNCT
ejpam-4734	206	36	then	then	ADV
ejpam-4734	206	37	cl⋆(a	cl⋆(a	PROPN
ejpam-4734	206	38	)	)	PUNCT
ejpam-4734	206	39	=	=	SYM
ejpam-4734	206	40	⋆θcl(a	⋆θcl(a	PROPN
ejpam-4734	206	41	)	)	PUNCT
ejpam-4734	206	42	.	.	PUNCT
ejpam-4734	207	1	(	(	PUNCT
ejpam-4734	207	2	2	2	X
ejpam-4734	207	3	)	)	PUNCT
ejpam-4734	207	4	⋆θcl(a	⋆θcl(a	PROPN
ejpam-4734	207	5	)	)	PUNCT
ejpam-4734	207	6	is	be	AUX
ejpam-4734	207	7	⋆-closed	⋆-close	VERB
ejpam-4734	207	8	in	in	ADP
ejpam-4734	207	9	x.	x.	NOUN
ejpam-4734	207	10	theorem	theorem	VERB
ejpam-4734	207	11	5	5	NUM
ejpam-4734	207	12	.	.	X
ejpam-4734	207	13	for	for	ADP
ejpam-4734	207	14	a	a	DET
ejpam-4734	207	15	multifunction	multifunction	NOUN
ejpam-4734	207	16	f	f	NOUN
ejpam-4734	207	17	:	:	PUNCT
ejpam-4734	207	18	(	(	PUNCT
ejpam-4734	207	19	x	x	X
ejpam-4734	207	20	,	,	PUNCT
ejpam-4734	207	21	τ	τ	PROPN
ejpam-4734	207	22	,	,	PUNCT
ejpam-4734	207	23	i	i	NOUN
ejpam-4734	207	24	)	)	PUNCT
ejpam-4734	207	25	→	→	PUNCT
ejpam-4734	207	26	(	(	PUNCT
ejpam-4734	207	27	y	y	PROPN
ejpam-4734	207	28	,	,	PUNCT
ejpam-4734	207	29	σ	σ	PROPN
ejpam-4734	207	30	,	,	PUNCT
ejpam-4734	207	31	j	j	PROPN
ejpam-4734	207	32	)	)	PUNCT
ejpam-4734	207	33	,	,	PUNCT
ejpam-4734	207	34	the	the	DET
ejpam-4734	207	35	following	follow	VERB
ejpam-4734	207	36	properties	property	NOUN
ejpam-4734	207	37	are	be	AUX
ejpam-4734	207	38	equivalent	equivalent	ADJ
ejpam-4734	207	39	:	:	PUNCT
ejpam-4734	207	40	(	(	PUNCT
ejpam-4734	207	41	1	1	X
ejpam-4734	207	42	)	)	PUNCT
ejpam-4734	207	43	f	f	PROPN
ejpam-4734	207	44	is	be	AUX
ejpam-4734	207	45	upper	upper	ADJ
ejpam-4734	207	46	weakly	weakly	ADJ
ejpam-4734	207	47	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	207	48	;	;	PUNCT
ejpam-4734	207	49	(	(	PUNCT
ejpam-4734	207	50	2	2	X
ejpam-4734	207	51	)	)	PUNCT
ejpam-4734	207	52	sβcli	sβcli	NOUN
ejpam-4734	207	53	(	(	PUNCT
ejpam-4734	207	54	f−(int⋆(⋆θcl(b	f−(int⋆(⋆θcl(b	NOUN
ejpam-4734	207	55	)	)	PUNCT
ejpam-4734	207	56	)	)	PUNCT
ejpam-4734	207	57	)	)	PUNCT
ejpam-4734	207	58	)	)	PUNCT
ejpam-4734	208	1	⊆	⊆	NUM
ejpam-4734	208	2	f−(⋆θcl(b	f−(⋆θcl(b	NOUN
ejpam-4734	208	3	)	)	PUNCT
ejpam-4734	208	4	)	)	PUNCT
ejpam-4734	208	5	for	for	ADP
ejpam-4734	208	6	every	every	DET
ejpam-4734	208	7	subset	subset	NOUN
ejpam-4734	208	8	b	b	PROPN
ejpam-4734	208	9	of	of	ADP
ejpam-4734	208	10	y	y	PROPN
ejpam-4734	208	11	;	;	PUNCT
ejpam-4734	208	12	(	(	PUNCT
ejpam-4734	208	13	3	3	X
ejpam-4734	208	14	)	)	PUNCT
ejpam-4734	208	15	sβcli	sβcli	NOUN
ejpam-4734	208	16	(	(	PUNCT
ejpam-4734	208	17	f−(int⋆(cl⋆(b	f−(int⋆(cl⋆(b	PROPN
ejpam-4734	208	18	)	)	PUNCT
ejpam-4734	208	19	)	)	PUNCT
ejpam-4734	208	20	)	)	PUNCT
ejpam-4734	208	21	)	)	PUNCT
ejpam-4734	209	1	⊆	⊆	NUM
ejpam-4734	209	2	f−(⋆θcl(b	f−(⋆θcl(b	NOUN
ejpam-4734	209	3	)	)	PUNCT
ejpam-4734	209	4	)	)	PUNCT
ejpam-4734	209	5	for	for	ADP
ejpam-4734	209	6	every	every	DET
ejpam-4734	209	7	subset	subset	NOUN
ejpam-4734	209	8	b	b	PROPN
ejpam-4734	209	9	of	of	ADP
ejpam-4734	209	10	y	y	PROPN
ejpam-4734	209	11	;	;	PUNCT
ejpam-4734	209	12	(	(	PUNCT
ejpam-4734	209	13	4	4	X
ejpam-4734	209	14	)	)	PUNCT
ejpam-4734	209	15	sβcli	sβcli	NOUN
ejpam-4734	209	16	(	(	PUNCT
ejpam-4734	209	17	f−(int⋆(cl⋆(v	f−(int⋆(cl⋆(v	PROPN
ejpam-4734	209	18	)	)	PUNCT
ejpam-4734	209	19	)	)	PUNCT
ejpam-4734	209	20	)	)	PUNCT
ejpam-4734	209	21	)	)	PUNCT
ejpam-4734	210	1	⊆	⊆	NUM
ejpam-4734	210	2	f−(cl⋆(v	f−(cl⋆(v	NOUN
ejpam-4734	210	3	)	)	PUNCT
ejpam-4734	210	4	)	)	PUNCT
ejpam-4734	210	5	for	for	ADP
ejpam-4734	210	6	every	every	DET
ejpam-4734	210	7	⋆-open	⋆-open	NOUN
ejpam-4734	210	8	set	set	VERB
ejpam-4734	210	9	v	v	NOUN
ejpam-4734	210	10	of	of	ADP
ejpam-4734	210	11	y	y	PROPN
ejpam-4734	210	12	;	;	PUNCT
ejpam-4734	210	13	(	(	PUNCT
ejpam-4734	210	14	5	5	X
ejpam-4734	210	15	)	)	PUNCT
ejpam-4734	210	16	sβcli	sβcli	NOUN
ejpam-4734	210	17	(	(	PUNCT
ejpam-4734	210	18	f−(int⋆(cl⋆(v	f−(int⋆(cl⋆(v	PROPN
ejpam-4734	210	19	)	)	PUNCT
ejpam-4734	210	20	)	)	PUNCT
ejpam-4734	210	21	)	)	PUNCT
ejpam-4734	210	22	)	)	PUNCT
ejpam-4734	211	1	⊆	⊆	NUM
ejpam-4734	211	2	f−(cl⋆(v	f−(cl⋆(v	NOUN
ejpam-4734	211	3	)	)	PUNCT
ejpam-4734	211	4	)	)	PUNCT
ejpam-4734	211	5	for	for	SCONJ
ejpam-4734	211	6	every	every	DET
ejpam-4734	211	7	j	j	PROPN
ejpam-4734	211	8	⋆-preopen	⋆-preopen	ADV
ejpam-4734	211	9	set	set	VERB
ejpam-4734	211	10	v	v	NUM
ejpam-4734	211	11	of	of	ADP
ejpam-4734	211	12	y	y	PROPN
ejpam-4734	211	13	;	;	PUNCT
ejpam-4734	211	14	(	(	PUNCT
ejpam-4734	211	15	6	6	X
ejpam-4734	211	16	)	)	PUNCT
ejpam-4734	211	17	sβcli	sβcli	NOUN
ejpam-4734	211	18	(	(	PUNCT
ejpam-4734	211	19	f−(int⋆(k	f−(int⋆(k	ADJ
ejpam-4734	211	20	)	)	PUNCT
ejpam-4734	211	21	)	)	PUNCT
ejpam-4734	211	22	)	)	PUNCT
ejpam-4734	211	23	⊆	⊆	X
ejpam-4734	211	24	f−(k	f−(k	PROPN
ejpam-4734	211	25	)	)	PUNCT
ejpam-4734	211	26	for	for	SCONJ
ejpam-4734	211	27	every	every	DET
ejpam-4734	211	28	r	r	PROPN
ejpam-4734	211	29	-	-	PUNCT
ejpam-4734	211	30	j	j	NOUN
ejpam-4734	211	31	⋆-closed	⋆-close	VERB
ejpam-4734	211	32	set	set	VERB
ejpam-4734	211	33	k	k	PROPN
ejpam-4734	211	34	of	of	ADP
ejpam-4734	211	35	y	y	PROPN
ejpam-4734	211	36	;	;	PUNCT
ejpam-4734	211	37	c.	c.	PROPN
ejpam-4734	211	38	boonpok	boonpok	PROPN
ejpam-4734	211	39	,	,	PUNCT
ejpam-4734	211	40	j.	j.	PROPN
ejpam-4734	211	41	khampakdee	khampakdee	PROPN
ejpam-4734	211	42	/	/	PUNCT
ejpam-4734	211	43	eur	eur	PROPN
ejpam-4734	211	44	.	.	PUNCT
ejpam-4734	212	1	j.	j.	PROPN
ejpam-4734	212	2	pure	pure	PROPN
ejpam-4734	212	3	appl	appl	PROPN
ejpam-4734	212	4	.	.	PROPN
ejpam-4734	212	5	math	math	PROPN
ejpam-4734	212	6	,	,	PUNCT
ejpam-4734	212	7	16	16	NUM
ejpam-4734	212	8	(	(	PUNCT
ejpam-4734	212	9	4	4	NUM
ejpam-4734	212	10	)	)	PUNCT
ejpam-4734	212	11	(	(	PUNCT
ejpam-4734	212	12	2023	2023	NUM
ejpam-4734	212	13	)	)	PUNCT
ejpam-4734	212	14	,	,	PUNCT
ejpam-4734	212	15	2544	2544	NUM
ejpam-4734	212	16	-	-	SYM
ejpam-4734	212	17	2556	2556	NUM
ejpam-4734	212	18	2551	2551	NUM
ejpam-4734	212	19	(	(	PUNCT
ejpam-4734	212	20	7	7	NUM
ejpam-4734	212	21	)	)	PUNCT
ejpam-4734	212	22	sβcli	sβcli	NOUN
ejpam-4734	212	23	(	(	PUNCT
ejpam-4734	212	24	f−(int⋆(cl⋆(v	f−(int⋆(cl⋆(v	PROPN
ejpam-4734	212	25	)	)	PUNCT
ejpam-4734	212	26	)	)	PUNCT
ejpam-4734	212	27	)	)	PUNCT
ejpam-4734	212	28	)	)	PUNCT
ejpam-4734	213	1	⊆	⊆	NUM
ejpam-4734	213	2	f−(cl⋆(v	f−(cl⋆(v	NOUN
ejpam-4734	213	3	)	)	PUNCT
ejpam-4734	213	4	)	)	PUNCT
ejpam-4734	213	5	for	for	ADP
ejpam-4734	213	6	every	every	DET
ejpam-4734	213	7	strong	strong	ADJ
ejpam-4734	213	8	β	β	PROPN
ejpam-4734	213	9	-	-	ADJ
ejpam-4734	213	10	j	j	ADJ
ejpam-4734	213	11	-open	-open	NOUN
ejpam-4734	213	12	set	set	VERB
ejpam-4734	213	13	v	v	NOUN
ejpam-4734	213	14	of	of	ADP
ejpam-4734	213	15	y	y	PROPN
ejpam-4734	213	16	;	;	PUNCT
ejpam-4734	213	17	(	(	PUNCT
ejpam-4734	213	18	8)	8)	NUM
ejpam-4734	213	19	sβcli	sβcli	NOUN
ejpam-4734	213	20	(	(	PUNCT
ejpam-4734	213	21	f−(int⋆(cl⋆(v	f−(int⋆(cl⋆(v	PROPN
ejpam-4734	213	22	)	)	PUNCT
ejpam-4734	213	23	)	)	PUNCT
ejpam-4734	213	24	)	)	PUNCT
ejpam-4734	213	25	)	)	PUNCT
ejpam-4734	213	26	⊆	⊆	NUM
ejpam-4734	213	27	f−(cl⋆(v	f−(cl⋆(v	NOUN
ejpam-4734	213	28	)	)	PUNCT
ejpam-4734	213	29	)	)	PUNCT
ejpam-4734	213	30	for	for	ADP
ejpam-4734	213	31	every	every	DET
ejpam-4734	213	32	j	j	PROPN
ejpam-4734	213	33	⋆-semi	⋆-semi	X
ejpam-4734	213	34	-	-	PUNCT
ejpam-4734	213	35	open	open	ADJ
ejpam-4734	213	36	set	set	VERB
ejpam-4734	213	37	v	v	NOUN
ejpam-4734	213	38	of	of	ADP
ejpam-4734	213	39	y	y	PROPN
ejpam-4734	213	40	.	.	PUNCT
ejpam-4734	214	1	proof	proof	NOUN
ejpam-4734	214	2	.	.	PUNCT
ejpam-4734	215	1	(	(	PUNCT
ejpam-4734	215	2	1	1	X
ejpam-4734	215	3	)	)	PUNCT
ejpam-4734	215	4	⇒	⇒	NOUN
ejpam-4734	215	5	(	(	PUNCT
ejpam-4734	215	6	2	2	NUM
ejpam-4734	215	7	):	):	PUNCT
ejpam-4734	215	8	let	let	VERB
ejpam-4734	215	9	b	b	X
ejpam-4734	215	10	be	be	AUX
ejpam-4734	215	11	any	any	DET
ejpam-4734	215	12	subset	subset	NOUN
ejpam-4734	215	13	of	of	ADP
ejpam-4734	215	14	y	y	PROPN
ejpam-4734	215	15	.	.	PUNCT
ejpam-4734	216	1	thus	thus	ADV
ejpam-4734	216	2	,	,	PUNCT
ejpam-4734	216	3	by	by	ADP
ejpam-4734	216	4	lemma	lemma	PROPN
ejpam-4734	216	5	6	6	NUM
ejpam-4734	216	6	,	,	PUNCT
ejpam-4734	216	7	⋆θcl(b	⋆θcl(b	NOUN
ejpam-4734	216	8	)	)	PUNCT
ejpam-4734	216	9	is	be	AUX
ejpam-4734	216	10	⋆-closed	⋆-close	VERB
ejpam-4734	216	11	in	in	ADP
ejpam-4734	216	12	y	y	PROPN
ejpam-4734	216	13	and	and	CCONJ
ejpam-4734	216	14	by	by	ADP
ejpam-4734	216	15	theorem	theorem	ADJ
ejpam-4734	216	16	3	3	NUM
ejpam-4734	216	17	,	,	PUNCT
ejpam-4734	216	18	sβcli	sβcli	NOUN
ejpam-4734	216	19	(	(	PUNCT
ejpam-4734	216	20	f−(int⋆(⋆θcl(b	f−(int⋆(⋆θcl(b	NOUN
ejpam-4734	216	21	)	)	PUNCT
ejpam-4734	216	22	)	)	PUNCT
ejpam-4734	216	23	)	)	PUNCT
ejpam-4734	216	24	)	)	PUNCT
ejpam-4734	217	1	⊆	⊆	NUM
ejpam-4734	217	2	f−(⋆θcl(b	f−(⋆θcl(b	NOUN
ejpam-4734	217	3	)	)	PUNCT
ejpam-4734	217	4	)	)	PUNCT
ejpam-4734	217	5	.	.	PUNCT
ejpam-4734	218	1	(	(	PUNCT
ejpam-4734	218	2	2	2	X
ejpam-4734	218	3	)	)	PUNCT
ejpam-4734	218	4	⇒	⇒	NOUN
ejpam-4734	218	5	(	(	PUNCT
ejpam-4734	218	6	3	3	NUM
ejpam-4734	218	7	):	):	PUNCT
ejpam-4734	218	8	this	this	PRON
ejpam-4734	218	9	is	be	AUX
ejpam-4734	218	10	obvious	obvious	ADJ
ejpam-4734	218	11	since	since	SCONJ
ejpam-4734	218	12	cl⋆(b	cl⋆(b	NOUN
ejpam-4734	218	13	)	)	PUNCT
ejpam-4734	218	14	⊆	⊆	NUM
ejpam-4734	218	15	⋆θcl(b	⋆θcl(b	NOUN
ejpam-4734	218	16	)	)	PUNCT
ejpam-4734	218	17	for	for	ADP
ejpam-4734	218	18	every	every	DET
ejpam-4734	218	19	subset	subset	NOUN
ejpam-4734	218	20	b	b	PROPN
ejpam-4734	218	21	of	of	ADP
ejpam-4734	218	22	y	y	PROPN
ejpam-4734	218	23	.	.	PUNCT
ejpam-4734	219	1	(	(	PUNCT
ejpam-4734	219	2	3	3	X
ejpam-4734	219	3	)	)	PUNCT
ejpam-4734	219	4	⇒	⇒	NOUN
ejpam-4734	219	5	(	(	PUNCT
ejpam-4734	219	6	4	4	NUM
ejpam-4734	219	7	):	):	PUNCT
ejpam-4734	219	8	this	this	PRON
ejpam-4734	219	9	is	be	AUX
ejpam-4734	219	10	obvious	obvious	ADJ
ejpam-4734	219	11	since	since	SCONJ
ejpam-4734	219	12	cl⋆(v	cl⋆(v	NOUN
ejpam-4734	219	13	)	)	PUNCT
ejpam-4734	220	1	=	=	SYM
ejpam-4734	220	2	⋆θcl(v	⋆θcl(v	PROPN
ejpam-4734	220	3	)	)	PUNCT
ejpam-4734	220	4	for	for	SCONJ
ejpam-4734	220	5	every	every	DET
ejpam-4734	220	6	⋆-open	⋆-open	NOUN
ejpam-4734	220	7	set	set	VERB
ejpam-4734	220	8	v	v	NOUN
ejpam-4734	220	9	of	of	ADP
ejpam-4734	220	10	y	y	PROPN
ejpam-4734	220	11	.	.	PUNCT
ejpam-4734	221	1	(	(	PUNCT
ejpam-4734	221	2	4	4	X
ejpam-4734	221	3	)	)	PUNCT
ejpam-4734	221	4	⇒	⇒	NOUN
ejpam-4734	221	5	(	(	PUNCT
ejpam-4734	221	6	5	5	NUM
ejpam-4734	221	7	):	):	PUNCT
ejpam-4734	221	8	let	let	VERB
ejpam-4734	221	9	v	v	PART
ejpam-4734	221	10	be	be	AUX
ejpam-4734	221	11	any	any	DET
ejpam-4734	221	12	j	j	PROPN
ejpam-4734	221	13	⋆-preopen	⋆-preopen	ADV
ejpam-4734	221	14	set	set	NOUN
ejpam-4734	221	15	of	of	ADP
ejpam-4734	221	16	y	y	PROPN
ejpam-4734	221	17	.	.	PUNCT
ejpam-4734	222	1	then	then	ADV
ejpam-4734	222	2	,	,	PUNCT
ejpam-4734	222	3	we	we	PRON
ejpam-4734	222	4	have	have	VERB
ejpam-4734	222	5	v	v	NUM
ejpam-4734	222	6	⊆	⊆	NUM
ejpam-4734	222	7	int⋆(cl⋆(v	int⋆(cl⋆(v	NOUN
ejpam-4734	222	8	)	)	PUNCT
ejpam-4734	222	9	)	)	PUNCT
ejpam-4734	223	1	and	and	CCONJ
ejpam-4734	223	2	so	so	ADV
ejpam-4734	223	3	cl⋆(v	cl⋆(v	NOUN
ejpam-4734	223	4	)	)	PUNCT
ejpam-4734	224	1	=	=	SYM
ejpam-4734	224	2	cl⋆(int⋆(cl⋆(v	cl⋆(int⋆(cl⋆(v	NOUN
ejpam-4734	224	3	)	)	PUNCT
ejpam-4734	224	4	)	)	PUNCT
ejpam-4734	224	5	)	)	PUNCT
ejpam-4734	224	6	.	.	PUNCT
ejpam-4734	225	1	now	now	ADV
ejpam-4734	225	2	,	,	PUNCT
ejpam-4734	225	3	put	put	VERB
ejpam-4734	225	4	g	g	NOUN
ejpam-4734	225	5	=	=	NOUN
ejpam-4734	225	6	int⋆(cl⋆(v	int⋆(cl⋆(v	PROPN
ejpam-4734	225	7	)	)	PUNCT
ejpam-4734	225	8	)	)	PUNCT
ejpam-4734	225	9	,	,	PUNCT
ejpam-4734	225	10	then	then	ADV
ejpam-4734	225	11	g	g	PROPN
ejpam-4734	225	12	is	be	AUX
ejpam-4734	225	13	⋆-open	⋆-open	ADJ
ejpam-4734	225	14	in	in	ADP
ejpam-4734	225	15	y	y	PROPN
ejpam-4734	225	16	and	and	CCONJ
ejpam-4734	225	17	cl⋆(g	cl⋆(g	PROPN
ejpam-4734	225	18	)	)	PUNCT
ejpam-4734	226	1	=	=	SYM
ejpam-4734	226	2	cl⋆(v	cl⋆(v	PROPN
ejpam-4734	226	3	)	)	PUNCT
ejpam-4734	226	4	.	.	PUNCT
ejpam-4734	227	1	thus	thus	ADV
ejpam-4734	227	2	,	,	PUNCT
ejpam-4734	227	3	by	by	ADP
ejpam-4734	227	4	(	(	PUNCT
ejpam-4734	227	5	4	4	NUM
ejpam-4734	227	6	)	)	PUNCT
ejpam-4734	227	7	,	,	PUNCT
ejpam-4734	227	8	we	we	PRON
ejpam-4734	227	9	have	have	VERB
ejpam-4734	227	10	sβcli	sβcli	NOUN
ejpam-4734	227	11	(	(	PUNCT
ejpam-4734	227	12	f−(int⋆(cl⋆(v	f−(int⋆(cl⋆(v	PROPN
ejpam-4734	227	13	)	)	PUNCT
ejpam-4734	227	14	)	)	PUNCT
ejpam-4734	227	15	)	)	PUNCT
ejpam-4734	227	16	)	)	PUNCT
ejpam-4734	228	1	⊆	⊆	NUM
ejpam-4734	228	2	f−(cl⋆(v	f−(cl⋆(v	NOUN
ejpam-4734	228	3	)	)	PUNCT
ejpam-4734	228	4	)	)	PUNCT
ejpam-4734	228	5	.	.	PUNCT
ejpam-4734	229	1	(	(	PUNCT
ejpam-4734	229	2	5	5	X
ejpam-4734	229	3	)	)	PUNCT
ejpam-4734	229	4	⇒	⇒	NOUN
ejpam-4734	229	5	(	(	PUNCT
ejpam-4734	229	6	6	6	NUM
ejpam-4734	229	7	):	):	PUNCT
ejpam-4734	229	8	let	let	VERB
ejpam-4734	229	9	k	k	PRON
ejpam-4734	229	10	be	be	AUX
ejpam-4734	229	11	any	any	PRON
ejpam-4734	229	12	r	r	NOUN
ejpam-4734	229	13	-	-	PUNCT
ejpam-4734	229	14	j	j	NOUN
ejpam-4734	229	15	⋆-closed	⋆-close	VERB
ejpam-4734	229	16	set	set	NOUN
ejpam-4734	229	17	of	of	ADP
ejpam-4734	229	18	y	y	PROPN
ejpam-4734	229	19	.	.	PUNCT
ejpam-4734	230	1	then	then	ADV
ejpam-4734	230	2	,	,	PUNCT
ejpam-4734	230	3	int⋆(k	int⋆(k	PUNCT
ejpam-4734	230	4	)	)	PUNCT
ejpam-4734	230	5	is	be	AUX
ejpam-4734	230	6	j	j	PROPN
ejpam-4734	230	7	⋆-preopen	⋆-preopen	NOUN
ejpam-4734	230	8	in	in	ADP
ejpam-4734	230	9	y	y	PROPN
ejpam-4734	230	10	,	,	PUNCT
ejpam-4734	230	11	by	by	ADP
ejpam-4734	230	12	(	(	PUNCT
ejpam-4734	230	13	5	5	NUM
ejpam-4734	230	14	)	)	PUNCT
ejpam-4734	230	15	,	,	PUNCT
ejpam-4734	230	16	sβcli	sβcli	NOUN
ejpam-4734	230	17	(	(	PUNCT
ejpam-4734	230	18	f−(int⋆(k	f−(int⋆(k	ADJ
ejpam-4734	230	19	)	)	PUNCT
ejpam-4734	230	20	)	)	PUNCT
ejpam-4734	230	21	)	)	PUNCT
ejpam-4734	231	1	=	=	SYM
ejpam-4734	231	2	sβcli	sβcli	X
ejpam-4734	231	3	(	(	PUNCT
ejpam-4734	231	4	f−(int⋆(cl⋆(int⋆(k	f−(int⋆(cl⋆(int⋆(k	ADJ
ejpam-4734	231	5	)	)	PUNCT
ejpam-4734	231	6	)	)	PUNCT
ejpam-4734	231	7	)	)	PUNCT
ejpam-4734	231	8	)	)	PUNCT
ejpam-4734	231	9	)	)	PUNCT
ejpam-4734	232	1	⊆	⊆	X
ejpam-4734	232	2	f−(cl⋆(int⋆(k	f−(cl⋆(int⋆(k	NOUN
ejpam-4734	232	3	)	)	PUNCT
ejpam-4734	232	4	)	)	PUNCT
ejpam-4734	232	5	)	)	PUNCT
ejpam-4734	233	1	=	=	SYM
ejpam-4734	233	2	f−(k	f−(k	PROPN
ejpam-4734	233	3	)	)	PUNCT
ejpam-4734	233	4	.	.	PUNCT
ejpam-4734	234	1	(	(	PUNCT
ejpam-4734	234	2	6	6	X
ejpam-4734	234	3	)	)	PUNCT
ejpam-4734	234	4	⇒	⇒	NOUN
ejpam-4734	234	5	(	(	PUNCT
ejpam-4734	234	6	7	7	NUM
ejpam-4734	234	7	):	):	PUNCT
ejpam-4734	234	8	let	let	VERB
ejpam-4734	234	9	v	v	PART
ejpam-4734	234	10	be	be	AUX
ejpam-4734	234	11	any	any	PRON
ejpam-4734	234	12	strong	strong	ADJ
ejpam-4734	234	13	β	β	NOUN
ejpam-4734	234	14	-	-	ADJ
ejpam-4734	234	15	j	j	PROPN
ejpam-4734	234	16	-open	-open	NOUN
ejpam-4734	234	17	set	set	NOUN
ejpam-4734	234	18	of	of	ADP
ejpam-4734	234	19	y	y	PROPN
ejpam-4734	234	20	.	.	PUNCT
ejpam-4734	235	1	then	then	ADV
ejpam-4734	235	2	,	,	PUNCT
ejpam-4734	235	3	v	v	ADP
ejpam-4734	235	4	⊆	⊆	NUM
ejpam-4734	235	5	cl⋆(int(cl⋆(v	cl⋆(int(cl⋆(v	PROPN
ejpam-4734	235	6	)	)	PUNCT
ejpam-4734	235	7	)	)	PUNCT
ejpam-4734	235	8	)	)	PUNCT
ejpam-4734	235	9	.	.	PUNCT
ejpam-4734	236	1	since	since	SCONJ
ejpam-4734	236	2	cl⋆(v	cl⋆(v	PROPN
ejpam-4734	236	3	)	)	PUNCT
ejpam-4734	236	4	isr	isr	PROPN
ejpam-4734	236	5	-	-	PUNCT
ejpam-4734	236	6	j	j	PROPN
ejpam-4734	236	7	⋆-closed	⋆-close	VERB
ejpam-4734	236	8	in	in	ADP
ejpam-4734	236	9	y	y	PROPN
ejpam-4734	236	10	.	.	PUNCT
ejpam-4734	237	1	thus	thus	ADV
ejpam-4734	237	2	,	,	PUNCT
ejpam-4734	237	3	by	by	ADP
ejpam-4734	237	4	(	(	PUNCT
ejpam-4734	237	5	6	6	NUM
ejpam-4734	237	6	)	)	PUNCT
ejpam-4734	237	7	,	,	PUNCT
ejpam-4734	237	8	sβcli	sβcli	NOUN
ejpam-4734	237	9	(	(	PUNCT
ejpam-4734	237	10	f−(int⋆(cl⋆(v	f−(int⋆(cl⋆(v	PROPN
ejpam-4734	237	11	)	)	PUNCT
ejpam-4734	237	12	)	)	PUNCT
ejpam-4734	237	13	)	)	PUNCT
ejpam-4734	237	14	)	)	PUNCT
ejpam-4734	238	1	⊆	⊆	NUM
ejpam-4734	238	2	f−(cl⋆(v	f−(cl⋆(v	NOUN
ejpam-4734	238	3	)	)	PUNCT
ejpam-4734	238	4	)	)	PUNCT
ejpam-4734	238	5	.	.	PUNCT
ejpam-4734	239	1	(	(	PUNCT
ejpam-4734	239	2	7	7	X
ejpam-4734	239	3	)	)	PUNCT
ejpam-4734	239	4	⇒	⇒	NOUN
ejpam-4734	239	5	(	(	PUNCT
ejpam-4734	239	6	8)	8)	NUM
ejpam-4734	239	7	:	:	PUNCT
ejpam-4734	239	8	this	this	PRON
ejpam-4734	239	9	is	be	AUX
ejpam-4734	239	10	obvious	obvious	ADJ
ejpam-4734	239	11	since	since	SCONJ
ejpam-4734	239	12	every	every	DET
ejpam-4734	239	13	j	j	PROPN
ejpam-4734	239	14	⋆-semi	⋆-semi	X
ejpam-4734	239	15	-	-	PUNCT
ejpam-4734	239	16	open	open	ADJ
ejpam-4734	239	17	set	set	NOUN
ejpam-4734	239	18	is	be	AUX
ejpam-4734	239	19	strong	strong	ADJ
ejpam-4734	239	20	β	β	NOUN
ejpam-4734	239	21	-	-	PUNCT
ejpam-4734	239	22	j	j	NOUN
ejpam-4734	239	23	-open	-open	NOUN
ejpam-4734	239	24	.	.	PUNCT
ejpam-4734	240	1	(	(	PUNCT
ejpam-4734	240	2	8)	8)	NUM
ejpam-4734	240	3	⇒	⇒	NOUN
ejpam-4734	240	4	(	(	PUNCT
ejpam-4734	240	5	1	1	NUM
ejpam-4734	240	6	):	):	PUNCT
ejpam-4734	240	7	let	let	VERB
ejpam-4734	240	8	v	v	PART
ejpam-4734	240	9	be	be	AUX
ejpam-4734	240	10	any	any	DET
ejpam-4734	240	11	⋆-open	⋆-open	ADJ
ejpam-4734	240	12	set	set	NOUN
ejpam-4734	240	13	of	of	ADP
ejpam-4734	240	14	y	y	PROPN
ejpam-4734	240	15	.	.	PUNCT
ejpam-4734	241	1	then	then	ADV
ejpam-4734	241	2	,	,	PUNCT
ejpam-4734	241	3	since	since	SCONJ
ejpam-4734	241	4	v	v	NOUN
ejpam-4734	241	5	is	be	AUX
ejpam-4734	241	6	j	j	PROPN
ejpam-4734	241	7	⋆-semi	⋆-semi	NOUN
ejpam-4734	241	8	-	-	PUNCT
ejpam-4734	241	9	open	open	ADJ
ejpam-4734	241	10	set	set	NOUN
ejpam-4734	241	11	in	in	ADP
ejpam-4734	241	12	y	y	PROPN
ejpam-4734	241	13	,	,	PUNCT
ejpam-4734	241	14	by	by	ADP
ejpam-4734	241	15	(	(	PUNCT
ejpam-4734	241	16	8)	8)	NUM
ejpam-4734	241	17	,	,	PUNCT
ejpam-4734	241	18	we	we	PRON
ejpam-4734	241	19	have	have	VERB
ejpam-4734	241	20	sβcli	sβcli	NOUN
ejpam-4734	241	21	(	(	PUNCT
ejpam-4734	241	22	f−(v	f−(v	NOUN
ejpam-4734	241	23	)	)	PUNCT
ejpam-4734	241	24	)	)	PUNCT
ejpam-4734	242	1	⊆	⊆	X
ejpam-4734	242	2	sβcli	sβcli	NOUN
ejpam-4734	242	3	(	(	PUNCT
ejpam-4734	242	4	f−(int⋆(cl⋆(v	f−(int⋆(cl⋆(v	PROPN
ejpam-4734	242	5	)	)	PUNCT
ejpam-4734	242	6	)	)	PUNCT
ejpam-4734	242	7	)	)	PUNCT
ejpam-4734	242	8	)	)	PUNCT
ejpam-4734	243	1	⊆	⊆	NUM
ejpam-4734	243	2	f−(cl⋆(v	f−(cl⋆(v	NOUN
ejpam-4734	243	3	)	)	PUNCT
ejpam-4734	243	4	)	)	PUNCT
ejpam-4734	243	5	.	.	PUNCT
ejpam-4734	244	1	by	by	ADP
ejpam-4734	244	2	theorem	theorem	NOUN
ejpam-4734	244	3	3	3	NUM
ejpam-4734	244	4	,	,	PUNCT
ejpam-4734	244	5	f	f	PROPN
ejpam-4734	244	6	is	be	AUX
ejpam-4734	244	7	upper	upper	ADJ
ejpam-4734	244	8	weakly	weakly	ADJ
ejpam-4734	244	9	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	244	10	.	.	PUNCT
ejpam-4734	244	11	theorem	theorem	PROPN
ejpam-4734	244	12	6	6	NUM
ejpam-4734	244	13	.	.	PUNCT
ejpam-4734	244	14	for	for	ADP
ejpam-4734	244	15	a	a	DET
ejpam-4734	244	16	multifunction	multifunction	NOUN
ejpam-4734	244	17	f	f	NOUN
ejpam-4734	244	18	:	:	PUNCT
ejpam-4734	244	19	(	(	PUNCT
ejpam-4734	244	20	x	x	X
ejpam-4734	244	21	,	,	PUNCT
ejpam-4734	244	22	τ	τ	PROPN
ejpam-4734	244	23	,	,	PUNCT
ejpam-4734	244	24	i	i	NOUN
ejpam-4734	244	25	)	)	PUNCT
ejpam-4734	244	26	→	→	PUNCT
ejpam-4734	244	27	(	(	PUNCT
ejpam-4734	244	28	y	y	PROPN
ejpam-4734	244	29	,	,	PUNCT
ejpam-4734	244	30	σ	σ	PROPN
ejpam-4734	244	31	,	,	PUNCT
ejpam-4734	244	32	j	j	PROPN
ejpam-4734	244	33	)	)	PUNCT
ejpam-4734	244	34	,	,	PUNCT
ejpam-4734	244	35	the	the	DET
ejpam-4734	244	36	following	follow	VERB
ejpam-4734	244	37	properties	property	NOUN
ejpam-4734	244	38	are	be	AUX
ejpam-4734	244	39	equivalent	equivalent	ADJ
ejpam-4734	244	40	:	:	PUNCT
ejpam-4734	244	41	(	(	PUNCT
ejpam-4734	244	42	1	1	X
ejpam-4734	244	43	)	)	PUNCT
ejpam-4734	244	44	f	f	PROPN
ejpam-4734	244	45	is	be	AUX
ejpam-4734	244	46	lower	low	ADJ
ejpam-4734	244	47	weakly	weakly	ADJ
ejpam-4734	244	48	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	244	49	;	;	PUNCT
ejpam-4734	244	50	(	(	PUNCT
ejpam-4734	244	51	2	2	X
ejpam-4734	244	52	)	)	PUNCT
ejpam-4734	244	53	sβcli	sβcli	NOUN
ejpam-4734	244	54	(	(	PUNCT
ejpam-4734	244	55	f+(int⋆(⋆θcl(b	f+(int⋆(⋆θcl(b	PROPN
ejpam-4734	244	56	)	)	PUNCT
ejpam-4734	244	57	)	)	PUNCT
ejpam-4734	244	58	)	)	PUNCT
ejpam-4734	244	59	)	)	PUNCT
ejpam-4734	245	1	⊆	⊆	NUM
ejpam-4734	245	2	f+(⋆θcl(b	f+(⋆θcl(b	NOUN
ejpam-4734	245	3	)	)	PUNCT
ejpam-4734	245	4	)	)	PUNCT
ejpam-4734	245	5	for	for	ADP
ejpam-4734	245	6	every	every	DET
ejpam-4734	245	7	subset	subset	NOUN
ejpam-4734	245	8	b	b	PROPN
ejpam-4734	245	9	of	of	ADP
ejpam-4734	245	10	y	y	PROPN
ejpam-4734	245	11	;	;	PUNCT
ejpam-4734	245	12	(	(	PUNCT
ejpam-4734	245	13	3	3	X
ejpam-4734	245	14	)	)	PUNCT
ejpam-4734	245	15	sβcli	sβcli	NOUN
ejpam-4734	245	16	(	(	PUNCT
ejpam-4734	245	17	f+(int⋆(cl⋆(b	f+(int⋆(cl⋆(b	NOUN
ejpam-4734	245	18	)	)	PUNCT
ejpam-4734	245	19	)	)	PUNCT
ejpam-4734	245	20	)	)	PUNCT
ejpam-4734	245	21	)	)	PUNCT
ejpam-4734	246	1	⊆	⊆	NUM
ejpam-4734	246	2	f+(⋆θcl(b	f+(⋆θcl(b	NOUN
ejpam-4734	246	3	)	)	PUNCT
ejpam-4734	246	4	)	)	PUNCT
ejpam-4734	246	5	for	for	ADP
ejpam-4734	246	6	every	every	DET
ejpam-4734	246	7	subset	subset	NOUN
ejpam-4734	246	8	b	b	PROPN
ejpam-4734	246	9	of	of	ADP
ejpam-4734	246	10	y	y	PROPN
ejpam-4734	246	11	;	;	PUNCT
ejpam-4734	246	12	(	(	PUNCT
ejpam-4734	246	13	4	4	X
ejpam-4734	246	14	)	)	PUNCT
ejpam-4734	246	15	sβcli	sβcli	NOUN
ejpam-4734	246	16	(	(	PUNCT
ejpam-4734	246	17	f+(int⋆(cl⋆(v	f+(int⋆(cl⋆(v	NOUN
ejpam-4734	246	18	)	)	PUNCT
ejpam-4734	246	19	)	)	PUNCT
ejpam-4734	246	20	)	)	PUNCT
ejpam-4734	246	21	)	)	PUNCT
ejpam-4734	247	1	⊆	⊆	NUM
ejpam-4734	247	2	f+(cl⋆(v	f+(cl⋆(v	PROPN
ejpam-4734	247	3	)	)	PUNCT
ejpam-4734	247	4	)	)	PUNCT
ejpam-4734	247	5	for	for	ADP
ejpam-4734	247	6	every	every	DET
ejpam-4734	247	7	⋆-open	⋆-open	NOUN
ejpam-4734	247	8	set	set	VERB
ejpam-4734	247	9	v	v	NOUN
ejpam-4734	247	10	of	of	ADP
ejpam-4734	247	11	y	y	PROPN
ejpam-4734	247	12	;	;	PUNCT
ejpam-4734	247	13	(	(	PUNCT
ejpam-4734	247	14	5	5	X
ejpam-4734	247	15	)	)	PUNCT
ejpam-4734	247	16	sβcli	sβcli	NOUN
ejpam-4734	247	17	(	(	PUNCT
ejpam-4734	247	18	f+(int⋆(cl⋆(v	f+(int⋆(cl⋆(v	NOUN
ejpam-4734	247	19	)	)	PUNCT
ejpam-4734	247	20	)	)	PUNCT
ejpam-4734	247	21	)	)	PUNCT
ejpam-4734	247	22	)	)	PUNCT
ejpam-4734	248	1	⊆	⊆	NUM
ejpam-4734	248	2	f+(cl⋆(v	f+(cl⋆(v	PROPN
ejpam-4734	248	3	)	)	PUNCT
ejpam-4734	248	4	)	)	PUNCT
ejpam-4734	248	5	for	for	SCONJ
ejpam-4734	248	6	every	every	DET
ejpam-4734	248	7	j	j	PROPN
ejpam-4734	248	8	⋆-preopen	⋆-preopen	ADV
ejpam-4734	248	9	set	set	VERB
ejpam-4734	248	10	v	v	NUM
ejpam-4734	248	11	of	of	ADP
ejpam-4734	248	12	y	y	PROPN
ejpam-4734	248	13	;	;	PUNCT
ejpam-4734	248	14	(	(	PUNCT
ejpam-4734	248	15	6	6	X
ejpam-4734	248	16	)	)	PUNCT
ejpam-4734	248	17	sβcli	sβcli	NOUN
ejpam-4734	248	18	(	(	PUNCT
ejpam-4734	248	19	f+(int⋆(k	f+(int⋆(k	NOUN
ejpam-4734	248	20	)	)	PUNCT
ejpam-4734	248	21	)	)	PUNCT
ejpam-4734	248	22	)	)	PUNCT
ejpam-4734	249	1	⊆	⊆	NUM
ejpam-4734	249	2	f+(k	f+(k	NOUN
ejpam-4734	249	3	)	)	PUNCT
ejpam-4734	249	4	for	for	SCONJ
ejpam-4734	249	5	every	every	DET
ejpam-4734	249	6	r	r	PROPN
ejpam-4734	249	7	-	-	PUNCT
ejpam-4734	249	8	j	j	NOUN
ejpam-4734	249	9	⋆-closed	⋆-close	VERB
ejpam-4734	249	10	set	set	VERB
ejpam-4734	249	11	k	k	PROPN
ejpam-4734	249	12	of	of	ADP
ejpam-4734	249	13	y	y	PROPN
ejpam-4734	249	14	;	;	PUNCT
ejpam-4734	249	15	(	(	PUNCT
ejpam-4734	249	16	7	7	X
ejpam-4734	249	17	)	)	PUNCT
ejpam-4734	249	18	sβcli	sβcli	NOUN
ejpam-4734	249	19	(	(	PUNCT
ejpam-4734	249	20	f+(int⋆(cl⋆(v	f+(int⋆(cl⋆(v	NOUN
ejpam-4734	249	21	)	)	PUNCT
ejpam-4734	249	22	)	)	PUNCT
ejpam-4734	249	23	)	)	PUNCT
ejpam-4734	249	24	)	)	PUNCT
ejpam-4734	250	1	⊆	⊆	NUM
ejpam-4734	250	2	f+(cl⋆(v	f+(cl⋆(v	PROPN
ejpam-4734	250	3	)	)	PUNCT
ejpam-4734	250	4	)	)	PUNCT
ejpam-4734	250	5	for	for	ADP
ejpam-4734	250	6	every	every	DET
ejpam-4734	250	7	strongly	strongly	ADV
ejpam-4734	250	8	β	β	NOUN
ejpam-4734	250	9	-	-	ADJ
ejpam-4734	250	10	j	j	ADJ
ejpam-4734	250	11	-open	-open	NOUN
ejpam-4734	250	12	set	set	VERB
ejpam-4734	250	13	v	v	NOUN
ejpam-4734	250	14	of	of	ADP
ejpam-4734	250	15	y	y	PROPN
ejpam-4734	250	16	;	;	PUNCT
ejpam-4734	250	17	(	(	PUNCT
ejpam-4734	250	18	8)	8)	NUM
ejpam-4734	250	19	sβcli	sβcli	NOUN
ejpam-4734	250	20	(	(	PUNCT
ejpam-4734	250	21	f+(int⋆(cl⋆(v	f+(int⋆(cl⋆(v	NOUN
ejpam-4734	250	22	)	)	PUNCT
ejpam-4734	250	23	)	)	PUNCT
ejpam-4734	250	24	)	)	PUNCT
ejpam-4734	250	25	)	)	PUNCT
ejpam-4734	251	1	⊆	⊆	NUM
ejpam-4734	251	2	f+(cl⋆(v	f+(cl⋆(v	PROPN
ejpam-4734	251	3	)	)	PUNCT
ejpam-4734	251	4	)	)	PUNCT
ejpam-4734	251	5	for	for	ADP
ejpam-4734	251	6	every	every	DET
ejpam-4734	251	7	j	j	PROPN
ejpam-4734	251	8	⋆-semi	⋆-semi	X
ejpam-4734	251	9	-	-	PUNCT
ejpam-4734	251	10	open	open	ADJ
ejpam-4734	251	11	set	set	VERB
ejpam-4734	251	12	v	v	NOUN
ejpam-4734	251	13	of	of	ADP
ejpam-4734	251	14	y	y	PROPN
ejpam-4734	251	15	.	.	PUNCT
ejpam-4734	252	1	proof	proof	NOUN
ejpam-4734	252	2	.	.	PUNCT
ejpam-4734	253	1	the	the	DET
ejpam-4734	253	2	proof	proof	NOUN
ejpam-4734	253	3	is	be	AUX
ejpam-4734	253	4	similar	similar	ADJ
ejpam-4734	253	5	to	to	ADP
ejpam-4734	253	6	that	that	PRON
ejpam-4734	253	7	of	of	ADP
ejpam-4734	253	8	theorem	theorem	NOUN
ejpam-4734	253	9	5	5	NUM
ejpam-4734	253	10	.	.	PUNCT
ejpam-4734	253	11	c.	c.	PROPN
ejpam-4734	253	12	boonpok	boonpok	PROPN
ejpam-4734	253	13	,	,	PUNCT
ejpam-4734	253	14	j.	j.	PROPN
ejpam-4734	253	15	khampakdee	khampakdee	PROPN
ejpam-4734	253	16	/	/	PUNCT
ejpam-4734	253	17	eur	eur	PROPN
ejpam-4734	253	18	.	.	PUNCT
ejpam-4734	254	1	j.	j.	PROPN
ejpam-4734	254	2	pure	pure	PROPN
ejpam-4734	254	3	appl	appl	PROPN
ejpam-4734	254	4	.	.	PROPN
ejpam-4734	254	5	math	math	PROPN
ejpam-4734	254	6	,	,	PUNCT
ejpam-4734	254	7	16	16	NUM
ejpam-4734	254	8	(	(	PUNCT
ejpam-4734	254	9	4	4	NUM
ejpam-4734	254	10	)	)	PUNCT
ejpam-4734	254	11	(	(	PUNCT
ejpam-4734	254	12	2023	2023	NUM
ejpam-4734	254	13	)	)	PUNCT
ejpam-4734	254	14	,	,	PUNCT
ejpam-4734	254	15	2544	2544	NUM
ejpam-4734	254	16	-	-	SYM
ejpam-4734	254	17	2556	2556	NUM
ejpam-4734	254	18	2552	2552	NUM
ejpam-4734	254	19	corollary	corollary	NOUN
ejpam-4734	254	20	3	3	NUM
ejpam-4734	254	21	.	.	PUNCT
ejpam-4734	255	1	for	for	ADP
ejpam-4734	255	2	a	a	DET
ejpam-4734	255	3	function	function	NOUN
ejpam-4734	255	4	f	f	NOUN
ejpam-4734	255	5	:	:	PUNCT
ejpam-4734	255	6	(	(	PUNCT
ejpam-4734	255	7	x	x	X
ejpam-4734	255	8	,	,	PUNCT
ejpam-4734	255	9	τ	τ	PROPN
ejpam-4734	255	10	,	,	PUNCT
ejpam-4734	255	11	i	i	NOUN
ejpam-4734	255	12	)	)	PUNCT
ejpam-4734	255	13	→	→	PUNCT
ejpam-4734	255	14	(	(	PUNCT
ejpam-4734	255	15	y	y	PROPN
ejpam-4734	255	16	,	,	PUNCT
ejpam-4734	255	17	σ	σ	PROPN
ejpam-4734	255	18	,	,	PUNCT
ejpam-4734	255	19	j	j	PROPN
ejpam-4734	255	20	)	)	PUNCT
ejpam-4734	255	21	,	,	PUNCT
ejpam-4734	255	22	the	the	DET
ejpam-4734	255	23	following	follow	VERB
ejpam-4734	255	24	properties	property	NOUN
ejpam-4734	255	25	are	be	AUX
ejpam-4734	255	26	equivalent	equivalent	ADJ
ejpam-4734	255	27	:	:	PUNCT
ejpam-4734	255	28	(	(	PUNCT
ejpam-4734	255	29	1	1	X
ejpam-4734	255	30	)	)	PUNCT
ejpam-4734	255	31	f	f	PROPN
ejpam-4734	255	32	is	be	AUX
ejpam-4734	255	33	weakly	weakly	ADV
ejpam-4734	255	34	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	255	35	;	;	PUNCT
ejpam-4734	255	36	(	(	PUNCT
ejpam-4734	255	37	2	2	X
ejpam-4734	255	38	)	)	PUNCT
ejpam-4734	255	39	sβcli	sβcli	NOUN
ejpam-4734	255	40	(	(	PUNCT
ejpam-4734	255	41	f−1(int⋆(⋆θcl(b	f−1(int⋆(⋆θcl(b	NOUN
ejpam-4734	255	42	)	)	PUNCT
ejpam-4734	255	43	)	)	PUNCT
ejpam-4734	255	44	)	)	PUNCT
ejpam-4734	255	45	)	)	PUNCT
ejpam-4734	256	1	⊆	⊆	NUM
ejpam-4734	256	2	f−1(⋆θcl(b	f−1(⋆θcl(b	NOUN
ejpam-4734	256	3	)	)	PUNCT
ejpam-4734	256	4	)	)	PUNCT
ejpam-4734	256	5	for	for	ADP
ejpam-4734	256	6	every	every	DET
ejpam-4734	256	7	subset	subset	NOUN
ejpam-4734	256	8	b	b	PROPN
ejpam-4734	256	9	of	of	ADP
ejpam-4734	256	10	y	y	PROPN
ejpam-4734	256	11	;	;	PUNCT
ejpam-4734	256	12	(	(	PUNCT
ejpam-4734	256	13	3	3	X
ejpam-4734	256	14	)	)	PUNCT
ejpam-4734	256	15	sβcli	sβcli	NOUN
ejpam-4734	256	16	(	(	PUNCT
ejpam-4734	256	17	f−1(int⋆(cl⋆(b	f−1(int⋆(cl⋆(b	PROPN
ejpam-4734	256	18	)	)	PUNCT
ejpam-4734	256	19	)	)	PUNCT
ejpam-4734	256	20	)	)	PUNCT
ejpam-4734	256	21	)	)	PUNCT
ejpam-4734	256	22	⊆	⊆	NUM
ejpam-4734	256	23	f−1(⋆θcl(b	f−1(⋆θcl(b	NOUN
ejpam-4734	256	24	)	)	PUNCT
ejpam-4734	256	25	)	)	PUNCT
ejpam-4734	256	26	for	for	ADP
ejpam-4734	256	27	every	every	DET
ejpam-4734	256	28	subset	subset	NOUN
ejpam-4734	256	29	b	b	PROPN
ejpam-4734	256	30	of	of	ADP
ejpam-4734	256	31	y	y	PROPN
ejpam-4734	256	32	;	;	PUNCT
ejpam-4734	256	33	(	(	PUNCT
ejpam-4734	256	34	4	4	X
ejpam-4734	256	35	)	)	PUNCT
ejpam-4734	256	36	sβcli	sβcli	NOUN
ejpam-4734	256	37	(	(	PUNCT
ejpam-4734	256	38	f−1(int⋆(cl⋆(v	f−1(int⋆(cl⋆(v	NOUN
ejpam-4734	256	39	)	)	PUNCT
ejpam-4734	256	40	)	)	PUNCT
ejpam-4734	256	41	)	)	PUNCT
ejpam-4734	256	42	)	)	PUNCT
ejpam-4734	257	1	⊆	⊆	NUM
ejpam-4734	257	2	f−1(cl⋆(v	f−1(cl⋆(v	NOUN
ejpam-4734	257	3	)	)	PUNCT
ejpam-4734	257	4	)	)	PUNCT
ejpam-4734	257	5	for	for	ADP
ejpam-4734	257	6	every	every	DET
ejpam-4734	257	7	⋆-open	⋆-open	NOUN
ejpam-4734	257	8	set	set	VERB
ejpam-4734	257	9	v	v	NOUN
ejpam-4734	257	10	of	of	ADP
ejpam-4734	257	11	y	y	PROPN
ejpam-4734	257	12	;	;	PUNCT
ejpam-4734	257	13	(	(	PUNCT
ejpam-4734	257	14	5	5	X
ejpam-4734	257	15	)	)	PUNCT
ejpam-4734	257	16	sβcli	sβcli	NOUN
ejpam-4734	257	17	(	(	PUNCT
ejpam-4734	257	18	f−1(int⋆(cl⋆(v	f−1(int⋆(cl⋆(v	NOUN
ejpam-4734	257	19	)	)	PUNCT
ejpam-4734	257	20	)	)	PUNCT
ejpam-4734	257	21	)	)	PUNCT
ejpam-4734	257	22	)	)	PUNCT
ejpam-4734	258	1	⊆	⊆	NUM
ejpam-4734	258	2	f−1(cl⋆(v	f−1(cl⋆(v	NOUN
ejpam-4734	258	3	)	)	PUNCT
ejpam-4734	258	4	)	)	PUNCT
ejpam-4734	258	5	for	for	SCONJ
ejpam-4734	258	6	every	every	DET
ejpam-4734	258	7	j	j	PROPN
ejpam-4734	258	8	⋆-preopen	⋆-preopen	ADV
ejpam-4734	258	9	set	set	VERB
ejpam-4734	258	10	v	v	NUM
ejpam-4734	258	11	of	of	ADP
ejpam-4734	258	12	y	y	PROPN
ejpam-4734	258	13	;	;	PUNCT
ejpam-4734	258	14	(	(	PUNCT
ejpam-4734	258	15	6	6	X
ejpam-4734	258	16	)	)	PUNCT
ejpam-4734	258	17	sβcli	sβcli	NOUN
ejpam-4734	258	18	(	(	PUNCT
ejpam-4734	258	19	f−1(int⋆(k	f−1(int⋆(k	NOUN
ejpam-4734	258	20	)	)	PUNCT
ejpam-4734	258	21	)	)	PUNCT
ejpam-4734	258	22	)	)	PUNCT
ejpam-4734	259	1	⊆	⊆	NUM
ejpam-4734	259	2	f−1(k	f−1(k	PROPN
ejpam-4734	259	3	)	)	PUNCT
ejpam-4734	259	4	for	for	SCONJ
ejpam-4734	259	5	every	every	DET
ejpam-4734	259	6	r	r	PROPN
ejpam-4734	259	7	-	-	PUNCT
ejpam-4734	259	8	j	j	NOUN
ejpam-4734	259	9	⋆-closed	⋆-close	VERB
ejpam-4734	259	10	set	set	VERB
ejpam-4734	259	11	k	k	PROPN
ejpam-4734	259	12	of	of	ADP
ejpam-4734	259	13	y	y	PROPN
ejpam-4734	259	14	;	;	PUNCT
ejpam-4734	259	15	(	(	PUNCT
ejpam-4734	259	16	7	7	X
ejpam-4734	259	17	)	)	PUNCT
ejpam-4734	259	18	sβcli	sβcli	NOUN
ejpam-4734	259	19	(	(	PUNCT
ejpam-4734	259	20	f−1(int⋆(cl⋆(v	f−1(int⋆(cl⋆(v	NOUN
ejpam-4734	259	21	)	)	PUNCT
ejpam-4734	259	22	)	)	PUNCT
ejpam-4734	259	23	)	)	PUNCT
ejpam-4734	259	24	)	)	PUNCT
ejpam-4734	260	1	⊆	⊆	NUM
ejpam-4734	260	2	f−1(cl⋆(v	f−1(cl⋆(v	NOUN
ejpam-4734	260	3	)	)	PUNCT
ejpam-4734	260	4	)	)	PUNCT
ejpam-4734	260	5	for	for	ADP
ejpam-4734	260	6	every	every	DET
ejpam-4734	260	7	strongly	strongly	ADV
ejpam-4734	260	8	β	β	NOUN
ejpam-4734	260	9	-	-	ADJ
ejpam-4734	260	10	j	j	ADJ
ejpam-4734	260	11	-open	-open	NOUN
ejpam-4734	260	12	set	set	VERB
ejpam-4734	260	13	v	v	NOUN
ejpam-4734	260	14	of	of	ADP
ejpam-4734	260	15	y	y	PROPN
ejpam-4734	260	16	;	;	PUNCT
ejpam-4734	260	17	(	(	PUNCT
ejpam-4734	260	18	8)	8)	NUM
ejpam-4734	260	19	sβcli	sβcli	NOUN
ejpam-4734	260	20	(	(	PUNCT
ejpam-4734	260	21	f−1(int⋆(cl⋆(v	f−1(int⋆(cl⋆(v	NOUN
ejpam-4734	260	22	)	)	PUNCT
ejpam-4734	260	23	)	)	PUNCT
ejpam-4734	260	24	)	)	PUNCT
ejpam-4734	260	25	)	)	PUNCT
ejpam-4734	260	26	⊆	⊆	NUM
ejpam-4734	260	27	f−1(cl⋆(v	f−1(cl⋆(v	NOUN
ejpam-4734	260	28	)	)	PUNCT
ejpam-4734	260	29	)	)	PUNCT
ejpam-4734	260	30	for	for	ADP
ejpam-4734	260	31	every	every	DET
ejpam-4734	260	32	j	j	PROPN
ejpam-4734	260	33	⋆-semi	⋆-semi	X
ejpam-4734	260	34	-	-	PUNCT
ejpam-4734	260	35	open	open	ADJ
ejpam-4734	260	36	set	set	VERB
ejpam-4734	260	37	v	v	NOUN
ejpam-4734	260	38	of	of	ADP
ejpam-4734	260	39	y	y	PROPN
ejpam-4734	260	40	.	.	PUNCT
ejpam-4734	260	41	theorem	theorem	VERB
ejpam-4734	260	42	7	7	NUM
ejpam-4734	260	43	.	.	X
ejpam-4734	260	44	for	for	ADP
ejpam-4734	260	45	a	a	DET
ejpam-4734	260	46	multifunction	multifunction	NOUN
ejpam-4734	260	47	f	f	NOUN
ejpam-4734	260	48	:	:	PUNCT
ejpam-4734	260	49	(	(	PUNCT
ejpam-4734	260	50	x	x	X
ejpam-4734	260	51	,	,	PUNCT
ejpam-4734	260	52	τ	τ	PROPN
ejpam-4734	260	53	,	,	PUNCT
ejpam-4734	260	54	i	i	NOUN
ejpam-4734	260	55	)	)	PUNCT
ejpam-4734	261	1	→	→	PUNCT
ejpam-4734	261	2	(	(	PUNCT
ejpam-4734	261	3	y	y	PROPN
ejpam-4734	261	4	,	,	PUNCT
ejpam-4734	261	5	σ	σ	PROPN
ejpam-4734	261	6	,	,	PUNCT
ejpam-4734	261	7	j	j	PROPN
ejpam-4734	261	8	)	)	PUNCT
ejpam-4734	261	9	,	,	PUNCT
ejpam-4734	261	10	the	the	DET
ejpam-4734	261	11	following	follow	VERB
ejpam-4734	261	12	properties	property	NOUN
ejpam-4734	261	13	are	be	AUX
ejpam-4734	261	14	equivalent	equivalent	ADJ
ejpam-4734	261	15	:	:	PUNCT
ejpam-4734	261	16	(	(	PUNCT
ejpam-4734	261	17	1	1	X
ejpam-4734	261	18	)	)	PUNCT
ejpam-4734	261	19	f	f	PROPN
ejpam-4734	261	20	is	be	AUX
ejpam-4734	261	21	upper	upper	ADJ
ejpam-4734	261	22	weakly	weakly	ADJ
ejpam-4734	261	23	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	261	24	;	;	PUNCT
ejpam-4734	261	25	(	(	PUNCT
ejpam-4734	261	26	2	2	X
ejpam-4734	261	27	)	)	PUNCT
ejpam-4734	261	28	sβcli	sβcli	NOUN
ejpam-4734	261	29	(	(	PUNCT
ejpam-4734	261	30	f−(v	f−(v	NOUN
ejpam-4734	261	31	)	)	PUNCT
ejpam-4734	261	32	)	)	PUNCT
ejpam-4734	262	1	⊆	⊆	NUM
ejpam-4734	262	2	f−(cl⋆(v	f−(cl⋆(v	NOUN
ejpam-4734	262	3	)	)	PUNCT
ejpam-4734	262	4	)	)	PUNCT
ejpam-4734	262	5	for	for	SCONJ
ejpam-4734	262	6	every	every	DET
ejpam-4734	262	7	j	j	PROPN
ejpam-4734	262	8	⋆-preopen	⋆-preopen	ADV
ejpam-4734	262	9	set	set	VERB
ejpam-4734	262	10	v	v	NUM
ejpam-4734	262	11	of	of	ADP
ejpam-4734	262	12	y	y	PROPN
ejpam-4734	262	13	;	;	PUNCT
ejpam-4734	262	14	(	(	PUNCT
ejpam-4734	262	15	3	3	X
ejpam-4734	262	16	)	)	PUNCT
ejpam-4734	262	17	f+(v	f+(v	NOUN
ejpam-4734	262	18	)	)	PUNCT
ejpam-4734	263	1	⊆	⊆	NUM
ejpam-4734	263	2	sβinti	sβinti	NOUN
ejpam-4734	263	3	(	(	PUNCT
ejpam-4734	263	4	f+(cl⋆(v	f+(cl⋆(v	PROPN
ejpam-4734	263	5	)	)	PUNCT
ejpam-4734	263	6	)	)	PUNCT
ejpam-4734	263	7	)	)	PUNCT
ejpam-4734	263	8	for	for	ADP
ejpam-4734	263	9	every	every	DET
ejpam-4734	263	10	j	j	PROPN
ejpam-4734	263	11	⋆-preopen	⋆-preopen	ADV
ejpam-4734	263	12	set	set	VERB
ejpam-4734	263	13	v	v	NUM
ejpam-4734	263	14	of	of	ADP
ejpam-4734	263	15	y	y	PROPN
ejpam-4734	263	16	.	.	PUNCT
ejpam-4734	264	1	proof	proof	NOUN
ejpam-4734	264	2	.	.	PUNCT
ejpam-4734	265	1	(	(	PUNCT
ejpam-4734	265	2	1	1	X
ejpam-4734	265	3	)	)	PUNCT
ejpam-4734	265	4	⇒	⇒	NOUN
ejpam-4734	265	5	(	(	PUNCT
ejpam-4734	265	6	2	2	NUM
ejpam-4734	265	7	):	):	PUNCT
ejpam-4734	265	8	let	let	VERB
ejpam-4734	265	9	v	v	PART
ejpam-4734	265	10	be	be	AUX
ejpam-4734	265	11	any	any	DET
ejpam-4734	265	12	j	j	PROPN
ejpam-4734	265	13	⋆-preopen	⋆-preopen	ADV
ejpam-4734	265	14	set	set	NOUN
ejpam-4734	265	15	of	of	ADP
ejpam-4734	265	16	y	y	PROPN
ejpam-4734	265	17	.	.	PUNCT
ejpam-4734	266	1	since	since	SCONJ
ejpam-4734	266	2	f	f	PROPN
ejpam-4734	266	3	is	be	AUX
ejpam-4734	266	4	upper	upper	ADJ
ejpam-4734	266	5	weakly	weakly	ADV
ejpam-4734	266	6	sβ(⋆)continuous	sβ(⋆)continuous	ADJ
ejpam-4734	266	7	,	,	PUNCT
ejpam-4734	266	8	by	by	ADP
ejpam-4734	266	9	theorem	theorem	NOUN
ejpam-4734	266	10	3	3	NUM
ejpam-4734	266	11	,	,	PUNCT
ejpam-4734	266	12	sβcli	sβcli	NOUN
ejpam-4734	266	13	(	(	PUNCT
ejpam-4734	266	14	f−(v	f−(v	NOUN
ejpam-4734	266	15	)	)	PUNCT
ejpam-4734	266	16	)	)	PUNCT
ejpam-4734	267	1	⊆	⊆	X
ejpam-4734	267	2	sβcli	sβcli	NOUN
ejpam-4734	267	3	(	(	PUNCT
ejpam-4734	267	4	f−(int⋆(cl⋆(v	f−(int⋆(cl⋆(v	PROPN
ejpam-4734	267	5	)	)	PUNCT
ejpam-4734	267	6	)	)	PUNCT
ejpam-4734	267	7	)	)	PUNCT
ejpam-4734	267	8	)	)	PUNCT
ejpam-4734	268	1	⊆	⊆	NUM
ejpam-4734	268	2	f−(cl⋆(v	f−(cl⋆(v	NOUN
ejpam-4734	268	3	)	)	PUNCT
ejpam-4734	268	4	)	)	PUNCT
ejpam-4734	268	5	.	.	PUNCT
ejpam-4734	269	1	(	(	PUNCT
ejpam-4734	269	2	2	2	X
ejpam-4734	269	3	)	)	PUNCT
ejpam-4734	269	4	⇒	⇒	NOUN
ejpam-4734	269	5	(	(	PUNCT
ejpam-4734	269	6	3	3	NUM
ejpam-4734	269	7	):	):	PUNCT
ejpam-4734	269	8	let	let	VERB
ejpam-4734	269	9	v	v	PART
ejpam-4734	269	10	be	be	AUX
ejpam-4734	269	11	any	any	DET
ejpam-4734	269	12	j	j	PROPN
ejpam-4734	269	13	⋆-preopen	⋆-preopen	ADV
ejpam-4734	269	14	set	set	NOUN
ejpam-4734	269	15	of	of	ADP
ejpam-4734	269	16	y	y	PROPN
ejpam-4734	269	17	.	.	PUNCT
ejpam-4734	270	1	then	then	ADV
ejpam-4734	270	2	,	,	PUNCT
ejpam-4734	270	3	we	we	PRON
ejpam-4734	270	4	have	have	VERB
ejpam-4734	270	5	v	v	NUM
ejpam-4734	270	6	⊆	⊆	NUM
ejpam-4734	270	7	int⋆(cl⋆(v	int⋆(cl⋆(v	NOUN
ejpam-4734	270	8	)	)	PUNCT
ejpam-4734	270	9	)	)	PUNCT
ejpam-4734	271	1	and	and	CCONJ
ejpam-4734	271	2	y	y	PROPN
ejpam-4734	271	3	−	−	PROPN
ejpam-4734	271	4	v	v	PROPN
ejpam-4734	271	5	⊇	⊇	PROPN
ejpam-4734	271	6	cl⋆(int⋆(y	cl⋆(int⋆(y	PROPN
ejpam-4734	271	7	−	−	PROPN
ejpam-4734	271	8	v	v	NOUN
ejpam-4734	271	9	)	)	PUNCT
ejpam-4734	271	10	)	)	PUNCT
ejpam-4734	271	11	.	.	PUNCT
ejpam-4734	272	1	thus	thus	ADV
ejpam-4734	272	2	,	,	PUNCT
ejpam-4734	272	3	by	by	ADP
ejpam-4734	272	4	(	(	PUNCT
ejpam-4734	272	5	3	3	NUM
ejpam-4734	272	6	)	)	PUNCT
ejpam-4734	272	7	,	,	PUNCT
ejpam-4734	272	8	x	x	PUNCT
ejpam-4734	272	9	−	−	NOUN
ejpam-4734	272	10	f+(v	f+(v	NOUN
ejpam-4734	272	11	)	)	PUNCT
ejpam-4734	272	12	=	=	PUNCT
ejpam-4734	272	13	f−(y	f−(y	NOUN
ejpam-4734	272	14	−	−	ADP
ejpam-4734	272	15	v	v	NOUN
ejpam-4734	272	16	)	)	PUNCT
ejpam-4734	272	17	⊇	⊇	NOUN
ejpam-4734	272	18	f−(cl⋆(int⋆(y	f−(cl⋆(int⋆(y	NUM
ejpam-4734	272	19	−	−	PROPN
ejpam-4734	272	20	v	v	NOUN
ejpam-4734	272	21	)	)	PUNCT
ejpam-4734	272	22	)	)	PUNCT
ejpam-4734	272	23	)	)	PUNCT
ejpam-4734	273	1	⊇	⊇	NOUN
ejpam-4734	273	2	sβcli	sβcli	NOUN
ejpam-4734	273	3	(	(	PUNCT
ejpam-4734	273	4	f−(int⋆(y	f−(int⋆(y	PROPN
ejpam-4734	273	5	−	−	PROPN
ejpam-4734	273	6	v	v	NOUN
ejpam-4734	273	7	)	)	PUNCT
ejpam-4734	273	8	)	)	PUNCT
ejpam-4734	273	9	)	)	PUNCT
ejpam-4734	274	1	=	=	SYM
ejpam-4734	274	2	sβcli	sβcli	NOUN
ejpam-4734	274	3	(	(	PUNCT
ejpam-4734	274	4	f−(y	f−(y	NOUN
ejpam-4734	274	5	−	−	NOUN
ejpam-4734	274	6	cl⋆(v	cl⋆(v	NOUN
ejpam-4734	274	7	)	)	PUNCT
ejpam-4734	274	8	)	)	PUNCT
ejpam-4734	274	9	)	)	PUNCT
ejpam-4734	275	1	=	=	SYM
ejpam-4734	275	2	sβcli	sβcli	NOUN
ejpam-4734	275	3	(	(	PUNCT
ejpam-4734	275	4	x	x	NOUN
ejpam-4734	275	5	−	−	PROPN
ejpam-4734	275	6	f+(cl⋆(v	f+(cl⋆(v	PROPN
ejpam-4734	275	7	)	)	PUNCT
ejpam-4734	275	8	)	)	PUNCT
ejpam-4734	275	9	)	)	PUNCT
ejpam-4734	276	1	=	=	PUNCT
ejpam-4734	276	2	x	x	PUNCT
ejpam-4734	277	1	−	−	PROPN
ejpam-4734	277	2	sβinti	sβinti	NOUN
ejpam-4734	277	3	(	(	PUNCT
ejpam-4734	277	4	f+(cl⋆(v	f+(cl⋆(v	PROPN
ejpam-4734	277	5	)	)	PUNCT
ejpam-4734	277	6	)	)	PUNCT
ejpam-4734	277	7	)	)	PUNCT
ejpam-4734	277	8	and	and	CCONJ
ejpam-4734	277	9	hence	hence	ADV
ejpam-4734	277	10	f+(v	f+(v	PROPN
ejpam-4734	277	11	)	)	PUNCT
ejpam-4734	278	1	⊆	⊆	NUM
ejpam-4734	278	2	sβinti	sβinti	NOUN
ejpam-4734	278	3	(	(	PUNCT
ejpam-4734	278	4	f+(cl⋆(v	f+(cl⋆(v	PROPN
ejpam-4734	278	5	)	)	PUNCT
ejpam-4734	278	6	)	)	PUNCT
ejpam-4734	278	7	)	)	PUNCT
ejpam-4734	278	8	.	.	PUNCT
ejpam-4734	279	1	(	(	PUNCT
ejpam-4734	279	2	3	3	X
ejpam-4734	279	3	)	)	PUNCT
ejpam-4734	279	4	⇒	⇒	NOUN
ejpam-4734	279	5	(	(	PUNCT
ejpam-4734	279	6	1	1	NUM
ejpam-4734	279	7	):	):	PUNCT
ejpam-4734	279	8	let	let	VERB
ejpam-4734	279	9	v	v	PART
ejpam-4734	279	10	be	be	AUX
ejpam-4734	279	11	any	any	DET
ejpam-4734	279	12	⋆-open	⋆-open	ADJ
ejpam-4734	279	13	set	set	NOUN
ejpam-4734	279	14	of	of	ADP
ejpam-4734	279	15	y	y	PROPN
ejpam-4734	279	16	.	.	PUNCT
ejpam-4734	280	1	then	then	ADV
ejpam-4734	280	2	,	,	PUNCT
ejpam-4734	280	3	v	v	NOUN
ejpam-4734	280	4	is	be	AUX
ejpam-4734	280	5	j	j	PROPN
ejpam-4734	280	6	⋆-preopen	⋆-preopen	NOUN
ejpam-4734	280	7	in	in	ADP
ejpam-4734	280	8	y	y	PROPN
ejpam-4734	280	9	,	,	PUNCT
ejpam-4734	280	10	by	by	ADP
ejpam-4734	280	11	(	(	PUNCT
ejpam-4734	280	12	4	4	NUM
ejpam-4734	280	13	)	)	PUNCT
ejpam-4734	280	14	,	,	PUNCT
ejpam-4734	280	15	f+(v	f+(v	PROPN
ejpam-4734	280	16	)	)	PUNCT
ejpam-4734	281	1	⊆	⊆	NUM
ejpam-4734	281	2	sβinti	sβinti	NOUN
ejpam-4734	281	3	(	(	PUNCT
ejpam-4734	281	4	f+(cl⋆(v	f+(cl⋆(v	PROPN
ejpam-4734	281	5	)	)	PUNCT
ejpam-4734	281	6	)	)	PUNCT
ejpam-4734	281	7	)	)	PUNCT
ejpam-4734	281	8	.	.	PUNCT
ejpam-4734	282	1	thus	thus	ADV
ejpam-4734	282	2	,	,	PUNCT
ejpam-4734	282	3	f	f	PROPN
ejpam-4734	282	4	is	be	AUX
ejpam-4734	282	5	upper	upper	ADJ
ejpam-4734	282	6	weakly	weakly	ADV
ejpam-4734	282	7	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	282	8	by	by	ADP
ejpam-4734	282	9	theorem	theorem	NOUN
ejpam-4734	282	10	3	3	NUM
ejpam-4734	282	11	.	.	PUNCT
ejpam-4734	282	12	theorem	theorem	NOUN
ejpam-4734	282	13	8	8	NUM
ejpam-4734	282	14	.	.	PUNCT
ejpam-4734	282	15	for	for	ADP
ejpam-4734	282	16	a	a	DET
ejpam-4734	282	17	multifunction	multifunction	NOUN
ejpam-4734	282	18	f	f	NOUN
ejpam-4734	282	19	:	:	PUNCT
ejpam-4734	282	20	(	(	PUNCT
ejpam-4734	282	21	x	x	X
ejpam-4734	282	22	,	,	PUNCT
ejpam-4734	282	23	τ	τ	PROPN
ejpam-4734	282	24	,	,	PUNCT
ejpam-4734	282	25	i	i	NOUN
ejpam-4734	282	26	)	)	PUNCT
ejpam-4734	282	27	→	→	PUNCT
ejpam-4734	282	28	(	(	PUNCT
ejpam-4734	282	29	y	y	PROPN
ejpam-4734	282	30	,	,	PUNCT
ejpam-4734	282	31	σ	σ	PROPN
ejpam-4734	282	32	,	,	PUNCT
ejpam-4734	282	33	j	j	PROPN
ejpam-4734	282	34	)	)	PUNCT
ejpam-4734	282	35	,	,	PUNCT
ejpam-4734	282	36	the	the	DET
ejpam-4734	282	37	following	follow	VERB
ejpam-4734	282	38	properties	property	NOUN
ejpam-4734	282	39	are	be	AUX
ejpam-4734	282	40	equivalent	equivalent	ADJ
ejpam-4734	282	41	:	:	PUNCT
ejpam-4734	282	42	c.	c.	PROPN
ejpam-4734	282	43	boonpok	boonpok	PROPN
ejpam-4734	282	44	,	,	PUNCT
ejpam-4734	282	45	j.	j.	PROPN
ejpam-4734	282	46	khampakdee	khampakdee	PROPN
ejpam-4734	282	47	/	/	PUNCT
ejpam-4734	282	48	eur	eur	PROPN
ejpam-4734	282	49	.	.	PUNCT
ejpam-4734	283	1	j.	j.	PROPN
ejpam-4734	283	2	pure	pure	PROPN
ejpam-4734	283	3	appl	appl	PROPN
ejpam-4734	283	4	.	.	PROPN
ejpam-4734	283	5	math	math	PROPN
ejpam-4734	283	6	,	,	PUNCT
ejpam-4734	283	7	16	16	NUM
ejpam-4734	283	8	(	(	PUNCT
ejpam-4734	283	9	4	4	NUM
ejpam-4734	283	10	)	)	PUNCT
ejpam-4734	283	11	(	(	PUNCT
ejpam-4734	283	12	2023	2023	NUM
ejpam-4734	283	13	)	)	PUNCT
ejpam-4734	283	14	,	,	PUNCT
ejpam-4734	283	15	2544	2544	NUM
ejpam-4734	283	16	-	-	SYM
ejpam-4734	283	17	2556	2556	NUM
ejpam-4734	283	18	2553	2553	NUM
ejpam-4734	283	19	(	(	PUNCT
ejpam-4734	283	20	1	1	NUM
ejpam-4734	283	21	)	)	PUNCT
ejpam-4734	283	22	f	f	PROPN
ejpam-4734	283	23	is	be	AUX
ejpam-4734	283	24	lower	low	ADJ
ejpam-4734	283	25	weakly	weakly	ADJ
ejpam-4734	283	26	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	283	27	;	;	PUNCT
ejpam-4734	283	28	(	(	PUNCT
ejpam-4734	283	29	2	2	X
ejpam-4734	283	30	)	)	PUNCT
ejpam-4734	283	31	sβcli	sβcli	NOUN
ejpam-4734	283	32	(	(	PUNCT
ejpam-4734	283	33	f+(v	f+(v	PROPN
ejpam-4734	283	34	)	)	PUNCT
ejpam-4734	283	35	)	)	PUNCT
ejpam-4734	284	1	⊆	⊆	NUM
ejpam-4734	284	2	f+(cl⋆(v	f+(cl⋆(v	PROPN
ejpam-4734	284	3	)	)	PUNCT
ejpam-4734	284	4	)	)	PUNCT
ejpam-4734	284	5	for	for	SCONJ
ejpam-4734	284	6	every	every	DET
ejpam-4734	284	7	j	j	PROPN
ejpam-4734	284	8	⋆-preopen	⋆-preopen	ADV
ejpam-4734	284	9	set	set	VERB
ejpam-4734	284	10	v	v	NUM
ejpam-4734	284	11	of	of	ADP
ejpam-4734	284	12	y	y	PROPN
ejpam-4734	284	13	;	;	PUNCT
ejpam-4734	284	14	(	(	PUNCT
ejpam-4734	284	15	3	3	X
ejpam-4734	284	16	)	)	PUNCT
ejpam-4734	284	17	f−(v	f−(v	NOUN
ejpam-4734	284	18	)	)	PUNCT
ejpam-4734	285	1	⊆	⊆	NUM
ejpam-4734	285	2	sβinti	sβinti	NOUN
ejpam-4734	285	3	(	(	PUNCT
ejpam-4734	285	4	f−(cl⋆(v	f−(cl⋆(v	PROPN
ejpam-4734	285	5	)	)	PUNCT
ejpam-4734	285	6	)	)	PUNCT
ejpam-4734	285	7	)	)	PUNCT
ejpam-4734	285	8	for	for	ADP
ejpam-4734	285	9	every	every	DET
ejpam-4734	285	10	j	j	PROPN
ejpam-4734	285	11	⋆-preopen	⋆-preopen	ADV
ejpam-4734	285	12	set	set	VERB
ejpam-4734	285	13	v	v	NUM
ejpam-4734	285	14	of	of	ADP
ejpam-4734	285	15	y	y	PROPN
ejpam-4734	285	16	.	.	PUNCT
ejpam-4734	286	1	proof	proof	NOUN
ejpam-4734	286	2	.	.	PUNCT
ejpam-4734	287	1	the	the	DET
ejpam-4734	287	2	proof	proof	NOUN
ejpam-4734	287	3	is	be	AUX
ejpam-4734	287	4	similar	similar	ADJ
ejpam-4734	287	5	to	to	ADP
ejpam-4734	287	6	that	that	PRON
ejpam-4734	287	7	of	of	ADP
ejpam-4734	287	8	theorem	theorem	ADJ
ejpam-4734	287	9	7	7	NUM
ejpam-4734	287	10	.	.	PUNCT
ejpam-4734	287	11	corollary	corollary	ADJ
ejpam-4734	287	12	4	4	NUM
ejpam-4734	287	13	.	.	PUNCT
ejpam-4734	287	14	for	for	ADP
ejpam-4734	287	15	a	a	DET
ejpam-4734	287	16	function	function	NOUN
ejpam-4734	287	17	f	f	NOUN
ejpam-4734	287	18	:	:	PUNCT
ejpam-4734	287	19	(	(	PUNCT
ejpam-4734	287	20	x	x	X
ejpam-4734	287	21	,	,	PUNCT
ejpam-4734	287	22	τ	τ	PROPN
ejpam-4734	287	23	,	,	PUNCT
ejpam-4734	287	24	i	i	NOUN
ejpam-4734	287	25	)	)	PUNCT
ejpam-4734	287	26	→	→	PUNCT
ejpam-4734	287	27	(	(	PUNCT
ejpam-4734	287	28	y	y	PROPN
ejpam-4734	287	29	,	,	PUNCT
ejpam-4734	287	30	σ	σ	PROPN
ejpam-4734	287	31	,	,	PUNCT
ejpam-4734	287	32	j	j	PROPN
ejpam-4734	287	33	)	)	PUNCT
ejpam-4734	287	34	,	,	PUNCT
ejpam-4734	287	35	the	the	DET
ejpam-4734	287	36	following	follow	VERB
ejpam-4734	287	37	properties	property	NOUN
ejpam-4734	287	38	are	be	AUX
ejpam-4734	287	39	equivalent	equivalent	ADJ
ejpam-4734	287	40	:	:	PUNCT
ejpam-4734	287	41	(	(	PUNCT
ejpam-4734	287	42	1	1	X
ejpam-4734	287	43	)	)	PUNCT
ejpam-4734	287	44	f	f	PROPN
ejpam-4734	287	45	is	be	AUX
ejpam-4734	287	46	weakly	weakly	ADV
ejpam-4734	287	47	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	287	48	;	;	PUNCT
ejpam-4734	287	49	(	(	PUNCT
ejpam-4734	287	50	2	2	X
ejpam-4734	287	51	)	)	PUNCT
ejpam-4734	287	52	sβcli	sβcli	NOUN
ejpam-4734	287	53	(	(	PUNCT
ejpam-4734	287	54	f−1(v	f−1(v	NOUN
ejpam-4734	287	55	)	)	PUNCT
ejpam-4734	287	56	)	)	PUNCT
ejpam-4734	288	1	⊆	⊆	NUM
ejpam-4734	288	2	f−1(cl⋆(v	f−1(cl⋆(v	NOUN
ejpam-4734	288	3	)	)	PUNCT
ejpam-4734	288	4	)	)	PUNCT
ejpam-4734	288	5	for	for	SCONJ
ejpam-4734	288	6	every	every	DET
ejpam-4734	288	7	j	j	PROPN
ejpam-4734	288	8	⋆-preopen	⋆-preopen	ADV
ejpam-4734	288	9	set	set	VERB
ejpam-4734	288	10	v	v	NUM
ejpam-4734	288	11	of	of	ADP
ejpam-4734	288	12	y	y	PROPN
ejpam-4734	288	13	;	;	PUNCT
ejpam-4734	288	14	(	(	PUNCT
ejpam-4734	288	15	3	3	X
ejpam-4734	288	16	)	)	PUNCT
ejpam-4734	288	17	f−1(v	f−1(v	NOUN
ejpam-4734	288	18	)	)	PUNCT
ejpam-4734	289	1	⊆	⊆	NUM
ejpam-4734	289	2	sβinti	sβinti	NOUN
ejpam-4734	289	3	(	(	PUNCT
ejpam-4734	289	4	f−1(cl⋆(v	f−1(cl⋆(v	PROPN
ejpam-4734	289	5	)	)	PUNCT
ejpam-4734	289	6	)	)	PUNCT
ejpam-4734	289	7	)	)	PUNCT
ejpam-4734	289	8	for	for	ADP
ejpam-4734	289	9	every	every	DET
ejpam-4734	289	10	j	j	PROPN
ejpam-4734	289	11	⋆-preopen	⋆-preopen	ADV
ejpam-4734	289	12	set	set	VERB
ejpam-4734	289	13	v	v	NUM
ejpam-4734	289	14	of	of	ADP
ejpam-4734	289	15	y	y	PROPN
ejpam-4734	289	16	.	.	PUNCT
ejpam-4734	290	1	definition	definition	NOUN
ejpam-4734	290	2	3	3	NUM
ejpam-4734	290	3	.	.	PUNCT
ejpam-4734	291	1	[	[	X
ejpam-4734	291	2	4	4	X
ejpam-4734	291	3	]	]	PUNCT
ejpam-4734	291	4	a	a	DET
ejpam-4734	291	5	multifunction	multifunction	NOUN
ejpam-4734	291	6	f	f	NOUN
ejpam-4734	291	7	:	:	PUNCT
ejpam-4734	291	8	(	(	PUNCT
ejpam-4734	291	9	x	x	X
ejpam-4734	291	10	,	,	PUNCT
ejpam-4734	291	11	τ	τ	PROPN
ejpam-4734	291	12	,	,	PUNCT
ejpam-4734	291	13	i	i	NOUN
ejpam-4734	291	14	)	)	PUNCT
ejpam-4734	291	15	→	→	PUNCT
ejpam-4734	291	16	(	(	PUNCT
ejpam-4734	291	17	y	y	PROPN
ejpam-4734	291	18	,	,	PUNCT
ejpam-4734	291	19	σ	σ	PROPN
ejpam-4734	291	20	,	,	PUNCT
ejpam-4734	291	21	j	j	PROPN
ejpam-4734	291	22	)	)	PUNCT
ejpam-4734	291	23	is	be	AUX
ejpam-4734	291	24	said	say	VERB
ejpam-4734	291	25	to	to	PART
ejpam-4734	291	26	be	be	AUX
ejpam-4734	291	27	:	:	PUNCT
ejpam-4734	291	28	(	(	PUNCT
ejpam-4734	291	29	1	1	X
ejpam-4734	291	30	)	)	PUNCT
ejpam-4734	291	31	upper	upper	ADJ
ejpam-4734	291	32	almost	almost	ADV
ejpam-4734	291	33	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	291	34	at	at	ADP
ejpam-4734	291	35	a	a	DET
ejpam-4734	291	36	point	point	NOUN
ejpam-4734	291	37	x	x	SYM
ejpam-4734	291	38	∈	∈	NOUN
ejpam-4734	291	39	x	x	INTJ
ejpam-4734	291	40	if	if	SCONJ
ejpam-4734	291	41	for	for	SCONJ
ejpam-4734	291	42	each	each	DET
ejpam-4734	291	43	⋆-open	⋆-open	ADV
ejpam-4734	291	44	set	set	VERB
ejpam-4734	291	45	v	v	NUM
ejpam-4734	291	46	of	of	ADP
ejpam-4734	291	47	y	y	PROPN
ejpam-4734	291	48	containing	contain	VERB
ejpam-4734	291	49	f	f	PROPN
ejpam-4734	291	50	(	(	PUNCT
ejpam-4734	291	51	x	x	NOUN
ejpam-4734	291	52	)	)	PUNCT
ejpam-4734	291	53	,	,	PUNCT
ejpam-4734	291	54	there	there	PRON
ejpam-4734	291	55	exists	exist	VERB
ejpam-4734	291	56	a	a	DET
ejpam-4734	291	57	strong	strong	ADJ
ejpam-4734	291	58	β	β	NOUN
ejpam-4734	291	59	-	-	ADJ
ejpam-4734	291	60	i	i	PRON
ejpam-4734	291	61	-open	-open	VERB
ejpam-4734	291	62	set	set	VERB
ejpam-4734	291	63	u	u	NOUN
ejpam-4734	291	64	of	of	ADP
ejpam-4734	291	65	x	x	PUNCT
ejpam-4734	291	66	containing	contain	VERB
ejpam-4734	291	67	x	x	PUNCT
ejpam-4734	291	68	such	such	ADJ
ejpam-4734	291	69	that	that	SCONJ
ejpam-4734	291	70	f	f	PROPN
ejpam-4734	291	71	(	(	PUNCT
ejpam-4734	291	72	u	u	NOUN
ejpam-4734	291	73	)	)	PUNCT
ejpam-4734	291	74	⊆	⊆	NUM
ejpam-4734	291	75	int⋆(cl(v	int⋆(cl(v	NOUN
ejpam-4734	291	76	)	)	PUNCT
ejpam-4734	291	77	)	)	PUNCT
ejpam-4734	291	78	;	;	PUNCT
ejpam-4734	291	79	(	(	PUNCT
ejpam-4734	291	80	2	2	X
ejpam-4734	291	81	)	)	PUNCT
ejpam-4734	291	82	lower	low	ADJ
ejpam-4734	291	83	almost	almost	ADV
ejpam-4734	291	84	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	291	85	at	at	ADP
ejpam-4734	291	86	a	a	DET
ejpam-4734	291	87	point	point	NOUN
ejpam-4734	291	88	x	x	SYM
ejpam-4734	291	89	∈	∈	NOUN
ejpam-4734	291	90	x	x	INTJ
ejpam-4734	291	91	if	if	SCONJ
ejpam-4734	291	92	for	for	SCONJ
ejpam-4734	291	93	each	each	DET
ejpam-4734	291	94	⋆-open	⋆-open	ADV
ejpam-4734	291	95	set	set	VERB
ejpam-4734	291	96	v	v	NUM
ejpam-4734	291	97	of	of	ADP
ejpam-4734	291	98	y	y	PRON
ejpam-4734	291	99	such	such	ADJ
ejpam-4734	291	100	that	that	SCONJ
ejpam-4734	291	101	f	f	PROPN
ejpam-4734	291	102	(	(	PUNCT
ejpam-4734	291	103	x	x	NOUN
ejpam-4734	291	104	)	)	PUNCT
ejpam-4734	291	105	∩	∩	NOUN
ejpam-4734	291	106	v	v	ADP
ejpam-4734	291	107	̸=	̸=	PROPN
ejpam-4734	291	108	∅	∅	NOUN
ejpam-4734	291	109	,	,	PUNCT
ejpam-4734	291	110	there	there	PRON
ejpam-4734	291	111	exists	exist	VERB
ejpam-4734	291	112	a	a	DET
ejpam-4734	291	113	strong	strong	ADJ
ejpam-4734	291	114	β	β	NOUN
ejpam-4734	291	115	-	-	ADJ
ejpam-4734	291	116	i	i	PRON
ejpam-4734	291	117	-open	-open	VERB
ejpam-4734	291	118	set	set	VERB
ejpam-4734	291	119	u	u	NOUN
ejpam-4734	291	120	of	of	ADP
ejpam-4734	291	121	x	x	PUNCT
ejpam-4734	291	122	containing	contain	VERB
ejpam-4734	291	123	x	x	PUNCT
ejpam-4734	291	124	such	such	ADJ
ejpam-4734	291	125	that	that	SCONJ
ejpam-4734	291	126	f	f	PROPN
ejpam-4734	291	127	(	(	PUNCT
ejpam-4734	291	128	z	z	NOUN
ejpam-4734	291	129	)	)	PUNCT
ejpam-4734	291	130	∩	∩	ADJ
ejpam-4734	291	131	int⋆(cl(v	int⋆(cl(v	NOUN
ejpam-4734	291	132	)	)	PUNCT
ejpam-4734	291	133	)	)	PUNCT
ejpam-4734	292	1	̸=	̸=	NOUN
ejpam-4734	292	2	∅	∅	NOUN
ejpam-4734	292	3	for	for	ADP
ejpam-4734	292	4	every	every	DET
ejpam-4734	292	5	z	z	NOUN
ejpam-4734	292	6	∈	∈	PROPN
ejpam-4734	292	7	u	u	NOUN
ejpam-4734	292	8	;	;	PUNCT
ejpam-4734	292	9	(	(	PUNCT
ejpam-4734	292	10	3	3	X
ejpam-4734	292	11	)	)	PUNCT
ejpam-4734	292	12	upper	upper	ADJ
ejpam-4734	292	13	(	(	PUNCT
ejpam-4734	292	14	resp	resp	NOUN
ejpam-4734	292	15	.	.	PUNCT
ejpam-4734	293	1	lower	low	ADJ
ejpam-4734	293	2	)	)	PUNCT
ejpam-4734	293	3	almost	almost	ADV
ejpam-4734	293	4	β(⋆)-continuous	β(⋆)-continuous	ADJ
ejpam-4734	293	5	if	if	SCONJ
ejpam-4734	293	6	f	f	PROPN
ejpam-4734	293	7	has	have	VERB
ejpam-4734	293	8	this	this	DET
ejpam-4734	293	9	property	property	NOUN
ejpam-4734	293	10	at	at	ADP
ejpam-4734	293	11	each	each	DET
ejpam-4734	293	12	point	point	NOUN
ejpam-4734	293	13	of	of	ADP
ejpam-4734	293	14	x.	x.	NOUN
ejpam-4734	293	15	remark	remark	PROPN
ejpam-4734	293	16	1	1	NUM
ejpam-4734	293	17	.	.	PUNCT
ejpam-4734	294	1	for	for	ADP
ejpam-4734	294	2	a	a	DET
ejpam-4734	294	3	multifunction	multifunction	NOUN
ejpam-4734	294	4	f	f	NOUN
ejpam-4734	294	5	:	:	PUNCT
ejpam-4734	294	6	(	(	PUNCT
ejpam-4734	294	7	x	x	X
ejpam-4734	294	8	,	,	PUNCT
ejpam-4734	294	9	τ	τ	PROPN
ejpam-4734	294	10	,	,	PUNCT
ejpam-4734	294	11	i	i	NOUN
ejpam-4734	294	12	)	)	PUNCT
ejpam-4734	294	13	→	→	PUNCT
ejpam-4734	294	14	(	(	PUNCT
ejpam-4734	294	15	y	y	PROPN
ejpam-4734	294	16	,	,	PUNCT
ejpam-4734	294	17	σ	σ	PROPN
ejpam-4734	294	18	,	,	PUNCT
ejpam-4734	294	19	j	j	PROPN
ejpam-4734	294	20	)	)	PUNCT
ejpam-4734	294	21	,	,	PUNCT
ejpam-4734	294	22	the	the	DET
ejpam-4734	294	23	following	follow	VERB
ejpam-4734	294	24	implication	implication	NOUN
ejpam-4734	294	25	holds	hold	VERB
ejpam-4734	294	26	:	:	PUNCT
ejpam-4734	294	27	upper	upper	ADJ
ejpam-4734	294	28	almost	almost	ADV
ejpam-4734	294	29	sβ(⋆)-continuity	sβ(⋆)-continuity	NOUN
ejpam-4734	294	30	⇒	⇒	NOUN
ejpam-4734	294	31	upper	upper	ADJ
ejpam-4734	294	32	weak	weak	ADJ
ejpam-4734	294	33	sβ(⋆)-continuity	sβ(⋆)-continuity	NOUN
ejpam-4734	294	34	.	.	PUNCT
ejpam-4734	295	1	the	the	DET
ejpam-4734	295	2	converse	converse	NOUN
ejpam-4734	295	3	of	of	ADP
ejpam-4734	295	4	the	the	DET
ejpam-4734	295	5	implication	implication	NOUN
ejpam-4734	295	6	is	be	AUX
ejpam-4734	295	7	not	not	PART
ejpam-4734	295	8	true	true	ADJ
ejpam-4734	295	9	in	in	ADP
ejpam-4734	295	10	general	general	ADJ
ejpam-4734	295	11	.	.	PUNCT
ejpam-4734	296	1	we	we	PRON
ejpam-4734	296	2	give	give	VERB
ejpam-4734	296	3	an	an	DET
ejpam-4734	296	4	example	example	NOUN
ejpam-4734	296	5	for	for	ADP
ejpam-4734	296	6	the	the	DET
ejpam-4734	296	7	implication	implication	NOUN
ejpam-4734	296	8	as	as	SCONJ
ejpam-4734	296	9	follows	follow	VERB
ejpam-4734	296	10	.	.	PUNCT
ejpam-4734	296	11	example	example	NOUN
ejpam-4734	297	1	1	1	NUM
ejpam-4734	297	2	.	.	PUNCT
ejpam-4734	297	3	let	let	VERB
ejpam-4734	297	4	x	x	PUNCT
ejpam-4734	297	5	=	=	PRON
ejpam-4734	297	6	{	{	PUNCT
ejpam-4734	297	7	1	1	NUM
ejpam-4734	297	8	,	,	PUNCT
ejpam-4734	297	9	2	2	NUM
ejpam-4734	297	10	,	,	PUNCT
ejpam-4734	297	11	3	3	NUM
ejpam-4734	297	12	}	}	PUNCT
ejpam-4734	297	13	with	with	ADP
ejpam-4734	297	14	a	a	DET
ejpam-4734	297	15	topology	topology	NOUN
ejpam-4734	297	16	τ	τ	X
ejpam-4734	297	17	=	=	SYM
ejpam-4734	297	18	{	{	PUNCT
ejpam-4734	297	19	∅	∅	NOUN
ejpam-4734	297	20	,	,	PUNCT
ejpam-4734	297	21	{	{	PUNCT
ejpam-4734	297	22	1	1	NUM
ejpam-4734	297	23	}	}	PUNCT
ejpam-4734	297	24	,	,	PUNCT
ejpam-4734	297	25	{	{	PUNCT
ejpam-4734	297	26	2	2	NUM
ejpam-4734	297	27	}	}	PUNCT
ejpam-4734	297	28	,	,	PUNCT
ejpam-4734	297	29	{	{	PUNCT
ejpam-4734	297	30	1	1	NUM
ejpam-4734	297	31	,	,	PUNCT
ejpam-4734	297	32	2	2	NUM
ejpam-4734	297	33	}	}	PUNCT
ejpam-4734	297	34	,	,	PUNCT
ejpam-4734	297	35	x	x	NOUN
ejpam-4734	297	36	}	}	PUNCT
ejpam-4734	297	37	and	and	CCONJ
ejpam-4734	297	38	an	an	DET
ejpam-4734	297	39	ideal	ideal	NOUN
ejpam-4734	297	40	i	i	X
ejpam-4734	297	41	=	=	SYM
ejpam-4734	297	42	{	{	PUNCT
ejpam-4734	297	43	∅	∅	NOUN
ejpam-4734	297	44	,	,	PUNCT
ejpam-4734	297	45	{	{	PUNCT
ejpam-4734	297	46	1	1	NUM
ejpam-4734	297	47	}	}	PUNCT
ejpam-4734	297	48	}	}	PUNCT
ejpam-4734	297	49	.	.	PUNCT
ejpam-4734	298	1	let	let	VERB
ejpam-4734	298	2	y	y	PROPN
ejpam-4734	298	3	=	=	PUNCT
ejpam-4734	298	4	{	{	PUNCT
ejpam-4734	298	5	a	a	PRON
ejpam-4734	298	6	,	,	PUNCT
ejpam-4734	298	7	b	b	NOUN
ejpam-4734	298	8	,	,	PUNCT
ejpam-4734	298	9	c	c	NOUN
ejpam-4734	298	10	}	}	PUNCT
ejpam-4734	298	11	with	with	ADP
ejpam-4734	298	12	a	a	DET
ejpam-4734	298	13	topology	topology	NOUN
ejpam-4734	298	14	σ	σ	NOUN
ejpam-4734	298	15	=	=	SYM
ejpam-4734	298	16	{	{	PUNCT
ejpam-4734	298	17	∅	∅	NOUN
ejpam-4734	298	18	,	,	PUNCT
ejpam-4734	298	19	{	{	PUNCT
ejpam-4734	298	20	a	a	X
ejpam-4734	298	21	}	}	PUNCT
ejpam-4734	298	22	,	,	PUNCT
ejpam-4734	298	23	{	{	PUNCT
ejpam-4734	298	24	a	a	DET
ejpam-4734	298	25	,	,	PUNCT
ejpam-4734	298	26	b	b	NOUN
ejpam-4734	298	27	}	}	PUNCT
ejpam-4734	298	28	,	,	PUNCT
ejpam-4734	298	29	y	y	PROPN
ejpam-4734	298	30	}	}	PUNCT
ejpam-4734	298	31	and	and	CCONJ
ejpam-4734	298	32	an	an	DET
ejpam-4734	298	33	ideal	ideal	NOUN
ejpam-4734	298	34	j	j	PROPN
ejpam-4734	299	1	=	=	PUNCT
ejpam-4734	299	2	{	{	PUNCT
ejpam-4734	299	3	∅	∅	NOUN
ejpam-4734	299	4	,	,	PUNCT
ejpam-4734	299	5	{	{	PUNCT
ejpam-4734	299	6	c	c	NOUN
ejpam-4734	299	7	}	}	PUNCT
ejpam-4734	299	8	}	}	PUNCT
ejpam-4734	299	9	.	.	PUNCT
ejpam-4734	300	1	a	a	DET
ejpam-4734	300	2	multifunction	multifunction	NOUN
ejpam-4734	300	3	f	f	NOUN
ejpam-4734	300	4	:	:	PUNCT
ejpam-4734	300	5	(	(	PUNCT
ejpam-4734	300	6	x	x	X
ejpam-4734	300	7	,	,	PUNCT
ejpam-4734	300	8	τ	τ	PROPN
ejpam-4734	300	9	,	,	PUNCT
ejpam-4734	300	10	i	i	NOUN
ejpam-4734	300	11	)	)	PUNCT
ejpam-4734	300	12	→	→	PUNCT
ejpam-4734	300	13	(	(	PUNCT
ejpam-4734	300	14	y	y	PROPN
ejpam-4734	300	15	,	,	PUNCT
ejpam-4734	300	16	σ	σ	PROPN
ejpam-4734	300	17	,	,	PUNCT
ejpam-4734	300	18	j	j	PROPN
ejpam-4734	300	19	)	)	PUNCT
ejpam-4734	300	20	is	be	AUX
ejpam-4734	300	21	defined	define	VERB
ejpam-4734	300	22	as	as	SCONJ
ejpam-4734	300	23	follows	follow	VERB
ejpam-4734	300	24	:	:	PUNCT
ejpam-4734	300	25	f	f	X
ejpam-4734	300	26	(	(	PUNCT
ejpam-4734	300	27	1	1	X
ejpam-4734	300	28	)	)	PUNCT
ejpam-4734	300	29	=	=	PRON
ejpam-4734	301	1	{	{	PUNCT
ejpam-4734	301	2	c	c	NOUN
ejpam-4734	301	3	}	}	PUNCT
ejpam-4734	301	4	and	and	CCONJ
ejpam-4734	301	5	f	f	X
ejpam-4734	301	6	(	(	PUNCT
ejpam-4734	301	7	2	2	NUM
ejpam-4734	301	8	)	)	PUNCT
ejpam-4734	301	9	=	=	SYM
ejpam-4734	301	10	f	f	PROPN
ejpam-4734	301	11	(	(	PUNCT
ejpam-4734	301	12	3	3	NUM
ejpam-4734	301	13	)	)	PUNCT
ejpam-4734	301	14	=	=	PRON
ejpam-4734	301	15	{	{	PUNCT
ejpam-4734	301	16	a	a	PRON
ejpam-4734	301	17	,	,	PUNCT
ejpam-4734	301	18	b	b	NOUN
ejpam-4734	301	19	}	}	PUNCT
ejpam-4734	301	20	.	.	PUNCT
ejpam-4734	302	1	then	then	ADV
ejpam-4734	302	2	,	,	PUNCT
ejpam-4734	302	3	f	f	PROPN
ejpam-4734	302	4	is	be	AUX
ejpam-4734	302	5	upper	upper	ADJ
ejpam-4734	302	6	weakly	weakly	ADV
ejpam-4734	302	7	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	303	1	but	but	CCONJ
ejpam-4734	303	2	f	f	PROPN
ejpam-4734	303	3	is	be	AUX
ejpam-4734	303	4	not	not	PART
ejpam-4734	303	5	upper	upper	ADJ
ejpam-4734	303	6	almost	almost	ADV
ejpam-4734	303	7	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	303	8	,	,	PUNCT
ejpam-4734	303	9	since	since	SCONJ
ejpam-4734	303	10	{	{	PUNCT
ejpam-4734	303	11	a	a	DET
ejpam-4734	303	12	,	,	PUNCT
ejpam-4734	303	13	b	b	NOUN
ejpam-4734	303	14	}	}	PUNCT
ejpam-4734	303	15	is	be	AUX
ejpam-4734	303	16	⋆-open	⋆-open	ADJ
ejpam-4734	303	17	in	in	ADP
ejpam-4734	303	18	y	y	PROPN
ejpam-4734	304	1	but	but	CCONJ
ejpam-4734	304	2	f+({a	f+({a	PROPN
ejpam-4734	304	3	,	,	PUNCT
ejpam-4734	304	4	b	b	NOUN
ejpam-4734	304	5	}	}	PUNCT
ejpam-4734	304	6	)	)	PUNCT
ejpam-4734	304	7	is	be	AUX
ejpam-4734	304	8	not	not	PART
ejpam-4734	304	9	strong	strong	ADJ
ejpam-4734	304	10	β	β	NOUN
ejpam-4734	304	11	-	-	PUNCT
ejpam-4734	304	12	i	i	PRON
ejpam-4734	304	13	-open	-open	ADJ
ejpam-4734	304	14	in	in	ADP
ejpam-4734	304	15	x.	x.	NOUN
ejpam-4734	304	16	lemma	lemma	PROPN
ejpam-4734	304	17	7	7	X
ejpam-4734	304	18	.	.	PUNCT
ejpam-4734	305	1	[	[	X
ejpam-4734	305	2	2	2	NUM
ejpam-4734	305	3	]	]	PUNCT
ejpam-4734	305	4	for	for	ADP
ejpam-4734	305	5	an	an	DET
ejpam-4734	305	6	ideal	ideal	ADJ
ejpam-4734	305	7	topological	topological	ADJ
ejpam-4734	305	8	space	space	NOUN
ejpam-4734	305	9	(	(	PUNCT
ejpam-4734	305	10	x	x	X
ejpam-4734	305	11	,	,	PUNCT
ejpam-4734	305	12	τ	τ	PROPN
ejpam-4734	305	13	,	,	PUNCT
ejpam-4734	305	14	i	i	NOUN
ejpam-4734	305	15	)	)	PUNCT
ejpam-4734	305	16	,	,	PUNCT
ejpam-4734	305	17	the	the	DET
ejpam-4734	305	18	following	follow	VERB
ejpam-4734	305	19	properties	property	NOUN
ejpam-4734	305	20	are	be	AUX
ejpam-4734	305	21	equivalent	equivalent	ADJ
ejpam-4734	305	22	:	:	PUNCT
ejpam-4734	305	23	(	(	PUNCT
ejpam-4734	305	24	1	1	X
ejpam-4734	305	25	)	)	PUNCT
ejpam-4734	305	26	(	(	PUNCT
ejpam-4734	305	27	x	x	X
ejpam-4734	305	28	,	,	PUNCT
ejpam-4734	305	29	τ	τ	PROPN
ejpam-4734	305	30	,	,	PUNCT
ejpam-4734	305	31	i	i	PROPN
ejpam-4734	305	32	)	)	PUNCT
ejpam-4734	305	33	is	be	AUX
ejpam-4734	305	34	⋆-i	⋆-i	NOUN
ejpam-4734	305	35	-normal	-normal	ADJ
ejpam-4734	305	36	.	.	PUNCT
ejpam-4734	306	1	c.	c.	PROPN
ejpam-4734	306	2	boonpok	boonpok	PROPN
ejpam-4734	306	3	,	,	PUNCT
ejpam-4734	306	4	j.	j.	PROPN
ejpam-4734	306	5	khampakdee	khampakdee	PROPN
ejpam-4734	306	6	/	/	PUNCT
ejpam-4734	306	7	eur	eur	PROPN
ejpam-4734	306	8	.	.	PUNCT
ejpam-4734	307	1	j.	j.	PROPN
ejpam-4734	307	2	pure	pure	PROPN
ejpam-4734	307	3	appl	appl	PROPN
ejpam-4734	307	4	.	.	PROPN
ejpam-4734	307	5	math	math	PROPN
ejpam-4734	307	6	,	,	PUNCT
ejpam-4734	307	7	16	16	NUM
ejpam-4734	307	8	(	(	PUNCT
ejpam-4734	307	9	4	4	NUM
ejpam-4734	307	10	)	)	PUNCT
ejpam-4734	307	11	(	(	PUNCT
ejpam-4734	307	12	2023	2023	NUM
ejpam-4734	307	13	)	)	PUNCT
ejpam-4734	307	14	,	,	PUNCT
ejpam-4734	307	15	2544	2544	NUM
ejpam-4734	307	16	-	-	SYM
ejpam-4734	307	17	2556	2556	NUM
ejpam-4734	307	18	2554	2554	NUM
ejpam-4734	307	19	(	(	PUNCT
ejpam-4734	307	20	2	2	NUM
ejpam-4734	307	21	)	)	PUNCT
ejpam-4734	307	22	for	for	ADP
ejpam-4734	307	23	each	each	DET
ejpam-4734	307	24	⋆-closed	⋆-close	VERB
ejpam-4734	307	25	set	set	VERB
ejpam-4734	307	26	f	f	PROPN
ejpam-4734	307	27	and	and	CCONJ
ejpam-4734	307	28	each	each	DET
ejpam-4734	307	29	⋆-open	⋆-open	ADV
ejpam-4734	307	30	set	set	VERB
ejpam-4734	307	31	v	v	NOUN
ejpam-4734	307	32	containing	contain	VERB
ejpam-4734	307	33	f	f	NOUN
ejpam-4734	307	34	,	,	PUNCT
ejpam-4734	307	35	there	there	PRON
ejpam-4734	307	36	exists	exist	VERB
ejpam-4734	307	37	a	a	DET
ejpam-4734	307	38	⋆-open	⋆-open	ADJ
ejpam-4734	307	39	set	set	NOUN
ejpam-4734	307	40	u	u	PRON
ejpam-4734	307	41	such	such	ADJ
ejpam-4734	307	42	that	that	SCONJ
ejpam-4734	307	43	f	f	PROPN
ejpam-4734	307	44	⊆	⊆	NUM
ejpam-4734	307	45	u	u	NOUN
ejpam-4734	307	46	⊆	⊆	NUM
ejpam-4734	307	47	cl⋆(u	cl⋆(u	NUM
ejpam-4734	307	48	)	)	PUNCT
ejpam-4734	307	49	⊆	⊆	NUM
ejpam-4734	307	50	v	v	NOUN
ejpam-4734	307	51	.	.	PUNCT
ejpam-4734	308	1	theorem	theorem	VERB
ejpam-4734	308	2	9	9	NUM
ejpam-4734	308	3	.	.	X
ejpam-4734	308	4	for	for	ADP
ejpam-4734	308	5	a	a	DET
ejpam-4734	308	6	multifunction	multifunction	NOUN
ejpam-4734	309	1	f	f	NOUN
ejpam-4734	309	2	:	:	PUNCT
ejpam-4734	309	3	(	(	PUNCT
ejpam-4734	309	4	x	x	X
ejpam-4734	309	5	,	,	PUNCT
ejpam-4734	309	6	τ	τ	PROPN
ejpam-4734	309	7	,	,	PUNCT
ejpam-4734	309	8	i	i	NOUN
ejpam-4734	309	9	)	)	PUNCT
ejpam-4734	309	10	→	→	PUNCT
ejpam-4734	309	11	(	(	PUNCT
ejpam-4734	309	12	y	y	PROPN
ejpam-4734	309	13	,	,	PUNCT
ejpam-4734	309	14	σ	σ	PROPN
ejpam-4734	309	15	,	,	PUNCT
ejpam-4734	309	16	j	j	PROPN
ejpam-4734	309	17	)	)	PUNCT
ejpam-4734	309	18	such	such	ADJ
ejpam-4734	309	19	that	that	SCONJ
ejpam-4734	309	20	f	f	PROPN
ejpam-4734	309	21	(	(	PUNCT
ejpam-4734	309	22	x	x	X
ejpam-4734	309	23	)	)	PUNCT
ejpam-4734	309	24	is	be	AUX
ejpam-4734	309	25	⋆-closed	⋆-close	VERB
ejpam-4734	309	26	in	in	ADP
ejpam-4734	309	27	y	y	PROPN
ejpam-4734	309	28	for	for	SCONJ
ejpam-4734	309	29	each	each	DET
ejpam-4734	309	30	x	x	SYM
ejpam-4734	309	31	∈	∈	PROPN
ejpam-4734	309	32	x	x	X
ejpam-4734	309	33	and	and	CCONJ
ejpam-4734	309	34	(	(	PUNCT
ejpam-4734	309	35	y	y	PROPN
ejpam-4734	309	36	,	,	PUNCT
ejpam-4734	309	37	σ	σ	PROPN
ejpam-4734	309	38	,	,	PUNCT
ejpam-4734	309	39	j	j	PROPN
ejpam-4734	309	40	)	)	PUNCT
ejpam-4734	309	41	is	be	AUX
ejpam-4734	309	42	a	a	DET
ejpam-4734	309	43	⋆-j	⋆-j	ADJ
ejpam-4734	309	44	-normal	-normal	ADJ
ejpam-4734	309	45	space	space	NOUN
ejpam-4734	309	46	,	,	PUNCT
ejpam-4734	309	47	the	the	DET
ejpam-4734	309	48	following	follow	VERB
ejpam-4734	309	49	properties	property	NOUN
ejpam-4734	309	50	are	be	AUX
ejpam-4734	309	51	equivalent	equivalent	ADJ
ejpam-4734	309	52	:	:	PUNCT
ejpam-4734	309	53	(	(	PUNCT
ejpam-4734	309	54	1	1	X
ejpam-4734	309	55	)	)	PUNCT
ejpam-4734	309	56	f	f	PROPN
ejpam-4734	309	57	is	be	AUX
ejpam-4734	309	58	upper	upper	ADJ
ejpam-4734	309	59	sβ(⋆)-continuous	sβ(⋆)-continuous	NOUN
ejpam-4734	309	60	;	;	PUNCT
ejpam-4734	309	61	(	(	PUNCT
ejpam-4734	309	62	2	2	X
ejpam-4734	309	63	)	)	PUNCT
ejpam-4734	309	64	f	f	PROPN
ejpam-4734	309	65	is	be	AUX
ejpam-4734	309	66	upper	upper	ADJ
ejpam-4734	309	67	almost	almost	ADV
ejpam-4734	309	68	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	309	69	;	;	PUNCT
ejpam-4734	309	70	(	(	PUNCT
ejpam-4734	309	71	3	3	X
ejpam-4734	309	72	)	)	PUNCT
ejpam-4734	309	73	f	f	PROPN
ejpam-4734	309	74	is	be	AUX
ejpam-4734	309	75	upper	upper	ADJ
ejpam-4734	309	76	weakly	weakly	ADJ
ejpam-4734	309	77	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	309	78	.	.	PUNCT
ejpam-4734	310	1	proof	proof	NOUN
ejpam-4734	310	2	.	.	PUNCT
ejpam-4734	311	1	we	we	PRON
ejpam-4734	311	2	show	show	VERB
ejpam-4734	311	3	only	only	ADV
ejpam-4734	311	4	the	the	DET
ejpam-4734	311	5	implication	implication	NOUN
ejpam-4734	311	6	(	(	PUNCT
ejpam-4734	311	7	3	3	X
ejpam-4734	311	8	)	)	PUNCT
ejpam-4734	311	9	⇒	⇒	NOUN
ejpam-4734	311	10	(	(	PUNCT
ejpam-4734	311	11	1	1	X
ejpam-4734	311	12	)	)	PUNCT
ejpam-4734	311	13	since	since	SCONJ
ejpam-4734	311	14	the	the	DET
ejpam-4734	311	15	others	other	NOUN
ejpam-4734	311	16	are	be	AUX
ejpam-4734	311	17	obvious	obvious	ADJ
ejpam-4734	311	18	.	.	PUNCT
ejpam-4734	312	1	suppose	suppose	VERB
ejpam-4734	312	2	that	that	SCONJ
ejpam-4734	312	3	f	f	PROPN
ejpam-4734	312	4	is	be	AUX
ejpam-4734	312	5	upper	upper	ADJ
ejpam-4734	312	6	weakly	weakly	ADJ
ejpam-4734	312	7	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	312	8	.	.	PUNCT
ejpam-4734	313	1	let	let	VERB
ejpam-4734	313	2	x	x	PUNCT
ejpam-4734	313	3	∈	∈	PROPN
ejpam-4734	313	4	x	x	X
ejpam-4734	313	5	and	and	CCONJ
ejpam-4734	313	6	v	v	X
ejpam-4734	313	7	be	be	AUX
ejpam-4734	313	8	any	any	DET
ejpam-4734	313	9	⋆-open	⋆-open	ADJ
ejpam-4734	313	10	set	set	NOUN
ejpam-4734	313	11	of	of	ADP
ejpam-4734	313	12	y	y	PRON
ejpam-4734	313	13	such	such	ADJ
ejpam-4734	313	14	that	that	SCONJ
ejpam-4734	313	15	f	f	PROPN
ejpam-4734	313	16	(	(	PUNCT
ejpam-4734	313	17	x	x	X
ejpam-4734	313	18	)	)	PUNCT
ejpam-4734	313	19	⊆	⊆	NUM
ejpam-4734	313	20	v	v	NOUN
ejpam-4734	313	21	.	.	PUNCT
ejpam-4734	314	1	since	since	SCONJ
ejpam-4734	314	2	f	f	PROPN
ejpam-4734	314	3	(	(	PUNCT
ejpam-4734	314	4	x	x	X
ejpam-4734	314	5	)	)	PUNCT
ejpam-4734	314	6	is	be	AUX
ejpam-4734	314	7	⋆-closed	⋆-close	VERB
ejpam-4734	314	8	in	in	ADP
ejpam-4734	314	9	y	y	PROPN
ejpam-4734	314	10	and	and	CCONJ
ejpam-4734	314	11	y	y	PROPN
ejpam-4734	314	12	is	be	AUX
ejpam-4734	314	13	⋆-j	⋆-j	ADJ
ejpam-4734	314	14	-normal	-normal	ADJ
ejpam-4734	314	15	,	,	PUNCT
ejpam-4734	314	16	there	there	PRON
ejpam-4734	314	17	exists	exist	VERB
ejpam-4734	314	18	a	a	DET
ejpam-4734	314	19	⋆-open	⋆-open	ADJ
ejpam-4734	314	20	set	set	VERB
ejpam-4734	314	21	g	g	NOUN
ejpam-4734	314	22	of	of	ADP
ejpam-4734	314	23	y	y	PRON
ejpam-4734	314	24	such	such	ADJ
ejpam-4734	314	25	that	that	SCONJ
ejpam-4734	314	26	f	f	PROPN
ejpam-4734	314	27	(	(	PUNCT
ejpam-4734	314	28	x	x	X
ejpam-4734	314	29	)	)	PUNCT
ejpam-4734	314	30	⊆	⊆	NUM
ejpam-4734	314	31	g	g	ADP
ejpam-4734	314	32	⊆	⊆	NUM
ejpam-4734	314	33	cl⋆(g	cl⋆(g	NUM
ejpam-4734	314	34	)	)	PUNCT
ejpam-4734	314	35	⊆	⊆	NUM
ejpam-4734	314	36	v	v	NOUN
ejpam-4734	314	37	.	.	PUNCT
ejpam-4734	315	1	since	since	SCONJ
ejpam-4734	315	2	f	f	PROPN
ejpam-4734	315	3	is	be	AUX
ejpam-4734	315	4	upper	upper	ADJ
ejpam-4734	315	5	weakly	weakly	ADJ
ejpam-4734	315	6	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	315	7	,	,	PUNCT
ejpam-4734	315	8	there	there	PRON
ejpam-4734	315	9	exists	exist	VERB
ejpam-4734	315	10	a	a	DET
ejpam-4734	315	11	strong	strong	ADJ
ejpam-4734	315	12	β	β	NOUN
ejpam-4734	315	13	-	-	ADJ
ejpam-4734	315	14	i	i	PRON
ejpam-4734	315	15	-open	-open	VERB
ejpam-4734	315	16	set	set	VERB
ejpam-4734	315	17	u	u	NOUN
ejpam-4734	315	18	of	of	ADP
ejpam-4734	315	19	x	x	PUNCT
ejpam-4734	315	20	containing	contain	VERB
ejpam-4734	315	21	x	x	PUNCT
ejpam-4734	315	22	such	such	ADJ
ejpam-4734	315	23	that	that	SCONJ
ejpam-4734	315	24	f	f	PROPN
ejpam-4734	315	25	(	(	PUNCT
ejpam-4734	315	26	u	u	NOUN
ejpam-4734	315	27	)	)	PUNCT
ejpam-4734	315	28	⊆	⊆	NUM
ejpam-4734	315	29	cl⋆(g	cl⋆(g	PROPN
ejpam-4734	315	30	)	)	PUNCT
ejpam-4734	315	31	;	;	PUNCT
ejpam-4734	315	32	hence	hence	ADV
ejpam-4734	315	33	f	f	PROPN
ejpam-4734	315	34	(	(	PUNCT
ejpam-4734	315	35	u	u	NOUN
ejpam-4734	315	36	)	)	PUNCT
ejpam-4734	315	37	⊆	⊆	NUM
ejpam-4734	315	38	v	v	NOUN
ejpam-4734	315	39	.	.	PUNCT
ejpam-4734	316	1	this	this	PRON
ejpam-4734	316	2	shows	show	VERB
ejpam-4734	316	3	that	that	SCONJ
ejpam-4734	316	4	f	f	PROPN
ejpam-4734	316	5	is	be	AUX
ejpam-4734	316	6	upper	upper	ADJ
ejpam-4734	316	7	sβ(⋆)-continuous	sβ(⋆)-continuous	PROPN
ejpam-4734	316	8	.	.	PUNCT
ejpam-4734	316	9	theorem	theorem	PROPN
ejpam-4734	316	10	10	10	NUM
ejpam-4734	316	11	.	.	PUNCT
ejpam-4734	316	12	for	for	ADP
ejpam-4734	316	13	a	a	DET
ejpam-4734	316	14	multifunction	multifunction	NOUN
ejpam-4734	316	15	f	f	NOUN
ejpam-4734	316	16	:	:	PUNCT
ejpam-4734	316	17	(	(	PUNCT
ejpam-4734	316	18	x	x	X
ejpam-4734	316	19	,	,	PUNCT
ejpam-4734	316	20	τ	τ	PROPN
ejpam-4734	316	21	,	,	PUNCT
ejpam-4734	316	22	i	i	NOUN
ejpam-4734	316	23	)	)	PUNCT
ejpam-4734	316	24	→	→	PUNCT
ejpam-4734	316	25	(	(	PUNCT
ejpam-4734	316	26	y	y	PROPN
ejpam-4734	316	27	,	,	PUNCT
ejpam-4734	316	28	σ	σ	PROPN
ejpam-4734	316	29	,	,	PUNCT
ejpam-4734	316	30	j	j	PROPN
ejpam-4734	316	31	)	)	PUNCT
ejpam-4734	316	32	such	such	ADJ
ejpam-4734	316	33	that	that	SCONJ
ejpam-4734	316	34	f	f	PROPN
ejpam-4734	316	35	(	(	PUNCT
ejpam-4734	316	36	x	x	X
ejpam-4734	316	37	)	)	PUNCT
ejpam-4734	316	38	is	be	AUX
ejpam-4734	316	39	⋆-open	⋆-open	ADJ
ejpam-4734	316	40	in	in	ADP
ejpam-4734	316	41	y	y	PROPN
ejpam-4734	316	42	for	for	ADP
ejpam-4734	316	43	each	each	DET
ejpam-4734	316	44	x	x	SYM
ejpam-4734	316	45	∈	∈	PROPN
ejpam-4734	316	46	x	x	NOUN
ejpam-4734	316	47	,	,	PUNCT
ejpam-4734	316	48	the	the	DET
ejpam-4734	316	49	following	follow	VERB
ejpam-4734	316	50	properties	property	NOUN
ejpam-4734	316	51	are	be	AUX
ejpam-4734	316	52	equivalent	equivalent	ADJ
ejpam-4734	316	53	:	:	PUNCT
ejpam-4734	316	54	(	(	PUNCT
ejpam-4734	316	55	1	1	X
ejpam-4734	316	56	)	)	PUNCT
ejpam-4734	316	57	f	f	PROPN
ejpam-4734	316	58	is	be	AUX
ejpam-4734	316	59	lower	low	ADJ
ejpam-4734	316	60	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	316	61	;	;	PUNCT
ejpam-4734	316	62	(	(	PUNCT
ejpam-4734	316	63	2	2	X
ejpam-4734	316	64	)	)	PUNCT
ejpam-4734	316	65	f	f	PROPN
ejpam-4734	316	66	is	be	AUX
ejpam-4734	316	67	lower	low	ADJ
ejpam-4734	316	68	almost	almost	ADV
ejpam-4734	316	69	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	316	70	;	;	PUNCT
ejpam-4734	316	71	(	(	PUNCT
ejpam-4734	316	72	3	3	X
ejpam-4734	316	73	)	)	PUNCT
ejpam-4734	316	74	f	f	PROPN
ejpam-4734	316	75	is	be	AUX
ejpam-4734	316	76	lower	low	ADJ
ejpam-4734	316	77	weakly	weakly	ADJ
ejpam-4734	316	78	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	316	79	.	.	PUNCT
ejpam-4734	316	80	proof	proof	NOUN
ejpam-4734	316	81	.	.	PUNCT
ejpam-4734	317	1	(	(	PUNCT
ejpam-4734	317	2	1	1	X
ejpam-4734	317	3	)	)	PUNCT
ejpam-4734	317	4	⇒	⇒	NOUN
ejpam-4734	317	5	(	(	PUNCT
ejpam-4734	317	6	2	2	NUM
ejpam-4734	317	7	)	)	PUNCT
ejpam-4734	317	8	and	and	CCONJ
ejpam-4734	317	9	(	(	PUNCT
ejpam-4734	317	10	2	2	X
ejpam-4734	317	11	)	)	PUNCT
ejpam-4734	317	12	⇒	⇒	NOUN
ejpam-4734	317	13	(	(	PUNCT
ejpam-4734	317	14	3	3	NUM
ejpam-4734	317	15	):	):	PUNCT
ejpam-4734	317	16	the	the	DET
ejpam-4734	317	17	proofs	proof	NOUN
ejpam-4734	317	18	of	of	ADP
ejpam-4734	317	19	these	these	DET
ejpam-4734	317	20	implications	implication	NOUN
ejpam-4734	317	21	are	be	AUX
ejpam-4734	317	22	obvious	obvious	ADJ
ejpam-4734	317	23	.	.	PUNCT
ejpam-4734	318	1	(	(	PUNCT
ejpam-4734	318	2	3	3	X
ejpam-4734	318	3	)	)	PUNCT
ejpam-4734	318	4	⇒	⇒	NOUN
ejpam-4734	318	5	(	(	PUNCT
ejpam-4734	318	6	1	1	NUM
ejpam-4734	318	7	):	):	PUNCT
ejpam-4734	318	8	suppose	suppose	VERB
ejpam-4734	318	9	that	that	SCONJ
ejpam-4734	318	10	f	f	PROPN
ejpam-4734	318	11	is	be	AUX
ejpam-4734	318	12	lower	low	ADJ
ejpam-4734	318	13	weakly	weakly	ADJ
ejpam-4734	318	14	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	318	15	.	.	PUNCT
ejpam-4734	319	1	let	let	VERB
ejpam-4734	319	2	x	x	PUNCT
ejpam-4734	319	3	∈	∈	PROPN
ejpam-4734	319	4	x	x	X
ejpam-4734	319	5	and	and	CCONJ
ejpam-4734	319	6	v	v	X
ejpam-4734	319	7	be	be	AUX
ejpam-4734	319	8	any	any	DET
ejpam-4734	319	9	⋆-open	⋆-open	ADJ
ejpam-4734	319	10	set	set	NOUN
ejpam-4734	319	11	such	such	ADJ
ejpam-4734	319	12	that	that	SCONJ
ejpam-4734	319	13	f	f	PROPN
ejpam-4734	319	14	(	(	PUNCT
ejpam-4734	319	15	x)∩	x)∩	PROPN
ejpam-4734	319	16	v	v	ADP
ejpam-4734	319	17	̸=	̸=	PROPN
ejpam-4734	319	18	∅.	∅.	ADP
ejpam-4734	319	19	then	then	ADV
ejpam-4734	319	20	,	,	PUNCT
ejpam-4734	319	21	there	there	PRON
ejpam-4734	319	22	exists	exist	VERB
ejpam-4734	319	23	a	a	DET
ejpam-4734	319	24	strong	strong	ADJ
ejpam-4734	319	25	β	β	NOUN
ejpam-4734	319	26	-	-	ADJ
ejpam-4734	319	27	i	i	PRON
ejpam-4734	319	28	-open	-open	VERB
ejpam-4734	319	29	set	set	VERB
ejpam-4734	319	30	u	u	NOUN
ejpam-4734	319	31	of	of	ADP
ejpam-4734	319	32	x	x	PUNCT
ejpam-4734	319	33	containing	contain	VERB
ejpam-4734	319	34	x	x	PUNCT
ejpam-4734	319	35	such	such	ADJ
ejpam-4734	319	36	that	that	SCONJ
ejpam-4734	319	37	f	f	PROPN
ejpam-4734	319	38	(	(	PUNCT
ejpam-4734	319	39	z	z	NOUN
ejpam-4734	319	40	)	)	PUNCT
ejpam-4734	319	41	∩	∩	NOUN
ejpam-4734	319	42	cl⋆(v	cl⋆(v	NOUN
ejpam-4734	319	43	)	)	PUNCT
ejpam-4734	319	44	̸=	̸=	PROPN
ejpam-4734	319	45	∅	∅	NOUN
ejpam-4734	319	46	for	for	ADP
ejpam-4734	319	47	each	each	DET
ejpam-4734	319	48	z	z	NOUN
ejpam-4734	319	49	∈	∈	PROPN
ejpam-4734	319	50	u	u	PROPN
ejpam-4734	319	51	.	.	PUNCT
ejpam-4734	320	1	since	since	SCONJ
ejpam-4734	320	2	f	f	PROPN
ejpam-4734	320	3	(	(	PUNCT
ejpam-4734	320	4	z	z	NOUN
ejpam-4734	320	5	)	)	PUNCT
ejpam-4734	320	6	is	be	AUX
ejpam-4734	320	7	⋆-open	⋆-open	ADJ
ejpam-4734	320	8	,	,	PUNCT
ejpam-4734	320	9	we	we	PRON
ejpam-4734	320	10	have	have	VERB
ejpam-4734	320	11	f	f	PROPN
ejpam-4734	320	12	(	(	PUNCT
ejpam-4734	320	13	z	z	NOUN
ejpam-4734	320	14	)	)	PUNCT
ejpam-4734	320	15	∩	∩	NOUN
ejpam-4734	320	16	v	v	ADP
ejpam-4734	320	17	̸=	̸=	PROPN
ejpam-4734	320	18	∅	∅	NOUN
ejpam-4734	320	19	for	for	ADP
ejpam-4734	320	20	each	each	DET
ejpam-4734	320	21	z	z	NOUN
ejpam-4734	320	22	∈	∈	PROPN
ejpam-4734	320	23	u	u	NOUN
ejpam-4734	320	24	and	and	CCONJ
ejpam-4734	320	25	so	so	ADV
ejpam-4734	320	26	f	f	PROPN
ejpam-4734	320	27	is	be	AUX
ejpam-4734	320	28	lower	low	ADJ
ejpam-4734	320	29	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	320	30	.	.	PROPN
ejpam-4734	320	31	definition	definition	NOUN
ejpam-4734	320	32	4	4	NUM
ejpam-4734	320	33	.	.	PUNCT
ejpam-4734	321	1	[	[	X
ejpam-4734	321	2	4	4	X
ejpam-4734	321	3	]	]	X
ejpam-4734	321	4	a	a	DET
ejpam-4734	321	5	function	function	NOUN
ejpam-4734	321	6	f	f	NOUN
ejpam-4734	321	7	:	:	PUNCT
ejpam-4734	321	8	(	(	PUNCT
ejpam-4734	321	9	x	x	X
ejpam-4734	321	10	,	,	PUNCT
ejpam-4734	321	11	τ	τ	PROPN
ejpam-4734	321	12	,	,	PUNCT
ejpam-4734	321	13	i	i	NOUN
ejpam-4734	321	14	)	)	PUNCT
ejpam-4734	321	15	→	→	PUNCT
ejpam-4734	321	16	(	(	PUNCT
ejpam-4734	321	17	y	y	PROPN
ejpam-4734	321	18	,	,	PUNCT
ejpam-4734	321	19	σ	σ	PROPN
ejpam-4734	321	20	,	,	PUNCT
ejpam-4734	321	21	j	j	PROPN
ejpam-4734	321	22	)	)	PUNCT
ejpam-4734	321	23	is	be	AUX
ejpam-4734	321	24	called	call	VERB
ejpam-4734	321	25	almost	almost	ADV
ejpam-4734	321	26	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	321	27	at	at	ADP
ejpam-4734	321	28	a	a	DET
ejpam-4734	321	29	point	point	NOUN
ejpam-4734	321	30	x	x	SYM
ejpam-4734	321	31	∈	∈	NOUN
ejpam-4734	321	32	x	x	INTJ
ejpam-4734	321	33	if	if	SCONJ
ejpam-4734	321	34	for	for	SCONJ
ejpam-4734	321	35	each	each	DET
ejpam-4734	321	36	⋆-open	⋆-open	ADV
ejpam-4734	321	37	set	set	VERB
ejpam-4734	321	38	v	v	NUM
ejpam-4734	321	39	of	of	ADP
ejpam-4734	321	40	y	y	NOUN
ejpam-4734	321	41	containing	contain	VERB
ejpam-4734	321	42	f(x	f(x	PROPN
ejpam-4734	321	43	)	)	PUNCT
ejpam-4734	321	44	,	,	PUNCT
ejpam-4734	321	45	there	there	PRON
ejpam-4734	321	46	exists	exist	VERB
ejpam-4734	321	47	a	a	DET
ejpam-4734	321	48	strong	strong	ADJ
ejpam-4734	321	49	β	β	NOUN
ejpam-4734	321	50	-	-	ADJ
ejpam-4734	321	51	i	i	PRON
ejpam-4734	321	52	-open	-open	VERB
ejpam-4734	321	53	set	set	VERB
ejpam-4734	321	54	u	u	NOUN
ejpam-4734	321	55	of	of	ADP
ejpam-4734	321	56	x	x	PUNCT
ejpam-4734	321	57	containing	contain	VERB
ejpam-4734	321	58	x	x	PUNCT
ejpam-4734	321	59	such	such	ADJ
ejpam-4734	321	60	that	that	DET
ejpam-4734	321	61	f(u	f(u	PROPN
ejpam-4734	321	62	)	)	PUNCT
ejpam-4734	321	63	⊆	⊆	NUM
ejpam-4734	321	64	int⋆(cl(v	int⋆(cl(v	PROPN
ejpam-4734	321	65	)	)	PUNCT
ejpam-4734	321	66	)	)	PUNCT
ejpam-4734	321	67	.	.	PUNCT
ejpam-4734	322	1	a	a	DET
ejpam-4734	322	2	function	function	NOUN
ejpam-4734	322	3	f	f	NOUN
ejpam-4734	322	4	:	:	PUNCT
ejpam-4734	322	5	(	(	PUNCT
ejpam-4734	322	6	x	x	X
ejpam-4734	322	7	,	,	PUNCT
ejpam-4734	322	8	τ	τ	PROPN
ejpam-4734	322	9	,	,	PUNCT
ejpam-4734	322	10	i	i	NOUN
ejpam-4734	322	11	)	)	PUNCT
ejpam-4734	322	12	→	→	PUNCT
ejpam-4734	322	13	(	(	PUNCT
ejpam-4734	322	14	y	y	PROPN
ejpam-4734	322	15	,	,	PUNCT
ejpam-4734	322	16	σ	σ	PROPN
ejpam-4734	322	17	,	,	PUNCT
ejpam-4734	322	18	j	j	PROPN
ejpam-4734	322	19	)	)	PUNCT
ejpam-4734	322	20	is	be	AUX
ejpam-4734	322	21	called	call	VERB
ejpam-4734	322	22	almost	almost	ADV
ejpam-4734	322	23	β(⋆)-continuous	β(⋆)-continuous	ADJ
ejpam-4734	322	24	if	if	SCONJ
ejpam-4734	322	25	f	f	PROPN
ejpam-4734	322	26	has	have	VERB
ejpam-4734	322	27	this	this	DET
ejpam-4734	322	28	property	property	NOUN
ejpam-4734	322	29	at	at	ADP
ejpam-4734	322	30	each	each	DET
ejpam-4734	322	31	point	point	NOUN
ejpam-4734	322	32	of	of	ADP
ejpam-4734	322	33	x.	x.	PROPN
ejpam-4734	322	34	corollary	corollary	NOUN
ejpam-4734	322	35	5	5	NUM
ejpam-4734	322	36	.	.	PUNCT
ejpam-4734	323	1	for	for	ADP
ejpam-4734	323	2	a	a	DET
ejpam-4734	323	3	function	function	NOUN
ejpam-4734	323	4	f	f	NOUN
ejpam-4734	323	5	:	:	PUNCT
ejpam-4734	323	6	(	(	PUNCT
ejpam-4734	323	7	x	x	X
ejpam-4734	323	8	,	,	PUNCT
ejpam-4734	323	9	τ	τ	PROPN
ejpam-4734	323	10	,	,	PUNCT
ejpam-4734	323	11	i	i	NOUN
ejpam-4734	323	12	)	)	PUNCT
ejpam-4734	323	13	→	→	PUNCT
ejpam-4734	323	14	(	(	PUNCT
ejpam-4734	323	15	y	y	PROPN
ejpam-4734	323	16	,	,	PUNCT
ejpam-4734	323	17	σ	σ	PROPN
ejpam-4734	323	18	,	,	PUNCT
ejpam-4734	323	19	j	j	PROPN
ejpam-4734	323	20	)	)	PUNCT
ejpam-4734	323	21	such	such	ADJ
ejpam-4734	323	22	that	that	SCONJ
ejpam-4734	323	23	f(x	f(x	PROPN
ejpam-4734	323	24	)	)	PUNCT
ejpam-4734	323	25	is	be	AUX
ejpam-4734	323	26	⋆-open	⋆-open	ADJ
ejpam-4734	323	27	in	in	ADP
ejpam-4734	323	28	y	y	PROPN
ejpam-4734	323	29	for	for	ADP
ejpam-4734	323	30	each	each	DET
ejpam-4734	323	31	x	x	SYM
ejpam-4734	323	32	∈	∈	PROPN
ejpam-4734	323	33	x	x	NOUN
ejpam-4734	323	34	,	,	PUNCT
ejpam-4734	323	35	the	the	DET
ejpam-4734	323	36	following	follow	VERB
ejpam-4734	323	37	properties	property	NOUN
ejpam-4734	323	38	are	be	AUX
ejpam-4734	323	39	equivalent	equivalent	ADJ
ejpam-4734	323	40	:	:	PUNCT
ejpam-4734	323	41	(	(	PUNCT
ejpam-4734	323	42	1	1	X
ejpam-4734	323	43	)	)	PUNCT
ejpam-4734	323	44	f	f	PROPN
ejpam-4734	323	45	is	be	AUX
ejpam-4734	323	46	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	323	47	;	;	PUNCT
ejpam-4734	323	48	(	(	PUNCT
ejpam-4734	323	49	2	2	X
ejpam-4734	323	50	)	)	PUNCT
ejpam-4734	323	51	f	f	PROPN
ejpam-4734	323	52	is	be	AUX
ejpam-4734	323	53	almost	almost	ADV
ejpam-4734	323	54	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	323	55	;	;	PUNCT
ejpam-4734	323	56	(	(	PUNCT
ejpam-4734	323	57	3	3	X
ejpam-4734	323	58	)	)	PUNCT
ejpam-4734	323	59	f	f	PROPN
ejpam-4734	323	60	is	be	AUX
ejpam-4734	323	61	weakly	weakly	ADV
ejpam-4734	323	62	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	323	63	.	.	PUNCT
ejpam-4734	324	1	references	reference	NOUN
ejpam-4734	324	2	2555	2555	NUM
ejpam-4734	324	3	acknowledgements	acknowledgement	NOUN
ejpam-4734	324	4	this	this	DET
ejpam-4734	324	5	research	research	NOUN
ejpam-4734	324	6	project	project	NOUN
ejpam-4734	324	7	was	be	AUX
ejpam-4734	324	8	financially	financially	ADV
ejpam-4734	324	9	supported	support	VERB
ejpam-4734	324	10	by	by	ADP
ejpam-4734	324	11	mahasarakham	mahasarakham	PROPN
ejpam-4734	324	12	university	university	PROPN
ejpam-4734	324	13	.	.	PUNCT
ejpam-4734	325	1	references	reference	NOUN
ejpam-4734	325	2	[	[	X
ejpam-4734	325	3	1	1	NUM
ejpam-4734	325	4	]	]	PUNCT
ejpam-4734	325	5	c.	c.	PROPN
ejpam-4734	325	6	berge	berge	PROPN
ejpam-4734	325	7	.	.	PUNCT
ejpam-4734	326	1	espaces	espace	VERB
ejpam-4734	326	2	topologiques	topologique	NOUN
ejpam-4734	326	3	fonctions	fonction	NOUN
ejpam-4734	326	4	multivoques	multivoque	NOUN
ejpam-4734	326	5	.	.	PUNCT
ejpam-4734	327	1	dunod	dunod	PROPN
ejpam-4734	327	2	,	,	PUNCT
ejpam-4734	327	3	paris	paris	PROPN
ejpam-4734	327	4	,	,	PUNCT
ejpam-4734	327	5	1959	1959	NUM
ejpam-4734	327	6	.	.	PUNCT
ejpam-4734	328	1	[	[	X
ejpam-4734	328	2	2	2	NUM
ejpam-4734	328	3	]	]	PUNCT
ejpam-4734	328	4	c.	c.	PROPN
ejpam-4734	328	5	boonpok	boonpok	PROPN
ejpam-4734	328	6	.	.	PUNCT
ejpam-4734	329	1	on	on	ADP
ejpam-4734	329	2	continuous	continuous	ADJ
ejpam-4734	329	3	multifunctions	multifunction	NOUN
ejpam-4734	329	4	in	in	ADP
ejpam-4734	329	5	ideal	ideal	ADJ
ejpam-4734	329	6	topological	topological	ADJ
ejpam-4734	329	7	spaces	space	NOUN
ejpam-4734	329	8	.	.	PUNCT
ejpam-4734	330	1	lobachevskii	lobachevskii	PROPN
ejpam-4734	330	2	journal	journal	PROPN
ejpam-4734	330	3	of	of	ADP
ejpam-4734	330	4	mathematics	mathematic	NOUN
ejpam-4734	330	5	,	,	PUNCT
ejpam-4734	330	6	40(1):24–35	40(1):24–35	NUM
ejpam-4734	330	7	,	,	PUNCT
ejpam-4734	330	8	2019	2019	NUM
ejpam-4734	330	9	.	.	PUNCT
ejpam-4734	331	1	[	[	X
ejpam-4734	331	2	3	3	X
ejpam-4734	331	3	]	]	PUNCT
ejpam-4734	331	4	c.	c.	PROPN
ejpam-4734	331	5	boonpok	boonpok	PROPN
ejpam-4734	331	6	.	.	PUNCT
ejpam-4734	332	1	upper	upper	ADJ
ejpam-4734	332	2	and	and	CCONJ
ejpam-4734	332	3	lower	low	ADJ
ejpam-4734	332	4	β(⋆)-continuity	β(⋆)-continuity	NOUN
ejpam-4734	332	5	.	.	PUNCT
ejpam-4734	332	6	heliyon	heliyon	NOUN
ejpam-4734	332	7	,	,	PUNCT
ejpam-4734	332	8	2021	2021	NUM
ejpam-4734	332	9	:	:	PUNCT
ejpam-4734	332	10	e05986	e05986	PROPN
ejpam-4734	332	11	,	,	PUNCT
ejpam-4734	332	12	2021	2021	NUM
ejpam-4734	332	13	.	.	PUNCT
ejpam-4734	333	1	[	[	X
ejpam-4734	333	2	4	4	NUM
ejpam-4734	333	3	]	]	PUNCT
ejpam-4734	333	4	c.	c.	NOUN
ejpam-4734	333	5	boonpok	boonpok	PROPN
ejpam-4734	333	6	and	and	CCONJ
ejpam-4734	333	7	p.	p.	NOUN
ejpam-4734	333	8	pue	pue	NOUN
ejpam-4734	333	9	-	-	PUNCT
ejpam-4734	333	10	on	on	ADP
ejpam-4734	333	11	.	.	PUNCT
ejpam-4734	334	1	upper	upper	ADJ
ejpam-4734	334	2	and	and	CCONJ
ejpam-4734	334	3	lower	low	ADJ
ejpam-4734	334	4	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-4734	334	5	multifunctions	multifunction	NOUN
ejpam-4734	334	6	.	.	PUNCT
ejpam-4734	335	1	european	european	ADJ
ejpam-4734	335	2	journal	journal	PROPN
ejpam-4734	335	3	of	of	ADP
ejpam-4734	335	4	pure	pure	ADJ
ejpam-4734	335	5	and	and	CCONJ
ejpam-4734	335	6	applied	applied	ADJ
ejpam-4734	335	7	mathematics	mathematic	NOUN
ejpam-4734	335	8	,	,	PUNCT
ejpam-4734	335	9	16(3):1634–1646	16(3):1634–1646	NUM
ejpam-4734	335	10	,	,	PUNCT
ejpam-4734	335	11	2023	2023	NUM
ejpam-4734	335	12	.	.	PUNCT
ejpam-4734	336	1	[	[	X
ejpam-4734	336	2	5	5	X
ejpam-4734	336	3	]	]	PUNCT
ejpam-4734	336	4	e.	e.	PROPN
ejpam-4734	336	5	ekici	ekici	PROPN
ejpam-4734	336	6	.	.	PUNCT
ejpam-4734	337	1	on	on	ADP
ejpam-4734	337	2	aci	aci	PROPN
ejpam-4734	337	3	-sets	-sets	PROPN
ejpam-4734	337	4	,	,	PUNCT
ejpam-4734	337	5	bci	bci	NOUN
ejpam-4734	337	6	-sets	-set	NOUN
ejpam-4734	337	7	,	,	PUNCT
ejpam-4734	337	8	β⋆	β⋆	PUNCT
ejpam-4734	337	9	i	i	PRON
ejpam-4734	337	10	-open	-open	VERB
ejpam-4734	337	11	sets	set	NOUN
ejpam-4734	337	12	and	and	CCONJ
ejpam-4734	337	13	decompositions	decomposition	NOUN
ejpam-4734	337	14	of	of	ADP
ejpam-4734	337	15	continuity	continuity	NOUN
ejpam-4734	337	16	in	in	ADP
ejpam-4734	337	17	ideal	ideal	ADJ
ejpam-4734	337	18	topological	topological	ADJ
ejpam-4734	337	19	spaces	space	NOUN
ejpam-4734	337	20	.	.	PUNCT
ejpam-4734	338	1	creative	creative	ADJ
ejpam-4734	338	2	mathematics	mathematic	NOUN
ejpam-4734	338	3	and	and	CCONJ
ejpam-4734	338	4	informatics	informatic	NOUN
ejpam-4734	338	5	,	,	PUNCT
ejpam-4734	338	6	20:47–54	20:47–54	NUM
ejpam-4734	338	7	,	,	PUNCT
ejpam-4734	338	8	2011	2011	NUM
ejpam-4734	338	9	.	.	PUNCT
ejpam-4734	339	1	[	[	X
ejpam-4734	339	2	6	6	NUM
ejpam-4734	339	3	]	]	PUNCT
ejpam-4734	339	4	e.	e.	PROPN
ejpam-4734	339	5	ekici	ekici	PROPN
ejpam-4734	339	6	and	and	CCONJ
ejpam-4734	339	7	t.	t.	PROPN
ejpam-4734	339	8	noiri	noiri	PROPN
ejpam-4734	339	9	.	.	PUNCT
ejpam-4734	340	1	⋆-hyperconnected	⋆-hyperconnecte	VERB
ejpam-4734	340	2	ideal	ideal	ADJ
ejpam-4734	340	3	topological	topological	ADJ
ejpam-4734	340	4	spaces	space	NOUN
ejpam-4734	340	5	.	.	PUNCT
ejpam-4734	341	1	analele	analele	ADP
ejpam-4734	341	2	stiintifice	stiintifice	PROPN
ejpam-4734	341	3	ale	ale	PROPN
ejpam-4734	341	4	universitatii	universitatii	PROPN
ejpam-4734	342	1	al	al	PROPN
ejpam-4734	342	2	i	i	PRON
ejpam-4734	342	3	cuza	cuza	VERB
ejpam-4734	342	4	din	din	VERB
ejpam-4734	342	5	iasi	iasi	PROPN
ejpam-4734	342	6	-	-	PUNCT
ejpam-4734	342	7	matematica	matematica	PROPN
ejpam-4734	342	8	,	,	PUNCT
ejpam-4734	342	9	58:121–129	58:121–129	PROPN
ejpam-4734	342	10	,	,	PUNCT
ejpam-4734	342	11	2012	2012	NUM
ejpam-4734	342	12	.	.	PUNCT
ejpam-4734	343	1	[	[	X
ejpam-4734	343	2	7	7	X
ejpam-4734	343	3	]	]	X
ejpam-4734	343	4	e.	e.	PROPN
ejpam-4734	343	5	hatir	hatir	PROPN
ejpam-4734	343	6	,	,	PUNCT
ejpam-4734	343	7	a.	a.	PROPN
ejpam-4734	343	8	keskin	keskin	PROPN
ejpam-4734	343	9	,	,	PUNCT
ejpam-4734	343	10	and	and	CCONJ
ejpam-4734	343	11	t.	t.	PROPN
ejpam-4734	343	12	noiri	noiri	PROPN
ejpam-4734	343	13	.	.	PUNCT
ejpam-4734	344	1	on	on	ADP
ejpam-4734	344	2	a	a	DET
ejpam-4734	344	3	new	new	ADJ
ejpam-4734	344	4	decomposition	decomposition	NOUN
ejpam-4734	344	5	of	of	ADP
ejpam-4734	344	6	continuity	continuity	NOUN
ejpam-4734	344	7	via	via	ADP
ejpam-4734	344	8	idealization	idealization	NOUN
ejpam-4734	344	9	.	.	PUNCT
ejpam-4734	345	1	jp	jp	PROPN
ejpam-4734	345	2	journal	journal	PROPN
ejpam-4734	345	3	of	of	ADP
ejpam-4734	345	4	geometry	geometry	NOUN
ejpam-4734	345	5	and	and	CCONJ
ejpam-4734	345	6	topology	topology	NOUN
ejpam-4734	345	7	,	,	PUNCT
ejpam-4734	345	8	3:53–64	3:53–64	NUM
ejpam-4734	345	9	,	,	PUNCT
ejpam-4734	345	10	2003	2003	NUM
ejpam-4734	345	11	.	.	PUNCT
ejpam-4734	346	1	[	[	X
ejpam-4734	346	2	8	8	X
ejpam-4734	346	3	]	]	X
ejpam-4734	346	4	e.	e.	PROPN
ejpam-4734	346	5	hatir	hatir	PROPN
ejpam-4734	346	6	,	,	PUNCT
ejpam-4734	346	7	a.	a.	PROPN
ejpam-4734	346	8	keskin	keskin	PROPN
ejpam-4734	346	9	,	,	PUNCT
ejpam-4734	346	10	and	and	CCONJ
ejpam-4734	346	11	t.	t.	PROPN
ejpam-4734	346	12	noiri	noiri	PROPN
ejpam-4734	346	13	.	.	PUNCT
ejpam-4734	347	1	a	a	DET
ejpam-4734	347	2	note	note	NOUN
ejpam-4734	347	3	on	on	ADP
ejpam-4734	347	4	strong	strong	ADJ
ejpam-4734	347	5	β	β	NOUN
ejpam-4734	347	6	-	-	ADJ
ejpam-4734	347	7	i	i	PRON
ejpam-4734	347	8	-open	-open	NOUN
ejpam-4734	347	9	sets	set	NOUN
ejpam-4734	347	10	and	and	CCONJ
ejpam-4734	347	11	strongly	strongly	ADV
ejpam-4734	347	12	β	β	X
ejpam-4734	347	13	-	-	ADJ
ejpam-4734	347	14	i	i	VERB
ejpam-4734	347	15	-continuous	-continuous	ADJ
ejpam-4734	347	16	functions	function	NOUN
ejpam-4734	347	17	.	.	PUNCT
ejpam-4734	348	1	acta	acta	PROPN
ejpam-4734	348	2	mathematica	mathematica	PROPN
ejpam-4734	348	3	hungarica	hungarica	PROPN
ejpam-4734	348	4	,	,	PUNCT
ejpam-4734	348	5	108:87–94	108:87–94	NUM
ejpam-4734	348	6	,	,	PUNCT
ejpam-4734	348	7	2005	2005	NUM
ejpam-4734	348	8	.	.	PUNCT
ejpam-4734	349	1	[	[	X
ejpam-4734	349	2	9	9	NUM
ejpam-4734	349	3	]	]	PUNCT
ejpam-4734	349	4	t.	t.	PROPN
ejpam-4734	349	5	husain	husain	PROPN
ejpam-4734	349	6	.	.	PUNCT
ejpam-4734	350	1	almost	almost	ADV
ejpam-4734	350	2	continuous	continuous	ADJ
ejpam-4734	350	3	mappings	mapping	NOUN
ejpam-4734	350	4	.	.	PUNCT
ejpam-4734	351	1	práce	práce	ADJ
ejpam-4734	351	2	matematika	matematika	X
ejpam-4734	351	3	,	,	PUNCT
ejpam-4734	351	4	10:1–7	10:1–7	NUM
ejpam-4734	351	5	,	,	PUNCT
ejpam-4734	351	6	1966	1966	NUM
ejpam-4734	351	7	.	.	PUNCT
ejpam-4734	352	1	[	[	X
ejpam-4734	352	2	10	10	NUM
ejpam-4734	352	3	]	]	X
ejpam-4734	352	4	d.	d.	PROPN
ejpam-4734	352	5	janković	janković	PROPN
ejpam-4734	352	6	and	and	CCONJ
ejpam-4734	352	7	t.	t.	PROPN
ejpam-4734	352	8	r.	r.	PROPN
ejpam-4734	352	9	hamlett	hamlett	PROPN
ejpam-4734	352	10	.	.	PUNCT
ejpam-4734	353	1	new	new	ADJ
ejpam-4734	353	2	topologies	topology	NOUN
ejpam-4734	353	3	from	from	ADP
ejpam-4734	353	4	old	old	ADJ
ejpam-4734	353	5	via	via	ADP
ejpam-4734	353	6	ideals	ideal	NOUN
ejpam-4734	353	7	.	.	PUNCT
ejpam-4734	354	1	the	the	DET
ejpam-4734	354	2	americal	americal	ADJ
ejpam-4734	354	3	mathematical	mathematical	NOUN
ejpam-4734	354	4	monthly	monthly	ADJ
ejpam-4734	354	5	,	,	PUNCT
ejpam-4734	354	6	97:295–310	97:295–310	PROPN
ejpam-4734	354	7	,	,	PUNCT
ejpam-4734	354	8	1990	1990	NUM
ejpam-4734	354	9	.	.	PUNCT
ejpam-4734	355	1	[	[	X
ejpam-4734	355	2	11	11	NUM
ejpam-4734	355	3	]	]	PUNCT
ejpam-4734	355	4	k.	k.	PROPN
ejpam-4734	355	5	kuratowski	kuratowski	PROPN
ejpam-4734	355	6	.	.	PUNCT
ejpam-4734	356	1	topology	topology	PROPN
ejpam-4734	356	2	,	,	PUNCT
ejpam-4734	356	3	vol	vol	NOUN
ejpam-4734	356	4	.	.	PUNCT
ejpam-4734	356	5	i.	i.	PROPN
ejpam-4734	356	6	academic	academic	PROPN
ejpam-4734	356	7	press	press	PROPN
ejpam-4734	356	8	,	,	PUNCT
ejpam-4734	356	9	new	new	PROPN
ejpam-4734	356	10	york	york	PROPN
ejpam-4734	356	11	,	,	PUNCT
ejpam-4734	356	12	1966	1966	NUM
ejpam-4734	356	13	.	.	PUNCT
ejpam-4734	357	1	[	[	X
ejpam-4734	357	2	12	12	NUM
ejpam-4734	357	3	]	]	X
ejpam-4734	357	4	n.	n.	PROPN
ejpam-4734	357	5	levine	levine	PROPN
ejpam-4734	357	6	.	.	PUNCT
ejpam-4734	358	1	a	a	DET
ejpam-4734	358	2	decomposition	decomposition	NOUN
ejpam-4734	358	3	of	of	ADP
ejpam-4734	358	4	continuity	continuity	NOUN
ejpam-4734	358	5	in	in	ADP
ejpam-4734	358	6	topological	topological	ADJ
ejpam-4734	358	7	spaces	space	NOUN
ejpam-4734	358	8	.	.	PUNCT
ejpam-4734	359	1	the	the	DET
ejpam-4734	359	2	american	american	PROPN
ejpam-4734	359	3	mathematical	mathematical	PROPN
ejpam-4734	359	4	monthly	monthly	ADV
ejpam-4734	359	5	,	,	PUNCT
ejpam-4734	359	6	68:44–46	68:44–46	NUM
ejpam-4734	359	7	,	,	PUNCT
ejpam-4734	359	8	1961	1961	NUM
ejpam-4734	359	9	.	.	PUNCT
ejpam-4734	360	1	[	[	X
ejpam-4734	360	2	13	13	NUM
ejpam-4734	360	3	]	]	X
ejpam-4734	360	4	n.	n.	PROPN
ejpam-4734	360	5	levine	levine	PROPN
ejpam-4734	360	6	.	.	PUNCT
ejpam-4734	361	1	semi	semi	ADJ
ejpam-4734	361	2	-	-	ADJ
ejpam-4734	361	3	open	open	ADJ
ejpam-4734	361	4	sets	set	NOUN
ejpam-4734	361	5	and	and	CCONJ
ejpam-4734	361	6	semi	semi	ADJ
ejpam-4734	361	7	-	-	NOUN
ejpam-4734	361	8	continuity	continuity	NOUN
ejpam-4734	361	9	in	in	ADP
ejpam-4734	361	10	topological	topological	ADJ
ejpam-4734	361	11	spaces	space	NOUN
ejpam-4734	361	12	.	.	PUNCT
ejpam-4734	362	1	the	the	DET
ejpam-4734	362	2	american	american	PROPN
ejpam-4734	362	3	mathematical	mathematical	PROPN
ejpam-4734	362	4	monthly	monthly	ADV
ejpam-4734	362	5	,	,	PUNCT
ejpam-4734	362	6	70:36–41	70:36–41	NUM
ejpam-4734	362	7	,	,	PUNCT
ejpam-4734	362	8	1963	1963	NUM
ejpam-4734	362	9	.	.	PUNCT
ejpam-4734	363	1	[	[	X
ejpam-4734	363	2	14	14	NUM
ejpam-4734	363	3	]	]	X
ejpam-4734	363	4	s.	s.	PROPN
ejpam-4734	363	5	marcus	marcus	PROPN
ejpam-4734	363	6	.	.	PUNCT
ejpam-4734	364	1	sur	sur	PROPN
ejpam-4734	364	2	les	les	PROPN
ejpam-4734	364	3	fonctions	fonctions	PROPN
ejpam-4734	364	4	quasicontinues	quasicontinue	NOUN
ejpam-4734	364	5	au	au	PROPN
ejpam-4734	364	6	sens	sens	X
ejpam-4734	364	7	de	de	PROPN
ejpam-4734	364	8	s.	s.	PROPN
ejpam-4734	364	9	kempisty	kempisty	PROPN
ejpam-4734	364	10	.	.	PUNCT
ejpam-4734	365	1	colloquium	colloquium	NOUN
ejpam-4734	365	2	mathematicum	mathematicum	PROPN
ejpam-4734	365	3	,	,	PUNCT
ejpam-4734	365	4	8:47–53	8:47–53	NUM
ejpam-4734	365	5	,	,	PUNCT
ejpam-4734	365	6	1961	1961	NUM
ejpam-4734	365	7	.	.	PUNCT
ejpam-4734	366	1	[	[	X
ejpam-4734	366	2	15	15	NUM
ejpam-4734	366	3	]	]	X
ejpam-4734	366	4	a.	a.	NOUN
ejpam-4734	366	5	neubrunnová.	neubrunnová.	PROPN
ejpam-4734	366	6	on	on	ADP
ejpam-4734	366	7	certain	certain	ADJ
ejpam-4734	366	8	generalizations	generalization	NOUN
ejpam-4734	366	9	of	of	ADP
ejpam-4734	366	10	the	the	DET
ejpam-4734	366	11	notion	notion	NOUN
ejpam-4734	366	12	of	of	ADP
ejpam-4734	366	13	continuity	continuity	NOUN
ejpam-4734	366	14	.	.	PUNCT
ejpam-4734	367	1	matematički	matematički	PROPN
ejpam-4734	368	1	časopis	časopis	PROPN
ejpam-4734	368	2	,	,	PUNCT
ejpam-4734	368	3	23:374–380	23:374–380	NUM
ejpam-4734	368	4	,	,	PUNCT
ejpam-4734	368	5	1973	1973	NUM
ejpam-4734	368	6	.	.	PUNCT
ejpam-4734	369	1	[	[	X
ejpam-4734	369	2	16	16	NUM
ejpam-4734	369	3	]	]	PUNCT
ejpam-4734	369	4	t.	t.	PROPN
ejpam-4734	369	5	noiri	noiri	PROPN
ejpam-4734	369	6	.	.	PUNCT
ejpam-4734	370	1	properties	property	NOUN
ejpam-4734	370	2	of	of	ADP
ejpam-4734	370	3	some	some	DET
ejpam-4734	370	4	weak	weak	ADJ
ejpam-4734	370	5	forms	form	NOUN
ejpam-4734	370	6	of	of	ADP
ejpam-4734	370	7	continuity	continuity	NOUN
ejpam-4734	370	8	.	.	PUNCT
ejpam-4734	371	1	international	international	ADJ
ejpam-4734	371	2	journal	journal	PROPN
ejpam-4734	371	3	of	of	ADP
ejpam-4734	371	4	mathematics	mathematics	PROPN
ejpam-4734	371	5	and	and	CCONJ
ejpam-4734	371	6	mathematical	mathematical	ADJ
ejpam-4734	371	7	sciences	science	NOUN
ejpam-4734	371	8	,	,	PUNCT
ejpam-4734	371	9	10(1):97–111	10(1):97–111	NUM
ejpam-4734	371	10	,	,	PUNCT
ejpam-4734	371	11	1987	1987	NUM
ejpam-4734	371	12	.	.	PUNCT
ejpam-4734	372	1	references	reference	NOUN
ejpam-4734	372	2	2556	2556	NUM
ejpam-4734	372	3	[	[	X
ejpam-4734	372	4	17	17	NUM
ejpam-4734	372	5	]	]	PUNCT
ejpam-4734	372	6	t.	t.	PROPN
ejpam-4734	372	7	noiri	noiri	PROPN
ejpam-4734	372	8	and	and	CCONJ
ejpam-4734	372	9	v.	v.	ADP
ejpam-4734	372	10	popa	popa	NOUN
ejpam-4734	372	11	.	.	PUNCT
ejpam-4734	373	1	on	on	ADP
ejpam-4734	373	2	upper	upper	ADJ
ejpam-4734	373	3	and	and	CCONJ
ejpam-4734	373	4	lower	low	ADJ
ejpam-4734	373	5	weakly	weakly	ADJ
ejpam-4734	373	6	quasicontinuous	quasicontinuous	ADJ
ejpam-4734	373	7	multifunctions	multifunction	NOUN
ejpam-4734	373	8	.	.	PUNCT
ejpam-4734	374	1	revue	revue	PROPN
ejpam-4734	374	2	roumaine	roumaine	NOUN
ejpam-4734	374	3	de	de	PROPN
ejpam-4734	374	4	mathématique	mathématique	PROPN
ejpam-4734	374	5	pures	pure	NOUN
ejpam-4734	374	6	et	et	NOUN
ejpam-4734	374	7	appliquées	appliquée	NOUN
ejpam-4734	374	8	,	,	PUNCT
ejpam-4734	374	9	36:499–508	36:499–508	NUM
ejpam-4734	374	10	,	,	PUNCT
ejpam-4734	374	11	1992	1992	NUM
ejpam-4734	374	12	.	.	PUNCT
ejpam-4734	375	1	[	[	X
ejpam-4734	375	2	18	18	NUM
ejpam-4734	375	3	]	]	PUNCT
ejpam-4734	375	4	t.	t.	PROPN
ejpam-4734	375	5	noiri	noiri	PROPN
ejpam-4734	375	6	and	and	CCONJ
ejpam-4734	375	7	v.	v.	ADP
ejpam-4734	375	8	popa	popa	NOUN
ejpam-4734	375	9	.	.	PUNCT
ejpam-4734	376	1	almost	almost	ADV
ejpam-4734	376	2	weakly	weakly	ADJ
ejpam-4734	376	3	continuous	continuous	ADJ
ejpam-4734	376	4	multifunctions	multifunction	NOUN
ejpam-4734	376	5	.	.	PUNCT
ejpam-4734	377	1	demonstratio	demonstratio	PROPN
ejpam-4734	377	2	mathematica	mathematica	PROPN
ejpam-4734	377	3	,	,	PUNCT
ejpam-4734	377	4	26:363–380	26:363–380	PROPN
ejpam-4734	377	5	,	,	PUNCT
ejpam-4734	377	6	1993	1993	NUM
ejpam-4734	377	7	.	.	PUNCT
ejpam-4734	378	1	[	[	X
ejpam-4734	378	2	19	19	NUM
ejpam-4734	378	3	]	]	X
ejpam-4734	378	4	t.	t.	PROPN
ejpam-4734	378	5	noiri	noiri	PROPN
ejpam-4734	378	6	and	and	CCONJ
ejpam-4734	378	7	v.	v.	ADP
ejpam-4734	378	8	popa	popa	NOUN
ejpam-4734	378	9	.	.	PUNCT
ejpam-4734	379	1	a	a	DET
ejpam-4734	379	2	unified	unified	ADJ
ejpam-4734	379	3	theory	theory	NOUN
ejpam-4734	379	4	of	of	ADP
ejpam-4734	379	5	weak	weak	ADJ
ejpam-4734	379	6	continuity	continuity	NOUN
ejpam-4734	379	7	for	for	ADP
ejpam-4734	379	8	multifunctions	multifunction	NOUN
ejpam-4734	379	9	.	.	PUNCT
ejpam-4734	380	1	studii	studii	PROPN
ejpam-4734	380	2	şi	şi	PROPN
ejpam-4734	380	3	cercetǎri	cercetǎri	VERB
ejpam-4734	380	4	ştiinţifice	ştiinţifice	NOUN
ejpam-4734	380	5	,	,	PUNCT
ejpam-4734	380	6	ser	ser	NOUN
ejpam-4734	380	7	.	.	PUNCT
ejpam-4734	381	1	matematicǎ-universitatea	matematicǎ-universitatea	PROPN
ejpam-4734	382	1	din	din	VERB
ejpam-4734	382	2	bacǎu	bacǎu	PROPN
ejpam-4734	382	3	,	,	PUNCT
ejpam-4734	382	4	16:167–200	16:167–200	NUM
ejpam-4734	382	5	,	,	PUNCT
ejpam-4734	382	6	2006	2006	NUM
ejpam-4734	382	7	.	.	PUNCT
ejpam-4734	383	1	[	[	X
ejpam-4734	383	2	20	20	NUM
ejpam-4734	383	3	]	]	PUNCT
ejpam-4734	383	4	v.	v.	CCONJ
ejpam-4734	383	5	popa	popa	NOUN
ejpam-4734	383	6	.	.	PUNCT
ejpam-4734	384	1	weakly	weakly	ADJ
ejpam-4734	384	2	continuous	continuous	ADJ
ejpam-4734	384	3	multifunctions	multifunction	NOUN
ejpam-4734	384	4	.	.	PUNCT
ejpam-4734	385	1	bollettino	bollettino	PROPN
ejpam-4734	385	2	dell’unione	dell’unione	PROPN
ejpam-4734	385	3	matematica	matematica	PROPN
ejpam-4734	385	4	italiana	italiana	PROPN
ejpam-4734	385	5	,	,	PUNCT
ejpam-4734	385	6	5(15(a)):379–388	5(15(a)):379–388	PROPN
ejpam-4734	385	7	,	,	PUNCT
ejpam-4734	385	8	1978	1978	NUM
ejpam-4734	385	9	.	.	PUNCT
ejpam-4734	386	1	[	[	X
ejpam-4734	386	2	21	21	NUM
ejpam-4734	386	3	]	]	X
ejpam-4734	386	4	v.	v.	CCONJ
ejpam-4734	386	5	popa	popa	NOUN
ejpam-4734	386	6	and	and	CCONJ
ejpam-4734	386	7	t.	t.	PROPN
ejpam-4734	386	8	noiri	noiri	PROPN
ejpam-4734	386	9	.	.	PUNCT
ejpam-4734	387	1	on	on	ADP
ejpam-4734	387	2	upper	upper	ADJ
ejpam-4734	387	3	and	and	CCONJ
ejpam-4734	387	4	lower	low	ADJ
ejpam-4734	387	5	weakly	weakly	ADJ
ejpam-4734	387	6	β	β	ADJ
ejpam-4734	387	7	-	-	ADJ
ejpam-4734	387	8	continuous	continuous	ADJ
ejpam-4734	387	9	multifunctions	multifunction	NOUN
ejpam-4734	387	10	.	.	PUNCT
ejpam-4734	388	1	annales	annales	PROPN
ejpam-4734	388	2	universitatis	universitatis	PROPN
ejpam-4734	388	3	scientiarium	scientiarium	PROPN
ejpam-4734	388	4	budapestinensis	budapestinensis	NOUN
ejpam-4734	388	5	de	de	PROPN
ejpam-4734	388	6	rolando	rolando	PROPN
ejpam-4734	388	7	eötvös	eötvös	PROPN
ejpam-4734	388	8	nominatae	nominatae	NOUN
ejpam-4734	388	9	sectio	sectio	NOUN
ejpam-4734	388	10	mathematica	mathematica	PROPN
ejpam-4734	388	11	,	,	PUNCT
ejpam-4734	388	12	43:25–48	43:25–48	PROPN
ejpam-4734	388	13	,	,	PUNCT
ejpam-4734	388	14	2000	2000	NUM
ejpam-4734	388	15	.	.	PUNCT
ejpam-4734	389	1	[	[	X
ejpam-4734	389	2	22	22	NUM
ejpam-4734	389	3	]	]	PUNCT
ejpam-4734	389	4	v.	v.	CCONJ
ejpam-4734	389	5	popa	popa	NOUN
ejpam-4734	389	6	and	and	CCONJ
ejpam-4734	389	7	t.	t.	PROPN
ejpam-4734	389	8	noiri	noiri	PROPN
ejpam-4734	389	9	.	.	PUNCT
ejpam-4734	390	1	on	on	ADP
ejpam-4734	390	2	upper	upper	ADJ
ejpam-4734	390	3	and	and	CCONJ
ejpam-4734	390	4	lower	low	ADJ
ejpam-4734	390	5	weakly	weakly	ADJ
ejpam-4734	390	6	α	α	ADJ
ejpam-4734	390	7	-	-	ADJ
ejpam-4734	390	8	continuous	continuous	ADJ
ejpam-4734	390	9	multifunctions	multifunction	NOUN
ejpam-4734	390	10	.	.	PUNCT
ejpam-4734	391	1	novi	novi	PROPN
ejpam-4734	391	2	sad	sad	PROPN
ejpam-4734	391	3	journal	journal	PROPN
ejpam-4734	391	4	of	of	ADP
ejpam-4734	391	5	mathematics	mathematic	NOUN
ejpam-4734	391	6	,	,	PUNCT
ejpam-4734	391	7	32(1):7–24	32(1):7–24	NUM
ejpam-4734	391	8	,	,	PUNCT
ejpam-4734	391	9	2002	2002	NUM
ejpam-4734	391	10	.	.	PUNCT
ejpam-4734	392	1	[	[	X
ejpam-4734	392	2	23	23	X
ejpam-4734	392	3	]	]	PUNCT
ejpam-4734	392	4	v.	v.	CCONJ
ejpam-4734	392	5	popa	popa	NOUN
ejpam-4734	392	6	and	and	CCONJ
ejpam-4734	392	7	c.	c.	PROPN
ejpam-4734	392	8	stan	stan	PROPN
ejpam-4734	392	9	.	.	PUNCT
ejpam-4734	393	1	on	on	ADP
ejpam-4734	393	2	a	a	DET
ejpam-4734	393	3	decomposition	decomposition	NOUN
ejpam-4734	393	4	of	of	ADP
ejpam-4734	393	5	quasi	quasi	NOUN
ejpam-4734	393	6	-	-	NOUN
ejpam-4734	393	7	continuity	continuity	NOUN
ejpam-4734	393	8	in	in	ADP
ejpam-4734	393	9	topological	topological	ADJ
ejpam-4734	393	10	spaces	space	NOUN
ejpam-4734	393	11	.	.	PUNCT
ejpam-4734	394	1	studii	studii	PROPN
ejpam-4734	394	2	şi	şi	PROPN
ejpam-4734	394	3	cercetǎri	cercetǎri	NOUN
ejpam-4734	394	4	matematicǎ	matematicǎ	VERB
ejpam-4734	394	5	,	,	PUNCT
ejpam-4734	394	6	25:41–43	25:41–43	NUM
ejpam-4734	394	7	,	,	PUNCT
ejpam-4734	394	8	1973	1973	NUM
ejpam-4734	394	9	.	.	PUNCT
ejpam-4734	395	1	[	[	X
ejpam-4734	395	2	24	24	NUM
ejpam-4734	395	3	]	]	PUNCT
ejpam-4734	395	4	r.	r.	PROPN
ejpam-4734	395	5	e.	e.	PROPN
ejpam-4734	395	6	smithson	smithson	PROPN
ejpam-4734	395	7	.	.	PUNCT
ejpam-4734	396	1	almost	almost	ADV
ejpam-4734	396	2	and	and	CCONJ
ejpam-4734	396	3	weak	weak	ADJ
ejpam-4734	396	4	continuity	continuity	NOUN
ejpam-4734	396	5	for	for	ADP
ejpam-4734	396	6	multifunctions	multifunction	NOUN
ejpam-4734	396	7	.	.	PUNCT
ejpam-4734	397	1	bulletin	bulletin	NOUN
ejpam-4734	397	2	of	of	ADP
ejpam-4734	397	3	the	the	DET
ejpam-4734	397	4	calcutta	calcutta	PROPN
ejpam-4734	397	5	mathematical	mathematical	ADJ
ejpam-4734	397	6	society	society	NOUN
ejpam-4734	397	7	,	,	PUNCT
ejpam-4734	397	8	70:383–390	70:383–390	NUM
ejpam-4734	397	9	,	,	PUNCT
ejpam-4734	397	10	1978	1978	NUM
ejpam-4734	397	11	.	.	PUNCT