id	sid	tid	token	lemma	pos
ejpam-4735	1	1	european	european	PROPN
ejpam-4735	1	2	journal	journal	PROPN
ejpam-4735	1	3	of	of	ADP
ejpam-4735	1	4	pure	pure	ADJ
ejpam-4735	1	5	and	and	CCONJ
ejpam-4735	1	6	applied	apply	VERB
ejpam-4735	1	7	mathematics	mathematic	NOUN
ejpam-4735	1	8	vol	vol	NOUN
ejpam-4735	1	9	.	.	PROPN
ejpam-4735	2	1	17	17	NUM
ejpam-4735	2	2	,	,	PUNCT
ejpam-4735	2	3	no	no	INTJ
ejpam-4735	2	4	.	.	NOUN
ejpam-4735	2	5	1	1	NUM
ejpam-4735	2	6	,	,	PUNCT
ejpam-4735	2	7	2024	2024	NUM
ejpam-4735	2	8	,	,	PUNCT
ejpam-4735	2	9	147	147	NUM
ejpam-4735	2	10	-	-	SYM
ejpam-4735	2	11	157	157	NUM
ejpam-4735	2	12	issn	issn	PROPN
ejpam-4735	2	13	1307	1307	NUM
ejpam-4735	2	14	-	-	SYM
ejpam-4735	2	15	5543	5543	NUM
ejpam-4735	2	16	–	–	PUNCT
ejpam-4735	2	17	ejpam.com	ejpam.com	X
ejpam-4735	2	18	published	publish	VERB
ejpam-4735	2	19	by	by	ADP
ejpam-4735	2	20	new	new	PROPN
ejpam-4735	2	21	york	york	PROPN
ejpam-4735	2	22	business	business	PROPN
ejpam-4735	2	23	global	global	ADJ
ejpam-4735	2	24	characterizations	characterization	NOUN
ejpam-4735	2	25	of	of	ADP
ejpam-4735	2	26	δp(λ	δp(λ	NOUN
ejpam-4735	2	27	,	,	PUNCT
ejpam-4735	2	28	s)-r0	s)-r0	PRON
ejpam-4735	2	29	spaces	space	VERB
ejpam-4735	2	30	chawalit	chawalit	VERB
ejpam-4735	2	31	boonpok1	boonpok1	PROPN
ejpam-4735	2	32	,	,	PUNCT
ejpam-4735	2	33	prapart	prapart	VERB
ejpam-4735	2	34	pue	pue	X
ejpam-4735	2	35	-	-	PUNCT
ejpam-4735	2	36	on1,∗	on1,∗	PROPN
ejpam-4735	2	37	1	1	NUM
ejpam-4735	2	38	mathematics	mathematic	NOUN
ejpam-4735	2	39	and	and	CCONJ
ejpam-4735	2	40	applied	apply	VERB
ejpam-4735	2	41	mathematics	mathematics	PROPN
ejpam-4735	2	42	research	research	NOUN
ejpam-4735	2	43	unit	unit	NOUN
ejpam-4735	2	44	,	,	PUNCT
ejpam-4735	2	45	department	department	NOUN
ejpam-4735	2	46	of	of	ADP
ejpam-4735	2	47	mathematics	mathematic	NOUN
ejpam-4735	2	48	,	,	PUNCT
ejpam-4735	2	49	faculty	faculty	NOUN
ejpam-4735	2	50	of	of	ADP
ejpam-4735	2	51	science	science	NOUN
ejpam-4735	2	52	,	,	PUNCT
ejpam-4735	2	53	mahasarakham	mahasarakham	PROPN
ejpam-4735	2	54	university	university	PROPN
ejpam-4735	2	55	,	,	PUNCT
ejpam-4735	2	56	maha	maha	PROPN
ejpam-4735	2	57	sarakham	sarakham	PROPN
ejpam-4735	2	58	,	,	PUNCT
ejpam-4735	2	59	44150	44150	NUM
ejpam-4735	2	60	,	,	PUNCT
ejpam-4735	2	61	thailand	thailand	PROPN
ejpam-4735	2	62	abstract	abstract	PROPN
ejpam-4735	2	63	.	.	PUNCT
ejpam-4735	3	1	our	our	PRON
ejpam-4735	3	2	main	main	ADJ
ejpam-4735	3	3	purpose	purpose	NOUN
ejpam-4735	3	4	is	be	AUX
ejpam-4735	3	5	to	to	PART
ejpam-4735	3	6	introduce	introduce	VERB
ejpam-4735	3	7	the	the	DET
ejpam-4735	3	8	concept	concept	NOUN
ejpam-4735	3	9	of	of	ADP
ejpam-4735	3	10	δp(λ	δp(λ	NOUN
ejpam-4735	3	11	,	,	PUNCT
ejpam-4735	3	12	s)-r0	s)-r0	PRON
ejpam-4735	3	13	spaces	space	VERB
ejpam-4735	3	14	.	.	PUNCT
ejpam-4735	4	1	moreover	moreover	ADV
ejpam-4735	4	2	,	,	PUNCT
ejpam-4735	4	3	some	some	DET
ejpam-4735	4	4	characterizations	characterization	NOUN
ejpam-4735	4	5	of	of	ADP
ejpam-4735	4	6	δp(λ	δp(λ	NOUN
ejpam-4735	4	7	,	,	PUNCT
ejpam-4735	4	8	s)-r0	s)-r0	PRON
ejpam-4735	4	9	spaces	space	NOUN
ejpam-4735	4	10	are	be	AUX
ejpam-4735	4	11	investigated	investigate	VERB
ejpam-4735	4	12	.	.	PUNCT
ejpam-4735	5	1	2020	2020	NUM
ejpam-4735	5	2	mathematics	mathematic	NOUN
ejpam-4735	5	3	subject	subject	NOUN
ejpam-4735	5	4	classifications	classification	NOUN
ejpam-4735	5	5	:	:	PUNCT
ejpam-4735	5	6	54a05	54a05	NUM
ejpam-4735	5	7	,	,	PUNCT
ejpam-4735	5	8	54d10	54d10	NUM
ejpam-4735	5	9	key	key	ADJ
ejpam-4735	5	10	words	word	NOUN
ejpam-4735	5	11	and	and	CCONJ
ejpam-4735	5	12	phrases	phrase	NOUN
ejpam-4735	5	13	:	:	PUNCT
ejpam-4735	5	14	δp(λ	δp(λ	NOUN
ejpam-4735	5	15	,	,	PUNCT
ejpam-4735	5	16	s)-open	s)-open	PUNCT
ejpam-4735	5	17	set	set	VERB
ejpam-4735	5	18	,	,	PUNCT
ejpam-4735	5	19	δp(λ	δp(λ	PROPN
ejpam-4735	5	20	,	,	PUNCT
ejpam-4735	5	21	s)-r0	s)-r0	PRON
ejpam-4735	5	22	space	space	NOUN
ejpam-4735	5	23	1	1	NUM
ejpam-4735	5	24	.	.	PUNCT
ejpam-4735	5	25	introduction	introduction	NOUN
ejpam-4735	5	26	in	in	ADP
ejpam-4735	5	27	1943	1943	NUM
ejpam-4735	5	28	,	,	PUNCT
ejpam-4735	5	29	shanin	shanin	ADJ
ejpam-4735	6	1	[	[	X
ejpam-4735	6	2	20	20	NUM
ejpam-4735	6	3	]	]	PUNCT
ejpam-4735	6	4	introduced	introduce	VERB
ejpam-4735	6	5	the	the	DET
ejpam-4735	6	6	concept	concept	NOUN
ejpam-4735	6	7	of	of	ADP
ejpam-4735	6	8	r0	r0	PROPN
ejpam-4735	6	9	topological	topological	ADJ
ejpam-4735	6	10	spaces	space	NOUN
ejpam-4735	6	11	.	.	PUNCT
ejpam-4735	7	1	davis	davis	PROPN
ejpam-4735	8	1	[	[	X
ejpam-4735	8	2	11	11	NUM
ejpam-4735	8	3	]	]	PUNCT
ejpam-4735	8	4	introduced	introduce	VERB
ejpam-4735	8	5	the	the	DET
ejpam-4735	8	6	concept	concept	NOUN
ejpam-4735	8	7	of	of	ADP
ejpam-4735	8	8	a	a	DET
ejpam-4735	8	9	separation	separation	NOUN
ejpam-4735	8	10	axiom	axiom	NOUN
ejpam-4735	8	11	called	call	VERB
ejpam-4735	8	12	r1	r1	PROPN
ejpam-4735	8	13	.	.	PUNCT
ejpam-4735	9	1	these	these	DET
ejpam-4735	9	2	concepts	concept	NOUN
ejpam-4735	9	3	are	be	AUX
ejpam-4735	9	4	further	far	ADV
ejpam-4735	9	5	investigated	investigate	VERB
ejpam-4735	9	6	by	by	ADP
ejpam-4735	9	7	naimpally	naimpally	ADV
ejpam-4735	9	8	[	[	X
ejpam-4735	9	9	16	16	NUM
ejpam-4735	9	10	]	]	PUNCT
ejpam-4735	9	11	,	,	PUNCT
ejpam-4735	9	12	dube	dube	PROPN
ejpam-4735	10	1	[	[	X
ejpam-4735	10	2	13	13	NUM
ejpam-4735	10	3	]	]	PUNCT
ejpam-4735	10	4	and	and	CCONJ
ejpam-4735	10	5	dorsett	dorsett	PROPN
ejpam-4735	10	6	[	[	X
ejpam-4735	10	7	12	12	NUM
ejpam-4735	10	8	]	]	PUNCT
ejpam-4735	10	9	.	.	PUNCT
ejpam-4735	11	1	cammaroto	cammaroto	NOUN
ejpam-4735	11	2	and	and	CCONJ
ejpam-4735	11	3	noiri	noiri	ADV
ejpam-4735	12	1	[	[	X
ejpam-4735	12	2	10	10	NUM
ejpam-4735	12	3	]	]	PUNCT
ejpam-4735	12	4	introduce	introduce	VERB
ejpam-4735	12	5	a	a	DET
ejpam-4735	12	6	weak	weak	ADJ
ejpam-4735	12	7	separation	separation	NOUN
ejpam-4735	12	8	axiom	axiom	NOUN
ejpam-4735	12	9	m	m	NOUN
ejpam-4735	12	10	-	-	PUNCT
ejpam-4735	12	11	r0	r0	NOUN
ejpam-4735	12	12	in	in	ADP
ejpam-4735	12	13	m	m	NOUN
ejpam-4735	12	14	-	-	NOUN
ejpam-4735	12	15	spaces	space	NOUN
ejpam-4735	12	16	which	which	PRON
ejpam-4735	12	17	are	be	AUX
ejpam-4735	12	18	equivalent	equivalent	ADJ
ejpam-4735	12	19	to	to	ADP
ejpam-4735	12	20	generalized	generalize	VERB
ejpam-4735	12	21	topological	topological	ADJ
ejpam-4735	12	22	spaces	space	NOUN
ejpam-4735	12	23	due	due	ADP
ejpam-4735	12	24	to	to	ADP
ejpam-4735	12	25	lugojan	lugojan	NOUN
ejpam-4735	12	26	[	[	X
ejpam-4735	12	27	15	15	NUM
ejpam-4735	12	28	]	]	PUNCT
ejpam-4735	12	29	.	.	PUNCT
ejpam-4735	13	1	noiri	noiri	PROPN
ejpam-4735	14	1	[	[	X
ejpam-4735	14	2	17	17	NUM
ejpam-4735	14	3	]	]	PUNCT
ejpam-4735	14	4	introduced	introduce	VERB
ejpam-4735	14	5	the	the	DET
ejpam-4735	14	6	notion	notion	NOUN
ejpam-4735	14	7	of	of	ADP
ejpam-4735	14	8	m	m	NOUN
ejpam-4735	14	9	-	-	PUNCT
ejpam-4735	14	10	r1	r1	ADJ
ejpam-4735	14	11	spaces	space	NOUN
ejpam-4735	14	12	and	and	CCONJ
ejpam-4735	14	13	investigated	investigate	VERB
ejpam-4735	14	14	several	several	ADJ
ejpam-4735	14	15	characterizations	characterization	NOUN
ejpam-4735	14	16	of	of	ADP
ejpam-4735	14	17	m	m	NOUN
ejpam-4735	14	18	-	-	PUNCT
ejpam-4735	14	19	r0	r0	NOUN
ejpam-4735	14	20	spaces	space	NOUN
ejpam-4735	14	21	and	and	CCONJ
ejpam-4735	14	22	m	m	NOUN
ejpam-4735	14	23	-	-	PUNCT
ejpam-4735	14	24	r1	r1	ADJ
ejpam-4735	14	25	spaces	space	NOUN
ejpam-4735	14	26	.	.	PUNCT
ejpam-4735	15	1	in	in	ADP
ejpam-4735	15	2	1963	1963	NUM
ejpam-4735	15	3	,	,	PUNCT
ejpam-4735	15	4	levine	levine	PROPN
ejpam-4735	15	5	[	[	X
ejpam-4735	15	6	14	14	NUM
ejpam-4735	15	7	]	]	PUNCT
ejpam-4735	15	8	introduced	introduce	VERB
ejpam-4735	15	9	the	the	DET
ejpam-4735	15	10	concept	concept	NOUN
ejpam-4735	15	11	of	of	ADP
ejpam-4735	15	12	semi	semi	ADJ
ejpam-4735	15	13	-	-	ADJ
ejpam-4735	15	14	open	open	ADJ
ejpam-4735	15	15	sets	set	NOUN
ejpam-4735	15	16	which	which	PRON
ejpam-4735	15	17	is	be	AUX
ejpam-4735	15	18	weaker	weak	ADJ
ejpam-4735	15	19	than	than	ADP
ejpam-4735	15	20	the	the	DET
ejpam-4735	15	21	concept	concept	NOUN
ejpam-4735	15	22	of	of	ADP
ejpam-4735	15	23	open	open	ADJ
ejpam-4735	15	24	sets	set	NOUN
ejpam-4735	15	25	in	in	ADP
ejpam-4735	15	26	topological	topological	ADJ
ejpam-4735	15	27	spaces	space	NOUN
ejpam-4735	15	28	.	.	PUNCT
ejpam-4735	16	1	veličko	veličko	PROPN
ejpam-4735	17	1	[	[	X
ejpam-4735	17	2	23	23	NUM
ejpam-4735	17	3	]	]	PUNCT
ejpam-4735	17	4	introduced	introduce	VERB
ejpam-4735	17	5	δ	δ	PROPN
ejpam-4735	17	6	-	-	ADJ
ejpam-4735	17	7	open	open	ADJ
ejpam-4735	17	8	sets	set	NOUN
ejpam-4735	17	9	,	,	PUNCT
ejpam-4735	17	10	which	which	PRON
ejpam-4735	17	11	are	be	AUX
ejpam-4735	17	12	stronger	strong	ADJ
ejpam-4735	17	13	than	than	ADP
ejpam-4735	17	14	open	open	ADJ
ejpam-4735	17	15	sets	set	NOUN
ejpam-4735	17	16	.	.	PUNCT
ejpam-4735	18	1	park	park	NOUN
ejpam-4735	18	2	et	et	PROPN
ejpam-4735	18	3	al	al	PROPN
ejpam-4735	18	4	.	.	PUNCT
ejpam-4735	19	1	[	[	X
ejpam-4735	19	2	18	18	NUM
ejpam-4735	19	3	]	]	PUNCT
ejpam-4735	19	4	have	have	AUX
ejpam-4735	19	5	offered	offer	VERB
ejpam-4735	19	6	new	new	ADJ
ejpam-4735	19	7	notion	notion	NOUN
ejpam-4735	19	8	called	call	VERB
ejpam-4735	19	9	δ	δ	PROPN
ejpam-4735	19	10	-	-	PUNCT
ejpam-4735	19	11	semiopen	semiopen	VERB
ejpam-4735	19	12	sets	set	NOUN
ejpam-4735	19	13	which	which	PRON
ejpam-4735	19	14	are	be	AUX
ejpam-4735	19	15	stronger	strong	ADJ
ejpam-4735	19	16	than	than	ADP
ejpam-4735	19	17	semi	semi	ADJ
ejpam-4735	19	18	-	-	ADJ
ejpam-4735	19	19	open	open	ADJ
ejpam-4735	19	20	sets	set	NOUN
ejpam-4735	19	21	but	but	CCONJ
ejpam-4735	19	22	weaker	weak	ADJ
ejpam-4735	19	23	than	than	ADP
ejpam-4735	19	24	δ	δ	NOUN
ejpam-4735	19	25	-	-	ADJ
ejpam-4735	19	26	open	open	ADJ
ejpam-4735	19	27	sets	set	NOUN
ejpam-4735	19	28	and	and	CCONJ
ejpam-4735	19	29	investigated	investigate	VERB
ejpam-4735	19	30	the	the	DET
ejpam-4735	19	31	relationships	relationship	NOUN
ejpam-4735	19	32	between	between	ADP
ejpam-4735	19	33	several	several	ADJ
ejpam-4735	19	34	types	type	NOUN
ejpam-4735	19	35	of	of	ADP
ejpam-4735	19	36	these	these	DET
ejpam-4735	19	37	open	open	ADJ
ejpam-4735	19	38	sets	set	NOUN
ejpam-4735	19	39	.	.	PUNCT
ejpam-4735	20	1	caldas	caldas	PROPN
ejpam-4735	20	2	and	and	CCONJ
ejpam-4735	20	3	dontchev	dontchev	ADJ
ejpam-4735	20	4	[	[	X
ejpam-4735	20	5	6	6	NUM
ejpam-4735	20	6	]	]	PUNCT
ejpam-4735	20	7	introduced	introduce	VERB
ejpam-4735	20	8	and	and	CCONJ
ejpam-4735	20	9	investigated	investigate	VERB
ejpam-4735	20	10	the	the	DET
ejpam-4735	20	11	notions	notion	NOUN
ejpam-4735	20	12	of	of	ADP
ejpam-4735	20	13	λssets	λsset	NOUN
ejpam-4735	20	14	and	and	CCONJ
ejpam-4735	20	15	vs	vs	NOUN
ejpam-4735	20	16	-	-	PUNCT
ejpam-4735	20	17	sets	set	NOUN
ejpam-4735	20	18	in	in	ADP
ejpam-4735	20	19	topological	topological	ADJ
ejpam-4735	20	20	spaces	space	NOUN
ejpam-4735	20	21	.	.	PUNCT
ejpam-4735	21	1	moreover	moreover	ADV
ejpam-4735	21	2	,	,	PUNCT
ejpam-4735	21	3	caldas	caldas	PROPN
ejpam-4735	21	4	et	et	PROPN
ejpam-4735	21	5	al	al	PROPN
ejpam-4735	21	6	.	.	PUNCT
ejpam-4735	22	1	[	[	X
ejpam-4735	22	2	9	9	NUM
ejpam-4735	22	3	]	]	PUNCT
ejpam-4735	22	4	investigated	investigate	VERB
ejpam-4735	22	5	some	some	DET
ejpam-4735	22	6	weak	weak	ADJ
ejpam-4735	22	7	separation	separation	NOUN
ejpam-4735	22	8	axioms	axiom	NOUN
ejpam-4735	22	9	by	by	ADP
ejpam-4735	22	10	utilizing	utilize	VERB
ejpam-4735	22	11	δ	δ	PROPN
ejpam-4735	22	12	-	-	PUNCT
ejpam-4735	22	13	semiopen	semiopen	ADJ
ejpam-4735	22	14	sets	set	NOUN
ejpam-4735	22	15	and	and	CCONJ
ejpam-4735	22	16	the	the	DET
ejpam-4735	22	17	δ	δ	PROPN
ejpam-4735	22	18	-	-	PUNCT
ejpam-4735	22	19	semiclosure	semiclosure	NOUN
ejpam-4735	22	20	operator	operator	NOUN
ejpam-4735	22	21	.	.	PUNCT
ejpam-4735	23	1	caldas	caldas	PROPN
ejpam-4735	23	2	et	et	PROPN
ejpam-4735	23	3	al	al	PROPN
ejpam-4735	23	4	.	.	PUNCT
ejpam-4735	24	1	[	[	X
ejpam-4735	24	2	8	8	NUM
ejpam-4735	24	3	]	]	PUNCT
ejpam-4735	24	4	investigated	investigate	VERB
ejpam-4735	24	5	the	the	DET
ejpam-4735	24	6	notion	notion	NOUN
ejpam-4735	24	7	of	of	ADP
ejpam-4735	24	8	δ	δ	PROPN
ejpam-4735	24	9	-	-	PUNCT
ejpam-4735	24	10	λs	λs	ADV
ejpam-4735	24	11	-	-	PUNCT
ejpam-4735	24	12	semiclosed	semiclose	VERB
ejpam-4735	24	13	sets	set	NOUN
ejpam-4735	24	14	which	which	PRON
ejpam-4735	24	15	is	be	AUX
ejpam-4735	24	16	defined	define	VERB
ejpam-4735	24	17	as	as	ADP
ejpam-4735	24	18	the	the	DET
ejpam-4735	24	19	intersection	intersection	NOUN
ejpam-4735	24	20	of	of	ADP
ejpam-4735	24	21	a	a	DET
ejpam-4735	24	22	δ	δ	PROPN
ejpam-4735	24	23	-	-	PUNCT
ejpam-4735	24	24	λs	λs	NOUN
ejpam-4735	24	25	-	-	PUNCT
ejpam-4735	24	26	set	set	NOUN
ejpam-4735	24	27	and	and	CCONJ
ejpam-4735	24	28	a	a	DET
ejpam-4735	24	29	δ	δ	NOUN
ejpam-4735	24	30	-	-	PUNCT
ejpam-4735	24	31	semiclosed	semiclose	VERB
ejpam-4735	24	32	set	set	NOUN
ejpam-4735	24	33	.	.	PUNCT
ejpam-4735	25	1	in	in	ADP
ejpam-4735	25	2	1982	1982	NUM
ejpam-4735	25	3	,	,	PUNCT
ejpam-4735	25	4	mashhour	mashhour	PROPN
ejpam-4735	25	5	et	et	PROPN
ejpam-4735	25	6	al	al	PROPN
ejpam-4735	25	7	.	.	PUNCT
ejpam-4735	26	1	[	[	X
ejpam-4735	26	2	1	1	X
ejpam-4735	26	3	]	]	PUNCT
ejpam-4735	26	4	introduced	introduce	VERB
ejpam-4735	26	5	and	and	CCONJ
ejpam-4735	26	6	studied	study	VERB
ejpam-4735	26	7	the	the	DET
ejpam-4735	26	8	concept	concept	NOUN
ejpam-4735	26	9	of	of	ADP
ejpam-4735	26	10	preopen	preopen	ADJ
ejpam-4735	26	11	sets	set	NOUN
ejpam-4735	26	12	.	.	PUNCT
ejpam-4735	27	1	raychaudhuri	raychaudhuri	PROPN
ejpam-4735	27	2	and	and	CCONJ
ejpam-4735	27	3	mukherjee	mukherjee	NOUN
ejpam-4735	28	1	[	[	X
ejpam-4735	28	2	19	19	NUM
ejpam-4735	28	3	]	]	PUNCT
ejpam-4735	28	4	introduced	introduce	VERB
ejpam-4735	28	5	the	the	DET
ejpam-4735	28	6	notions	notion	NOUN
ejpam-4735	28	7	of	of	ADP
ejpam-4735	28	8	δ	δ	PROPN
ejpam-4735	28	9	-	-	PUNCT
ejpam-4735	28	10	preopen	preopen	ADJ
ejpam-4735	28	11	sets	set	NOUN
ejpam-4735	28	12	and	and	CCONJ
ejpam-4735	28	13	δ	δ	NOUN
ejpam-4735	28	14	-	-	PUNCT
ejpam-4735	28	15	preclosure	preclosure	ADJ
ejpam-4735	28	16	.	.	PUNCT
ejpam-4735	29	1	the	the	DET
ejpam-4735	29	2	class	class	NOUN
ejpam-4735	29	3	of	of	ADP
ejpam-4735	29	4	δ	δ	PROPN
ejpam-4735	29	5	-	-	PUNCT
ejpam-4735	29	6	preopen	preopen	ADJ
ejpam-4735	29	7	sets	set	NOUN
ejpam-4735	29	8	is	be	AUX
ejpam-4735	29	9	larger	large	ADJ
ejpam-4735	29	10	than	than	ADP
ejpam-4735	29	11	that	that	PRON
ejpam-4735	29	12	of	of	ADP
ejpam-4735	29	13	preopen	preopen	ADJ
ejpam-4735	29	14	sets	set	NOUN
ejpam-4735	29	15	.	.	PUNCT
ejpam-4735	30	1	caldas	caldas	PROPN
ejpam-4735	30	2	et	et	PROPN
ejpam-4735	30	3	al	al	PROPN
ejpam-4735	30	4	.	.	PUNCT
ejpam-4735	31	1	[	[	X
ejpam-4735	31	2	7	7	X
ejpam-4735	31	3	]	]	PUNCT
ejpam-4735	31	4	introduced	introduce	VERB
ejpam-4735	31	5	some	some	DET
ejpam-4735	31	6	weak	weak	ADJ
ejpam-4735	31	7	separation	separation	NOUN
ejpam-4735	31	8	axioms	axiom	NOUN
ejpam-4735	31	9	by	by	ADP
ejpam-4735	31	10	utilizing	utilize	VERB
ejpam-4735	31	11	the	the	DET
ejpam-4735	31	12	notions	notion	NOUN
ejpam-4735	31	13	of	of	ADP
ejpam-4735	31	14	δ	δ	PROPN
ejpam-4735	31	15	-	-	PUNCT
ejpam-4735	31	16	preopen	preopen	ADJ
ejpam-4735	31	17	sets	set	NOUN
ejpam-4735	31	18	and	and	CCONJ
ejpam-4735	31	19	the	the	DET
ejpam-4735	31	20	δ	δ	NOUN
ejpam-4735	31	21	-	-	PUNCT
ejpam-4735	31	22	preclosure	preclosure	ADJ
ejpam-4735	31	23	operator	operator	NOUN
ejpam-4735	31	24	.	.	PUNCT
ejpam-4735	32	1	in	in	ADP
ejpam-4735	32	2	[	[	X
ejpam-4735	32	3	5	5	NUM
ejpam-4735	32	4	]	]	PUNCT
ejpam-4735	32	5	,	,	PUNCT
ejpam-4735	32	6	the	the	DET
ejpam-4735	32	7	present	present	ADJ
ejpam-4735	32	8	authors	author	NOUN
ejpam-4735	32	9	introduced	introduce	VERB
ejpam-4735	32	10	and	and	CCONJ
ejpam-4735	32	11	studied	study	VERB
ejpam-4735	32	12	the	the	DET
ejpam-4735	32	13	concept	concept	NOUN
ejpam-4735	32	14	of	of	ADP
ejpam-4735	32	15	(	(	PUNCT
ejpam-4735	32	16	λ	λ	PROPN
ejpam-4735	32	17	,	,	PUNCT
ejpam-4735	32	18	s)-closed	s)-close	VERB
ejpam-4735	32	19	sets	set	NOUN
ejpam-4735	32	20	by	by	ADP
ejpam-4735	32	21	utilizing	utilize	VERB
ejpam-4735	32	22	the	the	DET
ejpam-4735	32	23	notions	notion	NOUN
ejpam-4735	32	24	of	of	ADP
ejpam-4735	32	25	λs	λs	NOUN
ejpam-4735	32	26	-	-	PUNCT
ejpam-4735	32	27	sets	set	NOUN
ejpam-4735	32	28	∗corresponding	∗corresponde	VERB
ejpam-4735	32	29	author	author	NOUN
ejpam-4735	32	30	.	.	PUNCT
ejpam-4735	33	1	doi	doi	NOUN
ejpam-4735	33	2	:	:	PUNCT
ejpam-4735	33	3	https://doi.org/10.29020/nybg.ejpam.v17i1.4735	https://doi.org/10.29020/nybg.ejpam.v17i1.4735	NUM
ejpam-4735	33	4	email	email	NOUN
ejpam-4735	33	5	addresses	address	NOUN
ejpam-4735	33	6	:	:	PUNCT
ejpam-4735	34	1	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	INTJ
ejpam-4735	34	2	(	(	PUNCT
ejpam-4735	34	3	c.	c.	PROPN
ejpam-4735	34	4	boonpok	boonpok	PROPN
ejpam-4735	34	5	)	)	PUNCT
ejpam-4735	34	6	,	,	PUNCT
ejpam-4735	34	7	prapart.p@msu.ac.th	prapart.p@msu.ac.th	X
ejpam-4735	34	8	(	(	PUNCT
ejpam-4735	34	9	p.	p.	NOUN
ejpam-4735	34	10	pue	pue	NOUN
ejpam-4735	34	11	-	-	PUNCT
ejpam-4735	34	12	on	on	ADP
ejpam-4735	34	13	)	)	PUNCT
ejpam-4735	34	14	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4735	34	15	147	147	NUM
ejpam-4735	34	16	©	©	ADP
ejpam-4735	34	17	2024	2024	NUM
ejpam-4735	34	18	ejpam	ejpam	NOUN
ejpam-4735	34	19	all	all	DET
ejpam-4735	34	20	rights	right	NOUN
ejpam-4735	34	21	reserved	reserve	VERB
ejpam-4735	34	22	.	.	PUNCT
ejpam-4735	35	1	c.	c.	PROPN
ejpam-4735	35	2	boonpok	boonpok	PROPN
ejpam-4735	35	3	,	,	PUNCT
ejpam-4735	35	4	p.	p.	NOUN
ejpam-4735	35	5	pue	pue	NOUN
ejpam-4735	35	6	-	-	PUNCT
ejpam-4735	35	7	on	on	ADP
ejpam-4735	35	8	/	/	SYM
ejpam-4735	35	9	eur	eur	NOUN
ejpam-4735	35	10	.	.	PUNCT
ejpam-4735	36	1	j.	j.	PROPN
ejpam-4735	36	2	pure	pure	PROPN
ejpam-4735	36	3	appl	appl	PROPN
ejpam-4735	36	4	.	.	PROPN
ejpam-4735	36	5	math	math	PROPN
ejpam-4735	36	6	,	,	PUNCT
ejpam-4735	36	7	17	17	NUM
ejpam-4735	36	8	(	(	PUNCT
ejpam-4735	36	9	1	1	NUM
ejpam-4735	36	10	)	)	PUNCT
ejpam-4735	36	11	(	(	PUNCT
ejpam-4735	36	12	2024	2024	NUM
ejpam-4735	36	13	)	)	PUNCT
ejpam-4735	36	14	,	,	PUNCT
ejpam-4735	36	15	147	147	NUM
ejpam-4735	36	16	-	-	SYM
ejpam-4735	36	17	157	157	NUM
ejpam-4735	36	18	148	148	NUM
ejpam-4735	36	19	and	and	CCONJ
ejpam-4735	36	20	semi	semi	ADJ
ejpam-4735	36	21	-	-	ADJ
ejpam-4735	36	22	closed	closed	ADJ
ejpam-4735	36	23	sets	set	NOUN
ejpam-4735	36	24	.	.	PUNCT
ejpam-4735	37	1	furthermore	furthermore	ADV
ejpam-4735	37	2	,	,	PUNCT
ejpam-4735	37	3	several	several	ADJ
ejpam-4735	37	4	characterizations	characterization	NOUN
ejpam-4735	37	5	of	of	ADP
ejpam-4735	37	6	(	(	PUNCT
ejpam-4735	37	7	λ	λ	PROPN
ejpam-4735	37	8	,	,	PUNCT
ejpam-4735	37	9	s)-r0	s)-r0	PRON
ejpam-4735	37	10	spaces	space	VERB
ejpam-4735	37	11	and	and	CCONJ
ejpam-4735	37	12	λp	λp	ADJ
ejpam-4735	37	13	-	-	PUNCT
ejpam-4735	37	14	r0	r0	NOUN
ejpam-4735	37	15	spaces	space	NOUN
ejpam-4735	37	16	were	be	AUX
ejpam-4735	37	17	established	establish	VERB
ejpam-4735	37	18	in	in	ADP
ejpam-4735	37	19	[	[	X
ejpam-4735	37	20	5	5	NUM
ejpam-4735	37	21	]	]	PUNCT
ejpam-4735	37	22	and	and	CCONJ
ejpam-4735	37	23	[	[	X
ejpam-4735	37	24	4	4	NUM
ejpam-4735	37	25	]	]	PUNCT
ejpam-4735	37	26	,	,	PUNCT
ejpam-4735	37	27	respectively	respectively	ADV
ejpam-4735	37	28	.	.	PUNCT
ejpam-4735	38	1	boonpok	boonpok	PROPN
ejpam-4735	38	2	and	and	CCONJ
ejpam-4735	38	3	khampakdee	khampakdee	NOUN
ejpam-4735	39	1	[	[	X
ejpam-4735	39	2	2	2	X
ejpam-4735	39	3	]	]	PUNCT
ejpam-4735	39	4	introduced	introduce	VERB
ejpam-4735	39	5	and	and	CCONJ
ejpam-4735	39	6	investigated	investigate	VERB
ejpam-4735	39	7	the	the	DET
ejpam-4735	39	8	concepts	concept	NOUN
ejpam-4735	39	9	of	of	ADP
ejpam-4735	39	10	δs(λ	δs(λ	NOUN
ejpam-4735	39	11	,	,	PUNCT
ejpam-4735	39	12	s)-r0	s)-r0	PRON
ejpam-4735	39	13	spaces	space	VERB
ejpam-4735	39	14	and	and	CCONJ
ejpam-4735	39	15	δs(λ	δs(λ	NOUN
ejpam-4735	39	16	,	,	PUNCT
ejpam-4735	39	17	s)-r1	s)-r1	NOUN
ejpam-4735	39	18	spaces	space	NOUN
ejpam-4735	39	19	.	.	PUNCT
ejpam-4735	40	1	quite	quite	ADV
ejpam-4735	40	2	recently	recently	ADV
ejpam-4735	40	3	,	,	PUNCT
ejpam-4735	40	4	srisarakham	srisarakham	PROPN
ejpam-4735	40	5	and	and	CCONJ
ejpam-4735	40	6	boonpok	boonpok	PRON
ejpam-4735	40	7	[	[	X
ejpam-4735	40	8	21	21	NUM
ejpam-4735	40	9	]	]	PUNCT
ejpam-4735	40	10	defined	define	VERB
ejpam-4735	40	11	and	and	CCONJ
ejpam-4735	40	12	studied	study	VERB
ejpam-4735	40	13	the	the	DET
ejpam-4735	40	14	notion	notion	NOUN
ejpam-4735	40	15	of	of	ADP
ejpam-4735	40	16	δp(λ	δp(λ	NOUN
ejpam-4735	40	17	,	,	PUNCT
ejpam-4735	40	18	s)-open	s)-open	PUNCT
ejpam-4735	40	19	sets	set	NOUN
ejpam-4735	40	20	in	in	ADP
ejpam-4735	40	21	topological	topological	ADJ
ejpam-4735	40	22	spaces	space	NOUN
ejpam-4735	40	23	.	.	PUNCT
ejpam-4735	41	1	in	in	ADP
ejpam-4735	41	2	this	this	DET
ejpam-4735	41	3	paper	paper	NOUN
ejpam-4735	41	4	,	,	PUNCT
ejpam-4735	41	5	we	we	PRON
ejpam-4735	41	6	introduce	introduce	VERB
ejpam-4735	41	7	the	the	DET
ejpam-4735	41	8	concept	concept	NOUN
ejpam-4735	41	9	of	of	ADP
ejpam-4735	41	10	δp(λ	δp(λ	NOUN
ejpam-4735	41	11	,	,	PUNCT
ejpam-4735	41	12	s)-r0	s)-r0	PRON
ejpam-4735	41	13	spaces	space	VERB
ejpam-4735	41	14	.	.	PUNCT
ejpam-4735	42	1	moreover	moreover	ADV
ejpam-4735	42	2	,	,	PUNCT
ejpam-4735	42	3	some	some	DET
ejpam-4735	42	4	characterizations	characterization	NOUN
ejpam-4735	42	5	of	of	ADP
ejpam-4735	42	6	δp(λ	δp(λ	NOUN
ejpam-4735	42	7	,	,	PUNCT
ejpam-4735	42	8	s)-r0	s)-r0	PRON
ejpam-4735	42	9	spaces	space	NOUN
ejpam-4735	42	10	are	be	AUX
ejpam-4735	42	11	discussed	discuss	VERB
ejpam-4735	42	12	.	.	PUNCT
ejpam-4735	43	1	2	2	X
ejpam-4735	43	2	.	.	X
ejpam-4735	43	3	preliminaries	preliminary	NOUN
ejpam-4735	43	4	throughout	throughout	ADP
ejpam-4735	43	5	the	the	DET
ejpam-4735	43	6	present	present	ADJ
ejpam-4735	43	7	paper	paper	NOUN
ejpam-4735	43	8	,	,	PUNCT
ejpam-4735	43	9	spaces	space	NOUN
ejpam-4735	43	10	(	(	PUNCT
ejpam-4735	43	11	x	x	X
ejpam-4735	43	12	,	,	PUNCT
ejpam-4735	43	13	τ	τ	X
ejpam-4735	43	14	)	)	PUNCT
ejpam-4735	43	15	and	and	CCONJ
ejpam-4735	43	16	(	(	PUNCT
ejpam-4735	43	17	y	y	PROPN
ejpam-4735	43	18	,	,	PUNCT
ejpam-4735	43	19	σ	σ	PROPN
ejpam-4735	43	20	)	)	PUNCT
ejpam-4735	43	21	(	(	PUNCT
ejpam-4735	43	22	or	or	CCONJ
ejpam-4735	43	23	simply	simply	ADV
ejpam-4735	43	24	x	x	X
ejpam-4735	43	25	and	and	CCONJ
ejpam-4735	43	26	y	y	PROPN
ejpam-4735	43	27	)	)	PUNCT
ejpam-4735	43	28	always	always	ADV
ejpam-4735	43	29	mean	mean	VERB
ejpam-4735	43	30	topological	topological	ADJ
ejpam-4735	43	31	spaces	space	NOUN
ejpam-4735	43	32	on	on	ADP
ejpam-4735	43	33	which	which	PRON
ejpam-4735	43	34	no	no	DET
ejpam-4735	43	35	separation	separation	NOUN
ejpam-4735	43	36	axioms	axiom	NOUN
ejpam-4735	43	37	are	be	AUX
ejpam-4735	43	38	assumed	assume	VERB
ejpam-4735	43	39	unless	unless	SCONJ
ejpam-4735	43	40	explicitly	explicitly	ADV
ejpam-4735	43	41	stated	state	VERB
ejpam-4735	43	42	.	.	PUNCT
ejpam-4735	44	1	let	let	VERB
ejpam-4735	44	2	a	a	DET
ejpam-4735	44	3	be	be	AUX
ejpam-4735	44	4	a	a	DET
ejpam-4735	44	5	subset	subset	NOUN
ejpam-4735	44	6	of	of	ADP
ejpam-4735	44	7	a	a	DET
ejpam-4735	44	8	topological	topological	ADJ
ejpam-4735	44	9	space	space	NOUN
ejpam-4735	44	10	(	(	PUNCT
ejpam-4735	44	11	x	x	X
ejpam-4735	44	12	,	,	PUNCT
ejpam-4735	44	13	τ	τ	PROPN
ejpam-4735	44	14	)	)	PUNCT
ejpam-4735	44	15	.	.	PUNCT
ejpam-4735	45	1	the	the	DET
ejpam-4735	45	2	closure	closure	NOUN
ejpam-4735	45	3	of	of	ADP
ejpam-4735	45	4	a	a	PRON
ejpam-4735	45	5	and	and	CCONJ
ejpam-4735	45	6	the	the	DET
ejpam-4735	45	7	interior	interior	NOUN
ejpam-4735	45	8	of	of	ADP
ejpam-4735	45	9	a	a	PRON
ejpam-4735	45	10	are	be	AUX
ejpam-4735	45	11	denoted	denote	VERB
ejpam-4735	45	12	by	by	ADP
ejpam-4735	45	13	cl(a	cl(a	NOUN
ejpam-4735	45	14	)	)	PUNCT
ejpam-4735	45	15	and	and	CCONJ
ejpam-4735	45	16	int(a	int(a	PROPN
ejpam-4735	45	17	)	)	PUNCT
ejpam-4735	45	18	,	,	PUNCT
ejpam-4735	45	19	respectively	respectively	ADV
ejpam-4735	45	20	.	.	PUNCT
ejpam-4735	46	1	a	a	DET
ejpam-4735	46	2	subset	subset	NOUN
ejpam-4735	46	3	a	a	PRON
ejpam-4735	46	4	of	of	ADP
ejpam-4735	46	5	a	a	DET
ejpam-4735	46	6	topological	topological	ADJ
ejpam-4735	46	7	space	space	NOUN
ejpam-4735	46	8	(	(	PUNCT
ejpam-4735	46	9	x	x	X
ejpam-4735	46	10	,	,	PUNCT
ejpam-4735	46	11	τ	τ	X
ejpam-4735	46	12	)	)	PUNCT
ejpam-4735	46	13	is	be	AUX
ejpam-4735	46	14	called	call	VERB
ejpam-4735	46	15	semi	semi	ADJ
ejpam-4735	46	16	-	-	ADJ
ejpam-4735	46	17	open	open	ADJ
ejpam-4735	46	18	[	[	X
ejpam-4735	46	19	14	14	NUM
ejpam-4735	46	20	]	]	X
ejpam-4735	46	21	if	if	SCONJ
ejpam-4735	46	22	a	a	DET
ejpam-4735	46	23	⊆	⊆	NUM
ejpam-4735	46	24	cl(int(a	cl(int(a	NOUN
ejpam-4735	46	25	)	)	PUNCT
ejpam-4735	46	26	)	)	PUNCT
ejpam-4735	46	27	.	.	PUNCT
ejpam-4735	47	1	the	the	DET
ejpam-4735	47	2	complement	complement	NOUN
ejpam-4735	47	3	of	of	ADP
ejpam-4735	47	4	a	a	DET
ejpam-4735	47	5	semi	semi	ADJ
ejpam-4735	47	6	-	-	ADJ
ejpam-4735	47	7	open	open	ADJ
ejpam-4735	47	8	set	set	NOUN
ejpam-4735	47	9	is	be	AUX
ejpam-4735	47	10	called	call	VERB
ejpam-4735	47	11	semiclosed	semiclose	VERB
ejpam-4735	47	12	.	.	PUNCT
ejpam-4735	48	1	the	the	DET
ejpam-4735	48	2	family	family	NOUN
ejpam-4735	48	3	of	of	ADP
ejpam-4735	48	4	all	all	PRON
ejpam-4735	48	5	semi	semi	ADJ
ejpam-4735	48	6	-	-	ADJ
ejpam-4735	48	7	open	open	ADJ
ejpam-4735	48	8	(	(	PUNCT
ejpam-4735	48	9	resp	resp	NOUN
ejpam-4735	48	10	.	.	PUNCT
ejpam-4735	49	1	semi	semi	ADJ
ejpam-4735	49	2	-	-	ADJ
ejpam-4735	49	3	closed	closed	ADJ
ejpam-4735	49	4	)	)	PUNCT
ejpam-4735	49	5	sets	set	NOUN
ejpam-4735	49	6	in	in	ADP
ejpam-4735	49	7	a	a	DET
ejpam-4735	49	8	topological	topological	ADJ
ejpam-4735	49	9	space	space	NOUN
ejpam-4735	49	10	(	(	PUNCT
ejpam-4735	49	11	x	x	X
ejpam-4735	49	12	,	,	PUNCT
ejpam-4735	49	13	τ	τ	X
ejpam-4735	49	14	)	)	PUNCT
ejpam-4735	49	15	is	be	AUX
ejpam-4735	49	16	denoted	denote	VERB
ejpam-4735	49	17	by	by	ADP
ejpam-4735	49	18	so(x	so(x	NOUN
ejpam-4735	49	19	,	,	PUNCT
ejpam-4735	49	20	τ	τ	X
ejpam-4735	49	21	)	)	PUNCT
ejpam-4735	49	22	(	(	PUNCT
ejpam-4735	49	23	resp	resp	NOUN
ejpam-4735	49	24	.	.	PUNCT
ejpam-4735	50	1	sc(x	sc(x	PROPN
ejpam-4735	50	2	,	,	PUNCT
ejpam-4735	50	3	τ	τ	PROPN
ejpam-4735	50	4	)	)	PUNCT
ejpam-4735	50	5	)	)	PUNCT
ejpam-4735	50	6	.	.	PUNCT
ejpam-4735	51	1	a	a	DET
ejpam-4735	51	2	subset	subset	NOUN
ejpam-4735	51	3	aλs	aλs	NOUN
ejpam-4735	51	4	[	[	X
ejpam-4735	51	5	6	6	NUM
ejpam-4735	51	6	]	]	PUNCT
ejpam-4735	51	7	(	(	PUNCT
ejpam-4735	51	8	resp	resp	NOUN
ejpam-4735	51	9	.	.	PUNCT
ejpam-4735	52	1	avs	avs	PROPN
ejpam-4735	52	2	)	)	PUNCT
ejpam-4735	52	3	is	be	AUX
ejpam-4735	52	4	defined	define	VERB
ejpam-4735	52	5	as	as	SCONJ
ejpam-4735	52	6	follows	follow	VERB
ejpam-4735	52	7	:	:	PUNCT
ejpam-4735	52	8	aλs	aλs	PROPN
ejpam-4735	53	1	=	=	SYM
ejpam-4735	53	2	∩{u	∩{u	PROPN
ejpam-4735	54	1	|	|	ADV
ejpam-4735	54	2	u	u	PROPN
ejpam-4735	54	3	⊇	⊇	PROPN
ejpam-4735	54	4	a	a	PROPN
ejpam-4735	54	5	,	,	PUNCT
ejpam-4735	54	6	u	u	PROPN
ejpam-4735	54	7	∈	∈	PROPN
ejpam-4735	54	8	so(x	so(x	NOUN
ejpam-4735	54	9	,	,	PUNCT
ejpam-4735	54	10	τ	τ	PROPN
ejpam-4735	54	11	)	)	PUNCT
ejpam-4735	54	12	}	}	PUNCT
ejpam-4735	54	13	(	(	PUNCT
ejpam-4735	54	14	resp	resp	NOUN
ejpam-4735	54	15	.	.	PUNCT
ejpam-4735	55	1	avs	avs	PROPN
ejpam-4735	56	1	=	=	PROPN
ejpam-4735	56	2	∪{f	∪{f	PROPN
ejpam-4735	56	3	|	|	ADV
ejpam-4735	56	4	f	f	PROPN
ejpam-4735	57	1	⊆	⊆	NUM
ejpam-4735	57	2	a	a	PRON
ejpam-4735	57	3	,	,	PUNCT
ejpam-4735	57	4	f	f	PROPN
ejpam-4735	57	5	∈	∈	PROPN
ejpam-4735	57	6	sc(x	sc(x	PROPN
ejpam-4735	57	7	,	,	PUNCT
ejpam-4735	57	8	τ	τ	NOUN
ejpam-4735	57	9	)	)	PUNCT
ejpam-4735	57	10	}	}	PUNCT
ejpam-4735	57	11	)	)	PUNCT
ejpam-4735	57	12	.	.	PUNCT
ejpam-4735	58	1	a	a	DET
ejpam-4735	58	2	subset	subset	NOUN
ejpam-4735	58	3	a	a	PRON
ejpam-4735	58	4	of	of	ADP
ejpam-4735	58	5	a	a	DET
ejpam-4735	58	6	topological	topological	ADJ
ejpam-4735	58	7	space	space	NOUN
ejpam-4735	58	8	(	(	PUNCT
ejpam-4735	58	9	x	x	X
ejpam-4735	58	10	,	,	PUNCT
ejpam-4735	58	11	τ	τ	X
ejpam-4735	58	12	)	)	PUNCT
ejpam-4735	58	13	is	be	AUX
ejpam-4735	58	14	called	call	VERB
ejpam-4735	58	15	a	a	DET
ejpam-4735	58	16	λs	λs	ADV
ejpam-4735	58	17	-	-	PUNCT
ejpam-4735	58	18	set	set	VERB
ejpam-4735	58	19	(	(	PUNCT
ejpam-4735	58	20	resp	resp	NOUN
ejpam-4735	58	21	.	.	PUNCT
ejpam-4735	59	1	vs	vs	ADP
ejpam-4735	59	2	-	-	PUNCT
ejpam-4735	59	3	set	set	NOUN
ejpam-4735	59	4	)	)	PUNCT
ejpam-4735	60	1	[	[	X
ejpam-4735	60	2	6	6	X
ejpam-4735	60	3	]	]	X
ejpam-4735	60	4	if	if	SCONJ
ejpam-4735	60	5	a	a	PRON
ejpam-4735	60	6	=	=	X
ejpam-4735	60	7	aλs	aλs	NOUN
ejpam-4735	60	8	(	(	PUNCT
ejpam-4735	60	9	resp	resp	NOUN
ejpam-4735	60	10	.	.	PUNCT
ejpam-4735	61	1	a	a	DET
ejpam-4735	61	2	=	=	SYM
ejpam-4735	61	3	avs	avs	PROPN
ejpam-4735	61	4	)	)	PUNCT
ejpam-4735	61	5	.	.	PUNCT
ejpam-4735	62	1	a	a	DET
ejpam-4735	62	2	subset	subset	NOUN
ejpam-4735	62	3	a	a	PRON
ejpam-4735	62	4	of	of	ADP
ejpam-4735	62	5	a	a	DET
ejpam-4735	62	6	topological	topological	ADJ
ejpam-4735	62	7	space	space	NOUN
ejpam-4735	62	8	(	(	PUNCT
ejpam-4735	62	9	x	x	X
ejpam-4735	62	10	,	,	PUNCT
ejpam-4735	62	11	τ	τ	X
ejpam-4735	62	12	)	)	PUNCT
ejpam-4735	62	13	is	be	AUX
ejpam-4735	62	14	called	call	VERB
ejpam-4735	62	15	(	(	PUNCT
ejpam-4735	62	16	λ	λ	X
ejpam-4735	62	17	,	,	PUNCT
ejpam-4735	62	18	s)-closed	s)-close	VERB
ejpam-4735	62	19	[	[	X
ejpam-4735	62	20	5	5	X
ejpam-4735	62	21	]	]	PUNCT
ejpam-4735	62	22	if	if	SCONJ
ejpam-4735	62	23	a	a	DET
ejpam-4735	62	24	=	=	X
ejpam-4735	62	25	t	t	NOUN
ejpam-4735	62	26	∩c	∩c	NOUN
ejpam-4735	62	27	,	,	PUNCT
ejpam-4735	62	28	where	where	SCONJ
ejpam-4735	62	29	t	t	PROPN
ejpam-4735	62	30	is	be	AUX
ejpam-4735	62	31	a	a	DET
ejpam-4735	62	32	λs	λs	ADV
ejpam-4735	62	33	-	-	PUNCT
ejpam-4735	62	34	set	set	VERB
ejpam-4735	62	35	and	and	CCONJ
ejpam-4735	62	36	c	c	NOUN
ejpam-4735	62	37	is	be	AUX
ejpam-4735	62	38	a	a	DET
ejpam-4735	62	39	semi	semi	ADJ
ejpam-4735	62	40	-	-	ADJ
ejpam-4735	62	41	closed	closed	ADJ
ejpam-4735	62	42	set	set	NOUN
ejpam-4735	62	43	.	.	PUNCT
ejpam-4735	63	1	the	the	DET
ejpam-4735	63	2	complement	complement	NOUN
ejpam-4735	63	3	of	of	ADP
ejpam-4735	63	4	a	a	DET
ejpam-4735	63	5	(	(	PUNCT
ejpam-4735	63	6	λ	λ	PROPN
ejpam-4735	63	7	,	,	PUNCT
ejpam-4735	63	8	s)-closed	s)-close	VERB
ejpam-4735	63	9	set	set	NOUN
ejpam-4735	63	10	is	be	AUX
ejpam-4735	63	11	called	call	VERB
ejpam-4735	63	12	(	(	PUNCT
ejpam-4735	63	13	λ	λ	X
ejpam-4735	63	14	,	,	PUNCT
ejpam-4735	63	15	s)-open	s)-open	VERB
ejpam-4735	63	16	.	.	PUNCT
ejpam-4735	64	1	the	the	DET
ejpam-4735	64	2	family	family	NOUN
ejpam-4735	64	3	of	of	ADP
ejpam-4735	64	4	all	all	PRON
ejpam-4735	64	5	(	(	PUNCT
ejpam-4735	64	6	λ	λ	X
ejpam-4735	64	7	,	,	PUNCT
ejpam-4735	64	8	s)-closed	s)-close	VERB
ejpam-4735	64	9	(	(	PUNCT
ejpam-4735	64	10	resp	resp	NOUN
ejpam-4735	64	11	.	.	PUNCT
ejpam-4735	65	1	(	(	PUNCT
ejpam-4735	65	2	λ	λ	X
ejpam-4735	65	3	,	,	PUNCT
ejpam-4735	65	4	s)-open	s)-open	PUNCT
ejpam-4735	65	5	)	)	PUNCT
ejpam-4735	65	6	sets	set	NOUN
ejpam-4735	65	7	in	in	ADP
ejpam-4735	65	8	a	a	DET
ejpam-4735	65	9	topological	topological	ADJ
ejpam-4735	65	10	space	space	NOUN
ejpam-4735	65	11	(	(	PUNCT
ejpam-4735	65	12	x	x	X
ejpam-4735	65	13	,	,	PUNCT
ejpam-4735	65	14	τ	τ	X
ejpam-4735	65	15	)	)	PUNCT
ejpam-4735	65	16	is	be	AUX
ejpam-4735	65	17	denoted	denote	VERB
ejpam-4735	65	18	by	by	ADP
ejpam-4735	65	19	λsc(x	λsc(x	PROPN
ejpam-4735	65	20	,	,	PUNCT
ejpam-4735	65	21	τ	τ	PROPN
ejpam-4735	65	22	)	)	PUNCT
ejpam-4735	65	23	(	(	PUNCT
ejpam-4735	65	24	resp	resp	NOUN
ejpam-4735	65	25	.	.	PUNCT
ejpam-4735	66	1	λso(x	λso(x	NUM
ejpam-4735	66	2	,	,	PUNCT
ejpam-4735	66	3	τ	τ	NOUN
ejpam-4735	66	4	)	)	PUNCT
ejpam-4735	66	5	)	)	PUNCT
ejpam-4735	66	6	.	.	PUNCT
ejpam-4735	67	1	let	let	VERB
ejpam-4735	67	2	a	a	DET
ejpam-4735	67	3	be	be	AUX
ejpam-4735	67	4	a	a	DET
ejpam-4735	67	5	subset	subset	NOUN
ejpam-4735	67	6	of	of	ADP
ejpam-4735	67	7	a	a	DET
ejpam-4735	67	8	topological	topological	ADJ
ejpam-4735	67	9	space	space	NOUN
ejpam-4735	67	10	(	(	PUNCT
ejpam-4735	67	11	x	x	X
ejpam-4735	67	12	,	,	PUNCT
ejpam-4735	67	13	τ	τ	PROPN
ejpam-4735	67	14	)	)	PUNCT
ejpam-4735	67	15	.	.	PUNCT
ejpam-4735	68	1	a	a	DET
ejpam-4735	68	2	point	point	NOUN
ejpam-4735	68	3	x	x	X
ejpam-4735	68	4	∈	∈	NOUN
ejpam-4735	68	5	x	x	PUNCT
ejpam-4735	68	6	is	be	AUX
ejpam-4735	68	7	called	call	VERB
ejpam-4735	68	8	a	a	DET
ejpam-4735	68	9	(	(	PUNCT
ejpam-4735	68	10	λ	λ	NOUN
ejpam-4735	68	11	,	,	PUNCT
ejpam-4735	68	12	s)-cluster	s)-cluster	PUNCT
ejpam-4735	68	13	point	point	VERB
ejpam-4735	68	14	[	[	X
ejpam-4735	68	15	5	5	NUM
ejpam-4735	68	16	]	]	PUNCT
ejpam-4735	68	17	of	of	ADP
ejpam-4735	68	18	a	a	DET
ejpam-4735	68	19	if	if	NOUN
ejpam-4735	68	20	for	for	ADP
ejpam-4735	68	21	every	every	DET
ejpam-4735	68	22	(	(	PUNCT
ejpam-4735	68	23	λ	λ	NOUN
ejpam-4735	68	24	,	,	PUNCT
ejpam-4735	68	25	s)-open	s)-open	VERB
ejpam-4735	68	26	set	set	VERB
ejpam-4735	68	27	u	u	NOUN
ejpam-4735	68	28	of	of	ADP
ejpam-4735	68	29	x	x	PUNCT
ejpam-4735	68	30	containing	contain	VERB
ejpam-4735	68	31	x	x	VERB
ejpam-4735	68	32	we	we	PRON
ejpam-4735	68	33	have	have	VERB
ejpam-4735	68	34	a	a	DET
ejpam-4735	68	35	∩	∩	ADJ
ejpam-4735	68	36	u	u	ADJ
ejpam-4735	68	37	̸=	̸=	PROPN
ejpam-4735	68	38	∅.	∅.	ADP
ejpam-4735	68	39	the	the	DET
ejpam-4735	68	40	set	set	NOUN
ejpam-4735	68	41	of	of	ADP
ejpam-4735	68	42	all	all	DET
ejpam-4735	68	43	(	(	PUNCT
ejpam-4735	68	44	λ	λ	NOUN
ejpam-4735	68	45	,	,	PUNCT
ejpam-4735	69	1	s)-cluster	s)-cluster	PUNCT
ejpam-4735	69	2	points	point	NOUN
ejpam-4735	69	3	of	of	ADP
ejpam-4735	69	4	a	a	PRON
ejpam-4735	69	5	is	be	AUX
ejpam-4735	69	6	called	call	VERB
ejpam-4735	69	7	the	the	DET
ejpam-4735	69	8	(	(	PUNCT
ejpam-4735	69	9	λ	λ	PROPN
ejpam-4735	69	10	,	,	PUNCT
ejpam-4735	69	11	s)-closure	s)-closure	PUNCT
ejpam-4735	69	12	[	[	X
ejpam-4735	69	13	5	5	NUM
ejpam-4735	69	14	]	]	PUNCT
ejpam-4735	69	15	of	of	ADP
ejpam-4735	69	16	a	a	PRON
ejpam-4735	69	17	and	and	CCONJ
ejpam-4735	69	18	is	be	AUX
ejpam-4735	69	19	denoted	denote	VERB
ejpam-4735	69	20	by	by	ADP
ejpam-4735	69	21	a(λ	a(λ	PROPN
ejpam-4735	69	22	,	,	PUNCT
ejpam-4735	69	23	s	s	PART
ejpam-4735	69	24	)	)	PUNCT
ejpam-4735	69	25	.	.	PUNCT
ejpam-4735	70	1	the	the	DET
ejpam-4735	70	2	union	union	NOUN
ejpam-4735	70	3	of	of	ADP
ejpam-4735	70	4	all	all	DET
ejpam-4735	70	5	(	(	PUNCT
ejpam-4735	70	6	λ	λ	X
ejpam-4735	70	7	,	,	PUNCT
ejpam-4735	70	8	s)-open	s)-open	PUNCT
ejpam-4735	70	9	sets	set	NOUN
ejpam-4735	70	10	contained	contain	VERB
ejpam-4735	70	11	in	in	ADP
ejpam-4735	70	12	a	a	PRON
ejpam-4735	70	13	is	be	AUX
ejpam-4735	70	14	called	call	VERB
ejpam-4735	70	15	the	the	DET
ejpam-4735	70	16	(	(	PUNCT
ejpam-4735	70	17	λ	λ	PROPN
ejpam-4735	70	18	,	,	PUNCT
ejpam-4735	70	19	s)-interior	s)-interior	X
ejpam-4735	70	20	[	[	X
ejpam-4735	70	21	5	5	NUM
ejpam-4735	70	22	]	]	PUNCT
ejpam-4735	70	23	of	of	ADP
ejpam-4735	70	24	a	a	PRON
ejpam-4735	70	25	and	and	CCONJ
ejpam-4735	70	26	is	be	AUX
ejpam-4735	70	27	denoted	denote	VERB
ejpam-4735	70	28	by	by	ADP
ejpam-4735	70	29	a(λ	a(λ	PROPN
ejpam-4735	70	30	,	,	PUNCT
ejpam-4735	70	31	s	s	PART
ejpam-4735	70	32	)	)	PUNCT
ejpam-4735	70	33	.	.	PUNCT
ejpam-4735	71	1	let	let	VERB
ejpam-4735	71	2	a	a	DET
ejpam-4735	71	3	be	be	AUX
ejpam-4735	71	4	a	a	DET
ejpam-4735	71	5	subset	subset	NOUN
ejpam-4735	71	6	of	of	ADP
ejpam-4735	71	7	a	a	DET
ejpam-4735	71	8	topological	topological	ADJ
ejpam-4735	71	9	space	space	NOUN
ejpam-4735	71	10	(	(	PUNCT
ejpam-4735	71	11	x	x	X
ejpam-4735	71	12	,	,	PUNCT
ejpam-4735	71	13	τ	τ	PROPN
ejpam-4735	71	14	)	)	PUNCT
ejpam-4735	71	15	.	.	PUNCT
ejpam-4735	72	1	a	a	DET
ejpam-4735	72	2	point	point	NOUN
ejpam-4735	72	3	x	x	X
ejpam-4735	72	4	ofx	ofx	PROPN
ejpam-4735	72	5	is	be	AUX
ejpam-4735	72	6	called	call	VERB
ejpam-4735	72	7	a	a	DET
ejpam-4735	72	8	δ(λ	δ(λ	PROPN
ejpam-4735	72	9	,	,	PUNCT
ejpam-4735	72	10	s)-cluster	s)-cluster	PUNCT
ejpam-4735	72	11	point	point	NOUN
ejpam-4735	72	12	[	[	X
ejpam-4735	72	13	21	21	NUM
ejpam-4735	72	14	]	]	PUNCT
ejpam-4735	72	15	of	of	ADP
ejpam-4735	72	16	a	a	DET
ejpam-4735	72	17	if	if	SCONJ
ejpam-4735	72	18	a	a	DET
ejpam-4735	72	19	∩	∩	NOUN
ejpam-4735	72	20	[	[	X
ejpam-4735	72	21	v	v	X
ejpam-4735	72	22	(	(	PUNCT
ejpam-4735	72	23	λ	λ	PROPN
ejpam-4735	72	24	,	,	PUNCT
ejpam-4735	72	25	s)](λ	s)](λ	PROPN
ejpam-4735	72	26	,	,	PUNCT
ejpam-4735	72	27	s	s	PART
ejpam-4735	72	28	)	)	PUNCT
ejpam-4735	72	29	̸=	̸=	NOUN
ejpam-4735	72	30	∅	∅	NOUN
ejpam-4735	72	31	for	for	ADP
ejpam-4735	72	32	every	every	DET
ejpam-4735	72	33	(	(	PUNCT
ejpam-4735	72	34	λ	λ	NOUN
ejpam-4735	72	35	,	,	PUNCT
ejpam-4735	72	36	s)-open	s)-open	PUNCT
ejpam-4735	72	37	set	set	VERB
ejpam-4735	72	38	v	v	NUM
ejpam-4735	72	39	of	of	ADP
ejpam-4735	72	40	x	x	PUNCT
ejpam-4735	72	41	containing	contain	VERB
ejpam-4735	72	42	x.	x.	NOUN
ejpam-4735	72	43	the	the	DET
ejpam-4735	72	44	set	set	NOUN
ejpam-4735	72	45	of	of	ADP
ejpam-4735	72	46	all	all	DET
ejpam-4735	72	47	δ(λ	δ(λ	PROPN
ejpam-4735	72	48	,	,	PUNCT
ejpam-4735	72	49	s)-cluster	s)-cluster	PUNCT
ejpam-4735	72	50	points	point	NOUN
ejpam-4735	72	51	of	of	ADP
ejpam-4735	72	52	a	a	PRON
ejpam-4735	72	53	is	be	AUX
ejpam-4735	72	54	called	call	VERB
ejpam-4735	72	55	the	the	DET
ejpam-4735	72	56	δ(λ	δ(λ	PROPN
ejpam-4735	72	57	,	,	PUNCT
ejpam-4735	72	58	s)-closure	s)-closure	PUNCT
ejpam-4735	72	59	[	[	X
ejpam-4735	72	60	21	21	NUM
ejpam-4735	72	61	]	]	PUNCT
ejpam-4735	72	62	of	of	ADP
ejpam-4735	72	63	a	a	PRON
ejpam-4735	72	64	and	and	CCONJ
ejpam-4735	72	65	is	be	AUX
ejpam-4735	72	66	denoted	denote	VERB
ejpam-4735	72	67	by	by	ADP
ejpam-4735	72	68	aδ(λ	aδ(λ	NUM
ejpam-4735	72	69	,	,	PUNCT
ejpam-4735	72	70	s	s	NOUN
ejpam-4735	72	71	)	)	PUNCT
ejpam-4735	72	72	.	.	PUNCT
ejpam-4735	73	1	if	if	SCONJ
ejpam-4735	73	2	a	a	DET
ejpam-4735	73	3	=	=	NOUN
ejpam-4735	73	4	aδ(λ	aδ(λ	NUM
ejpam-4735	73	5	,	,	PUNCT
ejpam-4735	73	6	s	s	PART
ejpam-4735	73	7	)	)	PUNCT
ejpam-4735	73	8	,	,	PUNCT
ejpam-4735	73	9	then	then	ADV
ejpam-4735	73	10	a	a	PRON
ejpam-4735	73	11	is	be	AUX
ejpam-4735	73	12	said	say	VERB
ejpam-4735	73	13	to	to	PART
ejpam-4735	73	14	be	be	AUX
ejpam-4735	73	15	δ(λ	δ(λ	PROPN
ejpam-4735	73	16	,	,	PUNCT
ejpam-4735	73	17	s)-closed	s)-close	VERB
ejpam-4735	73	18	[	[	X
ejpam-4735	73	19	21	21	NUM
ejpam-4735	73	20	]	]	PUNCT
ejpam-4735	73	21	.	.	PUNCT
ejpam-4735	74	1	the	the	DET
ejpam-4735	74	2	complement	complement	NOUN
ejpam-4735	74	3	of	of	ADP
ejpam-4735	74	4	a	a	DET
ejpam-4735	74	5	δ(λ	δ(λ	PROPN
ejpam-4735	74	6	,	,	PUNCT
ejpam-4735	74	7	s)-closed	s)-close	VERB
ejpam-4735	74	8	set	set	NOUN
ejpam-4735	74	9	is	be	AUX
ejpam-4735	74	10	said	say	VERB
ejpam-4735	74	11	to	to	PART
ejpam-4735	74	12	be	be	AUX
ejpam-4735	74	13	δ(λ	δ(λ	PROPN
ejpam-4735	74	14	,	,	PUNCT
ejpam-4735	74	15	s)-open	s)-open	PUNCT
ejpam-4735	74	16	[	[	X
ejpam-4735	74	17	21	21	NUM
ejpam-4735	74	18	]	]	PUNCT
ejpam-4735	74	19	.	.	PUNCT
ejpam-4735	75	1	the	the	DET
ejpam-4735	75	2	union	union	NOUN
ejpam-4735	75	3	of	of	ADP
ejpam-4735	75	4	all	all	DET
ejpam-4735	75	5	δ(λ	δ(λ	PROPN
ejpam-4735	75	6	,	,	PUNCT
ejpam-4735	75	7	s)-open	s)-open	PUNCT
ejpam-4735	75	8	sets	set	NOUN
ejpam-4735	75	9	contained	contain	VERB
ejpam-4735	75	10	in	in	ADP
ejpam-4735	75	11	a	a	PRON
ejpam-4735	75	12	is	be	AUX
ejpam-4735	75	13	called	call	VERB
ejpam-4735	75	14	the	the	DET
ejpam-4735	75	15	δ(λ	δ(λ	PROPN
ejpam-4735	75	16	,	,	PUNCT
ejpam-4735	75	17	s)-interior	s)-interior	VERB
ejpam-4735	76	1	[	[	X
ejpam-4735	76	2	21	21	NUM
ejpam-4735	76	3	]	]	PUNCT
ejpam-4735	76	4	of	of	ADP
ejpam-4735	76	5	a	a	PRON
ejpam-4735	76	6	and	and	CCONJ
ejpam-4735	76	7	is	be	AUX
ejpam-4735	76	8	denoted	denote	VERB
ejpam-4735	76	9	by	by	ADP
ejpam-4735	76	10	aδ(λ	aδ(λ	NUM
ejpam-4735	76	11	,	,	PUNCT
ejpam-4735	76	12	s	s	NOUN
ejpam-4735	76	13	)	)	PUNCT
ejpam-4735	76	14	.	.	PUNCT
ejpam-4735	77	1	definition	definition	NOUN
ejpam-4735	77	2	1	1	NUM
ejpam-4735	77	3	.	.	PUNCT
ejpam-4735	78	1	[	[	X
ejpam-4735	78	2	21	21	NUM
ejpam-4735	78	3	]	]	X
ejpam-4735	78	4	a	a	DET
ejpam-4735	78	5	subset	subset	NOUN
ejpam-4735	78	6	a	a	PRON
ejpam-4735	78	7	of	of	ADP
ejpam-4735	78	8	a	a	DET
ejpam-4735	78	9	topological	topological	ADJ
ejpam-4735	78	10	space	space	NOUN
ejpam-4735	78	11	(	(	PUNCT
ejpam-4735	78	12	x	x	X
ejpam-4735	78	13	,	,	PUNCT
ejpam-4735	78	14	τ	τ	X
ejpam-4735	78	15	)	)	PUNCT
ejpam-4735	78	16	is	be	AUX
ejpam-4735	78	17	said	say	VERB
ejpam-4735	78	18	to	to	PART
ejpam-4735	78	19	be	be	AUX
ejpam-4735	78	20	δp(λ	δp(λ	NOUN
ejpam-4735	78	21	,	,	PUNCT
ejpam-4735	78	22	s)-open	s)-open	VERB
ejpam-4735	78	23	if	if	SCONJ
ejpam-4735	78	24	a	a	DET
ejpam-4735	78	25	⊆	⊆	NUM
ejpam-4735	78	26	[	[	X
ejpam-4735	78	27	a(λ	a(λ	ADJ
ejpam-4735	78	28	,	,	PUNCT
ejpam-4735	78	29	s)]δ(λ	s)]δ(λ	ADJ
ejpam-4735	78	30	,	,	PUNCT
ejpam-4735	78	31	s	s	PART
ejpam-4735	78	32	)	)	PUNCT
ejpam-4735	78	33	.	.	PUNCT
ejpam-4735	79	1	the	the	DET
ejpam-4735	79	2	complement	complement	NOUN
ejpam-4735	79	3	of	of	ADP
ejpam-4735	79	4	a	a	DET
ejpam-4735	79	5	δp(λ	δp(λ	NOUN
ejpam-4735	79	6	,	,	PUNCT
ejpam-4735	79	7	s)-open	s)-open	PUNCT
ejpam-4735	79	8	set	set	VERB
ejpam-4735	79	9	is	be	AUX
ejpam-4735	79	10	said	say	VERB
ejpam-4735	79	11	to	to	PART
ejpam-4735	79	12	be	be	AUX
ejpam-4735	79	13	δp(λ	δp(λ	NOUN
ejpam-4735	79	14	,	,	PUNCT
ejpam-4735	79	15	s)-closed	s)-close	VERB
ejpam-4735	79	16	.	.	PUNCT
ejpam-4735	80	1	the	the	DET
ejpam-4735	80	2	family	family	NOUN
ejpam-4735	80	3	of	of	ADP
ejpam-4735	80	4	all	all	DET
ejpam-4735	80	5	δp(λ	δp(λ	NOUN
ejpam-4735	80	6	,	,	PUNCT
ejpam-4735	80	7	s)-open	s)-open	PUNCT
ejpam-4735	80	8	(	(	PUNCT
ejpam-4735	80	9	resp	resp	NOUN
ejpam-4735	80	10	.	.	PUNCT
ejpam-4735	81	1	δp(λ	δp(λ	NOUN
ejpam-4735	81	2	,	,	PUNCT
ejpam-4735	81	3	s)-closed	s)-close	VERB
ejpam-4735	81	4	)	)	PUNCT
ejpam-4735	81	5	sets	set	NOUN
ejpam-4735	81	6	in	in	ADP
ejpam-4735	81	7	a	a	DET
ejpam-4735	81	8	topological	topological	ADJ
ejpam-4735	81	9	space	space	NOUN
ejpam-4735	81	10	(	(	PUNCT
ejpam-4735	81	11	x	x	X
ejpam-4735	81	12	,	,	PUNCT
ejpam-4735	81	13	τ	τ	X
ejpam-4735	81	14	)	)	PUNCT
ejpam-4735	81	15	is	be	AUX
ejpam-4735	81	16	denoted	denote	VERB
ejpam-4735	81	17	by	by	ADP
ejpam-4735	81	18	δp(λ	δp(λ	NOUN
ejpam-4735	81	19	,	,	PUNCT
ejpam-4735	81	20	s)o(x	s)o(x	PROPN
ejpam-4735	81	21	,	,	PUNCT
ejpam-4735	81	22	τ	τ	X
ejpam-4735	81	23	)	)	PUNCT
ejpam-4735	81	24	(	(	PUNCT
ejpam-4735	81	25	resp	resp	NOUN
ejpam-4735	81	26	.	.	PUNCT
ejpam-4735	82	1	δp(λ	δp(λ	PROPN
ejpam-4735	82	2	,	,	PUNCT
ejpam-4735	82	3	s)c(x	s)c(x	NOUN
ejpam-4735	82	4	,	,	PUNCT
ejpam-4735	82	5	τ	τ	PROPN
ejpam-4735	82	6	)	)	PUNCT
ejpam-4735	82	7	)	)	PUNCT
ejpam-4735	82	8	.	.	PUNCT
ejpam-4735	83	1	let	let	VERB
ejpam-4735	83	2	a	a	DET
ejpam-4735	83	3	be	be	AUX
ejpam-4735	83	4	a	a	DET
ejpam-4735	83	5	subset	subset	NOUN
ejpam-4735	83	6	of	of	ADP
ejpam-4735	83	7	a	a	DET
ejpam-4735	83	8	topological	topological	ADJ
ejpam-4735	83	9	space	space	NOUN
ejpam-4735	83	10	(	(	PUNCT
ejpam-4735	83	11	x	x	X
ejpam-4735	83	12	,	,	PUNCT
ejpam-4735	83	13	τ	τ	PROPN
ejpam-4735	83	14	)	)	PUNCT
ejpam-4735	83	15	.	.	PUNCT
ejpam-4735	84	1	the	the	DET
ejpam-4735	84	2	intersection	intersection	NOUN
ejpam-4735	84	3	of	of	ADP
ejpam-4735	84	4	all	all	DET
ejpam-4735	84	5	δp(λ	δp(λ	NOUN
ejpam-4735	84	6	,	,	PUNCT
ejpam-4735	84	7	s)-closed	s)-close	VERB
ejpam-4735	84	8	sets	set	NOUN
ejpam-4735	84	9	containing	contain	VERB
ejpam-4735	84	10	a	a	PRON
ejpam-4735	84	11	is	be	AUX
ejpam-4735	84	12	called	call	VERB
ejpam-4735	84	13	the	the	DET
ejpam-4735	84	14	δp(λ	δp(λ	NOUN
ejpam-4735	84	15	,	,	PUNCT
ejpam-4735	84	16	s)closure	s)closure	NOUN
ejpam-4735	85	1	[	[	X
ejpam-4735	85	2	22	22	NUM
ejpam-4735	85	3	]	]	PUNCT
ejpam-4735	85	4	of	of	ADP
ejpam-4735	85	5	a	a	PRON
ejpam-4735	85	6	and	and	CCONJ
ejpam-4735	85	7	is	be	AUX
ejpam-4735	85	8	denoted	denote	VERB
ejpam-4735	85	9	by	by	ADP
ejpam-4735	85	10	aδp(λ	aδp(λ	PROPN
ejpam-4735	85	11	,	,	PUNCT
ejpam-4735	85	12	s	s	NOUN
ejpam-4735	85	13	)	)	PUNCT
ejpam-4735	85	14	.	.	PUNCT
ejpam-4735	86	1	lemma	lemma	PROPN
ejpam-4735	86	2	1	1	NUM
ejpam-4735	86	3	.	.	PUNCT
ejpam-4735	87	1	[	[	X
ejpam-4735	87	2	21	21	NUM
ejpam-4735	87	3	]	]	PUNCT
ejpam-4735	87	4	for	for	ADP
ejpam-4735	87	5	the	the	DET
ejpam-4735	87	6	δp(λ	δp(λ	NOUN
ejpam-4735	87	7	,	,	PUNCT
ejpam-4735	87	8	s)-closure	s)-closure	NOUN
ejpam-4735	87	9	of	of	ADP
ejpam-4735	87	10	subsets	subset	NOUN
ejpam-4735	87	11	a	a	PRON
ejpam-4735	87	12	,	,	PUNCT
ejpam-4735	87	13	b	b	NOUN
ejpam-4735	87	14	in	in	ADP
ejpam-4735	87	15	a	a	DET
ejpam-4735	87	16	topological	topological	ADJ
ejpam-4735	87	17	space	space	NOUN
ejpam-4735	87	18	(	(	PUNCT
ejpam-4735	87	19	x	x	X
ejpam-4735	87	20	,	,	PUNCT
ejpam-4735	87	21	τ	τ	PROPN
ejpam-4735	87	22	)	)	PUNCT
ejpam-4735	87	23	,	,	PUNCT
ejpam-4735	87	24	the	the	DET
ejpam-4735	87	25	following	follow	VERB
ejpam-4735	87	26	properties	property	NOUN
ejpam-4735	87	27	hold	hold	VERB
ejpam-4735	87	28	:	:	PUNCT
ejpam-4735	87	29	(	(	PUNCT
ejpam-4735	87	30	1	1	X
ejpam-4735	87	31	)	)	PUNCT
ejpam-4735	88	1	if	if	SCONJ
ejpam-4735	88	2	a	a	DET
ejpam-4735	88	3	⊆	⊆	NUM
ejpam-4735	88	4	b	b	NOUN
ejpam-4735	88	5	,	,	PUNCT
ejpam-4735	88	6	then	then	ADV
ejpam-4735	88	7	aδp(λ	aδp(λ	PROPN
ejpam-4735	88	8	,	,	PUNCT
ejpam-4735	88	9	s	s	PART
ejpam-4735	88	10	)	)	PUNCT
ejpam-4735	88	11	⊆	⊆	NUM
ejpam-4735	88	12	bδp(λ	bδp(λ	PROPN
ejpam-4735	88	13	,	,	PUNCT
ejpam-4735	88	14	s	s	PART
ejpam-4735	88	15	)	)	PUNCT
ejpam-4735	88	16	.	.	PUNCT
ejpam-4735	89	1	c.	c.	PROPN
ejpam-4735	89	2	boonpok	boonpok	PROPN
ejpam-4735	89	3	,	,	PUNCT
ejpam-4735	89	4	p.	p.	NOUN
ejpam-4735	89	5	pue	pue	NOUN
ejpam-4735	89	6	-	-	PUNCT
ejpam-4735	89	7	on	on	ADP
ejpam-4735	89	8	/	/	SYM
ejpam-4735	89	9	eur	eur	NOUN
ejpam-4735	89	10	.	.	PUNCT
ejpam-4735	90	1	j.	j.	PROPN
ejpam-4735	90	2	pure	pure	PROPN
ejpam-4735	90	3	appl	appl	PROPN
ejpam-4735	90	4	.	.	PROPN
ejpam-4735	90	5	math	math	PROPN
ejpam-4735	90	6	,	,	PUNCT
ejpam-4735	90	7	17	17	NUM
ejpam-4735	90	8	(	(	PUNCT
ejpam-4735	90	9	1	1	NUM
ejpam-4735	90	10	)	)	PUNCT
ejpam-4735	90	11	(	(	PUNCT
ejpam-4735	90	12	2024	2024	NUM
ejpam-4735	90	13	)	)	PUNCT
ejpam-4735	90	14	,	,	PUNCT
ejpam-4735	90	15	147	147	NUM
ejpam-4735	90	16	-	-	SYM
ejpam-4735	90	17	157	157	NUM
ejpam-4735	90	18	149	149	NUM
ejpam-4735	90	19	(	(	PUNCT
ejpam-4735	90	20	2	2	NUM
ejpam-4735	90	21	)	)	PUNCT
ejpam-4735	90	22	a	a	PRON
ejpam-4735	90	23	is	is	NOUN
ejpam-4735	90	24	δp(λ	δp(λ	NOUN
ejpam-4735	90	25	,	,	PUNCT
ejpam-4735	90	26	s)-closed	s)-close	VERB
ejpam-4735	90	27	in	in	ADP
ejpam-4735	90	28	(	(	PUNCT
ejpam-4735	90	29	x	x	X
ejpam-4735	90	30	,	,	PUNCT
ejpam-4735	90	31	τ	τ	X
ejpam-4735	90	32	)	)	PUNCT
ejpam-4735	90	33	if	if	SCONJ
ejpam-4735	90	34	and	and	CCONJ
ejpam-4735	90	35	only	only	ADV
ejpam-4735	90	36	if	if	SCONJ
ejpam-4735	90	37	a	a	DET
ejpam-4735	90	38	=	=	X
ejpam-4735	90	39	aδp(λ	aδp(λ	PROPN
ejpam-4735	90	40	,	,	PUNCT
ejpam-4735	90	41	s	s	NOUN
ejpam-4735	90	42	)	)	PUNCT
ejpam-4735	90	43	.	.	PUNCT
ejpam-4735	91	1	(	(	PUNCT
ejpam-4735	91	2	3	3	X
ejpam-4735	91	3	)	)	PUNCT
ejpam-4735	91	4	aδp(λ	aδp(λ	PROPN
ejpam-4735	91	5	,	,	PUNCT
ejpam-4735	91	6	s	s	PART
ejpam-4735	91	7	)	)	PUNCT
ejpam-4735	91	8	is	be	AUX
ejpam-4735	91	9	δp(λ	δp(λ	NOUN
ejpam-4735	91	10	,	,	PUNCT
ejpam-4735	91	11	s)-closed	s)-close	VERB
ejpam-4735	91	12	,	,	PUNCT
ejpam-4735	91	13	that	that	ADV
ejpam-4735	91	14	is	is	ADV
ejpam-4735	91	15	,	,	PUNCT
ejpam-4735	91	16	aδp(λ	aδp(λ	PROPN
ejpam-4735	91	17	,	,	PUNCT
ejpam-4735	91	18	s	s	PART
ejpam-4735	91	19	)	)	PUNCT
ejpam-4735	91	20	=	=	PUNCT
ejpam-4735	92	1	[	[	X
ejpam-4735	92	2	aδp(λ	aδp(λ	PROPN
ejpam-4735	92	3	,	,	PUNCT
ejpam-4735	92	4	s)]δp(λ	s)]δp(λ	NOUN
ejpam-4735	92	5	,	,	PUNCT
ejpam-4735	92	6	s	s	NOUN
ejpam-4735	92	7	)	)	PUNCT
ejpam-4735	92	8	.	.	PUNCT
ejpam-4735	93	1	(	(	PUNCT
ejpam-4735	93	2	4	4	X
ejpam-4735	93	3	)	)	PUNCT
ejpam-4735	93	4	x	x	SYM
ejpam-4735	93	5	∈	∈	PROPN
ejpam-4735	93	6	aδp(λ	aδp(λ	PROPN
ejpam-4735	93	7	,	,	PUNCT
ejpam-4735	93	8	s	s	PART
ejpam-4735	93	9	)	)	PUNCT
ejpam-4735	93	10	if	if	SCONJ
ejpam-4735	93	11	and	and	CCONJ
ejpam-4735	93	12	only	only	ADV
ejpam-4735	93	13	if	if	SCONJ
ejpam-4735	93	14	a	a	DET
ejpam-4735	93	15	∩	∩	NOUN
ejpam-4735	93	16	v	v	ADP
ejpam-4735	93	17	̸=	̸=	PROPN
ejpam-4735	93	18	∅	∅	NOUN
ejpam-4735	93	19	for	for	ADP
ejpam-4735	93	20	every	every	DET
ejpam-4735	93	21	v	v	NOUN
ejpam-4735	93	22	∈	∈	PROPN
ejpam-4735	93	23	δp(λ	δp(λ	NOUN
ejpam-4735	93	24	,	,	PUNCT
ejpam-4735	93	25	s)o(x	s)o(x	PROPN
ejpam-4735	93	26	,	,	PUNCT
ejpam-4735	93	27	τ	τ	X
ejpam-4735	93	28	)	)	PUNCT
ejpam-4735	93	29	containing	contain	VERB
ejpam-4735	93	30	x.	x.	PROPN
ejpam-4735	93	31	lemma	lemma	PROPN
ejpam-4735	93	32	2	2	X
ejpam-4735	93	33	.	.	PUNCT
ejpam-4735	94	1	[	[	X
ejpam-4735	94	2	21	21	NUM
ejpam-4735	94	3	]	]	PUNCT
ejpam-4735	94	4	for	for	ADP
ejpam-4735	94	5	a	a	DET
ejpam-4735	94	6	family	family	NOUN
ejpam-4735	94	7	{	{	PUNCT
ejpam-4735	94	8	aγ	aγ	INTJ
ejpam-4735	94	9	|	|	ADV
ejpam-4735	94	10	γ	γ	X
ejpam-4735	94	11	∈	∈	PROPN
ejpam-4735	94	12	∇	∇	X
ejpam-4735	94	13	}	}	PUNCT
ejpam-4735	94	14	of	of	ADP
ejpam-4735	94	15	a	a	DET
ejpam-4735	94	16	topological	topological	ADJ
ejpam-4735	94	17	space	space	NOUN
ejpam-4735	94	18	(	(	PUNCT
ejpam-4735	94	19	x	x	X
ejpam-4735	94	20	,	,	PUNCT
ejpam-4735	94	21	τ	τ	PROPN
ejpam-4735	94	22	)	)	PUNCT
ejpam-4735	94	23	,	,	PUNCT
ejpam-4735	94	24	the	the	DET
ejpam-4735	94	25	following	follow	VERB
ejpam-4735	94	26	properties	property	NOUN
ejpam-4735	94	27	hold	hold	VERB
ejpam-4735	94	28	:	:	PUNCT
ejpam-4735	94	29	(	(	PUNCT
ejpam-4735	94	30	1	1	X
ejpam-4735	94	31	)	)	PUNCT
ejpam-4735	95	1	[	[	X
ejpam-4735	95	2	∩{aγ	∩{aγ	VERB
ejpam-4735	95	3	|	|	ADV
ejpam-4735	95	4	γ	γ	X
ejpam-4735	95	5	∈	∈	PROPN
ejpam-4735	95	6	∇}]δp(λ	∇}]δp(λ	X
ejpam-4735	95	7	,	,	PUNCT
ejpam-4735	95	8	s	s	PART
ejpam-4735	95	9	)	)	PUNCT
ejpam-4735	95	10	⊆	⊆	NUM
ejpam-4735	95	11	∩{aδp(λ	∩{aδp(λ	NOUN
ejpam-4735	95	12	,	,	PUNCT
ejpam-4735	95	13	s	s	PART
ejpam-4735	95	14	)	)	PUNCT
ejpam-4735	95	15	γ	γ	PROPN
ejpam-4735	95	16	|	|	ADV
ejpam-4735	95	17	γ	γ	X
ejpam-4735	95	18	∈	∈	NOUN
ejpam-4735	95	19	∇	∇	X
ejpam-4735	95	20	}	}	PUNCT
ejpam-4735	95	21	.	.	PUNCT
ejpam-4735	96	1	(	(	PUNCT
ejpam-4735	96	2	2	2	X
ejpam-4735	96	3	)	)	PUNCT
ejpam-4735	97	1	[	[	X
ejpam-4735	97	2	∪{aγ	∪{aγ	PROPN
ejpam-4735	97	3	|	|	ADV
ejpam-4735	97	4	γ	γ	X
ejpam-4735	97	5	∈	∈	PROPN
ejpam-4735	97	6	∇}]δp(λ	∇}]δp(λ	X
ejpam-4735	97	7	,	,	PUNCT
ejpam-4735	97	8	s	s	NOUN
ejpam-4735	97	9	)	)	PUNCT
ejpam-4735	97	10	⊇	⊇	NOUN
ejpam-4735	97	11	∪{aδp(λ	∪{aδp(λ	NOUN
ejpam-4735	97	12	,	,	PUNCT
ejpam-4735	97	13	s	s	PART
ejpam-4735	97	14	)	)	PUNCT
ejpam-4735	97	15	γ	γ	PROPN
ejpam-4735	97	16	|	|	ADV
ejpam-4735	97	17	γ	γ	X
ejpam-4735	97	18	∈	∈	NOUN
ejpam-4735	97	19	∇	∇	X
ejpam-4735	97	20	}	}	PUNCT
ejpam-4735	97	21	.	.	PUNCT
ejpam-4735	98	1	3	3	X
ejpam-4735	98	2	.	.	X
ejpam-4735	99	1	some	some	DET
ejpam-4735	99	2	characterizations	characterization	NOUN
ejpam-4735	99	3	of	of	ADP
ejpam-4735	99	4	δp(λ	δp(λ	NOUN
ejpam-4735	99	5	,	,	PUNCT
ejpam-4735	99	6	s)-r0	s)-r0	PRON
ejpam-4735	99	7	spaces	space	VERB
ejpam-4735	99	8	in	in	ADP
ejpam-4735	99	9	this	this	DET
ejpam-4735	99	10	section	section	NOUN
ejpam-4735	99	11	,	,	PUNCT
ejpam-4735	99	12	we	we	PRON
ejpam-4735	99	13	introduce	introduce	VERB
ejpam-4735	99	14	the	the	DET
ejpam-4735	99	15	notion	notion	NOUN
ejpam-4735	99	16	of	of	ADP
ejpam-4735	99	17	δp(λ	δp(λ	NOUN
ejpam-4735	99	18	,	,	PUNCT
ejpam-4735	99	19	s)-r0	s)-r0	PRON
ejpam-4735	99	20	spaces	space	VERB
ejpam-4735	99	21	.	.	PUNCT
ejpam-4735	100	1	moreover	moreover	ADV
ejpam-4735	100	2	,	,	PUNCT
ejpam-4735	100	3	several	several	ADJ
ejpam-4735	100	4	characterizations	characterization	NOUN
ejpam-4735	100	5	of	of	ADP
ejpam-4735	100	6	δp(λ	δp(λ	NOUN
ejpam-4735	100	7	,	,	PUNCT
ejpam-4735	100	8	s)-r0	s)-r0	PRON
ejpam-4735	100	9	spaces	space	NOUN
ejpam-4735	100	10	are	be	AUX
ejpam-4735	100	11	discussed	discuss	VERB
ejpam-4735	100	12	.	.	PUNCT
ejpam-4735	101	1	definition	definition	NOUN
ejpam-4735	101	2	2	2	NUM
ejpam-4735	101	3	.	.	PUNCT
ejpam-4735	102	1	a	a	DET
ejpam-4735	102	2	topological	topological	ADJ
ejpam-4735	102	3	space	space	NOUN
ejpam-4735	102	4	(	(	PUNCT
ejpam-4735	102	5	x	x	X
ejpam-4735	102	6	,	,	PUNCT
ejpam-4735	102	7	τ	τ	X
ejpam-4735	102	8	)	)	PUNCT
ejpam-4735	102	9	is	be	AUX
ejpam-4735	102	10	called	call	VERB
ejpam-4735	102	11	δp(λ	δp(λ	NOUN
ejpam-4735	102	12	,	,	PUNCT
ejpam-4735	102	13	s)-r0	s)-r0	PRON
ejpam-4735	102	14	if	if	SCONJ
ejpam-4735	102	15	,	,	PUNCT
ejpam-4735	102	16	for	for	ADP
ejpam-4735	102	17	each	each	DET
ejpam-4735	102	18	δp(λ	δp(λ	NOUN
ejpam-4735	102	19	,	,	PUNCT
ejpam-4735	102	20	s)-open	s)-open	VERB
ejpam-4735	102	21	set	set	VERB
ejpam-4735	102	22	u	u	NOUN
ejpam-4735	102	23	and	and	CCONJ
ejpam-4735	102	24	each	each	DET
ejpam-4735	102	25	x	x	SYM
ejpam-4735	102	26	∈	∈	PROPN
ejpam-4735	102	27	u	u	NOUN
ejpam-4735	102	28	,	,	PUNCT
ejpam-4735	102	29	{	{	PUNCT
ejpam-4735	102	30	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	102	31	,	,	PUNCT
ejpam-4735	102	32	s	s	PART
ejpam-4735	102	33	)	)	PUNCT
ejpam-4735	102	34	⊆	⊆	NUM
ejpam-4735	102	35	u	u	NOUN
ejpam-4735	102	36	.	.	PUNCT
ejpam-4735	103	1	theorem	theorem	NOUN
ejpam-4735	103	2	1	1	NUM
ejpam-4735	103	3	.	.	X
ejpam-4735	104	1	for	for	ADP
ejpam-4735	104	2	a	a	DET
ejpam-4735	104	3	topological	topological	ADJ
ejpam-4735	104	4	space	space	NOUN
ejpam-4735	104	5	(	(	PUNCT
ejpam-4735	104	6	x	x	X
ejpam-4735	104	7	,	,	PUNCT
ejpam-4735	104	8	τ	τ	PROPN
ejpam-4735	104	9	)	)	PUNCT
ejpam-4735	104	10	,	,	PUNCT
ejpam-4735	104	11	the	the	DET
ejpam-4735	104	12	following	follow	VERB
ejpam-4735	104	13	properties	property	NOUN
ejpam-4735	104	14	are	be	AUX
ejpam-4735	104	15	equivalent	equivalent	ADJ
ejpam-4735	104	16	:	:	PUNCT
ejpam-4735	104	17	(	(	PUNCT
ejpam-4735	104	18	1	1	X
ejpam-4735	104	19	)	)	PUNCT
ejpam-4735	104	20	(	(	PUNCT
ejpam-4735	104	21	x	x	X
ejpam-4735	104	22	,	,	PUNCT
ejpam-4735	104	23	τ	τ	X
ejpam-4735	104	24	)	)	PUNCT
ejpam-4735	104	25	is	be	AUX
ejpam-4735	104	26	δp(λ	δp(λ	NOUN
ejpam-4735	104	27	,	,	PUNCT
ejpam-4735	104	28	s)-r0	s)-r0	X
ejpam-4735	104	29	.	.	PUNCT
ejpam-4735	105	1	(	(	PUNCT
ejpam-4735	105	2	2	2	X
ejpam-4735	105	3	)	)	PUNCT
ejpam-4735	105	4	for	for	ADP
ejpam-4735	105	5	each	each	DET
ejpam-4735	105	6	δp(λ	δp(λ	NOUN
ejpam-4735	105	7	,	,	PUNCT
ejpam-4735	105	8	s)-closed	s)-close	VERB
ejpam-4735	105	9	set	set	ADJ
ejpam-4735	105	10	f	f	NOUN
ejpam-4735	105	11	and	and	CCONJ
ejpam-4735	105	12	each	each	DET
ejpam-4735	105	13	x	x	SYM
ejpam-4735	105	14	∈	∈	PROPN
ejpam-4735	105	15	x−f	x−f	PROPN
ejpam-4735	105	16	,	,	PUNCT
ejpam-4735	105	17	there	there	PRON
ejpam-4735	105	18	exists	exist	VERB
ejpam-4735	105	19	u	u	PROPN
ejpam-4735	105	20	∈	∈	PROPN
ejpam-4735	105	21	δp(λ	δp(λ	NOUN
ejpam-4735	105	22	,	,	PUNCT
ejpam-4735	105	23	s)o(x	s)o(x	PROPN
ejpam-4735	105	24	,	,	PUNCT
ejpam-4735	105	25	τ	τ	X
ejpam-4735	105	26	)	)	PUNCT
ejpam-4735	105	27	such	such	ADJ
ejpam-4735	105	28	that	that	SCONJ
ejpam-4735	105	29	f	f	PROPN
ejpam-4735	105	30	⊆	⊆	NUM
ejpam-4735	105	31	u	u	NOUN
ejpam-4735	105	32	and	and	CCONJ
ejpam-4735	105	33	x	x	PUNCT
ejpam-4735	105	34	̸∈	̸∈	PROPN
ejpam-4735	105	35	u	u	PROPN
ejpam-4735	105	36	.	.	PUNCT
ejpam-4735	106	1	(	(	PUNCT
ejpam-4735	106	2	3	3	X
ejpam-4735	106	3	)	)	PUNCT
ejpam-4735	106	4	for	for	ADP
ejpam-4735	106	5	each	each	DET
ejpam-4735	106	6	δp(λ	δp(λ	NOUN
ejpam-4735	106	7	,	,	PUNCT
ejpam-4735	106	8	s)-closed	s)-close	VERB
ejpam-4735	106	9	set	set	ADJ
ejpam-4735	106	10	f	f	NOUN
ejpam-4735	106	11	and	and	CCONJ
ejpam-4735	106	12	each	each	DET
ejpam-4735	106	13	x	x	SYM
ejpam-4735	106	14	∈	∈	PROPN
ejpam-4735	106	15	x	x	X
ejpam-4735	107	1	−	−	PROPN
ejpam-4735	107	2	f	f	PROPN
ejpam-4735	107	3	,	,	PUNCT
ejpam-4735	107	4	f	f	PROPN
ejpam-4735	107	5	∩	∩	X
ejpam-4735	107	6	{	{	PUNCT
ejpam-4735	107	7	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	107	8	,	,	PUNCT
ejpam-4735	107	9	s	s	PART
ejpam-4735	107	10	)	)	PUNCT
ejpam-4735	107	11	=	=	SYM
ejpam-4735	107	12	∅.	∅.	X
ejpam-4735	107	13	(	(	PUNCT
ejpam-4735	107	14	4	4	NUM
ejpam-4735	107	15	)	)	PUNCT
ejpam-4735	107	16	for	for	ADP
ejpam-4735	107	17	any	any	DET
ejpam-4735	107	18	distinct	distinct	ADJ
ejpam-4735	107	19	points	point	NOUN
ejpam-4735	107	20	x	x	NOUN
ejpam-4735	107	21	,	,	PUNCT
ejpam-4735	107	22	y	y	PROPN
ejpam-4735	107	23	in	in	ADP
ejpam-4735	107	24	x	x	PROPN
ejpam-4735	107	25	,	,	PUNCT
ejpam-4735	107	26	{	{	PUNCT
ejpam-4735	107	27	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	107	28	,	,	PUNCT
ejpam-4735	107	29	s	s	PART
ejpam-4735	107	30	)	)	PUNCT
ejpam-4735	107	31	=	=	PRON
ejpam-4735	107	32	{	{	PUNCT
ejpam-4735	107	33	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	107	34	,	,	PUNCT
ejpam-4735	107	35	s	s	NOUN
ejpam-4735	107	36	)	)	PUNCT
ejpam-4735	107	37	or	or	CCONJ
ejpam-4735	107	38	{	{	PUNCT
ejpam-4735	107	39	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	107	40	,	,	PUNCT
ejpam-4735	107	41	s)∩{y}δp(λ	s)∩{y}δp(λ	PROPN
ejpam-4735	107	42	,	,	PUNCT
ejpam-4735	107	43	s	s	PART
ejpam-4735	107	44	)	)	PUNCT
ejpam-4735	107	45	=	=	PUNCT
ejpam-4735	107	46	∅.	∅.	NOUN
ejpam-4735	107	47	proof	proof	NOUN
ejpam-4735	107	48	.	.	PUNCT
ejpam-4735	108	1	(	(	PUNCT
ejpam-4735	108	2	1	1	X
ejpam-4735	108	3	)	)	PUNCT
ejpam-4735	108	4	⇒	⇒	NOUN
ejpam-4735	108	5	(	(	PUNCT
ejpam-4735	108	6	2	2	NUM
ejpam-4735	108	7	):	):	PUNCT
ejpam-4735	108	8	let	let	VERB
ejpam-4735	108	9	f	f	PRON
ejpam-4735	108	10	be	be	AUX
ejpam-4735	108	11	a	a	DET
ejpam-4735	108	12	δp(λ	δp(λ	NOUN
ejpam-4735	108	13	,	,	PUNCT
ejpam-4735	108	14	s)-closed	s)-close	VERB
ejpam-4735	108	15	set	set	NOUN
ejpam-4735	108	16	and	and	CCONJ
ejpam-4735	108	17	x	x	SYM
ejpam-4735	108	18	∈	∈	PROPN
ejpam-4735	108	19	x	x	X
ejpam-4735	108	20	−	−	PROPN
ejpam-4735	108	21	f	f	X
ejpam-4735	108	22	.	.	PUNCT
ejpam-4735	109	1	since	since	SCONJ
ejpam-4735	109	2	(	(	PUNCT
ejpam-4735	109	3	x	x	X
ejpam-4735	109	4	,	,	PUNCT
ejpam-4735	109	5	τ	τ	X
ejpam-4735	109	6	)	)	PUNCT
ejpam-4735	109	7	is	be	AUX
ejpam-4735	109	8	δp(λ	δp(λ	NOUN
ejpam-4735	109	9	,	,	PUNCT
ejpam-4735	109	10	s)-r0	s)-r0	PRON
ejpam-4735	109	11	,	,	PUNCT
ejpam-4735	109	12	we	we	PRON
ejpam-4735	109	13	have	have	VERB
ejpam-4735	109	14	{	{	PUNCT
ejpam-4735	109	15	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	109	16	,	,	PUNCT
ejpam-4735	109	17	s	s	PART
ejpam-4735	109	18	)	)	PUNCT
ejpam-4735	109	19	⊆	⊆	NUM
ejpam-4735	110	1	x	x	SYM
ejpam-4735	110	2	−	−	PROPN
ejpam-4735	110	3	f	f	X
ejpam-4735	110	4	.	.	PUNCT
ejpam-4735	111	1	put	put	VERB
ejpam-4735	111	2	u	u	NOUN
ejpam-4735	111	3	=	=	NOUN
ejpam-4735	111	4	x	x	SYM
ejpam-4735	111	5	−	−	PROPN
ejpam-4735	111	6	{	{	PUNCT
ejpam-4735	111	7	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	111	8	,	,	PUNCT
ejpam-4735	111	9	s	s	NOUN
ejpam-4735	111	10	)	)	PUNCT
ejpam-4735	111	11	.	.	PUNCT
ejpam-4735	112	1	thus	thus	ADV
ejpam-4735	112	2	,	,	PUNCT
ejpam-4735	112	3	by	by	ADP
ejpam-4735	112	4	lemma	lemma	PROPN
ejpam-4735	112	5	1	1	NUM
ejpam-4735	112	6	,	,	PUNCT
ejpam-4735	112	7	u	u	PROPN
ejpam-4735	112	8	∈	∈	PROPN
ejpam-4735	112	9	δp(λ	δp(λ	NOUN
ejpam-4735	112	10	,	,	PUNCT
ejpam-4735	112	11	s)o(x	s)o(x	PROPN
ejpam-4735	112	12	,	,	PUNCT
ejpam-4735	112	13	τ	τ	PROPN
ejpam-4735	112	14	)	)	PUNCT
ejpam-4735	112	15	,	,	PUNCT
ejpam-4735	112	16	f	f	PROPN
ejpam-4735	112	17	⊆	⊆	NUM
ejpam-4735	112	18	u	u	NOUN
ejpam-4735	112	19	and	and	CCONJ
ejpam-4735	112	20	x	x	PUNCT
ejpam-4735	112	21	̸∈	̸∈	PROPN
ejpam-4735	112	22	u	u	PROPN
ejpam-4735	112	23	.	.	PUNCT
ejpam-4735	113	1	(	(	PUNCT
ejpam-4735	113	2	2	2	X
ejpam-4735	113	3	)	)	PUNCT
ejpam-4735	113	4	⇒	⇒	NOUN
ejpam-4735	113	5	(	(	PUNCT
ejpam-4735	113	6	3	3	NUM
ejpam-4735	113	7	):	):	PUNCT
ejpam-4735	113	8	let	let	VERB
ejpam-4735	113	9	f	f	PRON
ejpam-4735	113	10	be	be	AUX
ejpam-4735	113	11	a	a	DET
ejpam-4735	113	12	δp(λ	δp(λ	NOUN
ejpam-4735	113	13	,	,	PUNCT
ejpam-4735	113	14	s)-closed	s)-close	VERB
ejpam-4735	113	15	set	set	NOUN
ejpam-4735	113	16	and	and	CCONJ
ejpam-4735	113	17	x	x	SYM
ejpam-4735	113	18	∈	∈	PROPN
ejpam-4735	113	19	x	x	X
ejpam-4735	113	20	−	−	PROPN
ejpam-4735	113	21	f	f	X
ejpam-4735	113	22	.	.	PUNCT
ejpam-4735	114	1	thus	thus	ADV
ejpam-4735	114	2	,	,	PUNCT
ejpam-4735	114	3	by	by	ADP
ejpam-4735	114	4	(	(	PUNCT
ejpam-4735	114	5	2	2	NUM
ejpam-4735	114	6	)	)	PUNCT
ejpam-4735	114	7	,	,	PUNCT
ejpam-4735	114	8	there	there	PRON
ejpam-4735	114	9	exists	exist	VERB
ejpam-4735	114	10	u	u	PROPN
ejpam-4735	114	11	∈	∈	PROPN
ejpam-4735	114	12	δp(λ	δp(λ	NOUN
ejpam-4735	114	13	,	,	PUNCT
ejpam-4735	114	14	s)o(x	s)o(x	PROPN
ejpam-4735	114	15	,	,	PUNCT
ejpam-4735	114	16	τ	τ	X
ejpam-4735	114	17	)	)	PUNCT
ejpam-4735	114	18	such	such	ADJ
ejpam-4735	114	19	that	that	SCONJ
ejpam-4735	114	20	f	f	PROPN
ejpam-4735	114	21	⊆	⊆	NUM
ejpam-4735	114	22	u	u	NOUN
ejpam-4735	114	23	and	and	CCONJ
ejpam-4735	114	24	x	x	PUNCT
ejpam-4735	114	25	̸∈	̸∈	PROPN
ejpam-4735	114	26	u	u	PROPN
ejpam-4735	114	27	.	.	PUNCT
ejpam-4735	115	1	since	since	SCONJ
ejpam-4735	115	2	u	u	PROPN
ejpam-4735	115	3	∈	∈	PROPN
ejpam-4735	115	4	δp(λ	δp(λ	NOUN
ejpam-4735	115	5	,	,	PUNCT
ejpam-4735	115	6	s)o(x	s)o(x	PROPN
ejpam-4735	115	7	,	,	PUNCT
ejpam-4735	115	8	τ	τ	PROPN
ejpam-4735	115	9	)	)	PUNCT
ejpam-4735	115	10	,	,	PUNCT
ejpam-4735	115	11	u	u	PROPN
ejpam-4735	115	12	∩	∩	NOUN
ejpam-4735	115	13	{	{	PUNCT
ejpam-4735	115	14	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	115	15	,	,	PUNCT
ejpam-4735	115	16	s	s	PART
ejpam-4735	115	17	)	)	PUNCT
ejpam-4735	115	18	=	=	NOUN
ejpam-4735	115	19	∅	∅	NOUN
ejpam-4735	115	20	and	and	CCONJ
ejpam-4735	115	21	hence	hence	ADV
ejpam-4735	115	22	f	f	PROPN
ejpam-4735	115	23	∩	∩	PROPN
ejpam-4735	115	24	{	{	PUNCT
ejpam-4735	115	25	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	115	26	,	,	PUNCT
ejpam-4735	115	27	s	s	PART
ejpam-4735	115	28	)	)	PUNCT
ejpam-4735	115	29	=	=	SYM
ejpam-4735	115	30	∅.	∅.	X
ejpam-4735	115	31	(	(	PUNCT
ejpam-4735	115	32	3	3	NUM
ejpam-4735	115	33	)	)	PUNCT
ejpam-4735	115	34	⇒	⇒	NOUN
ejpam-4735	115	35	(	(	PUNCT
ejpam-4735	115	36	4	4	NUM
ejpam-4735	115	37	):	):	PUNCT
ejpam-4735	115	38	let	let	VERB
ejpam-4735	115	39	x	x	PRON
ejpam-4735	115	40	and	and	CCONJ
ejpam-4735	115	41	y	y	PROPN
ejpam-4735	115	42	be	be	AUX
ejpam-4735	115	43	distinct	distinct	ADJ
ejpam-4735	115	44	points	point	NOUN
ejpam-4735	115	45	of	of	ADP
ejpam-4735	115	46	x.	x.	NOUN
ejpam-4735	115	47	suppose	suppose	VERB
ejpam-4735	115	48	that	that	SCONJ
ejpam-4735	115	49	{	{	PUNCT
ejpam-4735	115	50	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	115	51	,	,	PUNCT
ejpam-4735	115	52	s)∩{y}δp(λ	s)∩{y}δp(λ	PROPN
ejpam-4735	115	53	,	,	PUNCT
ejpam-4735	115	54	s	s	PART
ejpam-4735	115	55	)	)	PUNCT
ejpam-4735	115	56	̸=	̸=	PROPN
ejpam-4735	115	57	∅.	∅.	VERB
ejpam-4735	115	58	by	by	ADP
ejpam-4735	115	59	(	(	PUNCT
ejpam-4735	115	60	3	3	NUM
ejpam-4735	115	61	)	)	PUNCT
ejpam-4735	115	62	,	,	PUNCT
ejpam-4735	115	63	x	x	PUNCT
ejpam-4735	115	64	∈	∈	NOUN
ejpam-4735	115	65	{	{	PUNCT
ejpam-4735	115	66	y}δp(λ	y}δp(λ	NOUN
ejpam-4735	115	67	,	,	PUNCT
ejpam-4735	115	68	s	s	NOUN
ejpam-4735	115	69	)	)	PUNCT
ejpam-4735	115	70	and	and	CCONJ
ejpam-4735	115	71	y	y	PROPN
ejpam-4735	115	72	∈	∈	PROPN
ejpam-4735	115	73	{	{	PUNCT
ejpam-4735	115	74	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	115	75	,	,	PUNCT
ejpam-4735	115	76	s	s	NOUN
ejpam-4735	115	77	)	)	PUNCT
ejpam-4735	115	78	.	.	PUNCT
ejpam-4735	116	1	by	by	ADP
ejpam-4735	116	2	lemma	lemma	PROPN
ejpam-4735	116	3	1	1	NUM
ejpam-4735	116	4	,	,	PUNCT
ejpam-4735	116	5	{	{	PUNCT
ejpam-4735	116	6	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	116	7	,	,	PUNCT
ejpam-4735	116	8	s	s	PART
ejpam-4735	116	9	)	)	PUNCT
ejpam-4735	116	10	⊆	⊆	NUM
ejpam-4735	116	11	{	{	PUNCT
ejpam-4735	116	12	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	116	13	,	,	PUNCT
ejpam-4735	116	14	s	s	NOUN
ejpam-4735	116	15	)	)	PUNCT
ejpam-4735	116	16	⊆	⊆	NUM
ejpam-4735	116	17	{	{	PUNCT
ejpam-4735	116	18	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	116	19	,	,	PUNCT
ejpam-4735	116	20	s	s	PART
ejpam-4735	116	21	)	)	PUNCT
ejpam-4735	116	22	and	and	CCONJ
ejpam-4735	116	23	hence	hence	ADV
ejpam-4735	116	24	{	{	PUNCT
ejpam-4735	116	25	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	116	26	,	,	PUNCT
ejpam-4735	116	27	s	s	PART
ejpam-4735	116	28	)	)	PUNCT
ejpam-4735	116	29	=	=	PRON
ejpam-4735	116	30	{	{	PUNCT
ejpam-4735	116	31	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	116	32	,	,	PUNCT
ejpam-4735	116	33	s	s	NOUN
ejpam-4735	116	34	)	)	PUNCT
ejpam-4735	116	35	.	.	PUNCT
ejpam-4735	117	1	(	(	PUNCT
ejpam-4735	117	2	4	4	X
ejpam-4735	117	3	)	)	PUNCT
ejpam-4735	117	4	⇒	⇒	NOUN
ejpam-4735	117	5	(	(	PUNCT
ejpam-4735	117	6	1	1	NUM
ejpam-4735	117	7	):	):	PUNCT
ejpam-4735	117	8	let	let	VERB
ejpam-4735	117	9	v	v	NUM
ejpam-4735	117	10	∈	∈	PROPN
ejpam-4735	117	11	δp(λ	δp(λ	NOUN
ejpam-4735	117	12	,	,	PUNCT
ejpam-4735	117	13	s)o(x	s)o(x	PROPN
ejpam-4735	117	14	,	,	PUNCT
ejpam-4735	117	15	τ	τ	X
ejpam-4735	117	16	)	)	PUNCT
ejpam-4735	117	17	and	and	CCONJ
ejpam-4735	117	18	x	x	PUNCT
ejpam-4735	117	19	∈	∈	NOUN
ejpam-4735	117	20	v	v	NOUN
ejpam-4735	117	21	.	.	PUNCT
ejpam-4735	118	1	for	for	ADP
ejpam-4735	118	2	each	each	DET
ejpam-4735	118	3	y	y	PROPN
ejpam-4735	118	4	̸∈	̸∈	PROPN
ejpam-4735	118	5	v	v	PROPN
ejpam-4735	118	6	,	,	PUNCT
ejpam-4735	118	7	v	v	NOUN
ejpam-4735	118	8	∩	∩	NOUN
ejpam-4735	118	9	{	{	PUNCT
ejpam-4735	118	10	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	118	11	,	,	PUNCT
ejpam-4735	118	12	s	s	NOUN
ejpam-4735	118	13	)	)	PUNCT
ejpam-4735	118	14	=	=	NOUN
ejpam-4735	118	15	∅	∅	NOUN
ejpam-4735	118	16	and	and	CCONJ
ejpam-4735	118	17	hence	hence	ADV
ejpam-4735	118	18	x	x	X
ejpam-4735	118	19	̸∈	̸∈	PROPN
ejpam-4735	118	20	{	{	PUNCT
ejpam-4735	118	21	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	118	22	,	,	PUNCT
ejpam-4735	118	23	s	s	NOUN
ejpam-4735	118	24	)	)	PUNCT
ejpam-4735	118	25	.	.	PUNCT
ejpam-4735	119	1	thus	thus	ADV
ejpam-4735	119	2	,	,	PUNCT
ejpam-4735	119	3	{	{	PUNCT
ejpam-4735	119	4	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	119	5	,	,	PUNCT
ejpam-4735	119	6	s	s	PART
ejpam-4735	119	7	)	)	PUNCT
ejpam-4735	119	8	̸=	̸=	PROPN
ejpam-4735	119	9	{	{	PUNCT
ejpam-4735	119	10	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	119	11	,	,	PUNCT
ejpam-4735	119	12	s	s	NOUN
ejpam-4735	119	13	)	)	PUNCT
ejpam-4735	119	14	.	.	PUNCT
ejpam-4735	120	1	by	by	ADP
ejpam-4735	120	2	(	(	PUNCT
ejpam-4735	120	3	4	4	NUM
ejpam-4735	120	4	)	)	PUNCT
ejpam-4735	120	5	,	,	PUNCT
ejpam-4735	120	6	for	for	ADP
ejpam-4735	120	7	each	each	DET
ejpam-4735	120	8	y	y	PROPN
ejpam-4735	120	9	̸∈	̸∈	PROPN
ejpam-4735	120	10	v	v	PROPN
ejpam-4735	120	11	,	,	PUNCT
ejpam-4735	120	12	{	{	PUNCT
ejpam-4735	120	13	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	120	14	,	,	PUNCT
ejpam-4735	120	15	s	s	NOUN
ejpam-4735	120	16	)	)	PUNCT
ejpam-4735	120	17	∩	∩	NOUN
ejpam-4735	120	18	{	{	PUNCT
ejpam-4735	120	19	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	120	20	,	,	PUNCT
ejpam-4735	120	21	s	s	NOUN
ejpam-4735	120	22	)	)	PUNCT
ejpam-4735	120	23	=	=	PUNCT
ejpam-4735	120	24	∅.	∅.	PROPN
ejpam-4735	120	25	c.	c.	PROPN
ejpam-4735	120	26	boonpok	boonpok	PROPN
ejpam-4735	120	27	,	,	PUNCT
ejpam-4735	120	28	p.	p.	NOUN
ejpam-4735	120	29	pue	pue	NOUN
ejpam-4735	120	30	-	-	PUNCT
ejpam-4735	120	31	on	on	ADP
ejpam-4735	120	32	/	/	SYM
ejpam-4735	120	33	eur	eur	NOUN
ejpam-4735	120	34	.	.	PUNCT
ejpam-4735	121	1	j.	j.	PROPN
ejpam-4735	121	2	pure	pure	PROPN
ejpam-4735	121	3	appl	appl	PROPN
ejpam-4735	121	4	.	.	PROPN
ejpam-4735	121	5	math	math	PROPN
ejpam-4735	121	6	,	,	PUNCT
ejpam-4735	121	7	17	17	NUM
ejpam-4735	121	8	(	(	PUNCT
ejpam-4735	121	9	1	1	NUM
ejpam-4735	121	10	)	)	PUNCT
ejpam-4735	121	11	(	(	PUNCT
ejpam-4735	121	12	2024	2024	NUM
ejpam-4735	121	13	)	)	PUNCT
ejpam-4735	121	14	,	,	PUNCT
ejpam-4735	121	15	147	147	NUM
ejpam-4735	121	16	-	-	SYM
ejpam-4735	121	17	157	157	NUM
ejpam-4735	121	18	150	150	NUM
ejpam-4735	121	19	since	since	SCONJ
ejpam-4735	121	20	x	x	INTJ
ejpam-4735	121	21	−	−	PROPN
ejpam-4735	121	22	v	v	NOUN
ejpam-4735	121	23	is	be	AUX
ejpam-4735	121	24	δp(λ	δp(λ	NOUN
ejpam-4735	121	25	,	,	PUNCT
ejpam-4735	121	26	s)-closed	s)-close	VERB
ejpam-4735	121	27	,	,	PUNCT
ejpam-4735	121	28	y	y	PROPN
ejpam-4735	121	29	∈	∈	PROPN
ejpam-4735	121	30	{	{	PUNCT
ejpam-4735	121	31	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	121	32	,	,	PUNCT
ejpam-4735	121	33	s	s	NOUN
ejpam-4735	121	34	)	)	PUNCT
ejpam-4735	121	35	⊆	⊆	NUM
ejpam-4735	121	36	x	x	SYM
ejpam-4735	121	37	−	−	PROPN
ejpam-4735	121	38	v	v	NOUN
ejpam-4735	121	39	and	and	CCONJ
ejpam-4735	121	40	∪y∈x−v	∪y∈x−v	PROPN
ejpam-4735	121	41	{	{	PUNCT
ejpam-4735	121	42	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	121	43	,	,	PUNCT
ejpam-4735	121	44	s	s	NOUN
ejpam-4735	121	45	)	)	PUNCT
ejpam-4735	121	46	=	=	PUNCT
ejpam-4735	122	1	x	x	PUNCT
ejpam-4735	122	2	−	−	NOUN
ejpam-4735	122	3	v	v	NOUN
ejpam-4735	122	4	.	.	PUNCT
ejpam-4735	123	1	thus	thus	ADV
ejpam-4735	123	2	,	,	PUNCT
ejpam-4735	123	3	{	{	PUNCT
ejpam-4735	123	4	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	123	5	,	,	PUNCT
ejpam-4735	123	6	s	s	NOUN
ejpam-4735	123	7	)	)	PUNCT
ejpam-4735	123	8	∩	∩	NOUN
ejpam-4735	123	9	(	(	PUNCT
ejpam-4735	123	10	x	x	SYM
ejpam-4735	123	11	−	−	PROPN
ejpam-4735	123	12	v	v	NOUN
ejpam-4735	123	13	)	)	PUNCT
ejpam-4735	123	14	=	=	SYM
ejpam-4735	123	15	{	{	PUNCT
ejpam-4735	123	16	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	123	17	,	,	PUNCT
ejpam-4735	123	18	s	s	NOUN
ejpam-4735	123	19	)	)	PUNCT
ejpam-4735	123	20	∩	∩	NOUN
ejpam-4735	123	21	[	[	X
ejpam-4735	123	22	∪y∈x−v	∪y∈x−v	ADJ
ejpam-4735	123	23	{	{	PUNCT
ejpam-4735	123	24	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	123	25	,	,	PUNCT
ejpam-4735	123	26	s	s	NOUN
ejpam-4735	123	27	)	)	PUNCT
ejpam-4735	123	28	]	]	PUNCT
ejpam-4735	124	1	=	=	PUNCT
ejpam-4735	124	2	∪y∈x−v	∪y∈x−v	PROPN
ejpam-4735	125	1	[	[	X
ejpam-4735	125	2	{	{	PUNCT
ejpam-4735	125	3	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	125	4	,	,	PUNCT
ejpam-4735	125	5	s	s	NOUN
ejpam-4735	125	6	)	)	PUNCT
ejpam-4735	125	7	∩	∩	NOUN
ejpam-4735	125	8	{	{	PUNCT
ejpam-4735	125	9	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	125	10	,	,	PUNCT
ejpam-4735	125	11	s	s	NOUN
ejpam-4735	125	12	)	)	PUNCT
ejpam-4735	125	13	]	]	PUNCT
ejpam-4735	126	1	=	=	PUNCT
ejpam-4735	126	2	∅	∅	NOUN
ejpam-4735	126	3	and	and	CCONJ
ejpam-4735	126	4	hence	hence	ADV
ejpam-4735	126	5	{	{	PUNCT
ejpam-4735	126	6	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	126	7	,	,	PUNCT
ejpam-4735	126	8	s	s	PART
ejpam-4735	126	9	)	)	PUNCT
ejpam-4735	126	10	⊆	⊆	NUM
ejpam-4735	126	11	v	v	NOUN
ejpam-4735	126	12	.	.	PUNCT
ejpam-4735	127	1	this	this	PRON
ejpam-4735	127	2	shows	show	VERB
ejpam-4735	127	3	that	that	SCONJ
ejpam-4735	127	4	(	(	PUNCT
ejpam-4735	127	5	x	x	X
ejpam-4735	127	6	,	,	PUNCT
ejpam-4735	127	7	τ	τ	X
ejpam-4735	127	8	)	)	PUNCT
ejpam-4735	127	9	is	be	AUX
ejpam-4735	127	10	δp(λ	δp(λ	NOUN
ejpam-4735	127	11	,	,	PUNCT
ejpam-4735	127	12	s)-r0	s)-r0	X
ejpam-4735	127	13	.	.	PUNCT
ejpam-4735	128	1	corollary	corollary	ADJ
ejpam-4735	128	2	1	1	NUM
ejpam-4735	128	3	.	.	PUNCT
ejpam-4735	129	1	a	a	DET
ejpam-4735	129	2	topological	topological	ADJ
ejpam-4735	129	3	space	space	NOUN
ejpam-4735	129	4	(	(	PUNCT
ejpam-4735	129	5	x	x	X
ejpam-4735	129	6	,	,	PUNCT
ejpam-4735	129	7	τ	τ	X
ejpam-4735	129	8	)	)	PUNCT
ejpam-4735	129	9	is	be	AUX
ejpam-4735	129	10	δp(λ	δp(λ	NOUN
ejpam-4735	129	11	,	,	PUNCT
ejpam-4735	129	12	s)-r0	s)-r0	PRON
ejpam-4735	129	13	if	if	SCONJ
ejpam-4735	129	14	and	and	CCONJ
ejpam-4735	129	15	only	only	ADV
ejpam-4735	129	16	if	if	SCONJ
ejpam-4735	129	17	for	for	ADP
ejpam-4735	129	18	any	any	DET
ejpam-4735	129	19	points	point	NOUN
ejpam-4735	129	20	x	x	PUNCT
ejpam-4735	129	21	and	and	CCONJ
ejpam-4735	129	22	y	y	PROPN
ejpam-4735	129	23	in	in	ADP
ejpam-4735	129	24	x	x	SYM
ejpam-4735	129	25	,	,	PUNCT
ejpam-4735	129	26	{	{	PUNCT
ejpam-4735	129	27	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	129	28	,	,	PUNCT
ejpam-4735	129	29	s	s	PART
ejpam-4735	129	30	)	)	PUNCT
ejpam-4735	129	31	̸=	̸=	PROPN
ejpam-4735	129	32	{	{	PUNCT
ejpam-4735	129	33	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	129	34	,	,	PUNCT
ejpam-4735	129	35	s	s	PART
ejpam-4735	129	36	)	)	PUNCT
ejpam-4735	129	37	implies	imply	VERB
ejpam-4735	129	38	{	{	PUNCT
ejpam-4735	129	39	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	129	40	,	,	PUNCT
ejpam-4735	129	41	s	s	NOUN
ejpam-4735	129	42	)	)	PUNCT
ejpam-4735	129	43	∩	∩	NOUN
ejpam-4735	129	44	{	{	PUNCT
ejpam-4735	129	45	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	129	46	,	,	PUNCT
ejpam-4735	129	47	s	s	NOUN
ejpam-4735	129	48	)	)	PUNCT
ejpam-4735	129	49	=	=	PUNCT
ejpam-4735	129	50	∅.	∅.	NOUN
ejpam-4735	129	51	proof	proof	NOUN
ejpam-4735	129	52	.	.	PUNCT
ejpam-4735	130	1	this	this	PRON
ejpam-4735	130	2	is	be	AUX
ejpam-4735	130	3	obvious	obvious	ADJ
ejpam-4735	130	4	by	by	ADP
ejpam-4735	130	5	theorem	theorem	NOUN
ejpam-4735	130	6	1	1	NUM
ejpam-4735	130	7	.	.	PUNCT
ejpam-4735	131	1	conversely	conversely	ADV
ejpam-4735	131	2	,	,	PUNCT
ejpam-4735	131	3	let	let	VERB
ejpam-4735	131	4	u	u	PRON
ejpam-4735	131	5	∈	∈	PROPN
ejpam-4735	131	6	δp(λ	δp(λ	NOUN
ejpam-4735	131	7	,	,	PUNCT
ejpam-4735	131	8	s)o(x	s)o(x	PROPN
ejpam-4735	131	9	,	,	PUNCT
ejpam-4735	131	10	τ	τ	X
ejpam-4735	131	11	)	)	PUNCT
ejpam-4735	131	12	and	and	CCONJ
ejpam-4735	131	13	x	x	PUNCT
ejpam-4735	131	14	∈	∈	PROPN
ejpam-4735	131	15	u	u	NOUN
ejpam-4735	131	16	.	.	PUNCT
ejpam-4735	132	1	if	if	SCONJ
ejpam-4735	132	2	y	y	PROPN
ejpam-4735	132	3	̸∈	̸∈	PROPN
ejpam-4735	132	4	u	u	PROPN
ejpam-4735	132	5	,	,	PUNCT
ejpam-4735	132	6	then	then	ADV
ejpam-4735	132	7	u∩{y}δp(λ	u∩{y}δp(λ	PROPN
ejpam-4735	132	8	,	,	PUNCT
ejpam-4735	132	9	s	s	PART
ejpam-4735	132	10	)	)	PUNCT
ejpam-4735	132	11	=	=	PUNCT
ejpam-4735	132	12	∅.	∅.	ADP
ejpam-4735	132	13	thus	thus	ADV
ejpam-4735	132	14	,	,	PUNCT
ejpam-4735	132	15	x	x	PROPN
ejpam-4735	132	16	̸∈	̸∈	PROPN
ejpam-4735	132	17	{	{	PUNCT
ejpam-4735	132	18	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	132	19	,	,	PUNCT
ejpam-4735	132	20	s	s	PART
ejpam-4735	132	21	)	)	PUNCT
ejpam-4735	132	22	and	and	CCONJ
ejpam-4735	132	23	{	{	PUNCT
ejpam-4735	132	24	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	132	25	,	,	PUNCT
ejpam-4735	132	26	s	s	PART
ejpam-4735	132	27	)	)	PUNCT
ejpam-4735	132	28	̸=	̸=	PROPN
ejpam-4735	132	29	{	{	PUNCT
ejpam-4735	132	30	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	132	31	,	,	PUNCT
ejpam-4735	132	32	s	s	NOUN
ejpam-4735	132	33	)	)	PUNCT
ejpam-4735	132	34	.	.	PUNCT
ejpam-4735	133	1	by	by	ADP
ejpam-4735	133	2	the	the	DET
ejpam-4735	133	3	hypothesis	hypothesis	NOUN
ejpam-4735	133	4	,	,	PUNCT
ejpam-4735	133	5	{	{	PUNCT
ejpam-4735	133	6	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	133	7	,	,	PUNCT
ejpam-4735	133	8	s	s	NOUN
ejpam-4735	133	9	)	)	PUNCT
ejpam-4735	133	10	∩	∩	NOUN
ejpam-4735	133	11	{	{	PUNCT
ejpam-4735	133	12	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	133	13	,	,	PUNCT
ejpam-4735	133	14	s	s	NOUN
ejpam-4735	133	15	)	)	PUNCT
ejpam-4735	133	16	=	=	NOUN
ejpam-4735	133	17	∅	∅	NOUN
ejpam-4735	133	18	and	and	CCONJ
ejpam-4735	133	19	hence	hence	ADV
ejpam-4735	133	20	y	y	PROPN
ejpam-4735	133	21	̸∈	̸∈	PROPN
ejpam-4735	133	22	{	{	PUNCT
ejpam-4735	133	23	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	133	24	,	,	PUNCT
ejpam-4735	133	25	s	s	NOUN
ejpam-4735	133	26	)	)	PUNCT
ejpam-4735	133	27	.	.	PUNCT
ejpam-4735	134	1	therefore	therefore	ADV
ejpam-4735	134	2	,	,	PUNCT
ejpam-4735	134	3	{	{	PUNCT
ejpam-4735	134	4	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	134	5	,	,	PUNCT
ejpam-4735	134	6	s	s	PART
ejpam-4735	134	7	)	)	PUNCT
ejpam-4735	134	8	⊆	⊆	NUM
ejpam-4735	134	9	u	u	NOUN
ejpam-4735	134	10	.	.	PUNCT
ejpam-4735	135	1	this	this	PRON
ejpam-4735	135	2	shows	show	VERB
ejpam-4735	135	3	that	that	SCONJ
ejpam-4735	135	4	(	(	PUNCT
ejpam-4735	135	5	x	x	X
ejpam-4735	135	6	,	,	PUNCT
ejpam-4735	135	7	τ	τ	X
ejpam-4735	135	8	)	)	PUNCT
ejpam-4735	135	9	is	be	AUX
ejpam-4735	135	10	δp(λ	δp(λ	NOUN
ejpam-4735	135	11	,	,	PUNCT
ejpam-4735	135	12	s)-r0	s)-r0	X
ejpam-4735	135	13	.	.	PUNCT
ejpam-4735	136	1	definition	definition	NOUN
ejpam-4735	136	2	3	3	NUM
ejpam-4735	136	3	.	.	PUNCT
ejpam-4735	137	1	[	[	X
ejpam-4735	137	2	22	22	NUM
ejpam-4735	137	3	]	]	PUNCT
ejpam-4735	137	4	let	let	VERB
ejpam-4735	137	5	a	a	PRON
ejpam-4735	137	6	be	be	AUX
ejpam-4735	137	7	a	a	DET
ejpam-4735	137	8	subset	subset	NOUN
ejpam-4735	137	9	of	of	ADP
ejpam-4735	137	10	a	a	DET
ejpam-4735	137	11	topological	topological	ADJ
ejpam-4735	137	12	space	space	NOUN
ejpam-4735	137	13	(	(	PUNCT
ejpam-4735	137	14	x	x	X
ejpam-4735	137	15	,	,	PUNCT
ejpam-4735	137	16	τ	τ	PROPN
ejpam-4735	137	17	)	)	PUNCT
ejpam-4735	137	18	.	.	PUNCT
ejpam-4735	138	1	the	the	DET
ejpam-4735	138	2	δp(λ	δp(λ	NOUN
ejpam-4735	138	3	,	,	PUNCT
ejpam-4735	138	4	s)-kernel	s)-kernel	NOUN
ejpam-4735	138	5	of	of	ADP
ejpam-4735	138	6	a	a	PRON
ejpam-4735	138	7	,	,	PUNCT
ejpam-4735	138	8	denoted	denote	VERB
ejpam-4735	138	9	by	by	ADP
ejpam-4735	138	10	δp(λ	δp(λ	NOUN
ejpam-4735	138	11	,	,	PUNCT
ejpam-4735	138	12	s)ker(a	s)ker(a	NOUN
ejpam-4735	138	13	)	)	PUNCT
ejpam-4735	138	14	,	,	PUNCT
ejpam-4735	138	15	is	be	AUX
ejpam-4735	138	16	defined	define	VERB
ejpam-4735	138	17	to	to	PART
ejpam-4735	138	18	be	be	AUX
ejpam-4735	138	19	the	the	DET
ejpam-4735	138	20	set	set	NOUN
ejpam-4735	138	21	δp(λ	δp(λ	NOUN
ejpam-4735	138	22	,	,	PUNCT
ejpam-4735	138	23	s)ker(a	s)ker(a	NOUN
ejpam-4735	138	24	)	)	PUNCT
ejpam-4735	138	25	=	=	SYM
ejpam-4735	138	26	∩{u	∩{u	PROPN
ejpam-4735	138	27	∈	∈	PROPN
ejpam-4735	138	28	δp(λ	δp(λ	NOUN
ejpam-4735	138	29	,	,	PUNCT
ejpam-4735	138	30	s)o(x	s)o(x	PROPN
ejpam-4735	138	31	,	,	PUNCT
ejpam-4735	138	32	τ	τ	X
ejpam-4735	138	33	)	)	PUNCT
ejpam-4735	138	34	|	|	ADV
ejpam-4735	138	35	a	a	DET
ejpam-4735	138	36	⊆	⊆	NUM
ejpam-4735	138	37	u	u	NOUN
ejpam-4735	138	38	}	}	PUNCT
ejpam-4735	138	39	.	.	PUNCT
ejpam-4735	139	1	lemma	lemma	PROPN
ejpam-4735	139	2	3	3	X
ejpam-4735	139	3	.	.	PUNCT
ejpam-4735	140	1	[	[	X
ejpam-4735	140	2	3	3	X
ejpam-4735	140	3	]	]	PUNCT
ejpam-4735	140	4	for	for	ADP
ejpam-4735	140	5	subsets	subset	NOUN
ejpam-4735	140	6	a	a	DET
ejpam-4735	140	7	,	,	PUNCT
ejpam-4735	140	8	b	b	PROPN
ejpam-4735	140	9	of	of	ADP
ejpam-4735	140	10	a	a	DET
ejpam-4735	140	11	topological	topological	ADJ
ejpam-4735	140	12	space	space	NOUN
ejpam-4735	140	13	(	(	PUNCT
ejpam-4735	140	14	x	x	X
ejpam-4735	140	15	,	,	PUNCT
ejpam-4735	140	16	τ	τ	PROPN
ejpam-4735	140	17	)	)	PUNCT
ejpam-4735	140	18	,	,	PUNCT
ejpam-4735	140	19	the	the	DET
ejpam-4735	140	20	following	follow	VERB
ejpam-4735	140	21	properties	property	NOUN
ejpam-4735	140	22	hold	hold	VERB
ejpam-4735	140	23	:	:	PUNCT
ejpam-4735	140	24	(	(	PUNCT
ejpam-4735	140	25	1	1	X
ejpam-4735	140	26	)	)	PUNCT
ejpam-4735	140	27	a	a	DET
ejpam-4735	140	28	⊆	⊆	NUM
ejpam-4735	140	29	δp(λ	δp(λ	NOUN
ejpam-4735	140	30	,	,	PUNCT
ejpam-4735	140	31	s)ker(a	s)ker(a	NOUN
ejpam-4735	140	32	)	)	PUNCT
ejpam-4735	140	33	.	.	PUNCT
ejpam-4735	141	1	(	(	PUNCT
ejpam-4735	141	2	2	2	X
ejpam-4735	141	3	)	)	PUNCT
ejpam-4735	141	4	if	if	SCONJ
ejpam-4735	141	5	a	a	DET
ejpam-4735	141	6	⊆	⊆	NUM
ejpam-4735	141	7	b	b	NOUN
ejpam-4735	141	8	,	,	PUNCT
ejpam-4735	141	9	then	then	ADV
ejpam-4735	141	10	δp(λ	δp(λ	NOUN
ejpam-4735	141	11	,	,	PUNCT
ejpam-4735	141	12	s)ker(a	s)ker(a	NOUN
ejpam-4735	141	13	)	)	PUNCT
ejpam-4735	141	14	⊆	⊆	NUM
ejpam-4735	141	15	δp(λ	δp(λ	NOUN
ejpam-4735	141	16	,	,	PUNCT
ejpam-4735	141	17	s)ker(b	s)ker(b	NUM
ejpam-4735	141	18	)	)	PUNCT
ejpam-4735	141	19	.	.	PUNCT
ejpam-4735	142	1	(	(	PUNCT
ejpam-4735	142	2	3	3	NUM
ejpam-4735	142	3	)	)	PUNCT
ejpam-4735	142	4	δp(λ	δp(λ	NOUN
ejpam-4735	142	5	,	,	PUNCT
ejpam-4735	142	6	s)ker(δp(λ	s)ker(δp(λ	NOUN
ejpam-4735	142	7	,	,	PUNCT
ejpam-4735	142	8	s)ker(a	s)ker(a	NOUN
ejpam-4735	142	9	)	)	PUNCT
ejpam-4735	142	10	)	)	PUNCT
ejpam-4735	143	1	=	=	SYM
ejpam-4735	143	2	δp(λ	δp(λ	NOUN
ejpam-4735	143	3	,	,	PUNCT
ejpam-4735	143	4	s)ker(a	s)ker(a	NOUN
ejpam-4735	143	5	)	)	PUNCT
ejpam-4735	143	6	.	.	PUNCT
ejpam-4735	144	1	(	(	PUNCT
ejpam-4735	144	2	4	4	X
ejpam-4735	144	3	)	)	PUNCT
ejpam-4735	144	4	if	if	SCONJ
ejpam-4735	144	5	a	a	PRON
ejpam-4735	144	6	is	be	AUX
ejpam-4735	144	7	δp(λ	δp(λ	NOUN
ejpam-4735	144	8	,	,	PUNCT
ejpam-4735	144	9	s)-open	s)-open	PUNCT
ejpam-4735	144	10	,	,	PUNCT
ejpam-4735	144	11	δp(λ	δp(λ	NOUN
ejpam-4735	144	12	,	,	PUNCT
ejpam-4735	144	13	s)ker(a	s)ker(a	NOUN
ejpam-4735	144	14	)	)	PUNCT
ejpam-4735	144	15	=	=	SYM
ejpam-4735	144	16	a.	a.	NOUN
ejpam-4735	144	17	theorem	theorem	NOUN
ejpam-4735	144	18	2	2	NUM
ejpam-4735	144	19	.	.	X
ejpam-4735	144	20	for	for	ADP
ejpam-4735	144	21	any	any	DET
ejpam-4735	144	22	points	point	NOUN
ejpam-4735	144	23	x	x	PUNCT
ejpam-4735	144	24	and	and	CCONJ
ejpam-4735	144	25	y	y	PROPN
ejpam-4735	144	26	in	in	ADP
ejpam-4735	144	27	a	a	DET
ejpam-4735	144	28	topological	topological	ADJ
ejpam-4735	144	29	space	space	NOUN
ejpam-4735	144	30	(	(	PUNCT
ejpam-4735	144	31	x	x	X
ejpam-4735	144	32	,	,	PUNCT
ejpam-4735	144	33	τ	τ	PROPN
ejpam-4735	144	34	)	)	PUNCT
ejpam-4735	144	35	,	,	PUNCT
ejpam-4735	144	36	the	the	DET
ejpam-4735	144	37	following	follow	VERB
ejpam-4735	144	38	properties	property	NOUN
ejpam-4735	144	39	are	be	AUX
ejpam-4735	144	40	equivalent	equivalent	ADJ
ejpam-4735	144	41	:	:	PUNCT
ejpam-4735	144	42	(	(	PUNCT
ejpam-4735	144	43	1	1	NUM
ejpam-4735	144	44	)	)	PUNCT
ejpam-4735	144	45	δp(λ	δp(λ	NOUN
ejpam-4735	144	46	,	,	PUNCT
ejpam-4735	144	47	s)ker({x	s)ker({x	NOUN
ejpam-4735	144	48	}	}	PUNCT
ejpam-4735	144	49	)	)	PUNCT
ejpam-4735	144	50	̸=	̸=	PROPN
ejpam-4735	144	51	δp(λ	δp(λ	NOUN
ejpam-4735	144	52	,	,	PUNCT
ejpam-4735	144	53	s)ker({y	s)ker({y	NOUN
ejpam-4735	144	54	}	}	PUNCT
ejpam-4735	144	55	)	)	PUNCT
ejpam-4735	144	56	.	.	PUNCT
ejpam-4735	145	1	(	(	PUNCT
ejpam-4735	145	2	2	2	X
ejpam-4735	145	3	)	)	PUNCT
ejpam-4735	145	4	{	{	PUNCT
ejpam-4735	145	5	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	145	6	,	,	PUNCT
ejpam-4735	145	7	s	s	PART
ejpam-4735	145	8	)	)	PUNCT
ejpam-4735	145	9	̸=	̸=	PROPN
ejpam-4735	145	10	{	{	PUNCT
ejpam-4735	145	11	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	145	12	,	,	PUNCT
ejpam-4735	145	13	s	s	NOUN
ejpam-4735	145	14	)	)	PUNCT
ejpam-4735	145	15	.	.	PUNCT
ejpam-4735	146	1	proof	proof	NOUN
ejpam-4735	146	2	.	.	PUNCT
ejpam-4735	147	1	(	(	PUNCT
ejpam-4735	147	2	1	1	X
ejpam-4735	147	3	)	)	PUNCT
ejpam-4735	147	4	⇒	⇒	NOUN
ejpam-4735	147	5	(	(	PUNCT
ejpam-4735	147	6	2	2	NUM
ejpam-4735	147	7	):	):	PUNCT
ejpam-4735	147	8	suppose	suppose	VERB
ejpam-4735	147	9	that	that	SCONJ
ejpam-4735	147	10	δp(λ	δp(λ	NOUN
ejpam-4735	147	11	,	,	PUNCT
ejpam-4735	147	12	s)ker({x	s)ker({x	NOUN
ejpam-4735	147	13	}	}	PUNCT
ejpam-4735	147	14	)	)	PUNCT
ejpam-4735	147	15	̸=	̸=	PROPN
ejpam-4735	147	16	δp(λ	δp(λ	NOUN
ejpam-4735	147	17	,	,	PUNCT
ejpam-4735	147	18	s)ker({y	s)ker({y	NOUN
ejpam-4735	147	19	}	}	PUNCT
ejpam-4735	147	20	)	)	PUNCT
ejpam-4735	147	21	.	.	PUNCT
ejpam-4735	148	1	then	then	ADV
ejpam-4735	148	2	,	,	PUNCT
ejpam-4735	148	3	there	there	PRON
ejpam-4735	148	4	exists	exist	VERB
ejpam-4735	148	5	a	a	DET
ejpam-4735	148	6	point	point	NOUN
ejpam-4735	148	7	z	z	NOUN
ejpam-4735	148	8	∈	∈	PROPN
ejpam-4735	148	9	x	x	PUNCT
ejpam-4735	148	10	such	such	ADJ
ejpam-4735	148	11	that	that	SCONJ
ejpam-4735	148	12	z	z	PROPN
ejpam-4735	148	13	∈	∈	PROPN
ejpam-4735	148	14	δp(λ	δp(λ	NOUN
ejpam-4735	148	15	,	,	PUNCT
ejpam-4735	148	16	s)ker({x	s)ker({x	NOUN
ejpam-4735	148	17	}	}	PUNCT
ejpam-4735	148	18	)	)	PUNCT
ejpam-4735	148	19	and	and	CCONJ
ejpam-4735	148	20	z	z	PROPN
ejpam-4735	148	21	̸∈	̸∈	PROPN
ejpam-4735	148	22	δp(λ	δp(λ	NOUN
ejpam-4735	148	23	,	,	PUNCT
ejpam-4735	148	24	s)ker({y	s)ker({y	NOUN
ejpam-4735	148	25	}	}	PUNCT
ejpam-4735	148	26	)	)	PUNCT
ejpam-4735	148	27	or	or	CCONJ
ejpam-4735	148	28	z	z	NOUN
ejpam-4735	148	29	∈	∈	PROPN
ejpam-4735	148	30	δp(λ	δp(λ	NOUN
ejpam-4735	148	31	,	,	PUNCT
ejpam-4735	148	32	s)ker({y	s)ker({y	NOUN
ejpam-4735	148	33	}	}	PUNCT
ejpam-4735	148	34	)	)	PUNCT
ejpam-4735	148	35	and	and	CCONJ
ejpam-4735	148	36	z	z	PROPN
ejpam-4735	148	37	̸∈	̸∈	PROPN
ejpam-4735	148	38	δp(λ	δp(λ	NOUN
ejpam-4735	148	39	,	,	PUNCT
ejpam-4735	148	40	s)ker({x	s)ker({x	NUM
ejpam-4735	148	41	}	}	PUNCT
ejpam-4735	148	42	)	)	PUNCT
ejpam-4735	148	43	.	.	PUNCT
ejpam-4735	149	1	we	we	PRON
ejpam-4735	149	2	prove	prove	VERB
ejpam-4735	149	3	only	only	ADV
ejpam-4735	149	4	the	the	DET
ejpam-4735	149	5	first	first	ADJ
ejpam-4735	149	6	case	case	NOUN
ejpam-4735	149	7	being	be	AUX
ejpam-4735	149	8	the	the	DET
ejpam-4735	149	9	second	second	ADJ
ejpam-4735	149	10	analogous	analogous	NOUN
ejpam-4735	149	11	.	.	PUNCT
ejpam-4735	150	1	from	from	ADP
ejpam-4735	150	2	z	z	PROPN
ejpam-4735	150	3	∈	∈	PROPN
ejpam-4735	150	4	δp(λ	δp(λ	NOUN
ejpam-4735	150	5	,	,	PUNCT
ejpam-4735	150	6	s)ker({x	s)ker({x	NUM
ejpam-4735	150	7	}	}	PUNCT
ejpam-4735	150	8	)	)	PUNCT
ejpam-4735	151	1	it	it	PRON
ejpam-4735	151	2	follows	follow	VERB
ejpam-4735	151	3	that	that	SCONJ
ejpam-4735	151	4	{	{	PUNCT
ejpam-4735	151	5	x	x	NOUN
ejpam-4735	151	6	}	}	PUNCT
ejpam-4735	151	7	∩	∩	ADJ
ejpam-4735	151	8	{	{	PUNCT
ejpam-4735	151	9	z}δp(λ	z}δp(λ	PROPN
ejpam-4735	151	10	,	,	PUNCT
ejpam-4735	151	11	s	s	PART
ejpam-4735	151	12	)	)	PUNCT
ejpam-4735	151	13	̸=	̸=	PROPN
ejpam-4735	151	14	∅	∅	NOUN
ejpam-4735	151	15	which	which	PRON
ejpam-4735	151	16	implies	imply	VERB
ejpam-4735	151	17	x	x	X
ejpam-4735	151	18	∈	∈	PROPN
ejpam-4735	151	19	{	{	PUNCT
ejpam-4735	151	20	z}δp(λ	z}δp(λ	PROPN
ejpam-4735	151	21	,	,	PUNCT
ejpam-4735	151	22	s	s	NOUN
ejpam-4735	151	23	)	)	PUNCT
ejpam-4735	151	24	.	.	PUNCT
ejpam-4735	152	1	by	by	ADP
ejpam-4735	152	2	z	z	PROPN
ejpam-4735	152	3	̸∈	̸∈	PROPN
ejpam-4735	152	4	δp(λ	δp(λ	NOUN
ejpam-4735	152	5	,	,	PUNCT
ejpam-4735	152	6	s)ker({y	s)ker({y	NOUN
ejpam-4735	152	7	}	}	PUNCT
ejpam-4735	152	8	)	)	PUNCT
ejpam-4735	152	9	,	,	PUNCT
ejpam-4735	152	10	we	we	PRON
ejpam-4735	152	11	have	have	VERB
ejpam-4735	152	12	{	{	PUNCT
ejpam-4735	152	13	y	y	NOUN
ejpam-4735	152	14	}	}	PUNCT
ejpam-4735	152	15	∩	∩	NOUN
ejpam-4735	152	16	{	{	PUNCT
ejpam-4735	152	17	z}δp(λ	z}δp(λ	PROPN
ejpam-4735	152	18	,	,	PUNCT
ejpam-4735	152	19	s	s	PART
ejpam-4735	152	20	)	)	PUNCT
ejpam-4735	152	21	=	=	PUNCT
ejpam-4735	152	22	∅.	∅.	NOUN
ejpam-4735	152	23	since	since	SCONJ
ejpam-4735	152	24	x	x	PROPN
ejpam-4735	152	25	∈	∈	PROPN
ejpam-4735	152	26	{	{	PUNCT
ejpam-4735	152	27	z}δp(λ	z}δp(λ	PROPN
ejpam-4735	152	28	,	,	PUNCT
ejpam-4735	152	29	s	s	PART
ejpam-4735	152	30	)	)	PUNCT
ejpam-4735	152	31	,	,	PUNCT
ejpam-4735	152	32	{	{	PUNCT
ejpam-4735	152	33	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	152	34	,	,	PUNCT
ejpam-4735	152	35	s	s	PART
ejpam-4735	152	36	)	)	PUNCT
ejpam-4735	152	37	⊆	⊆	NUM
ejpam-4735	152	38	{	{	PUNCT
ejpam-4735	152	39	z}δp(λ	z}δp(λ	PROPN
ejpam-4735	152	40	,	,	PUNCT
ejpam-4735	152	41	s	s	NOUN
ejpam-4735	152	42	)	)	PUNCT
ejpam-4735	152	43	c.	c.	PROPN
ejpam-4735	152	44	boonpok	boonpok	PROPN
ejpam-4735	152	45	,	,	PUNCT
ejpam-4735	152	46	p.	p.	NOUN
ejpam-4735	152	47	pue	pue	NOUN
ejpam-4735	152	48	-	-	PUNCT
ejpam-4735	152	49	on	on	ADP
ejpam-4735	152	50	/	/	SYM
ejpam-4735	152	51	eur	eur	NOUN
ejpam-4735	152	52	.	.	PUNCT
ejpam-4735	153	1	j.	j.	PROPN
ejpam-4735	153	2	pure	pure	PROPN
ejpam-4735	153	3	appl	appl	PROPN
ejpam-4735	153	4	.	.	PROPN
ejpam-4735	153	5	math	math	PROPN
ejpam-4735	153	6	,	,	PUNCT
ejpam-4735	153	7	17	17	NUM
ejpam-4735	153	8	(	(	PUNCT
ejpam-4735	153	9	1	1	NUM
ejpam-4735	153	10	)	)	PUNCT
ejpam-4735	153	11	(	(	PUNCT
ejpam-4735	153	12	2024	2024	NUM
ejpam-4735	153	13	)	)	PUNCT
ejpam-4735	153	14	,	,	PUNCT
ejpam-4735	153	15	147	147	NUM
ejpam-4735	153	16	-	-	SYM
ejpam-4735	153	17	157	157	NUM
ejpam-4735	153	18	151	151	NUM
ejpam-4735	153	19	and	and	CCONJ
ejpam-4735	153	20	{	{	PUNCT
ejpam-4735	153	21	y	y	NOUN
ejpam-4735	153	22	}	}	PUNCT
ejpam-4735	153	23	∩	∩	NOUN
ejpam-4735	153	24	{	{	PUNCT
ejpam-4735	153	25	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	153	26	,	,	PUNCT
ejpam-4735	153	27	s	s	PART
ejpam-4735	153	28	)	)	PUNCT
ejpam-4735	153	29	=	=	PUNCT
ejpam-4735	153	30	∅.	∅.	VERB
ejpam-4735	153	31	therefore	therefore	ADV
ejpam-4735	153	32	,	,	PUNCT
ejpam-4735	153	33	{	{	PUNCT
ejpam-4735	153	34	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	153	35	,	,	PUNCT
ejpam-4735	153	36	s	s	PART
ejpam-4735	153	37	)	)	PUNCT
ejpam-4735	153	38	̸=	̸=	PROPN
ejpam-4735	153	39	{	{	PUNCT
ejpam-4735	153	40	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	153	41	,	,	PUNCT
ejpam-4735	153	42	s	s	NOUN
ejpam-4735	153	43	)	)	PUNCT
ejpam-4735	153	44	.	.	PUNCT
ejpam-4735	154	1	thus	thus	ADV
ejpam-4735	154	2	,	,	PUNCT
ejpam-4735	154	3	δp(λ	δp(λ	NOUN
ejpam-4735	154	4	,	,	PUNCT
ejpam-4735	154	5	s)ker({x	s)ker({x	NOUN
ejpam-4735	154	6	}	}	PUNCT
ejpam-4735	154	7	)	)	PUNCT
ejpam-4735	155	1	̸=	̸=	PROPN
ejpam-4735	155	2	δp(λ	δp(λ	NOUN
ejpam-4735	155	3	,	,	PUNCT
ejpam-4735	155	4	s)ker({y	s)ker({y	NOUN
ejpam-4735	155	5	}	}	PUNCT
ejpam-4735	155	6	)	)	PUNCT
ejpam-4735	155	7	implies	imply	VERB
ejpam-4735	155	8	that	that	SCONJ
ejpam-4735	155	9	{	{	PUNCT
ejpam-4735	155	10	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	155	11	,	,	PUNCT
ejpam-4735	155	12	s	s	PART
ejpam-4735	155	13	)	)	PUNCT
ejpam-4735	155	14	̸=	̸=	PROPN
ejpam-4735	155	15	{	{	PUNCT
ejpam-4735	155	16	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	155	17	,	,	PUNCT
ejpam-4735	155	18	s	s	NOUN
ejpam-4735	155	19	)	)	PUNCT
ejpam-4735	155	20	.	.	PUNCT
ejpam-4735	156	1	(	(	PUNCT
ejpam-4735	156	2	2	2	X
ejpam-4735	156	3	)	)	PUNCT
ejpam-4735	156	4	⇒	⇒	NOUN
ejpam-4735	156	5	(	(	PUNCT
ejpam-4735	156	6	1	1	NUM
ejpam-4735	156	7	):	):	PUNCT
ejpam-4735	156	8	suppose	suppose	VERB
ejpam-4735	156	9	that	that	SCONJ
ejpam-4735	156	10	{	{	PUNCT
ejpam-4735	156	11	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	156	12	,	,	PUNCT
ejpam-4735	156	13	s	s	PART
ejpam-4735	156	14	)	)	PUNCT
ejpam-4735	156	15	̸=	̸=	PROPN
ejpam-4735	156	16	{	{	PUNCT
ejpam-4735	156	17	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	156	18	,	,	PUNCT
ejpam-4735	156	19	s	s	NOUN
ejpam-4735	156	20	)	)	PUNCT
ejpam-4735	156	21	.	.	PUNCT
ejpam-4735	157	1	there	there	PRON
ejpam-4735	157	2	exists	exist	VERB
ejpam-4735	157	3	a	a	DET
ejpam-4735	157	4	point	point	NOUN
ejpam-4735	157	5	z	z	NOUN
ejpam-4735	157	6	∈	∈	PROPN
ejpam-4735	157	7	x	x	PUNCT
ejpam-4735	157	8	such	such	ADJ
ejpam-4735	157	9	that	that	SCONJ
ejpam-4735	157	10	z	z	PROPN
ejpam-4735	157	11	∈	∈	PROPN
ejpam-4735	157	12	{	{	PUNCT
ejpam-4735	157	13	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	157	14	,	,	PUNCT
ejpam-4735	157	15	s	s	PART
ejpam-4735	157	16	)	)	PUNCT
ejpam-4735	157	17	and	and	CCONJ
ejpam-4735	157	18	z	z	PROPN
ejpam-4735	157	19	̸∈	̸∈	PROPN
ejpam-4735	157	20	{	{	PUNCT
ejpam-4735	157	21	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	157	22	,	,	PUNCT
ejpam-4735	157	23	s	s	NOUN
ejpam-4735	157	24	)	)	PUNCT
ejpam-4735	157	25	or	or	CCONJ
ejpam-4735	157	26	z	z	NOUN
ejpam-4735	157	27	∈	∈	PROPN
ejpam-4735	157	28	{	{	PUNCT
ejpam-4735	157	29	y}δp(λ	y}δp(λ	NOUN
ejpam-4735	157	30	,	,	PUNCT
ejpam-4735	157	31	s	s	PART
ejpam-4735	157	32	)	)	PUNCT
ejpam-4735	157	33	and	and	CCONJ
ejpam-4735	157	34	z	z	PROPN
ejpam-4735	157	35	̸∈	̸∈	PROPN
ejpam-4735	157	36	{	{	PUNCT
ejpam-4735	157	37	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	157	38	,	,	PUNCT
ejpam-4735	157	39	s	s	NOUN
ejpam-4735	157	40	)	)	PUNCT
ejpam-4735	157	41	.	.	PUNCT
ejpam-4735	158	1	we	we	PRON
ejpam-4735	158	2	prove	prove	VERB
ejpam-4735	158	3	only	only	ADV
ejpam-4735	158	4	the	the	DET
ejpam-4735	158	5	first	first	ADJ
ejpam-4735	158	6	case	case	NOUN
ejpam-4735	158	7	being	be	AUX
ejpam-4735	158	8	the	the	DET
ejpam-4735	158	9	second	second	ADJ
ejpam-4735	158	10	analogous	analogous	NOUN
ejpam-4735	158	11	.	.	PUNCT
ejpam-4735	159	1	it	it	PRON
ejpam-4735	159	2	follows	follow	VERB
ejpam-4735	159	3	that	that	SCONJ
ejpam-4735	159	4	there	there	PRON
ejpam-4735	159	5	exists	exist	VERB
ejpam-4735	159	6	a	a	DET
ejpam-4735	159	7	δp(λ	δp(λ	NOUN
ejpam-4735	159	8	,	,	PUNCT
ejpam-4735	159	9	s)open	s)open	NOUN
ejpam-4735	159	10	set	set	NOUN
ejpam-4735	159	11	containing	contain	VERB
ejpam-4735	159	12	z	z	NOUN
ejpam-4735	159	13	and	and	CCONJ
ejpam-4735	159	14	therefore	therefore	ADV
ejpam-4735	159	15	x	x	X
ejpam-4735	159	16	but	but	CCONJ
ejpam-4735	159	17	not	not	PART
ejpam-4735	159	18	y	y	NOUN
ejpam-4735	159	19	,	,	PUNCT
ejpam-4735	159	20	namely	namely	ADV
ejpam-4735	159	21	,	,	PUNCT
ejpam-4735	159	22	y	y	PROPN
ejpam-4735	159	23	̸∈	̸∈	PROPN
ejpam-4735	159	24	δp(λ	δp(λ	NOUN
ejpam-4735	159	25	,	,	PUNCT
ejpam-4735	159	26	s)ker({x	s)ker({x	NUM
ejpam-4735	159	27	}	}	PUNCT
ejpam-4735	159	28	)	)	PUNCT
ejpam-4735	159	29	and	and	CCONJ
ejpam-4735	159	30	thus	thus	ADV
ejpam-4735	159	31	δp(λ	δp(λ	NOUN
ejpam-4735	159	32	,	,	PUNCT
ejpam-4735	159	33	s)ker({x	s)ker({x	NOUN
ejpam-4735	159	34	}	}	PUNCT
ejpam-4735	159	35	)	)	PUNCT
ejpam-4735	159	36	̸=	̸=	PROPN
ejpam-4735	159	37	δp(λ	δp(λ	NOUN
ejpam-4735	159	38	,	,	PUNCT
ejpam-4735	159	39	s)ker({y	s)ker({y	NOUN
ejpam-4735	159	40	}	}	PUNCT
ejpam-4735	159	41	)	)	PUNCT
ejpam-4735	159	42	.	.	PUNCT
ejpam-4735	160	1	lemma	lemma	PROPN
ejpam-4735	160	2	4	4	X
ejpam-4735	160	3	.	.	PUNCT
ejpam-4735	161	1	let	let	AUX
ejpam-4735	161	2	(	(	PUNCT
ejpam-4735	161	3	x	x	NOUN
ejpam-4735	161	4	,	,	PUNCT
ejpam-4735	161	5	τ	τ	X
ejpam-4735	161	6	)	)	PUNCT
ejpam-4735	161	7	be	be	VERB
ejpam-4735	161	8	a	a	DET
ejpam-4735	161	9	topological	topological	ADJ
ejpam-4735	161	10	space	space	NOUN
ejpam-4735	161	11	and	and	CCONJ
ejpam-4735	161	12	x	x	NOUN
ejpam-4735	161	13	,	,	PUNCT
ejpam-4735	161	14	y	y	PROPN
ejpam-4735	161	15	∈	∈	PROPN
ejpam-4735	161	16	x.	x.	NOUN
ejpam-4735	161	17	then	then	ADV
ejpam-4735	161	18	,	,	PUNCT
ejpam-4735	161	19	the	the	DET
ejpam-4735	161	20	following	follow	VERB
ejpam-4735	161	21	properties	property	NOUN
ejpam-4735	161	22	hold	hold	VERB
ejpam-4735	161	23	:	:	PUNCT
ejpam-4735	161	24	(	(	PUNCT
ejpam-4735	161	25	1	1	X
ejpam-4735	161	26	)	)	PUNCT
ejpam-4735	161	27	y	y	PROPN
ejpam-4735	161	28	∈	∈	PROPN
ejpam-4735	161	29	δp(λ	δp(λ	NOUN
ejpam-4735	161	30	,	,	PUNCT
ejpam-4735	161	31	s)ker({x	s)ker({x	NUM
ejpam-4735	161	32	}	}	PUNCT
ejpam-4735	161	33	)	)	PUNCT
ejpam-4735	162	1	if	if	SCONJ
ejpam-4735	162	2	and	and	CCONJ
ejpam-4735	162	3	only	only	ADV
ejpam-4735	162	4	if	if	SCONJ
ejpam-4735	162	5	x	x	SYM
ejpam-4735	162	6	∈	∈	NOUN
ejpam-4735	162	7	{	{	PUNCT
ejpam-4735	162	8	y}δp(λ	y}δp(λ	NOUN
ejpam-4735	162	9	,	,	PUNCT
ejpam-4735	162	10	s	s	NOUN
ejpam-4735	162	11	)	)	PUNCT
ejpam-4735	162	12	.	.	PUNCT
ejpam-4735	163	1	(	(	PUNCT
ejpam-4735	163	2	2	2	NUM
ejpam-4735	163	3	)	)	PUNCT
ejpam-4735	163	4	δp(λ	δp(λ	NOUN
ejpam-4735	163	5	,	,	PUNCT
ejpam-4735	163	6	s)ker({x	s)ker({x	NUM
ejpam-4735	163	7	}	}	PUNCT
ejpam-4735	163	8	)	)	PUNCT
ejpam-4735	164	1	=	=	SYM
ejpam-4735	164	2	δp(λ	δp(λ	NOUN
ejpam-4735	164	3	,	,	PUNCT
ejpam-4735	164	4	s)ker({y	s)ker({y	NOUN
ejpam-4735	164	5	}	}	PUNCT
ejpam-4735	164	6	)	)	PUNCT
ejpam-4735	164	7	if	if	SCONJ
ejpam-4735	164	8	and	and	CCONJ
ejpam-4735	164	9	only	only	ADV
ejpam-4735	164	10	if	if	SCONJ
ejpam-4735	164	11	{	{	PUNCT
ejpam-4735	164	12	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	164	13	,	,	PUNCT
ejpam-4735	164	14	s	s	PART
ejpam-4735	164	15	)	)	PUNCT
ejpam-4735	164	16	=	=	PRON
ejpam-4735	164	17	{	{	PUNCT
ejpam-4735	164	18	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	164	19	,	,	PUNCT
ejpam-4735	164	20	s	s	NOUN
ejpam-4735	164	21	)	)	PUNCT
ejpam-4735	164	22	.	.	PUNCT
ejpam-4735	165	1	proof	proof	NOUN
ejpam-4735	165	2	.	.	PUNCT
ejpam-4735	166	1	(	(	PUNCT
ejpam-4735	166	2	1	1	X
ejpam-4735	166	3	)	)	PUNCT
ejpam-4735	166	4	let	let	VERB
ejpam-4735	166	5	x	x	SYM
ejpam-4735	166	6	̸∈	̸∈	PROPN
ejpam-4735	166	7	{	{	PUNCT
ejpam-4735	166	8	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	166	9	,	,	PUNCT
ejpam-4735	166	10	s	s	NOUN
ejpam-4735	166	11	)	)	PUNCT
ejpam-4735	166	12	.	.	PUNCT
ejpam-4735	167	1	then	then	ADV
ejpam-4735	167	2	,	,	PUNCT
ejpam-4735	167	3	there	there	PRON
ejpam-4735	167	4	exists	exist	VERB
ejpam-4735	167	5	u	u	PROPN
ejpam-4735	167	6	∈	∈	PROPN
ejpam-4735	167	7	δp(λ	δp(λ	NOUN
ejpam-4735	167	8	,	,	PUNCT
ejpam-4735	167	9	s)o(x	s)o(x	PROPN
ejpam-4735	167	10	,	,	PUNCT
ejpam-4735	167	11	τ	τ	X
ejpam-4735	167	12	)	)	PUNCT
ejpam-4735	167	13	such	such	ADJ
ejpam-4735	167	14	that	that	SCONJ
ejpam-4735	167	15	x	x	SYM
ejpam-4735	167	16	∈	∈	PROPN
ejpam-4735	167	17	u	u	NOUN
ejpam-4735	167	18	and	and	CCONJ
ejpam-4735	167	19	y	y	PROPN
ejpam-4735	167	20	̸∈	̸∈	PROPN
ejpam-4735	167	21	u	u	PROPN
ejpam-4735	167	22	.	.	PUNCT
ejpam-4735	168	1	thus	thus	ADV
ejpam-4735	168	2	,	,	PUNCT
ejpam-4735	168	3	y	y	PROPN
ejpam-4735	168	4	̸∈	̸∈	PROPN
ejpam-4735	168	5	δp(λ	δp(λ	NOUN
ejpam-4735	168	6	,	,	PUNCT
ejpam-4735	168	7	s)ker({x	s)ker({x	NUM
ejpam-4735	168	8	}	}	PUNCT
ejpam-4735	168	9	)	)	PUNCT
ejpam-4735	168	10	.	.	PUNCT
ejpam-4735	169	1	the	the	DET
ejpam-4735	169	2	converse	converse	NOUN
ejpam-4735	169	3	is	be	AUX
ejpam-4735	169	4	similarly	similarly	ADV
ejpam-4735	169	5	shown	show	VERB
ejpam-4735	169	6	.	.	PUNCT
ejpam-4735	170	1	(	(	PUNCT
ejpam-4735	170	2	2	2	X
ejpam-4735	170	3	)	)	PUNCT
ejpam-4735	170	4	suppose	suppose	VERB
ejpam-4735	170	5	that	that	SCONJ
ejpam-4735	170	6	δp(λ	δp(λ	NOUN
ejpam-4735	170	7	,	,	PUNCT
ejpam-4735	170	8	s)ker({x	s)ker({x	NUM
ejpam-4735	170	9	}	}	PUNCT
ejpam-4735	170	10	)	)	PUNCT
ejpam-4735	170	11	=	=	SYM
ejpam-4735	171	1	δp(λ	δp(λ	NOUN
ejpam-4735	171	2	,	,	PUNCT
ejpam-4735	171	3	s)ker({y	s)ker({y	NOUN
ejpam-4735	171	4	}	}	PUNCT
ejpam-4735	171	5	)	)	PUNCT
ejpam-4735	171	6	for	for	ADP
ejpam-4735	171	7	any	any	DET
ejpam-4735	171	8	x	x	NOUN
ejpam-4735	171	9	,	,	PUNCT
ejpam-4735	171	10	y	y	PROPN
ejpam-4735	171	11	∈	∈	PROPN
ejpam-4735	171	12	x.	x.	VERB
ejpam-4735	172	1	since	since	SCONJ
ejpam-4735	172	2	x	x	PROPN
ejpam-4735	172	3	∈	∈	PROPN
ejpam-4735	172	4	δp(λ	δp(λ	NOUN
ejpam-4735	172	5	,	,	PUNCT
ejpam-4735	172	6	s)ker({x	s)ker({x	NOUN
ejpam-4735	172	7	}	}	PUNCT
ejpam-4735	172	8	)	)	PUNCT
ejpam-4735	172	9	,	,	PUNCT
ejpam-4735	172	10	x	x	PUNCT
ejpam-4735	172	11	∈	∈	PROPN
ejpam-4735	172	12	δp(λ	δp(λ	NOUN
ejpam-4735	172	13	,	,	PUNCT
ejpam-4735	172	14	s)ker({y	s)ker({y	NOUN
ejpam-4735	172	15	}	}	PUNCT
ejpam-4735	172	16	)	)	PUNCT
ejpam-4735	172	17	,	,	PUNCT
ejpam-4735	172	18	by	by	ADP
ejpam-4735	172	19	(	(	PUNCT
ejpam-4735	172	20	1	1	NUM
ejpam-4735	172	21	)	)	PUNCT
ejpam-4735	172	22	,	,	PUNCT
ejpam-4735	172	23	y	y	PROPN
ejpam-4735	172	24	∈	∈	PROPN
ejpam-4735	172	25	{	{	PUNCT
ejpam-4735	172	26	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	172	27	,	,	PUNCT
ejpam-4735	172	28	s	s	NOUN
ejpam-4735	172	29	)	)	PUNCT
ejpam-4735	172	30	.	.	PUNCT
ejpam-4735	173	1	by	by	ADP
ejpam-4735	173	2	lemma	lemma	PROPN
ejpam-4735	173	3	1	1	NUM
ejpam-4735	173	4	,	,	PUNCT
ejpam-4735	173	5	{	{	PUNCT
ejpam-4735	173	6	y}δp(λ	y}δp(λ	NOUN
ejpam-4735	173	7	,	,	PUNCT
ejpam-4735	173	8	s	s	NOUN
ejpam-4735	173	9	)	)	PUNCT
ejpam-4735	173	10	⊆	⊆	NUM
ejpam-4735	173	11	{	{	PUNCT
ejpam-4735	173	12	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	173	13	,	,	PUNCT
ejpam-4735	173	14	s	s	NOUN
ejpam-4735	173	15	)	)	PUNCT
ejpam-4735	173	16	.	.	PUNCT
ejpam-4735	174	1	similarly	similarly	ADV
ejpam-4735	174	2	,	,	PUNCT
ejpam-4735	174	3	we	we	PRON
ejpam-4735	174	4	have	have	VERB
ejpam-4735	174	5	{	{	PUNCT
ejpam-4735	174	6	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	174	7	,	,	PUNCT
ejpam-4735	174	8	s	s	PART
ejpam-4735	174	9	)	)	PUNCT
ejpam-4735	174	10	⊆	⊆	NUM
ejpam-4735	174	11	{	{	PUNCT
ejpam-4735	174	12	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	174	13	,	,	PUNCT
ejpam-4735	174	14	s	s	NOUN
ejpam-4735	174	15	)	)	PUNCT
ejpam-4735	174	16	and	and	CCONJ
ejpam-4735	174	17	hence	hence	ADV
ejpam-4735	174	18	{	{	PUNCT
ejpam-4735	174	19	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	174	20	,	,	PUNCT
ejpam-4735	174	21	s	s	PART
ejpam-4735	174	22	)	)	PUNCT
ejpam-4735	174	23	=	=	PRON
ejpam-4735	174	24	{	{	PUNCT
ejpam-4735	174	25	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	174	26	,	,	PUNCT
ejpam-4735	174	27	s	s	NOUN
ejpam-4735	174	28	)	)	PUNCT
ejpam-4735	174	29	.	.	PUNCT
ejpam-4735	175	1	conversely	conversely	ADV
ejpam-4735	175	2	,	,	PUNCT
ejpam-4735	175	3	suppose	suppose	VERB
ejpam-4735	175	4	that	that	SCONJ
ejpam-4735	175	5	{	{	PUNCT
ejpam-4735	175	6	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	175	7	,	,	PUNCT
ejpam-4735	175	8	s	s	PART
ejpam-4735	175	9	)	)	PUNCT
ejpam-4735	175	10	=	=	PRON
ejpam-4735	175	11	{	{	PUNCT
ejpam-4735	175	12	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	175	13	,	,	PUNCT
ejpam-4735	175	14	s	s	NOUN
ejpam-4735	175	15	)	)	PUNCT
ejpam-4735	175	16	.	.	PUNCT
ejpam-4735	176	1	since	since	SCONJ
ejpam-4735	176	2	x	x	PROPN
ejpam-4735	176	3	∈	∈	PROPN
ejpam-4735	176	4	{	{	PUNCT
ejpam-4735	176	5	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	176	6	,	,	PUNCT
ejpam-4735	176	7	s	s	PART
ejpam-4735	176	8	)	)	PUNCT
ejpam-4735	176	9	,	,	PUNCT
ejpam-4735	176	10	x	x	PUNCT
ejpam-4735	176	11	∈	∈	NOUN
ejpam-4735	176	12	{	{	PUNCT
ejpam-4735	176	13	y}δp(λ	y}δp(λ	NOUN
ejpam-4735	176	14	,	,	PUNCT
ejpam-4735	176	15	s	s	NOUN
ejpam-4735	176	16	)	)	PUNCT
ejpam-4735	176	17	and	and	CCONJ
ejpam-4735	176	18	by	by	ADP
ejpam-4735	176	19	(	(	PUNCT
ejpam-4735	176	20	1	1	NUM
ejpam-4735	176	21	)	)	PUNCT
ejpam-4735	176	22	,	,	PUNCT
ejpam-4735	176	23	y	y	PROPN
ejpam-4735	176	24	∈	∈	PROPN
ejpam-4735	176	25	δp(λ	δp(λ	NOUN
ejpam-4735	176	26	,	,	PUNCT
ejpam-4735	176	27	s)ker({x	s)ker({x	NOUN
ejpam-4735	176	28	}	}	PUNCT
ejpam-4735	176	29	)	)	PUNCT
ejpam-4735	176	30	.	.	PUNCT
ejpam-4735	177	1	by	by	ADP
ejpam-4735	177	2	lemma	lemma	PROPN
ejpam-4735	177	3	3	3	NUM
ejpam-4735	177	4	,	,	PUNCT
ejpam-4735	177	5	δp(λ	δp(λ	NOUN
ejpam-4735	177	6	,	,	PUNCT
ejpam-4735	177	7	s)ker({y	s)ker({y	NOUN
ejpam-4735	177	8	}	}	PUNCT
ejpam-4735	177	9	)	)	PUNCT
ejpam-4735	177	10	⊆	⊆	NUM
ejpam-4735	177	11	δp(λ	δp(λ	NOUN
ejpam-4735	177	12	,	,	PUNCT
ejpam-4735	177	13	s)ker(δp(λ	s)ker(δp(λ	NOUN
ejpam-4735	177	14	,	,	PUNCT
ejpam-4735	177	15	s)ker({x	s)ker({x	NOUN
ejpam-4735	177	16	}	}	PUNCT
ejpam-4735	177	17	)	)	PUNCT
ejpam-4735	177	18	)	)	PUNCT
ejpam-4735	178	1	=	=	SYM
ejpam-4735	178	2	δp(λ	δp(λ	NOUN
ejpam-4735	178	3	,	,	PUNCT
ejpam-4735	178	4	s)ker({x	s)ker({x	NOUN
ejpam-4735	178	5	}	}	PUNCT
ejpam-4735	178	6	)	)	PUNCT
ejpam-4735	178	7	.	.	PUNCT
ejpam-4735	179	1	similarly	similarly	ADV
ejpam-4735	179	2	,	,	PUNCT
ejpam-4735	179	3	we	we	PRON
ejpam-4735	179	4	have	have	VERB
ejpam-4735	179	5	δp(λ	δp(λ	NOUN
ejpam-4735	179	6	,	,	PUNCT
ejpam-4735	179	7	s)ker({x	s)ker({x	NUM
ejpam-4735	179	8	}	}	PUNCT
ejpam-4735	179	9	)	)	PUNCT
ejpam-4735	180	1	⊆	⊆	NUM
ejpam-4735	180	2	δp(λ	δp(λ	NOUN
ejpam-4735	180	3	,	,	PUNCT
ejpam-4735	180	4	s)ker({y	s)ker({y	NOUN
ejpam-4735	180	5	}	}	PUNCT
ejpam-4735	180	6	)	)	PUNCT
ejpam-4735	180	7	and	and	CCONJ
ejpam-4735	180	8	hence	hence	ADV
ejpam-4735	180	9	δp(λ	δp(λ	NOUN
ejpam-4735	180	10	,	,	PUNCT
ejpam-4735	180	11	s)ker({x	s)ker({x	NUM
ejpam-4735	180	12	}	}	PUNCT
ejpam-4735	180	13	)	)	PUNCT
ejpam-4735	181	1	=	=	SYM
ejpam-4735	181	2	δp(λ	δp(λ	NOUN
ejpam-4735	181	3	,	,	PUNCT
ejpam-4735	181	4	s)ker({y	s)ker({y	NOUN
ejpam-4735	181	5	}	}	PUNCT
ejpam-4735	181	6	)	)	PUNCT
ejpam-4735	181	7	.	.	PUNCT
ejpam-4735	182	1	theorem	theorem	NOUN
ejpam-4735	182	2	3	3	NUM
ejpam-4735	182	3	.	.	PUNCT
ejpam-4735	183	1	a	a	DET
ejpam-4735	183	2	topological	topological	ADJ
ejpam-4735	183	3	space	space	NOUN
ejpam-4735	183	4	(	(	PUNCT
ejpam-4735	183	5	x	x	X
ejpam-4735	183	6	,	,	PUNCT
ejpam-4735	183	7	τ	τ	X
ejpam-4735	183	8	)	)	PUNCT
ejpam-4735	183	9	is	be	AUX
ejpam-4735	183	10	δp(λ	δp(λ	NOUN
ejpam-4735	183	11	,	,	PUNCT
ejpam-4735	183	12	s)-r0	s)-r0	PRON
ejpam-4735	183	13	if	if	SCONJ
ejpam-4735	183	14	and	and	CCONJ
ejpam-4735	183	15	only	only	ADV
ejpam-4735	183	16	if	if	SCONJ
ejpam-4735	183	17	,	,	PUNCT
ejpam-4735	183	18	for	for	ADP
ejpam-4735	183	19	each	each	DET
ejpam-4735	183	20	points	point	NOUN
ejpam-4735	183	21	x	x	PUNCT
ejpam-4735	183	22	and	and	CCONJ
ejpam-4735	183	23	y	y	PROPN
ejpam-4735	183	24	in	in	ADP
ejpam-4735	183	25	x	x	PROPN
ejpam-4735	183	26	,	,	PUNCT
ejpam-4735	183	27	δp(λ	δp(λ	NOUN
ejpam-4735	183	28	,	,	PUNCT
ejpam-4735	183	29	s)ker({x	s)ker({x	NOUN
ejpam-4735	183	30	}	}	PUNCT
ejpam-4735	183	31	)	)	PUNCT
ejpam-4735	183	32	̸=	̸=	PROPN
ejpam-4735	183	33	δp(λ	δp(λ	NOUN
ejpam-4735	183	34	,	,	PUNCT
ejpam-4735	183	35	s)ker({y	s)ker({y	NOUN
ejpam-4735	183	36	}	}	PUNCT
ejpam-4735	183	37	)	)	PUNCT
ejpam-4735	183	38	implies	imply	VERB
ejpam-4735	183	39	δp(λ	δp(λ	NOUN
ejpam-4735	183	40	,	,	PUNCT
ejpam-4735	183	41	s)ker({x	s)ker({x	NOUN
ejpam-4735	183	42	}	}	PUNCT
ejpam-4735	183	43	)	)	PUNCT
ejpam-4735	183	44	∩	∩	NOUN
ejpam-4735	183	45	δp(λ	δp(λ	NOUN
ejpam-4735	183	46	,	,	PUNCT
ejpam-4735	183	47	s)ker({y	s)ker({y	NOUN
ejpam-4735	183	48	}	}	PUNCT
ejpam-4735	183	49	)	)	PUNCT
ejpam-4735	183	50	=	=	PUNCT
ejpam-4735	183	51	∅.	∅.	NOUN
ejpam-4735	183	52	proof	proof	NOUN
ejpam-4735	183	53	.	.	PUNCT
ejpam-4735	184	1	let	let	VERB
ejpam-4735	184	2	(	(	PUNCT
ejpam-4735	184	3	x	x	NOUN
ejpam-4735	184	4	,	,	PUNCT
ejpam-4735	184	5	τ	τ	X
ejpam-4735	184	6	)	)	PUNCT
ejpam-4735	184	7	be	be	AUX
ejpam-4735	184	8	δp(λ	δp(λ	NOUN
ejpam-4735	184	9	,	,	PUNCT
ejpam-4735	184	10	s)-r0	s)-r0	X
ejpam-4735	184	11	.	.	PUNCT
ejpam-4735	185	1	suppose	suppose	VERB
ejpam-4735	185	2	that	that	SCONJ
ejpam-4735	185	3	δp(λ	δp(λ	NOUN
ejpam-4735	185	4	,	,	PUNCT
ejpam-4735	185	5	s)ker({x	s)ker({x	NOUN
ejpam-4735	185	6	}	}	PUNCT
ejpam-4735	185	7	)	)	PUNCT
ejpam-4735	185	8	∩	∩	NOUN
ejpam-4735	185	9	δp(λ	δp(λ	NOUN
ejpam-4735	185	10	,	,	PUNCT
ejpam-4735	185	11	s)ker({y	s)ker({y	NOUN
ejpam-4735	185	12	}	}	PUNCT
ejpam-4735	185	13	)	)	PUNCT
ejpam-4735	185	14	̸=	̸=	PROPN
ejpam-4735	185	15	∅.	∅.	PROPN
ejpam-4735	185	16	c.	c.	PROPN
ejpam-4735	185	17	boonpok	boonpok	PROPN
ejpam-4735	185	18	,	,	PUNCT
ejpam-4735	185	19	p.	p.	NOUN
ejpam-4735	185	20	pue	pue	NOUN
ejpam-4735	185	21	-	-	PUNCT
ejpam-4735	185	22	on	on	ADP
ejpam-4735	185	23	/	/	SYM
ejpam-4735	185	24	eur	eur	NOUN
ejpam-4735	185	25	.	.	PUNCT
ejpam-4735	186	1	j.	j.	PROPN
ejpam-4735	186	2	pure	pure	PROPN
ejpam-4735	186	3	appl	appl	PROPN
ejpam-4735	186	4	.	.	PROPN
ejpam-4735	186	5	math	math	PROPN
ejpam-4735	186	6	,	,	PUNCT
ejpam-4735	186	7	17	17	NUM
ejpam-4735	186	8	(	(	PUNCT
ejpam-4735	186	9	1	1	NUM
ejpam-4735	186	10	)	)	PUNCT
ejpam-4735	186	11	(	(	PUNCT
ejpam-4735	186	12	2024	2024	NUM
ejpam-4735	186	13	)	)	PUNCT
ejpam-4735	186	14	,	,	PUNCT
ejpam-4735	186	15	147	147	NUM
ejpam-4735	186	16	-	-	SYM
ejpam-4735	186	17	157	157	NUM
ejpam-4735	186	18	152	152	NUM
ejpam-4735	186	19	let	let	VERB
ejpam-4735	186	20	z	z	PROPN
ejpam-4735	186	21	∈	∈	PROPN
ejpam-4735	186	22	δp(λ	δp(λ	NOUN
ejpam-4735	186	23	,	,	PUNCT
ejpam-4735	186	24	s)ker({x})∩δp(λ	s)ker({x})∩δp(λ	PROPN
ejpam-4735	186	25	,	,	PUNCT
ejpam-4735	186	26	s)ker({y	s)ker({y	NOUN
ejpam-4735	186	27	}	}	PUNCT
ejpam-4735	186	28	)	)	PUNCT
ejpam-4735	186	29	.	.	PUNCT
ejpam-4735	187	1	then	then	ADV
ejpam-4735	187	2	,	,	PUNCT
ejpam-4735	187	3	z	z	PROPN
ejpam-4735	187	4	∈	∈	PROPN
ejpam-4735	187	5	δp(λ	δp(λ	NOUN
ejpam-4735	187	6	,	,	PUNCT
ejpam-4735	187	7	s)ker({x	s)ker({x	NOUN
ejpam-4735	187	8	}	}	PUNCT
ejpam-4735	187	9	)	)	PUNCT
ejpam-4735	187	10	and	and	CCONJ
ejpam-4735	187	11	by	by	ADP
ejpam-4735	187	12	lemma	lemma	PROPN
ejpam-4735	187	13	4	4	NUM
ejpam-4735	187	14	,	,	PUNCT
ejpam-4735	187	15	x	x	SYM
ejpam-4735	187	16	∈	∈	PROPN
ejpam-4735	187	17	{	{	PUNCT
ejpam-4735	187	18	z}δp(λ	z}δp(λ	PROPN
ejpam-4735	187	19	,	,	PUNCT
ejpam-4735	187	20	s	s	NOUN
ejpam-4735	187	21	)	)	PUNCT
ejpam-4735	187	22	.	.	PUNCT
ejpam-4735	188	1	thus	thus	ADV
ejpam-4735	188	2	,	,	PUNCT
ejpam-4735	188	3	x	x	SYM
ejpam-4735	188	4	∈	∈	PROPN
ejpam-4735	188	5	{	{	PUNCT
ejpam-4735	188	6	z}δp(λ	z}δp(λ	PROPN
ejpam-4735	188	7	,	,	PUNCT
ejpam-4735	188	8	s	s	NOUN
ejpam-4735	188	9	)	)	PUNCT
ejpam-4735	188	10	∩	∩	NOUN
ejpam-4735	188	11	{	{	PUNCT
ejpam-4735	188	12	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	188	13	,	,	PUNCT
ejpam-4735	188	14	s	s	PART
ejpam-4735	188	15	)	)	PUNCT
ejpam-4735	188	16	and	and	CCONJ
ejpam-4735	188	17	by	by	ADP
ejpam-4735	188	18	corollary	corollary	ADJ
ejpam-4735	188	19	1	1	NUM
ejpam-4735	188	20	,	,	PUNCT
ejpam-4735	188	21	{	{	PUNCT
ejpam-4735	188	22	z}δp(λ	z}δp(λ	PROPN
ejpam-4735	188	23	,	,	PUNCT
ejpam-4735	188	24	s	s	PART
ejpam-4735	188	25	)	)	PUNCT
ejpam-4735	188	26	=	=	SYM
ejpam-4735	188	27	{	{	PUNCT
ejpam-4735	188	28	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	188	29	,	,	PUNCT
ejpam-4735	188	30	s	s	NOUN
ejpam-4735	188	31	)	)	PUNCT
ejpam-4735	188	32	.	.	PUNCT
ejpam-4735	189	1	similarly	similarly	ADV
ejpam-4735	189	2	,	,	PUNCT
ejpam-4735	189	3	we	we	PRON
ejpam-4735	189	4	have	have	VERB
ejpam-4735	189	5	{	{	PUNCT
ejpam-4735	189	6	z}δp(λ	z}δp(λ	PROPN
ejpam-4735	189	7	,	,	PUNCT
ejpam-4735	189	8	s	s	PART
ejpam-4735	189	9	)	)	PUNCT
ejpam-4735	189	10	=	=	SYM
ejpam-4735	189	11	{	{	PUNCT
ejpam-4735	189	12	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	189	13	,	,	PUNCT
ejpam-4735	189	14	s	s	NOUN
ejpam-4735	189	15	)	)	PUNCT
ejpam-4735	189	16	and	and	CCONJ
ejpam-4735	189	17	hence	hence	ADV
ejpam-4735	189	18	{	{	PUNCT
ejpam-4735	189	19	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	189	20	,	,	PUNCT
ejpam-4735	189	21	s	s	PART
ejpam-4735	189	22	)	)	PUNCT
ejpam-4735	189	23	=	=	PRON
ejpam-4735	189	24	{	{	PUNCT
ejpam-4735	189	25	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	189	26	,	,	PUNCT
ejpam-4735	189	27	s	s	NOUN
ejpam-4735	189	28	)	)	PUNCT
ejpam-4735	189	29	,	,	PUNCT
ejpam-4735	189	30	by	by	ADP
ejpam-4735	189	31	lemma	lemma	PROPN
ejpam-4735	189	32	4	4	NUM
ejpam-4735	189	33	,	,	PUNCT
ejpam-4735	189	34	δp(λ	δp(λ	NOUN
ejpam-4735	189	35	,	,	PUNCT
ejpam-4735	189	36	s)ker({x	s)ker({x	NOUN
ejpam-4735	189	37	}	}	PUNCT
ejpam-4735	189	38	)	)	PUNCT
ejpam-4735	190	1	=	=	SYM
ejpam-4735	190	2	δp(λ	δp(λ	NOUN
ejpam-4735	190	3	,	,	PUNCT
ejpam-4735	190	4	s)ker({y	s)ker({y	NOUN
ejpam-4735	190	5	}	}	PUNCT
ejpam-4735	190	6	)	)	PUNCT
ejpam-4735	190	7	.	.	PUNCT
ejpam-4735	191	1	conversely	conversely	ADV
ejpam-4735	191	2	,	,	PUNCT
ejpam-4735	191	3	we	we	PRON
ejpam-4735	191	4	show	show	VERB
ejpam-4735	191	5	the	the	DET
ejpam-4735	191	6	sufficiency	sufficiency	NOUN
ejpam-4735	191	7	by	by	ADP
ejpam-4735	191	8	using	use	VERB
ejpam-4735	191	9	corollary	corollary	ADJ
ejpam-4735	191	10	1	1	NUM
ejpam-4735	191	11	.	.	PUNCT
ejpam-4735	191	12	suppose	suppose	VERB
ejpam-4735	191	13	that	that	SCONJ
ejpam-4735	191	14	{	{	PUNCT
ejpam-4735	191	15	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	191	16	,	,	PUNCT
ejpam-4735	191	17	s	s	PART
ejpam-4735	191	18	)	)	PUNCT
ejpam-4735	191	19	̸=	̸=	PROPN
ejpam-4735	191	20	{	{	PUNCT
ejpam-4735	191	21	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	191	22	,	,	PUNCT
ejpam-4735	191	23	s	s	NOUN
ejpam-4735	191	24	)	)	PUNCT
ejpam-4735	191	25	.	.	PUNCT
ejpam-4735	192	1	by	by	ADP
ejpam-4735	192	2	lemma	lemma	PROPN
ejpam-4735	192	3	4	4	NUM
ejpam-4735	192	4	,	,	PUNCT
ejpam-4735	192	5	δp(λ	δp(λ	NOUN
ejpam-4735	192	6	,	,	PUNCT
ejpam-4735	192	7	s)ker({x	s)ker({x	NOUN
ejpam-4735	192	8	}	}	PUNCT
ejpam-4735	192	9	)	)	PUNCT
ejpam-4735	193	1	̸=	̸=	PROPN
ejpam-4735	193	2	δp(λ	δp(λ	NOUN
ejpam-4735	193	3	,	,	PUNCT
ejpam-4735	193	4	s)ker({y	s)ker({y	NOUN
ejpam-4735	193	5	}	}	PUNCT
ejpam-4735	193	6	)	)	PUNCT
ejpam-4735	193	7	and	and	CCONJ
ejpam-4735	193	8	hence	hence	ADV
ejpam-4735	193	9	δp(λ	δp(λ	NOUN
ejpam-4735	193	10	,	,	PUNCT
ejpam-4735	193	11	s)ker({x	s)ker({x	NOUN
ejpam-4735	193	12	}	}	PUNCT
ejpam-4735	193	13	)	)	PUNCT
ejpam-4735	193	14	∩	∩	NOUN
ejpam-4735	193	15	δp(λ	δp(λ	NOUN
ejpam-4735	193	16	,	,	PUNCT
ejpam-4735	193	17	s)ker({y	s)ker({y	NOUN
ejpam-4735	193	18	}	}	PUNCT
ejpam-4735	193	19	)	)	PUNCT
ejpam-4735	193	20	=	=	PUNCT
ejpam-4735	193	21	∅.	∅.	ADP
ejpam-4735	193	22	thus	thus	ADV
ejpam-4735	193	23	,	,	PUNCT
ejpam-4735	193	24	{	{	PUNCT
ejpam-4735	193	25	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	193	26	,	,	PUNCT
ejpam-4735	193	27	s	s	NOUN
ejpam-4735	193	28	)	)	PUNCT
ejpam-4735	193	29	∩	∩	NOUN
ejpam-4735	193	30	{	{	PUNCT
ejpam-4735	193	31	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	193	32	,	,	PUNCT
ejpam-4735	193	33	s	s	NOUN
ejpam-4735	193	34	)	)	PUNCT
ejpam-4735	193	35	=	=	PUNCT
ejpam-4735	193	36	∅.	∅.	NOUN
ejpam-4735	193	37	in	in	ADP
ejpam-4735	193	38	fact	fact	NOUN
ejpam-4735	193	39	,	,	PUNCT
ejpam-4735	193	40	assume	assume	VERB
ejpam-4735	193	41	that	that	SCONJ
ejpam-4735	193	42	z	z	PROPN
ejpam-4735	193	43	∈	∈	PROPN
ejpam-4735	193	44	{	{	PUNCT
ejpam-4735	193	45	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	193	46	,	,	PUNCT
ejpam-4735	193	47	s	s	NOUN
ejpam-4735	193	48	)	)	PUNCT
ejpam-4735	193	49	∩	∩	NOUN
ejpam-4735	193	50	{	{	PUNCT
ejpam-4735	193	51	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	193	52	,	,	PUNCT
ejpam-4735	193	53	s	s	NOUN
ejpam-4735	193	54	)	)	PUNCT
ejpam-4735	193	55	.	.	PUNCT
ejpam-4735	194	1	then	then	ADV
ejpam-4735	194	2	,	,	PUNCT
ejpam-4735	194	3	z	z	PROPN
ejpam-4735	194	4	∈	∈	PROPN
ejpam-4735	194	5	{	{	PUNCT
ejpam-4735	194	6	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	194	7	,	,	PUNCT
ejpam-4735	194	8	s	s	PART
ejpam-4735	194	9	)	)	PUNCT
ejpam-4735	194	10	implies	imply	VERB
ejpam-4735	194	11	x	x	X
ejpam-4735	194	12	∈	∈	PROPN
ejpam-4735	194	13	δp(λ	δp(λ	NOUN
ejpam-4735	194	14	,	,	PUNCT
ejpam-4735	194	15	s)ker({z	s)ker({z	NOUN
ejpam-4735	194	16	}	}	PUNCT
ejpam-4735	194	17	)	)	PUNCT
ejpam-4735	194	18	and	and	CCONJ
ejpam-4735	194	19	hence	hence	ADV
ejpam-4735	194	20	x	x	PART
ejpam-4735	194	21	∈	∈	PROPN
ejpam-4735	194	22	δp(λ	δp(λ	NOUN
ejpam-4735	194	23	,	,	PUNCT
ejpam-4735	194	24	s)ker({z})∩δp(λ	s)ker({z})∩δp(λ	NOUN
ejpam-4735	194	25	,	,	PUNCT
ejpam-4735	194	26	s)ker({x	s)ker({x	NOUN
ejpam-4735	194	27	}	}	PUNCT
ejpam-4735	194	28	)	)	PUNCT
ejpam-4735	194	29	.	.	PUNCT
ejpam-4735	195	1	by	by	ADP
ejpam-4735	195	2	the	the	DET
ejpam-4735	195	3	hypothesis	hypothesis	NOUN
ejpam-4735	195	4	,	,	PUNCT
ejpam-4735	195	5	δp(λ	δp(λ	NOUN
ejpam-4735	195	6	,	,	PUNCT
ejpam-4735	195	7	s)ker({z	s)ker({z	NOUN
ejpam-4735	195	8	}	}	PUNCT
ejpam-4735	195	9	)	)	PUNCT
ejpam-4735	195	10	=	=	SYM
ejpam-4735	195	11	δp(λ	δp(λ	NOUN
ejpam-4735	195	12	,	,	PUNCT
ejpam-4735	195	13	s)ker({x	s)ker({x	NOUN
ejpam-4735	195	14	}	}	PUNCT
ejpam-4735	195	15	)	)	PUNCT
ejpam-4735	195	16	and	and	CCONJ
ejpam-4735	195	17	by	by	ADP
ejpam-4735	195	18	lemma	lemma	PROPN
ejpam-4735	195	19	4	4	NUM
ejpam-4735	195	20	,	,	PUNCT
ejpam-4735	195	21	{	{	PUNCT
ejpam-4735	195	22	z}δp(λ	z}δp(λ	PROPN
ejpam-4735	195	23	,	,	PUNCT
ejpam-4735	195	24	s	s	PART
ejpam-4735	195	25	)	)	PUNCT
ejpam-4735	195	26	=	=	SYM
ejpam-4735	195	27	{	{	PUNCT
ejpam-4735	195	28	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	195	29	,	,	PUNCT
ejpam-4735	195	30	s	s	NOUN
ejpam-4735	195	31	)	)	PUNCT
ejpam-4735	195	32	.	.	PUNCT
ejpam-4735	196	1	similarly	similarly	ADV
ejpam-4735	196	2	,	,	PUNCT
ejpam-4735	196	3	we	we	PRON
ejpam-4735	196	4	have	have	VERB
ejpam-4735	196	5	{	{	PUNCT
ejpam-4735	196	6	z}δp(λ	z}δp(λ	PROPN
ejpam-4735	196	7	,	,	PUNCT
ejpam-4735	196	8	s	s	PART
ejpam-4735	196	9	)	)	PUNCT
ejpam-4735	196	10	=	=	SYM
ejpam-4735	196	11	{	{	PUNCT
ejpam-4735	196	12	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	196	13	,	,	PUNCT
ejpam-4735	196	14	s	s	NOUN
ejpam-4735	196	15	)	)	PUNCT
ejpam-4735	196	16	and	and	CCONJ
ejpam-4735	196	17	hence	hence	ADV
ejpam-4735	196	18	{	{	PUNCT
ejpam-4735	196	19	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	196	20	,	,	PUNCT
ejpam-4735	196	21	s	s	PART
ejpam-4735	196	22	)	)	PUNCT
ejpam-4735	196	23	=	=	PRON
ejpam-4735	196	24	{	{	PUNCT
ejpam-4735	196	25	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	196	26	,	,	PUNCT
ejpam-4735	196	27	s	s	NOUN
ejpam-4735	196	28	)	)	PUNCT
ejpam-4735	196	29	.	.	PUNCT
ejpam-4735	197	1	this	this	PRON
ejpam-4735	197	2	contradicts	contradict	VERB
ejpam-4735	197	3	that	that	SCONJ
ejpam-4735	197	4	{	{	PUNCT
ejpam-4735	197	5	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	197	6	,	,	PUNCT
ejpam-4735	197	7	s	s	PART
ejpam-4735	197	8	)	)	PUNCT
ejpam-4735	197	9	̸=	̸=	PROPN
ejpam-4735	197	10	{	{	PUNCT
ejpam-4735	197	11	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	197	12	,	,	PUNCT
ejpam-4735	197	13	s	s	NOUN
ejpam-4735	197	14	)	)	PUNCT
ejpam-4735	197	15	.	.	PUNCT
ejpam-4735	198	1	thus	thus	ADV
ejpam-4735	198	2	,	,	PUNCT
ejpam-4735	198	3	{	{	PUNCT
ejpam-4735	198	4	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	198	5	,	,	PUNCT
ejpam-4735	198	6	s)∩{y}δp(λ	s)∩{y}δp(λ	PROPN
ejpam-4735	198	7	,	,	PUNCT
ejpam-4735	198	8	s	s	PART
ejpam-4735	198	9	)	)	PUNCT
ejpam-4735	198	10	=	=	PUNCT
ejpam-4735	198	11	∅.	∅.	ADP
ejpam-4735	198	12	this	this	PRON
ejpam-4735	198	13	shows	show	VERB
ejpam-4735	198	14	that	that	SCONJ
ejpam-4735	198	15	(	(	PUNCT
ejpam-4735	198	16	x	x	X
ejpam-4735	198	17	,	,	PUNCT
ejpam-4735	198	18	τ	τ	X
ejpam-4735	198	19	)	)	PUNCT
ejpam-4735	198	20	is	be	AUX
ejpam-4735	198	21	δp(λ	δp(λ	NOUN
ejpam-4735	198	22	,	,	PUNCT
ejpam-4735	198	23	s)-r0	s)-r0	X
ejpam-4735	198	24	.	.	PUNCT
ejpam-4735	199	1	theorem	theorem	VERB
ejpam-4735	199	2	4	4	NUM
ejpam-4735	199	3	.	.	X
ejpam-4735	200	1	for	for	ADP
ejpam-4735	200	2	a	a	DET
ejpam-4735	200	3	topological	topological	ADJ
ejpam-4735	200	4	space	space	NOUN
ejpam-4735	200	5	(	(	PUNCT
ejpam-4735	200	6	x	x	X
ejpam-4735	200	7	,	,	PUNCT
ejpam-4735	200	8	τ	τ	PROPN
ejpam-4735	200	9	)	)	PUNCT
ejpam-4735	200	10	,	,	PUNCT
ejpam-4735	200	11	the	the	DET
ejpam-4735	200	12	following	follow	VERB
ejpam-4735	200	13	properties	property	NOUN
ejpam-4735	200	14	are	be	AUX
ejpam-4735	200	15	equivalent	equivalent	ADJ
ejpam-4735	200	16	:	:	PUNCT
ejpam-4735	200	17	(	(	PUNCT
ejpam-4735	200	18	1	1	X
ejpam-4735	200	19	)	)	PUNCT
ejpam-4735	200	20	(	(	PUNCT
ejpam-4735	200	21	x	x	X
ejpam-4735	200	22	,	,	PUNCT
ejpam-4735	200	23	τ	τ	X
ejpam-4735	200	24	)	)	PUNCT
ejpam-4735	200	25	is	be	AUX
ejpam-4735	200	26	δp(λ	δp(λ	NOUN
ejpam-4735	200	27	,	,	PUNCT
ejpam-4735	200	28	s)-r0	s)-r0	X
ejpam-4735	200	29	.	.	PUNCT
ejpam-4735	201	1	(	(	PUNCT
ejpam-4735	201	2	2	2	X
ejpam-4735	201	3	)	)	PUNCT
ejpam-4735	201	4	x	x	SYM
ejpam-4735	201	5	∈	∈	PROPN
ejpam-4735	201	6	{	{	PUNCT
ejpam-4735	201	7	y}δp(λ	y}δp(λ	NOUN
ejpam-4735	201	8	,	,	PUNCT
ejpam-4735	201	9	s	s	NOUN
ejpam-4735	201	10	)	)	PUNCT
ejpam-4735	202	1	if	if	SCONJ
ejpam-4735	202	2	and	and	CCONJ
ejpam-4735	202	3	only	only	ADV
ejpam-4735	202	4	if	if	SCONJ
ejpam-4735	202	5	y	y	PROPN
ejpam-4735	202	6	∈	∈	PROPN
ejpam-4735	202	7	{	{	PUNCT
ejpam-4735	202	8	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	202	9	,	,	PUNCT
ejpam-4735	202	10	s	s	NOUN
ejpam-4735	202	11	)	)	PUNCT
ejpam-4735	202	12	.	.	PUNCT
ejpam-4735	203	1	proof	proof	NOUN
ejpam-4735	203	2	.	.	PUNCT
ejpam-4735	204	1	(	(	PUNCT
ejpam-4735	204	2	1	1	X
ejpam-4735	204	3	)	)	PUNCT
ejpam-4735	204	4	⇒	⇒	NOUN
ejpam-4735	204	5	(	(	PUNCT
ejpam-4735	204	6	2	2	NUM
ejpam-4735	204	7	):	):	PUNCT
ejpam-4735	204	8	suppose	suppose	VERB
ejpam-4735	204	9	that	that	SCONJ
ejpam-4735	204	10	x	x	SYM
ejpam-4735	204	11	∈	∈	PROPN
ejpam-4735	204	12	{	{	PUNCT
ejpam-4735	204	13	y}δp(λ	y}δp(λ	NOUN
ejpam-4735	204	14	,	,	PUNCT
ejpam-4735	204	15	s	s	NOUN
ejpam-4735	204	16	)	)	PUNCT
ejpam-4735	204	17	.	.	PUNCT
ejpam-4735	205	1	by	by	ADP
ejpam-4735	205	2	lemma	lemma	PROPN
ejpam-4735	205	3	4	4	NUM
ejpam-4735	205	4	,	,	PUNCT
ejpam-4735	205	5	y	y	PROPN
ejpam-4735	205	6	∈	∈	PROPN
ejpam-4735	205	7	δp(λ	δp(λ	NOUN
ejpam-4735	205	8	,	,	PUNCT
ejpam-4735	205	9	s)ker({x	s)ker({x	NOUN
ejpam-4735	205	10	}	}	PUNCT
ejpam-4735	205	11	)	)	PUNCT
ejpam-4735	205	12	and	and	CCONJ
ejpam-4735	205	13	hence	hence	ADV
ejpam-4735	205	14	δp(λ	δp(λ	NOUN
ejpam-4735	205	15	,	,	PUNCT
ejpam-4735	205	16	s)ker({x	s)ker({x	NOUN
ejpam-4735	205	17	}	}	PUNCT
ejpam-4735	205	18	)	)	PUNCT
ejpam-4735	205	19	∩	∩	NOUN
ejpam-4735	205	20	δp(λ	δp(λ	NOUN
ejpam-4735	205	21	,	,	PUNCT
ejpam-4735	205	22	s)ker({y	s)ker({y	NOUN
ejpam-4735	205	23	}	}	PUNCT
ejpam-4735	205	24	)	)	PUNCT
ejpam-4735	205	25	̸=	̸=	PROPN
ejpam-4735	205	26	∅.	∅.	VERB
ejpam-4735	205	27	by	by	ADP
ejpam-4735	205	28	theorem	theorem	ADJ
ejpam-4735	205	29	3	3	NUM
ejpam-4735	205	30	,	,	PUNCT
ejpam-4735	205	31	δp(λ	δp(λ	NOUN
ejpam-4735	205	32	,	,	PUNCT
ejpam-4735	205	33	s)ker({x	s)ker({x	NOUN
ejpam-4735	205	34	}	}	PUNCT
ejpam-4735	205	35	)	)	PUNCT
ejpam-4735	205	36	=	=	SYM
ejpam-4735	205	37	δp(λ	δp(λ	NOUN
ejpam-4735	205	38	,	,	PUNCT
ejpam-4735	205	39	s)ker({y	s)ker({y	NOUN
ejpam-4735	205	40	}	}	PUNCT
ejpam-4735	205	41	)	)	PUNCT
ejpam-4735	205	42	and	and	CCONJ
ejpam-4735	205	43	hence	hence	ADV
ejpam-4735	205	44	x	x	PART
ejpam-4735	205	45	∈	∈	PROPN
ejpam-4735	205	46	δp(λ	δp(λ	NOUN
ejpam-4735	205	47	,	,	PUNCT
ejpam-4735	205	48	s)ker({y	s)ker({y	NOUN
ejpam-4735	205	49	}	}	PUNCT
ejpam-4735	205	50	)	)	PUNCT
ejpam-4735	205	51	.	.	PUNCT
ejpam-4735	206	1	thus	thus	ADV
ejpam-4735	206	2	,	,	PUNCT
ejpam-4735	206	3	by	by	ADP
ejpam-4735	206	4	lemma	lemma	PROPN
ejpam-4735	206	5	4	4	NUM
ejpam-4735	206	6	,	,	PUNCT
ejpam-4735	206	7	y	y	PROPN
ejpam-4735	206	8	∈	∈	PROPN
ejpam-4735	206	9	{	{	PUNCT
ejpam-4735	206	10	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	206	11	,	,	PUNCT
ejpam-4735	206	12	s	s	NOUN
ejpam-4735	206	13	)	)	PUNCT
ejpam-4735	206	14	.	.	PUNCT
ejpam-4735	207	1	the	the	DET
ejpam-4735	207	2	converse	converse	NOUN
ejpam-4735	207	3	is	be	AUX
ejpam-4735	207	4	similarly	similarly	ADV
ejpam-4735	207	5	shown	show	VERB
ejpam-4735	207	6	.	.	PUNCT
ejpam-4735	208	1	(	(	PUNCT
ejpam-4735	208	2	2	2	X
ejpam-4735	208	3	)	)	PUNCT
ejpam-4735	208	4	⇒	⇒	NOUN
ejpam-4735	208	5	(	(	PUNCT
ejpam-4735	208	6	1	1	NUM
ejpam-4735	208	7	):	):	PUNCT
ejpam-4735	208	8	let	let	VERB
ejpam-4735	208	9	u	u	PRON
ejpam-4735	208	10	∈	∈	PROPN
ejpam-4735	208	11	δp(λ	δp(λ	NOUN
ejpam-4735	208	12	,	,	PUNCT
ejpam-4735	208	13	s)o(x	s)o(x	PROPN
ejpam-4735	208	14	,	,	PUNCT
ejpam-4735	208	15	τ	τ	X
ejpam-4735	208	16	)	)	PUNCT
ejpam-4735	208	17	and	and	CCONJ
ejpam-4735	208	18	x	x	PUNCT
ejpam-4735	208	19	∈	∈	PROPN
ejpam-4735	208	20	u	u	NOUN
ejpam-4735	208	21	.	.	PUNCT
ejpam-4735	209	1	if	if	SCONJ
ejpam-4735	209	2	y	y	PROPN
ejpam-4735	209	3	̸∈	̸∈	PROPN
ejpam-4735	209	4	u	u	PROPN
ejpam-4735	209	5	,	,	PUNCT
ejpam-4735	209	6	then	then	ADV
ejpam-4735	209	7	u	u	NOUN
ejpam-4735	209	8	∩	∩	NOUN
ejpam-4735	209	9	{	{	PUNCT
ejpam-4735	209	10	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	209	11	,	,	PUNCT
ejpam-4735	209	12	s	s	NOUN
ejpam-4735	209	13	)	)	PUNCT
ejpam-4735	209	14	=	=	PUNCT
ejpam-4735	209	15	∅.	∅.	ADP
ejpam-4735	209	16	thus	thus	ADV
ejpam-4735	209	17	,	,	PUNCT
ejpam-4735	209	18	x	x	PROPN
ejpam-4735	209	19	̸∈	̸∈	PROPN
ejpam-4735	209	20	{	{	PUNCT
ejpam-4735	209	21	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	209	22	,	,	PUNCT
ejpam-4735	209	23	s	s	PART
ejpam-4735	209	24	)	)	PUNCT
ejpam-4735	209	25	and	and	CCONJ
ejpam-4735	209	26	y	y	PROPN
ejpam-4735	209	27	̸∈	̸∈	PROPN
ejpam-4735	209	28	{	{	PUNCT
ejpam-4735	209	29	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	209	30	,	,	PUNCT
ejpam-4735	209	31	s	s	NOUN
ejpam-4735	209	32	)	)	PUNCT
ejpam-4735	209	33	.	.	PUNCT
ejpam-4735	210	1	this	this	PRON
ejpam-4735	210	2	implies	imply	VERB
ejpam-4735	210	3	that	that	SCONJ
ejpam-4735	210	4	{	{	PUNCT
ejpam-4735	210	5	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	210	6	,	,	PUNCT
ejpam-4735	210	7	s	s	PART
ejpam-4735	210	8	)	)	PUNCT
ejpam-4735	210	9	⊆	⊆	NUM
ejpam-4735	210	10	u	u	NOUN
ejpam-4735	210	11	.	.	PUNCT
ejpam-4735	211	1	therefore	therefore	ADV
ejpam-4735	211	2	,	,	PUNCT
ejpam-4735	211	3	(	(	PUNCT
ejpam-4735	211	4	x	x	X
ejpam-4735	211	5	,	,	PUNCT
ejpam-4735	211	6	τ	τ	X
ejpam-4735	211	7	)	)	PUNCT
ejpam-4735	211	8	is	be	AUX
ejpam-4735	211	9	δp(λ	δp(λ	NOUN
ejpam-4735	211	10	,	,	PUNCT
ejpam-4735	211	11	s)-r0	s)-r0	X
ejpam-4735	211	12	.	.	PUNCT
ejpam-4735	212	1	theorem	theorem	ADJ
ejpam-4735	212	2	5	5	NUM
ejpam-4735	212	3	.	.	X
ejpam-4735	213	1	for	for	ADP
ejpam-4735	213	2	a	a	DET
ejpam-4735	213	3	topological	topological	ADJ
ejpam-4735	213	4	space	space	NOUN
ejpam-4735	213	5	(	(	PUNCT
ejpam-4735	213	6	x	x	X
ejpam-4735	213	7	,	,	PUNCT
ejpam-4735	213	8	τ	τ	PROPN
ejpam-4735	213	9	)	)	PUNCT
ejpam-4735	213	10	,	,	PUNCT
ejpam-4735	213	11	the	the	DET
ejpam-4735	213	12	following	follow	VERB
ejpam-4735	213	13	properties	property	NOUN
ejpam-4735	213	14	are	be	AUX
ejpam-4735	213	15	equivalent	equivalent	ADJ
ejpam-4735	213	16	:	:	PUNCT
ejpam-4735	213	17	c.	c.	PROPN
ejpam-4735	213	18	boonpok	boonpok	PROPN
ejpam-4735	213	19	,	,	PUNCT
ejpam-4735	213	20	p.	p.	NOUN
ejpam-4735	213	21	pue	pue	NOUN
ejpam-4735	213	22	-	-	PUNCT
ejpam-4735	213	23	on	on	ADP
ejpam-4735	213	24	/	/	SYM
ejpam-4735	213	25	eur	eur	NOUN
ejpam-4735	213	26	.	.	PUNCT
ejpam-4735	214	1	j.	j.	PROPN
ejpam-4735	214	2	pure	pure	PROPN
ejpam-4735	214	3	appl	appl	PROPN
ejpam-4735	214	4	.	.	PROPN
ejpam-4735	214	5	math	math	PROPN
ejpam-4735	214	6	,	,	PUNCT
ejpam-4735	214	7	17	17	NUM
ejpam-4735	214	8	(	(	PUNCT
ejpam-4735	214	9	1	1	NUM
ejpam-4735	214	10	)	)	PUNCT
ejpam-4735	214	11	(	(	PUNCT
ejpam-4735	214	12	2024	2024	NUM
ejpam-4735	214	13	)	)	PUNCT
ejpam-4735	214	14	,	,	PUNCT
ejpam-4735	214	15	147	147	NUM
ejpam-4735	214	16	-	-	SYM
ejpam-4735	214	17	157	157	NUM
ejpam-4735	214	18	153	153	NUM
ejpam-4735	214	19	(	(	PUNCT
ejpam-4735	214	20	1	1	NUM
ejpam-4735	214	21	)	)	PUNCT
ejpam-4735	214	22	(	(	PUNCT
ejpam-4735	214	23	x	x	X
ejpam-4735	214	24	,	,	PUNCT
ejpam-4735	214	25	τ	τ	X
ejpam-4735	214	26	)	)	PUNCT
ejpam-4735	214	27	is	be	AUX
ejpam-4735	214	28	δp(λ	δp(λ	NOUN
ejpam-4735	214	29	,	,	PUNCT
ejpam-4735	214	30	s)-r0	s)-r0	X
ejpam-4735	214	31	.	.	PUNCT
ejpam-4735	215	1	(	(	PUNCT
ejpam-4735	215	2	2	2	X
ejpam-4735	215	3	)	)	PUNCT
ejpam-4735	215	4	for	for	ADP
ejpam-4735	215	5	each	each	DET
ejpam-4735	215	6	nonempty	nonempty	NOUN
ejpam-4735	215	7	subset	subset	VERB
ejpam-4735	215	8	a	a	PRON
ejpam-4735	215	9	of	of	ADP
ejpam-4735	215	10	x	x	PUNCT
ejpam-4735	215	11	and	and	CCONJ
ejpam-4735	215	12	each	each	DET
ejpam-4735	215	13	u	u	PROPN
ejpam-4735	215	14	∈	∈	PROPN
ejpam-4735	215	15	δp(λ	δp(λ	NOUN
ejpam-4735	215	16	,	,	PUNCT
ejpam-4735	215	17	s)o(x	s)o(x	PROPN
ejpam-4735	215	18	,	,	PUNCT
ejpam-4735	215	19	τ	τ	X
ejpam-4735	215	20	)	)	PUNCT
ejpam-4735	215	21	such	such	ADJ
ejpam-4735	215	22	that	that	DET
ejpam-4735	215	23	a∩u	a∩u	PROPN
ejpam-4735	215	24	̸=	̸=	NOUN
ejpam-4735	215	25	∅	∅	NOUN
ejpam-4735	215	26	,	,	PUNCT
ejpam-4735	215	27	there	there	PRON
ejpam-4735	215	28	exists	exist	VERB
ejpam-4735	215	29	a	a	DET
ejpam-4735	215	30	δp(λ	δp(λ	NOUN
ejpam-4735	215	31	,	,	PUNCT
ejpam-4735	215	32	s)-closed	s)-close	VERB
ejpam-4735	215	33	set	set	NOUN
ejpam-4735	215	34	f	f	PRON
ejpam-4735	215	35	such	such	ADJ
ejpam-4735	215	36	that	that	SCONJ
ejpam-4735	215	37	a	a	DET
ejpam-4735	215	38	∩	∩	ADJ
ejpam-4735	215	39	f	f	PROPN
ejpam-4735	215	40	̸=	̸=	PROPN
ejpam-4735	215	41	∅	∅	NOUN
ejpam-4735	215	42	and	and	CCONJ
ejpam-4735	215	43	f	f	PROPN
ejpam-4735	215	44	⊆	⊆	NUM
ejpam-4735	215	45	u	u	NOUN
ejpam-4735	215	46	.	.	PUNCT
ejpam-4735	216	1	(	(	PUNCT
ejpam-4735	216	2	3	3	X
ejpam-4735	216	3	)	)	PUNCT
ejpam-4735	216	4	f	f	NOUN
ejpam-4735	216	5	=	=	SYM
ejpam-4735	216	6	δp(λ	δp(λ	PROPN
ejpam-4735	216	7	,	,	PUNCT
ejpam-4735	216	8	s)ker(f	s)ker(f	NUM
ejpam-4735	216	9	)	)	PUNCT
ejpam-4735	216	10	for	for	ADP
ejpam-4735	216	11	each	each	DET
ejpam-4735	216	12	δp(λ	δp(λ	NOUN
ejpam-4735	216	13	,	,	PUNCT
ejpam-4735	216	14	s)-closed	s)-close	VERB
ejpam-4735	216	15	set	set	NOUN
ejpam-4735	216	16	f	f	X
ejpam-4735	216	17	.	.	PUNCT
ejpam-4735	217	1	(	(	PUNCT
ejpam-4735	217	2	4	4	X
ejpam-4735	217	3	)	)	PUNCT
ejpam-4735	217	4	{	{	PUNCT
ejpam-4735	217	5	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	217	6	,	,	PUNCT
ejpam-4735	217	7	s	s	NOUN
ejpam-4735	217	8	)	)	PUNCT
ejpam-4735	217	9	=	=	SYM
ejpam-4735	217	10	δp(λ	δp(λ	NOUN
ejpam-4735	217	11	,	,	PUNCT
ejpam-4735	217	12	s)ker({x	s)ker({x	NOUN
ejpam-4735	217	13	}	}	PUNCT
ejpam-4735	217	14	)	)	PUNCT
ejpam-4735	218	1	for	for	ADP
ejpam-4735	218	2	each	each	DET
ejpam-4735	218	3	x	x	SYM
ejpam-4735	218	4	∈	∈	PROPN
ejpam-4735	218	5	x.	x.	NOUN
ejpam-4735	218	6	(	(	PUNCT
ejpam-4735	218	7	5	5	NUM
ejpam-4735	218	8	)	)	PUNCT
ejpam-4735	218	9	{	{	PUNCT
ejpam-4735	218	10	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	218	11	,	,	PUNCT
ejpam-4735	218	12	s	s	PART
ejpam-4735	218	13	)	)	PUNCT
ejpam-4735	218	14	⊆	⊆	NUM
ejpam-4735	218	15	δp(λ	δp(λ	NOUN
ejpam-4735	218	16	,	,	PUNCT
ejpam-4735	218	17	s)ker({x	s)ker({x	NUM
ejpam-4735	218	18	}	}	PUNCT
ejpam-4735	218	19	)	)	PUNCT
ejpam-4735	218	20	for	for	ADP
ejpam-4735	218	21	each	each	DET
ejpam-4735	218	22	x	x	SYM
ejpam-4735	218	23	∈	∈	PROPN
ejpam-4735	218	24	x.	x.	NOUN
ejpam-4735	218	25	proof	proof	NOUN
ejpam-4735	218	26	.	.	PUNCT
ejpam-4735	219	1	(	(	PUNCT
ejpam-4735	219	2	1	1	X
ejpam-4735	219	3	)	)	PUNCT
ejpam-4735	219	4	⇒	⇒	NOUN
ejpam-4735	219	5	(	(	PUNCT
ejpam-4735	219	6	2	2	NUM
ejpam-4735	219	7	):	):	PUNCT
ejpam-4735	219	8	let	let	VERB
ejpam-4735	219	9	a	a	PRON
ejpam-4735	219	10	be	be	AUX
ejpam-4735	219	11	a	a	DET
ejpam-4735	219	12	nonempty	nonempty	ADJ
ejpam-4735	219	13	subset	subset	NOUN
ejpam-4735	219	14	of	of	ADP
ejpam-4735	219	15	x	x	PUNCT
ejpam-4735	219	16	and	and	CCONJ
ejpam-4735	219	17	u	u	PROPN
ejpam-4735	219	18	∈	∈	PROPN
ejpam-4735	219	19	δp(λ	δp(λ	NOUN
ejpam-4735	219	20	,	,	PUNCT
ejpam-4735	219	21	s)o(x	s)o(x	PROPN
ejpam-4735	219	22	,	,	PUNCT
ejpam-4735	219	23	τ	τ	X
ejpam-4735	219	24	)	)	PUNCT
ejpam-4735	219	25	such	such	ADJ
ejpam-4735	219	26	that	that	SCONJ
ejpam-4735	219	27	a	a	DET
ejpam-4735	219	28	∩	∩	ADJ
ejpam-4735	219	29	u	u	NOUN
ejpam-4735	219	30	̸=	̸=	PROPN
ejpam-4735	219	31	∅.	∅.	VERB
ejpam-4735	219	32	then	then	ADV
ejpam-4735	219	33	,	,	PUNCT
ejpam-4735	219	34	there	there	PRON
ejpam-4735	219	35	exists	exist	VERB
ejpam-4735	219	36	x	x	X
ejpam-4735	219	37	∈	∈	PROPN
ejpam-4735	219	38	a	a	DET
ejpam-4735	219	39	∩	∩	ADJ
ejpam-4735	219	40	u	u	NOUN
ejpam-4735	219	41	and	and	CCONJ
ejpam-4735	219	42	hence	hence	ADV
ejpam-4735	219	43	{	{	PUNCT
ejpam-4735	219	44	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	219	45	,	,	PUNCT
ejpam-4735	219	46	s	s	PART
ejpam-4735	219	47	)	)	PUNCT
ejpam-4735	219	48	⊆	⊆	NUM
ejpam-4735	219	49	u	u	NOUN
ejpam-4735	219	50	.	.	PUNCT
ejpam-4735	220	1	put	put	VERB
ejpam-4735	220	2	f	f	X
ejpam-4735	221	1	=	=	PRON
ejpam-4735	221	2	{	{	PUNCT
ejpam-4735	221	3	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	221	4	,	,	PUNCT
ejpam-4735	221	5	s	s	NOUN
ejpam-4735	221	6	)	)	PUNCT
ejpam-4735	221	7	.	.	PUNCT
ejpam-4735	222	1	then	then	ADV
ejpam-4735	222	2	,	,	PUNCT
ejpam-4735	222	3	f	f	PROPN
ejpam-4735	222	4	is	be	AUX
ejpam-4735	222	5	δp(λ	δp(λ	NOUN
ejpam-4735	222	6	,	,	PUNCT
ejpam-4735	222	7	s)-closed	s)-close	VERB
ejpam-4735	222	8	such	such	ADJ
ejpam-4735	222	9	that	that	SCONJ
ejpam-4735	222	10	a	a	DET
ejpam-4735	222	11	∩	∩	ADJ
ejpam-4735	222	12	f	f	PROPN
ejpam-4735	222	13	̸=	̸=	PROPN
ejpam-4735	222	14	∅	∅	NOUN
ejpam-4735	222	15	and	and	CCONJ
ejpam-4735	222	16	f	f	PROPN
ejpam-4735	222	17	⊆	⊆	NUM
ejpam-4735	222	18	u	u	NOUN
ejpam-4735	222	19	.	.	PUNCT
ejpam-4735	223	1	(	(	PUNCT
ejpam-4735	223	2	2	2	X
ejpam-4735	223	3	)	)	PUNCT
ejpam-4735	223	4	⇒	⇒	NOUN
ejpam-4735	223	5	(	(	PUNCT
ejpam-4735	223	6	3	3	NUM
ejpam-4735	223	7	):	):	PUNCT
ejpam-4735	223	8	let	let	VERB
ejpam-4735	223	9	f	f	PRON
ejpam-4735	223	10	be	be	AUX
ejpam-4735	223	11	any	any	DET
ejpam-4735	223	12	δp(λ	δp(λ	NOUN
ejpam-4735	223	13	,	,	PUNCT
ejpam-4735	223	14	s)-closed	s)-close	VERB
ejpam-4735	223	15	set	set	NOUN
ejpam-4735	223	16	of	of	ADP
ejpam-4735	223	17	x.	x.	NOUN
ejpam-4735	223	18	by	by	ADP
ejpam-4735	223	19	lemma	lemma	PROPN
ejpam-4735	223	20	3	3	NUM
ejpam-4735	223	21	,	,	PUNCT
ejpam-4735	223	22	we	we	PRON
ejpam-4735	223	23	have	have	VERB
ejpam-4735	223	24	f	f	PROPN
ejpam-4735	223	25	⊆	⊆	NUM
ejpam-4735	223	26	δp(λ	δp(λ	NOUN
ejpam-4735	223	27	,	,	PUNCT
ejpam-4735	223	28	s)ker(f	s)ker(f	NUM
ejpam-4735	223	29	)	)	PUNCT
ejpam-4735	223	30	.	.	PUNCT
ejpam-4735	224	1	next	next	ADV
ejpam-4735	224	2	,	,	PUNCT
ejpam-4735	224	3	we	we	PRON
ejpam-4735	224	4	show	show	VERB
ejpam-4735	224	5	f	f	PROPN
ejpam-4735	224	6	⊇	⊇	PROPN
ejpam-4735	224	7	δp(λ	δp(λ	PROPN
ejpam-4735	224	8	,	,	PUNCT
ejpam-4735	224	9	s)ker(f	s)ker(f	NUM
ejpam-4735	224	10	)	)	PUNCT
ejpam-4735	224	11	.	.	PUNCT
ejpam-4735	225	1	let	let	VERB
ejpam-4735	225	2	x	x	SYM
ejpam-4735	225	3	̸∈	̸∈	PROPN
ejpam-4735	225	4	f	f	PROPN
ejpam-4735	225	5	.	.	PUNCT
ejpam-4735	226	1	then	then	ADV
ejpam-4735	226	2	,	,	PUNCT
ejpam-4735	226	3	x	x	PUNCT
ejpam-4735	226	4	∈	∈	NOUN
ejpam-4735	226	5	x	x	X
ejpam-4735	226	6	−	−	PROPN
ejpam-4735	226	7	f	f	PROPN
ejpam-4735	226	8	∈	∈	PROPN
ejpam-4735	226	9	δp(λ	δp(λ	NOUN
ejpam-4735	226	10	,	,	PUNCT
ejpam-4735	226	11	s)o(x	s)o(x	PROPN
ejpam-4735	226	12	,	,	PUNCT
ejpam-4735	226	13	τ	τ	X
ejpam-4735	226	14	)	)	PUNCT
ejpam-4735	226	15	and	and	CCONJ
ejpam-4735	226	16	by	by	ADP
ejpam-4735	226	17	(	(	PUNCT
ejpam-4735	226	18	2	2	NUM
ejpam-4735	226	19	)	)	PUNCT
ejpam-4735	226	20	,	,	PUNCT
ejpam-4735	226	21	there	there	PRON
ejpam-4735	226	22	exists	exist	VERB
ejpam-4735	226	23	a	a	DET
ejpam-4735	226	24	δp(λ	δp(λ	NOUN
ejpam-4735	226	25	,	,	PUNCT
ejpam-4735	226	26	s)-closed	s)-close	VERB
ejpam-4735	226	27	set	set	NOUN
ejpam-4735	226	28	k	k	ADP
ejpam-4735	226	29	such	such	ADJ
ejpam-4735	226	30	that	that	SCONJ
ejpam-4735	226	31	x	x	SYM
ejpam-4735	226	32	∈	∈	PROPN
ejpam-4735	226	33	k	k	PROPN
ejpam-4735	226	34	and	and	CCONJ
ejpam-4735	226	35	k	k	PROPN
ejpam-4735	226	36	⊆	⊆	NUM
ejpam-4735	226	37	x	x	SYM
ejpam-4735	226	38	−	−	PROPN
ejpam-4735	226	39	f	f	NOUN
ejpam-4735	226	40	.	.	PUNCT
ejpam-4735	227	1	now	now	ADV
ejpam-4735	227	2	,	,	PUNCT
ejpam-4735	227	3	put	put	VERB
ejpam-4735	227	4	u	u	NOUN
ejpam-4735	227	5	=	=	NOUN
ejpam-4735	227	6	x−k	x−k	PROPN
ejpam-4735	227	7	.	.	PUNCT
ejpam-4735	228	1	then	then	ADV
ejpam-4735	228	2	,	,	PUNCT
ejpam-4735	228	3	f	f	PROPN
ejpam-4735	228	4	⊆	⊆	NUM
ejpam-4735	228	5	u	u	PROPN
ejpam-4735	228	6	∈	∈	PROPN
ejpam-4735	228	7	δp(λ	δp(λ	NOUN
ejpam-4735	228	8	,	,	PUNCT
ejpam-4735	228	9	s)o(x	s)o(x	PROPN
ejpam-4735	228	10	,	,	PUNCT
ejpam-4735	228	11	τ	τ	X
ejpam-4735	228	12	)	)	PUNCT
ejpam-4735	228	13	and	and	CCONJ
ejpam-4735	228	14	x	x	PUNCT
ejpam-4735	228	15	̸∈	̸∈	PROPN
ejpam-4735	228	16	u	u	PROPN
ejpam-4735	228	17	.	.	PUNCT
ejpam-4735	229	1	thus	thus	ADV
ejpam-4735	229	2	,	,	PUNCT
ejpam-4735	229	3	x	x	PROPN
ejpam-4735	229	4	̸∈	̸∈	PROPN
ejpam-4735	229	5	δp(λ	δp(λ	NOUN
ejpam-4735	229	6	,	,	PUNCT
ejpam-4735	229	7	s)ker(f	s)ker(f	NUM
ejpam-4735	229	8	)	)	PUNCT
ejpam-4735	229	9	.	.	PUNCT
ejpam-4735	230	1	this	this	PRON
ejpam-4735	230	2	shows	show	VERB
ejpam-4735	230	3	that	that	SCONJ
ejpam-4735	230	4	f	f	PROPN
ejpam-4735	230	5	⊇	⊇	PROPN
ejpam-4735	230	6	δp(λ	δp(λ	PROPN
ejpam-4735	230	7	,	,	PUNCT
ejpam-4735	230	8	s)ker(f	s)ker(f	NUM
ejpam-4735	230	9	)	)	PUNCT
ejpam-4735	230	10	.	.	PUNCT
ejpam-4735	231	1	(	(	PUNCT
ejpam-4735	231	2	3	3	X
ejpam-4735	231	3	)	)	PUNCT
ejpam-4735	231	4	⇒	⇒	NOUN
ejpam-4735	231	5	(	(	PUNCT
ejpam-4735	231	6	4	4	NUM
ejpam-4735	231	7	):	):	PUNCT
ejpam-4735	231	8	let	let	VERB
ejpam-4735	231	9	x	x	PUNCT
ejpam-4735	231	10	∈	∈	PROPN
ejpam-4735	231	11	x	x	X
ejpam-4735	231	12	and	and	CCONJ
ejpam-4735	231	13	y	y	PROPN
ejpam-4735	231	14	̸∈	̸∈	PROPN
ejpam-4735	231	15	δp(λ	δp(λ	NOUN
ejpam-4735	231	16	,	,	PUNCT
ejpam-4735	231	17	s)ker({x	s)ker({x	NUM
ejpam-4735	231	18	}	}	PUNCT
ejpam-4735	231	19	)	)	PUNCT
ejpam-4735	231	20	.	.	PUNCT
ejpam-4735	232	1	there	there	PRON
ejpam-4735	232	2	exists	exist	VERB
ejpam-4735	232	3	u	u	PROPN
ejpam-4735	232	4	∈	∈	PROPN
ejpam-4735	232	5	δp(λ	δp(λ	NOUN
ejpam-4735	232	6	,	,	PUNCT
ejpam-4735	232	7	s)o(x	s)o(x	PROPN
ejpam-4735	232	8	,	,	PUNCT
ejpam-4735	232	9	τ	τ	X
ejpam-4735	232	10	)	)	PUNCT
ejpam-4735	232	11	such	such	ADJ
ejpam-4735	232	12	that	that	SCONJ
ejpam-4735	232	13	x	x	SYM
ejpam-4735	232	14	∈	∈	PROPN
ejpam-4735	232	15	u	u	NOUN
ejpam-4735	232	16	and	and	CCONJ
ejpam-4735	232	17	y	y	PROPN
ejpam-4735	232	18	̸∈	̸∈	PROPN
ejpam-4735	232	19	u	u	PROPN
ejpam-4735	232	20	.	.	PUNCT
ejpam-4735	233	1	thus	thus	ADV
ejpam-4735	233	2	,	,	PUNCT
ejpam-4735	233	3	u	u	PROPN
ejpam-4735	233	4	∩	∩	NOUN
ejpam-4735	233	5	{	{	PUNCT
ejpam-4735	233	6	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	233	7	,	,	PUNCT
ejpam-4735	233	8	s	s	NOUN
ejpam-4735	233	9	)	)	PUNCT
ejpam-4735	233	10	=	=	PUNCT
ejpam-4735	233	11	∅.	∅.	X
ejpam-4735	233	12	by	by	ADP
ejpam-4735	233	13	(	(	PUNCT
ejpam-4735	233	14	3	3	NUM
ejpam-4735	233	15	)	)	PUNCT
ejpam-4735	233	16	,	,	PUNCT
ejpam-4735	233	17	u	u	PROPN
ejpam-4735	233	18	∩	∩	NOUN
ejpam-4735	233	19	δp(λ	δp(λ	NOUN
ejpam-4735	233	20	,	,	PUNCT
ejpam-4735	233	21	s)ker({y}δp(λ	s)ker({y}δp(λ	NOUN
ejpam-4735	233	22	,	,	PUNCT
ejpam-4735	233	23	s	s	NOUN
ejpam-4735	233	24	)	)	PUNCT
ejpam-4735	233	25	)	)	PUNCT
ejpam-4735	233	26	=	=	PUNCT
ejpam-4735	233	27	∅.	∅.	NOUN
ejpam-4735	233	28	since	since	SCONJ
ejpam-4735	233	29	x	x	PROPN
ejpam-4735	233	30	̸∈	̸∈	PROPN
ejpam-4735	233	31	δp(λ	δp(λ	NOUN
ejpam-4735	233	32	,	,	PUNCT
ejpam-4735	233	33	s)ker({y}δp(λ	s)ker({y}δp(λ	NOUN
ejpam-4735	233	34	,	,	PUNCT
ejpam-4735	233	35	s	s	NOUN
ejpam-4735	233	36	)	)	PUNCT
ejpam-4735	233	37	)	)	PUNCT
ejpam-4735	233	38	,	,	PUNCT
ejpam-4735	233	39	there	there	PRON
ejpam-4735	233	40	exists	exist	VERB
ejpam-4735	233	41	v	v	ADP
ejpam-4735	233	42	∈	∈	PROPN
ejpam-4735	233	43	δp(λ	δp(λ	NOUN
ejpam-4735	233	44	,	,	PUNCT
ejpam-4735	233	45	s)o(x	s)o(x	PROPN
ejpam-4735	233	46	,	,	PUNCT
ejpam-4735	233	47	τ	τ	X
ejpam-4735	233	48	)	)	PUNCT
ejpam-4735	233	49	such	such	ADJ
ejpam-4735	233	50	that	that	SCONJ
ejpam-4735	233	51	{	{	PUNCT
ejpam-4735	233	52	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	233	53	,	,	PUNCT
ejpam-4735	233	54	s	s	NOUN
ejpam-4735	233	55	)	)	PUNCT
ejpam-4735	233	56	⊆	⊆	NUM
ejpam-4735	233	57	v	v	NOUN
ejpam-4735	233	58	and	and	CCONJ
ejpam-4735	233	59	x	x	PART
ejpam-4735	233	60	̸∈	̸∈	PROPN
ejpam-4735	233	61	v	v	NUM
ejpam-4735	233	62	.	.	PUNCT
ejpam-4735	234	1	thus	thus	ADV
ejpam-4735	234	2	,	,	PUNCT
ejpam-4735	234	3	v	v	ADP
ejpam-4735	234	4	∩	∩	NOUN
ejpam-4735	234	5	{	{	PUNCT
ejpam-4735	234	6	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	234	7	,	,	PUNCT
ejpam-4735	234	8	s	s	PART
ejpam-4735	234	9	)	)	PUNCT
ejpam-4735	234	10	=	=	PUNCT
ejpam-4735	234	11	∅.	∅.	NOUN
ejpam-4735	234	12	since	since	SCONJ
ejpam-4735	234	13	y	y	PROPN
ejpam-4735	234	14	∈	∈	PROPN
ejpam-4735	234	15	v	v	NOUN
ejpam-4735	234	16	,	,	PUNCT
ejpam-4735	234	17	we	we	PRON
ejpam-4735	234	18	have	have	VERB
ejpam-4735	234	19	y	y	PROPN
ejpam-4735	234	20	̸∈	̸∈	PROPN
ejpam-4735	234	21	{	{	PUNCT
ejpam-4735	234	22	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	234	23	,	,	PUNCT
ejpam-4735	234	24	s	s	PART
ejpam-4735	234	25	)	)	PUNCT
ejpam-4735	234	26	and	and	CCONJ
ejpam-4735	234	27	hence	hence	ADV
ejpam-4735	234	28	{	{	PUNCT
ejpam-4735	234	29	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	234	30	,	,	PUNCT
ejpam-4735	234	31	s	s	PART
ejpam-4735	234	32	)	)	PUNCT
ejpam-4735	234	33	⊆	⊆	NUM
ejpam-4735	234	34	δp(λ	δp(λ	NOUN
ejpam-4735	234	35	,	,	PUNCT
ejpam-4735	234	36	s)ker({x	s)ker({x	NOUN
ejpam-4735	234	37	}	}	PUNCT
ejpam-4735	234	38	)	)	PUNCT
ejpam-4735	234	39	.	.	PUNCT
ejpam-4735	235	1	moreover	moreover	ADV
ejpam-4735	235	2	,	,	PUNCT
ejpam-4735	235	3	{	{	PUNCT
ejpam-4735	235	4	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	235	5	,	,	PUNCT
ejpam-4735	235	6	s	s	PART
ejpam-4735	235	7	)	)	PUNCT
ejpam-4735	235	8	⊆	⊆	NUM
ejpam-4735	235	9	δp(λ	δp(λ	NOUN
ejpam-4735	235	10	,	,	PUNCT
ejpam-4735	235	11	s)ker({x	s)ker({x	NUM
ejpam-4735	235	12	}	}	PUNCT
ejpam-4735	235	13	)	)	PUNCT
ejpam-4735	235	14	⊆	⊆	NUM
ejpam-4735	235	15	δp(λ	δp(λ	NOUN
ejpam-4735	235	16	,	,	PUNCT
ejpam-4735	235	17	s)ker({x}δp(λ	s)ker({x}δp(λ	NOUN
ejpam-4735	235	18	,	,	PUNCT
ejpam-4735	235	19	s	s	NOUN
ejpam-4735	235	20	)	)	PUNCT
ejpam-4735	235	21	)	)	PUNCT
ejpam-4735	236	1	=	=	PRON
ejpam-4735	236	2	{	{	PUNCT
ejpam-4735	236	3	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	236	4	,	,	PUNCT
ejpam-4735	236	5	s	s	NOUN
ejpam-4735	236	6	)	)	PUNCT
ejpam-4735	236	7	.	.	PUNCT
ejpam-4735	237	1	this	this	PRON
ejpam-4735	237	2	shows	show	VERB
ejpam-4735	237	3	that	that	SCONJ
ejpam-4735	237	4	{	{	PUNCT
ejpam-4735	237	5	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	237	6	,	,	PUNCT
ejpam-4735	237	7	s	s	NOUN
ejpam-4735	237	8	)	)	PUNCT
ejpam-4735	237	9	=	=	SYM
ejpam-4735	237	10	δp(λ	δp(λ	NOUN
ejpam-4735	237	11	,	,	PUNCT
ejpam-4735	237	12	s)ker({x	s)ker({x	NOUN
ejpam-4735	237	13	}	}	PUNCT
ejpam-4735	237	14	)	)	PUNCT
ejpam-4735	237	15	.	.	PUNCT
ejpam-4735	238	1	(	(	PUNCT
ejpam-4735	238	2	4	4	X
ejpam-4735	238	3	)	)	PUNCT
ejpam-4735	238	4	⇒	⇒	NOUN
ejpam-4735	238	5	(	(	PUNCT
ejpam-4735	238	6	5	5	NUM
ejpam-4735	238	7	):	):	PUNCT
ejpam-4735	238	8	the	the	DET
ejpam-4735	238	9	proof	proof	NOUN
ejpam-4735	238	10	is	be	AUX
ejpam-4735	238	11	obvious	obvious	ADJ
ejpam-4735	238	12	.	.	PUNCT
ejpam-4735	239	1	(	(	PUNCT
ejpam-4735	239	2	5	5	X
ejpam-4735	239	3	)	)	PUNCT
ejpam-4735	239	4	⇒	⇒	NOUN
ejpam-4735	239	5	(	(	PUNCT
ejpam-4735	239	6	1	1	NUM
ejpam-4735	239	7	):	):	PUNCT
ejpam-4735	239	8	let	let	VERB
ejpam-4735	239	9	u	u	PRON
ejpam-4735	239	10	∈	∈	PROPN
ejpam-4735	239	11	δp(λ	δp(λ	NOUN
ejpam-4735	239	12	,	,	PUNCT
ejpam-4735	239	13	s)o(x	s)o(x	PROPN
ejpam-4735	239	14	,	,	PUNCT
ejpam-4735	239	15	τ	τ	X
ejpam-4735	239	16	)	)	PUNCT
ejpam-4735	239	17	and	and	CCONJ
ejpam-4735	239	18	x	x	PUNCT
ejpam-4735	239	19	∈	∈	PROPN
ejpam-4735	239	20	u	u	NOUN
ejpam-4735	239	21	.	.	PUNCT
ejpam-4735	240	1	if	if	SCONJ
ejpam-4735	240	2	y	y	PROPN
ejpam-4735	240	3	̸∈	̸∈	PROPN
ejpam-4735	240	4	u	u	PROPN
ejpam-4735	240	5	,	,	PUNCT
ejpam-4735	240	6	then	then	ADV
ejpam-4735	240	7	u	u	NOUN
ejpam-4735	240	8	∩	∩	NOUN
ejpam-4735	240	9	{	{	PUNCT
ejpam-4735	240	10	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	240	11	,	,	PUNCT
ejpam-4735	240	12	s	s	NOUN
ejpam-4735	240	13	)	)	PUNCT
ejpam-4735	240	14	=	=	SYM
ejpam-4735	240	15	∅	∅	NOUN
ejpam-4735	240	16	and	and	CCONJ
ejpam-4735	240	17	x	x	PART
ejpam-4735	240	18	̸∈	̸∈	PROPN
ejpam-4735	240	19	{	{	PUNCT
ejpam-4735	240	20	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	240	21	,	,	PUNCT
ejpam-4735	240	22	s	s	NOUN
ejpam-4735	240	23	)	)	PUNCT
ejpam-4735	240	24	.	.	PUNCT
ejpam-4735	241	1	by	by	ADP
ejpam-4735	241	2	lemma	lemma	PROPN
ejpam-4735	241	3	4	4	NUM
ejpam-4735	241	4	,	,	PUNCT
ejpam-4735	241	5	y	y	PROPN
ejpam-4735	241	6	̸∈	̸∈	PROPN
ejpam-4735	241	7	δp(λ	δp(λ	NOUN
ejpam-4735	241	8	,	,	PUNCT
ejpam-4735	241	9	s)ker({x	s)ker({x	NUM
ejpam-4735	241	10	}	}	PUNCT
ejpam-4735	241	11	)	)	PUNCT
ejpam-4735	241	12	and	and	CCONJ
ejpam-4735	241	13	by	by	ADP
ejpam-4735	241	14	(	(	PUNCT
ejpam-4735	241	15	5	5	NUM
ejpam-4735	241	16	)	)	PUNCT
ejpam-4735	241	17	,	,	PUNCT
ejpam-4735	241	18	y	y	PROPN
ejpam-4735	241	19	̸∈	̸∈	PROPN
ejpam-4735	241	20	{	{	PUNCT
ejpam-4735	241	21	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	241	22	,	,	PUNCT
ejpam-4735	241	23	s	s	NOUN
ejpam-4735	241	24	)	)	PUNCT
ejpam-4735	241	25	.	.	PUNCT
ejpam-4735	242	1	thus	thus	ADV
ejpam-4735	242	2	,	,	PUNCT
ejpam-4735	242	3	{	{	PUNCT
ejpam-4735	242	4	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	242	5	,	,	PUNCT
ejpam-4735	242	6	s	s	PART
ejpam-4735	242	7	)	)	PUNCT
ejpam-4735	242	8	⊆	⊆	NUM
ejpam-4735	242	9	u	u	NOUN
ejpam-4735	242	10	and	and	CCONJ
ejpam-4735	242	11	hence	hence	ADV
ejpam-4735	242	12	(	(	PUNCT
ejpam-4735	242	13	x	x	X
ejpam-4735	242	14	,	,	PUNCT
ejpam-4735	242	15	τ	τ	X
ejpam-4735	242	16	)	)	PUNCT
ejpam-4735	242	17	is	be	AUX
ejpam-4735	242	18	δp(λ	δp(λ	NOUN
ejpam-4735	242	19	,	,	PUNCT
ejpam-4735	242	20	s)-r0	s)-r0	X
ejpam-4735	242	21	.	.	PUNCT
ejpam-4735	243	1	corollary	corollary	ADJ
ejpam-4735	243	2	2	2	NUM
ejpam-4735	243	3	.	.	PUNCT
ejpam-4735	244	1	a	a	DET
ejpam-4735	244	2	topological	topological	ADJ
ejpam-4735	244	3	space	space	NOUN
ejpam-4735	244	4	(	(	PUNCT
ejpam-4735	244	5	x	x	X
ejpam-4735	244	6	,	,	PUNCT
ejpam-4735	244	7	τ	τ	X
ejpam-4735	244	8	)	)	PUNCT
ejpam-4735	244	9	is	be	AUX
ejpam-4735	244	10	δp(λ	δp(λ	NOUN
ejpam-4735	244	11	,	,	PUNCT
ejpam-4735	244	12	s)-r0	s)-r0	PRON
ejpam-4735	244	13	if	if	SCONJ
ejpam-4735	244	14	and	and	CCONJ
ejpam-4735	244	15	only	only	ADV
ejpam-4735	244	16	if	if	SCONJ
ejpam-4735	244	17	δp(λ	δp(λ	NOUN
ejpam-4735	244	18	,	,	PUNCT
ejpam-4735	244	19	s)ker({x	s)ker({x	NOUN
ejpam-4735	244	20	}	}	PUNCT
ejpam-4735	244	21	)	)	PUNCT
ejpam-4735	245	1	⊆	⊆	NUM
ejpam-4735	245	2	{	{	PUNCT
ejpam-4735	245	3	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	245	4	,	,	PUNCT
ejpam-4735	245	5	s	s	NOUN
ejpam-4735	245	6	)	)	PUNCT
ejpam-4735	245	7	for	for	ADP
ejpam-4735	245	8	each	each	DET
ejpam-4735	245	9	x	x	SYM
ejpam-4735	245	10	∈	∈	PROPN
ejpam-4735	245	11	x.	x.	NOUN
ejpam-4735	245	12	c.	c.	PROPN
ejpam-4735	245	13	boonpok	boonpok	PROPN
ejpam-4735	245	14	,	,	PUNCT
ejpam-4735	245	15	p.	p.	NOUN
ejpam-4735	245	16	pue	pue	NOUN
ejpam-4735	245	17	-	-	PUNCT
ejpam-4735	245	18	on	on	ADP
ejpam-4735	245	19	/	/	SYM
ejpam-4735	245	20	eur	eur	NOUN
ejpam-4735	245	21	.	.	PUNCT
ejpam-4735	246	1	j.	j.	PROPN
ejpam-4735	246	2	pure	pure	PROPN
ejpam-4735	246	3	appl	appl	PROPN
ejpam-4735	246	4	.	.	PROPN
ejpam-4735	246	5	math	math	PROPN
ejpam-4735	246	6	,	,	PUNCT
ejpam-4735	246	7	17	17	NUM
ejpam-4735	246	8	(	(	PUNCT
ejpam-4735	246	9	1	1	NUM
ejpam-4735	246	10	)	)	PUNCT
ejpam-4735	246	11	(	(	PUNCT
ejpam-4735	246	12	2024	2024	NUM
ejpam-4735	246	13	)	)	PUNCT
ejpam-4735	246	14	,	,	PUNCT
ejpam-4735	246	15	147	147	NUM
ejpam-4735	246	16	-	-	SYM
ejpam-4735	246	17	157	157	NUM
ejpam-4735	246	18	154	154	NUM
ejpam-4735	246	19	proof	proof	NOUN
ejpam-4735	246	20	.	.	PUNCT
ejpam-4735	247	1	this	this	PRON
ejpam-4735	247	2	is	be	AUX
ejpam-4735	247	3	obvious	obvious	ADJ
ejpam-4735	247	4	by	by	ADP
ejpam-4735	247	5	theorem	theorem	NOUN
ejpam-4735	247	6	5	5	NUM
ejpam-4735	247	7	.	.	PUNCT
ejpam-4735	247	8	conversely	conversely	ADV
ejpam-4735	247	9	,	,	PUNCT
ejpam-4735	247	10	let	let	VERB
ejpam-4735	247	11	x	x	PRON
ejpam-4735	247	12	∈	∈	PROPN
ejpam-4735	247	13	{	{	PUNCT
ejpam-4735	247	14	y}δp(λ	y}δp(λ	NOUN
ejpam-4735	247	15	,	,	PUNCT
ejpam-4735	247	16	s	s	NOUN
ejpam-4735	247	17	)	)	PUNCT
ejpam-4735	247	18	.	.	PUNCT
ejpam-4735	248	1	thus	thus	ADV
ejpam-4735	248	2	,	,	PUNCT
ejpam-4735	248	3	by	by	ADP
ejpam-4735	248	4	lemma	lemma	PROPN
ejpam-4735	248	5	4	4	NUM
ejpam-4735	248	6	,	,	PUNCT
ejpam-4735	248	7	y	y	PROPN
ejpam-4735	248	8	∈	∈	PROPN
ejpam-4735	248	9	δp(λ	δp(λ	NOUN
ejpam-4735	248	10	,	,	PUNCT
ejpam-4735	248	11	s)ker({x	s)ker({x	NOUN
ejpam-4735	248	12	}	}	PUNCT
ejpam-4735	248	13	)	)	PUNCT
ejpam-4735	248	14	and	and	CCONJ
ejpam-4735	248	15	hence	hence	ADV
ejpam-4735	248	16	y	y	PROPN
ejpam-4735	248	17	∈	∈	PROPN
ejpam-4735	248	18	{	{	PUNCT
ejpam-4735	248	19	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	248	20	,	,	PUNCT
ejpam-4735	248	21	s	s	NOUN
ejpam-4735	248	22	)	)	PUNCT
ejpam-4735	248	23	.	.	PUNCT
ejpam-4735	249	1	similarly	similarly	ADV
ejpam-4735	249	2	,	,	PUNCT
ejpam-4735	249	3	if	if	SCONJ
ejpam-4735	249	4	y	y	PROPN
ejpam-4735	249	5	∈	∈	PROPN
ejpam-4735	249	6	{	{	PUNCT
ejpam-4735	249	7	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	249	8	,	,	PUNCT
ejpam-4735	249	9	s	s	PART
ejpam-4735	249	10	)	)	PUNCT
ejpam-4735	249	11	,	,	PUNCT
ejpam-4735	249	12	then	then	ADV
ejpam-4735	249	13	x	x	X
ejpam-4735	249	14	∈	∈	PROPN
ejpam-4735	249	15	{	{	PUNCT
ejpam-4735	249	16	y}δp(λ	y}δp(λ	NOUN
ejpam-4735	249	17	,	,	PUNCT
ejpam-4735	249	18	s	s	NOUN
ejpam-4735	249	19	)	)	PUNCT
ejpam-4735	249	20	.	.	PUNCT
ejpam-4735	250	1	it	it	PRON
ejpam-4735	250	2	follows	follow	VERB
ejpam-4735	250	3	from	from	ADP
ejpam-4735	250	4	theorem	theorem	ADJ
ejpam-4735	250	5	4	4	NUM
ejpam-4735	250	6	that	that	PRON
ejpam-4735	250	7	(	(	PUNCT
ejpam-4735	250	8	x	x	X
ejpam-4735	250	9	,	,	PUNCT
ejpam-4735	250	10	τ	τ	X
ejpam-4735	250	11	)	)	PUNCT
ejpam-4735	250	12	is	be	AUX
ejpam-4735	250	13	δp(λ	δp(λ	NOUN
ejpam-4735	250	14	,	,	PUNCT
ejpam-4735	250	15	s)-r0	s)-r0	X
ejpam-4735	250	16	.	.	PUNCT
ejpam-4735	251	1	definition	definition	NOUN
ejpam-4735	251	2	4	4	NUM
ejpam-4735	251	3	.	.	PUNCT
ejpam-4735	252	1	[	[	X
ejpam-4735	252	2	3	3	X
ejpam-4735	252	3	]	]	X
ejpam-4735	252	4	let	let	VERB
ejpam-4735	252	5	(	(	PUNCT
ejpam-4735	252	6	x	x	NOUN
ejpam-4735	252	7	,	,	PUNCT
ejpam-4735	252	8	τ	τ	X
ejpam-4735	252	9	)	)	PUNCT
ejpam-4735	252	10	be	be	VERB
ejpam-4735	252	11	a	a	DET
ejpam-4735	252	12	topological	topological	ADJ
ejpam-4735	252	13	space	space	NOUN
ejpam-4735	252	14	and	and	CCONJ
ejpam-4735	252	15	x	x	PUNCT
ejpam-4735	252	16	∈	∈	PROPN
ejpam-4735	252	17	x.	x.	NOUN
ejpam-4735	252	18	a	a	DET
ejpam-4735	252	19	subset	subset	NOUN
ejpam-4735	252	20	⟨x⟩δp(λ	⟨x⟩δp(λ	NOUN
ejpam-4735	252	21	,	,	PUNCT
ejpam-4735	252	22	s	s	PART
ejpam-4735	252	23	)	)	PUNCT
ejpam-4735	252	24	is	be	AUX
ejpam-4735	252	25	defined	define	VERB
ejpam-4735	252	26	as	as	SCONJ
ejpam-4735	252	27	follows	follow	VERB
ejpam-4735	252	28	:	:	PUNCT
ejpam-4735	253	1	⟨x⟩δp(λ	⟨x⟩δp(λ	NOUN
ejpam-4735	253	2	,	,	PUNCT
ejpam-4735	253	3	s	s	NOUN
ejpam-4735	253	4	)	)	PUNCT
ejpam-4735	253	5	=	=	SYM
ejpam-4735	253	6	δp(λ	δp(λ	NOUN
ejpam-4735	253	7	,	,	PUNCT
ejpam-4735	253	8	s)ker({x	s)ker({x	NOUN
ejpam-4735	253	9	}	}	PUNCT
ejpam-4735	253	10	)	)	PUNCT
ejpam-4735	253	11	∩	∩	NOUN
ejpam-4735	253	12	{	{	PUNCT
ejpam-4735	253	13	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	253	14	,	,	PUNCT
ejpam-4735	253	15	s	s	PART
ejpam-4735	253	16	)	)	PUNCT
ejpam-4735	253	17	.	.	PUNCT
ejpam-4735	254	1	theorem	theorem	VERB
ejpam-4735	254	2	6	6	NUM
ejpam-4735	254	3	.	.	PUNCT
ejpam-4735	255	1	a	a	DET
ejpam-4735	255	2	topological	topological	ADJ
ejpam-4735	255	3	space	space	NOUN
ejpam-4735	255	4	(	(	PUNCT
ejpam-4735	255	5	x	x	X
ejpam-4735	255	6	,	,	PUNCT
ejpam-4735	255	7	τ	τ	X
ejpam-4735	255	8	)	)	PUNCT
ejpam-4735	255	9	is	be	AUX
ejpam-4735	255	10	δp(λ	δp(λ	NOUN
ejpam-4735	255	11	,	,	PUNCT
ejpam-4735	255	12	s)-r0	s)-r0	PRON
ejpam-4735	255	13	if	if	SCONJ
ejpam-4735	255	14	and	and	CCONJ
ejpam-4735	255	15	only	only	ADV
ejpam-4735	255	16	if	if	SCONJ
ejpam-4735	255	17	⟨x⟩δp(λ	⟨x⟩δp(λ	NOUN
ejpam-4735	255	18	,	,	PUNCT
ejpam-4735	255	19	s	s	PART
ejpam-4735	255	20	)	)	PUNCT
ejpam-4735	255	21	=	=	SYM
ejpam-4735	255	22	{	{	PUNCT
ejpam-4735	255	23	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	255	24	,	,	PUNCT
ejpam-4735	255	25	s	s	NOUN
ejpam-4735	255	26	)	)	PUNCT
ejpam-4735	255	27	for	for	ADP
ejpam-4735	255	28	each	each	DET
ejpam-4735	255	29	x	x	SYM
ejpam-4735	255	30	∈	∈	PROPN
ejpam-4735	255	31	x.	x.	NOUN
ejpam-4735	255	32	proof	proof	NOUN
ejpam-4735	255	33	.	.	PUNCT
ejpam-4735	256	1	let	let	VERB
ejpam-4735	257	1	x	x	SYM
ejpam-4735	257	2	∈	∈	PROPN
ejpam-4735	257	3	x.	x.	NOUN
ejpam-4735	257	4	by	by	ADP
ejpam-4735	257	5	theorem	theorem	NOUN
ejpam-4735	257	6	5	5	NUM
ejpam-4735	257	7	,	,	PUNCT
ejpam-4735	257	8	δp(λ	δp(λ	NOUN
ejpam-4735	257	9	,	,	PUNCT
ejpam-4735	257	10	s)ker({x	s)ker({x	NOUN
ejpam-4735	257	11	}	}	PUNCT
ejpam-4735	257	12	)	)	PUNCT
ejpam-4735	258	1	=	=	PRON
ejpam-4735	258	2	{	{	PUNCT
ejpam-4735	258	3	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	258	4	,	,	PUNCT
ejpam-4735	258	5	s	s	NOUN
ejpam-4735	258	6	)	)	PUNCT
ejpam-4735	258	7	.	.	PUNCT
ejpam-4735	259	1	thus	thus	ADV
ejpam-4735	259	2	,	,	PUNCT
ejpam-4735	259	3	⟨x⟩δp(λ	⟨x⟩δp(λ	NOUN
ejpam-4735	259	4	,	,	PUNCT
ejpam-4735	259	5	s	s	PART
ejpam-4735	259	6	)	)	PUNCT
ejpam-4735	259	7	=	=	SYM
ejpam-4735	259	8	δp(λ	δp(λ	NOUN
ejpam-4735	259	9	,	,	PUNCT
ejpam-4735	259	10	s)ker({x	s)ker({x	NOUN
ejpam-4735	259	11	}	}	PUNCT
ejpam-4735	259	12	)	)	PUNCT
ejpam-4735	259	13	∩	∩	NOUN
ejpam-4735	259	14	{	{	PUNCT
ejpam-4735	259	15	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	259	16	,	,	PUNCT
ejpam-4735	259	17	s	s	PART
ejpam-4735	259	18	)	)	PUNCT
ejpam-4735	259	19	=	=	SYM
ejpam-4735	259	20	{	{	PUNCT
ejpam-4735	259	21	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	259	22	,	,	PUNCT
ejpam-4735	259	23	s	s	NOUN
ejpam-4735	259	24	)	)	PUNCT
ejpam-4735	259	25	.	.	PUNCT
ejpam-4735	260	1	conversely	conversely	ADV
ejpam-4735	260	2	,	,	PUNCT
ejpam-4735	260	3	let	let	VERB
ejpam-4735	260	4	x	x	X
ejpam-4735	260	5	∈	∈	PROPN
ejpam-4735	260	6	x.	x.	NOUN
ejpam-4735	260	7	by	by	ADP
ejpam-4735	260	8	the	the	DET
ejpam-4735	260	9	hypothesis	hypothesis	NOUN
ejpam-4735	260	10	,	,	PUNCT
ejpam-4735	260	11	{	{	PUNCT
ejpam-4735	260	12	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	260	13	,	,	PUNCT
ejpam-4735	260	14	s	s	NOUN
ejpam-4735	260	15	)	)	PUNCT
ejpam-4735	260	16	=	=	SYM
ejpam-4735	260	17	⟨x⟩δp(λ	⟨x⟩δp(λ	NOUN
ejpam-4735	260	18	,	,	PUNCT
ejpam-4735	260	19	s	s	NOUN
ejpam-4735	260	20	)	)	PUNCT
ejpam-4735	260	21	=	=	SYM
ejpam-4735	260	22	δp(λ	δp(λ	NOUN
ejpam-4735	260	23	,	,	PUNCT
ejpam-4735	260	24	s)ker({x	s)ker({x	NOUN
ejpam-4735	260	25	}	}	PUNCT
ejpam-4735	260	26	)	)	PUNCT
ejpam-4735	260	27	∩	∩	NOUN
ejpam-4735	260	28	{	{	PUNCT
ejpam-4735	260	29	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	260	30	,	,	PUNCT
ejpam-4735	260	31	s	s	PART
ejpam-4735	260	32	)	)	PUNCT
ejpam-4735	260	33	⊆	⊆	NUM
ejpam-4735	260	34	δp(λ	δp(λ	NOUN
ejpam-4735	260	35	,	,	PUNCT
ejpam-4735	260	36	s)ker({x	s)ker({x	NOUN
ejpam-4735	260	37	}	}	PUNCT
ejpam-4735	260	38	)	)	PUNCT
ejpam-4735	260	39	.	.	PUNCT
ejpam-4735	261	1	it	it	PRON
ejpam-4735	261	2	follows	follow	VERB
ejpam-4735	261	3	from	from	ADP
ejpam-4735	261	4	theorem	theorem	ADJ
ejpam-4735	261	5	5	5	NUM
ejpam-4735	261	6	that	that	PRON
ejpam-4735	261	7	(	(	PUNCT
ejpam-4735	261	8	x	x	X
ejpam-4735	261	9	,	,	PUNCT
ejpam-4735	261	10	τ	τ	X
ejpam-4735	261	11	)	)	PUNCT
ejpam-4735	261	12	is	be	AUX
ejpam-4735	261	13	δp(λ	δp(λ	NOUN
ejpam-4735	261	14	,	,	PUNCT
ejpam-4735	261	15	s)-r0	s)-r0	X
ejpam-4735	261	16	.	.	PUNCT
ejpam-4735	262	1	definition	definition	NOUN
ejpam-4735	262	2	5	5	NUM
ejpam-4735	262	3	.	.	PUNCT
ejpam-4735	263	1	a	a	DET
ejpam-4735	263	2	topological	topological	ADJ
ejpam-4735	263	3	space	space	NOUN
ejpam-4735	263	4	(	(	PUNCT
ejpam-4735	263	5	x	x	X
ejpam-4735	263	6	,	,	PUNCT
ejpam-4735	263	7	τ	τ	X
ejpam-4735	263	8	)	)	PUNCT
ejpam-4735	263	9	is	be	AUX
ejpam-4735	263	10	said	say	VERB
ejpam-4735	263	11	to	to	PART
ejpam-4735	263	12	be	be	AUX
ejpam-4735	263	13	δp(λ	δp(λ	NOUN
ejpam-4735	263	14	,	,	PUNCT
ejpam-4735	263	15	s)-r1	s)-r1	NOUN
ejpam-4735	263	16	if	if	SCONJ
ejpam-4735	263	17	for	for	ADP
ejpam-4735	263	18	each	each	DET
ejpam-4735	263	19	points	point	NOUN
ejpam-4735	263	20	x	x	PRON
ejpam-4735	263	21	,	,	PUNCT
ejpam-4735	263	22	y	y	PROPN
ejpam-4735	263	23	in	in	ADP
ejpam-4735	263	24	x	x	PUNCT
ejpam-4735	263	25	with	with	ADP
ejpam-4735	263	26	{	{	PUNCT
ejpam-4735	263	27	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	263	28	,	,	PUNCT
ejpam-4735	263	29	s	s	PART
ejpam-4735	263	30	)	)	PUNCT
ejpam-4735	263	31	̸=	̸=	PROPN
ejpam-4735	263	32	{	{	PUNCT
ejpam-4735	263	33	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	263	34	,	,	PUNCT
ejpam-4735	263	35	s	s	NOUN
ejpam-4735	263	36	)	)	PUNCT
ejpam-4735	263	37	,	,	PUNCT
ejpam-4735	263	38	there	there	PRON
ejpam-4735	263	39	exist	exist	VERB
ejpam-4735	263	40	disjoint	disjoint	NOUN
ejpam-4735	263	41	δp(λ	δp(λ	NOUN
ejpam-4735	263	42	,	,	PUNCT
ejpam-4735	263	43	s)-open	s)-open	PUNCT
ejpam-4735	263	44	sets	set	VERB
ejpam-4735	263	45	u	u	NOUN
ejpam-4735	263	46	and	and	CCONJ
ejpam-4735	263	47	v	v	ADP
ejpam-4735	263	48	such	such	ADJ
ejpam-4735	263	49	that	that	SCONJ
ejpam-4735	263	50	{	{	PUNCT
ejpam-4735	263	51	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	263	52	,	,	PUNCT
ejpam-4735	263	53	s	s	PART
ejpam-4735	263	54	)	)	PUNCT
ejpam-4735	263	55	⊆	⊆	NUM
ejpam-4735	263	56	u	u	NOUN
ejpam-4735	263	57	and	and	CCONJ
ejpam-4735	263	58	{	{	PUNCT
ejpam-4735	263	59	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	263	60	,	,	PUNCT
ejpam-4735	263	61	s	s	NOUN
ejpam-4735	263	62	)	)	PUNCT
ejpam-4735	263	63	⊆	⊆	NUM
ejpam-4735	263	64	v	v	NOUN
ejpam-4735	263	65	.	.	PUNCT
ejpam-4735	264	1	theorem	theorem	VERB
ejpam-4735	264	2	7	7	NUM
ejpam-4735	264	3	.	.	PUNCT
ejpam-4735	265	1	a	a	DET
ejpam-4735	265	2	topological	topological	ADJ
ejpam-4735	265	3	space	space	NOUN
ejpam-4735	265	4	(	(	PUNCT
ejpam-4735	265	5	x	x	X
ejpam-4735	265	6	,	,	PUNCT
ejpam-4735	265	7	τ	τ	X
ejpam-4735	265	8	)	)	PUNCT
ejpam-4735	265	9	is	be	AUX
ejpam-4735	265	10	δp(λ	δp(λ	NOUN
ejpam-4735	265	11	,	,	PUNCT
ejpam-4735	265	12	s)-r1	s)-r1	NOUN
ejpam-4735	265	13	if	if	SCONJ
ejpam-4735	265	14	and	and	CCONJ
ejpam-4735	265	15	only	only	ADV
ejpam-4735	265	16	if	if	SCONJ
ejpam-4735	265	17	for	for	ADP
ejpam-4735	265	18	any	any	DET
ejpam-4735	265	19	points	point	NOUN
ejpam-4735	265	20	x	x	X
ejpam-4735	265	21	,	,	PUNCT
ejpam-4735	265	22	y	y	PROPN
ejpam-4735	265	23	in	in	ADP
ejpam-4735	265	24	x	x	PUNCT
ejpam-4735	265	25	with	with	ADP
ejpam-4735	265	26	{	{	PUNCT
ejpam-4735	265	27	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	265	28	,	,	PUNCT
ejpam-4735	265	29	s	s	PART
ejpam-4735	265	30	)	)	PUNCT
ejpam-4735	265	31	̸=	̸=	PROPN
ejpam-4735	265	32	{	{	PUNCT
ejpam-4735	265	33	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	265	34	,	,	PUNCT
ejpam-4735	265	35	s	s	NOUN
ejpam-4735	265	36	)	)	PUNCT
ejpam-4735	265	37	,	,	PUNCT
ejpam-4735	265	38	there	there	PRON
ejpam-4735	265	39	exist	exist	VERB
ejpam-4735	265	40	δp(λ	δp(λ	NOUN
ejpam-4735	265	41	,	,	PUNCT
ejpam-4735	265	42	s)-closed	s)-close	VERB
ejpam-4735	265	43	sets	set	NOUN
ejpam-4735	265	44	f	f	PROPN
ejpam-4735	265	45	and	and	CCONJ
ejpam-4735	265	46	k	k	PROPN
ejpam-4735	265	47	such	such	ADJ
ejpam-4735	265	48	that	that	SCONJ
ejpam-4735	265	49	x	x	SYM
ejpam-4735	265	50	∈	∈	PROPN
ejpam-4735	265	51	f	f	PROPN
ejpam-4735	265	52	,	,	PUNCT
ejpam-4735	265	53	y	y	PROPN
ejpam-4735	265	54	̸∈	̸∈	PROPN
ejpam-4735	265	55	f	f	PROPN
ejpam-4735	265	56	,	,	PUNCT
ejpam-4735	265	57	y	y	PROPN
ejpam-4735	265	58	∈	∈	PROPN
ejpam-4735	265	59	k	k	PROPN
ejpam-4735	265	60	,	,	PUNCT
ejpam-4735	265	61	x	x	PROPN
ejpam-4735	265	62	̸∈	̸∈	PROPN
ejpam-4735	265	63	k	k	PROPN
ejpam-4735	265	64	and	and	CCONJ
ejpam-4735	265	65	x	x	X
ejpam-4735	265	66	=	=	SYM
ejpam-4735	265	67	f	f	PROPN
ejpam-4735	265	68	∪k	∪k	PROPN
ejpam-4735	265	69	.	.	PUNCT
ejpam-4735	266	1	proof	proof	NOUN
ejpam-4735	266	2	.	.	PUNCT
ejpam-4735	267	1	let	let	VERB
ejpam-4735	267	2	x	x	PRON
ejpam-4735	267	3	and	and	CCONJ
ejpam-4735	267	4	y	y	PROPN
ejpam-4735	267	5	be	be	AUX
ejpam-4735	267	6	any	any	DET
ejpam-4735	267	7	points	point	NOUN
ejpam-4735	267	8	in	in	ADP
ejpam-4735	267	9	x	x	PUNCT
ejpam-4735	267	10	with	with	ADP
ejpam-4735	267	11	{	{	PUNCT
ejpam-4735	267	12	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	267	13	,	,	PUNCT
ejpam-4735	267	14	s	s	PART
ejpam-4735	267	15	)	)	PUNCT
ejpam-4735	267	16	̸=	̸=	PROPN
ejpam-4735	267	17	{	{	PUNCT
ejpam-4735	267	18	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	267	19	,	,	PUNCT
ejpam-4735	267	20	s	s	NOUN
ejpam-4735	267	21	)	)	PUNCT
ejpam-4735	267	22	.	.	PUNCT
ejpam-4735	268	1	then	then	ADV
ejpam-4735	268	2	,	,	PUNCT
ejpam-4735	268	3	there	there	PRON
ejpam-4735	268	4	exist	exist	VERB
ejpam-4735	268	5	disjoint	disjoint	NOUN
ejpam-4735	268	6	u	u	NOUN
ejpam-4735	268	7	,	,	PUNCT
ejpam-4735	268	8	v	v	PROPN
ejpam-4735	268	9	∈	∈	PROPN
ejpam-4735	268	10	δp(λ	δp(λ	NOUN
ejpam-4735	268	11	,	,	PUNCT
ejpam-4735	268	12	s)o(x	s)o(x	PROPN
ejpam-4735	268	13	,	,	PUNCT
ejpam-4735	268	14	τ	τ	X
ejpam-4735	268	15	)	)	PUNCT
ejpam-4735	269	1	such	such	ADJ
ejpam-4735	269	2	that	that	SCONJ
ejpam-4735	269	3	{	{	PUNCT
ejpam-4735	269	4	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	269	5	,	,	PUNCT
ejpam-4735	269	6	s	s	PART
ejpam-4735	269	7	)	)	PUNCT
ejpam-4735	269	8	⊆	⊆	NUM
ejpam-4735	269	9	u	u	NOUN
ejpam-4735	269	10	and	and	CCONJ
ejpam-4735	269	11	{	{	PUNCT
ejpam-4735	269	12	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	269	13	,	,	PUNCT
ejpam-4735	269	14	s	s	NOUN
ejpam-4735	269	15	)	)	PUNCT
ejpam-4735	269	16	⊆	⊆	NUM
ejpam-4735	269	17	v	v	NOUN
ejpam-4735	269	18	.	.	PUNCT
ejpam-4735	270	1	now	now	ADV
ejpam-4735	270	2	,	,	PUNCT
ejpam-4735	270	3	put	put	VERB
ejpam-4735	270	4	f	f	NOUN
ejpam-4735	271	1	=	=	PUNCT
ejpam-4735	271	2	x	x	PROPN
ejpam-4735	271	3	−	−	PROPN
ejpam-4735	271	4	v	v	NOUN
ejpam-4735	271	5	and	and	CCONJ
ejpam-4735	271	6	k	k	NOUN
ejpam-4735	272	1	=	=	PUNCT
ejpam-4735	272	2	x	x	PUNCT
ejpam-4735	273	1	−	−	PROPN
ejpam-4735	273	2	u	u	NOUN
ejpam-4735	273	3	.	.	PUNCT
ejpam-4735	274	1	then	then	ADV
ejpam-4735	274	2	,	,	PUNCT
ejpam-4735	274	3	f	f	PROPN
ejpam-4735	274	4	and	and	CCONJ
ejpam-4735	274	5	k	k	PROPN
ejpam-4735	274	6	are	be	AUX
ejpam-4735	274	7	δp(λ	δp(λ	NOUN
ejpam-4735	274	8	,	,	PUNCT
ejpam-4735	274	9	s)-closed	s)-close	VERB
ejpam-4735	274	10	sets	set	NOUN
ejpam-4735	274	11	of	of	ADP
ejpam-4735	274	12	x	x	PUNCT
ejpam-4735	274	13	such	such	ADJ
ejpam-4735	274	14	that	that	SCONJ
ejpam-4735	274	15	x	x	SYM
ejpam-4735	274	16	∈	∈	PROPN
ejpam-4735	274	17	f	f	PROPN
ejpam-4735	274	18	,	,	PUNCT
ejpam-4735	274	19	y	y	PROPN
ejpam-4735	274	20	̸∈	̸∈	PROPN
ejpam-4735	274	21	f	f	PROPN
ejpam-4735	274	22	,	,	PUNCT
ejpam-4735	274	23	y	y	PROPN
ejpam-4735	274	24	∈	∈	PROPN
ejpam-4735	274	25	k	k	PROPN
ejpam-4735	274	26	,	,	PUNCT
ejpam-4735	274	27	x	x	PROPN
ejpam-4735	274	28	̸∈	̸∈	PROPN
ejpam-4735	274	29	k	k	PROPN
ejpam-4735	274	30	and	and	CCONJ
ejpam-4735	274	31	x	x	X
ejpam-4735	274	32	=	=	SYM
ejpam-4735	274	33	f	f	PROPN
ejpam-4735	274	34	∪k	∪k	PROPN
ejpam-4735	274	35	.	.	PUNCT
ejpam-4735	275	1	conversely	conversely	ADV
ejpam-4735	275	2	,	,	PUNCT
ejpam-4735	275	3	let	let	VERB
ejpam-4735	275	4	x	x	PRON
ejpam-4735	275	5	and	and	CCONJ
ejpam-4735	275	6	y	y	PROPN
ejpam-4735	275	7	be	be	AUX
ejpam-4735	275	8	any	any	DET
ejpam-4735	275	9	points	point	NOUN
ejpam-4735	275	10	in	in	ADP
ejpam-4735	275	11	x	x	INTJ
ejpam-4735	275	12	such	such	ADJ
ejpam-4735	275	13	that	that	SCONJ
ejpam-4735	275	14	{	{	PUNCT
ejpam-4735	275	15	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	275	16	,	,	PUNCT
ejpam-4735	275	17	s	s	PART
ejpam-4735	275	18	)	)	PUNCT
ejpam-4735	275	19	̸=	̸=	PROPN
ejpam-4735	275	20	{	{	PUNCT
ejpam-4735	275	21	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	275	22	,	,	PUNCT
ejpam-4735	275	23	s	s	NOUN
ejpam-4735	275	24	)	)	PUNCT
ejpam-4735	275	25	.	.	PUNCT
ejpam-4735	276	1	then	then	ADV
ejpam-4735	276	2	,	,	PUNCT
ejpam-4735	276	3	{	{	PUNCT
ejpam-4735	276	4	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	276	5	,	,	PUNCT
ejpam-4735	276	6	s)∩{y}δp(λ	s)∩{y}δp(λ	PROPN
ejpam-4735	276	7	,	,	PUNCT
ejpam-4735	276	8	s	s	PART
ejpam-4735	276	9	)	)	PUNCT
ejpam-4735	276	10	=	=	PUNCT
ejpam-4735	276	11	∅.	∅.	NOUN
ejpam-4735	276	12	in	in	ADP
ejpam-4735	276	13	fact	fact	NOUN
ejpam-4735	276	14	,	,	PUNCT
ejpam-4735	276	15	if	if	SCONJ
ejpam-4735	276	16	z	z	PROPN
ejpam-4735	276	17	∈	∈	PROPN
ejpam-4735	276	18	{	{	PUNCT
ejpam-4735	276	19	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	276	20	,	,	PUNCT
ejpam-4735	276	21	s)∩{y}δp(λ	s)∩{y}δp(λ	PROPN
ejpam-4735	276	22	,	,	PUNCT
ejpam-4735	276	23	s	s	PART
ejpam-4735	276	24	)	)	PUNCT
ejpam-4735	276	25	,	,	PUNCT
ejpam-4735	276	26	then	then	ADV
ejpam-4735	276	27	{	{	PUNCT
ejpam-4735	276	28	z}δp(λ	z}δp(λ	PROPN
ejpam-4735	276	29	,	,	PUNCT
ejpam-4735	276	30	s	s	PART
ejpam-4735	276	31	)	)	PUNCT
ejpam-4735	276	32	̸=	̸=	PROPN
ejpam-4735	276	33	{	{	PUNCT
ejpam-4735	276	34	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	276	35	,	,	PUNCT
ejpam-4735	276	36	s	s	PART
ejpam-4735	276	37	)	)	PUNCT
ejpam-4735	276	38	or	or	CCONJ
ejpam-4735	276	39	{	{	PUNCT
ejpam-4735	276	40	z}δp(λ	z}δp(λ	PROPN
ejpam-4735	276	41	,	,	PUNCT
ejpam-4735	276	42	s	s	PART
ejpam-4735	276	43	)	)	PUNCT
ejpam-4735	276	44	̸=	̸=	PROPN
ejpam-4735	276	45	{	{	PUNCT
ejpam-4735	276	46	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	276	47	,	,	PUNCT
ejpam-4735	276	48	s	s	NOUN
ejpam-4735	276	49	)	)	PUNCT
ejpam-4735	276	50	.	.	PUNCT
ejpam-4735	277	1	in	in	ADP
ejpam-4735	277	2	case	case	NOUN
ejpam-4735	277	3	{	{	PUNCT
ejpam-4735	277	4	z}δp(λ	z}δp(λ	PROPN
ejpam-4735	277	5	,	,	PUNCT
ejpam-4735	277	6	s	s	PART
ejpam-4735	277	7	)	)	PUNCT
ejpam-4735	277	8	̸=	̸=	PROPN
ejpam-4735	277	9	{	{	PUNCT
ejpam-4735	277	10	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	277	11	,	,	PUNCT
ejpam-4735	277	12	s	s	PART
ejpam-4735	277	13	)	)	PUNCT
ejpam-4735	277	14	,	,	PUNCT
ejpam-4735	277	15	by	by	ADP
ejpam-4735	277	16	the	the	DET
ejpam-4735	277	17	hypothesis	hypothesis	NOUN
ejpam-4735	277	18	,	,	PUNCT
ejpam-4735	277	19	there	there	PRON
ejpam-4735	277	20	exists	exist	VERB
ejpam-4735	277	21	a	a	DET
ejpam-4735	277	22	δp(λ	δp(λ	NOUN
ejpam-4735	277	23	,	,	PUNCT
ejpam-4735	277	24	s)-closed	s)-close	VERB
ejpam-4735	277	25	set	set	NOUN
ejpam-4735	277	26	f	f	PRON
ejpam-4735	277	27	such	such	ADJ
ejpam-4735	277	28	that	that	SCONJ
ejpam-4735	277	29	x	x	SYM
ejpam-4735	277	30	∈	∈	PROPN
ejpam-4735	277	31	f	f	PROPN
ejpam-4735	277	32	and	and	CCONJ
ejpam-4735	277	33	z	z	PROPN
ejpam-4735	277	34	̸∈	̸∈	PROPN
ejpam-4735	277	35	f	f	PROPN
ejpam-4735	277	36	.	.	PUNCT
ejpam-4735	278	1	then	then	ADV
ejpam-4735	278	2	,	,	PUNCT
ejpam-4735	278	3	z	z	PROPN
ejpam-4735	278	4	∈	∈	PROPN
ejpam-4735	278	5	{	{	PUNCT
ejpam-4735	278	6	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	278	7	,	,	PUNCT
ejpam-4735	278	8	s	s	PART
ejpam-4735	278	9	)	)	PUNCT
ejpam-4735	278	10	⊆	⊆	NUM
ejpam-4735	278	11	f	f	NOUN
ejpam-4735	278	12	.	.	PUNCT
ejpam-4735	279	1	this	this	PRON
ejpam-4735	279	2	contradicts	contradict	VERB
ejpam-4735	279	3	that	that	SCONJ
ejpam-4735	279	4	z	z	PROPN
ejpam-4735	279	5	̸∈	̸∈	PROPN
ejpam-4735	279	6	f	f	PROPN
ejpam-4735	279	7	.	.	PUNCT
ejpam-4735	280	1	in	in	ADP
ejpam-4735	280	2	case	case	NOUN
ejpam-4735	280	3	{	{	PUNCT
ejpam-4735	280	4	z}δp(λ	z}δp(λ	PROPN
ejpam-4735	280	5	,	,	PUNCT
ejpam-4735	280	6	s	s	PART
ejpam-4735	280	7	)	)	PUNCT
ejpam-4735	280	8	̸=	̸=	PROPN
ejpam-4735	280	9	{	{	PUNCT
ejpam-4735	280	10	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	280	11	,	,	PUNCT
ejpam-4735	280	12	s	s	NOUN
ejpam-4735	280	13	)	)	PUNCT
ejpam-4735	280	14	,	,	PUNCT
ejpam-4735	280	15	similarly	similarly	ADV
ejpam-4735	280	16	,	,	PUNCT
ejpam-4735	280	17	this	this	PRON
ejpam-4735	280	18	leads	lead	VERB
ejpam-4735	280	19	to	to	ADP
ejpam-4735	280	20	the	the	DET
ejpam-4735	280	21	contradiction	contradiction	NOUN
ejpam-4735	280	22	.	.	PUNCT
ejpam-4735	281	1	thus	thus	ADV
ejpam-4735	281	2	,	,	PUNCT
ejpam-4735	281	3	{	{	PUNCT
ejpam-4735	281	4	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	281	5	,	,	PUNCT
ejpam-4735	281	6	s	s	NOUN
ejpam-4735	281	7	)	)	PUNCT
ejpam-4735	281	8	∩	∩	NOUN
ejpam-4735	281	9	{	{	PUNCT
ejpam-4735	281	10	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	281	11	,	,	PUNCT
ejpam-4735	281	12	s	s	NOUN
ejpam-4735	281	13	)	)	PUNCT
ejpam-4735	281	14	=	=	NOUN
ejpam-4735	281	15	∅	∅	NOUN
ejpam-4735	281	16	,	,	PUNCT
ejpam-4735	281	17	by	by	ADP
ejpam-4735	281	18	corollary	corollary	ADJ
ejpam-4735	281	19	1	1	NUM
ejpam-4735	281	20	,	,	PUNCT
ejpam-4735	281	21	(	(	PUNCT
ejpam-4735	281	22	x	x	X
ejpam-4735	281	23	,	,	PUNCT
ejpam-4735	281	24	τ	τ	X
ejpam-4735	281	25	)	)	PUNCT
ejpam-4735	281	26	is	be	AUX
ejpam-4735	281	27	δp(λ	δp(λ	NOUN
ejpam-4735	281	28	,	,	PUNCT
ejpam-4735	281	29	s)-r0	s)-r0	X
ejpam-4735	281	30	.	.	PUNCT
ejpam-4735	282	1	by	by	ADP
ejpam-4735	282	2	the	the	DET
ejpam-4735	282	3	hypothesis	hypothesis	NOUN
ejpam-4735	282	4	,	,	PUNCT
ejpam-4735	282	5	there	there	PRON
ejpam-4735	282	6	exist	exist	VERB
ejpam-4735	282	7	δp(λ	δp(λ	NOUN
ejpam-4735	282	8	,	,	PUNCT
ejpam-4735	282	9	s)-closed	s)-close	VERB
ejpam-4735	282	10	sets	set	NOUN
ejpam-4735	282	11	f	f	PROPN
ejpam-4735	282	12	and	and	CCONJ
ejpam-4735	282	13	k	k	PROPN
ejpam-4735	282	14	such	such	ADJ
ejpam-4735	282	15	that	that	SCONJ
ejpam-4735	282	16	x	x	SYM
ejpam-4735	282	17	∈	∈	PROPN
ejpam-4735	282	18	f	f	PROPN
ejpam-4735	282	19	,	,	PUNCT
ejpam-4735	282	20	y	y	PROPN
ejpam-4735	282	21	̸∈	̸∈	PROPN
ejpam-4735	282	22	f	f	PROPN
ejpam-4735	282	23	,	,	PUNCT
ejpam-4735	282	24	y	y	PROPN
ejpam-4735	282	25	∈	∈	PROPN
ejpam-4735	282	26	k	k	PROPN
ejpam-4735	282	27	,	,	PUNCT
ejpam-4735	282	28	x	x	PROPN
ejpam-4735	282	29	̸∈	̸∈	PROPN
ejpam-4735	282	30	k	k	PROPN
ejpam-4735	282	31	and	and	CCONJ
ejpam-4735	282	32	x	x	X
ejpam-4735	282	33	=	=	SYM
ejpam-4735	282	34	f	f	PROPN
ejpam-4735	282	35	∪k	∪k	PROPN
ejpam-4735	282	36	.	.	PUNCT
ejpam-4735	283	1	put	put	VERB
ejpam-4735	283	2	u	u	NOUN
ejpam-4735	283	3	=	=	NOUN
ejpam-4735	283	4	x	x	SYM
ejpam-4735	283	5	−k	−k	ADJ
ejpam-4735	283	6	and	and	CCONJ
ejpam-4735	283	7	v	v	NOUN
ejpam-4735	283	8	=	=	NOUN
ejpam-4735	283	9	x	x	X
ejpam-4735	283	10	−	−	PROPN
ejpam-4735	283	11	f	f	X
ejpam-4735	283	12	.	.	PUNCT
ejpam-4735	284	1	then	then	ADV
ejpam-4735	284	2	,	,	PUNCT
ejpam-4735	284	3	x	x	PUNCT
ejpam-4735	284	4	∈	∈	PROPN
ejpam-4735	284	5	u	u	NOUN
ejpam-4735	284	6	∈	∈	PROPN
ejpam-4735	284	7	δp(λ	δp(λ	NOUN
ejpam-4735	284	8	,	,	PUNCT
ejpam-4735	284	9	s)o(x	s)o(x	PROPN
ejpam-4735	284	10	,	,	PUNCT
ejpam-4735	284	11	τ	τ	X
ejpam-4735	284	12	)	)	PUNCT
ejpam-4735	284	13	and	and	CCONJ
ejpam-4735	284	14	y	y	PROPN
ejpam-4735	284	15	∈	∈	PROPN
ejpam-4735	284	16	v	v	ADP
ejpam-4735	284	17	∈	∈	PROPN
ejpam-4735	284	18	δp(λ	δp(λ	NOUN
ejpam-4735	284	19	,	,	PUNCT
ejpam-4735	284	20	s)o(x	s)o(x	PROPN
ejpam-4735	284	21	,	,	PUNCT
ejpam-4735	284	22	τ	τ	PROPN
ejpam-4735	284	23	)	)	PUNCT
ejpam-4735	284	24	.	.	PUNCT
ejpam-4735	285	1	since	since	SCONJ
ejpam-4735	285	2	(	(	PUNCT
ejpam-4735	285	3	x	x	X
ejpam-4735	285	4	,	,	PUNCT
ejpam-4735	285	5	τ	τ	X
ejpam-4735	285	6	)	)	PUNCT
ejpam-4735	285	7	is	be	AUX
ejpam-4735	285	8	δp(λ	δp(λ	NOUN
ejpam-4735	285	9	,	,	PUNCT
ejpam-4735	285	10	s)-r0	s)-r0	PRON
ejpam-4735	285	11	,	,	PUNCT
ejpam-4735	285	12	we	we	PRON
ejpam-4735	285	13	have	have	AUX
ejpam-4735	285	14	{	{	PUNCT
ejpam-4735	285	15	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	285	16	,	,	PUNCT
ejpam-4735	285	17	s	s	PART
ejpam-4735	285	18	)	)	PUNCT
ejpam-4735	285	19	⊆	⊆	NUM
ejpam-4735	285	20	u	u	NOUN
ejpam-4735	285	21	,	,	PUNCT
ejpam-4735	285	22	{	{	PUNCT
ejpam-4735	285	23	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	285	24	,	,	PUNCT
ejpam-4735	285	25	s	s	NOUN
ejpam-4735	285	26	)	)	PUNCT
ejpam-4735	285	27	⊆	⊆	NUM
ejpam-4735	285	28	v	v	NOUN
ejpam-4735	285	29	and	and	CCONJ
ejpam-4735	285	30	also	also	ADV
ejpam-4735	285	31	u	u	NOUN
ejpam-4735	285	32	∩	∩	NOUN
ejpam-4735	285	33	v	v	NOUN
ejpam-4735	285	34	=	=	PUNCT
ejpam-4735	285	35	∅.	∅.	ADP
ejpam-4735	285	36	this	this	PRON
ejpam-4735	285	37	shows	show	VERB
ejpam-4735	285	38	that	that	SCONJ
ejpam-4735	285	39	(	(	PUNCT
ejpam-4735	285	40	x	x	X
ejpam-4735	285	41	,	,	PUNCT
ejpam-4735	285	42	τ	τ	X
ejpam-4735	285	43	)	)	PUNCT
ejpam-4735	285	44	is	be	AUX
ejpam-4735	285	45	δp(λ	δp(λ	NOUN
ejpam-4735	285	46	,	,	PUNCT
ejpam-4735	285	47	s)-r1	s)-r1	NOUN
ejpam-4735	285	48	.	.	PUNCT
ejpam-4735	286	1	c.	c.	PROPN
ejpam-4735	286	2	boonpok	boonpok	PROPN
ejpam-4735	286	3	,	,	PUNCT
ejpam-4735	286	4	p.	p.	NOUN
ejpam-4735	286	5	pue	pue	NOUN
ejpam-4735	286	6	-	-	PUNCT
ejpam-4735	286	7	on	on	ADP
ejpam-4735	286	8	/	/	SYM
ejpam-4735	286	9	eur	eur	NOUN
ejpam-4735	286	10	.	.	PUNCT
ejpam-4735	287	1	j.	j.	PROPN
ejpam-4735	287	2	pure	pure	PROPN
ejpam-4735	287	3	appl	appl	PROPN
ejpam-4735	287	4	.	.	PROPN
ejpam-4735	287	5	math	math	PROPN
ejpam-4735	287	6	,	,	PUNCT
ejpam-4735	287	7	17	17	NUM
ejpam-4735	287	8	(	(	PUNCT
ejpam-4735	287	9	1	1	NUM
ejpam-4735	287	10	)	)	PUNCT
ejpam-4735	287	11	(	(	PUNCT
ejpam-4735	287	12	2024	2024	NUM
ejpam-4735	287	13	)	)	PUNCT
ejpam-4735	287	14	,	,	PUNCT
ejpam-4735	287	15	147	147	NUM
ejpam-4735	287	16	-	-	SYM
ejpam-4735	287	17	157	157	NUM
ejpam-4735	287	18	155	155	NUM
ejpam-4735	287	19	definition	definition	NOUN
ejpam-4735	287	20	6	6	NUM
ejpam-4735	287	21	.	.	PUNCT
ejpam-4735	288	1	let	let	VERB
ejpam-4735	288	2	a	a	DET
ejpam-4735	288	3	be	be	AUX
ejpam-4735	288	4	a	a	DET
ejpam-4735	288	5	subset	subset	NOUN
ejpam-4735	288	6	of	of	ADP
ejpam-4735	288	7	a	a	DET
ejpam-4735	288	8	topological	topological	ADJ
ejpam-4735	288	9	space	space	NOUN
ejpam-4735	288	10	(	(	PUNCT
ejpam-4735	288	11	x	x	X
ejpam-4735	288	12	,	,	PUNCT
ejpam-4735	288	13	τ	τ	PROPN
ejpam-4735	288	14	)	)	PUNCT
ejpam-4735	288	15	.	.	PUNCT
ejpam-4735	289	1	the	the	DET
ejpam-4735	289	2	θδp(λ	θδp(λ	PROPN
ejpam-4735	289	3	,	,	PUNCT
ejpam-4735	289	4	s)-closure	s)-closure	NOUN
ejpam-4735	289	5	of	of	ADP
ejpam-4735	289	6	a	a	DET
ejpam-4735	289	7	,	,	PUNCT
ejpam-4735	289	8	aθδp(λ	aθδp(λ	PROPN
ejpam-4735	289	9	,	,	PUNCT
ejpam-4735	289	10	s	s	PART
ejpam-4735	289	11	)	)	PUNCT
ejpam-4735	289	12	,	,	PUNCT
ejpam-4735	289	13	is	be	AUX
ejpam-4735	289	14	defined	define	VERB
ejpam-4735	289	15	as	as	SCONJ
ejpam-4735	289	16	follows	follow	VERB
ejpam-4735	289	17	:	:	PUNCT
ejpam-4735	290	1	aθδp(λ	aθδp(λ	PROPN
ejpam-4735	290	2	,	,	PUNCT
ejpam-4735	290	3	s	s	PART
ejpam-4735	290	4	)	)	PUNCT
ejpam-4735	290	5	=	=	SYM
ejpam-4735	290	6	{	{	PUNCT
ejpam-4735	290	7	x	x	PUNCT
ejpam-4735	290	8	∈	∈	NOUN
ejpam-4735	290	9	x	x	PUNCT
ejpam-4735	290	10	|	|	ADV
ejpam-4735	290	11	a	a	DET
ejpam-4735	290	12	∩	∩	ADJ
ejpam-4735	290	13	u	u	NOUN
ejpam-4735	290	14	δp(λ	δp(λ	NOUN
ejpam-4735	290	15	,	,	PUNCT
ejpam-4735	290	16	s	s	PART
ejpam-4735	290	17	)	)	PUNCT
ejpam-4735	290	18	̸=	̸=	NOUN
ejpam-4735	290	19	∅	∅	NOUN
ejpam-4735	290	20	for	for	ADP
ejpam-4735	290	21	each	each	DET
ejpam-4735	290	22	u	u	PROPN
ejpam-4735	290	23	∈	∈	PROPN
ejpam-4735	290	24	δp(λ	δp(λ	NOUN
ejpam-4735	290	25	,	,	PUNCT
ejpam-4735	290	26	s)o(x	s)o(x	PROPN
ejpam-4735	290	27	,	,	PUNCT
ejpam-4735	290	28	τ	τ	X
ejpam-4735	290	29	)	)	PUNCT
ejpam-4735	290	30	containing	contain	VERB
ejpam-4735	290	31	x	x	X
ejpam-4735	290	32	}	}	PUNCT
ejpam-4735	290	33	.	.	PUNCT
ejpam-4735	291	1	lemma	lemma	PROPN
ejpam-4735	291	2	5	5	NUM
ejpam-4735	291	3	.	.	PUNCT
ejpam-4735	292	1	if	if	SCONJ
ejpam-4735	292	2	a	a	DET
ejpam-4735	292	3	topological	topological	ADJ
ejpam-4735	292	4	space	space	NOUN
ejpam-4735	292	5	(	(	PUNCT
ejpam-4735	292	6	x	x	X
ejpam-4735	292	7	,	,	PUNCT
ejpam-4735	292	8	τ	τ	X
ejpam-4735	292	9	)	)	PUNCT
ejpam-4735	292	10	is	be	AUX
ejpam-4735	292	11	δp(λ	δp(λ	NOUN
ejpam-4735	292	12	,	,	PUNCT
ejpam-4735	292	13	s)-r1	s)-r1	NOUN
ejpam-4735	292	14	,	,	PUNCT
ejpam-4735	292	15	then	then	ADV
ejpam-4735	292	16	(	(	PUNCT
ejpam-4735	292	17	x	x	X
ejpam-4735	292	18	,	,	PUNCT
ejpam-4735	292	19	τ	τ	X
ejpam-4735	292	20	)	)	PUNCT
ejpam-4735	292	21	is	be	AUX
ejpam-4735	292	22	δp(λ	δp(λ	NOUN
ejpam-4735	292	23	,	,	PUNCT
ejpam-4735	292	24	s)-r0	s)-r0	X
ejpam-4735	292	25	.	.	PUNCT
ejpam-4735	293	1	proof	proof	NOUN
ejpam-4735	293	2	.	.	PUNCT
ejpam-4735	294	1	let	let	VERB
ejpam-4735	294	2	u	u	PRON
ejpam-4735	294	3	∈	∈	PROPN
ejpam-4735	294	4	δp(λ	δp(λ	NOUN
ejpam-4735	294	5	,	,	PUNCT
ejpam-4735	294	6	s)o(x	s)o(x	PROPN
ejpam-4735	294	7	,	,	PUNCT
ejpam-4735	294	8	τ	τ	X
ejpam-4735	294	9	)	)	PUNCT
ejpam-4735	294	10	and	and	CCONJ
ejpam-4735	294	11	x	x	PUNCT
ejpam-4735	294	12	∈	∈	PROPN
ejpam-4735	294	13	u	u	NOUN
ejpam-4735	294	14	.	.	PUNCT
ejpam-4735	295	1	if	if	SCONJ
ejpam-4735	295	2	y	y	PROPN
ejpam-4735	295	3	̸∈	̸∈	PROPN
ejpam-4735	295	4	u	u	PROPN
ejpam-4735	295	5	,	,	PUNCT
ejpam-4735	295	6	then	then	ADV
ejpam-4735	295	7	u	u	NOUN
ejpam-4735	295	8	∩	∩	NOUN
ejpam-4735	295	9	{	{	PUNCT
ejpam-4735	295	10	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	295	11	,	,	PUNCT
ejpam-4735	295	12	s	s	NOUN
ejpam-4735	295	13	)	)	PUNCT
ejpam-4735	295	14	=	=	SYM
ejpam-4735	295	15	∅	∅	NOUN
ejpam-4735	295	16	and	and	CCONJ
ejpam-4735	295	17	x	x	PART
ejpam-4735	295	18	̸∈	̸∈	PROPN
ejpam-4735	295	19	{	{	PUNCT
ejpam-4735	295	20	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	295	21	,	,	PUNCT
ejpam-4735	295	22	s	s	NOUN
ejpam-4735	295	23	)	)	PUNCT
ejpam-4735	295	24	.	.	PUNCT
ejpam-4735	296	1	thus	thus	ADV
ejpam-4735	296	2	,	,	PUNCT
ejpam-4735	296	3	{	{	PUNCT
ejpam-4735	296	4	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	296	5	,	,	PUNCT
ejpam-4735	296	6	s	s	PART
ejpam-4735	296	7	)	)	PUNCT
ejpam-4735	296	8	̸=	̸=	PROPN
ejpam-4735	296	9	{	{	PUNCT
ejpam-4735	296	10	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	296	11	,	,	PUNCT
ejpam-4735	296	12	s	s	NOUN
ejpam-4735	296	13	)	)	PUNCT
ejpam-4735	296	14	.	.	PUNCT
ejpam-4735	297	1	since	since	SCONJ
ejpam-4735	297	2	(	(	PUNCT
ejpam-4735	297	3	x	x	X
ejpam-4735	297	4	,	,	PUNCT
ejpam-4735	297	5	τ	τ	X
ejpam-4735	297	6	)	)	PUNCT
ejpam-4735	297	7	is	be	AUX
ejpam-4735	297	8	δp(λ	δp(λ	NOUN
ejpam-4735	297	9	,	,	PUNCT
ejpam-4735	297	10	s)-r1	s)-r1	NOUN
ejpam-4735	297	11	,	,	PUNCT
ejpam-4735	297	12	there	there	PRON
ejpam-4735	297	13	exists	exist	VERB
ejpam-4735	297	14	v	v	ADP
ejpam-4735	297	15	∈	∈	PROPN
ejpam-4735	297	16	δp(λ	δp(λ	NOUN
ejpam-4735	297	17	,	,	PUNCT
ejpam-4735	297	18	s)o(x	s)o(x	PROPN
ejpam-4735	297	19	,	,	PUNCT
ejpam-4735	297	20	τ	τ	X
ejpam-4735	297	21	)	)	PUNCT
ejpam-4735	297	22	such	such	ADJ
ejpam-4735	297	23	that	that	SCONJ
ejpam-4735	297	24	{	{	PUNCT
ejpam-4735	297	25	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	297	26	,	,	PUNCT
ejpam-4735	297	27	s	s	NOUN
ejpam-4735	297	28	)	)	PUNCT
ejpam-4735	297	29	⊆	⊆	NUM
ejpam-4735	297	30	v	v	NOUN
ejpam-4735	297	31	and	and	CCONJ
ejpam-4735	297	32	x	x	PART
ejpam-4735	297	33	̸∈	̸∈	PROPN
ejpam-4735	297	34	v	v	NUM
ejpam-4735	297	35	.	.	PUNCT
ejpam-4735	298	1	thus	thus	ADV
ejpam-4735	298	2	,	,	PUNCT
ejpam-4735	298	3	v	v	ADP
ejpam-4735	298	4	∩	∩	NOUN
ejpam-4735	298	5	{	{	PUNCT
ejpam-4735	298	6	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	298	7	,	,	PUNCT
ejpam-4735	298	8	s	s	PART
ejpam-4735	298	9	)	)	PUNCT
ejpam-4735	298	10	=	=	NOUN
ejpam-4735	298	11	∅	∅	NOUN
ejpam-4735	298	12	and	and	CCONJ
ejpam-4735	298	13	hence	hence	ADV
ejpam-4735	298	14	y	y	PROPN
ejpam-4735	298	15	̸∈	̸∈	PROPN
ejpam-4735	298	16	{	{	PUNCT
ejpam-4735	298	17	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	298	18	,	,	PUNCT
ejpam-4735	298	19	s	s	NOUN
ejpam-4735	298	20	)	)	PUNCT
ejpam-4735	298	21	.	.	PUNCT
ejpam-4735	299	1	therefore	therefore	ADV
ejpam-4735	299	2	,	,	PUNCT
ejpam-4735	299	3	{	{	PUNCT
ejpam-4735	299	4	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	299	5	,	,	PUNCT
ejpam-4735	299	6	s	s	PART
ejpam-4735	299	7	)	)	PUNCT
ejpam-4735	299	8	⊆	⊆	NUM
ejpam-4735	299	9	u	u	NOUN
ejpam-4735	299	10	.	.	PUNCT
ejpam-4735	300	1	this	this	PRON
ejpam-4735	300	2	shows	show	VERB
ejpam-4735	300	3	that	that	SCONJ
ejpam-4735	300	4	(	(	PUNCT
ejpam-4735	300	5	x	x	X
ejpam-4735	300	6	,	,	PUNCT
ejpam-4735	300	7	τ	τ	X
ejpam-4735	300	8	)	)	PUNCT
ejpam-4735	300	9	is	be	AUX
ejpam-4735	300	10	δp(λ	δp(λ	NOUN
ejpam-4735	300	11	,	,	PUNCT
ejpam-4735	300	12	s)-r0	s)-r0	X
ejpam-4735	300	13	.	.	PUNCT
ejpam-4735	301	1	theorem	theorem	VERB
ejpam-4735	301	2	8	8	NUM
ejpam-4735	301	3	.	.	PUNCT
ejpam-4735	302	1	a	a	DET
ejpam-4735	302	2	topological	topological	ADJ
ejpam-4735	302	3	space	space	NOUN
ejpam-4735	302	4	(	(	PUNCT
ejpam-4735	302	5	x	x	X
ejpam-4735	302	6	,	,	PUNCT
ejpam-4735	302	7	τ	τ	X
ejpam-4735	302	8	)	)	PUNCT
ejpam-4735	302	9	is	be	AUX
ejpam-4735	302	10	δp(λ	δp(λ	NOUN
ejpam-4735	302	11	,	,	PUNCT
ejpam-4735	302	12	s)-r1	s)-r1	NOUN
ejpam-4735	302	13	if	if	SCONJ
ejpam-4735	302	14	and	and	CCONJ
ejpam-4735	302	15	only	only	ADV
ejpam-4735	302	16	if	if	SCONJ
ejpam-4735	302	17	⟨x⟩δp(λ	⟨x⟩δp(λ	NOUN
ejpam-4735	302	18	,	,	PUNCT
ejpam-4735	302	19	s	s	PART
ejpam-4735	302	20	)	)	PUNCT
ejpam-4735	302	21	=	=	SYM
ejpam-4735	302	22	{	{	PUNCT
ejpam-4735	302	23	x}θδp(λ	x}θδp(λ	PROPN
ejpam-4735	302	24	,	,	PUNCT
ejpam-4735	302	25	s	s	NOUN
ejpam-4735	302	26	)	)	PUNCT
ejpam-4735	302	27	for	for	ADP
ejpam-4735	302	28	each	each	DET
ejpam-4735	302	29	x	x	SYM
ejpam-4735	302	30	∈	∈	PROPN
ejpam-4735	302	31	x.	x.	NOUN
ejpam-4735	302	32	proof	proof	NOUN
ejpam-4735	302	33	.	.	PUNCT
ejpam-4735	303	1	let	let	VERB
ejpam-4735	303	2	(	(	PUNCT
ejpam-4735	303	3	x	x	NOUN
ejpam-4735	303	4	,	,	PUNCT
ejpam-4735	303	5	τ	τ	X
ejpam-4735	303	6	)	)	PUNCT
ejpam-4735	303	7	be	be	AUX
ejpam-4735	303	8	δp(λ	δp(λ	NOUN
ejpam-4735	303	9	,	,	PUNCT
ejpam-4735	303	10	s)-r1	s)-r1	NOUN
ejpam-4735	303	11	.	.	PUNCT
ejpam-4735	304	1	by	by	ADP
ejpam-4735	304	2	lemma	lemma	PROPN
ejpam-4735	304	3	5	5	NUM
ejpam-4735	304	4	,	,	PUNCT
ejpam-4735	304	5	(	(	PUNCT
ejpam-4735	304	6	x	x	X
ejpam-4735	304	7	,	,	PUNCT
ejpam-4735	304	8	τ	τ	X
ejpam-4735	304	9	)	)	PUNCT
ejpam-4735	304	10	is	be	AUX
ejpam-4735	304	11	δp(λ	δp(λ	NOUN
ejpam-4735	304	12	,	,	PUNCT
ejpam-4735	304	13	s)-r0	s)-r0	PRON
ejpam-4735	304	14	and	and	CCONJ
ejpam-4735	304	15	by	by	ADP
ejpam-4735	304	16	theorem	theorem	NOUN
ejpam-4735	304	17	6	6	NUM
ejpam-4735	304	18	,	,	PUNCT
ejpam-4735	304	19	⟨x⟩δp(λ	⟨x⟩δp(λ	NOUN
ejpam-4735	304	20	,	,	PUNCT
ejpam-4735	304	21	s	s	PART
ejpam-4735	304	22	)	)	PUNCT
ejpam-4735	304	23	=	=	SYM
ejpam-4735	304	24	{	{	PUNCT
ejpam-4735	304	25	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	304	26	,	,	PUNCT
ejpam-4735	304	27	s	s	PART
ejpam-4735	304	28	)	)	PUNCT
ejpam-4735	304	29	⊆	⊆	NUM
ejpam-4735	304	30	{	{	PUNCT
ejpam-4735	304	31	x}θδp(λ	x}θδp(λ	PROPN
ejpam-4735	304	32	,	,	PUNCT
ejpam-4735	304	33	s	s	NOUN
ejpam-4735	304	34	)	)	PUNCT
ejpam-4735	304	35	for	for	ADP
ejpam-4735	304	36	each	each	DET
ejpam-4735	304	37	x	x	SYM
ejpam-4735	304	38	∈	∈	PROPN
ejpam-4735	304	39	x.	x.	NOUN
ejpam-4735	304	40	thus	thus	ADV
ejpam-4735	304	41	,	,	PUNCT
ejpam-4735	304	42	⟨x⟩δp(λ	⟨x⟩δp(λ	AUX
ejpam-4735	304	43	,	,	PUNCT
ejpam-4735	304	44	s	s	PART
ejpam-4735	304	45	)	)	PUNCT
ejpam-4735	304	46	⊆	⊆	NUM
ejpam-4735	304	47	{	{	PUNCT
ejpam-4735	304	48	x}θδp(λ	x}θδp(λ	PROPN
ejpam-4735	304	49	,	,	PUNCT
ejpam-4735	304	50	s	s	NOUN
ejpam-4735	304	51	)	)	PUNCT
ejpam-4735	304	52	for	for	ADP
ejpam-4735	304	53	each	each	DET
ejpam-4735	304	54	x	x	SYM
ejpam-4735	304	55	∈	∈	PROPN
ejpam-4735	304	56	x.	x.	NOUN
ejpam-4735	304	57	in	in	ADP
ejpam-4735	304	58	order	order	NOUN
ejpam-4735	304	59	to	to	PART
ejpam-4735	304	60	show	show	VERB
ejpam-4735	304	61	the	the	DET
ejpam-4735	304	62	opposite	opposite	ADJ
ejpam-4735	304	63	inclusion	inclusion	NOUN
ejpam-4735	304	64	,	,	PUNCT
ejpam-4735	304	65	suppose	suppose	VERB
ejpam-4735	304	66	that	that	SCONJ
ejpam-4735	304	67	y	y	PROPN
ejpam-4735	304	68	̸∈	̸∈	PROPN
ejpam-4735	304	69	⟨x⟩δp(λ	⟨x⟩δp(λ	PROPN
ejpam-4735	304	70	,	,	PUNCT
ejpam-4735	304	71	s	s	NOUN
ejpam-4735	304	72	)	)	PUNCT
ejpam-4735	304	73	.	.	PUNCT
ejpam-4735	305	1	then	then	ADV
ejpam-4735	305	2	,	,	PUNCT
ejpam-4735	305	3	⟨x⟩δp(λ	⟨x⟩δp(λ	NOUN
ejpam-4735	305	4	,	,	PUNCT
ejpam-4735	305	5	s	s	PART
ejpam-4735	305	6	)	)	PUNCT
ejpam-4735	305	7	̸=	̸=	PROPN
ejpam-4735	305	8	⟨y⟩δp(λ	⟨y⟩δp(λ	PROPN
ejpam-4735	305	9	,	,	PUNCT
ejpam-4735	305	10	s	s	NOUN
ejpam-4735	305	11	)	)	PUNCT
ejpam-4735	305	12	.	.	PUNCT
ejpam-4735	306	1	since	since	SCONJ
ejpam-4735	306	2	(	(	PUNCT
ejpam-4735	306	3	x	x	X
ejpam-4735	306	4	,	,	PUNCT
ejpam-4735	306	5	τ	τ	X
ejpam-4735	306	6	)	)	PUNCT
ejpam-4735	306	7	is	be	AUX
ejpam-4735	306	8	δp(λ	δp(λ	NOUN
ejpam-4735	306	9	,	,	PUNCT
ejpam-4735	306	10	s)-r0	s)-r0	ADV
ejpam-4735	306	11	,	,	PUNCT
ejpam-4735	306	12	by	by	ADP
ejpam-4735	306	13	theorem	theorem	NOUN
ejpam-4735	306	14	6	6	NUM
ejpam-4735	306	15	,	,	PUNCT
ejpam-4735	306	16	{	{	PUNCT
ejpam-4735	306	17	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	306	18	,	,	PUNCT
ejpam-4735	306	19	s	s	PART
ejpam-4735	306	20	)	)	PUNCT
ejpam-4735	306	21	̸=	̸=	PROPN
ejpam-4735	306	22	{	{	PUNCT
ejpam-4735	306	23	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	306	24	,	,	PUNCT
ejpam-4735	306	25	s	s	NOUN
ejpam-4735	306	26	)	)	PUNCT
ejpam-4735	306	27	.	.	PUNCT
ejpam-4735	307	1	since	since	SCONJ
ejpam-4735	307	2	(	(	PUNCT
ejpam-4735	307	3	x	x	X
ejpam-4735	307	4	,	,	PUNCT
ejpam-4735	307	5	τ	τ	X
ejpam-4735	307	6	)	)	PUNCT
ejpam-4735	307	7	is	be	AUX
ejpam-4735	307	8	δp(λ	δp(λ	NOUN
ejpam-4735	307	9	,	,	PUNCT
ejpam-4735	307	10	s)-r1	s)-r1	NOUN
ejpam-4735	307	11	,	,	PUNCT
ejpam-4735	307	12	there	there	PRON
ejpam-4735	307	13	exist	exist	VERB
ejpam-4735	307	14	disjoint	disjoint	NOUN
ejpam-4735	307	15	δp(λ	δp(λ	NOUN
ejpam-4735	307	16	,	,	PUNCT
ejpam-4735	307	17	s)-open	s)-open	PUNCT
ejpam-4735	307	18	sets	set	VERB
ejpam-4735	307	19	u	u	NOUN
ejpam-4735	307	20	and	and	CCONJ
ejpam-4735	307	21	v	v	NOUN
ejpam-4735	307	22	of	of	ADP
ejpam-4735	307	23	x	x	PUNCT
ejpam-4735	307	24	such	such	ADJ
ejpam-4735	307	25	that	that	SCONJ
ejpam-4735	307	26	{	{	PUNCT
ejpam-4735	307	27	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	307	28	,	,	PUNCT
ejpam-4735	307	29	s	s	PART
ejpam-4735	307	30	)	)	PUNCT
ejpam-4735	308	1	⊆	⊆	NUM
ejpam-4735	308	2	u	u	NOUN
ejpam-4735	308	3	and	and	CCONJ
ejpam-4735	308	4	{	{	PUNCT
ejpam-4735	308	5	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	308	6	,	,	PUNCT
ejpam-4735	308	7	s	s	NOUN
ejpam-4735	308	8	)	)	PUNCT
ejpam-4735	308	9	⊆	⊆	NUM
ejpam-4735	308	10	v	v	NOUN
ejpam-4735	308	11	.	.	PUNCT
ejpam-4735	309	1	since	since	SCONJ
ejpam-4735	309	2	{	{	PUNCT
ejpam-4735	309	3	x}∩v	x}∩v	PRON
ejpam-4735	309	4	δp(λ	δp(λ	NOUN
ejpam-4735	309	5	,	,	PUNCT
ejpam-4735	309	6	s	s	PART
ejpam-4735	309	7	)	)	PUNCT
ejpam-4735	309	8	⊆	⊆	NUM
ejpam-4735	309	9	u	u	NOUN
ejpam-4735	309	10	∩v	∩v	NOUN
ejpam-4735	309	11	δp(λ	δp(λ	NOUN
ejpam-4735	309	12	,	,	PUNCT
ejpam-4735	309	13	s	s	PART
ejpam-4735	309	14	)	)	PUNCT
ejpam-4735	309	15	=	=	SYM
ejpam-4735	309	16	∅	∅	NOUN
ejpam-4735	309	17	,	,	PUNCT
ejpam-4735	309	18	y	y	PROPN
ejpam-4735	309	19	̸∈	̸∈	PROPN
ejpam-4735	309	20	{	{	PUNCT
ejpam-4735	309	21	x}θδp(λ	x}θδp(λ	PROPN
ejpam-4735	309	22	,	,	PUNCT
ejpam-4735	309	23	s	s	NOUN
ejpam-4735	309	24	)	)	PUNCT
ejpam-4735	309	25	.	.	PUNCT
ejpam-4735	310	1	thus	thus	ADV
ejpam-4735	310	2	,	,	PUNCT
ejpam-4735	310	3	{	{	PUNCT
ejpam-4735	310	4	x}θδp(λ	x}θδp(λ	NOUN
ejpam-4735	310	5	,	,	PUNCT
ejpam-4735	310	6	s	s	PART
ejpam-4735	310	7	)	)	PUNCT
ejpam-4735	310	8	⊆	⊆	NUM
ejpam-4735	310	9	⟨x⟩δp(λ	⟨x⟩δp(λ	NOUN
ejpam-4735	310	10	,	,	PUNCT
ejpam-4735	310	11	s	s	PART
ejpam-4735	310	12	)	)	PUNCT
ejpam-4735	310	13	and	and	CCONJ
ejpam-4735	310	14	hence	hence	ADV
ejpam-4735	310	15	{	{	PUNCT
ejpam-4735	310	16	x}θδp(λ	x}θδp(λ	PROPN
ejpam-4735	310	17	,	,	PUNCT
ejpam-4735	310	18	s	s	NOUN
ejpam-4735	310	19	)	)	PUNCT
ejpam-4735	310	20	=	=	SYM
ejpam-4735	310	21	⟨x⟩δp(λ	⟨x⟩δp(λ	NOUN
ejpam-4735	310	22	,	,	PUNCT
ejpam-4735	310	23	s	s	NOUN
ejpam-4735	310	24	)	)	PUNCT
ejpam-4735	310	25	.	.	PUNCT
ejpam-4735	311	1	conversely	conversely	ADV
ejpam-4735	311	2	,	,	PUNCT
ejpam-4735	311	3	suppose	suppose	VERB
ejpam-4735	311	4	that	that	SCONJ
ejpam-4735	311	5	{	{	PUNCT
ejpam-4735	311	6	x}θδp(λ	x}θδp(λ	NOUN
ejpam-4735	311	7	,	,	PUNCT
ejpam-4735	311	8	s	s	NOUN
ejpam-4735	311	9	)	)	PUNCT
ejpam-4735	311	10	=	=	SYM
ejpam-4735	311	11	⟨x⟩δp(λ	⟨x⟩δp(λ	NOUN
ejpam-4735	311	12	,	,	PUNCT
ejpam-4735	311	13	s	s	NOUN
ejpam-4735	311	14	)	)	PUNCT
ejpam-4735	311	15	for	for	ADP
ejpam-4735	311	16	each	each	DET
ejpam-4735	311	17	x	x	SYM
ejpam-4735	311	18	∈	∈	PROPN
ejpam-4735	311	19	x.	x.	NOUN
ejpam-4735	311	20	then	then	ADV
ejpam-4735	311	21	,	,	PUNCT
ejpam-4735	311	22	⟨x⟩δp(λ	⟨x⟩δp(λ	NOUN
ejpam-4735	311	23	,	,	PUNCT
ejpam-4735	311	24	s	s	PART
ejpam-4735	311	25	)	)	PUNCT
ejpam-4735	311	26	=	=	SYM
ejpam-4735	311	27	{	{	PUNCT
ejpam-4735	311	28	x}θδp(λ	x}θδp(λ	PROPN
ejpam-4735	311	29	,	,	PUNCT
ejpam-4735	311	30	s	s	PART
ejpam-4735	311	31	)	)	PUNCT
ejpam-4735	311	32	⊇	⊇	X
ejpam-4735	311	33	{	{	PUNCT
ejpam-4735	311	34	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	311	35	,	,	PUNCT
ejpam-4735	311	36	s	s	PART
ejpam-4735	311	37	)	)	PUNCT
ejpam-4735	311	38	⊇	⊇	NOUN
ejpam-4735	311	39	⟨x⟩δp(λ	⟨x⟩δp(λ	NOUN
ejpam-4735	311	40	,	,	PUNCT
ejpam-4735	311	41	s	s	PART
ejpam-4735	311	42	)	)	PUNCT
ejpam-4735	311	43	and	and	CCONJ
ejpam-4735	311	44	⟨x⟩δp(λ	⟨x⟩δp(λ	NOUN
ejpam-4735	311	45	,	,	PUNCT
ejpam-4735	311	46	s	s	PART
ejpam-4735	311	47	)	)	PUNCT
ejpam-4735	311	48	=	=	SYM
ejpam-4735	311	49	{	{	PUNCT
ejpam-4735	311	50	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	311	51	,	,	PUNCT
ejpam-4735	311	52	s	s	NOUN
ejpam-4735	311	53	)	)	PUNCT
ejpam-4735	311	54	for	for	ADP
ejpam-4735	311	55	each	each	DET
ejpam-4735	311	56	x	x	SYM
ejpam-4735	311	57	∈	∈	PROPN
ejpam-4735	311	58	x.	x.	NOUN
ejpam-4735	311	59	by	by	ADP
ejpam-4735	311	60	theorem	theorem	NOUN
ejpam-4735	311	61	6	6	NUM
ejpam-4735	311	62	,	,	PUNCT
ejpam-4735	311	63	(	(	PUNCT
ejpam-4735	311	64	x	x	X
ejpam-4735	311	65	,	,	PUNCT
ejpam-4735	311	66	τ	τ	X
ejpam-4735	311	67	)	)	PUNCT
ejpam-4735	311	68	is	be	AUX
ejpam-4735	311	69	δp(λ	δp(λ	NOUN
ejpam-4735	311	70	,	,	PUNCT
ejpam-4735	311	71	s)-r0	s)-r0	X
ejpam-4735	311	72	.	.	PUNCT
ejpam-4735	311	73	suppose	suppose	VERB
ejpam-4735	311	74	that	that	SCONJ
ejpam-4735	311	75	{	{	PUNCT
ejpam-4735	311	76	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	311	77	,	,	PUNCT
ejpam-4735	311	78	s	s	PART
ejpam-4735	311	79	)	)	PUNCT
ejpam-4735	311	80	̸=	̸=	PROPN
ejpam-4735	311	81	{	{	PUNCT
ejpam-4735	311	82	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	311	83	,	,	PUNCT
ejpam-4735	311	84	s	s	NOUN
ejpam-4735	311	85	)	)	PUNCT
ejpam-4735	311	86	.	.	PUNCT
ejpam-4735	312	1	thus	thus	ADV
ejpam-4735	312	2	,	,	PUNCT
ejpam-4735	312	3	by	by	ADP
ejpam-4735	312	4	corollary	corollary	ADJ
ejpam-4735	312	5	1	1	NUM
ejpam-4735	312	6	,	,	PUNCT
ejpam-4735	312	7	{	{	PUNCT
ejpam-4735	312	8	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	312	9	,	,	PUNCT
ejpam-4735	312	10	s)∩{y}δp(λ	s)∩{y}δp(λ	PROPN
ejpam-4735	312	11	,	,	PUNCT
ejpam-4735	312	12	s	s	PART
ejpam-4735	312	13	)	)	PUNCT
ejpam-4735	312	14	=	=	PUNCT
ejpam-4735	312	15	∅.	∅.	X
ejpam-4735	312	16	by	by	ADP
ejpam-4735	312	17	theorem	theorem	ADJ
ejpam-4735	312	18	6	6	NUM
ejpam-4735	312	19	,	,	PUNCT
ejpam-4735	312	20	⟨x⟩δp(λ	⟨x⟩δp(λ	NOUN
ejpam-4735	312	21	,	,	PUNCT
ejpam-4735	312	22	s	s	NOUN
ejpam-4735	312	23	)	)	PUNCT
ejpam-4735	312	24	∩	∩	ADJ
ejpam-4735	312	25	⟨y⟩δp(λ	⟨y⟩δp(λ	ADP
ejpam-4735	312	26	,	,	PUNCT
ejpam-4735	312	27	s	s	PART
ejpam-4735	312	28	)	)	PUNCT
ejpam-4735	312	29	=	=	NOUN
ejpam-4735	312	30	∅	∅	NOUN
ejpam-4735	312	31	and	and	CCONJ
ejpam-4735	312	32	hence	hence	ADV
ejpam-4735	312	33	{	{	PUNCT
ejpam-4735	312	34	x}θδ(λ	x}θδ(λ	PROPN
ejpam-4735	312	35	,	,	PUNCT
ejpam-4735	312	36	s	s	NOUN
ejpam-4735	312	37	)	)	PUNCT
ejpam-4735	312	38	∩	∩	NOUN
ejpam-4735	312	39	{	{	PUNCT
ejpam-4735	312	40	y}θδp(λ	y}θδp(λ	PROPN
ejpam-4735	312	41	,	,	PUNCT
ejpam-4735	312	42	s	s	PART
ejpam-4735	312	43	)	)	PUNCT
ejpam-4735	312	44	=	=	PUNCT
ejpam-4735	312	45	∅.	∅.	NOUN
ejpam-4735	312	46	since	since	SCONJ
ejpam-4735	312	47	y	y	PROPN
ejpam-4735	312	48	̸∈	̸∈	PROPN
ejpam-4735	312	49	{	{	PUNCT
ejpam-4735	312	50	x}θδp(λ	x}θδp(λ	PROPN
ejpam-4735	312	51	,	,	PUNCT
ejpam-4735	312	52	s	s	PART
ejpam-4735	312	53	)	)	PUNCT
ejpam-4735	312	54	,	,	PUNCT
ejpam-4735	312	55	there	there	PRON
ejpam-4735	312	56	exists	exist	VERB
ejpam-4735	312	57	a	a	DET
ejpam-4735	312	58	δp(λ	δp(λ	NOUN
ejpam-4735	312	59	,	,	PUNCT
ejpam-4735	312	60	s)-open	s)-open	VERB
ejpam-4735	312	61	set	set	VERB
ejpam-4735	312	62	u	u	NOUN
ejpam-4735	312	63	of	of	ADP
ejpam-4735	312	64	x	x	SYM
ejpam-4735	312	65	such	such	ADJ
ejpam-4735	312	66	that	that	SCONJ
ejpam-4735	312	67	y	y	PROPN
ejpam-4735	312	68	∈	∈	PROPN
ejpam-4735	312	69	u	u	NOUN
ejpam-4735	312	70	⊆	⊆	NUM
ejpam-4735	312	71	u	u	NOUN
ejpam-4735	312	72	δp(λ	δp(λ	NOUN
ejpam-4735	312	73	,	,	PUNCT
ejpam-4735	312	74	s	s	PART
ejpam-4735	312	75	)	)	PUNCT
ejpam-4735	312	76	⊆	⊆	NUM
ejpam-4735	312	77	x	x	SYM
ejpam-4735	312	78	−	−	PROPN
ejpam-4735	312	79	{	{	PUNCT
ejpam-4735	312	80	x	x	NOUN
ejpam-4735	312	81	}	}	PUNCT
ejpam-4735	312	82	.	.	PUNCT
ejpam-4735	313	1	let	let	VERB
ejpam-4735	313	2	v	v	VERB
ejpam-4735	313	3	=	=	NOUN
ejpam-4735	313	4	x	x	SYM
ejpam-4735	313	5	−	−	PROPN
ejpam-4735	313	6	u	u	PROPN
ejpam-4735	313	7	δp(λ	δp(λ	NOUN
ejpam-4735	313	8	,	,	PUNCT
ejpam-4735	313	9	s	s	PART
ejpam-4735	313	10	)	)	PUNCT
ejpam-4735	313	11	,	,	PUNCT
ejpam-4735	313	12	then	then	ADV
ejpam-4735	313	13	x	x	SYM
ejpam-4735	313	14	∈	∈	PROPN
ejpam-4735	313	15	v	v	ADP
ejpam-4735	313	16	∈	∈	PROPN
ejpam-4735	313	17	δp(λ	δp(λ	NOUN
ejpam-4735	313	18	,	,	PUNCT
ejpam-4735	313	19	s)o(x	s)o(x	PROPN
ejpam-4735	313	20	,	,	PUNCT
ejpam-4735	313	21	τ	τ	PROPN
ejpam-4735	313	22	)	)	PUNCT
ejpam-4735	313	23	.	.	PUNCT
ejpam-4735	314	1	since	since	SCONJ
ejpam-4735	314	2	(	(	PUNCT
ejpam-4735	314	3	x	x	X
ejpam-4735	314	4	,	,	PUNCT
ejpam-4735	314	5	τ	τ	X
ejpam-4735	314	6	)	)	PUNCT
ejpam-4735	314	7	is	be	AUX
ejpam-4735	314	8	δp(λ	δp(λ	NOUN
ejpam-4735	314	9	,	,	PUNCT
ejpam-4735	314	10	s)-r0	s)-r0	X
ejpam-4735	314	11	,	,	PUNCT
ejpam-4735	314	12	{	{	PUNCT
ejpam-4735	314	13	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	314	14	,	,	PUNCT
ejpam-4735	314	15	s	s	NOUN
ejpam-4735	314	16	)	)	PUNCT
ejpam-4735	314	17	⊆	⊆	NUM
ejpam-4735	314	18	u	u	NOUN
ejpam-4735	314	19	,	,	PUNCT
ejpam-4735	314	20	{	{	PUNCT
ejpam-4735	314	21	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	314	22	,	,	PUNCT
ejpam-4735	314	23	s	s	PART
ejpam-4735	314	24	)	)	PUNCT
ejpam-4735	314	25	⊆	⊆	NUM
ejpam-4735	314	26	v	v	NOUN
ejpam-4735	314	27	and	and	CCONJ
ejpam-4735	314	28	u	u	NOUN
ejpam-4735	314	29	∩	∩	NOUN
ejpam-4735	314	30	v	v	NOUN
ejpam-4735	314	31	=	=	PUNCT
ejpam-4735	314	32	∅.	∅.	ADP
ejpam-4735	314	33	this	this	DET
ejpam-4735	314	34	shows	show	VERB
ejpam-4735	314	35	that	that	SCONJ
ejpam-4735	314	36	(	(	PUNCT
ejpam-4735	314	37	x	x	X
ejpam-4735	314	38	,	,	PUNCT
ejpam-4735	314	39	τ	τ	X
ejpam-4735	314	40	)	)	PUNCT
ejpam-4735	314	41	is	be	AUX
ejpam-4735	314	42	δp(λ	δp(λ	NOUN
ejpam-4735	314	43	,	,	PUNCT
ejpam-4735	314	44	s)-r1	s)-r1	NOUN
ejpam-4735	314	45	.	.	PUNCT
ejpam-4735	315	1	corollary	corollary	ADJ
ejpam-4735	315	2	3	3	NUM
ejpam-4735	315	3	.	.	PUNCT
ejpam-4735	316	1	a	a	DET
ejpam-4735	316	2	topological	topological	ADJ
ejpam-4735	316	3	space	space	NOUN
ejpam-4735	316	4	(	(	PUNCT
ejpam-4735	316	5	x	x	X
ejpam-4735	316	6	,	,	PUNCT
ejpam-4735	316	7	τ	τ	X
ejpam-4735	316	8	)	)	PUNCT
ejpam-4735	316	9	is	be	AUX
ejpam-4735	316	10	δp(λ	δp(λ	NOUN
ejpam-4735	316	11	,	,	PUNCT
ejpam-4735	316	12	s)-r1	s)-r1	NOUN
ejpam-4735	316	13	if	if	SCONJ
ejpam-4735	316	14	and	and	CCONJ
ejpam-4735	316	15	only	only	ADV
ejpam-4735	316	16	if	if	SCONJ
ejpam-4735	316	17	{	{	PUNCT
ejpam-4735	316	18	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	316	19	,	,	PUNCT
ejpam-4735	316	20	s	s	PART
ejpam-4735	316	21	)	)	PUNCT
ejpam-4735	316	22	=	=	PRON
ejpam-4735	316	23	{	{	PUNCT
ejpam-4735	316	24	x}θδp(λ	x}θδp(λ	PROPN
ejpam-4735	316	25	,	,	PUNCT
ejpam-4735	316	26	s	s	NOUN
ejpam-4735	316	27	)	)	PUNCT
ejpam-4735	316	28	for	for	ADP
ejpam-4735	316	29	each	each	DET
ejpam-4735	316	30	x	x	SYM
ejpam-4735	316	31	∈	∈	PROPN
ejpam-4735	316	32	x.	x.	NOUN
ejpam-4735	316	33	proof	proof	NOUN
ejpam-4735	316	34	.	.	PUNCT
ejpam-4735	317	1	let	let	VERB
ejpam-4735	317	2	(	(	PUNCT
ejpam-4735	317	3	x	x	NOUN
ejpam-4735	317	4	,	,	PUNCT
ejpam-4735	317	5	τ	τ	X
ejpam-4735	317	6	)	)	PUNCT
ejpam-4735	317	7	be	be	AUX
ejpam-4735	317	8	a	a	DET
ejpam-4735	317	9	δp(λ	δp(λ	NOUN
ejpam-4735	317	10	,	,	PUNCT
ejpam-4735	317	11	s)-r1	s)-r1	NOUN
ejpam-4735	317	12	space	space	NOUN
ejpam-4735	317	13	.	.	PUNCT
ejpam-4735	318	1	by	by	ADP
ejpam-4735	318	2	theorem	theorem	NOUN
ejpam-4735	318	3	8	8	NUM
ejpam-4735	318	4	,	,	PUNCT
ejpam-4735	318	5	we	we	PRON
ejpam-4735	318	6	have	have	AUX
ejpam-4735	318	7	{	{	PUNCT
ejpam-4735	318	8	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	318	9	,	,	PUNCT
ejpam-4735	318	10	s	s	PART
ejpam-4735	318	11	)	)	PUNCT
ejpam-4735	318	12	⊇	⊇	NOUN
ejpam-4735	318	13	⟨x⟩δp(λ	⟨x⟩δp(λ	PROPN
ejpam-4735	318	14	,	,	PUNCT
ejpam-4735	318	15	s	s	PART
ejpam-4735	318	16	)	)	PUNCT
ejpam-4735	318	17	=	=	SYM
ejpam-4735	318	18	{	{	PUNCT
ejpam-4735	318	19	x}θδp(λ	x}θδp(λ	PROPN
ejpam-4735	318	20	,	,	PUNCT
ejpam-4735	318	21	s	s	PART
ejpam-4735	318	22	)	)	PUNCT
ejpam-4735	318	23	⊇	⊇	X
ejpam-4735	318	24	{	{	PUNCT
ejpam-4735	318	25	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	318	26	,	,	PUNCT
ejpam-4735	318	27	s	s	PART
ejpam-4735	318	28	)	)	PUNCT
ejpam-4735	318	29	and	and	CCONJ
ejpam-4735	318	30	hence	hence	ADV
ejpam-4735	318	31	{	{	PUNCT
ejpam-4735	318	32	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	318	33	,	,	PUNCT
ejpam-4735	318	34	s	s	PART
ejpam-4735	318	35	)	)	PUNCT
ejpam-4735	318	36	=	=	PRON
ejpam-4735	318	37	{	{	PUNCT
ejpam-4735	318	38	x}θδp(λ	x}θδp(λ	PROPN
ejpam-4735	318	39	,	,	PUNCT
ejpam-4735	318	40	s	s	NOUN
ejpam-4735	318	41	)	)	PUNCT
ejpam-4735	318	42	for	for	ADP
ejpam-4735	318	43	each	each	DET
ejpam-4735	318	44	x	x	SYM
ejpam-4735	318	45	∈	∈	PROPN
ejpam-4735	318	46	x.	x.	NOUN
ejpam-4735	318	47	references	reference	VERB
ejpam-4735	318	48	156	156	NUM
ejpam-4735	318	49	conversely	conversely	ADV
ejpam-4735	318	50	,	,	PUNCT
ejpam-4735	318	51	suppose	suppose	VERB
ejpam-4735	318	52	that	that	SCONJ
ejpam-4735	318	53	{	{	PUNCT
ejpam-4735	318	54	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	318	55	,	,	PUNCT
ejpam-4735	318	56	s	s	NOUN
ejpam-4735	318	57	)	)	PUNCT
ejpam-4735	318	58	=	=	PRON
ejpam-4735	318	59	{	{	PUNCT
ejpam-4735	318	60	x}θδp(λ	x}θδp(λ	PROPN
ejpam-4735	318	61	,	,	PUNCT
ejpam-4735	318	62	s	s	NOUN
ejpam-4735	318	63	)	)	PUNCT
ejpam-4735	318	64	for	for	ADP
ejpam-4735	318	65	each	each	DET
ejpam-4735	318	66	x	x	SYM
ejpam-4735	318	67	∈	∈	PROPN
ejpam-4735	318	68	x.	x.	NOUN
ejpam-4735	318	69	first	first	ADV
ejpam-4735	318	70	,	,	PUNCT
ejpam-4735	318	71	we	we	PRON
ejpam-4735	318	72	show	show	VERB
ejpam-4735	318	73	that	that	SCONJ
ejpam-4735	318	74	(	(	PUNCT
ejpam-4735	318	75	x	x	X
ejpam-4735	318	76	,	,	PUNCT
ejpam-4735	318	77	τ	τ	X
ejpam-4735	318	78	)	)	PUNCT
ejpam-4735	318	79	is	be	AUX
ejpam-4735	318	80	δp(λ	δp(λ	NOUN
ejpam-4735	318	81	,	,	PUNCT
ejpam-4735	318	82	s)-r0	s)-r0	X
ejpam-4735	318	83	.	.	PUNCT
ejpam-4735	319	1	let	let	VERB
ejpam-4735	319	2	u	u	PRON
ejpam-4735	319	3	∈	∈	PROPN
ejpam-4735	319	4	δp(λ	δp(λ	NOUN
ejpam-4735	319	5	,	,	PUNCT
ejpam-4735	319	6	s)o(x	s)o(x	PROPN
ejpam-4735	319	7	,	,	PUNCT
ejpam-4735	319	8	τ	τ	X
ejpam-4735	319	9	)	)	PUNCT
ejpam-4735	319	10	and	and	CCONJ
ejpam-4735	319	11	x	x	PUNCT
ejpam-4735	319	12	∈	∈	PROPN
ejpam-4735	319	13	u	u	NOUN
ejpam-4735	319	14	.	.	PUNCT
ejpam-4735	320	1	let	let	VERB
ejpam-4735	320	2	y	y	PROPN
ejpam-4735	320	3	̸∈	̸∈	PROPN
ejpam-4735	320	4	u	u	PROPN
ejpam-4735	320	5	.	.	PUNCT
ejpam-4735	321	1	then	then	ADV
ejpam-4735	321	2	,	,	PUNCT
ejpam-4735	321	3	u	u	PROPN
ejpam-4735	321	4	∩	∩	NOUN
ejpam-4735	321	5	{	{	PUNCT
ejpam-4735	321	6	y}δp(λ	y}δp(λ	PROPN
ejpam-4735	321	7	,	,	PUNCT
ejpam-4735	321	8	s	s	NOUN
ejpam-4735	321	9	)	)	PUNCT
ejpam-4735	321	10	=	=	SYM
ejpam-4735	321	11	u	u	PROPN
ejpam-4735	321	12	∩	∩	NOUN
ejpam-4735	321	13	{	{	PUNCT
ejpam-4735	321	14	y}θδp(λ	y}θδp(λ	PROPN
ejpam-4735	321	15	,	,	PUNCT
ejpam-4735	321	16	s	s	PART
ejpam-4735	321	17	)	)	PUNCT
ejpam-4735	321	18	=	=	PUNCT
ejpam-4735	321	19	∅.	∅.	ADP
ejpam-4735	321	20	thus	thus	ADV
ejpam-4735	321	21	,	,	PUNCT
ejpam-4735	321	22	x	x	PROPN
ejpam-4735	321	23	̸∈	̸∈	PROPN
ejpam-4735	321	24	{	{	PUNCT
ejpam-4735	321	25	y}θδp(λ	y}θδp(λ	PROPN
ejpam-4735	321	26	,	,	PUNCT
ejpam-4735	321	27	s	s	PROPN
ejpam-4735	321	28	)	)	PUNCT
ejpam-4735	321	29	.	.	PUNCT
ejpam-4735	322	1	there	there	PRON
ejpam-4735	322	2	exists	exist	VERB
ejpam-4735	322	3	v	v	ADP
ejpam-4735	322	4	∈	∈	PROPN
ejpam-4735	322	5	δp(λ	δp(λ	NOUN
ejpam-4735	322	6	,	,	PUNCT
ejpam-4735	322	7	s)o(x	s)o(x	PROPN
ejpam-4735	322	8	,	,	PUNCT
ejpam-4735	322	9	τ	τ	X
ejpam-4735	322	10	)	)	PUNCT
ejpam-4735	322	11	such	such	ADJ
ejpam-4735	322	12	that	that	SCONJ
ejpam-4735	322	13	x	x	SYM
ejpam-4735	322	14	∈	∈	PROPN
ejpam-4735	322	15	v	v	NOUN
ejpam-4735	322	16	and	and	CCONJ
ejpam-4735	322	17	y	y	PROPN
ejpam-4735	322	18	̸∈	̸∈	PROPN
ejpam-4735	322	19	v	v	PROPN
ejpam-4735	322	20	δp(λ	δp(λ	NOUN
ejpam-4735	322	21	,	,	PUNCT
ejpam-4735	322	22	s	s	NOUN
ejpam-4735	322	23	)	)	PUNCT
ejpam-4735	322	24	.	.	PUNCT
ejpam-4735	323	1	since	since	SCONJ
ejpam-4735	323	2	{	{	PUNCT
ejpam-4735	323	3	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	323	4	,	,	PUNCT
ejpam-4735	323	5	s	s	PART
ejpam-4735	323	6	)	)	PUNCT
ejpam-4735	323	7	⊆	⊆	NUM
ejpam-4735	323	8	v	v	NOUN
ejpam-4735	323	9	δp(λ	δp(λ	NOUN
ejpam-4735	323	10	,	,	PUNCT
ejpam-4735	323	11	s	s	PART
ejpam-4735	323	12	)	)	PUNCT
ejpam-4735	323	13	,	,	PUNCT
ejpam-4735	323	14	y	y	PROPN
ejpam-4735	323	15	̸∈	̸∈	PROPN
ejpam-4735	323	16	{	{	PUNCT
ejpam-4735	323	17	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	323	18	,	,	PUNCT
ejpam-4735	323	19	s	s	NOUN
ejpam-4735	323	20	)	)	PUNCT
ejpam-4735	323	21	.	.	PUNCT
ejpam-4735	324	1	this	this	PRON
ejpam-4735	324	2	shows	show	VERB
ejpam-4735	324	3	that	that	SCONJ
ejpam-4735	324	4	{	{	PUNCT
ejpam-4735	324	5	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	324	6	,	,	PUNCT
ejpam-4735	324	7	s	s	PART
ejpam-4735	324	8	)	)	PUNCT
ejpam-4735	324	9	⊆	⊆	NUM
ejpam-4735	324	10	u	u	NOUN
ejpam-4735	324	11	and	and	CCONJ
ejpam-4735	324	12	hence	hence	ADV
ejpam-4735	324	13	(	(	PUNCT
ejpam-4735	324	14	x	x	X
ejpam-4735	324	15	,	,	PUNCT
ejpam-4735	324	16	τ	τ	X
ejpam-4735	324	17	)	)	PUNCT
ejpam-4735	324	18	is	be	AUX
ejpam-4735	324	19	δp(λ	δp(λ	NOUN
ejpam-4735	324	20	,	,	PUNCT
ejpam-4735	324	21	s)-r0	s)-r0	X
ejpam-4735	324	22	.	.	PUNCT
ejpam-4735	325	1	by	by	ADP
ejpam-4735	325	2	theorem	theorem	NOUN
ejpam-4735	325	3	6	6	NUM
ejpam-4735	325	4	,	,	PUNCT
ejpam-4735	325	5	⟨x⟩δp(λ	⟨x⟩δp(λ	NOUN
ejpam-4735	325	6	,	,	PUNCT
ejpam-4735	325	7	s	s	PART
ejpam-4735	325	8	)	)	PUNCT
ejpam-4735	325	9	=	=	SYM
ejpam-4735	325	10	{	{	PUNCT
ejpam-4735	325	11	x}δp(λ	x}δp(λ	PROPN
ejpam-4735	325	12	,	,	PUNCT
ejpam-4735	325	13	s	s	PART
ejpam-4735	325	14	)	)	PUNCT
ejpam-4735	325	15	=	=	PRON
ejpam-4735	325	16	{	{	PUNCT
ejpam-4735	325	17	x}θδp(λ	x}θδp(λ	PROPN
ejpam-4735	325	18	,	,	PUNCT
ejpam-4735	325	19	s	s	NOUN
ejpam-4735	325	20	)	)	PUNCT
ejpam-4735	325	21	for	for	ADP
ejpam-4735	325	22	each	each	DET
ejpam-4735	325	23	x	x	SYM
ejpam-4735	325	24	∈	∈	PROPN
ejpam-4735	325	25	x.	x.	NOUN
ejpam-4735	325	26	thus	thus	ADV
ejpam-4735	325	27	,	,	PUNCT
ejpam-4735	325	28	by	by	SCONJ
ejpam-4735	325	29	theorem	theorem	NOUN
ejpam-4735	325	30	8	8	NUM
ejpam-4735	325	31	,	,	PUNCT
ejpam-4735	325	32	(	(	PUNCT
ejpam-4735	325	33	x	x	X
ejpam-4735	325	34	,	,	PUNCT
ejpam-4735	325	35	τ	τ	X
ejpam-4735	325	36	)	)	PUNCT
ejpam-4735	325	37	is	be	AUX
ejpam-4735	325	38	δp(λ	δp(λ	NOUN
ejpam-4735	325	39	,	,	PUNCT
ejpam-4735	325	40	s)-r1	s)-r1	NOUN
ejpam-4735	325	41	.	.	PUNCT
ejpam-4735	326	1	acknowledgements	acknowledgement	NOUN
ejpam-4735	326	2	this	this	DET
ejpam-4735	326	3	research	research	NOUN
ejpam-4735	326	4	project	project	NOUN
ejpam-4735	326	5	was	be	AUX
ejpam-4735	326	6	financially	financially	ADV
ejpam-4735	326	7	supported	support	VERB
ejpam-4735	326	8	by	by	ADP
ejpam-4735	326	9	mahasarakham	mahasarakham	PROPN
ejpam-4735	326	10	university	university	PROPN
ejpam-4735	326	11	.	.	PUNCT
ejpam-4735	327	1	references	reference	NOUN
ejpam-4735	327	2	[	[	X
ejpam-4735	327	3	1	1	NUM
ejpam-4735	327	4	]	]	PUNCT
ejpam-4735	327	5	m.	m.	NOUN
ejpam-4735	327	6	e.	e.	PROPN
ejpam-4735	327	7	abd	abd	PROPN
ejpam-4735	327	8	el	el	PROPN
ejpam-4735	327	9	-	-	PROPN
ejpam-4735	327	10	monsef	monsef	PROPN
ejpam-4735	327	11	a.	a.	PROPN
ejpam-4735	327	12	s.	s.	PROPN
ejpam-4735	327	13	mashhour	mashhour	PROPN
ejpam-4735	327	14	and	and	CCONJ
ejpam-4735	327	15	s.	s.	PROPN
ejpam-4735	327	16	n.	n.	PROPN
ejpam-4735	327	17	el	el	PROPN
ejpam-4735	327	18	-	-	PROPN
ejpam-4735	327	19	deeb	deeb	PROPN
ejpam-4735	327	20	.	.	PUNCT
ejpam-4735	328	1	on	on	ADP
ejpam-4735	328	2	precontinuous	precontinuous	ADJ
ejpam-4735	328	3	and	and	CCONJ
ejpam-4735	328	4	weak	weak	ADJ
ejpam-4735	328	5	precontinuous	precontinuous	ADJ
ejpam-4735	328	6	functions	function	NOUN
ejpam-4735	328	7	.	.	PUNCT
ejpam-4735	329	1	proceedings	proceeding	NOUN
ejpam-4735	329	2	of	of	ADP
ejpam-4735	329	3	the	the	DET
ejpam-4735	329	4	mathematical	mathematical	ADJ
ejpam-4735	329	5	and	and	CCONJ
ejpam-4735	329	6	physical	physical	ADJ
ejpam-4735	329	7	society	society	NOUN
ejpam-4735	329	8	of	of	ADP
ejpam-4735	329	9	egypt	egypt	PROPN
ejpam-4735	329	10	,	,	PUNCT
ejpam-4735	329	11	53:47–53	53:47–53	NUM
ejpam-4735	329	12	,	,	PUNCT
ejpam-4735	329	13	1982	1982	NUM
ejpam-4735	329	14	.	.	PUNCT
ejpam-4735	330	1	[	[	X
ejpam-4735	330	2	2	2	NUM
ejpam-4735	330	3	]	]	PUNCT
ejpam-4735	330	4	c.	c.	PROPN
ejpam-4735	330	5	boonpok	boonpok	PROPN
ejpam-4735	330	6	and	and	CCONJ
ejpam-4735	330	7	j.	j.	PROPN
ejpam-4735	330	8	khampakdee	khampakdee	PROPN
ejpam-4735	330	9	.	.	PUNCT
ejpam-4735	330	10	δs(λ	δs(λ	PROPN
ejpam-4735	330	11	,	,	PUNCT
ejpam-4735	330	12	s)-r0	s)-r0	PRON
ejpam-4735	330	13	spaces	space	VERB
ejpam-4735	330	14	and	and	CCONJ
ejpam-4735	330	15	δs(λ	δs(λ	NOUN
ejpam-4735	330	16	,	,	PUNCT
ejpam-4735	330	17	s)-r1	s)-r1	NOUN
ejpam-4735	330	18	spaces	space	NOUN
ejpam-4735	330	19	.	.	PUNCT
ejpam-4735	331	1	international	international	ADJ
ejpam-4735	331	2	journal	journal	NOUN
ejpam-4735	331	3	of	of	ADP
ejpam-4735	331	4	analysis	analysis	NOUN
ejpam-4735	331	5	and	and	CCONJ
ejpam-4735	331	6	applications	application	NOUN
ejpam-4735	331	7	,	,	PUNCT
ejpam-4735	331	8	21:99	21:99	NUM
ejpam-4735	331	9	,	,	PUNCT
ejpam-4735	331	10	2023	2023	NUM
ejpam-4735	331	11	.	.	PUNCT
ejpam-4735	332	1	[	[	X
ejpam-4735	332	2	3	3	X
ejpam-4735	332	3	]	]	PUNCT
ejpam-4735	332	4	c.	c.	PROPN
ejpam-4735	332	5	boonpok	boonpok	PROPN
ejpam-4735	332	6	and	and	CCONJ
ejpam-4735	332	7	n.	n.	PROPN
ejpam-4735	332	8	srisarakham	srisarakham	PROPN
ejpam-4735	332	9	.	.	PUNCT
ejpam-4735	333	1	properties	property	NOUN
ejpam-4735	333	2	of	of	ADP
ejpam-4735	333	3	generalized	generalized	ADJ
ejpam-4735	333	4	δp(λ	δp(λ	NOUN
ejpam-4735	333	5	,	,	PUNCT
ejpam-4735	333	6	s)-closed	s)-close	VERB
ejpam-4735	333	7	sets	set	NOUN
ejpam-4735	333	8	.	.	PUNCT
ejpam-4735	334	1	european	european	ADJ
ejpam-4735	334	2	journal	journal	PROPN
ejpam-4735	334	3	of	of	ADP
ejpam-4735	334	4	pure	pure	ADJ
ejpam-4735	334	5	and	and	CCONJ
ejpam-4735	334	6	applied	applied	ADJ
ejpam-4735	334	7	mathematics	mathematic	NOUN
ejpam-4735	334	8	,	,	PUNCT
ejpam-4735	334	9	16(4):2581–2596	16(4):2581–2596	NUM
ejpam-4735	334	10	,	,	PUNCT
ejpam-4735	334	11	2023	2023	NUM
ejpam-4735	334	12	.	.	PUNCT
ejpam-4735	335	1	[	[	X
ejpam-4735	335	2	4	4	NUM
ejpam-4735	335	3	]	]	PUNCT
ejpam-4735	335	4	c.	c.	PROPN
ejpam-4735	335	5	boonpok	boonpok	PROPN
ejpam-4735	335	6	and	and	CCONJ
ejpam-4735	335	7	c.	c.	PROPN
ejpam-4735	335	8	viriyapong	viriyapong	PROPN
ejpam-4735	335	9	.	.	PUNCT
ejpam-4735	336	1	on	on	ADP
ejpam-4735	336	2	(	(	PUNCT
ejpam-4735	336	3	λ	λ	PROPN
ejpam-4735	336	4	,	,	PUNCT
ejpam-4735	336	5	p)-closed	p)-close	VERB
ejpam-4735	336	6	sets	set	NOUN
ejpam-4735	336	7	and	and	CCONJ
ejpam-4735	336	8	the	the	DET
ejpam-4735	336	9	related	related	ADJ
ejpam-4735	336	10	notions	notion	NOUN
ejpam-4735	336	11	in	in	ADP
ejpam-4735	336	12	topological	topological	ADJ
ejpam-4735	336	13	spaces	space	NOUN
ejpam-4735	336	14	.	.	PUNCT
ejpam-4735	337	1	european	european	ADJ
ejpam-4735	337	2	journal	journal	PROPN
ejpam-4735	337	3	of	of	ADP
ejpam-4735	337	4	pure	pure	ADJ
ejpam-4735	337	5	and	and	CCONJ
ejpam-4735	337	6	applied	applied	ADJ
ejpam-4735	337	7	mathematics	mathematic	NOUN
ejpam-4735	337	8	,	,	PUNCT
ejpam-4735	337	9	15(2):415	15(2):415	PROPN
ejpam-4735	337	10	–	–	PUNCT
ejpam-4735	337	11	436	436	NUM
ejpam-4735	337	12	,	,	PUNCT
ejpam-4735	337	13	2022	2022	NUM
ejpam-4735	337	14	.	.	PUNCT
ejpam-4735	338	1	[	[	X
ejpam-4735	338	2	5	5	X
ejpam-4735	338	3	]	]	PUNCT
ejpam-4735	338	4	c.	c.	PROPN
ejpam-4735	338	5	boonpok	boonpok	PROPN
ejpam-4735	338	6	and	and	CCONJ
ejpam-4735	338	7	c.	c.	PROPN
ejpam-4735	338	8	viriyapong	viriyapong	PROPN
ejpam-4735	338	9	.	.	PUNCT
ejpam-4735	339	1	on	on	ADP
ejpam-4735	339	2	some	some	DET
ejpam-4735	339	3	forms	form	NOUN
ejpam-4735	339	4	of	of	ADP
ejpam-4735	339	5	closed	closed	ADJ
ejpam-4735	339	6	sets	set	NOUN
ejpam-4735	339	7	and	and	CCONJ
ejpam-4735	339	8	related	related	ADJ
ejpam-4735	339	9	topics	topic	NOUN
ejpam-4735	339	10	.	.	PUNCT
ejpam-4735	340	1	european	european	ADJ
ejpam-4735	340	2	journal	journal	PROPN
ejpam-4735	340	3	of	of	ADP
ejpam-4735	340	4	pure	pure	ADJ
ejpam-4735	340	5	and	and	CCONJ
ejpam-4735	340	6	applied	applied	ADJ
ejpam-4735	340	7	mathematics	mathematic	NOUN
ejpam-4735	340	8	,	,	PUNCT
ejpam-4735	340	9	16(1):336–362	16(1):336–362	NUM
ejpam-4735	340	10	,	,	PUNCT
ejpam-4735	340	11	2023	2023	NUM
ejpam-4735	340	12	.	.	PUNCT
ejpam-4735	341	1	[	[	X
ejpam-4735	341	2	6	6	NUM
ejpam-4735	341	3	]	]	PUNCT
ejpam-4735	341	4	m.	m.	NOUN
ejpam-4735	341	5	caldas	caldas	PROPN
ejpam-4735	341	6	and	and	CCONJ
ejpam-4735	341	7	j.	j.	PROPN
ejpam-4735	341	8	dontchev	dontchev	PROPN
ejpam-4735	341	9	.	.	PUNCT
ejpam-4735	342	1	g.λs	g.λs	ADJ
ejpam-4735	342	2	-	-	PUNCT
ejpam-4735	342	3	sets	set	NOUN
ejpam-4735	342	4	and	and	CCONJ
ejpam-4735	342	5	g.vs	g.vs	NOUN
ejpam-4735	342	6	-	-	PUNCT
ejpam-4735	342	7	sets	set	NOUN
ejpam-4735	342	8	.	.	PUNCT
ejpam-4735	343	1	arxiv	arxiv	NOUN
ejpam-4735	343	2	:	:	PUNCT
ejpam-4735	343	3	math/9810080v1	math/9810080v1	PROPN
ejpam-4735	344	1	[	[	X
ejpam-4735	344	2	math.gn	math.gn	X
ejpam-4735	344	3	]	]	X
ejpam-4735	344	4	,	,	PUNCT
ejpam-4735	344	5	1998	1998	NUM
ejpam-4735	344	6	.	.	PUNCT
ejpam-4735	345	1	[	[	X
ejpam-4735	345	2	7	7	X
ejpam-4735	345	3	]	]	X
ejpam-4735	345	4	m.	m.	NOUN
ejpam-4735	345	5	caldas	caldas	PROPN
ejpam-4735	345	6	,	,	PUNCT
ejpam-4735	345	7	t.	t.	NOUN
ejpam-4735	345	8	fukutake	fukutake	NOUN
ejpam-4735	345	9	,	,	PUNCT
ejpam-4735	345	10	s.	s.	PROPN
ejpam-4735	345	11	jafari	jafari	PROPN
ejpam-4735	345	12	,	,	PUNCT
ejpam-4735	345	13	and	and	CCONJ
ejpam-4735	345	14	t.	t.	PROPN
ejpam-4735	345	15	noiri	noiri	PROPN
ejpam-4735	345	16	.	.	PUNCT
ejpam-4735	346	1	some	some	DET
ejpam-4735	346	2	applications	application	NOUN
ejpam-4735	346	3	of	of	ADP
ejpam-4735	346	4	δ	δ	NOUN
ejpam-4735	346	5	-	-	PUNCT
ejpam-4735	346	6	preopen	preopen	ADJ
ejpam-4735	346	7	sets	set	NOUN
ejpam-4735	346	8	in	in	ADP
ejpam-4735	346	9	topological	topological	ADJ
ejpam-4735	346	10	spaces	space	NOUN
ejpam-4735	346	11	.	.	PUNCT
ejpam-4735	347	1	bulletin	bulletin	NOUN
ejpam-4735	347	2	of	of	ADP
ejpam-4735	347	3	the	the	DET
ejpam-4735	347	4	institute	institute	NOUN
ejpam-4735	347	5	of	of	ADP
ejpam-4735	347	6	mathematics	mathematics	PROPN
ejpam-4735	347	7	,	,	PUNCT
ejpam-4735	347	8	academia	academia	PROPN
ejpam-4735	347	9	sinica	sinica	PROPN
ejpam-4735	347	10	,	,	PUNCT
ejpam-4735	347	11	33(3):261–276	33(3):261–276	NOUN
ejpam-4735	347	12	,	,	PUNCT
ejpam-4735	347	13	2005	2005	NUM
ejpam-4735	347	14	.	.	PUNCT
ejpam-4735	348	1	[	[	X
ejpam-4735	348	2	8	8	NUM
ejpam-4735	348	3	]	]	PUNCT
ejpam-4735	348	4	m.	m.	NOUN
ejpam-4735	348	5	caldas	caldas	PROPN
ejpam-4735	348	6	,	,	PUNCT
ejpam-4735	348	7	m.	m.	NOUN
ejpam-4735	348	8	ganster	ganster	NOUN
ejpam-4735	348	9	,	,	PUNCT
ejpam-4735	348	10	d.	d.	PROPN
ejpam-4735	348	11	n.	n.	PROPN
ejpam-4735	348	12	georgiou	georgiou	PROPN
ejpam-4735	348	13	,	,	PUNCT
ejpam-4735	348	14	s.	s.	PROPN
ejpam-4735	348	15	jafari	jafari	PROPN
ejpam-4735	348	16	,	,	PUNCT
ejpam-4735	348	17	and	and	CCONJ
ejpam-4735	348	18	t.	t.	PROPN
ejpam-4735	348	19	noiri	noiri	PROPN
ejpam-4735	348	20	.	.	PUNCT
ejpam-4735	349	1	δ	δ	PROPN
ejpam-4735	349	2	-	-	PUNCT
ejpam-4735	349	3	semiopen	semiopen	ADJ
ejpam-4735	349	4	sets	set	NOUN
ejpam-4735	349	5	in	in	ADP
ejpam-4735	349	6	topological	topological	ADJ
ejpam-4735	349	7	spaces	space	NOUN
ejpam-4735	349	8	.	.	PUNCT
ejpam-4735	350	1	topology	topology	NOUN
ejpam-4735	350	2	proceedings	proceeding	NOUN
ejpam-4735	350	3	,	,	PUNCT
ejpam-4735	350	4	29(2):369–383	29(2):369–383	NUM
ejpam-4735	350	5	,	,	PUNCT
ejpam-4735	350	6	2005	2005	NUM
ejpam-4735	350	7	.	.	PUNCT
ejpam-4735	351	1	[	[	X
ejpam-4735	351	2	9	9	NUM
ejpam-4735	351	3	]	]	PUNCT
ejpam-4735	351	4	m.	m.	NOUN
ejpam-4735	351	5	caldas	caldas	PROPN
ejpam-4735	351	6	,	,	PUNCT
ejpam-4735	351	7	d.	d.	PROPN
ejpam-4735	351	8	n.	n.	PROPN
ejpam-4735	351	9	georgiou	georgiou	PROPN
ejpam-4735	351	10	,	,	PUNCT
ejpam-4735	351	11	s.	s.	PROPN
ejpam-4735	351	12	jafari	jafari	PROPN
ejpam-4735	351	13	,	,	PUNCT
ejpam-4735	351	14	and	and	CCONJ
ejpam-4735	351	15	t.	t.	PROPN
ejpam-4735	351	16	noiri	noiri	PROPN
ejpam-4735	351	17	.	.	PUNCT
ejpam-4735	352	1	more	more	ADV
ejpam-4735	352	2	on	on	ADP
ejpam-4735	352	3	δ	δ	PROPN
ejpam-4735	352	4	-	-	PUNCT
ejpam-4735	352	5	semiopen	semiopen	ADJ
ejpam-4735	352	6	sets	set	NOUN
ejpam-4735	352	7	.	.	PUNCT
ejpam-4735	353	1	note	note	VERB
ejpam-4735	353	2	di	di	PROPN
ejpam-4735	353	3	matematica	matematica	PROPN
ejpam-4735	353	4	,	,	PUNCT
ejpam-4735	353	5	22(2):1–14	22(2):1–14	PROPN
ejpam-4735	353	6	,	,	PUNCT
ejpam-4735	353	7	2003	2003	NUM
ejpam-4735	353	8	.	.	PUNCT
ejpam-4735	354	1	references	reference	NOUN
ejpam-4735	354	2	157	157	NUM
ejpam-4735	354	3	[	[	X
ejpam-4735	354	4	10	10	NUM
ejpam-4735	354	5	]	]	X
ejpam-4735	354	6	f.	f.	PROPN
ejpam-4735	354	7	cammaroto	cammaroto	NOUN
ejpam-4735	354	8	and	and	CCONJ
ejpam-4735	354	9	t.	t.	PROPN
ejpam-4735	354	10	noiri	noiri	PROPN
ejpam-4735	354	11	.	.	PUNCT
ejpam-4735	355	1	on	on	ADP
ejpam-4735	355	2	λm	λm	NOUN
ejpam-4735	355	3	-	-	PUNCT
ejpam-4735	355	4	sets	set	NOUN
ejpam-4735	355	5	and	and	CCONJ
ejpam-4735	355	6	related	relate	VERB
ejpam-4735	355	7	topological	topological	ADJ
ejpam-4735	355	8	spaces	space	NOUN
ejpam-4735	355	9	.	.	PUNCT
ejpam-4735	356	1	acta	acta	PROPN
ejpam-4735	356	2	mathematica	mathematica	PROPN
ejpam-4735	356	3	hungarica	hungarica	PROPN
ejpam-4735	356	4	,	,	PUNCT
ejpam-4735	356	5	109:261–279	109:261–279	NUM
ejpam-4735	356	6	,	,	PUNCT
ejpam-4735	356	7	2005	2005	NUM
ejpam-4735	356	8	.	.	PUNCT
ejpam-4735	357	1	[	[	X
ejpam-4735	357	2	11	11	NUM
ejpam-4735	357	3	]	]	PUNCT
ejpam-4735	357	4	a.	a.	PROPN
ejpam-4735	357	5	s.	s.	PROPN
ejpam-4735	357	6	davis	davis	PROPN
ejpam-4735	357	7	.	.	PUNCT
ejpam-4735	358	1	indexed	index	VERB
ejpam-4735	358	2	systems	system	NOUN
ejpam-4735	358	3	of	of	ADP
ejpam-4735	358	4	neighborhoods	neighborhood	NOUN
ejpam-4735	358	5	for	for	ADP
ejpam-4735	358	6	general	general	ADJ
ejpam-4735	358	7	topological	topological	ADJ
ejpam-4735	358	8	spaces	space	NOUN
ejpam-4735	358	9	.	.	PUNCT
ejpam-4735	359	1	the	the	DET
ejpam-4735	359	2	american	american	PROPN
ejpam-4735	359	3	mathematical	mathematical	PROPN
ejpam-4735	359	4	monthly	monthly	ADV
ejpam-4735	359	5	,	,	PUNCT
ejpam-4735	359	6	68:886–893	68:886–893	PROPN
ejpam-4735	359	7	,	,	PUNCT
ejpam-4735	359	8	1961	1961	NUM
ejpam-4735	359	9	.	.	PUNCT
ejpam-4735	360	1	[	[	X
ejpam-4735	360	2	12	12	NUM
ejpam-4735	360	3	]	]	X
ejpam-4735	360	4	c.	c.	PROPN
ejpam-4735	360	5	dorsett	dorsett	PROPN
ejpam-4735	360	6	.	.	PUNCT
ejpam-4735	361	1	r0	r0	NOUN
ejpam-4735	361	2	and	and	CCONJ
ejpam-4735	361	3	r1	r1	PROPN
ejpam-4735	361	4	topological	topological	ADJ
ejpam-4735	361	5	spaces	space	NOUN
ejpam-4735	361	6	.	.	PUNCT
ejpam-4735	362	1	matematički	matematički	PROPN
ejpam-4735	362	2	vesnik	vesnik	PROPN
ejpam-4735	362	3	,	,	PUNCT
ejpam-4735	362	4	2(15)(30):117–122	2(15)(30):117–122	NUM
ejpam-4735	362	5	,	,	PUNCT
ejpam-4735	362	6	1978	1978	NUM
ejpam-4735	362	7	.	.	PUNCT
ejpam-4735	363	1	[	[	X
ejpam-4735	363	2	13	13	NUM
ejpam-4735	363	3	]	]	PUNCT
ejpam-4735	363	4	k.	k.	PROPN
ejpam-4735	363	5	k.	k.	PROPN
ejpam-4735	363	6	dube	dube	PROPN
ejpam-4735	363	7	.	.	PUNCT
ejpam-4735	364	1	a	a	DET
ejpam-4735	364	2	note	note	NOUN
ejpam-4735	364	3	on	on	ADP
ejpam-4735	364	4	r0	r0	PROPN
ejpam-4735	364	5	topological	topological	ADJ
ejpam-4735	364	6	spaces	space	NOUN
ejpam-4735	364	7	.	.	PUNCT
ejpam-4735	365	1	matematički	matematički	PROPN
ejpam-4735	365	2	vesnik	vesnik	PROPN
ejpam-4735	365	3	,	,	PUNCT
ejpam-4735	365	4	11:203–208	11:203–208	NUM
ejpam-4735	365	5	,	,	PUNCT
ejpam-4735	365	6	1974	1974	NUM
ejpam-4735	365	7	.	.	PUNCT
ejpam-4735	366	1	[	[	X
ejpam-4735	366	2	14	14	NUM
ejpam-4735	366	3	]	]	X
ejpam-4735	366	4	n.	n.	PROPN
ejpam-4735	366	5	levine	levine	PROPN
ejpam-4735	366	6	.	.	PUNCT
ejpam-4735	367	1	semi	semi	ADJ
ejpam-4735	367	2	-	-	ADJ
ejpam-4735	367	3	open	open	ADJ
ejpam-4735	367	4	sets	set	NOUN
ejpam-4735	367	5	and	and	CCONJ
ejpam-4735	367	6	semi	semi	ADJ
ejpam-4735	367	7	-	-	NOUN
ejpam-4735	367	8	continuity	continuity	NOUN
ejpam-4735	367	9	in	in	ADP
ejpam-4735	367	10	topological	topological	ADJ
ejpam-4735	367	11	spaces	space	NOUN
ejpam-4735	367	12	.	.	PUNCT
ejpam-4735	368	1	the	the	DET
ejpam-4735	368	2	american	american	PROPN
ejpam-4735	368	3	mathematical	mathematical	PROPN
ejpam-4735	368	4	monthly	monthly	ADV
ejpam-4735	368	5	,	,	PUNCT
ejpam-4735	368	6	70:36–41	70:36–41	NUM
ejpam-4735	368	7	,	,	PUNCT
ejpam-4735	368	8	1963	1963	NUM
ejpam-4735	368	9	.	.	PUNCT
ejpam-4735	369	1	[	[	X
ejpam-4735	369	2	15	15	NUM
ejpam-4735	369	3	]	]	X
ejpam-4735	369	4	s.	s.	PROPN
ejpam-4735	369	5	lugojan	lugojan	PROPN
ejpam-4735	369	6	.	.	PUNCT
ejpam-4735	370	1	generalized	generalized	ADJ
ejpam-4735	370	2	topology	topology	NOUN
ejpam-4735	370	3	.	.	PUNCT
ejpam-4735	371	1	studii	studii	PROPN
ejpam-4735	371	2	ş	ş	PROPN
ejpam-4735	371	3	cercetǎri	cercetǎri	PROPN
ejpam-4735	371	4	de	de	X
ejpam-4735	371	5	matematicǎ	matematicǎ	X
ejpam-4735	371	6	,	,	PUNCT
ejpam-4735	371	7	34:348–360	34:348–360	PROPN
ejpam-4735	371	8	,	,	PUNCT
ejpam-4735	371	9	1982	1982	NUM
ejpam-4735	371	10	.	.	PUNCT
ejpam-4735	372	1	[	[	X
ejpam-4735	372	2	16	16	NUM
ejpam-4735	372	3	]	]	PUNCT
ejpam-4735	372	4	s.	s.	PROPN
ejpam-4735	372	5	a.	a.	PROPN
ejpam-4735	372	6	naimpally	naimpally	ADV
ejpam-4735	372	7	.	.	PUNCT
ejpam-4735	373	1	on	on	ADP
ejpam-4735	373	2	r0	r0	PROPN
ejpam-4735	373	3	topological	topological	ADJ
ejpam-4735	373	4	spaces	space	NOUN
ejpam-4735	373	5	.	.	PUNCT
ejpam-4735	374	1	annales	annales	PROPN
ejpam-4735	374	2	universitatis	universitatis	PROPN
ejpam-4735	374	3	scientiarium	scientiarium	PROPN
ejpam-4735	374	4	budapestinensis	budapestinensis	NOUN
ejpam-4735	374	5	de	de	PROPN
ejpam-4735	374	6	rolando	rolando	PROPN
ejpam-4735	374	7	eötvös	eötvös	PROPN
ejpam-4735	374	8	nominatae	nominatae	NOUN
ejpam-4735	374	9	sectio	sectio	NOUN
ejpam-4735	374	10	mathematica	mathematica	PROPN
ejpam-4735	374	11	,	,	PUNCT
ejpam-4735	374	12	10:53–54	10:53–54	NUM
ejpam-4735	374	13	,	,	PUNCT
ejpam-4735	374	14	1967	1967	NUM
ejpam-4735	374	15	.	.	PUNCT
ejpam-4735	375	1	[	[	X
ejpam-4735	375	2	17	17	NUM
ejpam-4735	375	3	]	]	PUNCT
ejpam-4735	375	4	t.	t.	PROPN
ejpam-4735	375	5	noiri	noiri	PROPN
ejpam-4735	375	6	.	.	PUNCT
ejpam-4735	376	1	unified	unify	VERB
ejpam-4735	376	2	characterizations	characterization	NOUN
ejpam-4735	376	3	for	for	ADP
ejpam-4735	376	4	modifications	modification	NOUN
ejpam-4735	376	5	of	of	ADP
ejpam-4735	376	6	r0	r0	NOUN
ejpam-4735	376	7	and	and	CCONJ
ejpam-4735	376	8	r1	r1	PROPN
ejpam-4735	376	9	topological	topological	ADJ
ejpam-4735	376	10	spaces	space	NOUN
ejpam-4735	376	11	.	.	PUNCT
ejpam-4735	377	1	rendiconti	rendiconti	ADJ
ejpam-4735	377	2	del	del	PROPN
ejpam-4735	377	3	circolo	circolo	PROPN
ejpam-4735	377	4	matematico	matematico	NOUN
ejpam-4735	377	5	di	di	PROPN
ejpam-4735	377	6	palermo	palermo	PROPN
ejpam-4735	377	7	series	series	PROPN
ejpam-4735	377	8	2	2	NUM
ejpam-4735	377	9	,	,	PUNCT
ejpam-4735	377	10	60:29–42	60:29–42	NUM
ejpam-4735	377	11	,	,	PUNCT
ejpam-4735	377	12	2006	2006	NUM
ejpam-4735	377	13	.	.	PUNCT
ejpam-4735	378	1	[	[	X
ejpam-4735	378	2	18	18	NUM
ejpam-4735	378	3	]	]	PUNCT
ejpam-4735	378	4	j.	j.	PROPN
ejpam-4735	378	5	h.	h.	PROPN
ejpam-4735	378	6	park	park	PROPN
ejpam-4735	378	7	,	,	PUNCT
ejpam-4735	378	8	b.	b.	PROPN
ejpam-4735	378	9	y.	y.	PROPN
ejpam-4735	378	10	lee	lee	PROPN
ejpam-4735	378	11	,	,	PUNCT
ejpam-4735	378	12	and	and	CCONJ
ejpam-4735	378	13	m.	m.	PROPN
ejpam-4735	378	14	j.	j.	PROPN
ejpam-4735	378	15	son	son	PROPN
ejpam-4735	378	16	.	.	PUNCT
ejpam-4735	379	1	on	on	ADP
ejpam-4735	379	2	δ	δ	PROPN
ejpam-4735	379	3	-	-	PUNCT
ejpam-4735	379	4	semiopen	semiopen	ADJ
ejpam-4735	379	5	sets	set	NOUN
ejpam-4735	379	6	in	in	ADP
ejpam-4735	379	7	topological	topological	ADJ
ejpam-4735	379	8	spaces	space	NOUN
ejpam-4735	379	9	.	.	PUNCT
ejpam-4735	380	1	the	the	DET
ejpam-4735	380	2	journal	journal	NOUN
ejpam-4735	380	3	of	of	ADP
ejpam-4735	380	4	the	the	DET
ejpam-4735	380	5	indian	indian	PROPN
ejpam-4735	380	6	academy	academy	PROPN
ejpam-4735	380	7	of	of	ADP
ejpam-4735	380	8	mathematics	mathematic	NOUN
ejpam-4735	380	9	,	,	PUNCT
ejpam-4735	380	10	19:59–67	19:59–67	NUM
ejpam-4735	380	11	,	,	PUNCT
ejpam-4735	380	12	1997	1997	NUM
ejpam-4735	380	13	.	.	PUNCT
ejpam-4735	381	1	[	[	X
ejpam-4735	381	2	19	19	NUM
ejpam-4735	381	3	]	]	X
ejpam-4735	381	4	s.	s.	PROPN
ejpam-4735	381	5	raychaudhuri	raychaudhuri	PROPN
ejpam-4735	381	6	and	and	CCONJ
ejpam-4735	381	7	m.	m.	PROPN
ejpam-4735	381	8	n.	n.	PROPN
ejpam-4735	381	9	mukherjee	mukherjee	PROPN
ejpam-4735	381	10	.	.	PUNCT
ejpam-4735	382	1	on	on	ADP
ejpam-4735	382	2	δ	δ	PROPN
ejpam-4735	382	3	-	-	PUNCT
ejpam-4735	382	4	almost	almost	ADV
ejpam-4735	382	5	continuity	continuity	NOUN
ejpam-4735	382	6	and	and	CCONJ
ejpam-4735	382	7	δ	δ	NOUN
ejpam-4735	382	8	-	-	PUNCT
ejpam-4735	382	9	preopen	preopen	ADJ
ejpam-4735	382	10	sets	set	NOUN
ejpam-4735	382	11	.	.	PUNCT
ejpam-4735	383	1	bulletin	bulletin	NOUN
ejpam-4735	383	2	of	of	ADP
ejpam-4735	383	3	the	the	DET
ejpam-4735	383	4	institute	institute	NOUN
ejpam-4735	383	5	of	of	ADP
ejpam-4735	383	6	mathematics	mathematics	PROPN
ejpam-4735	383	7	,	,	PUNCT
ejpam-4735	383	8	academia	academia	PROPN
ejpam-4735	383	9	sinica	sinica	PROPN
ejpam-4735	383	10	,	,	PUNCT
ejpam-4735	383	11	21:357–366	21:357–366	PROPN
ejpam-4735	383	12	,	,	PUNCT
ejpam-4735	383	13	1993	1993	NUM
ejpam-4735	383	14	.	.	PUNCT
ejpam-4735	384	1	[	[	X
ejpam-4735	384	2	20	20	NUM
ejpam-4735	384	3	]	]	X
ejpam-4735	384	4	n.	n.	NOUN
ejpam-4735	384	5	a.	a.	NOUN
ejpam-4735	384	6	shanin	shanin	PROPN
ejpam-4735	384	7	.	.	PUNCT
ejpam-4735	385	1	on	on	ADP
ejpam-4735	385	2	separation	separation	NOUN
ejpam-4735	385	3	in	in	ADP
ejpam-4735	385	4	topological	topological	ADJ
ejpam-4735	385	5	spaces	space	NOUN
ejpam-4735	385	6	.	.	PUNCT
ejpam-4735	386	1	doklady	doklady	PROPN
ejpam-4735	386	2	akademii	akademii	NOUN
ejpam-4735	386	3	nauk	nauk	NOUN
ejpam-4735	386	4	sssr	sssr	NOUN
ejpam-4735	386	5	,	,	PUNCT
ejpam-4735	386	6	38:110–113	38:110–113	NUM
ejpam-4735	386	7	,	,	PUNCT
ejpam-4735	386	8	1943	1943	NUM
ejpam-4735	386	9	.	.	PUNCT
ejpam-4735	387	1	[	[	X
ejpam-4735	387	2	21	21	NUM
ejpam-4735	387	3	]	]	X
ejpam-4735	387	4	n.	n.	PROPN
ejpam-4735	387	5	srisarakham	srisarakham	PROPN
ejpam-4735	387	6	and	and	CCONJ
ejpam-4735	387	7	c.	c.	PROPN
ejpam-4735	387	8	boonpok	boonpok	PROPN
ejpam-4735	387	9	.	.	PUNCT
ejpam-4735	388	1	on	on	ADP
ejpam-4735	388	2	characterizations	characterization	NOUN
ejpam-4735	388	3	of	of	ADP
ejpam-4735	388	4	δp(λ	δp(λ	NOUN
ejpam-4735	388	5	,	,	PUNCT
ejpam-4735	388	6	s)-d1	s)-d1	NOUN
ejpam-4735	388	7	spaces	space	NOUN
ejpam-4735	388	8	.	.	PUNCT
ejpam-4735	389	1	international	international	ADJ
ejpam-4735	389	2	journal	journal	PROPN
ejpam-4735	389	3	of	of	ADP
ejpam-4735	389	4	mathematics	mathematic	NOUN
ejpam-4735	389	5	and	and	CCONJ
ejpam-4735	389	6	computer	computer	NOUN
ejpam-4735	389	7	science	science	NOUN
ejpam-4735	389	8	,	,	PUNCT
ejpam-4735	389	9	18(4):743–747	18(4):743–747	PROPN
ejpam-4735	389	10	,	,	PUNCT
ejpam-4735	389	11	2023	2023	NUM
ejpam-4735	389	12	.	.	PUNCT
ejpam-4735	390	1	[	[	X
ejpam-4735	390	2	22	22	NUM
ejpam-4735	390	3	]	]	PUNCT
ejpam-4735	390	4	m.	m.	NOUN
ejpam-4735	390	5	thongmoon	thongmoon	NOUN
ejpam-4735	390	6	and	and	CCONJ
ejpam-4735	390	7	c.	c.	PROPN
ejpam-4735	390	8	boonpok	boonpok	PROPN
ejpam-4735	390	9	.	.	PUNCT
ejpam-4735	391	1	sober	sober	ADJ
ejpam-4735	391	2	δp(λ	δp(λ	PROPN
ejpam-4735	391	3	,	,	PUNCT
ejpam-4735	391	4	s)-r0	s)-r0	PRON
ejpam-4735	391	5	spaces	space	VERB
ejpam-4735	391	6	.	.	PUNCT
ejpam-4735	392	1	international	international	ADJ
ejpam-4735	392	2	journal	journal	PROPN
ejpam-4735	392	3	of	of	ADP
ejpam-4735	392	4	mathematics	mathematic	NOUN
ejpam-4735	392	5	and	and	CCONJ
ejpam-4735	392	6	computer	computer	NOUN
ejpam-4735	392	7	science	science	NOUN
ejpam-4735	392	8	,	,	PUNCT
ejpam-4735	392	9	18(4):761–765	18(4):761–765	NUM
ejpam-4735	392	10	,	,	PUNCT
ejpam-4735	392	11	2023	2023	NUM
ejpam-4735	392	12	.	.	PUNCT
ejpam-4735	393	1	[	[	X
ejpam-4735	393	2	23	23	NUM
ejpam-4735	393	3	]	]	X
ejpam-4735	393	4	n.	n.	NOUN
ejpam-4735	393	5	v.	v.	PROPN
ejpam-4735	393	6	veličko	veličko	PROPN
ejpam-4735	393	7	.	.	PUNCT
ejpam-4735	394	1	h	h	NOUN
ejpam-4735	394	2	-	-	PUNCT
ejpam-4735	394	3	closed	close	VERB
ejpam-4735	394	4	topological	topological	ADJ
ejpam-4735	394	5	spaces	space	NOUN
ejpam-4735	394	6	.	.	PUNCT
ejpam-4735	395	1	american	american	PROPN
ejpam-4735	395	2	mathematical	mathematical	ADJ
ejpam-4735	395	3	society	society	NOUN
ejpam-4735	395	4	translations	translation	NOUN
ejpam-4735	395	5	,	,	PUNCT
ejpam-4735	395	6	78(2):102–118	78(2):102–118	NUM
ejpam-4735	395	7	,	,	PUNCT
ejpam-4735	395	8	1968	1968	NUM
ejpam-4735	395	9	.	.	PUNCT