id	sid	tid	token	lemma	pos
ejpam-4573	1	1	european	european	PROPN
ejpam-4573	1	2	journal	journal	PROPN
ejpam-4573	1	3	of	of	ADP
ejpam-4573	1	4	pure	pure	ADJ
ejpam-4573	1	5	and	and	CCONJ
ejpam-4573	1	6	applied	apply	VERB
ejpam-4573	1	7	mathematics	mathematic	NOUN
ejpam-4573	1	8	vol	vol	NOUN
ejpam-4573	1	9	.	.	PUNCT
ejpam-4573	2	1	16	16	NUM
ejpam-4573	2	2	,	,	PUNCT
ejpam-4573	2	3	no	no	INTJ
ejpam-4573	2	4	.	.	NOUN
ejpam-4573	2	5	2	2	NUM
ejpam-4573	2	6	,	,	PUNCT
ejpam-4573	2	7	2023	2023	NUM
ejpam-4573	2	8	,	,	PUNCT
ejpam-4573	2	9	1047	1047	NUM
ejpam-4573	2	10	-	-	SYM
ejpam-4573	2	11	1058	1058	NUM
ejpam-4573	2	12	issn	issn	PROPN
ejpam-4573	2	13	1307	1307	NUM
ejpam-4573	2	14	-	-	SYM
ejpam-4573	2	15	5543	5543	NUM
ejpam-4573	2	16	–	–	PUNCT
ejpam-4573	2	17	ejpam.com	ejpam.com	X
ejpam-4573	2	18	published	publish	VERB
ejpam-4573	2	19	by	by	ADP
ejpam-4573	2	20	new	new	PROPN
ejpam-4573	2	21	york	york	PROPN
ejpam-4573	2	22	business	business	PROPN
ejpam-4573	2	23	global	global	PROPN
ejpam-4573	2	24	upper	upper	ADJ
ejpam-4573	2	25	and	and	CCONJ
ejpam-4573	2	26	lower	low	ADJ
ejpam-4573	2	27	weakly	weakly	ADJ
ejpam-4573	2	28	(	(	PUNCT
ejpam-4573	2	29	λ	λ	NOUN
ejpam-4573	2	30	,	,	PUNCT
ejpam-4573	2	31	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	2	32	multifunctions	multifunction	NOUN
ejpam-4573	2	33	chawalit	chawalit	VERB
ejpam-4573	2	34	boonpok1	boonpok1	PROPN
ejpam-4573	2	35	,	,	PUNCT
ejpam-4573	2	36	prapart	prapart	VERB
ejpam-4573	2	37	pue	pue	X
ejpam-4573	2	38	-	-	PUNCT
ejpam-4573	2	39	on1,∗	on1,∗	PROPN
ejpam-4573	2	40	1	1	NUM
ejpam-4573	2	41	mathematics	mathematic	NOUN
ejpam-4573	2	42	and	and	CCONJ
ejpam-4573	2	43	applied	apply	VERB
ejpam-4573	2	44	mathematics	mathematics	PROPN
ejpam-4573	2	45	research	research	NOUN
ejpam-4573	2	46	unit	unit	NOUN
ejpam-4573	2	47	,	,	PUNCT
ejpam-4573	2	48	department	department	NOUN
ejpam-4573	2	49	of	of	ADP
ejpam-4573	2	50	mathematics	mathematic	NOUN
ejpam-4573	2	51	,	,	PUNCT
ejpam-4573	2	52	faculty	faculty	NOUN
ejpam-4573	2	53	of	of	ADP
ejpam-4573	2	54	science	science	NOUN
ejpam-4573	2	55	,	,	PUNCT
ejpam-4573	2	56	mahasarakham	mahasarakham	PROPN
ejpam-4573	2	57	university	university	PROPN
ejpam-4573	2	58	,	,	PUNCT
ejpam-4573	2	59	maha	maha	PROPN
ejpam-4573	2	60	sarakham	sarakham	PROPN
ejpam-4573	2	61	,	,	PUNCT
ejpam-4573	2	62	44150	44150	NUM
ejpam-4573	2	63	,	,	PUNCT
ejpam-4573	2	64	thailand	thailand	PROPN
ejpam-4573	2	65	abstract	abstract	PROPN
ejpam-4573	2	66	.	.	PUNCT
ejpam-4573	3	1	our	our	PRON
ejpam-4573	3	2	main	main	ADJ
ejpam-4573	3	3	purpose	purpose	NOUN
ejpam-4573	3	4	is	be	AUX
ejpam-4573	3	5	to	to	PART
ejpam-4573	3	6	introduce	introduce	VERB
ejpam-4573	3	7	the	the	DET
ejpam-4573	3	8	concepts	concept	NOUN
ejpam-4573	3	9	of	of	ADP
ejpam-4573	3	10	upper	upper	ADJ
ejpam-4573	3	11	and	and	CCONJ
ejpam-4573	3	12	lower	low	ADJ
ejpam-4573	3	13	weakly	weakly	ADJ
ejpam-4573	3	14	(	(	PUNCT
ejpam-4573	3	15	λ	λ	NOUN
ejpam-4573	3	16	,	,	PUNCT
ejpam-4573	3	17	sp)continuous	sp)continuous	ADJ
ejpam-4573	3	18	multifunctions	multifunction	NOUN
ejpam-4573	3	19	.	.	PUNCT
ejpam-4573	4	1	in	in	ADP
ejpam-4573	4	2	particular	particular	ADJ
ejpam-4573	4	3	,	,	PUNCT
ejpam-4573	4	4	some	some	DET
ejpam-4573	4	5	characterizations	characterization	NOUN
ejpam-4573	4	6	of	of	ADP
ejpam-4573	4	7	upper	upper	ADJ
ejpam-4573	4	8	and	and	CCONJ
ejpam-4573	4	9	lower	low	ADJ
ejpam-4573	4	10	weakly	weakly	ADJ
ejpam-4573	4	11	(	(	PUNCT
ejpam-4573	4	12	λ	λ	NOUN
ejpam-4573	4	13	,	,	PUNCT
ejpam-4573	4	14	sp)continuous	sp)continuous	ADJ
ejpam-4573	4	15	multifunctions	multifunction	NOUN
ejpam-4573	4	16	are	be	AUX
ejpam-4573	4	17	investigated	investigate	VERB
ejpam-4573	4	18	.	.	PUNCT
ejpam-4573	5	1	2020	2020	NUM
ejpam-4573	5	2	mathematics	mathematic	NOUN
ejpam-4573	5	3	subject	subject	NOUN
ejpam-4573	5	4	classifications	classification	NOUN
ejpam-4573	5	5	:	:	PUNCT
ejpam-4573	5	6	54c08	54c08	NUM
ejpam-4573	5	7	,	,	PUNCT
ejpam-4573	5	8	54c60	54c60	NUM
ejpam-4573	5	9	key	key	ADJ
ejpam-4573	5	10	words	word	NOUN
ejpam-4573	5	11	and	and	CCONJ
ejpam-4573	5	12	phrases	phrase	NOUN
ejpam-4573	5	13	:	:	PUNCT
ejpam-4573	5	14	upper	upper	ADJ
ejpam-4573	5	15	weakly	weakly	ADJ
ejpam-4573	5	16	(	(	PUNCT
ejpam-4573	5	17	λ	λ	NOUN
ejpam-4573	5	18	,	,	PUNCT
ejpam-4573	5	19	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	5	20	multifunction	multifunction	NOUN
ejpam-4573	5	21	,	,	PUNCT
ejpam-4573	5	22	lower	low	ADJ
ejpam-4573	5	23	weakly	weakly	ADJ
ejpam-4573	5	24	(	(	PUNCT
ejpam-4573	5	25	λ	λ	NOUN
ejpam-4573	5	26	,	,	PUNCT
ejpam-4573	5	27	sp)continuous	sp)continuous	ADJ
ejpam-4573	5	28	multifunction	multifunction	NOUN
ejpam-4573	5	29	1	1	NUM
ejpam-4573	5	30	.	.	PUNCT
ejpam-4573	6	1	introduction	introduction	NOUN
ejpam-4573	6	2	in	in	ADP
ejpam-4573	6	3	topology	topology	NOUN
ejpam-4573	6	4	,	,	PUNCT
ejpam-4573	6	5	there	there	PRON
ejpam-4573	6	6	has	have	AUX
ejpam-4573	6	7	been	be	AUX
ejpam-4573	6	8	recently	recently	ADV
ejpam-4573	6	9	significant	significant	ADJ
ejpam-4573	6	10	interest	interest	NOUN
ejpam-4573	6	11	in	in	ADP
ejpam-4573	6	12	characterizing	characterize	VERB
ejpam-4573	6	13	and	and	CCONJ
ejpam-4573	6	14	investigating	investigate	VERB
ejpam-4573	6	15	the	the	DET
ejpam-4573	6	16	characterizations	characterization	NOUN
ejpam-4573	6	17	of	of	ADP
ejpam-4573	6	18	some	some	DET
ejpam-4573	6	19	weak	weak	ADJ
ejpam-4573	6	20	forms	form	NOUN
ejpam-4573	6	21	of	of	ADP
ejpam-4573	6	22	continuity	continuity	NOUN
ejpam-4573	6	23	for	for	ADP
ejpam-4573	6	24	functions	function	NOUN
ejpam-4573	6	25	and	and	CCONJ
ejpam-4573	6	26	multifunctions	multifunction	NOUN
ejpam-4573	6	27	.	.	PUNCT
ejpam-4573	7	1	as	as	ADP
ejpam-4573	7	2	weak	weak	ADJ
ejpam-4573	7	3	forms	form	NOUN
ejpam-4573	7	4	of	of	ADP
ejpam-4573	7	5	continuity	continuity	NOUN
ejpam-4573	7	6	in	in	ADP
ejpam-4573	7	7	topological	topological	ADJ
ejpam-4573	7	8	spaces	space	NOUN
ejpam-4573	7	9	,	,	PUNCT
ejpam-4573	7	10	weak	weak	ADJ
ejpam-4573	7	11	continuity	continuity	NOUN
ejpam-4573	7	12	[	[	X
ejpam-4573	7	13	9	9	NUM
ejpam-4573	7	14	]	]	PUNCT
ejpam-4573	7	15	,	,	PUNCT
ejpam-4573	7	16	quasicontinuity	quasicontinuity	NOUN
ejpam-4573	7	17	[	[	X
ejpam-4573	7	18	11	11	NUM
ejpam-4573	7	19	]	]	PUNCT
ejpam-4573	7	20	,	,	PUNCT
ejpam-4573	7	21	semi	semi	ADJ
ejpam-4573	7	22	-	-	NOUN
ejpam-4573	7	23	continuity	continuity	NOUN
ejpam-4573	7	24	[	[	X
ejpam-4573	7	25	10	10	NUM
ejpam-4573	7	26	]	]	PUNCT
ejpam-4573	7	27	and	and	CCONJ
ejpam-4573	7	28	almost	almost	ADV
ejpam-4573	7	29	continuity	continuity	NOUN
ejpam-4573	7	30	in	in	ADP
ejpam-4573	7	31	the	the	DET
ejpam-4573	7	32	sense	sense	NOUN
ejpam-4573	7	33	of	of	ADP
ejpam-4573	7	34	husain	husain	NOUN
ejpam-4573	7	35	[	[	X
ejpam-4573	7	36	7	7	NUM
ejpam-4573	7	37	]	]	PUNCT
ejpam-4573	7	38	are	be	AUX
ejpam-4573	7	39	well	well	ADV
ejpam-4573	7	40	-	-	PUNCT
ejpam-4573	7	41	known	know	VERB
ejpam-4573	7	42	.	.	PUNCT
ejpam-4573	8	1	it	it	PRON
ejpam-4573	8	2	is	be	AUX
ejpam-4573	8	3	shown	show	VERB
ejpam-4573	8	4	in	in	ADP
ejpam-4573	8	5	[	[	X
ejpam-4573	8	6	12	12	NUM
ejpam-4573	8	7	]	]	PUNCT
ejpam-4573	8	8	that	that	DET
ejpam-4573	8	9	quasicontinuity	quasicontinuity	NOUN
ejpam-4573	8	10	is	be	AUX
ejpam-4573	8	11	equivalent	equivalent	ADJ
ejpam-4573	8	12	to	to	ADP
ejpam-4573	8	13	semi	semi	NOUN
ejpam-4573	8	14	-	-	NOUN
ejpam-4573	8	15	continuity	continuity	NOUN
ejpam-4573	8	16	.	.	PUNCT
ejpam-4573	9	1	it	it	PRON
ejpam-4573	9	2	will	will	AUX
ejpam-4573	9	3	be	be	AUX
ejpam-4573	9	4	shown	show	VERB
ejpam-4573	9	5	that	that	SCONJ
ejpam-4573	9	6	weak	weak	ADJ
ejpam-4573	9	7	continuity	continuity	NOUN
ejpam-4573	9	8	,	,	PUNCT
ejpam-4573	9	9	semi	semi	ADJ
ejpam-4573	9	10	-	-	NOUN
ejpam-4573	9	11	continuity	continuity	NOUN
ejpam-4573	9	12	and	and	CCONJ
ejpam-4573	9	13	almost	almost	ADV
ejpam-4573	9	14	continuity	continuity	NOUN
ejpam-4573	9	15	are	be	AUX
ejpam-4573	9	16	respectively	respectively	ADV
ejpam-4573	9	17	independent	independent	ADJ
ejpam-4573	9	18	.	.	PUNCT
ejpam-4573	10	1	popa	popa	NOUN
ejpam-4573	10	2	and	and	CCONJ
ejpam-4573	10	3	stan	stan	PROPN
ejpam-4573	11	1	[	[	X
ejpam-4573	11	2	22	22	NUM
ejpam-4573	11	3	]	]	PUNCT
ejpam-4573	11	4	introduced	introduce	VERB
ejpam-4573	11	5	weak	weak	ADJ
ejpam-4573	11	6	quasi	quasi	NOUN
ejpam-4573	11	7	-	-	NOUN
ejpam-4573	11	8	continuity	continuity	NOUN
ejpam-4573	11	9	which	which	PRON
ejpam-4573	11	10	is	be	AUX
ejpam-4573	11	11	implied	imply	VERB
ejpam-4573	11	12	by	by	ADP
ejpam-4573	11	13	both	both	DET
ejpam-4573	11	14	weak	weak	ADJ
ejpam-4573	11	15	continuity	continuity	NOUN
ejpam-4573	11	16	and	and	CCONJ
ejpam-4573	11	17	quasicontinuity	quasicontinuity	NOUN
ejpam-4573	11	18	.	.	PUNCT
ejpam-4573	11	19	janković	janković	PUNCT
ejpam-4573	12	1	[	[	X
ejpam-4573	12	2	8	8	NUM
ejpam-4573	12	3	]	]	PUNCT
ejpam-4573	12	4	introduced	introduce	VERB
ejpam-4573	12	5	almost	almost	ADV
ejpam-4573	12	6	weak	weak	ADJ
ejpam-4573	12	7	continuity	continuity	NOUN
ejpam-4573	12	8	as	as	ADP
ejpam-4573	12	9	a	a	DET
ejpam-4573	12	10	generalization	generalization	NOUN
ejpam-4573	12	11	of	of	ADP
ejpam-4573	12	12	both	both	DET
ejpam-4573	12	13	weak	weak	ADJ
ejpam-4573	12	14	continuity	continuity	NOUN
ejpam-4573	12	15	and	and	CCONJ
ejpam-4573	12	16	almost	almost	ADV
ejpam-4573	12	17	continuity	continuity	NOUN
ejpam-4573	12	18	.	.	PUNCT
ejpam-4573	13	1	noiri	noiri	ADV
ejpam-4573	14	1	[	[	X
ejpam-4573	14	2	13	13	NUM
ejpam-4573	14	3	]	]	PUNCT
ejpam-4573	14	4	obtained	obtain	VERB
ejpam-4573	14	5	some	some	DET
ejpam-4573	14	6	characterizations	characterization	NOUN
ejpam-4573	14	7	of	of	ADP
ejpam-4573	14	8	almost	almost	ADV
ejpam-4573	14	9	weak	weak	ADJ
ejpam-4573	14	10	continuity	continuity	NOUN
ejpam-4573	14	11	and	and	CCONJ
ejpam-4573	14	12	some	some	DET
ejpam-4573	14	13	relations	relation	NOUN
ejpam-4573	14	14	between	between	ADP
ejpam-4573	14	15	almost	almost	ADV
ejpam-4573	14	16	weak	weak	ADJ
ejpam-4573	14	17	continuity	continuity	NOUN
ejpam-4573	14	18	and	and	CCONJ
ejpam-4573	14	19	weak	weak	ADJ
ejpam-4573	14	20	continuity	continuity	NOUN
ejpam-4573	14	21	.	.	PUNCT
ejpam-4573	15	1	popa	popa	NOUN
ejpam-4573	16	1	[	[	X
ejpam-4573	16	2	19	19	NUM
ejpam-4573	16	3	]	]	PUNCT
ejpam-4573	16	4	and	and	CCONJ
ejpam-4573	16	5	smithson	smithson	PROPN
ejpam-4573	16	6	[	[	X
ejpam-4573	16	7	23	23	NUM
ejpam-4573	16	8	]	]	PUNCT
ejpam-4573	16	9	independently	independently	ADV
ejpam-4573	16	10	introduced	introduce	VERB
ejpam-4573	16	11	the	the	DET
ejpam-4573	16	12	notion	notion	NOUN
ejpam-4573	16	13	of	of	ADP
ejpam-4573	16	14	weakly	weakly	ADJ
ejpam-4573	16	15	continuous	continuous	ADJ
ejpam-4573	16	16	multifunctions	multifunction	NOUN
ejpam-4573	16	17	.	.	PUNCT
ejpam-4573	17	1	the	the	DET
ejpam-4573	17	2	present	present	ADJ
ejpam-4573	17	3	authors	author	NOUN
ejpam-4573	17	4	introduced	introduce	VERB
ejpam-4573	17	5	and	and	CCONJ
ejpam-4573	17	6	studied	study	VERB
ejpam-4573	17	7	other	other	ADJ
ejpam-4573	17	8	weak	weak	ADJ
ejpam-4573	17	9	forms	form	NOUN
ejpam-4573	17	10	of	of	ADP
ejpam-4573	17	11	continuous	continuous	ADJ
ejpam-4573	17	12	multifunctions	multifunction	NOUN
ejpam-4573	17	13	:	:	PUNCT
ejpam-4573	17	14	weakly	weakly	ADJ
ejpam-4573	17	15	quasicontinuous	quasicontinuous	ADJ
ejpam-4573	17	16	multifunctions	multifunction	NOUN
ejpam-4573	18	1	[	[	X
ejpam-4573	18	2	15	15	NUM
ejpam-4573	18	3	]	]	PUNCT
ejpam-4573	18	4	,	,	PUNCT
ejpam-4573	18	5	almost	almost	ADV
ejpam-4573	18	6	weakly	weakly	ADJ
ejpam-4573	18	7	continuous	continuous	ADJ
ejpam-4573	18	8	multifunctions	multifunction	NOUN
ejpam-4573	19	1	[	[	X
ejpam-4573	19	2	16	16	NUM
ejpam-4573	19	3	]	]	PUNCT
ejpam-4573	19	4	,	,	PUNCT
ejpam-4573	19	5	weakly	weakly	ADJ
ejpam-4573	19	6	α	α	X
ejpam-4573	19	7	-	-	ADJ
ejpam-4573	19	8	continuous	continuous	ADJ
ejpam-4573	19	9	multifunctions	multifunction	NOUN
ejpam-4573	20	1	[	[	X
ejpam-4573	20	2	20	20	NUM
ejpam-4573	20	3	]	]	PUNCT
ejpam-4573	20	4	,	,	PUNCT
ejpam-4573	20	5	weakly	weakly	ADJ
ejpam-4573	20	6	β	β	ADJ
ejpam-4573	20	7	-	-	ADJ
ejpam-4573	20	8	continuous	continuous	ADJ
ejpam-4573	20	9	multifunctions	multifunction	NOUN
ejpam-4573	21	1	[	[	X
ejpam-4573	21	2	21	21	NUM
ejpam-4573	21	3	]	]	PUNCT
ejpam-4573	21	4	.	.	PUNCT
ejpam-4573	22	1	these	these	DET
ejpam-4573	22	2	multifunctions	multifunction	NOUN
ejpam-4573	22	3	have	have	VERB
ejpam-4573	22	4	similar	similar	ADJ
ejpam-4573	22	5	characterizations	characterization	NOUN
ejpam-4573	22	6	.	.	PUNCT
ejpam-4573	23	1	the	the	DET
ejpam-4573	23	2	analogy	analogy	NOUN
ejpam-4573	23	3	in	in	ADP
ejpam-4573	23	4	their	their	PRON
ejpam-4573	23	5	definitions	definition	NOUN
ejpam-4573	23	6	and	and	CCONJ
ejpam-4573	23	7	results	result	NOUN
ejpam-4573	23	8	suggests	suggest	VERB
ejpam-4573	23	9	the	the	DET
ejpam-4573	23	10	need	need	NOUN
ejpam-4573	23	11	of	of	ADP
ejpam-4573	23	12	formulating	formulate	VERB
ejpam-4573	23	13	a	a	DET
ejpam-4573	23	14	unified	unified	ADJ
ejpam-4573	23	15	theory	theory	NOUN
ejpam-4573	23	16	.	.	PUNCT
ejpam-4573	24	1	noiri	noiri	PROPN
ejpam-4573	24	2	and	and	CCONJ
ejpam-4573	24	3	popa	popa	NOUN
ejpam-4573	24	4	[	[	X
ejpam-4573	24	5	17	17	NUM
ejpam-4573	24	6	]	]	PUNCT
ejpam-4573	24	7	introduced	introduce	VERB
ejpam-4573	24	8	and	and	CCONJ
ejpam-4573	24	9	studied	study	VERB
ejpam-4573	24	10	the	the	DET
ejpam-4573	24	11	notions	notion	NOUN
ejpam-4573	24	12	of	of	ADP
ejpam-4573	24	13	upper	upper	ADJ
ejpam-4573	24	14	and	and	CCONJ
ejpam-4573	24	15	lower	low	ADJ
ejpam-4573	24	16	weakly	weakly	ADJ
ejpam-4573	24	17	m	m	ADJ
ejpam-4573	24	18	-	-	ADJ
ejpam-4573	24	19	continuous	continuous	ADJ
ejpam-4573	24	20	∗corresponding	∗corresponding	NOUN
ejpam-4573	24	21	author	author	NOUN
ejpam-4573	24	22	.	.	PUNCT
ejpam-4573	25	1	doi	doi	NOUN
ejpam-4573	25	2	:	:	PUNCT
ejpam-4573	25	3	https://doi.org/10.29020/nybg.ejpam.v16i2.4573	https://doi.org/10.29020/nybg.ejpam.v16i2.4573	DET
ejpam-4573	25	4	email	email	NOUN
ejpam-4573	25	5	addresses	address	NOUN
ejpam-4573	25	6	:	:	PUNCT
ejpam-4573	26	1	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	INTJ
ejpam-4573	26	2	(	(	PUNCT
ejpam-4573	26	3	c.	c.	PROPN
ejpam-4573	26	4	boonpok	boonpok	PROPN
ejpam-4573	26	5	)	)	PUNCT
ejpam-4573	26	6	,	,	PUNCT
ejpam-4573	26	7	prapart.p@msu.ac.th	prapart.p@msu.ac.th	X
ejpam-4573	26	8	(	(	PUNCT
ejpam-4573	26	9	p.	p.	NOUN
ejpam-4573	26	10	pue	pue	NOUN
ejpam-4573	26	11	-	-	PUNCT
ejpam-4573	26	12	on	on	ADP
ejpam-4573	26	13	)	)	PUNCT
ejpam-4573	26	14	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4573	26	15	1047	1047	NUM
ejpam-4573	26	16	©	©	ADP
ejpam-4573	26	17	2023	2023	NUM
ejpam-4573	26	18	ejpam	ejpam	NOUN
ejpam-4573	26	19	all	all	DET
ejpam-4573	26	20	rights	right	NOUN
ejpam-4573	26	21	reserved	reserve	VERB
ejpam-4573	26	22	.	.	PUNCT
ejpam-4573	27	1	c.	c.	PROPN
ejpam-4573	27	2	boonpok	boonpok	PROPN
ejpam-4573	27	3	,	,	PUNCT
ejpam-4573	27	4	p.	p.	NOUN
ejpam-4573	27	5	pue	pue	NOUN
ejpam-4573	27	6	-	-	PUNCT
ejpam-4573	27	7	on	on	ADP
ejpam-4573	27	8	/	/	SYM
ejpam-4573	27	9	eur	eur	NOUN
ejpam-4573	27	10	.	.	PUNCT
ejpam-4573	28	1	j.	j.	PROPN
ejpam-4573	28	2	pure	pure	PROPN
ejpam-4573	28	3	appl	appl	PROPN
ejpam-4573	28	4	.	.	PROPN
ejpam-4573	28	5	math	math	PROPN
ejpam-4573	28	6	,	,	PUNCT
ejpam-4573	28	7	16	16	NUM
ejpam-4573	28	8	(	(	PUNCT
ejpam-4573	28	9	2	2	NUM
ejpam-4573	28	10	)	)	PUNCT
ejpam-4573	28	11	(	(	PUNCT
ejpam-4573	28	12	2023	2023	NUM
ejpam-4573	28	13	)	)	PUNCT
ejpam-4573	28	14	,	,	PUNCT
ejpam-4573	28	15	1047	1047	NUM
ejpam-4573	28	16	-	-	SYM
ejpam-4573	28	17	1058	1058	NUM
ejpam-4573	28	18	1048	1048	NUM
ejpam-4573	28	19	multifunctions	multifunction	NOUN
ejpam-4573	28	20	as	as	ADP
ejpam-4573	28	21	a	a	DET
ejpam-4573	28	22	multifunction	multifunction	NOUN
ejpam-4573	28	23	from	from	ADP
ejpam-4573	28	24	a	a	DET
ejpam-4573	28	25	set	set	NOUN
ejpam-4573	28	26	satisfying	satisfy	VERB
ejpam-4573	28	27	certain	certain	ADJ
ejpam-4573	28	28	minimal	minimal	ADJ
ejpam-4573	28	29	condition	condition	NOUN
ejpam-4573	28	30	into	into	ADP
ejpam-4573	28	31	a	a	DET
ejpam-4573	28	32	topological	topological	ADJ
ejpam-4573	28	33	space	space	NOUN
ejpam-4573	28	34	.	.	PUNCT
ejpam-4573	29	1	in	in	ADP
ejpam-4573	29	2	[	[	X
ejpam-4573	29	3	5	5	NUM
ejpam-4573	29	4	]	]	PUNCT
ejpam-4573	29	5	,	,	PUNCT
ejpam-4573	29	6	the	the	DET
ejpam-4573	29	7	present	present	ADJ
ejpam-4573	29	8	authors	author	NOUN
ejpam-4573	29	9	introduced	introduce	VERB
ejpam-4573	29	10	and	and	CCONJ
ejpam-4573	29	11	studied	study	VERB
ejpam-4573	29	12	the	the	DET
ejpam-4573	29	13	notions	notion	NOUN
ejpam-4573	29	14	of	of	ADP
ejpam-4573	29	15	upper	upper	ADJ
ejpam-4573	29	16	and	and	CCONJ
ejpam-4573	29	17	lower	low	ADJ
ejpam-4573	29	18	(	(	PUNCT
ejpam-4573	29	19	τ1	τ1	NOUN
ejpam-4573	29	20	,	,	PUNCT
ejpam-4573	29	21	τ2)-precontinuous	τ2)-precontinuous	ADJ
ejpam-4573	29	22	multifunctions	multifunction	NOUN
ejpam-4573	29	23	.	.	PUNCT
ejpam-4573	30	1	viriyapong	viriyapong	PROPN
ejpam-4573	30	2	and	and	CCONJ
ejpam-4573	30	3	boonpok	boonpok	X
ejpam-4573	30	4	[	[	X
ejpam-4573	30	5	25	25	NUM
ejpam-4573	30	6	]	]	PUNCT
ejpam-4573	30	7	introduced	introduce	VERB
ejpam-4573	30	8	and	and	CCONJ
ejpam-4573	30	9	investigated	investigate	VERB
ejpam-4573	30	10	the	the	DET
ejpam-4573	30	11	concepts	concept	NOUN
ejpam-4573	30	12	of	of	ADP
ejpam-4573	30	13	upper	upper	ADJ
ejpam-4573	30	14	and	and	CCONJ
ejpam-4573	30	15	lower	low	ADJ
ejpam-4573	30	16	weakly	weakly	ADJ
ejpam-4573	30	17	(	(	PUNCT
ejpam-4573	30	18	τ1	τ1	NOUN
ejpam-4573	30	19	,	,	PUNCT
ejpam-4573	30	20	τ2)α	τ2)α	ADJ
ejpam-4573	30	21	-	-	PUNCT
ejpam-4573	30	22	continuous	continuous	ADJ
ejpam-4573	30	23	multifunctions	multifunction	NOUN
ejpam-4573	30	24	.	.	PUNCT
ejpam-4573	31	1	abd	abd	PROPN
ejpam-4573	31	2	el	el	PROPN
ejpam-4573	31	3	-	-	PROPN
ejpam-4573	31	4	monsef	monsef	PROPN
ejpam-4573	31	5	et	et	PROPN
ejpam-4573	31	6	al	al	PROPN
ejpam-4573	31	7	.	.	PUNCT
ejpam-4573	32	1	[	[	X
ejpam-4573	32	2	6	6	NUM
ejpam-4573	32	3	]	]	PUNCT
ejpam-4573	32	4	introduced	introduce	VERB
ejpam-4573	32	5	a	a	DET
ejpam-4573	32	6	weak	weak	ADJ
ejpam-4573	32	7	form	form	NOUN
ejpam-4573	32	8	of	of	ADP
ejpam-4573	32	9	open	open	ADJ
ejpam-4573	32	10	sets	set	NOUN
ejpam-4573	32	11	called	call	VERB
ejpam-4573	32	12	β	β	NOUN
ejpam-4573	32	13	-	-	ADJ
ejpam-4573	32	14	open	open	ADJ
ejpam-4573	32	15	sets	set	NOUN
ejpam-4573	32	16	.	.	PUNCT
ejpam-4573	33	1	the	the	DET
ejpam-4573	33	2	notion	notion	NOUN
ejpam-4573	33	3	of	of	ADP
ejpam-4573	33	4	β	β	ADJ
ejpam-4573	33	5	-	-	ADJ
ejpam-4573	33	6	open	open	ADJ
ejpam-4573	33	7	sets	set	NOUN
ejpam-4573	33	8	is	be	AUX
ejpam-4573	33	9	equivalent	equivalent	ADJ
ejpam-4573	33	10	to	to	ADP
ejpam-4573	33	11	that	that	PRON
ejpam-4573	33	12	of	of	ADP
ejpam-4573	33	13	semi	semi	ADJ
ejpam-4573	33	14	-	-	ADJ
ejpam-4573	33	15	preopen	preopen	ADJ
ejpam-4573	33	16	sets	set	NOUN
ejpam-4573	33	17	due	due	ADJ
ejpam-4573	33	18	to	to	PART
ejpam-4573	33	19	andrijević	andrijević	VERB
ejpam-4573	33	20	[	[	X
ejpam-4573	33	21	1	1	NUM
ejpam-4573	33	22	]	]	PUNCT
ejpam-4573	33	23	.	.	PUNCT
ejpam-4573	34	1	noiri	noiri	PROPN
ejpam-4573	34	2	and	and	CCONJ
ejpam-4573	34	3	hatir	hatir	PROPN
ejpam-4573	35	1	[	[	X
ejpam-4573	35	2	14	14	NUM
ejpam-4573	35	3	]	]	PUNCT
ejpam-4573	35	4	introduced	introduce	VERB
ejpam-4573	35	5	the	the	DET
ejpam-4573	35	6	concept	concept	NOUN
ejpam-4573	35	7	of	of	ADP
ejpam-4573	35	8	λsp	λsp	NOUN
ejpam-4573	35	9	-	-	PUNCT
ejpam-4573	35	10	sets	set	NOUN
ejpam-4573	35	11	in	in	ADP
ejpam-4573	35	12	terms	term	NOUN
ejpam-4573	35	13	of	of	ADP
ejpam-4573	35	14	the	the	DET
ejpam-4573	35	15	concept	concept	NOUN
ejpam-4573	35	16	of	of	ADP
ejpam-4573	35	17	β	β	ADJ
ejpam-4573	35	18	-	-	ADJ
ejpam-4573	35	19	open	open	ADJ
ejpam-4573	35	20	sets	set	NOUN
ejpam-4573	35	21	and	and	CCONJ
ejpam-4573	35	22	investigated	investigate	VERB
ejpam-4573	35	23	the	the	DET
ejpam-4573	35	24	notion	notion	NOUN
ejpam-4573	35	25	of	of	ADP
ejpam-4573	35	26	λsp	λsp	NOUN
ejpam-4573	35	27	-	-	PUNCT
ejpam-4573	35	28	closed	close	VERB
ejpam-4573	35	29	sets	set	NOUN
ejpam-4573	35	30	by	by	ADP
ejpam-4573	35	31	using	use	VERB
ejpam-4573	35	32	λsp	λsp	NOUN
ejpam-4573	35	33	-	-	PUNCT
ejpam-4573	35	34	sets	set	NOUN
ejpam-4573	35	35	.	.	PUNCT
ejpam-4573	36	1	in	in	ADP
ejpam-4573	36	2	[	[	X
ejpam-4573	36	3	3	3	NUM
ejpam-4573	36	4	]	]	PUNCT
ejpam-4573	36	5	,	,	PUNCT
ejpam-4573	36	6	the	the	DET
ejpam-4573	36	7	author	author	NOUN
ejpam-4573	36	8	introduced	introduce	VERB
ejpam-4573	36	9	the	the	DET
ejpam-4573	36	10	concepts	concept	NOUN
ejpam-4573	36	11	of	of	ADP
ejpam-4573	36	12	(	(	PUNCT
ejpam-4573	36	13	λ	λ	PROPN
ejpam-4573	36	14	,	,	PUNCT
ejpam-4573	36	15	sp)-open	sp)-open	ADJ
ejpam-4573	36	16	sets	set	NOUN
ejpam-4573	36	17	and	and	CCONJ
ejpam-4573	36	18	(	(	PUNCT
ejpam-4573	36	19	λ	λ	PROPN
ejpam-4573	36	20	,	,	PUNCT
ejpam-4573	36	21	sp)-closed	sp)-close	VERB
ejpam-4573	36	22	sets	set	NOUN
ejpam-4573	36	23	which	which	PRON
ejpam-4573	36	24	are	be	AUX
ejpam-4573	36	25	defined	define	VERB
ejpam-4573	36	26	by	by	ADP
ejpam-4573	36	27	utilizing	utilize	VERB
ejpam-4573	36	28	the	the	DET
ejpam-4573	36	29	notions	notion	NOUN
ejpam-4573	36	30	of	of	ADP
ejpam-4573	36	31	λsp	λsp	NOUN
ejpam-4573	36	32	-	-	PUNCT
ejpam-4573	36	33	sets	set	NOUN
ejpam-4573	36	34	and	and	CCONJ
ejpam-4573	36	35	β	β	NOUN
ejpam-4573	36	36	-	-	ADJ
ejpam-4573	36	37	closed	closed	ADJ
ejpam-4573	36	38	sets	set	NOUN
ejpam-4573	36	39	.	.	PUNCT
ejpam-4573	37	1	moreover	moreover	ADV
ejpam-4573	37	2	,	,	PUNCT
ejpam-4573	37	3	some	some	DET
ejpam-4573	37	4	characterizations	characterization	NOUN
ejpam-4573	37	5	of	of	ADP
ejpam-4573	37	6	upper	upper	ADJ
ejpam-4573	37	7	and	and	CCONJ
ejpam-4573	37	8	lower	low	ADJ
ejpam-4573	37	9	(	(	PUNCT
ejpam-4573	37	10	λ	λ	NOUN
ejpam-4573	37	11	,	,	PUNCT
ejpam-4573	37	12	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	37	13	multifunctions	multifunction	NOUN
ejpam-4573	37	14	were	be	AUX
ejpam-4573	37	15	provided	provide	VERB
ejpam-4573	37	16	in	in	ADP
ejpam-4573	37	17	[	[	X
ejpam-4573	37	18	3	3	NUM
ejpam-4573	37	19	]	]	PUNCT
ejpam-4573	37	20	.	.	PUNCT
ejpam-4573	38	1	the	the	DET
ejpam-4573	38	2	purpose	purpose	NOUN
ejpam-4573	38	3	of	of	ADP
ejpam-4573	38	4	the	the	DET
ejpam-4573	38	5	present	present	ADJ
ejpam-4573	38	6	paper	paper	NOUN
ejpam-4573	38	7	is	be	AUX
ejpam-4573	38	8	to	to	PART
ejpam-4573	38	9	introduce	introduce	VERB
ejpam-4573	38	10	the	the	DET
ejpam-4573	38	11	notions	notion	NOUN
ejpam-4573	38	12	of	of	ADP
ejpam-4573	38	13	upper	upper	ADJ
ejpam-4573	38	14	and	and	CCONJ
ejpam-4573	38	15	lower	low	ADJ
ejpam-4573	38	16	weakly	weakly	ADJ
ejpam-4573	38	17	(	(	PUNCT
ejpam-4573	38	18	λ	λ	NOUN
ejpam-4573	38	19	,	,	PUNCT
ejpam-4573	38	20	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	38	21	multifunctions	multifunction	NOUN
ejpam-4573	38	22	.	.	PUNCT
ejpam-4573	39	1	furthermore	furthermore	ADV
ejpam-4573	39	2	,	,	PUNCT
ejpam-4573	39	3	several	several	ADJ
ejpam-4573	39	4	characterizations	characterization	NOUN
ejpam-4573	39	5	of	of	ADP
ejpam-4573	39	6	upper	upper	ADJ
ejpam-4573	39	7	and	and	CCONJ
ejpam-4573	39	8	lower	low	ADJ
ejpam-4573	39	9	weakly	weakly	ADJ
ejpam-4573	39	10	(	(	PUNCT
ejpam-4573	39	11	λ	λ	NOUN
ejpam-4573	39	12	,	,	PUNCT
ejpam-4573	39	13	sp)continuous	sp)continuous	ADJ
ejpam-4573	39	14	multifunctions	multifunction	NOUN
ejpam-4573	39	15	are	be	AUX
ejpam-4573	39	16	discussed	discuss	VERB
ejpam-4573	39	17	.	.	PUNCT
ejpam-4573	40	1	2	2	X
ejpam-4573	40	2	.	.	X
ejpam-4573	40	3	preliminaries	preliminary	NOUN
ejpam-4573	40	4	let	let	VERB
ejpam-4573	40	5	a	a	PRON
ejpam-4573	40	6	be	be	AUX
ejpam-4573	40	7	a	a	DET
ejpam-4573	40	8	subset	subset	NOUN
ejpam-4573	40	9	of	of	ADP
ejpam-4573	40	10	a	a	DET
ejpam-4573	40	11	topological	topological	ADJ
ejpam-4573	40	12	space	space	NOUN
ejpam-4573	40	13	(	(	PUNCT
ejpam-4573	40	14	x	x	X
ejpam-4573	40	15	,	,	PUNCT
ejpam-4573	40	16	τ	τ	PROPN
ejpam-4573	40	17	)	)	PUNCT
ejpam-4573	40	18	.	.	PUNCT
ejpam-4573	41	1	the	the	DET
ejpam-4573	41	2	closure	closure	NOUN
ejpam-4573	41	3	of	of	ADP
ejpam-4573	41	4	a	a	PRON
ejpam-4573	41	5	and	and	CCONJ
ejpam-4573	41	6	the	the	DET
ejpam-4573	41	7	interior	interior	NOUN
ejpam-4573	41	8	of	of	ADP
ejpam-4573	41	9	a	a	PRON
ejpam-4573	41	10	are	be	AUX
ejpam-4573	41	11	denoted	denote	VERB
ejpam-4573	41	12	by	by	ADP
ejpam-4573	41	13	cl(a	cl(a	NOUN
ejpam-4573	41	14	)	)	PUNCT
ejpam-4573	41	15	and	and	CCONJ
ejpam-4573	41	16	int(a	int(a	PROPN
ejpam-4573	41	17	)	)	PUNCT
ejpam-4573	41	18	,	,	PUNCT
ejpam-4573	41	19	respectively	respectively	ADV
ejpam-4573	41	20	.	.	PUNCT
ejpam-4573	42	1	a	a	DET
ejpam-4573	42	2	subset	subset	NOUN
ejpam-4573	42	3	a	a	PRON
ejpam-4573	42	4	of	of	ADP
ejpam-4573	42	5	a	a	DET
ejpam-4573	42	6	topological	topological	ADJ
ejpam-4573	42	7	space	space	NOUN
ejpam-4573	42	8	(	(	PUNCT
ejpam-4573	42	9	x	x	X
ejpam-4573	42	10	,	,	PUNCT
ejpam-4573	42	11	τ	τ	X
ejpam-4573	42	12	)	)	PUNCT
ejpam-4573	42	13	is	be	AUX
ejpam-4573	42	14	said	say	VERB
ejpam-4573	42	15	to	to	PART
ejpam-4573	42	16	be	be	AUX
ejpam-4573	42	17	β	β	X
ejpam-4573	42	18	-	-	VERB
ejpam-4573	42	19	open	open	ADJ
ejpam-4573	43	1	[	[	X
ejpam-4573	43	2	6	6	NUM
ejpam-4573	43	3	]	]	PUNCT
ejpam-4573	43	4	if	if	SCONJ
ejpam-4573	43	5	a	a	DET
ejpam-4573	43	6	⊆	⊆	NUM
ejpam-4573	43	7	cl(int(cl(a	cl(int(cl(a	NOUN
ejpam-4573	43	8	)	)	PUNCT
ejpam-4573	43	9	)	)	PUNCT
ejpam-4573	43	10	)	)	PUNCT
ejpam-4573	43	11	.	.	PUNCT
ejpam-4573	44	1	the	the	DET
ejpam-4573	44	2	complement	complement	NOUN
ejpam-4573	44	3	of	of	ADP
ejpam-4573	44	4	a	a	DET
ejpam-4573	44	5	β	β	X
ejpam-4573	44	6	-	-	ADJ
ejpam-4573	44	7	open	open	ADJ
ejpam-4573	44	8	set	set	NOUN
ejpam-4573	44	9	is	be	AUX
ejpam-4573	44	10	called	call	VERB
ejpam-4573	44	11	β	β	NOUN
ejpam-4573	44	12	-	-	VERB
ejpam-4573	44	13	closed	closed	ADJ
ejpam-4573	44	14	.	.	PUNCT
ejpam-4573	45	1	the	the	DET
ejpam-4573	45	2	family	family	NOUN
ejpam-4573	45	3	of	of	ADP
ejpam-4573	45	4	all	all	DET
ejpam-4573	45	5	β	β	ADJ
ejpam-4573	45	6	-	-	ADJ
ejpam-4573	45	7	open	open	ADJ
ejpam-4573	45	8	sets	set	NOUN
ejpam-4573	45	9	of	of	ADP
ejpam-4573	45	10	a	a	DET
ejpam-4573	45	11	topological	topological	ADJ
ejpam-4573	45	12	space	space	NOUN
ejpam-4573	45	13	(	(	PUNCT
ejpam-4573	45	14	x	x	X
ejpam-4573	45	15	,	,	PUNCT
ejpam-4573	45	16	τ	τ	X
ejpam-4573	45	17	)	)	PUNCT
ejpam-4573	45	18	is	be	AUX
ejpam-4573	45	19	denoted	denote	VERB
ejpam-4573	45	20	by	by	ADP
ejpam-4573	45	21	β(x	β(x	PROPN
ejpam-4573	45	22	,	,	PUNCT
ejpam-4573	45	23	τ	τ	PROPN
ejpam-4573	45	24	)	)	PUNCT
ejpam-4573	45	25	.	.	PUNCT
ejpam-4573	46	1	a	a	DET
ejpam-4573	46	2	subset	subset	NOUN
ejpam-4573	46	3	λsp(a	λsp(a	NOUN
ejpam-4573	46	4	)	)	PUNCT
ejpam-4573	47	1	[	[	X
ejpam-4573	47	2	14	14	NUM
ejpam-4573	47	3	]	]	PUNCT
ejpam-4573	47	4	is	be	AUX
ejpam-4573	47	5	defined	define	VERB
ejpam-4573	47	6	as	as	SCONJ
ejpam-4573	47	7	follows	follow	VERB
ejpam-4573	47	8	:	:	PUNCT
ejpam-4573	47	9	λsp(a	λsp(a	NUM
ejpam-4573	47	10	)	)	PUNCT
ejpam-4573	47	11	=	=	PUNCT
ejpam-4573	48	1	∩{u	∩{u	PROPN
ejpam-4573	48	2	|	|	ADV
ejpam-4573	48	3	a	a	DET
ejpam-4573	48	4	⊆	⊆	NUM
ejpam-4573	48	5	u	u	NOUN
ejpam-4573	48	6	,	,	PUNCT
ejpam-4573	48	7	u	u	NOUN
ejpam-4573	48	8	∈	∈	PROPN
ejpam-4573	48	9	β(x	β(x	PROPN
ejpam-4573	48	10	,	,	PUNCT
ejpam-4573	48	11	τ	τ	X
ejpam-4573	48	12	)	)	PUNCT
ejpam-4573	48	13	}	}	PUNCT
ejpam-4573	48	14	.	.	PUNCT
ejpam-4573	49	1	a	a	DET
ejpam-4573	49	2	subset	subset	NOUN
ejpam-4573	49	3	a	a	PRON
ejpam-4573	49	4	of	of	ADP
ejpam-4573	49	5	a	a	DET
ejpam-4573	49	6	topological	topological	ADJ
ejpam-4573	49	7	space	space	NOUN
ejpam-4573	49	8	(	(	PUNCT
ejpam-4573	49	9	x	x	X
ejpam-4573	49	10	,	,	PUNCT
ejpam-4573	49	11	τ	τ	X
ejpam-4573	49	12	)	)	PUNCT
ejpam-4573	49	13	is	be	AUX
ejpam-4573	49	14	called	call	VERB
ejpam-4573	49	15	a	a	DET
ejpam-4573	49	16	λsp	λsp	NOUN
ejpam-4573	49	17	-	-	PUNCT
ejpam-4573	49	18	set	set	VERB
ejpam-4573	49	19	[	[	X
ejpam-4573	49	20	14	14	NUM
ejpam-4573	49	21	]	]	X
ejpam-4573	49	22	if	if	SCONJ
ejpam-4573	49	23	a	a	DET
ejpam-4573	49	24	=	=	NOUN
ejpam-4573	49	25	λsp(a	λsp(a	NOUN
ejpam-4573	49	26	)	)	PUNCT
ejpam-4573	49	27	.	.	PUNCT
ejpam-4573	50	1	a	a	DET
ejpam-4573	50	2	subset	subset	NOUN
ejpam-4573	50	3	a	a	PRON
ejpam-4573	50	4	of	of	ADP
ejpam-4573	50	5	a	a	DET
ejpam-4573	50	6	topological	topological	ADJ
ejpam-4573	50	7	space	space	NOUN
ejpam-4573	50	8	(	(	PUNCT
ejpam-4573	50	9	x	x	X
ejpam-4573	50	10	,	,	PUNCT
ejpam-4573	50	11	τ	τ	X
ejpam-4573	50	12	)	)	PUNCT
ejpam-4573	50	13	is	be	AUX
ejpam-4573	50	14	called	call	VERB
ejpam-4573	50	15	(	(	PUNCT
ejpam-4573	50	16	λ	λ	X
ejpam-4573	50	17	,	,	PUNCT
ejpam-4573	50	18	sp)-closed	sp)-close	VERB
ejpam-4573	50	19	[	[	PUNCT
ejpam-4573	50	20	3	3	X
ejpam-4573	50	21	]	]	X
ejpam-4573	50	22	if	if	SCONJ
ejpam-4573	50	23	a	a	DET
ejpam-4573	50	24	=	=	X
ejpam-4573	50	25	t	t	NOUN
ejpam-4573	50	26	∩c	∩c	NOUN
ejpam-4573	50	27	,	,	PUNCT
ejpam-4573	50	28	where	where	SCONJ
ejpam-4573	50	29	t	t	PROPN
ejpam-4573	50	30	is	be	AUX
ejpam-4573	50	31	a	a	DET
ejpam-4573	50	32	λsp	λsp	NOUN
ejpam-4573	50	33	-	-	PUNCT
ejpam-4573	50	34	set	set	VERB
ejpam-4573	50	35	and	and	CCONJ
ejpam-4573	50	36	c	c	NOUN
ejpam-4573	50	37	is	be	AUX
ejpam-4573	50	38	a	a	DET
ejpam-4573	50	39	β	β	NOUN
ejpam-4573	50	40	-	-	ADJ
ejpam-4573	50	41	closed	closed	ADJ
ejpam-4573	50	42	set	set	NOUN
ejpam-4573	50	43	.	.	PUNCT
ejpam-4573	51	1	the	the	DET
ejpam-4573	51	2	complement	complement	NOUN
ejpam-4573	51	3	of	of	ADP
ejpam-4573	51	4	a	a	DET
ejpam-4573	51	5	(	(	PUNCT
ejpam-4573	51	6	λ	λ	PROPN
ejpam-4573	51	7	,	,	PUNCT
ejpam-4573	51	8	sp)-closed	sp)-close	VERB
ejpam-4573	51	9	set	set	VERB
ejpam-4573	51	10	is	be	AUX
ejpam-4573	51	11	called	call	VERB
ejpam-4573	51	12	(	(	PUNCT
ejpam-4573	51	13	λ	λ	NOUN
ejpam-4573	51	14	,	,	PUNCT
ejpam-4573	51	15	sp)-open	sp)-open	NOUN
ejpam-4573	51	16	.	.	PUNCT
ejpam-4573	52	1	the	the	DET
ejpam-4573	52	2	family	family	NOUN
ejpam-4573	52	3	of	of	ADP
ejpam-4573	52	4	all	all	DET
ejpam-4573	52	5	(	(	PUNCT
ejpam-4573	52	6	λ	λ	NOUN
ejpam-4573	52	7	,	,	PUNCT
ejpam-4573	52	8	sp)-open	sp)-open	ADJ
ejpam-4573	52	9	sets	set	NOUN
ejpam-4573	52	10	in	in	ADP
ejpam-4573	52	11	a	a	DET
ejpam-4573	52	12	topological	topological	ADJ
ejpam-4573	52	13	space	space	NOUN
ejpam-4573	52	14	(	(	PUNCT
ejpam-4573	52	15	x	x	X
ejpam-4573	52	16	,	,	PUNCT
ejpam-4573	52	17	τ	τ	X
ejpam-4573	52	18	)	)	PUNCT
ejpam-4573	52	19	is	be	AUX
ejpam-4573	52	20	denoted	denote	VERB
ejpam-4573	52	21	by	by	ADP
ejpam-4573	52	22	λspo(x	λspo(x	PROPN
ejpam-4573	52	23	,	,	PUNCT
ejpam-4573	52	24	τ	τ	PROPN
ejpam-4573	52	25	)	)	PUNCT
ejpam-4573	52	26	.	.	PUNCT
ejpam-4573	53	1	let	let	VERB
ejpam-4573	53	2	a	a	DET
ejpam-4573	53	3	be	be	AUX
ejpam-4573	53	4	a	a	DET
ejpam-4573	53	5	subset	subset	NOUN
ejpam-4573	53	6	of	of	ADP
ejpam-4573	53	7	a	a	DET
ejpam-4573	53	8	topological	topological	ADJ
ejpam-4573	53	9	space	space	NOUN
ejpam-4573	53	10	(	(	PUNCT
ejpam-4573	53	11	x	x	X
ejpam-4573	53	12	,	,	PUNCT
ejpam-4573	53	13	τ	τ	PROPN
ejpam-4573	53	14	)	)	PUNCT
ejpam-4573	53	15	.	.	PUNCT
ejpam-4573	54	1	a	a	DET
ejpam-4573	54	2	point	point	NOUN
ejpam-4573	54	3	x	x	X
ejpam-4573	54	4	∈	∈	NOUN
ejpam-4573	54	5	x	x	PUNCT
ejpam-4573	54	6	is	be	AUX
ejpam-4573	54	7	called	call	VERB
ejpam-4573	54	8	a	a	DET
ejpam-4573	54	9	(	(	PUNCT
ejpam-4573	54	10	λ	λ	NOUN
ejpam-4573	54	11	,	,	PUNCT
ejpam-4573	54	12	sp)-cluster	sp)-cluster	NOUN
ejpam-4573	54	13	point	point	NOUN
ejpam-4573	54	14	[	[	X
ejpam-4573	54	15	3	3	X
ejpam-4573	54	16	]	]	PUNCT
ejpam-4573	54	17	of	of	ADP
ejpam-4573	54	18	a	a	PRON
ejpam-4573	54	19	if	if	SCONJ
ejpam-4573	54	20	a	a	DET
ejpam-4573	54	21	∩	∩	ADJ
ejpam-4573	54	22	u	u	ADJ
ejpam-4573	54	23	̸=	̸=	PROPN
ejpam-4573	54	24	∅	∅	NOUN
ejpam-4573	54	25	for	for	ADP
ejpam-4573	54	26	every	every	DET
ejpam-4573	54	27	(	(	PUNCT
ejpam-4573	54	28	λ	λ	NOUN
ejpam-4573	54	29	,	,	PUNCT
ejpam-4573	54	30	sp)-open	sp)-open	NOUN
ejpam-4573	54	31	set	set	VERB
ejpam-4573	54	32	u	u	NOUN
ejpam-4573	54	33	of	of	ADP
ejpam-4573	54	34	x	x	SYM
ejpam-4573	54	35	containing	contain	VERB
ejpam-4573	54	36	x.	x.	NOUN
ejpam-4573	54	37	the	the	DET
ejpam-4573	54	38	set	set	NOUN
ejpam-4573	54	39	of	of	ADP
ejpam-4573	54	40	all	all	DET
ejpam-4573	54	41	(	(	PUNCT
ejpam-4573	54	42	λ	λ	PROPN
ejpam-4573	54	43	,	,	PUNCT
ejpam-4573	54	44	sp)-cluster	sp)-cluster	NOUN
ejpam-4573	54	45	points	point	NOUN
ejpam-4573	54	46	of	of	ADP
ejpam-4573	54	47	a	a	PRON
ejpam-4573	54	48	is	be	AUX
ejpam-4573	54	49	called	call	VERB
ejpam-4573	54	50	the	the	DET
ejpam-4573	54	51	(	(	PUNCT
ejpam-4573	54	52	λ	λ	PROPN
ejpam-4573	54	53	,	,	PUNCT
ejpam-4573	54	54	sp)-closure	sp)-closure	NOUN
ejpam-4573	54	55	[	[	X
ejpam-4573	54	56	3	3	NUM
ejpam-4573	54	57	]	]	PUNCT
ejpam-4573	54	58	of	of	ADP
ejpam-4573	54	59	a	a	PRON
ejpam-4573	54	60	and	and	CCONJ
ejpam-4573	54	61	is	be	AUX
ejpam-4573	54	62	denoted	denote	VERB
ejpam-4573	54	63	by	by	ADP
ejpam-4573	54	64	a(λ	a(λ	ADV
ejpam-4573	54	65	,	,	PUNCT
ejpam-4573	54	66	sp	sp	NOUN
ejpam-4573	54	67	)	)	PUNCT
ejpam-4573	54	68	.	.	PUNCT
ejpam-4573	55	1	the	the	DET
ejpam-4573	55	2	union	union	NOUN
ejpam-4573	55	3	of	of	ADP
ejpam-4573	55	4	all	all	DET
ejpam-4573	55	5	(	(	PUNCT
ejpam-4573	55	6	λ	λ	NOUN
ejpam-4573	55	7	,	,	PUNCT
ejpam-4573	55	8	sp)-open	sp)-open	ADJ
ejpam-4573	55	9	sets	set	NOUN
ejpam-4573	55	10	contained	contain	VERB
ejpam-4573	55	11	in	in	ADP
ejpam-4573	55	12	a	a	PRON
ejpam-4573	55	13	is	be	AUX
ejpam-4573	55	14	called	call	VERB
ejpam-4573	55	15	the	the	DET
ejpam-4573	55	16	(	(	PUNCT
ejpam-4573	55	17	λ	λ	PROPN
ejpam-4573	55	18	,	,	PUNCT
ejpam-4573	55	19	sp)-interior	sp)-interior	NOUN
ejpam-4573	55	20	[	[	X
ejpam-4573	55	21	3	3	NUM
ejpam-4573	55	22	]	]	PUNCT
ejpam-4573	55	23	of	of	ADP
ejpam-4573	55	24	a	a	PRON
ejpam-4573	55	25	and	and	CCONJ
ejpam-4573	55	26	is	be	AUX
ejpam-4573	55	27	denoted	denote	VERB
ejpam-4573	55	28	by	by	ADP
ejpam-4573	55	29	a(λ	a(λ	ADV
ejpam-4573	55	30	,	,	PUNCT
ejpam-4573	55	31	sp	sp	NOUN
ejpam-4573	55	32	)	)	PUNCT
ejpam-4573	55	33	.	.	PUNCT
ejpam-4573	56	1	lemma	lemma	PROPN
ejpam-4573	56	2	1	1	NUM
ejpam-4573	56	3	.	.	PUNCT
ejpam-4573	57	1	[	[	X
ejpam-4573	57	2	3	3	X
ejpam-4573	57	3	]	]	PUNCT
ejpam-4573	57	4	let	let	VERB
ejpam-4573	57	5	a	a	PRON
ejpam-4573	57	6	and	and	CCONJ
ejpam-4573	57	7	b	b	NOUN
ejpam-4573	57	8	be	be	AUX
ejpam-4573	57	9	subsets	subset	NOUN
ejpam-4573	57	10	of	of	ADP
ejpam-4573	57	11	a	a	DET
ejpam-4573	57	12	topological	topological	ADJ
ejpam-4573	57	13	space	space	NOUN
ejpam-4573	57	14	(	(	PUNCT
ejpam-4573	57	15	x	x	X
ejpam-4573	57	16	,	,	PUNCT
ejpam-4573	57	17	τ	τ	PROPN
ejpam-4573	57	18	)	)	PUNCT
ejpam-4573	57	19	.	.	PUNCT
ejpam-4573	58	1	for	for	ADP
ejpam-4573	58	2	the	the	DET
ejpam-4573	58	3	(	(	PUNCT
ejpam-4573	58	4	λ	λ	PROPN
ejpam-4573	58	5	,	,	PUNCT
ejpam-4573	58	6	sp)-closure	sp)-closure	NOUN
ejpam-4573	58	7	,	,	PUNCT
ejpam-4573	58	8	the	the	DET
ejpam-4573	58	9	following	follow	VERB
ejpam-4573	58	10	properties	property	NOUN
ejpam-4573	58	11	hold	hold	VERB
ejpam-4573	58	12	:	:	PUNCT
ejpam-4573	58	13	(	(	PUNCT
ejpam-4573	58	14	1	1	X
ejpam-4573	58	15	)	)	PUNCT
ejpam-4573	58	16	a	a	DET
ejpam-4573	58	17	⊆	⊆	NUM
ejpam-4573	58	18	a(λ	a(λ	ADJ
ejpam-4573	58	19	,	,	PUNCT
ejpam-4573	58	20	sp	sp	NOUN
ejpam-4573	58	21	)	)	PUNCT
ejpam-4573	58	22	and	and	CCONJ
ejpam-4573	58	23	[	[	X
ejpam-4573	58	24	a(λ	a(λ	ADV
ejpam-4573	58	25	,	,	PUNCT
ejpam-4573	58	26	sp)](λ	sp)](λ	PROPN
ejpam-4573	58	27	,	,	PUNCT
ejpam-4573	58	28	sp	sp	NOUN
ejpam-4573	58	29	)	)	PUNCT
ejpam-4573	58	30	=	=	PUNCT
ejpam-4573	58	31	a(λ	a(λ	ADV
ejpam-4573	58	32	,	,	PUNCT
ejpam-4573	58	33	sp	sp	NOUN
ejpam-4573	58	34	)	)	PUNCT
ejpam-4573	58	35	.	.	PUNCT
ejpam-4573	59	1	(	(	PUNCT
ejpam-4573	59	2	2	2	X
ejpam-4573	59	3	)	)	PUNCT
ejpam-4573	59	4	if	if	SCONJ
ejpam-4573	59	5	a	a	DET
ejpam-4573	59	6	⊆	⊆	NUM
ejpam-4573	59	7	b	b	NOUN
ejpam-4573	59	8	,	,	PUNCT
ejpam-4573	59	9	then	then	ADV
ejpam-4573	59	10	a(λ	a(λ	ADV
ejpam-4573	59	11	,	,	PUNCT
ejpam-4573	59	12	sp	sp	NOUN
ejpam-4573	59	13	)	)	PUNCT
ejpam-4573	59	14	⊆	⊆	NUM
ejpam-4573	59	15	b(λ	b(λ	NOUN
ejpam-4573	59	16	,	,	PUNCT
ejpam-4573	59	17	sp	sp	NOUN
ejpam-4573	59	18	)	)	PUNCT
ejpam-4573	59	19	.	.	PUNCT
ejpam-4573	60	1	(	(	PUNCT
ejpam-4573	60	2	3	3	X
ejpam-4573	60	3	)	)	PUNCT
ejpam-4573	60	4	a(λ	a(λ	ADV
ejpam-4573	60	5	,	,	PUNCT
ejpam-4573	60	6	sp	sp	NOUN
ejpam-4573	60	7	)	)	PUNCT
ejpam-4573	60	8	is	be	AUX
ejpam-4573	60	9	(	(	PUNCT
ejpam-4573	60	10	λ	λ	X
ejpam-4573	60	11	,	,	PUNCT
ejpam-4573	60	12	sp)-closed	sp)-close	VERB
ejpam-4573	60	13	.	.	PUNCT
ejpam-4573	61	1	(	(	PUNCT
ejpam-4573	61	2	4	4	X
ejpam-4573	61	3	)	)	PUNCT
ejpam-4573	61	4	a	a	PRON
ejpam-4573	61	5	is	be	AUX
ejpam-4573	61	6	(	(	PUNCT
ejpam-4573	61	7	λ	λ	X
ejpam-4573	61	8	,	,	PUNCT
ejpam-4573	61	9	sp)-closed	sp)-close	VERB
ejpam-4573	61	10	if	if	SCONJ
ejpam-4573	61	11	and	and	CCONJ
ejpam-4573	61	12	only	only	ADV
ejpam-4573	61	13	if	if	SCONJ
ejpam-4573	61	14	a	a	DET
ejpam-4573	61	15	=	=	X
ejpam-4573	61	16	a(λ	a(λ	ADV
ejpam-4573	61	17	,	,	PUNCT
ejpam-4573	61	18	sp	sp	NOUN
ejpam-4573	61	19	)	)	PUNCT
ejpam-4573	61	20	.	.	PUNCT
ejpam-4573	62	1	lemma	lemma	PROPN
ejpam-4573	62	2	2	2	NUM
ejpam-4573	62	3	.	.	PUNCT
ejpam-4573	63	1	[	[	X
ejpam-4573	63	2	3	3	X
ejpam-4573	63	3	]	]	PUNCT
ejpam-4573	63	4	for	for	ADP
ejpam-4573	63	5	subsets	subset	NOUN
ejpam-4573	63	6	a	a	PRON
ejpam-4573	63	7	and	and	CCONJ
ejpam-4573	63	8	b	b	NOUN
ejpam-4573	63	9	of	of	ADP
ejpam-4573	63	10	a	a	DET
ejpam-4573	63	11	topological	topological	ADJ
ejpam-4573	63	12	space	space	NOUN
ejpam-4573	63	13	(	(	PUNCT
ejpam-4573	63	14	x	x	X
ejpam-4573	63	15	,	,	PUNCT
ejpam-4573	63	16	τ	τ	PROPN
ejpam-4573	63	17	)	)	PUNCT
ejpam-4573	63	18	,	,	PUNCT
ejpam-4573	63	19	the	the	DET
ejpam-4573	63	20	following	follow	VERB
ejpam-4573	63	21	properties	property	NOUN
ejpam-4573	63	22	hold	hold	VERB
ejpam-4573	63	23	:	:	PUNCT
ejpam-4573	63	24	c.	c.	PROPN
ejpam-4573	63	25	boonpok	boonpok	PROPN
ejpam-4573	63	26	,	,	PUNCT
ejpam-4573	63	27	p.	p.	NOUN
ejpam-4573	63	28	pue	pue	NOUN
ejpam-4573	63	29	-	-	PUNCT
ejpam-4573	63	30	on	on	ADP
ejpam-4573	63	31	/	/	SYM
ejpam-4573	63	32	eur	eur	NOUN
ejpam-4573	63	33	.	.	PUNCT
ejpam-4573	64	1	j.	j.	PROPN
ejpam-4573	64	2	pure	pure	PROPN
ejpam-4573	64	3	appl	appl	PROPN
ejpam-4573	64	4	.	.	PROPN
ejpam-4573	64	5	math	math	PROPN
ejpam-4573	64	6	,	,	PUNCT
ejpam-4573	64	7	16	16	NUM
ejpam-4573	64	8	(	(	PUNCT
ejpam-4573	64	9	2	2	NUM
ejpam-4573	64	10	)	)	PUNCT
ejpam-4573	64	11	(	(	PUNCT
ejpam-4573	64	12	2023	2023	NUM
ejpam-4573	64	13	)	)	PUNCT
ejpam-4573	64	14	,	,	PUNCT
ejpam-4573	64	15	1047	1047	NUM
ejpam-4573	64	16	-	-	SYM
ejpam-4573	64	17	1058	1058	NUM
ejpam-4573	64	18	1049	1049	NUM
ejpam-4573	64	19	(	(	PUNCT
ejpam-4573	64	20	1	1	NUM
ejpam-4573	64	21	)	)	PUNCT
ejpam-4573	64	22	a(λ	a(λ	ADV
ejpam-4573	64	23	,	,	PUNCT
ejpam-4573	64	24	sp	sp	NOUN
ejpam-4573	64	25	)	)	PUNCT
ejpam-4573	64	26	⊆	⊆	NUM
ejpam-4573	64	27	a	a	DET
ejpam-4573	64	28	and	and	CCONJ
ejpam-4573	64	29	[	[	X
ejpam-4573	64	30	a(λ	a(λ	ADV
ejpam-4573	64	31	,	,	PUNCT
ejpam-4573	64	32	sp)](λ	sp)](λ	PROPN
ejpam-4573	64	33	,	,	PUNCT
ejpam-4573	64	34	sp	sp	NOUN
ejpam-4573	64	35	)	)	PUNCT
ejpam-4573	64	36	=	=	PUNCT
ejpam-4573	65	1	a(λ	a(λ	ADV
ejpam-4573	65	2	,	,	PUNCT
ejpam-4573	65	3	sp	sp	NOUN
ejpam-4573	65	4	)	)	PUNCT
ejpam-4573	65	5	.	.	PUNCT
ejpam-4573	66	1	(	(	PUNCT
ejpam-4573	66	2	2	2	X
ejpam-4573	66	3	)	)	PUNCT
ejpam-4573	66	4	if	if	SCONJ
ejpam-4573	66	5	a	a	DET
ejpam-4573	66	6	⊆	⊆	NUM
ejpam-4573	66	7	b	b	NOUN
ejpam-4573	66	8	,	,	PUNCT
ejpam-4573	66	9	then	then	ADV
ejpam-4573	66	10	a(λ	a(λ	ADV
ejpam-4573	66	11	,	,	PUNCT
ejpam-4573	66	12	sp	sp	NOUN
ejpam-4573	66	13	)	)	PUNCT
ejpam-4573	66	14	⊆	⊆	NUM
ejpam-4573	66	15	b(λ	b(λ	NOUN
ejpam-4573	66	16	,	,	PUNCT
ejpam-4573	66	17	sp	sp	NOUN
ejpam-4573	66	18	)	)	PUNCT
ejpam-4573	66	19	.	.	PUNCT
ejpam-4573	67	1	(	(	PUNCT
ejpam-4573	67	2	3	3	X
ejpam-4573	67	3	)	)	PUNCT
ejpam-4573	67	4	a(λ	a(λ	ADV
ejpam-4573	67	5	,	,	PUNCT
ejpam-4573	67	6	sp	sp	NOUN
ejpam-4573	67	7	)	)	PUNCT
ejpam-4573	67	8	is	be	AUX
ejpam-4573	67	9	(	(	PUNCT
ejpam-4573	67	10	λ	λ	INTJ
ejpam-4573	67	11	,	,	PUNCT
ejpam-4573	67	12	sp)-open	sp)-open	NOUN
ejpam-4573	67	13	.	.	PUNCT
ejpam-4573	68	1	(	(	PUNCT
ejpam-4573	68	2	4	4	X
ejpam-4573	68	3	)	)	PUNCT
ejpam-4573	68	4	a	a	DET
ejpam-4573	68	5	is	be	AUX
ejpam-4573	68	6	(	(	PUNCT
ejpam-4573	68	7	λ	λ	NOUN
ejpam-4573	68	8	,	,	PUNCT
ejpam-4573	68	9	sp)-open	sp)-open	ADJ
ejpam-4573	68	10	if	if	SCONJ
ejpam-4573	68	11	and	and	CCONJ
ejpam-4573	68	12	only	only	ADV
ejpam-4573	68	13	if	if	SCONJ
ejpam-4573	68	14	a(λ	a(λ	ADV
ejpam-4573	68	15	,	,	PUNCT
ejpam-4573	68	16	sp	sp	NOUN
ejpam-4573	68	17	)	)	PUNCT
ejpam-4573	68	18	=	=	SYM
ejpam-4573	68	19	a.	a.	NOUN
ejpam-4573	68	20	(	(	PUNCT
ejpam-4573	68	21	5	5	NUM
ejpam-4573	68	22	)	)	PUNCT
ejpam-4573	69	1	[	[	X
ejpam-4573	69	2	x	x	X
ejpam-4573	69	3	−a](λ	−a](λ	PROPN
ejpam-4573	69	4	,	,	PUNCT
ejpam-4573	69	5	sp	sp	NOUN
ejpam-4573	69	6	)	)	PUNCT
ejpam-4573	69	7	=	=	SYM
ejpam-4573	69	8	x	x	SYM
ejpam-4573	69	9	−a(λ	−a(λ	NOUN
ejpam-4573	69	10	,	,	PUNCT
ejpam-4573	69	11	sp	sp	NOUN
ejpam-4573	69	12	)	)	PUNCT
ejpam-4573	69	13	.	.	PUNCT
ejpam-4573	70	1	(	(	PUNCT
ejpam-4573	70	2	6	6	NUM
ejpam-4573	70	3	)	)	PUNCT
ejpam-4573	71	1	[	[	X
ejpam-4573	71	2	x	x	X
ejpam-4573	71	3	−a](λ	−a](λ	PROPN
ejpam-4573	71	4	,	,	PUNCT
ejpam-4573	71	5	sp	sp	NOUN
ejpam-4573	71	6	)	)	PUNCT
ejpam-4573	71	7	=	=	SYM
ejpam-4573	71	8	x	x	SYM
ejpam-4573	71	9	−a(λ	−a(λ	NOUN
ejpam-4573	71	10	,	,	PUNCT
ejpam-4573	71	11	sp	sp	NOUN
ejpam-4573	71	12	)	)	PUNCT
ejpam-4573	71	13	.	.	PUNCT
ejpam-4573	72	1	a	a	DET
ejpam-4573	72	2	subset	subset	NOUN
ejpam-4573	72	3	a	a	PRON
ejpam-4573	72	4	of	of	ADP
ejpam-4573	72	5	a	a	DET
ejpam-4573	72	6	topological	topological	ADJ
ejpam-4573	72	7	space	space	NOUN
ejpam-4573	72	8	(	(	PUNCT
ejpam-4573	72	9	x	x	X
ejpam-4573	72	10	,	,	PUNCT
ejpam-4573	72	11	τ	τ	X
ejpam-4573	72	12	)	)	PUNCT
ejpam-4573	72	13	is	be	AUX
ejpam-4573	72	14	said	say	VERB
ejpam-4573	72	15	to	to	PART
ejpam-4573	72	16	be	be	AUX
ejpam-4573	72	17	s(λ	s(λ	NOUN
ejpam-4573	72	18	,	,	PUNCT
ejpam-4573	72	19	sp)-open	sp)-open	ADJ
ejpam-4573	72	20	(	(	PUNCT
ejpam-4573	72	21	resp	resp	NOUN
ejpam-4573	72	22	.	.	PUNCT
ejpam-4573	73	1	p(λ	p(λ	NOUN
ejpam-4573	73	2	,	,	PUNCT
ejpam-4573	73	3	sp)open	sp)open	VERB
ejpam-4573	73	4	,	,	PUNCT
ejpam-4573	73	5	β(λ	β(λ	X
ejpam-4573	73	6	,	,	PUNCT
ejpam-4573	73	7	sp)-open	sp)-open	NOUN
ejpam-4573	73	8	,	,	PUNCT
ejpam-4573	73	9	r(λ	r(λ	NOUN
ejpam-4573	73	10	,	,	PUNCT
ejpam-4573	73	11	sp)-open	sp)-open	NOUN
ejpam-4573	73	12	)	)	PUNCT
ejpam-4573	73	13	if	if	SCONJ
ejpam-4573	73	14	a	a	DET
ejpam-4573	73	15	⊆	⊆	NUM
ejpam-4573	73	16	[	[	X
ejpam-4573	73	17	a(λ	a(λ	ADV
ejpam-4573	73	18	,	,	PUNCT
ejpam-4573	73	19	sp	sp	NOUN
ejpam-4573	73	20	)	)	PUNCT
ejpam-4573	73	21	]	]	PUNCT
ejpam-4573	73	22	(	(	PUNCT
ejpam-4573	73	23	λ	λ	NOUN
ejpam-4573	73	24	,	,	PUNCT
ejpam-4573	73	25	sp	sp	NOUN
ejpam-4573	73	26	)	)	PUNCT
ejpam-4573	73	27	(	(	PUNCT
ejpam-4573	73	28	resp	resp	NOUN
ejpam-4573	73	29	.	.	PUNCT
ejpam-4573	74	1	a	a	DET
ejpam-4573	74	2	⊆	⊆	NUM
ejpam-4573	74	3	[	[	X
ejpam-4573	74	4	a(λ	a(λ	ADJ
ejpam-4573	74	5	,	,	PUNCT
ejpam-4573	74	6	sp)](λ	sp)](λ	PROPN
ejpam-4573	74	7	,	,	PUNCT
ejpam-4573	74	8	sp	sp	NOUN
ejpam-4573	74	9	)	)	PUNCT
ejpam-4573	74	10	,	,	PUNCT
ejpam-4573	74	11	a	a	PRON
ejpam-4573	74	12	⊆	⊆	NUM
ejpam-4573	75	1	[	[	X
ejpam-4573	75	2	[	[	X
ejpam-4573	75	3	a(λ	a(λ	ADJ
ejpam-4573	75	4	,	,	PUNCT
ejpam-4573	75	5	sp)](λ	sp)](λ	PROPN
ejpam-4573	75	6	,	,	PUNCT
ejpam-4573	75	7	sp	sp	NOUN
ejpam-4573	75	8	)	)	PUNCT
ejpam-4573	75	9	]	]	PUNCT
ejpam-4573	76	1	(	(	PUNCT
ejpam-4573	76	2	λ	λ	NOUN
ejpam-4573	76	3	,	,	PUNCT
ejpam-4573	76	4	sp	sp	NOUN
ejpam-4573	76	5	)	)	PUNCT
ejpam-4573	76	6	,	,	PUNCT
ejpam-4573	76	7	a	a	PRON
ejpam-4573	76	8	=	=	X
ejpam-4573	77	1	[	[	X
ejpam-4573	77	2	a(λ	a(λ	PROPN
ejpam-4573	77	3	,	,	PUNCT
ejpam-4573	77	4	sp)](λ	sp)](λ	PROPN
ejpam-4573	77	5	,	,	PUNCT
ejpam-4573	77	6	sp	sp	NOUN
ejpam-4573	77	7	)	)	PUNCT
ejpam-4573	77	8	)	)	PUNCT
ejpam-4573	78	1	[	[	X
ejpam-4573	78	2	3	3	NUM
ejpam-4573	78	3	]	]	PUNCT
ejpam-4573	78	4	.	.	PUNCT
ejpam-4573	79	1	the	the	DET
ejpam-4573	79	2	complement	complement	NOUN
ejpam-4573	79	3	of	of	ADP
ejpam-4573	79	4	a	a	DET
ejpam-4573	79	5	s(λ	s(λ	PROPN
ejpam-4573	79	6	,	,	PUNCT
ejpam-4573	79	7	sp)-open	sp)-open	ADJ
ejpam-4573	79	8	(	(	PUNCT
ejpam-4573	79	9	resp	resp	NOUN
ejpam-4573	79	10	.	.	PUNCT
ejpam-4573	80	1	p(λ	p(λ	NOUN
ejpam-4573	80	2	,	,	PUNCT
ejpam-4573	80	3	sp)-open	sp)-open	NOUN
ejpam-4573	80	4	,	,	PUNCT
ejpam-4573	80	5	β(λ	β(λ	X
ejpam-4573	80	6	,	,	PUNCT
ejpam-4573	80	7	sp)-open	sp)-open	NOUN
ejpam-4573	80	8	,	,	PUNCT
ejpam-4573	80	9	r(λ	r(λ	NOUN
ejpam-4573	80	10	,	,	PUNCT
ejpam-4573	80	11	sp)-open	sp)-open	NOUN
ejpam-4573	80	12	)	)	PUNCT
ejpam-4573	80	13	set	set	NOUN
ejpam-4573	80	14	is	be	AUX
ejpam-4573	80	15	said	say	VERB
ejpam-4573	80	16	to	to	PART
ejpam-4573	80	17	be	be	AUX
ejpam-4573	80	18	s(λ	s(λ	PROPN
ejpam-4573	80	19	,	,	PUNCT
ejpam-4573	80	20	sp)-closed	sp)-close	VERB
ejpam-4573	80	21	(	(	PUNCT
ejpam-4573	80	22	resp	resp	NOUN
ejpam-4573	80	23	.	.	PUNCT
ejpam-4573	81	1	p(λ	p(λ	NOUN
ejpam-4573	81	2	,	,	PUNCT
ejpam-4573	81	3	sp)-closed	sp)-close	VERB
ejpam-4573	81	4	,	,	PUNCT
ejpam-4573	81	5	β(λ	β(λ	X
ejpam-4573	81	6	,	,	PUNCT
ejpam-4573	81	7	sp)-closed	sp)-close	VERB
ejpam-4573	81	8	,	,	PUNCT
ejpam-4573	81	9	r(λ	r(λ	NOUN
ejpam-4573	81	10	,	,	PUNCT
ejpam-4573	81	11	sp)-closed	sp)-close	VERB
ejpam-4573	81	12	)	)	PUNCT
ejpam-4573	81	13	.	.	PUNCT
ejpam-4573	82	1	the	the	DET
ejpam-4573	82	2	family	family	NOUN
ejpam-4573	82	3	of	of	ADP
ejpam-4573	82	4	all	all	DET
ejpam-4573	82	5	s(λ	s(λ	NOUN
ejpam-4573	82	6	,	,	PUNCT
ejpam-4573	82	7	sp)-open	sp)-open	ADJ
ejpam-4573	82	8	(	(	PUNCT
ejpam-4573	82	9	resp	resp	NOUN
ejpam-4573	82	10	.	.	PUNCT
ejpam-4573	83	1	p(λ	p(λ	NOUN
ejpam-4573	83	2	,	,	PUNCT
ejpam-4573	83	3	sp)-open	sp)-open	NOUN
ejpam-4573	83	4	,	,	PUNCT
ejpam-4573	83	5	β(λ	β(λ	X
ejpam-4573	83	6	,	,	PUNCT
ejpam-4573	83	7	sp)-open	sp)-open	NOUN
ejpam-4573	83	8	,	,	PUNCT
ejpam-4573	83	9	r(λ	r(λ	NOUN
ejpam-4573	83	10	,	,	PUNCT
ejpam-4573	83	11	sp)-open	sp)-open	NOUN
ejpam-4573	83	12	)	)	PUNCT
ejpam-4573	83	13	sets	set	NOUN
ejpam-4573	83	14	in	in	ADP
ejpam-4573	83	15	a	a	DET
ejpam-4573	83	16	topological	topological	ADJ
ejpam-4573	83	17	space	space	NOUN
ejpam-4573	83	18	(	(	PUNCT
ejpam-4573	83	19	x	x	X
ejpam-4573	83	20	,	,	PUNCT
ejpam-4573	83	21	τ	τ	X
ejpam-4573	83	22	)	)	PUNCT
ejpam-4573	83	23	is	be	AUX
ejpam-4573	83	24	denoted	denote	VERB
ejpam-4573	83	25	by	by	ADP
ejpam-4573	83	26	sλspo(x	sλspo(x	PROPN
ejpam-4573	83	27	,	,	PUNCT
ejpam-4573	83	28	τ	τ	PROPN
ejpam-4573	83	29	)	)	PUNCT
ejpam-4573	83	30	(	(	PUNCT
ejpam-4573	83	31	resp	resp	NOUN
ejpam-4573	83	32	.	.	PUNCT
ejpam-4573	84	1	pλspo(x	pλspo(x	ADJ
ejpam-4573	84	2	,	,	PUNCT
ejpam-4573	84	3	τ	τ	PROPN
ejpam-4573	84	4	)	)	PUNCT
ejpam-4573	84	5	,	,	PUNCT
ejpam-4573	84	6	βλspo(x	βλspo(x	PROPN
ejpam-4573	84	7	,	,	PUNCT
ejpam-4573	84	8	τ	τ	PROPN
ejpam-4573	84	9	)	)	PUNCT
ejpam-4573	84	10	,	,	PUNCT
ejpam-4573	84	11	rλspo(x	rλspo(x	PROPN
ejpam-4573	84	12	,	,	PUNCT
ejpam-4573	84	13	τ	τ	PROPN
ejpam-4573	84	14	)	)	PUNCT
ejpam-4573	84	15	)	)	PUNCT
ejpam-4573	84	16	.	.	PUNCT
ejpam-4573	85	1	throughout	throughout	ADP
ejpam-4573	85	2	this	this	DET
ejpam-4573	85	3	paper	paper	NOUN
ejpam-4573	85	4	,	,	PUNCT
ejpam-4573	85	5	the	the	DET
ejpam-4573	85	6	spaces	space	NOUN
ejpam-4573	85	7	(	(	PUNCT
ejpam-4573	85	8	x	x	X
ejpam-4573	85	9	,	,	PUNCT
ejpam-4573	85	10	τ	τ	X
ejpam-4573	85	11	)	)	PUNCT
ejpam-4573	85	12	and	and	CCONJ
ejpam-4573	85	13	(	(	PUNCT
ejpam-4573	85	14	y	y	PROPN
ejpam-4573	85	15	,	,	PUNCT
ejpam-4573	85	16	σ	σ	PROPN
ejpam-4573	85	17	)	)	PUNCT
ejpam-4573	85	18	(	(	PUNCT
ejpam-4573	85	19	or	or	CCONJ
ejpam-4573	85	20	simply	simply	ADV
ejpam-4573	85	21	x	x	X
ejpam-4573	85	22	and	and	CCONJ
ejpam-4573	85	23	y	y	PROPN
ejpam-4573	85	24	)	)	PUNCT
ejpam-4573	85	25	always	always	ADV
ejpam-4573	85	26	mean	mean	VERB
ejpam-4573	85	27	topological	topological	ADJ
ejpam-4573	85	28	spaces	space	NOUN
ejpam-4573	85	29	and	and	CCONJ
ejpam-4573	85	30	f	f	NOUN
ejpam-4573	85	31	:	:	PUNCT
ejpam-4573	85	32	x	x	X
ejpam-4573	85	33	→	→	SYM
ejpam-4573	85	34	y	y	PROPN
ejpam-4573	85	35	(	(	PUNCT
ejpam-4573	85	36	resp	resp	PROPN
ejpam-4573	85	37	.	.	PUNCT
ejpam-4573	86	1	f	f	X
ejpam-4573	86	2	:	:	PUNCT
ejpam-4573	86	3	x	x	X
ejpam-4573	86	4	→	→	SYM
ejpam-4573	86	5	y	y	PROPN
ejpam-4573	86	6	)	)	PUNCT
ejpam-4573	86	7	presents	present	VERB
ejpam-4573	86	8	a	a	DET
ejpam-4573	86	9	multivalued	multivalue	VERB
ejpam-4573	86	10	(	(	PUNCT
ejpam-4573	86	11	resp	resp	NOUN
ejpam-4573	86	12	.	.	PUNCT
ejpam-4573	87	1	single	single	ADJ
ejpam-4573	87	2	valued	value	VERB
ejpam-4573	87	3	)	)	PUNCT
ejpam-4573	87	4	function	function	NOUN
ejpam-4573	87	5	.	.	PUNCT
ejpam-4573	88	1	for	for	ADP
ejpam-4573	88	2	a	a	DET
ejpam-4573	88	3	multifunction	multifunction	NOUN
ejpam-4573	88	4	f	f	NOUN
ejpam-4573	88	5	:	:	PUNCT
ejpam-4573	88	6	x	x	X
ejpam-4573	88	7	→	→	SYM
ejpam-4573	88	8	y	y	PROPN
ejpam-4573	88	9	,	,	PUNCT
ejpam-4573	88	10	following	follow	VERB
ejpam-4573	88	11	[	[	X
ejpam-4573	88	12	2	2	X
ejpam-4573	88	13	]	]	PUNCT
ejpam-4573	88	14	we	we	PRON
ejpam-4573	88	15	shall	shall	AUX
ejpam-4573	88	16	denote	denote	VERB
ejpam-4573	88	17	the	the	DET
ejpam-4573	88	18	upper	upper	ADJ
ejpam-4573	88	19	and	and	CCONJ
ejpam-4573	88	20	lower	low	ADJ
ejpam-4573	88	21	inverse	inverse	NOUN
ejpam-4573	88	22	of	of	ADP
ejpam-4573	88	23	a	a	DET
ejpam-4573	88	24	set	set	NOUN
ejpam-4573	88	25	b	b	PROPN
ejpam-4573	88	26	of	of	ADP
ejpam-4573	88	27	y	y	PROPN
ejpam-4573	88	28	by	by	ADP
ejpam-4573	88	29	f+(b	f+(b	NOUN
ejpam-4573	88	30	)	)	PUNCT
ejpam-4573	88	31	and	and	CCONJ
ejpam-4573	88	32	f−(b	f−(b	NOUN
ejpam-4573	88	33	)	)	PUNCT
ejpam-4573	88	34	,	,	PUNCT
ejpam-4573	88	35	respectively	respectively	ADV
ejpam-4573	88	36	,	,	PUNCT
ejpam-4573	88	37	that	that	ADV
ejpam-4573	88	38	is	is	ADV
ejpam-4573	88	39	,	,	PUNCT
ejpam-4573	88	40	f+(b	f+(b	NOUN
ejpam-4573	88	41	)	)	PUNCT
ejpam-4573	88	42	=	=	PRON
ejpam-4573	89	1	{	{	PUNCT
ejpam-4573	89	2	x	x	PUNCT
ejpam-4573	89	3	∈	∈	PROPN
ejpam-4573	89	4	x	x	INTJ
ejpam-4573	90	1	|	|	NOUN
ejpam-4573	90	2	f	f	X
ejpam-4573	90	3	(	(	PUNCT
ejpam-4573	90	4	x	x	NOUN
ejpam-4573	90	5	)	)	PUNCT
ejpam-4573	90	6	⊆	⊆	NUM
ejpam-4573	90	7	b	b	NOUN
ejpam-4573	90	8	}	}	PUNCT
ejpam-4573	90	9	and	and	CCONJ
ejpam-4573	90	10	f−(b	f−(b	PROPN
ejpam-4573	90	11	)	)	PUNCT
ejpam-4573	90	12	=	=	PRON
ejpam-4573	91	1	{	{	PUNCT
ejpam-4573	91	2	x	x	PUNCT
ejpam-4573	91	3	∈	∈	PROPN
ejpam-4573	91	4	x	x	INTJ
ejpam-4573	92	1	|	|	NOUN
ejpam-4573	92	2	f	f	X
ejpam-4573	92	3	(	(	PUNCT
ejpam-4573	92	4	x	x	NOUN
ejpam-4573	92	5	)	)	PUNCT
ejpam-4573	92	6	∩	∩	NOUN
ejpam-4573	92	7	b	b	PROPN
ejpam-4573	92	8	̸=	̸=	PROPN
ejpam-4573	92	9	∅	∅	NOUN
ejpam-4573	92	10	}	}	PUNCT
ejpam-4573	92	11	.	.	PUNCT
ejpam-4573	93	1	in	in	ADP
ejpam-4573	93	2	particular	particular	ADJ
ejpam-4573	93	3	,	,	PUNCT
ejpam-4573	93	4	f−(y	f−(y	NOUN
ejpam-4573	93	5	)	)	PUNCT
ejpam-4573	93	6	=	=	SYM
ejpam-4573	94	1	{	{	PUNCT
ejpam-4573	94	2	x	x	PUNCT
ejpam-4573	94	3	∈	∈	PROPN
ejpam-4573	94	4	x	x	INTJ
ejpam-4573	95	1	|	|	ADV
ejpam-4573	95	2	y	y	PROPN
ejpam-4573	95	3	∈	∈	PROPN
ejpam-4573	95	4	f	f	X
ejpam-4573	95	5	(	(	PUNCT
ejpam-4573	95	6	x	x	NOUN
ejpam-4573	95	7	)	)	PUNCT
ejpam-4573	95	8	}	}	PUNCT
ejpam-4573	95	9	for	for	ADP
ejpam-4573	95	10	each	each	DET
ejpam-4573	95	11	point	point	NOUN
ejpam-4573	95	12	y	y	PROPN
ejpam-4573	95	13	∈	∈	PROPN
ejpam-4573	95	14	y	y	PROPN
ejpam-4573	95	15	.	.	PUNCT
ejpam-4573	96	1	for	for	ADP
ejpam-4573	96	2	each	each	DET
ejpam-4573	96	3	a	a	DET
ejpam-4573	96	4	⊆	⊆	NUM
ejpam-4573	96	5	x	x	SYM
ejpam-4573	96	6	,	,	PUNCT
ejpam-4573	96	7	f	f	PROPN
ejpam-4573	96	8	(	(	PUNCT
ejpam-4573	96	9	a	a	NOUN
ejpam-4573	96	10	)	)	PUNCT
ejpam-4573	96	11	=	=	SYM
ejpam-4573	96	12	∪x∈af	∪x∈af	NOUN
ejpam-4573	96	13	(	(	PUNCT
ejpam-4573	96	14	x	x	NOUN
ejpam-4573	96	15	)	)	PUNCT
ejpam-4573	96	16	.	.	PUNCT
ejpam-4573	97	1	a	a	DET
ejpam-4573	97	2	multifunction	multifunction	NOUN
ejpam-4573	97	3	f	f	NOUN
ejpam-4573	97	4	:	:	PUNCT
ejpam-4573	97	5	x	x	X
ejpam-4573	97	6	→	→	SYM
ejpam-4573	97	7	y	y	PROPN
ejpam-4573	97	8	is	be	AUX
ejpam-4573	97	9	said	say	VERB
ejpam-4573	97	10	to	to	PART
ejpam-4573	97	11	be	be	AUX
ejpam-4573	97	12	injective	injective	ADJ
ejpam-4573	97	13	if	if	SCONJ
ejpam-4573	97	14	x	x	PROPN
ejpam-4573	97	15	̸=	̸=	PROPN
ejpam-4573	97	16	y	y	PROPN
ejpam-4573	97	17	implies	imply	VERB
ejpam-4573	97	18	that	that	SCONJ
ejpam-4573	97	19	f	f	PROPN
ejpam-4573	97	20	(	(	PUNCT
ejpam-4573	97	21	x	x	NOUN
ejpam-4573	97	22	)	)	PUNCT
ejpam-4573	97	23	∩	∩	ADJ
ejpam-4573	97	24	f	f	PROPN
ejpam-4573	97	25	(	(	PUNCT
ejpam-4573	97	26	y	y	NOUN
ejpam-4573	97	27	)	)	PUNCT
ejpam-4573	97	28	=	=	NOUN
ejpam-4573	97	29	∅.	∅.	VERB
ejpam-4573	97	30	moreover	moreover	ADV
ejpam-4573	97	31	,	,	PUNCT
ejpam-4573	97	32	f	f	X
ejpam-4573	97	33	:	:	PUNCT
ejpam-4573	97	34	x	x	X
ejpam-4573	97	35	→	→	SYM
ejpam-4573	97	36	y	y	PROPN
ejpam-4573	97	37	is	be	AUX
ejpam-4573	97	38	called	call	VERB
ejpam-4573	97	39	upper	upper	ADJ
ejpam-4573	97	40	semi	semi	ADJ
ejpam-4573	97	41	-	-	ADJ
ejpam-4573	97	42	continuous	continuous	ADJ
ejpam-4573	97	43	(	(	PUNCT
ejpam-4573	97	44	resp	resp	NOUN
ejpam-4573	97	45	.	.	PUNCT
ejpam-4573	98	1	lower	low	ADJ
ejpam-4573	98	2	semi	semi	ADJ
ejpam-4573	98	3	-	-	ADJ
ejpam-4573	98	4	continuous	continuous	ADJ
ejpam-4573	98	5	)	)	PUNCT
ejpam-4573	98	6	if	if	SCONJ
ejpam-4573	98	7	f+(v	f+(v	PROPN
ejpam-4573	98	8	)	)	PUNCT
ejpam-4573	98	9	(	(	PUNCT
ejpam-4573	98	10	resp	resp	NOUN
ejpam-4573	98	11	.	.	PUNCT
ejpam-4573	99	1	f−(v	f−(v	NOUN
ejpam-4573	99	2	)	)	PUNCT
ejpam-4573	99	3	)	)	PUNCT
ejpam-4573	100	1	is	be	AUX
ejpam-4573	100	2	open	open	ADJ
ejpam-4573	100	3	in	in	ADP
ejpam-4573	100	4	x	x	PUNCT
ejpam-4573	100	5	for	for	ADP
ejpam-4573	100	6	every	every	DET
ejpam-4573	100	7	open	open	ADJ
ejpam-4573	100	8	set	set	VERB
ejpam-4573	100	9	v	v	NOUN
ejpam-4573	100	10	of	of	ADP
ejpam-4573	100	11	y	y	PROPN
ejpam-4573	101	1	[	[	X
ejpam-4573	101	2	18	18	NUM
ejpam-4573	101	3	]	]	PUNCT
ejpam-4573	101	4	.	.	PUNCT
ejpam-4573	102	1	3	3	X
ejpam-4573	102	2	.	.	X
ejpam-4573	102	3	characterizations	characterization	NOUN
ejpam-4573	102	4	of	of	ADP
ejpam-4573	102	5	upper	upper	ADJ
ejpam-4573	102	6	and	and	CCONJ
ejpam-4573	102	7	lower	low	ADJ
ejpam-4573	102	8	weakly	weakly	ADJ
ejpam-4573	102	9	(	(	PUNCT
ejpam-4573	102	10	λ	λ	NOUN
ejpam-4573	102	11	,	,	PUNCT
ejpam-4573	102	12	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	102	13	multifunctions	multifunction	NOUN
ejpam-4573	102	14	in	in	ADP
ejpam-4573	102	15	this	this	DET
ejpam-4573	102	16	section	section	NOUN
ejpam-4573	102	17	,	,	PUNCT
ejpam-4573	102	18	we	we	PRON
ejpam-4573	102	19	introduce	introduce	VERB
ejpam-4573	102	20	the	the	DET
ejpam-4573	102	21	notions	notion	NOUN
ejpam-4573	102	22	of	of	ADP
ejpam-4573	102	23	upper	upper	ADJ
ejpam-4573	102	24	and	and	CCONJ
ejpam-4573	102	25	lower	low	ADJ
ejpam-4573	102	26	weakly	weakly	ADJ
ejpam-4573	102	27	(	(	PUNCT
ejpam-4573	102	28	λ	λ	NOUN
ejpam-4573	102	29	,	,	PUNCT
ejpam-4573	102	30	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	102	31	multifunctions	multifunction	NOUN
ejpam-4573	102	32	.	.	PUNCT
ejpam-4573	103	1	moreover	moreover	ADV
ejpam-4573	103	2	,	,	PUNCT
ejpam-4573	103	3	several	several	ADJ
ejpam-4573	103	4	characterizations	characterization	NOUN
ejpam-4573	103	5	of	of	ADP
ejpam-4573	103	6	upper	upper	ADJ
ejpam-4573	103	7	and	and	CCONJ
ejpam-4573	103	8	lower	low	ADJ
ejpam-4573	103	9	weakly	weakly	ADJ
ejpam-4573	103	10	(	(	PUNCT
ejpam-4573	103	11	λ	λ	NOUN
ejpam-4573	103	12	,	,	PUNCT
ejpam-4573	103	13	sp)continuous	sp)continuous	ADJ
ejpam-4573	103	14	multifunctions	multifunction	NOUN
ejpam-4573	103	15	are	be	AUX
ejpam-4573	103	16	discussed	discuss	VERB
ejpam-4573	103	17	.	.	PUNCT
ejpam-4573	104	1	definition	definition	NOUN
ejpam-4573	104	2	1	1	NUM
ejpam-4573	104	3	.	.	PUNCT
ejpam-4573	105	1	a	a	DET
ejpam-4573	105	2	multifunction	multifunction	NOUN
ejpam-4573	105	3	f	f	NOUN
ejpam-4573	105	4	:	:	PUNCT
ejpam-4573	105	5	(	(	PUNCT
ejpam-4573	105	6	x	x	X
ejpam-4573	105	7	,	,	PUNCT
ejpam-4573	105	8	τ	τ	X
ejpam-4573	105	9	)	)	PUNCT
ejpam-4573	105	10	→	→	SYM
ejpam-4573	105	11	(	(	PUNCT
ejpam-4573	105	12	y	y	PROPN
ejpam-4573	105	13	,	,	PUNCT
ejpam-4573	105	14	σ	σ	PROPN
ejpam-4573	105	15	)	)	PUNCT
ejpam-4573	105	16	is	be	AUX
ejpam-4573	105	17	said	say	VERB
ejpam-4573	105	18	to	to	PART
ejpam-4573	105	19	be	be	AUX
ejpam-4573	105	20	:	:	PUNCT
ejpam-4573	105	21	(	(	PUNCT
ejpam-4573	105	22	i	i	NOUN
ejpam-4573	105	23	)	)	PUNCT
ejpam-4573	105	24	upper	upper	ADJ
ejpam-4573	105	25	weakly	weakly	ADJ
ejpam-4573	105	26	(	(	PUNCT
ejpam-4573	105	27	λ	λ	NOUN
ejpam-4573	105	28	,	,	PUNCT
ejpam-4573	105	29	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	105	30	if	if	SCONJ
ejpam-4573	105	31	,	,	PUNCT
ejpam-4573	105	32	for	for	SCONJ
ejpam-4573	105	33	each	each	DET
ejpam-4573	105	34	x	x	SYM
ejpam-4573	105	35	∈	∈	PROPN
ejpam-4573	105	36	x	x	X
ejpam-4573	105	37	and	and	CCONJ
ejpam-4573	105	38	each	each	DET
ejpam-4573	105	39	(	(	PUNCT
ejpam-4573	105	40	λ	λ	PROPN
ejpam-4573	105	41	,	,	PUNCT
ejpam-4573	105	42	sp)-open	sp)-open	NOUN
ejpam-4573	105	43	set	set	VERB
ejpam-4573	105	44	v	v	NUM
ejpam-4573	105	45	of	of	ADP
ejpam-4573	105	46	y	y	PROPN
ejpam-4573	105	47	containing	contain	VERB
ejpam-4573	105	48	f	f	PROPN
ejpam-4573	105	49	(	(	PUNCT
ejpam-4573	105	50	x	x	NOUN
ejpam-4573	105	51	)	)	PUNCT
ejpam-4573	105	52	,	,	PUNCT
ejpam-4573	105	53	there	there	PRON
ejpam-4573	105	54	exists	exist	VERB
ejpam-4573	105	55	a	a	DET
ejpam-4573	105	56	(	(	PUNCT
ejpam-4573	105	57	λ	λ	NOUN
ejpam-4573	105	58	,	,	PUNCT
ejpam-4573	105	59	sp)-open	sp)-open	NOUN
ejpam-4573	105	60	set	set	VERB
ejpam-4573	105	61	u	u	NOUN
ejpam-4573	105	62	of	of	ADP
ejpam-4573	105	63	x	x	PUNCT
ejpam-4573	105	64	containing	contain	VERB
ejpam-4573	105	65	x	x	PUNCT
ejpam-4573	105	66	such	such	ADJ
ejpam-4573	105	67	that	that	SCONJ
ejpam-4573	105	68	f	f	PROPN
ejpam-4573	105	69	(	(	PUNCT
ejpam-4573	105	70	u	u	NOUN
ejpam-4573	105	71	)	)	PUNCT
ejpam-4573	105	72	⊆	⊆	NUM
ejpam-4573	105	73	v	v	NOUN
ejpam-4573	105	74	(	(	PUNCT
ejpam-4573	105	75	λ	λ	NOUN
ejpam-4573	105	76	,	,	PUNCT
ejpam-4573	105	77	sp	sp	NOUN
ejpam-4573	105	78	)	)	PUNCT
ejpam-4573	105	79	;	;	PUNCT
ejpam-4573	105	80	(	(	PUNCT
ejpam-4573	105	81	ii	ii	NOUN
ejpam-4573	105	82	)	)	PUNCT
ejpam-4573	105	83	lower	low	ADJ
ejpam-4573	105	84	weakly	weakly	ADJ
ejpam-4573	105	85	(	(	PUNCT
ejpam-4573	105	86	λ	λ	NOUN
ejpam-4573	105	87	,	,	PUNCT
ejpam-4573	105	88	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	105	89	if	if	SCONJ
ejpam-4573	105	90	,	,	PUNCT
ejpam-4573	105	91	for	for	SCONJ
ejpam-4573	105	92	each	each	DET
ejpam-4573	105	93	x	x	SYM
ejpam-4573	105	94	∈	∈	PROPN
ejpam-4573	105	95	x	x	X
ejpam-4573	105	96	and	and	CCONJ
ejpam-4573	105	97	each	each	DET
ejpam-4573	105	98	(	(	PUNCT
ejpam-4573	105	99	λ	λ	PROPN
ejpam-4573	105	100	,	,	PUNCT
ejpam-4573	105	101	sp)-open	sp)-open	NOUN
ejpam-4573	105	102	set	set	VERB
ejpam-4573	105	103	v	v	NUM
ejpam-4573	105	104	of	of	ADP
ejpam-4573	105	105	y	y	PRON
ejpam-4573	105	106	such	such	ADJ
ejpam-4573	105	107	that	that	SCONJ
ejpam-4573	105	108	f	f	PROPN
ejpam-4573	105	109	(	(	PUNCT
ejpam-4573	105	110	x	x	NOUN
ejpam-4573	105	111	)	)	PUNCT
ejpam-4573	105	112	∩	∩	NOUN
ejpam-4573	105	113	v	v	ADP
ejpam-4573	105	114	̸=	̸=	PROPN
ejpam-4573	105	115	∅	∅	NOUN
ejpam-4573	105	116	,	,	PUNCT
ejpam-4573	105	117	there	there	PRON
ejpam-4573	105	118	exists	exist	VERB
ejpam-4573	105	119	a	a	DET
ejpam-4573	105	120	(	(	PUNCT
ejpam-4573	105	121	λ	λ	NOUN
ejpam-4573	105	122	,	,	PUNCT
ejpam-4573	105	123	sp)-open	sp)-open	NOUN
ejpam-4573	105	124	set	set	VERB
ejpam-4573	105	125	u	u	NOUN
ejpam-4573	105	126	of	of	ADP
ejpam-4573	105	127	x	x	PUNCT
ejpam-4573	105	128	containing	contain	VERB
ejpam-4573	105	129	x	x	PUNCT
ejpam-4573	105	130	such	such	ADJ
ejpam-4573	105	131	that	that	SCONJ
ejpam-4573	105	132	f	f	PROPN
ejpam-4573	105	133	(	(	PUNCT
ejpam-4573	105	134	z	z	NOUN
ejpam-4573	105	135	)	)	PUNCT
ejpam-4573	105	136	∩	∩	ADJ
ejpam-4573	105	137	v	v	X
ejpam-4573	105	138	(	(	PUNCT
ejpam-4573	105	139	λ	λ	PROPN
ejpam-4573	105	140	,	,	PUNCT
ejpam-4573	105	141	sp	sp	NOUN
ejpam-4573	105	142	)	)	PUNCT
ejpam-4573	105	143	̸=	̸=	NOUN
ejpam-4573	105	144	∅	∅	NOUN
ejpam-4573	105	145	for	for	ADP
ejpam-4573	105	146	each	each	DET
ejpam-4573	105	147	z	z	NOUN
ejpam-4573	105	148	∈	∈	PROPN
ejpam-4573	105	149	u	u	PROPN
ejpam-4573	105	150	.	.	PUNCT
ejpam-4573	106	1	c.	c.	PROPN
ejpam-4573	106	2	boonpok	boonpok	PROPN
ejpam-4573	106	3	,	,	PUNCT
ejpam-4573	106	4	p.	p.	NOUN
ejpam-4573	106	5	pue	pue	NOUN
ejpam-4573	106	6	-	-	PUNCT
ejpam-4573	106	7	on	on	ADP
ejpam-4573	106	8	/	/	SYM
ejpam-4573	106	9	eur	eur	NOUN
ejpam-4573	106	10	.	.	PUNCT
ejpam-4573	107	1	j.	j.	PROPN
ejpam-4573	107	2	pure	pure	PROPN
ejpam-4573	107	3	appl	appl	PROPN
ejpam-4573	107	4	.	.	PROPN
ejpam-4573	107	5	math	math	PROPN
ejpam-4573	107	6	,	,	PUNCT
ejpam-4573	107	7	16	16	NUM
ejpam-4573	107	8	(	(	PUNCT
ejpam-4573	107	9	2	2	NUM
ejpam-4573	107	10	)	)	PUNCT
ejpam-4573	107	11	(	(	PUNCT
ejpam-4573	107	12	2023	2023	NUM
ejpam-4573	107	13	)	)	PUNCT
ejpam-4573	107	14	,	,	PUNCT
ejpam-4573	107	15	1047	1047	NUM
ejpam-4573	107	16	-	-	SYM
ejpam-4573	107	17	1058	1058	NUM
ejpam-4573	107	18	1050	1050	NUM
ejpam-4573	107	19	theorem	theorem	NOUN
ejpam-4573	107	20	1	1	NUM
ejpam-4573	107	21	.	.	X
ejpam-4573	107	22	for	for	ADP
ejpam-4573	107	23	a	a	DET
ejpam-4573	107	24	multifunction	multifunction	NOUN
ejpam-4573	107	25	f	f	NOUN
ejpam-4573	107	26	:	:	PUNCT
ejpam-4573	107	27	(	(	PUNCT
ejpam-4573	107	28	x	x	X
ejpam-4573	107	29	,	,	PUNCT
ejpam-4573	107	30	τ	τ	X
ejpam-4573	107	31	)	)	PUNCT
ejpam-4573	107	32	→	→	SYM
ejpam-4573	107	33	(	(	PUNCT
ejpam-4573	107	34	y	y	PROPN
ejpam-4573	107	35	,	,	PUNCT
ejpam-4573	107	36	σ	σ	PROPN
ejpam-4573	107	37	)	)	PUNCT
ejpam-4573	107	38	,	,	PUNCT
ejpam-4573	107	39	the	the	DET
ejpam-4573	107	40	following	follow	VERB
ejpam-4573	107	41	properties	property	NOUN
ejpam-4573	107	42	are	be	AUX
ejpam-4573	107	43	equivalent	equivalent	ADJ
ejpam-4573	107	44	:	:	PUNCT
ejpam-4573	107	45	(	(	PUNCT
ejpam-4573	107	46	1	1	X
ejpam-4573	107	47	)	)	PUNCT
ejpam-4573	107	48	f	f	PROPN
ejpam-4573	107	49	is	be	AUX
ejpam-4573	107	50	upper	upper	ADJ
ejpam-4573	107	51	weakly	weakly	ADJ
ejpam-4573	107	52	(	(	PUNCT
ejpam-4573	107	53	λ	λ	NOUN
ejpam-4573	107	54	,	,	PUNCT
ejpam-4573	107	55	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	107	56	;	;	PUNCT
ejpam-4573	107	57	(	(	PUNCT
ejpam-4573	107	58	2	2	NUM
ejpam-4573	107	59	)	)	PUNCT
ejpam-4573	107	60	f+(v	f+(v	NOUN
ejpam-4573	107	61	)	)	PUNCT
ejpam-4573	108	1	⊆	⊆	NUM
ejpam-4573	108	2	[	[	X
ejpam-4573	108	3	f+(v	f+(v	NOUN
ejpam-4573	108	4	(	(	PUNCT
ejpam-4573	108	5	λ	λ	PROPN
ejpam-4573	108	6	,	,	PUNCT
ejpam-4573	108	7	sp))](λ	sp))](λ	PROPN
ejpam-4573	108	8	,	,	PUNCT
ejpam-4573	108	9	sp	sp	NOUN
ejpam-4573	108	10	)	)	PUNCT
ejpam-4573	108	11	for	for	ADP
ejpam-4573	108	12	every	every	DET
ejpam-4573	108	13	(	(	PUNCT
ejpam-4573	108	14	λ	λ	NOUN
ejpam-4573	108	15	,	,	PUNCT
ejpam-4573	108	16	sp)-open	sp)-open	NOUN
ejpam-4573	108	17	set	set	VERB
ejpam-4573	108	18	v	v	NOUN
ejpam-4573	108	19	of	of	ADP
ejpam-4573	108	20	y	y	PROPN
ejpam-4573	108	21	;	;	PUNCT
ejpam-4573	108	22	(	(	PUNCT
ejpam-4573	108	23	3	3	X
ejpam-4573	108	24	)	)	PUNCT
ejpam-4573	109	1	[	[	X
ejpam-4573	109	2	f−(k(λ	f−(k(λ	NOUN
ejpam-4573	109	3	,	,	PUNCT
ejpam-4573	109	4	sp	sp	NOUN
ejpam-4573	109	5	)	)	PUNCT
ejpam-4573	109	6	)	)	PUNCT
ejpam-4573	109	7	]	]	PUNCT
ejpam-4573	110	1	(	(	PUNCT
ejpam-4573	110	2	λ	λ	NOUN
ejpam-4573	110	3	,	,	PUNCT
ejpam-4573	110	4	sp	sp	NOUN
ejpam-4573	110	5	)	)	PUNCT
ejpam-4573	110	6	⊆	⊆	NUM
ejpam-4573	110	7	f−(k	f−(k	PROPN
ejpam-4573	110	8	)	)	PUNCT
ejpam-4573	110	9	for	for	SCONJ
ejpam-4573	110	10	every	every	DET
ejpam-4573	110	11	(	(	PUNCT
ejpam-4573	110	12	λ	λ	PROPN
ejpam-4573	110	13	,	,	PUNCT
ejpam-4573	110	14	sp)-closed	sp)-close	VERB
ejpam-4573	110	15	set	set	VERB
ejpam-4573	110	16	k	k	PROPN
ejpam-4573	110	17	of	of	ADP
ejpam-4573	110	18	y	y	PROPN
ejpam-4573	110	19	;	;	PUNCT
ejpam-4573	110	20	(	(	PUNCT
ejpam-4573	110	21	4	4	X
ejpam-4573	110	22	)	)	PUNCT
ejpam-4573	111	1	[	[	X
ejpam-4573	111	2	f−([b(λ	f−([b(λ	PROPN
ejpam-4573	111	3	,	,	PUNCT
ejpam-4573	111	4	sp)](λ	sp)](λ	PROPN
ejpam-4573	111	5	,	,	PUNCT
ejpam-4573	111	6	sp	sp	NOUN
ejpam-4573	111	7	)	)	PUNCT
ejpam-4573	111	8	)	)	PUNCT
ejpam-4573	111	9	]	]	PUNCT
ejpam-4573	112	1	(	(	PUNCT
ejpam-4573	112	2	λ	λ	NOUN
ejpam-4573	112	3	,	,	PUNCT
ejpam-4573	112	4	sp	sp	NOUN
ejpam-4573	112	5	)	)	PUNCT
ejpam-4573	112	6	⊆	⊆	NUM
ejpam-4573	112	7	f−(b(λ	f−(b(λ	NOUN
ejpam-4573	112	8	,	,	PUNCT
ejpam-4573	112	9	sp	sp	NOUN
ejpam-4573	112	10	)	)	PUNCT
ejpam-4573	112	11	)	)	PUNCT
ejpam-4573	112	12	for	for	ADP
ejpam-4573	112	13	every	every	DET
ejpam-4573	112	14	subset	subset	NOUN
ejpam-4573	112	15	b	b	PROPN
ejpam-4573	112	16	of	of	ADP
ejpam-4573	112	17	y	y	PROPN
ejpam-4573	112	18	;	;	PUNCT
ejpam-4573	112	19	(	(	PUNCT
ejpam-4573	112	20	5	5	X
ejpam-4573	112	21	)	)	PUNCT
ejpam-4573	112	22	f+(b(λ	f+(b(λ	PROPN
ejpam-4573	112	23	,	,	PUNCT
ejpam-4573	112	24	sp	sp	NOUN
ejpam-4573	112	25	)	)	PUNCT
ejpam-4573	112	26	)	)	PUNCT
ejpam-4573	113	1	⊆	⊆	NUM
ejpam-4573	113	2	[	[	X
ejpam-4573	113	3	f+([b(λ	f+([b(λ	PROPN
ejpam-4573	113	4	,	,	PUNCT
ejpam-4573	113	5	sp	sp	NOUN
ejpam-4573	113	6	)	)	PUNCT
ejpam-4573	113	7	]	]	PUNCT
ejpam-4573	113	8	(	(	PUNCT
ejpam-4573	113	9	λ	λ	INTJ
ejpam-4573	113	10	,	,	PUNCT
ejpam-4573	113	11	sp))](λ	sp))](λ	PROPN
ejpam-4573	113	12	,	,	PUNCT
ejpam-4573	113	13	sp	sp	NOUN
ejpam-4573	113	14	)	)	PUNCT
ejpam-4573	113	15	for	for	ADP
ejpam-4573	113	16	every	every	DET
ejpam-4573	113	17	subset	subset	NOUN
ejpam-4573	113	18	b	b	PROPN
ejpam-4573	113	19	of	of	ADP
ejpam-4573	113	20	y	y	PROPN
ejpam-4573	113	21	;	;	PUNCT
ejpam-4573	113	22	(	(	PUNCT
ejpam-4573	113	23	6	6	X
ejpam-4573	113	24	)	)	PUNCT
ejpam-4573	114	1	[	[	X
ejpam-4573	114	2	f−([v	f−([v	ADJ
ejpam-4573	114	3	(	(	PUNCT
ejpam-4573	114	4	λ	λ	PROPN
ejpam-4573	114	5	,	,	PUNCT
ejpam-4573	114	6	sp)](λ	sp)](λ	PROPN
ejpam-4573	114	7	,	,	PUNCT
ejpam-4573	114	8	sp	sp	NOUN
ejpam-4573	114	9	)	)	PUNCT
ejpam-4573	114	10	)	)	PUNCT
ejpam-4573	114	11	]	]	PUNCT
ejpam-4573	114	12	(	(	PUNCT
ejpam-4573	114	13	λ	λ	NOUN
ejpam-4573	114	14	,	,	PUNCT
ejpam-4573	114	15	sp	sp	NOUN
ejpam-4573	114	16	)	)	PUNCT
ejpam-4573	114	17	⊆	⊆	NUM
ejpam-4573	114	18	f−(v	f−(v	NOUN
ejpam-4573	114	19	(	(	PUNCT
ejpam-4573	114	20	λ	λ	NOUN
ejpam-4573	114	21	,	,	PUNCT
ejpam-4573	114	22	sp	sp	NOUN
ejpam-4573	114	23	)	)	PUNCT
ejpam-4573	114	24	)	)	PUNCT
ejpam-4573	114	25	for	for	ADP
ejpam-4573	114	26	every	every	DET
ejpam-4573	114	27	(	(	PUNCT
ejpam-4573	114	28	λ	λ	NOUN
ejpam-4573	114	29	,	,	PUNCT
ejpam-4573	114	30	sp)-open	sp)-open	NOUN
ejpam-4573	114	31	set	set	VERB
ejpam-4573	114	32	v	v	NOUN
ejpam-4573	114	33	of	of	ADP
ejpam-4573	114	34	y	y	PROPN
ejpam-4573	114	35	;	;	PUNCT
ejpam-4573	114	36	(	(	PUNCT
ejpam-4573	114	37	7	7	X
ejpam-4573	114	38	)	)	PUNCT
ejpam-4573	115	1	[	[	X
ejpam-4573	115	2	f−(v	f−(v	NOUN
ejpam-4573	115	3	)	)	PUNCT
ejpam-4573	115	4	]	]	PUNCT
ejpam-4573	115	5	(	(	PUNCT
ejpam-4573	115	6	λ	λ	NOUN
ejpam-4573	115	7	,	,	PUNCT
ejpam-4573	115	8	sp	sp	NOUN
ejpam-4573	115	9	)	)	PUNCT
ejpam-4573	115	10	⊆	⊆	NUM
ejpam-4573	115	11	f−(v	f−(v	NOUN
ejpam-4573	115	12	(	(	PUNCT
ejpam-4573	115	13	λ	λ	NOUN
ejpam-4573	115	14	,	,	PUNCT
ejpam-4573	115	15	sp	sp	NOUN
ejpam-4573	115	16	)	)	PUNCT
ejpam-4573	115	17	)	)	PUNCT
ejpam-4573	115	18	for	for	ADP
ejpam-4573	115	19	every	every	DET
ejpam-4573	115	20	(	(	PUNCT
ejpam-4573	115	21	λ	λ	NOUN
ejpam-4573	115	22	,	,	PUNCT
ejpam-4573	115	23	sp)-open	sp)-open	NOUN
ejpam-4573	115	24	set	set	VERB
ejpam-4573	115	25	v	v	NOUN
ejpam-4573	115	26	of	of	ADP
ejpam-4573	115	27	y	y	PROPN
ejpam-4573	115	28	;	;	PUNCT
ejpam-4573	115	29	(	(	PUNCT
ejpam-4573	115	30	8)	8)	NUM
ejpam-4573	115	31	[	[	X
ejpam-4573	115	32	f−(k(λ	f−(k(λ	NOUN
ejpam-4573	115	33	,	,	PUNCT
ejpam-4573	115	34	sp	sp	NOUN
ejpam-4573	115	35	)	)	PUNCT
ejpam-4573	115	36	)	)	PUNCT
ejpam-4573	115	37	]	]	PUNCT
ejpam-4573	116	1	(	(	PUNCT
ejpam-4573	116	2	λ	λ	NOUN
ejpam-4573	116	3	,	,	PUNCT
ejpam-4573	116	4	sp	sp	NOUN
ejpam-4573	116	5	)	)	PUNCT
ejpam-4573	116	6	⊆	⊆	NUM
ejpam-4573	116	7	f−(k	f−(k	PROPN
ejpam-4573	116	8	)	)	PUNCT
ejpam-4573	116	9	for	for	ADP
ejpam-4573	116	10	every	every	DET
ejpam-4573	116	11	r(λ	r(λ	NOUN
ejpam-4573	116	12	,	,	PUNCT
ejpam-4573	116	13	sp)-closed	sp)-close	VERB
ejpam-4573	116	14	set	set	VERB
ejpam-4573	116	15	k	k	PROPN
ejpam-4573	116	16	of	of	ADP
ejpam-4573	116	17	y	y	PROPN
ejpam-4573	116	18	.	.	PUNCT
ejpam-4573	117	1	proof	proof	NOUN
ejpam-4573	117	2	.	.	PUNCT
ejpam-4573	118	1	(	(	PUNCT
ejpam-4573	118	2	1	1	X
ejpam-4573	118	3	)	)	PUNCT
ejpam-4573	118	4	⇒	⇒	NOUN
ejpam-4573	118	5	(	(	PUNCT
ejpam-4573	118	6	2	2	NUM
ejpam-4573	118	7	):	):	PUNCT
ejpam-4573	118	8	let	let	VERB
ejpam-4573	118	9	v	v	PART
ejpam-4573	118	10	be	be	AUX
ejpam-4573	118	11	any	any	DET
ejpam-4573	118	12	(	(	PUNCT
ejpam-4573	118	13	λ	λ	NOUN
ejpam-4573	118	14	,	,	PUNCT
ejpam-4573	118	15	sp)-open	sp)-open	ADJ
ejpam-4573	118	16	set	set	NOUN
ejpam-4573	118	17	of	of	ADP
ejpam-4573	118	18	y	y	PRON
ejpam-4573	118	19	such	such	ADJ
ejpam-4573	118	20	that	that	SCONJ
ejpam-4573	118	21	x	x	SYM
ejpam-4573	118	22	∈	∈	PROPN
ejpam-4573	118	23	f+(v	f+(v	NOUN
ejpam-4573	118	24	)	)	PUNCT
ejpam-4573	118	25	.	.	PUNCT
ejpam-4573	119	1	then	then	ADV
ejpam-4573	119	2	,	,	PUNCT
ejpam-4573	119	3	f	f	PROPN
ejpam-4573	119	4	(	(	PUNCT
ejpam-4573	119	5	x	x	X
ejpam-4573	119	6	)	)	PUNCT
ejpam-4573	119	7	⊆	⊆	NUM
ejpam-4573	119	8	v	v	NOUN
ejpam-4573	119	9	.	.	PUNCT
ejpam-4573	120	1	there	there	PRON
ejpam-4573	120	2	exists	exist	VERB
ejpam-4573	120	3	a	a	DET
ejpam-4573	120	4	(	(	PUNCT
ejpam-4573	120	5	λ	λ	NOUN
ejpam-4573	120	6	,	,	PUNCT
ejpam-4573	120	7	sp)-open	sp)-open	NOUN
ejpam-4573	120	8	set	set	VERB
ejpam-4573	120	9	u	u	NOUN
ejpam-4573	120	10	of	of	ADP
ejpam-4573	120	11	x	x	PUNCT
ejpam-4573	120	12	containing	contain	VERB
ejpam-4573	120	13	x	x	PUNCT
ejpam-4573	120	14	such	such	ADJ
ejpam-4573	120	15	that	that	SCONJ
ejpam-4573	120	16	f	f	PROPN
ejpam-4573	120	17	(	(	PUNCT
ejpam-4573	120	18	u	u	NOUN
ejpam-4573	120	19	)	)	PUNCT
ejpam-4573	120	20	⊆	⊆	NUM
ejpam-4573	120	21	v	v	NOUN
ejpam-4573	120	22	(	(	PUNCT
ejpam-4573	120	23	λ	λ	NOUN
ejpam-4573	120	24	,	,	PUNCT
ejpam-4573	120	25	sp	sp	NOUN
ejpam-4573	120	26	)	)	PUNCT
ejpam-4573	120	27	.	.	PUNCT
ejpam-4573	121	1	thus	thus	ADV
ejpam-4573	121	2	,	,	PUNCT
ejpam-4573	121	3	u	u	NOUN
ejpam-4573	121	4	⊆	⊆	NUM
ejpam-4573	121	5	f+(v	f+(v	NUM
ejpam-4573	121	6	(	(	PUNCT
ejpam-4573	121	7	λ	λ	NOUN
ejpam-4573	121	8	,	,	PUNCT
ejpam-4573	121	9	sp	sp	NOUN
ejpam-4573	121	10	)	)	PUNCT
ejpam-4573	121	11	)	)	PUNCT
ejpam-4573	121	12	.	.	PUNCT
ejpam-4573	122	1	since	since	SCONJ
ejpam-4573	122	2	u	u	NOUN
ejpam-4573	122	3	is	be	AUX
ejpam-4573	122	4	(	(	PUNCT
ejpam-4573	122	5	λ	λ	NOUN
ejpam-4573	122	6	,	,	PUNCT
ejpam-4573	122	7	sp)-open	sp)-open	ADJ
ejpam-4573	122	8	,	,	PUNCT
ejpam-4573	122	9	we	we	PRON
ejpam-4573	122	10	have	have	VERB
ejpam-4573	122	11	x	x	X
ejpam-4573	122	12	∈	∈	PROPN
ejpam-4573	122	13	[	[	X
ejpam-4573	122	14	f+(v	f+(v	NOUN
ejpam-4573	122	15	(	(	PUNCT
ejpam-4573	122	16	λ	λ	PROPN
ejpam-4573	122	17	,	,	PUNCT
ejpam-4573	122	18	sp))](λ	sp))](λ	PROPN
ejpam-4573	122	19	,	,	PUNCT
ejpam-4573	122	20	sp	sp	NOUN
ejpam-4573	122	21	)	)	PUNCT
ejpam-4573	122	22	and	and	CCONJ
ejpam-4573	122	23	hence	hence	ADV
ejpam-4573	122	24	f+(v	f+(v	NOUN
ejpam-4573	122	25	)	)	PUNCT
ejpam-4573	123	1	⊆	⊆	NUM
ejpam-4573	123	2	[	[	X
ejpam-4573	123	3	f+(v	f+(v	NOUN
ejpam-4573	123	4	(	(	PUNCT
ejpam-4573	123	5	λ	λ	PROPN
ejpam-4573	123	6	,	,	PUNCT
ejpam-4573	123	7	sp))](λ	sp))](λ	PROPN
ejpam-4573	123	8	,	,	PUNCT
ejpam-4573	123	9	sp	sp	NOUN
ejpam-4573	123	10	)	)	PUNCT
ejpam-4573	123	11	.	.	PUNCT
ejpam-4573	124	1	(	(	PUNCT
ejpam-4573	124	2	2	2	X
ejpam-4573	124	3	)	)	PUNCT
ejpam-4573	124	4	⇒	⇒	NOUN
ejpam-4573	124	5	(	(	PUNCT
ejpam-4573	124	6	3	3	NUM
ejpam-4573	124	7	):	):	PUNCT
ejpam-4573	124	8	let	let	VERB
ejpam-4573	124	9	k	k	PRON
ejpam-4573	124	10	be	be	AUX
ejpam-4573	124	11	any	any	DET
ejpam-4573	124	12	(	(	PUNCT
ejpam-4573	124	13	λ	λ	PROPN
ejpam-4573	124	14	,	,	PUNCT
ejpam-4573	124	15	sp)-closed	sp)-close	VERB
ejpam-4573	124	16	set	set	NOUN
ejpam-4573	124	17	of	of	ADP
ejpam-4573	124	18	y	y	PROPN
ejpam-4573	124	19	.	.	PUNCT
ejpam-4573	125	1	then	then	ADV
ejpam-4573	125	2	,	,	PUNCT
ejpam-4573	125	3	y	y	PROPN
ejpam-4573	125	4	−	−	PROPN
ejpam-4573	125	5	k	k	PROPN
ejpam-4573	125	6	is	be	AUX
ejpam-4573	125	7	(	(	PUNCT
ejpam-4573	125	8	λ	λ	INTJ
ejpam-4573	125	9	,	,	PUNCT
ejpam-4573	125	10	sp)-open	sp)-open	ADJ
ejpam-4573	125	11	in	in	ADP
ejpam-4573	125	12	y	y	PROPN
ejpam-4573	125	13	and	and	CCONJ
ejpam-4573	125	14	by	by	ADP
ejpam-4573	125	15	(	(	PUNCT
ejpam-4573	125	16	2	2	NUM
ejpam-4573	125	17	)	)	PUNCT
ejpam-4573	125	18	,	,	PUNCT
ejpam-4573	125	19	x	x	PUNCT
ejpam-4573	125	20	−	−	PRON
ejpam-4573	125	21	f−(k	f−(k	PROPN
ejpam-4573	125	22	)	)	PUNCT
ejpam-4573	125	23	=	=	PUNCT
ejpam-4573	126	1	f+(y	f+(y	PROPN
ejpam-4573	126	2	−k	−k	PROPN
ejpam-4573	126	3	)	)	PUNCT
ejpam-4573	126	4	⊆	⊆	NUM
ejpam-4573	126	5	[	[	X
ejpam-4573	126	6	f+([y	f+([y	NOUN
ejpam-4573	126	7	−k](λ	−k](λ	NUM
ejpam-4573	126	8	,	,	PUNCT
ejpam-4573	126	9	sp))](λ	sp))](λ	PROPN
ejpam-4573	126	10	,	,	PUNCT
ejpam-4573	126	11	sp	sp	NOUN
ejpam-4573	126	12	)	)	PUNCT
ejpam-4573	126	13	=	=	PUNCT
ejpam-4573	127	1	x	x	X
ejpam-4573	127	2	−	−	PROPN
ejpam-4573	128	1	[	[	X
ejpam-4573	128	2	f−(k(λ	f−(k(λ	NOUN
ejpam-4573	128	3	,	,	PUNCT
ejpam-4573	128	4	sp	sp	NOUN
ejpam-4573	128	5	)	)	PUNCT
ejpam-4573	128	6	)	)	PUNCT
ejpam-4573	128	7	]	]	PUNCT
ejpam-4573	129	1	(	(	PUNCT
ejpam-4573	129	2	λ	λ	NOUN
ejpam-4573	129	3	,	,	PUNCT
ejpam-4573	129	4	sp	sp	NOUN
ejpam-4573	129	5	)	)	PUNCT
ejpam-4573	129	6	.	.	PUNCT
ejpam-4573	130	1	thus	thus	ADV
ejpam-4573	130	2	,	,	PUNCT
ejpam-4573	130	3	[	[	X
ejpam-4573	130	4	f−(k(λ	f−(k(λ	NOUN
ejpam-4573	130	5	,	,	PUNCT
ejpam-4573	130	6	sp	sp	NOUN
ejpam-4573	130	7	)	)	PUNCT
ejpam-4573	130	8	)	)	PUNCT
ejpam-4573	130	9	]	]	PUNCT
ejpam-4573	130	10	(	(	PUNCT
ejpam-4573	130	11	λ	λ	NOUN
ejpam-4573	130	12	,	,	PUNCT
ejpam-4573	130	13	sp	sp	NOUN
ejpam-4573	130	14	)	)	PUNCT
ejpam-4573	130	15	⊆	⊆	NUM
ejpam-4573	130	16	f−(k	f−(k	PROPN
ejpam-4573	130	17	)	)	PUNCT
ejpam-4573	130	18	.	.	PUNCT
ejpam-4573	131	1	(	(	PUNCT
ejpam-4573	131	2	3	3	X
ejpam-4573	131	3	)	)	PUNCT
ejpam-4573	131	4	⇒	⇒	NOUN
ejpam-4573	131	5	(	(	PUNCT
ejpam-4573	131	6	4	4	NUM
ejpam-4573	131	7	):	):	PUNCT
ejpam-4573	131	8	let	let	VERB
ejpam-4573	131	9	b	b	X
ejpam-4573	131	10	be	be	AUX
ejpam-4573	131	11	any	any	DET
ejpam-4573	131	12	subset	subset	NOUN
ejpam-4573	131	13	of	of	ADP
ejpam-4573	131	14	y	y	PROPN
ejpam-4573	131	15	.	.	PUNCT
ejpam-4573	132	1	then	then	ADV
ejpam-4573	132	2	,	,	PUNCT
ejpam-4573	132	3	b(λ	b(λ	PROPN
ejpam-4573	132	4	,	,	PUNCT
ejpam-4573	132	5	sp	sp	NOUN
ejpam-4573	132	6	)	)	PUNCT
ejpam-4573	132	7	is	be	AUX
ejpam-4573	132	8	a	a	DET
ejpam-4573	132	9	(	(	PUNCT
ejpam-4573	132	10	λ	λ	PROPN
ejpam-4573	132	11	,	,	PUNCT
ejpam-4573	132	12	sp)-closed	sp)-close	VERB
ejpam-4573	132	13	set	set	NOUN
ejpam-4573	132	14	of	of	ADP
ejpam-4573	132	15	y	y	PROPN
ejpam-4573	132	16	and	and	CCONJ
ejpam-4573	132	17	by	by	ADP
ejpam-4573	132	18	(	(	PUNCT
ejpam-4573	132	19	3	3	NUM
ejpam-4573	132	20	)	)	PUNCT
ejpam-4573	132	21	,	,	PUNCT
ejpam-4573	132	22	[	[	X
ejpam-4573	132	23	f−([b(λ	f−([b(λ	PROPN
ejpam-4573	132	24	,	,	PUNCT
ejpam-4573	132	25	sp)](λ	sp)](λ	PROPN
ejpam-4573	132	26	,	,	PUNCT
ejpam-4573	132	27	sp	sp	NOUN
ejpam-4573	132	28	)	)	PUNCT
ejpam-4573	132	29	)	)	PUNCT
ejpam-4573	132	30	]	]	PUNCT
ejpam-4573	133	1	(	(	PUNCT
ejpam-4573	133	2	λ	λ	NOUN
ejpam-4573	133	3	,	,	PUNCT
ejpam-4573	133	4	sp	sp	NOUN
ejpam-4573	133	5	)	)	PUNCT
ejpam-4573	133	6	⊆	⊆	NUM
ejpam-4573	133	7	f−(b(λ	f−(b(λ	NOUN
ejpam-4573	133	8	,	,	PUNCT
ejpam-4573	133	9	sp	sp	NOUN
ejpam-4573	133	10	)	)	PUNCT
ejpam-4573	133	11	)	)	PUNCT
ejpam-4573	133	12	.	.	PUNCT
ejpam-4573	134	1	(	(	PUNCT
ejpam-4573	134	2	4	4	X
ejpam-4573	134	3	)	)	PUNCT
ejpam-4573	134	4	⇒	⇒	NOUN
ejpam-4573	134	5	(	(	PUNCT
ejpam-4573	134	6	5	5	NUM
ejpam-4573	134	7	):	):	PUNCT
ejpam-4573	134	8	let	let	VERB
ejpam-4573	134	9	b	b	X
ejpam-4573	134	10	be	be	AUX
ejpam-4573	134	11	any	any	DET
ejpam-4573	134	12	subset	subset	NOUN
ejpam-4573	134	13	of	of	ADP
ejpam-4573	134	14	y	y	PROPN
ejpam-4573	134	15	.	.	PUNCT
ejpam-4573	135	1	by	by	ADP
ejpam-4573	135	2	(	(	PUNCT
ejpam-4573	135	3	4	4	NUM
ejpam-4573	135	4	)	)	PUNCT
ejpam-4573	135	5	,	,	PUNCT
ejpam-4573	135	6	we	we	PRON
ejpam-4573	135	7	have	have	VERB
ejpam-4573	135	8	x	x	X
ejpam-4573	135	9	−	−	PROPN
ejpam-4573	136	1	[	[	X
ejpam-4573	136	2	f+([b(λ	f+([b(λ	PROPN
ejpam-4573	136	3	,	,	PUNCT
ejpam-4573	136	4	sp	sp	NOUN
ejpam-4573	136	5	)	)	PUNCT
ejpam-4573	136	6	]	]	PUNCT
ejpam-4573	136	7	(	(	PUNCT
ejpam-4573	136	8	λ	λ	INTJ
ejpam-4573	136	9	,	,	PUNCT
ejpam-4573	136	10	sp))](λ	sp))](λ	PROPN
ejpam-4573	136	11	,	,	PUNCT
ejpam-4573	136	12	sp	sp	NOUN
ejpam-4573	136	13	)	)	PUNCT
ejpam-4573	136	14	=	=	PUNCT
ejpam-4573	137	1	[	[	X
ejpam-4573	137	2	x	x	X
ejpam-4573	137	3	−	−	PROPN
ejpam-4573	137	4	f+([b(λ	f+([b(λ	PROPN
ejpam-4573	137	5	,	,	PUNCT
ejpam-4573	137	6	sp	sp	NOUN
ejpam-4573	137	7	)	)	PUNCT
ejpam-4573	137	8	]	]	PUNCT
ejpam-4573	137	9	(	(	PUNCT
ejpam-4573	137	10	λ	λ	INTJ
ejpam-4573	137	11	,	,	PUNCT
ejpam-4573	137	12	sp))](λ	sp))](λ	PROPN
ejpam-4573	137	13	,	,	PUNCT
ejpam-4573	137	14	sp	sp	NOUN
ejpam-4573	137	15	)	)	PUNCT
ejpam-4573	137	16	=	=	PUNCT
ejpam-4573	138	1	[	[	X
ejpam-4573	138	2	f−([[y	f−([[y	NUM
ejpam-4573	138	3	−b](λ	−b](λ	PROPN
ejpam-4573	138	4	,	,	PUNCT
ejpam-4573	138	5	sp)](λ	sp)](λ	PROPN
ejpam-4573	138	6	,	,	PUNCT
ejpam-4573	138	7	sp	sp	NOUN
ejpam-4573	138	8	)	)	PUNCT
ejpam-4573	138	9	)	)	PUNCT
ejpam-4573	138	10	]	]	PUNCT
ejpam-4573	138	11	(	(	PUNCT
ejpam-4573	138	12	λ	λ	NOUN
ejpam-4573	138	13	,	,	PUNCT
ejpam-4573	138	14	sp	sp	NOUN
ejpam-4573	138	15	)	)	PUNCT
ejpam-4573	138	16	⊆	⊆	NUM
ejpam-4573	138	17	f−([y	f−([y	NOUN
ejpam-4573	138	18	−b](λ	−b](λ	PROPN
ejpam-4573	138	19	,	,	PUNCT
ejpam-4573	138	20	sp	sp	NOUN
ejpam-4573	138	21	)	)	PUNCT
ejpam-4573	138	22	)	)	PUNCT
ejpam-4573	139	1	=	=	PUNCT
ejpam-4573	140	1	x	x	X
ejpam-4573	140	2	−	−	PROPN
ejpam-4573	140	3	f+(b(λ	f+(b(λ	PROPN
ejpam-4573	140	4	,	,	PUNCT
ejpam-4573	140	5	sp	sp	NOUN
ejpam-4573	140	6	)	)	PUNCT
ejpam-4573	140	7	)	)	PUNCT
ejpam-4573	140	8	and	and	CCONJ
ejpam-4573	140	9	hence	hence	ADV
ejpam-4573	140	10	f+(b(λ	f+(b(λ	PROPN
ejpam-4573	140	11	,	,	PUNCT
ejpam-4573	140	12	sp	sp	NOUN
ejpam-4573	140	13	)	)	PUNCT
ejpam-4573	140	14	)	)	PUNCT
ejpam-4573	141	1	⊆	⊆	NUM
ejpam-4573	142	1	[	[	X
ejpam-4573	142	2	f+([b(λ	f+([b(λ	PROPN
ejpam-4573	142	3	,	,	PUNCT
ejpam-4573	142	4	sp	sp	NOUN
ejpam-4573	142	5	)	)	PUNCT
ejpam-4573	142	6	]	]	PUNCT
ejpam-4573	142	7	(	(	PUNCT
ejpam-4573	142	8	λ	λ	INTJ
ejpam-4573	142	9	,	,	PUNCT
ejpam-4573	142	10	sp))](λ	sp))](λ	PROPN
ejpam-4573	142	11	,	,	PUNCT
ejpam-4573	142	12	sp	sp	NOUN
ejpam-4573	142	13	)	)	PUNCT
ejpam-4573	142	14	.	.	PUNCT
ejpam-4573	143	1	(	(	PUNCT
ejpam-4573	143	2	5	5	X
ejpam-4573	143	3	)	)	PUNCT
ejpam-4573	143	4	⇒	⇒	NOUN
ejpam-4573	143	5	(	(	PUNCT
ejpam-4573	143	6	1	1	NUM
ejpam-4573	143	7	):	):	PUNCT
ejpam-4573	143	8	let	let	VERB
ejpam-4573	143	9	x	x	PUNCT
ejpam-4573	143	10	∈	∈	PROPN
ejpam-4573	143	11	x	x	X
ejpam-4573	143	12	and	and	CCONJ
ejpam-4573	143	13	v	v	AUX
ejpam-4573	143	14	be	be	AUX
ejpam-4573	143	15	any	any	DET
ejpam-4573	143	16	(	(	PUNCT
ejpam-4573	143	17	λ	λ	NOUN
ejpam-4573	143	18	,	,	PUNCT
ejpam-4573	143	19	sp)-open	sp)-open	ADJ
ejpam-4573	143	20	set	set	NOUN
ejpam-4573	143	21	of	of	ADP
ejpam-4573	143	22	y	y	PRON
ejpam-4573	143	23	such	such	ADJ
ejpam-4573	143	24	that	that	SCONJ
ejpam-4573	143	25	f	f	PROPN
ejpam-4573	143	26	(	(	PUNCT
ejpam-4573	143	27	x	x	X
ejpam-4573	143	28	)	)	PUNCT
ejpam-4573	143	29	⊆	⊆	NUM
ejpam-4573	143	30	v	v	NOUN
ejpam-4573	143	31	.	.	PUNCT
ejpam-4573	144	1	then	then	ADV
ejpam-4573	144	2	,	,	PUNCT
ejpam-4573	144	3	x	x	X
ejpam-4573	144	4	∈	∈	PROPN
ejpam-4573	144	5	f+(v	f+(v	NOUN
ejpam-4573	144	6	)	)	PUNCT
ejpam-4573	145	1	⊆	⊆	NUM
ejpam-4573	145	2	[	[	X
ejpam-4573	145	3	f+(v	f+(v	NOUN
ejpam-4573	145	4	(	(	PUNCT
ejpam-4573	145	5	λ	λ	PROPN
ejpam-4573	145	6	,	,	PUNCT
ejpam-4573	145	7	sp))](λ	sp))](λ	PROPN
ejpam-4573	145	8	,	,	PUNCT
ejpam-4573	145	9	sp	sp	NOUN
ejpam-4573	145	10	)	)	PUNCT
ejpam-4573	145	11	and	and	CCONJ
ejpam-4573	145	12	there	there	PRON
ejpam-4573	145	13	exists	exist	VERB
ejpam-4573	145	14	a	a	DET
ejpam-4573	145	15	(	(	PUNCT
ejpam-4573	145	16	λ	λ	NOUN
ejpam-4573	145	17	,	,	PUNCT
ejpam-4573	145	18	sp)-open	sp)-open	NOUN
ejpam-4573	145	19	set	set	VERB
ejpam-4573	145	20	u	u	NOUN
ejpam-4573	145	21	of	of	ADP
ejpam-4573	145	22	x	x	PUNCT
ejpam-4573	145	23	containing	contain	VERB
ejpam-4573	145	24	x	x	PUNCT
ejpam-4573	145	25	such	such	ADJ
ejpam-4573	145	26	that	that	SCONJ
ejpam-4573	145	27	u	u	NOUN
ejpam-4573	145	28	⊆	⊆	NUM
ejpam-4573	145	29	f+(v	f+(v	NOUN
ejpam-4573	145	30	(	(	PUNCT
ejpam-4573	145	31	λ	λ	NOUN
ejpam-4573	145	32	,	,	PUNCT
ejpam-4573	145	33	sp	sp	NOUN
ejpam-4573	145	34	)	)	PUNCT
ejpam-4573	145	35	)	)	PUNCT
ejpam-4573	145	36	.	.	PUNCT
ejpam-4573	146	1	thus	thus	ADV
ejpam-4573	146	2	,	,	PUNCT
ejpam-4573	146	3	f	f	PROPN
ejpam-4573	146	4	(	(	PUNCT
ejpam-4573	146	5	u	u	NOUN
ejpam-4573	146	6	)	)	PUNCT
ejpam-4573	146	7	⊆	⊆	NUM
ejpam-4573	146	8	v	v	NOUN
ejpam-4573	146	9	(	(	PUNCT
ejpam-4573	146	10	λ	λ	NOUN
ejpam-4573	146	11	,	,	PUNCT
ejpam-4573	146	12	sp	sp	NOUN
ejpam-4573	146	13	)	)	PUNCT
ejpam-4573	146	14	and	and	CCONJ
ejpam-4573	146	15	hence	hence	ADV
ejpam-4573	146	16	f	f	PROPN
ejpam-4573	146	17	is	be	AUX
ejpam-4573	146	18	upper	upper	ADJ
ejpam-4573	146	19	weakly	weakly	ADJ
ejpam-4573	146	20	(	(	PUNCT
ejpam-4573	146	21	λ	λ	NOUN
ejpam-4573	146	22	,	,	PUNCT
ejpam-4573	146	23	sp)continuous	sp)continuous	ADJ
ejpam-4573	146	24	.	.	PUNCT
ejpam-4573	147	1	c.	c.	PROPN
ejpam-4573	147	2	boonpok	boonpok	PROPN
ejpam-4573	147	3	,	,	PUNCT
ejpam-4573	147	4	p.	p.	NOUN
ejpam-4573	147	5	pue	pue	NOUN
ejpam-4573	147	6	-	-	PUNCT
ejpam-4573	147	7	on	on	ADP
ejpam-4573	147	8	/	/	SYM
ejpam-4573	147	9	eur	eur	NOUN
ejpam-4573	147	10	.	.	PUNCT
ejpam-4573	148	1	j.	j.	PROPN
ejpam-4573	148	2	pure	pure	PROPN
ejpam-4573	148	3	appl	appl	PROPN
ejpam-4573	148	4	.	.	PROPN
ejpam-4573	148	5	math	math	PROPN
ejpam-4573	148	6	,	,	PUNCT
ejpam-4573	148	7	16	16	NUM
ejpam-4573	148	8	(	(	PUNCT
ejpam-4573	148	9	2	2	NUM
ejpam-4573	148	10	)	)	PUNCT
ejpam-4573	148	11	(	(	PUNCT
ejpam-4573	148	12	2023	2023	NUM
ejpam-4573	148	13	)	)	PUNCT
ejpam-4573	148	14	,	,	PUNCT
ejpam-4573	148	15	1047	1047	NUM
ejpam-4573	148	16	-	-	SYM
ejpam-4573	148	17	1058	1058	NUM
ejpam-4573	148	18	1051	1051	NUM
ejpam-4573	148	19	(	(	PUNCT
ejpam-4573	148	20	4	4	NUM
ejpam-4573	148	21	)	)	PUNCT
ejpam-4573	148	22	⇒	⇒	NOUN
ejpam-4573	148	23	(	(	PUNCT
ejpam-4573	148	24	6	6	NUM
ejpam-4573	148	25	)	)	PUNCT
ejpam-4573	148	26	and	and	CCONJ
ejpam-4573	148	27	(	(	PUNCT
ejpam-4573	148	28	6	6	NUM
ejpam-4573	148	29	)	)	PUNCT
ejpam-4573	148	30	⇒	⇒	NOUN
ejpam-4573	148	31	(	(	PUNCT
ejpam-4573	148	32	7	7	NUM
ejpam-4573	148	33	):	):	PUNCT
ejpam-4573	148	34	the	the	DET
ejpam-4573	148	35	proofs	proof	NOUN
ejpam-4573	148	36	are	be	AUX
ejpam-4573	148	37	obvious	obvious	ADJ
ejpam-4573	148	38	.	.	PUNCT
ejpam-4573	149	1	(	(	PUNCT
ejpam-4573	149	2	7	7	X
ejpam-4573	149	3	)	)	PUNCT
ejpam-4573	149	4	⇒	⇒	NOUN
ejpam-4573	149	5	(	(	PUNCT
ejpam-4573	149	6	8)	8)	NUM
ejpam-4573	149	7	:	:	PUNCT
ejpam-4573	149	8	let	let	VERB
ejpam-4573	149	9	k	k	X
ejpam-4573	149	10	be	be	AUX
ejpam-4573	149	11	any	any	DET
ejpam-4573	149	12	r(λ	r(λ	NOUN
ejpam-4573	149	13	,	,	PUNCT
ejpam-4573	149	14	sp)-closed	sp)-close	VERB
ejpam-4573	149	15	set	set	NOUN
ejpam-4573	149	16	of	of	ADP
ejpam-4573	149	17	y	y	PROPN
ejpam-4573	149	18	.	.	PUNCT
ejpam-4573	150	1	thus	thus	ADV
ejpam-4573	150	2	,	,	PUNCT
ejpam-4573	150	3	by	by	ADP
ejpam-4573	150	4	(	(	PUNCT
ejpam-4573	150	5	7	7	NUM
ejpam-4573	150	6	)	)	PUNCT
ejpam-4573	150	7	,	,	PUNCT
ejpam-4573	150	8	[	[	X
ejpam-4573	150	9	f−(k(λ	f−(k(λ	NOUN
ejpam-4573	150	10	,	,	PUNCT
ejpam-4573	150	11	sp	sp	NOUN
ejpam-4573	150	12	)	)	PUNCT
ejpam-4573	150	13	)	)	PUNCT
ejpam-4573	150	14	]	]	PUNCT
ejpam-4573	151	1	(	(	PUNCT
ejpam-4573	151	2	λ	λ	NOUN
ejpam-4573	151	3	,	,	PUNCT
ejpam-4573	151	4	sp	sp	NOUN
ejpam-4573	151	5	)	)	PUNCT
ejpam-4573	151	6	⊆	⊆	NUM
ejpam-4573	151	7	f−([k(λ	f−([k(λ	NOUN
ejpam-4573	151	8	,	,	PUNCT
ejpam-4573	151	9	sp	sp	NOUN
ejpam-4573	151	10	)	)	PUNCT
ejpam-4573	151	11	]	]	PUNCT
ejpam-4573	151	12	(	(	PUNCT
ejpam-4573	151	13	λ	λ	NOUN
ejpam-4573	151	14	,	,	PUNCT
ejpam-4573	151	15	sp	sp	NOUN
ejpam-4573	151	16	)	)	PUNCT
ejpam-4573	151	17	)	)	PUNCT
ejpam-4573	152	1	=	=	SYM
ejpam-4573	152	2	f−(k	f−(k	PROPN
ejpam-4573	152	3	)	)	PUNCT
ejpam-4573	152	4	.	.	PUNCT
ejpam-4573	153	1	(	(	PUNCT
ejpam-4573	153	2	8)	8)	NUM
ejpam-4573	153	3	⇒	⇒	NOUN
ejpam-4573	153	4	(	(	PUNCT
ejpam-4573	153	5	3	3	NUM
ejpam-4573	153	6	):	):	PUNCT
ejpam-4573	153	7	let	let	VERB
ejpam-4573	153	8	k	k	PRON
ejpam-4573	153	9	be	be	AUX
ejpam-4573	153	10	any	any	DET
ejpam-4573	153	11	(	(	PUNCT
ejpam-4573	153	12	λ	λ	PROPN
ejpam-4573	153	13	,	,	PUNCT
ejpam-4573	153	14	sp)-closed	sp)-close	VERB
ejpam-4573	153	15	set	set	NOUN
ejpam-4573	153	16	of	of	ADP
ejpam-4573	153	17	y	y	PROPN
ejpam-4573	153	18	.	.	PUNCT
ejpam-4573	154	1	then	then	ADV
ejpam-4573	154	2	,	,	PUNCT
ejpam-4573	154	3	[	[	X
ejpam-4573	154	4	k(λ	k(λ	X
ejpam-4573	154	5	,	,	PUNCT
ejpam-4573	154	6	sp	sp	NOUN
ejpam-4573	154	7	)	)	PUNCT
ejpam-4573	154	8	]	]	PUNCT
ejpam-4573	154	9	(	(	PUNCT
ejpam-4573	154	10	λ	λ	NOUN
ejpam-4573	154	11	,	,	PUNCT
ejpam-4573	154	12	sp	sp	NOUN
ejpam-4573	154	13	)	)	PUNCT
ejpam-4573	154	14	is	be	AUX
ejpam-4573	154	15	r(λ	r(λ	NOUN
ejpam-4573	154	16	,	,	PUNCT
ejpam-4573	154	17	sp)-closed	sp)-close	VERB
ejpam-4573	154	18	in	in	ADP
ejpam-4573	154	19	y	y	PROPN
ejpam-4573	154	20	and	and	CCONJ
ejpam-4573	154	21	[	[	X
ejpam-4573	154	22	[	[	X
ejpam-4573	154	23	k(λ	k(λ	NOUN
ejpam-4573	154	24	,	,	PUNCT
ejpam-4573	154	25	sp	sp	NOUN
ejpam-4573	154	26	)	)	PUNCT
ejpam-4573	154	27	]	]	PUNCT
ejpam-4573	155	1	(	(	PUNCT
ejpam-4573	155	2	λ	λ	X
ejpam-4573	155	3	,	,	PUNCT
ejpam-4573	155	4	sp)](λ	sp)](λ	PROPN
ejpam-4573	155	5	,	,	PUNCT
ejpam-4573	155	6	sp	sp	NOUN
ejpam-4573	155	7	)	)	PUNCT
ejpam-4573	155	8	=	=	PUNCT
ejpam-4573	156	1	[	[	X
ejpam-4573	156	2	k(λ	k(λ	X
ejpam-4573	156	3	,	,	PUNCT
ejpam-4573	156	4	sp)](λ	sp)](λ	PROPN
ejpam-4573	156	5	,	,	PUNCT
ejpam-4573	156	6	sp	sp	NOUN
ejpam-4573	156	7	)	)	PUNCT
ejpam-4573	156	8	=	=	PUNCT
ejpam-4573	156	9	k(λ	k(λ	NOUN
ejpam-4573	156	10	,	,	PUNCT
ejpam-4573	156	11	sp	sp	NOUN
ejpam-4573	156	12	)	)	PUNCT
ejpam-4573	156	13	,	,	PUNCT
ejpam-4573	156	14	by	by	ADP
ejpam-4573	156	15	(	(	PUNCT
ejpam-4573	156	16	8)	8)	NUM
ejpam-4573	156	17	,	,	PUNCT
ejpam-4573	156	18	[	[	X
ejpam-4573	156	19	f−(k(λ	f−(k(λ	NOUN
ejpam-4573	156	20	,	,	PUNCT
ejpam-4573	156	21	sp	sp	NOUN
ejpam-4573	156	22	)	)	PUNCT
ejpam-4573	156	23	)	)	PUNCT
ejpam-4573	156	24	]	]	PUNCT
ejpam-4573	156	25	(	(	PUNCT
ejpam-4573	156	26	λ	λ	NOUN
ejpam-4573	156	27	,	,	PUNCT
ejpam-4573	156	28	sp	sp	NOUN
ejpam-4573	156	29	)	)	PUNCT
ejpam-4573	156	30	=	=	PUNCT
ejpam-4573	157	1	[	[	X
ejpam-4573	157	2	f−([[k(λ	f−([[k(λ	X
ejpam-4573	157	3	,	,	PUNCT
ejpam-4573	157	4	sp	sp	NOUN
ejpam-4573	157	5	)	)	PUNCT
ejpam-4573	157	6	]	]	PUNCT
ejpam-4573	157	7	(	(	PUNCT
ejpam-4573	157	8	λ	λ	X
ejpam-4573	157	9	,	,	PUNCT
ejpam-4573	157	10	sp)](λ	sp)](λ	PROPN
ejpam-4573	157	11	,	,	PUNCT
ejpam-4573	157	12	sp	sp	NOUN
ejpam-4573	157	13	)	)	PUNCT
ejpam-4573	157	14	)	)	PUNCT
ejpam-4573	157	15	]	]	PUNCT
ejpam-4573	158	1	(	(	PUNCT
ejpam-4573	158	2	λ	λ	NOUN
ejpam-4573	158	3	,	,	PUNCT
ejpam-4573	158	4	sp	sp	NOUN
ejpam-4573	158	5	)	)	PUNCT
ejpam-4573	158	6	⊆	⊆	NUM
ejpam-4573	158	7	f−([k(λ	f−([k(λ	NOUN
ejpam-4573	158	8	,	,	PUNCT
ejpam-4573	158	9	sp	sp	NOUN
ejpam-4573	158	10	)	)	PUNCT
ejpam-4573	158	11	]	]	PUNCT
ejpam-4573	158	12	(	(	PUNCT
ejpam-4573	158	13	λ	λ	NOUN
ejpam-4573	158	14	,	,	PUNCT
ejpam-4573	158	15	sp	sp	NOUN
ejpam-4573	158	16	)	)	PUNCT
ejpam-4573	158	17	)	)	PUNCT
ejpam-4573	159	1	⊆	⊆	NUM
ejpam-4573	159	2	f−(k	f−(k	PROPN
ejpam-4573	159	3	)	)	PUNCT
ejpam-4573	159	4	.	.	PUNCT
ejpam-4573	160	1	theorem	theorem	NOUN
ejpam-4573	160	2	2	2	NUM
ejpam-4573	160	3	.	.	X
ejpam-4573	160	4	for	for	ADP
ejpam-4573	160	5	a	a	DET
ejpam-4573	160	6	multifunction	multifunction	NOUN
ejpam-4573	161	1	f	f	NOUN
ejpam-4573	161	2	:	:	PUNCT
ejpam-4573	161	3	(	(	PUNCT
ejpam-4573	161	4	x	x	X
ejpam-4573	161	5	,	,	PUNCT
ejpam-4573	161	6	τ	τ	X
ejpam-4573	161	7	)	)	PUNCT
ejpam-4573	161	8	→	→	SYM
ejpam-4573	161	9	(	(	PUNCT
ejpam-4573	161	10	y	y	PROPN
ejpam-4573	161	11	,	,	PUNCT
ejpam-4573	161	12	σ	σ	PROPN
ejpam-4573	161	13	)	)	PUNCT
ejpam-4573	161	14	,	,	PUNCT
ejpam-4573	161	15	the	the	DET
ejpam-4573	161	16	following	follow	VERB
ejpam-4573	161	17	properties	property	NOUN
ejpam-4573	161	18	are	be	AUX
ejpam-4573	161	19	equivalent	equivalent	ADJ
ejpam-4573	161	20	:	:	PUNCT
ejpam-4573	161	21	(	(	PUNCT
ejpam-4573	161	22	1	1	X
ejpam-4573	161	23	)	)	PUNCT
ejpam-4573	161	24	f	f	PROPN
ejpam-4573	161	25	is	be	AUX
ejpam-4573	161	26	lower	low	ADJ
ejpam-4573	161	27	weakly	weakly	ADJ
ejpam-4573	161	28	(	(	PUNCT
ejpam-4573	161	29	λ	λ	NOUN
ejpam-4573	161	30	,	,	PUNCT
ejpam-4573	161	31	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	161	32	;	;	PUNCT
ejpam-4573	161	33	(	(	PUNCT
ejpam-4573	161	34	2	2	X
ejpam-4573	161	35	)	)	PUNCT
ejpam-4573	161	36	f−(v	f−(v	NOUN
ejpam-4573	161	37	)	)	PUNCT
ejpam-4573	161	38	⊆	⊆	NUM
ejpam-4573	162	1	[	[	X
ejpam-4573	162	2	f−(v	f−(v	ADJ
ejpam-4573	162	3	(	(	PUNCT
ejpam-4573	162	4	λ	λ	PROPN
ejpam-4573	162	5	,	,	PUNCT
ejpam-4573	162	6	sp))](λ	sp))](λ	PROPN
ejpam-4573	162	7	,	,	PUNCT
ejpam-4573	162	8	sp	sp	NOUN
ejpam-4573	162	9	)	)	PUNCT
ejpam-4573	162	10	for	for	ADP
ejpam-4573	162	11	every	every	DET
ejpam-4573	162	12	(	(	PUNCT
ejpam-4573	162	13	λ	λ	NOUN
ejpam-4573	162	14	,	,	PUNCT
ejpam-4573	162	15	sp)-open	sp)-open	NOUN
ejpam-4573	162	16	set	set	VERB
ejpam-4573	162	17	v	v	NOUN
ejpam-4573	162	18	of	of	ADP
ejpam-4573	162	19	y	y	PROPN
ejpam-4573	162	20	;	;	PUNCT
ejpam-4573	162	21	(	(	PUNCT
ejpam-4573	162	22	3	3	X
ejpam-4573	162	23	)	)	PUNCT
ejpam-4573	163	1	[	[	X
ejpam-4573	163	2	f+(k(λ	f+(k(λ	NOUN
ejpam-4573	163	3	,	,	PUNCT
ejpam-4573	163	4	sp	sp	NOUN
ejpam-4573	163	5	)	)	PUNCT
ejpam-4573	163	6	)	)	PUNCT
ejpam-4573	163	7	]	]	PUNCT
ejpam-4573	164	1	(	(	PUNCT
ejpam-4573	164	2	λ	λ	NOUN
ejpam-4573	164	3	,	,	PUNCT
ejpam-4573	164	4	sp	sp	NOUN
ejpam-4573	164	5	)	)	PUNCT
ejpam-4573	164	6	⊆	⊆	NUM
ejpam-4573	164	7	f+(k	f+(k	NOUN
ejpam-4573	164	8	)	)	PUNCT
ejpam-4573	164	9	for	for	SCONJ
ejpam-4573	164	10	every	every	DET
ejpam-4573	164	11	(	(	PUNCT
ejpam-4573	164	12	λ	λ	PROPN
ejpam-4573	164	13	,	,	PUNCT
ejpam-4573	164	14	sp)-closed	sp)-close	VERB
ejpam-4573	164	15	set	set	VERB
ejpam-4573	164	16	k	k	PROPN
ejpam-4573	164	17	of	of	ADP
ejpam-4573	164	18	y	y	PROPN
ejpam-4573	164	19	;	;	PUNCT
ejpam-4573	164	20	(	(	PUNCT
ejpam-4573	164	21	4	4	X
ejpam-4573	164	22	)	)	PUNCT
ejpam-4573	165	1	[	[	X
ejpam-4573	165	2	f+([b(λ	f+([b(λ	PROPN
ejpam-4573	165	3	,	,	PUNCT
ejpam-4573	165	4	sp)](λ	sp)](λ	PROPN
ejpam-4573	165	5	,	,	PUNCT
ejpam-4573	165	6	sp	sp	NOUN
ejpam-4573	165	7	)	)	PUNCT
ejpam-4573	165	8	)	)	PUNCT
ejpam-4573	165	9	]	]	PUNCT
ejpam-4573	166	1	(	(	PUNCT
ejpam-4573	166	2	λ	λ	NOUN
ejpam-4573	166	3	,	,	PUNCT
ejpam-4573	166	4	sp	sp	NOUN
ejpam-4573	166	5	)	)	PUNCT
ejpam-4573	166	6	⊆	⊆	NUM
ejpam-4573	166	7	f+(b(λ	f+(b(λ	PROPN
ejpam-4573	166	8	,	,	PUNCT
ejpam-4573	166	9	sp	sp	NOUN
ejpam-4573	166	10	)	)	PUNCT
ejpam-4573	166	11	)	)	PUNCT
ejpam-4573	166	12	for	for	ADP
ejpam-4573	166	13	every	every	DET
ejpam-4573	166	14	subset	subset	NOUN
ejpam-4573	166	15	b	b	PROPN
ejpam-4573	166	16	of	of	ADP
ejpam-4573	166	17	y	y	PROPN
ejpam-4573	166	18	;	;	PUNCT
ejpam-4573	166	19	(	(	PUNCT
ejpam-4573	166	20	5	5	X
ejpam-4573	166	21	)	)	PUNCT
ejpam-4573	166	22	f−(b(λ	f−(b(λ	NOUN
ejpam-4573	166	23	,	,	PUNCT
ejpam-4573	166	24	sp	sp	NOUN
ejpam-4573	166	25	)	)	PUNCT
ejpam-4573	166	26	)	)	PUNCT
ejpam-4573	167	1	⊆	⊆	NUM
ejpam-4573	167	2	[	[	X
ejpam-4573	167	3	f−([b(λ	f−([b(λ	PROPN
ejpam-4573	167	4	,	,	PUNCT
ejpam-4573	167	5	sp	sp	NOUN
ejpam-4573	167	6	)	)	PUNCT
ejpam-4573	167	7	]	]	PUNCT
ejpam-4573	167	8	(	(	PUNCT
ejpam-4573	167	9	λ	λ	INTJ
ejpam-4573	167	10	,	,	PUNCT
ejpam-4573	167	11	sp))](λ	sp))](λ	PROPN
ejpam-4573	167	12	,	,	PUNCT
ejpam-4573	167	13	sp	sp	NOUN
ejpam-4573	167	14	)	)	PUNCT
ejpam-4573	167	15	for	for	ADP
ejpam-4573	167	16	every	every	DET
ejpam-4573	167	17	subset	subset	NOUN
ejpam-4573	167	18	b	b	PROPN
ejpam-4573	167	19	of	of	ADP
ejpam-4573	167	20	y	y	PROPN
ejpam-4573	167	21	;	;	PUNCT
ejpam-4573	167	22	(	(	PUNCT
ejpam-4573	167	23	6	6	X
ejpam-4573	167	24	)	)	PUNCT
ejpam-4573	168	1	[	[	X
ejpam-4573	168	2	f+([v	f+([v	X
ejpam-4573	168	3	(	(	PUNCT
ejpam-4573	168	4	λ	λ	PROPN
ejpam-4573	168	5	,	,	PUNCT
ejpam-4573	168	6	sp)](λ	sp)](λ	PROPN
ejpam-4573	168	7	,	,	PUNCT
ejpam-4573	168	8	sp	sp	NOUN
ejpam-4573	168	9	)	)	PUNCT
ejpam-4573	168	10	)	)	PUNCT
ejpam-4573	168	11	]	]	PUNCT
ejpam-4573	168	12	(	(	PUNCT
ejpam-4573	168	13	λ	λ	NOUN
ejpam-4573	168	14	,	,	PUNCT
ejpam-4573	168	15	sp	sp	NOUN
ejpam-4573	168	16	)	)	PUNCT
ejpam-4573	168	17	⊆	⊆	NUM
ejpam-4573	168	18	f+(v	f+(v	NUM
ejpam-4573	168	19	(	(	PUNCT
ejpam-4573	168	20	λ	λ	NOUN
ejpam-4573	168	21	,	,	PUNCT
ejpam-4573	168	22	sp	sp	NOUN
ejpam-4573	168	23	)	)	PUNCT
ejpam-4573	168	24	)	)	PUNCT
ejpam-4573	168	25	for	for	ADP
ejpam-4573	168	26	every	every	DET
ejpam-4573	168	27	(	(	PUNCT
ejpam-4573	168	28	λ	λ	NOUN
ejpam-4573	168	29	,	,	PUNCT
ejpam-4573	168	30	sp)-open	sp)-open	NOUN
ejpam-4573	168	31	set	set	VERB
ejpam-4573	168	32	v	v	NOUN
ejpam-4573	168	33	of	of	ADP
ejpam-4573	168	34	y	y	PROPN
ejpam-4573	168	35	;	;	PUNCT
ejpam-4573	168	36	(	(	PUNCT
ejpam-4573	168	37	7	7	X
ejpam-4573	168	38	)	)	PUNCT
ejpam-4573	168	39	[	[	X
ejpam-4573	168	40	f+(v	f+(v	NOUN
ejpam-4573	168	41	)	)	PUNCT
ejpam-4573	168	42	]	]	PUNCT
ejpam-4573	168	43	(	(	PUNCT
ejpam-4573	168	44	λ	λ	NOUN
ejpam-4573	168	45	,	,	PUNCT
ejpam-4573	168	46	sp	sp	NOUN
ejpam-4573	168	47	)	)	PUNCT
ejpam-4573	168	48	⊆	⊆	NUM
ejpam-4573	168	49	f+(v	f+(v	NUM
ejpam-4573	168	50	(	(	PUNCT
ejpam-4573	168	51	λ	λ	NOUN
ejpam-4573	168	52	,	,	PUNCT
ejpam-4573	168	53	sp	sp	NOUN
ejpam-4573	168	54	)	)	PUNCT
ejpam-4573	168	55	)	)	PUNCT
ejpam-4573	168	56	for	for	ADP
ejpam-4573	168	57	every	every	DET
ejpam-4573	168	58	(	(	PUNCT
ejpam-4573	168	59	λ	λ	NOUN
ejpam-4573	168	60	,	,	PUNCT
ejpam-4573	168	61	sp)-open	sp)-open	NOUN
ejpam-4573	168	62	set	set	VERB
ejpam-4573	168	63	v	v	NOUN
ejpam-4573	168	64	of	of	ADP
ejpam-4573	168	65	y	y	PROPN
ejpam-4573	168	66	;	;	PUNCT
ejpam-4573	168	67	(	(	PUNCT
ejpam-4573	168	68	8)	8)	NUM
ejpam-4573	168	69	[	[	X
ejpam-4573	168	70	f+(k(λ	f+(k(λ	NOUN
ejpam-4573	168	71	,	,	PUNCT
ejpam-4573	168	72	sp	sp	NOUN
ejpam-4573	168	73	)	)	PUNCT
ejpam-4573	168	74	)	)	PUNCT
ejpam-4573	168	75	]	]	PUNCT
ejpam-4573	168	76	(	(	PUNCT
ejpam-4573	168	77	λ	λ	NOUN
ejpam-4573	168	78	,	,	PUNCT
ejpam-4573	168	79	sp	sp	NOUN
ejpam-4573	168	80	)	)	PUNCT
ejpam-4573	168	81	⊆	⊆	NUM
ejpam-4573	168	82	f+(k	f+(k	NOUN
ejpam-4573	168	83	)	)	PUNCT
ejpam-4573	168	84	for	for	ADP
ejpam-4573	168	85	every	every	DET
ejpam-4573	168	86	r(λ	r(λ	NOUN
ejpam-4573	168	87	,	,	PUNCT
ejpam-4573	168	88	sp)-closed	sp)-close	VERB
ejpam-4573	168	89	set	set	VERB
ejpam-4573	168	90	k	k	PROPN
ejpam-4573	168	91	of	of	ADP
ejpam-4573	168	92	y	y	PROPN
ejpam-4573	168	93	.	.	PUNCT
ejpam-4573	169	1	proof	proof	NOUN
ejpam-4573	169	2	.	.	PUNCT
ejpam-4573	170	1	the	the	DET
ejpam-4573	170	2	proof	proof	NOUN
ejpam-4573	170	3	is	be	AUX
ejpam-4573	170	4	similar	similar	ADJ
ejpam-4573	170	5	to	to	ADP
ejpam-4573	170	6	that	that	PRON
ejpam-4573	170	7	of	of	ADP
ejpam-4573	170	8	theorem	theorem	NOUN
ejpam-4573	170	9	1	1	NUM
ejpam-4573	170	10	.	.	PUNCT
ejpam-4573	170	11	definition	definition	NOUN
ejpam-4573	170	12	2	2	NUM
ejpam-4573	170	13	.	.	PUNCT
ejpam-4573	171	1	a	a	DET
ejpam-4573	171	2	function	function	NOUN
ejpam-4573	171	3	f	f	NOUN
ejpam-4573	171	4	:	:	PUNCT
ejpam-4573	171	5	(	(	PUNCT
ejpam-4573	171	6	x	x	X
ejpam-4573	171	7	,	,	PUNCT
ejpam-4573	171	8	τ	τ	X
ejpam-4573	171	9	)	)	PUNCT
ejpam-4573	171	10	→	→	SYM
ejpam-4573	171	11	(	(	PUNCT
ejpam-4573	171	12	y	y	PROPN
ejpam-4573	171	13	,	,	PUNCT
ejpam-4573	171	14	σ	σ	PROPN
ejpam-4573	171	15	)	)	PUNCT
ejpam-4573	171	16	is	be	AUX
ejpam-4573	171	17	said	say	VERB
ejpam-4573	171	18	to	to	PART
ejpam-4573	171	19	be	be	AUX
ejpam-4573	171	20	weakly	weakly	ADJ
ejpam-4573	171	21	(	(	PUNCT
ejpam-4573	171	22	λ	λ	NOUN
ejpam-4573	171	23	,	,	PUNCT
ejpam-4573	171	24	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	171	25	if	if	SCONJ
ejpam-4573	171	26	,	,	PUNCT
ejpam-4573	171	27	for	for	SCONJ
ejpam-4573	171	28	each	each	DET
ejpam-4573	171	29	x	x	SYM
ejpam-4573	171	30	∈	∈	PROPN
ejpam-4573	171	31	x	x	X
ejpam-4573	171	32	and	and	CCONJ
ejpam-4573	171	33	each	each	DET
ejpam-4573	171	34	(	(	PUNCT
ejpam-4573	171	35	λ	λ	PROPN
ejpam-4573	171	36	,	,	PUNCT
ejpam-4573	171	37	sp)-open	sp)-open	NOUN
ejpam-4573	171	38	set	set	VERB
ejpam-4573	171	39	v	v	NUM
ejpam-4573	171	40	of	of	ADP
ejpam-4573	171	41	y	y	NOUN
ejpam-4573	171	42	containing	contain	VERB
ejpam-4573	171	43	f(x	f(x	PROPN
ejpam-4573	171	44	)	)	PUNCT
ejpam-4573	171	45	,	,	PUNCT
ejpam-4573	171	46	there	there	PRON
ejpam-4573	171	47	exists	exist	VERB
ejpam-4573	171	48	a	a	DET
ejpam-4573	171	49	(	(	PUNCT
ejpam-4573	171	50	λ	λ	NOUN
ejpam-4573	171	51	,	,	PUNCT
ejpam-4573	171	52	sp)-open	sp)-open	NOUN
ejpam-4573	171	53	set	set	VERB
ejpam-4573	171	54	u	u	NOUN
ejpam-4573	171	55	of	of	ADP
ejpam-4573	171	56	x	x	PUNCT
ejpam-4573	171	57	containing	contain	VERB
ejpam-4573	171	58	x	x	PUNCT
ejpam-4573	171	59	such	such	ADJ
ejpam-4573	171	60	that	that	DET
ejpam-4573	171	61	f(u	f(u	PROPN
ejpam-4573	171	62	)	)	PUNCT
ejpam-4573	171	63	⊆	⊆	NUM
ejpam-4573	171	64	v	v	NOUN
ejpam-4573	171	65	(	(	PUNCT
ejpam-4573	171	66	λ	λ	NOUN
ejpam-4573	171	67	,	,	PUNCT
ejpam-4573	171	68	sp	sp	NOUN
ejpam-4573	171	69	)	)	PUNCT
ejpam-4573	171	70	.	.	PUNCT
ejpam-4573	172	1	corollary	corollary	ADJ
ejpam-4573	172	2	1	1	NUM
ejpam-4573	172	3	.	.	PUNCT
ejpam-4573	173	1	for	for	ADP
ejpam-4573	173	2	a	a	DET
ejpam-4573	173	3	function	function	NOUN
ejpam-4573	173	4	f	f	NOUN
ejpam-4573	173	5	:	:	PUNCT
ejpam-4573	173	6	(	(	PUNCT
ejpam-4573	173	7	x	x	X
ejpam-4573	173	8	,	,	PUNCT
ejpam-4573	173	9	τ	τ	X
ejpam-4573	173	10	)	)	PUNCT
ejpam-4573	173	11	→	→	SYM
ejpam-4573	173	12	(	(	PUNCT
ejpam-4573	173	13	y	y	PROPN
ejpam-4573	173	14	,	,	PUNCT
ejpam-4573	173	15	σ	σ	PROPN
ejpam-4573	173	16	)	)	PUNCT
ejpam-4573	173	17	,	,	PUNCT
ejpam-4573	173	18	the	the	DET
ejpam-4573	173	19	following	follow	VERB
ejpam-4573	173	20	properties	property	NOUN
ejpam-4573	173	21	are	be	AUX
ejpam-4573	173	22	equivalent	equivalent	ADJ
ejpam-4573	173	23	:	:	PUNCT
ejpam-4573	173	24	(	(	PUNCT
ejpam-4573	173	25	1	1	X
ejpam-4573	173	26	)	)	PUNCT
ejpam-4573	173	27	f	f	PROPN
ejpam-4573	173	28	is	be	AUX
ejpam-4573	173	29	weakly	weakly	ADJ
ejpam-4573	173	30	(	(	PUNCT
ejpam-4573	173	31	λ	λ	NOUN
ejpam-4573	173	32	,	,	PUNCT
ejpam-4573	173	33	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	173	34	;	;	PUNCT
ejpam-4573	173	35	(	(	PUNCT
ejpam-4573	173	36	2	2	X
ejpam-4573	173	37	)	)	PUNCT
ejpam-4573	173	38	f−1(v	f−1(v	NOUN
ejpam-4573	173	39	)	)	PUNCT
ejpam-4573	174	1	⊆	⊆	NUM
ejpam-4573	174	2	[	[	X
ejpam-4573	174	3	f−1(v	f−1(v	NOUN
ejpam-4573	174	4	(	(	PUNCT
ejpam-4573	174	5	λ	λ	PROPN
ejpam-4573	174	6	,	,	PUNCT
ejpam-4573	174	7	sp))](λ	sp))](λ	PROPN
ejpam-4573	174	8	,	,	PUNCT
ejpam-4573	174	9	sp	sp	NOUN
ejpam-4573	174	10	)	)	PUNCT
ejpam-4573	174	11	for	for	ADP
ejpam-4573	174	12	every	every	DET
ejpam-4573	174	13	(	(	PUNCT
ejpam-4573	174	14	λ	λ	NOUN
ejpam-4573	174	15	,	,	PUNCT
ejpam-4573	174	16	sp)-open	sp)-open	NOUN
ejpam-4573	174	17	set	set	VERB
ejpam-4573	174	18	v	v	NOUN
ejpam-4573	174	19	of	of	ADP
ejpam-4573	174	20	y	y	PROPN
ejpam-4573	174	21	;	;	PUNCT
ejpam-4573	174	22	(	(	PUNCT
ejpam-4573	174	23	3	3	X
ejpam-4573	174	24	)	)	PUNCT
ejpam-4573	174	25	[	[	X
ejpam-4573	174	26	f−1(k(λ	f−1(k(λ	NOUN
ejpam-4573	174	27	,	,	PUNCT
ejpam-4573	174	28	sp	sp	NOUN
ejpam-4573	174	29	)	)	PUNCT
ejpam-4573	174	30	)	)	PUNCT
ejpam-4573	174	31	]	]	PUNCT
ejpam-4573	174	32	(	(	PUNCT
ejpam-4573	174	33	λ	λ	NOUN
ejpam-4573	174	34	,	,	PUNCT
ejpam-4573	174	35	sp	sp	NOUN
ejpam-4573	174	36	)	)	PUNCT
ejpam-4573	174	37	⊆	⊆	NUM
ejpam-4573	174	38	f−1(k	f−1(k	PROPN
ejpam-4573	174	39	)	)	PUNCT
ejpam-4573	174	40	for	for	ADP
ejpam-4573	174	41	every	every	DET
ejpam-4573	174	42	(	(	PUNCT
ejpam-4573	174	43	λ	λ	PROPN
ejpam-4573	174	44	,	,	PUNCT
ejpam-4573	174	45	sp)-closed	sp)-close	VERB
ejpam-4573	174	46	set	set	VERB
ejpam-4573	174	47	k	k	PROPN
ejpam-4573	174	48	of	of	ADP
ejpam-4573	174	49	y	y	PROPN
ejpam-4573	174	50	;	;	PUNCT
ejpam-4573	174	51	c.	c.	PROPN
ejpam-4573	174	52	boonpok	boonpok	PROPN
ejpam-4573	174	53	,	,	PUNCT
ejpam-4573	174	54	p.	p.	NOUN
ejpam-4573	174	55	pue	pue	NOUN
ejpam-4573	174	56	-	-	PUNCT
ejpam-4573	174	57	on	on	ADP
ejpam-4573	174	58	/	/	SYM
ejpam-4573	174	59	eur	eur	NOUN
ejpam-4573	174	60	.	.	PUNCT
ejpam-4573	175	1	j.	j.	PROPN
ejpam-4573	175	2	pure	pure	PROPN
ejpam-4573	175	3	appl	appl	PROPN
ejpam-4573	175	4	.	.	PROPN
ejpam-4573	175	5	math	math	PROPN
ejpam-4573	175	6	,	,	PUNCT
ejpam-4573	175	7	16	16	NUM
ejpam-4573	175	8	(	(	PUNCT
ejpam-4573	175	9	2	2	NUM
ejpam-4573	175	10	)	)	PUNCT
ejpam-4573	175	11	(	(	PUNCT
ejpam-4573	175	12	2023	2023	NUM
ejpam-4573	175	13	)	)	PUNCT
ejpam-4573	175	14	,	,	PUNCT
ejpam-4573	175	15	1047	1047	NUM
ejpam-4573	175	16	-	-	SYM
ejpam-4573	175	17	1058	1058	NUM
ejpam-4573	175	18	1052	1052	NUM
ejpam-4573	175	19	(	(	PUNCT
ejpam-4573	175	20	4	4	NUM
ejpam-4573	175	21	)	)	PUNCT
ejpam-4573	176	1	[	[	X
ejpam-4573	176	2	f−1([b(λ	f−1([b(λ	X
ejpam-4573	176	3	,	,	PUNCT
ejpam-4573	176	4	sp)](λ	sp)](λ	PROPN
ejpam-4573	176	5	,	,	PUNCT
ejpam-4573	176	6	sp	sp	NOUN
ejpam-4573	176	7	)	)	PUNCT
ejpam-4573	176	8	)	)	PUNCT
ejpam-4573	176	9	]	]	PUNCT
ejpam-4573	176	10	(	(	PUNCT
ejpam-4573	176	11	λ	λ	NOUN
ejpam-4573	176	12	,	,	PUNCT
ejpam-4573	176	13	sp	sp	NOUN
ejpam-4573	176	14	)	)	PUNCT
ejpam-4573	176	15	⊆	⊆	NUM
ejpam-4573	176	16	f−1(b(λ	f−1(b(λ	PROPN
ejpam-4573	176	17	,	,	PUNCT
ejpam-4573	176	18	sp	sp	NOUN
ejpam-4573	176	19	)	)	PUNCT
ejpam-4573	176	20	)	)	PUNCT
ejpam-4573	176	21	for	for	ADP
ejpam-4573	176	22	every	every	DET
ejpam-4573	176	23	subset	subset	NOUN
ejpam-4573	176	24	b	b	PROPN
ejpam-4573	176	25	of	of	ADP
ejpam-4573	176	26	y	y	PROPN
ejpam-4573	176	27	;	;	PUNCT
ejpam-4573	176	28	(	(	PUNCT
ejpam-4573	176	29	5	5	X
ejpam-4573	176	30	)	)	PUNCT
ejpam-4573	176	31	f−1(b(λ	f−1(b(λ	PROPN
ejpam-4573	176	32	,	,	PUNCT
ejpam-4573	176	33	sp	sp	NOUN
ejpam-4573	176	34	)	)	PUNCT
ejpam-4573	176	35	)	)	PUNCT
ejpam-4573	177	1	⊆	⊆	NUM
ejpam-4573	177	2	[	[	X
ejpam-4573	177	3	f−1([b(λ	f−1([b(λ	NOUN
ejpam-4573	177	4	,	,	PUNCT
ejpam-4573	177	5	sp	sp	NOUN
ejpam-4573	177	6	)	)	PUNCT
ejpam-4573	177	7	]	]	PUNCT
ejpam-4573	177	8	(	(	PUNCT
ejpam-4573	177	9	λ	λ	INTJ
ejpam-4573	177	10	,	,	PUNCT
ejpam-4573	177	11	sp))](λ	sp))](λ	PROPN
ejpam-4573	177	12	,	,	PUNCT
ejpam-4573	177	13	sp	sp	NOUN
ejpam-4573	177	14	)	)	PUNCT
ejpam-4573	177	15	for	for	ADP
ejpam-4573	177	16	every	every	DET
ejpam-4573	177	17	subset	subset	NOUN
ejpam-4573	177	18	b	b	PROPN
ejpam-4573	177	19	of	of	ADP
ejpam-4573	177	20	y	y	PROPN
ejpam-4573	177	21	;	;	PUNCT
ejpam-4573	177	22	(	(	PUNCT
ejpam-4573	177	23	6	6	X
ejpam-4573	177	24	)	)	PUNCT
ejpam-4573	177	25	[	[	X
ejpam-4573	177	26	f−1([v	f−1([v	ADJ
ejpam-4573	177	27	(	(	PUNCT
ejpam-4573	177	28	λ	λ	NOUN
ejpam-4573	177	29	,	,	PUNCT
ejpam-4573	177	30	sp)](λ	sp)](λ	PROPN
ejpam-4573	177	31	,	,	PUNCT
ejpam-4573	177	32	sp	sp	NOUN
ejpam-4573	177	33	)	)	PUNCT
ejpam-4573	177	34	)	)	PUNCT
ejpam-4573	177	35	]	]	PUNCT
ejpam-4573	177	36	(	(	PUNCT
ejpam-4573	177	37	λ	λ	NOUN
ejpam-4573	177	38	,	,	PUNCT
ejpam-4573	177	39	sp	sp	NOUN
ejpam-4573	177	40	)	)	PUNCT
ejpam-4573	177	41	⊆	⊆	NUM
ejpam-4573	177	42	f−1(v	f−1(v	NOUN
ejpam-4573	177	43	(	(	PUNCT
ejpam-4573	177	44	λ	λ	PROPN
ejpam-4573	177	45	,	,	PUNCT
ejpam-4573	177	46	sp	sp	NOUN
ejpam-4573	177	47	)	)	PUNCT
ejpam-4573	177	48	)	)	PUNCT
ejpam-4573	177	49	for	for	ADP
ejpam-4573	177	50	every	every	DET
ejpam-4573	177	51	(	(	PUNCT
ejpam-4573	177	52	λ	λ	NOUN
ejpam-4573	177	53	,	,	PUNCT
ejpam-4573	177	54	sp)-open	sp)-open	NOUN
ejpam-4573	177	55	set	set	VERB
ejpam-4573	177	56	v	v	NOUN
ejpam-4573	177	57	of	of	ADP
ejpam-4573	177	58	y	y	PROPN
ejpam-4573	177	59	;	;	PUNCT
ejpam-4573	177	60	(	(	PUNCT
ejpam-4573	177	61	7	7	X
ejpam-4573	177	62	)	)	PUNCT
ejpam-4573	178	1	[	[	X
ejpam-4573	178	2	f−1(v	f−1(v	NOUN
ejpam-4573	178	3	)	)	PUNCT
ejpam-4573	178	4	]	]	PUNCT
ejpam-4573	178	5	(	(	PUNCT
ejpam-4573	178	6	λ	λ	NOUN
ejpam-4573	178	7	,	,	PUNCT
ejpam-4573	178	8	sp	sp	NOUN
ejpam-4573	178	9	)	)	PUNCT
ejpam-4573	178	10	⊆	⊆	NUM
ejpam-4573	178	11	f−1(v	f−1(v	NOUN
ejpam-4573	178	12	(	(	PUNCT
ejpam-4573	178	13	λ	λ	PROPN
ejpam-4573	178	14	,	,	PUNCT
ejpam-4573	178	15	sp	sp	NOUN
ejpam-4573	178	16	)	)	PUNCT
ejpam-4573	178	17	)	)	PUNCT
ejpam-4573	178	18	for	for	ADP
ejpam-4573	178	19	every	every	DET
ejpam-4573	178	20	(	(	PUNCT
ejpam-4573	178	21	λ	λ	NOUN
ejpam-4573	178	22	,	,	PUNCT
ejpam-4573	178	23	sp)-open	sp)-open	NOUN
ejpam-4573	178	24	set	set	VERB
ejpam-4573	178	25	v	v	NOUN
ejpam-4573	178	26	of	of	ADP
ejpam-4573	178	27	y	y	PROPN
ejpam-4573	178	28	;	;	PUNCT
ejpam-4573	178	29	(	(	PUNCT
ejpam-4573	178	30	8)	8)	NUM
ejpam-4573	178	31	[	[	X
ejpam-4573	178	32	f−1(k(λ	f−1(k(λ	NOUN
ejpam-4573	178	33	,	,	PUNCT
ejpam-4573	178	34	sp	sp	NOUN
ejpam-4573	178	35	)	)	PUNCT
ejpam-4573	178	36	)	)	PUNCT
ejpam-4573	178	37	]	]	PUNCT
ejpam-4573	178	38	(	(	PUNCT
ejpam-4573	178	39	λ	λ	NOUN
ejpam-4573	178	40	,	,	PUNCT
ejpam-4573	178	41	sp	sp	NOUN
ejpam-4573	178	42	)	)	PUNCT
ejpam-4573	178	43	⊆	⊆	NUM
ejpam-4573	178	44	f−1(k	f−1(k	PROPN
ejpam-4573	178	45	)	)	PUNCT
ejpam-4573	178	46	for	for	ADP
ejpam-4573	178	47	every	every	DET
ejpam-4573	178	48	r(λ	r(λ	NOUN
ejpam-4573	178	49	,	,	PUNCT
ejpam-4573	178	50	sp)-closed	sp)-close	VERB
ejpam-4573	178	51	set	set	VERB
ejpam-4573	178	52	k	k	PROPN
ejpam-4573	178	53	of	of	ADP
ejpam-4573	178	54	y	y	PROPN
ejpam-4573	178	55	.	.	PUNCT
ejpam-4573	179	1	theorem	theorem	VERB
ejpam-4573	179	2	3	3	NUM
ejpam-4573	179	3	.	.	X
ejpam-4573	179	4	for	for	ADP
ejpam-4573	179	5	a	a	DET
ejpam-4573	179	6	multifunction	multifunction	NOUN
ejpam-4573	180	1	f	f	NOUN
ejpam-4573	180	2	:	:	PUNCT
ejpam-4573	180	3	(	(	PUNCT
ejpam-4573	180	4	x	x	X
ejpam-4573	180	5	,	,	PUNCT
ejpam-4573	180	6	τ	τ	X
ejpam-4573	180	7	)	)	PUNCT
ejpam-4573	180	8	→	→	SYM
ejpam-4573	180	9	(	(	PUNCT
ejpam-4573	180	10	y	y	PROPN
ejpam-4573	180	11	,	,	PUNCT
ejpam-4573	180	12	σ	σ	PROPN
ejpam-4573	180	13	)	)	PUNCT
ejpam-4573	180	14	,	,	PUNCT
ejpam-4573	180	15	the	the	DET
ejpam-4573	180	16	following	follow	VERB
ejpam-4573	180	17	properties	property	NOUN
ejpam-4573	180	18	are	be	AUX
ejpam-4573	180	19	equivalent	equivalent	ADJ
ejpam-4573	180	20	:	:	PUNCT
ejpam-4573	180	21	(	(	PUNCT
ejpam-4573	180	22	1	1	X
ejpam-4573	180	23	)	)	PUNCT
ejpam-4573	180	24	f	f	PROPN
ejpam-4573	180	25	is	be	AUX
ejpam-4573	180	26	upper	upper	ADJ
ejpam-4573	180	27	weakly	weakly	ADJ
ejpam-4573	180	28	(	(	PUNCT
ejpam-4573	180	29	λ	λ	NOUN
ejpam-4573	180	30	,	,	PUNCT
ejpam-4573	180	31	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	180	32	;	;	PUNCT
ejpam-4573	180	33	(	(	PUNCT
ejpam-4573	180	34	2	2	X
ejpam-4573	180	35	)	)	PUNCT
ejpam-4573	181	1	[	[	X
ejpam-4573	181	2	f−([v	f−([v	ADJ
ejpam-4573	181	3	(	(	PUNCT
ejpam-4573	181	4	λ	λ	PROPN
ejpam-4573	181	5	,	,	PUNCT
ejpam-4573	181	6	sp)](λ	sp)](λ	PROPN
ejpam-4573	181	7	,	,	PUNCT
ejpam-4573	181	8	sp	sp	NOUN
ejpam-4573	181	9	)	)	PUNCT
ejpam-4573	181	10	)	)	PUNCT
ejpam-4573	181	11	]	]	PUNCT
ejpam-4573	181	12	(	(	PUNCT
ejpam-4573	181	13	λ	λ	NOUN
ejpam-4573	181	14	,	,	PUNCT
ejpam-4573	181	15	sp	sp	NOUN
ejpam-4573	181	16	)	)	PUNCT
ejpam-4573	181	17	⊆	⊆	NUM
ejpam-4573	181	18	f−(v	f−(v	NOUN
ejpam-4573	181	19	(	(	PUNCT
ejpam-4573	181	20	λ	λ	NOUN
ejpam-4573	181	21	,	,	PUNCT
ejpam-4573	181	22	sp	sp	NOUN
ejpam-4573	181	23	)	)	PUNCT
ejpam-4573	181	24	)	)	PUNCT
ejpam-4573	181	25	for	for	ADP
ejpam-4573	181	26	every	every	DET
ejpam-4573	181	27	β(λ	β(λ	PROPN
ejpam-4573	181	28	,	,	PUNCT
ejpam-4573	181	29	sp)-open	sp)-open	NOUN
ejpam-4573	181	30	set	set	VERB
ejpam-4573	181	31	v	v	NOUN
ejpam-4573	181	32	of	of	ADP
ejpam-4573	181	33	y	y	PROPN
ejpam-4573	181	34	;	;	PUNCT
ejpam-4573	181	35	(	(	PUNCT
ejpam-4573	181	36	3	3	X
ejpam-4573	181	37	)	)	PUNCT
ejpam-4573	182	1	[	[	X
ejpam-4573	182	2	f−([v	f−([v	ADJ
ejpam-4573	182	3	(	(	PUNCT
ejpam-4573	182	4	λ	λ	PROPN
ejpam-4573	182	5	,	,	PUNCT
ejpam-4573	182	6	sp)](λ	sp)](λ	PROPN
ejpam-4573	182	7	,	,	PUNCT
ejpam-4573	182	8	sp	sp	NOUN
ejpam-4573	182	9	)	)	PUNCT
ejpam-4573	182	10	)	)	PUNCT
ejpam-4573	182	11	]	]	PUNCT
ejpam-4573	182	12	(	(	PUNCT
ejpam-4573	182	13	λ	λ	NOUN
ejpam-4573	182	14	,	,	PUNCT
ejpam-4573	182	15	sp	sp	NOUN
ejpam-4573	182	16	)	)	PUNCT
ejpam-4573	182	17	⊆	⊆	NUM
ejpam-4573	182	18	f−(v	f−(v	NOUN
ejpam-4573	182	19	(	(	PUNCT
ejpam-4573	182	20	λ	λ	NOUN
ejpam-4573	182	21	,	,	PUNCT
ejpam-4573	182	22	sp	sp	NOUN
ejpam-4573	182	23	)	)	PUNCT
ejpam-4573	182	24	)	)	PUNCT
ejpam-4573	182	25	for	for	ADP
ejpam-4573	182	26	every	every	DET
ejpam-4573	182	27	s(λ	s(λ	PROPN
ejpam-4573	182	28	,	,	PUNCT
ejpam-4573	182	29	sp)-open	sp)-open	VERB
ejpam-4573	182	30	set	set	VERB
ejpam-4573	182	31	v	v	NOUN
ejpam-4573	182	32	of	of	ADP
ejpam-4573	182	33	y	y	PROPN
ejpam-4573	182	34	.	.	PUNCT
ejpam-4573	183	1	proof	proof	NOUN
ejpam-4573	183	2	.	.	PUNCT
ejpam-4573	184	1	(	(	PUNCT
ejpam-4573	184	2	1	1	X
ejpam-4573	184	3	)	)	PUNCT
ejpam-4573	184	4	⇒	⇒	NOUN
ejpam-4573	184	5	(	(	PUNCT
ejpam-4573	184	6	2	2	NUM
ejpam-4573	184	7	):	):	PUNCT
ejpam-4573	184	8	this	this	PRON
ejpam-4573	184	9	follows	follow	VERB
ejpam-4573	184	10	from	from	ADP
ejpam-4573	184	11	(	(	PUNCT
ejpam-4573	184	12	4	4	NUM
ejpam-4573	184	13	)	)	PUNCT
ejpam-4573	184	14	of	of	ADP
ejpam-4573	184	15	theorem	theorem	NOUN
ejpam-4573	184	16	1	1	NUM
ejpam-4573	184	17	.	.	PUNCT
ejpam-4573	184	18	(	(	PUNCT
ejpam-4573	184	19	2	2	X
ejpam-4573	184	20	)	)	PUNCT
ejpam-4573	184	21	⇒	⇒	NOUN
ejpam-4573	184	22	(	(	PUNCT
ejpam-4573	184	23	3	3	NUM
ejpam-4573	184	24	):	):	PUNCT
ejpam-4573	184	25	the	the	DET
ejpam-4573	184	26	proof	proof	NOUN
ejpam-4573	184	27	is	be	AUX
ejpam-4573	184	28	obvious	obvious	ADJ
ejpam-4573	184	29	since	since	SCONJ
ejpam-4573	184	30	sλspo(y	sλspo(y	PROPN
ejpam-4573	184	31	,	,	PUNCT
ejpam-4573	184	32	σ	σ	PROPN
ejpam-4573	184	33	)	)	PUNCT
ejpam-4573	184	34	⊆	⊆	NUM
ejpam-4573	184	35	βλspo(y	βλspo(y	ADP
ejpam-4573	184	36	,	,	PUNCT
ejpam-4573	184	37	σ	σ	PROPN
ejpam-4573	184	38	)	)	PUNCT
ejpam-4573	184	39	.	.	PUNCT
ejpam-4573	185	1	(	(	PUNCT
ejpam-4573	185	2	3	3	X
ejpam-4573	185	3	)	)	PUNCT
ejpam-4573	185	4	⇒	⇒	NOUN
ejpam-4573	185	5	(	(	PUNCT
ejpam-4573	185	6	1	1	NUM
ejpam-4573	185	7	):	):	PUNCT
ejpam-4573	185	8	since	since	SCONJ
ejpam-4573	185	9	λspo(y	λspo(y	PROPN
ejpam-4573	185	10	,	,	PUNCT
ejpam-4573	185	11	σ	σ	PROPN
ejpam-4573	185	12	)	)	PUNCT
ejpam-4573	185	13	⊆	⊆	NUM
ejpam-4573	185	14	sλspo(y	sλspo(y	PROPN
ejpam-4573	185	15	,	,	PUNCT
ejpam-4573	185	16	σ	σ	PROPN
ejpam-4573	185	17	)	)	PUNCT
ejpam-4573	185	18	,	,	PUNCT
ejpam-4573	185	19	the	the	DET
ejpam-4573	185	20	proof	proof	NOUN
ejpam-4573	185	21	is	be	AUX
ejpam-4573	185	22	obvious	obvious	ADJ
ejpam-4573	185	23	by	by	ADP
ejpam-4573	185	24	(	(	PUNCT
ejpam-4573	185	25	7	7	NUM
ejpam-4573	185	26	)	)	PUNCT
ejpam-4573	185	27	of	of	ADP
ejpam-4573	185	28	theorem	theorem	ADJ
ejpam-4573	185	29	1	1	NUM
ejpam-4573	185	30	.	.	PUNCT
ejpam-4573	185	31	theorem	theorem	NOUN
ejpam-4573	185	32	4	4	NUM
ejpam-4573	185	33	.	.	X
ejpam-4573	185	34	for	for	ADP
ejpam-4573	185	35	a	a	DET
ejpam-4573	185	36	multifunction	multifunction	NOUN
ejpam-4573	185	37	f	f	NOUN
ejpam-4573	185	38	:	:	PUNCT
ejpam-4573	185	39	(	(	PUNCT
ejpam-4573	185	40	x	x	X
ejpam-4573	185	41	,	,	PUNCT
ejpam-4573	185	42	τ	τ	X
ejpam-4573	185	43	)	)	PUNCT
ejpam-4573	185	44	→	→	SYM
ejpam-4573	185	45	(	(	PUNCT
ejpam-4573	185	46	y	y	PROPN
ejpam-4573	185	47	,	,	PUNCT
ejpam-4573	185	48	σ	σ	PROPN
ejpam-4573	185	49	)	)	PUNCT
ejpam-4573	185	50	,	,	PUNCT
ejpam-4573	185	51	the	the	DET
ejpam-4573	185	52	following	follow	VERB
ejpam-4573	185	53	properties	property	NOUN
ejpam-4573	185	54	are	be	AUX
ejpam-4573	185	55	equivalent	equivalent	ADJ
ejpam-4573	185	56	:	:	PUNCT
ejpam-4573	185	57	(	(	PUNCT
ejpam-4573	185	58	1	1	X
ejpam-4573	185	59	)	)	PUNCT
ejpam-4573	185	60	f	f	PROPN
ejpam-4573	185	61	is	be	AUX
ejpam-4573	185	62	lower	low	ADJ
ejpam-4573	185	63	weakly	weakly	ADJ
ejpam-4573	185	64	(	(	PUNCT
ejpam-4573	185	65	λ	λ	NOUN
ejpam-4573	185	66	,	,	PUNCT
ejpam-4573	185	67	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	185	68	;	;	PUNCT
ejpam-4573	185	69	(	(	PUNCT
ejpam-4573	185	70	2	2	X
ejpam-4573	185	71	)	)	PUNCT
ejpam-4573	185	72	[	[	X
ejpam-4573	185	73	f+([v	f+([v	X
ejpam-4573	185	74	(	(	PUNCT
ejpam-4573	185	75	λ	λ	PROPN
ejpam-4573	185	76	,	,	PUNCT
ejpam-4573	185	77	sp)](λ	sp)](λ	PROPN
ejpam-4573	185	78	,	,	PUNCT
ejpam-4573	185	79	sp	sp	NOUN
ejpam-4573	185	80	)	)	PUNCT
ejpam-4573	185	81	)	)	PUNCT
ejpam-4573	185	82	]	]	PUNCT
ejpam-4573	185	83	(	(	PUNCT
ejpam-4573	185	84	λ	λ	NOUN
ejpam-4573	185	85	,	,	PUNCT
ejpam-4573	185	86	sp	sp	NOUN
ejpam-4573	185	87	)	)	PUNCT
ejpam-4573	185	88	⊆	⊆	NUM
ejpam-4573	185	89	f+(v	f+(v	NUM
ejpam-4573	185	90	(	(	PUNCT
ejpam-4573	185	91	λ	λ	NOUN
ejpam-4573	185	92	,	,	PUNCT
ejpam-4573	185	93	sp	sp	NOUN
ejpam-4573	185	94	)	)	PUNCT
ejpam-4573	185	95	)	)	PUNCT
ejpam-4573	185	96	for	for	ADP
ejpam-4573	185	97	every	every	DET
ejpam-4573	185	98	β(λ	β(λ	PROPN
ejpam-4573	185	99	,	,	PUNCT
ejpam-4573	185	100	sp)-open	sp)-open	NOUN
ejpam-4573	185	101	set	set	VERB
ejpam-4573	185	102	v	v	NOUN
ejpam-4573	185	103	of	of	ADP
ejpam-4573	185	104	y	y	PROPN
ejpam-4573	185	105	;	;	PUNCT
ejpam-4573	185	106	(	(	PUNCT
ejpam-4573	185	107	3	3	X
ejpam-4573	185	108	)	)	PUNCT
ejpam-4573	185	109	[	[	X
ejpam-4573	185	110	f+([v	f+([v	X
ejpam-4573	185	111	(	(	PUNCT
ejpam-4573	185	112	λ	λ	PROPN
ejpam-4573	185	113	,	,	PUNCT
ejpam-4573	185	114	sp)](λ	sp)](λ	PROPN
ejpam-4573	185	115	,	,	PUNCT
ejpam-4573	185	116	sp	sp	NOUN
ejpam-4573	185	117	)	)	PUNCT
ejpam-4573	185	118	)	)	PUNCT
ejpam-4573	185	119	]	]	PUNCT
ejpam-4573	185	120	(	(	PUNCT
ejpam-4573	185	121	λ	λ	NOUN
ejpam-4573	185	122	,	,	PUNCT
ejpam-4573	185	123	sp	sp	NOUN
ejpam-4573	185	124	)	)	PUNCT
ejpam-4573	185	125	⊆	⊆	NUM
ejpam-4573	185	126	f+(v	f+(v	NUM
ejpam-4573	185	127	(	(	PUNCT
ejpam-4573	185	128	λ	λ	NOUN
ejpam-4573	185	129	,	,	PUNCT
ejpam-4573	185	130	sp	sp	NOUN
ejpam-4573	185	131	)	)	PUNCT
ejpam-4573	185	132	)	)	PUNCT
ejpam-4573	185	133	for	for	ADP
ejpam-4573	185	134	every	every	DET
ejpam-4573	185	135	s(λ	s(λ	PROPN
ejpam-4573	185	136	,	,	PUNCT
ejpam-4573	185	137	sp)-open	sp)-open	VERB
ejpam-4573	185	138	set	set	VERB
ejpam-4573	185	139	v	v	NOUN
ejpam-4573	185	140	of	of	ADP
ejpam-4573	185	141	y	y	PROPN
ejpam-4573	185	142	.	.	PUNCT
ejpam-4573	186	1	proof	proof	NOUN
ejpam-4573	186	2	.	.	PUNCT
ejpam-4573	187	1	the	the	DET
ejpam-4573	187	2	proof	proof	NOUN
ejpam-4573	187	3	is	be	AUX
ejpam-4573	187	4	similar	similar	ADJ
ejpam-4573	187	5	to	to	ADP
ejpam-4573	187	6	that	that	PRON
ejpam-4573	187	7	of	of	ADP
ejpam-4573	187	8	theorem	theorem	ADJ
ejpam-4573	187	9	3	3	NUM
ejpam-4573	187	10	.	.	PUNCT
ejpam-4573	187	11	corollary	corollary	ADJ
ejpam-4573	187	12	2	2	NUM
ejpam-4573	187	13	.	.	PUNCT
ejpam-4573	187	14	for	for	ADP
ejpam-4573	187	15	a	a	DET
ejpam-4573	187	16	function	function	NOUN
ejpam-4573	187	17	f	f	NOUN
ejpam-4573	187	18	:	:	PUNCT
ejpam-4573	187	19	(	(	PUNCT
ejpam-4573	187	20	x	x	X
ejpam-4573	187	21	,	,	PUNCT
ejpam-4573	187	22	τ	τ	X
ejpam-4573	187	23	)	)	PUNCT
ejpam-4573	187	24	→	→	SYM
ejpam-4573	187	25	(	(	PUNCT
ejpam-4573	187	26	y	y	PROPN
ejpam-4573	187	27	,	,	PUNCT
ejpam-4573	187	28	σ	σ	PROPN
ejpam-4573	187	29	)	)	PUNCT
ejpam-4573	187	30	,	,	PUNCT
ejpam-4573	187	31	the	the	DET
ejpam-4573	187	32	following	follow	VERB
ejpam-4573	187	33	properties	property	NOUN
ejpam-4573	187	34	are	be	AUX
ejpam-4573	187	35	equivalent	equivalent	ADJ
ejpam-4573	187	36	:	:	PUNCT
ejpam-4573	187	37	(	(	PUNCT
ejpam-4573	187	38	1	1	X
ejpam-4573	187	39	)	)	PUNCT
ejpam-4573	187	40	f	f	PROPN
ejpam-4573	187	41	is	be	AUX
ejpam-4573	187	42	weakly	weakly	ADJ
ejpam-4573	187	43	(	(	PUNCT
ejpam-4573	187	44	λ	λ	NOUN
ejpam-4573	187	45	,	,	PUNCT
ejpam-4573	187	46	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	187	47	;	;	PUNCT
ejpam-4573	187	48	(	(	PUNCT
ejpam-4573	187	49	2	2	X
ejpam-4573	187	50	)	)	PUNCT
ejpam-4573	187	51	[	[	X
ejpam-4573	187	52	f−1([v	f−1([v	ADJ
ejpam-4573	187	53	(	(	PUNCT
ejpam-4573	187	54	λ	λ	NOUN
ejpam-4573	187	55	,	,	PUNCT
ejpam-4573	187	56	sp)](λ	sp)](λ	PROPN
ejpam-4573	187	57	,	,	PUNCT
ejpam-4573	187	58	sp	sp	NOUN
ejpam-4573	187	59	)	)	PUNCT
ejpam-4573	187	60	)	)	PUNCT
ejpam-4573	187	61	]	]	PUNCT
ejpam-4573	188	1	(	(	PUNCT
ejpam-4573	188	2	λ	λ	NOUN
ejpam-4573	188	3	,	,	PUNCT
ejpam-4573	188	4	sp	sp	NOUN
ejpam-4573	188	5	)	)	PUNCT
ejpam-4573	188	6	⊆	⊆	NUM
ejpam-4573	188	7	f−1(v	f−1(v	NOUN
ejpam-4573	188	8	(	(	PUNCT
ejpam-4573	188	9	λ	λ	PROPN
ejpam-4573	188	10	,	,	PUNCT
ejpam-4573	188	11	sp	sp	NOUN
ejpam-4573	188	12	)	)	PUNCT
ejpam-4573	188	13	)	)	PUNCT
ejpam-4573	188	14	for	for	ADP
ejpam-4573	188	15	every	every	DET
ejpam-4573	188	16	β(λ	β(λ	PROPN
ejpam-4573	188	17	,	,	PUNCT
ejpam-4573	188	18	sp)-open	sp)-open	NOUN
ejpam-4573	188	19	set	set	VERB
ejpam-4573	188	20	v	v	NOUN
ejpam-4573	188	21	of	of	ADP
ejpam-4573	188	22	y	y	PROPN
ejpam-4573	188	23	;	;	PUNCT
ejpam-4573	188	24	(	(	PUNCT
ejpam-4573	188	25	3	3	X
ejpam-4573	188	26	)	)	PUNCT
ejpam-4573	188	27	[	[	X
ejpam-4573	188	28	f−1([v	f−1([v	ADJ
ejpam-4573	188	29	(	(	PUNCT
ejpam-4573	188	30	λ	λ	NOUN
ejpam-4573	188	31	,	,	PUNCT
ejpam-4573	188	32	sp)](λ	sp)](λ	PROPN
ejpam-4573	188	33	,	,	PUNCT
ejpam-4573	188	34	sp	sp	NOUN
ejpam-4573	188	35	)	)	PUNCT
ejpam-4573	188	36	)	)	PUNCT
ejpam-4573	188	37	]	]	PUNCT
ejpam-4573	188	38	(	(	PUNCT
ejpam-4573	188	39	λ	λ	NOUN
ejpam-4573	188	40	,	,	PUNCT
ejpam-4573	188	41	sp	sp	NOUN
ejpam-4573	188	42	)	)	PUNCT
ejpam-4573	188	43	⊆	⊆	NUM
ejpam-4573	188	44	f−1(v	f−1(v	NOUN
ejpam-4573	188	45	(	(	PUNCT
ejpam-4573	188	46	λ	λ	PROPN
ejpam-4573	188	47	,	,	PUNCT
ejpam-4573	188	48	sp	sp	NOUN
ejpam-4573	188	49	)	)	PUNCT
ejpam-4573	188	50	)	)	PUNCT
ejpam-4573	188	51	for	for	ADP
ejpam-4573	188	52	every	every	DET
ejpam-4573	188	53	s(λ	s(λ	PROPN
ejpam-4573	188	54	,	,	PUNCT
ejpam-4573	188	55	sp)-open	sp)-open	VERB
ejpam-4573	188	56	set	set	VERB
ejpam-4573	188	57	v	v	NOUN
ejpam-4573	188	58	of	of	ADP
ejpam-4573	188	59	y	y	PROPN
ejpam-4573	188	60	.	.	PUNCT
ejpam-4573	189	1	theorem	theorem	ADJ
ejpam-4573	189	2	5	5	NUM
ejpam-4573	189	3	.	.	X
ejpam-4573	189	4	for	for	ADP
ejpam-4573	189	5	a	a	DET
ejpam-4573	189	6	multifunction	multifunction	NOUN
ejpam-4573	190	1	f	f	NOUN
ejpam-4573	190	2	:	:	PUNCT
ejpam-4573	190	3	(	(	PUNCT
ejpam-4573	190	4	x	x	X
ejpam-4573	190	5	,	,	PUNCT
ejpam-4573	190	6	τ	τ	X
ejpam-4573	190	7	)	)	PUNCT
ejpam-4573	190	8	→	→	SYM
ejpam-4573	190	9	(	(	PUNCT
ejpam-4573	190	10	y	y	PROPN
ejpam-4573	190	11	,	,	PUNCT
ejpam-4573	190	12	σ	σ	PROPN
ejpam-4573	190	13	)	)	PUNCT
ejpam-4573	190	14	,	,	PUNCT
ejpam-4573	190	15	the	the	DET
ejpam-4573	190	16	following	follow	VERB
ejpam-4573	190	17	properties	property	NOUN
ejpam-4573	190	18	are	be	AUX
ejpam-4573	190	19	equivalent	equivalent	ADJ
ejpam-4573	190	20	:	:	PUNCT
ejpam-4573	190	21	(	(	PUNCT
ejpam-4573	190	22	1	1	X
ejpam-4573	190	23	)	)	PUNCT
ejpam-4573	190	24	f	f	PROPN
ejpam-4573	190	25	is	be	AUX
ejpam-4573	190	26	upper	upper	ADJ
ejpam-4573	190	27	weakly	weakly	ADJ
ejpam-4573	190	28	(	(	PUNCT
ejpam-4573	190	29	λ	λ	NOUN
ejpam-4573	190	30	,	,	PUNCT
ejpam-4573	190	31	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	190	32	;	;	PUNCT
ejpam-4573	190	33	(	(	PUNCT
ejpam-4573	190	34	2	2	X
ejpam-4573	190	35	)	)	PUNCT
ejpam-4573	191	1	[	[	X
ejpam-4573	191	2	f−([v	f−([v	ADJ
ejpam-4573	191	3	(	(	PUNCT
ejpam-4573	191	4	λ	λ	PROPN
ejpam-4573	191	5	,	,	PUNCT
ejpam-4573	191	6	sp)](λ	sp)](λ	PROPN
ejpam-4573	191	7	,	,	PUNCT
ejpam-4573	191	8	sp	sp	NOUN
ejpam-4573	191	9	)	)	PUNCT
ejpam-4573	191	10	)	)	PUNCT
ejpam-4573	191	11	]	]	PUNCT
ejpam-4573	191	12	(	(	PUNCT
ejpam-4573	191	13	λ	λ	NOUN
ejpam-4573	191	14	,	,	PUNCT
ejpam-4573	191	15	sp	sp	NOUN
ejpam-4573	191	16	)	)	PUNCT
ejpam-4573	191	17	⊆	⊆	NUM
ejpam-4573	191	18	f−(v	f−(v	NOUN
ejpam-4573	191	19	(	(	PUNCT
ejpam-4573	191	20	λ	λ	NOUN
ejpam-4573	191	21	,	,	PUNCT
ejpam-4573	191	22	sp	sp	NOUN
ejpam-4573	191	23	)	)	PUNCT
ejpam-4573	191	24	)	)	PUNCT
ejpam-4573	191	25	for	for	ADP
ejpam-4573	191	26	every	every	DET
ejpam-4573	191	27	p(λ	p(λ	NOUN
ejpam-4573	191	28	,	,	PUNCT
ejpam-4573	191	29	sp)-open	sp)-open	NOUN
ejpam-4573	191	30	set	set	VERB
ejpam-4573	191	31	v	v	NOUN
ejpam-4573	191	32	of	of	ADP
ejpam-4573	191	33	y	y	PROPN
ejpam-4573	191	34	;	;	PUNCT
ejpam-4573	191	35	c.	c.	PROPN
ejpam-4573	191	36	boonpok	boonpok	PROPN
ejpam-4573	191	37	,	,	PUNCT
ejpam-4573	191	38	p.	p.	NOUN
ejpam-4573	191	39	pue	pue	NOUN
ejpam-4573	191	40	-	-	PUNCT
ejpam-4573	191	41	on	on	ADP
ejpam-4573	191	42	/	/	SYM
ejpam-4573	191	43	eur	eur	NOUN
ejpam-4573	191	44	.	.	PUNCT
ejpam-4573	192	1	j.	j.	PROPN
ejpam-4573	192	2	pure	pure	PROPN
ejpam-4573	192	3	appl	appl	PROPN
ejpam-4573	192	4	.	.	PROPN
ejpam-4573	192	5	math	math	PROPN
ejpam-4573	192	6	,	,	PUNCT
ejpam-4573	192	7	16	16	NUM
ejpam-4573	192	8	(	(	PUNCT
ejpam-4573	192	9	2	2	NUM
ejpam-4573	192	10	)	)	PUNCT
ejpam-4573	192	11	(	(	PUNCT
ejpam-4573	192	12	2023	2023	NUM
ejpam-4573	192	13	)	)	PUNCT
ejpam-4573	192	14	,	,	PUNCT
ejpam-4573	192	15	1047	1047	NUM
ejpam-4573	192	16	-	-	SYM
ejpam-4573	192	17	1058	1058	NUM
ejpam-4573	192	18	1053	1053	NUM
ejpam-4573	192	19	(	(	PUNCT
ejpam-4573	192	20	3	3	NUM
ejpam-4573	192	21	)	)	PUNCT
ejpam-4573	193	1	[	[	X
ejpam-4573	193	2	f−(v	f−(v	NOUN
ejpam-4573	193	3	)	)	PUNCT
ejpam-4573	193	4	]	]	PUNCT
ejpam-4573	193	5	(	(	PUNCT
ejpam-4573	193	6	λ	λ	NOUN
ejpam-4573	193	7	,	,	PUNCT
ejpam-4573	193	8	sp	sp	NOUN
ejpam-4573	193	9	)	)	PUNCT
ejpam-4573	193	10	⊆	⊆	NUM
ejpam-4573	193	11	f−(v	f−(v	NOUN
ejpam-4573	193	12	(	(	PUNCT
ejpam-4573	193	13	λ	λ	NOUN
ejpam-4573	193	14	,	,	PUNCT
ejpam-4573	193	15	sp	sp	NOUN
ejpam-4573	193	16	)	)	PUNCT
ejpam-4573	193	17	)	)	PUNCT
ejpam-4573	193	18	for	for	ADP
ejpam-4573	193	19	every	every	DET
ejpam-4573	193	20	p(λ	p(λ	NOUN
ejpam-4573	193	21	,	,	PUNCT
ejpam-4573	193	22	sp)-open	sp)-open	NOUN
ejpam-4573	193	23	set	set	VERB
ejpam-4573	193	24	v	v	NOUN
ejpam-4573	193	25	of	of	ADP
ejpam-4573	193	26	y	y	PROPN
ejpam-4573	193	27	;	;	PUNCT
ejpam-4573	193	28	(	(	PUNCT
ejpam-4573	193	29	4	4	X
ejpam-4573	193	30	)	)	PUNCT
ejpam-4573	193	31	f+(v	f+(v	NOUN
ejpam-4573	193	32	)	)	PUNCT
ejpam-4573	194	1	⊆	⊆	NUM
ejpam-4573	194	2	[	[	X
ejpam-4573	194	3	f+(v	f+(v	NOUN
ejpam-4573	194	4	(	(	PUNCT
ejpam-4573	194	5	λ	λ	PROPN
ejpam-4573	194	6	,	,	PUNCT
ejpam-4573	194	7	sp))](λ	sp))](λ	PROPN
ejpam-4573	194	8	,	,	PUNCT
ejpam-4573	194	9	sp	sp	NOUN
ejpam-4573	194	10	)	)	PUNCT
ejpam-4573	194	11	for	for	ADP
ejpam-4573	194	12	every	every	DET
ejpam-4573	194	13	p(λ	p(λ	NOUN
ejpam-4573	194	14	,	,	PUNCT
ejpam-4573	194	15	sp)-open	sp)-open	NOUN
ejpam-4573	194	16	set	set	VERB
ejpam-4573	194	17	v	v	NOUN
ejpam-4573	194	18	of	of	ADP
ejpam-4573	194	19	y	y	PROPN
ejpam-4573	194	20	.	.	PUNCT
ejpam-4573	195	1	proof	proof	NOUN
ejpam-4573	195	2	.	.	PUNCT
ejpam-4573	196	1	(	(	PUNCT
ejpam-4573	196	2	1	1	X
ejpam-4573	196	3	)	)	PUNCT
ejpam-4573	196	4	⇒	⇒	NOUN
ejpam-4573	196	5	(	(	PUNCT
ejpam-4573	196	6	2	2	NUM
ejpam-4573	196	7	):	):	PUNCT
ejpam-4573	196	8	let	let	VERB
ejpam-4573	196	9	v	v	PART
ejpam-4573	196	10	be	be	AUX
ejpam-4573	196	11	any	any	DET
ejpam-4573	196	12	p(λ	p(λ	NOUN
ejpam-4573	196	13	,	,	PUNCT
ejpam-4573	196	14	sp)-open	sp)-open	ADJ
ejpam-4573	196	15	set	set	NOUN
ejpam-4573	196	16	of	of	ADP
ejpam-4573	196	17	y	y	PROPN
ejpam-4573	196	18	.	.	PUNCT
ejpam-4573	197	1	since	since	SCONJ
ejpam-4573	197	2	[	[	X
ejpam-4573	197	3	v	v	X
ejpam-4573	197	4	(	(	PUNCT
ejpam-4573	197	5	λ	λ	PROPN
ejpam-4573	197	6	,	,	PUNCT
ejpam-4573	197	7	sp)](λ	sp)](λ	PROPN
ejpam-4573	197	8	,	,	PUNCT
ejpam-4573	197	9	sp	sp	NOUN
ejpam-4573	197	10	)	)	PUNCT
ejpam-4573	197	11	is	be	AUX
ejpam-4573	197	12	(	(	PUNCT
ejpam-4573	197	13	λ	λ	INTJ
ejpam-4573	197	14	,	,	PUNCT
ejpam-4573	197	15	sp)open	sp)open	VERB
ejpam-4573	197	16	,	,	PUNCT
ejpam-4573	197	17	by	by	ADP
ejpam-4573	197	18	theorem	theorem	NOUN
ejpam-4573	197	19	1(7	1(7	NUM
ejpam-4573	197	20	)	)	PUNCT
ejpam-4573	197	21	,	,	PUNCT
ejpam-4573	198	1	[	[	X
ejpam-4573	198	2	f−([v	f−([v	ADJ
ejpam-4573	198	3	(	(	PUNCT
ejpam-4573	198	4	λ	λ	PROPN
ejpam-4573	198	5	,	,	PUNCT
ejpam-4573	198	6	sp)](λ	sp)](λ	PROPN
ejpam-4573	198	7	,	,	PUNCT
ejpam-4573	198	8	sp	sp	NOUN
ejpam-4573	198	9	)	)	PUNCT
ejpam-4573	198	10	)	)	PUNCT
ejpam-4573	198	11	]	]	PUNCT
ejpam-4573	198	12	(	(	PUNCT
ejpam-4573	198	13	λ	λ	NOUN
ejpam-4573	198	14	,	,	PUNCT
ejpam-4573	198	15	sp	sp	NOUN
ejpam-4573	198	16	)	)	PUNCT
ejpam-4573	198	17	⊆	⊆	NUM
ejpam-4573	198	18	f−([[v	f−([[v	PROPN
ejpam-4573	198	19	(	(	PUNCT
ejpam-4573	198	20	λ	λ	PROPN
ejpam-4573	198	21	,	,	PUNCT
ejpam-4573	198	22	sp)](λ	sp)](λ	PROPN
ejpam-4573	198	23	,	,	PUNCT
ejpam-4573	198	24	sp	sp	NOUN
ejpam-4573	198	25	)	)	PUNCT
ejpam-4573	198	26	]	]	PUNCT
ejpam-4573	198	27	(	(	PUNCT
ejpam-4573	198	28	λ	λ	NOUN
ejpam-4573	198	29	,	,	PUNCT
ejpam-4573	198	30	sp	sp	NOUN
ejpam-4573	198	31	)	)	PUNCT
ejpam-4573	198	32	)	)	PUNCT
ejpam-4573	198	33	⊆	⊆	NUM
ejpam-4573	198	34	f−(v	f−(v	NOUN
ejpam-4573	198	35	(	(	PUNCT
ejpam-4573	198	36	λ	λ	NOUN
ejpam-4573	198	37	,	,	PUNCT
ejpam-4573	198	38	sp	sp	NOUN
ejpam-4573	198	39	)	)	PUNCT
ejpam-4573	198	40	)	)	PUNCT
ejpam-4573	198	41	.	.	PUNCT
ejpam-4573	199	1	(	(	PUNCT
ejpam-4573	199	2	2	2	X
ejpam-4573	199	3	)	)	PUNCT
ejpam-4573	199	4	⇒	⇒	NOUN
ejpam-4573	199	5	(	(	PUNCT
ejpam-4573	199	6	3	3	NUM
ejpam-4573	199	7	):	):	PUNCT
ejpam-4573	199	8	let	let	VERB
ejpam-4573	199	9	v	v	PART
ejpam-4573	199	10	be	be	AUX
ejpam-4573	199	11	any	any	DET
ejpam-4573	199	12	p(λ	p(λ	NOUN
ejpam-4573	199	13	,	,	PUNCT
ejpam-4573	199	14	sp)-open	sp)-open	ADJ
ejpam-4573	199	15	set	set	NOUN
ejpam-4573	199	16	of	of	ADP
ejpam-4573	199	17	y	y	PROPN
ejpam-4573	199	18	.	.	PUNCT
ejpam-4573	200	1	by	by	ADP
ejpam-4573	200	2	(	(	PUNCT
ejpam-4573	200	3	2	2	NUM
ejpam-4573	200	4	)	)	PUNCT
ejpam-4573	200	5	,	,	PUNCT
ejpam-4573	200	6	we	we	PRON
ejpam-4573	200	7	have	have	VERB
ejpam-4573	200	8	[	[	X
ejpam-4573	200	9	f−(v	f−(v	ADJ
ejpam-4573	200	10	)	)	PUNCT
ejpam-4573	200	11	]	]	PUNCT
ejpam-4573	200	12	(	(	PUNCT
ejpam-4573	200	13	λ	λ	NOUN
ejpam-4573	200	14	,	,	PUNCT
ejpam-4573	200	15	sp	sp	NOUN
ejpam-4573	200	16	)	)	PUNCT
ejpam-4573	200	17	⊆	⊆	NUM
ejpam-4573	201	1	[	[	X
ejpam-4573	201	2	f−([v	f−([v	ADJ
ejpam-4573	201	3	(	(	PUNCT
ejpam-4573	201	4	λ	λ	PROPN
ejpam-4573	201	5	,	,	PUNCT
ejpam-4573	201	6	sp)](λ	sp)](λ	PROPN
ejpam-4573	201	7	,	,	PUNCT
ejpam-4573	201	8	sp	sp	NOUN
ejpam-4573	201	9	)	)	PUNCT
ejpam-4573	201	10	)	)	PUNCT
ejpam-4573	201	11	]	]	PUNCT
ejpam-4573	201	12	(	(	PUNCT
ejpam-4573	201	13	λ	λ	NOUN
ejpam-4573	201	14	,	,	PUNCT
ejpam-4573	201	15	sp	sp	NOUN
ejpam-4573	201	16	)	)	PUNCT
ejpam-4573	201	17	⊆	⊆	NUM
ejpam-4573	201	18	f−(v	f−(v	NOUN
ejpam-4573	201	19	(	(	PUNCT
ejpam-4573	201	20	λ	λ	NOUN
ejpam-4573	201	21	,	,	PUNCT
ejpam-4573	201	22	sp	sp	NOUN
ejpam-4573	201	23	)	)	PUNCT
ejpam-4573	201	24	)	)	PUNCT
ejpam-4573	201	25	.	.	PUNCT
ejpam-4573	202	1	(	(	PUNCT
ejpam-4573	202	2	3	3	X
ejpam-4573	202	3	)	)	PUNCT
ejpam-4573	202	4	⇒	⇒	NOUN
ejpam-4573	202	5	(	(	PUNCT
ejpam-4573	202	6	4	4	NUM
ejpam-4573	202	7	):	):	PUNCT
ejpam-4573	202	8	let	let	VERB
ejpam-4573	202	9	v	v	PART
ejpam-4573	202	10	be	be	AUX
ejpam-4573	202	11	any	any	DET
ejpam-4573	202	12	p(λ	p(λ	NOUN
ejpam-4573	202	13	,	,	PUNCT
ejpam-4573	202	14	sp)-open	sp)-open	ADJ
ejpam-4573	202	15	set	set	NOUN
ejpam-4573	202	16	of	of	ADP
ejpam-4573	202	17	y	y	PROPN
ejpam-4573	202	18	.	.	PUNCT
ejpam-4573	203	1	thus	thus	ADV
ejpam-4573	203	2	,	,	PUNCT
ejpam-4573	203	3	by	by	ADP
ejpam-4573	203	4	(	(	PUNCT
ejpam-4573	203	5	3	3	NUM
ejpam-4573	203	6	)	)	PUNCT
ejpam-4573	203	7	,	,	PUNCT
ejpam-4573	203	8	x	x	X
ejpam-4573	203	9	−	−	NOUN
ejpam-4573	204	1	[	[	X
ejpam-4573	204	2	f+(v	f+(v	PROPN
ejpam-4573	204	3	(	(	PUNCT
ejpam-4573	204	4	λ	λ	PROPN
ejpam-4573	204	5	,	,	PUNCT
ejpam-4573	204	6	sp))](λ	sp))](λ	PROPN
ejpam-4573	204	7	,	,	PUNCT
ejpam-4573	204	8	sp	sp	NOUN
ejpam-4573	204	9	)	)	PUNCT
ejpam-4573	204	10	=	=	PUNCT
ejpam-4573	205	1	[	[	X
ejpam-4573	205	2	x	x	X
ejpam-4573	205	3	−	−	PROPN
ejpam-4573	205	4	f+(v	f+(v	PROPN
ejpam-4573	205	5	(	(	PUNCT
ejpam-4573	205	6	λ	λ	PROPN
ejpam-4573	205	7	,	,	PUNCT
ejpam-4573	205	8	sp))](λ	sp))](λ	PROPN
ejpam-4573	205	9	,	,	PUNCT
ejpam-4573	205	10	sp	sp	NOUN
ejpam-4573	205	11	)	)	PUNCT
ejpam-4573	205	12	=	=	PUNCT
ejpam-4573	206	1	[	[	X
ejpam-4573	206	2	f−(y	f−(y	NOUN
ejpam-4573	206	3	−	−	NOUN
ejpam-4573	206	4	v	v	NOUN
ejpam-4573	206	5	(	(	PUNCT
ejpam-4573	206	6	λ	λ	PROPN
ejpam-4573	206	7	,	,	PUNCT
ejpam-4573	206	8	sp))](λ	sp))](λ	PROPN
ejpam-4573	206	9	,	,	PUNCT
ejpam-4573	206	10	sp	sp	NOUN
ejpam-4573	206	11	)	)	PUNCT
ejpam-4573	206	12	⊆	⊆	NUM
ejpam-4573	206	13	f−([y	f−([y	PROPN
ejpam-4573	206	14	−	−	PROPN
ejpam-4573	206	15	v	v	NOUN
ejpam-4573	206	16	(	(	PUNCT
ejpam-4573	206	17	λ	λ	PROPN
ejpam-4573	206	18	,	,	PUNCT
ejpam-4573	206	19	sp)](λ	sp)](λ	PROPN
ejpam-4573	206	20	,	,	PUNCT
ejpam-4573	206	21	sp	sp	NOUN
ejpam-4573	206	22	)	)	PUNCT
ejpam-4573	206	23	)	)	PUNCT
ejpam-4573	206	24	=	=	PUNCT
ejpam-4573	206	25	x	x	PUNCT
ejpam-4573	206	26	−	−	PROPN
ejpam-4573	206	27	f+([v	f+([v	NOUN
ejpam-4573	206	28	(	(	PUNCT
ejpam-4573	206	29	λ	λ	PROPN
ejpam-4573	206	30	,	,	PUNCT
ejpam-4573	206	31	sp)](λ	sp)](λ	PROPN
ejpam-4573	206	32	,	,	PUNCT
ejpam-4573	206	33	sp	sp	NOUN
ejpam-4573	206	34	)	)	PUNCT
ejpam-4573	206	35	)	)	PUNCT
ejpam-4573	207	1	⊆	⊆	NUM
ejpam-4573	207	2	x	x	SYM
ejpam-4573	207	3	−	−	NOUN
ejpam-4573	207	4	f+(v	f+(v	NOUN
ejpam-4573	207	5	)	)	PUNCT
ejpam-4573	207	6	and	and	CCONJ
ejpam-4573	207	7	hence	hence	ADV
ejpam-4573	207	8	f+(v	f+(v	NOUN
ejpam-4573	207	9	)	)	PUNCT
ejpam-4573	208	1	⊆	⊆	NUM
ejpam-4573	208	2	[	[	X
ejpam-4573	208	3	f+(v	f+(v	NOUN
ejpam-4573	208	4	(	(	PUNCT
ejpam-4573	208	5	λ	λ	PROPN
ejpam-4573	208	6	,	,	PUNCT
ejpam-4573	208	7	sp))](λ	sp))](λ	PROPN
ejpam-4573	208	8	,	,	PUNCT
ejpam-4573	208	9	sp	sp	NOUN
ejpam-4573	208	10	)	)	PUNCT
ejpam-4573	208	11	.	.	PUNCT
ejpam-4573	209	1	(	(	PUNCT
ejpam-4573	209	2	4	4	X
ejpam-4573	209	3	)	)	PUNCT
ejpam-4573	209	4	⇒	⇒	NOUN
ejpam-4573	209	5	(	(	PUNCT
ejpam-4573	209	6	1	1	NUM
ejpam-4573	209	7	):	):	PUNCT
ejpam-4573	209	8	let	let	VERB
ejpam-4573	209	9	v	v	PART
ejpam-4573	209	10	be	be	AUX
ejpam-4573	209	11	any	any	DET
ejpam-4573	209	12	(	(	PUNCT
ejpam-4573	209	13	λ	λ	NOUN
ejpam-4573	209	14	,	,	PUNCT
ejpam-4573	209	15	sp)-open	sp)-open	ADJ
ejpam-4573	209	16	set	set	NOUN
ejpam-4573	209	17	of	of	ADP
ejpam-4573	209	18	y	y	PROPN
ejpam-4573	209	19	.	.	PUNCT
ejpam-4573	210	1	then	then	ADV
ejpam-4573	210	2	,	,	PUNCT
ejpam-4573	210	3	v	v	NOUN
ejpam-4573	210	4	is	be	AUX
ejpam-4573	210	5	p(λ	p(λ	NOUN
ejpam-4573	210	6	,	,	PUNCT
ejpam-4573	210	7	sp)-open	sp)-open	NOUN
ejpam-4573	210	8	,	,	PUNCT
ejpam-4573	210	9	by	by	ADP
ejpam-4573	210	10	(	(	PUNCT
ejpam-4573	210	11	4	4	NUM
ejpam-4573	210	12	)	)	PUNCT
ejpam-4573	210	13	,	,	PUNCT
ejpam-4573	210	14	f+(v	f+(v	PROPN
ejpam-4573	210	15	)	)	PUNCT
ejpam-4573	211	1	⊆	⊆	NUM
ejpam-4573	211	2	[	[	X
ejpam-4573	211	3	f+(v	f+(v	NOUN
ejpam-4573	211	4	(	(	PUNCT
ejpam-4573	211	5	λ	λ	PROPN
ejpam-4573	211	6	,	,	PUNCT
ejpam-4573	211	7	sp))](λ	sp))](λ	PROPN
ejpam-4573	211	8	,	,	PUNCT
ejpam-4573	211	9	sp	sp	NOUN
ejpam-4573	211	10	)	)	PUNCT
ejpam-4573	211	11	.	.	PUNCT
ejpam-4573	212	1	by	by	ADP
ejpam-4573	212	2	theorem	theorem	NOUN
ejpam-4573	212	3	1	1	NUM
ejpam-4573	212	4	,	,	PUNCT
ejpam-4573	212	5	f	f	PROPN
ejpam-4573	212	6	is	be	AUX
ejpam-4573	212	7	upper	upper	ADJ
ejpam-4573	212	8	weakly	weakly	ADJ
ejpam-4573	212	9	(	(	PUNCT
ejpam-4573	212	10	λ	λ	NOUN
ejpam-4573	212	11	,	,	PUNCT
ejpam-4573	212	12	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	212	13	.	.	PUNCT
ejpam-4573	213	1	theorem	theorem	VERB
ejpam-4573	213	2	6	6	NUM
ejpam-4573	213	3	.	.	PUNCT
ejpam-4573	213	4	for	for	ADP
ejpam-4573	213	5	a	a	DET
ejpam-4573	213	6	multifunction	multifunction	NOUN
ejpam-4573	214	1	f	f	NOUN
ejpam-4573	214	2	:	:	PUNCT
ejpam-4573	214	3	(	(	PUNCT
ejpam-4573	214	4	x	x	X
ejpam-4573	214	5	,	,	PUNCT
ejpam-4573	214	6	τ	τ	X
ejpam-4573	214	7	)	)	PUNCT
ejpam-4573	214	8	→	→	SYM
ejpam-4573	214	9	(	(	PUNCT
ejpam-4573	214	10	y	y	PROPN
ejpam-4573	214	11	,	,	PUNCT
ejpam-4573	214	12	σ	σ	PROPN
ejpam-4573	214	13	)	)	PUNCT
ejpam-4573	214	14	,	,	PUNCT
ejpam-4573	214	15	the	the	DET
ejpam-4573	214	16	following	follow	VERB
ejpam-4573	214	17	properties	property	NOUN
ejpam-4573	214	18	are	be	AUX
ejpam-4573	214	19	equivalent	equivalent	ADJ
ejpam-4573	214	20	:	:	PUNCT
ejpam-4573	214	21	(	(	PUNCT
ejpam-4573	214	22	1	1	X
ejpam-4573	214	23	)	)	PUNCT
ejpam-4573	214	24	f	f	PROPN
ejpam-4573	214	25	is	be	AUX
ejpam-4573	214	26	lower	low	ADJ
ejpam-4573	214	27	weakly	weakly	ADJ
ejpam-4573	214	28	(	(	PUNCT
ejpam-4573	214	29	λ	λ	NOUN
ejpam-4573	214	30	,	,	PUNCT
ejpam-4573	214	31	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	214	32	;	;	PUNCT
ejpam-4573	214	33	(	(	PUNCT
ejpam-4573	214	34	2	2	X
ejpam-4573	214	35	)	)	PUNCT
ejpam-4573	214	36	[	[	X
ejpam-4573	214	37	f+([v	f+([v	X
ejpam-4573	214	38	(	(	PUNCT
ejpam-4573	214	39	λ	λ	PROPN
ejpam-4573	214	40	,	,	PUNCT
ejpam-4573	214	41	sp)](λ	sp)](λ	PROPN
ejpam-4573	214	42	,	,	PUNCT
ejpam-4573	214	43	sp	sp	NOUN
ejpam-4573	214	44	)	)	PUNCT
ejpam-4573	214	45	)	)	PUNCT
ejpam-4573	214	46	]	]	PUNCT
ejpam-4573	214	47	(	(	PUNCT
ejpam-4573	214	48	λ	λ	NOUN
ejpam-4573	214	49	,	,	PUNCT
ejpam-4573	214	50	sp	sp	NOUN
ejpam-4573	214	51	)	)	PUNCT
ejpam-4573	214	52	⊆	⊆	NUM
ejpam-4573	214	53	f+(v	f+(v	NUM
ejpam-4573	214	54	(	(	PUNCT
ejpam-4573	214	55	λ	λ	NOUN
ejpam-4573	214	56	,	,	PUNCT
ejpam-4573	214	57	sp	sp	NOUN
ejpam-4573	214	58	)	)	PUNCT
ejpam-4573	214	59	)	)	PUNCT
ejpam-4573	214	60	for	for	ADP
ejpam-4573	214	61	every	every	DET
ejpam-4573	214	62	p(λ	p(λ	NOUN
ejpam-4573	214	63	,	,	PUNCT
ejpam-4573	214	64	sp)-open	sp)-open	NOUN
ejpam-4573	214	65	set	set	VERB
ejpam-4573	214	66	v	v	NOUN
ejpam-4573	214	67	of	of	ADP
ejpam-4573	214	68	y	y	PROPN
ejpam-4573	214	69	;	;	PUNCT
ejpam-4573	215	1	(	(	PUNCT
ejpam-4573	215	2	3	3	X
ejpam-4573	215	3	)	)	PUNCT
ejpam-4573	215	4	[	[	X
ejpam-4573	215	5	f+(v	f+(v	NOUN
ejpam-4573	215	6	)	)	PUNCT
ejpam-4573	215	7	]	]	PUNCT
ejpam-4573	215	8	(	(	PUNCT
ejpam-4573	215	9	λ	λ	NOUN
ejpam-4573	215	10	,	,	PUNCT
ejpam-4573	215	11	sp	sp	NOUN
ejpam-4573	215	12	)	)	PUNCT
ejpam-4573	215	13	⊆	⊆	NUM
ejpam-4573	215	14	f+(v	f+(v	NUM
ejpam-4573	215	15	(	(	PUNCT
ejpam-4573	215	16	λ	λ	NOUN
ejpam-4573	215	17	,	,	PUNCT
ejpam-4573	215	18	sp	sp	NOUN
ejpam-4573	215	19	)	)	PUNCT
ejpam-4573	215	20	)	)	PUNCT
ejpam-4573	215	21	for	for	ADP
ejpam-4573	215	22	every	every	DET
ejpam-4573	215	23	p(λ	p(λ	NOUN
ejpam-4573	215	24	,	,	PUNCT
ejpam-4573	215	25	sp)-open	sp)-open	NOUN
ejpam-4573	215	26	set	set	VERB
ejpam-4573	215	27	v	v	NOUN
ejpam-4573	215	28	of	of	ADP
ejpam-4573	215	29	y	y	PROPN
ejpam-4573	215	30	;	;	PUNCT
ejpam-4573	215	31	(	(	PUNCT
ejpam-4573	215	32	4	4	X
ejpam-4573	215	33	)	)	PUNCT
ejpam-4573	215	34	f−(v	f−(v	NOUN
ejpam-4573	215	35	)	)	PUNCT
ejpam-4573	215	36	⊆	⊆	NUM
ejpam-4573	216	1	[	[	X
ejpam-4573	216	2	f−(v	f−(v	ADJ
ejpam-4573	216	3	(	(	PUNCT
ejpam-4573	216	4	λ	λ	PROPN
ejpam-4573	216	5	,	,	PUNCT
ejpam-4573	216	6	sp))](λ	sp))](λ	PROPN
ejpam-4573	216	7	,	,	PUNCT
ejpam-4573	216	8	sp	sp	NOUN
ejpam-4573	216	9	)	)	PUNCT
ejpam-4573	216	10	for	for	ADP
ejpam-4573	216	11	every	every	DET
ejpam-4573	216	12	p(λ	p(λ	NOUN
ejpam-4573	216	13	,	,	PUNCT
ejpam-4573	216	14	sp)-open	sp)-open	NOUN
ejpam-4573	216	15	set	set	VERB
ejpam-4573	216	16	v	v	NOUN
ejpam-4573	216	17	of	of	ADP
ejpam-4573	216	18	y	y	PROPN
ejpam-4573	216	19	.	.	PUNCT
ejpam-4573	217	1	proof	proof	NOUN
ejpam-4573	217	2	.	.	PUNCT
ejpam-4573	218	1	the	the	DET
ejpam-4573	218	2	proof	proof	NOUN
ejpam-4573	218	3	is	be	AUX
ejpam-4573	218	4	similar	similar	ADJ
ejpam-4573	218	5	to	to	ADP
ejpam-4573	218	6	that	that	PRON
ejpam-4573	218	7	of	of	ADP
ejpam-4573	218	8	theorem	theorem	ADJ
ejpam-4573	218	9	5	5	NUM
ejpam-4573	218	10	.	.	PUNCT
ejpam-4573	218	11	corollary	corollary	ADJ
ejpam-4573	218	12	3	3	NUM
ejpam-4573	218	13	.	.	PUNCT
ejpam-4573	219	1	for	for	ADP
ejpam-4573	219	2	a	a	DET
ejpam-4573	219	3	function	function	NOUN
ejpam-4573	219	4	f	f	NOUN
ejpam-4573	219	5	:	:	PUNCT
ejpam-4573	219	6	(	(	PUNCT
ejpam-4573	219	7	x	x	X
ejpam-4573	219	8	,	,	PUNCT
ejpam-4573	219	9	τ	τ	X
ejpam-4573	219	10	)	)	PUNCT
ejpam-4573	219	11	→	→	SYM
ejpam-4573	219	12	(	(	PUNCT
ejpam-4573	219	13	y	y	PROPN
ejpam-4573	219	14	,	,	PUNCT
ejpam-4573	219	15	σ	σ	PROPN
ejpam-4573	219	16	)	)	PUNCT
ejpam-4573	219	17	,	,	PUNCT
ejpam-4573	219	18	the	the	DET
ejpam-4573	219	19	following	follow	VERB
ejpam-4573	219	20	properties	property	NOUN
ejpam-4573	219	21	are	be	AUX
ejpam-4573	219	22	equivalent	equivalent	ADJ
ejpam-4573	219	23	:	:	PUNCT
ejpam-4573	219	24	(	(	PUNCT
ejpam-4573	219	25	1	1	X
ejpam-4573	219	26	)	)	PUNCT
ejpam-4573	219	27	f	f	PROPN
ejpam-4573	219	28	is	be	AUX
ejpam-4573	219	29	weakly	weakly	ADJ
ejpam-4573	219	30	(	(	PUNCT
ejpam-4573	219	31	λ	λ	NOUN
ejpam-4573	219	32	,	,	PUNCT
ejpam-4573	219	33	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	219	34	;	;	PUNCT
ejpam-4573	219	35	(	(	PUNCT
ejpam-4573	219	36	2	2	X
ejpam-4573	219	37	)	)	PUNCT
ejpam-4573	219	38	[	[	X
ejpam-4573	219	39	f−1([v	f−1([v	ADJ
ejpam-4573	219	40	(	(	PUNCT
ejpam-4573	219	41	λ	λ	NOUN
ejpam-4573	219	42	,	,	PUNCT
ejpam-4573	219	43	sp)](λ	sp)](λ	PROPN
ejpam-4573	219	44	,	,	PUNCT
ejpam-4573	219	45	sp	sp	NOUN
ejpam-4573	219	46	)	)	PUNCT
ejpam-4573	219	47	)	)	PUNCT
ejpam-4573	219	48	]	]	PUNCT
ejpam-4573	220	1	(	(	PUNCT
ejpam-4573	220	2	λ	λ	NOUN
ejpam-4573	220	3	,	,	PUNCT
ejpam-4573	220	4	sp	sp	NOUN
ejpam-4573	220	5	)	)	PUNCT
ejpam-4573	220	6	⊆	⊆	NUM
ejpam-4573	220	7	f−1(v	f−1(v	NOUN
ejpam-4573	220	8	(	(	PUNCT
ejpam-4573	220	9	λ	λ	PROPN
ejpam-4573	220	10	,	,	PUNCT
ejpam-4573	220	11	sp	sp	NOUN
ejpam-4573	220	12	)	)	PUNCT
ejpam-4573	220	13	)	)	PUNCT
ejpam-4573	220	14	for	for	ADP
ejpam-4573	220	15	every	every	DET
ejpam-4573	220	16	p(λ	p(λ	NOUN
ejpam-4573	220	17	,	,	PUNCT
ejpam-4573	220	18	sp)-open	sp)-open	NOUN
ejpam-4573	220	19	set	set	VERB
ejpam-4573	220	20	v	v	NOUN
ejpam-4573	220	21	of	of	ADP
ejpam-4573	220	22	y	y	PROPN
ejpam-4573	220	23	;	;	PUNCT
ejpam-4573	220	24	c.	c.	PROPN
ejpam-4573	220	25	boonpok	boonpok	PROPN
ejpam-4573	220	26	,	,	PUNCT
ejpam-4573	220	27	p.	p.	NOUN
ejpam-4573	220	28	pue	pue	NOUN
ejpam-4573	220	29	-	-	PUNCT
ejpam-4573	220	30	on	on	ADP
ejpam-4573	220	31	/	/	SYM
ejpam-4573	220	32	eur	eur	NOUN
ejpam-4573	220	33	.	.	PUNCT
ejpam-4573	221	1	j.	j.	PROPN
ejpam-4573	221	2	pure	pure	PROPN
ejpam-4573	221	3	appl	appl	PROPN
ejpam-4573	221	4	.	.	PROPN
ejpam-4573	221	5	math	math	PROPN
ejpam-4573	221	6	,	,	PUNCT
ejpam-4573	221	7	16	16	NUM
ejpam-4573	221	8	(	(	PUNCT
ejpam-4573	221	9	2	2	NUM
ejpam-4573	221	10	)	)	PUNCT
ejpam-4573	221	11	(	(	PUNCT
ejpam-4573	221	12	2023	2023	NUM
ejpam-4573	221	13	)	)	PUNCT
ejpam-4573	221	14	,	,	PUNCT
ejpam-4573	221	15	1047	1047	NUM
ejpam-4573	221	16	-	-	SYM
ejpam-4573	221	17	1058	1058	NUM
ejpam-4573	221	18	1054	1054	NUM
ejpam-4573	221	19	(	(	PUNCT
ejpam-4573	221	20	3	3	NUM
ejpam-4573	221	21	)	)	PUNCT
ejpam-4573	222	1	[	[	X
ejpam-4573	222	2	f−1(v	f−1(v	NOUN
ejpam-4573	222	3	)	)	PUNCT
ejpam-4573	222	4	]	]	PUNCT
ejpam-4573	222	5	(	(	PUNCT
ejpam-4573	222	6	λ	λ	NOUN
ejpam-4573	222	7	,	,	PUNCT
ejpam-4573	222	8	sp	sp	NOUN
ejpam-4573	222	9	)	)	PUNCT
ejpam-4573	222	10	⊆	⊆	NUM
ejpam-4573	222	11	f−1(v	f−1(v	NOUN
ejpam-4573	222	12	(	(	PUNCT
ejpam-4573	222	13	λ	λ	PROPN
ejpam-4573	222	14	,	,	PUNCT
ejpam-4573	222	15	sp	sp	NOUN
ejpam-4573	222	16	)	)	PUNCT
ejpam-4573	222	17	)	)	PUNCT
ejpam-4573	222	18	for	for	ADP
ejpam-4573	222	19	every	every	DET
ejpam-4573	222	20	p(λ	p(λ	NOUN
ejpam-4573	222	21	,	,	PUNCT
ejpam-4573	222	22	sp)-open	sp)-open	NOUN
ejpam-4573	222	23	set	set	VERB
ejpam-4573	222	24	v	v	NOUN
ejpam-4573	222	25	of	of	ADP
ejpam-4573	222	26	y	y	PROPN
ejpam-4573	222	27	;	;	PUNCT
ejpam-4573	222	28	(	(	PUNCT
ejpam-4573	222	29	4	4	X
ejpam-4573	222	30	)	)	PUNCT
ejpam-4573	222	31	f−1(v	f−1(v	NOUN
ejpam-4573	222	32	)	)	PUNCT
ejpam-4573	222	33	⊆	⊆	NUM
ejpam-4573	223	1	[	[	X
ejpam-4573	223	2	f−1(v	f−1(v	NOUN
ejpam-4573	223	3	(	(	PUNCT
ejpam-4573	223	4	λ	λ	PROPN
ejpam-4573	223	5	,	,	PUNCT
ejpam-4573	223	6	sp))](λ	sp))](λ	PROPN
ejpam-4573	223	7	,	,	PUNCT
ejpam-4573	223	8	sp	sp	NOUN
ejpam-4573	223	9	)	)	PUNCT
ejpam-4573	223	10	for	for	ADP
ejpam-4573	223	11	every	every	DET
ejpam-4573	223	12	p(λ	p(λ	NOUN
ejpam-4573	223	13	,	,	PUNCT
ejpam-4573	223	14	sp)-open	sp)-open	NOUN
ejpam-4573	223	15	set	set	VERB
ejpam-4573	223	16	v	v	NOUN
ejpam-4573	223	17	of	of	ADP
ejpam-4573	223	18	y	y	PROPN
ejpam-4573	223	19	.	.	PUNCT
ejpam-4573	224	1	definition	definition	NOUN
ejpam-4573	224	2	3	3	NUM
ejpam-4573	224	3	.	.	PUNCT
ejpam-4573	225	1	[	[	X
ejpam-4573	225	2	3	3	X
ejpam-4573	225	3	]	]	PUNCT
ejpam-4573	225	4	let	let	VERB
ejpam-4573	225	5	a	a	PRON
ejpam-4573	225	6	be	be	AUX
ejpam-4573	225	7	a	a	DET
ejpam-4573	225	8	subset	subset	NOUN
ejpam-4573	225	9	of	of	ADP
ejpam-4573	225	10	a	a	DET
ejpam-4573	225	11	topological	topological	ADJ
ejpam-4573	225	12	space	space	NOUN
ejpam-4573	225	13	(	(	PUNCT
ejpam-4573	225	14	x	x	X
ejpam-4573	225	15	,	,	PUNCT
ejpam-4573	225	16	τ	τ	PROPN
ejpam-4573	225	17	)	)	PUNCT
ejpam-4573	225	18	.	.	PUNCT
ejpam-4573	226	1	the	the	DET
ejpam-4573	226	2	θ(λ	θ(λ	PROPN
ejpam-4573	226	3	,	,	PUNCT
ejpam-4573	226	4	sp)-closure	sp)-closure	NOUN
ejpam-4573	226	5	of	of	ADP
ejpam-4573	226	6	a	a	DET
ejpam-4573	226	7	,	,	PUNCT
ejpam-4573	226	8	aθ(λ	aθ(λ	NOUN
ejpam-4573	226	9	,	,	PUNCT
ejpam-4573	226	10	sp	sp	NOUN
ejpam-4573	226	11	)	)	PUNCT
ejpam-4573	226	12	,	,	PUNCT
ejpam-4573	226	13	is	be	AUX
ejpam-4573	226	14	defined	define	VERB
ejpam-4573	226	15	as	as	SCONJ
ejpam-4573	226	16	follows	follow	VERB
ejpam-4573	226	17	:	:	PUNCT
ejpam-4573	226	18	aθ(λ	aθ(λ	NOUN
ejpam-4573	226	19	,	,	PUNCT
ejpam-4573	226	20	sp	sp	NOUN
ejpam-4573	226	21	)	)	PUNCT
ejpam-4573	226	22	=	=	PRON
ejpam-4573	227	1	{	{	PUNCT
ejpam-4573	227	2	x	x	PUNCT
ejpam-4573	227	3	∈	∈	NOUN
ejpam-4573	227	4	x	x	PUNCT
ejpam-4573	227	5	|	|	ADV
ejpam-4573	227	6	a	a	DET
ejpam-4573	227	7	∩	∩	ADJ
ejpam-4573	227	8	u	u	NOUN
ejpam-4573	227	9	(	(	PUNCT
ejpam-4573	227	10	λ	λ	PROPN
ejpam-4573	227	11	,	,	PUNCT
ejpam-4573	227	12	sp	sp	NOUN
ejpam-4573	227	13	)	)	PUNCT
ejpam-4573	227	14	̸=	̸=	NOUN
ejpam-4573	227	15	∅	∅	NOUN
ejpam-4573	227	16	for	for	ADP
ejpam-4573	227	17	each	each	DET
ejpam-4573	227	18	u	u	PROPN
ejpam-4573	227	19	∈	∈	PROPN
ejpam-4573	227	20	λspo(x	λspo(x	PROPN
ejpam-4573	227	21	,	,	PUNCT
ejpam-4573	227	22	τ	τ	X
ejpam-4573	227	23	)	)	PUNCT
ejpam-4573	227	24	containing	contain	VERB
ejpam-4573	227	25	x	x	X
ejpam-4573	227	26	}	}	PUNCT
ejpam-4573	227	27	.	.	PUNCT
ejpam-4573	228	1	a	a	DET
ejpam-4573	228	2	subset	subset	NOUN
ejpam-4573	228	3	a	a	PRON
ejpam-4573	228	4	of	of	ADP
ejpam-4573	228	5	a	a	DET
ejpam-4573	228	6	topological	topological	ADJ
ejpam-4573	228	7	space	space	NOUN
ejpam-4573	228	8	(	(	PUNCT
ejpam-4573	228	9	x	x	X
ejpam-4573	228	10	,	,	PUNCT
ejpam-4573	228	11	τ	τ	X
ejpam-4573	228	12	)	)	PUNCT
ejpam-4573	228	13	is	be	AUX
ejpam-4573	228	14	said	say	VERB
ejpam-4573	228	15	to	to	PART
ejpam-4573	228	16	be	be	AUX
ejpam-4573	228	17	θ(λ	θ(λ	PROPN
ejpam-4573	228	18	,	,	PUNCT
ejpam-4573	228	19	sp)-closed	sp)-close	VERB
ejpam-4573	228	20	[	[	X
ejpam-4573	228	21	3	3	X
ejpam-4573	228	22	]	]	X
ejpam-4573	228	23	if	if	SCONJ
ejpam-4573	228	24	a	a	DET
ejpam-4573	228	25	=	=	NOUN
ejpam-4573	228	26	aθ(λ	aθ(λ	NOUN
ejpam-4573	228	27	,	,	PUNCT
ejpam-4573	228	28	sp	sp	NOUN
ejpam-4573	228	29	)	)	PUNCT
ejpam-4573	228	30	.	.	PUNCT
ejpam-4573	229	1	the	the	DET
ejpam-4573	229	2	complement	complement	NOUN
ejpam-4573	229	3	of	of	ADP
ejpam-4573	229	4	a	a	DET
ejpam-4573	229	5	θ(λ	θ(λ	PROPN
ejpam-4573	229	6	,	,	PUNCT
ejpam-4573	229	7	sp)-closed	sp)-close	VERB
ejpam-4573	229	8	set	set	NOUN
ejpam-4573	229	9	is	be	AUX
ejpam-4573	229	10	said	say	VERB
ejpam-4573	229	11	to	to	PART
ejpam-4573	229	12	be	be	AUX
ejpam-4573	229	13	θ(λ	θ(λ	PROPN
ejpam-4573	229	14	,	,	PUNCT
ejpam-4573	229	15	sp)-open	sp)-open	NOUN
ejpam-4573	229	16	.	.	PUNCT
ejpam-4573	230	1	the	the	DET
ejpam-4573	230	2	union	union	NOUN
ejpam-4573	230	3	of	of	ADP
ejpam-4573	230	4	all	all	DET
ejpam-4573	230	5	θ(λ	θ(λ	PROPN
ejpam-4573	230	6	,	,	PUNCT
ejpam-4573	230	7	sp)-open	sp)-open	ADJ
ejpam-4573	230	8	sets	set	NOUN
ejpam-4573	230	9	contained	contain	VERB
ejpam-4573	230	10	in	in	ADP
ejpam-4573	230	11	a	a	PRON
ejpam-4573	230	12	is	be	AUX
ejpam-4573	230	13	called	call	VERB
ejpam-4573	230	14	the	the	DET
ejpam-4573	230	15	θ(λ	θ(λ	PROPN
ejpam-4573	230	16	,	,	PUNCT
ejpam-4573	230	17	sp)-interior	sp)-interior	NOUN
ejpam-4573	230	18	of	of	ADP
ejpam-4573	230	19	a	a	PRON
ejpam-4573	230	20	and	and	CCONJ
ejpam-4573	230	21	is	be	AUX
ejpam-4573	230	22	denoted	denote	VERB
ejpam-4573	230	23	by	by	ADP
ejpam-4573	230	24	aθ(λ	aθ(λ	NOUN
ejpam-4573	230	25	,	,	PUNCT
ejpam-4573	230	26	sp	sp	NOUN
ejpam-4573	230	27	)	)	PUNCT
ejpam-4573	230	28	.	.	PUNCT
ejpam-4573	231	1	lemma	lemma	PROPN
ejpam-4573	231	2	3	3	X
ejpam-4573	231	3	.	.	PUNCT
ejpam-4573	232	1	[	[	X
ejpam-4573	232	2	3	3	X
ejpam-4573	232	3	]	]	PUNCT
ejpam-4573	232	4	for	for	ADP
ejpam-4573	232	5	a	a	DET
ejpam-4573	232	6	subset	subset	NOUN
ejpam-4573	232	7	a	a	PRON
ejpam-4573	232	8	of	of	ADP
ejpam-4573	232	9	a	a	DET
ejpam-4573	232	10	topological	topological	ADJ
ejpam-4573	232	11	space	space	NOUN
ejpam-4573	232	12	(	(	PUNCT
ejpam-4573	232	13	x	x	X
ejpam-4573	232	14	,	,	PUNCT
ejpam-4573	232	15	τ	τ	PROPN
ejpam-4573	232	16	)	)	PUNCT
ejpam-4573	232	17	,	,	PUNCT
ejpam-4573	232	18	the	the	DET
ejpam-4573	232	19	following	follow	VERB
ejpam-4573	232	20	properties	property	NOUN
ejpam-4573	232	21	hold	hold	VERB
ejpam-4573	232	22	:	:	PUNCT
ejpam-4573	232	23	(	(	PUNCT
ejpam-4573	232	24	1	1	X
ejpam-4573	232	25	)	)	PUNCT
ejpam-4573	232	26	if	if	SCONJ
ejpam-4573	232	27	a	a	PRON
ejpam-4573	232	28	is	be	AUX
ejpam-4573	232	29	(	(	PUNCT
ejpam-4573	232	30	λ	λ	NOUN
ejpam-4573	232	31	,	,	PUNCT
ejpam-4573	232	32	sp)-open	sp)-open	ADJ
ejpam-4573	232	33	in	in	ADP
ejpam-4573	232	34	x	x	NOUN
ejpam-4573	232	35	,	,	PUNCT
ejpam-4573	232	36	then	then	ADV
ejpam-4573	232	37	a(λ	a(λ	ADV
ejpam-4573	232	38	,	,	PUNCT
ejpam-4573	232	39	sp	sp	NOUN
ejpam-4573	232	40	)	)	PUNCT
ejpam-4573	232	41	=	=	SYM
ejpam-4573	232	42	aθ(λ	aθ(λ	NOUN
ejpam-4573	232	43	,	,	PUNCT
ejpam-4573	232	44	sp	sp	NOUN
ejpam-4573	232	45	)	)	PUNCT
ejpam-4573	232	46	.	.	PUNCT
ejpam-4573	233	1	(	(	PUNCT
ejpam-4573	233	2	2	2	X
ejpam-4573	233	3	)	)	PUNCT
ejpam-4573	233	4	aθ(λ	aθ(λ	NOUN
ejpam-4573	233	5	,	,	PUNCT
ejpam-4573	233	6	sp	sp	NOUN
ejpam-4573	233	7	)	)	PUNCT
ejpam-4573	233	8	is	be	AUX
ejpam-4573	233	9	(	(	PUNCT
ejpam-4573	233	10	λ	λ	X
ejpam-4573	233	11	,	,	PUNCT
ejpam-4573	233	12	sp)-closed	sp)-close	VERB
ejpam-4573	233	13	.	.	PUNCT
ejpam-4573	234	1	definition	definition	NOUN
ejpam-4573	234	2	4	4	NUM
ejpam-4573	234	3	.	.	PUNCT
ejpam-4573	235	1	[	[	X
ejpam-4573	235	2	3	3	X
ejpam-4573	235	3	]	]	PUNCT
ejpam-4573	235	4	a	a	DET
ejpam-4573	235	5	multifunction	multifunction	NOUN
ejpam-4573	235	6	f	f	NOUN
ejpam-4573	235	7	:	:	PUNCT
ejpam-4573	235	8	(	(	PUNCT
ejpam-4573	235	9	x	x	X
ejpam-4573	235	10	,	,	PUNCT
ejpam-4573	235	11	τ	τ	X
ejpam-4573	235	12	)	)	PUNCT
ejpam-4573	235	13	→	→	SYM
ejpam-4573	235	14	(	(	PUNCT
ejpam-4573	235	15	y	y	PROPN
ejpam-4573	235	16	,	,	PUNCT
ejpam-4573	235	17	σ	σ	PROPN
ejpam-4573	235	18	)	)	PUNCT
ejpam-4573	235	19	is	be	AUX
ejpam-4573	235	20	said	say	VERB
ejpam-4573	235	21	to	to	PART
ejpam-4573	235	22	be	be	AUX
ejpam-4573	235	23	:	:	PUNCT
ejpam-4573	235	24	(	(	PUNCT
ejpam-4573	235	25	i	i	NOUN
ejpam-4573	235	26	)	)	PUNCT
ejpam-4573	235	27	upper	upper	ADJ
ejpam-4573	235	28	(	(	PUNCT
ejpam-4573	235	29	λ	λ	PROPN
ejpam-4573	235	30	,	,	PUNCT
ejpam-4573	235	31	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	235	32	if	if	SCONJ
ejpam-4573	235	33	,	,	PUNCT
ejpam-4573	235	34	for	for	SCONJ
ejpam-4573	235	35	each	each	DET
ejpam-4573	235	36	x	x	SYM
ejpam-4573	235	37	∈	∈	PROPN
ejpam-4573	235	38	x	x	X
ejpam-4573	235	39	and	and	CCONJ
ejpam-4573	235	40	each	each	DET
ejpam-4573	235	41	(	(	PUNCT
ejpam-4573	235	42	λ	λ	PROPN
ejpam-4573	235	43	,	,	PUNCT
ejpam-4573	235	44	sp)-open	sp)-open	NOUN
ejpam-4573	235	45	set	set	VERB
ejpam-4573	235	46	v	v	NUM
ejpam-4573	235	47	of	of	ADP
ejpam-4573	235	48	y	y	PRON
ejpam-4573	235	49	such	such	ADJ
ejpam-4573	235	50	that	that	SCONJ
ejpam-4573	235	51	f	f	PROPN
ejpam-4573	235	52	(	(	PUNCT
ejpam-4573	235	53	x	x	X
ejpam-4573	235	54	)	)	PUNCT
ejpam-4573	235	55	⊆	⊆	NUM
ejpam-4573	235	56	v	v	NOUN
ejpam-4573	235	57	,	,	PUNCT
ejpam-4573	235	58	there	there	PRON
ejpam-4573	235	59	exists	exist	VERB
ejpam-4573	235	60	a	a	DET
ejpam-4573	235	61	(	(	PUNCT
ejpam-4573	235	62	λ	λ	NOUN
ejpam-4573	235	63	,	,	PUNCT
ejpam-4573	235	64	sp)-open	sp)-open	NOUN
ejpam-4573	235	65	set	set	VERB
ejpam-4573	235	66	u	u	NOUN
ejpam-4573	235	67	of	of	ADP
ejpam-4573	235	68	x	x	PUNCT
ejpam-4573	235	69	containing	contain	VERB
ejpam-4573	235	70	x	x	PUNCT
ejpam-4573	236	1	such	such	ADJ
ejpam-4573	236	2	that	that	SCONJ
ejpam-4573	236	3	f	f	PROPN
ejpam-4573	236	4	(	(	PUNCT
ejpam-4573	236	5	u	u	NOUN
ejpam-4573	236	6	)	)	PUNCT
ejpam-4573	236	7	⊆	⊆	NUM
ejpam-4573	236	8	v	v	NOUN
ejpam-4573	236	9	;	;	PUNCT
ejpam-4573	236	10	(	(	PUNCT
ejpam-4573	236	11	ii	ii	NOUN
ejpam-4573	236	12	)	)	PUNCT
ejpam-4573	236	13	lower	low	ADJ
ejpam-4573	236	14	(	(	PUNCT
ejpam-4573	236	15	λ	λ	NOUN
ejpam-4573	236	16	,	,	PUNCT
ejpam-4573	236	17	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	236	18	if	if	SCONJ
ejpam-4573	236	19	,	,	PUNCT
ejpam-4573	236	20	for	for	SCONJ
ejpam-4573	236	21	each	each	DET
ejpam-4573	236	22	x	x	SYM
ejpam-4573	236	23	∈	∈	PROPN
ejpam-4573	236	24	x	x	X
ejpam-4573	236	25	and	and	CCONJ
ejpam-4573	236	26	each	each	DET
ejpam-4573	236	27	(	(	PUNCT
ejpam-4573	236	28	λ	λ	PROPN
ejpam-4573	236	29	,	,	PUNCT
ejpam-4573	236	30	sp)-open	sp)-open	NOUN
ejpam-4573	236	31	set	set	VERB
ejpam-4573	236	32	v	v	NUM
ejpam-4573	236	33	of	of	ADP
ejpam-4573	236	34	y	y	PRON
ejpam-4573	236	35	such	such	ADJ
ejpam-4573	236	36	that	that	SCONJ
ejpam-4573	236	37	f	f	PROPN
ejpam-4573	236	38	(	(	PUNCT
ejpam-4573	236	39	x	x	NOUN
ejpam-4573	236	40	)	)	PUNCT
ejpam-4573	236	41	∩	∩	NOUN
ejpam-4573	236	42	v	v	ADP
ejpam-4573	236	43	̸=	̸=	PROPN
ejpam-4573	236	44	∅	∅	NOUN
ejpam-4573	236	45	,	,	PUNCT
ejpam-4573	236	46	there	there	PRON
ejpam-4573	236	47	exists	exist	VERB
ejpam-4573	236	48	a	a	DET
ejpam-4573	236	49	(	(	PUNCT
ejpam-4573	236	50	λ	λ	NOUN
ejpam-4573	236	51	,	,	PUNCT
ejpam-4573	236	52	sp)-open	sp)-open	NOUN
ejpam-4573	236	53	set	set	VERB
ejpam-4573	236	54	u	u	NOUN
ejpam-4573	236	55	of	of	ADP
ejpam-4573	236	56	x	x	PUNCT
ejpam-4573	236	57	containing	contain	VERB
ejpam-4573	236	58	x	x	PUNCT
ejpam-4573	236	59	such	such	ADJ
ejpam-4573	236	60	that	that	SCONJ
ejpam-4573	236	61	f	f	PROPN
ejpam-4573	236	62	(	(	PUNCT
ejpam-4573	236	63	z	z	NOUN
ejpam-4573	236	64	)	)	PUNCT
ejpam-4573	236	65	∩	∩	NOUN
ejpam-4573	236	66	v	v	ADP
ejpam-4573	236	67	̸=	̸=	PROPN
ejpam-4573	236	68	∅	∅	NOUN
ejpam-4573	236	69	for	for	ADP
ejpam-4573	236	70	each	each	DET
ejpam-4573	236	71	z	z	NOUN
ejpam-4573	236	72	∈	∈	PROPN
ejpam-4573	236	73	u	u	NOUN
ejpam-4573	236	74	.	.	PUNCT
ejpam-4573	237	1	definition	definition	NOUN
ejpam-4573	237	2	5	5	NUM
ejpam-4573	237	3	.	.	PUNCT
ejpam-4573	238	1	[	[	X
ejpam-4573	238	2	3	3	X
ejpam-4573	238	3	]	]	PUNCT
ejpam-4573	238	4	a	a	DET
ejpam-4573	238	5	topological	topological	ADJ
ejpam-4573	238	6	space	space	NOUN
ejpam-4573	238	7	(	(	PUNCT
ejpam-4573	238	8	x	x	X
ejpam-4573	238	9	,	,	PUNCT
ejpam-4573	238	10	τ	τ	X
ejpam-4573	238	11	)	)	PUNCT
ejpam-4573	238	12	is	be	AUX
ejpam-4573	238	13	said	say	VERB
ejpam-4573	238	14	to	to	PART
ejpam-4573	238	15	be	be	AUX
ejpam-4573	238	16	λsp	λsp	NOUN
ejpam-4573	238	17	-	-	ADJ
ejpam-4573	238	18	regular	regular	ADJ
ejpam-4573	238	19	if	if	SCONJ
ejpam-4573	238	20	,	,	PUNCT
ejpam-4573	238	21	for	for	ADP
ejpam-4573	238	22	each	each	DET
ejpam-4573	238	23	(	(	PUNCT
ejpam-4573	238	24	λ	λ	PROPN
ejpam-4573	238	25	,	,	PUNCT
ejpam-4573	238	26	sp)closed	sp)close	VERB
ejpam-4573	238	27	set	set	VERB
ejpam-4573	238	28	f	f	PROPN
ejpam-4573	238	29	and	and	CCONJ
ejpam-4573	238	30	each	each	DET
ejpam-4573	238	31	x	x	PROPN
ejpam-4573	238	32	̸∈	̸∈	PROPN
ejpam-4573	238	33	f	f	PROPN
ejpam-4573	238	34	,	,	PUNCT
ejpam-4573	238	35	there	there	PRON
ejpam-4573	238	36	exist	exist	VERB
ejpam-4573	238	37	disjoint	disjoint	NOUN
ejpam-4573	238	38	(	(	PUNCT
ejpam-4573	238	39	λ	λ	NOUN
ejpam-4573	238	40	,	,	PUNCT
ejpam-4573	238	41	sp)-open	sp)-open	NOUN
ejpam-4573	238	42	sets	set	VERB
ejpam-4573	238	43	u	u	NOUN
ejpam-4573	238	44	and	and	CCONJ
ejpam-4573	238	45	v	v	ADP
ejpam-4573	238	46	such	such	ADJ
ejpam-4573	238	47	that	that	SCONJ
ejpam-4573	238	48	x	x	SYM
ejpam-4573	238	49	∈	∈	PROPN
ejpam-4573	238	50	u	u	NOUN
ejpam-4573	238	51	and	and	CCONJ
ejpam-4573	238	52	f	f	PROPN
ejpam-4573	238	53	⊆	⊆	NUM
ejpam-4573	238	54	v	v	NOUN
ejpam-4573	238	55	.	.	PUNCT
ejpam-4573	239	1	lemma	lemma	PROPN
ejpam-4573	239	2	4	4	NUM
ejpam-4573	239	3	.	.	PUNCT
ejpam-4573	240	1	[	[	X
ejpam-4573	240	2	3	3	X
ejpam-4573	240	3	]	]	X
ejpam-4573	240	4	let	let	VERB
ejpam-4573	240	5	(	(	PUNCT
ejpam-4573	240	6	y	y	PROPN
ejpam-4573	240	7	,	,	PUNCT
ejpam-4573	240	8	σ	σ	PROPN
ejpam-4573	240	9	)	)	PUNCT
ejpam-4573	240	10	be	be	AUX
ejpam-4573	240	11	a	a	DET
ejpam-4573	240	12	λsp	λsp	NOUN
ejpam-4573	240	13	-	-	ADJ
ejpam-4573	240	14	regular	regular	ADJ
ejpam-4573	240	15	space	space	NOUN
ejpam-4573	240	16	.	.	PUNCT
ejpam-4573	241	1	for	for	ADP
ejpam-4573	241	2	a	a	DET
ejpam-4573	241	3	multifunction	multifunction	NOUN
ejpam-4573	241	4	f	f	NOUN
ejpam-4573	241	5	:	:	PUNCT
ejpam-4573	241	6	(	(	PUNCT
ejpam-4573	241	7	x	x	X
ejpam-4573	241	8	,	,	PUNCT
ejpam-4573	241	9	τ	τ	X
ejpam-4573	241	10	)	)	PUNCT
ejpam-4573	241	11	→	→	SYM
ejpam-4573	241	12	(	(	PUNCT
ejpam-4573	241	13	y	y	PROPN
ejpam-4573	241	14	,	,	PUNCT
ejpam-4573	241	15	σ	σ	PROPN
ejpam-4573	241	16	)	)	PUNCT
ejpam-4573	241	17	,	,	PUNCT
ejpam-4573	241	18	the	the	DET
ejpam-4573	241	19	following	follow	VERB
ejpam-4573	241	20	properties	property	NOUN
ejpam-4573	241	21	are	be	AUX
ejpam-4573	241	22	equivalent	equivalent	ADJ
ejpam-4573	241	23	:	:	PUNCT
ejpam-4573	241	24	(	(	PUNCT
ejpam-4573	241	25	1	1	X
ejpam-4573	241	26	)	)	PUNCT
ejpam-4573	241	27	f	f	PROPN
ejpam-4573	241	28	is	be	AUX
ejpam-4573	241	29	upper	upper	ADJ
ejpam-4573	241	30	(	(	PUNCT
ejpam-4573	241	31	λ	λ	NOUN
ejpam-4573	241	32	,	,	PUNCT
ejpam-4573	241	33	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	241	34	;	;	PUNCT
ejpam-4573	241	35	(	(	PUNCT
ejpam-4573	241	36	2	2	X
ejpam-4573	241	37	)	)	PUNCT
ejpam-4573	241	38	f−(bθ(λ	f−(bθ(λ	PROPN
ejpam-4573	241	39	,	,	PUNCT
ejpam-4573	241	40	sp	sp	NOUN
ejpam-4573	241	41	)	)	PUNCT
ejpam-4573	241	42	)	)	PUNCT
ejpam-4573	242	1	is	be	AUX
ejpam-4573	242	2	(	(	PUNCT
ejpam-4573	242	3	λ	λ	X
ejpam-4573	242	4	,	,	PUNCT
ejpam-4573	242	5	sp)-closed	sp)-close	VERB
ejpam-4573	242	6	in	in	ADP
ejpam-4573	242	7	x	x	PUNCT
ejpam-4573	242	8	for	for	ADP
ejpam-4573	242	9	every	every	DET
ejpam-4573	242	10	subset	subset	NOUN
ejpam-4573	242	11	b	b	PROPN
ejpam-4573	242	12	of	of	ADP
ejpam-4573	242	13	y	y	PROPN
ejpam-4573	242	14	;	;	PUNCT
ejpam-4573	242	15	(	(	PUNCT
ejpam-4573	242	16	3	3	X
ejpam-4573	242	17	)	)	PUNCT
ejpam-4573	242	18	f−(k	f−(k	PROPN
ejpam-4573	242	19	)	)	PUNCT
ejpam-4573	242	20	is	be	AUX
ejpam-4573	242	21	(	(	PUNCT
ejpam-4573	242	22	λ	λ	X
ejpam-4573	242	23	,	,	PUNCT
ejpam-4573	242	24	sp)-closed	sp)-close	VERB
ejpam-4573	242	25	in	in	ADP
ejpam-4573	242	26	x	x	PUNCT
ejpam-4573	242	27	for	for	ADP
ejpam-4573	242	28	every	every	DET
ejpam-4573	242	29	θ(λ	θ(λ	PROPN
ejpam-4573	242	30	,	,	PUNCT
ejpam-4573	242	31	sp)-closed	sp)-close	VERB
ejpam-4573	242	32	set	set	VERB
ejpam-4573	242	33	k	k	PROPN
ejpam-4573	242	34	of	of	ADP
ejpam-4573	242	35	y	y	PROPN
ejpam-4573	242	36	;	;	PUNCT
ejpam-4573	242	37	(	(	PUNCT
ejpam-4573	242	38	4	4	X
ejpam-4573	242	39	)	)	PUNCT
ejpam-4573	242	40	f+(v	f+(v	NOUN
ejpam-4573	242	41	)	)	PUNCT
ejpam-4573	243	1	is	be	AUX
ejpam-4573	243	2	(	(	PUNCT
ejpam-4573	243	3	λ	λ	INTJ
ejpam-4573	243	4	,	,	PUNCT
ejpam-4573	243	5	sp)-open	sp)-open	ADJ
ejpam-4573	243	6	in	in	ADP
ejpam-4573	243	7	x	x	PUNCT
ejpam-4573	243	8	for	for	ADP
ejpam-4573	243	9	every	every	DET
ejpam-4573	243	10	θ(λ	θ(λ	PROPN
ejpam-4573	243	11	,	,	PUNCT
ejpam-4573	243	12	sp)-open	sp)-open	NOUN
ejpam-4573	243	13	set	set	VERB
ejpam-4573	243	14	v	v	NOUN
ejpam-4573	243	15	of	of	ADP
ejpam-4573	243	16	y	y	PROPN
ejpam-4573	243	17	.	.	PUNCT
ejpam-4573	244	1	lemma	lemma	PROPN
ejpam-4573	244	2	5	5	NUM
ejpam-4573	244	3	.	.	PUNCT
ejpam-4573	245	1	[	[	X
ejpam-4573	245	2	3	3	X
ejpam-4573	245	3	]	]	X
ejpam-4573	245	4	let	let	VERB
ejpam-4573	245	5	(	(	PUNCT
ejpam-4573	245	6	x	x	NOUN
ejpam-4573	245	7	,	,	PUNCT
ejpam-4573	245	8	τ	τ	X
ejpam-4573	245	9	)	)	PUNCT
ejpam-4573	245	10	be	be	VERB
ejpam-4573	245	11	a	a	DET
ejpam-4573	245	12	λsp	λsp	NOUN
ejpam-4573	245	13	-	-	ADJ
ejpam-4573	245	14	regular	regular	ADJ
ejpam-4573	245	15	space	space	NOUN
ejpam-4573	245	16	.	.	PUNCT
ejpam-4573	246	1	then	then	ADV
ejpam-4573	246	2	,	,	PUNCT
ejpam-4573	246	3	the	the	DET
ejpam-4573	246	4	following	follow	VERB
ejpam-4573	246	5	properties	property	NOUN
ejpam-4573	246	6	hold	hold	VERB
ejpam-4573	246	7	:	:	PUNCT
ejpam-4573	246	8	(	(	PUNCT
ejpam-4573	246	9	1	1	X
ejpam-4573	246	10	)	)	PUNCT
ejpam-4573	246	11	a(λ	a(λ	ADV
ejpam-4573	246	12	,	,	PUNCT
ejpam-4573	246	13	sp	sp	NOUN
ejpam-4573	246	14	)	)	PUNCT
ejpam-4573	246	15	=	=	SYM
ejpam-4573	246	16	aθ(λ	aθ(λ	NOUN
ejpam-4573	246	17	,	,	PUNCT
ejpam-4573	246	18	sp	sp	NOUN
ejpam-4573	246	19	)	)	PUNCT
ejpam-4573	246	20	for	for	ADP
ejpam-4573	246	21	every	every	DET
ejpam-4573	246	22	subset	subset	NOUN
ejpam-4573	246	23	a	a	PRON
ejpam-4573	246	24	of	of	ADP
ejpam-4573	246	25	x.	x.	NOUN
ejpam-4573	246	26	(	(	PUNCT
ejpam-4573	246	27	2	2	X
ejpam-4573	246	28	)	)	PUNCT
ejpam-4573	246	29	every	every	DET
ejpam-4573	246	30	(	(	PUNCT
ejpam-4573	246	31	λ	λ	NOUN
ejpam-4573	246	32	,	,	PUNCT
ejpam-4573	246	33	sp)-open	sp)-open	ADJ
ejpam-4573	246	34	set	set	NOUN
ejpam-4573	246	35	is	be	AUX
ejpam-4573	246	36	θ(λ	θ(λ	PROPN
ejpam-4573	246	37	,	,	PUNCT
ejpam-4573	246	38	sp)-open	sp)-open	NOUN
ejpam-4573	246	39	.	.	PUNCT
ejpam-4573	247	1	c.	c.	PROPN
ejpam-4573	247	2	boonpok	boonpok	PROPN
ejpam-4573	247	3	,	,	PUNCT
ejpam-4573	247	4	p.	p.	NOUN
ejpam-4573	247	5	pue	pue	NOUN
ejpam-4573	247	6	-	-	PUNCT
ejpam-4573	247	7	on	on	ADP
ejpam-4573	247	8	/	/	SYM
ejpam-4573	247	9	eur	eur	NOUN
ejpam-4573	247	10	.	.	PUNCT
ejpam-4573	248	1	j.	j.	PROPN
ejpam-4573	248	2	pure	pure	PROPN
ejpam-4573	248	3	appl	appl	PROPN
ejpam-4573	248	4	.	.	PROPN
ejpam-4573	248	5	math	math	PROPN
ejpam-4573	248	6	,	,	PUNCT
ejpam-4573	248	7	16	16	NUM
ejpam-4573	248	8	(	(	PUNCT
ejpam-4573	248	9	2	2	NUM
ejpam-4573	248	10	)	)	PUNCT
ejpam-4573	248	11	(	(	PUNCT
ejpam-4573	248	12	2023	2023	NUM
ejpam-4573	248	13	)	)	PUNCT
ejpam-4573	248	14	,	,	PUNCT
ejpam-4573	248	15	1047	1047	NUM
ejpam-4573	248	16	-	-	SYM
ejpam-4573	248	17	1058	1058	NUM
ejpam-4573	248	18	1055	1055	NUM
ejpam-4573	248	19	theorem	theorem	NOUN
ejpam-4573	248	20	7	7	NUM
ejpam-4573	248	21	.	.	PUNCT
ejpam-4573	249	1	let	let	AUX
ejpam-4573	249	2	(	(	PUNCT
ejpam-4573	249	3	y	y	PROPN
ejpam-4573	249	4	,	,	PUNCT
ejpam-4573	249	5	σ	σ	PROPN
ejpam-4573	249	6	)	)	PUNCT
ejpam-4573	249	7	be	be	AUX
ejpam-4573	249	8	a	a	DET
ejpam-4573	249	9	λsp	λsp	NOUN
ejpam-4573	249	10	-	-	ADJ
ejpam-4573	249	11	regular	regular	ADJ
ejpam-4573	249	12	space	space	NOUN
ejpam-4573	249	13	.	.	PUNCT
ejpam-4573	250	1	for	for	ADP
ejpam-4573	250	2	a	a	DET
ejpam-4573	250	3	multifunction	multifunction	NOUN
ejpam-4573	250	4	f	f	NOUN
ejpam-4573	250	5	:	:	PUNCT
ejpam-4573	250	6	(	(	PUNCT
ejpam-4573	250	7	x	x	X
ejpam-4573	250	8	,	,	PUNCT
ejpam-4573	250	9	τ	τ	X
ejpam-4573	250	10	)	)	PUNCT
ejpam-4573	250	11	→	→	SYM
ejpam-4573	250	12	(	(	PUNCT
ejpam-4573	250	13	y	y	PROPN
ejpam-4573	250	14	,	,	PUNCT
ejpam-4573	250	15	σ	σ	PROPN
ejpam-4573	250	16	)	)	PUNCT
ejpam-4573	250	17	,	,	PUNCT
ejpam-4573	250	18	the	the	DET
ejpam-4573	250	19	following	follow	VERB
ejpam-4573	250	20	properties	property	NOUN
ejpam-4573	250	21	are	be	AUX
ejpam-4573	250	22	equivalent	equivalent	ADJ
ejpam-4573	250	23	:	:	PUNCT
ejpam-4573	250	24	(	(	PUNCT
ejpam-4573	250	25	1	1	X
ejpam-4573	250	26	)	)	PUNCT
ejpam-4573	250	27	f	f	PROPN
ejpam-4573	250	28	is	be	AUX
ejpam-4573	250	29	lower	low	ADJ
ejpam-4573	250	30	(	(	PUNCT
ejpam-4573	250	31	λ	λ	NOUN
ejpam-4573	250	32	,	,	PUNCT
ejpam-4573	250	33	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	250	34	;	;	PUNCT
ejpam-4573	250	35	(	(	PUNCT
ejpam-4573	250	36	2	2	X
ejpam-4573	250	37	)	)	PUNCT
ejpam-4573	250	38	f+[bθ(λ	f+[bθ(λ	PROPN
ejpam-4573	250	39	,	,	PUNCT
ejpam-4573	250	40	sp	sp	NOUN
ejpam-4573	250	41	)	)	PUNCT
ejpam-4573	250	42	]	]	PUNCT
ejpam-4573	251	1	is	be	AUX
ejpam-4573	251	2	(	(	PUNCT
ejpam-4573	251	3	λ	λ	X
ejpam-4573	251	4	,	,	PUNCT
ejpam-4573	251	5	sp)-closed	sp)-close	VERB
ejpam-4573	251	6	in	in	ADP
ejpam-4573	251	7	x	x	PUNCT
ejpam-4573	251	8	for	for	ADP
ejpam-4573	251	9	every	every	DET
ejpam-4573	251	10	subset	subset	NOUN
ejpam-4573	251	11	b	b	PROPN
ejpam-4573	251	12	of	of	ADP
ejpam-4573	251	13	y	y	PROPN
ejpam-4573	251	14	;	;	PUNCT
ejpam-4573	251	15	(	(	PUNCT
ejpam-4573	251	16	3	3	X
ejpam-4573	251	17	)	)	PUNCT
ejpam-4573	251	18	f+(k	f+(k	NUM
ejpam-4573	251	19	)	)	PUNCT
ejpam-4573	252	1	is	be	AUX
ejpam-4573	252	2	(	(	PUNCT
ejpam-4573	252	3	λ	λ	X
ejpam-4573	252	4	,	,	PUNCT
ejpam-4573	252	5	sp)-closed	sp)-close	VERB
ejpam-4573	252	6	in	in	ADP
ejpam-4573	252	7	x	x	PUNCT
ejpam-4573	252	8	for	for	ADP
ejpam-4573	252	9	every	every	DET
ejpam-4573	252	10	θ(λ	θ(λ	PROPN
ejpam-4573	252	11	,	,	PUNCT
ejpam-4573	252	12	sp)-closed	sp)-close	VERB
ejpam-4573	252	13	set	set	VERB
ejpam-4573	252	14	k	k	PROPN
ejpam-4573	252	15	of	of	ADP
ejpam-4573	252	16	y	y	PROPN
ejpam-4573	252	17	;	;	PUNCT
ejpam-4573	252	18	(	(	PUNCT
ejpam-4573	252	19	4	4	X
ejpam-4573	252	20	)	)	PUNCT
ejpam-4573	252	21	f−(v	f−(v	NOUN
ejpam-4573	252	22	)	)	PUNCT
ejpam-4573	252	23	is	be	AUX
ejpam-4573	252	24	(	(	PUNCT
ejpam-4573	252	25	λ	λ	INTJ
ejpam-4573	252	26	,	,	PUNCT
ejpam-4573	252	27	sp)-open	sp)-open	ADJ
ejpam-4573	252	28	in	in	ADP
ejpam-4573	252	29	x	x	PUNCT
ejpam-4573	252	30	for	for	ADP
ejpam-4573	252	31	every	every	DET
ejpam-4573	252	32	θ(λ	θ(λ	PROPN
ejpam-4573	252	33	,	,	PUNCT
ejpam-4573	252	34	sp)-open	sp)-open	NOUN
ejpam-4573	252	35	set	set	VERB
ejpam-4573	252	36	v	v	NOUN
ejpam-4573	252	37	of	of	ADP
ejpam-4573	252	38	y	y	PROPN
ejpam-4573	252	39	;	;	PUNCT
ejpam-4573	252	40	(	(	PUNCT
ejpam-4573	252	41	5	5	X
ejpam-4573	252	42	)	)	PUNCT
ejpam-4573	252	43	f	f	PROPN
ejpam-4573	252	44	is	be	AUX
ejpam-4573	252	45	lower	low	ADJ
ejpam-4573	252	46	weakly	weakly	ADJ
ejpam-4573	252	47	(	(	PUNCT
ejpam-4573	252	48	λ	λ	NOUN
ejpam-4573	252	49	,	,	PUNCT
ejpam-4573	252	50	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	252	51	.	.	PUNCT
ejpam-4573	253	1	proof	proof	NOUN
ejpam-4573	253	2	.	.	PUNCT
ejpam-4573	254	1	the	the	DET
ejpam-4573	254	2	proofs	proof	NOUN
ejpam-4573	254	3	of	of	ADP
ejpam-4573	254	4	the	the	DET
ejpam-4573	254	5	implications	implication	NOUN
ejpam-4573	254	6	:	:	PUNCT
ejpam-4573	254	7	(	(	PUNCT
ejpam-4573	254	8	1	1	X
ejpam-4573	254	9	)	)	PUNCT
ejpam-4573	254	10	⇒	⇒	NOUN
ejpam-4573	254	11	(	(	PUNCT
ejpam-4573	254	12	2	2	NUM
ejpam-4573	254	13	)	)	PUNCT
ejpam-4573	254	14	⇒	⇒	NOUN
ejpam-4573	254	15	(	(	PUNCT
ejpam-4573	254	16	3	3	NUM
ejpam-4573	254	17	)	)	PUNCT
ejpam-4573	254	18	⇒	⇒	NOUN
ejpam-4573	254	19	(	(	PUNCT
ejpam-4573	254	20	4	4	X
ejpam-4573	254	21	)	)	PUNCT
ejpam-4573	254	22	are	be	AUX
ejpam-4573	254	23	similar	similar	ADJ
ejpam-4573	254	24	as	as	ADP
ejpam-4573	254	25	in	in	ADP
ejpam-4573	254	26	lemma	lemma	PROPN
ejpam-4573	254	27	4	4	NUM
ejpam-4573	254	28	.	.	PUNCT
ejpam-4573	254	29	(	(	PUNCT
ejpam-4573	254	30	4	4	X
ejpam-4573	254	31	)	)	PUNCT
ejpam-4573	254	32	⇒	⇒	NOUN
ejpam-4573	254	33	(	(	PUNCT
ejpam-4573	254	34	5	5	NUM
ejpam-4573	254	35	):	):	PUNCT
ejpam-4573	254	36	let	let	VERB
ejpam-4573	254	37	v	v	PART
ejpam-4573	254	38	be	be	AUX
ejpam-4573	254	39	any	any	DET
ejpam-4573	254	40	(	(	PUNCT
ejpam-4573	254	41	λ	λ	NOUN
ejpam-4573	254	42	,	,	PUNCT
ejpam-4573	254	43	sp)-open	sp)-open	ADJ
ejpam-4573	254	44	set	set	NOUN
ejpam-4573	254	45	of	of	ADP
ejpam-4573	254	46	y	y	PROPN
ejpam-4573	254	47	.	.	PUNCT
ejpam-4573	255	1	since	since	SCONJ
ejpam-4573	255	2	(	(	PUNCT
ejpam-4573	255	3	y	y	PROPN
ejpam-4573	255	4	,	,	PUNCT
ejpam-4573	255	5	σ	σ	PROPN
ejpam-4573	255	6	)	)	PUNCT
ejpam-4573	255	7	is	be	AUX
ejpam-4573	255	8	λsp	λsp	NOUN
ejpam-4573	255	9	-	-	PUNCT
ejpam-4573	255	10	regular	regular	ADJ
ejpam-4573	255	11	,	,	PUNCT
ejpam-4573	255	12	by	by	ADP
ejpam-4573	255	13	lemma	lemma	PROPN
ejpam-4573	255	14	5	5	NUM
ejpam-4573	255	15	,	,	PUNCT
ejpam-4573	255	16	v	v	NOUN
ejpam-4573	255	17	is	be	AUX
ejpam-4573	255	18	θ(λ	θ(λ	PROPN
ejpam-4573	255	19	,	,	PUNCT
ejpam-4573	255	20	sp)-open	sp)-open	VERB
ejpam-4573	255	21	in	in	ADP
ejpam-4573	255	22	y	y	PROPN
ejpam-4573	255	23	and	and	CCONJ
ejpam-4573	255	24	by	by	ADP
ejpam-4573	255	25	(	(	PUNCT
ejpam-4573	255	26	4	4	NUM
ejpam-4573	255	27	)	)	PUNCT
ejpam-4573	255	28	,	,	PUNCT
ejpam-4573	255	29	f−(v	f−(v	ADJ
ejpam-4573	255	30	)	)	PUNCT
ejpam-4573	255	31	=	=	PUNCT
ejpam-4573	256	1	[	[	X
ejpam-4573	256	2	f−(v	f−(v	NOUN
ejpam-4573	256	3	)	)	PUNCT
ejpam-4573	256	4	]	]	PUNCT
ejpam-4573	256	5	(	(	PUNCT
ejpam-4573	256	6	λ	λ	NOUN
ejpam-4573	256	7	,	,	PUNCT
ejpam-4573	256	8	sp	sp	NOUN
ejpam-4573	256	9	)	)	PUNCT
ejpam-4573	256	10	⊆	⊆	NUM
ejpam-4573	257	1	[	[	X
ejpam-4573	257	2	f−(v	f−(v	ADJ
ejpam-4573	257	3	(	(	PUNCT
ejpam-4573	257	4	λ	λ	PROPN
ejpam-4573	257	5	,	,	PUNCT
ejpam-4573	257	6	sp))](λ	sp))](λ	PROPN
ejpam-4573	257	7	,	,	PUNCT
ejpam-4573	257	8	sp	sp	NOUN
ejpam-4573	257	9	)	)	PUNCT
ejpam-4573	257	10	.	.	PUNCT
ejpam-4573	258	1	thus	thus	ADV
ejpam-4573	258	2	,	,	PUNCT
ejpam-4573	258	3	by	by	ADP
ejpam-4573	258	4	theorem	theorem	NOUN
ejpam-4573	258	5	2	2	NUM
ejpam-4573	258	6	,	,	PUNCT
ejpam-4573	258	7	f	f	PROPN
ejpam-4573	258	8	is	be	AUX
ejpam-4573	258	9	lower	low	ADJ
ejpam-4573	258	10	weakly	weakly	ADJ
ejpam-4573	258	11	(	(	PUNCT
ejpam-4573	258	12	λ	λ	NOUN
ejpam-4573	258	13	,	,	PUNCT
ejpam-4573	258	14	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	258	15	.	.	PUNCT
ejpam-4573	259	1	(	(	PUNCT
ejpam-4573	259	2	5	5	X
ejpam-4573	259	3	)	)	PUNCT
ejpam-4573	259	4	⇒	⇒	NOUN
ejpam-4573	259	5	(	(	PUNCT
ejpam-4573	259	6	1	1	NUM
ejpam-4573	259	7	):	):	PUNCT
ejpam-4573	259	8	let	let	VERB
ejpam-4573	259	9	x	x	PUNCT
ejpam-4573	259	10	∈	∈	PROPN
ejpam-4573	259	11	x	x	X
ejpam-4573	259	12	and	and	CCONJ
ejpam-4573	259	13	v	v	AUX
ejpam-4573	259	14	be	be	AUX
ejpam-4573	259	15	any	any	DET
ejpam-4573	259	16	(	(	PUNCT
ejpam-4573	259	17	λ	λ	NOUN
ejpam-4573	259	18	,	,	PUNCT
ejpam-4573	259	19	sp)-open	sp)-open	ADJ
ejpam-4573	259	20	set	set	NOUN
ejpam-4573	259	21	of	of	ADP
ejpam-4573	259	22	y	y	PRON
ejpam-4573	259	23	such	such	ADJ
ejpam-4573	259	24	that	that	SCONJ
ejpam-4573	259	25	f	f	PROPN
ejpam-4573	259	26	(	(	PUNCT
ejpam-4573	259	27	x)∩v	x)∩v	PROPN
ejpam-4573	259	28	̸=	̸=	PROPN
ejpam-4573	259	29	∅.	∅.	NOUN
ejpam-4573	259	30	since	since	SCONJ
ejpam-4573	259	31	(	(	PUNCT
ejpam-4573	259	32	y	y	PROPN
ejpam-4573	259	33	,	,	PUNCT
ejpam-4573	259	34	σ	σ	PROPN
ejpam-4573	259	35	)	)	PUNCT
ejpam-4573	259	36	is	be	AUX
ejpam-4573	259	37	λsp	λsp	NOUN
ejpam-4573	259	38	-	-	PUNCT
ejpam-4573	259	39	regular	regular	ADJ
ejpam-4573	259	40	,	,	PUNCT
ejpam-4573	259	41	there	there	PRON
ejpam-4573	259	42	exists	exist	VERB
ejpam-4573	259	43	a	a	DET
ejpam-4573	259	44	(	(	PUNCT
ejpam-4573	259	45	λ	λ	NOUN
ejpam-4573	259	46	,	,	PUNCT
ejpam-4573	259	47	sp)-open	sp)-open	ADJ
ejpam-4573	259	48	set	set	VERB
ejpam-4573	259	49	w	w	PROPN
ejpam-4573	259	50	of	of	ADP
ejpam-4573	259	51	y	y	PRON
ejpam-4573	259	52	such	such	ADJ
ejpam-4573	259	53	that	that	SCONJ
ejpam-4573	259	54	f	f	PROPN
ejpam-4573	259	55	(	(	PUNCT
ejpam-4573	259	56	x	x	X
ejpam-4573	259	57	)	)	PUNCT
ejpam-4573	259	58	∩w	∩w	ADJ
ejpam-4573	259	59	̸=	̸=	NOUN
ejpam-4573	259	60	∅	∅	NOUN
ejpam-4573	259	61	and	and	CCONJ
ejpam-4573	259	62	w	w	PROPN
ejpam-4573	259	63	(	(	PUNCT
ejpam-4573	259	64	λ	λ	PROPN
ejpam-4573	259	65	,	,	PUNCT
ejpam-4573	259	66	sp	sp	NOUN
ejpam-4573	259	67	)	)	PUNCT
ejpam-4573	259	68	⊆	⊆	NUM
ejpam-4573	259	69	v	v	NOUN
ejpam-4573	259	70	.	.	PUNCT
ejpam-4573	260	1	since	since	SCONJ
ejpam-4573	260	2	f	f	PROPN
ejpam-4573	260	3	is	be	AUX
ejpam-4573	260	4	is	be	AUX
ejpam-4573	260	5	lower	low	ADJ
ejpam-4573	260	6	weakly	weakly	ADJ
ejpam-4573	260	7	(	(	PUNCT
ejpam-4573	260	8	λ	λ	NOUN
ejpam-4573	260	9	,	,	PUNCT
ejpam-4573	260	10	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	260	11	,	,	PUNCT
ejpam-4573	260	12	there	there	PRON
ejpam-4573	260	13	exists	exist	VERB
ejpam-4573	260	14	u	u	PROPN
ejpam-4573	260	15	∈	∈	PROPN
ejpam-4573	260	16	λspo(x	λspo(x	PROPN
ejpam-4573	260	17	,	,	PUNCT
ejpam-4573	260	18	τ	τ	X
ejpam-4573	260	19	)	)	PUNCT
ejpam-4573	260	20	containing	contain	VERB
ejpam-4573	260	21	x	x	PUNCT
ejpam-4573	260	22	such	such	ADJ
ejpam-4573	260	23	that	that	SCONJ
ejpam-4573	260	24	f	f	PROPN
ejpam-4573	260	25	(	(	PUNCT
ejpam-4573	260	26	z)∩w	z)∩w	PROPN
ejpam-4573	260	27	(	(	PUNCT
ejpam-4573	260	28	λ	λ	NOUN
ejpam-4573	260	29	,	,	PUNCT
ejpam-4573	260	30	sp	sp	NOUN
ejpam-4573	260	31	)	)	PUNCT
ejpam-4573	260	32	̸=	̸=	NOUN
ejpam-4573	260	33	∅	∅	NOUN
ejpam-4573	260	34	;	;	PUNCT
ejpam-4573	260	35	hence	hence	ADV
ejpam-4573	260	36	f	f	PROPN
ejpam-4573	260	37	(	(	PUNCT
ejpam-4573	260	38	z)∩v	z)∩v	PROPN
ejpam-4573	260	39	̸=	̸=	PROPN
ejpam-4573	260	40	∅	∅	NOUN
ejpam-4573	260	41	for	for	ADP
ejpam-4573	260	42	each	each	DET
ejpam-4573	260	43	z	z	NOUN
ejpam-4573	260	44	∈	∈	PROPN
ejpam-4573	260	45	u	u	NOUN
ejpam-4573	260	46	.	.	PUNCT
ejpam-4573	261	1	this	this	PRON
ejpam-4573	261	2	shows	show	VERB
ejpam-4573	261	3	that	that	SCONJ
ejpam-4573	261	4	f	f	PROPN
ejpam-4573	261	5	is	be	AUX
ejpam-4573	261	6	lower	low	ADJ
ejpam-4573	261	7	(	(	PUNCT
ejpam-4573	261	8	λ	λ	NOUN
ejpam-4573	261	9	,	,	PUNCT
ejpam-4573	261	10	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	261	11	.	.	PUNCT
ejpam-4573	262	1	definition	definition	NOUN
ejpam-4573	262	2	6	6	NUM
ejpam-4573	262	3	.	.	PUNCT
ejpam-4573	263	1	[	[	X
ejpam-4573	263	2	4	4	X
ejpam-4573	263	3	]	]	PUNCT
ejpam-4573	263	4	a	a	DET
ejpam-4573	263	5	topological	topological	ADJ
ejpam-4573	263	6	space	space	NOUN
ejpam-4573	263	7	(	(	PUNCT
ejpam-4573	263	8	x	x	X
ejpam-4573	263	9	,	,	PUNCT
ejpam-4573	263	10	τ	τ	X
ejpam-4573	263	11	)	)	PUNCT
ejpam-4573	263	12	is	be	AUX
ejpam-4573	263	13	said	say	VERB
ejpam-4573	263	14	to	to	PART
ejpam-4573	263	15	be	be	AUX
ejpam-4573	263	16	λsp	λsp	NOUN
ejpam-4573	263	17	-	-	ADJ
ejpam-4573	263	18	normal	normal	ADJ
ejpam-4573	263	19	if	if	SCONJ
ejpam-4573	263	20	,	,	PUNCT
ejpam-4573	263	21	for	for	ADP
ejpam-4573	263	22	any	any	DET
ejpam-4573	263	23	pair	pair	NOUN
ejpam-4573	263	24	of	of	ADP
ejpam-4573	263	25	disjoint	disjoint	NOUN
ejpam-4573	263	26	(	(	PUNCT
ejpam-4573	263	27	λ	λ	PROPN
ejpam-4573	263	28	,	,	PUNCT
ejpam-4573	263	29	sp)-closed	sp)-close	VERB
ejpam-4573	263	30	sets	set	VERB
ejpam-4573	263	31	f	f	PROPN
ejpam-4573	263	32	and	and	CCONJ
ejpam-4573	263	33	h	h	NOUN
ejpam-4573	263	34	,	,	PUNCT
ejpam-4573	263	35	there	there	PRON
ejpam-4573	263	36	exist	exist	VERB
ejpam-4573	263	37	disjoint	disjoint	NOUN
ejpam-4573	263	38	(	(	PUNCT
ejpam-4573	263	39	λ	λ	NOUN
ejpam-4573	263	40	,	,	PUNCT
ejpam-4573	263	41	sp)-open	sp)-open	NOUN
ejpam-4573	263	42	sets	set	VERB
ejpam-4573	263	43	u	u	NOUN
ejpam-4573	263	44	and	and	CCONJ
ejpam-4573	263	45	v	v	ADP
ejpam-4573	263	46	such	such	ADJ
ejpam-4573	263	47	that	that	SCONJ
ejpam-4573	263	48	f	f	PROPN
ejpam-4573	263	49	⊆	⊆	NUM
ejpam-4573	263	50	u	u	NOUN
ejpam-4573	263	51	and	and	CCONJ
ejpam-4573	263	52	h	h	NOUN
ejpam-4573	263	53	⊆	⊆	NUM
ejpam-4573	263	54	v	v	NOUN
ejpam-4573	263	55	.	.	PUNCT
ejpam-4573	264	1	lemma	lemma	PROPN
ejpam-4573	264	2	6	6	NUM
ejpam-4573	264	3	.	.	PUNCT
ejpam-4573	265	1	[	[	X
ejpam-4573	265	2	4	4	X
ejpam-4573	265	3	]	]	PUNCT
ejpam-4573	265	4	for	for	ADP
ejpam-4573	265	5	a	a	DET
ejpam-4573	265	6	topological	topological	ADJ
ejpam-4573	265	7	space	space	NOUN
ejpam-4573	265	8	(	(	PUNCT
ejpam-4573	265	9	x	x	X
ejpam-4573	265	10	,	,	PUNCT
ejpam-4573	265	11	τ	τ	PROPN
ejpam-4573	265	12	)	)	PUNCT
ejpam-4573	265	13	,	,	PUNCT
ejpam-4573	265	14	the	the	DET
ejpam-4573	265	15	following	follow	VERB
ejpam-4573	265	16	properties	property	NOUN
ejpam-4573	265	17	are	be	AUX
ejpam-4573	265	18	equivalent	equivalent	ADJ
ejpam-4573	265	19	:	:	PUNCT
ejpam-4573	265	20	(	(	PUNCT
ejpam-4573	265	21	1	1	X
ejpam-4573	265	22	)	)	PUNCT
ejpam-4573	265	23	(	(	PUNCT
ejpam-4573	265	24	x	x	X
ejpam-4573	265	25	,	,	PUNCT
ejpam-4573	265	26	τ	τ	X
ejpam-4573	265	27	)	)	PUNCT
ejpam-4573	265	28	is	be	AUX
ejpam-4573	265	29	λsp	λsp	ADJ
ejpam-4573	265	30	-	-	ADJ
ejpam-4573	265	31	normal	normal	ADJ
ejpam-4573	265	32	.	.	PUNCT
ejpam-4573	266	1	(	(	PUNCT
ejpam-4573	266	2	2	2	X
ejpam-4573	266	3	)	)	PUNCT
ejpam-4573	266	4	for	for	ADP
ejpam-4573	266	5	every	every	DET
ejpam-4573	266	6	pair	pair	NOUN
ejpam-4573	266	7	of	of	ADP
ejpam-4573	266	8	(	(	PUNCT
ejpam-4573	266	9	λ	λ	PROPN
ejpam-4573	266	10	,	,	PUNCT
ejpam-4573	266	11	sp)-open	sp)-open	NOUN
ejpam-4573	266	12	sets	set	VERB
ejpam-4573	266	13	u	u	NOUN
ejpam-4573	266	14	and	and	CCONJ
ejpam-4573	266	15	v	v	ADP
ejpam-4573	266	16	whose	whose	DET
ejpam-4573	266	17	union	union	NOUN
ejpam-4573	266	18	is	be	AUX
ejpam-4573	266	19	x	x	NOUN
ejpam-4573	266	20	,	,	PUNCT
ejpam-4573	266	21	there	there	PRON
ejpam-4573	266	22	exist	exist	VERB
ejpam-4573	266	23	(	(	PUNCT
ejpam-4573	266	24	λ	λ	NOUN
ejpam-4573	266	25	,	,	PUNCT
ejpam-4573	266	26	sp)closed	sp)close	VERB
ejpam-4573	266	27	sets	set	NOUN
ejpam-4573	266	28	f	f	PROPN
ejpam-4573	267	1	and	and	CCONJ
ejpam-4573	267	2	h	h	NOUN
ejpam-4573	267	3	such	such	ADJ
ejpam-4573	267	4	that	that	SCONJ
ejpam-4573	267	5	f	f	PROPN
ejpam-4573	267	6	⊆	⊆	NUM
ejpam-4573	267	7	u	u	NOUN
ejpam-4573	267	8	,	,	PUNCT
ejpam-4573	267	9	h	h	NOUN
ejpam-4573	267	10	⊆	⊆	NUM
ejpam-4573	267	11	v	v	NOUN
ejpam-4573	267	12	and	and	CCONJ
ejpam-4573	267	13	f	f	PROPN
ejpam-4573	267	14	∪h	∪h	PROPN
ejpam-4573	267	15	=	=	SYM
ejpam-4573	267	16	x.	x.	NOUN
ejpam-4573	267	17	(	(	PUNCT
ejpam-4573	267	18	3	3	NUM
ejpam-4573	267	19	)	)	PUNCT
ejpam-4573	267	20	for	for	ADP
ejpam-4573	267	21	every	every	DET
ejpam-4573	267	22	(	(	PUNCT
ejpam-4573	267	23	λ	λ	PROPN
ejpam-4573	267	24	,	,	PUNCT
ejpam-4573	267	25	sp)-closed	sp)-close	VERB
ejpam-4573	267	26	set	set	VERB
ejpam-4573	267	27	f	f	PROPN
ejpam-4573	267	28	and	and	CCONJ
ejpam-4573	267	29	every	every	DET
ejpam-4573	267	30	(	(	PUNCT
ejpam-4573	267	31	λ	λ	NOUN
ejpam-4573	267	32	,	,	PUNCT
ejpam-4573	267	33	sp)-open	sp)-open	NOUN
ejpam-4573	267	34	set	set	VERB
ejpam-4573	267	35	g	g	NOUN
ejpam-4573	267	36	containing	contain	VERB
ejpam-4573	267	37	f	f	NOUN
ejpam-4573	267	38	,	,	PUNCT
ejpam-4573	267	39	there	there	PRON
ejpam-4573	267	40	exists	exist	VERB
ejpam-4573	267	41	a	a	DET
ejpam-4573	267	42	(	(	PUNCT
ejpam-4573	267	43	λ	λ	NOUN
ejpam-4573	267	44	,	,	PUNCT
ejpam-4573	267	45	sp)-open	sp)-open	NOUN
ejpam-4573	267	46	set	set	VERB
ejpam-4573	267	47	u	u	PRON
ejpam-4573	267	48	such	such	ADJ
ejpam-4573	267	49	that	that	SCONJ
ejpam-4573	267	50	f	f	PROPN
ejpam-4573	267	51	⊆	⊆	NUM
ejpam-4573	267	52	u	u	NOUN
ejpam-4573	267	53	⊆	⊆	NUM
ejpam-4573	267	54	u	u	NOUN
ejpam-4573	267	55	(	(	PUNCT
ejpam-4573	267	56	λ	λ	PROPN
ejpam-4573	267	57	,	,	PUNCT
ejpam-4573	267	58	sp	sp	NOUN
ejpam-4573	267	59	)	)	PUNCT
ejpam-4573	267	60	⊆	⊆	NUM
ejpam-4573	267	61	g.	g.	NOUN
ejpam-4573	267	62	(	(	PUNCT
ejpam-4573	267	63	4	4	NUM
ejpam-4573	267	64	)	)	PUNCT
ejpam-4573	267	65	for	for	ADP
ejpam-4573	267	66	every	every	DET
ejpam-4573	267	67	pair	pair	NOUN
ejpam-4573	267	68	of	of	ADP
ejpam-4573	267	69	disjoint	disjoint	NOUN
ejpam-4573	267	70	(	(	PUNCT
ejpam-4573	267	71	λ	λ	PROPN
ejpam-4573	267	72	,	,	PUNCT
ejpam-4573	267	73	sp)-closed	sp)-close	VERB
ejpam-4573	267	74	sets	set	VERB
ejpam-4573	267	75	f	f	PROPN
ejpam-4573	267	76	and	and	CCONJ
ejpam-4573	267	77	h	h	NOUN
ejpam-4573	267	78	,	,	PUNCT
ejpam-4573	267	79	there	there	PRON
ejpam-4573	267	80	exist	exist	VERB
ejpam-4573	267	81	disjoint	disjoint	NOUN
ejpam-4573	267	82	(	(	PUNCT
ejpam-4573	267	83	λ	λ	NOUN
ejpam-4573	267	84	,	,	PUNCT
ejpam-4573	267	85	sp)open	sp)open	NOUN
ejpam-4573	267	86	sets	set	VERB
ejpam-4573	267	87	u	u	NOUN
ejpam-4573	267	88	and	and	CCONJ
ejpam-4573	267	89	v	v	ADP
ejpam-4573	267	90	such	such	ADJ
ejpam-4573	267	91	that	that	SCONJ
ejpam-4573	267	92	f	f	PROPN
ejpam-4573	267	93	⊆	⊆	NUM
ejpam-4573	267	94	u	u	NOUN
ejpam-4573	267	95	and	and	CCONJ
ejpam-4573	267	96	h	h	NOUN
ejpam-4573	267	97	⊆	⊆	NUM
ejpam-4573	267	98	v	v	NOUN
ejpam-4573	267	99	and	and	CCONJ
ejpam-4573	267	100	u	u	NOUN
ejpam-4573	267	101	(	(	PUNCT
ejpam-4573	267	102	λ	λ	PROPN
ejpam-4573	267	103	,	,	PUNCT
ejpam-4573	267	104	sp	sp	NOUN
ejpam-4573	267	105	)	)	PUNCT
ejpam-4573	267	106	∩	∩	ADJ
ejpam-4573	267	107	v	v	X
ejpam-4573	267	108	(	(	PUNCT
ejpam-4573	267	109	λ	λ	PROPN
ejpam-4573	267	110	,	,	PUNCT
ejpam-4573	267	111	sp	sp	NOUN
ejpam-4573	267	112	)	)	PUNCT
ejpam-4573	267	113	=	=	PUNCT
ejpam-4573	267	114	∅.	∅.	NOUN
ejpam-4573	267	115	theorem	theorem	VERB
ejpam-4573	267	116	8	8	NUM
ejpam-4573	267	117	.	.	PUNCT
ejpam-4573	268	1	let	let	AUX
ejpam-4573	268	2	(	(	PUNCT
ejpam-4573	268	3	y	y	PROPN
ejpam-4573	268	4	,	,	PUNCT
ejpam-4573	268	5	σ	σ	PROPN
ejpam-4573	268	6	)	)	PUNCT
ejpam-4573	268	7	be	be	AUX
ejpam-4573	268	8	a	a	DET
ejpam-4573	268	9	λsp	λsp	ADJ
ejpam-4573	268	10	-	-	ADJ
ejpam-4573	268	11	normal	normal	ADJ
ejpam-4573	268	12	space	space	NOUN
ejpam-4573	268	13	.	.	PUNCT
ejpam-4573	269	1	for	for	ADP
ejpam-4573	269	2	a	a	DET
ejpam-4573	269	3	multifunction	multifunction	NOUN
ejpam-4573	269	4	f	f	NOUN
ejpam-4573	269	5	:	:	PUNCT
ejpam-4573	269	6	(	(	PUNCT
ejpam-4573	269	7	x	x	X
ejpam-4573	269	8	,	,	PUNCT
ejpam-4573	269	9	τ	τ	X
ejpam-4573	269	10	)	)	PUNCT
ejpam-4573	269	11	→	→	SYM
ejpam-4573	269	12	(	(	PUNCT
ejpam-4573	269	13	y	y	PROPN
ejpam-4573	269	14	,	,	PUNCT
ejpam-4573	269	15	σ	σ	PROPN
ejpam-4573	269	16	)	)	PUNCT
ejpam-4573	269	17	such	such	ADJ
ejpam-4573	269	18	that	that	SCONJ
ejpam-4573	269	19	f	f	PROPN
ejpam-4573	269	20	(	(	PUNCT
ejpam-4573	269	21	x	x	X
ejpam-4573	269	22	)	)	PUNCT
ejpam-4573	269	23	is	be	AUX
ejpam-4573	269	24	(	(	PUNCT
ejpam-4573	269	25	λ	λ	X
ejpam-4573	269	26	,	,	PUNCT
ejpam-4573	269	27	sp)-closed	sp)-close	VERB
ejpam-4573	269	28	in	in	ADP
ejpam-4573	269	29	y	y	PROPN
ejpam-4573	269	30	for	for	ADP
ejpam-4573	269	31	each	each	DET
ejpam-4573	269	32	x	x	SYM
ejpam-4573	269	33	∈	∈	PROPN
ejpam-4573	269	34	x	x	NOUN
ejpam-4573	269	35	,	,	PUNCT
ejpam-4573	269	36	the	the	DET
ejpam-4573	269	37	following	follow	VERB
ejpam-4573	269	38	properties	property	NOUN
ejpam-4573	269	39	are	be	AUX
ejpam-4573	269	40	equivalent	equivalent	ADJ
ejpam-4573	269	41	:	:	PUNCT
ejpam-4573	269	42	(	(	PUNCT
ejpam-4573	269	43	1	1	X
ejpam-4573	269	44	)	)	PUNCT
ejpam-4573	269	45	f	f	PROPN
ejpam-4573	269	46	is	be	AUX
ejpam-4573	269	47	upper	upper	ADJ
ejpam-4573	269	48	(	(	PUNCT
ejpam-4573	269	49	λ	λ	NOUN
ejpam-4573	269	50	,	,	PUNCT
ejpam-4573	269	51	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	269	52	;	;	PUNCT
ejpam-4573	269	53	(	(	PUNCT
ejpam-4573	269	54	2	2	X
ejpam-4573	269	55	)	)	PUNCT
ejpam-4573	269	56	f	f	PROPN
ejpam-4573	269	57	is	be	AUX
ejpam-4573	269	58	upper	upper	ADJ
ejpam-4573	269	59	weakly	weakly	ADJ
ejpam-4573	269	60	(	(	PUNCT
ejpam-4573	269	61	λ	λ	NOUN
ejpam-4573	269	62	,	,	PUNCT
ejpam-4573	269	63	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	269	64	.	.	PUNCT
ejpam-4573	270	1	c.	c.	PROPN
ejpam-4573	270	2	boonpok	boonpok	PROPN
ejpam-4573	270	3	,	,	PUNCT
ejpam-4573	270	4	p.	p.	NOUN
ejpam-4573	270	5	pue	pue	NOUN
ejpam-4573	270	6	-	-	PUNCT
ejpam-4573	270	7	on	on	ADP
ejpam-4573	270	8	/	/	SYM
ejpam-4573	270	9	eur	eur	NOUN
ejpam-4573	270	10	.	.	PUNCT
ejpam-4573	271	1	j.	j.	PROPN
ejpam-4573	271	2	pure	pure	PROPN
ejpam-4573	271	3	appl	appl	PROPN
ejpam-4573	271	4	.	.	PROPN
ejpam-4573	271	5	math	math	PROPN
ejpam-4573	271	6	,	,	PUNCT
ejpam-4573	271	7	16	16	NUM
ejpam-4573	271	8	(	(	PUNCT
ejpam-4573	271	9	2	2	NUM
ejpam-4573	271	10	)	)	PUNCT
ejpam-4573	271	11	(	(	PUNCT
ejpam-4573	271	12	2023	2023	NUM
ejpam-4573	271	13	)	)	PUNCT
ejpam-4573	271	14	,	,	PUNCT
ejpam-4573	271	15	1047	1047	NUM
ejpam-4573	271	16	-	-	SYM
ejpam-4573	271	17	1058	1058	NUM
ejpam-4573	271	18	1056	1056	NUM
ejpam-4573	271	19	proof	proof	NOUN
ejpam-4573	271	20	.	.	PUNCT
ejpam-4573	272	1	(	(	PUNCT
ejpam-4573	272	2	1	1	X
ejpam-4573	272	3	)	)	PUNCT
ejpam-4573	272	4	⇒	⇒	NOUN
ejpam-4573	272	5	(	(	PUNCT
ejpam-4573	272	6	2	2	NUM
ejpam-4573	272	7	):	):	PUNCT
ejpam-4573	272	8	the	the	DET
ejpam-4573	272	9	proof	proof	NOUN
ejpam-4573	272	10	is	be	AUX
ejpam-4573	272	11	obvious	obvious	ADJ
ejpam-4573	272	12	.	.	PUNCT
ejpam-4573	273	1	(	(	PUNCT
ejpam-4573	273	2	2	2	X
ejpam-4573	273	3	)	)	PUNCT
ejpam-4573	273	4	⇒	⇒	NOUN
ejpam-4573	273	5	(	(	PUNCT
ejpam-4573	273	6	1	1	NUM
ejpam-4573	273	7	):	):	PUNCT
ejpam-4573	273	8	suppose	suppose	VERB
ejpam-4573	273	9	that	that	SCONJ
ejpam-4573	273	10	f	f	PROPN
ejpam-4573	273	11	is	be	AUX
ejpam-4573	273	12	upper	upper	ADJ
ejpam-4573	273	13	weakly	weakly	ADJ
ejpam-4573	273	14	(	(	PUNCT
ejpam-4573	273	15	λ	λ	NOUN
ejpam-4573	273	16	,	,	PUNCT
ejpam-4573	273	17	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	273	18	.	.	PUNCT
ejpam-4573	274	1	let	let	VERB
ejpam-4573	274	2	x	x	PUNCT
ejpam-4573	274	3	∈	∈	PROPN
ejpam-4573	274	4	x	x	X
ejpam-4573	274	5	and	and	CCONJ
ejpam-4573	274	6	v	v	X
ejpam-4573	274	7	be	be	AUX
ejpam-4573	274	8	any	any	DET
ejpam-4573	274	9	(	(	PUNCT
ejpam-4573	274	10	λ	λ	NOUN
ejpam-4573	274	11	,	,	PUNCT
ejpam-4573	274	12	sp)-open	sp)-open	ADJ
ejpam-4573	274	13	set	set	NOUN
ejpam-4573	274	14	of	of	ADP
ejpam-4573	274	15	y	y	PROPN
ejpam-4573	274	16	containing	contain	VERB
ejpam-4573	274	17	f	f	PROPN
ejpam-4573	274	18	(	(	PUNCT
ejpam-4573	274	19	x	x	NOUN
ejpam-4573	274	20	)	)	PUNCT
ejpam-4573	274	21	.	.	PUNCT
ejpam-4573	275	1	since	since	SCONJ
ejpam-4573	275	2	f	f	PROPN
ejpam-4573	275	3	(	(	PUNCT
ejpam-4573	275	4	x	x	X
ejpam-4573	275	5	)	)	PUNCT
ejpam-4573	275	6	is	be	AUX
ejpam-4573	275	7	(	(	PUNCT
ejpam-4573	275	8	λ	λ	X
ejpam-4573	275	9	,	,	PUNCT
ejpam-4573	275	10	sp)-closed	sp)-close	VERB
ejpam-4573	275	11	in	in	ADP
ejpam-4573	275	12	y	y	PROPN
ejpam-4573	275	13	,	,	PUNCT
ejpam-4573	275	14	by	by	ADP
ejpam-4573	275	15	the	the	DET
ejpam-4573	275	16	λsp	λsp	NOUN
ejpam-4573	275	17	-	-	NOUN
ejpam-4573	275	18	normality	normality	NOUN
ejpam-4573	275	19	of	of	ADP
ejpam-4573	275	20	(	(	PUNCT
ejpam-4573	275	21	y	y	PROPN
ejpam-4573	275	22	,	,	PUNCT
ejpam-4573	275	23	σ	σ	PROPN
ejpam-4573	275	24	)	)	PUNCT
ejpam-4573	275	25	,	,	PUNCT
ejpam-4573	275	26	there	there	PRON
ejpam-4573	275	27	exists	exist	VERB
ejpam-4573	275	28	a	a	DET
ejpam-4573	275	29	(	(	PUNCT
ejpam-4573	275	30	λ	λ	NOUN
ejpam-4573	275	31	,	,	PUNCT
ejpam-4573	275	32	sp)-open	sp)-open	NOUN
ejpam-4573	275	33	set	set	VERB
ejpam-4573	275	34	u	u	NOUN
ejpam-4573	275	35	of	of	ADP
ejpam-4573	275	36	y	y	PRON
ejpam-4573	275	37	such	such	ADJ
ejpam-4573	275	38	that	that	SCONJ
ejpam-4573	275	39	f	f	PROPN
ejpam-4573	275	40	(	(	PUNCT
ejpam-4573	275	41	x	x	X
ejpam-4573	275	42	)	)	PUNCT
ejpam-4573	275	43	⊆	⊆	NUM
ejpam-4573	275	44	u	u	NOUN
ejpam-4573	275	45	⊆	⊆	NUM
ejpam-4573	275	46	u	u	NOUN
ejpam-4573	275	47	(	(	PUNCT
ejpam-4573	275	48	λ	λ	PROPN
ejpam-4573	275	49	,	,	PUNCT
ejpam-4573	275	50	sp	sp	NOUN
ejpam-4573	275	51	)	)	PUNCT
ejpam-4573	275	52	⊆	⊆	NUM
ejpam-4573	275	53	v.	v.	ADV
ejpam-4573	275	54	since	since	SCONJ
ejpam-4573	275	55	f	f	PROPN
ejpam-4573	275	56	is	be	AUX
ejpam-4573	275	57	upper	upper	ADJ
ejpam-4573	275	58	weakly	weakly	ADJ
ejpam-4573	275	59	(	(	PUNCT
ejpam-4573	275	60	λ	λ	NOUN
ejpam-4573	275	61	,	,	PUNCT
ejpam-4573	275	62	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	275	63	,	,	PUNCT
ejpam-4573	275	64	there	there	PRON
ejpam-4573	275	65	exists	exist	VERB
ejpam-4573	275	66	w	w	PROPN
ejpam-4573	275	67	∈	∈	PROPN
ejpam-4573	275	68	λspo(x	λspo(x	PROPN
ejpam-4573	275	69	,	,	PUNCT
ejpam-4573	275	70	τ	τ	X
ejpam-4573	275	71	)	)	PUNCT
ejpam-4573	275	72	containing	contain	VERB
ejpam-4573	275	73	x	x	PUNCT
ejpam-4573	276	1	such	such	ADJ
ejpam-4573	276	2	that	that	SCONJ
ejpam-4573	276	3	f	f	PROPN
ejpam-4573	276	4	(	(	PUNCT
ejpam-4573	276	5	w	w	PROPN
ejpam-4573	276	6	)	)	PUNCT
ejpam-4573	276	7	⊆	⊆	NUM
ejpam-4573	276	8	u	u	NOUN
ejpam-4573	276	9	(	(	PUNCT
ejpam-4573	276	10	λ	λ	PROPN
ejpam-4573	276	11	,	,	PUNCT
ejpam-4573	276	12	sp	sp	NOUN
ejpam-4573	276	13	)	)	PUNCT
ejpam-4573	276	14	⊆	⊆	NUM
ejpam-4573	276	15	v	v	NOUN
ejpam-4573	276	16	.	.	PUNCT
ejpam-4573	277	1	this	this	PRON
ejpam-4573	277	2	shows	show	VERB
ejpam-4573	277	3	that	that	SCONJ
ejpam-4573	277	4	f	f	PROPN
ejpam-4573	277	5	is	be	AUX
ejpam-4573	277	6	upper	upper	ADJ
ejpam-4573	277	7	(	(	PUNCT
ejpam-4573	277	8	λ	λ	NOUN
ejpam-4573	277	9	,	,	PUNCT
ejpam-4573	277	10	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	277	11	.	.	PUNCT
ejpam-4573	278	1	definition	definition	NOUN
ejpam-4573	278	2	7	7	NUM
ejpam-4573	278	3	.	.	PUNCT
ejpam-4573	279	1	[	[	X
ejpam-4573	279	2	24	24	NUM
ejpam-4573	279	3	]	]	PUNCT
ejpam-4573	279	4	a	a	DET
ejpam-4573	279	5	topological	topological	ADJ
ejpam-4573	279	6	space	space	NOUN
ejpam-4573	279	7	(	(	PUNCT
ejpam-4573	279	8	x	x	X
ejpam-4573	279	9	,	,	PUNCT
ejpam-4573	279	10	τ	τ	X
ejpam-4573	279	11	)	)	PUNCT
ejpam-4573	279	12	is	be	AUX
ejpam-4573	279	13	said	say	VERB
ejpam-4573	279	14	to	to	PART
ejpam-4573	279	15	be	be	AUX
ejpam-4573	279	16	λsp	λsp	NOUN
ejpam-4573	279	17	-	-	ADJ
ejpam-4573	279	18	compact	compact	ADJ
ejpam-4573	279	19	if	if	SCONJ
ejpam-4573	279	20	every	every	DET
ejpam-4573	279	21	cover	cover	NOUN
ejpam-4573	279	22	of	of	ADP
ejpam-4573	279	23	x	x	PUNCT
ejpam-4573	279	24	by	by	ADP
ejpam-4573	279	25	(	(	PUNCT
ejpam-4573	279	26	λ	λ	PROPN
ejpam-4573	279	27	,	,	PUNCT
ejpam-4573	279	28	sp)-open	sp)-open	ADJ
ejpam-4573	279	29	sets	set	NOUN
ejpam-4573	279	30	of	of	ADP
ejpam-4573	279	31	x	x	PUNCT
ejpam-4573	279	32	has	have	VERB
ejpam-4573	279	33	a	a	DET
ejpam-4573	279	34	finite	finite	ADJ
ejpam-4573	279	35	subcover	subcover	PROPN
ejpam-4573	279	36	.	.	PUNCT
ejpam-4573	280	1	a	a	DET
ejpam-4573	280	2	subset	subset	NOUN
ejpam-4573	280	3	k	k	PROPN
ejpam-4573	280	4	of	of	ADP
ejpam-4573	280	5	a	a	DET
ejpam-4573	280	6	topological	topological	ADJ
ejpam-4573	280	7	space	space	NOUN
ejpam-4573	280	8	(	(	PUNCT
ejpam-4573	280	9	x	x	X
ejpam-4573	280	10	,	,	PUNCT
ejpam-4573	280	11	τ	τ	X
ejpam-4573	280	12	)	)	PUNCT
ejpam-4573	280	13	is	be	AUX
ejpam-4573	280	14	said	say	VERB
ejpam-4573	280	15	to	to	PART
ejpam-4573	280	16	be	be	AUX
ejpam-4573	280	17	λsp	λsp	NOUN
ejpam-4573	280	18	-	-	ADJ
ejpam-4573	280	19	compact	compact	ADJ
ejpam-4573	280	20	if	if	SCONJ
ejpam-4573	280	21	every	every	DET
ejpam-4573	280	22	cover	cover	NOUN
ejpam-4573	280	23	of	of	ADP
ejpam-4573	280	24	x	x	PUNCT
ejpam-4573	280	25	by	by	ADP
ejpam-4573	280	26	(	(	PUNCT
ejpam-4573	280	27	λ	λ	PROPN
ejpam-4573	280	28	,	,	PUNCT
ejpam-4573	280	29	sp)-open	sp)-open	ADJ
ejpam-4573	280	30	sets	set	NOUN
ejpam-4573	280	31	of	of	ADP
ejpam-4573	280	32	x	x	PUNCT
ejpam-4573	280	33	has	have	VERB
ejpam-4573	280	34	a	a	DET
ejpam-4573	280	35	finite	finite	ADJ
ejpam-4573	280	36	subcover	subcover	PROPN
ejpam-4573	280	37	.	.	PUNCT
ejpam-4573	281	1	definition	definition	NOUN
ejpam-4573	281	2	8	8	NUM
ejpam-4573	281	3	.	.	PUNCT
ejpam-4573	282	1	a	a	DET
ejpam-4573	282	2	topological	topological	ADJ
ejpam-4573	282	3	space	space	NOUN
ejpam-4573	282	4	(	(	PUNCT
ejpam-4573	282	5	x	x	X
ejpam-4573	282	6	,	,	PUNCT
ejpam-4573	282	7	τ	τ	X
ejpam-4573	282	8	)	)	PUNCT
ejpam-4573	282	9	is	be	AUX
ejpam-4573	282	10	called	call	VERB
ejpam-4573	282	11	λsp	λsp	INTJ
ejpam-4573	282	12	-	-	ADJ
ejpam-4573	282	13	urusohn	urusohn	ADJ
ejpam-4573	282	14	if	if	SCONJ
ejpam-4573	282	15	,	,	PUNCT
ejpam-4573	282	16	for	for	ADP
ejpam-4573	282	17	each	each	DET
ejpam-4573	282	18	distinct	distinct	ADJ
ejpam-4573	282	19	points	point	NOUN
ejpam-4573	282	20	x	x	PUNCT
ejpam-4573	282	21	and	and	CCONJ
ejpam-4573	282	22	y	y	PROPN
ejpam-4573	282	23	in	in	ADP
ejpam-4573	282	24	x	x	SYM
ejpam-4573	282	25	,	,	PUNCT
ejpam-4573	282	26	there	there	PRON
ejpam-4573	282	27	exist	exist	VERB
ejpam-4573	282	28	u	u	NOUN
ejpam-4573	282	29	,	,	PUNCT
ejpam-4573	282	30	v	v	NOUN
ejpam-4573	282	31	∈	∈	PROPN
ejpam-4573	282	32	λspo(x	λspo(x	NOUN
ejpam-4573	282	33	,	,	PUNCT
ejpam-4573	282	34	τ	τ	X
ejpam-4573	282	35	)	)	PUNCT
ejpam-4573	282	36	containing	contain	VERB
ejpam-4573	282	37	x	x	PROPN
ejpam-4573	282	38	and	and	CCONJ
ejpam-4573	282	39	y	y	PROPN
ejpam-4573	282	40	,	,	PUNCT
ejpam-4573	282	41	respectively	respectively	ADV
ejpam-4573	282	42	,	,	PUNCT
ejpam-4573	282	43	such	such	ADJ
ejpam-4573	282	44	that	that	SCONJ
ejpam-4573	282	45	u	u	PROPN
ejpam-4573	282	46	(	(	PUNCT
ejpam-4573	282	47	λ	λ	PROPN
ejpam-4573	282	48	,	,	PUNCT
ejpam-4573	282	49	sp	sp	NOUN
ejpam-4573	282	50	)	)	PUNCT
ejpam-4573	282	51	∩	∩	ADJ
ejpam-4573	282	52	v	v	X
ejpam-4573	282	53	(	(	PUNCT
ejpam-4573	282	54	λ	λ	PROPN
ejpam-4573	282	55	,	,	PUNCT
ejpam-4573	282	56	sp	sp	NOUN
ejpam-4573	282	57	)	)	PUNCT
ejpam-4573	282	58	=	=	PUNCT
ejpam-4573	282	59	∅.	∅.	PRON
ejpam-4573	282	60	lemma	lemma	PROPN
ejpam-4573	282	61	7	7	NUM
ejpam-4573	282	62	.	.	PUNCT
ejpam-4573	283	1	if	if	SCONJ
ejpam-4573	283	2	a	a	PRON
ejpam-4573	283	3	and	and	CCONJ
ejpam-4573	283	4	b	b	NOUN
ejpam-4573	283	5	are	be	AUX
ejpam-4573	283	6	disjoint	disjoint	ADJ
ejpam-4573	283	7	λsp	λsp	ADJ
ejpam-4573	283	8	-	-	ADJ
ejpam-4573	283	9	compact	compact	ADJ
ejpam-4573	283	10	subsets	subset	NOUN
ejpam-4573	283	11	of	of	ADP
ejpam-4573	283	12	a	a	DET
ejpam-4573	283	13	λsp	λsp	ADJ
ejpam-4573	283	14	-	-	ADJ
ejpam-4573	283	15	urusohn	urusohn	ADJ
ejpam-4573	283	16	space	space	NOUN
ejpam-4573	283	17	(	(	PUNCT
ejpam-4573	283	18	x	x	X
ejpam-4573	283	19	,	,	PUNCT
ejpam-4573	283	20	τ	τ	PROPN
ejpam-4573	283	21	)	)	PUNCT
ejpam-4573	283	22	,	,	PUNCT
ejpam-4573	283	23	then	then	ADV
ejpam-4573	283	24	there	there	PRON
ejpam-4573	283	25	exist	exist	VERB
ejpam-4573	283	26	u	u	NOUN
ejpam-4573	283	27	,	,	PUNCT
ejpam-4573	283	28	v	v	NOUN
ejpam-4573	283	29	∈	∈	PROPN
ejpam-4573	283	30	λspo(x	λspo(x	NOUN
ejpam-4573	283	31	,	,	PUNCT
ejpam-4573	283	32	τ	τ	PROPN
ejpam-4573	283	33	)	)	PUNCT
ejpam-4573	283	34	such	such	ADJ
ejpam-4573	283	35	that	that	SCONJ
ejpam-4573	283	36	a	a	DET
ejpam-4573	283	37	⊆	⊆	NUM
ejpam-4573	283	38	u	u	NOUN
ejpam-4573	283	39	,	,	PUNCT
ejpam-4573	283	40	b	b	PROPN
ejpam-4573	283	41	⊆	⊆	NUM
ejpam-4573	283	42	v	v	NOUN
ejpam-4573	283	43	and	and	CCONJ
ejpam-4573	283	44	u	u	NOUN
ejpam-4573	283	45	(	(	PUNCT
ejpam-4573	283	46	λ	λ	PROPN
ejpam-4573	283	47	,	,	PUNCT
ejpam-4573	283	48	sp	sp	NOUN
ejpam-4573	283	49	)	)	PUNCT
ejpam-4573	283	50	∩	∩	ADJ
ejpam-4573	283	51	v	v	X
ejpam-4573	283	52	(	(	PUNCT
ejpam-4573	283	53	λ	λ	PROPN
ejpam-4573	283	54	,	,	PUNCT
ejpam-4573	283	55	sp	sp	NOUN
ejpam-4573	283	56	)	)	PUNCT
ejpam-4573	283	57	=	=	PUNCT
ejpam-4573	283	58	∅.	∅.	PRON
ejpam-4573	283	59	definition	definition	NOUN
ejpam-4573	283	60	9	9	NUM
ejpam-4573	283	61	.	.	PUNCT
ejpam-4573	284	1	a	a	DET
ejpam-4573	284	2	topological	topological	ADJ
ejpam-4573	284	3	space	space	NOUN
ejpam-4573	284	4	(	(	PUNCT
ejpam-4573	284	5	x	x	X
ejpam-4573	284	6	,	,	PUNCT
ejpam-4573	284	7	τ	τ	X
ejpam-4573	284	8	)	)	PUNCT
ejpam-4573	284	9	is	be	AUX
ejpam-4573	284	10	called	call	VERB
ejpam-4573	284	11	λsp	λsp	NOUN
ejpam-4573	284	12	-	-	NOUN
ejpam-4573	284	13	t2	t2	NOUN
ejpam-4573	284	14	if	if	SCONJ
ejpam-4573	284	15	,	,	PUNCT
ejpam-4573	284	16	for	for	ADP
ejpam-4573	284	17	each	each	DET
ejpam-4573	284	18	distinct	distinct	ADJ
ejpam-4573	284	19	points	point	NOUN
ejpam-4573	284	20	x	x	PUNCT
ejpam-4573	284	21	and	and	CCONJ
ejpam-4573	284	22	y	y	PROPN
ejpam-4573	284	23	in	in	ADP
ejpam-4573	284	24	x	x	SYM
ejpam-4573	284	25	,	,	PUNCT
ejpam-4573	284	26	there	there	PRON
ejpam-4573	284	27	exist	exist	VERB
ejpam-4573	284	28	u	u	NOUN
ejpam-4573	284	29	,	,	PUNCT
ejpam-4573	284	30	v	v	NOUN
ejpam-4573	284	31	∈	∈	PROPN
ejpam-4573	284	32	λspo(x	λspo(x	NOUN
ejpam-4573	284	33	,	,	PUNCT
ejpam-4573	284	34	τ	τ	X
ejpam-4573	284	35	)	)	PUNCT
ejpam-4573	284	36	containing	contain	VERB
ejpam-4573	284	37	x	x	PROPN
ejpam-4573	284	38	and	and	CCONJ
ejpam-4573	284	39	y	y	PROPN
ejpam-4573	284	40	,	,	PUNCT
ejpam-4573	284	41	respectively	respectively	ADV
ejpam-4573	284	42	,	,	PUNCT
ejpam-4573	284	43	such	such	ADJ
ejpam-4573	284	44	that	that	SCONJ
ejpam-4573	284	45	u	u	PROPN
ejpam-4573	284	46	∩	∩	NOUN
ejpam-4573	284	47	v	v	NOUN
ejpam-4573	284	48	=	=	PUNCT
ejpam-4573	284	49	∅.	∅.	NOUN
ejpam-4573	284	50	theorem	theorem	VERB
ejpam-4573	284	51	9	9	NUM
ejpam-4573	284	52	.	.	PUNCT
ejpam-4573	285	1	if	if	SCONJ
ejpam-4573	285	2	f	f	PROPN
ejpam-4573	285	3	:	:	PUNCT
ejpam-4573	285	4	(	(	PUNCT
ejpam-4573	285	5	x	x	X
ejpam-4573	285	6	,	,	PUNCT
ejpam-4573	285	7	τ	τ	X
ejpam-4573	285	8	)	)	PUNCT
ejpam-4573	285	9	→	→	SYM
ejpam-4573	285	10	(	(	PUNCT
ejpam-4573	285	11	y	y	PROPN
ejpam-4573	285	12	,	,	PUNCT
ejpam-4573	285	13	σ	σ	PROPN
ejpam-4573	285	14	)	)	PUNCT
ejpam-4573	285	15	is	be	AUX
ejpam-4573	285	16	an	an	DET
ejpam-4573	285	17	upper	upper	ADJ
ejpam-4573	285	18	weakly	weakly	NOUN
ejpam-4573	285	19	(	(	PUNCT
ejpam-4573	285	20	λ	λ	NOUN
ejpam-4573	285	21	,	,	PUNCT
ejpam-4573	285	22	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	285	23	injective	injective	ADJ
ejpam-4573	285	24	multifunction	multifunction	NOUN
ejpam-4573	285	25	into	into	ADP
ejpam-4573	285	26	a	a	DET
ejpam-4573	285	27	λsp	λsp	ADJ
ejpam-4573	285	28	-	-	ADJ
ejpam-4573	285	29	urusohn	urusohn	ADJ
ejpam-4573	285	30	space	space	NOUN
ejpam-4573	285	31	(	(	PUNCT
ejpam-4573	285	32	y	y	PROPN
ejpam-4573	285	33	,	,	PUNCT
ejpam-4573	285	34	σ	σ	PROPN
ejpam-4573	285	35	)	)	PUNCT
ejpam-4573	285	36	and	and	CCONJ
ejpam-4573	285	37	f	f	PROPN
ejpam-4573	285	38	(	(	PUNCT
ejpam-4573	285	39	x	x	X
ejpam-4573	285	40	)	)	PUNCT
ejpam-4573	285	41	is	be	AUX
ejpam-4573	285	42	λsp	λsp	ADJ
ejpam-4573	285	43	-	-	ADJ
ejpam-4573	285	44	compact	compact	ADJ
ejpam-4573	285	45	for	for	ADP
ejpam-4573	285	46	each	each	DET
ejpam-4573	285	47	x	x	SYM
ejpam-4573	285	48	∈	∈	PROPN
ejpam-4573	285	49	x	x	NOUN
ejpam-4573	285	50	,	,	PUNCT
ejpam-4573	285	51	then	then	ADV
ejpam-4573	285	52	(	(	PUNCT
ejpam-4573	285	53	x	x	X
ejpam-4573	285	54	,	,	PUNCT
ejpam-4573	285	55	τ	τ	X
ejpam-4573	285	56	)	)	PUNCT
ejpam-4573	285	57	is	be	AUX
ejpam-4573	285	58	λsp	λsp	NOUN
ejpam-4573	285	59	-	-	PUNCT
ejpam-4573	285	60	t2	t2	NOUN
ejpam-4573	285	61	.	.	PUNCT
ejpam-4573	286	1	proof	proof	NOUN
ejpam-4573	286	2	.	.	PUNCT
ejpam-4573	287	1	for	for	ADP
ejpam-4573	287	2	any	any	DET
ejpam-4573	287	3	distinct	distinct	ADJ
ejpam-4573	287	4	points	point	NOUN
ejpam-4573	287	5	x1	x1	PROPN
ejpam-4573	287	6	,	,	PUNCT
ejpam-4573	287	7	x2	x2	PROPN
ejpam-4573	287	8	of	of	ADP
ejpam-4573	287	9	x	x	PRON
ejpam-4573	287	10	,	,	PUNCT
ejpam-4573	287	11	we	we	PRON
ejpam-4573	287	12	have	have	VERB
ejpam-4573	287	13	f	f	PROPN
ejpam-4573	287	14	(	(	PUNCT
ejpam-4573	287	15	x1	x1	PROPN
ejpam-4573	287	16	)	)	PUNCT
ejpam-4573	288	1	∩	∩	ADJ
ejpam-4573	288	2	f	f	PROPN
ejpam-4573	288	3	(	(	PUNCT
ejpam-4573	288	4	x2	x2	PROPN
ejpam-4573	288	5	)	)	PUNCT
ejpam-4573	288	6	=	=	NOUN
ejpam-4573	288	7	∅	∅	NOUN
ejpam-4573	288	8	since	since	SCONJ
ejpam-4573	288	9	f	f	PROPN
ejpam-4573	288	10	is	be	AUX
ejpam-4573	288	11	injective	injective	ADJ
ejpam-4573	288	12	.	.	PUNCT
ejpam-4573	289	1	since	since	SCONJ
ejpam-4573	289	2	f	f	PROPN
ejpam-4573	289	3	(	(	PUNCT
ejpam-4573	289	4	x	x	X
ejpam-4573	289	5	)	)	PUNCT
ejpam-4573	289	6	is	be	AUX
ejpam-4573	289	7	λsp	λsp	ADJ
ejpam-4573	289	8	-	-	ADJ
ejpam-4573	289	9	compact	compact	ADJ
ejpam-4573	289	10	for	for	SCONJ
ejpam-4573	289	11	each	each	DET
ejpam-4573	289	12	x	x	SYM
ejpam-4573	289	13	∈	∈	PROPN
ejpam-4573	289	14	x	x	X
ejpam-4573	289	15	and	and	CCONJ
ejpam-4573	289	16	(	(	PUNCT
ejpam-4573	289	17	y	y	PROPN
ejpam-4573	289	18	,	,	PUNCT
ejpam-4573	289	19	σ	σ	PROPN
ejpam-4573	289	20	)	)	PUNCT
ejpam-4573	289	21	is	be	AUX
ejpam-4573	289	22	λsp	λsp	NOUN
ejpam-4573	289	23	-	-	ADJ
ejpam-4573	289	24	urusohn	urusohn	ADJ
ejpam-4573	289	25	,	,	PUNCT
ejpam-4573	289	26	by	by	ADP
ejpam-4573	289	27	lemma	lemma	PROPN
ejpam-4573	289	28	7	7	NUM
ejpam-4573	289	29	,	,	PUNCT
ejpam-4573	289	30	there	there	PRON
ejpam-4573	289	31	exist	exist	VERB
ejpam-4573	289	32	v1	v1	NOUN
ejpam-4573	289	33	,	,	PUNCT
ejpam-4573	289	34	v2	v2	PROPN
ejpam-4573	289	35	∈	∈	PROPN
ejpam-4573	289	36	λspo(y	λspo(y	PROPN
ejpam-4573	289	37	,	,	PUNCT
ejpam-4573	289	38	σ	σ	PROPN
ejpam-4573	289	39	)	)	PUNCT
ejpam-4573	290	1	such	such	ADJ
ejpam-4573	290	2	that	that	PRON
ejpam-4573	290	3	v	v	NOUN
ejpam-4573	290	4	(	(	PUNCT
ejpam-4573	290	5	λ	λ	PROPN
ejpam-4573	290	6	,	,	PUNCT
ejpam-4573	290	7	sp	sp	NOUN
ejpam-4573	290	8	)	)	PUNCT
ejpam-4573	290	9	1	1	NUM
ejpam-4573	290	10	∩v	∩v	NOUN
ejpam-4573	290	11	(	(	PUNCT
ejpam-4573	290	12	λ	λ	NOUN
ejpam-4573	290	13	,	,	PUNCT
ejpam-4573	290	14	sp	sp	NOUN
ejpam-4573	290	15	)	)	PUNCT
ejpam-4573	290	16	2	2	NUM
ejpam-4573	290	17	=	=	PUNCT
ejpam-4573	290	18	∅.	∅.	NOUN
ejpam-4573	290	19	since	since	SCONJ
ejpam-4573	290	20	f	f	PROPN
ejpam-4573	290	21	is	be	AUX
ejpam-4573	290	22	upper	upper	ADJ
ejpam-4573	290	23	weakly	weakly	ADJ
ejpam-4573	290	24	(	(	PUNCT
ejpam-4573	290	25	λ	λ	NOUN
ejpam-4573	290	26	,	,	PUNCT
ejpam-4573	290	27	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	290	28	,	,	PUNCT
ejpam-4573	290	29	there	there	PRON
ejpam-4573	290	30	exist	exist	VERB
ejpam-4573	290	31	u1	u1	NOUN
ejpam-4573	290	32	,	,	PUNCT
ejpam-4573	290	33	u2	u2	PROPN
ejpam-4573	290	34	∈	∈	PROPN
ejpam-4573	290	35	λspo(x	λspo(x	PROPN
ejpam-4573	290	36	,	,	PUNCT
ejpam-4573	290	37	τ	τ	X
ejpam-4573	290	38	)	)	PUNCT
ejpam-4573	290	39	containing	contain	VERB
ejpam-4573	290	40	x1	x1	PROPN
ejpam-4573	290	41	and	and	CCONJ
ejpam-4573	290	42	x2	x2	PROPN
ejpam-4573	290	43	,	,	PUNCT
ejpam-4573	290	44	respectively	respectively	ADV
ejpam-4573	290	45	,	,	PUNCT
ejpam-4573	290	46	such	such	ADJ
ejpam-4573	290	47	that	that	SCONJ
ejpam-4573	290	48	f	f	PROPN
ejpam-4573	290	49	(	(	PUNCT
ejpam-4573	290	50	u1	u1	PROPN
ejpam-4573	290	51	)	)	PUNCT
ejpam-4573	290	52	⊆	⊆	NUM
ejpam-4573	290	53	v	v	NOUN
ejpam-4573	290	54	(	(	PUNCT
ejpam-4573	290	55	λ	λ	NOUN
ejpam-4573	290	56	,	,	PUNCT
ejpam-4573	290	57	sp	sp	NOUN
ejpam-4573	290	58	)	)	PUNCT
ejpam-4573	290	59	1	1	NUM
ejpam-4573	290	60	and	and	CCONJ
ejpam-4573	290	61	f	f	PROPN
ejpam-4573	290	62	(	(	PUNCT
ejpam-4573	290	63	u2	u2	PROPN
ejpam-4573	290	64	)	)	PUNCT
ejpam-4573	290	65	⊆	⊆	NUM
ejpam-4573	290	66	v	v	NOUN
ejpam-4573	290	67	(	(	PUNCT
ejpam-4573	290	68	λ	λ	NOUN
ejpam-4573	290	69	,	,	PUNCT
ejpam-4573	290	70	sp	sp	NOUN
ejpam-4573	290	71	)	)	PUNCT
ejpam-4573	290	72	2	2	NUM
ejpam-4573	290	73	.	.	PUNCT
ejpam-4573	291	1	thus	thus	ADV
ejpam-4573	291	2	,	,	PUNCT
ejpam-4573	291	3	u1	u1	NOUN
ejpam-4573	291	4	∩	∩	ADJ
ejpam-4573	291	5	u2	u2	NOUN
ejpam-4573	291	6	=	=	PUNCT
ejpam-4573	291	7	∅	∅	NOUN
ejpam-4573	291	8	and	and	CCONJ
ejpam-4573	291	9	hence	hence	ADV
ejpam-4573	291	10	(	(	PUNCT
ejpam-4573	291	11	x	x	X
ejpam-4573	291	12	,	,	PUNCT
ejpam-4573	291	13	τ	τ	X
ejpam-4573	291	14	)	)	PUNCT
ejpam-4573	291	15	is	be	AUX
ejpam-4573	291	16	λsp	λsp	NOUN
ejpam-4573	291	17	-	-	PUNCT
ejpam-4573	291	18	t2	t2	NOUN
ejpam-4573	291	19	.	.	PUNCT
ejpam-4573	292	1	4	4	X
ejpam-4573	292	2	.	.	X
ejpam-4573	292	3	conclusion	conclusion	VERB
ejpam-4573	292	4	the	the	DET
ejpam-4573	292	5	branch	branch	NOUN
ejpam-4573	292	6	of	of	ADP
ejpam-4573	292	7	mathematics	mathematic	NOUN
ejpam-4573	292	8	called	call	VERB
ejpam-4573	292	9	topology	topology	NOUN
ejpam-4573	292	10	is	be	AUX
ejpam-4573	292	11	concerned	concern	VERB
ejpam-4573	292	12	with	with	ADP
ejpam-4573	292	13	all	all	DET
ejpam-4573	292	14	questions	question	NOUN
ejpam-4573	292	15	directly	directly	ADV
ejpam-4573	292	16	or	or	CCONJ
ejpam-4573	292	17	indirectly	indirectly	ADV
ejpam-4573	292	18	related	relate	VERB
ejpam-4573	292	19	to	to	ADP
ejpam-4573	292	20	continuity	continuity	NOUN
ejpam-4573	292	21	.	.	PUNCT
ejpam-4573	293	1	this	this	DET
ejpam-4573	293	2	paper	paper	NOUN
ejpam-4573	293	3	deals	deal	NOUN
ejpam-4573	293	4	with	with	ADP
ejpam-4573	293	5	the	the	DET
ejpam-4573	293	6	concept	concept	NOUN
ejpam-4573	293	7	of	of	ADP
ejpam-4573	293	8	upper	upper	ADJ
ejpam-4573	293	9	(	(	PUNCT
ejpam-4573	293	10	resp	resp	NOUN
ejpam-4573	293	11	.	.	PUNCT
ejpam-4573	294	1	lower	low	ADJ
ejpam-4573	294	2	)	)	PUNCT
ejpam-4573	294	3	weak	weak	ADJ
ejpam-4573	294	4	(	(	PUNCT
ejpam-4573	294	5	λ	λ	NOUN
ejpam-4573	294	6	,	,	PUNCT
ejpam-4573	294	7	sp)-continuity	sp)-continuity	NOUN
ejpam-4573	294	8	.	.	PUNCT
ejpam-4573	295	1	a	a	DET
ejpam-4573	295	2	multifunction	multifunction	NOUN
ejpam-4573	295	3	f	f	NOUN
ejpam-4573	295	4	:	:	PUNCT
ejpam-4573	295	5	(	(	PUNCT
ejpam-4573	295	6	x	x	X
ejpam-4573	295	7	,	,	PUNCT
ejpam-4573	295	8	τ	τ	X
ejpam-4573	295	9	)	)	PUNCT
ejpam-4573	295	10	→	→	SYM
ejpam-4573	295	11	(	(	PUNCT
ejpam-4573	295	12	y	y	PROPN
ejpam-4573	295	13	,	,	PUNCT
ejpam-4573	295	14	σ	σ	PROPN
ejpam-4573	295	15	)	)	PUNCT
ejpam-4573	295	16	is	be	AUX
ejpam-4573	295	17	called	call	VERB
ejpam-4573	295	18	upper	upper	ADJ
ejpam-4573	295	19	(	(	PUNCT
ejpam-4573	295	20	resp	resp	NOUN
ejpam-4573	295	21	.	.	PUNCT
ejpam-4573	296	1	lower	low	ADJ
ejpam-4573	296	2	)	)	PUNCT
ejpam-4573	296	3	weakly	weakly	ADJ
ejpam-4573	296	4	(	(	PUNCT
ejpam-4573	296	5	λ	λ	NOUN
ejpam-4573	296	6	,	,	PUNCT
ejpam-4573	296	7	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	296	8	multifunctions	multifunction	NOUN
ejpam-4573	296	9	if	if	SCONJ
ejpam-4573	296	10	,	,	PUNCT
ejpam-4573	296	11	for	for	SCONJ
ejpam-4573	296	12	each	each	DET
ejpam-4573	296	13	x	x	SYM
ejpam-4573	296	14	∈	∈	PROPN
ejpam-4573	296	15	x	x	X
ejpam-4573	296	16	and	and	CCONJ
ejpam-4573	296	17	each	each	DET
ejpam-4573	296	18	(	(	PUNCT
ejpam-4573	296	19	λ	λ	PROPN
ejpam-4573	296	20	,	,	PUNCT
ejpam-4573	296	21	sp)-open	sp)-open	NOUN
ejpam-4573	296	22	set	set	VERB
ejpam-4573	296	23	v	v	NUM
ejpam-4573	296	24	of	of	ADP
ejpam-4573	296	25	y	y	PRON
ejpam-4573	297	1	such	such	ADJ
ejpam-4573	297	2	that	that	SCONJ
ejpam-4573	297	3	f	f	PROPN
ejpam-4573	297	4	(	(	PUNCT
ejpam-4573	297	5	x	x	X
ejpam-4573	297	6	)	)	PUNCT
ejpam-4573	297	7	⊆	⊆	NUM
ejpam-4573	297	8	v	v	NOUN
ejpam-4573	297	9	(	(	PUNCT
ejpam-4573	297	10	resp	resp	NOUN
ejpam-4573	297	11	.	.	PUNCT
ejpam-4573	298	1	f	f	X
ejpam-4573	298	2	(	(	PUNCT
ejpam-4573	298	3	x	x	NOUN
ejpam-4573	298	4	)	)	PUNCT
ejpam-4573	298	5	∩	∩	NOUN
ejpam-4573	298	6	v	v	ADP
ejpam-4573	298	7	̸=	̸=	PROPN
ejpam-4573	298	8	∅	∅	NOUN
ejpam-4573	298	9	)	)	PUNCT
ejpam-4573	298	10	,	,	PUNCT
ejpam-4573	298	11	there	there	PRON
ejpam-4573	298	12	exists	exist	VERB
ejpam-4573	298	13	a	a	DET
ejpam-4573	298	14	(	(	PUNCT
ejpam-4573	298	15	λ	λ	NOUN
ejpam-4573	298	16	,	,	PUNCT
ejpam-4573	298	17	sp)-open	sp)-open	NOUN
ejpam-4573	298	18	set	set	VERB
ejpam-4573	298	19	u	u	NOUN
ejpam-4573	298	20	of	of	ADP
ejpam-4573	298	21	references	reference	NOUN
ejpam-4573	298	22	1057	1057	NUM
ejpam-4573	298	23	x	x	SYM
ejpam-4573	298	24	containing	contain	VERB
ejpam-4573	298	25	x	x	PUNCT
ejpam-4573	298	26	such	such	ADJ
ejpam-4573	298	27	that	that	SCONJ
ejpam-4573	298	28	u	u	NOUN
ejpam-4573	298	29	⊆	⊆	NUM
ejpam-4573	298	30	f+(v	f+(v	NOUN
ejpam-4573	298	31	(	(	PUNCT
ejpam-4573	298	32	λ	λ	NOUN
ejpam-4573	298	33	,	,	PUNCT
ejpam-4573	298	34	sp	sp	NOUN
ejpam-4573	298	35	)	)	PUNCT
ejpam-4573	298	36	)	)	PUNCT
ejpam-4573	298	37	(	(	PUNCT
ejpam-4573	298	38	resp	resp	NOUN
ejpam-4573	298	39	.	.	PUNCT
ejpam-4573	299	1	u	u	NOUN
ejpam-4573	299	2	⊆	⊆	NUM
ejpam-4573	299	3	f−(v	f−(v	NOUN
ejpam-4573	299	4	(	(	PUNCT
ejpam-4573	299	5	λ	λ	NOUN
ejpam-4573	299	6	,	,	PUNCT
ejpam-4573	299	7	sp	sp	NOUN
ejpam-4573	299	8	)	)	PUNCT
ejpam-4573	299	9	)	)	PUNCT
ejpam-4573	299	10	)	)	PUNCT
ejpam-4573	299	11	.	.	PUNCT
ejpam-4573	300	1	moreover	moreover	ADV
ejpam-4573	300	2	,	,	PUNCT
ejpam-4573	300	3	some	some	DET
ejpam-4573	300	4	characterizations	characterization	NOUN
ejpam-4573	300	5	and	and	CCONJ
ejpam-4573	300	6	several	several	ADJ
ejpam-4573	300	7	properties	property	NOUN
ejpam-4573	300	8	concerning	concern	VERB
ejpam-4573	300	9	upper	upper	ADJ
ejpam-4573	300	10	(	(	PUNCT
ejpam-4573	300	11	resp	resp	NOUN
ejpam-4573	300	12	.	.	PUNCT
ejpam-4573	301	1	lower	low	ADJ
ejpam-4573	301	2	)	)	PUNCT
ejpam-4573	301	3	weakly	weakly	ADJ
ejpam-4573	301	4	(	(	PUNCT
ejpam-4573	301	5	λ	λ	PROPN
ejpam-4573	301	6	,	,	PUNCT
ejpam-4573	301	7	sp)continuous	sp)continuous	ADJ
ejpam-4573	301	8	multifunctions	multifunction	NOUN
ejpam-4573	301	9	are	be	AUX
ejpam-4573	301	10	explored	explore	VERB
ejpam-4573	301	11	.	.	PUNCT
ejpam-4573	302	1	the	the	DET
ejpam-4573	302	2	ideas	idea	NOUN
ejpam-4573	302	3	and	and	CCONJ
ejpam-4573	302	4	results	result	NOUN
ejpam-4573	302	5	of	of	ADP
ejpam-4573	302	6	this	this	DET
ejpam-4573	302	7	paper	paper	NOUN
ejpam-4573	302	8	may	may	AUX
ejpam-4573	302	9	motivate	motivate	VERB
ejpam-4573	302	10	further	further	ADJ
ejpam-4573	302	11	research	research	NOUN
ejpam-4573	302	12	.	.	PUNCT
ejpam-4573	303	1	acknowledgements	acknowledgement	NOUN
ejpam-4573	303	2	this	this	DET
ejpam-4573	303	3	research	research	NOUN
ejpam-4573	303	4	project	project	NOUN
ejpam-4573	303	5	was	be	AUX
ejpam-4573	303	6	financially	financially	ADV
ejpam-4573	303	7	supported	support	VERB
ejpam-4573	303	8	by	by	ADP
ejpam-4573	303	9	mahasarakham	mahasarakham	PROPN
ejpam-4573	303	10	university	university	PROPN
ejpam-4573	303	11	.	.	PUNCT
ejpam-4573	304	1	references	reference	NOUN
ejpam-4573	304	2	[	[	X
ejpam-4573	304	3	1	1	NUM
ejpam-4573	304	4	]	]	PUNCT
ejpam-4573	304	5	d.	d.	PROPN
ejpam-4573	304	6	andrijević.	andrijević.	PROPN
ejpam-4573	304	7	on	on	ADP
ejpam-4573	304	8	b	b	X
ejpam-4573	304	9	-	-	PUNCT
ejpam-4573	304	10	open	open	ADJ
ejpam-4573	304	11	sets	set	NOUN
ejpam-4573	304	12	.	.	PUNCT
ejpam-4573	305	1	matematiički	matematiički	PROPN
ejpam-4573	305	2	vesnik	vesnik	PROPN
ejpam-4573	305	3	,	,	PUNCT
ejpam-4573	305	4	48:59–64	48:59–64	PROPN
ejpam-4573	305	5	,	,	PUNCT
ejpam-4573	305	6	1996	1996	NUM
ejpam-4573	305	7	.	.	PUNCT
ejpam-4573	306	1	[	[	X
ejpam-4573	306	2	2	2	NUM
ejpam-4573	306	3	]	]	PUNCT
ejpam-4573	306	4	c.	c.	PROPN
ejpam-4573	306	5	berge	berge	PROPN
ejpam-4573	306	6	.	.	PUNCT
ejpam-4573	306	7	espaces	espace	VERB
ejpam-4573	306	8	topologiques	topologique	NOUN
ejpam-4573	306	9	fonctions	fonction	NOUN
ejpam-4573	306	10	multivoques	multivoque	NOUN
ejpam-4573	306	11	.	.	PUNCT
ejpam-4573	307	1	dunod	dunod	PROPN
ejpam-4573	307	2	,	,	PUNCT
ejpam-4573	307	3	paris	paris	PROPN
ejpam-4573	307	4	,	,	PUNCT
ejpam-4573	307	5	1959	1959	NUM
ejpam-4573	307	6	.	.	PUNCT
ejpam-4573	308	1	[	[	X
ejpam-4573	308	2	3	3	X
ejpam-4573	308	3	]	]	PUNCT
ejpam-4573	308	4	c.	c.	PROPN
ejpam-4573	308	5	boonpok	boonpok	PROPN
ejpam-4573	308	6	.	.	PUNCT
ejpam-4573	309	1	(	(	PUNCT
ejpam-4573	309	2	λ	λ	NOUN
ejpam-4573	309	3	,	,	PUNCT
ejpam-4573	309	4	sp)-closed	sp)-close	VERB
ejpam-4573	309	5	sets	set	NOUN
ejpam-4573	309	6	and	and	CCONJ
ejpam-4573	309	7	related	related	ADJ
ejpam-4573	309	8	topics	topic	NOUN
ejpam-4573	309	9	in	in	ADP
ejpam-4573	309	10	topological	topological	ADJ
ejpam-4573	309	11	spaces	space	NOUN
ejpam-4573	309	12	.	.	PUNCT
ejpam-4573	310	1	wseas	wseas	VERB
ejpam-4573	310	2	transactions	transaction	NOUN
ejpam-4573	310	3	on	on	ADP
ejpam-4573	310	4	mathematics	mathematic	NOUN
ejpam-4573	310	5	,	,	PUNCT
ejpam-4573	310	6	19:312–322	19:312–322	PROPN
ejpam-4573	310	7	,	,	PUNCT
ejpam-4573	310	8	2020	2020	NUM
ejpam-4573	310	9	.	.	PUNCT
ejpam-4573	311	1	[	[	X
ejpam-4573	311	2	4	4	NUM
ejpam-4573	311	3	]	]	PUNCT
ejpam-4573	311	4	c.	c.	PROPN
ejpam-4573	311	5	boonpok	boonpok	PROPN
ejpam-4573	311	6	and	and	CCONJ
ejpam-4573	311	7	c.	c.	PROPN
ejpam-4573	311	8	viriyapong	viriyapong	PROPN
ejpam-4573	311	9	.	.	PUNCT
ejpam-4573	312	1	on	on	ADP
ejpam-4573	312	2	generalized	generalized	ADJ
ejpam-4573	312	3	(	(	PUNCT
ejpam-4573	312	4	λ	λ	PROPN
ejpam-4573	312	5	,	,	PUNCT
ejpam-4573	312	6	sp)-closed	sp)-close	VERB
ejpam-4573	312	7	sets	set	NOUN
ejpam-4573	312	8	.	.	PUNCT
ejpam-4573	313	1	european	european	ADJ
ejpam-4573	313	2	journal	journal	PROPN
ejpam-4573	313	3	of	of	ADP
ejpam-4573	313	4	pure	pure	ADJ
ejpam-4573	313	5	and	and	CCONJ
ejpam-4573	313	6	applied	applied	ADJ
ejpam-4573	313	7	mathematics	mathematic	NOUN
ejpam-4573	313	8	,	,	PUNCT
ejpam-4573	313	9	15(4):2127–2140	15(4):2127–2140	NUM
ejpam-4573	313	10	,	,	PUNCT
ejpam-4573	313	11	2022	2022	NUM
ejpam-4573	313	12	.	.	PUNCT
ejpam-4573	314	1	[	[	X
ejpam-4573	314	2	5	5	X
ejpam-4573	314	3	]	]	PUNCT
ejpam-4573	314	4	c.	c.	PROPN
ejpam-4573	314	5	boonpok	boonpok	PROPN
ejpam-4573	314	6	,	,	PUNCT
ejpam-4573	314	7	c.	c.	PROPN
ejpam-4573	314	8	viriyapong	viriyapong	PROPN
ejpam-4573	314	9	,	,	PUNCT
ejpam-4573	314	10	and	and	CCONJ
ejpam-4573	314	11	m.	m.	NOUN
ejpam-4573	314	12	thongmoon	thongmoon	NOUN
ejpam-4573	314	13	.	.	PUNCT
ejpam-4573	315	1	on	on	ADP
ejpam-4573	315	2	upper	upper	ADJ
ejpam-4573	315	3	and	and	CCONJ
ejpam-4573	315	4	lower	low	ADJ
ejpam-4573	315	5	(	(	PUNCT
ejpam-4573	315	6	τ1	τ1	NOUN
ejpam-4573	315	7	,	,	PUNCT
ejpam-4573	315	8	τ2)precontinuous	τ2)precontinuous	ADJ
ejpam-4573	315	9	multifunctions	multifunction	NOUN
ejpam-4573	315	10	.	.	PUNCT
ejpam-4573	316	1	journal	journal	PROPN
ejpam-4573	316	2	of	of	ADP
ejpam-4573	316	3	mathematics	mathematics	PROPN
ejpam-4573	316	4	and	and	CCONJ
ejpam-4573	316	5	computer	computer	NOUN
ejpam-4573	316	6	science	science	NOUN
ejpam-4573	316	7	,	,	PUNCT
ejpam-4573	316	8	18:282–293	18:282–293	NUM
ejpam-4573	316	9	,	,	PUNCT
ejpam-4573	316	10	2018	2018	NUM
ejpam-4573	316	11	.	.	PUNCT
ejpam-4573	317	1	[	[	X
ejpam-4573	317	2	6	6	NUM
ejpam-4573	317	3	]	]	PUNCT
ejpam-4573	317	4	m.	m.	NOUN
ejpam-4573	317	5	e.	e.	PROPN
ejpam-4573	317	6	abd	abd	PROPN
ejpam-4573	317	7	el	el	PROPN
ejpam-4573	317	8	-	-	PROPN
ejpam-4573	317	9	monsef	monsef	PROPN
ejpam-4573	317	10	,	,	PUNCT
ejpam-4573	317	11	s.	s.	PROPN
ejpam-4573	317	12	n.	n.	PROPN
ejpam-4573	317	13	el	el	PROPN
ejpam-4573	317	14	-	-	PROPN
ejpam-4573	317	15	deeb	deeb	PROPN
ejpam-4573	317	16	,	,	PUNCT
ejpam-4573	317	17	and	and	CCONJ
ejpam-4573	317	18	r.	r.	PROPN
ejpam-4573	317	19	a.	a.	PROPN
ejpam-4573	317	20	mahmoud	mahmoud	PROPN
ejpam-4573	317	21	.	.	PUNCT
ejpam-4573	318	1	β	β	X
ejpam-4573	318	2	-	-	ADJ
ejpam-4573	318	3	open	open	ADJ
ejpam-4573	318	4	sets	set	NOUN
ejpam-4573	318	5	and	and	CCONJ
ejpam-4573	318	6	βcontinuous	βcontinuous	ADJ
ejpam-4573	318	7	mappings	mapping	NOUN
ejpam-4573	318	8	.	.	PUNCT
ejpam-4573	319	1	bulletin	bulletin	NOUN
ejpam-4573	319	2	of	of	ADP
ejpam-4573	319	3	the	the	DET
ejpam-4573	319	4	faculty	faculty	NOUN
ejpam-4573	319	5	of	of	ADP
ejpam-4573	319	6	science	science	NOUN
ejpam-4573	319	7	.	.	PUNCT
ejpam-4573	320	1	assiut	assiut	PROPN
ejpam-4573	320	2	university	university	PROPN
ejpam-4573	320	3	.	.	PUNCT
ejpam-4573	320	4	,	,	PUNCT
ejpam-4573	320	5	12:77–90	12:77–90	NUM
ejpam-4573	320	6	,	,	PUNCT
ejpam-4573	320	7	1983	1983	NUM
ejpam-4573	320	8	.	.	PUNCT
ejpam-4573	321	1	[	[	X
ejpam-4573	321	2	7	7	X
ejpam-4573	321	3	]	]	PUNCT
ejpam-4573	321	4	t.	t.	PROPN
ejpam-4573	321	5	husain	husain	PROPN
ejpam-4573	321	6	.	.	PUNCT
ejpam-4573	322	1	almost	almost	ADV
ejpam-4573	322	2	continuous	continuous	ADJ
ejpam-4573	322	3	mappings	mapping	NOUN
ejpam-4573	322	4	.	.	PUNCT
ejpam-4573	323	1	prace	prace	PROPN
ejpam-4573	323	2	matematika	matematika	PROPN
ejpam-4573	323	3	,	,	PUNCT
ejpam-4573	323	4	10:1–7	10:1–7	NUM
ejpam-4573	323	5	,	,	PUNCT
ejpam-4573	323	6	1966	1966	NUM
ejpam-4573	323	7	.	.	PUNCT
ejpam-4573	324	1	[	[	X
ejpam-4573	324	2	8	8	NUM
ejpam-4573	324	3	]	]	X
ejpam-4573	324	4	d.	d.	PROPN
ejpam-4573	324	5	s.	s.	PROPN
ejpam-4573	324	6	janković.	janković.	PROPN
ejpam-4573	324	7	θ	θ	PROPN
ejpam-4573	324	8	-	-	ADJ
ejpam-4573	324	9	regular	regular	ADJ
ejpam-4573	324	10	spaces	space	NOUN
ejpam-4573	324	11	.	.	PUNCT
ejpam-4573	325	1	international	international	ADJ
ejpam-4573	325	2	journal	journal	PROPN
ejpam-4573	325	3	of	of	ADP
ejpam-4573	325	4	mathematics	mathematics	PROPN
ejpam-4573	325	5	and	and	CCONJ
ejpam-4573	325	6	mathematical	mathematical	ADJ
ejpam-4573	325	7	sciences	science	NOUN
ejpam-4573	325	8	,	,	PUNCT
ejpam-4573	325	9	8:615–619	8:615–619	NUM
ejpam-4573	325	10	,	,	PUNCT
ejpam-4573	325	11	1985	1985	NUM
ejpam-4573	325	12	.	.	PUNCT
ejpam-4573	326	1	[	[	X
ejpam-4573	326	2	9	9	NUM
ejpam-4573	326	3	]	]	X
ejpam-4573	326	4	n.	n.	PROPN
ejpam-4573	326	5	levine	levine	PROPN
ejpam-4573	326	6	.	.	PUNCT
ejpam-4573	327	1	a	a	DET
ejpam-4573	327	2	decomposition	decomposition	NOUN
ejpam-4573	327	3	of	of	ADP
ejpam-4573	327	4	continuity	continuity	NOUN
ejpam-4573	327	5	in	in	ADP
ejpam-4573	327	6	topological	topological	ADJ
ejpam-4573	327	7	spaces	space	NOUN
ejpam-4573	327	8	.	.	PUNCT
ejpam-4573	328	1	the	the	DET
ejpam-4573	328	2	american	american	PROPN
ejpam-4573	328	3	mathematical	mathematical	PROPN
ejpam-4573	328	4	monthly	monthly	ADV
ejpam-4573	328	5	,	,	PUNCT
ejpam-4573	328	6	68:44–46	68:44–46	NUM
ejpam-4573	328	7	,	,	PUNCT
ejpam-4573	328	8	1961	1961	NUM
ejpam-4573	328	9	.	.	PUNCT
ejpam-4573	329	1	[	[	X
ejpam-4573	329	2	10	10	NUM
ejpam-4573	329	3	]	]	X
ejpam-4573	329	4	n.	n.	PROPN
ejpam-4573	329	5	levine	levine	PROPN
ejpam-4573	329	6	.	.	PUNCT
ejpam-4573	330	1	semi	semi	ADJ
ejpam-4573	330	2	-	-	ADJ
ejpam-4573	330	3	open	open	ADJ
ejpam-4573	330	4	sets	set	NOUN
ejpam-4573	330	5	and	and	CCONJ
ejpam-4573	330	6	semi	semi	ADJ
ejpam-4573	330	7	-	-	NOUN
ejpam-4573	330	8	continuity	continuity	NOUN
ejpam-4573	330	9	in	in	ADP
ejpam-4573	330	10	topological	topological	ADJ
ejpam-4573	330	11	spaces	space	NOUN
ejpam-4573	330	12	.	.	PUNCT
ejpam-4573	331	1	the	the	DET
ejpam-4573	331	2	american	american	PROPN
ejpam-4573	331	3	mathematical	mathematical	PROPN
ejpam-4573	331	4	monthly	monthly	ADV
ejpam-4573	331	5	,	,	PUNCT
ejpam-4573	331	6	70:36–41	70:36–41	NUM
ejpam-4573	331	7	,	,	PUNCT
ejpam-4573	331	8	1963	1963	NUM
ejpam-4573	331	9	.	.	PUNCT
ejpam-4573	332	1	[	[	X
ejpam-4573	332	2	11	11	NUM
ejpam-4573	332	3	]	]	PUNCT
ejpam-4573	332	4	s.	s.	PROPN
ejpam-4573	332	5	marcus	marcus	PROPN
ejpam-4573	332	6	.	.	PUNCT
ejpam-4573	333	1	sur	sur	PROPN
ejpam-4573	333	2	les	les	PROPN
ejpam-4573	333	3	fonctions	fonctions	PROPN
ejpam-4573	333	4	quasicontinues	quasicontinue	NOUN
ejpam-4573	333	5	au	au	PROPN
ejpam-4573	333	6	sens	sens	X
ejpam-4573	333	7	de	de	PROPN
ejpam-4573	333	8	s.	s.	PROPN
ejpam-4573	333	9	kempisty	kempisty	PROPN
ejpam-4573	333	10	.	.	PUNCT
ejpam-4573	334	1	colloquium	colloquium	NOUN
ejpam-4573	334	2	mathematicum	mathematicum	PROPN
ejpam-4573	334	3	,	,	PUNCT
ejpam-4573	334	4	8:47–53	8:47–53	NUM
ejpam-4573	334	5	,	,	PUNCT
ejpam-4573	334	6	1961	1961	NUM
ejpam-4573	334	7	.	.	PUNCT
ejpam-4573	335	1	[	[	X
ejpam-4573	335	2	12	12	NUM
ejpam-4573	335	3	]	]	PUNCT
ejpam-4573	335	4	a.	a.	NOUN
ejpam-4573	335	5	neubrunnová.	neubrunnová.	PROPN
ejpam-4573	335	6	on	on	ADP
ejpam-4573	335	7	certain	certain	ADJ
ejpam-4573	335	8	generalizations	generalization	NOUN
ejpam-4573	335	9	of	of	ADP
ejpam-4573	335	10	the	the	DET
ejpam-4573	335	11	notion	notion	NOUN
ejpam-4573	335	12	of	of	ADP
ejpam-4573	335	13	continuity	continuity	NOUN
ejpam-4573	335	14	.	.	PUNCT
ejpam-4573	336	1	matematický	matematický	ADJ
ejpam-4573	336	2	časopis	časopis	PROPN
ejpam-4573	336	3	,	,	PUNCT
ejpam-4573	336	4	23:374–380	23:374–380	NUM
ejpam-4573	336	5	,	,	PUNCT
ejpam-4573	336	6	1973	1973	NUM
ejpam-4573	336	7	.	.	PUNCT
ejpam-4573	337	1	references	reference	NOUN
ejpam-4573	337	2	1058	1058	NUM
ejpam-4573	337	3	[	[	X
ejpam-4573	337	4	13	13	NUM
ejpam-4573	337	5	]	]	PUNCT
ejpam-4573	337	6	t.	t.	PROPN
ejpam-4573	337	7	noiri	noiri	PROPN
ejpam-4573	337	8	.	.	PUNCT
ejpam-4573	338	1	properties	property	NOUN
ejpam-4573	338	2	of	of	ADP
ejpam-4573	338	3	some	some	DET
ejpam-4573	338	4	weak	weak	ADJ
ejpam-4573	338	5	forms	form	NOUN
ejpam-4573	338	6	of	of	ADP
ejpam-4573	338	7	continuity	continuity	NOUN
ejpam-4573	338	8	.	.	PUNCT
ejpam-4573	339	1	international	international	ADJ
ejpam-4573	339	2	journal	journal	PROPN
ejpam-4573	339	3	of	of	ADP
ejpam-4573	339	4	mathematics	mathematics	PROPN
ejpam-4573	339	5	and	and	CCONJ
ejpam-4573	339	6	mathematical	mathematical	ADJ
ejpam-4573	339	7	sciences	science	NOUN
ejpam-4573	339	8	,	,	PUNCT
ejpam-4573	339	9	10(1):97–111	10(1):97–111	NUM
ejpam-4573	339	10	,	,	PUNCT
ejpam-4573	339	11	1987	1987	NUM
ejpam-4573	339	12	.	.	PUNCT
ejpam-4573	340	1	[	[	X
ejpam-4573	340	2	14	14	NUM
ejpam-4573	340	3	]	]	PUNCT
ejpam-4573	340	4	t.	t.	PROPN
ejpam-4573	340	5	noiri	noiri	PROPN
ejpam-4573	340	6	and	and	CCONJ
ejpam-4573	340	7	e.	e.	PROPN
ejpam-4573	340	8	hatir	hatir	PROPN
ejpam-4573	340	9	.	.	PUNCT
ejpam-4573	341	1	λsp	λsp	NOUN
ejpam-4573	341	2	-	-	PUNCT
ejpam-4573	341	3	sets	set	NOUN
ejpam-4573	341	4	and	and	CCONJ
ejpam-4573	341	5	some	some	DET
ejpam-4573	341	6	weak	weak	ADJ
ejpam-4573	341	7	separation	separation	NOUN
ejpam-4573	341	8	axioms	axiom	NOUN
ejpam-4573	341	9	.	.	PUNCT
ejpam-4573	342	1	acta	acta	PROPN
ejpam-4573	342	2	mathematica	mathematica	PROPN
ejpam-4573	342	3	hungarica	hungarica	PROPN
ejpam-4573	342	4	,	,	PUNCT
ejpam-4573	342	5	103(3):225–232	103(3):225–232	NUM
ejpam-4573	342	6	,	,	PUNCT
ejpam-4573	342	7	2004	2004	NUM
ejpam-4573	342	8	.	.	PUNCT
ejpam-4573	343	1	[	[	X
ejpam-4573	343	2	15	15	X
ejpam-4573	343	3	]	]	X
ejpam-4573	343	4	t.	t.	PROPN
ejpam-4573	343	5	noiri	noiri	PROPN
ejpam-4573	343	6	and	and	CCONJ
ejpam-4573	343	7	v.	v.	ADP
ejpam-4573	343	8	popa	popa	NOUN
ejpam-4573	343	9	.	.	PUNCT
ejpam-4573	344	1	on	on	ADP
ejpam-4573	344	2	upper	upper	ADJ
ejpam-4573	344	3	and	and	CCONJ
ejpam-4573	344	4	lower	low	ADJ
ejpam-4573	344	5	weakly	weakly	ADJ
ejpam-4573	344	6	quasicontinuous	quasicontinuous	ADJ
ejpam-4573	344	7	multifunctions	multifunction	NOUN
ejpam-4573	344	8	.	.	PUNCT
ejpam-4573	345	1	revue	revue	PROPN
ejpam-4573	345	2	roumaine	roumaine	NOUN
ejpam-4573	345	3	de	de	X
ejpam-4573	345	4	mathematiques	mathematique	NOUN
ejpam-4573	345	5	pures	pure	NOUN
ejpam-4573	345	6	et	et	PROPN
ejpam-4573	345	7	appliquees	appliquee	NOUN
ejpam-4573	345	8	,	,	PUNCT
ejpam-4573	345	9	36:499–508	36:499–508	NUM
ejpam-4573	345	10	,	,	PUNCT
ejpam-4573	345	11	1992	1992	NUM
ejpam-4573	345	12	.	.	PUNCT
ejpam-4573	346	1	[	[	X
ejpam-4573	346	2	16	16	NUM
ejpam-4573	346	3	]	]	PUNCT
ejpam-4573	346	4	t.	t.	PROPN
ejpam-4573	346	5	noiri	noiri	PROPN
ejpam-4573	346	6	and	and	CCONJ
ejpam-4573	346	7	v.	v.	ADP
ejpam-4573	346	8	popa	popa	NOUN
ejpam-4573	346	9	.	.	PUNCT
ejpam-4573	347	1	almost	almost	ADV
ejpam-4573	347	2	weakly	weakly	ADJ
ejpam-4573	347	3	continuous	continuous	ADJ
ejpam-4573	347	4	multifunctions	multifunction	NOUN
ejpam-4573	347	5	.	.	PUNCT
ejpam-4573	348	1	demonstratio	demonstratio	PROPN
ejpam-4573	348	2	mathematica	mathematica	PROPN
ejpam-4573	348	3	,	,	PUNCT
ejpam-4573	348	4	26:363–380	26:363–380	PROPN
ejpam-4573	348	5	,	,	PUNCT
ejpam-4573	348	6	1993	1993	NUM
ejpam-4573	348	7	.	.	PUNCT
ejpam-4573	349	1	[	[	X
ejpam-4573	349	2	17	17	NUM
ejpam-4573	349	3	]	]	PUNCT
ejpam-4573	349	4	t.	t.	PROPN
ejpam-4573	349	5	noiri	noiri	PROPN
ejpam-4573	349	6	and	and	CCONJ
ejpam-4573	349	7	v.	v.	ADP
ejpam-4573	349	8	popa	popa	NOUN
ejpam-4573	349	9	.	.	PUNCT
ejpam-4573	350	1	a	a	DET
ejpam-4573	350	2	unified	unified	ADJ
ejpam-4573	350	3	theory	theory	NOUN
ejpam-4573	350	4	of	of	ADP
ejpam-4573	350	5	weak	weak	ADJ
ejpam-4573	350	6	continuity	continuity	NOUN
ejpam-4573	350	7	for	for	ADP
ejpam-4573	350	8	multifunctions	multifunction	NOUN
ejpam-4573	350	9	.	.	PUNCT
ejpam-4573	351	1	studii	studii	PROPN
ejpam-4573	351	2	şi	şi	PROPN
ejpam-4573	351	3	cercetǎri	cercetǎri	VERB
ejpam-4573	351	4	ştiinţifice	ştiinţifice	NOUN
ejpam-4573	351	5	,	,	PUNCT
ejpam-4573	351	6	ser	ser	NOUN
ejpam-4573	351	7	.	.	PUNCT
ejpam-4573	352	1	matematicǎuniversitatea	matematicǎuniversitatea	PROPN
ejpam-4573	352	2	din	din	VERB
ejpam-4573	352	3	bacǎu	bacǎu	PROPN
ejpam-4573	352	4	,	,	PUNCT
ejpam-4573	352	5	16:167–200	16:167–200	NUM
ejpam-4573	352	6	,	,	PUNCT
ejpam-4573	352	7	2006	2006	NUM
ejpam-4573	352	8	.	.	PUNCT
ejpam-4573	353	1	[	[	X
ejpam-4573	353	2	18	18	NUM
ejpam-4573	353	3	]	]	X
ejpam-4573	353	4	v.	v.	PROPN
ejpam-4573	353	5	i.	i.	PROPN
ejpam-4573	353	6	ponomarev	ponomarev	PROPN
ejpam-4573	353	7	.	.	PUNCT
ejpam-4573	354	1	properties	property	NOUN
ejpam-4573	354	2	of	of	ADP
ejpam-4573	354	3	topological	topological	ADJ
ejpam-4573	354	4	spaces	space	NOUN
ejpam-4573	354	5	preserved	preserve	VERB
ejpam-4573	354	6	under	under	ADP
ejpam-4573	354	7	multivalued	multivalued	ADJ
ejpam-4573	354	8	continuous	continuous	ADJ
ejpam-4573	354	9	mappings	mapping	NOUN
ejpam-4573	354	10	on	on	ADP
ejpam-4573	354	11	compacta	compacta	NOUN
ejpam-4573	354	12	.	.	PUNCT
ejpam-4573	355	1	american	american	PROPN
ejpam-4573	355	2	mathematical	mathematical	ADJ
ejpam-4573	355	3	society	society	NOUN
ejpam-4573	355	4	translations	translation	NOUN
ejpam-4573	355	5	,	,	PUNCT
ejpam-4573	355	6	38(2):119–140	38(2):119–140	NUM
ejpam-4573	355	7	,	,	PUNCT
ejpam-4573	355	8	1964	1964	NUM
ejpam-4573	355	9	.	.	PUNCT
ejpam-4573	356	1	[	[	X
ejpam-4573	356	2	19	19	NUM
ejpam-4573	356	3	]	]	X
ejpam-4573	356	4	v.	v.	CCONJ
ejpam-4573	356	5	popa	popa	NOUN
ejpam-4573	356	6	.	.	PUNCT
ejpam-4573	357	1	weakly	weakly	ADJ
ejpam-4573	357	2	continuous	continuous	ADJ
ejpam-4573	357	3	multifunctions	multifunction	NOUN
ejpam-4573	357	4	.	.	PUNCT
ejpam-4573	358	1	bollettino	bollettino	PROPN
ejpam-4573	358	2	dell	dell	PROPN
ejpam-4573	358	3	’	'	PUNCT
ejpam-4573	358	4	unione	unione	PROPN
ejpam-4573	358	5	matematica	matematica	PROPN
ejpam-4573	358	6	italiana	italiana	PROPN
ejpam-4573	358	7	,	,	PUNCT
ejpam-4573	358	8	5(15(a)):379–388	5(15(a)):379–388	PROPN
ejpam-4573	358	9	,	,	PUNCT
ejpam-4573	358	10	1978	1978	NUM
ejpam-4573	358	11	.	.	PUNCT
ejpam-4573	359	1	[	[	X
ejpam-4573	359	2	20	20	NUM
ejpam-4573	359	3	]	]	PUNCT
ejpam-4573	359	4	v.	v.	CCONJ
ejpam-4573	359	5	popa	popa	NOUN
ejpam-4573	359	6	and	and	CCONJ
ejpam-4573	359	7	t.	t.	PROPN
ejpam-4573	359	8	noiri	noiri	PROPN
ejpam-4573	359	9	.	.	PUNCT
ejpam-4573	360	1	on	on	ADP
ejpam-4573	360	2	upper	upper	ADJ
ejpam-4573	360	3	and	and	CCONJ
ejpam-4573	360	4	lower	low	ADJ
ejpam-4573	360	5	almost	almost	ADV
ejpam-4573	360	6	α	α	ADJ
ejpam-4573	360	7	-	-	ADJ
ejpam-4573	360	8	continuous	continuous	ADJ
ejpam-4573	360	9	multifunctions	multifunction	NOUN
ejpam-4573	360	10	.	.	PUNCT
ejpam-4573	361	1	demonstratio	demonstratio	PROPN
ejpam-4573	361	2	mathematica	mathematica	PROPN
ejpam-4573	361	3	,	,	PUNCT
ejpam-4573	361	4	29:381–396	29:381–396	PROPN
ejpam-4573	361	5	,	,	PUNCT
ejpam-4573	361	6	1996	1996	NUM
ejpam-4573	361	7	.	.	PUNCT
ejpam-4573	362	1	[	[	X
ejpam-4573	362	2	21	21	NUM
ejpam-4573	362	3	]	]	X
ejpam-4573	362	4	v.	v.	CCONJ
ejpam-4573	362	5	popa	popa	NOUN
ejpam-4573	362	6	and	and	CCONJ
ejpam-4573	362	7	t.	t.	PROPN
ejpam-4573	362	8	noiri	noiri	PROPN
ejpam-4573	362	9	.	.	PUNCT
ejpam-4573	363	1	on	on	ADP
ejpam-4573	363	2	upper	upper	ADJ
ejpam-4573	363	3	and	and	CCONJ
ejpam-4573	363	4	lower	low	ADJ
ejpam-4573	363	5	weakly	weakly	ADJ
ejpam-4573	363	6	β	β	ADJ
ejpam-4573	363	7	-	-	ADJ
ejpam-4573	363	8	continuous	continuous	ADJ
ejpam-4573	363	9	multifunctions	multifunction	NOUN
ejpam-4573	363	10	.	.	PUNCT
ejpam-4573	364	1	annales	annales	PROPN
ejpam-4573	364	2	universitatis	universitatis	PROPN
ejpam-4573	364	3	scientiarum	scientiarum	PROPN
ejpam-4573	364	4	budapestinensis	budapestinensis	PROPN
ejpam-4573	364	5	,	,	PUNCT
ejpam-4573	364	6	43:25–48	43:25–48	PROPN
ejpam-4573	364	7	,	,	PUNCT
ejpam-4573	364	8	2000	2000	NUM
ejpam-4573	364	9	.	.	PUNCT
ejpam-4573	365	1	[	[	X
ejpam-4573	365	2	22	22	NUM
ejpam-4573	365	3	]	]	PUNCT
ejpam-4573	365	4	v.	v.	CCONJ
ejpam-4573	365	5	popa	popa	NOUN
ejpam-4573	365	6	and	and	CCONJ
ejpam-4573	365	7	c.	c.	PROPN
ejpam-4573	365	8	stan	stan	PROPN
ejpam-4573	365	9	.	.	PUNCT
ejpam-4573	366	1	on	on	ADP
ejpam-4573	366	2	a	a	DET
ejpam-4573	366	3	decomposition	decomposition	NOUN
ejpam-4573	366	4	of	of	ADP
ejpam-4573	366	5	quasi	quasi	NOUN
ejpam-4573	366	6	-	-	NOUN
ejpam-4573	366	7	continuity	continuity	NOUN
ejpam-4573	366	8	in	in	ADP
ejpam-4573	366	9	topological	topological	ADJ
ejpam-4573	366	10	spaces	space	NOUN
ejpam-4573	366	11	.	.	PUNCT
ejpam-4573	367	1	studii	studii	PROPN
ejpam-4573	367	2	şi	şi	PROPN
ejpam-4573	367	3	cercetǎri	cercetǎri	PROPN
ejpam-4573	367	4	de	de	X
ejpam-4573	367	5	matematicǎ	matematicǎ	NOUN
ejpam-4573	367	6	,	,	PUNCT
ejpam-4573	367	7	25:41–43	25:41–43	NUM
ejpam-4573	367	8	,	,	PUNCT
ejpam-4573	367	9	1973	1973	NUM
ejpam-4573	367	10	.	.	PUNCT
ejpam-4573	368	1	[	[	X
ejpam-4573	368	2	23	23	NUM
ejpam-4573	368	3	]	]	X
ejpam-4573	368	4	r.	r.	PROPN
ejpam-4573	368	5	e.	e.	PROPN
ejpam-4573	368	6	smithson	smithson	PROPN
ejpam-4573	368	7	.	.	PUNCT
ejpam-4573	369	1	almost	almost	ADV
ejpam-4573	369	2	and	and	CCONJ
ejpam-4573	369	3	weak	weak	ADJ
ejpam-4573	369	4	continuity	continuity	NOUN
ejpam-4573	369	5	for	for	ADP
ejpam-4573	369	6	multifunctions	multifunction	NOUN
ejpam-4573	369	7	.	.	PUNCT
ejpam-4573	370	1	bulletin	bulletin	NOUN
ejpam-4573	370	2	of	of	ADP
ejpam-4573	370	3	the	the	DET
ejpam-4573	370	4	calcutta	calcutta	PROPN
ejpam-4573	370	5	mathematical	mathematical	ADJ
ejpam-4573	370	6	society	society	NOUN
ejpam-4573	370	7	,	,	PUNCT
ejpam-4573	370	8	70:383–390	70:383–390	NUM
ejpam-4573	370	9	,	,	PUNCT
ejpam-4573	370	10	1978	1978	NUM
ejpam-4573	370	11	.	.	PUNCT
ejpam-4573	371	1	[	[	X
ejpam-4573	371	2	24	24	NUM
ejpam-4573	371	3	]	]	X
ejpam-4573	371	4	c.	c.	PROPN
ejpam-4573	371	5	viriyapong	viriyapong	PROPN
ejpam-4573	371	6	and	and	CCONJ
ejpam-4573	371	7	c.	c.	PROPN
ejpam-4573	371	8	boonpok	boonpok	PROPN
ejpam-4573	371	9	.	.	PUNCT
ejpam-4573	372	1	(	(	PUNCT
ejpam-4573	372	2	λ	λ	X
ejpam-4573	372	3	,	,	PUNCT
ejpam-4573	372	4	sp)-continuous	sp)-continuous	ADJ
ejpam-4573	372	5	functions	function	NOUN
ejpam-4573	372	6	.	.	PUNCT
ejpam-4573	373	1	wseas	wseas	VERB
ejpam-4573	373	2	transactions	transaction	NOUN
ejpam-4573	373	3	on	on	ADP
ejpam-4573	373	4	mathematics	mathematic	NOUN
ejpam-4573	373	5	,	,	PUNCT
ejpam-4573	373	6	21:380–385	21:380–385	NUM
ejpam-4573	373	7	,	,	PUNCT
ejpam-4573	373	8	2022	2022	NUM
ejpam-4573	373	9	.	.	PUNCT
ejpam-4573	374	1	[	[	X
ejpam-4573	374	2	25	25	NUM
ejpam-4573	374	3	]	]	X
ejpam-4573	374	4	c.	c.	PROPN
ejpam-4573	374	5	viriyapong	viriyapong	PROPN
ejpam-4573	374	6	and	and	CCONJ
ejpam-4573	374	7	c.	c.	PROPN
ejpam-4573	374	8	boonpok	boonpok	PROPN
ejpam-4573	374	9	.	.	PUNCT
ejpam-4573	375	1	(	(	PUNCT
ejpam-4573	375	2	τ1	τ1	NOUN
ejpam-4573	375	3	,	,	PUNCT
ejpam-4573	375	4	τ2)α	τ2)α	NOUN
ejpam-4573	375	5	-	-	PUNCT
ejpam-4573	375	6	continuity	continuity	NOUN
ejpam-4573	375	7	for	for	ADP
ejpam-4573	375	8	multifunctions	multifunction	NOUN
ejpam-4573	375	9	.	.	PUNCT
ejpam-4573	376	1	journal	journal	PROPN
ejpam-4573	376	2	of	of	ADP
ejpam-4573	376	3	mathematics	mathematic	NOUN
ejpam-4573	376	4	,	,	PUNCT
ejpam-4573	376	5	2022:6285763	2022:6285763	NUM
ejpam-4573	376	6	,	,	PUNCT
ejpam-4573	376	7	2022	2022	NUM
ejpam-4573	376	8	.	.	PUNCT