id	sid	tid	token	lemma	pos
ejpam-4303	1	1	european	european	PROPN
ejpam-4303	1	2	journal	journal	PROPN
ejpam-4303	1	3	of	of	ADP
ejpam-4303	1	4	pure	pure	ADJ
ejpam-4303	1	5	and	and	CCONJ
ejpam-4303	1	6	applied	apply	VERB
ejpam-4303	1	7	mathematics	mathematic	NOUN
ejpam-4303	1	8	vol	vol	NOUN
ejpam-4303	1	9	.	.	PROPN
ejpam-4303	2	1	15	15	NUM
ejpam-4303	2	2	,	,	PUNCT
ejpam-4303	2	3	no	no	INTJ
ejpam-4303	2	4	.	.	NOUN
ejpam-4303	2	5	2	2	NUM
ejpam-4303	2	6	,	,	PUNCT
ejpam-4303	2	7	2022	2022	NUM
ejpam-4303	2	8	,	,	PUNCT
ejpam-4303	2	9	528	528	NUM
ejpam-4303	2	10	-	-	SYM
ejpam-4303	2	11	536	536	NUM
ejpam-4303	2	12	issn	issn	PROPN
ejpam-4303	2	13	1307	1307	NUM
ejpam-4303	2	14	-	-	SYM
ejpam-4303	2	15	5543	5543	NUM
ejpam-4303	2	16	–	–	PUNCT
ejpam-4303	2	17	ejpam.com	ejpam.com	X
ejpam-4303	2	18	published	publish	VERB
ejpam-4303	2	19	by	by	ADP
ejpam-4303	2	20	new	new	PROPN
ejpam-4303	2	21	york	york	PROPN
ejpam-4303	2	22	business	business	PROPN
ejpam-4303	2	23	global	global	ADJ
ejpam-4303	2	24	weakly	weakly	ADJ
ejpam-4303	2	25	(	(	PUNCT
ejpam-4303	2	26	λ	λ	NOUN
ejpam-4303	2	27	,	,	PUNCT
ejpam-4303	2	28	sp)-continuous	sp)-continuous	ADJ
ejpam-4303	2	29	multifunctions	multifunction	NOUN
ejpam-4303	2	30	chawalit	chawalit	VERB
ejpam-4303	2	31	boonpok1	boonpok1	PROPN
ejpam-4303	2	32	,	,	PUNCT
ejpam-4303	2	33	chokchai	chokchai	ADJ
ejpam-4303	2	34	viriyapong1,∗	viriyapong1,∗	NOUN
ejpam-4303	2	35	1	1	NUM
ejpam-4303	2	36	mathematics	mathematic	NOUN
ejpam-4303	2	37	and	and	CCONJ
ejpam-4303	2	38	applied	apply	VERB
ejpam-4303	2	39	mathematics	mathematics	PROPN
ejpam-4303	2	40	research	research	NOUN
ejpam-4303	2	41	unit	unit	NOUN
ejpam-4303	2	42	,	,	PUNCT
ejpam-4303	2	43	department	department	NOUN
ejpam-4303	2	44	of	of	ADP
ejpam-4303	2	45	mathematics	mathematic	NOUN
ejpam-4303	2	46	,	,	PUNCT
ejpam-4303	2	47	faculty	faculty	NOUN
ejpam-4303	2	48	of	of	ADP
ejpam-4303	2	49	science	science	NOUN
ejpam-4303	2	50	,	,	PUNCT
ejpam-4303	2	51	mahasarakham	mahasarakham	PROPN
ejpam-4303	2	52	university	university	PROPN
ejpam-4303	2	53	,	,	PUNCT
ejpam-4303	2	54	maha	maha	PROPN
ejpam-4303	2	55	sarakham	sarakham	PROPN
ejpam-4303	2	56	,	,	PUNCT
ejpam-4303	2	57	44150	44150	NUM
ejpam-4303	2	58	,	,	PUNCT
ejpam-4303	2	59	thailand	thailand	PROPN
ejpam-4303	2	60	abstract	abstract	PROPN
ejpam-4303	2	61	.	.	PUNCT
ejpam-4303	3	1	this	this	DET
ejpam-4303	3	2	paper	paper	NOUN
ejpam-4303	3	3	is	be	AUX
ejpam-4303	3	4	deals	deal	NOUN
ejpam-4303	3	5	with	with	ADP
ejpam-4303	3	6	the	the	DET
ejpam-4303	3	7	concept	concept	NOUN
ejpam-4303	3	8	of	of	ADP
ejpam-4303	3	9	weakly	weakly	ADJ
ejpam-4303	3	10	(	(	PUNCT
ejpam-4303	3	11	λ	λ	NOUN
ejpam-4303	3	12	,	,	PUNCT
ejpam-4303	3	13	sp)-continuous	sp)-continuous	ADJ
ejpam-4303	3	14	multifunctions	multifunction	NOUN
ejpam-4303	3	15	.	.	PUNCT
ejpam-4303	4	1	in	in	ADP
ejpam-4303	4	2	particular	particular	ADJ
ejpam-4303	4	3	,	,	PUNCT
ejpam-4303	4	4	some	some	DET
ejpam-4303	4	5	characterizations	characterization	NOUN
ejpam-4303	4	6	of	of	ADP
ejpam-4303	4	7	weakly	weakly	ADJ
ejpam-4303	4	8	(	(	PUNCT
ejpam-4303	4	9	λ	λ	NOUN
ejpam-4303	4	10	,	,	PUNCT
ejpam-4303	4	11	sp)-continuous	sp)-continuous	ADJ
ejpam-4303	4	12	multifunctions	multifunction	NOUN
ejpam-4303	4	13	are	be	AUX
ejpam-4303	4	14	investigated	investigate	VERB
ejpam-4303	4	15	.	.	PUNCT
ejpam-4303	5	1	2020	2020	NUM
ejpam-4303	5	2	mathematics	mathematic	NOUN
ejpam-4303	5	3	subject	subject	NOUN
ejpam-4303	5	4	classifications	classification	NOUN
ejpam-4303	5	5	:	:	PUNCT
ejpam-4303	5	6	54c08	54c08	NUM
ejpam-4303	5	7	,	,	PUNCT
ejpam-4303	5	8	54c60	54c60	NUM
ejpam-4303	5	9	key	key	ADJ
ejpam-4303	5	10	words	word	NOUN
ejpam-4303	5	11	and	and	CCONJ
ejpam-4303	5	12	phrases	phrase	NOUN
ejpam-4303	5	13	:	:	PUNCT
ejpam-4303	5	14	(	(	PUNCT
ejpam-4303	5	15	λ	λ	NOUN
ejpam-4303	5	16	,	,	PUNCT
ejpam-4303	5	17	sp)-open	sp)-open	ADJ
ejpam-4303	5	18	set	set	NOUN
ejpam-4303	5	19	,	,	PUNCT
ejpam-4303	5	20	weakly	weakly	ADJ
ejpam-4303	5	21	(	(	PUNCT
ejpam-4303	5	22	λ	λ	NOUN
ejpam-4303	5	23	,	,	PUNCT
ejpam-4303	5	24	sp)-continuous	sp)-continuous	ADJ
ejpam-4303	5	25	multifunction	multifunction	NOUN
ejpam-4303	5	26	1	1	NUM
ejpam-4303	5	27	.	.	PUNCT
ejpam-4303	5	28	introduction	introduction	NOUN
ejpam-4303	5	29	the	the	DET
ejpam-4303	5	30	branch	branch	NOUN
ejpam-4303	5	31	of	of	ADP
ejpam-4303	5	32	mathematics	mathematic	NOUN
ejpam-4303	5	33	called	call	VERB
ejpam-4303	5	34	topology	topology	NOUN
ejpam-4303	5	35	is	be	AUX
ejpam-4303	5	36	concerned	concern	VERB
ejpam-4303	5	37	with	with	ADP
ejpam-4303	5	38	all	all	DET
ejpam-4303	5	39	questions	question	NOUN
ejpam-4303	5	40	directly	directly	ADV
ejpam-4303	5	41	or	or	CCONJ
ejpam-4303	5	42	indirectly	indirectly	ADV
ejpam-4303	5	43	related	relate	VERB
ejpam-4303	5	44	to	to	ADP
ejpam-4303	5	45	continuity	continuity	NOUN
ejpam-4303	5	46	.	.	PUNCT
ejpam-4303	6	1	the	the	DET
ejpam-4303	6	2	topological	topological	ADJ
ejpam-4303	6	3	structures	structure	NOUN
ejpam-4303	6	4	of	of	ADP
ejpam-4303	6	5	set	set	NOUN
ejpam-4303	6	6	theories	theory	NOUN
ejpam-4303	6	7	dealing	deal	VERB
ejpam-4303	6	8	with	with	ADP
ejpam-4303	6	9	uncertainities	uncertainitie	NOUN
ejpam-4303	6	10	were	be	AUX
ejpam-4303	6	11	first	first	ADV
ejpam-4303	6	12	introduced	introduce	VERB
ejpam-4303	6	13	by	by	ADP
ejpam-4303	6	14	chang	chang	PROPN
ejpam-4303	7	1	[	[	X
ejpam-4303	7	2	5	5	NUM
ejpam-4303	7	3	]	]	PUNCT
ejpam-4303	7	4	.	.	PUNCT
ejpam-4303	8	1	lashin	lashin	PROPN
ejpam-4303	8	2	et	et	PROPN
ejpam-4303	8	3	al	al	PROPN
ejpam-4303	8	4	.	.	PUNCT
ejpam-4303	9	1	[	[	X
ejpam-4303	9	2	9	9	NUM
ejpam-4303	9	3	]	]	PUNCT
ejpam-4303	9	4	investigated	investigate	VERB
ejpam-4303	9	5	topological	topological	ADJ
ejpam-4303	9	6	spaces	space	NOUN
ejpam-4303	9	7	by	by	ADP
ejpam-4303	9	8	generalizing	generalize	VERB
ejpam-4303	9	9	rough	rough	ADJ
ejpam-4303	9	10	set	set	NOUN
ejpam-4303	9	11	theory	theory	NOUN
ejpam-4303	9	12	.	.	PUNCT
ejpam-4303	10	1	the	the	DET
ejpam-4303	10	2	concept	concept	NOUN
ejpam-4303	10	3	of	of	ADP
ejpam-4303	10	4	soft	soft	ADJ
ejpam-4303	10	5	topological	topological	ADJ
ejpam-4303	10	6	spaces	space	NOUN
ejpam-4303	10	7	defined	define	VERB
ejpam-4303	10	8	by	by	ADP
ejpam-4303	10	9	shabir	shabir	PROPN
ejpam-4303	10	10	and	and	CCONJ
ejpam-4303	10	11	naz	naz	PROPN
ejpam-4303	10	12	[	[	X
ejpam-4303	10	13	17	17	NUM
ejpam-4303	10	14	]	]	PUNCT
ejpam-4303	10	15	on	on	ADP
ejpam-4303	10	16	an	an	DET
ejpam-4303	10	17	initial	initial	ADJ
ejpam-4303	10	18	universe	universe	NOUN
ejpam-4303	10	19	with	with	ADP
ejpam-4303	10	20	a	a	DET
ejpam-4303	10	21	fixed	fix	VERB
ejpam-4303	10	22	set	set	NOUN
ejpam-4303	10	23	of	of	ADP
ejpam-4303	10	24	parameters	parameter	NOUN
ejpam-4303	10	25	.	.	PUNCT
ejpam-4303	11	1	şenel	şenel	PROPN
ejpam-4303	11	2	and	and	CCONJ
ejpam-4303	11	3	çağman	çağman	NOUN
ejpam-4303	11	4	[	[	X
ejpam-4303	11	5	7	7	NUM
ejpam-4303	11	6	]	]	PUNCT
ejpam-4303	11	7	extended	extend	VERB
ejpam-4303	11	8	the	the	DET
ejpam-4303	11	9	concept	concept	NOUN
ejpam-4303	11	10	of	of	ADP
ejpam-4303	11	11	bitopological	bitopological	ADJ
ejpam-4303	11	12	spaces	space	NOUN
ejpam-4303	11	13	to	to	ADP
ejpam-4303	11	14	soft	soft	ADJ
ejpam-4303	11	15	bitopological	bitopological	ADJ
ejpam-4303	11	16	spaces	space	NOUN
ejpam-4303	11	17	.	.	PUNCT
ejpam-4303	12	1	şenel	şenel	PROPN
ejpam-4303	13	1	[	[	X
ejpam-4303	13	2	6	6	NUM
ejpam-4303	13	3	]	]	PUNCT
ejpam-4303	13	4	presented	present	VERB
ejpam-4303	13	5	the	the	DET
ejpam-4303	13	6	notion	notion	NOUN
ejpam-4303	13	7	of	of	ADP
ejpam-4303	13	8	soft	soft	ADJ
ejpam-4303	13	9	bitopological	bitopological	ADJ
ejpam-4303	13	10	hausdorff	hausdorff	NOUN
ejpam-4303	13	11	spaces	space	NOUN
ejpam-4303	13	12	and	and	CCONJ
ejpam-4303	13	13	introduced	introduce	VERB
ejpam-4303	13	14	some	some	DET
ejpam-4303	13	15	new	new	ADJ
ejpam-4303	13	16	notions	notion	NOUN
ejpam-4303	13	17	in	in	ADP
ejpam-4303	13	18	soft	soft	ADJ
ejpam-4303	13	19	bitopological	bitopological	ADJ
ejpam-4303	13	20	spaces	space	NOUN
ejpam-4303	13	21	such	such	ADJ
ejpam-4303	13	22	as	as	ADP
ejpam-4303	13	23	sbt	sbt	PROPN
ejpam-4303	13	24	points	point	NOUN
ejpam-4303	13	25	,	,	PUNCT
ejpam-4303	13	26	sbt	sbt	PROPN
ejpam-4303	13	27	continuous	continuous	ADJ
ejpam-4303	13	28	functions	function	NOUN
ejpam-4303	13	29	and	and	CCONJ
ejpam-4303	13	30	sbt	sbt	PROPN
ejpam-4303	13	31	homeomorphisms	homeomorphisms	PROPN
ejpam-4303	13	32	.	.	PUNCT
ejpam-4303	14	1	continuity	continuity	NOUN
ejpam-4303	14	2	is	be	AUX
ejpam-4303	14	3	a	a	DET
ejpam-4303	14	4	basic	basic	ADJ
ejpam-4303	14	5	concept	concept	NOUN
ejpam-4303	14	6	for	for	ADP
ejpam-4303	14	7	the	the	DET
ejpam-4303	14	8	study	study	NOUN
ejpam-4303	14	9	in	in	ADP
ejpam-4303	14	10	topological	topological	ADJ
ejpam-4303	14	11	spaces	space	NOUN
ejpam-4303	14	12	.	.	PUNCT
ejpam-4303	15	1	semi	semi	ADJ
ejpam-4303	15	2	-	-	ADJ
ejpam-4303	15	3	open	open	ADJ
ejpam-4303	15	4	sets	set	NOUN
ejpam-4303	15	5	[	[	X
ejpam-4303	15	6	11	11	NUM
ejpam-4303	15	7	]	]	PUNCT
ejpam-4303	15	8	,	,	PUNCT
ejpam-4303	15	9	preopen	preopen	ADJ
ejpam-4303	15	10	sets	set	NOUN
ejpam-4303	15	11	[	[	X
ejpam-4303	15	12	12	12	NUM
ejpam-4303	15	13	]	]	PUNCT
ejpam-4303	15	14	and	and	CCONJ
ejpam-4303	15	15	β	β	X
ejpam-4303	15	16	-	-	ADJ
ejpam-4303	15	17	open	open	ADJ
ejpam-4303	15	18	sets	set	NOUN
ejpam-4303	15	19	[	[	X
ejpam-4303	15	20	8	8	NUM
ejpam-4303	15	21	]	]	PUNCT
ejpam-4303	15	22	play	play	VERB
ejpam-4303	15	23	an	an	DET
ejpam-4303	15	24	important	important	ADJ
ejpam-4303	15	25	role	role	NOUN
ejpam-4303	15	26	in	in	ADP
ejpam-4303	15	27	the	the	DET
ejpam-4303	15	28	researching	researching	NOUN
ejpam-4303	15	29	of	of	ADP
ejpam-4303	15	30	generalizations	generalization	NOUN
ejpam-4303	15	31	of	of	ADP
ejpam-4303	15	32	continuity	continuity	NOUN
ejpam-4303	15	33	in	in	ADP
ejpam-4303	15	34	topological	topological	ADJ
ejpam-4303	15	35	spaces	space	NOUN
ejpam-4303	15	36	.	.	PUNCT
ejpam-4303	16	1	by	by	ADP
ejpam-4303	16	2	using	use	VERB
ejpam-4303	16	3	these	these	DET
ejpam-4303	16	4	sets	set	NOUN
ejpam-4303	16	5	many	many	ADJ
ejpam-4303	16	6	authors	author	NOUN
ejpam-4303	16	7	introduced	introduce	VERB
ejpam-4303	16	8	and	and	CCONJ
ejpam-4303	16	9	studied	study	VERB
ejpam-4303	16	10	various	various	ADJ
ejpam-4303	16	11	types	type	NOUN
ejpam-4303	16	12	of	of	ADP
ejpam-4303	16	13	weak	weak	ADJ
ejpam-4303	16	14	forms	form	NOUN
ejpam-4303	16	15	of	of	ADP
ejpam-4303	16	16	continuity	continuity	NOUN
ejpam-4303	16	17	for	for	ADP
ejpam-4303	16	18	functions	function	NOUN
ejpam-4303	16	19	and	and	CCONJ
ejpam-4303	16	20	multifunctions	multifunction	NOUN
ejpam-4303	16	21	.	.	PUNCT
ejpam-4303	17	1	levine	levine	PROPN
ejpam-4303	18	1	[	[	X
ejpam-4303	18	2	10	10	NUM
ejpam-4303	18	3	]	]	PUNCT
ejpam-4303	18	4	introduced	introduce	VERB
ejpam-4303	18	5	the	the	DET
ejpam-4303	18	6	concept	concept	NOUN
ejpam-4303	18	7	of	of	ADP
ejpam-4303	18	8	weakly	weakly	ADJ
ejpam-4303	18	9	continuous	continuous	ADJ
ejpam-4303	18	10	functions	function	NOUN
ejpam-4303	18	11	.	.	PUNCT
ejpam-4303	19	1	popa	popa	NOUN
ejpam-4303	20	1	[	[	X
ejpam-4303	20	2	14	14	NUM
ejpam-4303	20	3	]	]	PUNCT
ejpam-4303	20	4	and	and	CCONJ
ejpam-4303	20	5	smithson	smithson	PROPN
ejpam-4303	20	6	[	[	X
ejpam-4303	20	7	18	18	NUM
ejpam-4303	20	8	]	]	PUNCT
ejpam-4303	20	9	independently	independently	ADV
ejpam-4303	20	10	introduced	introduce	VERB
ejpam-4303	20	11	the	the	DET
ejpam-4303	20	12	notion	notion	NOUN
ejpam-4303	20	13	of	of	ADP
ejpam-4303	20	14	weakly	weakly	ADJ
ejpam-4303	20	15	continuous	continuous	ADJ
ejpam-4303	20	16	multifunctions	multifunction	NOUN
ejpam-4303	20	17	.	.	PUNCT
ejpam-4303	21	1	in	in	ADP
ejpam-4303	21	2	[	[	X
ejpam-4303	21	3	15	15	NUM
ejpam-4303	21	4	]	]	PUNCT
ejpam-4303	21	5	,	,	PUNCT
ejpam-4303	21	6	the	the	DET
ejpam-4303	21	7	present	present	ADJ
ejpam-4303	21	8	authors	author	NOUN
ejpam-4303	21	9	introduced	introduce	VERB
ejpam-4303	21	10	a	a	DET
ejpam-4303	21	11	class	class	NOUN
ejpam-4303	21	12	of	of	ADP
ejpam-4303	21	13	multifunctions	multifunction	NOUN
ejpam-4303	21	14	called	call	VERB
ejpam-4303	21	15	weakly	weakly	ADJ
ejpam-4303	21	16	α	α	ADJ
ejpam-4303	21	17	-	-	ADJ
ejpam-4303	21	18	continuous	continuous	ADJ
ejpam-4303	21	19	multifunctions	multifunction	NOUN
ejpam-4303	21	20	.	.	PUNCT
ejpam-4303	22	1	some	some	DET
ejpam-4303	22	2	characterizations	characterization	NOUN
ejpam-4303	22	3	of	of	ADP
ejpam-4303	22	4	weakly	weakly	ADJ
ejpam-4303	22	5	α	α	ADJ
ejpam-4303	22	6	-	-	ADJ
ejpam-4303	22	7	continuous	continuous	ADJ
ejpam-4303	22	8	multifunctions	multifunction	NOUN
ejpam-4303	22	9	are	be	AUX
ejpam-4303	22	10	investigated	investigate	VERB
ejpam-4303	22	11	in	in	ADP
ejpam-4303	22	12	[	[	X
ejpam-4303	22	13	4	4	NUM
ejpam-4303	22	14	]	]	PUNCT
ejpam-4303	22	15	and	and	CCONJ
ejpam-4303	22	16	[	[	X
ejpam-4303	22	17	15	15	NUM
ejpam-4303	22	18	]	]	PUNCT
ejpam-4303	22	19	.	.	PUNCT
ejpam-4303	23	1	popa	popa	NOUN
ejpam-4303	23	2	and	and	CCONJ
ejpam-4303	23	3	noiri	noiri	ADV
ejpam-4303	24	1	[	[	X
ejpam-4303	24	2	16	16	NUM
ejpam-4303	24	3	]	]	PUNCT
ejpam-4303	24	4	investigated	investigate	VERB
ejpam-4303	24	5	several	several	ADJ
ejpam-4303	24	6	characterizations	characterization	NOUN
ejpam-4303	24	7	of	of	ADP
ejpam-4303	24	8	weakly	weakly	ADJ
ejpam-4303	24	9	β	β	ADJ
ejpam-4303	24	10	-	-	ADJ
ejpam-4303	24	11	continuous	continuous	ADJ
ejpam-4303	24	12	multifunctions	multifunction	NOUN
ejpam-4303	24	13	.	.	PUNCT
ejpam-4303	25	1	in	in	ADP
ejpam-4303	25	2	1983	1983	NUM
ejpam-4303	25	3	,	,	PUNCT
ejpam-4303	25	4	abd	abd	PROPN
ejpam-4303	25	5	el	el	PROPN
ejpam-4303	25	6	-	-	PROPN
ejpam-4303	25	7	monsef	monsef	PROPN
ejpam-4303	25	8	et	et	PROPN
ejpam-4303	25	9	al	al	PROPN
ejpam-4303	25	10	.	.	PUNCT
ejpam-4303	26	1	[	[	X
ejpam-4303	26	2	8	8	NUM
ejpam-4303	26	3	]	]	PUNCT
ejpam-4303	26	4	introduced	introduce	VERB
ejpam-4303	26	5	a	a	DET
ejpam-4303	26	6	weak	weak	ADJ
ejpam-4303	26	7	form	form	NOUN
ejpam-4303	26	8	of	of	ADP
ejpam-4303	26	9	open	open	ADJ
ejpam-4303	26	10	sets	set	NOUN
ejpam-4303	26	11	called	call	VERB
ejpam-4303	26	12	β	β	NOUN
ejpam-4303	26	13	-	-	ADJ
ejpam-4303	26	14	open	open	ADJ
ejpam-4303	26	15	sets	set	NOUN
ejpam-4303	26	16	.	.	PUNCT
ejpam-4303	27	1	this	this	DET
ejpam-4303	27	2	notion	notion	NOUN
ejpam-4303	27	3	was	be	AUX
ejpam-4303	27	4	also	also	ADV
ejpam-4303	27	5	called	call	VERB
ejpam-4303	27	6	semi	semi	ADJ
ejpam-4303	27	7	-	-	ADJ
ejpam-4303	27	8	preopen	preopen	ADJ
ejpam-4303	27	9	sets	set	NOUN
ejpam-4303	27	10	in	in	ADP
ejpam-4303	27	11	the	the	DET
ejpam-4303	27	12	sense	sense	NOUN
ejpam-4303	27	13	of	of	ADP
ejpam-4303	27	14	andrijević	andrijević	NOUN
ejpam-4303	27	15	[	[	X
ejpam-4303	27	16	1	1	NUM
ejpam-4303	27	17	]	]	PUNCT
ejpam-4303	27	18	.	.	PUNCT
ejpam-4303	28	1	in	in	ADP
ejpam-4303	28	2	2004	2004	NUM
ejpam-4303	28	3	,	,	PUNCT
ejpam-4303	28	4	noiri	noiri	PROPN
ejpam-4303	28	5	and	and	CCONJ
ejpam-4303	28	6	hatir	hatir	NOUN
ejpam-4303	29	1	[	[	X
ejpam-4303	29	2	13	13	NUM
ejpam-4303	29	3	]	]	PUNCT
ejpam-4303	29	4	introduced	introduce	VERB
ejpam-4303	29	5	the	the	DET
ejpam-4303	29	6	notion	notion	NOUN
ejpam-4303	29	7	of	of	ADP
ejpam-4303	29	8	∗corresponding	∗corresponde	VERB
ejpam-4303	29	9	author	author	NOUN
ejpam-4303	29	10	.	.	PUNCT
ejpam-4303	30	1	doi	doi	NOUN
ejpam-4303	30	2	:	:	PUNCT
ejpam-4303	30	3	https://doi.org/10.29020/nybg.ejpam.v15i2.4303	https://doi.org/10.29020/nybg.ejpam.v15i2.4303	ADJ
ejpam-4303	30	4	email	email	NOUN
ejpam-4303	30	5	addresses	address	NOUN
ejpam-4303	30	6	:	:	PUNCT
ejpam-4303	30	7	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	INTJ
ejpam-4303	30	8	(	(	PUNCT
ejpam-4303	30	9	c.	c.	PROPN
ejpam-4303	30	10	boonpok	boonpok	PROPN
ejpam-4303	30	11	)	)	PUNCT
ejpam-4303	30	12	,	,	PUNCT
ejpam-4303	30	13	chokchai.v@msu.ac.th	chokchai.v@msu.ac.th	INTJ
ejpam-4303	30	14	(	(	PUNCT
ejpam-4303	30	15	c.	c.	PROPN
ejpam-4303	30	16	viriyapong	viriyapong	PROPN
ejpam-4303	30	17	)	)	PUNCT
ejpam-4303	30	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4303	31	1	528	528	NUM
ejpam-4303	31	2	©	©	ADP
ejpam-4303	31	3	2022	2022	NUM
ejpam-4303	31	4	ejpam	ejpam	VERB
ejpam-4303	31	5	all	all	DET
ejpam-4303	31	6	rights	right	NOUN
ejpam-4303	31	7	reserved	reserve	VERB
ejpam-4303	31	8	.	.	PUNCT
ejpam-4303	32	1	c.	c.	PROPN
ejpam-4303	32	2	boonpok	boonpok	PROPN
ejpam-4303	32	3	,	,	PUNCT
ejpam-4303	32	4	c.	c.	PROPN
ejpam-4303	32	5	viriyapong	viriyapong	PROPN
ejpam-4303	32	6	/	/	SYM
ejpam-4303	32	7	eur	eur	PROPN
ejpam-4303	32	8	.	.	PUNCT
ejpam-4303	33	1	j.	j.	PROPN
ejpam-4303	33	2	pure	pure	PROPN
ejpam-4303	33	3	appl	appl	PROPN
ejpam-4303	33	4	.	.	PROPN
ejpam-4303	33	5	math	math	PROPN
ejpam-4303	33	6	,	,	PUNCT
ejpam-4303	33	7	15	15	NUM
ejpam-4303	33	8	(	(	PUNCT
ejpam-4303	33	9	2	2	NUM
ejpam-4303	33	10	)	)	PUNCT
ejpam-4303	33	11	(	(	PUNCT
ejpam-4303	33	12	2022	2022	NUM
ejpam-4303	33	13	)	)	PUNCT
ejpam-4303	33	14	,	,	PUNCT
ejpam-4303	33	15	528	528	NUM
ejpam-4303	33	16	-	-	SYM
ejpam-4303	33	17	536	536	NUM
ejpam-4303	33	18	529	529	NUM
ejpam-4303	33	19	λsp	λsp	NOUN
ejpam-4303	33	20	-	-	PUNCT
ejpam-4303	33	21	sets	set	NOUN
ejpam-4303	33	22	in	in	ADP
ejpam-4303	33	23	terms	term	NOUN
ejpam-4303	33	24	of	of	ADP
ejpam-4303	33	25	the	the	DET
ejpam-4303	33	26	concept	concept	NOUN
ejpam-4303	33	27	of	of	ADP
ejpam-4303	33	28	β	β	ADJ
ejpam-4303	33	29	-	-	ADJ
ejpam-4303	33	30	open	open	ADJ
ejpam-4303	33	31	sets	set	NOUN
ejpam-4303	33	32	and	and	CCONJ
ejpam-4303	33	33	investigated	investigate	VERB
ejpam-4303	33	34	the	the	DET
ejpam-4303	33	35	notion	notion	NOUN
ejpam-4303	33	36	of	of	ADP
ejpam-4303	33	37	λsp	λsp	NOUN
ejpam-4303	33	38	-	-	PUNCT
ejpam-4303	33	39	closed	close	VERB
ejpam-4303	33	40	sets	set	NOUN
ejpam-4303	33	41	by	by	ADP
ejpam-4303	33	42	using	use	VERB
ejpam-4303	33	43	λsp	λsp	NOUN
ejpam-4303	33	44	-	-	PUNCT
ejpam-4303	33	45	sets	set	NOUN
ejpam-4303	33	46	.	.	PUNCT
ejpam-4303	34	1	in	in	ADP
ejpam-4303	34	2	[	[	X
ejpam-4303	34	3	3	3	NUM
ejpam-4303	34	4	]	]	PUNCT
ejpam-4303	34	5	,	,	PUNCT
ejpam-4303	34	6	the	the	DET
ejpam-4303	34	7	author	author	NOUN
ejpam-4303	34	8	introduced	introduce	VERB
ejpam-4303	34	9	the	the	DET
ejpam-4303	34	10	concepts	concept	NOUN
ejpam-4303	34	11	of	of	ADP
ejpam-4303	34	12	(	(	PUNCT
ejpam-4303	34	13	λ	λ	PROPN
ejpam-4303	34	14	,	,	PUNCT
ejpam-4303	34	15	sp)-open	sp)-open	ADJ
ejpam-4303	34	16	sets	set	NOUN
ejpam-4303	34	17	and	and	CCONJ
ejpam-4303	34	18	(	(	PUNCT
ejpam-4303	34	19	λ	λ	PROPN
ejpam-4303	34	20	,	,	PUNCT
ejpam-4303	34	21	sp)-closed	sp)-close	VERB
ejpam-4303	34	22	sets	set	NOUN
ejpam-4303	34	23	which	which	PRON
ejpam-4303	34	24	are	be	AUX
ejpam-4303	34	25	defined	define	VERB
ejpam-4303	34	26	by	by	ADP
ejpam-4303	34	27	utilizing	utilize	VERB
ejpam-4303	34	28	the	the	DET
ejpam-4303	34	29	notions	notion	NOUN
ejpam-4303	34	30	of	of	ADP
ejpam-4303	34	31	λsp	λsp	NOUN
ejpam-4303	34	32	-	-	PUNCT
ejpam-4303	34	33	sets	set	NOUN
ejpam-4303	34	34	and	and	CCONJ
ejpam-4303	34	35	β	β	NOUN
ejpam-4303	34	36	-	-	ADJ
ejpam-4303	34	37	closed	closed	ADJ
ejpam-4303	34	38	sets	set	NOUN
ejpam-4303	34	39	.	.	PUNCT
ejpam-4303	35	1	the	the	DET
ejpam-4303	35	2	purpose	purpose	NOUN
ejpam-4303	35	3	of	of	ADP
ejpam-4303	35	4	the	the	DET
ejpam-4303	35	5	present	present	ADJ
ejpam-4303	35	6	paper	paper	NOUN
ejpam-4303	35	7	is	be	AUX
ejpam-4303	35	8	to	to	PART
ejpam-4303	35	9	introduce	introduce	VERB
ejpam-4303	35	10	the	the	DET
ejpam-4303	35	11	notion	notion	NOUN
ejpam-4303	35	12	of	of	ADP
ejpam-4303	35	13	weakly	weakly	ADJ
ejpam-4303	35	14	(	(	PUNCT
ejpam-4303	35	15	λ	λ	NOUN
ejpam-4303	35	16	,	,	PUNCT
ejpam-4303	35	17	sp)-continuous	sp)-continuous	ADJ
ejpam-4303	35	18	multifunctions	multifunction	NOUN
ejpam-4303	35	19	.	.	PUNCT
ejpam-4303	36	1	furthermore	furthermore	ADV
ejpam-4303	36	2	,	,	PUNCT
ejpam-4303	36	3	several	several	ADJ
ejpam-4303	36	4	characterizations	characterization	NOUN
ejpam-4303	36	5	of	of	ADP
ejpam-4303	36	6	weakly	weakly	ADJ
ejpam-4303	36	7	(	(	PUNCT
ejpam-4303	36	8	λ	λ	NOUN
ejpam-4303	36	9	,	,	PUNCT
ejpam-4303	36	10	sp)-continuous	sp)-continuous	ADJ
ejpam-4303	36	11	multifunctions	multifunction	NOUN
ejpam-4303	36	12	are	be	AUX
ejpam-4303	36	13	discussed	discuss	VERB
ejpam-4303	36	14	.	.	PUNCT
ejpam-4303	37	1	2	2	X
ejpam-4303	37	2	.	.	X
ejpam-4303	37	3	preliminaries	preliminary	NOUN
ejpam-4303	37	4	throughout	throughout	ADP
ejpam-4303	37	5	this	this	DET
ejpam-4303	37	6	paper	paper	NOUN
ejpam-4303	37	7	,	,	PUNCT
ejpam-4303	37	8	spaces	space	NOUN
ejpam-4303	37	9	(	(	PUNCT
ejpam-4303	37	10	x	x	X
ejpam-4303	37	11	,	,	PUNCT
ejpam-4303	37	12	τ	τ	X
ejpam-4303	37	13	)	)	PUNCT
ejpam-4303	37	14	and	and	CCONJ
ejpam-4303	37	15	(	(	PUNCT
ejpam-4303	37	16	y	y	PROPN
ejpam-4303	37	17	,	,	PUNCT
ejpam-4303	37	18	σ	σ	PROPN
ejpam-4303	37	19	)	)	PUNCT
ejpam-4303	37	20	(	(	PUNCT
ejpam-4303	37	21	or	or	CCONJ
ejpam-4303	37	22	simply	simply	ADV
ejpam-4303	37	23	x	x	X
ejpam-4303	37	24	and	and	CCONJ
ejpam-4303	37	25	y	y	PROPN
ejpam-4303	37	26	)	)	PUNCT
ejpam-4303	37	27	always	always	ADV
ejpam-4303	37	28	mean	mean	VERB
ejpam-4303	37	29	topological	topological	ADJ
ejpam-4303	37	30	spaces	space	NOUN
ejpam-4303	37	31	on	on	ADP
ejpam-4303	37	32	which	which	PRON
ejpam-4303	37	33	no	no	DET
ejpam-4303	37	34	separation	separation	NOUN
ejpam-4303	37	35	axioms	axiom	NOUN
ejpam-4303	37	36	are	be	AUX
ejpam-4303	37	37	assumed	assume	VERB
ejpam-4303	37	38	unless	unless	SCONJ
ejpam-4303	37	39	explicitly	explicitly	ADV
ejpam-4303	37	40	stated	state	VERB
ejpam-4303	37	41	.	.	PUNCT
ejpam-4303	38	1	let	let	VERB
ejpam-4303	38	2	a	a	DET
ejpam-4303	38	3	be	be	AUX
ejpam-4303	38	4	a	a	DET
ejpam-4303	38	5	subset	subset	NOUN
ejpam-4303	38	6	of	of	ADP
ejpam-4303	38	7	a	a	DET
ejpam-4303	38	8	topological	topological	ADJ
ejpam-4303	38	9	space	space	NOUN
ejpam-4303	38	10	(	(	PUNCT
ejpam-4303	38	11	x	x	X
ejpam-4303	38	12	,	,	PUNCT
ejpam-4303	38	13	τ	τ	PROPN
ejpam-4303	38	14	)	)	PUNCT
ejpam-4303	38	15	.	.	PUNCT
ejpam-4303	39	1	the	the	DET
ejpam-4303	39	2	closure	closure	NOUN
ejpam-4303	39	3	of	of	ADP
ejpam-4303	39	4	a	a	PRON
ejpam-4303	39	5	and	and	CCONJ
ejpam-4303	39	6	the	the	DET
ejpam-4303	39	7	interior	interior	NOUN
ejpam-4303	39	8	of	of	ADP
ejpam-4303	39	9	a	a	PRON
ejpam-4303	39	10	are	be	AUX
ejpam-4303	39	11	denoted	denote	VERB
ejpam-4303	39	12	by	by	ADP
ejpam-4303	39	13	cl(a	cl(a	NOUN
ejpam-4303	39	14	)	)	PUNCT
ejpam-4303	39	15	and	and	CCONJ
ejpam-4303	39	16	int(a	int(a	PROPN
ejpam-4303	39	17	)	)	PUNCT
ejpam-4303	39	18	,	,	PUNCT
ejpam-4303	39	19	respectively	respectively	ADV
ejpam-4303	39	20	.	.	PUNCT
ejpam-4303	40	1	a	a	DET
ejpam-4303	40	2	subset	subset	NOUN
ejpam-4303	40	3	a	a	PRON
ejpam-4303	40	4	of	of	ADP
ejpam-4303	40	5	a	a	DET
ejpam-4303	40	6	topological	topological	ADJ
ejpam-4303	40	7	space	space	NOUN
ejpam-4303	40	8	(	(	PUNCT
ejpam-4303	40	9	x	x	X
ejpam-4303	40	10	,	,	PUNCT
ejpam-4303	40	11	τ	τ	X
ejpam-4303	40	12	)	)	PUNCT
ejpam-4303	40	13	is	be	AUX
ejpam-4303	40	14	said	say	VERB
ejpam-4303	40	15	to	to	PART
ejpam-4303	40	16	be	be	AUX
ejpam-4303	40	17	β	β	X
ejpam-4303	40	18	-	-	ADJ
ejpam-4303	40	19	open	open	ADJ
ejpam-4303	40	20	[	[	X
ejpam-4303	40	21	8	8	NUM
ejpam-4303	40	22	]	]	X
ejpam-4303	40	23	if	if	SCONJ
ejpam-4303	40	24	a	a	DET
ejpam-4303	40	25	⊆	⊆	NUM
ejpam-4303	40	26	cl(int(cl(a	cl(int(cl(a	NOUN
ejpam-4303	40	27	)	)	PUNCT
ejpam-4303	40	28	)	)	PUNCT
ejpam-4303	40	29	)	)	PUNCT
ejpam-4303	40	30	.	.	PUNCT
ejpam-4303	41	1	the	the	DET
ejpam-4303	41	2	complement	complement	NOUN
ejpam-4303	41	3	of	of	ADP
ejpam-4303	41	4	a	a	DET
ejpam-4303	41	5	β	β	X
ejpam-4303	41	6	-	-	ADJ
ejpam-4303	41	7	open	open	ADJ
ejpam-4303	41	8	set	set	NOUN
ejpam-4303	41	9	is	be	AUX
ejpam-4303	41	10	called	call	VERB
ejpam-4303	41	11	β	β	NOUN
ejpam-4303	41	12	-	-	VERB
ejpam-4303	41	13	closed	closed	ADJ
ejpam-4303	41	14	.	.	PUNCT
ejpam-4303	42	1	the	the	DET
ejpam-4303	42	2	family	family	NOUN
ejpam-4303	42	3	of	of	ADP
ejpam-4303	42	4	all	all	DET
ejpam-4303	42	5	β	β	ADJ
ejpam-4303	42	6	-	-	ADJ
ejpam-4303	42	7	open	open	ADJ
ejpam-4303	42	8	sets	set	NOUN
ejpam-4303	42	9	of	of	ADP
ejpam-4303	42	10	a	a	DET
ejpam-4303	42	11	topological	topological	ADJ
ejpam-4303	42	12	space	space	NOUN
ejpam-4303	42	13	(	(	PUNCT
ejpam-4303	42	14	x	x	X
ejpam-4303	42	15	,	,	PUNCT
ejpam-4303	42	16	τ	τ	X
ejpam-4303	42	17	)	)	PUNCT
ejpam-4303	42	18	is	be	AUX
ejpam-4303	42	19	denoted	denote	VERB
ejpam-4303	42	20	by	by	ADP
ejpam-4303	42	21	β(x	β(x	PROPN
ejpam-4303	42	22	,	,	PUNCT
ejpam-4303	42	23	τ	τ	PROPN
ejpam-4303	42	24	)	)	PUNCT
ejpam-4303	42	25	.	.	PUNCT
ejpam-4303	43	1	a	a	DET
ejpam-4303	43	2	subset	subset	NOUN
ejpam-4303	43	3	λsp(a	λsp(a	NOUN
ejpam-4303	43	4	)	)	PUNCT
ejpam-4303	44	1	[	[	X
ejpam-4303	44	2	13	13	NUM
ejpam-4303	44	3	]	]	PUNCT
ejpam-4303	44	4	is	be	AUX
ejpam-4303	44	5	defined	define	VERB
ejpam-4303	44	6	as	as	SCONJ
ejpam-4303	44	7	follows	follow	VERB
ejpam-4303	44	8	:	:	PUNCT
ejpam-4303	44	9	λsp(a	λsp(a	NUM
ejpam-4303	44	10	)	)	PUNCT
ejpam-4303	44	11	=	=	PUNCT
ejpam-4303	45	1	∩{u	∩{u	PROPN
ejpam-4303	45	2	|	|	ADV
ejpam-4303	45	3	a	a	DET
ejpam-4303	45	4	⊆	⊆	NUM
ejpam-4303	45	5	u	u	NOUN
ejpam-4303	45	6	,	,	PUNCT
ejpam-4303	45	7	u	u	NOUN
ejpam-4303	45	8	∈	∈	PROPN
ejpam-4303	45	9	β(x	β(x	PROPN
ejpam-4303	45	10	,	,	PUNCT
ejpam-4303	45	11	τ	τ	X
ejpam-4303	45	12	)	)	PUNCT
ejpam-4303	45	13	}	}	PUNCT
ejpam-4303	45	14	.	.	PUNCT
ejpam-4303	46	1	a	a	DET
ejpam-4303	46	2	subset	subset	NOUN
ejpam-4303	46	3	b	b	NOUN
ejpam-4303	46	4	of	of	ADP
ejpam-4303	46	5	a	a	DET
ejpam-4303	46	6	topological	topological	ADJ
ejpam-4303	46	7	space	space	NOUN
ejpam-4303	46	8	(	(	PUNCT
ejpam-4303	46	9	x	x	X
ejpam-4303	46	10	,	,	PUNCT
ejpam-4303	46	11	τ	τ	X
ejpam-4303	46	12	)	)	PUNCT
ejpam-4303	46	13	is	be	AUX
ejpam-4303	46	14	called	call	VERB
ejpam-4303	46	15	a	a	DET
ejpam-4303	46	16	λsp	λsp	NOUN
ejpam-4303	46	17	-	-	PUNCT
ejpam-4303	46	18	set	set	VERB
ejpam-4303	46	19	[	[	X
ejpam-4303	46	20	13	13	NUM
ejpam-4303	46	21	]	]	PUNCT
ejpam-4303	46	22	if	if	SCONJ
ejpam-4303	46	23	b	b	PROPN
ejpam-4303	46	24	=	=	SYM
ejpam-4303	46	25	λsp(b	λsp(b	PROPN
ejpam-4303	46	26	)	)	PUNCT
ejpam-4303	46	27	.	.	PUNCT
ejpam-4303	47	1	a	a	DET
ejpam-4303	47	2	subset	subset	NOUN
ejpam-4303	47	3	a	a	PRON
ejpam-4303	47	4	of	of	ADP
ejpam-4303	47	5	a	a	DET
ejpam-4303	47	6	topological	topological	ADJ
ejpam-4303	47	7	space	space	NOUN
ejpam-4303	47	8	(	(	PUNCT
ejpam-4303	47	9	x	x	X
ejpam-4303	47	10	,	,	PUNCT
ejpam-4303	47	11	τ	τ	X
ejpam-4303	47	12	)	)	PUNCT
ejpam-4303	47	13	is	be	AUX
ejpam-4303	47	14	called	call	VERB
ejpam-4303	47	15	(	(	PUNCT
ejpam-4303	47	16	λ	λ	X
ejpam-4303	47	17	,	,	PUNCT
ejpam-4303	47	18	sp)-closed	sp)-close	VERB
ejpam-4303	47	19	[	[	PUNCT
ejpam-4303	47	20	3	3	X
ejpam-4303	47	21	]	]	X
ejpam-4303	47	22	if	if	SCONJ
ejpam-4303	47	23	a	a	DET
ejpam-4303	47	24	=	=	X
ejpam-4303	47	25	t	t	NOUN
ejpam-4303	47	26	∩c	∩c	NOUN
ejpam-4303	47	27	,	,	PUNCT
ejpam-4303	47	28	where	where	SCONJ
ejpam-4303	47	29	t	t	PROPN
ejpam-4303	47	30	is	be	AUX
ejpam-4303	47	31	a	a	DET
ejpam-4303	47	32	λsp	λsp	NOUN
ejpam-4303	47	33	-	-	PUNCT
ejpam-4303	47	34	set	set	VERB
ejpam-4303	47	35	and	and	CCONJ
ejpam-4303	47	36	c	c	NOUN
ejpam-4303	47	37	is	be	AUX
ejpam-4303	47	38	a	a	DET
ejpam-4303	47	39	β	β	NOUN
ejpam-4303	47	40	-	-	ADJ
ejpam-4303	47	41	closed	closed	ADJ
ejpam-4303	47	42	set	set	NOUN
ejpam-4303	47	43	.	.	PUNCT
ejpam-4303	48	1	the	the	DET
ejpam-4303	48	2	complement	complement	NOUN
ejpam-4303	48	3	of	of	ADP
ejpam-4303	48	4	a	a	DET
ejpam-4303	48	5	(	(	PUNCT
ejpam-4303	48	6	λ	λ	PROPN
ejpam-4303	48	7	,	,	PUNCT
ejpam-4303	48	8	sp)-closed	sp)-close	VERB
ejpam-4303	48	9	set	set	VERB
ejpam-4303	48	10	is	be	AUX
ejpam-4303	48	11	called	call	VERB
ejpam-4303	48	12	(	(	PUNCT
ejpam-4303	48	13	λ	λ	NOUN
ejpam-4303	48	14	,	,	PUNCT
ejpam-4303	48	15	sp)-open	sp)-open	NOUN
ejpam-4303	48	16	.	.	PUNCT
ejpam-4303	49	1	the	the	DET
ejpam-4303	49	2	family	family	NOUN
ejpam-4303	49	3	of	of	ADP
ejpam-4303	49	4	all	all	DET
ejpam-4303	49	5	(	(	PUNCT
ejpam-4303	49	6	λ	λ	NOUN
ejpam-4303	49	7	,	,	PUNCT
ejpam-4303	49	8	sp)-open	sp)-open	ADJ
ejpam-4303	49	9	sets	set	NOUN
ejpam-4303	49	10	in	in	ADP
ejpam-4303	49	11	a	a	DET
ejpam-4303	49	12	topological	topological	ADJ
ejpam-4303	49	13	space	space	NOUN
ejpam-4303	49	14	(	(	PUNCT
ejpam-4303	49	15	x	x	X
ejpam-4303	49	16	,	,	PUNCT
ejpam-4303	49	17	τ	τ	X
ejpam-4303	49	18	)	)	PUNCT
ejpam-4303	49	19	is	be	AUX
ejpam-4303	49	20	denoted	denote	VERB
ejpam-4303	49	21	by	by	ADP
ejpam-4303	49	22	λspo(x	λspo(x	PROPN
ejpam-4303	49	23	,	,	PUNCT
ejpam-4303	49	24	τ	τ	PROPN
ejpam-4303	49	25	)	)	PUNCT
ejpam-4303	49	26	.	.	PUNCT
ejpam-4303	50	1	let	let	VERB
ejpam-4303	50	2	a	a	DET
ejpam-4303	50	3	be	be	AUX
ejpam-4303	50	4	a	a	DET
ejpam-4303	50	5	subset	subset	NOUN
ejpam-4303	50	6	of	of	ADP
ejpam-4303	50	7	a	a	DET
ejpam-4303	50	8	topological	topological	ADJ
ejpam-4303	50	9	space	space	NOUN
ejpam-4303	50	10	(	(	PUNCT
ejpam-4303	50	11	x	x	X
ejpam-4303	50	12	,	,	PUNCT
ejpam-4303	50	13	τ	τ	PROPN
ejpam-4303	50	14	)	)	PUNCT
ejpam-4303	50	15	.	.	PUNCT
ejpam-4303	51	1	a	a	DET
ejpam-4303	51	2	point	point	NOUN
ejpam-4303	51	3	x	x	X
ejpam-4303	51	4	∈	∈	NOUN
ejpam-4303	51	5	x	x	PUNCT
ejpam-4303	51	6	is	be	AUX
ejpam-4303	51	7	called	call	VERB
ejpam-4303	51	8	a	a	DET
ejpam-4303	51	9	(	(	PUNCT
ejpam-4303	51	10	λ	λ	NOUN
ejpam-4303	51	11	,	,	PUNCT
ejpam-4303	51	12	sp)-cluster	sp)-cluster	NOUN
ejpam-4303	51	13	point	point	NOUN
ejpam-4303	51	14	[	[	X
ejpam-4303	51	15	3	3	X
ejpam-4303	51	16	]	]	PUNCT
ejpam-4303	51	17	of	of	ADP
ejpam-4303	51	18	a	a	PRON
ejpam-4303	52	1	if	if	SCONJ
ejpam-4303	52	2	a	a	DET
ejpam-4303	52	3	∩	∩	ADJ
ejpam-4303	52	4	u	u	NOUN
ejpam-4303	52	5	6=	6=	NOUN
ejpam-4303	52	6	∅	∅	NOUN
ejpam-4303	52	7	for	for	ADP
ejpam-4303	52	8	every	every	DET
ejpam-4303	52	9	(	(	PUNCT
ejpam-4303	52	10	λ	λ	NOUN
ejpam-4303	52	11	,	,	PUNCT
ejpam-4303	52	12	sp)-open	sp)-open	NOUN
ejpam-4303	52	13	set	set	VERB
ejpam-4303	52	14	u	u	NOUN
ejpam-4303	52	15	of	of	ADP
ejpam-4303	52	16	x	x	SYM
ejpam-4303	52	17	containing	contain	VERB
ejpam-4303	52	18	x.	x.	NOUN
ejpam-4303	52	19	the	the	DET
ejpam-4303	52	20	set	set	NOUN
ejpam-4303	52	21	of	of	ADP
ejpam-4303	52	22	all	all	DET
ejpam-4303	52	23	(	(	PUNCT
ejpam-4303	52	24	λ	λ	PROPN
ejpam-4303	52	25	,	,	PUNCT
ejpam-4303	52	26	sp)-cluster	sp)-cluster	NOUN
ejpam-4303	52	27	points	point	NOUN
ejpam-4303	52	28	of	of	ADP
ejpam-4303	52	29	a	a	PRON
ejpam-4303	52	30	is	be	AUX
ejpam-4303	52	31	called	call	VERB
ejpam-4303	52	32	the	the	DET
ejpam-4303	52	33	(	(	PUNCT
ejpam-4303	52	34	λ	λ	PROPN
ejpam-4303	52	35	,	,	PUNCT
ejpam-4303	52	36	sp)-closure	sp)-closure	NOUN
ejpam-4303	52	37	[	[	X
ejpam-4303	52	38	3	3	NUM
ejpam-4303	52	39	]	]	PUNCT
ejpam-4303	52	40	of	of	ADP
ejpam-4303	52	41	a	a	PRON
ejpam-4303	52	42	and	and	CCONJ
ejpam-4303	52	43	is	be	AUX
ejpam-4303	52	44	denoted	denote	VERB
ejpam-4303	52	45	by	by	ADP
ejpam-4303	52	46	a(λ	a(λ	ADV
ejpam-4303	52	47	,	,	PUNCT
ejpam-4303	52	48	sp	sp	NOUN
ejpam-4303	52	49	)	)	PUNCT
ejpam-4303	52	50	.	.	PUNCT
ejpam-4303	53	1	the	the	DET
ejpam-4303	53	2	union	union	NOUN
ejpam-4303	53	3	of	of	ADP
ejpam-4303	53	4	all	all	DET
ejpam-4303	53	5	(	(	PUNCT
ejpam-4303	53	6	λ	λ	NOUN
ejpam-4303	53	7	,	,	PUNCT
ejpam-4303	53	8	sp)-open	sp)-open	ADJ
ejpam-4303	53	9	sets	set	NOUN
ejpam-4303	53	10	contained	contain	VERB
ejpam-4303	53	11	in	in	ADP
ejpam-4303	53	12	a	a	PRON
ejpam-4303	53	13	is	be	AUX
ejpam-4303	53	14	called	call	VERB
ejpam-4303	53	15	the	the	DET
ejpam-4303	53	16	(	(	PUNCT
ejpam-4303	53	17	λ	λ	PROPN
ejpam-4303	53	18	,	,	PUNCT
ejpam-4303	53	19	sp)-interior	sp)-interior	NOUN
ejpam-4303	53	20	[	[	X
ejpam-4303	53	21	3	3	NUM
ejpam-4303	53	22	]	]	PUNCT
ejpam-4303	53	23	of	of	ADP
ejpam-4303	53	24	a	a	PRON
ejpam-4303	53	25	and	and	CCONJ
ejpam-4303	53	26	is	be	AUX
ejpam-4303	53	27	denoted	denote	VERB
ejpam-4303	53	28	by	by	ADP
ejpam-4303	53	29	a(λ	a(λ	ADV
ejpam-4303	53	30	,	,	PUNCT
ejpam-4303	53	31	sp	sp	NOUN
ejpam-4303	53	32	)	)	PUNCT
ejpam-4303	53	33	.	.	PUNCT
ejpam-4303	54	1	lemma	lemma	PROPN
ejpam-4303	54	2	1	1	NUM
ejpam-4303	54	3	.	.	PUNCT
ejpam-4303	55	1	[	[	X
ejpam-4303	55	2	3	3	X
ejpam-4303	55	3	]	]	PUNCT
ejpam-4303	55	4	let	let	VERB
ejpam-4303	55	5	a	a	PRON
ejpam-4303	55	6	and	and	CCONJ
ejpam-4303	55	7	b	b	NOUN
ejpam-4303	55	8	be	be	AUX
ejpam-4303	55	9	subsets	subset	NOUN
ejpam-4303	55	10	of	of	ADP
ejpam-4303	55	11	a	a	DET
ejpam-4303	55	12	topological	topological	ADJ
ejpam-4303	55	13	space	space	NOUN
ejpam-4303	55	14	(	(	PUNCT
ejpam-4303	55	15	x	x	X
ejpam-4303	55	16	,	,	PUNCT
ejpam-4303	55	17	τ	τ	PROPN
ejpam-4303	55	18	)	)	PUNCT
ejpam-4303	55	19	.	.	PUNCT
ejpam-4303	56	1	for	for	ADP
ejpam-4303	56	2	the	the	DET
ejpam-4303	56	3	(	(	PUNCT
ejpam-4303	56	4	λ	λ	PROPN
ejpam-4303	56	5	,	,	PUNCT
ejpam-4303	56	6	sp)-closure	sp)-closure	NOUN
ejpam-4303	56	7	,	,	PUNCT
ejpam-4303	56	8	the	the	DET
ejpam-4303	56	9	following	follow	VERB
ejpam-4303	56	10	properties	property	NOUN
ejpam-4303	56	11	hold	hold	VERB
ejpam-4303	56	12	:	:	PUNCT
ejpam-4303	56	13	(	(	PUNCT
ejpam-4303	56	14	1	1	X
ejpam-4303	56	15	)	)	PUNCT
ejpam-4303	56	16	a	a	DET
ejpam-4303	56	17	⊆	⊆	NUM
ejpam-4303	56	18	a(λ	a(λ	ADJ
ejpam-4303	56	19	,	,	PUNCT
ejpam-4303	56	20	sp	sp	NOUN
ejpam-4303	56	21	)	)	PUNCT
ejpam-4303	56	22	and	and	CCONJ
ejpam-4303	56	23	[	[	X
ejpam-4303	56	24	a(λ	a(λ	ADV
ejpam-4303	56	25	,	,	PUNCT
ejpam-4303	56	26	sp)](λ	sp)](λ	PROPN
ejpam-4303	56	27	,	,	PUNCT
ejpam-4303	56	28	sp	sp	NOUN
ejpam-4303	56	29	)	)	PUNCT
ejpam-4303	56	30	=	=	PUNCT
ejpam-4303	56	31	a(λ	a(λ	ADV
ejpam-4303	56	32	,	,	PUNCT
ejpam-4303	56	33	sp	sp	NOUN
ejpam-4303	56	34	)	)	PUNCT
ejpam-4303	56	35	.	.	PUNCT
ejpam-4303	57	1	(	(	PUNCT
ejpam-4303	57	2	2	2	X
ejpam-4303	57	3	)	)	PUNCT
ejpam-4303	57	4	if	if	SCONJ
ejpam-4303	57	5	a	a	DET
ejpam-4303	57	6	⊆	⊆	NUM
ejpam-4303	57	7	b	b	NOUN
ejpam-4303	57	8	,	,	PUNCT
ejpam-4303	57	9	then	then	ADV
ejpam-4303	57	10	a(λ	a(λ	ADV
ejpam-4303	57	11	,	,	PUNCT
ejpam-4303	57	12	sp	sp	NOUN
ejpam-4303	57	13	)	)	PUNCT
ejpam-4303	57	14	⊆	⊆	NUM
ejpam-4303	57	15	b(λ	b(λ	NOUN
ejpam-4303	57	16	,	,	PUNCT
ejpam-4303	57	17	sp	sp	NOUN
ejpam-4303	57	18	)	)	PUNCT
ejpam-4303	57	19	.	.	PUNCT
ejpam-4303	58	1	(	(	PUNCT
ejpam-4303	58	2	3	3	X
ejpam-4303	58	3	)	)	PUNCT
ejpam-4303	58	4	a(λ	a(λ	ADV
ejpam-4303	58	5	,	,	PUNCT
ejpam-4303	58	6	sp	sp	NOUN
ejpam-4303	58	7	)	)	PUNCT
ejpam-4303	58	8	=	=	SYM
ejpam-4303	58	9	∩{f	∩{f	NOUN
ejpam-4303	58	10	|a	|a	VERB
ejpam-4303	58	11	⊆	⊆	NUM
ejpam-4303	58	12	f	f	PROPN
ejpam-4303	58	13	and	and	CCONJ
ejpam-4303	58	14	f	f	PROPN
ejpam-4303	58	15	is	be	AUX
ejpam-4303	58	16	(	(	PUNCT
ejpam-4303	58	17	λ	λ	X
ejpam-4303	58	18	,	,	PUNCT
ejpam-4303	58	19	sp)-closed	sp)-close	VERB
ejpam-4303	58	20	}	}	PUNCT
ejpam-4303	58	21	.	.	PUNCT
ejpam-4303	59	1	(	(	PUNCT
ejpam-4303	59	2	4	4	NUM
ejpam-4303	59	3	)	)	PUNCT
ejpam-4303	59	4	a(λ	a(λ	ADV
ejpam-4303	59	5	,	,	PUNCT
ejpam-4303	59	6	sp	sp	NOUN
ejpam-4303	59	7	)	)	PUNCT
ejpam-4303	59	8	is	be	AUX
ejpam-4303	59	9	(	(	PUNCT
ejpam-4303	59	10	λ	λ	X
ejpam-4303	59	11	,	,	PUNCT
ejpam-4303	59	12	sp)-closed	sp)-close	VERB
ejpam-4303	59	13	.	.	PUNCT
ejpam-4303	60	1	(	(	PUNCT
ejpam-4303	60	2	5	5	X
ejpam-4303	60	3	)	)	PUNCT
ejpam-4303	60	4	a	a	PRON
ejpam-4303	60	5	is	be	AUX
ejpam-4303	60	6	(	(	PUNCT
ejpam-4303	60	7	λ	λ	X
ejpam-4303	60	8	,	,	PUNCT
ejpam-4303	60	9	sp)-closed	sp)-close	VERB
ejpam-4303	60	10	if	if	SCONJ
ejpam-4303	60	11	and	and	CCONJ
ejpam-4303	60	12	only	only	ADV
ejpam-4303	60	13	if	if	SCONJ
ejpam-4303	60	14	a	a	DET
ejpam-4303	60	15	=	=	X
ejpam-4303	60	16	a(λ	a(λ	ADV
ejpam-4303	60	17	,	,	PUNCT
ejpam-4303	60	18	sp	sp	NOUN
ejpam-4303	60	19	)	)	PUNCT
ejpam-4303	60	20	.	.	PUNCT
ejpam-4303	61	1	lemma	lemma	PROPN
ejpam-4303	61	2	2	2	NUM
ejpam-4303	61	3	.	.	PUNCT
ejpam-4303	62	1	[	[	X
ejpam-4303	62	2	3	3	X
ejpam-4303	62	3	]	]	PUNCT
ejpam-4303	62	4	let	let	VERB
ejpam-4303	62	5	a	a	PRON
ejpam-4303	62	6	and	and	CCONJ
ejpam-4303	62	7	b	b	NOUN
ejpam-4303	62	8	be	be	AUX
ejpam-4303	62	9	subsets	subset	NOUN
ejpam-4303	62	10	of	of	ADP
ejpam-4303	62	11	a	a	DET
ejpam-4303	62	12	topological	topological	ADJ
ejpam-4303	62	13	space	space	NOUN
ejpam-4303	62	14	(	(	PUNCT
ejpam-4303	62	15	x	x	X
ejpam-4303	62	16	,	,	PUNCT
ejpam-4303	62	17	τ	τ	PROPN
ejpam-4303	62	18	)	)	PUNCT
ejpam-4303	62	19	.	.	PUNCT
ejpam-4303	63	1	for	for	ADP
ejpam-4303	63	2	the	the	DET
ejpam-4303	63	3	(	(	PUNCT
ejpam-4303	63	4	λ	λ	PROPN
ejpam-4303	63	5	,	,	PUNCT
ejpam-4303	63	6	sp)interior	sp)interior	PROPN
ejpam-4303	63	7	,	,	PUNCT
ejpam-4303	63	8	the	the	DET
ejpam-4303	63	9	following	follow	VERB
ejpam-4303	63	10	properties	property	NOUN
ejpam-4303	63	11	hold	hold	VERB
ejpam-4303	63	12	:	:	PUNCT
ejpam-4303	63	13	(	(	PUNCT
ejpam-4303	63	14	1	1	X
ejpam-4303	63	15	)	)	PUNCT
ejpam-4303	63	16	a(λ	a(λ	ADV
ejpam-4303	63	17	,	,	PUNCT
ejpam-4303	63	18	sp	sp	NOUN
ejpam-4303	63	19	)	)	PUNCT
ejpam-4303	63	20	⊆	⊆	NUM
ejpam-4303	63	21	a	a	DET
ejpam-4303	63	22	and	and	CCONJ
ejpam-4303	63	23	[	[	X
ejpam-4303	63	24	a(λ	a(λ	ADV
ejpam-4303	63	25	,	,	PUNCT
ejpam-4303	63	26	sp)](λ	sp)](λ	PROPN
ejpam-4303	63	27	,	,	PUNCT
ejpam-4303	63	28	sp	sp	NOUN
ejpam-4303	63	29	)	)	PUNCT
ejpam-4303	63	30	=	=	PUNCT
ejpam-4303	63	31	a(λ	a(λ	ADV
ejpam-4303	63	32	,	,	PUNCT
ejpam-4303	63	33	sp	sp	NOUN
ejpam-4303	63	34	)	)	PUNCT
ejpam-4303	63	35	.	.	PUNCT
ejpam-4303	64	1	(	(	PUNCT
ejpam-4303	64	2	2	2	X
ejpam-4303	64	3	)	)	PUNCT
ejpam-4303	64	4	if	if	SCONJ
ejpam-4303	64	5	a	a	DET
ejpam-4303	64	6	⊆	⊆	NUM
ejpam-4303	64	7	b	b	NOUN
ejpam-4303	64	8	,	,	PUNCT
ejpam-4303	64	9	then	then	ADV
ejpam-4303	64	10	a(λ	a(λ	ADV
ejpam-4303	64	11	,	,	PUNCT
ejpam-4303	64	12	sp	sp	NOUN
ejpam-4303	64	13	)	)	PUNCT
ejpam-4303	64	14	⊆	⊆	NUM
ejpam-4303	64	15	b(λ	b(λ	NOUN
ejpam-4303	64	16	,	,	PUNCT
ejpam-4303	64	17	sp	sp	NOUN
ejpam-4303	64	18	)	)	PUNCT
ejpam-4303	64	19	.	.	PUNCT
ejpam-4303	65	1	(	(	PUNCT
ejpam-4303	65	2	3	3	X
ejpam-4303	65	3	)	)	PUNCT
ejpam-4303	65	4	a(λ	a(λ	ADV
ejpam-4303	65	5	,	,	PUNCT
ejpam-4303	65	6	sp	sp	NOUN
ejpam-4303	65	7	)	)	PUNCT
ejpam-4303	65	8	is	be	AUX
ejpam-4303	65	9	(	(	PUNCT
ejpam-4303	65	10	λ	λ	INTJ
ejpam-4303	65	11	,	,	PUNCT
ejpam-4303	65	12	sp)-open	sp)-open	NOUN
ejpam-4303	65	13	.	.	PUNCT
ejpam-4303	66	1	c.	c.	PROPN
ejpam-4303	66	2	boonpok	boonpok	PROPN
ejpam-4303	66	3	,	,	PUNCT
ejpam-4303	66	4	c.	c.	PROPN
ejpam-4303	66	5	viriyapong	viriyapong	PROPN
ejpam-4303	66	6	/	/	SYM
ejpam-4303	66	7	eur	eur	PROPN
ejpam-4303	66	8	.	.	PUNCT
ejpam-4303	67	1	j.	j.	PROPN
ejpam-4303	67	2	pure	pure	PROPN
ejpam-4303	67	3	appl	appl	PROPN
ejpam-4303	67	4	.	.	PROPN
ejpam-4303	67	5	math	math	PROPN
ejpam-4303	67	6	,	,	PUNCT
ejpam-4303	67	7	15	15	NUM
ejpam-4303	67	8	(	(	PUNCT
ejpam-4303	67	9	2	2	NUM
ejpam-4303	67	10	)	)	PUNCT
ejpam-4303	67	11	(	(	PUNCT
ejpam-4303	67	12	2022	2022	NUM
ejpam-4303	67	13	)	)	PUNCT
ejpam-4303	67	14	,	,	PUNCT
ejpam-4303	67	15	528	528	NUM
ejpam-4303	67	16	-	-	SYM
ejpam-4303	67	17	536	536	NUM
ejpam-4303	67	18	530	530	NUM
ejpam-4303	67	19	(	(	PUNCT
ejpam-4303	67	20	4	4	NUM
ejpam-4303	67	21	)	)	PUNCT
ejpam-4303	67	22	a	a	PRON
ejpam-4303	67	23	is	be	AUX
ejpam-4303	67	24	(	(	PUNCT
ejpam-4303	67	25	λ	λ	NOUN
ejpam-4303	67	26	,	,	PUNCT
ejpam-4303	67	27	sp)-open	sp)-open	ADJ
ejpam-4303	67	28	if	if	SCONJ
ejpam-4303	67	29	and	and	CCONJ
ejpam-4303	67	30	only	only	ADV
ejpam-4303	67	31	if	if	SCONJ
ejpam-4303	67	32	a(λ	a(λ	ADV
ejpam-4303	67	33	,	,	PUNCT
ejpam-4303	67	34	sp	sp	NOUN
ejpam-4303	67	35	)	)	PUNCT
ejpam-4303	67	36	=	=	SYM
ejpam-4303	67	37	a.	a.	NOUN
ejpam-4303	67	38	(	(	PUNCT
ejpam-4303	67	39	5	5	NUM
ejpam-4303	67	40	)	)	PUNCT
ejpam-4303	67	41	[	[	X
ejpam-4303	67	42	x	x	X
ejpam-4303	67	43	−a](λ	−a](λ	PROPN
ejpam-4303	67	44	,	,	PUNCT
ejpam-4303	67	45	sp	sp	NOUN
ejpam-4303	67	46	)	)	PUNCT
ejpam-4303	67	47	=	=	SYM
ejpam-4303	67	48	x	x	SYM
ejpam-4303	67	49	−a(λ	−a(λ	NOUN
ejpam-4303	67	50	,	,	PUNCT
ejpam-4303	67	51	sp	sp	NOUN
ejpam-4303	67	52	)	)	PUNCT
ejpam-4303	67	53	.	.	PUNCT
ejpam-4303	68	1	(	(	PUNCT
ejpam-4303	68	2	6	6	NUM
ejpam-4303	68	3	)	)	PUNCT
ejpam-4303	69	1	[	[	X
ejpam-4303	69	2	x	x	X
ejpam-4303	69	3	−a](λ	−a](λ	PROPN
ejpam-4303	69	4	,	,	PUNCT
ejpam-4303	69	5	sp	sp	NOUN
ejpam-4303	69	6	)	)	PUNCT
ejpam-4303	69	7	=	=	SYM
ejpam-4303	69	8	x	x	SYM
ejpam-4303	69	9	−a(λ	−a(λ	NOUN
ejpam-4303	69	10	,	,	PUNCT
ejpam-4303	69	11	sp	sp	NOUN
ejpam-4303	69	12	)	)	PUNCT
ejpam-4303	69	13	.	.	PUNCT
ejpam-4303	70	1	a	a	DET
ejpam-4303	70	2	subset	subset	NOUN
ejpam-4303	70	3	a	a	PRON
ejpam-4303	70	4	of	of	ADP
ejpam-4303	70	5	a	a	DET
ejpam-4303	70	6	topological	topological	ADJ
ejpam-4303	70	7	space	space	NOUN
ejpam-4303	70	8	(	(	PUNCT
ejpam-4303	70	9	x	x	X
ejpam-4303	70	10	,	,	PUNCT
ejpam-4303	70	11	τ	τ	X
ejpam-4303	70	12	)	)	PUNCT
ejpam-4303	70	13	is	be	AUX
ejpam-4303	70	14	said	say	VERB
ejpam-4303	70	15	to	to	PART
ejpam-4303	70	16	be	be	AUX
ejpam-4303	70	17	s(λ	s(λ	NOUN
ejpam-4303	70	18	,	,	PUNCT
ejpam-4303	70	19	sp)-open	sp)-open	ADJ
ejpam-4303	70	20	(	(	PUNCT
ejpam-4303	70	21	resp	resp	NOUN
ejpam-4303	70	22	.	.	PUNCT
ejpam-4303	71	1	p(λ	p(λ	NOUN
ejpam-4303	71	2	,	,	PUNCT
ejpam-4303	71	3	sp)-open	sp)-open	NOUN
ejpam-4303	71	4	,	,	PUNCT
ejpam-4303	71	5	r(λ	r(λ	NOUN
ejpam-4303	71	6	,	,	PUNCT
ejpam-4303	71	7	sp)-open	sp)-open	NOUN
ejpam-4303	71	8	,	,	PUNCT
ejpam-4303	71	9	α(λ	α(λ	PROPN
ejpam-4303	71	10	,	,	PUNCT
ejpam-4303	71	11	sp)-open	sp)-open	NOUN
ejpam-4303	71	12	,	,	PUNCT
ejpam-4303	71	13	β(λ	β(λ	X
ejpam-4303	71	14	,	,	PUNCT
ejpam-4303	71	15	sp)-open	sp)-open	NOUN
ejpam-4303	71	16	)	)	PUNCT
ejpam-4303	71	17	if	if	SCONJ
ejpam-4303	71	18	a	a	DET
ejpam-4303	71	19	⊆	⊆	NUM
ejpam-4303	71	20	[	[	X
ejpam-4303	71	21	a(λ	a(λ	ADV
ejpam-4303	71	22	,	,	PUNCT
ejpam-4303	71	23	sp	sp	NOUN
ejpam-4303	71	24	)	)	PUNCT
ejpam-4303	71	25	]	]	PUNCT
ejpam-4303	71	26	(	(	PUNCT
ejpam-4303	71	27	λ	λ	NOUN
ejpam-4303	71	28	,	,	PUNCT
ejpam-4303	71	29	sp	sp	NOUN
ejpam-4303	71	30	)	)	PUNCT
ejpam-4303	71	31	(	(	PUNCT
ejpam-4303	71	32	resp	resp	NOUN
ejpam-4303	71	33	.	.	PUNCT
ejpam-4303	72	1	a	a	DET
ejpam-4303	72	2	⊆	⊆	NUM
ejpam-4303	72	3	[	[	X
ejpam-4303	72	4	a(λ	a(λ	ADJ
ejpam-4303	72	5	,	,	PUNCT
ejpam-4303	72	6	sp)](λ	sp)](λ	PROPN
ejpam-4303	72	7	,	,	PUNCT
ejpam-4303	72	8	sp	sp	NOUN
ejpam-4303	72	9	)	)	PUNCT
ejpam-4303	72	10	,	,	PUNCT
ejpam-4303	73	1	a	a	DET
ejpam-4303	73	2	=	=	X
ejpam-4303	73	3	[	[	X
ejpam-4303	73	4	a(λ	a(λ	PROPN
ejpam-4303	73	5	,	,	PUNCT
ejpam-4303	73	6	sp)](λ	sp)](λ	PROPN
ejpam-4303	73	7	,	,	PUNCT
ejpam-4303	73	8	sp	sp	NOUN
ejpam-4303	73	9	)	)	PUNCT
ejpam-4303	73	10	,	,	PUNCT
ejpam-4303	73	11	a	a	DET
ejpam-4303	73	12	⊆	⊆	NUM
ejpam-4303	73	13	[	[	X
ejpam-4303	73	14	[	[	X
ejpam-4303	73	15	a(λ	a(λ	ADJ
ejpam-4303	73	16	,	,	PUNCT
ejpam-4303	73	17	sp	sp	NOUN
ejpam-4303	73	18	)	)	PUNCT
ejpam-4303	73	19	]	]	PUNCT
ejpam-4303	73	20	(	(	PUNCT
ejpam-4303	73	21	λ	λ	X
ejpam-4303	73	22	,	,	PUNCT
ejpam-4303	73	23	sp)](λ	sp)](λ	PROPN
ejpam-4303	73	24	,	,	PUNCT
ejpam-4303	73	25	sp	sp	NOUN
ejpam-4303	73	26	)	)	PUNCT
ejpam-4303	73	27	,	,	PUNCT
ejpam-4303	74	1	a	a	DET
ejpam-4303	74	2	⊆	⊆	NUM
ejpam-4303	74	3	[	[	X
ejpam-4303	74	4	[	[	X
ejpam-4303	74	5	a(λ	a(λ	ADJ
ejpam-4303	74	6	,	,	PUNCT
ejpam-4303	74	7	sp)](λ	sp)](λ	PROPN
ejpam-4303	74	8	,	,	PUNCT
ejpam-4303	74	9	sp	sp	NOUN
ejpam-4303	74	10	)	)	PUNCT
ejpam-4303	74	11	]	]	PUNCT
ejpam-4303	75	1	(	(	PUNCT
ejpam-4303	75	2	λ	λ	NOUN
ejpam-4303	75	3	,	,	PUNCT
ejpam-4303	75	4	sp	sp	NOUN
ejpam-4303	75	5	)	)	PUNCT
ejpam-4303	75	6	)	)	PUNCT
ejpam-4303	76	1	[	[	X
ejpam-4303	76	2	3	3	NUM
ejpam-4303	76	3	]	]	PUNCT
ejpam-4303	76	4	.	.	PUNCT
ejpam-4303	77	1	the	the	DET
ejpam-4303	77	2	complement	complement	NOUN
ejpam-4303	77	3	of	of	ADP
ejpam-4303	77	4	a	a	DET
ejpam-4303	77	5	s(λ	s(λ	PROPN
ejpam-4303	77	6	,	,	PUNCT
ejpam-4303	77	7	sp)-open	sp)-open	ADJ
ejpam-4303	77	8	(	(	PUNCT
ejpam-4303	77	9	resp	resp	NOUN
ejpam-4303	77	10	.	.	PUNCT
ejpam-4303	78	1	p(λ	p(λ	NOUN
ejpam-4303	78	2	,	,	PUNCT
ejpam-4303	78	3	sp)-open	sp)-open	NOUN
ejpam-4303	78	4	,	,	PUNCT
ejpam-4303	78	5	r(λ	r(λ	NOUN
ejpam-4303	78	6	,	,	PUNCT
ejpam-4303	78	7	sp)-open	sp)-open	NOUN
ejpam-4303	78	8	,	,	PUNCT
ejpam-4303	78	9	α(λ	α(λ	PROPN
ejpam-4303	78	10	,	,	PUNCT
ejpam-4303	78	11	sp)-open	sp)-open	NOUN
ejpam-4303	78	12	,	,	PUNCT
ejpam-4303	78	13	β(λ	β(λ	X
ejpam-4303	78	14	,	,	PUNCT
ejpam-4303	78	15	sp)-open	sp)-open	NOUN
ejpam-4303	78	16	)	)	PUNCT
ejpam-4303	78	17	set	set	NOUN
ejpam-4303	78	18	is	be	AUX
ejpam-4303	78	19	said	say	VERB
ejpam-4303	78	20	to	to	PART
ejpam-4303	78	21	be	be	AUX
ejpam-4303	78	22	s(λ	s(λ	PROPN
ejpam-4303	78	23	,	,	PUNCT
ejpam-4303	78	24	sp)-closed	sp)-close	VERB
ejpam-4303	78	25	(	(	PUNCT
ejpam-4303	78	26	resp	resp	NOUN
ejpam-4303	78	27	.	.	PUNCT
ejpam-4303	79	1	p(λ	p(λ	NOUN
ejpam-4303	79	2	,	,	PUNCT
ejpam-4303	79	3	sp)-closed	sp)-close	VERB
ejpam-4303	79	4	,	,	PUNCT
ejpam-4303	79	5	r(λ	r(λ	PROPN
ejpam-4303	79	6	,	,	PUNCT
ejpam-4303	79	7	sp)-closed	sp)-close	VERB
ejpam-4303	79	8	,	,	PUNCT
ejpam-4303	79	9	α(λ	α(λ	PROPN
ejpam-4303	79	10	,	,	PUNCT
ejpam-4303	79	11	sp)-closed	sp)-close	VERB
ejpam-4303	79	12	,	,	PUNCT
ejpam-4303	79	13	β(λ	β(λ	X
ejpam-4303	79	14	,	,	PUNCT
ejpam-4303	79	15	sp)-closed	sp)-close	VERB
ejpam-4303	79	16	)	)	PUNCT
ejpam-4303	79	17	.	.	PUNCT
ejpam-4303	80	1	the	the	DET
ejpam-4303	80	2	family	family	NOUN
ejpam-4303	80	3	of	of	ADP
ejpam-4303	80	4	all	all	DET
ejpam-4303	80	5	s(λ	s(λ	NOUN
ejpam-4303	80	6	,	,	PUNCT
ejpam-4303	80	7	sp)-open	sp)-open	ADJ
ejpam-4303	80	8	(	(	PUNCT
ejpam-4303	80	9	resp	resp	NOUN
ejpam-4303	80	10	.	.	PUNCT
ejpam-4303	81	1	p(λ	p(λ	NOUN
ejpam-4303	81	2	,	,	PUNCT
ejpam-4303	81	3	sp)-open	sp)-open	NOUN
ejpam-4303	81	4	,	,	PUNCT
ejpam-4303	81	5	r(λ	r(λ	NOUN
ejpam-4303	81	6	,	,	PUNCT
ejpam-4303	81	7	sp)-open	sp)-open	NOUN
ejpam-4303	81	8	,	,	PUNCT
ejpam-4303	81	9	α(λ	α(λ	PROPN
ejpam-4303	81	10	,	,	PUNCT
ejpam-4303	81	11	sp)-open	sp)-open	NOUN
ejpam-4303	81	12	,	,	PUNCT
ejpam-4303	81	13	β(λ	β(λ	X
ejpam-4303	81	14	,	,	PUNCT
ejpam-4303	81	15	sp)-open	sp)-open	NOUN
ejpam-4303	81	16	)	)	PUNCT
ejpam-4303	81	17	sets	set	NOUN
ejpam-4303	81	18	in	in	ADP
ejpam-4303	81	19	a	a	DET
ejpam-4303	81	20	topological	topological	ADJ
ejpam-4303	81	21	space	space	NOUN
ejpam-4303	81	22	(	(	PUNCT
ejpam-4303	81	23	x	x	X
ejpam-4303	81	24	,	,	PUNCT
ejpam-4303	81	25	τ	τ	X
ejpam-4303	81	26	)	)	PUNCT
ejpam-4303	81	27	is	be	AUX
ejpam-4303	81	28	denoted	denote	VERB
ejpam-4303	81	29	by	by	ADP
ejpam-4303	81	30	sλspo(x	sλspo(x	PROPN
ejpam-4303	81	31	,	,	PUNCT
ejpam-4303	81	32	τ	τ	PROPN
ejpam-4303	81	33	)	)	PUNCT
ejpam-4303	81	34	(	(	PUNCT
ejpam-4303	81	35	resp	resp	NOUN
ejpam-4303	81	36	.	.	PUNCT
ejpam-4303	82	1	pλspo(x	pλspo(x	ADJ
ejpam-4303	82	2	,	,	PUNCT
ejpam-4303	82	3	τ	τ	PROPN
ejpam-4303	82	4	)	)	PUNCT
ejpam-4303	82	5	,	,	PUNCT
ejpam-4303	82	6	rλspo(x	rλspo(x	PROPN
ejpam-4303	82	7	,	,	PUNCT
ejpam-4303	82	8	τ	τ	PROPN
ejpam-4303	82	9	)	)	PUNCT
ejpam-4303	82	10	,	,	PUNCT
ejpam-4303	82	11	αλspo(x	αλspo(x	NOUN
ejpam-4303	82	12	,	,	PUNCT
ejpam-4303	82	13	τ	τ	PROPN
ejpam-4303	82	14	)	)	PUNCT
ejpam-4303	82	15	,	,	PUNCT
ejpam-4303	82	16	βλspo(x	βλspo(x	PROPN
ejpam-4303	82	17	,	,	PUNCT
ejpam-4303	82	18	τ	τ	PROPN
ejpam-4303	82	19	)	)	PUNCT
ejpam-4303	82	20	)	)	PUNCT
ejpam-4303	82	21	.	.	PUNCT
ejpam-4303	83	1	by	by	ADP
ejpam-4303	83	2	a	a	DET
ejpam-4303	83	3	multifunction	multifunction	NOUN
ejpam-4303	83	4	f	f	NOUN
ejpam-4303	83	5	:	:	PUNCT
ejpam-4303	83	6	(	(	PUNCT
ejpam-4303	83	7	x	x	X
ejpam-4303	83	8	,	,	PUNCT
ejpam-4303	83	9	τ	τ	X
ejpam-4303	83	10	)	)	PUNCT
ejpam-4303	83	11	→	→	SYM
ejpam-4303	83	12	(	(	PUNCT
ejpam-4303	83	13	y	y	PROPN
ejpam-4303	83	14	,	,	PUNCT
ejpam-4303	83	15	σ	σ	PROPN
ejpam-4303	83	16	)	)	PUNCT
ejpam-4303	83	17	,	,	PUNCT
ejpam-4303	83	18	following	follow	VERB
ejpam-4303	83	19	[	[	X
ejpam-4303	83	20	2	2	NUM
ejpam-4303	83	21	]	]	PUNCT
ejpam-4303	83	22	,	,	PUNCT
ejpam-4303	83	23	we	we	PRON
ejpam-4303	83	24	shall	shall	AUX
ejpam-4303	83	25	denote	denote	VERB
ejpam-4303	83	26	the	the	DET
ejpam-4303	83	27	upper	upper	ADJ
ejpam-4303	83	28	and	and	CCONJ
ejpam-4303	83	29	lower	low	ADJ
ejpam-4303	83	30	inverse	inverse	NOUN
ejpam-4303	83	31	of	of	ADP
ejpam-4303	83	32	a	a	DET
ejpam-4303	83	33	set	set	NOUN
ejpam-4303	83	34	b	b	PROPN
ejpam-4303	83	35	of	of	ADP
ejpam-4303	83	36	y	y	PROPN
ejpam-4303	83	37	by	by	ADP
ejpam-4303	83	38	f+(b	f+(b	NOUN
ejpam-4303	83	39	)	)	PUNCT
ejpam-4303	83	40	and	and	CCONJ
ejpam-4303	83	41	f−(b	f−(b	NOUN
ejpam-4303	83	42	)	)	PUNCT
ejpam-4303	83	43	,	,	PUNCT
ejpam-4303	83	44	respectively	respectively	ADV
ejpam-4303	83	45	,	,	PUNCT
ejpam-4303	83	46	that	that	ADV
ejpam-4303	83	47	is	is	ADV
ejpam-4303	83	48	,	,	PUNCT
ejpam-4303	83	49	f+(b	f+(b	NOUN
ejpam-4303	83	50	)	)	PUNCT
ejpam-4303	83	51	=	=	PRON
ejpam-4303	84	1	{	{	PUNCT
ejpam-4303	84	2	x	x	PUNCT
ejpam-4303	84	3	∈	∈	PROPN
ejpam-4303	84	4	x	x	INTJ
ejpam-4303	85	1	|	|	NOUN
ejpam-4303	85	2	f	f	X
ejpam-4303	85	3	(	(	PUNCT
ejpam-4303	85	4	x	x	NOUN
ejpam-4303	85	5	)	)	PUNCT
ejpam-4303	85	6	⊆	⊆	NUM
ejpam-4303	85	7	b	b	NOUN
ejpam-4303	85	8	}	}	PUNCT
ejpam-4303	85	9	and	and	CCONJ
ejpam-4303	85	10	f−(b	f−(b	PROPN
ejpam-4303	85	11	)	)	PUNCT
ejpam-4303	85	12	=	=	PRON
ejpam-4303	86	1	{	{	PUNCT
ejpam-4303	86	2	x	x	PUNCT
ejpam-4303	86	3	∈	∈	PROPN
ejpam-4303	86	4	x	x	INTJ
ejpam-4303	87	1	|	|	NOUN
ejpam-4303	87	2	f	f	X
ejpam-4303	87	3	(	(	PUNCT
ejpam-4303	87	4	x	x	NOUN
ejpam-4303	87	5	)	)	PUNCT
ejpam-4303	87	6	∩	∩	PROPN
ejpam-4303	87	7	b	b	PROPN
ejpam-4303	87	8	6=	6=	ADP
ejpam-4303	87	9	∅	∅	NOUN
ejpam-4303	87	10	}	}	PUNCT
ejpam-4303	87	11	.	.	PUNCT
ejpam-4303	88	1	in	in	ADP
ejpam-4303	88	2	particular	particular	ADJ
ejpam-4303	88	3	,	,	PUNCT
ejpam-4303	88	4	f−(y	f−(y	NOUN
ejpam-4303	88	5	)	)	PUNCT
ejpam-4303	88	6	=	=	SYM
ejpam-4303	89	1	{	{	PUNCT
ejpam-4303	89	2	x	x	PUNCT
ejpam-4303	89	3	∈	∈	PROPN
ejpam-4303	89	4	x	x	INTJ
ejpam-4303	90	1	|	|	ADV
ejpam-4303	90	2	y	y	PROPN
ejpam-4303	90	3	∈	∈	PROPN
ejpam-4303	90	4	f	f	X
ejpam-4303	90	5	(	(	PUNCT
ejpam-4303	90	6	x	x	NOUN
ejpam-4303	90	7	)	)	PUNCT
ejpam-4303	90	8	}	}	PUNCT
ejpam-4303	90	9	for	for	ADP
ejpam-4303	90	10	each	each	DET
ejpam-4303	90	11	point	point	NOUN
ejpam-4303	90	12	y	y	PROPN
ejpam-4303	90	13	∈	∈	PROPN
ejpam-4303	90	14	y	y	PROPN
ejpam-4303	90	15	and	and	CCONJ
ejpam-4303	90	16	for	for	ADP
ejpam-4303	90	17	each	each	PRON
ejpam-4303	90	18	a	a	DET
ejpam-4303	90	19	⊆	⊆	NUM
ejpam-4303	90	20	x	x	SYM
ejpam-4303	90	21	,	,	PUNCT
ejpam-4303	90	22	f	f	PROPN
ejpam-4303	90	23	(	(	PUNCT
ejpam-4303	90	24	a	a	NOUN
ejpam-4303	90	25	)	)	PUNCT
ejpam-4303	90	26	=	=	SYM
ejpam-4303	90	27	∪x∈af	∪x∈af	NOUN
ejpam-4303	90	28	(	(	PUNCT
ejpam-4303	90	29	x	x	NOUN
ejpam-4303	90	30	)	)	PUNCT
ejpam-4303	90	31	.	.	PUNCT
ejpam-4303	91	1	let	let	VERB
ejpam-4303	91	2	p(y	p(y	PROPN
ejpam-4303	91	3	)	)	PUNCT
ejpam-4303	91	4	be	be	AUX
ejpam-4303	91	5	the	the	DET
ejpam-4303	91	6	collection	collection	NOUN
ejpam-4303	91	7	of	of	ADP
ejpam-4303	91	8	all	all	DET
ejpam-4303	91	9	nonempty	nonempty	ADJ
ejpam-4303	91	10	subsets	subset	NOUN
ejpam-4303	91	11	of	of	ADP
ejpam-4303	91	12	y	y	PROPN
ejpam-4303	91	13	.	.	PUNCT
ejpam-4303	92	1	for	for	ADP
ejpam-4303	92	2	any	any	DET
ejpam-4303	92	3	(	(	PUNCT
ejpam-4303	92	4	λ	λ	NOUN
ejpam-4303	92	5	,	,	PUNCT
ejpam-4303	92	6	sp)-open	sp)-open	NOUN
ejpam-4303	92	7	set	set	VERB
ejpam-4303	92	8	v	v	NUM
ejpam-4303	92	9	of	of	ADP
ejpam-4303	92	10	a	a	DET
ejpam-4303	92	11	topological	topological	ADJ
ejpam-4303	92	12	space	space	NOUN
ejpam-4303	92	13	(	(	PUNCT
ejpam-4303	92	14	y	y	PROPN
ejpam-4303	92	15	,	,	PUNCT
ejpam-4303	92	16	σ	σ	PROPN
ejpam-4303	92	17	)	)	PUNCT
ejpam-4303	92	18	,	,	PUNCT
ejpam-4303	92	19	we	we	PRON
ejpam-4303	92	20	denote	denote	VERB
ejpam-4303	92	21	v	v	ADP
ejpam-4303	92	22	+	+	NOUN
ejpam-4303	93	1	=	=	SYM
ejpam-4303	93	2	{	{	PUNCT
ejpam-4303	93	3	b	b	NOUN
ejpam-4303	93	4	∈	∈	PROPN
ejpam-4303	93	5	p(y	p(y	PROPN
ejpam-4303	93	6	)	)	PUNCT
ejpam-4303	93	7	|	|	ADV
ejpam-4303	93	8	b	b	X
ejpam-4303	93	9	⊆	⊆	NUM
ejpam-4303	93	10	v	v	NOUN
ejpam-4303	93	11	}	}	PUNCT
ejpam-4303	93	12	and	and	CCONJ
ejpam-4303	93	13	v	v	ADP
ejpam-4303	93	14	−	−	PROPN
ejpam-4303	93	15	=	=	PUNCT
ejpam-4303	93	16	{	{	PUNCT
ejpam-4303	93	17	b	b	NOUN
ejpam-4303	93	18	∈	∈	PROPN
ejpam-4303	93	19	p(y	p(y	PROPN
ejpam-4303	93	20	)	)	PUNCT
ejpam-4303	94	1	|	|	ADV
ejpam-4303	94	2	b	b	PROPN
ejpam-4303	94	3	∩	∩	X
ejpam-4303	94	4	v	v	ADP
ejpam-4303	94	5	6=	6=	ADP
ejpam-4303	94	6	∅	∅	NOUN
ejpam-4303	94	7	}	}	PUNCT
ejpam-4303	94	8	.	.	PUNCT
ejpam-4303	95	1	3	3	X
ejpam-4303	95	2	.	.	X
ejpam-4303	95	3	characterizations	characterization	NOUN
ejpam-4303	95	4	of	of	ADP
ejpam-4303	95	5	weakly	weakly	ADJ
ejpam-4303	95	6	(	(	PUNCT
ejpam-4303	95	7	λ	λ	NOUN
ejpam-4303	95	8	,	,	PUNCT
ejpam-4303	95	9	sp)-continuous	sp)-continuous	ADJ
ejpam-4303	95	10	multifunctions	multifunction	NOUN
ejpam-4303	95	11	in	in	ADP
ejpam-4303	95	12	this	this	DET
ejpam-4303	95	13	section	section	NOUN
ejpam-4303	95	14	,	,	PUNCT
ejpam-4303	95	15	we	we	PRON
ejpam-4303	95	16	introduce	introduce	VERB
ejpam-4303	95	17	the	the	DET
ejpam-4303	95	18	notion	notion	NOUN
ejpam-4303	95	19	of	of	ADP
ejpam-4303	95	20	weakly	weakly	ADJ
ejpam-4303	95	21	(	(	PUNCT
ejpam-4303	95	22	λ	λ	NOUN
ejpam-4303	95	23	,	,	PUNCT
ejpam-4303	95	24	sp)-continuous	sp)-continuous	ADJ
ejpam-4303	95	25	multifunctions	multifunction	NOUN
ejpam-4303	95	26	.	.	PUNCT
ejpam-4303	96	1	furthermore	furthermore	ADV
ejpam-4303	96	2	,	,	PUNCT
ejpam-4303	96	3	several	several	ADJ
ejpam-4303	96	4	characterizations	characterization	NOUN
ejpam-4303	96	5	of	of	ADP
ejpam-4303	96	6	weakly	weakly	ADJ
ejpam-4303	96	7	(	(	PUNCT
ejpam-4303	96	8	λ	λ	NOUN
ejpam-4303	96	9	,	,	PUNCT
ejpam-4303	96	10	sp)-continuous	sp)-continuous	ADJ
ejpam-4303	96	11	multifunctions	multifunction	NOUN
ejpam-4303	96	12	are	be	AUX
ejpam-4303	96	13	discussed	discuss	VERB
ejpam-4303	96	14	.	.	PUNCT
ejpam-4303	97	1	definition	definition	NOUN
ejpam-4303	97	2	1	1	NUM
ejpam-4303	97	3	.	.	PUNCT
ejpam-4303	98	1	a	a	DET
ejpam-4303	98	2	multifunction	multifunction	NOUN
ejpam-4303	98	3	f	f	NOUN
ejpam-4303	98	4	:	:	PUNCT
ejpam-4303	98	5	(	(	PUNCT
ejpam-4303	98	6	x	x	X
ejpam-4303	98	7	,	,	PUNCT
ejpam-4303	98	8	τ	τ	X
ejpam-4303	98	9	)	)	PUNCT
ejpam-4303	98	10	→	→	SYM
ejpam-4303	98	11	(	(	PUNCT
ejpam-4303	98	12	y	y	PROPN
ejpam-4303	98	13	,	,	PUNCT
ejpam-4303	98	14	σ	σ	PROPN
ejpam-4303	98	15	)	)	PUNCT
ejpam-4303	98	16	is	be	AUX
ejpam-4303	98	17	said	say	VERB
ejpam-4303	98	18	to	to	PART
ejpam-4303	98	19	be	be	AUX
ejpam-4303	98	20	weakly	weakly	ADJ
ejpam-4303	98	21	(	(	PUNCT
ejpam-4303	98	22	λ	λ	NOUN
ejpam-4303	98	23	,	,	PUNCT
ejpam-4303	98	24	sp)-continuous	sp)-continuous	ADJ
ejpam-4303	98	25	if	if	SCONJ
ejpam-4303	98	26	,	,	PUNCT
ejpam-4303	98	27	for	for	ADP
ejpam-4303	98	28	each	each	DET
ejpam-4303	98	29	x	x	SYM
ejpam-4303	98	30	∈	∈	PROPN
ejpam-4303	98	31	x	x	X
ejpam-4303	98	32	and	and	CCONJ
ejpam-4303	98	33	each	each	DET
ejpam-4303	98	34	(	(	PUNCT
ejpam-4303	98	35	λ	λ	PROPN
ejpam-4303	98	36	,	,	PUNCT
ejpam-4303	98	37	sp)-open	sp)-open	ADJ
ejpam-4303	98	38	sets	set	NOUN
ejpam-4303	98	39	v1	v1	NOUN
ejpam-4303	98	40	,	,	PUNCT
ejpam-4303	98	41	v2	v2	PROPN
ejpam-4303	98	42	of	of	ADP
ejpam-4303	98	43	y	y	PRON
ejpam-4303	98	44	such	such	ADJ
ejpam-4303	98	45	that	that	SCONJ
ejpam-4303	98	46	f	f	PROPN
ejpam-4303	98	47	(	(	PUNCT
ejpam-4303	98	48	x	x	X
ejpam-4303	98	49	)	)	PUNCT
ejpam-4303	98	50	∈	∈	NOUN
ejpam-4303	98	51	v	v	ADP
ejpam-4303	98	52	+	+	CCONJ
ejpam-4303	98	53	1	1	NUM
ejpam-4303	98	54	∩v	∩v	NOUN
ejpam-4303	98	55	−	−	PROPN
ejpam-4303	98	56	2	2	NUM
ejpam-4303	98	57	,	,	PUNCT
ejpam-4303	98	58	there	there	PRON
ejpam-4303	98	59	exists	exist	VERB
ejpam-4303	98	60	a	a	DET
ejpam-4303	98	61	(	(	PUNCT
ejpam-4303	98	62	λ	λ	NOUN
ejpam-4303	98	63	,	,	PUNCT
ejpam-4303	98	64	sp)-open	sp)-open	NOUN
ejpam-4303	98	65	set	set	VERB
ejpam-4303	98	66	u	u	NOUN
ejpam-4303	98	67	of	of	ADP
ejpam-4303	98	68	x	x	PUNCT
ejpam-4303	98	69	containing	contain	VERB
ejpam-4303	98	70	x	x	PUNCT
ejpam-4303	98	71	such	such	ADJ
ejpam-4303	98	72	that	that	SCONJ
ejpam-4303	98	73	f	f	PROPN
ejpam-4303	98	74	(	(	PUNCT
ejpam-4303	98	75	u	u	NOUN
ejpam-4303	98	76	)	)	PUNCT
ejpam-4303	98	77	⊆	⊆	NUM
ejpam-4303	98	78	v	v	NOUN
ejpam-4303	98	79	(	(	PUNCT
ejpam-4303	98	80	λ	λ	NOUN
ejpam-4303	98	81	,	,	PUNCT
ejpam-4303	98	82	sp	sp	NOUN
ejpam-4303	98	83	)	)	PUNCT
ejpam-4303	98	84	1	1	NUM
ejpam-4303	98	85	and	and	CCONJ
ejpam-4303	98	86	f	f	PROPN
ejpam-4303	98	87	(	(	PUNCT
ejpam-4303	98	88	z)∩v	z)∩v	PROPN
ejpam-4303	98	89	(	(	PUNCT
ejpam-4303	98	90	λ	λ	PROPN
ejpam-4303	98	91	,	,	PUNCT
ejpam-4303	98	92	sp	sp	NOUN
ejpam-4303	98	93	)	)	PUNCT
ejpam-4303	98	94	2	2	NUM
ejpam-4303	98	95	6=	6=	NOUN
ejpam-4303	98	96	∅	∅	NOUN
ejpam-4303	98	97	for	for	ADP
ejpam-4303	98	98	every	every	DET
ejpam-4303	98	99	z	z	NOUN
ejpam-4303	98	100	∈	∈	PROPN
ejpam-4303	98	101	u	u	PROPN
ejpam-4303	98	102	.	.	PUNCT
ejpam-4303	99	1	theorem	theorem	NOUN
ejpam-4303	99	2	1	1	NUM
ejpam-4303	99	3	.	.	X
ejpam-4303	99	4	for	for	ADP
ejpam-4303	99	5	a	a	DET
ejpam-4303	99	6	multifunction	multifunction	NOUN
ejpam-4303	100	1	f	f	NOUN
ejpam-4303	100	2	:	:	PUNCT
ejpam-4303	100	3	(	(	PUNCT
ejpam-4303	100	4	x	x	X
ejpam-4303	100	5	,	,	PUNCT
ejpam-4303	100	6	τ	τ	X
ejpam-4303	100	7	)	)	PUNCT
ejpam-4303	100	8	→	→	SYM
ejpam-4303	100	9	(	(	PUNCT
ejpam-4303	100	10	y	y	PROPN
ejpam-4303	100	11	,	,	PUNCT
ejpam-4303	100	12	σ	σ	PROPN
ejpam-4303	100	13	)	)	PUNCT
ejpam-4303	100	14	,	,	PUNCT
ejpam-4303	100	15	the	the	DET
ejpam-4303	100	16	following	follow	VERB
ejpam-4303	100	17	properties	property	NOUN
ejpam-4303	100	18	are	be	AUX
ejpam-4303	100	19	equivalent	equivalent	ADJ
ejpam-4303	100	20	:	:	PUNCT
ejpam-4303	100	21	(	(	PUNCT
ejpam-4303	100	22	1	1	X
ejpam-4303	100	23	)	)	PUNCT
ejpam-4303	100	24	f	f	PROPN
ejpam-4303	100	25	is	be	AUX
ejpam-4303	100	26	weakly	weakly	ADJ
ejpam-4303	100	27	(	(	PUNCT
ejpam-4303	100	28	λ	λ	NOUN
ejpam-4303	100	29	,	,	PUNCT
ejpam-4303	100	30	sp)-continuous	sp)-continuous	ADJ
ejpam-4303	100	31	;	;	PUNCT
ejpam-4303	100	32	(	(	PUNCT
ejpam-4303	100	33	2	2	X
ejpam-4303	100	34	)	)	PUNCT
ejpam-4303	100	35	f+(v1)∩f−(v2	f+(v1)∩f−(v2	NOUN
ejpam-4303	100	36	)	)	PUNCT
ejpam-4303	100	37	⊆	⊆	NUM
ejpam-4303	101	1	[	[	X
ejpam-4303	101	2	f+(v	f+(v	NOUN
ejpam-4303	101	3	(	(	PUNCT
ejpam-4303	101	4	λ	λ	NOUN
ejpam-4303	101	5	,	,	PUNCT
ejpam-4303	101	6	sp	sp	NOUN
ejpam-4303	101	7	)	)	PUNCT
ejpam-4303	101	8	1	1	NUM
ejpam-4303	101	9	)	)	PUNCT
ejpam-4303	101	10	∩f−(v	∩f−(v	NOUN
ejpam-4303	101	11	(	(	PUNCT
ejpam-4303	101	12	λ	λ	NOUN
ejpam-4303	101	13	,	,	PUNCT
ejpam-4303	101	14	sp	sp	NOUN
ejpam-4303	101	15	)	)	PUNCT
ejpam-4303	101	16	2	2	NUM
ejpam-4303	101	17	)	)	PUNCT
ejpam-4303	101	18	]	]	PUNCT
ejpam-4303	101	19	(	(	PUNCT
ejpam-4303	101	20	λ	λ	NOUN
ejpam-4303	101	21	,	,	PUNCT
ejpam-4303	101	22	sp	sp	NOUN
ejpam-4303	101	23	)	)	PUNCT
ejpam-4303	101	24	for	for	ADP
ejpam-4303	101	25	every	every	DET
ejpam-4303	101	26	(	(	PUNCT
ejpam-4303	101	27	λ	λ	NOUN
ejpam-4303	101	28	,	,	PUNCT
ejpam-4303	101	29	sp)-open	sp)-open	ADJ
ejpam-4303	101	30	sets	set	NOUN
ejpam-4303	101	31	v1	v1	NOUN
ejpam-4303	101	32	,	,	PUNCT
ejpam-4303	101	33	v2	v2	PROPN
ejpam-4303	101	34	of	of	ADP
ejpam-4303	101	35	y	y	PROPN
ejpam-4303	101	36	;	;	PUNCT
ejpam-4303	101	37	(	(	PUNCT
ejpam-4303	101	38	3	3	X
ejpam-4303	101	39	)	)	PUNCT
ejpam-4303	102	1	[	[	X
ejpam-4303	102	2	f−([k1](λ	f−([k1](λ	NOUN
ejpam-4303	102	3	,	,	PUNCT
ejpam-4303	102	4	sp	sp	NOUN
ejpam-4303	102	5	)	)	PUNCT
ejpam-4303	102	6	)	)	PUNCT
ejpam-4303	103	1	∪	∪	ADP
ejpam-4303	103	2	f+([k2](λ	f+([k2](λ	SYM
ejpam-4303	103	3	,	,	PUNCT
ejpam-4303	103	4	sp	sp	NOUN
ejpam-4303	103	5	)	)	PUNCT
ejpam-4303	103	6	)	)	PUNCT
ejpam-4303	103	7	]	]	PUNCT
ejpam-4303	104	1	(	(	PUNCT
ejpam-4303	104	2	λ	λ	NOUN
ejpam-4303	104	3	,	,	PUNCT
ejpam-4303	104	4	sp	sp	NOUN
ejpam-4303	104	5	)	)	PUNCT
ejpam-4303	104	6	⊆	⊆	NUM
ejpam-4303	104	7	f−(k1	f−(k1	NOUN
ejpam-4303	104	8	)	)	PUNCT
ejpam-4303	104	9	∪	∪	ADP
ejpam-4303	104	10	f+(k2	f+(k2	NOUN
ejpam-4303	104	11	)	)	PUNCT
ejpam-4303	104	12	for	for	ADP
ejpam-4303	104	13	every	every	DET
ejpam-4303	104	14	(	(	PUNCT
ejpam-4303	104	15	λ	λ	PROPN
ejpam-4303	104	16	,	,	PUNCT
ejpam-4303	104	17	sp)-closed	sp)-close	VERB
ejpam-4303	104	18	sets	set	VERB
ejpam-4303	104	19	k1,k2	k1,k2	PROPN
ejpam-4303	104	20	of	of	ADP
ejpam-4303	104	21	y	y	PROPN
ejpam-4303	104	22	;	;	PUNCT
ejpam-4303	104	23	c.	c.	PROPN
ejpam-4303	104	24	boonpok	boonpok	PROPN
ejpam-4303	104	25	,	,	PUNCT
ejpam-4303	104	26	c.	c.	PROPN
ejpam-4303	104	27	viriyapong	viriyapong	PROPN
ejpam-4303	104	28	/	/	SYM
ejpam-4303	104	29	eur	eur	PROPN
ejpam-4303	104	30	.	.	PUNCT
ejpam-4303	105	1	j.	j.	PROPN
ejpam-4303	105	2	pure	pure	PROPN
ejpam-4303	105	3	appl	appl	PROPN
ejpam-4303	105	4	.	.	PROPN
ejpam-4303	105	5	math	math	PROPN
ejpam-4303	105	6	,	,	PUNCT
ejpam-4303	105	7	15	15	NUM
ejpam-4303	105	8	(	(	PUNCT
ejpam-4303	105	9	2	2	NUM
ejpam-4303	105	10	)	)	PUNCT
ejpam-4303	105	11	(	(	PUNCT
ejpam-4303	105	12	2022	2022	NUM
ejpam-4303	105	13	)	)	PUNCT
ejpam-4303	105	14	,	,	PUNCT
ejpam-4303	105	15	528	528	NUM
ejpam-4303	105	16	-	-	SYM
ejpam-4303	105	17	536	536	NUM
ejpam-4303	105	18	531	531	NUM
ejpam-4303	105	19	(	(	PUNCT
ejpam-4303	105	20	4	4	NUM
ejpam-4303	105	21	)	)	PUNCT
ejpam-4303	106	1	[	[	X
ejpam-4303	106	2	f−([b	f−([b	PROPN
ejpam-4303	106	3	(	(	PUNCT
ejpam-4303	106	4	λ	λ	PROPN
ejpam-4303	106	5	,	,	PUNCT
ejpam-4303	106	6	sp	sp	NOUN
ejpam-4303	106	7	)	)	PUNCT
ejpam-4303	106	8	1	1	NUM
ejpam-4303	106	9	]	]	PUNCT
ejpam-4303	106	10	(	(	PUNCT
ejpam-4303	106	11	λ	λ	NOUN
ejpam-4303	106	12	,	,	PUNCT
ejpam-4303	106	13	sp))∪	sp))∪	ADJ
ejpam-4303	106	14	f+([b	f+([b	PROPN
ejpam-4303	106	15	(	(	PUNCT
ejpam-4303	106	16	λ	λ	PROPN
ejpam-4303	106	17	,	,	PUNCT
ejpam-4303	106	18	sp	sp	NOUN
ejpam-4303	106	19	)	)	PUNCT
ejpam-4303	106	20	2	2	NUM
ejpam-4303	106	21	]	]	PUNCT
ejpam-4303	106	22	(	(	PUNCT
ejpam-4303	106	23	λ	λ	NOUN
ejpam-4303	106	24	,	,	PUNCT
ejpam-4303	106	25	sp	sp	NOUN
ejpam-4303	106	26	)	)	PUNCT
ejpam-4303	106	27	)	)	PUNCT
ejpam-4303	106	28	]	]	PUNCT
ejpam-4303	106	29	(	(	PUNCT
ejpam-4303	106	30	λ	λ	NOUN
ejpam-4303	106	31	,	,	PUNCT
ejpam-4303	106	32	sp	sp	NOUN
ejpam-4303	106	33	)	)	PUNCT
ejpam-4303	106	34	⊆	⊆	NUM
ejpam-4303	106	35	f−(b	f−(b	PROPN
ejpam-4303	106	36	(	(	PUNCT
ejpam-4303	106	37	λ	λ	PROPN
ejpam-4303	106	38	,	,	PUNCT
ejpam-4303	106	39	sp	sp	NOUN
ejpam-4303	106	40	)	)	PUNCT
ejpam-4303	106	41	1	1	NUM
ejpam-4303	106	42	)	)	PUNCT
ejpam-4303	106	43	∪	∪	X
ejpam-4303	106	44	f+(b	f+(b	X
ejpam-4303	106	45	(	(	PUNCT
ejpam-4303	106	46	λ	λ	NOUN
ejpam-4303	106	47	,	,	PUNCT
ejpam-4303	106	48	sp	sp	NOUN
ejpam-4303	106	49	)	)	PUNCT
ejpam-4303	106	50	2	2	NUM
ejpam-4303	106	51	)	)	PUNCT
ejpam-4303	106	52	for	for	ADP
ejpam-4303	106	53	every	every	DET
ejpam-4303	106	54	subsets	subset	NOUN
ejpam-4303	106	55	b1	b1	NOUN
ejpam-4303	106	56	,	,	PUNCT
ejpam-4303	106	57	b2	b2	NOUN
ejpam-4303	106	58	of	of	ADP
ejpam-4303	106	59	y	y	PROPN
ejpam-4303	106	60	;	;	PUNCT
ejpam-4303	106	61	(	(	PUNCT
ejpam-4303	106	62	5	5	NUM
ejpam-4303	106	63	)	)	PUNCT
ejpam-4303	106	64	f+([b1](λ	f+([b1](λ	PROPN
ejpam-4303	106	65	,	,	PUNCT
ejpam-4303	106	66	sp	sp	NOUN
ejpam-4303	106	67	)	)	PUNCT
ejpam-4303	106	68	)	)	PUNCT
ejpam-4303	106	69	∩	∩	NOUN
ejpam-4303	106	70	f−([b2](λ	f−([b2](λ	NOUN
ejpam-4303	106	71	,	,	PUNCT
ejpam-4303	106	72	sp	sp	NOUN
ejpam-4303	106	73	)	)	PUNCT
ejpam-4303	106	74	)	)	PUNCT
ejpam-4303	107	1	⊆	⊆	NUM
ejpam-4303	107	2	[	[	X
ejpam-4303	107	3	f+(b	f+(b	X
ejpam-4303	107	4	(	(	PUNCT
ejpam-4303	107	5	λ	λ	NOUN
ejpam-4303	107	6	,	,	PUNCT
ejpam-4303	107	7	sp	sp	NOUN
ejpam-4303	107	8	)	)	PUNCT
ejpam-4303	107	9	1	1	NUM
ejpam-4303	107	10	)	)	PUNCT
ejpam-4303	107	11	∩	∩	PROPN
ejpam-4303	107	12	f−(b	f−(b	PROPN
ejpam-4303	107	13	(	(	PUNCT
ejpam-4303	107	14	λ	λ	PROPN
ejpam-4303	107	15	,	,	PUNCT
ejpam-4303	107	16	sp	sp	NOUN
ejpam-4303	107	17	)	)	PUNCT
ejpam-4303	107	18	2	2	NUM
ejpam-4303	107	19	)	)	PUNCT
ejpam-4303	107	20	]	]	PUNCT
ejpam-4303	107	21	(	(	PUNCT
ejpam-4303	107	22	λ	λ	NOUN
ejpam-4303	107	23	,	,	PUNCT
ejpam-4303	107	24	sp	sp	NOUN
ejpam-4303	107	25	)	)	PUNCT
ejpam-4303	107	26	for	for	ADP
ejpam-4303	107	27	every	every	DET
ejpam-4303	107	28	subsets	subset	NOUN
ejpam-4303	107	29	b1	b1	NOUN
ejpam-4303	107	30	,	,	PUNCT
ejpam-4303	107	31	b2	b2	NOUN
ejpam-4303	107	32	of	of	ADP
ejpam-4303	107	33	y	y	PROPN
ejpam-4303	107	34	;	;	PUNCT
ejpam-4303	107	35	(	(	PUNCT
ejpam-4303	107	36	6	6	X
ejpam-4303	107	37	)	)	PUNCT
ejpam-4303	107	38	[	[	X
ejpam-4303	107	39	f−(v1)∪f+(v2	f−(v1)∪f+(v2	NOUN
ejpam-4303	107	40	)	)	PUNCT
ejpam-4303	107	41	]	]	PUNCT
ejpam-4303	107	42	(	(	PUNCT
ejpam-4303	107	43	λ	λ	NOUN
ejpam-4303	107	44	,	,	PUNCT
ejpam-4303	107	45	sp	sp	NOUN
ejpam-4303	107	46	)	)	PUNCT
ejpam-4303	107	47	⊆	⊆	NUM
ejpam-4303	107	48	f−(v	f−(v	NOUN
ejpam-4303	107	49	(	(	PUNCT
ejpam-4303	107	50	λ	λ	NOUN
ejpam-4303	107	51	,	,	PUNCT
ejpam-4303	107	52	sp	sp	NOUN
ejpam-4303	107	53	)	)	PUNCT
ejpam-4303	107	54	1	1	NUM
ejpam-4303	107	55	)	)	PUNCT
ejpam-4303	107	56	∪f+(v	∪f+(v	X
ejpam-4303	107	57	(	(	PUNCT
ejpam-4303	107	58	λ	λ	NOUN
ejpam-4303	107	59	,	,	PUNCT
ejpam-4303	107	60	sp	sp	NOUN
ejpam-4303	107	61	)	)	PUNCT
ejpam-4303	107	62	2	2	NUM
ejpam-4303	107	63	)	)	PUNCT
ejpam-4303	107	64	for	for	ADP
ejpam-4303	107	65	every	every	DET
ejpam-4303	107	66	(	(	PUNCT
ejpam-4303	107	67	λ	λ	NOUN
ejpam-4303	107	68	,	,	PUNCT
ejpam-4303	107	69	sp)-open	sp)-open	ADJ
ejpam-4303	107	70	sets	set	NOUN
ejpam-4303	107	71	v1	v1	NOUN
ejpam-4303	107	72	,	,	PUNCT
ejpam-4303	107	73	v2	v2	PROPN
ejpam-4303	107	74	of	of	ADP
ejpam-4303	107	75	y	y	PROPN
ejpam-4303	107	76	.	.	PUNCT
ejpam-4303	108	1	proof	proof	NOUN
ejpam-4303	108	2	.	.	PUNCT
ejpam-4303	109	1	(	(	PUNCT
ejpam-4303	109	2	1	1	X
ejpam-4303	109	3	)	)	PUNCT
ejpam-4303	109	4	⇒	⇒	NOUN
ejpam-4303	109	5	(	(	PUNCT
ejpam-4303	109	6	2	2	NUM
ejpam-4303	109	7	):	):	PUNCT
ejpam-4303	109	8	let	let	VERB
ejpam-4303	109	9	v1	v1	NOUN
ejpam-4303	109	10	,	,	PUNCT
ejpam-4303	109	11	v2	v2	PROPN
ejpam-4303	109	12	be	be	AUX
ejpam-4303	109	13	any	any	DET
ejpam-4303	109	14	(	(	PUNCT
ejpam-4303	109	15	λ	λ	NOUN
ejpam-4303	109	16	,	,	PUNCT
ejpam-4303	109	17	sp)-open	sp)-open	ADJ
ejpam-4303	109	18	sets	set	NOUN
ejpam-4303	109	19	of	of	ADP
ejpam-4303	109	20	y	y	PRON
ejpam-4303	109	21	such	such	ADJ
ejpam-4303	109	22	that	that	SCONJ
ejpam-4303	109	23	x	x	SYM
ejpam-4303	109	24	∈	∈	NOUN
ejpam-4303	109	25	f+(v1	f+(v1	NOUN
ejpam-4303	109	26	)	)	PUNCT
ejpam-4303	109	27	∩	∩	NOUN
ejpam-4303	109	28	f−(v2	f−(v2	NUM
ejpam-4303	109	29	)	)	PUNCT
ejpam-4303	109	30	.	.	PUNCT
ejpam-4303	110	1	then	then	ADV
ejpam-4303	110	2	,	,	PUNCT
ejpam-4303	110	3	f	f	PROPN
ejpam-4303	110	4	(	(	PUNCT
ejpam-4303	110	5	x	x	X
ejpam-4303	110	6	)	)	PUNCT
ejpam-4303	110	7	∈	∈	NOUN
ejpam-4303	110	8	v	v	ADP
ejpam-4303	110	9	+	+	CCONJ
ejpam-4303	110	10	1	1	NUM
ejpam-4303	110	11	∩v	∩v	NOUN
ejpam-4303	110	12	−	−	PROPN
ejpam-4303	110	13	2	2	NUM
ejpam-4303	110	14	and	and	CCONJ
ejpam-4303	110	15	hence	hence	ADV
ejpam-4303	110	16	there	there	PRON
ejpam-4303	110	17	exists	exist	VERB
ejpam-4303	110	18	a	a	DET
ejpam-4303	110	19	(	(	PUNCT
ejpam-4303	110	20	λ	λ	NOUN
ejpam-4303	110	21	,	,	PUNCT
ejpam-4303	110	22	sp)-open	sp)-open	NOUN
ejpam-4303	110	23	set	set	VERB
ejpam-4303	110	24	u	u	NOUN
ejpam-4303	110	25	of	of	ADP
ejpam-4303	110	26	x	x	PUNCT
ejpam-4303	110	27	containing	contain	VERB
ejpam-4303	110	28	x	x	PUNCT
ejpam-4303	110	29	such	such	ADJ
ejpam-4303	110	30	that	that	SCONJ
ejpam-4303	110	31	f	f	PROPN
ejpam-4303	110	32	(	(	PUNCT
ejpam-4303	110	33	u	u	NOUN
ejpam-4303	110	34	)	)	PUNCT
ejpam-4303	110	35	⊆	⊆	NUM
ejpam-4303	110	36	v	v	NOUN
ejpam-4303	110	37	(	(	PUNCT
ejpam-4303	110	38	λ	λ	NOUN
ejpam-4303	110	39	,	,	PUNCT
ejpam-4303	110	40	sp	sp	NOUN
ejpam-4303	110	41	)	)	PUNCT
ejpam-4303	110	42	1	1	NUM
ejpam-4303	110	43	and	and	CCONJ
ejpam-4303	110	44	f	f	PROPN
ejpam-4303	110	45	(	(	PUNCT
ejpam-4303	110	46	z	z	NOUN
ejpam-4303	110	47	)	)	PUNCT
ejpam-4303	110	48	∩	∩	ADJ
ejpam-4303	110	49	v	v	X
ejpam-4303	110	50	(	(	PUNCT
ejpam-4303	110	51	λ	λ	PROPN
ejpam-4303	110	52	,	,	PUNCT
ejpam-4303	110	53	sp	sp	NOUN
ejpam-4303	110	54	)	)	PUNCT
ejpam-4303	110	55	2	2	NUM
ejpam-4303	110	56	6=	6=	NOUN
ejpam-4303	110	57	∅	∅	NOUN
ejpam-4303	110	58	for	for	ADP
ejpam-4303	110	59	each	each	DET
ejpam-4303	110	60	z	z	NOUN
ejpam-4303	110	61	∈	∈	PROPN
ejpam-4303	110	62	u	u	NOUN
ejpam-4303	110	63	.	.	PUNCT
ejpam-4303	111	1	thus	thus	ADV
ejpam-4303	111	2	,	,	PUNCT
ejpam-4303	111	3	x	x	PUNCT
ejpam-4303	111	4	∈	∈	PROPN
ejpam-4303	111	5	u	u	NOUN
ejpam-4303	111	6	⊆	⊆	NUM
ejpam-4303	111	7	f+(v	f+(v	NOUN
ejpam-4303	111	8	(	(	PUNCT
ejpam-4303	111	9	λ	λ	NOUN
ejpam-4303	111	10	,	,	PUNCT
ejpam-4303	111	11	sp	sp	NOUN
ejpam-4303	111	12	)	)	PUNCT
ejpam-4303	111	13	1	1	NUM
ejpam-4303	111	14	)	)	PUNCT
ejpam-4303	111	15	∩	∩	PROPN
ejpam-4303	111	16	f−(v	f−(v	NOUN
ejpam-4303	111	17	(	(	PUNCT
ejpam-4303	111	18	λ	λ	NOUN
ejpam-4303	111	19	,	,	PUNCT
ejpam-4303	111	20	sp	sp	NOUN
ejpam-4303	111	21	)	)	PUNCT
ejpam-4303	111	22	2	2	NUM
ejpam-4303	111	23	)	)	PUNCT
ejpam-4303	111	24	and	and	CCONJ
ejpam-4303	111	25	hence	hence	ADV
ejpam-4303	111	26	x	x	X
ejpam-4303	111	27	∈	∈	PROPN
ejpam-4303	112	1	[	[	X
ejpam-4303	112	2	f+(v	f+(v	NOUN
ejpam-4303	112	3	(	(	PUNCT
ejpam-4303	112	4	λ	λ	NOUN
ejpam-4303	112	5	,	,	PUNCT
ejpam-4303	112	6	sp	sp	NOUN
ejpam-4303	112	7	)	)	PUNCT
ejpam-4303	112	8	1	1	NUM
ejpam-4303	112	9	)	)	PUNCT
ejpam-4303	112	10	∩	∩	PROPN
ejpam-4303	112	11	f−(v	f−(v	NOUN
ejpam-4303	112	12	(	(	PUNCT
ejpam-4303	112	13	λ	λ	NOUN
ejpam-4303	112	14	,	,	PUNCT
ejpam-4303	112	15	sp	sp	NOUN
ejpam-4303	112	16	)	)	PUNCT
ejpam-4303	112	17	2	2	NUM
ejpam-4303	112	18	)	)	PUNCT
ejpam-4303	112	19	]	]	PUNCT
ejpam-4303	112	20	(	(	PUNCT
ejpam-4303	112	21	λ	λ	NOUN
ejpam-4303	112	22	,	,	PUNCT
ejpam-4303	112	23	sp	sp	NOUN
ejpam-4303	112	24	)	)	PUNCT
ejpam-4303	112	25	.	.	PUNCT
ejpam-4303	113	1	this	this	PRON
ejpam-4303	113	2	shows	show	VERB
ejpam-4303	113	3	that	that	SCONJ
ejpam-4303	113	4	f+(v1	f+(v1	VERB
ejpam-4303	113	5	)	)	PUNCT
ejpam-4303	113	6	∩	∩	NOUN
ejpam-4303	113	7	f−(v2	f−(v2	X
ejpam-4303	113	8	)	)	PUNCT
ejpam-4303	113	9	⊆	⊆	NUM
ejpam-4303	113	10	[	[	X
ejpam-4303	113	11	f+(v	f+(v	NOUN
ejpam-4303	113	12	(	(	PUNCT
ejpam-4303	113	13	λ	λ	NOUN
ejpam-4303	113	14	,	,	PUNCT
ejpam-4303	113	15	sp	sp	NOUN
ejpam-4303	113	16	)	)	PUNCT
ejpam-4303	113	17	1	1	NUM
ejpam-4303	113	18	)	)	PUNCT
ejpam-4303	113	19	∩	∩	PROPN
ejpam-4303	113	20	f−(v	f−(v	NOUN
ejpam-4303	113	21	(	(	PUNCT
ejpam-4303	113	22	λ	λ	NOUN
ejpam-4303	113	23	,	,	PUNCT
ejpam-4303	113	24	sp	sp	NOUN
ejpam-4303	113	25	)	)	PUNCT
ejpam-4303	113	26	2	2	NUM
ejpam-4303	113	27	)	)	PUNCT
ejpam-4303	113	28	]	]	PUNCT
ejpam-4303	113	29	(	(	PUNCT
ejpam-4303	113	30	λ	λ	NOUN
ejpam-4303	113	31	,	,	PUNCT
ejpam-4303	113	32	sp	sp	NOUN
ejpam-4303	113	33	)	)	PUNCT
ejpam-4303	113	34	.	.	PUNCT
ejpam-4303	114	1	(	(	PUNCT
ejpam-4303	114	2	2	2	X
ejpam-4303	114	3	)	)	PUNCT
ejpam-4303	114	4	⇒	⇒	NOUN
ejpam-4303	114	5	(	(	PUNCT
ejpam-4303	114	6	3	3	NUM
ejpam-4303	114	7	):	):	PUNCT
ejpam-4303	114	8	let	let	VERB
ejpam-4303	114	9	k1,k2	k1,k2	PROPN
ejpam-4303	114	10	be	be	AUX
ejpam-4303	114	11	any	any	DET
ejpam-4303	114	12	(	(	PUNCT
ejpam-4303	114	13	λ	λ	PROPN
ejpam-4303	114	14	,	,	PUNCT
ejpam-4303	114	15	sp)-closed	sp)-close	VERB
ejpam-4303	114	16	sets	set	NOUN
ejpam-4303	114	17	of	of	ADP
ejpam-4303	114	18	y	y	PROPN
ejpam-4303	114	19	.	.	PUNCT
ejpam-4303	115	1	then	then	ADV
ejpam-4303	115	2	,	,	PUNCT
ejpam-4303	115	3	y	y	PROPN
ejpam-4303	115	4	−k1	−k1	PROPN
ejpam-4303	115	5	and	and	CCONJ
ejpam-4303	115	6	y	y	PROPN
ejpam-4303	115	7	−k2	−k2	PROPN
ejpam-4303	115	8	are	be	AUX
ejpam-4303	115	9	(	(	PUNCT
ejpam-4303	115	10	λ	λ	X
ejpam-4303	115	11	,	,	PUNCT
ejpam-4303	115	12	sp)-open	sp)-open	ADJ
ejpam-4303	115	13	sets	set	NOUN
ejpam-4303	115	14	in	in	ADP
ejpam-4303	115	15	y	y	PROPN
ejpam-4303	115	16	,	,	PUNCT
ejpam-4303	115	17	by	by	ADP
ejpam-4303	115	18	(	(	PUNCT
ejpam-4303	115	19	2	2	NUM
ejpam-4303	115	20	)	)	PUNCT
ejpam-4303	115	21	,	,	PUNCT
ejpam-4303	115	22	x	x	PUNCT
ejpam-4303	115	23	−	−	NOUN
ejpam-4303	115	24	(	(	PUNCT
ejpam-4303	115	25	f−(k1	f−(k1	NOUN
ejpam-4303	115	26	)	)	PUNCT
ejpam-4303	115	27	∪	∪	ADP
ejpam-4303	115	28	f+(k2	f+(k2	NOUN
ejpam-4303	115	29	)	)	PUNCT
ejpam-4303	115	30	)	)	PUNCT
ejpam-4303	116	1	=	=	PUNCT
ejpam-4303	116	2	(	(	PUNCT
ejpam-4303	116	3	x	x	NOUN
ejpam-4303	116	4	−	−	NOUN
ejpam-4303	116	5	f−(k1	f−(k1	NOUN
ejpam-4303	116	6	)	)	PUNCT
ejpam-4303	116	7	)	)	PUNCT
ejpam-4303	117	1	∩	∩	NOUN
ejpam-4303	117	2	(	(	PUNCT
ejpam-4303	117	3	x	x	SYM
ejpam-4303	117	4	−	−	PROPN
ejpam-4303	117	5	f+(k2	f+(k2	NOUN
ejpam-4303	117	6	)	)	PUNCT
ejpam-4303	117	7	)	)	PUNCT
ejpam-4303	118	1	=	=	PUNCT
ejpam-4303	118	2	f+(y	f+(y	NOUN
ejpam-4303	118	3	−k1	−k1	NOUN
ejpam-4303	118	4	)	)	PUNCT
ejpam-4303	118	5	∩	∩	ADJ
ejpam-4303	118	6	f−(y	f−(y	NOUN
ejpam-4303	118	7	−k2	−k2	NOUN
ejpam-4303	118	8	)	)	PUNCT
ejpam-4303	118	9	⊆	⊆	NUM
ejpam-4303	119	1	[	[	X
ejpam-4303	119	2	f+([y	f+([y	ADJ
ejpam-4303	119	3	−k1	−k1	NOUN
ejpam-4303	119	4	]	]	X
ejpam-4303	119	5	(	(	PUNCT
ejpam-4303	119	6	λ	λ	NOUN
ejpam-4303	119	7	,	,	PUNCT
ejpam-4303	119	8	sp	sp	NOUN
ejpam-4303	119	9	)	)	PUNCT
ejpam-4303	119	10	)	)	PUNCT
ejpam-4303	119	11	∩	∩	ADJ
ejpam-4303	119	12	f−([y	f−([y	ADJ
ejpam-4303	119	13	−k2	−k2	PROPN
ejpam-4303	119	14	]	]	PUNCT
ejpam-4303	119	15	(	(	PUNCT
ejpam-4303	119	16	λ	λ	INTJ
ejpam-4303	119	17	,	,	PUNCT
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ejpam-4303	119	19	,	,	PUNCT
ejpam-4303	119	20	sp	sp	NOUN
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ejpam-4303	119	22	=	=	PUNCT
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ejpam-4303	120	2	(	(	PUNCT
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ejpam-4303	120	4	−	−	NOUN
ejpam-4303	120	5	f−([k1](λ	f−([k1](λ	NOUN
ejpam-4303	120	6	,	,	PUNCT
ejpam-4303	120	7	sp	sp	NOUN
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ejpam-4303	120	9	)	)	PUNCT
ejpam-4303	120	10	)	)	PUNCT
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ejpam-4303	120	15	f+([k2](λ	f+([k2](λ	NOUN
ejpam-4303	120	16	,	,	PUNCT
ejpam-4303	120	17	sp)))](λ	sp)))](λ	PROPN
ejpam-4303	120	18	,	,	PUNCT
ejpam-4303	120	19	sp	sp	NOUN
ejpam-4303	120	20	)	)	PUNCT
ejpam-4303	120	21	=	=	PUNCT
ejpam-4303	121	1	[	[	X
ejpam-4303	121	2	x	x	X
ejpam-4303	121	3	−	−	PROPN
ejpam-4303	122	1	[	[	X
ejpam-4303	122	2	f−([k1](λ	f−([k1](λ	NOUN
ejpam-4303	122	3	,	,	PUNCT
ejpam-4303	122	4	sp	sp	NOUN
ejpam-4303	122	5	)	)	PUNCT
ejpam-4303	122	6	)	)	PUNCT
ejpam-4303	122	7	∪	∪	ADP
ejpam-4303	122	8	f+([k2](λ	f+([k2](λ	NOUN
ejpam-4303	122	9	,	,	PUNCT
ejpam-4303	122	10	sp))]](λ	sp))]](λ	PROPN
ejpam-4303	122	11	,	,	PUNCT
ejpam-4303	122	12	sp	sp	NOUN
ejpam-4303	122	13	)	)	PUNCT
ejpam-4303	122	14	=	=	PUNCT
ejpam-4303	123	1	x	x	X
ejpam-4303	123	2	−	−	PROPN
ejpam-4303	124	1	[	[	X
ejpam-4303	124	2	f−([k1](λ	f−([k1](λ	NOUN
ejpam-4303	124	3	,	,	PUNCT
ejpam-4303	124	4	sp	sp	NOUN
ejpam-4303	124	5	)	)	PUNCT
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ejpam-4303	124	7	∪	∪	ADP
ejpam-4303	124	8	f+([k2](λ	f+([k2](λ	SYM
ejpam-4303	124	9	,	,	PUNCT
ejpam-4303	124	10	sp	sp	NOUN
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ejpam-4303	124	13	]	]	PUNCT
ejpam-4303	125	1	(	(	PUNCT
ejpam-4303	125	2	λ	λ	NOUN
ejpam-4303	125	3	,	,	PUNCT
ejpam-4303	125	4	sp	sp	NOUN
ejpam-4303	125	5	)	)	PUNCT
ejpam-4303	125	6	and	and	CCONJ
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ejpam-4303	125	8	[	[	X
ejpam-4303	125	9	f−([k1](λ	f−([k1](λ	NOUN
ejpam-4303	125	10	,	,	PUNCT
ejpam-4303	125	11	sp	sp	NOUN
ejpam-4303	125	12	)	)	PUNCT
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ejpam-4303	125	14	∪	∪	ADP
ejpam-4303	125	15	f+([k2](λ	f+([k2](λ	SYM
ejpam-4303	125	16	,	,	PUNCT
ejpam-4303	125	17	sp	sp	NOUN
ejpam-4303	125	18	)	)	PUNCT
ejpam-4303	125	19	)	)	PUNCT
ejpam-4303	125	20	]	]	PUNCT
ejpam-4303	125	21	(	(	PUNCT
ejpam-4303	125	22	λ	λ	NOUN
ejpam-4303	125	23	,	,	PUNCT
ejpam-4303	125	24	sp	sp	NOUN
ejpam-4303	125	25	)	)	PUNCT
ejpam-4303	125	26	⊆	⊆	NUM
ejpam-4303	125	27	f−(k1	f−(k1	NOUN
ejpam-4303	125	28	)	)	PUNCT
ejpam-4303	125	29	∪	∪	ADP
ejpam-4303	125	30	f+(k2	f+(k2	NOUN
ejpam-4303	125	31	)	)	PUNCT
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ejpam-4303	126	1	(	(	PUNCT
ejpam-4303	126	2	3	3	X
ejpam-4303	126	3	)	)	PUNCT
ejpam-4303	126	4	⇒	⇒	NOUN
ejpam-4303	126	5	(	(	PUNCT
ejpam-4303	126	6	4	4	NUM
ejpam-4303	126	7	):	):	PUNCT
ejpam-4303	126	8	let	let	VERB
ejpam-4303	126	9	b1	b1	NOUN
ejpam-4303	126	10	,	,	PUNCT
ejpam-4303	126	11	b2	b2	NOUN
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ejpam-4303	126	14	subsets	subset	NOUN
ejpam-4303	126	15	of	of	ADP
ejpam-4303	126	16	y	y	PROPN
ejpam-4303	126	17	.	.	PUNCT
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ejpam-4303	127	2	,	,	PUNCT
ejpam-4303	127	3	b(λ	b(λ	PROPN
ejpam-4303	127	4	,	,	PUNCT
ejpam-4303	127	5	sp	sp	NOUN
ejpam-4303	127	6	)	)	PUNCT
ejpam-4303	127	7	1	1	NUM
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ejpam-4303	127	9	b	b	PROPN
ejpam-4303	127	10	(	(	PUNCT
ejpam-4303	127	11	λ	λ	NOUN
ejpam-4303	127	12	,	,	PUNCT
ejpam-4303	127	13	sp	sp	NOUN
ejpam-4303	127	14	)	)	PUNCT
ejpam-4303	127	15	2	2	NUM
ejpam-4303	127	16	are	be	AUX
ejpam-4303	127	17	(	(	PUNCT
ejpam-4303	127	18	λ	λ	X
ejpam-4303	127	19	,	,	PUNCT
ejpam-4303	127	20	sp)-closed	sp)-close	VERB
ejpam-4303	127	21	in	in	ADP
ejpam-4303	127	22	y	y	PROPN
ejpam-4303	127	23	and	and	CCONJ
ejpam-4303	127	24	by	by	ADP
ejpam-4303	127	25	(	(	PUNCT
ejpam-4303	127	26	3	3	NUM
ejpam-4303	127	27	)	)	PUNCT
ejpam-4303	127	28	,	,	PUNCT
ejpam-4303	128	1	[	[	X
ejpam-4303	128	2	f−([b	f−([b	PROPN
ejpam-4303	128	3	(	(	PUNCT
ejpam-4303	128	4	λ	λ	PROPN
ejpam-4303	128	5	,	,	PUNCT
ejpam-4303	128	6	sp	sp	NOUN
ejpam-4303	128	7	)	)	PUNCT
ejpam-4303	128	8	1	1	NUM
ejpam-4303	128	9	]	]	PUNCT
ejpam-4303	128	10	(	(	PUNCT
ejpam-4303	128	11	λ	λ	NOUN
ejpam-4303	128	12	,	,	PUNCT
ejpam-4303	128	13	sp	sp	NOUN
ejpam-4303	128	14	)	)	PUNCT
ejpam-4303	128	15	)	)	PUNCT
ejpam-4303	128	16	∪	∪	ADP
ejpam-4303	128	17	f+([b	f+([b	PROPN
ejpam-4303	128	18	(	(	PUNCT
ejpam-4303	128	19	λ	λ	PROPN
ejpam-4303	128	20	,	,	PUNCT
ejpam-4303	128	21	sp	sp	NOUN
ejpam-4303	128	22	)	)	PUNCT
ejpam-4303	128	23	2	2	NUM
ejpam-4303	128	24	]	]	PUNCT
ejpam-4303	128	25	(	(	PUNCT
ejpam-4303	128	26	λ	λ	NOUN
ejpam-4303	128	27	,	,	PUNCT
ejpam-4303	128	28	sp	sp	NOUN
ejpam-4303	128	29	)	)	PUNCT
ejpam-4303	128	30	)	)	PUNCT
ejpam-4303	128	31	]	]	PUNCT
ejpam-4303	128	32	(	(	PUNCT
ejpam-4303	128	33	λ	λ	NOUN
ejpam-4303	128	34	,	,	PUNCT
ejpam-4303	128	35	sp	sp	NOUN
ejpam-4303	128	36	)	)	PUNCT
ejpam-4303	128	37	⊆	⊆	NUM
ejpam-4303	128	38	f−(b	f−(b	PROPN
ejpam-4303	128	39	(	(	PUNCT
ejpam-4303	128	40	λ	λ	PROPN
ejpam-4303	128	41	,	,	PUNCT
ejpam-4303	128	42	sp	sp	NOUN
ejpam-4303	128	43	)	)	PUNCT
ejpam-4303	128	44	1	1	NUM
ejpam-4303	128	45	)	)	PUNCT
ejpam-4303	128	46	∪	∪	ADP
ejpam-4303	128	47	f+(b	f+(b	X
ejpam-4303	128	48	(	(	PUNCT
ejpam-4303	128	49	λ	λ	NOUN
ejpam-4303	128	50	,	,	PUNCT
ejpam-4303	128	51	sp	sp	NOUN
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ejpam-4303	128	53	2	2	NUM
ejpam-4303	128	54	)	)	PUNCT
ejpam-4303	128	55	.	.	PUNCT
ejpam-4303	129	1	(	(	PUNCT
ejpam-4303	129	2	4	4	X
ejpam-4303	129	3	)	)	PUNCT
ejpam-4303	129	4	⇒	⇒	NOUN
ejpam-4303	129	5	(	(	PUNCT
ejpam-4303	129	6	5	5	NUM
ejpam-4303	129	7	):	):	PUNCT
ejpam-4303	129	8	let	let	VERB
ejpam-4303	129	9	b1	b1	NOUN
ejpam-4303	129	10	,	,	PUNCT
ejpam-4303	129	11	b2	b2	NOUN
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ejpam-4303	129	13	any	any	DET
ejpam-4303	129	14	subsets	subset	NOUN
ejpam-4303	129	15	of	of	ADP
ejpam-4303	129	16	y	y	PROPN
ejpam-4303	129	17	.	.	PUNCT
ejpam-4303	130	1	by	by	ADP
ejpam-4303	130	2	(	(	PUNCT
ejpam-4303	130	3	4	4	NUM
ejpam-4303	130	4	)	)	PUNCT
ejpam-4303	130	5	,	,	PUNCT
ejpam-4303	130	6	we	we	PRON
ejpam-4303	130	7	have	have	VERB
ejpam-4303	130	8	f−([b1](λ	f−([b1](λ	NOUN
ejpam-4303	130	9	,	,	PUNCT
ejpam-4303	130	10	sp	sp	NOUN
ejpam-4303	130	11	)	)	PUNCT
ejpam-4303	130	12	)	)	PUNCT
ejpam-4303	130	13	∩	∩	NOUN
ejpam-4303	130	14	f+([b2](λ	f+([b2](λ	NOUN
ejpam-4303	130	15	,	,	PUNCT
ejpam-4303	130	16	sp	sp	NOUN
ejpam-4303	130	17	)	)	PUNCT
ejpam-4303	130	18	)	)	PUNCT
ejpam-4303	131	1	=	=	PUNCT
ejpam-4303	131	2	x	x	X
ejpam-4303	132	1	−	−	PUNCT
ejpam-4303	132	2	[	[	X
ejpam-4303	132	3	f+([y	f+([y	NOUN
ejpam-4303	132	4	−b1	−b1	PROPN
ejpam-4303	132	5	]	]	PUNCT
ejpam-4303	132	6	(	(	PUNCT
ejpam-4303	132	7	λ	λ	NOUN
ejpam-4303	132	8	,	,	PUNCT
ejpam-4303	132	9	sp	sp	NOUN
ejpam-4303	132	10	)	)	PUNCT
ejpam-4303	132	11	)	)	PUNCT
ejpam-4303	132	12	∪	∪	ADP
ejpam-4303	132	13	f−([y	f−([y	ADJ
ejpam-4303	132	14	−b2	−b2	PROPN
ejpam-4303	132	15	]	]	PUNCT
ejpam-4303	132	16	(	(	PUNCT
ejpam-4303	132	17	λ	λ	NOUN
ejpam-4303	132	18	,	,	PUNCT
ejpam-4303	132	19	sp	sp	NOUN
ejpam-4303	132	20	)	)	PUNCT
ejpam-4303	132	21	)	)	PUNCT
ejpam-4303	132	22	]	]	PUNCT
ejpam-4303	133	1	⊆	⊆	NUM
ejpam-4303	133	2	x	x	SYM
ejpam-4303	133	3	−	−	PUNCT
ejpam-4303	133	4	[	[	X
ejpam-4303	133	5	f+([[y	f+([[y	X
ejpam-4303	133	6	−b1	−b1	PROPN
ejpam-4303	133	7	]	]	PUNCT
ejpam-4303	133	8	(	(	PUNCT
ejpam-4303	133	9	λ	λ	PROPN
ejpam-4303	133	10	,	,	PUNCT
ejpam-4303	133	11	sp)](λ	sp)](λ	PROPN
ejpam-4303	133	12	,	,	PUNCT
ejpam-4303	133	13	sp	sp	NOUN
ejpam-4303	133	14	)	)	PUNCT
ejpam-4303	133	15	)	)	PUNCT
ejpam-4303	133	16	∪	∪	ADP
ejpam-4303	133	17	f−([[y	f−([[y	NUM
ejpam-4303	133	18	−b2	−b2	PROPN
ejpam-4303	133	19	]	]	PUNCT
ejpam-4303	133	20	(	(	PUNCT
ejpam-4303	133	21	λ	λ	PROPN
ejpam-4303	133	22	,	,	PUNCT
ejpam-4303	133	23	sp)](λ	sp)](λ	PROPN
ejpam-4303	133	24	,	,	PUNCT
ejpam-4303	133	25	sp	sp	NOUN
ejpam-4303	133	26	)	)	PUNCT
ejpam-4303	133	27	)	)	PUNCT
ejpam-4303	133	28	]	]	PUNCT
ejpam-4303	133	29	(	(	PUNCT
ejpam-4303	133	30	λ	λ	NOUN
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ejpam-4303	133	32	sp	sp	NOUN
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ejpam-4303	133	34	c.	c.	NOUN
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ejpam-4303	133	36	,	,	PUNCT
ejpam-4303	133	37	c.	c.	PROPN
ejpam-4303	133	38	viriyapong	viriyapong	PROPN
ejpam-4303	133	39	/	/	SYM
ejpam-4303	133	40	eur	eur	PROPN
ejpam-4303	133	41	.	.	PUNCT
ejpam-4303	134	1	j.	j.	PROPN
ejpam-4303	134	2	pure	pure	PROPN
ejpam-4303	134	3	appl	appl	PROPN
ejpam-4303	134	4	.	.	PROPN
ejpam-4303	134	5	math	math	PROPN
ejpam-4303	134	6	,	,	PUNCT
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ejpam-4303	134	8	(	(	PUNCT
ejpam-4303	134	9	2	2	NUM
ejpam-4303	134	10	)	)	PUNCT
ejpam-4303	134	11	(	(	PUNCT
ejpam-4303	134	12	2022	2022	NUM
ejpam-4303	134	13	)	)	PUNCT
ejpam-4303	134	14	,	,	PUNCT
ejpam-4303	134	15	528	528	NUM
ejpam-4303	134	16	-	-	SYM
ejpam-4303	134	17	536	536	NUM
ejpam-4303	134	18	532	532	NUM
ejpam-4303	134	19	=	=	NOUN
ejpam-4303	134	20	x	x	SYM
ejpam-4303	134	21	−	−	PROPN
ejpam-4303	135	1	[	[	X
ejpam-4303	135	2	f+(y	f+(y	X
ejpam-4303	135	3	−	−	PROPN
ejpam-4303	136	1	[	[	X
ejpam-4303	136	2	[	[	X
ejpam-4303	136	3	b1](λ	b1](λ	PROPN
ejpam-4303	136	4	,	,	PUNCT
ejpam-4303	136	5	sp	sp	NOUN
ejpam-4303	136	6	)	)	PUNCT
ejpam-4303	136	7	]	]	PUNCT
ejpam-4303	136	8	(	(	PUNCT
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ejpam-4303	136	10	,	,	PUNCT
ejpam-4303	136	11	sp	sp	NOUN
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ejpam-4303	136	14	∪	∪	ADP
ejpam-4303	136	15	f−(y	f−(y	NOUN
ejpam-4303	136	16	−	−	PUNCT
ejpam-4303	137	1	[	[	X
ejpam-4303	137	2	[	[	X
ejpam-4303	137	3	b2](λ	b2](λ	NOUN
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ejpam-4303	137	5	sp	sp	NOUN
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ejpam-4303	137	7	]	]	PUNCT
ejpam-4303	137	8	(	(	PUNCT
ejpam-4303	137	9	λ	λ	INTJ
ejpam-4303	137	10	,	,	PUNCT
ejpam-4303	137	11	sp))](λ	sp))](λ	PROPN
ejpam-4303	137	12	,	,	PUNCT
ejpam-4303	137	13	sp	sp	NOUN
ejpam-4303	137	14	)	)	PUNCT
ejpam-4303	137	15	=	=	PUNCT
ejpam-4303	138	1	x	x	X
ejpam-4303	138	2	−	−	PROPN
ejpam-4303	139	1	[	[	X
ejpam-4303	139	2	(	(	PUNCT
ejpam-4303	139	3	x	x	INTJ
ejpam-4303	139	4	−	−	NOUN
ejpam-4303	139	5	f−([[b1](λ	f−([[b1](λ	NOUN
ejpam-4303	139	6	,	,	PUNCT
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ejpam-4303	139	9	]	]	PUNCT
ejpam-4303	139	10	(	(	PUNCT
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ejpam-4303	139	12	,	,	PUNCT
ejpam-4303	139	13	sp	sp	NOUN
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ejpam-4303	139	17	∪	∪	ADP
ejpam-4303	139	18	(	(	PUNCT
ejpam-4303	139	19	x	x	NOUN
ejpam-4303	139	20	−	−	NOUN
ejpam-4303	139	21	f+([[b2](λ	f+([[b2](λ	NOUN
ejpam-4303	139	22	,	,	PUNCT
ejpam-4303	139	23	sp	sp	NOUN
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ejpam-4303	139	25	]	]	PUNCT
ejpam-4303	139	26	(	(	PUNCT
ejpam-4303	139	27	λ	λ	X
ejpam-4303	139	28	,	,	PUNCT
ejpam-4303	139	29	sp)))](λ	sp)))](λ	PROPN
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ejpam-4303	139	33	=	=	PUNCT
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ejpam-4303	139	35	−	−	PUNCT
ejpam-4303	140	1	[	[	X
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ejpam-4303	140	3	−	−	PROPN
ejpam-4303	140	4	[	[	X
ejpam-4303	140	5	f−([[b1](λ	f−([[b1](λ	X
ejpam-4303	140	6	,	,	PUNCT
ejpam-4303	140	7	sp	sp	NOUN
ejpam-4303	140	8	)	)	PUNCT
ejpam-4303	140	9	]	]	PUNCT
ejpam-4303	140	10	(	(	PUNCT
ejpam-4303	140	11	λ	λ	NOUN
ejpam-4303	140	12	,	,	PUNCT
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ejpam-4303	140	15	)	)	PUNCT
ejpam-4303	140	16	∩	∩	NOUN
ejpam-4303	140	17	f+([[b2](λ	f+([[b2](λ	NOUN
ejpam-4303	140	18	,	,	PUNCT
ejpam-4303	140	19	sp	sp	NOUN
ejpam-4303	140	20	)	)	PUNCT
ejpam-4303	140	21	]	]	PUNCT
ejpam-4303	140	22	(	(	PUNCT
ejpam-4303	140	23	λ	λ	X
ejpam-4303	140	24	,	,	PUNCT
ejpam-4303	140	25	sp))]](λ	sp))]](λ	X
ejpam-4303	140	26	,	,	PUNCT
ejpam-4303	140	27	sp	sp	NOUN
ejpam-4303	140	28	)	)	PUNCT
ejpam-4303	140	29	=	=	PUNCT
ejpam-4303	141	1	[	[	X
ejpam-4303	141	2	f−([[b1](λ	f−([[b1](λ	X
ejpam-4303	141	3	,	,	PUNCT
ejpam-4303	141	4	sp	sp	NOUN
ejpam-4303	141	5	)	)	PUNCT
ejpam-4303	141	6	]	]	PUNCT
ejpam-4303	141	7	(	(	PUNCT
ejpam-4303	141	8	λ	λ	NOUN
ejpam-4303	141	9	,	,	PUNCT
ejpam-4303	141	10	sp	sp	NOUN
ejpam-4303	141	11	)	)	PUNCT
ejpam-4303	141	12	)	)	PUNCT
ejpam-4303	141	13	∩	∩	NOUN
ejpam-4303	141	14	f+([[b2](λ	f+([[b2](λ	NOUN
ejpam-4303	141	15	,	,	PUNCT
ejpam-4303	141	16	sp	sp	NOUN
ejpam-4303	141	17	)	)	PUNCT
ejpam-4303	141	18	]	]	PUNCT
ejpam-4303	141	19	(	(	PUNCT
ejpam-4303	141	20	λ	λ	INTJ
ejpam-4303	141	21	,	,	PUNCT
ejpam-4303	141	22	sp))](λ	sp))](λ	PROPN
ejpam-4303	141	23	,	,	PUNCT
ejpam-4303	141	24	sp	sp	NOUN
ejpam-4303	141	25	)	)	PUNCT
ejpam-4303	141	26	.	.	PUNCT
ejpam-4303	142	1	thus	thus	ADV
ejpam-4303	142	2	,	,	PUNCT
ejpam-4303	142	3	f+([b1](λ	f+([b1](λ	PROPN
ejpam-4303	142	4	,	,	PUNCT
ejpam-4303	142	5	sp	sp	NOUN
ejpam-4303	142	6	)	)	PUNCT
ejpam-4303	142	7	)	)	PUNCT
ejpam-4303	142	8	∩	∩	NOUN
ejpam-4303	142	9	f−([b2](λ	f−([b2](λ	NOUN
ejpam-4303	142	10	,	,	PUNCT
ejpam-4303	142	11	sp	sp	NOUN
ejpam-4303	142	12	)	)	PUNCT
ejpam-4303	142	13	)	)	PUNCT
ejpam-4303	143	1	⊆	⊆	NUM
ejpam-4303	143	2	[	[	X
ejpam-4303	143	3	f+(b	f+(b	X
ejpam-4303	143	4	(	(	PUNCT
ejpam-4303	143	5	λ	λ	NOUN
ejpam-4303	143	6	,	,	PUNCT
ejpam-4303	143	7	sp	sp	NOUN
ejpam-4303	143	8	)	)	PUNCT
ejpam-4303	143	9	1	1	NUM
ejpam-4303	143	10	)	)	PUNCT
ejpam-4303	143	11	∩	∩	PROPN
ejpam-4303	143	12	f−(b	f−(b	PROPN
ejpam-4303	143	13	(	(	PUNCT
ejpam-4303	143	14	λ	λ	PROPN
ejpam-4303	143	15	,	,	PUNCT
ejpam-4303	143	16	sp	sp	NOUN
ejpam-4303	143	17	)	)	PUNCT
ejpam-4303	143	18	2	2	NUM
ejpam-4303	143	19	)	)	PUNCT
ejpam-4303	143	20	]	]	PUNCT
ejpam-4303	143	21	(	(	PUNCT
ejpam-4303	143	22	λ	λ	NOUN
ejpam-4303	143	23	,	,	PUNCT
ejpam-4303	143	24	sp	sp	NOUN
ejpam-4303	143	25	)	)	PUNCT
ejpam-4303	143	26	.	.	PUNCT
ejpam-4303	144	1	(	(	PUNCT
ejpam-4303	144	2	5	5	X
ejpam-4303	144	3	)	)	PUNCT
ejpam-4303	144	4	⇒	⇒	NOUN
ejpam-4303	144	5	(	(	PUNCT
ejpam-4303	144	6	2	2	NUM
ejpam-4303	144	7	):	):	PUNCT
ejpam-4303	144	8	the	the	DET
ejpam-4303	144	9	proof	proof	NOUN
ejpam-4303	144	10	is	be	AUX
ejpam-4303	144	11	obvious	obvious	ADJ
ejpam-4303	144	12	.	.	PUNCT
ejpam-4303	145	1	(	(	PUNCT
ejpam-4303	145	2	2	2	X
ejpam-4303	145	3	)	)	PUNCT
ejpam-4303	145	4	⇒	⇒	NOUN
ejpam-4303	145	5	(	(	PUNCT
ejpam-4303	145	6	1	1	NUM
ejpam-4303	145	7	):	):	PUNCT
ejpam-4303	145	8	let	let	VERB
ejpam-4303	145	9	v1	v1	NOUN
ejpam-4303	145	10	,	,	PUNCT
ejpam-4303	145	11	v2	v2	PROPN
ejpam-4303	145	12	be	be	AUX
ejpam-4303	145	13	any	any	DET
ejpam-4303	145	14	(	(	PUNCT
ejpam-4303	145	15	λ	λ	NOUN
ejpam-4303	145	16	,	,	PUNCT
ejpam-4303	145	17	sp)-open	sp)-open	ADJ
ejpam-4303	145	18	sets	set	NOUN
ejpam-4303	145	19	of	of	ADP
ejpam-4303	145	20	y	y	PRON
ejpam-4303	145	21	such	such	ADJ
ejpam-4303	145	22	that	that	SCONJ
ejpam-4303	145	23	x	x	SYM
ejpam-4303	145	24	∈	∈	PROPN
ejpam-4303	145	25	f+(v1)∩f−(v2	f+(v1)∩f−(v2	NOUN
ejpam-4303	145	26	)	)	PUNCT
ejpam-4303	145	27	.	.	PUNCT
ejpam-4303	146	1	by	by	ADP
ejpam-4303	146	2	(	(	PUNCT
ejpam-4303	146	3	2	2	NUM
ejpam-4303	146	4	)	)	PUNCT
ejpam-4303	146	5	,	,	PUNCT
ejpam-4303	146	6	x	x	PUNCT
ejpam-4303	146	7	∈	∈	PROPN
ejpam-4303	146	8	f+(v1)∩f−(v2	f+(v1)∩f−(v2	NOUN
ejpam-4303	146	9	)	)	PUNCT
ejpam-4303	146	10	⊆	⊆	NUM
ejpam-4303	146	11	[	[	X
ejpam-4303	146	12	f+(v	f+(v	NOUN
ejpam-4303	146	13	(	(	PUNCT
ejpam-4303	146	14	λ	λ	NOUN
ejpam-4303	146	15	,	,	PUNCT
ejpam-4303	146	16	sp	sp	NOUN
ejpam-4303	146	17	)	)	PUNCT
ejpam-4303	146	18	1	1	NUM
ejpam-4303	146	19	)	)	PUNCT
ejpam-4303	146	20	∩f−(v	∩f−(v	NOUN
ejpam-4303	146	21	(	(	PUNCT
ejpam-4303	146	22	λ	λ	NOUN
ejpam-4303	146	23	,	,	PUNCT
ejpam-4303	146	24	sp	sp	NOUN
ejpam-4303	146	25	)	)	PUNCT
ejpam-4303	146	26	2	2	NUM
ejpam-4303	146	27	)	)	PUNCT
ejpam-4303	146	28	]	]	PUNCT
ejpam-4303	146	29	(	(	PUNCT
ejpam-4303	146	30	λ	λ	NOUN
ejpam-4303	146	31	,	,	PUNCT
ejpam-4303	146	32	sp	sp	NOUN
ejpam-4303	146	33	)	)	PUNCT
ejpam-4303	146	34	.	.	PUNCT
ejpam-4303	147	1	then	then	ADV
ejpam-4303	147	2	,	,	PUNCT
ejpam-4303	147	3	there	there	PRON
ejpam-4303	147	4	exists	exist	VERB
ejpam-4303	147	5	a	a	DET
ejpam-4303	147	6	(	(	PUNCT
ejpam-4303	147	7	λ	λ	NOUN
ejpam-4303	147	8	,	,	PUNCT
ejpam-4303	147	9	sp)open	sp)open	VERB
ejpam-4303	147	10	set	set	VERB
ejpam-4303	147	11	u	u	NOUN
ejpam-4303	147	12	of	of	ADP
ejpam-4303	147	13	x	x	SYM
ejpam-4303	147	14	such	such	ADJ
ejpam-4303	147	15	that	that	SCONJ
ejpam-4303	147	16	x	x	SYM
ejpam-4303	147	17	∈	∈	NOUN
ejpam-4303	147	18	u	u	NOUN
ejpam-4303	147	19	⊆	⊆	NUM
ejpam-4303	147	20	f+(v	f+(v	NOUN
ejpam-4303	147	21	(	(	PUNCT
ejpam-4303	147	22	λ	λ	NOUN
ejpam-4303	147	23	,	,	PUNCT
ejpam-4303	147	24	sp	sp	NOUN
ejpam-4303	147	25	)	)	PUNCT
ejpam-4303	147	26	1	1	NUM
ejpam-4303	147	27	)	)	PUNCT
ejpam-4303	147	28	∩f−(v	∩f−(v	NOUN
ejpam-4303	147	29	(	(	PUNCT
ejpam-4303	147	30	λ	λ	NOUN
ejpam-4303	147	31	,	,	PUNCT
ejpam-4303	147	32	sp	sp	NOUN
ejpam-4303	147	33	)	)	PUNCT
ejpam-4303	147	34	2	2	NUM
ejpam-4303	147	35	)	)	PUNCT
ejpam-4303	147	36	.	.	PUNCT
ejpam-4303	148	1	thus	thus	ADV
ejpam-4303	148	2	,	,	PUNCT
ejpam-4303	148	3	f	f	PROPN
ejpam-4303	148	4	(	(	PUNCT
ejpam-4303	148	5	u	u	NOUN
ejpam-4303	148	6	)	)	PUNCT
ejpam-4303	148	7	⊆	⊆	NUM
ejpam-4303	148	8	v	v	NOUN
ejpam-4303	148	9	(	(	PUNCT
ejpam-4303	148	10	λ	λ	NOUN
ejpam-4303	148	11	,	,	PUNCT
ejpam-4303	148	12	sp	sp	NOUN
ejpam-4303	148	13	)	)	PUNCT
ejpam-4303	148	14	1	1	NUM
ejpam-4303	148	15	and	and	CCONJ
ejpam-4303	148	16	f	f	PROPN
ejpam-4303	148	17	(	(	PUNCT
ejpam-4303	148	18	z	z	NOUN
ejpam-4303	148	19	)	)	PUNCT
ejpam-4303	148	20	∩	∩	ADJ
ejpam-4303	148	21	v	v	X
ejpam-4303	148	22	(	(	PUNCT
ejpam-4303	148	23	λ	λ	PROPN
ejpam-4303	148	24	,	,	PUNCT
ejpam-4303	148	25	sp	sp	NOUN
ejpam-4303	148	26	)	)	PUNCT
ejpam-4303	148	27	2	2	NUM
ejpam-4303	148	28	6=	6=	NOUN
ejpam-4303	148	29	∅	∅	NOUN
ejpam-4303	148	30	for	for	ADP
ejpam-4303	148	31	every	every	DET
ejpam-4303	148	32	z	z	NOUN
ejpam-4303	148	33	∈	∈	PROPN
ejpam-4303	148	34	u	u	NOUN
ejpam-4303	148	35	.	.	PUNCT
ejpam-4303	149	1	this	this	PRON
ejpam-4303	149	2	shows	show	VERB
ejpam-4303	149	3	that	that	SCONJ
ejpam-4303	149	4	f	f	PROPN
ejpam-4303	149	5	is	be	AUX
ejpam-4303	149	6	weakly	weakly	ADJ
ejpam-4303	149	7	(	(	PUNCT
ejpam-4303	149	8	λ	λ	NOUN
ejpam-4303	149	9	,	,	PUNCT
ejpam-4303	149	10	sp)-continuous	sp)-continuous	ADJ
ejpam-4303	149	11	.	.	PUNCT
ejpam-4303	150	1	(	(	PUNCT
ejpam-4303	150	2	4	4	X
ejpam-4303	150	3	)	)	PUNCT
ejpam-4303	150	4	⇒	⇒	NOUN
ejpam-4303	150	5	(	(	PUNCT
ejpam-4303	150	6	6	6	NUM
ejpam-4303	150	7	):	):	PUNCT
ejpam-4303	150	8	let	let	VERB
ejpam-4303	150	9	v1	v1	NOUN
ejpam-4303	150	10	,	,	PUNCT
ejpam-4303	150	11	v2	v2	PROPN
ejpam-4303	150	12	be	be	AUX
ejpam-4303	150	13	any	any	DET
ejpam-4303	150	14	(	(	PUNCT
ejpam-4303	150	15	λ	λ	NOUN
ejpam-4303	150	16	,	,	PUNCT
ejpam-4303	150	17	sp)-open	sp)-open	ADJ
ejpam-4303	150	18	sets	set	NOUN
ejpam-4303	150	19	of	of	ADP
ejpam-4303	150	20	y	y	PROPN
ejpam-4303	150	21	.	.	PUNCT
ejpam-4303	151	1	by	by	ADP
ejpam-4303	151	2	(	(	PUNCT
ejpam-4303	151	3	4	4	NUM
ejpam-4303	151	4	)	)	PUNCT
ejpam-4303	151	5	,	,	PUNCT
ejpam-4303	151	6	we	we	PRON
ejpam-4303	151	7	have	have	VERB
ejpam-4303	151	8	[	[	X
ejpam-4303	151	9	f−(v1	f−(v1	NOUN
ejpam-4303	151	10	)	)	PUNCT
ejpam-4303	151	11	∪	∪	ADJ
ejpam-4303	151	12	f+(v2	f+(v2	NOUN
ejpam-4303	151	13	)	)	PUNCT
ejpam-4303	151	14	]	]	PUNCT
ejpam-4303	152	1	(	(	PUNCT
ejpam-4303	152	2	λ	λ	NOUN
ejpam-4303	152	3	,	,	PUNCT
ejpam-4303	152	4	sp	sp	NOUN
ejpam-4303	152	5	)	)	PUNCT
ejpam-4303	152	6	⊆	⊆	NUM
ejpam-4303	153	1	[	[	X
ejpam-4303	153	2	f−([v	f−([v	ADJ
ejpam-4303	153	3	(	(	PUNCT
ejpam-4303	153	4	λ	λ	NOUN
ejpam-4303	153	5	,	,	PUNCT
ejpam-4303	153	6	sp	sp	NOUN
ejpam-4303	153	7	)	)	PUNCT
ejpam-4303	153	8	1	1	NUM
ejpam-4303	153	9	]	]	PUNCT
ejpam-4303	153	10	(	(	PUNCT
ejpam-4303	153	11	λ	λ	NOUN
ejpam-4303	153	12	,	,	PUNCT
ejpam-4303	153	13	sp	sp	NOUN
ejpam-4303	153	14	)	)	PUNCT
ejpam-4303	153	15	)	)	PUNCT
ejpam-4303	153	16	∪	∪	ADP
ejpam-4303	153	17	f+([v	f+([v	PROPN
ejpam-4303	153	18	(	(	PUNCT
ejpam-4303	153	19	λ	λ	PROPN
ejpam-4303	153	20	,	,	PUNCT
ejpam-4303	153	21	sp	sp	NOUN
ejpam-4303	153	22	)	)	PUNCT
ejpam-4303	153	23	2	2	NUM
ejpam-4303	153	24	]	]	PUNCT
ejpam-4303	153	25	(	(	PUNCT
ejpam-4303	153	26	λ	λ	NOUN
ejpam-4303	153	27	,	,	PUNCT
ejpam-4303	153	28	sp	sp	NOUN
ejpam-4303	153	29	)	)	PUNCT
ejpam-4303	153	30	)	)	PUNCT
ejpam-4303	153	31	]	]	PUNCT
ejpam-4303	153	32	(	(	PUNCT
ejpam-4303	153	33	λ	λ	NOUN
ejpam-4303	153	34	,	,	PUNCT
ejpam-4303	153	35	sp	sp	NOUN
ejpam-4303	153	36	)	)	PUNCT
ejpam-4303	153	37	⊆	⊆	NUM
ejpam-4303	153	38	f−(v	f−(v	NOUN
ejpam-4303	153	39	(	(	PUNCT
ejpam-4303	153	40	λ	λ	NOUN
ejpam-4303	153	41	,	,	PUNCT
ejpam-4303	153	42	sp	sp	NOUN
ejpam-4303	153	43	)	)	PUNCT
ejpam-4303	153	44	1	1	NUM
ejpam-4303	153	45	)	)	PUNCT
ejpam-4303	153	46	∪	∪	ADP
ejpam-4303	153	47	f+(v	f+(v	PROPN
ejpam-4303	153	48	(	(	PUNCT
ejpam-4303	153	49	λ	λ	NOUN
ejpam-4303	153	50	,	,	PUNCT
ejpam-4303	153	51	sp	sp	NOUN
ejpam-4303	153	52	)	)	PUNCT
ejpam-4303	153	53	2	2	NUM
ejpam-4303	153	54	)	)	PUNCT
ejpam-4303	153	55	.	.	PUNCT
ejpam-4303	154	1	(	(	PUNCT
ejpam-4303	154	2	6	6	X
ejpam-4303	154	3	)	)	PUNCT
ejpam-4303	154	4	⇒	⇒	NOUN
ejpam-4303	154	5	(	(	PUNCT
ejpam-4303	154	6	2	2	NUM
ejpam-4303	154	7	):	):	PUNCT
ejpam-4303	154	8	let	let	VERB
ejpam-4303	154	9	v1	v1	NOUN
ejpam-4303	154	10	,	,	PUNCT
ejpam-4303	154	11	v2	v2	PROPN
ejpam-4303	154	12	be	be	AUX
ejpam-4303	154	13	any	any	DET
ejpam-4303	154	14	(	(	PUNCT
ejpam-4303	154	15	λ	λ	NOUN
ejpam-4303	154	16	,	,	PUNCT
ejpam-4303	154	17	sp)-open	sp)-open	ADJ
ejpam-4303	154	18	sets	set	NOUN
ejpam-4303	154	19	of	of	ADP
ejpam-4303	154	20	y	y	PROPN
ejpam-4303	154	21	.	.	PUNCT
ejpam-4303	155	1	thus	thus	ADV
ejpam-4303	155	2	,	,	PUNCT
ejpam-4303	155	3	by	by	ADP
ejpam-4303	155	4	(	(	PUNCT
ejpam-4303	155	5	6	6	NUM
ejpam-4303	155	6	)	)	PUNCT
ejpam-4303	155	7	,	,	PUNCT
ejpam-4303	155	8	f+(v1	f+(v1	ADJ
ejpam-4303	155	9	)	)	PUNCT
ejpam-4303	155	10	∩	∩	NOUN
ejpam-4303	155	11	f−(v2	f−(v2	X
ejpam-4303	155	12	)	)	PUNCT
ejpam-4303	155	13	⊆	⊆	NUM
ejpam-4303	155	14	f+([v	f+([v	NOUN
ejpam-4303	155	15	(	(	PUNCT
ejpam-4303	155	16	λ	λ	PROPN
ejpam-4303	155	17	,	,	PUNCT
ejpam-4303	155	18	sp	sp	NOUN
ejpam-4303	155	19	)	)	PUNCT
ejpam-4303	155	20	1	1	NUM
ejpam-4303	155	21	]	]	PUNCT
ejpam-4303	155	22	(	(	PUNCT
ejpam-4303	155	23	λ	λ	NOUN
ejpam-4303	155	24	,	,	PUNCT
ejpam-4303	155	25	sp	sp	NOUN
ejpam-4303	155	26	)	)	PUNCT
ejpam-4303	155	27	)	)	PUNCT
ejpam-4303	155	28	∩	∩	ADJ
ejpam-4303	155	29	f−([v	f−([v	PROPN
ejpam-4303	155	30	(	(	PUNCT
ejpam-4303	155	31	λ	λ	NOUN
ejpam-4303	155	32	,	,	PUNCT
ejpam-4303	155	33	sp	sp	NOUN
ejpam-4303	155	34	)	)	PUNCT
ejpam-4303	155	35	2	2	NUM
ejpam-4303	155	36	]	]	PUNCT
ejpam-4303	155	37	(	(	PUNCT
ejpam-4303	155	38	λ	λ	NOUN
ejpam-4303	155	39	,	,	PUNCT
ejpam-4303	155	40	sp	sp	NOUN
ejpam-4303	155	41	)	)	PUNCT
ejpam-4303	155	42	)	)	PUNCT
ejpam-4303	156	1	=	=	PUNCT
ejpam-4303	156	2	x	x	X
ejpam-4303	157	1	−	−	PUNCT
ejpam-4303	158	1	[	[	X
ejpam-4303	158	2	f−([y	f−([y	ADJ
ejpam-4303	158	3	−	−	PROPN
ejpam-4303	158	4	v	v	NOUN
ejpam-4303	158	5	(	(	PUNCT
ejpam-4303	158	6	λ	λ	PROPN
ejpam-4303	158	7	,	,	PUNCT
ejpam-4303	158	8	sp	sp	NOUN
ejpam-4303	158	9	)	)	PUNCT
ejpam-4303	158	10	1	1	NUM
ejpam-4303	158	11	]	]	PUNCT
ejpam-4303	158	12	(	(	PUNCT
ejpam-4303	158	13	λ	λ	NOUN
ejpam-4303	158	14	,	,	PUNCT
ejpam-4303	158	15	sp	sp	NOUN
ejpam-4303	158	16	)	)	PUNCT
ejpam-4303	158	17	)	)	PUNCT
ejpam-4303	158	18	∪	∪	ADP
ejpam-4303	158	19	f+([y	f+([y	NOUN
ejpam-4303	158	20	−	−	PROPN
ejpam-4303	158	21	v	v	NOUN
ejpam-4303	158	22	(	(	PUNCT
ejpam-4303	158	23	λ	λ	PROPN
ejpam-4303	158	24	,	,	PUNCT
ejpam-4303	158	25	sp	sp	NOUN
ejpam-4303	158	26	)	)	PUNCT
ejpam-4303	158	27	2	2	NUM
ejpam-4303	158	28	]	]	PUNCT
ejpam-4303	158	29	(	(	PUNCT
ejpam-4303	158	30	λ	λ	NOUN
ejpam-4303	158	31	,	,	PUNCT
ejpam-4303	158	32	sp	sp	NOUN
ejpam-4303	158	33	)	)	PUNCT
ejpam-4303	158	34	)	)	PUNCT
ejpam-4303	158	35	]	]	PUNCT
ejpam-4303	159	1	⊆	⊆	NUM
ejpam-4303	159	2	x	x	SYM
ejpam-4303	159	3	−	−	X
ejpam-4303	159	4	[	[	X
ejpam-4303	159	5	f−(y	f−(y	NOUN
ejpam-4303	159	6	−	−	NOUN
ejpam-4303	159	7	v	v	NOUN
ejpam-4303	159	8	(	(	PUNCT
ejpam-4303	159	9	λ	λ	PROPN
ejpam-4303	159	10	,	,	PUNCT
ejpam-4303	159	11	sp	sp	NOUN
ejpam-4303	159	12	)	)	PUNCT
ejpam-4303	159	13	1	1	NUM
ejpam-4303	159	14	)	)	PUNCT
ejpam-4303	159	15	∪	∪	ADP
ejpam-4303	159	16	f+(y	f+(y	PROPN
ejpam-4303	159	17	−	−	PROPN
ejpam-4303	159	18	v	v	NOUN
ejpam-4303	159	19	(	(	PUNCT
ejpam-4303	159	20	λ	λ	PROPN
ejpam-4303	159	21	,	,	PUNCT
ejpam-4303	159	22	sp	sp	NOUN
ejpam-4303	159	23	)	)	PUNCT
ejpam-4303	159	24	2	2	NUM
ejpam-4303	159	25	)	)	PUNCT
ejpam-4303	159	26	]	]	PUNCT
ejpam-4303	159	27	(	(	PUNCT
ejpam-4303	159	28	λ	λ	NOUN
ejpam-4303	159	29	,	,	PUNCT
ejpam-4303	159	30	sp	sp	NOUN
ejpam-4303	159	31	)	)	PUNCT
ejpam-4303	159	32	=	=	PUNCT
ejpam-4303	160	1	[	[	X
ejpam-4303	160	2	f+(v	f+(v	INTJ
ejpam-4303	160	3	(	(	PUNCT
ejpam-4303	160	4	λ	λ	NOUN
ejpam-4303	160	5	,	,	PUNCT
ejpam-4303	160	6	sp	sp	NOUN
ejpam-4303	160	7	)	)	PUNCT
ejpam-4303	160	8	1	1	NUM
ejpam-4303	160	9	)	)	PUNCT
ejpam-4303	160	10	∩	∩	PROPN
ejpam-4303	160	11	f−(v	f−(v	NOUN
ejpam-4303	160	12	(	(	PUNCT
ejpam-4303	160	13	λ	λ	NOUN
ejpam-4303	160	14	,	,	PUNCT
ejpam-4303	160	15	sp	sp	NOUN
ejpam-4303	160	16	)	)	PUNCT
ejpam-4303	160	17	2	2	NUM
ejpam-4303	160	18	)	)	PUNCT
ejpam-4303	160	19	]	]	PUNCT
ejpam-4303	160	20	(	(	PUNCT
ejpam-4303	160	21	λ	λ	NOUN
ejpam-4303	160	22	,	,	PUNCT
ejpam-4303	160	23	sp	sp	NOUN
ejpam-4303	160	24	)	)	PUNCT
ejpam-4303	160	25	.	.	PUNCT
ejpam-4303	161	1	definition	definition	NOUN
ejpam-4303	161	2	2	2	NUM
ejpam-4303	161	3	.	.	PUNCT
ejpam-4303	162	1	a	a	DET
ejpam-4303	162	2	function	function	NOUN
ejpam-4303	162	3	f	f	NOUN
ejpam-4303	162	4	:	:	PUNCT
ejpam-4303	162	5	(	(	PUNCT
ejpam-4303	162	6	x	x	X
ejpam-4303	162	7	,	,	PUNCT
ejpam-4303	162	8	τ	τ	X
ejpam-4303	162	9	)	)	PUNCT
ejpam-4303	162	10	→	→	SYM
ejpam-4303	162	11	(	(	PUNCT
ejpam-4303	162	12	y	y	PROPN
ejpam-4303	162	13	,	,	PUNCT
ejpam-4303	162	14	σ	σ	PROPN
ejpam-4303	162	15	)	)	PUNCT
ejpam-4303	162	16	is	be	AUX
ejpam-4303	162	17	said	say	VERB
ejpam-4303	162	18	to	to	PART
ejpam-4303	162	19	be	be	AUX
ejpam-4303	162	20	weakly	weakly	ADJ
ejpam-4303	162	21	(	(	PUNCT
ejpam-4303	162	22	λ	λ	NOUN
ejpam-4303	162	23	,	,	PUNCT
ejpam-4303	162	24	sp)-continuous	sp)-continuous	ADJ
ejpam-4303	162	25	if	if	SCONJ
ejpam-4303	162	26	,	,	PUNCT
ejpam-4303	162	27	for	for	SCONJ
ejpam-4303	162	28	each	each	DET
ejpam-4303	162	29	x	x	SYM
ejpam-4303	162	30	∈	∈	PROPN
ejpam-4303	162	31	x	x	X
ejpam-4303	162	32	and	and	CCONJ
ejpam-4303	162	33	each	each	DET
ejpam-4303	162	34	(	(	PUNCT
ejpam-4303	162	35	λ	λ	PROPN
ejpam-4303	162	36	,	,	PUNCT
ejpam-4303	162	37	sp)-open	sp)-open	NOUN
ejpam-4303	162	38	set	set	VERB
ejpam-4303	162	39	v	v	NUM
ejpam-4303	162	40	of	of	ADP
ejpam-4303	162	41	y	y	NOUN
ejpam-4303	162	42	containing	contain	VERB
ejpam-4303	162	43	f(x	f(x	PROPN
ejpam-4303	162	44	)	)	PUNCT
ejpam-4303	162	45	,	,	PUNCT
ejpam-4303	162	46	there	there	PRON
ejpam-4303	162	47	exists	exist	VERB
ejpam-4303	162	48	a	a	DET
ejpam-4303	162	49	(	(	PUNCT
ejpam-4303	162	50	λ	λ	NOUN
ejpam-4303	162	51	,	,	PUNCT
ejpam-4303	162	52	sp)-open	sp)-open	NOUN
ejpam-4303	162	53	set	set	VERB
ejpam-4303	162	54	u	u	NOUN
ejpam-4303	162	55	of	of	ADP
ejpam-4303	162	56	x	x	PUNCT
ejpam-4303	162	57	containing	contain	VERB
ejpam-4303	162	58	x	x	PUNCT
ejpam-4303	162	59	such	such	ADJ
ejpam-4303	162	60	that	that	DET
ejpam-4303	162	61	f(u	f(u	PROPN
ejpam-4303	162	62	)	)	PUNCT
ejpam-4303	162	63	⊆	⊆	NUM
ejpam-4303	162	64	v	v	NOUN
ejpam-4303	162	65	(	(	PUNCT
ejpam-4303	162	66	λ	λ	NOUN
ejpam-4303	162	67	,	,	PUNCT
ejpam-4303	162	68	sp	sp	NOUN
ejpam-4303	162	69	)	)	PUNCT
ejpam-4303	162	70	.	.	PUNCT
ejpam-4303	163	1	corollary	corollary	ADJ
ejpam-4303	163	2	1	1	NUM
ejpam-4303	163	3	.	.	PUNCT
ejpam-4303	164	1	for	for	ADP
ejpam-4303	164	2	a	a	DET
ejpam-4303	164	3	function	function	NOUN
ejpam-4303	164	4	f	f	NOUN
ejpam-4303	164	5	:	:	PUNCT
ejpam-4303	164	6	(	(	PUNCT
ejpam-4303	164	7	x	x	X
ejpam-4303	164	8	,	,	PUNCT
ejpam-4303	164	9	τ	τ	X
ejpam-4303	164	10	)	)	PUNCT
ejpam-4303	164	11	→	→	SYM
ejpam-4303	164	12	(	(	PUNCT
ejpam-4303	164	13	y	y	PROPN
ejpam-4303	164	14	,	,	PUNCT
ejpam-4303	164	15	σ	σ	PROPN
ejpam-4303	164	16	)	)	PUNCT
ejpam-4303	164	17	,	,	PUNCT
ejpam-4303	164	18	the	the	DET
ejpam-4303	164	19	following	follow	VERB
ejpam-4303	164	20	properties	property	NOUN
ejpam-4303	164	21	are	be	AUX
ejpam-4303	164	22	equivalent	equivalent	ADJ
ejpam-4303	164	23	:	:	PUNCT
ejpam-4303	164	24	(	(	PUNCT
ejpam-4303	164	25	1	1	X
ejpam-4303	164	26	)	)	PUNCT
ejpam-4303	164	27	f	f	PROPN
ejpam-4303	164	28	is	be	AUX
ejpam-4303	164	29	weakly	weakly	ADJ
ejpam-4303	164	30	(	(	PUNCT
ejpam-4303	164	31	λ	λ	NOUN
ejpam-4303	164	32	,	,	PUNCT
ejpam-4303	164	33	sp)-continuous	sp)-continuous	ADJ
ejpam-4303	164	34	;	;	PUNCT
ejpam-4303	164	35	(	(	PUNCT
ejpam-4303	164	36	2	2	X
ejpam-4303	164	37	)	)	PUNCT
ejpam-4303	164	38	f−1(v	f−1(v	NOUN
ejpam-4303	164	39	)	)	PUNCT
ejpam-4303	165	1	⊆	⊆	NUM
ejpam-4303	165	2	[	[	X
ejpam-4303	165	3	f−(v	f−(v	ADJ
ejpam-4303	165	4	(	(	PUNCT
ejpam-4303	165	5	λ	λ	PROPN
ejpam-4303	165	6	,	,	PUNCT
ejpam-4303	165	7	sp))](λ	sp))](λ	PROPN
ejpam-4303	165	8	,	,	PUNCT
ejpam-4303	165	9	sp	sp	NOUN
ejpam-4303	165	10	)	)	PUNCT
ejpam-4303	165	11	for	for	ADP
ejpam-4303	165	12	every	every	DET
ejpam-4303	165	13	(	(	PUNCT
ejpam-4303	165	14	λ	λ	NOUN
ejpam-4303	165	15	,	,	PUNCT
ejpam-4303	165	16	sp)-open	sp)-open	NOUN
ejpam-4303	165	17	set	set	VERB
ejpam-4303	165	18	v	v	NOUN
ejpam-4303	165	19	of	of	ADP
ejpam-4303	165	20	y	y	PROPN
ejpam-4303	165	21	;	;	PUNCT
ejpam-4303	165	22	(	(	PUNCT
ejpam-4303	165	23	3	3	X
ejpam-4303	165	24	)	)	PUNCT
ejpam-4303	166	1	[	[	X
ejpam-4303	166	2	f−1([k(λ	f−1([k(λ	NOUN
ejpam-4303	166	3	,	,	PUNCT
ejpam-4303	166	4	sp	sp	NOUN
ejpam-4303	166	5	)	)	PUNCT
ejpam-4303	166	6	)	)	PUNCT
ejpam-4303	166	7	]	]	PUNCT
ejpam-4303	166	8	(	(	PUNCT
ejpam-4303	166	9	λ	λ	NOUN
ejpam-4303	166	10	,	,	PUNCT
ejpam-4303	166	11	sp	sp	NOUN
ejpam-4303	166	12	)	)	PUNCT
ejpam-4303	166	13	⊆	⊆	NUM
ejpam-4303	166	14	f−1(k	f−1(k	PROPN
ejpam-4303	166	15	)	)	PUNCT
ejpam-4303	166	16	for	for	ADP
ejpam-4303	166	17	every	every	DET
ejpam-4303	166	18	(	(	PUNCT
ejpam-4303	166	19	λ	λ	PROPN
ejpam-4303	166	20	,	,	PUNCT
ejpam-4303	166	21	sp)-closed	sp)-close	VERB
ejpam-4303	166	22	set	set	VERB
ejpam-4303	166	23	k	k	PROPN
ejpam-4303	166	24	of	of	ADP
ejpam-4303	166	25	y	y	PROPN
ejpam-4303	166	26	;	;	PUNCT
ejpam-4303	166	27	(	(	PUNCT
ejpam-4303	166	28	4	4	X
ejpam-4303	166	29	)	)	PUNCT
ejpam-4303	166	30	[	[	X
ejpam-4303	166	31	f−1([b(λ	f−1([b(λ	X
ejpam-4303	166	32	,	,	PUNCT
ejpam-4303	166	33	sp)](λ	sp)](λ	PROPN
ejpam-4303	166	34	,	,	PUNCT
ejpam-4303	166	35	sp	sp	NOUN
ejpam-4303	166	36	)	)	PUNCT
ejpam-4303	166	37	)	)	PUNCT
ejpam-4303	166	38	]	]	PUNCT
ejpam-4303	167	1	(	(	PUNCT
ejpam-4303	167	2	λ	λ	NOUN
ejpam-4303	167	3	,	,	PUNCT
ejpam-4303	167	4	sp	sp	NOUN
ejpam-4303	167	5	)	)	PUNCT
ejpam-4303	167	6	⊆	⊆	NUM
ejpam-4303	167	7	f−1(b(λ	f−1(b(λ	PROPN
ejpam-4303	167	8	,	,	PUNCT
ejpam-4303	167	9	sp	sp	NOUN
ejpam-4303	167	10	)	)	PUNCT
ejpam-4303	167	11	)	)	PUNCT
ejpam-4303	167	12	for	for	ADP
ejpam-4303	167	13	every	every	DET
ejpam-4303	167	14	subset	subset	NOUN
ejpam-4303	167	15	b	b	PROPN
ejpam-4303	167	16	of	of	ADP
ejpam-4303	167	17	y	y	PROPN
ejpam-4303	167	18	;	;	PUNCT
ejpam-4303	167	19	(	(	PUNCT
ejpam-4303	167	20	5	5	X
ejpam-4303	167	21	)	)	PUNCT
ejpam-4303	167	22	f−1(b(λ	f−1(b(λ	PROPN
ejpam-4303	167	23	,	,	PUNCT
ejpam-4303	167	24	sp	sp	NOUN
ejpam-4303	167	25	)	)	PUNCT
ejpam-4303	167	26	)	)	PUNCT
ejpam-4303	168	1	⊆	⊆	NUM
ejpam-4303	168	2	[	[	X
ejpam-4303	168	3	f−1(b(λ	f−1(b(λ	PROPN
ejpam-4303	168	4	,	,	PUNCT
ejpam-4303	168	5	sp))](λ	sp))](λ	PROPN
ejpam-4303	168	6	,	,	PUNCT
ejpam-4303	168	7	sp	sp	NOUN
ejpam-4303	168	8	)	)	PUNCT
ejpam-4303	168	9	for	for	ADP
ejpam-4303	168	10	every	every	DET
ejpam-4303	168	11	subset	subset	NOUN
ejpam-4303	168	12	b	b	PROPN
ejpam-4303	168	13	of	of	ADP
ejpam-4303	168	14	y	y	PROPN
ejpam-4303	168	15	;	;	PUNCT
ejpam-4303	168	16	(	(	PUNCT
ejpam-4303	168	17	6	6	X
ejpam-4303	168	18	)	)	PUNCT
ejpam-4303	169	1	[	[	X
ejpam-4303	169	2	f−1(v	f−1(v	NOUN
ejpam-4303	169	3	)	)	PUNCT
ejpam-4303	169	4	]	]	PUNCT
ejpam-4303	169	5	(	(	PUNCT
ejpam-4303	169	6	λ	λ	NOUN
ejpam-4303	169	7	,	,	PUNCT
ejpam-4303	169	8	sp	sp	NOUN
ejpam-4303	169	9	)	)	PUNCT
ejpam-4303	169	10	⊆	⊆	NUM
ejpam-4303	169	11	f−(v	f−(v	NOUN
ejpam-4303	169	12	(	(	PUNCT
ejpam-4303	169	13	λ	λ	NOUN
ejpam-4303	169	14	,	,	PUNCT
ejpam-4303	169	15	sp	sp	NOUN
ejpam-4303	169	16	)	)	PUNCT
ejpam-4303	169	17	)	)	PUNCT
ejpam-4303	169	18	for	for	ADP
ejpam-4303	169	19	every	every	DET
ejpam-4303	169	20	(	(	PUNCT
ejpam-4303	169	21	λ	λ	NOUN
ejpam-4303	169	22	,	,	PUNCT
ejpam-4303	169	23	sp)-open	sp)-open	NOUN
ejpam-4303	169	24	set	set	VERB
ejpam-4303	169	25	v	v	NOUN
ejpam-4303	169	26	of	of	ADP
ejpam-4303	169	27	y	y	PROPN
ejpam-4303	169	28	.	.	PUNCT
ejpam-4303	170	1	c.	c.	PROPN
ejpam-4303	170	2	boonpok	boonpok	PROPN
ejpam-4303	170	3	,	,	PUNCT
ejpam-4303	170	4	c.	c.	PROPN
ejpam-4303	170	5	viriyapong	viriyapong	PROPN
ejpam-4303	170	6	/	/	SYM
ejpam-4303	170	7	eur	eur	PROPN
ejpam-4303	170	8	.	.	PUNCT
ejpam-4303	171	1	j.	j.	PROPN
ejpam-4303	171	2	pure	pure	PROPN
ejpam-4303	171	3	appl	appl	PROPN
ejpam-4303	171	4	.	.	PROPN
ejpam-4303	171	5	math	math	PROPN
ejpam-4303	171	6	,	,	PUNCT
ejpam-4303	171	7	15	15	NUM
ejpam-4303	171	8	(	(	PUNCT
ejpam-4303	171	9	2	2	NUM
ejpam-4303	171	10	)	)	PUNCT
ejpam-4303	171	11	(	(	PUNCT
ejpam-4303	171	12	2022	2022	NUM
ejpam-4303	171	13	)	)	PUNCT
ejpam-4303	171	14	,	,	PUNCT
ejpam-4303	171	15	528	528	NUM
ejpam-4303	171	16	-	-	SYM
ejpam-4303	171	17	536	536	NUM
ejpam-4303	171	18	533	533	NUM
ejpam-4303	171	19	definition	definition	NOUN
ejpam-4303	171	20	3	3	NUM
ejpam-4303	171	21	.	.	PUNCT
ejpam-4303	172	1	[	[	X
ejpam-4303	172	2	3	3	X
ejpam-4303	172	3	]	]	PUNCT
ejpam-4303	172	4	let	let	VERB
ejpam-4303	172	5	a	a	PRON
ejpam-4303	172	6	be	be	AUX
ejpam-4303	172	7	a	a	DET
ejpam-4303	172	8	subset	subset	NOUN
ejpam-4303	172	9	of	of	ADP
ejpam-4303	172	10	a	a	DET
ejpam-4303	172	11	topological	topological	ADJ
ejpam-4303	172	12	space	space	NOUN
ejpam-4303	172	13	(	(	PUNCT
ejpam-4303	172	14	x	x	X
ejpam-4303	172	15	,	,	PUNCT
ejpam-4303	172	16	τ	τ	PROPN
ejpam-4303	172	17	)	)	PUNCT
ejpam-4303	172	18	.	.	PUNCT
ejpam-4303	173	1	the	the	DET
ejpam-4303	173	2	θ(λ	θ(λ	PROPN
ejpam-4303	173	3	,	,	PUNCT
ejpam-4303	173	4	sp)-closure	sp)-closure	NOUN
ejpam-4303	173	5	of	of	ADP
ejpam-4303	173	6	a	a	DET
ejpam-4303	173	7	,	,	PUNCT
ejpam-4303	173	8	aθ(λ	aθ(λ	NOUN
ejpam-4303	173	9	,	,	PUNCT
ejpam-4303	173	10	sp	sp	NOUN
ejpam-4303	173	11	)	)	PUNCT
ejpam-4303	173	12	,	,	PUNCT
ejpam-4303	173	13	is	be	AUX
ejpam-4303	173	14	defined	define	VERB
ejpam-4303	173	15	as	as	SCONJ
ejpam-4303	173	16	follows	follow	VERB
ejpam-4303	173	17	:	:	PUNCT
ejpam-4303	173	18	aθ(λ	aθ(λ	NOUN
ejpam-4303	173	19	,	,	PUNCT
ejpam-4303	173	20	sp	sp	NOUN
ejpam-4303	173	21	)	)	PUNCT
ejpam-4303	173	22	=	=	PRON
ejpam-4303	174	1	{	{	PUNCT
ejpam-4303	174	2	x	x	PUNCT
ejpam-4303	174	3	∈	∈	NOUN
ejpam-4303	174	4	x	x	PUNCT
ejpam-4303	174	5	|	|	ADV
ejpam-4303	174	6	a	a	DET
ejpam-4303	174	7	∩	∩	ADJ
ejpam-4303	174	8	u	u	NOUN
ejpam-4303	174	9	(	(	PUNCT
ejpam-4303	174	10	λ	λ	PROPN
ejpam-4303	174	11	,	,	PUNCT
ejpam-4303	174	12	sp	sp	NOUN
ejpam-4303	174	13	)	)	PUNCT
ejpam-4303	174	14	6=	6=	NOUN
ejpam-4303	174	15	∅	∅	NOUN
ejpam-4303	174	16	for	for	ADP
ejpam-4303	174	17	each	each	DET
ejpam-4303	174	18	u	u	PROPN
ejpam-4303	174	19	∈	∈	PROPN
ejpam-4303	174	20	λspo(x	λspo(x	PROPN
ejpam-4303	174	21	,	,	PUNCT
ejpam-4303	174	22	τ	τ	X
ejpam-4303	174	23	)	)	PUNCT
ejpam-4303	174	24	containing	contain	VERB
ejpam-4303	174	25	x	x	X
ejpam-4303	174	26	}	}	PUNCT
ejpam-4303	174	27	.	.	PUNCT
ejpam-4303	175	1	lemma	lemma	PROPN
ejpam-4303	175	2	3	3	X
ejpam-4303	175	3	.	.	PUNCT
ejpam-4303	176	1	[	[	X
ejpam-4303	176	2	3	3	X
ejpam-4303	176	3	]	]	PUNCT
ejpam-4303	176	4	for	for	ADP
ejpam-4303	176	5	a	a	DET
ejpam-4303	176	6	subset	subset	NOUN
ejpam-4303	176	7	a	a	PRON
ejpam-4303	176	8	of	of	ADP
ejpam-4303	176	9	a	a	DET
ejpam-4303	176	10	topological	topological	ADJ
ejpam-4303	176	11	space	space	NOUN
ejpam-4303	176	12	(	(	PUNCT
ejpam-4303	176	13	x	x	X
ejpam-4303	176	14	,	,	PUNCT
ejpam-4303	176	15	τ	τ	PROPN
ejpam-4303	176	16	)	)	PUNCT
ejpam-4303	176	17	,	,	PUNCT
ejpam-4303	176	18	the	the	DET
ejpam-4303	176	19	following	follow	VERB
ejpam-4303	176	20	properties	property	NOUN
ejpam-4303	176	21	hold	hold	VERB
ejpam-4303	176	22	:	:	PUNCT
ejpam-4303	176	23	(	(	PUNCT
ejpam-4303	176	24	1	1	X
ejpam-4303	176	25	)	)	PUNCT
ejpam-4303	176	26	if	if	SCONJ
ejpam-4303	176	27	a	a	PRON
ejpam-4303	176	28	is	be	AUX
ejpam-4303	176	29	(	(	PUNCT
ejpam-4303	176	30	λ	λ	NOUN
ejpam-4303	176	31	,	,	PUNCT
ejpam-4303	176	32	sp)-open	sp)-open	ADJ
ejpam-4303	176	33	in	in	ADP
ejpam-4303	176	34	x	x	NOUN
ejpam-4303	176	35	,	,	PUNCT
ejpam-4303	176	36	then	then	ADV
ejpam-4303	176	37	a(λ	a(λ	ADV
ejpam-4303	176	38	,	,	PUNCT
ejpam-4303	176	39	sp	sp	NOUN
ejpam-4303	176	40	)	)	PUNCT
ejpam-4303	176	41	=	=	SYM
ejpam-4303	176	42	aθ(λ	aθ(λ	NOUN
ejpam-4303	176	43	,	,	PUNCT
ejpam-4303	176	44	sp	sp	NOUN
ejpam-4303	176	45	)	)	PUNCT
ejpam-4303	176	46	.	.	PUNCT
ejpam-4303	177	1	(	(	PUNCT
ejpam-4303	177	2	2	2	X
ejpam-4303	177	3	)	)	PUNCT
ejpam-4303	177	4	aθ(λ	aθ(λ	NOUN
ejpam-4303	177	5	,	,	PUNCT
ejpam-4303	177	6	sp	sp	NOUN
ejpam-4303	177	7	)	)	PUNCT
ejpam-4303	177	8	is	be	AUX
ejpam-4303	177	9	(	(	PUNCT
ejpam-4303	177	10	λ	λ	X
ejpam-4303	177	11	,	,	PUNCT
ejpam-4303	177	12	sp)-closed	sp)-close	VERB
ejpam-4303	177	13	.	.	PUNCT
ejpam-4303	178	1	theorem	theorem	NOUN
ejpam-4303	178	2	2	2	NUM
ejpam-4303	178	3	.	.	X
ejpam-4303	178	4	for	for	ADP
ejpam-4303	178	5	a	a	DET
ejpam-4303	178	6	multifunction	multifunction	NOUN
ejpam-4303	179	1	f	f	NOUN
ejpam-4303	179	2	:	:	PUNCT
ejpam-4303	179	3	(	(	PUNCT
ejpam-4303	179	4	x	x	X
ejpam-4303	179	5	,	,	PUNCT
ejpam-4303	179	6	τ	τ	X
ejpam-4303	179	7	)	)	PUNCT
ejpam-4303	179	8	→	→	SYM
ejpam-4303	179	9	(	(	PUNCT
ejpam-4303	179	10	y	y	PROPN
ejpam-4303	179	11	,	,	PUNCT
ejpam-4303	179	12	σ	σ	PROPN
ejpam-4303	179	13	)	)	PUNCT
ejpam-4303	179	14	,	,	PUNCT
ejpam-4303	179	15	the	the	DET
ejpam-4303	179	16	following	follow	VERB
ejpam-4303	179	17	properties	property	NOUN
ejpam-4303	179	18	are	be	AUX
ejpam-4303	179	19	equivalent	equivalent	ADJ
ejpam-4303	179	20	:	:	PUNCT
ejpam-4303	179	21	(	(	PUNCT
ejpam-4303	179	22	1	1	X
ejpam-4303	179	23	)	)	PUNCT
ejpam-4303	179	24	f	f	PROPN
ejpam-4303	179	25	is	be	AUX
ejpam-4303	179	26	weakly	weakly	ADJ
ejpam-4303	179	27	(	(	PUNCT
ejpam-4303	179	28	λ	λ	NOUN
ejpam-4303	179	29	,	,	PUNCT
ejpam-4303	179	30	sp)-continuous	sp)-continuous	ADJ
ejpam-4303	179	31	;	;	PUNCT
ejpam-4303	179	32	(	(	PUNCT
ejpam-4303	179	33	2	2	X
ejpam-4303	179	34	)	)	PUNCT
ejpam-4303	180	1	[	[	X
ejpam-4303	180	2	f−([b	f−([b	PROPN
ejpam-4303	180	3	θ(λ	θ(λ	PROPN
ejpam-4303	180	4	,	,	PUNCT
ejpam-4303	180	5	sp	sp	NOUN
ejpam-4303	180	6	)	)	PUNCT
ejpam-4303	180	7	1	1	NUM
ejpam-4303	180	8	]	]	PUNCT
ejpam-4303	180	9	(	(	PUNCT
ejpam-4303	180	10	λ	λ	NOUN
ejpam-4303	180	11	,	,	PUNCT
ejpam-4303	180	12	sp	sp	NOUN
ejpam-4303	180	13	)	)	PUNCT
ejpam-4303	180	14	)	)	PUNCT
ejpam-4303	180	15	∩	∩	PROPN
ejpam-4303	180	16	f+([b	f+([b	PROPN
ejpam-4303	180	17	θ(λ	θ(λ	PROPN
ejpam-4303	180	18	,	,	PUNCT
ejpam-4303	180	19	sp	sp	NOUN
ejpam-4303	180	20	)	)	PUNCT
ejpam-4303	180	21	2	2	NUM
ejpam-4303	180	22	]	]	PUNCT
ejpam-4303	180	23	(	(	PUNCT
ejpam-4303	180	24	λ	λ	NOUN
ejpam-4303	180	25	,	,	PUNCT
ejpam-4303	180	26	sp	sp	NOUN
ejpam-4303	180	27	)	)	PUNCT
ejpam-4303	180	28	)	)	PUNCT
ejpam-4303	180	29	]	]	PUNCT
ejpam-4303	180	30	(	(	PUNCT
ejpam-4303	180	31	λ	λ	NOUN
ejpam-4303	180	32	,	,	PUNCT
ejpam-4303	180	33	sp	sp	NOUN
ejpam-4303	180	34	)	)	PUNCT
ejpam-4303	180	35	⊆	⊆	NUM
ejpam-4303	180	36	f−(b	f−(b	PROPN
ejpam-4303	180	37	θ(λ	θ(λ	PROPN
ejpam-4303	180	38	,	,	PUNCT
ejpam-4303	180	39	sp	sp	NOUN
ejpam-4303	180	40	)	)	PUNCT
ejpam-4303	180	41	1	1	NUM
ejpam-4303	180	42	)	)	PUNCT
ejpam-4303	180	43	∪	∪	ADP
ejpam-4303	180	44	f+(b	f+(b	PROPN
ejpam-4303	180	45	θ(λ	θ(λ	PROPN
ejpam-4303	180	46	,	,	PUNCT
ejpam-4303	180	47	sp	sp	NOUN
ejpam-4303	180	48	)	)	PUNCT
ejpam-4303	180	49	2	2	NUM
ejpam-4303	180	50	)	)	PUNCT
ejpam-4303	180	51	for	for	ADP
ejpam-4303	180	52	every	every	DET
ejpam-4303	180	53	subsets	subset	NOUN
ejpam-4303	180	54	b1	b1	NOUN
ejpam-4303	180	55	,	,	PUNCT
ejpam-4303	180	56	b2	b2	NOUN
ejpam-4303	180	57	of	of	ADP
ejpam-4303	180	58	y	y	PROPN
ejpam-4303	180	59	;	;	PUNCT
ejpam-4303	180	60	(	(	PUNCT
ejpam-4303	180	61	3	3	X
ejpam-4303	180	62	)	)	PUNCT
ejpam-4303	181	1	[	[	X
ejpam-4303	181	2	f−([b	f−([b	PROPN
ejpam-4303	181	3	(	(	PUNCT
ejpam-4303	181	4	λ	λ	PROPN
ejpam-4303	181	5	,	,	PUNCT
ejpam-4303	181	6	sp	sp	NOUN
ejpam-4303	181	7	)	)	PUNCT
ejpam-4303	181	8	1	1	NUM
ejpam-4303	181	9	]	]	PUNCT
ejpam-4303	181	10	(	(	PUNCT
ejpam-4303	181	11	λ	λ	X
ejpam-4303	181	12	,	,	PUNCT
ejpam-4303	181	13	sp))∪f+([b	sp))∪f+([b	PROPN
ejpam-4303	181	14	(	(	PUNCT
ejpam-4303	181	15	λ	λ	PROPN
ejpam-4303	181	16	,	,	PUNCT
ejpam-4303	181	17	sp	sp	NOUN
ejpam-4303	181	18	)	)	PUNCT
ejpam-4303	181	19	2	2	NUM
ejpam-4303	181	20	]	]	PUNCT
ejpam-4303	181	21	(	(	PUNCT
ejpam-4303	181	22	λ	λ	NOUN
ejpam-4303	181	23	,	,	PUNCT
ejpam-4303	181	24	sp	sp	NOUN
ejpam-4303	181	25	)	)	PUNCT
ejpam-4303	181	26	)	)	PUNCT
ejpam-4303	181	27	]	]	PUNCT
ejpam-4303	181	28	(	(	PUNCT
ejpam-4303	181	29	λ	λ	NOUN
ejpam-4303	181	30	,	,	PUNCT
ejpam-4303	181	31	sp	sp	NOUN
ejpam-4303	181	32	)	)	PUNCT
ejpam-4303	181	33	⊆	⊆	NUM
ejpam-4303	181	34	f−(b	f−(b	PROPN
ejpam-4303	181	35	θ(λ	θ(λ	PROPN
ejpam-4303	181	36	,	,	PUNCT
ejpam-4303	181	37	sp	sp	NOUN
ejpam-4303	181	38	)	)	PUNCT
ejpam-4303	181	39	1	1	NUM
ejpam-4303	181	40	)	)	PUNCT
ejpam-4303	181	41	∪f+(b	∪f+(b	PROPN
ejpam-4303	181	42	θ(λ	θ(λ	NOUN
ejpam-4303	181	43	,	,	PUNCT
ejpam-4303	181	44	sp	sp	NOUN
ejpam-4303	181	45	)	)	PUNCT
ejpam-4303	181	46	2	2	NUM
ejpam-4303	181	47	)	)	PUNCT
ejpam-4303	181	48	for	for	ADP
ejpam-4303	181	49	every	every	DET
ejpam-4303	181	50	subsets	subset	NOUN
ejpam-4303	181	51	b1	b1	NOUN
ejpam-4303	181	52	,	,	PUNCT
ejpam-4303	181	53	b2	b2	NOUN
ejpam-4303	181	54	of	of	ADP
ejpam-4303	181	55	y	y	PROPN
ejpam-4303	181	56	;	;	PUNCT
ejpam-4303	181	57	(	(	PUNCT
ejpam-4303	181	58	4	4	X
ejpam-4303	181	59	)	)	PUNCT
ejpam-4303	182	1	[	[	X
ejpam-4303	182	2	f−([v	f−([v	ADJ
ejpam-4303	182	3	(	(	PUNCT
ejpam-4303	182	4	λ	λ	NOUN
ejpam-4303	182	5	,	,	PUNCT
ejpam-4303	182	6	sp	sp	NOUN
ejpam-4303	182	7	)	)	PUNCT
ejpam-4303	182	8	1	1	NUM
ejpam-4303	182	9	]	]	PUNCT
ejpam-4303	182	10	(	(	PUNCT
ejpam-4303	182	11	λ	λ	NOUN
ejpam-4303	182	12	,	,	PUNCT
ejpam-4303	182	13	sp))∪	sp))∪	ADJ
ejpam-4303	182	14	f+([v	f+([v	NOUN
ejpam-4303	182	15	(	(	PUNCT
ejpam-4303	182	16	λ	λ	PROPN
ejpam-4303	182	17	,	,	PUNCT
ejpam-4303	182	18	sp	sp	NOUN
ejpam-4303	182	19	)	)	PUNCT
ejpam-4303	182	20	2	2	NUM
ejpam-4303	182	21	]	]	PUNCT
ejpam-4303	182	22	(	(	PUNCT
ejpam-4303	182	23	λ	λ	NOUN
ejpam-4303	182	24	,	,	PUNCT
ejpam-4303	182	25	sp	sp	NOUN
ejpam-4303	182	26	)	)	PUNCT
ejpam-4303	182	27	)	)	PUNCT
ejpam-4303	182	28	]	]	PUNCT
ejpam-4303	182	29	(	(	PUNCT
ejpam-4303	182	30	λ	λ	NOUN
ejpam-4303	182	31	,	,	PUNCT
ejpam-4303	182	32	sp	sp	NOUN
ejpam-4303	182	33	)	)	PUNCT
ejpam-4303	182	34	⊆	⊆	NUM
ejpam-4303	182	35	f−(v	f−(v	NOUN
ejpam-4303	182	36	(	(	PUNCT
ejpam-4303	182	37	λ	λ	NOUN
ejpam-4303	182	38	,	,	PUNCT
ejpam-4303	182	39	sp	sp	NOUN
ejpam-4303	182	40	)	)	PUNCT
ejpam-4303	182	41	1	1	NUM
ejpam-4303	182	42	)	)	PUNCT
ejpam-4303	182	43	∪	∪	NOUN
ejpam-4303	182	44	f+(v	f+(v	PROPN
ejpam-4303	182	45	(	(	PUNCT
ejpam-4303	182	46	λ	λ	NOUN
ejpam-4303	182	47	,	,	PUNCT
ejpam-4303	182	48	sp	sp	NOUN
ejpam-4303	182	49	)	)	PUNCT
ejpam-4303	182	50	2	2	NUM
ejpam-4303	182	51	)	)	PUNCT
ejpam-4303	182	52	for	for	ADP
ejpam-4303	182	53	every	every	DET
ejpam-4303	182	54	(	(	PUNCT
ejpam-4303	182	55	λ	λ	NOUN
ejpam-4303	182	56	,	,	PUNCT
ejpam-4303	182	57	sp)-open	sp)-open	ADJ
ejpam-4303	182	58	sets	set	NOUN
ejpam-4303	182	59	v1	v1	NOUN
ejpam-4303	182	60	,	,	PUNCT
ejpam-4303	182	61	v2	v2	PROPN
ejpam-4303	182	62	of	of	ADP
ejpam-4303	182	63	y	y	PROPN
ejpam-4303	182	64	;	;	PUNCT
ejpam-4303	182	65	(	(	PUNCT
ejpam-4303	182	66	5	5	X
ejpam-4303	182	67	)	)	PUNCT
ejpam-4303	183	1	[	[	X
ejpam-4303	183	2	f−([v	f−([v	ADJ
ejpam-4303	183	3	(	(	PUNCT
ejpam-4303	183	4	λ	λ	NOUN
ejpam-4303	183	5	,	,	PUNCT
ejpam-4303	183	6	sp	sp	NOUN
ejpam-4303	183	7	)	)	PUNCT
ejpam-4303	183	8	1	1	NUM
ejpam-4303	183	9	]	]	PUNCT
ejpam-4303	183	10	(	(	PUNCT
ejpam-4303	183	11	λ	λ	NOUN
ejpam-4303	183	12	,	,	PUNCT
ejpam-4303	183	13	sp))∪	sp))∪	ADJ
ejpam-4303	183	14	f+([v	f+([v	NOUN
ejpam-4303	183	15	(	(	PUNCT
ejpam-4303	183	16	λ	λ	PROPN
ejpam-4303	183	17	,	,	PUNCT
ejpam-4303	183	18	sp	sp	NOUN
ejpam-4303	183	19	)	)	PUNCT
ejpam-4303	183	20	2	2	NUM
ejpam-4303	183	21	]	]	PUNCT
ejpam-4303	183	22	(	(	PUNCT
ejpam-4303	183	23	λ	λ	NOUN
ejpam-4303	183	24	,	,	PUNCT
ejpam-4303	183	25	sp	sp	NOUN
ejpam-4303	183	26	)	)	PUNCT
ejpam-4303	183	27	)	)	PUNCT
ejpam-4303	183	28	]	]	PUNCT
ejpam-4303	183	29	(	(	PUNCT
ejpam-4303	183	30	λ	λ	NOUN
ejpam-4303	183	31	,	,	PUNCT
ejpam-4303	183	32	sp	sp	NOUN
ejpam-4303	183	33	)	)	PUNCT
ejpam-4303	183	34	⊆	⊆	NUM
ejpam-4303	183	35	f−(v	f−(v	NOUN
ejpam-4303	183	36	(	(	PUNCT
ejpam-4303	183	37	λ	λ	NOUN
ejpam-4303	183	38	,	,	PUNCT
ejpam-4303	183	39	sp	sp	NOUN
ejpam-4303	183	40	)	)	PUNCT
ejpam-4303	183	41	1	1	NUM
ejpam-4303	183	42	)	)	PUNCT
ejpam-4303	183	43	∪	∪	NOUN
ejpam-4303	183	44	f+(v	f+(v	PROPN
ejpam-4303	183	45	(	(	PUNCT
ejpam-4303	183	46	λ	λ	NOUN
ejpam-4303	183	47	,	,	PUNCT
ejpam-4303	183	48	sp	sp	NOUN
ejpam-4303	183	49	)	)	PUNCT
ejpam-4303	183	50	2	2	NUM
ejpam-4303	183	51	)	)	PUNCT
ejpam-4303	183	52	for	for	ADP
ejpam-4303	183	53	every	every	DET
ejpam-4303	183	54	p(λ	p(λ	NOUN
ejpam-4303	183	55	,	,	PUNCT
ejpam-4303	183	56	sp)-open	sp)-open	NOUN
ejpam-4303	183	57	sets	set	NOUN
ejpam-4303	183	58	v1	v1	NOUN
ejpam-4303	183	59	,	,	PUNCT
ejpam-4303	183	60	v2	v2	PROPN
ejpam-4303	183	61	of	of	ADP
ejpam-4303	183	62	y	y	PROPN
ejpam-4303	183	63	;	;	PUNCT
ejpam-4303	183	64	(	(	PUNCT
ejpam-4303	183	65	6	6	X
ejpam-4303	183	66	)	)	PUNCT
ejpam-4303	184	1	[	[	X
ejpam-4303	184	2	f−([k1](λ	f−([k1](λ	NOUN
ejpam-4303	184	3	,	,	PUNCT
ejpam-4303	184	4	sp	sp	NOUN
ejpam-4303	184	5	)	)	PUNCT
ejpam-4303	184	6	)	)	PUNCT
ejpam-4303	185	1	∪	∪	ADP
ejpam-4303	185	2	f+([k2](λ	f+([k2](λ	SYM
ejpam-4303	185	3	,	,	PUNCT
ejpam-4303	185	4	sp	sp	NOUN
ejpam-4303	185	5	)	)	PUNCT
ejpam-4303	185	6	)	)	PUNCT
ejpam-4303	185	7	]	]	PUNCT
ejpam-4303	186	1	(	(	PUNCT
ejpam-4303	186	2	λ	λ	NOUN
ejpam-4303	186	3	,	,	PUNCT
ejpam-4303	186	4	sp	sp	NOUN
ejpam-4303	186	5	)	)	PUNCT
ejpam-4303	186	6	⊆	⊆	NUM
ejpam-4303	186	7	f−(k1	f−(k1	NOUN
ejpam-4303	186	8	)	)	PUNCT
ejpam-4303	186	9	∪	∪	ADP
ejpam-4303	186	10	f+(k2	f+(k2	NOUN
ejpam-4303	186	11	)	)	PUNCT
ejpam-4303	186	12	for	for	ADP
ejpam-4303	186	13	every	every	DET
ejpam-4303	186	14	r(λ	r(λ	NOUN
ejpam-4303	186	15	,	,	PUNCT
ejpam-4303	186	16	sp)-closed	sp)-close	VERB
ejpam-4303	186	17	sets	set	VERB
ejpam-4303	186	18	k1,k2	k1,k2	PROPN
ejpam-4303	186	19	of	of	ADP
ejpam-4303	186	20	y	y	PROPN
ejpam-4303	186	21	.	.	PUNCT
ejpam-4303	187	1	proof	proof	NOUN
ejpam-4303	187	2	.	.	PUNCT
ejpam-4303	188	1	(	(	PUNCT
ejpam-4303	188	2	1	1	X
ejpam-4303	188	3	)	)	PUNCT
ejpam-4303	188	4	⇒	⇒	NOUN
ejpam-4303	188	5	(	(	PUNCT
ejpam-4303	188	6	2	2	NUM
ejpam-4303	188	7	):	):	PUNCT
ejpam-4303	188	8	let	let	VERB
ejpam-4303	188	9	b1	b1	NOUN
ejpam-4303	188	10	,	,	PUNCT
ejpam-4303	188	11	b2	b2	NOUN
ejpam-4303	188	12	be	be	VERB
ejpam-4303	188	13	any	any	DET
ejpam-4303	188	14	subsets	subset	NOUN
ejpam-4303	188	15	of	of	ADP
ejpam-4303	188	16	y	y	PROPN
ejpam-4303	188	17	.	.	PUNCT
ejpam-4303	189	1	then	then	ADV
ejpam-4303	189	2	,	,	PUNCT
ejpam-4303	189	3	b	b	PROPN
ejpam-4303	189	4	θ(λ	θ(λ	PROPN
ejpam-4303	189	5	,	,	PUNCT
ejpam-4303	189	6	sp	sp	NOUN
ejpam-4303	189	7	)	)	PUNCT
ejpam-4303	189	8	1	1	NUM
ejpam-4303	189	9	and	and	CCONJ
ejpam-4303	189	10	b	b	PROPN
ejpam-4303	189	11	θ(λ	θ(λ	PROPN
ejpam-4303	189	12	,	,	PUNCT
ejpam-4303	189	13	sp	sp	NOUN
ejpam-4303	189	14	)	)	PUNCT
ejpam-4303	189	15	2	2	NUM
ejpam-4303	189	16	are	be	AUX
ejpam-4303	189	17	(	(	PUNCT
ejpam-4303	189	18	λ	λ	X
ejpam-4303	189	19	,	,	PUNCT
ejpam-4303	189	20	sp)-closed	sp)-close	VERB
ejpam-4303	189	21	in	in	ADP
ejpam-4303	189	22	y	y	PROPN
ejpam-4303	189	23	,	,	PUNCT
ejpam-4303	189	24	by	by	ADP
ejpam-4303	189	25	theorem	theorem	NOUN
ejpam-4303	189	26	1	1	NUM
ejpam-4303	189	27	,	,	PUNCT
ejpam-4303	189	28	[	[	X
ejpam-4303	189	29	f−([b	f−([b	PROPN
ejpam-4303	189	30	θ(λ	θ(λ	PROPN
ejpam-4303	189	31	,	,	PUNCT
ejpam-4303	189	32	sp	sp	NOUN
ejpam-4303	189	33	)	)	PUNCT
ejpam-4303	189	34	1	1	NUM
ejpam-4303	189	35	]	]	PUNCT
ejpam-4303	189	36	(	(	PUNCT
ejpam-4303	189	37	λ	λ	NOUN
ejpam-4303	189	38	,	,	PUNCT
ejpam-4303	189	39	sp	sp	NOUN
ejpam-4303	189	40	)	)	PUNCT
ejpam-4303	189	41	)	)	PUNCT
ejpam-4303	189	42	∪	∪	ADP
ejpam-4303	189	43	f+([b	f+([b	PROPN
ejpam-4303	189	44	θ(λ	θ(λ	PROPN
ejpam-4303	189	45	,	,	PUNCT
ejpam-4303	189	46	sp	sp	NOUN
ejpam-4303	189	47	)	)	PUNCT
ejpam-4303	189	48	2	2	NUM
ejpam-4303	189	49	]	]	PUNCT
ejpam-4303	189	50	(	(	PUNCT
ejpam-4303	189	51	λ	λ	NOUN
ejpam-4303	189	52	,	,	PUNCT
ejpam-4303	189	53	sp	sp	NOUN
ejpam-4303	189	54	)	)	PUNCT
ejpam-4303	189	55	)	)	PUNCT
ejpam-4303	189	56	]	]	PUNCT
ejpam-4303	190	1	(	(	PUNCT
ejpam-4303	190	2	λ	λ	NOUN
ejpam-4303	190	3	,	,	PUNCT
ejpam-4303	190	4	sp	sp	NOUN
ejpam-4303	190	5	)	)	PUNCT
ejpam-4303	190	6	⊆	⊆	NUM
ejpam-4303	190	7	f−(b	f−(b	PROPN
ejpam-4303	190	8	θ(λ	θ(λ	PROPN
ejpam-4303	190	9	,	,	PUNCT
ejpam-4303	190	10	sp	sp	NOUN
ejpam-4303	190	11	)	)	PUNCT
ejpam-4303	190	12	1	1	NUM
ejpam-4303	190	13	)	)	PUNCT
ejpam-4303	190	14	∪	∪	ADP
ejpam-4303	190	15	f+(b	f+(b	PROPN
ejpam-4303	190	16	θ(λ	θ(λ	PROPN
ejpam-4303	190	17	,	,	PUNCT
ejpam-4303	190	18	sp	sp	NOUN
ejpam-4303	190	19	)	)	PUNCT
ejpam-4303	190	20	2	2	NUM
ejpam-4303	190	21	)	)	PUNCT
ejpam-4303	190	22	.	.	PUNCT
ejpam-4303	191	1	(	(	PUNCT
ejpam-4303	191	2	2	2	X
ejpam-4303	191	3	)	)	PUNCT
ejpam-4303	191	4	⇒	⇒	NOUN
ejpam-4303	191	5	(	(	PUNCT
ejpam-4303	191	6	3	3	NUM
ejpam-4303	191	7	):	):	PUNCT
ejpam-4303	191	8	this	this	PRON
ejpam-4303	191	9	is	be	AUX
ejpam-4303	191	10	obvious	obvious	ADJ
ejpam-4303	191	11	since	since	SCONJ
ejpam-4303	191	12	b(λ	b(λ	PROPN
ejpam-4303	191	13	,	,	PUNCT
ejpam-4303	191	14	sp	sp	NOUN
ejpam-4303	191	15	)	)	PUNCT
ejpam-4303	191	16	⊆	⊆	NUM
ejpam-4303	191	17	bθ(λ	bθ(λ	NOUN
ejpam-4303	191	18	,	,	PUNCT
ejpam-4303	191	19	sp	sp	NOUN
ejpam-4303	191	20	)	)	PUNCT
ejpam-4303	191	21	for	for	ADP
ejpam-4303	191	22	every	every	DET
ejpam-4303	191	23	subset	subset	NOUN
ejpam-4303	191	24	b	b	PROPN
ejpam-4303	191	25	of	of	ADP
ejpam-4303	191	26	y	y	PROPN
ejpam-4303	191	27	.	.	PUNCT
ejpam-4303	192	1	(	(	PUNCT
ejpam-4303	192	2	3	3	X
ejpam-4303	192	3	)	)	PUNCT
ejpam-4303	192	4	⇒	⇒	NOUN
ejpam-4303	192	5	(	(	PUNCT
ejpam-4303	192	6	4	4	NUM
ejpam-4303	192	7	):	):	PUNCT
ejpam-4303	192	8	this	this	PRON
ejpam-4303	192	9	is	be	AUX
ejpam-4303	192	10	obvious	obvious	ADJ
ejpam-4303	192	11	since	since	SCONJ
ejpam-4303	192	12	v	v	NOUN
ejpam-4303	192	13	(	(	PUNCT
ejpam-4303	192	14	λ	λ	NOUN
ejpam-4303	192	15	,	,	PUNCT
ejpam-4303	192	16	sp	sp	NOUN
ejpam-4303	192	17	)	)	PUNCT
ejpam-4303	192	18	=	=	SYM
ejpam-4303	192	19	v	v	ADP
ejpam-4303	192	20	θ(λ	θ(λ	PROPN
ejpam-4303	192	21	,	,	PUNCT
ejpam-4303	192	22	sp	sp	NOUN
ejpam-4303	192	23	)	)	PUNCT
ejpam-4303	192	24	for	for	ADP
ejpam-4303	192	25	every	every	DET
ejpam-4303	192	26	(	(	PUNCT
ejpam-4303	192	27	λ	λ	NOUN
ejpam-4303	192	28	,	,	PUNCT
ejpam-4303	192	29	sp)-open	sp)-open	NOUN
ejpam-4303	192	30	set	set	VERB
ejpam-4303	192	31	v	v	NOUN
ejpam-4303	192	32	of	of	ADP
ejpam-4303	192	33	y	y	PROPN
ejpam-4303	192	34	.	.	PUNCT
ejpam-4303	193	1	(	(	PUNCT
ejpam-4303	193	2	4	4	X
ejpam-4303	193	3	)	)	PUNCT
ejpam-4303	193	4	⇒	⇒	NOUN
ejpam-4303	193	5	(	(	PUNCT
ejpam-4303	193	6	5	5	NUM
ejpam-4303	193	7	):	):	PUNCT
ejpam-4303	193	8	let	let	VERB
ejpam-4303	193	9	v1	v1	NOUN
ejpam-4303	193	10	,	,	PUNCT
ejpam-4303	193	11	v2	v2	PROPN
ejpam-4303	193	12	be	be	AUX
ejpam-4303	193	13	any	any	DET
ejpam-4303	193	14	p(λ	p(λ	NOUN
ejpam-4303	193	15	,	,	PUNCT
ejpam-4303	193	16	sp)-open	sp)-open	ADJ
ejpam-4303	193	17	sets	set	NOUN
ejpam-4303	193	18	of	of	ADP
ejpam-4303	193	19	y	y	PROPN
ejpam-4303	193	20	.	.	PUNCT
ejpam-4303	194	1	since	since	SCONJ
ejpam-4303	194	2	vi	vi	NOUN
ejpam-4303	194	3	⊆	⊆	NUM
ejpam-4303	194	4	[	[	X
ejpam-4303	194	5	v	v	X
ejpam-4303	194	6	(	(	PUNCT
ejpam-4303	194	7	λ	λ	NOUN
ejpam-4303	194	8	,	,	PUNCT
ejpam-4303	194	9	sp	sp	NOUN
ejpam-4303	194	10	)	)	PUNCT
ejpam-4303	194	11	i	i	PRON
ejpam-4303	194	12	]	]	X
ejpam-4303	194	13	(	(	PUNCT
ejpam-4303	194	14	λ	λ	NOUN
ejpam-4303	194	15	,	,	PUNCT
ejpam-4303	194	16	sp	sp	NOUN
ejpam-4303	194	17	)	)	PUNCT
ejpam-4303	194	18	,	,	PUNCT
ejpam-4303	194	19	we	we	PRON
ejpam-4303	194	20	have	have	VERB
ejpam-4303	194	21	v	v	NUM
ejpam-4303	194	22	(	(	PUNCT
ejpam-4303	194	23	λ	λ	NOUN
ejpam-4303	194	24	,	,	PUNCT
ejpam-4303	194	25	sp	sp	NOUN
ejpam-4303	194	26	)	)	PUNCT
ejpam-4303	194	27	i	i	PRON
ejpam-4303	194	28	=	=	PUNCT
ejpam-4303	195	1	[	[	X
ejpam-4303	195	2	[	[	X
ejpam-4303	195	3	v	v	X
ejpam-4303	195	4	(	(	PUNCT
ejpam-4303	195	5	λ	λ	NOUN
ejpam-4303	195	6	,	,	PUNCT
ejpam-4303	195	7	sp	sp	NOUN
ejpam-4303	195	8	)	)	PUNCT
ejpam-4303	195	9	i	i	PRON
ejpam-4303	195	10	]	]	X
ejpam-4303	195	11	(	(	PUNCT
ejpam-4303	195	12	λ	λ	NOUN
ejpam-4303	195	13	,	,	PUNCT
ejpam-4303	195	14	sp	sp	NOUN
ejpam-4303	195	15	)	)	PUNCT
ejpam-4303	195	16	]	]	PUNCT
ejpam-4303	195	17	(	(	PUNCT
ejpam-4303	195	18	λ	λ	NOUN
ejpam-4303	195	19	,	,	PUNCT
ejpam-4303	195	20	sp	sp	NOUN
ejpam-4303	195	21	)	)	PUNCT
ejpam-4303	195	22	for	for	ADP
ejpam-4303	195	23	i	i	PROPN
ejpam-4303	195	24	=	=	SYM
ejpam-4303	195	25	1	1	NUM
ejpam-4303	195	26	,	,	PUNCT
ejpam-4303	195	27	2	2	NUM
ejpam-4303	195	28	.	.	PUNCT
ejpam-4303	195	29	now	now	ADV
ejpam-4303	195	30	,	,	PUNCT
ejpam-4303	195	31	put	put	VERB
ejpam-4303	195	32	ui	ui	NOUN
ejpam-4303	196	1	=	=	PUNCT
ejpam-4303	197	1	[	[	X
ejpam-4303	197	2	v	v	X
ejpam-4303	197	3	(	(	PUNCT
ejpam-4303	197	4	λ	λ	NOUN
ejpam-4303	197	5	,	,	PUNCT
ejpam-4303	197	6	sp	sp	NOUN
ejpam-4303	197	7	)	)	PUNCT
ejpam-4303	197	8	i	i	PRON
ejpam-4303	197	9	]	]	X
ejpam-4303	197	10	(	(	PUNCT
ejpam-4303	197	11	λ	λ	NOUN
ejpam-4303	197	12	,	,	PUNCT
ejpam-4303	197	13	sp	sp	NOUN
ejpam-4303	197	14	)	)	PUNCT
ejpam-4303	197	15	,	,	PUNCT
ejpam-4303	197	16	then	then	ADV
ejpam-4303	197	17	ui	ui	PROPN
ejpam-4303	197	18	is	be	AUX
ejpam-4303	197	19	(	(	PUNCT
ejpam-4303	197	20	λ	λ	INTJ
ejpam-4303	197	21	,	,	PUNCT
ejpam-4303	197	22	sp)-open	sp)-open	ADJ
ejpam-4303	197	23	in	in	ADP
ejpam-4303	197	24	y	y	PROPN
ejpam-4303	197	25	and	and	CCONJ
ejpam-4303	197	26	u	u	PROPN
ejpam-4303	197	27	(	(	PUNCT
ejpam-4303	197	28	λ	λ	PROPN
ejpam-4303	197	29	,	,	PUNCT
ejpam-4303	197	30	sp	sp	NOUN
ejpam-4303	197	31	)	)	PUNCT
ejpam-4303	198	1	i	i	NOUN
ejpam-4303	198	2	=	=	SYM
ejpam-4303	198	3	v	v	X
ejpam-4303	198	4	(	(	PUNCT
ejpam-4303	198	5	λ	λ	NOUN
ejpam-4303	198	6	,	,	PUNCT
ejpam-4303	198	7	sp	sp	NOUN
ejpam-4303	198	8	)	)	PUNCT
ejpam-4303	198	9	i	i	PRON
ejpam-4303	198	10	,	,	PUNCT
ejpam-4303	198	11	by	by	ADP
ejpam-4303	198	12	(	(	PUNCT
ejpam-4303	198	13	4	4	NUM
ejpam-4303	198	14	)	)	PUNCT
ejpam-4303	198	15	,	,	PUNCT
ejpam-4303	199	1	[	[	X
ejpam-4303	199	2	f−([v	f−([v	ADJ
ejpam-4303	199	3	(	(	PUNCT
ejpam-4303	199	4	λ	λ	NOUN
ejpam-4303	199	5	,	,	PUNCT
ejpam-4303	199	6	sp	sp	NOUN
ejpam-4303	199	7	)	)	PUNCT
ejpam-4303	199	8	1	1	NUM
ejpam-4303	199	9	]	]	PUNCT
ejpam-4303	199	10	(	(	PUNCT
ejpam-4303	199	11	λ	λ	NOUN
ejpam-4303	199	12	,	,	PUNCT
ejpam-4303	199	13	sp	sp	NOUN
ejpam-4303	199	14	)	)	PUNCT
ejpam-4303	199	15	)	)	PUNCT
ejpam-4303	199	16	∪	∪	ADP
ejpam-4303	199	17	f+([v	f+([v	PROPN
ejpam-4303	199	18	(	(	PUNCT
ejpam-4303	199	19	λ	λ	PROPN
ejpam-4303	199	20	,	,	PUNCT
ejpam-4303	199	21	sp	sp	NOUN
ejpam-4303	199	22	)	)	PUNCT
ejpam-4303	199	23	2	2	NUM
ejpam-4303	199	24	]	]	PUNCT
ejpam-4303	199	25	(	(	PUNCT
ejpam-4303	199	26	λ	λ	NOUN
ejpam-4303	199	27	,	,	PUNCT
ejpam-4303	199	28	sp	sp	NOUN
ejpam-4303	199	29	)	)	PUNCT
ejpam-4303	199	30	)	)	PUNCT
ejpam-4303	199	31	]	]	PUNCT
ejpam-4303	199	32	(	(	PUNCT
ejpam-4303	199	33	λ	λ	NOUN
ejpam-4303	199	34	,	,	PUNCT
ejpam-4303	199	35	sp	sp	NOUN
ejpam-4303	199	36	)	)	PUNCT
ejpam-4303	199	37	⊆	⊆	NUM
ejpam-4303	199	38	f−(v	f−(v	NOUN
ejpam-4303	199	39	(	(	PUNCT
ejpam-4303	199	40	λ	λ	NOUN
ejpam-4303	199	41	,	,	PUNCT
ejpam-4303	199	42	sp	sp	NOUN
ejpam-4303	199	43	)	)	PUNCT
ejpam-4303	199	44	1	1	NUM
ejpam-4303	199	45	)	)	PUNCT
ejpam-4303	199	46	∪	∪	ADP
ejpam-4303	199	47	f+(v	f+(v	PROPN
ejpam-4303	199	48	(	(	PUNCT
ejpam-4303	199	49	λ	λ	NOUN
ejpam-4303	199	50	,	,	PUNCT
ejpam-4303	199	51	sp	sp	NOUN
ejpam-4303	199	52	)	)	PUNCT
ejpam-4303	199	53	2	2	NUM
ejpam-4303	199	54	)	)	PUNCT
ejpam-4303	199	55	.	.	PUNCT
ejpam-4303	200	1	(	(	PUNCT
ejpam-4303	200	2	5	5	X
ejpam-4303	200	3	)	)	PUNCT
ejpam-4303	200	4	⇒	⇒	NOUN
ejpam-4303	200	5	(	(	PUNCT
ejpam-4303	200	6	6	6	NUM
ejpam-4303	200	7	):	):	PUNCT
ejpam-4303	200	8	let	let	VERB
ejpam-4303	200	9	k1,k2	k1,k2	PROPN
ejpam-4303	200	10	be	be	AUX
ejpam-4303	200	11	any	any	DET
ejpam-4303	200	12	r(λ	r(λ	NOUN
ejpam-4303	200	13	,	,	PUNCT
ejpam-4303	200	14	sp)-closed	sp)-close	VERB
ejpam-4303	200	15	sets	set	NOUN
ejpam-4303	200	16	of	of	ADP
ejpam-4303	200	17	y	y	PROPN
ejpam-4303	200	18	.	.	PUNCT
ejpam-4303	201	1	then	then	ADV
ejpam-4303	201	2	,	,	PUNCT
ejpam-4303	201	3	[	[	X
ejpam-4303	201	4	k1](λ	k1](λ	PROPN
ejpam-4303	201	5	,	,	PUNCT
ejpam-4303	201	6	sp	sp	NOUN
ejpam-4303	201	7	)	)	PUNCT
ejpam-4303	201	8	and	and	CCONJ
ejpam-4303	201	9	[	[	X
ejpam-4303	201	10	k2](λ	k2](λ	PROPN
ejpam-4303	201	11	,	,	PUNCT
ejpam-4303	201	12	sp	sp	NOUN
ejpam-4303	201	13	)	)	PUNCT
ejpam-4303	201	14	are	be	AUX
ejpam-4303	201	15	p(λ	p(λ	NOUN
ejpam-4303	201	16	,	,	PUNCT
ejpam-4303	201	17	sp)-open	sp)-open	ADJ
ejpam-4303	201	18	in	in	ADP
ejpam-4303	201	19	y	y	PROPN
ejpam-4303	201	20	and	and	CCONJ
ejpam-4303	201	21	by	by	ADP
ejpam-4303	201	22	(	(	PUNCT
ejpam-4303	201	23	5	5	NUM
ejpam-4303	201	24	)	)	PUNCT
ejpam-4303	201	25	,	,	PUNCT
ejpam-4303	202	1	[	[	X
ejpam-4303	202	2	f−([k1](λ	f−([k1](λ	NOUN
ejpam-4303	202	3	,	,	PUNCT
ejpam-4303	202	4	sp	sp	NOUN
ejpam-4303	202	5	)	)	PUNCT
ejpam-4303	202	6	)	)	PUNCT
ejpam-4303	202	7	∪	∪	ADP
ejpam-4303	202	8	f+([k2](λ	f+([k2](λ	SYM
ejpam-4303	202	9	,	,	PUNCT
ejpam-4303	202	10	sp	sp	NOUN
ejpam-4303	202	11	)	)	PUNCT
ejpam-4303	202	12	)	)	PUNCT
ejpam-4303	202	13	]	]	PUNCT
ejpam-4303	203	1	(	(	PUNCT
ejpam-4303	203	2	λ	λ	NOUN
ejpam-4303	203	3	,	,	PUNCT
ejpam-4303	203	4	sp	sp	NOUN
ejpam-4303	203	5	)	)	PUNCT
ejpam-4303	203	6	c.	c.	NOUN
ejpam-4303	203	7	boonpok	boonpok	PROPN
ejpam-4303	203	8	,	,	PUNCT
ejpam-4303	203	9	c.	c.	PROPN
ejpam-4303	203	10	viriyapong	viriyapong	PROPN
ejpam-4303	203	11	/	/	SYM
ejpam-4303	203	12	eur	eur	PROPN
ejpam-4303	203	13	.	.	PUNCT
ejpam-4303	204	1	j.	j.	PROPN
ejpam-4303	204	2	pure	pure	PROPN
ejpam-4303	204	3	appl	appl	PROPN
ejpam-4303	204	4	.	.	PROPN
ejpam-4303	204	5	math	math	PROPN
ejpam-4303	204	6	,	,	PUNCT
ejpam-4303	204	7	15	15	NUM
ejpam-4303	204	8	(	(	PUNCT
ejpam-4303	204	9	2	2	NUM
ejpam-4303	204	10	)	)	PUNCT
ejpam-4303	204	11	(	(	PUNCT
ejpam-4303	204	12	2022	2022	NUM
ejpam-4303	204	13	)	)	PUNCT
ejpam-4303	204	14	,	,	PUNCT
ejpam-4303	204	15	528	528	NUM
ejpam-4303	204	16	-	-	SYM
ejpam-4303	204	17	536	536	NUM
ejpam-4303	204	18	534	534	NUM
ejpam-4303	204	19	=	=	SYM
ejpam-4303	205	1	[	[	X
ejpam-4303	205	2	f−([[[k1](λ	f−([[[k1](λ	ADP
ejpam-4303	205	3	,	,	PUNCT
ejpam-4303	205	4	sp	sp	NOUN
ejpam-4303	205	5	)	)	PUNCT
ejpam-4303	205	6	]	]	PUNCT
ejpam-4303	205	7	(	(	PUNCT
ejpam-4303	205	8	λ	λ	X
ejpam-4303	205	9	,	,	PUNCT
ejpam-4303	205	10	sp)](λ	sp)](λ	PROPN
ejpam-4303	205	11	,	,	PUNCT
ejpam-4303	205	12	sp	sp	NOUN
ejpam-4303	205	13	)	)	PUNCT
ejpam-4303	205	14	)	)	PUNCT
ejpam-4303	205	15	∪	∪	ADP
ejpam-4303	205	16	f+([[[k2](λ	f+([[[k2](λ	PROPN
ejpam-4303	205	17	,	,	PUNCT
ejpam-4303	205	18	sp	sp	NOUN
ejpam-4303	205	19	)	)	PUNCT
ejpam-4303	205	20	]	]	PUNCT
ejpam-4303	205	21	(	(	PUNCT
ejpam-4303	205	22	λ	λ	X
ejpam-4303	205	23	,	,	PUNCT
ejpam-4303	205	24	sp)](λ	sp)](λ	PROPN
ejpam-4303	205	25	,	,	PUNCT
ejpam-4303	205	26	sp	sp	NOUN
ejpam-4303	205	27	)	)	PUNCT
ejpam-4303	205	28	)	)	PUNCT
ejpam-4303	205	29	]	]	PUNCT
ejpam-4303	205	30	(	(	PUNCT
ejpam-4303	205	31	λ	λ	NOUN
ejpam-4303	205	32	,	,	PUNCT
ejpam-4303	205	33	sp	sp	NOUN
ejpam-4303	205	34	)	)	PUNCT
ejpam-4303	205	35	⊆	⊆	NUM
ejpam-4303	205	36	f−(k1	f−(k1	NOUN
ejpam-4303	205	37	)	)	PUNCT
ejpam-4303	205	38	∪	∪	ADP
ejpam-4303	205	39	f+(k2	f+(k2	NOUN
ejpam-4303	205	40	)	)	PUNCT
ejpam-4303	205	41	.	.	PUNCT
ejpam-4303	206	1	(	(	PUNCT
ejpam-4303	206	2	6	6	X
ejpam-4303	206	3	)	)	PUNCT
ejpam-4303	206	4	⇒	⇒	NOUN
ejpam-4303	206	5	(	(	PUNCT
ejpam-4303	206	6	1	1	NUM
ejpam-4303	206	7	):	):	PUNCT
ejpam-4303	206	8	let	let	VERB
ejpam-4303	206	9	v1	v1	NOUN
ejpam-4303	206	10	,	,	PUNCT
ejpam-4303	206	11	v2	v2	PROPN
ejpam-4303	206	12	be	be	AUX
ejpam-4303	206	13	any	any	DET
ejpam-4303	206	14	(	(	PUNCT
ejpam-4303	206	15	λ	λ	NOUN
ejpam-4303	206	16	,	,	PUNCT
ejpam-4303	206	17	sp)-open	sp)-open	ADJ
ejpam-4303	206	18	sets	set	NOUN
ejpam-4303	206	19	of	of	ADP
ejpam-4303	206	20	y	y	PROPN
ejpam-4303	206	21	.	.	PUNCT
ejpam-4303	207	1	then	then	ADV
ejpam-4303	207	2	,	,	PUNCT
ejpam-4303	207	3	v	v	INTJ
ejpam-4303	207	4	(	(	PUNCT
ejpam-4303	207	5	λ	λ	NOUN
ejpam-4303	207	6	,	,	PUNCT
ejpam-4303	207	7	sp	sp	NOUN
ejpam-4303	207	8	)	)	PUNCT
ejpam-4303	207	9	1	1	NUM
ejpam-4303	207	10	and	and	CCONJ
ejpam-4303	207	11	v	v	NOUN
ejpam-4303	207	12	(	(	PUNCT
ejpam-4303	207	13	λ	λ	NOUN
ejpam-4303	207	14	,	,	PUNCT
ejpam-4303	207	15	sp	sp	NOUN
ejpam-4303	207	16	)	)	PUNCT
ejpam-4303	207	17	2	2	NUM
ejpam-4303	207	18	are	be	AUX
ejpam-4303	207	19	r(λ	r(λ	NOUN
ejpam-4303	207	20	,	,	PUNCT
ejpam-4303	207	21	sp)-closed	sp)-close	VERB
ejpam-4303	207	22	in	in	ADP
ejpam-4303	207	23	y	y	PROPN
ejpam-4303	207	24	and	and	CCONJ
ejpam-4303	207	25	by	by	ADP
ejpam-4303	207	26	(	(	PUNCT
ejpam-4303	207	27	6	6	NUM
ejpam-4303	207	28	)	)	PUNCT
ejpam-4303	207	29	,	,	PUNCT
ejpam-4303	207	30	we	we	PRON
ejpam-4303	207	31	have	have	VERB
ejpam-4303	207	32	[	[	X
ejpam-4303	207	33	f−(v1	f−(v1	NOUN
ejpam-4303	207	34	)	)	PUNCT
ejpam-4303	207	35	∪	∪	ADJ
ejpam-4303	207	36	f+(v2	f+(v2	NOUN
ejpam-4303	207	37	)	)	PUNCT
ejpam-4303	207	38	]	]	PUNCT
ejpam-4303	208	1	(	(	PUNCT
ejpam-4303	208	2	λ	λ	NOUN
ejpam-4303	208	3	,	,	PUNCT
ejpam-4303	208	4	sp	sp	NOUN
ejpam-4303	208	5	)	)	PUNCT
ejpam-4303	208	6	⊆	⊆	NUM
ejpam-4303	209	1	[	[	X
ejpam-4303	209	2	f−([v	f−([v	ADJ
ejpam-4303	209	3	(	(	PUNCT
ejpam-4303	209	4	λ	λ	NOUN
ejpam-4303	209	5	,	,	PUNCT
ejpam-4303	209	6	sp	sp	NOUN
ejpam-4303	209	7	)	)	PUNCT
ejpam-4303	209	8	1	1	NUM
ejpam-4303	209	9	]	]	PUNCT
ejpam-4303	209	10	(	(	PUNCT
ejpam-4303	209	11	λ	λ	NOUN
ejpam-4303	209	12	,	,	PUNCT
ejpam-4303	209	13	sp	sp	NOUN
ejpam-4303	209	14	)	)	PUNCT
ejpam-4303	209	15	)	)	PUNCT
ejpam-4303	209	16	∪	∪	ADP
ejpam-4303	209	17	f+([v	f+([v	PROPN
ejpam-4303	209	18	(	(	PUNCT
ejpam-4303	209	19	λ	λ	PROPN
ejpam-4303	209	20	,	,	PUNCT
ejpam-4303	209	21	sp	sp	NOUN
ejpam-4303	209	22	)	)	PUNCT
ejpam-4303	209	23	2	2	NUM
ejpam-4303	209	24	]	]	PUNCT
ejpam-4303	209	25	(	(	PUNCT
ejpam-4303	209	26	λ	λ	NOUN
ejpam-4303	209	27	,	,	PUNCT
ejpam-4303	209	28	sp	sp	NOUN
ejpam-4303	209	29	)	)	PUNCT
ejpam-4303	209	30	)	)	PUNCT
ejpam-4303	209	31	]	]	PUNCT
ejpam-4303	209	32	(	(	PUNCT
ejpam-4303	209	33	λ	λ	NOUN
ejpam-4303	209	34	,	,	PUNCT
ejpam-4303	209	35	sp	sp	NOUN
ejpam-4303	209	36	)	)	PUNCT
ejpam-4303	209	37	⊆	⊆	NUM
ejpam-4303	209	38	f−(v	f−(v	NOUN
ejpam-4303	209	39	(	(	PUNCT
ejpam-4303	209	40	λ	λ	NOUN
ejpam-4303	209	41	,	,	PUNCT
ejpam-4303	209	42	sp	sp	NOUN
ejpam-4303	209	43	)	)	PUNCT
ejpam-4303	209	44	1	1	NUM
ejpam-4303	209	45	)	)	PUNCT
ejpam-4303	209	46	∪	∪	ADP
ejpam-4303	209	47	f+(v	f+(v	PROPN
ejpam-4303	209	48	(	(	PUNCT
ejpam-4303	209	49	λ	λ	NOUN
ejpam-4303	209	50	,	,	PUNCT
ejpam-4303	209	51	sp	sp	NOUN
ejpam-4303	209	52	)	)	PUNCT
ejpam-4303	209	53	2	2	NUM
ejpam-4303	209	54	)	)	PUNCT
ejpam-4303	209	55	.	.	PUNCT
ejpam-4303	210	1	it	it	PRON
ejpam-4303	210	2	follows	follow	VERB
ejpam-4303	210	3	from	from	ADP
ejpam-4303	210	4	theorem	theorem	ADJ
ejpam-4303	210	5	1	1	NUM
ejpam-4303	210	6	that	that	SCONJ
ejpam-4303	210	7	f	f	PROPN
ejpam-4303	210	8	is	be	AUX
ejpam-4303	210	9	weakly	weakly	ADJ
ejpam-4303	210	10	(	(	PUNCT
ejpam-4303	210	11	λ	λ	NOUN
ejpam-4303	210	12	,	,	PUNCT
ejpam-4303	210	13	sp)-continuous	sp)-continuous	ADJ
ejpam-4303	210	14	.	.	PUNCT
ejpam-4303	211	1	corollary	corollary	ADJ
ejpam-4303	211	2	2	2	NUM
ejpam-4303	211	3	.	.	PUNCT
ejpam-4303	212	1	for	for	ADP
ejpam-4303	212	2	a	a	DET
ejpam-4303	212	3	function	function	NOUN
ejpam-4303	212	4	f	f	NOUN
ejpam-4303	212	5	:	:	PUNCT
ejpam-4303	212	6	(	(	PUNCT
ejpam-4303	212	7	x	x	X
ejpam-4303	212	8	,	,	PUNCT
ejpam-4303	212	9	τ	τ	X
ejpam-4303	212	10	)	)	PUNCT
ejpam-4303	212	11	→	→	SYM
ejpam-4303	212	12	(	(	PUNCT
ejpam-4303	212	13	y	y	PROPN
ejpam-4303	212	14	,	,	PUNCT
ejpam-4303	212	15	σ	σ	PROPN
ejpam-4303	212	16	)	)	PUNCT
ejpam-4303	212	17	,	,	PUNCT
ejpam-4303	212	18	the	the	DET
ejpam-4303	212	19	following	follow	VERB
ejpam-4303	212	20	properties	property	NOUN
ejpam-4303	212	21	are	be	AUX
ejpam-4303	212	22	equivalent	equivalent	ADJ
ejpam-4303	212	23	:	:	PUNCT
ejpam-4303	212	24	(	(	PUNCT
ejpam-4303	212	25	1	1	X
ejpam-4303	212	26	)	)	PUNCT
ejpam-4303	212	27	f	f	PROPN
ejpam-4303	212	28	is	be	AUX
ejpam-4303	212	29	weakly	weakly	ADJ
ejpam-4303	212	30	(	(	PUNCT
ejpam-4303	212	31	λ	λ	NOUN
ejpam-4303	212	32	,	,	PUNCT
ejpam-4303	212	33	sp)-continuous	sp)-continuous	ADJ
ejpam-4303	212	34	;	;	PUNCT
ejpam-4303	212	35	(	(	PUNCT
ejpam-4303	212	36	2	2	X
ejpam-4303	212	37	)	)	PUNCT
ejpam-4303	212	38	[	[	X
ejpam-4303	212	39	f−1([bθ(λ	f−1([bθ(λ	NOUN
ejpam-4303	212	40	,	,	PUNCT
ejpam-4303	212	41	sp)](λ	sp)](λ	PROPN
ejpam-4303	212	42	,	,	PUNCT
ejpam-4303	212	43	sp	sp	NOUN
ejpam-4303	212	44	)	)	PUNCT
ejpam-4303	212	45	)	)	PUNCT
ejpam-4303	212	46	]	]	PUNCT
ejpam-4303	213	1	(	(	PUNCT
ejpam-4303	213	2	λ	λ	NOUN
ejpam-4303	213	3	,	,	PUNCT
ejpam-4303	213	4	sp	sp	NOUN
ejpam-4303	213	5	)	)	PUNCT
ejpam-4303	213	6	⊆	⊆	NUM
ejpam-4303	213	7	f−1(bθ(λ	f−1(bθ(λ	NOUN
ejpam-4303	213	8	,	,	PUNCT
ejpam-4303	213	9	sp	sp	NOUN
ejpam-4303	213	10	)	)	PUNCT
ejpam-4303	213	11	)	)	PUNCT
ejpam-4303	213	12	for	for	ADP
ejpam-4303	213	13	every	every	DET
ejpam-4303	213	14	subset	subset	NOUN
ejpam-4303	213	15	b	b	PROPN
ejpam-4303	213	16	of	of	ADP
ejpam-4303	213	17	y	y	PROPN
ejpam-4303	213	18	;	;	PUNCT
ejpam-4303	213	19	(	(	PUNCT
ejpam-4303	213	20	3	3	X
ejpam-4303	213	21	)	)	PUNCT
ejpam-4303	213	22	[	[	X
ejpam-4303	213	23	f−1([b(λ	f−1([b(λ	X
ejpam-4303	213	24	,	,	PUNCT
ejpam-4303	213	25	sp)](λ	sp)](λ	PROPN
ejpam-4303	213	26	,	,	PUNCT
ejpam-4303	213	27	sp	sp	NOUN
ejpam-4303	213	28	)	)	PUNCT
ejpam-4303	213	29	)	)	PUNCT
ejpam-4303	213	30	]	]	PUNCT
ejpam-4303	213	31	(	(	PUNCT
ejpam-4303	213	32	λ	λ	NOUN
ejpam-4303	213	33	,	,	PUNCT
ejpam-4303	213	34	sp	sp	NOUN
ejpam-4303	213	35	)	)	PUNCT
ejpam-4303	213	36	⊆	⊆	NUM
ejpam-4303	213	37	f−1(bθ(λ	f−1(bθ(λ	NOUN
ejpam-4303	213	38	,	,	PUNCT
ejpam-4303	213	39	sp	sp	NOUN
ejpam-4303	213	40	)	)	PUNCT
ejpam-4303	213	41	)	)	PUNCT
ejpam-4303	213	42	for	for	ADP
ejpam-4303	213	43	every	every	DET
ejpam-4303	213	44	subset	subset	NOUN
ejpam-4303	213	45	b	b	PROPN
ejpam-4303	213	46	of	of	ADP
ejpam-4303	213	47	y	y	PROPN
ejpam-4303	213	48	;	;	PUNCT
ejpam-4303	213	49	(	(	PUNCT
ejpam-4303	213	50	4	4	X
ejpam-4303	213	51	)	)	PUNCT
ejpam-4303	214	1	[	[	X
ejpam-4303	214	2	f−1([v	f−1([v	ADJ
ejpam-4303	214	3	(	(	PUNCT
ejpam-4303	214	4	λ	λ	NOUN
ejpam-4303	214	5	,	,	PUNCT
ejpam-4303	214	6	sp)](λ	sp)](λ	PROPN
ejpam-4303	214	7	,	,	PUNCT
ejpam-4303	214	8	sp	sp	NOUN
ejpam-4303	214	9	)	)	PUNCT
ejpam-4303	214	10	)	)	PUNCT
ejpam-4303	214	11	]	]	PUNCT
ejpam-4303	214	12	(	(	PUNCT
ejpam-4303	214	13	λ	λ	NOUN
ejpam-4303	214	14	,	,	PUNCT
ejpam-4303	214	15	sp	sp	NOUN
ejpam-4303	214	16	)	)	PUNCT
ejpam-4303	214	17	⊆	⊆	NUM
ejpam-4303	214	18	f−1(v	f−1(v	NOUN
ejpam-4303	214	19	(	(	PUNCT
ejpam-4303	214	20	λ	λ	PROPN
ejpam-4303	214	21	,	,	PUNCT
ejpam-4303	214	22	sp	sp	NOUN
ejpam-4303	214	23	)	)	PUNCT
ejpam-4303	214	24	)	)	PUNCT
ejpam-4303	214	25	for	for	ADP
ejpam-4303	214	26	every	every	DET
ejpam-4303	214	27	(	(	PUNCT
ejpam-4303	214	28	λ	λ	NOUN
ejpam-4303	214	29	,	,	PUNCT
ejpam-4303	214	30	sp)-open	sp)-open	NOUN
ejpam-4303	214	31	set	set	VERB
ejpam-4303	214	32	v	v	NOUN
ejpam-4303	214	33	of	of	ADP
ejpam-4303	214	34	y	y	PROPN
ejpam-4303	214	35	;	;	PUNCT
ejpam-4303	214	36	(	(	PUNCT
ejpam-4303	214	37	5	5	X
ejpam-4303	214	38	)	)	PUNCT
ejpam-4303	214	39	[	[	X
ejpam-4303	214	40	f−1([v	f−1([v	ADJ
ejpam-4303	214	41	(	(	PUNCT
ejpam-4303	214	42	λ	λ	NOUN
ejpam-4303	214	43	,	,	PUNCT
ejpam-4303	214	44	sp)](λ	sp)](λ	PROPN
ejpam-4303	214	45	,	,	PUNCT
ejpam-4303	214	46	sp	sp	NOUN
ejpam-4303	214	47	)	)	PUNCT
ejpam-4303	214	48	)	)	PUNCT
ejpam-4303	214	49	]	]	PUNCT
ejpam-4303	214	50	(	(	PUNCT
ejpam-4303	214	51	λ	λ	NOUN
ejpam-4303	214	52	,	,	PUNCT
ejpam-4303	214	53	sp	sp	NOUN
ejpam-4303	214	54	)	)	PUNCT
ejpam-4303	214	55	⊆	⊆	NUM
ejpam-4303	214	56	f−1(v	f−1(v	NOUN
ejpam-4303	214	57	(	(	PUNCT
ejpam-4303	214	58	λ	λ	PROPN
ejpam-4303	214	59	,	,	PUNCT
ejpam-4303	214	60	sp	sp	NOUN
ejpam-4303	214	61	)	)	PUNCT
ejpam-4303	214	62	)	)	PUNCT
ejpam-4303	214	63	for	for	ADP
ejpam-4303	214	64	every	every	DET
ejpam-4303	214	65	p(λ	p(λ	NOUN
ejpam-4303	214	66	,	,	PUNCT
ejpam-4303	214	67	sp)-open	sp)-open	NOUN
ejpam-4303	214	68	set	set	VERB
ejpam-4303	214	69	v	v	NOUN
ejpam-4303	214	70	of	of	ADP
ejpam-4303	214	71	y	y	PROPN
ejpam-4303	214	72	;	;	PUNCT
ejpam-4303	214	73	(	(	PUNCT
ejpam-4303	214	74	6	6	X
ejpam-4303	214	75	)	)	PUNCT
ejpam-4303	215	1	[	[	X
ejpam-4303	215	2	f−1(k(λ	f−1(k(λ	NOUN
ejpam-4303	215	3	,	,	PUNCT
ejpam-4303	215	4	sp	sp	NOUN
ejpam-4303	215	5	)	)	PUNCT
ejpam-4303	215	6	)	)	PUNCT
ejpam-4303	215	7	]	]	PUNCT
ejpam-4303	215	8	(	(	PUNCT
ejpam-4303	215	9	λ	λ	NOUN
ejpam-4303	215	10	,	,	PUNCT
ejpam-4303	215	11	sp	sp	NOUN
ejpam-4303	215	12	)	)	PUNCT
ejpam-4303	215	13	⊆	⊆	NUM
ejpam-4303	215	14	f−1(k	f−1(k	PROPN
ejpam-4303	215	15	)	)	PUNCT
ejpam-4303	215	16	for	for	ADP
ejpam-4303	215	17	every	every	DET
ejpam-4303	215	18	r(λ	r(λ	NOUN
ejpam-4303	215	19	,	,	PUNCT
ejpam-4303	215	20	sp)-closed	sp)-close	VERB
ejpam-4303	215	21	set	set	VERB
ejpam-4303	215	22	k	k	PROPN
ejpam-4303	215	23	of	of	ADP
ejpam-4303	215	24	y	y	PROPN
ejpam-4303	215	25	.	.	PUNCT
ejpam-4303	216	1	theorem	theorem	VERB
ejpam-4303	216	2	3	3	NUM
ejpam-4303	216	3	.	.	X
ejpam-4303	216	4	for	for	ADP
ejpam-4303	216	5	a	a	DET
ejpam-4303	216	6	multifunction	multifunction	NOUN
ejpam-4303	217	1	f	f	NOUN
ejpam-4303	217	2	:	:	PUNCT
ejpam-4303	217	3	(	(	PUNCT
ejpam-4303	217	4	x	x	X
ejpam-4303	217	5	,	,	PUNCT
ejpam-4303	217	6	τ	τ	X
ejpam-4303	217	7	)	)	PUNCT
ejpam-4303	217	8	→	→	SYM
ejpam-4303	217	9	(	(	PUNCT
ejpam-4303	217	10	y	y	PROPN
ejpam-4303	217	11	,	,	PUNCT
ejpam-4303	217	12	σ	σ	PROPN
ejpam-4303	217	13	)	)	PUNCT
ejpam-4303	217	14	,	,	PUNCT
ejpam-4303	217	15	the	the	DET
ejpam-4303	217	16	following	follow	VERB
ejpam-4303	217	17	properties	property	NOUN
ejpam-4303	217	18	are	be	AUX
ejpam-4303	217	19	equivalent	equivalent	ADJ
ejpam-4303	217	20	:	:	PUNCT
ejpam-4303	217	21	(	(	PUNCT
ejpam-4303	217	22	1	1	X
ejpam-4303	217	23	)	)	PUNCT
ejpam-4303	217	24	f	f	PROPN
ejpam-4303	217	25	is	be	AUX
ejpam-4303	217	26	weakly	weakly	ADJ
ejpam-4303	217	27	(	(	PUNCT
ejpam-4303	217	28	λ	λ	NOUN
ejpam-4303	217	29	,	,	PUNCT
ejpam-4303	217	30	sp)-continuous	sp)-continuous	ADJ
ejpam-4303	217	31	;	;	PUNCT
ejpam-4303	217	32	(	(	PUNCT
ejpam-4303	217	33	2	2	X
ejpam-4303	217	34	)	)	PUNCT
ejpam-4303	218	1	[	[	X
ejpam-4303	218	2	f−([v	f−([v	ADJ
ejpam-4303	218	3	(	(	PUNCT
ejpam-4303	218	4	λ	λ	NOUN
ejpam-4303	218	5	,	,	PUNCT
ejpam-4303	218	6	sp	sp	NOUN
ejpam-4303	218	7	)	)	PUNCT
ejpam-4303	218	8	1	1	NUM
ejpam-4303	218	9	]	]	PUNCT
ejpam-4303	218	10	(	(	PUNCT
ejpam-4303	218	11	λ	λ	NOUN
ejpam-4303	218	12	,	,	PUNCT
ejpam-4303	218	13	sp	sp	NOUN
ejpam-4303	218	14	)	)	PUNCT
ejpam-4303	218	15	)	)	PUNCT
ejpam-4303	218	16	∪	∪	ADP
ejpam-4303	218	17	f+(v	f+(v	PROPN
ejpam-4303	218	18	(	(	PUNCT
ejpam-4303	218	19	λ	λ	NOUN
ejpam-4303	218	20	,	,	PUNCT
ejpam-4303	218	21	sp	sp	NOUN
ejpam-4303	218	22	)	)	PUNCT
ejpam-4303	218	23	2	2	NUM
ejpam-4303	218	24	]	]	PUNCT
ejpam-4303	218	25	(	(	PUNCT
ejpam-4303	218	26	λ	λ	NOUN
ejpam-4303	218	27	,	,	PUNCT
ejpam-4303	218	28	sp	sp	NOUN
ejpam-4303	218	29	)	)	PUNCT
ejpam-4303	218	30	)	)	PUNCT
ejpam-4303	218	31	]	]	PUNCT
ejpam-4303	218	32	(	(	PUNCT
ejpam-4303	218	33	λ	λ	NOUN
ejpam-4303	218	34	,	,	PUNCT
ejpam-4303	218	35	sp	sp	NOUN
ejpam-4303	218	36	)	)	PUNCT
ejpam-4303	218	37	⊆	⊆	NUM
ejpam-4303	218	38	f−(v	f−(v	NOUN
ejpam-4303	218	39	(	(	PUNCT
ejpam-4303	218	40	λ	λ	NOUN
ejpam-4303	218	41	,	,	PUNCT
ejpam-4303	218	42	sp	sp	NOUN
ejpam-4303	218	43	)	)	PUNCT
ejpam-4303	218	44	1	1	NUM
ejpam-4303	218	45	)	)	PUNCT
ejpam-4303	218	46	∪	∪	ADP
ejpam-4303	218	47	f+(v	f+(v	PROPN
ejpam-4303	218	48	(	(	PUNCT
ejpam-4303	218	49	λ	λ	NOUN
ejpam-4303	218	50	,	,	PUNCT
ejpam-4303	218	51	sp	sp	NOUN
ejpam-4303	218	52	)	)	PUNCT
ejpam-4303	218	53	2	2	NUM
ejpam-4303	218	54	)	)	PUNCT
ejpam-4303	218	55	for	for	ADP
ejpam-4303	218	56	every	every	DET
ejpam-4303	218	57	β(λ	β(λ	NOUN
ejpam-4303	218	58	,	,	PUNCT
ejpam-4303	218	59	sp)-open	sp)-open	NOUN
ejpam-4303	218	60	sets	set	NOUN
ejpam-4303	218	61	v1	v1	NOUN
ejpam-4303	218	62	,	,	PUNCT
ejpam-4303	218	63	v2	v2	PROPN
ejpam-4303	218	64	of	of	ADP
ejpam-4303	218	65	y	y	PROPN
ejpam-4303	218	66	;	;	PUNCT
ejpam-4303	218	67	(	(	PUNCT
ejpam-4303	218	68	3	3	X
ejpam-4303	218	69	)	)	PUNCT
ejpam-4303	219	1	[	[	X
ejpam-4303	219	2	f−([v	f−([v	ADJ
ejpam-4303	219	3	(	(	PUNCT
ejpam-4303	219	4	λ	λ	NOUN
ejpam-4303	219	5	,	,	PUNCT
ejpam-4303	219	6	sp	sp	NOUN
ejpam-4303	219	7	)	)	PUNCT
ejpam-4303	219	8	1	1	NUM
ejpam-4303	219	9	]	]	PUNCT
ejpam-4303	219	10	(	(	PUNCT
ejpam-4303	219	11	λ	λ	NOUN
ejpam-4303	219	12	,	,	PUNCT
ejpam-4303	219	13	sp))∪	sp))∪	ADJ
ejpam-4303	219	14	f+([v	f+([v	NOUN
ejpam-4303	219	15	(	(	PUNCT
ejpam-4303	219	16	λ	λ	PROPN
ejpam-4303	219	17	,	,	PUNCT
ejpam-4303	219	18	sp	sp	NOUN
ejpam-4303	219	19	)	)	PUNCT
ejpam-4303	219	20	2	2	NUM
ejpam-4303	219	21	]	]	PUNCT
ejpam-4303	219	22	(	(	PUNCT
ejpam-4303	219	23	λ	λ	NOUN
ejpam-4303	219	24	,	,	PUNCT
ejpam-4303	219	25	sp	sp	NOUN
ejpam-4303	219	26	)	)	PUNCT
ejpam-4303	219	27	)	)	PUNCT
ejpam-4303	219	28	]	]	PUNCT
ejpam-4303	219	29	(	(	PUNCT
ejpam-4303	219	30	λ	λ	NOUN
ejpam-4303	219	31	,	,	PUNCT
ejpam-4303	219	32	sp	sp	NOUN
ejpam-4303	219	33	)	)	PUNCT
ejpam-4303	219	34	⊆	⊆	NUM
ejpam-4303	219	35	f−(v	f−(v	NOUN
ejpam-4303	219	36	(	(	PUNCT
ejpam-4303	219	37	λ	λ	NOUN
ejpam-4303	219	38	,	,	PUNCT
ejpam-4303	219	39	sp	sp	NOUN
ejpam-4303	219	40	)	)	PUNCT
ejpam-4303	219	41	1	1	NUM
ejpam-4303	219	42	)	)	PUNCT
ejpam-4303	219	43	∪	∪	NOUN
ejpam-4303	219	44	f+(v	f+(v	PROPN
ejpam-4303	219	45	(	(	PUNCT
ejpam-4303	219	46	λ	λ	NOUN
ejpam-4303	219	47	,	,	PUNCT
ejpam-4303	219	48	sp	sp	NOUN
ejpam-4303	219	49	)	)	PUNCT
ejpam-4303	219	50	2	2	NUM
ejpam-4303	219	51	)	)	PUNCT
ejpam-4303	219	52	for	for	ADP
ejpam-4303	219	53	every	every	DET
ejpam-4303	219	54	s(λ	s(λ	PROPN
ejpam-4303	219	55	,	,	PUNCT
ejpam-4303	219	56	sp)-open	sp)-open	NOUN
ejpam-4303	219	57	sets	set	NOUN
ejpam-4303	219	58	v1	v1	NOUN
ejpam-4303	219	59	,	,	PUNCT
ejpam-4303	219	60	v2	v2	PROPN
ejpam-4303	219	61	of	of	ADP
ejpam-4303	219	62	y	y	PROPN
ejpam-4303	219	63	.	.	PUNCT
ejpam-4303	220	1	proof	proof	NOUN
ejpam-4303	220	2	.	.	PUNCT
ejpam-4303	221	1	(	(	PUNCT
ejpam-4303	221	2	1	1	X
ejpam-4303	221	3	)	)	PUNCT
ejpam-4303	221	4	⇒	⇒	NOUN
ejpam-4303	221	5	(	(	PUNCT
ejpam-4303	221	6	2	2	NUM
ejpam-4303	221	7	):	):	PUNCT
ejpam-4303	221	8	let	let	VERB
ejpam-4303	221	9	v1	v1	NOUN
ejpam-4303	221	10	,	,	PUNCT
ejpam-4303	221	11	v2	v2	PROPN
ejpam-4303	221	12	be	be	AUX
ejpam-4303	221	13	any	any	DET
ejpam-4303	221	14	β(λ	β(λ	NOUN
ejpam-4303	221	15	,	,	PUNCT
ejpam-4303	221	16	sp)-open	sp)-open	ADJ
ejpam-4303	221	17	sets	set	NOUN
ejpam-4303	221	18	of	of	ADP
ejpam-4303	221	19	y	y	PROPN
ejpam-4303	221	20	.	.	PUNCT
ejpam-4303	222	1	then	then	ADV
ejpam-4303	222	2	,	,	PUNCT
ejpam-4303	222	3	we	we	PRON
ejpam-4303	222	4	have	have	VERB
ejpam-4303	222	5	vi	vi	NOUN
ejpam-4303	222	6	⊆	⊆	NUM
ejpam-4303	223	1	[	[	X
ejpam-4303	223	2	[	[	X
ejpam-4303	223	3	v	v	X
ejpam-4303	223	4	(	(	PUNCT
ejpam-4303	223	5	λ	λ	NOUN
ejpam-4303	223	6	,	,	PUNCT
ejpam-4303	223	7	sp	sp	NOUN
ejpam-4303	223	8	)	)	PUNCT
ejpam-4303	224	1	i	i	PRON
ejpam-4303	224	2	]	]	X
ejpam-4303	224	3	(	(	PUNCT
ejpam-4303	224	4	λ	λ	NOUN
ejpam-4303	224	5	,	,	PUNCT
ejpam-4303	224	6	sp	sp	NOUN
ejpam-4303	224	7	)	)	PUNCT
ejpam-4303	224	8	]	]	PUNCT
ejpam-4303	224	9	(	(	PUNCT
ejpam-4303	224	10	λ	λ	NOUN
ejpam-4303	224	11	,	,	PUNCT
ejpam-4303	224	12	sp	sp	NOUN
ejpam-4303	224	13	)	)	PUNCT
ejpam-4303	224	14	and	and	CCONJ
ejpam-4303	224	15	v	v	NOUN
ejpam-4303	224	16	(	(	PUNCT
ejpam-4303	224	17	λ	λ	NOUN
ejpam-4303	224	18	,	,	PUNCT
ejpam-4303	224	19	sp	sp	NOUN
ejpam-4303	224	20	)	)	PUNCT
ejpam-4303	224	21	i	i	PRON
ejpam-4303	225	1	=	=	PUNCT
ejpam-4303	226	1	[	[	X
ejpam-4303	226	2	[	[	X
ejpam-4303	226	3	v	v	X
ejpam-4303	226	4	(	(	PUNCT
ejpam-4303	226	5	λ	λ	NOUN
ejpam-4303	226	6	,	,	PUNCT
ejpam-4303	226	7	sp	sp	NOUN
ejpam-4303	226	8	)	)	PUNCT
ejpam-4303	226	9	i	i	PRON
ejpam-4303	226	10	]	]	X
ejpam-4303	226	11	(	(	PUNCT
ejpam-4303	226	12	λ	λ	NOUN
ejpam-4303	226	13	,	,	PUNCT
ejpam-4303	226	14	sp	sp	NOUN
ejpam-4303	226	15	)	)	PUNCT
ejpam-4303	226	16	]	]	PUNCT
ejpam-4303	226	17	(	(	PUNCT
ejpam-4303	226	18	λ	λ	NOUN
ejpam-4303	226	19	,	,	PUNCT
ejpam-4303	226	20	sp	sp	NOUN
ejpam-4303	226	21	)	)	PUNCT
ejpam-4303	226	22	for	for	ADP
ejpam-4303	226	23	i	i	PROPN
ejpam-4303	226	24	=	=	SYM
ejpam-4303	226	25	1	1	NUM
ejpam-4303	226	26	,	,	PUNCT
ejpam-4303	226	27	2	2	NUM
ejpam-4303	226	28	.	.	PUNCT
ejpam-4303	227	1	since	since	SCONJ
ejpam-4303	227	2	v	v	NOUN
ejpam-4303	227	3	(	(	PUNCT
ejpam-4303	227	4	λ	λ	NOUN
ejpam-4303	227	5	,	,	PUNCT
ejpam-4303	227	6	sp	sp	NOUN
ejpam-4303	227	7	)	)	PUNCT
ejpam-4303	227	8	1	1	NUM
ejpam-4303	227	9	and	and	CCONJ
ejpam-4303	227	10	v	v	NOUN
ejpam-4303	227	11	(	(	PUNCT
ejpam-4303	227	12	λ	λ	NOUN
ejpam-4303	227	13	,	,	PUNCT
ejpam-4303	227	14	sp	sp	NOUN
ejpam-4303	227	15	)	)	PUNCT
ejpam-4303	227	16	2	2	NUM
ejpam-4303	227	17	are	be	AUX
ejpam-4303	227	18	r(λ	r(λ	NOUN
ejpam-4303	227	19	,	,	PUNCT
ejpam-4303	227	20	sp)-closed	sp)-close	VERB
ejpam-4303	227	21	in	in	ADP
ejpam-4303	227	22	y	y	PROPN
ejpam-4303	227	23	,	,	PUNCT
ejpam-4303	227	24	by	by	ADP
ejpam-4303	227	25	theorem	theorem	NOUN
ejpam-4303	227	26	2	2	NUM
ejpam-4303	227	27	,	,	PUNCT
ejpam-4303	227	28	[	[	X
ejpam-4303	227	29	f−([v	f−([v	ADJ
ejpam-4303	227	30	(	(	PUNCT
ejpam-4303	227	31	λ	λ	NOUN
ejpam-4303	227	32	,	,	PUNCT
ejpam-4303	227	33	sp	sp	NOUN
ejpam-4303	227	34	)	)	PUNCT
ejpam-4303	227	35	1	1	NUM
ejpam-4303	227	36	]	]	PUNCT
ejpam-4303	227	37	(	(	PUNCT
ejpam-4303	227	38	λ	λ	NOUN
ejpam-4303	227	39	,	,	PUNCT
ejpam-4303	227	40	sp	sp	NOUN
ejpam-4303	227	41	)	)	PUNCT
ejpam-4303	227	42	)	)	PUNCT
ejpam-4303	227	43	∪	∪	ADP
ejpam-4303	227	44	f+([v	f+([v	PROPN
ejpam-4303	227	45	(	(	PUNCT
ejpam-4303	227	46	λ	λ	PROPN
ejpam-4303	227	47	,	,	PUNCT
ejpam-4303	227	48	sp	sp	NOUN
ejpam-4303	227	49	)	)	PUNCT
ejpam-4303	227	50	2	2	NUM
ejpam-4303	227	51	]	]	PUNCT
ejpam-4303	227	52	(	(	PUNCT
ejpam-4303	227	53	λ	λ	NOUN
ejpam-4303	227	54	,	,	PUNCT
ejpam-4303	227	55	sp	sp	NOUN
ejpam-4303	227	56	)	)	PUNCT
ejpam-4303	227	57	)	)	PUNCT
ejpam-4303	227	58	]	]	PUNCT
ejpam-4303	228	1	(	(	PUNCT
ejpam-4303	228	2	λ	λ	NOUN
ejpam-4303	228	3	,	,	PUNCT
ejpam-4303	228	4	sp	sp	NOUN
ejpam-4303	228	5	)	)	PUNCT
ejpam-4303	228	6	⊆	⊆	NUM
ejpam-4303	228	7	f−(v	f−(v	NOUN
ejpam-4303	228	8	(	(	PUNCT
ejpam-4303	228	9	λ	λ	NOUN
ejpam-4303	228	10	,	,	PUNCT
ejpam-4303	228	11	sp	sp	NOUN
ejpam-4303	228	12	)	)	PUNCT
ejpam-4303	228	13	1	1	NUM
ejpam-4303	228	14	)	)	PUNCT
ejpam-4303	228	15	∪	∪	ADP
ejpam-4303	228	16	f+(v	f+(v	PROPN
ejpam-4303	228	17	(	(	PUNCT
ejpam-4303	228	18	λ	λ	NOUN
ejpam-4303	228	19	,	,	PUNCT
ejpam-4303	228	20	sp	sp	NOUN
ejpam-4303	228	21	)	)	PUNCT
ejpam-4303	228	22	2	2	NUM
ejpam-4303	228	23	)	)	PUNCT
ejpam-4303	228	24	.	.	PUNCT
ejpam-4303	229	1	(	(	PUNCT
ejpam-4303	229	2	2	2	X
ejpam-4303	229	3	)	)	PUNCT
ejpam-4303	229	4	⇒	⇒	NOUN
ejpam-4303	229	5	(	(	PUNCT
ejpam-4303	229	6	3	3	NUM
ejpam-4303	229	7	):	):	PUNCT
ejpam-4303	229	8	this	this	PRON
ejpam-4303	229	9	is	be	AUX
ejpam-4303	229	10	obvious	obvious	ADJ
ejpam-4303	229	11	since	since	SCONJ
ejpam-4303	229	12	every	every	DET
ejpam-4303	229	13	s(λ	s(λ	PROPN
ejpam-4303	229	14	,	,	PUNCT
ejpam-4303	229	15	sp)-open	sp)-open	ADJ
ejpam-4303	229	16	set	set	NOUN
ejpam-4303	229	17	is	be	AUX
ejpam-4303	229	18	β(λ	β(λ	X
ejpam-4303	229	19	,	,	PUNCT
ejpam-4303	229	20	sp)-open	sp)-open	NOUN
ejpam-4303	229	21	.	.	PUNCT
ejpam-4303	230	1	references	reference	NOUN
ejpam-4303	230	2	535	535	NUM
ejpam-4303	230	3	(	(	PUNCT
ejpam-4303	230	4	3	3	NUM
ejpam-4303	230	5	)	)	PUNCT
ejpam-4303	230	6	⇒	⇒	NOUN
ejpam-4303	230	7	(	(	PUNCT
ejpam-4303	230	8	1	1	NUM
ejpam-4303	230	9	):	):	PUNCT
ejpam-4303	230	10	let	let	VERB
ejpam-4303	230	11	v1	v1	NOUN
ejpam-4303	230	12	,	,	PUNCT
ejpam-4303	230	13	v2	v2	PROPN
ejpam-4303	230	14	be	be	AUX
ejpam-4303	230	15	any	any	DET
ejpam-4303	230	16	β(λ	β(λ	NOUN
ejpam-4303	230	17	,	,	PUNCT
ejpam-4303	230	18	sp)-open	sp)-open	ADJ
ejpam-4303	230	19	sets	set	NOUN
ejpam-4303	230	20	of	of	ADP
ejpam-4303	230	21	y	y	PROPN
ejpam-4303	230	22	.	.	PUNCT
ejpam-4303	231	1	then	then	ADV
ejpam-4303	231	2	,	,	PUNCT
ejpam-4303	231	3	v	v	INTJ
ejpam-4303	231	4	(	(	PUNCT
ejpam-4303	231	5	λ	λ	NOUN
ejpam-4303	231	6	,	,	PUNCT
ejpam-4303	231	7	sp	sp	NOUN
ejpam-4303	231	8	)	)	PUNCT
ejpam-4303	231	9	1	1	NUM
ejpam-4303	231	10	and	and	CCONJ
ejpam-4303	231	11	v	v	NOUN
ejpam-4303	231	12	(	(	PUNCT
ejpam-4303	231	13	λ	λ	NOUN
ejpam-4303	231	14	,	,	PUNCT
ejpam-4303	231	15	sp	sp	NOUN
ejpam-4303	231	16	)	)	PUNCT
ejpam-4303	231	17	2	2	NUM
ejpam-4303	231	18	are	be	AUX
ejpam-4303	231	19	r(λ	r(λ	NOUN
ejpam-4303	231	20	,	,	PUNCT
ejpam-4303	231	21	sp)-closed	sp)-close	VERB
ejpam-4303	231	22	sets	set	NOUN
ejpam-4303	231	23	of	of	ADP
ejpam-4303	231	24	y	y	PROPN
ejpam-4303	231	25	and	and	CCONJ
ejpam-4303	231	26	hence	hence	ADV
ejpam-4303	231	27	v	v	NOUN
ejpam-4303	231	28	(	(	PUNCT
ejpam-4303	231	29	λ	λ	NOUN
ejpam-4303	231	30	,	,	PUNCT
ejpam-4303	231	31	sp	sp	NOUN
ejpam-4303	231	32	)	)	PUNCT
ejpam-4303	231	33	1	1	NUM
ejpam-4303	231	34	and	and	CCONJ
ejpam-4303	231	35	v	v	NOUN
ejpam-4303	231	36	(	(	PUNCT
ejpam-4303	231	37	λ	λ	NOUN
ejpam-4303	231	38	,	,	PUNCT
ejpam-4303	231	39	sp	sp	NOUN
ejpam-4303	231	40	)	)	PUNCT
ejpam-4303	231	41	2	2	NUM
ejpam-4303	231	42	are	be	AUX
ejpam-4303	231	43	s(λ	s(λ	NOUN
ejpam-4303	231	44	,	,	PUNCT
ejpam-4303	231	45	sp)-open	sp)-open	ADJ
ejpam-4303	231	46	in	in	ADP
ejpam-4303	231	47	y	y	PROPN
ejpam-4303	231	48	,	,	PUNCT
ejpam-4303	231	49	by	by	ADP
ejpam-4303	231	50	(	(	PUNCT
ejpam-4303	231	51	3	3	NUM
ejpam-4303	231	52	)	)	PUNCT
ejpam-4303	231	53	,	,	PUNCT
ejpam-4303	231	54	we	we	PRON
ejpam-4303	231	55	have	have	VERB
ejpam-4303	231	56	[	[	X
ejpam-4303	231	57	f−([v	f−([v	ADJ
ejpam-4303	231	58	(	(	PUNCT
ejpam-4303	231	59	λ	λ	NOUN
ejpam-4303	231	60	,	,	PUNCT
ejpam-4303	231	61	sp	sp	NOUN
ejpam-4303	231	62	)	)	PUNCT
ejpam-4303	231	63	1	1	NUM
ejpam-4303	231	64	]	]	PUNCT
ejpam-4303	231	65	(	(	PUNCT
ejpam-4303	231	66	λ	λ	NOUN
ejpam-4303	231	67	,	,	PUNCT
ejpam-4303	231	68	sp	sp	NOUN
ejpam-4303	231	69	)	)	PUNCT
ejpam-4303	231	70	)	)	PUNCT
ejpam-4303	231	71	∪	∪	ADP
ejpam-4303	231	72	f+([v	f+([v	PROPN
ejpam-4303	231	73	(	(	PUNCT
ejpam-4303	231	74	λ	λ	PROPN
ejpam-4303	231	75	,	,	PUNCT
ejpam-4303	231	76	sp	sp	NOUN
ejpam-4303	231	77	)	)	PUNCT
ejpam-4303	231	78	2	2	NUM
ejpam-4303	231	79	]	]	PUNCT
ejpam-4303	231	80	(	(	PUNCT
ejpam-4303	231	81	λ	λ	NOUN
ejpam-4303	231	82	,	,	PUNCT
ejpam-4303	231	83	sp	sp	NOUN
ejpam-4303	231	84	)	)	PUNCT
ejpam-4303	231	85	)	)	PUNCT
ejpam-4303	231	86	]	]	PUNCT
ejpam-4303	232	1	(	(	PUNCT
ejpam-4303	232	2	λ	λ	NOUN
ejpam-4303	232	3	,	,	PUNCT
ejpam-4303	232	4	sp	sp	NOUN
ejpam-4303	232	5	)	)	PUNCT
ejpam-4303	232	6	⊆	⊆	NUM
ejpam-4303	232	7	f−(v	f−(v	NOUN
ejpam-4303	232	8	(	(	PUNCT
ejpam-4303	232	9	λ	λ	NOUN
ejpam-4303	232	10	,	,	PUNCT
ejpam-4303	232	11	sp	sp	NOUN
ejpam-4303	232	12	)	)	PUNCT
ejpam-4303	232	13	1	1	NUM
ejpam-4303	232	14	)	)	PUNCT
ejpam-4303	232	15	∪	∪	ADP
ejpam-4303	232	16	f+(v	f+(v	PROPN
ejpam-4303	232	17	(	(	PUNCT
ejpam-4303	232	18	λ	λ	NOUN
ejpam-4303	232	19	,	,	PUNCT
ejpam-4303	232	20	sp	sp	NOUN
ejpam-4303	232	21	)	)	PUNCT
ejpam-4303	232	22	2	2	NUM
ejpam-4303	232	23	)	)	PUNCT
ejpam-4303	232	24	and	and	CCONJ
ejpam-4303	232	25	by	by	ADP
ejpam-4303	232	26	theorem	theorem	NOUN
ejpam-4303	232	27	2	2	NUM
ejpam-4303	232	28	,	,	PUNCT
ejpam-4303	232	29	f	f	PROPN
ejpam-4303	232	30	is	be	AUX
ejpam-4303	232	31	weakly	weakly	ADJ
ejpam-4303	232	32	(	(	PUNCT
ejpam-4303	232	33	λ	λ	NOUN
ejpam-4303	232	34	,	,	PUNCT
ejpam-4303	232	35	sp)-continuous	sp)-continuous	ADJ
ejpam-4303	232	36	.	.	PUNCT
ejpam-4303	233	1	corollary	corollary	ADJ
ejpam-4303	233	2	3	3	NUM
ejpam-4303	233	3	.	.	PUNCT
ejpam-4303	234	1	for	for	ADP
ejpam-4303	234	2	a	a	DET
ejpam-4303	234	3	function	function	NOUN
ejpam-4303	234	4	f	f	NOUN
ejpam-4303	234	5	:	:	PUNCT
ejpam-4303	234	6	(	(	PUNCT
ejpam-4303	234	7	x	x	X
ejpam-4303	234	8	,	,	PUNCT
ejpam-4303	234	9	τ	τ	X
ejpam-4303	234	10	)	)	PUNCT
ejpam-4303	234	11	→	→	SYM
ejpam-4303	234	12	(	(	PUNCT
ejpam-4303	234	13	y	y	PROPN
ejpam-4303	234	14	,	,	PUNCT
ejpam-4303	234	15	σ	σ	PROPN
ejpam-4303	234	16	)	)	PUNCT
ejpam-4303	234	17	,	,	PUNCT
ejpam-4303	234	18	the	the	DET
ejpam-4303	234	19	following	follow	VERB
ejpam-4303	234	20	properties	property	NOUN
ejpam-4303	234	21	are	be	AUX
ejpam-4303	234	22	equivalent	equivalent	ADJ
ejpam-4303	234	23	:	:	PUNCT
ejpam-4303	234	24	(	(	PUNCT
ejpam-4303	234	25	1	1	X
ejpam-4303	234	26	)	)	PUNCT
ejpam-4303	234	27	f	f	PROPN
ejpam-4303	234	28	is	be	AUX
ejpam-4303	234	29	weakly	weakly	ADJ
ejpam-4303	234	30	(	(	PUNCT
ejpam-4303	234	31	λ	λ	NOUN
ejpam-4303	234	32	,	,	PUNCT
ejpam-4303	234	33	sp)-continuous	sp)-continuous	ADJ
ejpam-4303	234	34	;	;	PUNCT
ejpam-4303	234	35	(	(	PUNCT
ejpam-4303	234	36	2	2	X
ejpam-4303	234	37	)	)	PUNCT
ejpam-4303	234	38	[	[	X
ejpam-4303	234	39	f−1([v	f−1([v	ADJ
ejpam-4303	234	40	(	(	PUNCT
ejpam-4303	234	41	λ	λ	NOUN
ejpam-4303	234	42	,	,	PUNCT
ejpam-4303	234	43	sp)](λ	sp)](λ	PROPN
ejpam-4303	234	44	,	,	PUNCT
ejpam-4303	234	45	sp	sp	NOUN
ejpam-4303	234	46	)	)	PUNCT
ejpam-4303	234	47	)	)	PUNCT
ejpam-4303	234	48	]	]	PUNCT
ejpam-4303	235	1	(	(	PUNCT
ejpam-4303	235	2	λ	λ	NOUN
ejpam-4303	235	3	,	,	PUNCT
ejpam-4303	235	4	sp	sp	NOUN
ejpam-4303	235	5	)	)	PUNCT
ejpam-4303	235	6	⊆	⊆	NUM
ejpam-4303	235	7	f−1(v	f−1(v	NOUN
ejpam-4303	235	8	(	(	PUNCT
ejpam-4303	235	9	λ	λ	PROPN
ejpam-4303	235	10	,	,	PUNCT
ejpam-4303	235	11	sp	sp	NOUN
ejpam-4303	235	12	)	)	PUNCT
ejpam-4303	235	13	)	)	PUNCT
ejpam-4303	235	14	for	for	ADP
ejpam-4303	235	15	every	every	DET
ejpam-4303	235	16	β(λ	β(λ	PROPN
ejpam-4303	235	17	,	,	PUNCT
ejpam-4303	235	18	sp)-open	sp)-open	NOUN
ejpam-4303	235	19	set	set	VERB
ejpam-4303	235	20	v	v	NOUN
ejpam-4303	235	21	of	of	ADP
ejpam-4303	235	22	y	y	PROPN
ejpam-4303	235	23	;	;	PUNCT
ejpam-4303	235	24	(	(	PUNCT
ejpam-4303	235	25	3	3	X
ejpam-4303	235	26	)	)	PUNCT
ejpam-4303	235	27	[	[	X
ejpam-4303	235	28	f−1([v	f−1([v	ADJ
ejpam-4303	235	29	(	(	PUNCT
ejpam-4303	235	30	λ	λ	NOUN
ejpam-4303	235	31	,	,	PUNCT
ejpam-4303	235	32	sp)](λ	sp)](λ	PROPN
ejpam-4303	235	33	,	,	PUNCT
ejpam-4303	235	34	sp	sp	NOUN
ejpam-4303	235	35	)	)	PUNCT
ejpam-4303	235	36	)	)	PUNCT
ejpam-4303	235	37	]	]	PUNCT
ejpam-4303	235	38	(	(	PUNCT
ejpam-4303	235	39	λ	λ	NOUN
ejpam-4303	235	40	,	,	PUNCT
ejpam-4303	235	41	sp	sp	NOUN
ejpam-4303	235	42	)	)	PUNCT
ejpam-4303	235	43	⊆	⊆	NUM
ejpam-4303	235	44	f−1(v	f−1(v	NOUN
ejpam-4303	235	45	(	(	PUNCT
ejpam-4303	235	46	λ	λ	PROPN
ejpam-4303	235	47	,	,	PUNCT
ejpam-4303	235	48	sp	sp	NOUN
ejpam-4303	235	49	)	)	PUNCT
ejpam-4303	235	50	)	)	PUNCT
ejpam-4303	235	51	for	for	ADP
ejpam-4303	235	52	every	every	DET
ejpam-4303	235	53	s(λ	s(λ	PROPN
ejpam-4303	235	54	,	,	PUNCT
ejpam-4303	235	55	sp)-open	sp)-open	VERB
ejpam-4303	235	56	set	set	VERB
ejpam-4303	235	57	v	v	NOUN
ejpam-4303	235	58	of	of	ADP
ejpam-4303	235	59	y	y	PROPN
ejpam-4303	235	60	.	.	PUNCT
ejpam-4303	236	1	acknowledgements	acknowledgement	NOUN
ejpam-4303	236	2	this	this	DET
ejpam-4303	236	3	research	research	NOUN
ejpam-4303	236	4	project	project	NOUN
ejpam-4303	236	5	was	be	AUX
ejpam-4303	236	6	financially	financially	ADV
ejpam-4303	236	7	supported	support	VERB
ejpam-4303	236	8	by	by	ADP
ejpam-4303	236	9	mahasarakham	mahasarakham	PROPN
ejpam-4303	236	10	university	university	PROPN
ejpam-4303	236	11	.	.	PUNCT
ejpam-4303	237	1	references	reference	NOUN
ejpam-4303	237	2	[	[	X
ejpam-4303	237	3	1	1	X
ejpam-4303	237	4	]	]	PUNCT
ejpam-4303	237	5	d.	d.	PROPN
ejpam-4303	237	6	andrijević	andrijević	PROPN
ejpam-4303	237	7	.	.	PUNCT
ejpam-4303	238	1	on	on	ADP
ejpam-4303	238	2	b	b	X
ejpam-4303	238	3	-	-	PUNCT
ejpam-4303	238	4	open	open	ADJ
ejpam-4303	238	5	sets	set	NOUN
ejpam-4303	238	6	.	.	PUNCT
ejpam-4303	239	1	matematički	matematički	PROPN
ejpam-4303	239	2	vesnik	vesnik	PROPN
ejpam-4303	239	3	,	,	PUNCT
ejpam-4303	239	4	48:59–64	48:59–64	PROPN
ejpam-4303	239	5	,	,	PUNCT
ejpam-4303	239	6	1996	1996	NUM
ejpam-4303	239	7	.	.	PUNCT
ejpam-4303	240	1	[	[	X
ejpam-4303	240	2	2	2	NUM
ejpam-4303	240	3	]	]	PUNCT
ejpam-4303	240	4	c.	c.	PROPN
ejpam-4303	240	5	berge	berge	PROPN
ejpam-4303	240	6	.	.	PUNCT
ejpam-4303	240	7	espaces	espace	VERB
ejpam-4303	240	8	topologiques	topologique	NOUN
ejpam-4303	240	9	fonctions	fonction	NOUN
ejpam-4303	240	10	multivoques	multivoque	NOUN
ejpam-4303	240	11	.	.	PUNCT
ejpam-4303	241	1	dunod	dunod	PROPN
ejpam-4303	241	2	,	,	PUNCT
ejpam-4303	241	3	paris	paris	PROPN
ejpam-4303	241	4	,	,	PUNCT
ejpam-4303	241	5	1959	1959	NUM
ejpam-4303	241	6	.	.	PUNCT
ejpam-4303	242	1	[	[	X
ejpam-4303	242	2	3	3	X
ejpam-4303	242	3	]	]	PUNCT
ejpam-4303	242	4	c.	c.	PROPN
ejpam-4303	242	5	boonpok	boonpok	PROPN
ejpam-4303	242	6	.	.	PUNCT
ejpam-4303	243	1	(	(	PUNCT
ejpam-4303	243	2	λ	λ	NOUN
ejpam-4303	243	3	,	,	PUNCT
ejpam-4303	243	4	sp)-closed	sp)-close	VERB
ejpam-4303	243	5	sets	set	NOUN
ejpam-4303	243	6	and	and	CCONJ
ejpam-4303	243	7	related	related	ADJ
ejpam-4303	243	8	topics	topic	NOUN
ejpam-4303	243	9	in	in	ADP
ejpam-4303	243	10	topological	topological	ADJ
ejpam-4303	243	11	spaces	space	NOUN
ejpam-4303	243	12	.	.	PUNCT
ejpam-4303	244	1	wseas	wseas	VERB
ejpam-4303	244	2	transactions	transaction	NOUN
ejpam-4303	244	3	on	on	ADP
ejpam-4303	244	4	mathematics	mathematic	NOUN
ejpam-4303	244	5	,	,	PUNCT
ejpam-4303	244	6	19:321–322	19:321–322	PROPN
ejpam-4303	244	7	,	,	PUNCT
ejpam-4303	244	8	2020	2020	NUM
ejpam-4303	244	9	.	.	PUNCT
ejpam-4303	245	1	[	[	X
ejpam-4303	245	2	4	4	X
ejpam-4303	245	3	]	]	PUNCT
ejpam-4303	245	4	j.	j.	PROPN
ejpam-4303	245	5	cao	cao	PROPN
ejpam-4303	245	6	and	and	CCONJ
ejpam-4303	245	7	j.	j.	PROPN
ejpam-4303	245	8	dontchev	dontchev	PROPN
ejpam-4303	245	9	.	.	PUNCT
ejpam-4303	246	1	on	on	ADP
ejpam-4303	246	2	some	some	DET
ejpam-4303	246	3	weaker	weak	ADJ
ejpam-4303	246	4	forms	form	NOUN
ejpam-4303	246	5	of	of	ADP
ejpam-4303	246	6	continuity	continuity	NOUN
ejpam-4303	246	7	for	for	ADP
ejpam-4303	246	8	multifunctions	multifunction	NOUN
ejpam-4303	246	9	.	.	PUNCT
ejpam-4303	247	1	real	real	ADJ
ejpam-4303	247	2	analysis	analysis	NOUN
ejpam-4303	247	3	exchange	exchange	NOUN
ejpam-4303	247	4	,	,	PUNCT
ejpam-4303	247	5	22:842–852	22:842–852	PROPN
ejpam-4303	247	6	,	,	PUNCT
ejpam-4303	247	7	1996	1996	NUM
ejpam-4303	247	8	-	-	SYM
ejpam-4303	247	9	97	97	NUM
ejpam-4303	247	10	.	.	PUNCT
ejpam-4303	248	1	[	[	X
ejpam-4303	248	2	5	5	X
ejpam-4303	248	3	]	]	PUNCT
ejpam-4303	248	4	c.	c.	PROPN
ejpam-4303	248	5	l.	l.	PROPN
ejpam-4303	248	6	chang	chang	PROPN
ejpam-4303	248	7	.	.	PUNCT
ejpam-4303	249	1	fuzzy	fuzzy	ADJ
ejpam-4303	249	2	topological	topological	ADJ
ejpam-4303	249	3	spaces	space	NOUN
ejpam-4303	249	4	.	.	PUNCT
ejpam-4303	250	1	journal	journal	PROPN
ejpam-4303	250	2	of	of	ADP
ejpam-4303	250	3	mathematical	mathematical	ADJ
ejpam-4303	250	4	analysis	analysis	NOUN
ejpam-4303	250	5	and	and	CCONJ
ejpam-4303	250	6	applications	application	NOUN
ejpam-4303	250	7	,	,	PUNCT
ejpam-4303	250	8	24:182–190	24:182–190	NUM
ejpam-4303	250	9	,	,	PUNCT
ejpam-4303	250	10	1968	1968	NUM
ejpam-4303	250	11	.	.	PUNCT
ejpam-4303	251	1	[	[	X
ejpam-4303	251	2	6	6	NUM
ejpam-4303	251	3	]	]	PUNCT
ejpam-4303	251	4	g.	g.	PROPN
ejpam-4303	251	5	şenel	şenel	PROPN
ejpam-4303	251	6	.	.	PUNCT
ejpam-4303	252	1	a	a	DET
ejpam-4303	252	2	new	new	ADJ
ejpam-4303	252	3	approach	approach	NOUN
ejpam-4303	252	4	to	to	ADP
ejpam-4303	252	5	hausdorff	hausdorff	NOUN
ejpam-4303	252	6	space	space	NOUN
ejpam-4303	252	7	theory	theory	NOUN
ejpam-4303	252	8	via	via	ADP
ejpam-4303	252	9	the	the	DET
ejpam-4303	252	10	soft	soft	ADJ
ejpam-4303	252	11	sets	set	NOUN
ejpam-4303	252	12	.	.	PUNCT
ejpam-4303	253	1	mathematical	mathematical	ADJ
ejpam-4303	253	2	problems	problem	NOUN
ejpam-4303	253	3	in	in	ADP
ejpam-4303	253	4	engineering	engineering	NOUN
ejpam-4303	253	5	,	,	PUNCT
ejpam-4303	253	6	2016(article	2016(article	NOUN
ejpam-4303	254	1	i	i	PROPN
ejpam-4303	254	2	d	d	PROPN
ejpam-4303	254	3	2196743):6	2196743):6	NUM
ejpam-4303	254	4	pages	page	NOUN
ejpam-4303	254	5	,	,	PUNCT
ejpam-4303	254	6	2016	2016	NUM
ejpam-4303	254	7	.	.	PUNCT
ejpam-4303	255	1	[	[	X
ejpam-4303	255	2	7	7	X
ejpam-4303	255	3	]	]	X
ejpam-4303	255	4	g.	g.	PROPN
ejpam-4303	255	5	şenel	şenel	PROPN
ejpam-4303	255	6	and	and	CCONJ
ejpam-4303	255	7	n.	n.	PROPN
ejpam-4303	255	8	çağman	çağman	NOUN
ejpam-4303	255	9	.	.	PUNCT
ejpam-4303	256	1	soft	soft	ADJ
ejpam-4303	256	2	topological	topological	ADJ
ejpam-4303	256	3	subspaces	subspace	NOUN
ejpam-4303	256	4	.	.	PUNCT
ejpam-4303	257	1	annals	annal	NOUN
ejpam-4303	257	2	of	of	ADP
ejpam-4303	257	3	fuzzy	fuzzy	ADJ
ejpam-4303	257	4	mathematics	mathematic	NOUN
ejpam-4303	257	5	and	and	CCONJ
ejpam-4303	257	6	informatics	informatic	NOUN
ejpam-4303	257	7	,	,	PUNCT
ejpam-4303	257	8	10(4):525–535	10(4):525–535	NUM
ejpam-4303	257	9	,	,	PUNCT
ejpam-4303	257	10	2015	2015	NUM
ejpam-4303	257	11	.	.	PUNCT
ejpam-4303	258	1	[	[	X
ejpam-4303	258	2	8	8	NUM
ejpam-4303	258	3	]	]	PUNCT
ejpam-4303	258	4	m.	m.	NOUN
ejpam-4303	258	5	e.	e.	PROPN
ejpam-4303	258	6	abd	abd	PROPN
ejpam-4303	258	7	el	el	PROPN
ejpam-4303	258	8	-	-	PROPN
ejpam-4303	258	9	monsef	monsef	PROPN
ejpam-4303	258	10	,	,	PUNCT
ejpam-4303	258	11	s.	s.	PROPN
ejpam-4303	258	12	n.	n.	PROPN
ejpam-4303	258	13	el	el	PROPN
ejpam-4303	258	14	-	-	PROPN
ejpam-4303	258	15	deeb	deeb	PROPN
ejpam-4303	258	16	,	,	PUNCT
ejpam-4303	258	17	and	and	CCONJ
ejpam-4303	258	18	r.	r.	PROPN
ejpam-4303	258	19	a.	a.	PROPN
ejpam-4303	258	20	mahmoud	mahmoud	PROPN
ejpam-4303	258	21	.	.	PUNCT
ejpam-4303	259	1	β	β	X
ejpam-4303	259	2	-	-	ADJ
ejpam-4303	259	3	open	open	ADJ
ejpam-4303	259	4	sets	set	NOUN
ejpam-4303	259	5	and	and	CCONJ
ejpam-4303	259	6	βcontinuous	βcontinuous	ADJ
ejpam-4303	259	7	mappings	mapping	NOUN
ejpam-4303	259	8	.	.	PUNCT
ejpam-4303	260	1	bulletin	bulletin	NOUN
ejpam-4303	260	2	of	of	ADP
ejpam-4303	260	3	the	the	DET
ejpam-4303	260	4	faculty	faculty	NOUN
ejpam-4303	260	5	of	of	ADP
ejpam-4303	260	6	science	science	NOUN
ejpam-4303	260	7	.	.	PUNCT
ejpam-4303	261	1	assiut	assiut	PROPN
ejpam-4303	261	2	university	university	PROPN
ejpam-4303	261	3	.	.	PUNCT
ejpam-4303	261	4	,	,	PUNCT
ejpam-4303	261	5	12:77–90	12:77–90	NUM
ejpam-4303	261	6	,	,	PUNCT
ejpam-4303	261	7	1983	1983	NUM
ejpam-4303	261	8	.	.	PUNCT
ejpam-4303	262	1	[	[	X
ejpam-4303	262	2	9	9	NUM
ejpam-4303	262	3	]	]	PUNCT
ejpam-4303	262	4	e.	e.	PROPN
ejpam-4303	262	5	f.	f.	PROPN
ejpam-4303	262	6	lashin	lashin	PROPN
ejpam-4303	262	7	,	,	PUNCT
ejpam-4303	262	8	a.	a.	NOUN
ejpam-4303	262	9	m.	m.	NOUN
ejpam-4303	262	10	kozae	kozae	PROPN
ejpam-4303	262	11	,	,	PUNCT
ejpam-4303	262	12	a.	a.	NOUN
ejpam-4303	262	13	a.	a.	NOUN
ejpam-4303	262	14	abo	abo	PROPN
ejpam-4303	262	15	khadra	khadra	NOUN
ejpam-4303	262	16	,	,	PUNCT
ejpam-4303	262	17	and	and	CCONJ
ejpam-4303	262	18	t.	t.	PROPN
ejpam-4303	262	19	medhat	medhat	PROPN
ejpam-4303	262	20	.	.	PUNCT
ejpam-4303	263	1	rough	rough	ADJ
ejpam-4303	263	2	set	set	NOUN
ejpam-4303	263	3	for	for	ADP
ejpam-4303	263	4	topological	topological	ADJ
ejpam-4303	263	5	spaces	space	NOUN
ejpam-4303	263	6	.	.	PUNCT
ejpam-4303	264	1	international	international	ADJ
ejpam-4303	264	2	journal	journal	PROPN
ejpam-4303	264	3	of	of	ADP
ejpam-4303	264	4	approximate	approximate	ADJ
ejpam-4303	264	5	reasoning	reasoning	NOUN
ejpam-4303	264	6	,	,	PUNCT
ejpam-4303	264	7	40:35–43	40:35–43	NUM
ejpam-4303	264	8	,	,	PUNCT
ejpam-4303	264	9	2005	2005	NUM
ejpam-4303	264	10	.	.	PUNCT
ejpam-4303	265	1	[	[	X
ejpam-4303	265	2	10	10	NUM
ejpam-4303	265	3	]	]	X
ejpam-4303	265	4	n.	n.	PROPN
ejpam-4303	265	5	levine	levine	PROPN
ejpam-4303	265	6	.	.	PUNCT
ejpam-4303	266	1	a	a	DET
ejpam-4303	266	2	decomposition	decomposition	NOUN
ejpam-4303	266	3	of	of	ADP
ejpam-4303	266	4	continuity	continuity	NOUN
ejpam-4303	266	5	in	in	ADP
ejpam-4303	266	6	topological	topological	ADJ
ejpam-4303	266	7	spaces	space	NOUN
ejpam-4303	266	8	.	.	PUNCT
ejpam-4303	267	1	the	the	DET
ejpam-4303	267	2	american	american	PROPN
ejpam-4303	267	3	mathematical	mathematical	PROPN
ejpam-4303	267	4	monthly	monthly	ADV
ejpam-4303	267	5	,	,	PUNCT
ejpam-4303	267	6	68:44–46	68:44–46	NUM
ejpam-4303	267	7	,	,	PUNCT
ejpam-4303	267	8	1961	1961	NUM
ejpam-4303	267	9	.	.	PUNCT
ejpam-4303	267	10	references	reference	NOUN
ejpam-4303	267	11	536	536	NUM
ejpam-4303	267	12	[	[	SYM
ejpam-4303	267	13	11	11	NUM
ejpam-4303	267	14	]	]	X
ejpam-4303	267	15	n.	n.	PROPN
ejpam-4303	267	16	levine	levine	PROPN
ejpam-4303	267	17	.	.	PUNCT
ejpam-4303	268	1	semi	semi	ADJ
ejpam-4303	268	2	-	-	ADJ
ejpam-4303	268	3	open	open	ADJ
ejpam-4303	268	4	sets	set	NOUN
ejpam-4303	268	5	and	and	CCONJ
ejpam-4303	268	6	semi	semi	ADJ
ejpam-4303	268	7	-	-	NOUN
ejpam-4303	268	8	continuity	continuity	NOUN
ejpam-4303	268	9	in	in	ADP
ejpam-4303	268	10	topological	topological	ADJ
ejpam-4303	268	11	spaces	space	NOUN
ejpam-4303	268	12	.	.	PUNCT
ejpam-4303	269	1	the	the	DET
ejpam-4303	269	2	american	american	PROPN
ejpam-4303	269	3	mathematical	mathematical	PROPN
ejpam-4303	269	4	monthly	monthly	ADV
ejpam-4303	269	5	,	,	PUNCT
ejpam-4303	269	6	70:36–41	70:36–41	NUM
ejpam-4303	269	7	,	,	PUNCT
ejpam-4303	269	8	1963	1963	NUM
ejpam-4303	269	9	.	.	PUNCT
ejpam-4303	270	1	[	[	X
ejpam-4303	270	2	12	12	NUM
ejpam-4303	270	3	]	]	PUNCT
ejpam-4303	270	4	a.	a.	NOUN
ejpam-4303	270	5	s.	s.	PROPN
ejpam-4303	270	6	mashhour	mashhour	PROPN
ejpam-4303	270	7	,	,	PUNCT
ejpam-4303	270	8	m.	m.	PROPN
ejpam-4303	270	9	e.	e.	PROPN
ejpam-4303	270	10	el	el	PROPN
ejpam-4303	270	11	-	-	PROPN
ejpam-4303	270	12	monsef	monsef	ADJ
ejpam-4303	270	13	,	,	PUNCT
ejpam-4303	270	14	and	and	CCONJ
ejpam-4303	270	15	s.	s.	PROPN
ejpam-4303	270	16	n.	n.	PROPN
ejpam-4303	270	17	el	el	PROPN
ejpam-4303	270	18	-	-	PROPN
ejpam-4303	270	19	deeb	deeb	PROPN
ejpam-4303	270	20	.	.	PUNCT
ejpam-4303	271	1	on	on	ADP
ejpam-4303	271	2	precontinuous	precontinuous	ADJ
ejpam-4303	271	3	and	and	CCONJ
ejpam-4303	271	4	weak	weak	ADJ
ejpam-4303	271	5	precontinuous	precontinuous	ADJ
ejpam-4303	271	6	mappings	mapping	NOUN
ejpam-4303	271	7	.	.	PUNCT
ejpam-4303	272	1	proceedings	proceeding	NOUN
ejpam-4303	272	2	of	of	ADP
ejpam-4303	272	3	the	the	DET
ejpam-4303	272	4	mathematical	mathematical	ADJ
ejpam-4303	272	5	and	and	CCONJ
ejpam-4303	272	6	physical	physical	ADJ
ejpam-4303	272	7	society	society	NOUN
ejpam-4303	272	8	of	of	ADP
ejpam-4303	272	9	egypt	egypt	PROPN
ejpam-4303	272	10	,	,	PUNCT
ejpam-4303	272	11	53:47–53	53:47–53	NUM
ejpam-4303	272	12	,	,	PUNCT
ejpam-4303	272	13	1982	1982	NUM
ejpam-4303	272	14	.	.	PUNCT
ejpam-4303	273	1	[	[	X
ejpam-4303	273	2	13	13	NUM
ejpam-4303	273	3	]	]	PUNCT
ejpam-4303	273	4	t.	t.	PROPN
ejpam-4303	273	5	noiri	noiri	PROPN
ejpam-4303	273	6	and	and	CCONJ
ejpam-4303	273	7	e.	e.	PROPN
ejpam-4303	273	8	hatir	hatir	PROPN
ejpam-4303	273	9	.	.	PUNCT
ejpam-4303	274	1	λsp	λsp	NOUN
ejpam-4303	274	2	-	-	PUNCT
ejpam-4303	274	3	sets	set	NOUN
ejpam-4303	274	4	and	and	CCONJ
ejpam-4303	274	5	some	some	DET
ejpam-4303	274	6	weak	weak	ADJ
ejpam-4303	274	7	separation	separation	NOUN
ejpam-4303	274	8	axioms	axiom	NOUN
ejpam-4303	274	9	.	.	PUNCT
ejpam-4303	275	1	acta	acta	PROPN
ejpam-4303	275	2	mathematica	mathematica	PROPN
ejpam-4303	275	3	hungarica	hungarica	PROPN
ejpam-4303	275	4	,	,	PUNCT
ejpam-4303	275	5	103(3):225–232	103(3):225–232	NUM
ejpam-4303	275	6	,	,	PUNCT
ejpam-4303	275	7	2004	2004	NUM
ejpam-4303	275	8	.	.	PUNCT
ejpam-4303	276	1	[	[	X
ejpam-4303	276	2	14	14	NUM
ejpam-4303	276	3	]	]	X
ejpam-4303	276	4	v.	v.	CCONJ
ejpam-4303	276	5	popa	popa	NOUN
ejpam-4303	276	6	.	.	PUNCT
ejpam-4303	277	1	weakly	weakly	ADJ
ejpam-4303	277	2	continuous	continuous	ADJ
ejpam-4303	277	3	multifunctions	multifunction	NOUN
ejpam-4303	277	4	.	.	PUNCT
ejpam-4303	278	1	bollettino	bollettino	PROPN
ejpam-4303	278	2	dell	dell	PROPN
ejpam-4303	278	3	’	'	PUNCT
ejpam-4303	278	4	unione	unione	PROPN
ejpam-4303	278	5	matematica	matematica	PROPN
ejpam-4303	278	6	italiana	italiana	PROPN
ejpam-4303	278	7	(	(	PUNCT
ejpam-4303	278	8	5	5	NUM
ejpam-4303	278	9	)	)	PUNCT
ejpam-4303	278	10	,	,	PUNCT
ejpam-4303	278	11	15(a):379–388	15(a):379–388	NUM
ejpam-4303	278	12	,	,	PUNCT
ejpam-4303	278	13	1978	1978	NUM
ejpam-4303	278	14	.	.	PUNCT
ejpam-4303	279	1	[	[	X
ejpam-4303	279	2	15	15	NUM
ejpam-4303	279	3	]	]	X
ejpam-4303	279	4	v.	v.	CCONJ
ejpam-4303	279	5	popa	popa	NOUN
ejpam-4303	279	6	and	and	CCONJ
ejpam-4303	279	7	t.	t.	PROPN
ejpam-4303	279	8	noiri	noiri	PROPN
ejpam-4303	279	9	.	.	PUNCT
ejpam-4303	280	1	on	on	ADP
ejpam-4303	280	2	upper	upper	ADJ
ejpam-4303	280	3	and	and	CCONJ
ejpam-4303	280	4	lower	low	ADJ
ejpam-4303	280	5	almost	almost	ADV
ejpam-4303	280	6	α	α	ADJ
ejpam-4303	280	7	-	-	ADJ
ejpam-4303	280	8	continuous	continuous	ADJ
ejpam-4303	280	9	multifunctions	multifunction	NOUN
ejpam-4303	280	10	.	.	PUNCT
ejpam-4303	281	1	demonstratio	demonstratio	PROPN
ejpam-4303	281	2	mathematica	mathematica	PROPN
ejpam-4303	281	3	,	,	PUNCT
ejpam-4303	281	4	29:381–396	29:381–396	PROPN
ejpam-4303	281	5	,	,	PUNCT
ejpam-4303	281	6	1996	1996	NUM
ejpam-4303	281	7	.	.	PUNCT
ejpam-4303	282	1	[	[	X
ejpam-4303	282	2	16	16	NUM
ejpam-4303	282	3	]	]	PUNCT
ejpam-4303	282	4	v.	v.	CCONJ
ejpam-4303	282	5	popa	popa	NOUN
ejpam-4303	282	6	and	and	CCONJ
ejpam-4303	282	7	t.	t.	PROPN
ejpam-4303	282	8	noiri	noiri	PROPN
ejpam-4303	282	9	.	.	PUNCT
ejpam-4303	283	1	on	on	ADP
ejpam-4303	283	2	upper	upper	ADJ
ejpam-4303	283	3	and	and	CCONJ
ejpam-4303	283	4	lower	low	ADJ
ejpam-4303	283	5	weakly	weakly	ADJ
ejpam-4303	283	6	β	β	ADJ
ejpam-4303	283	7	-	-	ADJ
ejpam-4303	283	8	continuous	continuous	ADJ
ejpam-4303	283	9	multifunctions	multifunction	NOUN
ejpam-4303	283	10	.	.	PUNCT
ejpam-4303	284	1	annales	annales	PROPN
ejpam-4303	284	2	universitatis	universitatis	PROPN
ejpam-4303	284	3	scientiarum	scientiarum	PROPN
ejpam-4303	284	4	budapestinensis	budapestinensis	PROPN
ejpam-4303	284	5	de	de	PROPN
ejpam-4303	284	6	rolando	rolando	PROPN
ejpam-4303	284	7	eötvös	eötvös	PROPN
ejpam-4303	284	8	nominatae	nominatae	NOUN
ejpam-4303	284	9	,	,	PUNCT
ejpam-4303	284	10	43:25–48	43:25–48	NUM
ejpam-4303	284	11	,	,	PUNCT
ejpam-4303	284	12	2000	2000	NUM
ejpam-4303	284	13	.	.	PUNCT
ejpam-4303	285	1	[	[	X
ejpam-4303	285	2	17	17	NUM
ejpam-4303	285	3	]	]	PUNCT
ejpam-4303	285	4	m.	m.	NOUN
ejpam-4303	285	5	shabir	shabir	PROPN
ejpam-4303	285	6	and	and	CCONJ
ejpam-4303	285	7	m.	m.	PROPN
ejpam-4303	285	8	naz	naz	PROPN
ejpam-4303	285	9	.	.	PUNCT
ejpam-4303	286	1	on	on	ADP
ejpam-4303	286	2	soft	soft	ADJ
ejpam-4303	286	3	topological	topological	ADJ
ejpam-4303	286	4	spaces	space	NOUN
ejpam-4303	286	5	.	.	PUNCT
ejpam-4303	287	1	computers	computer	NOUN
ejpam-4303	287	2	and	and	CCONJ
ejpam-4303	287	3	mathematics	mathematic	NOUN
ejpam-4303	287	4	with	with	ADP
ejpam-4303	287	5	applications	application	NOUN
ejpam-4303	287	6	,	,	PUNCT
ejpam-4303	287	7	61:1786–1799	61:1786–1799	NUM
ejpam-4303	287	8	,	,	PUNCT
ejpam-4303	287	9	2011	2011	NUM
ejpam-4303	287	10	.	.	PUNCT
ejpam-4303	288	1	[	[	X
ejpam-4303	288	2	18	18	NUM
ejpam-4303	288	3	]	]	X
ejpam-4303	288	4	r.	r.	PROPN
ejpam-4303	288	5	e.	e.	PROPN
ejpam-4303	288	6	smithson	smithson	PROPN
ejpam-4303	288	7	.	.	PUNCT
ejpam-4303	289	1	almost	almost	ADV
ejpam-4303	289	2	and	and	CCONJ
ejpam-4303	289	3	weak	weak	ADJ
ejpam-4303	289	4	continuity	continuity	NOUN
ejpam-4303	289	5	for	for	ADP
ejpam-4303	289	6	multifunctions	multifunction	NOUN
ejpam-4303	289	7	.	.	PUNCT
ejpam-4303	290	1	bulletin	bulletin	NOUN
ejpam-4303	290	2	of	of	ADP
ejpam-4303	290	3	the	the	DET
ejpam-4303	290	4	calcutta	calcutta	PROPN
ejpam-4303	290	5	mathematical	mathematical	ADJ
ejpam-4303	290	6	society	society	NOUN
ejpam-4303	290	7	,	,	PUNCT
ejpam-4303	290	8	70:383–390	70:383–390	NUM
ejpam-4303	290	9	,	,	PUNCT
ejpam-4303	290	10	1978	1978	NUM
ejpam-4303	290	11	.	.	PUNCT