id	sid	tid	token	lemma	pos
ejpam-4369	1	1	european	european	PROPN
ejpam-4369	1	2	journal	journal	PROPN
ejpam-4369	1	3	of	of	ADP
ejpam-4369	1	4	pure	pure	ADJ
ejpam-4369	1	5	and	and	CCONJ
ejpam-4369	1	6	applied	apply	VERB
ejpam-4369	1	7	mathematics	mathematic	NOUN
ejpam-4369	1	8	vol	vol	NOUN
ejpam-4369	1	9	.	.	PROPN
ejpam-4369	2	1	15	15	NUM
ejpam-4369	2	2	,	,	PUNCT
ejpam-4369	2	3	no	no	INTJ
ejpam-4369	2	4	.	.	NOUN
ejpam-4369	2	5	3	3	NUM
ejpam-4369	2	6	,	,	PUNCT
ejpam-4369	2	7	2022	2022	NUM
ejpam-4369	2	8	,	,	PUNCT
ejpam-4369	2	9	1180	1180	NUM
ejpam-4369	2	10	-	-	SYM
ejpam-4369	2	11	1188	1188	NUM
ejpam-4369	2	12	issn	issn	PROPN
ejpam-4369	2	13	1307	1307	NUM
ejpam-4369	2	14	-	-	SYM
ejpam-4369	2	15	5543	5543	NUM
ejpam-4369	2	16	–	–	PUNCT
ejpam-4369	2	17	ejpam.com	ejpam.com	X
ejpam-4369	2	18	published	publish	VERB
ejpam-4369	2	19	by	by	ADP
ejpam-4369	2	20	new	new	PROPN
ejpam-4369	2	21	york	york	PROPN
ejpam-4369	2	22	business	business	PROPN
ejpam-4369	2	23	global	global	ADJ
ejpam-4369	2	24	slight	slight	NOUN
ejpam-4369	2	25	(	(	PUNCT
ejpam-4369	2	26	λ	λ	NOUN
ejpam-4369	2	27	,	,	PUNCT
ejpam-4369	2	28	sp)-continuity	sp)-continuity	NOUN
ejpam-4369	2	29	and	and	CCONJ
ejpam-4369	2	30	λsp	λsp	PROPN
ejpam-4369	2	31	-	-	PUNCT
ejpam-4369	2	32	extremally	extremally	ADV
ejpam-4369	2	33	disconnectedness	disconnectedness	NOUN
ejpam-4369	2	34	chawalit	chawalit	VERB
ejpam-4369	2	35	boonpok1	boonpok1	NOUN
ejpam-4369	2	36	,	,	PUNCT
ejpam-4369	2	37	jeeranunt	jeeranunt	PROPN
ejpam-4369	2	38	khampakdee1,∗	khampakdee1,∗	PROPN
ejpam-4369	2	39	1	1	NUM
ejpam-4369	2	40	mathematics	mathematic	NOUN
ejpam-4369	2	41	and	and	CCONJ
ejpam-4369	2	42	applied	apply	VERB
ejpam-4369	2	43	mathematics	mathematics	PROPN
ejpam-4369	2	44	research	research	NOUN
ejpam-4369	2	45	unit	unit	NOUN
ejpam-4369	2	46	,	,	PUNCT
ejpam-4369	2	47	department	department	NOUN
ejpam-4369	2	48	of	of	ADP
ejpam-4369	2	49	mathematics	mathematic	NOUN
ejpam-4369	2	50	,	,	PUNCT
ejpam-4369	2	51	faculty	faculty	NOUN
ejpam-4369	2	52	of	of	ADP
ejpam-4369	2	53	science	science	NOUN
ejpam-4369	2	54	,	,	PUNCT
ejpam-4369	2	55	mahasarakham	mahasarakham	PROPN
ejpam-4369	2	56	university	university	PROPN
ejpam-4369	2	57	,	,	PUNCT
ejpam-4369	2	58	maha	maha	PROPN
ejpam-4369	2	59	sarakham	sarakham	PROPN
ejpam-4369	2	60	,	,	PUNCT
ejpam-4369	2	61	44150	44150	NUM
ejpam-4369	2	62	,	,	PUNCT
ejpam-4369	2	63	thailand	thailand	PROPN
ejpam-4369	2	64	abstract	abstract	PROPN
ejpam-4369	2	65	.	.	PUNCT
ejpam-4369	3	1	this	this	DET
ejpam-4369	3	2	paper	paper	NOUN
ejpam-4369	3	3	is	be	AUX
ejpam-4369	3	4	concerned	concern	VERB
ejpam-4369	3	5	with	with	ADP
ejpam-4369	3	6	the	the	DET
ejpam-4369	3	7	concepts	concept	NOUN
ejpam-4369	3	8	of	of	ADP
ejpam-4369	3	9	upper	upper	ADJ
ejpam-4369	3	10	and	and	CCONJ
ejpam-4369	3	11	lower	lower	ADV
ejpam-4369	3	12	slightly	slightly	ADV
ejpam-4369	3	13	(	(	PUNCT
ejpam-4369	3	14	λ	λ	NOUN
ejpam-4369	3	15	,	,	PUNCT
ejpam-4369	3	16	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	3	17	multifunctions	multifunction	NOUN
ejpam-4369	3	18	.	.	PUNCT
ejpam-4369	4	1	moreover	moreover	ADV
ejpam-4369	4	2	,	,	PUNCT
ejpam-4369	4	3	some	some	DET
ejpam-4369	4	4	characterizations	characterization	NOUN
ejpam-4369	4	5	of	of	ADP
ejpam-4369	4	6	upper	upper	ADJ
ejpam-4369	4	7	and	and	CCONJ
ejpam-4369	4	8	lower	lower	ADV
ejpam-4369	4	9	slightly	slightly	ADV
ejpam-4369	4	10	(	(	PUNCT
ejpam-4369	4	11	λ	λ	NOUN
ejpam-4369	4	12	,	,	PUNCT
ejpam-4369	4	13	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	4	14	multifunctions	multifunction	NOUN
ejpam-4369	4	15	are	be	AUX
ejpam-4369	4	16	established	establish	VERB
ejpam-4369	4	17	.	.	PUNCT
ejpam-4369	5	1	2020	2020	NUM
ejpam-4369	5	2	mathematics	mathematics	PROPN
ejpam-4369	5	3	subject	subject	NOUN
ejpam-4369	5	4	classifications	classification	NOUN
ejpam-4369	5	5	:	:	PUNCT
ejpam-4369	5	6	54c08	54c08	NUM
ejpam-4369	5	7	,	,	PUNCT
ejpam-4369	5	8	54c60	54c60	NUM
ejpam-4369	5	9	,	,	PUNCT
ejpam-4369	5	10	54g05	54g05	NUM
ejpam-4369	5	11	key	key	ADJ
ejpam-4369	5	12	words	word	NOUN
ejpam-4369	5	13	and	and	CCONJ
ejpam-4369	5	14	phrases	phrase	NOUN
ejpam-4369	5	15	:	:	PUNCT
ejpam-4369	5	16	upper	upper	ADJ
ejpam-4369	5	17	slight	slight	NOUN
ejpam-4369	5	18	(	(	PUNCT
ejpam-4369	5	19	λ	λ	NOUN
ejpam-4369	5	20	,	,	PUNCT
ejpam-4369	5	21	sp)-continuity	sp)-continuity	NOUN
ejpam-4369	5	22	,	,	PUNCT
ejpam-4369	5	23	lower	low	ADJ
ejpam-4369	5	24	slight	slight	ADJ
ejpam-4369	5	25	(	(	PUNCT
ejpam-4369	5	26	λ	λ	NOUN
ejpam-4369	5	27	,	,	PUNCT
ejpam-4369	5	28	sp)-continuity	sp)-continuity	NOUN
ejpam-4369	5	29	,	,	PUNCT
ejpam-4369	5	30	λspextremally	λspextremally	ADV
ejpam-4369	5	31	disconnectedness	disconnectedness	VERB
ejpam-4369	5	32	1	1	NUM
ejpam-4369	5	33	.	.	PUNCT
ejpam-4369	6	1	introduction	introduction	NOUN
ejpam-4369	6	2	stronger	strong	ADJ
ejpam-4369	6	3	and	and	CCONJ
ejpam-4369	6	4	weaker	weak	ADJ
ejpam-4369	6	5	forms	form	NOUN
ejpam-4369	6	6	of	of	ADP
ejpam-4369	6	7	open	open	ADJ
ejpam-4369	6	8	sets	set	NOUN
ejpam-4369	6	9	play	play	VERB
ejpam-4369	6	10	an	an	DET
ejpam-4369	6	11	important	important	ADJ
ejpam-4369	6	12	role	role	NOUN
ejpam-4369	6	13	in	in	ADP
ejpam-4369	6	14	the	the	DET
ejpam-4369	6	15	researches	research	NOUN
ejpam-4369	6	16	of	of	ADP
ejpam-4369	6	17	generalizations	generalization	NOUN
ejpam-4369	6	18	of	of	ADP
ejpam-4369	6	19	continuity	continuity	NOUN
ejpam-4369	6	20	for	for	ADP
ejpam-4369	6	21	functions	function	NOUN
ejpam-4369	6	22	and	and	CCONJ
ejpam-4369	6	23	multifunctions	multifunction	NOUN
ejpam-4369	6	24	in	in	ADP
ejpam-4369	6	25	topological	topological	ADJ
ejpam-4369	6	26	spaces	space	NOUN
ejpam-4369	6	27	.	.	PUNCT
ejpam-4369	7	1	the	the	DET
ejpam-4369	7	2	concept	concept	NOUN
ejpam-4369	7	3	of	of	ADP
ejpam-4369	7	4	slightly	slightly	ADV
ejpam-4369	7	5	continuous	continuous	ADJ
ejpam-4369	7	6	functions	function	NOUN
ejpam-4369	7	7	was	be	AUX
ejpam-4369	7	8	first	first	ADV
ejpam-4369	7	9	introduced	introduce	VERB
ejpam-4369	7	10	by	by	ADP
ejpam-4369	7	11	jain	jain	NOUN
ejpam-4369	7	12	[	[	X
ejpam-4369	7	13	6	6	NUM
ejpam-4369	7	14	]	]	PUNCT
ejpam-4369	7	15	.	.	PUNCT
ejpam-4369	8	1	in	in	ADP
ejpam-4369	8	2	1995	1995	NUM
ejpam-4369	8	3	,	,	PUNCT
ejpam-4369	8	4	nour	nour	PROPN
ejpam-4369	9	1	[	[	X
ejpam-4369	9	2	11	11	NUM
ejpam-4369	9	3	]	]	PUNCT
ejpam-4369	9	4	defined	define	VERB
ejpam-4369	9	5	slightly	slightly	ADV
ejpam-4369	9	6	semi	semi	ADJ
ejpam-4369	9	7	-	-	ADJ
ejpam-4369	9	8	continuous	continuous	ADJ
ejpam-4369	9	9	functions	function	NOUN
ejpam-4369	9	10	as	as	ADP
ejpam-4369	9	11	a	a	DET
ejpam-4369	9	12	weak	weak	ADJ
ejpam-4369	9	13	form	form	NOUN
ejpam-4369	9	14	of	of	ADP
ejpam-4369	9	15	slight	slight	ADJ
ejpam-4369	9	16	continuity	continuity	NOUN
ejpam-4369	9	17	and	and	CCONJ
ejpam-4369	9	18	investigated	investigate	VERB
ejpam-4369	9	19	several	several	ADJ
ejpam-4369	9	20	characterizations	characterization	NOUN
ejpam-4369	9	21	of	of	ADP
ejpam-4369	9	22	slightly	slightly	ADV
ejpam-4369	9	23	semi	semi	ADJ
ejpam-4369	9	24	-	-	ADJ
ejpam-4369	9	25	continuous	continuous	ADJ
ejpam-4369	9	26	functions	function	NOUN
ejpam-4369	9	27	.	.	PUNCT
ejpam-4369	10	1	noiri	noiri	PROPN
ejpam-4369	10	2	and	and	CCONJ
ejpam-4369	10	3	chae	chae	PROPN
ejpam-4369	10	4	[	[	X
ejpam-4369	10	5	8	8	NUM
ejpam-4369	10	6	]	]	PUNCT
ejpam-4369	10	7	further	far	ADV
ejpam-4369	10	8	investigated	investigate	VERB
ejpam-4369	10	9	slight	slight	ADJ
ejpam-4369	10	10	semi	semi	NOUN
ejpam-4369	10	11	-	-	NOUN
ejpam-4369	10	12	continuity	continuity	NOUN
ejpam-4369	10	13	.	.	PUNCT
ejpam-4369	11	1	pal	pal	NOUN
ejpam-4369	11	2	and	and	CCONJ
ejpam-4369	11	3	bhattacharya	bhattacharya	NOUN
ejpam-4369	12	1	[	[	X
ejpam-4369	12	2	12	12	NUM
ejpam-4369	12	3	]	]	PUNCT
ejpam-4369	12	4	defined	define	VERB
ejpam-4369	12	5	a	a	DET
ejpam-4369	12	6	function	function	NOUN
ejpam-4369	12	7	to	to	PART
ejpam-4369	12	8	be	be	AUX
ejpam-4369	12	9	faintly	faintly	ADV
ejpam-4369	12	10	precontinuous	precontinuous	ADJ
ejpam-4369	12	11	if	if	SCONJ
ejpam-4369	12	12	the	the	DET
ejpam-4369	12	13	preimage	preimage	NOUN
ejpam-4369	12	14	of	of	ADP
ejpam-4369	12	15	each	each	DET
ejpam-4369	12	16	clopen	clopen	ADJ
ejpam-4369	12	17	set	set	NOUN
ejpam-4369	12	18	of	of	ADP
ejpam-4369	12	19	the	the	DET
ejpam-4369	12	20	codomain	codomain	NOUN
ejpam-4369	12	21	is	be	AUX
ejpam-4369	12	22	preopen	preopen	ADJ
ejpam-4369	12	23	and	and	CCONJ
ejpam-4369	12	24	obtained	obtain	VERB
ejpam-4369	12	25	some	some	DET
ejpam-4369	12	26	properties	property	NOUN
ejpam-4369	12	27	of	of	ADP
ejpam-4369	12	28	such	such	ADJ
ejpam-4369	12	29	functions	function	NOUN
ejpam-4369	12	30	.	.	PUNCT
ejpam-4369	13	1	slight	slight	ADJ
ejpam-4369	13	2	continuity	continuity	NOUN
ejpam-4369	13	3	implies	imply	VERB
ejpam-4369	13	4	both	both	DET
ejpam-4369	13	5	slight	slight	ADJ
ejpam-4369	13	6	semi	semi	ADJ
ejpam-4369	13	7	-	-	ADJ
ejpam-4369	13	8	continuity	continuity	ADJ
ejpam-4369	13	9	and	and	CCONJ
ejpam-4369	13	10	faint	faint	ADJ
ejpam-4369	13	11	precontinuity	precontinuity	NOUN
ejpam-4369	13	12	.	.	PUNCT
ejpam-4369	14	1	in	in	ADP
ejpam-4369	14	2	2001	2001	NUM
ejpam-4369	14	3	,	,	PUNCT
ejpam-4369	14	4	noiri	noiri	ADV
ejpam-4369	14	5	[	[	X
ejpam-4369	14	6	7	7	X
ejpam-4369	14	7	]	]	PUNCT
ejpam-4369	14	8	introduced	introduce	VERB
ejpam-4369	14	9	the	the	DET
ejpam-4369	14	10	concept	concept	NOUN
ejpam-4369	14	11	of	of	ADP
ejpam-4369	14	12	slight	slight	ADJ
ejpam-4369	14	13	β	β	NOUN
ejpam-4369	14	14	-	-	NOUN
ejpam-4369	14	15	continuity	continuity	NOUN
ejpam-4369	14	16	which	which	PRON
ejpam-4369	14	17	is	be	AUX
ejpam-4369	14	18	implies	imply	VERB
ejpam-4369	14	19	by	by	ADP
ejpam-4369	14	20	both	both	DET
ejpam-4369	14	21	slight	slight	ADJ
ejpam-4369	14	22	semi	semi	ADJ
ejpam-4369	14	23	-	-	ADJ
ejpam-4369	14	24	continuity	continuity	ADJ
ejpam-4369	14	25	and	and	CCONJ
ejpam-4369	14	26	faint	faint	ADJ
ejpam-4369	14	27	precontinuity	precontinuity	NOUN
ejpam-4369	14	28	.	.	PUNCT
ejpam-4369	15	1	a	a	DET
ejpam-4369	15	2	unified	unified	ADJ
ejpam-4369	15	3	theory	theory	NOUN
ejpam-4369	15	4	of	of	ADP
ejpam-4369	15	5	slight	slight	ADJ
ejpam-4369	15	6	continuity	continuity	NOUN
ejpam-4369	15	7	is	be	AUX
ejpam-4369	15	8	presented	present	VERB
ejpam-4369	15	9	in	in	ADP
ejpam-4369	15	10	[	[	X
ejpam-4369	15	11	14	14	NUM
ejpam-4369	15	12	]	]	PUNCT
ejpam-4369	15	13	,	,	PUNCT
ejpam-4369	15	14	the	the	DET
ejpam-4369	15	15	present	present	ADJ
ejpam-4369	15	16	authors	author	NOUN
ejpam-4369	15	17	introduced	introduce	VERB
ejpam-4369	15	18	and	and	CCONJ
ejpam-4369	15	19	investigated	investigate	VERB
ejpam-4369	15	20	the	the	DET
ejpam-4369	15	21	concept	concept	NOUN
ejpam-4369	15	22	of	of	ADP
ejpam-4369	15	23	slightly	slightly	ADJ
ejpam-4369	15	24	m	m	ADJ
ejpam-4369	15	25	-	-	ADJ
ejpam-4369	15	26	continuous	continuous	ADJ
ejpam-4369	15	27	functions	function	NOUN
ejpam-4369	15	28	.	.	PUNCT
ejpam-4369	16	1	noiri	noiri	PROPN
ejpam-4369	16	2	and	and	CCONJ
ejpam-4369	16	3	popa	popa	NOUN
ejpam-4369	17	1	[	[	X
ejpam-4369	17	2	10	10	NUM
ejpam-4369	17	3	]	]	PUNCT
ejpam-4369	17	4	introduced	introduce	VERB
ejpam-4369	17	5	the	the	DET
ejpam-4369	17	6	notion	notion	NOUN
ejpam-4369	17	7	of	of	ADP
ejpam-4369	17	8	slightlym	slightlym	NOUN
ejpam-4369	17	9	-	-	PUNCT
ejpam-4369	17	10	continuous	continuous	ADJ
ejpam-4369	17	11	multifunctions	multifunction	NOUN
ejpam-4369	17	12	and	and	CCONJ
ejpam-4369	17	13	studied	study	VERB
ejpam-4369	17	14	the	the	DET
ejpam-4369	17	15	relationships	relationship	NOUN
ejpam-4369	17	16	among	among	ADP
ejpam-4369	17	17	m	m	NOUN
ejpam-4369	17	18	-	-	NOUN
ejpam-4369	17	19	continuity	continuity	NOUN
ejpam-4369	17	20	,	,	PUNCT
ejpam-4369	17	21	almost	almost	ADV
ejpam-4369	17	22	m	m	NOUN
ejpam-4369	17	23	-	-	NOUN
ejpam-4369	17	24	continuity	continuity	NOUN
ejpam-4369	17	25	,	,	PUNCT
ejpam-4369	17	26	weak	weak	ADJ
ejpam-4369	17	27	m	m	NOUN
ejpam-4369	17	28	-	-	NOUN
ejpam-4369	17	29	continuity	continuity	NOUN
ejpam-4369	17	30	and	and	CCONJ
ejpam-4369	17	31	slight	slight	ADJ
ejpam-4369	17	32	m	m	NOUN
ejpam-4369	17	33	-	-	NOUN
ejpam-4369	17	34	continuity	continuity	NOUN
ejpam-4369	17	35	for	for	ADP
ejpam-4369	17	36	multifunctions	multifunction	NOUN
ejpam-4369	17	37	.	.	PUNCT
ejpam-4369	18	1	the	the	DET
ejpam-4369	18	2	concept	concept	NOUN
ejpam-4369	18	3	of	of	ADP
ejpam-4369	18	4	β	β	ADJ
ejpam-4369	18	5	-	-	ADJ
ejpam-4369	18	6	open	open	ADJ
ejpam-4369	18	7	sets	set	NOUN
ejpam-4369	18	8	due	due	ADP
ejpam-4369	18	9	to	to	ADP
ejpam-4369	18	10	abd	abd	PROPN
ejpam-4369	18	11	el	el	PROPN
ejpam-4369	18	12	-	-	PROPN
ejpam-4369	18	13	monsef	monsef	PROPN
ejpam-4369	18	14	et	et	PROPN
ejpam-4369	18	15	al	al	PROPN
ejpam-4369	18	16	.	.	PUNCT
ejpam-4369	19	1	[	[	X
ejpam-4369	19	2	5	5	NUM
ejpam-4369	19	3	]	]	PUNCT
ejpam-4369	19	4	or	or	CCONJ
ejpam-4369	19	5	semi	semi	ADJ
ejpam-4369	19	6	-	-	ADJ
ejpam-4369	19	7	preopen	preopen	ADJ
ejpam-4369	19	8	sets	set	NOUN
ejpam-4369	19	9	in	in	ADP
ejpam-4369	19	10	the	the	DET
ejpam-4369	19	11	sense	sense	NOUN
ejpam-4369	19	12	of	of	ADP
ejpam-4369	19	13	andrijević	andrijević	NOUN
ejpam-4369	19	14	[	[	X
ejpam-4369	19	15	1	1	X
ejpam-4369	19	16	]	]	PUNCT
ejpam-4369	19	17	plays	play	VERB
ejpam-4369	19	18	a	a	DET
ejpam-4369	19	19	significant	significant	ADJ
ejpam-4369	19	20	role	role	NOUN
ejpam-4369	19	21	in	in	ADP
ejpam-4369	19	22	general	general	ADJ
ejpam-4369	19	23	topology	topology	NOUN
ejpam-4369	19	24	.	.	PUNCT
ejpam-4369	20	1	in	in	ADP
ejpam-4369	20	2	2004	2004	NUM
ejpam-4369	20	3	,	,	PUNCT
ejpam-4369	20	4	noiri	noiri	PRON
ejpam-4369	20	5	and	and	CCONJ
ejpam-4369	20	6	hatir	hatir	PROPN
ejpam-4369	20	7	∗corresponding	∗corresponde	VERB
ejpam-4369	20	8	author	author	NOUN
ejpam-4369	20	9	.	.	PUNCT
ejpam-4369	21	1	doi	doi	NOUN
ejpam-4369	21	2	:	:	PUNCT
ejpam-4369	21	3	https://doi.org/10.29020/nybg.ejpam.v15i3.4369	https://doi.org/10.29020/nybg.ejpam.v15i3.4369	NOUN
ejpam-4369	21	4	email	email	NOUN
ejpam-4369	21	5	addresses	address	NOUN
ejpam-4369	21	6	:	:	PUNCT
ejpam-4369	21	7	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	INTJ
ejpam-4369	21	8	(	(	PUNCT
ejpam-4369	21	9	c.	c.	PROPN
ejpam-4369	21	10	boonpok	boonpok	PROPN
ejpam-4369	21	11	)	)	PUNCT
ejpam-4369	21	12	,	,	PUNCT
ejpam-4369	21	13	jeeranunt.k@msu.ac.th	jeeranunt.k@msu.ac.th	INTJ
ejpam-4369	21	14	(	(	PUNCT
ejpam-4369	21	15	j.	j.	PROPN
ejpam-4369	21	16	khampakdee	khampakdee	PROPN
ejpam-4369	21	17	)	)	PUNCT
ejpam-4369	21	18	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4369	21	19	1180	1180	NUM
ejpam-4369	22	1	©	©	ADP
ejpam-4369	22	2	2022	2022	NUM
ejpam-4369	22	3	ejpam	ejpam	VERB
ejpam-4369	22	4	all	all	DET
ejpam-4369	22	5	rights	right	NOUN
ejpam-4369	22	6	reserved	reserve	VERB
ejpam-4369	22	7	.	.	PUNCT
ejpam-4369	23	1	c.	c.	PROPN
ejpam-4369	23	2	boonpok	boonpok	PROPN
ejpam-4369	23	3	,	,	PUNCT
ejpam-4369	23	4	j.	j.	PROPN
ejpam-4369	23	5	khampakdee	khampakdee	PROPN
ejpam-4369	23	6	/	/	PUNCT
ejpam-4369	23	7	eur	eur	PROPN
ejpam-4369	23	8	.	.	PUNCT
ejpam-4369	24	1	j.	j.	PROPN
ejpam-4369	24	2	pure	pure	PROPN
ejpam-4369	24	3	appl	appl	PROPN
ejpam-4369	24	4	.	.	PROPN
ejpam-4369	24	5	math	math	PROPN
ejpam-4369	24	6	,	,	PUNCT
ejpam-4369	24	7	15	15	NUM
ejpam-4369	24	8	(	(	PUNCT
ejpam-4369	24	9	3	3	NUM
ejpam-4369	24	10	)	)	PUNCT
ejpam-4369	24	11	(	(	PUNCT
ejpam-4369	24	12	2022	2022	NUM
ejpam-4369	24	13	)	)	PUNCT
ejpam-4369	24	14	,	,	PUNCT
ejpam-4369	24	15	1180	1180	NUM
ejpam-4369	24	16	-	-	SYM
ejpam-4369	24	17	1188	1188	NUM
ejpam-4369	24	18	1181	1181	NUM
ejpam-4369	24	19	[	[	X
ejpam-4369	24	20	9	9	NUM
ejpam-4369	24	21	]	]	PUNCT
ejpam-4369	24	22	introduced	introduce	VERB
ejpam-4369	24	23	the	the	DET
ejpam-4369	24	24	notion	notion	NOUN
ejpam-4369	24	25	of	of	ADP
ejpam-4369	24	26	λsp	λsp	NOUN
ejpam-4369	24	27	-	-	PUNCT
ejpam-4369	24	28	sets	set	NOUN
ejpam-4369	24	29	in	in	ADP
ejpam-4369	24	30	terms	term	NOUN
ejpam-4369	24	31	of	of	ADP
ejpam-4369	24	32	the	the	DET
ejpam-4369	24	33	concept	concept	NOUN
ejpam-4369	24	34	of	of	ADP
ejpam-4369	24	35	β	β	ADJ
ejpam-4369	24	36	-	-	ADJ
ejpam-4369	24	37	open	open	ADJ
ejpam-4369	24	38	sets	set	NOUN
ejpam-4369	24	39	and	and	CCONJ
ejpam-4369	24	40	investigated	investigate	VERB
ejpam-4369	24	41	the	the	DET
ejpam-4369	24	42	notion	notion	NOUN
ejpam-4369	24	43	of	of	ADP
ejpam-4369	24	44	λsp	λsp	NOUN
ejpam-4369	24	45	-	-	PUNCT
ejpam-4369	24	46	closed	close	VERB
ejpam-4369	24	47	sets	set	NOUN
ejpam-4369	24	48	by	by	ADP
ejpam-4369	24	49	using	use	VERB
ejpam-4369	24	50	λsp	λsp	NOUN
ejpam-4369	24	51	-	-	PUNCT
ejpam-4369	24	52	sets	set	NOUN
ejpam-4369	24	53	.	.	PUNCT
ejpam-4369	25	1	in	in	ADP
ejpam-4369	25	2	[	[	X
ejpam-4369	25	3	3	3	NUM
ejpam-4369	25	4	]	]	PUNCT
ejpam-4369	25	5	,	,	PUNCT
ejpam-4369	25	6	the	the	DET
ejpam-4369	25	7	author	author	NOUN
ejpam-4369	25	8	introduced	introduce	VERB
ejpam-4369	25	9	the	the	DET
ejpam-4369	25	10	concepts	concept	NOUN
ejpam-4369	25	11	of	of	ADP
ejpam-4369	25	12	(	(	PUNCT
ejpam-4369	25	13	λ	λ	PROPN
ejpam-4369	25	14	,	,	PUNCT
ejpam-4369	25	15	sp)-open	sp)-open	ADJ
ejpam-4369	25	16	sets	set	NOUN
ejpam-4369	25	17	and	and	CCONJ
ejpam-4369	25	18	(	(	PUNCT
ejpam-4369	25	19	λ	λ	PROPN
ejpam-4369	25	20	,	,	PUNCT
ejpam-4369	25	21	sp)-closed	sp)-close	VERB
ejpam-4369	25	22	sets	set	NOUN
ejpam-4369	25	23	which	which	PRON
ejpam-4369	25	24	are	be	AUX
ejpam-4369	25	25	defined	define	VERB
ejpam-4369	25	26	by	by	ADP
ejpam-4369	25	27	utilizing	utilize	VERB
ejpam-4369	25	28	the	the	DET
ejpam-4369	25	29	notions	notion	NOUN
ejpam-4369	25	30	of	of	ADP
ejpam-4369	25	31	λsp	λsp	NOUN
ejpam-4369	25	32	-	-	PUNCT
ejpam-4369	25	33	sets	set	NOUN
ejpam-4369	25	34	and	and	CCONJ
ejpam-4369	25	35	β	β	NOUN
ejpam-4369	25	36	-	-	ADJ
ejpam-4369	25	37	closed	closed	ADJ
ejpam-4369	25	38	sets	set	NOUN
ejpam-4369	25	39	.	.	PUNCT
ejpam-4369	26	1	in	in	ADP
ejpam-4369	26	2	particular	particular	ADJ
ejpam-4369	26	3	,	,	PUNCT
ejpam-4369	26	4	some	some	DET
ejpam-4369	26	5	characterizations	characterization	NOUN
ejpam-4369	26	6	of	of	ADP
ejpam-4369	26	7	λsp	λsp	NOUN
ejpam-4369	26	8	-	-	PUNCT
ejpam-4369	26	9	extremally	extremally	ADV
ejpam-4369	26	10	disconnected	disconnected	ADJ
ejpam-4369	26	11	spaces	space	NOUN
ejpam-4369	26	12	are	be	AUX
ejpam-4369	26	13	investigated	investigate	VERB
ejpam-4369	26	14	in	in	ADP
ejpam-4369	26	15	[	[	X
ejpam-4369	26	16	3	3	NUM
ejpam-4369	26	17	]	]	PUNCT
ejpam-4369	26	18	.	.	PUNCT
ejpam-4369	27	1	the	the	DET
ejpam-4369	27	2	purpose	purpose	NOUN
ejpam-4369	27	3	of	of	ADP
ejpam-4369	27	4	the	the	DET
ejpam-4369	27	5	present	present	ADJ
ejpam-4369	27	6	paper	paper	NOUN
ejpam-4369	27	7	is	be	AUX
ejpam-4369	27	8	to	to	PART
ejpam-4369	27	9	introduce	introduce	VERB
ejpam-4369	27	10	the	the	DET
ejpam-4369	27	11	notions	notion	NOUN
ejpam-4369	27	12	of	of	ADP
ejpam-4369	27	13	upper	upper	ADJ
ejpam-4369	27	14	and	and	CCONJ
ejpam-4369	27	15	lower	lower	ADV
ejpam-4369	27	16	slightly	slightly	ADV
ejpam-4369	27	17	(	(	PUNCT
ejpam-4369	27	18	λ	λ	NOUN
ejpam-4369	27	19	,	,	PUNCT
ejpam-4369	27	20	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	27	21	multifunctions	multifunction	NOUN
ejpam-4369	27	22	.	.	PUNCT
ejpam-4369	28	1	furthermore	furthermore	ADV
ejpam-4369	28	2	,	,	PUNCT
ejpam-4369	28	3	some	some	DET
ejpam-4369	28	4	characterizations	characterization	NOUN
ejpam-4369	28	5	of	of	ADP
ejpam-4369	28	6	upper	upper	ADJ
ejpam-4369	28	7	and	and	CCONJ
ejpam-4369	28	8	lower	lower	ADV
ejpam-4369	28	9	slightly	slightly	ADV
ejpam-4369	28	10	(	(	PUNCT
ejpam-4369	28	11	λ	λ	NOUN
ejpam-4369	28	12	,	,	PUNCT
ejpam-4369	28	13	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	28	14	multifunctions	multifunction	NOUN
ejpam-4369	28	15	are	be	AUX
ejpam-4369	28	16	discussed	discuss	VERB
ejpam-4369	28	17	.	.	PUNCT
ejpam-4369	29	1	2	2	X
ejpam-4369	29	2	.	.	X
ejpam-4369	29	3	preliminaries	preliminary	NOUN
ejpam-4369	29	4	throughout	throughout	ADP
ejpam-4369	29	5	this	this	DET
ejpam-4369	29	6	paper	paper	NOUN
ejpam-4369	29	7	,	,	PUNCT
ejpam-4369	29	8	spaces	space	NOUN
ejpam-4369	29	9	(	(	PUNCT
ejpam-4369	29	10	x	x	X
ejpam-4369	29	11	,	,	PUNCT
ejpam-4369	29	12	τ	τ	X
ejpam-4369	29	13	)	)	PUNCT
ejpam-4369	29	14	and	and	CCONJ
ejpam-4369	29	15	(	(	PUNCT
ejpam-4369	29	16	y	y	PROPN
ejpam-4369	29	17	,	,	PUNCT
ejpam-4369	29	18	σ	σ	PROPN
ejpam-4369	29	19	)	)	PUNCT
ejpam-4369	29	20	(	(	PUNCT
ejpam-4369	29	21	or	or	CCONJ
ejpam-4369	29	22	simply	simply	ADV
ejpam-4369	29	23	x	x	X
ejpam-4369	29	24	and	and	CCONJ
ejpam-4369	29	25	y	y	PROPN
ejpam-4369	29	26	)	)	PUNCT
ejpam-4369	29	27	always	always	ADV
ejpam-4369	29	28	mean	mean	VERB
ejpam-4369	29	29	topological	topological	ADJ
ejpam-4369	29	30	spaces	space	NOUN
ejpam-4369	29	31	on	on	ADP
ejpam-4369	29	32	which	which	PRON
ejpam-4369	29	33	no	no	DET
ejpam-4369	29	34	separation	separation	NOUN
ejpam-4369	29	35	axioms	axiom	NOUN
ejpam-4369	29	36	are	be	AUX
ejpam-4369	29	37	assumed	assume	VERB
ejpam-4369	29	38	unless	unless	SCONJ
ejpam-4369	29	39	explicitly	explicitly	ADV
ejpam-4369	29	40	stated	state	VERB
ejpam-4369	29	41	.	.	PUNCT
ejpam-4369	30	1	let	let	VERB
ejpam-4369	30	2	a	a	DET
ejpam-4369	30	3	be	be	AUX
ejpam-4369	30	4	a	a	DET
ejpam-4369	30	5	subset	subset	NOUN
ejpam-4369	30	6	of	of	ADP
ejpam-4369	30	7	a	a	DET
ejpam-4369	30	8	topological	topological	ADJ
ejpam-4369	30	9	space	space	NOUN
ejpam-4369	30	10	(	(	PUNCT
ejpam-4369	30	11	x	x	X
ejpam-4369	30	12	,	,	PUNCT
ejpam-4369	30	13	τ	τ	PROPN
ejpam-4369	30	14	)	)	PUNCT
ejpam-4369	30	15	.	.	PUNCT
ejpam-4369	31	1	the	the	DET
ejpam-4369	31	2	closure	closure	NOUN
ejpam-4369	31	3	of	of	ADP
ejpam-4369	31	4	a	a	PRON
ejpam-4369	31	5	and	and	CCONJ
ejpam-4369	31	6	the	the	DET
ejpam-4369	31	7	interior	interior	NOUN
ejpam-4369	31	8	of	of	ADP
ejpam-4369	31	9	a	a	PRON
ejpam-4369	31	10	are	be	AUX
ejpam-4369	31	11	denoted	denote	VERB
ejpam-4369	31	12	by	by	ADP
ejpam-4369	31	13	cl(a	cl(a	NOUN
ejpam-4369	31	14	)	)	PUNCT
ejpam-4369	31	15	and	and	CCONJ
ejpam-4369	31	16	int(a	int(a	PROPN
ejpam-4369	31	17	)	)	PUNCT
ejpam-4369	31	18	,	,	PUNCT
ejpam-4369	31	19	respectively	respectively	ADV
ejpam-4369	31	20	.	.	PUNCT
ejpam-4369	32	1	a	a	DET
ejpam-4369	32	2	subset	subset	NOUN
ejpam-4369	32	3	a	a	PRON
ejpam-4369	32	4	of	of	ADP
ejpam-4369	32	5	a	a	DET
ejpam-4369	32	6	topological	topological	ADJ
ejpam-4369	32	7	space	space	NOUN
ejpam-4369	32	8	(	(	PUNCT
ejpam-4369	32	9	x	x	X
ejpam-4369	32	10	,	,	PUNCT
ejpam-4369	32	11	τ	τ	X
ejpam-4369	32	12	)	)	PUNCT
ejpam-4369	32	13	is	be	AUX
ejpam-4369	32	14	said	say	VERB
ejpam-4369	32	15	to	to	PART
ejpam-4369	32	16	be	be	AUX
ejpam-4369	32	17	β	β	X
ejpam-4369	32	18	-	-	ADJ
ejpam-4369	32	19	open	open	ADJ
ejpam-4369	32	20	[	[	X
ejpam-4369	32	21	5	5	NUM
ejpam-4369	32	22	]	]	PUNCT
ejpam-4369	32	23	if	if	SCONJ
ejpam-4369	32	24	a	a	DET
ejpam-4369	32	25	⊆	⊆	NUM
ejpam-4369	32	26	cl(int(cl(a	cl(int(cl(a	NOUN
ejpam-4369	32	27	)	)	PUNCT
ejpam-4369	32	28	)	)	PUNCT
ejpam-4369	32	29	)	)	PUNCT
ejpam-4369	32	30	.	.	PUNCT
ejpam-4369	33	1	the	the	DET
ejpam-4369	33	2	complement	complement	NOUN
ejpam-4369	33	3	of	of	ADP
ejpam-4369	33	4	a	a	DET
ejpam-4369	33	5	β	β	X
ejpam-4369	33	6	-	-	ADJ
ejpam-4369	33	7	open	open	ADJ
ejpam-4369	33	8	set	set	NOUN
ejpam-4369	33	9	is	be	AUX
ejpam-4369	33	10	called	call	VERB
ejpam-4369	33	11	β	β	NOUN
ejpam-4369	33	12	-	-	VERB
ejpam-4369	33	13	closed	closed	ADJ
ejpam-4369	33	14	.	.	PUNCT
ejpam-4369	34	1	the	the	DET
ejpam-4369	34	2	family	family	NOUN
ejpam-4369	34	3	of	of	ADP
ejpam-4369	34	4	all	all	DET
ejpam-4369	34	5	β	β	ADJ
ejpam-4369	34	6	-	-	ADJ
ejpam-4369	34	7	open	open	ADJ
ejpam-4369	34	8	sets	set	NOUN
ejpam-4369	34	9	of	of	ADP
ejpam-4369	34	10	a	a	DET
ejpam-4369	34	11	topological	topological	ADJ
ejpam-4369	34	12	space	space	NOUN
ejpam-4369	34	13	(	(	PUNCT
ejpam-4369	34	14	x	x	X
ejpam-4369	34	15	,	,	PUNCT
ejpam-4369	34	16	τ	τ	X
ejpam-4369	34	17	)	)	PUNCT
ejpam-4369	34	18	is	be	AUX
ejpam-4369	34	19	denoted	denote	VERB
ejpam-4369	34	20	by	by	ADP
ejpam-4369	34	21	β(x	β(x	PROPN
ejpam-4369	34	22	,	,	PUNCT
ejpam-4369	34	23	τ	τ	PROPN
ejpam-4369	34	24	)	)	PUNCT
ejpam-4369	34	25	.	.	PUNCT
ejpam-4369	35	1	a	a	DET
ejpam-4369	35	2	subset	subset	NOUN
ejpam-4369	35	3	λsp(a	λsp(a	NOUN
ejpam-4369	35	4	)	)	PUNCT
ejpam-4369	36	1	[	[	X
ejpam-4369	36	2	9	9	NUM
ejpam-4369	36	3	]	]	PUNCT
ejpam-4369	36	4	is	be	AUX
ejpam-4369	36	5	defined	define	VERB
ejpam-4369	36	6	as	as	SCONJ
ejpam-4369	36	7	follows	follow	VERB
ejpam-4369	36	8	:	:	PUNCT
ejpam-4369	36	9	λsp(a	λsp(a	NUM
ejpam-4369	36	10	)	)	PUNCT
ejpam-4369	36	11	=	=	PUNCT
ejpam-4369	37	1	∩{u	∩{u	PROPN
ejpam-4369	37	2	|	|	ADV
ejpam-4369	37	3	a	a	DET
ejpam-4369	37	4	⊆	⊆	NUM
ejpam-4369	37	5	u	u	NOUN
ejpam-4369	37	6	,	,	PUNCT
ejpam-4369	37	7	u	u	NOUN
ejpam-4369	37	8	∈	∈	PROPN
ejpam-4369	37	9	β(x	β(x	PROPN
ejpam-4369	37	10	,	,	PUNCT
ejpam-4369	37	11	τ	τ	X
ejpam-4369	37	12	)	)	PUNCT
ejpam-4369	37	13	}	}	PUNCT
ejpam-4369	37	14	.	.	PUNCT
ejpam-4369	38	1	a	a	DET
ejpam-4369	38	2	subset	subset	NOUN
ejpam-4369	38	3	a	a	PRON
ejpam-4369	38	4	of	of	ADP
ejpam-4369	38	5	a	a	DET
ejpam-4369	38	6	topological	topological	ADJ
ejpam-4369	38	7	space	space	NOUN
ejpam-4369	38	8	(	(	PUNCT
ejpam-4369	38	9	x	x	X
ejpam-4369	38	10	,	,	PUNCT
ejpam-4369	38	11	τ	τ	X
ejpam-4369	38	12	)	)	PUNCT
ejpam-4369	38	13	is	be	AUX
ejpam-4369	38	14	called	call	VERB
ejpam-4369	38	15	a	a	DET
ejpam-4369	38	16	λsp	λsp	NOUN
ejpam-4369	38	17	-	-	PUNCT
ejpam-4369	38	18	set	set	VERB
ejpam-4369	38	19	[	[	X
ejpam-4369	38	20	9	9	NUM
ejpam-4369	38	21	]	]	X
ejpam-4369	38	22	if	if	SCONJ
ejpam-4369	38	23	a	a	DET
ejpam-4369	38	24	=	=	NOUN
ejpam-4369	38	25	λsp(a	λsp(a	NOUN
ejpam-4369	38	26	)	)	PUNCT
ejpam-4369	38	27	.	.	PUNCT
ejpam-4369	39	1	a	a	DET
ejpam-4369	39	2	subset	subset	NOUN
ejpam-4369	39	3	a	a	PRON
ejpam-4369	39	4	of	of	ADP
ejpam-4369	39	5	a	a	DET
ejpam-4369	39	6	topological	topological	ADJ
ejpam-4369	39	7	space	space	NOUN
ejpam-4369	39	8	(	(	PUNCT
ejpam-4369	39	9	x	x	X
ejpam-4369	39	10	,	,	PUNCT
ejpam-4369	39	11	τ	τ	X
ejpam-4369	39	12	)	)	PUNCT
ejpam-4369	39	13	is	be	AUX
ejpam-4369	39	14	called	call	VERB
ejpam-4369	39	15	(	(	PUNCT
ejpam-4369	39	16	λ	λ	X
ejpam-4369	39	17	,	,	PUNCT
ejpam-4369	39	18	sp)-closed	sp)-close	VERB
ejpam-4369	39	19	[	[	PUNCT
ejpam-4369	39	20	3	3	X
ejpam-4369	39	21	]	]	X
ejpam-4369	39	22	if	if	SCONJ
ejpam-4369	39	23	a	a	DET
ejpam-4369	39	24	=	=	X
ejpam-4369	39	25	t	t	NOUN
ejpam-4369	39	26	∩c	∩c	NOUN
ejpam-4369	39	27	,	,	PUNCT
ejpam-4369	39	28	where	where	SCONJ
ejpam-4369	39	29	t	t	PROPN
ejpam-4369	39	30	is	be	AUX
ejpam-4369	39	31	a	a	DET
ejpam-4369	39	32	λsp	λsp	NOUN
ejpam-4369	39	33	-	-	PUNCT
ejpam-4369	39	34	set	set	VERB
ejpam-4369	39	35	and	and	CCONJ
ejpam-4369	39	36	c	c	NOUN
ejpam-4369	39	37	is	be	AUX
ejpam-4369	39	38	a	a	DET
ejpam-4369	39	39	β	β	NOUN
ejpam-4369	39	40	-	-	ADJ
ejpam-4369	39	41	closed	closed	ADJ
ejpam-4369	39	42	set	set	NOUN
ejpam-4369	39	43	.	.	PUNCT
ejpam-4369	40	1	the	the	DET
ejpam-4369	40	2	complement	complement	NOUN
ejpam-4369	40	3	of	of	ADP
ejpam-4369	40	4	a	a	DET
ejpam-4369	40	5	(	(	PUNCT
ejpam-4369	40	6	λ	λ	PROPN
ejpam-4369	40	7	,	,	PUNCT
ejpam-4369	40	8	sp)-closed	sp)-close	VERB
ejpam-4369	40	9	set	set	VERB
ejpam-4369	40	10	is	be	AUX
ejpam-4369	40	11	called	call	VERB
ejpam-4369	40	12	(	(	PUNCT
ejpam-4369	40	13	λ	λ	NOUN
ejpam-4369	40	14	,	,	PUNCT
ejpam-4369	40	15	sp)-open	sp)-open	NOUN
ejpam-4369	40	16	.	.	PUNCT
ejpam-4369	41	1	the	the	DET
ejpam-4369	41	2	family	family	NOUN
ejpam-4369	41	3	of	of	ADP
ejpam-4369	41	4	all	all	DET
ejpam-4369	41	5	(	(	PUNCT
ejpam-4369	41	6	λ	λ	NOUN
ejpam-4369	41	7	,	,	PUNCT
ejpam-4369	41	8	sp)-open	sp)-open	ADJ
ejpam-4369	41	9	sets	set	NOUN
ejpam-4369	41	10	in	in	ADP
ejpam-4369	41	11	a	a	DET
ejpam-4369	41	12	topological	topological	ADJ
ejpam-4369	41	13	space	space	NOUN
ejpam-4369	41	14	(	(	PUNCT
ejpam-4369	41	15	x	x	X
ejpam-4369	41	16	,	,	PUNCT
ejpam-4369	41	17	τ	τ	X
ejpam-4369	41	18	)	)	PUNCT
ejpam-4369	41	19	is	be	AUX
ejpam-4369	41	20	denoted	denote	VERB
ejpam-4369	41	21	by	by	ADP
ejpam-4369	41	22	λspo(x	λspo(x	PROPN
ejpam-4369	41	23	,	,	PUNCT
ejpam-4369	41	24	τ	τ	PROPN
ejpam-4369	41	25	)	)	PUNCT
ejpam-4369	41	26	.	.	PUNCT
ejpam-4369	42	1	let	let	VERB
ejpam-4369	42	2	a	a	DET
ejpam-4369	42	3	be	be	AUX
ejpam-4369	42	4	a	a	DET
ejpam-4369	42	5	subset	subset	NOUN
ejpam-4369	42	6	of	of	ADP
ejpam-4369	42	7	a	a	DET
ejpam-4369	42	8	topological	topological	ADJ
ejpam-4369	42	9	space	space	NOUN
ejpam-4369	42	10	(	(	PUNCT
ejpam-4369	42	11	x	x	X
ejpam-4369	42	12	,	,	PUNCT
ejpam-4369	42	13	τ	τ	PROPN
ejpam-4369	42	14	)	)	PUNCT
ejpam-4369	42	15	.	.	PUNCT
ejpam-4369	43	1	a	a	DET
ejpam-4369	43	2	point	point	NOUN
ejpam-4369	43	3	x	x	X
ejpam-4369	43	4	∈	∈	NOUN
ejpam-4369	43	5	x	x	PUNCT
ejpam-4369	43	6	is	be	AUX
ejpam-4369	43	7	called	call	VERB
ejpam-4369	43	8	a	a	DET
ejpam-4369	43	9	(	(	PUNCT
ejpam-4369	43	10	λ	λ	NOUN
ejpam-4369	43	11	,	,	PUNCT
ejpam-4369	43	12	sp)-cluster	sp)-cluster	NOUN
ejpam-4369	43	13	point	point	NOUN
ejpam-4369	43	14	[	[	X
ejpam-4369	43	15	3	3	X
ejpam-4369	43	16	]	]	PUNCT
ejpam-4369	43	17	of	of	ADP
ejpam-4369	43	18	a	a	PRON
ejpam-4369	43	19	if	if	SCONJ
ejpam-4369	43	20	a	a	DET
ejpam-4369	43	21	∩	∩	ADJ
ejpam-4369	43	22	u	u	ADJ
ejpam-4369	43	23	̸=	̸=	PROPN
ejpam-4369	43	24	∅	∅	NOUN
ejpam-4369	43	25	for	for	ADP
ejpam-4369	43	26	every	every	DET
ejpam-4369	43	27	(	(	PUNCT
ejpam-4369	43	28	λ	λ	NOUN
ejpam-4369	43	29	,	,	PUNCT
ejpam-4369	43	30	sp)-open	sp)-open	NOUN
ejpam-4369	43	31	set	set	VERB
ejpam-4369	43	32	u	u	NOUN
ejpam-4369	43	33	of	of	ADP
ejpam-4369	43	34	x	x	SYM
ejpam-4369	43	35	containing	contain	VERB
ejpam-4369	43	36	x.	x.	NOUN
ejpam-4369	43	37	the	the	DET
ejpam-4369	43	38	set	set	NOUN
ejpam-4369	43	39	of	of	ADP
ejpam-4369	43	40	all	all	DET
ejpam-4369	43	41	(	(	PUNCT
ejpam-4369	43	42	λ	λ	PROPN
ejpam-4369	43	43	,	,	PUNCT
ejpam-4369	43	44	sp)-cluster	sp)-cluster	NOUN
ejpam-4369	43	45	points	point	NOUN
ejpam-4369	43	46	of	of	ADP
ejpam-4369	43	47	a	a	PRON
ejpam-4369	43	48	is	be	AUX
ejpam-4369	43	49	called	call	VERB
ejpam-4369	43	50	the	the	DET
ejpam-4369	43	51	(	(	PUNCT
ejpam-4369	43	52	λ	λ	PROPN
ejpam-4369	43	53	,	,	PUNCT
ejpam-4369	43	54	sp)-closure	sp)-closure	NOUN
ejpam-4369	43	55	[	[	X
ejpam-4369	43	56	3	3	NUM
ejpam-4369	43	57	]	]	PUNCT
ejpam-4369	43	58	of	of	ADP
ejpam-4369	43	59	a	a	PRON
ejpam-4369	43	60	and	and	CCONJ
ejpam-4369	43	61	is	be	AUX
ejpam-4369	43	62	denoted	denote	VERB
ejpam-4369	43	63	by	by	ADP
ejpam-4369	43	64	a(λ	a(λ	ADV
ejpam-4369	43	65	,	,	PUNCT
ejpam-4369	43	66	sp	sp	NOUN
ejpam-4369	43	67	)	)	PUNCT
ejpam-4369	43	68	.	.	PUNCT
ejpam-4369	44	1	the	the	DET
ejpam-4369	44	2	union	union	NOUN
ejpam-4369	44	3	of	of	ADP
ejpam-4369	44	4	all	all	DET
ejpam-4369	44	5	(	(	PUNCT
ejpam-4369	44	6	λ	λ	NOUN
ejpam-4369	44	7	,	,	PUNCT
ejpam-4369	44	8	sp)-open	sp)-open	ADJ
ejpam-4369	44	9	sets	set	NOUN
ejpam-4369	44	10	contained	contain	VERB
ejpam-4369	44	11	in	in	ADP
ejpam-4369	44	12	a	a	PRON
ejpam-4369	44	13	is	be	AUX
ejpam-4369	44	14	called	call	VERB
ejpam-4369	44	15	the	the	DET
ejpam-4369	44	16	(	(	PUNCT
ejpam-4369	44	17	λ	λ	PROPN
ejpam-4369	44	18	,	,	PUNCT
ejpam-4369	44	19	sp)-interior	sp)-interior	NOUN
ejpam-4369	44	20	[	[	X
ejpam-4369	44	21	3	3	NUM
ejpam-4369	44	22	]	]	PUNCT
ejpam-4369	44	23	of	of	ADP
ejpam-4369	44	24	a	a	PRON
ejpam-4369	44	25	and	and	CCONJ
ejpam-4369	44	26	is	be	AUX
ejpam-4369	44	27	denoted	denote	VERB
ejpam-4369	44	28	by	by	ADP
ejpam-4369	44	29	a(λ	a(λ	ADV
ejpam-4369	44	30	,	,	PUNCT
ejpam-4369	44	31	sp	sp	NOUN
ejpam-4369	44	32	)	)	PUNCT
ejpam-4369	44	33	.	.	PUNCT
ejpam-4369	45	1	lemma	lemma	PROPN
ejpam-4369	45	2	1	1	NUM
ejpam-4369	45	3	.	.	PUNCT
ejpam-4369	46	1	[	[	X
ejpam-4369	46	2	3	3	X
ejpam-4369	46	3	]	]	PUNCT
ejpam-4369	46	4	let	let	VERB
ejpam-4369	46	5	a	a	PRON
ejpam-4369	46	6	and	and	CCONJ
ejpam-4369	46	7	b	b	NOUN
ejpam-4369	46	8	be	be	AUX
ejpam-4369	46	9	subsets	subset	NOUN
ejpam-4369	46	10	of	of	ADP
ejpam-4369	46	11	a	a	DET
ejpam-4369	46	12	topological	topological	ADJ
ejpam-4369	46	13	space	space	NOUN
ejpam-4369	46	14	(	(	PUNCT
ejpam-4369	46	15	x	x	X
ejpam-4369	46	16	,	,	PUNCT
ejpam-4369	46	17	τ	τ	PROPN
ejpam-4369	46	18	)	)	PUNCT
ejpam-4369	46	19	.	.	PUNCT
ejpam-4369	47	1	for	for	ADP
ejpam-4369	47	2	the	the	DET
ejpam-4369	47	3	(	(	PUNCT
ejpam-4369	47	4	λ	λ	PROPN
ejpam-4369	47	5	,	,	PUNCT
ejpam-4369	47	6	sp)-closure	sp)-closure	NOUN
ejpam-4369	47	7	,	,	PUNCT
ejpam-4369	47	8	the	the	DET
ejpam-4369	47	9	following	follow	VERB
ejpam-4369	47	10	properties	property	NOUN
ejpam-4369	47	11	hold	hold	VERB
ejpam-4369	47	12	:	:	PUNCT
ejpam-4369	47	13	(	(	PUNCT
ejpam-4369	47	14	1	1	X
ejpam-4369	47	15	)	)	PUNCT
ejpam-4369	47	16	a	a	DET
ejpam-4369	47	17	⊆	⊆	NUM
ejpam-4369	47	18	a(λ	a(λ	ADJ
ejpam-4369	47	19	,	,	PUNCT
ejpam-4369	47	20	sp	sp	NOUN
ejpam-4369	47	21	)	)	PUNCT
ejpam-4369	47	22	and	and	CCONJ
ejpam-4369	47	23	[	[	X
ejpam-4369	47	24	a(λ	a(λ	ADV
ejpam-4369	47	25	,	,	PUNCT
ejpam-4369	47	26	sp)](λ	sp)](λ	PROPN
ejpam-4369	47	27	,	,	PUNCT
ejpam-4369	47	28	sp	sp	NOUN
ejpam-4369	47	29	)	)	PUNCT
ejpam-4369	47	30	=	=	PUNCT
ejpam-4369	47	31	a(λ	a(λ	ADV
ejpam-4369	47	32	,	,	PUNCT
ejpam-4369	47	33	sp	sp	NOUN
ejpam-4369	47	34	)	)	PUNCT
ejpam-4369	47	35	.	.	PUNCT
ejpam-4369	48	1	(	(	PUNCT
ejpam-4369	48	2	2	2	X
ejpam-4369	48	3	)	)	PUNCT
ejpam-4369	48	4	if	if	SCONJ
ejpam-4369	48	5	a	a	DET
ejpam-4369	48	6	⊆	⊆	NUM
ejpam-4369	48	7	b	b	NOUN
ejpam-4369	48	8	,	,	PUNCT
ejpam-4369	48	9	then	then	ADV
ejpam-4369	48	10	a(λ	a(λ	ADV
ejpam-4369	48	11	,	,	PUNCT
ejpam-4369	48	12	sp	sp	NOUN
ejpam-4369	48	13	)	)	PUNCT
ejpam-4369	48	14	⊆	⊆	NUM
ejpam-4369	48	15	b(λ	b(λ	NOUN
ejpam-4369	48	16	,	,	PUNCT
ejpam-4369	48	17	sp	sp	NOUN
ejpam-4369	48	18	)	)	PUNCT
ejpam-4369	48	19	.	.	PUNCT
ejpam-4369	49	1	(	(	PUNCT
ejpam-4369	49	2	3	3	X
ejpam-4369	49	3	)	)	PUNCT
ejpam-4369	49	4	a(λ	a(λ	ADV
ejpam-4369	49	5	,	,	PUNCT
ejpam-4369	49	6	sp	sp	NOUN
ejpam-4369	49	7	)	)	PUNCT
ejpam-4369	49	8	=	=	SYM
ejpam-4369	49	9	∩{f	∩{f	NOUN
ejpam-4369	49	10	|a	|a	VERB
ejpam-4369	49	11	⊆	⊆	NUM
ejpam-4369	49	12	f	f	PROPN
ejpam-4369	49	13	and	and	CCONJ
ejpam-4369	49	14	f	f	PROPN
ejpam-4369	49	15	is	be	AUX
ejpam-4369	49	16	(	(	PUNCT
ejpam-4369	49	17	λ	λ	X
ejpam-4369	49	18	,	,	PUNCT
ejpam-4369	49	19	sp)-closed	sp)-close	VERB
ejpam-4369	49	20	}	}	PUNCT
ejpam-4369	49	21	.	.	PUNCT
ejpam-4369	50	1	(	(	PUNCT
ejpam-4369	50	2	4	4	NUM
ejpam-4369	50	3	)	)	PUNCT
ejpam-4369	50	4	a(λ	a(λ	ADV
ejpam-4369	50	5	,	,	PUNCT
ejpam-4369	50	6	sp	sp	NOUN
ejpam-4369	50	7	)	)	PUNCT
ejpam-4369	50	8	is	be	AUX
ejpam-4369	50	9	(	(	PUNCT
ejpam-4369	50	10	λ	λ	X
ejpam-4369	50	11	,	,	PUNCT
ejpam-4369	50	12	sp)-closed	sp)-close	VERB
ejpam-4369	50	13	.	.	PUNCT
ejpam-4369	51	1	(	(	PUNCT
ejpam-4369	51	2	5	5	X
ejpam-4369	51	3	)	)	PUNCT
ejpam-4369	51	4	a	a	PRON
ejpam-4369	51	5	is	be	AUX
ejpam-4369	51	6	(	(	PUNCT
ejpam-4369	51	7	λ	λ	X
ejpam-4369	51	8	,	,	PUNCT
ejpam-4369	51	9	sp)-closed	sp)-close	VERB
ejpam-4369	51	10	if	if	SCONJ
ejpam-4369	51	11	and	and	CCONJ
ejpam-4369	51	12	only	only	ADV
ejpam-4369	51	13	if	if	SCONJ
ejpam-4369	51	14	a	a	DET
ejpam-4369	51	15	=	=	X
ejpam-4369	51	16	a(λ	a(λ	ADV
ejpam-4369	51	17	,	,	PUNCT
ejpam-4369	51	18	sp	sp	NOUN
ejpam-4369	51	19	)	)	PUNCT
ejpam-4369	51	20	.	.	PUNCT
ejpam-4369	52	1	lemma	lemma	PROPN
ejpam-4369	52	2	2	2	NUM
ejpam-4369	52	3	.	.	PUNCT
ejpam-4369	53	1	[	[	X
ejpam-4369	53	2	3	3	X
ejpam-4369	53	3	]	]	PUNCT
ejpam-4369	53	4	let	let	VERB
ejpam-4369	53	5	a	a	PRON
ejpam-4369	53	6	and	and	CCONJ
ejpam-4369	53	7	b	b	NOUN
ejpam-4369	53	8	be	be	AUX
ejpam-4369	53	9	subsets	subset	NOUN
ejpam-4369	53	10	of	of	ADP
ejpam-4369	53	11	a	a	DET
ejpam-4369	53	12	topological	topological	ADJ
ejpam-4369	53	13	space	space	NOUN
ejpam-4369	53	14	(	(	PUNCT
ejpam-4369	53	15	x	x	X
ejpam-4369	53	16	,	,	PUNCT
ejpam-4369	53	17	τ	τ	PROPN
ejpam-4369	53	18	)	)	PUNCT
ejpam-4369	53	19	.	.	PUNCT
ejpam-4369	54	1	for	for	ADP
ejpam-4369	54	2	the	the	DET
ejpam-4369	54	3	(	(	PUNCT
ejpam-4369	54	4	λ	λ	PROPN
ejpam-4369	54	5	,	,	PUNCT
ejpam-4369	54	6	sp)interior	sp)interior	PROPN
ejpam-4369	54	7	,	,	PUNCT
ejpam-4369	54	8	the	the	DET
ejpam-4369	54	9	following	follow	VERB
ejpam-4369	54	10	properties	property	NOUN
ejpam-4369	54	11	hold	hold	VERB
ejpam-4369	54	12	:	:	PUNCT
ejpam-4369	54	13	(	(	PUNCT
ejpam-4369	54	14	1	1	X
ejpam-4369	54	15	)	)	PUNCT
ejpam-4369	54	16	a(λ	a(λ	ADV
ejpam-4369	54	17	,	,	PUNCT
ejpam-4369	54	18	sp	sp	NOUN
ejpam-4369	54	19	)	)	PUNCT
ejpam-4369	54	20	⊆	⊆	NUM
ejpam-4369	54	21	a	a	DET
ejpam-4369	54	22	and	and	CCONJ
ejpam-4369	54	23	[	[	X
ejpam-4369	54	24	a(λ	a(λ	ADV
ejpam-4369	54	25	,	,	PUNCT
ejpam-4369	54	26	sp)](λ	sp)](λ	PROPN
ejpam-4369	54	27	,	,	PUNCT
ejpam-4369	54	28	sp	sp	NOUN
ejpam-4369	54	29	)	)	PUNCT
ejpam-4369	54	30	=	=	PUNCT
ejpam-4369	54	31	a(λ	a(λ	ADV
ejpam-4369	54	32	,	,	PUNCT
ejpam-4369	54	33	sp	sp	NOUN
ejpam-4369	54	34	)	)	PUNCT
ejpam-4369	54	35	.	.	PUNCT
ejpam-4369	55	1	(	(	PUNCT
ejpam-4369	55	2	2	2	X
ejpam-4369	55	3	)	)	PUNCT
ejpam-4369	55	4	if	if	SCONJ
ejpam-4369	55	5	a	a	DET
ejpam-4369	55	6	⊆	⊆	NUM
ejpam-4369	55	7	b	b	NOUN
ejpam-4369	55	8	,	,	PUNCT
ejpam-4369	55	9	then	then	ADV
ejpam-4369	55	10	a(λ	a(λ	ADV
ejpam-4369	55	11	,	,	PUNCT
ejpam-4369	55	12	sp	sp	NOUN
ejpam-4369	55	13	)	)	PUNCT
ejpam-4369	55	14	⊆	⊆	NUM
ejpam-4369	55	15	b(λ	b(λ	NOUN
ejpam-4369	55	16	,	,	PUNCT
ejpam-4369	55	17	sp	sp	NOUN
ejpam-4369	55	18	)	)	PUNCT
ejpam-4369	55	19	.	.	PUNCT
ejpam-4369	56	1	c.	c.	PROPN
ejpam-4369	56	2	boonpok	boonpok	PROPN
ejpam-4369	56	3	,	,	PUNCT
ejpam-4369	56	4	j.	j.	PROPN
ejpam-4369	56	5	khampakdee	khampakdee	PROPN
ejpam-4369	56	6	/	/	PUNCT
ejpam-4369	56	7	eur	eur	PROPN
ejpam-4369	56	8	.	.	PUNCT
ejpam-4369	57	1	j.	j.	PROPN
ejpam-4369	57	2	pure	pure	PROPN
ejpam-4369	57	3	appl	appl	PROPN
ejpam-4369	57	4	.	.	PROPN
ejpam-4369	57	5	math	math	PROPN
ejpam-4369	57	6	,	,	PUNCT
ejpam-4369	57	7	15	15	NUM
ejpam-4369	57	8	(	(	PUNCT
ejpam-4369	57	9	3	3	NUM
ejpam-4369	57	10	)	)	PUNCT
ejpam-4369	57	11	(	(	PUNCT
ejpam-4369	57	12	2022	2022	NUM
ejpam-4369	57	13	)	)	PUNCT
ejpam-4369	57	14	,	,	PUNCT
ejpam-4369	57	15	1180	1180	NUM
ejpam-4369	57	16	-	-	SYM
ejpam-4369	57	17	1188	1188	NUM
ejpam-4369	57	18	1182	1182	NUM
ejpam-4369	57	19	(	(	PUNCT
ejpam-4369	57	20	3	3	NUM
ejpam-4369	57	21	)	)	PUNCT
ejpam-4369	57	22	a(λ	a(λ	ADV
ejpam-4369	57	23	,	,	PUNCT
ejpam-4369	57	24	sp	sp	NOUN
ejpam-4369	57	25	)	)	PUNCT
ejpam-4369	57	26	is	be	AUX
ejpam-4369	57	27	(	(	PUNCT
ejpam-4369	57	28	λ	λ	INTJ
ejpam-4369	57	29	,	,	PUNCT
ejpam-4369	57	30	sp)-open	sp)-open	NOUN
ejpam-4369	57	31	.	.	PUNCT
ejpam-4369	58	1	(	(	PUNCT
ejpam-4369	58	2	4	4	X
ejpam-4369	58	3	)	)	PUNCT
ejpam-4369	58	4	a	a	DET
ejpam-4369	58	5	is	be	AUX
ejpam-4369	58	6	(	(	PUNCT
ejpam-4369	58	7	λ	λ	NOUN
ejpam-4369	58	8	,	,	PUNCT
ejpam-4369	58	9	sp)-open	sp)-open	ADJ
ejpam-4369	58	10	if	if	SCONJ
ejpam-4369	58	11	and	and	CCONJ
ejpam-4369	58	12	only	only	ADV
ejpam-4369	58	13	if	if	SCONJ
ejpam-4369	58	14	a(λ	a(λ	ADV
ejpam-4369	58	15	,	,	PUNCT
ejpam-4369	58	16	sp	sp	NOUN
ejpam-4369	58	17	)	)	PUNCT
ejpam-4369	58	18	=	=	SYM
ejpam-4369	58	19	a.	a.	NOUN
ejpam-4369	58	20	(	(	PUNCT
ejpam-4369	58	21	5	5	NUM
ejpam-4369	58	22	)	)	PUNCT
ejpam-4369	59	1	[	[	X
ejpam-4369	59	2	x	x	X
ejpam-4369	59	3	−a](λ	−a](λ	PROPN
ejpam-4369	59	4	,	,	PUNCT
ejpam-4369	59	5	sp	sp	NOUN
ejpam-4369	59	6	)	)	PUNCT
ejpam-4369	59	7	=	=	SYM
ejpam-4369	59	8	x	x	SYM
ejpam-4369	59	9	−a(λ	−a(λ	NOUN
ejpam-4369	59	10	,	,	PUNCT
ejpam-4369	59	11	sp	sp	NOUN
ejpam-4369	59	12	)	)	PUNCT
ejpam-4369	59	13	.	.	PUNCT
ejpam-4369	60	1	(	(	PUNCT
ejpam-4369	60	2	6	6	NUM
ejpam-4369	60	3	)	)	PUNCT
ejpam-4369	61	1	[	[	X
ejpam-4369	61	2	x	x	X
ejpam-4369	61	3	−a](λ	−a](λ	PROPN
ejpam-4369	61	4	,	,	PUNCT
ejpam-4369	61	5	sp	sp	NOUN
ejpam-4369	61	6	)	)	PUNCT
ejpam-4369	61	7	=	=	SYM
ejpam-4369	61	8	x	x	SYM
ejpam-4369	61	9	−a(λ	−a(λ	NOUN
ejpam-4369	61	10	,	,	PUNCT
ejpam-4369	61	11	sp	sp	NOUN
ejpam-4369	61	12	)	)	PUNCT
ejpam-4369	61	13	.	.	PUNCT
ejpam-4369	62	1	a	a	DET
ejpam-4369	62	2	subset	subset	NOUN
ejpam-4369	62	3	a	a	PRON
ejpam-4369	62	4	of	of	ADP
ejpam-4369	62	5	a	a	DET
ejpam-4369	62	6	topological	topological	ADJ
ejpam-4369	62	7	space	space	NOUN
ejpam-4369	62	8	(	(	PUNCT
ejpam-4369	62	9	x	x	X
ejpam-4369	62	10	,	,	PUNCT
ejpam-4369	62	11	τ	τ	X
ejpam-4369	62	12	)	)	PUNCT
ejpam-4369	62	13	is	be	AUX
ejpam-4369	62	14	said	say	VERB
ejpam-4369	62	15	to	to	PART
ejpam-4369	62	16	be	be	AUX
ejpam-4369	62	17	s(λ	s(λ	NOUN
ejpam-4369	62	18	,	,	PUNCT
ejpam-4369	62	19	sp)-open	sp)-open	ADJ
ejpam-4369	62	20	(	(	PUNCT
ejpam-4369	62	21	resp	resp	NOUN
ejpam-4369	62	22	.	.	PUNCT
ejpam-4369	63	1	p(λ	p(λ	NOUN
ejpam-4369	63	2	,	,	PUNCT
ejpam-4369	63	3	sp)open	sp)open	VERB
ejpam-4369	63	4	,	,	PUNCT
ejpam-4369	63	5	r(λ	r(λ	NOUN
ejpam-4369	63	6	,	,	PUNCT
ejpam-4369	63	7	sp)-open	sp)-open	NOUN
ejpam-4369	63	8	,	,	PUNCT
ejpam-4369	63	9	β(λ	β(λ	X
ejpam-4369	63	10	,	,	PUNCT
ejpam-4369	63	11	sp)-open	sp)-open	NOUN
ejpam-4369	63	12	)	)	PUNCT
ejpam-4369	63	13	if	if	SCONJ
ejpam-4369	63	14	a	a	DET
ejpam-4369	63	15	⊆	⊆	NUM
ejpam-4369	63	16	[	[	X
ejpam-4369	63	17	a(λ	a(λ	ADV
ejpam-4369	63	18	,	,	PUNCT
ejpam-4369	63	19	sp	sp	NOUN
ejpam-4369	63	20	)	)	PUNCT
ejpam-4369	63	21	]	]	PUNCT
ejpam-4369	64	1	(	(	PUNCT
ejpam-4369	64	2	λ	λ	NOUN
ejpam-4369	64	3	,	,	PUNCT
ejpam-4369	64	4	sp	sp	NOUN
ejpam-4369	64	5	)	)	PUNCT
ejpam-4369	64	6	(	(	PUNCT
ejpam-4369	64	7	resp	resp	NOUN
ejpam-4369	64	8	.	.	PUNCT
ejpam-4369	65	1	a	a	DET
ejpam-4369	65	2	⊆	⊆	NUM
ejpam-4369	65	3	[	[	X
ejpam-4369	65	4	a(λ	a(λ	ADJ
ejpam-4369	65	5	,	,	PUNCT
ejpam-4369	65	6	sp)](λ	sp)](λ	PROPN
ejpam-4369	65	7	,	,	PUNCT
ejpam-4369	65	8	sp	sp	NOUN
ejpam-4369	65	9	)	)	PUNCT
ejpam-4369	65	10	,	,	PUNCT
ejpam-4369	66	1	a	a	DET
ejpam-4369	66	2	=	=	X
ejpam-4369	66	3	[	[	X
ejpam-4369	66	4	a(λ	a(λ	PROPN
ejpam-4369	66	5	,	,	PUNCT
ejpam-4369	66	6	sp)](λ	sp)](λ	PROPN
ejpam-4369	66	7	,	,	PUNCT
ejpam-4369	66	8	sp	sp	NOUN
ejpam-4369	66	9	)	)	PUNCT
ejpam-4369	66	10	,	,	PUNCT
ejpam-4369	66	11	a	a	DET
ejpam-4369	66	12	⊆	⊆	NUM
ejpam-4369	66	13	[	[	X
ejpam-4369	66	14	[	[	X
ejpam-4369	66	15	a(λ	a(λ	ADJ
ejpam-4369	66	16	,	,	PUNCT
ejpam-4369	66	17	sp)](λ	sp)](λ	PROPN
ejpam-4369	66	18	,	,	PUNCT
ejpam-4369	66	19	sp	sp	NOUN
ejpam-4369	66	20	)	)	PUNCT
ejpam-4369	66	21	]	]	PUNCT
ejpam-4369	67	1	(	(	PUNCT
ejpam-4369	67	2	λ	λ	NOUN
ejpam-4369	67	3	,	,	PUNCT
ejpam-4369	67	4	sp	sp	NOUN
ejpam-4369	67	5	)	)	PUNCT
ejpam-4369	67	6	)	)	PUNCT
ejpam-4369	68	1	[	[	X
ejpam-4369	68	2	3	3	NUM
ejpam-4369	68	3	]	]	PUNCT
ejpam-4369	68	4	.	.	PUNCT
ejpam-4369	69	1	the	the	DET
ejpam-4369	69	2	complement	complement	NOUN
ejpam-4369	69	3	of	of	ADP
ejpam-4369	69	4	a	a	DET
ejpam-4369	69	5	s(λ	s(λ	PROPN
ejpam-4369	69	6	,	,	PUNCT
ejpam-4369	69	7	sp)-open	sp)-open	ADJ
ejpam-4369	69	8	(	(	PUNCT
ejpam-4369	69	9	resp	resp	NOUN
ejpam-4369	69	10	.	.	PUNCT
ejpam-4369	70	1	p(λ	p(λ	NOUN
ejpam-4369	70	2	,	,	PUNCT
ejpam-4369	70	3	sp)-open	sp)-open	NOUN
ejpam-4369	70	4	,	,	PUNCT
ejpam-4369	70	5	r(λ	r(λ	NOUN
ejpam-4369	70	6	,	,	PUNCT
ejpam-4369	70	7	sp)-open	sp)-open	NOUN
ejpam-4369	70	8	,	,	PUNCT
ejpam-4369	70	9	β(λ	β(λ	X
ejpam-4369	70	10	,	,	PUNCT
ejpam-4369	70	11	sp)-open	sp)-open	NOUN
ejpam-4369	70	12	)	)	PUNCT
ejpam-4369	70	13	set	set	NOUN
ejpam-4369	70	14	is	be	AUX
ejpam-4369	70	15	called	call	VERB
ejpam-4369	70	16	s(λ	s(λ	PROPN
ejpam-4369	70	17	,	,	PUNCT
ejpam-4369	70	18	sp)-closed	sp)-close	VERB
ejpam-4369	70	19	(	(	PUNCT
ejpam-4369	70	20	resp	resp	NOUN
ejpam-4369	70	21	.	.	PUNCT
ejpam-4369	71	1	p(λ	p(λ	NOUN
ejpam-4369	71	2	,	,	PUNCT
ejpam-4369	71	3	sp)closed	sp)close	VERB
ejpam-4369	71	4	,	,	PUNCT
ejpam-4369	71	5	r(λ	r(λ	PROPN
ejpam-4369	71	6	,	,	PUNCT
ejpam-4369	71	7	sp)-closed	sp)-close	VERB
ejpam-4369	71	8	,	,	PUNCT
ejpam-4369	71	9	β(λ	β(λ	X
ejpam-4369	71	10	,	,	PUNCT
ejpam-4369	71	11	sp)-closed	sp)-close	VERB
ejpam-4369	71	12	)	)	PUNCT
ejpam-4369	71	13	.	.	PUNCT
ejpam-4369	72	1	the	the	DET
ejpam-4369	72	2	family	family	NOUN
ejpam-4369	72	3	of	of	ADP
ejpam-4369	72	4	all	all	DET
ejpam-4369	72	5	s(λ	s(λ	NOUN
ejpam-4369	72	6	,	,	PUNCT
ejpam-4369	72	7	sp)-open	sp)-open	ADJ
ejpam-4369	72	8	(	(	PUNCT
ejpam-4369	72	9	resp	resp	NOUN
ejpam-4369	72	10	.	.	PUNCT
ejpam-4369	73	1	p(λ	p(λ	NOUN
ejpam-4369	73	2	,	,	PUNCT
ejpam-4369	73	3	sp)-open	sp)-open	NOUN
ejpam-4369	73	4	,	,	PUNCT
ejpam-4369	73	5	r(λ	r(λ	NOUN
ejpam-4369	73	6	,	,	PUNCT
ejpam-4369	73	7	sp)-open	sp)-open	NOUN
ejpam-4369	73	8	,	,	PUNCT
ejpam-4369	73	9	β(λ	β(λ	X
ejpam-4369	73	10	,	,	PUNCT
ejpam-4369	73	11	sp)-open	sp)-open	NOUN
ejpam-4369	73	12	)	)	PUNCT
ejpam-4369	73	13	sets	set	NOUN
ejpam-4369	73	14	in	in	ADP
ejpam-4369	73	15	a	a	DET
ejpam-4369	73	16	topological	topological	ADJ
ejpam-4369	73	17	space	space	NOUN
ejpam-4369	73	18	(	(	PUNCT
ejpam-4369	73	19	x	x	X
ejpam-4369	73	20	,	,	PUNCT
ejpam-4369	73	21	τ	τ	X
ejpam-4369	73	22	)	)	PUNCT
ejpam-4369	73	23	is	be	AUX
ejpam-4369	73	24	denoted	denote	VERB
ejpam-4369	73	25	by	by	ADP
ejpam-4369	73	26	sλspo(x	sλspo(x	PROPN
ejpam-4369	73	27	,	,	PUNCT
ejpam-4369	73	28	τ	τ	PROPN
ejpam-4369	73	29	)	)	PUNCT
ejpam-4369	73	30	(	(	PUNCT
ejpam-4369	73	31	resp	resp	NOUN
ejpam-4369	73	32	.	.	PUNCT
ejpam-4369	74	1	pλspo(x	pλspo(x	ADJ
ejpam-4369	74	2	,	,	PUNCT
ejpam-4369	74	3	τ	τ	PROPN
ejpam-4369	74	4	)	)	PUNCT
ejpam-4369	74	5	,	,	PUNCT
ejpam-4369	74	6	rλspo(x	rλspo(x	PROPN
ejpam-4369	74	7	,	,	PUNCT
ejpam-4369	74	8	τ	τ	PROPN
ejpam-4369	74	9	)	)	PUNCT
ejpam-4369	74	10	,	,	PUNCT
ejpam-4369	74	11	βλspo(x	βλspo(x	PROPN
ejpam-4369	74	12	,	,	PUNCT
ejpam-4369	74	13	τ	τ	PROPN
ejpam-4369	74	14	)	)	PUNCT
ejpam-4369	74	15	)	)	PUNCT
ejpam-4369	74	16	.	.	PUNCT
ejpam-4369	75	1	a	a	DET
ejpam-4369	75	2	subset	subset	NOUN
ejpam-4369	75	3	a	a	PRON
ejpam-4369	75	4	of	of	ADP
ejpam-4369	75	5	a	a	DET
ejpam-4369	75	6	topological	topological	ADJ
ejpam-4369	75	7	space	space	NOUN
ejpam-4369	75	8	(	(	PUNCT
ejpam-4369	75	9	x	x	X
ejpam-4369	75	10	,	,	PUNCT
ejpam-4369	75	11	τ	τ	X
ejpam-4369	75	12	)	)	PUNCT
ejpam-4369	75	13	is	be	AUX
ejpam-4369	75	14	called	call	VERB
ejpam-4369	75	15	(	(	PUNCT
ejpam-4369	75	16	λ	λ	PROPN
ejpam-4369	75	17	,	,	PUNCT
ejpam-4369	75	18	sp)-clopen	sp)-clopen	NOUN
ejpam-4369	76	1	[	[	X
ejpam-4369	76	2	4	4	X
ejpam-4369	76	3	]	]	X
ejpam-4369	76	4	if	if	SCONJ
ejpam-4369	76	5	a	a	PRON
ejpam-4369	76	6	is	be	AUX
ejpam-4369	76	7	both	both	PRON
ejpam-4369	76	8	(	(	PUNCT
ejpam-4369	76	9	λ	λ	NOUN
ejpam-4369	76	10	,	,	PUNCT
ejpam-4369	76	11	sp)-open	sp)-open	ADJ
ejpam-4369	76	12	and	and	CCONJ
ejpam-4369	76	13	(	(	PUNCT
ejpam-4369	76	14	λ	λ	PROPN
ejpam-4369	76	15	,	,	PUNCT
ejpam-4369	76	16	sp)-closed	sp)-close	VERB
ejpam-4369	76	17	.	.	PUNCT
ejpam-4369	77	1	by	by	ADP
ejpam-4369	77	2	a	a	DET
ejpam-4369	77	3	multifunction	multifunction	NOUN
ejpam-4369	77	4	f	f	NOUN
ejpam-4369	77	5	:	:	PUNCT
ejpam-4369	77	6	x	x	X
ejpam-4369	77	7	→	→	SYM
ejpam-4369	77	8	y	y	PROPN
ejpam-4369	77	9	,	,	PUNCT
ejpam-4369	77	10	we	we	PRON
ejpam-4369	77	11	mean	mean	VERB
ejpam-4369	77	12	a	a	DET
ejpam-4369	77	13	point	point	NOUN
ejpam-4369	77	14	-	-	PUNCT
ejpam-4369	77	15	to	to	ADP
ejpam-4369	77	16	-	-	PUNCT
ejpam-4369	77	17	set	set	VERB
ejpam-4369	77	18	correspondence	correspondence	NOUN
ejpam-4369	77	19	from	from	ADP
ejpam-4369	77	20	x	x	PUNCT
ejpam-4369	77	21	into	into	ADP
ejpam-4369	77	22	y	y	PROPN
ejpam-4369	77	23	,	,	PUNCT
ejpam-4369	77	24	and	and	CCONJ
ejpam-4369	77	25	always	always	ADV
ejpam-4369	77	26	assume	assume	VERB
ejpam-4369	77	27	that	that	SCONJ
ejpam-4369	78	1	f	f	PROPN
ejpam-4369	78	2	(	(	PUNCT
ejpam-4369	78	3	x	x	X
ejpam-4369	78	4	)	)	PUNCT
ejpam-4369	78	5	̸=	̸=	NOUN
ejpam-4369	78	6	∅	∅	NOUN
ejpam-4369	78	7	for	for	ADP
ejpam-4369	78	8	all	all	PRON
ejpam-4369	78	9	x	x	SYM
ejpam-4369	78	10	∈	∈	ADJ
ejpam-4369	78	11	x.	x.	NOUN
ejpam-4369	78	12	for	for	ADP
ejpam-4369	78	13	a	a	DET
ejpam-4369	78	14	multifunction	multifunction	NOUN
ejpam-4369	78	15	f	f	NOUN
ejpam-4369	78	16	:	:	PUNCT
ejpam-4369	78	17	x	x	X
ejpam-4369	78	18	→	→	SYM
ejpam-4369	78	19	y	y	PROPN
ejpam-4369	78	20	,	,	PUNCT
ejpam-4369	78	21	following	follow	VERB
ejpam-4369	78	22	[	[	X
ejpam-4369	78	23	2	2	X
ejpam-4369	78	24	]	]	PUNCT
ejpam-4369	78	25	we	we	PRON
ejpam-4369	78	26	shall	shall	AUX
ejpam-4369	78	27	denote	denote	VERB
ejpam-4369	78	28	the	the	DET
ejpam-4369	78	29	upper	upper	ADJ
ejpam-4369	78	30	and	and	CCONJ
ejpam-4369	78	31	lower	low	ADJ
ejpam-4369	78	32	inverse	inverse	NOUN
ejpam-4369	78	33	of	of	ADP
ejpam-4369	78	34	a	a	DET
ejpam-4369	78	35	set	set	NOUN
ejpam-4369	78	36	b	b	PROPN
ejpam-4369	78	37	of	of	ADP
ejpam-4369	78	38	y	y	PROPN
ejpam-4369	78	39	by	by	ADP
ejpam-4369	78	40	f+(b	f+(b	NOUN
ejpam-4369	78	41	)	)	PUNCT
ejpam-4369	78	42	and	and	CCONJ
ejpam-4369	78	43	f−(b	f−(b	NOUN
ejpam-4369	78	44	)	)	PUNCT
ejpam-4369	78	45	,	,	PUNCT
ejpam-4369	78	46	respectively	respectively	ADV
ejpam-4369	78	47	,	,	PUNCT
ejpam-4369	78	48	that	that	ADV
ejpam-4369	78	49	is	is	ADV
ejpam-4369	78	50	,	,	PUNCT
ejpam-4369	78	51	f+(b	f+(b	NOUN
ejpam-4369	78	52	)	)	PUNCT
ejpam-4369	78	53	=	=	PRON
ejpam-4369	79	1	{	{	PUNCT
ejpam-4369	79	2	x	x	PUNCT
ejpam-4369	79	3	∈	∈	PROPN
ejpam-4369	79	4	x	x	INTJ
ejpam-4369	80	1	|	|	NOUN
ejpam-4369	80	2	f	f	X
ejpam-4369	80	3	(	(	PUNCT
ejpam-4369	80	4	x	x	NOUN
ejpam-4369	80	5	)	)	PUNCT
ejpam-4369	80	6	⊆	⊆	NUM
ejpam-4369	80	7	b	b	NOUN
ejpam-4369	80	8	}	}	PUNCT
ejpam-4369	80	9	and	and	CCONJ
ejpam-4369	80	10	f−(b	f−(b	PROPN
ejpam-4369	80	11	)	)	PUNCT
ejpam-4369	80	12	=	=	PRON
ejpam-4369	81	1	{	{	PUNCT
ejpam-4369	81	2	x	x	PUNCT
ejpam-4369	81	3	∈	∈	PROPN
ejpam-4369	81	4	x	x	INTJ
ejpam-4369	82	1	|	|	NOUN
ejpam-4369	82	2	f	f	X
ejpam-4369	82	3	(	(	PUNCT
ejpam-4369	82	4	x)∩b	x)∩b	PROPN
ejpam-4369	82	5	̸=	̸=	PROPN
ejpam-4369	82	6	∅	∅	NOUN
ejpam-4369	82	7	}	}	PUNCT
ejpam-4369	82	8	.	.	PUNCT
ejpam-4369	83	1	in	in	ADP
ejpam-4369	83	2	particular	particular	ADJ
ejpam-4369	83	3	,	,	PUNCT
ejpam-4369	83	4	f−(y	f−(y	NOUN
ejpam-4369	83	5	)	)	PUNCT
ejpam-4369	83	6	=	=	SYM
ejpam-4369	84	1	{	{	PUNCT
ejpam-4369	84	2	x	x	PUNCT
ejpam-4369	84	3	∈	∈	PROPN
ejpam-4369	84	4	x	x	INTJ
ejpam-4369	85	1	|	|	ADV
ejpam-4369	85	2	y	y	PROPN
ejpam-4369	85	3	∈	∈	PROPN
ejpam-4369	85	4	f	f	X
ejpam-4369	85	5	(	(	PUNCT
ejpam-4369	85	6	x	x	NOUN
ejpam-4369	85	7	)	)	PUNCT
ejpam-4369	85	8	}	}	PUNCT
ejpam-4369	85	9	for	for	ADP
ejpam-4369	85	10	each	each	DET
ejpam-4369	85	11	point	point	NOUN
ejpam-4369	85	12	y	y	PROPN
ejpam-4369	85	13	∈	∈	PROPN
ejpam-4369	85	14	y	y	PROPN
ejpam-4369	85	15	.	.	PUNCT
ejpam-4369	86	1	for	for	ADP
ejpam-4369	86	2	each	each	PRON
ejpam-4369	86	3	a	a	DET
ejpam-4369	86	4	⊆	⊆	NUM
ejpam-4369	86	5	x	x	SYM
ejpam-4369	86	6	,	,	PUNCT
ejpam-4369	86	7	f	f	PROPN
ejpam-4369	86	8	(	(	PUNCT
ejpam-4369	86	9	a	a	NOUN
ejpam-4369	86	10	)	)	PUNCT
ejpam-4369	86	11	=	=	SYM
ejpam-4369	86	12	∪x∈af	∪x∈af	NOUN
ejpam-4369	86	13	(	(	PUNCT
ejpam-4369	86	14	x	x	NOUN
ejpam-4369	86	15	)	)	PUNCT
ejpam-4369	86	16	.	.	PUNCT
ejpam-4369	87	1	then	then	ADV
ejpam-4369	87	2	,	,	PUNCT
ejpam-4369	87	3	f	f	PROPN
ejpam-4369	87	4	is	be	AUX
ejpam-4369	87	5	said	say	VERB
ejpam-4369	87	6	to	to	PART
ejpam-4369	87	7	be	be	AUX
ejpam-4369	87	8	a	a	DET
ejpam-4369	87	9	surjection	surjection	NOUN
ejpam-4369	87	10	if	if	SCONJ
ejpam-4369	87	11	f	f	PROPN
ejpam-4369	87	12	(	(	PUNCT
ejpam-4369	87	13	x	x	X
ejpam-4369	87	14	)	)	PUNCT
ejpam-4369	87	15	=	=	SYM
ejpam-4369	87	16	y	y	PROPN
ejpam-4369	87	17	,	,	PUNCT
ejpam-4369	87	18	or	or	CCONJ
ejpam-4369	87	19	equivalently	equivalently	ADV
ejpam-4369	87	20	,	,	PUNCT
ejpam-4369	87	21	if	if	SCONJ
ejpam-4369	87	22	for	for	ADP
ejpam-4369	87	23	each	each	DET
ejpam-4369	87	24	y	y	PROPN
ejpam-4369	87	25	∈	∈	PROPN
ejpam-4369	87	26	y	y	PROPN
ejpam-4369	87	27	,	,	PUNCT
ejpam-4369	87	28	there	there	PRON
ejpam-4369	87	29	exists	exist	VERB
ejpam-4369	87	30	an	an	DET
ejpam-4369	87	31	x	x	SYM
ejpam-4369	87	32	∈	∈	PROPN
ejpam-4369	87	33	x	x	X
ejpam-4369	87	34	such	such	ADJ
ejpam-4369	87	35	that	that	SCONJ
ejpam-4369	87	36	y	y	PROPN
ejpam-4369	87	37	∈	∈	PROPN
ejpam-4369	87	38	f	f	X
ejpam-4369	87	39	(	(	PUNCT
ejpam-4369	87	40	x	x	NOUN
ejpam-4369	87	41	)	)	PUNCT
ejpam-4369	87	42	.	.	PUNCT
ejpam-4369	88	1	moreover	moreover	ADV
ejpam-4369	88	2	,	,	PUNCT
ejpam-4369	88	3	f	f	X
ejpam-4369	88	4	:	:	PUNCT
ejpam-4369	88	5	x	x	X
ejpam-4369	88	6	→	→	SYM
ejpam-4369	88	7	y	y	PROPN
ejpam-4369	88	8	is	be	AUX
ejpam-4369	88	9	called	call	VERB
ejpam-4369	88	10	upper	upper	ADJ
ejpam-4369	88	11	semi	semi	ADJ
ejpam-4369	88	12	-	-	ADJ
ejpam-4369	88	13	continuous	continuous	ADJ
ejpam-4369	88	14	(	(	PUNCT
ejpam-4369	88	15	resp	resp	NOUN
ejpam-4369	88	16	.	.	PUNCT
ejpam-4369	89	1	lower	low	ADJ
ejpam-4369	89	2	semi	semi	ADJ
ejpam-4369	89	3	-	-	ADJ
ejpam-4369	89	4	continuous	continuous	ADJ
ejpam-4369	89	5	)	)	PUNCT
ejpam-4369	89	6	if	if	SCONJ
ejpam-4369	89	7	f+(v	f+(v	PROPN
ejpam-4369	89	8	)	)	PUNCT
ejpam-4369	89	9	(	(	PUNCT
ejpam-4369	89	10	resp	resp	NOUN
ejpam-4369	89	11	.	.	PUNCT
ejpam-4369	90	1	f−(v	f−(v	NOUN
ejpam-4369	90	2	)	)	PUNCT
ejpam-4369	90	3	)	)	PUNCT
ejpam-4369	91	1	is	be	AUX
ejpam-4369	91	2	open	open	ADJ
ejpam-4369	91	3	in	in	ADP
ejpam-4369	91	4	x	x	PUNCT
ejpam-4369	91	5	for	for	ADP
ejpam-4369	91	6	every	every	DET
ejpam-4369	91	7	open	open	ADJ
ejpam-4369	91	8	set	set	VERB
ejpam-4369	91	9	v	v	NOUN
ejpam-4369	91	10	of	of	ADP
ejpam-4369	91	11	y	y	PROPN
ejpam-4369	92	1	[	[	X
ejpam-4369	92	2	13	13	NUM
ejpam-4369	92	3	]	]	PUNCT
ejpam-4369	92	4	.	.	PUNCT
ejpam-4369	93	1	3	3	X
ejpam-4369	93	2	.	.	X
ejpam-4369	93	3	upper	upper	ADJ
ejpam-4369	93	4	and	and	CCONJ
ejpam-4369	93	5	lower	lower	ADV
ejpam-4369	93	6	slightly	slightly	ADV
ejpam-4369	93	7	(	(	PUNCT
ejpam-4369	93	8	λ	λ	NOUN
ejpam-4369	93	9	,	,	PUNCT
ejpam-4369	93	10	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	93	11	multifunctions	multifunction	NOUN
ejpam-4369	93	12	in	in	ADP
ejpam-4369	93	13	this	this	DET
ejpam-4369	93	14	section	section	NOUN
ejpam-4369	93	15	,	,	PUNCT
ejpam-4369	93	16	we	we	PRON
ejpam-4369	93	17	introduce	introduce	VERB
ejpam-4369	93	18	of	of	ADP
ejpam-4369	93	19	the	the	DET
ejpam-4369	93	20	concepts	concept	NOUN
ejpam-4369	93	21	of	of	ADP
ejpam-4369	93	22	upper	upper	ADJ
ejpam-4369	93	23	and	and	CCONJ
ejpam-4369	93	24	lower	lower	ADV
ejpam-4369	93	25	slightly	slightly	ADV
ejpam-4369	93	26	(	(	PUNCT
ejpam-4369	93	27	λ	λ	NOUN
ejpam-4369	93	28	,	,	PUNCT
ejpam-4369	93	29	sp)continuous	sp)continuous	ADJ
ejpam-4369	93	30	multifunctions	multifunction	NOUN
ejpam-4369	93	31	.	.	PUNCT
ejpam-4369	94	1	moreover	moreover	ADV
ejpam-4369	94	2	,	,	PUNCT
ejpam-4369	94	3	some	some	DET
ejpam-4369	94	4	characterizations	characterization	NOUN
ejpam-4369	94	5	of	of	ADP
ejpam-4369	94	6	upper	upper	ADJ
ejpam-4369	94	7	and	and	CCONJ
ejpam-4369	94	8	lower	lower	ADV
ejpam-4369	94	9	slightly	slightly	ADV
ejpam-4369	94	10	(	(	PUNCT
ejpam-4369	94	11	λ	λ	NOUN
ejpam-4369	94	12	,	,	PUNCT
ejpam-4369	94	13	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	94	14	multifunctions	multifunction	NOUN
ejpam-4369	94	15	are	be	AUX
ejpam-4369	94	16	discussed	discuss	VERB
ejpam-4369	94	17	.	.	PUNCT
ejpam-4369	95	1	definition	definition	NOUN
ejpam-4369	95	2	1	1	NUM
ejpam-4369	95	3	.	.	PUNCT
ejpam-4369	96	1	a	a	DET
ejpam-4369	96	2	multifunction	multifunction	NOUN
ejpam-4369	96	3	f	f	NOUN
ejpam-4369	96	4	:	:	PUNCT
ejpam-4369	96	5	(	(	PUNCT
ejpam-4369	96	6	x	x	X
ejpam-4369	96	7	,	,	PUNCT
ejpam-4369	96	8	τ	τ	X
ejpam-4369	96	9	)	)	PUNCT
ejpam-4369	96	10	→	→	SYM
ejpam-4369	96	11	(	(	PUNCT
ejpam-4369	96	12	y	y	PROPN
ejpam-4369	96	13	,	,	PUNCT
ejpam-4369	96	14	σ	σ	PROPN
ejpam-4369	96	15	)	)	PUNCT
ejpam-4369	96	16	is	be	AUX
ejpam-4369	96	17	said	say	VERB
ejpam-4369	96	18	to	to	PART
ejpam-4369	96	19	be	be	AUX
ejpam-4369	96	20	:	:	PUNCT
ejpam-4369	96	21	(	(	PUNCT
ejpam-4369	96	22	i	i	NOUN
ejpam-4369	96	23	)	)	PUNCT
ejpam-4369	96	24	upper	upper	ADJ
ejpam-4369	96	25	slightly	slightly	ADV
ejpam-4369	96	26	(	(	PUNCT
ejpam-4369	96	27	λ	λ	NOUN
ejpam-4369	96	28	,	,	PUNCT
ejpam-4369	96	29	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	96	30	if	if	SCONJ
ejpam-4369	96	31	,	,	PUNCT
ejpam-4369	96	32	for	for	ADP
ejpam-4369	96	33	each	each	DET
ejpam-4369	96	34	x	x	SYM
ejpam-4369	96	35	∈	∈	PROPN
ejpam-4369	96	36	x	x	X
ejpam-4369	96	37	and	and	CCONJ
ejpam-4369	96	38	each	each	DET
ejpam-4369	96	39	(	(	PUNCT
ejpam-4369	96	40	λ	λ	PROPN
ejpam-4369	96	41	,	,	PUNCT
ejpam-4369	96	42	sp)-clopen	sp)-clopen	NOUN
ejpam-4369	96	43	set	set	VERB
ejpam-4369	96	44	v	v	NUM
ejpam-4369	96	45	of	of	ADP
ejpam-4369	96	46	y	y	PRON
ejpam-4369	96	47	such	such	ADJ
ejpam-4369	96	48	that	that	SCONJ
ejpam-4369	96	49	f	f	PROPN
ejpam-4369	96	50	(	(	PUNCT
ejpam-4369	96	51	x	x	X
ejpam-4369	96	52	)	)	PUNCT
ejpam-4369	96	53	⊆	⊆	NUM
ejpam-4369	96	54	v	v	NOUN
ejpam-4369	96	55	,	,	PUNCT
ejpam-4369	96	56	there	there	PRON
ejpam-4369	96	57	exists	exist	VERB
ejpam-4369	96	58	a	a	DET
ejpam-4369	96	59	(	(	PUNCT
ejpam-4369	96	60	λ	λ	NOUN
ejpam-4369	96	61	,	,	PUNCT
ejpam-4369	96	62	sp)-open	sp)-open	NOUN
ejpam-4369	96	63	set	set	VERB
ejpam-4369	96	64	u	u	NOUN
ejpam-4369	96	65	of	of	ADP
ejpam-4369	96	66	x	x	PUNCT
ejpam-4369	96	67	containing	contain	VERB
ejpam-4369	96	68	x	x	PUNCT
ejpam-4369	97	1	such	such	ADJ
ejpam-4369	97	2	that	that	SCONJ
ejpam-4369	97	3	f	f	PROPN
ejpam-4369	97	4	(	(	PUNCT
ejpam-4369	97	5	u	u	NOUN
ejpam-4369	97	6	)	)	PUNCT
ejpam-4369	97	7	⊆	⊆	NUM
ejpam-4369	97	8	v	v	NOUN
ejpam-4369	97	9	;	;	PUNCT
ejpam-4369	97	10	(	(	PUNCT
ejpam-4369	97	11	ii	ii	NOUN
ejpam-4369	97	12	)	)	PUNCT
ejpam-4369	97	13	lower	lower	ADV
ejpam-4369	97	14	slightly	slightly	ADV
ejpam-4369	97	15	(	(	PUNCT
ejpam-4369	97	16	λ	λ	NOUN
ejpam-4369	97	17	,	,	PUNCT
ejpam-4369	97	18	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	97	19	if	if	SCONJ
ejpam-4369	97	20	,	,	PUNCT
ejpam-4369	97	21	for	for	ADP
ejpam-4369	97	22	each	each	DET
ejpam-4369	97	23	x	x	SYM
ejpam-4369	97	24	∈	∈	PROPN
ejpam-4369	97	25	x	x	X
ejpam-4369	97	26	and	and	CCONJ
ejpam-4369	97	27	each	each	DET
ejpam-4369	97	28	(	(	PUNCT
ejpam-4369	97	29	λ	λ	PROPN
ejpam-4369	97	30	,	,	PUNCT
ejpam-4369	97	31	sp)-clopen	sp)-clopen	NOUN
ejpam-4369	97	32	set	set	VERB
ejpam-4369	97	33	v	v	NUM
ejpam-4369	97	34	of	of	ADP
ejpam-4369	97	35	y	y	PRON
ejpam-4369	97	36	such	such	ADJ
ejpam-4369	97	37	that	that	SCONJ
ejpam-4369	97	38	f	f	PROPN
ejpam-4369	97	39	(	(	PUNCT
ejpam-4369	97	40	x	x	NOUN
ejpam-4369	97	41	)	)	PUNCT
ejpam-4369	97	42	∩	∩	NOUN
ejpam-4369	97	43	v	v	ADP
ejpam-4369	97	44	̸=	̸=	PROPN
ejpam-4369	97	45	∅	∅	NOUN
ejpam-4369	97	46	,	,	PUNCT
ejpam-4369	97	47	there	there	PRON
ejpam-4369	97	48	exists	exist	VERB
ejpam-4369	97	49	a	a	DET
ejpam-4369	97	50	(	(	PUNCT
ejpam-4369	97	51	λ	λ	NOUN
ejpam-4369	97	52	,	,	PUNCT
ejpam-4369	97	53	sp)-open	sp)-open	NOUN
ejpam-4369	97	54	set	set	VERB
ejpam-4369	97	55	u	u	NOUN
ejpam-4369	97	56	of	of	ADP
ejpam-4369	97	57	x	x	PUNCT
ejpam-4369	97	58	containing	contain	VERB
ejpam-4369	97	59	x	x	PUNCT
ejpam-4369	97	60	such	such	ADJ
ejpam-4369	97	61	that	that	SCONJ
ejpam-4369	97	62	f	f	PROPN
ejpam-4369	97	63	(	(	PUNCT
ejpam-4369	97	64	z	z	NOUN
ejpam-4369	97	65	)	)	PUNCT
ejpam-4369	97	66	∩	∩	NOUN
ejpam-4369	97	67	v	v	ADP
ejpam-4369	97	68	̸=	̸=	PROPN
ejpam-4369	97	69	∅	∅	NOUN
ejpam-4369	97	70	for	for	ADP
ejpam-4369	97	71	each	each	DET
ejpam-4369	97	72	z	z	NOUN
ejpam-4369	97	73	∈	∈	PROPN
ejpam-4369	97	74	u	u	PROPN
ejpam-4369	97	75	.	.	PUNCT
ejpam-4369	98	1	theorem	theorem	NOUN
ejpam-4369	98	2	1	1	NUM
ejpam-4369	98	3	.	.	X
ejpam-4369	98	4	for	for	ADP
ejpam-4369	98	5	a	a	DET
ejpam-4369	98	6	multifunction	multifunction	NOUN
ejpam-4369	99	1	f	f	NOUN
ejpam-4369	99	2	:	:	PUNCT
ejpam-4369	99	3	(	(	PUNCT
ejpam-4369	99	4	x	x	X
ejpam-4369	99	5	,	,	PUNCT
ejpam-4369	99	6	τ	τ	X
ejpam-4369	99	7	)	)	PUNCT
ejpam-4369	99	8	→	→	SYM
ejpam-4369	99	9	(	(	PUNCT
ejpam-4369	99	10	y	y	PROPN
ejpam-4369	99	11	,	,	PUNCT
ejpam-4369	99	12	σ	σ	PROPN
ejpam-4369	99	13	)	)	PUNCT
ejpam-4369	99	14	,	,	PUNCT
ejpam-4369	99	15	the	the	DET
ejpam-4369	99	16	following	follow	VERB
ejpam-4369	99	17	properties	property	NOUN
ejpam-4369	99	18	are	be	AUX
ejpam-4369	99	19	equivalent	equivalent	ADJ
ejpam-4369	99	20	:	:	PUNCT
ejpam-4369	99	21	c.	c.	PROPN
ejpam-4369	99	22	boonpok	boonpok	PROPN
ejpam-4369	99	23	,	,	PUNCT
ejpam-4369	99	24	j.	j.	PROPN
ejpam-4369	99	25	khampakdee	khampakdee	PROPN
ejpam-4369	99	26	/	/	PUNCT
ejpam-4369	99	27	eur	eur	PROPN
ejpam-4369	99	28	.	.	PUNCT
ejpam-4369	100	1	j.	j.	PROPN
ejpam-4369	100	2	pure	pure	PROPN
ejpam-4369	100	3	appl	appl	PROPN
ejpam-4369	100	4	.	.	PROPN
ejpam-4369	100	5	math	math	PROPN
ejpam-4369	100	6	,	,	PUNCT
ejpam-4369	100	7	15	15	NUM
ejpam-4369	100	8	(	(	PUNCT
ejpam-4369	100	9	3	3	NUM
ejpam-4369	100	10	)	)	PUNCT
ejpam-4369	100	11	(	(	PUNCT
ejpam-4369	100	12	2022	2022	NUM
ejpam-4369	100	13	)	)	PUNCT
ejpam-4369	100	14	,	,	PUNCT
ejpam-4369	100	15	1180	1180	NUM
ejpam-4369	100	16	-	-	SYM
ejpam-4369	100	17	1188	1188	NUM
ejpam-4369	100	18	1183	1183	NUM
ejpam-4369	100	19	(	(	PUNCT
ejpam-4369	100	20	1	1	X
ejpam-4369	100	21	)	)	PUNCT
ejpam-4369	100	22	f	f	PROPN
ejpam-4369	100	23	is	be	AUX
ejpam-4369	100	24	upper	upper	ADJ
ejpam-4369	100	25	slightly	slightly	ADV
ejpam-4369	100	26	(	(	PUNCT
ejpam-4369	100	27	λ	λ	NOUN
ejpam-4369	100	28	,	,	PUNCT
ejpam-4369	100	29	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	100	30	;	;	PUNCT
ejpam-4369	100	31	(	(	PUNCT
ejpam-4369	100	32	2	2	NUM
ejpam-4369	100	33	)	)	PUNCT
ejpam-4369	100	34	f+(v	f+(v	NOUN
ejpam-4369	100	35	)	)	PUNCT
ejpam-4369	101	1	is	be	AUX
ejpam-4369	101	2	(	(	PUNCT
ejpam-4369	101	3	λ	λ	INTJ
ejpam-4369	101	4	,	,	PUNCT
ejpam-4369	101	5	sp)-open	sp)-open	ADJ
ejpam-4369	101	6	in	in	ADP
ejpam-4369	101	7	x	x	PUNCT
ejpam-4369	101	8	for	for	ADP
ejpam-4369	101	9	every	every	DET
ejpam-4369	101	10	(	(	PUNCT
ejpam-4369	101	11	λ	λ	PROPN
ejpam-4369	101	12	,	,	PUNCT
ejpam-4369	101	13	sp)-clopen	sp)-clopen	NOUN
ejpam-4369	101	14	set	set	VERB
ejpam-4369	101	15	v	v	NOUN
ejpam-4369	101	16	of	of	ADP
ejpam-4369	101	17	y	y	PROPN
ejpam-4369	101	18	;	;	PUNCT
ejpam-4369	101	19	(	(	PUNCT
ejpam-4369	101	20	3	3	X
ejpam-4369	101	21	)	)	PUNCT
ejpam-4369	101	22	f−(v	f−(v	NOUN
ejpam-4369	101	23	)	)	PUNCT
ejpam-4369	101	24	is	be	AUX
ejpam-4369	101	25	(	(	PUNCT
ejpam-4369	101	26	λ	λ	X
ejpam-4369	101	27	,	,	PUNCT
ejpam-4369	101	28	sp)-closed	sp)-close	VERB
ejpam-4369	101	29	in	in	ADP
ejpam-4369	101	30	x	x	PUNCT
ejpam-4369	101	31	for	for	ADP
ejpam-4369	101	32	every	every	DET
ejpam-4369	101	33	(	(	PUNCT
ejpam-4369	101	34	λ	λ	PROPN
ejpam-4369	101	35	,	,	PUNCT
ejpam-4369	101	36	sp)-clopen	sp)-clopen	NOUN
ejpam-4369	101	37	set	set	VERB
ejpam-4369	101	38	v	v	NOUN
ejpam-4369	101	39	of	of	ADP
ejpam-4369	101	40	y	y	PROPN
ejpam-4369	101	41	.	.	PUNCT
ejpam-4369	102	1	proof	proof	NOUN
ejpam-4369	102	2	.	.	PUNCT
ejpam-4369	103	1	(	(	PUNCT
ejpam-4369	103	2	1	1	X
ejpam-4369	103	3	)	)	PUNCT
ejpam-4369	103	4	⇒	⇒	NOUN
ejpam-4369	103	5	(	(	PUNCT
ejpam-4369	103	6	2	2	NUM
ejpam-4369	103	7	):	):	PUNCT
ejpam-4369	103	8	let	let	VERB
ejpam-4369	103	9	v	v	PART
ejpam-4369	103	10	be	be	AUX
ejpam-4369	103	11	any	any	DET
ejpam-4369	103	12	(	(	PUNCT
ejpam-4369	103	13	λ	λ	PROPN
ejpam-4369	103	14	,	,	PUNCT
ejpam-4369	103	15	sp)-clopen	sp)-clopen	ADJ
ejpam-4369	103	16	set	set	NOUN
ejpam-4369	103	17	of	of	ADP
ejpam-4369	103	18	y	y	PROPN
ejpam-4369	103	19	and	and	CCONJ
ejpam-4369	103	20	let	let	VERB
ejpam-4369	103	21	x	x	X
ejpam-4369	103	22	∈	∈	PROPN
ejpam-4369	103	23	f+(v	f+(v	NOUN
ejpam-4369	103	24	)	)	PUNCT
ejpam-4369	103	25	.	.	PUNCT
ejpam-4369	104	1	then	then	ADV
ejpam-4369	104	2	,	,	PUNCT
ejpam-4369	104	3	f	f	PROPN
ejpam-4369	104	4	(	(	PUNCT
ejpam-4369	104	5	x	x	X
ejpam-4369	104	6	)	)	PUNCT
ejpam-4369	104	7	⊆	⊆	NUM
ejpam-4369	104	8	v	v	NOUN
ejpam-4369	104	9	.	.	PUNCT
ejpam-4369	105	1	since	since	SCONJ
ejpam-4369	105	2	f	f	PROPN
ejpam-4369	105	3	is	be	AUX
ejpam-4369	105	4	upper	upper	ADJ
ejpam-4369	105	5	slightly	slightly	ADV
ejpam-4369	105	6	(	(	PUNCT
ejpam-4369	105	7	λ	λ	NOUN
ejpam-4369	105	8	,	,	PUNCT
ejpam-4369	105	9	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	105	10	,	,	PUNCT
ejpam-4369	105	11	there	there	PRON
ejpam-4369	105	12	exists	exist	VERB
ejpam-4369	105	13	u	u	PROPN
ejpam-4369	105	14	∈	∈	PROPN
ejpam-4369	105	15	λspo(x	λspo(x	PROPN
ejpam-4369	105	16	,	,	PUNCT
ejpam-4369	105	17	τ	τ	X
ejpam-4369	105	18	)	)	PUNCT
ejpam-4369	105	19	containing	contain	VERB
ejpam-4369	105	20	x	x	PUNCT
ejpam-4369	105	21	such	such	ADJ
ejpam-4369	105	22	that	that	SCONJ
ejpam-4369	105	23	f	f	PROPN
ejpam-4369	105	24	(	(	PUNCT
ejpam-4369	105	25	u	u	NOUN
ejpam-4369	105	26	)	)	PUNCT
ejpam-4369	105	27	⊆	⊆	NUM
ejpam-4369	105	28	v	v	NOUN
ejpam-4369	105	29	.	.	PUNCT
ejpam-4369	106	1	thus	thus	ADV
ejpam-4369	106	2	,	,	PUNCT
ejpam-4369	106	3	x	x	PUNCT
ejpam-4369	106	4	∈	∈	PROPN
ejpam-4369	106	5	u	u	NOUN
ejpam-4369	106	6	⊆	⊆	NUM
ejpam-4369	106	7	f+(v	f+(v	NOUN
ejpam-4369	106	8	)	)	PUNCT
ejpam-4369	106	9	and	and	CCONJ
ejpam-4369	106	10	hence	hence	ADV
ejpam-4369	106	11	x	x	X
ejpam-4369	106	12	∈	∈	PROPN
ejpam-4369	107	1	[	[	X
ejpam-4369	107	2	f+(v	f+(v	NOUN
ejpam-4369	107	3	)	)	PUNCT
ejpam-4369	107	4	]	]	PUNCT
ejpam-4369	107	5	(	(	PUNCT
ejpam-4369	107	6	λ	λ	NOUN
ejpam-4369	107	7	,	,	PUNCT
ejpam-4369	107	8	sp	sp	NOUN
ejpam-4369	107	9	)	)	PUNCT
ejpam-4369	107	10	.	.	PUNCT
ejpam-4369	108	1	therefore	therefore	ADV
ejpam-4369	108	2	,	,	PUNCT
ejpam-4369	108	3	f+(v	f+(v	PROPN
ejpam-4369	108	4	)	)	PUNCT
ejpam-4369	109	1	⊆	⊆	NUM
ejpam-4369	109	2	[	[	X
ejpam-4369	109	3	f+(v	f+(v	NOUN
ejpam-4369	109	4	)	)	PUNCT
ejpam-4369	109	5	]	]	PUNCT
ejpam-4369	109	6	(	(	PUNCT
ejpam-4369	109	7	λ	λ	NOUN
ejpam-4369	109	8	,	,	PUNCT
ejpam-4369	109	9	sp	sp	NOUN
ejpam-4369	109	10	)	)	PUNCT
ejpam-4369	109	11	.	.	PUNCT
ejpam-4369	110	1	this	this	PRON
ejpam-4369	110	2	shows	show	VERB
ejpam-4369	110	3	that	that	SCONJ
ejpam-4369	110	4	f	f	PROPN
ejpam-4369	110	5	+	+	ADJ
ejpam-4369	110	6	(	(	PUNCT
ejpam-4369	110	7	v	v	NOUN
ejpam-4369	110	8	)	)	PUNCT
ejpam-4369	110	9	is	be	AUX
ejpam-4369	110	10	(	(	PUNCT
ejpam-4369	110	11	λ	λ	INTJ
ejpam-4369	110	12	,	,	PUNCT
ejpam-4369	110	13	sp)-open	sp)-open	ADJ
ejpam-4369	110	14	in	in	ADP
ejpam-4369	110	15	x.	x.	NOUN
ejpam-4369	110	16	(	(	PUNCT
ejpam-4369	110	17	2	2	NUM
ejpam-4369	110	18	)	)	PUNCT
ejpam-4369	110	19	⇒	⇒	NOUN
ejpam-4369	110	20	(	(	PUNCT
ejpam-4369	110	21	3	3	NUM
ejpam-4369	110	22	)	)	PUNCT
ejpam-4369	110	23	and	and	CCONJ
ejpam-4369	110	24	(	(	PUNCT
ejpam-4369	110	25	3	3	X
ejpam-4369	110	26	)	)	PUNCT
ejpam-4369	110	27	⇒	⇒	NOUN
ejpam-4369	110	28	(	(	PUNCT
ejpam-4369	110	29	2	2	NUM
ejpam-4369	110	30	):	):	PUNCT
ejpam-4369	110	31	the	the	DET
ejpam-4369	110	32	proofs	proof	NOUN
ejpam-4369	110	33	are	be	AUX
ejpam-4369	110	34	obvious	obvious	ADJ
ejpam-4369	110	35	.	.	PUNCT
ejpam-4369	111	1	(	(	PUNCT
ejpam-4369	111	2	2	2	X
ejpam-4369	111	3	)	)	PUNCT
ejpam-4369	111	4	⇒	⇒	NOUN
ejpam-4369	111	5	(	(	PUNCT
ejpam-4369	111	6	1	1	NUM
ejpam-4369	111	7	):	):	PUNCT
ejpam-4369	111	8	let	let	VERB
ejpam-4369	111	9	x	x	PUNCT
ejpam-4369	111	10	∈	∈	PROPN
ejpam-4369	111	11	x	x	PUNCT
ejpam-4369	111	12	and	and	CCONJ
ejpam-4369	111	13	let	let	VERB
ejpam-4369	111	14	v	v	PART
ejpam-4369	111	15	be	be	AUX
ejpam-4369	111	16	any	any	DET
ejpam-4369	111	17	(	(	PUNCT
ejpam-4369	111	18	λ	λ	PROPN
ejpam-4369	111	19	,	,	PUNCT
ejpam-4369	111	20	sp)-clopen	sp)-clopen	ADJ
ejpam-4369	111	21	set	set	NOUN
ejpam-4369	111	22	of	of	ADP
ejpam-4369	111	23	y	y	PROPN
ejpam-4369	111	24	containing	contain	VERB
ejpam-4369	111	25	f	f	PROPN
ejpam-4369	111	26	(	(	PUNCT
ejpam-4369	111	27	x	x	NOUN
ejpam-4369	111	28	)	)	PUNCT
ejpam-4369	111	29	.	.	PUNCT
ejpam-4369	112	1	then	then	ADV
ejpam-4369	112	2	,	,	PUNCT
ejpam-4369	112	3	x	x	X
ejpam-4369	112	4	∈	∈	PROPN
ejpam-4369	112	5	f+(v	f+(v	NOUN
ejpam-4369	112	6	)	)	PUNCT
ejpam-4369	112	7	,	,	PUNCT
ejpam-4369	112	8	by	by	ADP
ejpam-4369	112	9	(	(	PUNCT
ejpam-4369	112	10	2	2	NUM
ejpam-4369	112	11	)	)	PUNCT
ejpam-4369	112	12	,	,	PUNCT
ejpam-4369	112	13	f+(v	f+(v	PROPN
ejpam-4369	112	14	)	)	PUNCT
ejpam-4369	112	15	is	be	AUX
ejpam-4369	112	16	(	(	PUNCT
ejpam-4369	112	17	λ	λ	INTJ
ejpam-4369	112	18	,	,	PUNCT
ejpam-4369	112	19	sp)-open	sp)-open	ADJ
ejpam-4369	112	20	in	in	ADP
ejpam-4369	112	21	x.	x.	NOUN
ejpam-4369	112	22	put	put	VERB
ejpam-4369	112	23	u	u	NOUN
ejpam-4369	112	24	=	=	NOUN
ejpam-4369	112	25	f+(v	f+(v	PROPN
ejpam-4369	112	26	)	)	PUNCT
ejpam-4369	112	27	,	,	PUNCT
ejpam-4369	112	28	then	then	ADV
ejpam-4369	112	29	u	u	NOUN
ejpam-4369	112	30	is	be	AUX
ejpam-4369	112	31	a	a	DET
ejpam-4369	112	32	(	(	PUNCT
ejpam-4369	112	33	λ	λ	NOUN
ejpam-4369	112	34	,	,	PUNCT
ejpam-4369	112	35	sp)-open	sp)-open	ADJ
ejpam-4369	112	36	set	set	NOUN
ejpam-4369	112	37	of	of	ADP
ejpam-4369	112	38	x	x	PUNCT
ejpam-4369	112	39	containing	contain	VERB
ejpam-4369	112	40	x	x	PUNCT
ejpam-4369	112	41	such	such	ADJ
ejpam-4369	112	42	that	that	SCONJ
ejpam-4369	112	43	f	f	PROPN
ejpam-4369	112	44	(	(	PUNCT
ejpam-4369	112	45	u	u	NOUN
ejpam-4369	112	46	)	)	PUNCT
ejpam-4369	112	47	⊆	⊆	NUM
ejpam-4369	112	48	v	v	NOUN
ejpam-4369	112	49	.	.	PUNCT
ejpam-4369	113	1	thus	thus	ADV
ejpam-4369	113	2	,	,	PUNCT
ejpam-4369	113	3	f	f	PROPN
ejpam-4369	113	4	is	be	AUX
ejpam-4369	113	5	upper	upper	ADJ
ejpam-4369	113	6	slightly	slightly	ADV
ejpam-4369	113	7	(	(	PUNCT
ejpam-4369	113	8	λ	λ	NOUN
ejpam-4369	113	9	,	,	PUNCT
ejpam-4369	113	10	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	113	11	.	.	PUNCT
ejpam-4369	114	1	theorem	theorem	NOUN
ejpam-4369	114	2	2	2	NUM
ejpam-4369	114	3	.	.	X
ejpam-4369	114	4	for	for	ADP
ejpam-4369	114	5	a	a	DET
ejpam-4369	114	6	multifunction	multifunction	NOUN
ejpam-4369	115	1	f	f	NOUN
ejpam-4369	115	2	:	:	PUNCT
ejpam-4369	115	3	(	(	PUNCT
ejpam-4369	115	4	x	x	X
ejpam-4369	115	5	,	,	PUNCT
ejpam-4369	115	6	τ	τ	X
ejpam-4369	115	7	)	)	PUNCT
ejpam-4369	115	8	→	→	SYM
ejpam-4369	115	9	(	(	PUNCT
ejpam-4369	115	10	y	y	PROPN
ejpam-4369	115	11	,	,	PUNCT
ejpam-4369	115	12	σ	σ	PROPN
ejpam-4369	115	13	)	)	PUNCT
ejpam-4369	115	14	,	,	PUNCT
ejpam-4369	115	15	the	the	DET
ejpam-4369	115	16	following	follow	VERB
ejpam-4369	115	17	properties	property	NOUN
ejpam-4369	115	18	are	be	AUX
ejpam-4369	115	19	equivalent	equivalent	ADJ
ejpam-4369	115	20	:	:	PUNCT
ejpam-4369	115	21	(	(	PUNCT
ejpam-4369	115	22	1	1	X
ejpam-4369	115	23	)	)	PUNCT
ejpam-4369	115	24	f	f	PROPN
ejpam-4369	115	25	is	be	AUX
ejpam-4369	115	26	lower	lower	ADV
ejpam-4369	115	27	slightly	slightly	ADV
ejpam-4369	115	28	(	(	PUNCT
ejpam-4369	115	29	λ	λ	NOUN
ejpam-4369	115	30	,	,	PUNCT
ejpam-4369	115	31	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	115	32	;	;	PUNCT
ejpam-4369	115	33	(	(	PUNCT
ejpam-4369	115	34	2	2	X
ejpam-4369	115	35	)	)	PUNCT
ejpam-4369	115	36	f−(v	f−(v	NOUN
ejpam-4369	115	37	)	)	PUNCT
ejpam-4369	115	38	is	be	AUX
ejpam-4369	115	39	(	(	PUNCT
ejpam-4369	115	40	λ	λ	INTJ
ejpam-4369	115	41	,	,	PUNCT
ejpam-4369	115	42	sp)-open	sp)-open	ADJ
ejpam-4369	115	43	in	in	ADP
ejpam-4369	115	44	x	x	PUNCT
ejpam-4369	115	45	for	for	ADP
ejpam-4369	115	46	every	every	DET
ejpam-4369	115	47	(	(	PUNCT
ejpam-4369	115	48	λ	λ	PROPN
ejpam-4369	115	49	,	,	PUNCT
ejpam-4369	115	50	sp)-clopen	sp)-clopen	NOUN
ejpam-4369	115	51	set	set	VERB
ejpam-4369	115	52	v	v	NOUN
ejpam-4369	115	53	of	of	ADP
ejpam-4369	115	54	y	y	PROPN
ejpam-4369	115	55	;	;	PUNCT
ejpam-4369	115	56	(	(	PUNCT
ejpam-4369	115	57	3	3	X
ejpam-4369	115	58	)	)	PUNCT
ejpam-4369	116	1	f+(v	f+(v	NOUN
ejpam-4369	116	2	)	)	PUNCT
ejpam-4369	117	1	is	be	AUX
ejpam-4369	117	2	(	(	PUNCT
ejpam-4369	117	3	λ	λ	X
ejpam-4369	117	4	,	,	PUNCT
ejpam-4369	117	5	sp)-closed	sp)-close	VERB
ejpam-4369	117	6	in	in	ADP
ejpam-4369	117	7	x	x	PUNCT
ejpam-4369	117	8	for	for	ADP
ejpam-4369	117	9	every	every	DET
ejpam-4369	117	10	(	(	PUNCT
ejpam-4369	117	11	λ	λ	PROPN
ejpam-4369	117	12	,	,	PUNCT
ejpam-4369	117	13	sp)-clopen	sp)-clopen	NOUN
ejpam-4369	117	14	set	set	VERB
ejpam-4369	117	15	v	v	NOUN
ejpam-4369	117	16	of	of	ADP
ejpam-4369	117	17	y	y	PROPN
ejpam-4369	117	18	.	.	PUNCT
ejpam-4369	118	1	proof	proof	NOUN
ejpam-4369	118	2	.	.	PUNCT
ejpam-4369	119	1	the	the	DET
ejpam-4369	119	2	proof	proof	NOUN
ejpam-4369	119	3	is	be	AUX
ejpam-4369	119	4	similar	similar	ADJ
ejpam-4369	119	5	to	to	ADP
ejpam-4369	119	6	that	that	PRON
ejpam-4369	119	7	of	of	ADP
ejpam-4369	119	8	theorem	theorem	NOUN
ejpam-4369	119	9	1	1	NUM
ejpam-4369	119	10	.	.	PUNCT
ejpam-4369	119	11	definition	definition	NOUN
ejpam-4369	119	12	2	2	NUM
ejpam-4369	119	13	.	.	PUNCT
ejpam-4369	120	1	a	a	DET
ejpam-4369	120	2	function	function	NOUN
ejpam-4369	120	3	f	f	NOUN
ejpam-4369	120	4	:	:	PUNCT
ejpam-4369	120	5	(	(	PUNCT
ejpam-4369	120	6	x	x	X
ejpam-4369	120	7	,	,	PUNCT
ejpam-4369	120	8	τ	τ	X
ejpam-4369	120	9	)	)	PUNCT
ejpam-4369	120	10	→	→	SYM
ejpam-4369	120	11	(	(	PUNCT
ejpam-4369	120	12	y	y	PROPN
ejpam-4369	120	13	,	,	PUNCT
ejpam-4369	120	14	σ	σ	PROPN
ejpam-4369	120	15	)	)	PUNCT
ejpam-4369	120	16	is	be	AUX
ejpam-4369	120	17	called	call	VERB
ejpam-4369	120	18	slightly	slightly	ADV
ejpam-4369	120	19	(	(	PUNCT
ejpam-4369	120	20	λ	λ	NOUN
ejpam-4369	120	21	,	,	PUNCT
ejpam-4369	120	22	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	120	23	if	if	SCONJ
ejpam-4369	120	24	,	,	PUNCT
ejpam-4369	120	25	for	for	ADP
ejpam-4369	120	26	each	each	DET
ejpam-4369	120	27	x	x	SYM
ejpam-4369	120	28	∈	∈	PROPN
ejpam-4369	120	29	x	x	X
ejpam-4369	120	30	and	and	CCONJ
ejpam-4369	120	31	each	each	DET
ejpam-4369	120	32	(	(	PUNCT
ejpam-4369	120	33	λ	λ	PROPN
ejpam-4369	120	34	,	,	PUNCT
ejpam-4369	120	35	sp)-clopen	sp)-clopen	NOUN
ejpam-4369	120	36	set	set	VERB
ejpam-4369	120	37	v	v	NUM
ejpam-4369	120	38	of	of	ADP
ejpam-4369	120	39	y	y	NOUN
ejpam-4369	120	40	containing	contain	VERB
ejpam-4369	120	41	f(x	f(x	PROPN
ejpam-4369	120	42	)	)	PUNCT
ejpam-4369	120	43	,	,	PUNCT
ejpam-4369	120	44	there	there	PRON
ejpam-4369	120	45	exists	exist	VERB
ejpam-4369	120	46	a	a	DET
ejpam-4369	120	47	(	(	PUNCT
ejpam-4369	120	48	λ	λ	NOUN
ejpam-4369	120	49	,	,	PUNCT
ejpam-4369	120	50	sp)-open	sp)-open	NOUN
ejpam-4369	120	51	set	set	VERB
ejpam-4369	120	52	u	u	NOUN
ejpam-4369	120	53	of	of	ADP
ejpam-4369	120	54	x	x	PUNCT
ejpam-4369	120	55	containing	contain	VERB
ejpam-4369	120	56	x	x	PUNCT
ejpam-4369	120	57	such	such	ADJ
ejpam-4369	120	58	that	that	DET
ejpam-4369	120	59	f(u	f(u	PROPN
ejpam-4369	120	60	)	)	PUNCT
ejpam-4369	120	61	⊆	⊆	NUM
ejpam-4369	120	62	v	v	NOUN
ejpam-4369	120	63	.	.	PUNCT
ejpam-4369	121	1	corollary	corollary	ADJ
ejpam-4369	121	2	1	1	NUM
ejpam-4369	121	3	.	.	PUNCT
ejpam-4369	122	1	for	for	ADP
ejpam-4369	122	2	a	a	DET
ejpam-4369	122	3	function	function	NOUN
ejpam-4369	122	4	f	f	NOUN
ejpam-4369	122	5	:	:	PUNCT
ejpam-4369	122	6	(	(	PUNCT
ejpam-4369	122	7	x	x	X
ejpam-4369	122	8	,	,	PUNCT
ejpam-4369	122	9	τ	τ	X
ejpam-4369	122	10	)	)	PUNCT
ejpam-4369	122	11	→	→	SYM
ejpam-4369	122	12	(	(	PUNCT
ejpam-4369	122	13	y	y	PROPN
ejpam-4369	122	14	,	,	PUNCT
ejpam-4369	122	15	σ	σ	PROPN
ejpam-4369	122	16	)	)	PUNCT
ejpam-4369	122	17	,	,	PUNCT
ejpam-4369	122	18	the	the	DET
ejpam-4369	122	19	following	follow	VERB
ejpam-4369	122	20	properties	property	NOUN
ejpam-4369	122	21	are	be	AUX
ejpam-4369	122	22	equivalent	equivalent	ADJ
ejpam-4369	122	23	:	:	PUNCT
ejpam-4369	122	24	(	(	PUNCT
ejpam-4369	122	25	1	1	X
ejpam-4369	122	26	)	)	PUNCT
ejpam-4369	122	27	f	f	PROPN
ejpam-4369	122	28	is	be	AUX
ejpam-4369	122	29	slightly	slightly	ADV
ejpam-4369	122	30	(	(	PUNCT
ejpam-4369	122	31	λ	λ	NOUN
ejpam-4369	122	32	,	,	PUNCT
ejpam-4369	122	33	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	122	34	;	;	PUNCT
ejpam-4369	122	35	(	(	PUNCT
ejpam-4369	122	36	2	2	X
ejpam-4369	122	37	)	)	PUNCT
ejpam-4369	122	38	f−1(v	f−1(v	NOUN
ejpam-4369	122	39	)	)	PUNCT
ejpam-4369	122	40	is	be	AUX
ejpam-4369	122	41	(	(	PUNCT
ejpam-4369	122	42	λ	λ	INTJ
ejpam-4369	122	43	,	,	PUNCT
ejpam-4369	122	44	sp)-open	sp)-open	ADJ
ejpam-4369	122	45	in	in	ADP
ejpam-4369	122	46	x	x	PUNCT
ejpam-4369	122	47	for	for	ADP
ejpam-4369	122	48	every	every	DET
ejpam-4369	122	49	(	(	PUNCT
ejpam-4369	122	50	λ	λ	PROPN
ejpam-4369	122	51	,	,	PUNCT
ejpam-4369	122	52	sp)-clopen	sp)-clopen	NOUN
ejpam-4369	122	53	set	set	VERB
ejpam-4369	122	54	v	v	NOUN
ejpam-4369	122	55	of	of	ADP
ejpam-4369	122	56	y	y	PROPN
ejpam-4369	122	57	;	;	PUNCT
ejpam-4369	122	58	(	(	PUNCT
ejpam-4369	122	59	3	3	X
ejpam-4369	122	60	)	)	PUNCT
ejpam-4369	122	61	f−1(v	f−1(v	NOUN
ejpam-4369	122	62	)	)	PUNCT
ejpam-4369	123	1	is	be	AUX
ejpam-4369	123	2	(	(	PUNCT
ejpam-4369	123	3	λ	λ	X
ejpam-4369	123	4	,	,	PUNCT
ejpam-4369	123	5	sp)-closed	sp)-close	VERB
ejpam-4369	123	6	in	in	ADP
ejpam-4369	123	7	x	x	PUNCT
ejpam-4369	123	8	for	for	ADP
ejpam-4369	123	9	every	every	DET
ejpam-4369	123	10	(	(	PUNCT
ejpam-4369	123	11	λ	λ	PROPN
ejpam-4369	123	12	,	,	PUNCT
ejpam-4369	123	13	sp)-clopen	sp)-clopen	NOUN
ejpam-4369	123	14	set	set	VERB
ejpam-4369	123	15	v	v	NOUN
ejpam-4369	123	16	of	of	ADP
ejpam-4369	123	17	y	y	PROPN
ejpam-4369	123	18	.	.	PUNCT
ejpam-4369	124	1	definition	definition	NOUN
ejpam-4369	124	2	3	3	NUM
ejpam-4369	124	3	.	.	PUNCT
ejpam-4369	125	1	let	let	VERB
ejpam-4369	125	2	a	a	DET
ejpam-4369	125	3	be	be	AUX
ejpam-4369	125	4	a	a	DET
ejpam-4369	125	5	subset	subset	NOUN
ejpam-4369	125	6	of	of	ADP
ejpam-4369	125	7	a	a	DET
ejpam-4369	125	8	topological	topological	ADJ
ejpam-4369	125	9	space	space	NOUN
ejpam-4369	125	10	(	(	PUNCT
ejpam-4369	125	11	x	x	X
ejpam-4369	125	12	,	,	PUNCT
ejpam-4369	125	13	τ	τ	PROPN
ejpam-4369	125	14	)	)	PUNCT
ejpam-4369	125	15	.	.	PUNCT
ejpam-4369	126	1	the	the	DET
ejpam-4369	126	2	(	(	PUNCT
ejpam-4369	126	3	λ	λ	NOUN
ejpam-4369	126	4	,	,	PUNCT
ejpam-4369	126	5	sp)-frontier	sp)-fronti	ADJ
ejpam-4369	126	6	of	of	ADP
ejpam-4369	126	7	a	a	PRON
ejpam-4369	126	8	,	,	PUNCT
ejpam-4369	126	9	denoted	denote	VERB
ejpam-4369	126	10	by	by	ADP
ejpam-4369	126	11	(	(	PUNCT
ejpam-4369	126	12	λ	λ	X
ejpam-4369	126	13	,	,	PUNCT
ejpam-4369	126	14	sp)-fr(a	sp)-fr(a	NOUN
ejpam-4369	126	15	)	)	PUNCT
ejpam-4369	126	16	,	,	PUNCT
ejpam-4369	126	17	(	(	PUNCT
ejpam-4369	126	18	λ	λ	X
ejpam-4369	126	19	,	,	PUNCT
ejpam-4369	126	20	sp)-fr(a	sp)-fr(a	NOUN
ejpam-4369	126	21	)	)	PUNCT
ejpam-4369	126	22	=	=	PUNCT
ejpam-4369	126	23	a(λ	a(λ	ADV
ejpam-4369	126	24	,	,	PUNCT
ejpam-4369	126	25	sp	sp	NOUN
ejpam-4369	126	26	)	)	PUNCT
ejpam-4369	126	27	∩	∩	NOUN
ejpam-4369	126	28	[	[	X
ejpam-4369	126	29	x	x	SYM
ejpam-4369	126	30	−a](λ	−a](λ	PROPN
ejpam-4369	126	31	,	,	PUNCT
ejpam-4369	126	32	sp	sp	NOUN
ejpam-4369	126	33	)	)	PUNCT
ejpam-4369	126	34	=	=	PUNCT
ejpam-4369	126	35	a(λ	a(λ	ADV
ejpam-4369	126	36	,	,	PUNCT
ejpam-4369	126	37	sp	sp	NOUN
ejpam-4369	126	38	)	)	PUNCT
ejpam-4369	126	39	−a(λ	−a(λ	NOUN
ejpam-4369	126	40	,	,	PUNCT
ejpam-4369	126	41	sp	sp	NOUN
ejpam-4369	126	42	)	)	PUNCT
ejpam-4369	126	43	.	.	PUNCT
ejpam-4369	127	1	theorem	theorem	NOUN
ejpam-4369	127	2	3	3	NUM
ejpam-4369	127	3	.	.	PUNCT
ejpam-4369	128	1	the	the	DET
ejpam-4369	128	2	set	set	NOUN
ejpam-4369	128	3	of	of	ADP
ejpam-4369	128	4	all	all	DET
ejpam-4369	128	5	points	point	NOUN
ejpam-4369	128	6	x	x	X
ejpam-4369	128	7	∈	∈	NOUN
ejpam-4369	128	8	x	x	PUNCT
ejpam-4369	128	9	at	at	ADP
ejpam-4369	128	10	which	which	PRON
ejpam-4369	128	11	a	a	DET
ejpam-4369	128	12	multifunction	multifunction	NOUN
ejpam-4369	128	13	f	f	NOUN
ejpam-4369	128	14	:	:	PUNCT
ejpam-4369	128	15	(	(	PUNCT
ejpam-4369	128	16	x	x	X
ejpam-4369	128	17	,	,	PUNCT
ejpam-4369	128	18	τ	τ	X
ejpam-4369	128	19	)	)	PUNCT
ejpam-4369	128	20	→	→	SYM
ejpam-4369	128	21	(	(	PUNCT
ejpam-4369	128	22	y	y	PROPN
ejpam-4369	128	23	,	,	PUNCT
ejpam-4369	128	24	σ	σ	PROPN
ejpam-4369	128	25	)	)	PUNCT
ejpam-4369	128	26	is	be	AUX
ejpam-4369	128	27	not	not	PART
ejpam-4369	128	28	upper	upper	ADJ
ejpam-4369	128	29	slightly	slightly	ADV
ejpam-4369	128	30	(	(	PUNCT
ejpam-4369	128	31	λ	λ	NOUN
ejpam-4369	128	32	,	,	PUNCT
ejpam-4369	128	33	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	128	34	is	be	AUX
ejpam-4369	128	35	identical	identical	ADJ
ejpam-4369	128	36	with	with	ADP
ejpam-4369	128	37	the	the	DET
ejpam-4369	128	38	union	union	NOUN
ejpam-4369	128	39	of	of	ADP
ejpam-4369	128	40	(	(	PUNCT
ejpam-4369	128	41	λ	λ	PROPN
ejpam-4369	128	42	,	,	PUNCT
ejpam-4369	128	43	sp)-frontiers	sp)-frontier	NOUN
ejpam-4369	128	44	of	of	ADP
ejpam-4369	128	45	the	the	DET
ejpam-4369	128	46	upper	upper	ADJ
ejpam-4369	128	47	inverse	inverse	NOUN
ejpam-4369	128	48	images	image	NOUN
ejpam-4369	128	49	of	of	ADP
ejpam-4369	128	50	(	(	PUNCT
ejpam-4369	128	51	λ	λ	PROPN
ejpam-4369	128	52	,	,	PUNCT
ejpam-4369	128	53	sp)-clopen	sp)-clopen	ADJ
ejpam-4369	128	54	sets	set	NOUN
ejpam-4369	128	55	containing	contain	VERB
ejpam-4369	128	56	f	f	X
ejpam-4369	128	57	(	(	PUNCT
ejpam-4369	128	58	x	x	NOUN
ejpam-4369	128	59	)	)	PUNCT
ejpam-4369	128	60	.	.	PUNCT
ejpam-4369	129	1	c.	c.	PROPN
ejpam-4369	129	2	boonpok	boonpok	PROPN
ejpam-4369	129	3	,	,	PUNCT
ejpam-4369	129	4	j.	j.	PROPN
ejpam-4369	129	5	khampakdee	khampakdee	PROPN
ejpam-4369	129	6	/	/	PUNCT
ejpam-4369	129	7	eur	eur	PROPN
ejpam-4369	129	8	.	.	PUNCT
ejpam-4369	130	1	j.	j.	PROPN
ejpam-4369	130	2	pure	pure	PROPN
ejpam-4369	130	3	appl	appl	PROPN
ejpam-4369	130	4	.	.	PROPN
ejpam-4369	130	5	math	math	PROPN
ejpam-4369	130	6	,	,	PUNCT
ejpam-4369	130	7	15	15	NUM
ejpam-4369	130	8	(	(	PUNCT
ejpam-4369	130	9	3	3	NUM
ejpam-4369	130	10	)	)	PUNCT
ejpam-4369	130	11	(	(	PUNCT
ejpam-4369	130	12	2022	2022	NUM
ejpam-4369	130	13	)	)	PUNCT
ejpam-4369	130	14	,	,	PUNCT
ejpam-4369	130	15	1180	1180	NUM
ejpam-4369	130	16	-	-	SYM
ejpam-4369	130	17	1188	1188	NUM
ejpam-4369	130	18	1184	1184	NUM
ejpam-4369	130	19	proof	proof	NOUN
ejpam-4369	130	20	.	.	PUNCT
ejpam-4369	130	21	suppose	suppose	VERB
ejpam-4369	130	22	that	that	SCONJ
ejpam-4369	130	23	f	f	PROPN
ejpam-4369	130	24	is	be	AUX
ejpam-4369	130	25	not	not	PART
ejpam-4369	130	26	upper	upper	ADJ
ejpam-4369	130	27	slightly	slightly	ADV
ejpam-4369	130	28	(	(	PUNCT
ejpam-4369	130	29	λ	λ	NOUN
ejpam-4369	130	30	,	,	PUNCT
ejpam-4369	130	31	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	130	32	at	at	ADP
ejpam-4369	130	33	x	x	PROPN
ejpam-4369	130	34	∈	∈	PROPN
ejpam-4369	130	35	x.	x.	NOUN
ejpam-4369	130	36	then	then	ADV
ejpam-4369	130	37	,	,	PUNCT
ejpam-4369	130	38	there	there	PRON
ejpam-4369	130	39	exists	exist	VERB
ejpam-4369	130	40	a	a	DET
ejpam-4369	130	41	(	(	PUNCT
ejpam-4369	130	42	λ	λ	NOUN
ejpam-4369	130	43	,	,	PUNCT
ejpam-4369	130	44	sp)-clopen	sp)-clopen	NOUN
ejpam-4369	130	45	set	set	VERB
ejpam-4369	130	46	v	v	NUM
ejpam-4369	130	47	of	of	ADP
ejpam-4369	130	48	y	y	PROPN
ejpam-4369	130	49	containing	contain	VERB
ejpam-4369	130	50	f	f	PROPN
ejpam-4369	130	51	(	(	PUNCT
ejpam-4369	130	52	x	x	X
ejpam-4369	130	53	)	)	PUNCT
ejpam-4369	130	54	such	such	ADJ
ejpam-4369	130	55	that	that	SCONJ
ejpam-4369	130	56	u	u	PROPN
ejpam-4369	130	57	∩	∩	NOUN
ejpam-4369	130	58	(	(	PUNCT
ejpam-4369	130	59	x	x	NOUN
ejpam-4369	130	60	−	−	PROPN
ejpam-4369	130	61	f+(v	f+(v	NOUN
ejpam-4369	130	62	)	)	PUNCT
ejpam-4369	130	63	)	)	PUNCT
ejpam-4369	131	1	̸=	̸=	NOUN
ejpam-4369	131	2	∅	∅	NOUN
ejpam-4369	131	3	for	for	ADP
ejpam-4369	131	4	every	every	DET
ejpam-4369	131	5	u	u	PROPN
ejpam-4369	131	6	∈	∈	PROPN
ejpam-4369	131	7	λspo(x	λspo(x	PROPN
ejpam-4369	131	8	,	,	PUNCT
ejpam-4369	131	9	τ	τ	X
ejpam-4369	131	10	)	)	PUNCT
ejpam-4369	131	11	containing	contain	VERB
ejpam-4369	131	12	x.	x.	NOUN
ejpam-4369	131	13	thus	thus	ADV
ejpam-4369	131	14	,	,	PUNCT
ejpam-4369	131	15	x	x	PUNCT
ejpam-4369	131	16	∈	∈	PROPN
ejpam-4369	132	1	[	[	X
ejpam-4369	132	2	x	x	X
ejpam-4369	132	3	−	−	PROPN
ejpam-4369	132	4	f+(v	f+(v	NOUN
ejpam-4369	132	5	)	)	PUNCT
ejpam-4369	132	6	]	]	PUNCT
ejpam-4369	132	7	(	(	PUNCT
ejpam-4369	132	8	λ	λ	NOUN
ejpam-4369	132	9	,	,	PUNCT
ejpam-4369	132	10	sp	sp	NOUN
ejpam-4369	132	11	)	)	PUNCT
ejpam-4369	132	12	.	.	PUNCT
ejpam-4369	133	1	on	on	ADP
ejpam-4369	133	2	the	the	DET
ejpam-4369	133	3	other	other	ADJ
ejpam-4369	133	4	hand	hand	NOUN
ejpam-4369	133	5	,	,	PUNCT
ejpam-4369	133	6	we	we	PRON
ejpam-4369	133	7	have	have	VERB
ejpam-4369	133	8	x	x	X
ejpam-4369	133	9	∈	∈	PROPN
ejpam-4369	133	10	f+(v	f+(v	NOUN
ejpam-4369	133	11	)	)	PUNCT
ejpam-4369	134	1	⊆	⊆	NUM
ejpam-4369	134	2	[	[	X
ejpam-4369	134	3	f+(v	f+(v	NOUN
ejpam-4369	134	4	)	)	PUNCT
ejpam-4369	134	5	]	]	PUNCT
ejpam-4369	134	6	(	(	PUNCT
ejpam-4369	134	7	λ	λ	NOUN
ejpam-4369	134	8	,	,	PUNCT
ejpam-4369	134	9	sp	sp	NOUN
ejpam-4369	134	10	)	)	PUNCT
ejpam-4369	134	11	and	and	CCONJ
ejpam-4369	134	12	hence	hence	ADV
ejpam-4369	134	13	x	x	X
ejpam-4369	134	14	∈	∈	PROPN
ejpam-4369	134	15	(	(	PUNCT
ejpam-4369	134	16	λ	λ	NOUN
ejpam-4369	134	17	,	,	PUNCT
ejpam-4369	134	18	sp)-fr(f+(v	sp)-fr(f+(v	PROPN
ejpam-4369	134	19	)	)	PUNCT
ejpam-4369	134	20	)	)	PUNCT
ejpam-4369	134	21	.	.	PUNCT
ejpam-4369	135	1	conversely	conversely	ADV
ejpam-4369	135	2	,	,	PUNCT
ejpam-4369	135	3	suppose	suppose	VERB
ejpam-4369	135	4	that	that	SCONJ
ejpam-4369	135	5	f	f	PROPN
ejpam-4369	135	6	is	be	AUX
ejpam-4369	135	7	upper	upper	ADJ
ejpam-4369	135	8	slightly	slightly	ADV
ejpam-4369	135	9	(	(	PUNCT
ejpam-4369	135	10	λ	λ	NOUN
ejpam-4369	135	11	,	,	PUNCT
ejpam-4369	135	12	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	135	13	at	at	ADP
ejpam-4369	135	14	x	x	PROPN
ejpam-4369	135	15	∈	∈	PROPN
ejpam-4369	135	16	x.	x.	NOUN
ejpam-4369	135	17	let	let	VERB
ejpam-4369	135	18	v	v	PART
ejpam-4369	135	19	be	be	AUX
ejpam-4369	135	20	any	any	DET
ejpam-4369	135	21	(	(	PUNCT
ejpam-4369	135	22	λ	λ	PROPN
ejpam-4369	135	23	,	,	PUNCT
ejpam-4369	135	24	sp)-clopen	sp)-clopen	ADJ
ejpam-4369	135	25	set	set	NOUN
ejpam-4369	135	26	of	of	ADP
ejpam-4369	135	27	y	y	PROPN
ejpam-4369	135	28	containing	contain	VERB
ejpam-4369	135	29	f	f	PROPN
ejpam-4369	135	30	(	(	PUNCT
ejpam-4369	135	31	x	x	NOUN
ejpam-4369	135	32	)	)	PUNCT
ejpam-4369	135	33	.	.	PUNCT
ejpam-4369	136	1	then	then	ADV
ejpam-4369	136	2	,	,	PUNCT
ejpam-4369	136	3	there	there	PRON
ejpam-4369	136	4	exists	exist	VERB
ejpam-4369	136	5	u	u	PROPN
ejpam-4369	136	6	∈	∈	PROPN
ejpam-4369	136	7	λspo(x	λspo(x	PROPN
ejpam-4369	136	8	,	,	PUNCT
ejpam-4369	136	9	τ	τ	X
ejpam-4369	136	10	)	)	PUNCT
ejpam-4369	136	11	containing	contain	VERB
ejpam-4369	136	12	x	x	PUNCT
ejpam-4369	136	13	such	such	ADJ
ejpam-4369	136	14	that	that	SCONJ
ejpam-4369	136	15	u	u	NOUN
ejpam-4369	136	16	⊆	⊆	NUM
ejpam-4369	136	17	f+(v	f+(v	NOUN
ejpam-4369	136	18	)	)	PUNCT
ejpam-4369	136	19	;	;	PUNCT
ejpam-4369	136	20	hence	hence	ADV
ejpam-4369	136	21	x	x	X
ejpam-4369	136	22	∈	∈	PROPN
ejpam-4369	136	23	[	[	X
ejpam-4369	136	24	f+(v	f+(v	NOUN
ejpam-4369	136	25	)	)	PUNCT
ejpam-4369	136	26	]	]	PUNCT
ejpam-4369	136	27	(	(	PUNCT
ejpam-4369	136	28	λ	λ	NOUN
ejpam-4369	136	29	,	,	PUNCT
ejpam-4369	136	30	sp	sp	NOUN
ejpam-4369	136	31	)	)	PUNCT
ejpam-4369	136	32	.	.	PUNCT
ejpam-4369	137	1	thus	thus	ADV
ejpam-4369	137	2	,	,	PUNCT
ejpam-4369	137	3	x	x	PROPN
ejpam-4369	137	4	̸∈	̸∈	PROPN
ejpam-4369	137	5	(	(	PUNCT
ejpam-4369	137	6	λ	λ	PROPN
ejpam-4369	137	7	,	,	PUNCT
ejpam-4369	137	8	sp)-fr(f+(v	sp)-fr(f+(v	PROPN
ejpam-4369	137	9	)	)	PUNCT
ejpam-4369	137	10	)	)	PUNCT
ejpam-4369	137	11	for	for	ADP
ejpam-4369	137	12	every	every	DET
ejpam-4369	137	13	(	(	PUNCT
ejpam-4369	137	14	λ	λ	PROPN
ejpam-4369	137	15	,	,	PUNCT
ejpam-4369	137	16	sp)-clopen	sp)-clopen	NOUN
ejpam-4369	137	17	set	set	VERB
ejpam-4369	137	18	v	v	NUM
ejpam-4369	137	19	of	of	ADP
ejpam-4369	137	20	y	y	PROPN
ejpam-4369	137	21	containing	contain	VERB
ejpam-4369	137	22	f	f	PROPN
ejpam-4369	137	23	(	(	PUNCT
ejpam-4369	137	24	x	x	NOUN
ejpam-4369	137	25	)	)	PUNCT
ejpam-4369	137	26	.	.	PUNCT
ejpam-4369	138	1	theorem	theorem	NOUN
ejpam-4369	138	2	4	4	NUM
ejpam-4369	138	3	.	.	PUNCT
ejpam-4369	139	1	the	the	DET
ejpam-4369	139	2	set	set	NOUN
ejpam-4369	139	3	of	of	ADP
ejpam-4369	139	4	all	all	DET
ejpam-4369	139	5	points	point	NOUN
ejpam-4369	139	6	x	x	X
ejpam-4369	139	7	∈	∈	NOUN
ejpam-4369	139	8	x	x	PUNCT
ejpam-4369	139	9	at	at	ADP
ejpam-4369	139	10	which	which	PRON
ejpam-4369	139	11	a	a	DET
ejpam-4369	139	12	multifunction	multifunction	NOUN
ejpam-4369	139	13	f	f	NOUN
ejpam-4369	139	14	:	:	PUNCT
ejpam-4369	139	15	(	(	PUNCT
ejpam-4369	139	16	x	x	X
ejpam-4369	139	17	,	,	PUNCT
ejpam-4369	139	18	τ	τ	X
ejpam-4369	139	19	)	)	PUNCT
ejpam-4369	139	20	→	→	SYM
ejpam-4369	139	21	(	(	PUNCT
ejpam-4369	139	22	y	y	PROPN
ejpam-4369	139	23	,	,	PUNCT
ejpam-4369	139	24	σ	σ	PROPN
ejpam-4369	139	25	)	)	PUNCT
ejpam-4369	139	26	is	be	AUX
ejpam-4369	139	27	not	not	PART
ejpam-4369	139	28	lower	low	ADJ
ejpam-4369	139	29	slightly	slightly	ADV
ejpam-4369	139	30	(	(	PUNCT
ejpam-4369	139	31	λ	λ	NOUN
ejpam-4369	139	32	,	,	PUNCT
ejpam-4369	139	33	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	139	34	is	be	AUX
ejpam-4369	139	35	identical	identical	ADJ
ejpam-4369	139	36	with	with	ADP
ejpam-4369	139	37	the	the	DET
ejpam-4369	139	38	union	union	NOUN
ejpam-4369	139	39	of	of	ADP
ejpam-4369	139	40	(	(	PUNCT
ejpam-4369	139	41	λ	λ	PROPN
ejpam-4369	139	42	,	,	PUNCT
ejpam-4369	139	43	sp)-frontiers	sp)-frontier	NOUN
ejpam-4369	139	44	of	of	ADP
ejpam-4369	139	45	the	the	DET
ejpam-4369	139	46	lower	low	ADJ
ejpam-4369	139	47	inverse	inverse	NOUN
ejpam-4369	139	48	images	image	NOUN
ejpam-4369	139	49	of	of	ADP
ejpam-4369	139	50	(	(	PUNCT
ejpam-4369	139	51	λ	λ	PROPN
ejpam-4369	139	52	,	,	PUNCT
ejpam-4369	139	53	sp)-clopen	sp)-clopen	ADJ
ejpam-4369	139	54	sets	set	NOUN
ejpam-4369	139	55	meeting	meet	VERB
ejpam-4369	139	56	f	f	X
ejpam-4369	139	57	(	(	PUNCT
ejpam-4369	139	58	x	x	NOUN
ejpam-4369	139	59	)	)	PUNCT
ejpam-4369	139	60	.	.	PUNCT
ejpam-4369	140	1	proof	proof	NOUN
ejpam-4369	140	2	.	.	PUNCT
ejpam-4369	141	1	the	the	DET
ejpam-4369	141	2	proof	proof	NOUN
ejpam-4369	141	3	is	be	AUX
ejpam-4369	141	4	similar	similar	ADJ
ejpam-4369	141	5	to	to	ADP
ejpam-4369	141	6	that	that	PRON
ejpam-4369	141	7	of	of	ADP
ejpam-4369	141	8	theorem	theorem	ADJ
ejpam-4369	141	9	3	3	NUM
ejpam-4369	141	10	.	.	PUNCT
ejpam-4369	141	11	definition	definition	NOUN
ejpam-4369	141	12	4	4	NUM
ejpam-4369	141	13	.	.	PUNCT
ejpam-4369	142	1	[	[	X
ejpam-4369	142	2	3	3	X
ejpam-4369	142	3	]	]	PUNCT
ejpam-4369	142	4	a	a	DET
ejpam-4369	142	5	topological	topological	ADJ
ejpam-4369	142	6	space	space	NOUN
ejpam-4369	142	7	(	(	PUNCT
ejpam-4369	142	8	x	x	X
ejpam-4369	142	9	,	,	PUNCT
ejpam-4369	142	10	τ	τ	X
ejpam-4369	142	11	)	)	PUNCT
ejpam-4369	142	12	is	be	AUX
ejpam-4369	142	13	called	call	VERB
ejpam-4369	142	14	λsp	λsp	INTJ
ejpam-4369	142	15	-	-	PUNCT
ejpam-4369	142	16	extremally	extremally	ADV
ejpam-4369	142	17	disconnected	disconnected	ADJ
ejpam-4369	142	18	if	if	SCONJ
ejpam-4369	142	19	v	v	X
ejpam-4369	142	20	(	(	PUNCT
ejpam-4369	142	21	λ	λ	NOUN
ejpam-4369	142	22	,	,	PUNCT
ejpam-4369	142	23	sp	sp	NOUN
ejpam-4369	142	24	)	)	PUNCT
ejpam-4369	142	25	is	be	AUX
ejpam-4369	142	26	(	(	PUNCT
ejpam-4369	142	27	λ	λ	X
ejpam-4369	142	28	,	,	PUNCT
ejpam-4369	142	29	sp)-open	sp)-open	ADJ
ejpam-4369	142	30	in	in	ADP
ejpam-4369	142	31	x	x	PUNCT
ejpam-4369	142	32	for	for	SCONJ
ejpam-4369	142	33	every	every	DET
ejpam-4369	142	34	(	(	PUNCT
ejpam-4369	142	35	λ	λ	NOUN
ejpam-4369	142	36	,	,	PUNCT
ejpam-4369	142	37	sp)-open	sp)-open	NOUN
ejpam-4369	142	38	set	set	VERB
ejpam-4369	142	39	v	v	ADP
ejpam-4369	142	40	of	of	ADP
ejpam-4369	142	41	x.	x.	NOUN
ejpam-4369	142	42	theorem	theorem	VERB
ejpam-4369	142	43	5	5	NUM
ejpam-4369	142	44	.	.	X
ejpam-4369	142	45	for	for	ADP
ejpam-4369	142	46	a	a	DET
ejpam-4369	142	47	multifunction	multifunction	NOUN
ejpam-4369	142	48	f	f	NOUN
ejpam-4369	142	49	:	:	PUNCT
ejpam-4369	142	50	(	(	PUNCT
ejpam-4369	142	51	x	x	X
ejpam-4369	142	52	,	,	PUNCT
ejpam-4369	142	53	τ	τ	X
ejpam-4369	142	54	)	)	PUNCT
ejpam-4369	142	55	→	→	SYM
ejpam-4369	142	56	(	(	PUNCT
ejpam-4369	142	57	y	y	PROPN
ejpam-4369	142	58	,	,	PUNCT
ejpam-4369	142	59	σ	σ	PROPN
ejpam-4369	142	60	)	)	PUNCT
ejpam-4369	142	61	,	,	PUNCT
ejpam-4369	142	62	where	where	SCONJ
ejpam-4369	142	63	(	(	PUNCT
ejpam-4369	142	64	y	y	PROPN
ejpam-4369	142	65	,	,	PUNCT
ejpam-4369	142	66	σ	σ	PROPN
ejpam-4369	142	67	)	)	PUNCT
ejpam-4369	142	68	is	be	AUX
ejpam-4369	142	69	a	a	DET
ejpam-4369	142	70	λsp	λsp	ADV
ejpam-4369	142	71	-	-	PUNCT
ejpam-4369	142	72	extremally	extremally	ADV
ejpam-4369	142	73	disconnected	disconnected	ADJ
ejpam-4369	142	74	space	space	NOUN
ejpam-4369	142	75	,	,	PUNCT
ejpam-4369	142	76	the	the	DET
ejpam-4369	142	77	following	follow	VERB
ejpam-4369	142	78	properties	property	NOUN
ejpam-4369	142	79	are	be	AUX
ejpam-4369	142	80	equivalent	equivalent	ADJ
ejpam-4369	142	81	:	:	PUNCT
ejpam-4369	142	82	(	(	PUNCT
ejpam-4369	142	83	1	1	X
ejpam-4369	142	84	)	)	PUNCT
ejpam-4369	142	85	f	f	PROPN
ejpam-4369	142	86	is	be	AUX
ejpam-4369	142	87	upper	upper	ADJ
ejpam-4369	142	88	slightly	slightly	ADV
ejpam-4369	142	89	(	(	PUNCT
ejpam-4369	142	90	λ	λ	NOUN
ejpam-4369	142	91	,	,	PUNCT
ejpam-4369	142	92	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	142	93	;	;	PUNCT
ejpam-4369	142	94	(	(	PUNCT
ejpam-4369	142	95	2	2	X
ejpam-4369	142	96	)	)	PUNCT
ejpam-4369	143	1	[	[	X
ejpam-4369	143	2	f−(v	f−(v	NOUN
ejpam-4369	143	3	)	)	PUNCT
ejpam-4369	143	4	]	]	PUNCT
ejpam-4369	143	5	(	(	PUNCT
ejpam-4369	143	6	λ	λ	NOUN
ejpam-4369	143	7	,	,	PUNCT
ejpam-4369	143	8	sp	sp	NOUN
ejpam-4369	143	9	)	)	PUNCT
ejpam-4369	143	10	⊆	⊆	NUM
ejpam-4369	143	11	f−(v	f−(v	NOUN
ejpam-4369	143	12	(	(	PUNCT
ejpam-4369	143	13	λ	λ	NOUN
ejpam-4369	143	14	,	,	PUNCT
ejpam-4369	143	15	sp	sp	NOUN
ejpam-4369	143	16	)	)	PUNCT
ejpam-4369	143	17	)	)	PUNCT
ejpam-4369	143	18	for	for	ADP
ejpam-4369	143	19	every	every	DET
ejpam-4369	143	20	(	(	PUNCT
ejpam-4369	143	21	λ	λ	NOUN
ejpam-4369	143	22	,	,	PUNCT
ejpam-4369	143	23	sp)-open	sp)-open	NOUN
ejpam-4369	143	24	set	set	VERB
ejpam-4369	143	25	v	v	NOUN
ejpam-4369	143	26	of	of	ADP
ejpam-4369	143	27	y	y	PROPN
ejpam-4369	143	28	;	;	PUNCT
ejpam-4369	143	29	(	(	PUNCT
ejpam-4369	143	30	3	3	X
ejpam-4369	143	31	)	)	PUNCT
ejpam-4369	143	32	f+(k(λ	f+(k(λ	NOUN
ejpam-4369	143	33	,	,	PUNCT
ejpam-4369	143	34	sp	sp	NOUN
ejpam-4369	143	35	)	)	PUNCT
ejpam-4369	143	36	)	)	PUNCT
ejpam-4369	144	1	⊆	⊆	NUM
ejpam-4369	144	2	[	[	X
ejpam-4369	144	3	f+(k)](λ	f+(k)](λ	NUM
ejpam-4369	144	4	,	,	PUNCT
ejpam-4369	144	5	sp	sp	NOUN
ejpam-4369	144	6	)	)	PUNCT
ejpam-4369	144	7	for	for	SCONJ
ejpam-4369	144	8	every	every	DET
ejpam-4369	144	9	(	(	PUNCT
ejpam-4369	144	10	λ	λ	PROPN
ejpam-4369	144	11	,	,	PUNCT
ejpam-4369	144	12	sp)-closed	sp)-close	VERB
ejpam-4369	144	13	set	set	VERB
ejpam-4369	144	14	k	k	PROPN
ejpam-4369	144	15	of	of	ADP
ejpam-4369	144	16	y	y	PROPN
ejpam-4369	144	17	.	.	PUNCT
ejpam-4369	145	1	proof	proof	NOUN
ejpam-4369	145	2	.	.	PUNCT
ejpam-4369	146	1	(	(	PUNCT
ejpam-4369	146	2	1	1	X
ejpam-4369	146	3	)	)	PUNCT
ejpam-4369	146	4	⇒	⇒	NOUN
ejpam-4369	146	5	(	(	PUNCT
ejpam-4369	146	6	2	2	NUM
ejpam-4369	146	7	):	):	PUNCT
ejpam-4369	146	8	let	let	VERB
ejpam-4369	146	9	v	v	PART
ejpam-4369	146	10	be	be	AUX
ejpam-4369	146	11	any	any	DET
ejpam-4369	146	12	(	(	PUNCT
ejpam-4369	146	13	λ	λ	NOUN
ejpam-4369	146	14	,	,	PUNCT
ejpam-4369	146	15	sp)-open	sp)-open	ADJ
ejpam-4369	146	16	set	set	NOUN
ejpam-4369	146	17	of	of	ADP
ejpam-4369	146	18	y	y	PROPN
ejpam-4369	146	19	.	.	PUNCT
ejpam-4369	147	1	since	since	SCONJ
ejpam-4369	147	2	(	(	PUNCT
ejpam-4369	147	3	y	y	PROPN
ejpam-4369	147	4	,	,	PUNCT
ejpam-4369	147	5	σ	σ	PROPN
ejpam-4369	147	6	)	)	PUNCT
ejpam-4369	147	7	is	be	AUX
ejpam-4369	147	8	λsp	λsp	VERB
ejpam-4369	147	9	-	-	PUNCT
ejpam-4369	147	10	extremally	extremally	ADV
ejpam-4369	147	11	disconnected	disconnected	ADJ
ejpam-4369	147	12	,	,	PUNCT
ejpam-4369	147	13	v	v	INTJ
ejpam-4369	147	14	(	(	PUNCT
ejpam-4369	147	15	λ	λ	NOUN
ejpam-4369	147	16	,	,	PUNCT
ejpam-4369	147	17	sp	sp	NOUN
ejpam-4369	147	18	)	)	PUNCT
ejpam-4369	147	19	is	be	AUX
ejpam-4369	147	20	(	(	PUNCT
ejpam-4369	147	21	λ	λ	X
ejpam-4369	147	22	,	,	PUNCT
ejpam-4369	147	23	sp)-open	sp)-open	ADJ
ejpam-4369	147	24	in	in	ADP
ejpam-4369	147	25	y	y	PROPN
ejpam-4369	147	26	.	.	PUNCT
ejpam-4369	148	1	thus	thus	ADV
ejpam-4369	148	2	,	,	PUNCT
ejpam-4369	148	3	v	v	INTJ
ejpam-4369	148	4	(	(	PUNCT
ejpam-4369	148	5	λ	λ	NOUN
ejpam-4369	148	6	,	,	PUNCT
ejpam-4369	148	7	sp	sp	NOUN
ejpam-4369	148	8	)	)	PUNCT
ejpam-4369	148	9	is	be	AUX
ejpam-4369	148	10	(	(	PUNCT
ejpam-4369	148	11	λ	λ	PROPN
ejpam-4369	148	12	,	,	PUNCT
ejpam-4369	148	13	sp)-clopen	sp)-clopen	ADJ
ejpam-4369	148	14	in	in	ADP
ejpam-4369	148	15	y	y	PROPN
ejpam-4369	148	16	.	.	PUNCT
ejpam-4369	149	1	by	by	ADP
ejpam-4369	149	2	theorem	theorem	NOUN
ejpam-4369	149	3	1	1	NUM
ejpam-4369	149	4	,	,	PUNCT
ejpam-4369	149	5	f−(v	f−(v	ADJ
ejpam-4369	149	6	(	(	PUNCT
ejpam-4369	149	7	λ	λ	NOUN
ejpam-4369	149	8	,	,	PUNCT
ejpam-4369	149	9	sp	sp	NOUN
ejpam-4369	149	10	)	)	PUNCT
ejpam-4369	149	11	)	)	PUNCT
ejpam-4369	149	12	is	be	AUX
ejpam-4369	149	13	(	(	PUNCT
ejpam-4369	149	14	λ	λ	X
ejpam-4369	149	15	,	,	PUNCT
ejpam-4369	149	16	sp)-closed	sp)-close	VERB
ejpam-4369	149	17	and	and	CCONJ
ejpam-4369	149	18	hence	hence	ADV
ejpam-4369	150	1	[	[	X
ejpam-4369	150	2	f−(v	f−(v	NOUN
ejpam-4369	150	3	)	)	PUNCT
ejpam-4369	150	4	]	]	PUNCT
ejpam-4369	150	5	(	(	PUNCT
ejpam-4369	150	6	λ	λ	NOUN
ejpam-4369	150	7	,	,	PUNCT
ejpam-4369	150	8	sp	sp	NOUN
ejpam-4369	150	9	)	)	PUNCT
ejpam-4369	150	10	⊆	⊆	NUM
ejpam-4369	150	11	[	[	X
ejpam-4369	150	12	f−(v	f−(v	ADJ
ejpam-4369	150	13	(	(	PUNCT
ejpam-4369	150	14	λ	λ	PROPN
ejpam-4369	150	15	,	,	PUNCT
ejpam-4369	150	16	sp))](λ	sp))](λ	PROPN
ejpam-4369	150	17	,	,	PUNCT
ejpam-4369	150	18	sp	sp	NOUN
ejpam-4369	150	19	)	)	PUNCT
ejpam-4369	150	20	=	=	VERB
ejpam-4369	150	21	f−(v	f−(v	NOUN
ejpam-4369	150	22	(	(	PUNCT
ejpam-4369	150	23	λ	λ	NOUN
ejpam-4369	150	24	,	,	PUNCT
ejpam-4369	150	25	sp	sp	NOUN
ejpam-4369	150	26	)	)	PUNCT
ejpam-4369	150	27	)	)	PUNCT
ejpam-4369	150	28	.	.	PUNCT
ejpam-4369	151	1	(	(	PUNCT
ejpam-4369	151	2	2	2	X
ejpam-4369	151	3	)	)	PUNCT
ejpam-4369	151	4	⇒	⇒	NOUN
ejpam-4369	151	5	(	(	PUNCT
ejpam-4369	151	6	3	3	NUM
ejpam-4369	151	7	):	):	PUNCT
ejpam-4369	151	8	let	let	VERB
ejpam-4369	151	9	k	k	PRON
ejpam-4369	151	10	be	be	AUX
ejpam-4369	151	11	any	any	DET
ejpam-4369	151	12	(	(	PUNCT
ejpam-4369	151	13	λ	λ	PROPN
ejpam-4369	151	14	,	,	PUNCT
ejpam-4369	151	15	sp)-closed	sp)-close	VERB
ejpam-4369	151	16	set	set	NOUN
ejpam-4369	151	17	of	of	ADP
ejpam-4369	151	18	y	y	PROPN
ejpam-4369	151	19	.	.	PUNCT
ejpam-4369	152	1	then	then	ADV
ejpam-4369	152	2	,	,	PUNCT
ejpam-4369	152	3	y	y	PROPN
ejpam-4369	152	4	−k	−k	PROPN
ejpam-4369	152	5	is	be	AUX
ejpam-4369	152	6	(	(	PUNCT
ejpam-4369	152	7	λ	λ	X
ejpam-4369	152	8	,	,	PUNCT
ejpam-4369	152	9	sp)-open	sp)-open	ADJ
ejpam-4369	152	10	in	in	ADP
ejpam-4369	152	11	y	y	PROPN
ejpam-4369	152	12	,	,	PUNCT
ejpam-4369	152	13	by	by	ADP
ejpam-4369	152	14	(	(	PUNCT
ejpam-4369	152	15	2	2	NUM
ejpam-4369	152	16	)	)	PUNCT
ejpam-4369	152	17	,	,	PUNCT
ejpam-4369	152	18	we	we	PRON
ejpam-4369	152	19	have	have	VERB
ejpam-4369	152	20	x	x	X
ejpam-4369	152	21	−	−	PROPN
ejpam-4369	153	1	[	[	X
ejpam-4369	153	2	f+(k)](λ	f+(k)](λ	NUM
ejpam-4369	153	3	,	,	PUNCT
ejpam-4369	153	4	sp	sp	NOUN
ejpam-4369	153	5	)	)	PUNCT
ejpam-4369	153	6	=	=	PUNCT
ejpam-4369	154	1	[	[	X
ejpam-4369	154	2	x	x	X
ejpam-4369	154	3	−	−	NOUN
ejpam-4369	154	4	f+(k)](λ	f+(k)](λ	NUM
ejpam-4369	154	5	,	,	PUNCT
ejpam-4369	154	6	sp	sp	NOUN
ejpam-4369	154	7	)	)	PUNCT
ejpam-4369	154	8	=	=	NOUN
ejpam-4369	155	1	[	[	X
ejpam-4369	155	2	f−(y	f−(y	NOUN
ejpam-4369	155	3	−k)](λ	−k)](λ	NOUN
ejpam-4369	155	4	,	,	PUNCT
ejpam-4369	155	5	sp	sp	NOUN
ejpam-4369	155	6	)	)	PUNCT
ejpam-4369	155	7	⊆	⊆	NUM
ejpam-4369	155	8	f−([y	f−([y	NOUN
ejpam-4369	155	9	−k](λ	−k](λ	NUM
ejpam-4369	155	10	,	,	PUNCT
ejpam-4369	155	11	sp	sp	NOUN
ejpam-4369	155	12	)	)	PUNCT
ejpam-4369	155	13	)	)	PUNCT
ejpam-4369	156	1	=	=	SYM
ejpam-4369	156	2	f−(y	f−(y	NOUN
ejpam-4369	156	3	−k(λ	−k(λ	NOUN
ejpam-4369	156	4	,	,	PUNCT
ejpam-4369	156	5	sp	sp	NOUN
ejpam-4369	156	6	)	)	PUNCT
ejpam-4369	156	7	)	)	PUNCT
ejpam-4369	157	1	=	=	PUNCT
ejpam-4369	157	2	x	x	X
ejpam-4369	158	1	−	−	PROPN
ejpam-4369	158	2	f+(k(λ	f+(k(λ	PROPN
ejpam-4369	158	3	,	,	PUNCT
ejpam-4369	158	4	sp	sp	NOUN
ejpam-4369	158	5	)	)	PUNCT
ejpam-4369	158	6	)	)	PUNCT
ejpam-4369	158	7	and	and	CCONJ
ejpam-4369	158	8	hence	hence	ADV
ejpam-4369	158	9	f+(k(λ	f+(k(λ	PROPN
ejpam-4369	158	10	,	,	PUNCT
ejpam-4369	158	11	sp	sp	NOUN
ejpam-4369	158	12	)	)	PUNCT
ejpam-4369	158	13	)	)	PUNCT
ejpam-4369	159	1	⊆	⊆	NUM
ejpam-4369	159	2	[	[	X
ejpam-4369	159	3	f+(k)](λ	f+(k)](λ	NUM
ejpam-4369	159	4	,	,	PUNCT
ejpam-4369	159	5	sp	sp	NOUN
ejpam-4369	159	6	)	)	PUNCT
ejpam-4369	159	7	.	.	PUNCT
ejpam-4369	160	1	(	(	PUNCT
ejpam-4369	160	2	3	3	X
ejpam-4369	160	3	)	)	PUNCT
ejpam-4369	160	4	⇒	⇒	NOUN
ejpam-4369	160	5	(	(	PUNCT
ejpam-4369	160	6	1	1	NUM
ejpam-4369	160	7	):	):	PUNCT
ejpam-4369	160	8	let	let	VERB
ejpam-4369	160	9	x	x	PUNCT
ejpam-4369	160	10	∈	∈	PROPN
ejpam-4369	160	11	x	x	PUNCT
ejpam-4369	160	12	and	and	CCONJ
ejpam-4369	160	13	let	let	VERB
ejpam-4369	160	14	v	v	PART
ejpam-4369	160	15	be	be	AUX
ejpam-4369	160	16	any	any	DET
ejpam-4369	160	17	(	(	PUNCT
ejpam-4369	160	18	λ	λ	PROPN
ejpam-4369	160	19	,	,	PUNCT
ejpam-4369	160	20	sp)-clopen	sp)-clopen	ADJ
ejpam-4369	160	21	set	set	NOUN
ejpam-4369	160	22	of	of	ADP
ejpam-4369	160	23	y	y	PROPN
ejpam-4369	160	24	containing	contain	VERB
ejpam-4369	160	25	f	f	PROPN
ejpam-4369	160	26	(	(	PUNCT
ejpam-4369	160	27	x	x	NOUN
ejpam-4369	160	28	)	)	PUNCT
ejpam-4369	160	29	.	.	PUNCT
ejpam-4369	161	1	thus	thus	ADV
ejpam-4369	161	2	,	,	PUNCT
ejpam-4369	161	3	by	by	ADP
ejpam-4369	161	4	(	(	PUNCT
ejpam-4369	161	5	3	3	NUM
ejpam-4369	161	6	)	)	PUNCT
ejpam-4369	161	7	,	,	PUNCT
ejpam-4369	161	8	x	x	PUNCT
ejpam-4369	161	9	∈	∈	NOUN
ejpam-4369	161	10	f+(v	f+(v	NOUN
ejpam-4369	161	11	)	)	PUNCT
ejpam-4369	162	1	=	=	SYM
ejpam-4369	162	2	f+(v(λ	f+(v(λ	NOUN
ejpam-4369	162	3	,	,	PUNCT
ejpam-4369	162	4	sp	sp	NOUN
ejpam-4369	162	5	)	)	PUNCT
ejpam-4369	162	6	)	)	PUNCT
ejpam-4369	163	1	⊆	⊆	NUM
ejpam-4369	164	1	[	[	X
ejpam-4369	164	2	f+(v	f+(v	NOUN
ejpam-4369	164	3	)	)	PUNCT
ejpam-4369	164	4	]	]	PUNCT
ejpam-4369	164	5	(	(	PUNCT
ejpam-4369	164	6	λ	λ	NOUN
ejpam-4369	164	7	,	,	PUNCT
ejpam-4369	164	8	sp	sp	NOUN
ejpam-4369	164	9	)	)	PUNCT
ejpam-4369	164	10	.	.	PUNCT
ejpam-4369	165	1	then	then	ADV
ejpam-4369	165	2	,	,	PUNCT
ejpam-4369	165	3	there	there	PRON
ejpam-4369	165	4	exists	exist	VERB
ejpam-4369	165	5	u	u	PROPN
ejpam-4369	165	6	∈	∈	PROPN
ejpam-4369	165	7	λspo(x	λspo(x	PROPN
ejpam-4369	165	8	,	,	PUNCT
ejpam-4369	165	9	τ	τ	PROPN
ejpam-4369	165	10	)	)	PUNCT
ejpam-4369	165	11	such	such	ADJ
ejpam-4369	165	12	that	that	SCONJ
ejpam-4369	165	13	x	x	SYM
ejpam-4369	165	14	∈	∈	NUM
ejpam-4369	165	15	u	u	NOUN
ejpam-4369	165	16	⊆	⊆	NUM
ejpam-4369	165	17	f+(v	f+(v	NOUN
ejpam-4369	165	18	)	)	PUNCT
ejpam-4369	165	19	;	;	PUNCT
ejpam-4369	165	20	hence	hence	ADV
ejpam-4369	165	21	f	f	PROPN
ejpam-4369	165	22	(	(	PUNCT
ejpam-4369	165	23	u	u	NOUN
ejpam-4369	165	24	)	)	PUNCT
ejpam-4369	165	25	⊆	⊆	NUM
ejpam-4369	165	26	v	v	NOUN
ejpam-4369	165	27	.	.	PUNCT
ejpam-4369	166	1	this	this	PRON
ejpam-4369	166	2	shows	show	VERB
ejpam-4369	166	3	that	that	SCONJ
ejpam-4369	166	4	f	f	PROPN
ejpam-4369	166	5	is	be	AUX
ejpam-4369	166	6	upper	upper	ADJ
ejpam-4369	166	7	slightly	slightly	ADV
ejpam-4369	166	8	(	(	PUNCT
ejpam-4369	166	9	λ	λ	NOUN
ejpam-4369	166	10	,	,	PUNCT
ejpam-4369	166	11	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	166	12	.	.	PUNCT
ejpam-4369	167	1	c.	c.	PROPN
ejpam-4369	167	2	boonpok	boonpok	PROPN
ejpam-4369	167	3	,	,	PUNCT
ejpam-4369	167	4	j.	j.	PROPN
ejpam-4369	167	5	khampakdee	khampakdee	PROPN
ejpam-4369	167	6	/	/	PUNCT
ejpam-4369	167	7	eur	eur	PROPN
ejpam-4369	167	8	.	.	PUNCT
ejpam-4369	168	1	j.	j.	PROPN
ejpam-4369	168	2	pure	pure	PROPN
ejpam-4369	168	3	appl	appl	PROPN
ejpam-4369	168	4	.	.	PROPN
ejpam-4369	168	5	math	math	PROPN
ejpam-4369	168	6	,	,	PUNCT
ejpam-4369	168	7	15	15	NUM
ejpam-4369	168	8	(	(	PUNCT
ejpam-4369	168	9	3	3	NUM
ejpam-4369	168	10	)	)	PUNCT
ejpam-4369	168	11	(	(	PUNCT
ejpam-4369	168	12	2022	2022	NUM
ejpam-4369	168	13	)	)	PUNCT
ejpam-4369	168	14	,	,	PUNCT
ejpam-4369	168	15	1180	1180	NUM
ejpam-4369	168	16	-	-	SYM
ejpam-4369	168	17	1188	1188	NUM
ejpam-4369	168	18	1185	1185	NUM
ejpam-4369	168	19	theorem	theorem	NOUN
ejpam-4369	168	20	6	6	NUM
ejpam-4369	168	21	.	.	X
ejpam-4369	168	22	for	for	ADP
ejpam-4369	168	23	a	a	DET
ejpam-4369	168	24	multifunction	multifunction	NOUN
ejpam-4369	168	25	f	f	NOUN
ejpam-4369	168	26	:	:	PUNCT
ejpam-4369	168	27	(	(	PUNCT
ejpam-4369	168	28	x	x	X
ejpam-4369	168	29	,	,	PUNCT
ejpam-4369	168	30	τ	τ	X
ejpam-4369	168	31	)	)	PUNCT
ejpam-4369	168	32	→	→	SYM
ejpam-4369	168	33	(	(	PUNCT
ejpam-4369	168	34	y	y	PROPN
ejpam-4369	168	35	,	,	PUNCT
ejpam-4369	168	36	σ	σ	PROPN
ejpam-4369	168	37	)	)	PUNCT
ejpam-4369	168	38	,	,	PUNCT
ejpam-4369	168	39	where	where	SCONJ
ejpam-4369	168	40	(	(	PUNCT
ejpam-4369	168	41	y	y	PROPN
ejpam-4369	168	42	,	,	PUNCT
ejpam-4369	168	43	σ	σ	PROPN
ejpam-4369	168	44	)	)	PUNCT
ejpam-4369	168	45	is	be	AUX
ejpam-4369	168	46	a	a	DET
ejpam-4369	168	47	λsp	λsp	ADV
ejpam-4369	168	48	-	-	PUNCT
ejpam-4369	168	49	extremally	extremally	ADV
ejpam-4369	168	50	disconnected	disconnected	ADJ
ejpam-4369	168	51	space	space	NOUN
ejpam-4369	168	52	,	,	PUNCT
ejpam-4369	168	53	the	the	DET
ejpam-4369	168	54	following	follow	VERB
ejpam-4369	168	55	properties	property	NOUN
ejpam-4369	168	56	are	be	AUX
ejpam-4369	168	57	equivalent	equivalent	ADJ
ejpam-4369	168	58	:	:	PUNCT
ejpam-4369	168	59	(	(	PUNCT
ejpam-4369	168	60	1	1	X
ejpam-4369	168	61	)	)	PUNCT
ejpam-4369	168	62	f	f	PROPN
ejpam-4369	168	63	is	be	AUX
ejpam-4369	168	64	lower	lower	ADV
ejpam-4369	168	65	slightly	slightly	ADV
ejpam-4369	168	66	(	(	PUNCT
ejpam-4369	168	67	λ	λ	NOUN
ejpam-4369	168	68	,	,	PUNCT
ejpam-4369	168	69	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	168	70	;	;	PUNCT
ejpam-4369	168	71	(	(	PUNCT
ejpam-4369	168	72	2	2	X
ejpam-4369	168	73	)	)	PUNCT
ejpam-4369	168	74	[	[	X
ejpam-4369	168	75	f+(v	f+(v	NOUN
ejpam-4369	168	76	)	)	PUNCT
ejpam-4369	168	77	]	]	PUNCT
ejpam-4369	168	78	(	(	PUNCT
ejpam-4369	168	79	λ	λ	NOUN
ejpam-4369	168	80	,	,	PUNCT
ejpam-4369	168	81	sp	sp	NOUN
ejpam-4369	168	82	)	)	PUNCT
ejpam-4369	168	83	⊆	⊆	NUM
ejpam-4369	168	84	f+(v	f+(v	NUM
ejpam-4369	168	85	(	(	PUNCT
ejpam-4369	168	86	λ	λ	NOUN
ejpam-4369	168	87	,	,	PUNCT
ejpam-4369	168	88	sp	sp	NOUN
ejpam-4369	168	89	)	)	PUNCT
ejpam-4369	168	90	)	)	PUNCT
ejpam-4369	168	91	for	for	SCONJ
ejpam-4369	168	92	every	every	DET
ejpam-4369	168	93	(	(	PUNCT
ejpam-4369	168	94	λ	λ	NOUN
ejpam-4369	168	95	,	,	PUNCT
ejpam-4369	168	96	sp)-open	sp)-open	NOUN
ejpam-4369	168	97	set	set	VERB
ejpam-4369	168	98	v	v	NOUN
ejpam-4369	168	99	of	of	ADP
ejpam-4369	168	100	y	y	PROPN
ejpam-4369	168	101	;	;	PUNCT
ejpam-4369	168	102	(	(	PUNCT
ejpam-4369	168	103	3	3	X
ejpam-4369	168	104	)	)	PUNCT
ejpam-4369	168	105	f−(k(λ	f−(k(λ	NOUN
ejpam-4369	168	106	,	,	PUNCT
ejpam-4369	168	107	sp	sp	NOUN
ejpam-4369	168	108	)	)	PUNCT
ejpam-4369	168	109	)	)	PUNCT
ejpam-4369	169	1	⊆	⊆	NUM
ejpam-4369	169	2	[	[	X
ejpam-4369	169	3	f−(k)](λ	f−(k)](λ	PROPN
ejpam-4369	169	4	,	,	PUNCT
ejpam-4369	169	5	sp	sp	NOUN
ejpam-4369	169	6	)	)	PUNCT
ejpam-4369	169	7	for	for	SCONJ
ejpam-4369	169	8	every	every	DET
ejpam-4369	169	9	(	(	PUNCT
ejpam-4369	169	10	λ	λ	PROPN
ejpam-4369	169	11	,	,	PUNCT
ejpam-4369	169	12	sp)-closed	sp)-close	VERB
ejpam-4369	169	13	set	set	VERB
ejpam-4369	169	14	k	k	PROPN
ejpam-4369	169	15	of	of	ADP
ejpam-4369	169	16	y	y	PROPN
ejpam-4369	169	17	.	.	PUNCT
ejpam-4369	170	1	proof	proof	NOUN
ejpam-4369	170	2	.	.	PUNCT
ejpam-4369	171	1	the	the	DET
ejpam-4369	171	2	proof	proof	NOUN
ejpam-4369	171	3	is	be	AUX
ejpam-4369	171	4	similar	similar	ADJ
ejpam-4369	171	5	to	to	ADP
ejpam-4369	171	6	that	that	PRON
ejpam-4369	171	7	of	of	ADP
ejpam-4369	171	8	theorem	theorem	NOUN
ejpam-4369	171	9	5	5	NUM
ejpam-4369	171	10	.	.	PUNCT
ejpam-4369	171	11	lemma	lemma	PROPN
ejpam-4369	171	12	3	3	X
ejpam-4369	171	13	.	.	PUNCT
ejpam-4369	172	1	[	[	X
ejpam-4369	172	2	3	3	X
ejpam-4369	172	3	]	]	PUNCT
ejpam-4369	172	4	for	for	ADP
ejpam-4369	172	5	a	a	DET
ejpam-4369	172	6	topological	topological	ADJ
ejpam-4369	172	7	space	space	NOUN
ejpam-4369	172	8	(	(	PUNCT
ejpam-4369	172	9	x	x	X
ejpam-4369	172	10	,	,	PUNCT
ejpam-4369	172	11	τ	τ	PROPN
ejpam-4369	172	12	)	)	PUNCT
ejpam-4369	172	13	,	,	PUNCT
ejpam-4369	172	14	the	the	DET
ejpam-4369	172	15	following	follow	VERB
ejpam-4369	172	16	properties	property	NOUN
ejpam-4369	172	17	are	be	AUX
ejpam-4369	172	18	equivalent	equivalent	ADJ
ejpam-4369	172	19	:	:	PUNCT
ejpam-4369	172	20	(	(	PUNCT
ejpam-4369	172	21	1	1	X
ejpam-4369	172	22	)	)	PUNCT
ejpam-4369	172	23	(	(	PUNCT
ejpam-4369	172	24	x	x	X
ejpam-4369	172	25	,	,	PUNCT
ejpam-4369	172	26	τ	τ	X
ejpam-4369	172	27	)	)	PUNCT
ejpam-4369	172	28	is	be	AUX
ejpam-4369	172	29	λsp	λsp	VERB
ejpam-4369	172	30	-	-	PUNCT
ejpam-4369	172	31	extremally	extremally	ADV
ejpam-4369	172	32	disconnected	disconnected	ADJ
ejpam-4369	172	33	.	.	PUNCT
ejpam-4369	173	1	(	(	PUNCT
ejpam-4369	173	2	2	2	X
ejpam-4369	173	3	)	)	PUNCT
ejpam-4369	173	4	the	the	DET
ejpam-4369	173	5	(	(	PUNCT
ejpam-4369	173	6	λ	λ	PROPN
ejpam-4369	173	7	,	,	PUNCT
ejpam-4369	173	8	sp)-closure	sp)-closure	NOUN
ejpam-4369	173	9	of	of	ADP
ejpam-4369	173	10	every	every	DET
ejpam-4369	173	11	s(λ	s(λ	PROPN
ejpam-4369	173	12	,	,	PUNCT
ejpam-4369	173	13	sp)-open	sp)-open	ADJ
ejpam-4369	173	14	set	set	NOUN
ejpam-4369	173	15	of	of	ADP
ejpam-4369	173	16	x	x	PUNCT
ejpam-4369	173	17	is	be	AUX
ejpam-4369	173	18	(	(	PUNCT
ejpam-4369	173	19	λ	λ	NOUN
ejpam-4369	173	20	,	,	PUNCT
ejpam-4369	173	21	sp)-open	sp)-open	NOUN
ejpam-4369	173	22	.	.	PUNCT
ejpam-4369	174	1	(	(	PUNCT
ejpam-4369	174	2	3	3	X
ejpam-4369	174	3	)	)	PUNCT
ejpam-4369	174	4	the	the	DET
ejpam-4369	174	5	(	(	PUNCT
ejpam-4369	174	6	λ	λ	PROPN
ejpam-4369	174	7	,	,	PUNCT
ejpam-4369	174	8	sp)-closure	sp)-closure	NOUN
ejpam-4369	174	9	of	of	ADP
ejpam-4369	174	10	every	every	DET
ejpam-4369	174	11	p(λ	p(λ	NOUN
ejpam-4369	174	12	,	,	PUNCT
ejpam-4369	174	13	sp)-open	sp)-open	ADJ
ejpam-4369	174	14	set	set	NOUN
ejpam-4369	174	15	of	of	ADP
ejpam-4369	174	16	x	x	PUNCT
ejpam-4369	174	17	is	be	AUX
ejpam-4369	174	18	(	(	PUNCT
ejpam-4369	174	19	λ	λ	NOUN
ejpam-4369	174	20	,	,	PUNCT
ejpam-4369	174	21	sp)-open	sp)-open	NOUN
ejpam-4369	174	22	.	.	PUNCT
ejpam-4369	175	1	(	(	PUNCT
ejpam-4369	175	2	4	4	X
ejpam-4369	175	3	)	)	PUNCT
ejpam-4369	175	4	the	the	DET
ejpam-4369	175	5	(	(	PUNCT
ejpam-4369	175	6	λ	λ	PROPN
ejpam-4369	175	7	,	,	PUNCT
ejpam-4369	175	8	sp)-closure	sp)-closure	NOUN
ejpam-4369	175	9	of	of	ADP
ejpam-4369	175	10	every	every	DET
ejpam-4369	175	11	r(λ	r(λ	NOUN
ejpam-4369	175	12	,	,	PUNCT
ejpam-4369	175	13	sp)-open	sp)-open	ADJ
ejpam-4369	175	14	set	set	NOUN
ejpam-4369	175	15	of	of	ADP
ejpam-4369	175	16	x	x	PUNCT
ejpam-4369	175	17	is	be	AUX
ejpam-4369	175	18	(	(	PUNCT
ejpam-4369	175	19	λ	λ	NOUN
ejpam-4369	175	20	,	,	PUNCT
ejpam-4369	175	21	sp)-open	sp)-open	NOUN
ejpam-4369	175	22	.	.	PUNCT
ejpam-4369	176	1	theorem	theorem	VERB
ejpam-4369	176	2	7	7	NUM
ejpam-4369	176	3	.	.	X
ejpam-4369	176	4	for	for	ADP
ejpam-4369	176	5	a	a	DET
ejpam-4369	176	6	multifunction	multifunction	NOUN
ejpam-4369	177	1	f	f	NOUN
ejpam-4369	177	2	:	:	PUNCT
ejpam-4369	177	3	(	(	PUNCT
ejpam-4369	177	4	x	x	X
ejpam-4369	177	5	,	,	PUNCT
ejpam-4369	177	6	τ	τ	X
ejpam-4369	177	7	)	)	PUNCT
ejpam-4369	177	8	→	→	SYM
ejpam-4369	177	9	(	(	PUNCT
ejpam-4369	177	10	y	y	PROPN
ejpam-4369	177	11	,	,	PUNCT
ejpam-4369	177	12	σ	σ	PROPN
ejpam-4369	177	13	)	)	PUNCT
ejpam-4369	177	14	,	,	PUNCT
ejpam-4369	177	15	where	where	SCONJ
ejpam-4369	177	16	(	(	PUNCT
ejpam-4369	177	17	y	y	PROPN
ejpam-4369	177	18	,	,	PUNCT
ejpam-4369	177	19	σ	σ	PROPN
ejpam-4369	177	20	)	)	PUNCT
ejpam-4369	177	21	is	be	AUX
ejpam-4369	177	22	a	a	DET
ejpam-4369	177	23	λsp	λsp	ADV
ejpam-4369	177	24	-	-	PUNCT
ejpam-4369	177	25	extremally	extremally	ADV
ejpam-4369	177	26	disconnected	disconnected	ADJ
ejpam-4369	177	27	space	space	NOUN
ejpam-4369	177	28	,	,	PUNCT
ejpam-4369	177	29	the	the	DET
ejpam-4369	177	30	following	follow	VERB
ejpam-4369	177	31	properties	property	NOUN
ejpam-4369	177	32	are	be	AUX
ejpam-4369	177	33	equivalent	equivalent	ADJ
ejpam-4369	177	34	:	:	PUNCT
ejpam-4369	177	35	(	(	PUNCT
ejpam-4369	177	36	1	1	X
ejpam-4369	177	37	)	)	PUNCT
ejpam-4369	177	38	f	f	PROPN
ejpam-4369	177	39	is	be	AUX
ejpam-4369	177	40	upper	upper	ADJ
ejpam-4369	177	41	slightly	slightly	ADV
ejpam-4369	177	42	(	(	PUNCT
ejpam-4369	177	43	λ	λ	NOUN
ejpam-4369	177	44	,	,	PUNCT
ejpam-4369	177	45	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	177	46	;	;	PUNCT
ejpam-4369	177	47	(	(	PUNCT
ejpam-4369	177	48	2	2	X
ejpam-4369	177	49	)	)	PUNCT
ejpam-4369	178	1	[	[	X
ejpam-4369	178	2	f−(v	f−(v	NOUN
ejpam-4369	178	3	)	)	PUNCT
ejpam-4369	178	4	]	]	PUNCT
ejpam-4369	178	5	(	(	PUNCT
ejpam-4369	178	6	λ	λ	NOUN
ejpam-4369	178	7	,	,	PUNCT
ejpam-4369	178	8	sp	sp	NOUN
ejpam-4369	178	9	)	)	PUNCT
ejpam-4369	178	10	⊆	⊆	NUM
ejpam-4369	178	11	f−(v	f−(v	NOUN
ejpam-4369	178	12	(	(	PUNCT
ejpam-4369	178	13	λ	λ	NOUN
ejpam-4369	178	14	,	,	PUNCT
ejpam-4369	178	15	sp	sp	NOUN
ejpam-4369	178	16	)	)	PUNCT
ejpam-4369	178	17	)	)	PUNCT
ejpam-4369	178	18	for	for	ADP
ejpam-4369	178	19	every	every	DET
ejpam-4369	178	20	s(λ	s(λ	PROPN
ejpam-4369	178	21	,	,	PUNCT
ejpam-4369	178	22	sp)-open	sp)-open	VERB
ejpam-4369	178	23	set	set	VERB
ejpam-4369	178	24	v	v	NOUN
ejpam-4369	178	25	of	of	ADP
ejpam-4369	178	26	y	y	PROPN
ejpam-4369	178	27	;	;	PUNCT
ejpam-4369	178	28	(	(	PUNCT
ejpam-4369	178	29	3	3	X
ejpam-4369	178	30	)	)	PUNCT
ejpam-4369	178	31	f+(k(λ	f+(k(λ	NOUN
ejpam-4369	178	32	,	,	PUNCT
ejpam-4369	178	33	sp	sp	NOUN
ejpam-4369	178	34	)	)	PUNCT
ejpam-4369	178	35	)	)	PUNCT
ejpam-4369	179	1	⊆	⊆	NUM
ejpam-4369	179	2	[	[	X
ejpam-4369	179	3	f+(k)](λ	f+(k)](λ	NUM
ejpam-4369	179	4	,	,	PUNCT
ejpam-4369	179	5	sp	sp	NOUN
ejpam-4369	179	6	)	)	PUNCT
ejpam-4369	179	7	for	for	ADP
ejpam-4369	179	8	every	every	DET
ejpam-4369	179	9	s(λ	s(λ	PROPN
ejpam-4369	179	10	,	,	PUNCT
ejpam-4369	179	11	sp)-closed	sp)-close	VERB
ejpam-4369	179	12	set	set	VERB
ejpam-4369	179	13	k	k	PROPN
ejpam-4369	179	14	of	of	ADP
ejpam-4369	179	15	y	y	PROPN
ejpam-4369	179	16	.	.	PUNCT
ejpam-4369	180	1	proof	proof	NOUN
ejpam-4369	180	2	.	.	PUNCT
ejpam-4369	181	1	the	the	DET
ejpam-4369	181	2	proof	proof	NOUN
ejpam-4369	181	3	is	be	AUX
ejpam-4369	181	4	similar	similar	ADJ
ejpam-4369	181	5	to	to	ADP
ejpam-4369	181	6	that	that	PRON
ejpam-4369	181	7	of	of	ADP
ejpam-4369	181	8	theorem	theorem	NOUN
ejpam-4369	181	9	5	5	NUM
ejpam-4369	181	10	and	and	CCONJ
ejpam-4369	181	11	it	it	PRON
ejpam-4369	181	12	follows	follow	VERB
ejpam-4369	181	13	from	from	ADP
ejpam-4369	181	14	theorem	theorem	ADJ
ejpam-4369	181	15	1	1	NUM
ejpam-4369	181	16	and	and	CCONJ
ejpam-4369	181	17	lemma	lemma	PROPN
ejpam-4369	181	18	3	3	X
ejpam-4369	181	19	.	.	PUNCT
ejpam-4369	181	20	theorem	theorem	VERB
ejpam-4369	181	21	8	8	NUM
ejpam-4369	181	22	.	.	PUNCT
ejpam-4369	181	23	for	for	ADP
ejpam-4369	181	24	a	a	DET
ejpam-4369	181	25	multifunction	multifunction	NOUN
ejpam-4369	181	26	f	f	NOUN
ejpam-4369	181	27	:	:	PUNCT
ejpam-4369	181	28	(	(	PUNCT
ejpam-4369	181	29	x	x	X
ejpam-4369	181	30	,	,	PUNCT
ejpam-4369	181	31	τ	τ	X
ejpam-4369	181	32	)	)	PUNCT
ejpam-4369	181	33	→	→	SYM
ejpam-4369	181	34	(	(	PUNCT
ejpam-4369	181	35	y	y	PROPN
ejpam-4369	181	36	,	,	PUNCT
ejpam-4369	181	37	σ	σ	PROPN
ejpam-4369	181	38	)	)	PUNCT
ejpam-4369	181	39	,	,	PUNCT
ejpam-4369	181	40	where	where	SCONJ
ejpam-4369	181	41	(	(	PUNCT
ejpam-4369	181	42	y	y	PROPN
ejpam-4369	181	43	,	,	PUNCT
ejpam-4369	181	44	σ	σ	PROPN
ejpam-4369	181	45	)	)	PUNCT
ejpam-4369	181	46	is	be	AUX
ejpam-4369	181	47	a	a	DET
ejpam-4369	181	48	λsp	λsp	ADV
ejpam-4369	181	49	-	-	PUNCT
ejpam-4369	181	50	extremally	extremally	ADV
ejpam-4369	181	51	disconnected	disconnected	ADJ
ejpam-4369	181	52	space	space	NOUN
ejpam-4369	181	53	,	,	PUNCT
ejpam-4369	181	54	the	the	DET
ejpam-4369	181	55	following	follow	VERB
ejpam-4369	181	56	properties	property	NOUN
ejpam-4369	181	57	are	be	AUX
ejpam-4369	181	58	equivalent	equivalent	ADJ
ejpam-4369	181	59	:	:	PUNCT
ejpam-4369	181	60	(	(	PUNCT
ejpam-4369	181	61	1	1	X
ejpam-4369	181	62	)	)	PUNCT
ejpam-4369	181	63	f	f	PROPN
ejpam-4369	181	64	is	be	AUX
ejpam-4369	181	65	lower	lower	ADV
ejpam-4369	181	66	slightly	slightly	ADV
ejpam-4369	181	67	(	(	PUNCT
ejpam-4369	181	68	λ	λ	NOUN
ejpam-4369	181	69	,	,	PUNCT
ejpam-4369	181	70	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	181	71	;	;	PUNCT
ejpam-4369	181	72	(	(	PUNCT
ejpam-4369	181	73	2	2	X
ejpam-4369	181	74	)	)	PUNCT
ejpam-4369	181	75	[	[	X
ejpam-4369	181	76	f+(v	f+(v	NOUN
ejpam-4369	181	77	)	)	PUNCT
ejpam-4369	181	78	]	]	PUNCT
ejpam-4369	181	79	(	(	PUNCT
ejpam-4369	181	80	λ	λ	NOUN
ejpam-4369	181	81	,	,	PUNCT
ejpam-4369	181	82	sp	sp	NOUN
ejpam-4369	181	83	)	)	PUNCT
ejpam-4369	181	84	⊆	⊆	NUM
ejpam-4369	181	85	f+(v	f+(v	NUM
ejpam-4369	181	86	(	(	PUNCT
ejpam-4369	181	87	λ	λ	NOUN
ejpam-4369	181	88	,	,	PUNCT
ejpam-4369	181	89	sp	sp	NOUN
ejpam-4369	181	90	)	)	PUNCT
ejpam-4369	181	91	)	)	PUNCT
ejpam-4369	181	92	for	for	ADP
ejpam-4369	181	93	every	every	DET
ejpam-4369	181	94	s(λ	s(λ	PROPN
ejpam-4369	181	95	,	,	PUNCT
ejpam-4369	181	96	sp)-open	sp)-open	VERB
ejpam-4369	181	97	set	set	VERB
ejpam-4369	181	98	v	v	NOUN
ejpam-4369	181	99	of	of	ADP
ejpam-4369	181	100	y	y	PROPN
ejpam-4369	181	101	;	;	PUNCT
ejpam-4369	181	102	(	(	PUNCT
ejpam-4369	181	103	3	3	X
ejpam-4369	181	104	)	)	PUNCT
ejpam-4369	181	105	f−(k(λ	f−(k(λ	NOUN
ejpam-4369	181	106	,	,	PUNCT
ejpam-4369	181	107	sp	sp	NOUN
ejpam-4369	181	108	)	)	PUNCT
ejpam-4369	181	109	)	)	PUNCT
ejpam-4369	182	1	⊆	⊆	NUM
ejpam-4369	182	2	[	[	X
ejpam-4369	182	3	f−(k)](λ	f−(k)](λ	PROPN
ejpam-4369	182	4	,	,	PUNCT
ejpam-4369	182	5	sp	sp	NOUN
ejpam-4369	182	6	)	)	PUNCT
ejpam-4369	182	7	for	for	ADP
ejpam-4369	182	8	every	every	DET
ejpam-4369	182	9	s(λ	s(λ	PROPN
ejpam-4369	182	10	,	,	PUNCT
ejpam-4369	182	11	sp)-closed	sp)-close	VERB
ejpam-4369	182	12	set	set	VERB
ejpam-4369	182	13	k	k	PROPN
ejpam-4369	182	14	of	of	ADP
ejpam-4369	182	15	y	y	PROPN
ejpam-4369	182	16	.	.	PUNCT
ejpam-4369	183	1	proof	proof	NOUN
ejpam-4369	183	2	.	.	PUNCT
ejpam-4369	184	1	the	the	DET
ejpam-4369	184	2	proof	proof	NOUN
ejpam-4369	184	3	is	be	AUX
ejpam-4369	184	4	similar	similar	ADJ
ejpam-4369	184	5	to	to	ADP
ejpam-4369	184	6	that	that	PRON
ejpam-4369	184	7	of	of	ADP
ejpam-4369	184	8	theorem	theorem	NOUN
ejpam-4369	184	9	6	6	NUM
ejpam-4369	184	10	and	and	CCONJ
ejpam-4369	184	11	it	it	PRON
ejpam-4369	184	12	follows	follow	VERB
ejpam-4369	184	13	from	from	ADP
ejpam-4369	184	14	theorem	theorem	ADJ
ejpam-4369	184	15	2	2	NUM
ejpam-4369	184	16	and	and	CCONJ
ejpam-4369	184	17	lemma	lemma	PROPN
ejpam-4369	184	18	3	3	X
ejpam-4369	184	19	.	.	PUNCT
ejpam-4369	184	20	corollary	corollary	ADJ
ejpam-4369	184	21	2	2	NUM
ejpam-4369	184	22	.	.	PUNCT
ejpam-4369	185	1	for	for	ADP
ejpam-4369	185	2	a	a	DET
ejpam-4369	185	3	function	function	NOUN
ejpam-4369	185	4	f	f	NOUN
ejpam-4369	185	5	:	:	PUNCT
ejpam-4369	185	6	(	(	PUNCT
ejpam-4369	185	7	x	x	X
ejpam-4369	185	8	,	,	PUNCT
ejpam-4369	185	9	τ	τ	X
ejpam-4369	185	10	)	)	PUNCT
ejpam-4369	185	11	→	→	SYM
ejpam-4369	185	12	(	(	PUNCT
ejpam-4369	185	13	y	y	PROPN
ejpam-4369	185	14	,	,	PUNCT
ejpam-4369	185	15	σ	σ	PROPN
ejpam-4369	185	16	)	)	PUNCT
ejpam-4369	185	17	,	,	PUNCT
ejpam-4369	185	18	where	where	SCONJ
ejpam-4369	185	19	(	(	PUNCT
ejpam-4369	185	20	y	y	PROPN
ejpam-4369	185	21	,	,	PUNCT
ejpam-4369	185	22	σ	σ	PROPN
ejpam-4369	185	23	)	)	PUNCT
ejpam-4369	185	24	is	be	AUX
ejpam-4369	185	25	a	a	DET
ejpam-4369	185	26	λsp	λsp	ADV
ejpam-4369	185	27	-	-	PUNCT
ejpam-4369	185	28	extremally	extremally	ADV
ejpam-4369	185	29	disconnected	disconnected	ADJ
ejpam-4369	185	30	space	space	NOUN
ejpam-4369	185	31	,	,	PUNCT
ejpam-4369	185	32	the	the	DET
ejpam-4369	185	33	following	follow	VERB
ejpam-4369	185	34	properties	property	NOUN
ejpam-4369	185	35	are	be	AUX
ejpam-4369	185	36	equivalent	equivalent	ADJ
ejpam-4369	185	37	:	:	PUNCT
ejpam-4369	185	38	(	(	PUNCT
ejpam-4369	185	39	1	1	X
ejpam-4369	185	40	)	)	PUNCT
ejpam-4369	185	41	f	f	PROPN
ejpam-4369	185	42	is	be	AUX
ejpam-4369	185	43	slightly	slightly	ADV
ejpam-4369	185	44	(	(	PUNCT
ejpam-4369	185	45	λ	λ	NOUN
ejpam-4369	185	46	,	,	PUNCT
ejpam-4369	185	47	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	185	48	;	;	PUNCT
ejpam-4369	185	49	c.	c.	PROPN
ejpam-4369	185	50	boonpok	boonpok	PROPN
ejpam-4369	185	51	,	,	PUNCT
ejpam-4369	185	52	j.	j.	PROPN
ejpam-4369	185	53	khampakdee	khampakdee	PROPN
ejpam-4369	185	54	/	/	PUNCT
ejpam-4369	185	55	eur	eur	PROPN
ejpam-4369	185	56	.	.	PUNCT
ejpam-4369	186	1	j.	j.	PROPN
ejpam-4369	186	2	pure	pure	PROPN
ejpam-4369	186	3	appl	appl	PROPN
ejpam-4369	186	4	.	.	PROPN
ejpam-4369	186	5	math	math	PROPN
ejpam-4369	186	6	,	,	PUNCT
ejpam-4369	186	7	15	15	NUM
ejpam-4369	186	8	(	(	PUNCT
ejpam-4369	186	9	3	3	NUM
ejpam-4369	186	10	)	)	PUNCT
ejpam-4369	186	11	(	(	PUNCT
ejpam-4369	186	12	2022	2022	NUM
ejpam-4369	186	13	)	)	PUNCT
ejpam-4369	186	14	,	,	PUNCT
ejpam-4369	186	15	1180	1180	NUM
ejpam-4369	186	16	-	-	SYM
ejpam-4369	186	17	1188	1188	NUM
ejpam-4369	186	18	1186	1186	NUM
ejpam-4369	186	19	(	(	PUNCT
ejpam-4369	186	20	2	2	NUM
ejpam-4369	186	21	)	)	PUNCT
ejpam-4369	187	1	[	[	X
ejpam-4369	187	2	f−1(v	f−1(v	NOUN
ejpam-4369	187	3	)	)	PUNCT
ejpam-4369	187	4	]	]	PUNCT
ejpam-4369	187	5	(	(	PUNCT
ejpam-4369	187	6	λ	λ	NOUN
ejpam-4369	187	7	,	,	PUNCT
ejpam-4369	187	8	sp	sp	NOUN
ejpam-4369	187	9	)	)	PUNCT
ejpam-4369	187	10	⊆	⊆	NUM
ejpam-4369	187	11	f−1(v	f−1(v	NOUN
ejpam-4369	187	12	(	(	PUNCT
ejpam-4369	187	13	λ	λ	PROPN
ejpam-4369	187	14	,	,	PUNCT
ejpam-4369	187	15	sp	sp	NOUN
ejpam-4369	187	16	)	)	PUNCT
ejpam-4369	187	17	)	)	PUNCT
ejpam-4369	187	18	for	for	ADP
ejpam-4369	187	19	every	every	DET
ejpam-4369	187	20	s(λ	s(λ	PROPN
ejpam-4369	187	21	,	,	PUNCT
ejpam-4369	187	22	sp)-open	sp)-open	VERB
ejpam-4369	187	23	set	set	VERB
ejpam-4369	187	24	v	v	NOUN
ejpam-4369	187	25	of	of	ADP
ejpam-4369	187	26	y	y	PROPN
ejpam-4369	187	27	;	;	PUNCT
ejpam-4369	187	28	(	(	PUNCT
ejpam-4369	187	29	3	3	X
ejpam-4369	187	30	)	)	PUNCT
ejpam-4369	187	31	f−1(k(λ	f−1(k(λ	NOUN
ejpam-4369	187	32	,	,	PUNCT
ejpam-4369	187	33	sp	sp	NOUN
ejpam-4369	187	34	)	)	PUNCT
ejpam-4369	187	35	)	)	PUNCT
ejpam-4369	187	36	⊆	⊆	NUM
ejpam-4369	187	37	[	[	X
ejpam-4369	187	38	f−1(k)](λ	f−1(k)](λ	PROPN
ejpam-4369	187	39	,	,	PUNCT
ejpam-4369	187	40	sp	sp	NOUN
ejpam-4369	187	41	)	)	PUNCT
ejpam-4369	187	42	for	for	ADP
ejpam-4369	187	43	every	every	DET
ejpam-4369	187	44	s(λ	s(λ	PROPN
ejpam-4369	187	45	,	,	PUNCT
ejpam-4369	187	46	sp)-closed	sp)-close	VERB
ejpam-4369	187	47	set	set	VERB
ejpam-4369	187	48	k	k	PROPN
ejpam-4369	187	49	of	of	ADP
ejpam-4369	187	50	y	y	PROPN
ejpam-4369	187	51	.	.	PUNCT
ejpam-4369	188	1	theorem	theorem	VERB
ejpam-4369	188	2	9	9	NUM
ejpam-4369	188	3	.	.	X
ejpam-4369	188	4	for	for	ADP
ejpam-4369	188	5	a	a	DET
ejpam-4369	188	6	multifunction	multifunction	NOUN
ejpam-4369	189	1	f	f	NOUN
ejpam-4369	189	2	:	:	PUNCT
ejpam-4369	189	3	(	(	PUNCT
ejpam-4369	189	4	x	x	X
ejpam-4369	189	5	,	,	PUNCT
ejpam-4369	189	6	τ	τ	X
ejpam-4369	189	7	)	)	PUNCT
ejpam-4369	189	8	→	→	SYM
ejpam-4369	189	9	(	(	PUNCT
ejpam-4369	189	10	y	y	PROPN
ejpam-4369	189	11	,	,	PUNCT
ejpam-4369	189	12	σ	σ	PROPN
ejpam-4369	189	13	)	)	PUNCT
ejpam-4369	189	14	,	,	PUNCT
ejpam-4369	189	15	where	where	SCONJ
ejpam-4369	189	16	(	(	PUNCT
ejpam-4369	189	17	y	y	PROPN
ejpam-4369	189	18	,	,	PUNCT
ejpam-4369	189	19	σ	σ	PROPN
ejpam-4369	189	20	)	)	PUNCT
ejpam-4369	189	21	is	be	AUX
ejpam-4369	189	22	a	a	DET
ejpam-4369	189	23	λsp	λsp	ADV
ejpam-4369	189	24	-	-	PUNCT
ejpam-4369	189	25	extremally	extremally	ADV
ejpam-4369	189	26	disconnected	disconnected	ADJ
ejpam-4369	189	27	space	space	NOUN
ejpam-4369	189	28	,	,	PUNCT
ejpam-4369	189	29	the	the	DET
ejpam-4369	189	30	following	follow	VERB
ejpam-4369	189	31	properties	property	NOUN
ejpam-4369	189	32	are	be	AUX
ejpam-4369	189	33	equivalent	equivalent	ADJ
ejpam-4369	189	34	:	:	PUNCT
ejpam-4369	189	35	(	(	PUNCT
ejpam-4369	189	36	1	1	X
ejpam-4369	189	37	)	)	PUNCT
ejpam-4369	189	38	f	f	PROPN
ejpam-4369	189	39	is	be	AUX
ejpam-4369	189	40	upper	upper	ADJ
ejpam-4369	189	41	slightly	slightly	ADV
ejpam-4369	189	42	(	(	PUNCT
ejpam-4369	189	43	λ	λ	NOUN
ejpam-4369	189	44	,	,	PUNCT
ejpam-4369	189	45	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	189	46	;	;	PUNCT
ejpam-4369	189	47	(	(	PUNCT
ejpam-4369	189	48	2	2	X
ejpam-4369	189	49	)	)	PUNCT
ejpam-4369	190	1	[	[	X
ejpam-4369	190	2	f−(v	f−(v	NOUN
ejpam-4369	190	3	)	)	PUNCT
ejpam-4369	190	4	]	]	PUNCT
ejpam-4369	190	5	(	(	PUNCT
ejpam-4369	190	6	λ	λ	NOUN
ejpam-4369	190	7	,	,	PUNCT
ejpam-4369	190	8	sp	sp	NOUN
ejpam-4369	190	9	)	)	PUNCT
ejpam-4369	190	10	⊆	⊆	NUM
ejpam-4369	190	11	f−(v	f−(v	NOUN
ejpam-4369	190	12	(	(	PUNCT
ejpam-4369	190	13	λ	λ	NOUN
ejpam-4369	190	14	,	,	PUNCT
ejpam-4369	190	15	sp	sp	NOUN
ejpam-4369	190	16	)	)	PUNCT
ejpam-4369	190	17	)	)	PUNCT
ejpam-4369	190	18	for	for	ADP
ejpam-4369	190	19	every	every	DET
ejpam-4369	190	20	p(λ	p(λ	NOUN
ejpam-4369	190	21	,	,	PUNCT
ejpam-4369	190	22	sp)-open	sp)-open	NOUN
ejpam-4369	190	23	set	set	VERB
ejpam-4369	190	24	v	v	NOUN
ejpam-4369	190	25	of	of	ADP
ejpam-4369	190	26	y	y	PROPN
ejpam-4369	190	27	;	;	PUNCT
ejpam-4369	190	28	(	(	PUNCT
ejpam-4369	190	29	3	3	X
ejpam-4369	190	30	)	)	PUNCT
ejpam-4369	190	31	f+(k(λ	f+(k(λ	NOUN
ejpam-4369	190	32	,	,	PUNCT
ejpam-4369	190	33	sp	sp	NOUN
ejpam-4369	190	34	)	)	PUNCT
ejpam-4369	190	35	)	)	PUNCT
ejpam-4369	191	1	⊆	⊆	NUM
ejpam-4369	191	2	[	[	X
ejpam-4369	191	3	f+(k)](λ	f+(k)](λ	NUM
ejpam-4369	191	4	,	,	PUNCT
ejpam-4369	191	5	sp	sp	NOUN
ejpam-4369	191	6	)	)	PUNCT
ejpam-4369	191	7	for	for	ADP
ejpam-4369	191	8	every	every	DET
ejpam-4369	191	9	p(λ	p(λ	NOUN
ejpam-4369	191	10	,	,	PUNCT
ejpam-4369	191	11	sp)-closed	sp)-close	VERB
ejpam-4369	191	12	set	set	VERB
ejpam-4369	191	13	k	k	PROPN
ejpam-4369	191	14	of	of	ADP
ejpam-4369	191	15	y	y	PROPN
ejpam-4369	191	16	.	.	PUNCT
ejpam-4369	192	1	proof	proof	NOUN
ejpam-4369	192	2	.	.	PUNCT
ejpam-4369	193	1	the	the	DET
ejpam-4369	193	2	proof	proof	NOUN
ejpam-4369	193	3	is	be	AUX
ejpam-4369	193	4	similar	similar	ADJ
ejpam-4369	193	5	to	to	ADP
ejpam-4369	193	6	that	that	PRON
ejpam-4369	193	7	of	of	ADP
ejpam-4369	193	8	theorem	theorem	NOUN
ejpam-4369	193	9	5	5	NUM
ejpam-4369	193	10	and	and	CCONJ
ejpam-4369	193	11	it	it	PRON
ejpam-4369	193	12	follows	follow	VERB
ejpam-4369	193	13	from	from	ADP
ejpam-4369	193	14	theorem	theorem	ADJ
ejpam-4369	193	15	1	1	NUM
ejpam-4369	193	16	and	and	CCONJ
ejpam-4369	193	17	lemma	lemma	PROPN
ejpam-4369	193	18	3	3	X
ejpam-4369	193	19	.	.	PUNCT
ejpam-4369	193	20	theorem	theorem	VERB
ejpam-4369	193	21	10	10	NUM
ejpam-4369	193	22	.	.	PUNCT
ejpam-4369	194	1	for	for	ADP
ejpam-4369	194	2	a	a	DET
ejpam-4369	194	3	multifunction	multifunction	NOUN
ejpam-4369	194	4	f	f	NOUN
ejpam-4369	194	5	:	:	PUNCT
ejpam-4369	194	6	(	(	PUNCT
ejpam-4369	194	7	x	x	X
ejpam-4369	194	8	,	,	PUNCT
ejpam-4369	194	9	τ	τ	X
ejpam-4369	194	10	)	)	PUNCT
ejpam-4369	194	11	→	→	SYM
ejpam-4369	194	12	(	(	PUNCT
ejpam-4369	194	13	y	y	PROPN
ejpam-4369	194	14	,	,	PUNCT
ejpam-4369	194	15	σ	σ	PROPN
ejpam-4369	194	16	)	)	PUNCT
ejpam-4369	194	17	,	,	PUNCT
ejpam-4369	194	18	where	where	SCONJ
ejpam-4369	194	19	(	(	PUNCT
ejpam-4369	194	20	y	y	PROPN
ejpam-4369	194	21	,	,	PUNCT
ejpam-4369	194	22	σ	σ	PROPN
ejpam-4369	194	23	)	)	PUNCT
ejpam-4369	194	24	is	be	AUX
ejpam-4369	194	25	a	a	DET
ejpam-4369	194	26	λsp	λsp	ADV
ejpam-4369	194	27	-	-	PUNCT
ejpam-4369	194	28	extremally	extremally	ADV
ejpam-4369	194	29	disconnected	disconnected	ADJ
ejpam-4369	194	30	space	space	NOUN
ejpam-4369	194	31	,	,	PUNCT
ejpam-4369	194	32	the	the	DET
ejpam-4369	194	33	following	follow	VERB
ejpam-4369	194	34	properties	property	NOUN
ejpam-4369	194	35	are	be	AUX
ejpam-4369	194	36	equivalent	equivalent	ADJ
ejpam-4369	194	37	:	:	PUNCT
ejpam-4369	194	38	(	(	PUNCT
ejpam-4369	194	39	1	1	X
ejpam-4369	194	40	)	)	PUNCT
ejpam-4369	194	41	f	f	PROPN
ejpam-4369	194	42	is	be	AUX
ejpam-4369	194	43	lower	lower	ADV
ejpam-4369	194	44	slightly	slightly	ADV
ejpam-4369	194	45	(	(	PUNCT
ejpam-4369	194	46	λ	λ	NOUN
ejpam-4369	194	47	,	,	PUNCT
ejpam-4369	194	48	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	194	49	;	;	PUNCT
ejpam-4369	194	50	(	(	PUNCT
ejpam-4369	194	51	2	2	X
ejpam-4369	194	52	)	)	PUNCT
ejpam-4369	194	53	[	[	X
ejpam-4369	194	54	f+(v	f+(v	NOUN
ejpam-4369	194	55	)	)	PUNCT
ejpam-4369	194	56	]	]	PUNCT
ejpam-4369	194	57	(	(	PUNCT
ejpam-4369	194	58	λ	λ	NOUN
ejpam-4369	194	59	,	,	PUNCT
ejpam-4369	194	60	sp	sp	NOUN
ejpam-4369	194	61	)	)	PUNCT
ejpam-4369	194	62	⊆	⊆	NUM
ejpam-4369	194	63	f+(v	f+(v	NUM
ejpam-4369	194	64	(	(	PUNCT
ejpam-4369	194	65	λ	λ	NOUN
ejpam-4369	194	66	,	,	PUNCT
ejpam-4369	194	67	sp	sp	NOUN
ejpam-4369	194	68	)	)	PUNCT
ejpam-4369	194	69	)	)	PUNCT
ejpam-4369	194	70	for	for	ADP
ejpam-4369	194	71	every	every	DET
ejpam-4369	194	72	p(λ	p(λ	NOUN
ejpam-4369	194	73	,	,	PUNCT
ejpam-4369	194	74	sp)-open	sp)-open	NOUN
ejpam-4369	194	75	set	set	VERB
ejpam-4369	194	76	v	v	NOUN
ejpam-4369	194	77	of	of	ADP
ejpam-4369	194	78	y	y	PROPN
ejpam-4369	194	79	;	;	PUNCT
ejpam-4369	194	80	(	(	PUNCT
ejpam-4369	194	81	3	3	X
ejpam-4369	194	82	)	)	PUNCT
ejpam-4369	194	83	f−(k(λ	f−(k(λ	NOUN
ejpam-4369	194	84	,	,	PUNCT
ejpam-4369	194	85	sp	sp	NOUN
ejpam-4369	194	86	)	)	PUNCT
ejpam-4369	194	87	)	)	PUNCT
ejpam-4369	195	1	⊆	⊆	NUM
ejpam-4369	195	2	[	[	X
ejpam-4369	195	3	f−(k)](λ	f−(k)](λ	PROPN
ejpam-4369	195	4	,	,	PUNCT
ejpam-4369	195	5	sp	sp	NOUN
ejpam-4369	195	6	)	)	PUNCT
ejpam-4369	195	7	for	for	ADP
ejpam-4369	195	8	every	every	DET
ejpam-4369	195	9	p(λ	p(λ	NOUN
ejpam-4369	195	10	,	,	PUNCT
ejpam-4369	195	11	sp)-closed	sp)-close	VERB
ejpam-4369	195	12	set	set	VERB
ejpam-4369	195	13	k	k	PROPN
ejpam-4369	195	14	of	of	ADP
ejpam-4369	195	15	y	y	PROPN
ejpam-4369	195	16	.	.	PUNCT
ejpam-4369	196	1	proof	proof	NOUN
ejpam-4369	196	2	.	.	PUNCT
ejpam-4369	197	1	the	the	DET
ejpam-4369	197	2	proof	proof	NOUN
ejpam-4369	197	3	is	be	AUX
ejpam-4369	197	4	similar	similar	ADJ
ejpam-4369	197	5	to	to	ADP
ejpam-4369	197	6	that	that	PRON
ejpam-4369	197	7	of	of	ADP
ejpam-4369	197	8	theorem	theorem	NOUN
ejpam-4369	197	9	6	6	NUM
ejpam-4369	197	10	and	and	CCONJ
ejpam-4369	197	11	it	it	PRON
ejpam-4369	197	12	follows	follow	VERB
ejpam-4369	197	13	from	from	ADP
ejpam-4369	197	14	theorem	theorem	ADJ
ejpam-4369	197	15	2	2	NUM
ejpam-4369	197	16	and	and	CCONJ
ejpam-4369	197	17	lemma	lemma	PROPN
ejpam-4369	197	18	3	3	X
ejpam-4369	197	19	.	.	PUNCT
ejpam-4369	197	20	corollary	corollary	ADJ
ejpam-4369	197	21	3	3	NUM
ejpam-4369	197	22	.	.	PUNCT
ejpam-4369	198	1	for	for	ADP
ejpam-4369	198	2	a	a	DET
ejpam-4369	198	3	function	function	NOUN
ejpam-4369	198	4	f	f	NOUN
ejpam-4369	198	5	:	:	PUNCT
ejpam-4369	198	6	(	(	PUNCT
ejpam-4369	198	7	x	x	X
ejpam-4369	198	8	,	,	PUNCT
ejpam-4369	198	9	τ	τ	X
ejpam-4369	198	10	)	)	PUNCT
ejpam-4369	198	11	→	→	SYM
ejpam-4369	198	12	(	(	PUNCT
ejpam-4369	198	13	y	y	PROPN
ejpam-4369	198	14	,	,	PUNCT
ejpam-4369	198	15	σ	σ	PROPN
ejpam-4369	198	16	)	)	PUNCT
ejpam-4369	198	17	,	,	PUNCT
ejpam-4369	198	18	where	where	SCONJ
ejpam-4369	198	19	(	(	PUNCT
ejpam-4369	198	20	y	y	PROPN
ejpam-4369	198	21	,	,	PUNCT
ejpam-4369	198	22	σ	σ	PROPN
ejpam-4369	198	23	)	)	PUNCT
ejpam-4369	198	24	is	be	AUX
ejpam-4369	198	25	a	a	DET
ejpam-4369	198	26	λsp	λsp	ADV
ejpam-4369	198	27	-	-	PUNCT
ejpam-4369	198	28	extremally	extremally	ADV
ejpam-4369	198	29	disconnected	disconnected	ADJ
ejpam-4369	198	30	space	space	NOUN
ejpam-4369	198	31	,	,	PUNCT
ejpam-4369	198	32	the	the	DET
ejpam-4369	198	33	following	follow	VERB
ejpam-4369	198	34	properties	property	NOUN
ejpam-4369	198	35	are	be	AUX
ejpam-4369	198	36	equivalent	equivalent	ADJ
ejpam-4369	198	37	:	:	PUNCT
ejpam-4369	198	38	(	(	PUNCT
ejpam-4369	198	39	1	1	X
ejpam-4369	198	40	)	)	PUNCT
ejpam-4369	198	41	f	f	PROPN
ejpam-4369	198	42	is	be	AUX
ejpam-4369	198	43	slightly	slightly	ADV
ejpam-4369	198	44	(	(	PUNCT
ejpam-4369	198	45	λ	λ	NOUN
ejpam-4369	198	46	,	,	PUNCT
ejpam-4369	198	47	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	198	48	;	;	PUNCT
ejpam-4369	198	49	(	(	PUNCT
ejpam-4369	198	50	2	2	X
ejpam-4369	198	51	)	)	PUNCT
ejpam-4369	199	1	[	[	X
ejpam-4369	199	2	f−1(v	f−1(v	NOUN
ejpam-4369	199	3	)	)	PUNCT
ejpam-4369	199	4	]	]	PUNCT
ejpam-4369	199	5	(	(	PUNCT
ejpam-4369	199	6	λ	λ	NOUN
ejpam-4369	199	7	,	,	PUNCT
ejpam-4369	199	8	sp	sp	NOUN
ejpam-4369	199	9	)	)	PUNCT
ejpam-4369	199	10	⊆	⊆	NUM
ejpam-4369	199	11	f−1(v	f−1(v	NOUN
ejpam-4369	199	12	(	(	PUNCT
ejpam-4369	199	13	λ	λ	PROPN
ejpam-4369	199	14	,	,	PUNCT
ejpam-4369	199	15	sp	sp	NOUN
ejpam-4369	199	16	)	)	PUNCT
ejpam-4369	199	17	)	)	PUNCT
ejpam-4369	199	18	for	for	ADP
ejpam-4369	199	19	every	every	DET
ejpam-4369	199	20	p(λ	p(λ	NOUN
ejpam-4369	199	21	,	,	PUNCT
ejpam-4369	199	22	sp)-open	sp)-open	NOUN
ejpam-4369	199	23	set	set	VERB
ejpam-4369	199	24	v	v	NOUN
ejpam-4369	199	25	of	of	ADP
ejpam-4369	199	26	y	y	PROPN
ejpam-4369	199	27	;	;	PUNCT
ejpam-4369	199	28	(	(	PUNCT
ejpam-4369	199	29	3	3	X
ejpam-4369	199	30	)	)	PUNCT
ejpam-4369	199	31	f−1(k(λ	f−1(k(λ	NOUN
ejpam-4369	199	32	,	,	PUNCT
ejpam-4369	199	33	sp	sp	NOUN
ejpam-4369	199	34	)	)	PUNCT
ejpam-4369	199	35	)	)	PUNCT
ejpam-4369	199	36	⊆	⊆	NUM
ejpam-4369	199	37	[	[	X
ejpam-4369	199	38	f−1(k)](λ	f−1(k)](λ	PROPN
ejpam-4369	199	39	,	,	PUNCT
ejpam-4369	199	40	sp	sp	NOUN
ejpam-4369	199	41	)	)	PUNCT
ejpam-4369	199	42	for	for	ADP
ejpam-4369	199	43	every	every	DET
ejpam-4369	199	44	p(λ	p(λ	NOUN
ejpam-4369	199	45	,	,	PUNCT
ejpam-4369	199	46	sp)-closed	sp)-close	VERB
ejpam-4369	199	47	set	set	VERB
ejpam-4369	199	48	k	k	PROPN
ejpam-4369	199	49	of	of	ADP
ejpam-4369	199	50	y	y	PROPN
ejpam-4369	199	51	.	.	PUNCT
ejpam-4369	200	1	theorem	theorem	VERB
ejpam-4369	200	2	11	11	NUM
ejpam-4369	200	3	.	.	PUNCT
ejpam-4369	201	1	for	for	ADP
ejpam-4369	201	2	a	a	DET
ejpam-4369	201	3	multifunction	multifunction	NOUN
ejpam-4369	201	4	f	f	NOUN
ejpam-4369	201	5	:	:	PUNCT
ejpam-4369	201	6	(	(	PUNCT
ejpam-4369	201	7	x	x	X
ejpam-4369	201	8	,	,	PUNCT
ejpam-4369	201	9	τ	τ	X
ejpam-4369	201	10	)	)	PUNCT
ejpam-4369	201	11	→	→	SYM
ejpam-4369	201	12	(	(	PUNCT
ejpam-4369	201	13	y	y	PROPN
ejpam-4369	201	14	,	,	PUNCT
ejpam-4369	201	15	σ	σ	PROPN
ejpam-4369	201	16	)	)	PUNCT
ejpam-4369	201	17	,	,	PUNCT
ejpam-4369	201	18	where	where	SCONJ
ejpam-4369	201	19	(	(	PUNCT
ejpam-4369	201	20	y	y	PROPN
ejpam-4369	201	21	,	,	PUNCT
ejpam-4369	201	22	σ	σ	PROPN
ejpam-4369	201	23	)	)	PUNCT
ejpam-4369	201	24	is	be	AUX
ejpam-4369	201	25	a	a	DET
ejpam-4369	201	26	λsp	λsp	ADV
ejpam-4369	201	27	-	-	PUNCT
ejpam-4369	201	28	extremally	extremally	ADV
ejpam-4369	201	29	disconnected	disconnected	ADJ
ejpam-4369	201	30	space	space	NOUN
ejpam-4369	201	31	,	,	PUNCT
ejpam-4369	201	32	the	the	DET
ejpam-4369	201	33	following	follow	VERB
ejpam-4369	201	34	properties	property	NOUN
ejpam-4369	201	35	are	be	AUX
ejpam-4369	201	36	equivalent	equivalent	ADJ
ejpam-4369	201	37	:	:	PUNCT
ejpam-4369	201	38	(	(	PUNCT
ejpam-4369	201	39	1	1	X
ejpam-4369	201	40	)	)	PUNCT
ejpam-4369	201	41	f	f	PROPN
ejpam-4369	201	42	is	be	AUX
ejpam-4369	201	43	upper	upper	ADJ
ejpam-4369	201	44	slightly	slightly	ADV
ejpam-4369	201	45	(	(	PUNCT
ejpam-4369	201	46	λ	λ	NOUN
ejpam-4369	201	47	,	,	PUNCT
ejpam-4369	201	48	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	201	49	;	;	PUNCT
ejpam-4369	201	50	(	(	PUNCT
ejpam-4369	201	51	2	2	X
ejpam-4369	201	52	)	)	PUNCT
ejpam-4369	202	1	[	[	X
ejpam-4369	202	2	f−(v	f−(v	NOUN
ejpam-4369	202	3	)	)	PUNCT
ejpam-4369	202	4	]	]	PUNCT
ejpam-4369	202	5	(	(	PUNCT
ejpam-4369	202	6	λ	λ	NOUN
ejpam-4369	202	7	,	,	PUNCT
ejpam-4369	202	8	sp	sp	NOUN
ejpam-4369	202	9	)	)	PUNCT
ejpam-4369	202	10	⊆	⊆	NUM
ejpam-4369	202	11	f−(v	f−(v	NOUN
ejpam-4369	202	12	(	(	PUNCT
ejpam-4369	202	13	λ	λ	NOUN
ejpam-4369	202	14	,	,	PUNCT
ejpam-4369	202	15	sp	sp	NOUN
ejpam-4369	202	16	)	)	PUNCT
ejpam-4369	202	17	)	)	PUNCT
ejpam-4369	202	18	for	for	ADP
ejpam-4369	202	19	every	every	DET
ejpam-4369	202	20	β(λ	β(λ	PROPN
ejpam-4369	202	21	,	,	PUNCT
ejpam-4369	202	22	sp)-open	sp)-open	NOUN
ejpam-4369	202	23	set	set	VERB
ejpam-4369	202	24	v	v	NOUN
ejpam-4369	202	25	of	of	ADP
ejpam-4369	202	26	y	y	PROPN
ejpam-4369	202	27	;	;	PUNCT
ejpam-4369	202	28	(	(	PUNCT
ejpam-4369	202	29	3	3	X
ejpam-4369	202	30	)	)	PUNCT
ejpam-4369	202	31	f+(k(λ	f+(k(λ	NOUN
ejpam-4369	202	32	,	,	PUNCT
ejpam-4369	202	33	sp	sp	NOUN
ejpam-4369	202	34	)	)	PUNCT
ejpam-4369	202	35	)	)	PUNCT
ejpam-4369	202	36	⊆	⊆	NUM
ejpam-4369	203	1	[	[	X
ejpam-4369	203	2	f+(k)](λ	f+(k)](λ	NUM
ejpam-4369	203	3	,	,	PUNCT
ejpam-4369	203	4	sp	sp	NOUN
ejpam-4369	203	5	)	)	PUNCT
ejpam-4369	203	6	for	for	ADP
ejpam-4369	203	7	every	every	DET
ejpam-4369	203	8	β(λ	β(λ	NOUN
ejpam-4369	203	9	,	,	PUNCT
ejpam-4369	203	10	sp)-closed	sp)-close	VERB
ejpam-4369	203	11	set	set	VERB
ejpam-4369	203	12	k	k	PROPN
ejpam-4369	203	13	of	of	ADP
ejpam-4369	203	14	y	y	PROPN
ejpam-4369	203	15	.	.	PUNCT
ejpam-4369	204	1	proof	proof	NOUN
ejpam-4369	204	2	.	.	PUNCT
ejpam-4369	205	1	the	the	DET
ejpam-4369	205	2	proof	proof	NOUN
ejpam-4369	205	3	is	be	AUX
ejpam-4369	205	4	similar	similar	ADJ
ejpam-4369	205	5	to	to	ADP
ejpam-4369	205	6	that	that	PRON
ejpam-4369	205	7	of	of	ADP
ejpam-4369	205	8	theorem	theorem	NOUN
ejpam-4369	205	9	5	5	NUM
ejpam-4369	205	10	and	and	CCONJ
ejpam-4369	205	11	it	it	PRON
ejpam-4369	205	12	follows	follow	VERB
ejpam-4369	205	13	from	from	ADP
ejpam-4369	205	14	theorem	theorem	ADJ
ejpam-4369	205	15	1	1	NUM
ejpam-4369	205	16	and	and	CCONJ
ejpam-4369	205	17	lemma	lemma	PROPN
ejpam-4369	205	18	3	3	NUM
ejpam-4369	205	19	.	.	PUNCT
ejpam-4369	205	20	references	reference	NOUN
ejpam-4369	205	21	1187	1187	NUM
ejpam-4369	205	22	theorem	theorem	VERB
ejpam-4369	205	23	12	12	NUM
ejpam-4369	205	24	.	.	PUNCT
ejpam-4369	206	1	for	for	ADP
ejpam-4369	206	2	a	a	DET
ejpam-4369	206	3	multifunction	multifunction	NOUN
ejpam-4369	206	4	f	f	NOUN
ejpam-4369	206	5	:	:	PUNCT
ejpam-4369	206	6	(	(	PUNCT
ejpam-4369	206	7	x	x	X
ejpam-4369	206	8	,	,	PUNCT
ejpam-4369	206	9	τ	τ	X
ejpam-4369	206	10	)	)	PUNCT
ejpam-4369	206	11	→	→	SYM
ejpam-4369	206	12	(	(	PUNCT
ejpam-4369	206	13	y	y	PROPN
ejpam-4369	206	14	,	,	PUNCT
ejpam-4369	206	15	σ	σ	PROPN
ejpam-4369	206	16	)	)	PUNCT
ejpam-4369	206	17	,	,	PUNCT
ejpam-4369	206	18	where	where	SCONJ
ejpam-4369	206	19	(	(	PUNCT
ejpam-4369	206	20	y	y	PROPN
ejpam-4369	206	21	,	,	PUNCT
ejpam-4369	206	22	σ	σ	PROPN
ejpam-4369	206	23	)	)	PUNCT
ejpam-4369	206	24	is	be	AUX
ejpam-4369	206	25	a	a	DET
ejpam-4369	206	26	λsp	λsp	ADV
ejpam-4369	206	27	-	-	PUNCT
ejpam-4369	206	28	extremally	extremally	ADV
ejpam-4369	206	29	disconnected	disconnected	ADJ
ejpam-4369	206	30	space	space	NOUN
ejpam-4369	206	31	,	,	PUNCT
ejpam-4369	206	32	the	the	DET
ejpam-4369	206	33	following	follow	VERB
ejpam-4369	206	34	properties	property	NOUN
ejpam-4369	206	35	are	be	AUX
ejpam-4369	206	36	equivalent	equivalent	ADJ
ejpam-4369	206	37	:	:	PUNCT
ejpam-4369	206	38	(	(	PUNCT
ejpam-4369	206	39	1	1	X
ejpam-4369	206	40	)	)	PUNCT
ejpam-4369	206	41	f	f	PROPN
ejpam-4369	206	42	is	be	AUX
ejpam-4369	206	43	lower	lower	ADV
ejpam-4369	206	44	slightly	slightly	ADV
ejpam-4369	206	45	(	(	PUNCT
ejpam-4369	206	46	λ	λ	NOUN
ejpam-4369	206	47	,	,	PUNCT
ejpam-4369	206	48	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	206	49	;	;	PUNCT
ejpam-4369	206	50	(	(	PUNCT
ejpam-4369	206	51	2	2	X
ejpam-4369	206	52	)	)	PUNCT
ejpam-4369	206	53	[	[	X
ejpam-4369	206	54	f+(v	f+(v	NOUN
ejpam-4369	206	55	)	)	PUNCT
ejpam-4369	206	56	]	]	PUNCT
ejpam-4369	206	57	(	(	PUNCT
ejpam-4369	206	58	λ	λ	NOUN
ejpam-4369	206	59	,	,	PUNCT
ejpam-4369	206	60	sp	sp	NOUN
ejpam-4369	206	61	)	)	PUNCT
ejpam-4369	206	62	⊆	⊆	NUM
ejpam-4369	206	63	f+(v	f+(v	NUM
ejpam-4369	206	64	(	(	PUNCT
ejpam-4369	206	65	λ	λ	NOUN
ejpam-4369	206	66	,	,	PUNCT
ejpam-4369	206	67	sp	sp	NOUN
ejpam-4369	206	68	)	)	PUNCT
ejpam-4369	206	69	)	)	PUNCT
ejpam-4369	206	70	for	for	ADP
ejpam-4369	206	71	every	every	DET
ejpam-4369	206	72	β(λ	β(λ	PROPN
ejpam-4369	206	73	,	,	PUNCT
ejpam-4369	206	74	sp)-open	sp)-open	NOUN
ejpam-4369	206	75	set	set	VERB
ejpam-4369	206	76	v	v	NOUN
ejpam-4369	206	77	of	of	ADP
ejpam-4369	206	78	y	y	PROPN
ejpam-4369	206	79	;	;	PUNCT
ejpam-4369	206	80	(	(	PUNCT
ejpam-4369	206	81	3	3	X
ejpam-4369	206	82	)	)	PUNCT
ejpam-4369	206	83	f−(k(λ	f−(k(λ	NOUN
ejpam-4369	206	84	,	,	PUNCT
ejpam-4369	206	85	sp	sp	NOUN
ejpam-4369	206	86	)	)	PUNCT
ejpam-4369	206	87	)	)	PUNCT
ejpam-4369	207	1	⊆	⊆	NUM
ejpam-4369	207	2	[	[	X
ejpam-4369	207	3	f−(k)](λ	f−(k)](λ	PROPN
ejpam-4369	207	4	,	,	PUNCT
ejpam-4369	207	5	sp	sp	NOUN
ejpam-4369	207	6	)	)	PUNCT
ejpam-4369	207	7	for	for	ADP
ejpam-4369	207	8	every	every	DET
ejpam-4369	207	9	β(λ	β(λ	NOUN
ejpam-4369	207	10	,	,	PUNCT
ejpam-4369	207	11	sp)-closed	sp)-close	VERB
ejpam-4369	207	12	set	set	VERB
ejpam-4369	207	13	k	k	PROPN
ejpam-4369	207	14	of	of	ADP
ejpam-4369	207	15	y	y	PROPN
ejpam-4369	207	16	.	.	PUNCT
ejpam-4369	208	1	proof	proof	NOUN
ejpam-4369	208	2	.	.	PUNCT
ejpam-4369	209	1	the	the	DET
ejpam-4369	209	2	proof	proof	NOUN
ejpam-4369	209	3	is	be	AUX
ejpam-4369	209	4	similar	similar	ADJ
ejpam-4369	209	5	to	to	ADP
ejpam-4369	209	6	that	that	PRON
ejpam-4369	209	7	of	of	ADP
ejpam-4369	209	8	theorem	theorem	NOUN
ejpam-4369	209	9	6	6	NUM
ejpam-4369	209	10	and	and	CCONJ
ejpam-4369	209	11	it	it	PRON
ejpam-4369	209	12	follows	follow	VERB
ejpam-4369	209	13	from	from	ADP
ejpam-4369	209	14	theorem	theorem	ADJ
ejpam-4369	209	15	2	2	NUM
ejpam-4369	209	16	and	and	CCONJ
ejpam-4369	209	17	lemma	lemma	PROPN
ejpam-4369	209	18	3	3	X
ejpam-4369	209	19	.	.	PUNCT
ejpam-4369	209	20	corollary	corollary	ADJ
ejpam-4369	209	21	4	4	NUM
ejpam-4369	209	22	.	.	PUNCT
ejpam-4369	210	1	for	for	ADP
ejpam-4369	210	2	a	a	DET
ejpam-4369	210	3	function	function	NOUN
ejpam-4369	210	4	f	f	NOUN
ejpam-4369	210	5	:	:	PUNCT
ejpam-4369	210	6	(	(	PUNCT
ejpam-4369	210	7	x	x	X
ejpam-4369	210	8	,	,	PUNCT
ejpam-4369	210	9	τ	τ	X
ejpam-4369	210	10	)	)	PUNCT
ejpam-4369	210	11	→	→	SYM
ejpam-4369	210	12	(	(	PUNCT
ejpam-4369	210	13	y	y	PROPN
ejpam-4369	210	14	,	,	PUNCT
ejpam-4369	210	15	σ	σ	PROPN
ejpam-4369	210	16	)	)	PUNCT
ejpam-4369	210	17	,	,	PUNCT
ejpam-4369	210	18	where	where	SCONJ
ejpam-4369	210	19	(	(	PUNCT
ejpam-4369	210	20	y	y	PROPN
ejpam-4369	210	21	,	,	PUNCT
ejpam-4369	210	22	σ	σ	PROPN
ejpam-4369	210	23	)	)	PUNCT
ejpam-4369	210	24	is	be	AUX
ejpam-4369	210	25	a	a	DET
ejpam-4369	210	26	λsp	λsp	ADV
ejpam-4369	210	27	-	-	PUNCT
ejpam-4369	210	28	extremally	extremally	ADV
ejpam-4369	210	29	disconnected	disconnected	ADJ
ejpam-4369	210	30	space	space	NOUN
ejpam-4369	210	31	,	,	PUNCT
ejpam-4369	210	32	the	the	DET
ejpam-4369	210	33	following	follow	VERB
ejpam-4369	210	34	properties	property	NOUN
ejpam-4369	210	35	are	be	AUX
ejpam-4369	210	36	equivalent	equivalent	ADJ
ejpam-4369	210	37	:	:	PUNCT
ejpam-4369	210	38	(	(	PUNCT
ejpam-4369	210	39	1	1	X
ejpam-4369	210	40	)	)	PUNCT
ejpam-4369	210	41	f	f	PROPN
ejpam-4369	210	42	is	be	AUX
ejpam-4369	210	43	slightly	slightly	ADV
ejpam-4369	210	44	(	(	PUNCT
ejpam-4369	210	45	λ	λ	NOUN
ejpam-4369	210	46	,	,	PUNCT
ejpam-4369	210	47	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	210	48	;	;	PUNCT
ejpam-4369	210	49	(	(	PUNCT
ejpam-4369	210	50	2	2	X
ejpam-4369	210	51	)	)	PUNCT
ejpam-4369	211	1	[	[	X
ejpam-4369	211	2	f−1(v	f−1(v	NOUN
ejpam-4369	211	3	)	)	PUNCT
ejpam-4369	211	4	]	]	PUNCT
ejpam-4369	211	5	(	(	PUNCT
ejpam-4369	211	6	λ	λ	NOUN
ejpam-4369	211	7	,	,	PUNCT
ejpam-4369	211	8	sp	sp	NOUN
ejpam-4369	211	9	)	)	PUNCT
ejpam-4369	211	10	⊆	⊆	NUM
ejpam-4369	211	11	f−1(v	f−1(v	NOUN
ejpam-4369	211	12	(	(	PUNCT
ejpam-4369	211	13	λ	λ	PROPN
ejpam-4369	211	14	,	,	PUNCT
ejpam-4369	211	15	sp	sp	NOUN
ejpam-4369	211	16	)	)	PUNCT
ejpam-4369	211	17	)	)	PUNCT
ejpam-4369	211	18	for	for	ADP
ejpam-4369	211	19	every	every	DET
ejpam-4369	211	20	β(λ	β(λ	PROPN
ejpam-4369	211	21	,	,	PUNCT
ejpam-4369	211	22	sp)-open	sp)-open	NOUN
ejpam-4369	211	23	set	set	VERB
ejpam-4369	211	24	v	v	NOUN
ejpam-4369	211	25	of	of	ADP
ejpam-4369	211	26	y	y	PROPN
ejpam-4369	211	27	;	;	PUNCT
ejpam-4369	211	28	(	(	PUNCT
ejpam-4369	211	29	3	3	X
ejpam-4369	211	30	)	)	PUNCT
ejpam-4369	211	31	f−1(k(λ	f−1(k(λ	NOUN
ejpam-4369	211	32	,	,	PUNCT
ejpam-4369	211	33	sp	sp	NOUN
ejpam-4369	211	34	)	)	PUNCT
ejpam-4369	211	35	)	)	PUNCT
ejpam-4369	211	36	⊆	⊆	NUM
ejpam-4369	211	37	[	[	X
ejpam-4369	211	38	f−1(k)](λ	f−1(k)](λ	PROPN
ejpam-4369	211	39	,	,	PUNCT
ejpam-4369	211	40	sp	sp	NOUN
ejpam-4369	211	41	)	)	PUNCT
ejpam-4369	211	42	for	for	ADP
ejpam-4369	211	43	every	every	DET
ejpam-4369	211	44	β(λ	β(λ	NOUN
ejpam-4369	211	45	,	,	PUNCT
ejpam-4369	211	46	sp)-closed	sp)-close	VERB
ejpam-4369	211	47	set	set	VERB
ejpam-4369	211	48	k	k	PROPN
ejpam-4369	211	49	of	of	ADP
ejpam-4369	211	50	y	y	PROPN
ejpam-4369	211	51	.	.	PUNCT
ejpam-4369	212	1	4	4	X
ejpam-4369	212	2	.	.	X
ejpam-4369	212	3	conclusion	conclusion	VERB
ejpam-4369	212	4	the	the	DET
ejpam-4369	212	5	field	field	NOUN
ejpam-4369	212	6	of	of	ADP
ejpam-4369	212	7	the	the	DET
ejpam-4369	212	8	mathematical	mathematical	ADJ
ejpam-4369	212	9	science	science	NOUN
ejpam-4369	212	10	which	which	PRON
ejpam-4369	212	11	goes	go	VERB
ejpam-4369	212	12	under	under	ADP
ejpam-4369	212	13	the	the	DET
ejpam-4369	212	14	name	name	NOUN
ejpam-4369	212	15	of	of	ADP
ejpam-4369	212	16	topology	topology	NOUN
ejpam-4369	212	17	is	be	AUX
ejpam-4369	212	18	concerned	concern	VERB
ejpam-4369	212	19	with	with	ADP
ejpam-4369	212	20	all	all	DET
ejpam-4369	212	21	questions	question	NOUN
ejpam-4369	212	22	directly	directly	ADV
ejpam-4369	212	23	or	or	CCONJ
ejpam-4369	212	24	indirectly	indirectly	ADV
ejpam-4369	212	25	related	relate	VERB
ejpam-4369	212	26	to	to	ADP
ejpam-4369	212	27	continuity	continuity	NOUN
ejpam-4369	212	28	.	.	PUNCT
ejpam-4369	213	1	this	this	DET
ejpam-4369	213	2	paper	paper	NOUN
ejpam-4369	213	3	deals	deal	NOUN
ejpam-4369	213	4	with	with	ADP
ejpam-4369	213	5	the	the	DET
ejpam-4369	213	6	concepts	concept	NOUN
ejpam-4369	213	7	of	of	ADP
ejpam-4369	213	8	upper	upper	ADJ
ejpam-4369	213	9	and	and	CCONJ
ejpam-4369	213	10	lower	low	ADJ
ejpam-4369	213	11	slight	slight	ADJ
ejpam-4369	213	12	(	(	PUNCT
ejpam-4369	213	13	λ	λ	NOUN
ejpam-4369	213	14	,	,	PUNCT
ejpam-4369	213	15	sp)-continuity	sp)-continuity	NOUN
ejpam-4369	213	16	.	.	PUNCT
ejpam-4369	214	1	in	in	ADP
ejpam-4369	214	2	particular	particular	ADJ
ejpam-4369	214	3	,	,	PUNCT
ejpam-4369	214	4	some	some	DET
ejpam-4369	214	5	characterizations	characterization	NOUN
ejpam-4369	214	6	of	of	ADP
ejpam-4369	214	7	upper	upper	ADJ
ejpam-4369	214	8	and	and	CCONJ
ejpam-4369	214	9	lower	lower	ADV
ejpam-4369	214	10	slightly	slightly	ADV
ejpam-4369	214	11	(	(	PUNCT
ejpam-4369	214	12	λ	λ	NOUN
ejpam-4369	214	13	,	,	PUNCT
ejpam-4369	214	14	sp)-continuous	sp)-continuous	ADJ
ejpam-4369	214	15	multifunctions	multifunction	NOUN
ejpam-4369	214	16	are	be	AUX
ejpam-4369	214	17	obtained	obtain	VERB
ejpam-4369	214	18	.	.	PUNCT
ejpam-4369	215	1	the	the	DET
ejpam-4369	215	2	ideas	idea	NOUN
ejpam-4369	215	3	and	and	CCONJ
ejpam-4369	215	4	results	result	NOUN
ejpam-4369	215	5	of	of	ADP
ejpam-4369	215	6	this	this	DET
ejpam-4369	215	7	paper	paper	NOUN
ejpam-4369	215	8	may	may	AUX
ejpam-4369	215	9	motivate	motivate	VERB
ejpam-4369	215	10	further	further	ADJ
ejpam-4369	215	11	research	research	NOUN
ejpam-4369	215	12	.	.	PUNCT
ejpam-4369	216	1	acknowledgements	acknowledgement	NOUN
ejpam-4369	216	2	this	this	DET
ejpam-4369	216	3	research	research	NOUN
ejpam-4369	216	4	project	project	NOUN
ejpam-4369	216	5	was	be	AUX
ejpam-4369	216	6	financially	financially	ADV
ejpam-4369	216	7	supported	support	VERB
ejpam-4369	216	8	by	by	ADP
ejpam-4369	216	9	mahasarakham	mahasarakham	PROPN
ejpam-4369	216	10	university	university	PROPN
ejpam-4369	216	11	.	.	PUNCT
ejpam-4369	217	1	references	reference	NOUN
ejpam-4369	217	2	[	[	X
ejpam-4369	217	3	1	1	NUM
ejpam-4369	217	4	]	]	PUNCT
ejpam-4369	217	5	d.	d.	PROPN
ejpam-4369	217	6	andrijević.	andrijević.	PROPN
ejpam-4369	217	7	on	on	ADP
ejpam-4369	217	8	b	b	X
ejpam-4369	217	9	-	-	PUNCT
ejpam-4369	217	10	open	open	ADJ
ejpam-4369	217	11	sets	set	NOUN
ejpam-4369	217	12	.	.	PUNCT
ejpam-4369	218	1	matematički	matematički	PROPN
ejpam-4369	218	2	vesnik	vesnik	PROPN
ejpam-4369	218	3	,	,	PUNCT
ejpam-4369	218	4	48:59–64	48:59–64	PROPN
ejpam-4369	218	5	,	,	PUNCT
ejpam-4369	218	6	1996	1996	NUM
ejpam-4369	218	7	.	.	PUNCT
ejpam-4369	219	1	[	[	X
ejpam-4369	219	2	2	2	NUM
ejpam-4369	219	3	]	]	PUNCT
ejpam-4369	219	4	c.	c.	PROPN
ejpam-4369	219	5	berge	berge	PROPN
ejpam-4369	219	6	.	.	PUNCT
ejpam-4369	219	7	espaces	espace	VERB
ejpam-4369	219	8	topologiques	topologique	NOUN
ejpam-4369	219	9	fonctions	fonction	NOUN
ejpam-4369	219	10	multivoques	multivoque	NOUN
ejpam-4369	219	11	.	.	PUNCT
ejpam-4369	220	1	dunod	dunod	PROPN
ejpam-4369	220	2	,	,	PUNCT
ejpam-4369	220	3	paris	paris	PROPN
ejpam-4369	220	4	,	,	PUNCT
ejpam-4369	220	5	1959	1959	NUM
ejpam-4369	220	6	.	.	PUNCT
ejpam-4369	221	1	[	[	X
ejpam-4369	221	2	3	3	X
ejpam-4369	221	3	]	]	PUNCT
ejpam-4369	221	4	c.	c.	PROPN
ejpam-4369	221	5	boonpok	boonpok	PROPN
ejpam-4369	221	6	.	.	PUNCT
ejpam-4369	222	1	(	(	PUNCT
ejpam-4369	222	2	λ	λ	NOUN
ejpam-4369	222	3	,	,	PUNCT
ejpam-4369	222	4	sp)-closed	sp)-close	VERB
ejpam-4369	222	5	sets	set	NOUN
ejpam-4369	222	6	and	and	CCONJ
ejpam-4369	222	7	related	related	ADJ
ejpam-4369	222	8	topics	topic	NOUN
ejpam-4369	222	9	in	in	ADP
ejpam-4369	222	10	topological	topological	ADJ
ejpam-4369	222	11	spaces	space	NOUN
ejpam-4369	222	12	.	.	PUNCT
ejpam-4369	223	1	wseas	wseas	VERB
ejpam-4369	223	2	transactions	transaction	NOUN
ejpam-4369	223	3	on	on	ADP
ejpam-4369	223	4	mathematics	mathematic	NOUN
ejpam-4369	223	5	,	,	PUNCT
ejpam-4369	223	6	19:321–322	19:321–322	PROPN
ejpam-4369	223	7	,	,	PUNCT
ejpam-4369	223	8	2020	2020	NUM
ejpam-4369	223	9	.	.	PUNCT
ejpam-4369	224	1	[	[	X
ejpam-4369	224	2	4	4	NUM
ejpam-4369	224	3	]	]	PUNCT
ejpam-4369	224	4	c.	c.	PROPN
ejpam-4369	224	5	boonpok	boonpok	PROPN
ejpam-4369	224	6	and	and	CCONJ
ejpam-4369	224	7	j.	j.	PROPN
ejpam-4369	224	8	khampakdee	khampakdee	PROPN
ejpam-4369	224	9	.	.	PUNCT
ejpam-4369	225	1	(	(	PUNCT
ejpam-4369	225	2	λ	λ	NOUN
ejpam-4369	225	3	,	,	PUNCT
ejpam-4369	225	4	sp)-open	sp)-open	ADJ
ejpam-4369	225	5	sets	set	NOUN
ejpam-4369	225	6	in	in	ADP
ejpam-4369	225	7	topological	topological	ADJ
ejpam-4369	225	8	spaces	space	NOUN
ejpam-4369	225	9	.	.	PUNCT
ejpam-4369	226	1	european	european	ADJ
ejpam-4369	226	2	journal	journal	PROPN
ejpam-4369	226	3	of	of	ADP
ejpam-4369	226	4	pure	pure	ADJ
ejpam-4369	226	5	and	and	CCONJ
ejpam-4369	226	6	applied	applied	ADJ
ejpam-4369	226	7	mathematics	mathematic	NOUN
ejpam-4369	226	8	,	,	PUNCT
ejpam-4369	226	9	15(2):572–588	15(2):572–588	NUM
ejpam-4369	226	10	,	,	PUNCT
ejpam-4369	226	11	2022	2022	NUM
ejpam-4369	226	12	.	.	PUNCT
ejpam-4369	227	1	[	[	X
ejpam-4369	227	2	5	5	NUM
ejpam-4369	227	3	]	]	PUNCT
ejpam-4369	227	4	m.	m.	NOUN
ejpam-4369	227	5	e.	e.	PROPN
ejpam-4369	227	6	abd	abd	PROPN
ejpam-4369	228	1	el	el	PROPN
ejpam-4369	228	2	-	-	PROPN
ejpam-4369	228	3	monsef	monsef	PROPN
ejpam-4369	228	4	,	,	PUNCT
ejpam-4369	228	5	s.	s.	PROPN
ejpam-4369	228	6	n.	n.	PROPN
ejpam-4369	228	7	el	el	PROPN
ejpam-4369	228	8	-	-	PROPN
ejpam-4369	228	9	deeb	deeb	PROPN
ejpam-4369	228	10	,	,	PUNCT
ejpam-4369	228	11	and	and	CCONJ
ejpam-4369	228	12	r.	r.	PROPN
ejpam-4369	228	13	a.	a.	PROPN
ejpam-4369	228	14	mahmoud	mahmoud	PROPN
ejpam-4369	228	15	.	.	PUNCT
ejpam-4369	229	1	β	β	X
ejpam-4369	229	2	-	-	ADJ
ejpam-4369	229	3	open	open	ADJ
ejpam-4369	229	4	sets	set	NOUN
ejpam-4369	229	5	and	and	CCONJ
ejpam-4369	229	6	βcontinuous	βcontinuous	ADJ
ejpam-4369	229	7	mappings	mapping	NOUN
ejpam-4369	229	8	.	.	PUNCT
ejpam-4369	230	1	bulletin	bulletin	NOUN
ejpam-4369	230	2	of	of	ADP
ejpam-4369	230	3	the	the	DET
ejpam-4369	230	4	faculty	faculty	NOUN
ejpam-4369	230	5	of	of	ADP
ejpam-4369	230	6	science	science	NOUN
ejpam-4369	230	7	.	.	PUNCT
ejpam-4369	231	1	assiut	assiut	PROPN
ejpam-4369	231	2	university	university	PROPN
ejpam-4369	231	3	.	.	PUNCT
ejpam-4369	231	4	,	,	PUNCT
ejpam-4369	231	5	12:77–90	12:77–90	NUM
ejpam-4369	231	6	,	,	PUNCT
ejpam-4369	231	7	1983	1983	NUM
ejpam-4369	231	8	.	.	PUNCT
ejpam-4369	232	1	references	reference	NOUN
ejpam-4369	232	2	1188	1188	NUM
ejpam-4369	232	3	[	[	X
ejpam-4369	232	4	6	6	NUM
ejpam-4369	232	5	]	]	PUNCT
ejpam-4369	232	6	r.	r.	PROPN
ejpam-4369	232	7	c.	c.	PROPN
ejpam-4369	232	8	jain	jain	PROPN
ejpam-4369	232	9	.	.	PUNCT
ejpam-4369	233	1	the	the	DET
ejpam-4369	233	2	role	role	NOUN
ejpam-4369	233	3	of	of	ADP
ejpam-4369	233	4	regularly	regularly	ADV
ejpam-4369	233	5	open	open	ADJ
ejpam-4369	233	6	sets	set	NOUN
ejpam-4369	233	7	in	in	ADP
ejpam-4369	233	8	general	general	ADJ
ejpam-4369	233	9	topology	topology	NOUN
ejpam-4369	233	10	.	.	PUNCT
ejpam-4369	234	1	ph.d	ph.d	PROPN
ejpam-4369	234	2	.	.	PUNCT
ejpam-4369	235	1	thesis	thesis	PROPN
ejpam-4369	235	2	,	,	PUNCT
ejpam-4369	235	3	meerut	meerut	PROPN
ejpam-4369	235	4	university	university	PROPN
ejpam-4369	235	5	,	,	PUNCT
ejpam-4369	235	6	meerut	meerut	PROPN
ejpam-4369	235	7	,	,	PUNCT
ejpam-4369	235	8	1980	1980	NUM
ejpam-4369	235	9	.	.	PUNCT
ejpam-4369	236	1	[	[	X
ejpam-4369	236	2	7	7	X
ejpam-4369	236	3	]	]	PUNCT
ejpam-4369	236	4	t.	t.	PROPN
ejpam-4369	236	5	noiri	noiri	PROPN
ejpam-4369	236	6	.	.	PUNCT
ejpam-4369	237	1	on	on	ADP
ejpam-4369	237	2	slightly	slightly	ADV
ejpam-4369	237	3	β	β	ADJ
ejpam-4369	237	4	-	-	ADJ
ejpam-4369	237	5	continuous	continuous	ADJ
ejpam-4369	237	6	functions	function	NOUN
ejpam-4369	237	7	.	.	PUNCT
ejpam-4369	238	1	international	international	ADJ
ejpam-4369	238	2	journal	journal	PROPN
ejpam-4369	238	3	of	of	ADP
ejpam-4369	238	4	mathematics	mathematics	PROPN
ejpam-4369	238	5	and	and	CCONJ
ejpam-4369	238	6	mathematical	mathematical	ADJ
ejpam-4369	238	7	sciences	science	NOUN
ejpam-4369	238	8	,	,	PUNCT
ejpam-4369	238	9	28:469–478	28:469–478	NUM
ejpam-4369	238	10	,	,	PUNCT
ejpam-4369	238	11	2001	2001	NUM
ejpam-4369	238	12	.	.	PUNCT
ejpam-4369	239	1	[	[	X
ejpam-4369	239	2	8	8	X
ejpam-4369	239	3	]	]	PUNCT
ejpam-4369	239	4	t.	t.	PROPN
ejpam-4369	239	5	noiri	noiri	PROPN
ejpam-4369	239	6	and	and	CCONJ
ejpam-4369	239	7	g.	g.	PROPN
ejpam-4369	239	8	i.	i.	PROPN
ejpam-4369	239	9	chae	chae	PROPN
ejpam-4369	239	10	.	.	PUNCT
ejpam-4369	240	1	a	a	DET
ejpam-4369	240	2	note	note	NOUN
ejpam-4369	240	3	on	on	ADP
ejpam-4369	240	4	slightly	slightly	ADV
ejpam-4369	240	5	semi	semi	ADJ
ejpam-4369	240	6	-	-	ADJ
ejpam-4369	240	7	continuous	continuous	ADJ
ejpam-4369	240	8	functions	function	NOUN
ejpam-4369	240	9	.	.	PUNCT
ejpam-4369	241	1	bulletin	bulletin	NOUN
ejpam-4369	241	2	of	of	ADP
ejpam-4369	241	3	the	the	DET
ejpam-4369	241	4	calcutta	calcutta	PROPN
ejpam-4369	241	5	mathematical	mathematical	ADJ
ejpam-4369	241	6	society	society	NOUN
ejpam-4369	241	7	,	,	PUNCT
ejpam-4369	241	8	92:87–92	92:87–92	PROPN
ejpam-4369	241	9	,	,	PUNCT
ejpam-4369	241	10	2000	2000	NUM
ejpam-4369	241	11	.	.	PUNCT
ejpam-4369	242	1	[	[	X
ejpam-4369	242	2	9	9	NUM
ejpam-4369	242	3	]	]	PUNCT
ejpam-4369	242	4	t.	t.	PROPN
ejpam-4369	242	5	noiri	noiri	PROPN
ejpam-4369	242	6	and	and	CCONJ
ejpam-4369	242	7	e.	e.	PROPN
ejpam-4369	242	8	hatir	hatir	PROPN
ejpam-4369	242	9	.	.	PUNCT
ejpam-4369	243	1	λsp	λsp	NOUN
ejpam-4369	243	2	-	-	PUNCT
ejpam-4369	243	3	sets	set	NOUN
ejpam-4369	243	4	and	and	CCONJ
ejpam-4369	243	5	some	some	DET
ejpam-4369	243	6	weak	weak	ADJ
ejpam-4369	243	7	separation	separation	NOUN
ejpam-4369	243	8	axioms	axiom	NOUN
ejpam-4369	243	9	.	.	PUNCT
ejpam-4369	244	1	acta	acta	PROPN
ejpam-4369	244	2	mathematica	mathematica	PROPN
ejpam-4369	244	3	hungarica	hungarica	PROPN
ejpam-4369	244	4	,	,	PUNCT
ejpam-4369	244	5	103(3):225–232	103(3):225–232	NUM
ejpam-4369	244	6	,	,	PUNCT
ejpam-4369	244	7	2004	2004	NUM
ejpam-4369	244	8	.	.	PUNCT
ejpam-4369	245	1	[	[	X
ejpam-4369	245	2	10	10	NUM
ejpam-4369	245	3	]	]	PUNCT
ejpam-4369	245	4	t.	t.	PROPN
ejpam-4369	245	5	noiri	noiri	PROPN
ejpam-4369	245	6	and	and	CCONJ
ejpam-4369	245	7	v.	v.	ADP
ejpam-4369	245	8	popa	popa	NOUN
ejpam-4369	245	9	.	.	PUNCT
ejpam-4369	246	1	slightly	slightly	ADV
ejpam-4369	246	2	m	m	ADJ
ejpam-4369	246	3	-	-	ADJ
ejpam-4369	246	4	continuous	continuous	ADJ
ejpam-4369	246	5	multifunctions	multifunction	NOUN
ejpam-4369	246	6	.	.	PUNCT
ejpam-4369	247	1	bulletin	bulletin	NOUN
ejpam-4369	247	2	of	of	ADP
ejpam-4369	247	3	the	the	DET
ejpam-4369	247	4	institute	institute	PROPN
ejpam-4369	247	5	of	of	ADP
ejpam-4369	247	6	mathematics	mathematics	PROPN
ejpam-4369	247	7	academia	academia	PROPN
ejpam-4369	247	8	sinica	sinica	PROPN
ejpam-4369	247	9	(	(	PUNCT
ejpam-4369	247	10	new	new	ADJ
ejpam-4369	247	11	series	series	NOUN
ejpam-4369	247	12	)	)	PUNCT
ejpam-4369	247	13	,	,	PUNCT
ejpam-4369	247	14	1(4):485–501	1(4):485–501	NUM
ejpam-4369	247	15	,	,	PUNCT
ejpam-4369	247	16	2006	2006	NUM
ejpam-4369	247	17	.	.	PUNCT
ejpam-4369	248	1	[	[	X
ejpam-4369	248	2	11	11	NUM
ejpam-4369	248	3	]	]	PUNCT
ejpam-4369	248	4	t.	t.	PROPN
ejpam-4369	248	5	m.	m.	PROPN
ejpam-4369	248	6	nour	nour	PROPN
ejpam-4369	248	7	.	.	PUNCT
ejpam-4369	249	1	slightly	slightly	ADV
ejpam-4369	249	2	semi	semi	ADJ
ejpam-4369	249	3	-	-	ADJ
ejpam-4369	249	4	continuous	continuous	ADJ
ejpam-4369	249	5	functions	function	NOUN
ejpam-4369	249	6	.	.	PUNCT
ejpam-4369	250	1	bulletin	bulletin	NOUN
ejpam-4369	250	2	of	of	ADP
ejpam-4369	250	3	the	the	DET
ejpam-4369	250	4	calcutta	calcutta	PROPN
ejpam-4369	250	5	mathematical	mathematical	ADJ
ejpam-4369	250	6	society	society	NOUN
ejpam-4369	250	7	,	,	PUNCT
ejpam-4369	250	8	87:187–190	87:187–190	NUM
ejpam-4369	250	9	,	,	PUNCT
ejpam-4369	250	10	1995	1995	NUM
ejpam-4369	250	11	.	.	PUNCT
ejpam-4369	251	1	[	[	X
ejpam-4369	251	2	12	12	NUM
ejpam-4369	251	3	]	]	PUNCT
ejpam-4369	251	4	m.	m.	NOUN
ejpam-4369	251	5	c.	c.	PROPN
ejpam-4369	251	6	pal	pal	PROPN
ejpam-4369	251	7	and	and	CCONJ
ejpam-4369	251	8	p.	p.	PROPN
ejpam-4369	251	9	bhattacharya	bhattacharya	PROPN
ejpam-4369	251	10	.	.	PUNCT
ejpam-4369	252	1	faint	faint	ADJ
ejpam-4369	252	2	precontinuous	precontinuous	ADJ
ejpam-4369	252	3	functions	function	NOUN
ejpam-4369	252	4	.	.	PUNCT
ejpam-4369	253	1	soochow	soochow	PROPN
ejpam-4369	253	2	journal	journal	PROPN
ejpam-4369	253	3	of	of	ADP
ejpam-4369	253	4	mathematics	mathematic	NOUN
ejpam-4369	253	5	,	,	PUNCT
ejpam-4369	253	6	21:273–289	21:273–289	NUM
ejpam-4369	253	7	,	,	PUNCT
ejpam-4369	253	8	1995	1995	NUM
ejpam-4369	253	9	.	.	PUNCT
ejpam-4369	254	1	[	[	X
ejpam-4369	254	2	13	13	NUM
ejpam-4369	254	3	]	]	PUNCT
ejpam-4369	254	4	v.	v.	PROPN
ejpam-4369	254	5	i.	i.	PROPN
ejpam-4369	254	6	ponomarev	ponomarev	PROPN
ejpam-4369	254	7	.	.	PUNCT
ejpam-4369	255	1	properties	property	NOUN
ejpam-4369	255	2	of	of	ADP
ejpam-4369	255	3	topological	topological	ADJ
ejpam-4369	255	4	spaces	space	NOUN
ejpam-4369	255	5	preserved	preserve	VERB
ejpam-4369	255	6	under	under	ADP
ejpam-4369	255	7	multivalued	multivalued	ADJ
ejpam-4369	255	8	continuous	continuous	ADJ
ejpam-4369	255	9	mapping	mapping	NOUN
ejpam-4369	255	10	on	on	ADP
ejpam-4369	255	11	compacta	compacta	NOUN
ejpam-4369	255	12	.	.	PUNCT
ejpam-4369	256	1	american	american	PROPN
ejpam-4369	256	2	mathematical	mathematical	ADJ
ejpam-4369	256	3	society	society	NOUN
ejpam-4369	256	4	translations	translation	NOUN
ejpam-4369	256	5	,	,	PUNCT
ejpam-4369	256	6	38(2):119	38(2):119	NUM
ejpam-4369	256	7	–	–	PUNCT
ejpam-4369	256	8	140	140	NUM
ejpam-4369	256	9	,	,	PUNCT
ejpam-4369	256	10	1964	1964	NUM
ejpam-4369	256	11	.	.	PUNCT
ejpam-4369	257	1	[	[	X
ejpam-4369	257	2	14	14	NUM
ejpam-4369	257	3	]	]	PUNCT
ejpam-4369	257	4	v.	v.	CCONJ
ejpam-4369	257	5	popa	popa	NOUN
ejpam-4369	257	6	and	and	CCONJ
ejpam-4369	257	7	t.	t.	PROPN
ejpam-4369	257	8	noiri	noiri	PROPN
ejpam-4369	257	9	.	.	PUNCT
ejpam-4369	258	1	slightly	slightly	ADV
ejpam-4369	258	2	m	m	ADJ
ejpam-4369	258	3	-	-	ADJ
ejpam-4369	258	4	continuous	continuous	ADJ
ejpam-4369	258	5	functions	function	NOUN
ejpam-4369	258	6	.	.	PUNCT
ejpam-4369	259	1	radovi	radovi	PROPN
ejpam-4369	259	2	matematički	matematički	PROPN
ejpam-4369	259	3	,	,	PUNCT
ejpam-4369	259	4	10:1–14	10:1–14	NUM
ejpam-4369	259	5	,	,	PUNCT
ejpam-4369	259	6	2001	2001	NUM
ejpam-4369	259	7	.	.	PUNCT