id	sid	tid	token	lemma	pos
ejpam-5192	1	1	european	european	PROPN
ejpam-5192	1	2	journal	journal	PROPN
ejpam-5192	1	3	of	of	ADP
ejpam-5192	1	4	pure	pure	ADJ
ejpam-5192	1	5	and	and	CCONJ
ejpam-5192	1	6	applied	apply	VERB
ejpam-5192	1	7	mathematics	mathematic	NOUN
ejpam-5192	1	8	vol	vol	NOUN
ejpam-5192	1	9	.	.	PROPN
ejpam-5192	2	1	17	17	NUM
ejpam-5192	2	2	,	,	PUNCT
ejpam-5192	2	3	no	no	INTJ
ejpam-5192	2	4	.	.	NOUN
ejpam-5192	2	5	2	2	NUM
ejpam-5192	2	6	,	,	PUNCT
ejpam-5192	2	7	2024	2024	NUM
ejpam-5192	2	8	,	,	PUNCT
ejpam-5192	2	9	1244	1244	NUM
ejpam-5192	2	10	-	-	SYM
ejpam-5192	2	11	1253	1253	NUM
ejpam-5192	2	12	issn	issn	PROPN
ejpam-5192	2	13	1307	1307	NUM
ejpam-5192	2	14	-	-	SYM
ejpam-5192	2	15	5543	5543	NUM
ejpam-5192	2	16	–	–	PUNCT
ejpam-5192	3	1	ejpam.com	ejpam.com	X
ejpam-5192	3	2	published	publish	VERB
ejpam-5192	3	3	by	by	ADP
ejpam-5192	3	4	new	new	PROPN
ejpam-5192	3	5	york	york	PROPN
ejpam-5192	3	6	business	business	PROPN
ejpam-5192	3	7	global	global	PROPN
ejpam-5192	3	8	upper	upper	ADJ
ejpam-5192	3	9	and	and	CCONJ
ejpam-5192	3	10	lower	low	ADJ
ejpam-5192	3	11	almost	almost	ADV
ejpam-5192	3	12	(	(	PUNCT
ejpam-5192	3	13	τ1	τ1	NOUN
ejpam-5192	3	14	,	,	PUNCT
ejpam-5192	3	15	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	3	16	multifunctions	multifunction	NOUN
ejpam-5192	3	17	chalongchai	chalongchai	PROPN
ejpam-5192	3	18	klanarong1	klanarong1	PROPN
ejpam-5192	3	19	,	,	PUNCT
ejpam-5192	3	20	supannee	supannee	PROPN
ejpam-5192	3	21	sompong2	sompong2	PROPN
ejpam-5192	3	22	,	,	PUNCT
ejpam-5192	3	23	chawalit	chawalit	VERB
ejpam-5192	3	24	boonpok1,∗	boonpok1,∗	NOUN
ejpam-5192	3	25	1	1	NUM
ejpam-5192	3	26	mathematics	mathematic	NOUN
ejpam-5192	3	27	and	and	CCONJ
ejpam-5192	3	28	applied	apply	VERB
ejpam-5192	3	29	mathematics	mathematics	PROPN
ejpam-5192	3	30	research	research	NOUN
ejpam-5192	3	31	unit	unit	NOUN
ejpam-5192	3	32	,	,	PUNCT
ejpam-5192	3	33	department	department	NOUN
ejpam-5192	3	34	of	of	ADP
ejpam-5192	3	35	mathematics	mathematic	NOUN
ejpam-5192	3	36	,	,	PUNCT
ejpam-5192	3	37	faculty	faculty	NOUN
ejpam-5192	3	38	of	of	ADP
ejpam-5192	3	39	science	science	NOUN
ejpam-5192	3	40	,	,	PUNCT
ejpam-5192	3	41	mahasarakham	mahasarakham	PROPN
ejpam-5192	3	42	university	university	PROPN
ejpam-5192	3	43	,	,	PUNCT
ejpam-5192	3	44	maha	maha	PROPN
ejpam-5192	3	45	sarakham	sarakham	PROPN
ejpam-5192	3	46	,	,	PUNCT
ejpam-5192	3	47	44150	44150	NUM
ejpam-5192	3	48	,	,	PUNCT
ejpam-5192	3	49	thailand	thailand	PROPN
ejpam-5192	3	50	2	2	NUM
ejpam-5192	3	51	department	department	NOUN
ejpam-5192	3	52	of	of	ADP
ejpam-5192	3	53	mathematics	mathematic	NOUN
ejpam-5192	3	54	and	and	CCONJ
ejpam-5192	3	55	statistics	statistic	NOUN
ejpam-5192	3	56	,	,	PUNCT
ejpam-5192	3	57	faculty	faculty	NOUN
ejpam-5192	3	58	of	of	ADP
ejpam-5192	3	59	science	science	NOUN
ejpam-5192	3	60	and	and	CCONJ
ejpam-5192	3	61	technology	technology	NOUN
ejpam-5192	3	62	,	,	PUNCT
ejpam-5192	3	63	sakon	sakon	PROPN
ejpam-5192	3	64	nakhon	nakhon	PROPN
ejpam-5192	3	65	rajbhat	rajbhat	PROPN
ejpam-5192	3	66	university	university	PROPN
ejpam-5192	3	67	,	,	PUNCT
ejpam-5192	3	68	sakon	sakon	PROPN
ejpam-5192	3	69	nakhon	nakhon	PROPN
ejpam-5192	3	70	,	,	PUNCT
ejpam-5192	3	71	47000	47000	NUM
ejpam-5192	3	72	,	,	PUNCT
ejpam-5192	3	73	thailand	thailand	PROPN
ejpam-5192	3	74	abstract	abstract	NOUN
ejpam-5192	3	75	.	.	PUNCT
ejpam-5192	4	1	this	this	DET
ejpam-5192	4	2	paper	paper	NOUN
ejpam-5192	4	3	is	be	AUX
ejpam-5192	4	4	concerned	concern	VERB
ejpam-5192	4	5	with	with	ADP
ejpam-5192	4	6	the	the	DET
ejpam-5192	4	7	concepts	concept	NOUN
ejpam-5192	4	8	of	of	ADP
ejpam-5192	4	9	upper	upper	ADJ
ejpam-5192	4	10	and	and	CCONJ
ejpam-5192	4	11	lower	low	ADJ
ejpam-5192	4	12	almost	almost	ADV
ejpam-5192	4	13	(	(	PUNCT
ejpam-5192	4	14	τ1	τ1	NOUN
ejpam-5192	4	15	,	,	PUNCT
ejpam-5192	4	16	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	4	17	multifunctions	multifunction	NOUN
ejpam-5192	4	18	.	.	PUNCT
ejpam-5192	5	1	furthermore	furthermore	ADV
ejpam-5192	5	2	,	,	PUNCT
ejpam-5192	5	3	some	some	DET
ejpam-5192	5	4	characterizations	characterization	NOUN
ejpam-5192	5	5	of	of	ADP
ejpam-5192	5	6	upper	upper	ADJ
ejpam-5192	5	7	and	and	CCONJ
ejpam-5192	5	8	lower	low	ADJ
ejpam-5192	5	9	almost	almost	ADV
ejpam-5192	5	10	(	(	PUNCT
ejpam-5192	5	11	τ1	τ1	NOUN
ejpam-5192	5	12	,	,	PUNCT
ejpam-5192	5	13	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	5	14	multifunctions	multifunction	NOUN
ejpam-5192	5	15	are	be	AUX
ejpam-5192	5	16	investigated	investigate	VERB
ejpam-5192	5	17	.	.	PUNCT
ejpam-5192	6	1	2020	2020	NUM
ejpam-5192	6	2	mathematics	mathematic	NOUN
ejpam-5192	6	3	subject	subject	NOUN
ejpam-5192	6	4	classifications	classification	NOUN
ejpam-5192	6	5	:	:	PUNCT
ejpam-5192	6	6	54c08	54c08	NUM
ejpam-5192	6	7	,	,	PUNCT
ejpam-5192	6	8	54c60	54c60	NUM
ejpam-5192	6	9	,	,	PUNCT
ejpam-5192	6	10	54e55	54e55	NUM
ejpam-5192	6	11	key	key	ADJ
ejpam-5192	6	12	words	word	NOUN
ejpam-5192	6	13	and	and	CCONJ
ejpam-5192	6	14	phrases	phrase	NOUN
ejpam-5192	6	15	:	:	PUNCT
ejpam-5192	6	16	upper	upper	ADJ
ejpam-5192	6	17	almost	almost	ADV
ejpam-5192	6	18	(	(	PUNCT
ejpam-5192	6	19	τ1	τ1	NOUN
ejpam-5192	6	20	,	,	PUNCT
ejpam-5192	6	21	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	6	22	multifunction	multifunction	NOUN
ejpam-5192	6	23	;	;	PUNCT
ejpam-5192	6	24	lower	low	ADJ
ejpam-5192	6	25	almost	almost	ADV
ejpam-5192	6	26	(	(	PUNCT
ejpam-5192	6	27	τ1	τ1	NOUN
ejpam-5192	6	28	,	,	PUNCT
ejpam-5192	6	29	τ2)continuous	τ2)continuous	ADJ
ejpam-5192	6	30	multifunction	multifunction	NOUN
ejpam-5192	6	31	1	1	NUM
ejpam-5192	6	32	.	.	PUNCT
ejpam-5192	7	1	introduction	introduction	NOUN
ejpam-5192	7	2	it	it	PRON
ejpam-5192	7	3	is	be	AUX
ejpam-5192	7	4	well	well	ADV
ejpam-5192	7	5	-	-	PUNCT
ejpam-5192	7	6	known	know	VERB
ejpam-5192	7	7	that	that	SCONJ
ejpam-5192	7	8	the	the	DET
ejpam-5192	7	9	branch	branch	NOUN
ejpam-5192	7	10	of	of	ADP
ejpam-5192	7	11	mathematics	mathematic	NOUN
ejpam-5192	7	12	called	call	VERB
ejpam-5192	7	13	topology	topology	NOUN
ejpam-5192	7	14	is	be	AUX
ejpam-5192	7	15	related	relate	VERB
ejpam-5192	7	16	to	to	ADP
ejpam-5192	7	17	all	all	DET
ejpam-5192	7	18	questions	question	NOUN
ejpam-5192	7	19	directly	directly	ADV
ejpam-5192	7	20	or	or	CCONJ
ejpam-5192	7	21	indirectly	indirectly	ADV
ejpam-5192	7	22	concerned	concerned	ADJ
ejpam-5192	7	23	with	with	ADP
ejpam-5192	7	24	continuity	continuity	NOUN
ejpam-5192	7	25	.	.	PUNCT
ejpam-5192	8	1	semi	semi	ADJ
ejpam-5192	8	2	-	-	ADJ
ejpam-5192	8	3	open	open	ADJ
ejpam-5192	8	4	sets	set	NOUN
ejpam-5192	8	5	,	,	PUNCT
ejpam-5192	8	6	preopen	preopen	ADJ
ejpam-5192	8	7	sets	set	NOUN
ejpam-5192	8	8	,	,	PUNCT
ejpam-5192	8	9	α	α	NOUN
ejpam-5192	8	10	-	-	ADJ
ejpam-5192	8	11	open	open	ADJ
ejpam-5192	8	12	sets	set	NOUN
ejpam-5192	8	13	,	,	PUNCT
ejpam-5192	8	14	β	β	ADJ
ejpam-5192	8	15	-	-	ADJ
ejpam-5192	8	16	open	open	ADJ
ejpam-5192	8	17	sets	set	NOUN
ejpam-5192	8	18	and	and	CCONJ
ejpam-5192	8	19	δ	δ	NOUN
ejpam-5192	8	20	-	-	PUNCT
ejpam-5192	8	21	open	open	ADJ
ejpam-5192	8	22	sets	set	NOUN
ejpam-5192	8	23	play	play	VERB
ejpam-5192	8	24	an	an	DET
ejpam-5192	8	25	important	important	ADJ
ejpam-5192	8	26	role	role	NOUN
ejpam-5192	8	27	in	in	ADP
ejpam-5192	8	28	the	the	DET
ejpam-5192	8	29	researches	research	NOUN
ejpam-5192	8	30	of	of	ADP
ejpam-5192	8	31	generalizations	generalization	NOUN
ejpam-5192	8	32	of	of	ADP
ejpam-5192	8	33	continuity	continuity	NOUN
ejpam-5192	8	34	in	in	ADP
ejpam-5192	8	35	topological	topological	ADJ
ejpam-5192	8	36	spaces	space	NOUN
ejpam-5192	8	37	.	.	PUNCT
ejpam-5192	9	1	by	by	ADP
ejpam-5192	9	2	using	use	VERB
ejpam-5192	9	3	these	these	DET
ejpam-5192	9	4	sets	set	NOUN
ejpam-5192	9	5	many	many	ADJ
ejpam-5192	9	6	authors	author	NOUN
ejpam-5192	9	7	introduced	introduce	VERB
ejpam-5192	9	8	and	and	CCONJ
ejpam-5192	9	9	studied	study	VERB
ejpam-5192	9	10	various	various	ADJ
ejpam-5192	9	11	types	type	NOUN
ejpam-5192	9	12	of	of	ADP
ejpam-5192	9	13	weak	weak	ADJ
ejpam-5192	9	14	forms	form	NOUN
ejpam-5192	9	15	of	of	ADP
ejpam-5192	9	16	continuity	continuity	NOUN
ejpam-5192	9	17	for	for	ADP
ejpam-5192	9	18	functions	function	NOUN
ejpam-5192	9	19	and	and	CCONJ
ejpam-5192	9	20	multifunctions	multifunction	NOUN
ejpam-5192	9	21	.	.	PUNCT
ejpam-5192	10	1	singal	singal	ADJ
ejpam-5192	10	2	and	and	CCONJ
ejpam-5192	10	3	singal	singal	ADJ
ejpam-5192	10	4	[	[	X
ejpam-5192	10	5	28	28	NUM
ejpam-5192	10	6	]	]	PUNCT
ejpam-5192	10	7	introduced	introduce	VERB
ejpam-5192	10	8	the	the	DET
ejpam-5192	10	9	concept	concept	NOUN
ejpam-5192	10	10	of	of	ADP
ejpam-5192	10	11	almost	almost	ADV
ejpam-5192	10	12	continuous	continuous	ADJ
ejpam-5192	10	13	functions	function	NOUN
ejpam-5192	10	14	as	as	ADP
ejpam-5192	10	15	a	a	DET
ejpam-5192	10	16	generalization	generalization	NOUN
ejpam-5192	10	17	of	of	ADP
ejpam-5192	10	18	continuity	continuity	NOUN
ejpam-5192	10	19	.	.	PUNCT
ejpam-5192	11	1	munshi	munshi	PROPN
ejpam-5192	11	2	and	and	CCONJ
ejpam-5192	11	3	bassan	bassan	NOUN
ejpam-5192	11	4	[	[	X
ejpam-5192	11	5	16	16	NUM
ejpam-5192	11	6	]	]	PUNCT
ejpam-5192	11	7	studied	study	VERB
ejpam-5192	11	8	the	the	DET
ejpam-5192	11	9	notion	notion	NOUN
ejpam-5192	11	10	of	of	ADP
ejpam-5192	11	11	almost	almost	ADV
ejpam-5192	11	12	semi	semi	ADJ
ejpam-5192	11	13	-	-	ADJ
ejpam-5192	11	14	continuous	continuous	ADJ
ejpam-5192	11	15	functions	function	NOUN
ejpam-5192	11	16	.	.	PUNCT
ejpam-5192	12	1	noiri	noiri	PROPN
ejpam-5192	13	1	[	[	X
ejpam-5192	13	2	18	18	NUM
ejpam-5192	13	3	]	]	PUNCT
ejpam-5192	13	4	introduced	introduce	VERB
ejpam-5192	13	5	and	and	CCONJ
ejpam-5192	13	6	investigated	investigate	VERB
ejpam-5192	13	7	the	the	DET
ejpam-5192	13	8	concept	concept	NOUN
ejpam-5192	13	9	of	of	ADP
ejpam-5192	13	10	almost	almost	ADV
ejpam-5192	13	11	α	α	NUM
ejpam-5192	13	12	-	-	ADJ
ejpam-5192	13	13	continuous	continuous	ADJ
ejpam-5192	13	14	functions	function	NOUN
ejpam-5192	13	15	.	.	PUNCT
ejpam-5192	14	1	nasef	nasef	NOUN
ejpam-5192	14	2	and	and	CCONJ
ejpam-5192	14	3	noiri	noiri	ADV
ejpam-5192	15	1	[	[	X
ejpam-5192	15	2	17	17	NUM
ejpam-5192	15	3	]	]	PUNCT
ejpam-5192	15	4	introduced	introduce	VERB
ejpam-5192	15	5	two	two	NUM
ejpam-5192	15	6	classes	class	NOUN
ejpam-5192	15	7	of	of	ADP
ejpam-5192	15	8	functions	function	NOUN
ejpam-5192	15	9	,	,	PUNCT
ejpam-5192	15	10	namely	namely	ADV
ejpam-5192	15	11	almost	almost	ADV
ejpam-5192	15	12	precontinuous	precontinuous	ADJ
ejpam-5192	15	13	functions	function	NOUN
ejpam-5192	15	14	and	and	CCONJ
ejpam-5192	15	15	almost	almost	ADV
ejpam-5192	15	16	β	β	ADJ
ejpam-5192	15	17	-	-	ADJ
ejpam-5192	15	18	continuous	continuous	ADJ
ejpam-5192	15	19	functions	function	NOUN
ejpam-5192	15	20	by	by	ADP
ejpam-5192	15	21	utilizing	utilize	VERB
ejpam-5192	15	22	the	the	DET
ejpam-5192	15	23	notions	notion	NOUN
ejpam-5192	15	24	of	of	ADP
ejpam-5192	15	25	preopen	preopen	ADJ
ejpam-5192	15	26	sets	set	NOUN
ejpam-5192	15	27	and	and	CCONJ
ejpam-5192	15	28	β	β	NOUN
ejpam-5192	15	29	-	-	ADJ
ejpam-5192	15	30	open	open	ADJ
ejpam-5192	15	31	sets	set	NOUN
ejpam-5192	15	32	due	due	ADP
ejpam-5192	15	33	to	to	ADP
ejpam-5192	15	34	mashhour	mashhour	PROPN
ejpam-5192	15	35	et	et	PROPN
ejpam-5192	15	36	al	al	PROPN
ejpam-5192	16	1	[	[	X
ejpam-5192	16	2	15	15	NUM
ejpam-5192	16	3	]	]	PUNCT
ejpam-5192	16	4	and	and	CCONJ
ejpam-5192	16	5	abd	abd	PROPN
ejpam-5192	16	6	el	el	PROPN
ejpam-5192	16	7	-	-	PROPN
ejpam-5192	16	8	monsef	monsef	PROPN
ejpam-5192	16	9	et	et	PROPN
ejpam-5192	16	10	al	al	PROPN
ejpam-5192	16	11	.	.	PUNCT
ejpam-5192	17	1	[	[	X
ejpam-5192	17	2	12	12	NUM
ejpam-5192	17	3	]	]	PUNCT
ejpam-5192	17	4	,	,	PUNCT
ejpam-5192	17	5	respectively	respectively	ADV
ejpam-5192	17	6	.	.	PUNCT
ejpam-5192	18	1	the	the	DET
ejpam-5192	18	2	class	class	NOUN
ejpam-5192	18	3	of	of	ADP
ejpam-5192	18	4	almost	almost	ADV
ejpam-5192	18	5	precontinuity	precontinuity	NOUN
ejpam-5192	18	6	is	be	AUX
ejpam-5192	18	7	a	a	DET
ejpam-5192	18	8	generalization	generalization	NOUN
ejpam-5192	18	9	of	of	ADP
ejpam-5192	18	10	almost	almost	ADV
ejpam-5192	18	11	α	α	NOUN
ejpam-5192	18	12	-	-	NOUN
ejpam-5192	18	13	continuity	continuity	NOUN
ejpam-5192	18	14	.	.	PUNCT
ejpam-5192	19	1	the	the	DET
ejpam-5192	19	2	class	class	NOUN
ejpam-5192	19	3	of	of	ADP
ejpam-5192	19	4	almost	almost	ADV
ejpam-5192	19	5	β	β	NOUN
ejpam-5192	19	6	-	-	NOUN
ejpam-5192	19	7	continuity	continuity	NOUN
ejpam-5192	19	8	is	be	AUX
ejpam-5192	19	9	a	a	DET
ejpam-5192	19	10	generalization	generalization	NOUN
ejpam-5192	19	11	of	of	ADP
ejpam-5192	19	12	almost	almost	ADV
ejpam-5192	19	13	semi	semi	NOUN
ejpam-5192	19	14	-	-	NOUN
ejpam-5192	19	15	continuity	continuity	NOUN
ejpam-5192	19	16	.	.	PUNCT
ejpam-5192	20	1	keskin	keskin	NOUN
ejpam-5192	20	2	and	and	CCONJ
ejpam-5192	20	3	noiri	noiri	ADV
ejpam-5192	21	1	[	[	X
ejpam-5192	21	2	13	13	NUM
ejpam-5192	21	3	]	]	PUNCT
ejpam-5192	21	4	introduced	introduce	VERB
ejpam-5192	21	5	the	the	DET
ejpam-5192	21	6	concept	concept	NOUN
ejpam-5192	21	7	of	of	ADP
ejpam-5192	21	8	almost	almost	ADV
ejpam-5192	21	9	b	b	NOUN
ejpam-5192	21	10	-	-	PUNCT
ejpam-5192	21	11	continuous	continuous	ADJ
ejpam-5192	21	12	functions	function	NOUN
ejpam-5192	21	13	by	by	ADP
ejpam-5192	21	14	utilizing	utilize	VERB
ejpam-5192	21	15	the	the	DET
ejpam-5192	21	16	notion	notion	NOUN
ejpam-5192	21	17	of	of	ADP
ejpam-5192	21	18	b	b	NOUN
ejpam-5192	21	19	-	-	PUNCT
ejpam-5192	21	20	open	open	ADJ
ejpam-5192	21	21	∗corresponding	∗corresponde	VERB
ejpam-5192	21	22	author	author	NOUN
ejpam-5192	21	23	.	.	PUNCT
ejpam-5192	22	1	doi	doi	NOUN
ejpam-5192	22	2	:	:	PUNCT
ejpam-5192	22	3	https://doi.org/10.29020/nybg.ejpam.v17i2.5192	https://doi.org/10.29020/nybg.ejpam.v17i2.5192	ADP
ejpam-5192	22	4	email	email	NOUN
ejpam-5192	22	5	addresses	address	NOUN
ejpam-5192	22	6	:	:	PUNCT
ejpam-5192	22	7	chalongchai.k@msu.ac.th	chalongchai.k@msu.ac.th	PROPN
ejpam-5192	22	8	(	(	PUNCT
ejpam-5192	22	9	c.	c.	PROPN
ejpam-5192	22	10	klanarong	klanarong	PROPN
ejpam-5192	22	11	)	)	PUNCT
ejpam-5192	22	12	,	,	PUNCT
ejpam-5192	22	13	s−sompong@snru.ac.th	s−sompong@snru.ac.th	PRON
ejpam-5192	22	14	(	(	PUNCT
ejpam-5192	22	15	s.	s.	PROPN
ejpam-5192	22	16	sompong	sompong	PROPN
ejpam-5192	22	17	)	)	PUNCT
ejpam-5192	22	18	,	,	PUNCT
ejpam-5192	22	19	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	PROPN
ejpam-5192	22	20	(	(	PUNCT
ejpam-5192	22	21	c.	c.	PROPN
ejpam-5192	22	22	boonpok	boonpok	PROPN
ejpam-5192	22	23	)	)	PUNCT
ejpam-5192	22	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5192	22	25	1244	1244	NUM
ejpam-5192	23	1	©	©	PROPN
ejpam-5192	23	2	2024	2024	NUM
ejpam-5192	23	3	ejpam	ejpam	NOUN
ejpam-5192	23	4	all	all	DET
ejpam-5192	23	5	rights	right	NOUN
ejpam-5192	23	6	reserved	reserve	VERB
ejpam-5192	23	7	.	.	PUNCT
ejpam-5192	24	1	c.	c.	PROPN
ejpam-5192	24	2	klanarong	klanarong	PROPN
ejpam-5192	24	3	,	,	PUNCT
ejpam-5192	24	4	s.	s.	PROPN
ejpam-5192	24	5	sompong	sompong	PROPN
ejpam-5192	24	6	,	,	PUNCT
ejpam-5192	24	7	c.	c.	PROPN
ejpam-5192	24	8	boonpok	boonpok	PROPN
ejpam-5192	24	9	/	/	SYM
ejpam-5192	24	10	eur	eur	PROPN
ejpam-5192	24	11	.	.	PUNCT
ejpam-5192	25	1	j.	j.	PROPN
ejpam-5192	25	2	pure	pure	PROPN
ejpam-5192	25	3	appl	appl	PROPN
ejpam-5192	25	4	.	.	PROPN
ejpam-5192	25	5	math	math	PROPN
ejpam-5192	25	6	,	,	PUNCT
ejpam-5192	25	7	17	17	NUM
ejpam-5192	25	8	(	(	PUNCT
ejpam-5192	25	9	2	2	NUM
ejpam-5192	25	10	)	)	PUNCT
ejpam-5192	25	11	(	(	PUNCT
ejpam-5192	25	12	2024	2024	NUM
ejpam-5192	25	13	)	)	PUNCT
ejpam-5192	25	14	,	,	PUNCT
ejpam-5192	25	15	1244	1244	NUM
ejpam-5192	25	16	-	-	SYM
ejpam-5192	25	17	1253	1253	NUM
ejpam-5192	25	18	1245	1245	NUM
ejpam-5192	25	19	sets	set	NOUN
ejpam-5192	25	20	due	due	ADJ
ejpam-5192	25	21	to	to	PART
ejpam-5192	25	22	andrijević	andrijević	VERB
ejpam-5192	25	23	[	[	X
ejpam-5192	25	24	1	1	NUM
ejpam-5192	25	25	]	]	PUNCT
ejpam-5192	25	26	.	.	PUNCT
ejpam-5192	26	1	the	the	DET
ejpam-5192	26	2	class	class	NOUN
ejpam-5192	26	3	of	of	ADP
ejpam-5192	26	4	almost	almost	ADV
ejpam-5192	26	5	b	b	NOUN
ejpam-5192	26	6	-	-	PUNCT
ejpam-5192	26	7	continuity	continuity	NOUN
ejpam-5192	26	8	is	be	AUX
ejpam-5192	26	9	a	a	DET
ejpam-5192	26	10	generalization	generalization	NOUN
ejpam-5192	26	11	of	of	ADP
ejpam-5192	26	12	almost	almost	ADV
ejpam-5192	26	13	precontinuity	precontinuity	NOUN
ejpam-5192	26	14	and	and	CCONJ
ejpam-5192	26	15	almost	almost	ADV
ejpam-5192	26	16	semi	semi	ADJ
ejpam-5192	26	17	-	-	NOUN
ejpam-5192	26	18	continuity	continuity	NOUN
ejpam-5192	26	19	.	.	PUNCT
ejpam-5192	27	1	the	the	DET
ejpam-5192	27	2	class	class	NOUN
ejpam-5192	27	3	of	of	ADP
ejpam-5192	27	4	almost	almost	ADV
ejpam-5192	27	5	β	β	NOUN
ejpam-5192	27	6	-	-	NOUN
ejpam-5192	27	7	continuity	continuity	NOUN
ejpam-5192	27	8	is	be	AUX
ejpam-5192	27	9	a	a	DET
ejpam-5192	27	10	generalization	generalization	NOUN
ejpam-5192	27	11	of	of	ADP
ejpam-5192	27	12	almost	almost	ADV
ejpam-5192	27	13	b	b	NOUN
ejpam-5192	27	14	-	-	PUNCT
ejpam-5192	27	15	continuity	continuity	NOUN
ejpam-5192	27	16	.	.	PUNCT
ejpam-5192	28	1	popa	popa	NOUN
ejpam-5192	29	1	[	[	X
ejpam-5192	29	2	22	22	NUM
ejpam-5192	29	3	]	]	PUNCT
ejpam-5192	29	4	introduced	introduce	VERB
ejpam-5192	29	5	the	the	DET
ejpam-5192	29	6	concepts	concept	NOUN
ejpam-5192	29	7	of	of	ADP
ejpam-5192	29	8	upper	upper	ADJ
ejpam-5192	29	9	and	and	CCONJ
ejpam-5192	29	10	lower	low	ADJ
ejpam-5192	29	11	almost	almost	ADV
ejpam-5192	29	12	continuous	continuous	ADJ
ejpam-5192	29	13	multifunctions	multifunction	NOUN
ejpam-5192	29	14	.	.	PUNCT
ejpam-5192	30	1	popa	popa	NOUN
ejpam-5192	30	2	and	and	CCONJ
ejpam-5192	30	3	noiri	noiri	ADV
ejpam-5192	31	1	[	[	X
ejpam-5192	31	2	23	23	NUM
ejpam-5192	31	3	]	]	PUNCT
ejpam-5192	31	4	introduced	introduce	VERB
ejpam-5192	31	5	the	the	DET
ejpam-5192	31	6	notions	notion	NOUN
ejpam-5192	31	7	of	of	ADP
ejpam-5192	31	8	upper	upper	ADJ
ejpam-5192	31	9	and	and	CCONJ
ejpam-5192	31	10	lower	low	ADJ
ejpam-5192	31	11	almost	almost	ADV
ejpam-5192	31	12	quasi	quasi	ADJ
ejpam-5192	31	13	-	-	ADJ
ejpam-5192	31	14	continuous	continuous	ADJ
ejpam-5192	31	15	multifunctions	multifunction	NOUN
ejpam-5192	31	16	.	.	PUNCT
ejpam-5192	32	1	several	several	ADJ
ejpam-5192	32	2	characterizations	characterization	NOUN
ejpam-5192	32	3	of	of	ADP
ejpam-5192	32	4	upper	upper	ADJ
ejpam-5192	32	5	and	and	CCONJ
ejpam-5192	32	6	lower	low	ADJ
ejpam-5192	32	7	almost	almost	ADV
ejpam-5192	32	8	quasi	quasi	ADJ
ejpam-5192	32	9	-	-	ADJ
ejpam-5192	32	10	continuous	continuous	ADJ
ejpam-5192	32	11	multifunctions	multifunction	NOUN
ejpam-5192	32	12	were	be	AUX
ejpam-5192	32	13	investigated	investigate	VERB
ejpam-5192	32	14	in	in	ADP
ejpam-5192	32	15	[	[	X
ejpam-5192	32	16	19	19	NUM
ejpam-5192	32	17	]	]	PUNCT
ejpam-5192	32	18	.	.	PUNCT
ejpam-5192	33	1	in	in	ADP
ejpam-5192	33	2	1996	1996	NUM
ejpam-5192	33	3	,	,	PUNCT
ejpam-5192	33	4	popa	popa	NOUN
ejpam-5192	33	5	and	and	CCONJ
ejpam-5192	33	6	noiri	noiri	ADV
ejpam-5192	33	7	[	[	X
ejpam-5192	33	8	24	24	NUM
ejpam-5192	33	9	]	]	PUNCT
ejpam-5192	33	10	introduced	introduce	VERB
ejpam-5192	33	11	and	and	CCONJ
ejpam-5192	33	12	investigated	investigate	VERB
ejpam-5192	33	13	the	the	DET
ejpam-5192	33	14	notions	notion	NOUN
ejpam-5192	33	15	of	of	ADP
ejpam-5192	33	16	upper	upper	ADJ
ejpam-5192	33	17	and	and	CCONJ
ejpam-5192	33	18	lower	low	ADJ
ejpam-5192	33	19	almost	almost	ADV
ejpam-5192	33	20	α	α	ADJ
ejpam-5192	33	21	-	-	ADJ
ejpam-5192	33	22	continuous	continuous	ADJ
ejpam-5192	33	23	multifunctions	multifunction	NOUN
ejpam-5192	33	24	.	.	PUNCT
ejpam-5192	34	1	in	in	ADP
ejpam-5192	34	2	1997	1997	NUM
ejpam-5192	34	3	,	,	PUNCT
ejpam-5192	34	4	popa	popa	NOUN
ejpam-5192	34	5	et	et	PROPN
ejpam-5192	34	6	al	al	PROPN
ejpam-5192	34	7	.	.	PUNCT
ejpam-5192	35	1	[	[	X
ejpam-5192	35	2	26	26	NUM
ejpam-5192	35	3	]	]	PUNCT
ejpam-5192	35	4	introduced	introduce	VERB
ejpam-5192	35	5	the	the	DET
ejpam-5192	35	6	concepts	concept	NOUN
ejpam-5192	35	7	of	of	ADP
ejpam-5192	35	8	upper	upper	ADJ
ejpam-5192	35	9	and	and	CCONJ
ejpam-5192	35	10	lower	low	ADJ
ejpam-5192	35	11	almost	almost	ADV
ejpam-5192	35	12	precontinuous	precontinuous	ADJ
ejpam-5192	35	13	multifunctions	multifunction	NOUN
ejpam-5192	35	14	.	.	PUNCT
ejpam-5192	36	1	in	in	ADP
ejpam-5192	36	2	particular	particular	ADJ
ejpam-5192	36	3	,	,	PUNCT
ejpam-5192	36	4	several	several	ADJ
ejpam-5192	36	5	characterizations	characterization	NOUN
ejpam-5192	36	6	of	of	ADP
ejpam-5192	36	7	upper	upper	ADJ
ejpam-5192	36	8	and	and	CCONJ
ejpam-5192	36	9	lower	low	ADJ
ejpam-5192	36	10	almost	almost	ADV
ejpam-5192	36	11	precontinuous	precontinuous	ADJ
ejpam-5192	36	12	multifunctions	multifunction	NOUN
ejpam-5192	36	13	were	be	AUX
ejpam-5192	36	14	presented	present	VERB
ejpam-5192	36	15	in	in	ADP
ejpam-5192	36	16	[	[	X
ejpam-5192	36	17	27	27	NUM
ejpam-5192	36	18	]	]	PUNCT
ejpam-5192	36	19	.	.	PUNCT
ejpam-5192	37	1	in	in	ADP
ejpam-5192	37	2	1999	1999	NUM
ejpam-5192	37	3	,	,	PUNCT
ejpam-5192	37	4	noiri	noiri	PRON
ejpam-5192	37	5	and	and	CCONJ
ejpam-5192	37	6	popa	popa	NOUN
ejpam-5192	37	7	[	[	X
ejpam-5192	37	8	20	20	NUM
ejpam-5192	37	9	]	]	PUNCT
ejpam-5192	37	10	introduced	introduce	VERB
ejpam-5192	37	11	the	the	DET
ejpam-5192	37	12	concepts	concept	NOUN
ejpam-5192	37	13	of	of	ADP
ejpam-5192	37	14	upper	upper	ADJ
ejpam-5192	37	15	and	and	CCONJ
ejpam-5192	37	16	lower	low	ADJ
ejpam-5192	37	17	almost	almost	ADV
ejpam-5192	37	18	β	β	ADJ
ejpam-5192	37	19	-	-	ADJ
ejpam-5192	37	20	continuous	continuous	ADJ
ejpam-5192	37	21	multifunctions	multifunction	NOUN
ejpam-5192	37	22	.	.	PUNCT
ejpam-5192	38	1	some	some	DET
ejpam-5192	38	2	characterizations	characterization	NOUN
ejpam-5192	38	3	of	of	ADP
ejpam-5192	38	4	upper	upper	ADJ
ejpam-5192	38	5	and	and	CCONJ
ejpam-5192	38	6	lower	low	ADJ
ejpam-5192	38	7	almost	almost	ADV
ejpam-5192	38	8	β	β	ADJ
ejpam-5192	38	9	-	-	ADJ
ejpam-5192	38	10	continuous	continuous	ADJ
ejpam-5192	38	11	multifunctions	multifunction	NOUN
ejpam-5192	38	12	were	be	AUX
ejpam-5192	38	13	investigated	investigate	VERB
ejpam-5192	38	14	in	in	ADP
ejpam-5192	38	15	[	[	X
ejpam-5192	38	16	25	25	NUM
ejpam-5192	38	17	]	]	PUNCT
ejpam-5192	38	18	.	.	PUNCT
ejpam-5192	39	1	in	in	ADP
ejpam-5192	39	2	2006	2006	NUM
ejpam-5192	39	3	,	,	PUNCT
ejpam-5192	39	4	ekici	ekici	NOUN
ejpam-5192	39	5	and	and	CCONJ
ejpam-5192	39	6	park	park	NOUN
ejpam-5192	39	7	[	[	X
ejpam-5192	39	8	11	11	NUM
ejpam-5192	39	9	]	]	PUNCT
ejpam-5192	39	10	introduced	introduce	VERB
ejpam-5192	39	11	and	and	CCONJ
ejpam-5192	39	12	studied	study	VERB
ejpam-5192	39	13	almost	almost	ADV
ejpam-5192	39	14	γ	γ	ADJ
ejpam-5192	39	15	-	-	ADJ
ejpam-5192	39	16	continuous	continuous	ADJ
ejpam-5192	39	17	multifunctions	multifunction	NOUN
ejpam-5192	39	18	.	.	PUNCT
ejpam-5192	40	1	noiri	noiri	PROPN
ejpam-5192	40	2	and	and	CCONJ
ejpam-5192	40	3	popa	popa	NOUN
ejpam-5192	40	4	[	[	X
ejpam-5192	40	5	21	21	NUM
ejpam-5192	40	6	]	]	PUNCT
ejpam-5192	40	7	introduced	introduce	VERB
ejpam-5192	40	8	and	and	CCONJ
ejpam-5192	40	9	investigated	investigate	VERB
ejpam-5192	40	10	the	the	DET
ejpam-5192	40	11	notions	notion	NOUN
ejpam-5192	40	12	of	of	ADP
ejpam-5192	40	13	upper	upper	ADJ
ejpam-5192	40	14	and	and	CCONJ
ejpam-5192	40	15	lower	low	ADJ
ejpam-5192	40	16	almost	almost	ADV
ejpam-5192	40	17	m	m	ADJ
ejpam-5192	40	18	-	-	ADJ
ejpam-5192	40	19	continuous	continuous	ADJ
ejpam-5192	40	20	multifunctions	multifunction	NOUN
ejpam-5192	40	21	as	as	ADP
ejpam-5192	40	22	multifunctions	multifunction	NOUN
ejpam-5192	40	23	from	from	ADP
ejpam-5192	40	24	a	a	DET
ejpam-5192	40	25	set	set	NOUN
ejpam-5192	40	26	satisfying	satisfy	VERB
ejpam-5192	40	27	some	some	DET
ejpam-5192	40	28	minimal	minimal	ADJ
ejpam-5192	40	29	conditions	condition	NOUN
ejpam-5192	40	30	into	into	ADP
ejpam-5192	40	31	a	a	DET
ejpam-5192	40	32	topological	topological	ADJ
ejpam-5192	40	33	space	space	NOUN
ejpam-5192	40	34	.	.	PUNCT
ejpam-5192	41	1	in	in	ADP
ejpam-5192	41	2	[	[	X
ejpam-5192	41	3	3	3	NUM
ejpam-5192	41	4	]	]	PUNCT
ejpam-5192	41	5	,	,	PUNCT
ejpam-5192	41	6	the	the	DET
ejpam-5192	41	7	present	present	ADJ
ejpam-5192	41	8	author	author	NOUN
ejpam-5192	41	9	introduced	introduce	VERB
ejpam-5192	41	10	and	and	CCONJ
ejpam-5192	41	11	studied	study	VERB
ejpam-5192	41	12	the	the	DET
ejpam-5192	41	13	concept	concept	NOUN
ejpam-5192	41	14	of	of	ADP
ejpam-5192	41	15	pairwise	pairwise	NOUN
ejpam-5192	41	16	almost	almost	ADV
ejpam-5192	41	17	m	m	VERB
ejpam-5192	41	18	-continuous	-continuous	ADJ
ejpam-5192	41	19	functions	function	NOUN
ejpam-5192	41	20	in	in	ADP
ejpam-5192	41	21	biminimal	biminimal	NOUN
ejpam-5192	41	22	structure	structure	NOUN
ejpam-5192	41	23	spaces	space	VERB
ejpam-5192	41	24	.	.	PUNCT
ejpam-5192	42	1	laprom	laprom	ADP
ejpam-5192	42	2	et	et	PROPN
ejpam-5192	42	3	al	al	PROPN
ejpam-5192	42	4	.	.	PUNCT
ejpam-5192	43	1	[	[	X
ejpam-5192	43	2	14	14	NUM
ejpam-5192	43	3	]	]	PUNCT
ejpam-5192	43	4	introduced	introduce	VERB
ejpam-5192	43	5	and	and	CCONJ
ejpam-5192	43	6	investigated	investigate	VERB
ejpam-5192	43	7	the	the	DET
ejpam-5192	43	8	notion	notion	NOUN
ejpam-5192	43	9	of	of	ADP
ejpam-5192	43	10	almost	almost	ADV
ejpam-5192	43	11	β(τ1	β(τ1	NOUN
ejpam-5192	43	12	,	,	PUNCT
ejpam-5192	43	13	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	43	14	multifunctions	multifunction	NOUN
ejpam-5192	43	15	.	.	PUNCT
ejpam-5192	44	1	viriyapong	viriyapong	PROPN
ejpam-5192	44	2	and	and	CCONJ
ejpam-5192	44	3	boonpok	boonpok	X
ejpam-5192	44	4	[	[	X
ejpam-5192	44	5	29	29	NUM
ejpam-5192	44	6	]	]	PUNCT
ejpam-5192	44	7	introduced	introduce	VERB
ejpam-5192	44	8	and	and	CCONJ
ejpam-5192	44	9	studied	study	VERB
ejpam-5192	44	10	the	the	DET
ejpam-5192	44	11	concept	concept	NOUN
ejpam-5192	44	12	of	of	ADP
ejpam-5192	44	13	almost	almost	ADV
ejpam-5192	44	14	(	(	PUNCT
ejpam-5192	44	15	τ1	τ1	NOUN
ejpam-5192	44	16	,	,	PUNCT
ejpam-5192	44	17	τ2)α	τ2)α	ADJ
ejpam-5192	44	18	-	-	PUNCT
ejpam-5192	44	19	continuous	continuous	ADJ
ejpam-5192	44	20	multifunctions	multifunction	NOUN
ejpam-5192	44	21	.	.	PUNCT
ejpam-5192	45	1	moreover	moreover	ADV
ejpam-5192	45	2	,	,	PUNCT
ejpam-5192	45	3	some	some	DET
ejpam-5192	45	4	characterizations	characterization	NOUN
ejpam-5192	45	5	of	of	ADP
ejpam-5192	45	6	almost	almost	ADV
ejpam-5192	45	7	(	(	PUNCT
ejpam-5192	45	8	τ1	τ1	NOUN
ejpam-5192	45	9	,	,	PUNCT
ejpam-5192	45	10	τ2)δ	τ2)δ	ADJ
ejpam-5192	45	11	-	-	PUNCT
ejpam-5192	45	12	semicontinuous	semicontinuous	ADJ
ejpam-5192	45	13	multifunctions	multifunction	NOUN
ejpam-5192	45	14	,	,	PUNCT
ejpam-5192	45	15	almost	almost	ADV
ejpam-5192	45	16	weakly	weakly	ADJ
ejpam-5192	45	17	(	(	PUNCT
ejpam-5192	45	18	τ1	τ1	NOUN
ejpam-5192	45	19	,	,	PUNCT
ejpam-5192	45	20	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	45	21	multifunctions	multifunction	NOUN
ejpam-5192	45	22	,	,	PUNCT
ejpam-5192	45	23	almost	almost	ADV
ejpam-5192	45	24	(	(	PUNCT
ejpam-5192	45	25	λ	λ	NOUN
ejpam-5192	45	26	,	,	PUNCT
ejpam-5192	45	27	sp)-continuous	sp)-continuous	ADJ
ejpam-5192	45	28	multifunctions	multifunction	NOUN
ejpam-5192	45	29	,	,	PUNCT
ejpam-5192	45	30	almost	almost	ADV
ejpam-5192	45	31	β(⋆)-continuous	β(⋆)-continuous	ADJ
ejpam-5192	45	32	multifunctions	multifunction	NOUN
ejpam-5192	45	33	and	and	CCONJ
ejpam-5192	45	34	almost	almost	ADV
ejpam-5192	45	35	⋆-continuous	⋆-continuous	ADJ
ejpam-5192	45	36	multifunctions	multifunction	NOUN
ejpam-5192	45	37	were	be	AUX
ejpam-5192	45	38	established	establish	VERB
ejpam-5192	45	39	in	in	ADP
ejpam-5192	45	40	[	[	X
ejpam-5192	45	41	5	5	NUM
ejpam-5192	45	42	]	]	PUNCT
ejpam-5192	45	43	,	,	PUNCT
ejpam-5192	45	44	[	[	X
ejpam-5192	45	45	8	8	NUM
ejpam-5192	45	46	]	]	PUNCT
ejpam-5192	45	47	,	,	PUNCT
ejpam-5192	45	48	[	[	X
ejpam-5192	45	49	10	10	NUM
ejpam-5192	45	50	]	]	PUNCT
ejpam-5192	45	51	,	,	PUNCT
ejpam-5192	45	52	[	[	X
ejpam-5192	45	53	6	6	NUM
ejpam-5192	45	54	]	]	PUNCT
ejpam-5192	45	55	and	and	CCONJ
ejpam-5192	45	56	[	[	X
ejpam-5192	45	57	4	4	X
ejpam-5192	45	58	]	]	PUNCT
ejpam-5192	45	59	respectively	respectively	ADV
ejpam-5192	45	60	.	.	PUNCT
ejpam-5192	46	1	in	in	ADP
ejpam-5192	46	2	this	this	DET
ejpam-5192	46	3	paper	paper	NOUN
ejpam-5192	46	4	,	,	PUNCT
ejpam-5192	46	5	we	we	PRON
ejpam-5192	46	6	introduce	introduce	VERB
ejpam-5192	46	7	the	the	DET
ejpam-5192	46	8	concepts	concept	NOUN
ejpam-5192	46	9	of	of	ADP
ejpam-5192	46	10	upper	upper	ADJ
ejpam-5192	46	11	and	and	CCONJ
ejpam-5192	46	12	lower	low	ADJ
ejpam-5192	46	13	almost	almost	ADV
ejpam-5192	46	14	(	(	PUNCT
ejpam-5192	46	15	τ1	τ1	NOUN
ejpam-5192	46	16	,	,	PUNCT
ejpam-5192	46	17	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	46	18	multifunctions	multifunction	NOUN
ejpam-5192	46	19	.	.	PUNCT
ejpam-5192	47	1	furthermore	furthermore	ADV
ejpam-5192	47	2	,	,	PUNCT
ejpam-5192	47	3	several	several	ADJ
ejpam-5192	47	4	characterizations	characterization	NOUN
ejpam-5192	47	5	of	of	ADP
ejpam-5192	47	6	upper	upper	ADJ
ejpam-5192	47	7	and	and	CCONJ
ejpam-5192	47	8	lower	low	ADJ
ejpam-5192	47	9	almost	almost	ADV
ejpam-5192	47	10	(	(	PUNCT
ejpam-5192	47	11	τ1	τ1	NOUN
ejpam-5192	47	12	,	,	PUNCT
ejpam-5192	47	13	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	47	14	multifunctions	multifunction	NOUN
ejpam-5192	47	15	are	be	AUX
ejpam-5192	47	16	investigated	investigate	VERB
ejpam-5192	47	17	.	.	PUNCT
ejpam-5192	48	1	2	2	X
ejpam-5192	48	2	.	.	X
ejpam-5192	48	3	preliminaries	preliminary	NOUN
ejpam-5192	48	4	throughout	throughout	ADP
ejpam-5192	48	5	the	the	DET
ejpam-5192	48	6	present	present	ADJ
ejpam-5192	48	7	paper	paper	NOUN
ejpam-5192	48	8	,	,	PUNCT
ejpam-5192	48	9	spaces	space	NOUN
ejpam-5192	48	10	(	(	PUNCT
ejpam-5192	48	11	x	x	NOUN
ejpam-5192	48	12	,	,	PUNCT
ejpam-5192	48	13	τ1	τ1	NOUN
ejpam-5192	48	14	,	,	PUNCT
ejpam-5192	48	15	τ2	τ2	NOUN
ejpam-5192	48	16	)	)	PUNCT
ejpam-5192	48	17	and	and	CCONJ
ejpam-5192	48	18	(	(	PUNCT
ejpam-5192	48	19	y	y	PROPN
ejpam-5192	48	20	,	,	PUNCT
ejpam-5192	48	21	σ1	σ1	PROPN
ejpam-5192	48	22	,	,	PUNCT
ejpam-5192	48	23	σ2	σ2	NOUN
ejpam-5192	48	24	)	)	PUNCT
ejpam-5192	48	25	(	(	PUNCT
ejpam-5192	48	26	or	or	CCONJ
ejpam-5192	48	27	simply	simply	ADV
ejpam-5192	48	28	x	x	X
ejpam-5192	48	29	and	and	CCONJ
ejpam-5192	48	30	y	y	PROPN
ejpam-5192	48	31	)	)	PUNCT
ejpam-5192	48	32	always	always	ADV
ejpam-5192	48	33	mean	mean	VERB
ejpam-5192	48	34	bitopological	bitopological	ADJ
ejpam-5192	48	35	spaces	space	NOUN
ejpam-5192	48	36	on	on	ADP
ejpam-5192	48	37	which	which	PRON
ejpam-5192	48	38	no	no	DET
ejpam-5192	48	39	separation	separation	NOUN
ejpam-5192	48	40	axioms	axiom	NOUN
ejpam-5192	48	41	are	be	AUX
ejpam-5192	48	42	assumed	assume	VERB
ejpam-5192	48	43	unless	unless	SCONJ
ejpam-5192	48	44	explicitly	explicitly	ADV
ejpam-5192	48	45	stated	state	VERB
ejpam-5192	48	46	.	.	PUNCT
ejpam-5192	49	1	let	let	VERB
ejpam-5192	49	2	a	a	DET
ejpam-5192	49	3	be	be	AUX
ejpam-5192	49	4	a	a	DET
ejpam-5192	49	5	subset	subset	NOUN
ejpam-5192	49	6	of	of	ADP
ejpam-5192	49	7	a	a	DET
ejpam-5192	49	8	bitopological	bitopological	ADJ
ejpam-5192	49	9	space	space	NOUN
ejpam-5192	49	10	(	(	PUNCT
ejpam-5192	49	11	x	x	NOUN
ejpam-5192	49	12	,	,	PUNCT
ejpam-5192	49	13	τ1	τ1	NOUN
ejpam-5192	49	14	,	,	PUNCT
ejpam-5192	49	15	τ2	τ2	NOUN
ejpam-5192	49	16	)	)	PUNCT
ejpam-5192	49	17	.	.	PUNCT
ejpam-5192	50	1	the	the	DET
ejpam-5192	50	2	closure	closure	NOUN
ejpam-5192	50	3	of	of	ADP
ejpam-5192	50	4	a	a	PRON
ejpam-5192	50	5	and	and	CCONJ
ejpam-5192	50	6	the	the	DET
ejpam-5192	50	7	interior	interior	NOUN
ejpam-5192	50	8	of	of	ADP
ejpam-5192	50	9	a	a	PRON
ejpam-5192	50	10	with	with	ADP
ejpam-5192	50	11	respect	respect	NOUN
ejpam-5192	50	12	to	to	ADP
ejpam-5192	50	13	τi	τi	PROPN
ejpam-5192	50	14	are	be	AUX
ejpam-5192	50	15	denoted	denote	VERB
ejpam-5192	50	16	by	by	ADP
ejpam-5192	50	17	τi	τi	NOUN
ejpam-5192	50	18	-	-	PUNCT
ejpam-5192	50	19	cl(a	cl(a	NUM
ejpam-5192	50	20	)	)	PUNCT
ejpam-5192	50	21	and	and	CCONJ
ejpam-5192	50	22	τi	τi	NOUN
ejpam-5192	50	23	-	-	PUNCT
ejpam-5192	50	24	int(a	int(a	NOUN
ejpam-5192	50	25	)	)	PUNCT
ejpam-5192	50	26	,	,	PUNCT
ejpam-5192	50	27	respectively	respectively	ADV
ejpam-5192	50	28	,	,	PUNCT
ejpam-5192	50	29	for	for	ADP
ejpam-5192	50	30	i	i	PROPN
ejpam-5192	50	31	=	=	SYM
ejpam-5192	50	32	1	1	NUM
ejpam-5192	50	33	,	,	PUNCT
ejpam-5192	50	34	2	2	NUM
ejpam-5192	50	35	.	.	X
ejpam-5192	50	36	a	a	DET
ejpam-5192	50	37	subset	subset	NOUN
ejpam-5192	50	38	a	a	PRON
ejpam-5192	50	39	of	of	ADP
ejpam-5192	50	40	a	a	DET
ejpam-5192	50	41	bitopological	bitopological	ADJ
ejpam-5192	50	42	space	space	NOUN
ejpam-5192	50	43	(	(	PUNCT
ejpam-5192	50	44	x	x	NOUN
ejpam-5192	50	45	,	,	PUNCT
ejpam-5192	50	46	τ1	τ1	NOUN
ejpam-5192	50	47	,	,	PUNCT
ejpam-5192	50	48	τ2	τ2	NOUN
ejpam-5192	50	49	)	)	PUNCT
ejpam-5192	50	50	is	be	AUX
ejpam-5192	50	51	called	call	VERB
ejpam-5192	50	52	τ1τ2	τ1τ2	VERB
ejpam-5192	50	53	-	-	ADJ
ejpam-5192	50	54	closed	closed	ADJ
ejpam-5192	50	55	[	[	X
ejpam-5192	50	56	9	9	NUM
ejpam-5192	50	57	]	]	X
ejpam-5192	50	58	if	if	SCONJ
ejpam-5192	50	59	a	a	DET
ejpam-5192	50	60	=	=	NOUN
ejpam-5192	50	61	τ1	τ1	NOUN
ejpam-5192	50	62	-	-	PUNCT
ejpam-5192	50	63	cl(τ2	cl(τ2	NOUN
ejpam-5192	50	64	-	-	PUNCT
ejpam-5192	50	65	cl(a	cl(a	NUM
ejpam-5192	50	66	)	)	PUNCT
ejpam-5192	50	67	)	)	PUNCT
ejpam-5192	50	68	.	.	PUNCT
ejpam-5192	51	1	the	the	DET
ejpam-5192	51	2	complement	complement	NOUN
ejpam-5192	51	3	of	of	ADP
ejpam-5192	51	4	a	a	DET
ejpam-5192	51	5	τ1τ2	τ1τ2	ADJ
ejpam-5192	51	6	-	-	ADJ
ejpam-5192	51	7	closed	closed	ADJ
ejpam-5192	51	8	set	set	NOUN
ejpam-5192	51	9	is	be	AUX
ejpam-5192	51	10	called	call	VERB
ejpam-5192	51	11	τ1τ2	τ1τ2	NOUN
ejpam-5192	51	12	-	-	ADJ
ejpam-5192	51	13	open	open	ADJ
ejpam-5192	51	14	.	.	PUNCT
ejpam-5192	52	1	let	let	VERB
ejpam-5192	52	2	a	a	DET
ejpam-5192	52	3	be	be	AUX
ejpam-5192	52	4	a	a	DET
ejpam-5192	52	5	subset	subset	NOUN
ejpam-5192	52	6	of	of	ADP
ejpam-5192	52	7	a	a	DET
ejpam-5192	52	8	bitopological	bitopological	ADJ
ejpam-5192	52	9	space	space	NOUN
ejpam-5192	52	10	(	(	PUNCT
ejpam-5192	52	11	x	x	NOUN
ejpam-5192	52	12	,	,	PUNCT
ejpam-5192	52	13	τ1	τ1	NOUN
ejpam-5192	52	14	,	,	PUNCT
ejpam-5192	52	15	τ2	τ2	NOUN
ejpam-5192	52	16	)	)	PUNCT
ejpam-5192	52	17	.	.	PUNCT
ejpam-5192	53	1	the	the	DET
ejpam-5192	53	2	intersection	intersection	NOUN
ejpam-5192	53	3	of	of	ADP
ejpam-5192	53	4	all	all	DET
ejpam-5192	53	5	τ1τ2	τ1τ2	ADJ
ejpam-5192	53	6	-	-	ADJ
ejpam-5192	53	7	closed	closed	ADJ
ejpam-5192	53	8	sets	set	NOUN
ejpam-5192	53	9	of	of	ADP
ejpam-5192	53	10	x	x	PUNCT
ejpam-5192	53	11	containing	contain	VERB
ejpam-5192	53	12	a	a	PRON
ejpam-5192	53	13	is	be	AUX
ejpam-5192	53	14	called	call	VERB
ejpam-5192	53	15	the	the	DET
ejpam-5192	53	16	τ1τ2	τ1τ2	NOUN
ejpam-5192	53	17	-	-	NOUN
ejpam-5192	53	18	closure	closure	NOUN
ejpam-5192	53	19	[	[	X
ejpam-5192	53	20	9	9	NUM
ejpam-5192	53	21	]	]	PUNCT
ejpam-5192	53	22	of	of	ADP
ejpam-5192	53	23	a	a	PRON
ejpam-5192	53	24	and	and	CCONJ
ejpam-5192	53	25	is	be	AUX
ejpam-5192	53	26	denoted	denote	VERB
ejpam-5192	53	27	by	by	ADP
ejpam-5192	53	28	τ1τ2	τ1τ2	NOUN
ejpam-5192	53	29	-	-	NUM
ejpam-5192	53	30	cl(a	cl(a	NUM
ejpam-5192	53	31	)	)	PUNCT
ejpam-5192	53	32	.	.	PUNCT
ejpam-5192	54	1	the	the	DET
ejpam-5192	54	2	union	union	NOUN
ejpam-5192	54	3	of	of	ADP
ejpam-5192	54	4	all	all	DET
ejpam-5192	54	5	τ1τ2	τ1τ2	ADJ
ejpam-5192	54	6	-	-	ADJ
ejpam-5192	54	7	open	open	ADJ
ejpam-5192	54	8	sets	set	NOUN
ejpam-5192	54	9	of	of	ADP
ejpam-5192	54	10	x	x	PUNCT
ejpam-5192	54	11	contained	contain	VERB
ejpam-5192	54	12	in	in	ADP
ejpam-5192	54	13	a	a	PRON
ejpam-5192	54	14	is	be	AUX
ejpam-5192	54	15	called	call	VERB
ejpam-5192	54	16	the	the	DET
ejpam-5192	54	17	τ1τ2	τ1τ2	NOUN
ejpam-5192	54	18	-	-	ADJ
ejpam-5192	54	19	interior	interior	ADJ
ejpam-5192	54	20	[	[	X
ejpam-5192	54	21	9	9	NUM
ejpam-5192	54	22	]	]	PUNCT
ejpam-5192	54	23	of	of	ADP
ejpam-5192	54	24	a	a	PRON
ejpam-5192	54	25	and	and	CCONJ
ejpam-5192	54	26	is	be	AUX
ejpam-5192	54	27	denoted	denote	VERB
ejpam-5192	54	28	by	by	ADP
ejpam-5192	54	29	τ1τ2	τ1τ2	NOUN
ejpam-5192	54	30	-	-	ADJ
ejpam-5192	54	31	int(a	int(a	NOUN
ejpam-5192	54	32	)	)	PUNCT
ejpam-5192	54	33	.	.	PUNCT
ejpam-5192	55	1	lemma	lemma	PROPN
ejpam-5192	55	2	1	1	NUM
ejpam-5192	55	3	.	.	PUNCT
ejpam-5192	56	1	[	[	X
ejpam-5192	56	2	9	9	NUM
ejpam-5192	56	3	]	]	PUNCT
ejpam-5192	56	4	let	let	VERB
ejpam-5192	56	5	a	a	PRON
ejpam-5192	56	6	and	and	CCONJ
ejpam-5192	56	7	b	b	NOUN
ejpam-5192	56	8	be	be	AUX
ejpam-5192	56	9	subsets	subset	NOUN
ejpam-5192	56	10	of	of	ADP
ejpam-5192	56	11	a	a	DET
ejpam-5192	56	12	bitopological	bitopological	ADJ
ejpam-5192	56	13	space	space	NOUN
ejpam-5192	56	14	(	(	PUNCT
ejpam-5192	56	15	x	x	NOUN
ejpam-5192	56	16	,	,	PUNCT
ejpam-5192	56	17	τ1	τ1	NOUN
ejpam-5192	56	18	,	,	PUNCT
ejpam-5192	56	19	τ2	τ2	NOUN
ejpam-5192	56	20	)	)	PUNCT
ejpam-5192	56	21	.	.	PUNCT
ejpam-5192	57	1	for	for	ADP
ejpam-5192	57	2	the	the	DET
ejpam-5192	57	3	τ1τ2closure	τ1τ2closure	NOUN
ejpam-5192	57	4	,	,	PUNCT
ejpam-5192	57	5	the	the	DET
ejpam-5192	57	6	following	follow	VERB
ejpam-5192	57	7	properties	property	NOUN
ejpam-5192	57	8	hold	hold	VERB
ejpam-5192	57	9	:	:	PUNCT
ejpam-5192	57	10	(	(	PUNCT
ejpam-5192	57	11	1	1	X
ejpam-5192	57	12	)	)	PUNCT
ejpam-5192	57	13	a	a	DET
ejpam-5192	57	14	⊆	⊆	NUM
ejpam-5192	57	15	τ1τ2	τ1τ2	NOUN
ejpam-5192	57	16	-	-	NUM
ejpam-5192	57	17	cl(a	cl(a	NUM
ejpam-5192	57	18	)	)	PUNCT
ejpam-5192	57	19	and	and	CCONJ
ejpam-5192	57	20	τ1τ2	τ1τ2	NOUN
ejpam-5192	57	21	-	-	ADJ
ejpam-5192	57	22	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5192	57	23	-	-	PUNCT
ejpam-5192	57	24	cl(a	cl(a	NUM
ejpam-5192	57	25	)	)	PUNCT
ejpam-5192	57	26	)	)	PUNCT
ejpam-5192	58	1	=	=	PUNCT
ejpam-5192	58	2	τ1τ2	τ1τ2	NOUN
ejpam-5192	58	3	-	-	NUM
ejpam-5192	58	4	cl(a	cl(a	NUM
ejpam-5192	58	5	)	)	PUNCT
ejpam-5192	58	6	.	.	PUNCT
ejpam-5192	59	1	c.	c.	PROPN
ejpam-5192	59	2	klanarong	klanarong	PROPN
ejpam-5192	59	3	,	,	PUNCT
ejpam-5192	59	4	s.	s.	PROPN
ejpam-5192	59	5	sompong	sompong	PROPN
ejpam-5192	59	6	,	,	PUNCT
ejpam-5192	59	7	c.	c.	PROPN
ejpam-5192	59	8	boonpok	boonpok	PROPN
ejpam-5192	59	9	/	/	SYM
ejpam-5192	59	10	eur	eur	PROPN
ejpam-5192	59	11	.	.	PUNCT
ejpam-5192	60	1	j.	j.	PROPN
ejpam-5192	60	2	pure	pure	PROPN
ejpam-5192	60	3	appl	appl	PROPN
ejpam-5192	60	4	.	.	PROPN
ejpam-5192	60	5	math	math	PROPN
ejpam-5192	60	6	,	,	PUNCT
ejpam-5192	60	7	17	17	NUM
ejpam-5192	60	8	(	(	PUNCT
ejpam-5192	60	9	2	2	NUM
ejpam-5192	60	10	)	)	PUNCT
ejpam-5192	60	11	(	(	PUNCT
ejpam-5192	60	12	2024	2024	NUM
ejpam-5192	60	13	)	)	PUNCT
ejpam-5192	60	14	,	,	PUNCT
ejpam-5192	60	15	1244	1244	NUM
ejpam-5192	60	16	-	-	SYM
ejpam-5192	60	17	1253	1253	NUM
ejpam-5192	60	18	1246	1246	NUM
ejpam-5192	60	19	(	(	PUNCT
ejpam-5192	60	20	2	2	NUM
ejpam-5192	60	21	)	)	PUNCT
ejpam-5192	60	22	if	if	SCONJ
ejpam-5192	60	23	a	a	DET
ejpam-5192	60	24	⊆	⊆	NUM
ejpam-5192	60	25	b	b	NOUN
ejpam-5192	60	26	,	,	PUNCT
ejpam-5192	60	27	then	then	ADV
ejpam-5192	60	28	τ1τ2	τ1τ2	NOUN
ejpam-5192	60	29	-	-	NUM
ejpam-5192	60	30	cl(a	cl(a	NUM
ejpam-5192	60	31	)	)	PUNCT
ejpam-5192	60	32	⊆	⊆	NUM
ejpam-5192	60	33	τ1τ2	τ1τ2	NOUN
ejpam-5192	60	34	-	-	NOUN
ejpam-5192	60	35	cl(b	cl(b	NOUN
ejpam-5192	60	36	)	)	PUNCT
ejpam-5192	60	37	.	.	PUNCT
ejpam-5192	61	1	(	(	PUNCT
ejpam-5192	61	2	3	3	X
ejpam-5192	61	3	)	)	PUNCT
ejpam-5192	61	4	τ1τ2	τ1τ2	NOUN
ejpam-5192	61	5	-	-	NUM
ejpam-5192	61	6	cl(a	cl(a	NUM
ejpam-5192	61	7	)	)	PUNCT
ejpam-5192	61	8	is	be	AUX
ejpam-5192	61	9	τ1τ2	τ1τ2	NOUN
ejpam-5192	61	10	-	-	ADJ
ejpam-5192	61	11	closed	closed	ADJ
ejpam-5192	61	12	.	.	PUNCT
ejpam-5192	62	1	(	(	PUNCT
ejpam-5192	62	2	4	4	X
ejpam-5192	62	3	)	)	PUNCT
ejpam-5192	62	4	a	a	PRON
ejpam-5192	62	5	is	be	AUX
ejpam-5192	62	6	τ1τ2	τ1τ2	NOUN
ejpam-5192	62	7	-	-	ADJ
ejpam-5192	62	8	closed	closed	ADJ
ejpam-5192	62	9	if	if	SCONJ
ejpam-5192	62	10	and	and	CCONJ
ejpam-5192	62	11	only	only	ADV
ejpam-5192	62	12	if	if	SCONJ
ejpam-5192	62	13	a	a	DET
ejpam-5192	62	14	=	=	PUNCT
ejpam-5192	62	15	τ1τ2	τ1τ2	NOUN
ejpam-5192	62	16	-	-	NUM
ejpam-5192	62	17	cl(a	cl(a	NUM
ejpam-5192	62	18	)	)	PUNCT
ejpam-5192	62	19	.	.	PUNCT
ejpam-5192	63	1	(	(	PUNCT
ejpam-5192	63	2	5	5	X
ejpam-5192	63	3	)	)	PUNCT
ejpam-5192	63	4	τ1τ2	τ1τ2	NOUN
ejpam-5192	63	5	-	-	NOUN
ejpam-5192	63	6	cl(x	cl(x	X
ejpam-5192	63	7	−a	−a	NOUN
ejpam-5192	63	8	)	)	PUNCT
ejpam-5192	64	1	=	=	PUNCT
ejpam-5192	64	2	x	x	X
ejpam-5192	65	1	−	−	ADP
ejpam-5192	65	2	τ1τ2	τ1τ2	NOUN
ejpam-5192	65	3	-	-	PUNCT
ejpam-5192	65	4	int(a	int(a	NOUN
ejpam-5192	65	5	)	)	PUNCT
ejpam-5192	65	6	.	.	PUNCT
ejpam-5192	66	1	a	a	DET
ejpam-5192	66	2	subset	subset	NOUN
ejpam-5192	66	3	a	a	PRON
ejpam-5192	66	4	of	of	ADP
ejpam-5192	66	5	a	a	DET
ejpam-5192	66	6	bitopological	bitopological	ADJ
ejpam-5192	66	7	space	space	NOUN
ejpam-5192	66	8	(	(	PUNCT
ejpam-5192	66	9	x	x	NOUN
ejpam-5192	66	10	,	,	PUNCT
ejpam-5192	66	11	τ1	τ1	NOUN
ejpam-5192	66	12	,	,	PUNCT
ejpam-5192	66	13	τ2	τ2	NOUN
ejpam-5192	66	14	)	)	PUNCT
ejpam-5192	66	15	is	be	AUX
ejpam-5192	66	16	said	say	VERB
ejpam-5192	66	17	to	to	PART
ejpam-5192	66	18	be	be	AUX
ejpam-5192	66	19	(	(	PUNCT
ejpam-5192	66	20	τ1	τ1	NOUN
ejpam-5192	66	21	,	,	PUNCT
ejpam-5192	66	22	τ2)r	τ2)r	NOUN
ejpam-5192	66	23	-	-	PUNCT
ejpam-5192	66	24	open	open	NOUN
ejpam-5192	66	25	[	[	X
ejpam-5192	66	26	29	29	NUM
ejpam-5192	66	27	]	]	PUNCT
ejpam-5192	66	28	(	(	PUNCT
ejpam-5192	66	29	resp	resp	NOUN
ejpam-5192	66	30	.	.	PUNCT
ejpam-5192	67	1	(	(	PUNCT
ejpam-5192	67	2	τ1	τ1	NOUN
ejpam-5192	67	3	,	,	PUNCT
ejpam-5192	67	4	τ2)s	τ2)s	NOUN
ejpam-5192	67	5	-	-	PUNCT
ejpam-5192	67	6	open	open	ADJ
ejpam-5192	67	7	[	[	X
ejpam-5192	67	8	5	5	NUM
ejpam-5192	67	9	]	]	PUNCT
ejpam-5192	67	10	,	,	PUNCT
ejpam-5192	67	11	(	(	PUNCT
ejpam-5192	67	12	τ1	τ1	NOUN
ejpam-5192	67	13	,	,	PUNCT
ejpam-5192	67	14	τ2)p	τ2)p	NOUN
ejpam-5192	67	15	-	-	ADJ
ejpam-5192	67	16	open	open	ADJ
ejpam-5192	67	17	[	[	X
ejpam-5192	67	18	5	5	NUM
ejpam-5192	67	19	]	]	PUNCT
ejpam-5192	67	20	,	,	PUNCT
ejpam-5192	67	21	(	(	PUNCT
ejpam-5192	67	22	τ1	τ1	NOUN
ejpam-5192	67	23	,	,	PUNCT
ejpam-5192	67	24	τ2)β	τ2)β	ADJ
ejpam-5192	67	25	-	-	PUNCT
ejpam-5192	67	26	open	open	ADJ
ejpam-5192	67	27	[	[	X
ejpam-5192	67	28	5	5	NUM
ejpam-5192	67	29	]	]	PUNCT
ejpam-5192	67	30	)	)	PUNCT
ejpam-5192	67	31	if	if	SCONJ
ejpam-5192	67	32	a	a	DET
ejpam-5192	67	33	=	=	PUNCT
ejpam-5192	67	34	τ1τ2	τ1τ2	NOUN
ejpam-5192	67	35	-	-	NOUN
ejpam-5192	67	36	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5192	67	37	-	-	PUNCT
ejpam-5192	67	38	cl(a	cl(a	NUM
ejpam-5192	67	39	)	)	PUNCT
ejpam-5192	67	40	)	)	PUNCT
ejpam-5192	67	41	(	(	PUNCT
ejpam-5192	67	42	resp	resp	NOUN
ejpam-5192	67	43	.	.	PUNCT
ejpam-5192	68	1	a	a	DET
ejpam-5192	68	2	⊆	⊆	NUM
ejpam-5192	68	3	τ1τ2	τ1τ2	NOUN
ejpam-5192	68	4	-	-	ADJ
ejpam-5192	68	5	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5192	68	6	-	-	PUNCT
ejpam-5192	68	7	int(a	int(a	NOUN
ejpam-5192	68	8	)	)	PUNCT
ejpam-5192	68	9	)	)	PUNCT
ejpam-5192	68	10	,	,	PUNCT
ejpam-5192	68	11	a	a	DET
ejpam-5192	68	12	⊆	⊆	NUM
ejpam-5192	68	13	τ1τ2	τ1τ2	NOUN
ejpam-5192	68	14	-	-	NOUN
ejpam-5192	68	15	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5192	68	16	-	-	PUNCT
ejpam-5192	68	17	cl(a	cl(a	NUM
ejpam-5192	68	18	)	)	PUNCT
ejpam-5192	68	19	)	)	PUNCT
ejpam-5192	68	20	,	,	PUNCT
ejpam-5192	68	21	a	a	DET
ejpam-5192	68	22	⊆	⊆	NUM
ejpam-5192	68	23	τ1τ2	τ1τ2	NOUN
ejpam-5192	68	24	-	-	PUNCT
ejpam-5192	68	25	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5192	68	26	-	-	PUNCT
ejpam-5192	68	27	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5192	68	28	-	-	PUNCT
ejpam-5192	68	29	cl(a	cl(a	NUM
ejpam-5192	68	30	)	)	PUNCT
ejpam-5192	68	31	)	)	PUNCT
ejpam-5192	68	32	)	)	PUNCT
ejpam-5192	68	33	)	)	PUNCT
ejpam-5192	68	34	.	.	PUNCT
ejpam-5192	69	1	the	the	DET
ejpam-5192	69	2	complement	complement	NOUN
ejpam-5192	69	3	of	of	ADP
ejpam-5192	69	4	a	a	DET
ejpam-5192	69	5	(	(	PUNCT
ejpam-5192	69	6	τ1	τ1	NOUN
ejpam-5192	69	7	,	,	PUNCT
ejpam-5192	69	8	τ2)r	τ2)r	NOUN
ejpam-5192	69	9	-	-	PUNCT
ejpam-5192	69	10	open	open	ADJ
ejpam-5192	69	11	(	(	PUNCT
ejpam-5192	69	12	resp	resp	NOUN
ejpam-5192	69	13	.	.	PUNCT
ejpam-5192	70	1	(	(	PUNCT
ejpam-5192	70	2	τ1	τ1	NOUN
ejpam-5192	70	3	,	,	PUNCT
ejpam-5192	70	4	τ2)s	τ2)s	NOUN
ejpam-5192	70	5	-	-	PUNCT
ejpam-5192	70	6	open	open	ADJ
ejpam-5192	70	7	,	,	PUNCT
ejpam-5192	70	8	(	(	PUNCT
ejpam-5192	70	9	τ1	τ1	NOUN
ejpam-5192	70	10	,	,	PUNCT
ejpam-5192	70	11	τ2)p	τ2)p	NOUN
ejpam-5192	70	12	-	-	ADJ
ejpam-5192	70	13	open	open	ADJ
ejpam-5192	70	14	,	,	PUNCT
ejpam-5192	70	15	(	(	PUNCT
ejpam-5192	70	16	τ1	τ1	NOUN
ejpam-5192	70	17	,	,	PUNCT
ejpam-5192	70	18	τ2)β	τ2)β	ADJ
ejpam-5192	70	19	-	-	PUNCT
ejpam-5192	70	20	open	open	ADJ
ejpam-5192	70	21	)	)	PUNCT
ejpam-5192	70	22	set	set	NOUN
ejpam-5192	70	23	is	be	AUX
ejpam-5192	70	24	called	call	VERB
ejpam-5192	70	25	(	(	PUNCT
ejpam-5192	70	26	τ1	τ1	NOUN
ejpam-5192	70	27	,	,	PUNCT
ejpam-5192	70	28	τ2)r	τ2)r	NOUN
ejpam-5192	70	29	-	-	PUNCT
ejpam-5192	70	30	closed	closed	ADJ
ejpam-5192	70	31	,	,	PUNCT
ejpam-5192	70	32	(	(	PUNCT
ejpam-5192	70	33	τ1	τ1	NOUN
ejpam-5192	70	34	,	,	PUNCT
ejpam-5192	70	35	τ2)s	τ2)s	NOUN
ejpam-5192	70	36	-	-	PUNCT
ejpam-5192	70	37	closed	closed	ADJ
ejpam-5192	70	38	,	,	PUNCT
ejpam-5192	70	39	(	(	PUNCT
ejpam-5192	70	40	τ1	τ1	NOUN
ejpam-5192	70	41	,	,	PUNCT
ejpam-5192	70	42	τ2)p	τ2)p	NOUN
ejpam-5192	70	43	-	-	PUNCT
ejpam-5192	70	44	closed	closed	ADJ
ejpam-5192	70	45	,	,	PUNCT
ejpam-5192	70	46	(	(	PUNCT
ejpam-5192	70	47	τ1	τ1	NOUN
ejpam-5192	70	48	,	,	PUNCT
ejpam-5192	70	49	τ2)β	τ2)β	NOUN
ejpam-5192	70	50	-	-	PUNCT
ejpam-5192	70	51	closed	closed	ADJ
ejpam-5192	70	52	.	.	PUNCT
ejpam-5192	71	1	let	let	VERB
ejpam-5192	71	2	a	a	DET
ejpam-5192	71	3	be	be	AUX
ejpam-5192	71	4	a	a	DET
ejpam-5192	71	5	subset	subset	NOUN
ejpam-5192	71	6	of	of	ADP
ejpam-5192	71	7	a	a	DET
ejpam-5192	71	8	bitopological	bitopological	ADJ
ejpam-5192	71	9	space	space	NOUN
ejpam-5192	71	10	(	(	PUNCT
ejpam-5192	71	11	x	x	NOUN
ejpam-5192	71	12	,	,	PUNCT
ejpam-5192	71	13	τ1	τ1	NOUN
ejpam-5192	71	14	,	,	PUNCT
ejpam-5192	71	15	τ2	τ2	NOUN
ejpam-5192	71	16	)	)	PUNCT
ejpam-5192	71	17	.	.	PUNCT
ejpam-5192	72	1	the	the	DET
ejpam-5192	72	2	intersection	intersection	NOUN
ejpam-5192	72	3	of	of	ADP
ejpam-5192	72	4	all	all	DET
ejpam-5192	72	5	(	(	PUNCT
ejpam-5192	72	6	τ1	τ1	NOUN
ejpam-5192	72	7	,	,	PUNCT
ejpam-5192	72	8	τ2)s	τ2)s	NOUN
ejpam-5192	72	9	-	-	PUNCT
ejpam-5192	72	10	closed	close	VERB
ejpam-5192	72	11	sets	set	NOUN
ejpam-5192	72	12	of	of	ADP
ejpam-5192	72	13	x	x	PUNCT
ejpam-5192	72	14	containing	contain	VERB
ejpam-5192	72	15	a	a	PRON
ejpam-5192	72	16	is	be	AUX
ejpam-5192	72	17	called	call	VERB
ejpam-5192	72	18	the	the	DET
ejpam-5192	72	19	(	(	PUNCT
ejpam-5192	72	20	τ1	τ1	NOUN
ejpam-5192	72	21	,	,	PUNCT
ejpam-5192	72	22	τ2)s	τ2)s	NOUN
ejpam-5192	72	23	-	-	PUNCT
ejpam-5192	72	24	closure	closure	NOUN
ejpam-5192	72	25	[	[	X
ejpam-5192	72	26	5	5	NUM
ejpam-5192	72	27	]	]	PUNCT
ejpam-5192	72	28	of	of	ADP
ejpam-5192	72	29	a	a	PRON
ejpam-5192	72	30	and	and	CCONJ
ejpam-5192	72	31	is	be	AUX
ejpam-5192	72	32	denoted	denote	VERB
ejpam-5192	72	33	by	by	ADP
ejpam-5192	72	34	(	(	PUNCT
ejpam-5192	72	35	τ1	τ1	NOUN
ejpam-5192	72	36	,	,	PUNCT
ejpam-5192	72	37	τ2)-scl(a	τ2)-scl(a	PROPN
ejpam-5192	72	38	)	)	PUNCT
ejpam-5192	72	39	.	.	PUNCT
ejpam-5192	73	1	the	the	DET
ejpam-5192	73	2	union	union	NOUN
ejpam-5192	73	3	of	of	ADP
ejpam-5192	73	4	all	all	DET
ejpam-5192	73	5	(	(	PUNCT
ejpam-5192	73	6	τ1	τ1	NOUN
ejpam-5192	73	7	,	,	PUNCT
ejpam-5192	73	8	τ2)s	τ2)s	NOUN
ejpam-5192	73	9	-	-	PUNCT
ejpam-5192	73	10	open	open	ADJ
ejpam-5192	73	11	sets	set	NOUN
ejpam-5192	73	12	of	of	ADP
ejpam-5192	73	13	x	x	PUNCT
ejpam-5192	73	14	contained	contain	VERB
ejpam-5192	73	15	in	in	ADP
ejpam-5192	73	16	a	a	PRON
ejpam-5192	73	17	is	be	AUX
ejpam-5192	73	18	called	call	VERB
ejpam-5192	73	19	the	the	DET
ejpam-5192	73	20	(	(	PUNCT
ejpam-5192	73	21	τ1	τ1	NOUN
ejpam-5192	73	22	,	,	PUNCT
ejpam-5192	73	23	τ2)s	τ2)s	NOUN
ejpam-5192	73	24	-	-	ADJ
ejpam-5192	73	25	interior	interior	ADJ
ejpam-5192	73	26	[	[	X
ejpam-5192	73	27	5	5	NUM
ejpam-5192	73	28	]	]	PUNCT
ejpam-5192	73	29	of	of	ADP
ejpam-5192	73	30	a	a	PRON
ejpam-5192	73	31	and	and	CCONJ
ejpam-5192	73	32	is	be	AUX
ejpam-5192	73	33	denoted	denote	VERB
ejpam-5192	73	34	by	by	ADP
ejpam-5192	73	35	(	(	PUNCT
ejpam-5192	73	36	τ1	τ1	NOUN
ejpam-5192	73	37	,	,	PUNCT
ejpam-5192	73	38	τ2)-sint(a	τ2)-sint(a	PROPN
ejpam-5192	73	39	)	)	PUNCT
ejpam-5192	73	40	.	.	PUNCT
ejpam-5192	74	1	a	a	DET
ejpam-5192	74	2	subset	subset	NOUN
ejpam-5192	74	3	a	a	PRON
ejpam-5192	74	4	of	of	ADP
ejpam-5192	74	5	a	a	DET
ejpam-5192	74	6	bitopological	bitopological	ADJ
ejpam-5192	74	7	space	space	NOUN
ejpam-5192	74	8	(	(	PUNCT
ejpam-5192	74	9	x	x	NOUN
ejpam-5192	74	10	,	,	PUNCT
ejpam-5192	74	11	τ1	τ1	NOUN
ejpam-5192	74	12	,	,	PUNCT
ejpam-5192	74	13	τ2	τ2	NOUN
ejpam-5192	74	14	)	)	PUNCT
ejpam-5192	74	15	is	be	AUX
ejpam-5192	74	16	said	say	VERB
ejpam-5192	74	17	to	to	PART
ejpam-5192	74	18	be	be	AUX
ejpam-5192	74	19	α(τ1	α(τ1	NOUN
ejpam-5192	74	20	,	,	PUNCT
ejpam-5192	74	21	τ2)-open	τ2)-open	ADJ
ejpam-5192	74	22	[	[	X
ejpam-5192	74	23	30	30	NUM
ejpam-5192	74	24	]	]	X
ejpam-5192	74	25	if	if	SCONJ
ejpam-5192	74	26	a	a	DET
ejpam-5192	74	27	⊆	⊆	NUM
ejpam-5192	74	28	τ1τ2	τ1τ2	NOUN
ejpam-5192	74	29	-	-	PUNCT
ejpam-5192	74	30	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5192	74	31	-	-	PUNCT
ejpam-5192	74	32	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5192	74	33	-	-	PUNCT
ejpam-5192	74	34	int(a	int(a	NOUN
ejpam-5192	74	35	)	)	PUNCT
ejpam-5192	74	36	)	)	PUNCT
ejpam-5192	74	37	)	)	PUNCT
ejpam-5192	74	38	.	.	PUNCT
ejpam-5192	75	1	the	the	DET
ejpam-5192	75	2	complement	complement	NOUN
ejpam-5192	75	3	of	of	ADP
ejpam-5192	75	4	an	an	DET
ejpam-5192	75	5	α(τ1	α(τ1	NOUN
ejpam-5192	75	6	,	,	PUNCT
ejpam-5192	75	7	τ2)-open	τ2)-open	ADJ
ejpam-5192	75	8	set	set	NOUN
ejpam-5192	75	9	is	be	AUX
ejpam-5192	75	10	called	call	VERB
ejpam-5192	75	11	α(τ1	α(τ1	NOUN
ejpam-5192	75	12	,	,	PUNCT
ejpam-5192	75	13	τ2)-closed	τ2)-closed	PROPN
ejpam-5192	75	14	.	.	PUNCT
ejpam-5192	76	1	let	let	VERB
ejpam-5192	76	2	a	a	DET
ejpam-5192	76	3	be	be	AUX
ejpam-5192	76	4	a	a	DET
ejpam-5192	76	5	subset	subset	NOUN
ejpam-5192	76	6	of	of	ADP
ejpam-5192	76	7	a	a	DET
ejpam-5192	76	8	bitopological	bitopological	ADJ
ejpam-5192	76	9	space	space	NOUN
ejpam-5192	76	10	(	(	PUNCT
ejpam-5192	76	11	x	x	NOUN
ejpam-5192	76	12	,	,	PUNCT
ejpam-5192	76	13	τ1	τ1	NOUN
ejpam-5192	76	14	,	,	PUNCT
ejpam-5192	76	15	τ2	τ2	NOUN
ejpam-5192	76	16	)	)	PUNCT
ejpam-5192	76	17	.	.	PUNCT
ejpam-5192	77	1	the	the	DET
ejpam-5192	77	2	intersection	intersection	NOUN
ejpam-5192	77	3	of	of	ADP
ejpam-5192	77	4	all	all	PRON
ejpam-5192	77	5	(	(	PUNCT
ejpam-5192	77	6	τ1	τ1	NOUN
ejpam-5192	77	7	,	,	PUNCT
ejpam-5192	77	8	τ2)p	τ2)p	NOUN
ejpam-5192	77	9	-	-	PUNCT
ejpam-5192	77	10	closed	closed	ADJ
ejpam-5192	77	11	(	(	PUNCT
ejpam-5192	77	12	resp	resp	NOUN
ejpam-5192	77	13	.	.	PUNCT
ejpam-5192	78	1	α(τ1	α(τ1	NOUN
ejpam-5192	78	2	,	,	PUNCT
ejpam-5192	78	3	τ2)-closed	τ2)-closed	ADJ
ejpam-5192	78	4	)	)	PUNCT
ejpam-5192	78	5	sets	set	NOUN
ejpam-5192	78	6	of	of	ADP
ejpam-5192	78	7	x	x	PUNCT
ejpam-5192	78	8	containing	contain	VERB
ejpam-5192	78	9	a	a	PRON
ejpam-5192	78	10	is	be	AUX
ejpam-5192	78	11	called	call	VERB
ejpam-5192	78	12	the	the	DET
ejpam-5192	78	13	(	(	PUNCT
ejpam-5192	78	14	τ1	τ1	NOUN
ejpam-5192	78	15	,	,	PUNCT
ejpam-5192	78	16	τ2)p	τ2)p	NOUN
ejpam-5192	78	17	-	-	PUNCT
ejpam-5192	78	18	closure	closure	NOUN
ejpam-5192	78	19	(	(	PUNCT
ejpam-5192	78	20	resp	resp	NOUN
ejpam-5192	78	21	.	.	PUNCT
ejpam-5192	78	22	α(τ1	α(τ1	NOUN
ejpam-5192	78	23	,	,	PUNCT
ejpam-5192	78	24	τ2)-closure	τ2)-closure	NOUN
ejpam-5192	78	25	)	)	PUNCT
ejpam-5192	78	26	and	and	CCONJ
ejpam-5192	78	27	is	be	AUX
ejpam-5192	78	28	denoted	denote	VERB
ejpam-5192	78	29	by	by	ADP
ejpam-5192	78	30	(	(	PUNCT
ejpam-5192	78	31	τ1	τ1	NOUN
ejpam-5192	78	32	,	,	PUNCT
ejpam-5192	78	33	τ2)-pcl(a	τ2)-pcl(a	NOUN
ejpam-5192	78	34	)	)	PUNCT
ejpam-5192	78	35	(	(	PUNCT
ejpam-5192	78	36	resp	resp	NOUN
ejpam-5192	78	37	.	.	PUNCT
ejpam-5192	79	1	(	(	PUNCT
ejpam-5192	79	2	τ1	τ1	NOUN
ejpam-5192	79	3	,	,	PUNCT
ejpam-5192	79	4	τ2)-αcl(a	τ2)-αcl(a	ADJ
ejpam-5192	79	5	)	)	PUNCT
ejpam-5192	79	6	)	)	PUNCT
ejpam-5192	79	7	.	.	PUNCT
ejpam-5192	80	1	by	by	ADP
ejpam-5192	80	2	a	a	DET
ejpam-5192	80	3	multifunction	multifunction	NOUN
ejpam-5192	80	4	f	f	NOUN
ejpam-5192	80	5	:	:	PUNCT
ejpam-5192	80	6	x	x	X
ejpam-5192	80	7	→	→	SYM
ejpam-5192	80	8	y	y	PROPN
ejpam-5192	80	9	,	,	PUNCT
ejpam-5192	80	10	we	we	PRON
ejpam-5192	80	11	mean	mean	VERB
ejpam-5192	80	12	a	a	DET
ejpam-5192	80	13	point	point	NOUN
ejpam-5192	80	14	-	-	PUNCT
ejpam-5192	80	15	to	to	ADP
ejpam-5192	80	16	-	-	PUNCT
ejpam-5192	80	17	set	set	VERB
ejpam-5192	80	18	correspondence	correspondence	NOUN
ejpam-5192	80	19	from	from	ADP
ejpam-5192	80	20	x	x	PUNCT
ejpam-5192	80	21	into	into	ADP
ejpam-5192	80	22	y	y	PROPN
ejpam-5192	80	23	,	,	PUNCT
ejpam-5192	80	24	and	and	CCONJ
ejpam-5192	80	25	we	we	PRON
ejpam-5192	80	26	always	always	ADV
ejpam-5192	80	27	assume	assume	VERB
ejpam-5192	80	28	that	that	SCONJ
ejpam-5192	80	29	f	f	PROPN
ejpam-5192	80	30	(	(	PUNCT
ejpam-5192	80	31	x	x	X
ejpam-5192	80	32	)	)	PUNCT
ejpam-5192	80	33	̸=	̸=	NOUN
ejpam-5192	80	34	∅	∅	NOUN
ejpam-5192	80	35	for	for	ADP
ejpam-5192	80	36	all	all	PRON
ejpam-5192	80	37	x	x	SYM
ejpam-5192	80	38	∈	∈	ADJ
ejpam-5192	80	39	x.	x.	NOUN
ejpam-5192	80	40	for	for	ADP
ejpam-5192	80	41	a	a	DET
ejpam-5192	80	42	multifunction	multifunction	NOUN
ejpam-5192	80	43	f	f	NOUN
ejpam-5192	81	1	:	:	PUNCT
ejpam-5192	81	2	x	x	X
ejpam-5192	81	3	→	→	SYM
ejpam-5192	81	4	y	y	PROPN
ejpam-5192	81	5	,	,	PUNCT
ejpam-5192	81	6	following	follow	VERB
ejpam-5192	81	7	[	[	X
ejpam-5192	81	8	2	2	X
ejpam-5192	81	9	]	]	PUNCT
ejpam-5192	81	10	we	we	PRON
ejpam-5192	81	11	shall	shall	AUX
ejpam-5192	81	12	denote	denote	VERB
ejpam-5192	81	13	the	the	DET
ejpam-5192	81	14	upper	upper	ADJ
ejpam-5192	81	15	and	and	CCONJ
ejpam-5192	81	16	lower	low	ADJ
ejpam-5192	81	17	inverse	inverse	NOUN
ejpam-5192	81	18	of	of	ADP
ejpam-5192	81	19	a	a	DET
ejpam-5192	81	20	set	set	NOUN
ejpam-5192	81	21	b	b	PROPN
ejpam-5192	81	22	of	of	ADP
ejpam-5192	81	23	y	y	PROPN
ejpam-5192	81	24	by	by	ADP
ejpam-5192	81	25	f+(b	f+(b	NOUN
ejpam-5192	81	26	)	)	PUNCT
ejpam-5192	81	27	and	and	CCONJ
ejpam-5192	81	28	f−(b	f−(b	NOUN
ejpam-5192	81	29	)	)	PUNCT
ejpam-5192	81	30	,	,	PUNCT
ejpam-5192	81	31	respectively	respectively	ADV
ejpam-5192	81	32	,	,	PUNCT
ejpam-5192	81	33	that	that	ADV
ejpam-5192	81	34	is	is	ADV
ejpam-5192	81	35	,	,	PUNCT
ejpam-5192	81	36	f+(b	f+(b	NOUN
ejpam-5192	81	37	)	)	PUNCT
ejpam-5192	81	38	=	=	PRON
ejpam-5192	82	1	{	{	PUNCT
ejpam-5192	82	2	x	x	PUNCT
ejpam-5192	82	3	∈	∈	PROPN
ejpam-5192	82	4	x	x	INTJ
ejpam-5192	83	1	|	|	NOUN
ejpam-5192	83	2	f	f	X
ejpam-5192	83	3	(	(	PUNCT
ejpam-5192	83	4	x	x	NOUN
ejpam-5192	83	5	)	)	PUNCT
ejpam-5192	83	6	⊆	⊆	NUM
ejpam-5192	83	7	b	b	NOUN
ejpam-5192	83	8	}	}	PUNCT
ejpam-5192	83	9	and	and	CCONJ
ejpam-5192	83	10	f−(b	f−(b	PROPN
ejpam-5192	83	11	)	)	PUNCT
ejpam-5192	83	12	=	=	PRON
ejpam-5192	84	1	{	{	PUNCT
ejpam-5192	84	2	x	x	PUNCT
ejpam-5192	84	3	∈	∈	PROPN
ejpam-5192	84	4	x	x	INTJ
ejpam-5192	85	1	|	|	NOUN
ejpam-5192	85	2	f	f	X
ejpam-5192	85	3	(	(	PUNCT
ejpam-5192	85	4	x	x	NOUN
ejpam-5192	85	5	)	)	PUNCT
ejpam-5192	85	6	∩b	∩b	NOUN
ejpam-5192	85	7	̸=	̸=	PROPN
ejpam-5192	85	8	∅	∅	NOUN
ejpam-5192	85	9	}	}	PUNCT
ejpam-5192	85	10	.	.	PUNCT
ejpam-5192	86	1	in	in	ADP
ejpam-5192	86	2	particular	particular	ADJ
ejpam-5192	86	3	,	,	PUNCT
ejpam-5192	86	4	f−(y	f−(y	NOUN
ejpam-5192	86	5	)	)	PUNCT
ejpam-5192	86	6	=	=	SYM
ejpam-5192	87	1	{	{	PUNCT
ejpam-5192	87	2	x	x	PUNCT
ejpam-5192	87	3	∈	∈	PROPN
ejpam-5192	87	4	x	x	INTJ
ejpam-5192	88	1	|	|	ADV
ejpam-5192	88	2	y	y	PROPN
ejpam-5192	88	3	∈	∈	PROPN
ejpam-5192	88	4	f	f	X
ejpam-5192	88	5	(	(	PUNCT
ejpam-5192	88	6	x	x	NOUN
ejpam-5192	88	7	)	)	PUNCT
ejpam-5192	88	8	}	}	PUNCT
ejpam-5192	88	9	for	for	ADP
ejpam-5192	88	10	each	each	DET
ejpam-5192	88	11	point	point	NOUN
ejpam-5192	88	12	y	y	PROPN
ejpam-5192	88	13	∈	∈	PROPN
ejpam-5192	88	14	y	y	PROPN
ejpam-5192	88	15	.	.	PUNCT
ejpam-5192	89	1	for	for	ADP
ejpam-5192	89	2	each	each	DET
ejpam-5192	89	3	a	a	DET
ejpam-5192	89	4	⊆	⊆	NUM
ejpam-5192	89	5	x	x	SYM
ejpam-5192	89	6	,	,	PUNCT
ejpam-5192	89	7	f	f	PROPN
ejpam-5192	89	8	(	(	PUNCT
ejpam-5192	89	9	a	a	NOUN
ejpam-5192	89	10	)	)	PUNCT
ejpam-5192	89	11	=	=	SYM
ejpam-5192	89	12	∪x∈af	∪x∈af	NOUN
ejpam-5192	89	13	(	(	PUNCT
ejpam-5192	89	14	x	x	NOUN
ejpam-5192	89	15	)	)	PUNCT
ejpam-5192	89	16	.	.	PUNCT
ejpam-5192	90	1	3	3	X
ejpam-5192	90	2	.	.	X
ejpam-5192	90	3	upper	upper	ADJ
ejpam-5192	90	4	and	and	CCONJ
ejpam-5192	90	5	lower	low	ADJ
ejpam-5192	90	6	almost	almost	ADV
ejpam-5192	90	7	(	(	PUNCT
ejpam-5192	90	8	τ1	τ1	NOUN
ejpam-5192	90	9	,	,	PUNCT
ejpam-5192	90	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	90	11	multifunctions	multifunction	NOUN
ejpam-5192	90	12	in	in	ADP
ejpam-5192	90	13	this	this	DET
ejpam-5192	90	14	section	section	NOUN
ejpam-5192	90	15	,	,	PUNCT
ejpam-5192	90	16	we	we	PRON
ejpam-5192	90	17	introduce	introduce	VERB
ejpam-5192	90	18	the	the	DET
ejpam-5192	90	19	notions	notion	NOUN
ejpam-5192	90	20	of	of	ADP
ejpam-5192	90	21	upper	upper	ADJ
ejpam-5192	90	22	and	and	CCONJ
ejpam-5192	90	23	lower	low	ADJ
ejpam-5192	90	24	almost	almost	ADV
ejpam-5192	90	25	(	(	PUNCT
ejpam-5192	90	26	τ1	τ1	NOUN
ejpam-5192	90	27	,	,	PUNCT
ejpam-5192	90	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	90	29	multifunctions	multifunction	NOUN
ejpam-5192	90	30	.	.	PUNCT
ejpam-5192	91	1	moreover	moreover	ADV
ejpam-5192	91	2	,	,	PUNCT
ejpam-5192	91	3	several	several	ADJ
ejpam-5192	91	4	characterizations	characterization	NOUN
ejpam-5192	91	5	of	of	ADP
ejpam-5192	91	6	upper	upper	ADJ
ejpam-5192	91	7	and	and	CCONJ
ejpam-5192	91	8	lower	low	ADJ
ejpam-5192	91	9	almost	almost	ADV
ejpam-5192	91	10	(	(	PUNCT
ejpam-5192	91	11	τ1	τ1	NOUN
ejpam-5192	91	12	,	,	PUNCT
ejpam-5192	91	13	τ2)continuous	τ2)continuous	ADJ
ejpam-5192	91	14	multifunctions	multifunction	NOUN
ejpam-5192	91	15	are	be	AUX
ejpam-5192	91	16	discussed	discuss	VERB
ejpam-5192	91	17	.	.	PUNCT
ejpam-5192	92	1	definition	definition	NOUN
ejpam-5192	92	2	1	1	NUM
ejpam-5192	92	3	.	.	PUNCT
ejpam-5192	93	1	a	a	DET
ejpam-5192	93	2	multifunction	multifunction	NOUN
ejpam-5192	93	3	f	f	NOUN
ejpam-5192	93	4	:	:	PUNCT
ejpam-5192	93	5	(	(	PUNCT
ejpam-5192	93	6	x	x	NOUN
ejpam-5192	93	7	,	,	PUNCT
ejpam-5192	93	8	τ1	τ1	NOUN
ejpam-5192	93	9	,	,	PUNCT
ejpam-5192	93	10	τ2	τ2	NOUN
ejpam-5192	93	11	)	)	PUNCT
ejpam-5192	93	12	→	→	SYM
ejpam-5192	93	13	(	(	PUNCT
ejpam-5192	93	14	y	y	PROPN
ejpam-5192	93	15	,	,	PUNCT
ejpam-5192	93	16	σ1	σ1	PROPN
ejpam-5192	93	17	,	,	PUNCT
ejpam-5192	93	18	σ2	σ2	PROPN
ejpam-5192	93	19	)	)	PUNCT
ejpam-5192	93	20	is	be	AUX
ejpam-5192	93	21	said	say	VERB
ejpam-5192	93	22	to	to	PART
ejpam-5192	93	23	be	be	AUX
ejpam-5192	93	24	upper	upper	ADJ
ejpam-5192	93	25	almost	almost	ADV
ejpam-5192	93	26	(	(	PUNCT
ejpam-5192	93	27	τ1	τ1	NOUN
ejpam-5192	93	28	,	,	PUNCT
ejpam-5192	93	29	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	93	30	at	at	ADP
ejpam-5192	93	31	a	a	DET
ejpam-5192	93	32	point	point	NOUN
ejpam-5192	93	33	x	x	SYM
ejpam-5192	93	34	∈	∈	NOUN
ejpam-5192	93	35	x	x	PUNCT
ejpam-5192	93	36	if	if	SCONJ
ejpam-5192	93	37	for	for	ADP
ejpam-5192	93	38	each	each	DET
ejpam-5192	93	39	σ1σ2	σ1σ2	VERB
ejpam-5192	93	40	-	-	ADJ
ejpam-5192	93	41	open	open	ADJ
ejpam-5192	93	42	set	set	NOUN
ejpam-5192	93	43	v	v	NOUN
ejpam-5192	93	44	of	of	ADP
ejpam-5192	93	45	y	y	PROPN
ejpam-5192	93	46	containing	contain	VERB
ejpam-5192	93	47	f	f	PROPN
ejpam-5192	93	48	(	(	PUNCT
ejpam-5192	93	49	x	x	NOUN
ejpam-5192	93	50	)	)	PUNCT
ejpam-5192	93	51	,	,	PUNCT
ejpam-5192	93	52	there	there	PRON
ejpam-5192	93	53	exists	exist	VERB
ejpam-5192	93	54	a	a	DET
ejpam-5192	93	55	τ1τ2	τ1τ2	NOUN
ejpam-5192	93	56	-	-	ADJ
ejpam-5192	93	57	open	open	ADJ
ejpam-5192	93	58	set	set	ADJ
ejpam-5192	93	59	u	u	NOUN
ejpam-5192	93	60	of	of	ADP
ejpam-5192	93	61	x	x	PUNCT
ejpam-5192	93	62	containing	contain	VERB
ejpam-5192	93	63	x	x	PUNCT
ejpam-5192	93	64	such	such	ADJ
ejpam-5192	93	65	that	that	SCONJ
ejpam-5192	93	66	f	f	PROPN
ejpam-5192	93	67	(	(	PUNCT
ejpam-5192	93	68	u	u	NOUN
ejpam-5192	93	69	)	)	PUNCT
ejpam-5192	93	70	⊆	⊆	NUM
ejpam-5192	93	71	σ1σ2	σ1σ2	X
ejpam-5192	93	72	-	-	PUNCT
ejpam-5192	93	73	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5192	93	74	-	-	PUNCT
ejpam-5192	93	75	cl(v	cl(v	NOUN
ejpam-5192	93	76	)	)	PUNCT
ejpam-5192	93	77	)	)	PUNCT
ejpam-5192	93	78	.	.	PUNCT
ejpam-5192	94	1	a	a	DET
ejpam-5192	94	2	multifunction	multifunction	NOUN
ejpam-5192	94	3	f	f	NOUN
ejpam-5192	94	4	:	:	PUNCT
ejpam-5192	94	5	(	(	PUNCT
ejpam-5192	94	6	x	x	NOUN
ejpam-5192	94	7	,	,	PUNCT
ejpam-5192	94	8	τ1	τ1	NOUN
ejpam-5192	94	9	,	,	PUNCT
ejpam-5192	94	10	τ2	τ2	NOUN
ejpam-5192	94	11	)	)	PUNCT
ejpam-5192	94	12	→	→	SYM
ejpam-5192	94	13	(	(	PUNCT
ejpam-5192	94	14	y	y	PROPN
ejpam-5192	94	15	,	,	PUNCT
ejpam-5192	94	16	σ1	σ1	PROPN
ejpam-5192	94	17	,	,	PUNCT
ejpam-5192	94	18	σ2	σ2	PROPN
ejpam-5192	94	19	)	)	PUNCT
ejpam-5192	94	20	is	be	AUX
ejpam-5192	94	21	said	say	VERB
ejpam-5192	94	22	to	to	PART
ejpam-5192	94	23	be	be	AUX
ejpam-5192	94	24	upper	upper	ADJ
ejpam-5192	94	25	almost	almost	ADV
ejpam-5192	94	26	(	(	PUNCT
ejpam-5192	94	27	τ1	τ1	NOUN
ejpam-5192	94	28	,	,	PUNCT
ejpam-5192	94	29	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	94	30	if	if	SCONJ
ejpam-5192	94	31	f	f	PROPN
ejpam-5192	94	32	has	have	VERB
ejpam-5192	94	33	this	this	DET
ejpam-5192	94	34	property	property	NOUN
ejpam-5192	94	35	at	at	ADP
ejpam-5192	94	36	each	each	DET
ejpam-5192	94	37	point	point	NOUN
ejpam-5192	94	38	of	of	ADP
ejpam-5192	94	39	x.	x.	PROPN
ejpam-5192	94	40	lemma	lemma	PROPN
ejpam-5192	95	1	2	2	NUM
ejpam-5192	95	2	.	.	X
ejpam-5192	95	3	for	for	ADP
ejpam-5192	95	4	a	a	DET
ejpam-5192	95	5	subset	subset	NOUN
ejpam-5192	95	6	a	a	PRON
ejpam-5192	95	7	of	of	ADP
ejpam-5192	95	8	a	a	DET
ejpam-5192	95	9	bitopological	bitopological	ADJ
ejpam-5192	95	10	space	space	NOUN
ejpam-5192	95	11	(	(	PUNCT
ejpam-5192	95	12	x	x	NOUN
ejpam-5192	95	13	,	,	PUNCT
ejpam-5192	95	14	τ1	τ1	NOUN
ejpam-5192	95	15	,	,	PUNCT
ejpam-5192	95	16	τ2	τ2	NOUN
ejpam-5192	95	17	)	)	PUNCT
ejpam-5192	95	18	,	,	PUNCT
ejpam-5192	95	19	the	the	DET
ejpam-5192	95	20	following	follow	VERB
ejpam-5192	95	21	properties	property	NOUN
ejpam-5192	95	22	hold	hold	VERB
ejpam-5192	95	23	:	:	PUNCT
ejpam-5192	95	24	c.	c.	PROPN
ejpam-5192	95	25	klanarong	klanarong	PROPN
ejpam-5192	95	26	,	,	PUNCT
ejpam-5192	95	27	s.	s.	PROPN
ejpam-5192	95	28	sompong	sompong	PROPN
ejpam-5192	95	29	,	,	PUNCT
ejpam-5192	95	30	c.	c.	PROPN
ejpam-5192	95	31	boonpok	boonpok	PROPN
ejpam-5192	95	32	/	/	SYM
ejpam-5192	95	33	eur	eur	PROPN
ejpam-5192	95	34	.	.	PUNCT
ejpam-5192	96	1	j.	j.	PROPN
ejpam-5192	96	2	pure	pure	PROPN
ejpam-5192	96	3	appl	appl	PROPN
ejpam-5192	96	4	.	.	PROPN
ejpam-5192	96	5	math	math	PROPN
ejpam-5192	96	6	,	,	PUNCT
ejpam-5192	96	7	17	17	NUM
ejpam-5192	96	8	(	(	PUNCT
ejpam-5192	96	9	2	2	NUM
ejpam-5192	96	10	)	)	PUNCT
ejpam-5192	96	11	(	(	PUNCT
ejpam-5192	96	12	2024	2024	NUM
ejpam-5192	96	13	)	)	PUNCT
ejpam-5192	96	14	,	,	PUNCT
ejpam-5192	96	15	1244	1244	NUM
ejpam-5192	96	16	-	-	SYM
ejpam-5192	96	17	1253	1253	NUM
ejpam-5192	96	18	1247	1247	NUM
ejpam-5192	96	19	(	(	PUNCT
ejpam-5192	96	20	1	1	NUM
ejpam-5192	96	21	)	)	PUNCT
ejpam-5192	96	22	(	(	PUNCT
ejpam-5192	96	23	τ1	τ1	NOUN
ejpam-5192	96	24	,	,	PUNCT
ejpam-5192	96	25	τ2)-scl(a	τ2)-scl(a	NOUN
ejpam-5192	96	26	)	)	PUNCT
ejpam-5192	96	27	=	=	PUNCT
ejpam-5192	97	1	τ1τ2	τ1τ2	NOUN
ejpam-5192	97	2	-	-	NOUN
ejpam-5192	97	3	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5192	97	4	-	-	PUNCT
ejpam-5192	97	5	cl(a	cl(a	NUM
ejpam-5192	97	6	)	)	PUNCT
ejpam-5192	97	7	)	)	PUNCT
ejpam-5192	97	8	∪a	∪a	X
ejpam-5192	98	1	[	[	X
ejpam-5192	98	2	5	5	NUM
ejpam-5192	98	3	]	]	PUNCT
ejpam-5192	98	4	;	;	PUNCT
ejpam-5192	98	5	(	(	PUNCT
ejpam-5192	98	6	2	2	X
ejpam-5192	98	7	)	)	PUNCT
ejpam-5192	98	8	(	(	PUNCT
ejpam-5192	98	9	τ1	τ1	NOUN
ejpam-5192	98	10	,	,	PUNCT
ejpam-5192	98	11	τ2)-sint(a	τ2)-sint(a	PROPN
ejpam-5192	98	12	)	)	PUNCT
ejpam-5192	98	13	=	=	PUNCT
ejpam-5192	99	1	τ1τ2	τ1τ2	NOUN
ejpam-5192	99	2	-	-	ADJ
ejpam-5192	99	3	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5192	99	4	-	-	PUNCT
ejpam-5192	99	5	int(a	int(a	NOUN
ejpam-5192	99	6	)	)	PUNCT
ejpam-5192	99	7	)	)	PUNCT
ejpam-5192	100	1	∩a	∩a	PROPN
ejpam-5192	100	2	.	.	PUNCT
ejpam-5192	101	1	lemma	lemma	PROPN
ejpam-5192	101	2	3	3	X
ejpam-5192	101	3	.	.	PUNCT
ejpam-5192	102	1	let	let	VERB
ejpam-5192	102	2	a	a	DET
ejpam-5192	102	3	be	be	AUX
ejpam-5192	102	4	a	a	DET
ejpam-5192	102	5	subset	subset	NOUN
ejpam-5192	102	6	of	of	ADP
ejpam-5192	102	7	a	a	DET
ejpam-5192	102	8	bitopological	bitopological	ADJ
ejpam-5192	102	9	space	space	NOUN
ejpam-5192	102	10	(	(	PUNCT
ejpam-5192	102	11	x	x	NOUN
ejpam-5192	102	12	,	,	PUNCT
ejpam-5192	102	13	τ1	τ1	NOUN
ejpam-5192	102	14	,	,	PUNCT
ejpam-5192	102	15	τ2	τ2	NOUN
ejpam-5192	102	16	)	)	PUNCT
ejpam-5192	102	17	.	.	PUNCT
ejpam-5192	103	1	if	if	SCONJ
ejpam-5192	103	2	a	a	PRON
ejpam-5192	103	3	is	be	AUX
ejpam-5192	103	4	τ1τ2	τ1τ2	NOUN
ejpam-5192	103	5	-	-	ADJ
ejpam-5192	103	6	open	open	ADJ
ejpam-5192	103	7	in	in	ADP
ejpam-5192	103	8	x	x	NOUN
ejpam-5192	103	9	,	,	PUNCT
ejpam-5192	103	10	then	then	ADV
ejpam-5192	103	11	(	(	PUNCT
ejpam-5192	103	12	τ1	τ1	NOUN
ejpam-5192	103	13	,	,	PUNCT
ejpam-5192	103	14	τ2)-scl(a	τ2)-scl(a	NOUN
ejpam-5192	103	15	)	)	PUNCT
ejpam-5192	103	16	=	=	PUNCT
ejpam-5192	104	1	τ1τ2	τ1τ2	NOUN
ejpam-5192	104	2	-	-	NOUN
ejpam-5192	104	3	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5192	104	4	-	-	PUNCT
ejpam-5192	104	5	cl(a	cl(a	NUM
ejpam-5192	104	6	)	)	PUNCT
ejpam-5192	104	7	)	)	PUNCT
ejpam-5192	104	8	.	.	PUNCT
ejpam-5192	105	1	theorem	theorem	NOUN
ejpam-5192	105	2	1	1	NUM
ejpam-5192	105	3	.	.	X
ejpam-5192	105	4	for	for	ADP
ejpam-5192	105	5	a	a	DET
ejpam-5192	105	6	multifunction	multifunction	NOUN
ejpam-5192	106	1	f	f	NOUN
ejpam-5192	106	2	:	:	PUNCT
ejpam-5192	106	3	(	(	PUNCT
ejpam-5192	106	4	x	x	NOUN
ejpam-5192	106	5	,	,	PUNCT
ejpam-5192	106	6	τ1	τ1	NOUN
ejpam-5192	106	7	,	,	PUNCT
ejpam-5192	106	8	τ2	τ2	NOUN
ejpam-5192	106	9	)	)	PUNCT
ejpam-5192	106	10	→	→	SYM
ejpam-5192	106	11	(	(	PUNCT
ejpam-5192	106	12	y	y	PROPN
ejpam-5192	106	13	,	,	PUNCT
ejpam-5192	106	14	σ1	σ1	PROPN
ejpam-5192	106	15	,	,	PUNCT
ejpam-5192	106	16	σ2	σ2	NOUN
ejpam-5192	106	17	)	)	PUNCT
ejpam-5192	106	18	,	,	PUNCT
ejpam-5192	106	19	the	the	DET
ejpam-5192	106	20	following	follow	VERB
ejpam-5192	106	21	properties	property	NOUN
ejpam-5192	106	22	are	be	AUX
ejpam-5192	106	23	equivalent	equivalent	ADJ
ejpam-5192	106	24	:	:	PUNCT
ejpam-5192	106	25	(	(	PUNCT
ejpam-5192	106	26	1	1	X
ejpam-5192	106	27	)	)	PUNCT
ejpam-5192	106	28	f	f	PROPN
ejpam-5192	106	29	is	be	AUX
ejpam-5192	106	30	upper	upper	ADJ
ejpam-5192	106	31	almost	almost	ADV
ejpam-5192	106	32	(	(	PUNCT
ejpam-5192	106	33	τ1	τ1	NOUN
ejpam-5192	106	34	,	,	PUNCT
ejpam-5192	106	35	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	106	36	at	at	ADP
ejpam-5192	106	37	x	x	X
ejpam-5192	106	38	∈	∈	PROPN
ejpam-5192	106	39	x	x	X
ejpam-5192	106	40	;	;	PUNCT
ejpam-5192	106	41	(	(	PUNCT
ejpam-5192	106	42	2	2	X
ejpam-5192	106	43	)	)	PUNCT
ejpam-5192	106	44	x	x	SYM
ejpam-5192	106	45	∈	∈	PRON
ejpam-5192	106	46	τ1τ2	τ1τ2	NOUN
ejpam-5192	106	47	-	-	NUM
ejpam-5192	106	48	int(f	int(f	VERB
ejpam-5192	106	49	+	+	ADJ
ejpam-5192	106	50	(	(	PUNCT
ejpam-5192	106	51	σ1σ2	σ1σ2	NUM
ejpam-5192	106	52	-	-	PUNCT
ejpam-5192	106	53	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5192	106	54	-	-	PUNCT
ejpam-5192	106	55	cl(v	cl(v	NOUN
ejpam-5192	106	56	)	)	PUNCT
ejpam-5192	106	57	)	)	PUNCT
ejpam-5192	106	58	)	)	PUNCT
ejpam-5192	106	59	)	)	PUNCT
ejpam-5192	106	60	for	for	ADP
ejpam-5192	106	61	every	every	DET
ejpam-5192	106	62	σ1σ2	σ1σ2	NOUN
ejpam-5192	106	63	-	-	ADJ
ejpam-5192	106	64	open	open	ADJ
ejpam-5192	106	65	set	set	NOUN
ejpam-5192	106	66	v	v	NOUN
ejpam-5192	106	67	of	of	ADP
ejpam-5192	106	68	y	y	PROPN
ejpam-5192	106	69	containing	contain	VERB
ejpam-5192	106	70	f	f	PROPN
ejpam-5192	106	71	(	(	PUNCT
ejpam-5192	106	72	x	x	NOUN
ejpam-5192	106	73	)	)	PUNCT
ejpam-5192	106	74	;	;	PUNCT
ejpam-5192	106	75	(	(	PUNCT
ejpam-5192	106	76	3	3	X
ejpam-5192	106	77	)	)	PUNCT
ejpam-5192	106	78	x	x	SYM
ejpam-5192	106	79	∈	∈	PRON
ejpam-5192	106	80	τ1τ2	τ1τ2	PUNCT
ejpam-5192	106	81	-	-	NUM
ejpam-5192	106	82	int(f	int(f	VERB
ejpam-5192	106	83	+	+	ADJ
ejpam-5192	106	84	(	(	PUNCT
ejpam-5192	106	85	(	(	PUNCT
ejpam-5192	106	86	σ1	σ1	PROPN
ejpam-5192	106	87	,	,	PUNCT
ejpam-5192	106	88	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-5192	106	89	)	)	PUNCT
ejpam-5192	106	90	)	)	PUNCT
ejpam-5192	106	91	)	)	PUNCT
ejpam-5192	106	92	for	for	ADP
ejpam-5192	106	93	every	every	DET
ejpam-5192	106	94	σ1σ2	σ1σ2	NOUN
ejpam-5192	106	95	-	-	ADJ
ejpam-5192	106	96	open	open	ADJ
ejpam-5192	106	97	set	set	NOUN
ejpam-5192	106	98	v	v	NOUN
ejpam-5192	106	99	of	of	ADP
ejpam-5192	106	100	y	y	PROPN
ejpam-5192	106	101	containing	contain	VERB
ejpam-5192	106	102	f	f	PROPN
ejpam-5192	106	103	(	(	PUNCT
ejpam-5192	106	104	x	x	NOUN
ejpam-5192	106	105	)	)	PUNCT
ejpam-5192	106	106	;	;	PUNCT
ejpam-5192	106	107	(	(	PUNCT
ejpam-5192	106	108	4	4	X
ejpam-5192	106	109	)	)	PUNCT
ejpam-5192	106	110	x	x	SYM
ejpam-5192	106	111	∈	∈	PRON
ejpam-5192	106	112	τ1τ2	τ1τ2	PUNCT
ejpam-5192	106	113	-	-	NUM
ejpam-5192	106	114	int(f	int(f	VERB
ejpam-5192	106	115	+	+	ADJ
ejpam-5192	106	116	(	(	PUNCT
ejpam-5192	106	117	v	v	NOUN
ejpam-5192	106	118	)	)	PUNCT
ejpam-5192	106	119	)	)	PUNCT
ejpam-5192	106	120	for	for	ADP
ejpam-5192	106	121	every	every	DET
ejpam-5192	106	122	(	(	PUNCT
ejpam-5192	106	123	σ1	σ1	PROPN
ejpam-5192	106	124	,	,	PUNCT
ejpam-5192	106	125	σ2)r	σ2)r	NOUN
ejpam-5192	106	126	-	-	PUNCT
ejpam-5192	106	127	open	open	ADJ
ejpam-5192	106	128	set	set	VERB
ejpam-5192	106	129	v	v	NOUN
ejpam-5192	106	130	of	of	ADP
ejpam-5192	106	131	y	y	PROPN
ejpam-5192	106	132	containing	contain	VERB
ejpam-5192	106	133	f	f	PROPN
ejpam-5192	106	134	(	(	PUNCT
ejpam-5192	106	135	x	x	NOUN
ejpam-5192	106	136	)	)	PUNCT
ejpam-5192	106	137	;	;	PUNCT
ejpam-5192	106	138	(	(	PUNCT
ejpam-5192	106	139	5	5	X
ejpam-5192	106	140	)	)	PUNCT
ejpam-5192	106	141	for	for	ADP
ejpam-5192	106	142	each	each	DET
ejpam-5192	106	143	(	(	PUNCT
ejpam-5192	106	144	σ1	σ1	PROPN
ejpam-5192	106	145	,	,	PUNCT
ejpam-5192	106	146	σ2)r	σ2)r	NOUN
ejpam-5192	106	147	-	-	PUNCT
ejpam-5192	106	148	open	open	ADJ
ejpam-5192	106	149	set	set	VERB
ejpam-5192	106	150	v	v	NOUN
ejpam-5192	106	151	of	of	ADP
ejpam-5192	106	152	y	y	PROPN
ejpam-5192	106	153	containing	contain	VERB
ejpam-5192	106	154	f	f	PROPN
ejpam-5192	106	155	(	(	PUNCT
ejpam-5192	106	156	x	x	NOUN
ejpam-5192	106	157	)	)	PUNCT
ejpam-5192	106	158	,	,	PUNCT
ejpam-5192	106	159	there	there	PRON
ejpam-5192	106	160	exists	exist	VERB
ejpam-5192	106	161	a	a	DET
ejpam-5192	106	162	τ1τ2	τ1τ2	NOUN
ejpam-5192	106	163	-	-	ADJ
ejpam-5192	106	164	open	open	ADJ
ejpam-5192	106	165	set	set	ADJ
ejpam-5192	106	166	u	u	NOUN
ejpam-5192	106	167	of	of	ADP
ejpam-5192	106	168	x	x	PUNCT
ejpam-5192	106	169	containing	contain	VERB
ejpam-5192	106	170	x	x	PUNCT
ejpam-5192	106	171	such	such	ADJ
ejpam-5192	106	172	that	that	SCONJ
ejpam-5192	106	173	f	f	PROPN
ejpam-5192	106	174	(	(	PUNCT
ejpam-5192	106	175	u	u	NOUN
ejpam-5192	106	176	)	)	PUNCT
ejpam-5192	106	177	⊆	⊆	NUM
ejpam-5192	106	178	v	v	NOUN
ejpam-5192	106	179	.	.	PUNCT
ejpam-5192	107	1	proof	proof	NOUN
ejpam-5192	107	2	.	.	PUNCT
ejpam-5192	108	1	(	(	PUNCT
ejpam-5192	108	2	1	1	X
ejpam-5192	108	3	)	)	PUNCT
ejpam-5192	108	4	⇒	⇒	NOUN
ejpam-5192	108	5	(	(	PUNCT
ejpam-5192	108	6	2	2	NUM
ejpam-5192	108	7	):	):	PUNCT
ejpam-5192	108	8	let	let	VERB
ejpam-5192	108	9	v	v	PART
ejpam-5192	108	10	be	be	AUX
ejpam-5192	108	11	any	any	DET
ejpam-5192	108	12	σ1σ2	σ1σ2	NOUN
ejpam-5192	108	13	-	-	ADJ
ejpam-5192	108	14	open	open	ADJ
ejpam-5192	108	15	set	set	NOUN
ejpam-5192	108	16	of	of	ADP
ejpam-5192	108	17	y	y	PROPN
ejpam-5192	108	18	containing	contain	VERB
ejpam-5192	108	19	f	f	PROPN
ejpam-5192	108	20	(	(	PUNCT
ejpam-5192	108	21	x	x	NOUN
ejpam-5192	108	22	)	)	PUNCT
ejpam-5192	108	23	.	.	PUNCT
ejpam-5192	109	1	there	there	PRON
ejpam-5192	109	2	exists	exist	VERB
ejpam-5192	109	3	a	a	DET
ejpam-5192	109	4	τ1τ2	τ1τ2	NOUN
ejpam-5192	109	5	-	-	ADJ
ejpam-5192	109	6	open	open	ADJ
ejpam-5192	109	7	set	set	ADJ
ejpam-5192	109	8	u	u	NOUN
ejpam-5192	109	9	of	of	ADP
ejpam-5192	109	10	x	x	PUNCT
ejpam-5192	109	11	containing	contain	VERB
ejpam-5192	109	12	x	x	PUNCT
ejpam-5192	109	13	such	such	ADJ
ejpam-5192	109	14	that	that	SCONJ
ejpam-5192	109	15	f	f	PROPN
ejpam-5192	109	16	(	(	PUNCT
ejpam-5192	109	17	u	u	NOUN
ejpam-5192	109	18	)	)	PUNCT
ejpam-5192	109	19	⊆	⊆	NUM
ejpam-5192	109	20	σ1σ2	σ1σ2	X
ejpam-5192	109	21	-	-	PUNCT
ejpam-5192	109	22	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5192	109	23	-	-	PUNCT
ejpam-5192	109	24	cl(v	cl(v	NOUN
ejpam-5192	109	25	)	)	PUNCT
ejpam-5192	109	26	)	)	PUNCT
ejpam-5192	109	27	.	.	PUNCT
ejpam-5192	110	1	thus	thus	ADV
ejpam-5192	110	2	,	,	PUNCT
ejpam-5192	110	3	x	x	PUNCT
ejpam-5192	110	4	∈	∈	PROPN
ejpam-5192	110	5	u	u	NOUN
ejpam-5192	110	6	⊆	⊆	NUM
ejpam-5192	110	7	f+(σ1σ2	f+(σ1σ2	ADJ
ejpam-5192	110	8	-	-	PUNCT
ejpam-5192	110	9	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5192	110	10	-	-	PUNCT
ejpam-5192	110	11	cl(v	cl(v	NOUN
ejpam-5192	110	12	)	)	PUNCT
ejpam-5192	110	13	)	)	PUNCT
ejpam-5192	110	14	)	)	PUNCT
ejpam-5192	110	15	and	and	CCONJ
ejpam-5192	110	16	hence	hence	ADV
ejpam-5192	110	17	x	x	X
ejpam-5192	110	18	∈	∈	PRON
ejpam-5192	110	19	τ1τ2	τ1τ2	NOUN
ejpam-5192	110	20	-	-	NUM
ejpam-5192	110	21	int(f	int(f	VERB
ejpam-5192	110	22	+	+	ADJ
ejpam-5192	110	23	(	(	PUNCT
ejpam-5192	110	24	σ1σ2	σ1σ2	NUM
ejpam-5192	110	25	-	-	PUNCT
ejpam-5192	110	26	int(σ1σ2	int(σ1σ2	VERB
ejpam-5192	110	27	-	-	PUNCT
ejpam-5192	110	28	int(v	int(v	NOUN
ejpam-5192	110	29	)	)	PUNCT
ejpam-5192	110	30	)	)	PUNCT
ejpam-5192	110	31	)	)	PUNCT
ejpam-5192	110	32	)	)	PUNCT
ejpam-5192	110	33	.	.	PUNCT
ejpam-5192	111	1	(	(	PUNCT
ejpam-5192	111	2	2	2	X
ejpam-5192	111	3	)	)	PUNCT
ejpam-5192	111	4	⇒	⇒	NOUN
ejpam-5192	111	5	(	(	PUNCT
ejpam-5192	111	6	3	3	NUM
ejpam-5192	111	7	):	):	PUNCT
ejpam-5192	111	8	this	this	PRON
ejpam-5192	111	9	follows	follow	VERB
ejpam-5192	111	10	from	from	ADP
ejpam-5192	111	11	lemma	lemma	PROPN
ejpam-5192	111	12	3	3	NUM
ejpam-5192	111	13	.	.	PUNCT
ejpam-5192	111	14	(	(	PUNCT
ejpam-5192	111	15	3	3	X
ejpam-5192	111	16	)	)	PUNCT
ejpam-5192	111	17	⇒	⇒	NOUN
ejpam-5192	111	18	(	(	PUNCT
ejpam-5192	111	19	4	4	NUM
ejpam-5192	111	20	):	):	PUNCT
ejpam-5192	111	21	let	let	VERB
ejpam-5192	111	22	v	v	PART
ejpam-5192	111	23	be	be	AUX
ejpam-5192	111	24	any	any	DET
ejpam-5192	111	25	(	(	PUNCT
ejpam-5192	111	26	σ1	σ1	NOUN
ejpam-5192	111	27	,	,	PUNCT
ejpam-5192	111	28	σ2)r	σ2)r	NOUN
ejpam-5192	111	29	-	-	PUNCT
ejpam-5192	111	30	open	open	ADJ
ejpam-5192	111	31	set	set	NOUN
ejpam-5192	111	32	of	of	ADP
ejpam-5192	111	33	y	y	PROPN
ejpam-5192	111	34	containing	contain	VERB
ejpam-5192	111	35	f	f	PROPN
ejpam-5192	111	36	(	(	PUNCT
ejpam-5192	111	37	x	x	NOUN
ejpam-5192	111	38	)	)	PUNCT
ejpam-5192	111	39	.	.	PUNCT
ejpam-5192	112	1	then	then	ADV
ejpam-5192	112	2	,	,	PUNCT
ejpam-5192	112	3	it	it	PRON
ejpam-5192	112	4	follows	follow	VERB
ejpam-5192	112	5	from	from	ADP
ejpam-5192	112	6	lemma	lemma	PROPN
ejpam-5192	112	7	3	3	NUM
ejpam-5192	112	8	that	that	PRON
ejpam-5192	112	9	v	v	NOUN
ejpam-5192	112	10	=	=	SYM
ejpam-5192	112	11	σ1σ2	σ1σ2	NOUN
ejpam-5192	112	12	-	-	PUNCT
ejpam-5192	112	13	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5192	112	14	-	-	PUNCT
ejpam-5192	112	15	cl(v	cl(v	NOUN
ejpam-5192	112	16	)	)	PUNCT
ejpam-5192	112	17	)	)	PUNCT
ejpam-5192	113	1	=	=	SYM
ejpam-5192	113	2	(	(	PUNCT
ejpam-5192	113	3	σ1	σ1	PROPN
ejpam-5192	113	4	,	,	PUNCT
ejpam-5192	113	5	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-5192	113	6	)	)	PUNCT
ejpam-5192	113	7	.	.	PUNCT
ejpam-5192	114	1	(	(	PUNCT
ejpam-5192	114	2	4	4	X
ejpam-5192	114	3	)	)	PUNCT
ejpam-5192	114	4	⇒	⇒	NOUN
ejpam-5192	114	5	(	(	PUNCT
ejpam-5192	114	6	5	5	NUM
ejpam-5192	114	7	):	):	PUNCT
ejpam-5192	114	8	let	let	VERB
ejpam-5192	114	9	v	v	PART
ejpam-5192	114	10	be	be	AUX
ejpam-5192	114	11	any	any	DET
ejpam-5192	114	12	(	(	PUNCT
ejpam-5192	114	13	σ1	σ1	NOUN
ejpam-5192	114	14	,	,	PUNCT
ejpam-5192	114	15	σ2)r	σ2)r	NOUN
ejpam-5192	114	16	-	-	PUNCT
ejpam-5192	114	17	open	open	ADJ
ejpam-5192	114	18	set	set	NOUN
ejpam-5192	114	19	of	of	ADP
ejpam-5192	114	20	y	y	PROPN
ejpam-5192	114	21	containing	contain	VERB
ejpam-5192	114	22	f	f	PROPN
ejpam-5192	114	23	(	(	PUNCT
ejpam-5192	114	24	x	x	NOUN
ejpam-5192	114	25	)	)	PUNCT
ejpam-5192	114	26	.	.	PUNCT
ejpam-5192	115	1	then	then	ADV
ejpam-5192	115	2	by	by	ADP
ejpam-5192	115	3	(	(	PUNCT
ejpam-5192	115	4	4	4	NUM
ejpam-5192	115	5	)	)	PUNCT
ejpam-5192	115	6	,	,	PUNCT
ejpam-5192	115	7	x	x	PUNCT
ejpam-5192	115	8	∈	∈	PROPN
ejpam-5192	115	9	τ1τ2	τ1τ2	PUNCT
ejpam-5192	115	10	-	-	NUM
ejpam-5192	115	11	int(f	int(f	VERB
ejpam-5192	115	12	+	+	ADJ
ejpam-5192	115	13	(	(	PUNCT
ejpam-5192	115	14	v	v	NOUN
ejpam-5192	115	15	)	)	PUNCT
ejpam-5192	115	16	)	)	PUNCT
ejpam-5192	115	17	and	and	CCONJ
ejpam-5192	115	18	there	there	PRON
ejpam-5192	115	19	exists	exist	VERB
ejpam-5192	115	20	a	a	DET
ejpam-5192	115	21	τ1τ2	τ1τ2	NOUN
ejpam-5192	115	22	-	-	ADJ
ejpam-5192	115	23	open	open	ADJ
ejpam-5192	115	24	set	set	ADJ
ejpam-5192	115	25	u	u	NOUN
ejpam-5192	115	26	of	of	ADP
ejpam-5192	115	27	x	x	PUNCT
ejpam-5192	115	28	containing	contain	VERB
ejpam-5192	115	29	x	x	PUNCT
ejpam-5192	115	30	such	such	ADJ
ejpam-5192	115	31	that	that	SCONJ
ejpam-5192	115	32	x	x	SYM
ejpam-5192	115	33	∈	∈	NUM
ejpam-5192	115	34	u	u	NOUN
ejpam-5192	115	35	⊆	⊆	NUM
ejpam-5192	115	36	f+(v	f+(v	NOUN
ejpam-5192	115	37	)	)	PUNCT
ejpam-5192	115	38	;	;	PUNCT
ejpam-5192	115	39	hence	hence	ADV
ejpam-5192	115	40	f	f	PROPN
ejpam-5192	115	41	(	(	PUNCT
ejpam-5192	115	42	u	u	NOUN
ejpam-5192	115	43	)	)	PUNCT
ejpam-5192	115	44	⊆	⊆	NUM
ejpam-5192	115	45	v	v	NOUN
ejpam-5192	115	46	.	.	PUNCT
ejpam-5192	116	1	(	(	PUNCT
ejpam-5192	116	2	5	5	X
ejpam-5192	116	3	)	)	PUNCT
ejpam-5192	116	4	⇒	⇒	NOUN
ejpam-5192	116	5	(	(	PUNCT
ejpam-5192	116	6	1	1	NUM
ejpam-5192	116	7	):	):	PUNCT
ejpam-5192	116	8	let	let	VERB
ejpam-5192	116	9	v	v	PART
ejpam-5192	116	10	be	be	AUX
ejpam-5192	116	11	any	any	DET
ejpam-5192	116	12	σ1σ2	σ1σ2	NOUN
ejpam-5192	116	13	-	-	ADJ
ejpam-5192	116	14	open	open	ADJ
ejpam-5192	116	15	set	set	NOUN
ejpam-5192	116	16	of	of	ADP
ejpam-5192	116	17	y	y	PROPN
ejpam-5192	116	18	containing	contain	VERB
ejpam-5192	116	19	f	f	PROPN
ejpam-5192	116	20	(	(	PUNCT
ejpam-5192	116	21	x	x	NOUN
ejpam-5192	116	22	)	)	PUNCT
ejpam-5192	116	23	.	.	PUNCT
ejpam-5192	117	1	since	since	SCONJ
ejpam-5192	117	2	σ1σ2	σ1σ2	NOUN
ejpam-5192	117	3	-	-	PUNCT
ejpam-5192	117	4	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5192	117	5	-	-	PUNCT
ejpam-5192	117	6	cl(v	cl(v	NOUN
ejpam-5192	117	7	)	)	PUNCT
ejpam-5192	117	8	)	)	PUNCT
ejpam-5192	117	9	is	be	AUX
ejpam-5192	117	10	(	(	PUNCT
ejpam-5192	117	11	σ1	σ1	NOUN
ejpam-5192	117	12	,	,	PUNCT
ejpam-5192	117	13	σ2)r	σ2)r	NOUN
ejpam-5192	117	14	-	-	PUNCT
ejpam-5192	117	15	open	open	ADJ
ejpam-5192	117	16	,	,	PUNCT
ejpam-5192	117	17	there	there	PRON
ejpam-5192	117	18	exists	exist	VERB
ejpam-5192	117	19	a	a	DET
ejpam-5192	117	20	τ1τ2	τ1τ2	NOUN
ejpam-5192	117	21	-	-	ADJ
ejpam-5192	117	22	open	open	ADJ
ejpam-5192	117	23	set	set	ADJ
ejpam-5192	117	24	u	u	NOUN
ejpam-5192	117	25	of	of	ADP
ejpam-5192	117	26	x	x	PUNCT
ejpam-5192	117	27	containing	contain	VERB
ejpam-5192	117	28	x	x	PUNCT
ejpam-5192	117	29	such	such	ADJ
ejpam-5192	117	30	that	that	SCONJ
ejpam-5192	117	31	f	f	PROPN
ejpam-5192	117	32	(	(	PUNCT
ejpam-5192	117	33	u	u	NOUN
ejpam-5192	117	34	)	)	PUNCT
ejpam-5192	117	35	⊆	⊆	NUM
ejpam-5192	117	36	σ1σ2	σ1σ2	X
ejpam-5192	117	37	-	-	PUNCT
ejpam-5192	117	38	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5192	117	39	-	-	PUNCT
ejpam-5192	117	40	cl(v	cl(v	NOUN
ejpam-5192	117	41	)	)	PUNCT
ejpam-5192	117	42	)	)	PUNCT
ejpam-5192	117	43	.	.	PUNCT
ejpam-5192	118	1	this	this	PRON
ejpam-5192	118	2	shows	show	VERB
ejpam-5192	118	3	that	that	SCONJ
ejpam-5192	118	4	f	f	PROPN
ejpam-5192	118	5	is	be	AUX
ejpam-5192	118	6	upper	upper	ADJ
ejpam-5192	118	7	almost	almost	ADV
ejpam-5192	118	8	(	(	PUNCT
ejpam-5192	118	9	τ1	τ1	NOUN
ejpam-5192	118	10	,	,	PUNCT
ejpam-5192	118	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	118	12	at	at	ADP
ejpam-5192	118	13	x	x	SYM
ejpam-5192	118	14	∈	∈	PROPN
ejpam-5192	118	15	x.	x.	NOUN
ejpam-5192	118	16	definition	definition	NOUN
ejpam-5192	118	17	2	2	NUM
ejpam-5192	118	18	.	.	PUNCT
ejpam-5192	118	19	a	a	DET
ejpam-5192	118	20	multifunction	multifunction	NOUN
ejpam-5192	119	1	f	f	NOUN
ejpam-5192	119	2	:	:	PUNCT
ejpam-5192	119	3	(	(	PUNCT
ejpam-5192	119	4	x	x	NOUN
ejpam-5192	119	5	,	,	PUNCT
ejpam-5192	119	6	τ1	τ1	NOUN
ejpam-5192	119	7	,	,	PUNCT
ejpam-5192	119	8	τ2	τ2	NOUN
ejpam-5192	119	9	)	)	PUNCT
ejpam-5192	119	10	→	→	SYM
ejpam-5192	119	11	(	(	PUNCT
ejpam-5192	119	12	y	y	PROPN
ejpam-5192	119	13	,	,	PUNCT
ejpam-5192	119	14	σ1	σ1	PROPN
ejpam-5192	119	15	,	,	PUNCT
ejpam-5192	119	16	σ2	σ2	PROPN
ejpam-5192	119	17	)	)	PUNCT
ejpam-5192	119	18	is	be	AUX
ejpam-5192	119	19	said	say	VERB
ejpam-5192	119	20	to	to	PART
ejpam-5192	119	21	be	be	AUX
ejpam-5192	119	22	lower	low	ADJ
ejpam-5192	119	23	almost	almost	ADV
ejpam-5192	119	24	(	(	PUNCT
ejpam-5192	119	25	τ1	τ1	NOUN
ejpam-5192	119	26	,	,	PUNCT
ejpam-5192	119	27	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	119	28	at	at	ADP
ejpam-5192	119	29	a	a	DET
ejpam-5192	119	30	point	point	NOUN
ejpam-5192	119	31	x	x	SYM
ejpam-5192	119	32	∈	∈	NOUN
ejpam-5192	119	33	x	x	PUNCT
ejpam-5192	119	34	if	if	SCONJ
ejpam-5192	119	35	for	for	ADP
ejpam-5192	119	36	each	each	DET
ejpam-5192	119	37	σ1σ2	σ1σ2	VERB
ejpam-5192	119	38	-	-	ADJ
ejpam-5192	119	39	open	open	ADJ
ejpam-5192	119	40	set	set	NOUN
ejpam-5192	119	41	v	v	NOUN
ejpam-5192	119	42	of	of	ADP
ejpam-5192	119	43	y	y	PRON
ejpam-5192	119	44	such	such	ADJ
ejpam-5192	119	45	that	that	SCONJ
ejpam-5192	119	46	f	f	PROPN
ejpam-5192	119	47	(	(	PUNCT
ejpam-5192	119	48	x	x	NOUN
ejpam-5192	119	49	)	)	PUNCT
ejpam-5192	119	50	∩	∩	NOUN
ejpam-5192	119	51	v	v	ADP
ejpam-5192	119	52	̸=	̸=	PROPN
ejpam-5192	119	53	∅	∅	NOUN
ejpam-5192	119	54	,	,	PUNCT
ejpam-5192	119	55	there	there	PRON
ejpam-5192	119	56	exists	exist	VERB
ejpam-5192	119	57	a	a	DET
ejpam-5192	119	58	τ1τ2	τ1τ2	NOUN
ejpam-5192	119	59	-	-	ADJ
ejpam-5192	119	60	open	open	ADJ
ejpam-5192	119	61	set	set	ADJ
ejpam-5192	119	62	u	u	NOUN
ejpam-5192	119	63	of	of	ADP
ejpam-5192	119	64	x	x	PUNCT
ejpam-5192	119	65	containing	contain	VERB
ejpam-5192	119	66	x	x	PUNCT
ejpam-5192	119	67	such	such	ADJ
ejpam-5192	119	68	that	that	SCONJ
ejpam-5192	119	69	σ1σ2	σ1σ2	ADV
ejpam-5192	119	70	-	-	PUNCT
ejpam-5192	119	71	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5192	119	72	-	-	PUNCT
ejpam-5192	119	73	cl(v	cl(v	NOUN
ejpam-5192	119	74	)	)	PUNCT
ejpam-5192	119	75	)	)	PUNCT
ejpam-5192	120	1	∩f	∩f	NOUN
ejpam-5192	120	2	(	(	PUNCT
ejpam-5192	120	3	z	z	X
ejpam-5192	120	4	)	)	PUNCT
ejpam-5192	120	5	̸=	̸=	NOUN
ejpam-5192	120	6	∅	∅	NOUN
ejpam-5192	120	7	for	for	ADP
ejpam-5192	120	8	each	each	DET
ejpam-5192	120	9	z	z	NOUN
ejpam-5192	120	10	∈	∈	PROPN
ejpam-5192	120	11	u	u	NOUN
ejpam-5192	120	12	.	.	PUNCT
ejpam-5192	121	1	a	a	DET
ejpam-5192	121	2	multifunction	multifunction	NOUN
ejpam-5192	121	3	f	f	NOUN
ejpam-5192	121	4	:	:	PUNCT
ejpam-5192	121	5	(	(	PUNCT
ejpam-5192	121	6	x	x	NOUN
ejpam-5192	121	7	,	,	PUNCT
ejpam-5192	121	8	τ1	τ1	NOUN
ejpam-5192	121	9	,	,	PUNCT
ejpam-5192	121	10	τ2	τ2	NOUN
ejpam-5192	121	11	)	)	PUNCT
ejpam-5192	121	12	→	→	SYM
ejpam-5192	121	13	(	(	PUNCT
ejpam-5192	121	14	y	y	PROPN
ejpam-5192	121	15	,	,	PUNCT
ejpam-5192	121	16	σ1	σ1	PROPN
ejpam-5192	121	17	,	,	PUNCT
ejpam-5192	121	18	σ2	σ2	PROPN
ejpam-5192	121	19	)	)	PUNCT
ejpam-5192	121	20	is	be	AUX
ejpam-5192	121	21	said	say	VERB
ejpam-5192	121	22	to	to	PART
ejpam-5192	121	23	be	be	AUX
ejpam-5192	121	24	lower	low	ADJ
ejpam-5192	121	25	almost	almost	ADV
ejpam-5192	121	26	(	(	PUNCT
ejpam-5192	121	27	τ1	τ1	NOUN
ejpam-5192	121	28	,	,	PUNCT
ejpam-5192	121	29	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	121	30	if	if	SCONJ
ejpam-5192	121	31	f	f	PROPN
ejpam-5192	121	32	has	have	VERB
ejpam-5192	121	33	this	this	DET
ejpam-5192	121	34	property	property	NOUN
ejpam-5192	121	35	at	at	ADP
ejpam-5192	121	36	each	each	DET
ejpam-5192	121	37	point	point	NOUN
ejpam-5192	121	38	of	of	ADP
ejpam-5192	121	39	x.	x.	NOUN
ejpam-5192	121	40	theorem	theorem	VERB
ejpam-5192	121	41	2	2	NUM
ejpam-5192	121	42	.	.	X
ejpam-5192	121	43	for	for	ADP
ejpam-5192	121	44	a	a	DET
ejpam-5192	121	45	multifunction	multifunction	NOUN
ejpam-5192	121	46	f	f	NOUN
ejpam-5192	121	47	:	:	PUNCT
ejpam-5192	121	48	(	(	PUNCT
ejpam-5192	121	49	x	x	NOUN
ejpam-5192	121	50	,	,	PUNCT
ejpam-5192	121	51	τ1	τ1	NOUN
ejpam-5192	121	52	,	,	PUNCT
ejpam-5192	121	53	τ2	τ2	NOUN
ejpam-5192	121	54	)	)	PUNCT
ejpam-5192	121	55	→	→	SYM
ejpam-5192	121	56	(	(	PUNCT
ejpam-5192	121	57	y	y	PROPN
ejpam-5192	121	58	,	,	PUNCT
ejpam-5192	121	59	σ1	σ1	PROPN
ejpam-5192	121	60	,	,	PUNCT
ejpam-5192	121	61	σ2	σ2	NOUN
ejpam-5192	121	62	)	)	PUNCT
ejpam-5192	121	63	,	,	PUNCT
ejpam-5192	121	64	the	the	DET
ejpam-5192	121	65	following	follow	VERB
ejpam-5192	121	66	properties	property	NOUN
ejpam-5192	121	67	are	be	AUX
ejpam-5192	121	68	equivalent	equivalent	ADJ
ejpam-5192	121	69	:	:	PUNCT
ejpam-5192	121	70	(	(	PUNCT
ejpam-5192	121	71	1	1	X
ejpam-5192	121	72	)	)	PUNCT
ejpam-5192	121	73	f	f	PROPN
ejpam-5192	121	74	is	be	AUX
ejpam-5192	121	75	lower	low	ADJ
ejpam-5192	121	76	almost	almost	ADV
ejpam-5192	121	77	(	(	PUNCT
ejpam-5192	121	78	τ1	τ1	NOUN
ejpam-5192	121	79	,	,	PUNCT
ejpam-5192	121	80	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	121	81	at	at	ADP
ejpam-5192	121	82	x	x	X
ejpam-5192	121	83	∈	∈	PROPN
ejpam-5192	121	84	x	x	NOUN
ejpam-5192	121	85	;	;	PUNCT
ejpam-5192	121	86	c.	c.	PROPN
ejpam-5192	121	87	klanarong	klanarong	PROPN
ejpam-5192	121	88	,	,	PUNCT
ejpam-5192	121	89	s.	s.	PROPN
ejpam-5192	121	90	sompong	sompong	PROPN
ejpam-5192	121	91	,	,	PUNCT
ejpam-5192	121	92	c.	c.	PROPN
ejpam-5192	121	93	boonpok	boonpok	PROPN
ejpam-5192	121	94	/	/	SYM
ejpam-5192	121	95	eur	eur	PROPN
ejpam-5192	121	96	.	.	PUNCT
ejpam-5192	122	1	j.	j.	PROPN
ejpam-5192	122	2	pure	pure	PROPN
ejpam-5192	122	3	appl	appl	PROPN
ejpam-5192	122	4	.	.	PROPN
ejpam-5192	122	5	math	math	PROPN
ejpam-5192	122	6	,	,	PUNCT
ejpam-5192	122	7	17	17	NUM
ejpam-5192	122	8	(	(	PUNCT
ejpam-5192	122	9	2	2	NUM
ejpam-5192	122	10	)	)	PUNCT
ejpam-5192	122	11	(	(	PUNCT
ejpam-5192	122	12	2024	2024	NUM
ejpam-5192	122	13	)	)	PUNCT
ejpam-5192	122	14	,	,	PUNCT
ejpam-5192	122	15	1244	1244	NUM
ejpam-5192	122	16	-	-	SYM
ejpam-5192	122	17	1253	1253	NUM
ejpam-5192	122	18	1248	1248	NUM
ejpam-5192	122	19	(	(	PUNCT
ejpam-5192	122	20	2	2	NUM
ejpam-5192	122	21	)	)	PUNCT
ejpam-5192	122	22	x	x	SYM
ejpam-5192	122	23	∈	∈	PRON
ejpam-5192	122	24	τ1τ2	τ1τ2	NOUN
ejpam-5192	122	25	-	-	PUNCT
ejpam-5192	122	26	int(f	int(f	NOUN
ejpam-5192	122	27	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5192	122	28	-	-	PUNCT
ejpam-5192	122	29	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5192	122	30	-	-	PUNCT
ejpam-5192	122	31	cl(v	cl(v	NOUN
ejpam-5192	122	32	)	)	PUNCT
ejpam-5192	122	33	)	)	PUNCT
ejpam-5192	122	34	)	)	PUNCT
ejpam-5192	122	35	)	)	PUNCT
ejpam-5192	123	1	for	for	ADP
ejpam-5192	123	2	every	every	DET
ejpam-5192	123	3	σ1σ2	σ1σ2	NOUN
ejpam-5192	123	4	-	-	ADJ
ejpam-5192	123	5	open	open	ADJ
ejpam-5192	123	6	set	set	NOUN
ejpam-5192	123	7	v	v	NOUN
ejpam-5192	123	8	of	of	ADP
ejpam-5192	123	9	y	y	PRON
ejpam-5192	123	10	such	such	ADJ
ejpam-5192	123	11	that	that	SCONJ
ejpam-5192	123	12	f	f	PROPN
ejpam-5192	123	13	(	(	PUNCT
ejpam-5192	123	14	x	x	NOUN
ejpam-5192	123	15	)	)	PUNCT
ejpam-5192	123	16	∩	∩	NOUN
ejpam-5192	123	17	v	v	ADP
ejpam-5192	123	18	̸=	̸=	PROPN
ejpam-5192	123	19	∅	∅	NOUN
ejpam-5192	123	20	;	;	PUNCT
ejpam-5192	123	21	(	(	PUNCT
ejpam-5192	123	22	3	3	X
ejpam-5192	123	23	)	)	PUNCT
ejpam-5192	123	24	x	x	SYM
ejpam-5192	123	25	∈	∈	PRON
ejpam-5192	123	26	τ1τ2	τ1τ2	NOUN
ejpam-5192	123	27	-	-	ADJ
ejpam-5192	123	28	int(f	int(f	NUM
ejpam-5192	123	29	−((σ1	−((σ1	NOUN
ejpam-5192	123	30	,	,	PUNCT
ejpam-5192	123	31	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-5192	123	32	)	)	PUNCT
ejpam-5192	123	33	)	)	PUNCT
ejpam-5192	123	34	)	)	PUNCT
ejpam-5192	123	35	for	for	ADP
ejpam-5192	123	36	every	every	DET
ejpam-5192	123	37	σ1σ2	σ1σ2	NOUN
ejpam-5192	123	38	-	-	ADJ
ejpam-5192	123	39	open	open	ADJ
ejpam-5192	123	40	set	set	NOUN
ejpam-5192	123	41	v	v	NOUN
ejpam-5192	123	42	of	of	ADP
ejpam-5192	123	43	y	y	PRON
ejpam-5192	123	44	such	such	ADJ
ejpam-5192	123	45	that	that	SCONJ
ejpam-5192	123	46	f	f	PROPN
ejpam-5192	123	47	(	(	PUNCT
ejpam-5192	123	48	x	x	NOUN
ejpam-5192	123	49	)	)	PUNCT
ejpam-5192	123	50	∩	∩	NOUN
ejpam-5192	123	51	v	v	ADP
ejpam-5192	123	52	̸=	̸=	PROPN
ejpam-5192	123	53	∅	∅	NOUN
ejpam-5192	123	54	;	;	PUNCT
ejpam-5192	123	55	(	(	PUNCT
ejpam-5192	123	56	4	4	X
ejpam-5192	123	57	)	)	PUNCT
ejpam-5192	123	58	x	x	SYM
ejpam-5192	123	59	∈	∈	PRON
ejpam-5192	123	60	τ1τ2	τ1τ2	NOUN
ejpam-5192	123	61	-	-	ADJ
ejpam-5192	123	62	int(f	int(f	NUM
ejpam-5192	123	63	−(v	−(v	NOUN
ejpam-5192	123	64	)	)	PUNCT
ejpam-5192	123	65	)	)	PUNCT
ejpam-5192	123	66	for	for	ADP
ejpam-5192	123	67	every	every	DET
ejpam-5192	123	68	(	(	PUNCT
ejpam-5192	123	69	σ1	σ1	PROPN
ejpam-5192	123	70	,	,	PUNCT
ejpam-5192	123	71	σ2)r	σ2)r	NOUN
ejpam-5192	123	72	-	-	PUNCT
ejpam-5192	123	73	open	open	ADJ
ejpam-5192	123	74	set	set	VERB
ejpam-5192	123	75	v	v	NOUN
ejpam-5192	123	76	of	of	ADP
ejpam-5192	123	77	y	y	PRON
ejpam-5192	123	78	such	such	ADJ
ejpam-5192	123	79	that	that	SCONJ
ejpam-5192	123	80	f	f	PROPN
ejpam-5192	123	81	(	(	PUNCT
ejpam-5192	123	82	x	x	NOUN
ejpam-5192	123	83	)	)	PUNCT
ejpam-5192	123	84	∩	∩	NOUN
ejpam-5192	123	85	v	v	ADP
ejpam-5192	123	86	̸=	̸=	PROPN
ejpam-5192	123	87	∅	∅	NOUN
ejpam-5192	123	88	;	;	PUNCT
ejpam-5192	123	89	(	(	PUNCT
ejpam-5192	123	90	5	5	X
ejpam-5192	123	91	)	)	PUNCT
ejpam-5192	123	92	for	for	ADP
ejpam-5192	123	93	each	each	DET
ejpam-5192	123	94	(	(	PUNCT
ejpam-5192	123	95	σ1	σ1	PROPN
ejpam-5192	123	96	,	,	PUNCT
ejpam-5192	123	97	σ2)r	σ2)r	NOUN
ejpam-5192	123	98	-	-	PUNCT
ejpam-5192	123	99	open	open	ADJ
ejpam-5192	123	100	set	set	VERB
ejpam-5192	123	101	v	v	NOUN
ejpam-5192	123	102	of	of	ADP
ejpam-5192	123	103	y	y	PRON
ejpam-5192	123	104	such	such	ADJ
ejpam-5192	123	105	that	that	SCONJ
ejpam-5192	123	106	f	f	PROPN
ejpam-5192	123	107	(	(	PUNCT
ejpam-5192	123	108	x	x	NOUN
ejpam-5192	123	109	)	)	PUNCT
ejpam-5192	123	110	∩	∩	NOUN
ejpam-5192	123	111	v	v	ADP
ejpam-5192	123	112	̸=	̸=	PROPN
ejpam-5192	123	113	∅	∅	NOUN
ejpam-5192	123	114	,	,	PUNCT
ejpam-5192	123	115	there	there	PRON
ejpam-5192	123	116	exists	exist	VERB
ejpam-5192	123	117	a	a	DET
ejpam-5192	123	118	τ1τ2	τ1τ2	NOUN
ejpam-5192	123	119	-	-	ADJ
ejpam-5192	123	120	open	open	ADJ
ejpam-5192	123	121	set	set	ADJ
ejpam-5192	123	122	u	u	NOUN
ejpam-5192	123	123	of	of	ADP
ejpam-5192	123	124	x	x	PUNCT
ejpam-5192	123	125	containing	contain	VERB
ejpam-5192	123	126	x	x	PUNCT
ejpam-5192	123	127	such	such	ADJ
ejpam-5192	123	128	that	that	SCONJ
ejpam-5192	123	129	u	u	NOUN
ejpam-5192	123	130	⊆	⊆	NUM
ejpam-5192	123	131	f−(v	f−(v	NOUN
ejpam-5192	123	132	)	)	PUNCT
ejpam-5192	123	133	.	.	PUNCT
ejpam-5192	124	1	proof	proof	NOUN
ejpam-5192	124	2	.	.	PUNCT
ejpam-5192	125	1	the	the	DET
ejpam-5192	125	2	proof	proof	NOUN
ejpam-5192	125	3	is	be	AUX
ejpam-5192	125	4	similar	similar	ADJ
ejpam-5192	125	5	to	to	ADP
ejpam-5192	125	6	that	that	PRON
ejpam-5192	125	7	of	of	ADP
ejpam-5192	125	8	theorem	theorem	NOUN
ejpam-5192	125	9	1	1	NUM
ejpam-5192	125	10	.	.	PUNCT
ejpam-5192	125	11	definition	definition	NOUN
ejpam-5192	125	12	3	3	NUM
ejpam-5192	125	13	.	.	PUNCT
ejpam-5192	126	1	[	[	X
ejpam-5192	126	2	7	7	X
ejpam-5192	126	3	]	]	X
ejpam-5192	126	4	a	a	DET
ejpam-5192	126	5	function	function	NOUN
ejpam-5192	126	6	f	f	NOUN
ejpam-5192	126	7	:	:	PUNCT
ejpam-5192	126	8	(	(	PUNCT
ejpam-5192	126	9	x	x	NOUN
ejpam-5192	126	10	,	,	PUNCT
ejpam-5192	126	11	τ1	τ1	NOUN
ejpam-5192	126	12	,	,	PUNCT
ejpam-5192	126	13	τ2	τ2	NOUN
ejpam-5192	126	14	)	)	PUNCT
ejpam-5192	126	15	→	→	SYM
ejpam-5192	126	16	(	(	PUNCT
ejpam-5192	126	17	y	y	PROPN
ejpam-5192	126	18	,	,	PUNCT
ejpam-5192	126	19	σ1	σ1	PROPN
ejpam-5192	126	20	,	,	PUNCT
ejpam-5192	126	21	σ2	σ2	PROPN
ejpam-5192	126	22	)	)	PUNCT
ejpam-5192	126	23	is	be	AUX
ejpam-5192	126	24	said	say	VERB
ejpam-5192	126	25	to	to	PART
ejpam-5192	126	26	be	be	AUX
ejpam-5192	126	27	almost	almost	ADV
ejpam-5192	126	28	(	(	PUNCT
ejpam-5192	126	29	τ1	τ1	NOUN
ejpam-5192	126	30	,	,	PUNCT
ejpam-5192	126	31	τ2)continuous	τ2)continuous	ADJ
ejpam-5192	126	32	at	at	ADP
ejpam-5192	126	33	a	a	DET
ejpam-5192	126	34	point	point	NOUN
ejpam-5192	126	35	x	x	SYM
ejpam-5192	126	36	∈	∈	NOUN
ejpam-5192	126	37	x	x	PUNCT
ejpam-5192	126	38	if	if	SCONJ
ejpam-5192	126	39	for	for	ADP
ejpam-5192	126	40	each	each	DET
ejpam-5192	126	41	σ1σ2	σ1σ2	VERB
ejpam-5192	126	42	-	-	ADJ
ejpam-5192	126	43	open	open	ADJ
ejpam-5192	126	44	set	set	NOUN
ejpam-5192	126	45	v	v	NOUN
ejpam-5192	126	46	of	of	ADP
ejpam-5192	126	47	y	y	NOUN
ejpam-5192	126	48	containing	contain	VERB
ejpam-5192	126	49	f(x	f(x	PROPN
ejpam-5192	126	50	)	)	PUNCT
ejpam-5192	126	51	,	,	PUNCT
ejpam-5192	126	52	there	there	PRON
ejpam-5192	126	53	exists	exist	VERB
ejpam-5192	126	54	a	a	DET
ejpam-5192	126	55	τ1τ2	τ1τ2	NOUN
ejpam-5192	126	56	-	-	ADJ
ejpam-5192	126	57	open	open	ADJ
ejpam-5192	126	58	set	set	ADJ
ejpam-5192	126	59	u	u	NOUN
ejpam-5192	126	60	of	of	ADP
ejpam-5192	126	61	x	x	PUNCT
ejpam-5192	126	62	containing	contain	VERB
ejpam-5192	126	63	x	x	PUNCT
ejpam-5192	126	64	such	such	ADJ
ejpam-5192	126	65	that	that	DET
ejpam-5192	126	66	f(u	f(u	PROPN
ejpam-5192	126	67	)	)	PUNCT
ejpam-5192	126	68	⊆	⊆	NUM
ejpam-5192	126	69	σ1σ2	σ1σ2	X
ejpam-5192	126	70	-	-	PUNCT
ejpam-5192	126	71	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5192	126	72	-	-	PUNCT
ejpam-5192	126	73	cl(v	cl(v	NOUN
ejpam-5192	126	74	)	)	PUNCT
ejpam-5192	126	75	)	)	PUNCT
ejpam-5192	126	76	.	.	PUNCT
ejpam-5192	127	1	a	a	DET
ejpam-5192	127	2	function	function	NOUN
ejpam-5192	127	3	f	f	NOUN
ejpam-5192	127	4	:	:	PUNCT
ejpam-5192	127	5	(	(	PUNCT
ejpam-5192	127	6	x	x	NOUN
ejpam-5192	127	7	,	,	PUNCT
ejpam-5192	127	8	τ1	τ1	NOUN
ejpam-5192	127	9	,	,	PUNCT
ejpam-5192	127	10	τ2	τ2	NOUN
ejpam-5192	127	11	)	)	PUNCT
ejpam-5192	127	12	→	→	SYM
ejpam-5192	127	13	(	(	PUNCT
ejpam-5192	127	14	y	y	PROPN
ejpam-5192	127	15	,	,	PUNCT
ejpam-5192	127	16	σ1	σ1	PROPN
ejpam-5192	127	17	,	,	PUNCT
ejpam-5192	127	18	σ2	σ2	PROPN
ejpam-5192	127	19	)	)	PUNCT
ejpam-5192	127	20	is	be	AUX
ejpam-5192	127	21	said	say	VERB
ejpam-5192	127	22	to	to	PART
ejpam-5192	127	23	be	be	AUX
ejpam-5192	127	24	almost	almost	ADV
ejpam-5192	127	25	(	(	PUNCT
ejpam-5192	127	26	τ1	τ1	NOUN
ejpam-5192	127	27	,	,	PUNCT
ejpam-5192	127	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	127	29	if	if	SCONJ
ejpam-5192	127	30	f	f	PROPN
ejpam-5192	127	31	has	have	VERB
ejpam-5192	127	32	this	this	DET
ejpam-5192	127	33	property	property	NOUN
ejpam-5192	127	34	at	at	ADP
ejpam-5192	127	35	each	each	DET
ejpam-5192	127	36	point	point	NOUN
ejpam-5192	127	37	of	of	ADP
ejpam-5192	127	38	x.	x.	PROPN
ejpam-5192	127	39	corollary	corollary	NOUN
ejpam-5192	127	40	1	1	NUM
ejpam-5192	127	41	.	.	PUNCT
ejpam-5192	128	1	for	for	ADP
ejpam-5192	128	2	a	a	DET
ejpam-5192	128	3	function	function	NOUN
ejpam-5192	128	4	f	f	NOUN
ejpam-5192	128	5	:	:	PUNCT
ejpam-5192	128	6	(	(	PUNCT
ejpam-5192	128	7	x	x	NOUN
ejpam-5192	128	8	,	,	PUNCT
ejpam-5192	128	9	τ1	τ1	NOUN
ejpam-5192	128	10	,	,	PUNCT
ejpam-5192	128	11	τ2	τ2	NOUN
ejpam-5192	128	12	)	)	PUNCT
ejpam-5192	128	13	→	→	SYM
ejpam-5192	128	14	(	(	PUNCT
ejpam-5192	128	15	y	y	PROPN
ejpam-5192	128	16	,	,	PUNCT
ejpam-5192	128	17	σ1	σ1	PROPN
ejpam-5192	128	18	,	,	PUNCT
ejpam-5192	128	19	σ2	σ2	NOUN
ejpam-5192	128	20	)	)	PUNCT
ejpam-5192	128	21	,	,	PUNCT
ejpam-5192	128	22	the	the	DET
ejpam-5192	128	23	following	follow	VERB
ejpam-5192	128	24	properties	property	NOUN
ejpam-5192	128	25	are	be	AUX
ejpam-5192	128	26	equivalent	equivalent	ADJ
ejpam-5192	128	27	:	:	PUNCT
ejpam-5192	128	28	(	(	PUNCT
ejpam-5192	128	29	1	1	X
ejpam-5192	128	30	)	)	PUNCT
ejpam-5192	128	31	f	f	NOUN
ejpam-5192	128	32	is	be	AUX
ejpam-5192	128	33	almost	almost	ADV
ejpam-5192	128	34	(	(	PUNCT
ejpam-5192	128	35	τ1	τ1	NOUN
ejpam-5192	128	36	,	,	PUNCT
ejpam-5192	128	37	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	128	38	at	at	ADP
ejpam-5192	128	39	x	x	X
ejpam-5192	128	40	∈	∈	PROPN
ejpam-5192	128	41	x	x	X
ejpam-5192	128	42	;	;	PUNCT
ejpam-5192	128	43	(	(	PUNCT
ejpam-5192	128	44	2	2	X
ejpam-5192	128	45	)	)	PUNCT
ejpam-5192	128	46	x	x	SYM
ejpam-5192	128	47	∈	∈	PRON
ejpam-5192	128	48	τ1τ2	τ1τ2	PUNCT
ejpam-5192	128	49	-	-	NUM
ejpam-5192	128	50	int(f	int(f	VERB
ejpam-5192	128	51	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5192	128	52	-	-	PUNCT
ejpam-5192	128	53	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5192	128	54	-	-	PUNCT
ejpam-5192	128	55	cl(v	cl(v	NOUN
ejpam-5192	128	56	)	)	PUNCT
ejpam-5192	128	57	)	)	PUNCT
ejpam-5192	128	58	)	)	PUNCT
ejpam-5192	128	59	)	)	PUNCT
ejpam-5192	129	1	for	for	ADP
ejpam-5192	129	2	every	every	DET
ejpam-5192	129	3	σ1σ2	σ1σ2	NOUN
ejpam-5192	129	4	-	-	ADJ
ejpam-5192	129	5	open	open	ADJ
ejpam-5192	129	6	set	set	NOUN
ejpam-5192	129	7	v	v	NOUN
ejpam-5192	129	8	of	of	ADP
ejpam-5192	129	9	y	y	NOUN
ejpam-5192	129	10	containing	contain	VERB
ejpam-5192	129	11	f(x	f(x	PROPN
ejpam-5192	129	12	)	)	PUNCT
ejpam-5192	129	13	;	;	PUNCT
ejpam-5192	129	14	(	(	PUNCT
ejpam-5192	129	15	3	3	X
ejpam-5192	129	16	)	)	PUNCT
ejpam-5192	129	17	x	x	SYM
ejpam-5192	129	18	∈	∈	PRON
ejpam-5192	129	19	τ1τ2	τ1τ2	NOUN
ejpam-5192	129	20	-	-	ADJ
ejpam-5192	129	21	int(f	int(f	VERB
ejpam-5192	129	22	−1((σ1	−1((σ1	NOUN
ejpam-5192	129	23	,	,	PUNCT
ejpam-5192	129	24	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-5192	129	25	)	)	PUNCT
ejpam-5192	129	26	)	)	PUNCT
ejpam-5192	129	27	)	)	PUNCT
ejpam-5192	129	28	for	for	ADP
ejpam-5192	129	29	every	every	DET
ejpam-5192	129	30	σ1σ2	σ1σ2	NOUN
ejpam-5192	129	31	-	-	ADJ
ejpam-5192	129	32	open	open	ADJ
ejpam-5192	129	33	set	set	NOUN
ejpam-5192	129	34	v	v	NOUN
ejpam-5192	129	35	of	of	ADP
ejpam-5192	129	36	y	y	NOUN
ejpam-5192	129	37	containing	contain	VERB
ejpam-5192	129	38	f(x	f(x	PROPN
ejpam-5192	129	39	)	)	PUNCT
ejpam-5192	129	40	;	;	PUNCT
ejpam-5192	129	41	(	(	PUNCT
ejpam-5192	129	42	4	4	X
ejpam-5192	129	43	)	)	PUNCT
ejpam-5192	129	44	x	x	SYM
ejpam-5192	129	45	∈	∈	PRON
ejpam-5192	129	46	τ1τ2	τ1τ2	NOUN
ejpam-5192	129	47	-	-	NUM
ejpam-5192	129	48	int(f	int(f	X
ejpam-5192	129	49	−1(v	−1(v	NOUN
ejpam-5192	129	50	)	)	PUNCT
ejpam-5192	129	51	)	)	PUNCT
ejpam-5192	129	52	for	for	ADP
ejpam-5192	129	53	every	every	DET
ejpam-5192	129	54	(	(	PUNCT
ejpam-5192	129	55	σ1	σ1	PROPN
ejpam-5192	129	56	,	,	PUNCT
ejpam-5192	129	57	σ2)r	σ2)r	NOUN
ejpam-5192	129	58	-	-	PUNCT
ejpam-5192	129	59	open	open	ADJ
ejpam-5192	129	60	set	set	VERB
ejpam-5192	129	61	v	v	NOUN
ejpam-5192	129	62	of	of	ADP
ejpam-5192	129	63	y	y	NOUN
ejpam-5192	129	64	containing	contain	VERB
ejpam-5192	129	65	f(x	f(x	PROPN
ejpam-5192	129	66	)	)	PUNCT
ejpam-5192	129	67	;	;	PUNCT
ejpam-5192	129	68	(	(	PUNCT
ejpam-5192	129	69	5	5	X
ejpam-5192	129	70	)	)	PUNCT
ejpam-5192	129	71	for	for	ADP
ejpam-5192	129	72	each	each	DET
ejpam-5192	129	73	(	(	PUNCT
ejpam-5192	129	74	σ1	σ1	PROPN
ejpam-5192	129	75	,	,	PUNCT
ejpam-5192	129	76	σ2)r	σ2)r	NOUN
ejpam-5192	129	77	-	-	PUNCT
ejpam-5192	129	78	open	open	ADJ
ejpam-5192	129	79	set	set	VERB
ejpam-5192	129	80	v	v	NOUN
ejpam-5192	129	81	of	of	ADP
ejpam-5192	129	82	y	y	NOUN
ejpam-5192	129	83	containing	contain	VERB
ejpam-5192	129	84	f(x	f(x	PROPN
ejpam-5192	129	85	)	)	PUNCT
ejpam-5192	129	86	,	,	PUNCT
ejpam-5192	129	87	there	there	PRON
ejpam-5192	129	88	exists	exist	VERB
ejpam-5192	129	89	a	a	DET
ejpam-5192	129	90	τ1τ2	τ1τ2	NOUN
ejpam-5192	129	91	-	-	ADJ
ejpam-5192	129	92	open	open	ADJ
ejpam-5192	129	93	set	set	ADJ
ejpam-5192	129	94	u	u	NOUN
ejpam-5192	129	95	of	of	ADP
ejpam-5192	129	96	x	x	PUNCT
ejpam-5192	129	97	containing	contain	VERB
ejpam-5192	129	98	x	x	PUNCT
ejpam-5192	129	99	such	such	ADJ
ejpam-5192	129	100	that	that	DET
ejpam-5192	129	101	f(u	f(u	PROPN
ejpam-5192	129	102	)	)	PUNCT
ejpam-5192	129	103	⊆	⊆	NUM
ejpam-5192	129	104	v	v	NOUN
ejpam-5192	129	105	.	.	PUNCT
ejpam-5192	130	1	theorem	theorem	NOUN
ejpam-5192	130	2	3	3	NUM
ejpam-5192	130	3	.	.	X
ejpam-5192	130	4	for	for	ADP
ejpam-5192	130	5	a	a	DET
ejpam-5192	130	6	multifunction	multifunction	NOUN
ejpam-5192	131	1	f	f	NOUN
ejpam-5192	131	2	:	:	PUNCT
ejpam-5192	131	3	(	(	PUNCT
ejpam-5192	131	4	x	x	NOUN
ejpam-5192	131	5	,	,	PUNCT
ejpam-5192	131	6	τ1	τ1	NOUN
ejpam-5192	131	7	,	,	PUNCT
ejpam-5192	131	8	τ2	τ2	NOUN
ejpam-5192	131	9	)	)	PUNCT
ejpam-5192	131	10	→	→	SYM
ejpam-5192	131	11	(	(	PUNCT
ejpam-5192	131	12	y	y	PROPN
ejpam-5192	131	13	,	,	PUNCT
ejpam-5192	131	14	σ1	σ1	PROPN
ejpam-5192	131	15	,	,	PUNCT
ejpam-5192	131	16	σ2	σ2	NOUN
ejpam-5192	131	17	)	)	PUNCT
ejpam-5192	131	18	,	,	PUNCT
ejpam-5192	131	19	the	the	DET
ejpam-5192	131	20	following	follow	VERB
ejpam-5192	131	21	properties	property	NOUN
ejpam-5192	131	22	are	be	AUX
ejpam-5192	131	23	equivalent	equivalent	ADJ
ejpam-5192	131	24	:	:	PUNCT
ejpam-5192	131	25	(	(	PUNCT
ejpam-5192	131	26	1	1	X
ejpam-5192	131	27	)	)	PUNCT
ejpam-5192	131	28	f	f	PROPN
ejpam-5192	131	29	is	be	AUX
ejpam-5192	131	30	upper	upper	ADJ
ejpam-5192	131	31	almost	almost	ADV
ejpam-5192	131	32	(	(	PUNCT
ejpam-5192	131	33	τ1	τ1	NOUN
ejpam-5192	131	34	,	,	PUNCT
ejpam-5192	131	35	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	131	36	;	;	PUNCT
ejpam-5192	131	37	(	(	PUNCT
ejpam-5192	131	38	2	2	NUM
ejpam-5192	131	39	)	)	PUNCT
ejpam-5192	131	40	f+(v	f+(v	NOUN
ejpam-5192	131	41	)	)	PUNCT
ejpam-5192	132	1	⊆	⊆	X
ejpam-5192	132	2	τ1τ2	τ1τ2	NOUN
ejpam-5192	132	3	-	-	NUM
ejpam-5192	132	4	int(f	int(f	VERB
ejpam-5192	132	5	+	+	ADJ
ejpam-5192	132	6	(	(	PUNCT
ejpam-5192	132	7	σ1σ2	σ1σ2	NUM
ejpam-5192	132	8	-	-	PUNCT
ejpam-5192	132	9	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5192	132	10	-	-	PUNCT
ejpam-5192	132	11	cl(v	cl(v	NOUN
ejpam-5192	132	12	)	)	PUNCT
ejpam-5192	132	13	)	)	PUNCT
ejpam-5192	132	14	)	)	PUNCT
ejpam-5192	132	15	)	)	PUNCT
ejpam-5192	132	16	for	for	ADP
ejpam-5192	132	17	every	every	DET
ejpam-5192	132	18	σ1σ2	σ1σ2	NOUN
ejpam-5192	132	19	-	-	ADJ
ejpam-5192	132	20	open	open	ADJ
ejpam-5192	132	21	set	set	NOUN
ejpam-5192	132	22	v	v	NOUN
ejpam-5192	132	23	of	of	ADP
ejpam-5192	132	24	y	y	PROPN
ejpam-5192	132	25	;	;	PUNCT
ejpam-5192	132	26	(	(	PUNCT
ejpam-5192	132	27	3	3	X
ejpam-5192	132	28	)	)	PUNCT
ejpam-5192	132	29	τ1τ2	τ1τ2	NOUN
ejpam-5192	132	30	-	-	NOUN
ejpam-5192	132	31	cl(f	cl(f	NOUN
ejpam-5192	132	32	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5192	132	33	-	-	PUNCT
ejpam-5192	132	34	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5192	132	35	-	-	PUNCT
ejpam-5192	132	36	int(k	int(k	NOUN
ejpam-5192	132	37	)	)	PUNCT
ejpam-5192	132	38	)	)	PUNCT
ejpam-5192	132	39	)	)	PUNCT
ejpam-5192	132	40	)	)	PUNCT
ejpam-5192	133	1	⊆	⊆	X
ejpam-5192	133	2	f−(k	f−(k	PROPN
ejpam-5192	133	3	)	)	PUNCT
ejpam-5192	133	4	for	for	ADP
ejpam-5192	133	5	every	every	DET
ejpam-5192	133	6	σ1σ2	σ1σ2	NUM
ejpam-5192	133	7	-	-	PUNCT
ejpam-5192	133	8	closed	closed	ADJ
ejpam-5192	133	9	set	set	NOUN
ejpam-5192	133	10	k	k	PROPN
ejpam-5192	133	11	of	of	ADP
ejpam-5192	133	12	y	y	PROPN
ejpam-5192	133	13	;	;	PUNCT
ejpam-5192	133	14	(	(	PUNCT
ejpam-5192	133	15	4	4	X
ejpam-5192	133	16	)	)	PUNCT
ejpam-5192	133	17	τ1τ2	τ1τ2	NOUN
ejpam-5192	133	18	-	-	NOUN
ejpam-5192	133	19	cl(f	cl(f	NOUN
ejpam-5192	133	20	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5192	133	21	-	-	PUNCT
ejpam-5192	133	22	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5192	133	23	-	-	PUNCT
ejpam-5192	133	24	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5192	133	25	-	-	PUNCT
ejpam-5192	133	26	cl(b	cl(b	NOUN
ejpam-5192	133	27	)	)	PUNCT
ejpam-5192	133	28	)	)	PUNCT
ejpam-5192	133	29	)	)	PUNCT
ejpam-5192	133	30	)	)	PUNCT
ejpam-5192	133	31	)	)	PUNCT
ejpam-5192	134	1	⊆	⊆	X
ejpam-5192	134	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5192	134	3	-	-	PUNCT
ejpam-5192	134	4	cl(b	cl(b	NOUN
ejpam-5192	134	5	)	)	PUNCT
ejpam-5192	134	6	)	)	PUNCT
ejpam-5192	135	1	for	for	ADP
ejpam-5192	135	2	every	every	DET
ejpam-5192	135	3	subset	subset	NOUN
ejpam-5192	135	4	b	b	PROPN
ejpam-5192	135	5	of	of	ADP
ejpam-5192	135	6	y	y	PROPN
ejpam-5192	135	7	;	;	PUNCT
ejpam-5192	135	8	(	(	PUNCT
ejpam-5192	135	9	5	5	X
ejpam-5192	135	10	)	)	PUNCT
ejpam-5192	135	11	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5192	135	12	-	-	PUNCT
ejpam-5192	135	13	int(b	int(b	NOUN
ejpam-5192	135	14	)	)	PUNCT
ejpam-5192	135	15	)	)	PUNCT
ejpam-5192	136	1	⊆	⊆	X
ejpam-5192	136	2	τ1τ2	τ1τ2	NOUN
ejpam-5192	136	3	-	-	NUM
ejpam-5192	136	4	int(f	int(f	VERB
ejpam-5192	136	5	+	+	ADJ
ejpam-5192	136	6	(	(	PUNCT
ejpam-5192	136	7	σ1σ2	σ1σ2	NUM
ejpam-5192	136	8	-	-	PUNCT
ejpam-5192	136	9	int(σ1σ2	int(σ1σ2	ADV
ejpam-5192	136	10	-	-	PUNCT
ejpam-5192	136	11	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5192	136	12	-	-	PUNCT
ejpam-5192	136	13	int(b	int(b	NOUN
ejpam-5192	136	14	)	)	PUNCT
ejpam-5192	136	15	)	)	PUNCT
ejpam-5192	136	16	)	)	PUNCT
ejpam-5192	136	17	)	)	PUNCT
ejpam-5192	136	18	)	)	PUNCT
ejpam-5192	136	19	for	for	ADP
ejpam-5192	136	20	every	every	DET
ejpam-5192	136	21	subset	subset	NOUN
ejpam-5192	136	22	b	b	PROPN
ejpam-5192	136	23	of	of	ADP
ejpam-5192	136	24	y	y	PROPN
ejpam-5192	136	25	;	;	PUNCT
ejpam-5192	136	26	c.	c.	PROPN
ejpam-5192	136	27	klanarong	klanarong	PROPN
ejpam-5192	136	28	,	,	PUNCT
ejpam-5192	136	29	s.	s.	PROPN
ejpam-5192	136	30	sompong	sompong	PROPN
ejpam-5192	136	31	,	,	PUNCT
ejpam-5192	136	32	c.	c.	PROPN
ejpam-5192	136	33	boonpok	boonpok	PROPN
ejpam-5192	136	34	/	/	SYM
ejpam-5192	136	35	eur	eur	PROPN
ejpam-5192	136	36	.	.	PUNCT
ejpam-5192	137	1	j.	j.	PROPN
ejpam-5192	137	2	pure	pure	PROPN
ejpam-5192	137	3	appl	appl	PROPN
ejpam-5192	137	4	.	.	PROPN
ejpam-5192	137	5	math	math	PROPN
ejpam-5192	137	6	,	,	PUNCT
ejpam-5192	137	7	17	17	NUM
ejpam-5192	137	8	(	(	PUNCT
ejpam-5192	137	9	2	2	NUM
ejpam-5192	137	10	)	)	PUNCT
ejpam-5192	137	11	(	(	PUNCT
ejpam-5192	137	12	2024	2024	NUM
ejpam-5192	137	13	)	)	PUNCT
ejpam-5192	137	14	,	,	PUNCT
ejpam-5192	137	15	1244	1244	NUM
ejpam-5192	137	16	-	-	SYM
ejpam-5192	137	17	1253	1253	NUM
ejpam-5192	137	18	1249	1249	NUM
ejpam-5192	137	19	(	(	PUNCT
ejpam-5192	137	20	6	6	NUM
ejpam-5192	137	21	)	)	PUNCT
ejpam-5192	137	22	f+(v	f+(v	NOUN
ejpam-5192	137	23	)	)	PUNCT
ejpam-5192	137	24	is	be	AUX
ejpam-5192	137	25	τ1τ2	τ1τ2	NOUN
ejpam-5192	137	26	-	-	ADJ
ejpam-5192	137	27	open	open	ADJ
ejpam-5192	137	28	in	in	ADP
ejpam-5192	137	29	x	x	PUNCT
ejpam-5192	137	30	for	for	ADP
ejpam-5192	137	31	every	every	DET
ejpam-5192	137	32	(	(	PUNCT
ejpam-5192	137	33	σ1	σ1	PROPN
ejpam-5192	137	34	,	,	PUNCT
ejpam-5192	137	35	σ2)r	σ2)r	NOUN
ejpam-5192	137	36	-	-	PUNCT
ejpam-5192	137	37	open	open	ADJ
ejpam-5192	137	38	set	set	VERB
ejpam-5192	137	39	v	v	NOUN
ejpam-5192	137	40	of	of	ADP
ejpam-5192	137	41	y	y	PROPN
ejpam-5192	137	42	;	;	PUNCT
ejpam-5192	137	43	(	(	PUNCT
ejpam-5192	137	44	7	7	X
ejpam-5192	137	45	)	)	PUNCT
ejpam-5192	137	46	f−(k	f−(k	PROPN
ejpam-5192	137	47	)	)	PUNCT
ejpam-5192	137	48	is	be	AUX
ejpam-5192	137	49	τ1τ2	τ1τ2	NOUN
ejpam-5192	137	50	-	-	ADJ
ejpam-5192	137	51	closed	closed	ADJ
ejpam-5192	137	52	in	in	ADP
ejpam-5192	137	53	x	x	PUNCT
ejpam-5192	137	54	for	for	ADP
ejpam-5192	137	55	every	every	DET
ejpam-5192	137	56	(	(	PUNCT
ejpam-5192	137	57	σ1	σ1	PROPN
ejpam-5192	137	58	,	,	PUNCT
ejpam-5192	138	1	σ2)r	σ2)r	NOUN
ejpam-5192	138	2	-	-	PUNCT
ejpam-5192	138	3	closed	close	VERB
ejpam-5192	138	4	set	set	ADJ
ejpam-5192	138	5	k	k	PROPN
ejpam-5192	138	6	of	of	ADP
ejpam-5192	138	7	y	y	PROPN
ejpam-5192	138	8	.	.	PUNCT
ejpam-5192	139	1	proof	proof	NOUN
ejpam-5192	139	2	.	.	PUNCT
ejpam-5192	140	1	(	(	PUNCT
ejpam-5192	140	2	1	1	X
ejpam-5192	140	3	)	)	PUNCT
ejpam-5192	140	4	⇒	⇒	NOUN
ejpam-5192	140	5	(	(	PUNCT
ejpam-5192	140	6	2	2	NUM
ejpam-5192	140	7	):	):	PUNCT
ejpam-5192	140	8	let	let	VERB
ejpam-5192	140	9	v	v	PART
ejpam-5192	140	10	be	be	AUX
ejpam-5192	140	11	any	any	DET
ejpam-5192	140	12	σ1σ2	σ1σ2	NOUN
ejpam-5192	140	13	-	-	ADJ
ejpam-5192	140	14	open	open	ADJ
ejpam-5192	140	15	set	set	NOUN
ejpam-5192	140	16	of	of	ADP
ejpam-5192	140	17	y	y	PROPN
ejpam-5192	140	18	and	and	CCONJ
ejpam-5192	140	19	x	x	PROPN
ejpam-5192	140	20	∈	∈	PROPN
ejpam-5192	140	21	f+(v	f+(v	NOUN
ejpam-5192	140	22	)	)	PUNCT
ejpam-5192	140	23	.	.	PUNCT
ejpam-5192	141	1	then	then	ADV
ejpam-5192	141	2	,	,	PUNCT
ejpam-5192	141	3	f	f	PROPN
ejpam-5192	141	4	(	(	PUNCT
ejpam-5192	141	5	x	x	X
ejpam-5192	141	6	)	)	PUNCT
ejpam-5192	141	7	⊆	⊆	NUM
ejpam-5192	141	8	v	v	NOUN
ejpam-5192	141	9	.	.	PUNCT
ejpam-5192	142	1	thus	thus	ADV
ejpam-5192	142	2	,	,	PUNCT
ejpam-5192	142	3	by	by	ADP
ejpam-5192	142	4	theorem	theorem	NOUN
ejpam-5192	142	5	1	1	NUM
ejpam-5192	142	6	,	,	PUNCT
ejpam-5192	142	7	x	x	SYM
ejpam-5192	142	8	∈	∈	PRON
ejpam-5192	142	9	τ1τ2	τ1τ2	PUNCT
ejpam-5192	142	10	-	-	NUM
ejpam-5192	142	11	int(f	int(f	VERB
ejpam-5192	142	12	+	+	ADJ
ejpam-5192	142	13	(	(	PUNCT
ejpam-5192	142	14	σ1σ2	σ1σ2	NUM
ejpam-5192	142	15	-	-	PUNCT
ejpam-5192	142	16	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5192	142	17	-	-	PUNCT
ejpam-5192	142	18	cl(v	cl(v	NOUN
ejpam-5192	142	19	)	)	PUNCT
ejpam-5192	142	20	)	)	PUNCT
ejpam-5192	142	21	)	)	PUNCT
ejpam-5192	142	22	)	)	PUNCT
ejpam-5192	142	23	and	and	CCONJ
ejpam-5192	142	24	hence	hence	ADV
ejpam-5192	142	25	f+(v	f+(v	NOUN
ejpam-5192	142	26	)	)	PUNCT
ejpam-5192	143	1	⊆	⊆	X
ejpam-5192	143	2	τ1τ2	τ1τ2	NOUN
ejpam-5192	143	3	-	-	NUM
ejpam-5192	143	4	int(f	int(f	VERB
ejpam-5192	143	5	+	+	ADJ
ejpam-5192	143	6	(	(	PUNCT
ejpam-5192	143	7	σ1σ2	σ1σ2	NUM
ejpam-5192	143	8	-	-	PUNCT
ejpam-5192	143	9	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5192	143	10	-	-	PUNCT
ejpam-5192	143	11	cl(v	cl(v	NOUN
ejpam-5192	143	12	)	)	PUNCT
ejpam-5192	143	13	)	)	PUNCT
ejpam-5192	143	14	)	)	PUNCT
ejpam-5192	143	15	)	)	PUNCT
ejpam-5192	143	16	.	.	PUNCT
ejpam-5192	144	1	(	(	PUNCT
ejpam-5192	144	2	2	2	X
ejpam-5192	144	3	)	)	PUNCT
ejpam-5192	144	4	⇒	⇒	NOUN
ejpam-5192	144	5	(	(	PUNCT
ejpam-5192	144	6	3	3	NUM
ejpam-5192	144	7	):	):	PUNCT
ejpam-5192	144	8	let	let	VERB
ejpam-5192	144	9	k	k	PRON
ejpam-5192	144	10	be	be	AUX
ejpam-5192	144	11	any	any	DET
ejpam-5192	144	12	σ1σ2	σ1σ2	NUM
ejpam-5192	144	13	-	-	PUNCT
ejpam-5192	144	14	closed	closed	ADJ
ejpam-5192	144	15	set	set	NOUN
ejpam-5192	144	16	of	of	ADP
ejpam-5192	144	17	y	y	PROPN
ejpam-5192	144	18	.	.	PUNCT
ejpam-5192	145	1	then	then	ADV
ejpam-5192	145	2	,	,	PUNCT
ejpam-5192	145	3	y	y	PROPN
ejpam-5192	145	4	−k	−k	PROPN
ejpam-5192	145	5	is	be	AUX
ejpam-5192	145	6	σ1σ2	σ1σ2	NOUN
ejpam-5192	145	7	-	-	ADJ
ejpam-5192	145	8	open	open	ADJ
ejpam-5192	145	9	in	in	ADP
ejpam-5192	145	10	y	y	PROPN
ejpam-5192	145	11	and	and	CCONJ
ejpam-5192	145	12	by	by	ADP
ejpam-5192	145	13	(	(	PUNCT
ejpam-5192	145	14	2	2	NUM
ejpam-5192	145	15	)	)	PUNCT
ejpam-5192	145	16	,	,	PUNCT
ejpam-5192	145	17	x	x	PUNCT
ejpam-5192	145	18	−	−	DET
ejpam-5192	145	19	f−(k	f−(k	PROPN
ejpam-5192	145	20	)	)	PUNCT
ejpam-5192	145	21	=	=	PUNCT
ejpam-5192	146	1	f+(y	f+(y	PROPN
ejpam-5192	146	2	−k	−k	PROPN
ejpam-5192	146	3	)	)	PUNCT
ejpam-5192	146	4	⊆	⊆	NUM
ejpam-5192	146	5	τ1τ2	τ1τ2	NOUN
ejpam-5192	146	6	-	-	NUM
ejpam-5192	146	7	int(f	int(f	VERB
ejpam-5192	146	8	+	+	ADJ
ejpam-5192	146	9	(	(	PUNCT
ejpam-5192	146	10	σ1σ2	σ1σ2	NUM
ejpam-5192	146	11	-	-	PUNCT
ejpam-5192	146	12	int(σ1σ2	int(σ1σ2	VERB
ejpam-5192	146	13	-	-	PUNCT
ejpam-5192	146	14	cl(y	cl(y	NOUN
ejpam-5192	146	15	−k	−k	NOUN
ejpam-5192	146	16	)	)	PUNCT
ejpam-5192	146	17	)	)	PUNCT
ejpam-5192	146	18	)	)	PUNCT
ejpam-5192	146	19	)	)	PUNCT
ejpam-5192	147	1	=	=	PUNCT
ejpam-5192	148	1	τ1τ2	τ1τ2	NOUN
ejpam-5192	148	2	-	-	ADJ
ejpam-5192	148	3	int(x	int(x	ADJ
ejpam-5192	148	4	−	−	NOUN
ejpam-5192	148	5	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-5192	148	6	-	-	PUNCT
ejpam-5192	148	7	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5192	148	8	-	-	PUNCT
ejpam-5192	148	9	int(k	int(k	NOUN
ejpam-5192	148	10	)	)	PUNCT
ejpam-5192	148	11	)	)	PUNCT
ejpam-5192	148	12	)	)	PUNCT
ejpam-5192	148	13	)	)	PUNCT
ejpam-5192	149	1	=	=	PUNCT
ejpam-5192	149	2	x	x	X
ejpam-5192	150	1	−	−	ADP
ejpam-5192	150	2	τ1τ2	τ1τ2	NOUN
ejpam-5192	150	3	-	-	ADJ
ejpam-5192	150	4	cl(f	cl(f	NOUN
ejpam-5192	150	5	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5192	150	6	-	-	PUNCT
ejpam-5192	150	7	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5192	150	8	-	-	PUNCT
ejpam-5192	150	9	int(k	int(k	NOUN
ejpam-5192	150	10	)	)	PUNCT
ejpam-5192	150	11	)	)	PUNCT
ejpam-5192	150	12	)	)	PUNCT
ejpam-5192	150	13	)	)	PUNCT
ejpam-5192	150	14	.	.	PUNCT
ejpam-5192	151	1	thus	thus	ADV
ejpam-5192	151	2	,	,	PUNCT
ejpam-5192	151	3	τ1τ2	τ1τ2	NOUN
ejpam-5192	151	4	-	-	ADJ
ejpam-5192	151	5	cl(f	cl(f	NOUN
ejpam-5192	151	6	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5192	151	7	-	-	PUNCT
ejpam-5192	151	8	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5192	151	9	-	-	PUNCT
ejpam-5192	151	10	int(k	int(k	NOUN
ejpam-5192	151	11	)	)	PUNCT
ejpam-5192	151	12	)	)	PUNCT
ejpam-5192	151	13	)	)	PUNCT
ejpam-5192	151	14	)	)	PUNCT
ejpam-5192	152	1	⊆	⊆	NUM
ejpam-5192	152	2	f−(k	f−(k	PROPN
ejpam-5192	152	3	)	)	PUNCT
ejpam-5192	152	4	.	.	PUNCT
ejpam-5192	153	1	(	(	PUNCT
ejpam-5192	153	2	3	3	X
ejpam-5192	153	3	)	)	PUNCT
ejpam-5192	153	4	⇒	⇒	NOUN
ejpam-5192	153	5	(	(	PUNCT
ejpam-5192	153	6	4	4	NUM
ejpam-5192	153	7	):	):	PUNCT
ejpam-5192	153	8	let	let	VERB
ejpam-5192	153	9	b	b	X
ejpam-5192	153	10	be	be	AUX
ejpam-5192	153	11	any	any	DET
ejpam-5192	153	12	subset	subset	NOUN
ejpam-5192	153	13	of	of	ADP
ejpam-5192	153	14	y	y	PROPN
ejpam-5192	153	15	.	.	PUNCT
ejpam-5192	154	1	then	then	ADV
ejpam-5192	154	2	,	,	PUNCT
ejpam-5192	154	3	σ1σ2	σ1σ2	NOUN
ejpam-5192	154	4	-	-	NOUN
ejpam-5192	154	5	cl(b	cl(b	NOUN
ejpam-5192	154	6	)	)	PUNCT
ejpam-5192	154	7	is	be	AUX
ejpam-5192	154	8	a	a	DET
ejpam-5192	154	9	σ1σ2	σ1σ2	NUM
ejpam-5192	154	10	-	-	PUNCT
ejpam-5192	154	11	closed	closed	ADJ
ejpam-5192	154	12	set	set	NOUN
ejpam-5192	154	13	of	of	ADP
ejpam-5192	154	14	y	y	PROPN
ejpam-5192	154	15	and	and	CCONJ
ejpam-5192	154	16	by	by	ADP
ejpam-5192	154	17	(	(	PUNCT
ejpam-5192	154	18	3	3	NUM
ejpam-5192	154	19	)	)	PUNCT
ejpam-5192	154	20	,	,	PUNCT
ejpam-5192	154	21	τ1τ2	τ1τ2	NOUN
ejpam-5192	154	22	-	-	ADJ
ejpam-5192	154	23	cl(f	cl(f	NOUN
ejpam-5192	154	24	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5192	154	25	-	-	PUNCT
ejpam-5192	154	26	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5192	154	27	-	-	PUNCT
ejpam-5192	154	28	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5192	154	29	-	-	PUNCT
ejpam-5192	154	30	cl(b	cl(b	NOUN
ejpam-5192	154	31	)	)	PUNCT
ejpam-5192	154	32	)	)	PUNCT
ejpam-5192	154	33	)	)	PUNCT
ejpam-5192	154	34	)	)	PUNCT
ejpam-5192	154	35	)	)	PUNCT
ejpam-5192	155	1	⊆	⊆	X
ejpam-5192	155	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5192	155	3	-	-	PUNCT
ejpam-5192	155	4	cl(b	cl(b	NOUN
ejpam-5192	155	5	)	)	PUNCT
ejpam-5192	155	6	)	)	PUNCT
ejpam-5192	155	7	.	.	PUNCT
ejpam-5192	156	1	(	(	PUNCT
ejpam-5192	156	2	4	4	X
ejpam-5192	156	3	)	)	PUNCT
ejpam-5192	156	4	⇒	⇒	NOUN
ejpam-5192	156	5	(	(	PUNCT
ejpam-5192	156	6	5	5	NUM
ejpam-5192	156	7	):	):	PUNCT
ejpam-5192	156	8	let	let	VERB
ejpam-5192	156	9	b	b	X
ejpam-5192	156	10	be	be	AUX
ejpam-5192	156	11	any	any	DET
ejpam-5192	156	12	subset	subset	NOUN
ejpam-5192	156	13	of	of	ADP
ejpam-5192	156	14	y	y	PROPN
ejpam-5192	156	15	.	.	PUNCT
ejpam-5192	157	1	then	then	ADV
ejpam-5192	157	2	,	,	PUNCT
ejpam-5192	157	3	we	we	PRON
ejpam-5192	157	4	have	have	VERB
ejpam-5192	157	5	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5192	157	6	-	-	PUNCT
ejpam-5192	157	7	int(b	int(b	NOUN
ejpam-5192	157	8	)	)	PUNCT
ejpam-5192	157	9	)	)	PUNCT
ejpam-5192	158	1	=	=	PUNCT
ejpam-5192	159	1	x	x	PUNCT
ejpam-5192	159	2	−	−	ADP
ejpam-5192	159	3	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5192	159	4	-	-	PUNCT
ejpam-5192	159	5	cl(y	cl(y	NOUN
ejpam-5192	159	6	−b	−b	NOUN
ejpam-5192	159	7	)	)	PUNCT
ejpam-5192	159	8	)	)	PUNCT
ejpam-5192	160	1	⊆	⊆	NUM
ejpam-5192	160	2	x	x	SYM
ejpam-5192	160	3	−	−	NUM
ejpam-5192	160	4	τ1τ2	τ1τ2	NOUN
ejpam-5192	160	5	-	-	ADJ
ejpam-5192	160	6	cl(f	cl(f	NOUN
ejpam-5192	160	7	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5192	160	8	-	-	PUNCT
ejpam-5192	160	9	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5192	160	10	-	-	PUNCT
ejpam-5192	160	11	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5192	160	12	-	-	PUNCT
ejpam-5192	160	13	cl(y	cl(y	NOUN
ejpam-5192	160	14	−b	−b	NOUN
ejpam-5192	160	15	)	)	PUNCT
ejpam-5192	160	16	)	)	PUNCT
ejpam-5192	160	17	)	)	PUNCT
ejpam-5192	160	18	)	)	PUNCT
ejpam-5192	160	19	)	)	PUNCT
ejpam-5192	161	1	=	=	PUNCT
ejpam-5192	162	1	x	x	X
ejpam-5192	162	2	−	−	ADP
ejpam-5192	162	3	τ1τ2	τ1τ2	NOUN
ejpam-5192	162	4	-	-	NOUN
ejpam-5192	162	5	cl(f	cl(f	NOUN
ejpam-5192	162	6	−(y	−(y	NOUN
ejpam-5192	162	7	−	−	NOUN
ejpam-5192	162	8	σ1σ2	σ1σ2	SYM
ejpam-5192	162	9	-	-	PUNCT
ejpam-5192	162	10	int(σ1σ2	int(σ1σ2	ADV
ejpam-5192	162	11	-	-	PUNCT
ejpam-5192	162	12	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5192	162	13	-	-	PUNCT
ejpam-5192	162	14	int(b	int(b	NOUN
ejpam-5192	162	15	)	)	PUNCT
ejpam-5192	162	16	)	)	PUNCT
ejpam-5192	162	17	)	)	PUNCT
ejpam-5192	162	18	)	)	PUNCT
ejpam-5192	162	19	)	)	PUNCT
ejpam-5192	163	1	=	=	PUNCT
ejpam-5192	163	2	τ1τ2	τ1τ2	NOUN
ejpam-5192	163	3	-	-	NUM
ejpam-5192	163	4	int(f	int(f	VERB
ejpam-5192	163	5	+	+	ADJ
ejpam-5192	163	6	(	(	PUNCT
ejpam-5192	163	7	σ1σ2	σ1σ2	NUM
ejpam-5192	163	8	-	-	PUNCT
ejpam-5192	163	9	int(σ1σ2	int(σ1σ2	ADV
ejpam-5192	163	10	-	-	PUNCT
ejpam-5192	163	11	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5192	163	12	-	-	PUNCT
ejpam-5192	163	13	int(b	int(b	NOUN
ejpam-5192	163	14	)	)	PUNCT
ejpam-5192	163	15	)	)	PUNCT
ejpam-5192	163	16	)	)	PUNCT
ejpam-5192	163	17	)	)	PUNCT
ejpam-5192	163	18	)	)	PUNCT
ejpam-5192	163	19	.	.	PUNCT
ejpam-5192	164	1	(	(	PUNCT
ejpam-5192	164	2	5	5	X
ejpam-5192	164	3	)	)	PUNCT
ejpam-5192	164	4	⇒	⇒	NOUN
ejpam-5192	164	5	(	(	PUNCT
ejpam-5192	164	6	6	6	NUM
ejpam-5192	164	7	):	):	PUNCT
ejpam-5192	164	8	let	let	VERB
ejpam-5192	164	9	v	v	PART
ejpam-5192	164	10	be	be	AUX
ejpam-5192	164	11	any	any	DET
ejpam-5192	164	12	(	(	PUNCT
ejpam-5192	164	13	σ1	σ1	NOUN
ejpam-5192	164	14	,	,	PUNCT
ejpam-5192	164	15	σ2)r	σ2)r	NOUN
ejpam-5192	164	16	-	-	PUNCT
ejpam-5192	164	17	open	open	ADJ
ejpam-5192	164	18	set	set	NOUN
ejpam-5192	164	19	of	of	ADP
ejpam-5192	164	20	y	y	PROPN
ejpam-5192	164	21	.	.	PUNCT
ejpam-5192	165	1	by	by	ADP
ejpam-5192	165	2	(	(	PUNCT
ejpam-5192	165	3	5	5	NUM
ejpam-5192	165	4	)	)	PUNCT
ejpam-5192	165	5	,	,	PUNCT
ejpam-5192	165	6	we	we	PRON
ejpam-5192	165	7	have	have	VERB
ejpam-5192	165	8	f+(v	f+(v	NOUN
ejpam-5192	165	9	)	)	PUNCT
ejpam-5192	166	1	⊆	⊆	X
ejpam-5192	166	2	τ1τ2	τ1τ2	NOUN
ejpam-5192	166	3	-	-	NUM
ejpam-5192	166	4	int(f	int(f	VERB
ejpam-5192	166	5	+	+	ADJ
ejpam-5192	166	6	(	(	PUNCT
ejpam-5192	166	7	v	v	NOUN
ejpam-5192	166	8	)	)	PUNCT
ejpam-5192	166	9	)	)	PUNCT
ejpam-5192	166	10	and	and	CCONJ
ejpam-5192	166	11	hence	hence	ADV
ejpam-5192	166	12	f+(v	f+(v	PROPN
ejpam-5192	166	13	)	)	PUNCT
ejpam-5192	166	14	is	be	AUX
ejpam-5192	166	15	τ1τ2	τ1τ2	NOUN
ejpam-5192	166	16	-	-	ADJ
ejpam-5192	166	17	open	open	ADJ
ejpam-5192	166	18	in	in	ADP
ejpam-5192	166	19	x.	x.	NOUN
ejpam-5192	166	20	(	(	PUNCT
ejpam-5192	166	21	6	6	NUM
ejpam-5192	166	22	)	)	PUNCT
ejpam-5192	166	23	⇒	⇒	NOUN
ejpam-5192	166	24	(	(	PUNCT
ejpam-5192	166	25	7	7	NUM
ejpam-5192	166	26	):	):	PUNCT
ejpam-5192	166	27	the	the	DET
ejpam-5192	166	28	proof	proof	NOUN
ejpam-5192	166	29	is	be	AUX
ejpam-5192	166	30	obvious	obvious	ADJ
ejpam-5192	166	31	.	.	PUNCT
ejpam-5192	167	1	(	(	PUNCT
ejpam-5192	167	2	7	7	X
ejpam-5192	167	3	)	)	PUNCT
ejpam-5192	167	4	⇒	⇒	NOUN
ejpam-5192	167	5	(	(	PUNCT
ejpam-5192	167	6	1	1	NUM
ejpam-5192	167	7	):	):	PUNCT
ejpam-5192	167	8	let	let	VERB
ejpam-5192	167	9	x	x	PUNCT
ejpam-5192	167	10	∈	∈	PROPN
ejpam-5192	167	11	x	x	X
ejpam-5192	167	12	and	and	CCONJ
ejpam-5192	167	13	v	v	AUX
ejpam-5192	167	14	be	be	AUX
ejpam-5192	167	15	any	any	DET
ejpam-5192	167	16	(	(	PUNCT
ejpam-5192	167	17	σ1	σ1	NOUN
ejpam-5192	167	18	,	,	PUNCT
ejpam-5192	167	19	σ2)r	σ2)r	NOUN
ejpam-5192	167	20	-	-	PUNCT
ejpam-5192	167	21	open	open	ADJ
ejpam-5192	167	22	set	set	NOUN
ejpam-5192	167	23	of	of	ADP
ejpam-5192	167	24	y	y	PROPN
ejpam-5192	167	25	containing	contain	VERB
ejpam-5192	167	26	f	f	PROPN
ejpam-5192	167	27	(	(	PUNCT
ejpam-5192	167	28	x	x	NOUN
ejpam-5192	167	29	)	)	PUNCT
ejpam-5192	167	30	.	.	PUNCT
ejpam-5192	168	1	since	since	SCONJ
ejpam-5192	168	2	y	y	PROPN
ejpam-5192	168	3	−v	−v	PROPN
ejpam-5192	168	4	is	be	AUX
ejpam-5192	168	5	(	(	PUNCT
ejpam-5192	168	6	σ1	σ1	NOUN
ejpam-5192	168	7	,	,	PUNCT
ejpam-5192	168	8	σ2)r	σ2)r	NOUN
ejpam-5192	168	9	-	-	PUNCT
ejpam-5192	168	10	closed	closed	ADJ
ejpam-5192	168	11	and	and	CCONJ
ejpam-5192	168	12	by	by	ADP
ejpam-5192	168	13	(	(	PUNCT
ejpam-5192	168	14	7	7	NUM
ejpam-5192	168	15	)	)	PUNCT
ejpam-5192	168	16	,	,	PUNCT
ejpam-5192	168	17	x	x	PUNCT
ejpam-5192	168	18	−f+(v	−f+(v	X
ejpam-5192	168	19	)	)	PUNCT
ejpam-5192	168	20	=	=	SYM
ejpam-5192	168	21	f−(y	f−(y	NOUN
ejpam-5192	168	22	−v	−v	NOUN
ejpam-5192	168	23	)	)	PUNCT
ejpam-5192	168	24	is	be	AUX
ejpam-5192	168	25	τ1τ2	τ1τ2	NOUN
ejpam-5192	168	26	-	-	ADJ
ejpam-5192	168	27	closed	closed	ADJ
ejpam-5192	168	28	in	in	ADP
ejpam-5192	168	29	x.	x.	NOUN
ejpam-5192	168	30	thus	thus	ADV
ejpam-5192	168	31	,	,	PUNCT
ejpam-5192	168	32	f+(v	f+(v	PROPN
ejpam-5192	168	33	)	)	PUNCT
ejpam-5192	169	1	is	be	AUX
ejpam-5192	169	2	τ1τ2	τ1τ2	NOUN
ejpam-5192	169	3	-	-	ADJ
ejpam-5192	169	4	open	open	ADJ
ejpam-5192	169	5	and	and	CCONJ
ejpam-5192	169	6	hence	hence	ADV
ejpam-5192	169	7	x	x	X
ejpam-5192	169	8	∈	∈	PRON
ejpam-5192	169	9	τ1τ2	τ1τ2	NOUN
ejpam-5192	169	10	-	-	NUM
ejpam-5192	169	11	int(f	int(f	VERB
ejpam-5192	169	12	+	+	ADJ
ejpam-5192	169	13	(	(	PUNCT
ejpam-5192	169	14	v	v	NOUN
ejpam-5192	169	15	)	)	PUNCT
ejpam-5192	169	16	)	)	PUNCT
ejpam-5192	169	17	.	.	PUNCT
ejpam-5192	170	1	then	then	ADV
ejpam-5192	170	2	,	,	PUNCT
ejpam-5192	170	3	there	there	PRON
ejpam-5192	170	4	exists	exist	VERB
ejpam-5192	170	5	a	a	DET
ejpam-5192	170	6	τ1τ2	τ1τ2	NOUN
ejpam-5192	170	7	-	-	ADJ
ejpam-5192	170	8	open	open	ADJ
ejpam-5192	170	9	set	set	ADJ
ejpam-5192	170	10	u	u	NOUN
ejpam-5192	170	11	of	of	ADP
ejpam-5192	170	12	x	x	PUNCT
ejpam-5192	170	13	containing	contain	VERB
ejpam-5192	170	14	x	x	PUNCT
ejpam-5192	170	15	such	such	ADJ
ejpam-5192	170	16	that	that	SCONJ
ejpam-5192	170	17	f	f	PROPN
ejpam-5192	170	18	(	(	PUNCT
ejpam-5192	170	19	u	u	NOUN
ejpam-5192	170	20	)	)	PUNCT
ejpam-5192	170	21	⊆	⊆	NUM
ejpam-5192	170	22	v	v	NOUN
ejpam-5192	170	23	.	.	PUNCT
ejpam-5192	171	1	it	it	PRON
ejpam-5192	171	2	follows	follow	VERB
ejpam-5192	171	3	from	from	ADP
ejpam-5192	171	4	theorem	theorem	ADJ
ejpam-5192	171	5	1	1	NUM
ejpam-5192	171	6	that	that	SCONJ
ejpam-5192	171	7	f	f	PROPN
ejpam-5192	171	8	is	be	AUX
ejpam-5192	171	9	upper	upper	ADJ
ejpam-5192	171	10	almost	almost	ADV
ejpam-5192	171	11	(	(	PUNCT
ejpam-5192	171	12	τ1	τ1	NOUN
ejpam-5192	171	13	,	,	PUNCT
ejpam-5192	171	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	171	15	.	.	PUNCT
ejpam-5192	172	1	theorem	theorem	NOUN
ejpam-5192	172	2	4	4	NUM
ejpam-5192	172	3	.	.	X
ejpam-5192	172	4	for	for	ADP
ejpam-5192	172	5	a	a	DET
ejpam-5192	172	6	multifunction	multifunction	NOUN
ejpam-5192	173	1	f	f	NOUN
ejpam-5192	173	2	:	:	PUNCT
ejpam-5192	173	3	(	(	PUNCT
ejpam-5192	173	4	x	x	NOUN
ejpam-5192	173	5	,	,	PUNCT
ejpam-5192	173	6	τ1	τ1	NOUN
ejpam-5192	173	7	,	,	PUNCT
ejpam-5192	173	8	τ2	τ2	NOUN
ejpam-5192	173	9	)	)	PUNCT
ejpam-5192	173	10	→	→	SYM
ejpam-5192	173	11	(	(	PUNCT
ejpam-5192	173	12	y	y	PROPN
ejpam-5192	173	13	,	,	PUNCT
ejpam-5192	173	14	σ1	σ1	PROPN
ejpam-5192	173	15	,	,	PUNCT
ejpam-5192	173	16	σ2	σ2	NOUN
ejpam-5192	173	17	)	)	PUNCT
ejpam-5192	173	18	,	,	PUNCT
ejpam-5192	173	19	the	the	DET
ejpam-5192	173	20	following	follow	VERB
ejpam-5192	173	21	properties	property	NOUN
ejpam-5192	173	22	are	be	AUX
ejpam-5192	173	23	equivalent	equivalent	ADJ
ejpam-5192	173	24	:	:	PUNCT
ejpam-5192	173	25	(	(	PUNCT
ejpam-5192	173	26	1	1	X
ejpam-5192	173	27	)	)	PUNCT
ejpam-5192	173	28	f	f	PROPN
ejpam-5192	173	29	is	be	AUX
ejpam-5192	173	30	lower	low	ADJ
ejpam-5192	173	31	almost	almost	ADV
ejpam-5192	173	32	(	(	PUNCT
ejpam-5192	173	33	τ1	τ1	NOUN
ejpam-5192	173	34	,	,	PUNCT
ejpam-5192	173	35	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	173	36	;	;	PUNCT
ejpam-5192	173	37	(	(	PUNCT
ejpam-5192	173	38	2	2	X
ejpam-5192	173	39	)	)	PUNCT
ejpam-5192	173	40	f−(v	f−(v	NOUN
ejpam-5192	173	41	)	)	PUNCT
ejpam-5192	173	42	⊆	⊆	NUM
ejpam-5192	173	43	τ1τ2	τ1τ2	NOUN
ejpam-5192	173	44	-	-	NUM
ejpam-5192	173	45	int(f	int(f	VERB
ejpam-5192	173	46	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5192	173	47	-	-	PUNCT
ejpam-5192	173	48	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5192	173	49	-	-	PUNCT
ejpam-5192	173	50	cl(v	cl(v	NOUN
ejpam-5192	173	51	)	)	PUNCT
ejpam-5192	173	52	)	)	PUNCT
ejpam-5192	173	53	)	)	PUNCT
ejpam-5192	173	54	)	)	PUNCT
ejpam-5192	174	1	for	for	ADP
ejpam-5192	174	2	every	every	DET
ejpam-5192	174	3	σ1σ2	σ1σ2	NOUN
ejpam-5192	174	4	-	-	ADJ
ejpam-5192	174	5	open	open	ADJ
ejpam-5192	174	6	set	set	NOUN
ejpam-5192	174	7	v	v	NOUN
ejpam-5192	174	8	of	of	ADP
ejpam-5192	174	9	y	y	PROPN
ejpam-5192	174	10	;	;	PUNCT
ejpam-5192	174	11	(	(	PUNCT
ejpam-5192	174	12	3	3	X
ejpam-5192	174	13	)	)	PUNCT
ejpam-5192	174	14	τ1τ2	τ1τ2	NOUN
ejpam-5192	174	15	-	-	NOUN
ejpam-5192	174	16	cl(f	cl(f	NOUN
ejpam-5192	174	17	+	+	NOUN
ejpam-5192	174	18	(	(	PUNCT
ejpam-5192	174	19	σ1σ2	σ1σ2	NUM
ejpam-5192	174	20	-	-	PUNCT
ejpam-5192	174	21	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5192	174	22	-	-	PUNCT
ejpam-5192	174	23	int(k	int(k	NOUN
ejpam-5192	174	24	)	)	PUNCT
ejpam-5192	174	25	)	)	PUNCT
ejpam-5192	174	26	)	)	PUNCT
ejpam-5192	174	27	)	)	PUNCT
ejpam-5192	174	28	⊆	⊆	NUM
ejpam-5192	174	29	f+(k	f+(k	NOUN
ejpam-5192	174	30	)	)	PUNCT
ejpam-5192	174	31	for	for	ADP
ejpam-5192	174	32	every	every	DET
ejpam-5192	174	33	σ1σ2	σ1σ2	NUM
ejpam-5192	174	34	-	-	PUNCT
ejpam-5192	174	35	closed	closed	ADJ
ejpam-5192	174	36	set	set	NOUN
ejpam-5192	174	37	k	k	PROPN
ejpam-5192	174	38	of	of	ADP
ejpam-5192	174	39	y	y	PROPN
ejpam-5192	174	40	;	;	PUNCT
ejpam-5192	174	41	(	(	PUNCT
ejpam-5192	174	42	4	4	X
ejpam-5192	174	43	)	)	PUNCT
ejpam-5192	174	44	τ1τ2	τ1τ2	NOUN
ejpam-5192	174	45	-	-	NOUN
ejpam-5192	174	46	cl(f	cl(f	NOUN
ejpam-5192	174	47	+	+	NOUN
ejpam-5192	174	48	(	(	PUNCT
ejpam-5192	174	49	σ1σ2	σ1σ2	NUM
ejpam-5192	174	50	-	-	PUNCT
ejpam-5192	174	51	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5192	174	52	-	-	PUNCT
ejpam-5192	174	53	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5192	174	54	-	-	PUNCT
ejpam-5192	174	55	cl(b	cl(b	NOUN
ejpam-5192	174	56	)	)	PUNCT
ejpam-5192	174	57	)	)	PUNCT
ejpam-5192	174	58	)	)	PUNCT
ejpam-5192	174	59	)	)	PUNCT
ejpam-5192	174	60	)	)	PUNCT
ejpam-5192	174	61	⊆	⊆	X
ejpam-5192	174	62	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5192	174	63	-	-	PUNCT
ejpam-5192	174	64	cl(b	cl(b	NOUN
ejpam-5192	174	65	)	)	PUNCT
ejpam-5192	174	66	)	)	PUNCT
ejpam-5192	174	67	for	for	ADP
ejpam-5192	174	68	every	every	DET
ejpam-5192	174	69	subset	subset	NOUN
ejpam-5192	174	70	b	b	PROPN
ejpam-5192	174	71	of	of	ADP
ejpam-5192	174	72	y	y	PROPN
ejpam-5192	174	73	;	;	PUNCT
ejpam-5192	174	74	c.	c.	PROPN
ejpam-5192	174	75	klanarong	klanarong	PROPN
ejpam-5192	174	76	,	,	PUNCT
ejpam-5192	174	77	s.	s.	PROPN
ejpam-5192	174	78	sompong	sompong	PROPN
ejpam-5192	174	79	,	,	PUNCT
ejpam-5192	174	80	c.	c.	PROPN
ejpam-5192	174	81	boonpok	boonpok	PROPN
ejpam-5192	174	82	/	/	SYM
ejpam-5192	174	83	eur	eur	PROPN
ejpam-5192	174	84	.	.	PUNCT
ejpam-5192	175	1	j.	j.	PROPN
ejpam-5192	175	2	pure	pure	PROPN
ejpam-5192	175	3	appl	appl	PROPN
ejpam-5192	175	4	.	.	PROPN
ejpam-5192	175	5	math	math	PROPN
ejpam-5192	175	6	,	,	PUNCT
ejpam-5192	175	7	17	17	NUM
ejpam-5192	175	8	(	(	PUNCT
ejpam-5192	175	9	2	2	NUM
ejpam-5192	175	10	)	)	PUNCT
ejpam-5192	175	11	(	(	PUNCT
ejpam-5192	175	12	2024	2024	NUM
ejpam-5192	175	13	)	)	PUNCT
ejpam-5192	175	14	,	,	PUNCT
ejpam-5192	175	15	1244	1244	NUM
ejpam-5192	175	16	-	-	SYM
ejpam-5192	175	17	1253	1253	NUM
ejpam-5192	175	18	1250	1250	NUM
ejpam-5192	175	19	(	(	PUNCT
ejpam-5192	175	20	5	5	X
ejpam-5192	175	21	)	)	PUNCT
ejpam-5192	175	22	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5192	175	23	-	-	PUNCT
ejpam-5192	175	24	int(b	int(b	NOUN
ejpam-5192	175	25	)	)	PUNCT
ejpam-5192	175	26	)	)	PUNCT
ejpam-5192	176	1	⊆	⊆	X
ejpam-5192	176	2	τ1τ2	τ1τ2	NOUN
ejpam-5192	176	3	-	-	NUM
ejpam-5192	176	4	int(f	int(f	VERB
ejpam-5192	176	5	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5192	176	6	-	-	PUNCT
ejpam-5192	176	7	int(σ1σ2	int(σ1σ2	ADV
ejpam-5192	176	8	-	-	PUNCT
ejpam-5192	176	9	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5192	176	10	-	-	PUNCT
ejpam-5192	176	11	int(b	int(b	NOUN
ejpam-5192	176	12	)	)	PUNCT
ejpam-5192	176	13	)	)	PUNCT
ejpam-5192	176	14	)	)	PUNCT
ejpam-5192	176	15	)	)	PUNCT
ejpam-5192	176	16	)	)	PUNCT
ejpam-5192	176	17	for	for	ADP
ejpam-5192	176	18	every	every	DET
ejpam-5192	176	19	subset	subset	NOUN
ejpam-5192	176	20	b	b	PROPN
ejpam-5192	176	21	of	of	ADP
ejpam-5192	176	22	y	y	PROPN
ejpam-5192	176	23	;	;	PUNCT
ejpam-5192	176	24	(	(	PUNCT
ejpam-5192	176	25	6	6	X
ejpam-5192	176	26	)	)	PUNCT
ejpam-5192	176	27	f−(v	f−(v	NOUN
ejpam-5192	176	28	)	)	PUNCT
ejpam-5192	176	29	is	be	AUX
ejpam-5192	176	30	τ1τ2	τ1τ2	NOUN
ejpam-5192	176	31	-	-	ADJ
ejpam-5192	176	32	open	open	ADJ
ejpam-5192	176	33	in	in	ADP
ejpam-5192	176	34	x	x	PUNCT
ejpam-5192	176	35	for	for	ADP
ejpam-5192	176	36	every	every	DET
ejpam-5192	176	37	(	(	PUNCT
ejpam-5192	176	38	σ1	σ1	PROPN
ejpam-5192	176	39	,	,	PUNCT
ejpam-5192	176	40	σ2)r	σ2)r	NOUN
ejpam-5192	176	41	-	-	PUNCT
ejpam-5192	176	42	open	open	ADJ
ejpam-5192	176	43	set	set	VERB
ejpam-5192	176	44	v	v	NOUN
ejpam-5192	176	45	of	of	ADP
ejpam-5192	176	46	y	y	PROPN
ejpam-5192	176	47	;	;	PUNCT
ejpam-5192	176	48	(	(	PUNCT
ejpam-5192	176	49	7	7	X
ejpam-5192	176	50	)	)	PUNCT
ejpam-5192	176	51	f+(k	f+(k	NOUN
ejpam-5192	176	52	)	)	PUNCT
ejpam-5192	176	53	is	be	AUX
ejpam-5192	176	54	τ1τ2	τ1τ2	NOUN
ejpam-5192	176	55	-	-	ADJ
ejpam-5192	176	56	closed	closed	ADJ
ejpam-5192	176	57	in	in	ADP
ejpam-5192	176	58	x	x	PUNCT
ejpam-5192	176	59	for	for	ADP
ejpam-5192	176	60	every	every	DET
ejpam-5192	176	61	(	(	PUNCT
ejpam-5192	176	62	σ1	σ1	PROPN
ejpam-5192	176	63	,	,	PUNCT
ejpam-5192	176	64	σ2)r	σ2)r	NOUN
ejpam-5192	176	65	-	-	PUNCT
ejpam-5192	176	66	closed	close	VERB
ejpam-5192	176	67	set	set	ADJ
ejpam-5192	176	68	k	k	PROPN
ejpam-5192	176	69	of	of	ADP
ejpam-5192	176	70	y	y	PROPN
ejpam-5192	176	71	.	.	PUNCT
ejpam-5192	177	1	proof	proof	NOUN
ejpam-5192	177	2	.	.	PUNCT
ejpam-5192	178	1	the	the	DET
ejpam-5192	178	2	proof	proof	NOUN
ejpam-5192	178	3	is	be	AUX
ejpam-5192	178	4	similar	similar	ADJ
ejpam-5192	178	5	to	to	ADP
ejpam-5192	178	6	that	that	PRON
ejpam-5192	178	7	of	of	ADP
ejpam-5192	178	8	theorem	theorem	ADJ
ejpam-5192	178	9	3	3	NUM
ejpam-5192	178	10	.	.	PUNCT
ejpam-5192	178	11	corollary	corollary	ADJ
ejpam-5192	178	12	2	2	NUM
ejpam-5192	178	13	.	.	PUNCT
ejpam-5192	178	14	for	for	ADP
ejpam-5192	178	15	a	a	DET
ejpam-5192	178	16	function	function	NOUN
ejpam-5192	178	17	f	f	NOUN
ejpam-5192	178	18	:	:	PUNCT
ejpam-5192	178	19	(	(	PUNCT
ejpam-5192	178	20	x	x	NOUN
ejpam-5192	178	21	,	,	PUNCT
ejpam-5192	178	22	τ1	τ1	NOUN
ejpam-5192	178	23	,	,	PUNCT
ejpam-5192	178	24	τ2	τ2	NOUN
ejpam-5192	178	25	)	)	PUNCT
ejpam-5192	178	26	→	→	SYM
ejpam-5192	178	27	(	(	PUNCT
ejpam-5192	178	28	y	y	PROPN
ejpam-5192	178	29	,	,	PUNCT
ejpam-5192	178	30	σ1	σ1	PROPN
ejpam-5192	178	31	,	,	PUNCT
ejpam-5192	178	32	σ2	σ2	NOUN
ejpam-5192	178	33	)	)	PUNCT
ejpam-5192	178	34	,	,	PUNCT
ejpam-5192	178	35	the	the	DET
ejpam-5192	178	36	following	follow	VERB
ejpam-5192	178	37	properties	property	NOUN
ejpam-5192	178	38	are	be	AUX
ejpam-5192	178	39	equivalent	equivalent	ADJ
ejpam-5192	178	40	:	:	PUNCT
ejpam-5192	178	41	(	(	PUNCT
ejpam-5192	178	42	1	1	X
ejpam-5192	178	43	)	)	PUNCT
ejpam-5192	178	44	f	f	NOUN
ejpam-5192	178	45	is	be	AUX
ejpam-5192	178	46	almost	almost	ADV
ejpam-5192	178	47	(	(	PUNCT
ejpam-5192	178	48	τ1	τ1	NOUN
ejpam-5192	178	49	,	,	PUNCT
ejpam-5192	178	50	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	178	51	;	;	PUNCT
ejpam-5192	178	52	(	(	PUNCT
ejpam-5192	178	53	2	2	X
ejpam-5192	178	54	)	)	PUNCT
ejpam-5192	178	55	f−1(v	f−1(v	NOUN
ejpam-5192	178	56	)	)	PUNCT
ejpam-5192	179	1	⊆	⊆	X
ejpam-5192	179	2	τ1τ2	τ1τ2	NOUN
ejpam-5192	179	3	-	-	NUM
ejpam-5192	179	4	int(f	int(f	VERB
ejpam-5192	179	5	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5192	179	6	-	-	PUNCT
ejpam-5192	179	7	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5192	179	8	-	-	PUNCT
ejpam-5192	179	9	cl(v	cl(v	NOUN
ejpam-5192	179	10	)	)	PUNCT
ejpam-5192	179	11	)	)	PUNCT
ejpam-5192	179	12	)	)	PUNCT
ejpam-5192	179	13	)	)	PUNCT
ejpam-5192	180	1	for	for	ADP
ejpam-5192	180	2	every	every	DET
ejpam-5192	180	3	σ1σ2	σ1σ2	NOUN
ejpam-5192	180	4	-	-	ADJ
ejpam-5192	180	5	open	open	ADJ
ejpam-5192	180	6	set	set	NOUN
ejpam-5192	180	7	v	v	NOUN
ejpam-5192	180	8	of	of	ADP
ejpam-5192	180	9	y	y	PROPN
ejpam-5192	180	10	;	;	PUNCT
ejpam-5192	180	11	(	(	PUNCT
ejpam-5192	180	12	3	3	X
ejpam-5192	180	13	)	)	PUNCT
ejpam-5192	180	14	τ1τ2	τ1τ2	NOUN
ejpam-5192	180	15	-	-	NOUN
ejpam-5192	180	16	cl(f	cl(f	NOUN
ejpam-5192	180	17	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5192	180	18	-	-	PUNCT
ejpam-5192	180	19	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5192	180	20	-	-	PUNCT
ejpam-5192	180	21	int(k	int(k	NOUN
ejpam-5192	180	22	)	)	PUNCT
ejpam-5192	180	23	)	)	PUNCT
ejpam-5192	180	24	)	)	PUNCT
ejpam-5192	180	25	)	)	PUNCT
ejpam-5192	180	26	⊆	⊆	NUM
ejpam-5192	180	27	f−1(k	f−1(k	PROPN
ejpam-5192	180	28	)	)	PUNCT
ejpam-5192	180	29	for	for	ADP
ejpam-5192	180	30	every	every	DET
ejpam-5192	180	31	σ1σ2	σ1σ2	NUM
ejpam-5192	180	32	-	-	PUNCT
ejpam-5192	180	33	closed	closed	ADJ
ejpam-5192	180	34	set	set	NOUN
ejpam-5192	180	35	k	k	PROPN
ejpam-5192	180	36	of	of	ADP
ejpam-5192	180	37	y	y	PROPN
ejpam-5192	180	38	;	;	PUNCT
ejpam-5192	180	39	(	(	PUNCT
ejpam-5192	180	40	4	4	X
ejpam-5192	180	41	)	)	PUNCT
ejpam-5192	180	42	τ1τ2	τ1τ2	NOUN
ejpam-5192	180	43	-	-	NOUN
ejpam-5192	180	44	cl(f	cl(f	NOUN
ejpam-5192	180	45	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5192	180	46	-	-	PUNCT
ejpam-5192	180	47	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5192	180	48	-	-	PUNCT
ejpam-5192	180	49	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5192	180	50	-	-	PUNCT
ejpam-5192	180	51	cl(b	cl(b	NOUN
ejpam-5192	180	52	)	)	PUNCT
ejpam-5192	180	53	)	)	PUNCT
ejpam-5192	180	54	)	)	PUNCT
ejpam-5192	180	55	)	)	PUNCT
ejpam-5192	180	56	)	)	PUNCT
ejpam-5192	181	1	⊆	⊆	NUM
ejpam-5192	181	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5192	181	3	-	-	PUNCT
ejpam-5192	181	4	cl(b	cl(b	NOUN
ejpam-5192	181	5	)	)	PUNCT
ejpam-5192	181	6	)	)	PUNCT
ejpam-5192	181	7	for	for	ADP
ejpam-5192	181	8	every	every	DET
ejpam-5192	181	9	subset	subset	NOUN
ejpam-5192	181	10	b	b	PROPN
ejpam-5192	181	11	of	of	ADP
ejpam-5192	181	12	y	y	PROPN
ejpam-5192	181	13	;	;	PUNCT
ejpam-5192	181	14	(	(	PUNCT
ejpam-5192	181	15	5	5	X
ejpam-5192	181	16	)	)	PUNCT
ejpam-5192	181	17	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5192	181	18	-	-	PUNCT
ejpam-5192	181	19	int(b	int(b	NOUN
ejpam-5192	181	20	)	)	PUNCT
ejpam-5192	181	21	)	)	PUNCT
ejpam-5192	182	1	⊆	⊆	X
ejpam-5192	182	2	τ1τ2	τ1τ2	NOUN
ejpam-5192	182	3	-	-	NUM
ejpam-5192	182	4	int(f	int(f	VERB
ejpam-5192	182	5	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5192	182	6	-	-	PUNCT
ejpam-5192	182	7	int(σ1σ2	int(σ1σ2	ADV
ejpam-5192	182	8	-	-	PUNCT
ejpam-5192	182	9	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5192	182	10	-	-	PUNCT
ejpam-5192	182	11	int(b	int(b	NOUN
ejpam-5192	182	12	)	)	PUNCT
ejpam-5192	182	13	)	)	PUNCT
ejpam-5192	182	14	)	)	PUNCT
ejpam-5192	182	15	)	)	PUNCT
ejpam-5192	182	16	)	)	PUNCT
ejpam-5192	182	17	for	for	ADP
ejpam-5192	182	18	every	every	DET
ejpam-5192	182	19	subset	subset	NOUN
ejpam-5192	182	20	b	b	PROPN
ejpam-5192	182	21	of	of	ADP
ejpam-5192	182	22	y	y	PROPN
ejpam-5192	182	23	;	;	PUNCT
ejpam-5192	182	24	(	(	PUNCT
ejpam-5192	182	25	6	6	X
ejpam-5192	182	26	)	)	PUNCT
ejpam-5192	182	27	f−1(v	f−1(v	NOUN
ejpam-5192	182	28	)	)	PUNCT
ejpam-5192	182	29	is	be	AUX
ejpam-5192	182	30	τ1τ2	τ1τ2	NOUN
ejpam-5192	182	31	-	-	ADJ
ejpam-5192	182	32	open	open	ADJ
ejpam-5192	182	33	in	in	ADP
ejpam-5192	182	34	x	x	PUNCT
ejpam-5192	182	35	for	for	ADP
ejpam-5192	182	36	every	every	DET
ejpam-5192	182	37	(	(	PUNCT
ejpam-5192	182	38	σ1	σ1	PROPN
ejpam-5192	182	39	,	,	PUNCT
ejpam-5192	182	40	σ2)r	σ2)r	NOUN
ejpam-5192	182	41	-	-	PUNCT
ejpam-5192	182	42	open	open	ADJ
ejpam-5192	182	43	set	set	VERB
ejpam-5192	182	44	v	v	NOUN
ejpam-5192	182	45	of	of	ADP
ejpam-5192	182	46	y	y	PROPN
ejpam-5192	182	47	;	;	PUNCT
ejpam-5192	182	48	(	(	PUNCT
ejpam-5192	182	49	7	7	X
ejpam-5192	182	50	)	)	PUNCT
ejpam-5192	182	51	f−1(k	f−1(k	PROPN
ejpam-5192	182	52	)	)	PUNCT
ejpam-5192	182	53	is	be	AUX
ejpam-5192	182	54	τ1τ2	τ1τ2	NOUN
ejpam-5192	182	55	-	-	ADJ
ejpam-5192	182	56	closed	closed	ADJ
ejpam-5192	182	57	in	in	ADP
ejpam-5192	182	58	x	x	PUNCT
ejpam-5192	182	59	for	for	ADP
ejpam-5192	182	60	every	every	DET
ejpam-5192	182	61	(	(	PUNCT
ejpam-5192	182	62	σ1	σ1	PROPN
ejpam-5192	182	63	,	,	PUNCT
ejpam-5192	182	64	σ2)r	σ2)r	NOUN
ejpam-5192	182	65	-	-	PUNCT
ejpam-5192	182	66	closed	close	VERB
ejpam-5192	182	67	set	set	ADJ
ejpam-5192	182	68	k	k	PROPN
ejpam-5192	182	69	of	of	ADP
ejpam-5192	182	70	y	y	PROPN
ejpam-5192	182	71	.	.	PUNCT
ejpam-5192	183	1	theorem	theorem	ADJ
ejpam-5192	183	2	5	5	NUM
ejpam-5192	183	3	.	.	X
ejpam-5192	183	4	for	for	ADP
ejpam-5192	183	5	a	a	DET
ejpam-5192	183	6	multifunction	multifunction	NOUN
ejpam-5192	184	1	f	f	NOUN
ejpam-5192	184	2	:	:	PUNCT
ejpam-5192	184	3	(	(	PUNCT
ejpam-5192	184	4	x	x	NOUN
ejpam-5192	184	5	,	,	PUNCT
ejpam-5192	184	6	τ1	τ1	NOUN
ejpam-5192	184	7	,	,	PUNCT
ejpam-5192	184	8	τ2	τ2	NOUN
ejpam-5192	184	9	)	)	PUNCT
ejpam-5192	184	10	→	→	SYM
ejpam-5192	184	11	(	(	PUNCT
ejpam-5192	184	12	y	y	PROPN
ejpam-5192	184	13	,	,	PUNCT
ejpam-5192	184	14	σ1	σ1	PROPN
ejpam-5192	184	15	,	,	PUNCT
ejpam-5192	184	16	σ2	σ2	NOUN
ejpam-5192	184	17	)	)	PUNCT
ejpam-5192	184	18	,	,	PUNCT
ejpam-5192	184	19	the	the	DET
ejpam-5192	184	20	following	follow	VERB
ejpam-5192	184	21	properties	property	NOUN
ejpam-5192	184	22	are	be	AUX
ejpam-5192	184	23	equivalent	equivalent	ADJ
ejpam-5192	184	24	:	:	PUNCT
ejpam-5192	184	25	(	(	PUNCT
ejpam-5192	184	26	1	1	X
ejpam-5192	184	27	)	)	PUNCT
ejpam-5192	184	28	f	f	PROPN
ejpam-5192	184	29	is	be	AUX
ejpam-5192	184	30	upper	upper	ADJ
ejpam-5192	184	31	almost	almost	ADV
ejpam-5192	184	32	(	(	PUNCT
ejpam-5192	184	33	τ1	τ1	NOUN
ejpam-5192	184	34	,	,	PUNCT
ejpam-5192	184	35	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	184	36	;	;	PUNCT
ejpam-5192	184	37	(	(	PUNCT
ejpam-5192	184	38	2	2	X
ejpam-5192	184	39	)	)	PUNCT
ejpam-5192	184	40	τ1τ2	τ1τ2	NOUN
ejpam-5192	184	41	-	-	NOUN
ejpam-5192	184	42	cl(f	cl(f	NUM
ejpam-5192	184	43	−(v	−(v	NOUN
ejpam-5192	184	44	)	)	PUNCT
ejpam-5192	184	45	)	)	PUNCT
ejpam-5192	185	1	⊆	⊆	X
ejpam-5192	185	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5192	185	3	-	-	PUNCT
ejpam-5192	185	4	cl(v	cl(v	NOUN
ejpam-5192	185	5	)	)	PUNCT
ejpam-5192	185	6	)	)	PUNCT
ejpam-5192	185	7	for	for	ADP
ejpam-5192	185	8	every	every	DET
ejpam-5192	185	9	(	(	PUNCT
ejpam-5192	185	10	σ1	σ1	PROPN
ejpam-5192	185	11	,	,	PUNCT
ejpam-5192	185	12	σ2)β	σ2)β	NOUN
ejpam-5192	185	13	-	-	PUNCT
ejpam-5192	185	14	open	open	NOUN
ejpam-5192	185	15	set	set	NOUN
ejpam-5192	185	16	v	v	NOUN
ejpam-5192	185	17	of	of	ADP
ejpam-5192	185	18	y	y	PROPN
ejpam-5192	185	19	;	;	PUNCT
ejpam-5192	185	20	(	(	PUNCT
ejpam-5192	185	21	3	3	X
ejpam-5192	185	22	)	)	PUNCT
ejpam-5192	185	23	τ1τ2	τ1τ2	NOUN
ejpam-5192	185	24	-	-	NOUN
ejpam-5192	185	25	cl(f	cl(f	NUM
ejpam-5192	185	26	−(v	−(v	NOUN
ejpam-5192	185	27	)	)	PUNCT
ejpam-5192	185	28	)	)	PUNCT
ejpam-5192	186	1	⊆	⊆	X
ejpam-5192	186	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5192	186	3	-	-	PUNCT
ejpam-5192	186	4	cl(v	cl(v	NOUN
ejpam-5192	186	5	)	)	PUNCT
ejpam-5192	186	6	)	)	PUNCT
ejpam-5192	186	7	for	for	ADP
ejpam-5192	186	8	every	every	DET
ejpam-5192	186	9	(	(	PUNCT
ejpam-5192	186	10	σ1	σ1	PROPN
ejpam-5192	186	11	,	,	PUNCT
ejpam-5192	186	12	σ2)s	σ2)s	NOUN
ejpam-5192	186	13	-	-	PUNCT
ejpam-5192	186	14	open	open	NOUN
ejpam-5192	186	15	set	set	NOUN
ejpam-5192	186	16	v	v	NOUN
ejpam-5192	186	17	of	of	ADP
ejpam-5192	186	18	y	y	PROPN
ejpam-5192	186	19	.	.	PUNCT
ejpam-5192	187	1	proof	proof	NOUN
ejpam-5192	187	2	.	.	PUNCT
ejpam-5192	188	1	(	(	PUNCT
ejpam-5192	188	2	1	1	X
ejpam-5192	188	3	)	)	PUNCT
ejpam-5192	188	4	⇒	⇒	NOUN
ejpam-5192	188	5	(	(	PUNCT
ejpam-5192	188	6	2	2	NUM
ejpam-5192	188	7	):	):	PUNCT
ejpam-5192	188	8	let	let	VERB
ejpam-5192	188	9	v	v	PART
ejpam-5192	188	10	be	be	AUX
ejpam-5192	188	11	any	any	DET
ejpam-5192	188	12	(	(	PUNCT
ejpam-5192	188	13	σ1	σ1	PROPN
ejpam-5192	188	14	,	,	PUNCT
ejpam-5192	188	15	σ2)β	σ2)β	NOUN
ejpam-5192	188	16	-	-	PUNCT
ejpam-5192	188	17	open	open	ADJ
ejpam-5192	188	18	set	set	NOUN
ejpam-5192	188	19	of	of	ADP
ejpam-5192	188	20	y	y	PROPN
ejpam-5192	188	21	.	.	PUNCT
ejpam-5192	189	1	then	then	ADV
ejpam-5192	189	2	,	,	PUNCT
ejpam-5192	189	3	σ1σ2	σ1σ2	NOUN
ejpam-5192	189	4	-	-	NUM
ejpam-5192	189	5	cl(v	cl(v	NOUN
ejpam-5192	189	6	)	)	PUNCT
ejpam-5192	189	7	is	be	AUX
ejpam-5192	189	8	a	a	DET
ejpam-5192	189	9	(	(	PUNCT
ejpam-5192	189	10	σ1	σ1	NOUN
ejpam-5192	189	11	,	,	PUNCT
ejpam-5192	189	12	σ2)r	σ2)r	NOUN
ejpam-5192	189	13	-	-	PUNCT
ejpam-5192	189	14	closed	close	VERB
ejpam-5192	189	15	set	set	NOUN
ejpam-5192	189	16	of	of	ADP
ejpam-5192	189	17	y	y	PROPN
ejpam-5192	189	18	.	.	PUNCT
ejpam-5192	190	1	since	since	SCONJ
ejpam-5192	190	2	f	f	PROPN
ejpam-5192	190	3	is	be	AUX
ejpam-5192	190	4	upper	upper	ADJ
ejpam-5192	190	5	almost	almost	ADV
ejpam-5192	190	6	(	(	PUNCT
ejpam-5192	190	7	τ1	τ1	NOUN
ejpam-5192	190	8	,	,	PUNCT
ejpam-5192	190	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	190	10	and	and	CCONJ
ejpam-5192	190	11	by	by	ADP
ejpam-5192	190	12	theorem	theorem	ADJ
ejpam-5192	190	13	3	3	NUM
ejpam-5192	190	14	,	,	PUNCT
ejpam-5192	190	15	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5192	190	16	-	-	PUNCT
ejpam-5192	190	17	cl(v	cl(v	NOUN
ejpam-5192	190	18	)	)	PUNCT
ejpam-5192	190	19	)	)	PUNCT
ejpam-5192	190	20	is	be	AUX
ejpam-5192	190	21	τ1τ2	τ1τ2	NOUN
ejpam-5192	190	22	-	-	ADJ
ejpam-5192	190	23	closed	closed	ADJ
ejpam-5192	190	24	in	in	ADP
ejpam-5192	190	25	x.	x.	NOUN
ejpam-5192	190	26	thus	thus	ADV
ejpam-5192	190	27	,	,	PUNCT
ejpam-5192	190	28	τ1τ2	τ1τ2	NOUN
ejpam-5192	190	29	-	-	ADJ
ejpam-5192	190	30	cl(f	cl(f	NUM
ejpam-5192	190	31	−(v	−(v	NOUN
ejpam-5192	190	32	)	)	PUNCT
ejpam-5192	190	33	)	)	PUNCT
ejpam-5192	191	1	⊆	⊆	X
ejpam-5192	191	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5192	191	3	-	-	PUNCT
ejpam-5192	191	4	cl(v	cl(v	NOUN
ejpam-5192	191	5	)	)	PUNCT
ejpam-5192	191	6	)	)	PUNCT
ejpam-5192	191	7	.	.	PUNCT
ejpam-5192	192	1	(	(	PUNCT
ejpam-5192	192	2	2	2	X
ejpam-5192	192	3	)	)	PUNCT
ejpam-5192	192	4	⇒	⇒	NOUN
ejpam-5192	192	5	(	(	PUNCT
ejpam-5192	192	6	3	3	NUM
ejpam-5192	192	7	):	):	PUNCT
ejpam-5192	192	8	the	the	DET
ejpam-5192	192	9	proof	proof	NOUN
ejpam-5192	192	10	is	be	AUX
ejpam-5192	192	11	obvious	obvious	ADJ
ejpam-5192	192	12	.	.	PUNCT
ejpam-5192	193	1	(	(	PUNCT
ejpam-5192	193	2	3	3	X
ejpam-5192	193	3	)	)	PUNCT
ejpam-5192	193	4	⇒	⇒	NOUN
ejpam-5192	193	5	(	(	PUNCT
ejpam-5192	193	6	1	1	NUM
ejpam-5192	193	7	):	):	PUNCT
ejpam-5192	193	8	let	let	VERB
ejpam-5192	193	9	k	k	PRON
ejpam-5192	193	10	be	be	AUX
ejpam-5192	193	11	any	any	DET
ejpam-5192	193	12	(	(	PUNCT
ejpam-5192	193	13	σ1	σ1	NOUN
ejpam-5192	193	14	,	,	PUNCT
ejpam-5192	193	15	σ2)r	σ2)r	NOUN
ejpam-5192	193	16	-	-	PUNCT
ejpam-5192	193	17	closed	close	VERB
ejpam-5192	193	18	set	set	NOUN
ejpam-5192	193	19	of	of	ADP
ejpam-5192	193	20	y	y	PROPN
ejpam-5192	193	21	.	.	PUNCT
ejpam-5192	194	1	then	then	ADV
ejpam-5192	194	2	,	,	PUNCT
ejpam-5192	194	3	k	k	X
ejpam-5192	194	4	is	be	AUX
ejpam-5192	194	5	(	(	PUNCT
ejpam-5192	194	6	σ1	σ1	PROPN
ejpam-5192	194	7	,	,	PUNCT
ejpam-5192	194	8	σ2)s	σ2)s	NOUN
ejpam-5192	194	9	-	-	PUNCT
ejpam-5192	194	10	open	open	ADJ
ejpam-5192	194	11	in	in	ADP
ejpam-5192	194	12	y	y	PROPN
ejpam-5192	194	13	.	.	PUNCT
ejpam-5192	195	1	then	then	ADV
ejpam-5192	195	2	by	by	ADP
ejpam-5192	195	3	(	(	PUNCT
ejpam-5192	195	4	3	3	NUM
ejpam-5192	195	5	)	)	PUNCT
ejpam-5192	195	6	,	,	PUNCT
ejpam-5192	195	7	τ1τ2	τ1τ2	PROPN
ejpam-5192	195	8	-	-	ADJ
ejpam-5192	195	9	cl(f	cl(f	NOUN
ejpam-5192	195	10	−(k	−(k	NOUN
ejpam-5192	195	11	)	)	PUNCT
ejpam-5192	195	12	)	)	PUNCT
ejpam-5192	196	1	⊆	⊆	X
ejpam-5192	196	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5192	196	3	-	-	PUNCT
ejpam-5192	196	4	cl(k	cl(k	NOUN
ejpam-5192	196	5	)	)	PUNCT
ejpam-5192	196	6	)	)	PUNCT
ejpam-5192	197	1	=	=	SYM
ejpam-5192	197	2	f−(k	f−(k	PROPN
ejpam-5192	197	3	)	)	PUNCT
ejpam-5192	197	4	and	and	CCONJ
ejpam-5192	197	5	hence	hence	ADV
ejpam-5192	197	6	f−(k	f−(k	PROPN
ejpam-5192	197	7	)	)	PUNCT
ejpam-5192	197	8	is	be	AUX
ejpam-5192	197	9	τ1τ2	τ1τ2	NOUN
ejpam-5192	197	10	-	-	ADJ
ejpam-5192	197	11	closed	closed	ADJ
ejpam-5192	197	12	in	in	ADP
ejpam-5192	197	13	x.	x.	NOUN
ejpam-5192	197	14	by	by	ADP
ejpam-5192	197	15	theorem	theorem	NOUN
ejpam-5192	197	16	3	3	NUM
ejpam-5192	197	17	,	,	PUNCT
ejpam-5192	197	18	f	f	PROPN
ejpam-5192	197	19	is	be	AUX
ejpam-5192	197	20	upper	upper	ADJ
ejpam-5192	197	21	almost	almost	ADV
ejpam-5192	197	22	(	(	PUNCT
ejpam-5192	197	23	τ1	τ1	NOUN
ejpam-5192	197	24	,	,	PUNCT
ejpam-5192	197	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	197	26	.	.	PUNCT
ejpam-5192	198	1	theorem	theorem	VERB
ejpam-5192	198	2	6	6	NUM
ejpam-5192	198	3	.	.	PUNCT
ejpam-5192	198	4	for	for	ADP
ejpam-5192	198	5	a	a	DET
ejpam-5192	198	6	multifunction	multifunction	NOUN
ejpam-5192	199	1	f	f	NOUN
ejpam-5192	199	2	:	:	PUNCT
ejpam-5192	199	3	(	(	PUNCT
ejpam-5192	199	4	x	x	NOUN
ejpam-5192	199	5	,	,	PUNCT
ejpam-5192	199	6	τ1	τ1	NOUN
ejpam-5192	199	7	,	,	PUNCT
ejpam-5192	199	8	τ2	τ2	NOUN
ejpam-5192	199	9	)	)	PUNCT
ejpam-5192	199	10	→	→	SYM
ejpam-5192	199	11	(	(	PUNCT
ejpam-5192	199	12	y	y	PROPN
ejpam-5192	199	13	,	,	PUNCT
ejpam-5192	199	14	σ1	σ1	PROPN
ejpam-5192	199	15	,	,	PUNCT
ejpam-5192	199	16	σ2	σ2	NOUN
ejpam-5192	199	17	)	)	PUNCT
ejpam-5192	199	18	,	,	PUNCT
ejpam-5192	199	19	the	the	DET
ejpam-5192	199	20	following	follow	VERB
ejpam-5192	199	21	properties	property	NOUN
ejpam-5192	199	22	are	be	AUX
ejpam-5192	199	23	equivalent	equivalent	ADJ
ejpam-5192	199	24	:	:	PUNCT
ejpam-5192	199	25	(	(	PUNCT
ejpam-5192	199	26	1	1	X
ejpam-5192	199	27	)	)	PUNCT
ejpam-5192	199	28	f	f	PROPN
ejpam-5192	199	29	is	be	AUX
ejpam-5192	199	30	lower	low	ADJ
ejpam-5192	199	31	almost	almost	ADV
ejpam-5192	199	32	(	(	PUNCT
ejpam-5192	199	33	τ1	τ1	NOUN
ejpam-5192	199	34	,	,	PUNCT
ejpam-5192	199	35	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	199	36	;	;	PUNCT
ejpam-5192	199	37	c.	c.	PROPN
ejpam-5192	199	38	klanarong	klanarong	PROPN
ejpam-5192	199	39	,	,	PUNCT
ejpam-5192	199	40	s.	s.	PROPN
ejpam-5192	199	41	sompong	sompong	PROPN
ejpam-5192	199	42	,	,	PUNCT
ejpam-5192	199	43	c.	c.	PROPN
ejpam-5192	199	44	boonpok	boonpok	PROPN
ejpam-5192	199	45	/	/	SYM
ejpam-5192	199	46	eur	eur	PROPN
ejpam-5192	199	47	.	.	PUNCT
ejpam-5192	200	1	j.	j.	PROPN
ejpam-5192	200	2	pure	pure	PROPN
ejpam-5192	200	3	appl	appl	PROPN
ejpam-5192	200	4	.	.	PROPN
ejpam-5192	200	5	math	math	PROPN
ejpam-5192	200	6	,	,	PUNCT
ejpam-5192	200	7	17	17	NUM
ejpam-5192	200	8	(	(	PUNCT
ejpam-5192	200	9	2	2	NUM
ejpam-5192	200	10	)	)	PUNCT
ejpam-5192	200	11	(	(	PUNCT
ejpam-5192	200	12	2024	2024	NUM
ejpam-5192	200	13	)	)	PUNCT
ejpam-5192	200	14	,	,	PUNCT
ejpam-5192	200	15	1244	1244	NUM
ejpam-5192	200	16	-	-	SYM
ejpam-5192	200	17	1253	1253	NUM
ejpam-5192	200	18	1251	1251	NUM
ejpam-5192	200	19	(	(	PUNCT
ejpam-5192	200	20	2	2	NUM
ejpam-5192	200	21	)	)	PUNCT
ejpam-5192	200	22	τ1τ2	τ1τ2	NOUN
ejpam-5192	200	23	-	-	NOUN
ejpam-5192	200	24	cl(f	cl(f	NOUN
ejpam-5192	200	25	+	+	NOUN
ejpam-5192	200	26	(	(	PUNCT
ejpam-5192	200	27	v	v	NOUN
ejpam-5192	200	28	)	)	PUNCT
ejpam-5192	200	29	)	)	PUNCT
ejpam-5192	201	1	⊆	⊆	NUM
ejpam-5192	201	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5192	201	3	-	-	PUNCT
ejpam-5192	201	4	cl(v	cl(v	NOUN
ejpam-5192	201	5	)	)	PUNCT
ejpam-5192	201	6	)	)	PUNCT
ejpam-5192	201	7	for	for	ADP
ejpam-5192	201	8	every	every	DET
ejpam-5192	201	9	(	(	PUNCT
ejpam-5192	201	10	σ1	σ1	PROPN
ejpam-5192	201	11	,	,	PUNCT
ejpam-5192	201	12	σ2)β	σ2)β	NOUN
ejpam-5192	201	13	-	-	PUNCT
ejpam-5192	201	14	open	open	NOUN
ejpam-5192	201	15	set	set	NOUN
ejpam-5192	201	16	v	v	NOUN
ejpam-5192	201	17	of	of	ADP
ejpam-5192	201	18	y	y	PROPN
ejpam-5192	201	19	;	;	PUNCT
ejpam-5192	201	20	(	(	PUNCT
ejpam-5192	201	21	3	3	X
ejpam-5192	201	22	)	)	PUNCT
ejpam-5192	201	23	τ1τ2	τ1τ2	NOUN
ejpam-5192	201	24	-	-	NOUN
ejpam-5192	201	25	cl(f	cl(f	NOUN
ejpam-5192	201	26	+	+	NOUN
ejpam-5192	201	27	(	(	PUNCT
ejpam-5192	201	28	v	v	NOUN
ejpam-5192	201	29	)	)	PUNCT
ejpam-5192	201	30	)	)	PUNCT
ejpam-5192	202	1	⊆	⊆	NUM
ejpam-5192	202	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5192	202	3	-	-	PUNCT
ejpam-5192	202	4	cl(v	cl(v	NOUN
ejpam-5192	202	5	)	)	PUNCT
ejpam-5192	202	6	)	)	PUNCT
ejpam-5192	202	7	for	for	ADP
ejpam-5192	202	8	every	every	DET
ejpam-5192	202	9	(	(	PUNCT
ejpam-5192	202	10	σ1	σ1	PROPN
ejpam-5192	202	11	,	,	PUNCT
ejpam-5192	202	12	σ2)s	σ2)s	NOUN
ejpam-5192	202	13	-	-	PUNCT
ejpam-5192	202	14	open	open	NOUN
ejpam-5192	202	15	set	set	NOUN
ejpam-5192	202	16	v	v	NOUN
ejpam-5192	202	17	of	of	ADP
ejpam-5192	202	18	y	y	PROPN
ejpam-5192	202	19	.	.	PUNCT
ejpam-5192	203	1	proof	proof	NOUN
ejpam-5192	203	2	.	.	PUNCT
ejpam-5192	204	1	the	the	DET
ejpam-5192	204	2	proof	proof	NOUN
ejpam-5192	204	3	is	be	AUX
ejpam-5192	204	4	similar	similar	ADJ
ejpam-5192	204	5	to	to	ADP
ejpam-5192	204	6	that	that	PRON
ejpam-5192	204	7	of	of	ADP
ejpam-5192	204	8	theorem	theorem	ADJ
ejpam-5192	204	9	5	5	NUM
ejpam-5192	204	10	.	.	PUNCT
ejpam-5192	204	11	corollary	corollary	ADJ
ejpam-5192	204	12	3	3	NUM
ejpam-5192	204	13	.	.	PUNCT
ejpam-5192	205	1	for	for	ADP
ejpam-5192	205	2	a	a	DET
ejpam-5192	205	3	function	function	NOUN
ejpam-5192	205	4	f	f	NOUN
ejpam-5192	205	5	:	:	PUNCT
ejpam-5192	205	6	(	(	PUNCT
ejpam-5192	205	7	x	x	NOUN
ejpam-5192	205	8	,	,	PUNCT
ejpam-5192	205	9	τ1	τ1	NOUN
ejpam-5192	205	10	,	,	PUNCT
ejpam-5192	205	11	τ2	τ2	NOUN
ejpam-5192	205	12	)	)	PUNCT
ejpam-5192	205	13	→	→	SYM
ejpam-5192	205	14	(	(	PUNCT
ejpam-5192	205	15	y	y	PROPN
ejpam-5192	205	16	,	,	PUNCT
ejpam-5192	205	17	σ1	σ1	PROPN
ejpam-5192	205	18	,	,	PUNCT
ejpam-5192	205	19	σ2	σ2	NOUN
ejpam-5192	205	20	)	)	PUNCT
ejpam-5192	205	21	,	,	PUNCT
ejpam-5192	205	22	the	the	DET
ejpam-5192	205	23	following	follow	VERB
ejpam-5192	205	24	properties	property	NOUN
ejpam-5192	205	25	are	be	AUX
ejpam-5192	205	26	equivalent	equivalent	ADJ
ejpam-5192	205	27	:	:	PUNCT
ejpam-5192	205	28	(	(	PUNCT
ejpam-5192	205	29	1	1	X
ejpam-5192	205	30	)	)	PUNCT
ejpam-5192	205	31	f	f	NOUN
ejpam-5192	205	32	is	be	AUX
ejpam-5192	205	33	almost	almost	ADV
ejpam-5192	205	34	(	(	PUNCT
ejpam-5192	205	35	τ1	τ1	NOUN
ejpam-5192	205	36	,	,	PUNCT
ejpam-5192	205	37	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	205	38	;	;	PUNCT
ejpam-5192	205	39	(	(	PUNCT
ejpam-5192	205	40	2	2	X
ejpam-5192	205	41	)	)	PUNCT
ejpam-5192	205	42	τ1τ2	τ1τ2	NOUN
ejpam-5192	205	43	-	-	NOUN
ejpam-5192	205	44	cl(f	cl(f	PRON
ejpam-5192	205	45	−1(v	−1(v	NOUN
ejpam-5192	205	46	)	)	PUNCT
ejpam-5192	205	47	)	)	PUNCT
ejpam-5192	206	1	⊆	⊆	NUM
ejpam-5192	206	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5192	206	3	-	-	PUNCT
ejpam-5192	206	4	cl(v	cl(v	NOUN
ejpam-5192	206	5	)	)	PUNCT
ejpam-5192	206	6	)	)	PUNCT
ejpam-5192	206	7	for	for	ADP
ejpam-5192	206	8	every	every	DET
ejpam-5192	206	9	(	(	PUNCT
ejpam-5192	206	10	σ1	σ1	PROPN
ejpam-5192	206	11	,	,	PUNCT
ejpam-5192	206	12	σ2)β	σ2)β	NOUN
ejpam-5192	206	13	-	-	PUNCT
ejpam-5192	206	14	open	open	NOUN
ejpam-5192	206	15	set	set	NOUN
ejpam-5192	206	16	v	v	NOUN
ejpam-5192	206	17	of	of	ADP
ejpam-5192	206	18	y	y	PROPN
ejpam-5192	206	19	;	;	PUNCT
ejpam-5192	206	20	(	(	PUNCT
ejpam-5192	206	21	3	3	X
ejpam-5192	206	22	)	)	PUNCT
ejpam-5192	206	23	τ1τ2	τ1τ2	NOUN
ejpam-5192	206	24	-	-	NOUN
ejpam-5192	206	25	cl(f	cl(f	PRON
ejpam-5192	206	26	−1(v	−1(v	NOUN
ejpam-5192	206	27	)	)	PUNCT
ejpam-5192	206	28	)	)	PUNCT
ejpam-5192	207	1	⊆	⊆	NUM
ejpam-5192	207	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5192	207	3	-	-	PUNCT
ejpam-5192	207	4	cl(v	cl(v	NOUN
ejpam-5192	207	5	)	)	PUNCT
ejpam-5192	207	6	)	)	PUNCT
ejpam-5192	207	7	for	for	ADP
ejpam-5192	207	8	every	every	DET
ejpam-5192	207	9	(	(	PUNCT
ejpam-5192	207	10	σ1	σ1	PROPN
ejpam-5192	207	11	,	,	PUNCT
ejpam-5192	207	12	σ2)s	σ2)s	NOUN
ejpam-5192	207	13	-	-	PUNCT
ejpam-5192	207	14	open	open	NOUN
ejpam-5192	207	15	set	set	NOUN
ejpam-5192	207	16	v	v	NOUN
ejpam-5192	207	17	of	of	ADP
ejpam-5192	207	18	y	y	PROPN
ejpam-5192	207	19	.	.	PUNCT
ejpam-5192	208	1	lemma	lemma	PROPN
ejpam-5192	208	2	4	4	NUM
ejpam-5192	208	3	.	.	PUNCT
ejpam-5192	209	1	for	for	ADP
ejpam-5192	209	2	a	a	DET
ejpam-5192	209	3	bitopological	bitopological	ADJ
ejpam-5192	209	4	space	space	NOUN
ejpam-5192	209	5	(	(	PUNCT
ejpam-5192	209	6	x	x	NOUN
ejpam-5192	209	7	,	,	PUNCT
ejpam-5192	209	8	τ1	τ1	NOUN
ejpam-5192	209	9	,	,	PUNCT
ejpam-5192	209	10	τ2	τ2	NOUN
ejpam-5192	209	11	)	)	PUNCT
ejpam-5192	209	12	,	,	PUNCT
ejpam-5192	209	13	the	the	DET
ejpam-5192	209	14	following	follow	VERB
ejpam-5192	209	15	properties	property	NOUN
ejpam-5192	209	16	hold	hold	VERB
ejpam-5192	209	17	:	:	PUNCT
ejpam-5192	209	18	(	(	PUNCT
ejpam-5192	209	19	1	1	X
ejpam-5192	209	20	)	)	PUNCT
ejpam-5192	209	21	(	(	PUNCT
ejpam-5192	209	22	τ1	τ1	NOUN
ejpam-5192	209	23	,	,	PUNCT
ejpam-5192	209	24	τ2)-αcl(v	τ2)-αcl(v	NOUN
ejpam-5192	209	25	)	)	PUNCT
ejpam-5192	209	26	=	=	PUNCT
ejpam-5192	210	1	τ1τ2	τ1τ2	NOUN
ejpam-5192	210	2	-	-	NOUN
ejpam-5192	210	3	cl(v	cl(v	X
ejpam-5192	210	4	)	)	PUNCT
ejpam-5192	210	5	for	for	ADP
ejpam-5192	210	6	every	every	DET
ejpam-5192	210	7	(	(	PUNCT
ejpam-5192	210	8	τ1	τ1	NOUN
ejpam-5192	210	9	,	,	PUNCT
ejpam-5192	210	10	τ2)β	τ2)β	ADJ
ejpam-5192	210	11	-	-	PUNCT
ejpam-5192	210	12	open	open	NOUN
ejpam-5192	210	13	set	set	NOUN
ejpam-5192	210	14	v	v	NOUN
ejpam-5192	210	15	of	of	ADP
ejpam-5192	210	16	y	y	PROPN
ejpam-5192	210	17	;	;	PUNCT
ejpam-5192	210	18	(	(	PUNCT
ejpam-5192	210	19	2	2	X
ejpam-5192	210	20	)	)	PUNCT
ejpam-5192	210	21	(	(	PUNCT
ejpam-5192	210	22	τ1	τ1	NOUN
ejpam-5192	210	23	,	,	PUNCT
ejpam-5192	210	24	τ2)-pcl(v	τ2)-pcl(v	NOUN
ejpam-5192	210	25	)	)	PUNCT
ejpam-5192	211	1	=	=	PUNCT
ejpam-5192	211	2	τ1τ2	τ1τ2	NOUN
ejpam-5192	211	3	-	-	NOUN
ejpam-5192	211	4	cl(v	cl(v	X
ejpam-5192	211	5	)	)	PUNCT
ejpam-5192	211	6	for	for	ADP
ejpam-5192	211	7	every	every	DET
ejpam-5192	211	8	(	(	PUNCT
ejpam-5192	211	9	τ1	τ1	NOUN
ejpam-5192	211	10	,	,	PUNCT
ejpam-5192	211	11	τ2)s	τ2)s	NOUN
ejpam-5192	211	12	-	-	PUNCT
ejpam-5192	211	13	open	open	ADJ
ejpam-5192	211	14	set	set	NOUN
ejpam-5192	211	15	v	v	NOUN
ejpam-5192	211	16	of	of	ADP
ejpam-5192	211	17	y	y	PROPN
ejpam-5192	211	18	.	.	PUNCT
ejpam-5192	212	1	corollary	corollary	ADJ
ejpam-5192	212	2	4	4	NUM
ejpam-5192	212	3	.	.	PUNCT
ejpam-5192	212	4	for	for	ADP
ejpam-5192	212	5	a	a	DET
ejpam-5192	212	6	multifunction	multifunction	NOUN
ejpam-5192	213	1	f	f	NOUN
ejpam-5192	213	2	:	:	PUNCT
ejpam-5192	213	3	(	(	PUNCT
ejpam-5192	213	4	x	x	NOUN
ejpam-5192	213	5	,	,	PUNCT
ejpam-5192	213	6	τ1	τ1	NOUN
ejpam-5192	213	7	,	,	PUNCT
ejpam-5192	213	8	τ2	τ2	NOUN
ejpam-5192	213	9	)	)	PUNCT
ejpam-5192	213	10	→	→	SYM
ejpam-5192	213	11	(	(	PUNCT
ejpam-5192	213	12	y	y	PROPN
ejpam-5192	213	13	,	,	PUNCT
ejpam-5192	213	14	σ1	σ1	PROPN
ejpam-5192	213	15	,	,	PUNCT
ejpam-5192	213	16	σ2	σ2	NOUN
ejpam-5192	213	17	)	)	PUNCT
ejpam-5192	213	18	,	,	PUNCT
ejpam-5192	213	19	the	the	DET
ejpam-5192	213	20	following	follow	VERB
ejpam-5192	213	21	properties	property	NOUN
ejpam-5192	213	22	are	be	AUX
ejpam-5192	213	23	equivalent	equivalent	ADJ
ejpam-5192	213	24	:	:	PUNCT
ejpam-5192	213	25	(	(	PUNCT
ejpam-5192	213	26	1	1	X
ejpam-5192	213	27	)	)	PUNCT
ejpam-5192	213	28	f	f	PROPN
ejpam-5192	213	29	is	be	AUX
ejpam-5192	213	30	upper	upper	ADJ
ejpam-5192	213	31	almost	almost	ADV
ejpam-5192	213	32	(	(	PUNCT
ejpam-5192	213	33	τ1	τ1	NOUN
ejpam-5192	213	34	,	,	PUNCT
ejpam-5192	213	35	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	213	36	;	;	PUNCT
ejpam-5192	213	37	(	(	PUNCT
ejpam-5192	213	38	2	2	X
ejpam-5192	213	39	)	)	PUNCT
ejpam-5192	213	40	τ1τ2	τ1τ2	NOUN
ejpam-5192	213	41	-	-	NOUN
ejpam-5192	213	42	cl(f	cl(f	NUM
ejpam-5192	213	43	−(v	−(v	NOUN
ejpam-5192	213	44	)	)	PUNCT
ejpam-5192	213	45	)	)	PUNCT
ejpam-5192	214	1	⊆	⊆	NUM
ejpam-5192	214	2	f−((σ1	f−((σ1	NOUN
ejpam-5192	214	3	,	,	PUNCT
ejpam-5192	214	4	σ2)-αcl(v	σ2)-αcl(v	NOUN
ejpam-5192	214	5	)	)	PUNCT
ejpam-5192	214	6	)	)	PUNCT
ejpam-5192	214	7	for	for	ADP
ejpam-5192	214	8	every	every	DET
ejpam-5192	214	9	(	(	PUNCT
ejpam-5192	214	10	σ1	σ1	PROPN
ejpam-5192	214	11	,	,	PUNCT
ejpam-5192	214	12	σ2)β	σ2)β	NOUN
ejpam-5192	214	13	-	-	PUNCT
ejpam-5192	214	14	open	open	NOUN
ejpam-5192	214	15	set	set	NOUN
ejpam-5192	214	16	v	v	NOUN
ejpam-5192	214	17	of	of	ADP
ejpam-5192	214	18	y	y	PROPN
ejpam-5192	214	19	;	;	PUNCT
ejpam-5192	214	20	(	(	PUNCT
ejpam-5192	214	21	3	3	X
ejpam-5192	214	22	)	)	PUNCT
ejpam-5192	214	23	τ1τ2	τ1τ2	NOUN
ejpam-5192	214	24	-	-	NOUN
ejpam-5192	214	25	cl(f	cl(f	NUM
ejpam-5192	214	26	−(v	−(v	NOUN
ejpam-5192	214	27	)	)	PUNCT
ejpam-5192	214	28	)	)	PUNCT
ejpam-5192	215	1	⊆	⊆	NUM
ejpam-5192	215	2	f−((σ1	f−((σ1	NOUN
ejpam-5192	215	3	,	,	PUNCT
ejpam-5192	215	4	σ2)-pcl(v	σ2)-pcl(v	NOUN
ejpam-5192	215	5	)	)	PUNCT
ejpam-5192	215	6	)	)	PUNCT
ejpam-5192	215	7	for	for	ADP
ejpam-5192	215	8	every	every	DET
ejpam-5192	215	9	(	(	PUNCT
ejpam-5192	215	10	σ1	σ1	PROPN
ejpam-5192	215	11	,	,	PUNCT
ejpam-5192	215	12	σ2)s	σ2)s	NOUN
ejpam-5192	215	13	-	-	PUNCT
ejpam-5192	215	14	open	open	NOUN
ejpam-5192	215	15	set	set	NOUN
ejpam-5192	215	16	v	v	NOUN
ejpam-5192	215	17	of	of	ADP
ejpam-5192	215	18	y	y	PROPN
ejpam-5192	215	19	.	.	PUNCT
ejpam-5192	216	1	corollary	corollary	ADJ
ejpam-5192	216	2	5	5	NUM
ejpam-5192	216	3	.	.	PUNCT
ejpam-5192	217	1	for	for	ADP
ejpam-5192	217	2	a	a	DET
ejpam-5192	217	3	multifunction	multifunction	NOUN
ejpam-5192	217	4	f	f	NOUN
ejpam-5192	217	5	:	:	PUNCT
ejpam-5192	217	6	(	(	PUNCT
ejpam-5192	217	7	x	x	NOUN
ejpam-5192	217	8	,	,	PUNCT
ejpam-5192	217	9	τ1	τ1	NOUN
ejpam-5192	217	10	,	,	PUNCT
ejpam-5192	217	11	τ2	τ2	NOUN
ejpam-5192	217	12	)	)	PUNCT
ejpam-5192	217	13	→	→	SYM
ejpam-5192	217	14	(	(	PUNCT
ejpam-5192	217	15	y	y	PROPN
ejpam-5192	217	16	,	,	PUNCT
ejpam-5192	217	17	σ1	σ1	PROPN
ejpam-5192	217	18	,	,	PUNCT
ejpam-5192	217	19	σ2	σ2	NOUN
ejpam-5192	217	20	)	)	PUNCT
ejpam-5192	217	21	,	,	PUNCT
ejpam-5192	217	22	the	the	DET
ejpam-5192	217	23	following	follow	VERB
ejpam-5192	217	24	properties	property	NOUN
ejpam-5192	217	25	are	be	AUX
ejpam-5192	217	26	equivalent	equivalent	ADJ
ejpam-5192	217	27	:	:	PUNCT
ejpam-5192	217	28	(	(	PUNCT
ejpam-5192	217	29	1	1	X
ejpam-5192	217	30	)	)	PUNCT
ejpam-5192	217	31	f	f	PROPN
ejpam-5192	217	32	is	be	AUX
ejpam-5192	217	33	lower	low	ADJ
ejpam-5192	217	34	almost	almost	ADV
ejpam-5192	217	35	(	(	PUNCT
ejpam-5192	217	36	τ1	τ1	NOUN
ejpam-5192	217	37	,	,	PUNCT
ejpam-5192	217	38	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	217	39	;	;	PUNCT
ejpam-5192	217	40	(	(	PUNCT
ejpam-5192	217	41	2	2	X
ejpam-5192	217	42	)	)	PUNCT
ejpam-5192	217	43	τ1τ2	τ1τ2	NOUN
ejpam-5192	217	44	-	-	NOUN
ejpam-5192	217	45	cl(f	cl(f	NOUN
ejpam-5192	217	46	+	+	NOUN
ejpam-5192	217	47	(	(	PUNCT
ejpam-5192	217	48	v	v	NOUN
ejpam-5192	217	49	)	)	PUNCT
ejpam-5192	217	50	)	)	PUNCT
ejpam-5192	218	1	⊆	⊆	NUM
ejpam-5192	218	2	f+((σ1	f+((σ1	NOUN
ejpam-5192	218	3	,	,	PUNCT
ejpam-5192	218	4	σ2)-αcl(v	σ2)-αcl(v	NOUN
ejpam-5192	218	5	)	)	PUNCT
ejpam-5192	218	6	)	)	PUNCT
ejpam-5192	218	7	for	for	ADP
ejpam-5192	218	8	every	every	DET
ejpam-5192	218	9	(	(	PUNCT
ejpam-5192	218	10	σ1	σ1	PROPN
ejpam-5192	218	11	,	,	PUNCT
ejpam-5192	218	12	σ2)β	σ2)β	NOUN
ejpam-5192	218	13	-	-	PUNCT
ejpam-5192	218	14	open	open	NOUN
ejpam-5192	218	15	set	set	NOUN
ejpam-5192	218	16	v	v	NOUN
ejpam-5192	218	17	of	of	ADP
ejpam-5192	218	18	y	y	PROPN
ejpam-5192	218	19	;	;	PUNCT
ejpam-5192	218	20	(	(	PUNCT
ejpam-5192	218	21	3	3	X
ejpam-5192	218	22	)	)	PUNCT
ejpam-5192	218	23	τ1τ2	τ1τ2	NOUN
ejpam-5192	218	24	-	-	NOUN
ejpam-5192	218	25	cl(f	cl(f	NOUN
ejpam-5192	218	26	+	+	NOUN
ejpam-5192	218	27	(	(	PUNCT
ejpam-5192	218	28	v	v	NOUN
ejpam-5192	218	29	)	)	PUNCT
ejpam-5192	218	30	)	)	PUNCT
ejpam-5192	218	31	⊆	⊆	NUM
ejpam-5192	218	32	f+((σ1	f+((σ1	NOUN
ejpam-5192	218	33	,	,	PUNCT
ejpam-5192	218	34	σ2)-pcl(v	σ2)-pcl(v	NOUN
ejpam-5192	218	35	)	)	PUNCT
ejpam-5192	218	36	)	)	PUNCT
ejpam-5192	218	37	for	for	ADP
ejpam-5192	218	38	every	every	DET
ejpam-5192	218	39	(	(	PUNCT
ejpam-5192	218	40	σ1	σ1	PROPN
ejpam-5192	218	41	,	,	PUNCT
ejpam-5192	218	42	σ2)s	σ2)s	NOUN
ejpam-5192	218	43	-	-	PUNCT
ejpam-5192	218	44	open	open	NOUN
ejpam-5192	218	45	set	set	NOUN
ejpam-5192	218	46	v	v	NOUN
ejpam-5192	218	47	of	of	ADP
ejpam-5192	218	48	y	y	PROPN
ejpam-5192	218	49	.	.	PUNCT
ejpam-5192	219	1	acknowledgements	acknowledgement	NOUN
ejpam-5192	219	2	this	this	DET
ejpam-5192	219	3	research	research	NOUN
ejpam-5192	219	4	project	project	NOUN
ejpam-5192	219	5	was	be	AUX
ejpam-5192	219	6	financially	financially	ADV
ejpam-5192	219	7	supported	support	VERB
ejpam-5192	219	8	by	by	ADP
ejpam-5192	219	9	mahasarakham	mahasarakham	PROPN
ejpam-5192	219	10	university	university	PROPN
ejpam-5192	219	11	.	.	PUNCT
ejpam-5192	220	1	references	reference	NOUN
ejpam-5192	220	2	1252	1252	NUM
ejpam-5192	220	3	references	reference	NOUN
ejpam-5192	220	4	[	[	X
ejpam-5192	220	5	1	1	NUM
ejpam-5192	220	6	]	]	PUNCT
ejpam-5192	220	7	d.	d.	PROPN
ejpam-5192	220	8	andrijević.	andrijević.	PROPN
ejpam-5192	220	9	on	on	ADP
ejpam-5192	220	10	b	b	X
ejpam-5192	220	11	-	-	PUNCT
ejpam-5192	220	12	open	open	ADJ
ejpam-5192	220	13	sets	set	NOUN
ejpam-5192	220	14	.	.	PUNCT
ejpam-5192	221	1	matematički	matematički	PROPN
ejpam-5192	221	2	vesnik	vesnik	PROPN
ejpam-5192	221	3	,	,	PUNCT
ejpam-5192	221	4	48:59–64	48:59–64	PROPN
ejpam-5192	221	5	,	,	PUNCT
ejpam-5192	221	6	1996	1996	NUM
ejpam-5192	221	7	.	.	PUNCT
ejpam-5192	222	1	[	[	X
ejpam-5192	222	2	2	2	NUM
ejpam-5192	222	3	]	]	PUNCT
ejpam-5192	222	4	c.	c.	PROPN
ejpam-5192	222	5	berge	berge	PROPN
ejpam-5192	222	6	.	.	PUNCT
ejpam-5192	222	7	espaces	espace	VERB
ejpam-5192	222	8	topologiques	topologique	NOUN
ejpam-5192	222	9	fonctions	fonction	NOUN
ejpam-5192	222	10	multivoques	multivoque	NOUN
ejpam-5192	222	11	.	.	PUNCT
ejpam-5192	223	1	dunod	dunod	PROPN
ejpam-5192	223	2	,	,	PUNCT
ejpam-5192	223	3	paris	paris	PROPN
ejpam-5192	223	4	,	,	PUNCT
ejpam-5192	223	5	1959	1959	NUM
ejpam-5192	223	6	.	.	PUNCT
ejpam-5192	224	1	[	[	X
ejpam-5192	224	2	3	3	X
ejpam-5192	224	3	]	]	PUNCT
ejpam-5192	224	4	c.	c.	PROPN
ejpam-5192	224	5	boonpok	boonpok	PROPN
ejpam-5192	224	6	.	.	PUNCT
ejpam-5192	225	1	m	m	VERB
ejpam-5192	225	2	-continuous	-continuous	ADJ
ejpam-5192	225	3	functions	function	NOUN
ejpam-5192	225	4	in	in	ADP
ejpam-5192	225	5	biminimal	biminimal	NOUN
ejpam-5192	225	6	structure	structure	NOUN
ejpam-5192	225	7	spaces	space	NOUN
ejpam-5192	225	8	.	.	PUNCT
ejpam-5192	226	1	far	far	PROPN
ejpam-5192	226	2	east	east	PROPN
ejpam-5192	226	3	journal	journal	PROPN
ejpam-5192	226	4	of	of	ADP
ejpam-5192	226	5	mathematical	mathematical	ADJ
ejpam-5192	226	6	sciences	science	NOUN
ejpam-5192	226	7	,	,	PUNCT
ejpam-5192	226	8	43(1):41–58	43(1):41–58	NUM
ejpam-5192	226	9	,	,	PUNCT
ejpam-5192	226	10	2010	2010	NUM
ejpam-5192	226	11	.	.	PUNCT
ejpam-5192	227	1	[	[	X
ejpam-5192	227	2	4	4	NUM
ejpam-5192	227	3	]	]	PUNCT
ejpam-5192	227	4	c.	c.	PROPN
ejpam-5192	227	5	boonpok	boonpok	PROPN
ejpam-5192	227	6	.	.	PUNCT
ejpam-5192	228	1	on	on	ADP
ejpam-5192	228	2	continuous	continuous	ADJ
ejpam-5192	228	3	multifunctions	multifunction	NOUN
ejpam-5192	228	4	in	in	ADP
ejpam-5192	228	5	ideal	ideal	ADJ
ejpam-5192	228	6	topological	topological	ADJ
ejpam-5192	228	7	spaces	space	NOUN
ejpam-5192	228	8	.	.	PUNCT
ejpam-5192	229	1	lobachevskii	lobachevskii	PROPN
ejpam-5192	229	2	journal	journal	PROPN
ejpam-5192	229	3	of	of	ADP
ejpam-5192	229	4	mathematics	mathematic	NOUN
ejpam-5192	229	5	,	,	PUNCT
ejpam-5192	229	6	40(1):24–35	40(1):24–35	NUM
ejpam-5192	229	7	,	,	PUNCT
ejpam-5192	229	8	2019	2019	NUM
ejpam-5192	229	9	.	.	PUNCT
ejpam-5192	230	1	[	[	X
ejpam-5192	230	2	5	5	X
ejpam-5192	230	3	]	]	PUNCT
ejpam-5192	230	4	c.	c.	PROPN
ejpam-5192	230	5	boonpok	boonpok	PROPN
ejpam-5192	230	6	.	.	PUNCT
ejpam-5192	231	1	(	(	PUNCT
ejpam-5192	231	2	τ1	τ1	NOUN
ejpam-5192	231	3	,	,	PUNCT
ejpam-5192	231	4	τ2)δ	τ2)δ	ADJ
ejpam-5192	231	5	-	-	PUNCT
ejpam-5192	231	6	semicontinuous	semicontinuous	ADJ
ejpam-5192	231	7	multifunctions	multifunction	NOUN
ejpam-5192	231	8	.	.	PUNCT
ejpam-5192	232	1	heliyon	heliyon	NOUN
ejpam-5192	232	2	,	,	PUNCT
ejpam-5192	232	3	6	6	NUM
ejpam-5192	232	4	:	:	SYM
ejpam-5192	232	5	e05367	e05367	PROPN
ejpam-5192	232	6	,	,	PUNCT
ejpam-5192	232	7	2020	2020	NUM
ejpam-5192	232	8	.	.	PUNCT
ejpam-5192	233	1	[	[	X
ejpam-5192	233	2	6	6	NUM
ejpam-5192	233	3	]	]	PUNCT
ejpam-5192	233	4	c.	c.	PROPN
ejpam-5192	233	5	boonpok	boonpok	PROPN
ejpam-5192	233	6	.	.	PUNCT
ejpam-5192	234	1	upper	upper	ADJ
ejpam-5192	234	2	and	and	CCONJ
ejpam-5192	234	3	lower	low	ADJ
ejpam-5192	234	4	β(⋆)-continuity	β(⋆)-continuity	NOUN
ejpam-5192	234	5	.	.	PUNCT
ejpam-5192	234	6	heliyon	heliyon	NOUN
ejpam-5192	234	7	,	,	PUNCT
ejpam-5192	234	8	7	7	NUM
ejpam-5192	234	9	:	:	PUNCT
ejpam-5192	234	10	e05986	e05986	PROPN
ejpam-5192	234	11	,	,	PUNCT
ejpam-5192	234	12	2021	2021	NUM
ejpam-5192	234	13	.	.	PUNCT
ejpam-5192	235	1	[	[	X
ejpam-5192	235	2	7	7	X
ejpam-5192	235	3	]	]	X
ejpam-5192	235	4	c.	c.	NOUN
ejpam-5192	235	5	boonpok	boonpok	PROPN
ejpam-5192	235	6	and	and	CCONJ
ejpam-5192	235	7	p.	p.	NOUN
ejpam-5192	235	8	pue	pue	NOUN
ejpam-5192	235	9	-	-	PUNCT
ejpam-5192	235	10	on	on	ADP
ejpam-5192	235	11	.	.	PUNCT
ejpam-5192	236	1	characterizations	characterization	NOUN
ejpam-5192	236	2	of	of	ADP
ejpam-5192	236	3	almost	almost	ADV
ejpam-5192	236	4	(	(	PUNCT
ejpam-5192	236	5	τ1	τ1	NOUN
ejpam-5192	236	6	,	,	PUNCT
ejpam-5192	236	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	236	8	functions	function	NOUN
ejpam-5192	236	9	.	.	PUNCT
ejpam-5192	237	1	international	international	ADJ
ejpam-5192	237	2	journal	journal	NOUN
ejpam-5192	237	3	of	of	ADP
ejpam-5192	237	4	analysis	analysis	NOUN
ejpam-5192	237	5	and	and	CCONJ
ejpam-5192	237	6	applications	application	NOUN
ejpam-5192	237	7	,	,	PUNCT
ejpam-5192	237	8	22:33	22:33	NUM
ejpam-5192	237	9	,	,	PUNCT
ejpam-5192	237	10	2024	2024	NUM
ejpam-5192	237	11	.	.	PUNCT
ejpam-5192	238	1	[	[	X
ejpam-5192	238	2	8	8	NUM
ejpam-5192	238	3	]	]	X
ejpam-5192	238	4	c.	c.	PROPN
ejpam-5192	238	5	boonpok	boonpok	PROPN
ejpam-5192	238	6	and	and	CCONJ
ejpam-5192	238	7	c.	c.	PROPN
ejpam-5192	238	8	viriyapong	viriyapong	PROPN
ejpam-5192	238	9	.	.	PUNCT
ejpam-5192	239	1	upper	upper	ADJ
ejpam-5192	239	2	and	and	CCONJ
ejpam-5192	239	3	lower	low	ADJ
ejpam-5192	239	4	almost	almost	ADV
ejpam-5192	239	5	weak	weak	ADJ
ejpam-5192	239	6	(	(	PUNCT
ejpam-5192	239	7	τ1	τ1	NOUN
ejpam-5192	239	8	,	,	PUNCT
ejpam-5192	239	9	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5192	239	10	.	.	PUNCT
ejpam-5192	240	1	european	european	PROPN
ejpam-5192	240	2	journal	journal	PROPN
ejpam-5192	240	3	of	of	ADP
ejpam-5192	240	4	pure	pure	ADJ
ejpam-5192	240	5	and	and	CCONJ
ejpam-5192	240	6	applied	applied	ADJ
ejpam-5192	240	7	mathematics	mathematic	NOUN
ejpam-5192	240	8	,	,	PUNCT
ejpam-5192	240	9	14(4):1212–1225	14(4):1212–1225	NUM
ejpam-5192	240	10	,	,	PUNCT
ejpam-5192	240	11	2021	2021	NUM
ejpam-5192	240	12	.	.	PUNCT
ejpam-5192	241	1	[	[	X
ejpam-5192	241	2	9	9	NUM
ejpam-5192	241	3	]	]	PUNCT
ejpam-5192	241	4	c.	c.	PROPN
ejpam-5192	241	5	boonpok	boonpok	PROPN
ejpam-5192	241	6	,	,	PUNCT
ejpam-5192	241	7	c.	c.	PROPN
ejpam-5192	241	8	viriyapong	viriyapong	PROPN
ejpam-5192	241	9	,	,	PUNCT
ejpam-5192	241	10	and	and	CCONJ
ejpam-5192	241	11	m.	m.	NOUN
ejpam-5192	241	12	thongmoon	thongmoon	NOUN
ejpam-5192	241	13	.	.	PUNCT
ejpam-5192	242	1	on	on	ADP
ejpam-5192	242	2	upper	upper	ADJ
ejpam-5192	242	3	and	and	CCONJ
ejpam-5192	242	4	lower	low	ADJ
ejpam-5192	242	5	(	(	PUNCT
ejpam-5192	242	6	τ1	τ1	NOUN
ejpam-5192	242	7	,	,	PUNCT
ejpam-5192	242	8	τ2)precontinuous	τ2)precontinuous	ADJ
ejpam-5192	242	9	multifunctions	multifunction	NOUN
ejpam-5192	242	10	.	.	PUNCT
ejpam-5192	243	1	journal	journal	PROPN
ejpam-5192	243	2	of	of	ADP
ejpam-5192	243	3	mathematics	mathematics	PROPN
ejpam-5192	243	4	and	and	CCONJ
ejpam-5192	243	5	computer	computer	NOUN
ejpam-5192	243	6	science	science	NOUN
ejpam-5192	243	7	,	,	PUNCT
ejpam-5192	243	8	18:282–293	18:282–293	NUM
ejpam-5192	243	9	,	,	PUNCT
ejpam-5192	243	10	2018	2018	NUM
ejpam-5192	243	11	.	.	PUNCT
ejpam-5192	244	1	[	[	X
ejpam-5192	244	2	10	10	NUM
ejpam-5192	244	3	]	]	X
ejpam-5192	244	4	c.	c.	PROPN
ejpam-5192	244	5	boonpok	boonpok	PROPN
ejpam-5192	244	6	and	and	CCONJ
ejpam-5192	244	7	n.	n.	PROPN
ejpam-5192	244	8	viriyapong	viriyapong	PROPN
ejpam-5192	244	9	.	.	PUNCT
ejpam-5192	245	1	almost	almost	ADV
ejpam-5192	245	2	(	(	PUNCT
ejpam-5192	245	3	λ	λ	PROPN
ejpam-5192	245	4	,	,	PUNCT
ejpam-5192	245	5	sp)-continuity	sp)-continuity	NOUN
ejpam-5192	245	6	for	for	ADP
ejpam-5192	245	7	multifunctions	multifunction	NOUN
ejpam-5192	245	8	.	.	PUNCT
ejpam-5192	246	1	european	european	ADJ
ejpam-5192	246	2	journal	journal	PROPN
ejpam-5192	246	3	of	of	ADP
ejpam-5192	246	4	pure	pure	ADJ
ejpam-5192	246	5	and	and	CCONJ
ejpam-5192	246	6	applied	applied	ADJ
ejpam-5192	246	7	mathematics	mathematic	NOUN
ejpam-5192	246	8	,	,	PUNCT
ejpam-5192	246	9	16(1):84–96	16(1):84–96	NUM
ejpam-5192	246	10	,	,	PUNCT
ejpam-5192	246	11	2023	2023	NUM
ejpam-5192	246	12	.	.	PUNCT
ejpam-5192	247	1	[	[	X
ejpam-5192	247	2	11	11	NUM
ejpam-5192	247	3	]	]	X
ejpam-5192	247	4	e.	e.	PROPN
ejpam-5192	247	5	ekici	ekici	PROPN
ejpam-5192	247	6	and	and	CCONJ
ejpam-5192	247	7	j.	j.	PROPN
ejpam-5192	247	8	h.	h.	PROPN
ejpam-5192	247	9	park	park	PROPN
ejpam-5192	247	10	.	.	PUNCT
ejpam-5192	248	1	a	a	DET
ejpam-5192	248	2	weak	weak	ADJ
ejpam-5192	248	3	form	form	NOUN
ejpam-5192	248	4	of	of	ADP
ejpam-5192	248	5	some	some	DET
ejpam-5192	248	6	types	type	NOUN
ejpam-5192	248	7	of	of	ADP
ejpam-5192	248	8	continuous	continuous	ADJ
ejpam-5192	248	9	multifunctions	multifunction	NOUN
ejpam-5192	248	10	.	.	PUNCT
ejpam-5192	249	1	filomat	filomat	NOUN
ejpam-5192	249	2	,	,	PUNCT
ejpam-5192	249	3	20(2):13–32	20(2):13–32	NUM
ejpam-5192	249	4	,	,	PUNCT
ejpam-5192	249	5	2006	2006	NUM
ejpam-5192	249	6	.	.	PUNCT
ejpam-5192	250	1	[	[	X
ejpam-5192	250	2	12	12	NUM
ejpam-5192	250	3	]	]	PUNCT
ejpam-5192	250	4	m.	m.	NOUN
ejpam-5192	250	5	e.	e.	PROPN
ejpam-5192	250	6	abd	abd	PROPN
ejpam-5192	251	1	el	el	PROPN
ejpam-5192	251	2	-	-	PROPN
ejpam-5192	251	3	monsef	monsef	PROPN
ejpam-5192	251	4	,	,	PUNCT
ejpam-5192	251	5	s.	s.	PROPN
ejpam-5192	251	6	n.	n.	PROPN
ejpam-5192	251	7	el	el	PROPN
ejpam-5192	251	8	-	-	PROPN
ejpam-5192	251	9	deeb	deeb	PROPN
ejpam-5192	251	10	,	,	PUNCT
ejpam-5192	251	11	and	and	CCONJ
ejpam-5192	251	12	r.	r.	PROPN
ejpam-5192	251	13	a.	a.	PROPN
ejpam-5192	251	14	mahmoud	mahmoud	PROPN
ejpam-5192	251	15	.	.	PUNCT
ejpam-5192	252	1	β	β	X
ejpam-5192	252	2	-	-	ADJ
ejpam-5192	252	3	open	open	ADJ
ejpam-5192	252	4	sets	set	NOUN
ejpam-5192	252	5	and	and	CCONJ
ejpam-5192	252	6	βcontinuous	βcontinuous	ADJ
ejpam-5192	252	7	mappings	mapping	NOUN
ejpam-5192	252	8	.	.	PUNCT
ejpam-5192	253	1	bulletin	bulletin	NOUN
ejpam-5192	253	2	of	of	ADP
ejpam-5192	253	3	the	the	DET
ejpam-5192	253	4	faculty	faculty	NOUN
ejpam-5192	253	5	of	of	ADP
ejpam-5192	253	6	science	science	NOUN
ejpam-5192	253	7	.	.	PUNCT
ejpam-5192	254	1	assiut	assiut	PROPN
ejpam-5192	254	2	university	university	PROPN
ejpam-5192	254	3	.	.	PUNCT
ejpam-5192	254	4	,	,	PUNCT
ejpam-5192	254	5	12:77–90	12:77–90	NUM
ejpam-5192	254	6	,	,	PUNCT
ejpam-5192	254	7	1983	1983	NUM
ejpam-5192	254	8	.	.	PUNCT
ejpam-5192	255	1	[	[	X
ejpam-5192	255	2	13	13	NUM
ejpam-5192	255	3	]	]	PUNCT
ejpam-5192	255	4	a.	a.	NOUN
ejpam-5192	255	5	keskin	keskin	PROPN
ejpam-5192	255	6	and	and	CCONJ
ejpam-5192	255	7	t.	t.	PROPN
ejpam-5192	255	8	noiri	noiri	PROPN
ejpam-5192	255	9	.	.	PUNCT
ejpam-5192	256	1	almost	almost	ADV
ejpam-5192	256	2	b	b	X
ejpam-5192	256	3	-	-	PUNCT
ejpam-5192	256	4	continuous	continuous	ADJ
ejpam-5192	256	5	functions	function	NOUN
ejpam-5192	256	6	.	.	PUNCT
ejpam-5192	257	1	chaos	chaos	NOUN
ejpam-5192	257	2	,	,	PUNCT
ejpam-5192	257	3	solitons	soliton	NOUN
ejpam-5192	257	4	&	&	CCONJ
ejpam-5192	257	5	fractals	fractal	NOUN
ejpam-5192	257	6	,	,	PUNCT
ejpam-5192	257	7	41:72–81	41:72–81	NUM
ejpam-5192	257	8	,	,	PUNCT
ejpam-5192	257	9	2009	2009	NUM
ejpam-5192	257	10	.	.	PUNCT
ejpam-5192	258	1	[	[	X
ejpam-5192	258	2	14	14	NUM
ejpam-5192	258	3	]	]	PUNCT
ejpam-5192	258	4	k.	k.	PROPN
ejpam-5192	259	1	laprom	laprom	PROPN
ejpam-5192	259	2	,	,	PUNCT
ejpam-5192	259	3	c.	c.	PROPN
ejpam-5192	259	4	boonpok	boonpok	PROPN
ejpam-5192	259	5	,	,	PUNCT
ejpam-5192	259	6	and	and	CCONJ
ejpam-5192	259	7	c.	c.	PROPN
ejpam-5192	259	8	viriyapong	viriyapong	PROPN
ejpam-5192	259	9	.	.	PUNCT
ejpam-5192	260	1	β(τ1	β(τ1	PROPN
ejpam-5192	260	2	,	,	PUNCT
ejpam-5192	260	3	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5192	260	4	multifunctions	multifunction	NOUN
ejpam-5192	260	5	on	on	ADP
ejpam-5192	260	6	bitopological	bitopological	ADJ
ejpam-5192	260	7	spaces	space	NOUN
ejpam-5192	260	8	.	.	PUNCT
ejpam-5192	261	1	journal	journal	NOUN
ejpam-5192	261	2	of	of	ADP
ejpam-5192	261	3	mathematics	mathematic	NOUN
ejpam-5192	261	4	,	,	PUNCT
ejpam-5192	261	5	2020:4020971	2020:4020971	NUM
ejpam-5192	261	6	,	,	PUNCT
ejpam-5192	261	7	2020	2020	NUM
ejpam-5192	261	8	.	.	PUNCT
ejpam-5192	262	1	[	[	X
ejpam-5192	262	2	15	15	NUM
ejpam-5192	262	3	]	]	X
ejpam-5192	262	4	a.	a.	NOUN
ejpam-5192	262	5	s.	s.	PROPN
ejpam-5192	262	6	mashhour	mashhour	PROPN
ejpam-5192	262	7	,	,	PUNCT
ejpam-5192	262	8	m.	m.	PROPN
ejpam-5192	262	9	e.	e.	PROPN
ejpam-5192	262	10	abd	abd	PROPN
ejpam-5192	262	11	el	el	PROPN
ejpam-5192	262	12	-	-	PROPN
ejpam-5192	262	13	monsef	monsef	ADJ
ejpam-5192	262	14	,	,	PUNCT
ejpam-5192	262	15	and	and	CCONJ
ejpam-5192	262	16	s.	s.	PROPN
ejpam-5192	262	17	n.	n.	PROPN
ejpam-5192	262	18	el	el	PROPN
ejpam-5192	262	19	-	-	PROPN
ejpam-5192	262	20	deeb	deeb	PROPN
ejpam-5192	262	21	.	.	PUNCT
ejpam-5192	263	1	on	on	ADP
ejpam-5192	263	2	precontinuous	precontinuous	ADJ
ejpam-5192	263	3	and	and	CCONJ
ejpam-5192	263	4	weak	weak	ADJ
ejpam-5192	263	5	precontinuous	precontinuous	ADJ
ejpam-5192	263	6	mappings	mapping	NOUN
ejpam-5192	263	7	.	.	PUNCT
ejpam-5192	264	1	proceedings	proceeding	NOUN
ejpam-5192	264	2	of	of	ADP
ejpam-5192	264	3	the	the	DET
ejpam-5192	264	4	mathematical	mathematical	ADJ
ejpam-5192	264	5	and	and	CCONJ
ejpam-5192	264	6	physical	physical	ADJ
ejpam-5192	264	7	society	society	NOUN
ejpam-5192	264	8	of	of	ADP
ejpam-5192	264	9	egypt	egypt	PROPN
ejpam-5192	264	10	,	,	PUNCT
ejpam-5192	264	11	53:47–53	53:47–53	NUM
ejpam-5192	264	12	,	,	PUNCT
ejpam-5192	264	13	1982	1982	NUM
ejpam-5192	264	14	.	.	PUNCT
ejpam-5192	265	1	[	[	X
ejpam-5192	265	2	16	16	NUM
ejpam-5192	265	3	]	]	X
ejpam-5192	265	4	b.	b.	PROPN
ejpam-5192	265	5	m.	m.	PROPN
ejpam-5192	265	6	munshi	munshi	PROPN
ejpam-5192	265	7	and	and	CCONJ
ejpam-5192	265	8	d.	d.	PROPN
ejpam-5192	265	9	s.	s.	PROPN
ejpam-5192	265	10	bassan	bassan	PROPN
ejpam-5192	265	11	.	.	PUNCT
ejpam-5192	266	1	almost	almost	ADV
ejpam-5192	266	2	semi	semi	ADJ
ejpam-5192	266	3	-	-	ADJ
ejpam-5192	266	4	continuous	continuous	ADJ
ejpam-5192	266	5	mappings	mapping	NOUN
ejpam-5192	266	6	.	.	PUNCT
ejpam-5192	267	1	mathematics	mathematic	NOUN
ejpam-5192	267	2	student	student	NOUN
ejpam-5192	267	3	,	,	PUNCT
ejpam-5192	267	4	49:239–248	49:239–248	PROPN
ejpam-5192	267	5	,	,	PUNCT
ejpam-5192	267	6	1981	1981	NUM
ejpam-5192	267	7	.	.	PUNCT
ejpam-5192	268	1	references	reference	NOUN
ejpam-5192	268	2	1253	1253	NUM
ejpam-5192	269	1	[	[	X
ejpam-5192	269	2	17	17	NUM
ejpam-5192	269	3	]	]	PUNCT
ejpam-5192	269	4	a.	a.	NOUN
ejpam-5192	269	5	a.	a.	NOUN
ejpam-5192	269	6	nasef	nasef	PROPN
ejpam-5192	269	7	and	and	CCONJ
ejpam-5192	269	8	t.	t.	PROPN
ejpam-5192	269	9	noiri	noiri	PROPN
ejpam-5192	269	10	.	.	PUNCT
ejpam-5192	270	1	some	some	DET
ejpam-5192	270	2	weak	weak	ADJ
ejpam-5192	270	3	forms	form	NOUN
ejpam-5192	270	4	of	of	ADP
ejpam-5192	270	5	almost	almost	ADV
ejpam-5192	270	6	continuity	continuity	NOUN
ejpam-5192	270	7	.	.	PUNCT
ejpam-5192	271	1	acta	acta	PROPN
ejpam-5192	271	2	mathematica	mathematica	PROPN
ejpam-5192	271	3	hungarica	hungarica	PROPN
ejpam-5192	271	4	,	,	PUNCT
ejpam-5192	271	5	74(3):211–219	74(3):211–219	PROPN
ejpam-5192	271	6	,	,	PUNCT
ejpam-5192	271	7	1997	1997	NUM
ejpam-5192	271	8	.	.	PUNCT
ejpam-5192	272	1	[	[	X
ejpam-5192	272	2	18	18	NUM
ejpam-5192	272	3	]	]	PUNCT
ejpam-5192	272	4	t.	t.	PROPN
ejpam-5192	272	5	noiri	noiri	PROPN
ejpam-5192	272	6	.	.	PUNCT
ejpam-5192	273	1	almost	almost	ADV
ejpam-5192	273	2	α	α	NUM
ejpam-5192	273	3	-	-	ADJ
ejpam-5192	273	4	continuous	continuous	ADJ
ejpam-5192	273	5	functions	function	NOUN
ejpam-5192	273	6	.	.	PUNCT
ejpam-5192	274	1	kyungpook	kyungpook	PROPN
ejpam-5192	274	2	mathematical	mathematical	PROPN
ejpam-5192	274	3	journal	journal	PROPN
ejpam-5192	274	4	,	,	PUNCT
ejpam-5192	274	5	28:71–77	28:71–77	PROPN
ejpam-5192	274	6	,	,	PUNCT
ejpam-5192	274	7	1988	1988	NUM
ejpam-5192	274	8	.	.	PUNCT
ejpam-5192	275	1	[	[	X
ejpam-5192	275	2	19	19	NUM
ejpam-5192	275	3	]	]	X
ejpam-5192	275	4	t.	t.	PROPN
ejpam-5192	275	5	noiri	noiri	PROPN
ejpam-5192	275	6	and	and	CCONJ
ejpam-5192	275	7	v.	v.	ADP
ejpam-5192	275	8	popa	popa	NOUN
ejpam-5192	275	9	.	.	PUNCT
ejpam-5192	276	1	characterizations	characterization	NOUN
ejpam-5192	276	2	of	of	ADP
ejpam-5192	276	3	almost	almost	ADV
ejpam-5192	276	4	quasi	quasi	ADJ
ejpam-5192	276	5	-	-	ADJ
ejpam-5192	276	6	continuous	continuous	ADJ
ejpam-5192	276	7	multifunctions	multifunction	NOUN
ejpam-5192	276	8	.	.	PUNCT
ejpam-5192	277	1	research	research	NOUN
ejpam-5192	277	2	reports	report	NOUN
ejpam-5192	277	3	of	of	ADP
ejpam-5192	277	4	yatsushiro	yatsushiro	PROPN
ejpam-5192	277	5	national	national	PROPN
ejpam-5192	277	6	college	college	PROPN
ejpam-5192	277	7	of	of	ADP
ejpam-5192	277	8	technology	technology	NOUN
ejpam-5192	277	9	,	,	PUNCT
ejpam-5192	277	10	15:97–101	15:97–101	NUM
ejpam-5192	277	11	,	,	PUNCT
ejpam-5192	277	12	1993	1993	NUM
ejpam-5192	277	13	.	.	PUNCT
ejpam-5192	278	1	[	[	X
ejpam-5192	278	2	20	20	NUM
ejpam-5192	278	3	]	]	PUNCT
ejpam-5192	278	4	t.	t.	PROPN
ejpam-5192	278	5	noiri	noiri	PROPN
ejpam-5192	278	6	and	and	CCONJ
ejpam-5192	278	7	v.	v.	ADP
ejpam-5192	278	8	popa	popa	NOUN
ejpam-5192	278	9	.	.	PUNCT
ejpam-5192	279	1	on	on	ADP
ejpam-5192	279	2	upper	upper	ADJ
ejpam-5192	279	3	and	and	CCONJ
ejpam-5192	279	4	lower	low	ADJ
ejpam-5192	279	5	almost	almost	ADV
ejpam-5192	279	6	β	β	ADJ
ejpam-5192	279	7	-	-	ADJ
ejpam-5192	279	8	continuous	continuous	ADJ
ejpam-5192	279	9	multifunctions	multifunction	NOUN
ejpam-5192	279	10	.	.	PUNCT
ejpam-5192	280	1	acta	acta	PROPN
ejpam-5192	280	2	mathematica	mathematica	PROPN
ejpam-5192	280	3	hungarica	hungarica	PROPN
ejpam-5192	280	4	,	,	PUNCT
ejpam-5192	280	5	82:57–73	82:57–73	PROPN
ejpam-5192	280	6	,	,	PUNCT
ejpam-5192	280	7	1999	1999	NUM
ejpam-5192	280	8	.	.	PUNCT
ejpam-5192	281	1	[	[	X
ejpam-5192	281	2	21	21	NUM
ejpam-5192	281	3	]	]	X
ejpam-5192	281	4	t.	t.	PROPN
ejpam-5192	281	5	noiri	noiri	PROPN
ejpam-5192	281	6	and	and	CCONJ
ejpam-5192	281	7	v.	v.	ADP
ejpam-5192	281	8	popa	popa	NOUN
ejpam-5192	281	9	.	.	PUNCT
ejpam-5192	282	1	a	a	DET
ejpam-5192	282	2	unified	unified	ADJ
ejpam-5192	282	3	theory	theory	NOUN
ejpam-5192	282	4	of	of	ADP
ejpam-5192	282	5	almost	almost	ADV
ejpam-5192	282	6	continuity	continuity	NOUN
ejpam-5192	282	7	for	for	ADP
ejpam-5192	282	8	multifunctions	multifunction	NOUN
ejpam-5192	282	9	.	.	PUNCT
ejpam-5192	283	1	scientific	scientific	ADJ
ejpam-5192	283	2	studies	study	NOUN
ejpam-5192	283	3	and	and	CCONJ
ejpam-5192	283	4	research	research	NOUN
ejpam-5192	283	5	.	.	PUNCT
ejpam-5192	284	1	series	series	PROPN
ejpam-5192	284	2	mathematics	mathematics	PROPN
ejpam-5192	284	3	and	and	CCONJ
ejpam-5192	284	4	informatics	informatic	NOUN
ejpam-5192	284	5	,	,	PUNCT
ejpam-5192	284	6	20(1):185–214	20(1):185–214	PROPN
ejpam-5192	284	7	,	,	PUNCT
ejpam-5192	284	8	2010	2010	NUM
ejpam-5192	284	9	.	.	PUNCT
ejpam-5192	285	1	[	[	X
ejpam-5192	285	2	22	22	NUM
ejpam-5192	285	3	]	]	PUNCT
ejpam-5192	285	4	v.	v.	CCONJ
ejpam-5192	285	5	popa	popa	NOUN
ejpam-5192	285	6	.	.	PUNCT
ejpam-5192	286	1	almost	almost	ADV
ejpam-5192	286	2	continuous	continuous	ADJ
ejpam-5192	286	3	multifunctions	multifunction	NOUN
ejpam-5192	286	4	.	.	PUNCT
ejpam-5192	287	1	matematički	matematički	PROPN
ejpam-5192	287	2	vesnik	vesnik	PROPN
ejpam-5192	287	3	,	,	PUNCT
ejpam-5192	287	4	6(9)(34):75–84	6(9)(34):75–84	NOUN
ejpam-5192	287	5	,	,	PUNCT
ejpam-5192	287	6	1982	1982	NUM
ejpam-5192	287	7	.	.	PUNCT
ejpam-5192	288	1	[	[	X
ejpam-5192	288	2	23	23	X
ejpam-5192	288	3	]	]	PUNCT
ejpam-5192	288	4	v.	v.	CCONJ
ejpam-5192	288	5	popa	popa	NOUN
ejpam-5192	288	6	and	and	CCONJ
ejpam-5192	288	7	t.	t.	PROPN
ejpam-5192	288	8	noiri	noiri	PROPN
ejpam-5192	288	9	.	.	PUNCT
ejpam-5192	289	1	on	on	ADP
ejpam-5192	289	2	upper	upper	ADJ
ejpam-5192	289	3	and	and	CCONJ
ejpam-5192	289	4	lower	low	ADJ
ejpam-5192	289	5	almost	almost	ADV
ejpam-5192	289	6	quasi	quasi	ADJ
ejpam-5192	289	7	-	-	ADJ
ejpam-5192	289	8	continuous	continuous	ADJ
ejpam-5192	289	9	multifunctions	multifunction	NOUN
ejpam-5192	289	10	.	.	PUNCT
ejpam-5192	290	1	bulletin	bulletin	NOUN
ejpam-5192	290	2	of	of	ADP
ejpam-5192	290	3	the	the	DET
ejpam-5192	290	4	institute	institute	NOUN
ejpam-5192	290	5	of	of	ADP
ejpam-5192	290	6	mathematics	mathematics	PROPN
ejpam-5192	290	7	,	,	PUNCT
ejpam-5192	290	8	academia	academia	PROPN
ejpam-5192	290	9	sinica	sinica	PROPN
ejpam-5192	290	10	,	,	PUNCT
ejpam-5192	290	11	21:337–349	21:337–349	NUM
ejpam-5192	290	12	,	,	PUNCT
ejpam-5192	290	13	1993	1993	NUM
ejpam-5192	290	14	.	.	PUNCT
ejpam-5192	291	1	[	[	X
ejpam-5192	291	2	24	24	NUM
ejpam-5192	291	3	]	]	PUNCT
ejpam-5192	291	4	v.	v.	CCONJ
ejpam-5192	291	5	popa	popa	NOUN
ejpam-5192	291	6	and	and	CCONJ
ejpam-5192	291	7	t.	t.	PROPN
ejpam-5192	291	8	noiri	noiri	PROPN
ejpam-5192	291	9	.	.	PUNCT
ejpam-5192	292	1	on	on	ADP
ejpam-5192	292	2	upper	upper	ADJ
ejpam-5192	292	3	and	and	CCONJ
ejpam-5192	292	4	lower	low	ADJ
ejpam-5192	292	5	almost	almost	ADV
ejpam-5192	292	6	α	α	ADJ
ejpam-5192	292	7	-	-	ADJ
ejpam-5192	292	8	continuous	continuous	ADJ
ejpam-5192	292	9	multifunctions	multifunction	NOUN
ejpam-5192	292	10	.	.	PUNCT
ejpam-5192	293	1	demonstratio	demonstratio	PROPN
ejpam-5192	293	2	mathematica	mathematica	PROPN
ejpam-5192	293	3	,	,	PUNCT
ejpam-5192	293	4	29:381–396	29:381–396	PROPN
ejpam-5192	293	5	,	,	PUNCT
ejpam-5192	293	6	1996	1996	NUM
ejpam-5192	293	7	.	.	PUNCT
ejpam-5192	294	1	[	[	X
ejpam-5192	294	2	25	25	NUM
ejpam-5192	294	3	]	]	PUNCT
ejpam-5192	294	4	v.	v.	CCONJ
ejpam-5192	294	5	popa	popa	NOUN
ejpam-5192	294	6	and	and	CCONJ
ejpam-5192	294	7	t.	t.	PROPN
ejpam-5192	294	8	noiri	noiri	PROPN
ejpam-5192	294	9	.	.	PUNCT
ejpam-5192	295	1	on	on	ADP
ejpam-5192	295	2	upper	upper	ADJ
ejpam-5192	295	3	and	and	CCONJ
ejpam-5192	295	4	lower	low	ADJ
ejpam-5192	295	5	weakly	weakly	ADJ
ejpam-5192	295	6	β	β	ADJ
ejpam-5192	295	7	-	-	ADJ
ejpam-5192	295	8	continuous	continuous	ADJ
ejpam-5192	295	9	multifunctions	multifunction	NOUN
ejpam-5192	295	10	.	.	PUNCT
ejpam-5192	296	1	annales	annales	PROPN
ejpam-5192	296	2	universitatis	universitatis	PROPN
ejpam-5192	296	3	scientiarum	scientiarum	PROPN
ejpam-5192	296	4	budapestinensis	budapestinensis	PROPN
ejpam-5192	296	5	,	,	PUNCT
ejpam-5192	296	6	43:25–48	43:25–48	PROPN
ejpam-5192	296	7	,	,	PUNCT
ejpam-5192	296	8	2000	2000	NUM
ejpam-5192	296	9	.	.	PUNCT
ejpam-5192	297	1	[	[	X
ejpam-5192	297	2	26	26	NUM
ejpam-5192	297	3	]	]	PUNCT
ejpam-5192	297	4	v.	v.	CCONJ
ejpam-5192	297	5	popa	popa	NOUN
ejpam-5192	297	6	,	,	PUNCT
ejpam-5192	297	7	t.	t.	PROPN
ejpam-5192	297	8	noiri	noiri	PROPN
ejpam-5192	297	9	,	,	PUNCT
ejpam-5192	297	10	and	and	CCONJ
ejpam-5192	297	11	m.	m.	NOUN
ejpam-5192	297	12	ganster	ganster	NOUN
ejpam-5192	297	13	.	.	PUNCT
ejpam-5192	298	1	on	on	ADP
ejpam-5192	298	2	upper	upper	ADJ
ejpam-5192	298	3	and	and	CCONJ
ejpam-5192	298	4	lower	low	ADJ
ejpam-5192	298	5	almost	almost	ADV
ejpam-5192	298	6	precontinuous	precontinuous	ADJ
ejpam-5192	298	7	multifunctions	multifunction	NOUN
ejpam-5192	298	8	.	.	PUNCT
ejpam-5192	299	1	far	far	PROPN
ejpam-5192	299	2	east	east	PROPN
ejpam-5192	299	3	journal	journal	PROPN
ejpam-5192	299	4	of	of	ADP
ejpam-5192	299	5	mathematical	mathematical	ADJ
ejpam-5192	299	6	sciences	science	NOUN
ejpam-5192	299	7	,	,	PUNCT
ejpam-5192	299	8	special	special	ADJ
ejpam-5192	299	9	volume(part	volume(part	NOUN
ejpam-5192	299	10	i):49–68	i):49–68	NOUN
ejpam-5192	299	11	,	,	PUNCT
ejpam-5192	299	12	1997	1997	NUM
ejpam-5192	299	13	.	.	PUNCT
ejpam-5192	300	1	[	[	X
ejpam-5192	300	2	27	27	NUM
ejpam-5192	300	3	]	]	X
ejpam-5192	300	4	v.	v.	CCONJ
ejpam-5192	300	5	popa	popa	NOUN
ejpam-5192	300	6	,	,	PUNCT
ejpam-5192	300	7	t.	t.	PROPN
ejpam-5192	300	8	noiri	noiri	PROPN
ejpam-5192	300	9	,	,	PUNCT
ejpam-5192	300	10	m.	m.	NOUN
ejpam-5192	300	11	ganster	ganster	NOUN
ejpam-5192	300	12	,	,	PUNCT
ejpam-5192	300	13	and	and	CCONJ
ejpam-5192	300	14	k.	k.	PROPN
ejpam-5192	300	15	dlaska	dlaska	PROPN
ejpam-5192	300	16	.	.	PUNCT
ejpam-5192	301	1	on	on	ADP
ejpam-5192	301	2	upper	upper	ADJ
ejpam-5192	301	3	and	and	CCONJ
ejpam-5192	301	4	lower	low	ADJ
ejpam-5192	301	5	θ	θ	ADJ
ejpam-5192	301	6	-	-	PUNCT
ejpam-5192	301	7	irresolute	irresolute	ADJ
ejpam-5192	301	8	multifunctions	multifunction	NOUN
ejpam-5192	301	9	.	.	PUNCT
ejpam-5192	302	1	journal	journal	PROPN
ejpam-5192	302	2	of	of	ADP
ejpam-5192	302	3	institute	institute	PROPN
ejpam-5192	302	4	of	of	ADP
ejpam-5192	302	5	mathematics	mathematics	PROPN
ejpam-5192	302	6	&	&	CCONJ
ejpam-5192	302	7	computer	computer	PROPN
ejpam-5192	302	8	sciences	sciences	PROPN
ejpam-5192	302	9	.	.	PUNCT
ejpam-5192	303	1	mathematics	mathematic	NOUN
ejpam-5192	303	2	series	series	PROPN
ejpam-5192	303	3	,	,	PUNCT
ejpam-5192	303	4	6:137–149	6:137–149	NOUN
ejpam-5192	303	5	,	,	PUNCT
ejpam-5192	303	6	1993	1993	NUM
ejpam-5192	303	7	.	.	PUNCT
ejpam-5192	304	1	[	[	X
ejpam-5192	304	2	28	28	NUM
ejpam-5192	304	3	]	]	X
ejpam-5192	304	4	m.	m.	NOUN
ejpam-5192	304	5	k.	k.	PROPN
ejpam-5192	304	6	singal	singal	PROPN
ejpam-5192	304	7	and	and	CCONJ
ejpam-5192	304	8	a.	a.	PROPN
ejpam-5192	304	9	r.	r.	PROPN
ejpam-5192	304	10	singal	singal	PROPN
ejpam-5192	304	11	.	.	PUNCT
ejpam-5192	305	1	almost	almost	ADV
ejpam-5192	305	2	continuous	continuous	ADJ
ejpam-5192	305	3	mappings	mapping	NOUN
ejpam-5192	305	4	.	.	PUNCT
ejpam-5192	306	1	yokohama	yokohama	PROPN
ejpam-5192	306	2	mathematical	mathematical	PROPN
ejpam-5192	306	3	journal	journal	PROPN
ejpam-5192	306	4	,	,	PUNCT
ejpam-5192	306	5	16:63–73	16:63–73	PROPN
ejpam-5192	306	6	,	,	PUNCT
ejpam-5192	306	7	1968	1968	NUM
ejpam-5192	306	8	.	.	PUNCT
ejpam-5192	307	1	[	[	X
ejpam-5192	307	2	29	29	NUM
ejpam-5192	307	3	]	]	X
ejpam-5192	307	4	c.	c.	PROPN
ejpam-5192	307	5	viriyapong	viriyapong	PROPN
ejpam-5192	307	6	and	and	CCONJ
ejpam-5192	307	7	c.	c.	PROPN
ejpam-5192	307	8	boonpok	boonpok	PROPN
ejpam-5192	307	9	.	.	PUNCT
ejpam-5192	308	1	(	(	PUNCT
ejpam-5192	308	2	τ1	τ1	NOUN
ejpam-5192	308	3	,	,	PUNCT
ejpam-5192	308	4	τ2)α	τ2)α	NOUN
ejpam-5192	308	5	-	-	PUNCT
ejpam-5192	308	6	continuity	continuity	NOUN
ejpam-5192	308	7	for	for	ADP
ejpam-5192	308	8	multifunctions	multifunction	NOUN
ejpam-5192	308	9	.	.	PUNCT
ejpam-5192	309	1	journal	journal	PROPN
ejpam-5192	309	2	of	of	ADP
ejpam-5192	309	3	mathematics	mathematic	NOUN
ejpam-5192	309	4	,	,	PUNCT
ejpam-5192	309	5	2020:6285763	2020:6285763	NUM
ejpam-5192	309	6	,	,	PUNCT
ejpam-5192	309	7	2020	2020	NUM
ejpam-5192	309	8	.	.	PUNCT
ejpam-5192	310	1	[	[	X
ejpam-5192	310	2	30	30	NUM
ejpam-5192	310	3	]	]	X
ejpam-5192	310	4	n.	n.	PROPN
ejpam-5192	310	5	viriyapong	viriyapong	PROPN
ejpam-5192	310	6	,	,	PUNCT
ejpam-5192	310	7	s.	s.	PROPN
ejpam-5192	310	8	sompong	sompong	PROPN
ejpam-5192	310	9	,	,	PUNCT
ejpam-5192	310	10	and	and	CCONJ
ejpam-5192	310	11	c.	c.	PROPN
ejpam-5192	310	12	boonpok	boonpok	PROPN
ejpam-5192	310	13	.	.	PUNCT
ejpam-5192	311	1	(	(	PUNCT
ejpam-5192	311	2	τ1	τ1	NOUN
ejpam-5192	311	3	,	,	PUNCT
ejpam-5192	311	4	τ2)-extremal	τ2)-extremal	ADJ
ejpam-5192	311	5	disconnectedness	disconnectedness	NOUN
ejpam-5192	311	6	in	in	ADP
ejpam-5192	311	7	bitopological	bitopological	ADJ
ejpam-5192	311	8	spaces	space	NOUN
ejpam-5192	311	9	.	.	PUNCT
ejpam-5192	312	1	international	international	ADJ
ejpam-5192	312	2	journal	journal	PROPN
ejpam-5192	312	3	of	of	ADP
ejpam-5192	312	4	mathematics	mathematic	NOUN
ejpam-5192	312	5	and	and	CCONJ
ejpam-5192	312	6	computer	computer	NOUN
ejpam-5192	312	7	science	science	NOUN
ejpam-5192	312	8	,	,	PUNCT
ejpam-5192	312	9	19(3):855–860	19(3):855–860	PROPN
ejpam-5192	312	10	,	,	PUNCT
ejpam-5192	312	11	2024	2024	NUM
ejpam-5192	312	12	.	.	PUNCT