id	sid	tid	token	lemma	pos
ejpam-4975	1	1	european	european	PROPN
ejpam-4975	1	2	journal	journal	PROPN
ejpam-4975	1	3	of	of	ADP
ejpam-4975	1	4	pure	pure	ADJ
ejpam-4975	1	5	and	and	CCONJ
ejpam-4975	1	6	applied	apply	VERB
ejpam-4975	1	7	mathematics	mathematic	NOUN
ejpam-4975	1	8	vol	vol	NOUN
ejpam-4975	1	9	.	.	PROPN
ejpam-4975	2	1	17	17	NUM
ejpam-4975	2	2	,	,	PUNCT
ejpam-4975	2	3	no	no	INTJ
ejpam-4975	2	4	.	.	NOUN
ejpam-4975	2	5	1	1	NUM
ejpam-4975	2	6	,	,	PUNCT
ejpam-4975	2	7	2024	2024	NUM
ejpam-4975	2	8	,	,	PUNCT
ejpam-4975	2	9	300	300	NUM
ejpam-4975	2	10	-	-	SYM
ejpam-4975	2	11	309	309	NUM
ejpam-4975	2	12	issn	issn	PROPN
ejpam-4975	2	13	1307	1307	NUM
ejpam-4975	2	14	-	-	SYM
ejpam-4975	2	15	5543	5543	NUM
ejpam-4975	2	16	–	–	PUNCT
ejpam-4975	3	1	ejpam.com	ejpam.com	X
ejpam-4975	3	2	published	publish	VERB
ejpam-4975	3	3	by	by	ADP
ejpam-4975	3	4	new	new	PROPN
ejpam-4975	3	5	york	york	PROPN
ejpam-4975	3	6	business	business	PROPN
ejpam-4975	3	7	global	global	ADJ
ejpam-4975	3	8	almost	almost	ADV
ejpam-4975	3	9	strong	strong	ADJ
ejpam-4975	3	10	θ(λ	θ(λ	PROPN
ejpam-4975	3	11	,	,	PUNCT
ejpam-4975	3	12	p)-continuity	p)-continuity	NOUN
ejpam-4975	3	13	for	for	ADP
ejpam-4975	3	14	functions	function	NOUN
ejpam-4975	3	15	chawalit	chawalit	VERB
ejpam-4975	3	16	boonpok1	boonpok1	PROPN
ejpam-4975	3	17	,	,	PUNCT
ejpam-4975	3	18	jeeranunt	jeeranunt	PROPN
ejpam-4975	3	19	khampakdee1,∗	khampakdee1,∗	PROPN
ejpam-4975	3	20	1	1	NUM
ejpam-4975	3	21	mathematics	mathematic	NOUN
ejpam-4975	3	22	and	and	CCONJ
ejpam-4975	3	23	applied	apply	VERB
ejpam-4975	3	24	mathematics	mathematics	PROPN
ejpam-4975	3	25	research	research	NOUN
ejpam-4975	3	26	unit	unit	NOUN
ejpam-4975	3	27	,	,	PUNCT
ejpam-4975	3	28	department	department	NOUN
ejpam-4975	3	29	of	of	ADP
ejpam-4975	3	30	mathematics	mathematic	NOUN
ejpam-4975	3	31	,	,	PUNCT
ejpam-4975	3	32	faculty	faculty	NOUN
ejpam-4975	3	33	of	of	ADP
ejpam-4975	3	34	science	science	NOUN
ejpam-4975	3	35	,	,	PUNCT
ejpam-4975	3	36	mahasarakham	mahasarakham	PROPN
ejpam-4975	3	37	university	university	PROPN
ejpam-4975	3	38	,	,	PUNCT
ejpam-4975	3	39	maha	maha	PROPN
ejpam-4975	3	40	sarakham	sarakham	PROPN
ejpam-4975	3	41	,	,	PUNCT
ejpam-4975	3	42	44150	44150	NUM
ejpam-4975	3	43	,	,	PUNCT
ejpam-4975	3	44	thailand	thailand	PROPN
ejpam-4975	3	45	abstract	abstract	PROPN
ejpam-4975	3	46	.	.	PUNCT
ejpam-4975	4	1	our	our	PRON
ejpam-4975	4	2	main	main	ADJ
ejpam-4975	4	3	purpose	purpose	NOUN
ejpam-4975	4	4	is	be	AUX
ejpam-4975	4	5	to	to	PART
ejpam-4975	4	6	introduce	introduce	VERB
ejpam-4975	4	7	the	the	DET
ejpam-4975	4	8	concept	concept	NOUN
ejpam-4975	4	9	of	of	ADP
ejpam-4975	4	10	almost	almost	ADV
ejpam-4975	4	11	strongly	strongly	ADV
ejpam-4975	4	12	θ(λ	θ(λ	VERB
ejpam-4975	4	13	,	,	PUNCT
ejpam-4975	4	14	p)-continuous	p)-continuous	ADJ
ejpam-4975	4	15	functions	function	NOUN
ejpam-4975	4	16	.	.	PUNCT
ejpam-4975	5	1	moreover	moreover	ADV
ejpam-4975	5	2	,	,	PUNCT
ejpam-4975	5	3	some	some	DET
ejpam-4975	5	4	characterizations	characterization	NOUN
ejpam-4975	5	5	of	of	ADP
ejpam-4975	5	6	almost	almost	ADV
ejpam-4975	5	7	strongly	strongly	ADV
ejpam-4975	5	8	θ(λ	θ(λ	VERB
ejpam-4975	5	9	,	,	PUNCT
ejpam-4975	5	10	p)-continuous	p)-continuous	ADJ
ejpam-4975	5	11	functions	function	NOUN
ejpam-4975	5	12	are	be	AUX
ejpam-4975	5	13	considered	consider	VERB
ejpam-4975	5	14	.	.	PUNCT
ejpam-4975	6	1	2020	2020	NUM
ejpam-4975	6	2	mathematics	mathematic	NOUN
ejpam-4975	6	3	subject	subject	NOUN
ejpam-4975	6	4	classifications	classification	NOUN
ejpam-4975	6	5	:	:	PUNCT
ejpam-4975	6	6	54a05	54a05	NUM
ejpam-4975	6	7	,	,	PUNCT
ejpam-4975	6	8	54c08	54c08	NUM
ejpam-4975	6	9	key	key	ADJ
ejpam-4975	6	10	words	word	NOUN
ejpam-4975	6	11	and	and	CCONJ
ejpam-4975	6	12	phrases	phrase	NOUN
ejpam-4975	6	13	:	:	PUNCT
ejpam-4975	6	14	θ(λ	θ(λ	VERB
ejpam-4975	6	15	,	,	PUNCT
ejpam-4975	6	16	p)-open	p)-open	VERB
ejpam-4975	6	17	set	set	VERB
ejpam-4975	6	18	,	,	PUNCT
ejpam-4975	6	19	almost	almost	ADV
ejpam-4975	6	20	strongly	strongly	ADV
ejpam-4975	6	21	θ(λ	θ(λ	VERB
ejpam-4975	6	22	,	,	PUNCT
ejpam-4975	6	23	p)-continuous	p)-continuous	ADJ
ejpam-4975	6	24	function	function	NOUN
ejpam-4975	6	25	1	1	NUM
ejpam-4975	6	26	.	.	PUNCT
ejpam-4975	6	27	introduction	introduction	NOUN
ejpam-4975	6	28	the	the	DET
ejpam-4975	6	29	notion	notion	NOUN
ejpam-4975	6	30	of	of	ADP
ejpam-4975	6	31	θ	θ	ADJ
ejpam-4975	6	32	-	-	ADJ
ejpam-4975	6	33	continuous	continuous	ADJ
ejpam-4975	6	34	functions	function	NOUN
ejpam-4975	6	35	was	be	AUX
ejpam-4975	6	36	introduced	introduce	VERB
ejpam-4975	6	37	by	by	ADP
ejpam-4975	6	38	fomin	fomin	NOUN
ejpam-4975	7	1	[	[	X
ejpam-4975	7	2	10	10	NUM
ejpam-4975	7	3	]	]	PUNCT
ejpam-4975	7	4	.	.	PUNCT
ejpam-4975	8	1	noiri	noiri	PROPN
ejpam-4975	9	1	[	[	X
ejpam-4975	9	2	20	20	NUM
ejpam-4975	9	3	]	]	PUNCT
ejpam-4975	9	4	studied	study	VERB
ejpam-4975	9	5	some	some	DET
ejpam-4975	9	6	properties	property	NOUN
ejpam-4975	9	7	of	of	ADP
ejpam-4975	9	8	θ	θ	ADJ
ejpam-4975	9	9	-	-	ADJ
ejpam-4975	9	10	continuous	continuous	ADJ
ejpam-4975	9	11	functions	function	NOUN
ejpam-4975	9	12	.	.	PUNCT
ejpam-4975	10	1	arya	arya	PROPN
ejpam-4975	10	2	and	and	CCONJ
ejpam-4975	10	3	bhamini	bhamini	PROPN
ejpam-4975	11	1	[	[	X
ejpam-4975	11	2	1	1	NUM
ejpam-4975	11	3	]	]	PUNCT
ejpam-4975	11	4	introduced	introduce	VERB
ejpam-4975	11	5	the	the	DET
ejpam-4975	11	6	notion	notion	NOUN
ejpam-4975	11	7	of	of	ADP
ejpam-4975	11	8	θ	θ	NOUN
ejpam-4975	11	9	-	-	PUNCT
ejpam-4975	11	10	semi	semi	ADJ
ejpam-4975	11	11	-	-	ADJ
ejpam-4975	11	12	continuous	continuous	ADJ
ejpam-4975	11	13	functions	function	NOUN
ejpam-4975	11	14	.	.	PUNCT
ejpam-4975	12	1	noiri	noiri	PROPN
ejpam-4975	13	1	[	[	X
ejpam-4975	13	2	22	22	NUM
ejpam-4975	13	3	]	]	PUNCT
ejpam-4975	13	4	investigated	investigate	VERB
ejpam-4975	13	5	several	several	ADJ
ejpam-4975	13	6	characterizations	characterization	NOUN
ejpam-4975	13	7	of	of	ADP
ejpam-4975	13	8	θ	θ	ADJ
ejpam-4975	13	9	-	-	PUNCT
ejpam-4975	13	10	semicontinuous	semicontinuous	ADJ
ejpam-4975	13	11	functions	function	NOUN
ejpam-4975	13	12	.	.	PUNCT
ejpam-4975	14	1	moreover	moreover	ADV
ejpam-4975	14	2	,	,	PUNCT
ejpam-4975	14	3	jafari	jafari	ADJ
ejpam-4975	14	4	and	and	CCONJ
ejpam-4975	14	5	noiri	noiri	ADV
ejpam-4975	15	1	[	[	X
ejpam-4975	15	2	15	15	NUM
ejpam-4975	15	3	]	]	PUNCT
ejpam-4975	15	4	obtained	obtain	VERB
ejpam-4975	15	5	some	some	DET
ejpam-4975	15	6	properties	property	NOUN
ejpam-4975	15	7	of	of	ADP
ejpam-4975	15	8	θ	θ	ADJ
ejpam-4975	15	9	-	-	PUNCT
ejpam-4975	15	10	semicontinuous	semicontinuous	ADJ
ejpam-4975	15	11	functions	function	NOUN
ejpam-4975	15	12	.	.	PUNCT
ejpam-4975	16	1	di	di	PROPN
ejpam-4975	16	2	maio	maio	PROPN
ejpam-4975	16	3	and	and	CCONJ
ejpam-4975	16	4	noiri	noiri	ADV
ejpam-4975	17	1	[	[	X
ejpam-4975	17	2	18	18	NUM
ejpam-4975	17	3	]	]	PUNCT
ejpam-4975	17	4	introduced	introduce	VERB
ejpam-4975	17	5	the	the	DET
ejpam-4975	17	6	concept	concept	NOUN
ejpam-4975	17	7	of	of	ADP
ejpam-4975	17	8	quasi	quasi	ADJ
ejpam-4975	17	9	-	-	ADJ
ejpam-4975	17	10	irresolute	irresolute	ADJ
ejpam-4975	17	11	functions	function	NOUN
ejpam-4975	17	12	.	.	PUNCT
ejpam-4975	18	1	it	it	PRON
ejpam-4975	18	2	is	be	AUX
ejpam-4975	18	3	shown	show	VERB
ejpam-4975	18	4	in	in	ADP
ejpam-4975	18	5	[	[	X
ejpam-4975	18	6	8	8	NUM
ejpam-4975	18	7	]	]	PUNCT
ejpam-4975	18	8	that	that	SCONJ
ejpam-4975	18	9	a	a	DET
ejpam-4975	18	10	function	function	NOUN
ejpam-4975	18	11	is	be	AUX
ejpam-4975	18	12	quasi	quasi	ADJ
ejpam-4975	18	13	-	-	NOUN
ejpam-4975	18	14	irresolute	irresolute	ADJ
ejpam-4975	18	15	if	if	SCONJ
ejpam-4975	18	16	and	and	CCONJ
ejpam-4975	18	17	only	only	ADV
ejpam-4975	18	18	if	if	SCONJ
ejpam-4975	18	19	it	it	PRON
ejpam-4975	18	20	is	be	AUX
ejpam-4975	18	21	θ	θ	NOUN
ejpam-4975	18	22	-	-	PUNCT
ejpam-4975	18	23	irresolute	irresolute	ADJ
ejpam-4975	18	24	.	.	PUNCT
ejpam-4975	19	1	noiri	noiri	PROPN
ejpam-4975	20	1	[	[	X
ejpam-4975	20	2	24	24	NUM
ejpam-4975	20	3	]	]	PUNCT
ejpam-4975	20	4	introduced	introduce	VERB
ejpam-4975	20	5	and	and	CCONJ
ejpam-4975	20	6	investigated	investigate	VERB
ejpam-4975	20	7	the	the	DET
ejpam-4975	20	8	notion	notion	NOUN
ejpam-4975	20	9	of	of	ADP
ejpam-4975	20	10	θ	θ	PROPN
ejpam-4975	20	11	-	-	PUNCT
ejpam-4975	20	12	preirresolute	preirresolute	ADJ
ejpam-4975	20	13	functions	function	NOUN
ejpam-4975	20	14	.	.	PUNCT
ejpam-4975	21	1	the	the	DET
ejpam-4975	21	2	notion	notion	NOUN
ejpam-4975	21	3	of	of	ADP
ejpam-4975	21	4	weakly	weakly	ADJ
ejpam-4975	21	5	β	β	NOUN
ejpam-4975	21	6	-	-	ADJ
ejpam-4975	21	7	irresolute	irresolute	ADJ
ejpam-4975	21	8	functions	function	NOUN
ejpam-4975	21	9	has	have	AUX
ejpam-4975	21	10	been	be	AUX
ejpam-4975	21	11	defined	define	VERB
ejpam-4975	21	12	and	and	CCONJ
ejpam-4975	21	13	studied	study	VERB
ejpam-4975	21	14	in	in	ADP
ejpam-4975	21	15	[	[	X
ejpam-4975	21	16	25	25	NUM
ejpam-4975	21	17	]	]	PUNCT
ejpam-4975	21	18	.	.	PUNCT
ejpam-4975	22	1	these	these	DET
ejpam-4975	22	2	four	four	NUM
ejpam-4975	22	3	classes	class	NOUN
ejpam-4975	22	4	of	of	ADP
ejpam-4975	22	5	functions	function	NOUN
ejpam-4975	22	6	have	have	VERB
ejpam-4975	22	7	properties	property	NOUN
ejpam-4975	22	8	similar	similar	ADJ
ejpam-4975	22	9	to	to	ADP
ejpam-4975	22	10	the	the	DET
ejpam-4975	22	11	class	class	NOUN
ejpam-4975	22	12	of	of	ADP
ejpam-4975	22	13	θ	θ	ADJ
ejpam-4975	22	14	-	-	ADJ
ejpam-4975	22	15	continuous	continuous	ADJ
ejpam-4975	22	16	functions	function	NOUN
ejpam-4975	22	17	.	.	PUNCT
ejpam-4975	23	1	in	in	ADP
ejpam-4975	23	2	1980	1980	NUM
ejpam-4975	23	3	,	,	PUNCT
ejpam-4975	23	4	noiri	noiri	ADV
ejpam-4975	23	5	[	[	X
ejpam-4975	23	6	21	21	NUM
ejpam-4975	23	7	]	]	PUNCT
ejpam-4975	23	8	introduced	introduce	VERB
ejpam-4975	23	9	the	the	DET
ejpam-4975	23	10	notion	notion	NOUN
ejpam-4975	23	11	of	of	ADP
ejpam-4975	23	12	strongly	strongly	ADV
ejpam-4975	23	13	θ	θ	ADJ
ejpam-4975	23	14	-	-	ADJ
ejpam-4975	23	15	continuous	continuous	ADJ
ejpam-4975	23	16	functions	function	NOUN
ejpam-4975	23	17	.	.	PUNCT
ejpam-4975	24	1	long	long	ADV
ejpam-4975	24	2	et	et	PROPN
ejpam-4975	24	3	al	al	PROPN
ejpam-4975	24	4	.	.	PUNCT
ejpam-4975	25	1	[	[	X
ejpam-4975	25	2	17	17	NUM
ejpam-4975	25	3	]	]	PUNCT
ejpam-4975	25	4	studied	study	VERB
ejpam-4975	25	5	some	some	DET
ejpam-4975	25	6	properties	property	NOUN
ejpam-4975	25	7	of	of	ADP
ejpam-4975	25	8	strongly	strongly	ADV
ejpam-4975	25	9	θ	θ	ADJ
ejpam-4975	25	10	-	-	ADJ
ejpam-4975	25	11	continuous	continuous	ADJ
ejpam-4975	25	12	functions	function	NOUN
ejpam-4975	25	13	.	.	PUNCT
ejpam-4975	26	1	in	in	ADP
ejpam-4975	26	2	1998	1998	NUM
ejpam-4975	26	3	,	,	PUNCT
ejpam-4975	26	4	jafari	jafari	ADJ
ejpam-4975	26	5	and	and	CCONJ
ejpam-4975	26	6	noiri	noiri	ADV
ejpam-4975	26	7	[	[	X
ejpam-4975	26	8	12	12	NUM
ejpam-4975	26	9	]	]	PUNCT
ejpam-4975	26	10	introduced	introduce	VERB
ejpam-4975	26	11	and	and	CCONJ
ejpam-4975	26	12	studied	study	VERB
ejpam-4975	26	13	the	the	DET
ejpam-4975	26	14	concept	concept	NOUN
ejpam-4975	26	15	of	of	ADP
ejpam-4975	26	16	strongly	strongly	ADV
ejpam-4975	26	17	θ	θ	NOUN
ejpam-4975	26	18	-	-	PUNCT
ejpam-4975	26	19	semi	semi	ADJ
ejpam-4975	26	20	-	-	ADJ
ejpam-4975	26	21	continuous	continuous	ADJ
ejpam-4975	26	22	functions	function	NOUN
ejpam-4975	26	23	.	.	PUNCT
ejpam-4975	27	1	moreover	moreover	ADV
ejpam-4975	27	2	,	,	PUNCT
ejpam-4975	27	3	jafari	jafari	ADJ
ejpam-4975	27	4	and	and	CCONJ
ejpam-4975	27	5	noiri	noiri	ADV
ejpam-4975	28	1	[	[	X
ejpam-4975	28	2	14	14	NUM
ejpam-4975	28	3	]	]	PUNCT
ejpam-4975	28	4	studied	study	VERB
ejpam-4975	28	5	the	the	DET
ejpam-4975	28	6	notion	notion	NOUN
ejpam-4975	28	7	of	of	ADP
ejpam-4975	28	8	strongly	strongly	ADV
ejpam-4975	28	9	sober	sober	ADJ
ejpam-4975	28	10	θ	θ	ADJ
ejpam-4975	28	11	-	-	ADJ
ejpam-4975	28	12	continuous	continuous	ADJ
ejpam-4975	28	13	functions	function	NOUN
ejpam-4975	28	14	.	.	PUNCT
ejpam-4975	29	1	noiri	noiri	PROPN
ejpam-4975	30	1	[	[	X
ejpam-4975	30	2	23	23	NUM
ejpam-4975	30	3	]	]	PUNCT
ejpam-4975	30	4	introduced	introduce	VERB
ejpam-4975	30	5	the	the	DET
ejpam-4975	30	6	concept	concept	NOUN
ejpam-4975	30	7	of	of	ADP
ejpam-4975	30	8	θ	θ	ADJ
ejpam-4975	30	9	-	-	ADJ
ejpam-4975	30	10	precontinuous	precontinuous	ADJ
ejpam-4975	30	11	functions	function	NOUN
ejpam-4975	30	12	.	.	PUNCT
ejpam-4975	31	1	in	in	ADP
ejpam-4975	31	2	2002	2002	NUM
ejpam-4975	31	3	,	,	PUNCT
ejpam-4975	31	4	noiri	noiri	ADV
ejpam-4975	31	5	and	and	CCONJ
ejpam-4975	31	6	popa	popa	NOUN
ejpam-4975	31	7	[	[	X
ejpam-4975	31	8	27	27	NUM
ejpam-4975	31	9	]	]	PUNCT
ejpam-4975	31	10	introduced	introduce	VERB
ejpam-4975	31	11	and	and	CCONJ
ejpam-4975	31	12	investigated	investigate	VERB
ejpam-4975	31	13	the	the	DET
ejpam-4975	31	14	notion	notion	NOUN
ejpam-4975	31	15	of	of	ADP
ejpam-4975	31	16	strongly	strongly	ADV
ejpam-4975	31	17	θ	θ	NOUN
ejpam-4975	31	18	-	-	PUNCT
ejpam-4975	31	19	β	β	ADJ
ejpam-4975	31	20	-	-	ADJ
ejpam-4975	31	21	continuous	continuous	ADJ
ejpam-4975	31	22	functions	function	NOUN
ejpam-4975	31	23	.	.	PUNCT
ejpam-4975	32	1	in	in	ADP
ejpam-4975	32	2	2005	2005	NUM
ejpam-4975	32	3	,	,	PUNCT
ejpam-4975	32	4	noiri	noiri	ADV
ejpam-4975	32	5	and	and	CCONJ
ejpam-4975	32	6	popa	popa	NOUN
ejpam-4975	32	7	[	[	X
ejpam-4975	32	8	29	29	NUM
ejpam-4975	32	9	]	]	PUNCT
ejpam-4975	32	10	defined	define	VERB
ejpam-4975	32	11	a	a	DET
ejpam-4975	32	12	new	new	ADJ
ejpam-4975	32	13	notion	notion	NOUN
ejpam-4975	32	14	of	of	ADP
ejpam-4975	32	15	strongly	strongly	ADV
ejpam-4975	32	16	θ	θ	ADJ
ejpam-4975	32	17	-	-	ADJ
ejpam-4975	32	18	m	m	VERB
ejpam-4975	32	19	-continuous	-continuous	ADJ
ejpam-4975	32	20	functions	function	NOUN
ejpam-4975	32	21	as	as	ADP
ejpam-4975	32	22	functions	function	NOUN
ejpam-4975	32	23	from	from	ADP
ejpam-4975	32	24	a	a	DET
ejpam-4975	32	25	set	set	NOUN
ejpam-4975	32	26	satisfying	satisfy	VERB
ejpam-4975	32	27	some	some	DET
ejpam-4975	32	28	minimal	minimal	ADJ
ejpam-4975	32	29	conditions	condition	NOUN
ejpam-4975	32	30	into	into	ADP
ejpam-4975	32	31	a	a	DET
ejpam-4975	32	32	set	set	NOUN
ejpam-4975	32	33	satisfying	satisfy	VERB
ejpam-4975	32	34	some	some	DET
ejpam-4975	32	35	minimal	minimal	ADJ
ejpam-4975	32	36	conditions	condition	NOUN
ejpam-4975	32	37	.	.	PUNCT
ejpam-4975	33	1	noiri	noiri	PROPN
ejpam-4975	33	2	and	and	CCONJ
ejpam-4975	33	3	kang	kang	PROPN
ejpam-4975	34	1	[	[	X
ejpam-4975	34	2	26	26	NUM
ejpam-4975	34	3	]	]	PUNCT
ejpam-4975	34	4	introduced	introduce	VERB
ejpam-4975	34	5	and	and	CCONJ
ejpam-4975	34	6	studied	study	VERB
ejpam-4975	34	7	the	the	DET
ejpam-4975	34	8	notion	notion	NOUN
ejpam-4975	34	9	of	of	ADP
ejpam-4975	34	10	almost	almost	ADV
ejpam-4975	34	11	strongly	strongly	ADV
ejpam-4975	34	12	θ	θ	ADJ
ejpam-4975	34	13	-	-	ADJ
ejpam-4975	34	14	continuous	continuous	ADJ
ejpam-4975	34	15	functions	function	NOUN
ejpam-4975	34	16	.	.	PUNCT
ejpam-4975	35	1	jafari	jafari	PROPN
ejpam-4975	35	2	and	and	CCONJ
ejpam-4975	35	3	noiri	noiri	ADV
ejpam-4975	36	1	[	[	X
ejpam-4975	36	2	16	16	NUM
ejpam-4975	36	3	]	]	PUNCT
ejpam-4975	36	4	investigated	investigate	VERB
ejpam-4975	36	5	some	some	DET
ejpam-4975	36	6	properties	property	NOUN
ejpam-4975	36	7	of	of	ADP
ejpam-4975	36	8	almost	almost	ADV
ejpam-4975	36	9	strongly	strongly	ADV
ejpam-4975	36	10	θ	θ	ADJ
ejpam-4975	36	11	-	-	ADJ
ejpam-4975	36	12	continuous	continuous	ADJ
ejpam-4975	36	13	functions	function	NOUN
ejpam-4975	36	14	.	.	PUNCT
ejpam-4975	37	1	beceren	beceren	NOUN
ejpam-4975	37	2	∗corresponding	∗corresponde	VERB
ejpam-4975	37	3	author	author	NOUN
ejpam-4975	37	4	.	.	PUNCT
ejpam-4975	38	1	doi	doi	NOUN
ejpam-4975	38	2	:	:	PUNCT
ejpam-4975	38	3	https://doi.org/10.29020/nybg.ejpam.v17i1.4975	https://doi.org/10.29020/nybg.ejpam.v17i1.4975	PROPN
ejpam-4975	38	4	email	email	NOUN
ejpam-4975	38	5	addresses	address	NOUN
ejpam-4975	38	6	:	:	PUNCT
ejpam-4975	39	1	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	INTJ
ejpam-4975	39	2	(	(	PUNCT
ejpam-4975	39	3	c.	c.	PROPN
ejpam-4975	39	4	boonpok	boonpok	PROPN
ejpam-4975	39	5	)	)	PUNCT
ejpam-4975	39	6	,	,	PUNCT
ejpam-4975	39	7	jeeranunt.k@msu.ac.th	jeeranunt.k@msu.ac.th	INTJ
ejpam-4975	39	8	(	(	PUNCT
ejpam-4975	39	9	j.	j.	PROPN
ejpam-4975	39	10	khampakdee	khampakdee	PROPN
ejpam-4975	39	11	)	)	PUNCT
ejpam-4975	39	12	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4975	40	1	300	300	NUM
ejpam-4975	40	2	©	©	ADP
ejpam-4975	40	3	2024	2024	NUM
ejpam-4975	40	4	ejpam	ejpam	NOUN
ejpam-4975	40	5	all	all	DET
ejpam-4975	40	6	rights	right	NOUN
ejpam-4975	40	7	reserved	reserve	VERB
ejpam-4975	40	8	.	.	PUNCT
ejpam-4975	41	1	c.	c.	PROPN
ejpam-4975	41	2	boonpok	boonpok	PROPN
ejpam-4975	41	3	,	,	PUNCT
ejpam-4975	41	4	j.	j.	PROPN
ejpam-4975	41	5	khampakdee	khampakdee	PROPN
ejpam-4975	41	6	/	/	PUNCT
ejpam-4975	41	7	eur	eur	PROPN
ejpam-4975	41	8	.	.	PUNCT
ejpam-4975	42	1	j.	j.	PROPN
ejpam-4975	42	2	pure	pure	PROPN
ejpam-4975	42	3	appl	appl	PROPN
ejpam-4975	42	4	.	.	PROPN
ejpam-4975	42	5	math	math	PROPN
ejpam-4975	42	6	,	,	PUNCT
ejpam-4975	42	7	17	17	NUM
ejpam-4975	42	8	(	(	PUNCT
ejpam-4975	42	9	1	1	NUM
ejpam-4975	42	10	)	)	PUNCT
ejpam-4975	42	11	(	(	PUNCT
ejpam-4975	42	12	2024	2024	NUM
ejpam-4975	42	13	)	)	PUNCT
ejpam-4975	42	14	,	,	PUNCT
ejpam-4975	42	15	300	300	NUM
ejpam-4975	42	16	-	-	SYM
ejpam-4975	42	17	309	309	NUM
ejpam-4975	42	18	301	301	NUM
ejpam-4975	42	19	et	et	NOUN
ejpam-4975	42	20	al	al	PROPN
ejpam-4975	42	21	.	.	PUNCT
ejpam-4975	43	1	[	[	X
ejpam-4975	43	2	2	2	X
ejpam-4975	43	3	]	]	PUNCT
ejpam-4975	43	4	introduced	introduce	VERB
ejpam-4975	43	5	and	and	CCONJ
ejpam-4975	43	6	studied	study	VERB
ejpam-4975	43	7	the	the	DET
ejpam-4975	43	8	concept	concept	NOUN
ejpam-4975	43	9	of	of	ADP
ejpam-4975	43	10	almost	almost	ADV
ejpam-4975	43	11	strongly	strongly	ADV
ejpam-4975	43	12	θ	θ	NOUN
ejpam-4975	43	13	-	-	PUNCT
ejpam-4975	43	14	semi	semi	ADJ
ejpam-4975	43	15	-	-	ADJ
ejpam-4975	43	16	continuous	continuous	ADJ
ejpam-4975	43	17	functions	function	NOUN
ejpam-4975	43	18	.	.	PUNCT
ejpam-4975	44	1	furthermore	furthermore	ADV
ejpam-4975	44	2	,	,	PUNCT
ejpam-4975	44	3	jafari	jafari	ADJ
ejpam-4975	44	4	and	and	CCONJ
ejpam-4975	44	5	noiri	noiri	ADV
ejpam-4975	45	1	[	[	X
ejpam-4975	45	2	13	13	NUM
ejpam-4975	45	3	]	]	PUNCT
ejpam-4975	45	4	investigated	investigate	VERB
ejpam-4975	45	5	several	several	ADJ
ejpam-4975	45	6	characterizations	characterization	NOUN
ejpam-4975	45	7	of	of	ADP
ejpam-4975	45	8	almost	almost	ADV
ejpam-4975	45	9	strongly	strongly	ADV
ejpam-4975	45	10	θ	θ	NOUN
ejpam-4975	45	11	-	-	PUNCT
ejpam-4975	45	12	semi	semi	ADJ
ejpam-4975	45	13	-	-	ADJ
ejpam-4975	45	14	continuous	continuous	ADJ
ejpam-4975	45	15	functions	function	NOUN
ejpam-4975	45	16	.	.	PUNCT
ejpam-4975	46	1	dube	dube	PROPN
ejpam-4975	46	2	and	and	CCONJ
ejpam-4975	46	3	chauhan	chauhan	PROPN
ejpam-4975	47	1	[	[	X
ejpam-4975	47	2	9	9	NUM
ejpam-4975	47	3	]	]	PUNCT
ejpam-4975	47	4	introduced	introduce	VERB
ejpam-4975	47	5	the	the	DET
ejpam-4975	47	6	notion	notion	NOUN
ejpam-4975	47	7	of	of	ADP
ejpam-4975	47	8	strongly	strongly	ADV
ejpam-4975	47	9	closure	closure	ADJ
ejpam-4975	47	10	semi	semi	ADJ
ejpam-4975	47	11	-	-	ADJ
ejpam-4975	47	12	continuous	continuous	ADJ
ejpam-4975	47	13	functions	function	NOUN
ejpam-4975	47	14	which	which	PRON
ejpam-4975	47	15	are	be	AUX
ejpam-4975	47	16	equivalent	equivalent	ADJ
ejpam-4975	47	17	to	to	ADP
ejpam-4975	47	18	almost	almost	ADV
ejpam-4975	47	19	strongly	strongly	ADV
ejpam-4975	47	20	θ	θ	ADJ
ejpam-4975	47	21	-	-	PUNCT
ejpam-4975	47	22	semicontinuous	semicontinuous	ADJ
ejpam-4975	47	23	functions	function	NOUN
ejpam-4975	47	24	.	.	PUNCT
ejpam-4975	48	1	these	these	DET
ejpam-4975	48	2	classes	class	NOUN
ejpam-4975	48	3	of	of	ADP
ejpam-4975	48	4	functions	function	NOUN
ejpam-4975	48	5	have	have	VERB
ejpam-4975	48	6	properties	property	NOUN
ejpam-4975	48	7	similar	similar	ADJ
ejpam-4975	48	8	to	to	ADP
ejpam-4975	48	9	the	the	DET
ejpam-4975	48	10	class	class	NOUN
ejpam-4975	48	11	of	of	ADP
ejpam-4975	48	12	θ	θ	ADJ
ejpam-4975	48	13	-	-	ADJ
ejpam-4975	48	14	continuous	continuous	ADJ
ejpam-4975	48	15	functions	function	NOUN
ejpam-4975	48	16	.	.	PUNCT
ejpam-4975	49	1	noiri	noiri	PROPN
ejpam-4975	49	2	and	and	CCONJ
ejpam-4975	49	3	popa	popa	NOUN
ejpam-4975	50	1	[	[	X
ejpam-4975	50	2	28	28	NUM
ejpam-4975	50	3	]	]	PUNCT
ejpam-4975	50	4	introduced	introduce	VERB
ejpam-4975	50	5	and	and	CCONJ
ejpam-4975	50	6	studied	study	VERB
ejpam-4975	50	7	the	the	DET
ejpam-4975	50	8	notion	notion	NOUN
ejpam-4975	50	9	of	of	ADP
ejpam-4975	50	10	almost	almost	ADV
ejpam-4975	50	11	strongly	strongly	ADV
ejpam-4975	50	12	θ	θ	ADJ
ejpam-4975	50	13	-	-	PUNCT
ejpam-4975	50	14	m	m	NOUN
ejpam-4975	50	15	-	-	ADJ
ejpam-4975	50	16	continuous	continuous	ADJ
ejpam-4975	50	17	functions	function	NOUN
ejpam-4975	50	18	as	as	ADP
ejpam-4975	50	19	functions	function	NOUN
ejpam-4975	50	20	from	from	ADP
ejpam-4975	50	21	a	a	DET
ejpam-4975	50	22	set	set	NOUN
ejpam-4975	50	23	satisfying	satisfy	VERB
ejpam-4975	50	24	some	some	DET
ejpam-4975	50	25	minimal	minimal	ADJ
ejpam-4975	50	26	conditions	condition	NOUN
ejpam-4975	50	27	into	into	ADP
ejpam-4975	50	28	a	a	DET
ejpam-4975	50	29	topological	topological	ADJ
ejpam-4975	50	30	space	space	NOUN
ejpam-4975	50	31	.	.	PUNCT
ejpam-4975	51	1	in	in	ADP
ejpam-4975	51	2	[	[	X
ejpam-4975	51	3	7	7	NUM
ejpam-4975	51	4	]	]	PUNCT
ejpam-4975	51	5	,	,	PUNCT
ejpam-4975	51	6	the	the	DET
ejpam-4975	51	7	present	present	ADJ
ejpam-4975	51	8	authors	author	NOUN
ejpam-4975	51	9	introduced	introduce	VERB
ejpam-4975	51	10	and	and	CCONJ
ejpam-4975	51	11	investigated	investigate	VERB
ejpam-4975	51	12	the	the	DET
ejpam-4975	51	13	concept	concept	NOUN
ejpam-4975	51	14	of	of	ADP
ejpam-4975	51	15	almost	almost	ADV
ejpam-4975	51	16	(	(	PUNCT
ejpam-4975	51	17	λ	λ	PROPN
ejpam-4975	51	18	,	,	PUNCT
ejpam-4975	51	19	s)-continuous	s)-continuous	ADJ
ejpam-4975	51	20	functions	function	NOUN
ejpam-4975	51	21	.	.	PUNCT
ejpam-4975	52	1	the	the	DET
ejpam-4975	52	2	notions	notion	NOUN
ejpam-4975	52	3	of	of	ADP
ejpam-4975	52	4	(	(	PUNCT
ejpam-4975	52	5	λ	λ	PROPN
ejpam-4975	52	6	,	,	PUNCT
ejpam-4975	52	7	sp)-open	sp)-open	ADJ
ejpam-4975	52	8	sets	set	NOUN
ejpam-4975	52	9	,	,	PUNCT
ejpam-4975	52	10	s(λ	s(λ	PROPN
ejpam-4975	52	11	,	,	PUNCT
ejpam-4975	52	12	sp)open	sp)open	NOUN
ejpam-4975	52	13	sets	set	NOUN
ejpam-4975	52	14	,	,	PUNCT
ejpam-4975	52	15	p(λ	p(λ	NOUN
ejpam-4975	52	16	,	,	PUNCT
ejpam-4975	52	17	sp)-open	sp)-open	ADJ
ejpam-4975	52	18	sets	set	NOUN
ejpam-4975	52	19	,	,	PUNCT
ejpam-4975	52	20	α(λ	α(λ	PROPN
ejpam-4975	52	21	,	,	PUNCT
ejpam-4975	52	22	sp)-open	sp)-open	ADJ
ejpam-4975	52	23	sets	set	NOUN
ejpam-4975	52	24	,	,	PUNCT
ejpam-4975	52	25	β(λ	β(λ	X
ejpam-4975	52	26	,	,	PUNCT
ejpam-4975	52	27	sp)-open	sp)-open	ADJ
ejpam-4975	52	28	sets	set	NOUN
ejpam-4975	52	29	and	and	CCONJ
ejpam-4975	52	30	b(λ	b(λ	NOUN
ejpam-4975	52	31	,	,	PUNCT
ejpam-4975	52	32	sp)-open	sp)-open	ADJ
ejpam-4975	52	33	sets	set	NOUN
ejpam-4975	52	34	were	be	AUX
ejpam-4975	52	35	studied	study	VERB
ejpam-4975	52	36	in	in	ADP
ejpam-4975	52	37	[	[	X
ejpam-4975	52	38	4	4	NUM
ejpam-4975	52	39	]	]	PUNCT
ejpam-4975	52	40	.	.	PUNCT
ejpam-4975	53	1	viriyapong	viriyapong	PROPN
ejpam-4975	53	2	and	and	CCONJ
ejpam-4975	53	3	boonpok	boonpok	VERB
ejpam-4975	53	4	[	[	X
ejpam-4975	53	5	31	31	NUM
ejpam-4975	53	6	]	]	PUNCT
ejpam-4975	53	7	investigated	investigate	VERB
ejpam-4975	53	8	some	some	DET
ejpam-4975	53	9	characterizations	characterization	NOUN
ejpam-4975	53	10	of	of	ADP
ejpam-4975	53	11	(	(	PUNCT
ejpam-4975	53	12	λ	λ	PROPN
ejpam-4975	53	13	,	,	PUNCT
ejpam-4975	53	14	sp)-continuous	sp)-continuous	ADJ
ejpam-4975	53	15	functions	function	NOUN
ejpam-4975	53	16	.	.	PUNCT
ejpam-4975	54	1	furthermore	furthermore	ADV
ejpam-4975	54	2	,	,	PUNCT
ejpam-4975	54	3	several	several	ADJ
ejpam-4975	54	4	characterizations	characterization	NOUN
ejpam-4975	54	5	of	of	ADP
ejpam-4975	54	6	pairwise	pairwise	NOUN
ejpam-4975	54	7	almost	almost	ADV
ejpam-4975	54	8	m	m	VERB
ejpam-4975	54	9	-continuous	-continuous	ADJ
ejpam-4975	54	10	functions	function	NOUN
ejpam-4975	54	11	were	be	AUX
ejpam-4975	54	12	established	establish	VERB
ejpam-4975	54	13	in	in	ADP
ejpam-4975	54	14	[	[	X
ejpam-4975	54	15	3	3	NUM
ejpam-4975	54	16	]	]	PUNCT
ejpam-4975	54	17	.	.	PUNCT
ejpam-4975	55	1	in	in	ADP
ejpam-4975	55	2	this	this	DET
ejpam-4975	55	3	paper	paper	NOUN
ejpam-4975	55	4	,	,	PUNCT
ejpam-4975	55	5	we	we	PRON
ejpam-4975	55	6	introduce	introduce	VERB
ejpam-4975	55	7	the	the	DET
ejpam-4975	55	8	concept	concept	NOUN
ejpam-4975	55	9	of	of	ADP
ejpam-4975	55	10	almost	almost	ADV
ejpam-4975	55	11	strongly	strongly	ADV
ejpam-4975	55	12	θ(λ	θ(λ	VERB
ejpam-4975	55	13	,	,	PUNCT
ejpam-4975	55	14	p)-continuous	p)-continuous	ADJ
ejpam-4975	55	15	functions	function	NOUN
ejpam-4975	55	16	.	.	PUNCT
ejpam-4975	56	1	in	in	ADP
ejpam-4975	56	2	particular	particular	ADJ
ejpam-4975	56	3	,	,	PUNCT
ejpam-4975	56	4	several	several	ADJ
ejpam-4975	56	5	characterizations	characterization	NOUN
ejpam-4975	56	6	of	of	ADP
ejpam-4975	56	7	almost	almost	ADV
ejpam-4975	56	8	strongly	strongly	ADV
ejpam-4975	56	9	θ(λ	θ(λ	VERB
ejpam-4975	56	10	,	,	PUNCT
ejpam-4975	56	11	p)-continuous	p)-continuous	ADJ
ejpam-4975	56	12	functions	function	NOUN
ejpam-4975	56	13	are	be	AUX
ejpam-4975	56	14	discussed	discuss	VERB
ejpam-4975	56	15	.	.	PUNCT
ejpam-4975	57	1	2	2	X
ejpam-4975	57	2	.	.	X
ejpam-4975	57	3	preliminaries	preliminary	NOUN
ejpam-4975	57	4	throughout	throughout	ADP
ejpam-4975	57	5	the	the	DET
ejpam-4975	57	6	present	present	ADJ
ejpam-4975	57	7	paper	paper	NOUN
ejpam-4975	57	8	,	,	PUNCT
ejpam-4975	57	9	spaces	space	NOUN
ejpam-4975	57	10	(	(	PUNCT
ejpam-4975	57	11	x	x	X
ejpam-4975	57	12	,	,	PUNCT
ejpam-4975	57	13	τ	τ	X
ejpam-4975	57	14	)	)	PUNCT
ejpam-4975	57	15	and	and	CCONJ
ejpam-4975	57	16	(	(	PUNCT
ejpam-4975	57	17	y	y	PROPN
ejpam-4975	57	18	,	,	PUNCT
ejpam-4975	57	19	σ	σ	PROPN
ejpam-4975	57	20	)	)	PUNCT
ejpam-4975	57	21	(	(	PUNCT
ejpam-4975	57	22	or	or	CCONJ
ejpam-4975	57	23	simply	simply	ADV
ejpam-4975	57	24	x	x	X
ejpam-4975	57	25	and	and	CCONJ
ejpam-4975	57	26	y	y	PROPN
ejpam-4975	57	27	)	)	PUNCT
ejpam-4975	57	28	always	always	ADV
ejpam-4975	57	29	mean	mean	VERB
ejpam-4975	57	30	topological	topological	ADJ
ejpam-4975	57	31	spaces	space	NOUN
ejpam-4975	57	32	on	on	ADP
ejpam-4975	57	33	which	which	PRON
ejpam-4975	57	34	no	no	DET
ejpam-4975	57	35	separation	separation	NOUN
ejpam-4975	57	36	axioms	axiom	NOUN
ejpam-4975	57	37	are	be	AUX
ejpam-4975	57	38	assumed	assume	VERB
ejpam-4975	57	39	unless	unless	SCONJ
ejpam-4975	57	40	explicitly	explicitly	ADV
ejpam-4975	57	41	stated	state	VERB
ejpam-4975	57	42	.	.	PUNCT
ejpam-4975	58	1	for	for	ADP
ejpam-4975	58	2	a	a	DET
ejpam-4975	58	3	subset	subset	NOUN
ejpam-4975	58	4	a	a	PRON
ejpam-4975	58	5	of	of	ADP
ejpam-4975	58	6	a	a	DET
ejpam-4975	58	7	topological	topological	ADJ
ejpam-4975	58	8	space	space	NOUN
ejpam-4975	58	9	(	(	PUNCT
ejpam-4975	58	10	x	x	X
ejpam-4975	58	11	,	,	PUNCT
ejpam-4975	58	12	τ	τ	PROPN
ejpam-4975	58	13	)	)	PUNCT
ejpam-4975	58	14	,	,	PUNCT
ejpam-4975	58	15	cl(a	cl(a	NUM
ejpam-4975	58	16	)	)	PUNCT
ejpam-4975	58	17	and	and	CCONJ
ejpam-4975	58	18	int(a	int(a	PROPN
ejpam-4975	58	19	)	)	PUNCT
ejpam-4975	58	20	,	,	PUNCT
ejpam-4975	58	21	represent	represent	VERB
ejpam-4975	58	22	the	the	DET
ejpam-4975	58	23	closure	closure	NOUN
ejpam-4975	58	24	and	and	CCONJ
ejpam-4975	58	25	the	the	DET
ejpam-4975	58	26	interior	interior	NOUN
ejpam-4975	58	27	of	of	ADP
ejpam-4975	58	28	a	a	PRON
ejpam-4975	58	29	,	,	PUNCT
ejpam-4975	58	30	respectively	respectively	ADV
ejpam-4975	58	31	.	.	PUNCT
ejpam-4975	59	1	a	a	DET
ejpam-4975	59	2	subset	subset	NOUN
ejpam-4975	59	3	a	a	PRON
ejpam-4975	59	4	of	of	ADP
ejpam-4975	59	5	a	a	DET
ejpam-4975	59	6	topological	topological	ADJ
ejpam-4975	59	7	space	space	NOUN
ejpam-4975	59	8	(	(	PUNCT
ejpam-4975	59	9	x	x	X
ejpam-4975	59	10	,	,	PUNCT
ejpam-4975	59	11	τ	τ	X
ejpam-4975	59	12	)	)	PUNCT
ejpam-4975	59	13	is	be	AUX
ejpam-4975	59	14	said	say	VERB
ejpam-4975	59	15	to	to	PART
ejpam-4975	59	16	be	be	AUX
ejpam-4975	59	17	preopen	preopen	ADJ
ejpam-4975	59	18	[	[	X
ejpam-4975	59	19	19	19	NUM
ejpam-4975	59	20	]	]	X
ejpam-4975	59	21	if	if	SCONJ
ejpam-4975	59	22	a	a	DET
ejpam-4975	59	23	⊆	⊆	NUM
ejpam-4975	59	24	int(cl(a	int(cl(a	PROPN
ejpam-4975	59	25	)	)	PUNCT
ejpam-4975	59	26	)	)	PUNCT
ejpam-4975	59	27	.	.	PUNCT
ejpam-4975	60	1	the	the	DET
ejpam-4975	60	2	complement	complement	NOUN
ejpam-4975	60	3	of	of	ADP
ejpam-4975	60	4	a	a	DET
ejpam-4975	60	5	preopen	preopen	ADJ
ejpam-4975	60	6	set	set	NOUN
ejpam-4975	60	7	is	be	AUX
ejpam-4975	60	8	called	call	VERB
ejpam-4975	60	9	preclosed	preclose	VERB
ejpam-4975	60	10	.	.	PUNCT
ejpam-4975	61	1	the	the	DET
ejpam-4975	61	2	family	family	NOUN
ejpam-4975	61	3	of	of	ADP
ejpam-4975	61	4	all	all	DET
ejpam-4975	61	5	preopen	preopen	ADJ
ejpam-4975	61	6	sets	set	NOUN
ejpam-4975	61	7	of	of	ADP
ejpam-4975	61	8	a	a	DET
ejpam-4975	61	9	topological	topological	ADJ
ejpam-4975	61	10	space	space	NOUN
ejpam-4975	61	11	(	(	PUNCT
ejpam-4975	61	12	x	x	X
ejpam-4975	61	13	,	,	PUNCT
ejpam-4975	61	14	τ	τ	X
ejpam-4975	61	15	)	)	PUNCT
ejpam-4975	61	16	is	be	AUX
ejpam-4975	61	17	denoted	denote	VERB
ejpam-4975	61	18	by	by	ADP
ejpam-4975	61	19	po(x	po(x	NUM
ejpam-4975	61	20	,	,	PUNCT
ejpam-4975	61	21	τ	τ	PROPN
ejpam-4975	61	22	)	)	PUNCT
ejpam-4975	61	23	.	.	PUNCT
ejpam-4975	62	1	a	a	DET
ejpam-4975	62	2	subset	subset	NOUN
ejpam-4975	62	3	λp(a	λp(a	NOUN
ejpam-4975	62	4	)	)	PUNCT
ejpam-4975	63	1	[	[	X
ejpam-4975	63	2	11	11	NUM
ejpam-4975	63	3	]	]	PUNCT
ejpam-4975	63	4	is	be	AUX
ejpam-4975	63	5	defined	define	VERB
ejpam-4975	63	6	as	as	SCONJ
ejpam-4975	63	7	follows	follow	VERB
ejpam-4975	63	8	:	:	PUNCT
ejpam-4975	63	9	λp(a	λp(a	NUM
ejpam-4975	63	10	)	)	PUNCT
ejpam-4975	64	1	=	=	PUNCT
ejpam-4975	65	1	∩{u	∩{u	PROPN
ejpam-4975	65	2	|	|	ADV
ejpam-4975	65	3	a	a	DET
ejpam-4975	65	4	⊆	⊆	NUM
ejpam-4975	65	5	u	u	NOUN
ejpam-4975	65	6	,	,	PUNCT
ejpam-4975	65	7	u	u	PROPN
ejpam-4975	65	8	∈	∈	PROPN
ejpam-4975	65	9	po(x	po(x	NOUN
ejpam-4975	65	10	,	,	PUNCT
ejpam-4975	65	11	τ	τ	NOUN
ejpam-4975	65	12	)	)	PUNCT
ejpam-4975	65	13	}	}	PUNCT
ejpam-4975	65	14	.	.	PUNCT
ejpam-4975	66	1	a	a	DET
ejpam-4975	66	2	subset	subset	NOUN
ejpam-4975	66	3	a	a	PRON
ejpam-4975	66	4	of	of	ADP
ejpam-4975	66	5	a	a	DET
ejpam-4975	66	6	topological	topological	ADJ
ejpam-4975	66	7	space	space	NOUN
ejpam-4975	66	8	(	(	PUNCT
ejpam-4975	66	9	x	x	X
ejpam-4975	66	10	,	,	PUNCT
ejpam-4975	66	11	τ	τ	X
ejpam-4975	66	12	)	)	PUNCT
ejpam-4975	66	13	is	be	AUX
ejpam-4975	66	14	called	call	VERB
ejpam-4975	66	15	a	a	DET
ejpam-4975	66	16	λp	λp	NOUN
ejpam-4975	66	17	-	-	PUNCT
ejpam-4975	66	18	set	set	VERB
ejpam-4975	66	19	[	[	X
ejpam-4975	66	20	6	6	NUM
ejpam-4975	66	21	]	]	PUNCT
ejpam-4975	66	22	(	(	PUNCT
ejpam-4975	66	23	pre	pre	ADJ
ejpam-4975	66	24	-	-	ADJ
ejpam-4975	66	25	λ	λ	NOUN
ejpam-4975	66	26	-	-	NOUN
ejpam-4975	66	27	set	set	NOUN
ejpam-4975	66	28	[	[	X
ejpam-4975	66	29	11	11	NUM
ejpam-4975	66	30	]	]	SYM
ejpam-4975	66	31	)	)	PUNCT
ejpam-4975	66	32	if	if	SCONJ
ejpam-4975	66	33	a	a	DET
ejpam-4975	66	34	=	=	NOUN
ejpam-4975	66	35	λp(a	λp(a	NOUN
ejpam-4975	66	36	)	)	PUNCT
ejpam-4975	66	37	.	.	PUNCT
ejpam-4975	67	1	a	a	DET
ejpam-4975	67	2	subset	subset	NOUN
ejpam-4975	67	3	a	a	PRON
ejpam-4975	67	4	of	of	ADP
ejpam-4975	67	5	a	a	DET
ejpam-4975	67	6	topological	topological	ADJ
ejpam-4975	67	7	space	space	NOUN
ejpam-4975	67	8	(	(	PUNCT
ejpam-4975	67	9	x	x	X
ejpam-4975	67	10	,	,	PUNCT
ejpam-4975	67	11	τ	τ	X
ejpam-4975	67	12	)	)	PUNCT
ejpam-4975	67	13	is	be	AUX
ejpam-4975	67	14	called	call	VERB
ejpam-4975	67	15	(	(	PUNCT
ejpam-4975	67	16	λ	λ	X
ejpam-4975	67	17	,	,	PUNCT
ejpam-4975	67	18	p)-closed	p)-close	VERB
ejpam-4975	67	19	[	[	X
ejpam-4975	67	20	6	6	NUM
ejpam-4975	67	21	]	]	PUNCT
ejpam-4975	67	22	if	if	SCONJ
ejpam-4975	67	23	a	a	DET
ejpam-4975	67	24	=	=	X
ejpam-4975	67	25	t	t	NOUN
ejpam-4975	67	26	∩c	∩c	NOUN
ejpam-4975	67	27	,	,	PUNCT
ejpam-4975	67	28	where	where	SCONJ
ejpam-4975	67	29	t	t	PROPN
ejpam-4975	67	30	is	be	AUX
ejpam-4975	67	31	a	a	DET
ejpam-4975	67	32	λp	λp	ADV
ejpam-4975	67	33	-	-	PUNCT
ejpam-4975	67	34	set	set	NOUN
ejpam-4975	67	35	and	and	CCONJ
ejpam-4975	67	36	c	c	NOUN
ejpam-4975	67	37	is	be	AUX
ejpam-4975	67	38	a	a	DET
ejpam-4975	67	39	preclosed	preclose	VERB
ejpam-4975	67	40	set	set	NOUN
ejpam-4975	67	41	.	.	PUNCT
ejpam-4975	68	1	the	the	DET
ejpam-4975	68	2	complement	complement	NOUN
ejpam-4975	68	3	of	of	ADP
ejpam-4975	68	4	a	a	DET
ejpam-4975	68	5	(	(	PUNCT
ejpam-4975	68	6	λ	λ	PROPN
ejpam-4975	68	7	,	,	PUNCT
ejpam-4975	68	8	p)-closed	p)-close	VERB
ejpam-4975	68	9	set	set	NOUN
ejpam-4975	68	10	is	be	AUX
ejpam-4975	68	11	called	call	VERB
ejpam-4975	68	12	(	(	PUNCT
ejpam-4975	68	13	λ	λ	X
ejpam-4975	68	14	,	,	PUNCT
ejpam-4975	68	15	p)-open	p)-open	ADJ
ejpam-4975	68	16	.	.	PUNCT
ejpam-4975	69	1	the	the	DET
ejpam-4975	69	2	family	family	NOUN
ejpam-4975	69	3	of	of	ADP
ejpam-4975	69	4	all	all	DET
ejpam-4975	69	5	(	(	PUNCT
ejpam-4975	69	6	λ	λ	X
ejpam-4975	69	7	,	,	PUNCT
ejpam-4975	69	8	p)-open	p)-open	ADJ
ejpam-4975	69	9	(	(	PUNCT
ejpam-4975	69	10	resp	resp	NOUN
ejpam-4975	69	11	.	.	PUNCT
ejpam-4975	70	1	(	(	PUNCT
ejpam-4975	70	2	λ	λ	X
ejpam-4975	70	3	,	,	PUNCT
ejpam-4975	70	4	p)-closed	p)-close	VERB
ejpam-4975	70	5	)	)	PUNCT
ejpam-4975	70	6	sets	set	NOUN
ejpam-4975	70	7	in	in	ADP
ejpam-4975	70	8	a	a	DET
ejpam-4975	70	9	topological	topological	ADJ
ejpam-4975	70	10	space	space	NOUN
ejpam-4975	70	11	(	(	PUNCT
ejpam-4975	70	12	x	x	X
ejpam-4975	70	13	,	,	PUNCT
ejpam-4975	70	14	τ	τ	X
ejpam-4975	70	15	)	)	PUNCT
ejpam-4975	70	16	is	be	AUX
ejpam-4975	70	17	denoted	denote	VERB
ejpam-4975	70	18	by	by	ADP
ejpam-4975	70	19	λpo(x	λpo(x	PROPN
ejpam-4975	70	20	,	,	PUNCT
ejpam-4975	70	21	τ	τ	X
ejpam-4975	70	22	)	)	PUNCT
ejpam-4975	70	23	(	(	PUNCT
ejpam-4975	70	24	resp	resp	NOUN
ejpam-4975	70	25	.	.	PUNCT
ejpam-4975	71	1	λpc(x	λpc(x	PROPN
ejpam-4975	71	2	,	,	PUNCT
ejpam-4975	71	3	τ	τ	PROPN
ejpam-4975	71	4	)	)	PUNCT
ejpam-4975	71	5	)	)	PUNCT
ejpam-4975	71	6	.	.	PUNCT
ejpam-4975	72	1	let	let	VERB
ejpam-4975	72	2	a	a	DET
ejpam-4975	72	3	be	be	AUX
ejpam-4975	72	4	a	a	DET
ejpam-4975	72	5	subset	subset	NOUN
ejpam-4975	72	6	of	of	ADP
ejpam-4975	72	7	a	a	DET
ejpam-4975	72	8	topological	topological	ADJ
ejpam-4975	72	9	space	space	NOUN
ejpam-4975	72	10	(	(	PUNCT
ejpam-4975	72	11	x	x	X
ejpam-4975	72	12	,	,	PUNCT
ejpam-4975	72	13	τ	τ	PROPN
ejpam-4975	72	14	)	)	PUNCT
ejpam-4975	72	15	.	.	PUNCT
ejpam-4975	73	1	a	a	DET
ejpam-4975	73	2	point	point	NOUN
ejpam-4975	73	3	x	x	X
ejpam-4975	73	4	∈	∈	NOUN
ejpam-4975	73	5	x	x	PUNCT
ejpam-4975	73	6	is	be	AUX
ejpam-4975	73	7	called	call	VERB
ejpam-4975	73	8	a	a	DET
ejpam-4975	73	9	(	(	PUNCT
ejpam-4975	73	10	λ	λ	NOUN
ejpam-4975	73	11	,	,	PUNCT
ejpam-4975	73	12	p)-cluster	p)-cluster	NOUN
ejpam-4975	73	13	point	point	NOUN
ejpam-4975	73	14	[	[	X
ejpam-4975	73	15	6	6	NUM
ejpam-4975	73	16	]	]	PUNCT
ejpam-4975	73	17	of	of	ADP
ejpam-4975	73	18	a	a	DET
ejpam-4975	73	19	if	if	SCONJ
ejpam-4975	73	20	a∩u	a∩u	VERB
ejpam-4975	73	21	̸=	̸=	NOUN
ejpam-4975	73	22	∅	∅	NOUN
ejpam-4975	73	23	for	for	ADP
ejpam-4975	73	24	every	every	DET
ejpam-4975	73	25	(	(	PUNCT
ejpam-4975	73	26	λ	λ	NOUN
ejpam-4975	73	27	,	,	PUNCT
ejpam-4975	73	28	p)-open	p)-open	VERB
ejpam-4975	73	29	set	set	VERB
ejpam-4975	73	30	u	u	NOUN
ejpam-4975	73	31	of	of	ADP
ejpam-4975	73	32	x	x	SYM
ejpam-4975	73	33	containing	contain	VERB
ejpam-4975	73	34	x.	x.	NOUN
ejpam-4975	73	35	the	the	DET
ejpam-4975	73	36	set	set	NOUN
ejpam-4975	73	37	of	of	ADP
ejpam-4975	73	38	all	all	DET
ejpam-4975	73	39	(	(	PUNCT
ejpam-4975	73	40	λ	λ	NOUN
ejpam-4975	73	41	,	,	PUNCT
ejpam-4975	73	42	p)-cluster	p)-cluster	VERB
ejpam-4975	73	43	points	point	NOUN
ejpam-4975	73	44	of	of	ADP
ejpam-4975	73	45	a	a	PRON
ejpam-4975	73	46	is	be	AUX
ejpam-4975	73	47	called	call	VERB
ejpam-4975	73	48	the	the	DET
ejpam-4975	73	49	(	(	PUNCT
ejpam-4975	73	50	λ	λ	PROPN
ejpam-4975	73	51	,	,	PUNCT
ejpam-4975	73	52	p)-closure	p)-closure	PUNCT
ejpam-4975	74	1	[	[	X
ejpam-4975	74	2	6	6	NUM
ejpam-4975	74	3	]	]	PUNCT
ejpam-4975	74	4	of	of	ADP
ejpam-4975	74	5	a	a	PRON
ejpam-4975	74	6	and	and	CCONJ
ejpam-4975	74	7	is	be	AUX
ejpam-4975	74	8	denoted	denote	VERB
ejpam-4975	74	9	by	by	ADP
ejpam-4975	74	10	a(λ	a(λ	PROPN
ejpam-4975	74	11	,	,	PUNCT
ejpam-4975	74	12	p	p	NOUN
ejpam-4975	74	13	)	)	PUNCT
ejpam-4975	74	14	.	.	PUNCT
ejpam-4975	75	1	the	the	DET
ejpam-4975	75	2	union	union	NOUN
ejpam-4975	75	3	of	of	ADP
ejpam-4975	75	4	all	all	PRON
ejpam-4975	75	5	(	(	PUNCT
ejpam-4975	75	6	λ	λ	NOUN
ejpam-4975	75	7	,	,	PUNCT
ejpam-4975	75	8	p)-open	p)-open	VERB
ejpam-4975	75	9	sets	set	NOUN
ejpam-4975	75	10	of	of	ADP
ejpam-4975	75	11	x	x	PUNCT
ejpam-4975	75	12	contained	contain	VERB
ejpam-4975	75	13	in	in	ADP
ejpam-4975	75	14	a	a	PRON
ejpam-4975	75	15	is	be	AUX
ejpam-4975	75	16	called	call	VERB
ejpam-4975	75	17	the	the	DET
ejpam-4975	75	18	(	(	PUNCT
ejpam-4975	75	19	λ	λ	PROPN
ejpam-4975	75	20	,	,	PUNCT
ejpam-4975	75	21	p)-interior	p)-interior	ADJ
ejpam-4975	76	1	[	[	X
ejpam-4975	76	2	6	6	NUM
ejpam-4975	76	3	]	]	PUNCT
ejpam-4975	76	4	of	of	ADP
ejpam-4975	76	5	a	a	PRON
ejpam-4975	76	6	and	and	CCONJ
ejpam-4975	76	7	is	be	AUX
ejpam-4975	76	8	denoted	denote	VERB
ejpam-4975	76	9	by	by	ADP
ejpam-4975	76	10	a(λ	a(λ	PROPN
ejpam-4975	76	11	,	,	PUNCT
ejpam-4975	76	12	p	p	NOUN
ejpam-4975	76	13	)	)	PUNCT
ejpam-4975	76	14	.	.	PUNCT
ejpam-4975	77	1	the	the	DET
ejpam-4975	77	2	θ(λ	θ(λ	PROPN
ejpam-4975	77	3	,	,	PUNCT
ejpam-4975	77	4	p)-closure	p)-closure	X
ejpam-4975	78	1	[	[	X
ejpam-4975	78	2	6	6	NUM
ejpam-4975	78	3	]	]	PUNCT
ejpam-4975	78	4	of	of	ADP
ejpam-4975	78	5	a	a	DET
ejpam-4975	78	6	,	,	PUNCT
ejpam-4975	78	7	aθ(λ	aθ(λ	ADJ
ejpam-4975	78	8	,	,	PUNCT
ejpam-4975	78	9	p	p	NOUN
ejpam-4975	78	10	)	)	PUNCT
ejpam-4975	78	11	,	,	PUNCT
ejpam-4975	78	12	is	be	AUX
ejpam-4975	78	13	defined	define	VERB
ejpam-4975	78	14	as	as	SCONJ
ejpam-4975	78	15	follows	follow	VERB
ejpam-4975	78	16	:	:	PUNCT
ejpam-4975	79	1	aθ(λ	aθ(λ	NOUN
ejpam-4975	79	2	,	,	PUNCT
ejpam-4975	79	3	p	p	NOUN
ejpam-4975	79	4	)	)	PUNCT
ejpam-4975	79	5	=	=	SYM
ejpam-4975	79	6	{	{	PUNCT
ejpam-4975	79	7	x	x	PUNCT
ejpam-4975	79	8	∈	∈	NOUN
ejpam-4975	79	9	x	x	PUNCT
ejpam-4975	79	10	|	|	ADV
ejpam-4975	79	11	a	a	DET
ejpam-4975	79	12	∩	∩	ADJ
ejpam-4975	79	13	u	u	NOUN
ejpam-4975	79	14	(	(	PUNCT
ejpam-4975	79	15	λ	λ	PROPN
ejpam-4975	79	16	,	,	PUNCT
ejpam-4975	79	17	p	p	NOUN
ejpam-4975	79	18	)	)	PUNCT
ejpam-4975	79	19	̸=	̸=	PROPN
ejpam-4975	79	20	∅	∅	NOUN
ejpam-4975	79	21	for	for	ADP
ejpam-4975	79	22	each	each	DET
ejpam-4975	79	23	(	(	PUNCT
ejpam-4975	79	24	λ	λ	PROPN
ejpam-4975	79	25	,	,	PUNCT
ejpam-4975	79	26	p)-open	p)-open	VERB
ejpam-4975	79	27	set	set	VERB
ejpam-4975	79	28	u	u	NOUN
ejpam-4975	79	29	containing	contain	VERB
ejpam-4975	79	30	x	x	X
ejpam-4975	79	31	}	}	PUNCT
ejpam-4975	79	32	.	.	PUNCT
ejpam-4975	80	1	a	a	DET
ejpam-4975	80	2	subset	subset	NOUN
ejpam-4975	80	3	a	a	PRON
ejpam-4975	80	4	of	of	ADP
ejpam-4975	80	5	a	a	DET
ejpam-4975	80	6	topological	topological	ADJ
ejpam-4975	80	7	space	space	NOUN
ejpam-4975	80	8	(	(	PUNCT
ejpam-4975	80	9	x	x	X
ejpam-4975	80	10	,	,	PUNCT
ejpam-4975	80	11	τ	τ	X
ejpam-4975	80	12	)	)	PUNCT
ejpam-4975	80	13	is	be	AUX
ejpam-4975	80	14	called	call	VERB
ejpam-4975	80	15	θ(λ	θ(λ	PROPN
ejpam-4975	80	16	,	,	PUNCT
ejpam-4975	80	17	p)-closed	p)-close	VERB
ejpam-4975	80	18	[	[	X
ejpam-4975	80	19	6	6	NUM
ejpam-4975	80	20	]	]	PUNCT
ejpam-4975	80	21	if	if	SCONJ
ejpam-4975	80	22	a	a	PRON
ejpam-4975	80	23	=	=	NOUN
ejpam-4975	80	24	aθ(λ	aθ(λ	NOUN
ejpam-4975	80	25	,	,	PUNCT
ejpam-4975	80	26	p	p	NOUN
ejpam-4975	80	27	)	)	PUNCT
ejpam-4975	80	28	.	.	PUNCT
ejpam-4975	81	1	the	the	DET
ejpam-4975	81	2	complement	complement	NOUN
ejpam-4975	81	3	of	of	ADP
ejpam-4975	81	4	a	a	DET
ejpam-4975	81	5	θ(λ	θ(λ	PROPN
ejpam-4975	81	6	,	,	PUNCT
ejpam-4975	81	7	p)-closed	p)-close	VERB
ejpam-4975	81	8	set	set	NOUN
ejpam-4975	81	9	is	be	AUX
ejpam-4975	81	10	said	say	VERB
ejpam-4975	81	11	to	to	PART
ejpam-4975	81	12	be	be	AUX
ejpam-4975	81	13	θ(λ	θ(λ	PROPN
ejpam-4975	81	14	,	,	PUNCT
ejpam-4975	81	15	p)-open	p)-open	VERB
ejpam-4975	81	16	.	.	PUNCT
ejpam-4975	82	1	let	let	VERB
ejpam-4975	82	2	a	a	DET
ejpam-4975	82	3	be	be	AUX
ejpam-4975	82	4	a	a	DET
ejpam-4975	82	5	subset	subset	NOUN
ejpam-4975	82	6	of	of	ADP
ejpam-4975	82	7	a	a	DET
ejpam-4975	82	8	topological	topological	ADJ
ejpam-4975	82	9	space	space	NOUN
ejpam-4975	82	10	(	(	PUNCT
ejpam-4975	82	11	x	x	X
ejpam-4975	82	12	,	,	PUNCT
ejpam-4975	82	13	τ	τ	PROPN
ejpam-4975	82	14	)	)	PUNCT
ejpam-4975	82	15	.	.	PUNCT
ejpam-4975	83	1	a	a	DET
ejpam-4975	83	2	point	point	NOUN
ejpam-4975	83	3	x	x	X
ejpam-4975	83	4	∈	∈	NOUN
ejpam-4975	83	5	x	x	PUNCT
ejpam-4975	83	6	is	be	AUX
ejpam-4975	83	7	called	call	VERB
ejpam-4975	83	8	a	a	DET
ejpam-4975	83	9	θ(λ	θ(λ	PROPN
ejpam-4975	83	10	,	,	PUNCT
ejpam-4975	83	11	p)-interior	p)-interior	ADJ
ejpam-4975	83	12	point	point	NOUN
ejpam-4975	83	13	[	[	X
ejpam-4975	83	14	30	30	NUM
ejpam-4975	83	15	]	]	PUNCT
ejpam-4975	83	16	of	of	ADP
ejpam-4975	83	17	a	a	PRON
ejpam-4975	83	18	if	if	NOUN
ejpam-4975	83	19	x	x	SYM
ejpam-4975	83	20	∈	∈	PROPN
ejpam-4975	83	21	u	u	NOUN
ejpam-4975	83	22	⊆	⊆	NUM
ejpam-4975	83	23	u	u	PROPN
ejpam-4975	83	24	(	(	PUNCT
ejpam-4975	83	25	λ	λ	PROPN
ejpam-4975	83	26	,	,	PUNCT
ejpam-4975	83	27	p	p	NOUN
ejpam-4975	83	28	)	)	PUNCT
ejpam-4975	83	29	⊆	⊆	NUM
ejpam-4975	83	30	a	a	PRON
ejpam-4975	83	31	for	for	ADP
ejpam-4975	83	32	some	some	DET
ejpam-4975	83	33	u	u	NOUN
ejpam-4975	83	34	∈	∈	PROPN
ejpam-4975	83	35	λpo(x	λpo(x	PROPN
ejpam-4975	83	36	,	,	PUNCT
ejpam-4975	83	37	τ	τ	PROPN
ejpam-4975	83	38	)	)	PUNCT
ejpam-4975	83	39	.	.	PUNCT
ejpam-4975	84	1	the	the	DET
ejpam-4975	84	2	set	set	NOUN
ejpam-4975	84	3	of	of	ADP
ejpam-4975	84	4	all	all	DET
ejpam-4975	84	5	θ(λ	θ(λ	PROPN
ejpam-4975	84	6	,	,	PUNCT
ejpam-4975	84	7	p)-interior	p)-interior	ADJ
ejpam-4975	84	8	points	point	NOUN
ejpam-4975	84	9	of	of	ADP
ejpam-4975	84	10	a	a	PRON
ejpam-4975	84	11	is	be	AUX
ejpam-4975	84	12	called	call	VERB
ejpam-4975	84	13	the	the	DET
ejpam-4975	84	14	θ(λ	θ(λ	PROPN
ejpam-4975	84	15	,	,	PUNCT
ejpam-4975	84	16	p)-interior	p)-interior	ADJ
ejpam-4975	84	17	[	[	X
ejpam-4975	84	18	30	30	NUM
ejpam-4975	84	19	]	]	PUNCT
ejpam-4975	84	20	of	of	ADP
ejpam-4975	84	21	a	a	PRON
ejpam-4975	84	22	and	and	CCONJ
ejpam-4975	84	23	is	be	AUX
ejpam-4975	84	24	denoted	denote	VERB
ejpam-4975	84	25	by	by	ADP
ejpam-4975	84	26	aθ(λ	aθ(λ	NOUN
ejpam-4975	84	27	,	,	PUNCT
ejpam-4975	84	28	p	p	NOUN
ejpam-4975	84	29	)	)	PUNCT
ejpam-4975	84	30	.	.	PUNCT
ejpam-4975	85	1	c.	c.	PROPN
ejpam-4975	85	2	boonpok	boonpok	PROPN
ejpam-4975	85	3	,	,	PUNCT
ejpam-4975	85	4	j.	j.	PROPN
ejpam-4975	85	5	khampakdee	khampakdee	PROPN
ejpam-4975	85	6	/	/	PUNCT
ejpam-4975	85	7	eur	eur	PROPN
ejpam-4975	85	8	.	.	PUNCT
ejpam-4975	86	1	j.	j.	PROPN
ejpam-4975	86	2	pure	pure	PROPN
ejpam-4975	86	3	appl	appl	PROPN
ejpam-4975	86	4	.	.	PROPN
ejpam-4975	86	5	math	math	PROPN
ejpam-4975	86	6	,	,	PUNCT
ejpam-4975	86	7	17	17	NUM
ejpam-4975	86	8	(	(	PUNCT
ejpam-4975	86	9	1	1	NUM
ejpam-4975	86	10	)	)	PUNCT
ejpam-4975	86	11	(	(	PUNCT
ejpam-4975	86	12	2024	2024	NUM
ejpam-4975	86	13	)	)	PUNCT
ejpam-4975	86	14	,	,	PUNCT
ejpam-4975	86	15	300	300	NUM
ejpam-4975	86	16	-	-	SYM
ejpam-4975	86	17	309	309	NUM
ejpam-4975	86	18	302	302	NUM
ejpam-4975	86	19	lemma	lemma	PROPN
ejpam-4975	86	20	1	1	NUM
ejpam-4975	86	21	.	.	PUNCT
ejpam-4975	87	1	[	[	X
ejpam-4975	87	2	30	30	NUM
ejpam-4975	87	3	]	]	PUNCT
ejpam-4975	87	4	for	for	ADP
ejpam-4975	87	5	subsets	subset	NOUN
ejpam-4975	87	6	a	a	PRON
ejpam-4975	87	7	and	and	CCONJ
ejpam-4975	87	8	b	b	NOUN
ejpam-4975	87	9	of	of	ADP
ejpam-4975	87	10	a	a	DET
ejpam-4975	87	11	topological	topological	ADJ
ejpam-4975	87	12	space	space	NOUN
ejpam-4975	87	13	(	(	PUNCT
ejpam-4975	87	14	x	x	X
ejpam-4975	87	15	,	,	PUNCT
ejpam-4975	87	16	τ	τ	PROPN
ejpam-4975	87	17	)	)	PUNCT
ejpam-4975	87	18	,	,	PUNCT
ejpam-4975	87	19	the	the	DET
ejpam-4975	87	20	following	follow	VERB
ejpam-4975	87	21	properties	property	NOUN
ejpam-4975	87	22	hold	hold	VERB
ejpam-4975	87	23	:	:	PUNCT
ejpam-4975	87	24	(	(	PUNCT
ejpam-4975	87	25	1	1	X
ejpam-4975	87	26	)	)	PUNCT
ejpam-4975	87	27	x	x	PUNCT
ejpam-4975	88	1	−aθ(λ	−aθ(λ	NOUN
ejpam-4975	88	2	,	,	PUNCT
ejpam-4975	88	3	p	p	NOUN
ejpam-4975	88	4	)	)	PUNCT
ejpam-4975	88	5	=	=	PUNCT
ejpam-4975	89	1	[	[	X
ejpam-4975	89	2	x	x	X
ejpam-4975	89	3	−a]θ(λ	−a]θ(λ	NOUN
ejpam-4975	89	4	,	,	PUNCT
ejpam-4975	89	5	p	p	NOUN
ejpam-4975	89	6	)	)	PUNCT
ejpam-4975	89	7	and	and	CCONJ
ejpam-4975	89	8	x	x	PUNCT
ejpam-4975	89	9	−aθ(λ	−aθ(λ	NOUN
ejpam-4975	89	10	,	,	PUNCT
ejpam-4975	89	11	p	p	NOUN
ejpam-4975	89	12	)	)	PUNCT
ejpam-4975	89	13	=	=	PUNCT
ejpam-4975	90	1	[	[	X
ejpam-4975	90	2	x	x	X
ejpam-4975	90	3	−a]θ(λ	−a]θ(λ	NOUN
ejpam-4975	90	4	,	,	PUNCT
ejpam-4975	90	5	p	p	NOUN
ejpam-4975	90	6	)	)	PUNCT
ejpam-4975	90	7	.	.	PUNCT
ejpam-4975	91	1	(	(	PUNCT
ejpam-4975	91	2	2	2	X
ejpam-4975	91	3	)	)	PUNCT
ejpam-4975	91	4	a	a	PRON
ejpam-4975	91	5	is	be	AUX
ejpam-4975	91	6	θ(λ	θ(λ	PROPN
ejpam-4975	91	7	,	,	PUNCT
ejpam-4975	91	8	p)-open	p)-open	VERB
ejpam-4975	91	9	if	if	SCONJ
ejpam-4975	91	10	and	and	CCONJ
ejpam-4975	91	11	only	only	ADV
ejpam-4975	91	12	if	if	SCONJ
ejpam-4975	91	13	a	a	PRON
ejpam-4975	91	14	=	=	NOUN
ejpam-4975	91	15	aθ(λ	aθ(λ	NOUN
ejpam-4975	91	16	,	,	PUNCT
ejpam-4975	91	17	p	p	NOUN
ejpam-4975	91	18	)	)	PUNCT
ejpam-4975	91	19	.	.	PUNCT
ejpam-4975	92	1	(	(	PUNCT
ejpam-4975	92	2	3	3	X
ejpam-4975	92	3	)	)	PUNCT
ejpam-4975	92	4	a	a	DET
ejpam-4975	92	5	⊆	⊆	NUM
ejpam-4975	92	6	a(λ	a(λ	ADJ
ejpam-4975	92	7	,	,	PUNCT
ejpam-4975	92	8	p	p	X
ejpam-4975	92	9	)	)	PUNCT
ejpam-4975	92	10	⊆	⊆	NUM
ejpam-4975	92	11	aθ(λ	aθ(λ	NOUN
ejpam-4975	92	12	,	,	PUNCT
ejpam-4975	92	13	p	p	NOUN
ejpam-4975	92	14	)	)	PUNCT
ejpam-4975	92	15	and	and	CCONJ
ejpam-4975	92	16	aθ(λ	aθ(λ	NOUN
ejpam-4975	92	17	,	,	PUNCT
ejpam-4975	92	18	p	p	NOUN
ejpam-4975	92	19	)	)	PUNCT
ejpam-4975	92	20	⊆	⊆	NUM
ejpam-4975	92	21	a(λ	a(λ	ADV
ejpam-4975	92	22	,	,	PUNCT
ejpam-4975	92	23	p	p	NOUN
ejpam-4975	92	24	)	)	PUNCT
ejpam-4975	92	25	⊆	⊆	NUM
ejpam-4975	92	26	a.	a.	NOUN
ejpam-4975	92	27	(	(	PUNCT
ejpam-4975	92	28	4	4	NUM
ejpam-4975	92	29	)	)	PUNCT
ejpam-4975	92	30	if	if	SCONJ
ejpam-4975	92	31	a	a	DET
ejpam-4975	92	32	⊆	⊆	NUM
ejpam-4975	92	33	b	b	NOUN
ejpam-4975	92	34	,	,	PUNCT
ejpam-4975	92	35	then	then	ADV
ejpam-4975	92	36	aθ(λ	aθ(λ	NOUN
ejpam-4975	92	37	,	,	PUNCT
ejpam-4975	92	38	p	p	NOUN
ejpam-4975	92	39	)	)	PUNCT
ejpam-4975	92	40	⊆	⊆	NUM
ejpam-4975	92	41	bθ(λ	bθ(λ	NOUN
ejpam-4975	92	42	,	,	PUNCT
ejpam-4975	92	43	p	p	NOUN
ejpam-4975	92	44	)	)	PUNCT
ejpam-4975	92	45	and	and	CCONJ
ejpam-4975	92	46	aθ(λ	aθ(λ	NOUN
ejpam-4975	92	47	,	,	PUNCT
ejpam-4975	92	48	p	p	NOUN
ejpam-4975	92	49	)	)	PUNCT
ejpam-4975	92	50	⊆	⊆	NUM
ejpam-4975	92	51	bθ(λ	bθ(λ	NOUN
ejpam-4975	92	52	,	,	PUNCT
ejpam-4975	92	53	p	p	NOUN
ejpam-4975	92	54	)	)	PUNCT
ejpam-4975	92	55	.	.	PUNCT
ejpam-4975	93	1	(	(	PUNCT
ejpam-4975	93	2	5	5	X
ejpam-4975	93	3	)	)	PUNCT
ejpam-4975	93	4	if	if	SCONJ
ejpam-4975	93	5	a	a	PRON
ejpam-4975	93	6	is	be	AUX
ejpam-4975	93	7	(	(	PUNCT
ejpam-4975	93	8	λ	λ	NOUN
ejpam-4975	93	9	,	,	PUNCT
ejpam-4975	93	10	p)-open	p)-open	ADJ
ejpam-4975	93	11	,	,	PUNCT
ejpam-4975	93	12	then	then	ADV
ejpam-4975	93	13	a(λ	a(λ	ADV
ejpam-4975	93	14	,	,	PUNCT
ejpam-4975	93	15	p	p	X
ejpam-4975	93	16	)	)	PUNCT
ejpam-4975	93	17	=	=	PUNCT
ejpam-4975	93	18	aθ(λ	aθ(λ	NOUN
ejpam-4975	93	19	,	,	PUNCT
ejpam-4975	93	20	p	p	NOUN
ejpam-4975	93	21	)	)	PUNCT
ejpam-4975	93	22	.	.	PUNCT
ejpam-4975	94	1	a	a	DET
ejpam-4975	94	2	subset	subset	NOUN
ejpam-4975	94	3	a	a	PRON
ejpam-4975	94	4	of	of	ADP
ejpam-4975	94	5	a	a	DET
ejpam-4975	94	6	topological	topological	ADJ
ejpam-4975	94	7	space	space	NOUN
ejpam-4975	94	8	(	(	PUNCT
ejpam-4975	94	9	x	x	X
ejpam-4975	94	10	,	,	PUNCT
ejpam-4975	94	11	τ	τ	X
ejpam-4975	94	12	)	)	PUNCT
ejpam-4975	94	13	is	be	AUX
ejpam-4975	94	14	said	say	VERB
ejpam-4975	94	15	to	to	PART
ejpam-4975	94	16	be	be	AUX
ejpam-4975	94	17	s(λ	s(λ	NOUN
ejpam-4975	94	18	,	,	PUNCT
ejpam-4975	94	19	p)-open	p)-open	VERB
ejpam-4975	95	1	[	[	X
ejpam-4975	95	2	6	6	NUM
ejpam-4975	95	3	]	]	PUNCT
ejpam-4975	95	4	(	(	PUNCT
ejpam-4975	95	5	resp	resp	NOUN
ejpam-4975	95	6	.	.	PUNCT
ejpam-4975	96	1	p(λ	p(λ	PROPN
ejpam-4975	96	2	,	,	PUNCT
ejpam-4975	96	3	p)open	p)open	PROPN
ejpam-4975	97	1	[	[	X
ejpam-4975	97	2	6	6	NUM
ejpam-4975	97	3	]	]	PUNCT
ejpam-4975	97	4	,	,	PUNCT
ejpam-4975	97	5	β(λ	β(λ	X
ejpam-4975	97	6	,	,	PUNCT
ejpam-4975	97	7	p)-open	p)-open	VERB
ejpam-4975	97	8	[	[	X
ejpam-4975	97	9	6	6	NUM
ejpam-4975	97	10	]	]	PUNCT
ejpam-4975	97	11	,	,	PUNCT
ejpam-4975	97	12	α(λ	α(λ	PROPN
ejpam-4975	97	13	,	,	PUNCT
ejpam-4975	97	14	p)-open	p)-open	VERB
ejpam-4975	97	15	[	[	X
ejpam-4975	97	16	32	32	NUM
ejpam-4975	97	17	]	]	PUNCT
ejpam-4975	97	18	,	,	PUNCT
ejpam-4975	97	19	r(λ	r(λ	PROPN
ejpam-4975	97	20	,	,	PUNCT
ejpam-4975	97	21	p)-open	p)-open	VERB
ejpam-4975	97	22	[	[	X
ejpam-4975	97	23	6	6	NUM
ejpam-4975	97	24	]	]	SYM
ejpam-4975	97	25	)	)	PUNCT
ejpam-4975	97	26	if	if	SCONJ
ejpam-4975	97	27	a	a	DET
ejpam-4975	97	28	⊆	⊆	NUM
ejpam-4975	97	29	[	[	X
ejpam-4975	97	30	a(λ	a(λ	ADV
ejpam-4975	97	31	,	,	PUNCT
ejpam-4975	97	32	p	p	NOUN
ejpam-4975	97	33	)	)	PUNCT
ejpam-4975	97	34	]	]	PUNCT
ejpam-4975	97	35	(	(	PUNCT
ejpam-4975	97	36	λ	λ	X
ejpam-4975	97	37	,	,	PUNCT
ejpam-4975	97	38	p	p	NOUN
ejpam-4975	97	39	)	)	PUNCT
ejpam-4975	97	40	(	(	PUNCT
ejpam-4975	97	41	resp	resp	NOUN
ejpam-4975	97	42	.	.	PUNCT
ejpam-4975	98	1	a	a	DET
ejpam-4975	98	2	⊆	⊆	NUM
ejpam-4975	98	3	[	[	X
ejpam-4975	98	4	a(λ	a(λ	ADV
ejpam-4975	98	5	,	,	PUNCT
ejpam-4975	98	6	p)](λ	p)](λ	X
ejpam-4975	98	7	,	,	PUNCT
ejpam-4975	98	8	p	p	NOUN
ejpam-4975	98	9	)	)	PUNCT
ejpam-4975	98	10	,	,	PUNCT
ejpam-4975	98	11	a	a	DET
ejpam-4975	98	12	⊆	⊆	NUM
ejpam-4975	98	13	[	[	X
ejpam-4975	98	14	[	[	X
ejpam-4975	98	15	a(λ	a(λ	ADJ
ejpam-4975	98	16	,	,	PUNCT
ejpam-4975	98	17	p)](λ	p)](λ	X
ejpam-4975	98	18	,	,	PUNCT
ejpam-4975	98	19	p	p	NOUN
ejpam-4975	98	20	)	)	PUNCT
ejpam-4975	98	21	]	]	PUNCT
ejpam-4975	98	22	(	(	PUNCT
ejpam-4975	98	23	λ	λ	X
ejpam-4975	98	24	,	,	PUNCT
ejpam-4975	98	25	p	p	NOUN
ejpam-4975	98	26	)	)	PUNCT
ejpam-4975	98	27	,	,	PUNCT
ejpam-4975	98	28	a	a	DET
ejpam-4975	98	29	⊆	⊆	NUM
ejpam-4975	98	30	[	[	X
ejpam-4975	98	31	[	[	X
ejpam-4975	98	32	a(λ	a(λ	ADJ
ejpam-4975	98	33	,	,	PUNCT
ejpam-4975	98	34	p	p	NOUN
ejpam-4975	98	35	)	)	PUNCT
ejpam-4975	98	36	]	]	PUNCT
ejpam-4975	98	37	(	(	PUNCT
ejpam-4975	98	38	λ	λ	X
ejpam-4975	98	39	,	,	PUNCT
ejpam-4975	98	40	p)](λ	p)](λ	ADJ
ejpam-4975	98	41	,	,	PUNCT
ejpam-4975	98	42	p	p	NOUN
ejpam-4975	98	43	)	)	PUNCT
ejpam-4975	98	44	,	,	PUNCT
ejpam-4975	98	45	a	a	PRON
ejpam-4975	98	46	=	=	X
ejpam-4975	99	1	[	[	X
ejpam-4975	99	2	a(λ	a(λ	ADV
ejpam-4975	99	3	,	,	PUNCT
ejpam-4975	99	4	p)](λ	p)](λ	X
ejpam-4975	99	5	,	,	PUNCT
ejpam-4975	99	6	p	p	NOUN
ejpam-4975	99	7	)	)	PUNCT
ejpam-4975	99	8	)	)	PUNCT
ejpam-4975	99	9	.	.	PUNCT
ejpam-4975	100	1	the	the	DET
ejpam-4975	100	2	family	family	NOUN
ejpam-4975	100	3	of	of	ADP
ejpam-4975	100	4	all	all	DET
ejpam-4975	100	5	s(λ	s(λ	NOUN
ejpam-4975	100	6	,	,	PUNCT
ejpam-4975	100	7	p)-open	p)-open	ADJ
ejpam-4975	100	8	(	(	PUNCT
ejpam-4975	100	9	resp	resp	NOUN
ejpam-4975	100	10	.	.	PUNCT
ejpam-4975	101	1	p(λ	p(λ	NOUN
ejpam-4975	101	2	,	,	PUNCT
ejpam-4975	101	3	p)-open	p)-open	ADJ
ejpam-4975	101	4	,	,	PUNCT
ejpam-4975	101	5	β(λ	β(λ	X
ejpam-4975	101	6	,	,	PUNCT
ejpam-4975	101	7	p)-open	p)-open	NOUN
ejpam-4975	101	8	,	,	PUNCT
ejpam-4975	101	9	α(λ	α(λ	PROPN
ejpam-4975	101	10	,	,	PUNCT
ejpam-4975	101	11	p)-open	p)-open	NOUN
ejpam-4975	101	12	,	,	PUNCT
ejpam-4975	101	13	r(λ	r(λ	NOUN
ejpam-4975	101	14	,	,	PUNCT
ejpam-4975	101	15	p)-open	p)-open	ADJ
ejpam-4975	101	16	)	)	PUNCT
ejpam-4975	101	17	sets	set	NOUN
ejpam-4975	101	18	in	in	ADP
ejpam-4975	101	19	a	a	DET
ejpam-4975	101	20	topological	topological	ADJ
ejpam-4975	101	21	space	space	NOUN
ejpam-4975	101	22	(	(	PUNCT
ejpam-4975	101	23	x	x	X
ejpam-4975	101	24	,	,	PUNCT
ejpam-4975	101	25	τ	τ	X
ejpam-4975	101	26	)	)	PUNCT
ejpam-4975	101	27	is	be	AUX
ejpam-4975	101	28	denoted	denote	VERB
ejpam-4975	101	29	by	by	ADP
ejpam-4975	101	30	s(λ	s(λ	PROPN
ejpam-4975	101	31	,	,	PUNCT
ejpam-4975	101	32	p)o(x	p)o(x	ADJ
ejpam-4975	101	33	,	,	PUNCT
ejpam-4975	101	34	τ	τ	PROPN
ejpam-4975	101	35	)	)	PUNCT
ejpam-4975	101	36	(	(	PUNCT
ejpam-4975	101	37	resp	resp	NOUN
ejpam-4975	101	38	.	.	PUNCT
ejpam-4975	102	1	p(λ	p(λ	PROPN
ejpam-4975	102	2	,	,	PUNCT
ejpam-4975	102	3	p)o(x	p)o(x	ADJ
ejpam-4975	102	4	,	,	PUNCT
ejpam-4975	102	5	τ	τ	PROPN
ejpam-4975	102	6	)	)	PUNCT
ejpam-4975	102	7	,	,	PUNCT
ejpam-4975	102	8	β(λ	β(λ	X
ejpam-4975	102	9	,	,	PUNCT
ejpam-4975	102	10	p)o(x	p)o(x	ADJ
ejpam-4975	102	11	,	,	PUNCT
ejpam-4975	102	12	τ	τ	PROPN
ejpam-4975	102	13	)	)	PUNCT
ejpam-4975	102	14	,	,	PUNCT
ejpam-4975	102	15	α(λ	α(λ	PROPN
ejpam-4975	102	16	,	,	PUNCT
ejpam-4975	102	17	p)o(x	p)o(x	ADJ
ejpam-4975	102	18	,	,	PUNCT
ejpam-4975	102	19	τ	τ	PROPN
ejpam-4975	102	20	)	)	PUNCT
ejpam-4975	102	21	,	,	PUNCT
ejpam-4975	102	22	r(λ	r(λ	PROPN
ejpam-4975	102	23	,	,	PUNCT
ejpam-4975	102	24	p)o(x	p)o(x	ADJ
ejpam-4975	102	25	,	,	PUNCT
ejpam-4975	102	26	τ	τ	PROPN
ejpam-4975	102	27	)	)	PUNCT
ejpam-4975	102	28	)	)	PUNCT
ejpam-4975	102	29	.	.	PUNCT
ejpam-4975	103	1	the	the	DET
ejpam-4975	103	2	union	union	NOUN
ejpam-4975	103	3	of	of	ADP
ejpam-4975	103	4	all	all	DET
ejpam-4975	103	5	s(λ	s(λ	NOUN
ejpam-4975	103	6	,	,	PUNCT
ejpam-4975	103	7	p)-open	p)-open	ADJ
ejpam-4975	103	8	(	(	PUNCT
ejpam-4975	103	9	resp	resp	NOUN
ejpam-4975	103	10	.	.	PUNCT
ejpam-4975	104	1	p(λ	p(λ	NOUN
ejpam-4975	104	2	,	,	PUNCT
ejpam-4975	104	3	p)-open	p)-open	NOUN
ejpam-4975	104	4	,	,	PUNCT
ejpam-4975	104	5	α(λ	α(λ	PROPN
ejpam-4975	104	6	,	,	PUNCT
ejpam-4975	104	7	p)-open	p)-open	NOUN
ejpam-4975	104	8	)	)	PUNCT
ejpam-4975	104	9	sets	set	NOUN
ejpam-4975	104	10	of	of	ADP
ejpam-4975	104	11	x	x	PUNCT
ejpam-4975	104	12	contained	contain	VERB
ejpam-4975	104	13	in	in	ADP
ejpam-4975	104	14	a	a	PRON
ejpam-4975	104	15	is	be	AUX
ejpam-4975	104	16	called	call	VERB
ejpam-4975	104	17	the	the	DET
ejpam-4975	104	18	s(λ	s(λ	NOUN
ejpam-4975	104	19	,	,	PUNCT
ejpam-4975	104	20	p)-interior	p)-interior	ADJ
ejpam-4975	104	21	(	(	PUNCT
ejpam-4975	104	22	resp	resp	NOUN
ejpam-4975	104	23	.	.	PUNCT
ejpam-4975	105	1	p(λ	p(λ	NOUN
ejpam-4975	105	2	,	,	PUNCT
ejpam-4975	105	3	p)-interior	p)-interior	PROPN
ejpam-4975	105	4	,	,	PUNCT
ejpam-4975	105	5	α(λ	α(λ	PROPN
ejpam-4975	105	6	,	,	PUNCT
ejpam-4975	105	7	p)-interior	p)-interior	ADJ
ejpam-4975	105	8	)	)	PUNCT
ejpam-4975	105	9	of	of	ADP
ejpam-4975	105	10	a	a	PRON
ejpam-4975	105	11	and	and	CCONJ
ejpam-4975	105	12	is	be	AUX
ejpam-4975	105	13	denoted	denote	VERB
ejpam-4975	105	14	by	by	ADP
ejpam-4975	105	15	as(λ	as(λ	NOUN
ejpam-4975	105	16	,	,	PUNCT
ejpam-4975	105	17	p	p	NOUN
ejpam-4975	105	18	)	)	PUNCT
ejpam-4975	105	19	(	(	PUNCT
ejpam-4975	105	20	resp	resp	NOUN
ejpam-4975	105	21	.	.	PUNCT
ejpam-4975	106	1	ap(λ	ap(λ	PROPN
ejpam-4975	106	2	,	,	PUNCT
ejpam-4975	106	3	p	p	NOUN
ejpam-4975	106	4	)	)	PUNCT
ejpam-4975	106	5	,	,	PUNCT
ejpam-4975	106	6	aα(λ	aα(λ	PROPN
ejpam-4975	106	7	,	,	PUNCT
ejpam-4975	106	8	p	p	NOUN
ejpam-4975	106	9	)	)	PUNCT
ejpam-4975	106	10	)	)	PUNCT
ejpam-4975	106	11	.	.	PUNCT
ejpam-4975	107	1	the	the	DET
ejpam-4975	107	2	complement	complement	NOUN
ejpam-4975	107	3	of	of	ADP
ejpam-4975	107	4	a	a	DET
ejpam-4975	107	5	s(λ	s(λ	PROPN
ejpam-4975	107	6	,	,	PUNCT
ejpam-4975	107	7	p)-open	p)-open	ADJ
ejpam-4975	107	8	(	(	PUNCT
ejpam-4975	107	9	resp	resp	NOUN
ejpam-4975	107	10	.	.	PUNCT
ejpam-4975	108	1	p(λ	p(λ	NOUN
ejpam-4975	108	2	,	,	PUNCT
ejpam-4975	108	3	p)-open	p)-open	ADJ
ejpam-4975	108	4	,	,	PUNCT
ejpam-4975	108	5	β(λ	β(λ	X
ejpam-4975	108	6	,	,	PUNCT
ejpam-4975	108	7	p)-open	p)-open	NOUN
ejpam-4975	108	8	,	,	PUNCT
ejpam-4975	108	9	α(λ	α(λ	PROPN
ejpam-4975	108	10	,	,	PUNCT
ejpam-4975	108	11	p)-open	p)-open	NOUN
ejpam-4975	108	12	,	,	PUNCT
ejpam-4975	108	13	r(λ	r(λ	NOUN
ejpam-4975	108	14	,	,	PUNCT
ejpam-4975	108	15	p)open	p)open	ADJ
ejpam-4975	108	16	)	)	PUNCT
ejpam-4975	108	17	set	set	NOUN
ejpam-4975	108	18	is	be	AUX
ejpam-4975	108	19	called	call	VERB
ejpam-4975	108	20	s(λ	s(λ	PROPN
ejpam-4975	108	21	,	,	PUNCT
ejpam-4975	108	22	p)-closed	p)-close	VERB
ejpam-4975	108	23	(	(	PUNCT
ejpam-4975	108	24	resp	resp	NOUN
ejpam-4975	108	25	.	.	PUNCT
ejpam-4975	109	1	p(λ	p(λ	NOUN
ejpam-4975	109	2	,	,	PUNCT
ejpam-4975	109	3	p)-closed	p)-close	VERB
ejpam-4975	109	4	,	,	PUNCT
ejpam-4975	109	5	β(λ	β(λ	PROPN
ejpam-4975	109	6	,	,	PUNCT
ejpam-4975	109	7	p)-closed	p)-close	VERB
ejpam-4975	109	8	,	,	PUNCT
ejpam-4975	109	9	α(λ	α(λ	PROPN
ejpam-4975	109	10	,	,	PUNCT
ejpam-4975	109	11	p)-closed	p)-close	VERB
ejpam-4975	109	12	,	,	PUNCT
ejpam-4975	109	13	r(λ	r(λ	NOUN
ejpam-4975	109	14	,	,	PUNCT
ejpam-4975	109	15	p)closed	p)close	VERB
ejpam-4975	109	16	)	)	PUNCT
ejpam-4975	109	17	.	.	PUNCT
ejpam-4975	110	1	the	the	DET
ejpam-4975	110	2	family	family	NOUN
ejpam-4975	110	3	of	of	ADP
ejpam-4975	110	4	all	all	DET
ejpam-4975	110	5	s(λ	s(λ	PROPN
ejpam-4975	110	6	,	,	PUNCT
ejpam-4975	110	7	p)-closed	p)-close	VERB
ejpam-4975	110	8	(	(	PUNCT
ejpam-4975	110	9	resp	resp	NOUN
ejpam-4975	110	10	.	.	PUNCT
ejpam-4975	111	1	p(λ	p(λ	NOUN
ejpam-4975	111	2	,	,	PUNCT
ejpam-4975	111	3	p)-closed	p)-close	VERB
ejpam-4975	111	4	,	,	PUNCT
ejpam-4975	111	5	β(λ	β(λ	PROPN
ejpam-4975	111	6	,	,	PUNCT
ejpam-4975	111	7	p)-closed	p)-close	VERB
ejpam-4975	111	8	,	,	PUNCT
ejpam-4975	111	9	α(λ	α(λ	PROPN
ejpam-4975	111	10	,	,	PUNCT
ejpam-4975	111	11	p)closed	p)close	VERB
ejpam-4975	111	12	,	,	PUNCT
ejpam-4975	111	13	r(λ	r(λ	PROPN
ejpam-4975	111	14	,	,	PUNCT
ejpam-4975	111	15	p)-closed	p)-close	VERB
ejpam-4975	111	16	)	)	PUNCT
ejpam-4975	111	17	sets	set	NOUN
ejpam-4975	111	18	in	in	ADP
ejpam-4975	111	19	a	a	DET
ejpam-4975	111	20	topological	topological	ADJ
ejpam-4975	111	21	space	space	NOUN
ejpam-4975	111	22	(	(	PUNCT
ejpam-4975	111	23	x	x	X
ejpam-4975	111	24	,	,	PUNCT
ejpam-4975	111	25	τ	τ	X
ejpam-4975	111	26	)	)	PUNCT
ejpam-4975	111	27	is	be	AUX
ejpam-4975	111	28	denoted	denote	VERB
ejpam-4975	111	29	by	by	ADP
ejpam-4975	111	30	s(λ	s(λ	PROPN
ejpam-4975	111	31	,	,	PUNCT
ejpam-4975	111	32	p)c(x	p)c(x	NOUN
ejpam-4975	111	33	,	,	PUNCT
ejpam-4975	111	34	τ	τ	X
ejpam-4975	111	35	)	)	PUNCT
ejpam-4975	111	36	(	(	PUNCT
ejpam-4975	111	37	resp	resp	NOUN
ejpam-4975	111	38	.	.	PUNCT
ejpam-4975	112	1	p(λ	p(λ	NOUN
ejpam-4975	112	2	,	,	PUNCT
ejpam-4975	112	3	p)c(x	p)c(x	NOUN
ejpam-4975	112	4	,	,	PUNCT
ejpam-4975	112	5	τ	τ	PROPN
ejpam-4975	112	6	)	)	PUNCT
ejpam-4975	112	7	,	,	PUNCT
ejpam-4975	112	8	β(λ	β(λ	X
ejpam-4975	112	9	,	,	PUNCT
ejpam-4975	112	10	p)c(x	p)c(x	NOUN
ejpam-4975	112	11	,	,	PUNCT
ejpam-4975	112	12	τ	τ	PROPN
ejpam-4975	112	13	)	)	PUNCT
ejpam-4975	112	14	,	,	PUNCT
ejpam-4975	112	15	α(λ	α(λ	PROPN
ejpam-4975	112	16	,	,	PUNCT
ejpam-4975	112	17	p)c(x	p)c(x	PROPN
ejpam-4975	112	18	,	,	PUNCT
ejpam-4975	112	19	τ	τ	PROPN
ejpam-4975	112	20	)	)	PUNCT
ejpam-4975	112	21	,	,	PUNCT
ejpam-4975	112	22	r(λ	r(λ	PROPN
ejpam-4975	112	23	,	,	PUNCT
ejpam-4975	112	24	p)c(x	p)c(x	NOUN
ejpam-4975	112	25	,	,	PUNCT
ejpam-4975	112	26	τ	τ	NOUN
ejpam-4975	112	27	)	)	PUNCT
ejpam-4975	112	28	)	)	PUNCT
ejpam-4975	112	29	.	.	PUNCT
ejpam-4975	113	1	the	the	DET
ejpam-4975	113	2	intersection	intersection	NOUN
ejpam-4975	113	3	of	of	ADP
ejpam-4975	113	4	all	all	DET
ejpam-4975	113	5	s(λ	s(λ	NOUN
ejpam-4975	113	6	,	,	PUNCT
ejpam-4975	113	7	p)-closed	p)-close	VERB
ejpam-4975	113	8	(	(	PUNCT
ejpam-4975	113	9	resp	resp	NOUN
ejpam-4975	113	10	.	.	PUNCT
ejpam-4975	114	1	p(λ	p(λ	NOUN
ejpam-4975	114	2	,	,	PUNCT
ejpam-4975	114	3	p)-closed	p)-close	VERB
ejpam-4975	114	4	,	,	PUNCT
ejpam-4975	114	5	α(λ	α(λ	PROPN
ejpam-4975	114	6	,	,	PUNCT
ejpam-4975	114	7	p)-closed	p)-close	VERB
ejpam-4975	114	8	)	)	PUNCT
ejpam-4975	114	9	sets	set	NOUN
ejpam-4975	114	10	of	of	ADP
ejpam-4975	114	11	x	x	PUNCT
ejpam-4975	114	12	containing	contain	VERB
ejpam-4975	114	13	a	a	PRON
ejpam-4975	114	14	is	be	AUX
ejpam-4975	114	15	called	call	VERB
ejpam-4975	114	16	the	the	DET
ejpam-4975	114	17	s(λ	s(λ	NOUN
ejpam-4975	114	18	,	,	PUNCT
ejpam-4975	114	19	p)-closure	p)-closure	X
ejpam-4975	114	20	(	(	PUNCT
ejpam-4975	114	21	resp	resp	NOUN
ejpam-4975	114	22	.	.	PUNCT
ejpam-4975	115	1	p(λ	p(λ	NOUN
ejpam-4975	115	2	,	,	PUNCT
ejpam-4975	115	3	p)-closure	p)-closure	NOUN
ejpam-4975	115	4	,	,	PUNCT
ejpam-4975	115	5	α(λ	α(λ	PROPN
ejpam-4975	115	6	,	,	PUNCT
ejpam-4975	115	7	p)-closure	p)-closure	NOUN
ejpam-4975	115	8	)	)	PUNCT
ejpam-4975	115	9	of	of	ADP
ejpam-4975	115	10	a	a	PRON
ejpam-4975	115	11	and	and	CCONJ
ejpam-4975	115	12	is	be	AUX
ejpam-4975	115	13	denoted	denote	VERB
ejpam-4975	115	14	by	by	ADP
ejpam-4975	115	15	as(λ	as(λ	NOUN
ejpam-4975	115	16	,	,	PUNCT
ejpam-4975	115	17	p	p	NOUN
ejpam-4975	115	18	)	)	PUNCT
ejpam-4975	115	19	(	(	PUNCT
ejpam-4975	115	20	resp	resp	NOUN
ejpam-4975	115	21	.	.	PUNCT
ejpam-4975	116	1	ap(λ	ap(λ	PROPN
ejpam-4975	116	2	,	,	PUNCT
ejpam-4975	116	3	p	p	NOUN
ejpam-4975	116	4	)	)	PUNCT
ejpam-4975	116	5	,	,	PUNCT
ejpam-4975	116	6	aα(λ	aα(λ	PROPN
ejpam-4975	116	7	,	,	PUNCT
ejpam-4975	116	8	p	p	NOUN
ejpam-4975	116	9	)	)	PUNCT
ejpam-4975	116	10	)	)	PUNCT
ejpam-4975	116	11	.	.	PUNCT
ejpam-4975	117	1	let	let	VERB
ejpam-4975	117	2	a	a	DET
ejpam-4975	117	3	be	be	AUX
ejpam-4975	117	4	a	a	DET
ejpam-4975	117	5	subset	subset	NOUN
ejpam-4975	117	6	of	of	ADP
ejpam-4975	117	7	a	a	DET
ejpam-4975	117	8	topological	topological	ADJ
ejpam-4975	117	9	space	space	NOUN
ejpam-4975	117	10	(	(	PUNCT
ejpam-4975	117	11	x	x	X
ejpam-4975	117	12	,	,	PUNCT
ejpam-4975	117	13	τ	τ	PROPN
ejpam-4975	117	14	)	)	PUNCT
ejpam-4975	117	15	.	.	PUNCT
ejpam-4975	118	1	a	a	DET
ejpam-4975	118	2	point	point	NOUN
ejpam-4975	118	3	x	x	PUNCT
ejpam-4975	118	4	of	of	ADP
ejpam-4975	118	5	x	x	PROPN
ejpam-4975	118	6	is	be	AUX
ejpam-4975	118	7	called	call	VERB
ejpam-4975	118	8	a	a	DET
ejpam-4975	118	9	δ(λ	δ(λ	PROPN
ejpam-4975	118	10	,	,	PUNCT
ejpam-4975	118	11	p)-cluster	p)-cluster	NOUN
ejpam-4975	118	12	point	point	NOUN
ejpam-4975	118	13	[	[	X
ejpam-4975	118	14	5	5	NUM
ejpam-4975	118	15	]	]	PUNCT
ejpam-4975	118	16	of	of	ADP
ejpam-4975	118	17	a	a	DET
ejpam-4975	118	18	if	if	SCONJ
ejpam-4975	118	19	a	a	DET
ejpam-4975	118	20	∩	∩	NOUN
ejpam-4975	118	21	[	[	X
ejpam-4975	118	22	v	v	X
ejpam-4975	118	23	(	(	PUNCT
ejpam-4975	118	24	λ	λ	PROPN
ejpam-4975	118	25	,	,	PUNCT
ejpam-4975	118	26	p)](λ	p)](λ	ADJ
ejpam-4975	118	27	,	,	PUNCT
ejpam-4975	118	28	p	p	NOUN
ejpam-4975	118	29	)	)	PUNCT
ejpam-4975	118	30	̸=	̸=	PROPN
ejpam-4975	118	31	∅	∅	NOUN
ejpam-4975	118	32	for	for	ADP
ejpam-4975	118	33	every	every	DET
ejpam-4975	118	34	(	(	PUNCT
ejpam-4975	118	35	λ	λ	NOUN
ejpam-4975	118	36	,	,	PUNCT
ejpam-4975	118	37	p)-open	p)-open	VERB
ejpam-4975	118	38	set	set	VERB
ejpam-4975	118	39	v	v	NOUN
ejpam-4975	118	40	of	of	ADP
ejpam-4975	118	41	x	x	PUNCT
ejpam-4975	118	42	containing	contain	VERB
ejpam-4975	118	43	x.	x.	NOUN
ejpam-4975	118	44	the	the	DET
ejpam-4975	118	45	set	set	NOUN
ejpam-4975	118	46	of	of	ADP
ejpam-4975	118	47	all	all	DET
ejpam-4975	118	48	δ(λ	δ(λ	PROPN
ejpam-4975	118	49	,	,	PUNCT
ejpam-4975	118	50	p)-cluster	p)-cluster	VERB
ejpam-4975	118	51	points	point	NOUN
ejpam-4975	118	52	of	of	ADP
ejpam-4975	118	53	a	a	PRON
ejpam-4975	118	54	is	be	AUX
ejpam-4975	118	55	called	call	VERB
ejpam-4975	118	56	the	the	DET
ejpam-4975	118	57	δ(λ	δ(λ	PROPN
ejpam-4975	118	58	,	,	PUNCT
ejpam-4975	118	59	p)-closure	p)-closure	PUNCT
ejpam-4975	119	1	[	[	X
ejpam-4975	119	2	5	5	NUM
ejpam-4975	119	3	]	]	PUNCT
ejpam-4975	119	4	of	of	ADP
ejpam-4975	119	5	a	a	PRON
ejpam-4975	119	6	and	and	CCONJ
ejpam-4975	119	7	is	be	AUX
ejpam-4975	119	8	denoted	denote	VERB
ejpam-4975	119	9	by	by	ADP
ejpam-4975	119	10	aδ(λ	aδ(λ	NUM
ejpam-4975	119	11	,	,	PUNCT
ejpam-4975	119	12	p	p	NOUN
ejpam-4975	119	13	)	)	PUNCT
ejpam-4975	119	14	.	.	PUNCT
ejpam-4975	120	1	if	if	SCONJ
ejpam-4975	120	2	a	a	DET
ejpam-4975	120	3	=	=	NOUN
ejpam-4975	120	4	aδ(λ	aδ(λ	NUM
ejpam-4975	120	5	,	,	PUNCT
ejpam-4975	120	6	p	p	NOUN
ejpam-4975	120	7	)	)	PUNCT
ejpam-4975	120	8	,	,	PUNCT
ejpam-4975	120	9	then	then	ADV
ejpam-4975	120	10	a	a	PRON
ejpam-4975	120	11	is	be	AUX
ejpam-4975	120	12	said	say	VERB
ejpam-4975	120	13	to	to	PART
ejpam-4975	120	14	be	be	AUX
ejpam-4975	120	15	δ(λ	δ(λ	PROPN
ejpam-4975	120	16	,	,	PUNCT
ejpam-4975	120	17	p)-closed	p)-close	VERB
ejpam-4975	120	18	[	[	X
ejpam-4975	120	19	5	5	NUM
ejpam-4975	120	20	]	]	PUNCT
ejpam-4975	120	21	.	.	PUNCT
ejpam-4975	121	1	the	the	DET
ejpam-4975	121	2	complement	complement	NOUN
ejpam-4975	121	3	of	of	ADP
ejpam-4975	121	4	a	a	DET
ejpam-4975	121	5	δ(λ	δ(λ	PROPN
ejpam-4975	121	6	,	,	PUNCT
ejpam-4975	121	7	p)-closed	p)-close	VERB
ejpam-4975	121	8	set	set	NOUN
ejpam-4975	121	9	is	be	AUX
ejpam-4975	121	10	said	say	VERB
ejpam-4975	121	11	to	to	PART
ejpam-4975	121	12	be	be	AUX
ejpam-4975	121	13	δ(λ	δ(λ	PROPN
ejpam-4975	121	14	,	,	PUNCT
ejpam-4975	121	15	p)-open	p)-open	NOUN
ejpam-4975	121	16	.	.	PUNCT
ejpam-4975	122	1	the	the	DET
ejpam-4975	122	2	union	union	NOUN
ejpam-4975	122	3	of	of	ADP
ejpam-4975	122	4	all	all	DET
ejpam-4975	122	5	δ(λ	δ(λ	PROPN
ejpam-4975	122	6	,	,	PUNCT
ejpam-4975	122	7	p)-open	p)-open	VERB
ejpam-4975	122	8	sets	set	NOUN
ejpam-4975	122	9	of	of	ADP
ejpam-4975	122	10	x	x	PUNCT
ejpam-4975	122	11	contained	contain	VERB
ejpam-4975	122	12	in	in	ADP
ejpam-4975	122	13	a	a	PRON
ejpam-4975	122	14	is	be	AUX
ejpam-4975	122	15	called	call	VERB
ejpam-4975	122	16	the	the	DET
ejpam-4975	122	17	δ(λ	δ(λ	PROPN
ejpam-4975	122	18	,	,	PUNCT
ejpam-4975	122	19	p)-interior	p)-interior	ADJ
ejpam-4975	122	20	[	[	X
ejpam-4975	122	21	5	5	NUM
ejpam-4975	122	22	]	]	PUNCT
ejpam-4975	122	23	of	of	ADP
ejpam-4975	122	24	a	a	PRON
ejpam-4975	122	25	and	and	CCONJ
ejpam-4975	122	26	is	be	AUX
ejpam-4975	122	27	denoted	denote	VERB
ejpam-4975	122	28	by	by	ADP
ejpam-4975	122	29	aδ(λ	aδ(λ	NUM
ejpam-4975	122	30	,	,	PUNCT
ejpam-4975	122	31	p	p	NOUN
ejpam-4975	122	32	)	)	PUNCT
ejpam-4975	122	33	.	.	PUNCT
ejpam-4975	123	1	3	3	X
ejpam-4975	123	2	.	.	X
ejpam-4975	123	3	on	on	ADP
ejpam-4975	123	4	almost	almost	ADV
ejpam-4975	123	5	strongly	strongly	ADV
ejpam-4975	123	6	θ(λ	θ(λ	VERB
ejpam-4975	123	7	,	,	PUNCT
ejpam-4975	123	8	p)-continuous	p)-continuous	ADJ
ejpam-4975	123	9	functions	function	NOUN
ejpam-4975	123	10	we	we	PRON
ejpam-4975	123	11	begin	begin	VERB
ejpam-4975	123	12	this	this	DET
ejpam-4975	123	13	section	section	NOUN
ejpam-4975	123	14	by	by	ADP
ejpam-4975	123	15	introducing	introduce	VERB
ejpam-4975	123	16	the	the	DET
ejpam-4975	123	17	concept	concept	NOUN
ejpam-4975	123	18	of	of	ADP
ejpam-4975	123	19	almost	almost	ADV
ejpam-4975	123	20	strongly	strongly	ADV
ejpam-4975	123	21	θ(λ	θ(λ	VERB
ejpam-4975	123	22	,	,	PUNCT
ejpam-4975	123	23	p)-continuous	p)-continuous	ADJ
ejpam-4975	123	24	functions	function	NOUN
ejpam-4975	123	25	.	.	PUNCT
ejpam-4975	124	1	definition	definition	NOUN
ejpam-4975	124	2	1	1	NUM
ejpam-4975	124	3	.	.	PUNCT
ejpam-4975	125	1	a	a	DET
ejpam-4975	125	2	function	function	NOUN
ejpam-4975	125	3	f	f	NOUN
ejpam-4975	125	4	:	:	PUNCT
ejpam-4975	125	5	(	(	PUNCT
ejpam-4975	125	6	x	x	X
ejpam-4975	125	7	,	,	PUNCT
ejpam-4975	125	8	τ	τ	X
ejpam-4975	125	9	)	)	PUNCT
ejpam-4975	125	10	→	→	SYM
ejpam-4975	125	11	(	(	PUNCT
ejpam-4975	125	12	y	y	PROPN
ejpam-4975	125	13	,	,	PUNCT
ejpam-4975	125	14	σ	σ	PROPN
ejpam-4975	125	15	)	)	PUNCT
ejpam-4975	125	16	is	be	AUX
ejpam-4975	125	17	said	say	VERB
ejpam-4975	125	18	to	to	PART
ejpam-4975	125	19	be	be	AUX
ejpam-4975	125	20	almost	almost	ADV
ejpam-4975	125	21	strongly	strongly	ADV
ejpam-4975	125	22	θ(λ	θ(λ	VERB
ejpam-4975	125	23	,	,	PUNCT
ejpam-4975	125	24	p)continuous	p)continuous	ADJ
ejpam-4975	125	25	functions	function	NOUN
ejpam-4975	125	26	at	at	ADP
ejpam-4975	125	27	x	x	X
ejpam-4975	125	28	∈	∈	PROPN
ejpam-4975	125	29	x	x	SYM
ejpam-4975	125	30	if	if	SCONJ
ejpam-4975	125	31	for	for	SCONJ
ejpam-4975	125	32	each	each	DET
ejpam-4975	125	33	(	(	PUNCT
ejpam-4975	125	34	λ	λ	PROPN
ejpam-4975	125	35	,	,	PUNCT
ejpam-4975	125	36	p)-open	p)-open	VERB
ejpam-4975	125	37	set	set	VERB
ejpam-4975	125	38	v	v	NOUN
ejpam-4975	125	39	of	of	ADP
ejpam-4975	125	40	y	y	NOUN
ejpam-4975	125	41	containing	contain	VERB
ejpam-4975	125	42	f(x	f(x	PROPN
ejpam-4975	125	43	)	)	PUNCT
ejpam-4975	125	44	,	,	PUNCT
ejpam-4975	125	45	there	there	PRON
ejpam-4975	125	46	exists	exist	VERB
ejpam-4975	125	47	a	a	DET
ejpam-4975	125	48	(	(	PUNCT
ejpam-4975	125	49	λ	λ	NOUN
ejpam-4975	125	50	,	,	PUNCT
ejpam-4975	125	51	p)-open	p)-open	VERB
ejpam-4975	125	52	set	set	VERB
ejpam-4975	125	53	u	u	NOUN
ejpam-4975	125	54	of	of	ADP
ejpam-4975	125	55	x	x	PUNCT
ejpam-4975	125	56	containing	contain	VERB
ejpam-4975	125	57	x	x	PUNCT
ejpam-4975	125	58	such	such	ADJ
ejpam-4975	125	59	that	that	DET
ejpam-4975	125	60	f(u	f(u	PROPN
ejpam-4975	125	61	(	(	PUNCT
ejpam-4975	125	62	λ	λ	PROPN
ejpam-4975	125	63	,	,	PUNCT
ejpam-4975	125	64	p	p	NOUN
ejpam-4975	125	65	)	)	PUNCT
ejpam-4975	125	66	)	)	PUNCT
ejpam-4975	126	1	⊆	⊆	NUM
ejpam-4975	126	2	v	v	ADP
ejpam-4975	126	3	s(λ	s(λ	PROPN
ejpam-4975	126	4	,	,	PUNCT
ejpam-4975	126	5	p	p	NOUN
ejpam-4975	126	6	)	)	PUNCT
ejpam-4975	126	7	.	.	PUNCT
ejpam-4975	127	1	a	a	DET
ejpam-4975	127	2	function	function	NOUN
ejpam-4975	127	3	f	f	NOUN
ejpam-4975	127	4	:	:	PUNCT
ejpam-4975	127	5	(	(	PUNCT
ejpam-4975	127	6	x	x	X
ejpam-4975	127	7	,	,	PUNCT
ejpam-4975	127	8	τ	τ	X
ejpam-4975	127	9	)	)	PUNCT
ejpam-4975	127	10	→	→	SYM
ejpam-4975	127	11	(	(	PUNCT
ejpam-4975	127	12	y	y	PROPN
ejpam-4975	127	13	,	,	PUNCT
ejpam-4975	127	14	σ	σ	PROPN
ejpam-4975	127	15	)	)	PUNCT
ejpam-4975	127	16	is	be	AUX
ejpam-4975	127	17	said	say	VERB
ejpam-4975	127	18	to	to	PART
ejpam-4975	127	19	be	be	AUX
ejpam-4975	127	20	almost	almost	ADV
ejpam-4975	127	21	strongly	strongly	ADV
ejpam-4975	127	22	θ(λ	θ(λ	VERB
ejpam-4975	127	23	,	,	PUNCT
ejpam-4975	127	24	p)-continuous	p)-continuous	ADJ
ejpam-4975	127	25	if	if	SCONJ
ejpam-4975	127	26	f	f	PROPN
ejpam-4975	127	27	has	have	VERB
ejpam-4975	127	28	the	the	DET
ejpam-4975	127	29	property	property	NOUN
ejpam-4975	127	30	at	at	ADP
ejpam-4975	127	31	each	each	DET
ejpam-4975	127	32	point	point	NOUN
ejpam-4975	127	33	x	x	X
ejpam-4975	127	34	∈	∈	PROPN
ejpam-4975	127	35	x.	x.	NOUN
ejpam-4975	127	36	c.	c.	PROPN
ejpam-4975	127	37	boonpok	boonpok	PROPN
ejpam-4975	127	38	,	,	PUNCT
ejpam-4975	127	39	j.	j.	PROPN
ejpam-4975	127	40	khampakdee	khampakdee	PROPN
ejpam-4975	127	41	/	/	PUNCT
ejpam-4975	127	42	eur	eur	PROPN
ejpam-4975	127	43	.	.	PUNCT
ejpam-4975	128	1	j.	j.	PROPN
ejpam-4975	128	2	pure	pure	PROPN
ejpam-4975	128	3	appl	appl	PROPN
ejpam-4975	128	4	.	.	PROPN
ejpam-4975	128	5	math	math	PROPN
ejpam-4975	128	6	,	,	PUNCT
ejpam-4975	128	7	17	17	NUM
ejpam-4975	128	8	(	(	PUNCT
ejpam-4975	128	9	1	1	NUM
ejpam-4975	128	10	)	)	PUNCT
ejpam-4975	128	11	(	(	PUNCT
ejpam-4975	128	12	2024	2024	NUM
ejpam-4975	128	13	)	)	PUNCT
ejpam-4975	128	14	,	,	PUNCT
ejpam-4975	128	15	300	300	NUM
ejpam-4975	128	16	-	-	SYM
ejpam-4975	128	17	309	309	NUM
ejpam-4975	128	18	303	303	NUM
ejpam-4975	128	19	theorem	theorem	NOUN
ejpam-4975	128	20	1	1	NUM
ejpam-4975	128	21	.	.	PUNCT
ejpam-4975	128	22	for	for	ADP
ejpam-4975	128	23	a	a	DET
ejpam-4975	128	24	function	function	NOUN
ejpam-4975	128	25	f	f	NOUN
ejpam-4975	128	26	:	:	PUNCT
ejpam-4975	128	27	(	(	PUNCT
ejpam-4975	128	28	x	x	X
ejpam-4975	128	29	,	,	PUNCT
ejpam-4975	128	30	τ	τ	X
ejpam-4975	128	31	)	)	PUNCT
ejpam-4975	128	32	→	→	SYM
ejpam-4975	128	33	(	(	PUNCT
ejpam-4975	128	34	y	y	PROPN
ejpam-4975	128	35	,	,	PUNCT
ejpam-4975	128	36	σ	σ	PROPN
ejpam-4975	128	37	)	)	PUNCT
ejpam-4975	128	38	,	,	PUNCT
ejpam-4975	128	39	the	the	DET
ejpam-4975	128	40	following	follow	VERB
ejpam-4975	128	41	properties	property	NOUN
ejpam-4975	128	42	are	be	AUX
ejpam-4975	128	43	equivalent	equivalent	ADJ
ejpam-4975	128	44	:	:	PUNCT
ejpam-4975	128	45	(	(	PUNCT
ejpam-4975	128	46	1	1	X
ejpam-4975	128	47	)	)	PUNCT
ejpam-4975	128	48	f	f	NOUN
ejpam-4975	128	49	is	be	AUX
ejpam-4975	128	50	almost	almost	ADV
ejpam-4975	128	51	strongly	strongly	ADV
ejpam-4975	128	52	θ(λ	θ(λ	VERB
ejpam-4975	128	53	,	,	PUNCT
ejpam-4975	128	54	p)-continuous	p)-continuous	ADJ
ejpam-4975	128	55	;	;	PUNCT
ejpam-4975	128	56	(	(	PUNCT
ejpam-4975	128	57	2	2	X
ejpam-4975	128	58	)	)	PUNCT
ejpam-4975	128	59	f−1(v	f−1(v	NOUN
ejpam-4975	128	60	)	)	PUNCT
ejpam-4975	128	61	is	be	AUX
ejpam-4975	128	62	θ(λ	θ(λ	PROPN
ejpam-4975	128	63	,	,	PUNCT
ejpam-4975	128	64	p)-open	p)-open	VERB
ejpam-4975	128	65	in	in	ADP
ejpam-4975	128	66	x	x	PUNCT
ejpam-4975	128	67	for	for	ADP
ejpam-4975	128	68	every	every	DET
ejpam-4975	128	69	r(λ	r(λ	NOUN
ejpam-4975	128	70	,	,	PUNCT
ejpam-4975	128	71	p)-open	p)-open	VERB
ejpam-4975	128	72	set	set	VERB
ejpam-4975	128	73	v	v	NOUN
ejpam-4975	128	74	of	of	ADP
ejpam-4975	128	75	y	y	PROPN
ejpam-4975	128	76	;	;	PUNCT
ejpam-4975	128	77	(	(	PUNCT
ejpam-4975	128	78	3	3	X
ejpam-4975	128	79	)	)	PUNCT
ejpam-4975	128	80	f−1(k	f−1(k	PROPN
ejpam-4975	128	81	)	)	PUNCT
ejpam-4975	128	82	is	be	AUX
ejpam-4975	128	83	θ(λ	θ(λ	PROPN
ejpam-4975	128	84	,	,	PUNCT
ejpam-4975	128	85	p)-closed	p)-close	VERB
ejpam-4975	128	86	in	in	ADP
ejpam-4975	128	87	x	x	PUNCT
ejpam-4975	128	88	for	for	ADP
ejpam-4975	128	89	every	every	DET
ejpam-4975	128	90	r(λ	r(λ	NOUN
ejpam-4975	128	91	,	,	PUNCT
ejpam-4975	128	92	p)-closed	p)-close	VERB
ejpam-4975	128	93	set	set	NOUN
ejpam-4975	128	94	k	k	PROPN
ejpam-4975	128	95	of	of	ADP
ejpam-4975	128	96	y	y	PROPN
ejpam-4975	128	97	;	;	PUNCT
ejpam-4975	128	98	(	(	PUNCT
ejpam-4975	128	99	4	4	X
ejpam-4975	128	100	)	)	PUNCT
ejpam-4975	128	101	for	for	ADP
ejpam-4975	128	102	each	each	DET
ejpam-4975	128	103	x	x	SYM
ejpam-4975	128	104	∈	∈	PROPN
ejpam-4975	128	105	x	x	X
ejpam-4975	128	106	and	and	CCONJ
ejpam-4975	128	107	each	each	DET
ejpam-4975	128	108	r(λ	r(λ	NOUN
ejpam-4975	128	109	,	,	PUNCT
ejpam-4975	128	110	p)-open	p)-open	VERB
ejpam-4975	128	111	set	set	VERB
ejpam-4975	128	112	v	v	NOUN
ejpam-4975	128	113	of	of	ADP
ejpam-4975	128	114	y	y	NOUN
ejpam-4975	128	115	containing	contain	VERB
ejpam-4975	128	116	f(x	f(x	PROPN
ejpam-4975	128	117	)	)	PUNCT
ejpam-4975	128	118	,	,	PUNCT
ejpam-4975	128	119	there	there	PRON
ejpam-4975	128	120	exists	exist	VERB
ejpam-4975	128	121	a	a	DET
ejpam-4975	128	122	(	(	PUNCT
ejpam-4975	128	123	λ	λ	NOUN
ejpam-4975	128	124	,	,	PUNCT
ejpam-4975	128	125	p)-open	p)-open	VERB
ejpam-4975	128	126	set	set	VERB
ejpam-4975	128	127	u	u	NOUN
ejpam-4975	128	128	of	of	ADP
ejpam-4975	128	129	x	x	PUNCT
ejpam-4975	128	130	containing	contain	VERB
ejpam-4975	128	131	x	x	PUNCT
ejpam-4975	129	1	such	such	ADJ
ejpam-4975	129	2	that	that	PRON
ejpam-4975	129	3	f(u	f(u	PROPN
ejpam-4975	129	4	(	(	PUNCT
ejpam-4975	129	5	λ	λ	PROPN
ejpam-4975	129	6	,	,	PUNCT
ejpam-4975	129	7	p	p	NOUN
ejpam-4975	129	8	)	)	PUNCT
ejpam-4975	129	9	)	)	PUNCT
ejpam-4975	129	10	⊆	⊆	NUM
ejpam-4975	129	11	v	v	NOUN
ejpam-4975	129	12	;	;	PUNCT
ejpam-4975	129	13	(	(	PUNCT
ejpam-4975	129	14	5	5	X
ejpam-4975	129	15	)	)	PUNCT
ejpam-4975	129	16	f−1(v	f−1(v	NOUN
ejpam-4975	129	17	)	)	PUNCT
ejpam-4975	129	18	is	be	AUX
ejpam-4975	129	19	θ(λ	θ(λ	PROPN
ejpam-4975	129	20	,	,	PUNCT
ejpam-4975	129	21	p)-open	p)-open	VERB
ejpam-4975	129	22	in	in	ADP
ejpam-4975	129	23	x	x	PUNCT
ejpam-4975	129	24	for	for	ADP
ejpam-4975	129	25	every	every	DET
ejpam-4975	129	26	δ(λ	δ(λ	PROPN
ejpam-4975	129	27	,	,	PUNCT
ejpam-4975	129	28	p)-open	p)-open	VERB
ejpam-4975	129	29	set	set	VERB
ejpam-4975	129	30	v	v	NOUN
ejpam-4975	129	31	of	of	ADP
ejpam-4975	129	32	y	y	PROPN
ejpam-4975	129	33	;	;	PUNCT
ejpam-4975	129	34	(	(	PUNCT
ejpam-4975	129	35	6	6	X
ejpam-4975	129	36	)	)	PUNCT
ejpam-4975	129	37	f−1(k	f−1(k	PROPN
ejpam-4975	129	38	)	)	PUNCT
ejpam-4975	129	39	is	be	AUX
ejpam-4975	129	40	θ(λ	θ(λ	PROPN
ejpam-4975	129	41	,	,	PUNCT
ejpam-4975	129	42	p)-closed	p)-close	VERB
ejpam-4975	129	43	in	in	ADP
ejpam-4975	129	44	x	x	PUNCT
ejpam-4975	129	45	for	for	ADP
ejpam-4975	129	46	every	every	DET
ejpam-4975	129	47	δ(λ	δ(λ	PROPN
ejpam-4975	129	48	,	,	PUNCT
ejpam-4975	129	49	p)-closed	p)-close	VERB
ejpam-4975	129	50	set	set	NOUN
ejpam-4975	129	51	k	k	PROPN
ejpam-4975	129	52	of	of	ADP
ejpam-4975	129	53	y	y	PROPN
ejpam-4975	129	54	;	;	PUNCT
ejpam-4975	129	55	(	(	PUNCT
ejpam-4975	129	56	7	7	X
ejpam-4975	129	57	)	)	PUNCT
ejpam-4975	129	58	f(aθ(λ	f(aθ(λ	PROPN
ejpam-4975	129	59	,	,	PUNCT
ejpam-4975	129	60	p	p	NOUN
ejpam-4975	129	61	)	)	PUNCT
ejpam-4975	129	62	)	)	PUNCT
ejpam-4975	130	1	⊆	⊆	NUM
ejpam-4975	130	2	[	[	X
ejpam-4975	130	3	f(a)]δ(λ	f(a)]δ(λ	NOUN
ejpam-4975	130	4	,	,	PUNCT
ejpam-4975	130	5	p	p	NOUN
ejpam-4975	130	6	)	)	PUNCT
ejpam-4975	130	7	for	for	ADP
ejpam-4975	130	8	every	every	DET
ejpam-4975	130	9	subset	subset	NOUN
ejpam-4975	130	10	a	a	PRON
ejpam-4975	130	11	of	of	ADP
ejpam-4975	130	12	x	x	PRON
ejpam-4975	130	13	;	;	PUNCT
ejpam-4975	130	14	(	(	PUNCT
ejpam-4975	130	15	8)	8)	NUM
ejpam-4975	130	16	[	[	X
ejpam-4975	130	17	f−1(b)]θ(λ	f−1(b)]θ(λ	PROPN
ejpam-4975	130	18	,	,	PUNCT
ejpam-4975	130	19	p	p	NOUN
ejpam-4975	130	20	)	)	PUNCT
ejpam-4975	130	21	⊆	⊆	NUM
ejpam-4975	130	22	f−1(bδ(λ	f−1(bδ(λ	NOUN
ejpam-4975	130	23	,	,	PUNCT
ejpam-4975	130	24	p	p	NOUN
ejpam-4975	130	25	)	)	PUNCT
ejpam-4975	130	26	)	)	PUNCT
ejpam-4975	130	27	for	for	ADP
ejpam-4975	130	28	every	every	DET
ejpam-4975	130	29	subset	subset	NOUN
ejpam-4975	130	30	b	b	PROPN
ejpam-4975	130	31	of	of	ADP
ejpam-4975	130	32	y	y	PROPN
ejpam-4975	130	33	;	;	PUNCT
ejpam-4975	130	34	(	(	PUNCT
ejpam-4975	130	35	9	9	X
ejpam-4975	130	36	)	)	PUNCT
ejpam-4975	130	37	f−1(bδ(λ	f−1(bδ(λ	NOUN
ejpam-4975	130	38	,	,	PUNCT
ejpam-4975	130	39	p	p	NOUN
ejpam-4975	130	40	)	)	PUNCT
ejpam-4975	130	41	)	)	PUNCT
ejpam-4975	131	1	⊆	⊆	NUM
ejpam-4975	131	2	[	[	X
ejpam-4975	131	3	f−1(b)]θ(λ	f−1(b)]θ(λ	NOUN
ejpam-4975	131	4	,	,	PUNCT
ejpam-4975	131	5	p	p	NOUN
ejpam-4975	131	6	)	)	PUNCT
ejpam-4975	131	7	for	for	ADP
ejpam-4975	131	8	every	every	DET
ejpam-4975	131	9	subset	subset	NOUN
ejpam-4975	131	10	b	b	PROPN
ejpam-4975	131	11	of	of	ADP
ejpam-4975	131	12	y	y	PROPN
ejpam-4975	131	13	;	;	PUNCT
ejpam-4975	131	14	(	(	PUNCT
ejpam-4975	131	15	10	10	X
ejpam-4975	131	16	)	)	PUNCT
ejpam-4975	131	17	f−1(v	f−1(v	NOUN
ejpam-4975	131	18	)	)	PUNCT
ejpam-4975	131	19	⊆	⊆	NUM
ejpam-4975	132	1	[	[	X
ejpam-4975	132	2	f−1(v	f−1(v	NOUN
ejpam-4975	132	3	s(λ	s(λ	PROPN
ejpam-4975	132	4	,	,	PUNCT
ejpam-4975	132	5	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	132	6	,	,	PUNCT
ejpam-4975	132	7	p	p	NOUN
ejpam-4975	132	8	)	)	PUNCT
ejpam-4975	132	9	for	for	ADP
ejpam-4975	132	10	every	every	DET
ejpam-4975	132	11	(	(	PUNCT
ejpam-4975	132	12	λ	λ	NOUN
ejpam-4975	132	13	,	,	PUNCT
ejpam-4975	132	14	p)-open	p)-open	VERB
ejpam-4975	132	15	set	set	VERB
ejpam-4975	132	16	v	v	NOUN
ejpam-4975	132	17	of	of	ADP
ejpam-4975	132	18	y	y	PROPN
ejpam-4975	132	19	.	.	PUNCT
ejpam-4975	133	1	proof	proof	NOUN
ejpam-4975	133	2	.	.	PUNCT
ejpam-4975	134	1	(	(	PUNCT
ejpam-4975	134	2	1	1	X
ejpam-4975	134	3	)	)	PUNCT
ejpam-4975	134	4	⇒	⇒	NOUN
ejpam-4975	134	5	(	(	PUNCT
ejpam-4975	134	6	2	2	NUM
ejpam-4975	134	7	):	):	PUNCT
ejpam-4975	134	8	let	let	VERB
ejpam-4975	134	9	v	v	PART
ejpam-4975	134	10	be	be	AUX
ejpam-4975	134	11	any	any	DET
ejpam-4975	134	12	r(λ	r(λ	NOUN
ejpam-4975	134	13	,	,	PUNCT
ejpam-4975	134	14	p)-open	p)-open	VERB
ejpam-4975	134	15	set	set	VERB
ejpam-4975	134	16	of	of	ADP
ejpam-4975	134	17	y	y	PROPN
ejpam-4975	134	18	and	and	CCONJ
ejpam-4975	134	19	x	x	PROPN
ejpam-4975	134	20	∈	∈	PROPN
ejpam-4975	134	21	f−1(v	f−1(v	NOUN
ejpam-4975	134	22	)	)	PUNCT
ejpam-4975	134	23	.	.	PUNCT
ejpam-4975	135	1	since	since	SCONJ
ejpam-4975	135	2	f	f	PROPN
ejpam-4975	135	3	is	be	AUX
ejpam-4975	135	4	almost	almost	ADV
ejpam-4975	135	5	strongly	strongly	ADV
ejpam-4975	135	6	θ(λ	θ(λ	VERB
ejpam-4975	135	7	,	,	PUNCT
ejpam-4975	135	8	p)-continuous	p)-continuous	ADJ
ejpam-4975	135	9	,	,	PUNCT
ejpam-4975	135	10	there	there	PRON
ejpam-4975	135	11	exists	exist	VERB
ejpam-4975	135	12	a	a	DET
ejpam-4975	135	13	(	(	PUNCT
ejpam-4975	135	14	λ	λ	NOUN
ejpam-4975	135	15	,	,	PUNCT
ejpam-4975	135	16	p)-open	p)-open	VERB
ejpam-4975	135	17	set	set	VERB
ejpam-4975	135	18	u	u	NOUN
ejpam-4975	135	19	of	of	ADP
ejpam-4975	135	20	x	x	PUNCT
ejpam-4975	135	21	containing	contain	VERB
ejpam-4975	135	22	x	x	PUNCT
ejpam-4975	135	23	such	such	ADJ
ejpam-4975	135	24	that	that	DET
ejpam-4975	135	25	f(u	f(u	PROPN
ejpam-4975	135	26	(	(	PUNCT
ejpam-4975	135	27	λ	λ	PROPN
ejpam-4975	135	28	,	,	PUNCT
ejpam-4975	135	29	p	p	NOUN
ejpam-4975	135	30	)	)	PUNCT
ejpam-4975	135	31	)	)	PUNCT
ejpam-4975	136	1	⊆	⊆	NUM
ejpam-4975	136	2	v	v	ADP
ejpam-4975	136	3	s(λ	s(λ	PROPN
ejpam-4975	136	4	,	,	PUNCT
ejpam-4975	136	5	p	p	NOUN
ejpam-4975	136	6	)	)	PUNCT
ejpam-4975	136	7	=	=	NOUN
ejpam-4975	136	8	v	v	NOUN
ejpam-4975	136	9	.	.	PUNCT
ejpam-4975	137	1	thus	thus	ADV
ejpam-4975	137	2	,	,	PUNCT
ejpam-4975	137	3	x	x	PUNCT
ejpam-4975	137	4	∈	∈	PROPN
ejpam-4975	137	5	u	u	NOUN
ejpam-4975	137	6	⊆	⊆	NUM
ejpam-4975	137	7	u	u	PROPN
ejpam-4975	137	8	(	(	PUNCT
ejpam-4975	137	9	λ	λ	PROPN
ejpam-4975	137	10	,	,	PUNCT
ejpam-4975	137	11	p	p	NOUN
ejpam-4975	137	12	)	)	PUNCT
ejpam-4975	137	13	⊆	⊆	NUM
ejpam-4975	137	14	f−1(v	f−1(v	NOUN
ejpam-4975	137	15	)	)	PUNCT
ejpam-4975	137	16	which	which	PRON
ejpam-4975	137	17	implies	imply	VERB
ejpam-4975	137	18	that	that	SCONJ
ejpam-4975	137	19	x	x	PUNCT
ejpam-4975	137	20	∈	∈	PROPN
ejpam-4975	137	21	[	[	X
ejpam-4975	137	22	f−1(v	f−1(v	NOUN
ejpam-4975	137	23	)	)	PUNCT
ejpam-4975	137	24	]	]	X
ejpam-4975	138	1	θ(λ	θ(λ	PROPN
ejpam-4975	138	2	,	,	PUNCT
ejpam-4975	138	3	p	p	NOUN
ejpam-4975	138	4	)	)	PUNCT
ejpam-4975	138	5	.	.	PUNCT
ejpam-4975	139	1	this	this	PRON
ejpam-4975	139	2	shows	show	VERB
ejpam-4975	139	3	that	that	DET
ejpam-4975	139	4	f−1(v	f−1(v	NOUN
ejpam-4975	139	5	)	)	PUNCT
ejpam-4975	140	1	⊆	⊆	NUM
ejpam-4975	140	2	[	[	X
ejpam-4975	140	3	f−1(v	f−1(v	NOUN
ejpam-4975	140	4	)	)	PUNCT
ejpam-4975	140	5	]	]	X
ejpam-4975	141	1	θ(λ	θ(λ	PROPN
ejpam-4975	141	2	,	,	PUNCT
ejpam-4975	141	3	p	p	NOUN
ejpam-4975	141	4	)	)	PUNCT
ejpam-4975	141	5	.	.	PUNCT
ejpam-4975	142	1	by	by	ADP
ejpam-4975	142	2	lemma	lemma	PROPN
ejpam-4975	142	3	1	1	NUM
ejpam-4975	142	4	,	,	PUNCT
ejpam-4975	142	5	f−1(v	f−1(v	NOUN
ejpam-4975	142	6	)	)	PUNCT
ejpam-4975	142	7	=	=	PUNCT
ejpam-4975	143	1	[	[	X
ejpam-4975	143	2	f−1(v	f−1(v	NOUN
ejpam-4975	143	3	)	)	PUNCT
ejpam-4975	143	4	]	]	X
ejpam-4975	143	5	θ(λ	θ(λ	PROPN
ejpam-4975	143	6	,	,	PUNCT
ejpam-4975	143	7	p	p	NOUN
ejpam-4975	143	8	)	)	PUNCT
ejpam-4975	143	9	and	and	CCONJ
ejpam-4975	143	10	hence	hence	ADV
ejpam-4975	143	11	f−1(v	f−1(v	PROPN
ejpam-4975	143	12	)	)	PUNCT
ejpam-4975	143	13	is	be	AUX
ejpam-4975	143	14	θ(λ	θ(λ	PROPN
ejpam-4975	143	15	,	,	PUNCT
ejpam-4975	143	16	p)-open	p)-open	ADJ
ejpam-4975	143	17	.	.	PUNCT
ejpam-4975	144	1	(	(	PUNCT
ejpam-4975	144	2	2	2	X
ejpam-4975	144	3	)	)	PUNCT
ejpam-4975	144	4	⇒	⇒	NOUN
ejpam-4975	144	5	(	(	PUNCT
ejpam-4975	144	6	3	3	NUM
ejpam-4975	144	7	):	):	PUNCT
ejpam-4975	144	8	let	let	VERB
ejpam-4975	144	9	k	k	PRON
ejpam-4975	144	10	be	be	AUX
ejpam-4975	144	11	any	any	DET
ejpam-4975	144	12	r(λ	r(λ	NOUN
ejpam-4975	144	13	,	,	PUNCT
ejpam-4975	144	14	p)-closed	p)-close	VERB
ejpam-4975	144	15	set	set	NOUN
ejpam-4975	144	16	of	of	ADP
ejpam-4975	144	17	y	y	PROPN
ejpam-4975	144	18	.	.	PUNCT
ejpam-4975	145	1	by	by	ADP
ejpam-4975	145	2	(	(	PUNCT
ejpam-4975	145	3	2	2	NUM
ejpam-4975	145	4	)	)	PUNCT
ejpam-4975	145	5	,	,	PUNCT
ejpam-4975	145	6	we	we	PRON
ejpam-4975	145	7	have	have	VERB
ejpam-4975	145	8	f−1(k	f−1(k	PROPN
ejpam-4975	145	9	)	)	PUNCT
ejpam-4975	146	1	=	=	PUNCT
ejpam-4975	147	1	x	x	PUNCT
ejpam-4975	147	2	−	−	NOUN
ejpam-4975	147	3	f−1(y	f−1(y	PROPN
ejpam-4975	147	4	−k	−k	NOUN
ejpam-4975	147	5	)	)	PUNCT
ejpam-4975	147	6	=	=	PUNCT
ejpam-4975	148	1	x	x	X
ejpam-4975	148	2	−	−	PROPN
ejpam-4975	149	1	[	[	X
ejpam-4975	149	2	f−1(y	f−1(y	PROPN
ejpam-4975	149	3	−k)]θ(λ	−k)]θ(λ	PROPN
ejpam-4975	149	4	,	,	PUNCT
ejpam-4975	149	5	p	p	NOUN
ejpam-4975	149	6	)	)	PUNCT
ejpam-4975	149	7	=	=	PUNCT
ejpam-4975	150	1	x	x	X
ejpam-4975	150	2	−	−	PUNCT
ejpam-4975	151	1	[	[	X
ejpam-4975	151	2	x	x	X
ejpam-4975	151	3	−	−	X
ejpam-4975	151	4	f−1(k)]θ(λ	f−1(k)]θ(λ	PROPN
ejpam-4975	151	5	,	,	PUNCT
ejpam-4975	151	6	p	p	NOUN
ejpam-4975	151	7	)	)	PUNCT
ejpam-4975	151	8	=	=	NOUN
ejpam-4975	152	1	[	[	X
ejpam-4975	152	2	f−1(k)]θ(λ	f−1(k)]θ(λ	PROPN
ejpam-4975	152	3	,	,	PUNCT
ejpam-4975	152	4	p	p	NOUN
ejpam-4975	152	5	)	)	PUNCT
ejpam-4975	152	6	.	.	PUNCT
ejpam-4975	153	1	thus	thus	ADV
ejpam-4975	153	2	,	,	PUNCT
ejpam-4975	153	3	f−1(k	f−1(k	PROPN
ejpam-4975	153	4	)	)	PUNCT
ejpam-4975	153	5	is	be	AUX
ejpam-4975	153	6	θ(λ	θ(λ	PROPN
ejpam-4975	153	7	,	,	PUNCT
ejpam-4975	153	8	p)-closed	p)-close	VERB
ejpam-4975	153	9	in	in	ADP
ejpam-4975	153	10	x.	x.	NOUN
ejpam-4975	153	11	(	(	PUNCT
ejpam-4975	153	12	3	3	NUM
ejpam-4975	153	13	)	)	PUNCT
ejpam-4975	153	14	⇒	⇒	NOUN
ejpam-4975	153	15	(	(	PUNCT
ejpam-4975	153	16	4	4	NUM
ejpam-4975	153	17	):	):	PUNCT
ejpam-4975	153	18	let	let	VERB
ejpam-4975	153	19	x	x	PUNCT
ejpam-4975	153	20	∈	∈	PROPN
ejpam-4975	153	21	x	x	X
ejpam-4975	153	22	and	and	CCONJ
ejpam-4975	153	23	v	v	X
ejpam-4975	153	24	be	be	AUX
ejpam-4975	153	25	any	any	DET
ejpam-4975	153	26	r(λ	r(λ	NOUN
ejpam-4975	153	27	,	,	PUNCT
ejpam-4975	153	28	p)-open	p)-open	VERB
ejpam-4975	153	29	set	set	VERB
ejpam-4975	153	30	of	of	ADP
ejpam-4975	153	31	y	y	PROPN
ejpam-4975	153	32	containing	contain	VERB
ejpam-4975	153	33	f(x	f(x	PROPN
ejpam-4975	153	34	)	)	PUNCT
ejpam-4975	153	35	.	.	PUNCT
ejpam-4975	154	1	by	by	ADP
ejpam-4975	154	2	(	(	PUNCT
ejpam-4975	154	3	3	3	NUM
ejpam-4975	154	4	)	)	PUNCT
ejpam-4975	154	5	,	,	PUNCT
ejpam-4975	154	6	x	x	PUNCT
ejpam-4975	154	7	−	−	PROPN
ejpam-4975	154	8	f−1(v	f−1(v	NOUN
ejpam-4975	154	9	)	)	PUNCT
ejpam-4975	155	1	=	=	PUNCT
ejpam-4975	155	2	f−1(y	f−1(y	PROPN
ejpam-4975	155	3	−	−	PROPN
ejpam-4975	155	4	v	v	NOUN
ejpam-4975	155	5	)	)	PUNCT
ejpam-4975	155	6	=	=	PUNCT
ejpam-4975	156	1	[	[	X
ejpam-4975	156	2	f−1(y	f−1(y	NOUN
ejpam-4975	156	3	−	−	PROPN
ejpam-4975	156	4	v	v	NOUN
ejpam-4975	156	5	)	)	PUNCT
ejpam-4975	156	6	]	]	X
ejpam-4975	156	7	θ(λ	θ(λ	PROPN
ejpam-4975	156	8	,	,	PUNCT
ejpam-4975	156	9	p	p	NOUN
ejpam-4975	156	10	)	)	PUNCT
ejpam-4975	156	11	=	=	PUNCT
ejpam-4975	156	12	x	x	X
ejpam-4975	156	13	−	−	PROPN
ejpam-4975	157	1	[	[	X
ejpam-4975	157	2	f−1(v	f−1(v	NOUN
ejpam-4975	157	3	)	)	PUNCT
ejpam-4975	157	4	]	]	X
ejpam-4975	158	1	θ(λ	θ(λ	PROPN
ejpam-4975	158	2	,	,	PUNCT
ejpam-4975	158	3	p	p	NOUN
ejpam-4975	158	4	)	)	PUNCT
ejpam-4975	158	5	.	.	PUNCT
ejpam-4975	159	1	this	this	PRON
ejpam-4975	159	2	implies	imply	VERB
ejpam-4975	159	3	that	that	DET
ejpam-4975	159	4	f−1(v	f−1(v	NOUN
ejpam-4975	159	5	)	)	PUNCT
ejpam-4975	159	6	=	=	PUNCT
ejpam-4975	160	1	[	[	X
ejpam-4975	160	2	f−1(v	f−1(v	NOUN
ejpam-4975	160	3	)	)	PUNCT
ejpam-4975	160	4	]	]	X
ejpam-4975	161	1	θ(λ	θ(λ	PROPN
ejpam-4975	161	2	,	,	PUNCT
ejpam-4975	161	3	p	p	NOUN
ejpam-4975	161	4	)	)	PUNCT
ejpam-4975	161	5	.	.	PUNCT
ejpam-4975	162	1	then	then	ADV
ejpam-4975	162	2	,	,	PUNCT
ejpam-4975	162	3	there	there	PRON
ejpam-4975	162	4	exists	exist	VERB
ejpam-4975	162	5	a	a	DET
ejpam-4975	162	6	(	(	PUNCT
ejpam-4975	162	7	λ	λ	NOUN
ejpam-4975	162	8	,	,	PUNCT
ejpam-4975	162	9	p)-open	p)-open	VERB
ejpam-4975	162	10	set	set	VERB
ejpam-4975	162	11	u	u	NOUN
ejpam-4975	162	12	of	of	ADP
ejpam-4975	162	13	x	x	PUNCT
ejpam-4975	162	14	containing	contain	VERB
ejpam-4975	162	15	x	x	PUNCT
ejpam-4975	162	16	such	such	ADJ
ejpam-4975	162	17	that	that	DET
ejpam-4975	162	18	u	u	PROPN
ejpam-4975	162	19	(	(	PUNCT
ejpam-4975	162	20	λ	λ	PROPN
ejpam-4975	162	21	,	,	PUNCT
ejpam-4975	162	22	p	p	NOUN
ejpam-4975	162	23	)	)	PUNCT
ejpam-4975	162	24	⊆	⊆	NUM
ejpam-4975	162	25	f−1(v	f−1(v	NOUN
ejpam-4975	162	26	)	)	PUNCT
ejpam-4975	162	27	;	;	PUNCT
ejpam-4975	162	28	hence	hence	ADV
ejpam-4975	162	29	f(u	f(u	PROPN
ejpam-4975	162	30	(	(	PUNCT
ejpam-4975	162	31	λ	λ	PROPN
ejpam-4975	162	32	,	,	PUNCT
ejpam-4975	162	33	p	p	NOUN
ejpam-4975	162	34	)	)	PUNCT
ejpam-4975	162	35	)	)	PUNCT
ejpam-4975	162	36	⊆	⊆	NUM
ejpam-4975	162	37	v	v	NOUN
ejpam-4975	162	38	.	.	PUNCT
ejpam-4975	163	1	(	(	PUNCT
ejpam-4975	163	2	4	4	X
ejpam-4975	163	3	)	)	PUNCT
ejpam-4975	163	4	⇒	⇒	NOUN
ejpam-4975	163	5	(	(	PUNCT
ejpam-4975	163	6	5	5	NUM
ejpam-4975	163	7	):	):	PUNCT
ejpam-4975	163	8	let	let	VERB
ejpam-4975	163	9	v	v	PART
ejpam-4975	163	10	be	be	AUX
ejpam-4975	163	11	any	any	DET
ejpam-4975	163	12	δ(λ	δ(λ	PROPN
ejpam-4975	163	13	,	,	PUNCT
ejpam-4975	163	14	p)-open	p)-open	VERB
ejpam-4975	163	15	set	set	VERB
ejpam-4975	163	16	of	of	ADP
ejpam-4975	163	17	y	y	PROPN
ejpam-4975	163	18	and	and	CCONJ
ejpam-4975	163	19	x	x	PROPN
ejpam-4975	163	20	∈	∈	PROPN
ejpam-4975	163	21	f−1(v	f−1(v	NOUN
ejpam-4975	163	22	)	)	PUNCT
ejpam-4975	163	23	.	.	PUNCT
ejpam-4975	164	1	there	there	PRON
ejpam-4975	164	2	exists	exist	VERB
ejpam-4975	164	3	a	a	DET
ejpam-4975	164	4	r(λ	r(λ	NOUN
ejpam-4975	164	5	,	,	PUNCT
ejpam-4975	164	6	p)-open	p)-open	VERB
ejpam-4975	164	7	set	set	VERB
ejpam-4975	164	8	g	g	NOUN
ejpam-4975	164	9	of	of	ADP
ejpam-4975	164	10	y	y	PRON
ejpam-4975	164	11	such	such	ADJ
ejpam-4975	164	12	that	that	SCONJ
ejpam-4975	164	13	f(x	f(x	PROPN
ejpam-4975	164	14	)	)	PUNCT
ejpam-4975	164	15	∈	∈	PROPN
ejpam-4975	164	16	g	g	ADP
ejpam-4975	164	17	⊆	⊆	NUM
ejpam-4975	164	18	v	v	NOUN
ejpam-4975	164	19	.	.	PUNCT
ejpam-4975	165	1	by	by	ADP
ejpam-4975	165	2	(	(	PUNCT
ejpam-4975	165	3	4	4	NUM
ejpam-4975	165	4	)	)	PUNCT
ejpam-4975	165	5	,	,	PUNCT
ejpam-4975	165	6	there	there	PRON
ejpam-4975	165	7	exists	exist	VERB
ejpam-4975	165	8	a	a	DET
ejpam-4975	165	9	(	(	PUNCT
ejpam-4975	165	10	λ	λ	NOUN
ejpam-4975	165	11	,	,	PUNCT
ejpam-4975	165	12	p)-open	p)-open	VERB
ejpam-4975	165	13	set	set	VERB
ejpam-4975	165	14	u	u	NOUN
ejpam-4975	165	15	of	of	ADP
ejpam-4975	165	16	x	x	PUNCT
ejpam-4975	165	17	containing	contain	VERB
ejpam-4975	165	18	x	x	PUNCT
ejpam-4975	165	19	such	such	ADJ
ejpam-4975	165	20	that	that	DET
ejpam-4975	165	21	f(u	f(u	PROPN
ejpam-4975	165	22	(	(	PUNCT
ejpam-4975	165	23	λ	λ	PROPN
ejpam-4975	165	24	,	,	PUNCT
ejpam-4975	165	25	p	p	NOUN
ejpam-4975	165	26	)	)	PUNCT
ejpam-4975	165	27	)	)	PUNCT
ejpam-4975	166	1	⊆	⊆	NUM
ejpam-4975	166	2	g.	g.	NOUN
ejpam-4975	166	3	thus	thus	ADV
ejpam-4975	166	4	,	,	PUNCT
ejpam-4975	166	5	x	x	PUNCT
ejpam-4975	166	6	∈	∈	PROPN
ejpam-4975	166	7	u	u	NOUN
ejpam-4975	166	8	⊆	⊆	NUM
ejpam-4975	166	9	u	u	PROPN
ejpam-4975	166	10	(	(	PUNCT
ejpam-4975	166	11	λ	λ	PROPN
ejpam-4975	166	12	,	,	PUNCT
ejpam-4975	166	13	p	p	NOUN
ejpam-4975	166	14	)	)	PUNCT
ejpam-4975	166	15	⊆	⊆	NUM
ejpam-4975	166	16	f−1(v	f−1(v	NOUN
ejpam-4975	166	17	)	)	PUNCT
ejpam-4975	166	18	which	which	PRON
ejpam-4975	166	19	implies	imply	VERB
ejpam-4975	166	20	that	that	SCONJ
ejpam-4975	166	21	x	x	PUNCT
ejpam-4975	166	22	∈	∈	PROPN
ejpam-4975	166	23	[	[	X
ejpam-4975	166	24	f−1(v	f−1(v	NOUN
ejpam-4975	166	25	)	)	PUNCT
ejpam-4975	166	26	]	]	X
ejpam-4975	167	1	θ(λ	θ(λ	PROPN
ejpam-4975	167	2	,	,	PUNCT
ejpam-4975	167	3	p	p	NOUN
ejpam-4975	167	4	)	)	PUNCT
ejpam-4975	167	5	.	.	PUNCT
ejpam-4975	168	1	therefore	therefore	ADV
ejpam-4975	168	2	,	,	PUNCT
ejpam-4975	168	3	f−1(v	f−1(v	PROPN
ejpam-4975	168	4	)	)	PUNCT
ejpam-4975	169	1	⊆	⊆	NUM
ejpam-4975	169	2	[	[	X
ejpam-4975	169	3	f−1(v	f−1(v	NOUN
ejpam-4975	169	4	)	)	PUNCT
ejpam-4975	169	5	]	]	X
ejpam-4975	170	1	θ(λ	θ(λ	PROPN
ejpam-4975	170	2	,	,	PUNCT
ejpam-4975	170	3	p	p	NOUN
ejpam-4975	170	4	)	)	PUNCT
ejpam-4975	170	5	and	and	CCONJ
ejpam-4975	170	6	hence	hence	ADV
ejpam-4975	170	7	f−1(v	f−1(v	NOUN
ejpam-4975	170	8	)	)	PUNCT
ejpam-4975	170	9	=	=	PUNCT
ejpam-4975	171	1	[	[	X
ejpam-4975	171	2	f−1(v	f−1(v	NOUN
ejpam-4975	171	3	)	)	PUNCT
ejpam-4975	171	4	]	]	X
ejpam-4975	171	5	θ(λ	θ(λ	PROPN
ejpam-4975	171	6	,	,	PUNCT
ejpam-4975	171	7	p	p	NOUN
ejpam-4975	171	8	)	)	PUNCT
ejpam-4975	171	9	,	,	PUNCT
ejpam-4975	171	10	by	by	ADP
ejpam-4975	171	11	lemma	lemma	PROPN
ejpam-4975	171	12	1	1	NUM
ejpam-4975	171	13	,	,	PUNCT
ejpam-4975	171	14	f−1(v	f−1(v	PROPN
ejpam-4975	171	15	)	)	PUNCT
ejpam-4975	171	16	is	be	AUX
ejpam-4975	171	17	θ(λ	θ(λ	PROPN
ejpam-4975	171	18	,	,	PUNCT
ejpam-4975	171	19	p)-open	p)-open	NOUN
ejpam-4975	171	20	.	.	PUNCT
ejpam-4975	172	1	c.	c.	PROPN
ejpam-4975	172	2	boonpok	boonpok	PROPN
ejpam-4975	172	3	,	,	PUNCT
ejpam-4975	172	4	j.	j.	PROPN
ejpam-4975	172	5	khampakdee	khampakdee	PROPN
ejpam-4975	172	6	/	/	PUNCT
ejpam-4975	172	7	eur	eur	PROPN
ejpam-4975	172	8	.	.	PUNCT
ejpam-4975	173	1	j.	j.	PROPN
ejpam-4975	173	2	pure	pure	PROPN
ejpam-4975	173	3	appl	appl	PROPN
ejpam-4975	173	4	.	.	PROPN
ejpam-4975	173	5	math	math	PROPN
ejpam-4975	173	6	,	,	PUNCT
ejpam-4975	173	7	17	17	NUM
ejpam-4975	173	8	(	(	PUNCT
ejpam-4975	173	9	1	1	NUM
ejpam-4975	173	10	)	)	PUNCT
ejpam-4975	173	11	(	(	PUNCT
ejpam-4975	173	12	2024	2024	NUM
ejpam-4975	173	13	)	)	PUNCT
ejpam-4975	173	14	,	,	PUNCT
ejpam-4975	173	15	300	300	NUM
ejpam-4975	173	16	-	-	SYM
ejpam-4975	173	17	309	309	NUM
ejpam-4975	173	18	304	304	NUM
ejpam-4975	173	19	(	(	PUNCT
ejpam-4975	173	20	5	5	NUM
ejpam-4975	173	21	)	)	PUNCT
ejpam-4975	173	22	⇒	⇒	NOUN
ejpam-4975	173	23	(	(	PUNCT
ejpam-4975	173	24	6	6	NUM
ejpam-4975	173	25	):	):	PUNCT
ejpam-4975	173	26	let	let	VERB
ejpam-4975	173	27	k	k	PRON
ejpam-4975	173	28	be	be	AUX
ejpam-4975	173	29	any	any	DET
ejpam-4975	173	30	δ(λ	δ(λ	PROPN
ejpam-4975	173	31	,	,	PUNCT
ejpam-4975	173	32	p)-closed	p)-close	VERB
ejpam-4975	173	33	set	set	NOUN
ejpam-4975	173	34	of	of	ADP
ejpam-4975	173	35	y	y	PROPN
ejpam-4975	173	36	.	.	PUNCT
ejpam-4975	174	1	by	by	ADP
ejpam-4975	174	2	(	(	PUNCT
ejpam-4975	174	3	5	5	NUM
ejpam-4975	174	4	)	)	PUNCT
ejpam-4975	174	5	,	,	PUNCT
ejpam-4975	174	6	we	we	PRON
ejpam-4975	174	7	have	have	VERB
ejpam-4975	174	8	f−1(k	f−1(k	PROPN
ejpam-4975	174	9	)	)	PUNCT
ejpam-4975	175	1	=	=	PUNCT
ejpam-4975	176	1	x	x	PUNCT
ejpam-4975	176	2	−	−	NOUN
ejpam-4975	176	3	f−1(y	f−1(y	PROPN
ejpam-4975	176	4	−k	−k	NOUN
ejpam-4975	176	5	)	)	PUNCT
ejpam-4975	176	6	=	=	PUNCT
ejpam-4975	177	1	x	x	X
ejpam-4975	177	2	−	−	PROPN
ejpam-4975	178	1	[	[	X
ejpam-4975	178	2	f−1(y	f−1(y	PROPN
ejpam-4975	178	3	−k)]θ(λ	−k)]θ(λ	PROPN
ejpam-4975	178	4	,	,	PUNCT
ejpam-4975	178	5	p	p	NOUN
ejpam-4975	178	6	)	)	PUNCT
ejpam-4975	178	7	=	=	NOUN
ejpam-4975	179	1	[	[	X
ejpam-4975	179	2	f−1(k)]θ(λ	f−1(k)]θ(λ	PROPN
ejpam-4975	179	3	,	,	PUNCT
ejpam-4975	179	4	p	p	NOUN
ejpam-4975	179	5	)	)	PUNCT
ejpam-4975	179	6	.	.	PUNCT
ejpam-4975	180	1	thus	thus	ADV
ejpam-4975	180	2	,	,	PUNCT
ejpam-4975	180	3	f−1(k	f−1(k	PROPN
ejpam-4975	180	4	)	)	PUNCT
ejpam-4975	180	5	=	=	PUNCT
ejpam-4975	181	1	[	[	X
ejpam-4975	181	2	f−1(k)]θ(λ	f−1(k)]θ(λ	PROPN
ejpam-4975	181	3	,	,	PUNCT
ejpam-4975	181	4	p	p	NOUN
ejpam-4975	181	5	)	)	PUNCT
ejpam-4975	181	6	and	and	CCONJ
ejpam-4975	181	7	hence	hence	ADV
ejpam-4975	181	8	f−1(k	f−1(k	PROPN
ejpam-4975	181	9	)	)	PUNCT
ejpam-4975	181	10	is	be	AUX
ejpam-4975	181	11	θ(λ	θ(λ	PROPN
ejpam-4975	181	12	,	,	PUNCT
ejpam-4975	181	13	p)-closed	p)-close	VERB
ejpam-4975	181	14	.	.	PUNCT
ejpam-4975	182	1	(	(	PUNCT
ejpam-4975	182	2	6	6	NUM
ejpam-4975	182	3	)	)	PUNCT
ejpam-4975	182	4	⇒	⇒	NOUN
ejpam-4975	182	5	(	(	PUNCT
ejpam-4975	182	6	7	7	NUM
ejpam-4975	182	7	):	):	PUNCT
ejpam-4975	182	8	let	let	VERB
ejpam-4975	182	9	a	a	DET
ejpam-4975	182	10	be	be	AUX
ejpam-4975	182	11	any	any	DET
ejpam-4975	182	12	subset	subset	NOUN
ejpam-4975	182	13	of	of	ADP
ejpam-4975	182	14	x.	x.	NOUN
ejpam-4975	182	15	since	since	SCONJ
ejpam-4975	182	16	[	[	X
ejpam-4975	182	17	f(a)]δ(λ	f(a)]δ(λ	PROPN
ejpam-4975	182	18	,	,	PUNCT
ejpam-4975	182	19	p	p	NOUN
ejpam-4975	182	20	)	)	PUNCT
ejpam-4975	182	21	is	be	AUX
ejpam-4975	182	22	δ(λ	δ(λ	PROPN
ejpam-4975	182	23	,	,	PUNCT
ejpam-4975	182	24	p)-closed	p)-close	VERB
ejpam-4975	182	25	in	in	ADP
ejpam-4975	182	26	y	y	PROPN
ejpam-4975	182	27	,	,	PUNCT
ejpam-4975	182	28	by	by	ADP
ejpam-4975	182	29	(	(	PUNCT
ejpam-4975	182	30	6	6	X
ejpam-4975	182	31	)	)	PUNCT
ejpam-4975	182	32	we	we	PRON
ejpam-4975	182	33	have	have	VERB
ejpam-4975	182	34	f−1([f(a)]δ(λ	f−1([f(a)]δ(λ	NOUN
ejpam-4975	182	35	,	,	PUNCT
ejpam-4975	182	36	p	p	NOUN
ejpam-4975	182	37	)	)	PUNCT
ejpam-4975	182	38	)	)	PUNCT
ejpam-4975	183	1	=	=	PUNCT
ejpam-4975	184	1	[	[	X
ejpam-4975	184	2	f−1([f(a)]δ(λ	f−1([f(a)]δ(λ	NOUN
ejpam-4975	184	3	,	,	PUNCT
ejpam-4975	184	4	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	184	5	,	,	PUNCT
ejpam-4975	184	6	p	p	NOUN
ejpam-4975	184	7	)	)	PUNCT
ejpam-4975	184	8	.	.	PUNCT
ejpam-4975	185	1	let	let	VERB
ejpam-4975	185	2	x	x	SYM
ejpam-4975	185	3	̸∈	̸∈	PROPN
ejpam-4975	185	4	f−1([f(a)]δ(λ	f−1([f(a)]δ(λ	PROPN
ejpam-4975	185	5	,	,	PUNCT
ejpam-4975	185	6	p	p	NOUN
ejpam-4975	185	7	)	)	PUNCT
ejpam-4975	185	8	)	)	PUNCT
ejpam-4975	185	9	.	.	PUNCT
ejpam-4975	186	1	then	then	ADV
ejpam-4975	186	2	,	,	PUNCT
ejpam-4975	186	3	there	there	PRON
ejpam-4975	186	4	exists	exist	VERB
ejpam-4975	186	5	a	a	DET
ejpam-4975	186	6	(	(	PUNCT
ejpam-4975	186	7	λ	λ	NOUN
ejpam-4975	186	8	,	,	PUNCT
ejpam-4975	186	9	p)-open	p)-open	VERB
ejpam-4975	186	10	set	set	VERB
ejpam-4975	186	11	u	u	NOUN
ejpam-4975	186	12	of	of	ADP
ejpam-4975	186	13	x	x	PUNCT
ejpam-4975	186	14	containing	contain	VERB
ejpam-4975	186	15	x	x	PUNCT
ejpam-4975	187	1	such	such	ADJ
ejpam-4975	187	2	that	that	PRON
ejpam-4975	187	3	u	u	PROPN
ejpam-4975	187	4	(	(	PUNCT
ejpam-4975	187	5	λ	λ	PROPN
ejpam-4975	187	6	,	,	PUNCT
ejpam-4975	187	7	p)∩f−1([f(a)]δ(λ	p)∩f−1([f(a)]δ(λ	NOUN
ejpam-4975	187	8	,	,	PUNCT
ejpam-4975	187	9	p	p	NOUN
ejpam-4975	187	10	)	)	PUNCT
ejpam-4975	187	11	)	)	PUNCT
ejpam-4975	187	12	=	=	PUNCT
ejpam-4975	187	13	∅.	∅.	PRON
ejpam-4975	187	14	this	this	PRON
ejpam-4975	187	15	implies	imply	VERB
ejpam-4975	187	16	that	that	SCONJ
ejpam-4975	187	17	u	u	PROPN
ejpam-4975	187	18	(	(	PUNCT
ejpam-4975	187	19	λ	λ	PROPN
ejpam-4975	187	20	,	,	PUNCT
ejpam-4975	187	21	p	p	NOUN
ejpam-4975	187	22	)	)	PUNCT
ejpam-4975	187	23	∩a	∩a	PROPN
ejpam-4975	187	24	=	=	PUNCT
ejpam-4975	187	25	∅.	∅.	VERB
ejpam-4975	187	26	thus	thus	ADV
ejpam-4975	187	27	,	,	PUNCT
ejpam-4975	187	28	x	x	PROPN
ejpam-4975	187	29	̸∈	̸∈	PROPN
ejpam-4975	187	30	aθ(λ	aθ(λ	NOUN
ejpam-4975	187	31	,	,	PUNCT
ejpam-4975	187	32	p	p	NOUN
ejpam-4975	187	33	)	)	PUNCT
ejpam-4975	187	34	and	and	CCONJ
ejpam-4975	187	35	hence	hence	ADV
ejpam-4975	187	36	f(aθ(λ	f(aθ(λ	PROPN
ejpam-4975	187	37	,	,	PUNCT
ejpam-4975	187	38	p	p	NOUN
ejpam-4975	187	39	)	)	PUNCT
ejpam-4975	187	40	)	)	PUNCT
ejpam-4975	187	41	⊆	⊆	NUM
ejpam-4975	188	1	[	[	X
ejpam-4975	188	2	f(a)]δ(λ	f(a)]δ(λ	NOUN
ejpam-4975	188	3	,	,	PUNCT
ejpam-4975	188	4	p	p	NOUN
ejpam-4975	188	5	)	)	PUNCT
ejpam-4975	188	6	.	.	PUNCT
ejpam-4975	189	1	(	(	PUNCT
ejpam-4975	189	2	7	7	X
ejpam-4975	189	3	)	)	PUNCT
ejpam-4975	189	4	⇒	⇒	NOUN
ejpam-4975	189	5	(	(	PUNCT
ejpam-4975	189	6	8)	8)	NUM
ejpam-4975	189	7	:	:	PUNCT
ejpam-4975	189	8	let	let	VERB
ejpam-4975	189	9	b	b	X
ejpam-4975	189	10	be	be	AUX
ejpam-4975	189	11	any	any	DET
ejpam-4975	189	12	subset	subset	NOUN
ejpam-4975	189	13	of	of	ADP
ejpam-4975	189	14	y	y	PROPN
ejpam-4975	189	15	.	.	PUNCT
ejpam-4975	190	1	then	then	ADV
ejpam-4975	190	2	,	,	PUNCT
ejpam-4975	190	3	by	by	ADP
ejpam-4975	190	4	(	(	PUNCT
ejpam-4975	190	5	7	7	X
ejpam-4975	190	6	)	)	PUNCT
ejpam-4975	190	7	we	we	PRON
ejpam-4975	190	8	have	have	VERB
ejpam-4975	190	9	f([f−1(b)]θ(λ	f([f−1(b)]θ(λ	PROPN
ejpam-4975	190	10	,	,	PUNCT
ejpam-4975	190	11	p	p	NOUN
ejpam-4975	190	12	)	)	PUNCT
ejpam-4975	190	13	)	)	PUNCT
ejpam-4975	191	1	⊆	⊆	NUM
ejpam-4975	191	2	bδ(λ	bδ(λ	NUM
ejpam-4975	191	3	,	,	PUNCT
ejpam-4975	191	4	p	p	NOUN
ejpam-4975	191	5	)	)	PUNCT
ejpam-4975	191	6	and	and	CCONJ
ejpam-4975	191	7	hence	hence	ADV
ejpam-4975	191	8	[	[	X
ejpam-4975	191	9	f−1(b)]θ(λ	f−1(b)]θ(λ	PROPN
ejpam-4975	191	10	,	,	PUNCT
ejpam-4975	191	11	p	p	NOUN
ejpam-4975	191	12	)	)	PUNCT
ejpam-4975	191	13	⊆	⊆	NUM
ejpam-4975	191	14	f−1(bδ(λ	f−1(bδ(λ	NOUN
ejpam-4975	191	15	,	,	PUNCT
ejpam-4975	191	16	p	p	NOUN
ejpam-4975	191	17	)	)	PUNCT
ejpam-4975	191	18	)	)	PUNCT
ejpam-4975	191	19	.	.	PUNCT
ejpam-4975	192	1	(	(	PUNCT
ejpam-4975	192	2	8)	8)	NUM
ejpam-4975	192	3	⇒	⇒	NOUN
ejpam-4975	192	4	(	(	PUNCT
ejpam-4975	192	5	9	9	NUM
ejpam-4975	192	6	):	):	PUNCT
ejpam-4975	192	7	let	let	VERB
ejpam-4975	192	8	b	b	X
ejpam-4975	192	9	be	be	AUX
ejpam-4975	192	10	any	any	DET
ejpam-4975	192	11	subset	subset	NOUN
ejpam-4975	192	12	of	of	ADP
ejpam-4975	192	13	y	y	PROPN
ejpam-4975	192	14	.	.	PUNCT
ejpam-4975	193	1	let	let	VERB
ejpam-4975	193	2	x	x	X
ejpam-4975	193	3	∈	∈	PROPN
ejpam-4975	193	4	f−1(bδ(λ	f−1(bδ(λ	NOUN
ejpam-4975	193	5	,	,	PUNCT
ejpam-4975	193	6	p	p	NOUN
ejpam-4975	193	7	)	)	PUNCT
ejpam-4975	193	8	)	)	PUNCT
ejpam-4975	193	9	.	.	PUNCT
ejpam-4975	194	1	then	then	ADV
ejpam-4975	194	2	,	,	PUNCT
ejpam-4975	194	3	f(x	f(x	PROPN
ejpam-4975	194	4	)	)	PUNCT
ejpam-4975	194	5	∈	∈	PROPN
ejpam-4975	194	6	bδ(λ	bδ(λ	NUM
ejpam-4975	194	7	,	,	PUNCT
ejpam-4975	194	8	p	p	NOUN
ejpam-4975	194	9	)	)	PUNCT
ejpam-4975	194	10	and	and	CCONJ
ejpam-4975	194	11	f(x	f(x	PROPN
ejpam-4975	194	12	)	)	PUNCT
ejpam-4975	195	1	̸∈	̸∈	PROPN
ejpam-4975	195	2	y	y	PROPN
ejpam-4975	195	3	−	−	PROPN
ejpam-4975	195	4	bδ(λ	bδ(λ	PROPN
ejpam-4975	195	5	,	,	PUNCT
ejpam-4975	195	6	p	p	NOUN
ejpam-4975	195	7	)	)	PUNCT
ejpam-4975	195	8	=	=	PUNCT
ejpam-4975	196	1	[	[	X
ejpam-4975	196	2	y	y	NOUN
ejpam-4975	196	3	−	−	PROPN
ejpam-4975	196	4	b]δ(λ	b]δ(λ	PROPN
ejpam-4975	196	5	,	,	PUNCT
ejpam-4975	196	6	p	p	NOUN
ejpam-4975	196	7	)	)	PUNCT
ejpam-4975	196	8	.	.	PUNCT
ejpam-4975	197	1	therefore	therefore	ADV
ejpam-4975	197	2	,	,	PUNCT
ejpam-4975	197	3	x	x	PROPN
ejpam-4975	197	4	̸∈	̸∈	PROPN
ejpam-4975	197	5	f−1([y	f−1([y	NOUN
ejpam-4975	197	6	−	−	ADP
ejpam-4975	197	7	b]δ(λ	b]δ(λ	NOUN
ejpam-4975	197	8	,	,	PUNCT
ejpam-4975	197	9	p	p	NOUN
ejpam-4975	197	10	)	)	PUNCT
ejpam-4975	197	11	)	)	PUNCT
ejpam-4975	197	12	.	.	PUNCT
ejpam-4975	198	1	by	by	ADP
ejpam-4975	198	2	(	(	PUNCT
ejpam-4975	198	3	8)	8)	NUM
ejpam-4975	198	4	,	,	PUNCT
ejpam-4975	198	5	x	x	PROPN
ejpam-4975	198	6	̸∈	̸∈	PROPN
ejpam-4975	198	7	[	[	X
ejpam-4975	198	8	f−1(y	f−1(y	PROPN
ejpam-4975	198	9	−b)]θ(λ	−b)]θ(λ	PROPN
ejpam-4975	198	10	,	,	PUNCT
ejpam-4975	198	11	p	p	NOUN
ejpam-4975	198	12	)	)	PUNCT
ejpam-4975	198	13	.	.	PUNCT
ejpam-4975	199	1	there	there	PRON
ejpam-4975	199	2	exists	exist	VERB
ejpam-4975	199	3	a	a	DET
ejpam-4975	199	4	(	(	PUNCT
ejpam-4975	199	5	λ	λ	NOUN
ejpam-4975	199	6	,	,	PUNCT
ejpam-4975	199	7	p)-open	p)-open	VERB
ejpam-4975	199	8	set	set	VERB
ejpam-4975	199	9	u	u	NOUN
ejpam-4975	199	10	of	of	ADP
ejpam-4975	199	11	x	x	PUNCT
ejpam-4975	199	12	containing	contain	VERB
ejpam-4975	199	13	x	x	PUNCT
ejpam-4975	199	14	such	such	ADJ
ejpam-4975	199	15	that	that	SCONJ
ejpam-4975	199	16	x	x	SYM
ejpam-4975	199	17	∈	∈	NOUN
ejpam-4975	199	18	u	u	NOUN
ejpam-4975	199	19	⊆	⊆	NUM
ejpam-4975	199	20	u	u	PROPN
ejpam-4975	199	21	(	(	PUNCT
ejpam-4975	199	22	λ	λ	PROPN
ejpam-4975	199	23	,	,	PUNCT
ejpam-4975	199	24	p	p	NOUN
ejpam-4975	199	25	)	)	PUNCT
ejpam-4975	199	26	⊆	⊆	NUM
ejpam-4975	199	27	f−1(b	f−1(b	PROPN
ejpam-4975	199	28	)	)	PUNCT
ejpam-4975	199	29	.	.	PUNCT
ejpam-4975	200	1	thus	thus	ADV
ejpam-4975	200	2	,	,	PUNCT
ejpam-4975	200	3	x	x	PUNCT
ejpam-4975	200	4	∈	∈	PROPN
ejpam-4975	200	5	[	[	X
ejpam-4975	200	6	f−1(b)]θ(λ	f−1(b)]θ(λ	PROPN
ejpam-4975	200	7	,	,	PUNCT
ejpam-4975	200	8	p	p	NOUN
ejpam-4975	200	9	)	)	PUNCT
ejpam-4975	200	10	and	and	CCONJ
ejpam-4975	200	11	hence	hence	ADV
ejpam-4975	200	12	f−1(bδ(λ	f−1(bδ(λ	ADJ
ejpam-4975	200	13	,	,	PUNCT
ejpam-4975	200	14	p	p	NOUN
ejpam-4975	200	15	)	)	PUNCT
ejpam-4975	200	16	)	)	PUNCT
ejpam-4975	201	1	⊆	⊆	NUM
ejpam-4975	201	2	[	[	X
ejpam-4975	201	3	f−1(b)]θ(λ	f−1(b)]θ(λ	NOUN
ejpam-4975	201	4	,	,	PUNCT
ejpam-4975	201	5	p	p	NOUN
ejpam-4975	201	6	)	)	PUNCT
ejpam-4975	201	7	.	.	PUNCT
ejpam-4975	202	1	(	(	PUNCT
ejpam-4975	202	2	9	9	X
ejpam-4975	202	3	)	)	PUNCT
ejpam-4975	202	4	⇒	⇒	NOUN
ejpam-4975	202	5	(	(	PUNCT
ejpam-4975	202	6	10	10	NUM
ejpam-4975	202	7	):	):	PUNCT
ejpam-4975	202	8	let	let	VERB
ejpam-4975	202	9	v	v	PART
ejpam-4975	202	10	be	be	AUX
ejpam-4975	202	11	any	any	DET
ejpam-4975	202	12	(	(	PUNCT
ejpam-4975	202	13	λ	λ	NOUN
ejpam-4975	202	14	,	,	PUNCT
ejpam-4975	202	15	p)-open	p)-open	VERB
ejpam-4975	202	16	set	set	VERB
ejpam-4975	202	17	of	of	ADP
ejpam-4975	202	18	y	y	PROPN
ejpam-4975	202	19	.	.	PUNCT
ejpam-4975	203	1	then	then	ADV
ejpam-4975	203	2	,	,	PUNCT
ejpam-4975	203	3	we	we	PRON
ejpam-4975	203	4	have	have	VERB
ejpam-4975	203	5	v	v	ADP
ejpam-4975	203	6	⊆	⊆	NUM
ejpam-4975	203	7	[	[	X
ejpam-4975	203	8	v	v	X
ejpam-4975	203	9	(	(	PUNCT
ejpam-4975	203	10	λ	λ	PROPN
ejpam-4975	203	11	,	,	PUNCT
ejpam-4975	203	12	p)](λ	p)](λ	ADJ
ejpam-4975	203	13	,	,	PUNCT
ejpam-4975	203	14	p	p	NOUN
ejpam-4975	203	15	)	)	PUNCT
ejpam-4975	203	16	⊆	⊆	NUM
ejpam-4975	204	1	[	[	X
ejpam-4975	204	2	v	v	ADP
ejpam-4975	204	3	s(λ	s(λ	PROPN
ejpam-4975	204	4	,	,	PUNCT
ejpam-4975	204	5	p)]δ(λ	p)]δ(λ	PROPN
ejpam-4975	204	6	,	,	PUNCT
ejpam-4975	204	7	p	p	NOUN
ejpam-4975	204	8	)	)	PUNCT
ejpam-4975	204	9	and	and	CCONJ
ejpam-4975	204	10	by	by	ADP
ejpam-4975	204	11	(	(	PUNCT
ejpam-4975	204	12	9	9	NUM
ejpam-4975	204	13	)	)	PUNCT
ejpam-4975	204	14	,	,	PUNCT
ejpam-4975	204	15	f−1(v	f−1(v	PROPN
ejpam-4975	204	16	)	)	PUNCT
ejpam-4975	204	17	⊆	⊆	NUM
ejpam-4975	204	18	f−1([v	f−1([v	NUM
ejpam-4975	204	19	s(λ	s(λ	NOUN
ejpam-4975	204	20	,	,	PUNCT
ejpam-4975	204	21	p)]δ(λ	p)]δ(λ	PROPN
ejpam-4975	204	22	,	,	PUNCT
ejpam-4975	204	23	p	p	NOUN
ejpam-4975	204	24	)	)	PUNCT
ejpam-4975	204	25	)	)	PUNCT
ejpam-4975	204	26	⊆	⊆	NUM
ejpam-4975	205	1	[	[	X
ejpam-4975	205	2	f−1(v	f−1(v	NOUN
ejpam-4975	205	3	s(λ	s(λ	PROPN
ejpam-4975	205	4	,	,	PUNCT
ejpam-4975	205	5	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	205	6	,	,	PUNCT
ejpam-4975	205	7	p	p	NOUN
ejpam-4975	205	8	)	)	PUNCT
ejpam-4975	205	9	.	.	PUNCT
ejpam-4975	206	1	(	(	PUNCT
ejpam-4975	206	2	10	10	NUM
ejpam-4975	206	3	)	)	PUNCT
ejpam-4975	206	4	⇒	⇒	NOUN
ejpam-4975	206	5	(	(	PUNCT
ejpam-4975	206	6	1	1	NUM
ejpam-4975	206	7	):	):	PUNCT
ejpam-4975	206	8	let	let	VERB
ejpam-4975	206	9	x	x	PUNCT
ejpam-4975	206	10	∈	∈	PROPN
ejpam-4975	206	11	x	x	X
ejpam-4975	206	12	and	and	CCONJ
ejpam-4975	206	13	v	v	AUX
ejpam-4975	206	14	be	be	AUX
ejpam-4975	206	15	any	any	DET
ejpam-4975	206	16	(	(	PUNCT
ejpam-4975	206	17	λ	λ	NOUN
ejpam-4975	206	18	,	,	PUNCT
ejpam-4975	206	19	p)-open	p)-open	VERB
ejpam-4975	206	20	set	set	VERB
ejpam-4975	206	21	of	of	ADP
ejpam-4975	206	22	y	y	PROPN
ejpam-4975	206	23	containing	contain	VERB
ejpam-4975	206	24	f(x	f(x	PROPN
ejpam-4975	206	25	)	)	PUNCT
ejpam-4975	206	26	.	.	PUNCT
ejpam-4975	207	1	then	then	ADV
ejpam-4975	207	2	,	,	PUNCT
ejpam-4975	207	3	x	x	PROPN
ejpam-4975	207	4	∈	∈	PROPN
ejpam-4975	207	5	f−1(v	f−1(v	NOUN
ejpam-4975	207	6	)	)	PUNCT
ejpam-4975	208	1	⊆	⊆	NUM
ejpam-4975	208	2	[	[	X
ejpam-4975	208	3	f−1(v	f−1(v	NOUN
ejpam-4975	208	4	s(λ	s(λ	PROPN
ejpam-4975	208	5	,	,	PUNCT
ejpam-4975	208	6	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	208	7	,	,	PUNCT
ejpam-4975	208	8	p	p	NOUN
ejpam-4975	208	9	)	)	PUNCT
ejpam-4975	208	10	.	.	PUNCT
ejpam-4975	209	1	then	then	ADV
ejpam-4975	209	2	,	,	PUNCT
ejpam-4975	209	3	there	there	PRON
ejpam-4975	209	4	exists	exist	VERB
ejpam-4975	209	5	a	a	DET
ejpam-4975	209	6	(	(	PUNCT
ejpam-4975	209	7	λ	λ	NOUN
ejpam-4975	209	8	,	,	PUNCT
ejpam-4975	209	9	p)-open	p)-open	VERB
ejpam-4975	209	10	set	set	VERB
ejpam-4975	209	11	u	u	NOUN
ejpam-4975	209	12	of	of	ADP
ejpam-4975	209	13	x	x	PUNCT
ejpam-4975	209	14	containing	contain	VERB
ejpam-4975	209	15	x	x	PUNCT
ejpam-4975	209	16	such	such	ADJ
ejpam-4975	209	17	that	that	SCONJ
ejpam-4975	209	18	x	x	SYM
ejpam-4975	209	19	∈	∈	NOUN
ejpam-4975	209	20	u	u	NOUN
ejpam-4975	209	21	⊆	⊆	NUM
ejpam-4975	209	22	u	u	PROPN
ejpam-4975	209	23	(	(	PUNCT
ejpam-4975	209	24	λ	λ	PROPN
ejpam-4975	209	25	,	,	PUNCT
ejpam-4975	209	26	p	p	NOUN
ejpam-4975	209	27	)	)	PUNCT
ejpam-4975	209	28	⊆	⊆	NUM
ejpam-4975	209	29	f−1(v	f−1(v	PROPN
ejpam-4975	209	30	s(λ	s(λ	PROPN
ejpam-4975	209	31	,	,	PUNCT
ejpam-4975	209	32	p	p	NOUN
ejpam-4975	209	33	)	)	PUNCT
ejpam-4975	209	34	)	)	PUNCT
ejpam-4975	209	35	which	which	PRON
ejpam-4975	209	36	implies	imply	VERB
ejpam-4975	209	37	that	that	SCONJ
ejpam-4975	209	38	f(u	f(u	PROPN
ejpam-4975	209	39	(	(	PUNCT
ejpam-4975	209	40	λ	λ	PROPN
ejpam-4975	209	41	,	,	PUNCT
ejpam-4975	209	42	p	p	NOUN
ejpam-4975	209	43	)	)	PUNCT
ejpam-4975	209	44	)	)	PUNCT
ejpam-4975	210	1	⊆	⊆	NUM
ejpam-4975	210	2	v	v	ADP
ejpam-4975	210	3	s(λ	s(λ	PROPN
ejpam-4975	210	4	,	,	PUNCT
ejpam-4975	210	5	p	p	NOUN
ejpam-4975	210	6	)	)	PUNCT
ejpam-4975	210	7	.	.	PUNCT
ejpam-4975	211	1	thus	thus	ADV
ejpam-4975	211	2	,	,	PUNCT
ejpam-4975	211	3	f	f	PROPN
ejpam-4975	211	4	is	be	AUX
ejpam-4975	211	5	almost	almost	ADV
ejpam-4975	211	6	strongly	strongly	ADV
ejpam-4975	211	7	θ(λ	θ(λ	VERB
ejpam-4975	211	8	,	,	PUNCT
ejpam-4975	211	9	p)-continuous	p)-continuous	ADJ
ejpam-4975	211	10	.	.	PUNCT
ejpam-4975	212	1	theorem	theorem	NOUN
ejpam-4975	212	2	2	2	NUM
ejpam-4975	212	3	.	.	X
ejpam-4975	212	4	for	for	ADP
ejpam-4975	212	5	a	a	DET
ejpam-4975	212	6	function	function	NOUN
ejpam-4975	212	7	f	f	NOUN
ejpam-4975	212	8	:	:	PUNCT
ejpam-4975	212	9	(	(	PUNCT
ejpam-4975	212	10	x	x	X
ejpam-4975	212	11	,	,	PUNCT
ejpam-4975	212	12	τ	τ	X
ejpam-4975	212	13	)	)	PUNCT
ejpam-4975	212	14	→	→	SYM
ejpam-4975	212	15	(	(	PUNCT
ejpam-4975	212	16	y	y	PROPN
ejpam-4975	212	17	,	,	PUNCT
ejpam-4975	212	18	σ	σ	PROPN
ejpam-4975	212	19	)	)	PUNCT
ejpam-4975	212	20	,	,	PUNCT
ejpam-4975	212	21	the	the	DET
ejpam-4975	212	22	following	follow	VERB
ejpam-4975	212	23	properties	property	NOUN
ejpam-4975	212	24	are	be	AUX
ejpam-4975	212	25	equivalent	equivalent	ADJ
ejpam-4975	212	26	:	:	PUNCT
ejpam-4975	212	27	(	(	PUNCT
ejpam-4975	212	28	1	1	X
ejpam-4975	212	29	)	)	PUNCT
ejpam-4975	212	30	f	f	NOUN
ejpam-4975	212	31	is	be	AUX
ejpam-4975	212	32	almost	almost	ADV
ejpam-4975	212	33	strongly	strongly	ADV
ejpam-4975	212	34	θ(λ	θ(λ	VERB
ejpam-4975	212	35	,	,	PUNCT
ejpam-4975	212	36	p)-continuous	p)-continuous	ADJ
ejpam-4975	212	37	;	;	PUNCT
ejpam-4975	212	38	(	(	PUNCT
ejpam-4975	212	39	2	2	X
ejpam-4975	212	40	)	)	PUNCT
ejpam-4975	212	41	[	[	X
ejpam-4975	212	42	f−1([k(λ	f−1([k(λ	NOUN
ejpam-4975	212	43	,	,	PUNCT
ejpam-4975	212	44	p	p	NOUN
ejpam-4975	212	45	)	)	PUNCT
ejpam-4975	212	46	]	]	PUNCT
ejpam-4975	212	47	(	(	PUNCT
ejpam-4975	212	48	λ	λ	INTJ
ejpam-4975	212	49	,	,	PUNCT
ejpam-4975	212	50	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	212	51	,	,	PUNCT
ejpam-4975	212	52	p	p	NOUN
ejpam-4975	212	53	)	)	PUNCT
ejpam-4975	212	54	⊆	⊆	NUM
ejpam-4975	212	55	f−1(k	f−1(k	PROPN
ejpam-4975	212	56	)	)	PUNCT
ejpam-4975	212	57	for	for	SCONJ
ejpam-4975	212	58	every	every	DET
ejpam-4975	212	59	(	(	PUNCT
ejpam-4975	212	60	λ	λ	PROPN
ejpam-4975	212	61	,	,	PUNCT
ejpam-4975	212	62	p)-closed	p)-close	VERB
ejpam-4975	212	63	set	set	NOUN
ejpam-4975	212	64	k	k	PROPN
ejpam-4975	212	65	of	of	ADP
ejpam-4975	212	66	y	y	PROPN
ejpam-4975	212	67	;	;	PUNCT
ejpam-4975	212	68	(	(	PUNCT
ejpam-4975	212	69	3	3	X
ejpam-4975	212	70	)	)	PUNCT
ejpam-4975	213	1	[	[	X
ejpam-4975	213	2	f−1([[b(λ	f−1([[b(λ	X
ejpam-4975	213	3	,	,	PUNCT
ejpam-4975	213	4	p)](λ	p)](λ	ADJ
ejpam-4975	213	5	,	,	PUNCT
ejpam-4975	213	6	p	p	NOUN
ejpam-4975	213	7	)	)	PUNCT
ejpam-4975	213	8	]	]	PUNCT
ejpam-4975	213	9	(	(	PUNCT
ejpam-4975	213	10	λ	λ	INTJ
ejpam-4975	213	11	,	,	PUNCT
ejpam-4975	213	12	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	213	13	,	,	PUNCT
ejpam-4975	213	14	p	p	NOUN
ejpam-4975	213	15	)	)	PUNCT
ejpam-4975	213	16	⊆	⊆	NUM
ejpam-4975	213	17	f−1(b(λ	f−1(b(λ	PROPN
ejpam-4975	213	18	,	,	PUNCT
ejpam-4975	213	19	p	p	NOUN
ejpam-4975	213	20	)	)	PUNCT
ejpam-4975	213	21	)	)	PUNCT
ejpam-4975	213	22	for	for	ADP
ejpam-4975	213	23	every	every	DET
ejpam-4975	213	24	subset	subset	NOUN
ejpam-4975	213	25	b	b	PROPN
ejpam-4975	213	26	of	of	ADP
ejpam-4975	213	27	y	y	PROPN
ejpam-4975	213	28	;	;	PUNCT
ejpam-4975	213	29	(	(	PUNCT
ejpam-4975	213	30	4	4	X
ejpam-4975	213	31	)	)	PUNCT
ejpam-4975	213	32	f−1(b(λ	f−1(b(λ	PROPN
ejpam-4975	213	33	,	,	PUNCT
ejpam-4975	213	34	p	p	NOUN
ejpam-4975	213	35	)	)	PUNCT
ejpam-4975	213	36	)	)	PUNCT
ejpam-4975	214	1	⊆	⊆	NUM
ejpam-4975	214	2	[	[	X
ejpam-4975	214	3	f−1([[b(λ	f−1([[b(λ	PROPN
ejpam-4975	214	4	,	,	PUNCT
ejpam-4975	214	5	p	p	NOUN
ejpam-4975	214	6	)	)	PUNCT
ejpam-4975	214	7	]	]	PUNCT
ejpam-4975	214	8	(	(	PUNCT
ejpam-4975	214	9	λ	λ	X
ejpam-4975	214	10	,	,	PUNCT
ejpam-4975	214	11	p)](λ	p)](λ	ADJ
ejpam-4975	214	12	,	,	PUNCT
ejpam-4975	214	13	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	214	14	,	,	PUNCT
ejpam-4975	214	15	p	p	NOUN
ejpam-4975	214	16	)	)	PUNCT
ejpam-4975	214	17	for	for	ADP
ejpam-4975	214	18	every	every	DET
ejpam-4975	214	19	subset	subset	NOUN
ejpam-4975	214	20	b	b	PROPN
ejpam-4975	214	21	of	of	ADP
ejpam-4975	214	22	y	y	PROPN
ejpam-4975	214	23	.	.	PUNCT
ejpam-4975	215	1	proof	proof	NOUN
ejpam-4975	215	2	.	.	PUNCT
ejpam-4975	216	1	(	(	PUNCT
ejpam-4975	216	2	1	1	X
ejpam-4975	216	3	)	)	PUNCT
ejpam-4975	216	4	⇒	⇒	NOUN
ejpam-4975	216	5	(	(	PUNCT
ejpam-4975	216	6	2	2	NUM
ejpam-4975	216	7	):	):	PUNCT
ejpam-4975	216	8	let	let	VERB
ejpam-4975	216	9	k	k	PRON
ejpam-4975	216	10	be	be	AUX
ejpam-4975	216	11	any	any	DET
ejpam-4975	216	12	(	(	PUNCT
ejpam-4975	216	13	λ	λ	PROPN
ejpam-4975	216	14	,	,	PUNCT
ejpam-4975	216	15	p)-closed	p)-close	VERB
ejpam-4975	216	16	set	set	NOUN
ejpam-4975	216	17	of	of	ADP
ejpam-4975	216	18	y	y	PROPN
ejpam-4975	216	19	.	.	PUNCT
ejpam-4975	217	1	then	then	ADV
ejpam-4975	217	2	,	,	PUNCT
ejpam-4975	217	3	y	y	PROPN
ejpam-4975	217	4	−k	−k	PROPN
ejpam-4975	217	5	is	be	AUX
ejpam-4975	217	6	(	(	PUNCT
ejpam-4975	217	7	λ	λ	X
ejpam-4975	217	8	,	,	PUNCT
ejpam-4975	217	9	p)-open	p)-open	VERB
ejpam-4975	217	10	in	in	ADP
ejpam-4975	217	11	y	y	PROPN
ejpam-4975	217	12	.	.	PUNCT
ejpam-4975	218	1	thus	thus	ADV
ejpam-4975	218	2	,	,	PUNCT
ejpam-4975	218	3	by	by	ADP
ejpam-4975	218	4	theorem	theorem	NOUN
ejpam-4975	218	5	1	1	NUM
ejpam-4975	218	6	and	and	CCONJ
ejpam-4975	218	7	lemma	lemma	PROPN
ejpam-4975	218	8	1	1	NUM
ejpam-4975	218	9	,	,	PUNCT
ejpam-4975	218	10	we	we	PRON
ejpam-4975	218	11	have	have	VERB
ejpam-4975	218	12	x	x	X
ejpam-4975	218	13	−	−	PROPN
ejpam-4975	218	14	f−1(k	f−1(k	PROPN
ejpam-4975	218	15	)	)	PUNCT
ejpam-4975	219	1	=	=	SYM
ejpam-4975	219	2	f−1(y	f−1(y	PROPN
ejpam-4975	219	3	−k	−k	PROPN
ejpam-4975	219	4	)	)	PUNCT
ejpam-4975	219	5	⊆	⊆	NUM
ejpam-4975	220	1	[	[	X
ejpam-4975	220	2	f−1([[y	f−1([[y	NOUN
ejpam-4975	220	3	−k](λ	−k](λ	NUM
ejpam-4975	220	4	,	,	PUNCT
ejpam-4975	220	5	p)](λ	p)](λ	ADJ
ejpam-4975	220	6	,	,	PUNCT
ejpam-4975	220	7	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	220	8	,	,	PUNCT
ejpam-4975	220	9	p	p	NOUN
ejpam-4975	220	10	)	)	PUNCT
ejpam-4975	220	11	c.	c.	PROPN
ejpam-4975	220	12	boonpok	boonpok	PROPN
ejpam-4975	220	13	,	,	PUNCT
ejpam-4975	220	14	j.	j.	PROPN
ejpam-4975	220	15	khampakdee	khampakdee	PROPN
ejpam-4975	220	16	/	/	PUNCT
ejpam-4975	220	17	eur	eur	PROPN
ejpam-4975	220	18	.	.	PUNCT
ejpam-4975	221	1	j.	j.	PROPN
ejpam-4975	221	2	pure	pure	PROPN
ejpam-4975	221	3	appl	appl	PROPN
ejpam-4975	221	4	.	.	PROPN
ejpam-4975	221	5	math	math	PROPN
ejpam-4975	221	6	,	,	PUNCT
ejpam-4975	221	7	17	17	NUM
ejpam-4975	221	8	(	(	PUNCT
ejpam-4975	221	9	1	1	NUM
ejpam-4975	221	10	)	)	PUNCT
ejpam-4975	221	11	(	(	PUNCT
ejpam-4975	221	12	2024	2024	NUM
ejpam-4975	221	13	)	)	PUNCT
ejpam-4975	221	14	,	,	PUNCT
ejpam-4975	221	15	300	300	NUM
ejpam-4975	221	16	-	-	SYM
ejpam-4975	221	17	309	309	NUM
ejpam-4975	221	18	305	305	NUM
ejpam-4975	221	19	=	=	SYM
ejpam-4975	222	1	[	[	X
ejpam-4975	222	2	x	x	X
ejpam-4975	222	3	−	−	NOUN
ejpam-4975	222	4	f−1([k(λ	f−1([k(λ	NOUN
ejpam-4975	222	5	,	,	PUNCT
ejpam-4975	222	6	p	p	NOUN
ejpam-4975	222	7	)	)	PUNCT
ejpam-4975	222	8	]	]	PUNCT
ejpam-4975	222	9	(	(	PUNCT
ejpam-4975	222	10	λ	λ	INTJ
ejpam-4975	222	11	,	,	PUNCT
ejpam-4975	222	12	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	222	13	,	,	PUNCT
ejpam-4975	222	14	p	p	NOUN
ejpam-4975	222	15	)	)	PUNCT
ejpam-4975	222	16	=	=	PUNCT
ejpam-4975	223	1	x	x	X
ejpam-4975	223	2	−	−	PROPN
ejpam-4975	224	1	[	[	X
ejpam-4975	224	2	f−1([k(λ	f−1([k(λ	NOUN
ejpam-4975	224	3	,	,	PUNCT
ejpam-4975	224	4	p	p	NOUN
ejpam-4975	224	5	)	)	PUNCT
ejpam-4975	224	6	]	]	PUNCT
ejpam-4975	224	7	(	(	PUNCT
ejpam-4975	224	8	λ	λ	INTJ
ejpam-4975	224	9	,	,	PUNCT
ejpam-4975	224	10	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	224	11	,	,	PUNCT
ejpam-4975	224	12	p	p	NOUN
ejpam-4975	224	13	)	)	PUNCT
ejpam-4975	224	14	and	and	CCONJ
ejpam-4975	224	15	hence	hence	ADV
ejpam-4975	224	16	[	[	X
ejpam-4975	224	17	f−1([k(λ	f−1([k(λ	NOUN
ejpam-4975	224	18	,	,	PUNCT
ejpam-4975	224	19	p	p	NOUN
ejpam-4975	224	20	)	)	PUNCT
ejpam-4975	224	21	]	]	PUNCT
ejpam-4975	224	22	(	(	PUNCT
ejpam-4975	224	23	λ	λ	INTJ
ejpam-4975	224	24	,	,	PUNCT
ejpam-4975	224	25	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	224	26	,	,	PUNCT
ejpam-4975	224	27	p	p	NOUN
ejpam-4975	224	28	)	)	PUNCT
ejpam-4975	224	29	⊆	⊆	NUM
ejpam-4975	224	30	f−1(k	f−1(k	PROPN
ejpam-4975	224	31	)	)	PUNCT
ejpam-4975	224	32	.	.	PUNCT
ejpam-4975	225	1	(	(	PUNCT
ejpam-4975	225	2	2	2	X
ejpam-4975	225	3	)	)	PUNCT
ejpam-4975	225	4	⇒	⇒	NOUN
ejpam-4975	225	5	(	(	PUNCT
ejpam-4975	225	6	3	3	NUM
ejpam-4975	225	7	):	):	PUNCT
ejpam-4975	225	8	let	let	VERB
ejpam-4975	225	9	b	b	X
ejpam-4975	225	10	be	be	AUX
ejpam-4975	225	11	any	any	DET
ejpam-4975	225	12	subset	subset	NOUN
ejpam-4975	225	13	of	of	ADP
ejpam-4975	225	14	y	y	PROPN
ejpam-4975	225	15	.	.	PUNCT
ejpam-4975	226	1	then	then	ADV
ejpam-4975	226	2	,	,	PUNCT
ejpam-4975	226	3	b(λ	b(λ	PROPN
ejpam-4975	226	4	,	,	PUNCT
ejpam-4975	226	5	p	p	NOUN
ejpam-4975	226	6	)	)	PUNCT
ejpam-4975	226	7	is	be	AUX
ejpam-4975	226	8	(	(	PUNCT
ejpam-4975	226	9	λ	λ	X
ejpam-4975	226	10	,	,	PUNCT
ejpam-4975	226	11	p)-closed	p)-close	VERB
ejpam-4975	226	12	in	in	ADP
ejpam-4975	226	13	y	y	PROPN
ejpam-4975	226	14	and	and	CCONJ
ejpam-4975	226	15	by	by	ADP
ejpam-4975	226	16	(	(	PUNCT
ejpam-4975	226	17	2	2	NUM
ejpam-4975	226	18	)	)	PUNCT
ejpam-4975	226	19	,	,	PUNCT
ejpam-4975	227	1	[	[	X
ejpam-4975	227	2	f−1([[b(λ	f−1([[b(λ	X
ejpam-4975	227	3	,	,	PUNCT
ejpam-4975	227	4	p)](λ	p)](λ	ADJ
ejpam-4975	227	5	,	,	PUNCT
ejpam-4975	227	6	p	p	NOUN
ejpam-4975	227	7	)	)	PUNCT
ejpam-4975	227	8	]	]	PUNCT
ejpam-4975	227	9	(	(	PUNCT
ejpam-4975	227	10	λ	λ	INTJ
ejpam-4975	227	11	,	,	PUNCT
ejpam-4975	227	12	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	227	13	,	,	PUNCT
ejpam-4975	227	14	p	p	NOUN
ejpam-4975	227	15	)	)	PUNCT
ejpam-4975	227	16	⊆	⊆	NUM
ejpam-4975	227	17	f−1(b(λ	f−1(b(λ	PROPN
ejpam-4975	227	18	,	,	PUNCT
ejpam-4975	227	19	p	p	NOUN
ejpam-4975	227	20	)	)	PUNCT
ejpam-4975	227	21	)	)	PUNCT
ejpam-4975	227	22	.	.	PUNCT
ejpam-4975	228	1	(	(	PUNCT
ejpam-4975	228	2	3	3	X
ejpam-4975	228	3	)	)	PUNCT
ejpam-4975	228	4	⇒	⇒	NOUN
ejpam-4975	228	5	(	(	PUNCT
ejpam-4975	228	6	4	4	NUM
ejpam-4975	228	7	):	):	PUNCT
ejpam-4975	228	8	let	let	VERB
ejpam-4975	228	9	b	b	X
ejpam-4975	228	10	be	be	AUX
ejpam-4975	228	11	any	any	DET
ejpam-4975	228	12	subset	subset	NOUN
ejpam-4975	228	13	of	of	ADP
ejpam-4975	228	14	y	y	PROPN
ejpam-4975	228	15	.	.	PUNCT
ejpam-4975	229	1	then	then	ADV
ejpam-4975	229	2	,	,	PUNCT
ejpam-4975	229	3	we	we	PRON
ejpam-4975	229	4	have	have	VERB
ejpam-4975	229	5	f−1(b(λ	f−1(b(λ	PROPN
ejpam-4975	229	6	,	,	PUNCT
ejpam-4975	229	7	p	p	NOUN
ejpam-4975	229	8	)	)	PUNCT
ejpam-4975	229	9	)	)	PUNCT
ejpam-4975	230	1	=	=	PUNCT
ejpam-4975	230	2	x	x	X
ejpam-4975	231	1	−	−	NOUN
ejpam-4975	231	2	f−1([y	f−1([y	NOUN
ejpam-4975	231	3	−b](λ	−b](λ	NOUN
ejpam-4975	231	4	,	,	PUNCT
ejpam-4975	231	5	p	p	NOUN
ejpam-4975	231	6	)	)	PUNCT
ejpam-4975	231	7	)	)	PUNCT
ejpam-4975	232	1	⊆	⊆	NUM
ejpam-4975	232	2	x	x	SYM
ejpam-4975	232	3	−	−	PROPN
ejpam-4975	233	1	[	[	X
ejpam-4975	233	2	f−1([[[y	f−1([[[y	NOUN
ejpam-4975	233	3	−b](λ	−b](λ	PROPN
ejpam-4975	233	4	,	,	PUNCT
ejpam-4975	233	5	p)](λ	p)](λ	NOUN
ejpam-4975	233	6	,	,	PUNCT
ejpam-4975	233	7	p	p	NOUN
ejpam-4975	233	8	)	)	PUNCT
ejpam-4975	233	9	]	]	PUNCT
ejpam-4975	233	10	(	(	PUNCT
ejpam-4975	233	11	λ	λ	INTJ
ejpam-4975	233	12	,	,	PUNCT
ejpam-4975	233	13	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	233	14	,	,	PUNCT
ejpam-4975	233	15	p	p	NOUN
ejpam-4975	233	16	)	)	PUNCT
ejpam-4975	234	1	=	=	PUNCT
ejpam-4975	235	1	[	[	X
ejpam-4975	235	2	f−1([[b(λ	f−1([[b(λ	X
ejpam-4975	235	3	,	,	PUNCT
ejpam-4975	235	4	p	p	NOUN
ejpam-4975	235	5	)	)	PUNCT
ejpam-4975	235	6	]	]	PUNCT
ejpam-4975	235	7	(	(	PUNCT
ejpam-4975	235	8	λ	λ	X
ejpam-4975	235	9	,	,	PUNCT
ejpam-4975	235	10	p)](λ	p)](λ	ADJ
ejpam-4975	235	11	,	,	PUNCT
ejpam-4975	235	12	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	235	13	,	,	PUNCT
ejpam-4975	235	14	p	p	NOUN
ejpam-4975	235	15	)	)	PUNCT
ejpam-4975	235	16	and	and	CCONJ
ejpam-4975	235	17	hence	hence	ADV
ejpam-4975	235	18	f−1(b(λ	f−1(b(λ	PROPN
ejpam-4975	235	19	,	,	PUNCT
ejpam-4975	235	20	p	p	NOUN
ejpam-4975	235	21	)	)	PUNCT
ejpam-4975	235	22	)	)	PUNCT
ejpam-4975	236	1	⊆	⊆	NUM
ejpam-4975	236	2	[	[	X
ejpam-4975	236	3	f−1([[b(λ	f−1([[b(λ	PROPN
ejpam-4975	236	4	,	,	PUNCT
ejpam-4975	236	5	p	p	NOUN
ejpam-4975	236	6	)	)	PUNCT
ejpam-4975	236	7	]	]	PUNCT
ejpam-4975	236	8	(	(	PUNCT
ejpam-4975	236	9	λ	λ	X
ejpam-4975	236	10	,	,	PUNCT
ejpam-4975	236	11	p)](λ	p)](λ	ADJ
ejpam-4975	236	12	,	,	PUNCT
ejpam-4975	236	13	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	236	14	,	,	PUNCT
ejpam-4975	236	15	p	p	NOUN
ejpam-4975	236	16	)	)	PUNCT
ejpam-4975	236	17	.	.	PUNCT
ejpam-4975	237	1	(	(	PUNCT
ejpam-4975	237	2	4	4	X
ejpam-4975	237	3	)	)	PUNCT
ejpam-4975	237	4	⇒	⇒	NOUN
ejpam-4975	237	5	(	(	PUNCT
ejpam-4975	237	6	1	1	NUM
ejpam-4975	237	7	):	):	PUNCT
ejpam-4975	237	8	let	let	VERB
ejpam-4975	237	9	v	v	PART
ejpam-4975	237	10	be	be	AUX
ejpam-4975	237	11	any	any	DET
ejpam-4975	237	12	r(λ	r(λ	NOUN
ejpam-4975	237	13	,	,	PUNCT
ejpam-4975	237	14	p)-open	p)-open	VERB
ejpam-4975	237	15	set	set	NOUN
ejpam-4975	237	16	of	of	ADP
ejpam-4975	237	17	y	y	PROPN
ejpam-4975	237	18	.	.	PUNCT
ejpam-4975	238	1	by	by	ADP
ejpam-4975	238	2	(	(	PUNCT
ejpam-4975	238	3	4	4	NUM
ejpam-4975	238	4	)	)	PUNCT
ejpam-4975	238	5	,	,	PUNCT
ejpam-4975	238	6	f−1(v	f−1(v	NOUN
ejpam-4975	238	7	)	)	PUNCT
ejpam-4975	238	8	⊆	⊆	NUM
ejpam-4975	238	9	[	[	X
ejpam-4975	238	10	f−1(v	f−1(v	NOUN
ejpam-4975	238	11	)	)	PUNCT
ejpam-4975	238	12	]	]	X
ejpam-4975	238	13	θ(λ	θ(λ	PROPN
ejpam-4975	238	14	,	,	PUNCT
ejpam-4975	238	15	p	p	NOUN
ejpam-4975	238	16	)	)	PUNCT
ejpam-4975	238	17	and	and	CCONJ
ejpam-4975	238	18	hence	hence	ADV
ejpam-4975	238	19	f−1(v	f−1(v	NOUN
ejpam-4975	238	20	)	)	PUNCT
ejpam-4975	238	21	=	=	PUNCT
ejpam-4975	239	1	[	[	X
ejpam-4975	239	2	f−1(v	f−1(v	NOUN
ejpam-4975	239	3	)	)	PUNCT
ejpam-4975	239	4	]	]	X
ejpam-4975	240	1	θ(λ	θ(λ	PROPN
ejpam-4975	240	2	,	,	PUNCT
ejpam-4975	240	3	p	p	NOUN
ejpam-4975	240	4	)	)	PUNCT
ejpam-4975	240	5	.	.	PUNCT
ejpam-4975	241	1	thus	thus	ADV
ejpam-4975	241	2	,	,	PUNCT
ejpam-4975	241	3	f−1(v	f−1(v	PROPN
ejpam-4975	241	4	)	)	PUNCT
ejpam-4975	241	5	is	be	AUX
ejpam-4975	241	6	θ(λ	θ(λ	PROPN
ejpam-4975	241	7	,	,	PUNCT
ejpam-4975	241	8	p)-open	p)-open	ADJ
ejpam-4975	241	9	and	and	CCONJ
ejpam-4975	241	10	by	by	ADP
ejpam-4975	241	11	theorem	theorem	NOUN
ejpam-4975	241	12	1	1	NUM
ejpam-4975	241	13	,	,	PUNCT
ejpam-4975	241	14	f	f	PROPN
ejpam-4975	241	15	is	be	AUX
ejpam-4975	241	16	almost	almost	ADV
ejpam-4975	241	17	strongly	strongly	ADV
ejpam-4975	241	18	θ(λ	θ(λ	VERB
ejpam-4975	241	19	,	,	PUNCT
ejpam-4975	241	20	p)-continuous	p)-continuous	ADJ
ejpam-4975	241	21	.	.	PUNCT
ejpam-4975	242	1	theorem	theorem	NOUN
ejpam-4975	242	2	3	3	NUM
ejpam-4975	242	3	.	.	X
ejpam-4975	242	4	for	for	ADP
ejpam-4975	242	5	a	a	DET
ejpam-4975	242	6	function	function	NOUN
ejpam-4975	242	7	f	f	NOUN
ejpam-4975	242	8	:	:	PUNCT
ejpam-4975	242	9	(	(	PUNCT
ejpam-4975	242	10	x	x	X
ejpam-4975	242	11	,	,	PUNCT
ejpam-4975	242	12	τ	τ	X
ejpam-4975	242	13	)	)	PUNCT
ejpam-4975	242	14	→	→	SYM
ejpam-4975	242	15	(	(	PUNCT
ejpam-4975	242	16	y	y	PROPN
ejpam-4975	242	17	,	,	PUNCT
ejpam-4975	242	18	σ	σ	PROPN
ejpam-4975	242	19	)	)	PUNCT
ejpam-4975	242	20	,	,	PUNCT
ejpam-4975	242	21	the	the	DET
ejpam-4975	242	22	following	follow	VERB
ejpam-4975	242	23	properties	property	NOUN
ejpam-4975	242	24	are	be	AUX
ejpam-4975	242	25	equivalent	equivalent	ADJ
ejpam-4975	242	26	:	:	PUNCT
ejpam-4975	242	27	(	(	PUNCT
ejpam-4975	242	28	1	1	X
ejpam-4975	242	29	)	)	PUNCT
ejpam-4975	242	30	f	f	NOUN
ejpam-4975	242	31	is	be	AUX
ejpam-4975	242	32	almost	almost	ADV
ejpam-4975	242	33	strongly	strongly	ADV
ejpam-4975	242	34	θ(λ	θ(λ	VERB
ejpam-4975	242	35	,	,	PUNCT
ejpam-4975	242	36	p)-continuous	p)-continuous	ADJ
ejpam-4975	242	37	;	;	PUNCT
ejpam-4975	242	38	(	(	PUNCT
ejpam-4975	242	39	2	2	X
ejpam-4975	242	40	)	)	PUNCT
ejpam-4975	243	1	[	[	X
ejpam-4975	243	2	f−1(v	f−1(v	NOUN
ejpam-4975	243	3	)	)	PUNCT
ejpam-4975	243	4	]	]	X
ejpam-4975	244	1	θ(λ	θ(λ	PROPN
ejpam-4975	244	2	,	,	PUNCT
ejpam-4975	244	3	p	p	NOUN
ejpam-4975	244	4	)	)	PUNCT
ejpam-4975	244	5	⊆	⊆	NUM
ejpam-4975	244	6	f−1(v	f−1(v	NOUN
ejpam-4975	244	7	(	(	PUNCT
ejpam-4975	244	8	λ	λ	PROPN
ejpam-4975	244	9	,	,	PUNCT
ejpam-4975	244	10	p	p	NOUN
ejpam-4975	244	11	)	)	PUNCT
ejpam-4975	244	12	)	)	PUNCT
ejpam-4975	244	13	for	for	ADP
ejpam-4975	244	14	every	every	DET
ejpam-4975	244	15	β(λ	β(λ	NOUN
ejpam-4975	244	16	,	,	PUNCT
ejpam-4975	244	17	p)-open	p)-open	VERB
ejpam-4975	244	18	set	set	VERB
ejpam-4975	244	19	v	v	NOUN
ejpam-4975	244	20	of	of	ADP
ejpam-4975	244	21	y	y	PROPN
ejpam-4975	244	22	;	;	PUNCT
ejpam-4975	244	23	(	(	PUNCT
ejpam-4975	244	24	3	3	X
ejpam-4975	244	25	)	)	PUNCT
ejpam-4975	245	1	[	[	X
ejpam-4975	245	2	f−1(v	f−1(v	NOUN
ejpam-4975	245	3	)	)	PUNCT
ejpam-4975	245	4	]	]	X
ejpam-4975	246	1	θ(λ	θ(λ	PROPN
ejpam-4975	246	2	,	,	PUNCT
ejpam-4975	246	3	p	p	NOUN
ejpam-4975	246	4	)	)	PUNCT
ejpam-4975	246	5	⊆	⊆	NUM
ejpam-4975	246	6	f−1(v	f−1(v	NOUN
ejpam-4975	246	7	(	(	PUNCT
ejpam-4975	246	8	λ	λ	PROPN
ejpam-4975	246	9	,	,	PUNCT
ejpam-4975	246	10	p	p	NOUN
ejpam-4975	246	11	)	)	PUNCT
ejpam-4975	246	12	)	)	PUNCT
ejpam-4975	246	13	for	for	ADP
ejpam-4975	246	14	every	every	DET
ejpam-4975	246	15	s(λ	s(λ	PROPN
ejpam-4975	246	16	,	,	PUNCT
ejpam-4975	246	17	p)-open	p)-open	AUX
ejpam-4975	246	18	set	set	VERB
ejpam-4975	246	19	v	v	NOUN
ejpam-4975	246	20	of	of	ADP
ejpam-4975	246	21	y	y	PROPN
ejpam-4975	246	22	;	;	PUNCT
ejpam-4975	246	23	(	(	PUNCT
ejpam-4975	246	24	4	4	X
ejpam-4975	246	25	)	)	PUNCT
ejpam-4975	246	26	f−1(v	f−1(v	NOUN
ejpam-4975	246	27	)	)	PUNCT
ejpam-4975	246	28	⊆	⊆	NUM
ejpam-4975	247	1	[	[	X
ejpam-4975	247	2	f−1([v	f−1([v	ADJ
ejpam-4975	247	3	(	(	PUNCT
ejpam-4975	247	4	λ	λ	NOUN
ejpam-4975	247	5	,	,	PUNCT
ejpam-4975	247	6	p)](λ	p)](λ	ADJ
ejpam-4975	247	7	,	,	PUNCT
ejpam-4975	247	8	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	247	9	,	,	PUNCT
ejpam-4975	247	10	p	p	NOUN
ejpam-4975	247	11	)	)	PUNCT
ejpam-4975	247	12	for	for	ADP
ejpam-4975	247	13	every	every	DET
ejpam-4975	247	14	p(λ	p(λ	NOUN
ejpam-4975	247	15	,	,	PUNCT
ejpam-4975	247	16	p)-open	p)-open	VERB
ejpam-4975	247	17	set	set	VERB
ejpam-4975	247	18	v	v	NOUN
ejpam-4975	247	19	of	of	ADP
ejpam-4975	247	20	y	y	PROPN
ejpam-4975	247	21	.	.	PUNCT
ejpam-4975	248	1	proof	proof	NOUN
ejpam-4975	248	2	.	.	PUNCT
ejpam-4975	249	1	(	(	PUNCT
ejpam-4975	249	2	1	1	X
ejpam-4975	249	3	)	)	PUNCT
ejpam-4975	249	4	⇒	⇒	NOUN
ejpam-4975	249	5	(	(	PUNCT
ejpam-4975	249	6	2	2	NUM
ejpam-4975	249	7	):	):	PUNCT
ejpam-4975	249	8	let	let	VERB
ejpam-4975	249	9	v	v	PART
ejpam-4975	249	10	be	be	AUX
ejpam-4975	249	11	any	any	DET
ejpam-4975	249	12	β(λ	β(λ	NOUN
ejpam-4975	249	13	,	,	PUNCT
ejpam-4975	249	14	p)-open	p)-open	VERB
ejpam-4975	249	15	set	set	NOUN
ejpam-4975	249	16	of	of	ADP
ejpam-4975	249	17	y	y	PROPN
ejpam-4975	249	18	.	.	PUNCT
ejpam-4975	250	1	then	then	ADV
ejpam-4975	250	2	,	,	PUNCT
ejpam-4975	250	3	v	v	INTJ
ejpam-4975	250	4	(	(	PUNCT
ejpam-4975	250	5	λ	λ	PROPN
ejpam-4975	250	6	,	,	PUNCT
ejpam-4975	250	7	p	p	NOUN
ejpam-4975	250	8	)	)	PUNCT
ejpam-4975	250	9	is	be	AUX
ejpam-4975	250	10	r(λ	r(λ	PROPN
ejpam-4975	250	11	,	,	PUNCT
ejpam-4975	250	12	p)-closed	p)-close	VERB
ejpam-4975	250	13	.	.	PUNCT
ejpam-4975	251	1	since	since	SCONJ
ejpam-4975	251	2	f	f	PROPN
ejpam-4975	251	3	is	be	AUX
ejpam-4975	251	4	almost	almost	ADV
ejpam-4975	251	5	strongly	strongly	ADV
ejpam-4975	251	6	θ(λ	θ(λ	VERB
ejpam-4975	251	7	,	,	PUNCT
ejpam-4975	251	8	p)-continuous	p)-continuous	ADJ
ejpam-4975	251	9	,	,	PUNCT
ejpam-4975	251	10	by	by	ADP
ejpam-4975	251	11	theorem	theorem	NOUN
ejpam-4975	251	12	2	2	NUM
ejpam-4975	251	13	we	we	PRON
ejpam-4975	251	14	have	have	VERB
ejpam-4975	251	15	[	[	X
ejpam-4975	251	16	f−1(v	f−1(v	NOUN
ejpam-4975	251	17	)	)	PUNCT
ejpam-4975	251	18	]	]	X
ejpam-4975	252	1	θ(λ	θ(λ	PROPN
ejpam-4975	252	2	,	,	PUNCT
ejpam-4975	252	3	p	p	NOUN
ejpam-4975	252	4	)	)	PUNCT
ejpam-4975	252	5	⊆	⊆	NUM
ejpam-4975	253	1	[	[	X
ejpam-4975	253	2	f−1([[v	f−1([[v	PROPN
ejpam-4975	253	3	(	(	PUNCT
ejpam-4975	253	4	λ	λ	PROPN
ejpam-4975	253	5	,	,	PUNCT
ejpam-4975	253	6	p)](λ	p)](λ	ADJ
ejpam-4975	253	7	,	,	PUNCT
ejpam-4975	253	8	p	p	NOUN
ejpam-4975	253	9	)	)	PUNCT
ejpam-4975	253	10	]	]	PUNCT
ejpam-4975	253	11	(	(	PUNCT
ejpam-4975	253	12	λ	λ	INTJ
ejpam-4975	253	13	,	,	PUNCT
ejpam-4975	253	14	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	253	15	,	,	PUNCT
ejpam-4975	253	16	p	p	NOUN
ejpam-4975	253	17	)	)	PUNCT
ejpam-4975	253	18	⊆	⊆	NUM
ejpam-4975	253	19	f−1(v	f−1(v	NOUN
ejpam-4975	253	20	(	(	PUNCT
ejpam-4975	253	21	λ	λ	PROPN
ejpam-4975	253	22	,	,	PUNCT
ejpam-4975	253	23	p	p	NOUN
ejpam-4975	253	24	)	)	PUNCT
ejpam-4975	253	25	)	)	PUNCT
ejpam-4975	253	26	and	and	CCONJ
ejpam-4975	253	27	hence	hence	ADV
ejpam-4975	253	28	[	[	X
ejpam-4975	253	29	f−1(v	f−1(v	NOUN
ejpam-4975	253	30	)	)	PUNCT
ejpam-4975	253	31	]	]	X
ejpam-4975	253	32	θ(λ	θ(λ	PROPN
ejpam-4975	253	33	,	,	PUNCT
ejpam-4975	253	34	p	p	NOUN
ejpam-4975	253	35	)	)	PUNCT
ejpam-4975	253	36	⊆	⊆	NUM
ejpam-4975	253	37	f−1(v	f−1(v	NOUN
ejpam-4975	253	38	(	(	PUNCT
ejpam-4975	253	39	λ	λ	PROPN
ejpam-4975	253	40	,	,	PUNCT
ejpam-4975	253	41	p	p	NOUN
ejpam-4975	253	42	)	)	PUNCT
ejpam-4975	253	43	)	)	PUNCT
ejpam-4975	253	44	.	.	PUNCT
ejpam-4975	254	1	(	(	PUNCT
ejpam-4975	254	2	2	2	X
ejpam-4975	254	3	)	)	PUNCT
ejpam-4975	254	4	⇒	⇒	NOUN
ejpam-4975	254	5	(	(	PUNCT
ejpam-4975	254	6	3	3	NUM
ejpam-4975	254	7	):	):	PUNCT
ejpam-4975	254	8	this	this	PRON
ejpam-4975	254	9	is	be	AUX
ejpam-4975	254	10	obvious	obvious	ADJ
ejpam-4975	254	11	since	since	SCONJ
ejpam-4975	254	12	s(λ	s(λ	PROPN
ejpam-4975	254	13	,	,	PUNCT
ejpam-4975	254	14	p)o(x	p)o(x	ADJ
ejpam-4975	254	15	,	,	PUNCT
ejpam-4975	254	16	τ	τ	PROPN
ejpam-4975	254	17	)	)	PUNCT
ejpam-4975	254	18	⊆	⊆	NUM
ejpam-4975	254	19	β(λ	β(λ	NOUN
ejpam-4975	254	20	,	,	PUNCT
ejpam-4975	254	21	p)o(x	p)o(x	ADJ
ejpam-4975	254	22	,	,	PUNCT
ejpam-4975	254	23	τ	τ	PROPN
ejpam-4975	254	24	)	)	PUNCT
ejpam-4975	254	25	.	.	PUNCT
ejpam-4975	255	1	(	(	PUNCT
ejpam-4975	255	2	3	3	X
ejpam-4975	255	3	)	)	PUNCT
ejpam-4975	255	4	⇒	⇒	NOUN
ejpam-4975	255	5	(	(	PUNCT
ejpam-4975	255	6	4	4	NUM
ejpam-4975	255	7	):	):	PUNCT
ejpam-4975	255	8	let	let	VERB
ejpam-4975	255	9	v	v	PART
ejpam-4975	255	10	be	be	AUX
ejpam-4975	255	11	any	any	DET
ejpam-4975	255	12	p(λ	p(λ	NOUN
ejpam-4975	255	13	,	,	PUNCT
ejpam-4975	255	14	p)-open	p)-open	VERB
ejpam-4975	255	15	set	set	NOUN
ejpam-4975	255	16	of	of	ADP
ejpam-4975	255	17	y	y	PROPN
ejpam-4975	255	18	.	.	PUNCT
ejpam-4975	256	1	then	then	ADV
ejpam-4975	256	2	,	,	PUNCT
ejpam-4975	256	3	y	y	PROPN
ejpam-4975	256	4	−	−	PROPN
ejpam-4975	256	5	v	v	PROPN
ejpam-4975	256	6	is	be	AUX
ejpam-4975	256	7	p(λ	p(λ	NOUN
ejpam-4975	256	8	,	,	PUNCT
ejpam-4975	256	9	p)-closed	p)-close	VERB
ejpam-4975	256	10	in	in	ADP
ejpam-4975	256	11	y	y	NOUN
ejpam-4975	256	12	and	and	CCONJ
ejpam-4975	257	1	hence	hence	ADV
ejpam-4975	257	2	[	[	X
ejpam-4975	257	3	[	[	X
ejpam-4975	257	4	y	y	INTJ
ejpam-4975	257	5	−	−	PROPN
ejpam-4975	257	6	v	v	NOUN
ejpam-4975	257	7	]	]	X
ejpam-4975	257	8	(	(	PUNCT
ejpam-4975	257	9	λ	λ	X
ejpam-4975	257	10	,	,	PUNCT
ejpam-4975	257	11	p	p	NOUN
ejpam-4975	257	12	)	)	PUNCT
ejpam-4975	257	13	]	]	PUNCT
ejpam-4975	257	14	(	(	PUNCT
ejpam-4975	257	15	λ	λ	X
ejpam-4975	257	16	,	,	PUNCT
ejpam-4975	257	17	p	p	NOUN
ejpam-4975	257	18	)	)	PUNCT
ejpam-4975	257	19	⊆	⊆	NUM
ejpam-4975	257	20	y	y	PROPN
ejpam-4975	257	21	−	−	PROPN
ejpam-4975	257	22	v	v	NOUN
ejpam-4975	257	23	.	.	PUNCT
ejpam-4975	258	1	since	since	SCONJ
ejpam-4975	258	2	[	[	X
ejpam-4975	258	3	[	[	X
ejpam-4975	258	4	y	y	INTJ
ejpam-4975	258	5	−	−	PROPN
ejpam-4975	258	6	v	v	NOUN
ejpam-4975	258	7	]	]	X
ejpam-4975	258	8	(	(	PUNCT
ejpam-4975	258	9	λ	λ	X
ejpam-4975	258	10	,	,	PUNCT
ejpam-4975	258	11	p	p	NOUN
ejpam-4975	258	12	)	)	PUNCT
ejpam-4975	258	13	]	]	PUNCT
ejpam-4975	258	14	(	(	PUNCT
ejpam-4975	258	15	λ	λ	X
ejpam-4975	258	16	,	,	PUNCT
ejpam-4975	258	17	p	p	NOUN
ejpam-4975	258	18	)	)	PUNCT
ejpam-4975	258	19	is	be	AUX
ejpam-4975	258	20	r(λ	r(λ	PROPN
ejpam-4975	258	21	,	,	PUNCT
ejpam-4975	258	22	p)-closed	p)-close	VERB
ejpam-4975	258	23	,	,	PUNCT
ejpam-4975	258	24	we	we	PRON
ejpam-4975	258	25	have	have	VERB
ejpam-4975	258	26	[	[	X
ejpam-4975	258	27	[	[	X
ejpam-4975	258	28	y	y	INTJ
ejpam-4975	258	29	−	−	PROPN
ejpam-4975	258	30	v	v	NOUN
ejpam-4975	258	31	]	]	X
ejpam-4975	258	32	(	(	PUNCT
ejpam-4975	258	33	λ	λ	X
ejpam-4975	258	34	,	,	PUNCT
ejpam-4975	258	35	p	p	NOUN
ejpam-4975	258	36	)	)	PUNCT
ejpam-4975	258	37	]	]	PUNCT
ejpam-4975	258	38	(	(	PUNCT
ejpam-4975	258	39	λ	λ	X
ejpam-4975	258	40	,	,	PUNCT
ejpam-4975	258	41	p	p	NOUN
ejpam-4975	258	42	)	)	PUNCT
ejpam-4975	258	43	is	be	AUX
ejpam-4975	258	44	s(λ	s(λ	PROPN
ejpam-4975	258	45	,	,	PUNCT
ejpam-4975	258	46	p)-open	p)-open	VERB
ejpam-4975	258	47	in	in	ADP
ejpam-4975	258	48	y	y	PROPN
ejpam-4975	258	49	.	.	PUNCT
ejpam-4975	259	1	then	then	ADV
ejpam-4975	259	2	by	by	ADP
ejpam-4975	259	3	(	(	PUNCT
ejpam-4975	259	4	3	3	NUM
ejpam-4975	259	5	)	)	PUNCT
ejpam-4975	259	6	,	,	PUNCT
ejpam-4975	260	1	[	[	X
ejpam-4975	260	2	f−1([[y	f−1([[y	NOUN
ejpam-4975	260	3	−	−	NOUN
ejpam-4975	260	4	v	v	NOUN
ejpam-4975	260	5	]	]	X
ejpam-4975	260	6	(	(	PUNCT
ejpam-4975	260	7	λ	λ	X
ejpam-4975	260	8	,	,	PUNCT
ejpam-4975	260	9	p	p	NOUN
ejpam-4975	260	10	)	)	PUNCT
ejpam-4975	260	11	]	]	PUNCT
ejpam-4975	260	12	(	(	PUNCT
ejpam-4975	260	13	λ	λ	INTJ
ejpam-4975	260	14	,	,	PUNCT
ejpam-4975	260	15	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	260	16	,	,	PUNCT
ejpam-4975	260	17	p	p	NOUN
ejpam-4975	260	18	)	)	PUNCT
ejpam-4975	260	19	⊆	⊆	NUM
ejpam-4975	260	20	f−1([[y	f−1([[y	NOUN
ejpam-4975	260	21	−	−	NOUN
ejpam-4975	260	22	v	v	NOUN
ejpam-4975	260	23	]	]	X
ejpam-4975	260	24	(	(	PUNCT
ejpam-4975	260	25	λ	λ	X
ejpam-4975	260	26	,	,	PUNCT
ejpam-4975	260	27	p	p	NOUN
ejpam-4975	260	28	)	)	PUNCT
ejpam-4975	260	29	]	]	PUNCT
ejpam-4975	260	30	(	(	PUNCT
ejpam-4975	260	31	λ	λ	X
ejpam-4975	260	32	,	,	PUNCT
ejpam-4975	260	33	p	p	NOUN
ejpam-4975	260	34	)	)	PUNCT
ejpam-4975	260	35	)	)	PUNCT
ejpam-4975	261	1	⊆	⊆	NUM
ejpam-4975	261	2	f−1(y	f−1(y	NOUN
ejpam-4975	261	3	−	−	PROPN
ejpam-4975	261	4	v	v	NOUN
ejpam-4975	261	5	)	)	PUNCT
ejpam-4975	261	6	.	.	PUNCT
ejpam-4975	262	1	thus	thus	ADV
ejpam-4975	262	2	,	,	PUNCT
ejpam-4975	262	3	f−1(v	f−1(v	PROPN
ejpam-4975	262	4	)	)	PUNCT
ejpam-4975	263	1	⊆	⊆	NUM
ejpam-4975	263	2	x	x	SYM
ejpam-4975	263	3	−	−	NOUN
ejpam-4975	264	1	[	[	X
ejpam-4975	264	2	f−1([[y	f−1([[y	NOUN
ejpam-4975	264	3	−	−	NOUN
ejpam-4975	264	4	v	v	NOUN
ejpam-4975	264	5	]	]	X
ejpam-4975	264	6	(	(	PUNCT
ejpam-4975	264	7	λ	λ	X
ejpam-4975	264	8	,	,	PUNCT
ejpam-4975	264	9	p	p	NOUN
ejpam-4975	264	10	)	)	PUNCT
ejpam-4975	264	11	]	]	PUNCT
ejpam-4975	264	12	(	(	PUNCT
ejpam-4975	264	13	λ	λ	INTJ
ejpam-4975	264	14	,	,	PUNCT
ejpam-4975	264	15	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	264	16	,	,	PUNCT
ejpam-4975	264	17	p	p	NOUN
ejpam-4975	264	18	)	)	PUNCT
ejpam-4975	264	19	=	=	PUNCT
ejpam-4975	264	20	x	x	X
ejpam-4975	264	21	−	−	PUNCT
ejpam-4975	265	1	[	[	X
ejpam-4975	265	2	x	x	X
ejpam-4975	265	3	−	−	PROPN
ejpam-4975	265	4	f−1([v	f−1([v	ADJ
ejpam-4975	265	5	(	(	PUNCT
ejpam-4975	265	6	λ	λ	NOUN
ejpam-4975	265	7	,	,	PUNCT
ejpam-4975	265	8	p)](λ	p)](λ	ADJ
ejpam-4975	265	9	,	,	PUNCT
ejpam-4975	265	10	p	p	NOUN
ejpam-4975	265	11	)	)	PUNCT
ejpam-4975	265	12	)	)	PUNCT
ejpam-4975	265	13	]	]	PUNCT
ejpam-4975	266	1	θ(λ	θ(λ	PROPN
ejpam-4975	266	2	,	,	PUNCT
ejpam-4975	266	3	p	p	NOUN
ejpam-4975	266	4	)	)	PUNCT
ejpam-4975	266	5	c.	c.	PROPN
ejpam-4975	266	6	boonpok	boonpok	PROPN
ejpam-4975	266	7	,	,	PUNCT
ejpam-4975	266	8	j.	j.	PROPN
ejpam-4975	266	9	khampakdee	khampakdee	PROPN
ejpam-4975	266	10	/	/	PUNCT
ejpam-4975	266	11	eur	eur	PROPN
ejpam-4975	266	12	.	.	PUNCT
ejpam-4975	267	1	j.	j.	PROPN
ejpam-4975	267	2	pure	pure	PROPN
ejpam-4975	267	3	appl	appl	PROPN
ejpam-4975	267	4	.	.	PROPN
ejpam-4975	267	5	math	math	PROPN
ejpam-4975	267	6	,	,	PUNCT
ejpam-4975	267	7	17	17	NUM
ejpam-4975	267	8	(	(	PUNCT
ejpam-4975	267	9	1	1	NUM
ejpam-4975	267	10	)	)	PUNCT
ejpam-4975	267	11	(	(	PUNCT
ejpam-4975	267	12	2024	2024	NUM
ejpam-4975	267	13	)	)	PUNCT
ejpam-4975	267	14	,	,	PUNCT
ejpam-4975	267	15	300	300	NUM
ejpam-4975	267	16	-	-	SYM
ejpam-4975	267	17	309	309	NUM
ejpam-4975	267	18	306	306	NUM
ejpam-4975	267	19	=	=	PUNCT
ejpam-4975	268	1	[	[	PUNCT
ejpam-4975	268	2	f−1([v	f−1([v	ADJ
ejpam-4975	268	3	(	(	PUNCT
ejpam-4975	268	4	λ	λ	NOUN
ejpam-4975	268	5	,	,	PUNCT
ejpam-4975	268	6	p)](λ	p)](λ	ADJ
ejpam-4975	268	7	,	,	PUNCT
ejpam-4975	268	8	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	268	9	,	,	PUNCT
ejpam-4975	268	10	p	p	NOUN
ejpam-4975	268	11	)	)	PUNCT
ejpam-4975	268	12	.	.	PUNCT
ejpam-4975	269	1	(	(	PUNCT
ejpam-4975	269	2	4	4	X
ejpam-4975	269	3	)	)	PUNCT
ejpam-4975	269	4	⇒	⇒	NOUN
ejpam-4975	269	5	(	(	PUNCT
ejpam-4975	269	6	1	1	NUM
ejpam-4975	269	7	):	):	PUNCT
ejpam-4975	269	8	let	let	VERB
ejpam-4975	269	9	v	v	PART
ejpam-4975	269	10	be	be	AUX
ejpam-4975	269	11	any	any	DET
ejpam-4975	269	12	r(λ	r(λ	NOUN
ejpam-4975	269	13	,	,	PUNCT
ejpam-4975	269	14	p)-open	p)-open	VERB
ejpam-4975	269	15	set	set	NOUN
ejpam-4975	269	16	of	of	ADP
ejpam-4975	269	17	y	y	PROPN
ejpam-4975	269	18	.	.	PUNCT
ejpam-4975	270	1	then	then	ADV
ejpam-4975	270	2	,	,	PUNCT
ejpam-4975	270	3	v	v	NOUN
ejpam-4975	270	4	is	be	AUX
ejpam-4975	270	5	p(λ	p(λ	NOUN
ejpam-4975	270	6	,	,	PUNCT
ejpam-4975	270	7	p)-open	p)-open	VERB
ejpam-4975	270	8	and	and	CCONJ
ejpam-4975	270	9	f−1(v	f−1(v	PROPN
ejpam-4975	270	10	)	)	PUNCT
ejpam-4975	271	1	⊆	⊆	NUM
ejpam-4975	271	2	[	[	X
ejpam-4975	271	3	f−1([v	f−1([v	ADJ
ejpam-4975	271	4	(	(	PUNCT
ejpam-4975	271	5	λ	λ	NOUN
ejpam-4975	271	6	,	,	PUNCT
ejpam-4975	271	7	p)](λ	p)](λ	ADJ
ejpam-4975	271	8	,	,	PUNCT
ejpam-4975	271	9	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	271	10	,	,	PUNCT
ejpam-4975	271	11	p	p	NOUN
ejpam-4975	271	12	)	)	PUNCT
ejpam-4975	271	13	=	=	PUNCT
ejpam-4975	272	1	[	[	X
ejpam-4975	272	2	f−1(v	f−1(v	NOUN
ejpam-4975	272	3	)	)	PUNCT
ejpam-4975	272	4	]	]	X
ejpam-4975	273	1	θ(λ	θ(λ	PROPN
ejpam-4975	273	2	,	,	PUNCT
ejpam-4975	273	3	p	p	NOUN
ejpam-4975	273	4	)	)	PUNCT
ejpam-4975	273	5	.	.	PUNCT
ejpam-4975	274	1	thus	thus	ADV
ejpam-4975	274	2	,	,	PUNCT
ejpam-4975	274	3	f−1(v	f−1(v	PROPN
ejpam-4975	274	4	)	)	PUNCT
ejpam-4975	274	5	=	=	PUNCT
ejpam-4975	275	1	[	[	X
ejpam-4975	275	2	f−1(v	f−1(v	NOUN
ejpam-4975	275	3	)	)	PUNCT
ejpam-4975	275	4	]	]	X
ejpam-4975	275	5	θ(λ	θ(λ	PROPN
ejpam-4975	275	6	,	,	PUNCT
ejpam-4975	275	7	p	p	NOUN
ejpam-4975	275	8	)	)	PUNCT
ejpam-4975	275	9	and	and	CCONJ
ejpam-4975	275	10	by	by	ADP
ejpam-4975	275	11	lemma	lemma	PROPN
ejpam-4975	275	12	1	1	NUM
ejpam-4975	275	13	,	,	PUNCT
ejpam-4975	275	14	f−1(v	f−1(v	PROPN
ejpam-4975	275	15	)	)	PUNCT
ejpam-4975	275	16	is	be	AUX
ejpam-4975	275	17	θ(λ	θ(λ	PROPN
ejpam-4975	275	18	,	,	PUNCT
ejpam-4975	275	19	p)-open	p)-open	VERB
ejpam-4975	275	20	in	in	ADP
ejpam-4975	275	21	x.	x.	NOUN
ejpam-4975	275	22	it	it	PRON
ejpam-4975	275	23	follows	follow	VERB
ejpam-4975	275	24	from	from	ADP
ejpam-4975	275	25	theorem	theorem	ADJ
ejpam-4975	275	26	1	1	NUM
ejpam-4975	275	27	that	that	SCONJ
ejpam-4975	275	28	f	f	PROPN
ejpam-4975	275	29	is	be	AUX
ejpam-4975	275	30	almost	almost	ADV
ejpam-4975	275	31	strongly	strongly	ADV
ejpam-4975	275	32	θ(λ	θ(λ	VERB
ejpam-4975	275	33	,	,	PUNCT
ejpam-4975	275	34	p)-continuous	p)-continuous	ADJ
ejpam-4975	275	35	.	.	PUNCT
ejpam-4975	276	1	lemma	lemma	PROPN
ejpam-4975	276	2	2	2	NUM
ejpam-4975	276	3	.	.	X
ejpam-4975	277	1	for	for	ADP
ejpam-4975	277	2	a	a	DET
ejpam-4975	277	3	topological	topological	ADJ
ejpam-4975	277	4	space	space	NOUN
ejpam-4975	277	5	(	(	PUNCT
ejpam-4975	277	6	x	x	X
ejpam-4975	277	7	,	,	PUNCT
ejpam-4975	277	8	τ	τ	PROPN
ejpam-4975	277	9	)	)	PUNCT
ejpam-4975	277	10	,	,	PUNCT
ejpam-4975	277	11	the	the	DET
ejpam-4975	277	12	following	follow	VERB
ejpam-4975	277	13	properties	property	NOUN
ejpam-4975	277	14	hold	hold	VERB
ejpam-4975	277	15	:	:	PUNCT
ejpam-4975	277	16	(	(	PUNCT
ejpam-4975	277	17	1	1	X
ejpam-4975	277	18	)	)	PUNCT
ejpam-4975	277	19	v	v	ADP
ejpam-4975	277	20	α(λ	α(λ	PROPN
ejpam-4975	277	21	,	,	PUNCT
ejpam-4975	277	22	p	p	NOUN
ejpam-4975	277	23	)	)	PUNCT
ejpam-4975	277	24	=	=	SYM
ejpam-4975	277	25	v	v	X
ejpam-4975	277	26	(	(	PUNCT
ejpam-4975	277	27	λ	λ	PROPN
ejpam-4975	277	28	,	,	PUNCT
ejpam-4975	277	29	p	p	NOUN
ejpam-4975	277	30	)	)	PUNCT
ejpam-4975	277	31	for	for	ADP
ejpam-4975	277	32	every	every	DET
ejpam-4975	277	33	v	v	NOUN
ejpam-4975	277	34	∈	∈	PROPN
ejpam-4975	277	35	β(λ	β(λ	X
ejpam-4975	277	36	,	,	PUNCT
ejpam-4975	277	37	p)o(x	p)o(x	ADJ
ejpam-4975	277	38	,	,	PUNCT
ejpam-4975	277	39	τ	τ	PROPN
ejpam-4975	277	40	)	)	PUNCT
ejpam-4975	277	41	;	;	PUNCT
ejpam-4975	277	42	(	(	PUNCT
ejpam-4975	277	43	2	2	X
ejpam-4975	277	44	)	)	PUNCT
ejpam-4975	277	45	v	v	NOUN
ejpam-4975	277	46	p(λ	p(λ	NOUN
ejpam-4975	277	47	,	,	PUNCT
ejpam-4975	277	48	p	p	NOUN
ejpam-4975	277	49	)	)	PUNCT
ejpam-4975	277	50	=	=	SYM
ejpam-4975	277	51	v	v	X
ejpam-4975	277	52	(	(	PUNCT
ejpam-4975	277	53	λ	λ	PROPN
ejpam-4975	277	54	,	,	PUNCT
ejpam-4975	277	55	p	p	NOUN
ejpam-4975	277	56	)	)	PUNCT
ejpam-4975	277	57	for	for	ADP
ejpam-4975	277	58	every	every	DET
ejpam-4975	277	59	v	v	PROPN
ejpam-4975	277	60	∈	∈	PROPN
ejpam-4975	277	61	s(λ	s(λ	PROPN
ejpam-4975	277	62	,	,	PUNCT
ejpam-4975	277	63	p)o(x	p)o(x	ADJ
ejpam-4975	277	64	,	,	PUNCT
ejpam-4975	277	65	τ	τ	PROPN
ejpam-4975	277	66	)	)	PUNCT
ejpam-4975	277	67	;	;	PUNCT
ejpam-4975	277	68	(	(	PUNCT
ejpam-4975	277	69	3	3	X
ejpam-4975	277	70	)	)	PUNCT
ejpam-4975	277	71	v	v	ADP
ejpam-4975	277	72	s(λ	s(λ	PROPN
ejpam-4975	277	73	,	,	PUNCT
ejpam-4975	277	74	p	p	NOUN
ejpam-4975	277	75	)	)	PUNCT
ejpam-4975	277	76	=	=	PUNCT
ejpam-4975	278	1	[	[	X
ejpam-4975	278	2	v	v	X
ejpam-4975	278	3	(	(	PUNCT
ejpam-4975	278	4	λ	λ	PROPN
ejpam-4975	278	5	,	,	PUNCT
ejpam-4975	278	6	p)](λ	p)](λ	ADJ
ejpam-4975	278	7	,	,	PUNCT
ejpam-4975	278	8	p	p	NOUN
ejpam-4975	278	9	)	)	PUNCT
ejpam-4975	278	10	for	for	ADP
ejpam-4975	278	11	every	every	DET
ejpam-4975	278	12	v	v	NOUN
ejpam-4975	278	13	∈	∈	PROPN
ejpam-4975	278	14	p(λ	p(λ	NOUN
ejpam-4975	278	15	,	,	PUNCT
ejpam-4975	278	16	p)o(x	p)o(x	ADJ
ejpam-4975	278	17	,	,	PUNCT
ejpam-4975	278	18	τ	τ	PROPN
ejpam-4975	278	19	)	)	PUNCT
ejpam-4975	278	20	.	.	PUNCT
ejpam-4975	279	1	corollary	corollary	ADJ
ejpam-4975	279	2	1	1	NUM
ejpam-4975	279	3	.	.	PUNCT
ejpam-4975	280	1	for	for	ADP
ejpam-4975	280	2	a	a	DET
ejpam-4975	280	3	function	function	NOUN
ejpam-4975	280	4	f	f	NOUN
ejpam-4975	280	5	:	:	PUNCT
ejpam-4975	280	6	(	(	PUNCT
ejpam-4975	280	7	x	x	X
ejpam-4975	280	8	,	,	PUNCT
ejpam-4975	280	9	τ	τ	X
ejpam-4975	280	10	)	)	PUNCT
ejpam-4975	280	11	→	→	SYM
ejpam-4975	280	12	(	(	PUNCT
ejpam-4975	280	13	y	y	PROPN
ejpam-4975	280	14	,	,	PUNCT
ejpam-4975	280	15	σ	σ	PROPN
ejpam-4975	280	16	)	)	PUNCT
ejpam-4975	280	17	,	,	PUNCT
ejpam-4975	280	18	the	the	DET
ejpam-4975	280	19	following	follow	VERB
ejpam-4975	280	20	properties	property	NOUN
ejpam-4975	280	21	are	be	AUX
ejpam-4975	280	22	equivalent	equivalent	ADJ
ejpam-4975	280	23	:	:	PUNCT
ejpam-4975	280	24	(	(	PUNCT
ejpam-4975	280	25	1	1	X
ejpam-4975	280	26	)	)	PUNCT
ejpam-4975	280	27	f	f	NOUN
ejpam-4975	280	28	is	be	AUX
ejpam-4975	280	29	almost	almost	ADV
ejpam-4975	280	30	strongly	strongly	ADV
ejpam-4975	280	31	θ(λ	θ(λ	VERB
ejpam-4975	280	32	,	,	PUNCT
ejpam-4975	280	33	p)-continuous	p)-continuous	ADJ
ejpam-4975	280	34	;	;	PUNCT
ejpam-4975	280	35	(	(	PUNCT
ejpam-4975	280	36	2	2	X
ejpam-4975	280	37	)	)	PUNCT
ejpam-4975	281	1	[	[	X
ejpam-4975	281	2	f−1(v	f−1(v	NOUN
ejpam-4975	281	3	)	)	PUNCT
ejpam-4975	281	4	]	]	X
ejpam-4975	282	1	θ(λ	θ(λ	PROPN
ejpam-4975	282	2	,	,	PUNCT
ejpam-4975	282	3	p	p	NOUN
ejpam-4975	282	4	)	)	PUNCT
ejpam-4975	282	5	⊆	⊆	NUM
ejpam-4975	282	6	f−1(v	f−1(v	PROPN
ejpam-4975	282	7	α(λ	α(λ	PROPN
ejpam-4975	282	8	,	,	PUNCT
ejpam-4975	282	9	p	p	NOUN
ejpam-4975	282	10	)	)	PUNCT
ejpam-4975	282	11	)	)	PUNCT
ejpam-4975	282	12	for	for	ADP
ejpam-4975	282	13	every	every	DET
ejpam-4975	282	14	β(λ	β(λ	NOUN
ejpam-4975	282	15	,	,	PUNCT
ejpam-4975	282	16	p)-open	p)-open	VERB
ejpam-4975	282	17	set	set	VERB
ejpam-4975	282	18	v	v	NOUN
ejpam-4975	282	19	of	of	ADP
ejpam-4975	282	20	y	y	PROPN
ejpam-4975	282	21	;	;	PUNCT
ejpam-4975	282	22	(	(	PUNCT
ejpam-4975	282	23	3	3	X
ejpam-4975	282	24	)	)	PUNCT
ejpam-4975	283	1	[	[	X
ejpam-4975	283	2	f−1(v	f−1(v	NOUN
ejpam-4975	283	3	)	)	PUNCT
ejpam-4975	283	4	]	]	X
ejpam-4975	284	1	θ(λ	θ(λ	PROPN
ejpam-4975	284	2	,	,	PUNCT
ejpam-4975	284	3	p	p	NOUN
ejpam-4975	284	4	)	)	PUNCT
ejpam-4975	284	5	⊆	⊆	NUM
ejpam-4975	284	6	f−1(v	f−1(v	NOUN
ejpam-4975	284	7	p(λ	p(λ	PROPN
ejpam-4975	284	8	,	,	PUNCT
ejpam-4975	284	9	p	p	NOUN
ejpam-4975	284	10	)	)	PUNCT
ejpam-4975	284	11	)	)	PUNCT
ejpam-4975	284	12	for	for	ADP
ejpam-4975	284	13	every	every	DET
ejpam-4975	284	14	s(λ	s(λ	PROPN
ejpam-4975	284	15	,	,	PUNCT
ejpam-4975	284	16	p)-open	p)-open	AUX
ejpam-4975	284	17	set	set	VERB
ejpam-4975	284	18	v	v	NOUN
ejpam-4975	284	19	of	of	ADP
ejpam-4975	284	20	y	y	PROPN
ejpam-4975	284	21	;	;	PUNCT
ejpam-4975	284	22	(	(	PUNCT
ejpam-4975	284	23	4	4	X
ejpam-4975	284	24	)	)	PUNCT
ejpam-4975	284	25	f−1(v	f−1(v	NOUN
ejpam-4975	284	26	)	)	PUNCT
ejpam-4975	284	27	⊆	⊆	NUM
ejpam-4975	285	1	[	[	X
ejpam-4975	285	2	f−1(v	f−1(v	NOUN
ejpam-4975	285	3	s(λ	s(λ	PROPN
ejpam-4975	285	4	,	,	PUNCT
ejpam-4975	285	5	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	285	6	,	,	PUNCT
ejpam-4975	285	7	p	p	NOUN
ejpam-4975	285	8	)	)	PUNCT
ejpam-4975	285	9	for	for	ADP
ejpam-4975	285	10	every	every	DET
ejpam-4975	285	11	p(λ	p(λ	NOUN
ejpam-4975	285	12	,	,	PUNCT
ejpam-4975	285	13	p)-open	p)-open	VERB
ejpam-4975	285	14	set	set	VERB
ejpam-4975	285	15	v	v	NOUN
ejpam-4975	285	16	of	of	ADP
ejpam-4975	285	17	y	y	PROPN
ejpam-4975	285	18	.	.	PUNCT
ejpam-4975	286	1	theorem	theorem	ADJ
ejpam-4975	286	2	4	4	NUM
ejpam-4975	286	3	.	.	X
ejpam-4975	286	4	for	for	ADP
ejpam-4975	286	5	a	a	DET
ejpam-4975	286	6	function	function	NOUN
ejpam-4975	286	7	f	f	NOUN
ejpam-4975	286	8	:	:	PUNCT
ejpam-4975	286	9	(	(	PUNCT
ejpam-4975	286	10	x	x	X
ejpam-4975	286	11	,	,	PUNCT
ejpam-4975	286	12	τ	τ	X
ejpam-4975	286	13	)	)	PUNCT
ejpam-4975	286	14	→	→	SYM
ejpam-4975	286	15	(	(	PUNCT
ejpam-4975	286	16	y	y	PROPN
ejpam-4975	286	17	,	,	PUNCT
ejpam-4975	286	18	σ	σ	PROPN
ejpam-4975	286	19	)	)	PUNCT
ejpam-4975	286	20	,	,	PUNCT
ejpam-4975	286	21	the	the	DET
ejpam-4975	286	22	following	follow	VERB
ejpam-4975	286	23	properties	property	NOUN
ejpam-4975	286	24	are	be	AUX
ejpam-4975	286	25	equivalent	equivalent	ADJ
ejpam-4975	286	26	:	:	PUNCT
ejpam-4975	286	27	(	(	PUNCT
ejpam-4975	286	28	1	1	X
ejpam-4975	286	29	)	)	PUNCT
ejpam-4975	286	30	f	f	NOUN
ejpam-4975	286	31	is	be	AUX
ejpam-4975	286	32	almost	almost	ADV
ejpam-4975	286	33	strongly	strongly	ADV
ejpam-4975	286	34	θ(λ	θ(λ	VERB
ejpam-4975	286	35	,	,	PUNCT
ejpam-4975	286	36	p)-continuous	p)-continuous	ADJ
ejpam-4975	286	37	;	;	PUNCT
ejpam-4975	286	38	(	(	PUNCT
ejpam-4975	286	39	2	2	X
ejpam-4975	286	40	)	)	PUNCT
ejpam-4975	286	41	[	[	X
ejpam-4975	286	42	f−1([[bδ(λ	f−1([[bδ(λ	NOUN
ejpam-4975	286	43	,	,	PUNCT
ejpam-4975	286	44	p)](λ	p)](λ	ADJ
ejpam-4975	286	45	,	,	PUNCT
ejpam-4975	286	46	p	p	NOUN
ejpam-4975	286	47	)	)	PUNCT
ejpam-4975	286	48	]	]	PUNCT
ejpam-4975	286	49	(	(	PUNCT
ejpam-4975	286	50	λ	λ	INTJ
ejpam-4975	286	51	,	,	PUNCT
ejpam-4975	286	52	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	286	53	,	,	PUNCT
ejpam-4975	286	54	p	p	NOUN
ejpam-4975	286	55	)	)	PUNCT
ejpam-4975	286	56	⊆	⊆	NUM
ejpam-4975	286	57	f−1(bδ(λ	f−1(bδ(λ	NOUN
ejpam-4975	286	58	,	,	PUNCT
ejpam-4975	286	59	p	p	NOUN
ejpam-4975	286	60	)	)	PUNCT
ejpam-4975	286	61	)	)	PUNCT
ejpam-4975	286	62	for	for	ADP
ejpam-4975	286	63	every	every	DET
ejpam-4975	286	64	subset	subset	NOUN
ejpam-4975	286	65	b	b	PROPN
ejpam-4975	286	66	of	of	ADP
ejpam-4975	286	67	y	y	PROPN
ejpam-4975	286	68	;	;	PUNCT
ejpam-4975	286	69	(	(	PUNCT
ejpam-4975	286	70	3	3	X
ejpam-4975	286	71	)	)	PUNCT
ejpam-4975	287	1	[	[	X
ejpam-4975	287	2	f−1([[b(λ	f−1([[b(λ	X
ejpam-4975	287	3	,	,	PUNCT
ejpam-4975	287	4	p)](λ	p)](λ	ADJ
ejpam-4975	287	5	,	,	PUNCT
ejpam-4975	287	6	p	p	NOUN
ejpam-4975	287	7	)	)	PUNCT
ejpam-4975	287	8	]	]	PUNCT
ejpam-4975	287	9	(	(	PUNCT
ejpam-4975	287	10	λ	λ	INTJ
ejpam-4975	287	11	,	,	PUNCT
ejpam-4975	287	12	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	287	13	,	,	PUNCT
ejpam-4975	287	14	p	p	NOUN
ejpam-4975	287	15	)	)	PUNCT
ejpam-4975	287	16	⊆	⊆	NUM
ejpam-4975	287	17	f−1(bδ(λ	f−1(bδ(λ	NOUN
ejpam-4975	287	18	,	,	PUNCT
ejpam-4975	287	19	p	p	NOUN
ejpam-4975	287	20	)	)	PUNCT
ejpam-4975	287	21	)	)	PUNCT
ejpam-4975	287	22	for	for	ADP
ejpam-4975	287	23	every	every	DET
ejpam-4975	287	24	subset	subset	NOUN
ejpam-4975	287	25	b	b	PROPN
ejpam-4975	287	26	of	of	ADP
ejpam-4975	287	27	y	y	PROPN
ejpam-4975	287	28	;	;	PUNCT
ejpam-4975	287	29	(	(	PUNCT
ejpam-4975	287	30	4	4	X
ejpam-4975	287	31	)	)	PUNCT
ejpam-4975	288	1	[	[	X
ejpam-4975	288	2	f−1([[v	f−1([[v	PROPN
ejpam-4975	288	3	(	(	PUNCT
ejpam-4975	288	4	λ	λ	PROPN
ejpam-4975	288	5	,	,	PUNCT
ejpam-4975	288	6	p)](λ	p)](λ	ADJ
ejpam-4975	288	7	,	,	PUNCT
ejpam-4975	288	8	p	p	NOUN
ejpam-4975	288	9	)	)	PUNCT
ejpam-4975	288	10	]	]	PUNCT
ejpam-4975	288	11	(	(	PUNCT
ejpam-4975	288	12	λ	λ	INTJ
ejpam-4975	288	13	,	,	PUNCT
ejpam-4975	288	14	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	288	15	,	,	PUNCT
ejpam-4975	288	16	p	p	NOUN
ejpam-4975	288	17	)	)	PUNCT
ejpam-4975	288	18	⊆	⊆	NUM
ejpam-4975	288	19	f−1(v	f−1(v	NOUN
ejpam-4975	288	20	(	(	PUNCT
ejpam-4975	288	21	λ	λ	PROPN
ejpam-4975	288	22	,	,	PUNCT
ejpam-4975	288	23	p	p	NOUN
ejpam-4975	288	24	)	)	PUNCT
ejpam-4975	288	25	)	)	PUNCT
ejpam-4975	288	26	for	for	ADP
ejpam-4975	288	27	every	every	DET
ejpam-4975	288	28	(	(	PUNCT
ejpam-4975	288	29	λ	λ	NOUN
ejpam-4975	288	30	,	,	PUNCT
ejpam-4975	288	31	p)-open	p)-open	VERB
ejpam-4975	288	32	set	set	VERB
ejpam-4975	288	33	v	v	NOUN
ejpam-4975	288	34	of	of	ADP
ejpam-4975	288	35	y	y	PROPN
ejpam-4975	288	36	;	;	PUNCT
ejpam-4975	288	37	(	(	PUNCT
ejpam-4975	288	38	5	5	X
ejpam-4975	288	39	)	)	PUNCT
ejpam-4975	289	1	[	[	X
ejpam-4975	289	2	f−1([[v	f−1([[v	PROPN
ejpam-4975	289	3	(	(	PUNCT
ejpam-4975	289	4	λ	λ	PROPN
ejpam-4975	289	5	,	,	PUNCT
ejpam-4975	289	6	p)](λ	p)](λ	ADJ
ejpam-4975	289	7	,	,	PUNCT
ejpam-4975	289	8	p	p	NOUN
ejpam-4975	289	9	)	)	PUNCT
ejpam-4975	289	10	]	]	PUNCT
ejpam-4975	289	11	(	(	PUNCT
ejpam-4975	289	12	λ	λ	INTJ
ejpam-4975	289	13	,	,	PUNCT
ejpam-4975	289	14	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	289	15	,	,	PUNCT
ejpam-4975	289	16	p	p	NOUN
ejpam-4975	289	17	)	)	PUNCT
ejpam-4975	289	18	⊆	⊆	NUM
ejpam-4975	289	19	f−1(v	f−1(v	NOUN
ejpam-4975	289	20	(	(	PUNCT
ejpam-4975	289	21	λ	λ	PROPN
ejpam-4975	289	22	,	,	PUNCT
ejpam-4975	289	23	p	p	NOUN
ejpam-4975	289	24	)	)	PUNCT
ejpam-4975	289	25	)	)	PUNCT
ejpam-4975	289	26	for	for	ADP
ejpam-4975	289	27	every	every	DET
ejpam-4975	289	28	p(λ	p(λ	NOUN
ejpam-4975	289	29	,	,	PUNCT
ejpam-4975	289	30	p)-open	p)-open	VERB
ejpam-4975	289	31	set	set	VERB
ejpam-4975	289	32	v	v	NOUN
ejpam-4975	289	33	of	of	ADP
ejpam-4975	289	34	y	y	PROPN
ejpam-4975	289	35	.	.	PUNCT
ejpam-4975	290	1	proof	proof	NOUN
ejpam-4975	290	2	.	.	PUNCT
ejpam-4975	291	1	(	(	PUNCT
ejpam-4975	291	2	1	1	X
ejpam-4975	291	3	)	)	PUNCT
ejpam-4975	291	4	⇒	⇒	NOUN
ejpam-4975	291	5	(	(	PUNCT
ejpam-4975	291	6	2	2	NUM
ejpam-4975	291	7	):	):	PUNCT
ejpam-4975	291	8	let	let	VERB
ejpam-4975	291	9	b	b	X
ejpam-4975	291	10	be	be	AUX
ejpam-4975	291	11	any	any	DET
ejpam-4975	291	12	subset	subset	NOUN
ejpam-4975	291	13	of	of	ADP
ejpam-4975	291	14	y	y	PROPN
ejpam-4975	291	15	.	.	PUNCT
ejpam-4975	292	1	then	then	ADV
ejpam-4975	292	2	,	,	PUNCT
ejpam-4975	292	3	bδ(λ	bδ(λ	NUM
ejpam-4975	292	4	,	,	PUNCT
ejpam-4975	292	5	p	p	NOUN
ejpam-4975	292	6	)	)	PUNCT
ejpam-4975	292	7	is	be	AUX
ejpam-4975	292	8	(	(	PUNCT
ejpam-4975	292	9	λ	λ	X
ejpam-4975	292	10	,	,	PUNCT
ejpam-4975	292	11	p)-closed	p)-close	VERB
ejpam-4975	292	12	in	in	ADP
ejpam-4975	292	13	y	y	PROPN
ejpam-4975	292	14	.	.	PUNCT
ejpam-4975	293	1	by	by	ADP
ejpam-4975	293	2	theorem	theorem	NOUN
ejpam-4975	293	3	2	2	NUM
ejpam-4975	293	4	,	,	PUNCT
ejpam-4975	293	5	[	[	X
ejpam-4975	293	6	f−1([[bδ(λ	f−1([[bδ(λ	NOUN
ejpam-4975	293	7	,	,	PUNCT
ejpam-4975	293	8	p)](λ	p)](λ	ADJ
ejpam-4975	293	9	,	,	PUNCT
ejpam-4975	293	10	p	p	NOUN
ejpam-4975	293	11	)	)	PUNCT
ejpam-4975	293	12	]	]	PUNCT
ejpam-4975	293	13	(	(	PUNCT
ejpam-4975	293	14	λ	λ	INTJ
ejpam-4975	293	15	,	,	PUNCT
ejpam-4975	293	16	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	293	17	,	,	PUNCT
ejpam-4975	293	18	p	p	NOUN
ejpam-4975	293	19	)	)	PUNCT
ejpam-4975	293	20	⊆	⊆	NUM
ejpam-4975	293	21	f−1(bδ(λ	f−1(bδ(λ	NOUN
ejpam-4975	293	22	,	,	PUNCT
ejpam-4975	293	23	p	p	NOUN
ejpam-4975	293	24	)	)	PUNCT
ejpam-4975	293	25	)	)	PUNCT
ejpam-4975	293	26	.	.	PUNCT
ejpam-4975	294	1	(	(	PUNCT
ejpam-4975	294	2	2	2	X
ejpam-4975	294	3	)	)	PUNCT
ejpam-4975	294	4	⇒	⇒	NOUN
ejpam-4975	294	5	(	(	PUNCT
ejpam-4975	294	6	3	3	NUM
ejpam-4975	294	7	):	):	PUNCT
ejpam-4975	294	8	this	this	PRON
ejpam-4975	294	9	is	be	AUX
ejpam-4975	294	10	obvious	obvious	ADJ
ejpam-4975	294	11	since	since	SCONJ
ejpam-4975	294	12	b(λ	b(λ	PROPN
ejpam-4975	294	13	,	,	PUNCT
ejpam-4975	294	14	p	p	NOUN
ejpam-4975	294	15	)	)	PUNCT
ejpam-4975	294	16	⊆	⊆	NUM
ejpam-4975	294	17	bδ(λ	bδ(λ	NUM
ejpam-4975	294	18	,	,	PUNCT
ejpam-4975	294	19	p	p	NOUN
ejpam-4975	294	20	)	)	PUNCT
ejpam-4975	294	21	for	for	ADP
ejpam-4975	294	22	every	every	DET
ejpam-4975	294	23	subset	subset	NOUN
ejpam-4975	294	24	b	b	PROPN
ejpam-4975	294	25	of	of	ADP
ejpam-4975	294	26	y	y	PROPN
ejpam-4975	294	27	.	.	PUNCT
ejpam-4975	295	1	(	(	PUNCT
ejpam-4975	295	2	3	3	X
ejpam-4975	295	3	)	)	PUNCT
ejpam-4975	295	4	⇒	⇒	NOUN
ejpam-4975	295	5	(	(	PUNCT
ejpam-4975	295	6	4	4	NUM
ejpam-4975	295	7	):	):	PUNCT
ejpam-4975	295	8	this	this	PRON
ejpam-4975	295	9	is	be	AUX
ejpam-4975	295	10	obvious	obvious	ADJ
ejpam-4975	295	11	since	since	SCONJ
ejpam-4975	295	12	v	v	NOUN
ejpam-4975	295	13	(	(	PUNCT
ejpam-4975	295	14	λ	λ	PROPN
ejpam-4975	295	15	,	,	PUNCT
ejpam-4975	295	16	p	p	NOUN
ejpam-4975	295	17	)	)	PUNCT
ejpam-4975	295	18	=	=	SYM
ejpam-4975	295	19	v	v	ADP
ejpam-4975	295	20	δ(λ	δ(λ	PROPN
ejpam-4975	295	21	,	,	PUNCT
ejpam-4975	295	22	p	p	NOUN
ejpam-4975	295	23	)	)	PUNCT
ejpam-4975	295	24	for	for	ADP
ejpam-4975	295	25	every	every	DET
ejpam-4975	295	26	(	(	PUNCT
ejpam-4975	295	27	λ	λ	NOUN
ejpam-4975	295	28	,	,	PUNCT
ejpam-4975	295	29	p)-open	p)-open	VERB
ejpam-4975	295	30	set	set	VERB
ejpam-4975	295	31	v	v	NOUN
ejpam-4975	295	32	of	of	ADP
ejpam-4975	295	33	y	y	PROPN
ejpam-4975	295	34	.	.	PUNCT
ejpam-4975	296	1	(	(	PUNCT
ejpam-4975	296	2	4	4	X
ejpam-4975	296	3	)	)	PUNCT
ejpam-4975	296	4	⇒	⇒	NOUN
ejpam-4975	296	5	(	(	PUNCT
ejpam-4975	296	6	5	5	NUM
ejpam-4975	296	7	):	):	PUNCT
ejpam-4975	296	8	let	let	VERB
ejpam-4975	296	9	v	v	PART
ejpam-4975	296	10	be	be	AUX
ejpam-4975	296	11	any	any	DET
ejpam-4975	296	12	p(λ	p(λ	NOUN
ejpam-4975	296	13	,	,	PUNCT
ejpam-4975	296	14	p)-open	p)-open	VERB
ejpam-4975	296	15	set	set	NOUN
ejpam-4975	296	16	of	of	ADP
ejpam-4975	296	17	y	y	PROPN
ejpam-4975	296	18	.	.	PUNCT
ejpam-4975	297	1	then	then	ADV
ejpam-4975	297	2	,	,	PUNCT
ejpam-4975	297	3	we	we	PRON
ejpam-4975	297	4	have	have	VERB
ejpam-4975	297	5	v	v	ADP
ejpam-4975	297	6	⊆	⊆	NUM
ejpam-4975	297	7	[	[	X
ejpam-4975	297	8	v	v	X
ejpam-4975	297	9	(	(	PUNCT
ejpam-4975	297	10	λ	λ	PROPN
ejpam-4975	297	11	,	,	PUNCT
ejpam-4975	297	12	p)](λ	p)](λ	ADJ
ejpam-4975	297	13	,	,	PUNCT
ejpam-4975	297	14	p	p	NOUN
ejpam-4975	297	15	)	)	PUNCT
ejpam-4975	297	16	and	and	CCONJ
ejpam-4975	297	17	v	v	NOUN
ejpam-4975	297	18	(	(	PUNCT
ejpam-4975	297	19	λ	λ	X
ejpam-4975	297	20	,	,	PUNCT
ejpam-4975	297	21	p	p	NOUN
ejpam-4975	297	22	)	)	PUNCT
ejpam-4975	297	23	=	=	NOUN
ejpam-4975	298	1	[	[	X
ejpam-4975	298	2	[	[	X
ejpam-4975	298	3	v	v	X
ejpam-4975	298	4	(	(	PUNCT
ejpam-4975	298	5	λ	λ	PROPN
ejpam-4975	298	6	,	,	PUNCT
ejpam-4975	298	7	p)](λ	p)](λ	ADJ
ejpam-4975	298	8	,	,	PUNCT
ejpam-4975	298	9	p	p	NOUN
ejpam-4975	298	10	)	)	PUNCT
ejpam-4975	298	11	]	]	PUNCT
ejpam-4975	298	12	(	(	PUNCT
ejpam-4975	298	13	λ	λ	X
ejpam-4975	298	14	,	,	PUNCT
ejpam-4975	298	15	p	p	NOUN
ejpam-4975	298	16	)	)	PUNCT
ejpam-4975	298	17	.	.	PUNCT
ejpam-4975	299	1	thus	thus	ADV
ejpam-4975	299	2	,	,	PUNCT
ejpam-4975	299	3	by	by	ADP
ejpam-4975	299	4	(	(	PUNCT
ejpam-4975	299	5	4	4	NUM
ejpam-4975	299	6	)	)	PUNCT
ejpam-4975	299	7	,	,	PUNCT
ejpam-4975	300	1	[	[	X
ejpam-4975	300	2	f−1([[v	f−1([[v	PROPN
ejpam-4975	300	3	(	(	PUNCT
ejpam-4975	300	4	λ	λ	PROPN
ejpam-4975	300	5	,	,	PUNCT
ejpam-4975	300	6	p)](λ	p)](λ	ADJ
ejpam-4975	300	7	,	,	PUNCT
ejpam-4975	300	8	p	p	NOUN
ejpam-4975	300	9	)	)	PUNCT
ejpam-4975	300	10	]	]	PUNCT
ejpam-4975	300	11	(	(	PUNCT
ejpam-4975	300	12	λ	λ	INTJ
ejpam-4975	300	13	,	,	PUNCT
ejpam-4975	300	14	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	300	15	,	,	PUNCT
ejpam-4975	300	16	p	p	NOUN
ejpam-4975	300	17	)	)	PUNCT
ejpam-4975	300	18	⊆	⊆	NUM
ejpam-4975	300	19	f−1(v	f−1(v	NOUN
ejpam-4975	300	20	(	(	PUNCT
ejpam-4975	300	21	λ	λ	PROPN
ejpam-4975	300	22	,	,	PUNCT
ejpam-4975	300	23	p	p	NOUN
ejpam-4975	300	24	)	)	PUNCT
ejpam-4975	300	25	)	)	PUNCT
ejpam-4975	300	26	.	.	PUNCT
ejpam-4975	301	1	(	(	PUNCT
ejpam-4975	301	2	5	5	X
ejpam-4975	301	3	)	)	PUNCT
ejpam-4975	301	4	⇒	⇒	NOUN
ejpam-4975	301	5	(	(	PUNCT
ejpam-4975	301	6	1	1	NUM
ejpam-4975	301	7	):	):	PUNCT
ejpam-4975	301	8	let	let	VERB
ejpam-4975	301	9	k	k	PRON
ejpam-4975	301	10	be	be	AUX
ejpam-4975	301	11	any	any	DET
ejpam-4975	301	12	r(λ	r(λ	NOUN
ejpam-4975	301	13	,	,	PUNCT
ejpam-4975	301	14	p)-closed	p)-close	VERB
ejpam-4975	301	15	set	set	NOUN
ejpam-4975	301	16	of	of	ADP
ejpam-4975	301	17	y	y	PROPN
ejpam-4975	301	18	.	.	PUNCT
ejpam-4975	302	1	then	then	ADV
ejpam-4975	302	2	,	,	PUNCT
ejpam-4975	302	3	we	we	PRON
ejpam-4975	302	4	have	have	VERB
ejpam-4975	302	5	k(λ	k(λ	NOUN
ejpam-4975	302	6	,	,	PUNCT
ejpam-4975	302	7	p	p	NOUN
ejpam-4975	302	8	)	)	PUNCT
ejpam-4975	302	9	is	be	AUX
ejpam-4975	302	10	p(λ	p(λ	NOUN
ejpam-4975	302	11	,	,	PUNCT
ejpam-4975	302	12	p)-open	p)-open	VERB
ejpam-4975	302	13	in	in	ADP
ejpam-4975	302	14	y	y	PROPN
ejpam-4975	302	15	and	and	CCONJ
ejpam-4975	302	16	by	by	ADP
ejpam-4975	302	17	(	(	PUNCT
ejpam-4975	302	18	5	5	NUM
ejpam-4975	302	19	)	)	PUNCT
ejpam-4975	302	20	,	,	PUNCT
ejpam-4975	303	1	[	[	X
ejpam-4975	303	2	f−1(k)]θ(λ	f−1(k)]θ(λ	X
ejpam-4975	303	3	,	,	PUNCT
ejpam-4975	303	4	p	p	NOUN
ejpam-4975	303	5	)	)	PUNCT
ejpam-4975	303	6	=	=	NOUN
ejpam-4975	304	1	[	[	X
ejpam-4975	304	2	f−1([k(λ	f−1([k(λ	NOUN
ejpam-4975	304	3	,	,	PUNCT
ejpam-4975	304	4	p	p	NOUN
ejpam-4975	304	5	)	)	PUNCT
ejpam-4975	304	6	]	]	PUNCT
ejpam-4975	304	7	(	(	PUNCT
ejpam-4975	304	8	λ	λ	INTJ
ejpam-4975	304	9	,	,	PUNCT
ejpam-4975	304	10	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	304	11	,	,	PUNCT
ejpam-4975	304	12	p	p	NOUN
ejpam-4975	304	13	)	)	PUNCT
ejpam-4975	304	14	references	reference	NOUN
ejpam-4975	304	15	307	307	NUM
ejpam-4975	304	16	=	=	SYM
ejpam-4975	305	1	[	[	X
ejpam-4975	305	2	f−1([[[k(λ	f−1([[[k(λ	NOUN
ejpam-4975	305	3	,	,	PUNCT
ejpam-4975	305	4	p	p	NOUN
ejpam-4975	305	5	)	)	PUNCT
ejpam-4975	305	6	]	]	PUNCT
ejpam-4975	305	7	(	(	PUNCT
ejpam-4975	305	8	λ	λ	X
ejpam-4975	305	9	,	,	PUNCT
ejpam-4975	305	10	p)](λ	p)](λ	ADJ
ejpam-4975	305	11	,	,	PUNCT
ejpam-4975	305	12	p	p	NOUN
ejpam-4975	305	13	)	)	PUNCT
ejpam-4975	305	14	]	]	PUNCT
ejpam-4975	305	15	(	(	PUNCT
ejpam-4975	305	16	λ	λ	INTJ
ejpam-4975	305	17	,	,	PUNCT
ejpam-4975	305	18	p))]θ(λ	p))]θ(λ	NOUN
ejpam-4975	305	19	,	,	PUNCT
ejpam-4975	305	20	p	p	NOUN
ejpam-4975	305	21	)	)	PUNCT
ejpam-4975	305	22	⊆	⊆	NUM
ejpam-4975	305	23	f−1([k(λ	f−1([k(λ	NOUN
ejpam-4975	305	24	,	,	PUNCT
ejpam-4975	305	25	p	p	NOUN
ejpam-4975	305	26	)	)	PUNCT
ejpam-4975	305	27	]	]	PUNCT
ejpam-4975	305	28	(	(	PUNCT
ejpam-4975	305	29	λ	λ	X
ejpam-4975	305	30	,	,	PUNCT
ejpam-4975	305	31	p	p	NOUN
ejpam-4975	305	32	)	)	PUNCT
ejpam-4975	305	33	)	)	PUNCT
ejpam-4975	305	34	=	=	SYM
ejpam-4975	305	35	f−1(k	f−1(k	PROPN
ejpam-4975	305	36	)	)	PUNCT
ejpam-4975	305	37	.	.	PUNCT
ejpam-4975	306	1	thus	thus	ADV
ejpam-4975	306	2	,	,	PUNCT
ejpam-4975	306	3	[	[	X
ejpam-4975	306	4	f−1(k)]θ(λ	f−1(k)]θ(λ	X
ejpam-4975	306	5	,	,	PUNCT
ejpam-4975	306	6	p	p	NOUN
ejpam-4975	306	7	)	)	PUNCT
ejpam-4975	306	8	=	=	SYM
ejpam-4975	306	9	f−1(k	f−1(k	PROPN
ejpam-4975	306	10	)	)	PUNCT
ejpam-4975	306	11	and	and	CCONJ
ejpam-4975	306	12	by	by	ADP
ejpam-4975	306	13	lemma	lemma	PROPN
ejpam-4975	306	14	1	1	NUM
ejpam-4975	306	15	,	,	PUNCT
ejpam-4975	306	16	f−1(k	f−1(k	PROPN
ejpam-4975	306	17	)	)	PUNCT
ejpam-4975	306	18	is	be	AUX
ejpam-4975	306	19	θ(λ	θ(λ	PROPN
ejpam-4975	306	20	,	,	PUNCT
ejpam-4975	306	21	p)-closed	p)-close	VERB
ejpam-4975	306	22	in	in	ADP
ejpam-4975	306	23	x.	x.	NOUN
ejpam-4975	306	24	by	by	ADP
ejpam-4975	306	25	theorem	theorem	NOUN
ejpam-4975	306	26	1	1	NUM
ejpam-4975	306	27	,	,	PUNCT
ejpam-4975	306	28	f	f	PROPN
ejpam-4975	306	29	is	be	AUX
ejpam-4975	306	30	almost	almost	ADV
ejpam-4975	306	31	strongly	strongly	ADV
ejpam-4975	306	32	θ(λ	θ(λ	VERB
ejpam-4975	306	33	,	,	PUNCT
ejpam-4975	306	34	p)-continuous	p)-continuous	ADJ
ejpam-4975	306	35	.	.	PUNCT
ejpam-4975	307	1	acknowledgements	acknowledgement	NOUN
ejpam-4975	307	2	this	this	DET
ejpam-4975	307	3	research	research	NOUN
ejpam-4975	307	4	project	project	NOUN
ejpam-4975	307	5	was	be	AUX
ejpam-4975	307	6	financially	financially	ADV
ejpam-4975	307	7	supported	support	VERB
ejpam-4975	307	8	by	by	ADP
ejpam-4975	307	9	mahasarakham	mahasarakham	PROPN
ejpam-4975	307	10	university	university	PROPN
ejpam-4975	307	11	.	.	PUNCT
ejpam-4975	308	1	references	reference	NOUN
ejpam-4975	308	2	[	[	X
ejpam-4975	308	3	1	1	X
ejpam-4975	308	4	]	]	PUNCT
ejpam-4975	308	5	s.	s.	PROPN
ejpam-4975	308	6	p.	p.	PROPN
ejpam-4975	308	7	arya	arya	PROPN
ejpam-4975	308	8	and	and	CCONJ
ejpam-4975	308	9	m.	m.	PROPN
ejpam-4975	308	10	p.	p.	PROPN
ejpam-4975	308	11	bhamini	bhamini	PROPN
ejpam-4975	308	12	.	.	PUNCT
ejpam-4975	309	1	some	some	DET
ejpam-4975	309	2	weaker	weak	ADJ
ejpam-4975	309	3	forms	form	NOUN
ejpam-4975	309	4	of	of	ADP
ejpam-4975	309	5	semi	semi	ADJ
ejpam-4975	309	6	-	-	ADJ
ejpam-4975	309	7	continuous	continuous	ADJ
ejpam-4975	309	8	functions	function	NOUN
ejpam-4975	309	9	.	.	PUNCT
ejpam-4975	310	1	ganita	ganita	NOUN
ejpam-4975	310	2	,	,	PUNCT
ejpam-4975	310	3	33:124–134	33:124–134	NUM
ejpam-4975	310	4	,	,	PUNCT
ejpam-4975	310	5	1982	1982	NUM
ejpam-4975	310	6	.	.	PUNCT
ejpam-4975	311	1	[	[	X
ejpam-4975	311	2	2	2	X
ejpam-4975	311	3	]	]	X
ejpam-4975	311	4	y.	y.	PROPN
ejpam-4975	311	5	beceren	beceren	PROPN
ejpam-4975	311	6	,	,	PUNCT
ejpam-4975	311	7	s.	s.	PROPN
ejpam-4975	311	8	yuksel	yuksel	PROPN
ejpam-4975	311	9	,	,	PUNCT
ejpam-4975	311	10	and	and	CCONJ
ejpam-4975	311	11	e.	e.	PROPN
ejpam-4975	311	12	hatir	hatir	PROPN
ejpam-4975	311	13	.	.	PUNCT
ejpam-4975	312	1	on	on	ADP
ejpam-4975	312	2	almost	almost	ADV
ejpam-4975	312	3	strongly	strongly	ADV
ejpam-4975	312	4	θ	θ	NOUN
ejpam-4975	312	5	-	-	PUNCT
ejpam-4975	312	6	semi	semi	ADJ
ejpam-4975	312	7	-	-	ADJ
ejpam-4975	312	8	continuous	continuous	ADJ
ejpam-4975	312	9	functions	function	NOUN
ejpam-4975	312	10	.	.	PUNCT
ejpam-4975	313	1	bulletin	bulletin	NOUN
ejpam-4975	313	2	of	of	ADP
ejpam-4975	313	3	the	the	DET
ejpam-4975	313	4	calcutta	calcutta	PROPN
ejpam-4975	313	5	mathematical	mathematical	ADJ
ejpam-4975	313	6	society	society	NOUN
ejpam-4975	313	7	,	,	PUNCT
ejpam-4975	313	8	87:329–334	87:329–334	PROPN
ejpam-4975	313	9	,	,	PUNCT
ejpam-4975	313	10	1995	1995	NUM
ejpam-4975	313	11	.	.	PUNCT
ejpam-4975	314	1	[	[	X
ejpam-4975	314	2	3	3	X
ejpam-4975	314	3	]	]	PUNCT
ejpam-4975	314	4	c.	c.	PROPN
ejpam-4975	314	5	boonpok	boonpok	PROPN
ejpam-4975	314	6	.	.	PUNCT
ejpam-4975	315	1	m	m	VERB
ejpam-4975	315	2	-continuous	-continuous	ADJ
ejpam-4975	315	3	functions	function	NOUN
ejpam-4975	315	4	on	on	ADP
ejpam-4975	315	5	biminimal	biminimal	NOUN
ejpam-4975	315	6	structure	structure	NOUN
ejpam-4975	315	7	spaces	space	NOUN
ejpam-4975	315	8	.	.	PUNCT
ejpam-4975	316	1	far	far	PROPN
ejpam-4975	316	2	east	east	PROPN
ejpam-4975	316	3	journal	journal	PROPN
ejpam-4975	316	4	of	of	ADP
ejpam-4975	316	5	mathematical	mathematical	ADJ
ejpam-4975	316	6	sciences	science	NOUN
ejpam-4975	316	7	,	,	PUNCT
ejpam-4975	316	8	43(1):41–58	43(1):41–58	NUM
ejpam-4975	316	9	,	,	PUNCT
ejpam-4975	316	10	2010	2010	NUM
ejpam-4975	316	11	.	.	PUNCT
ejpam-4975	317	1	[	[	X
ejpam-4975	317	2	4	4	X
ejpam-4975	317	3	]	]	PUNCT
ejpam-4975	317	4	c.	c.	PROPN
ejpam-4975	317	5	boonpok	boonpok	PROPN
ejpam-4975	317	6	and	and	CCONJ
ejpam-4975	317	7	j.	j.	PROPN
ejpam-4975	317	8	khampakdee	khampakdee	PROPN
ejpam-4975	317	9	.	.	PUNCT
ejpam-4975	318	1	(	(	PUNCT
ejpam-4975	318	2	λ	λ	NOUN
ejpam-4975	318	3	,	,	PUNCT
ejpam-4975	318	4	sp)-open	sp)-open	ADJ
ejpam-4975	318	5	sets	set	NOUN
ejpam-4975	318	6	in	in	ADP
ejpam-4975	318	7	topological	topological	ADJ
ejpam-4975	318	8	spaces	space	NOUN
ejpam-4975	318	9	.	.	PUNCT
ejpam-4975	319	1	european	european	ADJ
ejpam-4975	319	2	journal	journal	PROPN
ejpam-4975	319	3	of	of	ADP
ejpam-4975	319	4	pure	pure	ADJ
ejpam-4975	319	5	and	and	CCONJ
ejpam-4975	319	6	applied	applied	ADJ
ejpam-4975	319	7	mathematics	mathematic	NOUN
ejpam-4975	319	8	,	,	PUNCT
ejpam-4975	319	9	15(2):572–588	15(2):572–588	NUM
ejpam-4975	319	10	,	,	PUNCT
ejpam-4975	319	11	2022	2022	NUM
ejpam-4975	319	12	.	.	PUNCT
ejpam-4975	320	1	[	[	X
ejpam-4975	320	2	5	5	X
ejpam-4975	320	3	]	]	PUNCT
ejpam-4975	320	4	c.	c.	PROPN
ejpam-4975	320	5	boonpok	boonpok	PROPN
ejpam-4975	320	6	and	and	CCONJ
ejpam-4975	320	7	m.	m.	NOUN
ejpam-4975	320	8	thongmoon	thongmoon	NOUN
ejpam-4975	320	9	.	.	PUNCT
ejpam-4975	321	1	δp(λ	δp(λ	NOUN
ejpam-4975	321	2	,	,	PUNCT
ejpam-4975	321	3	p)-open	p)-open	VERB
ejpam-4975	321	4	sets	set	NOUN
ejpam-4975	321	5	in	in	ADP
ejpam-4975	321	6	topological	topological	ADJ
ejpam-4975	321	7	spaces	space	NOUN
ejpam-4975	321	8	.	.	PUNCT
ejpam-4975	322	1	european	european	ADJ
ejpam-4975	322	2	journal	journal	PROPN
ejpam-4975	322	3	of	of	ADP
ejpam-4975	322	4	pure	pure	ADJ
ejpam-4975	322	5	and	and	CCONJ
ejpam-4975	322	6	applied	applied	ADJ
ejpam-4975	322	7	mathematics	mathematic	NOUN
ejpam-4975	322	8	,	,	PUNCT
ejpam-4975	322	9	16(3):1533–1542	16(3):1533–1542	NUM
ejpam-4975	322	10	,	,	PUNCT
ejpam-4975	322	11	2023	2023	NUM
ejpam-4975	322	12	.	.	PUNCT
ejpam-4975	323	1	[	[	X
ejpam-4975	323	2	6	6	NUM
ejpam-4975	323	3	]	]	PUNCT
ejpam-4975	323	4	c.	c.	PROPN
ejpam-4975	323	5	boonpok	boonpok	PROPN
ejpam-4975	323	6	and	and	CCONJ
ejpam-4975	323	7	c.	c.	PROPN
ejpam-4975	323	8	viriyapong	viriyapong	PROPN
ejpam-4975	323	9	.	.	PUNCT
ejpam-4975	324	1	on	on	ADP
ejpam-4975	324	2	(	(	PUNCT
ejpam-4975	324	3	λ	λ	PROPN
ejpam-4975	324	4	,	,	PUNCT
ejpam-4975	324	5	p)-closed	p)-close	VERB
ejpam-4975	324	6	sets	set	NOUN
ejpam-4975	324	7	and	and	CCONJ
ejpam-4975	324	8	the	the	DET
ejpam-4975	324	9	related	related	ADJ
ejpam-4975	324	10	notions	notion	NOUN
ejpam-4975	324	11	in	in	ADP
ejpam-4975	324	12	topological	topological	ADJ
ejpam-4975	324	13	spaces	space	NOUN
ejpam-4975	324	14	.	.	PUNCT
ejpam-4975	325	1	european	european	ADJ
ejpam-4975	325	2	journal	journal	PROPN
ejpam-4975	325	3	of	of	ADP
ejpam-4975	325	4	pure	pure	ADJ
ejpam-4975	325	5	and	and	CCONJ
ejpam-4975	325	6	applied	applied	ADJ
ejpam-4975	325	7	mathematics	mathematic	NOUN
ejpam-4975	325	8	,	,	PUNCT
ejpam-4975	325	9	15(2):415	15(2):415	PROPN
ejpam-4975	325	10	–	–	PUNCT
ejpam-4975	325	11	436	436	NUM
ejpam-4975	325	12	,	,	PUNCT
ejpam-4975	325	13	2022	2022	NUM
ejpam-4975	325	14	.	.	PUNCT
ejpam-4975	326	1	[	[	X
ejpam-4975	326	2	7	7	X
ejpam-4975	326	3	]	]	X
ejpam-4975	326	4	c.	c.	PROPN
ejpam-4975	326	5	boonpok	boonpok	PROPN
ejpam-4975	326	6	and	and	CCONJ
ejpam-4975	326	7	c.	c.	PROPN
ejpam-4975	326	8	viriyapong	viriyapong	PROPN
ejpam-4975	326	9	.	.	PUNCT
ejpam-4975	327	1	on	on	ADP
ejpam-4975	327	2	some	some	DET
ejpam-4975	327	3	forms	form	NOUN
ejpam-4975	327	4	of	of	ADP
ejpam-4975	327	5	closed	closed	ADJ
ejpam-4975	327	6	sets	set	NOUN
ejpam-4975	327	7	and	and	CCONJ
ejpam-4975	327	8	related	related	ADJ
ejpam-4975	327	9	topics	topic	NOUN
ejpam-4975	327	10	.	.	PUNCT
ejpam-4975	328	1	european	european	ADJ
ejpam-4975	328	2	journal	journal	PROPN
ejpam-4975	328	3	of	of	ADP
ejpam-4975	328	4	pure	pure	ADJ
ejpam-4975	328	5	and	and	CCONJ
ejpam-4975	328	6	applied	applied	ADJ
ejpam-4975	328	7	mathematics	mathematic	NOUN
ejpam-4975	328	8	,	,	PUNCT
ejpam-4975	328	9	16(1):336–362	16(1):336–362	NUM
ejpam-4975	328	10	,	,	PUNCT
ejpam-4975	328	11	2023	2023	NUM
ejpam-4975	328	12	.	.	PUNCT
ejpam-4975	329	1	[	[	X
ejpam-4975	329	2	8	8	NUM
ejpam-4975	329	3	]	]	X
ejpam-4975	329	4	f.	f.	PROPN
ejpam-4975	329	5	cammaroto	cammaroto	NOUN
ejpam-4975	329	6	and	and	CCONJ
ejpam-4975	329	7	t.	t.	PROPN
ejpam-4975	329	8	noiri	noiri	PROPN
ejpam-4975	329	9	.	.	PUNCT
ejpam-4975	330	1	almost	almost	ADV
ejpam-4975	330	2	irresolute	irresolute	ADJ
ejpam-4975	330	3	functions	function	NOUN
ejpam-4975	330	4	.	.	PUNCT
ejpam-4975	331	1	indian	indian	ADJ
ejpam-4975	331	2	journal	journal	PROPN
ejpam-4975	331	3	of	of	ADP
ejpam-4975	331	4	pure	pure	ADJ
ejpam-4975	331	5	and	and	CCONJ
ejpam-4975	331	6	applied	applied	ADJ
ejpam-4975	331	7	mathematics	mathematic	NOUN
ejpam-4975	331	8	,	,	PUNCT
ejpam-4975	331	9	20:472–482	20:472–482	PROPN
ejpam-4975	331	10	,	,	PUNCT
ejpam-4975	331	11	1989	1989	NUM
ejpam-4975	331	12	.	.	PUNCT
ejpam-4975	332	1	[	[	X
ejpam-4975	332	2	9	9	NUM
ejpam-4975	332	3	]	]	PUNCT
ejpam-4975	332	4	k.	k.	PROPN
ejpam-4975	332	5	k.	k.	PROPN
ejpam-4975	333	1	dube	dube	PROPN
ejpam-4975	333	2	and	and	CCONJ
ejpam-4975	333	3	s.	s.	PROPN
ejpam-4975	333	4	s.	s.	PROPN
ejpam-4975	333	5	chauhan	chauhan	PROPN
ejpam-4975	333	6	.	.	PUNCT
ejpam-4975	334	1	strongly	strongly	ADV
ejpam-4975	334	2	closure	closure	VERB
ejpam-4975	334	3	semi	semi	ADJ
ejpam-4975	334	4	-	-	ADJ
ejpam-4975	334	5	continuous	continuous	ADJ
ejpam-4975	334	6	mappings	mapping	NOUN
ejpam-4975	334	7	.	.	PUNCT
ejpam-4975	335	1	the	the	DET
ejpam-4975	335	2	journal	journal	NOUN
ejpam-4975	335	3	of	of	ADP
ejpam-4975	335	4	the	the	DET
ejpam-4975	335	5	indian	indian	PROPN
ejpam-4975	335	6	academy	academy	PROPN
ejpam-4975	335	7	of	of	ADP
ejpam-4975	335	8	mathematics	mathematics	PROPN
ejpam-4975	335	9	,	,	PUNCT
ejpam-4975	335	10	19:139–147	19:139–147	NUM
ejpam-4975	335	11	,	,	PUNCT
ejpam-4975	335	12	1997	1997	NUM
ejpam-4975	335	13	.	.	PUNCT
ejpam-4975	336	1	[	[	X
ejpam-4975	336	2	10	10	NUM
ejpam-4975	336	3	]	]	X
ejpam-4975	336	4	s.	s.	PROPN
ejpam-4975	336	5	fomin	fomin	PROPN
ejpam-4975	336	6	.	.	PUNCT
ejpam-4975	337	1	extensions	extension	NOUN
ejpam-4975	337	2	of	of	ADP
ejpam-4975	337	3	topological	topological	ADJ
ejpam-4975	337	4	spaces	space	NOUN
ejpam-4975	337	5	.	.	PUNCT
ejpam-4975	338	1	doklady	doklady	PROPN
ejpam-4975	338	2	akademii	akademii	NOUN
ejpam-4975	338	3	nauk	nauk	NOUN
ejpam-4975	338	4	sssr	sssr	NOUN
ejpam-4975	338	5	,	,	PUNCT
ejpam-4975	338	6	32:114	32:114	NUM
ejpam-4975	338	7	–	–	PUNCT
ejpam-4975	338	8	116	116	NUM
ejpam-4975	338	9	,	,	PUNCT
ejpam-4975	338	10	1941	1941	NUM
ejpam-4975	338	11	.	.	PUNCT
ejpam-4975	339	1	[	[	X
ejpam-4975	339	2	11	11	NUM
ejpam-4975	339	3	]	]	PUNCT
ejpam-4975	339	4	m.	m.	NOUN
ejpam-4975	339	5	ganster	ganster	NOUN
ejpam-4975	339	6	,	,	PUNCT
ejpam-4975	339	7	s.	s.	PROPN
ejpam-4975	339	8	jafari	jafari	PROPN
ejpam-4975	339	9	,	,	PUNCT
ejpam-4975	339	10	and	and	CCONJ
ejpam-4975	339	11	t.	t.	PROPN
ejpam-4975	339	12	noiri	noiri	PROPN
ejpam-4975	339	13	.	.	PUNCT
ejpam-4975	340	1	on	on	ADP
ejpam-4975	340	2	pre	pre	ADJ
ejpam-4975	340	3	-	-	ADJ
ejpam-4975	340	4	λ	λ	NOUN
ejpam-4975	340	5	-	-	NOUN
ejpam-4975	340	6	sets	set	NOUN
ejpam-4975	340	7	and	and	CCONJ
ejpam-4975	340	8	pre	pre	ADJ
ejpam-4975	340	9	-	-	ADJ
ejpam-4975	340	10	v	v	ADJ
ejpam-4975	340	11	-sets	-set	NOUN
ejpam-4975	340	12	.	.	PUNCT
ejpam-4975	341	1	acta	acta	PROPN
ejpam-4975	341	2	mathematica	mathematica	PROPN
ejpam-4975	341	3	hungarica	hungarica	PROPN
ejpam-4975	341	4	,	,	PUNCT
ejpam-4975	341	5	95:337–343	95:337–343	PROPN
ejpam-4975	341	6	,	,	PUNCT
ejpam-4975	341	7	2002	2002	NUM
ejpam-4975	341	8	.	.	PUNCT
ejpam-4975	342	1	references	reference	NOUN
ejpam-4975	342	2	308	308	NUM
ejpam-4975	343	1	[	[	X
ejpam-4975	343	2	12	12	NUM
ejpam-4975	343	3	]	]	PUNCT
ejpam-4975	343	4	s.	s.	PROPN
ejpam-4975	343	5	jafari	jafari	PROPN
ejpam-4975	343	6	and	and	CCONJ
ejpam-4975	343	7	t.	t.	PROPN
ejpam-4975	343	8	noiri	noiri	PROPN
ejpam-4975	343	9	.	.	PUNCT
ejpam-4975	344	1	strongly	strongly	ADV
ejpam-4975	344	2	θ	θ	VERB
ejpam-4975	344	3	-	-	PUNCT
ejpam-4975	344	4	semi	semi	ADJ
ejpam-4975	344	5	-	-	ADJ
ejpam-4975	344	6	continuous	continuous	ADJ
ejpam-4975	344	7	functions	function	NOUN
ejpam-4975	344	8	.	.	PUNCT
ejpam-4975	345	1	indian	indian	ADJ
ejpam-4975	345	2	journal	journal	PROPN
ejpam-4975	345	3	of	of	ADP
ejpam-4975	345	4	pure	pure	ADJ
ejpam-4975	345	5	and	and	CCONJ
ejpam-4975	345	6	applied	applied	ADJ
ejpam-4975	345	7	mathematics	mathematic	NOUN
ejpam-4975	345	8	,	,	PUNCT
ejpam-4975	345	9	29:1195–1201	29:1195–1201	NUM
ejpam-4975	345	10	,	,	PUNCT
ejpam-4975	345	11	1998	1998	NUM
ejpam-4975	345	12	.	.	PUNCT
ejpam-4975	346	1	[	[	X
ejpam-4975	346	2	13	13	NUM
ejpam-4975	346	3	]	]	PUNCT
ejpam-4975	346	4	s.	s.	PROPN
ejpam-4975	346	5	jafari	jafari	PROPN
ejpam-4975	346	6	and	and	CCONJ
ejpam-4975	346	7	t.	t.	PROPN
ejpam-4975	346	8	noiri	noiri	PROPN
ejpam-4975	346	9	.	.	PUNCT
ejpam-4975	347	1	on	on	ADP
ejpam-4975	347	2	almost	almost	ADV
ejpam-4975	347	3	strongly	strongly	ADV
ejpam-4975	347	4	θ	θ	NOUN
ejpam-4975	347	5	-	-	PUNCT
ejpam-4975	347	6	semi	semi	ADJ
ejpam-4975	347	7	-	-	ADJ
ejpam-4975	347	8	continuous	continuous	ADJ
ejpam-4975	347	9	functions	function	NOUN
ejpam-4975	347	10	.	.	PUNCT
ejpam-4975	348	1	acta	acta	PROPN
ejpam-4975	348	2	mathematica	mathematica	PROPN
ejpam-4975	348	3	hungarica	hungarica	PROPN
ejpam-4975	348	4	,	,	PUNCT
ejpam-4975	348	5	85:167–173	85:167–173	PROPN
ejpam-4975	348	6	,	,	PUNCT
ejpam-4975	348	7	1999	1999	NUM
ejpam-4975	348	8	.	.	PUNCT
ejpam-4975	349	1	[	[	X
ejpam-4975	349	2	14	14	NUM
ejpam-4975	349	3	]	]	X
ejpam-4975	349	4	s.	s.	PROPN
ejpam-4975	349	5	jafari	jafari	PROPN
ejpam-4975	349	6	and	and	CCONJ
ejpam-4975	349	7	t.	t.	PROPN
ejpam-4975	349	8	noiri	noiri	PROPN
ejpam-4975	349	9	.	.	PUNCT
ejpam-4975	350	1	strongly	strongly	ADV
ejpam-4975	350	2	sober	sober	ADJ
ejpam-4975	350	3	θ	θ	ADJ
ejpam-4975	350	4	-	-	ADJ
ejpam-4975	350	5	continuous	continuous	ADJ
ejpam-4975	350	6	functions	function	NOUN
ejpam-4975	350	7	.	.	PUNCT
ejpam-4975	351	1	journal	journal	NOUN
ejpam-4975	351	2	of	of	ADP
ejpam-4975	351	3	pure	pure	ADJ
ejpam-4975	351	4	mathematics	mathematic	NOUN
ejpam-4975	351	5	,	,	PUNCT
ejpam-4975	351	6	16:9–17	16:9–17	NUM
ejpam-4975	351	7	,	,	PUNCT
ejpam-4975	351	8	1999	1999	NUM
ejpam-4975	351	9	.	.	PUNCT
ejpam-4975	352	1	[	[	X
ejpam-4975	352	2	15	15	NUM
ejpam-4975	352	3	]	]	X
ejpam-4975	352	4	s.	s.	PROPN
ejpam-4975	352	5	jafari	jafari	PROPN
ejpam-4975	352	6	and	and	CCONJ
ejpam-4975	352	7	t.	t.	PROPN
ejpam-4975	352	8	noiri	noiri	PROPN
ejpam-4975	352	9	.	.	PUNCT
ejpam-4975	353	1	properties	property	NOUN
ejpam-4975	353	2	of	of	ADP
ejpam-4975	353	3	θ	θ	NOUN
ejpam-4975	353	4	-	-	PUNCT
ejpam-4975	353	5	semi	semi	ADJ
ejpam-4975	353	6	-	-	ADJ
ejpam-4975	353	7	continuous	continuous	ADJ
ejpam-4975	353	8	functions	function	NOUN
ejpam-4975	353	9	.	.	PUNCT
ejpam-4975	354	1	journal	journal	PROPN
ejpam-4975	354	2	of	of	ADP
ejpam-4975	354	3	institute	institute	PROPN
ejpam-4975	354	4	of	of	ADP
ejpam-4975	354	5	mathematics	mathematics	PROPN
ejpam-4975	354	6	and	and	CCONJ
ejpam-4975	354	7	computer	computer	NOUN
ejpam-4975	354	8	sciences	science	NOUN
ejpam-4975	354	9	.	.	PUNCT
ejpam-4975	355	1	mathematics	mathematic	NOUN
ejpam-4975	355	2	series	series	PROPN
ejpam-4975	355	3	,	,	PUNCT
ejpam-4975	355	4	13:123–128	13:123–128	NUM
ejpam-4975	355	5	,	,	PUNCT
ejpam-4975	355	6	2000	2000	NUM
ejpam-4975	355	7	.	.	PUNCT
ejpam-4975	356	1	[	[	X
ejpam-4975	356	2	16	16	NUM
ejpam-4975	356	3	]	]	PUNCT
ejpam-4975	356	4	s.	s.	PROPN
ejpam-4975	356	5	jafari	jafari	PROPN
ejpam-4975	356	6	and	and	CCONJ
ejpam-4975	356	7	t.	t.	PROPN
ejpam-4975	356	8	noiri	noiri	PROPN
ejpam-4975	356	9	.	.	PUNCT
ejpam-4975	357	1	some	some	DET
ejpam-4975	357	2	properties	property	NOUN
ejpam-4975	357	3	of	of	ADP
ejpam-4975	357	4	almost	almost	ADV
ejpam-4975	357	5	strongly	strongly	ADV
ejpam-4975	357	6	θ	θ	ADJ
ejpam-4975	357	7	-	-	ADJ
ejpam-4975	357	8	continuous	continuous	ADJ
ejpam-4975	357	9	functions	function	NOUN
ejpam-4975	357	10	.	.	PUNCT
ejpam-4975	358	1	memoirs	memoir	NOUN
ejpam-4975	358	2	of	of	ADP
ejpam-4975	358	3	the	the	DET
ejpam-4975	358	4	faculty	faculty	NOUN
ejpam-4975	358	5	of	of	ADP
ejpam-4975	358	6	science	science	PROPN
ejpam-4975	358	7	kochi	kochi	PROPN
ejpam-4975	358	8	university	university	PROPN
ejpam-4975	358	9	series	series	NOUN
ejpam-4975	358	10	a	a	DET
ejpam-4975	358	11	mathematics	mathematic	NOUN
ejpam-4975	358	12	,	,	PUNCT
ejpam-4975	358	13	25:71–76	25:71–76	NUM
ejpam-4975	358	14	,	,	PUNCT
ejpam-4975	358	15	2004	2004	NUM
ejpam-4975	358	16	.	.	PUNCT
ejpam-4975	359	1	[	[	X
ejpam-4975	359	2	17	17	NUM
ejpam-4975	359	3	]	]	PUNCT
ejpam-4975	360	1	p.	p.	PROPN
ejpam-4975	360	2	e.	e.	PROPN
ejpam-4975	361	1	long	long	PROPN
ejpam-4975	361	2	and	and	CCONJ
ejpam-4975	361	3	l.	l.	PROPN
ejpam-4975	361	4	l.	l.	PROPN
ejpam-4975	361	5	herrington	herrington	PROPN
ejpam-4975	361	6	.	.	PUNCT
ejpam-4975	362	1	strongly	strongly	ADV
ejpam-4975	362	2	θ	θ	ADJ
ejpam-4975	362	3	-	-	ADJ
ejpam-4975	362	4	continuous	continuous	ADJ
ejpam-4975	362	5	functions	function	NOUN
ejpam-4975	362	6	.	.	PUNCT
ejpam-4975	363	1	journal	journal	NOUN
ejpam-4975	363	2	of	of	ADP
ejpam-4975	363	3	the	the	DET
ejpam-4975	363	4	korean	korean	PROPN
ejpam-4975	363	5	mathematical	mathematical	ADJ
ejpam-4975	363	6	society	society	NOUN
ejpam-4975	363	7	,	,	PUNCT
ejpam-4975	363	8	18:21–28	18:21–28	NUM
ejpam-4975	363	9	,	,	PUNCT
ejpam-4975	363	10	1981	1981	NUM
ejpam-4975	363	11	.	.	PUNCT
ejpam-4975	364	1	[	[	X
ejpam-4975	364	2	18	18	NUM
ejpam-4975	364	3	]	]	X
ejpam-4975	364	4	g.	g.	PROPN
ejpam-4975	364	5	di	di	PROPN
ejpam-4975	364	6	maio	maio	PROPN
ejpam-4975	364	7	and	and	CCONJ
ejpam-4975	364	8	t.	t.	PROPN
ejpam-4975	364	9	noiri	noiri	PROPN
ejpam-4975	364	10	.	.	PUNCT
ejpam-4975	365	1	weak	weak	ADJ
ejpam-4975	365	2	and	and	CCONJ
ejpam-4975	365	3	strong	strong	ADJ
ejpam-4975	365	4	forms	form	NOUN
ejpam-4975	365	5	of	of	ADP
ejpam-4975	365	6	irresolute	irresolute	ADJ
ejpam-4975	365	7	functions	function	NOUN
ejpam-4975	365	8	.	.	PUNCT
ejpam-4975	366	1	rendiconti	rendiconti	ADJ
ejpam-4975	366	2	del	del	PROPN
ejpam-4975	366	3	circolo	circolo	PROPN
ejpam-4975	366	4	matematico	matematico	NOUN
ejpam-4975	366	5	di	di	X
ejpam-4975	366	6	palermo	palermo	NOUN
ejpam-4975	366	7	(	(	PUNCT
ejpam-4975	366	8	2	2	NUM
ejpam-4975	366	9	)	)	PUNCT
ejpam-4975	366	10	supplemento	supplemento	NOUN
ejpam-4975	366	11	,	,	PUNCT
ejpam-4975	366	12	18:255–273	18:255–273	NUM
ejpam-4975	366	13	,	,	PUNCT
ejpam-4975	366	14	1988	1988	NUM
ejpam-4975	366	15	.	.	PUNCT
ejpam-4975	367	1	[	[	X
ejpam-4975	367	2	19	19	NUM
ejpam-4975	367	3	]	]	PUNCT
ejpam-4975	367	4	a.	a.	NOUN
ejpam-4975	367	5	s.	s.	PROPN
ejpam-4975	367	6	mashhour	mashhour	PROPN
ejpam-4975	367	7	,	,	PUNCT
ejpam-4975	367	8	m.	m.	PROPN
ejpam-4975	367	9	e.	e.	PROPN
ejpam-4975	367	10	abd	abd	PROPN
ejpam-4975	367	11	el	el	PROPN
ejpam-4975	367	12	-	-	PROPN
ejpam-4975	367	13	monsef	monsef	ADJ
ejpam-4975	367	14	,	,	PUNCT
ejpam-4975	367	15	and	and	CCONJ
ejpam-4975	367	16	s.	s.	PROPN
ejpam-4975	367	17	n.	n.	PROPN
ejpam-4975	367	18	el	el	PROPN
ejpam-4975	367	19	-	-	PROPN
ejpam-4975	367	20	deeb	deeb	PROPN
ejpam-4975	367	21	.	.	PUNCT
ejpam-4975	368	1	on	on	ADP
ejpam-4975	368	2	precontinuous	precontinuous	ADJ
ejpam-4975	368	3	and	and	CCONJ
ejpam-4975	368	4	weak	weak	ADJ
ejpam-4975	368	5	precontinuous	precontinuous	ADJ
ejpam-4975	368	6	mappings	mapping	NOUN
ejpam-4975	368	7	.	.	PUNCT
ejpam-4975	369	1	proceedings	proceeding	NOUN
ejpam-4975	369	2	of	of	ADP
ejpam-4975	369	3	the	the	DET
ejpam-4975	369	4	mathematical	mathematical	ADJ
ejpam-4975	369	5	and	and	CCONJ
ejpam-4975	369	6	physical	physical	ADJ
ejpam-4975	369	7	society	society	NOUN
ejpam-4975	369	8	of	of	ADP
ejpam-4975	369	9	egypt	egypt	PROPN
ejpam-4975	369	10	,	,	PUNCT
ejpam-4975	369	11	53:47–53	53:47–53	NUM
ejpam-4975	369	12	,	,	PUNCT
ejpam-4975	369	13	1982	1982	NUM
ejpam-4975	369	14	.	.	PUNCT
ejpam-4975	370	1	[	[	X
ejpam-4975	370	2	20	20	NUM
ejpam-4975	370	3	]	]	PUNCT
ejpam-4975	370	4	t.	t.	PROPN
ejpam-4975	370	5	noiri	noiri	PROPN
ejpam-4975	370	6	.	.	PUNCT
ejpam-4975	371	1	properties	property	NOUN
ejpam-4975	371	2	of	of	ADP
ejpam-4975	371	3	θ	θ	ADJ
ejpam-4975	371	4	-	-	ADJ
ejpam-4975	371	5	continuous	continuous	ADJ
ejpam-4975	371	6	functions	function	NOUN
ejpam-4975	371	7	.	.	PUNCT
ejpam-4975	372	1	atti	atti	PROPN
ejpam-4975	372	2	della	della	PROPN
ejpam-4975	372	3	accademia	accademia	PROPN
ejpam-4975	372	4	nazionale	nazionale	PROPN
ejpam-4975	372	5	dei	dei	PROPN
ejpam-4975	372	6	lincei	lincei	NOUN
ejpam-4975	372	7	,	,	PUNCT
ejpam-4975	372	8	classe	classe	PROPN
ejpam-4975	372	9	di	di	PROPN
ejpam-4975	372	10	scienze	scienze	PROPN
ejpam-4975	372	11	fisiche	fisiche	PROPN
ejpam-4975	372	12	,	,	PUNCT
ejpam-4975	372	13	matematiche	matematiche	PROPN
ejpam-4975	372	14	e	e	X
ejpam-4975	372	15	naturali	naturali	X
ejpam-4975	372	16	.	.	PUNCT
ejpam-4975	373	1	rendiconti	rendiconti	PROPN
ejpam-4975	373	2	,	,	PUNCT
ejpam-4975	373	3	series	series	NOUN
ejpam-4975	373	4	(	(	PUNCT
ejpam-4975	373	5	8)	8)	NUM
ejpam-4975	373	6	,	,	PUNCT
ejpam-4975	373	7	58:887–891	58:887–891	NUM
ejpam-4975	373	8	,	,	PUNCT
ejpam-4975	373	9	1975	1975	NUM
ejpam-4975	373	10	.	.	PUNCT
ejpam-4975	374	1	[	[	X
ejpam-4975	374	2	21	21	NUM
ejpam-4975	374	3	]	]	PUNCT
ejpam-4975	374	4	t.	t.	PROPN
ejpam-4975	374	5	noiri	noiri	PROPN
ejpam-4975	374	6	.	.	PUNCT
ejpam-4975	375	1	on	on	ADP
ejpam-4975	375	2	δ	δ	PROPN
ejpam-4975	375	3	-	-	ADJ
ejpam-4975	375	4	continuous	continuous	ADJ
ejpam-4975	375	5	functions	function	NOUN
ejpam-4975	375	6	.	.	PUNCT
ejpam-4975	376	1	journal	journal	NOUN
ejpam-4975	376	2	of	of	ADP
ejpam-4975	376	3	the	the	DET
ejpam-4975	376	4	korean	korean	PROPN
ejpam-4975	376	5	mathematical	mathematical	ADJ
ejpam-4975	376	6	society	society	NOUN
ejpam-4975	376	7	,	,	PUNCT
ejpam-4975	376	8	16:161–166	16:161–166	PROPN
ejpam-4975	376	9	,	,	PUNCT
ejpam-4975	376	10	1980	1980	NUM
ejpam-4975	376	11	.	.	PUNCT
ejpam-4975	377	1	[	[	X
ejpam-4975	377	2	22	22	NUM
ejpam-4975	377	3	]	]	PUNCT
ejpam-4975	377	4	t.	t.	PROPN
ejpam-4975	377	5	noiri	noiri	PROPN
ejpam-4975	377	6	.	.	PUNCT
ejpam-4975	378	1	on	on	ADP
ejpam-4975	378	2	θ	θ	PROPN
ejpam-4975	378	3	-	-	PUNCT
ejpam-4975	378	4	semi	semi	ADJ
ejpam-4975	378	5	-	-	ADJ
ejpam-4975	378	6	continuous	continuous	ADJ
ejpam-4975	378	7	functions	function	NOUN
ejpam-4975	378	8	.	.	PUNCT
ejpam-4975	379	1	indian	indian	ADJ
ejpam-4975	379	2	journal	journal	PROPN
ejpam-4975	379	3	of	of	ADP
ejpam-4975	379	4	pure	pure	ADJ
ejpam-4975	379	5	and	and	CCONJ
ejpam-4975	379	6	applied	applied	ADJ
ejpam-4975	379	7	mathematics	mathematic	NOUN
ejpam-4975	379	8	,	,	PUNCT
ejpam-4975	379	9	21:410–415	21:410–415	NUM
ejpam-4975	379	10	,	,	PUNCT
ejpam-4975	379	11	1990	1990	NUM
ejpam-4975	379	12	.	.	PUNCT
ejpam-4975	380	1	[	[	X
ejpam-4975	380	2	23	23	NUM
ejpam-4975	380	3	]	]	PUNCT
ejpam-4975	380	4	t.	t.	PROPN
ejpam-4975	380	5	noiri	noiri	PROPN
ejpam-4975	380	6	.	.	PUNCT
ejpam-4975	381	1	strongly	strongly	ADV
ejpam-4975	381	2	θ	θ	ADJ
ejpam-4975	381	3	-	-	ADJ
ejpam-4975	381	4	precontinuous	precontinuous	ADJ
ejpam-4975	381	5	functions	function	NOUN
ejpam-4975	381	6	.	.	PUNCT
ejpam-4975	382	1	acta	acta	PROPN
ejpam-4975	382	2	mathematica	mathematica	PROPN
ejpam-4975	382	3	hungarica	hungarica	PROPN
ejpam-4975	382	4	,	,	PUNCT
ejpam-4975	382	5	90:307	90:307	NUM
ejpam-4975	382	6	–	–	PUNCT
ejpam-4975	382	7	316	316	NUM
ejpam-4975	382	8	,	,	PUNCT
ejpam-4975	382	9	2001	2001	NUM
ejpam-4975	382	10	.	.	PUNCT
ejpam-4975	383	1	[	[	X
ejpam-4975	383	2	24	24	NUM
ejpam-4975	383	3	]	]	PUNCT
ejpam-4975	383	4	t.	t.	PROPN
ejpam-4975	383	5	noiri	noiri	PROPN
ejpam-4975	383	6	.	.	PUNCT
ejpam-4975	384	1	on	on	ADP
ejpam-4975	384	2	θ	θ	PROPN
ejpam-4975	384	3	-	-	PUNCT
ejpam-4975	384	4	preirresolute	preirresolute	ADJ
ejpam-4975	384	5	functions	function	NOUN
ejpam-4975	384	6	.	.	PUNCT
ejpam-4975	385	1	acta	acta	PROPN
ejpam-4975	385	2	mathematica	mathematica	PROPN
ejpam-4975	385	3	hungarica	hungarica	PROPN
ejpam-4975	385	4	,	,	PUNCT
ejpam-4975	385	5	95:287–298	95:287–298	NUM
ejpam-4975	385	6	,	,	PUNCT
ejpam-4975	385	7	2002	2002	NUM
ejpam-4975	385	8	.	.	PUNCT
ejpam-4975	386	1	[	[	X
ejpam-4975	386	2	25	25	NUM
ejpam-4975	386	3	]	]	PUNCT
ejpam-4975	386	4	t.	t.	PROPN
ejpam-4975	386	5	noiri	noiri	PROPN
ejpam-4975	386	6	.	.	PUNCT
ejpam-4975	387	1	weak	weak	ADJ
ejpam-4975	387	2	and	and	CCONJ
ejpam-4975	387	3	strong	strong	ADJ
ejpam-4975	387	4	forms	form	NOUN
ejpam-4975	387	5	of	of	ADP
ejpam-4975	387	6	β	β	NOUN
ejpam-4975	387	7	-	-	ADJ
ejpam-4975	387	8	irresolute	irresolute	ADJ
ejpam-4975	387	9	functions	function	NOUN
ejpam-4975	387	10	.	.	PUNCT
ejpam-4975	388	1	acta	acta	PROPN
ejpam-4975	388	2	mathematica	mathematica	PROPN
ejpam-4975	388	3	hungarica	hungarica	PROPN
ejpam-4975	388	4	,	,	PUNCT
ejpam-4975	388	5	99:305–318	99:305–318	PROPN
ejpam-4975	388	6	,	,	PUNCT
ejpam-4975	388	7	2003	2003	NUM
ejpam-4975	388	8	.	.	PUNCT
ejpam-4975	389	1	[	[	X
ejpam-4975	389	2	26	26	NUM
ejpam-4975	389	3	]	]	PUNCT
ejpam-4975	389	4	t.	t.	PROPN
ejpam-4975	389	5	noiri	noiri	PROPN
ejpam-4975	389	6	and	and	CCONJ
ejpam-4975	389	7	s.	s.	PROPN
ejpam-4975	389	8	m.	m.	PROPN
ejpam-4975	389	9	kang	kang	PROPN
ejpam-4975	389	10	.	.	PUNCT
ejpam-4975	390	1	on	on	ADP
ejpam-4975	390	2	almost	almost	ADV
ejpam-4975	390	3	strongly	strongly	ADV
ejpam-4975	390	4	θ	θ	ADJ
ejpam-4975	390	5	-	-	ADJ
ejpam-4975	390	6	continuous	continuous	ADJ
ejpam-4975	390	7	functions	function	NOUN
ejpam-4975	390	8	.	.	PUNCT
ejpam-4975	391	1	indian	indian	ADJ
ejpam-4975	391	2	journal	journal	PROPN
ejpam-4975	391	3	of	of	ADP
ejpam-4975	391	4	pure	pure	ADJ
ejpam-4975	391	5	and	and	CCONJ
ejpam-4975	391	6	applied	applied	ADJ
ejpam-4975	391	7	mathematics	mathematic	NOUN
ejpam-4975	391	8	,	,	PUNCT
ejpam-4975	391	9	15:1–8	15:1–8	NUM
ejpam-4975	391	10	,	,	PUNCT
ejpam-4975	391	11	1984	1984	NUM
ejpam-4975	391	12	.	.	PUNCT
ejpam-4975	392	1	references	reference	NOUN
ejpam-4975	392	2	309	309	NUM
ejpam-4975	393	1	[	[	X
ejpam-4975	393	2	27	27	NUM
ejpam-4975	393	3	]	]	PUNCT
ejpam-4975	393	4	t.	t.	PROPN
ejpam-4975	393	5	noiri	noiri	PROPN
ejpam-4975	393	6	and	and	CCONJ
ejpam-4975	393	7	v.	v.	ADP
ejpam-4975	393	8	popa	popa	NOUN
ejpam-4975	393	9	.	.	PUNCT
ejpam-4975	394	1	strongly	strongly	ADV
ejpam-4975	394	2	θ	θ	VERB
ejpam-4975	394	3	-	-	PUNCT
ejpam-4975	394	4	β	β	ADJ
ejpam-4975	394	5	-	-	ADJ
ejpam-4975	394	6	precontinuous	precontinuous	ADJ
ejpam-4975	394	7	functions	function	NOUN
ejpam-4975	394	8	.	.	PUNCT
ejpam-4975	395	1	journal	journal	NOUN
ejpam-4975	395	2	of	of	ADP
ejpam-4975	395	3	pure	pure	ADJ
ejpam-4975	395	4	mathematics	mathematic	NOUN
ejpam-4975	395	5	,	,	PUNCT
ejpam-4975	395	6	19:31–39	19:31–39	NUM
ejpam-4975	395	7	,	,	PUNCT
ejpam-4975	395	8	2002	2002	NUM
ejpam-4975	395	9	.	.	PUNCT
ejpam-4975	396	1	[	[	X
ejpam-4975	396	2	28	28	NUM
ejpam-4975	396	3	]	]	X
ejpam-4975	396	4	t.	t.	PROPN
ejpam-4975	396	5	noiri	noiri	PROPN
ejpam-4975	396	6	and	and	CCONJ
ejpam-4975	396	7	v.	v.	ADP
ejpam-4975	396	8	popa	popa	NOUN
ejpam-4975	396	9	.	.	PUNCT
ejpam-4975	397	1	on	on	ADP
ejpam-4975	397	2	almost	almost	ADV
ejpam-4975	397	3	strongly	strongly	ADV
ejpam-4975	397	4	θ	θ	ADJ
ejpam-4975	397	5	-	-	PUNCT
ejpam-4975	397	6	m	m	NOUN
ejpam-4975	397	7	-	-	PUNCT
ejpam-4975	397	8	continuous	continuous	ADJ
ejpam-4975	397	9	functions	function	NOUN
ejpam-4975	397	10	.	.	PUNCT
ejpam-4975	398	1	istanbul	istanbul	PROPN
ejpam-4975	398	2	üniversitesi	üniversitesi	PROPN
ejpam-4975	398	3	fen	fen	PROPN
ejpam-4975	398	4	fakültesi	fakültesi	X
ejpam-4975	398	5	matematik	matematik	PROPN
ejpam-4975	398	6	,	,	PUNCT
ejpam-4975	398	7	fizik	fizik	ADJ
ejpam-4975	398	8	astronomi	astronomi	PROPN
ejpam-4975	398	9	dergisi	dergisi	VERB
ejpam-4975	398	10	,	,	PUNCT
ejpam-4975	398	11	1:69–92	1:69–92	NUM
ejpam-4975	398	12	,	,	PUNCT
ejpam-4975	398	13	2004	2004	NUM
ejpam-4975	398	14	-	-	SYM
ejpam-4975	398	15	2005	2005	NUM
ejpam-4975	398	16	.	.	PUNCT
ejpam-4975	399	1	[	[	X
ejpam-4975	399	2	29	29	NUM
ejpam-4975	399	3	]	]	PUNCT
ejpam-4975	399	4	t.	t.	PROPN
ejpam-4975	399	5	noiri	noiri	PROPN
ejpam-4975	399	6	and	and	CCONJ
ejpam-4975	399	7	v.	v.	ADP
ejpam-4975	399	8	popa	popa	NOUN
ejpam-4975	399	9	.	.	PUNCT
ejpam-4975	400	1	a	a	DET
ejpam-4975	400	2	unified	unified	ADJ
ejpam-4975	400	3	theory	theory	NOUN
ejpam-4975	400	4	for	for	ADP
ejpam-4975	400	5	strongly	strongly	ADV
ejpam-4975	400	6	θ	θ	NOUN
ejpam-4975	400	7	-	-	NOUN
ejpam-4975	400	8	continuity	continuity	NOUN
ejpam-4975	400	9	for	for	ADP
ejpam-4975	400	10	functions	function	NOUN
ejpam-4975	400	11	.	.	PUNCT
ejpam-4975	401	1	acta	acta	PROPN
ejpam-4975	401	2	mathematica	mathematica	PROPN
ejpam-4975	401	3	hungarica	hungarica	PROPN
ejpam-4975	401	4	,	,	PUNCT
ejpam-4975	401	5	106(3):167–186	106(3):167–186	NUM
ejpam-4975	401	6	,	,	PUNCT
ejpam-4975	401	7	2005	2005	NUM
ejpam-4975	401	8	.	.	PUNCT
ejpam-4975	402	1	[	[	X
ejpam-4975	402	2	30	30	NUM
ejpam-4975	402	3	]	]	X
ejpam-4975	402	4	m.	m.	NOUN
ejpam-4975	402	5	thongmoon	thongmoon	NOUN
ejpam-4975	402	6	and	and	CCONJ
ejpam-4975	402	7	c.	c.	PROPN
ejpam-4975	402	8	boonpok	boonpok	PROPN
ejpam-4975	402	9	.	.	PUNCT
ejpam-4975	403	1	θ(λ	θ(λ	PROPN
ejpam-4975	403	2	,	,	PUNCT
ejpam-4975	403	3	p)-continuous	p)-continuous	ADJ
ejpam-4975	403	4	functions	function	NOUN
ejpam-4975	403	5	.	.	PUNCT
ejpam-4975	404	1	international	international	ADJ
ejpam-4975	404	2	journal	journal	PROPN
ejpam-4975	404	3	of	of	ADP
ejpam-4975	404	4	mathematics	mathematic	NOUN
ejpam-4975	404	5	and	and	CCONJ
ejpam-4975	404	6	computer	computer	NOUN
ejpam-4975	404	7	science	science	NOUN
ejpam-4975	404	8	,	,	PUNCT
ejpam-4975	404	9	19(2):475–479	19(2):475–479	PROPN
ejpam-4975	404	10	,	,	PUNCT
ejpam-4975	404	11	2024	2024	NUM
ejpam-4975	404	12	.	.	PUNCT
ejpam-4975	405	1	[	[	X
ejpam-4975	405	2	31	31	NUM
ejpam-4975	405	3	]	]	PUNCT
ejpam-4975	405	4	c.	c.	PROPN
ejpam-4975	405	5	viriyapong	viriyapong	PROPN
ejpam-4975	405	6	and	and	CCONJ
ejpam-4975	405	7	c.	c.	PROPN
ejpam-4975	405	8	boonpok	boonpok	PROPN
ejpam-4975	405	9	.	.	PUNCT
ejpam-4975	406	1	(	(	PUNCT
ejpam-4975	406	2	λ	λ	X
ejpam-4975	406	3	,	,	PUNCT
ejpam-4975	406	4	sp)-continuous	sp)-continuous	ADJ
ejpam-4975	406	5	functions	function	NOUN
ejpam-4975	406	6	.	.	PUNCT
ejpam-4975	407	1	wseas	wseas	VERB
ejpam-4975	407	2	transactions	transaction	NOUN
ejpam-4975	407	3	on	on	ADP
ejpam-4975	407	4	mathematics	mathematic	NOUN
ejpam-4975	407	5	,	,	PUNCT
ejpam-4975	407	6	21:380–385	21:380–385	NUM
ejpam-4975	407	7	,	,	PUNCT
ejpam-4975	407	8	2022	2022	NUM
ejpam-4975	407	9	.	.	PUNCT
ejpam-4975	408	1	[	[	X
ejpam-4975	408	2	32	32	NUM
ejpam-4975	408	3	]	]	X
ejpam-4975	408	4	n.	n.	PROPN
ejpam-4975	408	5	viriyapong	viriyapong	PROPN
ejpam-4975	408	6	and	and	CCONJ
ejpam-4975	408	7	c.	c.	PROPN
ejpam-4975	408	8	boonpok	boonpok	PROPN
ejpam-4975	408	9	.	.	PUNCT
ejpam-4975	409	1	on	on	ADP
ejpam-4975	409	2	(	(	PUNCT
ejpam-4975	409	3	λ	λ	INTJ
ejpam-4975	409	4	,	,	PUNCT
ejpam-4975	409	5	p)-extremally	p)-extremally	ADV
ejpam-4975	409	6	disconnected	disconnected	ADJ
ejpam-4975	409	7	spaces	space	NOUN
ejpam-4975	409	8	.	.	PUNCT
ejpam-4975	410	1	international	international	ADJ
ejpam-4975	410	2	journal	journal	PROPN
ejpam-4975	410	3	of	of	ADP
ejpam-4975	410	4	mathematics	mathematic	NOUN
ejpam-4975	410	5	and	and	CCONJ
ejpam-4975	410	6	computer	computer	NOUN
ejpam-4975	410	7	science	science	NOUN
ejpam-4975	410	8	,	,	PUNCT
ejpam-4975	410	9	18(2):289–293	18(2):289–293	NUM
ejpam-4975	410	10	,	,	PUNCT
ejpam-4975	410	11	2023	2023	NUM
ejpam-4975	410	12	.	.	PUNCT