id	sid	tid	token	lemma	pos
ejpam-4277	1	1	european	european	PROPN
ejpam-4277	1	2	journal	journal	PROPN
ejpam-4277	1	3	of	of	ADP
ejpam-4277	1	4	pure	pure	ADJ
ejpam-4277	1	5	and	and	CCONJ
ejpam-4277	1	6	applied	apply	VERB
ejpam-4277	1	7	mathematics	mathematic	NOUN
ejpam-4277	1	8	vol	vol	NOUN
ejpam-4277	1	9	.	.	PROPN
ejpam-4277	2	1	15	15	NUM
ejpam-4277	2	2	,	,	PUNCT
ejpam-4277	2	3	no	no	INTJ
ejpam-4277	2	4	.	.	NOUN
ejpam-4277	2	5	2	2	NUM
ejpam-4277	2	6	,	,	PUNCT
ejpam-4277	2	7	2022	2022	NUM
ejpam-4277	2	8	,	,	PUNCT
ejpam-4277	2	9	626	626	NUM
ejpam-4277	2	10	-	-	SYM
ejpam-4277	2	11	634	634	NUM
ejpam-4277	2	12	issn	issn	PROPN
ejpam-4277	2	13	1307	1307	NUM
ejpam-4277	2	14	-	-	SYM
ejpam-4277	2	15	5543	5543	NUM
ejpam-4277	2	16	–	–	PUNCT
ejpam-4277	2	17	ejpam.com	ejpam.com	X
ejpam-4277	2	18	published	publish	VERB
ejpam-4277	2	19	by	by	ADP
ejpam-4277	2	20	new	new	PROPN
ejpam-4277	2	21	york	york	PROPN
ejpam-4277	2	22	business	business	PROPN
ejpam-4277	2	23	global	global	ADJ
ejpam-4277	2	24	on	on	ADP
ejpam-4277	2	25	almost	almost	ADV
ejpam-4277	2	26	α(λ	α(λ	PROPN
ejpam-4277	2	27	,	,	PUNCT
ejpam-4277	2	28	sp)-continuous	sp)-continuous	ADJ
ejpam-4277	2	29	multifunctions	multifunction	NOUN
ejpam-4277	2	30	chawalit	chawalit	VERB
ejpam-4277	2	31	boonpok1	boonpok1	PROPN
ejpam-4277	2	32	,	,	PUNCT
ejpam-4277	2	33	jeeranunt	jeeranunt	PROPN
ejpam-4277	2	34	khampakdee1,∗	khampakdee1,∗	PROPN
ejpam-4277	2	35	1	1	NUM
ejpam-4277	2	36	mathematics	mathematic	NOUN
ejpam-4277	2	37	and	and	CCONJ
ejpam-4277	2	38	applied	apply	VERB
ejpam-4277	2	39	mathematics	mathematics	PROPN
ejpam-4277	2	40	research	research	NOUN
ejpam-4277	2	41	unit	unit	NOUN
ejpam-4277	2	42	,	,	PUNCT
ejpam-4277	2	43	department	department	NOUN
ejpam-4277	2	44	of	of	ADP
ejpam-4277	2	45	mathematics	mathematic	NOUN
ejpam-4277	2	46	,	,	PUNCT
ejpam-4277	2	47	faculty	faculty	NOUN
ejpam-4277	2	48	of	of	ADP
ejpam-4277	2	49	science	science	NOUN
ejpam-4277	2	50	,	,	PUNCT
ejpam-4277	2	51	mahasarakham	mahasarakham	PROPN
ejpam-4277	2	52	university	university	PROPN
ejpam-4277	2	53	,	,	PUNCT
ejpam-4277	2	54	maha	maha	PROPN
ejpam-4277	2	55	sarakham	sarakham	PROPN
ejpam-4277	2	56	,	,	PUNCT
ejpam-4277	2	57	44150	44150	NUM
ejpam-4277	2	58	,	,	PUNCT
ejpam-4277	2	59	thailand	thailand	PROPN
ejpam-4277	2	60	abstract	abstract	PROPN
ejpam-4277	2	61	.	.	PUNCT
ejpam-4277	3	1	our	our	PRON
ejpam-4277	3	2	main	main	ADJ
ejpam-4277	3	3	purpose	purpose	NOUN
ejpam-4277	3	4	is	be	AUX
ejpam-4277	3	5	to	to	PART
ejpam-4277	3	6	introduce	introduce	VERB
ejpam-4277	3	7	the	the	DET
ejpam-4277	3	8	notion	notion	NOUN
ejpam-4277	3	9	of	of	ADP
ejpam-4277	3	10	almost	almost	ADV
ejpam-4277	3	11	α(λ	α(λ	PROPN
ejpam-4277	3	12	,	,	PUNCT
ejpam-4277	3	13	sp)-continuous	sp)-continuous	ADJ
ejpam-4277	3	14	multifunctions	multifunction	NOUN
ejpam-4277	3	15	.	.	PUNCT
ejpam-4277	4	1	moreover	moreover	ADV
ejpam-4277	4	2	,	,	PUNCT
ejpam-4277	4	3	some	some	DET
ejpam-4277	4	4	characterizations	characterization	NOUN
ejpam-4277	4	5	of	of	ADP
ejpam-4277	4	6	almost	almost	ADV
ejpam-4277	4	7	α(λ	α(λ	PROPN
ejpam-4277	4	8	,	,	PUNCT
ejpam-4277	4	9	sp)-continuous	sp)-continuous	ADJ
ejpam-4277	4	10	multifunctions	multifunction	NOUN
ejpam-4277	4	11	are	be	AUX
ejpam-4277	4	12	established	establish	VERB
ejpam-4277	4	13	.	.	PUNCT
ejpam-4277	5	1	2020	2020	NUM
ejpam-4277	5	2	mathematics	mathematics	PROPN
ejpam-4277	5	3	subject	subject	NOUN
ejpam-4277	5	4	classifications	classification	NOUN
ejpam-4277	5	5	:	:	PUNCT
ejpam-4277	5	6	54c08	54c08	NUM
ejpam-4277	5	7	,	,	PUNCT
ejpam-4277	5	8	54c60	54c60	NUM
ejpam-4277	5	9	key	key	ADJ
ejpam-4277	5	10	words	word	NOUN
ejpam-4277	5	11	and	and	CCONJ
ejpam-4277	5	12	phrases	phrase	NOUN
ejpam-4277	5	13	:	:	PUNCT
ejpam-4277	5	14	α(λ	α(λ	NOUN
ejpam-4277	5	15	,	,	PUNCT
ejpam-4277	5	16	sp)-open	sp)-open	ADJ
ejpam-4277	5	17	set	set	NOUN
ejpam-4277	5	18	,	,	PUNCT
ejpam-4277	5	19	almost	almost	ADV
ejpam-4277	5	20	α(λ	α(λ	PROPN
ejpam-4277	5	21	,	,	PUNCT
ejpam-4277	5	22	sp)-continuous	sp)-continuous	ADJ
ejpam-4277	5	23	multifunction	multifunction	NOUN
ejpam-4277	5	24	1	1	NUM
ejpam-4277	5	25	.	.	PUNCT
ejpam-4277	5	26	introduction	introduction	NOUN
ejpam-4277	5	27	the	the	DET
ejpam-4277	5	28	notion	notion	NOUN
ejpam-4277	5	29	of	of	ADP
ejpam-4277	5	30	continuity	continuity	NOUN
ejpam-4277	5	31	is	be	AUX
ejpam-4277	5	32	an	an	DET
ejpam-4277	5	33	important	important	ADJ
ejpam-4277	5	34	concept	concept	NOUN
ejpam-4277	5	35	in	in	ADP
ejpam-4277	5	36	topological	topological	ADJ
ejpam-4277	5	37	spaces	space	NOUN
ejpam-4277	5	38	.	.	PUNCT
ejpam-4277	6	1	many	many	ADJ
ejpam-4277	6	2	mathematicians	mathematician	NOUN
ejpam-4277	6	3	studied	study	VERB
ejpam-4277	6	4	the	the	DET
ejpam-4277	6	5	various	various	ADJ
ejpam-4277	6	6	types	type	NOUN
ejpam-4277	6	7	of	of	ADP
ejpam-4277	6	8	generalizations	generalization	NOUN
ejpam-4277	6	9	of	of	ADP
ejpam-4277	6	10	continuity	continuity	NOUN
ejpam-4277	6	11	.	.	PUNCT
ejpam-4277	7	1	in	in	ADP
ejpam-4277	7	2	1988	1988	NUM
ejpam-4277	7	3	,	,	PUNCT
ejpam-4277	7	4	noiri	noiri	ADV
ejpam-4277	7	5	[	[	X
ejpam-4277	7	6	6	6	NUM
ejpam-4277	7	7	]	]	PUNCT
ejpam-4277	7	8	introduced	introduce	VERB
ejpam-4277	7	9	and	and	CCONJ
ejpam-4277	7	10	studied	study	VERB
ejpam-4277	7	11	the	the	DET
ejpam-4277	7	12	notion	notion	NOUN
ejpam-4277	7	13	of	of	ADP
ejpam-4277	7	14	almost	almost	ADV
ejpam-4277	7	15	α	α	NOUN
ejpam-4277	7	16	-	-	NOUN
ejpam-4277	7	17	continuity	continuity	NOUN
ejpam-4277	7	18	in	in	ADP
ejpam-4277	7	19	topological	topological	ADJ
ejpam-4277	7	20	spaces	space	NOUN
ejpam-4277	7	21	as	as	ADP
ejpam-4277	7	22	a	a	DET
ejpam-4277	7	23	generalization	generalization	NOUN
ejpam-4277	7	24	of	of	ADP
ejpam-4277	7	25	α	α	NOUN
ejpam-4277	7	26	-	-	NOUN
ejpam-4277	7	27	continuity	continuity	NOUN
ejpam-4277	7	28	due	due	ADP
ejpam-4277	7	29	to	to	ADP
ejpam-4277	7	30	mashhour	mashhour	PROPN
ejpam-4277	7	31	et	et	PROPN
ejpam-4277	7	32	al	al	PROPN
ejpam-4277	7	33	.	.	PUNCT
ejpam-4277	8	1	[	[	X
ejpam-4277	8	2	5	5	NUM
ejpam-4277	8	3	]	]	PUNCT
ejpam-4277	8	4	.	.	PUNCT
ejpam-4277	9	1	in	in	ADP
ejpam-4277	9	2	1998	1998	NUM
ejpam-4277	9	3	,	,	PUNCT
ejpam-4277	9	4	popa	popa	NOUN
ejpam-4277	9	5	and	and	CCONJ
ejpam-4277	9	6	noiri	noiri	ADV
ejpam-4277	9	7	[	[	X
ejpam-4277	9	8	8	8	NUM
ejpam-4277	9	9	]	]	PUNCT
ejpam-4277	9	10	extended	extend	VERB
ejpam-4277	9	11	the	the	DET
ejpam-4277	9	12	concept	concept	NOUN
ejpam-4277	9	13	of	of	ADP
ejpam-4277	9	14	almost	almost	ADV
ejpam-4277	9	15	α	α	ADJ
ejpam-4277	9	16	-	-	ADJ
ejpam-4277	9	17	continuous	continuous	ADJ
ejpam-4277	9	18	functions	function	NOUN
ejpam-4277	9	19	to	to	ADP
ejpam-4277	9	20	multifunctions	multifunction	NOUN
ejpam-4277	9	21	and	and	CCONJ
ejpam-4277	9	22	defined	define	VERB
ejpam-4277	9	23	almost	almost	ADV
ejpam-4277	9	24	αcontinuous	αcontinuous	ADJ
ejpam-4277	9	25	multifunctions	multifunction	NOUN
ejpam-4277	9	26	and	and	CCONJ
ejpam-4277	9	27	obtained	obtain	VERB
ejpam-4277	9	28	several	several	ADJ
ejpam-4277	9	29	characterizations	characterization	NOUN
ejpam-4277	9	30	of	of	ADP
ejpam-4277	9	31	almost	almost	ADV
ejpam-4277	9	32	α	α	NUM
ejpam-4277	9	33	-	-	ADJ
ejpam-4277	9	34	continuous	continuous	ADJ
ejpam-4277	9	35	multifunctions	multifunction	NOUN
ejpam-4277	9	36	.	.	PUNCT
ejpam-4277	10	1	abd	abd	PROPN
ejpam-4277	10	2	el	el	PROPN
ejpam-4277	10	3	-	-	PROPN
ejpam-4277	10	4	monsef	monsef	PROPN
ejpam-4277	10	5	et	et	PROPN
ejpam-4277	10	6	al	al	PROPN
ejpam-4277	10	7	.	.	PUNCT
ejpam-4277	11	1	[	[	X
ejpam-4277	11	2	4	4	X
ejpam-4277	11	3	]	]	PUNCT
ejpam-4277	11	4	introduced	introduce	VERB
ejpam-4277	11	5	a	a	DET
ejpam-4277	11	6	weak	weak	ADJ
ejpam-4277	11	7	form	form	NOUN
ejpam-4277	11	8	of	of	ADP
ejpam-4277	11	9	open	open	ADJ
ejpam-4277	11	10	sets	set	NOUN
ejpam-4277	11	11	called	call	VERB
ejpam-4277	11	12	β	β	NOUN
ejpam-4277	11	13	-	-	ADJ
ejpam-4277	11	14	open	open	ADJ
ejpam-4277	11	15	sets	set	NOUN
ejpam-4277	11	16	.	.	PUNCT
ejpam-4277	12	1	this	this	DET
ejpam-4277	12	2	notion	notion	NOUN
ejpam-4277	12	3	was	be	AUX
ejpam-4277	12	4	also	also	ADV
ejpam-4277	12	5	called	call	VERB
ejpam-4277	12	6	semi	semi	ADJ
ejpam-4277	12	7	-	-	ADJ
ejpam-4277	12	8	preopen	preopen	ADJ
ejpam-4277	12	9	sets	set	NOUN
ejpam-4277	12	10	in	in	ADP
ejpam-4277	12	11	the	the	DET
ejpam-4277	12	12	sense	sense	NOUN
ejpam-4277	12	13	of	of	ADP
ejpam-4277	12	14	andrijević	andrijević	NOUN
ejpam-4277	12	15	[	[	X
ejpam-4277	12	16	1	1	NUM
ejpam-4277	12	17	]	]	PUNCT
ejpam-4277	12	18	.	.	PUNCT
ejpam-4277	13	1	in	in	ADP
ejpam-4277	13	2	2004	2004	NUM
ejpam-4277	13	3	,	,	PUNCT
ejpam-4277	13	4	noiri	noiri	PROPN
ejpam-4277	13	5	and	and	CCONJ
ejpam-4277	13	6	hatir	hatir	NOUN
ejpam-4277	13	7	[	[	X
ejpam-4277	13	8	7	7	NUM
ejpam-4277	13	9	]	]	PUNCT
ejpam-4277	13	10	introduced	introduce	VERB
ejpam-4277	13	11	the	the	DET
ejpam-4277	13	12	notion	notion	NOUN
ejpam-4277	13	13	of	of	ADP
ejpam-4277	13	14	λsp	λsp	NOUN
ejpam-4277	13	15	-	-	PUNCT
ejpam-4277	13	16	sets	set	NOUN
ejpam-4277	13	17	in	in	ADP
ejpam-4277	13	18	terms	term	NOUN
ejpam-4277	13	19	of	of	ADP
ejpam-4277	13	20	the	the	DET
ejpam-4277	13	21	concept	concept	NOUN
ejpam-4277	13	22	of	of	ADP
ejpam-4277	13	23	β	β	ADJ
ejpam-4277	13	24	-	-	ADJ
ejpam-4277	13	25	open	open	ADJ
ejpam-4277	13	26	sets	set	NOUN
ejpam-4277	13	27	and	and	CCONJ
ejpam-4277	13	28	investigated	investigate	VERB
ejpam-4277	13	29	the	the	DET
ejpam-4277	13	30	notion	notion	NOUN
ejpam-4277	13	31	of	of	ADP
ejpam-4277	13	32	λsp	λsp	NOUN
ejpam-4277	13	33	-	-	PUNCT
ejpam-4277	13	34	closed	close	VERB
ejpam-4277	13	35	sets	set	NOUN
ejpam-4277	13	36	by	by	ADP
ejpam-4277	13	37	using	use	VERB
ejpam-4277	13	38	λsp	λsp	NOUN
ejpam-4277	13	39	-	-	PUNCT
ejpam-4277	13	40	sets	set	NOUN
ejpam-4277	13	41	.	.	PUNCT
ejpam-4277	14	1	in	in	ADP
ejpam-4277	14	2	[	[	X
ejpam-4277	14	3	3	3	NUM
ejpam-4277	14	4	]	]	PUNCT
ejpam-4277	14	5	,	,	PUNCT
ejpam-4277	14	6	the	the	DET
ejpam-4277	14	7	author	author	NOUN
ejpam-4277	14	8	introduced	introduce	VERB
ejpam-4277	14	9	the	the	DET
ejpam-4277	14	10	concepts	concept	NOUN
ejpam-4277	14	11	of	of	ADP
ejpam-4277	14	12	(	(	PUNCT
ejpam-4277	14	13	λ	λ	PROPN
ejpam-4277	14	14	,	,	PUNCT
ejpam-4277	14	15	sp)-open	sp)-open	ADJ
ejpam-4277	14	16	sets	set	NOUN
ejpam-4277	14	17	and	and	CCONJ
ejpam-4277	14	18	(	(	PUNCT
ejpam-4277	14	19	λ	λ	PROPN
ejpam-4277	14	20	,	,	PUNCT
ejpam-4277	14	21	sp)-closed	sp)-close	VERB
ejpam-4277	14	22	sets	set	NOUN
ejpam-4277	14	23	which	which	PRON
ejpam-4277	14	24	are	be	AUX
ejpam-4277	14	25	defined	define	VERB
ejpam-4277	14	26	by	by	ADP
ejpam-4277	14	27	utilizing	utilize	VERB
ejpam-4277	14	28	the	the	DET
ejpam-4277	14	29	notions	notion	NOUN
ejpam-4277	14	30	of	of	ADP
ejpam-4277	14	31	λsp	λsp	NOUN
ejpam-4277	14	32	-	-	PUNCT
ejpam-4277	14	33	sets	set	NOUN
ejpam-4277	14	34	and	and	CCONJ
ejpam-4277	14	35	β	β	NOUN
ejpam-4277	14	36	-	-	ADJ
ejpam-4277	14	37	closed	closed	ADJ
ejpam-4277	14	38	sets	set	NOUN
ejpam-4277	14	39	.	.	PUNCT
ejpam-4277	15	1	in	in	ADP
ejpam-4277	15	2	particular	particular	ADJ
ejpam-4277	15	3	,	,	PUNCT
ejpam-4277	15	4	some	some	DET
ejpam-4277	15	5	characterizations	characterization	NOUN
ejpam-4277	15	6	of	of	ADP
ejpam-4277	15	7	upper	upper	ADJ
ejpam-4277	15	8	and	and	CCONJ
ejpam-4277	15	9	lower	low	ADJ
ejpam-4277	15	10	(	(	PUNCT
ejpam-4277	15	11	λ	λ	NOUN
ejpam-4277	15	12	,	,	PUNCT
ejpam-4277	15	13	sp)-continuous	sp)-continuous	ADJ
ejpam-4277	15	14	multifunctions	multifunction	NOUN
ejpam-4277	15	15	are	be	AUX
ejpam-4277	15	16	investigated	investigate	VERB
ejpam-4277	15	17	in	in	ADP
ejpam-4277	15	18	[	[	X
ejpam-4277	15	19	3	3	NUM
ejpam-4277	15	20	]	]	PUNCT
ejpam-4277	15	21	.	.	PUNCT
ejpam-4277	16	1	the	the	DET
ejpam-4277	16	2	purpose	purpose	NOUN
ejpam-4277	16	3	of	of	ADP
ejpam-4277	16	4	the	the	DET
ejpam-4277	16	5	present	present	ADJ
ejpam-4277	16	6	paper	paper	NOUN
ejpam-4277	16	7	is	be	AUX
ejpam-4277	16	8	to	to	PART
ejpam-4277	16	9	introduce	introduce	VERB
ejpam-4277	16	10	the	the	DET
ejpam-4277	16	11	notion	notion	NOUN
ejpam-4277	16	12	of	of	ADP
ejpam-4277	16	13	almost	almost	ADV
ejpam-4277	16	14	α(λ	α(λ	PROPN
ejpam-4277	16	15	,	,	PUNCT
ejpam-4277	16	16	sp)-continuous	sp)-continuous	ADJ
ejpam-4277	16	17	multifunctions	multifunction	NOUN
ejpam-4277	16	18	.	.	PUNCT
ejpam-4277	17	1	furthermore	furthermore	ADV
ejpam-4277	17	2	,	,	PUNCT
ejpam-4277	17	3	several	several	ADJ
ejpam-4277	17	4	characterizations	characterization	NOUN
ejpam-4277	17	5	of	of	ADP
ejpam-4277	17	6	almost	almost	ADV
ejpam-4277	17	7	α(λ	α(λ	PROPN
ejpam-4277	17	8	,	,	PUNCT
ejpam-4277	17	9	sp)-continuous	sp)-continuous	ADJ
ejpam-4277	17	10	multifunctions	multifunction	NOUN
ejpam-4277	17	11	are	be	AUX
ejpam-4277	17	12	discussed	discuss	VERB
ejpam-4277	17	13	.	.	PUNCT
ejpam-4277	18	1	∗corresponding	∗corresponde	VERB
ejpam-4277	18	2	author	author	NOUN
ejpam-4277	18	3	.	.	PUNCT
ejpam-4277	19	1	doi	doi	NOUN
ejpam-4277	19	2	:	:	PUNCT
ejpam-4277	19	3	https://doi.org/10.29020/nybg.ejpam.v15i2.4277	https://doi.org/10.29020/nybg.ejpam.v15i2.4277	PROPN
ejpam-4277	19	4	email	email	NOUN
ejpam-4277	19	5	addresses	address	NOUN
ejpam-4277	19	6	:	:	PUNCT
ejpam-4277	19	7	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	INTJ
ejpam-4277	19	8	(	(	PUNCT
ejpam-4277	19	9	c.	c.	PROPN
ejpam-4277	19	10	boonpok	boonpok	PROPN
ejpam-4277	19	11	)	)	PUNCT
ejpam-4277	19	12	,	,	PUNCT
ejpam-4277	19	13	jeeranunt.k@msu.ac.th	jeeranunt.k@msu.ac.th	INTJ
ejpam-4277	19	14	(	(	PUNCT
ejpam-4277	19	15	j.	j.	PROPN
ejpam-4277	19	16	khampakdee	khampakdee	PROPN
ejpam-4277	19	17	)	)	PUNCT
ejpam-4277	19	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4277	20	1	626	626	NUM
ejpam-4277	21	1	©	©	ADP
ejpam-4277	21	2	2022	2022	NUM
ejpam-4277	21	3	ejpam	ejpam	VERB
ejpam-4277	21	4	all	all	DET
ejpam-4277	21	5	rights	right	NOUN
ejpam-4277	21	6	reserved	reserve	VERB
ejpam-4277	21	7	.	.	PUNCT
ejpam-4277	22	1	c.	c.	PROPN
ejpam-4277	22	2	boonpok	boonpok	PROPN
ejpam-4277	22	3	,	,	PUNCT
ejpam-4277	22	4	j.	j.	PROPN
ejpam-4277	22	5	khampakdee	khampakdee	PROPN
ejpam-4277	22	6	/	/	PUNCT
ejpam-4277	22	7	eur	eur	PROPN
ejpam-4277	22	8	.	.	PUNCT
ejpam-4277	23	1	j.	j.	PROPN
ejpam-4277	23	2	pure	pure	PROPN
ejpam-4277	23	3	appl	appl	PROPN
ejpam-4277	23	4	.	.	PROPN
ejpam-4277	23	5	math	math	PROPN
ejpam-4277	23	6	,	,	PUNCT
ejpam-4277	23	7	15	15	NUM
ejpam-4277	23	8	(	(	PUNCT
ejpam-4277	23	9	2	2	NUM
ejpam-4277	23	10	)	)	PUNCT
ejpam-4277	23	11	(	(	PUNCT
ejpam-4277	23	12	2022	2022	NUM
ejpam-4277	23	13	)	)	PUNCT
ejpam-4277	23	14	,	,	PUNCT
ejpam-4277	23	15	626	626	NUM
ejpam-4277	23	16	-	-	SYM
ejpam-4277	23	17	634	634	NUM
ejpam-4277	23	18	627	627	NUM
ejpam-4277	23	19	2	2	NUM
ejpam-4277	23	20	.	.	PUNCT
ejpam-4277	23	21	preliminaries	preliminary	NOUN
ejpam-4277	23	22	throughout	throughout	ADP
ejpam-4277	23	23	this	this	DET
ejpam-4277	23	24	paper	paper	NOUN
ejpam-4277	23	25	,	,	PUNCT
ejpam-4277	23	26	spaces	space	NOUN
ejpam-4277	23	27	(	(	PUNCT
ejpam-4277	23	28	x	x	X
ejpam-4277	23	29	,	,	PUNCT
ejpam-4277	23	30	τ	τ	X
ejpam-4277	23	31	)	)	PUNCT
ejpam-4277	23	32	and	and	CCONJ
ejpam-4277	23	33	(	(	PUNCT
ejpam-4277	23	34	y	y	PROPN
ejpam-4277	23	35	,	,	PUNCT
ejpam-4277	23	36	σ	σ	PROPN
ejpam-4277	23	37	)	)	PUNCT
ejpam-4277	23	38	(	(	PUNCT
ejpam-4277	23	39	or	or	CCONJ
ejpam-4277	23	40	simply	simply	ADV
ejpam-4277	23	41	x	x	X
ejpam-4277	23	42	and	and	CCONJ
ejpam-4277	23	43	y	y	PROPN
ejpam-4277	23	44	)	)	PUNCT
ejpam-4277	23	45	always	always	ADV
ejpam-4277	23	46	mean	mean	VERB
ejpam-4277	23	47	topological	topological	ADJ
ejpam-4277	23	48	spaces	space	NOUN
ejpam-4277	23	49	on	on	ADP
ejpam-4277	23	50	which	which	PRON
ejpam-4277	23	51	no	no	DET
ejpam-4277	23	52	separation	separation	NOUN
ejpam-4277	23	53	axioms	axiom	NOUN
ejpam-4277	23	54	are	be	AUX
ejpam-4277	23	55	assumed	assume	VERB
ejpam-4277	23	56	unless	unless	SCONJ
ejpam-4277	23	57	explicitly	explicitly	ADV
ejpam-4277	23	58	stated	state	VERB
ejpam-4277	23	59	.	.	PUNCT
ejpam-4277	24	1	let	let	VERB
ejpam-4277	24	2	a	a	DET
ejpam-4277	24	3	be	be	AUX
ejpam-4277	24	4	a	a	DET
ejpam-4277	24	5	subset	subset	NOUN
ejpam-4277	24	6	of	of	ADP
ejpam-4277	24	7	a	a	DET
ejpam-4277	24	8	topological	topological	ADJ
ejpam-4277	24	9	space	space	NOUN
ejpam-4277	24	10	(	(	PUNCT
ejpam-4277	24	11	x	x	X
ejpam-4277	24	12	,	,	PUNCT
ejpam-4277	24	13	τ	τ	PROPN
ejpam-4277	24	14	)	)	PUNCT
ejpam-4277	24	15	.	.	PUNCT
ejpam-4277	25	1	the	the	DET
ejpam-4277	25	2	closure	closure	NOUN
ejpam-4277	25	3	of	of	ADP
ejpam-4277	25	4	a	a	PRON
ejpam-4277	25	5	and	and	CCONJ
ejpam-4277	25	6	the	the	DET
ejpam-4277	25	7	interior	interior	NOUN
ejpam-4277	25	8	of	of	ADP
ejpam-4277	25	9	a	a	PRON
ejpam-4277	25	10	are	be	AUX
ejpam-4277	25	11	denoted	denote	VERB
ejpam-4277	25	12	by	by	ADP
ejpam-4277	25	13	cl(a	cl(a	NOUN
ejpam-4277	25	14	)	)	PUNCT
ejpam-4277	25	15	and	and	CCONJ
ejpam-4277	25	16	int(a	int(a	PROPN
ejpam-4277	25	17	)	)	PUNCT
ejpam-4277	25	18	,	,	PUNCT
ejpam-4277	25	19	respectively	respectively	ADV
ejpam-4277	25	20	.	.	PUNCT
ejpam-4277	26	1	a	a	DET
ejpam-4277	26	2	subset	subset	NOUN
ejpam-4277	26	3	a	a	PRON
ejpam-4277	26	4	of	of	ADP
ejpam-4277	26	5	a	a	DET
ejpam-4277	26	6	topological	topological	ADJ
ejpam-4277	26	7	space	space	NOUN
ejpam-4277	26	8	(	(	PUNCT
ejpam-4277	26	9	x	x	X
ejpam-4277	26	10	,	,	PUNCT
ejpam-4277	26	11	τ	τ	X
ejpam-4277	26	12	)	)	PUNCT
ejpam-4277	26	13	is	be	AUX
ejpam-4277	26	14	said	say	VERB
ejpam-4277	26	15	to	to	PART
ejpam-4277	26	16	be	be	AUX
ejpam-4277	26	17	β	β	X
ejpam-4277	26	18	-	-	ADJ
ejpam-4277	26	19	open	open	ADJ
ejpam-4277	26	20	[	[	X
ejpam-4277	26	21	4	4	NUM
ejpam-4277	26	22	]	]	X
ejpam-4277	26	23	if	if	SCONJ
ejpam-4277	26	24	a	a	DET
ejpam-4277	26	25	⊆	⊆	NUM
ejpam-4277	26	26	cl(int(cl(a	cl(int(cl(a	NOUN
ejpam-4277	26	27	)	)	PUNCT
ejpam-4277	26	28	)	)	PUNCT
ejpam-4277	26	29	)	)	PUNCT
ejpam-4277	26	30	.	.	PUNCT
ejpam-4277	27	1	the	the	DET
ejpam-4277	27	2	complement	complement	NOUN
ejpam-4277	27	3	of	of	ADP
ejpam-4277	27	4	a	a	DET
ejpam-4277	27	5	β	β	X
ejpam-4277	27	6	-	-	ADJ
ejpam-4277	27	7	open	open	ADJ
ejpam-4277	27	8	set	set	NOUN
ejpam-4277	27	9	is	be	AUX
ejpam-4277	27	10	called	call	VERB
ejpam-4277	27	11	β	β	NOUN
ejpam-4277	27	12	-	-	VERB
ejpam-4277	27	13	closed	closed	ADJ
ejpam-4277	27	14	.	.	PUNCT
ejpam-4277	28	1	the	the	DET
ejpam-4277	28	2	family	family	NOUN
ejpam-4277	28	3	of	of	ADP
ejpam-4277	28	4	all	all	DET
ejpam-4277	28	5	β	β	ADJ
ejpam-4277	28	6	-	-	ADJ
ejpam-4277	28	7	open	open	ADJ
ejpam-4277	28	8	sets	set	NOUN
ejpam-4277	28	9	of	of	ADP
ejpam-4277	28	10	a	a	DET
ejpam-4277	28	11	topological	topological	ADJ
ejpam-4277	28	12	space	space	NOUN
ejpam-4277	28	13	(	(	PUNCT
ejpam-4277	28	14	x	x	X
ejpam-4277	28	15	,	,	PUNCT
ejpam-4277	28	16	τ	τ	X
ejpam-4277	28	17	)	)	PUNCT
ejpam-4277	28	18	is	be	AUX
ejpam-4277	28	19	denoted	denote	VERB
ejpam-4277	28	20	by	by	ADP
ejpam-4277	28	21	β(x	β(x	PROPN
ejpam-4277	28	22	,	,	PUNCT
ejpam-4277	28	23	τ	τ	PROPN
ejpam-4277	28	24	)	)	PUNCT
ejpam-4277	28	25	.	.	PUNCT
ejpam-4277	29	1	a	a	DET
ejpam-4277	29	2	subset	subset	NOUN
ejpam-4277	29	3	λsp(a	λsp(a	NOUN
ejpam-4277	29	4	)	)	PUNCT
ejpam-4277	30	1	[	[	X
ejpam-4277	30	2	7	7	X
ejpam-4277	30	3	]	]	PUNCT
ejpam-4277	30	4	is	be	AUX
ejpam-4277	30	5	defined	define	VERB
ejpam-4277	30	6	as	as	SCONJ
ejpam-4277	30	7	follows	follow	VERB
ejpam-4277	30	8	:	:	PUNCT
ejpam-4277	30	9	λsp(a	λsp(a	NUM
ejpam-4277	30	10	)	)	PUNCT
ejpam-4277	30	11	=	=	PUNCT
ejpam-4277	31	1	∩{u	∩{u	PROPN
ejpam-4277	31	2	|	|	ADV
ejpam-4277	31	3	a	a	DET
ejpam-4277	31	4	⊆	⊆	NUM
ejpam-4277	31	5	u	u	NOUN
ejpam-4277	31	6	,	,	PUNCT
ejpam-4277	31	7	u	u	NOUN
ejpam-4277	31	8	∈	∈	PROPN
ejpam-4277	31	9	β(x	β(x	PROPN
ejpam-4277	31	10	,	,	PUNCT
ejpam-4277	31	11	τ	τ	X
ejpam-4277	31	12	)	)	PUNCT
ejpam-4277	31	13	}	}	PUNCT
ejpam-4277	31	14	.	.	PUNCT
ejpam-4277	32	1	a	a	DET
ejpam-4277	32	2	subset	subset	NOUN
ejpam-4277	32	3	a	a	PRON
ejpam-4277	32	4	of	of	ADP
ejpam-4277	32	5	a	a	DET
ejpam-4277	32	6	topological	topological	ADJ
ejpam-4277	32	7	space	space	NOUN
ejpam-4277	32	8	(	(	PUNCT
ejpam-4277	32	9	x	x	X
ejpam-4277	32	10	,	,	PUNCT
ejpam-4277	32	11	τ	τ	X
ejpam-4277	32	12	)	)	PUNCT
ejpam-4277	32	13	is	be	AUX
ejpam-4277	32	14	called	call	VERB
ejpam-4277	32	15	a	a	DET
ejpam-4277	32	16	λsp	λsp	NOUN
ejpam-4277	32	17	-	-	PUNCT
ejpam-4277	32	18	set	set	VERB
ejpam-4277	32	19	[	[	X
ejpam-4277	32	20	7	7	X
ejpam-4277	32	21	]	]	X
ejpam-4277	32	22	if	if	SCONJ
ejpam-4277	32	23	a	a	DET
ejpam-4277	32	24	=	=	NOUN
ejpam-4277	32	25	λsp(a	λsp(a	NOUN
ejpam-4277	32	26	)	)	PUNCT
ejpam-4277	32	27	.	.	PUNCT
ejpam-4277	33	1	a	a	DET
ejpam-4277	33	2	subset	subset	NOUN
ejpam-4277	33	3	a	a	PRON
ejpam-4277	33	4	of	of	ADP
ejpam-4277	33	5	a	a	DET
ejpam-4277	33	6	topological	topological	ADJ
ejpam-4277	33	7	space	space	NOUN
ejpam-4277	33	8	(	(	PUNCT
ejpam-4277	33	9	x	x	X
ejpam-4277	33	10	,	,	PUNCT
ejpam-4277	33	11	τ	τ	X
ejpam-4277	33	12	)	)	PUNCT
ejpam-4277	33	13	is	be	AUX
ejpam-4277	33	14	called	call	VERB
ejpam-4277	33	15	(	(	PUNCT
ejpam-4277	33	16	λ	λ	X
ejpam-4277	33	17	,	,	PUNCT
ejpam-4277	33	18	sp)-closed	sp)-close	VERB
ejpam-4277	33	19	[	[	PUNCT
ejpam-4277	33	20	3	3	X
ejpam-4277	33	21	]	]	X
ejpam-4277	33	22	if	if	SCONJ
ejpam-4277	33	23	a	a	DET
ejpam-4277	33	24	=	=	X
ejpam-4277	33	25	t	t	NOUN
ejpam-4277	33	26	∩c	∩c	NOUN
ejpam-4277	33	27	,	,	PUNCT
ejpam-4277	33	28	where	where	SCONJ
ejpam-4277	33	29	t	t	PROPN
ejpam-4277	33	30	is	be	AUX
ejpam-4277	33	31	a	a	DET
ejpam-4277	33	32	λsp	λsp	NOUN
ejpam-4277	33	33	-	-	PUNCT
ejpam-4277	33	34	set	set	VERB
ejpam-4277	33	35	and	and	CCONJ
ejpam-4277	33	36	c	c	NOUN
ejpam-4277	33	37	is	be	AUX
ejpam-4277	33	38	a	a	DET
ejpam-4277	33	39	β	β	NOUN
ejpam-4277	33	40	-	-	ADJ
ejpam-4277	33	41	closed	closed	ADJ
ejpam-4277	33	42	set	set	NOUN
ejpam-4277	33	43	.	.	PUNCT
ejpam-4277	34	1	the	the	DET
ejpam-4277	34	2	complement	complement	NOUN
ejpam-4277	34	3	of	of	ADP
ejpam-4277	34	4	a	a	DET
ejpam-4277	34	5	(	(	PUNCT
ejpam-4277	34	6	λ	λ	PROPN
ejpam-4277	34	7	,	,	PUNCT
ejpam-4277	34	8	sp)-closed	sp)-close	VERB
ejpam-4277	34	9	set	set	VERB
ejpam-4277	34	10	is	be	AUX
ejpam-4277	34	11	called	call	VERB
ejpam-4277	34	12	(	(	PUNCT
ejpam-4277	34	13	λ	λ	NOUN
ejpam-4277	34	14	,	,	PUNCT
ejpam-4277	34	15	sp)-open	sp)-open	NOUN
ejpam-4277	34	16	.	.	PUNCT
ejpam-4277	35	1	let	let	VERB
ejpam-4277	35	2	a	a	DET
ejpam-4277	35	3	be	be	AUX
ejpam-4277	35	4	a	a	DET
ejpam-4277	35	5	subset	subset	NOUN
ejpam-4277	35	6	of	of	ADP
ejpam-4277	35	7	a	a	DET
ejpam-4277	35	8	topological	topological	ADJ
ejpam-4277	35	9	space	space	NOUN
ejpam-4277	35	10	(	(	PUNCT
ejpam-4277	35	11	x	x	X
ejpam-4277	35	12	,	,	PUNCT
ejpam-4277	35	13	τ	τ	PROPN
ejpam-4277	35	14	)	)	PUNCT
ejpam-4277	35	15	.	.	PUNCT
ejpam-4277	36	1	a	a	DET
ejpam-4277	36	2	point	point	NOUN
ejpam-4277	36	3	x	x	X
ejpam-4277	36	4	∈	∈	NOUN
ejpam-4277	36	5	x	x	PUNCT
ejpam-4277	36	6	is	be	AUX
ejpam-4277	36	7	called	call	VERB
ejpam-4277	36	8	a	a	DET
ejpam-4277	36	9	(	(	PUNCT
ejpam-4277	36	10	λ	λ	PROPN
ejpam-4277	36	11	,	,	PUNCT
ejpam-4277	36	12	sp)cluster	sp)cluster	NOUN
ejpam-4277	36	13	point	point	NOUN
ejpam-4277	36	14	[	[	X
ejpam-4277	36	15	3	3	X
ejpam-4277	36	16	]	]	PUNCT
ejpam-4277	36	17	of	of	ADP
ejpam-4277	36	18	a	a	PRON
ejpam-4277	37	1	if	if	SCONJ
ejpam-4277	37	2	a	a	DET
ejpam-4277	37	3	∩	∩	ADJ
ejpam-4277	37	4	u	u	NOUN
ejpam-4277	37	5	6=	6=	NOUN
ejpam-4277	37	6	∅	∅	NOUN
ejpam-4277	37	7	for	for	ADP
ejpam-4277	37	8	every	every	DET
ejpam-4277	37	9	(	(	PUNCT
ejpam-4277	37	10	λ	λ	NOUN
ejpam-4277	37	11	,	,	PUNCT
ejpam-4277	37	12	sp)-open	sp)-open	NOUN
ejpam-4277	37	13	set	set	VERB
ejpam-4277	37	14	u	u	NOUN
ejpam-4277	37	15	of	of	ADP
ejpam-4277	37	16	x	x	SYM
ejpam-4277	37	17	containing	contain	VERB
ejpam-4277	37	18	x.	x.	NOUN
ejpam-4277	37	19	the	the	DET
ejpam-4277	37	20	set	set	NOUN
ejpam-4277	37	21	of	of	ADP
ejpam-4277	37	22	all	all	DET
ejpam-4277	37	23	(	(	PUNCT
ejpam-4277	37	24	λ	λ	PROPN
ejpam-4277	37	25	,	,	PUNCT
ejpam-4277	37	26	sp)-cluster	sp)-cluster	NOUN
ejpam-4277	37	27	points	point	NOUN
ejpam-4277	37	28	of	of	ADP
ejpam-4277	37	29	a	a	PRON
ejpam-4277	37	30	is	be	AUX
ejpam-4277	37	31	called	call	VERB
ejpam-4277	37	32	the	the	DET
ejpam-4277	37	33	(	(	PUNCT
ejpam-4277	37	34	λ	λ	PROPN
ejpam-4277	37	35	,	,	PUNCT
ejpam-4277	37	36	sp)-closure	sp)-closure	NOUN
ejpam-4277	37	37	[	[	X
ejpam-4277	37	38	3	3	NUM
ejpam-4277	37	39	]	]	PUNCT
ejpam-4277	37	40	of	of	ADP
ejpam-4277	37	41	a	a	PRON
ejpam-4277	37	42	and	and	CCONJ
ejpam-4277	37	43	is	be	AUX
ejpam-4277	37	44	denoted	denote	VERB
ejpam-4277	37	45	by	by	ADP
ejpam-4277	37	46	a(λ	a(λ	ADV
ejpam-4277	37	47	,	,	PUNCT
ejpam-4277	37	48	sp	sp	NOUN
ejpam-4277	37	49	)	)	PUNCT
ejpam-4277	37	50	.	.	PUNCT
ejpam-4277	38	1	the	the	DET
ejpam-4277	38	2	union	union	NOUN
ejpam-4277	38	3	of	of	ADP
ejpam-4277	38	4	all	all	DET
ejpam-4277	38	5	(	(	PUNCT
ejpam-4277	38	6	λ	λ	NOUN
ejpam-4277	38	7	,	,	PUNCT
ejpam-4277	38	8	sp)-open	sp)-open	ADJ
ejpam-4277	38	9	sets	set	NOUN
ejpam-4277	38	10	contained	contain	VERB
ejpam-4277	38	11	in	in	ADP
ejpam-4277	38	12	a	a	PRON
ejpam-4277	38	13	is	be	AUX
ejpam-4277	38	14	called	call	VERB
ejpam-4277	38	15	the	the	DET
ejpam-4277	38	16	(	(	PUNCT
ejpam-4277	38	17	λ	λ	PROPN
ejpam-4277	38	18	,	,	PUNCT
ejpam-4277	38	19	sp)-interior	sp)-interior	NOUN
ejpam-4277	38	20	[	[	X
ejpam-4277	38	21	3	3	NUM
ejpam-4277	38	22	]	]	PUNCT
ejpam-4277	38	23	of	of	ADP
ejpam-4277	38	24	a	a	PRON
ejpam-4277	38	25	and	and	CCONJ
ejpam-4277	38	26	is	be	AUX
ejpam-4277	38	27	denoted	denote	VERB
ejpam-4277	38	28	by	by	ADP
ejpam-4277	38	29	a(λ	a(λ	ADV
ejpam-4277	38	30	,	,	PUNCT
ejpam-4277	38	31	sp	sp	NOUN
ejpam-4277	38	32	)	)	PUNCT
ejpam-4277	38	33	.	.	PUNCT
ejpam-4277	39	1	lemma	lemma	PROPN
ejpam-4277	39	2	1	1	NUM
ejpam-4277	39	3	.	.	PUNCT
ejpam-4277	40	1	[	[	X
ejpam-4277	40	2	3	3	X
ejpam-4277	40	3	]	]	PUNCT
ejpam-4277	40	4	let	let	VERB
ejpam-4277	40	5	a	a	PRON
ejpam-4277	40	6	and	and	CCONJ
ejpam-4277	40	7	b	b	NOUN
ejpam-4277	40	8	be	be	AUX
ejpam-4277	40	9	subsets	subset	NOUN
ejpam-4277	40	10	of	of	ADP
ejpam-4277	40	11	a	a	DET
ejpam-4277	40	12	topological	topological	ADJ
ejpam-4277	40	13	space	space	NOUN
ejpam-4277	40	14	(	(	PUNCT
ejpam-4277	40	15	x	x	X
ejpam-4277	40	16	,	,	PUNCT
ejpam-4277	40	17	τ	τ	PROPN
ejpam-4277	40	18	)	)	PUNCT
ejpam-4277	40	19	.	.	PUNCT
ejpam-4277	41	1	for	for	ADP
ejpam-4277	41	2	the	the	DET
ejpam-4277	41	3	(	(	PUNCT
ejpam-4277	41	4	λ	λ	PROPN
ejpam-4277	41	5	,	,	PUNCT
ejpam-4277	41	6	sp)-closure	sp)-closure	NOUN
ejpam-4277	41	7	,	,	PUNCT
ejpam-4277	41	8	the	the	DET
ejpam-4277	41	9	following	follow	VERB
ejpam-4277	41	10	properties	property	NOUN
ejpam-4277	41	11	hold	hold	VERB
ejpam-4277	41	12	:	:	PUNCT
ejpam-4277	41	13	(	(	PUNCT
ejpam-4277	41	14	1	1	X
ejpam-4277	41	15	)	)	PUNCT
ejpam-4277	41	16	a	a	DET
ejpam-4277	41	17	⊆	⊆	NUM
ejpam-4277	41	18	a(λ	a(λ	ADJ
ejpam-4277	41	19	,	,	PUNCT
ejpam-4277	41	20	sp	sp	NOUN
ejpam-4277	41	21	)	)	PUNCT
ejpam-4277	41	22	and	and	CCONJ
ejpam-4277	41	23	[	[	X
ejpam-4277	41	24	a(λ	a(λ	ADV
ejpam-4277	41	25	,	,	PUNCT
ejpam-4277	41	26	sp)](λ	sp)](λ	PROPN
ejpam-4277	41	27	,	,	PUNCT
ejpam-4277	41	28	sp	sp	NOUN
ejpam-4277	41	29	)	)	PUNCT
ejpam-4277	41	30	=	=	PUNCT
ejpam-4277	41	31	a(λ	a(λ	ADV
ejpam-4277	41	32	,	,	PUNCT
ejpam-4277	41	33	sp	sp	NOUN
ejpam-4277	41	34	)	)	PUNCT
ejpam-4277	41	35	.	.	PUNCT
ejpam-4277	42	1	(	(	PUNCT
ejpam-4277	42	2	2	2	X
ejpam-4277	42	3	)	)	PUNCT
ejpam-4277	42	4	if	if	SCONJ
ejpam-4277	42	5	a	a	DET
ejpam-4277	42	6	⊆	⊆	NUM
ejpam-4277	42	7	b	b	NOUN
ejpam-4277	42	8	,	,	PUNCT
ejpam-4277	42	9	then	then	ADV
ejpam-4277	42	10	a(λ	a(λ	ADV
ejpam-4277	42	11	,	,	PUNCT
ejpam-4277	42	12	sp	sp	NOUN
ejpam-4277	42	13	)	)	PUNCT
ejpam-4277	42	14	⊆	⊆	NUM
ejpam-4277	42	15	b(λ	b(λ	NOUN
ejpam-4277	42	16	,	,	PUNCT
ejpam-4277	42	17	sp	sp	NOUN
ejpam-4277	42	18	)	)	PUNCT
ejpam-4277	42	19	.	.	PUNCT
ejpam-4277	43	1	(	(	PUNCT
ejpam-4277	43	2	3	3	X
ejpam-4277	43	3	)	)	PUNCT
ejpam-4277	43	4	a(λ	a(λ	ADV
ejpam-4277	43	5	,	,	PUNCT
ejpam-4277	43	6	sp	sp	NOUN
ejpam-4277	43	7	)	)	PUNCT
ejpam-4277	43	8	=	=	SYM
ejpam-4277	43	9	∩{f	∩{f	NOUN
ejpam-4277	43	10	|a	|a	VERB
ejpam-4277	43	11	⊆	⊆	NUM
ejpam-4277	43	12	f	f	PROPN
ejpam-4277	43	13	and	and	CCONJ
ejpam-4277	43	14	f	f	PROPN
ejpam-4277	43	15	is	be	AUX
ejpam-4277	43	16	(	(	PUNCT
ejpam-4277	43	17	λ	λ	X
ejpam-4277	43	18	,	,	PUNCT
ejpam-4277	43	19	sp)-closed	sp)-close	VERB
ejpam-4277	43	20	}	}	PUNCT
ejpam-4277	43	21	.	.	PUNCT
ejpam-4277	44	1	(	(	PUNCT
ejpam-4277	44	2	4	4	NUM
ejpam-4277	44	3	)	)	PUNCT
ejpam-4277	44	4	a(λ	a(λ	ADV
ejpam-4277	44	5	,	,	PUNCT
ejpam-4277	44	6	sp	sp	NOUN
ejpam-4277	44	7	)	)	PUNCT
ejpam-4277	44	8	is	be	AUX
ejpam-4277	44	9	(	(	PUNCT
ejpam-4277	44	10	λ	λ	X
ejpam-4277	44	11	,	,	PUNCT
ejpam-4277	44	12	sp)-closed	sp)-close	VERB
ejpam-4277	44	13	.	.	PUNCT
ejpam-4277	45	1	(	(	PUNCT
ejpam-4277	45	2	5	5	X
ejpam-4277	45	3	)	)	PUNCT
ejpam-4277	45	4	a	a	PRON
ejpam-4277	45	5	is	be	AUX
ejpam-4277	45	6	(	(	PUNCT
ejpam-4277	45	7	λ	λ	X
ejpam-4277	45	8	,	,	PUNCT
ejpam-4277	45	9	sp)-closed	sp)-close	VERB
ejpam-4277	45	10	if	if	SCONJ
ejpam-4277	45	11	and	and	CCONJ
ejpam-4277	45	12	only	only	ADV
ejpam-4277	45	13	if	if	SCONJ
ejpam-4277	45	14	a	a	DET
ejpam-4277	45	15	=	=	X
ejpam-4277	45	16	a(λ	a(λ	ADV
ejpam-4277	45	17	,	,	PUNCT
ejpam-4277	45	18	sp	sp	NOUN
ejpam-4277	45	19	)	)	PUNCT
ejpam-4277	45	20	.	.	PUNCT
ejpam-4277	46	1	lemma	lemma	PROPN
ejpam-4277	46	2	2	2	NUM
ejpam-4277	46	3	.	.	PUNCT
ejpam-4277	47	1	[	[	X
ejpam-4277	47	2	3	3	X
ejpam-4277	47	3	]	]	PUNCT
ejpam-4277	47	4	let	let	VERB
ejpam-4277	47	5	a	a	PRON
ejpam-4277	47	6	and	and	CCONJ
ejpam-4277	47	7	b	b	NOUN
ejpam-4277	47	8	be	be	AUX
ejpam-4277	47	9	subsets	subset	NOUN
ejpam-4277	47	10	of	of	ADP
ejpam-4277	47	11	a	a	DET
ejpam-4277	47	12	topological	topological	ADJ
ejpam-4277	47	13	space	space	NOUN
ejpam-4277	47	14	(	(	PUNCT
ejpam-4277	47	15	x	x	X
ejpam-4277	47	16	,	,	PUNCT
ejpam-4277	47	17	τ	τ	PROPN
ejpam-4277	47	18	)	)	PUNCT
ejpam-4277	47	19	.	.	PUNCT
ejpam-4277	48	1	for	for	ADP
ejpam-4277	48	2	the	the	DET
ejpam-4277	48	3	(	(	PUNCT
ejpam-4277	48	4	λ	λ	PROPN
ejpam-4277	48	5	,	,	PUNCT
ejpam-4277	48	6	sp)interior	sp)interior	PROPN
ejpam-4277	48	7	,	,	PUNCT
ejpam-4277	48	8	the	the	DET
ejpam-4277	48	9	following	follow	VERB
ejpam-4277	48	10	properties	property	NOUN
ejpam-4277	48	11	hold	hold	VERB
ejpam-4277	48	12	:	:	PUNCT
ejpam-4277	48	13	(	(	PUNCT
ejpam-4277	48	14	1	1	X
ejpam-4277	48	15	)	)	PUNCT
ejpam-4277	48	16	a(λ	a(λ	ADV
ejpam-4277	48	17	,	,	PUNCT
ejpam-4277	48	18	sp	sp	NOUN
ejpam-4277	48	19	)	)	PUNCT
ejpam-4277	48	20	⊆	⊆	NUM
ejpam-4277	48	21	a	a	DET
ejpam-4277	48	22	and	and	CCONJ
ejpam-4277	48	23	[	[	X
ejpam-4277	48	24	a(λ	a(λ	ADV
ejpam-4277	48	25	,	,	PUNCT
ejpam-4277	48	26	sp)](λ	sp)](λ	PROPN
ejpam-4277	48	27	,	,	PUNCT
ejpam-4277	48	28	sp	sp	NOUN
ejpam-4277	48	29	)	)	PUNCT
ejpam-4277	48	30	=	=	PUNCT
ejpam-4277	48	31	a(λ	a(λ	ADV
ejpam-4277	48	32	,	,	PUNCT
ejpam-4277	48	33	sp	sp	NOUN
ejpam-4277	48	34	)	)	PUNCT
ejpam-4277	48	35	.	.	PUNCT
ejpam-4277	49	1	(	(	PUNCT
ejpam-4277	49	2	2	2	X
ejpam-4277	49	3	)	)	PUNCT
ejpam-4277	49	4	if	if	SCONJ
ejpam-4277	49	5	a	a	DET
ejpam-4277	49	6	⊆	⊆	NUM
ejpam-4277	49	7	b	b	NOUN
ejpam-4277	49	8	,	,	PUNCT
ejpam-4277	49	9	then	then	ADV
ejpam-4277	49	10	a(λ	a(λ	ADV
ejpam-4277	49	11	,	,	PUNCT
ejpam-4277	49	12	sp	sp	NOUN
ejpam-4277	49	13	)	)	PUNCT
ejpam-4277	49	14	⊆	⊆	NUM
ejpam-4277	49	15	b(λ	b(λ	NOUN
ejpam-4277	49	16	,	,	PUNCT
ejpam-4277	49	17	sp	sp	NOUN
ejpam-4277	49	18	)	)	PUNCT
ejpam-4277	49	19	.	.	PUNCT
ejpam-4277	50	1	(	(	PUNCT
ejpam-4277	50	2	3	3	X
ejpam-4277	50	3	)	)	PUNCT
ejpam-4277	50	4	a(λ	a(λ	ADV
ejpam-4277	50	5	,	,	PUNCT
ejpam-4277	50	6	sp	sp	NOUN
ejpam-4277	50	7	)	)	PUNCT
ejpam-4277	50	8	is	be	AUX
ejpam-4277	50	9	(	(	PUNCT
ejpam-4277	50	10	λ	λ	INTJ
ejpam-4277	50	11	,	,	PUNCT
ejpam-4277	50	12	sp)-open	sp)-open	NOUN
ejpam-4277	50	13	.	.	PUNCT
ejpam-4277	51	1	(	(	PUNCT
ejpam-4277	51	2	4	4	X
ejpam-4277	51	3	)	)	PUNCT
ejpam-4277	51	4	a	a	DET
ejpam-4277	51	5	is	be	AUX
ejpam-4277	51	6	(	(	PUNCT
ejpam-4277	51	7	λ	λ	NOUN
ejpam-4277	51	8	,	,	PUNCT
ejpam-4277	51	9	sp)-open	sp)-open	ADJ
ejpam-4277	51	10	if	if	SCONJ
ejpam-4277	51	11	and	and	CCONJ
ejpam-4277	51	12	only	only	ADV
ejpam-4277	51	13	if	if	SCONJ
ejpam-4277	51	14	a(λ	a(λ	ADV
ejpam-4277	51	15	,	,	PUNCT
ejpam-4277	51	16	sp	sp	NOUN
ejpam-4277	51	17	)	)	PUNCT
ejpam-4277	51	18	=	=	SYM
ejpam-4277	51	19	a.	a.	NOUN
ejpam-4277	51	20	(	(	PUNCT
ejpam-4277	51	21	5	5	NUM
ejpam-4277	51	22	)	)	PUNCT
ejpam-4277	52	1	[	[	X
ejpam-4277	52	2	x	x	X
ejpam-4277	52	3	−a](λ	−a](λ	PROPN
ejpam-4277	52	4	,	,	PUNCT
ejpam-4277	52	5	sp	sp	NOUN
ejpam-4277	52	6	)	)	PUNCT
ejpam-4277	52	7	=	=	SYM
ejpam-4277	52	8	x	x	SYM
ejpam-4277	52	9	−a(λ	−a(λ	NOUN
ejpam-4277	52	10	,	,	PUNCT
ejpam-4277	52	11	sp	sp	NOUN
ejpam-4277	52	12	)	)	PUNCT
ejpam-4277	52	13	.	.	PUNCT
ejpam-4277	53	1	(	(	PUNCT
ejpam-4277	53	2	6	6	NUM
ejpam-4277	53	3	)	)	PUNCT
ejpam-4277	54	1	[	[	X
ejpam-4277	54	2	x	x	X
ejpam-4277	54	3	−a](λ	−a](λ	PROPN
ejpam-4277	54	4	,	,	PUNCT
ejpam-4277	54	5	sp	sp	NOUN
ejpam-4277	54	6	)	)	PUNCT
ejpam-4277	54	7	=	=	SYM
ejpam-4277	54	8	x	x	SYM
ejpam-4277	54	9	−a(λ	−a(λ	NOUN
ejpam-4277	54	10	,	,	PUNCT
ejpam-4277	54	11	sp	sp	NOUN
ejpam-4277	54	12	)	)	PUNCT
ejpam-4277	54	13	.	.	PUNCT
ejpam-4277	55	1	c.	c.	PROPN
ejpam-4277	55	2	boonpok	boonpok	PROPN
ejpam-4277	55	3	,	,	PUNCT
ejpam-4277	55	4	j.	j.	PROPN
ejpam-4277	55	5	khampakdee	khampakdee	PROPN
ejpam-4277	55	6	/	/	PUNCT
ejpam-4277	55	7	eur	eur	PROPN
ejpam-4277	55	8	.	.	PUNCT
ejpam-4277	56	1	j.	j.	PROPN
ejpam-4277	56	2	pure	pure	PROPN
ejpam-4277	56	3	appl	appl	PROPN
ejpam-4277	56	4	.	.	PROPN
ejpam-4277	56	5	math	math	PROPN
ejpam-4277	56	6	,	,	PUNCT
ejpam-4277	56	7	15	15	NUM
ejpam-4277	56	8	(	(	PUNCT
ejpam-4277	56	9	2	2	NUM
ejpam-4277	56	10	)	)	PUNCT
ejpam-4277	56	11	(	(	PUNCT
ejpam-4277	56	12	2022	2022	NUM
ejpam-4277	56	13	)	)	PUNCT
ejpam-4277	56	14	,	,	PUNCT
ejpam-4277	56	15	626	626	NUM
ejpam-4277	56	16	-	-	SYM
ejpam-4277	56	17	634	634	NUM
ejpam-4277	56	18	628	628	NUM
ejpam-4277	56	19	a	a	DET
ejpam-4277	56	20	subset	subset	NOUN
ejpam-4277	56	21	a	a	PRON
ejpam-4277	56	22	of	of	ADP
ejpam-4277	56	23	a	a	DET
ejpam-4277	56	24	topological	topological	ADJ
ejpam-4277	56	25	space	space	NOUN
ejpam-4277	56	26	(	(	PUNCT
ejpam-4277	56	27	x	x	X
ejpam-4277	56	28	,	,	PUNCT
ejpam-4277	56	29	τ	τ	X
ejpam-4277	56	30	)	)	PUNCT
ejpam-4277	56	31	is	be	AUX
ejpam-4277	56	32	said	say	VERB
ejpam-4277	56	33	to	to	PART
ejpam-4277	56	34	be	be	AUX
ejpam-4277	56	35	s(λ	s(λ	NOUN
ejpam-4277	56	36	,	,	PUNCT
ejpam-4277	56	37	sp)-open	sp)-open	ADJ
ejpam-4277	56	38	(	(	PUNCT
ejpam-4277	56	39	resp	resp	NOUN
ejpam-4277	56	40	.	.	PUNCT
ejpam-4277	57	1	p(λ	p(λ	NOUN
ejpam-4277	57	2	,	,	PUNCT
ejpam-4277	57	3	sp)-open	sp)-open	NOUN
ejpam-4277	57	4	,	,	PUNCT
ejpam-4277	57	5	r(λ	r(λ	NOUN
ejpam-4277	57	6	,	,	PUNCT
ejpam-4277	57	7	sp)-open	sp)-open	NOUN
ejpam-4277	57	8	,	,	PUNCT
ejpam-4277	57	9	α(λ	α(λ	PROPN
ejpam-4277	57	10	,	,	PUNCT
ejpam-4277	57	11	sp)-open	sp)-open	NOUN
ejpam-4277	57	12	,	,	PUNCT
ejpam-4277	57	13	β(λ	β(λ	X
ejpam-4277	57	14	,	,	PUNCT
ejpam-4277	57	15	sp)-open	sp)-open	NOUN
ejpam-4277	57	16	)	)	PUNCT
ejpam-4277	57	17	if	if	SCONJ
ejpam-4277	57	18	a	a	DET
ejpam-4277	57	19	⊆	⊆	NUM
ejpam-4277	57	20	[	[	X
ejpam-4277	57	21	a(λ	a(λ	ADV
ejpam-4277	57	22	,	,	PUNCT
ejpam-4277	57	23	sp	sp	NOUN
ejpam-4277	57	24	)	)	PUNCT
ejpam-4277	57	25	]	]	PUNCT
ejpam-4277	57	26	(	(	PUNCT
ejpam-4277	57	27	λ	λ	NOUN
ejpam-4277	57	28	,	,	PUNCT
ejpam-4277	57	29	sp	sp	NOUN
ejpam-4277	57	30	)	)	PUNCT
ejpam-4277	57	31	(	(	PUNCT
ejpam-4277	57	32	resp	resp	NOUN
ejpam-4277	57	33	.	.	PUNCT
ejpam-4277	58	1	a	a	DET
ejpam-4277	58	2	⊆	⊆	NUM
ejpam-4277	58	3	[	[	X
ejpam-4277	58	4	a(λ	a(λ	ADJ
ejpam-4277	58	5	,	,	PUNCT
ejpam-4277	58	6	sp)](λ	sp)](λ	PROPN
ejpam-4277	58	7	,	,	PUNCT
ejpam-4277	58	8	sp	sp	NOUN
ejpam-4277	58	9	)	)	PUNCT
ejpam-4277	58	10	,	,	PUNCT
ejpam-4277	59	1	a	a	DET
ejpam-4277	59	2	=	=	X
ejpam-4277	59	3	[	[	X
ejpam-4277	59	4	a(λ	a(λ	PROPN
ejpam-4277	59	5	,	,	PUNCT
ejpam-4277	59	6	sp)](λ	sp)](λ	PROPN
ejpam-4277	59	7	,	,	PUNCT
ejpam-4277	59	8	sp	sp	NOUN
ejpam-4277	59	9	)	)	PUNCT
ejpam-4277	59	10	,	,	PUNCT
ejpam-4277	59	11	a	a	DET
ejpam-4277	59	12	⊆	⊆	NUM
ejpam-4277	59	13	[	[	X
ejpam-4277	59	14	[	[	X
ejpam-4277	59	15	a(λ	a(λ	ADJ
ejpam-4277	59	16	,	,	PUNCT
ejpam-4277	59	17	sp	sp	NOUN
ejpam-4277	59	18	)	)	PUNCT
ejpam-4277	59	19	]	]	PUNCT
ejpam-4277	59	20	(	(	PUNCT
ejpam-4277	59	21	λ	λ	X
ejpam-4277	59	22	,	,	PUNCT
ejpam-4277	59	23	sp)](λ	sp)](λ	PROPN
ejpam-4277	59	24	,	,	PUNCT
ejpam-4277	59	25	sp	sp	NOUN
ejpam-4277	59	26	)	)	PUNCT
ejpam-4277	59	27	,	,	PUNCT
ejpam-4277	60	1	a	a	DET
ejpam-4277	60	2	⊆	⊆	NUM
ejpam-4277	60	3	[	[	X
ejpam-4277	60	4	[	[	X
ejpam-4277	60	5	a(λ	a(λ	ADJ
ejpam-4277	60	6	,	,	PUNCT
ejpam-4277	60	7	sp)](λ	sp)](λ	PROPN
ejpam-4277	60	8	,	,	PUNCT
ejpam-4277	60	9	sp	sp	NOUN
ejpam-4277	60	10	)	)	PUNCT
ejpam-4277	60	11	]	]	PUNCT
ejpam-4277	61	1	(	(	PUNCT
ejpam-4277	61	2	λ	λ	NOUN
ejpam-4277	61	3	,	,	PUNCT
ejpam-4277	61	4	sp	sp	NOUN
ejpam-4277	61	5	)	)	PUNCT
ejpam-4277	61	6	)	)	PUNCT
ejpam-4277	62	1	[	[	X
ejpam-4277	62	2	3	3	NUM
ejpam-4277	62	3	]	]	PUNCT
ejpam-4277	62	4	.	.	PUNCT
ejpam-4277	63	1	the	the	DET
ejpam-4277	63	2	complement	complement	NOUN
ejpam-4277	63	3	of	of	ADP
ejpam-4277	63	4	a	a	DET
ejpam-4277	63	5	s(λ	s(λ	PROPN
ejpam-4277	63	6	,	,	PUNCT
ejpam-4277	63	7	sp)-open	sp)-open	ADJ
ejpam-4277	63	8	(	(	PUNCT
ejpam-4277	63	9	resp	resp	NOUN
ejpam-4277	63	10	.	.	PUNCT
ejpam-4277	64	1	p(λ	p(λ	NOUN
ejpam-4277	64	2	,	,	PUNCT
ejpam-4277	64	3	sp)-open	sp)-open	NOUN
ejpam-4277	64	4	,	,	PUNCT
ejpam-4277	64	5	r(λ	r(λ	NOUN
ejpam-4277	64	6	,	,	PUNCT
ejpam-4277	64	7	sp)-open	sp)-open	NOUN
ejpam-4277	64	8	,	,	PUNCT
ejpam-4277	64	9	α(λ	α(λ	PROPN
ejpam-4277	64	10	,	,	PUNCT
ejpam-4277	64	11	sp)-open	sp)-open	NOUN
ejpam-4277	64	12	,	,	PUNCT
ejpam-4277	64	13	β(λ	β(λ	X
ejpam-4277	64	14	,	,	PUNCT
ejpam-4277	64	15	sp)-open	sp)-open	NOUN
ejpam-4277	64	16	)	)	PUNCT
ejpam-4277	64	17	set	set	NOUN
ejpam-4277	64	18	is	be	AUX
ejpam-4277	64	19	said	say	VERB
ejpam-4277	64	20	to	to	PART
ejpam-4277	64	21	be	be	AUX
ejpam-4277	64	22	s(λ	s(λ	PROPN
ejpam-4277	64	23	,	,	PUNCT
ejpam-4277	64	24	sp)-closed	sp)-close	VERB
ejpam-4277	64	25	(	(	PUNCT
ejpam-4277	64	26	resp	resp	NOUN
ejpam-4277	64	27	.	.	PUNCT
ejpam-4277	65	1	p(λ	p(λ	NOUN
ejpam-4277	65	2	,	,	PUNCT
ejpam-4277	65	3	sp)-closed	sp)-close	VERB
ejpam-4277	65	4	,	,	PUNCT
ejpam-4277	65	5	r(λ	r(λ	PROPN
ejpam-4277	65	6	,	,	PUNCT
ejpam-4277	65	7	sp)-closed	sp)-close	VERB
ejpam-4277	65	8	,	,	PUNCT
ejpam-4277	65	9	α(λ	α(λ	PROPN
ejpam-4277	65	10	,	,	PUNCT
ejpam-4277	65	11	sp)-closed	sp)-close	VERB
ejpam-4277	65	12	,	,	PUNCT
ejpam-4277	65	13	β(λ	β(λ	X
ejpam-4277	65	14	,	,	PUNCT
ejpam-4277	65	15	sp)-closed	sp)-close	VERB
ejpam-4277	65	16	)	)	PUNCT
ejpam-4277	65	17	.	.	PUNCT
ejpam-4277	66	1	the	the	DET
ejpam-4277	66	2	family	family	NOUN
ejpam-4277	66	3	of	of	ADP
ejpam-4277	66	4	all	all	DET
ejpam-4277	66	5	s(λ	s(λ	NOUN
ejpam-4277	66	6	,	,	PUNCT
ejpam-4277	66	7	sp)-open	sp)-open	ADJ
ejpam-4277	66	8	(	(	PUNCT
ejpam-4277	66	9	resp	resp	NOUN
ejpam-4277	66	10	.	.	PUNCT
ejpam-4277	67	1	p(λ	p(λ	NOUN
ejpam-4277	67	2	,	,	PUNCT
ejpam-4277	67	3	sp)-open	sp)-open	NOUN
ejpam-4277	67	4	,	,	PUNCT
ejpam-4277	67	5	r(λ	r(λ	NOUN
ejpam-4277	67	6	,	,	PUNCT
ejpam-4277	67	7	sp)-open	sp)-open	NOUN
ejpam-4277	67	8	,	,	PUNCT
ejpam-4277	67	9	α(λ	α(λ	PROPN
ejpam-4277	67	10	,	,	PUNCT
ejpam-4277	67	11	sp)-open	sp)-open	NOUN
ejpam-4277	67	12	,	,	PUNCT
ejpam-4277	67	13	β(λ	β(λ	X
ejpam-4277	67	14	,	,	PUNCT
ejpam-4277	67	15	sp)-open	sp)-open	NOUN
ejpam-4277	67	16	)	)	PUNCT
ejpam-4277	67	17	sets	set	NOUN
ejpam-4277	67	18	in	in	ADP
ejpam-4277	67	19	a	a	DET
ejpam-4277	67	20	topological	topological	ADJ
ejpam-4277	67	21	space	space	NOUN
ejpam-4277	67	22	(	(	PUNCT
ejpam-4277	67	23	x	x	X
ejpam-4277	67	24	,	,	PUNCT
ejpam-4277	67	25	τ	τ	X
ejpam-4277	67	26	)	)	PUNCT
ejpam-4277	67	27	is	be	AUX
ejpam-4277	67	28	denoted	denote	VERB
ejpam-4277	67	29	by	by	ADP
ejpam-4277	67	30	sλspo(x	sλspo(x	PROPN
ejpam-4277	67	31	,	,	PUNCT
ejpam-4277	67	32	τ	τ	PROPN
ejpam-4277	67	33	)	)	PUNCT
ejpam-4277	67	34	(	(	PUNCT
ejpam-4277	67	35	resp	resp	NOUN
ejpam-4277	67	36	.	.	PUNCT
ejpam-4277	68	1	pλspo(x	pλspo(x	ADJ
ejpam-4277	68	2	,	,	PUNCT
ejpam-4277	68	3	τ	τ	PROPN
ejpam-4277	68	4	)	)	PUNCT
ejpam-4277	68	5	,	,	PUNCT
ejpam-4277	68	6	rλspo(x	rλspo(x	PROPN
ejpam-4277	68	7	,	,	PUNCT
ejpam-4277	68	8	τ	τ	PROPN
ejpam-4277	68	9	)	)	PUNCT
ejpam-4277	68	10	,	,	PUNCT
ejpam-4277	68	11	αλspo(x	αλspo(x	NOUN
ejpam-4277	68	12	,	,	PUNCT
ejpam-4277	68	13	τ	τ	PROPN
ejpam-4277	68	14	)	)	PUNCT
ejpam-4277	68	15	,	,	PUNCT
ejpam-4277	68	16	βλspo(x	βλspo(x	PROPN
ejpam-4277	68	17	,	,	PUNCT
ejpam-4277	68	18	τ	τ	PROPN
ejpam-4277	68	19	)	)	PUNCT
ejpam-4277	68	20	)	)	PUNCT
ejpam-4277	68	21	.	.	PUNCT
ejpam-4277	69	1	the	the	DET
ejpam-4277	69	2	intersection	intersection	NOUN
ejpam-4277	69	3	of	of	ADP
ejpam-4277	69	4	all	all	DET
ejpam-4277	69	5	α(λ	α(λ	PROPN
ejpam-4277	69	6	,	,	PUNCT
ejpam-4277	69	7	sp)-closed	sp)-close	VERB
ejpam-4277	69	8	(	(	PUNCT
ejpam-4277	69	9	resp	resp	NOUN
ejpam-4277	69	10	.	.	PUNCT
ejpam-4277	70	1	s(λ	s(λ	NOUN
ejpam-4277	70	2	,	,	PUNCT
ejpam-4277	70	3	sp)-closed	sp)-close	VERB
ejpam-4277	70	4	)	)	PUNCT
ejpam-4277	70	5	sets	set	NOUN
ejpam-4277	70	6	containing	contain	VERB
ejpam-4277	70	7	a	a	PRON
ejpam-4277	70	8	is	be	AUX
ejpam-4277	70	9	called	call	VERB
ejpam-4277	70	10	the	the	DET
ejpam-4277	70	11	α(λ	α(λ	PROPN
ejpam-4277	70	12	,	,	PUNCT
ejpam-4277	70	13	sp)-closure	sp)-closure	NOUN
ejpam-4277	70	14	(	(	PUNCT
ejpam-4277	70	15	resp	resp	NOUN
ejpam-4277	70	16	.	.	PUNCT
ejpam-4277	71	1	s(λ	s(λ	NOUN
ejpam-4277	71	2	,	,	PUNCT
ejpam-4277	71	3	sp)-closure	sp)-closure	NOUN
ejpam-4277	71	4	)	)	PUNCT
ejpam-4277	71	5	of	of	ADP
ejpam-4277	71	6	a	a	PRON
ejpam-4277	71	7	and	and	CCONJ
ejpam-4277	71	8	is	be	AUX
ejpam-4277	71	9	denoted	denote	VERB
ejpam-4277	71	10	by	by	ADP
ejpam-4277	71	11	aα(λ	aα(λ	PROPN
ejpam-4277	71	12	,	,	PUNCT
ejpam-4277	71	13	sp	sp	NOUN
ejpam-4277	71	14	)	)	PUNCT
ejpam-4277	71	15	(	(	PUNCT
ejpam-4277	71	16	resp	resp	NOUN
ejpam-4277	71	17	.	.	PUNCT
ejpam-4277	72	1	as(λ	as(λ	PROPN
ejpam-4277	72	2	,	,	PUNCT
ejpam-4277	72	3	sp	sp	NOUN
ejpam-4277	72	4	)	)	PUNCT
ejpam-4277	72	5	)	)	PUNCT
ejpam-4277	72	6	.	.	PUNCT
ejpam-4277	73	1	the	the	DET
ejpam-4277	73	2	union	union	NOUN
ejpam-4277	73	3	of	of	ADP
ejpam-4277	73	4	all	all	DET
ejpam-4277	73	5	α(λ	α(λ	PROPN
ejpam-4277	73	6	,	,	PUNCT
ejpam-4277	73	7	sp)-open	sp)-open	ADJ
ejpam-4277	73	8	(	(	PUNCT
ejpam-4277	73	9	resp	resp	NOUN
ejpam-4277	73	10	.	.	PUNCT
ejpam-4277	74	1	s(λ	s(λ	NOUN
ejpam-4277	74	2	,	,	PUNCT
ejpam-4277	74	3	sp)-open	sp)-open	NOUN
ejpam-4277	74	4	)	)	PUNCT
ejpam-4277	74	5	sets	set	NOUN
ejpam-4277	74	6	contained	contain	VERB
ejpam-4277	74	7	in	in	ADP
ejpam-4277	74	8	a	a	PRON
ejpam-4277	74	9	is	be	AUX
ejpam-4277	74	10	called	call	VERB
ejpam-4277	74	11	the	the	DET
ejpam-4277	74	12	α(λ	α(λ	PROPN
ejpam-4277	74	13	,	,	PUNCT
ejpam-4277	74	14	sp)-interior	sp)-interior	NOUN
ejpam-4277	74	15	(	(	PUNCT
ejpam-4277	74	16	resp	resp	NOUN
ejpam-4277	74	17	.	.	PUNCT
ejpam-4277	75	1	s(λ	s(λ	NOUN
ejpam-4277	75	2	,	,	PUNCT
ejpam-4277	75	3	sp)-interior	sp)-interior	NOUN
ejpam-4277	75	4	)	)	PUNCT
ejpam-4277	75	5	of	of	ADP
ejpam-4277	75	6	a	a	PRON
ejpam-4277	75	7	and	and	CCONJ
ejpam-4277	75	8	is	be	AUX
ejpam-4277	75	9	denoted	denote	VERB
ejpam-4277	75	10	by	by	ADP
ejpam-4277	75	11	aα(λ	aα(λ	PROPN
ejpam-4277	75	12	,	,	PUNCT
ejpam-4277	75	13	sp	sp	NOUN
ejpam-4277	75	14	)	)	PUNCT
ejpam-4277	75	15	(	(	PUNCT
ejpam-4277	75	16	resp	resp	NOUN
ejpam-4277	75	17	.	.	PUNCT
ejpam-4277	76	1	as(λ	as(λ	PROPN
ejpam-4277	76	2	,	,	PUNCT
ejpam-4277	76	3	sp	sp	NOUN
ejpam-4277	76	4	)	)	PUNCT
ejpam-4277	76	5	)	)	PUNCT
ejpam-4277	76	6	.	.	PUNCT
ejpam-4277	77	1	lemma	lemma	PROPN
ejpam-4277	77	2	3	3	X
ejpam-4277	77	3	.	.	PUNCT
ejpam-4277	78	1	let	let	VERB
ejpam-4277	78	2	a	a	DET
ejpam-4277	78	3	be	be	AUX
ejpam-4277	78	4	a	a	DET
ejpam-4277	78	5	subset	subset	NOUN
ejpam-4277	78	6	of	of	ADP
ejpam-4277	78	7	a	a	DET
ejpam-4277	78	8	topological	topological	ADJ
ejpam-4277	78	9	space	space	NOUN
ejpam-4277	78	10	(	(	PUNCT
ejpam-4277	78	11	x	x	X
ejpam-4277	78	12	,	,	PUNCT
ejpam-4277	78	13	τ	τ	PROPN
ejpam-4277	78	14	)	)	PUNCT
ejpam-4277	78	15	.	.	PUNCT
ejpam-4277	79	1	then	then	ADV
ejpam-4277	79	2	,	,	PUNCT
ejpam-4277	79	3	x	x	PUNCT
ejpam-4277	79	4	∈	∈	NOUN
ejpam-4277	79	5	as(λ	as(λ	NOUN
ejpam-4277	79	6	,	,	PUNCT
ejpam-4277	79	7	sp	sp	NOUN
ejpam-4277	79	8	)	)	PUNCT
ejpam-4277	79	9	if	if	SCONJ
ejpam-4277	79	10	and	and	CCONJ
ejpam-4277	79	11	only	only	ADV
ejpam-4277	79	12	if	if	SCONJ
ejpam-4277	79	13	u	u	PROPN
ejpam-4277	79	14	∩a	∩a	PROPN
ejpam-4277	79	15	6=	6=	ADP
ejpam-4277	79	16	∅	∅	NOUN
ejpam-4277	79	17	for	for	ADP
ejpam-4277	79	18	every	every	DET
ejpam-4277	79	19	u	u	PROPN
ejpam-4277	79	20	∈	∈	PROPN
ejpam-4277	79	21	sλspo(x	sλspo(x	PROPN
ejpam-4277	79	22	,	,	PUNCT
ejpam-4277	79	23	τ	τ	X
ejpam-4277	79	24	)	)	PUNCT
ejpam-4277	79	25	containing	contain	VERB
ejpam-4277	79	26	x.	x.	PROPN
ejpam-4277	79	27	lemma	lemma	PROPN
ejpam-4277	79	28	4	4	X
ejpam-4277	79	29	.	.	PUNCT
ejpam-4277	79	30	let	let	VERB
ejpam-4277	79	31	a	a	DET
ejpam-4277	79	32	be	be	AUX
ejpam-4277	79	33	a	a	DET
ejpam-4277	79	34	subset	subset	NOUN
ejpam-4277	79	35	of	of	ADP
ejpam-4277	79	36	a	a	DET
ejpam-4277	79	37	topological	topological	ADJ
ejpam-4277	79	38	space	space	NOUN
ejpam-4277	79	39	(	(	PUNCT
ejpam-4277	79	40	x	x	X
ejpam-4277	79	41	,	,	PUNCT
ejpam-4277	79	42	τ	τ	PROPN
ejpam-4277	79	43	)	)	PUNCT
ejpam-4277	79	44	.	.	PUNCT
ejpam-4277	80	1	then	then	ADV
ejpam-4277	80	2	,	,	PUNCT
ejpam-4277	80	3	aα(λ	aα(λ	PROPN
ejpam-4277	80	4	,	,	PUNCT
ejpam-4277	80	5	sp	sp	NOUN
ejpam-4277	80	6	)	)	PUNCT
ejpam-4277	80	7	=	=	NOUN
ejpam-4277	81	1	a	a	DET
ejpam-4277	81	2	∪	∪	ADJ
ejpam-4277	81	3	[	[	X
ejpam-4277	81	4	[	[	X
ejpam-4277	81	5	a(λ	a(λ	ADJ
ejpam-4277	81	6	,	,	PUNCT
ejpam-4277	81	7	sp)](λ	sp)](λ	PROPN
ejpam-4277	81	8	,	,	PUNCT
ejpam-4277	81	9	sp	sp	NOUN
ejpam-4277	81	10	)	)	PUNCT
ejpam-4277	81	11	]	]	PUNCT
ejpam-4277	81	12	(	(	PUNCT
ejpam-4277	81	13	λ	λ	NOUN
ejpam-4277	81	14	,	,	PUNCT
ejpam-4277	81	15	sp	sp	NOUN
ejpam-4277	81	16	)	)	PUNCT
ejpam-4277	81	17	.	.	PUNCT
ejpam-4277	82	1	by	by	ADP
ejpam-4277	82	2	a	a	DET
ejpam-4277	82	3	multifunction	multifunction	NOUN
ejpam-4277	82	4	f	f	NOUN
ejpam-4277	82	5	:	:	PUNCT
ejpam-4277	82	6	x	x	X
ejpam-4277	82	7	→	→	SYM
ejpam-4277	82	8	y	y	PROPN
ejpam-4277	82	9	,	,	PUNCT
ejpam-4277	82	10	we	we	PRON
ejpam-4277	82	11	mean	mean	VERB
ejpam-4277	82	12	a	a	DET
ejpam-4277	82	13	point	point	NOUN
ejpam-4277	82	14	-	-	PUNCT
ejpam-4277	82	15	to	to	ADP
ejpam-4277	82	16	-	-	PUNCT
ejpam-4277	82	17	set	set	VERB
ejpam-4277	82	18	correspondence	correspondence	NOUN
ejpam-4277	82	19	from	from	ADP
ejpam-4277	82	20	x	x	PUNCT
ejpam-4277	82	21	into	into	ADP
ejpam-4277	82	22	y	y	PROPN
ejpam-4277	82	23	,	,	PUNCT
ejpam-4277	82	24	and	and	CCONJ
ejpam-4277	82	25	always	always	ADV
ejpam-4277	82	26	assume	assume	VERB
ejpam-4277	82	27	that	that	SCONJ
ejpam-4277	82	28	f	f	PROPN
ejpam-4277	82	29	(	(	PUNCT
ejpam-4277	82	30	x	x	X
ejpam-4277	82	31	)	)	PUNCT
ejpam-4277	82	32	6=	6=	ADP
ejpam-4277	82	33	∅	∅	NOUN
ejpam-4277	82	34	for	for	ADP
ejpam-4277	82	35	all	all	PRON
ejpam-4277	82	36	x	x	SYM
ejpam-4277	82	37	∈	∈	ADJ
ejpam-4277	82	38	x.	x.	NOUN
ejpam-4277	82	39	for	for	ADP
ejpam-4277	82	40	a	a	DET
ejpam-4277	82	41	multifunction	multifunction	NOUN
ejpam-4277	83	1	f	f	NOUN
ejpam-4277	83	2	:	:	PUNCT
ejpam-4277	83	3	x	x	X
ejpam-4277	83	4	→	→	SYM
ejpam-4277	83	5	y	y	PROPN
ejpam-4277	83	6	,	,	PUNCT
ejpam-4277	83	7	following	follow	VERB
ejpam-4277	83	8	[	[	X
ejpam-4277	83	9	2	2	X
ejpam-4277	83	10	]	]	PUNCT
ejpam-4277	83	11	we	we	PRON
ejpam-4277	83	12	shall	shall	AUX
ejpam-4277	83	13	denote	denote	VERB
ejpam-4277	83	14	the	the	DET
ejpam-4277	83	15	upper	upper	ADJ
ejpam-4277	83	16	and	and	CCONJ
ejpam-4277	83	17	lower	low	ADJ
ejpam-4277	83	18	inverse	inverse	NOUN
ejpam-4277	83	19	of	of	ADP
ejpam-4277	83	20	a	a	DET
ejpam-4277	83	21	set	set	NOUN
ejpam-4277	83	22	b	b	PROPN
ejpam-4277	83	23	of	of	ADP
ejpam-4277	83	24	y	y	PROPN
ejpam-4277	83	25	by	by	ADP
ejpam-4277	83	26	f+(b	f+(b	NOUN
ejpam-4277	83	27	)	)	PUNCT
ejpam-4277	83	28	and	and	CCONJ
ejpam-4277	83	29	f−(b	f−(b	NOUN
ejpam-4277	83	30	)	)	PUNCT
ejpam-4277	83	31	,	,	PUNCT
ejpam-4277	83	32	respectively	respectively	ADV
ejpam-4277	83	33	,	,	PUNCT
ejpam-4277	83	34	that	that	ADV
ejpam-4277	83	35	is	is	ADV
ejpam-4277	83	36	,	,	PUNCT
ejpam-4277	83	37	f+(b	f+(b	NOUN
ejpam-4277	83	38	)	)	PUNCT
ejpam-4277	83	39	=	=	PRON
ejpam-4277	84	1	{	{	PUNCT
ejpam-4277	84	2	x	x	PUNCT
ejpam-4277	84	3	∈	∈	PROPN
ejpam-4277	84	4	x	x	INTJ
ejpam-4277	85	1	|	|	NOUN
ejpam-4277	85	2	f	f	X
ejpam-4277	85	3	(	(	PUNCT
ejpam-4277	85	4	x	x	NOUN
ejpam-4277	85	5	)	)	PUNCT
ejpam-4277	85	6	⊆	⊆	NUM
ejpam-4277	85	7	b	b	NOUN
ejpam-4277	85	8	}	}	PUNCT
ejpam-4277	85	9	and	and	CCONJ
ejpam-4277	85	10	f−(b	f−(b	PROPN
ejpam-4277	85	11	)	)	PUNCT
ejpam-4277	85	12	=	=	PRON
ejpam-4277	86	1	{	{	PUNCT
ejpam-4277	86	2	x	x	PUNCT
ejpam-4277	86	3	∈	∈	PROPN
ejpam-4277	86	4	x	x	INTJ
ejpam-4277	87	1	|	|	NOUN
ejpam-4277	87	2	f	f	X
ejpam-4277	87	3	(	(	PUNCT
ejpam-4277	87	4	x)∩b	x)∩b	PROPN
ejpam-4277	87	5	6=	6=	NUM
ejpam-4277	87	6	∅	∅	NOUN
ejpam-4277	87	7	}	}	PUNCT
ejpam-4277	87	8	.	.	PUNCT
ejpam-4277	88	1	in	in	ADP
ejpam-4277	88	2	particular	particular	ADJ
ejpam-4277	88	3	,	,	PUNCT
ejpam-4277	88	4	f−(y	f−(y	NOUN
ejpam-4277	88	5	)	)	PUNCT
ejpam-4277	88	6	=	=	SYM
ejpam-4277	89	1	{	{	PUNCT
ejpam-4277	89	2	x	x	PUNCT
ejpam-4277	89	3	∈	∈	PROPN
ejpam-4277	89	4	x	x	INTJ
ejpam-4277	90	1	|	|	ADV
ejpam-4277	90	2	y	y	PROPN
ejpam-4277	90	3	∈	∈	PROPN
ejpam-4277	90	4	f	f	X
ejpam-4277	90	5	(	(	PUNCT
ejpam-4277	90	6	x	x	NOUN
ejpam-4277	90	7	)	)	PUNCT
ejpam-4277	90	8	}	}	PUNCT
ejpam-4277	90	9	for	for	ADP
ejpam-4277	90	10	each	each	DET
ejpam-4277	90	11	point	point	NOUN
ejpam-4277	90	12	y	y	PROPN
ejpam-4277	90	13	∈	∈	PROPN
ejpam-4277	90	14	y	y	PROPN
ejpam-4277	90	15	.	.	PUNCT
ejpam-4277	91	1	for	for	ADP
ejpam-4277	91	2	each	each	PRON
ejpam-4277	91	3	a	a	DET
ejpam-4277	91	4	⊆	⊆	NUM
ejpam-4277	91	5	x	x	SYM
ejpam-4277	91	6	,	,	PUNCT
ejpam-4277	91	7	f	f	PROPN
ejpam-4277	91	8	(	(	PUNCT
ejpam-4277	91	9	a	a	NOUN
ejpam-4277	91	10	)	)	PUNCT
ejpam-4277	91	11	=	=	SYM
ejpam-4277	91	12	∪x∈af	∪x∈af	NOUN
ejpam-4277	91	13	(	(	PUNCT
ejpam-4277	91	14	x	x	NOUN
ejpam-4277	91	15	)	)	PUNCT
ejpam-4277	91	16	.	.	PUNCT
ejpam-4277	92	1	let	let	VERB
ejpam-4277	92	2	p(y	p(y	PROPN
ejpam-4277	92	3	)	)	PUNCT
ejpam-4277	92	4	be	be	AUX
ejpam-4277	92	5	the	the	DET
ejpam-4277	92	6	collection	collection	NOUN
ejpam-4277	92	7	of	of	ADP
ejpam-4277	92	8	all	all	DET
ejpam-4277	92	9	nonempty	nonempty	ADJ
ejpam-4277	92	10	subsets	subset	NOUN
ejpam-4277	92	11	of	of	ADP
ejpam-4277	92	12	y	y	PROPN
ejpam-4277	92	13	.	.	PUNCT
ejpam-4277	93	1	for	for	ADP
ejpam-4277	93	2	any	any	DET
ejpam-4277	93	3	(	(	PUNCT
ejpam-4277	93	4	λ	λ	NOUN
ejpam-4277	93	5	,	,	PUNCT
ejpam-4277	93	6	sp)-open	sp)-open	NOUN
ejpam-4277	93	7	set	set	VERB
ejpam-4277	93	8	v	v	NUM
ejpam-4277	93	9	of	of	ADP
ejpam-4277	93	10	a	a	DET
ejpam-4277	93	11	topological	topological	ADJ
ejpam-4277	93	12	space	space	NOUN
ejpam-4277	93	13	(	(	PUNCT
ejpam-4277	93	14	y	y	PROPN
ejpam-4277	93	15	,	,	PUNCT
ejpam-4277	93	16	σ	σ	PROPN
ejpam-4277	93	17	)	)	PUNCT
ejpam-4277	93	18	,	,	PUNCT
ejpam-4277	93	19	we	we	PRON
ejpam-4277	93	20	denote	denote	VERB
ejpam-4277	93	21	v	v	ADP
ejpam-4277	93	22	+	+	NOUN
ejpam-4277	94	1	=	=	SYM
ejpam-4277	94	2	{	{	PUNCT
ejpam-4277	94	3	b	b	NOUN
ejpam-4277	94	4	∈	∈	PROPN
ejpam-4277	94	5	p(y	p(y	PROPN
ejpam-4277	94	6	)	)	PUNCT
ejpam-4277	94	7	|	|	ADV
ejpam-4277	94	8	b	b	X
ejpam-4277	94	9	⊆	⊆	NUM
ejpam-4277	94	10	v	v	NOUN
ejpam-4277	94	11	}	}	PUNCT
ejpam-4277	94	12	and	and	CCONJ
ejpam-4277	94	13	v	v	ADP
ejpam-4277	94	14	−	−	PROPN
ejpam-4277	94	15	=	=	PUNCT
ejpam-4277	94	16	{	{	PUNCT
ejpam-4277	94	17	b	b	NOUN
ejpam-4277	94	18	∈	∈	PROPN
ejpam-4277	94	19	p(y	p(y	PROPN
ejpam-4277	94	20	)	)	PUNCT
ejpam-4277	95	1	|	|	ADV
ejpam-4277	95	2	b	b	PROPN
ejpam-4277	95	3	∩	∩	X
ejpam-4277	95	4	v	v	ADP
ejpam-4277	95	5	6=	6=	ADP
ejpam-4277	95	6	∅	∅	NOUN
ejpam-4277	95	7	}	}	PUNCT
ejpam-4277	95	8	.	.	PUNCT
ejpam-4277	96	1	3	3	X
ejpam-4277	96	2	.	.	X
ejpam-4277	96	3	almost	almost	ADV
ejpam-4277	96	4	α(λ	α(λ	PROPN
ejpam-4277	96	5	,	,	PUNCT
ejpam-4277	96	6	sp)-continuous	sp)-continuous	ADJ
ejpam-4277	96	7	multifunctions	multifunction	NOUN
ejpam-4277	96	8	in	in	ADP
ejpam-4277	96	9	this	this	DET
ejpam-4277	96	10	section	section	NOUN
ejpam-4277	96	11	,	,	PUNCT
ejpam-4277	96	12	we	we	PRON
ejpam-4277	96	13	introduce	introduce	VERB
ejpam-4277	96	14	the	the	DET
ejpam-4277	96	15	notion	notion	NOUN
ejpam-4277	96	16	of	of	ADP
ejpam-4277	96	17	almost	almost	ADV
ejpam-4277	96	18	α(λ	α(λ	PROPN
ejpam-4277	96	19	,	,	PUNCT
ejpam-4277	96	20	sp)-continuous	sp)-continuous	ADJ
ejpam-4277	96	21	multifunctions	multifunction	NOUN
ejpam-4277	96	22	.	.	PUNCT
ejpam-4277	97	1	moreover	moreover	ADV
ejpam-4277	97	2	,	,	PUNCT
ejpam-4277	97	3	some	some	DET
ejpam-4277	97	4	characterizations	characterization	NOUN
ejpam-4277	97	5	of	of	ADP
ejpam-4277	97	6	almost	almost	ADV
ejpam-4277	97	7	α(λ	α(λ	PROPN
ejpam-4277	97	8	,	,	PUNCT
ejpam-4277	97	9	sp)-continuous	sp)-continuous	ADJ
ejpam-4277	97	10	multifunctions	multifunction	NOUN
ejpam-4277	97	11	are	be	AUX
ejpam-4277	97	12	discussed	discuss	VERB
ejpam-4277	97	13	.	.	PUNCT
ejpam-4277	98	1	definition	definition	NOUN
ejpam-4277	98	2	1	1	NUM
ejpam-4277	98	3	.	.	PUNCT
ejpam-4277	99	1	a	a	DET
ejpam-4277	99	2	multifunction	multifunction	NOUN
ejpam-4277	99	3	f	f	NOUN
ejpam-4277	99	4	:	:	PUNCT
ejpam-4277	99	5	(	(	PUNCT
ejpam-4277	99	6	x	x	X
ejpam-4277	99	7	,	,	PUNCT
ejpam-4277	99	8	τ	τ	X
ejpam-4277	99	9	)	)	PUNCT
ejpam-4277	99	10	→	→	SYM
ejpam-4277	99	11	(	(	PUNCT
ejpam-4277	99	12	y	y	PROPN
ejpam-4277	99	13	,	,	PUNCT
ejpam-4277	99	14	σ	σ	PROPN
ejpam-4277	99	15	)	)	PUNCT
ejpam-4277	99	16	is	be	AUX
ejpam-4277	99	17	said	say	VERB
ejpam-4277	99	18	to	to	PART
ejpam-4277	99	19	be	be	AUX
ejpam-4277	99	20	almost	almost	ADV
ejpam-4277	99	21	α(λ	α(λ	PROPN
ejpam-4277	99	22	,	,	PUNCT
ejpam-4277	99	23	sp)-continuous	sp)-continuous	ADJ
ejpam-4277	99	24	at	at	ADP
ejpam-4277	99	25	x	x	X
ejpam-4277	99	26	∈	∈	PROPN
ejpam-4277	99	27	x	x	INTJ
ejpam-4277	99	28	if	if	SCONJ
ejpam-4277	99	29	,	,	PUNCT
ejpam-4277	99	30	for	for	ADP
ejpam-4277	99	31	any	any	DET
ejpam-4277	99	32	(	(	PUNCT
ejpam-4277	99	33	λ	λ	NOUN
ejpam-4277	99	34	,	,	PUNCT
ejpam-4277	99	35	sp)-open	sp)-open	ADJ
ejpam-4277	99	36	sets	set	NOUN
ejpam-4277	99	37	g1	g1	NOUN
ejpam-4277	99	38	,	,	PUNCT
ejpam-4277	99	39	g2	g2	PROPN
ejpam-4277	99	40	of	of	ADP
ejpam-4277	99	41	y	y	PRON
ejpam-4277	99	42	such	such	ADJ
ejpam-4277	99	43	that	that	SCONJ
ejpam-4277	99	44	f	f	PROPN
ejpam-4277	99	45	(	(	PUNCT
ejpam-4277	99	46	x	x	X
ejpam-4277	99	47	)	)	PUNCT
ejpam-4277	99	48	∈	∈	PROPN
ejpam-4277	99	49	g+	g+	NOUN
ejpam-4277	99	50	1	1	NUM
ejpam-4277	99	51	∩	∩	X
ejpam-4277	99	52	g+	g+	X
ejpam-4277	99	53	2	2	NUM
ejpam-4277	99	54	and	and	CCONJ
ejpam-4277	99	55	each	each	DET
ejpam-4277	99	56	s(λ	s(λ	PROPN
ejpam-4277	99	57	,	,	PUNCT
ejpam-4277	99	58	sp)-open	sp)-open	VERB
ejpam-4277	99	59	set	set	VERB
ejpam-4277	99	60	u	u	NOUN
ejpam-4277	99	61	of	of	ADP
ejpam-4277	99	62	x	x	SYM
ejpam-4277	99	63	containing	contain	VERB
ejpam-4277	99	64	x	x	PRON
ejpam-4277	99	65	,	,	PUNCT
ejpam-4277	99	66	there	there	PRON
ejpam-4277	99	67	exists	exist	VERB
ejpam-4277	99	68	a	a	DET
ejpam-4277	99	69	nonempty	nonempty	ADJ
ejpam-4277	99	70	(	(	PUNCT
ejpam-4277	99	71	λ	λ	NOUN
ejpam-4277	99	72	,	,	PUNCT
ejpam-4277	99	73	sp)-open	sp)-open	ADJ
ejpam-4277	99	74	set	set	NOUN
ejpam-4277	99	75	gu	gu	NOUN
ejpam-4277	99	76	of	of	ADP
ejpam-4277	99	77	x	x	SYM
ejpam-4277	99	78	such	such	ADJ
ejpam-4277	99	79	that	that	PRON
ejpam-4277	99	80	gu	gu	NOUN
ejpam-4277	99	81	⊆	⊆	NUM
ejpam-4277	99	82	u	u	NOUN
ejpam-4277	99	83	,	,	PUNCT
ejpam-4277	99	84	f	f	PROPN
ejpam-4277	99	85	(	(	PUNCT
ejpam-4277	99	86	gu	gu	NOUN
ejpam-4277	99	87	)	)	PUNCT
ejpam-4277	99	88	⊆	⊆	PROPN
ejpam-4277	99	89	g	g	PROPN
ejpam-4277	99	90	s(λ	s(λ	PROPN
ejpam-4277	99	91	,	,	PUNCT
ejpam-4277	99	92	sp	sp	NOUN
ejpam-4277	99	93	)	)	PUNCT
ejpam-4277	99	94	1	1	NUM
ejpam-4277	99	95	and	and	CCONJ
ejpam-4277	99	96	f	f	PROPN
ejpam-4277	99	97	(	(	PUNCT
ejpam-4277	99	98	z	z	NOUN
ejpam-4277	99	99	)	)	PUNCT
ejpam-4277	99	100	∩	∩	PROPN
ejpam-4277	99	101	g	g	PROPN
ejpam-4277	99	102	s(λ	s(λ	PROPN
ejpam-4277	99	103	,	,	PUNCT
ejpam-4277	99	104	sp	sp	NOUN
ejpam-4277	99	105	)	)	PUNCT
ejpam-4277	99	106	2	2	NUM
ejpam-4277	99	107	6=	6=	NOUN
ejpam-4277	99	108	∅	∅	NOUN
ejpam-4277	99	109	for	for	ADP
ejpam-4277	99	110	every	every	DET
ejpam-4277	99	111	z	z	PROPN
ejpam-4277	99	112	∈	∈	PROPN
ejpam-4277	99	113	gu	gu	NOUN
ejpam-4277	99	114	.	.	PUNCT
ejpam-4277	100	1	a	a	DET
ejpam-4277	100	2	multifunction	multifunction	NOUN
ejpam-4277	100	3	f	f	NOUN
ejpam-4277	100	4	:	:	PUNCT
ejpam-4277	100	5	(	(	PUNCT
ejpam-4277	100	6	x	x	X
ejpam-4277	100	7	,	,	PUNCT
ejpam-4277	100	8	τ	τ	X
ejpam-4277	100	9	)	)	PUNCT
ejpam-4277	100	10	→	→	SYM
ejpam-4277	100	11	(	(	PUNCT
ejpam-4277	100	12	y	y	PROPN
ejpam-4277	100	13	,	,	PUNCT
ejpam-4277	100	14	σ	σ	PROPN
ejpam-4277	100	15	)	)	PUNCT
ejpam-4277	100	16	is	be	AUX
ejpam-4277	100	17	said	say	VERB
ejpam-4277	100	18	to	to	PART
ejpam-4277	100	19	be	be	AUX
ejpam-4277	100	20	almost	almost	ADV
ejpam-4277	100	21	α(λ	α(λ	NOUN
ejpam-4277	100	22	,	,	PUNCT
ejpam-4277	100	23	sp)-continuous	sp)-continuous	ADJ
ejpam-4277	100	24	if	if	SCONJ
ejpam-4277	100	25	f	f	PROPN
ejpam-4277	100	26	has	have	VERB
ejpam-4277	100	27	this	this	DET
ejpam-4277	100	28	property	property	NOUN
ejpam-4277	100	29	at	at	ADP
ejpam-4277	100	30	each	each	DET
ejpam-4277	100	31	point	point	NOUN
ejpam-4277	100	32	of	of	ADP
ejpam-4277	100	33	x.	x.	NOUN
ejpam-4277	100	34	theorem	theorem	VERB
ejpam-4277	100	35	1	1	NUM
ejpam-4277	100	36	.	.	X
ejpam-4277	100	37	for	for	ADP
ejpam-4277	100	38	a	a	DET
ejpam-4277	100	39	multifunction	multifunction	NOUN
ejpam-4277	100	40	f	f	NOUN
ejpam-4277	100	41	:	:	PUNCT
ejpam-4277	100	42	(	(	PUNCT
ejpam-4277	100	43	x	x	X
ejpam-4277	100	44	,	,	PUNCT
ejpam-4277	100	45	τ	τ	X
ejpam-4277	100	46	)	)	PUNCT
ejpam-4277	100	47	→	→	SYM
ejpam-4277	100	48	(	(	PUNCT
ejpam-4277	100	49	y	y	PROPN
ejpam-4277	100	50	,	,	PUNCT
ejpam-4277	100	51	σ	σ	PROPN
ejpam-4277	100	52	)	)	PUNCT
ejpam-4277	100	53	,	,	PUNCT
ejpam-4277	100	54	the	the	DET
ejpam-4277	100	55	following	follow	VERB
ejpam-4277	100	56	properties	property	NOUN
ejpam-4277	100	57	are	be	AUX
ejpam-4277	100	58	equivalent	equivalent	ADJ
ejpam-4277	100	59	:	:	PUNCT
ejpam-4277	100	60	c.	c.	PROPN
ejpam-4277	100	61	boonpok	boonpok	PROPN
ejpam-4277	100	62	,	,	PUNCT
ejpam-4277	100	63	j.	j.	PROPN
ejpam-4277	100	64	khampakdee	khampakdee	PROPN
ejpam-4277	100	65	/	/	PUNCT
ejpam-4277	100	66	eur	eur	PROPN
ejpam-4277	100	67	.	.	PUNCT
ejpam-4277	101	1	j.	j.	PROPN
ejpam-4277	101	2	pure	pure	PROPN
ejpam-4277	101	3	appl	appl	PROPN
ejpam-4277	101	4	.	.	PROPN
ejpam-4277	101	5	math	math	PROPN
ejpam-4277	101	6	,	,	PUNCT
ejpam-4277	101	7	15	15	NUM
ejpam-4277	101	8	(	(	PUNCT
ejpam-4277	101	9	2	2	NUM
ejpam-4277	101	10	)	)	PUNCT
ejpam-4277	101	11	(	(	PUNCT
ejpam-4277	101	12	2022	2022	NUM
ejpam-4277	101	13	)	)	PUNCT
ejpam-4277	101	14	,	,	PUNCT
ejpam-4277	101	15	626	626	NUM
ejpam-4277	101	16	-	-	SYM
ejpam-4277	101	17	634	634	NUM
ejpam-4277	101	18	629	629	NUM
ejpam-4277	101	19	(	(	PUNCT
ejpam-4277	101	20	1	1	NUM
ejpam-4277	101	21	)	)	PUNCT
ejpam-4277	101	22	f	f	PROPN
ejpam-4277	101	23	is	be	AUX
ejpam-4277	101	24	almost	almost	ADV
ejpam-4277	101	25	α(λ	α(λ	NOUN
ejpam-4277	101	26	,	,	PUNCT
ejpam-4277	101	27	sp)-continuous	sp)-continuous	ADJ
ejpam-4277	101	28	at	at	ADP
ejpam-4277	101	29	a	a	DET
ejpam-4277	101	30	point	point	NOUN
ejpam-4277	101	31	x	x	X
ejpam-4277	101	32	∈	∈	NOUN
ejpam-4277	101	33	x	x	X
ejpam-4277	101	34	;	;	PUNCT
ejpam-4277	101	35	(	(	PUNCT
ejpam-4277	101	36	2	2	X
ejpam-4277	101	37	)	)	PUNCT
ejpam-4277	101	38	for	for	ADP
ejpam-4277	101	39	any	any	DET
ejpam-4277	101	40	(	(	PUNCT
ejpam-4277	101	41	λ	λ	NOUN
ejpam-4277	101	42	,	,	PUNCT
ejpam-4277	101	43	sp)-open	sp)-open	ADJ
ejpam-4277	101	44	sets	set	NOUN
ejpam-4277	101	45	g1	g1	NOUN
ejpam-4277	101	46	,	,	PUNCT
ejpam-4277	101	47	g2	g2	PROPN
ejpam-4277	101	48	of	of	ADP
ejpam-4277	101	49	y	y	PRON
ejpam-4277	101	50	such	such	ADJ
ejpam-4277	101	51	that	that	SCONJ
ejpam-4277	101	52	f	f	PROPN
ejpam-4277	101	53	(	(	PUNCT
ejpam-4277	101	54	x	x	X
ejpam-4277	101	55	)	)	PUNCT
ejpam-4277	101	56	∈	∈	PROPN
ejpam-4277	101	57	g+	g+	NOUN
ejpam-4277	101	58	1	1	NUM
ejpam-4277	101	59	∩	∩	X
ejpam-4277	101	60	g−	g−	ADJ
ejpam-4277	101	61	2	2	NUM
ejpam-4277	101	62	,	,	PUNCT
ejpam-4277	101	63	there	there	PRON
ejpam-4277	101	64	exists	exist	VERB
ejpam-4277	101	65	an	an	DET
ejpam-4277	101	66	α(λ	α(λ	PROPN
ejpam-4277	101	67	,	,	PUNCT
ejpam-4277	101	68	sp)-open	sp)-open	VERB
ejpam-4277	101	69	set	set	VERB
ejpam-4277	101	70	u	u	PRON
ejpam-4277	101	71	containing	contain	VERB
ejpam-4277	101	72	x	x	PUNCT
ejpam-4277	101	73	such	such	ADJ
ejpam-4277	101	74	that	that	SCONJ
ejpam-4277	101	75	f	f	PROPN
ejpam-4277	101	76	(	(	PUNCT
ejpam-4277	101	77	u	u	NOUN
ejpam-4277	101	78	)	)	PUNCT
ejpam-4277	101	79	⊆	⊆	NUM
ejpam-4277	101	80	g	g	PROPN
ejpam-4277	101	81	s(λ	s(λ	PROPN
ejpam-4277	101	82	,	,	PUNCT
ejpam-4277	101	83	sp	sp	NOUN
ejpam-4277	101	84	)	)	PUNCT
ejpam-4277	101	85	1	1	NUM
ejpam-4277	101	86	and	and	CCONJ
ejpam-4277	101	87	f	f	PROPN
ejpam-4277	101	88	(	(	PUNCT
ejpam-4277	101	89	z)∩g	z)∩g	PROPN
ejpam-4277	101	90	s(λ	s(λ	PROPN
ejpam-4277	101	91	,	,	PUNCT
ejpam-4277	101	92	sp	sp	NOUN
ejpam-4277	101	93	)	)	PUNCT
ejpam-4277	101	94	2	2	NUM
ejpam-4277	101	95	6=	6=	NOUN
ejpam-4277	101	96	∅	∅	NOUN
ejpam-4277	101	97	for	for	ADP
ejpam-4277	101	98	every	every	DET
ejpam-4277	101	99	z	z	NOUN
ejpam-4277	101	100	∈	∈	PROPN
ejpam-4277	101	101	u	u	NOUN
ejpam-4277	101	102	;	;	PUNCT
ejpam-4277	101	103	(	(	PUNCT
ejpam-4277	101	104	3	3	X
ejpam-4277	101	105	)	)	PUNCT
ejpam-4277	102	1	x	x	SYM
ejpam-4277	102	2	∈	∈	PROPN
ejpam-4277	103	1	[	[	X
ejpam-4277	103	2	f+(g	f+(g	NOUN
ejpam-4277	103	3	s(λ	s(λ	NOUN
ejpam-4277	103	4	,	,	PUNCT
ejpam-4277	103	5	sp	sp	NOUN
ejpam-4277	103	6	)	)	PUNCT
ejpam-4277	103	7	1	1	NUM
ejpam-4277	103	8	)	)	PUNCT
ejpam-4277	103	9	∩	∩	PROPN
ejpam-4277	103	10	f−(g	f−(g	VERB
ejpam-4277	103	11	s(λ	s(λ	PROPN
ejpam-4277	103	12	,	,	PUNCT
ejpam-4277	103	13	sp	sp	NOUN
ejpam-4277	103	14	)	)	PUNCT
ejpam-4277	103	15	2	2	NUM
ejpam-4277	103	16	)	)	PUNCT
ejpam-4277	103	17	]	]	PUNCT
ejpam-4277	103	18	α(λ	α(λ	PROPN
ejpam-4277	103	19	,	,	PUNCT
ejpam-4277	103	20	sp	sp	NOUN
ejpam-4277	103	21	)	)	PUNCT
ejpam-4277	103	22	for	for	ADP
ejpam-4277	103	23	any	any	DET
ejpam-4277	103	24	(	(	PUNCT
ejpam-4277	103	25	λ	λ	NOUN
ejpam-4277	103	26	,	,	PUNCT
ejpam-4277	103	27	sp)-open	sp)-open	ADJ
ejpam-4277	103	28	sets	set	NOUN
ejpam-4277	103	29	g1	g1	NOUN
ejpam-4277	103	30	,	,	PUNCT
ejpam-4277	103	31	g2	g2	PROPN
ejpam-4277	103	32	of	of	ADP
ejpam-4277	103	33	y	y	PRON
ejpam-4277	103	34	such	such	ADJ
ejpam-4277	103	35	that	that	SCONJ
ejpam-4277	103	36	f	f	PROPN
ejpam-4277	103	37	(	(	PUNCT
ejpam-4277	103	38	x	x	X
ejpam-4277	103	39	)	)	PUNCT
ejpam-4277	103	40	∈	∈	NOUN
ejpam-4277	103	41	g+	g+	NOUN
ejpam-4277	103	42	1	1	NUM
ejpam-4277	103	43	∩g−	∩g−	PROPN
ejpam-4277	103	44	2	2	NUM
ejpam-4277	103	45	;	;	PUNCT
ejpam-4277	103	46	(	(	PUNCT
ejpam-4277	103	47	4	4	X
ejpam-4277	103	48	)	)	PUNCT
ejpam-4277	103	49	x	x	SYM
ejpam-4277	103	50	∈	∈	PROPN
ejpam-4277	104	1	[	[	X
ejpam-4277	104	2	[	[	X
ejpam-4277	104	3	[	[	X
ejpam-4277	104	4	f+(g	f+(g	NOUN
ejpam-4277	104	5	s(λ	s(λ	NOUN
ejpam-4277	104	6	,	,	PUNCT
ejpam-4277	104	7	sp	sp	NOUN
ejpam-4277	104	8	)	)	PUNCT
ejpam-4277	104	9	1	1	NUM
ejpam-4277	104	10	)	)	PUNCT
ejpam-4277	104	11	∩	∩	PROPN
ejpam-4277	104	12	f−(g	f−(g	VERB
ejpam-4277	104	13	s(λ	s(λ	PROPN
ejpam-4277	104	14	,	,	PUNCT
ejpam-4277	104	15	sp	sp	NOUN
ejpam-4277	104	16	)	)	PUNCT
ejpam-4277	104	17	2	2	NUM
ejpam-4277	104	18	)	)	PUNCT
ejpam-4277	104	19	]	]	PUNCT
ejpam-4277	104	20	(	(	PUNCT
ejpam-4277	104	21	λ	λ	NOUN
ejpam-4277	104	22	,	,	PUNCT
ejpam-4277	104	23	sp	sp	NOUN
ejpam-4277	104	24	)	)	PUNCT
ejpam-4277	104	25	]	]	PUNCT
ejpam-4277	104	26	(	(	PUNCT
ejpam-4277	104	27	λ	λ	X
ejpam-4277	104	28	,	,	PUNCT
ejpam-4277	104	29	sp)](λ	sp)](λ	PROPN
ejpam-4277	104	30	,	,	PUNCT
ejpam-4277	104	31	sp	sp	NOUN
ejpam-4277	104	32	)	)	PUNCT
ejpam-4277	104	33	for	for	ADP
ejpam-4277	104	34	any	any	DET
ejpam-4277	104	35	(	(	PUNCT
ejpam-4277	104	36	λ	λ	NOUN
ejpam-4277	104	37	,	,	PUNCT
ejpam-4277	104	38	sp)-open	sp)-open	ADJ
ejpam-4277	104	39	sets	set	NOUN
ejpam-4277	104	40	g1	g1	NOUN
ejpam-4277	104	41	,	,	PUNCT
ejpam-4277	104	42	g2	g2	PROPN
ejpam-4277	104	43	of	of	ADP
ejpam-4277	104	44	y	y	PRON
ejpam-4277	104	45	such	such	ADJ
ejpam-4277	104	46	that	that	SCONJ
ejpam-4277	104	47	f	f	PROPN
ejpam-4277	104	48	(	(	PUNCT
ejpam-4277	104	49	x	x	X
ejpam-4277	104	50	)	)	PUNCT
ejpam-4277	104	51	∈	∈	NOUN
ejpam-4277	104	52	g+	g+	NOUN
ejpam-4277	105	1	1	1	NUM
ejpam-4277	105	2	∩g−	∩g−	PROPN
ejpam-4277	105	3	2	2	NUM
ejpam-4277	105	4	.	.	PUNCT
ejpam-4277	106	1	proof	proof	NOUN
ejpam-4277	106	2	.	.	PUNCT
ejpam-4277	107	1	(	(	PUNCT
ejpam-4277	107	2	1	1	X
ejpam-4277	107	3	)	)	PUNCT
ejpam-4277	107	4	⇒	⇒	NOUN
ejpam-4277	107	5	(	(	PUNCT
ejpam-4277	107	6	2	2	NUM
ejpam-4277	107	7	):	):	PUNCT
ejpam-4277	107	8	let	let	VERB
ejpam-4277	107	9	g1	g1	PROPN
ejpam-4277	107	10	,	,	PUNCT
ejpam-4277	107	11	g2	g2	PROPN
ejpam-4277	107	12	be	be	VERB
ejpam-4277	107	13	any	any	DET
ejpam-4277	107	14	(	(	PUNCT
ejpam-4277	107	15	λ	λ	NOUN
ejpam-4277	107	16	,	,	PUNCT
ejpam-4277	107	17	sp)-open	sp)-open	ADJ
ejpam-4277	107	18	sets	set	NOUN
ejpam-4277	107	19	of	of	ADP
ejpam-4277	107	20	y	y	PRON
ejpam-4277	107	21	such	such	ADJ
ejpam-4277	107	22	that	that	SCONJ
ejpam-4277	107	23	f	f	PROPN
ejpam-4277	107	24	(	(	PUNCT
ejpam-4277	107	25	x	x	X
ejpam-4277	107	26	)	)	PUNCT
ejpam-4277	107	27	∈	∈	NOUN
ejpam-4277	107	28	g+	g+	NOUN
ejpam-4277	107	29	1	1	NUM
ejpam-4277	107	30	∩g−	∩g−	PROPN
ejpam-4277	107	31	2	2	NUM
ejpam-4277	107	32	.	.	PUNCT
ejpam-4277	108	1	for	for	ADP
ejpam-4277	108	2	each	each	DET
ejpam-4277	108	3	s(λ	s(λ	PROPN
ejpam-4277	108	4	,	,	PUNCT
ejpam-4277	108	5	sp)-open	sp)-open	ADJ
ejpam-4277	108	6	set	set	VERB
ejpam-4277	108	7	h	h	NOUN
ejpam-4277	108	8	containing	contain	VERB
ejpam-4277	108	9	x	x	X
ejpam-4277	108	10	,	,	PUNCT
ejpam-4277	108	11	there	there	PRON
ejpam-4277	108	12	exists	exist	VERB
ejpam-4277	108	13	a	a	DET
ejpam-4277	108	14	nonempty	nonempty	ADJ
ejpam-4277	108	15	(	(	PUNCT
ejpam-4277	108	16	λ	λ	NOUN
ejpam-4277	108	17	,	,	PUNCT
ejpam-4277	108	18	sp)-open	sp)-open	ADJ
ejpam-4277	108	19	set	set	VERB
ejpam-4277	108	20	gh	gh	PROPN
ejpam-4277	108	21	such	such	ADJ
ejpam-4277	108	22	that	that	SCONJ
ejpam-4277	108	23	gh	gh	PROPN
ejpam-4277	108	24	⊆	⊆	NUM
ejpam-4277	108	25	h	h	NOUN
ejpam-4277	108	26	,	,	PUNCT
ejpam-4277	108	27	f	f	PROPN
ejpam-4277	108	28	(	(	PUNCT
ejpam-4277	108	29	gh	gh	PROPN
ejpam-4277	108	30	)	)	PUNCT
ejpam-4277	108	31	⊆	⊆	PROPN
ejpam-4277	108	32	g	g	PROPN
ejpam-4277	108	33	s(λ	s(λ	PROPN
ejpam-4277	108	34	,	,	PUNCT
ejpam-4277	108	35	sp	sp	NOUN
ejpam-4277	108	36	)	)	PUNCT
ejpam-4277	108	37	1	1	NUM
ejpam-4277	108	38	and	and	CCONJ
ejpam-4277	108	39	f	f	PROPN
ejpam-4277	108	40	(	(	PUNCT
ejpam-4277	108	41	z	z	NOUN
ejpam-4277	108	42	)	)	PUNCT
ejpam-4277	108	43	∩g	∩g	PROPN
ejpam-4277	108	44	s(λ	s(λ	PROPN
ejpam-4277	108	45	,	,	PUNCT
ejpam-4277	108	46	sp	sp	NOUN
ejpam-4277	108	47	)	)	PUNCT
ejpam-4277	108	48	2	2	NUM
ejpam-4277	108	49	6=	6=	NOUN
ejpam-4277	108	50	∅	∅	NOUN
ejpam-4277	108	51	for	for	ADP
ejpam-4277	108	52	every	every	DET
ejpam-4277	108	53	z	z	PROPN
ejpam-4277	108	54	∈	∈	PROPN
ejpam-4277	108	55	gh	gh	PROPN
ejpam-4277	108	56	.	.	PUNCT
ejpam-4277	109	1	let	let	VERB
ejpam-4277	109	2	w	w	NOUN
ejpam-4277	109	3	=	=	PUNCT
ejpam-4277	109	4	∪{gh	∪{gh	ADP
ejpam-4277	109	5	|	|	ADV
ejpam-4277	109	6	h	h	NOUN
ejpam-4277	109	7	∈	∈	PROPN
ejpam-4277	109	8	sλspo(x	sλspo(x	PROPN
ejpam-4277	109	9	,	,	PUNCT
ejpam-4277	109	10	τ	τ	X
ejpam-4277	109	11	)	)	PUNCT
ejpam-4277	109	12	containing	contain	VERB
ejpam-4277	109	13	x	x	X
ejpam-4277	109	14	}	}	PUNCT
ejpam-4277	109	15	.	.	PUNCT
ejpam-4277	110	1	then	then	ADV
ejpam-4277	110	2	,	,	PUNCT
ejpam-4277	110	3	w	w	NOUN
ejpam-4277	110	4	is	be	AUX
ejpam-4277	110	5	(	(	PUNCT
ejpam-4277	110	6	λ	λ	X
ejpam-4277	110	7	,	,	PUNCT
ejpam-4277	110	8	sp)-open	sp)-open	ADJ
ejpam-4277	110	9	in	in	ADP
ejpam-4277	110	10	x	x	X
ejpam-4277	110	11	,	,	PUNCT
ejpam-4277	110	12	x	x	SYM
ejpam-4277	110	13	∈	∈	PROPN
ejpam-4277	110	14	w	w	PROPN
ejpam-4277	110	15	s(λ	s(λ	PROPN
ejpam-4277	110	16	,	,	PUNCT
ejpam-4277	110	17	sp	sp	NOUN
ejpam-4277	110	18	)	)	PUNCT
ejpam-4277	110	19	,	,	PUNCT
ejpam-4277	110	20	f	f	PROPN
ejpam-4277	110	21	(	(	PUNCT
ejpam-4277	110	22	w	w	PROPN
ejpam-4277	110	23	)	)	PUNCT
ejpam-4277	110	24	⊆	⊆	NUM
ejpam-4277	110	25	g	g	PROPN
ejpam-4277	110	26	s(λ	s(λ	PROPN
ejpam-4277	110	27	,	,	PUNCT
ejpam-4277	110	28	sp	sp	NOUN
ejpam-4277	110	29	)	)	PUNCT
ejpam-4277	110	30	1	1	NUM
ejpam-4277	110	31	and	and	CCONJ
ejpam-4277	110	32	f	f	PROPN
ejpam-4277	110	33	(	(	PUNCT
ejpam-4277	110	34	w)∩g	w)∩g	PROPN
ejpam-4277	110	35	s(λ	s(λ	PROPN
ejpam-4277	110	36	,	,	PUNCT
ejpam-4277	110	37	sp	sp	NOUN
ejpam-4277	110	38	)	)	PUNCT
ejpam-4277	110	39	2	2	NUM
ejpam-4277	110	40	6=	6=	NOUN
ejpam-4277	110	41	∅	∅	NOUN
ejpam-4277	110	42	for	for	ADP
ejpam-4277	110	43	every	every	DET
ejpam-4277	110	44	w	w	PROPN
ejpam-4277	110	45	∈	∈	PROPN
ejpam-4277	110	46	w	w	PROPN
ejpam-4277	110	47	.	.	PUNCT
ejpam-4277	111	1	put	put	VERB
ejpam-4277	111	2	u	u	NOUN
ejpam-4277	112	1	=	=	NOUN
ejpam-4277	112	2	w	w	NOUN
ejpam-4277	112	3	∪	∪	X
ejpam-4277	112	4	{	{	PUNCT
ejpam-4277	112	5	x	x	NOUN
ejpam-4277	112	6	}	}	PUNCT
ejpam-4277	112	7	,	,	PUNCT
ejpam-4277	112	8	then	then	ADV
ejpam-4277	112	9	w	w	PROPN
ejpam-4277	112	10	⊆	⊆	NUM
ejpam-4277	112	11	u	u	NOUN
ejpam-4277	112	12	⊆	⊆	NUM
ejpam-4277	112	13	w	w	PROPN
ejpam-4277	112	14	s(λ	s(λ	PROPN
ejpam-4277	112	15	,	,	PUNCT
ejpam-4277	112	16	sp	sp	NOUN
ejpam-4277	112	17	)	)	PUNCT
ejpam-4277	112	18	=	=	NOUN
ejpam-4277	113	1	[	[	X
ejpam-4277	113	2	w	w	X
ejpam-4277	113	3	(	(	PUNCT
ejpam-4277	113	4	λ	λ	PROPN
ejpam-4277	113	5	,	,	PUNCT
ejpam-4277	113	6	sp)](λ	sp)](λ	PROPN
ejpam-4277	113	7	,	,	PUNCT
ejpam-4277	113	8	sp	sp	NOUN
ejpam-4277	113	9	)	)	PUNCT
ejpam-4277	113	10	.	.	PUNCT
ejpam-4277	114	1	thus	thus	ADV
ejpam-4277	114	2	,	,	PUNCT
ejpam-4277	114	3	u	u	NOUN
ejpam-4277	114	4	is	be	AUX
ejpam-4277	114	5	an	an	DET
ejpam-4277	114	6	α(λ	α(λ	PROPN
ejpam-4277	114	7	,	,	PUNCT
ejpam-4277	114	8	sp)-open	sp)-open	ADJ
ejpam-4277	114	9	set	set	NOUN
ejpam-4277	114	10	containing	contain	VERB
ejpam-4277	114	11	x	x	PUNCT
ejpam-4277	114	12	such	such	ADJ
ejpam-4277	114	13	that	that	SCONJ
ejpam-4277	114	14	f	f	PROPN
ejpam-4277	114	15	(	(	PUNCT
ejpam-4277	114	16	u	u	NOUN
ejpam-4277	114	17	)	)	PUNCT
ejpam-4277	114	18	⊆	⊆	NUM
ejpam-4277	114	19	g	g	PROPN
ejpam-4277	114	20	s(λ	s(λ	PROPN
ejpam-4277	114	21	,	,	PUNCT
ejpam-4277	114	22	sp	sp	NOUN
ejpam-4277	114	23	)	)	PUNCT
ejpam-4277	114	24	1	1	NUM
ejpam-4277	114	25	and	and	CCONJ
ejpam-4277	114	26	f	f	PROPN
ejpam-4277	114	27	(	(	PUNCT
ejpam-4277	114	28	u	u	NOUN
ejpam-4277	114	29	)	)	PUNCT
ejpam-4277	114	30	∩	∩	NOUN
ejpam-4277	114	31	g	g	PROPN
ejpam-4277	114	32	s(λ	s(λ	PROPN
ejpam-4277	114	33	,	,	PUNCT
ejpam-4277	114	34	sp	sp	NOUN
ejpam-4277	114	35	)	)	PUNCT
ejpam-4277	114	36	2	2	NUM
ejpam-4277	114	37	6=	6=	NOUN
ejpam-4277	114	38	∅	∅	NOUN
ejpam-4277	114	39	for	for	ADP
ejpam-4277	114	40	every	every	DET
ejpam-4277	114	41	u	u	PROPN
ejpam-4277	114	42	∈	∈	PROPN
ejpam-4277	114	43	u	u	NOUN
ejpam-4277	114	44	.	.	PUNCT
ejpam-4277	115	1	(	(	PUNCT
ejpam-4277	115	2	2	2	X
ejpam-4277	115	3	)	)	PUNCT
ejpam-4277	115	4	⇒	⇒	NOUN
ejpam-4277	115	5	(	(	PUNCT
ejpam-4277	115	6	3	3	NUM
ejpam-4277	115	7	):	):	PUNCT
ejpam-4277	115	8	let	let	VERB
ejpam-4277	115	9	g1	g1	PROPN
ejpam-4277	115	10	,	,	PUNCT
ejpam-4277	115	11	g2	g2	PROPN
ejpam-4277	115	12	be	be	VERB
ejpam-4277	115	13	any	any	DET
ejpam-4277	115	14	(	(	PUNCT
ejpam-4277	115	15	λ	λ	NOUN
ejpam-4277	115	16	,	,	PUNCT
ejpam-4277	115	17	sp)-open	sp)-open	ADJ
ejpam-4277	115	18	sets	set	NOUN
ejpam-4277	115	19	of	of	ADP
ejpam-4277	115	20	y	y	PRON
ejpam-4277	115	21	such	such	ADJ
ejpam-4277	115	22	that	that	SCONJ
ejpam-4277	115	23	f	f	PROPN
ejpam-4277	115	24	(	(	PUNCT
ejpam-4277	115	25	x	x	X
ejpam-4277	115	26	)	)	PUNCT
ejpam-4277	115	27	∈	∈	NOUN
ejpam-4277	115	28	g+	g+	NOUN
ejpam-4277	115	29	1	1	NUM
ejpam-4277	115	30	∩g−	∩g−	PROPN
ejpam-4277	115	31	2	2	NUM
ejpam-4277	115	32	.	.	PUNCT
ejpam-4277	116	1	then	then	ADV
ejpam-4277	116	2	,	,	PUNCT
ejpam-4277	116	3	there	there	PRON
ejpam-4277	116	4	exists	exist	VERB
ejpam-4277	116	5	an	an	DET
ejpam-4277	116	6	α(λ	α(λ	PROPN
ejpam-4277	116	7	,	,	PUNCT
ejpam-4277	116	8	sp)-open	sp)-open	VERB
ejpam-4277	116	9	set	set	VERB
ejpam-4277	116	10	u	u	NOUN
ejpam-4277	116	11	of	of	ADP
ejpam-4277	116	12	x	x	PUNCT
ejpam-4277	116	13	containing	contain	VERB
ejpam-4277	116	14	x	x	PUNCT
ejpam-4277	116	15	such	such	ADJ
ejpam-4277	116	16	that	that	SCONJ
ejpam-4277	116	17	f	f	PROPN
ejpam-4277	116	18	(	(	PUNCT
ejpam-4277	116	19	u	u	NOUN
ejpam-4277	116	20	)	)	PUNCT
ejpam-4277	116	21	⊆	⊆	NUM
ejpam-4277	116	22	g	g	PROPN
ejpam-4277	116	23	s(λ	s(λ	PROPN
ejpam-4277	116	24	,	,	PUNCT
ejpam-4277	116	25	sp	sp	NOUN
ejpam-4277	116	26	)	)	PUNCT
ejpam-4277	116	27	1	1	NUM
ejpam-4277	116	28	and	and	CCONJ
ejpam-4277	116	29	f	f	PROPN
ejpam-4277	116	30	(	(	PUNCT
ejpam-4277	116	31	z	z	NOUN
ejpam-4277	116	32	)	)	PUNCT
ejpam-4277	116	33	∩	∩	PROPN
ejpam-4277	116	34	g	g	PROPN
ejpam-4277	116	35	s(λ	s(λ	PROPN
ejpam-4277	116	36	,	,	PUNCT
ejpam-4277	116	37	sp	sp	NOUN
ejpam-4277	116	38	)	)	PUNCT
ejpam-4277	116	39	2	2	NUM
ejpam-4277	116	40	6=	6=	NOUN
ejpam-4277	116	41	∅	∅	NOUN
ejpam-4277	116	42	for	for	ADP
ejpam-4277	116	43	every	every	DET
ejpam-4277	116	44	z	z	NOUN
ejpam-4277	116	45	∈	∈	PROPN
ejpam-4277	116	46	u	u	NOUN
ejpam-4277	116	47	.	.	PUNCT
ejpam-4277	117	1	thus	thus	ADV
ejpam-4277	117	2	,	,	PUNCT
ejpam-4277	117	3	x	x	PUNCT
ejpam-4277	117	4	∈	∈	PROPN
ejpam-4277	117	5	u	u	NOUN
ejpam-4277	117	6	⊆	⊆	NUM
ejpam-4277	117	7	f+(g	f+(g	NOUN
ejpam-4277	117	8	s(λ	s(λ	NOUN
ejpam-4277	117	9	,	,	PUNCT
ejpam-4277	117	10	sp	sp	NOUN
ejpam-4277	117	11	)	)	PUNCT
ejpam-4277	117	12	1	1	NUM
ejpam-4277	117	13	)	)	PUNCT
ejpam-4277	117	14	∩	∩	PROPN
ejpam-4277	117	15	f−(g	f−(g	VERB
ejpam-4277	117	16	s(λ	s(λ	PROPN
ejpam-4277	117	17	,	,	PUNCT
ejpam-4277	117	18	sp	sp	NOUN
ejpam-4277	117	19	)	)	PUNCT
ejpam-4277	117	20	2	2	NUM
ejpam-4277	117	21	)	)	PUNCT
ejpam-4277	117	22	.	.	PUNCT
ejpam-4277	118	1	since	since	SCONJ
ejpam-4277	118	2	u	u	PROPN
ejpam-4277	118	3	∈	∈	PROPN
ejpam-4277	118	4	αλspo(x	αλspo(x	PROPN
ejpam-4277	118	5	,	,	PUNCT
ejpam-4277	118	6	τ	τ	PROPN
ejpam-4277	118	7	)	)	PUNCT
ejpam-4277	118	8	,	,	PUNCT
ejpam-4277	118	9	we	we	PRON
ejpam-4277	118	10	have	have	VERB
ejpam-4277	118	11	x	x	X
ejpam-4277	118	12	∈	∈	PROPN
ejpam-4277	118	13	u	u	NOUN
ejpam-4277	119	1	⊆	⊆	NUM
ejpam-4277	119	2	[	[	SYM
ejpam-4277	119	3	f+(g	f+(g	NOUN
ejpam-4277	119	4	s(λ	s(λ	NOUN
ejpam-4277	119	5	,	,	PUNCT
ejpam-4277	119	6	sp	sp	NOUN
ejpam-4277	119	7	)	)	PUNCT
ejpam-4277	119	8	1	1	NUM
ejpam-4277	119	9	)	)	PUNCT
ejpam-4277	119	10	∩	∩	PROPN
ejpam-4277	119	11	f−(g	f−(g	VERB
ejpam-4277	119	12	s(λ	s(λ	PROPN
ejpam-4277	119	13	,	,	PUNCT
ejpam-4277	119	14	sp	sp	NOUN
ejpam-4277	119	15	)	)	PUNCT
ejpam-4277	119	16	2	2	NUM
ejpam-4277	119	17	)	)	PUNCT
ejpam-4277	119	18	]	]	PUNCT
ejpam-4277	119	19	α(λ	α(λ	PROPN
ejpam-4277	119	20	,	,	PUNCT
ejpam-4277	119	21	sp	sp	NOUN
ejpam-4277	119	22	)	)	PUNCT
ejpam-4277	119	23	.	.	PUNCT
ejpam-4277	120	1	(	(	PUNCT
ejpam-4277	120	2	3	3	X
ejpam-4277	120	3	)	)	PUNCT
ejpam-4277	120	4	⇒	⇒	NOUN
ejpam-4277	120	5	(	(	PUNCT
ejpam-4277	120	6	4	4	NUM
ejpam-4277	120	7	):	):	PUNCT
ejpam-4277	120	8	let	let	VERB
ejpam-4277	120	9	g1	g1	PROPN
ejpam-4277	120	10	,	,	PUNCT
ejpam-4277	120	11	g2	g2	PROPN
ejpam-4277	120	12	be	be	VERB
ejpam-4277	120	13	any	any	DET
ejpam-4277	120	14	(	(	PUNCT
ejpam-4277	120	15	λ	λ	NOUN
ejpam-4277	120	16	,	,	PUNCT
ejpam-4277	120	17	sp)-open	sp)-open	ADJ
ejpam-4277	120	18	sets	set	NOUN
ejpam-4277	120	19	of	of	ADP
ejpam-4277	120	20	y	y	PRON
ejpam-4277	120	21	such	such	ADJ
ejpam-4277	120	22	that	that	SCONJ
ejpam-4277	120	23	f	f	PROPN
ejpam-4277	120	24	(	(	PUNCT
ejpam-4277	120	25	x	x	X
ejpam-4277	120	26	)	)	PUNCT
ejpam-4277	120	27	∈	∈	PROPN
ejpam-4277	120	28	g+	g+	NOUN
ejpam-4277	120	29	1	1	NUM
ejpam-4277	120	30	∩	∩	X
ejpam-4277	120	31	g−	g−	ADJ
ejpam-4277	120	32	2	2	NUM
ejpam-4277	120	33	.	.	PUNCT
ejpam-4277	121	1	now	now	ADV
ejpam-4277	121	2	,	,	PUNCT
ejpam-4277	121	3	put	put	VERB
ejpam-4277	121	4	u	u	NOUN
ejpam-4277	121	5	=	=	PUNCT
ejpam-4277	122	1	[	[	X
ejpam-4277	122	2	f+(g	f+(g	NOUN
ejpam-4277	122	3	s(λ	s(λ	NOUN
ejpam-4277	122	4	,	,	PUNCT
ejpam-4277	122	5	sp	sp	NOUN
ejpam-4277	122	6	)	)	PUNCT
ejpam-4277	122	7	1	1	NUM
ejpam-4277	122	8	)	)	PUNCT
ejpam-4277	122	9	∩	∩	PROPN
ejpam-4277	122	10	f−(g	f−(g	VERB
ejpam-4277	122	11	s(λ	s(λ	PROPN
ejpam-4277	122	12	,	,	PUNCT
ejpam-4277	122	13	sp	sp	NOUN
ejpam-4277	122	14	)	)	PUNCT
ejpam-4277	122	15	2	2	NUM
ejpam-4277	122	16	)	)	PUNCT
ejpam-4277	122	17	]	]	PUNCT
ejpam-4277	122	18	α(λ	α(λ	PROPN
ejpam-4277	122	19	,	,	PUNCT
ejpam-4277	122	20	sp	sp	NOUN
ejpam-4277	122	21	)	)	PUNCT
ejpam-4277	122	22	.	.	PUNCT
ejpam-4277	123	1	then	then	ADV
ejpam-4277	123	2	,	,	PUNCT
ejpam-4277	123	3	u	u	NOUN
ejpam-4277	123	4	is	be	AUX
ejpam-4277	123	5	an	an	DET
ejpam-4277	123	6	α(λ	α(λ	PROPN
ejpam-4277	123	7	,	,	PUNCT
ejpam-4277	123	8	sp)-open	sp)-open	NOUN
ejpam-4277	123	9	set	set	NOUN
ejpam-4277	123	10	and	and	CCONJ
ejpam-4277	123	11	x	x	SYM
ejpam-4277	123	12	∈	∈	PROPN
ejpam-4277	123	13	u	u	NOUN
ejpam-4277	123	14	⊆	⊆	NUM
ejpam-4277	123	15	f+(g	f+(g	NOUN
ejpam-4277	123	16	s(λ	s(λ	NOUN
ejpam-4277	123	17	,	,	PUNCT
ejpam-4277	123	18	sp	sp	NOUN
ejpam-4277	123	19	)	)	PUNCT
ejpam-4277	123	20	1	1	NUM
ejpam-4277	123	21	)	)	PUNCT
ejpam-4277	123	22	∩	∩	PROPN
ejpam-4277	123	23	f−(g	f−(g	VERB
ejpam-4277	123	24	s(λ	s(λ	PROPN
ejpam-4277	123	25	,	,	PUNCT
ejpam-4277	123	26	sp	sp	NOUN
ejpam-4277	123	27	)	)	PUNCT
ejpam-4277	123	28	2	2	NUM
ejpam-4277	123	29	)	)	PUNCT
ejpam-4277	123	30	.	.	PUNCT
ejpam-4277	124	1	thus	thus	ADV
ejpam-4277	124	2	,	,	PUNCT
ejpam-4277	124	3	x	x	PUNCT
ejpam-4277	124	4	∈	∈	PROPN
ejpam-4277	124	5	u	u	NOUN
ejpam-4277	124	6	⊆	⊆	NUM
ejpam-4277	124	7	[	[	X
ejpam-4277	124	8	[	[	X
ejpam-4277	124	9	u(λ	u(λ	PROPN
ejpam-4277	124	10	,	,	PUNCT
ejpam-4277	124	11	sp	sp	NOUN
ejpam-4277	124	12	)	)	PUNCT
ejpam-4277	124	13	]	]	PUNCT
ejpam-4277	124	14	(	(	PUNCT
ejpam-4277	124	15	λ	λ	X
ejpam-4277	124	16	,	,	PUNCT
ejpam-4277	124	17	sp)](λ	sp)](λ	PROPN
ejpam-4277	124	18	,	,	PUNCT
ejpam-4277	124	19	sp	sp	NOUN
ejpam-4277	124	20	)	)	PUNCT
ejpam-4277	124	21	⊆	⊆	NUM
ejpam-4277	125	1	[	[	X
ejpam-4277	125	2	[	[	X
ejpam-4277	125	3	[	[	X
ejpam-4277	125	4	f+(g	f+(g	NOUN
ejpam-4277	125	5	s(λ	s(λ	NOUN
ejpam-4277	125	6	,	,	PUNCT
ejpam-4277	125	7	sp	sp	NOUN
ejpam-4277	125	8	)	)	PUNCT
ejpam-4277	125	9	1	1	NUM
ejpam-4277	125	10	)	)	PUNCT
ejpam-4277	125	11	∩	∩	PROPN
ejpam-4277	125	12	f−(g	f−(g	VERB
ejpam-4277	125	13	s(λ	s(λ	PROPN
ejpam-4277	125	14	,	,	PUNCT
ejpam-4277	125	15	sp	sp	NOUN
ejpam-4277	125	16	)	)	PUNCT
ejpam-4277	125	17	2	2	NUM
ejpam-4277	125	18	)	)	PUNCT
ejpam-4277	125	19	]	]	PUNCT
ejpam-4277	125	20	(	(	PUNCT
ejpam-4277	125	21	λ	λ	NOUN
ejpam-4277	125	22	,	,	PUNCT
ejpam-4277	125	23	sp	sp	NOUN
ejpam-4277	125	24	)	)	PUNCT
ejpam-4277	125	25	]	]	PUNCT
ejpam-4277	125	26	(	(	PUNCT
ejpam-4277	125	27	λ	λ	X
ejpam-4277	125	28	,	,	PUNCT
ejpam-4277	125	29	sp)](λ	sp)](λ	PROPN
ejpam-4277	125	30	,	,	PUNCT
ejpam-4277	125	31	sp	sp	NOUN
ejpam-4277	125	32	)	)	PUNCT
ejpam-4277	125	33	.	.	PUNCT
ejpam-4277	126	1	(	(	PUNCT
ejpam-4277	126	2	4	4	X
ejpam-4277	126	3	)	)	PUNCT
ejpam-4277	126	4	⇒	⇒	NOUN
ejpam-4277	126	5	(	(	PUNCT
ejpam-4277	126	6	1	1	NUM
ejpam-4277	126	7	):	):	PUNCT
ejpam-4277	126	8	let	let	VERB
ejpam-4277	126	9	u	u	PRON
ejpam-4277	126	10	∈	∈	PROPN
ejpam-4277	126	11	sλspo(x	sλspo(x	PROPN
ejpam-4277	126	12	,	,	PUNCT
ejpam-4277	126	13	τ	τ	X
ejpam-4277	126	14	)	)	PUNCT
ejpam-4277	126	15	containing	contain	VERB
ejpam-4277	126	16	x	x	PUNCT
ejpam-4277	126	17	and	and	CCONJ
ejpam-4277	126	18	let	let	VERB
ejpam-4277	126	19	g1	g1	PROPN
ejpam-4277	126	20	,	,	PUNCT
ejpam-4277	126	21	g2	g2	PROPN
ejpam-4277	126	22	be	be	VERB
ejpam-4277	126	23	any	any	DET
ejpam-4277	126	24	(	(	PUNCT
ejpam-4277	126	25	λ	λ	NOUN
ejpam-4277	126	26	,	,	PUNCT
ejpam-4277	126	27	sp)-open	sp)-open	ADJ
ejpam-4277	126	28	sets	set	NOUN
ejpam-4277	126	29	of	of	ADP
ejpam-4277	126	30	y	y	PRON
ejpam-4277	126	31	such	such	ADJ
ejpam-4277	126	32	that	that	SCONJ
ejpam-4277	126	33	f	f	PROPN
ejpam-4277	126	34	(	(	PUNCT
ejpam-4277	126	35	x	x	X
ejpam-4277	126	36	)	)	PUNCT
ejpam-4277	126	37	∈	∈	NOUN
ejpam-4277	126	38	g+	g+	NOUN
ejpam-4277	126	39	1	1	NUM
ejpam-4277	126	40	∩g−	∩g−	PROPN
ejpam-4277	126	41	2	2	NUM
ejpam-4277	126	42	.	.	PUNCT
ejpam-4277	127	1	then	then	ADV
ejpam-4277	127	2	,	,	PUNCT
ejpam-4277	127	3	x	x	PUNCT
ejpam-4277	127	4	∈	∈	PROPN
ejpam-4277	128	1	[	[	X
ejpam-4277	128	2	[	[	X
ejpam-4277	128	3	[	[	X
ejpam-4277	128	4	f+(g	f+(g	NOUN
ejpam-4277	128	5	s(λ	s(λ	NOUN
ejpam-4277	128	6	,	,	PUNCT
ejpam-4277	128	7	sp	sp	NOUN
ejpam-4277	128	8	)	)	PUNCT
ejpam-4277	128	9	1	1	NUM
ejpam-4277	128	10	)	)	PUNCT
ejpam-4277	128	11	∩f−(g	∩f−(g	PROPN
ejpam-4277	128	12	s(λ	s(λ	PROPN
ejpam-4277	128	13	,	,	PUNCT
ejpam-4277	128	14	sp	sp	NOUN
ejpam-4277	128	15	)	)	PUNCT
ejpam-4277	128	16	2	2	NUM
ejpam-4277	128	17	)	)	PUNCT
ejpam-4277	128	18	]	]	PUNCT
ejpam-4277	128	19	(	(	PUNCT
ejpam-4277	128	20	λ	λ	NOUN
ejpam-4277	128	21	,	,	PUNCT
ejpam-4277	128	22	sp	sp	NOUN
ejpam-4277	128	23	)	)	PUNCT
ejpam-4277	128	24	]	]	PUNCT
ejpam-4277	128	25	(	(	PUNCT
ejpam-4277	128	26	λ	λ	X
ejpam-4277	128	27	,	,	PUNCT
ejpam-4277	128	28	sp)](λ	sp)](λ	PROPN
ejpam-4277	128	29	,	,	PUNCT
ejpam-4277	128	30	sp	sp	NOUN
ejpam-4277	128	31	)	)	PUNCT
ejpam-4277	128	32	=	=	NOUN
ejpam-4277	129	1	[	[	X
ejpam-4277	129	2	[	[	X
ejpam-4277	129	3	f+(g	f+(g	NOUN
ejpam-4277	129	4	s(λ	s(λ	NOUN
ejpam-4277	129	5	,	,	PUNCT
ejpam-4277	129	6	sp	sp	NOUN
ejpam-4277	129	7	)	)	PUNCT
ejpam-4277	129	8	1	1	NUM
ejpam-4277	129	9	)	)	PUNCT
ejpam-4277	129	10	∩	∩	PROPN
ejpam-4277	129	11	f−(g	f−(g	VERB
ejpam-4277	129	12	s(λ	s(λ	PROPN
ejpam-4277	129	13	,	,	PUNCT
ejpam-4277	129	14	sp	sp	NOUN
ejpam-4277	129	15	)	)	PUNCT
ejpam-4277	129	16	2	2	NUM
ejpam-4277	129	17	)	)	PUNCT
ejpam-4277	129	18	]	]	PUNCT
ejpam-4277	129	19	(	(	PUNCT
ejpam-4277	129	20	λ	λ	NOUN
ejpam-4277	129	21	,	,	PUNCT
ejpam-4277	129	22	sp	sp	NOUN
ejpam-4277	129	23	)	)	PUNCT
ejpam-4277	129	24	]	]	PUNCT
ejpam-4277	130	1	s(λ	s(λ	PROPN
ejpam-4277	130	2	,	,	PUNCT
ejpam-4277	130	3	sp	sp	NOUN
ejpam-4277	130	4	)	)	PUNCT
ejpam-4277	130	5	,	,	PUNCT
ejpam-4277	130	6	by	by	ADP
ejpam-4277	130	7	lemma	lemma	PROPN
ejpam-4277	130	8	3	3	NUM
ejpam-4277	130	9	,	,	PUNCT
ejpam-4277	130	10	∅	∅	NOUN
ejpam-4277	130	11	6=	6=	ADP
ejpam-4277	130	12	u	u	NOUN
ejpam-4277	130	13	∩	∩	NOUN
ejpam-4277	130	14	[	[	X
ejpam-4277	130	15	f+(g	f+(g	NUM
ejpam-4277	130	16	s(λ	s(λ	NOUN
ejpam-4277	130	17	,	,	PUNCT
ejpam-4277	130	18	sp	sp	NOUN
ejpam-4277	130	19	)	)	PUNCT
ejpam-4277	130	20	1	1	NUM
ejpam-4277	130	21	)	)	PUNCT
ejpam-4277	130	22	∩	∩	PROPN
ejpam-4277	130	23	f−(g	f−(g	VERB
ejpam-4277	130	24	s(λ	s(λ	PROPN
ejpam-4277	130	25	,	,	PUNCT
ejpam-4277	130	26	sp	sp	NOUN
ejpam-4277	130	27	)	)	PUNCT
ejpam-4277	130	28	2	2	NUM
ejpam-4277	130	29	)	)	PUNCT
ejpam-4277	130	30	]	]	PUNCT
ejpam-4277	130	31	(	(	PUNCT
ejpam-4277	130	32	λ	λ	NOUN
ejpam-4277	130	33	,	,	PUNCT
ejpam-4277	130	34	sp	sp	NOUN
ejpam-4277	130	35	)	)	PUNCT
ejpam-4277	130	36	.	.	PUNCT
ejpam-4277	131	1	put	put	VERB
ejpam-4277	131	2	gu	gu	NOUN
ejpam-4277	132	1	=	=	PUNCT
ejpam-4277	133	1	[	[	X
ejpam-4277	133	2	u	u	NOUN
ejpam-4277	133	3	∩	∩	NOUN
ejpam-4277	133	4	[	[	X
ejpam-4277	133	5	f+(g	f+(g	NUM
ejpam-4277	133	6	s(λ	s(λ	NOUN
ejpam-4277	133	7	,	,	PUNCT
ejpam-4277	133	8	sp	sp	NOUN
ejpam-4277	133	9	)	)	PUNCT
ejpam-4277	133	10	1	1	NUM
ejpam-4277	133	11	)	)	PUNCT
ejpam-4277	133	12	∩	∩	PROPN
ejpam-4277	133	13	f−(g	f−(g	VERB
ejpam-4277	133	14	s(λ	s(λ	PROPN
ejpam-4277	133	15	,	,	PUNCT
ejpam-4277	133	16	sp	sp	NOUN
ejpam-4277	133	17	)	)	PUNCT
ejpam-4277	133	18	2	2	NUM
ejpam-4277	133	19	)	)	PUNCT
ejpam-4277	133	20	]	]	PUNCT
ejpam-4277	133	21	(	(	PUNCT
ejpam-4277	133	22	λ	λ	PROPN
ejpam-4277	133	23	,	,	PUNCT
ejpam-4277	133	24	sp)](λ	sp)](λ	PROPN
ejpam-4277	133	25	,	,	PUNCT
ejpam-4277	133	26	sp	sp	NOUN
ejpam-4277	133	27	)	)	PUNCT
ejpam-4277	133	28	,	,	PUNCT
ejpam-4277	133	29	then	then	ADV
ejpam-4277	133	30	gu	gu	PROPN
ejpam-4277	133	31	is	be	AUX
ejpam-4277	133	32	a	a	DET
ejpam-4277	133	33	nonempty	nonempty	ADJ
ejpam-4277	133	34	(	(	PUNCT
ejpam-4277	133	35	λ	λ	NOUN
ejpam-4277	133	36	,	,	PUNCT
ejpam-4277	133	37	sp)open	sp)open	VERB
ejpam-4277	133	38	set	set	NOUN
ejpam-4277	133	39	of	of	ADP
ejpam-4277	133	40	x	x	SYM
ejpam-4277	133	41	such	such	ADJ
ejpam-4277	133	42	that	that	PRON
ejpam-4277	133	43	gu	gu	NOUN
ejpam-4277	133	44	⊆	⊆	NUM
ejpam-4277	133	45	u	u	NOUN
ejpam-4277	133	46	,	,	PUNCT
ejpam-4277	133	47	f	f	PROPN
ejpam-4277	133	48	(	(	PUNCT
ejpam-4277	133	49	gu	gu	NOUN
ejpam-4277	133	50	)	)	PUNCT
ejpam-4277	133	51	⊆	⊆	PROPN
ejpam-4277	133	52	g	g	PROPN
ejpam-4277	133	53	s(λ	s(λ	PROPN
ejpam-4277	133	54	,	,	PUNCT
ejpam-4277	133	55	sp	sp	NOUN
ejpam-4277	133	56	)	)	PUNCT
ejpam-4277	133	57	1	1	NUM
ejpam-4277	133	58	and	and	CCONJ
ejpam-4277	133	59	f	f	PROPN
ejpam-4277	133	60	(	(	PUNCT
ejpam-4277	133	61	z	z	NOUN
ejpam-4277	133	62	)	)	PUNCT
ejpam-4277	133	63	∩	∩	PROPN
ejpam-4277	133	64	g	g	PROPN
ejpam-4277	133	65	s(λ	s(λ	PROPN
ejpam-4277	133	66	,	,	PUNCT
ejpam-4277	133	67	sp	sp	NOUN
ejpam-4277	133	68	)	)	PUNCT
ejpam-4277	133	69	2	2	NUM
ejpam-4277	133	70	6=	6=	NOUN
ejpam-4277	133	71	∅	∅	NOUN
ejpam-4277	133	72	for	for	ADP
ejpam-4277	133	73	each	each	DET
ejpam-4277	133	74	z	z	NOUN
ejpam-4277	133	75	∈	∈	PROPN
ejpam-4277	133	76	gu	gu	NOUN
ejpam-4277	133	77	.	.	PUNCT
ejpam-4277	134	1	this	this	PRON
ejpam-4277	134	2	shows	show	VERB
ejpam-4277	134	3	that	that	SCONJ
ejpam-4277	134	4	f	f	PROPN
ejpam-4277	134	5	is	be	AUX
ejpam-4277	134	6	almost	almost	ADV
ejpam-4277	134	7	α(λ	α(λ	PROPN
ejpam-4277	134	8	,	,	PUNCT
ejpam-4277	134	9	sp)-continuous	sp)-continuous	ADJ
ejpam-4277	134	10	at	at	ADP
ejpam-4277	134	11	x.	x.	PROPN
ejpam-4277	134	12	c.	c.	PROPN
ejpam-4277	134	13	boonpok	boonpok	PROPN
ejpam-4277	134	14	,	,	PUNCT
ejpam-4277	134	15	j.	j.	PROPN
ejpam-4277	134	16	khampakdee	khampakdee	PROPN
ejpam-4277	134	17	/	/	PUNCT
ejpam-4277	134	18	eur	eur	PROPN
ejpam-4277	134	19	.	.	PUNCT
ejpam-4277	135	1	j.	j.	PROPN
ejpam-4277	135	2	pure	pure	PROPN
ejpam-4277	135	3	appl	appl	PROPN
ejpam-4277	135	4	.	.	PROPN
ejpam-4277	135	5	math	math	PROPN
ejpam-4277	135	6	,	,	PUNCT
ejpam-4277	135	7	15	15	NUM
ejpam-4277	135	8	(	(	PUNCT
ejpam-4277	135	9	2	2	NUM
ejpam-4277	135	10	)	)	PUNCT
ejpam-4277	135	11	(	(	PUNCT
ejpam-4277	135	12	2022	2022	NUM
ejpam-4277	135	13	)	)	PUNCT
ejpam-4277	135	14	,	,	PUNCT
ejpam-4277	135	15	626	626	NUM
ejpam-4277	135	16	-	-	SYM
ejpam-4277	135	17	634	634	NUM
ejpam-4277	135	18	630	630	NUM
ejpam-4277	135	19	theorem	theorem	NOUN
ejpam-4277	135	20	2	2	NUM
ejpam-4277	135	21	.	.	X
ejpam-4277	135	22	for	for	ADP
ejpam-4277	135	23	a	a	DET
ejpam-4277	135	24	multifunction	multifunction	NOUN
ejpam-4277	135	25	f	f	NOUN
ejpam-4277	135	26	:	:	PUNCT
ejpam-4277	135	27	(	(	PUNCT
ejpam-4277	135	28	x	x	X
ejpam-4277	135	29	,	,	PUNCT
ejpam-4277	135	30	τ	τ	X
ejpam-4277	135	31	)	)	PUNCT
ejpam-4277	135	32	→	→	SYM
ejpam-4277	135	33	(	(	PUNCT
ejpam-4277	135	34	y	y	PROPN
ejpam-4277	135	35	,	,	PUNCT
ejpam-4277	135	36	σ	σ	PROPN
ejpam-4277	135	37	)	)	PUNCT
ejpam-4277	135	38	,	,	PUNCT
ejpam-4277	135	39	the	the	DET
ejpam-4277	135	40	following	follow	VERB
ejpam-4277	135	41	properties	property	NOUN
ejpam-4277	135	42	are	be	AUX
ejpam-4277	135	43	equivalent	equivalent	ADJ
ejpam-4277	135	44	:	:	PUNCT
ejpam-4277	135	45	(	(	PUNCT
ejpam-4277	135	46	1	1	X
ejpam-4277	135	47	)	)	PUNCT
ejpam-4277	135	48	f	f	PROPN
ejpam-4277	135	49	is	be	AUX
ejpam-4277	135	50	almost	almost	ADV
ejpam-4277	135	51	α(λ	α(λ	NOUN
ejpam-4277	135	52	,	,	PUNCT
ejpam-4277	135	53	sp)-continuous	sp)-continuous	ADJ
ejpam-4277	135	54	at	at	ADP
ejpam-4277	135	55	a	a	DET
ejpam-4277	135	56	point	point	NOUN
ejpam-4277	135	57	x	x	X
ejpam-4277	135	58	∈	∈	NOUN
ejpam-4277	135	59	x	x	X
ejpam-4277	135	60	;	;	PUNCT
ejpam-4277	135	61	(	(	PUNCT
ejpam-4277	135	62	2	2	X
ejpam-4277	135	63	)	)	PUNCT
ejpam-4277	135	64	for	for	ADP
ejpam-4277	135	65	each	each	DET
ejpam-4277	135	66	x	x	SYM
ejpam-4277	135	67	∈	∈	PROPN
ejpam-4277	135	68	x	x	X
ejpam-4277	135	69	and	and	CCONJ
ejpam-4277	135	70	any	any	DET
ejpam-4277	135	71	(	(	PUNCT
ejpam-4277	135	72	λ	λ	NOUN
ejpam-4277	135	73	,	,	PUNCT
ejpam-4277	135	74	sp)-open	sp)-open	ADJ
ejpam-4277	135	75	sets	set	NOUN
ejpam-4277	135	76	g1	g1	NOUN
ejpam-4277	135	77	,	,	PUNCT
ejpam-4277	135	78	g2	g2	PROPN
ejpam-4277	135	79	of	of	ADP
ejpam-4277	135	80	y	y	PRON
ejpam-4277	135	81	such	such	ADJ
ejpam-4277	135	82	that	that	SCONJ
ejpam-4277	135	83	f	f	PROPN
ejpam-4277	135	84	(	(	PUNCT
ejpam-4277	135	85	x	x	X
ejpam-4277	135	86	)	)	PUNCT
ejpam-4277	135	87	∈	∈	PROPN
ejpam-4277	135	88	g+	g+	NOUN
ejpam-4277	135	89	1	1	NUM
ejpam-4277	135	90	∩	∩	X
ejpam-4277	135	91	g−	g−	ADJ
ejpam-4277	135	92	2	2	NUM
ejpam-4277	135	93	,	,	PUNCT
ejpam-4277	135	94	there	there	PRON
ejpam-4277	135	95	exists	exist	VERB
ejpam-4277	135	96	an	an	DET
ejpam-4277	135	97	α(λ	α(λ	PROPN
ejpam-4277	135	98	,	,	PUNCT
ejpam-4277	135	99	sp)-open	sp)-open	VERB
ejpam-4277	135	100	set	set	VERB
ejpam-4277	135	101	u	u	PRON
ejpam-4277	135	102	containing	contain	VERB
ejpam-4277	135	103	x	x	PUNCT
ejpam-4277	135	104	such	such	ADJ
ejpam-4277	135	105	that	that	SCONJ
ejpam-4277	135	106	f	f	PROPN
ejpam-4277	135	107	(	(	PUNCT
ejpam-4277	135	108	u	u	NOUN
ejpam-4277	135	109	)	)	PUNCT
ejpam-4277	135	110	⊆	⊆	NUM
ejpam-4277	135	111	g	g	PROPN
ejpam-4277	135	112	s(λ	s(λ	PROPN
ejpam-4277	135	113	,	,	PUNCT
ejpam-4277	135	114	sp	sp	NOUN
ejpam-4277	135	115	)	)	PUNCT
ejpam-4277	135	116	1	1	NUM
ejpam-4277	135	117	and	and	CCONJ
ejpam-4277	135	118	f	f	PROPN
ejpam-4277	135	119	(	(	PUNCT
ejpam-4277	135	120	z	z	NOUN
ejpam-4277	135	121	)	)	PUNCT
ejpam-4277	135	122	∩g	∩g	PROPN
ejpam-4277	135	123	s(λ	s(λ	PROPN
ejpam-4277	135	124	,	,	PUNCT
ejpam-4277	135	125	sp	sp	NOUN
ejpam-4277	135	126	)	)	PUNCT
ejpam-4277	135	127	2	2	NUM
ejpam-4277	135	128	6=	6=	NOUN
ejpam-4277	135	129	∅	∅	NOUN
ejpam-4277	135	130	for	for	ADP
ejpam-4277	135	131	every	every	DET
ejpam-4277	135	132	z	z	NOUN
ejpam-4277	135	133	∈	∈	PROPN
ejpam-4277	135	134	u	u	NOUN
ejpam-4277	135	135	;	;	PUNCT
ejpam-4277	135	136	(	(	PUNCT
ejpam-4277	135	137	3	3	X
ejpam-4277	135	138	)	)	PUNCT
ejpam-4277	135	139	for	for	ADP
ejpam-4277	135	140	each	each	DET
ejpam-4277	135	141	x	x	SYM
ejpam-4277	135	142	∈	∈	PROPN
ejpam-4277	135	143	x	x	X
ejpam-4277	135	144	and	and	CCONJ
ejpam-4277	135	145	any	any	DET
ejpam-4277	135	146	r(λ	r(λ	NOUN
ejpam-4277	135	147	,	,	PUNCT
ejpam-4277	135	148	sp)-open	sp)-open	NOUN
ejpam-4277	135	149	sets	set	NOUN
ejpam-4277	135	150	g1	g1	NOUN
ejpam-4277	135	151	,	,	PUNCT
ejpam-4277	135	152	g2	g2	PROPN
ejpam-4277	135	153	of	of	ADP
ejpam-4277	135	154	y	y	PRON
ejpam-4277	135	155	such	such	ADJ
ejpam-4277	135	156	that	that	SCONJ
ejpam-4277	135	157	f	f	PROPN
ejpam-4277	135	158	(	(	PUNCT
ejpam-4277	135	159	x	x	X
ejpam-4277	135	160	)	)	PUNCT
ejpam-4277	135	161	∈	∈	NOUN
ejpam-4277	135	162	g+	g+	NOUN
ejpam-4277	136	1	1	1	NUM
ejpam-4277	136	2	∩g−	∩g−	PROPN
ejpam-4277	136	3	2	2	NUM
ejpam-4277	136	4	,	,	PUNCT
ejpam-4277	136	5	there	there	PRON
ejpam-4277	136	6	exists	exist	VERB
ejpam-4277	136	7	u	u	PROPN
ejpam-4277	136	8	∈	∈	PROPN
ejpam-4277	136	9	αλspo(x	αλspo(x	PROPN
ejpam-4277	136	10	,	,	PUNCT
ejpam-4277	136	11	τ	τ	X
ejpam-4277	136	12	)	)	PUNCT
ejpam-4277	136	13	containing	contain	VERB
ejpam-4277	136	14	x	x	PUNCT
ejpam-4277	136	15	such	such	ADJ
ejpam-4277	136	16	that	that	SCONJ
ejpam-4277	136	17	f	f	PROPN
ejpam-4277	136	18	(	(	PUNCT
ejpam-4277	136	19	u	u	NOUN
ejpam-4277	136	20	)	)	PUNCT
ejpam-4277	136	21	⊆	⊆	NUM
ejpam-4277	136	22	g1	g1	NOUN
ejpam-4277	136	23	and	and	CCONJ
ejpam-4277	136	24	f	f	PROPN
ejpam-4277	136	25	(	(	PUNCT
ejpam-4277	136	26	z)∩g2	z)∩g2	X
ejpam-4277	136	27	6=	6=	NOUN
ejpam-4277	136	28	∅	∅	NOUN
ejpam-4277	136	29	for	for	ADP
ejpam-4277	136	30	every	every	DET
ejpam-4277	136	31	z	z	NOUN
ejpam-4277	136	32	∈	∈	PROPN
ejpam-4277	136	33	u	u	NOUN
ejpam-4277	136	34	;	;	PUNCT
ejpam-4277	136	35	(	(	PUNCT
ejpam-4277	136	36	4	4	X
ejpam-4277	136	37	)	)	PUNCT
ejpam-4277	136	38	f+(g1	f+(g1	NOUN
ejpam-4277	136	39	)	)	PUNCT
ejpam-4277	136	40	∩	∩	NOUN
ejpam-4277	136	41	f−(g2	f−(g2	PRON
ejpam-4277	136	42	)	)	PUNCT
ejpam-4277	136	43	∈	∈	PROPN
ejpam-4277	136	44	αλspo(x	αλspo(x	PROPN
ejpam-4277	136	45	,	,	PUNCT
ejpam-4277	136	46	τ	τ	PROPN
ejpam-4277	136	47	)	)	PUNCT
ejpam-4277	136	48	for	for	ADP
ejpam-4277	136	49	every	every	DET
ejpam-4277	136	50	g1	g1	NOUN
ejpam-4277	136	51	,	,	PUNCT
ejpam-4277	136	52	g2	g2	PROPN
ejpam-4277	136	53	∈	∈	PROPN
ejpam-4277	136	54	rλspo(y	rλspo(y	PROPN
ejpam-4277	136	55	,	,	PUNCT
ejpam-4277	136	56	σ	σ	PROPN
ejpam-4277	136	57	)	)	PUNCT
ejpam-4277	136	58	;	;	PUNCT
ejpam-4277	136	59	(	(	PUNCT
ejpam-4277	136	60	5	5	X
ejpam-4277	136	61	)	)	PUNCT
ejpam-4277	136	62	f+(k1	f+(k1	NOUN
ejpam-4277	136	63	)	)	PUNCT
ejpam-4277	136	64	∪	∪	ADP
ejpam-4277	136	65	f−(k2	f−(k2	NOUN
ejpam-4277	136	66	)	)	PUNCT
ejpam-4277	136	67	is	be	AUX
ejpam-4277	136	68	α(λ	α(λ	PROPN
ejpam-4277	136	69	,	,	PUNCT
ejpam-4277	136	70	sp)-closed	sp)-close	VERB
ejpam-4277	136	71	in	in	ADP
ejpam-4277	136	72	x	x	PUNCT
ejpam-4277	136	73	for	for	ADP
ejpam-4277	136	74	every	every	DET
ejpam-4277	136	75	r(λ	r(λ	NOUN
ejpam-4277	136	76	,	,	PUNCT
ejpam-4277	136	77	sp)-closed	sp)-close	VERB
ejpam-4277	136	78	sets	set	VERB
ejpam-4277	136	79	k1,k2	k1,k2	PROPN
ejpam-4277	136	80	of	of	ADP
ejpam-4277	136	81	y	y	PROPN
ejpam-4277	136	82	;	;	PUNCT
ejpam-4277	136	83	(	(	PUNCT
ejpam-4277	136	84	6	6	X
ejpam-4277	136	85	)	)	PUNCT
ejpam-4277	136	86	f+(g1	f+(g1	NOUN
ejpam-4277	136	87	)	)	PUNCT
ejpam-4277	136	88	∪	∪	ADP
ejpam-4277	136	89	f−(g2	f−(g2	NOUN
ejpam-4277	136	90	)	)	PUNCT
ejpam-4277	136	91	⊆	⊆	NUM
ejpam-4277	137	1	[	[	SYM
ejpam-4277	137	2	f+(g	f+(g	NOUN
ejpam-4277	137	3	s(λ	s(λ	NOUN
ejpam-4277	137	4	,	,	PUNCT
ejpam-4277	137	5	sp	sp	NOUN
ejpam-4277	137	6	)	)	PUNCT
ejpam-4277	137	7	1	1	NUM
ejpam-4277	137	8	)	)	PUNCT
ejpam-4277	137	9	∩	∩	PROPN
ejpam-4277	137	10	f−(g	f−(g	VERB
ejpam-4277	137	11	s(λ	s(λ	PROPN
ejpam-4277	137	12	,	,	PUNCT
ejpam-4277	137	13	sp	sp	NOUN
ejpam-4277	137	14	)	)	PUNCT
ejpam-4277	137	15	2	2	NUM
ejpam-4277	137	16	)	)	PUNCT
ejpam-4277	137	17	]	]	PUNCT
ejpam-4277	137	18	α(λ	α(λ	PROPN
ejpam-4277	137	19	,	,	PUNCT
ejpam-4277	137	20	sp	sp	NOUN
ejpam-4277	137	21	)	)	PUNCT
ejpam-4277	137	22	for	for	ADP
ejpam-4277	137	23	any	any	DET
ejpam-4277	137	24	(	(	PUNCT
ejpam-4277	137	25	λ	λ	NOUN
ejpam-4277	137	26	,	,	PUNCT
ejpam-4277	137	27	sp)-open	sp)-open	ADJ
ejpam-4277	137	28	sets	set	NOUN
ejpam-4277	137	29	g1	g1	NOUN
ejpam-4277	137	30	,	,	PUNCT
ejpam-4277	137	31	g2	g2	PROPN
ejpam-4277	137	32	of	of	ADP
ejpam-4277	137	33	y	y	PROPN
ejpam-4277	137	34	;	;	PUNCT
ejpam-4277	137	35	(	(	PUNCT
ejpam-4277	137	36	7	7	X
ejpam-4277	137	37	)	)	PUNCT
ejpam-4277	138	1	[	[	X
ejpam-4277	138	2	f−([k1]s(λ	f−([k1]s(λ	ADJ
ejpam-4277	138	3	,	,	PUNCT
ejpam-4277	138	4	sp	sp	NOUN
ejpam-4277	138	5	)	)	PUNCT
ejpam-4277	138	6	)	)	PUNCT
ejpam-4277	138	7	∪	∪	ADP
ejpam-4277	138	8	f+([k2]s(λ	f+([k2]s(λ	PROPN
ejpam-4277	138	9	,	,	PUNCT
ejpam-4277	138	10	sp	sp	NOUN
ejpam-4277	138	11	)	)	PUNCT
ejpam-4277	138	12	)	)	PUNCT
ejpam-4277	138	13	]	]	PUNCT
ejpam-4277	139	1	α(λ	α(λ	PROPN
ejpam-4277	139	2	,	,	PUNCT
ejpam-4277	139	3	sp	sp	NOUN
ejpam-4277	139	4	)	)	PUNCT
ejpam-4277	139	5	⊆	⊆	NUM
ejpam-4277	139	6	f−(k1	f−(k1	NOUN
ejpam-4277	139	7	)	)	PUNCT
ejpam-4277	139	8	∪	∪	ADP
ejpam-4277	139	9	f+(k2	f+(k2	NOUN
ejpam-4277	139	10	)	)	PUNCT
ejpam-4277	139	11	for	for	ADP
ejpam-4277	139	12	any	any	DET
ejpam-4277	139	13	(	(	PUNCT
ejpam-4277	139	14	λ	λ	PROPN
ejpam-4277	139	15	,	,	PUNCT
ejpam-4277	139	16	sp)-closed	sp)-close	VERB
ejpam-4277	139	17	sets	set	VERB
ejpam-4277	139	18	k1,k2	k1,k2	PROPN
ejpam-4277	139	19	of	of	ADP
ejpam-4277	139	20	y	y	PROPN
ejpam-4277	139	21	;	;	PUNCT
ejpam-4277	139	22	(	(	PUNCT
ejpam-4277	139	23	8)	8)	NUM
ejpam-4277	139	24	[	[	X
ejpam-4277	139	25	f−([[k1](λ	f−([[k1](λ	NOUN
ejpam-4277	139	26	,	,	PUNCT
ejpam-4277	139	27	sp	sp	NOUN
ejpam-4277	139	28	)	)	PUNCT
ejpam-4277	139	29	]	]	PUNCT
ejpam-4277	139	30	(	(	PUNCT
ejpam-4277	139	31	λ	λ	NOUN
ejpam-4277	139	32	,	,	PUNCT
ejpam-4277	139	33	sp	sp	NOUN
ejpam-4277	139	34	)	)	PUNCT
ejpam-4277	139	35	)	)	PUNCT
ejpam-4277	139	36	∪	∪	ADP
ejpam-4277	139	37	f+([[k2](λ	f+([[k2](λ	PROPN
ejpam-4277	139	38	,	,	PUNCT
ejpam-4277	139	39	sp	sp	NOUN
ejpam-4277	139	40	)	)	PUNCT
ejpam-4277	139	41	]	]	PUNCT
ejpam-4277	139	42	(	(	PUNCT
ejpam-4277	139	43	λ	λ	NOUN
ejpam-4277	139	44	,	,	PUNCT
ejpam-4277	139	45	sp))]α(λ	sp))]α(λ	NOUN
ejpam-4277	139	46	,	,	PUNCT
ejpam-4277	139	47	sp	sp	NOUN
ejpam-4277	139	48	)	)	PUNCT
ejpam-4277	139	49	⊆	⊆	NUM
ejpam-4277	139	50	f−(k1	f−(k1	NOUN
ejpam-4277	139	51	)	)	PUNCT
ejpam-4277	139	52	∪	∪	ADP
ejpam-4277	139	53	f+(k2	f+(k2	NOUN
ejpam-4277	139	54	)	)	PUNCT
ejpam-4277	139	55	for	for	ADP
ejpam-4277	139	56	any	any	DET
ejpam-4277	139	57	(	(	PUNCT
ejpam-4277	139	58	λ	λ	PROPN
ejpam-4277	139	59	,	,	PUNCT
ejpam-4277	139	60	sp)-closed	sp)-close	VERB
ejpam-4277	139	61	sets	set	VERB
ejpam-4277	139	62	k1,k2	k1,k2	PROPN
ejpam-4277	139	63	of	of	ADP
ejpam-4277	139	64	y	y	PROPN
ejpam-4277	139	65	;	;	PUNCT
ejpam-4277	139	66	(	(	PUNCT
ejpam-4277	139	67	9	9	X
ejpam-4277	139	68	)	)	PUNCT
ejpam-4277	139	69	[	[	X
ejpam-4277	139	70	f−([[b	f−([[b	X
ejpam-4277	139	71	(	(	PUNCT
ejpam-4277	139	72	λ	λ	PROPN
ejpam-4277	139	73	,	,	PUNCT
ejpam-4277	139	74	sp	sp	NOUN
ejpam-4277	139	75	)	)	PUNCT
ejpam-4277	139	76	1	1	NUM
ejpam-4277	139	77	]	]	PUNCT
ejpam-4277	139	78	(	(	PUNCT
ejpam-4277	139	79	λ	λ	NOUN
ejpam-4277	139	80	,	,	PUNCT
ejpam-4277	139	81	sp	sp	NOUN
ejpam-4277	139	82	)	)	PUNCT
ejpam-4277	139	83	]	]	PUNCT
ejpam-4277	139	84	(	(	PUNCT
ejpam-4277	139	85	λ	λ	X
ejpam-4277	139	86	,	,	PUNCT
ejpam-4277	139	87	sp))∪f+([[b	sp))∪f+([[b	PROPN
ejpam-4277	139	88	(	(	PUNCT
ejpam-4277	139	89	λ	λ	NOUN
ejpam-4277	139	90	,	,	PUNCT
ejpam-4277	139	91	sp	sp	NOUN
ejpam-4277	139	92	)	)	PUNCT
ejpam-4277	139	93	2	2	NUM
ejpam-4277	139	94	]	]	PUNCT
ejpam-4277	139	95	(	(	PUNCT
ejpam-4277	139	96	λ	λ	NOUN
ejpam-4277	139	97	,	,	PUNCT
ejpam-4277	139	98	sp	sp	NOUN
ejpam-4277	139	99	)	)	PUNCT
ejpam-4277	139	100	]	]	PUNCT
ejpam-4277	139	101	(	(	PUNCT
ejpam-4277	139	102	λ	λ	NOUN
ejpam-4277	139	103	,	,	PUNCT
ejpam-4277	139	104	sp))]α(λ	sp))]α(λ	NOUN
ejpam-4277	139	105	,	,	PUNCT
ejpam-4277	139	106	sp	sp	NOUN
ejpam-4277	139	107	)	)	PUNCT
ejpam-4277	139	108	⊆	⊆	NUM
ejpam-4277	139	109	f−(b	f−(b	PROPN
ejpam-4277	139	110	(	(	PUNCT
ejpam-4277	139	111	λ	λ	PROPN
ejpam-4277	139	112	,	,	PUNCT
ejpam-4277	139	113	sp	sp	NOUN
ejpam-4277	139	114	)	)	PUNCT
ejpam-4277	139	115	1	1	NUM
ejpam-4277	139	116	)	)	PUNCT
ejpam-4277	139	117	∪f+(b	∪f+(b	NOUN
ejpam-4277	139	118	(	(	PUNCT
ejpam-4277	139	119	λ	λ	NOUN
ejpam-4277	139	120	,	,	PUNCT
ejpam-4277	139	121	sp	sp	NOUN
ejpam-4277	139	122	)	)	PUNCT
ejpam-4277	139	123	2	2	NUM
ejpam-4277	139	124	)	)	PUNCT
ejpam-4277	139	125	for	for	ADP
ejpam-4277	139	126	any	any	DET
ejpam-4277	139	127	subsets	subset	NOUN
ejpam-4277	139	128	b1	b1	NOUN
ejpam-4277	139	129	,	,	PUNCT
ejpam-4277	139	130	b2	b2	NOUN
ejpam-4277	139	131	of	of	ADP
ejpam-4277	139	132	y	y	PROPN
ejpam-4277	139	133	;	;	PUNCT
ejpam-4277	139	134	(	(	PUNCT
ejpam-4277	139	135	10	10	NUM
ejpam-4277	139	136	)	)	PUNCT
ejpam-4277	140	1	[	[	X
ejpam-4277	140	2	[	[	X
ejpam-4277	140	3	[	[	X
ejpam-4277	140	4	f−([[k1](λ	f−([[k1](λ	NOUN
ejpam-4277	140	5	,	,	PUNCT
ejpam-4277	140	6	sp	sp	NOUN
ejpam-4277	140	7	)	)	PUNCT
ejpam-4277	140	8	]	]	PUNCT
ejpam-4277	141	1	(	(	PUNCT
ejpam-4277	141	2	λ	λ	NOUN
ejpam-4277	141	3	,	,	PUNCT
ejpam-4277	141	4	sp	sp	NOUN
ejpam-4277	141	5	)	)	PUNCT
ejpam-4277	141	6	)	)	PUNCT
ejpam-4277	141	7	∪	∪	ADP
ejpam-4277	141	8	f+([[k2](λ	f+([[k2](λ	PROPN
ejpam-4277	141	9	,	,	PUNCT
ejpam-4277	141	10	sp	sp	NOUN
ejpam-4277	141	11	)	)	PUNCT
ejpam-4277	141	12	]	]	PUNCT
ejpam-4277	141	13	(	(	PUNCT
ejpam-4277	141	14	λ	λ	INTJ
ejpam-4277	141	15	,	,	PUNCT
ejpam-4277	141	16	sp))](λ	sp))](λ	PROPN
ejpam-4277	141	17	,	,	PUNCT
ejpam-4277	141	18	sp)](λ	sp)](λ	PROPN
ejpam-4277	141	19	,	,	PUNCT
ejpam-4277	141	20	sp	sp	NOUN
ejpam-4277	141	21	)	)	PUNCT
ejpam-4277	141	22	]	]	PUNCT
ejpam-4277	141	23	(	(	PUNCT
ejpam-4277	141	24	λ	λ	NOUN
ejpam-4277	141	25	,	,	PUNCT
ejpam-4277	141	26	sp	sp	NOUN
ejpam-4277	141	27	)	)	PUNCT
ejpam-4277	141	28	⊆	⊆	NUM
ejpam-4277	141	29	f−(k1	f−(k1	NOUN
ejpam-4277	141	30	)	)	PUNCT
ejpam-4277	141	31	∪	∪	ADP
ejpam-4277	141	32	f+(k2	f+(k2	NOUN
ejpam-4277	141	33	)	)	PUNCT
ejpam-4277	141	34	for	for	ADP
ejpam-4277	141	35	any	any	DET
ejpam-4277	141	36	(	(	PUNCT
ejpam-4277	141	37	λ	λ	PROPN
ejpam-4277	141	38	,	,	PUNCT
ejpam-4277	141	39	sp)-closed	sp)-close	VERB
ejpam-4277	141	40	sets	set	VERB
ejpam-4277	141	41	k1,k2	k1,k2	PROPN
ejpam-4277	141	42	of	of	ADP
ejpam-4277	141	43	y	y	PROPN
ejpam-4277	141	44	;	;	PUNCT
ejpam-4277	141	45	(	(	PUNCT
ejpam-4277	141	46	11	11	NUM
ejpam-4277	141	47	)	)	PUNCT
ejpam-4277	142	1	[	[	X
ejpam-4277	142	2	[	[	X
ejpam-4277	142	3	[	[	X
ejpam-4277	142	4	f−([k1]s(λ	f−([k1]s(λ	ADJ
ejpam-4277	142	5	,	,	PUNCT
ejpam-4277	142	6	sp	sp	NOUN
ejpam-4277	142	7	)	)	PUNCT
ejpam-4277	142	8	)	)	PUNCT
ejpam-4277	142	9	∪	∪	ADP
ejpam-4277	142	10	f+([k2]s(λ	f+([k2]s(λ	PROPN
ejpam-4277	142	11	,	,	PUNCT
ejpam-4277	142	12	sp	sp	NOUN
ejpam-4277	142	13	)	)	PUNCT
ejpam-4277	142	14	)	)	PUNCT
ejpam-4277	142	15	]	]	PUNCT
ejpam-4277	143	1	(	(	PUNCT
ejpam-4277	143	2	λ	λ	X
ejpam-4277	143	3	,	,	PUNCT
ejpam-4277	143	4	sp)](λ	sp)](λ	PROPN
ejpam-4277	143	5	,	,	PUNCT
ejpam-4277	143	6	sp	sp	NOUN
ejpam-4277	143	7	)	)	PUNCT
ejpam-4277	143	8	]	]	PUNCT
ejpam-4277	143	9	(	(	PUNCT
ejpam-4277	143	10	λ	λ	NOUN
ejpam-4277	143	11	,	,	PUNCT
ejpam-4277	143	12	sp	sp	NOUN
ejpam-4277	143	13	)	)	PUNCT
ejpam-4277	143	14	⊆	⊆	NUM
ejpam-4277	143	15	f−(k1	f−(k1	NOUN
ejpam-4277	143	16	)	)	PUNCT
ejpam-4277	143	17	∪	∪	ADP
ejpam-4277	143	18	f+(k2	f+(k2	NOUN
ejpam-4277	143	19	)	)	PUNCT
ejpam-4277	143	20	for	for	ADP
ejpam-4277	143	21	any	any	DET
ejpam-4277	143	22	(	(	PUNCT
ejpam-4277	143	23	λ	λ	PROPN
ejpam-4277	143	24	,	,	PUNCT
ejpam-4277	143	25	sp)-closed	sp)-close	VERB
ejpam-4277	143	26	sets	set	VERB
ejpam-4277	143	27	k1,k2	k1,k2	PROPN
ejpam-4277	143	28	of	of	ADP
ejpam-4277	143	29	y	y	PROPN
ejpam-4277	143	30	;	;	PUNCT
ejpam-4277	143	31	(	(	PUNCT
ejpam-4277	143	32	12	12	NUM
ejpam-4277	143	33	)	)	PUNCT
ejpam-4277	143	34	f+(g1)∩f−(g2	f+(g1)∩f−(g2	NOUN
ejpam-4277	143	35	)	)	PUNCT
ejpam-4277	143	36	⊆	⊆	NUM
ejpam-4277	144	1	[	[	X
ejpam-4277	144	2	[	[	X
ejpam-4277	144	3	[	[	X
ejpam-4277	144	4	f+(g	f+(g	NOUN
ejpam-4277	144	5	s(λ	s(λ	NOUN
ejpam-4277	144	6	,	,	PUNCT
ejpam-4277	144	7	sp	sp	NOUN
ejpam-4277	144	8	)	)	PUNCT
ejpam-4277	144	9	1	1	NUM
ejpam-4277	144	10	)	)	PUNCT
ejpam-4277	144	11	∩f−(g	∩f−(g	PROPN
ejpam-4277	144	12	s(λ	s(λ	PROPN
ejpam-4277	144	13	,	,	PUNCT
ejpam-4277	144	14	sp	sp	NOUN
ejpam-4277	144	15	)	)	PUNCT
ejpam-4277	144	16	2	2	NUM
ejpam-4277	144	17	)	)	PUNCT
ejpam-4277	144	18	]	]	PUNCT
ejpam-4277	144	19	(	(	PUNCT
ejpam-4277	144	20	λ	λ	NOUN
ejpam-4277	144	21	,	,	PUNCT
ejpam-4277	144	22	sp	sp	NOUN
ejpam-4277	144	23	)	)	PUNCT
ejpam-4277	144	24	]	]	PUNCT
ejpam-4277	144	25	(	(	PUNCT
ejpam-4277	144	26	λ	λ	X
ejpam-4277	144	27	,	,	PUNCT
ejpam-4277	144	28	sp)](λ	sp)](λ	PROPN
ejpam-4277	144	29	,	,	PUNCT
ejpam-4277	144	30	sp	sp	NOUN
ejpam-4277	144	31	)	)	PUNCT
ejpam-4277	144	32	for	for	ADP
ejpam-4277	144	33	any	any	DET
ejpam-4277	144	34	(	(	PUNCT
ejpam-4277	144	35	λ	λ	NOUN
ejpam-4277	144	36	,	,	PUNCT
ejpam-4277	144	37	sp)open	sp)open	NOUN
ejpam-4277	144	38	sets	set	NOUN
ejpam-4277	144	39	g1	g1	NOUN
ejpam-4277	144	40	,	,	PUNCT
ejpam-4277	144	41	g2	g2	PROPN
ejpam-4277	144	42	of	of	ADP
ejpam-4277	144	43	y	y	PROPN
ejpam-4277	144	44	.	.	PUNCT
ejpam-4277	145	1	proof	proof	NOUN
ejpam-4277	145	2	.	.	PUNCT
ejpam-4277	146	1	(	(	PUNCT
ejpam-4277	146	2	1	1	X
ejpam-4277	146	3	)	)	PUNCT
ejpam-4277	146	4	⇒	⇒	NOUN
ejpam-4277	146	5	(	(	PUNCT
ejpam-4277	146	6	2	2	NUM
ejpam-4277	146	7	):	):	PUNCT
ejpam-4277	146	8	the	the	DET
ejpam-4277	146	9	proof	proof	NOUN
ejpam-4277	146	10	follows	follow	VERB
ejpam-4277	146	11	from	from	ADP
ejpam-4277	146	12	theorem	theorem	ADJ
ejpam-4277	146	13	1	1	NUM
ejpam-4277	146	14	.	.	PUNCT
ejpam-4277	146	15	(	(	PUNCT
ejpam-4277	146	16	2	2	X
ejpam-4277	146	17	)	)	PUNCT
ejpam-4277	146	18	⇒	⇒	NOUN
ejpam-4277	146	19	(	(	PUNCT
ejpam-4277	146	20	3	3	NUM
ejpam-4277	146	21	):	):	PUNCT
ejpam-4277	146	22	the	the	DET
ejpam-4277	146	23	proof	proof	NOUN
ejpam-4277	146	24	is	be	AUX
ejpam-4277	146	25	obvious	obvious	ADJ
ejpam-4277	146	26	.	.	PUNCT
ejpam-4277	147	1	(	(	PUNCT
ejpam-4277	147	2	3	3	X
ejpam-4277	147	3	)	)	PUNCT
ejpam-4277	147	4	⇒	⇒	NOUN
ejpam-4277	147	5	(	(	PUNCT
ejpam-4277	147	6	4	4	NUM
ejpam-4277	147	7	):	):	PUNCT
ejpam-4277	147	8	let	let	VERB
ejpam-4277	147	9	g1	g1	NOUN
ejpam-4277	147	10	,	,	PUNCT
ejpam-4277	147	11	g2	g2	PROPN
ejpam-4277	147	12	∈	∈	PROPN
ejpam-4277	147	13	rλspo(y	rλspo(y	PROPN
ejpam-4277	147	14	,	,	PUNCT
ejpam-4277	147	15	σ	σ	NOUN
ejpam-4277	147	16	)	)	PUNCT
ejpam-4277	147	17	and	and	CCONJ
ejpam-4277	147	18	let	let	VERB
ejpam-4277	147	19	x	x	X
ejpam-4277	147	20	∈	∈	PROPN
ejpam-4277	147	21	f+(g1	f+(g1	NOUN
ejpam-4277	147	22	)	)	PUNCT
ejpam-4277	147	23	∩	∩	NOUN
ejpam-4277	147	24	f−(g2	f−(g2	NUM
ejpam-4277	147	25	)	)	PUNCT
ejpam-4277	147	26	.	.	PUNCT
ejpam-4277	148	1	then	then	ADV
ejpam-4277	148	2	,	,	PUNCT
ejpam-4277	148	3	f	f	PROPN
ejpam-4277	148	4	(	(	PUNCT
ejpam-4277	148	5	x	x	X
ejpam-4277	148	6	)	)	PUNCT
ejpam-4277	148	7	∈	∈	NOUN
ejpam-4277	148	8	g+	g+	NOUN
ejpam-4277	148	9	1	1	NUM
ejpam-4277	148	10	∩g−	∩g−	PROPN
ejpam-4277	148	11	2	2	NUM
ejpam-4277	148	12	and	and	CCONJ
ejpam-4277	148	13	there	there	PRON
ejpam-4277	148	14	exists	exist	VERB
ejpam-4277	148	15	u	u	PROPN
ejpam-4277	148	16	∈	∈	PROPN
ejpam-4277	148	17	αλspo(x	αλspo(x	PROPN
ejpam-4277	148	18	,	,	PUNCT
ejpam-4277	148	19	τ	τ	X
ejpam-4277	148	20	)	)	PUNCT
ejpam-4277	148	21	containing	contain	VERB
ejpam-4277	148	22	x	x	PUNCT
ejpam-4277	148	23	such	such	ADJ
ejpam-4277	148	24	that	that	SCONJ
ejpam-4277	148	25	f	f	PROPN
ejpam-4277	148	26	(	(	PUNCT
ejpam-4277	148	27	u	u	NOUN
ejpam-4277	148	28	)	)	PUNCT
ejpam-4277	148	29	⊆	⊆	NUM
ejpam-4277	148	30	g1	g1	NOUN
ejpam-4277	148	31	and	and	CCONJ
ejpam-4277	148	32	f	f	PROPN
ejpam-4277	148	33	(	(	PUNCT
ejpam-4277	148	34	z	z	NOUN
ejpam-4277	148	35	)	)	PUNCT
ejpam-4277	148	36	∩g2	∩g2	PROPN
ejpam-4277	148	37	6=	6=	NOUN
ejpam-4277	148	38	∅	∅	NOUN
ejpam-4277	148	39	for	for	ADP
ejpam-4277	148	40	every	every	DET
ejpam-4277	148	41	z	z	NOUN
ejpam-4277	148	42	∈	∈	PROPN
ejpam-4277	148	43	u	u	NOUN
ejpam-4277	148	44	.	.	PUNCT
ejpam-4277	149	1	thus	thus	ADV
ejpam-4277	149	2	,	,	PUNCT
ejpam-4277	149	3	x	x	PUNCT
ejpam-4277	149	4	∈	∈	PROPN
ejpam-4277	149	5	u	u	NOUN
ejpam-4277	149	6	⊆	⊆	NUM
ejpam-4277	149	7	f+(g1	f+(g1	NOUN
ejpam-4277	149	8	)	)	PUNCT
ejpam-4277	149	9	∩	∩	NOUN
ejpam-4277	149	10	f−(g2	f−(g2	NUM
ejpam-4277	149	11	)	)	PUNCT
ejpam-4277	149	12	and	and	CCONJ
ejpam-4277	149	13	hence	hence	ADV
ejpam-4277	149	14	f+(g1	f+(g1	ADJ
ejpam-4277	149	15	)	)	PUNCT
ejpam-4277	149	16	∩	∩	NOUN
ejpam-4277	149	17	f−(g2	f−(g2	PRON
ejpam-4277	149	18	)	)	PUNCT
ejpam-4277	149	19	∈	∈	PROPN
ejpam-4277	149	20	αλspo(x	αλspo(x	PROPN
ejpam-4277	149	21	,	,	PUNCT
ejpam-4277	149	22	τ	τ	PROPN
ejpam-4277	149	23	)	)	PUNCT
ejpam-4277	149	24	.	.	PUNCT
ejpam-4277	150	1	c.	c.	PROPN
ejpam-4277	150	2	boonpok	boonpok	PROPN
ejpam-4277	150	3	,	,	PUNCT
ejpam-4277	150	4	j.	j.	PROPN
ejpam-4277	150	5	khampakdee	khampakdee	PROPN
ejpam-4277	150	6	/	/	PUNCT
ejpam-4277	150	7	eur	eur	PROPN
ejpam-4277	150	8	.	.	PUNCT
ejpam-4277	151	1	j.	j.	PROPN
ejpam-4277	151	2	pure	pure	PROPN
ejpam-4277	151	3	appl	appl	PROPN
ejpam-4277	151	4	.	.	PROPN
ejpam-4277	151	5	math	math	PROPN
ejpam-4277	151	6	,	,	PUNCT
ejpam-4277	151	7	15	15	NUM
ejpam-4277	151	8	(	(	PUNCT
ejpam-4277	151	9	2	2	NUM
ejpam-4277	151	10	)	)	PUNCT
ejpam-4277	151	11	(	(	PUNCT
ejpam-4277	151	12	2022	2022	NUM
ejpam-4277	151	13	)	)	PUNCT
ejpam-4277	151	14	,	,	PUNCT
ejpam-4277	151	15	626	626	NUM
ejpam-4277	151	16	-	-	SYM
ejpam-4277	151	17	634	634	NUM
ejpam-4277	151	18	631	631	NUM
ejpam-4277	151	19	(	(	PUNCT
ejpam-4277	151	20	4	4	NUM
ejpam-4277	151	21	)	)	PUNCT
ejpam-4277	151	22	⇒	⇒	NOUN
ejpam-4277	151	23	(	(	PUNCT
ejpam-4277	151	24	5	5	NUM
ejpam-4277	151	25	):	):	PUNCT
ejpam-4277	151	26	this	this	PRON
ejpam-4277	151	27	follows	follow	VERB
ejpam-4277	151	28	from	from	ADP
ejpam-4277	151	29	the	the	DET
ejpam-4277	151	30	fact	fact	NOUN
ejpam-4277	151	31	that	that	SCONJ
ejpam-4277	151	32	f+(y	f+(y	PROPN
ejpam-4277	151	33	−b	−b	ADV
ejpam-4277	151	34	)	)	PUNCT
ejpam-4277	151	35	=	=	SYM
ejpam-4277	152	1	x−f−(b	x−f−(b	X
ejpam-4277	152	2	)	)	PUNCT
ejpam-4277	152	3	and	and	CCONJ
ejpam-4277	152	4	f−(y	f−(y	NOUN
ejpam-4277	152	5	−b	−b	NOUN
ejpam-4277	152	6	)	)	PUNCT
ejpam-4277	152	7	=	=	PUNCT
ejpam-4277	153	1	x	x	PUNCT
ejpam-4277	153	2	−	−	NOUN
ejpam-4277	153	3	f+(b	f+(b	NOUN
ejpam-4277	153	4	)	)	PUNCT
ejpam-4277	153	5	for	for	ADP
ejpam-4277	153	6	every	every	DET
ejpam-4277	153	7	subset	subset	NOUN
ejpam-4277	153	8	b	b	PROPN
ejpam-4277	153	9	of	of	ADP
ejpam-4277	153	10	y	y	PROPN
ejpam-4277	153	11	.	.	PUNCT
ejpam-4277	154	1	(	(	PUNCT
ejpam-4277	154	2	5	5	X
ejpam-4277	154	3	)	)	PUNCT
ejpam-4277	154	4	⇒	⇒	NOUN
ejpam-4277	154	5	(	(	PUNCT
ejpam-4277	154	6	6	6	NUM
ejpam-4277	154	7	):	):	PUNCT
ejpam-4277	154	8	let	let	VERB
ejpam-4277	154	9	g1	g1	PROPN
ejpam-4277	154	10	,	,	PUNCT
ejpam-4277	154	11	g2	g2	PROPN
ejpam-4277	154	12	be	be	VERB
ejpam-4277	154	13	any	any	DET
ejpam-4277	154	14	(	(	PUNCT
ejpam-4277	154	15	λ	λ	NOUN
ejpam-4277	154	16	,	,	PUNCT
ejpam-4277	154	17	sp)-open	sp)-open	ADJ
ejpam-4277	154	18	sets	set	NOUN
ejpam-4277	154	19	of	of	ADP
ejpam-4277	154	20	y	y	PROPN
ejpam-4277	154	21	and	and	CCONJ
ejpam-4277	154	22	let	let	VERB
ejpam-4277	154	23	x	x	X
ejpam-4277	154	24	∈	∈	PROPN
ejpam-4277	154	25	f+(g1	f+(g1	NOUN
ejpam-4277	154	26	)	)	PUNCT
ejpam-4277	154	27	∩	∩	NOUN
ejpam-4277	154	28	f−(g2	f−(g2	NUM
ejpam-4277	154	29	)	)	PUNCT
ejpam-4277	154	30	.	.	PUNCT
ejpam-4277	155	1	then	then	ADV
ejpam-4277	155	2	,	,	PUNCT
ejpam-4277	155	3	f	f	PROPN
ejpam-4277	155	4	(	(	PUNCT
ejpam-4277	155	5	x	x	X
ejpam-4277	155	6	)	)	PUNCT
ejpam-4277	155	7	⊆	⊆	NUM
ejpam-4277	155	8	g1	g1	PROPN
ejpam-4277	155	9	⊆	⊆	NUM
ejpam-4277	155	10	g	g	PROPN
ejpam-4277	155	11	s(λ	s(λ	PROPN
ejpam-4277	155	12	,	,	PUNCT
ejpam-4277	155	13	sp	sp	NOUN
ejpam-4277	155	14	)	)	PUNCT
ejpam-4277	155	15	1	1	NUM
ejpam-4277	155	16	and	and	CCONJ
ejpam-4277	155	17	∅	∅	NOUN
ejpam-4277	155	18	6=	6=	ADP
ejpam-4277	155	19	f	f	PROPN
ejpam-4277	155	20	(	(	PUNCT
ejpam-4277	155	21	x	x	X
ejpam-4277	155	22	)	)	PUNCT
ejpam-4277	155	23	∩g2	∩g2	PROPN
ejpam-4277	155	24	⊆	⊆	NUM
ejpam-4277	155	25	f	f	X
ejpam-4277	155	26	(	(	PUNCT
ejpam-4277	155	27	x	x	NOUN
ejpam-4277	155	28	)	)	PUNCT
ejpam-4277	155	29	∩g	∩g	PROPN
ejpam-4277	155	30	s(λ	s(λ	PROPN
ejpam-4277	155	31	,	,	PUNCT
ejpam-4277	155	32	sp	sp	NOUN
ejpam-4277	155	33	)	)	PUNCT
ejpam-4277	155	34	2	2	NUM
ejpam-4277	155	35	.	.	PUNCT
ejpam-4277	156	1	thus	thus	ADV
ejpam-4277	156	2	,	,	PUNCT
ejpam-4277	156	3	x	x	SYM
ejpam-4277	156	4	∈	∈	NOUN
ejpam-4277	156	5	f+(g	f+(g	NOUN
ejpam-4277	156	6	s(λ	s(λ	NOUN
ejpam-4277	156	7	,	,	PUNCT
ejpam-4277	156	8	sp	sp	NOUN
ejpam-4277	156	9	)	)	PUNCT
ejpam-4277	156	10	1	1	NUM
ejpam-4277	156	11	)	)	PUNCT
ejpam-4277	156	12	=	=	PUNCT
ejpam-4277	156	13	x	x	SYM
ejpam-4277	156	14	−	−	NOUN
ejpam-4277	156	15	f−(y	f−(y	NOUN
ejpam-4277	156	16	−g	−g	NOUN
ejpam-4277	156	17	s(λ	s(λ	NOUN
ejpam-4277	156	18	,	,	PUNCT
ejpam-4277	156	19	sp	sp	NOUN
ejpam-4277	156	20	)	)	PUNCT
ejpam-4277	156	21	1	1	NUM
ejpam-4277	156	22	)	)	PUNCT
ejpam-4277	156	23	and	and	CCONJ
ejpam-4277	156	24	x	x	PUNCT
ejpam-4277	156	25	∈	∈	PROPN
ejpam-4277	156	26	f−(g	f−(g	PROPN
ejpam-4277	156	27	s(λ	s(λ	PROPN
ejpam-4277	156	28	,	,	PUNCT
ejpam-4277	156	29	sp	sp	NOUN
ejpam-4277	156	30	)	)	PUNCT
ejpam-4277	156	31	2	2	NUM
ejpam-4277	156	32	)	)	PUNCT
ejpam-4277	156	33	=	=	PUNCT
ejpam-4277	156	34	x	x	PUNCT
ejpam-4277	156	35	−	−	NOUN
ejpam-4277	156	36	f−(y	f−(y	NOUN
ejpam-4277	156	37	−	−	NOUN
ejpam-4277	156	38	g	g	PROPN
ejpam-4277	156	39	s(λ	s(λ	PROPN
ejpam-4277	156	40	,	,	PUNCT
ejpam-4277	156	41	sp	sp	NOUN
ejpam-4277	156	42	)	)	PUNCT
ejpam-4277	156	43	2	2	NUM
ejpam-4277	156	44	)	)	PUNCT
ejpam-4277	156	45	.	.	PUNCT
ejpam-4277	157	1	since	since	SCONJ
ejpam-4277	157	2	y	y	PROPN
ejpam-4277	157	3	−	−	PROPN
ejpam-4277	157	4	g	g	PROPN
ejpam-4277	157	5	s(λ	s(λ	PROPN
ejpam-4277	157	6	,	,	PUNCT
ejpam-4277	157	7	sp	sp	NOUN
ejpam-4277	157	8	)	)	PUNCT
ejpam-4277	157	9	1	1	NUM
ejpam-4277	157	10	and	and	CCONJ
ejpam-4277	157	11	y	y	PROPN
ejpam-4277	157	12	−	−	PROPN
ejpam-4277	157	13	g	g	PROPN
ejpam-4277	157	14	s(λ	s(λ	PROPN
ejpam-4277	157	15	,	,	PUNCT
ejpam-4277	157	16	sp	sp	NOUN
ejpam-4277	157	17	)	)	PUNCT
ejpam-4277	157	18	2	2	NUM
ejpam-4277	157	19	are	be	AUX
ejpam-4277	157	20	r(λ	r(λ	NOUN
ejpam-4277	157	21	,	,	PUNCT
ejpam-4277	157	22	sp)-closed	sp)-close	VERB
ejpam-4277	157	23	,	,	PUNCT
ejpam-4277	157	24	f−(y	f−(y	NOUN
ejpam-4277	157	25	−g	−g	NOUN
ejpam-4277	157	26	s(λ	s(λ	NOUN
ejpam-4277	157	27	,	,	PUNCT
ejpam-4277	157	28	sp	sp	NOUN
ejpam-4277	157	29	)	)	PUNCT
ejpam-4277	157	30	1	1	NUM
ejpam-4277	157	31	)	)	PUNCT
ejpam-4277	157	32	∪	∪	ADP
ejpam-4277	157	33	f+(y	f+(y	PROPN
ejpam-4277	157	34	−g	−g	PROPN
ejpam-4277	157	35	s(λ	s(λ	PROPN
ejpam-4277	157	36	,	,	PUNCT
ejpam-4277	157	37	sp	sp	NOUN
ejpam-4277	157	38	)	)	PUNCT
ejpam-4277	157	39	2	2	NUM
ejpam-4277	157	40	)	)	PUNCT
ejpam-4277	157	41	is	be	AUX
ejpam-4277	157	42	α(λ	α(λ	PROPN
ejpam-4277	157	43	,	,	PUNCT
ejpam-4277	157	44	sp)-closed	sp)-close	VERB
ejpam-4277	157	45	in	in	ADP
ejpam-4277	157	46	x.	x.	NOUN
ejpam-4277	157	47	since	since	SCONJ
ejpam-4277	157	48	f−(y	f−(y	NOUN
ejpam-4277	157	49	−g	−g	NOUN
ejpam-4277	157	50	s(λ	s(λ	NOUN
ejpam-4277	157	51	,	,	PUNCT
ejpam-4277	157	52	sp	sp	NOUN
ejpam-4277	157	53	)	)	PUNCT
ejpam-4277	157	54	1	1	NUM
ejpam-4277	157	55	)	)	PUNCT
ejpam-4277	157	56	∪	∪	ADP
ejpam-4277	157	57	f+(y	f+(y	PROPN
ejpam-4277	157	58	−g	−g	PROPN
ejpam-4277	157	59	s(λ	s(λ	PROPN
ejpam-4277	157	60	,	,	PUNCT
ejpam-4277	157	61	sp	sp	NOUN
ejpam-4277	157	62	)	)	PUNCT
ejpam-4277	157	63	2	2	NUM
ejpam-4277	157	64	)	)	PUNCT
ejpam-4277	157	65	=	=	NOUN
ejpam-4277	158	1	[	[	X
ejpam-4277	158	2	x	x	X
ejpam-4277	158	3	−	−	NOUN
ejpam-4277	158	4	f+(g	f+(g	PUNCT
ejpam-4277	158	5	s(λ	s(λ	NOUN
ejpam-4277	158	6	,	,	PUNCT
ejpam-4277	158	7	sp	sp	NOUN
ejpam-4277	158	8	)	)	PUNCT
ejpam-4277	158	9	1	1	NUM
ejpam-4277	158	10	)	)	PUNCT
ejpam-4277	158	11	]	]	PUNCT
ejpam-4277	158	12	∪	∪	X
ejpam-4277	158	13	[	[	X
ejpam-4277	158	14	x	x	X
ejpam-4277	158	15	−	−	PROPN
ejpam-4277	158	16	f−(g	f−(g	PROPN
ejpam-4277	158	17	s(λ	s(λ	PROPN
ejpam-4277	158	18	,	,	PUNCT
ejpam-4277	158	19	sp	sp	NOUN
ejpam-4277	158	20	)	)	PUNCT
ejpam-4277	158	21	2	2	NUM
ejpam-4277	158	22	)	)	PUNCT
ejpam-4277	158	23	]	]	PUNCT
ejpam-4277	159	1	=	=	PUNCT
ejpam-4277	159	2	x	x	X
ejpam-4277	159	3	−	−	PUNCT
ejpam-4277	160	1	[	[	X
ejpam-4277	160	2	f+(g	f+(g	NOUN
ejpam-4277	160	3	s(λ	s(λ	NOUN
ejpam-4277	160	4	,	,	PUNCT
ejpam-4277	160	5	sp	sp	NOUN
ejpam-4277	160	6	)	)	PUNCT
ejpam-4277	160	7	1	1	NUM
ejpam-4277	160	8	)	)	PUNCT
ejpam-4277	160	9	∪	∪	ADP
ejpam-4277	160	10	f−(g	f−(g	NOUN
ejpam-4277	160	11	s(λ	s(λ	PROPN
ejpam-4277	160	12	,	,	PUNCT
ejpam-4277	160	13	sp	sp	NOUN
ejpam-4277	160	14	)	)	PUNCT
ejpam-4277	160	15	2	2	NUM
ejpam-4277	160	16	)	)	PUNCT
ejpam-4277	160	17	]	]	PUNCT
ejpam-4277	160	18	,	,	PUNCT
ejpam-4277	160	19	we	we	PRON
ejpam-4277	160	20	have	have	VERB
ejpam-4277	160	21	f+(g	f+(g	NOUN
ejpam-4277	160	22	s(λ	s(λ	NOUN
ejpam-4277	160	23	,	,	PUNCT
ejpam-4277	160	24	sp	sp	NOUN
ejpam-4277	160	25	)	)	PUNCT
ejpam-4277	160	26	1	1	NUM
ejpam-4277	160	27	)	)	PUNCT
ejpam-4277	160	28	∪	∪	ADP
ejpam-4277	160	29	f−(g	f−(g	NOUN
ejpam-4277	160	30	s(λ	s(λ	PROPN
ejpam-4277	160	31	,	,	PUNCT
ejpam-4277	160	32	sp	sp	NOUN
ejpam-4277	160	33	)	)	PUNCT
ejpam-4277	160	34	2	2	NUM
ejpam-4277	160	35	)	)	PUNCT
ejpam-4277	160	36	is	be	AUX
ejpam-4277	160	37	α(λ	α(λ	PROPN
ejpam-4277	160	38	,	,	PUNCT
ejpam-4277	160	39	sp)-open	sp)-open	VERB
ejpam-4277	160	40	in	in	ADP
ejpam-4277	160	41	x	x	PUNCT
ejpam-4277	160	42	and	and	CCONJ
ejpam-4277	161	1	hence	hence	ADV
ejpam-4277	161	2	x	x	X
ejpam-4277	161	3	∈	∈	PROPN
ejpam-4277	162	1	[	[	X
ejpam-4277	162	2	f+(g	f+(g	NOUN
ejpam-4277	162	3	s(λ	s(λ	NOUN
ejpam-4277	162	4	,	,	PUNCT
ejpam-4277	162	5	sp	sp	NOUN
ejpam-4277	162	6	)	)	PUNCT
ejpam-4277	162	7	1	1	NUM
ejpam-4277	162	8	)	)	PUNCT
ejpam-4277	162	9	∪	∪	ADP
ejpam-4277	162	10	f−(g	f−(g	NOUN
ejpam-4277	162	11	s(λ	s(λ	PROPN
ejpam-4277	162	12	,	,	PUNCT
ejpam-4277	162	13	sp	sp	NOUN
ejpam-4277	162	14	)	)	PUNCT
ejpam-4277	162	15	2	2	NUM
ejpam-4277	162	16	)	)	PUNCT
ejpam-4277	162	17	]	]	PUNCT
ejpam-4277	162	18	α(λ	α(λ	PROPN
ejpam-4277	162	19	,	,	PUNCT
ejpam-4277	162	20	sp	sp	NOUN
ejpam-4277	162	21	)	)	PUNCT
ejpam-4277	162	22	.	.	PUNCT
ejpam-4277	163	1	thus	thus	ADV
ejpam-4277	163	2	,	,	PUNCT
ejpam-4277	163	3	f+(g1	f+(g1	NOUN
ejpam-4277	163	4	)	)	PUNCT
ejpam-4277	163	5	∪	∪	NOUN
ejpam-4277	163	6	f−(g2	f−(g2	NOUN
ejpam-4277	163	7	)	)	PUNCT
ejpam-4277	163	8	⊆	⊆	NUM
ejpam-4277	164	1	[	[	SYM
ejpam-4277	164	2	f+(g	f+(g	NOUN
ejpam-4277	164	3	s(λ	s(λ	NOUN
ejpam-4277	164	4	,	,	PUNCT
ejpam-4277	164	5	sp	sp	NOUN
ejpam-4277	164	6	)	)	PUNCT
ejpam-4277	164	7	1	1	NUM
ejpam-4277	164	8	)	)	PUNCT
ejpam-4277	164	9	∩	∩	PROPN
ejpam-4277	164	10	f−(g	f−(g	VERB
ejpam-4277	164	11	s(λ	s(λ	PROPN
ejpam-4277	164	12	,	,	PUNCT
ejpam-4277	164	13	sp	sp	NOUN
ejpam-4277	164	14	)	)	PUNCT
ejpam-4277	164	15	2	2	NUM
ejpam-4277	164	16	)	)	PUNCT
ejpam-4277	164	17	]	]	PUNCT
ejpam-4277	164	18	α(λ	α(λ	PROPN
ejpam-4277	164	19	,	,	PUNCT
ejpam-4277	164	20	sp	sp	NOUN
ejpam-4277	164	21	)	)	PUNCT
ejpam-4277	164	22	.	.	PUNCT
ejpam-4277	165	1	(	(	PUNCT
ejpam-4277	165	2	6	6	X
ejpam-4277	165	3	)	)	PUNCT
ejpam-4277	165	4	⇒	⇒	NOUN
ejpam-4277	165	5	(	(	PUNCT
ejpam-4277	165	6	7	7	NUM
ejpam-4277	165	7	):	):	PUNCT
ejpam-4277	165	8	let	let	VERB
ejpam-4277	165	9	k1,k2	k1,k2	PROPN
ejpam-4277	165	10	be	be	AUX
ejpam-4277	165	11	any	any	DET
ejpam-4277	165	12	(	(	PUNCT
ejpam-4277	165	13	λ	λ	PROPN
ejpam-4277	165	14	,	,	PUNCT
ejpam-4277	165	15	sp)-closed	sp)-close	VERB
ejpam-4277	165	16	sets	set	NOUN
ejpam-4277	165	17	of	of	ADP
ejpam-4277	165	18	y	y	PROPN
ejpam-4277	165	19	.	.	PUNCT
ejpam-4277	166	1	then	then	ADV
ejpam-4277	166	2	,	,	PUNCT
ejpam-4277	166	3	y	y	PROPN
ejpam-4277	166	4	−k1	−k1	PROPN
ejpam-4277	166	5	and	and	CCONJ
ejpam-4277	166	6	y	y	PROPN
ejpam-4277	166	7	−k2	−k2	PROPN
ejpam-4277	166	8	are	be	AUX
ejpam-4277	166	9	(	(	PUNCT
ejpam-4277	166	10	λ	λ	X
ejpam-4277	166	11	,	,	PUNCT
ejpam-4277	166	12	sp)-open	sp)-open	ADJ
ejpam-4277	166	13	,	,	PUNCT
ejpam-4277	166	14	by	by	ADP
ejpam-4277	166	15	(	(	PUNCT
ejpam-4277	166	16	6	6	NUM
ejpam-4277	166	17	)	)	PUNCT
ejpam-4277	166	18	,	,	PUNCT
ejpam-4277	166	19	x	x	X
ejpam-4277	167	1	−	−	PROPN
ejpam-4277	168	1	[	[	X
ejpam-4277	168	2	f−(k1	f−(k1	ADP
ejpam-4277	168	3	)	)	PUNCT
ejpam-4277	168	4	∪	∪	ADP
ejpam-4277	168	5	f+(k2	f+(k2	NOUN
ejpam-4277	168	6	)	)	PUNCT
ejpam-4277	168	7	]	]	PUNCT
ejpam-4277	169	1	=	=	PUNCT
ejpam-4277	170	1	[	[	X
ejpam-4277	170	2	x	x	X
ejpam-4277	170	3	−	−	NOUN
ejpam-4277	170	4	f−(k1	f−(k1	NOUN
ejpam-4277	170	5	)	)	PUNCT
ejpam-4277	170	6	]	]	PUNCT
ejpam-4277	170	7	∩	∩	NOUN
ejpam-4277	170	8	[	[	X
ejpam-4277	170	9	x	x	X
ejpam-4277	170	10	−	−	NUM
ejpam-4277	170	11	f+(k2	f+(k2	NOUN
ejpam-4277	170	12	)	)	PUNCT
ejpam-4277	170	13	]	]	PUNCT
ejpam-4277	171	1	=	=	SYM
ejpam-4277	171	2	f+(y	f+(y	NUM
ejpam-4277	171	3	−k1	−k1	NOUN
ejpam-4277	171	4	)	)	PUNCT
ejpam-4277	171	5	∩	∩	ADJ
ejpam-4277	171	6	f−(y	f−(y	NOUN
ejpam-4277	171	7	−k2	−k2	NOUN
ejpam-4277	171	8	)	)	PUNCT
ejpam-4277	171	9	⊆	⊆	NUM
ejpam-4277	172	1	[	[	X
ejpam-4277	172	2	f+([y	f+([y	ADJ
ejpam-4277	172	3	−k1	−k1	NOUN
ejpam-4277	172	4	]	]	PUNCT
ejpam-4277	172	5	s(λ	s(λ	PROPN
ejpam-4277	172	6	,	,	PUNCT
ejpam-4277	172	7	sp	sp	NOUN
ejpam-4277	172	8	)	)	PUNCT
ejpam-4277	172	9	)	)	PUNCT
ejpam-4277	172	10	∩	∩	ADJ
ejpam-4277	172	11	f−([y	f−([y	ADJ
ejpam-4277	172	12	−k2	−k2	PROPN
ejpam-4277	172	13	]	]	PUNCT
ejpam-4277	172	14	s(λ	s(λ	PROPN
ejpam-4277	172	15	,	,	PUNCT
ejpam-4277	172	16	sp))]α(λ	sp))]α(λ	NOUN
ejpam-4277	172	17	,	,	PUNCT
ejpam-4277	172	18	sp	sp	NOUN
ejpam-4277	172	19	)	)	PUNCT
ejpam-4277	172	20	=	=	NOUN
ejpam-4277	173	1	[	[	X
ejpam-4277	173	2	f+(y	f+(y	X
ejpam-4277	173	3	−	−	PROPN
ejpam-4277	173	4	[	[	X
ejpam-4277	173	5	k1]s(λ	k1]s(λ	PROPN
ejpam-4277	173	6	,	,	PUNCT
ejpam-4277	173	7	sp	sp	NOUN
ejpam-4277	173	8	)	)	PUNCT
ejpam-4277	173	9	)	)	PUNCT
ejpam-4277	173	10	∩	∩	NOUN
ejpam-4277	173	11	f−(y	f−(y	NOUN
ejpam-4277	173	12	−	−	PROPN
ejpam-4277	174	1	[	[	X
ejpam-4277	174	2	k2]s(λ	k2]s(λ	PROPN
ejpam-4277	174	3	,	,	PUNCT
ejpam-4277	174	4	sp))]α(λ	sp))]α(λ	NOUN
ejpam-4277	174	5	,	,	PUNCT
ejpam-4277	174	6	sp	sp	NOUN
ejpam-4277	174	7	)	)	PUNCT
ejpam-4277	174	8	=	=	PUNCT
ejpam-4277	175	1	[	[	X
ejpam-4277	175	2	[	[	X
ejpam-4277	175	3	x	x	X
ejpam-4277	175	4	−	−	PROPN
ejpam-4277	175	5	f−([k1]s(λ	f−([k1]s(λ	PROPN
ejpam-4277	175	6	,	,	PUNCT
ejpam-4277	175	7	sp	sp	NOUN
ejpam-4277	175	8	)	)	PUNCT
ejpam-4277	175	9	)	)	PUNCT
ejpam-4277	175	10	]	]	PUNCT
ejpam-4277	176	1	∩	∩	NOUN
ejpam-4277	176	2	[	[	X
ejpam-4277	176	3	x	x	X
ejpam-4277	176	4	−	−	PROPN
ejpam-4277	176	5	f+([k2]s(λ	f+([k2]s(λ	PROPN
ejpam-4277	176	6	,	,	PUNCT
ejpam-4277	176	7	sp))]]α(λ	sp))]]α(λ	PROPN
ejpam-4277	176	8	,	,	PUNCT
ejpam-4277	176	9	sp	sp	NOUN
ejpam-4277	176	10	)	)	PUNCT
ejpam-4277	176	11	=	=	PUNCT
ejpam-4277	176	12	x	x	X
ejpam-4277	176	13	−	−	PROPN
ejpam-4277	177	1	[	[	X
ejpam-4277	177	2	f−([k1]s(λ	f−([k1]s(λ	PROPN
ejpam-4277	177	3	,	,	PUNCT
ejpam-4277	177	4	sp	sp	NOUN
ejpam-4277	177	5	)	)	PUNCT
ejpam-4277	177	6	)	)	PUNCT
ejpam-4277	177	7	∪	∪	ADP
ejpam-4277	177	8	f+([k2]s(λ	f+([k2]s(λ	PROPN
ejpam-4277	177	9	,	,	PUNCT
ejpam-4277	177	10	sp	sp	NOUN
ejpam-4277	177	11	)	)	PUNCT
ejpam-4277	177	12	)	)	PUNCT
ejpam-4277	177	13	]	]	PUNCT
ejpam-4277	178	1	α(λ	α(λ	PROPN
ejpam-4277	178	2	,	,	PUNCT
ejpam-4277	178	3	sp	sp	NOUN
ejpam-4277	178	4	)	)	PUNCT
ejpam-4277	178	5	.	.	PUNCT
ejpam-4277	179	1	thus	thus	ADV
ejpam-4277	179	2	,	,	PUNCT
ejpam-4277	179	3	[	[	X
ejpam-4277	179	4	f−([k1]s(λ	f−([k1]s(λ	ADJ
ejpam-4277	179	5	,	,	PUNCT
ejpam-4277	179	6	sp	sp	NOUN
ejpam-4277	179	7	)	)	PUNCT
ejpam-4277	179	8	)	)	PUNCT
ejpam-4277	179	9	∪	∪	ADP
ejpam-4277	179	10	f+([k2]s(λ	f+([k2]s(λ	PROPN
ejpam-4277	179	11	,	,	PUNCT
ejpam-4277	179	12	sp	sp	NOUN
ejpam-4277	179	13	)	)	PUNCT
ejpam-4277	179	14	)	)	PUNCT
ejpam-4277	179	15	]	]	PUNCT
ejpam-4277	180	1	α(λ	α(λ	PROPN
ejpam-4277	180	2	,	,	PUNCT
ejpam-4277	180	3	sp	sp	NOUN
ejpam-4277	180	4	)	)	PUNCT
ejpam-4277	180	5	⊆	⊆	NUM
ejpam-4277	180	6	f−(k1	f−(k1	NOUN
ejpam-4277	180	7	)	)	PUNCT
ejpam-4277	180	8	∪	∪	ADP
ejpam-4277	180	9	f+(k2	f+(k2	NOUN
ejpam-4277	180	10	)	)	PUNCT
ejpam-4277	180	11	.	.	PUNCT
ejpam-4277	181	1	(	(	PUNCT
ejpam-4277	181	2	7	7	X
ejpam-4277	181	3	)	)	PUNCT
ejpam-4277	181	4	⇒	⇒	NOUN
ejpam-4277	181	5	(	(	PUNCT
ejpam-4277	181	6	8)	8)	NUM
ejpam-4277	181	7	:	:	PUNCT
ejpam-4277	181	8	the	the	DET
ejpam-4277	181	9	proof	proof	NOUN
ejpam-4277	181	10	is	be	AUX
ejpam-4277	181	11	obvious	obvious	ADJ
ejpam-4277	181	12	since	since	SCONJ
ejpam-4277	181	13	ks(λ	ks(λ	NOUN
ejpam-4277	181	14	,	,	PUNCT
ejpam-4277	181	15	sp	sp	NOUN
ejpam-4277	181	16	)	)	PUNCT
ejpam-4277	181	17	=	=	PUNCT
ejpam-4277	182	1	[	[	X
ejpam-4277	182	2	k(λ	k(λ	X
ejpam-4277	182	3	,	,	PUNCT
ejpam-4277	182	4	sp	sp	NOUN
ejpam-4277	182	5	)	)	PUNCT
ejpam-4277	182	6	]	]	PUNCT
ejpam-4277	182	7	(	(	PUNCT
ejpam-4277	182	8	λ	λ	NOUN
ejpam-4277	182	9	,	,	PUNCT
ejpam-4277	182	10	sp	sp	NOUN
ejpam-4277	182	11	)	)	PUNCT
ejpam-4277	182	12	for	for	ADP
ejpam-4277	182	13	every	every	DET
ejpam-4277	182	14	(	(	PUNCT
ejpam-4277	182	15	λ	λ	PROPN
ejpam-4277	182	16	,	,	PUNCT
ejpam-4277	182	17	sp)-closed	sp)-close	VERB
ejpam-4277	182	18	set	set	VERB
ejpam-4277	182	19	k.	k.	PROPN
ejpam-4277	182	20	(	(	PUNCT
ejpam-4277	182	21	8)	8)	NUM
ejpam-4277	182	22	⇒	⇒	NOUN
ejpam-4277	182	23	(	(	PUNCT
ejpam-4277	182	24	9	9	NUM
ejpam-4277	182	25	):	):	PUNCT
ejpam-4277	182	26	the	the	DET
ejpam-4277	182	27	proof	proof	NOUN
ejpam-4277	182	28	is	be	AUX
ejpam-4277	182	29	obvious	obvious	ADJ
ejpam-4277	182	30	.	.	PUNCT
ejpam-4277	183	1	(	(	PUNCT
ejpam-4277	183	2	9	9	X
ejpam-4277	183	3	)	)	PUNCT
ejpam-4277	183	4	⇒	⇒	NOUN
ejpam-4277	183	5	(	(	PUNCT
ejpam-4277	183	6	10	10	NUM
ejpam-4277	183	7	):	):	PUNCT
ejpam-4277	183	8	let	let	VERB
ejpam-4277	183	9	k1,k2	k1,k2	PROPN
ejpam-4277	183	10	be	be	AUX
ejpam-4277	183	11	any	any	DET
ejpam-4277	183	12	(	(	PUNCT
ejpam-4277	183	13	λ	λ	PROPN
ejpam-4277	183	14	,	,	PUNCT
ejpam-4277	183	15	sp)-closed	sp)-close	VERB
ejpam-4277	183	16	sets	set	NOUN
ejpam-4277	183	17	of	of	ADP
ejpam-4277	183	18	y	y	PROPN
ejpam-4277	183	19	.	.	PUNCT
ejpam-4277	184	1	thus	thus	ADV
ejpam-4277	184	2	,	,	PUNCT
ejpam-4277	184	3	by	by	ADP
ejpam-4277	184	4	(	(	PUNCT
ejpam-4277	184	5	9	9	NUM
ejpam-4277	184	6	)	)	PUNCT
ejpam-4277	184	7	and	and	CCONJ
ejpam-4277	184	8	lemma	lemma	PROPN
ejpam-4277	184	9	4	4	NUM
ejpam-4277	184	10	,	,	PUNCT
ejpam-4277	184	11	[	[	X
ejpam-4277	184	12	[	[	X
ejpam-4277	184	13	[	[	X
ejpam-4277	184	14	f−([[k1](λ	f−([[k1](λ	NOUN
ejpam-4277	184	15	,	,	PUNCT
ejpam-4277	184	16	sp	sp	NOUN
ejpam-4277	184	17	)	)	PUNCT
ejpam-4277	184	18	]	]	PUNCT
ejpam-4277	184	19	(	(	PUNCT
ejpam-4277	184	20	λ	λ	NOUN
ejpam-4277	184	21	,	,	PUNCT
ejpam-4277	184	22	sp	sp	NOUN
ejpam-4277	184	23	)	)	PUNCT
ejpam-4277	184	24	)	)	PUNCT
ejpam-4277	184	25	∪	∪	ADP
ejpam-4277	184	26	f+([[k2](λ	f+([[k2](λ	PROPN
ejpam-4277	184	27	,	,	PUNCT
ejpam-4277	184	28	sp	sp	NOUN
ejpam-4277	184	29	)	)	PUNCT
ejpam-4277	184	30	]	]	PUNCT
ejpam-4277	184	31	(	(	PUNCT
ejpam-4277	184	32	λ	λ	INTJ
ejpam-4277	184	33	,	,	PUNCT
ejpam-4277	184	34	sp))](λ	sp))](λ	PROPN
ejpam-4277	184	35	,	,	PUNCT
ejpam-4277	184	36	sp)](λ	sp)](λ	PROPN
ejpam-4277	184	37	,	,	PUNCT
ejpam-4277	184	38	sp	sp	NOUN
ejpam-4277	184	39	)	)	PUNCT
ejpam-4277	184	40	]	]	PUNCT
ejpam-4277	184	41	(	(	PUNCT
ejpam-4277	184	42	λ	λ	NOUN
ejpam-4277	184	43	,	,	PUNCT
ejpam-4277	184	44	sp	sp	NOUN
ejpam-4277	184	45	)	)	PUNCT
ejpam-4277	184	46	⊆	⊆	NUM
ejpam-4277	184	47	[	[	X
ejpam-4277	184	48	f−([[k1](λ	f−([[k1](λ	NOUN
ejpam-4277	184	49	,	,	PUNCT
ejpam-4277	184	50	sp	sp	NOUN
ejpam-4277	184	51	)	)	PUNCT
ejpam-4277	184	52	]	]	PUNCT
ejpam-4277	184	53	(	(	PUNCT
ejpam-4277	184	54	λ	λ	NOUN
ejpam-4277	184	55	,	,	PUNCT
ejpam-4277	184	56	sp	sp	NOUN
ejpam-4277	184	57	)	)	PUNCT
ejpam-4277	184	58	)	)	PUNCT
ejpam-4277	184	59	∪	∪	ADP
ejpam-4277	184	60	f+([[k2](λ	f+([[k2](λ	PROPN
ejpam-4277	184	61	,	,	PUNCT
ejpam-4277	184	62	sp	sp	NOUN
ejpam-4277	184	63	)	)	PUNCT
ejpam-4277	184	64	]	]	PUNCT
ejpam-4277	184	65	(	(	PUNCT
ejpam-4277	184	66	λ	λ	NOUN
ejpam-4277	184	67	,	,	PUNCT
ejpam-4277	184	68	sp))]α(λ	sp))]α(λ	NOUN
ejpam-4277	184	69	,	,	PUNCT
ejpam-4277	184	70	sp	sp	NOUN
ejpam-4277	184	71	)	)	PUNCT
ejpam-4277	184	72	=	=	PUNCT
ejpam-4277	185	1	[	[	X
ejpam-4277	185	2	f−([[k	f−([[k	NOUN
ejpam-4277	185	3	(	(	PUNCT
ejpam-4277	185	4	λ	λ	NOUN
ejpam-4277	185	5	,	,	PUNCT
ejpam-4277	185	6	sp	sp	NOUN
ejpam-4277	185	7	)	)	PUNCT
ejpam-4277	185	8	1	1	NUM
ejpam-4277	185	9	]	]	PUNCT
ejpam-4277	185	10	(	(	PUNCT
ejpam-4277	185	11	λ	λ	NOUN
ejpam-4277	185	12	,	,	PUNCT
ejpam-4277	185	13	sp	sp	NOUN
ejpam-4277	185	14	)	)	PUNCT
ejpam-4277	185	15	]	]	PUNCT
ejpam-4277	185	16	(	(	PUNCT
ejpam-4277	185	17	λ	λ	NOUN
ejpam-4277	185	18	,	,	PUNCT
ejpam-4277	185	19	sp	sp	NOUN
ejpam-4277	185	20	)	)	PUNCT
ejpam-4277	185	21	)	)	PUNCT
ejpam-4277	185	22	∪	∪	ADP
ejpam-4277	185	23	f+([[k	f+([[k	X
ejpam-4277	185	24	(	(	PUNCT
ejpam-4277	185	25	λ	λ	NOUN
ejpam-4277	185	26	,	,	PUNCT
ejpam-4277	185	27	sp	sp	NOUN
ejpam-4277	185	28	)	)	PUNCT
ejpam-4277	185	29	2	2	NUM
ejpam-4277	185	30	]	]	PUNCT
ejpam-4277	185	31	(	(	PUNCT
ejpam-4277	185	32	λ	λ	NOUN
ejpam-4277	185	33	,	,	PUNCT
ejpam-4277	185	34	sp	sp	NOUN
ejpam-4277	185	35	)	)	PUNCT
ejpam-4277	185	36	]	]	PUNCT
ejpam-4277	185	37	(	(	PUNCT
ejpam-4277	185	38	λ	λ	NOUN
ejpam-4277	185	39	,	,	PUNCT
ejpam-4277	185	40	sp))]α(λ	sp))]α(λ	NOUN
ejpam-4277	185	41	,	,	PUNCT
ejpam-4277	185	42	sp	sp	NOUN
ejpam-4277	185	43	)	)	PUNCT
ejpam-4277	185	44	⊆	⊆	NUM
ejpam-4277	185	45	f−(k1	f−(k1	NOUN
ejpam-4277	185	46	)	)	PUNCT
ejpam-4277	185	47	∪	∪	ADP
ejpam-4277	185	48	f+(k2	f+(k2	NOUN
ejpam-4277	185	49	)	)	PUNCT
ejpam-4277	185	50	.	.	PUNCT
ejpam-4277	186	1	(	(	PUNCT
ejpam-4277	186	2	10	10	NUM
ejpam-4277	186	3	)	)	PUNCT
ejpam-4277	186	4	⇒	⇒	NOUN
ejpam-4277	186	5	(	(	PUNCT
ejpam-4277	186	6	11	11	NUM
ejpam-4277	186	7	):	):	PUNCT
ejpam-4277	186	8	the	the	DET
ejpam-4277	186	9	proof	proof	NOUN
ejpam-4277	186	10	is	be	AUX
ejpam-4277	186	11	obvious	obvious	ADJ
ejpam-4277	186	12	since	since	SCONJ
ejpam-4277	186	13	ks(λ	ks(λ	NOUN
ejpam-4277	186	14	,	,	PUNCT
ejpam-4277	186	15	sp	sp	NOUN
ejpam-4277	186	16	)	)	PUNCT
ejpam-4277	186	17	=	=	PUNCT
ejpam-4277	187	1	[	[	X
ejpam-4277	187	2	k(λ	k(λ	X
ejpam-4277	187	3	,	,	PUNCT
ejpam-4277	187	4	sp	sp	NOUN
ejpam-4277	187	5	)	)	PUNCT
ejpam-4277	187	6	]	]	PUNCT
ejpam-4277	187	7	(	(	PUNCT
ejpam-4277	187	8	λ	λ	NOUN
ejpam-4277	187	9	,	,	PUNCT
ejpam-4277	187	10	sp	sp	NOUN
ejpam-4277	187	11	)	)	PUNCT
ejpam-4277	187	12	for	for	ADP
ejpam-4277	187	13	every	every	DET
ejpam-4277	187	14	(	(	PUNCT
ejpam-4277	187	15	λ	λ	PROPN
ejpam-4277	187	16	,	,	PUNCT
ejpam-4277	187	17	sp)closed	sp)close	VERB
ejpam-4277	187	18	set	set	VERB
ejpam-4277	187	19	k.	k.	PROPN
ejpam-4277	187	20	c.	c.	PROPN
ejpam-4277	187	21	boonpok	boonpok	PROPN
ejpam-4277	187	22	,	,	PUNCT
ejpam-4277	187	23	j.	j.	PROPN
ejpam-4277	187	24	khampakdee	khampakdee	PROPN
ejpam-4277	187	25	/	/	PUNCT
ejpam-4277	187	26	eur	eur	PROPN
ejpam-4277	187	27	.	.	PUNCT
ejpam-4277	188	1	j.	j.	PROPN
ejpam-4277	188	2	pure	pure	PROPN
ejpam-4277	188	3	appl	appl	PROPN
ejpam-4277	188	4	.	.	PROPN
ejpam-4277	188	5	math	math	PROPN
ejpam-4277	188	6	,	,	PUNCT
ejpam-4277	188	7	15	15	NUM
ejpam-4277	188	8	(	(	PUNCT
ejpam-4277	188	9	2	2	NUM
ejpam-4277	188	10	)	)	PUNCT
ejpam-4277	188	11	(	(	PUNCT
ejpam-4277	188	12	2022	2022	NUM
ejpam-4277	188	13	)	)	PUNCT
ejpam-4277	188	14	,	,	PUNCT
ejpam-4277	188	15	626	626	NUM
ejpam-4277	188	16	-	-	SYM
ejpam-4277	188	17	634	634	NUM
ejpam-4277	188	18	632	632	NUM
ejpam-4277	188	19	(	(	PUNCT
ejpam-4277	188	20	11	11	NUM
ejpam-4277	188	21	)	)	PUNCT
ejpam-4277	188	22	⇒	⇒	NOUN
ejpam-4277	188	23	(	(	PUNCT
ejpam-4277	188	24	12	12	NUM
ejpam-4277	188	25	):	):	PUNCT
ejpam-4277	188	26	let	let	VERB
ejpam-4277	188	27	g1	g1	PROPN
ejpam-4277	188	28	,	,	PUNCT
ejpam-4277	188	29	g2	g2	PROPN
ejpam-4277	188	30	be	be	VERB
ejpam-4277	188	31	any	any	DET
ejpam-4277	188	32	(	(	PUNCT
ejpam-4277	188	33	λ	λ	NOUN
ejpam-4277	188	34	,	,	PUNCT
ejpam-4277	188	35	sp)-open	sp)-open	ADJ
ejpam-4277	188	36	sets	set	NOUN
ejpam-4277	188	37	of	of	ADP
ejpam-4277	188	38	y	y	PROPN
ejpam-4277	188	39	.	.	PUNCT
ejpam-4277	189	1	then	then	ADV
ejpam-4277	189	2	,	,	PUNCT
ejpam-4277	189	3	y	y	PROPN
ejpam-4277	189	4	−g1	−g1	VERB
ejpam-4277	189	5	and	and	CCONJ
ejpam-4277	189	6	y	y	PROPN
ejpam-4277	189	7	−g2	−g2	PROPN
ejpam-4277	189	8	are	be	AUX
ejpam-4277	189	9	(	(	PUNCT
ejpam-4277	189	10	λ	λ	X
ejpam-4277	189	11	,	,	PUNCT
ejpam-4277	189	12	sp)-closed	sp)-close	VERB
ejpam-4277	189	13	sets	set	NOUN
ejpam-4277	189	14	of	of	ADP
ejpam-4277	189	15	y	y	PROPN
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ejpam-4277	189	21	,	,	PUNCT
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ejpam-4277	191	4	sp)](λ	sp)](λ	PROPN
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ejpam-4277	191	9	(	(	PUNCT
ejpam-4277	191	10	λ	λ	NOUN
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ejpam-4277	191	12	sp	sp	NOUN
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ejpam-4277	191	14	⊆	⊆	NUM
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ejpam-4277	191	16	−g1	−g1	VERB
ejpam-4277	191	17	)	)	PUNCT
ejpam-4277	191	18	∪	∪	ADP
ejpam-4277	191	19	f+(y	f+(y	X
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ejpam-4277	191	21	)	)	PUNCT
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ejpam-4277	192	4	f+(g1	f+(g1	NOUN
ejpam-4277	192	5	)	)	PUNCT
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ejpam-4277	192	7	∪	∪	ADP
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ejpam-4277	192	11	f−(g2	f−(g2	NUM
ejpam-4277	192	12	)	)	PUNCT
ejpam-4277	192	13	]	]	PUNCT
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ejpam-4277	194	2	[	[	X
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ejpam-4277	194	4	)	)	PUNCT
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ejpam-4277	194	7	)	)	PUNCT
ejpam-4277	194	8	]	]	PUNCT
ejpam-4277	194	9	.	.	PUNCT
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ejpam-4277	195	2	,	,	PUNCT
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ejpam-4277	195	7	[	[	X
ejpam-4277	195	8	f−([y	f−([y	ADJ
ejpam-4277	195	9	−g1]s(λ	−g1]s(λ	ADJ
ejpam-4277	195	10	,	,	PUNCT
ejpam-4277	195	11	sp	sp	NOUN
ejpam-4277	195	12	)	)	PUNCT
ejpam-4277	195	13	)	)	PUNCT
ejpam-4277	195	14	∪	∪	ADP
ejpam-4277	195	15	f+([y	f+([y	PROPN
ejpam-4277	195	16	−g2]s(λ	−g2]s(λ	PROPN
ejpam-4277	195	17	,	,	PUNCT
ejpam-4277	195	18	sp	sp	NOUN
ejpam-4277	195	19	)	)	PUNCT
ejpam-4277	195	20	)	)	PUNCT
ejpam-4277	195	21	]	]	PUNCT
ejpam-4277	196	1	(	(	PUNCT
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ejpam-4277	196	4	sp)](λ	sp)](λ	PROPN
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ejpam-4277	196	7	)	)	PUNCT
ejpam-4277	196	8	]	]	PUNCT
ejpam-4277	196	9	(	(	PUNCT
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ejpam-4277	196	12	sp	sp	NOUN
ejpam-4277	196	13	)	)	PUNCT
ejpam-4277	196	14	=	=	PUNCT
ejpam-4277	197	1	[	[	X
ejpam-4277	197	2	[	[	X
ejpam-4277	197	3	[	[	X
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ejpam-4277	197	6	s(λ	s(λ	NOUN
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ejpam-4277	197	9	)	)	PUNCT
ejpam-4277	197	10	1	1	NUM
ejpam-4277	197	11	)	)	PUNCT
ejpam-4277	197	12	∪	∪	ADP
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ejpam-4277	197	15	s(λ	s(λ	PROPN
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ejpam-4277	197	18	)	)	PUNCT
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ejpam-4277	197	20	)	)	PUNCT
ejpam-4277	197	21	]	]	PUNCT
ejpam-4277	197	22	(	(	PUNCT
ejpam-4277	197	23	λ	λ	PROPN
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ejpam-4277	197	25	sp)](λ	sp)](λ	PROPN
ejpam-4277	197	26	,	,	PUNCT
ejpam-4277	197	27	sp	sp	NOUN
ejpam-4277	197	28	)	)	PUNCT
ejpam-4277	197	29	]	]	PUNCT
ejpam-4277	197	30	(	(	PUNCT
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ejpam-4277	197	33	sp	sp	NOUN
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ejpam-4277	198	1	[	[	X
ejpam-4277	198	2	[	[	X
ejpam-4277	198	3	[	[	X
ejpam-4277	198	4	[	[	X
ejpam-4277	198	5	x	x	X
ejpam-4277	198	6	−	−	X
ejpam-4277	199	1	[	[	X
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ejpam-4277	199	3	s(λ	s(λ	NOUN
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ejpam-4277	199	5	sp	sp	NOUN
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ejpam-4277	200	1	]	]	X
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ejpam-4277	200	3	∪	∪	ADP
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ejpam-4277	200	5	x	x	X
ejpam-4277	200	6	−	−	X
ejpam-4277	200	7	[	[	X
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ejpam-4277	200	9	s(λ	s(λ	PROPN
ejpam-4277	200	10	,	,	PUNCT
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ejpam-4277	200	15	]	]	PUNCT
ejpam-4277	200	16	]	]	X
ejpam-4277	200	17	]	]	X
ejpam-4277	200	18	(	(	PUNCT
ejpam-4277	200	19	λ	λ	PROPN
ejpam-4277	200	20	,	,	PUNCT
ejpam-4277	200	21	sp)](λ	sp)](λ	PROPN
ejpam-4277	200	22	,	,	PUNCT
ejpam-4277	200	23	sp	sp	NOUN
ejpam-4277	200	24	)	)	PUNCT
ejpam-4277	200	25	]	]	PUNCT
ejpam-4277	200	26	(	(	PUNCT
ejpam-4277	200	27	λ	λ	NOUN
ejpam-4277	200	28	,	,	PUNCT
ejpam-4277	200	29	sp	sp	NOUN
ejpam-4277	200	30	)	)	PUNCT
ejpam-4277	200	31	=	=	PUNCT
ejpam-4277	201	1	[	[	X
ejpam-4277	201	2	[	[	X
ejpam-4277	201	3	[	[	X
ejpam-4277	201	4	x	x	X
ejpam-4277	201	5	−	−	X
ejpam-4277	201	6	[	[	X
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ejpam-4277	201	8	s(λ	s(λ	NOUN
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ejpam-4277	201	13	)	)	PUNCT
ejpam-4277	201	14	∩	∩	PROPN
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ejpam-4277	201	16	s(λ	s(λ	PROPN
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ejpam-4277	201	19	)	)	PUNCT
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ejpam-4277	201	21	)	)	PUNCT
ejpam-4277	202	1	]	]	X
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ejpam-4277	202	3	s(λ	s(λ	PROPN
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ejpam-4277	202	5	sp)]s(λ	sp)]s(λ	PROPN
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ejpam-4277	203	1	s(λ	s(λ	PROPN
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ejpam-4277	203	4	)	)	PUNCT
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ejpam-4277	203	6	x	x	X
ejpam-4277	204	1	−	−	PROPN
ejpam-4277	205	1	[	[	X
ejpam-4277	205	2	[	[	X
ejpam-4277	205	3	[	[	X
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ejpam-4277	205	5	s(λ	s(λ	NOUN
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ejpam-4277	205	8	)	)	PUNCT
ejpam-4277	205	9	1	1	NUM
ejpam-4277	205	10	)	)	PUNCT
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ejpam-4277	205	13	s(λ	s(λ	PROPN
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ejpam-4277	205	19	]	]	PUNCT
ejpam-4277	205	20	(	(	PUNCT
ejpam-4277	205	21	λ	λ	NOUN
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ejpam-4277	205	23	sp	sp	NOUN
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ejpam-4277	205	26	(	(	PUNCT
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ejpam-4277	205	29	sp)](λ	sp)](λ	PROPN
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ejpam-4277	205	31	sp	sp	NOUN
ejpam-4277	205	32	)	)	PUNCT
ejpam-4277	205	33	.	.	PUNCT
ejpam-4277	206	1	thus	thus	ADV
ejpam-4277	206	2	,	,	PUNCT
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ejpam-4277	206	4	)	)	PUNCT
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ejpam-4277	206	6	f−(g2	f−(g2	NUM
ejpam-4277	206	7	)	)	PUNCT
ejpam-4277	206	8	⊆	⊆	NUM
ejpam-4277	207	1	[	[	X
ejpam-4277	207	2	[	[	X
ejpam-4277	207	3	[	[	X
ejpam-4277	207	4	f+(g	f+(g	NOUN
ejpam-4277	207	5	s(λ	s(λ	NOUN
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ejpam-4277	207	8	)	)	PUNCT
ejpam-4277	207	9	1	1	NUM
ejpam-4277	207	10	)	)	PUNCT
ejpam-4277	207	11	∩	∩	PROPN
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ejpam-4277	207	13	s(λ	s(λ	PROPN
ejpam-4277	207	14	,	,	PUNCT
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ejpam-4277	207	16	)	)	PUNCT
ejpam-4277	207	17	2	2	NUM
ejpam-4277	207	18	)	)	PUNCT
ejpam-4277	207	19	]	]	PUNCT
ejpam-4277	207	20	(	(	PUNCT
ejpam-4277	207	21	λ	λ	NOUN
ejpam-4277	207	22	,	,	PUNCT
ejpam-4277	207	23	sp	sp	NOUN
ejpam-4277	207	24	)	)	PUNCT
ejpam-4277	207	25	]	]	PUNCT
ejpam-4277	207	26	(	(	PUNCT
ejpam-4277	207	27	λ	λ	X
ejpam-4277	207	28	,	,	PUNCT
ejpam-4277	207	29	sp)](λ	sp)](λ	PROPN
ejpam-4277	207	30	,	,	PUNCT
ejpam-4277	207	31	sp	sp	NOUN
ejpam-4277	207	32	)	)	PUNCT
ejpam-4277	207	33	.	.	PUNCT
ejpam-4277	208	1	(	(	PUNCT
ejpam-4277	208	2	12	12	NUM
ejpam-4277	208	3	)	)	PUNCT
ejpam-4277	208	4	⇒	⇒	NOUN
ejpam-4277	208	5	(	(	PUNCT
ejpam-4277	208	6	1	1	NUM
ejpam-4277	208	7	):	):	PUNCT
ejpam-4277	208	8	let	let	VERB
ejpam-4277	208	9	x	x	PUNCT
ejpam-4277	208	10	∈	∈	PROPN
ejpam-4277	208	11	x	x	PUNCT
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ejpam-4277	208	13	let	let	VERB
ejpam-4277	208	14	g1	g1	PROPN
ejpam-4277	208	15	,	,	PUNCT
ejpam-4277	208	16	g2	g2	PROPN
ejpam-4277	208	17	be	be	VERB
ejpam-4277	208	18	any	any	DET
ejpam-4277	208	19	(	(	PUNCT
ejpam-4277	208	20	λ	λ	NOUN
ejpam-4277	208	21	,	,	PUNCT
ejpam-4277	208	22	sp)-open	sp)-open	ADJ
ejpam-4277	208	23	sets	set	NOUN
ejpam-4277	208	24	of	of	ADP
ejpam-4277	208	25	y	y	PRON
ejpam-4277	208	26	such	such	ADJ
ejpam-4277	208	27	that	that	SCONJ
ejpam-4277	208	28	f	f	PROPN
ejpam-4277	208	29	(	(	PUNCT
ejpam-4277	208	30	x	x	X
ejpam-4277	208	31	)	)	PUNCT
ejpam-4277	208	32	∈	∈	NOUN
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ejpam-4277	208	34	1	1	NUM
ejpam-4277	208	35	∩g−	∩g−	PROPN
ejpam-4277	208	36	2	2	NUM
ejpam-4277	208	37	.	.	PUNCT
ejpam-4277	209	1	then	then	ADV
ejpam-4277	209	2	,	,	PUNCT
ejpam-4277	209	3	x	x	PUNCT
ejpam-4277	209	4	∈	∈	NOUN
ejpam-4277	209	5	f+(g1	f+(g1	NOUN
ejpam-4277	209	6	)	)	PUNCT
ejpam-4277	209	7	∩	∩	NOUN
ejpam-4277	209	8	f−(g2	f−(g2	NUM
ejpam-4277	209	9	)	)	PUNCT
ejpam-4277	209	10	⊆	⊆	NUM
ejpam-4277	210	1	[	[	X
ejpam-4277	210	2	[	[	X
ejpam-4277	210	3	[	[	X
ejpam-4277	210	4	f+(g	f+(g	NOUN
ejpam-4277	210	5	s(λ	s(λ	NOUN
ejpam-4277	210	6	,	,	PUNCT
ejpam-4277	210	7	sp	sp	NOUN
ejpam-4277	210	8	)	)	PUNCT
ejpam-4277	210	9	1	1	NUM
ejpam-4277	210	10	)	)	PUNCT
ejpam-4277	210	11	∩	∩	PROPN
ejpam-4277	210	12	f−(g	f−(g	VERB
ejpam-4277	210	13	s(λ	s(λ	PROPN
ejpam-4277	210	14	,	,	PUNCT
ejpam-4277	210	15	sp	sp	NOUN
ejpam-4277	210	16	)	)	PUNCT
ejpam-4277	210	17	2	2	NUM
ejpam-4277	210	18	)	)	PUNCT
ejpam-4277	210	19	]	]	PUNCT
ejpam-4277	210	20	(	(	PUNCT
ejpam-4277	210	21	λ	λ	NOUN
ejpam-4277	210	22	,	,	PUNCT
ejpam-4277	210	23	sp	sp	NOUN
ejpam-4277	210	24	)	)	PUNCT
ejpam-4277	210	25	]	]	PUNCT
ejpam-4277	210	26	(	(	PUNCT
ejpam-4277	210	27	λ	λ	X
ejpam-4277	210	28	,	,	PUNCT
ejpam-4277	210	29	sp)](λ	sp)](λ	PROPN
ejpam-4277	210	30	,	,	PUNCT
ejpam-4277	210	31	sp	sp	NOUN
ejpam-4277	210	32	)	)	PUNCT
ejpam-4277	210	33	and	and	CCONJ
ejpam-4277	210	34	hence	hence	ADV
ejpam-4277	210	35	f	f	PROPN
ejpam-4277	210	36	is	be	AUX
ejpam-4277	210	37	almost	almost	ADV
ejpam-4277	210	38	α(λ	α(λ	NOUN
ejpam-4277	210	39	,	,	PUNCT
ejpam-4277	210	40	sp)-continuous	sp)-continuous	ADJ
ejpam-4277	210	41	at	at	ADP
ejpam-4277	210	42	x	x	PUNCT
ejpam-4277	210	43	by	by	ADP
ejpam-4277	210	44	theorem	theorem	NOUN
ejpam-4277	210	45	1	1	NUM
ejpam-4277	210	46	.	.	PUNCT
ejpam-4277	211	1	this	this	PRON
ejpam-4277	211	2	shows	show	VERB
ejpam-4277	211	3	that	that	SCONJ
ejpam-4277	211	4	f	f	PROPN
ejpam-4277	211	5	is	be	AUX
ejpam-4277	211	6	almost	almost	ADV
ejpam-4277	211	7	α(λ	α(λ	NOUN
ejpam-4277	211	8	,	,	PUNCT
ejpam-4277	211	9	sp)-continuous	sp)-continuous	ADJ
ejpam-4277	211	10	.	.	PUNCT
ejpam-4277	212	1	definition	definition	NOUN
ejpam-4277	212	2	2	2	NUM
ejpam-4277	212	3	.	.	PUNCT
ejpam-4277	213	1	a	a	DET
ejpam-4277	213	2	function	function	NOUN
ejpam-4277	213	3	f	f	NOUN
ejpam-4277	213	4	:	:	PUNCT
ejpam-4277	213	5	(	(	PUNCT
ejpam-4277	213	6	x	x	X
ejpam-4277	213	7	,	,	PUNCT
ejpam-4277	213	8	τ	τ	X
ejpam-4277	213	9	)	)	PUNCT
ejpam-4277	213	10	→	→	SYM
ejpam-4277	213	11	(	(	PUNCT
ejpam-4277	213	12	y	y	PROPN
ejpam-4277	213	13	,	,	PUNCT
ejpam-4277	213	14	σ	σ	PROPN
ejpam-4277	213	15	)	)	PUNCT
ejpam-4277	213	16	is	be	AUX
ejpam-4277	213	17	said	say	VERB
ejpam-4277	213	18	to	to	PART
ejpam-4277	213	19	be	be	AUX
ejpam-4277	213	20	almost	almost	ADV
ejpam-4277	213	21	α(λ	α(λ	NOUN
ejpam-4277	213	22	,	,	PUNCT
ejpam-4277	213	23	sp)-continuous	sp)-continuous	ADJ
ejpam-4277	213	24	if	if	SCONJ
ejpam-4277	213	25	f−1(v	f−1(v	PROPN
ejpam-4277	213	26	)	)	PUNCT
ejpam-4277	213	27	∈	∈	PROPN
ejpam-4277	213	28	αλspo(x	αλspo(x	PROPN
ejpam-4277	213	29	,	,	PUNCT
ejpam-4277	213	30	τ	τ	PROPN
ejpam-4277	213	31	)	)	PUNCT
ejpam-4277	213	32	for	for	ADP
ejpam-4277	213	33	every	every	DET
ejpam-4277	213	34	v	v	NOUN
ejpam-4277	213	35	∈	∈	NOUN
ejpam-4277	213	36	rλspo(y	rλspo(y	PROPN
ejpam-4277	213	37	,	,	PUNCT
ejpam-4277	213	38	σ	σ	PROPN
ejpam-4277	213	39	)	)	PUNCT
ejpam-4277	213	40	.	.	PUNCT
ejpam-4277	214	1	corollary	corollary	ADJ
ejpam-4277	214	2	1	1	NUM
ejpam-4277	214	3	.	.	PUNCT
ejpam-4277	215	1	for	for	ADP
ejpam-4277	215	2	a	a	DET
ejpam-4277	215	3	function	function	NOUN
ejpam-4277	215	4	f	f	NOUN
ejpam-4277	215	5	:	:	PUNCT
ejpam-4277	215	6	(	(	PUNCT
ejpam-4277	215	7	x	x	X
ejpam-4277	215	8	,	,	PUNCT
ejpam-4277	215	9	τ	τ	X
ejpam-4277	215	10	)	)	PUNCT
ejpam-4277	215	11	→	→	SYM
ejpam-4277	215	12	(	(	PUNCT
ejpam-4277	215	13	y	y	PROPN
ejpam-4277	215	14	,	,	PUNCT
ejpam-4277	215	15	σ	σ	PROPN
ejpam-4277	215	16	)	)	PUNCT
ejpam-4277	215	17	,	,	PUNCT
ejpam-4277	215	18	the	the	DET
ejpam-4277	215	19	following	follow	VERB
ejpam-4277	215	20	properties	property	NOUN
ejpam-4277	215	21	are	be	AUX
ejpam-4277	215	22	equivalent	equivalent	ADJ
ejpam-4277	215	23	:	:	PUNCT
ejpam-4277	215	24	(	(	PUNCT
ejpam-4277	215	25	1	1	X
ejpam-4277	215	26	)	)	PUNCT
ejpam-4277	215	27	f	f	PROPN
ejpam-4277	215	28	is	be	AUX
ejpam-4277	215	29	almost	almost	ADV
ejpam-4277	215	30	α(λ	α(λ	NOUN
ejpam-4277	215	31	,	,	PUNCT
ejpam-4277	215	32	sp)-continuous	sp)-continuous	ADJ
ejpam-4277	215	33	;	;	PUNCT
ejpam-4277	215	34	(	(	PUNCT
ejpam-4277	215	35	2	2	X
ejpam-4277	215	36	)	)	PUNCT
ejpam-4277	215	37	for	for	ADP
ejpam-4277	215	38	each	each	DET
ejpam-4277	215	39	x	x	SYM
ejpam-4277	215	40	∈	∈	PROPN
ejpam-4277	215	41	x	x	X
ejpam-4277	215	42	and	and	CCONJ
ejpam-4277	215	43	any	any	DET
ejpam-4277	215	44	(	(	PUNCT
ejpam-4277	215	45	λ	λ	NOUN
ejpam-4277	215	46	,	,	PUNCT
ejpam-4277	215	47	sp)-open	sp)-open	NOUN
ejpam-4277	215	48	set	set	VERB
ejpam-4277	215	49	g	g	NOUN
ejpam-4277	215	50	of	of	ADP
ejpam-4277	215	51	y	y	PROPN
ejpam-4277	215	52	containing	contain	VERB
ejpam-4277	215	53	f(x	f(x	PROPN
ejpam-4277	215	54	)	)	PUNCT
ejpam-4277	215	55	,	,	PUNCT
ejpam-4277	215	56	there	there	PRON
ejpam-4277	215	57	exists	exist	VERB
ejpam-4277	215	58	an	an	DET
ejpam-4277	215	59	α(λ	α(λ	PROPN
ejpam-4277	215	60	,	,	PUNCT
ejpam-4277	215	61	sp)-open	sp)-open	VERB
ejpam-4277	215	62	set	set	VERB
ejpam-4277	215	63	u	u	NOUN
ejpam-4277	215	64	of	of	ADP
ejpam-4277	215	65	x	x	PUNCT
ejpam-4277	215	66	containing	contain	VERB
ejpam-4277	215	67	x	x	PUNCT
ejpam-4277	215	68	such	such	ADJ
ejpam-4277	215	69	that	that	DET
ejpam-4277	215	70	f(u	f(u	PROPN
ejpam-4277	215	71	)	)	PUNCT
ejpam-4277	215	72	⊆	⊆	NUM
ejpam-4277	215	73	gs(λ	gs(λ	NOUN
ejpam-4277	215	74	,	,	PUNCT
ejpam-4277	215	75	sp	sp	NOUN
ejpam-4277	215	76	)	)	PUNCT
ejpam-4277	215	77	;	;	PUNCT
ejpam-4277	215	78	(	(	PUNCT
ejpam-4277	215	79	3	3	X
ejpam-4277	215	80	)	)	PUNCT
ejpam-4277	215	81	for	for	ADP
ejpam-4277	215	82	each	each	DET
ejpam-4277	215	83	x	x	SYM
ejpam-4277	215	84	∈	∈	PROPN
ejpam-4277	215	85	x	x	X
ejpam-4277	215	86	and	and	CCONJ
ejpam-4277	215	87	any	any	DET
ejpam-4277	215	88	r(λ	r(λ	NOUN
ejpam-4277	215	89	,	,	PUNCT
ejpam-4277	215	90	sp)-open	sp)-open	NOUN
ejpam-4277	215	91	set	set	VERB
ejpam-4277	215	92	g	g	NOUN
ejpam-4277	215	93	of	of	ADP
ejpam-4277	215	94	y	y	PROPN
ejpam-4277	215	95	containing	contain	VERB
ejpam-4277	215	96	f(x	f(x	PROPN
ejpam-4277	215	97	)	)	PUNCT
ejpam-4277	215	98	,	,	PUNCT
ejpam-4277	215	99	there	there	PRON
ejpam-4277	215	100	exists	exist	VERB
ejpam-4277	215	101	an	an	DET
ejpam-4277	215	102	α(λ	α(λ	PROPN
ejpam-4277	215	103	,	,	PUNCT
ejpam-4277	215	104	sp)-open	sp)-open	VERB
ejpam-4277	215	105	set	set	VERB
ejpam-4277	215	106	u	u	NOUN
ejpam-4277	215	107	of	of	ADP
ejpam-4277	215	108	x	x	PUNCT
ejpam-4277	215	109	containing	contain	VERB
ejpam-4277	215	110	x	x	PUNCT
ejpam-4277	215	111	such	such	ADJ
ejpam-4277	215	112	that	that	DET
ejpam-4277	215	113	f(u	f(u	PROPN
ejpam-4277	215	114	)	)	PUNCT
ejpam-4277	215	115	⊆	⊆	NUM
ejpam-4277	215	116	g	g	NOUN
ejpam-4277	215	117	;	;	PUNCT
ejpam-4277	215	118	(	(	PUNCT
ejpam-4277	215	119	4	4	X
ejpam-4277	215	120	)	)	PUNCT
ejpam-4277	215	121	f−1(g	f−1(g	PROPN
ejpam-4277	215	122	)	)	PUNCT
ejpam-4277	215	123	∈	∈	PROPN
ejpam-4277	215	124	αλspo(x	αλspo(x	PROPN
ejpam-4277	215	125	,	,	PUNCT
ejpam-4277	215	126	τ	τ	PROPN
ejpam-4277	215	127	)	)	PUNCT
ejpam-4277	215	128	for	for	ADP
ejpam-4277	215	129	every	every	DET
ejpam-4277	215	130	g	g	PROPN
ejpam-4277	215	131	∈	∈	PROPN
ejpam-4277	215	132	rλspo(y	rλspo(y	PROPN
ejpam-4277	215	133	,	,	PUNCT
ejpam-4277	215	134	σ	σ	PROPN
ejpam-4277	215	135	)	)	PUNCT
ejpam-4277	215	136	;	;	PUNCT
ejpam-4277	215	137	(	(	PUNCT
ejpam-4277	215	138	5	5	X
ejpam-4277	215	139	)	)	PUNCT
ejpam-4277	215	140	f−1(k	f−1(k	PROPN
ejpam-4277	215	141	)	)	PUNCT
ejpam-4277	215	142	∈	∈	PROPN
ejpam-4277	215	143	αλspc(x	αλspc(x	PROPN
ejpam-4277	215	144	,	,	PUNCT
ejpam-4277	215	145	τ	τ	PROPN
ejpam-4277	215	146	)	)	PUNCT
ejpam-4277	215	147	for	for	ADP
ejpam-4277	215	148	every	every	DET
ejpam-4277	215	149	k	k	PROPN
ejpam-4277	215	150	∈	∈	PROPN
ejpam-4277	215	151	rλspc(y	rλspc(y	PROPN
ejpam-4277	215	152	,	,	PUNCT
ejpam-4277	215	153	σ	σ	PROPN
ejpam-4277	215	154	)	)	PUNCT
ejpam-4277	215	155	;	;	PUNCT
ejpam-4277	215	156	(	(	PUNCT
ejpam-4277	215	157	6	6	X
ejpam-4277	215	158	)	)	PUNCT
ejpam-4277	215	159	f−1(g	f−1(g	PROPN
ejpam-4277	215	160	)	)	PUNCT
ejpam-4277	216	1	⊆	⊆	NUM
ejpam-4277	217	1	[	[	X
ejpam-4277	217	2	f−1(gs(λ	f−1(gs(λ	NOUN
ejpam-4277	217	3	,	,	PUNCT
ejpam-4277	217	4	sp))]α(λ	sp))]α(λ	NOUN
ejpam-4277	217	5	,	,	PUNCT
ejpam-4277	217	6	sp	sp	NOUN
ejpam-4277	217	7	)	)	PUNCT
ejpam-4277	217	8	for	for	ADP
ejpam-4277	217	9	any	any	DET
ejpam-4277	217	10	(	(	PUNCT
ejpam-4277	217	11	λ	λ	NOUN
ejpam-4277	217	12	,	,	PUNCT
ejpam-4277	217	13	sp)-open	sp)-open	NOUN
ejpam-4277	217	14	set	set	VERB
ejpam-4277	217	15	g	g	NOUN
ejpam-4277	217	16	of	of	ADP
ejpam-4277	217	17	y	y	PROPN
ejpam-4277	217	18	;	;	PUNCT
ejpam-4277	217	19	c.	c.	PROPN
ejpam-4277	217	20	boonpok	boonpok	PROPN
ejpam-4277	217	21	,	,	PUNCT
ejpam-4277	217	22	j.	j.	PROPN
ejpam-4277	217	23	khampakdee	khampakdee	PROPN
ejpam-4277	217	24	/	/	PUNCT
ejpam-4277	217	25	eur	eur	PROPN
ejpam-4277	217	26	.	.	PUNCT
ejpam-4277	218	1	j.	j.	PROPN
ejpam-4277	218	2	pure	pure	PROPN
ejpam-4277	218	3	appl	appl	PROPN
ejpam-4277	218	4	.	.	PROPN
ejpam-4277	218	5	math	math	PROPN
ejpam-4277	218	6	,	,	PUNCT
ejpam-4277	218	7	15	15	NUM
ejpam-4277	218	8	(	(	PUNCT
ejpam-4277	218	9	2	2	NUM
ejpam-4277	218	10	)	)	PUNCT
ejpam-4277	218	11	(	(	PUNCT
ejpam-4277	218	12	2022	2022	NUM
ejpam-4277	218	13	)	)	PUNCT
ejpam-4277	218	14	,	,	PUNCT
ejpam-4277	218	15	626	626	NUM
ejpam-4277	218	16	-	-	SYM
ejpam-4277	218	17	634	634	NUM
ejpam-4277	218	18	633	633	NUM
ejpam-4277	218	19	(	(	PUNCT
ejpam-4277	218	20	7	7	NUM
ejpam-4277	218	21	)	)	PUNCT
ejpam-4277	218	22	[	[	X
ejpam-4277	218	23	f−1(ks(λ	f−1(ks(λ	ADJ
ejpam-4277	218	24	,	,	PUNCT
ejpam-4277	218	25	sp	sp	NOUN
ejpam-4277	218	26	)	)	PUNCT
ejpam-4277	218	27	)	)	PUNCT
ejpam-4277	218	28	]	]	PUNCT
ejpam-4277	219	1	α(λ	α(λ	PROPN
ejpam-4277	219	2	,	,	PUNCT
ejpam-4277	219	3	sp	sp	NOUN
ejpam-4277	219	4	)	)	PUNCT
ejpam-4277	219	5	⊆	⊆	NUM
ejpam-4277	219	6	f−1(k	f−1(k	PROPN
ejpam-4277	219	7	)	)	PUNCT
ejpam-4277	219	8	for	for	ADP
ejpam-4277	219	9	any	any	DET
ejpam-4277	219	10	(	(	PUNCT
ejpam-4277	219	11	λ	λ	PROPN
ejpam-4277	219	12	,	,	PUNCT
ejpam-4277	219	13	sp)-closed	sp)-close	VERB
ejpam-4277	219	14	set	set	VERB
ejpam-4277	219	15	k	k	PROPN
ejpam-4277	219	16	of	of	ADP
ejpam-4277	219	17	y	y	PROPN
ejpam-4277	219	18	;	;	PUNCT
ejpam-4277	219	19	(	(	PUNCT
ejpam-4277	219	20	8)	8)	NUM
ejpam-4277	219	21	[	[	NOUN
ejpam-4277	219	22	f−1([k(λ	f−1([k(λ	NOUN
ejpam-4277	219	23	,	,	PUNCT
ejpam-4277	219	24	sp	sp	NOUN
ejpam-4277	219	25	)	)	PUNCT
ejpam-4277	219	26	]	]	PUNCT
ejpam-4277	219	27	(	(	PUNCT
ejpam-4277	219	28	λ	λ	NOUN
ejpam-4277	219	29	,	,	PUNCT
ejpam-4277	219	30	sp))]α(λ	sp))]α(λ	NOUN
ejpam-4277	219	31	,	,	PUNCT
ejpam-4277	219	32	sp	sp	NOUN
ejpam-4277	219	33	)	)	PUNCT
ejpam-4277	219	34	⊆	⊆	NUM
ejpam-4277	219	35	f−1(k	f−1(k	PROPN
ejpam-4277	219	36	)	)	PUNCT
ejpam-4277	219	37	for	for	SCONJ
ejpam-4277	219	38	any	any	DET
ejpam-4277	219	39	(	(	PUNCT
ejpam-4277	219	40	λ	λ	PROPN
ejpam-4277	219	41	,	,	PUNCT
ejpam-4277	219	42	sp)-closed	sp)-close	VERB
ejpam-4277	219	43	set	set	VERB
ejpam-4277	219	44	k	k	PROPN
ejpam-4277	219	45	of	of	ADP
ejpam-4277	219	46	y	y	PROPN
ejpam-4277	219	47	;	;	PUNCT
ejpam-4277	219	48	(	(	PUNCT
ejpam-4277	219	49	9	9	X
ejpam-4277	219	50	)	)	PUNCT
ejpam-4277	220	1	[	[	X
ejpam-4277	220	2	f−1([[b(λ	f−1([[b(λ	X
ejpam-4277	220	3	,	,	PUNCT
ejpam-4277	220	4	sp)](λ	sp)](λ	PROPN
ejpam-4277	220	5	,	,	PUNCT
ejpam-4277	220	6	sp	sp	NOUN
ejpam-4277	220	7	)	)	PUNCT
ejpam-4277	220	8	]	]	PUNCT
ejpam-4277	220	9	(	(	PUNCT
ejpam-4277	220	10	λ	λ	NOUN
ejpam-4277	220	11	,	,	PUNCT
ejpam-4277	220	12	sp))]α(λ	sp))]α(λ	NOUN
ejpam-4277	220	13	,	,	PUNCT
ejpam-4277	220	14	sp	sp	NOUN
ejpam-4277	220	15	)	)	PUNCT
ejpam-4277	220	16	⊆	⊆	NUM
ejpam-4277	220	17	f−1(b(λ	f−1(b(λ	PROPN
ejpam-4277	220	18	,	,	PUNCT
ejpam-4277	220	19	sp	sp	NOUN
ejpam-4277	220	20	)	)	PUNCT
ejpam-4277	220	21	)	)	PUNCT
ejpam-4277	220	22	for	for	ADP
ejpam-4277	220	23	any	any	DET
ejpam-4277	220	24	subset	subset	NOUN
ejpam-4277	220	25	b	b	PROPN
ejpam-4277	220	26	of	of	ADP
ejpam-4277	220	27	y	y	PROPN
ejpam-4277	220	28	;	;	PUNCT
ejpam-4277	220	29	(	(	PUNCT
ejpam-4277	220	30	10	10	NUM
ejpam-4277	220	31	)	)	PUNCT
ejpam-4277	221	1	[	[	X
ejpam-4277	221	2	[	[	X
ejpam-4277	221	3	[	[	X
ejpam-4277	221	4	f−1([k(λ	f−1([k(λ	NOUN
ejpam-4277	221	5	,	,	PUNCT
ejpam-4277	221	6	sp	sp	NOUN
ejpam-4277	221	7	)	)	PUNCT
ejpam-4277	221	8	]	]	PUNCT
ejpam-4277	221	9	(	(	PUNCT
ejpam-4277	221	10	λ	λ	INTJ
ejpam-4277	221	11	,	,	PUNCT
ejpam-4277	221	12	sp))](λ	sp))](λ	PROPN
ejpam-4277	221	13	,	,	PUNCT
ejpam-4277	221	14	sp)](λ	sp)](λ	PROPN
ejpam-4277	221	15	,	,	PUNCT
ejpam-4277	221	16	sp	sp	NOUN
ejpam-4277	221	17	)	)	PUNCT
ejpam-4277	221	18	]	]	PUNCT
ejpam-4277	221	19	(	(	PUNCT
ejpam-4277	221	20	λ	λ	NOUN
ejpam-4277	221	21	,	,	PUNCT
ejpam-4277	221	22	sp	sp	NOUN
ejpam-4277	221	23	)	)	PUNCT
ejpam-4277	221	24	⊆	⊆	NUM
ejpam-4277	221	25	f−1(k	f−1(k	PROPN
ejpam-4277	221	26	)	)	PUNCT
ejpam-4277	221	27	for	for	ADP
ejpam-4277	221	28	any	any	DET
ejpam-4277	221	29	(	(	PUNCT
ejpam-4277	221	30	λ	λ	PROPN
ejpam-4277	221	31	,	,	PUNCT
ejpam-4277	221	32	sp)-closed	sp)-close	VERB
ejpam-4277	221	33	set	set	VERB
ejpam-4277	221	34	k	k	PROPN
ejpam-4277	221	35	of	of	ADP
ejpam-4277	221	36	y	y	PROPN
ejpam-4277	221	37	;	;	PUNCT
ejpam-4277	221	38	(	(	PUNCT
ejpam-4277	221	39	11	11	NUM
ejpam-4277	221	40	)	)	PUNCT
ejpam-4277	222	1	[	[	X
ejpam-4277	222	2	[	[	X
ejpam-4277	222	3	[	[	X
ejpam-4277	222	4	f−1(ks(λ	f−1(ks(λ	ADJ
ejpam-4277	222	5	,	,	PUNCT
ejpam-4277	222	6	sp	sp	NOUN
ejpam-4277	222	7	)	)	PUNCT
ejpam-4277	222	8	)	)	PUNCT
ejpam-4277	222	9	]	]	PUNCT
ejpam-4277	223	1	(	(	PUNCT
ejpam-4277	223	2	λ	λ	X
ejpam-4277	223	3	,	,	PUNCT
ejpam-4277	223	4	sp)](λ	sp)](λ	PROPN
ejpam-4277	223	5	,	,	PUNCT
ejpam-4277	223	6	sp	sp	NOUN
ejpam-4277	223	7	)	)	PUNCT
ejpam-4277	223	8	]	]	PUNCT
ejpam-4277	223	9	(	(	PUNCT
ejpam-4277	223	10	λ	λ	NOUN
ejpam-4277	223	11	,	,	PUNCT
ejpam-4277	223	12	sp	sp	NOUN
ejpam-4277	223	13	)	)	PUNCT
ejpam-4277	223	14	⊆	⊆	NUM
ejpam-4277	223	15	f−(k	f−(k	PROPN
ejpam-4277	223	16	)	)	PUNCT
ejpam-4277	223	17	for	for	ADP
ejpam-4277	223	18	any	any	DET
ejpam-4277	223	19	(	(	PUNCT
ejpam-4277	223	20	λ	λ	PROPN
ejpam-4277	223	21	,	,	PUNCT
ejpam-4277	223	22	sp)-closed	sp)-close	VERB
ejpam-4277	223	23	set	set	VERB
ejpam-4277	223	24	k	k	PROPN
ejpam-4277	223	25	of	of	ADP
ejpam-4277	223	26	y	y	PROPN
ejpam-4277	223	27	;	;	PUNCT
ejpam-4277	223	28	(	(	PUNCT
ejpam-4277	223	29	12	12	NUM
ejpam-4277	223	30	)	)	PUNCT
ejpam-4277	223	31	f−1(g	f−1(g	PROPN
ejpam-4277	223	32	)	)	PUNCT
ejpam-4277	224	1	⊆	⊆	NUM
ejpam-4277	225	1	[	[	X
ejpam-4277	225	2	[	[	X
ejpam-4277	225	3	[	[	X
ejpam-4277	225	4	f−1(gs(λ	f−1(gs(λ	NOUN
ejpam-4277	225	5	,	,	PUNCT
ejpam-4277	225	6	sp))](λ	sp))](λ	PROPN
ejpam-4277	225	7	,	,	PUNCT
ejpam-4277	225	8	sp	sp	NOUN
ejpam-4277	225	9	)	)	PUNCT
ejpam-4277	225	10	]	]	PUNCT
ejpam-4277	225	11	(	(	PUNCT
ejpam-4277	225	12	λ	λ	X
ejpam-4277	225	13	,	,	PUNCT
ejpam-4277	225	14	sp)](λ	sp)](λ	PROPN
ejpam-4277	225	15	,	,	PUNCT
ejpam-4277	225	16	sp	sp	NOUN
ejpam-4277	225	17	)	)	PUNCT
ejpam-4277	225	18	for	for	ADP
ejpam-4277	225	19	any	any	DET
ejpam-4277	225	20	(	(	PUNCT
ejpam-4277	225	21	λ	λ	NOUN
ejpam-4277	225	22	,	,	PUNCT
ejpam-4277	225	23	sp)-open	sp)-open	NOUN
ejpam-4277	225	24	set	set	VERB
ejpam-4277	225	25	g	g	NOUN
ejpam-4277	225	26	of	of	ADP
ejpam-4277	225	27	y	y	PROPN
ejpam-4277	225	28	.	.	PUNCT
ejpam-4277	226	1	theorem	theorem	VERB
ejpam-4277	226	2	3	3	NUM
ejpam-4277	226	3	.	.	X
ejpam-4277	226	4	for	for	ADP
ejpam-4277	226	5	a	a	DET
ejpam-4277	226	6	multifunction	multifunction	NOUN
ejpam-4277	227	1	f	f	NOUN
ejpam-4277	227	2	:	:	PUNCT
ejpam-4277	227	3	(	(	PUNCT
ejpam-4277	227	4	x	x	X
ejpam-4277	227	5	,	,	PUNCT
ejpam-4277	227	6	τ	τ	X
ejpam-4277	227	7	)	)	PUNCT
ejpam-4277	227	8	→	→	SYM
ejpam-4277	227	9	(	(	PUNCT
ejpam-4277	227	10	y	y	PROPN
ejpam-4277	227	11	,	,	PUNCT
ejpam-4277	227	12	σ	σ	PROPN
ejpam-4277	227	13	)	)	PUNCT
ejpam-4277	227	14	,	,	PUNCT
ejpam-4277	227	15	the	the	DET
ejpam-4277	227	16	following	follow	VERB
ejpam-4277	227	17	properties	property	NOUN
ejpam-4277	227	18	are	be	AUX
ejpam-4277	227	19	equivalent	equivalent	ADJ
ejpam-4277	227	20	:	:	PUNCT
ejpam-4277	227	21	(	(	PUNCT
ejpam-4277	227	22	1	1	X
ejpam-4277	227	23	)	)	PUNCT
ejpam-4277	227	24	f	f	PROPN
ejpam-4277	227	25	is	be	AUX
ejpam-4277	227	26	almost	almost	ADV
ejpam-4277	227	27	α(λ	α(λ	NOUN
ejpam-4277	227	28	,	,	PUNCT
ejpam-4277	227	29	sp)-continuous	sp)-continuous	ADJ
ejpam-4277	227	30	;	;	PUNCT
ejpam-4277	227	31	(	(	PUNCT
ejpam-4277	227	32	2	2	X
ejpam-4277	227	33	)	)	PUNCT
ejpam-4277	227	34	[	[	X
ejpam-4277	227	35	f−(g1)∪f+(g2	f−(g1)∪f+(g2	NOUN
ejpam-4277	227	36	)	)	PUNCT
ejpam-4277	227	37	]	]	PUNCT
ejpam-4277	228	1	α(λ	α(λ	PROPN
ejpam-4277	228	2	,	,	PUNCT
ejpam-4277	228	3	sp	sp	NOUN
ejpam-4277	228	4	)	)	PUNCT
ejpam-4277	228	5	⊆	⊆	NUM
ejpam-4277	228	6	f−(g	f−(g	NOUN
ejpam-4277	228	7	(	(	PUNCT
ejpam-4277	228	8	λ	λ	NOUN
ejpam-4277	228	9	,	,	PUNCT
ejpam-4277	228	10	sp	sp	NOUN
ejpam-4277	228	11	)	)	PUNCT
ejpam-4277	228	12	1	1	NUM
ejpam-4277	228	13	)	)	PUNCT
ejpam-4277	228	14	∪f+(g	∪f+(g	NOUN
ejpam-4277	228	15	(	(	PUNCT
ejpam-4277	228	16	λ	λ	NOUN
ejpam-4277	228	17	,	,	PUNCT
ejpam-4277	228	18	sp	sp	NOUN
ejpam-4277	228	19	)	)	PUNCT
ejpam-4277	228	20	2	2	NUM
ejpam-4277	228	21	)	)	PUNCT
ejpam-4277	228	22	for	for	ADP
ejpam-4277	228	23	any	any	DET
ejpam-4277	228	24	g1	g1	NOUN
ejpam-4277	228	25	,	,	PUNCT
ejpam-4277	228	26	g2	g2	PROPN
ejpam-4277	228	27	∈	∈	PROPN
ejpam-4277	229	1	βλspo(y	βλspo(y	PROPN
ejpam-4277	229	2	,	,	PUNCT
ejpam-4277	229	3	σ	σ	PROPN
ejpam-4277	229	4	)	)	PUNCT
ejpam-4277	229	5	;	;	PUNCT
ejpam-4277	229	6	(	(	PUNCT
ejpam-4277	229	7	3	3	X
ejpam-4277	229	8	)	)	PUNCT
ejpam-4277	229	9	[	[	X
ejpam-4277	229	10	f−(g1)∪f+(g2	f−(g1)∪f+(g2	NOUN
ejpam-4277	229	11	)	)	PUNCT
ejpam-4277	229	12	]	]	PUNCT
ejpam-4277	230	1	α(λ	α(λ	PROPN
ejpam-4277	230	2	,	,	PUNCT
ejpam-4277	230	3	sp	sp	NOUN
ejpam-4277	230	4	)	)	PUNCT
ejpam-4277	230	5	⊆	⊆	NUM
ejpam-4277	230	6	f−(g	f−(g	NOUN
ejpam-4277	230	7	(	(	PUNCT
ejpam-4277	230	8	λ	λ	NOUN
ejpam-4277	230	9	,	,	PUNCT
ejpam-4277	230	10	sp	sp	NOUN
ejpam-4277	230	11	)	)	PUNCT
ejpam-4277	230	12	1	1	NUM
ejpam-4277	230	13	)	)	PUNCT
ejpam-4277	230	14	∪f+(g	∪f+(g	NOUN
ejpam-4277	230	15	(	(	PUNCT
ejpam-4277	230	16	λ	λ	NOUN
ejpam-4277	230	17	,	,	PUNCT
ejpam-4277	230	18	sp	sp	NOUN
ejpam-4277	230	19	)	)	PUNCT
ejpam-4277	230	20	2	2	NUM
ejpam-4277	230	21	)	)	PUNCT
ejpam-4277	230	22	for	for	ADP
ejpam-4277	230	23	any	any	DET
ejpam-4277	230	24	g1	g1	NOUN
ejpam-4277	230	25	,	,	PUNCT
ejpam-4277	230	26	g2	g2	PROPN
ejpam-4277	230	27	∈	∈	PROPN
ejpam-4277	230	28	sλspo(y	sλspo(y	PROPN
ejpam-4277	230	29	,	,	PUNCT
ejpam-4277	230	30	σ	σ	PROPN
ejpam-4277	230	31	)	)	PUNCT
ejpam-4277	230	32	;	;	PUNCT
ejpam-4277	230	33	(	(	PUNCT
ejpam-4277	230	34	4	4	X
ejpam-4277	230	35	)	)	PUNCT
ejpam-4277	230	36	f+(g1)∩f−(g2	f+(g1)∩f−(g2	NOUN
ejpam-4277	230	37	)	)	PUNCT
ejpam-4277	230	38	⊆	⊆	NUM
ejpam-4277	231	1	[	[	SYM
ejpam-4277	231	2	f+(g	f+(g	NOUN
ejpam-4277	231	3	s(λ	s(λ	NOUN
ejpam-4277	231	4	,	,	PUNCT
ejpam-4277	231	5	sp	sp	NOUN
ejpam-4277	231	6	)	)	PUNCT
ejpam-4277	231	7	1	1	NUM
ejpam-4277	231	8	)	)	PUNCT
ejpam-4277	231	9	∩f−(g	∩f−(g	PROPN
ejpam-4277	231	10	s(λ	s(λ	PROPN
ejpam-4277	231	11	,	,	PUNCT
ejpam-4277	231	12	sp	sp	NOUN
ejpam-4277	231	13	)	)	PUNCT
ejpam-4277	231	14	2	2	NUM
ejpam-4277	231	15	)	)	PUNCT
ejpam-4277	231	16	]	]	PUNCT
ejpam-4277	231	17	α(λ	α(λ	PROPN
ejpam-4277	231	18	,	,	PUNCT
ejpam-4277	231	19	sp	sp	NOUN
ejpam-4277	231	20	)	)	PUNCT
ejpam-4277	231	21	for	for	ADP
ejpam-4277	231	22	any	any	DET
ejpam-4277	231	23	g1	g1	NOUN
ejpam-4277	231	24	,	,	PUNCT
ejpam-4277	231	25	g2	g2	PROPN
ejpam-4277	231	26	∈	∈	PROPN
ejpam-4277	231	27	pλspo(y	pλspo(y	PROPN
ejpam-4277	231	28	,	,	PUNCT
ejpam-4277	231	29	σ	σ	PROPN
ejpam-4277	231	30	)	)	PUNCT
ejpam-4277	231	31	.	.	PUNCT
ejpam-4277	232	1	proof	proof	NOUN
ejpam-4277	232	2	.	.	PUNCT
ejpam-4277	233	1	(	(	PUNCT
ejpam-4277	233	2	1	1	X
ejpam-4277	233	3	)	)	PUNCT
ejpam-4277	233	4	⇒	⇒	NOUN
ejpam-4277	233	5	(	(	PUNCT
ejpam-4277	233	6	2	2	NUM
ejpam-4277	233	7	):	):	PUNCT
ejpam-4277	233	8	let	let	VERB
ejpam-4277	233	9	g1	g1	PROPN
ejpam-4277	233	10	,	,	PUNCT
ejpam-4277	233	11	g2	g2	PROPN
ejpam-4277	233	12	be	be	VERB
ejpam-4277	233	13	any	any	DET
ejpam-4277	233	14	β(λ	β(λ	NOUN
ejpam-4277	233	15	,	,	PUNCT
ejpam-4277	233	16	sp)-open	sp)-open	ADJ
ejpam-4277	233	17	sets	set	NOUN
ejpam-4277	233	18	of	of	ADP
ejpam-4277	233	19	y	y	PROPN
ejpam-4277	233	20	.	.	PUNCT
ejpam-4277	234	1	since	since	SCONJ
ejpam-4277	234	2	g	g	PROPN
ejpam-4277	234	3	(	(	PUNCT
ejpam-4277	234	4	λ	λ	PROPN
ejpam-4277	234	5	,	,	PUNCT
ejpam-4277	234	6	sp	sp	NOUN
ejpam-4277	234	7	)	)	PUNCT
ejpam-4277	234	8	1	1	NUM
ejpam-4277	234	9	and	and	CCONJ
ejpam-4277	234	10	g	g	PROPN
ejpam-4277	234	11	(	(	PUNCT
ejpam-4277	234	12	λ	λ	PROPN
ejpam-4277	234	13	,	,	PUNCT
ejpam-4277	234	14	sp	sp	NOUN
ejpam-4277	234	15	)	)	PUNCT
ejpam-4277	234	16	2	2	NUM
ejpam-4277	234	17	are	be	AUX
ejpam-4277	234	18	r(λ	r(λ	NOUN
ejpam-4277	234	19	,	,	PUNCT
ejpam-4277	234	20	sp)-closed	sp)-close	VERB
ejpam-4277	234	21	,	,	PUNCT
ejpam-4277	234	22	by	by	ADP
ejpam-4277	234	23	theorem	theorem	NOUN
ejpam-4277	234	24	2	2	NUM
ejpam-4277	234	25	,	,	PUNCT
ejpam-4277	234	26	f−(g	f−(g	NOUN
ejpam-4277	234	27	(	(	PUNCT
ejpam-4277	234	28	λ	λ	NOUN
ejpam-4277	234	29	,	,	PUNCT
ejpam-4277	234	30	sp	sp	NOUN
ejpam-4277	234	31	)	)	PUNCT
ejpam-4277	234	32	1	1	NUM
ejpam-4277	234	33	)	)	PUNCT
ejpam-4277	234	34	∪	∪	X
ejpam-4277	234	35	f+(g	f+(g	X
ejpam-4277	234	36	(	(	PUNCT
ejpam-4277	234	37	λ	λ	NOUN
ejpam-4277	234	38	,	,	PUNCT
ejpam-4277	234	39	sp	sp	NOUN
ejpam-4277	234	40	)	)	PUNCT
ejpam-4277	234	41	2	2	NUM
ejpam-4277	234	42	)	)	PUNCT
ejpam-4277	234	43	is	be	AUX
ejpam-4277	234	44	α(λ	α(λ	PROPN
ejpam-4277	234	45	,	,	PUNCT
ejpam-4277	234	46	sp)-closed	sp)-close	VERB
ejpam-4277	234	47	in	in	ADP
ejpam-4277	234	48	x	x	X
ejpam-4277	234	49	and	and	CCONJ
ejpam-4277	234	50	f−(g1	f−(g1	NUM
ejpam-4277	234	51	)	)	PUNCT
ejpam-4277	234	52	∪	∪	ADP
ejpam-4277	234	53	f+(g2	f+(g2	NOUN
ejpam-4277	234	54	)	)	PUNCT
ejpam-4277	234	55	⊆	⊆	NUM
ejpam-4277	234	56	f−(g	f−(g	NOUN
ejpam-4277	234	57	(	(	PUNCT
ejpam-4277	234	58	λ	λ	NOUN
ejpam-4277	234	59	,	,	PUNCT
ejpam-4277	234	60	sp	sp	NOUN
ejpam-4277	234	61	)	)	PUNCT
ejpam-4277	234	62	1	1	NUM
ejpam-4277	234	63	)	)	PUNCT
ejpam-4277	234	64	∪	∪	X
ejpam-4277	234	65	f+(g	f+(g	X
ejpam-4277	234	66	(	(	PUNCT
ejpam-4277	234	67	λ	λ	NOUN
ejpam-4277	234	68	,	,	PUNCT
ejpam-4277	234	69	sp	sp	NOUN
ejpam-4277	234	70	)	)	PUNCT
ejpam-4277	234	71	2	2	NUM
ejpam-4277	234	72	)	)	PUNCT
ejpam-4277	234	73	.	.	PUNCT
ejpam-4277	235	1	thus	thus	ADV
ejpam-4277	235	2	,	,	PUNCT
ejpam-4277	235	3	[	[	X
ejpam-4277	235	4	f−(g1	f−(g1	X
ejpam-4277	235	5	)	)	PUNCT
ejpam-4277	235	6	∪	∪	ADP
ejpam-4277	235	7	f+(g2	f+(g2	NOUN
ejpam-4277	235	8	)	)	PUNCT
ejpam-4277	235	9	]	]	PUNCT
ejpam-4277	235	10	α(λ	α(λ	PROPN
ejpam-4277	235	11	,	,	PUNCT
ejpam-4277	235	12	sp	sp	NOUN
ejpam-4277	235	13	)	)	PUNCT
ejpam-4277	235	14	⊆	⊆	NUM
ejpam-4277	235	15	f−(g	f−(g	NOUN
ejpam-4277	235	16	(	(	PUNCT
ejpam-4277	235	17	λ	λ	NOUN
ejpam-4277	235	18	,	,	PUNCT
ejpam-4277	235	19	sp	sp	NOUN
ejpam-4277	235	20	)	)	PUNCT
ejpam-4277	235	21	1	1	NUM
ejpam-4277	235	22	)	)	PUNCT
ejpam-4277	235	23	∪	∪	X
ejpam-4277	235	24	f+(g	f+(g	X
ejpam-4277	235	25	(	(	PUNCT
ejpam-4277	235	26	λ	λ	NOUN
ejpam-4277	235	27	,	,	PUNCT
ejpam-4277	235	28	sp	sp	NOUN
ejpam-4277	235	29	)	)	PUNCT
ejpam-4277	235	30	2	2	NUM
ejpam-4277	235	31	)	)	PUNCT
ejpam-4277	235	32	.	.	PUNCT
ejpam-4277	236	1	(	(	PUNCT
ejpam-4277	236	2	2	2	X
ejpam-4277	236	3	)	)	PUNCT
ejpam-4277	236	4	⇒	⇒	NOUN
ejpam-4277	236	5	(	(	PUNCT
ejpam-4277	236	6	3	3	NUM
ejpam-4277	236	7	):	):	PUNCT
ejpam-4277	236	8	this	this	PRON
ejpam-4277	236	9	is	be	AUX
ejpam-4277	236	10	obvious	obvious	ADJ
ejpam-4277	236	11	since	since	SCONJ
ejpam-4277	236	12	sλspo(y	sλspo(y	PROPN
ejpam-4277	236	13	,	,	PUNCT
ejpam-4277	236	14	σ	σ	PROPN
ejpam-4277	236	15	)	)	PUNCT
ejpam-4277	236	16	⊆	⊆	NUM
ejpam-4277	236	17	βλspo(y	βλspo(y	ADP
ejpam-4277	236	18	,	,	PUNCT
ejpam-4277	236	19	σ	σ	PROPN
ejpam-4277	236	20	)	)	PUNCT
ejpam-4277	236	21	.	.	PUNCT
ejpam-4277	237	1	(	(	PUNCT
ejpam-4277	237	2	3	3	X
ejpam-4277	237	3	)	)	PUNCT
ejpam-4277	237	4	⇒	⇒	NOUN
ejpam-4277	237	5	(	(	PUNCT
ejpam-4277	237	6	1	1	NUM
ejpam-4277	237	7	):	):	PUNCT
ejpam-4277	237	8	let	let	VERB
ejpam-4277	237	9	k1,k2	k1,k2	PROPN
ejpam-4277	237	10	∈	∈	PROPN
ejpam-4277	237	11	rλspc(y	rλspc(y	PROPN
ejpam-4277	237	12	,	,	PUNCT
ejpam-4277	237	13	σ	σ	PROPN
ejpam-4277	237	14	)	)	PUNCT
ejpam-4277	237	15	.	.	PUNCT
ejpam-4277	238	1	then	then	ADV
ejpam-4277	238	2	,	,	PUNCT
ejpam-4277	238	3	k1,k2	k1,k2	PROPN
ejpam-4277	238	4	∈	∈	PROPN
ejpam-4277	238	5	sλspo(y	sλspo(y	PROPN
ejpam-4277	238	6	,	,	PUNCT
ejpam-4277	238	7	σ	σ	PROPN
ejpam-4277	238	8	)	)	PUNCT
ejpam-4277	238	9	and	and	CCONJ
ejpam-4277	238	10	hence	hence	ADV
ejpam-4277	238	11	[	[	X
ejpam-4277	238	12	f−(k1	f−(k1	NOUN
ejpam-4277	238	13	)	)	PUNCT
ejpam-4277	238	14	∪	∪	ADP
ejpam-4277	238	15	f+(k2	f+(k2	NOUN
ejpam-4277	238	16	)	)	PUNCT
ejpam-4277	238	17	]	]	PUNCT
ejpam-4277	239	1	α(λ	α(λ	PROPN
ejpam-4277	239	2	,	,	PUNCT
ejpam-4277	239	3	sp	sp	NOUN
ejpam-4277	239	4	)	)	PUNCT
ejpam-4277	239	5	⊆	⊆	NUM
ejpam-4277	239	6	f−(k1	f−(k1	NOUN
ejpam-4277	239	7	)	)	PUNCT
ejpam-4277	239	8	∪	∪	ADP
ejpam-4277	239	9	f+(k2	f+(k2	NOUN
ejpam-4277	239	10	)	)	PUNCT
ejpam-4277	239	11	.	.	PUNCT
ejpam-4277	240	1	thus	thus	ADV
ejpam-4277	240	2	,	,	PUNCT
ejpam-4277	240	3	we	we	PRON
ejpam-4277	240	4	have	have	AUX
ejpam-4277	240	5	f−(k1	f−(k1	NOUN
ejpam-4277	240	6	)	)	PUNCT
ejpam-4277	240	7	∪	∪	ADP
ejpam-4277	240	8	f+(k2	f+(k2	NOUN
ejpam-4277	240	9	)	)	PUNCT
ejpam-4277	240	10	is	be	AUX
ejpam-4277	240	11	α(λ	α(λ	PROPN
ejpam-4277	240	12	,	,	PUNCT
ejpam-4277	240	13	sp)-closed	sp)-close	VERB
ejpam-4277	240	14	in	in	ADP
ejpam-4277	240	15	x	x	PUNCT
ejpam-4277	240	16	and	and	CCONJ
ejpam-4277	240	17	hence	hence	ADV
ejpam-4277	240	18	f	f	PROPN
ejpam-4277	240	19	is	be	AUX
ejpam-4277	240	20	almost	almost	ADV
ejpam-4277	240	21	α(λ	α(λ	NOUN
ejpam-4277	240	22	,	,	PUNCT
ejpam-4277	240	23	sp)-continuous	sp)-continuous	ADJ
ejpam-4277	240	24	by	by	ADP
ejpam-4277	240	25	theorem	theorem	NOUN
ejpam-4277	240	26	2	2	NUM
ejpam-4277	240	27	.	.	PUNCT
ejpam-4277	240	28	(	(	PUNCT
ejpam-4277	240	29	1	1	X
ejpam-4277	240	30	)	)	PUNCT
ejpam-4277	240	31	⇒	⇒	NOUN
ejpam-4277	240	32	(	(	PUNCT
ejpam-4277	240	33	4	4	NUM
ejpam-4277	240	34	):	):	PUNCT
ejpam-4277	240	35	let	let	VERB
ejpam-4277	240	36	g1	g1	PROPN
ejpam-4277	240	37	,	,	PUNCT
ejpam-4277	240	38	g2	g2	PROPN
ejpam-4277	240	39	be	be	VERB
ejpam-4277	240	40	any	any	DET
ejpam-4277	240	41	p(λ	p(λ	NOUN
ejpam-4277	240	42	,	,	PUNCT
ejpam-4277	240	43	sp)-open	sp)-open	ADJ
ejpam-4277	240	44	sets	set	NOUN
ejpam-4277	240	45	of	of	ADP
ejpam-4277	240	46	y	y	PROPN
ejpam-4277	240	47	.	.	PUNCT
ejpam-4277	241	1	since	since	SCONJ
ejpam-4277	241	2	[	[	X
ejpam-4277	241	3	g	g	PROPN
ejpam-4277	241	4	(	(	PUNCT
ejpam-4277	241	5	λ	λ	PROPN
ejpam-4277	241	6	,	,	PUNCT
ejpam-4277	241	7	sp	sp	NOUN
ejpam-4277	241	8	)	)	PUNCT
ejpam-4277	241	9	1	1	NUM
ejpam-4277	241	10	]	]	PUNCT
ejpam-4277	241	11	(	(	PUNCT
ejpam-4277	241	12	λ	λ	NOUN
ejpam-4277	241	13	,	,	PUNCT
ejpam-4277	241	14	sp	sp	NOUN
ejpam-4277	241	15	)	)	PUNCT
ejpam-4277	241	16	and	and	CCONJ
ejpam-4277	241	17	[	[	X
ejpam-4277	241	18	g	g	X
ejpam-4277	241	19	(	(	PUNCT
ejpam-4277	241	20	λ	λ	PROPN
ejpam-4277	241	21	,	,	PUNCT
ejpam-4277	241	22	sp	sp	NOUN
ejpam-4277	241	23	)	)	PUNCT
ejpam-4277	241	24	2	2	NUM
ejpam-4277	241	25	]	]	PUNCT
ejpam-4277	241	26	(	(	PUNCT
ejpam-4277	241	27	λ	λ	NOUN
ejpam-4277	241	28	,	,	PUNCT
ejpam-4277	241	29	sp	sp	NOUN
ejpam-4277	241	30	)	)	PUNCT
ejpam-4277	241	31	are	be	AUX
ejpam-4277	241	32	r(λ	r(λ	NOUN
ejpam-4277	241	33	,	,	PUNCT
ejpam-4277	241	34	sp)-open	sp)-open	ADJ
ejpam-4277	241	35	in	in	ADP
ejpam-4277	241	36	y	y	PROPN
ejpam-4277	241	37	,	,	PUNCT
ejpam-4277	241	38	we	we	PRON
ejpam-4277	241	39	have	have	VERB
ejpam-4277	241	40	[	[	X
ejpam-4277	241	41	g	g	PROPN
ejpam-4277	241	42	(	(	PUNCT
ejpam-4277	241	43	λ	λ	PROPN
ejpam-4277	241	44	,	,	PUNCT
ejpam-4277	241	45	sp	sp	NOUN
ejpam-4277	241	46	)	)	PUNCT
ejpam-4277	241	47	1	1	NUM
ejpam-4277	241	48	]	]	PUNCT
ejpam-4277	241	49	(	(	PUNCT
ejpam-4277	241	50	λ	λ	NOUN
ejpam-4277	241	51	,	,	PUNCT
ejpam-4277	241	52	sp	sp	NOUN
ejpam-4277	241	53	)	)	PUNCT
ejpam-4277	241	54	=	=	SYM
ejpam-4277	241	55	g	g	PROPN
ejpam-4277	241	56	s(λ	s(λ	PROPN
ejpam-4277	241	57	,	,	PUNCT
ejpam-4277	241	58	sp	sp	NOUN
ejpam-4277	241	59	)	)	PUNCT
ejpam-4277	241	60	1	1	NUM
ejpam-4277	242	1	and	and	CCONJ
ejpam-4277	243	1	[	[	X
ejpam-4277	243	2	g	g	PROPN
ejpam-4277	243	3	(	(	PUNCT
ejpam-4277	243	4	λ	λ	PROPN
ejpam-4277	243	5	,	,	PUNCT
ejpam-4277	243	6	sp	sp	NOUN
ejpam-4277	243	7	)	)	PUNCT
ejpam-4277	243	8	1	1	NUM
ejpam-4277	243	9	]	]	PUNCT
ejpam-4277	243	10	(	(	PUNCT
ejpam-4277	243	11	λ	λ	NOUN
ejpam-4277	243	12	,	,	PUNCT
ejpam-4277	243	13	sp	sp	NOUN
ejpam-4277	243	14	)	)	PUNCT
ejpam-4277	243	15	=	=	SYM
ejpam-4277	243	16	g	g	PROPN
ejpam-4277	243	17	s(λ	s(λ	PROPN
ejpam-4277	243	18	,	,	PUNCT
ejpam-4277	243	19	sp	sp	NOUN
ejpam-4277	243	20	)	)	PUNCT
ejpam-4277	243	21	2	2	NUM
ejpam-4277	243	22	,	,	PUNCT
ejpam-4277	243	23	by	by	ADP
ejpam-4277	243	24	theorem	theorem	NOUN
ejpam-4277	243	25	2	2	NUM
ejpam-4277	243	26	,	,	PUNCT
ejpam-4277	243	27	f+(g	f+(g	NOUN
ejpam-4277	243	28	s(λ	s(λ	PROPN
ejpam-4277	243	29	,	,	PUNCT
ejpam-4277	243	30	sp	sp	NOUN
ejpam-4277	243	31	)	)	PUNCT
ejpam-4277	243	32	1	1	NUM
ejpam-4277	243	33	)	)	PUNCT
ejpam-4277	243	34	∩	∩	PROPN
ejpam-4277	243	35	f−(g	f−(g	VERB
ejpam-4277	243	36	s(λ	s(λ	PROPN
ejpam-4277	243	37	,	,	PUNCT
ejpam-4277	243	38	sp	sp	NOUN
ejpam-4277	243	39	)	)	PUNCT
ejpam-4277	243	40	2	2	NUM
ejpam-4277	243	41	)	)	PUNCT
ejpam-4277	243	42	is	be	AUX
ejpam-4277	243	43	α(λ	α(λ	PROPN
ejpam-4277	243	44	,	,	PUNCT
ejpam-4277	243	45	sp)-open	sp)-open	ADJ
ejpam-4277	243	46	in	in	ADP
ejpam-4277	243	47	x.	x.	NOUN
ejpam-4277	243	48	thus	thus	ADV
ejpam-4277	243	49	,	,	PUNCT
ejpam-4277	243	50	f+(g1	f+(g1	ADJ
ejpam-4277	243	51	)	)	PUNCT
ejpam-4277	243	52	∩	∩	NOUN
ejpam-4277	243	53	f−(g2	f−(g2	NUM
ejpam-4277	243	54	)	)	PUNCT
ejpam-4277	243	55	⊆	⊆	NUM
ejpam-4277	243	56	f+(g	f+(g	NOUN
ejpam-4277	243	57	s(λ	s(λ	NOUN
ejpam-4277	243	58	,	,	PUNCT
ejpam-4277	243	59	sp	sp	NOUN
ejpam-4277	243	60	)	)	PUNCT
ejpam-4277	243	61	1	1	NUM
ejpam-4277	243	62	)	)	PUNCT
ejpam-4277	243	63	∩	∩	PROPN
ejpam-4277	243	64	f−(g	f−(g	VERB
ejpam-4277	243	65	s(λ	s(λ	PROPN
ejpam-4277	243	66	,	,	PUNCT
ejpam-4277	243	67	sp	sp	NOUN
ejpam-4277	243	68	)	)	PUNCT
ejpam-4277	243	69	2	2	NUM
ejpam-4277	243	70	)	)	PUNCT
ejpam-4277	243	71	=	=	NOUN
ejpam-4277	244	1	[	[	X
ejpam-4277	244	2	f+(g	f+(g	NOUN
ejpam-4277	244	3	s(λ	s(λ	NOUN
ejpam-4277	244	4	,	,	PUNCT
ejpam-4277	244	5	sp	sp	NOUN
ejpam-4277	244	6	)	)	PUNCT
ejpam-4277	244	7	1	1	NUM
ejpam-4277	244	8	)	)	PUNCT
ejpam-4277	244	9	∩	∩	PROPN
ejpam-4277	244	10	f−(g	f−(g	VERB
ejpam-4277	244	11	s(λ	s(λ	PROPN
ejpam-4277	244	12	,	,	PUNCT
ejpam-4277	244	13	sp	sp	NOUN
ejpam-4277	244	14	)	)	PUNCT
ejpam-4277	244	15	2	2	NUM
ejpam-4277	244	16	)	)	PUNCT
ejpam-4277	244	17	]	]	PUNCT
ejpam-4277	244	18	α(λ	α(λ	PROPN
ejpam-4277	244	19	,	,	PUNCT
ejpam-4277	244	20	sp	sp	NOUN
ejpam-4277	244	21	)	)	PUNCT
ejpam-4277	244	22	.	.	PUNCT
ejpam-4277	245	1	(	(	PUNCT
ejpam-4277	245	2	4	4	X
ejpam-4277	245	3	)	)	PUNCT
ejpam-4277	245	4	⇒	⇒	NOUN
ejpam-4277	245	5	(	(	PUNCT
ejpam-4277	245	6	1	1	NUM
ejpam-4277	245	7	):	):	PUNCT
ejpam-4277	245	8	let	let	VERB
ejpam-4277	245	9	g1	g1	PROPN
ejpam-4277	245	10	,	,	PUNCT
ejpam-4277	245	11	g2	g2	PROPN
ejpam-4277	245	12	be	be	VERB
ejpam-4277	245	13	any	any	DET
ejpam-4277	245	14	r(λ	r(λ	NOUN
ejpam-4277	245	15	,	,	PUNCT
ejpam-4277	245	16	sp)-open	sp)-open	ADJ
ejpam-4277	245	17	sets	set	NOUN
ejpam-4277	245	18	of	of	ADP
ejpam-4277	245	19	y	y	PROPN
ejpam-4277	245	20	.	.	PUNCT
ejpam-4277	246	1	since	since	SCONJ
ejpam-4277	246	2	g1	g1	PROPN
ejpam-4277	246	3	,	,	PUNCT
ejpam-4277	246	4	g2	g2	PROPN
ejpam-4277	246	5	∈	∈	PROPN
ejpam-4277	246	6	pλspo(y	pλspo(y	PROPN
ejpam-4277	246	7	,	,	PUNCT
ejpam-4277	246	8	σ	σ	PROPN
ejpam-4277	246	9	)	)	PUNCT
ejpam-4277	246	10	,	,	PUNCT
ejpam-4277	246	11	we	we	PRON
ejpam-4277	246	12	have	have	VERB
ejpam-4277	246	13	f+(g1)∩f−(g2	f+(g1)∩f−(g2	NOUN
ejpam-4277	246	14	)	)	PUNCT
ejpam-4277	246	15	⊆	⊆	NUM
ejpam-4277	246	16	[	[	SYM
ejpam-4277	246	17	f+(g	f+(g	NOUN
ejpam-4277	246	18	s(λ	s(λ	NOUN
ejpam-4277	246	19	,	,	PUNCT
ejpam-4277	246	20	sp	sp	NOUN
ejpam-4277	246	21	)	)	PUNCT
ejpam-4277	246	22	1	1	NUM
ejpam-4277	246	23	)	)	PUNCT
ejpam-4277	246	24	∩f−(g	∩f−(g	PROPN
ejpam-4277	246	25	s(λ	s(λ	PROPN
ejpam-4277	246	26	,	,	PUNCT
ejpam-4277	246	27	sp	sp	NOUN
ejpam-4277	246	28	)	)	PUNCT
ejpam-4277	246	29	2	2	NUM
ejpam-4277	246	30	)	)	PUNCT
ejpam-4277	247	1	]	]	PUNCT
ejpam-4277	247	2	α(λ	α(λ	PROPN
ejpam-4277	247	3	,	,	PUNCT
ejpam-4277	247	4	sp	sp	NOUN
ejpam-4277	247	5	)	)	PUNCT
ejpam-4277	247	6	=	=	PUNCT
ejpam-4277	248	1	[	[	X
ejpam-4277	248	2	f+(g1)∩f−(g2)]α(λ	f+(g1)∩f−(g2)]α(λ	NOUN
ejpam-4277	248	3	,	,	PUNCT
ejpam-4277	248	4	sp	sp	NOUN
ejpam-4277	248	5	)	)	PUNCT
ejpam-4277	248	6	and	and	CCONJ
ejpam-4277	248	7	hence	hence	ADV
ejpam-4277	248	8	f+(g1)∩	f+(g1)∩	NUM
ejpam-4277	248	9	f−(g2	f−(g2	NOUN
ejpam-4277	248	10	)	)	PUNCT
ejpam-4277	248	11	∈	∈	PROPN
ejpam-4277	248	12	αλspo(x	αλspo(x	PROPN
ejpam-4277	248	13	,	,	PUNCT
ejpam-4277	248	14	τ	τ	PROPN
ejpam-4277	248	15	)	)	PUNCT
ejpam-4277	248	16	.	.	PUNCT
ejpam-4277	249	1	it	it	PRON
ejpam-4277	249	2	follows	follow	VERB
ejpam-4277	249	3	from	from	ADP
ejpam-4277	249	4	theorem	theorem	ADJ
ejpam-4277	249	5	2	2	NUM
ejpam-4277	249	6	that	that	PRON
ejpam-4277	249	7	f	f	PROPN
ejpam-4277	249	8	is	be	AUX
ejpam-4277	249	9	almost	almost	ADV
ejpam-4277	249	10	α(λ	α(λ	NOUN
ejpam-4277	249	11	,	,	PUNCT
ejpam-4277	249	12	sp)-continuous	sp)-continuous	ADJ
ejpam-4277	249	13	.	.	PUNCT
ejpam-4277	250	1	references	reference	NOUN
ejpam-4277	250	2	634	634	NUM
ejpam-4277	250	3	corollary	corollary	ADJ
ejpam-4277	250	4	2	2	NUM
ejpam-4277	250	5	.	.	PUNCT
ejpam-4277	250	6	for	for	ADP
ejpam-4277	250	7	a	a	DET
ejpam-4277	250	8	function	function	NOUN
ejpam-4277	250	9	f	f	NOUN
ejpam-4277	250	10	:	:	PUNCT
ejpam-4277	250	11	(	(	PUNCT
ejpam-4277	250	12	x	x	X
ejpam-4277	250	13	,	,	PUNCT
ejpam-4277	250	14	τ	τ	X
ejpam-4277	250	15	)	)	PUNCT
ejpam-4277	250	16	→	→	SYM
ejpam-4277	250	17	(	(	PUNCT
ejpam-4277	250	18	y	y	PROPN
ejpam-4277	250	19	,	,	PUNCT
ejpam-4277	250	20	σ	σ	PROPN
ejpam-4277	250	21	)	)	PUNCT
ejpam-4277	250	22	,	,	PUNCT
ejpam-4277	250	23	the	the	DET
ejpam-4277	250	24	following	follow	VERB
ejpam-4277	250	25	properties	property	NOUN
ejpam-4277	250	26	are	be	AUX
ejpam-4277	250	27	equivalent	equivalent	ADJ
ejpam-4277	250	28	:	:	PUNCT
ejpam-4277	250	29	(	(	PUNCT
ejpam-4277	250	30	1	1	X
ejpam-4277	250	31	)	)	PUNCT
ejpam-4277	250	32	f	f	PROPN
ejpam-4277	250	33	is	be	AUX
ejpam-4277	250	34	almost	almost	ADV
ejpam-4277	250	35	α(λ	α(λ	NOUN
ejpam-4277	250	36	,	,	PUNCT
ejpam-4277	250	37	sp)-continuous	sp)-continuous	ADJ
ejpam-4277	250	38	;	;	PUNCT
ejpam-4277	250	39	(	(	PUNCT
ejpam-4277	250	40	2	2	X
ejpam-4277	250	41	)	)	PUNCT
ejpam-4277	251	1	[	[	X
ejpam-4277	251	2	f−1(v	f−1(v	NOUN
ejpam-4277	251	3	)	)	PUNCT
ejpam-4277	251	4	]	]	PUNCT
ejpam-4277	251	5	α(λ	α(λ	PROPN
ejpam-4277	251	6	,	,	PUNCT
ejpam-4277	251	7	sp	sp	NOUN
ejpam-4277	251	8	)	)	PUNCT
ejpam-4277	251	9	⊆	⊆	NUM
ejpam-4277	251	10	f−1(v	f−1(v	NOUN
ejpam-4277	251	11	(	(	PUNCT
ejpam-4277	251	12	λ	λ	PROPN
ejpam-4277	251	13	,	,	PUNCT
ejpam-4277	251	14	sp	sp	NOUN
ejpam-4277	251	15	)	)	PUNCT
ejpam-4277	251	16	)	)	PUNCT
ejpam-4277	251	17	for	for	ADP
ejpam-4277	251	18	any	any	PRON
ejpam-4277	251	19	v	v	NOUN
ejpam-4277	251	20	∈	∈	PROPN
ejpam-4277	251	21	βλspo(y	βλspo(y	ADP
ejpam-4277	251	22	,	,	PUNCT
ejpam-4277	251	23	σ	σ	PROPN
ejpam-4277	251	24	)	)	PUNCT
ejpam-4277	251	25	;	;	PUNCT
ejpam-4277	251	26	(	(	PUNCT
ejpam-4277	251	27	3	3	X
ejpam-4277	251	28	)	)	PUNCT
ejpam-4277	252	1	[	[	X
ejpam-4277	252	2	f−1(v	f−1(v	NOUN
ejpam-4277	252	3	)	)	PUNCT
ejpam-4277	252	4	]	]	PUNCT
ejpam-4277	252	5	α(λ	α(λ	PROPN
ejpam-4277	252	6	,	,	PUNCT
ejpam-4277	252	7	sp	sp	NOUN
ejpam-4277	252	8	)	)	PUNCT
ejpam-4277	252	9	⊆	⊆	NUM
ejpam-4277	252	10	f−1(v	f−1(v	NOUN
ejpam-4277	252	11	(	(	PUNCT
ejpam-4277	252	12	λ	λ	PROPN
ejpam-4277	252	13	,	,	PUNCT
ejpam-4277	252	14	sp	sp	NOUN
ejpam-4277	252	15	)	)	PUNCT
ejpam-4277	252	16	)	)	PUNCT
ejpam-4277	252	17	for	for	ADP
ejpam-4277	252	18	any	any	DET
ejpam-4277	252	19	v	v	NOUN
ejpam-4277	252	20	∈	∈	PROPN
ejpam-4277	252	21	sλspo(y	sλspo(y	NOUN
ejpam-4277	252	22	,	,	PUNCT
ejpam-4277	252	23	σ	σ	PROPN
ejpam-4277	252	24	)	)	PUNCT
ejpam-4277	252	25	;	;	PUNCT
ejpam-4277	252	26	(	(	PUNCT
ejpam-4277	252	27	4	4	X
ejpam-4277	252	28	)	)	PUNCT
ejpam-4277	252	29	f−1(v	f−1(v	NOUN
ejpam-4277	252	30	)	)	PUNCT
ejpam-4277	252	31	⊆	⊆	NUM
ejpam-4277	253	1	[	[	X
ejpam-4277	253	2	f−1(v	f−1(v	NOUN
ejpam-4277	253	3	s(λ	s(λ	PROPN
ejpam-4277	253	4	,	,	PUNCT
ejpam-4277	253	5	sp))]α(λ	sp))]α(λ	NOUN
ejpam-4277	253	6	,	,	PUNCT
ejpam-4277	253	7	sp	sp	NOUN
ejpam-4277	253	8	)	)	PUNCT
ejpam-4277	253	9	for	for	ADP
ejpam-4277	253	10	any	any	DET
ejpam-4277	253	11	v	v	NOUN
ejpam-4277	253	12	∈	∈	PROPN
ejpam-4277	253	13	pλspo(y	pλspo(y	PROPN
ejpam-4277	253	14	,	,	PUNCT
ejpam-4277	253	15	σ	σ	PROPN
ejpam-4277	253	16	)	)	PUNCT
ejpam-4277	253	17	.	.	PUNCT
ejpam-4277	254	1	acknowledgements	acknowledgement	NOUN
ejpam-4277	254	2	this	this	DET
ejpam-4277	254	3	research	research	NOUN
ejpam-4277	254	4	project	project	NOUN
ejpam-4277	254	5	was	be	AUX
ejpam-4277	254	6	financially	financially	ADV
ejpam-4277	254	7	supported	support	VERB
ejpam-4277	254	8	by	by	ADP
ejpam-4277	254	9	mahasarakham	mahasarakham	PROPN
ejpam-4277	254	10	university	university	PROPN
ejpam-4277	254	11	.	.	PUNCT
ejpam-4277	255	1	references	reference	NOUN
ejpam-4277	255	2	[	[	X
ejpam-4277	255	3	1	1	X
ejpam-4277	255	4	]	]	PUNCT
ejpam-4277	255	5	d.	d.	PROPN
ejpam-4277	255	6	andrijević	andrijević	PROPN
ejpam-4277	255	7	.	.	PUNCT
ejpam-4277	256	1	on	on	ADP
ejpam-4277	256	2	b	b	X
ejpam-4277	256	3	-	-	PUNCT
ejpam-4277	256	4	open	open	ADJ
ejpam-4277	256	5	sets	set	NOUN
ejpam-4277	256	6	.	.	PUNCT
ejpam-4277	257	1	matematički	matematički	PROPN
ejpam-4277	257	2	vesnik	vesnik	PROPN
ejpam-4277	257	3	,	,	PUNCT
ejpam-4277	257	4	48:56–64	48:56–64	PROPN
ejpam-4277	257	5	,	,	PUNCT
ejpam-4277	257	6	1996	1996	NUM
ejpam-4277	257	7	.	.	PUNCT
ejpam-4277	258	1	[	[	X
ejpam-4277	258	2	2	2	NUM
ejpam-4277	258	3	]	]	PUNCT
ejpam-4277	258	4	c.	c.	PROPN
ejpam-4277	258	5	berge	berge	PROPN
ejpam-4277	258	6	.	.	PUNCT
ejpam-4277	258	7	espaces	espace	VERB
ejpam-4277	258	8	topologiques	topologique	NOUN
ejpam-4277	258	9	fonctions	fonction	NOUN
ejpam-4277	258	10	multivoques	multivoque	NOUN
ejpam-4277	258	11	.	.	PUNCT
ejpam-4277	259	1	dunod	dunod	PROPN
ejpam-4277	259	2	,	,	PUNCT
ejpam-4277	259	3	paris	paris	PROPN
ejpam-4277	259	4	,	,	PUNCT
ejpam-4277	259	5	1959	1959	NUM
ejpam-4277	259	6	.	.	PUNCT
ejpam-4277	260	1	[	[	X
ejpam-4277	260	2	3	3	X
ejpam-4277	260	3	]	]	PUNCT
ejpam-4277	260	4	c.	c.	PROPN
ejpam-4277	260	5	boonpok	boonpok	PROPN
ejpam-4277	260	6	.	.	PUNCT
ejpam-4277	261	1	(	(	PUNCT
ejpam-4277	261	2	λ	λ	NOUN
ejpam-4277	261	3	,	,	PUNCT
ejpam-4277	261	4	sp)-closed	sp)-close	VERB
ejpam-4277	261	5	sets	set	NOUN
ejpam-4277	261	6	and	and	CCONJ
ejpam-4277	261	7	related	related	ADJ
ejpam-4277	261	8	topics	topic	NOUN
ejpam-4277	261	9	in	in	ADP
ejpam-4277	261	10	topological	topological	ADJ
ejpam-4277	261	11	spaces	space	NOUN
ejpam-4277	261	12	.	.	PUNCT
ejpam-4277	262	1	wseas	wseas	VERB
ejpam-4277	262	2	transactions	transaction	NOUN
ejpam-4277	262	3	on	on	ADP
ejpam-4277	262	4	mathematics	mathematic	NOUN
ejpam-4277	262	5	,	,	PUNCT
ejpam-4277	262	6	19:312–322	19:312–322	PROPN
ejpam-4277	262	7	,	,	PUNCT
ejpam-4277	262	8	2020	2020	NUM
ejpam-4277	262	9	.	.	PUNCT
ejpam-4277	263	1	[	[	X
ejpam-4277	263	2	4	4	X
ejpam-4277	263	3	]	]	PUNCT
ejpam-4277	263	4	m.	m.	NOUN
ejpam-4277	263	5	e.	e.	PROPN
ejpam-4277	263	6	abd	abd	PROPN
ejpam-4277	264	1	el	el	PROPN
ejpam-4277	264	2	-	-	PROPN
ejpam-4277	264	3	monsef	monsef	PROPN
ejpam-4277	264	4	,	,	PUNCT
ejpam-4277	264	5	s.	s.	PROPN
ejpam-4277	264	6	n.	n.	PROPN
ejpam-4277	264	7	el	el	PROPN
ejpam-4277	264	8	-	-	PROPN
ejpam-4277	264	9	deeb	deeb	PROPN
ejpam-4277	264	10	,	,	PUNCT
ejpam-4277	264	11	and	and	CCONJ
ejpam-4277	264	12	r.	r.	PROPN
ejpam-4277	264	13	a.	a.	PROPN
ejpam-4277	264	14	mahmoud	mahmoud	PROPN
ejpam-4277	264	15	.	.	PUNCT
ejpam-4277	265	1	β	β	X
ejpam-4277	265	2	-	-	ADJ
ejpam-4277	265	3	open	open	ADJ
ejpam-4277	265	4	sets	set	NOUN
ejpam-4277	265	5	and	and	CCONJ
ejpam-4277	265	6	βcontinuous	βcontinuous	ADJ
ejpam-4277	265	7	mappings	mapping	NOUN
ejpam-4277	265	8	.	.	PUNCT
ejpam-4277	266	1	bulletin	bulletin	NOUN
ejpam-4277	266	2	of	of	ADP
ejpam-4277	266	3	the	the	DET
ejpam-4277	266	4	faculty	faculty	NOUN
ejpam-4277	266	5	of	of	ADP
ejpam-4277	266	6	science	science	NOUN
ejpam-4277	266	7	.	.	PUNCT
ejpam-4277	267	1	assiut	assiut	PROPN
ejpam-4277	267	2	university	university	PROPN
ejpam-4277	267	3	.	.	PUNCT
ejpam-4277	267	4	,	,	PUNCT
ejpam-4277	267	5	12:77–90	12:77–90	NUM
ejpam-4277	267	6	,	,	PUNCT
ejpam-4277	267	7	1983	1983	NUM
ejpam-4277	267	8	.	.	PUNCT
ejpam-4277	268	1	[	[	X
ejpam-4277	268	2	5	5	NUM
ejpam-4277	268	3	]	]	PUNCT
ejpam-4277	268	4	a.	a.	NOUN
ejpam-4277	268	5	s.	s.	PROPN
ejpam-4277	268	6	mashhour	mashhour	PROPN
ejpam-4277	268	7	,	,	PUNCT
ejpam-4277	268	8	i.	i.	PROPN
ejpam-4277	268	9	a.	a.	PROPN
ejpam-4277	268	10	hasanein	hasanein	PROPN
ejpam-4277	268	11	,	,	PUNCT
ejpam-4277	268	12	and	and	CCONJ
ejpam-4277	268	13	s.	s.	PROPN
ejpam-4277	268	14	n.	n.	PROPN
ejpam-4277	268	15	el	el	PROPN
ejpam-4277	268	16	-	-	PROPN
ejpam-4277	268	17	deeb	deeb	PROPN
ejpam-4277	268	18	.	.	PUNCT
ejpam-4277	269	1	α	α	X
ejpam-4277	269	2	-	-	ADJ
ejpam-4277	269	3	continuous	continuous	ADJ
ejpam-4277	269	4	and	and	CCONJ
ejpam-4277	269	5	α	α	NOUN
ejpam-4277	269	6	-	-	ADJ
ejpam-4277	269	7	open	open	ADJ
ejpam-4277	269	8	mappings	mapping	NOUN
ejpam-4277	269	9	.	.	PUNCT
ejpam-4277	270	1	acta	acta	PROPN
ejpam-4277	270	2	mathematica	mathematica	PROPN
ejpam-4277	270	3	hungarica	hungarica	PROPN
ejpam-4277	270	4	,	,	PUNCT
ejpam-4277	270	5	41:213–218	41:213–218	PROPN
ejpam-4277	270	6	,	,	PUNCT
ejpam-4277	270	7	1983	1983	NUM
ejpam-4277	270	8	.	.	PUNCT
ejpam-4277	271	1	[	[	X
ejpam-4277	271	2	6	6	NUM
ejpam-4277	271	3	]	]	PUNCT
ejpam-4277	271	4	t.	t.	PROPN
ejpam-4277	271	5	noiri	noiri	PROPN
ejpam-4277	271	6	.	.	PUNCT
ejpam-4277	272	1	almost	almost	ADV
ejpam-4277	272	2	α	α	NUM
ejpam-4277	272	3	-	-	ADJ
ejpam-4277	272	4	continuous	continuous	ADJ
ejpam-4277	272	5	functions	function	NOUN
ejpam-4277	272	6	.	.	PUNCT
ejpam-4277	273	1	kyungpook	kyungpook	PROPN
ejpam-4277	273	2	mathematical	mathematical	PROPN
ejpam-4277	273	3	journal	journal	NOUN
ejpam-4277	273	4	,	,	PUNCT
ejpam-4277	273	5	28(1):71–77	28(1):71–77	NUM
ejpam-4277	273	6	,	,	PUNCT
ejpam-4277	273	7	1988	1988	NUM
ejpam-4277	273	8	.	.	PUNCT
ejpam-4277	274	1	[	[	X
ejpam-4277	274	2	7	7	X
ejpam-4277	274	3	]	]	PUNCT
ejpam-4277	274	4	t.	t.	PROPN
ejpam-4277	274	5	noiri	noiri	PROPN
ejpam-4277	274	6	and	and	CCONJ
ejpam-4277	274	7	e.	e.	PROPN
ejpam-4277	274	8	hatir	hatir	PROPN
ejpam-4277	274	9	.	.	PUNCT
ejpam-4277	274	10	λsp	λsp	NOUN
ejpam-4277	274	11	-	-	PUNCT
ejpam-4277	274	12	sets	set	NOUN
ejpam-4277	274	13	and	and	CCONJ
ejpam-4277	274	14	some	some	DET
ejpam-4277	274	15	weak	weak	ADJ
ejpam-4277	274	16	separation	separation	NOUN
ejpam-4277	274	17	axioms	axiom	NOUN
ejpam-4277	274	18	.	.	PUNCT
ejpam-4277	275	1	acta	acta	PROPN
ejpam-4277	275	2	mathematica	mathematica	PROPN
ejpam-4277	275	3	hungarica	hungarica	PROPN
ejpam-4277	275	4	,	,	PUNCT
ejpam-4277	275	5	103(3):225–232	103(3):225–232	NUM
ejpam-4277	275	6	,	,	PUNCT
ejpam-4277	275	7	2004	2004	NUM
ejpam-4277	275	8	.	.	PUNCT
ejpam-4277	276	1	[	[	X
ejpam-4277	276	2	8	8	NUM
ejpam-4277	276	3	]	]	PUNCT
ejpam-4277	276	4	v.	v.	CCONJ
ejpam-4277	276	5	popa	popa	NOUN
ejpam-4277	276	6	and	and	CCONJ
ejpam-4277	276	7	t.	t.	PROPN
ejpam-4277	276	8	noiri	noiri	PROPN
ejpam-4277	276	9	.	.	PUNCT
ejpam-4277	277	1	almost	almost	ADV
ejpam-4277	277	2	α	α	NUM
ejpam-4277	277	3	-	-	ADJ
ejpam-4277	277	4	continuous	continuous	ADJ
ejpam-4277	277	5	multifunctions	multifunction	NOUN
ejpam-4277	277	6	.	.	PUNCT
ejpam-4277	278	1	filomat	filomat	NOUN
ejpam-4277	278	2	,	,	PUNCT
ejpam-4277	278	3	12(1):39–52	12(1):39–52	NUM
ejpam-4277	278	4	,	,	PUNCT
ejpam-4277	278	5	1998	1998	NUM
ejpam-4277	278	6	.	.	PUNCT