id	sid	tid	token	lemma	pos
ejpam-4581	1	1	european	european	PROPN
ejpam-4581	1	2	journal	journal	PROPN
ejpam-4581	1	3	of	of	ADP
ejpam-4581	1	4	pure	pure	ADJ
ejpam-4581	1	5	and	and	CCONJ
ejpam-4581	1	6	applied	apply	VERB
ejpam-4581	1	7	mathematics	mathematic	NOUN
ejpam-4581	1	8	vol	vol	NOUN
ejpam-4581	1	9	.	.	PUNCT
ejpam-4581	2	1	16	16	NUM
ejpam-4581	2	2	,	,	PUNCT
ejpam-4581	2	3	no	no	INTJ
ejpam-4581	2	4	.	.	NOUN
ejpam-4581	2	5	1	1	NUM
ejpam-4581	2	6	,	,	PUNCT
ejpam-4581	2	7	2023	2023	NUM
ejpam-4581	2	8	,	,	PUNCT
ejpam-4581	2	9	156	156	NUM
ejpam-4581	2	10	-	-	SYM
ejpam-4581	2	11	168	168	NUM
ejpam-4581	2	12	issn	issn	PROPN
ejpam-4581	2	13	1307	1307	NUM
ejpam-4581	2	14	-	-	SYM
ejpam-4581	2	15	5543	5543	NUM
ejpam-4581	2	16	–	–	PUNCT
ejpam-4581	3	1	ejpam.com	ejpam.com	X
ejpam-4581	3	2	published	publish	VERB
ejpam-4581	3	3	by	by	ADP
ejpam-4581	3	4	new	new	PROPN
ejpam-4581	3	5	york	york	PROPN
ejpam-4581	3	6	business	business	PROPN
ejpam-4581	3	7	global	global	PROPN
ejpam-4581	3	8	upper	upper	ADJ
ejpam-4581	3	9	and	and	CCONJ
ejpam-4581	3	10	lower	low	ADJ
ejpam-4581	3	11	almost	almost	ADV
ejpam-4581	3	12	contra-(λ	contra-(λ	PROPN
ejpam-4581	3	13	,	,	PUNCT
ejpam-4581	3	14	sp)-continuity	sp)-continuity	NOUN
ejpam-4581	3	15	chawalit	chawalit	VERB
ejpam-4581	3	16	boonpok1	boonpok1	PROPN
ejpam-4581	3	17	,	,	PUNCT
ejpam-4581	3	18	jeeranunt	jeeranunt	PROPN
ejpam-4581	3	19	khampakdee1,∗	khampakdee1,∗	PROPN
ejpam-4581	3	20	1	1	NUM
ejpam-4581	3	21	mathematics	mathematic	NOUN
ejpam-4581	3	22	and	and	CCONJ
ejpam-4581	3	23	applied	apply	VERB
ejpam-4581	3	24	mathematics	mathematics	PROPN
ejpam-4581	3	25	research	research	NOUN
ejpam-4581	3	26	unit	unit	NOUN
ejpam-4581	3	27	,	,	PUNCT
ejpam-4581	3	28	department	department	NOUN
ejpam-4581	3	29	of	of	ADP
ejpam-4581	3	30	mathematics	mathematic	NOUN
ejpam-4581	3	31	,	,	PUNCT
ejpam-4581	3	32	faculty	faculty	NOUN
ejpam-4581	3	33	of	of	ADP
ejpam-4581	3	34	science	science	NOUN
ejpam-4581	3	35	,	,	PUNCT
ejpam-4581	3	36	mahasarakham	mahasarakham	PROPN
ejpam-4581	3	37	university	university	PROPN
ejpam-4581	3	38	,	,	PUNCT
ejpam-4581	3	39	maha	maha	PROPN
ejpam-4581	3	40	sarakham	sarakham	PROPN
ejpam-4581	3	41	,	,	PUNCT
ejpam-4581	3	42	44150	44150	NUM
ejpam-4581	3	43	,	,	PUNCT
ejpam-4581	3	44	thailand	thailand	PROPN
ejpam-4581	3	45	abstract	abstract	PROPN
ejpam-4581	3	46	.	.	PUNCT
ejpam-4581	4	1	our	our	PRON
ejpam-4581	4	2	main	main	ADJ
ejpam-4581	4	3	purpose	purpose	NOUN
ejpam-4581	4	4	is	be	AUX
ejpam-4581	4	5	to	to	PART
ejpam-4581	4	6	introduce	introduce	VERB
ejpam-4581	4	7	the	the	DET
ejpam-4581	4	8	concepts	concept	NOUN
ejpam-4581	4	9	of	of	ADP
ejpam-4581	4	10	upper	upper	ADJ
ejpam-4581	4	11	and	and	CCONJ
ejpam-4581	4	12	lower	low	ADJ
ejpam-4581	4	13	almost	almost	ADV
ejpam-4581	4	14	contra(λ	contra(λ	PROPN
ejpam-4581	4	15	,	,	PUNCT
ejpam-4581	4	16	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	4	17	multifunctions	multifunction	NOUN
ejpam-4581	4	18	.	.	PUNCT
ejpam-4581	5	1	moreover	moreover	ADV
ejpam-4581	5	2	,	,	PUNCT
ejpam-4581	5	3	several	several	ADJ
ejpam-4581	5	4	characterizations	characterization	NOUN
ejpam-4581	5	5	of	of	ADP
ejpam-4581	5	6	upper	upper	ADJ
ejpam-4581	5	7	and	and	CCONJ
ejpam-4581	5	8	lower	low	ADJ
ejpam-4581	5	9	almost	almost	ADV
ejpam-4581	5	10	contra-(λ	contra-(λ	PROPN
ejpam-4581	5	11	,	,	PUNCT
ejpam-4581	5	12	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	5	13	multifunctions	multifunction	NOUN
ejpam-4581	5	14	are	be	AUX
ejpam-4581	5	15	investigated	investigate	VERB
ejpam-4581	5	16	.	.	PUNCT
ejpam-4581	6	1	2020	2020	NUM
ejpam-4581	6	2	mathematics	mathematic	NOUN
ejpam-4581	6	3	subject	subject	NOUN
ejpam-4581	6	4	classifications	classification	NOUN
ejpam-4581	6	5	:	:	PUNCT
ejpam-4581	6	6	54c08	54c08	NUM
ejpam-4581	6	7	,	,	PUNCT
ejpam-4581	6	8	54c60	54c60	NUM
ejpam-4581	6	9	key	key	ADJ
ejpam-4581	6	10	words	word	NOUN
ejpam-4581	6	11	and	and	CCONJ
ejpam-4581	6	12	phrases	phrase	NOUN
ejpam-4581	6	13	:	:	PUNCT
ejpam-4581	6	14	(	(	PUNCT
ejpam-4581	6	15	λ	λ	NOUN
ejpam-4581	6	16	,	,	PUNCT
ejpam-4581	6	17	sp)-open	sp)-open	ADJ
ejpam-4581	6	18	set	set	NOUN
ejpam-4581	6	19	,	,	PUNCT
ejpam-4581	6	20	upper	upper	ADJ
ejpam-4581	6	21	almost	almost	ADV
ejpam-4581	6	22	contra-(λ	contra-(λ	PROPN
ejpam-4581	6	23	,	,	PUNCT
ejpam-4581	6	24	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	6	25	multifunction	multifunction	NOUN
ejpam-4581	6	26	,	,	PUNCT
ejpam-4581	6	27	lower	low	ADJ
ejpam-4581	6	28	almost	almost	ADV
ejpam-4581	6	29	contra-(λ	contra-(λ	PROPN
ejpam-4581	6	30	,	,	PUNCT
ejpam-4581	6	31	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	6	32	multifunction	multifunction	NOUN
ejpam-4581	6	33	1	1	NUM
ejpam-4581	6	34	.	.	PUNCT
ejpam-4581	6	35	introduction	introduction	NOUN
ejpam-4581	6	36	in	in	ADP
ejpam-4581	6	37	1996	1996	NUM
ejpam-4581	6	38	,	,	PUNCT
ejpam-4581	6	39	dontchev	dontchev	ADJ
ejpam-4581	6	40	[	[	X
ejpam-4581	6	41	8	8	NUM
ejpam-4581	6	42	]	]	PUNCT
ejpam-4581	6	43	introduced	introduce	VERB
ejpam-4581	6	44	and	and	CCONJ
ejpam-4581	6	45	studied	study	VERB
ejpam-4581	6	46	the	the	DET
ejpam-4581	6	47	concept	concept	NOUN
ejpam-4581	6	48	of	of	ADP
ejpam-4581	6	49	contra	contra	ADJ
ejpam-4581	6	50	-	-	ADJ
ejpam-4581	6	51	continuous	continuous	ADJ
ejpam-4581	6	52	functions	function	NOUN
ejpam-4581	6	53	.	.	PUNCT
ejpam-4581	7	1	in	in	ADP
ejpam-4581	7	2	1999	1999	NUM
ejpam-4581	7	3	,	,	PUNCT
ejpam-4581	7	4	dontchev	dontchev	NOUN
ejpam-4581	7	5	and	and	CCONJ
ejpam-4581	7	6	noiri	noiri	ADV
ejpam-4581	7	7	[	[	X
ejpam-4581	7	8	10	10	NUM
ejpam-4581	7	9	]	]	PUNCT
ejpam-4581	7	10	considered	consider	VERB
ejpam-4581	7	11	a	a	DET
ejpam-4581	7	12	slightly	slightly	ADV
ejpam-4581	7	13	weaker	weak	ADJ
ejpam-4581	7	14	form	form	NOUN
ejpam-4581	7	15	of	of	ADP
ejpam-4581	7	16	contracontinuity	contracontinuity	NOUN
ejpam-4581	7	17	called	call	VERB
ejpam-4581	7	18	contra	contra	PROPN
ejpam-4581	7	19	-	-	NOUN
ejpam-4581	7	20	semicontinuity	semicontinuity	NOUN
ejpam-4581	7	21	and	and	CCONJ
ejpam-4581	7	22	investigated	investigate	VERB
ejpam-4581	7	23	the	the	DET
ejpam-4581	7	24	class	class	NOUN
ejpam-4581	7	25	of	of	ADP
ejpam-4581	7	26	strongly	strongly	ADV
ejpam-4581	7	27	s	s	NOUN
ejpam-4581	7	28	-	-	PUNCT
ejpam-4581	7	29	closed	closed	ADJ
ejpam-4581	7	30	spaces	space	NOUN
ejpam-4581	7	31	.	.	PUNCT
ejpam-4581	8	1	in	in	ADP
ejpam-4581	8	2	2001	2001	NUM
ejpam-4581	8	3	,	,	PUNCT
ejpam-4581	8	4	caldas	caldas	PROPN
ejpam-4581	8	5	and	and	CCONJ
ejpam-4581	8	6	jafari	jafari	PROPN
ejpam-4581	8	7	[	[	X
ejpam-4581	8	8	7	7	X
ejpam-4581	8	9	]	]	PUNCT
ejpam-4581	8	10	introduced	introduce	VERB
ejpam-4581	8	11	and	and	CCONJ
ejpam-4581	8	12	investigated	investigate	VERB
ejpam-4581	8	13	the	the	DET
ejpam-4581	8	14	concept	concept	NOUN
ejpam-4581	8	15	of	of	ADP
ejpam-4581	8	16	contraβ	contraβ	NOUN
ejpam-4581	8	17	-	-	PUNCT
ejpam-4581	8	18	continuous	continuous	ADJ
ejpam-4581	8	19	functions	function	NOUN
ejpam-4581	8	20	.	.	PUNCT
ejpam-4581	9	1	in	in	ADP
ejpam-4581	9	2	2002	2002	NUM
ejpam-4581	9	3	,	,	PUNCT
ejpam-4581	9	4	jafari	jafari	ADJ
ejpam-4581	9	5	and	and	CCONJ
ejpam-4581	9	6	noiri	noiri	ADV
ejpam-4581	10	1	[	[	X
ejpam-4581	10	2	16	16	NUM
ejpam-4581	10	3	]	]	PUNCT
ejpam-4581	10	4	introduced	introduce	VERB
ejpam-4581	10	5	and	and	CCONJ
ejpam-4581	10	6	studied	study	VERB
ejpam-4581	10	7	a	a	DET
ejpam-4581	10	8	new	new	ADJ
ejpam-4581	10	9	form	form	NOUN
ejpam-4581	10	10	of	of	ADP
ejpam-4581	10	11	functions	function	NOUN
ejpam-4581	10	12	called	call	VERB
ejpam-4581	10	13	contra	contra	ADJ
ejpam-4581	10	14	-	-	ADJ
ejpam-4581	10	15	precontinuous	precontinuous	ADJ
ejpam-4581	10	16	functions	function	NOUN
ejpam-4581	10	17	.	.	PUNCT
ejpam-4581	11	1	in	in	ADP
ejpam-4581	11	2	2004	2004	NUM
ejpam-4581	11	3	,	,	PUNCT
ejpam-4581	11	4	ekici	ekici	NOUN
ejpam-4581	11	5	[	[	X
ejpam-4581	11	6	11	11	NUM
ejpam-4581	11	7	]	]	PUNCT
ejpam-4581	11	8	introduced	introduce	VERB
ejpam-4581	11	9	and	and	CCONJ
ejpam-4581	11	10	investigated	investigate	VERB
ejpam-4581	11	11	almost	almost	ADV
ejpam-4581	11	12	contra	contra	NOUN
ejpam-4581	11	13	-	-	NOUN
ejpam-4581	11	14	precontinuity	precontinuity	NOUN
ejpam-4581	11	15	as	as	ADP
ejpam-4581	11	16	a	a	DET
ejpam-4581	11	17	new	new	ADJ
ejpam-4581	11	18	generalization	generalization	NOUN
ejpam-4581	11	19	of	of	ADP
ejpam-4581	11	20	regular	regular	ADJ
ejpam-4581	11	21	set	set	NOUN
ejpam-4581	11	22	-	-	PUNCT
ejpam-4581	11	23	connectedness	connectedness	NOUN
ejpam-4581	11	24	[	[	X
ejpam-4581	11	25	9	9	NUM
ejpam-4581	11	26	]	]	PUNCT
ejpam-4581	11	27	,	,	PUNCT
ejpam-4581	11	28	contra	contra	PROPN
ejpam-4581	11	29	-	-	NOUN
ejpam-4581	11	30	precontinuity	precontinuity	NOUN
ejpam-4581	11	31	[	[	X
ejpam-4581	11	32	16	16	NUM
ejpam-4581	11	33	]	]	PUNCT
ejpam-4581	11	34	,	,	PUNCT
ejpam-4581	11	35	contra	contra	NOUN
ejpam-4581	11	36	-	-	NOUN
ejpam-4581	11	37	continuity	continuity	NOUN
ejpam-4581	11	38	[	[	X
ejpam-4581	11	39	8	8	NUM
ejpam-4581	11	40	]	]	PUNCT
ejpam-4581	11	41	,	,	PUNCT
ejpam-4581	11	42	almost	almost	ADV
ejpam-4581	11	43	s	s	NOUN
ejpam-4581	11	44	-	-	NOUN
ejpam-4581	11	45	continuity	continuity	NOUN
ejpam-4581	11	46	[	[	X
ejpam-4581	11	47	19	19	NUM
ejpam-4581	11	48	]	]	PUNCT
ejpam-4581	11	49	and	and	CCONJ
ejpam-4581	11	50	perfect	perfect	ADJ
ejpam-4581	11	51	continuity	continuity	NOUN
ejpam-4581	11	52	[	[	X
ejpam-4581	11	53	18	18	NUM
ejpam-4581	11	54	]	]	PUNCT
ejpam-4581	11	55	.	.	PUNCT
ejpam-4581	12	1	in	in	ADP
ejpam-4581	12	2	2005	2005	NUM
ejpam-4581	12	3	,	,	PUNCT
ejpam-4581	12	4	nasef	nasef	PROPN
ejpam-4581	12	5	[	[	X
ejpam-4581	12	6	17	17	NUM
ejpam-4581	12	7	]	]	PUNCT
ejpam-4581	12	8	defined	define	VERB
ejpam-4581	12	9	a	a	DET
ejpam-4581	12	10	new	new	ADJ
ejpam-4581	12	11	class	class	NOUN
ejpam-4581	12	12	of	of	ADP
ejpam-4581	12	13	functions	function	NOUN
ejpam-4581	12	14	called	call	VERB
ejpam-4581	12	15	contra	contra	ADJ
ejpam-4581	12	16	-	-	ADJ
ejpam-4581	12	17	γcontinuous	γcontinuous	ADJ
ejpam-4581	12	18	functions	function	NOUN
ejpam-4581	12	19	which	which	PRON
ejpam-4581	12	20	lies	lie	VERB
ejpam-4581	12	21	between	between	ADP
ejpam-4581	12	22	classes	class	NOUN
ejpam-4581	12	23	of	of	ADP
ejpam-4581	12	24	contra	contra	ADJ
ejpam-4581	12	25	-	-	ADJ
ejpam-4581	12	26	semicontinuous	semicontinuous	ADJ
ejpam-4581	12	27	functions	function	NOUN
ejpam-4581	12	28	and	and	CCONJ
ejpam-4581	12	29	contra	contra	PROPN
ejpam-4581	12	30	-	-	PUNCT
ejpam-4581	12	31	β	β	ADJ
ejpam-4581	12	32	-	-	ADJ
ejpam-4581	12	33	continuous	continuous	ADJ
ejpam-4581	12	34	functions	function	NOUN
ejpam-4581	12	35	.	.	PUNCT
ejpam-4581	13	1	the	the	DET
ejpam-4581	13	2	first	first	ADJ
ejpam-4581	13	3	initiation	initiation	NOUN
ejpam-4581	13	4	of	of	ADP
ejpam-4581	13	5	the	the	DET
ejpam-4581	13	6	concept	concept	NOUN
ejpam-4581	13	7	of	of	ADP
ejpam-4581	13	8	contra	contra	ADJ
ejpam-4581	13	9	-	-	ADJ
ejpam-4581	13	10	continuous	continuous	ADJ
ejpam-4581	13	11	multifunctions	multifunction	NOUN
ejpam-4581	13	12	has	have	AUX
ejpam-4581	13	13	been	be	AUX
ejpam-4581	13	14	done	do	VERB
ejpam-4581	13	15	by	by	ADP
ejpam-4581	13	16	ekici	ekici	PROPN
ejpam-4581	13	17	et	et	PROPN
ejpam-4581	13	18	al	al	PROPN
ejpam-4581	13	19	.	.	PUNCT
ejpam-4581	14	1	[	[	X
ejpam-4581	14	2	12	12	NUM
ejpam-4581	14	3	]	]	PUNCT
ejpam-4581	14	4	.	.	PUNCT
ejpam-4581	15	1	in	in	ADP
ejpam-4581	15	2	2009	2009	NUM
ejpam-4581	15	3	,	,	PUNCT
ejpam-4581	15	4	ekici	ekici	NOUN
ejpam-4581	15	5	et	et	PROPN
ejpam-4581	15	6	al	al	PROPN
ejpam-4581	15	7	.	.	PUNCT
ejpam-4581	16	1	[	[	X
ejpam-4581	16	2	13	13	NUM
ejpam-4581	16	3	]	]	PUNCT
ejpam-4581	16	4	introduced	introduce	VERB
ejpam-4581	16	5	and	and	CCONJ
ejpam-4581	16	6	studied	study	VERB
ejpam-4581	16	7	a	a	DET
ejpam-4581	16	8	new	new	ADJ
ejpam-4581	16	9	generalization	generalization	NOUN
ejpam-4581	16	10	of	of	ADP
ejpam-4581	16	11	contra	contra	ADJ
ejpam-4581	16	12	-	-	ADJ
ejpam-4581	16	13	continuous	continuous	ADJ
ejpam-4581	16	14	multifunctions	multifunction	NOUN
ejpam-4581	16	15	called	call	VERB
ejpam-4581	16	16	almost	almost	ADV
ejpam-4581	16	17	contracontinuous	contracontinuous	ADJ
ejpam-4581	16	18	multifunctions	multifunction	NOUN
ejpam-4581	16	19	.	.	PUNCT
ejpam-4581	17	1	in	in	ADP
ejpam-4581	17	2	2010	2010	NUM
ejpam-4581	17	3	,	,	PUNCT
ejpam-4581	17	4	ekici	ekici	NOUN
ejpam-4581	17	5	et	et	PROPN
ejpam-4581	17	6	al	al	PROPN
ejpam-4581	17	7	.	.	PUNCT
ejpam-4581	18	1	[	[	X
ejpam-4581	18	2	14	14	NUM
ejpam-4581	18	3	]	]	PUNCT
ejpam-4581	18	4	introduced	introduce	VERB
ejpam-4581	18	5	and	and	CCONJ
ejpam-4581	18	6	studied	study	VERB
ejpam-4581	18	7	two	two	NUM
ejpam-4581	18	8	new	new	ADJ
ejpam-4581	18	9	concepts	concept	NOUN
ejpam-4581	18	10	namely	namely	ADV
ejpam-4581	18	11	contra	contra	ADJ
ejpam-4581	18	12	-	-	ADJ
ejpam-4581	18	13	precontinuous	precontinuous	ADJ
ejpam-4581	18	14	multifunctions	multifunction	NOUN
ejpam-4581	18	15	and	and	CCONJ
ejpam-4581	18	16	almost	almost	ADV
ejpam-4581	18	17	contra	contra	ADJ
ejpam-4581	18	18	-	-	ADJ
ejpam-4581	18	19	precontinuous	precontinuous	ADJ
ejpam-4581	18	20	multifunctions	multifunction	NOUN
ejpam-4581	18	21	which	which	PRON
ejpam-4581	18	22	are	be	AUX
ejpam-4581	18	23	containing	contain	VERB
ejpam-4581	18	24	the	the	DET
ejpam-4581	18	25	class	class	NOUN
ejpam-4581	18	26	of	of	ADP
ejpam-4581	18	27	contra	contra	ADJ
ejpam-4581	18	28	-	-	ADJ
ejpam-4581	18	29	continuous	continuous	ADJ
ejpam-4581	18	30	multifunctions	multifunction	NOUN
ejpam-4581	18	31	and	and	CCONJ
ejpam-4581	18	32	contained	contain	VERB
ejpam-4581	18	33	in	in	ADP
ejpam-4581	18	34	the	the	DET
ejpam-4581	18	35	class	class	NOUN
ejpam-4581	18	36	of	of	ADP
ejpam-4581	18	37	weakly	weakly	ADJ
ejpam-4581	18	38	precontinuous	precontinuous	ADJ
ejpam-4581	18	39	multifunctions	multifunction	NOUN
ejpam-4581	18	40	.	.	PUNCT
ejpam-4581	19	1	in	in	ADP
ejpam-4581	19	2	2018	2018	NUM
ejpam-4581	19	3	,	,	PUNCT
ejpam-4581	19	4	boonpok	boonpok	PROPN
ejpam-4581	19	5	et	et	PROPN
ejpam-4581	19	6	al	al	PROPN
ejpam-4581	19	7	.	.	PUNCT
ejpam-4581	20	1	[	[	X
ejpam-4581	20	2	6	6	NUM
ejpam-4581	20	3	]	]	PUNCT
ejpam-4581	20	4	introduced	introduce	VERB
ejpam-4581	20	5	and	and	CCONJ
ejpam-4581	20	6	studied	study	VERB
ejpam-4581	20	7	the	the	DET
ejpam-4581	20	8	notions	notion	NOUN
ejpam-4581	20	9	of	of	ADP
ejpam-4581	20	10	upper	upper	ADJ
ejpam-4581	20	11	and	and	CCONJ
ejpam-4581	20	12	lower	low	ADJ
ejpam-4581	20	13	almost	almost	ADV
ejpam-4581	20	14	(	(	PUNCT
ejpam-4581	20	15	τ1	τ1	NOUN
ejpam-4581	20	16	,	,	PUNCT
ejpam-4581	20	17	τ2)-precontinuous	τ2)-precontinuous	ADJ
ejpam-4581	20	18	multifunctions	multifunction	NOUN
ejpam-4581	20	19	.	.	PUNCT
ejpam-4581	21	1	∗corresponding	∗corresponde	VERB
ejpam-4581	21	2	author	author	NOUN
ejpam-4581	21	3	.	.	PUNCT
ejpam-4581	22	1	doi	doi	NOUN
ejpam-4581	22	2	:	:	PUNCT
ejpam-4581	22	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4581	https://doi.org/10.29020/nybg.ejpam.v16i1.4581	NOUN
ejpam-4581	22	4	email	email	NOUN
ejpam-4581	22	5	addresses	address	VERB
ejpam-4581	22	6	:	:	PUNCT
ejpam-4581	22	7	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	INTJ
ejpam-4581	22	8	(	(	PUNCT
ejpam-4581	22	9	c.	c.	PROPN
ejpam-4581	22	10	boonpok	boonpok	PROPN
ejpam-4581	22	11	)	)	PUNCT
ejpam-4581	22	12	,	,	PUNCT
ejpam-4581	23	1	jeeranunt.k@msu.ac.th	jeeranunt.k@msu.ac.th	INTJ
ejpam-4581	23	2	(	(	PUNCT
ejpam-4581	23	3	j.	j.	PROPN
ejpam-4581	23	4	khampakdee	khampakdee	PROPN
ejpam-4581	23	5	)	)	PUNCT
ejpam-4581	23	6	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4581	24	1	156	156	NUM
ejpam-4581	25	1	©	©	PROPN
ejpam-4581	25	2	2023	2023	NUM
ejpam-4581	25	3	ejpam	ejpam	NOUN
ejpam-4581	25	4	all	all	DET
ejpam-4581	25	5	rights	right	NOUN
ejpam-4581	25	6	reserved	reserve	VERB
ejpam-4581	25	7	.	.	PUNCT
ejpam-4581	26	1	c.	c.	PROPN
ejpam-4581	26	2	boonpok	boonpok	PROPN
ejpam-4581	26	3	,	,	PUNCT
ejpam-4581	26	4	j.	j.	PROPN
ejpam-4581	26	5	khampakdee	khampakdee	PROPN
ejpam-4581	26	6	/	/	PUNCT
ejpam-4581	26	7	eur	eur	PROPN
ejpam-4581	26	8	.	.	PUNCT
ejpam-4581	27	1	j.	j.	PROPN
ejpam-4581	27	2	pure	pure	PROPN
ejpam-4581	27	3	appl	appl	PROPN
ejpam-4581	27	4	.	.	PROPN
ejpam-4581	27	5	math	math	PROPN
ejpam-4581	27	6	,	,	PUNCT
ejpam-4581	27	7	16	16	NUM
ejpam-4581	27	8	(	(	PUNCT
ejpam-4581	27	9	1	1	NUM
ejpam-4581	27	10	)	)	PUNCT
ejpam-4581	27	11	(	(	PUNCT
ejpam-4581	27	12	2023	2023	NUM
ejpam-4581	27	13	)	)	PUNCT
ejpam-4581	27	14	,	,	PUNCT
ejpam-4581	27	15	156	156	NUM
ejpam-4581	27	16	-	-	SYM
ejpam-4581	27	17	168	168	NUM
ejpam-4581	27	18	157	157	NUM
ejpam-4581	27	19	abd	abd	PROPN
ejpam-4581	27	20	el	el	PROPN
ejpam-4581	27	21	-	-	PROPN
ejpam-4581	27	22	monsef	monsef	PROPN
ejpam-4581	27	23	et	et	PROPN
ejpam-4581	27	24	al	al	PROPN
ejpam-4581	27	25	.	.	PUNCT
ejpam-4581	28	1	[	[	X
ejpam-4581	28	2	15	15	NUM
ejpam-4581	28	3	]	]	PUNCT
ejpam-4581	28	4	introduced	introduce	VERB
ejpam-4581	28	5	a	a	DET
ejpam-4581	28	6	weak	weak	ADJ
ejpam-4581	28	7	form	form	NOUN
ejpam-4581	28	8	of	of	ADP
ejpam-4581	28	9	open	open	ADJ
ejpam-4581	28	10	sets	set	NOUN
ejpam-4581	28	11	called	call	VERB
ejpam-4581	28	12	β	β	NOUN
ejpam-4581	28	13	-	-	ADJ
ejpam-4581	28	14	open	open	ADJ
ejpam-4581	28	15	sets	set	NOUN
ejpam-4581	28	16	.	.	PUNCT
ejpam-4581	29	1	the	the	DET
ejpam-4581	29	2	notion	notion	NOUN
ejpam-4581	29	3	of	of	ADP
ejpam-4581	29	4	β	β	ADJ
ejpam-4581	29	5	-	-	ADJ
ejpam-4581	29	6	open	open	ADJ
ejpam-4581	29	7	sets	set	NOUN
ejpam-4581	29	8	is	be	AUX
ejpam-4581	29	9	equivalent	equivalent	ADJ
ejpam-4581	29	10	to	to	ADP
ejpam-4581	29	11	that	that	PRON
ejpam-4581	29	12	of	of	ADP
ejpam-4581	29	13	semi	semi	ADJ
ejpam-4581	29	14	-	-	ADJ
ejpam-4581	29	15	preopen	preopen	ADJ
ejpam-4581	29	16	sets	set	NOUN
ejpam-4581	29	17	[	[	X
ejpam-4581	29	18	1	1	NUM
ejpam-4581	29	19	]	]	PUNCT
ejpam-4581	29	20	.	.	PUNCT
ejpam-4581	30	1	noiri	noiri	PROPN
ejpam-4581	30	2	and	and	CCONJ
ejpam-4581	30	3	hatir	hatir	PROPN
ejpam-4581	31	1	[	[	X
ejpam-4581	31	2	20	20	NUM
ejpam-4581	31	3	]	]	PUNCT
ejpam-4581	31	4	introduced	introduce	VERB
ejpam-4581	31	5	the	the	DET
ejpam-4581	31	6	concept	concept	NOUN
ejpam-4581	31	7	of	of	ADP
ejpam-4581	31	8	λsp	λsp	NOUN
ejpam-4581	31	9	-	-	PUNCT
ejpam-4581	31	10	sets	set	NOUN
ejpam-4581	31	11	in	in	ADP
ejpam-4581	31	12	terms	term	NOUN
ejpam-4581	31	13	of	of	ADP
ejpam-4581	31	14	the	the	DET
ejpam-4581	31	15	concept	concept	NOUN
ejpam-4581	31	16	of	of	ADP
ejpam-4581	31	17	β	β	ADJ
ejpam-4581	31	18	-	-	ADJ
ejpam-4581	31	19	open	open	ADJ
ejpam-4581	31	20	sets	set	NOUN
ejpam-4581	31	21	and	and	CCONJ
ejpam-4581	31	22	investigated	investigate	VERB
ejpam-4581	31	23	the	the	DET
ejpam-4581	31	24	notion	notion	NOUN
ejpam-4581	31	25	of	of	ADP
ejpam-4581	31	26	λsp	λsp	NOUN
ejpam-4581	31	27	-	-	PUNCT
ejpam-4581	31	28	closed	close	VERB
ejpam-4581	31	29	sets	set	NOUN
ejpam-4581	31	30	by	by	ADP
ejpam-4581	31	31	using	use	VERB
ejpam-4581	31	32	λsp	λsp	NOUN
ejpam-4581	31	33	-	-	PUNCT
ejpam-4581	31	34	sets	set	NOUN
ejpam-4581	31	35	.	.	PUNCT
ejpam-4581	32	1	in	in	ADP
ejpam-4581	32	2	[	[	X
ejpam-4581	32	3	3	3	NUM
ejpam-4581	32	4	]	]	PUNCT
ejpam-4581	32	5	,	,	PUNCT
ejpam-4581	32	6	the	the	DET
ejpam-4581	32	7	author	author	NOUN
ejpam-4581	32	8	introduced	introduce	VERB
ejpam-4581	32	9	the	the	DET
ejpam-4581	32	10	concepts	concept	NOUN
ejpam-4581	32	11	of	of	ADP
ejpam-4581	32	12	(	(	PUNCT
ejpam-4581	32	13	λ	λ	PROPN
ejpam-4581	32	14	,	,	PUNCT
ejpam-4581	32	15	sp)-open	sp)-open	ADJ
ejpam-4581	32	16	sets	set	NOUN
ejpam-4581	32	17	and	and	CCONJ
ejpam-4581	32	18	(	(	PUNCT
ejpam-4581	32	19	λ	λ	PROPN
ejpam-4581	32	20	,	,	PUNCT
ejpam-4581	32	21	sp)-closed	sp)-close	VERB
ejpam-4581	32	22	sets	set	NOUN
ejpam-4581	32	23	which	which	PRON
ejpam-4581	32	24	are	be	AUX
ejpam-4581	32	25	defined	define	VERB
ejpam-4581	32	26	by	by	ADP
ejpam-4581	32	27	utilizing	utilize	VERB
ejpam-4581	32	28	the	the	DET
ejpam-4581	32	29	notions	notion	NOUN
ejpam-4581	32	30	of	of	ADP
ejpam-4581	32	31	λsp	λsp	NOUN
ejpam-4581	32	32	-	-	PUNCT
ejpam-4581	32	33	sets	set	NOUN
ejpam-4581	32	34	and	and	CCONJ
ejpam-4581	32	35	β	β	NOUN
ejpam-4581	32	36	-	-	ADJ
ejpam-4581	32	37	closed	closed	ADJ
ejpam-4581	32	38	sets	set	NOUN
ejpam-4581	32	39	.	.	PUNCT
ejpam-4581	33	1	the	the	DET
ejpam-4581	33	2	concept	concept	NOUN
ejpam-4581	33	3	of	of	ADP
ejpam-4581	33	4	(	(	PUNCT
ejpam-4581	33	5	λ	λ	PROPN
ejpam-4581	33	6	,	,	PUNCT
ejpam-4581	33	7	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	33	8	multifunctions	multifunction	NOUN
ejpam-4581	33	9	was	be	AUX
ejpam-4581	33	10	introduced	introduce	VERB
ejpam-4581	33	11	and	and	CCONJ
ejpam-4581	33	12	investigated	investigate	VERB
ejpam-4581	33	13	in	in	ADP
ejpam-4581	33	14	[	[	X
ejpam-4581	33	15	3	3	NUM
ejpam-4581	33	16	]	]	PUNCT
ejpam-4581	33	17	.	.	PUNCT
ejpam-4581	34	1	the	the	DET
ejpam-4581	34	2	purpose	purpose	NOUN
ejpam-4581	34	3	of	of	ADP
ejpam-4581	34	4	the	the	DET
ejpam-4581	34	5	present	present	ADJ
ejpam-4581	34	6	paper	paper	NOUN
ejpam-4581	34	7	is	be	AUX
ejpam-4581	34	8	to	to	PART
ejpam-4581	34	9	introduce	introduce	VERB
ejpam-4581	34	10	the	the	DET
ejpam-4581	34	11	notions	notion	NOUN
ejpam-4581	34	12	of	of	ADP
ejpam-4581	34	13	upper	upper	ADJ
ejpam-4581	34	14	and	and	CCONJ
ejpam-4581	34	15	lower	low	ADJ
ejpam-4581	34	16	almost	almost	ADV
ejpam-4581	34	17	contra-(λ	contra-(λ	PROPN
ejpam-4581	34	18	,	,	PUNCT
ejpam-4581	34	19	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	34	20	multifunctions	multifunction	NOUN
ejpam-4581	34	21	.	.	PUNCT
ejpam-4581	35	1	in	in	ADP
ejpam-4581	35	2	particular	particular	ADJ
ejpam-4581	35	3	,	,	PUNCT
ejpam-4581	35	4	several	several	ADJ
ejpam-4581	35	5	characterizations	characterization	NOUN
ejpam-4581	35	6	of	of	ADP
ejpam-4581	35	7	upper	upper	ADJ
ejpam-4581	35	8	and	and	CCONJ
ejpam-4581	35	9	lower	low	ADJ
ejpam-4581	35	10	almost	almost	ADV
ejpam-4581	35	11	contra-(λ	contra-(λ	PROPN
ejpam-4581	35	12	,	,	PUNCT
ejpam-4581	35	13	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	35	14	multifunctions	multifunction	NOUN
ejpam-4581	35	15	are	be	AUX
ejpam-4581	35	16	discussed	discuss	VERB
ejpam-4581	35	17	.	.	PUNCT
ejpam-4581	36	1	2	2	X
ejpam-4581	36	2	.	.	X
ejpam-4581	36	3	preliminaries	preliminary	NOUN
ejpam-4581	36	4	let	let	VERB
ejpam-4581	36	5	a	a	PRON
ejpam-4581	36	6	be	be	AUX
ejpam-4581	36	7	a	a	DET
ejpam-4581	36	8	subset	subset	NOUN
ejpam-4581	36	9	of	of	ADP
ejpam-4581	36	10	a	a	DET
ejpam-4581	36	11	topological	topological	ADJ
ejpam-4581	36	12	space	space	NOUN
ejpam-4581	36	13	(	(	PUNCT
ejpam-4581	36	14	x	x	X
ejpam-4581	36	15	,	,	PUNCT
ejpam-4581	36	16	τ	τ	PROPN
ejpam-4581	36	17	)	)	PUNCT
ejpam-4581	36	18	.	.	PUNCT
ejpam-4581	37	1	the	the	DET
ejpam-4581	37	2	closure	closure	NOUN
ejpam-4581	37	3	of	of	ADP
ejpam-4581	37	4	a	a	PRON
ejpam-4581	37	5	and	and	CCONJ
ejpam-4581	37	6	the	the	DET
ejpam-4581	37	7	interior	interior	NOUN
ejpam-4581	37	8	of	of	ADP
ejpam-4581	37	9	a	a	PRON
ejpam-4581	37	10	are	be	AUX
ejpam-4581	37	11	denoted	denote	VERB
ejpam-4581	37	12	by	by	ADP
ejpam-4581	37	13	cl(a	cl(a	NOUN
ejpam-4581	37	14	)	)	PUNCT
ejpam-4581	37	15	and	and	CCONJ
ejpam-4581	37	16	int(a	int(a	PROPN
ejpam-4581	37	17	)	)	PUNCT
ejpam-4581	37	18	,	,	PUNCT
ejpam-4581	37	19	respectively	respectively	ADV
ejpam-4581	37	20	.	.	PUNCT
ejpam-4581	38	1	a	a	DET
ejpam-4581	38	2	subset	subset	NOUN
ejpam-4581	38	3	a	a	PRON
ejpam-4581	38	4	of	of	ADP
ejpam-4581	38	5	a	a	DET
ejpam-4581	38	6	topological	topological	ADJ
ejpam-4581	38	7	space	space	NOUN
ejpam-4581	38	8	(	(	PUNCT
ejpam-4581	38	9	x	x	X
ejpam-4581	38	10	,	,	PUNCT
ejpam-4581	38	11	τ	τ	X
ejpam-4581	38	12	)	)	PUNCT
ejpam-4581	38	13	is	be	AUX
ejpam-4581	38	14	said	say	VERB
ejpam-4581	38	15	to	to	PART
ejpam-4581	38	16	be	be	AUX
ejpam-4581	38	17	β	β	X
ejpam-4581	38	18	-	-	ADJ
ejpam-4581	38	19	open	open	ADJ
ejpam-4581	38	20	[	[	X
ejpam-4581	38	21	15	15	NUM
ejpam-4581	38	22	]	]	X
ejpam-4581	38	23	if	if	SCONJ
ejpam-4581	38	24	a	a	DET
ejpam-4581	38	25	⊆	⊆	NUM
ejpam-4581	38	26	cl(int(cl(a	cl(int(cl(a	NOUN
ejpam-4581	38	27	)	)	PUNCT
ejpam-4581	38	28	)	)	PUNCT
ejpam-4581	38	29	)	)	PUNCT
ejpam-4581	38	30	.	.	PUNCT
ejpam-4581	39	1	the	the	DET
ejpam-4581	39	2	complement	complement	NOUN
ejpam-4581	39	3	of	of	ADP
ejpam-4581	39	4	a	a	DET
ejpam-4581	39	5	β	β	X
ejpam-4581	39	6	-	-	ADJ
ejpam-4581	39	7	open	open	ADJ
ejpam-4581	39	8	set	set	NOUN
ejpam-4581	39	9	is	be	AUX
ejpam-4581	39	10	called	call	VERB
ejpam-4581	39	11	β	β	NOUN
ejpam-4581	39	12	-	-	VERB
ejpam-4581	39	13	closed	closed	ADJ
ejpam-4581	39	14	.	.	PUNCT
ejpam-4581	40	1	the	the	DET
ejpam-4581	40	2	family	family	NOUN
ejpam-4581	40	3	of	of	ADP
ejpam-4581	40	4	all	all	DET
ejpam-4581	40	5	β	β	ADJ
ejpam-4581	40	6	-	-	ADJ
ejpam-4581	40	7	open	open	ADJ
ejpam-4581	40	8	sets	set	NOUN
ejpam-4581	40	9	of	of	ADP
ejpam-4581	40	10	a	a	DET
ejpam-4581	40	11	topological	topological	ADJ
ejpam-4581	40	12	space	space	NOUN
ejpam-4581	40	13	(	(	PUNCT
ejpam-4581	40	14	x	x	X
ejpam-4581	40	15	,	,	PUNCT
ejpam-4581	40	16	τ	τ	X
ejpam-4581	40	17	)	)	PUNCT
ejpam-4581	40	18	is	be	AUX
ejpam-4581	40	19	denoted	denote	VERB
ejpam-4581	40	20	by	by	ADP
ejpam-4581	40	21	β(x	β(x	PROPN
ejpam-4581	40	22	,	,	PUNCT
ejpam-4581	40	23	τ	τ	PROPN
ejpam-4581	40	24	)	)	PUNCT
ejpam-4581	40	25	.	.	PUNCT
ejpam-4581	41	1	a	a	DET
ejpam-4581	41	2	subset	subset	NOUN
ejpam-4581	41	3	λsp(a	λsp(a	NOUN
ejpam-4581	41	4	)	)	PUNCT
ejpam-4581	42	1	[	[	X
ejpam-4581	42	2	20	20	NUM
ejpam-4581	42	3	]	]	PUNCT
ejpam-4581	42	4	is	be	AUX
ejpam-4581	42	5	defined	define	VERB
ejpam-4581	42	6	as	as	SCONJ
ejpam-4581	42	7	follows	follow	VERB
ejpam-4581	42	8	:	:	PUNCT
ejpam-4581	42	9	λsp(a	λsp(a	NUM
ejpam-4581	42	10	)	)	PUNCT
ejpam-4581	42	11	=	=	PUNCT
ejpam-4581	43	1	∩{u	∩{u	PROPN
ejpam-4581	43	2	|	|	ADV
ejpam-4581	43	3	a	a	DET
ejpam-4581	43	4	⊆	⊆	NUM
ejpam-4581	43	5	u	u	NOUN
ejpam-4581	43	6	,	,	PUNCT
ejpam-4581	43	7	u	u	NOUN
ejpam-4581	43	8	∈	∈	PROPN
ejpam-4581	43	9	β(x	β(x	PROPN
ejpam-4581	43	10	,	,	PUNCT
ejpam-4581	43	11	τ	τ	X
ejpam-4581	43	12	)	)	PUNCT
ejpam-4581	43	13	}	}	PUNCT
ejpam-4581	43	14	.	.	PUNCT
ejpam-4581	44	1	a	a	DET
ejpam-4581	44	2	subset	subset	NOUN
ejpam-4581	44	3	a	a	PRON
ejpam-4581	44	4	of	of	ADP
ejpam-4581	44	5	a	a	DET
ejpam-4581	44	6	topological	topological	ADJ
ejpam-4581	44	7	space	space	NOUN
ejpam-4581	44	8	(	(	PUNCT
ejpam-4581	44	9	x	x	X
ejpam-4581	44	10	,	,	PUNCT
ejpam-4581	44	11	τ	τ	X
ejpam-4581	44	12	)	)	PUNCT
ejpam-4581	44	13	is	be	AUX
ejpam-4581	44	14	called	call	VERB
ejpam-4581	44	15	a	a	DET
ejpam-4581	44	16	λsp	λsp	NOUN
ejpam-4581	44	17	-	-	PUNCT
ejpam-4581	44	18	set	set	VERB
ejpam-4581	44	19	[	[	X
ejpam-4581	44	20	20	20	NUM
ejpam-4581	44	21	]	]	PUNCT
ejpam-4581	44	22	if	if	SCONJ
ejpam-4581	44	23	a	a	DET
ejpam-4581	44	24	=	=	NOUN
ejpam-4581	44	25	λsp(a	λsp(a	NOUN
ejpam-4581	44	26	)	)	PUNCT
ejpam-4581	44	27	.	.	PUNCT
ejpam-4581	45	1	a	a	DET
ejpam-4581	45	2	subset	subset	NOUN
ejpam-4581	45	3	a	a	PRON
ejpam-4581	45	4	of	of	ADP
ejpam-4581	45	5	a	a	DET
ejpam-4581	45	6	topological	topological	ADJ
ejpam-4581	45	7	space	space	NOUN
ejpam-4581	45	8	(	(	PUNCT
ejpam-4581	45	9	x	x	X
ejpam-4581	45	10	,	,	PUNCT
ejpam-4581	45	11	τ	τ	X
ejpam-4581	45	12	)	)	PUNCT
ejpam-4581	45	13	is	be	AUX
ejpam-4581	45	14	called	call	VERB
ejpam-4581	45	15	(	(	PUNCT
ejpam-4581	45	16	λ	λ	X
ejpam-4581	45	17	,	,	PUNCT
ejpam-4581	45	18	sp)-closed	sp)-close	VERB
ejpam-4581	45	19	[	[	PUNCT
ejpam-4581	45	20	3	3	X
ejpam-4581	45	21	]	]	X
ejpam-4581	45	22	if	if	SCONJ
ejpam-4581	45	23	a	a	DET
ejpam-4581	45	24	=	=	X
ejpam-4581	45	25	t	t	NOUN
ejpam-4581	45	26	∩c	∩c	NOUN
ejpam-4581	45	27	,	,	PUNCT
ejpam-4581	45	28	where	where	SCONJ
ejpam-4581	45	29	t	t	PROPN
ejpam-4581	45	30	is	be	AUX
ejpam-4581	45	31	a	a	DET
ejpam-4581	45	32	λsp	λsp	NOUN
ejpam-4581	45	33	-	-	PUNCT
ejpam-4581	45	34	set	set	VERB
ejpam-4581	45	35	and	and	CCONJ
ejpam-4581	45	36	c	c	NOUN
ejpam-4581	45	37	is	be	AUX
ejpam-4581	45	38	a	a	DET
ejpam-4581	45	39	β	β	NOUN
ejpam-4581	45	40	-	-	ADJ
ejpam-4581	45	41	closed	closed	ADJ
ejpam-4581	45	42	set	set	NOUN
ejpam-4581	45	43	.	.	PUNCT
ejpam-4581	46	1	the	the	DET
ejpam-4581	46	2	complement	complement	NOUN
ejpam-4581	46	3	of	of	ADP
ejpam-4581	46	4	a	a	DET
ejpam-4581	46	5	(	(	PUNCT
ejpam-4581	46	6	λ	λ	PROPN
ejpam-4581	46	7	,	,	PUNCT
ejpam-4581	46	8	sp)-closed	sp)-close	VERB
ejpam-4581	46	9	set	set	VERB
ejpam-4581	46	10	is	be	AUX
ejpam-4581	46	11	called	call	VERB
ejpam-4581	46	12	(	(	PUNCT
ejpam-4581	46	13	λ	λ	NOUN
ejpam-4581	46	14	,	,	PUNCT
ejpam-4581	46	15	sp)-open	sp)-open	NOUN
ejpam-4581	46	16	.	.	PUNCT
ejpam-4581	47	1	let	let	VERB
ejpam-4581	47	2	a	a	DET
ejpam-4581	47	3	be	be	AUX
ejpam-4581	47	4	a	a	DET
ejpam-4581	47	5	subset	subset	NOUN
ejpam-4581	47	6	of	of	ADP
ejpam-4581	47	7	a	a	DET
ejpam-4581	47	8	topological	topological	ADJ
ejpam-4581	47	9	space	space	NOUN
ejpam-4581	47	10	(	(	PUNCT
ejpam-4581	47	11	x	x	X
ejpam-4581	47	12	,	,	PUNCT
ejpam-4581	47	13	τ	τ	PROPN
ejpam-4581	47	14	)	)	PUNCT
ejpam-4581	47	15	.	.	PUNCT
ejpam-4581	48	1	a	a	DET
ejpam-4581	48	2	point	point	NOUN
ejpam-4581	48	3	x	x	X
ejpam-4581	48	4	∈	∈	NOUN
ejpam-4581	48	5	x	x	PUNCT
ejpam-4581	48	6	is	be	AUX
ejpam-4581	48	7	called	call	VERB
ejpam-4581	48	8	a	a	DET
ejpam-4581	48	9	(	(	PUNCT
ejpam-4581	48	10	λ	λ	NOUN
ejpam-4581	48	11	,	,	PUNCT
ejpam-4581	48	12	sp)-cluster	sp)-cluster	NOUN
ejpam-4581	48	13	point	point	NOUN
ejpam-4581	48	14	[	[	X
ejpam-4581	48	15	3	3	X
ejpam-4581	48	16	]	]	PUNCT
ejpam-4581	48	17	of	of	ADP
ejpam-4581	48	18	a	a	PRON
ejpam-4581	48	19	if	if	SCONJ
ejpam-4581	48	20	a	a	DET
ejpam-4581	48	21	∩	∩	ADJ
ejpam-4581	48	22	u	u	ADJ
ejpam-4581	48	23	̸=	̸=	PROPN
ejpam-4581	48	24	∅	∅	NOUN
ejpam-4581	48	25	for	for	ADP
ejpam-4581	48	26	every	every	DET
ejpam-4581	48	27	(	(	PUNCT
ejpam-4581	48	28	λ	λ	NOUN
ejpam-4581	48	29	,	,	PUNCT
ejpam-4581	48	30	sp)-open	sp)-open	NOUN
ejpam-4581	48	31	set	set	VERB
ejpam-4581	48	32	u	u	NOUN
ejpam-4581	48	33	of	of	ADP
ejpam-4581	48	34	x	x	SYM
ejpam-4581	48	35	containing	contain	VERB
ejpam-4581	48	36	x.	x.	NOUN
ejpam-4581	48	37	the	the	DET
ejpam-4581	48	38	set	set	NOUN
ejpam-4581	48	39	of	of	ADP
ejpam-4581	48	40	all	all	DET
ejpam-4581	48	41	(	(	PUNCT
ejpam-4581	48	42	λ	λ	PROPN
ejpam-4581	48	43	,	,	PUNCT
ejpam-4581	48	44	sp)-cluster	sp)-cluster	NOUN
ejpam-4581	48	45	points	point	NOUN
ejpam-4581	48	46	of	of	ADP
ejpam-4581	48	47	a	a	PRON
ejpam-4581	48	48	is	be	AUX
ejpam-4581	48	49	called	call	VERB
ejpam-4581	48	50	the	the	DET
ejpam-4581	48	51	(	(	PUNCT
ejpam-4581	48	52	λ	λ	PROPN
ejpam-4581	48	53	,	,	PUNCT
ejpam-4581	48	54	sp)-closure	sp)-closure	NOUN
ejpam-4581	48	55	[	[	X
ejpam-4581	48	56	3	3	NUM
ejpam-4581	48	57	]	]	PUNCT
ejpam-4581	48	58	of	of	ADP
ejpam-4581	48	59	a	a	PRON
ejpam-4581	48	60	and	and	CCONJ
ejpam-4581	48	61	is	be	AUX
ejpam-4581	48	62	denoted	denote	VERB
ejpam-4581	48	63	by	by	ADP
ejpam-4581	48	64	a(λ	a(λ	ADV
ejpam-4581	48	65	,	,	PUNCT
ejpam-4581	48	66	sp	sp	NOUN
ejpam-4581	48	67	)	)	PUNCT
ejpam-4581	48	68	.	.	PUNCT
ejpam-4581	49	1	the	the	DET
ejpam-4581	49	2	union	union	NOUN
ejpam-4581	49	3	of	of	ADP
ejpam-4581	49	4	all	all	DET
ejpam-4581	49	5	(	(	PUNCT
ejpam-4581	49	6	λ	λ	NOUN
ejpam-4581	49	7	,	,	PUNCT
ejpam-4581	49	8	sp)-open	sp)-open	ADJ
ejpam-4581	49	9	sets	set	NOUN
ejpam-4581	49	10	contained	contain	VERB
ejpam-4581	49	11	in	in	ADP
ejpam-4581	49	12	a	a	PRON
ejpam-4581	49	13	is	be	AUX
ejpam-4581	49	14	called	call	VERB
ejpam-4581	49	15	the	the	DET
ejpam-4581	49	16	(	(	PUNCT
ejpam-4581	49	17	λ	λ	PROPN
ejpam-4581	49	18	,	,	PUNCT
ejpam-4581	49	19	sp)-interior	sp)-interior	NOUN
ejpam-4581	49	20	[	[	X
ejpam-4581	49	21	3	3	NUM
ejpam-4581	49	22	]	]	PUNCT
ejpam-4581	49	23	of	of	ADP
ejpam-4581	49	24	a	a	PRON
ejpam-4581	49	25	and	and	CCONJ
ejpam-4581	49	26	is	be	AUX
ejpam-4581	49	27	denoted	denote	VERB
ejpam-4581	49	28	by	by	ADP
ejpam-4581	49	29	a(λ	a(λ	ADV
ejpam-4581	49	30	,	,	PUNCT
ejpam-4581	49	31	sp	sp	NOUN
ejpam-4581	49	32	)	)	PUNCT
ejpam-4581	49	33	.	.	PUNCT
ejpam-4581	50	1	lemma	lemma	PROPN
ejpam-4581	50	2	1	1	NUM
ejpam-4581	50	3	.	.	PUNCT
ejpam-4581	51	1	[	[	X
ejpam-4581	51	2	3	3	X
ejpam-4581	51	3	]	]	PUNCT
ejpam-4581	51	4	let	let	VERB
ejpam-4581	51	5	a	a	PRON
ejpam-4581	51	6	and	and	CCONJ
ejpam-4581	51	7	b	b	NOUN
ejpam-4581	51	8	be	be	AUX
ejpam-4581	51	9	subsets	subset	NOUN
ejpam-4581	51	10	of	of	ADP
ejpam-4581	51	11	a	a	DET
ejpam-4581	51	12	topological	topological	ADJ
ejpam-4581	51	13	space	space	NOUN
ejpam-4581	51	14	(	(	PUNCT
ejpam-4581	51	15	x	x	X
ejpam-4581	51	16	,	,	PUNCT
ejpam-4581	51	17	τ	τ	PROPN
ejpam-4581	51	18	)	)	PUNCT
ejpam-4581	51	19	.	.	PUNCT
ejpam-4581	52	1	for	for	ADP
ejpam-4581	52	2	the	the	DET
ejpam-4581	52	3	(	(	PUNCT
ejpam-4581	52	4	λ	λ	PROPN
ejpam-4581	52	5	,	,	PUNCT
ejpam-4581	52	6	sp)-closure	sp)-closure	NOUN
ejpam-4581	52	7	,	,	PUNCT
ejpam-4581	52	8	the	the	DET
ejpam-4581	52	9	following	follow	VERB
ejpam-4581	52	10	properties	property	NOUN
ejpam-4581	52	11	hold	hold	VERB
ejpam-4581	52	12	:	:	PUNCT
ejpam-4581	52	13	(	(	PUNCT
ejpam-4581	52	14	1	1	X
ejpam-4581	52	15	)	)	PUNCT
ejpam-4581	52	16	a	a	DET
ejpam-4581	52	17	⊆	⊆	NUM
ejpam-4581	52	18	a(λ	a(λ	ADJ
ejpam-4581	52	19	,	,	PUNCT
ejpam-4581	52	20	sp	sp	NOUN
ejpam-4581	52	21	)	)	PUNCT
ejpam-4581	52	22	and	and	CCONJ
ejpam-4581	52	23	[	[	X
ejpam-4581	52	24	a(λ	a(λ	ADV
ejpam-4581	52	25	,	,	PUNCT
ejpam-4581	52	26	sp)](λ	sp)](λ	PROPN
ejpam-4581	52	27	,	,	PUNCT
ejpam-4581	52	28	sp	sp	NOUN
ejpam-4581	52	29	)	)	PUNCT
ejpam-4581	52	30	=	=	PUNCT
ejpam-4581	52	31	a(λ	a(λ	ADV
ejpam-4581	52	32	,	,	PUNCT
ejpam-4581	52	33	sp	sp	NOUN
ejpam-4581	52	34	)	)	PUNCT
ejpam-4581	52	35	.	.	PUNCT
ejpam-4581	53	1	(	(	PUNCT
ejpam-4581	53	2	2	2	X
ejpam-4581	53	3	)	)	PUNCT
ejpam-4581	53	4	if	if	SCONJ
ejpam-4581	53	5	a	a	DET
ejpam-4581	53	6	⊆	⊆	NUM
ejpam-4581	53	7	b	b	NOUN
ejpam-4581	53	8	,	,	PUNCT
ejpam-4581	53	9	then	then	ADV
ejpam-4581	53	10	a(λ	a(λ	ADV
ejpam-4581	53	11	,	,	PUNCT
ejpam-4581	53	12	sp	sp	NOUN
ejpam-4581	53	13	)	)	PUNCT
ejpam-4581	53	14	⊆	⊆	NUM
ejpam-4581	53	15	b(λ	b(λ	NOUN
ejpam-4581	53	16	,	,	PUNCT
ejpam-4581	53	17	sp	sp	NOUN
ejpam-4581	53	18	)	)	PUNCT
ejpam-4581	53	19	.	.	PUNCT
ejpam-4581	54	1	(	(	PUNCT
ejpam-4581	54	2	3	3	X
ejpam-4581	54	3	)	)	PUNCT
ejpam-4581	54	4	a(λ	a(λ	ADV
ejpam-4581	54	5	,	,	PUNCT
ejpam-4581	54	6	sp	sp	NOUN
ejpam-4581	54	7	)	)	PUNCT
ejpam-4581	54	8	is	be	AUX
ejpam-4581	54	9	(	(	PUNCT
ejpam-4581	54	10	λ	λ	X
ejpam-4581	54	11	,	,	PUNCT
ejpam-4581	54	12	sp)-closed	sp)-close	VERB
ejpam-4581	54	13	.	.	PUNCT
ejpam-4581	55	1	(	(	PUNCT
ejpam-4581	55	2	4	4	X
ejpam-4581	55	3	)	)	PUNCT
ejpam-4581	55	4	a	a	PRON
ejpam-4581	55	5	is	be	AUX
ejpam-4581	55	6	(	(	PUNCT
ejpam-4581	55	7	λ	λ	X
ejpam-4581	55	8	,	,	PUNCT
ejpam-4581	55	9	sp)-closed	sp)-close	VERB
ejpam-4581	55	10	if	if	SCONJ
ejpam-4581	55	11	and	and	CCONJ
ejpam-4581	55	12	only	only	ADV
ejpam-4581	55	13	if	if	SCONJ
ejpam-4581	55	14	a	a	DET
ejpam-4581	55	15	=	=	X
ejpam-4581	55	16	a(λ	a(λ	ADV
ejpam-4581	55	17	,	,	PUNCT
ejpam-4581	55	18	sp	sp	NOUN
ejpam-4581	55	19	)	)	PUNCT
ejpam-4581	55	20	.	.	PUNCT
ejpam-4581	56	1	lemma	lemma	PROPN
ejpam-4581	56	2	2	2	NUM
ejpam-4581	56	3	.	.	PUNCT
ejpam-4581	57	1	[	[	X
ejpam-4581	57	2	3	3	X
ejpam-4581	57	3	]	]	PUNCT
ejpam-4581	57	4	let	let	VERB
ejpam-4581	57	5	a	a	PRON
ejpam-4581	57	6	and	and	CCONJ
ejpam-4581	57	7	b	b	NOUN
ejpam-4581	57	8	be	be	AUX
ejpam-4581	57	9	subsets	subset	NOUN
ejpam-4581	57	10	of	of	ADP
ejpam-4581	57	11	a	a	DET
ejpam-4581	57	12	topological	topological	ADJ
ejpam-4581	57	13	space	space	NOUN
ejpam-4581	57	14	(	(	PUNCT
ejpam-4581	57	15	x	x	X
ejpam-4581	57	16	,	,	PUNCT
ejpam-4581	57	17	τ	τ	PROPN
ejpam-4581	57	18	)	)	PUNCT
ejpam-4581	57	19	.	.	PUNCT
ejpam-4581	58	1	for	for	ADP
ejpam-4581	58	2	the	the	DET
ejpam-4581	58	3	(	(	PUNCT
ejpam-4581	58	4	λ	λ	PROPN
ejpam-4581	58	5	,	,	PUNCT
ejpam-4581	58	6	sp)interior	sp)interior	PROPN
ejpam-4581	58	7	,	,	PUNCT
ejpam-4581	58	8	the	the	DET
ejpam-4581	58	9	following	follow	VERB
ejpam-4581	58	10	properties	property	NOUN
ejpam-4581	58	11	hold	hold	VERB
ejpam-4581	58	12	:	:	PUNCT
ejpam-4581	58	13	(	(	PUNCT
ejpam-4581	58	14	1	1	X
ejpam-4581	58	15	)	)	PUNCT
ejpam-4581	58	16	a(λ	a(λ	ADV
ejpam-4581	58	17	,	,	PUNCT
ejpam-4581	58	18	sp	sp	NOUN
ejpam-4581	58	19	)	)	PUNCT
ejpam-4581	58	20	⊆	⊆	NUM
ejpam-4581	58	21	a	a	DET
ejpam-4581	58	22	and	and	CCONJ
ejpam-4581	58	23	[	[	X
ejpam-4581	58	24	a(λ	a(λ	ADV
ejpam-4581	58	25	,	,	PUNCT
ejpam-4581	58	26	sp)](λ	sp)](λ	PROPN
ejpam-4581	58	27	,	,	PUNCT
ejpam-4581	58	28	sp	sp	NOUN
ejpam-4581	58	29	)	)	PUNCT
ejpam-4581	58	30	=	=	PUNCT
ejpam-4581	58	31	a(λ	a(λ	ADV
ejpam-4581	58	32	,	,	PUNCT
ejpam-4581	58	33	sp	sp	NOUN
ejpam-4581	58	34	)	)	PUNCT
ejpam-4581	58	35	.	.	PUNCT
ejpam-4581	59	1	(	(	PUNCT
ejpam-4581	59	2	2	2	X
ejpam-4581	59	3	)	)	PUNCT
ejpam-4581	59	4	if	if	SCONJ
ejpam-4581	59	5	a	a	DET
ejpam-4581	59	6	⊆	⊆	NUM
ejpam-4581	59	7	b	b	NOUN
ejpam-4581	59	8	,	,	PUNCT
ejpam-4581	59	9	then	then	ADV
ejpam-4581	59	10	a(λ	a(λ	ADV
ejpam-4581	59	11	,	,	PUNCT
ejpam-4581	59	12	sp	sp	NOUN
ejpam-4581	59	13	)	)	PUNCT
ejpam-4581	59	14	⊆	⊆	NUM
ejpam-4581	59	15	b(λ	b(λ	NOUN
ejpam-4581	59	16	,	,	PUNCT
ejpam-4581	59	17	sp	sp	NOUN
ejpam-4581	59	18	)	)	PUNCT
ejpam-4581	59	19	.	.	PUNCT
ejpam-4581	60	1	(	(	PUNCT
ejpam-4581	60	2	3	3	X
ejpam-4581	60	3	)	)	PUNCT
ejpam-4581	60	4	a(λ	a(λ	ADV
ejpam-4581	60	5	,	,	PUNCT
ejpam-4581	60	6	sp	sp	NOUN
ejpam-4581	60	7	)	)	PUNCT
ejpam-4581	60	8	is	be	AUX
ejpam-4581	60	9	(	(	PUNCT
ejpam-4581	60	10	λ	λ	INTJ
ejpam-4581	60	11	,	,	PUNCT
ejpam-4581	60	12	sp)-open	sp)-open	NOUN
ejpam-4581	60	13	.	.	PUNCT
ejpam-4581	61	1	c.	c.	PROPN
ejpam-4581	61	2	boonpok	boonpok	PROPN
ejpam-4581	61	3	,	,	PUNCT
ejpam-4581	61	4	j.	j.	PROPN
ejpam-4581	61	5	khampakdee	khampakdee	PROPN
ejpam-4581	61	6	/	/	PUNCT
ejpam-4581	61	7	eur	eur	PROPN
ejpam-4581	61	8	.	.	PUNCT
ejpam-4581	62	1	j.	j.	PROPN
ejpam-4581	62	2	pure	pure	PROPN
ejpam-4581	62	3	appl	appl	PROPN
ejpam-4581	62	4	.	.	PROPN
ejpam-4581	62	5	math	math	PROPN
ejpam-4581	62	6	,	,	PUNCT
ejpam-4581	62	7	16	16	NUM
ejpam-4581	62	8	(	(	PUNCT
ejpam-4581	62	9	1	1	NUM
ejpam-4581	62	10	)	)	PUNCT
ejpam-4581	62	11	(	(	PUNCT
ejpam-4581	62	12	2023	2023	NUM
ejpam-4581	62	13	)	)	PUNCT
ejpam-4581	62	14	,	,	PUNCT
ejpam-4581	62	15	156	156	NUM
ejpam-4581	62	16	-	-	SYM
ejpam-4581	62	17	168	168	NUM
ejpam-4581	62	18	158	158	NUM
ejpam-4581	62	19	(	(	PUNCT
ejpam-4581	62	20	4	4	NUM
ejpam-4581	62	21	)	)	PUNCT
ejpam-4581	62	22	a	a	DET
ejpam-4581	62	23	is	be	AUX
ejpam-4581	62	24	(	(	PUNCT
ejpam-4581	62	25	λ	λ	NOUN
ejpam-4581	62	26	,	,	PUNCT
ejpam-4581	62	27	sp)-open	sp)-open	ADJ
ejpam-4581	62	28	if	if	SCONJ
ejpam-4581	62	29	and	and	CCONJ
ejpam-4581	62	30	only	only	ADV
ejpam-4581	62	31	if	if	SCONJ
ejpam-4581	62	32	a(λ	a(λ	ADV
ejpam-4581	62	33	,	,	PUNCT
ejpam-4581	62	34	sp	sp	NOUN
ejpam-4581	62	35	)	)	PUNCT
ejpam-4581	62	36	=	=	SYM
ejpam-4581	62	37	a.	a.	NOUN
ejpam-4581	62	38	(	(	PUNCT
ejpam-4581	62	39	5	5	NUM
ejpam-4581	62	40	)	)	PUNCT
ejpam-4581	63	1	[	[	X
ejpam-4581	63	2	x	x	X
ejpam-4581	63	3	−a](λ	−a](λ	PROPN
ejpam-4581	63	4	,	,	PUNCT
ejpam-4581	63	5	sp	sp	NOUN
ejpam-4581	63	6	)	)	PUNCT
ejpam-4581	63	7	=	=	SYM
ejpam-4581	63	8	x	x	SYM
ejpam-4581	63	9	−a(λ	−a(λ	NOUN
ejpam-4581	63	10	,	,	PUNCT
ejpam-4581	63	11	sp	sp	NOUN
ejpam-4581	63	12	)	)	PUNCT
ejpam-4581	63	13	.	.	PUNCT
ejpam-4581	64	1	(	(	PUNCT
ejpam-4581	64	2	6	6	NUM
ejpam-4581	64	3	)	)	PUNCT
ejpam-4581	65	1	[	[	X
ejpam-4581	65	2	x	x	X
ejpam-4581	65	3	−a](λ	−a](λ	PROPN
ejpam-4581	65	4	,	,	PUNCT
ejpam-4581	65	5	sp	sp	NOUN
ejpam-4581	65	6	)	)	PUNCT
ejpam-4581	65	7	=	=	SYM
ejpam-4581	65	8	x	x	SYM
ejpam-4581	65	9	−a(λ	−a(λ	NOUN
ejpam-4581	65	10	,	,	PUNCT
ejpam-4581	65	11	sp	sp	NOUN
ejpam-4581	65	12	)	)	PUNCT
ejpam-4581	65	13	.	.	PUNCT
ejpam-4581	66	1	a	a	DET
ejpam-4581	66	2	subset	subset	NOUN
ejpam-4581	66	3	a	a	PRON
ejpam-4581	66	4	of	of	ADP
ejpam-4581	66	5	a	a	DET
ejpam-4581	66	6	topological	topological	ADJ
ejpam-4581	66	7	space	space	NOUN
ejpam-4581	66	8	(	(	PUNCT
ejpam-4581	66	9	x	x	X
ejpam-4581	66	10	,	,	PUNCT
ejpam-4581	66	11	τ	τ	X
ejpam-4581	66	12	)	)	PUNCT
ejpam-4581	66	13	is	be	AUX
ejpam-4581	66	14	said	say	VERB
ejpam-4581	66	15	to	to	PART
ejpam-4581	66	16	be	be	AUX
ejpam-4581	66	17	s(λ	s(λ	NOUN
ejpam-4581	66	18	,	,	PUNCT
ejpam-4581	66	19	sp)-open	sp)-open	ADJ
ejpam-4581	66	20	(	(	PUNCT
ejpam-4581	66	21	resp	resp	NOUN
ejpam-4581	66	22	.	.	PUNCT
ejpam-4581	67	1	p(λ	p(λ	NOUN
ejpam-4581	67	2	,	,	PUNCT
ejpam-4581	67	3	sp)-open	sp)-open	NOUN
ejpam-4581	67	4	,	,	PUNCT
ejpam-4581	67	5	β(λ	β(λ	X
ejpam-4581	67	6	,	,	PUNCT
ejpam-4581	67	7	sp)-open	sp)-open	NOUN
ejpam-4581	67	8	,	,	PUNCT
ejpam-4581	67	9	α(λ	α(λ	PROPN
ejpam-4581	67	10	,	,	PUNCT
ejpam-4581	67	11	sp)-open	sp)-open	NOUN
ejpam-4581	67	12	,	,	PUNCT
ejpam-4581	67	13	r(λ	r(λ	NOUN
ejpam-4581	67	14	,	,	PUNCT
ejpam-4581	67	15	sp)-open	sp)-open	NOUN
ejpam-4581	67	16	)	)	PUNCT
ejpam-4581	67	17	if	if	SCONJ
ejpam-4581	67	18	a	a	DET
ejpam-4581	67	19	⊆	⊆	NUM
ejpam-4581	67	20	[	[	X
ejpam-4581	67	21	a(λ	a(λ	ADV
ejpam-4581	67	22	,	,	PUNCT
ejpam-4581	67	23	sp	sp	NOUN
ejpam-4581	67	24	)	)	PUNCT
ejpam-4581	67	25	]	]	PUNCT
ejpam-4581	67	26	(	(	PUNCT
ejpam-4581	67	27	λ	λ	NOUN
ejpam-4581	67	28	,	,	PUNCT
ejpam-4581	67	29	sp	sp	NOUN
ejpam-4581	67	30	)	)	PUNCT
ejpam-4581	67	31	(	(	PUNCT
ejpam-4581	67	32	resp	resp	NOUN
ejpam-4581	67	33	.	.	PUNCT
ejpam-4581	68	1	a	a	DET
ejpam-4581	68	2	⊆	⊆	NUM
ejpam-4581	68	3	[	[	X
ejpam-4581	68	4	a(λ	a(λ	ADJ
ejpam-4581	68	5	,	,	PUNCT
ejpam-4581	68	6	sp)](λ	sp)](λ	PROPN
ejpam-4581	68	7	,	,	PUNCT
ejpam-4581	68	8	sp	sp	NOUN
ejpam-4581	68	9	)	)	PUNCT
ejpam-4581	68	10	,	,	PUNCT
ejpam-4581	68	11	a	a	PRON
ejpam-4581	68	12	⊆	⊆	NUM
ejpam-4581	69	1	[	[	X
ejpam-4581	69	2	[	[	X
ejpam-4581	69	3	a(λ	a(λ	ADJ
ejpam-4581	69	4	,	,	PUNCT
ejpam-4581	69	5	sp)](λ	sp)](λ	PROPN
ejpam-4581	69	6	,	,	PUNCT
ejpam-4581	69	7	sp	sp	NOUN
ejpam-4581	69	8	)	)	PUNCT
ejpam-4581	69	9	]	]	PUNCT
ejpam-4581	70	1	(	(	PUNCT
ejpam-4581	70	2	λ	λ	NOUN
ejpam-4581	70	3	,	,	PUNCT
ejpam-4581	70	4	sp	sp	NOUN
ejpam-4581	70	5	)	)	PUNCT
ejpam-4581	70	6	,	,	PUNCT
ejpam-4581	70	7	a	a	DET
ejpam-4581	70	8	⊆	⊆	NUM
ejpam-4581	70	9	[	[	X
ejpam-4581	70	10	[	[	X
ejpam-4581	70	11	a(λ	a(λ	ADJ
ejpam-4581	70	12	,	,	PUNCT
ejpam-4581	70	13	sp	sp	NOUN
ejpam-4581	70	14	)	)	PUNCT
ejpam-4581	70	15	]	]	PUNCT
ejpam-4581	70	16	(	(	PUNCT
ejpam-4581	70	17	λ	λ	X
ejpam-4581	70	18	,	,	PUNCT
ejpam-4581	70	19	sp)](λ	sp)](λ	PROPN
ejpam-4581	70	20	,	,	PUNCT
ejpam-4581	70	21	sp	sp	NOUN
ejpam-4581	70	22	)	)	PUNCT
ejpam-4581	70	23	,	,	PUNCT
ejpam-4581	70	24	a	a	PRON
ejpam-4581	70	25	=	=	X
ejpam-4581	71	1	[	[	X
ejpam-4581	71	2	a(λ	a(λ	PROPN
ejpam-4581	71	3	,	,	PUNCT
ejpam-4581	71	4	sp)](λ	sp)](λ	PROPN
ejpam-4581	71	5	,	,	PUNCT
ejpam-4581	71	6	sp	sp	NOUN
ejpam-4581	71	7	)	)	PUNCT
ejpam-4581	71	8	)	)	PUNCT
ejpam-4581	72	1	[	[	X
ejpam-4581	72	2	3	3	NUM
ejpam-4581	72	3	]	]	PUNCT
ejpam-4581	72	4	.	.	PUNCT
ejpam-4581	73	1	the	the	DET
ejpam-4581	73	2	family	family	NOUN
ejpam-4581	73	3	of	of	ADP
ejpam-4581	73	4	all	all	DET
ejpam-4581	73	5	s(λ	s(λ	NOUN
ejpam-4581	73	6	,	,	PUNCT
ejpam-4581	73	7	sp)-open	sp)-open	ADJ
ejpam-4581	73	8	(	(	PUNCT
ejpam-4581	73	9	resp	resp	NOUN
ejpam-4581	73	10	.	.	PUNCT
ejpam-4581	74	1	p(λ	p(λ	NOUN
ejpam-4581	74	2	,	,	PUNCT
ejpam-4581	74	3	sp)-open	sp)-open	NOUN
ejpam-4581	74	4	,	,	PUNCT
ejpam-4581	74	5	β(λ	β(λ	X
ejpam-4581	74	6	,	,	PUNCT
ejpam-4581	74	7	sp)-open	sp)-open	NOUN
ejpam-4581	74	8	,	,	PUNCT
ejpam-4581	74	9	α(λ	α(λ	PROPN
ejpam-4581	74	10	,	,	PUNCT
ejpam-4581	74	11	sp)-open	sp)-open	NOUN
ejpam-4581	74	12	,	,	PUNCT
ejpam-4581	74	13	r(λ	r(λ	NOUN
ejpam-4581	74	14	,	,	PUNCT
ejpam-4581	74	15	sp)-open	sp)-open	NOUN
ejpam-4581	74	16	)	)	PUNCT
ejpam-4581	74	17	sets	set	NOUN
ejpam-4581	74	18	in	in	ADP
ejpam-4581	74	19	a	a	DET
ejpam-4581	74	20	topological	topological	ADJ
ejpam-4581	74	21	space	space	NOUN
ejpam-4581	74	22	(	(	PUNCT
ejpam-4581	74	23	x	x	X
ejpam-4581	74	24	,	,	PUNCT
ejpam-4581	74	25	τ	τ	X
ejpam-4581	74	26	)	)	PUNCT
ejpam-4581	74	27	is	be	AUX
ejpam-4581	74	28	denoted	denote	VERB
ejpam-4581	74	29	by	by	ADP
ejpam-4581	74	30	sλspo(x	sλspo(x	PROPN
ejpam-4581	74	31	,	,	PUNCT
ejpam-4581	74	32	τ	τ	PROPN
ejpam-4581	74	33	)	)	PUNCT
ejpam-4581	74	34	(	(	PUNCT
ejpam-4581	74	35	resp	resp	NOUN
ejpam-4581	74	36	.	.	PUNCT
ejpam-4581	75	1	pλspo(x	pλspo(x	ADJ
ejpam-4581	75	2	,	,	PUNCT
ejpam-4581	75	3	τ	τ	PROPN
ejpam-4581	75	4	)	)	PUNCT
ejpam-4581	75	5	,	,	PUNCT
ejpam-4581	75	6	βλspo(x	βλspo(x	PROPN
ejpam-4581	75	7	,	,	PUNCT
ejpam-4581	75	8	τ	τ	PROPN
ejpam-4581	75	9	)	)	PUNCT
ejpam-4581	75	10	,	,	PUNCT
ejpam-4581	75	11	αλspo(x	αλspo(x	NOUN
ejpam-4581	75	12	,	,	PUNCT
ejpam-4581	75	13	τ	τ	PROPN
ejpam-4581	75	14	)	)	PUNCT
ejpam-4581	75	15	,	,	PUNCT
ejpam-4581	75	16	rλspo(x	rλspo(x	PROPN
ejpam-4581	75	17	,	,	PUNCT
ejpam-4581	75	18	τ	τ	PROPN
ejpam-4581	75	19	)	)	PUNCT
ejpam-4581	75	20	)	)	PUNCT
ejpam-4581	75	21	.	.	PUNCT
ejpam-4581	76	1	the	the	DET
ejpam-4581	76	2	complement	complement	NOUN
ejpam-4581	76	3	of	of	ADP
ejpam-4581	76	4	a	a	DET
ejpam-4581	76	5	s(λ	s(λ	PROPN
ejpam-4581	76	6	,	,	PUNCT
ejpam-4581	76	7	sp)-open	sp)-open	ADJ
ejpam-4581	76	8	(	(	PUNCT
ejpam-4581	76	9	resp	resp	NOUN
ejpam-4581	76	10	.	.	PUNCT
ejpam-4581	77	1	p(λ	p(λ	NOUN
ejpam-4581	77	2	,	,	PUNCT
ejpam-4581	77	3	sp)-open	sp)-open	NOUN
ejpam-4581	77	4	,	,	PUNCT
ejpam-4581	77	5	β(λ	β(λ	X
ejpam-4581	77	6	,	,	PUNCT
ejpam-4581	77	7	sp)-open	sp)-open	NOUN
ejpam-4581	77	8	,	,	PUNCT
ejpam-4581	77	9	α(λ	α(λ	PROPN
ejpam-4581	77	10	,	,	PUNCT
ejpam-4581	77	11	sp)-open	sp)-open	NOUN
ejpam-4581	77	12	,	,	PUNCT
ejpam-4581	77	13	r(λ	r(λ	NOUN
ejpam-4581	77	14	,	,	PUNCT
ejpam-4581	77	15	sp)-open	sp)-open	NOUN
ejpam-4581	77	16	)	)	PUNCT
ejpam-4581	77	17	set	set	NOUN
ejpam-4581	77	18	is	be	AUX
ejpam-4581	77	19	said	say	VERB
ejpam-4581	77	20	to	to	PART
ejpam-4581	77	21	be	be	AUX
ejpam-4581	77	22	s(λ	s(λ	PROPN
ejpam-4581	77	23	,	,	PUNCT
ejpam-4581	77	24	sp)-closed	sp)-close	VERB
ejpam-4581	77	25	(	(	PUNCT
ejpam-4581	77	26	resp	resp	NOUN
ejpam-4581	77	27	.	.	PUNCT
ejpam-4581	78	1	p(λ	p(λ	NOUN
ejpam-4581	78	2	,	,	PUNCT
ejpam-4581	78	3	sp)closed	sp)close	VERB
ejpam-4581	78	4	,	,	PUNCT
ejpam-4581	78	5	β(λ	β(λ	X
ejpam-4581	78	6	,	,	PUNCT
ejpam-4581	78	7	sp)-closed	sp)-close	VERB
ejpam-4581	78	8	,	,	PUNCT
ejpam-4581	78	9	α(λ	α(λ	PROPN
ejpam-4581	78	10	,	,	PUNCT
ejpam-4581	78	11	sp)-closed	sp)-close	VERB
ejpam-4581	78	12	,	,	PUNCT
ejpam-4581	78	13	r(λ	r(λ	NOUN
ejpam-4581	78	14	,	,	PUNCT
ejpam-4581	78	15	sp)-closed	sp)-close	VERB
ejpam-4581	78	16	)	)	PUNCT
ejpam-4581	78	17	.	.	PUNCT
ejpam-4581	79	1	the	the	DET
ejpam-4581	79	2	family	family	NOUN
ejpam-4581	79	3	of	of	ADP
ejpam-4581	79	4	all	all	DET
ejpam-4581	79	5	s(λ	s(λ	NOUN
ejpam-4581	79	6	,	,	PUNCT
ejpam-4581	79	7	sp)-closed	sp)-close	VERB
ejpam-4581	79	8	(	(	PUNCT
ejpam-4581	79	9	resp	resp	NOUN
ejpam-4581	79	10	.	.	PUNCT
ejpam-4581	80	1	p(λ	p(λ	NOUN
ejpam-4581	80	2	,	,	PUNCT
ejpam-4581	80	3	sp)-closed	sp)-close	VERB
ejpam-4581	80	4	,	,	PUNCT
ejpam-4581	80	5	β(λ	β(λ	X
ejpam-4581	80	6	,	,	PUNCT
ejpam-4581	80	7	sp)-closed	sp)-close	VERB
ejpam-4581	80	8	,	,	PUNCT
ejpam-4581	80	9	α(λ	α(λ	PROPN
ejpam-4581	80	10	,	,	PUNCT
ejpam-4581	80	11	sp)-closed	sp)-close	VERB
ejpam-4581	80	12	,	,	PUNCT
ejpam-4581	80	13	r(λ	r(λ	NOUN
ejpam-4581	80	14	,	,	PUNCT
ejpam-4581	80	15	sp)-closed	sp)-close	VERB
ejpam-4581	80	16	)	)	PUNCT
ejpam-4581	80	17	sets	set	NOUN
ejpam-4581	80	18	in	in	ADP
ejpam-4581	80	19	a	a	DET
ejpam-4581	80	20	topological	topological	ADJ
ejpam-4581	80	21	space	space	NOUN
ejpam-4581	80	22	(	(	PUNCT
ejpam-4581	80	23	x	x	X
ejpam-4581	80	24	,	,	PUNCT
ejpam-4581	80	25	τ	τ	X
ejpam-4581	80	26	)	)	PUNCT
ejpam-4581	80	27	is	be	AUX
ejpam-4581	80	28	denoted	denote	VERB
ejpam-4581	80	29	by	by	ADP
ejpam-4581	80	30	sλspc(x	sλspc(x	PROPN
ejpam-4581	80	31	,	,	PUNCT
ejpam-4581	80	32	τ	τ	PROPN
ejpam-4581	80	33	)	)	PUNCT
ejpam-4581	80	34	(	(	PUNCT
ejpam-4581	80	35	resp	resp	NOUN
ejpam-4581	80	36	.	.	PUNCT
ejpam-4581	81	1	pλspc(x	pλspc(x	NOUN
ejpam-4581	81	2	,	,	PUNCT
ejpam-4581	81	3	τ	τ	PROPN
ejpam-4581	81	4	)	)	PUNCT
ejpam-4581	81	5	,	,	PUNCT
ejpam-4581	81	6	βλspc(x	βλspc(x	PROPN
ejpam-4581	81	7	,	,	PUNCT
ejpam-4581	81	8	τ	τ	PROPN
ejpam-4581	81	9	)	)	PUNCT
ejpam-4581	81	10	,	,	PUNCT
ejpam-4581	81	11	αλspc(x	αλspc(x	NOUN
ejpam-4581	81	12	,	,	PUNCT
ejpam-4581	81	13	τ	τ	PROPN
ejpam-4581	81	14	)	)	PUNCT
ejpam-4581	81	15	,	,	PUNCT
ejpam-4581	81	16	rλspc(x	rλspc(x	PROPN
ejpam-4581	81	17	,	,	PUNCT
ejpam-4581	81	18	τ	τ	PROPN
ejpam-4581	81	19	)	)	PUNCT
ejpam-4581	81	20	)	)	PUNCT
ejpam-4581	81	21	.	.	PUNCT
ejpam-4581	82	1	let	let	VERB
ejpam-4581	82	2	a	a	DET
ejpam-4581	82	3	be	be	AUX
ejpam-4581	82	4	a	a	DET
ejpam-4581	82	5	subset	subset	NOUN
ejpam-4581	82	6	of	of	ADP
ejpam-4581	82	7	a	a	DET
ejpam-4581	82	8	topological	topological	ADJ
ejpam-4581	82	9	space	space	NOUN
ejpam-4581	82	10	(	(	PUNCT
ejpam-4581	82	11	x	x	X
ejpam-4581	82	12	,	,	PUNCT
ejpam-4581	82	13	τ	τ	PROPN
ejpam-4581	82	14	)	)	PUNCT
ejpam-4581	82	15	.	.	PUNCT
ejpam-4581	83	1	the	the	DET
ejpam-4581	83	2	intersection	intersection	NOUN
ejpam-4581	83	3	of	of	ADP
ejpam-4581	83	4	all	all	DET
ejpam-4581	83	5	s(λ	s(λ	NOUN
ejpam-4581	83	6	,	,	PUNCT
ejpam-4581	83	7	sp)-closed	sp)-close	VERB
ejpam-4581	83	8	(	(	PUNCT
ejpam-4581	83	9	resp	resp	NOUN
ejpam-4581	83	10	.	.	PUNCT
ejpam-4581	84	1	p(λ	p(λ	NOUN
ejpam-4581	84	2	,	,	PUNCT
ejpam-4581	84	3	sp)-closed	sp)-close	VERB
ejpam-4581	84	4	,	,	PUNCT
ejpam-4581	84	5	α(λ	α(λ	PROPN
ejpam-4581	84	6	,	,	PUNCT
ejpam-4581	84	7	sp)-closed	sp)-close	VERB
ejpam-4581	84	8	)	)	PUNCT
ejpam-4581	84	9	sets	set	NOUN
ejpam-4581	84	10	containing	contain	VERB
ejpam-4581	84	11	a	a	PRON
ejpam-4581	84	12	is	be	AUX
ejpam-4581	84	13	called	call	VERB
ejpam-4581	84	14	the	the	DET
ejpam-4581	84	15	s(λ	s(λ	PROPN
ejpam-4581	84	16	,	,	PUNCT
ejpam-4581	84	17	sp)-closure	sp)-closure	NOUN
ejpam-4581	84	18	[	[	X
ejpam-4581	84	19	23	23	NUM
ejpam-4581	84	20	]	]	PUNCT
ejpam-4581	84	21	(	(	PUNCT
ejpam-4581	84	22	resp	resp	NOUN
ejpam-4581	84	23	.	.	PUNCT
ejpam-4581	85	1	p(λ	p(λ	NOUN
ejpam-4581	85	2	,	,	PUNCT
ejpam-4581	85	3	sp)-closure	sp)-closure	NOUN
ejpam-4581	85	4	,	,	PUNCT
ejpam-4581	85	5	α(λ	α(λ	PROPN
ejpam-4581	85	6	,	,	PUNCT
ejpam-4581	85	7	sp)-closure	sp)-closure	NOUN
ejpam-4581	86	1	[	[	X
ejpam-4581	86	2	5	5	NUM
ejpam-4581	86	3	,	,	PUNCT
ejpam-4581	86	4	22	22	NUM
ejpam-4581	86	5	]	]	PUNCT
ejpam-4581	86	6	)	)	PUNCT
ejpam-4581	86	7	of	of	ADP
ejpam-4581	86	8	a	a	PRON
ejpam-4581	86	9	and	and	CCONJ
ejpam-4581	86	10	is	be	AUX
ejpam-4581	86	11	denoted	denote	VERB
ejpam-4581	86	12	by	by	ADP
ejpam-4581	86	13	as(λ	as(λ	NUM
ejpam-4581	86	14	,	,	PUNCT
ejpam-4581	86	15	sp	sp	NOUN
ejpam-4581	86	16	)	)	PUNCT
ejpam-4581	86	17	(	(	PUNCT
ejpam-4581	86	18	resp	resp	NOUN
ejpam-4581	86	19	.	.	PUNCT
ejpam-4581	87	1	ap(λ	ap(λ	PROPN
ejpam-4581	87	2	,	,	PUNCT
ejpam-4581	87	3	sp	sp	NOUN
ejpam-4581	87	4	)	)	PUNCT
ejpam-4581	87	5	,	,	PUNCT
ejpam-4581	87	6	aα(λ	aα(λ	NOUN
ejpam-4581	87	7	,	,	PUNCT
ejpam-4581	87	8	sp	sp	NOUN
ejpam-4581	87	9	)	)	PUNCT
ejpam-4581	87	10	)	)	PUNCT
ejpam-4581	87	11	.	.	PUNCT
ejpam-4581	88	1	throughout	throughout	ADP
ejpam-4581	88	2	this	this	DET
ejpam-4581	88	3	paper	paper	NOUN
ejpam-4581	88	4	,	,	PUNCT
ejpam-4581	88	5	the	the	DET
ejpam-4581	88	6	spaces	space	NOUN
ejpam-4581	88	7	(	(	PUNCT
ejpam-4581	88	8	x	x	X
ejpam-4581	88	9	,	,	PUNCT
ejpam-4581	88	10	τ	τ	X
ejpam-4581	88	11	)	)	PUNCT
ejpam-4581	88	12	and	and	CCONJ
ejpam-4581	88	13	(	(	PUNCT
ejpam-4581	88	14	y	y	PROPN
ejpam-4581	88	15	,	,	PUNCT
ejpam-4581	88	16	σ	σ	PROPN
ejpam-4581	88	17	)	)	PUNCT
ejpam-4581	88	18	(	(	PUNCT
ejpam-4581	88	19	or	or	CCONJ
ejpam-4581	88	20	simply	simply	ADV
ejpam-4581	88	21	x	x	X
ejpam-4581	88	22	and	and	CCONJ
ejpam-4581	88	23	y	y	PROPN
ejpam-4581	88	24	)	)	PUNCT
ejpam-4581	88	25	always	always	ADV
ejpam-4581	88	26	mean	mean	VERB
ejpam-4581	88	27	topological	topological	ADJ
ejpam-4581	88	28	spaces	space	NOUN
ejpam-4581	88	29	and	and	CCONJ
ejpam-4581	88	30	f	f	NOUN
ejpam-4581	88	31	:	:	PUNCT
ejpam-4581	88	32	x	x	X
ejpam-4581	88	33	→	→	SYM
ejpam-4581	88	34	y	y	PROPN
ejpam-4581	88	35	(	(	PUNCT
ejpam-4581	88	36	resp	resp	PROPN
ejpam-4581	88	37	.	.	PUNCT
ejpam-4581	89	1	f	f	X
ejpam-4581	89	2	:	:	PUNCT
ejpam-4581	89	3	x	x	X
ejpam-4581	89	4	→	→	SYM
ejpam-4581	89	5	y	y	PROPN
ejpam-4581	89	6	)	)	PUNCT
ejpam-4581	89	7	presents	present	VERB
ejpam-4581	89	8	a	a	DET
ejpam-4581	89	9	multivalued	multivalue	VERB
ejpam-4581	89	10	(	(	PUNCT
ejpam-4581	89	11	resp	resp	NOUN
ejpam-4581	89	12	.	.	PUNCT
ejpam-4581	90	1	single	single	ADJ
ejpam-4581	90	2	valued	value	VERB
ejpam-4581	90	3	)	)	PUNCT
ejpam-4581	90	4	function	function	NOUN
ejpam-4581	90	5	.	.	PUNCT
ejpam-4581	91	1	for	for	ADP
ejpam-4581	91	2	a	a	DET
ejpam-4581	91	3	multifunction	multifunction	NOUN
ejpam-4581	91	4	f	f	NOUN
ejpam-4581	91	5	:	:	PUNCT
ejpam-4581	91	6	x	x	X
ejpam-4581	91	7	→	→	SYM
ejpam-4581	91	8	y	y	PROPN
ejpam-4581	91	9	,	,	PUNCT
ejpam-4581	91	10	following	follow	VERB
ejpam-4581	91	11	[	[	X
ejpam-4581	91	12	2	2	X
ejpam-4581	91	13	]	]	PUNCT
ejpam-4581	91	14	we	we	PRON
ejpam-4581	91	15	shall	shall	AUX
ejpam-4581	91	16	denote	denote	VERB
ejpam-4581	91	17	the	the	DET
ejpam-4581	91	18	upper	upper	ADJ
ejpam-4581	91	19	and	and	CCONJ
ejpam-4581	91	20	lower	low	ADJ
ejpam-4581	91	21	inverse	inverse	NOUN
ejpam-4581	91	22	of	of	ADP
ejpam-4581	91	23	a	a	DET
ejpam-4581	91	24	set	set	NOUN
ejpam-4581	91	25	b	b	PROPN
ejpam-4581	91	26	of	of	ADP
ejpam-4581	91	27	y	y	PROPN
ejpam-4581	91	28	by	by	ADP
ejpam-4581	91	29	f+(b	f+(b	NOUN
ejpam-4581	91	30	)	)	PUNCT
ejpam-4581	91	31	and	and	CCONJ
ejpam-4581	91	32	f−(b	f−(b	NOUN
ejpam-4581	91	33	)	)	PUNCT
ejpam-4581	91	34	,	,	PUNCT
ejpam-4581	91	35	respectively	respectively	ADV
ejpam-4581	91	36	,	,	PUNCT
ejpam-4581	91	37	that	that	ADV
ejpam-4581	91	38	is	is	ADV
ejpam-4581	91	39	,	,	PUNCT
ejpam-4581	91	40	f+(b	f+(b	NOUN
ejpam-4581	91	41	)	)	PUNCT
ejpam-4581	91	42	=	=	PRON
ejpam-4581	92	1	{	{	PUNCT
ejpam-4581	92	2	x	x	PUNCT
ejpam-4581	92	3	∈	∈	PROPN
ejpam-4581	92	4	x	x	INTJ
ejpam-4581	93	1	|	|	NOUN
ejpam-4581	93	2	f	f	X
ejpam-4581	93	3	(	(	PUNCT
ejpam-4581	93	4	x	x	NOUN
ejpam-4581	93	5	)	)	PUNCT
ejpam-4581	93	6	⊆	⊆	NUM
ejpam-4581	93	7	b	b	NOUN
ejpam-4581	93	8	}	}	PUNCT
ejpam-4581	93	9	and	and	CCONJ
ejpam-4581	93	10	f−(b	f−(b	PROPN
ejpam-4581	93	11	)	)	PUNCT
ejpam-4581	93	12	=	=	PRON
ejpam-4581	94	1	{	{	PUNCT
ejpam-4581	94	2	x	x	PUNCT
ejpam-4581	94	3	∈	∈	PROPN
ejpam-4581	94	4	x	x	INTJ
ejpam-4581	95	1	|	|	NOUN
ejpam-4581	95	2	f	f	X
ejpam-4581	95	3	(	(	PUNCT
ejpam-4581	95	4	x	x	NOUN
ejpam-4581	95	5	)	)	PUNCT
ejpam-4581	95	6	∩	∩	NOUN
ejpam-4581	95	7	b	b	PROPN
ejpam-4581	95	8	̸=	̸=	PROPN
ejpam-4581	95	9	∅	∅	NOUN
ejpam-4581	95	10	}	}	PUNCT
ejpam-4581	95	11	.	.	PUNCT
ejpam-4581	96	1	in	in	ADP
ejpam-4581	96	2	particular	particular	ADJ
ejpam-4581	96	3	,	,	PUNCT
ejpam-4581	96	4	f−(y	f−(y	NOUN
ejpam-4581	96	5	)	)	PUNCT
ejpam-4581	96	6	=	=	SYM
ejpam-4581	97	1	{	{	PUNCT
ejpam-4581	97	2	x	x	PUNCT
ejpam-4581	97	3	∈	∈	PROPN
ejpam-4581	97	4	x	x	INTJ
ejpam-4581	98	1	|	|	ADV
ejpam-4581	98	2	y	y	PROPN
ejpam-4581	98	3	∈	∈	PROPN
ejpam-4581	98	4	f	f	X
ejpam-4581	98	5	(	(	PUNCT
ejpam-4581	98	6	x	x	NOUN
ejpam-4581	98	7	)	)	PUNCT
ejpam-4581	98	8	}	}	PUNCT
ejpam-4581	98	9	for	for	ADP
ejpam-4581	98	10	each	each	DET
ejpam-4581	98	11	point	point	NOUN
ejpam-4581	98	12	y	y	PROPN
ejpam-4581	98	13	∈	∈	PROPN
ejpam-4581	98	14	y	y	PROPN
ejpam-4581	98	15	.	.	PUNCT
ejpam-4581	99	1	for	for	ADP
ejpam-4581	99	2	each	each	PRON
ejpam-4581	99	3	a	a	DET
ejpam-4581	99	4	⊆	⊆	NUM
ejpam-4581	99	5	x	x	SYM
ejpam-4581	99	6	,	,	PUNCT
ejpam-4581	99	7	f	f	PROPN
ejpam-4581	99	8	(	(	PUNCT
ejpam-4581	99	9	a	a	NOUN
ejpam-4581	99	10	)	)	PUNCT
ejpam-4581	99	11	=	=	SYM
ejpam-4581	99	12	∪x∈af	∪x∈af	NOUN
ejpam-4581	99	13	(	(	PUNCT
ejpam-4581	99	14	x	x	NOUN
ejpam-4581	99	15	)	)	PUNCT
ejpam-4581	99	16	.	.	PUNCT
ejpam-4581	100	1	moreover	moreover	ADV
ejpam-4581	100	2	,	,	PUNCT
ejpam-4581	100	3	f	f	X
ejpam-4581	100	4	:	:	PUNCT
ejpam-4581	100	5	x	x	X
ejpam-4581	100	6	→	→	SYM
ejpam-4581	100	7	y	y	PROPN
ejpam-4581	100	8	is	be	AUX
ejpam-4581	100	9	called	call	VERB
ejpam-4581	100	10	upper	upper	ADJ
ejpam-4581	100	11	semi	semi	ADJ
ejpam-4581	100	12	-	-	ADJ
ejpam-4581	100	13	continuous	continuous	ADJ
ejpam-4581	100	14	(	(	PUNCT
ejpam-4581	100	15	resp	resp	NOUN
ejpam-4581	100	16	.	.	PUNCT
ejpam-4581	101	1	lower	low	ADJ
ejpam-4581	101	2	semi	semi	ADJ
ejpam-4581	101	3	-	-	ADJ
ejpam-4581	101	4	continuous	continuous	ADJ
ejpam-4581	101	5	)	)	PUNCT
ejpam-4581	101	6	if	if	SCONJ
ejpam-4581	101	7	f+(v	f+(v	PROPN
ejpam-4581	101	8	)	)	PUNCT
ejpam-4581	101	9	(	(	PUNCT
ejpam-4581	101	10	resp	resp	NOUN
ejpam-4581	101	11	.	.	PUNCT
ejpam-4581	102	1	f−(v	f−(v	NOUN
ejpam-4581	102	2	)	)	PUNCT
ejpam-4581	102	3	)	)	PUNCT
ejpam-4581	103	1	is	be	AUX
ejpam-4581	103	2	open	open	ADJ
ejpam-4581	103	3	in	in	ADP
ejpam-4581	103	4	x	x	PUNCT
ejpam-4581	103	5	for	for	ADP
ejpam-4581	103	6	every	every	DET
ejpam-4581	103	7	open	open	ADJ
ejpam-4581	103	8	set	set	VERB
ejpam-4581	103	9	v	v	NOUN
ejpam-4581	103	10	of	of	ADP
ejpam-4581	103	11	y	y	PROPN
ejpam-4581	104	1	[	[	X
ejpam-4581	104	2	21	21	NUM
ejpam-4581	104	3	]	]	PUNCT
ejpam-4581	104	4	.	.	PUNCT
ejpam-4581	105	1	3	3	X
ejpam-4581	105	2	.	.	X
ejpam-4581	105	3	on	on	ADP
ejpam-4581	105	4	upper	upper	ADJ
ejpam-4581	105	5	and	and	CCONJ
ejpam-4581	105	6	lower	low	ADJ
ejpam-4581	105	7	almost	almost	ADV
ejpam-4581	105	8	contra-(λ	contra-(λ	PROPN
ejpam-4581	105	9	,	,	PUNCT
ejpam-4581	105	10	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	105	11	multifunctions	multifunction	NOUN
ejpam-4581	105	12	we	we	PRON
ejpam-4581	105	13	begin	begin	VERB
ejpam-4581	105	14	this	this	DET
ejpam-4581	105	15	section	section	NOUN
ejpam-4581	105	16	by	by	ADP
ejpam-4581	105	17	introducing	introduce	VERB
ejpam-4581	105	18	the	the	DET
ejpam-4581	105	19	concepts	concept	NOUN
ejpam-4581	105	20	of	of	ADP
ejpam-4581	105	21	upper	upper	ADJ
ejpam-4581	105	22	and	and	CCONJ
ejpam-4581	105	23	lower	low	ADJ
ejpam-4581	105	24	almost	almost	ADV
ejpam-4581	105	25	contra(λ	contra(λ	PROPN
ejpam-4581	105	26	,	,	PUNCT
ejpam-4581	105	27	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	105	28	multifunctions	multifunction	NOUN
ejpam-4581	105	29	.	.	PUNCT
ejpam-4581	106	1	definition	definition	NOUN
ejpam-4581	106	2	1	1	NUM
ejpam-4581	106	3	.	.	PUNCT
ejpam-4581	107	1	a	a	DET
ejpam-4581	107	2	multifunction	multifunction	NOUN
ejpam-4581	107	3	f	f	NOUN
ejpam-4581	107	4	:	:	PUNCT
ejpam-4581	107	5	(	(	PUNCT
ejpam-4581	107	6	x	x	X
ejpam-4581	107	7	,	,	PUNCT
ejpam-4581	107	8	τ	τ	X
ejpam-4581	107	9	)	)	PUNCT
ejpam-4581	107	10	→	→	SYM
ejpam-4581	107	11	(	(	PUNCT
ejpam-4581	107	12	y	y	PROPN
ejpam-4581	107	13	,	,	PUNCT
ejpam-4581	107	14	σ	σ	PROPN
ejpam-4581	107	15	)	)	PUNCT
ejpam-4581	107	16	is	be	AUX
ejpam-4581	107	17	said	say	VERB
ejpam-4581	107	18	to	to	PART
ejpam-4581	107	19	be	be	AUX
ejpam-4581	107	20	:	:	PUNCT
ejpam-4581	107	21	(	(	PUNCT
ejpam-4581	107	22	i	i	NOUN
ejpam-4581	107	23	)	)	PUNCT
ejpam-4581	107	24	lower	low	ADJ
ejpam-4581	107	25	almost	almost	ADV
ejpam-4581	107	26	contra-(λ	contra-(λ	PROPN
ejpam-4581	107	27	,	,	PUNCT
ejpam-4581	107	28	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	107	29	at	at	ADP
ejpam-4581	107	30	x	x	X
ejpam-4581	107	31	∈	∈	PROPN
ejpam-4581	107	32	x	x	INTJ
ejpam-4581	107	33	if	if	SCONJ
ejpam-4581	107	34	,	,	PUNCT
ejpam-4581	107	35	for	for	ADP
ejpam-4581	107	36	each	each	DET
ejpam-4581	107	37	r(λ	r(λ	NOUN
ejpam-4581	107	38	,	,	PUNCT
ejpam-4581	107	39	sp)-closed	sp)-close	VERB
ejpam-4581	107	40	set	set	VERB
ejpam-4581	107	41	k	k	PROPN
ejpam-4581	107	42	of	of	ADP
ejpam-4581	107	43	y	y	PROPN
ejpam-4581	107	44	with	with	ADP
ejpam-4581	107	45	x	x	PROPN
ejpam-4581	107	46	∈	∈	PROPN
ejpam-4581	107	47	f−(k	f−(k	PROPN
ejpam-4581	107	48	)	)	PUNCT
ejpam-4581	107	49	,	,	PUNCT
ejpam-4581	107	50	there	there	PRON
ejpam-4581	107	51	exists	exist	VERB
ejpam-4581	107	52	a	a	DET
ejpam-4581	107	53	(	(	PUNCT
ejpam-4581	107	54	λ	λ	NOUN
ejpam-4581	107	55	,	,	PUNCT
ejpam-4581	107	56	sp)-open	sp)-open	NOUN
ejpam-4581	107	57	set	set	VERB
ejpam-4581	107	58	u	u	NOUN
ejpam-4581	107	59	of	of	ADP
ejpam-4581	107	60	x	x	PUNCT
ejpam-4581	107	61	containing	contain	VERB
ejpam-4581	107	62	x	x	PUNCT
ejpam-4581	107	63	such	such	ADJ
ejpam-4581	107	64	that	that	SCONJ
ejpam-4581	107	65	u	u	PROPN
ejpam-4581	107	66	⊆	⊆	NUM
ejpam-4581	107	67	f−(k	f−(k	PROPN
ejpam-4581	107	68	)	)	PUNCT
ejpam-4581	107	69	;	;	PUNCT
ejpam-4581	107	70	(	(	PUNCT
ejpam-4581	107	71	ii	ii	NOUN
ejpam-4581	107	72	)	)	PUNCT
ejpam-4581	107	73	upper	upper	ADJ
ejpam-4581	107	74	almost	almost	ADV
ejpam-4581	107	75	contra-(λ	contra-(λ	PROPN
ejpam-4581	107	76	,	,	PUNCT
ejpam-4581	107	77	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	107	78	at	at	ADP
ejpam-4581	107	79	x	x	X
ejpam-4581	107	80	∈	∈	PROPN
ejpam-4581	107	81	x	x	INTJ
ejpam-4581	107	82	if	if	SCONJ
ejpam-4581	107	83	,	,	PUNCT
ejpam-4581	107	84	for	for	ADP
ejpam-4581	107	85	each	each	DET
ejpam-4581	107	86	r(λ	r(λ	NOUN
ejpam-4581	107	87	,	,	PUNCT
ejpam-4581	107	88	sp)-closed	sp)-close	VERB
ejpam-4581	107	89	set	set	VERB
ejpam-4581	107	90	k	k	PROPN
ejpam-4581	107	91	of	of	ADP
ejpam-4581	107	92	y	y	PROPN
ejpam-4581	107	93	with	with	ADP
ejpam-4581	107	94	x	x	PROPN
ejpam-4581	107	95	∈	∈	PROPN
ejpam-4581	107	96	f+(k	f+(k	PROPN
ejpam-4581	107	97	)	)	PUNCT
ejpam-4581	107	98	,	,	PUNCT
ejpam-4581	107	99	there	there	PRON
ejpam-4581	107	100	exists	exist	VERB
ejpam-4581	107	101	a	a	DET
ejpam-4581	107	102	(	(	PUNCT
ejpam-4581	107	103	λ	λ	NOUN
ejpam-4581	107	104	,	,	PUNCT
ejpam-4581	107	105	sp)-open	sp)-open	NOUN
ejpam-4581	107	106	set	set	VERB
ejpam-4581	107	107	u	u	NOUN
ejpam-4581	107	108	of	of	ADP
ejpam-4581	107	109	x	x	PUNCT
ejpam-4581	107	110	containing	contain	VERB
ejpam-4581	107	111	x	x	PUNCT
ejpam-4581	107	112	such	such	ADJ
ejpam-4581	107	113	that	that	SCONJ
ejpam-4581	107	114	u	u	PROPN
ejpam-4581	107	115	⊆	⊆	NUM
ejpam-4581	107	116	f+(k	f+(k	NOUN
ejpam-4581	107	117	)	)	PUNCT
ejpam-4581	107	118	;	;	PUNCT
ejpam-4581	107	119	(	(	PUNCT
ejpam-4581	107	120	iii	iii	X
ejpam-4581	107	121	)	)	PUNCT
ejpam-4581	107	122	lower	low	ADJ
ejpam-4581	107	123	(	(	PUNCT
ejpam-4581	107	124	upper	upper	ADJ
ejpam-4581	107	125	)	)	PUNCT
ejpam-4581	107	126	almost	almost	ADV
ejpam-4581	107	127	contra-(λ	contra-(λ	PROPN
ejpam-4581	107	128	,	,	PUNCT
ejpam-4581	107	129	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	107	130	if	if	SCONJ
ejpam-4581	107	131	f	f	PROPN
ejpam-4581	107	132	has	have	VERB
ejpam-4581	107	133	this	this	DET
ejpam-4581	107	134	property	property	NOUN
ejpam-4581	107	135	at	at	ADP
ejpam-4581	107	136	each	each	DET
ejpam-4581	107	137	point	point	NOUN
ejpam-4581	107	138	of	of	ADP
ejpam-4581	107	139	x.	x.	PROPN
ejpam-4581	107	140	c.	c.	PROPN
ejpam-4581	107	141	boonpok	boonpok	PROPN
ejpam-4581	107	142	,	,	PUNCT
ejpam-4581	107	143	j.	j.	PROPN
ejpam-4581	107	144	khampakdee	khampakdee	PROPN
ejpam-4581	107	145	/	/	PUNCT
ejpam-4581	107	146	eur	eur	PROPN
ejpam-4581	107	147	.	.	PUNCT
ejpam-4581	108	1	j.	j.	PROPN
ejpam-4581	108	2	pure	pure	PROPN
ejpam-4581	108	3	appl	appl	PROPN
ejpam-4581	108	4	.	.	PROPN
ejpam-4581	108	5	math	math	PROPN
ejpam-4581	108	6	,	,	PUNCT
ejpam-4581	108	7	16	16	NUM
ejpam-4581	108	8	(	(	PUNCT
ejpam-4581	108	9	1	1	NUM
ejpam-4581	108	10	)	)	PUNCT
ejpam-4581	108	11	(	(	PUNCT
ejpam-4581	108	12	2023	2023	NUM
ejpam-4581	108	13	)	)	PUNCT
ejpam-4581	108	14	,	,	PUNCT
ejpam-4581	108	15	156	156	NUM
ejpam-4581	108	16	-	-	SYM
ejpam-4581	108	17	168	168	NUM
ejpam-4581	108	18	159	159	NUM
ejpam-4581	108	19	theorem	theorem	NOUN
ejpam-4581	108	20	1	1	NUM
ejpam-4581	108	21	.	.	X
ejpam-4581	108	22	for	for	ADP
ejpam-4581	108	23	a	a	DET
ejpam-4581	108	24	multifunction	multifunction	NOUN
ejpam-4581	108	25	f	f	NOUN
ejpam-4581	108	26	:	:	PUNCT
ejpam-4581	108	27	(	(	PUNCT
ejpam-4581	108	28	x	x	X
ejpam-4581	108	29	,	,	PUNCT
ejpam-4581	108	30	τ	τ	X
ejpam-4581	108	31	)	)	PUNCT
ejpam-4581	108	32	→	→	SYM
ejpam-4581	108	33	(	(	PUNCT
ejpam-4581	108	34	y	y	PROPN
ejpam-4581	108	35	,	,	PUNCT
ejpam-4581	108	36	σ	σ	PROPN
ejpam-4581	108	37	)	)	PUNCT
ejpam-4581	108	38	,	,	PUNCT
ejpam-4581	108	39	the	the	DET
ejpam-4581	108	40	following	follow	VERB
ejpam-4581	108	41	properties	property	NOUN
ejpam-4581	108	42	are	be	AUX
ejpam-4581	108	43	equivalent	equivalent	ADJ
ejpam-4581	108	44	:	:	PUNCT
ejpam-4581	108	45	(	(	PUNCT
ejpam-4581	108	46	1	1	X
ejpam-4581	108	47	)	)	PUNCT
ejpam-4581	108	48	f	f	PROPN
ejpam-4581	108	49	is	be	AUX
ejpam-4581	108	50	upper	upper	ADJ
ejpam-4581	108	51	almost	almost	ADV
ejpam-4581	108	52	contra-(λ	contra-(λ	PROPN
ejpam-4581	108	53	,	,	PUNCT
ejpam-4581	108	54	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	108	55	;	;	PUNCT
ejpam-4581	108	56	(	(	PUNCT
ejpam-4581	108	57	2	2	X
ejpam-4581	108	58	)	)	PUNCT
ejpam-4581	108	59	f+(k	f+(k	NOUN
ejpam-4581	108	60	)	)	PUNCT
ejpam-4581	108	61	is	be	AUX
ejpam-4581	108	62	(	(	PUNCT
ejpam-4581	108	63	λ	λ	INTJ
ejpam-4581	108	64	,	,	PUNCT
ejpam-4581	108	65	sp)-open	sp)-open	ADJ
ejpam-4581	108	66	in	in	ADP
ejpam-4581	108	67	x	x	PUNCT
ejpam-4581	108	68	for	for	ADP
ejpam-4581	108	69	every	every	DET
ejpam-4581	108	70	r(λ	r(λ	NOUN
ejpam-4581	108	71	,	,	PUNCT
ejpam-4581	108	72	sp)-closed	sp)-close	VERB
ejpam-4581	108	73	set	set	VERB
ejpam-4581	109	1	k	k	PROPN
ejpam-4581	109	2	of	of	ADP
ejpam-4581	109	3	y	y	PROPN
ejpam-4581	109	4	;	;	PUNCT
ejpam-4581	109	5	(	(	PUNCT
ejpam-4581	109	6	3	3	X
ejpam-4581	109	7	)	)	PUNCT
ejpam-4581	109	8	f−(v	f−(v	NOUN
ejpam-4581	109	9	)	)	PUNCT
ejpam-4581	109	10	is	be	AUX
ejpam-4581	109	11	(	(	PUNCT
ejpam-4581	109	12	λ	λ	X
ejpam-4581	109	13	,	,	PUNCT
ejpam-4581	109	14	sp)-closed	sp)-close	VERB
ejpam-4581	109	15	in	in	ADP
ejpam-4581	109	16	x	x	PUNCT
ejpam-4581	109	17	for	for	ADP
ejpam-4581	109	18	every	every	DET
ejpam-4581	109	19	r(λ	r(λ	NOUN
ejpam-4581	109	20	,	,	PUNCT
ejpam-4581	109	21	sp)-open	sp)-open	ADJ
ejpam-4581	109	22	set	set	VERB
ejpam-4581	109	23	v	v	NOUN
ejpam-4581	109	24	of	of	ADP
ejpam-4581	109	25	y	y	PROPN
ejpam-4581	109	26	;	;	PUNCT
ejpam-4581	109	27	(	(	PUNCT
ejpam-4581	109	28	4	4	X
ejpam-4581	109	29	)	)	PUNCT
ejpam-4581	109	30	f−([v	f−([v	NOUN
ejpam-4581	109	31	(	(	PUNCT
ejpam-4581	109	32	λ	λ	PROPN
ejpam-4581	109	33	,	,	PUNCT
ejpam-4581	109	34	sp)](λ	sp)](λ	PROPN
ejpam-4581	109	35	,	,	PUNCT
ejpam-4581	109	36	sp	sp	NOUN
ejpam-4581	109	37	)	)	PUNCT
ejpam-4581	109	38	)	)	PUNCT
ejpam-4581	109	39	is	be	AUX
ejpam-4581	109	40	(	(	PUNCT
ejpam-4581	109	41	λ	λ	X
ejpam-4581	109	42	,	,	PUNCT
ejpam-4581	109	43	sp)-closed	sp)-close	VERB
ejpam-4581	109	44	in	in	ADP
ejpam-4581	109	45	x	x	PUNCT
ejpam-4581	109	46	for	for	ADP
ejpam-4581	109	47	every	every	DET
ejpam-4581	109	48	(	(	PUNCT
ejpam-4581	109	49	λ	λ	NOUN
ejpam-4581	109	50	,	,	PUNCT
ejpam-4581	109	51	sp)-open	sp)-open	NOUN
ejpam-4581	109	52	set	set	VERB
ejpam-4581	109	53	v	v	NOUN
ejpam-4581	109	54	of	of	ADP
ejpam-4581	109	55	y	y	PROPN
ejpam-4581	109	56	;	;	PUNCT
ejpam-4581	109	57	(	(	PUNCT
ejpam-4581	109	58	5	5	X
ejpam-4581	109	59	)	)	PUNCT
ejpam-4581	109	60	f+([k(λ	f+([k(λ	NOUN
ejpam-4581	109	61	,	,	PUNCT
ejpam-4581	109	62	sp	sp	NOUN
ejpam-4581	109	63	)	)	PUNCT
ejpam-4581	109	64	]	]	PUNCT
ejpam-4581	110	1	(	(	PUNCT
ejpam-4581	110	2	λ	λ	NOUN
ejpam-4581	110	3	,	,	PUNCT
ejpam-4581	110	4	sp	sp	NOUN
ejpam-4581	110	5	)	)	PUNCT
ejpam-4581	110	6	)	)	PUNCT
ejpam-4581	110	7	is	be	AUX
ejpam-4581	110	8	(	(	PUNCT
ejpam-4581	110	9	λ	λ	INTJ
ejpam-4581	110	10	,	,	PUNCT
ejpam-4581	110	11	sp)-open	sp)-open	ADJ
ejpam-4581	110	12	in	in	ADP
ejpam-4581	110	13	x	x	PUNCT
ejpam-4581	110	14	for	for	SCONJ
ejpam-4581	110	15	every	every	DET
ejpam-4581	110	16	(	(	PUNCT
ejpam-4581	110	17	λ	λ	PROPN
ejpam-4581	110	18	,	,	PUNCT
ejpam-4581	110	19	sp)-closed	sp)-close	VERB
ejpam-4581	110	20	set	set	VERB
ejpam-4581	110	21	k	k	PROPN
ejpam-4581	110	22	of	of	ADP
ejpam-4581	110	23	y	y	PROPN
ejpam-4581	110	24	;	;	PUNCT
ejpam-4581	110	25	(	(	PUNCT
ejpam-4581	110	26	6	6	NUM
ejpam-4581	110	27	)	)	PUNCT
ejpam-4581	110	28	for	for	ADP
ejpam-4581	110	29	each	each	DET
ejpam-4581	110	30	x	x	SYM
ejpam-4581	110	31	∈	∈	PROPN
ejpam-4581	110	32	x	x	X
ejpam-4581	110	33	and	and	CCONJ
ejpam-4581	110	34	for	for	ADP
ejpam-4581	110	35	each	each	DET
ejpam-4581	110	36	s(λ	s(λ	PROPN
ejpam-4581	110	37	,	,	PUNCT
ejpam-4581	110	38	sp)-open	sp)-open	VERB
ejpam-4581	110	39	set	set	VERB
ejpam-4581	110	40	v	v	NUM
ejpam-4581	110	41	of	of	ADP
ejpam-4581	110	42	y	y	PROPN
ejpam-4581	110	43	with	with	ADP
ejpam-4581	110	44	f	f	PROPN
ejpam-4581	110	45	(	(	PUNCT
ejpam-4581	110	46	x	x	NOUN
ejpam-4581	110	47	)	)	PUNCT
ejpam-4581	110	48	⊆	⊆	NUM
ejpam-4581	110	49	v	v	NOUN
ejpam-4581	110	50	,	,	PUNCT
ejpam-4581	110	51	there	there	PRON
ejpam-4581	110	52	exists	exist	VERB
ejpam-4581	110	53	a	a	DET
ejpam-4581	110	54	(	(	PUNCT
ejpam-4581	110	55	λ	λ	NOUN
ejpam-4581	110	56	,	,	PUNCT
ejpam-4581	110	57	sp)-open	sp)-open	NOUN
ejpam-4581	110	58	set	set	VERB
ejpam-4581	110	59	u	u	NOUN
ejpam-4581	110	60	of	of	ADP
ejpam-4581	110	61	x	x	PUNCT
ejpam-4581	110	62	containing	contain	VERB
ejpam-4581	110	63	x	x	PUNCT
ejpam-4581	111	1	such	such	ADJ
ejpam-4581	111	2	that	that	SCONJ
ejpam-4581	111	3	f	f	PROPN
ejpam-4581	111	4	(	(	PUNCT
ejpam-4581	111	5	u	u	NOUN
ejpam-4581	111	6	)	)	PUNCT
ejpam-4581	111	7	⊆	⊆	NUM
ejpam-4581	111	8	v	v	NOUN
ejpam-4581	111	9	(	(	PUNCT
ejpam-4581	111	10	λ	λ	NOUN
ejpam-4581	111	11	,	,	PUNCT
ejpam-4581	111	12	sp	sp	NOUN
ejpam-4581	111	13	)	)	PUNCT
ejpam-4581	111	14	;	;	PUNCT
ejpam-4581	111	15	(	(	PUNCT
ejpam-4581	111	16	7	7	X
ejpam-4581	111	17	)	)	PUNCT
ejpam-4581	111	18	f+(v	f+(v	NOUN
ejpam-4581	111	19	)	)	PUNCT
ejpam-4581	111	20	⊆	⊆	NUM
ejpam-4581	111	21	[	[	X
ejpam-4581	111	22	f+(v	f+(v	NOUN
ejpam-4581	111	23	(	(	PUNCT
ejpam-4581	111	24	λ	λ	PROPN
ejpam-4581	111	25	,	,	PUNCT
ejpam-4581	111	26	sp))](λ	sp))](λ	PROPN
ejpam-4581	111	27	,	,	PUNCT
ejpam-4581	111	28	sp	sp	NOUN
ejpam-4581	111	29	)	)	PUNCT
ejpam-4581	111	30	for	for	ADP
ejpam-4581	111	31	every	every	DET
ejpam-4581	111	32	s(λ	s(λ	PROPN
ejpam-4581	111	33	,	,	PUNCT
ejpam-4581	111	34	sp)-open	sp)-open	VERB
ejpam-4581	111	35	set	set	VERB
ejpam-4581	111	36	v	v	NOUN
ejpam-4581	111	37	of	of	ADP
ejpam-4581	111	38	y	y	PROPN
ejpam-4581	111	39	.	.	PUNCT
ejpam-4581	112	1	proof	proof	NOUN
ejpam-4581	112	2	.	.	PUNCT
ejpam-4581	113	1	(	(	PUNCT
ejpam-4581	113	2	1	1	X
ejpam-4581	113	3	)	)	PUNCT
ejpam-4581	113	4	⇒	⇒	NOUN
ejpam-4581	113	5	(	(	PUNCT
ejpam-4581	113	6	2	2	NUM
ejpam-4581	113	7	):	):	PUNCT
ejpam-4581	113	8	let	let	VERB
ejpam-4581	113	9	k	k	PRON
ejpam-4581	113	10	be	be	AUX
ejpam-4581	113	11	any	any	DET
ejpam-4581	113	12	r(λ	r(λ	NOUN
ejpam-4581	113	13	,	,	PUNCT
ejpam-4581	113	14	sp)-closed	sp)-close	VERB
ejpam-4581	113	15	set	set	NOUN
ejpam-4581	113	16	of	of	ADP
ejpam-4581	113	17	y	y	PROPN
ejpam-4581	113	18	and	and	CCONJ
ejpam-4581	113	19	x	x	PUNCT
ejpam-4581	113	20	∈	∈	PROPN
ejpam-4581	113	21	f+(k	f+(k	PROPN
ejpam-4581	113	22	)	)	PUNCT
ejpam-4581	113	23	.	.	PUNCT
ejpam-4581	114	1	since	since	SCONJ
ejpam-4581	114	2	f	f	PROPN
ejpam-4581	114	3	is	be	AUX
ejpam-4581	114	4	upper	upper	ADJ
ejpam-4581	114	5	almost	almost	ADV
ejpam-4581	114	6	contra	contra	PROPN
ejpam-4581	114	7	(	(	PUNCT
ejpam-4581	114	8	λ	λ	PROPN
ejpam-4581	114	9	,	,	PUNCT
ejpam-4581	114	10	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	114	11	,	,	PUNCT
ejpam-4581	114	12	there	there	PRON
ejpam-4581	114	13	exists	exist	VERB
ejpam-4581	114	14	a	a	DET
ejpam-4581	114	15	(	(	PUNCT
ejpam-4581	114	16	λ	λ	NOUN
ejpam-4581	114	17	,	,	PUNCT
ejpam-4581	114	18	sp)-open	sp)-open	NOUN
ejpam-4581	114	19	set	set	VERB
ejpam-4581	114	20	u	u	NOUN
ejpam-4581	114	21	of	of	ADP
ejpam-4581	114	22	x	x	PUNCT
ejpam-4581	114	23	containing	contain	VERB
ejpam-4581	114	24	x	x	PUNCT
ejpam-4581	114	25	such	such	ADJ
ejpam-4581	114	26	that	that	SCONJ
ejpam-4581	114	27	u	u	PROPN
ejpam-4581	114	28	⊆	⊆	NUM
ejpam-4581	114	29	f+(k	f+(k	NUM
ejpam-4581	114	30	)	)	PUNCT
ejpam-4581	114	31	.	.	PUNCT
ejpam-4581	115	1	thus	thus	ADV
ejpam-4581	115	2	,	,	PUNCT
ejpam-4581	115	3	f+(k	f+(k	X
ejpam-4581	115	4	)	)	PUNCT
ejpam-4581	115	5	is	be	AUX
ejpam-4581	115	6	(	(	PUNCT
ejpam-4581	115	7	λ	λ	INTJ
ejpam-4581	115	8	,	,	PUNCT
ejpam-4581	115	9	sp)-open	sp)-open	ADJ
ejpam-4581	115	10	in	in	ADP
ejpam-4581	115	11	x.	x.	NOUN
ejpam-4581	115	12	(	(	PUNCT
ejpam-4581	115	13	2	2	NUM
ejpam-4581	115	14	)	)	PUNCT
ejpam-4581	115	15	⇒	⇒	NOUN
ejpam-4581	115	16	(	(	PUNCT
ejpam-4581	115	17	1	1	NUM
ejpam-4581	115	18	):	):	PUNCT
ejpam-4581	115	19	the	the	DET
ejpam-4581	115	20	proof	proof	NOUN
ejpam-4581	115	21	is	be	AUX
ejpam-4581	115	22	obvious	obvious	ADJ
ejpam-4581	115	23	.	.	PUNCT
ejpam-4581	116	1	(	(	PUNCT
ejpam-4581	116	2	2	2	X
ejpam-4581	116	3	)	)	PUNCT
ejpam-4581	116	4	⇔	⇔	X
ejpam-4581	116	5	(	(	PUNCT
ejpam-4581	116	6	3	3	NUM
ejpam-4581	116	7	):	):	PUNCT
ejpam-4581	116	8	it	it	PRON
ejpam-4581	116	9	follows	follow	VERB
ejpam-4581	116	10	from	from	ADP
ejpam-4581	116	11	the	the	DET
ejpam-4581	116	12	fact	fact	NOUN
ejpam-4581	116	13	that	that	SCONJ
ejpam-4581	116	14	f+(y	f+(y	PROPN
ejpam-4581	116	15	−k	−k	ADJ
ejpam-4581	116	16	)	)	PUNCT
ejpam-4581	116	17	=	=	PUNCT
ejpam-4581	117	1	x	x	X
ejpam-4581	117	2	−	−	DET
ejpam-4581	117	3	f−(k	f−(k	PROPN
ejpam-4581	117	4	)	)	PUNCT
ejpam-4581	117	5	for	for	ADP
ejpam-4581	117	6	every	every	DET
ejpam-4581	117	7	subset	subset	NOUN
ejpam-4581	117	8	k	k	PROPN
ejpam-4581	117	9	of	of	ADP
ejpam-4581	117	10	y	y	PROPN
ejpam-4581	117	11	.	.	PUNCT
ejpam-4581	118	1	(	(	PUNCT
ejpam-4581	118	2	3	3	X
ejpam-4581	118	3	)	)	PUNCT
ejpam-4581	118	4	⇔	⇔	X
ejpam-4581	118	5	(	(	PUNCT
ejpam-4581	118	6	4	4	NUM
ejpam-4581	118	7	):	):	PUNCT
ejpam-4581	118	8	let	let	VERB
ejpam-4581	118	9	v	v	PART
ejpam-4581	118	10	be	be	AUX
ejpam-4581	118	11	any	any	DET
ejpam-4581	118	12	(	(	PUNCT
ejpam-4581	118	13	λ	λ	NOUN
ejpam-4581	118	14	,	,	PUNCT
ejpam-4581	118	15	sp)-open	sp)-open	ADJ
ejpam-4581	118	16	set	set	NOUN
ejpam-4581	118	17	of	of	ADP
ejpam-4581	118	18	y	y	PROPN
ejpam-4581	118	19	.	.	PUNCT
ejpam-4581	119	1	then	then	ADV
ejpam-4581	119	2	[	[	X
ejpam-4581	119	3	v	v	X
ejpam-4581	119	4	(	(	PUNCT
ejpam-4581	119	5	λ	λ	PROPN
ejpam-4581	119	6	,	,	PUNCT
ejpam-4581	119	7	sp)](λ	sp)](λ	PROPN
ejpam-4581	119	8	,	,	PUNCT
ejpam-4581	119	9	sp	sp	NOUN
ejpam-4581	119	10	)	)	PUNCT
ejpam-4581	119	11	is	be	AUX
ejpam-4581	119	12	r(λ	r(λ	NOUN
ejpam-4581	119	13	,	,	PUNCT
ejpam-4581	119	14	sp)-open	sp)-open	ADJ
ejpam-4581	119	15	in	in	ADP
ejpam-4581	119	16	y	y	PROPN
ejpam-4581	119	17	and	and	CCONJ
ejpam-4581	119	18	by	by	ADP
ejpam-4581	119	19	(	(	PUNCT
ejpam-4581	119	20	3	3	NUM
ejpam-4581	119	21	)	)	PUNCT
ejpam-4581	119	22	,	,	PUNCT
ejpam-4581	119	23	f−([v	f−([v	PROPN
ejpam-4581	119	24	(	(	PUNCT
ejpam-4581	119	25	λ	λ	PROPN
ejpam-4581	119	26	,	,	PUNCT
ejpam-4581	119	27	sp)](λ	sp)](λ	PROPN
ejpam-4581	119	28	,	,	PUNCT
ejpam-4581	119	29	sp	sp	NOUN
ejpam-4581	119	30	)	)	PUNCT
ejpam-4581	119	31	)	)	PUNCT
ejpam-4581	120	1	is	be	AUX
ejpam-4581	120	2	(	(	PUNCT
ejpam-4581	120	3	λ	λ	X
ejpam-4581	120	4	,	,	PUNCT
ejpam-4581	120	5	sp)-closed	sp)-close	VERB
ejpam-4581	120	6	in	in	ADP
ejpam-4581	120	7	x.	x.	NOUN
ejpam-4581	120	8	the	the	DET
ejpam-4581	120	9	converse	converse	NOUN
ejpam-4581	120	10	is	be	AUX
ejpam-4581	120	11	obvious	obvious	ADJ
ejpam-4581	120	12	.	.	PUNCT
ejpam-4581	121	1	(	(	PUNCT
ejpam-4581	121	2	4	4	X
ejpam-4581	121	3	)	)	PUNCT
ejpam-4581	121	4	⇔	⇔	X
ejpam-4581	121	5	(	(	PUNCT
ejpam-4581	121	6	5	5	NUM
ejpam-4581	121	7	):	):	PUNCT
ejpam-4581	121	8	it	it	PRON
ejpam-4581	121	9	follows	follow	VERB
ejpam-4581	121	10	from	from	ADP
ejpam-4581	121	11	the	the	DET
ejpam-4581	121	12	fact	fact	NOUN
ejpam-4581	121	13	that	that	SCONJ
ejpam-4581	121	14	f+(y	f+(y	PROPN
ejpam-4581	121	15	−k	−k	ADJ
ejpam-4581	121	16	)	)	PUNCT
ejpam-4581	121	17	=	=	PUNCT
ejpam-4581	122	1	x	x	X
ejpam-4581	122	2	−	−	DET
ejpam-4581	122	3	f−(k	f−(k	PROPN
ejpam-4581	122	4	)	)	PUNCT
ejpam-4581	122	5	for	for	ADP
ejpam-4581	122	6	every	every	DET
ejpam-4581	122	7	subset	subset	NOUN
ejpam-4581	122	8	k	k	PROPN
ejpam-4581	122	9	of	of	ADP
ejpam-4581	122	10	y	y	PROPN
ejpam-4581	122	11	.	.	PUNCT
ejpam-4581	123	1	(	(	PUNCT
ejpam-4581	123	2	5	5	X
ejpam-4581	123	3	)	)	PUNCT
ejpam-4581	123	4	⇔	⇔	X
ejpam-4581	123	5	(	(	PUNCT
ejpam-4581	123	6	2	2	NUM
ejpam-4581	123	7	):	):	PUNCT
ejpam-4581	123	8	it	it	PRON
ejpam-4581	123	9	similar	similar	ADJ
ejpam-4581	123	10	to	to	ADP
ejpam-4581	123	11	that	that	PRON
ejpam-4581	123	12	(	(	PUNCT
ejpam-4581	123	13	3	3	X
ejpam-4581	123	14	)	)	PUNCT
ejpam-4581	123	15	⇔	⇔	X
ejpam-4581	123	16	(	(	PUNCT
ejpam-4581	123	17	4	4	NUM
ejpam-4581	123	18	)	)	PUNCT
ejpam-4581	123	19	.	.	PUNCT
ejpam-4581	124	1	(	(	PUNCT
ejpam-4581	124	2	6	6	X
ejpam-4581	124	3	)	)	PUNCT
ejpam-4581	124	4	⇒	⇒	NOUN
ejpam-4581	124	5	(	(	PUNCT
ejpam-4581	124	6	7	7	NUM
ejpam-4581	124	7	):	):	PUNCT
ejpam-4581	124	8	let	let	VERB
ejpam-4581	124	9	v	v	PART
ejpam-4581	124	10	be	be	AUX
ejpam-4581	124	11	any	any	DET
ejpam-4581	124	12	s(λ	s(λ	NOUN
ejpam-4581	124	13	,	,	PUNCT
ejpam-4581	124	14	sp)-open	sp)-open	ADJ
ejpam-4581	124	15	set	set	NOUN
ejpam-4581	124	16	of	of	ADP
ejpam-4581	124	17	y	y	PROPN
ejpam-4581	124	18	and	and	CCONJ
ejpam-4581	124	19	x	x	PROPN
ejpam-4581	124	20	∈	∈	PROPN
ejpam-4581	124	21	f+(v	f+(v	NOUN
ejpam-4581	124	22	)	)	PUNCT
ejpam-4581	124	23	.	.	PUNCT
ejpam-4581	125	1	then	then	ADV
ejpam-4581	125	2	f	f	X
ejpam-4581	125	3	(	(	PUNCT
ejpam-4581	125	4	x	x	X
ejpam-4581	125	5	)	)	PUNCT
ejpam-4581	125	6	⊆	⊆	NUM
ejpam-4581	125	7	v	v	NOUN
ejpam-4581	125	8	.	.	PUNCT
ejpam-4581	126	1	by	by	ADP
ejpam-4581	126	2	(	(	PUNCT
ejpam-4581	126	3	6	6	NUM
ejpam-4581	126	4	)	)	PUNCT
ejpam-4581	126	5	,	,	PUNCT
ejpam-4581	126	6	there	there	PRON
ejpam-4581	126	7	exists	exist	VERB
ejpam-4581	126	8	a	a	DET
ejpam-4581	126	9	(	(	PUNCT
ejpam-4581	126	10	λ	λ	NOUN
ejpam-4581	126	11	,	,	PUNCT
ejpam-4581	126	12	sp)-open	sp)-open	NOUN
ejpam-4581	126	13	set	set	VERB
ejpam-4581	126	14	u	u	NOUN
ejpam-4581	126	15	of	of	ADP
ejpam-4581	126	16	x	x	PUNCT
ejpam-4581	126	17	containing	contain	VERB
ejpam-4581	126	18	x	x	PUNCT
ejpam-4581	126	19	such	such	ADJ
ejpam-4581	126	20	that	that	SCONJ
ejpam-4581	126	21	f	f	PROPN
ejpam-4581	126	22	(	(	PUNCT
ejpam-4581	126	23	u	u	NOUN
ejpam-4581	126	24	)	)	PUNCT
ejpam-4581	126	25	⊆	⊆	NUM
ejpam-4581	126	26	v	v	NOUN
ejpam-4581	126	27	(	(	PUNCT
ejpam-4581	126	28	λ	λ	NOUN
ejpam-4581	126	29	,	,	PUNCT
ejpam-4581	126	30	sp	sp	NOUN
ejpam-4581	126	31	)	)	PUNCT
ejpam-4581	126	32	.	.	PUNCT
ejpam-4581	127	1	thus	thus	ADV
ejpam-4581	127	2	,	,	PUNCT
ejpam-4581	127	3	x	x	PUNCT
ejpam-4581	127	4	∈	∈	PROPN
ejpam-4581	127	5	u	u	NOUN
ejpam-4581	127	6	⊆	⊆	NUM
ejpam-4581	127	7	f+(v	f+(v	NOUN
ejpam-4581	127	8	(	(	PUNCT
ejpam-4581	127	9	λ	λ	NOUN
ejpam-4581	127	10	,	,	PUNCT
ejpam-4581	127	11	sp	sp	NOUN
ejpam-4581	127	12	)	)	PUNCT
ejpam-4581	127	13	)	)	PUNCT
ejpam-4581	127	14	and	and	CCONJ
ejpam-4581	127	15	hence	hence	ADV
ejpam-4581	127	16	x	x	X
ejpam-4581	127	17	∈	∈	PROPN
ejpam-4581	128	1	[	[	X
ejpam-4581	128	2	f+(v	f+(v	NOUN
ejpam-4581	128	3	(	(	PUNCT
ejpam-4581	128	4	λ	λ	PROPN
ejpam-4581	128	5	,	,	PUNCT
ejpam-4581	128	6	sp))](λ	sp))](λ	PROPN
ejpam-4581	128	7	,	,	PUNCT
ejpam-4581	128	8	sp	sp	NOUN
ejpam-4581	128	9	)	)	PUNCT
ejpam-4581	128	10	.	.	PUNCT
ejpam-4581	129	1	this	this	PRON
ejpam-4581	129	2	shows	show	VERB
ejpam-4581	129	3	that	that	SCONJ
ejpam-4581	129	4	f+(v	f+(v	PROPN
ejpam-4581	129	5	)	)	PUNCT
ejpam-4581	130	1	⊆	⊆	NUM
ejpam-4581	130	2	[	[	X
ejpam-4581	130	3	f+(v	f+(v	NOUN
ejpam-4581	130	4	(	(	PUNCT
ejpam-4581	130	5	λ	λ	PROPN
ejpam-4581	130	6	,	,	PUNCT
ejpam-4581	130	7	sp))](λ	sp))](λ	PROPN
ejpam-4581	130	8	,	,	PUNCT
ejpam-4581	130	9	sp	sp	NOUN
ejpam-4581	130	10	)	)	PUNCT
ejpam-4581	130	11	.	.	PUNCT
ejpam-4581	131	1	(	(	PUNCT
ejpam-4581	131	2	7	7	X
ejpam-4581	131	3	)	)	PUNCT
ejpam-4581	131	4	⇒	⇒	NOUN
ejpam-4581	131	5	(	(	PUNCT
ejpam-4581	131	6	2	2	NUM
ejpam-4581	131	7	):	):	PUNCT
ejpam-4581	131	8	let	let	VERB
ejpam-4581	131	9	k	k	PRON
ejpam-4581	131	10	be	be	AUX
ejpam-4581	131	11	any	any	DET
ejpam-4581	131	12	r(λ	r(λ	NOUN
ejpam-4581	131	13	,	,	PUNCT
ejpam-4581	131	14	sp)-closed	sp)-close	VERB
ejpam-4581	131	15	set	set	NOUN
ejpam-4581	131	16	of	of	ADP
ejpam-4581	131	17	y	y	PROPN
ejpam-4581	131	18	.	.	PUNCT
ejpam-4581	132	1	then	then	ADV
ejpam-4581	132	2	k	k	PROPN
ejpam-4581	132	3	is	be	AUX
ejpam-4581	132	4	s(λ	s(λ	PROPN
ejpam-4581	132	5	,	,	PUNCT
ejpam-4581	132	6	sp)-open	sp)-open	ADJ
ejpam-4581	132	7	in	in	ADP
ejpam-4581	132	8	y	y	PROPN
ejpam-4581	132	9	.	.	PUNCT
ejpam-4581	133	1	by	by	ADP
ejpam-4581	133	2	(	(	PUNCT
ejpam-4581	133	3	7	7	NUM
ejpam-4581	133	4	)	)	PUNCT
ejpam-4581	133	5	,	,	PUNCT
ejpam-4581	133	6	we	we	PRON
ejpam-4581	133	7	have	have	VERB
ejpam-4581	133	8	f+(k	f+(k	NUM
ejpam-4581	133	9	)	)	PUNCT
ejpam-4581	134	1	⊆	⊆	NUM
ejpam-4581	134	2	[	[	X
ejpam-4581	134	3	f+(k)](λ	f+(k)](λ	NUM
ejpam-4581	134	4	,	,	PUNCT
ejpam-4581	134	5	sp	sp	NOUN
ejpam-4581	134	6	)	)	PUNCT
ejpam-4581	134	7	and	and	CCONJ
ejpam-4581	134	8	hence	hence	ADV
ejpam-4581	134	9	f+(k	f+(k	NUM
ejpam-4581	134	10	)	)	PUNCT
ejpam-4581	134	11	is	be	AUX
ejpam-4581	134	12	(	(	PUNCT
ejpam-4581	134	13	λ	λ	INTJ
ejpam-4581	134	14	,	,	PUNCT
ejpam-4581	134	15	sp)-open	sp)-open	ADJ
ejpam-4581	134	16	in	in	ADP
ejpam-4581	134	17	x.	x.	NOUN
ejpam-4581	134	18	(	(	PUNCT
ejpam-4581	134	19	2	2	NUM
ejpam-4581	134	20	)	)	PUNCT
ejpam-4581	134	21	⇒	⇒	NOUN
ejpam-4581	134	22	(	(	PUNCT
ejpam-4581	134	23	6	6	NUM
ejpam-4581	134	24	):	):	PUNCT
ejpam-4581	134	25	let	let	VERB
ejpam-4581	134	26	x	x	PUNCT
ejpam-4581	134	27	∈	∈	PROPN
ejpam-4581	134	28	x	x	X
ejpam-4581	134	29	and	and	CCONJ
ejpam-4581	134	30	v	v	X
ejpam-4581	134	31	be	be	AUX
ejpam-4581	134	32	any	any	DET
ejpam-4581	134	33	s(λ	s(λ	NOUN
ejpam-4581	134	34	,	,	PUNCT
ejpam-4581	134	35	sp)-open	sp)-open	ADJ
ejpam-4581	134	36	set	set	NOUN
ejpam-4581	134	37	of	of	ADP
ejpam-4581	134	38	y	y	PROPN
ejpam-4581	134	39	with	with	ADP
ejpam-4581	134	40	f	f	PROPN
ejpam-4581	134	41	(	(	PUNCT
ejpam-4581	134	42	x	x	NOUN
ejpam-4581	134	43	)	)	PUNCT
ejpam-4581	134	44	⊆	⊆	NUM
ejpam-4581	134	45	v	v	NOUN
ejpam-4581	134	46	.	.	PUNCT
ejpam-4581	135	1	since	since	SCONJ
ejpam-4581	135	2	v	v	NOUN
ejpam-4581	135	3	(	(	PUNCT
ejpam-4581	135	4	λ	λ	NOUN
ejpam-4581	135	5	,	,	PUNCT
ejpam-4581	135	6	sp	sp	NOUN
ejpam-4581	135	7	)	)	PUNCT
ejpam-4581	135	8	is	be	AUX
ejpam-4581	135	9	r(λ	r(λ	NOUN
ejpam-4581	135	10	,	,	PUNCT
ejpam-4581	135	11	sp)-closed	sp)-close	VERB
ejpam-4581	135	12	and	and	CCONJ
ejpam-4581	135	13	by	by	ADP
ejpam-4581	135	14	(	(	PUNCT
ejpam-4581	135	15	2	2	NUM
ejpam-4581	135	16	)	)	PUNCT
ejpam-4581	135	17	,	,	PUNCT
ejpam-4581	135	18	f+(v	f+(v	PROPN
ejpam-4581	135	19	(	(	PUNCT
ejpam-4581	135	20	λ	λ	NOUN
ejpam-4581	135	21	,	,	PUNCT
ejpam-4581	135	22	sp	sp	NOUN
ejpam-4581	135	23	)	)	PUNCT
ejpam-4581	135	24	)	)	PUNCT
ejpam-4581	136	1	is	be	AUX
ejpam-4581	136	2	(	(	PUNCT
ejpam-4581	136	3	λ	λ	INTJ
ejpam-4581	136	4	,	,	PUNCT
ejpam-4581	136	5	sp)-open	sp)-open	ADJ
ejpam-4581	136	6	in	in	ADP
ejpam-4581	136	7	x.	x.	NOUN
ejpam-4581	136	8	then	then	ADV
ejpam-4581	136	9	,	,	PUNCT
ejpam-4581	136	10	there	there	PRON
ejpam-4581	136	11	exists	exist	VERB
ejpam-4581	136	12	a	a	DET
ejpam-4581	136	13	(	(	PUNCT
ejpam-4581	136	14	λ	λ	NOUN
ejpam-4581	136	15	,	,	PUNCT
ejpam-4581	136	16	sp)-open	sp)-open	NOUN
ejpam-4581	136	17	set	set	VERB
ejpam-4581	136	18	u	u	NOUN
ejpam-4581	136	19	of	of	ADP
ejpam-4581	136	20	x	x	PUNCT
ejpam-4581	136	21	containing	contain	VERB
ejpam-4581	136	22	x	x	PUNCT
ejpam-4581	136	23	such	such	ADJ
ejpam-4581	136	24	that	that	SCONJ
ejpam-4581	136	25	u	u	NOUN
ejpam-4581	136	26	⊆	⊆	NUM
ejpam-4581	136	27	f+(v	f+(v	NOUN
ejpam-4581	136	28	(	(	PUNCT
ejpam-4581	136	29	λ	λ	NOUN
ejpam-4581	136	30	,	,	PUNCT
ejpam-4581	136	31	sp	sp	NOUN
ejpam-4581	136	32	)	)	PUNCT
ejpam-4581	136	33	)	)	PUNCT
ejpam-4581	136	34	.	.	PUNCT
ejpam-4581	137	1	thus	thus	ADV
ejpam-4581	137	2	,	,	PUNCT
ejpam-4581	137	3	f	f	PROPN
ejpam-4581	137	4	(	(	PUNCT
ejpam-4581	137	5	u	u	NOUN
ejpam-4581	137	6	)	)	PUNCT
ejpam-4581	137	7	⊆	⊆	NUM
ejpam-4581	137	8	v	v	NOUN
ejpam-4581	137	9	(	(	PUNCT
ejpam-4581	137	10	λ	λ	NOUN
ejpam-4581	137	11	,	,	PUNCT
ejpam-4581	137	12	sp	sp	NOUN
ejpam-4581	137	13	)	)	PUNCT
ejpam-4581	137	14	.	.	PUNCT
ejpam-4581	137	15	theorem	theorem	NOUN
ejpam-4581	137	16	2	2	NUM
ejpam-4581	137	17	.	.	X
ejpam-4581	137	18	for	for	ADP
ejpam-4581	137	19	a	a	DET
ejpam-4581	137	20	multifunction	multifunction	NOUN
ejpam-4581	137	21	f	f	NOUN
ejpam-4581	137	22	:	:	PUNCT
ejpam-4581	137	23	(	(	PUNCT
ejpam-4581	137	24	x	x	X
ejpam-4581	137	25	,	,	PUNCT
ejpam-4581	137	26	τ	τ	X
ejpam-4581	137	27	)	)	PUNCT
ejpam-4581	137	28	→	→	SYM
ejpam-4581	137	29	(	(	PUNCT
ejpam-4581	137	30	y	y	PROPN
ejpam-4581	137	31	,	,	PUNCT
ejpam-4581	137	32	σ	σ	PROPN
ejpam-4581	137	33	)	)	PUNCT
ejpam-4581	137	34	,	,	PUNCT
ejpam-4581	137	35	the	the	DET
ejpam-4581	137	36	following	follow	VERB
ejpam-4581	137	37	properties	property	NOUN
ejpam-4581	137	38	are	be	AUX
ejpam-4581	137	39	equivalent	equivalent	ADJ
ejpam-4581	137	40	:	:	PUNCT
ejpam-4581	137	41	(	(	PUNCT
ejpam-4581	137	42	1	1	X
ejpam-4581	137	43	)	)	PUNCT
ejpam-4581	137	44	f	f	PROPN
ejpam-4581	137	45	is	be	AUX
ejpam-4581	137	46	lower	low	ADJ
ejpam-4581	137	47	almost	almost	ADV
ejpam-4581	137	48	contra-(λ	contra-(λ	PROPN
ejpam-4581	137	49	,	,	PUNCT
ejpam-4581	137	50	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	137	51	;	;	PUNCT
ejpam-4581	137	52	(	(	PUNCT
ejpam-4581	137	53	2	2	X
ejpam-4581	137	54	)	)	PUNCT
ejpam-4581	137	55	f−(k	f−(k	PROPN
ejpam-4581	137	56	)	)	PUNCT
ejpam-4581	137	57	is	be	AUX
ejpam-4581	137	58	(	(	PUNCT
ejpam-4581	137	59	λ	λ	INTJ
ejpam-4581	137	60	,	,	PUNCT
ejpam-4581	137	61	sp)-open	sp)-open	ADJ
ejpam-4581	137	62	in	in	ADP
ejpam-4581	137	63	x	x	PUNCT
ejpam-4581	137	64	for	for	ADP
ejpam-4581	137	65	every	every	DET
ejpam-4581	137	66	r(λ	r(λ	NOUN
ejpam-4581	137	67	,	,	PUNCT
ejpam-4581	137	68	sp)-closed	sp)-close	VERB
ejpam-4581	137	69	set	set	VERB
ejpam-4581	137	70	k	k	PROPN
ejpam-4581	137	71	of	of	ADP
ejpam-4581	137	72	y	y	PROPN
ejpam-4581	137	73	;	;	PUNCT
ejpam-4581	137	74	(	(	PUNCT
ejpam-4581	137	75	3	3	X
ejpam-4581	137	76	)	)	PUNCT
ejpam-4581	137	77	f+(v	f+(v	NOUN
ejpam-4581	137	78	)	)	PUNCT
ejpam-4581	138	1	is	be	AUX
ejpam-4581	138	2	(	(	PUNCT
ejpam-4581	138	3	λ	λ	X
ejpam-4581	138	4	,	,	PUNCT
ejpam-4581	138	5	sp)-closed	sp)-close	VERB
ejpam-4581	138	6	in	in	ADP
ejpam-4581	138	7	x	x	PUNCT
ejpam-4581	138	8	for	for	ADP
ejpam-4581	138	9	every	every	DET
ejpam-4581	138	10	r(λ	r(λ	NOUN
ejpam-4581	138	11	,	,	PUNCT
ejpam-4581	138	12	sp)-open	sp)-open	ADJ
ejpam-4581	138	13	set	set	VERB
ejpam-4581	138	14	v	v	NOUN
ejpam-4581	138	15	of	of	ADP
ejpam-4581	138	16	y	y	PROPN
ejpam-4581	138	17	;	;	PUNCT
ejpam-4581	138	18	c.	c.	PROPN
ejpam-4581	138	19	boonpok	boonpok	PROPN
ejpam-4581	138	20	,	,	PUNCT
ejpam-4581	138	21	j.	j.	PROPN
ejpam-4581	138	22	khampakdee	khampakdee	PROPN
ejpam-4581	138	23	/	/	PUNCT
ejpam-4581	138	24	eur	eur	PROPN
ejpam-4581	138	25	.	.	PUNCT
ejpam-4581	139	1	j.	j.	PROPN
ejpam-4581	139	2	pure	pure	PROPN
ejpam-4581	139	3	appl	appl	PROPN
ejpam-4581	139	4	.	.	PROPN
ejpam-4581	139	5	math	math	PROPN
ejpam-4581	139	6	,	,	PUNCT
ejpam-4581	139	7	16	16	NUM
ejpam-4581	139	8	(	(	PUNCT
ejpam-4581	139	9	1	1	NUM
ejpam-4581	139	10	)	)	PUNCT
ejpam-4581	139	11	(	(	PUNCT
ejpam-4581	139	12	2023	2023	NUM
ejpam-4581	139	13	)	)	PUNCT
ejpam-4581	139	14	,	,	PUNCT
ejpam-4581	139	15	156	156	NUM
ejpam-4581	139	16	-	-	SYM
ejpam-4581	139	17	168	168	NUM
ejpam-4581	139	18	160	160	NUM
ejpam-4581	139	19	(	(	PUNCT
ejpam-4581	139	20	4	4	NUM
ejpam-4581	139	21	)	)	PUNCT
ejpam-4581	139	22	f+([v	f+([v	NOUN
ejpam-4581	139	23	(	(	PUNCT
ejpam-4581	139	24	λ	λ	PROPN
ejpam-4581	139	25	,	,	PUNCT
ejpam-4581	139	26	sp)](λ	sp)](λ	PROPN
ejpam-4581	139	27	,	,	PUNCT
ejpam-4581	139	28	sp	sp	NOUN
ejpam-4581	139	29	)	)	PUNCT
ejpam-4581	139	30	)	)	PUNCT
ejpam-4581	139	31	is	be	AUX
ejpam-4581	139	32	(	(	PUNCT
ejpam-4581	139	33	λ	λ	X
ejpam-4581	139	34	,	,	PUNCT
ejpam-4581	139	35	sp)-closed	sp)-close	VERB
ejpam-4581	139	36	in	in	ADP
ejpam-4581	139	37	x	x	PUNCT
ejpam-4581	139	38	for	for	ADP
ejpam-4581	139	39	every	every	DET
ejpam-4581	139	40	(	(	PUNCT
ejpam-4581	139	41	λ	λ	NOUN
ejpam-4581	139	42	,	,	PUNCT
ejpam-4581	139	43	sp)-open	sp)-open	NOUN
ejpam-4581	139	44	set	set	VERB
ejpam-4581	139	45	v	v	NOUN
ejpam-4581	139	46	of	of	ADP
ejpam-4581	139	47	y	y	PROPN
ejpam-4581	139	48	;	;	PUNCT
ejpam-4581	139	49	(	(	PUNCT
ejpam-4581	139	50	5	5	X
ejpam-4581	139	51	)	)	PUNCT
ejpam-4581	139	52	f−([k(λ	f−([k(λ	NOUN
ejpam-4581	139	53	,	,	PUNCT
ejpam-4581	139	54	sp	sp	NOUN
ejpam-4581	139	55	)	)	PUNCT
ejpam-4581	139	56	]	]	PUNCT
ejpam-4581	139	57	(	(	PUNCT
ejpam-4581	139	58	λ	λ	NOUN
ejpam-4581	139	59	,	,	PUNCT
ejpam-4581	139	60	sp	sp	NOUN
ejpam-4581	139	61	)	)	PUNCT
ejpam-4581	139	62	)	)	PUNCT
ejpam-4581	140	1	is	be	AUX
ejpam-4581	140	2	(	(	PUNCT
ejpam-4581	140	3	λ	λ	INTJ
ejpam-4581	140	4	,	,	PUNCT
ejpam-4581	140	5	sp)-open	sp)-open	ADJ
ejpam-4581	140	6	in	in	ADP
ejpam-4581	140	7	x	x	PUNCT
ejpam-4581	140	8	for	for	SCONJ
ejpam-4581	140	9	every	every	DET
ejpam-4581	140	10	(	(	PUNCT
ejpam-4581	140	11	λ	λ	PROPN
ejpam-4581	140	12	,	,	PUNCT
ejpam-4581	140	13	sp)-closed	sp)-close	VERB
ejpam-4581	140	14	set	set	VERB
ejpam-4581	140	15	k	k	PROPN
ejpam-4581	140	16	of	of	ADP
ejpam-4581	140	17	y	y	PROPN
ejpam-4581	140	18	;	;	PUNCT
ejpam-4581	140	19	(	(	PUNCT
ejpam-4581	140	20	6	6	NUM
ejpam-4581	140	21	)	)	PUNCT
ejpam-4581	140	22	for	for	ADP
ejpam-4581	140	23	each	each	DET
ejpam-4581	140	24	x	x	SYM
ejpam-4581	140	25	∈	∈	PROPN
ejpam-4581	140	26	x	x	X
ejpam-4581	140	27	and	and	CCONJ
ejpam-4581	140	28	for	for	ADP
ejpam-4581	140	29	each	each	DET
ejpam-4581	140	30	s(λ	s(λ	PROPN
ejpam-4581	140	31	,	,	PUNCT
ejpam-4581	140	32	sp)-open	sp)-open	VERB
ejpam-4581	140	33	set	set	VERB
ejpam-4581	140	34	v	v	NUM
ejpam-4581	140	35	of	of	ADP
ejpam-4581	140	36	y	y	PROPN
ejpam-4581	140	37	with	with	ADP
ejpam-4581	140	38	f	f	PROPN
ejpam-4581	140	39	(	(	PUNCT
ejpam-4581	140	40	x)∩v	x)∩v	PROPN
ejpam-4581	140	41	̸=	̸=	PROPN
ejpam-4581	140	42	∅	∅	NOUN
ejpam-4581	140	43	,	,	PUNCT
ejpam-4581	140	44	there	there	PRON
ejpam-4581	140	45	exists	exist	VERB
ejpam-4581	140	46	a	a	DET
ejpam-4581	140	47	(	(	PUNCT
ejpam-4581	140	48	λ	λ	NOUN
ejpam-4581	140	49	,	,	PUNCT
ejpam-4581	140	50	sp)-open	sp)-open	NOUN
ejpam-4581	140	51	set	set	VERB
ejpam-4581	140	52	u	u	NOUN
ejpam-4581	140	53	of	of	ADP
ejpam-4581	140	54	x	x	PUNCT
ejpam-4581	140	55	containing	contain	VERB
ejpam-4581	140	56	x	x	PUNCT
ejpam-4581	141	1	such	such	ADJ
ejpam-4581	141	2	that	that	SCONJ
ejpam-4581	141	3	f	f	PROPN
ejpam-4581	141	4	(	(	PUNCT
ejpam-4581	141	5	z)∩	z)∩	PROPN
ejpam-4581	141	6	v	v	NOUN
ejpam-4581	141	7	(	(	PUNCT
ejpam-4581	141	8	λ	λ	PROPN
ejpam-4581	141	9	,	,	PUNCT
ejpam-4581	141	10	sp	sp	NOUN
ejpam-4581	141	11	)	)	PUNCT
ejpam-4581	141	12	̸=	̸=	NOUN
ejpam-4581	141	13	∅	∅	NOUN
ejpam-4581	141	14	for	for	ADP
ejpam-4581	141	15	each	each	DET
ejpam-4581	141	16	z	z	NOUN
ejpam-4581	141	17	∈	∈	PROPN
ejpam-4581	141	18	u	u	NOUN
ejpam-4581	141	19	;	;	PUNCT
ejpam-4581	141	20	(	(	PUNCT
ejpam-4581	141	21	7	7	X
ejpam-4581	141	22	)	)	PUNCT
ejpam-4581	141	23	f−(v	f−(v	NOUN
ejpam-4581	141	24	)	)	PUNCT
ejpam-4581	141	25	⊆	⊆	NUM
ejpam-4581	141	26	[	[	X
ejpam-4581	141	27	f−(v	f−(v	ADJ
ejpam-4581	141	28	(	(	PUNCT
ejpam-4581	141	29	λ	λ	PROPN
ejpam-4581	141	30	,	,	PUNCT
ejpam-4581	141	31	sp))](λ	sp))](λ	PROPN
ejpam-4581	141	32	,	,	PUNCT
ejpam-4581	141	33	sp	sp	NOUN
ejpam-4581	141	34	)	)	PUNCT
ejpam-4581	141	35	for	for	ADP
ejpam-4581	141	36	every	every	DET
ejpam-4581	141	37	s(λ	s(λ	PROPN
ejpam-4581	141	38	,	,	PUNCT
ejpam-4581	141	39	sp)-open	sp)-open	VERB
ejpam-4581	141	40	set	set	VERB
ejpam-4581	141	41	v	v	NOUN
ejpam-4581	141	42	of	of	ADP
ejpam-4581	141	43	y	y	PROPN
ejpam-4581	141	44	.	.	PUNCT
ejpam-4581	142	1	proof	proof	NOUN
ejpam-4581	142	2	.	.	PUNCT
ejpam-4581	143	1	the	the	DET
ejpam-4581	143	2	proof	proof	NOUN
ejpam-4581	143	3	is	be	AUX
ejpam-4581	143	4	similar	similar	ADJ
ejpam-4581	143	5	to	to	ADP
ejpam-4581	143	6	that	that	PRON
ejpam-4581	143	7	of	of	ADP
ejpam-4581	143	8	theorem	theorem	NOUN
ejpam-4581	143	9	1	1	NUM
ejpam-4581	143	10	.	.	PUNCT
ejpam-4581	143	11	definition	definition	NOUN
ejpam-4581	143	12	2	2	NUM
ejpam-4581	143	13	.	.	PUNCT
ejpam-4581	144	1	a	a	DET
ejpam-4581	144	2	function	function	NOUN
ejpam-4581	144	3	f	f	NOUN
ejpam-4581	144	4	:	:	PUNCT
ejpam-4581	144	5	(	(	PUNCT
ejpam-4581	144	6	x	x	X
ejpam-4581	144	7	,	,	PUNCT
ejpam-4581	144	8	τ	τ	X
ejpam-4581	144	9	)	)	PUNCT
ejpam-4581	144	10	→	→	SYM
ejpam-4581	144	11	(	(	PUNCT
ejpam-4581	144	12	y	y	PROPN
ejpam-4581	144	13	,	,	PUNCT
ejpam-4581	144	14	σ	σ	PROPN
ejpam-4581	144	15	)	)	PUNCT
ejpam-4581	144	16	is	be	AUX
ejpam-4581	144	17	called	call	VERB
ejpam-4581	144	18	almost	almost	ADV
ejpam-4581	144	19	contra-(λ	contra-(λ	PROPN
ejpam-4581	144	20	,	,	PUNCT
ejpam-4581	144	21	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	144	22	if	if	SCONJ
ejpam-4581	144	23	,	,	PUNCT
ejpam-4581	144	24	for	for	ADP
ejpam-4581	144	25	each	each	DET
ejpam-4581	144	26	x	x	SYM
ejpam-4581	144	27	∈	∈	PROPN
ejpam-4581	144	28	x	x	X
ejpam-4581	144	29	and	and	CCONJ
ejpam-4581	144	30	each	each	DET
ejpam-4581	144	31	r(λ	r(λ	NOUN
ejpam-4581	144	32	,	,	PUNCT
ejpam-4581	144	33	sp)-closed	sp)-close	VERB
ejpam-4581	144	34	set	set	VERB
ejpam-4581	144	35	k	k	PROPN
ejpam-4581	144	36	of	of	ADP
ejpam-4581	144	37	y	y	PROPN
ejpam-4581	144	38	containing	contain	VERB
ejpam-4581	144	39	f(x	f(x	PROPN
ejpam-4581	144	40	)	)	PUNCT
ejpam-4581	144	41	,	,	PUNCT
ejpam-4581	144	42	there	there	PRON
ejpam-4581	144	43	exists	exist	VERB
ejpam-4581	144	44	a	a	DET
ejpam-4581	144	45	(	(	PUNCT
ejpam-4581	144	46	λ	λ	NOUN
ejpam-4581	144	47	,	,	PUNCT
ejpam-4581	144	48	sp)-open	sp)-open	NOUN
ejpam-4581	144	49	set	set	VERB
ejpam-4581	144	50	u	u	NOUN
ejpam-4581	144	51	of	of	ADP
ejpam-4581	144	52	x	x	PUNCT
ejpam-4581	144	53	containing	contain	VERB
ejpam-4581	144	54	x	x	PUNCT
ejpam-4581	144	55	such	such	ADJ
ejpam-4581	144	56	that	that	DET
ejpam-4581	144	57	f(u	f(u	PROPN
ejpam-4581	144	58	)	)	PUNCT
ejpam-4581	144	59	⊆	⊆	PROPN
ejpam-4581	144	60	k.	k.	PROPN
ejpam-4581	144	61	corollary	corollary	NOUN
ejpam-4581	144	62	1	1	NUM
ejpam-4581	144	63	.	.	PUNCT
ejpam-4581	145	1	for	for	ADP
ejpam-4581	145	2	a	a	DET
ejpam-4581	145	3	function	function	NOUN
ejpam-4581	145	4	f	f	NOUN
ejpam-4581	145	5	:	:	PUNCT
ejpam-4581	145	6	(	(	PUNCT
ejpam-4581	145	7	x	x	X
ejpam-4581	145	8	,	,	PUNCT
ejpam-4581	145	9	τ	τ	X
ejpam-4581	145	10	)	)	PUNCT
ejpam-4581	145	11	→	→	SYM
ejpam-4581	145	12	(	(	PUNCT
ejpam-4581	145	13	y	y	PROPN
ejpam-4581	145	14	,	,	PUNCT
ejpam-4581	145	15	σ	σ	PROPN
ejpam-4581	145	16	)	)	PUNCT
ejpam-4581	145	17	,	,	PUNCT
ejpam-4581	145	18	the	the	DET
ejpam-4581	145	19	following	follow	VERB
ejpam-4581	145	20	properties	property	NOUN
ejpam-4581	145	21	are	be	AUX
ejpam-4581	145	22	equivalent	equivalent	ADJ
ejpam-4581	145	23	:	:	PUNCT
ejpam-4581	145	24	(	(	PUNCT
ejpam-4581	145	25	1	1	X
ejpam-4581	145	26	)	)	PUNCT
ejpam-4581	145	27	f	f	PROPN
ejpam-4581	145	28	is	be	AUX
ejpam-4581	145	29	almost	almost	ADV
ejpam-4581	145	30	contra-(λ	contra-(λ	PROPN
ejpam-4581	145	31	,	,	PUNCT
ejpam-4581	145	32	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	145	33	;	;	PUNCT
ejpam-4581	145	34	(	(	PUNCT
ejpam-4581	145	35	2	2	X
ejpam-4581	145	36	)	)	PUNCT
ejpam-4581	145	37	f−1(k	f−1(k	PROPN
ejpam-4581	145	38	)	)	PUNCT
ejpam-4581	145	39	is	be	AUX
ejpam-4581	145	40	(	(	PUNCT
ejpam-4581	145	41	λ	λ	INTJ
ejpam-4581	145	42	,	,	PUNCT
ejpam-4581	145	43	sp)-open	sp)-open	ADJ
ejpam-4581	145	44	in	in	ADP
ejpam-4581	145	45	x	x	PUNCT
ejpam-4581	145	46	for	for	ADP
ejpam-4581	145	47	every	every	DET
ejpam-4581	145	48	r(λ	r(λ	NOUN
ejpam-4581	145	49	,	,	PUNCT
ejpam-4581	145	50	sp)-closed	sp)-close	VERB
ejpam-4581	146	1	set	set	VERB
ejpam-4581	146	2	k	k	PROPN
ejpam-4581	146	3	of	of	ADP
ejpam-4581	146	4	y	y	PROPN
ejpam-4581	146	5	;	;	PUNCT
ejpam-4581	146	6	(	(	PUNCT
ejpam-4581	146	7	3	3	X
ejpam-4581	146	8	)	)	PUNCT
ejpam-4581	146	9	f−1(v	f−1(v	NOUN
ejpam-4581	146	10	)	)	PUNCT
ejpam-4581	147	1	is	be	AUX
ejpam-4581	147	2	(	(	PUNCT
ejpam-4581	147	3	λ	λ	X
ejpam-4581	147	4	,	,	PUNCT
ejpam-4581	147	5	sp)-closed	sp)-close	VERB
ejpam-4581	147	6	in	in	ADP
ejpam-4581	147	7	x	x	PUNCT
ejpam-4581	147	8	for	for	ADP
ejpam-4581	147	9	every	every	DET
ejpam-4581	147	10	r(λ	r(λ	NOUN
ejpam-4581	147	11	,	,	PUNCT
ejpam-4581	147	12	sp)-open	sp)-open	ADJ
ejpam-4581	147	13	set	set	VERB
ejpam-4581	147	14	v	v	NOUN
ejpam-4581	147	15	of	of	ADP
ejpam-4581	147	16	y	y	PROPN
ejpam-4581	147	17	;	;	PUNCT
ejpam-4581	147	18	(	(	PUNCT
ejpam-4581	147	19	4	4	X
ejpam-4581	147	20	)	)	PUNCT
ejpam-4581	147	21	f−1([v	f−1([v	NOUN
ejpam-4581	147	22	(	(	PUNCT
ejpam-4581	147	23	λ	λ	PROPN
ejpam-4581	147	24	,	,	PUNCT
ejpam-4581	147	25	sp)](λ	sp)](λ	PROPN
ejpam-4581	147	26	,	,	PUNCT
ejpam-4581	147	27	sp	sp	NOUN
ejpam-4581	147	28	)	)	PUNCT
ejpam-4581	147	29	)	)	PUNCT
ejpam-4581	148	1	is	be	AUX
ejpam-4581	148	2	(	(	PUNCT
ejpam-4581	148	3	λ	λ	X
ejpam-4581	148	4	,	,	PUNCT
ejpam-4581	148	5	sp)-closed	sp)-close	VERB
ejpam-4581	148	6	in	in	ADP
ejpam-4581	148	7	x	x	PUNCT
ejpam-4581	148	8	for	for	ADP
ejpam-4581	148	9	every	every	DET
ejpam-4581	148	10	(	(	PUNCT
ejpam-4581	148	11	λ	λ	NOUN
ejpam-4581	148	12	,	,	PUNCT
ejpam-4581	148	13	sp)-open	sp)-open	NOUN
ejpam-4581	148	14	set	set	VERB
ejpam-4581	148	15	v	v	NOUN
ejpam-4581	148	16	of	of	ADP
ejpam-4581	148	17	y	y	PROPN
ejpam-4581	148	18	;	;	PUNCT
ejpam-4581	148	19	(	(	PUNCT
ejpam-4581	148	20	5	5	X
ejpam-4581	148	21	)	)	PUNCT
ejpam-4581	148	22	f−1([k(λ	f−1([k(λ	NOUN
ejpam-4581	148	23	,	,	PUNCT
ejpam-4581	148	24	sp	sp	NOUN
ejpam-4581	148	25	)	)	PUNCT
ejpam-4581	148	26	]	]	PUNCT
ejpam-4581	148	27	(	(	PUNCT
ejpam-4581	148	28	λ	λ	NOUN
ejpam-4581	148	29	,	,	PUNCT
ejpam-4581	148	30	sp	sp	NOUN
ejpam-4581	148	31	)	)	PUNCT
ejpam-4581	148	32	)	)	PUNCT
ejpam-4581	149	1	is	be	AUX
ejpam-4581	149	2	(	(	PUNCT
ejpam-4581	149	3	λ	λ	INTJ
ejpam-4581	149	4	,	,	PUNCT
ejpam-4581	149	5	sp)-open	sp)-open	ADJ
ejpam-4581	149	6	in	in	ADP
ejpam-4581	149	7	x	x	PUNCT
ejpam-4581	149	8	for	for	SCONJ
ejpam-4581	149	9	every	every	DET
ejpam-4581	149	10	(	(	PUNCT
ejpam-4581	149	11	λ	λ	PROPN
ejpam-4581	149	12	,	,	PUNCT
ejpam-4581	149	13	sp)-closed	sp)-close	VERB
ejpam-4581	149	14	set	set	VERB
ejpam-4581	149	15	k	k	PROPN
ejpam-4581	149	16	of	of	ADP
ejpam-4581	149	17	y	y	PROPN
ejpam-4581	149	18	;	;	PUNCT
ejpam-4581	149	19	(	(	PUNCT
ejpam-4581	149	20	6	6	NUM
ejpam-4581	149	21	)	)	PUNCT
ejpam-4581	149	22	for	for	ADP
ejpam-4581	149	23	each	each	DET
ejpam-4581	149	24	x	x	SYM
ejpam-4581	149	25	∈	∈	PROPN
ejpam-4581	149	26	x	x	X
ejpam-4581	149	27	and	and	CCONJ
ejpam-4581	149	28	for	for	ADP
ejpam-4581	149	29	each	each	DET
ejpam-4581	149	30	s(λ	s(λ	PROPN
ejpam-4581	149	31	,	,	PUNCT
ejpam-4581	149	32	sp)-open	sp)-open	VERB
ejpam-4581	149	33	set	set	VERB
ejpam-4581	149	34	v	v	NUM
ejpam-4581	149	35	of	of	ADP
ejpam-4581	149	36	y	y	NOUN
ejpam-4581	149	37	containing	contain	VERB
ejpam-4581	149	38	f(x	f(x	PROPN
ejpam-4581	149	39	)	)	PUNCT
ejpam-4581	149	40	,	,	PUNCT
ejpam-4581	149	41	there	there	PRON
ejpam-4581	149	42	exists	exist	VERB
ejpam-4581	149	43	a	a	DET
ejpam-4581	149	44	(	(	PUNCT
ejpam-4581	149	45	λ	λ	NOUN
ejpam-4581	149	46	,	,	PUNCT
ejpam-4581	149	47	sp)-open	sp)-open	NOUN
ejpam-4581	149	48	set	set	VERB
ejpam-4581	149	49	u	u	NOUN
ejpam-4581	149	50	of	of	ADP
ejpam-4581	149	51	x	x	PUNCT
ejpam-4581	149	52	containing	contain	VERB
ejpam-4581	149	53	x	x	PUNCT
ejpam-4581	149	54	such	such	ADJ
ejpam-4581	149	55	that	that	DET
ejpam-4581	149	56	f(u	f(u	PROPN
ejpam-4581	149	57	)	)	PUNCT
ejpam-4581	149	58	⊆	⊆	NUM
ejpam-4581	149	59	v	v	NOUN
ejpam-4581	149	60	(	(	PUNCT
ejpam-4581	149	61	λ	λ	NOUN
ejpam-4581	149	62	,	,	PUNCT
ejpam-4581	149	63	sp	sp	NOUN
ejpam-4581	149	64	)	)	PUNCT
ejpam-4581	149	65	;	;	PUNCT
ejpam-4581	149	66	(	(	PUNCT
ejpam-4581	149	67	7	7	X
ejpam-4581	149	68	)	)	PUNCT
ejpam-4581	149	69	f−1(v	f−1(v	NOUN
ejpam-4581	149	70	)	)	PUNCT
ejpam-4581	149	71	⊆	⊆	NUM
ejpam-4581	150	1	[	[	X
ejpam-4581	150	2	f−1(v	f−1(v	NOUN
ejpam-4581	150	3	(	(	PUNCT
ejpam-4581	150	4	λ	λ	PROPN
ejpam-4581	150	5	,	,	PUNCT
ejpam-4581	150	6	sp))](λ	sp))](λ	PROPN
ejpam-4581	150	7	,	,	PUNCT
ejpam-4581	150	8	sp	sp	NOUN
ejpam-4581	150	9	)	)	PUNCT
ejpam-4581	150	10	for	for	ADP
ejpam-4581	150	11	every	every	DET
ejpam-4581	150	12	s(λ	s(λ	PROPN
ejpam-4581	150	13	,	,	PUNCT
ejpam-4581	150	14	sp)-open	sp)-open	VERB
ejpam-4581	150	15	set	set	VERB
ejpam-4581	150	16	v	v	NOUN
ejpam-4581	150	17	of	of	ADP
ejpam-4581	150	18	y	y	PROPN
ejpam-4581	150	19	.	.	PUNCT
ejpam-4581	151	1	lemma	lemma	PROPN
ejpam-4581	151	2	3	3	X
ejpam-4581	151	3	.	.	PUNCT
ejpam-4581	152	1	[	[	X
ejpam-4581	152	2	4	4	X
ejpam-4581	152	3	]	]	PUNCT
ejpam-4581	152	4	let	let	VERB
ejpam-4581	152	5	v	v	PART
ejpam-4581	152	6	be	be	AUX
ejpam-4581	152	7	a	a	DET
ejpam-4581	152	8	subset	subset	NOUN
ejpam-4581	152	9	of	of	ADP
ejpam-4581	152	10	a	a	DET
ejpam-4581	152	11	topological	topological	ADJ
ejpam-4581	152	12	space	space	NOUN
ejpam-4581	152	13	(	(	PUNCT
ejpam-4581	152	14	x	x	X
ejpam-4581	152	15	,	,	PUNCT
ejpam-4581	152	16	τ	τ	PROPN
ejpam-4581	152	17	)	)	PUNCT
ejpam-4581	152	18	.	.	PUNCT
ejpam-4581	153	1	if	if	SCONJ
ejpam-4581	153	2	v	v	NUM
ejpam-4581	153	3	∈	∈	PROPN
ejpam-4581	153	4	βλspo(x	βλspo(x	PROPN
ejpam-4581	153	5	,	,	PUNCT
ejpam-4581	153	6	τ	τ	PROPN
ejpam-4581	153	7	)	)	PUNCT
ejpam-4581	153	8	,	,	PUNCT
ejpam-4581	153	9	then	then	ADV
ejpam-4581	153	10	v	v	X
ejpam-4581	153	11	(	(	PUNCT
ejpam-4581	153	12	λ	λ	PROPN
ejpam-4581	153	13	,	,	PUNCT
ejpam-4581	153	14	sp	sp	NOUN
ejpam-4581	153	15	)	)	PUNCT
ejpam-4581	153	16	∈	∈	PROPN
ejpam-4581	153	17	rλspc(x	rλspc(x	PROPN
ejpam-4581	153	18	,	,	PUNCT
ejpam-4581	153	19	τ	τ	PROPN
ejpam-4581	153	20	)	)	PUNCT
ejpam-4581	153	21	.	.	PUNCT
ejpam-4581	154	1	theorem	theorem	NOUN
ejpam-4581	154	2	3	3	NUM
ejpam-4581	154	3	.	.	X
ejpam-4581	154	4	for	for	ADP
ejpam-4581	154	5	a	a	DET
ejpam-4581	154	6	multifunction	multifunction	NOUN
ejpam-4581	155	1	f	f	NOUN
ejpam-4581	155	2	:	:	PUNCT
ejpam-4581	155	3	(	(	PUNCT
ejpam-4581	155	4	x	x	X
ejpam-4581	155	5	,	,	PUNCT
ejpam-4581	155	6	τ	τ	X
ejpam-4581	155	7	)	)	PUNCT
ejpam-4581	155	8	→	→	SYM
ejpam-4581	155	9	(	(	PUNCT
ejpam-4581	155	10	y	y	PROPN
ejpam-4581	155	11	,	,	PUNCT
ejpam-4581	155	12	σ	σ	PROPN
ejpam-4581	155	13	)	)	PUNCT
ejpam-4581	155	14	,	,	PUNCT
ejpam-4581	155	15	the	the	DET
ejpam-4581	155	16	following	follow	VERB
ejpam-4581	155	17	properties	property	NOUN
ejpam-4581	155	18	are	be	AUX
ejpam-4581	155	19	equivalent	equivalent	ADJ
ejpam-4581	155	20	:	:	PUNCT
ejpam-4581	155	21	(	(	PUNCT
ejpam-4581	155	22	1	1	X
ejpam-4581	155	23	)	)	PUNCT
ejpam-4581	155	24	f	f	PROPN
ejpam-4581	155	25	is	be	AUX
ejpam-4581	155	26	upper	upper	ADJ
ejpam-4581	155	27	almost	almost	ADV
ejpam-4581	155	28	contra-(λ	contra-(λ	PROPN
ejpam-4581	155	29	,	,	PUNCT
ejpam-4581	155	30	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	155	31	;	;	PUNCT
ejpam-4581	155	32	(	(	PUNCT
ejpam-4581	155	33	2	2	NUM
ejpam-4581	155	34	)	)	PUNCT
ejpam-4581	155	35	f+(v	f+(v	NOUN
ejpam-4581	155	36	(	(	PUNCT
ejpam-4581	155	37	λ	λ	NOUN
ejpam-4581	155	38	,	,	PUNCT
ejpam-4581	155	39	sp	sp	NOUN
ejpam-4581	155	40	)	)	PUNCT
ejpam-4581	155	41	)	)	PUNCT
ejpam-4581	156	1	is	be	AUX
ejpam-4581	156	2	(	(	PUNCT
ejpam-4581	156	3	λ	λ	INTJ
ejpam-4581	156	4	,	,	PUNCT
ejpam-4581	156	5	sp)-open	sp)-open	ADJ
ejpam-4581	156	6	in	in	ADP
ejpam-4581	156	7	x	x	PUNCT
ejpam-4581	156	8	for	for	ADP
ejpam-4581	156	9	every	every	DET
ejpam-4581	156	10	β(λ	β(λ	NOUN
ejpam-4581	156	11	,	,	PUNCT
ejpam-4581	156	12	sp)-open	sp)-open	NOUN
ejpam-4581	156	13	set	set	VERB
ejpam-4581	156	14	v	v	NOUN
ejpam-4581	156	15	of	of	ADP
ejpam-4581	156	16	y	y	PROPN
ejpam-4581	156	17	;	;	PUNCT
ejpam-4581	156	18	(	(	PUNCT
ejpam-4581	156	19	3	3	X
ejpam-4581	156	20	)	)	PUNCT
ejpam-4581	156	21	f+(v	f+(v	NOUN
ejpam-4581	156	22	(	(	PUNCT
ejpam-4581	156	23	λ	λ	NOUN
ejpam-4581	156	24	,	,	PUNCT
ejpam-4581	156	25	sp	sp	NOUN
ejpam-4581	156	26	)	)	PUNCT
ejpam-4581	156	27	)	)	PUNCT
ejpam-4581	157	1	is	be	AUX
ejpam-4581	157	2	(	(	PUNCT
ejpam-4581	157	3	λ	λ	INTJ
ejpam-4581	157	4	,	,	PUNCT
ejpam-4581	157	5	sp)-open	sp)-open	ADJ
ejpam-4581	157	6	in	in	ADP
ejpam-4581	157	7	x	x	PUNCT
ejpam-4581	157	8	for	for	ADP
ejpam-4581	157	9	every	every	DET
ejpam-4581	157	10	s(λ	s(λ	PROPN
ejpam-4581	157	11	,	,	PUNCT
ejpam-4581	157	12	sp)-open	sp)-open	VERB
ejpam-4581	157	13	set	set	VERB
ejpam-4581	157	14	v	v	NOUN
ejpam-4581	157	15	of	of	ADP
ejpam-4581	157	16	y	y	PROPN
ejpam-4581	157	17	;	;	PUNCT
ejpam-4581	157	18	(	(	PUNCT
ejpam-4581	157	19	4	4	X
ejpam-4581	157	20	)	)	PUNCT
ejpam-4581	157	21	f−([v	f−([v	NOUN
ejpam-4581	157	22	(	(	PUNCT
ejpam-4581	157	23	λ	λ	PROPN
ejpam-4581	157	24	,	,	PUNCT
ejpam-4581	157	25	sp)](λ	sp)](λ	PROPN
ejpam-4581	157	26	,	,	PUNCT
ejpam-4581	157	27	sp	sp	NOUN
ejpam-4581	157	28	)	)	PUNCT
ejpam-4581	157	29	)	)	PUNCT
ejpam-4581	158	1	is	be	AUX
ejpam-4581	158	2	(	(	PUNCT
ejpam-4581	158	3	λ	λ	X
ejpam-4581	158	4	,	,	PUNCT
ejpam-4581	158	5	sp)-closed	sp)-close	VERB
ejpam-4581	158	6	in	in	ADP
ejpam-4581	158	7	x	x	PUNCT
ejpam-4581	158	8	for	for	ADP
ejpam-4581	158	9	every	every	DET
ejpam-4581	158	10	p(λ	p(λ	NOUN
ejpam-4581	158	11	,	,	PUNCT
ejpam-4581	158	12	sp)-open	sp)-open	NOUN
ejpam-4581	158	13	set	set	VERB
ejpam-4581	158	14	v	v	NOUN
ejpam-4581	158	15	of	of	ADP
ejpam-4581	158	16	y	y	PROPN
ejpam-4581	158	17	.	.	PUNCT
ejpam-4581	159	1	c.	c.	PROPN
ejpam-4581	159	2	boonpok	boonpok	PROPN
ejpam-4581	159	3	,	,	PUNCT
ejpam-4581	159	4	j.	j.	PROPN
ejpam-4581	159	5	khampakdee	khampakdee	PROPN
ejpam-4581	159	6	/	/	PUNCT
ejpam-4581	159	7	eur	eur	PROPN
ejpam-4581	159	8	.	.	PUNCT
ejpam-4581	160	1	j.	j.	PROPN
ejpam-4581	160	2	pure	pure	PROPN
ejpam-4581	160	3	appl	appl	PROPN
ejpam-4581	160	4	.	.	PROPN
ejpam-4581	160	5	math	math	PROPN
ejpam-4581	160	6	,	,	PUNCT
ejpam-4581	160	7	16	16	NUM
ejpam-4581	160	8	(	(	PUNCT
ejpam-4581	160	9	1	1	NUM
ejpam-4581	160	10	)	)	PUNCT
ejpam-4581	160	11	(	(	PUNCT
ejpam-4581	160	12	2023	2023	NUM
ejpam-4581	160	13	)	)	PUNCT
ejpam-4581	160	14	,	,	PUNCT
ejpam-4581	160	15	156	156	NUM
ejpam-4581	160	16	-	-	SYM
ejpam-4581	160	17	168	168	NUM
ejpam-4581	160	18	161	161	NUM
ejpam-4581	160	19	proof	proof	NOUN
ejpam-4581	160	20	.	.	PUNCT
ejpam-4581	161	1	(	(	PUNCT
ejpam-4581	161	2	1	1	X
ejpam-4581	161	3	)	)	PUNCT
ejpam-4581	161	4	⇒	⇒	NOUN
ejpam-4581	161	5	(	(	PUNCT
ejpam-4581	161	6	2	2	NUM
ejpam-4581	161	7	):	):	PUNCT
ejpam-4581	161	8	let	let	VERB
ejpam-4581	161	9	v	v	PART
ejpam-4581	161	10	be	be	AUX
ejpam-4581	161	11	any	any	DET
ejpam-4581	161	12	β(λ	β(λ	NOUN
ejpam-4581	161	13	,	,	PUNCT
ejpam-4581	161	14	sp)-open	sp)-open	ADJ
ejpam-4581	161	15	set	set	NOUN
ejpam-4581	161	16	of	of	ADP
ejpam-4581	161	17	y	y	PROPN
ejpam-4581	161	18	.	.	PUNCT
ejpam-4581	162	1	by	by	ADP
ejpam-4581	162	2	lemma	lemma	PROPN
ejpam-4581	162	3	3	3	NUM
ejpam-4581	162	4	,	,	PUNCT
ejpam-4581	162	5	v	v	PROPN
ejpam-4581	162	6	(	(	PUNCT
ejpam-4581	162	7	λ	λ	NOUN
ejpam-4581	162	8	,	,	PUNCT
ejpam-4581	162	9	sp	sp	NOUN
ejpam-4581	162	10	)	)	PUNCT
ejpam-4581	162	11	is	be	AUX
ejpam-4581	162	12	r(λ	r(λ	NOUN
ejpam-4581	162	13	,	,	PUNCT
ejpam-4581	162	14	sp)-closed	sp)-close	VERB
ejpam-4581	162	15	and	and	CCONJ
ejpam-4581	162	16	by	by	ADP
ejpam-4581	162	17	theorem	theorem	NOUN
ejpam-4581	162	18	1	1	NUM
ejpam-4581	162	19	,	,	PUNCT
ejpam-4581	162	20	f+(v	f+(v	PROPN
ejpam-4581	162	21	(	(	PUNCT
ejpam-4581	162	22	λ	λ	NOUN
ejpam-4581	162	23	,	,	PUNCT
ejpam-4581	162	24	sp	sp	NOUN
ejpam-4581	162	25	)	)	PUNCT
ejpam-4581	162	26	)	)	PUNCT
ejpam-4581	163	1	is	be	AUX
ejpam-4581	163	2	(	(	PUNCT
ejpam-4581	163	3	λ	λ	INTJ
ejpam-4581	163	4	,	,	PUNCT
ejpam-4581	163	5	sp)-open	sp)-open	ADJ
ejpam-4581	163	6	in	in	ADP
ejpam-4581	163	7	x.	x.	NOUN
ejpam-4581	163	8	(	(	PUNCT
ejpam-4581	163	9	2	2	NUM
ejpam-4581	163	10	)	)	PUNCT
ejpam-4581	163	11	⇒	⇒	NOUN
ejpam-4581	163	12	(	(	PUNCT
ejpam-4581	163	13	3	3	NUM
ejpam-4581	163	14	):	):	PUNCT
ejpam-4581	163	15	the	the	DET
ejpam-4581	163	16	proof	proof	NOUN
ejpam-4581	163	17	is	be	AUX
ejpam-4581	163	18	obvious	obvious	ADJ
ejpam-4581	163	19	.	.	PUNCT
ejpam-4581	164	1	(	(	PUNCT
ejpam-4581	164	2	3	3	X
ejpam-4581	164	3	)	)	PUNCT
ejpam-4581	164	4	⇒	⇒	NOUN
ejpam-4581	164	5	(	(	PUNCT
ejpam-4581	164	6	4	4	NUM
ejpam-4581	164	7	):	):	PUNCT
ejpam-4581	164	8	let	let	VERB
ejpam-4581	164	9	v	v	PART
ejpam-4581	164	10	be	be	AUX
ejpam-4581	164	11	any	any	DET
ejpam-4581	164	12	p(λ	p(λ	NOUN
ejpam-4581	164	13	,	,	PUNCT
ejpam-4581	164	14	sp)-open	sp)-open	ADJ
ejpam-4581	164	15	set	set	NOUN
ejpam-4581	164	16	of	of	ADP
ejpam-4581	164	17	y	y	PROPN
ejpam-4581	164	18	.	.	PUNCT
ejpam-4581	165	1	then	then	ADV
ejpam-4581	165	2	y	y	PROPN
ejpam-4581	166	1	−	−	PROPN
ejpam-4581	167	1	[	[	X
ejpam-4581	167	2	v	v	X
ejpam-4581	167	3	(	(	PUNCT
ejpam-4581	167	4	λ	λ	PROPN
ejpam-4581	167	5	,	,	PUNCT
ejpam-4581	167	6	sp)](λ	sp)](λ	PROPN
ejpam-4581	167	7	,	,	PUNCT
ejpam-4581	167	8	sp	sp	NOUN
ejpam-4581	167	9	)	)	PUNCT
ejpam-4581	167	10	is	be	AUX
ejpam-4581	167	11	r(λ	r(λ	NOUN
ejpam-4581	167	12	,	,	PUNCT
ejpam-4581	167	13	sp)closed	sp)close	VERB
ejpam-4581	167	14	and	and	CCONJ
ejpam-4581	167	15	s(λ	s(λ	PROPN
ejpam-4581	167	16	,	,	PUNCT
ejpam-4581	167	17	sp)-open	sp)-open	NOUN
ejpam-4581	167	18	.	.	PUNCT
ejpam-4581	168	1	by	by	ADP
ejpam-4581	168	2	(	(	PUNCT
ejpam-4581	168	3	3	3	NUM
ejpam-4581	168	4	)	)	PUNCT
ejpam-4581	168	5	,	,	PUNCT
ejpam-4581	168	6	we	we	PRON
ejpam-4581	168	7	have	have	VERB
ejpam-4581	168	8	x	x	X
ejpam-4581	168	9	−	−	PROPN
ejpam-4581	168	10	f−([v	f−([v	ADJ
ejpam-4581	168	11	(	(	PUNCT
ejpam-4581	168	12	λ	λ	PROPN
ejpam-4581	168	13	,	,	PUNCT
ejpam-4581	168	14	sp)](λ	sp)](λ	PROPN
ejpam-4581	168	15	,	,	PUNCT
ejpam-4581	168	16	sp	sp	NOUN
ejpam-4581	168	17	)	)	PUNCT
ejpam-4581	168	18	)	)	PUNCT
ejpam-4581	169	1	=	=	PUNCT
ejpam-4581	170	1	f+(y	f+(y	NOUN
ejpam-4581	171	1	−	−	PROPN
ejpam-4581	172	1	[	[	X
ejpam-4581	172	2	v	v	X
ejpam-4581	172	3	(	(	PUNCT
ejpam-4581	172	4	λ	λ	PROPN
ejpam-4581	172	5	,	,	PUNCT
ejpam-4581	172	6	sp)](λ	sp)](λ	PROPN
ejpam-4581	172	7	,	,	PUNCT
ejpam-4581	172	8	sp	sp	NOUN
ejpam-4581	172	9	)	)	PUNCT
ejpam-4581	172	10	)	)	PUNCT
ejpam-4581	172	11	=	=	PUNCT
ejpam-4581	172	12	f+([y	f+([y	NOUN
ejpam-4581	172	13	−	−	PROPN
ejpam-4581	173	1	[	[	X
ejpam-4581	173	2	v	v	X
ejpam-4581	173	3	(	(	PUNCT
ejpam-4581	173	4	λ	λ	PROPN
ejpam-4581	173	5	,	,	PUNCT
ejpam-4581	173	6	sp)](λ	sp)](λ	PROPN
ejpam-4581	173	7	,	,	PUNCT
ejpam-4581	173	8	sp	sp	NOUN
ejpam-4581	173	9	)	)	PUNCT
ejpam-4581	173	10	]	]	PUNCT
ejpam-4581	173	11	(	(	PUNCT
ejpam-4581	173	12	λ	λ	NOUN
ejpam-4581	173	13	,	,	PUNCT
ejpam-4581	173	14	sp	sp	NOUN
ejpam-4581	173	15	)	)	PUNCT
ejpam-4581	173	16	)	)	PUNCT
ejpam-4581	173	17	is	be	AUX
ejpam-4581	173	18	(	(	PUNCT
ejpam-4581	173	19	λ	λ	X
ejpam-4581	173	20	,	,	PUNCT
ejpam-4581	173	21	sp)-open	sp)-open	ADJ
ejpam-4581	173	22	and	and	CCONJ
ejpam-4581	173	23	hence	hence	ADV
ejpam-4581	173	24	f−([v	f−([v	ADJ
ejpam-4581	173	25	(	(	PUNCT
ejpam-4581	173	26	λ	λ	PROPN
ejpam-4581	173	27	,	,	PUNCT
ejpam-4581	173	28	sp)](λ	sp)](λ	PROPN
ejpam-4581	173	29	,	,	PUNCT
ejpam-4581	173	30	sp	sp	NOUN
ejpam-4581	173	31	)	)	PUNCT
ejpam-4581	173	32	)	)	PUNCT
ejpam-4581	174	1	is	be	AUX
ejpam-4581	174	2	(	(	PUNCT
ejpam-4581	174	3	λ	λ	X
ejpam-4581	174	4	,	,	PUNCT
ejpam-4581	174	5	sp)-closed	sp)-close	VERB
ejpam-4581	174	6	in	in	ADP
ejpam-4581	174	7	x.	x.	NOUN
ejpam-4581	174	8	(	(	PUNCT
ejpam-4581	174	9	4	4	NUM
ejpam-4581	174	10	)	)	PUNCT
ejpam-4581	174	11	⇒	⇒	NOUN
ejpam-4581	174	12	(	(	PUNCT
ejpam-4581	174	13	1	1	NUM
ejpam-4581	174	14	):	):	PUNCT
ejpam-4581	174	15	let	let	VERB
ejpam-4581	174	16	v	v	PART
ejpam-4581	174	17	be	be	AUX
ejpam-4581	174	18	any	any	DET
ejpam-4581	174	19	r(λ	r(λ	NOUN
ejpam-4581	174	20	,	,	PUNCT
ejpam-4581	174	21	sp)-open	sp)-open	ADJ
ejpam-4581	174	22	set	set	NOUN
ejpam-4581	174	23	of	of	ADP
ejpam-4581	174	24	y	y	PROPN
ejpam-4581	174	25	.	.	PUNCT
ejpam-4581	175	1	then	then	ADV
ejpam-4581	175	2	v	v	NOUN
ejpam-4581	175	3	is	be	AUX
ejpam-4581	175	4	p(λ	p(λ	NOUN
ejpam-4581	175	5	,	,	PUNCT
ejpam-4581	175	6	sp)-open	sp)-open	ADJ
ejpam-4581	175	7	in	in	ADP
ejpam-4581	175	8	y	y	PROPN
ejpam-4581	175	9	and	and	CCONJ
ejpam-4581	175	10	by	by	ADP
ejpam-4581	175	11	(	(	PUNCT
ejpam-4581	175	12	4	4	NUM
ejpam-4581	175	13	)	)	PUNCT
ejpam-4581	175	14	,	,	PUNCT
ejpam-4581	175	15	f−(v	f−(v	ADJ
ejpam-4581	175	16	)	)	PUNCT
ejpam-4581	176	1	=	=	SYM
ejpam-4581	176	2	f−([v	f−([v	ADJ
ejpam-4581	176	3	(	(	PUNCT
ejpam-4581	176	4	λ	λ	PROPN
ejpam-4581	176	5	,	,	PUNCT
ejpam-4581	176	6	sp)](λ	sp)](λ	PROPN
ejpam-4581	176	7	,	,	PUNCT
ejpam-4581	176	8	sp	sp	NOUN
ejpam-4581	176	9	)	)	PUNCT
ejpam-4581	176	10	)	)	PUNCT
ejpam-4581	176	11	is	be	AUX
ejpam-4581	176	12	(	(	PUNCT
ejpam-4581	176	13	λ	λ	X
ejpam-4581	176	14	,	,	PUNCT
ejpam-4581	176	15	sp)-closed	sp)-close	VERB
ejpam-4581	176	16	in	in	ADP
ejpam-4581	176	17	x.	x.	NOUN
ejpam-4581	176	18	thus	thus	ADV
ejpam-4581	176	19	,	,	PUNCT
ejpam-4581	176	20	by	by	ADP
ejpam-4581	176	21	theorem	theorem	NOUN
ejpam-4581	176	22	1	1	NUM
ejpam-4581	176	23	,	,	PUNCT
ejpam-4581	176	24	f	f	PROPN
ejpam-4581	176	25	is	be	AUX
ejpam-4581	176	26	upper	upper	ADJ
ejpam-4581	176	27	almost	almost	ADV
ejpam-4581	176	28	contra-(λ	contra-(λ	PROPN
ejpam-4581	176	29	,	,	PUNCT
ejpam-4581	176	30	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	176	31	.	.	PUNCT
ejpam-4581	177	1	theorem	theorem	VERB
ejpam-4581	177	2	4	4	NUM
ejpam-4581	177	3	.	.	X
ejpam-4581	177	4	for	for	ADP
ejpam-4581	177	5	a	a	DET
ejpam-4581	177	6	multifunction	multifunction	NOUN
ejpam-4581	178	1	f	f	NOUN
ejpam-4581	178	2	:	:	PUNCT
ejpam-4581	178	3	(	(	PUNCT
ejpam-4581	178	4	x	x	X
ejpam-4581	178	5	,	,	PUNCT
ejpam-4581	178	6	τ	τ	X
ejpam-4581	178	7	)	)	PUNCT
ejpam-4581	178	8	→	→	SYM
ejpam-4581	178	9	(	(	PUNCT
ejpam-4581	178	10	y	y	PROPN
ejpam-4581	178	11	,	,	PUNCT
ejpam-4581	178	12	σ	σ	PROPN
ejpam-4581	178	13	)	)	PUNCT
ejpam-4581	178	14	,	,	PUNCT
ejpam-4581	178	15	the	the	DET
ejpam-4581	178	16	following	follow	VERB
ejpam-4581	178	17	properties	property	NOUN
ejpam-4581	178	18	are	be	AUX
ejpam-4581	178	19	equivalent	equivalent	ADJ
ejpam-4581	178	20	:	:	PUNCT
ejpam-4581	178	21	(	(	PUNCT
ejpam-4581	178	22	1	1	X
ejpam-4581	178	23	)	)	PUNCT
ejpam-4581	178	24	f	f	PROPN
ejpam-4581	178	25	is	be	AUX
ejpam-4581	178	26	lower	low	ADJ
ejpam-4581	178	27	almost	almost	ADV
ejpam-4581	178	28	contra-(λ	contra-(λ	PROPN
ejpam-4581	178	29	,	,	PUNCT
ejpam-4581	178	30	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	178	31	;	;	PUNCT
ejpam-4581	178	32	(	(	PUNCT
ejpam-4581	178	33	2	2	X
ejpam-4581	178	34	)	)	PUNCT
ejpam-4581	178	35	f−(v	f−(v	NOUN
ejpam-4581	178	36	(	(	PUNCT
ejpam-4581	178	37	λ	λ	NOUN
ejpam-4581	178	38	,	,	PUNCT
ejpam-4581	178	39	sp	sp	NOUN
ejpam-4581	178	40	)	)	PUNCT
ejpam-4581	178	41	)	)	PUNCT
ejpam-4581	179	1	is	be	AUX
ejpam-4581	179	2	(	(	PUNCT
ejpam-4581	179	3	λ	λ	INTJ
ejpam-4581	179	4	,	,	PUNCT
ejpam-4581	179	5	sp)-open	sp)-open	ADJ
ejpam-4581	179	6	in	in	ADP
ejpam-4581	179	7	x	x	PUNCT
ejpam-4581	179	8	for	for	ADP
ejpam-4581	179	9	every	every	DET
ejpam-4581	179	10	β(λ	β(λ	NOUN
ejpam-4581	179	11	,	,	PUNCT
ejpam-4581	179	12	sp)-open	sp)-open	NOUN
ejpam-4581	179	13	set	set	VERB
ejpam-4581	179	14	v	v	NOUN
ejpam-4581	179	15	of	of	ADP
ejpam-4581	179	16	y	y	PROPN
ejpam-4581	179	17	;	;	PUNCT
ejpam-4581	179	18	(	(	PUNCT
ejpam-4581	179	19	3	3	X
ejpam-4581	179	20	)	)	PUNCT
ejpam-4581	179	21	f−(v	f−(v	NOUN
ejpam-4581	179	22	(	(	PUNCT
ejpam-4581	179	23	λ	λ	NOUN
ejpam-4581	179	24	,	,	PUNCT
ejpam-4581	179	25	sp	sp	NOUN
ejpam-4581	179	26	)	)	PUNCT
ejpam-4581	179	27	)	)	PUNCT
ejpam-4581	180	1	is	be	AUX
ejpam-4581	180	2	(	(	PUNCT
ejpam-4581	180	3	λ	λ	INTJ
ejpam-4581	180	4	,	,	PUNCT
ejpam-4581	180	5	sp)-open	sp)-open	ADJ
ejpam-4581	180	6	in	in	ADP
ejpam-4581	180	7	x	x	PUNCT
ejpam-4581	180	8	for	for	ADP
ejpam-4581	180	9	every	every	DET
ejpam-4581	180	10	s(λ	s(λ	PROPN
ejpam-4581	180	11	,	,	PUNCT
ejpam-4581	180	12	sp)-open	sp)-open	VERB
ejpam-4581	180	13	set	set	VERB
ejpam-4581	180	14	v	v	NOUN
ejpam-4581	180	15	of	of	ADP
ejpam-4581	180	16	y	y	PROPN
ejpam-4581	180	17	;	;	PUNCT
ejpam-4581	180	18	(	(	PUNCT
ejpam-4581	180	19	4	4	X
ejpam-4581	180	20	)	)	PUNCT
ejpam-4581	180	21	f+([v	f+([v	NOUN
ejpam-4581	180	22	(	(	PUNCT
ejpam-4581	180	23	λ	λ	PROPN
ejpam-4581	180	24	,	,	PUNCT
ejpam-4581	180	25	sp)](λ	sp)](λ	PROPN
ejpam-4581	180	26	,	,	PUNCT
ejpam-4581	180	27	sp	sp	NOUN
ejpam-4581	180	28	)	)	PUNCT
ejpam-4581	180	29	)	)	PUNCT
ejpam-4581	181	1	is	be	AUX
ejpam-4581	181	2	(	(	PUNCT
ejpam-4581	181	3	λ	λ	X
ejpam-4581	181	4	,	,	PUNCT
ejpam-4581	181	5	sp)-closed	sp)-close	VERB
ejpam-4581	181	6	in	in	ADP
ejpam-4581	181	7	x	x	PUNCT
ejpam-4581	181	8	for	for	ADP
ejpam-4581	181	9	every	every	DET
ejpam-4581	181	10	p(λ	p(λ	NOUN
ejpam-4581	181	11	,	,	PUNCT
ejpam-4581	181	12	sp)-open	sp)-open	NOUN
ejpam-4581	181	13	set	set	VERB
ejpam-4581	181	14	v	v	NOUN
ejpam-4581	181	15	of	of	ADP
ejpam-4581	181	16	y	y	PROPN
ejpam-4581	181	17	.	.	PUNCT
ejpam-4581	182	1	proof	proof	NOUN
ejpam-4581	182	2	.	.	PUNCT
ejpam-4581	183	1	the	the	DET
ejpam-4581	183	2	proof	proof	NOUN
ejpam-4581	183	3	is	be	AUX
ejpam-4581	183	4	similar	similar	ADJ
ejpam-4581	183	5	to	to	ADP
ejpam-4581	183	6	that	that	PRON
ejpam-4581	183	7	of	of	ADP
ejpam-4581	183	8	theorem	theorem	ADJ
ejpam-4581	183	9	3	3	NUM
ejpam-4581	183	10	.	.	PUNCT
ejpam-4581	183	11	corollary	corollary	ADJ
ejpam-4581	183	12	2	2	NUM
ejpam-4581	183	13	.	.	PUNCT
ejpam-4581	183	14	for	for	ADP
ejpam-4581	183	15	a	a	DET
ejpam-4581	183	16	function	function	NOUN
ejpam-4581	183	17	f	f	NOUN
ejpam-4581	183	18	:	:	PUNCT
ejpam-4581	183	19	(	(	PUNCT
ejpam-4581	183	20	x	x	X
ejpam-4581	183	21	,	,	PUNCT
ejpam-4581	183	22	τ	τ	X
ejpam-4581	183	23	)	)	PUNCT
ejpam-4581	183	24	→	→	SYM
ejpam-4581	183	25	(	(	PUNCT
ejpam-4581	183	26	y	y	PROPN
ejpam-4581	183	27	,	,	PUNCT
ejpam-4581	183	28	σ	σ	PROPN
ejpam-4581	183	29	)	)	PUNCT
ejpam-4581	183	30	,	,	PUNCT
ejpam-4581	183	31	the	the	DET
ejpam-4581	183	32	following	follow	VERB
ejpam-4581	183	33	properties	property	NOUN
ejpam-4581	183	34	are	be	AUX
ejpam-4581	183	35	equivalent	equivalent	ADJ
ejpam-4581	183	36	:	:	PUNCT
ejpam-4581	183	37	(	(	PUNCT
ejpam-4581	183	38	1	1	X
ejpam-4581	183	39	)	)	PUNCT
ejpam-4581	183	40	f	f	PROPN
ejpam-4581	183	41	is	be	AUX
ejpam-4581	183	42	almost	almost	ADV
ejpam-4581	183	43	contra-(λ	contra-(λ	PROPN
ejpam-4581	183	44	,	,	PUNCT
ejpam-4581	183	45	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	183	46	;	;	PUNCT
ejpam-4581	183	47	(	(	PUNCT
ejpam-4581	183	48	2	2	X
ejpam-4581	183	49	)	)	PUNCT
ejpam-4581	183	50	f−1(v	f−1(v	NOUN
ejpam-4581	183	51	(	(	PUNCT
ejpam-4581	183	52	λ	λ	NOUN
ejpam-4581	183	53	,	,	PUNCT
ejpam-4581	183	54	sp	sp	NOUN
ejpam-4581	183	55	)	)	PUNCT
ejpam-4581	183	56	)	)	PUNCT
ejpam-4581	184	1	is	be	AUX
ejpam-4581	184	2	(	(	PUNCT
ejpam-4581	184	3	λ	λ	INTJ
ejpam-4581	184	4	,	,	PUNCT
ejpam-4581	184	5	sp)-open	sp)-open	ADJ
ejpam-4581	184	6	in	in	ADP
ejpam-4581	184	7	x	x	PUNCT
ejpam-4581	184	8	for	for	ADP
ejpam-4581	184	9	every	every	DET
ejpam-4581	184	10	β(λ	β(λ	NOUN
ejpam-4581	184	11	,	,	PUNCT
ejpam-4581	184	12	sp)-open	sp)-open	NOUN
ejpam-4581	184	13	set	set	VERB
ejpam-4581	184	14	v	v	NOUN
ejpam-4581	184	15	of	of	ADP
ejpam-4581	184	16	y	y	PROPN
ejpam-4581	184	17	;	;	PUNCT
ejpam-4581	184	18	(	(	PUNCT
ejpam-4581	184	19	3	3	X
ejpam-4581	184	20	)	)	PUNCT
ejpam-4581	184	21	f−1(v	f−1(v	NOUN
ejpam-4581	184	22	(	(	PUNCT
ejpam-4581	184	23	λ	λ	NOUN
ejpam-4581	184	24	,	,	PUNCT
ejpam-4581	184	25	sp	sp	NOUN
ejpam-4581	184	26	)	)	PUNCT
ejpam-4581	184	27	)	)	PUNCT
ejpam-4581	185	1	is	be	AUX
ejpam-4581	185	2	(	(	PUNCT
ejpam-4581	185	3	λ	λ	INTJ
ejpam-4581	185	4	,	,	PUNCT
ejpam-4581	185	5	sp)-open	sp)-open	ADJ
ejpam-4581	185	6	in	in	ADP
ejpam-4581	185	7	x	x	PUNCT
ejpam-4581	185	8	for	for	ADP
ejpam-4581	185	9	every	every	DET
ejpam-4581	185	10	s(λ	s(λ	PROPN
ejpam-4581	185	11	,	,	PUNCT
ejpam-4581	185	12	sp)-open	sp)-open	VERB
ejpam-4581	185	13	set	set	VERB
ejpam-4581	185	14	v	v	NOUN
ejpam-4581	185	15	of	of	ADP
ejpam-4581	185	16	y	y	PROPN
ejpam-4581	185	17	;	;	PUNCT
ejpam-4581	185	18	(	(	PUNCT
ejpam-4581	185	19	4	4	X
ejpam-4581	185	20	)	)	PUNCT
ejpam-4581	185	21	f−1([v	f−1([v	NOUN
ejpam-4581	185	22	(	(	PUNCT
ejpam-4581	185	23	λ	λ	PROPN
ejpam-4581	185	24	,	,	PUNCT
ejpam-4581	185	25	sp)](λ	sp)](λ	PROPN
ejpam-4581	185	26	,	,	PUNCT
ejpam-4581	185	27	sp	sp	NOUN
ejpam-4581	185	28	)	)	PUNCT
ejpam-4581	185	29	)	)	PUNCT
ejpam-4581	186	1	is	be	AUX
ejpam-4581	186	2	(	(	PUNCT
ejpam-4581	186	3	λ	λ	X
ejpam-4581	186	4	,	,	PUNCT
ejpam-4581	186	5	sp)-closed	sp)-close	VERB
ejpam-4581	186	6	in	in	ADP
ejpam-4581	186	7	x	x	PUNCT
ejpam-4581	186	8	for	for	ADP
ejpam-4581	186	9	every	every	DET
ejpam-4581	186	10	p(λ	p(λ	NOUN
ejpam-4581	186	11	,	,	PUNCT
ejpam-4581	186	12	sp)-open	sp)-open	NOUN
ejpam-4581	186	13	set	set	VERB
ejpam-4581	186	14	v	v	NOUN
ejpam-4581	186	15	of	of	ADP
ejpam-4581	186	16	y	y	PROPN
ejpam-4581	186	17	.	.	PUNCT
ejpam-4581	187	1	lemma	lemma	PROPN
ejpam-4581	187	2	4	4	NUM
ejpam-4581	187	3	.	.	X
ejpam-4581	188	1	for	for	ADP
ejpam-4581	188	2	a	a	DET
ejpam-4581	188	3	subset	subset	NOUN
ejpam-4581	188	4	a	a	PRON
ejpam-4581	188	5	of	of	ADP
ejpam-4581	188	6	a	a	DET
ejpam-4581	188	7	topological	topological	ADJ
ejpam-4581	188	8	space	space	NOUN
ejpam-4581	188	9	(	(	PUNCT
ejpam-4581	188	10	x	x	X
ejpam-4581	188	11	,	,	PUNCT
ejpam-4581	188	12	τ	τ	PROPN
ejpam-4581	188	13	)	)	PUNCT
ejpam-4581	188	14	,	,	PUNCT
ejpam-4581	188	15	the	the	DET
ejpam-4581	188	16	following	follow	VERB
ejpam-4581	188	17	properties	property	NOUN
ejpam-4581	188	18	hold	hold	VERB
ejpam-4581	188	19	:	:	PUNCT
ejpam-4581	188	20	(	(	PUNCT
ejpam-4581	188	21	1	1	X
ejpam-4581	188	22	)	)	PUNCT
ejpam-4581	188	23	aα(λ	aα(λ	NOUN
ejpam-4581	188	24	,	,	PUNCT
ejpam-4581	188	25	sp	sp	NOUN
ejpam-4581	188	26	)	)	PUNCT
ejpam-4581	188	27	=	=	NOUN
ejpam-4581	188	28	a	a	DET
ejpam-4581	188	29	∪	∪	ADJ
ejpam-4581	188	30	[	[	X
ejpam-4581	188	31	[	[	X
ejpam-4581	188	32	a(λ	a(λ	ADJ
ejpam-4581	188	33	,	,	PUNCT
ejpam-4581	188	34	sp)](λ	sp)](λ	PROPN
ejpam-4581	188	35	,	,	PUNCT
ejpam-4581	188	36	sp	sp	NOUN
ejpam-4581	188	37	)	)	PUNCT
ejpam-4581	188	38	]	]	PUNCT
ejpam-4581	189	1	(	(	PUNCT
ejpam-4581	189	2	λ	λ	NOUN
ejpam-4581	189	3	,	,	PUNCT
ejpam-4581	189	4	sp	sp	NOUN
ejpam-4581	189	5	)	)	PUNCT
ejpam-4581	190	1	[	[	X
ejpam-4581	190	2	5	5	NUM
ejpam-4581	190	3	,	,	PUNCT
ejpam-4581	190	4	22	22	NUM
ejpam-4581	190	5	]	]	PUNCT
ejpam-4581	190	6	.	.	PUNCT
ejpam-4581	191	1	(	(	PUNCT
ejpam-4581	191	2	2	2	X
ejpam-4581	191	3	)	)	PUNCT
ejpam-4581	191	4	as(λ	as(λ	NUM
ejpam-4581	191	5	,	,	PUNCT
ejpam-4581	191	6	sp	sp	NOUN
ejpam-4581	191	7	)	)	PUNCT
ejpam-4581	192	1	=	=	NOUN
ejpam-4581	192	2	a	a	DET
ejpam-4581	192	3	∪	∪	ADJ
ejpam-4581	192	4	[	[	X
ejpam-4581	192	5	a(λ	a(λ	ADJ
ejpam-4581	192	6	,	,	PUNCT
ejpam-4581	192	7	sp)](λ	sp)](λ	PROPN
ejpam-4581	192	8	,	,	PUNCT
ejpam-4581	192	9	sp	sp	NOUN
ejpam-4581	192	10	)	)	PUNCT
ejpam-4581	193	1	[	[	X
ejpam-4581	193	2	23	23	NUM
ejpam-4581	193	3	]	]	PUNCT
ejpam-4581	193	4	.	.	PUNCT
ejpam-4581	194	1	(	(	PUNCT
ejpam-4581	194	2	3	3	X
ejpam-4581	194	3	)	)	PUNCT
ejpam-4581	194	4	ap(λ	ap(λ	NOUN
ejpam-4581	194	5	,	,	PUNCT
ejpam-4581	194	6	sp	sp	NOUN
ejpam-4581	194	7	)	)	PUNCT
ejpam-4581	194	8	=	=	NOUN
ejpam-4581	194	9	a	a	DET
ejpam-4581	194	10	∪	∪	ADJ
ejpam-4581	194	11	[	[	X
ejpam-4581	194	12	a(λ	a(λ	ADJ
ejpam-4581	194	13	,	,	PUNCT
ejpam-4581	194	14	sp	sp	NOUN
ejpam-4581	194	15	)	)	PUNCT
ejpam-4581	194	16	]	]	PUNCT
ejpam-4581	194	17	(	(	PUNCT
ejpam-4581	194	18	λ	λ	NOUN
ejpam-4581	194	19	,	,	PUNCT
ejpam-4581	194	20	sp	sp	NOUN
ejpam-4581	194	21	)	)	PUNCT
ejpam-4581	194	22	.	.	PUNCT
ejpam-4581	195	1	lemma	lemma	PROPN
ejpam-4581	195	2	5	5	NUM
ejpam-4581	195	3	.	.	PUNCT
ejpam-4581	196	1	for	for	ADP
ejpam-4581	196	2	a	a	DET
ejpam-4581	196	3	subset	subset	NOUN
ejpam-4581	196	4	v	v	NOUN
ejpam-4581	196	5	of	of	ADP
ejpam-4581	196	6	a	a	DET
ejpam-4581	196	7	topological	topological	ADJ
ejpam-4581	196	8	space	space	NOUN
ejpam-4581	196	9	(	(	PUNCT
ejpam-4581	196	10	x	x	X
ejpam-4581	196	11	,	,	PUNCT
ejpam-4581	196	12	τ	τ	PROPN
ejpam-4581	196	13	)	)	PUNCT
ejpam-4581	196	14	,	,	PUNCT
ejpam-4581	196	15	the	the	DET
ejpam-4581	196	16	following	follow	VERB
ejpam-4581	196	17	properties	property	NOUN
ejpam-4581	196	18	hold	hold	VERB
ejpam-4581	196	19	:	:	PUNCT
ejpam-4581	196	20	(	(	PUNCT
ejpam-4581	196	21	1	1	X
ejpam-4581	196	22	)	)	PUNCT
ejpam-4581	196	23	v	v	ADP
ejpam-4581	196	24	α(λ	α(λ	PROPN
ejpam-4581	196	25	,	,	PUNCT
ejpam-4581	196	26	sp	sp	NOUN
ejpam-4581	196	27	)	)	PUNCT
ejpam-4581	196	28	=	=	SYM
ejpam-4581	196	29	v	v	X
ejpam-4581	196	30	(	(	PUNCT
ejpam-4581	196	31	λ	λ	NOUN
ejpam-4581	196	32	,	,	PUNCT
ejpam-4581	196	33	sp	sp	NOUN
ejpam-4581	196	34	)	)	PUNCT
ejpam-4581	196	35	for	for	ADP
ejpam-4581	196	36	every	every	DET
ejpam-4581	196	37	v	v	PROPN
ejpam-4581	196	38	∈	∈	PROPN
ejpam-4581	196	39	βλspo(x	βλspo(x	PROPN
ejpam-4581	196	40	,	,	PUNCT
ejpam-4581	196	41	τ	τ	PROPN
ejpam-4581	196	42	)	)	PUNCT
ejpam-4581	196	43	.	.	PUNCT
ejpam-4581	197	1	c.	c.	PROPN
ejpam-4581	197	2	boonpok	boonpok	PROPN
ejpam-4581	197	3	,	,	PUNCT
ejpam-4581	197	4	j.	j.	PROPN
ejpam-4581	197	5	khampakdee	khampakdee	PROPN
ejpam-4581	197	6	/	/	PUNCT
ejpam-4581	197	7	eur	eur	PROPN
ejpam-4581	197	8	.	.	PUNCT
ejpam-4581	198	1	j.	j.	PROPN
ejpam-4581	198	2	pure	pure	PROPN
ejpam-4581	198	3	appl	appl	PROPN
ejpam-4581	198	4	.	.	PROPN
ejpam-4581	198	5	math	math	PROPN
ejpam-4581	198	6	,	,	PUNCT
ejpam-4581	198	7	16	16	NUM
ejpam-4581	198	8	(	(	PUNCT
ejpam-4581	198	9	1	1	NUM
ejpam-4581	198	10	)	)	PUNCT
ejpam-4581	198	11	(	(	PUNCT
ejpam-4581	198	12	2023	2023	NUM
ejpam-4581	198	13	)	)	PUNCT
ejpam-4581	198	14	,	,	PUNCT
ejpam-4581	198	15	156	156	NUM
ejpam-4581	198	16	-	-	SYM
ejpam-4581	198	17	168	168	NUM
ejpam-4581	198	18	162	162	NUM
ejpam-4581	198	19	(	(	PUNCT
ejpam-4581	198	20	2	2	NUM
ejpam-4581	198	21	)	)	PUNCT
ejpam-4581	198	22	v	v	NOUN
ejpam-4581	198	23	p(λ	p(λ	NOUN
ejpam-4581	198	24	,	,	PUNCT
ejpam-4581	198	25	sp	sp	NOUN
ejpam-4581	198	26	)	)	PUNCT
ejpam-4581	198	27	=	=	SYM
ejpam-4581	198	28	v	v	X
ejpam-4581	198	29	(	(	PUNCT
ejpam-4581	198	30	λ	λ	NOUN
ejpam-4581	198	31	,	,	PUNCT
ejpam-4581	198	32	sp	sp	NOUN
ejpam-4581	198	33	)	)	PUNCT
ejpam-4581	198	34	for	for	ADP
ejpam-4581	198	35	every	every	DET
ejpam-4581	198	36	v	v	PROPN
ejpam-4581	198	37	∈	∈	PROPN
ejpam-4581	198	38	sλspo(x	sλspo(x	PROPN
ejpam-4581	198	39	,	,	PUNCT
ejpam-4581	198	40	τ	τ	PROPN
ejpam-4581	198	41	)	)	PUNCT
ejpam-4581	198	42	.	.	PUNCT
ejpam-4581	199	1	(	(	PUNCT
ejpam-4581	199	2	3	3	X
ejpam-4581	199	3	)	)	PUNCT
ejpam-4581	199	4	v	v	ADP
ejpam-4581	199	5	s(λ	s(λ	PROPN
ejpam-4581	199	6	,	,	PUNCT
ejpam-4581	199	7	sp	sp	NOUN
ejpam-4581	199	8	)	)	PUNCT
ejpam-4581	199	9	=	=	SYM
ejpam-4581	199	10	v	v	X
ejpam-4581	199	11	(	(	PUNCT
ejpam-4581	199	12	λ	λ	NOUN
ejpam-4581	199	13	,	,	PUNCT
ejpam-4581	199	14	sp	sp	NOUN
ejpam-4581	199	15	)	)	PUNCT
ejpam-4581	199	16	for	for	ADP
ejpam-4581	199	17	every	every	DET
ejpam-4581	199	18	v	v	NUM
ejpam-4581	199	19	∈	∈	PROPN
ejpam-4581	199	20	pλspo(x	pλspo(x	NOUN
ejpam-4581	199	21	,	,	PUNCT
ejpam-4581	199	22	τ	τ	PROPN
ejpam-4581	199	23	)	)	PUNCT
ejpam-4581	199	24	.	.	PUNCT
ejpam-4581	200	1	theorem	theorem	NOUN
ejpam-4581	200	2	5	5	NUM
ejpam-4581	200	3	.	.	X
ejpam-4581	200	4	for	for	ADP
ejpam-4581	200	5	a	a	DET
ejpam-4581	200	6	multifunction	multifunction	NOUN
ejpam-4581	201	1	f	f	NOUN
ejpam-4581	201	2	:	:	PUNCT
ejpam-4581	201	3	(	(	PUNCT
ejpam-4581	201	4	x	x	X
ejpam-4581	201	5	,	,	PUNCT
ejpam-4581	201	6	τ	τ	X
ejpam-4581	201	7	)	)	PUNCT
ejpam-4581	201	8	→	→	SYM
ejpam-4581	201	9	(	(	PUNCT
ejpam-4581	201	10	y	y	PROPN
ejpam-4581	201	11	,	,	PUNCT
ejpam-4581	201	12	σ	σ	PROPN
ejpam-4581	201	13	)	)	PUNCT
ejpam-4581	201	14	,	,	PUNCT
ejpam-4581	201	15	the	the	DET
ejpam-4581	201	16	following	follow	VERB
ejpam-4581	201	17	properties	property	NOUN
ejpam-4581	201	18	are	be	AUX
ejpam-4581	201	19	equivalent	equivalent	ADJ
ejpam-4581	201	20	:	:	PUNCT
ejpam-4581	201	21	(	(	PUNCT
ejpam-4581	201	22	1	1	X
ejpam-4581	201	23	)	)	PUNCT
ejpam-4581	201	24	f	f	PROPN
ejpam-4581	201	25	is	be	AUX
ejpam-4581	201	26	upper	upper	ADJ
ejpam-4581	201	27	almost	almost	ADV
ejpam-4581	201	28	contra-(λ	contra-(λ	PROPN
ejpam-4581	201	29	,	,	PUNCT
ejpam-4581	201	30	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	201	31	;	;	PUNCT
ejpam-4581	201	32	(	(	PUNCT
ejpam-4581	201	33	2	2	X
ejpam-4581	201	34	)	)	PUNCT
ejpam-4581	201	35	f+(v	f+(v	PROPN
ejpam-4581	201	36	α(λ	α(λ	PROPN
ejpam-4581	201	37	,	,	PUNCT
ejpam-4581	201	38	sp	sp	NOUN
ejpam-4581	201	39	)	)	PUNCT
ejpam-4581	201	40	)	)	PUNCT
ejpam-4581	201	41	is	be	AUX
ejpam-4581	201	42	(	(	PUNCT
ejpam-4581	201	43	λ	λ	INTJ
ejpam-4581	201	44	,	,	PUNCT
ejpam-4581	201	45	sp)-open	sp)-open	ADJ
ejpam-4581	201	46	in	in	ADP
ejpam-4581	201	47	x	x	PUNCT
ejpam-4581	201	48	for	for	ADP
ejpam-4581	201	49	every	every	DET
ejpam-4581	201	50	β(λ	β(λ	NOUN
ejpam-4581	201	51	,	,	PUNCT
ejpam-4581	201	52	sp)-open	sp)-open	NOUN
ejpam-4581	201	53	set	set	VERB
ejpam-4581	201	54	v	v	NOUN
ejpam-4581	201	55	of	of	ADP
ejpam-4581	201	56	y	y	PROPN
ejpam-4581	201	57	;	;	PUNCT
ejpam-4581	201	58	(	(	PUNCT
ejpam-4581	201	59	3	3	X
ejpam-4581	201	60	)	)	PUNCT
ejpam-4581	201	61	f+(v	f+(v	NOUN
ejpam-4581	201	62	p(λ	p(λ	NOUN
ejpam-4581	201	63	,	,	PUNCT
ejpam-4581	201	64	sp	sp	NOUN
ejpam-4581	201	65	)	)	PUNCT
ejpam-4581	201	66	)	)	PUNCT
ejpam-4581	202	1	is	be	AUX
ejpam-4581	202	2	(	(	PUNCT
ejpam-4581	202	3	λ	λ	INTJ
ejpam-4581	202	4	,	,	PUNCT
ejpam-4581	202	5	sp)-open	sp)-open	ADJ
ejpam-4581	202	6	in	in	ADP
ejpam-4581	202	7	x	x	PUNCT
ejpam-4581	202	8	for	for	ADP
ejpam-4581	202	9	every	every	DET
ejpam-4581	202	10	s(λ	s(λ	PROPN
ejpam-4581	202	11	,	,	PUNCT
ejpam-4581	202	12	sp)-open	sp)-open	VERB
ejpam-4581	202	13	set	set	VERB
ejpam-4581	202	14	v	v	NOUN
ejpam-4581	202	15	of	of	ADP
ejpam-4581	202	16	y	y	PROPN
ejpam-4581	202	17	;	;	PUNCT
ejpam-4581	202	18	(	(	PUNCT
ejpam-4581	202	19	4	4	X
ejpam-4581	202	20	)	)	PUNCT
ejpam-4581	202	21	f−([v	f−([v	PROPN
ejpam-4581	202	22	s(λ	s(λ	PROPN
ejpam-4581	202	23	,	,	PUNCT
ejpam-4581	202	24	sp)](λ	sp)](λ	PROPN
ejpam-4581	202	25	,	,	PUNCT
ejpam-4581	202	26	sp	sp	NOUN
ejpam-4581	202	27	)	)	PUNCT
ejpam-4581	202	28	)	)	PUNCT
ejpam-4581	203	1	is	be	AUX
ejpam-4581	203	2	(	(	PUNCT
ejpam-4581	203	3	λ	λ	X
ejpam-4581	203	4	,	,	PUNCT
ejpam-4581	203	5	sp)-closed	sp)-close	VERB
ejpam-4581	203	6	in	in	ADP
ejpam-4581	203	7	x	x	PUNCT
ejpam-4581	203	8	for	for	ADP
ejpam-4581	203	9	every	every	DET
ejpam-4581	203	10	p(λ	p(λ	NOUN
ejpam-4581	203	11	,	,	PUNCT
ejpam-4581	203	12	sp)-open	sp)-open	NOUN
ejpam-4581	203	13	set	set	VERB
ejpam-4581	203	14	v	v	NOUN
ejpam-4581	203	15	of	of	ADP
ejpam-4581	203	16	y	y	PROPN
ejpam-4581	203	17	.	.	PUNCT
ejpam-4581	204	1	proof	proof	NOUN
ejpam-4581	204	2	.	.	PUNCT
ejpam-4581	205	1	this	this	PRON
ejpam-4581	205	2	is	be	AUX
ejpam-4581	205	3	an	an	DET
ejpam-4581	205	4	immediate	immediate	ADJ
ejpam-4581	205	5	consequence	consequence	NOUN
ejpam-4581	205	6	of	of	ADP
ejpam-4581	205	7	theorem	theorem	NOUN
ejpam-4581	205	8	3	3	NUM
ejpam-4581	205	9	and	and	CCONJ
ejpam-4581	205	10	lemma	lemma	PROPN
ejpam-4581	205	11	5	5	NUM
ejpam-4581	205	12	.	.	PUNCT
ejpam-4581	205	13	theorem	theorem	VERB
ejpam-4581	205	14	6	6	NUM
ejpam-4581	205	15	.	.	PUNCT
ejpam-4581	205	16	for	for	ADP
ejpam-4581	205	17	a	a	DET
ejpam-4581	205	18	multifunction	multifunction	NOUN
ejpam-4581	205	19	f	f	NOUN
ejpam-4581	205	20	:	:	PUNCT
ejpam-4581	205	21	(	(	PUNCT
ejpam-4581	205	22	x	x	X
ejpam-4581	205	23	,	,	PUNCT
ejpam-4581	205	24	τ	τ	X
ejpam-4581	205	25	)	)	PUNCT
ejpam-4581	205	26	→	→	SYM
ejpam-4581	205	27	(	(	PUNCT
ejpam-4581	205	28	y	y	PROPN
ejpam-4581	205	29	,	,	PUNCT
ejpam-4581	205	30	σ	σ	PROPN
ejpam-4581	205	31	)	)	PUNCT
ejpam-4581	205	32	,	,	PUNCT
ejpam-4581	205	33	the	the	DET
ejpam-4581	205	34	following	follow	VERB
ejpam-4581	205	35	properties	property	NOUN
ejpam-4581	205	36	are	be	AUX
ejpam-4581	205	37	equivalent	equivalent	ADJ
ejpam-4581	205	38	:	:	PUNCT
ejpam-4581	205	39	(	(	PUNCT
ejpam-4581	205	40	1	1	X
ejpam-4581	205	41	)	)	PUNCT
ejpam-4581	205	42	f	f	PROPN
ejpam-4581	205	43	is	be	AUX
ejpam-4581	205	44	lower	low	ADJ
ejpam-4581	205	45	almost	almost	ADV
ejpam-4581	205	46	contra-(λ	contra-(λ	PROPN
ejpam-4581	205	47	,	,	PUNCT
ejpam-4581	205	48	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	205	49	;	;	PUNCT
ejpam-4581	205	50	(	(	PUNCT
ejpam-4581	205	51	2	2	X
ejpam-4581	205	52	)	)	PUNCT
ejpam-4581	205	53	f−(v	f−(v	PROPN
ejpam-4581	205	54	α(λ	α(λ	PROPN
ejpam-4581	205	55	,	,	PUNCT
ejpam-4581	205	56	sp	sp	NOUN
ejpam-4581	205	57	)	)	PUNCT
ejpam-4581	205	58	)	)	PUNCT
ejpam-4581	205	59	is	be	AUX
ejpam-4581	205	60	(	(	PUNCT
ejpam-4581	205	61	λ	λ	INTJ
ejpam-4581	205	62	,	,	PUNCT
ejpam-4581	205	63	sp)-open	sp)-open	ADJ
ejpam-4581	205	64	in	in	ADP
ejpam-4581	205	65	x	x	PUNCT
ejpam-4581	205	66	for	for	ADP
ejpam-4581	205	67	every	every	DET
ejpam-4581	205	68	β(λ	β(λ	NOUN
ejpam-4581	205	69	,	,	PUNCT
ejpam-4581	205	70	sp)-open	sp)-open	NOUN
ejpam-4581	205	71	set	set	VERB
ejpam-4581	205	72	v	v	NOUN
ejpam-4581	205	73	of	of	ADP
ejpam-4581	205	74	y	y	PROPN
ejpam-4581	205	75	;	;	PUNCT
ejpam-4581	205	76	(	(	PUNCT
ejpam-4581	205	77	3	3	X
ejpam-4581	205	78	)	)	PUNCT
ejpam-4581	205	79	f−(v	f−(v	ADJ
ejpam-4581	205	80	p(λ	p(λ	NOUN
ejpam-4581	205	81	,	,	PUNCT
ejpam-4581	205	82	sp	sp	NOUN
ejpam-4581	205	83	)	)	PUNCT
ejpam-4581	205	84	)	)	PUNCT
ejpam-4581	206	1	is	be	AUX
ejpam-4581	206	2	(	(	PUNCT
ejpam-4581	206	3	λ	λ	INTJ
ejpam-4581	206	4	,	,	PUNCT
ejpam-4581	206	5	sp)-open	sp)-open	ADJ
ejpam-4581	206	6	in	in	ADP
ejpam-4581	206	7	x	x	PUNCT
ejpam-4581	206	8	for	for	ADP
ejpam-4581	206	9	every	every	DET
ejpam-4581	206	10	s(λ	s(λ	PROPN
ejpam-4581	206	11	,	,	PUNCT
ejpam-4581	206	12	sp)-open	sp)-open	VERB
ejpam-4581	206	13	set	set	VERB
ejpam-4581	206	14	v	v	NOUN
ejpam-4581	206	15	of	of	ADP
ejpam-4581	206	16	y	y	PROPN
ejpam-4581	206	17	;	;	PUNCT
ejpam-4581	206	18	(	(	PUNCT
ejpam-4581	206	19	4	4	X
ejpam-4581	206	20	)	)	PUNCT
ejpam-4581	206	21	f+([v	f+([v	PROPN
ejpam-4581	206	22	s(λ	s(λ	PROPN
ejpam-4581	206	23	,	,	PUNCT
ejpam-4581	206	24	sp)](λ	sp)](λ	PROPN
ejpam-4581	206	25	,	,	PUNCT
ejpam-4581	206	26	sp	sp	NOUN
ejpam-4581	206	27	)	)	PUNCT
ejpam-4581	206	28	)	)	PUNCT
ejpam-4581	207	1	is	be	AUX
ejpam-4581	207	2	(	(	PUNCT
ejpam-4581	207	3	λ	λ	X
ejpam-4581	207	4	,	,	PUNCT
ejpam-4581	207	5	sp)-closed	sp)-close	VERB
ejpam-4581	207	6	in	in	ADP
ejpam-4581	207	7	x	x	PUNCT
ejpam-4581	207	8	for	for	ADP
ejpam-4581	207	9	every	every	DET
ejpam-4581	207	10	p(λ	p(λ	NOUN
ejpam-4581	207	11	,	,	PUNCT
ejpam-4581	207	12	sp)-open	sp)-open	NOUN
ejpam-4581	207	13	set	set	VERB
ejpam-4581	207	14	v	v	NOUN
ejpam-4581	207	15	of	of	ADP
ejpam-4581	207	16	y	y	PROPN
ejpam-4581	207	17	.	.	PUNCT
ejpam-4581	208	1	proof	proof	NOUN
ejpam-4581	208	2	.	.	PUNCT
ejpam-4581	209	1	this	this	PRON
ejpam-4581	209	2	is	be	AUX
ejpam-4581	209	3	an	an	DET
ejpam-4581	209	4	immediate	immediate	ADJ
ejpam-4581	209	5	consequence	consequence	NOUN
ejpam-4581	209	6	of	of	ADP
ejpam-4581	209	7	theorem	theorem	NOUN
ejpam-4581	209	8	4	4	NUM
ejpam-4581	209	9	and	and	CCONJ
ejpam-4581	209	10	lemma	lemma	PROPN
ejpam-4581	209	11	5	5	NUM
ejpam-4581	209	12	.	.	PUNCT
ejpam-4581	209	13	corollary	corollary	ADJ
ejpam-4581	209	14	3	3	NUM
ejpam-4581	209	15	.	.	PUNCT
ejpam-4581	209	16	for	for	ADP
ejpam-4581	209	17	a	a	DET
ejpam-4581	209	18	function	function	NOUN
ejpam-4581	209	19	f	f	NOUN
ejpam-4581	209	20	:	:	PUNCT
ejpam-4581	209	21	(	(	PUNCT
ejpam-4581	209	22	x	x	X
ejpam-4581	209	23	,	,	PUNCT
ejpam-4581	209	24	τ	τ	X
ejpam-4581	209	25	)	)	PUNCT
ejpam-4581	209	26	→	→	SYM
ejpam-4581	209	27	(	(	PUNCT
ejpam-4581	209	28	y	y	PROPN
ejpam-4581	209	29	,	,	PUNCT
ejpam-4581	209	30	σ	σ	PROPN
ejpam-4581	209	31	)	)	PUNCT
ejpam-4581	209	32	,	,	PUNCT
ejpam-4581	209	33	the	the	DET
ejpam-4581	209	34	following	follow	VERB
ejpam-4581	209	35	properties	property	NOUN
ejpam-4581	209	36	are	be	AUX
ejpam-4581	209	37	equivalent	equivalent	ADJ
ejpam-4581	209	38	:	:	PUNCT
ejpam-4581	209	39	(	(	PUNCT
ejpam-4581	209	40	1	1	X
ejpam-4581	209	41	)	)	PUNCT
ejpam-4581	209	42	f	f	PROPN
ejpam-4581	209	43	is	be	AUX
ejpam-4581	209	44	almost	almost	ADV
ejpam-4581	209	45	contra-(λ	contra-(λ	PROPN
ejpam-4581	209	46	,	,	PUNCT
ejpam-4581	209	47	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	209	48	;	;	PUNCT
ejpam-4581	209	49	(	(	PUNCT
ejpam-4581	209	50	2	2	X
ejpam-4581	209	51	)	)	PUNCT
ejpam-4581	209	52	f−1(v	f−1(v	NOUN
ejpam-4581	209	53	α(λ	α(λ	PROPN
ejpam-4581	209	54	,	,	PUNCT
ejpam-4581	209	55	sp	sp	NOUN
ejpam-4581	209	56	)	)	PUNCT
ejpam-4581	209	57	)	)	PUNCT
ejpam-4581	209	58	is	be	AUX
ejpam-4581	209	59	(	(	PUNCT
ejpam-4581	209	60	λ	λ	INTJ
ejpam-4581	209	61	,	,	PUNCT
ejpam-4581	209	62	sp)-open	sp)-open	ADJ
ejpam-4581	209	63	in	in	ADP
ejpam-4581	209	64	x	x	PUNCT
ejpam-4581	209	65	for	for	ADP
ejpam-4581	209	66	every	every	DET
ejpam-4581	209	67	β(λ	β(λ	NOUN
ejpam-4581	209	68	,	,	PUNCT
ejpam-4581	209	69	sp)-open	sp)-open	NOUN
ejpam-4581	209	70	set	set	VERB
ejpam-4581	209	71	v	v	NOUN
ejpam-4581	209	72	of	of	ADP
ejpam-4581	209	73	y	y	PROPN
ejpam-4581	209	74	;	;	PUNCT
ejpam-4581	209	75	(	(	PUNCT
ejpam-4581	209	76	3	3	X
ejpam-4581	209	77	)	)	PUNCT
ejpam-4581	209	78	f−1(v	f−1(v	NOUN
ejpam-4581	209	79	p(λ	p(λ	PROPN
ejpam-4581	209	80	,	,	PUNCT
ejpam-4581	209	81	sp	sp	NOUN
ejpam-4581	209	82	)	)	PUNCT
ejpam-4581	209	83	)	)	PUNCT
ejpam-4581	210	1	is	be	AUX
ejpam-4581	210	2	(	(	PUNCT
ejpam-4581	210	3	λ	λ	INTJ
ejpam-4581	210	4	,	,	PUNCT
ejpam-4581	210	5	sp)-open	sp)-open	ADJ
ejpam-4581	210	6	in	in	ADP
ejpam-4581	210	7	x	x	PUNCT
ejpam-4581	210	8	for	for	ADP
ejpam-4581	210	9	every	every	DET
ejpam-4581	210	10	s(λ	s(λ	PROPN
ejpam-4581	210	11	,	,	PUNCT
ejpam-4581	210	12	sp)-open	sp)-open	VERB
ejpam-4581	210	13	set	set	VERB
ejpam-4581	210	14	v	v	NOUN
ejpam-4581	210	15	of	of	ADP
ejpam-4581	210	16	y	y	PROPN
ejpam-4581	210	17	;	;	PUNCT
ejpam-4581	210	18	(	(	PUNCT
ejpam-4581	210	19	4	4	X
ejpam-4581	210	20	)	)	PUNCT
ejpam-4581	210	21	f−1([v	f−1([v	NOUN
ejpam-4581	210	22	s(λ	s(λ	NOUN
ejpam-4581	210	23	,	,	PUNCT
ejpam-4581	210	24	sp)](λ	sp)](λ	PROPN
ejpam-4581	210	25	,	,	PUNCT
ejpam-4581	210	26	sp	sp	NOUN
ejpam-4581	210	27	)	)	PUNCT
ejpam-4581	210	28	)	)	PUNCT
ejpam-4581	211	1	is	be	AUX
ejpam-4581	211	2	(	(	PUNCT
ejpam-4581	211	3	λ	λ	X
ejpam-4581	211	4	,	,	PUNCT
ejpam-4581	211	5	sp)-closed	sp)-close	VERB
ejpam-4581	211	6	in	in	ADP
ejpam-4581	211	7	x	x	PUNCT
ejpam-4581	211	8	for	for	ADP
ejpam-4581	211	9	every	every	DET
ejpam-4581	211	10	p(λ	p(λ	NOUN
ejpam-4581	211	11	,	,	PUNCT
ejpam-4581	211	12	sp)-open	sp)-open	NOUN
ejpam-4581	211	13	set	set	VERB
ejpam-4581	211	14	v	v	NOUN
ejpam-4581	211	15	of	of	ADP
ejpam-4581	211	16	y	y	PROPN
ejpam-4581	211	17	.	.	PUNCT
ejpam-4581	212	1	theorem	theorem	VERB
ejpam-4581	212	2	7	7	NUM
ejpam-4581	212	3	.	.	X
ejpam-4581	212	4	for	for	ADP
ejpam-4581	212	5	a	a	DET
ejpam-4581	212	6	multifunction	multifunction	NOUN
ejpam-4581	213	1	f	f	NOUN
ejpam-4581	213	2	:	:	PUNCT
ejpam-4581	213	3	(	(	PUNCT
ejpam-4581	213	4	x	x	X
ejpam-4581	213	5	,	,	PUNCT
ejpam-4581	213	6	τ	τ	X
ejpam-4581	213	7	)	)	PUNCT
ejpam-4581	213	8	→	→	SYM
ejpam-4581	213	9	(	(	PUNCT
ejpam-4581	213	10	y	y	PROPN
ejpam-4581	213	11	,	,	PUNCT
ejpam-4581	213	12	σ	σ	PROPN
ejpam-4581	213	13	)	)	PUNCT
ejpam-4581	213	14	,	,	PUNCT
ejpam-4581	213	15	the	the	DET
ejpam-4581	213	16	following	follow	VERB
ejpam-4581	213	17	properties	property	NOUN
ejpam-4581	213	18	are	be	AUX
ejpam-4581	213	19	equivalent	equivalent	ADJ
ejpam-4581	213	20	:	:	PUNCT
ejpam-4581	213	21	(	(	PUNCT
ejpam-4581	213	22	1	1	X
ejpam-4581	213	23	)	)	PUNCT
ejpam-4581	213	24	f	f	PROPN
ejpam-4581	213	25	is	be	AUX
ejpam-4581	213	26	upper	upper	ADJ
ejpam-4581	213	27	almost	almost	ADV
ejpam-4581	213	28	contra-(λ	contra-(λ	PROPN
ejpam-4581	213	29	,	,	PUNCT
ejpam-4581	213	30	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	213	31	;	;	PUNCT
ejpam-4581	213	32	(	(	PUNCT
ejpam-4581	213	33	2	2	X
ejpam-4581	213	34	)	)	PUNCT
ejpam-4581	214	1	[	[	X
ejpam-4581	214	2	f−(v	f−(v	NOUN
ejpam-4581	214	3	)	)	PUNCT
ejpam-4581	214	4	]	]	PUNCT
ejpam-4581	214	5	(	(	PUNCT
ejpam-4581	214	6	λ	λ	NOUN
ejpam-4581	214	7	,	,	PUNCT
ejpam-4581	214	8	sp	sp	NOUN
ejpam-4581	214	9	)	)	PUNCT
ejpam-4581	214	10	⊆	⊆	NUM
ejpam-4581	214	11	f−([v	f−([v	ADJ
ejpam-4581	214	12	(	(	PUNCT
ejpam-4581	214	13	λ	λ	PROPN
ejpam-4581	214	14	,	,	PUNCT
ejpam-4581	214	15	sp)](λ	sp)](λ	PROPN
ejpam-4581	214	16	,	,	PUNCT
ejpam-4581	214	17	sp	sp	NOUN
ejpam-4581	214	18	)	)	PUNCT
ejpam-4581	214	19	)	)	PUNCT
ejpam-4581	214	20	for	for	ADP
ejpam-4581	214	21	every	every	DET
ejpam-4581	214	22	(	(	PUNCT
ejpam-4581	214	23	λ	λ	NOUN
ejpam-4581	214	24	,	,	PUNCT
ejpam-4581	214	25	sp)-open	sp)-open	NOUN
ejpam-4581	214	26	set	set	VERB
ejpam-4581	214	27	v	v	NOUN
ejpam-4581	214	28	of	of	ADP
ejpam-4581	214	29	y	y	PROPN
ejpam-4581	214	30	;	;	PUNCT
ejpam-4581	214	31	(	(	PUNCT
ejpam-4581	214	32	3	3	X
ejpam-4581	214	33	)	)	PUNCT
ejpam-4581	215	1	[	[	X
ejpam-4581	215	2	f−(v	f−(v	NOUN
ejpam-4581	215	3	)	)	PUNCT
ejpam-4581	215	4	]	]	PUNCT
ejpam-4581	215	5	(	(	PUNCT
ejpam-4581	215	6	λ	λ	NOUN
ejpam-4581	215	7	,	,	PUNCT
ejpam-4581	215	8	sp	sp	NOUN
ejpam-4581	215	9	)	)	PUNCT
ejpam-4581	215	10	⊆	⊆	NUM
ejpam-4581	215	11	f−(v	f−(v	PROPN
ejpam-4581	215	12	s(λ	s(λ	PROPN
ejpam-4581	215	13	,	,	PUNCT
ejpam-4581	215	14	sp	sp	NOUN
ejpam-4581	215	15	)	)	PUNCT
ejpam-4581	215	16	)	)	PUNCT
ejpam-4581	215	17	for	for	ADP
ejpam-4581	215	18	every	every	DET
ejpam-4581	215	19	(	(	PUNCT
ejpam-4581	215	20	λ	λ	NOUN
ejpam-4581	215	21	,	,	PUNCT
ejpam-4581	215	22	sp)-open	sp)-open	NOUN
ejpam-4581	215	23	set	set	VERB
ejpam-4581	215	24	v	v	NOUN
ejpam-4581	215	25	of	of	ADP
ejpam-4581	215	26	y	y	PROPN
ejpam-4581	215	27	.	.	PUNCT
ejpam-4581	216	1	c.	c.	PROPN
ejpam-4581	216	2	boonpok	boonpok	PROPN
ejpam-4581	216	3	,	,	PUNCT
ejpam-4581	216	4	j.	j.	PROPN
ejpam-4581	216	5	khampakdee	khampakdee	PROPN
ejpam-4581	216	6	/	/	PUNCT
ejpam-4581	216	7	eur	eur	PROPN
ejpam-4581	216	8	.	.	PUNCT
ejpam-4581	217	1	j.	j.	PROPN
ejpam-4581	217	2	pure	pure	PROPN
ejpam-4581	217	3	appl	appl	PROPN
ejpam-4581	217	4	.	.	PROPN
ejpam-4581	217	5	math	math	PROPN
ejpam-4581	217	6	,	,	PUNCT
ejpam-4581	217	7	16	16	NUM
ejpam-4581	217	8	(	(	PUNCT
ejpam-4581	217	9	1	1	NUM
ejpam-4581	217	10	)	)	PUNCT
ejpam-4581	217	11	(	(	PUNCT
ejpam-4581	217	12	2023	2023	NUM
ejpam-4581	217	13	)	)	PUNCT
ejpam-4581	217	14	,	,	PUNCT
ejpam-4581	217	15	156	156	NUM
ejpam-4581	217	16	-	-	SYM
ejpam-4581	217	17	168	168	NUM
ejpam-4581	217	18	163	163	NUM
ejpam-4581	217	19	proof	proof	NOUN
ejpam-4581	217	20	.	.	PUNCT
ejpam-4581	218	1	(	(	PUNCT
ejpam-4581	218	2	1	1	X
ejpam-4581	218	3	)	)	PUNCT
ejpam-4581	218	4	⇒	⇒	NOUN
ejpam-4581	218	5	(	(	PUNCT
ejpam-4581	218	6	2	2	NUM
ejpam-4581	218	7	):	):	PUNCT
ejpam-4581	218	8	let	let	VERB
ejpam-4581	218	9	v	v	PART
ejpam-4581	218	10	be	be	AUX
ejpam-4581	218	11	any	any	DET
ejpam-4581	218	12	(	(	PUNCT
ejpam-4581	218	13	λ	λ	NOUN
ejpam-4581	218	14	,	,	PUNCT
ejpam-4581	218	15	sp)-open	sp)-open	ADJ
ejpam-4581	218	16	set	set	NOUN
ejpam-4581	218	17	of	of	ADP
ejpam-4581	218	18	y	y	PROPN
ejpam-4581	218	19	.	.	PUNCT
ejpam-4581	219	1	then	then	ADV
ejpam-4581	219	2	[	[	X
ejpam-4581	219	3	v	v	X
ejpam-4581	219	4	(	(	PUNCT
ejpam-4581	219	5	λ	λ	PROPN
ejpam-4581	219	6	,	,	PUNCT
ejpam-4581	219	7	sp)](λ	sp)](λ	PROPN
ejpam-4581	219	8	,	,	PUNCT
ejpam-4581	219	9	sp	sp	NOUN
ejpam-4581	219	10	)	)	PUNCT
ejpam-4581	219	11	is	be	AUX
ejpam-4581	219	12	r(λ	r(λ	NOUN
ejpam-4581	219	13	,	,	PUNCT
ejpam-4581	219	14	sp)-open	sp)-open	ADJ
ejpam-4581	219	15	in	in	ADP
ejpam-4581	219	16	y	y	PROPN
ejpam-4581	219	17	.	.	PUNCT
ejpam-4581	220	1	by	by	ADP
ejpam-4581	220	2	theorem	theorem	NOUN
ejpam-4581	220	3	1	1	NUM
ejpam-4581	220	4	,	,	PUNCT
ejpam-4581	220	5	f−([v	f−([v	ADJ
ejpam-4581	220	6	(	(	PUNCT
ejpam-4581	220	7	λ	λ	PROPN
ejpam-4581	220	8	,	,	PUNCT
ejpam-4581	220	9	sp)](λ	sp)](λ	PROPN
ejpam-4581	220	10	,	,	PUNCT
ejpam-4581	220	11	sp	sp	NOUN
ejpam-4581	220	12	)	)	PUNCT
ejpam-4581	220	13	)	)	PUNCT
ejpam-4581	220	14	is	be	AUX
ejpam-4581	220	15	(	(	PUNCT
ejpam-4581	220	16	λ	λ	X
ejpam-4581	220	17	,	,	PUNCT
ejpam-4581	220	18	sp)-closed	sp)-close	VERB
ejpam-4581	220	19	in	in	ADP
ejpam-4581	220	20	x.	x.	NOUN
ejpam-4581	220	21	since	since	SCONJ
ejpam-4581	220	22	v	v	NUM
ejpam-4581	220	23	⊆	⊆	NUM
ejpam-4581	220	24	[	[	X
ejpam-4581	220	25	v	v	X
ejpam-4581	220	26	(	(	PUNCT
ejpam-4581	220	27	λ	λ	PROPN
ejpam-4581	220	28	,	,	PUNCT
ejpam-4581	220	29	sp)](λ	sp)](λ	PROPN
ejpam-4581	220	30	,	,	PUNCT
ejpam-4581	220	31	sp	sp	NOUN
ejpam-4581	220	32	)	)	PUNCT
ejpam-4581	220	33	,	,	PUNCT
ejpam-4581	220	34	f	f	PROPN
ejpam-4581	220	35	−(v	−(v	NOUN
ejpam-4581	220	36	)	)	PUNCT
ejpam-4581	221	1	⊆	⊆	NUM
ejpam-4581	221	2	f−([v	f−([v	ADJ
ejpam-4581	221	3	(	(	PUNCT
ejpam-4581	221	4	λ	λ	PROPN
ejpam-4581	221	5	,	,	PUNCT
ejpam-4581	221	6	sp)](λ	sp)](λ	PROPN
ejpam-4581	221	7	,	,	PUNCT
ejpam-4581	221	8	sp	sp	NOUN
ejpam-4581	221	9	)	)	PUNCT
ejpam-4581	221	10	)	)	PUNCT
ejpam-4581	221	11	and	and	CCONJ
ejpam-4581	221	12	hence	hence	ADV
ejpam-4581	221	13	[	[	X
ejpam-4581	221	14	f−(v	f−(v	ADJ
ejpam-4581	221	15	)	)	PUNCT
ejpam-4581	221	16	]	]	PUNCT
ejpam-4581	221	17	(	(	PUNCT
ejpam-4581	221	18	λ	λ	NOUN
ejpam-4581	221	19	,	,	PUNCT
ejpam-4581	221	20	sp	sp	NOUN
ejpam-4581	221	21	)	)	PUNCT
ejpam-4581	221	22	⊆	⊆	NUM
ejpam-4581	221	23	f−([v	f−([v	ADJ
ejpam-4581	221	24	(	(	PUNCT
ejpam-4581	221	25	λ	λ	PROPN
ejpam-4581	221	26	,	,	PUNCT
ejpam-4581	221	27	sp)](λ	sp)](λ	PROPN
ejpam-4581	221	28	,	,	PUNCT
ejpam-4581	221	29	sp	sp	NOUN
ejpam-4581	221	30	)	)	PUNCT
ejpam-4581	221	31	)	)	PUNCT
ejpam-4581	221	32	.	.	PUNCT
ejpam-4581	222	1	(	(	PUNCT
ejpam-4581	222	2	2	2	X
ejpam-4581	222	3	)	)	PUNCT
ejpam-4581	222	4	⇒	⇒	NOUN
ejpam-4581	222	5	(	(	PUNCT
ejpam-4581	222	6	1	1	NUM
ejpam-4581	222	7	):	):	PUNCT
ejpam-4581	222	8	let	let	VERB
ejpam-4581	222	9	v	v	PART
ejpam-4581	222	10	be	be	AUX
ejpam-4581	222	11	any	any	DET
ejpam-4581	222	12	r(λ	r(λ	NOUN
ejpam-4581	222	13	,	,	PUNCT
ejpam-4581	222	14	sp)-open	sp)-open	ADJ
ejpam-4581	222	15	set	set	NOUN
ejpam-4581	222	16	of	of	ADP
ejpam-4581	222	17	y	y	PROPN
ejpam-4581	222	18	.	.	PUNCT
ejpam-4581	223	1	then	then	ADV
ejpam-4581	223	2	v	v	NOUN
ejpam-4581	223	3	is	be	AUX
ejpam-4581	223	4	(	(	PUNCT
ejpam-4581	223	5	λ	λ	X
ejpam-4581	223	6	,	,	PUNCT
ejpam-4581	223	7	sp)-open	sp)-open	ADJ
ejpam-4581	223	8	in	in	ADP
ejpam-4581	223	9	y	y	PROPN
ejpam-4581	223	10	.	.	PUNCT
ejpam-4581	224	1	by	by	ADP
ejpam-4581	224	2	(	(	PUNCT
ejpam-4581	224	3	2	2	NUM
ejpam-4581	224	4	)	)	PUNCT
ejpam-4581	224	5	,	,	PUNCT
ejpam-4581	224	6	we	we	PRON
ejpam-4581	224	7	have	have	VERB
ejpam-4581	224	8	[	[	X
ejpam-4581	224	9	f−(v	f−(v	ADJ
ejpam-4581	224	10	)	)	PUNCT
ejpam-4581	224	11	]	]	PUNCT
ejpam-4581	224	12	(	(	PUNCT
ejpam-4581	224	13	λ	λ	NOUN
ejpam-4581	224	14	,	,	PUNCT
ejpam-4581	224	15	sp	sp	NOUN
ejpam-4581	224	16	)	)	PUNCT
ejpam-4581	224	17	⊆	⊆	NUM
ejpam-4581	224	18	f−([v	f−([v	ADJ
ejpam-4581	224	19	(	(	PUNCT
ejpam-4581	224	20	λ	λ	PROPN
ejpam-4581	224	21	,	,	PUNCT
ejpam-4581	224	22	sp)](λ	sp)](λ	PROPN
ejpam-4581	224	23	,	,	PUNCT
ejpam-4581	224	24	sp	sp	NOUN
ejpam-4581	224	25	)	)	PUNCT
ejpam-4581	224	26	)	)	PUNCT
ejpam-4581	225	1	=	=	SYM
ejpam-4581	225	2	f−(v	f−(v	ADJ
ejpam-4581	225	3	)	)	PUNCT
ejpam-4581	225	4	and	and	CCONJ
ejpam-4581	225	5	hence	hence	ADV
ejpam-4581	225	6	f−(v	f−(v	ADJ
ejpam-4581	225	7	)	)	PUNCT
ejpam-4581	225	8	is	be	AUX
ejpam-4581	225	9	(	(	PUNCT
ejpam-4581	225	10	λ	λ	X
ejpam-4581	225	11	,	,	PUNCT
ejpam-4581	225	12	sp)-closed	sp)-close	VERB
ejpam-4581	225	13	in	in	ADP
ejpam-4581	225	14	x.	x.	NOUN
ejpam-4581	225	15	thus	thus	ADV
ejpam-4581	225	16	,	,	PUNCT
ejpam-4581	225	17	by	by	ADP
ejpam-4581	225	18	theorem	theorem	NOUN
ejpam-4581	225	19	1	1	NUM
ejpam-4581	225	20	,	,	PUNCT
ejpam-4581	225	21	f	f	PROPN
ejpam-4581	225	22	is	be	AUX
ejpam-4581	225	23	upper	upper	ADJ
ejpam-4581	225	24	almost	almost	ADV
ejpam-4581	225	25	contra-(λ	contra-(λ	PROPN
ejpam-4581	225	26	,	,	PUNCT
ejpam-4581	225	27	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	225	28	.	.	PUNCT
ejpam-4581	226	1	(	(	PUNCT
ejpam-4581	226	2	2	2	X
ejpam-4581	226	3	)	)	PUNCT
ejpam-4581	226	4	⇔	⇔	X
ejpam-4581	226	5	(	(	PUNCT
ejpam-4581	226	6	3	3	NUM
ejpam-4581	226	7	):	):	PUNCT
ejpam-4581	226	8	it	it	PRON
ejpam-4581	226	9	follows	follow	VERB
ejpam-4581	226	10	from	from	ADP
ejpam-4581	226	11	lemma	lemma	PROPN
ejpam-4581	226	12	4	4	NUM
ejpam-4581	226	13	.	.	PUNCT
ejpam-4581	226	14	theorem	theorem	VERB
ejpam-4581	226	15	8	8	NUM
ejpam-4581	226	16	.	.	PUNCT
ejpam-4581	226	17	for	for	ADP
ejpam-4581	226	18	a	a	DET
ejpam-4581	226	19	multifunction	multifunction	NOUN
ejpam-4581	226	20	f	f	NOUN
ejpam-4581	226	21	:	:	PUNCT
ejpam-4581	226	22	(	(	PUNCT
ejpam-4581	226	23	x	x	X
ejpam-4581	226	24	,	,	PUNCT
ejpam-4581	226	25	τ	τ	X
ejpam-4581	226	26	)	)	PUNCT
ejpam-4581	226	27	→	→	SYM
ejpam-4581	226	28	(	(	PUNCT
ejpam-4581	226	29	y	y	PROPN
ejpam-4581	226	30	,	,	PUNCT
ejpam-4581	226	31	σ	σ	PROPN
ejpam-4581	226	32	)	)	PUNCT
ejpam-4581	226	33	,	,	PUNCT
ejpam-4581	226	34	the	the	DET
ejpam-4581	226	35	following	follow	VERB
ejpam-4581	226	36	properties	property	NOUN
ejpam-4581	226	37	are	be	AUX
ejpam-4581	226	38	equivalent	equivalent	ADJ
ejpam-4581	226	39	:	:	PUNCT
ejpam-4581	226	40	(	(	PUNCT
ejpam-4581	226	41	1	1	X
ejpam-4581	226	42	)	)	PUNCT
ejpam-4581	226	43	f	f	PROPN
ejpam-4581	226	44	is	be	AUX
ejpam-4581	226	45	lower	low	ADJ
ejpam-4581	226	46	almost	almost	ADV
ejpam-4581	226	47	contra-(λ	contra-(λ	PROPN
ejpam-4581	226	48	,	,	PUNCT
ejpam-4581	226	49	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	226	50	;	;	PUNCT
ejpam-4581	227	1	(	(	PUNCT
ejpam-4581	227	2	2	2	X
ejpam-4581	227	3	)	)	PUNCT
ejpam-4581	227	4	[	[	X
ejpam-4581	227	5	f+(v	f+(v	NOUN
ejpam-4581	227	6	)	)	PUNCT
ejpam-4581	227	7	]	]	PUNCT
ejpam-4581	227	8	(	(	PUNCT
ejpam-4581	227	9	λ	λ	NOUN
ejpam-4581	227	10	,	,	PUNCT
ejpam-4581	227	11	sp	sp	NOUN
ejpam-4581	227	12	)	)	PUNCT
ejpam-4581	227	13	⊆	⊆	NUM
ejpam-4581	227	14	f+([v	f+([v	NOUN
ejpam-4581	227	15	(	(	PUNCT
ejpam-4581	227	16	λ	λ	PROPN
ejpam-4581	227	17	,	,	PUNCT
ejpam-4581	227	18	sp)](λ	sp)](λ	PROPN
ejpam-4581	227	19	,	,	PUNCT
ejpam-4581	227	20	sp	sp	NOUN
ejpam-4581	227	21	)	)	PUNCT
ejpam-4581	227	22	)	)	PUNCT
ejpam-4581	227	23	for	for	ADP
ejpam-4581	227	24	every	every	DET
ejpam-4581	227	25	(	(	PUNCT
ejpam-4581	227	26	λ	λ	NOUN
ejpam-4581	227	27	,	,	PUNCT
ejpam-4581	227	28	sp)-open	sp)-open	NOUN
ejpam-4581	227	29	set	set	VERB
ejpam-4581	227	30	v	v	NOUN
ejpam-4581	227	31	of	of	ADP
ejpam-4581	227	32	y	y	PROPN
ejpam-4581	227	33	;	;	PUNCT
ejpam-4581	227	34	(	(	PUNCT
ejpam-4581	227	35	3	3	X
ejpam-4581	227	36	)	)	PUNCT
ejpam-4581	227	37	[	[	X
ejpam-4581	227	38	f+(v	f+(v	NOUN
ejpam-4581	227	39	)	)	PUNCT
ejpam-4581	227	40	]	]	PUNCT
ejpam-4581	227	41	(	(	PUNCT
ejpam-4581	227	42	λ	λ	NOUN
ejpam-4581	227	43	,	,	PUNCT
ejpam-4581	227	44	sp	sp	NOUN
ejpam-4581	227	45	)	)	PUNCT
ejpam-4581	227	46	⊆	⊆	NUM
ejpam-4581	227	47	f+(v	f+(v	NOUN
ejpam-4581	227	48	s(λ	s(λ	PROPN
ejpam-4581	227	49	,	,	PUNCT
ejpam-4581	227	50	sp	sp	NOUN
ejpam-4581	227	51	)	)	PUNCT
ejpam-4581	227	52	)	)	PUNCT
ejpam-4581	227	53	for	for	SCONJ
ejpam-4581	227	54	every	every	DET
ejpam-4581	227	55	(	(	PUNCT
ejpam-4581	227	56	λ	λ	NOUN
ejpam-4581	227	57	,	,	PUNCT
ejpam-4581	227	58	sp)-open	sp)-open	NOUN
ejpam-4581	227	59	set	set	VERB
ejpam-4581	227	60	v	v	NOUN
ejpam-4581	227	61	of	of	ADP
ejpam-4581	227	62	y	y	PROPN
ejpam-4581	227	63	.	.	PUNCT
ejpam-4581	228	1	proof	proof	NOUN
ejpam-4581	228	2	.	.	PUNCT
ejpam-4581	229	1	the	the	DET
ejpam-4581	229	2	proof	proof	NOUN
ejpam-4581	229	3	is	be	AUX
ejpam-4581	229	4	similar	similar	ADJ
ejpam-4581	229	5	to	to	ADP
ejpam-4581	229	6	that	that	PRON
ejpam-4581	229	7	of	of	ADP
ejpam-4581	229	8	theorem	theorem	ADJ
ejpam-4581	229	9	7	7	NUM
ejpam-4581	229	10	.	.	PUNCT
ejpam-4581	229	11	corollary	corollary	ADJ
ejpam-4581	229	12	4	4	NUM
ejpam-4581	229	13	.	.	PUNCT
ejpam-4581	229	14	for	for	ADP
ejpam-4581	229	15	a	a	DET
ejpam-4581	229	16	function	function	NOUN
ejpam-4581	229	17	f	f	NOUN
ejpam-4581	229	18	:	:	PUNCT
ejpam-4581	229	19	(	(	PUNCT
ejpam-4581	229	20	x	x	X
ejpam-4581	229	21	,	,	PUNCT
ejpam-4581	229	22	τ	τ	X
ejpam-4581	229	23	)	)	PUNCT
ejpam-4581	229	24	→	→	SYM
ejpam-4581	229	25	(	(	PUNCT
ejpam-4581	229	26	y	y	PROPN
ejpam-4581	229	27	,	,	PUNCT
ejpam-4581	229	28	σ	σ	PROPN
ejpam-4581	229	29	)	)	PUNCT
ejpam-4581	229	30	,	,	PUNCT
ejpam-4581	229	31	the	the	DET
ejpam-4581	229	32	following	follow	VERB
ejpam-4581	229	33	properties	property	NOUN
ejpam-4581	229	34	are	be	AUX
ejpam-4581	229	35	equivalent	equivalent	ADJ
ejpam-4581	229	36	:	:	PUNCT
ejpam-4581	229	37	(	(	PUNCT
ejpam-4581	229	38	1	1	X
ejpam-4581	229	39	)	)	PUNCT
ejpam-4581	229	40	f	f	PROPN
ejpam-4581	229	41	is	be	AUX
ejpam-4581	229	42	almost	almost	ADV
ejpam-4581	229	43	contra-(λ	contra-(λ	PROPN
ejpam-4581	229	44	,	,	PUNCT
ejpam-4581	229	45	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	229	46	;	;	PUNCT
ejpam-4581	229	47	(	(	PUNCT
ejpam-4581	229	48	2	2	X
ejpam-4581	229	49	)	)	PUNCT
ejpam-4581	230	1	[	[	X
ejpam-4581	230	2	f−1(v	f−1(v	NOUN
ejpam-4581	230	3	)	)	PUNCT
ejpam-4581	230	4	]	]	PUNCT
ejpam-4581	230	5	(	(	PUNCT
ejpam-4581	230	6	λ	λ	NOUN
ejpam-4581	230	7	,	,	PUNCT
ejpam-4581	230	8	sp	sp	NOUN
ejpam-4581	230	9	)	)	PUNCT
ejpam-4581	230	10	⊆	⊆	NUM
ejpam-4581	230	11	f−1([v	f−1([v	ADJ
ejpam-4581	230	12	(	(	PUNCT
ejpam-4581	230	13	λ	λ	PROPN
ejpam-4581	230	14	,	,	PUNCT
ejpam-4581	230	15	sp)](λ	sp)](λ	PROPN
ejpam-4581	230	16	,	,	PUNCT
ejpam-4581	230	17	sp	sp	NOUN
ejpam-4581	230	18	)	)	PUNCT
ejpam-4581	230	19	)	)	PUNCT
ejpam-4581	230	20	for	for	ADP
ejpam-4581	230	21	every	every	DET
ejpam-4581	230	22	(	(	PUNCT
ejpam-4581	230	23	λ	λ	NOUN
ejpam-4581	230	24	,	,	PUNCT
ejpam-4581	230	25	sp)-open	sp)-open	NOUN
ejpam-4581	230	26	set	set	VERB
ejpam-4581	230	27	v	v	NOUN
ejpam-4581	230	28	of	of	ADP
ejpam-4581	230	29	y	y	PROPN
ejpam-4581	230	30	;	;	PUNCT
ejpam-4581	230	31	(	(	PUNCT
ejpam-4581	230	32	3	3	X
ejpam-4581	230	33	)	)	PUNCT
ejpam-4581	231	1	[	[	X
ejpam-4581	231	2	f−1(v	f−1(v	NOUN
ejpam-4581	231	3	)	)	PUNCT
ejpam-4581	231	4	]	]	PUNCT
ejpam-4581	231	5	(	(	PUNCT
ejpam-4581	231	6	λ	λ	NOUN
ejpam-4581	231	7	,	,	PUNCT
ejpam-4581	231	8	sp	sp	NOUN
ejpam-4581	231	9	)	)	PUNCT
ejpam-4581	231	10	⊆	⊆	NUM
ejpam-4581	231	11	f−1(v	f−1(v	PROPN
ejpam-4581	231	12	s(λ	s(λ	PROPN
ejpam-4581	231	13	,	,	PUNCT
ejpam-4581	231	14	sp	sp	NOUN
ejpam-4581	231	15	)	)	PUNCT
ejpam-4581	231	16	)	)	PUNCT
ejpam-4581	231	17	for	for	ADP
ejpam-4581	231	18	every	every	DET
ejpam-4581	231	19	(	(	PUNCT
ejpam-4581	231	20	λ	λ	NOUN
ejpam-4581	231	21	,	,	PUNCT
ejpam-4581	231	22	sp)-open	sp)-open	NOUN
ejpam-4581	231	23	set	set	VERB
ejpam-4581	231	24	v	v	NOUN
ejpam-4581	231	25	of	of	ADP
ejpam-4581	231	26	y	y	PROPN
ejpam-4581	231	27	.	.	PUNCT
ejpam-4581	232	1	let	let	VERB
ejpam-4581	232	2	a	a	DET
ejpam-4581	232	3	be	be	AUX
ejpam-4581	232	4	a	a	DET
ejpam-4581	232	5	subset	subset	NOUN
ejpam-4581	232	6	of	of	ADP
ejpam-4581	232	7	a	a	DET
ejpam-4581	232	8	topological	topological	ADJ
ejpam-4581	232	9	space	space	NOUN
ejpam-4581	232	10	(	(	PUNCT
ejpam-4581	232	11	x	x	X
ejpam-4581	232	12	,	,	PUNCT
ejpam-4581	232	13	τ	τ	PROPN
ejpam-4581	232	14	)	)	PUNCT
ejpam-4581	232	15	.	.	PUNCT
ejpam-4581	233	1	a	a	DET
ejpam-4581	233	2	point	point	NOUN
ejpam-4581	233	3	x	x	X
ejpam-4581	233	4	∈	∈	NOUN
ejpam-4581	233	5	x	x	PUNCT
ejpam-4581	233	6	is	be	AUX
ejpam-4581	233	7	said	say	VERB
ejpam-4581	233	8	to	to	PART
ejpam-4581	233	9	be	be	AUX
ejpam-4581	233	10	in	in	ADP
ejpam-4581	233	11	the	the	DET
ejpam-4581	233	12	θs(λ	θs(λ	NOUN
ejpam-4581	233	13	,	,	PUNCT
ejpam-4581	233	14	sp)-closure	sp)-closure	NOUN
ejpam-4581	233	15	of	of	ADP
ejpam-4581	233	16	a	a	PRON
ejpam-4581	233	17	,	,	PUNCT
ejpam-4581	233	18	denoted	denote	VERB
ejpam-4581	233	19	by	by	ADP
ejpam-4581	233	20	aθs(λ	aθs(λ	PROPN
ejpam-4581	233	21	,	,	PUNCT
ejpam-4581	233	22	sp	sp	NOUN
ejpam-4581	233	23	)	)	PUNCT
ejpam-4581	233	24	,	,	PUNCT
ejpam-4581	233	25	if	if	SCONJ
ejpam-4581	233	26	a	a	DET
ejpam-4581	233	27	∩	∩	ADJ
ejpam-4581	233	28	u	u	NOUN
ejpam-4581	233	29	(	(	PUNCT
ejpam-4581	233	30	λ	λ	PROPN
ejpam-4581	233	31	,	,	PUNCT
ejpam-4581	233	32	sp	sp	NOUN
ejpam-4581	233	33	)	)	PUNCT
ejpam-4581	233	34	̸=	̸=	NOUN
ejpam-4581	233	35	∅	∅	NOUN
ejpam-4581	233	36	for	for	ADP
ejpam-4581	233	37	each	each	DET
ejpam-4581	233	38	s(λ	s(λ	PROPN
ejpam-4581	233	39	,	,	PUNCT
ejpam-4581	233	40	sp)-open	sp)-open	VERB
ejpam-4581	233	41	set	set	VERB
ejpam-4581	233	42	u	u	NOUN
ejpam-4581	233	43	of	of	ADP
ejpam-4581	233	44	x	x	SYM
ejpam-4581	233	45	containing	contain	VERB
ejpam-4581	233	46	x.	x.	NOUN
ejpam-4581	233	47	a	a	DET
ejpam-4581	233	48	subset	subset	NOUN
ejpam-4581	233	49	a	a	PRON
ejpam-4581	233	50	of	of	ADP
ejpam-4581	233	51	a	a	DET
ejpam-4581	233	52	topological	topological	ADJ
ejpam-4581	233	53	space	space	NOUN
ejpam-4581	233	54	(	(	PUNCT
ejpam-4581	233	55	x	x	X
ejpam-4581	233	56	,	,	PUNCT
ejpam-4581	233	57	τ	τ	X
ejpam-4581	233	58	)	)	PUNCT
ejpam-4581	233	59	is	be	AUX
ejpam-4581	233	60	called	call	VERB
ejpam-4581	233	61	θs(λ	θs(λ	NOUN
ejpam-4581	233	62	,	,	PUNCT
ejpam-4581	233	63	sp)-closed	sp)-close	VERB
ejpam-4581	233	64	if	if	SCONJ
ejpam-4581	233	65	a	a	DET
ejpam-4581	233	66	=	=	SYM
ejpam-4581	233	67	aθs(λ	aθs(λ	PROPN
ejpam-4581	233	68	,	,	PUNCT
ejpam-4581	233	69	sp	sp	NOUN
ejpam-4581	233	70	)	)	PUNCT
ejpam-4581	233	71	.	.	PUNCT
ejpam-4581	234	1	the	the	DET
ejpam-4581	234	2	complement	complement	NOUN
ejpam-4581	234	3	of	of	ADP
ejpam-4581	234	4	a	a	DET
ejpam-4581	234	5	θs(λ	θs(λ	NOUN
ejpam-4581	234	6	,	,	PUNCT
ejpam-4581	234	7	sp)-closed	sp)-close	VERB
ejpam-4581	234	8	set	set	VERB
ejpam-4581	234	9	is	be	AUX
ejpam-4581	234	10	called	call	VERB
ejpam-4581	234	11	θs(λ	θs(λ	NOUN
ejpam-4581	234	12	,	,	PUNCT
ejpam-4581	234	13	sp)-open	sp)-open	NOUN
ejpam-4581	234	14	.	.	PUNCT
ejpam-4581	235	1	theorem	theorem	VERB
ejpam-4581	235	2	9	9	NUM
ejpam-4581	235	3	.	.	X
ejpam-4581	235	4	for	for	ADP
ejpam-4581	235	5	a	a	DET
ejpam-4581	235	6	multifunction	multifunction	NOUN
ejpam-4581	236	1	f	f	NOUN
ejpam-4581	236	2	:	:	PUNCT
ejpam-4581	236	3	(	(	PUNCT
ejpam-4581	236	4	x	x	X
ejpam-4581	236	5	,	,	PUNCT
ejpam-4581	236	6	τ	τ	X
ejpam-4581	236	7	)	)	PUNCT
ejpam-4581	236	8	→	→	SYM
ejpam-4581	236	9	(	(	PUNCT
ejpam-4581	236	10	y	y	PROPN
ejpam-4581	236	11	,	,	PUNCT
ejpam-4581	236	12	σ	σ	PROPN
ejpam-4581	236	13	)	)	PUNCT
ejpam-4581	236	14	,	,	PUNCT
ejpam-4581	236	15	the	the	DET
ejpam-4581	236	16	following	follow	VERB
ejpam-4581	236	17	properties	property	NOUN
ejpam-4581	236	18	are	be	AUX
ejpam-4581	236	19	equivalent	equivalent	ADJ
ejpam-4581	236	20	:	:	PUNCT
ejpam-4581	236	21	(	(	PUNCT
ejpam-4581	236	22	1	1	X
ejpam-4581	236	23	)	)	PUNCT
ejpam-4581	236	24	f	f	PROPN
ejpam-4581	236	25	is	be	AUX
ejpam-4581	236	26	lower	low	ADJ
ejpam-4581	236	27	almost	almost	ADV
ejpam-4581	236	28	contra-(λ	contra-(λ	PROPN
ejpam-4581	236	29	,	,	PUNCT
ejpam-4581	236	30	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	236	31	;	;	PUNCT
ejpam-4581	236	32	(	(	PUNCT
ejpam-4581	236	33	2	2	X
ejpam-4581	236	34	)	)	PUNCT
ejpam-4581	236	35	f−(v	f−(v	NOUN
ejpam-4581	236	36	)	)	PUNCT
ejpam-4581	236	37	is	be	AUX
ejpam-4581	236	38	(	(	PUNCT
ejpam-4581	236	39	λ	λ	INTJ
ejpam-4581	236	40	,	,	PUNCT
ejpam-4581	236	41	sp)-open	sp)-open	ADJ
ejpam-4581	236	42	in	in	ADP
ejpam-4581	236	43	x	x	PUNCT
ejpam-4581	236	44	for	for	ADP
ejpam-4581	236	45	every	every	DET
ejpam-4581	236	46	θs(λ	θs(λ	NOUN
ejpam-4581	236	47	,	,	PUNCT
ejpam-4581	236	48	sp)-open	sp)-open	VERB
ejpam-4581	236	49	set	set	VERB
ejpam-4581	236	50	v	v	NOUN
ejpam-4581	236	51	of	of	ADP
ejpam-4581	236	52	y	y	PROPN
ejpam-4581	236	53	;	;	PUNCT
ejpam-4581	236	54	(	(	PUNCT
ejpam-4581	236	55	3	3	X
ejpam-4581	236	56	)	)	PUNCT
ejpam-4581	236	57	f+(k	f+(k	NUM
ejpam-4581	236	58	)	)	PUNCT
ejpam-4581	237	1	is	be	AUX
ejpam-4581	237	2	(	(	PUNCT
ejpam-4581	237	3	λ	λ	X
ejpam-4581	237	4	,	,	PUNCT
ejpam-4581	237	5	sp)-closed	sp)-close	VERB
ejpam-4581	237	6	in	in	ADP
ejpam-4581	237	7	x	x	PUNCT
ejpam-4581	237	8	for	for	ADP
ejpam-4581	237	9	every	every	DET
ejpam-4581	237	10	θs(λ	θs(λ	NOUN
ejpam-4581	237	11	,	,	PUNCT
ejpam-4581	237	12	sp)-closed	sp)-close	VERB
ejpam-4581	237	13	set	set	VERB
ejpam-4581	237	14	k	k	PROPN
ejpam-4581	237	15	of	of	ADP
ejpam-4581	237	16	y	y	PROPN
ejpam-4581	237	17	;	;	PUNCT
ejpam-4581	237	18	(	(	PUNCT
ejpam-4581	237	19	4	4	X
ejpam-4581	237	20	)	)	PUNCT
ejpam-4581	238	1	[	[	X
ejpam-4581	238	2	f+([b(λ	f+([b(λ	PROPN
ejpam-4581	238	3	,	,	PUNCT
ejpam-4581	238	4	sp)](λ	sp)](λ	PROPN
ejpam-4581	238	5	,	,	PUNCT
ejpam-4581	238	6	sp	sp	NOUN
ejpam-4581	238	7	)	)	PUNCT
ejpam-4581	238	8	)	)	PUNCT
ejpam-4581	238	9	]	]	PUNCT
ejpam-4581	239	1	(	(	PUNCT
ejpam-4581	239	2	λ	λ	NOUN
ejpam-4581	239	3	,	,	PUNCT
ejpam-4581	239	4	sp	sp	NOUN
ejpam-4581	239	5	)	)	PUNCT
ejpam-4581	239	6	⊆	⊆	NUM
ejpam-4581	239	7	f+(bs(λ	f+(bs(λ	PROPN
ejpam-4581	239	8	,	,	PUNCT
ejpam-4581	239	9	sp	sp	NOUN
ejpam-4581	239	10	)	)	PUNCT
ejpam-4581	239	11	)	)	PUNCT
ejpam-4581	239	12	for	for	ADP
ejpam-4581	239	13	every	every	DET
ejpam-4581	239	14	subset	subset	NOUN
ejpam-4581	239	15	b	b	PROPN
ejpam-4581	239	16	of	of	ADP
ejpam-4581	239	17	y	y	PROPN
ejpam-4581	239	18	;	;	PUNCT
ejpam-4581	239	19	(	(	PUNCT
ejpam-4581	239	20	5	5	X
ejpam-4581	239	21	)	)	PUNCT
ejpam-4581	239	22	[	[	X
ejpam-4581	239	23	f+(b)](λ	f+(b)](λ	NUM
ejpam-4581	239	24	,	,	PUNCT
ejpam-4581	239	25	sp	sp	NOUN
ejpam-4581	239	26	)	)	PUNCT
ejpam-4581	239	27	⊆	⊆	NUM
ejpam-4581	239	28	f+(bθs(λ	f+(bθs(λ	NOUN
ejpam-4581	239	29	,	,	PUNCT
ejpam-4581	239	30	sp	sp	NOUN
ejpam-4581	239	31	)	)	PUNCT
ejpam-4581	239	32	)	)	PUNCT
ejpam-4581	239	33	for	for	ADP
ejpam-4581	239	34	every	every	DET
ejpam-4581	239	35	subset	subset	NOUN
ejpam-4581	239	36	b	b	PROPN
ejpam-4581	239	37	of	of	ADP
ejpam-4581	239	38	y	y	PROPN
ejpam-4581	239	39	;	;	PUNCT
ejpam-4581	239	40	(	(	PUNCT
ejpam-4581	239	41	6	6	X
ejpam-4581	239	42	)	)	PUNCT
ejpam-4581	239	43	f	f	NOUN
ejpam-4581	239	44	(	(	PUNCT
ejpam-4581	239	45	a(λ	a(λ	ADV
ejpam-4581	239	46	,	,	PUNCT
ejpam-4581	239	47	sp	sp	NOUN
ejpam-4581	239	48	)	)	PUNCT
ejpam-4581	239	49	)	)	PUNCT
ejpam-4581	240	1	⊆	⊆	NUM
ejpam-4581	241	1	[	[	X
ejpam-4581	241	2	f	f	X
ejpam-4581	241	3	(	(	PUNCT
ejpam-4581	241	4	a)]θs(λ	a)]θs(λ	NOUN
ejpam-4581	241	5	,	,	PUNCT
ejpam-4581	241	6	sp	sp	NOUN
ejpam-4581	241	7	)	)	PUNCT
ejpam-4581	241	8	for	for	ADP
ejpam-4581	241	9	every	every	DET
ejpam-4581	241	10	subset	subset	NOUN
ejpam-4581	241	11	a	a	PRON
ejpam-4581	241	12	of	of	ADP
ejpam-4581	241	13	x.	x.	PROPN
ejpam-4581	241	14	c.	c.	PROPN
ejpam-4581	241	15	boonpok	boonpok	PROPN
ejpam-4581	241	16	,	,	PUNCT
ejpam-4581	241	17	j.	j.	PROPN
ejpam-4581	241	18	khampakdee	khampakdee	PROPN
ejpam-4581	241	19	/	/	PUNCT
ejpam-4581	241	20	eur	eur	PROPN
ejpam-4581	241	21	.	.	PUNCT
ejpam-4581	242	1	j.	j.	PROPN
ejpam-4581	242	2	pure	pure	PROPN
ejpam-4581	242	3	appl	appl	PROPN
ejpam-4581	242	4	.	.	PROPN
ejpam-4581	242	5	math	math	PROPN
ejpam-4581	242	6	,	,	PUNCT
ejpam-4581	242	7	16	16	NUM
ejpam-4581	242	8	(	(	PUNCT
ejpam-4581	242	9	1	1	NUM
ejpam-4581	242	10	)	)	PUNCT
ejpam-4581	242	11	(	(	PUNCT
ejpam-4581	242	12	2023	2023	NUM
ejpam-4581	242	13	)	)	PUNCT
ejpam-4581	242	14	,	,	PUNCT
ejpam-4581	242	15	156	156	NUM
ejpam-4581	242	16	-	-	SYM
ejpam-4581	242	17	168	168	NUM
ejpam-4581	242	18	164	164	NUM
ejpam-4581	242	19	proof	proof	NOUN
ejpam-4581	242	20	.	.	PUNCT
ejpam-4581	243	1	(	(	PUNCT
ejpam-4581	243	2	1	1	X
ejpam-4581	243	3	)	)	PUNCT
ejpam-4581	243	4	⇒	⇒	NOUN
ejpam-4581	243	5	(	(	PUNCT
ejpam-4581	243	6	2	2	NUM
ejpam-4581	243	7	):	):	PUNCT
ejpam-4581	243	8	let	let	VERB
ejpam-4581	243	9	v	v	PART
ejpam-4581	243	10	be	be	AUX
ejpam-4581	243	11	any	any	DET
ejpam-4581	243	12	θs(λ	θs(λ	NOUN
ejpam-4581	243	13	,	,	PUNCT
ejpam-4581	243	14	sp)-open	sp)-open	VERB
ejpam-4581	243	15	set	set	NOUN
ejpam-4581	243	16	of	of	ADP
ejpam-4581	243	17	y	y	PROPN
ejpam-4581	243	18	.	.	PUNCT
ejpam-4581	244	1	there	there	PRON
ejpam-4581	244	2	exists	exist	VERB
ejpam-4581	244	3	a	a	DET
ejpam-4581	244	4	family	family	NOUN
ejpam-4581	244	5	of	of	ADP
ejpam-4581	244	6	r(λ	r(λ	PROPN
ejpam-4581	244	7	,	,	PUNCT
ejpam-4581	244	8	sp)-closed	sp)-close	VERB
ejpam-4581	244	9	sets	set	NOUN
ejpam-4581	244	10	{	{	PUNCT
ejpam-4581	244	11	kγ	kγ	INTJ
ejpam-4581	244	12	|	|	ADV
ejpam-4581	244	13	γ	γ	PROPN
ejpam-4581	244	14	∈	∈	PROPN
ejpam-4581	244	15	γ	γ	X
ejpam-4581	244	16	}	}	PUNCT
ejpam-4581	244	17	such	such	ADJ
ejpam-4581	244	18	that	that	DET
ejpam-4581	244	19	v	v	NOUN
ejpam-4581	244	20	=	=	SYM
ejpam-4581	244	21	∪{kγ	∪{kγ	PROPN
ejpam-4581	244	22	|	|	ADV
ejpam-4581	244	23	γ	γ	X
ejpam-4581	244	24	∈	∈	PROPN
ejpam-4581	244	25	γ	γ	X
ejpam-4581	244	26	}	}	PUNCT
ejpam-4581	244	27	.	.	PUNCT
ejpam-4581	245	1	it	it	PRON
ejpam-4581	245	2	follows	follow	VERB
ejpam-4581	245	3	from	from	ADP
ejpam-4581	245	4	theorem	theorem	ADJ
ejpam-4581	245	5	2	2	NUM
ejpam-4581	245	6	that	that	DET
ejpam-4581	245	7	f−(v	f−(v	VERB
ejpam-4581	245	8	)	)	PUNCT
ejpam-4581	245	9	=	=	SYM
ejpam-4581	245	10	∪{f−(kγ	∪{f−(kγ	PROPN
ejpam-4581	245	11	)	)	PUNCT
ejpam-4581	245	12	|	|	ADV
ejpam-4581	245	13	γ	γ	PROPN
ejpam-4581	245	14	∈	∈	PROPN
ejpam-4581	245	15	γ	γ	X
ejpam-4581	245	16	}	}	PUNCT
ejpam-4581	245	17	is	be	AUX
ejpam-4581	245	18	(	(	PUNCT
ejpam-4581	245	19	λ	λ	X
ejpam-4581	245	20	,	,	PUNCT
ejpam-4581	245	21	sp)-open	sp)-open	ADJ
ejpam-4581	245	22	in	in	ADP
ejpam-4581	245	23	x.	x.	NOUN
ejpam-4581	245	24	(	(	PUNCT
ejpam-4581	245	25	2	2	NUM
ejpam-4581	245	26	)	)	PUNCT
ejpam-4581	245	27	⇒	⇒	NOUN
ejpam-4581	245	28	(	(	PUNCT
ejpam-4581	245	29	3	3	NUM
ejpam-4581	245	30	):	):	PUNCT
ejpam-4581	245	31	the	the	DET
ejpam-4581	245	32	proof	proof	NOUN
ejpam-4581	245	33	is	be	AUX
ejpam-4581	245	34	obvious	obvious	ADJ
ejpam-4581	245	35	.	.	PUNCT
ejpam-4581	246	1	(	(	PUNCT
ejpam-4581	246	2	3	3	X
ejpam-4581	246	3	)	)	PUNCT
ejpam-4581	246	4	⇒	⇒	NOUN
ejpam-4581	246	5	(	(	PUNCT
ejpam-4581	246	6	4	4	NUM
ejpam-4581	246	7	):	):	PUNCT
ejpam-4581	246	8	let	let	VERB
ejpam-4581	246	9	b	b	X
ejpam-4581	246	10	be	be	AUX
ejpam-4581	246	11	any	any	DET
ejpam-4581	246	12	subset	subset	NOUN
ejpam-4581	246	13	of	of	ADP
ejpam-4581	246	14	y	y	PROPN
ejpam-4581	246	15	.	.	PUNCT
ejpam-4581	247	1	then	then	ADV
ejpam-4581	247	2	[	[	X
ejpam-4581	247	3	b(λ	b(λ	X
ejpam-4581	247	4	,	,	PUNCT
ejpam-4581	247	5	sp)](λ	sp)](λ	PROPN
ejpam-4581	247	6	,	,	PUNCT
ejpam-4581	247	7	sp	sp	NOUN
ejpam-4581	247	8	)	)	PUNCT
ejpam-4581	247	9	is	be	AUX
ejpam-4581	247	10	r(λ	r(λ	NOUN
ejpam-4581	247	11	,	,	PUNCT
ejpam-4581	247	12	sp)-open	sp)-open	ADJ
ejpam-4581	247	13	and	and	CCONJ
ejpam-4581	247	14	hence	hence	ADV
ejpam-4581	247	15	[	[	X
ejpam-4581	247	16	b(λ	b(λ	PROPN
ejpam-4581	247	17	,	,	PUNCT
ejpam-4581	247	18	sp)](λ	sp)](λ	PROPN
ejpam-4581	247	19	,	,	PUNCT
ejpam-4581	247	20	sp	sp	NOUN
ejpam-4581	247	21	)	)	PUNCT
ejpam-4581	247	22	is	be	AUX
ejpam-4581	247	23	θs(λ	θs(λ	NOUN
ejpam-4581	247	24	,	,	PUNCT
ejpam-4581	247	25	sp)-open	sp)-open	VERB
ejpam-4581	247	26	in	in	ADP
ejpam-4581	247	27	y	y	PROPN
ejpam-4581	247	28	.	.	PUNCT
ejpam-4581	248	1	by	by	ADP
ejpam-4581	248	2	(	(	PUNCT
ejpam-4581	248	3	3	3	NUM
ejpam-4581	248	4	)	)	PUNCT
ejpam-4581	248	5	,	,	PUNCT
ejpam-4581	248	6	f+([b(λ	f+([b(λ	PROPN
ejpam-4581	248	7	,	,	PUNCT
ejpam-4581	248	8	sp)](λ	sp)](λ	PROPN
ejpam-4581	248	9	,	,	PUNCT
ejpam-4581	248	10	sp	sp	NOUN
ejpam-4581	248	11	)	)	PUNCT
ejpam-4581	248	12	)	)	PUNCT
ejpam-4581	248	13	is	be	AUX
ejpam-4581	248	14	(	(	PUNCT
ejpam-4581	248	15	λ	λ	X
ejpam-4581	248	16	,	,	PUNCT
ejpam-4581	248	17	sp)-closed	sp)-close	VERB
ejpam-4581	248	18	in	in	ADP
ejpam-4581	248	19	x.	x.	NOUN
ejpam-4581	248	20	thus	thus	ADV
ejpam-4581	248	21	,	,	PUNCT
ejpam-4581	248	22	[	[	X
ejpam-4581	248	23	f+([b(λ	f+([b(λ	PROPN
ejpam-4581	248	24	,	,	PUNCT
ejpam-4581	248	25	sp)](λ	sp)](λ	PROPN
ejpam-4581	248	26	,	,	PUNCT
ejpam-4581	248	27	sp	sp	NOUN
ejpam-4581	248	28	)	)	PUNCT
ejpam-4581	248	29	)	)	PUNCT
ejpam-4581	248	30	]	]	PUNCT
ejpam-4581	249	1	(	(	PUNCT
ejpam-4581	249	2	λ	λ	NOUN
ejpam-4581	249	3	,	,	PUNCT
ejpam-4581	249	4	sp	sp	NOUN
ejpam-4581	249	5	)	)	PUNCT
ejpam-4581	249	6	=	=	SYM
ejpam-4581	250	1	f+([b(λ	f+([b(λ	PROPN
ejpam-4581	250	2	,	,	PUNCT
ejpam-4581	250	3	sp)](λ	sp)](λ	PROPN
ejpam-4581	250	4	,	,	PUNCT
ejpam-4581	250	5	sp	sp	NOUN
ejpam-4581	250	6	)	)	PUNCT
ejpam-4581	250	7	)	)	PUNCT
ejpam-4581	251	1	⊆	⊆	NUM
ejpam-4581	251	2	f+(bs(λ	f+(bs(λ	NOUN
ejpam-4581	251	3	,	,	PUNCT
ejpam-4581	251	4	sp	sp	NOUN
ejpam-4581	251	5	)	)	PUNCT
ejpam-4581	251	6	)	)	PUNCT
ejpam-4581	251	7	.	.	PUNCT
ejpam-4581	252	1	(	(	PUNCT
ejpam-4581	252	2	4	4	X
ejpam-4581	252	3	)	)	PUNCT
ejpam-4581	252	4	⇒	⇒	NOUN
ejpam-4581	252	5	(	(	PUNCT
ejpam-4581	252	6	5	5	NUM
ejpam-4581	252	7	):	):	PUNCT
ejpam-4581	252	8	let	let	VERB
ejpam-4581	252	9	b	b	X
ejpam-4581	252	10	be	be	AUX
ejpam-4581	252	11	any	any	DET
ejpam-4581	252	12	subset	subset	NOUN
ejpam-4581	252	13	of	of	ADP
ejpam-4581	252	14	y	y	PROPN
ejpam-4581	252	15	.	.	PUNCT
ejpam-4581	253	1	for	for	ADP
ejpam-4581	253	2	any	any	DET
ejpam-4581	253	3	r(λ	r(λ	NOUN
ejpam-4581	253	4	,	,	PUNCT
ejpam-4581	253	5	sp)-open	sp)-open	ADJ
ejpam-4581	253	6	set	set	VERB
ejpam-4581	253	7	v	v	NOUN
ejpam-4581	253	8	with	with	ADP
ejpam-4581	253	9	b	b	PROPN
ejpam-4581	253	10	⊆	⊆	NUM
ejpam-4581	253	11	v	v	NOUN
ejpam-4581	253	12	,	,	PUNCT
ejpam-4581	253	13	we	we	PRON
ejpam-4581	253	14	have	have	VERB
ejpam-4581	253	15	[	[	X
ejpam-4581	253	16	f+(b)](λ	f+(b)](λ	NUM
ejpam-4581	253	17	,	,	PUNCT
ejpam-4581	253	18	sp	sp	NOUN
ejpam-4581	253	19	)	)	PUNCT
ejpam-4581	253	20	⊆	⊆	NUM
ejpam-4581	254	1	[	[	NOUN
ejpam-4581	254	2	f+(v	f+(v	NOUN
ejpam-4581	254	3	)	)	PUNCT
ejpam-4581	254	4	]	]	PUNCT
ejpam-4581	254	5	(	(	PUNCT
ejpam-4581	254	6	λ	λ	NOUN
ejpam-4581	254	7	,	,	PUNCT
ejpam-4581	254	8	sp	sp	NOUN
ejpam-4581	254	9	)	)	PUNCT
ejpam-4581	254	10	=	=	PUNCT
ejpam-4581	255	1	[	[	X
ejpam-4581	255	2	f+([v	f+([v	X
ejpam-4581	255	3	(	(	PUNCT
ejpam-4581	255	4	λ	λ	PROPN
ejpam-4581	255	5	,	,	PUNCT
ejpam-4581	255	6	sp)](λ	sp)](λ	PROPN
ejpam-4581	255	7	,	,	PUNCT
ejpam-4581	255	8	sp	sp	NOUN
ejpam-4581	255	9	)	)	PUNCT
ejpam-4581	255	10	)	)	PUNCT
ejpam-4581	255	11	]	]	PUNCT
ejpam-4581	255	12	(	(	PUNCT
ejpam-4581	255	13	λ	λ	NOUN
ejpam-4581	255	14	,	,	PUNCT
ejpam-4581	255	15	sp	sp	NOUN
ejpam-4581	255	16	)	)	PUNCT
ejpam-4581	255	17	⊆	⊆	NUM
ejpam-4581	255	18	f+(v	f+(v	NOUN
ejpam-4581	255	19	s(λ	s(λ	PROPN
ejpam-4581	255	20	,	,	PUNCT
ejpam-4581	255	21	sp	sp	NOUN
ejpam-4581	255	22	)	)	PUNCT
ejpam-4581	255	23	)	)	PUNCT
ejpam-4581	255	24	=	=	PUNCT
ejpam-4581	255	25	f+(v	f+(v	NOUN
ejpam-4581	255	26	)	)	PUNCT
ejpam-4581	255	27	.	.	PUNCT
ejpam-4581	256	1	thus	thus	ADV
ejpam-4581	256	2	,	,	PUNCT
ejpam-4581	256	3	[	[	X
ejpam-4581	256	4	f+(b)](λ	f+(b)](λ	VERB
ejpam-4581	256	5	,	,	PUNCT
ejpam-4581	256	6	sp	sp	NOUN
ejpam-4581	256	7	)	)	PUNCT
ejpam-4581	256	8	⊆	⊆	NUM
ejpam-4581	256	9	f+(∩{v	f+(∩{v	PROPN
ejpam-4581	256	10	∈	∈	PROPN
ejpam-4581	256	11	rλspo(x	rλspo(x	PROPN
ejpam-4581	256	12	,	,	PUNCT
ejpam-4581	256	13	τ	τ	PROPN
ejpam-4581	256	14	)	)	PUNCT
ejpam-4581	257	1	|	|	ADV
ejpam-4581	257	2	b	b	NOUN
ejpam-4581	257	3	⊆	⊆	NUM
ejpam-4581	257	4	v	v	NOUN
ejpam-4581	257	5	}	}	PUNCT
ejpam-4581	257	6	)	)	PUNCT
ejpam-4581	257	7	=	=	SYM
ejpam-4581	257	8	f+(bθs(λ	f+(bθs(λ	NOUN
ejpam-4581	257	9	,	,	PUNCT
ejpam-4581	257	10	sp	sp	NOUN
ejpam-4581	257	11	)	)	PUNCT
ejpam-4581	257	12	)	)	PUNCT
ejpam-4581	257	13	.	.	PUNCT
ejpam-4581	258	1	(	(	PUNCT
ejpam-4581	258	2	5	5	X
ejpam-4581	258	3	)	)	PUNCT
ejpam-4581	258	4	⇒	⇒	NOUN
ejpam-4581	258	5	(	(	PUNCT
ejpam-4581	258	6	1	1	NUM
ejpam-4581	258	7	):	):	PUNCT
ejpam-4581	258	8	let	let	VERB
ejpam-4581	258	9	v	v	PART
ejpam-4581	258	10	be	be	AUX
ejpam-4581	258	11	any	any	DET
ejpam-4581	258	12	s(λ	s(λ	NOUN
ejpam-4581	258	13	,	,	PUNCT
ejpam-4581	258	14	sp)-open	sp)-open	ADJ
ejpam-4581	258	15	set	set	NOUN
ejpam-4581	258	16	of	of	ADP
ejpam-4581	258	17	y	y	PROPN
ejpam-4581	258	18	.	.	PUNCT
ejpam-4581	259	1	by	by	ADP
ejpam-4581	259	2	(	(	PUNCT
ejpam-4581	259	3	5	5	NUM
ejpam-4581	259	4	)	)	PUNCT
ejpam-4581	259	5	,	,	PUNCT
ejpam-4581	259	6	x	x	X
ejpam-4581	259	7	−	−	PROPN
ejpam-4581	260	1	[	[	X
ejpam-4581	260	2	f−(v	f−(v	ADJ
ejpam-4581	260	3	(	(	PUNCT
ejpam-4581	260	4	λ	λ	PROPN
ejpam-4581	260	5	,	,	PUNCT
ejpam-4581	260	6	sp))](λ	sp))](λ	PROPN
ejpam-4581	260	7	,	,	PUNCT
ejpam-4581	260	8	sp	sp	NOUN
ejpam-4581	260	9	)	)	PUNCT
ejpam-4581	260	10	=	=	NOUN
ejpam-4581	261	1	[	[	X
ejpam-4581	261	2	f+(y	f+(y	X
ejpam-4581	261	3	−	−	PROPN
ejpam-4581	261	4	v	v	NOUN
ejpam-4581	261	5	(	(	PUNCT
ejpam-4581	261	6	λ	λ	PROPN
ejpam-4581	261	7	,	,	PUNCT
ejpam-4581	261	8	sp))](λ	sp))](λ	PROPN
ejpam-4581	261	9	,	,	PUNCT
ejpam-4581	261	10	sp	sp	NOUN
ejpam-4581	261	11	)	)	PUNCT
ejpam-4581	261	12	⊆	⊆	NUM
ejpam-4581	261	13	f+([y	f+([y	NOUN
ejpam-4581	261	14	−	−	PROPN
ejpam-4581	261	15	v	v	NOUN
ejpam-4581	261	16	(	(	PUNCT
ejpam-4581	261	17	λ	λ	PROPN
ejpam-4581	261	18	,	,	PUNCT
ejpam-4581	261	19	sp)]θs(λ	sp)]θs(λ	ADV
ejpam-4581	261	20	,	,	PUNCT
ejpam-4581	261	21	sp	sp	NOUN
ejpam-4581	261	22	)	)	PUNCT
ejpam-4581	261	23	)	)	PUNCT
ejpam-4581	262	1	=	=	PUNCT
ejpam-4581	263	1	f+(y	f+(y	NOUN
ejpam-4581	263	2	−	−	PROPN
ejpam-4581	263	3	v	v	NOUN
ejpam-4581	263	4	(	(	PUNCT
ejpam-4581	263	5	λ	λ	PROPN
ejpam-4581	263	6	,	,	PUNCT
ejpam-4581	263	7	sp	sp	NOUN
ejpam-4581	263	8	)	)	PUNCT
ejpam-4581	263	9	)	)	PUNCT
ejpam-4581	264	1	=	=	PUNCT
ejpam-4581	264	2	x	x	PUNCT
ejpam-4581	265	1	−	−	PROPN
ejpam-4581	265	2	f−(v	f−(v	NOUN
ejpam-4581	265	3	(	(	PUNCT
ejpam-4581	265	4	λ	λ	NOUN
ejpam-4581	265	5	,	,	PUNCT
ejpam-4581	265	6	sp	sp	NOUN
ejpam-4581	265	7	)	)	PUNCT
ejpam-4581	265	8	)	)	PUNCT
ejpam-4581	265	9	and	and	CCONJ
ejpam-4581	265	10	hence	hence	ADV
ejpam-4581	265	11	f−(v	f−(v	ADJ
ejpam-4581	265	12	)	)	PUNCT
ejpam-4581	265	13	⊆	⊆	NUM
ejpam-4581	265	14	f−(v	f−(v	NOUN
ejpam-4581	265	15	(	(	PUNCT
ejpam-4581	265	16	λ	λ	NOUN
ejpam-4581	265	17	,	,	PUNCT
ejpam-4581	265	18	sp	sp	NOUN
ejpam-4581	265	19	)	)	PUNCT
ejpam-4581	265	20	)	)	PUNCT
ejpam-4581	266	1	⊆	⊆	NUM
ejpam-4581	267	1	[	[	X
ejpam-4581	267	2	f−(v	f−(v	ADJ
ejpam-4581	267	3	(	(	PUNCT
ejpam-4581	267	4	λ	λ	PROPN
ejpam-4581	267	5	,	,	PUNCT
ejpam-4581	267	6	sp))](λ	sp))](λ	PROPN
ejpam-4581	267	7	,	,	PUNCT
ejpam-4581	267	8	sp	sp	NOUN
ejpam-4581	267	9	)	)	PUNCT
ejpam-4581	267	10	.	.	PUNCT
ejpam-4581	268	1	by	by	ADP
ejpam-4581	268	2	theorem	theorem	NOUN
ejpam-4581	268	3	2	2	NUM
ejpam-4581	268	4	,	,	PUNCT
ejpam-4581	268	5	f	f	PROPN
ejpam-4581	268	6	is	be	AUX
ejpam-4581	268	7	lower	low	ADJ
ejpam-4581	268	8	almost	almost	ADV
ejpam-4581	268	9	contra-(λ	contra-(λ	PROPN
ejpam-4581	268	10	,	,	PUNCT
ejpam-4581	268	11	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	268	12	.	.	PUNCT
ejpam-4581	269	1	(	(	PUNCT
ejpam-4581	269	2	5	5	X
ejpam-4581	269	3	)	)	PUNCT
ejpam-4581	269	4	⇒	⇒	NOUN
ejpam-4581	269	5	(	(	PUNCT
ejpam-4581	269	6	6	6	NUM
ejpam-4581	269	7	):	):	PUNCT
ejpam-4581	269	8	let	let	VERB
ejpam-4581	269	9	a	a	PRON
ejpam-4581	269	10	be	be	AUX
ejpam-4581	269	11	any	any	DET
ejpam-4581	269	12	subset	subset	NOUN
ejpam-4581	269	13	of	of	ADP
ejpam-4581	269	14	x	x	PROPN
ejpam-4581	269	15	and	and	CCONJ
ejpam-4581	269	16	b	b	X
ejpam-4581	269	17	=	=	SYM
ejpam-4581	269	18	f	f	PROPN
ejpam-4581	269	19	(	(	PUNCT
ejpam-4581	269	20	a	a	NOUN
ejpam-4581	269	21	)	)	PUNCT
ejpam-4581	269	22	.	.	PUNCT
ejpam-4581	270	1	then	then	ADV
ejpam-4581	270	2	a	a	DET
ejpam-4581	270	3	⊆	⊆	NUM
ejpam-4581	270	4	f+(b	f+(b	NOUN
ejpam-4581	270	5	)	)	PUNCT
ejpam-4581	270	6	and	and	CCONJ
ejpam-4581	270	7	by	by	ADP
ejpam-4581	270	8	(	(	PUNCT
ejpam-4581	270	9	5	5	NUM
ejpam-4581	270	10	)	)	PUNCT
ejpam-4581	270	11	,	,	PUNCT
ejpam-4581	270	12	a(λ	a(λ	ADV
ejpam-4581	270	13	,	,	PUNCT
ejpam-4581	270	14	sp	sp	NOUN
ejpam-4581	270	15	)	)	PUNCT
ejpam-4581	270	16	⊆	⊆	NUM
ejpam-4581	270	17	[	[	X
ejpam-4581	270	18	f+(b)](λ	f+(b)](λ	NUM
ejpam-4581	270	19	,	,	PUNCT
ejpam-4581	270	20	sp	sp	NOUN
ejpam-4581	270	21	)	)	PUNCT
ejpam-4581	270	22	⊆	⊆	NUM
ejpam-4581	270	23	f+(bθs(λ	f+(bθs(λ	NOUN
ejpam-4581	270	24	,	,	PUNCT
ejpam-4581	270	25	sp	sp	NOUN
ejpam-4581	270	26	)	)	PUNCT
ejpam-4581	270	27	)	)	PUNCT
ejpam-4581	270	28	.	.	PUNCT
ejpam-4581	271	1	thus	thus	ADV
ejpam-4581	271	2	,	,	PUNCT
ejpam-4581	271	3	f	f	PROPN
ejpam-4581	271	4	(	(	PUNCT
ejpam-4581	271	5	a(λ	a(λ	ADV
ejpam-4581	271	6	,	,	PUNCT
ejpam-4581	271	7	sp	sp	NOUN
ejpam-4581	271	8	)	)	PUNCT
ejpam-4581	271	9	)	)	PUNCT
ejpam-4581	271	10	⊆	⊆	NUM
ejpam-4581	271	11	f	f	X
ejpam-4581	271	12	(	(	PUNCT
ejpam-4581	271	13	f+(bθs(λ	f+(bθs(λ	PROPN
ejpam-4581	271	14	,	,	PUNCT
ejpam-4581	271	15	sp	sp	NOUN
ejpam-4581	271	16	)	)	PUNCT
ejpam-4581	271	17	)	)	PUNCT
ejpam-4581	271	18	)	)	PUNCT
ejpam-4581	271	19	⊆	⊆	NUM
ejpam-4581	271	20	bθs(λ	bθs(λ	NOUN
ejpam-4581	271	21	,	,	PUNCT
ejpam-4581	271	22	sp	sp	NOUN
ejpam-4581	271	23	)	)	PUNCT
ejpam-4581	271	24	=	=	PUNCT
ejpam-4581	272	1	[	[	X
ejpam-4581	272	2	f	f	X
ejpam-4581	272	3	(	(	PUNCT
ejpam-4581	272	4	a)]θs(λ	a)]θs(λ	NOUN
ejpam-4581	272	5	,	,	PUNCT
ejpam-4581	272	6	sp	sp	NOUN
ejpam-4581	272	7	)	)	PUNCT
ejpam-4581	272	8	.	.	PUNCT
ejpam-4581	273	1	(	(	PUNCT
ejpam-4581	273	2	6	6	X
ejpam-4581	273	3	)	)	PUNCT
ejpam-4581	273	4	⇒	⇒	NOUN
ejpam-4581	273	5	(	(	PUNCT
ejpam-4581	273	6	5	5	NUM
ejpam-4581	273	7	):	):	PUNCT
ejpam-4581	273	8	let	let	VERB
ejpam-4581	273	9	b	b	X
ejpam-4581	273	10	be	be	AUX
ejpam-4581	273	11	any	any	DET
ejpam-4581	273	12	subset	subset	NOUN
ejpam-4581	273	13	of	of	ADP
ejpam-4581	273	14	y	y	PROPN
ejpam-4581	273	15	.	.	PUNCT
ejpam-4581	274	1	by	by	ADP
ejpam-4581	274	2	(	(	PUNCT
ejpam-4581	274	3	6	6	NUM
ejpam-4581	274	4	)	)	PUNCT
ejpam-4581	274	5	,	,	PUNCT
ejpam-4581	274	6	we	we	PRON
ejpam-4581	274	7	have	have	VERB
ejpam-4581	274	8	f	f	X
ejpam-4581	274	9	(	(	PUNCT
ejpam-4581	274	10	[	[	X
ejpam-4581	274	11	f+(b)](λ	f+(b)](λ	NUM
ejpam-4581	274	12	,	,	PUNCT
ejpam-4581	274	13	sp	sp	NOUN
ejpam-4581	274	14	)	)	PUNCT
ejpam-4581	274	15	)	)	PUNCT
ejpam-4581	275	1	⊆	⊆	NUM
ejpam-4581	276	1	[	[	X
ejpam-4581	276	2	f	f	X
ejpam-4581	276	3	(	(	PUNCT
ejpam-4581	276	4	f+(b))]θs(λ	f+(b))]θs(λ	NOUN
ejpam-4581	276	5	,	,	PUNCT
ejpam-4581	276	6	sp	sp	NOUN
ejpam-4581	276	7	)	)	PUNCT
ejpam-4581	276	8	⊆	⊆	NUM
ejpam-4581	276	9	bθs(λ	bθs(λ	PROPN
ejpam-4581	276	10	,	,	PUNCT
ejpam-4581	276	11	sp	sp	NOUN
ejpam-4581	276	12	)	)	PUNCT
ejpam-4581	276	13	and	and	CCONJ
ejpam-4581	276	14	hence	hence	ADV
ejpam-4581	276	15	[	[	X
ejpam-4581	276	16	f+(b)](λ	f+(b)](λ	NUM
ejpam-4581	276	17	,	,	PUNCT
ejpam-4581	276	18	sp	sp	NOUN
ejpam-4581	276	19	)	)	PUNCT
ejpam-4581	276	20	⊆	⊆	NUM
ejpam-4581	276	21	f+(bθs(λ	f+(bθs(λ	NOUN
ejpam-4581	276	22	,	,	PUNCT
ejpam-4581	276	23	sp	sp	NOUN
ejpam-4581	276	24	)	)	PUNCT
ejpam-4581	276	25	)	)	PUNCT
ejpam-4581	276	26	.	.	PUNCT
ejpam-4581	277	1	corollary	corollary	ADJ
ejpam-4581	277	2	5	5	NUM
ejpam-4581	277	3	.	.	PUNCT
ejpam-4581	278	1	for	for	ADP
ejpam-4581	278	2	a	a	DET
ejpam-4581	278	3	function	function	NOUN
ejpam-4581	278	4	f	f	NOUN
ejpam-4581	278	5	:	:	PUNCT
ejpam-4581	278	6	(	(	PUNCT
ejpam-4581	278	7	x	x	X
ejpam-4581	278	8	,	,	PUNCT
ejpam-4581	278	9	τ	τ	X
ejpam-4581	278	10	)	)	PUNCT
ejpam-4581	278	11	→	→	SYM
ejpam-4581	278	12	(	(	PUNCT
ejpam-4581	278	13	y	y	PROPN
ejpam-4581	278	14	,	,	PUNCT
ejpam-4581	278	15	σ	σ	PROPN
ejpam-4581	278	16	)	)	PUNCT
ejpam-4581	278	17	,	,	PUNCT
ejpam-4581	278	18	the	the	DET
ejpam-4581	278	19	following	follow	VERB
ejpam-4581	278	20	properties	property	NOUN
ejpam-4581	278	21	are	be	AUX
ejpam-4581	278	22	equivalent	equivalent	ADJ
ejpam-4581	278	23	:	:	PUNCT
ejpam-4581	278	24	(	(	PUNCT
ejpam-4581	278	25	1	1	X
ejpam-4581	278	26	)	)	PUNCT
ejpam-4581	278	27	f	f	PROPN
ejpam-4581	278	28	is	be	AUX
ejpam-4581	278	29	almost	almost	ADV
ejpam-4581	278	30	contra-(λ	contra-(λ	PROPN
ejpam-4581	278	31	,	,	PUNCT
ejpam-4581	278	32	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	278	33	;	;	PUNCT
ejpam-4581	278	34	(	(	PUNCT
ejpam-4581	278	35	2	2	X
ejpam-4581	278	36	)	)	PUNCT
ejpam-4581	278	37	f−1(v	f−1(v	NOUN
ejpam-4581	278	38	)	)	PUNCT
ejpam-4581	278	39	is	be	AUX
ejpam-4581	278	40	(	(	PUNCT
ejpam-4581	278	41	λ	λ	INTJ
ejpam-4581	278	42	,	,	PUNCT
ejpam-4581	278	43	sp)-open	sp)-open	ADJ
ejpam-4581	278	44	in	in	ADP
ejpam-4581	278	45	x	x	PUNCT
ejpam-4581	278	46	for	for	ADP
ejpam-4581	278	47	every	every	DET
ejpam-4581	278	48	θs(λ	θs(λ	NOUN
ejpam-4581	278	49	,	,	PUNCT
ejpam-4581	278	50	sp)-open	sp)-open	VERB
ejpam-4581	278	51	set	set	VERB
ejpam-4581	278	52	v	v	NOUN
ejpam-4581	278	53	of	of	ADP
ejpam-4581	278	54	y	y	PROPN
ejpam-4581	278	55	;	;	PUNCT
ejpam-4581	278	56	(	(	PUNCT
ejpam-4581	278	57	3	3	X
ejpam-4581	278	58	)	)	PUNCT
ejpam-4581	278	59	f−1(k	f−1(k	PROPN
ejpam-4581	278	60	)	)	PUNCT
ejpam-4581	278	61	is	be	AUX
ejpam-4581	278	62	(	(	PUNCT
ejpam-4581	278	63	λ	λ	X
ejpam-4581	278	64	,	,	PUNCT
ejpam-4581	278	65	sp)-closed	sp)-close	VERB
ejpam-4581	278	66	in	in	ADP
ejpam-4581	278	67	x	x	PUNCT
ejpam-4581	278	68	for	for	ADP
ejpam-4581	278	69	every	every	DET
ejpam-4581	278	70	θs(λ	θs(λ	NOUN
ejpam-4581	278	71	,	,	PUNCT
ejpam-4581	278	72	sp)-closed	sp)-close	VERB
ejpam-4581	278	73	set	set	VERB
ejpam-4581	278	74	k	k	PROPN
ejpam-4581	278	75	of	of	ADP
ejpam-4581	278	76	y	y	PROPN
ejpam-4581	278	77	;	;	PUNCT
ejpam-4581	278	78	(	(	PUNCT
ejpam-4581	278	79	4	4	X
ejpam-4581	278	80	)	)	PUNCT
ejpam-4581	278	81	[	[	X
ejpam-4581	278	82	f−1([b(λ	f−1([b(λ	X
ejpam-4581	278	83	,	,	PUNCT
ejpam-4581	278	84	sp)](λ	sp)](λ	PROPN
ejpam-4581	278	85	,	,	PUNCT
ejpam-4581	278	86	sp	sp	NOUN
ejpam-4581	278	87	)	)	PUNCT
ejpam-4581	278	88	)	)	PUNCT
ejpam-4581	278	89	]	]	PUNCT
ejpam-4581	279	1	(	(	PUNCT
ejpam-4581	279	2	λ	λ	NOUN
ejpam-4581	279	3	,	,	PUNCT
ejpam-4581	279	4	sp	sp	NOUN
ejpam-4581	279	5	)	)	PUNCT
ejpam-4581	279	6	⊆	⊆	NUM
ejpam-4581	279	7	f−1(bs(λ	f−1(bs(λ	NOUN
ejpam-4581	279	8	,	,	PUNCT
ejpam-4581	279	9	sp	sp	NOUN
ejpam-4581	279	10	)	)	PUNCT
ejpam-4581	279	11	)	)	PUNCT
ejpam-4581	279	12	for	for	ADP
ejpam-4581	279	13	every	every	DET
ejpam-4581	279	14	subset	subset	NOUN
ejpam-4581	279	15	b	b	PROPN
ejpam-4581	279	16	of	of	ADP
ejpam-4581	279	17	y	y	PROPN
ejpam-4581	279	18	;	;	PUNCT
ejpam-4581	279	19	(	(	PUNCT
ejpam-4581	279	20	5	5	X
ejpam-4581	279	21	)	)	PUNCT
ejpam-4581	279	22	[	[	X
ejpam-4581	279	23	f−1(b)](λ	f−1(b)](λ	PROPN
ejpam-4581	279	24	,	,	PUNCT
ejpam-4581	279	25	sp	sp	NOUN
ejpam-4581	279	26	)	)	PUNCT
ejpam-4581	279	27	⊆	⊆	NUM
ejpam-4581	279	28	f−1(bθs(λ	f−1(bθs(λ	NOUN
ejpam-4581	279	29	,	,	PUNCT
ejpam-4581	279	30	sp	sp	NOUN
ejpam-4581	279	31	)	)	PUNCT
ejpam-4581	279	32	)	)	PUNCT
ejpam-4581	279	33	for	for	ADP
ejpam-4581	279	34	every	every	DET
ejpam-4581	279	35	subset	subset	NOUN
ejpam-4581	279	36	b	b	PROPN
ejpam-4581	279	37	of	of	ADP
ejpam-4581	279	38	y	y	PROPN
ejpam-4581	279	39	;	;	PUNCT
ejpam-4581	279	40	(	(	PUNCT
ejpam-4581	279	41	6	6	X
ejpam-4581	279	42	)	)	PUNCT
ejpam-4581	279	43	f(a(λ	f(a(λ	NOUN
ejpam-4581	279	44	,	,	PUNCT
ejpam-4581	279	45	sp	sp	NOUN
ejpam-4581	279	46	)	)	PUNCT
ejpam-4581	279	47	)	)	PUNCT
ejpam-4581	279	48	⊆	⊆	NUM
ejpam-4581	280	1	[	[	X
ejpam-4581	280	2	f(a)]θs(λ	f(a)]θs(λ	PROPN
ejpam-4581	280	3	,	,	PUNCT
ejpam-4581	280	4	sp	sp	NOUN
ejpam-4581	280	5	)	)	PUNCT
ejpam-4581	280	6	for	for	ADP
ejpam-4581	280	7	every	every	DET
ejpam-4581	280	8	subset	subset	NOUN
ejpam-4581	280	9	a	a	PRON
ejpam-4581	280	10	of	of	ADP
ejpam-4581	280	11	x.	x.	NOUN
ejpam-4581	280	12	definition	definition	NOUN
ejpam-4581	280	13	3	3	NUM
ejpam-4581	280	14	.	.	PUNCT
ejpam-4581	281	1	a	a	DET
ejpam-4581	281	2	multifunction	multifunction	NOUN
ejpam-4581	281	3	f	f	NOUN
ejpam-4581	281	4	:	:	PUNCT
ejpam-4581	281	5	(	(	PUNCT
ejpam-4581	281	6	x	x	X
ejpam-4581	281	7	,	,	PUNCT
ejpam-4581	281	8	τ	τ	X
ejpam-4581	281	9	)	)	PUNCT
ejpam-4581	281	10	→	→	SYM
ejpam-4581	281	11	(	(	PUNCT
ejpam-4581	281	12	y	y	PROPN
ejpam-4581	281	13	,	,	PUNCT
ejpam-4581	281	14	σ	σ	PROPN
ejpam-4581	281	15	)	)	PUNCT
ejpam-4581	281	16	is	be	AUX
ejpam-4581	281	17	said	say	VERB
ejpam-4581	281	18	to	to	PART
ejpam-4581	281	19	be	be	AUX
ejpam-4581	281	20	upper	upper	ADJ
ejpam-4581	281	21	strongly	strongly	ADV
ejpam-4581	281	22	s(λ	s(λ	NOUN
ejpam-4581	281	23	,	,	PUNCT
ejpam-4581	281	24	sp)continuous	sp)continuous	ADJ
ejpam-4581	281	25	if	if	SCONJ
ejpam-4581	281	26	,	,	PUNCT
ejpam-4581	281	27	for	for	ADP
ejpam-4581	281	28	each	each	DET
ejpam-4581	281	29	x	x	SYM
ejpam-4581	281	30	∈	∈	PROPN
ejpam-4581	281	31	x	x	X
ejpam-4581	281	32	and	and	CCONJ
ejpam-4581	281	33	each	each	DET
ejpam-4581	281	34	s(λ	s(λ	PROPN
ejpam-4581	281	35	,	,	PUNCT
ejpam-4581	281	36	sp)-open	sp)-open	VERB
ejpam-4581	281	37	set	set	VERB
ejpam-4581	281	38	v	v	NUM
ejpam-4581	281	39	of	of	ADP
ejpam-4581	281	40	y	y	PRON
ejpam-4581	281	41	such	such	ADJ
ejpam-4581	281	42	that	that	SCONJ
ejpam-4581	281	43	f	f	PROPN
ejpam-4581	281	44	(	(	PUNCT
ejpam-4581	281	45	x	x	X
ejpam-4581	281	46	)	)	PUNCT
ejpam-4581	281	47	⊆	⊆	NUM
ejpam-4581	281	48	v	v	NOUN
ejpam-4581	281	49	,	,	PUNCT
ejpam-4581	281	50	there	there	PRON
ejpam-4581	281	51	exists	exist	VERB
ejpam-4581	281	52	a	a	DET
ejpam-4581	281	53	(	(	PUNCT
ejpam-4581	281	54	λ	λ	NOUN
ejpam-4581	281	55	,	,	PUNCT
ejpam-4581	281	56	sp)-open	sp)-open	NOUN
ejpam-4581	281	57	set	set	VERB
ejpam-4581	281	58	u	u	NOUN
ejpam-4581	281	59	of	of	ADP
ejpam-4581	281	60	x	x	PUNCT
ejpam-4581	281	61	containing	contain	VERB
ejpam-4581	281	62	x	x	PUNCT
ejpam-4581	281	63	such	such	ADJ
ejpam-4581	281	64	that	that	SCONJ
ejpam-4581	281	65	f	f	PROPN
ejpam-4581	281	66	(	(	PUNCT
ejpam-4581	281	67	u	u	NOUN
ejpam-4581	281	68	)	)	PUNCT
ejpam-4581	281	69	⊆	⊆	NUM
ejpam-4581	281	70	v	v	NOUN
ejpam-4581	281	71	.	.	PUNCT
ejpam-4581	282	1	c.	c.	PROPN
ejpam-4581	282	2	boonpok	boonpok	PROPN
ejpam-4581	282	3	,	,	PUNCT
ejpam-4581	282	4	j.	j.	PROPN
ejpam-4581	282	5	khampakdee	khampakdee	PROPN
ejpam-4581	282	6	/	/	PUNCT
ejpam-4581	282	7	eur	eur	PROPN
ejpam-4581	282	8	.	.	PUNCT
ejpam-4581	283	1	j.	j.	PROPN
ejpam-4581	283	2	pure	pure	PROPN
ejpam-4581	283	3	appl	appl	PROPN
ejpam-4581	283	4	.	.	PROPN
ejpam-4581	283	5	math	math	PROPN
ejpam-4581	283	6	,	,	PUNCT
ejpam-4581	283	7	16	16	NUM
ejpam-4581	283	8	(	(	PUNCT
ejpam-4581	283	9	1	1	NUM
ejpam-4581	283	10	)	)	PUNCT
ejpam-4581	283	11	(	(	PUNCT
ejpam-4581	283	12	2023	2023	NUM
ejpam-4581	283	13	)	)	PUNCT
ejpam-4581	283	14	,	,	PUNCT
ejpam-4581	283	15	156	156	NUM
ejpam-4581	283	16	-	-	SYM
ejpam-4581	283	17	168	168	NUM
ejpam-4581	283	18	165	165	NUM
ejpam-4581	283	19	theorem	theorem	NOUN
ejpam-4581	283	20	10	10	NUM
ejpam-4581	283	21	.	.	PUNCT
ejpam-4581	284	1	for	for	ADP
ejpam-4581	284	2	a	a	DET
ejpam-4581	284	3	multifunction	multifunction	NOUN
ejpam-4581	284	4	f	f	NOUN
ejpam-4581	284	5	:	:	PUNCT
ejpam-4581	284	6	(	(	PUNCT
ejpam-4581	284	7	x	x	X
ejpam-4581	284	8	,	,	PUNCT
ejpam-4581	284	9	τ	τ	X
ejpam-4581	284	10	)	)	PUNCT
ejpam-4581	284	11	→	→	SYM
ejpam-4581	284	12	(	(	PUNCT
ejpam-4581	284	13	y	y	PROPN
ejpam-4581	284	14	,	,	PUNCT
ejpam-4581	284	15	σ	σ	PROPN
ejpam-4581	284	16	)	)	PUNCT
ejpam-4581	284	17	,	,	PUNCT
ejpam-4581	284	18	the	the	DET
ejpam-4581	284	19	following	follow	VERB
ejpam-4581	284	20	properties	property	NOUN
ejpam-4581	284	21	are	be	AUX
ejpam-4581	284	22	equivalent	equivalent	ADJ
ejpam-4581	284	23	:	:	PUNCT
ejpam-4581	284	24	(	(	PUNCT
ejpam-4581	284	25	1	1	X
ejpam-4581	284	26	)	)	PUNCT
ejpam-4581	284	27	f	f	PROPN
ejpam-4581	284	28	is	be	AUX
ejpam-4581	284	29	upper	upper	ADJ
ejpam-4581	284	30	strongly	strongly	ADV
ejpam-4581	284	31	s(λ	s(λ	NOUN
ejpam-4581	284	32	,	,	PUNCT
ejpam-4581	284	33	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	284	34	;	;	PUNCT
ejpam-4581	284	35	(	(	PUNCT
ejpam-4581	284	36	2	2	NUM
ejpam-4581	284	37	)	)	PUNCT
ejpam-4581	284	38	f+(v	f+(v	NOUN
ejpam-4581	284	39	)	)	PUNCT
ejpam-4581	285	1	is	be	AUX
ejpam-4581	285	2	(	(	PUNCT
ejpam-4581	285	3	λ	λ	INTJ
ejpam-4581	285	4	,	,	PUNCT
ejpam-4581	285	5	sp)-open	sp)-open	ADJ
ejpam-4581	285	6	in	in	ADP
ejpam-4581	285	7	x	x	PUNCT
ejpam-4581	285	8	for	for	ADP
ejpam-4581	285	9	every	every	DET
ejpam-4581	285	10	s(λ	s(λ	PROPN
ejpam-4581	285	11	,	,	PUNCT
ejpam-4581	285	12	sp)-open	sp)-open	VERB
ejpam-4581	285	13	set	set	VERB
ejpam-4581	285	14	v	v	NOUN
ejpam-4581	285	15	of	of	ADP
ejpam-4581	285	16	y	y	PROPN
ejpam-4581	285	17	;	;	PUNCT
ejpam-4581	285	18	(	(	PUNCT
ejpam-4581	285	19	3	3	X
ejpam-4581	285	20	)	)	PUNCT
ejpam-4581	285	21	f−(k	f−(k	PROPN
ejpam-4581	285	22	)	)	PUNCT
ejpam-4581	285	23	is	be	AUX
ejpam-4581	285	24	(	(	PUNCT
ejpam-4581	285	25	λ	λ	X
ejpam-4581	285	26	,	,	PUNCT
ejpam-4581	285	27	sp)-closed	sp)-close	VERB
ejpam-4581	285	28	in	in	ADP
ejpam-4581	285	29	x	x	PUNCT
ejpam-4581	285	30	for	for	ADP
ejpam-4581	285	31	every	every	DET
ejpam-4581	285	32	s(λ	s(λ	PROPN
ejpam-4581	285	33	,	,	PUNCT
ejpam-4581	285	34	sp)-closed	sp)-close	VERB
ejpam-4581	285	35	set	set	VERB
ejpam-4581	285	36	k	k	PROPN
ejpam-4581	285	37	of	of	ADP
ejpam-4581	285	38	y	y	PROPN
ejpam-4581	285	39	;	;	PUNCT
ejpam-4581	285	40	(	(	PUNCT
ejpam-4581	285	41	4	4	X
ejpam-4581	285	42	)	)	PUNCT
ejpam-4581	285	43	[	[	X
ejpam-4581	285	44	f−(b)](λ	f−(b)](λ	PROPN
ejpam-4581	285	45	,	,	PUNCT
ejpam-4581	285	46	sp	sp	NOUN
ejpam-4581	285	47	)	)	PUNCT
ejpam-4581	285	48	⊆	⊆	NUM
ejpam-4581	285	49	f−(bs(λ	f−(bs(λ	PROPN
ejpam-4581	285	50	,	,	PUNCT
ejpam-4581	285	51	sp	sp	NOUN
ejpam-4581	285	52	)	)	PUNCT
ejpam-4581	285	53	)	)	PUNCT
ejpam-4581	285	54	for	for	ADP
ejpam-4581	285	55	every	every	DET
ejpam-4581	285	56	subset	subset	NOUN
ejpam-4581	285	57	b	b	PROPN
ejpam-4581	285	58	of	of	ADP
ejpam-4581	285	59	y	y	PROPN
ejpam-4581	285	60	;	;	PUNCT
ejpam-4581	285	61	(	(	PUNCT
ejpam-4581	285	62	5	5	X
ejpam-4581	285	63	)	)	PUNCT
ejpam-4581	285	64	f+(bs(λ	f+(bs(λ	PROPN
ejpam-4581	285	65	,	,	PUNCT
ejpam-4581	285	66	sp	sp	NOUN
ejpam-4581	285	67	)	)	PUNCT
ejpam-4581	285	68	)	)	PUNCT
ejpam-4581	286	1	⊆	⊆	NUM
ejpam-4581	286	2	[	[	X
ejpam-4581	286	3	f+(b)](λ	f+(b)](λ	NUM
ejpam-4581	286	4	,	,	PUNCT
ejpam-4581	286	5	sp	sp	NOUN
ejpam-4581	286	6	)	)	PUNCT
ejpam-4581	286	7	for	for	ADP
ejpam-4581	286	8	every	every	DET
ejpam-4581	286	9	subset	subset	NOUN
ejpam-4581	286	10	b	b	PROPN
ejpam-4581	286	11	of	of	ADP
ejpam-4581	286	12	y	y	PROPN
ejpam-4581	286	13	.	.	PUNCT
ejpam-4581	287	1	proof	proof	NOUN
ejpam-4581	287	2	.	.	PUNCT
ejpam-4581	288	1	(	(	PUNCT
ejpam-4581	288	2	1	1	X
ejpam-4581	288	3	)	)	PUNCT
ejpam-4581	288	4	⇒	⇒	NOUN
ejpam-4581	288	5	(	(	PUNCT
ejpam-4581	288	6	2	2	NUM
ejpam-4581	288	7	):	):	PUNCT
ejpam-4581	288	8	let	let	VERB
ejpam-4581	288	9	v	v	PART
ejpam-4581	288	10	be	be	AUX
ejpam-4581	288	11	any	any	DET
ejpam-4581	288	12	s(λ	s(λ	NOUN
ejpam-4581	288	13	,	,	PUNCT
ejpam-4581	288	14	sp)-open	sp)-open	ADJ
ejpam-4581	288	15	set	set	NOUN
ejpam-4581	288	16	of	of	ADP
ejpam-4581	288	17	y	y	PROPN
ejpam-4581	288	18	and	and	CCONJ
ejpam-4581	288	19	x	x	PROPN
ejpam-4581	288	20	∈	∈	PROPN
ejpam-4581	288	21	f+(v	f+(v	NOUN
ejpam-4581	288	22	)	)	PUNCT
ejpam-4581	288	23	.	.	PUNCT
ejpam-4581	289	1	then	then	ADV
ejpam-4581	289	2	f	f	X
ejpam-4581	289	3	(	(	PUNCT
ejpam-4581	289	4	x	x	X
ejpam-4581	289	5	)	)	PUNCT
ejpam-4581	289	6	⊆	⊆	NUM
ejpam-4581	289	7	v	v	NOUN
ejpam-4581	289	8	.	.	PUNCT
ejpam-4581	290	1	since	since	SCONJ
ejpam-4581	290	2	f	f	PROPN
ejpam-4581	290	3	is	be	AUX
ejpam-4581	290	4	upper	upper	ADJ
ejpam-4581	290	5	strongly	strongly	ADV
ejpam-4581	290	6	s(λ	s(λ	NOUN
ejpam-4581	290	7	,	,	PUNCT
ejpam-4581	290	8	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	290	9	,	,	PUNCT
ejpam-4581	290	10	there	there	PRON
ejpam-4581	290	11	exists	exist	VERB
ejpam-4581	290	12	a	a	DET
ejpam-4581	290	13	(	(	PUNCT
ejpam-4581	290	14	λ	λ	NOUN
ejpam-4581	290	15	,	,	PUNCT
ejpam-4581	290	16	sp)-open	sp)-open	NOUN
ejpam-4581	290	17	set	set	VERB
ejpam-4581	290	18	u	u	NOUN
ejpam-4581	290	19	of	of	ADP
ejpam-4581	290	20	x	x	PUNCT
ejpam-4581	290	21	containing	contain	VERB
ejpam-4581	290	22	x	x	PUNCT
ejpam-4581	290	23	such	such	ADJ
ejpam-4581	290	24	that	that	SCONJ
ejpam-4581	290	25	u	u	NOUN
ejpam-4581	290	26	⊆	⊆	NUM
ejpam-4581	290	27	f+(v	f+(v	NOUN
ejpam-4581	290	28	)	)	PUNCT
ejpam-4581	290	29	.	.	PUNCT
ejpam-4581	291	1	thus	thus	ADV
ejpam-4581	291	2	,	,	PUNCT
ejpam-4581	291	3	f+(v	f+(v	PROPN
ejpam-4581	291	4	)	)	PUNCT
ejpam-4581	292	1	⊆	⊆	NUM
ejpam-4581	292	2	[	[	X
ejpam-4581	292	3	f+(v	f+(v	NOUN
ejpam-4581	292	4	)	)	PUNCT
ejpam-4581	292	5	]	]	PUNCT
ejpam-4581	292	6	(	(	PUNCT
ejpam-4581	292	7	λ	λ	NOUN
ejpam-4581	292	8	,	,	PUNCT
ejpam-4581	292	9	sp	sp	NOUN
ejpam-4581	292	10	)	)	PUNCT
ejpam-4581	292	11	and	and	CCONJ
ejpam-4581	292	12	hence	hence	ADV
ejpam-4581	292	13	f+(v	f+(v	PROPN
ejpam-4581	292	14	)	)	PUNCT
ejpam-4581	292	15	is	be	AUX
ejpam-4581	292	16	(	(	PUNCT
ejpam-4581	292	17	λ	λ	INTJ
ejpam-4581	292	18	,	,	PUNCT
ejpam-4581	292	19	sp)-open	sp)-open	ADJ
ejpam-4581	292	20	in	in	ADP
ejpam-4581	292	21	x.	x.	NOUN
ejpam-4581	292	22	(	(	PUNCT
ejpam-4581	292	23	2	2	NUM
ejpam-4581	292	24	)	)	PUNCT
ejpam-4581	292	25	⇒	⇒	NOUN
ejpam-4581	292	26	(	(	PUNCT
ejpam-4581	292	27	3	3	NUM
ejpam-4581	292	28	):	):	PUNCT
ejpam-4581	292	29	the	the	DET
ejpam-4581	292	30	proof	proof	NOUN
ejpam-4581	292	31	is	be	AUX
ejpam-4581	292	32	obvious	obvious	ADJ
ejpam-4581	292	33	.	.	PUNCT
ejpam-4581	293	1	(	(	PUNCT
ejpam-4581	293	2	3	3	X
ejpam-4581	293	3	)	)	PUNCT
ejpam-4581	293	4	⇒	⇒	NOUN
ejpam-4581	293	5	(	(	PUNCT
ejpam-4581	293	6	4	4	NUM
ejpam-4581	293	7	):	):	PUNCT
ejpam-4581	293	8	let	let	VERB
ejpam-4581	293	9	b	b	X
ejpam-4581	293	10	be	be	AUX
ejpam-4581	293	11	any	any	DET
ejpam-4581	293	12	subset	subset	NOUN
ejpam-4581	293	13	of	of	ADP
ejpam-4581	293	14	y	y	PROPN
ejpam-4581	293	15	.	.	PUNCT
ejpam-4581	294	1	then	then	ADV
ejpam-4581	294	2	bs(λ	bs(λ	NUM
ejpam-4581	294	3	,	,	PUNCT
ejpam-4581	294	4	sp	sp	NOUN
ejpam-4581	294	5	)	)	PUNCT
ejpam-4581	294	6	is	be	AUX
ejpam-4581	294	7	s(λ	s(λ	PROPN
ejpam-4581	294	8	,	,	PUNCT
ejpam-4581	294	9	sp)-closed	sp)-close	VERB
ejpam-4581	294	10	and	and	CCONJ
ejpam-4581	294	11	by	by	ADP
ejpam-4581	294	12	(	(	PUNCT
ejpam-4581	294	13	3	3	NUM
ejpam-4581	294	14	)	)	PUNCT
ejpam-4581	294	15	,	,	PUNCT
ejpam-4581	294	16	f−(bs(λ	f−(bs(λ	PROPN
ejpam-4581	294	17	,	,	PUNCT
ejpam-4581	294	18	sp	sp	NOUN
ejpam-4581	294	19	)	)	PUNCT
ejpam-4581	294	20	)	)	PUNCT
ejpam-4581	295	1	is	be	AUX
ejpam-4581	295	2	(	(	PUNCT
ejpam-4581	295	3	λ	λ	X
ejpam-4581	295	4	,	,	PUNCT
ejpam-4581	295	5	sp)-closed	sp)-close	VERB
ejpam-4581	295	6	in	in	ADP
ejpam-4581	295	7	x.	x.	NOUN
ejpam-4581	295	8	thus	thus	ADV
ejpam-4581	295	9	,	,	PUNCT
ejpam-4581	295	10	[	[	X
ejpam-4581	295	11	f−(b)](λ	f−(b)](λ	PROPN
ejpam-4581	295	12	,	,	PUNCT
ejpam-4581	295	13	sp	sp	NOUN
ejpam-4581	295	14	)	)	PUNCT
ejpam-4581	295	15	⊆	⊆	NUM
ejpam-4581	295	16	[	[	X
ejpam-4581	295	17	f−(bs(λ	f−(bs(λ	PROPN
ejpam-4581	295	18	,	,	PUNCT
ejpam-4581	295	19	sp))](λ	sp))](λ	PROPN
ejpam-4581	295	20	,	,	PUNCT
ejpam-4581	295	21	sp	sp	NOUN
ejpam-4581	295	22	)	)	PUNCT
ejpam-4581	295	23	=	=	SYM
ejpam-4581	295	24	f−(bs(λ	f−(bs(λ	PROPN
ejpam-4581	295	25	,	,	PUNCT
ejpam-4581	295	26	sp	sp	NOUN
ejpam-4581	295	27	)	)	PUNCT
ejpam-4581	295	28	)	)	PUNCT
ejpam-4581	295	29	.	.	PUNCT
ejpam-4581	296	1	(	(	PUNCT
ejpam-4581	296	2	4	4	X
ejpam-4581	296	3	)	)	PUNCT
ejpam-4581	296	4	⇒	⇒	NOUN
ejpam-4581	296	5	(	(	PUNCT
ejpam-4581	296	6	5	5	NUM
ejpam-4581	296	7	):	):	PUNCT
ejpam-4581	296	8	let	let	VERB
ejpam-4581	296	9	b	b	X
ejpam-4581	296	10	be	be	AUX
ejpam-4581	296	11	any	any	DET
ejpam-4581	296	12	subset	subset	NOUN
ejpam-4581	296	13	of	of	ADP
ejpam-4581	296	14	y	y	PROPN
ejpam-4581	296	15	.	.	PUNCT
ejpam-4581	297	1	by	by	ADP
ejpam-4581	297	2	(	(	PUNCT
ejpam-4581	297	3	4	4	NUM
ejpam-4581	297	4	)	)	PUNCT
ejpam-4581	297	5	,	,	PUNCT
ejpam-4581	297	6	x−	x−	PROPN
ejpam-4581	298	1	[	[	X
ejpam-4581	298	2	f+(b)](λ	f+(b)](λ	NUM
ejpam-4581	298	3	,	,	PUNCT
ejpam-4581	298	4	sp	sp	NOUN
ejpam-4581	298	5	)	)	PUNCT
ejpam-4581	298	6	=	=	PUNCT
ejpam-4581	299	1	[	[	X
ejpam-4581	299	2	x−f+(b)](λ	x−f+(b)](λ	PROPN
ejpam-4581	299	3	,	,	PUNCT
ejpam-4581	299	4	sp	sp	NOUN
ejpam-4581	299	5	)	)	PUNCT
ejpam-4581	299	6	=	=	PUNCT
ejpam-4581	300	1	[	[	X
ejpam-4581	300	2	f−(y	f−(y	NOUN
ejpam-4581	300	3	−b)](λ	−b)](λ	NOUN
ejpam-4581	300	4	,	,	PUNCT
ejpam-4581	300	5	sp	sp	NOUN
ejpam-4581	300	6	)	)	PUNCT
ejpam-4581	300	7	⊆	⊆	NUM
ejpam-4581	300	8	f−([y	f−([y	ADJ
ejpam-4581	300	9	−b]s(λ	−b]s(λ	NOUN
ejpam-4581	300	10	,	,	PUNCT
ejpam-4581	300	11	sp	sp	NOUN
ejpam-4581	300	12	)	)	PUNCT
ejpam-4581	300	13	)	)	PUNCT
ejpam-4581	301	1	=	=	PUNCT
ejpam-4581	301	2	f−(y	f−(y	NOUN
ejpam-4581	301	3	−bs(λ	−bs(λ	NOUN
ejpam-4581	301	4	,	,	PUNCT
ejpam-4581	301	5	sp	sp	NOUN
ejpam-4581	301	6	)	)	PUNCT
ejpam-4581	301	7	)	)	PUNCT
ejpam-4581	302	1	=	=	SYM
ejpam-4581	302	2	x−f+(bs(λ	x−f+(bs(λ	PROPN
ejpam-4581	302	3	,	,	PUNCT
ejpam-4581	302	4	sp	sp	NOUN
ejpam-4581	302	5	)	)	PUNCT
ejpam-4581	302	6	)	)	PUNCT
ejpam-4581	302	7	.	.	PUNCT
ejpam-4581	303	1	therefore	therefore	ADV
ejpam-4581	303	2	,	,	PUNCT
ejpam-4581	303	3	f+(bs(λ	f+(bs(λ	PROPN
ejpam-4581	303	4	,	,	PUNCT
ejpam-4581	303	5	sp	sp	NOUN
ejpam-4581	303	6	)	)	PUNCT
ejpam-4581	303	7	)	)	PUNCT
ejpam-4581	304	1	⊆	⊆	NUM
ejpam-4581	304	2	[	[	X
ejpam-4581	304	3	f+(b)](λ	f+(b)](λ	NUM
ejpam-4581	304	4	,	,	PUNCT
ejpam-4581	304	5	sp	sp	NOUN
ejpam-4581	304	6	)	)	PUNCT
ejpam-4581	304	7	.	.	PUNCT
ejpam-4581	305	1	(	(	PUNCT
ejpam-4581	305	2	5	5	X
ejpam-4581	305	3	)	)	PUNCT
ejpam-4581	305	4	⇒	⇒	NOUN
ejpam-4581	305	5	(	(	PUNCT
ejpam-4581	305	6	1	1	NUM
ejpam-4581	305	7	):	):	PUNCT
ejpam-4581	305	8	let	let	VERB
ejpam-4581	305	9	x	x	PUNCT
ejpam-4581	305	10	∈	∈	PROPN
ejpam-4581	305	11	x	x	X
ejpam-4581	305	12	and	and	CCONJ
ejpam-4581	305	13	v	v	X
ejpam-4581	305	14	be	be	AUX
ejpam-4581	305	15	any	any	DET
ejpam-4581	305	16	s(λ	s(λ	NOUN
ejpam-4581	305	17	,	,	PUNCT
ejpam-4581	305	18	sp)-open	sp)-open	ADJ
ejpam-4581	305	19	set	set	NOUN
ejpam-4581	305	20	of	of	ADP
ejpam-4581	305	21	y	y	PRON
ejpam-4581	305	22	such	such	ADJ
ejpam-4581	305	23	that	that	SCONJ
ejpam-4581	305	24	f	f	PROPN
ejpam-4581	305	25	(	(	PUNCT
ejpam-4581	305	26	x	x	X
ejpam-4581	305	27	)	)	PUNCT
ejpam-4581	305	28	⊆	⊆	NUM
ejpam-4581	305	29	v	v	NOUN
ejpam-4581	305	30	.	.	PUNCT
ejpam-4581	306	1	by	by	ADP
ejpam-4581	306	2	(	(	PUNCT
ejpam-4581	306	3	5	5	NUM
ejpam-4581	306	4	)	)	PUNCT
ejpam-4581	306	5	,	,	PUNCT
ejpam-4581	306	6	we	we	PRON
ejpam-4581	306	7	have	have	VERB
ejpam-4581	306	8	f+(v	f+(v	NOUN
ejpam-4581	306	9	)	)	PUNCT
ejpam-4581	307	1	⊆	⊆	NUM
ejpam-4581	307	2	[	[	X
ejpam-4581	307	3	f+(v	f+(v	NOUN
ejpam-4581	307	4	)	)	PUNCT
ejpam-4581	307	5	]	]	PUNCT
ejpam-4581	307	6	(	(	PUNCT
ejpam-4581	307	7	λ	λ	NOUN
ejpam-4581	307	8	,	,	PUNCT
ejpam-4581	307	9	sp	sp	NOUN
ejpam-4581	307	10	)	)	PUNCT
ejpam-4581	307	11	and	and	CCONJ
ejpam-4581	307	12	hence	hence	ADV
ejpam-4581	307	13	f+(v	f+(v	PROPN
ejpam-4581	307	14	)	)	PUNCT
ejpam-4581	307	15	is	be	AUX
ejpam-4581	307	16	(	(	PUNCT
ejpam-4581	307	17	λ	λ	INTJ
ejpam-4581	307	18	,	,	PUNCT
ejpam-4581	307	19	sp)-open	sp)-open	ADJ
ejpam-4581	307	20	in	in	ADP
ejpam-4581	307	21	x.	x.	NOUN
ejpam-4581	307	22	put	put	VERB
ejpam-4581	307	23	u	u	NOUN
ejpam-4581	307	24	=	=	NOUN
ejpam-4581	307	25	f+(v	f+(v	PROPN
ejpam-4581	307	26	)	)	PUNCT
ejpam-4581	307	27	,	,	PUNCT
ejpam-4581	307	28	then	then	ADV
ejpam-4581	307	29	u	u	NOUN
ejpam-4581	307	30	is	be	AUX
ejpam-4581	307	31	a	a	DET
ejpam-4581	307	32	(	(	PUNCT
ejpam-4581	307	33	λ	λ	NOUN
ejpam-4581	307	34	,	,	PUNCT
ejpam-4581	307	35	sp)-open	sp)-open	ADJ
ejpam-4581	307	36	set	set	NOUN
ejpam-4581	307	37	of	of	ADP
ejpam-4581	307	38	x	x	PUNCT
ejpam-4581	307	39	containing	contain	VERB
ejpam-4581	307	40	x	x	PUNCT
ejpam-4581	307	41	such	such	ADJ
ejpam-4581	307	42	that	that	SCONJ
ejpam-4581	307	43	f	f	PROPN
ejpam-4581	307	44	(	(	PUNCT
ejpam-4581	307	45	u	u	NOUN
ejpam-4581	307	46	)	)	PUNCT
ejpam-4581	307	47	⊆	⊆	NUM
ejpam-4581	307	48	v	v	NOUN
ejpam-4581	307	49	.	.	PUNCT
ejpam-4581	308	1	this	this	PRON
ejpam-4581	308	2	shows	show	VERB
ejpam-4581	308	3	that	that	SCONJ
ejpam-4581	308	4	f	f	PROPN
ejpam-4581	308	5	is	be	AUX
ejpam-4581	308	6	upper	upper	ADJ
ejpam-4581	308	7	strongly	strongly	ADV
ejpam-4581	308	8	s(λ	s(λ	NOUN
ejpam-4581	308	9	,	,	PUNCT
ejpam-4581	308	10	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	308	11	.	.	PUNCT
ejpam-4581	309	1	definition	definition	NOUN
ejpam-4581	309	2	4	4	NUM
ejpam-4581	309	3	.	.	PUNCT
ejpam-4581	310	1	a	a	DET
ejpam-4581	310	2	multifunction	multifunction	NOUN
ejpam-4581	310	3	f	f	NOUN
ejpam-4581	310	4	:	:	PUNCT
ejpam-4581	310	5	(	(	PUNCT
ejpam-4581	310	6	x	x	X
ejpam-4581	310	7	,	,	PUNCT
ejpam-4581	310	8	τ	τ	X
ejpam-4581	310	9	)	)	PUNCT
ejpam-4581	310	10	→	→	SYM
ejpam-4581	310	11	(	(	PUNCT
ejpam-4581	310	12	y	y	PROPN
ejpam-4581	310	13	,	,	PUNCT
ejpam-4581	310	14	σ	σ	PROPN
ejpam-4581	310	15	)	)	PUNCT
ejpam-4581	310	16	is	be	AUX
ejpam-4581	310	17	said	say	VERB
ejpam-4581	310	18	to	to	PART
ejpam-4581	310	19	be	be	AUX
ejpam-4581	310	20	lower	lower	ADV
ejpam-4581	310	21	strongly	strongly	ADV
ejpam-4581	310	22	s(λ	s(λ	NOUN
ejpam-4581	310	23	,	,	PUNCT
ejpam-4581	310	24	sp)continuous	sp)continuous	ADJ
ejpam-4581	310	25	if	if	SCONJ
ejpam-4581	310	26	,	,	PUNCT
ejpam-4581	310	27	for	for	ADP
ejpam-4581	310	28	each	each	DET
ejpam-4581	310	29	x	x	SYM
ejpam-4581	310	30	∈	∈	PROPN
ejpam-4581	310	31	x	x	X
ejpam-4581	310	32	and	and	CCONJ
ejpam-4581	310	33	each	each	DET
ejpam-4581	310	34	s(λ	s(λ	PROPN
ejpam-4581	310	35	,	,	PUNCT
ejpam-4581	310	36	sp)-open	sp)-open	VERB
ejpam-4581	310	37	set	set	VERB
ejpam-4581	310	38	v	v	NUM
ejpam-4581	310	39	of	of	ADP
ejpam-4581	310	40	y	y	PRON
ejpam-4581	310	41	such	such	ADJ
ejpam-4581	310	42	that	that	SCONJ
ejpam-4581	310	43	f	f	PROPN
ejpam-4581	310	44	(	(	PUNCT
ejpam-4581	310	45	x	x	NOUN
ejpam-4581	310	46	)	)	PUNCT
ejpam-4581	310	47	∩	∩	NOUN
ejpam-4581	310	48	v	v	ADP
ejpam-4581	310	49	̸=	̸=	PROPN
ejpam-4581	310	50	∅	∅	NOUN
ejpam-4581	310	51	,	,	PUNCT
ejpam-4581	310	52	there	there	PRON
ejpam-4581	310	53	exists	exist	VERB
ejpam-4581	310	54	a	a	DET
ejpam-4581	310	55	(	(	PUNCT
ejpam-4581	310	56	λ	λ	NOUN
ejpam-4581	310	57	,	,	PUNCT
ejpam-4581	310	58	sp)-open	sp)-open	NOUN
ejpam-4581	310	59	set	set	VERB
ejpam-4581	310	60	u	u	NOUN
ejpam-4581	310	61	of	of	ADP
ejpam-4581	310	62	x	x	PUNCT
ejpam-4581	310	63	containing	contain	VERB
ejpam-4581	310	64	x	x	PUNCT
ejpam-4581	311	1	such	such	ADJ
ejpam-4581	311	2	that	that	SCONJ
ejpam-4581	311	3	f	f	PROPN
ejpam-4581	311	4	(	(	PUNCT
ejpam-4581	311	5	z)∩v	z)∩v	PROPN
ejpam-4581	311	6	̸=	̸=	PROPN
ejpam-4581	311	7	∅	∅	NOUN
ejpam-4581	311	8	for	for	ADP
ejpam-4581	311	9	each	each	DET
ejpam-4581	311	10	z	z	NOUN
ejpam-4581	311	11	∈	∈	PROPN
ejpam-4581	311	12	u	u	PROPN
ejpam-4581	311	13	.	.	PUNCT
ejpam-4581	312	1	theorem	theorem	VERB
ejpam-4581	312	2	11	11	NUM
ejpam-4581	312	3	.	.	PUNCT
ejpam-4581	313	1	for	for	ADP
ejpam-4581	313	2	a	a	DET
ejpam-4581	313	3	multifunction	multifunction	NOUN
ejpam-4581	313	4	f	f	NOUN
ejpam-4581	313	5	:	:	PUNCT
ejpam-4581	313	6	(	(	PUNCT
ejpam-4581	313	7	x	x	X
ejpam-4581	313	8	,	,	PUNCT
ejpam-4581	313	9	τ	τ	X
ejpam-4581	313	10	)	)	PUNCT
ejpam-4581	313	11	→	→	SYM
ejpam-4581	313	12	(	(	PUNCT
ejpam-4581	313	13	y	y	PROPN
ejpam-4581	313	14	,	,	PUNCT
ejpam-4581	313	15	σ	σ	PROPN
ejpam-4581	313	16	)	)	PUNCT
ejpam-4581	313	17	,	,	PUNCT
ejpam-4581	313	18	the	the	DET
ejpam-4581	313	19	following	follow	VERB
ejpam-4581	313	20	properties	property	NOUN
ejpam-4581	313	21	are	be	AUX
ejpam-4581	313	22	equivalent	equivalent	ADJ
ejpam-4581	313	23	:	:	PUNCT
ejpam-4581	313	24	(	(	PUNCT
ejpam-4581	313	25	1	1	X
ejpam-4581	313	26	)	)	PUNCT
ejpam-4581	313	27	f	f	PROPN
ejpam-4581	313	28	is	be	AUX
ejpam-4581	313	29	lower	low	ADJ
ejpam-4581	313	30	strongly	strongly	ADV
ejpam-4581	313	31	s(λ	s(λ	NOUN
ejpam-4581	313	32	,	,	PUNCT
ejpam-4581	313	33	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	313	34	;	;	PUNCT
ejpam-4581	313	35	(	(	PUNCT
ejpam-4581	313	36	2	2	X
ejpam-4581	313	37	)	)	PUNCT
ejpam-4581	313	38	f−(v	f−(v	NOUN
ejpam-4581	313	39	)	)	PUNCT
ejpam-4581	313	40	is	be	AUX
ejpam-4581	313	41	(	(	PUNCT
ejpam-4581	313	42	λ	λ	INTJ
ejpam-4581	313	43	,	,	PUNCT
ejpam-4581	313	44	sp)-open	sp)-open	ADJ
ejpam-4581	313	45	in	in	ADP
ejpam-4581	313	46	x	x	PUNCT
ejpam-4581	313	47	for	for	ADP
ejpam-4581	313	48	every	every	DET
ejpam-4581	313	49	s(λ	s(λ	PROPN
ejpam-4581	313	50	,	,	PUNCT
ejpam-4581	313	51	sp)-open	sp)-open	VERB
ejpam-4581	313	52	set	set	VERB
ejpam-4581	313	53	v	v	NOUN
ejpam-4581	313	54	of	of	ADP
ejpam-4581	313	55	y	y	PROPN
ejpam-4581	313	56	;	;	PUNCT
ejpam-4581	313	57	(	(	PUNCT
ejpam-4581	313	58	3	3	X
ejpam-4581	313	59	)	)	PUNCT
ejpam-4581	313	60	f+(k	f+(k	NUM
ejpam-4581	313	61	)	)	PUNCT
ejpam-4581	314	1	is	be	AUX
ejpam-4581	314	2	(	(	PUNCT
ejpam-4581	314	3	λ	λ	X
ejpam-4581	314	4	,	,	PUNCT
ejpam-4581	314	5	sp)-closed	sp)-close	VERB
ejpam-4581	314	6	in	in	ADP
ejpam-4581	314	7	x	x	PUNCT
ejpam-4581	314	8	for	for	ADP
ejpam-4581	314	9	every	every	DET
ejpam-4581	314	10	s(λ	s(λ	PROPN
ejpam-4581	314	11	,	,	PUNCT
ejpam-4581	314	12	sp)-closed	sp)-close	VERB
ejpam-4581	314	13	set	set	VERB
ejpam-4581	314	14	k	k	PROPN
ejpam-4581	314	15	of	of	ADP
ejpam-4581	314	16	y	y	PROPN
ejpam-4581	314	17	;	;	PUNCT
ejpam-4581	314	18	(	(	PUNCT
ejpam-4581	314	19	4	4	X
ejpam-4581	314	20	)	)	PUNCT
ejpam-4581	315	1	[	[	X
ejpam-4581	315	2	f+(b)](λ	f+(b)](λ	NUM
ejpam-4581	315	3	,	,	PUNCT
ejpam-4581	315	4	sp	sp	NOUN
ejpam-4581	315	5	)	)	PUNCT
ejpam-4581	315	6	⊆	⊆	NUM
ejpam-4581	315	7	f+(bs(λ	f+(bs(λ	PROPN
ejpam-4581	315	8	,	,	PUNCT
ejpam-4581	315	9	sp	sp	NOUN
ejpam-4581	315	10	)	)	PUNCT
ejpam-4581	315	11	)	)	PUNCT
ejpam-4581	315	12	for	for	ADP
ejpam-4581	315	13	every	every	DET
ejpam-4581	315	14	subset	subset	NOUN
ejpam-4581	315	15	b	b	PROPN
ejpam-4581	315	16	of	of	ADP
ejpam-4581	315	17	y	y	PROPN
ejpam-4581	315	18	;	;	PUNCT
ejpam-4581	315	19	(	(	PUNCT
ejpam-4581	315	20	5	5	X
ejpam-4581	315	21	)	)	PUNCT
ejpam-4581	315	22	f−(bs(λ	f−(bs(λ	PROPN
ejpam-4581	315	23	,	,	PUNCT
ejpam-4581	315	24	sp	sp	NOUN
ejpam-4581	315	25	)	)	PUNCT
ejpam-4581	315	26	)	)	PUNCT
ejpam-4581	316	1	⊆	⊆	NUM
ejpam-4581	316	2	[	[	X
ejpam-4581	316	3	f−(b)](λ	f−(b)](λ	PROPN
ejpam-4581	316	4	,	,	PUNCT
ejpam-4581	316	5	sp	sp	NOUN
ejpam-4581	316	6	)	)	PUNCT
ejpam-4581	316	7	for	for	ADP
ejpam-4581	316	8	every	every	DET
ejpam-4581	316	9	subset	subset	NOUN
ejpam-4581	316	10	b	b	PROPN
ejpam-4581	316	11	of	of	ADP
ejpam-4581	316	12	y	y	PROPN
ejpam-4581	316	13	.	.	PUNCT
ejpam-4581	317	1	proof	proof	NOUN
ejpam-4581	317	2	.	.	PUNCT
ejpam-4581	318	1	the	the	DET
ejpam-4581	318	2	proof	proof	NOUN
ejpam-4581	318	3	is	be	AUX
ejpam-4581	318	4	similar	similar	ADJ
ejpam-4581	318	5	to	to	ADP
ejpam-4581	318	6	that	that	PRON
ejpam-4581	318	7	of	of	ADP
ejpam-4581	318	8	theorem	theorem	ADJ
ejpam-4581	318	9	10	10	NUM
ejpam-4581	318	10	.	.	PUNCT
ejpam-4581	319	1	c.	c.	PROPN
ejpam-4581	319	2	boonpok	boonpok	PROPN
ejpam-4581	319	3	,	,	PUNCT
ejpam-4581	319	4	j.	j.	PROPN
ejpam-4581	319	5	khampakdee	khampakdee	PROPN
ejpam-4581	319	6	/	/	PUNCT
ejpam-4581	319	7	eur	eur	PROPN
ejpam-4581	319	8	.	.	PUNCT
ejpam-4581	320	1	j.	j.	PROPN
ejpam-4581	320	2	pure	pure	PROPN
ejpam-4581	320	3	appl	appl	PROPN
ejpam-4581	320	4	.	.	PROPN
ejpam-4581	320	5	math	math	PROPN
ejpam-4581	320	6	,	,	PUNCT
ejpam-4581	320	7	16	16	NUM
ejpam-4581	320	8	(	(	PUNCT
ejpam-4581	320	9	1	1	NUM
ejpam-4581	320	10	)	)	PUNCT
ejpam-4581	320	11	(	(	PUNCT
ejpam-4581	320	12	2023	2023	NUM
ejpam-4581	320	13	)	)	PUNCT
ejpam-4581	320	14	,	,	PUNCT
ejpam-4581	320	15	156	156	NUM
ejpam-4581	320	16	-	-	SYM
ejpam-4581	320	17	168	168	NUM
ejpam-4581	320	18	166	166	NUM
ejpam-4581	320	19	definition	definition	NOUN
ejpam-4581	320	20	5	5	NUM
ejpam-4581	320	21	.	.	PUNCT
ejpam-4581	321	1	a	a	DET
ejpam-4581	321	2	topological	topological	ADJ
ejpam-4581	321	3	space	space	NOUN
ejpam-4581	321	4	(	(	PUNCT
ejpam-4581	321	5	x	x	X
ejpam-4581	321	6	,	,	PUNCT
ejpam-4581	321	7	τ	τ	X
ejpam-4581	321	8	)	)	PUNCT
ejpam-4581	321	9	is	be	AUX
ejpam-4581	321	10	called	call	VERB
ejpam-4581	321	11	strongly	strongly	ADV
ejpam-4581	321	12	s(λ	s(λ	NOUN
ejpam-4581	321	13	,	,	PUNCT
ejpam-4581	321	14	sp)-regular	sp)-regular	ADJ
ejpam-4581	321	15	if	if	SCONJ
ejpam-4581	321	16	,	,	PUNCT
ejpam-4581	321	17	for	for	ADP
ejpam-4581	321	18	each	each	DET
ejpam-4581	321	19	s(λ	s(λ	PROPN
ejpam-4581	321	20	,	,	PUNCT
ejpam-4581	321	21	sp)-closed	sp)-close	VERB
ejpam-4581	321	22	set	set	VERB
ejpam-4581	321	23	k	k	PROPN
ejpam-4581	321	24	and	and	CCONJ
ejpam-4581	321	25	each	each	DET
ejpam-4581	321	26	x	x	SYM
ejpam-4581	321	27	∈	∈	PROPN
ejpam-4581	321	28	x	x	PUNCT
ejpam-4581	321	29	−k	−k	PROPN
ejpam-4581	321	30	,	,	PUNCT
ejpam-4581	321	31	there	there	PRON
ejpam-4581	321	32	exists	exist	VERB
ejpam-4581	321	33	a	a	DET
ejpam-4581	321	34	r(λ	r(λ	NOUN
ejpam-4581	321	35	,	,	PUNCT
ejpam-4581	321	36	sp)-closed	sp)-close	VERB
ejpam-4581	321	37	set	set	VERB
ejpam-4581	321	38	f	f	PROPN
ejpam-4581	321	39	containing	contain	VERB
ejpam-4581	321	40	x	x	PUNCT
ejpam-4581	321	41	such	such	ADJ
ejpam-4581	321	42	that	that	SCONJ
ejpam-4581	321	43	f	f	NOUN
ejpam-4581	321	44	∩k	∩k	PROPN
ejpam-4581	321	45	=	=	PUNCT
ejpam-4581	322	1	∅.	∅.	PRON
ejpam-4581	322	2	lemma	lemma	PROPN
ejpam-4581	322	3	6	6	NUM
ejpam-4581	322	4	.	.	PUNCT
ejpam-4581	323	1	for	for	ADP
ejpam-4581	323	2	a	a	DET
ejpam-4581	323	3	topological	topological	ADJ
ejpam-4581	323	4	space	space	NOUN
ejpam-4581	323	5	(	(	PUNCT
ejpam-4581	323	6	x	x	X
ejpam-4581	323	7	,	,	PUNCT
ejpam-4581	323	8	τ	τ	PROPN
ejpam-4581	323	9	)	)	PUNCT
ejpam-4581	323	10	,	,	PUNCT
ejpam-4581	323	11	the	the	DET
ejpam-4581	323	12	following	follow	VERB
ejpam-4581	323	13	properties	property	NOUN
ejpam-4581	323	14	are	be	AUX
ejpam-4581	323	15	equivalent	equivalent	ADJ
ejpam-4581	323	16	:	:	PUNCT
ejpam-4581	323	17	(	(	PUNCT
ejpam-4581	323	18	1	1	X
ejpam-4581	323	19	)	)	PUNCT
ejpam-4581	323	20	(	(	PUNCT
ejpam-4581	323	21	x	x	X
ejpam-4581	323	22	,	,	PUNCT
ejpam-4581	323	23	τ	τ	X
ejpam-4581	323	24	)	)	PUNCT
ejpam-4581	323	25	is	be	AUX
ejpam-4581	323	26	strongly	strongly	ADV
ejpam-4581	323	27	s(λ	s(λ	NOUN
ejpam-4581	323	28	,	,	PUNCT
ejpam-4581	323	29	sp)-regular	sp)-regular	NOUN
ejpam-4581	323	30	;	;	PUNCT
ejpam-4581	323	31	(	(	PUNCT
ejpam-4581	323	32	2	2	X
ejpam-4581	323	33	)	)	PUNCT
ejpam-4581	323	34	for	for	ADP
ejpam-4581	323	35	each	each	DET
ejpam-4581	323	36	s(λ	s(λ	PROPN
ejpam-4581	323	37	,	,	PUNCT
ejpam-4581	323	38	sp)-open	sp)-open	VERB
ejpam-4581	323	39	set	set	VERB
ejpam-4581	323	40	w	w	PROPN
ejpam-4581	323	41	of	of	ADP
ejpam-4581	323	42	x	x	PUNCT
ejpam-4581	323	43	and	and	CCONJ
ejpam-4581	323	44	each	each	DET
ejpam-4581	323	45	x	x	SYM
ejpam-4581	323	46	∈	∈	PROPN
ejpam-4581	323	47	w	w	NOUN
ejpam-4581	323	48	,	,	PUNCT
ejpam-4581	323	49	there	there	PRON
ejpam-4581	323	50	exists	exist	VERB
ejpam-4581	323	51	a	a	DET
ejpam-4581	323	52	s(λ	s(λ	PROPN
ejpam-4581	323	53	,	,	PUNCT
ejpam-4581	323	54	sp)-open	sp)-open	NOUN
ejpam-4581	323	55	set	set	VERB
ejpam-4581	323	56	v	v	ADP
ejpam-4581	323	57	such	such	ADJ
ejpam-4581	323	58	that	that	SCONJ
ejpam-4581	323	59	x	x	SYM
ejpam-4581	323	60	∈	∈	NOUN
ejpam-4581	323	61	v	v	ADP
ejpam-4581	323	62	⊆	⊆	NUM
ejpam-4581	323	63	v	v	NOUN
ejpam-4581	323	64	(	(	PUNCT
ejpam-4581	323	65	λ	λ	NOUN
ejpam-4581	323	66	,	,	PUNCT
ejpam-4581	323	67	sp	sp	NOUN
ejpam-4581	323	68	)	)	PUNCT
ejpam-4581	323	69	⊆	⊆	NUM
ejpam-4581	323	70	w	w	NOUN
ejpam-4581	323	71	;	;	PUNCT
ejpam-4581	323	72	(	(	PUNCT
ejpam-4581	323	73	3	3	X
ejpam-4581	323	74	)	)	PUNCT
ejpam-4581	323	75	for	for	ADP
ejpam-4581	323	76	each	each	DET
ejpam-4581	323	77	s(λ	s(λ	PROPN
ejpam-4581	323	78	,	,	PUNCT
ejpam-4581	323	79	sp)-open	sp)-open	VERB
ejpam-4581	323	80	set	set	VERB
ejpam-4581	323	81	w	w	PROPN
ejpam-4581	323	82	of	of	ADP
ejpam-4581	323	83	x	x	PUNCT
ejpam-4581	323	84	and	and	CCONJ
ejpam-4581	323	85	each	each	DET
ejpam-4581	323	86	x	x	SYM
ejpam-4581	323	87	∈	∈	PROPN
ejpam-4581	323	88	w	w	NOUN
ejpam-4581	323	89	,	,	PUNCT
ejpam-4581	323	90	there	there	PRON
ejpam-4581	323	91	exists	exist	VERB
ejpam-4581	323	92	a	a	DET
ejpam-4581	323	93	r(λ	r(λ	NOUN
ejpam-4581	323	94	,	,	PUNCT
ejpam-4581	323	95	sp)-closed	sp)-close	VERB
ejpam-4581	323	96	set	set	VERB
ejpam-4581	323	97	f	f	PROPN
ejpam-4581	323	98	such	such	ADJ
ejpam-4581	323	99	that	that	SCONJ
ejpam-4581	323	100	x	x	SYM
ejpam-4581	323	101	∈	∈	NOUN
ejpam-4581	323	102	f	f	PROPN
ejpam-4581	323	103	⊆	⊆	NUM
ejpam-4581	323	104	w	w	NOUN
ejpam-4581	323	105	;	;	PUNCT
ejpam-4581	323	106	(	(	PUNCT
ejpam-4581	323	107	4	4	X
ejpam-4581	323	108	)	)	PUNCT
ejpam-4581	323	109	as(λ	as(λ	NUM
ejpam-4581	323	110	,	,	PUNCT
ejpam-4581	323	111	sp	sp	NOUN
ejpam-4581	323	112	)	)	PUNCT
ejpam-4581	323	113	=	=	SYM
ejpam-4581	323	114	aθs(λ	aθs(λ	PROPN
ejpam-4581	323	115	,	,	PUNCT
ejpam-4581	323	116	sp	sp	NOUN
ejpam-4581	323	117	)	)	PUNCT
ejpam-4581	323	118	for	for	ADP
ejpam-4581	323	119	every	every	DET
ejpam-4581	323	120	subset	subset	NOUN
ejpam-4581	323	121	a	a	PRON
ejpam-4581	323	122	of	of	ADP
ejpam-4581	323	123	x	x	PRON
ejpam-4581	323	124	;	;	PUNCT
ejpam-4581	323	125	(	(	PUNCT
ejpam-4581	323	126	5	5	X
ejpam-4581	323	127	)	)	PUNCT
ejpam-4581	323	128	every	every	DET
ejpam-4581	323	129	s(λ	s(λ	PROPN
ejpam-4581	323	130	,	,	PUNCT
ejpam-4581	323	131	sp)-open	sp)-open	ADJ
ejpam-4581	323	132	set	set	NOUN
ejpam-4581	323	133	of	of	ADP
ejpam-4581	323	134	x	x	PROPN
ejpam-4581	323	135	is	be	AUX
ejpam-4581	323	136	θs(λ	θs(λ	NOUN
ejpam-4581	323	137	,	,	PUNCT
ejpam-4581	323	138	sp)-open	sp)-open	NOUN
ejpam-4581	323	139	.	.	PUNCT
ejpam-4581	324	1	theorem	theorem	NOUN
ejpam-4581	324	2	12	12	NUM
ejpam-4581	324	3	.	.	PUNCT
ejpam-4581	325	1	let	let	AUX
ejpam-4581	325	2	(	(	PUNCT
ejpam-4581	325	3	y	y	PROPN
ejpam-4581	325	4	,	,	PUNCT
ejpam-4581	325	5	σ	σ	PROPN
ejpam-4581	325	6	)	)	PUNCT
ejpam-4581	325	7	be	be	VERB
ejpam-4581	325	8	a	a	DET
ejpam-4581	325	9	strongly	strongly	ADV
ejpam-4581	325	10	s(λ	s(λ	VERB
ejpam-4581	325	11	,	,	PUNCT
ejpam-4581	325	12	sp)-regular	sp)-regular	ADJ
ejpam-4581	325	13	space	space	NOUN
ejpam-4581	325	14	.	.	PUNCT
ejpam-4581	326	1	for	for	ADP
ejpam-4581	326	2	a	a	DET
ejpam-4581	326	3	multifunction	multifunction	NOUN
ejpam-4581	326	4	f	f	NOUN
ejpam-4581	326	5	:	:	PUNCT
ejpam-4581	326	6	(	(	PUNCT
ejpam-4581	326	7	x	x	X
ejpam-4581	326	8	,	,	PUNCT
ejpam-4581	326	9	τ	τ	X
ejpam-4581	326	10	)	)	PUNCT
ejpam-4581	326	11	→	→	SYM
ejpam-4581	326	12	(	(	PUNCT
ejpam-4581	326	13	y	y	PROPN
ejpam-4581	326	14	,	,	PUNCT
ejpam-4581	326	15	σ	σ	PROPN
ejpam-4581	326	16	)	)	PUNCT
ejpam-4581	326	17	,	,	PUNCT
ejpam-4581	326	18	the	the	DET
ejpam-4581	326	19	following	follow	VERB
ejpam-4581	326	20	properties	property	NOUN
ejpam-4581	326	21	are	be	AUX
ejpam-4581	326	22	equivalent	equivalent	ADJ
ejpam-4581	326	23	:	:	PUNCT
ejpam-4581	326	24	(	(	PUNCT
ejpam-4581	326	25	1	1	X
ejpam-4581	326	26	)	)	PUNCT
ejpam-4581	326	27	f	f	PROPN
ejpam-4581	326	28	is	be	AUX
ejpam-4581	326	29	lower	low	ADJ
ejpam-4581	326	30	strongly	strongly	ADV
ejpam-4581	326	31	s(λ	s(λ	NOUN
ejpam-4581	326	32	,	,	PUNCT
ejpam-4581	326	33	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	326	34	;	;	PUNCT
ejpam-4581	326	35	(	(	PUNCT
ejpam-4581	326	36	2	2	X
ejpam-4581	326	37	)	)	PUNCT
ejpam-4581	326	38	f+(bθs(λ	f+(bθs(λ	NOUN
ejpam-4581	326	39	,	,	PUNCT
ejpam-4581	326	40	sp	sp	NOUN
ejpam-4581	326	41	)	)	PUNCT
ejpam-4581	326	42	)	)	PUNCT
ejpam-4581	327	1	is	be	AUX
ejpam-4581	327	2	(	(	PUNCT
ejpam-4581	327	3	λ	λ	X
ejpam-4581	327	4	,	,	PUNCT
ejpam-4581	327	5	sp)-closed	sp)-close	VERB
ejpam-4581	327	6	in	in	ADP
ejpam-4581	327	7	x	x	PUNCT
ejpam-4581	327	8	for	for	ADP
ejpam-4581	327	9	every	every	DET
ejpam-4581	327	10	subset	subset	NOUN
ejpam-4581	327	11	b	b	PROPN
ejpam-4581	327	12	of	of	ADP
ejpam-4581	327	13	y	y	PROPN
ejpam-4581	327	14	;	;	PUNCT
ejpam-4581	327	15	(	(	PUNCT
ejpam-4581	327	16	3	3	X
ejpam-4581	327	17	)	)	PUNCT
ejpam-4581	327	18	f	f	PROPN
ejpam-4581	327	19	is	be	AUX
ejpam-4581	327	20	lower	low	ADJ
ejpam-4581	327	21	almost	almost	ADV
ejpam-4581	327	22	contra-(λ	contra-(λ	PROPN
ejpam-4581	327	23	,	,	PUNCT
ejpam-4581	327	24	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	327	25	.	.	PUNCT
ejpam-4581	328	1	proof	proof	NOUN
ejpam-4581	328	2	.	.	PUNCT
ejpam-4581	329	1	(	(	PUNCT
ejpam-4581	329	2	1	1	X
ejpam-4581	329	3	)	)	PUNCT
ejpam-4581	329	4	⇒	⇒	NOUN
ejpam-4581	329	5	(	(	PUNCT
ejpam-4581	329	6	2	2	NUM
ejpam-4581	329	7	):	):	PUNCT
ejpam-4581	329	8	let	let	VERB
ejpam-4581	329	9	b	b	X
ejpam-4581	329	10	be	be	AUX
ejpam-4581	329	11	any	any	DET
ejpam-4581	329	12	subset	subset	NOUN
ejpam-4581	329	13	of	of	ADP
ejpam-4581	329	14	y	y	PROPN
ejpam-4581	329	15	.	.	PUNCT
ejpam-4581	330	1	by	by	ADP
ejpam-4581	330	2	lemma	lemma	PROPN
ejpam-4581	330	3	6	6	NUM
ejpam-4581	330	4	,	,	PUNCT
ejpam-4581	330	5	bθs(λ	bθs(λ	PROPN
ejpam-4581	330	6	,	,	PUNCT
ejpam-4581	330	7	sp	sp	NOUN
ejpam-4581	330	8	)	)	PUNCT
ejpam-4581	330	9	is	be	AUX
ejpam-4581	330	10	s(λ	s(λ	PROPN
ejpam-4581	330	11	,	,	PUNCT
ejpam-4581	330	12	sp)-closed	sp)-close	VERB
ejpam-4581	330	13	and	and	CCONJ
ejpam-4581	330	14	by	by	ADP
ejpam-4581	330	15	theorem	theorem	NOUN
ejpam-4581	330	16	11	11	NUM
ejpam-4581	330	17	,	,	PUNCT
ejpam-4581	330	18	f+(bθs(λ	f+(bθs(λ	NOUN
ejpam-4581	330	19	,	,	PUNCT
ejpam-4581	330	20	sp	sp	NOUN
ejpam-4581	330	21	)	)	PUNCT
ejpam-4581	330	22	)	)	PUNCT
ejpam-4581	330	23	is	be	AUX
ejpam-4581	330	24	(	(	PUNCT
ejpam-4581	330	25	λ	λ	X
ejpam-4581	330	26	,	,	PUNCT
ejpam-4581	330	27	sp)-closed	sp)-close	VERB
ejpam-4581	330	28	.	.	PUNCT
ejpam-4581	331	1	(	(	PUNCT
ejpam-4581	331	2	2	2	X
ejpam-4581	331	3	)	)	PUNCT
ejpam-4581	331	4	⇒	⇒	NOUN
ejpam-4581	331	5	(	(	PUNCT
ejpam-4581	331	6	3	3	NUM
ejpam-4581	331	7	):	):	PUNCT
ejpam-4581	331	8	let	let	VERB
ejpam-4581	331	9	b	b	X
ejpam-4581	331	10	be	be	AUX
ejpam-4581	331	11	any	any	DET
ejpam-4581	331	12	subset	subset	NOUN
ejpam-4581	331	13	of	of	ADP
ejpam-4581	331	14	y	y	PROPN
ejpam-4581	331	15	.	.	PUNCT
ejpam-4581	332	1	by	by	ADP
ejpam-4581	332	2	(	(	PUNCT
ejpam-4581	332	3	2	2	NUM
ejpam-4581	332	4	)	)	PUNCT
ejpam-4581	332	5	,	,	PUNCT
ejpam-4581	332	6	we	we	PRON
ejpam-4581	332	7	have	have	VERB
ejpam-4581	332	8	[	[	X
ejpam-4581	332	9	f+(b)](λ	f+(b)](λ	NUM
ejpam-4581	332	10	,	,	PUNCT
ejpam-4581	332	11	sp	sp	NOUN
ejpam-4581	332	12	)	)	PUNCT
ejpam-4581	332	13	⊆	⊆	NUM
ejpam-4581	333	1	[	[	X
ejpam-4581	333	2	f+(bθs(λ	f+(bθs(λ	NOUN
ejpam-4581	333	3	,	,	PUNCT
ejpam-4581	333	4	sp))](λ	sp))](λ	PROPN
ejpam-4581	333	5	,	,	PUNCT
ejpam-4581	333	6	sp	sp	NOUN
ejpam-4581	333	7	)	)	PUNCT
ejpam-4581	333	8	=	=	NOUN
ejpam-4581	333	9	f+(bθs(λ	f+(bθs(λ	NOUN
ejpam-4581	333	10	,	,	PUNCT
ejpam-4581	333	11	sp	sp	NOUN
ejpam-4581	333	12	)	)	PUNCT
ejpam-4581	333	13	)	)	PUNCT
ejpam-4581	333	14	and	and	CCONJ
ejpam-4581	333	15	by	by	ADP
ejpam-4581	333	16	theorem	theorem	NOUN
ejpam-4581	333	17	9	9	NUM
ejpam-4581	333	18	,	,	PUNCT
ejpam-4581	333	19	f	f	PROPN
ejpam-4581	333	20	is	be	AUX
ejpam-4581	333	21	lower	low	ADJ
ejpam-4581	333	22	almost	almost	ADV
ejpam-4581	333	23	contra-(λ	contra-(λ	PROPN
ejpam-4581	333	24	,	,	PUNCT
ejpam-4581	333	25	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	333	26	.	.	PUNCT
ejpam-4581	334	1	(	(	PUNCT
ejpam-4581	334	2	3	3	X
ejpam-4581	334	3	)	)	PUNCT
ejpam-4581	334	4	⇒	⇒	NOUN
ejpam-4581	334	5	(	(	PUNCT
ejpam-4581	334	6	1	1	NUM
ejpam-4581	334	7	):	):	PUNCT
ejpam-4581	334	8	let	let	VERB
ejpam-4581	334	9	v	v	PART
ejpam-4581	334	10	be	be	AUX
ejpam-4581	334	11	any	any	DET
ejpam-4581	334	12	s(λ	s(λ	NOUN
ejpam-4581	334	13	,	,	PUNCT
ejpam-4581	334	14	sp)-open	sp)-open	ADJ
ejpam-4581	334	15	set	set	NOUN
ejpam-4581	334	16	of	of	ADP
ejpam-4581	334	17	y	y	PROPN
ejpam-4581	334	18	.	.	PUNCT
ejpam-4581	335	1	since	since	SCONJ
ejpam-4581	335	2	(	(	PUNCT
ejpam-4581	335	3	y	y	PROPN
ejpam-4581	335	4	,	,	PUNCT
ejpam-4581	335	5	σ	σ	PROPN
ejpam-4581	335	6	)	)	PUNCT
ejpam-4581	335	7	is	be	AUX
ejpam-4581	335	8	strongly	strongly	ADV
ejpam-4581	335	9	s(λ	s(λ	NOUN
ejpam-4581	335	10	,	,	PUNCT
ejpam-4581	335	11	sp)regular	sp)regular	ADJ
ejpam-4581	335	12	,	,	PUNCT
ejpam-4581	335	13	by	by	ADP
ejpam-4581	335	14	lemma	lemma	PROPN
ejpam-4581	335	15	6	6	NUM
ejpam-4581	335	16	,	,	PUNCT
ejpam-4581	335	17	v	v	NOUN
ejpam-4581	335	18	is	be	AUX
ejpam-4581	335	19	θs(λ	θs(λ	NOUN
ejpam-4581	335	20	,	,	PUNCT
ejpam-4581	335	21	sp)-open	sp)-open	NOUN
ejpam-4581	335	22	.	.	PUNCT
ejpam-4581	336	1	by	by	ADP
ejpam-4581	336	2	theorem	theorem	NOUN
ejpam-4581	336	3	9	9	NUM
ejpam-4581	336	4	,	,	PUNCT
ejpam-4581	336	5	f−(v	f−(v	ADJ
ejpam-4581	336	6	)	)	PUNCT
ejpam-4581	336	7	is	be	AUX
ejpam-4581	336	8	(	(	PUNCT
ejpam-4581	336	9	λ	λ	INTJ
ejpam-4581	336	10	,	,	PUNCT
ejpam-4581	336	11	sp)-open	sp)-open	ADJ
ejpam-4581	336	12	in	in	ADP
ejpam-4581	336	13	x.	x.	NOUN
ejpam-4581	336	14	thus	thus	ADV
ejpam-4581	336	15	,	,	PUNCT
ejpam-4581	336	16	by	by	ADP
ejpam-4581	336	17	theorem	theorem	NOUN
ejpam-4581	336	18	11	11	NUM
ejpam-4581	336	19	,	,	PUNCT
ejpam-4581	336	20	f	f	PROPN
ejpam-4581	336	21	is	be	AUX
ejpam-4581	336	22	lower	low	ADJ
ejpam-4581	336	23	strongly	strongly	ADV
ejpam-4581	336	24	s(λ	s(λ	NOUN
ejpam-4581	336	25	,	,	PUNCT
ejpam-4581	336	26	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	336	27	.	.	PUNCT
ejpam-4581	337	1	theorem	theorem	VERB
ejpam-4581	337	2	13	13	NUM
ejpam-4581	337	3	.	.	PUNCT
ejpam-4581	338	1	if	if	SCONJ
ejpam-4581	338	2	f	f	PROPN
ejpam-4581	338	3	:	:	PUNCT
ejpam-4581	338	4	(	(	PUNCT
ejpam-4581	338	5	x	x	X
ejpam-4581	338	6	,	,	PUNCT
ejpam-4581	338	7	τ	τ	X
ejpam-4581	338	8	)	)	PUNCT
ejpam-4581	338	9	→	→	SYM
ejpam-4581	338	10	(	(	PUNCT
ejpam-4581	338	11	y	y	PROPN
ejpam-4581	338	12	,	,	PUNCT
ejpam-4581	338	13	σ	σ	PROPN
ejpam-4581	338	14	)	)	PUNCT
ejpam-4581	338	15	is	be	AUX
ejpam-4581	338	16	an	an	DET
ejpam-4581	338	17	upper	upper	ADJ
ejpam-4581	338	18	strongly	strongly	ADV
ejpam-4581	338	19	s(λ	s(λ	NOUN
ejpam-4581	338	20	,	,	PUNCT
ejpam-4581	338	21	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	338	22	multifunction	multifunction	NOUN
ejpam-4581	338	23	and	and	CCONJ
ejpam-4581	338	24	g	g	NOUN
ejpam-4581	338	25	:	:	PUNCT
ejpam-4581	338	26	(	(	PUNCT
ejpam-4581	338	27	y	y	PROPN
ejpam-4581	338	28	,	,	PUNCT
ejpam-4581	338	29	σ	σ	PROPN
ejpam-4581	338	30	)	)	PUNCT
ejpam-4581	338	31	→	→	SYM
ejpam-4581	338	32	(	(	PUNCT
ejpam-4581	338	33	z	z	PROPN
ejpam-4581	338	34	,	,	PUNCT
ejpam-4581	338	35	η	η	NOUN
ejpam-4581	338	36	)	)	PUNCT
ejpam-4581	338	37	is	be	AUX
ejpam-4581	338	38	an	an	DET
ejpam-4581	338	39	upper	upper	ADJ
ejpam-4581	338	40	almost	almost	ADV
ejpam-4581	338	41	contra-(λ	contra-(λ	PROPN
ejpam-4581	338	42	,	,	PUNCT
ejpam-4581	338	43	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	338	44	multifunction	multifunction	NOUN
ejpam-4581	338	45	,	,	PUNCT
ejpam-4581	338	46	then	then	ADV
ejpam-4581	338	47	g	g	PROPN
ejpam-4581	338	48	◦	◦	NOUN
ejpam-4581	338	49	f	f	X
ejpam-4581	338	50	:	:	PUNCT
ejpam-4581	338	51	(	(	PUNCT
ejpam-4581	338	52	x	x	X
ejpam-4581	338	53	,	,	PUNCT
ejpam-4581	338	54	τ	τ	X
ejpam-4581	338	55	)	)	PUNCT
ejpam-4581	338	56	→	→	SYM
ejpam-4581	338	57	(	(	PUNCT
ejpam-4581	338	58	z	z	PROPN
ejpam-4581	338	59	,	,	PUNCT
ejpam-4581	338	60	η	η	NOUN
ejpam-4581	338	61	)	)	PUNCT
ejpam-4581	338	62	is	be	AUX
ejpam-4581	338	63	upper	upper	ADJ
ejpam-4581	338	64	almost	almost	ADV
ejpam-4581	338	65	contra-(λ	contra-(λ	PROPN
ejpam-4581	338	66	,	,	PUNCT
ejpam-4581	338	67	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	338	68	.	.	PUNCT
ejpam-4581	339	1	proof	proof	NOUN
ejpam-4581	339	2	.	.	PUNCT
ejpam-4581	340	1	let	let	VERB
ejpam-4581	340	2	k	k	PRON
ejpam-4581	340	3	be	be	AUX
ejpam-4581	340	4	any	any	DET
ejpam-4581	340	5	r(λ	r(λ	NOUN
ejpam-4581	340	6	,	,	PUNCT
ejpam-4581	340	7	sp)-closed	sp)-close	VERB
ejpam-4581	340	8	set	set	NOUN
ejpam-4581	340	9	of	of	ADP
ejpam-4581	340	10	z.	z.	PROPN
ejpam-4581	340	11	we	we	PRON
ejpam-4581	340	12	have	have	VERB
ejpam-4581	340	13	(	(	PUNCT
ejpam-4581	340	14	g	g	NOUN
ejpam-4581	340	15	◦	◦	NOUN
ejpam-4581	340	16	f	f	PROPN
ejpam-4581	340	17	)	)	PUNCT
ejpam-4581	341	1	+	+	ADJ
ejpam-4581	341	2	(	(	PUNCT
ejpam-4581	341	3	k	k	NOUN
ejpam-4581	341	4	)	)	PUNCT
ejpam-4581	341	5	=	=	SYM
ejpam-4581	341	6	f−(g+(k	f−(g+(k	NOUN
ejpam-4581	341	7	)	)	PUNCT
ejpam-4581	341	8	)	)	PUNCT
ejpam-4581	341	9	.	.	PUNCT
ejpam-4581	342	1	since	since	SCONJ
ejpam-4581	342	2	g	g	PROPN
ejpam-4581	342	3	is	be	AUX
ejpam-4581	342	4	lower	low	ADJ
ejpam-4581	342	5	almost	almost	ADV
ejpam-4581	342	6	contra-(λ	contra-(λ	PROPN
ejpam-4581	342	7	,	,	PUNCT
ejpam-4581	342	8	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	342	9	,	,	PUNCT
ejpam-4581	342	10	by	by	ADP
ejpam-4581	342	11	theorem	theorem	NOUN
ejpam-4581	342	12	1	1	NUM
ejpam-4581	342	13	,	,	PUNCT
ejpam-4581	342	14	g+(k	g+(k	NOUN
ejpam-4581	342	15	)	)	PUNCT
ejpam-4581	342	16	is	be	AUX
ejpam-4581	342	17	(	(	PUNCT
ejpam-4581	342	18	λ	λ	INTJ
ejpam-4581	342	19	,	,	PUNCT
ejpam-4581	342	20	sp)-open	sp)-open	ADJ
ejpam-4581	342	21	in	in	ADP
ejpam-4581	342	22	x	x	PUNCT
ejpam-4581	342	23	and	and	CCONJ
ejpam-4581	342	24	hence	hence	ADV
ejpam-4581	342	25	g+(k	g+(k	NOUN
ejpam-4581	342	26	)	)	PUNCT
ejpam-4581	342	27	is	be	AUX
ejpam-4581	342	28	s(λ	s(λ	PROPN
ejpam-4581	342	29	,	,	PUNCT
ejpam-4581	342	30	sp)-open	sp)-open	NOUN
ejpam-4581	342	31	.	.	PUNCT
ejpam-4581	343	1	since	since	SCONJ
ejpam-4581	343	2	f	f	PROPN
ejpam-4581	343	3	is	be	AUX
ejpam-4581	343	4	lower	low	ADJ
ejpam-4581	343	5	strongly	strongly	ADV
ejpam-4581	343	6	s(λ	s(λ	NOUN
ejpam-4581	343	7	,	,	PUNCT
ejpam-4581	343	8	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	343	9	,	,	PUNCT
ejpam-4581	343	10	by	by	ADP
ejpam-4581	343	11	theorem	theorem	NOUN
ejpam-4581	343	12	10	10	NUM
ejpam-4581	343	13	,	,	PUNCT
ejpam-4581	343	14	f+(g+(k	f+(g+(k	NOUN
ejpam-4581	343	15	)	)	PUNCT
ejpam-4581	343	16	)	)	PUNCT
ejpam-4581	343	17	is	be	AUX
ejpam-4581	343	18	(	(	PUNCT
ejpam-4581	343	19	λ	λ	INTJ
ejpam-4581	343	20	,	,	PUNCT
ejpam-4581	343	21	sp)-open	sp)-open	NOUN
ejpam-4581	343	22	.	.	PUNCT
ejpam-4581	344	1	thus	thus	ADV
ejpam-4581	344	2	,	,	PUNCT
ejpam-4581	344	3	g	g	PROPN
ejpam-4581	344	4	◦	◦	NOUN
ejpam-4581	344	5	f	f	PROPN
ejpam-4581	344	6	is	be	AUX
ejpam-4581	344	7	upper	upper	ADJ
ejpam-4581	344	8	almost	almost	ADV
ejpam-4581	344	9	contra-(λ	contra-(λ	PROPN
ejpam-4581	344	10	,	,	PUNCT
ejpam-4581	344	11	sp)continuous	sp)continuous	ADJ
ejpam-4581	344	12	.	.	PUNCT
ejpam-4581	345	1	references	reference	NOUN
ejpam-4581	345	2	167	167	NUM
ejpam-4581	345	3	theorem	theorem	NOUN
ejpam-4581	345	4	14	14	NUM
ejpam-4581	345	5	.	.	PUNCT
ejpam-4581	346	1	if	if	SCONJ
ejpam-4581	346	2	f	f	PROPN
ejpam-4581	346	3	:	:	PUNCT
ejpam-4581	346	4	(	(	PUNCT
ejpam-4581	346	5	x	x	X
ejpam-4581	346	6	,	,	PUNCT
ejpam-4581	346	7	τ	τ	X
ejpam-4581	346	8	)	)	PUNCT
ejpam-4581	346	9	→	→	SYM
ejpam-4581	346	10	(	(	PUNCT
ejpam-4581	346	11	y	y	PROPN
ejpam-4581	346	12	,	,	PUNCT
ejpam-4581	346	13	σ	σ	PROPN
ejpam-4581	346	14	)	)	PUNCT
ejpam-4581	346	15	is	be	AUX
ejpam-4581	346	16	a	a	DET
ejpam-4581	346	17	lower	low	ADJ
ejpam-4581	346	18	strongly	strongly	ADV
ejpam-4581	346	19	s(λ	s(λ	NOUN
ejpam-4581	346	20	,	,	PUNCT
ejpam-4581	346	21	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	346	22	multifunction	multifunction	NOUN
ejpam-4581	346	23	and	and	CCONJ
ejpam-4581	346	24	g	g	NOUN
ejpam-4581	346	25	:	:	PUNCT
ejpam-4581	346	26	(	(	PUNCT
ejpam-4581	346	27	y	y	PROPN
ejpam-4581	346	28	,	,	PUNCT
ejpam-4581	346	29	σ	σ	PROPN
ejpam-4581	346	30	)	)	PUNCT
ejpam-4581	346	31	→	→	SYM
ejpam-4581	346	32	(	(	PUNCT
ejpam-4581	346	33	z	z	PROPN
ejpam-4581	346	34	,	,	PUNCT
ejpam-4581	346	35	η	η	NOUN
ejpam-4581	346	36	)	)	PUNCT
ejpam-4581	346	37	is	be	AUX
ejpam-4581	346	38	a	a	DET
ejpam-4581	346	39	lower	low	ADJ
ejpam-4581	346	40	almost	almost	ADV
ejpam-4581	346	41	contra-(λ	contra-(λ	PROPN
ejpam-4581	346	42	,	,	PUNCT
ejpam-4581	346	43	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	346	44	multifunction	multifunction	NOUN
ejpam-4581	346	45	,	,	PUNCT
ejpam-4581	347	1	then	then	ADV
ejpam-4581	347	2	g	g	PROPN
ejpam-4581	347	3	◦	◦	NOUN
ejpam-4581	347	4	f	f	X
ejpam-4581	347	5	:	:	PUNCT
ejpam-4581	347	6	(	(	PUNCT
ejpam-4581	347	7	x	x	X
ejpam-4581	347	8	,	,	PUNCT
ejpam-4581	347	9	τ	τ	X
ejpam-4581	347	10	)	)	PUNCT
ejpam-4581	347	11	→	→	SYM
ejpam-4581	347	12	(	(	PUNCT
ejpam-4581	347	13	z	z	PROPN
ejpam-4581	347	14	,	,	PUNCT
ejpam-4581	347	15	η	η	NOUN
ejpam-4581	347	16	)	)	PUNCT
ejpam-4581	347	17	is	be	AUX
ejpam-4581	347	18	lower	low	ADJ
ejpam-4581	347	19	almost	almost	ADV
ejpam-4581	347	20	contra-(λ	contra-(λ	PROPN
ejpam-4581	347	21	,	,	PUNCT
ejpam-4581	347	22	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	347	23	.	.	PUNCT
ejpam-4581	348	1	proof	proof	NOUN
ejpam-4581	348	2	.	.	PUNCT
ejpam-4581	349	1	the	the	DET
ejpam-4581	349	2	proof	proof	NOUN
ejpam-4581	349	3	is	be	AUX
ejpam-4581	349	4	similar	similar	ADJ
ejpam-4581	349	5	to	to	ADP
ejpam-4581	349	6	that	that	PRON
ejpam-4581	349	7	of	of	ADP
ejpam-4581	349	8	theorem	theorem	ADJ
ejpam-4581	349	9	13	13	NUM
ejpam-4581	349	10	.	.	PUNCT
ejpam-4581	350	1	acknowledgements	acknowledgement	NOUN
ejpam-4581	350	2	this	this	DET
ejpam-4581	350	3	research	research	NOUN
ejpam-4581	350	4	project	project	NOUN
ejpam-4581	350	5	was	be	AUX
ejpam-4581	350	6	financially	financially	ADV
ejpam-4581	350	7	supported	support	VERB
ejpam-4581	350	8	by	by	ADP
ejpam-4581	350	9	mahasarakham	mahasarakham	PROPN
ejpam-4581	350	10	university	university	PROPN
ejpam-4581	350	11	.	.	PUNCT
ejpam-4581	351	1	references	reference	NOUN
ejpam-4581	351	2	[	[	X
ejpam-4581	351	3	1	1	NUM
ejpam-4581	351	4	]	]	PUNCT
ejpam-4581	351	5	d.	d.	PROPN
ejpam-4581	351	6	andrijević.	andrijević.	PROPN
ejpam-4581	351	7	on	on	ADP
ejpam-4581	351	8	b	b	X
ejpam-4581	351	9	-	-	PUNCT
ejpam-4581	351	10	open	open	ADJ
ejpam-4581	351	11	sets	set	NOUN
ejpam-4581	351	12	.	.	PUNCT
ejpam-4581	352	1	matematički	matematički	PROPN
ejpam-4581	352	2	vesnik	vesnik	PROPN
ejpam-4581	352	3	,	,	PUNCT
ejpam-4581	352	4	48:59–64	48:59–64	PROPN
ejpam-4581	352	5	,	,	PUNCT
ejpam-4581	352	6	1996	1996	NUM
ejpam-4581	352	7	.	.	PUNCT
ejpam-4581	353	1	[	[	X
ejpam-4581	353	2	2	2	NUM
ejpam-4581	353	3	]	]	PUNCT
ejpam-4581	353	4	c.	c.	PROPN
ejpam-4581	353	5	berge	berge	PROPN
ejpam-4581	353	6	.	.	PUNCT
ejpam-4581	353	7	espaces	espace	VERB
ejpam-4581	353	8	topologiques	topologique	NOUN
ejpam-4581	353	9	fonctions	fonction	NOUN
ejpam-4581	353	10	multivoques	multivoque	NOUN
ejpam-4581	353	11	.	.	PUNCT
ejpam-4581	354	1	dunod	dunod	PROPN
ejpam-4581	354	2	,	,	PUNCT
ejpam-4581	354	3	paris	paris	PROPN
ejpam-4581	354	4	,	,	PUNCT
ejpam-4581	354	5	1959	1959	NUM
ejpam-4581	354	6	.	.	PUNCT
ejpam-4581	355	1	[	[	X
ejpam-4581	355	2	3	3	X
ejpam-4581	355	3	]	]	PUNCT
ejpam-4581	355	4	c.	c.	PROPN
ejpam-4581	355	5	boonpok	boonpok	PROPN
ejpam-4581	355	6	.	.	PUNCT
ejpam-4581	356	1	(	(	PUNCT
ejpam-4581	356	2	λ	λ	NOUN
ejpam-4581	356	3	,	,	PUNCT
ejpam-4581	356	4	sp)-closed	sp)-close	VERB
ejpam-4581	356	5	sets	set	NOUN
ejpam-4581	356	6	and	and	CCONJ
ejpam-4581	356	7	related	related	ADJ
ejpam-4581	356	8	topics	topic	NOUN
ejpam-4581	356	9	in	in	ADP
ejpam-4581	356	10	topological	topological	ADJ
ejpam-4581	356	11	spaces	space	NOUN
ejpam-4581	356	12	.	.	PUNCT
ejpam-4581	357	1	wseas	wseas	VERB
ejpam-4581	357	2	transactions	transaction	NOUN
ejpam-4581	357	3	on	on	ADP
ejpam-4581	357	4	mathematics	mathematic	NOUN
ejpam-4581	357	5	,	,	PUNCT
ejpam-4581	357	6	19:321–322	19:321–322	PROPN
ejpam-4581	357	7	,	,	PUNCT
ejpam-4581	357	8	2020	2020	NUM
ejpam-4581	357	9	.	.	PUNCT
ejpam-4581	358	1	[	[	X
ejpam-4581	358	2	4	4	NUM
ejpam-4581	358	3	]	]	PUNCT
ejpam-4581	358	4	c.	c.	PROPN
ejpam-4581	358	5	boonpok	boonpok	PROPN
ejpam-4581	358	6	and	and	CCONJ
ejpam-4581	358	7	j.	j.	PROPN
ejpam-4581	358	8	khampakdee	khampakdee	PROPN
ejpam-4581	358	9	.	.	PUNCT
ejpam-4581	359	1	(	(	PUNCT
ejpam-4581	359	2	λ	λ	NOUN
ejpam-4581	359	3	,	,	PUNCT
ejpam-4581	359	4	sp)-open	sp)-open	ADJ
ejpam-4581	359	5	sets	set	NOUN
ejpam-4581	359	6	in	in	ADP
ejpam-4581	359	7	topological	topological	ADJ
ejpam-4581	359	8	spaces	space	NOUN
ejpam-4581	359	9	.	.	PUNCT
ejpam-4581	360	1	european	european	ADJ
ejpam-4581	360	2	journal	journal	PROPN
ejpam-4581	360	3	of	of	ADP
ejpam-4581	360	4	pure	pure	ADJ
ejpam-4581	360	5	and	and	CCONJ
ejpam-4581	360	6	applied	applied	ADJ
ejpam-4581	360	7	mathematics	mathematic	NOUN
ejpam-4581	360	8	,	,	PUNCT
ejpam-4581	360	9	15(2):572–588	15(2):572–588	NUM
ejpam-4581	360	10	,	,	PUNCT
ejpam-4581	360	11	2022	2022	NUM
ejpam-4581	360	12	.	.	PUNCT
ejpam-4581	361	1	[	[	X
ejpam-4581	361	2	5	5	X
ejpam-4581	361	3	]	]	PUNCT
ejpam-4581	361	4	c.	c.	PROPN
ejpam-4581	361	5	boonpok	boonpok	PROPN
ejpam-4581	361	6	and	and	CCONJ
ejpam-4581	361	7	j.	j.	PROPN
ejpam-4581	361	8	khampakdee	khampakdee	PROPN
ejpam-4581	361	9	.	.	PUNCT
ejpam-4581	362	1	on	on	ADP
ejpam-4581	362	2	almost	almost	ADV
ejpam-4581	362	3	α(λ	α(λ	PROPN
ejpam-4581	362	4	,	,	PUNCT
ejpam-4581	362	5	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	362	6	multifunctions	multifunction	NOUN
ejpam-4581	362	7	.	.	PUNCT
ejpam-4581	363	1	european	european	PROPN
ejpam-4581	363	2	journal	journal	PROPN
ejpam-4581	363	3	of	of	ADP
ejpam-4581	363	4	pure	pure	ADJ
ejpam-4581	363	5	and	and	CCONJ
ejpam-4581	363	6	applied	applied	ADJ
ejpam-4581	363	7	mathematics	mathematic	NOUN
ejpam-4581	363	8	,	,	PUNCT
ejpam-4581	363	9	15(2):626–634	15(2):626–634	PROPN
ejpam-4581	363	10	,	,	PUNCT
ejpam-4581	363	11	2022	2022	NUM
ejpam-4581	363	12	.	.	PUNCT
ejpam-4581	364	1	[	[	X
ejpam-4581	364	2	6	6	NUM
ejpam-4581	364	3	]	]	PUNCT
ejpam-4581	364	4	c.	c.	PROPN
ejpam-4581	364	5	boonpok	boonpok	PROPN
ejpam-4581	364	6	,	,	PUNCT
ejpam-4581	364	7	c.	c.	PROPN
ejpam-4581	364	8	viriyapong	viriyapong	PROPN
ejpam-4581	364	9	,	,	PUNCT
ejpam-4581	364	10	and	and	CCONJ
ejpam-4581	364	11	m.	m.	NOUN
ejpam-4581	364	12	thongmoon	thongmoon	NOUN
ejpam-4581	364	13	.	.	PUNCT
ejpam-4581	365	1	on	on	ADP
ejpam-4581	365	2	upper	upper	ADJ
ejpam-4581	365	3	and	and	CCONJ
ejpam-4581	365	4	lower	low	ADJ
ejpam-4581	365	5	(	(	PUNCT
ejpam-4581	365	6	τ1	τ1	NOUN
ejpam-4581	365	7	,	,	PUNCT
ejpam-4581	365	8	τ2)precontinuous	τ2)precontinuous	ADJ
ejpam-4581	365	9	multifunctions	multifunction	NOUN
ejpam-4581	365	10	.	.	PUNCT
ejpam-4581	366	1	journal	journal	PROPN
ejpam-4581	366	2	of	of	ADP
ejpam-4581	366	3	mathematics	mathematics	PROPN
ejpam-4581	366	4	and	and	CCONJ
ejpam-4581	366	5	computer	computer	NOUN
ejpam-4581	366	6	science	science	NOUN
ejpam-4581	366	7	,	,	PUNCT
ejpam-4581	366	8	18:282–293	18:282–293	NUM
ejpam-4581	366	9	,	,	PUNCT
ejpam-4581	366	10	2018	2018	NUM
ejpam-4581	366	11	.	.	PUNCT
ejpam-4581	367	1	[	[	X
ejpam-4581	367	2	7	7	X
ejpam-4581	367	3	]	]	PUNCT
ejpam-4581	367	4	m.	m.	NOUN
ejpam-4581	367	5	caldas	caldas	PROPN
ejpam-4581	367	6	and	and	CCONJ
ejpam-4581	367	7	s.	s.	PROPN
ejpam-4581	367	8	jafari	jafari	PROPN
ejpam-4581	367	9	.	.	PUNCT
ejpam-4581	368	1	some	some	DET
ejpam-4581	368	2	properties	property	NOUN
ejpam-4581	368	3	of	of	ADP
ejpam-4581	368	4	contra	contra	PROPN
ejpam-4581	368	5	-	-	PUNCT
ejpam-4581	368	6	β	β	ADJ
ejpam-4581	368	7	-	-	ADJ
ejpam-4581	368	8	continuous	continuous	ADJ
ejpam-4581	368	9	functions	function	NOUN
ejpam-4581	368	10	.	.	PUNCT
ejpam-4581	369	1	memoirs	memoir	NOUN
ejpam-4581	369	2	of	of	ADP
ejpam-4581	369	3	the	the	DET
ejpam-4581	369	4	faculty	faculty	NOUN
ejpam-4581	369	5	of	of	ADP
ejpam-4581	369	6	science	science	NOUN
ejpam-4581	369	7	,	,	PUNCT
ejpam-4581	369	8	kochi	kochi	PROPN
ejpam-4581	369	9	university	university	PROPN
ejpam-4581	369	10	.	.	PUNCT
ejpam-4581	370	1	series	series	PROPN
ejpam-4581	370	2	a	a	PROPN
ejpam-4581	370	3	,	,	PUNCT
ejpam-4581	370	4	mathematics	mathematic	NOUN
ejpam-4581	370	5	,	,	PUNCT
ejpam-4581	370	6	22:19–28	22:19–28	NUM
ejpam-4581	370	7	,	,	PUNCT
ejpam-4581	370	8	2001	2001	NUM
ejpam-4581	370	9	.	.	PUNCT
ejpam-4581	371	1	[	[	X
ejpam-4581	371	2	8	8	X
ejpam-4581	371	3	]	]	PUNCT
ejpam-4581	371	4	j.	j.	PROPN
ejpam-4581	371	5	dontchev	dontchev	PROPN
ejpam-4581	371	6	.	.	PUNCT
ejpam-4581	372	1	contra	contra	ADJ
ejpam-4581	372	2	-	-	ADJ
ejpam-4581	372	3	continuous	continuous	ADJ
ejpam-4581	372	4	functions	function	NOUN
ejpam-4581	372	5	and	and	CCONJ
ejpam-4581	372	6	strongly	strongly	ADV
ejpam-4581	372	7	s	s	NOUN
ejpam-4581	372	8	-	-	PUNCT
ejpam-4581	372	9	closed	closed	ADJ
ejpam-4581	372	10	spaces	space	NOUN
ejpam-4581	372	11	.	.	PUNCT
ejpam-4581	373	1	international	international	ADJ
ejpam-4581	373	2	journal	journal	PROPN
ejpam-4581	373	3	of	of	ADP
ejpam-4581	373	4	mathematics	mathematics	PROPN
ejpam-4581	373	5	and	and	CCONJ
ejpam-4581	373	6	mathematical	mathematical	ADJ
ejpam-4581	373	7	sciences	science	NOUN
ejpam-4581	373	8	,	,	PUNCT
ejpam-4581	373	9	19(2):303–310	19(2):303–310	NUM
ejpam-4581	373	10	,	,	PUNCT
ejpam-4581	373	11	1996	1996	NUM
ejpam-4581	373	12	.	.	PUNCT
ejpam-4581	374	1	[	[	X
ejpam-4581	374	2	9	9	NUM
ejpam-4581	374	3	]	]	PUNCT
ejpam-4581	374	4	j.	j.	PROPN
ejpam-4581	374	5	dontchev	dontchev	PROPN
ejpam-4581	374	6	,	,	PUNCT
ejpam-4581	374	7	m.	m.	NOUN
ejpam-4581	374	8	ganster	ganster	NOUN
ejpam-4581	374	9	,	,	PUNCT
ejpam-4581	374	10	and	and	CCONJ
ejpam-4581	374	11	i.	i.	PROPN
ejpam-4581	374	12	reilly	reilly	PROPN
ejpam-4581	374	13	.	.	PUNCT
ejpam-4581	375	1	more	more	ADV
ejpam-4581	375	2	on	on	ADP
ejpam-4581	375	3	almost	almost	ADV
ejpam-4581	375	4	s	s	NOUN
ejpam-4581	375	5	-	-	NOUN
ejpam-4581	375	6	continuity	continuity	NOUN
ejpam-4581	375	7	.	.	PUNCT
ejpam-4581	376	1	indian	indian	ADJ
ejpam-4581	376	2	journal	journal	PROPN
ejpam-4581	376	3	of	of	ADP
ejpam-4581	376	4	mathematics	mathematics	PROPN
ejpam-4581	376	5	,	,	PUNCT
ejpam-4581	376	6	41:139–146	41:139–146	PROPN
ejpam-4581	376	7	,	,	PUNCT
ejpam-4581	376	8	1999	1999	NUM
ejpam-4581	376	9	.	.	PUNCT
ejpam-4581	377	1	[	[	X
ejpam-4581	377	2	10	10	NUM
ejpam-4581	377	3	]	]	X
ejpam-4581	377	4	j.	j.	PROPN
ejpam-4581	377	5	dontchev	dontchev	PROPN
ejpam-4581	377	6	and	and	CCONJ
ejpam-4581	377	7	t.	t.	PROPN
ejpam-4581	377	8	noiri	noiri	PROPN
ejpam-4581	377	9	.	.	PUNCT
ejpam-4581	378	1	contra	contra	ADJ
ejpam-4581	378	2	-	-	ADJ
ejpam-4581	378	3	semicontinuous	semicontinuous	ADJ
ejpam-4581	378	4	functions	function	NOUN
ejpam-4581	378	5	.	.	PUNCT
ejpam-4581	379	1	mathematica	mathematica	PROPN
ejpam-4581	379	2	pannonica	pannonica	PROPN
ejpam-4581	379	3	,	,	PUNCT
ejpam-4581	379	4	10(2):159–168	10(2):159–168	PROPN
ejpam-4581	379	5	,	,	PUNCT
ejpam-4581	379	6	1999	1999	NUM
ejpam-4581	379	7	.	.	PUNCT
ejpam-4581	380	1	[	[	X
ejpam-4581	380	2	11	11	NUM
ejpam-4581	380	3	]	]	X
ejpam-4581	380	4	e.	e.	PROPN
ejpam-4581	380	5	ekici	ekici	PROPN
ejpam-4581	380	6	.	.	PUNCT
ejpam-4581	381	1	almost	almost	ADV
ejpam-4581	381	2	contra	contra	ADJ
ejpam-4581	381	3	-	-	ADJ
ejpam-4581	381	4	precontinuous	precontinuous	ADJ
ejpam-4581	381	5	functions	function	NOUN
ejpam-4581	381	6	.	.	PUNCT
ejpam-4581	382	1	bulletin	bulletin	NOUN
ejpam-4581	382	2	of	of	ADP
ejpam-4581	382	3	the	the	DET
ejpam-4581	382	4	malaysian	malaysian	PROPN
ejpam-4581	382	5	mathematical	mathematical	PROPN
ejpam-4581	382	6	sciences	sciences	PROPN
ejpam-4581	382	7	society	society	NOUN
ejpam-4581	382	8	,	,	PUNCT
ejpam-4581	382	9	27:53–65	27:53–65	NUM
ejpam-4581	382	10	,	,	PUNCT
ejpam-4581	382	11	2004	2004	NUM
ejpam-4581	382	12	.	.	PUNCT
ejpam-4581	383	1	[	[	X
ejpam-4581	383	2	12	12	NUM
ejpam-4581	383	3	]	]	X
ejpam-4581	383	4	e.	e.	PROPN
ejpam-4581	383	5	ekici	ekici	PROPN
ejpam-4581	383	6	,	,	PUNCT
ejpam-4581	383	7	s.	s.	PROPN
ejpam-4581	383	8	jafari	jafari	PROPN
ejpam-4581	383	9	,	,	PUNCT
ejpam-4581	383	10	and	and	CCONJ
ejpam-4581	383	11	t.	t.	PROPN
ejpam-4581	383	12	noiri	noiri	PROPN
ejpam-4581	383	13	.	.	PUNCT
ejpam-4581	384	1	on	on	ADP
ejpam-4581	384	2	upper	upper	ADJ
ejpam-4581	384	3	and	and	CCONJ
ejpam-4581	384	4	lower	low	ADJ
ejpam-4581	384	5	contra	contra	ADJ
ejpam-4581	384	6	-	-	ADJ
ejpam-4581	384	7	continuous	continuous	ADJ
ejpam-4581	384	8	multifunctions	multifunction	NOUN
ejpam-4581	384	9	.	.	PUNCT
ejpam-4581	385	1	analele	analele	ADP
ejpam-4581	385	2	stiintifice	stiintifice	PROPN
ejpam-4581	385	3	ale	ale	PROPN
ejpam-4581	385	4	universitatii	universitatii	PROPN
ejpam-4581	386	1	al	al	PROPN
ejpam-4581	386	2	i	i	PRON
ejpam-4581	386	3	cuza	cuza	VERB
ejpam-4581	386	4	din	din	VERB
ejpam-4581	386	5	iasi	iasi	PROPN
ejpam-4581	386	6	-	-	PUNCT
ejpam-4581	386	7	matematica	matematica	PROPN
ejpam-4581	386	8	,	,	PUNCT
ejpam-4581	386	9	54(1):75–85	54(1):75–85	NUM
ejpam-4581	386	10	,	,	PUNCT
ejpam-4581	386	11	2008	2008	NUM
ejpam-4581	386	12	.	.	PUNCT
ejpam-4581	387	1	references	reference	NOUN
ejpam-4581	387	2	168	168	NUM
ejpam-4581	387	3	[	[	X
ejpam-4581	387	4	13	13	NUM
ejpam-4581	387	5	]	]	PUNCT
ejpam-4581	387	6	e.	e.	PROPN
ejpam-4581	387	7	ekici	ekici	PROPN
ejpam-4581	387	8	,	,	PUNCT
ejpam-4581	387	9	s.	s.	PROPN
ejpam-4581	387	10	jafari	jafari	PROPN
ejpam-4581	387	11	,	,	PUNCT
ejpam-4581	387	12	and	and	CCONJ
ejpam-4581	387	13	v.	v.	ADP
ejpam-4581	387	14	popa	popa	NOUN
ejpam-4581	387	15	.	.	PUNCT
ejpam-4581	388	1	on	on	ADP
ejpam-4581	388	2	almost	almost	ADV
ejpam-4581	388	3	contra	contra	ADJ
ejpam-4581	388	4	-	-	ADJ
ejpam-4581	388	5	continuous	continuous	ADJ
ejpam-4581	388	6	multifunctions	multifunction	NOUN
ejpam-4581	388	7	.	.	PUNCT
ejpam-4581	389	1	lobachevskii	lobachevskii	PROPN
ejpam-4581	389	2	journal	journal	PROPN
ejpam-4581	389	3	of	of	ADP
ejpam-4581	389	4	mathematics	mathematic	NOUN
ejpam-4581	389	5	,	,	PUNCT
ejpam-4581	389	6	30(2):124–131	30(2):124–131	PROPN
ejpam-4581	389	7	,	,	PUNCT
ejpam-4581	389	8	2009	2009	NUM
ejpam-4581	389	9	.	.	PUNCT
ejpam-4581	390	1	[	[	X
ejpam-4581	390	2	14	14	NUM
ejpam-4581	390	3	]	]	X
ejpam-4581	390	4	e.	e.	PROPN
ejpam-4581	390	5	ekici	ekici	PROPN
ejpam-4581	390	6	,	,	PUNCT
ejpam-4581	390	7	s.	s.	PROPN
ejpam-4581	390	8	jafari	jafari	PROPN
ejpam-4581	390	9	,	,	PUNCT
ejpam-4581	390	10	and	and	CCONJ
ejpam-4581	390	11	v.	v.	ADP
ejpam-4581	390	12	popa	popa	NOUN
ejpam-4581	390	13	.	.	PUNCT
ejpam-4581	391	1	on	on	ADP
ejpam-4581	391	2	contra	contra	PROPN
ejpam-4581	391	3	-	-	ADJ
ejpam-4581	391	4	precontinuous	precontinuous	ADJ
ejpam-4581	391	5	and	and	CCONJ
ejpam-4581	391	6	almost	almost	ADV
ejpam-4581	391	7	contraprecontinuous	contraprecontinuous	ADJ
ejpam-4581	391	8	multifunctions	multifunction	NOUN
ejpam-4581	391	9	.	.	PUNCT
ejpam-4581	392	1	journal	journal	PROPN
ejpam-4581	392	2	of	of	ADP
ejpam-4581	392	3	advanced	advanced	ADJ
ejpam-4581	392	4	research	research	NOUN
ejpam-4581	392	5	in	in	ADP
ejpam-4581	392	6	pure	pure	ADJ
ejpam-4581	392	7	mathematics	mathematic	NOUN
ejpam-4581	392	8	,	,	PUNCT
ejpam-4581	392	9	2(1):11–25	2(1):11–25	NUM
ejpam-4581	392	10	,	,	PUNCT
ejpam-4581	392	11	2010	2010	NUM
ejpam-4581	392	12	.	.	PUNCT
ejpam-4581	393	1	[	[	X
ejpam-4581	393	2	15	15	NUM
ejpam-4581	393	3	]	]	PUNCT
ejpam-4581	393	4	m.	m.	NOUN
ejpam-4581	393	5	e.	e.	PROPN
ejpam-4581	393	6	abd	abd	PROPN
ejpam-4581	394	1	el	el	PROPN
ejpam-4581	394	2	-	-	PROPN
ejpam-4581	394	3	monsef	monsef	PROPN
ejpam-4581	394	4	,	,	PUNCT
ejpam-4581	394	5	s.	s.	PROPN
ejpam-4581	394	6	n.	n.	PROPN
ejpam-4581	394	7	el	el	PROPN
ejpam-4581	394	8	-	-	PROPN
ejpam-4581	394	9	deeb	deeb	PROPN
ejpam-4581	394	10	,	,	PUNCT
ejpam-4581	394	11	and	and	CCONJ
ejpam-4581	394	12	r.	r.	PROPN
ejpam-4581	394	13	a.	a.	PROPN
ejpam-4581	394	14	mahmoud	mahmoud	PROPN
ejpam-4581	394	15	.	.	PUNCT
ejpam-4581	395	1	β	β	X
ejpam-4581	395	2	-	-	ADJ
ejpam-4581	395	3	open	open	ADJ
ejpam-4581	395	4	sets	set	NOUN
ejpam-4581	395	5	and	and	CCONJ
ejpam-4581	395	6	βcontinuous	βcontinuous	ADJ
ejpam-4581	395	7	mappings	mapping	NOUN
ejpam-4581	395	8	.	.	PUNCT
ejpam-4581	396	1	bulletin	bulletin	NOUN
ejpam-4581	396	2	of	of	ADP
ejpam-4581	396	3	the	the	DET
ejpam-4581	396	4	faculty	faculty	NOUN
ejpam-4581	396	5	of	of	ADP
ejpam-4581	396	6	science	science	NOUN
ejpam-4581	396	7	.	.	PUNCT
ejpam-4581	397	1	assiut	assiut	PROPN
ejpam-4581	397	2	university	university	PROPN
ejpam-4581	397	3	.	.	PUNCT
ejpam-4581	397	4	,	,	PUNCT
ejpam-4581	397	5	12:77–90	12:77–90	NUM
ejpam-4581	397	6	,	,	PUNCT
ejpam-4581	397	7	1983	1983	NUM
ejpam-4581	397	8	.	.	PUNCT
ejpam-4581	398	1	[	[	X
ejpam-4581	398	2	16	16	NUM
ejpam-4581	398	3	]	]	PUNCT
ejpam-4581	398	4	s.	s.	PROPN
ejpam-4581	398	5	jafari	jafari	PROPN
ejpam-4581	398	6	and	and	CCONJ
ejpam-4581	398	7	t.	t.	PROPN
ejpam-4581	398	8	noiri	noiri	PROPN
ejpam-4581	398	9	.	.	PUNCT
ejpam-4581	399	1	on	on	ADP
ejpam-4581	399	2	contra	contra	ADJ
ejpam-4581	399	3	-	-	ADJ
ejpam-4581	399	4	precontinuous	precontinuous	ADJ
ejpam-4581	399	5	functions	function	NOUN
ejpam-4581	399	6	.	.	PUNCT
ejpam-4581	400	1	bulletin	bulletin	NOUN
ejpam-4581	400	2	of	of	ADP
ejpam-4581	400	3	the	the	DET
ejpam-4581	400	4	malaysian	malaysian	PROPN
ejpam-4581	400	5	mathematical	mathematical	PROPN
ejpam-4581	400	6	sciences	sciences	PROPN
ejpam-4581	400	7	society	society	NOUN
ejpam-4581	400	8	,	,	PUNCT
ejpam-4581	400	9	25:115–128	25:115–128	PROPN
ejpam-4581	400	10	,	,	PUNCT
ejpam-4581	400	11	2002	2002	NUM
ejpam-4581	400	12	.	.	PUNCT
ejpam-4581	401	1	[	[	X
ejpam-4581	401	2	17	17	NUM
ejpam-4581	401	3	]	]	PUNCT
ejpam-4581	401	4	a.	a.	NOUN
ejpam-4581	401	5	a.	a.	NOUN
ejpam-4581	401	6	nasef	nasef	PROPN
ejpam-4581	401	7	.	.	PUNCT
ejpam-4581	402	1	some	some	DET
ejpam-4581	402	2	properties	property	NOUN
ejpam-4581	402	3	of	of	ADP
ejpam-4581	402	4	contra	contra	PROPN
ejpam-4581	402	5	-	-	PUNCT
ejpam-4581	402	6	γ	γ	ADJ
ejpam-4581	402	7	-	-	ADJ
ejpam-4581	402	8	continuous	continuous	ADJ
ejpam-4581	402	9	functions	function	NOUN
ejpam-4581	402	10	.	.	PUNCT
ejpam-4581	403	1	chaos	chaos	NOUN
ejpam-4581	403	2	,	,	PUNCT
ejpam-4581	403	3	solitons	soliton	NOUN
ejpam-4581	403	4	&	&	CCONJ
ejpam-4581	403	5	fractals	fractal	NOUN
ejpam-4581	403	6	,	,	PUNCT
ejpam-4581	403	7	24:471–477	24:471–477	NUM
ejpam-4581	403	8	,	,	PUNCT
ejpam-4581	403	9	2005	2005	NUM
ejpam-4581	403	10	.	.	PUNCT
ejpam-4581	404	1	[	[	X
ejpam-4581	404	2	18	18	NUM
ejpam-4581	404	3	]	]	PUNCT
ejpam-4581	404	4	t.	t.	PROPN
ejpam-4581	404	5	noiri	noiri	PROPN
ejpam-4581	404	6	.	.	PUNCT
ejpam-4581	405	1	super	super	ADJ
ejpam-4581	405	2	-	-	NOUN
ejpam-4581	405	3	continuity	continuity	NOUN
ejpam-4581	405	4	and	and	CCONJ
ejpam-4581	405	5	some	some	DET
ejpam-4581	405	6	strong	strong	ADJ
ejpam-4581	405	7	forms	form	NOUN
ejpam-4581	405	8	of	of	ADP
ejpam-4581	405	9	continuity	continuity	NOUN
ejpam-4581	405	10	.	.	PUNCT
ejpam-4581	406	1	indian	indian	ADJ
ejpam-4581	406	2	journal	journal	PROPN
ejpam-4581	406	3	of	of	ADP
ejpam-4581	406	4	pure	pure	ADJ
ejpam-4581	406	5	and	and	CCONJ
ejpam-4581	406	6	applied	applied	ADJ
ejpam-4581	406	7	mathematics	mathematic	NOUN
ejpam-4581	406	8	,	,	PUNCT
ejpam-4581	406	9	15:241–250	15:241–250	NUM
ejpam-4581	406	10	,	,	PUNCT
ejpam-4581	406	11	1984	1984	NUM
ejpam-4581	406	12	.	.	PUNCT
ejpam-4581	407	1	[	[	X
ejpam-4581	407	2	19	19	NUM
ejpam-4581	407	3	]	]	X
ejpam-4581	407	4	t.	t.	PROPN
ejpam-4581	407	5	noiri	noiri	PROPN
ejpam-4581	407	6	,	,	PUNCT
ejpam-4581	407	7	b.	b.	PROPN
ejpam-4581	407	8	ahmad	ahmad	PROPN
ejpam-4581	407	9	,	,	PUNCT
ejpam-4581	407	10	and	and	CCONJ
ejpam-4581	407	11	m.	m.	PROPN
ejpam-4581	407	12	khan	khan	PROPN
ejpam-4581	407	13	.	.	PUNCT
ejpam-4581	408	1	almost	almost	ADV
ejpam-4581	408	2	s	s	NOUN
ejpam-4581	408	3	-	-	PUNCT
ejpam-4581	408	4	continuous	continuous	ADJ
ejpam-4581	408	5	functions	function	NOUN
ejpam-4581	408	6	.	.	PUNCT
ejpam-4581	409	1	kyungpook	kyungpook	PROPN
ejpam-4581	409	2	mathematical	mathematical	PROPN
ejpam-4581	409	3	journal	journal	PROPN
ejpam-4581	409	4	,	,	PUNCT
ejpam-4581	409	5	35:311–322	35:311–322	PROPN
ejpam-4581	409	6	,	,	PUNCT
ejpam-4581	409	7	1995	1995	NUM
ejpam-4581	409	8	.	.	PUNCT
ejpam-4581	410	1	[	[	X
ejpam-4581	410	2	20	20	NUM
ejpam-4581	410	3	]	]	PUNCT
ejpam-4581	410	4	t.	t.	PROPN
ejpam-4581	410	5	noiri	noiri	PROPN
ejpam-4581	410	6	and	and	CCONJ
ejpam-4581	410	7	e.	e.	PROPN
ejpam-4581	410	8	hatir	hatir	PROPN
ejpam-4581	410	9	.	.	PUNCT
ejpam-4581	411	1	λsp	λsp	NOUN
ejpam-4581	411	2	-	-	PUNCT
ejpam-4581	411	3	sets	set	NOUN
ejpam-4581	411	4	and	and	CCONJ
ejpam-4581	411	5	some	some	DET
ejpam-4581	411	6	weak	weak	ADJ
ejpam-4581	411	7	separation	separation	NOUN
ejpam-4581	411	8	axioms	axiom	NOUN
ejpam-4581	411	9	.	.	PUNCT
ejpam-4581	412	1	acta	acta	PROPN
ejpam-4581	412	2	mathematica	mathematica	PROPN
ejpam-4581	412	3	hungarica	hungarica	PROPN
ejpam-4581	412	4	,	,	PUNCT
ejpam-4581	412	5	103(3):225–232	103(3):225–232	NUM
ejpam-4581	412	6	,	,	PUNCT
ejpam-4581	412	7	2004	2004	NUM
ejpam-4581	412	8	.	.	PUNCT
ejpam-4581	413	1	[	[	X
ejpam-4581	413	2	21	21	NUM
ejpam-4581	413	3	]	]	X
ejpam-4581	413	4	v.	v.	PROPN
ejpam-4581	413	5	i.	i.	PROPN
ejpam-4581	413	6	ponomarev	ponomarev	PROPN
ejpam-4581	413	7	.	.	PUNCT
ejpam-4581	414	1	properties	property	NOUN
ejpam-4581	414	2	of	of	ADP
ejpam-4581	414	3	topological	topological	ADJ
ejpam-4581	414	4	spaces	space	NOUN
ejpam-4581	414	5	preserved	preserve	VERB
ejpam-4581	414	6	under	under	ADP
ejpam-4581	414	7	multivalued	multivalued	ADJ
ejpam-4581	414	8	continuous	continuous	ADJ
ejpam-4581	414	9	mappings	mapping	NOUN
ejpam-4581	414	10	on	on	ADP
ejpam-4581	414	11	compacta	compacta	NOUN
ejpam-4581	414	12	.	.	PUNCT
ejpam-4581	415	1	american	american	PROPN
ejpam-4581	415	2	mathematical	mathematical	ADJ
ejpam-4581	415	3	society	society	NOUN
ejpam-4581	415	4	translations	translation	NOUN
ejpam-4581	415	5	,	,	PUNCT
ejpam-4581	415	6	38(2):119–140	38(2):119–140	NUM
ejpam-4581	415	7	,	,	PUNCT
ejpam-4581	415	8	1964	1964	NUM
ejpam-4581	415	9	.	.	PUNCT
ejpam-4581	416	1	[	[	X
ejpam-4581	416	2	22	22	NUM
ejpam-4581	416	3	]	]	X
ejpam-4581	416	4	c.	c.	PROPN
ejpam-4581	416	5	viriyapong	viriyapong	PROPN
ejpam-4581	416	6	and	and	CCONJ
ejpam-4581	416	7	c.	c.	PROPN
ejpam-4581	416	8	boonpok	boonpok	PROPN
ejpam-4581	416	9	.	.	PUNCT
ejpam-4581	417	1	on	on	ADP
ejpam-4581	417	2	α(λ	α(λ	PROPN
ejpam-4581	417	3	,	,	PUNCT
ejpam-4581	417	4	sp)-continuous	sp)-continuous	ADJ
ejpam-4581	417	5	multifunctions	multifunction	NOUN
ejpam-4581	417	6	.	.	PUNCT
ejpam-4581	418	1	international	international	ADJ
ejpam-4581	418	2	journal	journal	PROPN
ejpam-4581	418	3	of	of	ADP
ejpam-4581	418	4	mathematics	mathematic	NOUN
ejpam-4581	418	5	and	and	CCONJ
ejpam-4581	418	6	computer	computer	NOUN
ejpam-4581	418	7	science	science	NOUN
ejpam-4581	418	8	,	,	PUNCT
ejpam-4581	418	9	17(3):1375–1381	17(3):1375–1381	NUM
ejpam-4581	418	10	,	,	PUNCT
ejpam-4581	418	11	2022	2022	NUM
ejpam-4581	418	12	.	.	PUNCT
ejpam-4581	419	1	[	[	X
ejpam-4581	419	2	23	23	NUM
ejpam-4581	419	3	]	]	X
ejpam-4581	419	4	c.	c.	PROPN
ejpam-4581	419	5	viriyapong	viriyapong	PROPN
ejpam-4581	419	6	and	and	CCONJ
ejpam-4581	419	7	c.	c.	PROPN
ejpam-4581	419	8	boonpok	boonpok	PROPN
ejpam-4581	419	9	.	.	PUNCT
ejpam-4581	420	1	weak	weak	ADJ
ejpam-4581	420	2	quasi	quasi	NOUN
ejpam-4581	420	3	(	(	PUNCT
ejpam-4581	420	4	λ	λ	PROPN
ejpam-4581	420	5	,	,	PUNCT
ejpam-4581	420	6	sp)-continuity	sp)-continuity	NOUN
ejpam-4581	420	7	for	for	ADP
ejpam-4581	420	8	multifunctions	multifunction	NOUN
ejpam-4581	420	9	.	.	PUNCT
ejpam-4581	421	1	international	international	ADJ
ejpam-4581	421	2	journal	journal	PROPN
ejpam-4581	421	3	of	of	ADP
ejpam-4581	421	4	mathematics	mathematic	NOUN
ejpam-4581	421	5	and	and	CCONJ
ejpam-4581	421	6	computer	computer	NOUN
ejpam-4581	421	7	science	science	NOUN
ejpam-4581	421	8	,	,	PUNCT
ejpam-4581	421	9	17(3):1201–1209	17(3):1201–1209	NUM
ejpam-4581	421	10	,	,	PUNCT
ejpam-4581	421	11	2022	2022	NUM
ejpam-4581	421	12	.	.	PUNCT