id	sid	tid	token	lemma	pos
ejpam-5393	1	1	european	european	PROPN
ejpam-5393	1	2	journal	journal	PROPN
ejpam-5393	1	3	of	of	ADP
ejpam-5393	1	4	pure	pure	ADJ
ejpam-5393	1	5	and	and	CCONJ
ejpam-5393	1	6	applied	apply	VERB
ejpam-5393	1	7	mathematics	mathematic	NOUN
ejpam-5393	1	8	vol	vol	NOUN
ejpam-5393	1	9	.	.	PROPN
ejpam-5393	2	1	17	17	NUM
ejpam-5393	2	2	,	,	PUNCT
ejpam-5393	2	3	no	no	INTJ
ejpam-5393	2	4	.	.	NOUN
ejpam-5393	2	5	4	4	NUM
ejpam-5393	2	6	,	,	PUNCT
ejpam-5393	2	7	2024	2024	NUM
ejpam-5393	2	8	,	,	PUNCT
ejpam-5393	2	9	3242	3242	NUM
ejpam-5393	2	10	-	-	SYM
ejpam-5393	2	11	3253	3253	NUM
ejpam-5393	2	12	issn	issn	PROPN
ejpam-5393	2	13	1307	1307	NUM
ejpam-5393	2	14	-	-	SYM
ejpam-5393	2	15	5543	5543	NUM
ejpam-5393	2	16	–	–	PUNCT
ejpam-5393	2	17	ejpam.com	ejpam.com	X
ejpam-5393	2	18	published	publish	VERB
ejpam-5393	2	19	by	by	ADP
ejpam-5393	2	20	new	new	PROPN
ejpam-5393	2	21	york	york	PROPN
ejpam-5393	2	22	business	business	PROPN
ejpam-5393	2	23	global	global	PROPN
ejpam-5393	2	24	c	c	NOUN
ejpam-5393	2	25	-	-	PUNCT
ejpam-5393	2	26	quasi	quasi	NOUN
ejpam-5393	2	27	(	(	PUNCT
ejpam-5393	2	28	τ1	τ1	PROPN
ejpam-5393	2	29	,	,	PUNCT
ejpam-5393	2	30	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	2	31	multifunctions	multifunction	NOUN
ejpam-5393	2	32	prapart	prapart	VERB
ejpam-5393	2	33	pue	pue	PROPN
ejpam-5393	2	34	-	-	PUNCT
ejpam-5393	2	35	on1	on1	PROPN
ejpam-5393	2	36	,	,	PUNCT
ejpam-5393	2	37	areeyuth	areeyuth	NOUN
ejpam-5393	2	38	sama	sama	NOUN
ejpam-5393	2	39	-	-	PUNCT
ejpam-5393	2	40	ae2	ae2	PROPN
ejpam-5393	2	41	,	,	PUNCT
ejpam-5393	2	42	chawalit	chawalit	VERB
ejpam-5393	2	43	boonpok1,∗	boonpok1,∗	NOUN
ejpam-5393	2	44	1	1	NUM
ejpam-5393	2	45	mathematics	mathematic	NOUN
ejpam-5393	2	46	and	and	CCONJ
ejpam-5393	2	47	applied	apply	VERB
ejpam-5393	2	48	mathematics	mathematics	PROPN
ejpam-5393	2	49	research	research	NOUN
ejpam-5393	2	50	unit	unit	NOUN
ejpam-5393	2	51	,	,	PUNCT
ejpam-5393	2	52	department	department	NOUN
ejpam-5393	2	53	of	of	ADP
ejpam-5393	2	54	mathematics	mathematic	NOUN
ejpam-5393	2	55	,	,	PUNCT
ejpam-5393	2	56	faculty	faculty	NOUN
ejpam-5393	2	57	of	of	ADP
ejpam-5393	2	58	science	science	NOUN
ejpam-5393	2	59	,	,	PUNCT
ejpam-5393	2	60	mahasarakham	mahasarakham	PROPN
ejpam-5393	2	61	university	university	PROPN
ejpam-5393	2	62	,	,	PUNCT
ejpam-5393	2	63	maha	maha	PROPN
ejpam-5393	2	64	sarakham	sarakham	PROPN
ejpam-5393	2	65	,	,	PUNCT
ejpam-5393	2	66	44150	44150	NUM
ejpam-5393	2	67	,	,	PUNCT
ejpam-5393	2	68	thailand	thailand	PROPN
ejpam-5393	2	69	2	2	NUM
ejpam-5393	2	70	department	department	NOUN
ejpam-5393	2	71	of	of	ADP
ejpam-5393	2	72	mathematics	mathematic	NOUN
ejpam-5393	2	73	and	and	CCONJ
ejpam-5393	2	74	computer	computer	NOUN
ejpam-5393	2	75	science	science	NOUN
ejpam-5393	2	76	,	,	PUNCT
ejpam-5393	2	77	faculty	faculty	NOUN
ejpam-5393	2	78	of	of	ADP
ejpam-5393	2	79	science	science	NOUN
ejpam-5393	2	80	and	and	CCONJ
ejpam-5393	2	81	technology	technology	NOUN
ejpam-5393	2	82	,	,	PUNCT
ejpam-5393	2	83	prince	prince	NOUN
ejpam-5393	2	84	of	of	ADP
ejpam-5393	2	85	songkla	songkla	PROPN
ejpam-5393	2	86	university	university	PROPN
ejpam-5393	2	87	,	,	PUNCT
ejpam-5393	2	88	pattani	pattani	NOUN
ejpam-5393	2	89	campus	campus	NOUN
ejpam-5393	2	90	,	,	PUNCT
ejpam-5393	2	91	pattani	pattani	NOUN
ejpam-5393	2	92	,	,	PUNCT
ejpam-5393	2	93	94000	94000	NUM
ejpam-5393	2	94	,	,	PUNCT
ejpam-5393	2	95	thailand	thailand	PROPN
ejpam-5393	2	96	abstract	abstract	PROPN
ejpam-5393	2	97	.	.	PUNCT
ejpam-5393	3	1	our	our	PRON
ejpam-5393	3	2	main	main	ADJ
ejpam-5393	3	3	purpose	purpose	NOUN
ejpam-5393	3	4	is	be	AUX
ejpam-5393	3	5	to	to	PART
ejpam-5393	3	6	introduce	introduce	VERB
ejpam-5393	3	7	the	the	DET
ejpam-5393	3	8	concepts	concept	NOUN
ejpam-5393	3	9	of	of	ADP
ejpam-5393	3	10	upper	upper	ADJ
ejpam-5393	3	11	and	and	CCONJ
ejpam-5393	3	12	lower	low	ADJ
ejpam-5393	3	13	c	c	NOUN
ejpam-5393	3	14	-	-	PUNCT
ejpam-5393	3	15	quasi	quasi	ADJ
ejpam-5393	3	16	(	(	PUNCT
ejpam-5393	3	17	τ1	τ1	NOUN
ejpam-5393	3	18	,	,	PUNCT
ejpam-5393	3	19	τ2)continuous	τ2)continuous	ADJ
ejpam-5393	3	20	multifunctions	multifunction	NOUN
ejpam-5393	3	21	.	.	PUNCT
ejpam-5393	4	1	moerover	moerover	NOUN
ejpam-5393	4	2	,	,	PUNCT
ejpam-5393	4	3	several	several	ADJ
ejpam-5393	4	4	characterizations	characterization	NOUN
ejpam-5393	4	5	of	of	ADP
ejpam-5393	4	6	upper	upper	ADJ
ejpam-5393	4	7	and	and	CCONJ
ejpam-5393	4	8	lower	low	ADJ
ejpam-5393	4	9	c	c	NOUN
ejpam-5393	4	10	-	-	PUNCT
ejpam-5393	4	11	quasi	quasi	ADJ
ejpam-5393	4	12	(	(	PUNCT
ejpam-5393	4	13	τ1	τ1	NOUN
ejpam-5393	4	14	,	,	PUNCT
ejpam-5393	4	15	τ2)continuous	τ2)continuous	ADJ
ejpam-5393	4	16	multifunctions	multifunction	NOUN
ejpam-5393	4	17	are	be	AUX
ejpam-5393	4	18	established	establish	VERB
ejpam-5393	4	19	.	.	PUNCT
ejpam-5393	5	1	2020	2020	NUM
ejpam-5393	5	2	mathematics	mathematics	PROPN
ejpam-5393	5	3	subject	subject	NOUN
ejpam-5393	5	4	classifications	classification	NOUN
ejpam-5393	5	5	:	:	PUNCT
ejpam-5393	5	6	54c08	54c08	NUM
ejpam-5393	5	7	,	,	PUNCT
ejpam-5393	5	8	54c60	54c60	NUM
ejpam-5393	5	9	,	,	PUNCT
ejpam-5393	5	10	54e55	54e55	NUM
ejpam-5393	5	11	key	key	ADJ
ejpam-5393	5	12	words	word	NOUN
ejpam-5393	5	13	and	and	CCONJ
ejpam-5393	5	14	phrases	phrase	NOUN
ejpam-5393	5	15	:	:	PUNCT
ejpam-5393	5	16	τ1τ2	τ1τ2	ADJ
ejpam-5393	5	17	-	-	ADJ
ejpam-5393	5	18	open	open	ADJ
ejpam-5393	5	19	set	set	NOUN
ejpam-5393	5	20	,	,	PUNCT
ejpam-5393	5	21	upper	upper	ADJ
ejpam-5393	5	22	c	c	NOUN
ejpam-5393	5	23	-	-	PUNCT
ejpam-5393	5	24	quasi	quasi	ADJ
ejpam-5393	5	25	(	(	PUNCT
ejpam-5393	5	26	τ1	τ1	PROPN
ejpam-5393	5	27	,	,	PUNCT
ejpam-5393	5	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	5	29	multifunction	multifunction	NOUN
ejpam-5393	5	30	,	,	PUNCT
ejpam-5393	5	31	lower	low	ADJ
ejpam-5393	5	32	c	c	NOUN
ejpam-5393	5	33	-	-	PUNCT
ejpam-5393	5	34	quasi	quasi	ADJ
ejpam-5393	5	35	(	(	PUNCT
ejpam-5393	5	36	τ1	τ1	PROPN
ejpam-5393	5	37	,	,	PUNCT
ejpam-5393	5	38	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	5	39	multifunction	multifunction	NOUN
ejpam-5393	5	40	1	1	NUM
ejpam-5393	5	41	.	.	PUNCT
ejpam-5393	6	1	introduction	introduction	NOUN
ejpam-5393	6	2	it	it	PRON
ejpam-5393	6	3	is	be	AUX
ejpam-5393	6	4	well	well	ADV
ejpam-5393	6	5	-	-	PUNCT
ejpam-5393	6	6	known	know	VERB
ejpam-5393	6	7	that	that	SCONJ
ejpam-5393	6	8	the	the	DET
ejpam-5393	6	9	branch	branch	NOUN
ejpam-5393	6	10	of	of	ADP
ejpam-5393	6	11	mathematics	mathematic	NOUN
ejpam-5393	6	12	called	call	VERB
ejpam-5393	6	13	topology	topology	NOUN
ejpam-5393	6	14	is	be	AUX
ejpam-5393	6	15	concerned	concern	VERB
ejpam-5393	6	16	with	with	ADP
ejpam-5393	6	17	all	all	DET
ejpam-5393	6	18	questions	question	NOUN
ejpam-5393	6	19	directly	directly	ADV
ejpam-5393	6	20	or	or	CCONJ
ejpam-5393	6	21	indirectly	indirectly	ADV
ejpam-5393	6	22	related	relate	VERB
ejpam-5393	6	23	to	to	ADP
ejpam-5393	6	24	continuity	continuity	NOUN
ejpam-5393	6	25	.	.	PUNCT
ejpam-5393	7	1	continuity	continuity	NOUN
ejpam-5393	7	2	is	be	AUX
ejpam-5393	7	3	an	an	DET
ejpam-5393	7	4	important	important	ADJ
ejpam-5393	7	5	concept	concept	NOUN
ejpam-5393	7	6	for	for	ADP
ejpam-5393	7	7	the	the	DET
ejpam-5393	7	8	study	study	NOUN
ejpam-5393	7	9	and	and	CCONJ
ejpam-5393	7	10	investigation	investigation	NOUN
ejpam-5393	7	11	in	in	ADP
ejpam-5393	7	12	the	the	DET
ejpam-5393	7	13	theory	theory	NOUN
ejpam-5393	7	14	of	of	ADP
ejpam-5393	7	15	classical	classical	ADJ
ejpam-5393	7	16	point	point	NOUN
ejpam-5393	7	17	set	set	VERB
ejpam-5393	7	18	topology	topology	NOUN
ejpam-5393	7	19	.	.	PUNCT
ejpam-5393	8	1	generalization	generalization	NOUN
ejpam-5393	8	2	of	of	ADP
ejpam-5393	8	3	this	this	DET
ejpam-5393	8	4	concept	concept	NOUN
ejpam-5393	8	5	by	by	ADP
ejpam-5393	8	6	using	use	VERB
ejpam-5393	8	7	stronger	strong	ADJ
ejpam-5393	8	8	and	and	CCONJ
ejpam-5393	8	9	weaker	weak	ADJ
ejpam-5393	8	10	forms	form	NOUN
ejpam-5393	8	11	of	of	ADP
ejpam-5393	8	12	open	open	ADJ
ejpam-5393	8	13	sets	set	NOUN
ejpam-5393	8	14	.	.	PUNCT
ejpam-5393	9	1	many	many	ADJ
ejpam-5393	9	2	authors	author	NOUN
ejpam-5393	9	3	have	have	AUX
ejpam-5393	9	4	researched	research	VERB
ejpam-5393	9	5	and	and	CCONJ
ejpam-5393	9	6	investigated	investigate	VERB
ejpam-5393	9	7	several	several	ADJ
ejpam-5393	9	8	stronger	strong	ADJ
ejpam-5393	9	9	and	and	CCONJ
ejpam-5393	9	10	weaker	weak	ADJ
ejpam-5393	9	11	forms	form	NOUN
ejpam-5393	9	12	of	of	ADP
ejpam-5393	9	13	continuous	continuous	ADJ
ejpam-5393	9	14	functions	function	NOUN
ejpam-5393	9	15	and	and	CCONJ
ejpam-5393	9	16	multifunctions	multifunction	NOUN
ejpam-5393	9	17	.	.	PUNCT
ejpam-5393	10	1	viriyapong	viriyapong	PROPN
ejpam-5393	10	2	and	and	CCONJ
ejpam-5393	10	3	boonpok	boonpok	VERB
ejpam-5393	11	1	[	[	X
ejpam-5393	11	2	58	58	NUM
ejpam-5393	11	3	]	]	PUNCT
ejpam-5393	11	4	investigated	investigate	VERB
ejpam-5393	11	5	some	some	DET
ejpam-5393	11	6	characterizations	characterization	NOUN
ejpam-5393	11	7	of	of	ADP
ejpam-5393	11	8	(	(	PUNCT
ejpam-5393	11	9	λ	λ	PROPN
ejpam-5393	11	10	,	,	PUNCT
ejpam-5393	11	11	sp)-continuous	sp)-continuous	ADJ
ejpam-5393	11	12	functions	function	NOUN
ejpam-5393	11	13	by	by	ADP
ejpam-5393	11	14	utilizing	utilize	VERB
ejpam-5393	11	15	the	the	DET
ejpam-5393	11	16	notions	notion	NOUN
ejpam-5393	11	17	of	of	ADP
ejpam-5393	11	18	(	(	PUNCT
ejpam-5393	11	19	λ	λ	PROPN
ejpam-5393	11	20	,	,	PUNCT
ejpam-5393	11	21	sp)-open	sp)-open	ADJ
ejpam-5393	11	22	sets	set	NOUN
ejpam-5393	11	23	and	and	CCONJ
ejpam-5393	11	24	(	(	PUNCT
ejpam-5393	11	25	λ	λ	PROPN
ejpam-5393	11	26	,	,	PUNCT
ejpam-5393	11	27	sp)closed	sp)close	VERB
ejpam-5393	11	28	sets	set	NOUN
ejpam-5393	11	29	due	due	ADP
ejpam-5393	11	30	to	to	ADP
ejpam-5393	11	31	boonpok	boonpok	NOUN
ejpam-5393	11	32	and	and	CCONJ
ejpam-5393	11	33	khampakdee	khampakdee	NOUN
ejpam-5393	11	34	[	[	X
ejpam-5393	11	35	13	13	NUM
ejpam-5393	11	36	]	]	PUNCT
ejpam-5393	11	37	.	.	PUNCT
ejpam-5393	12	1	dungthaisong	dungthaisong	NOUN
ejpam-5393	12	2	et	et	PROPN
ejpam-5393	12	3	al	al	PROPN
ejpam-5393	12	4	.	.	PUNCT
ejpam-5393	13	1	[	[	X
ejpam-5393	13	2	33	33	NUM
ejpam-5393	13	3	]	]	PUNCT
ejpam-5393	13	4	introduced	introduce	VERB
ejpam-5393	13	5	and	and	CCONJ
ejpam-5393	13	6	studied	study	VERB
ejpam-5393	13	7	the	the	DET
ejpam-5393	13	8	concept	concept	NOUN
ejpam-5393	13	9	of	of	ADP
ejpam-5393	13	10	g(m	g(m	ADJ
ejpam-5393	13	11	,	,	PUNCT
ejpam-5393	13	12	n)-continuous	n)-continuous	ADJ
ejpam-5393	13	13	functions	function	NOUN
ejpam-5393	13	14	.	.	PUNCT
ejpam-5393	14	1	duangphui	duangphui	NOUN
ejpam-5393	14	2	et	et	PROPN
ejpam-5393	14	3	al	al	PROPN
ejpam-5393	14	4	.	.	PUNCT
ejpam-5393	15	1	[	[	X
ejpam-5393	15	2	32	32	NUM
ejpam-5393	15	3	]	]	PUNCT
ejpam-5393	15	4	introduced	introduce	VERB
ejpam-5393	15	5	and	and	CCONJ
ejpam-5393	15	6	investigated	investigate	VERB
ejpam-5393	15	7	the	the	DET
ejpam-5393	15	8	notion	notion	NOUN
ejpam-5393	15	9	of	of	ADP
ejpam-5393	15	10	(	(	PUNCT
ejpam-5393	15	11	µ	µ	NOUN
ejpam-5393	15	12	,	,	PUNCT
ejpam-5393	15	13	µ′)(m	µ′)(m	VERB
ejpam-5393	15	14	,	,	PUNCT
ejpam-5393	15	15	n)-continuous	n)-continuous	ADJ
ejpam-5393	15	16	functions	function	NOUN
ejpam-5393	15	17	.	.	PUNCT
ejpam-5393	16	1	moreover	moreover	ADV
ejpam-5393	16	2	,	,	PUNCT
ejpam-5393	16	3	several	several	ADJ
ejpam-5393	16	4	characterizations	characterization	NOUN
ejpam-5393	16	5	of	of	ADP
ejpam-5393	16	6	almost	almost	ADV
ejpam-5393	16	7	(	(	PUNCT
ejpam-5393	16	8	λ	λ	PROPN
ejpam-5393	16	9	,	,	PUNCT
ejpam-5393	16	10	p)-continuous	p)-continuous	ADJ
ejpam-5393	16	11	functions	function	NOUN
ejpam-5393	16	12	,	,	PUNCT
ejpam-5393	16	13	strongly	strongly	ADV
ejpam-5393	16	14	θ(λ	θ(λ	PROPN
ejpam-5393	16	15	,	,	PUNCT
ejpam-5393	16	16	p)-continuous	p)-continuous	ADJ
ejpam-5393	16	17	functions	function	NOUN
ejpam-5393	16	18	,	,	PUNCT
ejpam-5393	16	19	almost	almost	ADV
ejpam-5393	16	20	strongly	strongly	ADV
ejpam-5393	16	21	θ(λ	θ(λ	VERB
ejpam-5393	16	22	,	,	PUNCT
ejpam-5393	16	23	p)-continuous	p)-continuous	ADJ
ejpam-5393	16	24	functions	function	NOUN
ejpam-5393	16	25	,	,	PUNCT
ejpam-5393	16	26	θ(λ	θ(λ	PROPN
ejpam-5393	16	27	,	,	PUNCT
ejpam-5393	16	28	p)-continuous	p)-continuous	ADJ
ejpam-5393	16	29	functions	function	NOUN
ejpam-5393	16	30	,	,	PUNCT
ejpam-5393	16	31	weakly	weakly	ADJ
ejpam-5393	16	32	(	(	PUNCT
ejpam-5393	16	33	λ	λ	PROPN
ejpam-5393	16	34	,	,	PUNCT
ejpam-5393	16	35	b)-continuous	b)-continuous	ADJ
ejpam-5393	16	36	functions	function	NOUN
ejpam-5393	16	37	,	,	PUNCT
ejpam-5393	16	38	θ(⋆)-precontinuous	θ(⋆)-precontinuous	ADJ
ejpam-5393	16	39	functions	function	NOUN
ejpam-5393	16	40	,	,	PUNCT
ejpam-5393	16	41	(	(	PUNCT
ejpam-5393	16	42	λ	λ	NOUN
ejpam-5393	16	43	,	,	PUNCT
ejpam-5393	16	44	p(⋆))-continuous	p(⋆))-continuous	ADJ
ejpam-5393	16	45	functions	function	NOUN
ejpam-5393	16	46	,	,	PUNCT
ejpam-5393	16	47	⋆-continuous	⋆-continuous	ADJ
ejpam-5393	16	48	functions	function	NOUN
ejpam-5393	16	49	,	,	PUNCT
ejpam-5393	16	50	θ	θ	PROPN
ejpam-5393	16	51	-	-	ADJ
ejpam-5393	16	52	i	i	NOUN
ejpam-5393	16	53	-continuous	-continuous	ADJ
ejpam-5393	16	54	functions	function	NOUN
ejpam-5393	16	55	,	,	PUNCT
ejpam-5393	16	56	almost	almost	ADV
ejpam-5393	16	57	(	(	PUNCT
ejpam-5393	16	58	g	g	NOUN
ejpam-5393	16	59	,	,	PUNCT
ejpam-5393	16	60	m)-continuous	m)-continuous	ADJ
ejpam-5393	16	61	functions	function	NOUN
ejpam-5393	16	62	,	,	PUNCT
ejpam-5393	16	63	pairwise	pairwise	PROPN
ejpam-5393	16	64	m	m	PROPN
ejpam-5393	16	65	-continuous	-continuous	ADJ
ejpam-5393	16	66	functions	function	NOUN
ejpam-5393	16	67	,	,	PUNCT
ejpam-5393	16	68	(	(	PUNCT
ejpam-5393	16	69	τ1	τ1	NOUN
ejpam-5393	16	70	,	,	PUNCT
ejpam-5393	16	71	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	16	72	functions	function	NOUN
ejpam-5393	16	73	,	,	PUNCT
ejpam-5393	16	74	almost	almost	ADV
ejpam-5393	16	75	(	(	PUNCT
ejpam-5393	16	76	τ1	τ1	NOUN
ejpam-5393	16	77	,	,	PUNCT
ejpam-5393	16	78	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	16	79	functions	function	NOUN
ejpam-5393	16	80	,	,	PUNCT
ejpam-5393	16	81	weakly	weakly	ADJ
ejpam-5393	16	82	(	(	PUNCT
ejpam-5393	16	83	τ1	τ1	NOUN
ejpam-5393	16	84	,	,	PUNCT
ejpam-5393	16	85	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	16	86	functions	function	NOUN
ejpam-5393	16	87	,	,	PUNCT
ejpam-5393	16	88	almost	almost	ADV
ejpam-5393	16	89	quasi	quasi	NOUN
ejpam-5393	16	90	(	(	PUNCT
ejpam-5393	16	91	τ1	τ1	NOUN
ejpam-5393	16	92	,	,	PUNCT
ejpam-5393	16	93	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	16	94	functions	function	NOUN
ejpam-5393	16	95	∗corresponding	∗corresponde	VERB
ejpam-5393	16	96	author	author	NOUN
ejpam-5393	16	97	.	.	PUNCT
ejpam-5393	17	1	doi	doi	NOUN
ejpam-5393	17	2	:	:	PUNCT
ejpam-5393	17	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5393	https://doi.org/10.29020/nybg.ejpam.v17i4.5393	ADJ
ejpam-5393	17	4	email	email	NOUN
ejpam-5393	17	5	addresses	address	NOUN
ejpam-5393	17	6	:	:	PUNCT
ejpam-5393	17	7	prapart.p@msu.ac.th	prapart.p@msu.ac.th	PROPN
ejpam-5393	17	8	(	(	PUNCT
ejpam-5393	17	9	p.	p.	NOUN
ejpam-5393	17	10	pue	pue	NOUN
ejpam-5393	17	11	-	-	PUNCT
ejpam-5393	17	12	on	on	ADP
ejpam-5393	17	13	)	)	PUNCT
ejpam-5393	17	14	,	,	PUNCT
ejpam-5393	17	15	areeyuth.s@psu.ac.th	areeyuth.s@psu.ac.th	X
ejpam-5393	17	16	(	(	PUNCT
ejpam-5393	17	17	a.	a.	PROPN
ejpam-5393	17	18	sama	sama	PROPN
ejpam-5393	17	19	-	-	PUNCT
ejpam-5393	17	20	ae	ae	PROPN
ejpam-5393	17	21	)	)	PUNCT
ejpam-5393	17	22	,	,	PUNCT
ejpam-5393	17	23	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	PROPN
ejpam-5393	17	24	(	(	PUNCT
ejpam-5393	17	25	c.	c.	PROPN
ejpam-5393	17	26	boonpok	boonpok	PROPN
ejpam-5393	17	27	)	)	PUNCT
ejpam-5393	17	28	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5393	17	29	3242	3242	NUM
ejpam-5393	18	1	copyright	copyright	NOUN
ejpam-5393	18	2	:	:	PUNCT
ejpam-5393	18	3	©	©	PROPN
ejpam-5393	18	4	2024	2024	NUM
ejpam-5393	18	5	the	the	DET
ejpam-5393	18	6	author(s	author(s	NOUN
ejpam-5393	18	7	)	)	PUNCT
ejpam-5393	18	8	.	.	PUNCT
ejpam-5393	19	1	(	(	PUNCT
ejpam-5393	19	2	cc	cc	NOUN
ejpam-5393	19	3	by	by	ADP
ejpam-5393	19	4	-	-	PUNCT
ejpam-5393	19	5	nc	nc	PROPN
ejpam-5393	19	6	4.0	4.0	NUM
ejpam-5393	19	7	)	)	PUNCT
ejpam-5393	19	8	p.	p.	NOUN
ejpam-5393	19	9	pue	pue	NOUN
ejpam-5393	19	10	-	-	PUNCT
ejpam-5393	19	11	on	on	ADP
ejpam-5393	19	12	,	,	PUNCT
ejpam-5393	19	13	a.	a.	PROPN
ejpam-5393	19	14	sama	sama	PROPN
ejpam-5393	19	15	-	-	PUNCT
ejpam-5393	19	16	ae	ae	PROPN
ejpam-5393	19	17	,	,	PUNCT
ejpam-5393	19	18	c.	c.	PROPN
ejpam-5393	19	19	boonpok	boonpok	PROPN
ejpam-5393	19	20	/	/	SYM
ejpam-5393	19	21	eur	eur	PROPN
ejpam-5393	19	22	.	.	PUNCT
ejpam-5393	20	1	j.	j.	PROPN
ejpam-5393	20	2	pure	pure	PROPN
ejpam-5393	20	3	appl	appl	PROPN
ejpam-5393	20	4	.	.	PROPN
ejpam-5393	20	5	math	math	PROPN
ejpam-5393	20	6	,	,	PUNCT
ejpam-5393	20	7	17	17	NUM
ejpam-5393	20	8	(	(	PUNCT
ejpam-5393	20	9	4	4	NUM
ejpam-5393	20	10	)	)	PUNCT
ejpam-5393	20	11	(	(	PUNCT
ejpam-5393	20	12	2024	2024	NUM
ejpam-5393	20	13	)	)	PUNCT
ejpam-5393	20	14	,	,	PUNCT
ejpam-5393	20	15	3242	3242	NUM
ejpam-5393	20	16	-	-	SYM
ejpam-5393	20	17	3253	3253	NUM
ejpam-5393	20	18	3243	3243	NUM
ejpam-5393	20	19	and	and	CCONJ
ejpam-5393	20	20	weakly	weakly	ADJ
ejpam-5393	20	21	quasi	quasi	NOUN
ejpam-5393	20	22	(	(	PUNCT
ejpam-5393	20	23	τ1	τ1	PROPN
ejpam-5393	20	24	,	,	PUNCT
ejpam-5393	20	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	20	26	functions	function	NOUN
ejpam-5393	20	27	were	be	AUX
ejpam-5393	20	28	presented	present	VERB
ejpam-5393	20	29	in	in	ADP
ejpam-5393	20	30	[	[	X
ejpam-5393	20	31	53	53	NUM
ejpam-5393	20	32	]	]	PUNCT
ejpam-5393	20	33	,	,	PUNCT
ejpam-5393	20	34	[	[	X
ejpam-5393	20	35	55	55	NUM
ejpam-5393	20	36	]	]	PUNCT
ejpam-5393	20	37	,	,	PUNCT
ejpam-5393	20	38	[	[	X
ejpam-5393	20	39	17	17	NUM
ejpam-5393	20	40	]	]	PUNCT
ejpam-5393	20	41	,	,	PUNCT
ejpam-5393	20	42	[	[	X
ejpam-5393	20	43	49	49	NUM
ejpam-5393	20	44	]	]	PUNCT
ejpam-5393	20	45	,	,	PUNCT
ejpam-5393	20	46	[	[	X
ejpam-5393	20	47	26	26	NUM
ejpam-5393	20	48	]	]	PUNCT
ejpam-5393	20	49	,	,	PUNCT
ejpam-5393	20	50	[	[	X
ejpam-5393	20	51	12	12	NUM
ejpam-5393	20	52	]	]	PUNCT
ejpam-5393	20	53	,	,	PUNCT
ejpam-5393	20	54	[	[	X
ejpam-5393	20	55	9	9	NUM
ejpam-5393	20	56	]	]	PUNCT
ejpam-5393	20	57	,	,	PUNCT
ejpam-5393	20	58	[	[	X
ejpam-5393	20	59	11	11	NUM
ejpam-5393	20	60	]	]	PUNCT
ejpam-5393	20	61	,	,	PUNCT
ejpam-5393	20	62	[	[	X
ejpam-5393	20	63	5	5	NUM
ejpam-5393	20	64	]	]	PUNCT
ejpam-5393	20	65	,	,	PUNCT
ejpam-5393	20	66	[	[	X
ejpam-5393	20	67	2	2	NUM
ejpam-5393	20	68	]	]	PUNCT
ejpam-5393	20	69	,	,	PUNCT
ejpam-5393	20	70	[	[	X
ejpam-5393	20	71	3	3	NUM
ejpam-5393	20	72	]	]	PUNCT
ejpam-5393	20	73	,	,	PUNCT
ejpam-5393	20	74	[	[	X
ejpam-5393	20	75	27	27	NUM
ejpam-5393	20	76	]	]	PUNCT
ejpam-5393	20	77	,	,	PUNCT
ejpam-5393	20	78	[	[	X
ejpam-5393	20	79	24	24	NUM
ejpam-5393	20	80	]	]	PUNCT
ejpam-5393	20	81	,	,	PUNCT
ejpam-5393	20	82	[	[	X
ejpam-5393	20	83	19	19	NUM
ejpam-5393	20	84	]	]	PUNCT
ejpam-5393	20	85	,	,	PUNCT
ejpam-5393	20	86	[	[	X
ejpam-5393	20	87	39	39	NUM
ejpam-5393	20	88	]	]	PUNCT
ejpam-5393	20	89	and	and	CCONJ
ejpam-5393	21	1	[	[	X
ejpam-5393	21	2	31	31	NUM
ejpam-5393	21	3	]	]	PUNCT
ejpam-5393	21	4	,	,	PUNCT
ejpam-5393	21	5	respectively	respectively	ADV
ejpam-5393	21	6	.	.	PUNCT
ejpam-5393	21	7	gentry	gentry	NOUN
ejpam-5393	21	8	and	and	CCONJ
ejpam-5393	21	9	hoyle	hoyle	PROPN
ejpam-5393	21	10	iii	iii	PROPN
ejpam-5393	22	1	[	[	X
ejpam-5393	22	2	34	34	NUM
ejpam-5393	22	3	]	]	PUNCT
ejpam-5393	22	4	introduced	introduce	VERB
ejpam-5393	22	5	and	and	CCONJ
ejpam-5393	22	6	investigated	investigate	VERB
ejpam-5393	22	7	the	the	DET
ejpam-5393	22	8	concept	concept	NOUN
ejpam-5393	22	9	of	of	ADP
ejpam-5393	22	10	c	c	NOUN
ejpam-5393	22	11	-	-	PUNCT
ejpam-5393	22	12	continuous	continuous	ADJ
ejpam-5393	22	13	functions	function	NOUN
ejpam-5393	22	14	.	.	PUNCT
ejpam-5393	23	1	in	in	ADP
ejpam-5393	23	2	particular	particular	ADJ
ejpam-5393	23	3	,	,	PUNCT
ejpam-5393	23	4	some	some	DET
ejpam-5393	23	5	characterizations	characterization	NOUN
ejpam-5393	23	6	of	of	ADP
ejpam-5393	23	7	c	c	NOUN
ejpam-5393	23	8	-	-	PUNCT
ejpam-5393	23	9	continuous	continuous	ADJ
ejpam-5393	23	10	functions	function	NOUN
ejpam-5393	23	11	were	be	AUX
ejpam-5393	23	12	studied	study	VERB
ejpam-5393	23	13	in	in	ADP
ejpam-5393	23	14	[	[	X
ejpam-5393	23	15	41	41	NUM
ejpam-5393	23	16	]	]	PUNCT
ejpam-5393	23	17	,	,	PUNCT
ejpam-5393	24	1	[	[	X
ejpam-5393	24	2	42	42	NUM
ejpam-5393	24	3	]	]	PUNCT
ejpam-5393	24	4	and	and	CCONJ
ejpam-5393	24	5	[	[	X
ejpam-5393	24	6	46	46	NUM
ejpam-5393	24	7	]	]	X
ejpam-5393	24	8	,	,	PUNCT
ejpam-5393	24	9	respectively	respectively	ADV
ejpam-5393	24	10	.	.	PUNCT
ejpam-5393	25	1	in	in	ADP
ejpam-5393	25	2	1961	1961	NUM
ejpam-5393	25	3	,	,	PUNCT
ejpam-5393	25	4	marcus	marcus	PROPN
ejpam-5393	26	1	[	[	X
ejpam-5393	26	2	43	43	NUM
ejpam-5393	26	3	]	]	PUNCT
ejpam-5393	26	4	introduced	introduce	VERB
ejpam-5393	26	5	the	the	DET
ejpam-5393	26	6	notion	notion	NOUN
ejpam-5393	26	7	of	of	ADP
ejpam-5393	26	8	quasicontinuous	quasicontinuous	ADJ
ejpam-5393	26	9	functions	function	NOUN
ejpam-5393	26	10	.	.	PUNCT
ejpam-5393	27	1	popa	popa	NOUN
ejpam-5393	27	2	[	[	X
ejpam-5393	27	3	47	47	NUM
ejpam-5393	27	4	]	]	PUNCT
ejpam-5393	27	5	introduced	introduce	VERB
ejpam-5393	27	6	and	and	CCONJ
ejpam-5393	27	7	studied	study	VERB
ejpam-5393	27	8	the	the	DET
ejpam-5393	27	9	notion	notion	NOUN
ejpam-5393	27	10	of	of	ADP
ejpam-5393	27	11	quasi	quasi	ADJ
ejpam-5393	27	12	-	-	ADJ
ejpam-5393	27	13	continuous	continuous	ADJ
ejpam-5393	27	14	multifunctions	multifunction	NOUN
ejpam-5393	27	15	.	.	PUNCT
ejpam-5393	28	1	viriyapong	viriyapong	PROPN
ejpam-5393	28	2	and	and	CCONJ
ejpam-5393	28	3	boonpok	boonpok	VERB
ejpam-5393	29	1	[	[	X
ejpam-5393	29	2	59	59	NUM
ejpam-5393	29	3	]	]	PUNCT
ejpam-5393	29	4	introduced	introduce	VERB
ejpam-5393	29	5	and	and	CCONJ
ejpam-5393	29	6	studied	study	VERB
ejpam-5393	29	7	the	the	DET
ejpam-5393	29	8	concept	concept	NOUN
ejpam-5393	29	9	of	of	ADP
ejpam-5393	29	10	weakly	weakly	ADJ
ejpam-5393	29	11	quasi	quasi	NOUN
ejpam-5393	29	12	(	(	PUNCT
ejpam-5393	29	13	λ	λ	PROPN
ejpam-5393	29	14	,	,	PUNCT
ejpam-5393	29	15	sp)-continuous	sp)-continuous	ADJ
ejpam-5393	29	16	multifunctions	multifunction	NOUN
ejpam-5393	29	17	.	.	PUNCT
ejpam-5393	30	1	furthermore	furthermore	ADV
ejpam-5393	30	2	,	,	PUNCT
ejpam-5393	30	3	several	several	ADJ
ejpam-5393	30	4	characterizations	characterization	NOUN
ejpam-5393	30	5	of	of	ADP
ejpam-5393	30	6	(	(	PUNCT
ejpam-5393	30	7	τ1	τ1	NOUN
ejpam-5393	30	8	,	,	PUNCT
ejpam-5393	30	9	τ2)δ	τ2)δ	ADJ
ejpam-5393	30	10	-	-	PUNCT
ejpam-5393	30	11	semicontinuous	semicontinuous	ADJ
ejpam-5393	30	12	multifunctions	multifunction	NOUN
ejpam-5393	30	13	,	,	PUNCT
ejpam-5393	30	14	almost	almost	ADV
ejpam-5393	30	15	weakly	weakly	ADJ
ejpam-5393	30	16	(	(	PUNCT
ejpam-5393	30	17	τ1	τ1	NOUN
ejpam-5393	30	18	,	,	PUNCT
ejpam-5393	30	19	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	30	20	multifunctions	multifunction	NOUN
ejpam-5393	30	21	,	,	PUNCT
ejpam-5393	30	22	⋆-continuous	⋆-continuous	ADJ
ejpam-5393	30	23	multifunctions	multifunction	NOUN
ejpam-5393	30	24	,	,	PUNCT
ejpam-5393	30	25	β(⋆)continuous	β(⋆)continuous	ADJ
ejpam-5393	30	26	multifunctions	multifunction	NOUN
ejpam-5393	30	27	,	,	PUNCT
ejpam-5393	30	28	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5393	30	29	multifunctions	multifunction	NOUN
ejpam-5393	30	30	,	,	PUNCT
ejpam-5393	30	31	almost	almost	ADV
ejpam-5393	30	32	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5393	30	33	multifunctions	multifunction	NOUN
ejpam-5393	30	34	,	,	PUNCT
ejpam-5393	30	35	almost	almost	ADV
ejpam-5393	30	36	quasi	quasi	VERB
ejpam-5393	30	37	⋆-continuous	⋆-continuous	ADJ
ejpam-5393	30	38	multifunctions	multifunction	NOUN
ejpam-5393	30	39	,	,	PUNCT
ejpam-5393	30	40	weakly	weakly	ADJ
ejpam-5393	30	41	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5393	30	42	multifunctions	multifunction	NOUN
ejpam-5393	30	43	,	,	PUNCT
ejpam-5393	30	44	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-5393	30	45	multifunctions	multifunction	NOUN
ejpam-5393	30	46	,	,	PUNCT
ejpam-5393	30	47	weakly	weakly	ADJ
ejpam-5393	30	48	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-5393	30	49	multifunctions	multifunction	NOUN
ejpam-5393	30	50	,	,	PUNCT
ejpam-5393	30	51	θ(⋆)-quasi	θ(⋆)-quasi	NUM
ejpam-5393	30	52	continuous	continuous	ADJ
ejpam-5393	30	53	multifunctions	multifunction	NOUN
ejpam-5393	30	54	,	,	PUNCT
ejpam-5393	30	55	almost	almost	ADV
ejpam-5393	30	56	ı⋆-continuous	ı⋆-continuous	ADJ
ejpam-5393	30	57	multifunctions	multifunction	NOUN
ejpam-5393	30	58	,	,	PUNCT
ejpam-5393	30	59	weakly	weakly	ADJ
ejpam-5393	30	60	(	(	PUNCT
ejpam-5393	30	61	λ	λ	NOUN
ejpam-5393	30	62	,	,	PUNCT
ejpam-5393	30	63	sp)-continuous	sp)-continuous	ADJ
ejpam-5393	30	64	multifunctions	multifunction	NOUN
ejpam-5393	30	65	,	,	PUNCT
ejpam-5393	30	66	α(λ	α(λ	PROPN
ejpam-5393	30	67	,	,	PUNCT
ejpam-5393	30	68	sp)-continuous	sp)-continuous	ADJ
ejpam-5393	30	69	multifunctions	multifunction	NOUN
ejpam-5393	30	70	,	,	PUNCT
ejpam-5393	30	71	almost	almost	ADV
ejpam-5393	30	72	α(λ	α(λ	PROPN
ejpam-5393	30	73	,	,	PUNCT
ejpam-5393	30	74	sp)-continuous	sp)-continuous	ADJ
ejpam-5393	30	75	multifunctions	multifunction	NOUN
ejpam-5393	30	76	,	,	PUNCT
ejpam-5393	30	77	weakly	weakly	ADJ
ejpam-5393	30	78	α(λ	α(λ	PROPN
ejpam-5393	30	79	,	,	PUNCT
ejpam-5393	30	80	sp)-continuous	sp)-continuous	ADJ
ejpam-5393	30	81	multifunctions	multifunction	NOUN
ejpam-5393	30	82	,	,	PUNCT
ejpam-5393	30	83	almost	almost	ADV
ejpam-5393	30	84	β(λ	β(λ	NOUN
ejpam-5393	30	85	,	,	PUNCT
ejpam-5393	30	86	sp)-continuous	sp)-continuous	ADJ
ejpam-5393	30	87	multifunctions	multifunction	NOUN
ejpam-5393	30	88	,	,	PUNCT
ejpam-5393	30	89	slightly	slightly	ADV
ejpam-5393	30	90	(	(	PUNCT
ejpam-5393	30	91	λ	λ	NOUN
ejpam-5393	30	92	,	,	PUNCT
ejpam-5393	30	93	sp)-continuous	sp)-continuous	ADJ
ejpam-5393	30	94	multifunctions	multifunction	NOUN
ejpam-5393	30	95	,	,	PUNCT
ejpam-5393	30	96	(	(	PUNCT
ejpam-5393	30	97	τ1	τ1	NOUN
ejpam-5393	30	98	,	,	PUNCT
ejpam-5393	30	99	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	30	100	multifunctions	multifunction	NOUN
ejpam-5393	30	101	,	,	PUNCT
ejpam-5393	30	102	almost	almost	ADV
ejpam-5393	30	103	(	(	PUNCT
ejpam-5393	30	104	τ1	τ1	NOUN
ejpam-5393	30	105	,	,	PUNCT
ejpam-5393	30	106	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	30	107	multifunctions	multifunction	NOUN
ejpam-5393	30	108	,	,	PUNCT
ejpam-5393	30	109	weakly	weakly	ADJ
ejpam-5393	30	110	(	(	PUNCT
ejpam-5393	30	111	τ1	τ1	NOUN
ejpam-5393	30	112	,	,	PUNCT
ejpam-5393	30	113	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	30	114	multifunctions	multifunction	NOUN
ejpam-5393	30	115	and	and	CCONJ
ejpam-5393	30	116	weakly	weakly	ADJ
ejpam-5393	30	117	quasi	quasi	NOUN
ejpam-5393	30	118	(	(	PUNCT
ejpam-5393	30	119	τ1	τ1	PROPN
ejpam-5393	30	120	,	,	PUNCT
ejpam-5393	30	121	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	30	122	multifunctions	multifunction	NOUN
ejpam-5393	30	123	were	be	AUX
ejpam-5393	30	124	investigated	investigate	VERB
ejpam-5393	30	125	in	in	ADP
ejpam-5393	30	126	[	[	X
ejpam-5393	30	127	6	6	NUM
ejpam-5393	30	128	]	]	PUNCT
ejpam-5393	30	129	,	,	PUNCT
ejpam-5393	30	130	[	[	X
ejpam-5393	30	131	29	29	NUM
ejpam-5393	30	132	]	]	PUNCT
ejpam-5393	30	133	,	,	PUNCT
ejpam-5393	30	134	[	[	X
ejpam-5393	30	135	4	4	NUM
ejpam-5393	30	136	]	]	PUNCT
ejpam-5393	30	137	,	,	PUNCT
ejpam-5393	30	138	[	[	X
ejpam-5393	30	139	8	8	NUM
ejpam-5393	30	140	]	]	PUNCT
ejpam-5393	30	141	,	,	PUNCT
ejpam-5393	30	142	[	[	X
ejpam-5393	30	143	18	18	NUM
ejpam-5393	30	144	]	]	PUNCT
ejpam-5393	30	145	,	,	PUNCT
ejpam-5393	30	146	[	[	X
ejpam-5393	30	147	25	25	NUM
ejpam-5393	30	148	]	]	PUNCT
ejpam-5393	30	149	,	,	PUNCT
ejpam-5393	30	150	[	[	X
ejpam-5393	30	151	7	7	NUM
ejpam-5393	30	152	]	]	PUNCT
ejpam-5393	30	153	,	,	PUNCT
ejpam-5393	30	154	[	[	X
ejpam-5393	30	155	22	22	NUM
ejpam-5393	30	156	]	]	PUNCT
ejpam-5393	30	157	,	,	PUNCT
ejpam-5393	30	158	[	[	X
ejpam-5393	30	159	21	21	NUM
ejpam-5393	30	160	]	]	PUNCT
ejpam-5393	30	161	,	,	PUNCT
ejpam-5393	31	1	[	[	X
ejpam-5393	31	2	16	16	NUM
ejpam-5393	31	3	]	]	PUNCT
ejpam-5393	31	4	,	,	PUNCT
ejpam-5393	31	5	[	[	X
ejpam-5393	31	6	10	10	NUM
ejpam-5393	31	7	]	]	PUNCT
ejpam-5393	31	8	,	,	PUNCT
ejpam-5393	31	9	[	[	X
ejpam-5393	31	10	20	20	NUM
ejpam-5393	31	11	]	]	PUNCT
ejpam-5393	31	12	,	,	PUNCT
ejpam-5393	31	13	[	[	X
ejpam-5393	31	14	23	23	NUM
ejpam-5393	31	15	]	]	PUNCT
ejpam-5393	31	16	,	,	PUNCT
ejpam-5393	31	17	[	[	X
ejpam-5393	31	18	36	36	NUM
ejpam-5393	31	19	]	]	PUNCT
ejpam-5393	31	20	,	,	PUNCT
ejpam-5393	31	21	[	[	X
ejpam-5393	31	22	14	14	NUM
ejpam-5393	31	23	]	]	PUNCT
ejpam-5393	31	24	,	,	PUNCT
ejpam-5393	32	1	[	[	X
ejpam-5393	32	2	28	28	NUM
ejpam-5393	32	3	]	]	PUNCT
ejpam-5393	32	4	,	,	PUNCT
ejpam-5393	32	5	[	[	X
ejpam-5393	32	6	54	54	NUM
ejpam-5393	32	7	]	]	PUNCT
ejpam-5393	32	8	,	,	PUNCT
ejpam-5393	32	9	[	[	X
ejpam-5393	32	10	15	15	NUM
ejpam-5393	32	11	]	]	PUNCT
ejpam-5393	32	12	,	,	PUNCT
ejpam-5393	32	13	[	[	X
ejpam-5393	32	14	51	51	NUM
ejpam-5393	32	15	]	]	PUNCT
ejpam-5393	32	16	,	,	PUNCT
ejpam-5393	33	1	[	[	X
ejpam-5393	33	2	38	38	NUM
ejpam-5393	33	3	]	]	PUNCT
ejpam-5393	33	4	,	,	PUNCT
ejpam-5393	34	1	[	[	X
ejpam-5393	34	2	56	56	NUM
ejpam-5393	34	3	]	]	PUNCT
ejpam-5393	34	4	and	and	CCONJ
ejpam-5393	34	5	[	[	X
ejpam-5393	34	6	52	52	NUM
ejpam-5393	34	7	]	]	PUNCT
ejpam-5393	34	8	,	,	PUNCT
ejpam-5393	34	9	respectively	respectively	ADV
ejpam-5393	34	10	.	.	PUNCT
ejpam-5393	35	1	neubrunn	neubrunn	PROPN
ejpam-5393	36	1	[	[	X
ejpam-5393	36	2	44	44	NUM
ejpam-5393	36	3	]	]	PUNCT
ejpam-5393	36	4	and	and	CCONJ
ejpam-5393	36	5	holá	holá	NOUN
ejpam-5393	36	6	et	et	PROPN
ejpam-5393	36	7	al	al	PROPN
ejpam-5393	36	8	.	.	PUNCT
ejpam-5393	37	1	[	[	X
ejpam-5393	37	2	35	35	NUM
ejpam-5393	37	3	]	]	PUNCT
ejpam-5393	37	4	extended	extend	VERB
ejpam-5393	37	5	the	the	DET
ejpam-5393	37	6	concept	concept	NOUN
ejpam-5393	37	7	of	of	ADP
ejpam-5393	37	8	c	c	NOUN
ejpam-5393	37	9	-	-	PUNCT
ejpam-5393	37	10	continuous	continuous	ADJ
ejpam-5393	37	11	functions	function	NOUN
ejpam-5393	37	12	to	to	ADP
ejpam-5393	37	13	the	the	DET
ejpam-5393	37	14	setting	setting	NOUN
ejpam-5393	37	15	of	of	ADP
ejpam-5393	37	16	multifunctions	multifunction	NOUN
ejpam-5393	37	17	.	.	PUNCT
ejpam-5393	38	1	lipski	lipski	ADJ
ejpam-5393	39	1	[	[	X
ejpam-5393	39	2	40	40	NUM
ejpam-5393	39	3	]	]	PUNCT
ejpam-5393	39	4	introduced	introduce	VERB
ejpam-5393	39	5	the	the	DET
ejpam-5393	39	6	notion	notion	NOUN
ejpam-5393	39	7	of	of	ADP
ejpam-5393	39	8	c	c	NOUN
ejpam-5393	39	9	-	-	PUNCT
ejpam-5393	39	10	quasicontinuous	quasicontinuous	ADJ
ejpam-5393	39	11	multifunctions	multifunction	NOUN
ejpam-5393	39	12	as	as	ADP
ejpam-5393	39	13	a	a	DET
ejpam-5393	39	14	generalization	generalization	NOUN
ejpam-5393	39	15	of	of	ADP
ejpam-5393	39	16	c	c	NOUN
ejpam-5393	39	17	-	-	PUNCT
ejpam-5393	39	18	continuous	continuous	ADJ
ejpam-5393	39	19	multifunctions	multifunction	NOUN
ejpam-5393	39	20	[	[	X
ejpam-5393	39	21	44	44	NUM
ejpam-5393	39	22	]	]	PUNCT
ejpam-5393	39	23	and	and	CCONJ
ejpam-5393	39	24	quasi	quasi	ADJ
ejpam-5393	39	25	-	-	ADJ
ejpam-5393	39	26	continuous	continuous	ADJ
ejpam-5393	39	27	multifunctions	multifunction	NOUN
ejpam-5393	40	1	[	[	X
ejpam-5393	40	2	47	47	NUM
ejpam-5393	40	3	]	]	PUNCT
ejpam-5393	40	4	.	.	PUNCT
ejpam-5393	41	1	noiri	noiri	PROPN
ejpam-5393	41	2	and	and	CCONJ
ejpam-5393	41	3	popa	popa	NOUN
ejpam-5393	41	4	[	[	X
ejpam-5393	41	5	45	45	NUM
ejpam-5393	41	6	]	]	PUNCT
ejpam-5393	41	7	introduced	introduce	VERB
ejpam-5393	41	8	and	and	CCONJ
ejpam-5393	41	9	investigated	investigate	VERB
ejpam-5393	41	10	the	the	DET
ejpam-5393	41	11	notion	notion	NOUN
ejpam-5393	41	12	of	of	ADP
ejpam-5393	41	13	cm	cm	NOUN
ejpam-5393	41	14	-	-	PUNCT
ejpam-5393	41	15	continuous	continuous	ADJ
ejpam-5393	41	16	multifunctions	multifunction	NOUN
ejpam-5393	41	17	.	.	PUNCT
ejpam-5393	42	1	popa	popa	NOUN
ejpam-5393	42	2	and	and	CCONJ
ejpam-5393	42	3	noiri	noiri	ADV
ejpam-5393	43	1	[	[	X
ejpam-5393	43	2	48	48	NUM
ejpam-5393	43	3	]	]	PUNCT
ejpam-5393	43	4	investigated	investigate	VERB
ejpam-5393	43	5	some	some	DET
ejpam-5393	43	6	characterizations	characterization	NOUN
ejpam-5393	43	7	of	of	ADP
ejpam-5393	43	8	c	c	NOUN
ejpam-5393	43	9	-	-	PUNCT
ejpam-5393	43	10	quasicontinuous	quasicontinuous	ADJ
ejpam-5393	43	11	multifunctions	multifunction	NOUN
ejpam-5393	43	12	.	.	PUNCT
ejpam-5393	44	1	khampakdee	khampakdee	NOUN
ejpam-5393	44	2	et	et	PROPN
ejpam-5393	44	3	al	al	PROPN
ejpam-5393	44	4	.	.	PUNCT
ejpam-5393	45	1	[	[	X
ejpam-5393	45	2	37	37	NUM
ejpam-5393	45	3	]	]	PUNCT
ejpam-5393	45	4	introduced	introduce	VERB
ejpam-5393	45	5	and	and	CCONJ
ejpam-5393	45	6	studied	study	VERB
ejpam-5393	45	7	the	the	DET
ejpam-5393	45	8	notion	notion	NOUN
ejpam-5393	45	9	of	of	ADP
ejpam-5393	45	10	c-(τ1	c-(τ1	PROPN
ejpam-5393	45	11	,	,	PUNCT
ejpam-5393	45	12	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	45	13	multifunctions	multifunction	NOUN
ejpam-5393	45	14	.	.	PUNCT
ejpam-5393	46	1	in	in	ADP
ejpam-5393	46	2	this	this	DET
ejpam-5393	46	3	paper	paper	NOUN
ejpam-5393	46	4	,	,	PUNCT
ejpam-5393	46	5	we	we	PRON
ejpam-5393	46	6	introduce	introduce	VERB
ejpam-5393	46	7	the	the	DET
ejpam-5393	46	8	concepts	concept	NOUN
ejpam-5393	46	9	of	of	ADP
ejpam-5393	46	10	upper	upper	ADJ
ejpam-5393	46	11	and	and	CCONJ
ejpam-5393	46	12	lower	low	ADJ
ejpam-5393	46	13	c	c	NOUN
ejpam-5393	46	14	-	-	PUNCT
ejpam-5393	46	15	qausi	qausi	NOUN
ejpam-5393	46	16	(	(	PUNCT
ejpam-5393	46	17	τ1	τ1	PROPN
ejpam-5393	46	18	,	,	PUNCT
ejpam-5393	46	19	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	46	20	multifunctions	multifunction	NOUN
ejpam-5393	46	21	.	.	PUNCT
ejpam-5393	47	1	we	we	PRON
ejpam-5393	47	2	also	also	ADV
ejpam-5393	47	3	investigate	investigate	VERB
ejpam-5393	47	4	several	several	ADJ
ejpam-5393	47	5	characterizations	characterization	NOUN
ejpam-5393	47	6	of	of	ADP
ejpam-5393	47	7	upper	upper	ADJ
ejpam-5393	47	8	and	and	CCONJ
ejpam-5393	47	9	lower	low	ADJ
ejpam-5393	47	10	c	c	NOUN
ejpam-5393	47	11	-	-	PUNCT
ejpam-5393	47	12	qausi	qausi	NOUN
ejpam-5393	47	13	(	(	PUNCT
ejpam-5393	47	14	τ1	τ1	PROPN
ejpam-5393	47	15	,	,	PUNCT
ejpam-5393	47	16	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	47	17	multifunctions	multifunction	NOUN
ejpam-5393	47	18	.	.	PUNCT
ejpam-5393	48	1	2	2	X
ejpam-5393	48	2	.	.	X
ejpam-5393	48	3	preliminaries	preliminary	NOUN
ejpam-5393	48	4	throughout	throughout	ADP
ejpam-5393	48	5	the	the	DET
ejpam-5393	48	6	present	present	ADJ
ejpam-5393	48	7	paper	paper	NOUN
ejpam-5393	48	8	,	,	PUNCT
ejpam-5393	48	9	spaces	space	NOUN
ejpam-5393	48	10	(	(	PUNCT
ejpam-5393	48	11	x	x	NOUN
ejpam-5393	48	12	,	,	PUNCT
ejpam-5393	48	13	τ1	τ1	NOUN
ejpam-5393	48	14	,	,	PUNCT
ejpam-5393	48	15	τ2	τ2	NOUN
ejpam-5393	48	16	)	)	PUNCT
ejpam-5393	48	17	and	and	CCONJ
ejpam-5393	48	18	(	(	PUNCT
ejpam-5393	48	19	y	y	PROPN
ejpam-5393	48	20	,	,	PUNCT
ejpam-5393	48	21	σ1	σ1	PROPN
ejpam-5393	48	22	,	,	PUNCT
ejpam-5393	48	23	σ2	σ2	NOUN
ejpam-5393	48	24	)	)	PUNCT
ejpam-5393	48	25	(	(	PUNCT
ejpam-5393	48	26	or	or	CCONJ
ejpam-5393	48	27	simply	simply	ADV
ejpam-5393	48	28	x	x	X
ejpam-5393	48	29	and	and	CCONJ
ejpam-5393	48	30	y	y	PROPN
ejpam-5393	48	31	)	)	PUNCT
ejpam-5393	48	32	always	always	ADV
ejpam-5393	48	33	mean	mean	VERB
ejpam-5393	48	34	bitopological	bitopological	ADJ
ejpam-5393	48	35	spaces	space	NOUN
ejpam-5393	48	36	on	on	ADP
ejpam-5393	48	37	which	which	PRON
ejpam-5393	48	38	no	no	DET
ejpam-5393	48	39	separation	separation	NOUN
ejpam-5393	48	40	axioms	axiom	NOUN
ejpam-5393	48	41	are	be	AUX
ejpam-5393	48	42	assumed	assume	VERB
ejpam-5393	48	43	unless	unless	SCONJ
ejpam-5393	48	44	explicitly	explicitly	ADV
ejpam-5393	48	45	stated	state	VERB
ejpam-5393	48	46	.	.	PUNCT
ejpam-5393	49	1	let	let	VERB
ejpam-5393	49	2	a	a	DET
ejpam-5393	49	3	be	be	AUX
ejpam-5393	49	4	a	a	DET
ejpam-5393	49	5	subset	subset	NOUN
ejpam-5393	49	6	of	of	ADP
ejpam-5393	49	7	a	a	DET
ejpam-5393	49	8	bitopological	bitopological	ADJ
ejpam-5393	49	9	space	space	NOUN
ejpam-5393	49	10	(	(	PUNCT
ejpam-5393	49	11	x	x	NOUN
ejpam-5393	49	12	,	,	PUNCT
ejpam-5393	49	13	τ1	τ1	NOUN
ejpam-5393	49	14	,	,	PUNCT
ejpam-5393	49	15	τ2	τ2	NOUN
ejpam-5393	49	16	)	)	PUNCT
ejpam-5393	49	17	.	.	PUNCT
ejpam-5393	50	1	the	the	DET
ejpam-5393	50	2	closure	closure	NOUN
ejpam-5393	50	3	of	of	ADP
ejpam-5393	50	4	a	a	PRON
ejpam-5393	50	5	and	and	CCONJ
ejpam-5393	50	6	the	the	DET
ejpam-5393	50	7	interior	interior	NOUN
ejpam-5393	50	8	of	of	ADP
ejpam-5393	50	9	a	a	PRON
ejpam-5393	50	10	with	with	ADP
ejpam-5393	50	11	respect	respect	NOUN
ejpam-5393	50	12	to	to	ADP
ejpam-5393	50	13	τi	τi	PROPN
ejpam-5393	50	14	are	be	AUX
ejpam-5393	50	15	denoted	denote	VERB
ejpam-5393	50	16	by	by	ADP
ejpam-5393	50	17	τi	τi	NOUN
ejpam-5393	50	18	-	-	PUNCT
ejpam-5393	50	19	cl(a	cl(a	NUM
ejpam-5393	50	20	)	)	PUNCT
ejpam-5393	50	21	and	and	CCONJ
ejpam-5393	50	22	τi	τi	NOUN
ejpam-5393	50	23	-	-	PUNCT
ejpam-5393	50	24	int(a	int(a	NOUN
ejpam-5393	50	25	)	)	PUNCT
ejpam-5393	50	26	,	,	PUNCT
ejpam-5393	50	27	respectively	respectively	ADV
ejpam-5393	50	28	,	,	PUNCT
ejpam-5393	50	29	for	for	ADP
ejpam-5393	50	30	i	i	PROPN
ejpam-5393	50	31	=	=	SYM
ejpam-5393	50	32	1	1	NUM
ejpam-5393	50	33	,	,	PUNCT
ejpam-5393	50	34	2	2	NUM
ejpam-5393	50	35	.	.	X
ejpam-5393	50	36	a	a	DET
ejpam-5393	50	37	subset	subset	NOUN
ejpam-5393	50	38	a	a	PRON
ejpam-5393	50	39	of	of	ADP
ejpam-5393	50	40	a	a	DET
ejpam-5393	50	41	bitopological	bitopological	ADJ
ejpam-5393	50	42	space	space	NOUN
ejpam-5393	50	43	(	(	PUNCT
ejpam-5393	50	44	x	x	NOUN
ejpam-5393	50	45	,	,	PUNCT
ejpam-5393	50	46	τ1	τ1	NOUN
ejpam-5393	50	47	,	,	PUNCT
ejpam-5393	50	48	τ2	τ2	NOUN
ejpam-5393	50	49	)	)	PUNCT
ejpam-5393	50	50	is	be	AUX
ejpam-5393	50	51	called	call	VERB
ejpam-5393	50	52	τ1τ2	τ1τ2	VERB
ejpam-5393	50	53	-	-	ADJ
ejpam-5393	50	54	closed	closed	ADJ
ejpam-5393	50	55	[	[	X
ejpam-5393	50	56	30	30	NUM
ejpam-5393	50	57	]	]	X
ejpam-5393	50	58	if	if	SCONJ
ejpam-5393	50	59	a	a	DET
ejpam-5393	50	60	=	=	NOUN
ejpam-5393	50	61	τ1	τ1	NOUN
ejpam-5393	50	62	-	-	PUNCT
ejpam-5393	50	63	cl(τ2	cl(τ2	NOUN
ejpam-5393	50	64	-	-	PUNCT
ejpam-5393	50	65	cl(a	cl(a	NUM
ejpam-5393	50	66	)	)	PUNCT
ejpam-5393	50	67	)	)	PUNCT
ejpam-5393	50	68	.	.	PUNCT
ejpam-5393	51	1	the	the	DET
ejpam-5393	51	2	complement	complement	NOUN
ejpam-5393	51	3	of	of	ADP
ejpam-5393	51	4	a	a	DET
ejpam-5393	51	5	τ1τ2	τ1τ2	ADJ
ejpam-5393	51	6	-	-	ADJ
ejpam-5393	51	7	closed	closed	ADJ
ejpam-5393	51	8	set	set	NOUN
ejpam-5393	51	9	is	be	AUX
ejpam-5393	51	10	called	call	VERB
ejpam-5393	51	11	τ1τ2	τ1τ2	NOUN
ejpam-5393	51	12	-	-	ADJ
ejpam-5393	51	13	open	open	ADJ
ejpam-5393	51	14	.	.	PUNCT
ejpam-5393	52	1	let	let	VERB
ejpam-5393	52	2	a	a	DET
ejpam-5393	52	3	be	be	AUX
ejpam-5393	52	4	a	a	DET
ejpam-5393	52	5	subset	subset	NOUN
ejpam-5393	52	6	of	of	ADP
ejpam-5393	52	7	a	a	DET
ejpam-5393	52	8	bitopological	bitopological	ADJ
ejpam-5393	52	9	space	space	NOUN
ejpam-5393	52	10	(	(	PUNCT
ejpam-5393	52	11	x	x	NOUN
ejpam-5393	52	12	,	,	PUNCT
ejpam-5393	52	13	τ1	τ1	NOUN
ejpam-5393	52	14	,	,	PUNCT
ejpam-5393	52	15	τ2	τ2	NOUN
ejpam-5393	52	16	)	)	PUNCT
ejpam-5393	52	17	.	.	PUNCT
ejpam-5393	53	1	the	the	DET
ejpam-5393	53	2	intersection	intersection	NOUN
ejpam-5393	53	3	of	of	ADP
ejpam-5393	53	4	all	all	DET
ejpam-5393	53	5	τ1τ2	τ1τ2	ADJ
ejpam-5393	53	6	-	-	ADJ
ejpam-5393	53	7	closed	closed	ADJ
ejpam-5393	53	8	sets	set	NOUN
ejpam-5393	53	9	of	of	ADP
ejpam-5393	53	10	x	x	PUNCT
ejpam-5393	53	11	containing	contain	VERB
ejpam-5393	53	12	a	a	PRON
ejpam-5393	53	13	is	be	AUX
ejpam-5393	53	14	called	call	VERB
ejpam-5393	53	15	the	the	DET
ejpam-5393	53	16	τ1τ2	τ1τ2	NOUN
ejpam-5393	53	17	-	-	NOUN
ejpam-5393	53	18	closure	closure	NOUN
ejpam-5393	53	19	[	[	X
ejpam-5393	53	20	30	30	NUM
ejpam-5393	53	21	]	]	PUNCT
ejpam-5393	53	22	of	of	ADP
ejpam-5393	53	23	a	a	PRON
ejpam-5393	53	24	and	and	CCONJ
ejpam-5393	53	25	is	be	AUX
ejpam-5393	53	26	denoted	denote	VERB
ejpam-5393	53	27	by	by	ADP
ejpam-5393	53	28	τ1τ2	τ1τ2	NOUN
ejpam-5393	53	29	-	-	NUM
ejpam-5393	53	30	cl(a	cl(a	NUM
ejpam-5393	53	31	)	)	PUNCT
ejpam-5393	53	32	.	.	PUNCT
ejpam-5393	54	1	the	the	DET
ejpam-5393	54	2	union	union	NOUN
ejpam-5393	54	3	of	of	ADP
ejpam-5393	54	4	all	all	DET
ejpam-5393	54	5	τ1τ2	τ1τ2	ADJ
ejpam-5393	54	6	-	-	ADJ
ejpam-5393	54	7	open	open	ADJ
ejpam-5393	54	8	sets	set	NOUN
ejpam-5393	54	9	of	of	ADP
ejpam-5393	54	10	x	x	PUNCT
ejpam-5393	54	11	contained	contain	VERB
ejpam-5393	54	12	in	in	ADP
ejpam-5393	54	13	a	a	PRON
ejpam-5393	54	14	is	be	AUX
ejpam-5393	54	15	called	call	VERB
ejpam-5393	54	16	the	the	DET
ejpam-5393	54	17	τ1τ2	τ1τ2	NOUN
ejpam-5393	54	18	-	-	ADJ
ejpam-5393	54	19	interior	interior	ADJ
ejpam-5393	54	20	[	[	X
ejpam-5393	54	21	30	30	NUM
ejpam-5393	54	22	]	]	PUNCT
ejpam-5393	54	23	of	of	ADP
ejpam-5393	54	24	a	a	PRON
ejpam-5393	54	25	and	and	CCONJ
ejpam-5393	54	26	is	be	AUX
ejpam-5393	54	27	denoted	denote	VERB
ejpam-5393	54	28	by	by	ADP
ejpam-5393	54	29	τ1τ2	τ1τ2	NOUN
ejpam-5393	54	30	-	-	ADJ
ejpam-5393	54	31	int(a	int(a	NOUN
ejpam-5393	54	32	)	)	PUNCT
ejpam-5393	54	33	.	.	PUNCT
ejpam-5393	55	1	lemma	lemma	PROPN
ejpam-5393	55	2	1	1	NUM
ejpam-5393	55	3	.	.	PUNCT
ejpam-5393	56	1	[	[	X
ejpam-5393	56	2	30	30	NUM
ejpam-5393	56	3	]	]	PUNCT
ejpam-5393	56	4	let	let	VERB
ejpam-5393	56	5	a	a	PRON
ejpam-5393	56	6	and	and	CCONJ
ejpam-5393	56	7	b	b	NOUN
ejpam-5393	56	8	be	be	AUX
ejpam-5393	56	9	subsets	subset	NOUN
ejpam-5393	56	10	of	of	ADP
ejpam-5393	56	11	a	a	DET
ejpam-5393	56	12	bitopological	bitopological	ADJ
ejpam-5393	56	13	space	space	NOUN
ejpam-5393	56	14	(	(	PUNCT
ejpam-5393	56	15	x	x	NOUN
ejpam-5393	56	16	,	,	PUNCT
ejpam-5393	56	17	τ1	τ1	NOUN
ejpam-5393	56	18	,	,	PUNCT
ejpam-5393	56	19	τ2	τ2	NOUN
ejpam-5393	56	20	)	)	PUNCT
ejpam-5393	56	21	.	.	PUNCT
ejpam-5393	57	1	for	for	ADP
ejpam-5393	57	2	the	the	DET
ejpam-5393	57	3	τ1τ2closure	τ1τ2closure	NOUN
ejpam-5393	57	4	,	,	PUNCT
ejpam-5393	57	5	the	the	DET
ejpam-5393	57	6	following	follow	VERB
ejpam-5393	57	7	properties	property	NOUN
ejpam-5393	57	8	hold	hold	VERB
ejpam-5393	57	9	:	:	PUNCT
ejpam-5393	57	10	p.	p.	NOUN
ejpam-5393	57	11	pue	pue	NOUN
ejpam-5393	57	12	-	-	PUNCT
ejpam-5393	57	13	on	on	ADP
ejpam-5393	57	14	,	,	PUNCT
ejpam-5393	57	15	a.	a.	PROPN
ejpam-5393	57	16	sama	sama	PROPN
ejpam-5393	57	17	-	-	PUNCT
ejpam-5393	57	18	ae	ae	PROPN
ejpam-5393	57	19	,	,	PUNCT
ejpam-5393	57	20	c.	c.	PROPN
ejpam-5393	57	21	boonpok	boonpok	PROPN
ejpam-5393	57	22	/	/	SYM
ejpam-5393	57	23	eur	eur	PROPN
ejpam-5393	57	24	.	.	PUNCT
ejpam-5393	58	1	j.	j.	PROPN
ejpam-5393	58	2	pure	pure	PROPN
ejpam-5393	58	3	appl	appl	PROPN
ejpam-5393	58	4	.	.	PROPN
ejpam-5393	58	5	math	math	PROPN
ejpam-5393	58	6	,	,	PUNCT
ejpam-5393	58	7	17	17	NUM
ejpam-5393	58	8	(	(	PUNCT
ejpam-5393	58	9	4	4	NUM
ejpam-5393	58	10	)	)	PUNCT
ejpam-5393	58	11	(	(	PUNCT
ejpam-5393	58	12	2024	2024	NUM
ejpam-5393	58	13	)	)	PUNCT
ejpam-5393	58	14	,	,	PUNCT
ejpam-5393	58	15	3242	3242	NUM
ejpam-5393	58	16	-	-	SYM
ejpam-5393	58	17	3253	3253	NUM
ejpam-5393	58	18	3244	3244	NUM
ejpam-5393	58	19	(	(	PUNCT
ejpam-5393	58	20	1	1	X
ejpam-5393	58	21	)	)	PUNCT
ejpam-5393	58	22	a	a	DET
ejpam-5393	58	23	⊆	⊆	NUM
ejpam-5393	58	24	τ1τ2	τ1τ2	NOUN
ejpam-5393	58	25	-	-	NUM
ejpam-5393	58	26	cl(a	cl(a	NUM
ejpam-5393	58	27	)	)	PUNCT
ejpam-5393	58	28	and	and	CCONJ
ejpam-5393	58	29	τ1τ2	τ1τ2	NOUN
ejpam-5393	58	30	-	-	ADJ
ejpam-5393	58	31	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5393	58	32	-	-	PUNCT
ejpam-5393	58	33	cl(a	cl(a	NUM
ejpam-5393	58	34	)	)	PUNCT
ejpam-5393	58	35	)	)	PUNCT
ejpam-5393	59	1	=	=	PUNCT
ejpam-5393	59	2	τ1τ2	τ1τ2	NOUN
ejpam-5393	59	3	-	-	NUM
ejpam-5393	59	4	cl(a	cl(a	NUM
ejpam-5393	59	5	)	)	PUNCT
ejpam-5393	59	6	.	.	PUNCT
ejpam-5393	60	1	(	(	PUNCT
ejpam-5393	60	2	2	2	X
ejpam-5393	60	3	)	)	PUNCT
ejpam-5393	60	4	if	if	SCONJ
ejpam-5393	60	5	a	a	DET
ejpam-5393	60	6	⊆	⊆	NUM
ejpam-5393	60	7	b	b	NOUN
ejpam-5393	60	8	,	,	PUNCT
ejpam-5393	60	9	then	then	ADV
ejpam-5393	60	10	τ1τ2	τ1τ2	NOUN
ejpam-5393	60	11	-	-	NUM
ejpam-5393	60	12	cl(a	cl(a	NUM
ejpam-5393	60	13	)	)	PUNCT
ejpam-5393	60	14	⊆	⊆	NUM
ejpam-5393	60	15	τ1τ2	τ1τ2	NOUN
ejpam-5393	60	16	-	-	NOUN
ejpam-5393	60	17	cl(b	cl(b	NOUN
ejpam-5393	60	18	)	)	PUNCT
ejpam-5393	60	19	.	.	PUNCT
ejpam-5393	61	1	(	(	PUNCT
ejpam-5393	61	2	3	3	X
ejpam-5393	61	3	)	)	PUNCT
ejpam-5393	61	4	τ1τ2	τ1τ2	NOUN
ejpam-5393	61	5	-	-	NUM
ejpam-5393	61	6	cl(a	cl(a	NUM
ejpam-5393	61	7	)	)	PUNCT
ejpam-5393	61	8	is	be	AUX
ejpam-5393	61	9	τ1τ2	τ1τ2	NOUN
ejpam-5393	61	10	-	-	ADJ
ejpam-5393	61	11	closed	closed	ADJ
ejpam-5393	61	12	.	.	PUNCT
ejpam-5393	62	1	(	(	PUNCT
ejpam-5393	62	2	4	4	X
ejpam-5393	62	3	)	)	PUNCT
ejpam-5393	62	4	a	a	PRON
ejpam-5393	62	5	is	be	AUX
ejpam-5393	62	6	τ1τ2	τ1τ2	NOUN
ejpam-5393	62	7	-	-	ADJ
ejpam-5393	62	8	closed	closed	ADJ
ejpam-5393	62	9	if	if	SCONJ
ejpam-5393	62	10	and	and	CCONJ
ejpam-5393	62	11	only	only	ADV
ejpam-5393	62	12	if	if	SCONJ
ejpam-5393	62	13	a	a	DET
ejpam-5393	62	14	=	=	PUNCT
ejpam-5393	62	15	τ1τ2	τ1τ2	NOUN
ejpam-5393	62	16	-	-	NUM
ejpam-5393	62	17	cl(a	cl(a	NUM
ejpam-5393	62	18	)	)	PUNCT
ejpam-5393	62	19	.	.	PUNCT
ejpam-5393	63	1	(	(	PUNCT
ejpam-5393	63	2	5	5	X
ejpam-5393	63	3	)	)	PUNCT
ejpam-5393	63	4	τ1τ2	τ1τ2	NOUN
ejpam-5393	63	5	-	-	NOUN
ejpam-5393	63	6	cl(x	cl(x	X
ejpam-5393	63	7	−a	−a	NOUN
ejpam-5393	63	8	)	)	PUNCT
ejpam-5393	64	1	=	=	PUNCT
ejpam-5393	64	2	x	x	X
ejpam-5393	65	1	−	−	ADP
ejpam-5393	65	2	τ1τ2	τ1τ2	NOUN
ejpam-5393	65	3	-	-	PUNCT
ejpam-5393	65	4	int(a	int(a	NOUN
ejpam-5393	65	5	)	)	PUNCT
ejpam-5393	65	6	.	.	PUNCT
ejpam-5393	66	1	a	a	DET
ejpam-5393	66	2	bitopological	bitopological	ADJ
ejpam-5393	66	3	space	space	NOUN
ejpam-5393	66	4	(	(	PUNCT
ejpam-5393	66	5	x	x	NOUN
ejpam-5393	66	6	,	,	PUNCT
ejpam-5393	66	7	τ1	τ1	NOUN
ejpam-5393	66	8	,	,	PUNCT
ejpam-5393	66	9	τ2	τ2	NOUN
ejpam-5393	66	10	)	)	PUNCT
ejpam-5393	66	11	is	be	AUX
ejpam-5393	66	12	called	call	VERB
ejpam-5393	66	13	τ1τ2	τ1τ2	ADJ
ejpam-5393	66	14	-	-	ADJ
ejpam-5393	66	15	compact	compact	ADJ
ejpam-5393	66	16	[	[	X
ejpam-5393	66	17	30	30	NUM
ejpam-5393	66	18	]	]	PUNCT
ejpam-5393	66	19	if	if	SCONJ
ejpam-5393	66	20	every	every	DET
ejpam-5393	66	21	cover	cover	NOUN
ejpam-5393	66	22	of	of	ADP
ejpam-5393	66	23	x	x	PUNCT
ejpam-5393	66	24	by	by	ADP
ejpam-5393	66	25	τ1τ2open	τ1τ2open	NOUN
ejpam-5393	66	26	sets	set	NOUN
ejpam-5393	66	27	of	of	ADP
ejpam-5393	66	28	x	x	PUNCT
ejpam-5393	66	29	has	have	VERB
ejpam-5393	66	30	a	a	DET
ejpam-5393	66	31	finite	finite	ADJ
ejpam-5393	66	32	subcover	subcover	PROPN
ejpam-5393	66	33	.	.	PUNCT
ejpam-5393	67	1	a	a	DET
ejpam-5393	67	2	subset	subset	NOUN
ejpam-5393	67	3	a	a	PRON
ejpam-5393	67	4	of	of	ADP
ejpam-5393	67	5	a	a	DET
ejpam-5393	67	6	bitopological	bitopological	ADJ
ejpam-5393	67	7	space	space	NOUN
ejpam-5393	67	8	(	(	PUNCT
ejpam-5393	67	9	x	x	NOUN
ejpam-5393	67	10	,	,	PUNCT
ejpam-5393	67	11	τ1	τ1	NOUN
ejpam-5393	67	12	,	,	PUNCT
ejpam-5393	67	13	τ2	τ2	NOUN
ejpam-5393	67	14	)	)	PUNCT
ejpam-5393	67	15	is	be	AUX
ejpam-5393	67	16	said	say	VERB
ejpam-5393	67	17	to	to	PART
ejpam-5393	67	18	be	be	AUX
ejpam-5393	67	19	(	(	PUNCT
ejpam-5393	67	20	τ1	τ1	NOUN
ejpam-5393	67	21	,	,	PUNCT
ejpam-5393	67	22	τ2)r	τ2)r	NOUN
ejpam-5393	67	23	-	-	PUNCT
ejpam-5393	67	24	open	open	ADJ
ejpam-5393	68	1	[	[	X
ejpam-5393	68	2	57	57	NUM
ejpam-5393	68	3	]	]	PUNCT
ejpam-5393	68	4	(	(	PUNCT
ejpam-5393	68	5	resp	resp	NOUN
ejpam-5393	68	6	.	.	PUNCT
ejpam-5393	69	1	(	(	PUNCT
ejpam-5393	69	2	τ1	τ1	NOUN
ejpam-5393	69	3	,	,	PUNCT
ejpam-5393	69	4	τ2)s	τ2)s	NOUN
ejpam-5393	69	5	-	-	PUNCT
ejpam-5393	69	6	open	open	ADJ
ejpam-5393	69	7	[	[	X
ejpam-5393	69	8	6	6	NUM
ejpam-5393	69	9	]	]	PUNCT
ejpam-5393	69	10	,	,	PUNCT
ejpam-5393	69	11	(	(	PUNCT
ejpam-5393	69	12	τ1	τ1	NOUN
ejpam-5393	69	13	,	,	PUNCT
ejpam-5393	69	14	τ2)p	τ2)p	NOUN
ejpam-5393	69	15	-	-	ADJ
ejpam-5393	69	16	open	open	ADJ
ejpam-5393	69	17	[	[	X
ejpam-5393	69	18	6	6	NUM
ejpam-5393	69	19	]	]	PUNCT
ejpam-5393	69	20	,	,	PUNCT
ejpam-5393	69	21	(	(	PUNCT
ejpam-5393	69	22	τ1	τ1	NOUN
ejpam-5393	69	23	,	,	PUNCT
ejpam-5393	69	24	τ2)β	τ2)β	ADJ
ejpam-5393	69	25	-	-	PUNCT
ejpam-5393	69	26	open	open	NOUN
ejpam-5393	70	1	[	[	X
ejpam-5393	70	2	6	6	NUM
ejpam-5393	70	3	]	]	PUNCT
ejpam-5393	70	4	)	)	PUNCT
ejpam-5393	70	5	if	if	SCONJ
ejpam-5393	70	6	a	a	DET
ejpam-5393	70	7	=	=	PUNCT
ejpam-5393	70	8	τ1τ2	τ1τ2	NOUN
ejpam-5393	70	9	-	-	NOUN
ejpam-5393	70	10	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5393	70	11	-	-	PUNCT
ejpam-5393	70	12	cl(a	cl(a	NUM
ejpam-5393	70	13	)	)	PUNCT
ejpam-5393	70	14	)	)	PUNCT
ejpam-5393	70	15	(	(	PUNCT
ejpam-5393	70	16	resp	resp	NOUN
ejpam-5393	70	17	.	.	PUNCT
ejpam-5393	71	1	a	a	DET
ejpam-5393	71	2	⊆	⊆	NUM
ejpam-5393	71	3	τ1τ2	τ1τ2	NOUN
ejpam-5393	71	4	-	-	ADJ
ejpam-5393	71	5	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5393	71	6	-	-	PUNCT
ejpam-5393	71	7	int(a	int(a	NOUN
ejpam-5393	71	8	)	)	PUNCT
ejpam-5393	71	9	)	)	PUNCT
ejpam-5393	71	10	,	,	PUNCT
ejpam-5393	71	11	a	a	DET
ejpam-5393	71	12	⊆	⊆	NUM
ejpam-5393	71	13	τ1τ2	τ1τ2	NOUN
ejpam-5393	71	14	-	-	NOUN
ejpam-5393	71	15	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5393	71	16	-	-	PUNCT
ejpam-5393	71	17	cl(a	cl(a	NUM
ejpam-5393	71	18	)	)	PUNCT
ejpam-5393	71	19	)	)	PUNCT
ejpam-5393	71	20	,	,	PUNCT
ejpam-5393	71	21	a	a	DET
ejpam-5393	71	22	⊆	⊆	NUM
ejpam-5393	71	23	τ1τ2	τ1τ2	NOUN
ejpam-5393	71	24	-	-	PUNCT
ejpam-5393	71	25	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5393	71	26	-	-	PUNCT
ejpam-5393	71	27	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5393	71	28	-	-	PUNCT
ejpam-5393	71	29	cl(a	cl(a	NUM
ejpam-5393	71	30	)	)	PUNCT
ejpam-5393	71	31	)	)	PUNCT
ejpam-5393	71	32	)	)	PUNCT
ejpam-5393	71	33	)	)	PUNCT
ejpam-5393	71	34	.	.	PUNCT
ejpam-5393	72	1	the	the	DET
ejpam-5393	72	2	complement	complement	NOUN
ejpam-5393	72	3	of	of	ADP
ejpam-5393	72	4	a	a	DET
ejpam-5393	72	5	(	(	PUNCT
ejpam-5393	72	6	τ1	τ1	NOUN
ejpam-5393	72	7	,	,	PUNCT
ejpam-5393	72	8	τ2)r	τ2)r	NOUN
ejpam-5393	72	9	-	-	PUNCT
ejpam-5393	72	10	open	open	ADJ
ejpam-5393	72	11	(	(	PUNCT
ejpam-5393	72	12	resp	resp	NOUN
ejpam-5393	72	13	.	.	PUNCT
ejpam-5393	73	1	(	(	PUNCT
ejpam-5393	73	2	τ1	τ1	NOUN
ejpam-5393	73	3	,	,	PUNCT
ejpam-5393	73	4	τ2)sopen	τ2)sopen	ADJ
ejpam-5393	73	5	,	,	PUNCT
ejpam-5393	73	6	(	(	PUNCT
ejpam-5393	73	7	τ1	τ1	NOUN
ejpam-5393	73	8	,	,	PUNCT
ejpam-5393	73	9	τ2)p	τ2)p	NOUN
ejpam-5393	73	10	-	-	ADJ
ejpam-5393	73	11	open	open	ADJ
ejpam-5393	73	12	,	,	PUNCT
ejpam-5393	73	13	(	(	PUNCT
ejpam-5393	73	14	τ1	τ1	NOUN
ejpam-5393	73	15	,	,	PUNCT
ejpam-5393	73	16	τ2)β	τ2)β	ADJ
ejpam-5393	73	17	-	-	PUNCT
ejpam-5393	73	18	open	open	ADJ
ejpam-5393	73	19	)	)	PUNCT
ejpam-5393	73	20	set	set	NOUN
ejpam-5393	73	21	is	be	AUX
ejpam-5393	73	22	said	say	VERB
ejpam-5393	73	23	to	to	PART
ejpam-5393	73	24	be	be	AUX
ejpam-5393	73	25	(	(	PUNCT
ejpam-5393	73	26	τ1	τ1	NOUN
ejpam-5393	73	27	,	,	PUNCT
ejpam-5393	73	28	τ2)r	τ2)r	NOUN
ejpam-5393	73	29	-	-	PUNCT
ejpam-5393	73	30	closed	closed	ADJ
ejpam-5393	73	31	(	(	PUNCT
ejpam-5393	73	32	resp	resp	NOUN
ejpam-5393	73	33	.	.	PUNCT
ejpam-5393	74	1	(	(	PUNCT
ejpam-5393	74	2	τ1	τ1	NOUN
ejpam-5393	74	3	,	,	PUNCT
ejpam-5393	74	4	τ2)s	τ2)s	NOUN
ejpam-5393	74	5	-	-	PUNCT
ejpam-5393	74	6	closed	closed	ADJ
ejpam-5393	74	7	,	,	PUNCT
ejpam-5393	74	8	(	(	PUNCT
ejpam-5393	74	9	τ1	τ1	NOUN
ejpam-5393	74	10	,	,	PUNCT
ejpam-5393	74	11	τ2)p	τ2)p	NOUN
ejpam-5393	74	12	-	-	PUNCT
ejpam-5393	74	13	closed	closed	ADJ
ejpam-5393	74	14	,	,	PUNCT
ejpam-5393	74	15	(	(	PUNCT
ejpam-5393	74	16	τ1	τ1	NOUN
ejpam-5393	74	17	,	,	PUNCT
ejpam-5393	74	18	τ2)β	τ2)β	ADJ
ejpam-5393	74	19	-	-	PUNCT
ejpam-5393	74	20	closed	closed	ADJ
ejpam-5393	74	21	)	)	PUNCT
ejpam-5393	74	22	.	.	PUNCT
ejpam-5393	75	1	a	a	DET
ejpam-5393	75	2	subset	subset	NOUN
ejpam-5393	75	3	a	a	PRON
ejpam-5393	75	4	of	of	ADP
ejpam-5393	75	5	a	a	DET
ejpam-5393	75	6	bitopological	bitopological	ADJ
ejpam-5393	75	7	space	space	NOUN
ejpam-5393	75	8	(	(	PUNCT
ejpam-5393	75	9	x	x	NOUN
ejpam-5393	75	10	,	,	PUNCT
ejpam-5393	75	11	τ1	τ1	NOUN
ejpam-5393	75	12	,	,	PUNCT
ejpam-5393	75	13	τ2	τ2	NOUN
ejpam-5393	75	14	)	)	PUNCT
ejpam-5393	75	15	is	be	AUX
ejpam-5393	75	16	called	call	VERB
ejpam-5393	75	17	α(τ1	α(τ1	NOUN
ejpam-5393	75	18	,	,	PUNCT
ejpam-5393	75	19	τ2)-open	τ2)-open	ADJ
ejpam-5393	75	20	[	[	X
ejpam-5393	75	21	60	60	NUM
ejpam-5393	75	22	]	]	X
ejpam-5393	75	23	if	if	SCONJ
ejpam-5393	75	24	a	a	DET
ejpam-5393	75	25	⊆	⊆	NUM
ejpam-5393	75	26	τ1τ2	τ1τ2	NOUN
ejpam-5393	75	27	-	-	PUNCT
ejpam-5393	75	28	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5393	75	29	-	-	PUNCT
ejpam-5393	75	30	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5393	75	31	-	-	PUNCT
ejpam-5393	75	32	int(a	int(a	NOUN
ejpam-5393	75	33	)	)	PUNCT
ejpam-5393	75	34	)	)	PUNCT
ejpam-5393	75	35	)	)	PUNCT
ejpam-5393	75	36	.	.	PUNCT
ejpam-5393	76	1	the	the	DET
ejpam-5393	76	2	complement	complement	NOUN
ejpam-5393	76	3	of	of	ADP
ejpam-5393	76	4	an	an	DET
ejpam-5393	76	5	α(τ1	α(τ1	NOUN
ejpam-5393	76	6	,	,	PUNCT
ejpam-5393	76	7	τ2)open	τ2)open	PROPN
ejpam-5393	76	8	set	set	NOUN
ejpam-5393	76	9	is	be	AUX
ejpam-5393	76	10	called	call	VERB
ejpam-5393	76	11	α(τ1	α(τ1	NOUN
ejpam-5393	76	12	,	,	PUNCT
ejpam-5393	76	13	τ2)-closed	τ2)-closed	PROPN
ejpam-5393	76	14	.	.	PUNCT
ejpam-5393	77	1	the	the	DET
ejpam-5393	77	2	intersection	intersection	NOUN
ejpam-5393	77	3	of	of	ADP
ejpam-5393	77	4	all	all	DET
ejpam-5393	77	5	(	(	PUNCT
ejpam-5393	77	6	τ1	τ1	NOUN
ejpam-5393	77	7	,	,	PUNCT
ejpam-5393	77	8	τ2)s	τ2)s	NOUN
ejpam-5393	77	9	-	-	PUNCT
ejpam-5393	77	10	closed	close	VERB
ejpam-5393	77	11	sets	set	NOUN
ejpam-5393	77	12	of	of	ADP
ejpam-5393	77	13	x	x	PUNCT
ejpam-5393	77	14	containing	contain	VERB
ejpam-5393	77	15	a	a	PRON
ejpam-5393	77	16	is	be	AUX
ejpam-5393	77	17	called	call	VERB
ejpam-5393	77	18	the	the	DET
ejpam-5393	77	19	(	(	PUNCT
ejpam-5393	77	20	τ1	τ1	NOUN
ejpam-5393	77	21	,	,	PUNCT
ejpam-5393	77	22	τ2)s	τ2)s	NOUN
ejpam-5393	77	23	-	-	PUNCT
ejpam-5393	77	24	closure	closure	NOUN
ejpam-5393	77	25	[	[	X
ejpam-5393	77	26	6	6	NUM
ejpam-5393	77	27	]	]	PUNCT
ejpam-5393	77	28	of	of	ADP
ejpam-5393	77	29	a	a	PRON
ejpam-5393	77	30	and	and	CCONJ
ejpam-5393	77	31	is	be	AUX
ejpam-5393	77	32	denoted	denote	VERB
ejpam-5393	77	33	by	by	ADP
ejpam-5393	77	34	(	(	PUNCT
ejpam-5393	77	35	τ1	τ1	NOUN
ejpam-5393	77	36	,	,	PUNCT
ejpam-5393	77	37	τ2)-scl(a	τ2)-scl(a	PROPN
ejpam-5393	77	38	)	)	PUNCT
ejpam-5393	77	39	.	.	PUNCT
ejpam-5393	78	1	the	the	DET
ejpam-5393	78	2	union	union	NOUN
ejpam-5393	78	3	of	of	ADP
ejpam-5393	78	4	all	all	DET
ejpam-5393	78	5	(	(	PUNCT
ejpam-5393	78	6	τ1	τ1	NOUN
ejpam-5393	78	7	,	,	PUNCT
ejpam-5393	78	8	τ2)s	τ2)s	NOUN
ejpam-5393	78	9	-	-	PUNCT
ejpam-5393	78	10	open	open	ADJ
ejpam-5393	78	11	sets	set	NOUN
ejpam-5393	78	12	of	of	ADP
ejpam-5393	78	13	x	x	PUNCT
ejpam-5393	78	14	contained	contain	VERB
ejpam-5393	78	15	in	in	ADP
ejpam-5393	78	16	a	a	PRON
ejpam-5393	78	17	is	be	AUX
ejpam-5393	78	18	called	call	VERB
ejpam-5393	78	19	the	the	DET
ejpam-5393	78	20	(	(	PUNCT
ejpam-5393	78	21	τ1	τ1	NOUN
ejpam-5393	78	22	,	,	PUNCT
ejpam-5393	78	23	τ2)s	τ2)s	NOUN
ejpam-5393	78	24	-	-	ADJ
ejpam-5393	78	25	interior	interior	ADJ
ejpam-5393	78	26	[	[	X
ejpam-5393	78	27	6	6	NUM
ejpam-5393	78	28	]	]	PUNCT
ejpam-5393	78	29	of	of	ADP
ejpam-5393	78	30	a	a	PRON
ejpam-5393	78	31	and	and	CCONJ
ejpam-5393	78	32	is	be	AUX
ejpam-5393	78	33	denoted	denote	VERB
ejpam-5393	78	34	by	by	ADP
ejpam-5393	78	35	(	(	PUNCT
ejpam-5393	78	36	τ1	τ1	NOUN
ejpam-5393	78	37	,	,	PUNCT
ejpam-5393	78	38	τ2)-sint(a	τ2)-sint(a	PROPN
ejpam-5393	78	39	)	)	PUNCT
ejpam-5393	78	40	.	.	PUNCT
ejpam-5393	79	1	lemma	lemma	PROPN
ejpam-5393	79	2	2	2	NUM
ejpam-5393	79	3	.	.	X
ejpam-5393	80	1	for	for	ADP
ejpam-5393	80	2	a	a	DET
ejpam-5393	80	3	subset	subset	NOUN
ejpam-5393	80	4	a	a	PRON
ejpam-5393	80	5	of	of	ADP
ejpam-5393	80	6	a	a	DET
ejpam-5393	80	7	bitopological	bitopological	ADJ
ejpam-5393	80	8	space	space	NOUN
ejpam-5393	80	9	(	(	PUNCT
ejpam-5393	80	10	x	x	NOUN
ejpam-5393	80	11	,	,	PUNCT
ejpam-5393	80	12	τ1	τ1	NOUN
ejpam-5393	80	13	,	,	PUNCT
ejpam-5393	80	14	τ2	τ2	NOUN
ejpam-5393	80	15	)	)	PUNCT
ejpam-5393	80	16	,	,	PUNCT
ejpam-5393	80	17	the	the	DET
ejpam-5393	80	18	following	follow	VERB
ejpam-5393	80	19	properties	property	NOUN
ejpam-5393	80	20	hold	hold	VERB
ejpam-5393	80	21	:	:	PUNCT
ejpam-5393	80	22	(	(	PUNCT
ejpam-5393	80	23	1	1	X
ejpam-5393	80	24	)	)	PUNCT
ejpam-5393	80	25	(	(	PUNCT
ejpam-5393	80	26	τ1	τ1	NOUN
ejpam-5393	80	27	,	,	PUNCT
ejpam-5393	80	28	τ2)-scl(a	τ2)-scl(a	NOUN
ejpam-5393	80	29	)	)	PUNCT
ejpam-5393	80	30	=	=	PUNCT
ejpam-5393	81	1	τ1τ2	τ1τ2	NOUN
ejpam-5393	81	2	-	-	NOUN
ejpam-5393	81	3	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5393	81	4	-	-	PUNCT
ejpam-5393	81	5	cl(a	cl(a	NUM
ejpam-5393	81	6	)	)	PUNCT
ejpam-5393	81	7	)	)	PUNCT
ejpam-5393	82	1	∪a	∪a	X
ejpam-5393	83	1	[	[	X
ejpam-5393	83	2	6	6	NUM
ejpam-5393	83	3	]	]	PUNCT
ejpam-5393	83	4	;	;	PUNCT
ejpam-5393	83	5	(	(	PUNCT
ejpam-5393	83	6	2	2	X
ejpam-5393	83	7	)	)	PUNCT
ejpam-5393	83	8	(	(	PUNCT
ejpam-5393	83	9	τ1	τ1	NOUN
ejpam-5393	83	10	,	,	PUNCT
ejpam-5393	83	11	τ2)-sint(a	τ2)-sint(a	PROPN
ejpam-5393	83	12	)	)	PUNCT
ejpam-5393	84	1	=	=	PUNCT
ejpam-5393	84	2	τ1τ2	τ1τ2	NOUN
ejpam-5393	84	3	-	-	ADJ
ejpam-5393	84	4	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5393	84	5	-	-	PUNCT
ejpam-5393	84	6	int(a	int(a	NOUN
ejpam-5393	84	7	)	)	PUNCT
ejpam-5393	84	8	)	)	PUNCT
ejpam-5393	85	1	∩a	∩a	PROPN
ejpam-5393	86	1	[	[	X
ejpam-5393	86	2	50	50	NUM
ejpam-5393	86	3	]	]	PUNCT
ejpam-5393	86	4	.	.	PUNCT
ejpam-5393	87	1	by	by	ADP
ejpam-5393	87	2	a	a	DET
ejpam-5393	87	3	multifunction	multifunction	NOUN
ejpam-5393	87	4	f	f	NOUN
ejpam-5393	87	5	:	:	PUNCT
ejpam-5393	87	6	x	x	X
ejpam-5393	87	7	→	→	SYM
ejpam-5393	87	8	y	y	PROPN
ejpam-5393	87	9	,	,	PUNCT
ejpam-5393	87	10	we	we	PRON
ejpam-5393	87	11	mean	mean	VERB
ejpam-5393	87	12	a	a	DET
ejpam-5393	87	13	point	point	NOUN
ejpam-5393	87	14	-	-	PUNCT
ejpam-5393	87	15	to	to	ADP
ejpam-5393	87	16	-	-	PUNCT
ejpam-5393	87	17	set	set	VERB
ejpam-5393	87	18	correspondence	correspondence	NOUN
ejpam-5393	87	19	from	from	ADP
ejpam-5393	87	20	x	x	PUNCT
ejpam-5393	87	21	into	into	ADP
ejpam-5393	87	22	y	y	PROPN
ejpam-5393	87	23	,	,	PUNCT
ejpam-5393	87	24	and	and	CCONJ
ejpam-5393	87	25	we	we	PRON
ejpam-5393	87	26	always	always	ADV
ejpam-5393	87	27	assume	assume	VERB
ejpam-5393	87	28	that	that	SCONJ
ejpam-5393	87	29	f	f	PROPN
ejpam-5393	87	30	(	(	PUNCT
ejpam-5393	87	31	x	x	X
ejpam-5393	87	32	)	)	PUNCT
ejpam-5393	87	33	̸=	̸=	NOUN
ejpam-5393	87	34	∅	∅	NOUN
ejpam-5393	87	35	for	for	ADP
ejpam-5393	87	36	all	all	PRON
ejpam-5393	87	37	x	x	SYM
ejpam-5393	87	38	∈	∈	ADJ
ejpam-5393	87	39	x.	x.	NOUN
ejpam-5393	87	40	for	for	ADP
ejpam-5393	87	41	a	a	DET
ejpam-5393	87	42	multifunction	multifunction	NOUN
ejpam-5393	87	43	f	f	NOUN
ejpam-5393	88	1	:	:	PUNCT
ejpam-5393	88	2	x	x	X
ejpam-5393	88	3	→	→	SYM
ejpam-5393	88	4	y	y	PROPN
ejpam-5393	88	5	,	,	PUNCT
ejpam-5393	88	6	following	follow	VERB
ejpam-5393	88	7	[	[	X
ejpam-5393	88	8	1	1	X
ejpam-5393	88	9	]	]	PUNCT
ejpam-5393	88	10	we	we	PRON
ejpam-5393	88	11	shall	shall	AUX
ejpam-5393	88	12	denote	denote	VERB
ejpam-5393	88	13	the	the	DET
ejpam-5393	88	14	upper	upper	ADJ
ejpam-5393	88	15	and	and	CCONJ
ejpam-5393	88	16	lower	low	ADJ
ejpam-5393	88	17	inverse	inverse	NOUN
ejpam-5393	88	18	of	of	ADP
ejpam-5393	88	19	a	a	DET
ejpam-5393	88	20	set	set	NOUN
ejpam-5393	88	21	b	b	PROPN
ejpam-5393	88	22	of	of	ADP
ejpam-5393	88	23	y	y	PROPN
ejpam-5393	88	24	by	by	ADP
ejpam-5393	88	25	f+(b	f+(b	NOUN
ejpam-5393	88	26	)	)	PUNCT
ejpam-5393	88	27	and	and	CCONJ
ejpam-5393	88	28	f−(b	f−(b	NOUN
ejpam-5393	88	29	)	)	PUNCT
ejpam-5393	88	30	,	,	PUNCT
ejpam-5393	88	31	respectively	respectively	ADV
ejpam-5393	88	32	,	,	PUNCT
ejpam-5393	88	33	that	that	ADV
ejpam-5393	88	34	is	is	ADV
ejpam-5393	88	35	,	,	PUNCT
ejpam-5393	88	36	f+(b	f+(b	NOUN
ejpam-5393	88	37	)	)	PUNCT
ejpam-5393	88	38	=	=	PRON
ejpam-5393	89	1	{	{	PUNCT
ejpam-5393	89	2	x	x	PUNCT
ejpam-5393	89	3	∈	∈	PROPN
ejpam-5393	89	4	x	x	INTJ
ejpam-5393	90	1	|	|	NOUN
ejpam-5393	90	2	f	f	X
ejpam-5393	90	3	(	(	PUNCT
ejpam-5393	90	4	x	x	NOUN
ejpam-5393	90	5	)	)	PUNCT
ejpam-5393	90	6	⊆	⊆	NUM
ejpam-5393	90	7	b	b	NOUN
ejpam-5393	90	8	}	}	PUNCT
ejpam-5393	90	9	and	and	CCONJ
ejpam-5393	90	10	f−(b	f−(b	PROPN
ejpam-5393	90	11	)	)	PUNCT
ejpam-5393	90	12	=	=	PRON
ejpam-5393	91	1	{	{	PUNCT
ejpam-5393	91	2	x	x	PUNCT
ejpam-5393	91	3	∈	∈	PROPN
ejpam-5393	91	4	x	x	INTJ
ejpam-5393	92	1	|	|	NOUN
ejpam-5393	92	2	f	f	X
ejpam-5393	92	3	(	(	PUNCT
ejpam-5393	92	4	x	x	NOUN
ejpam-5393	92	5	)	)	PUNCT
ejpam-5393	92	6	∩b	∩b	NOUN
ejpam-5393	92	7	̸=	̸=	PROPN
ejpam-5393	92	8	∅	∅	NOUN
ejpam-5393	92	9	}	}	PUNCT
ejpam-5393	92	10	.	.	PUNCT
ejpam-5393	93	1	in	in	ADP
ejpam-5393	93	2	particular	particular	ADJ
ejpam-5393	93	3	,	,	PUNCT
ejpam-5393	93	4	f−(y	f−(y	NOUN
ejpam-5393	93	5	)	)	PUNCT
ejpam-5393	93	6	=	=	SYM
ejpam-5393	94	1	{	{	PUNCT
ejpam-5393	94	2	x	x	PUNCT
ejpam-5393	94	3	∈	∈	PROPN
ejpam-5393	94	4	x	x	INTJ
ejpam-5393	95	1	|	|	ADV
ejpam-5393	95	2	y	y	PROPN
ejpam-5393	95	3	∈	∈	PROPN
ejpam-5393	95	4	f	f	X
ejpam-5393	95	5	(	(	PUNCT
ejpam-5393	95	6	x	x	NOUN
ejpam-5393	95	7	)	)	PUNCT
ejpam-5393	95	8	}	}	PUNCT
ejpam-5393	95	9	for	for	ADP
ejpam-5393	95	10	each	each	DET
ejpam-5393	95	11	point	point	NOUN
ejpam-5393	95	12	y	y	PROPN
ejpam-5393	95	13	∈	∈	PROPN
ejpam-5393	95	14	y	y	PROPN
ejpam-5393	95	15	.	.	PUNCT
ejpam-5393	96	1	for	for	ADP
ejpam-5393	96	2	each	each	DET
ejpam-5393	96	3	a	a	DET
ejpam-5393	96	4	⊆	⊆	NUM
ejpam-5393	96	5	x	x	SYM
ejpam-5393	96	6	,	,	PUNCT
ejpam-5393	96	7	f	f	PROPN
ejpam-5393	96	8	(	(	PUNCT
ejpam-5393	96	9	a	a	NOUN
ejpam-5393	96	10	)	)	PUNCT
ejpam-5393	96	11	=	=	SYM
ejpam-5393	96	12	∪x∈af	∪x∈af	NOUN
ejpam-5393	96	13	(	(	PUNCT
ejpam-5393	96	14	x	x	NOUN
ejpam-5393	96	15	)	)	PUNCT
ejpam-5393	96	16	.	.	PUNCT
ejpam-5393	97	1	3	3	X
ejpam-5393	97	2	.	.	X
ejpam-5393	97	3	upper	upper	ADJ
ejpam-5393	97	4	and	and	CCONJ
ejpam-5393	97	5	lower	low	ADJ
ejpam-5393	97	6	c	c	NOUN
ejpam-5393	97	7	-	-	PUNCT
ejpam-5393	97	8	quasi	quasi	ADJ
ejpam-5393	97	9	(	(	PUNCT
ejpam-5393	97	10	τ1	τ1	PROPN
ejpam-5393	97	11	,	,	PUNCT
ejpam-5393	97	12	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	97	13	multifunctions	multifunction	NOUN
ejpam-5393	97	14	in	in	ADP
ejpam-5393	97	15	this	this	DET
ejpam-5393	97	16	section	section	NOUN
ejpam-5393	97	17	,	,	PUNCT
ejpam-5393	97	18	we	we	PRON
ejpam-5393	97	19	introduce	introduce	VERB
ejpam-5393	97	20	the	the	DET
ejpam-5393	97	21	notions	notion	NOUN
ejpam-5393	97	22	of	of	ADP
ejpam-5393	97	23	upper	upper	ADJ
ejpam-5393	97	24	and	and	CCONJ
ejpam-5393	97	25	lower	low	ADJ
ejpam-5393	97	26	c	c	NOUN
ejpam-5393	97	27	-	-	PUNCT
ejpam-5393	97	28	quasi	quasi	ADJ
ejpam-5393	97	29	(	(	PUNCT
ejpam-5393	97	30	τ1	τ1	PROPN
ejpam-5393	97	31	,	,	PUNCT
ejpam-5393	97	32	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	97	33	multifunctions	multifunction	NOUN
ejpam-5393	97	34	.	.	PUNCT
ejpam-5393	98	1	moreover	moreover	ADV
ejpam-5393	98	2	,	,	PUNCT
ejpam-5393	98	3	we	we	PRON
ejpam-5393	98	4	investigate	investigate	VERB
ejpam-5393	98	5	some	some	DET
ejpam-5393	98	6	characterizations	characterization	NOUN
ejpam-5393	98	7	of	of	ADP
ejpam-5393	98	8	upper	upper	ADJ
ejpam-5393	98	9	and	and	CCONJ
ejpam-5393	98	10	lower	low	ADJ
ejpam-5393	98	11	c	c	NOUN
ejpam-5393	98	12	-	-	PUNCT
ejpam-5393	98	13	quasi	quasi	ADJ
ejpam-5393	98	14	(	(	PUNCT
ejpam-5393	98	15	τ1	τ1	PROPN
ejpam-5393	98	16	,	,	PUNCT
ejpam-5393	98	17	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	98	18	multifunctions	multifunction	NOUN
ejpam-5393	98	19	.	.	PUNCT
ejpam-5393	99	1	p.	p.	NOUN
ejpam-5393	99	2	pue	pue	NOUN
ejpam-5393	99	3	-	-	PUNCT
ejpam-5393	99	4	on	on	ADP
ejpam-5393	99	5	,	,	PUNCT
ejpam-5393	99	6	a.	a.	PROPN
ejpam-5393	99	7	sama	sama	PROPN
ejpam-5393	99	8	-	-	PUNCT
ejpam-5393	99	9	ae	ae	PROPN
ejpam-5393	99	10	,	,	PUNCT
ejpam-5393	99	11	c.	c.	PROPN
ejpam-5393	99	12	boonpok	boonpok	PROPN
ejpam-5393	99	13	/	/	SYM
ejpam-5393	99	14	eur	eur	PROPN
ejpam-5393	99	15	.	.	PUNCT
ejpam-5393	100	1	j.	j.	PROPN
ejpam-5393	100	2	pure	pure	PROPN
ejpam-5393	100	3	appl	appl	PROPN
ejpam-5393	100	4	.	.	PROPN
ejpam-5393	100	5	math	math	PROPN
ejpam-5393	100	6	,	,	PUNCT
ejpam-5393	100	7	17	17	NUM
ejpam-5393	100	8	(	(	PUNCT
ejpam-5393	100	9	4	4	NUM
ejpam-5393	100	10	)	)	PUNCT
ejpam-5393	100	11	(	(	PUNCT
ejpam-5393	100	12	2024	2024	NUM
ejpam-5393	100	13	)	)	PUNCT
ejpam-5393	100	14	,	,	PUNCT
ejpam-5393	100	15	3242	3242	NUM
ejpam-5393	100	16	-	-	SYM
ejpam-5393	100	17	3253	3253	NUM
ejpam-5393	100	18	3245	3245	NUM
ejpam-5393	100	19	definition	definition	NOUN
ejpam-5393	100	20	1	1	NUM
ejpam-5393	100	21	.	.	PUNCT
ejpam-5393	101	1	a	a	DET
ejpam-5393	101	2	multifunction	multifunction	NOUN
ejpam-5393	101	3	f	f	NOUN
ejpam-5393	101	4	:	:	PUNCT
ejpam-5393	101	5	(	(	PUNCT
ejpam-5393	101	6	x	x	NOUN
ejpam-5393	101	7	,	,	PUNCT
ejpam-5393	101	8	τ1	τ1	NOUN
ejpam-5393	101	9	,	,	PUNCT
ejpam-5393	101	10	τ2	τ2	NOUN
ejpam-5393	101	11	)	)	PUNCT
ejpam-5393	101	12	→	→	SYM
ejpam-5393	101	13	(	(	PUNCT
ejpam-5393	101	14	y	y	PROPN
ejpam-5393	101	15	,	,	PUNCT
ejpam-5393	101	16	σ1	σ1	PROPN
ejpam-5393	101	17	,	,	PUNCT
ejpam-5393	101	18	σ2	σ2	PROPN
ejpam-5393	101	19	)	)	PUNCT
ejpam-5393	101	20	is	be	AUX
ejpam-5393	101	21	called	call	VERB
ejpam-5393	101	22	upper	upper	ADJ
ejpam-5393	101	23	c	c	NOUN
ejpam-5393	101	24	-	-	PUNCT
ejpam-5393	101	25	quasi	quasi	ADJ
ejpam-5393	101	26	(	(	PUNCT
ejpam-5393	101	27	τ1	τ1	NOUN
ejpam-5393	101	28	,	,	PUNCT
ejpam-5393	101	29	τ2)continuous	τ2)continuous	ADJ
ejpam-5393	101	30	at	at	ADP
ejpam-5393	101	31	a	a	DET
ejpam-5393	101	32	point	point	NOUN
ejpam-5393	101	33	x	x	SYM
ejpam-5393	101	34	∈	∈	NOUN
ejpam-5393	101	35	x	x	PUNCT
ejpam-5393	101	36	if	if	SCONJ
ejpam-5393	101	37	for	for	ADP
ejpam-5393	101	38	each	each	DET
ejpam-5393	101	39	σ1σ2	σ1σ2	VERB
ejpam-5393	101	40	-	-	ADJ
ejpam-5393	101	41	open	open	ADJ
ejpam-5393	101	42	set	set	NOUN
ejpam-5393	101	43	v	v	NOUN
ejpam-5393	101	44	of	of	ADP
ejpam-5393	101	45	y	y	PROPN
ejpam-5393	101	46	containing	contain	VERB
ejpam-5393	101	47	f	f	PROPN
ejpam-5393	101	48	(	(	PUNCT
ejpam-5393	101	49	x	x	NOUN
ejpam-5393	101	50	)	)	PUNCT
ejpam-5393	101	51	and	and	CCONJ
ejpam-5393	101	52	having	have	VERB
ejpam-5393	101	53	σ1σ2	σ1σ2	NOUN
ejpam-5393	101	54	-	-	ADJ
ejpam-5393	101	55	compact	compact	ADJ
ejpam-5393	101	56	complement	complement	NOUN
ejpam-5393	101	57	and	and	CCONJ
ejpam-5393	101	58	for	for	ADP
ejpam-5393	101	59	each	each	DET
ejpam-5393	101	60	τ1τ2	τ1τ2	ADJ
ejpam-5393	101	61	-	-	ADJ
ejpam-5393	101	62	open	open	ADJ
ejpam-5393	101	63	set	set	ADJ
ejpam-5393	101	64	u	u	NOUN
ejpam-5393	101	65	of	of	ADP
ejpam-5393	101	66	x	x	PUNCT
ejpam-5393	101	67	containing	contain	VERB
ejpam-5393	101	68	x	x	PRON
ejpam-5393	101	69	,	,	PUNCT
ejpam-5393	101	70	there	there	PRON
ejpam-5393	101	71	exists	exist	VERB
ejpam-5393	101	72	a	a	DET
ejpam-5393	101	73	nonempty	nonempty	ADJ
ejpam-5393	101	74	τ1τ2	τ1τ2	NOUN
ejpam-5393	101	75	-	-	ADJ
ejpam-5393	101	76	open	open	ADJ
ejpam-5393	101	77	set	set	NOUN
ejpam-5393	101	78	g	g	PROPN
ejpam-5393	101	79	such	such	ADJ
ejpam-5393	101	80	that	that	SCONJ
ejpam-5393	101	81	g	g	PROPN
ejpam-5393	101	82	⊆	⊆	NUM
ejpam-5393	101	83	u	u	NOUN
ejpam-5393	101	84	and	and	CCONJ
ejpam-5393	101	85	f	f	PROPN
ejpam-5393	101	86	(	(	PUNCT
ejpam-5393	101	87	g	g	NOUN
ejpam-5393	101	88	)	)	PUNCT
ejpam-5393	101	89	⊆	⊆	NUM
ejpam-5393	101	90	v	v	NOUN
ejpam-5393	101	91	.	.	PUNCT
ejpam-5393	102	1	a	a	DET
ejpam-5393	102	2	multifunction	multifunction	NOUN
ejpam-5393	102	3	f	f	NOUN
ejpam-5393	102	4	:	:	PUNCT
ejpam-5393	102	5	(	(	PUNCT
ejpam-5393	102	6	x	x	NOUN
ejpam-5393	102	7	,	,	PUNCT
ejpam-5393	102	8	τ1	τ1	NOUN
ejpam-5393	102	9	,	,	PUNCT
ejpam-5393	102	10	τ2	τ2	NOUN
ejpam-5393	102	11	)	)	PUNCT
ejpam-5393	102	12	→	→	SYM
ejpam-5393	102	13	(	(	PUNCT
ejpam-5393	102	14	y	y	PROPN
ejpam-5393	102	15	,	,	PUNCT
ejpam-5393	102	16	σ1	σ1	PROPN
ejpam-5393	102	17	,	,	PUNCT
ejpam-5393	102	18	σ2	σ2	PROPN
ejpam-5393	102	19	)	)	PUNCT
ejpam-5393	102	20	is	be	AUX
ejpam-5393	102	21	called	call	VERB
ejpam-5393	102	22	upper	upper	ADJ
ejpam-5393	102	23	c	c	NOUN
ejpam-5393	102	24	-	-	PUNCT
ejpam-5393	102	25	quasi	quasi	ADJ
ejpam-5393	102	26	(	(	PUNCT
ejpam-5393	102	27	τ1	τ1	NOUN
ejpam-5393	102	28	,	,	PUNCT
ejpam-5393	102	29	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	102	30	if	if	SCONJ
ejpam-5393	102	31	f	f	PROPN
ejpam-5393	102	32	has	have	VERB
ejpam-5393	102	33	this	this	DET
ejpam-5393	102	34	property	property	NOUN
ejpam-5393	102	35	at	at	ADP
ejpam-5393	102	36	every	every	DET
ejpam-5393	102	37	point	point	NOUN
ejpam-5393	102	38	of	of	ADP
ejpam-5393	102	39	x.	x.	NOUN
ejpam-5393	102	40	theorem	theorem	VERB
ejpam-5393	102	41	1	1	NUM
ejpam-5393	102	42	.	.	PUNCT
ejpam-5393	102	43	a	a	DET
ejpam-5393	102	44	multifunction	multifunction	NOUN
ejpam-5393	102	45	f	f	NOUN
ejpam-5393	102	46	:	:	PUNCT
ejpam-5393	102	47	(	(	PUNCT
ejpam-5393	102	48	x	x	NOUN
ejpam-5393	102	49	,	,	PUNCT
ejpam-5393	102	50	τ1	τ1	NOUN
ejpam-5393	102	51	,	,	PUNCT
ejpam-5393	102	52	τ2	τ2	NOUN
ejpam-5393	102	53	)	)	PUNCT
ejpam-5393	102	54	→	→	SYM
ejpam-5393	102	55	(	(	PUNCT
ejpam-5393	102	56	y	y	PROPN
ejpam-5393	102	57	,	,	PUNCT
ejpam-5393	102	58	σ1	σ1	PROPN
ejpam-5393	102	59	,	,	PUNCT
ejpam-5393	102	60	σ2	σ2	PROPN
ejpam-5393	102	61	)	)	PUNCT
ejpam-5393	102	62	is	be	AUX
ejpam-5393	102	63	upper	upper	ADJ
ejpam-5393	102	64	c	c	NOUN
ejpam-5393	102	65	-	-	PUNCT
ejpam-5393	102	66	quasi	quasi	ADJ
ejpam-5393	102	67	(	(	PUNCT
ejpam-5393	102	68	τ1	τ1	NOUN
ejpam-5393	102	69	,	,	PUNCT
ejpam-5393	102	70	τ2)continuous	τ2)continuous	ADJ
ejpam-5393	102	71	at	at	ADP
ejpam-5393	102	72	x	x	X
ejpam-5393	102	73	∈	∈	PROPN
ejpam-5393	102	74	x	x	SYM
ejpam-5393	102	75	if	if	SCONJ
ejpam-5393	102	76	and	and	CCONJ
ejpam-5393	102	77	only	only	ADV
ejpam-5393	102	78	if	if	SCONJ
ejpam-5393	102	79	for	for	ADP
ejpam-5393	102	80	every	every	DET
ejpam-5393	102	81	σ1σ2	σ1σ2	NUM
ejpam-5393	102	82	-	-	ADJ
ejpam-5393	102	83	open	open	ADJ
ejpam-5393	102	84	set	set	NOUN
ejpam-5393	102	85	v	v	NOUN
ejpam-5393	102	86	of	of	ADP
ejpam-5393	102	87	y	y	PROPN
ejpam-5393	102	88	containing	contain	VERB
ejpam-5393	102	89	f	f	PROPN
ejpam-5393	102	90	(	(	PUNCT
ejpam-5393	102	91	x	x	NOUN
ejpam-5393	102	92	)	)	PUNCT
ejpam-5393	102	93	and	and	CCONJ
ejpam-5393	102	94	having	have	VERB
ejpam-5393	102	95	σ1σ2	σ1σ2	NOUN
ejpam-5393	102	96	-	-	ADJ
ejpam-5393	102	97	compact	compact	ADJ
ejpam-5393	102	98	complement	complement	NOUN
ejpam-5393	102	99	,	,	PUNCT
ejpam-5393	102	100	there	there	PRON
ejpam-5393	102	101	exists	exist	VERB
ejpam-5393	102	102	a	a	DET
ejpam-5393	102	103	(	(	PUNCT
ejpam-5393	102	104	τ1	τ1	NOUN
ejpam-5393	102	105	,	,	PUNCT
ejpam-5393	102	106	τ2)s	τ2)s	NOUN
ejpam-5393	102	107	-	-	PUNCT
ejpam-5393	102	108	open	open	ADJ
ejpam-5393	102	109	set	set	NOUN
ejpam-5393	102	110	u	u	NOUN
ejpam-5393	102	111	of	of	ADP
ejpam-5393	102	112	x	x	PUNCT
ejpam-5393	102	113	containing	contain	VERB
ejpam-5393	102	114	x	x	PUNCT
ejpam-5393	102	115	such	such	ADJ
ejpam-5393	102	116	that	that	SCONJ
ejpam-5393	102	117	f	f	PROPN
ejpam-5393	102	118	(	(	PUNCT
ejpam-5393	102	119	u	u	NOUN
ejpam-5393	102	120	)	)	PUNCT
ejpam-5393	102	121	⊆	⊆	NUM
ejpam-5393	102	122	v	v	NOUN
ejpam-5393	102	123	.	.	PUNCT
ejpam-5393	103	1	proof	proof	NOUN
ejpam-5393	103	2	.	.	PUNCT
ejpam-5393	104	1	suppose	suppose	VERB
ejpam-5393	104	2	that	that	SCONJ
ejpam-5393	104	3	f	f	PROPN
ejpam-5393	104	4	is	be	AUX
ejpam-5393	104	5	upper	upper	ADJ
ejpam-5393	104	6	c	c	NOUN
ejpam-5393	104	7	-	-	PUNCT
ejpam-5393	104	8	quasi	quasi	ADJ
ejpam-5393	104	9	(	(	PUNCT
ejpam-5393	104	10	τ1	τ1	NOUN
ejpam-5393	104	11	,	,	PUNCT
ejpam-5393	104	12	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	104	13	at	at	ADP
ejpam-5393	104	14	x	x	SYM
ejpam-5393	104	15	∈	∈	PROPN
ejpam-5393	104	16	x.	x.	NOUN
ejpam-5393	104	17	let	let	VERB
ejpam-5393	104	18	v	v	PART
ejpam-5393	104	19	be	be	AUX
ejpam-5393	104	20	any	any	DET
ejpam-5393	104	21	σ1σ2	σ1σ2	NOUN
ejpam-5393	104	22	-	-	ADJ
ejpam-5393	104	23	open	open	ADJ
ejpam-5393	104	24	set	set	NOUN
ejpam-5393	104	25	of	of	ADP
ejpam-5393	104	26	y	y	PROPN
ejpam-5393	104	27	having	have	VERB
ejpam-5393	104	28	σ1σ2	σ1σ2	VERB
ejpam-5393	104	29	-	-	ADJ
ejpam-5393	104	30	compact	compact	ADJ
ejpam-5393	104	31	complement	complement	NOUN
ejpam-5393	104	32	such	such	ADJ
ejpam-5393	104	33	that	that	SCONJ
ejpam-5393	104	34	f	f	PROPN
ejpam-5393	104	35	(	(	PUNCT
ejpam-5393	104	36	x	x	X
ejpam-5393	104	37	)	)	PUNCT
ejpam-5393	104	38	⊆	⊆	NUM
ejpam-5393	104	39	v	v	NOUN
ejpam-5393	104	40	.	.	PUNCT
ejpam-5393	105	1	for	for	ADP
ejpam-5393	105	2	each	each	DET
ejpam-5393	105	3	τ1τ2	τ1τ2	ADJ
ejpam-5393	105	4	-	-	ADJ
ejpam-5393	105	5	open	open	ADJ
ejpam-5393	105	6	set	set	ADJ
ejpam-5393	105	7	u	u	NOUN
ejpam-5393	105	8	of	of	ADP
ejpam-5393	105	9	x	x	PUNCT
ejpam-5393	105	10	containing	contain	VERB
ejpam-5393	105	11	x	x	PRON
ejpam-5393	105	12	,	,	PUNCT
ejpam-5393	105	13	there	there	PRON
ejpam-5393	105	14	exists	exist	VERB
ejpam-5393	105	15	a	a	DET
ejpam-5393	105	16	nonempty	nonempty	ADJ
ejpam-5393	105	17	τ1τ2	τ1τ2	NOUN
ejpam-5393	105	18	-	-	ADJ
ejpam-5393	105	19	open	open	ADJ
ejpam-5393	105	20	set	set	ADJ
ejpam-5393	105	21	gu	gu	NOUN
ejpam-5393	105	22	of	of	ADP
ejpam-5393	105	23	x	x	SYM
ejpam-5393	105	24	such	such	ADJ
ejpam-5393	105	25	that	that	DET
ejpam-5393	105	26	gu	gu	NOUN
ejpam-5393	105	27	⊆	⊆	NUM
ejpam-5393	105	28	u	u	NOUN
ejpam-5393	105	29	and	and	CCONJ
ejpam-5393	105	30	f	f	PROPN
ejpam-5393	105	31	(	(	PUNCT
ejpam-5393	105	32	gu	gu	NOUN
ejpam-5393	105	33	)	)	PUNCT
ejpam-5393	105	34	⊆	⊆	NUM
ejpam-5393	105	35	v	v	NOUN
ejpam-5393	105	36	.	.	PUNCT
ejpam-5393	106	1	put	put	VERB
ejpam-5393	106	2	w	w	NOUN
ejpam-5393	106	3	=	=	SYM
ejpam-5393	107	1	∪{gu	∪{gu	PROPN
ejpam-5393	107	2	|	|	ADV
ejpam-5393	107	3	u	u	NOUN
ejpam-5393	107	4	is	be	AUX
ejpam-5393	107	5	τ1τ2	τ1τ2	VERB
ejpam-5393	107	6	-	-	ADJ
ejpam-5393	107	7	open	open	ADJ
ejpam-5393	107	8	,	,	PUNCT
ejpam-5393	107	9	x	x	SYM
ejpam-5393	107	10	∈	∈	NOUN
ejpam-5393	107	11	u	u	NOUN
ejpam-5393	107	12	}	}	PUNCT
ejpam-5393	107	13	.	.	PUNCT
ejpam-5393	108	1	then	then	ADV
ejpam-5393	108	2	,	,	PUNCT
ejpam-5393	108	3	w	w	PROPN
ejpam-5393	108	4	is	be	AUX
ejpam-5393	108	5	a	a	DET
ejpam-5393	108	6	τ1τ2	τ1τ2	ADJ
ejpam-5393	108	7	-	-	ADJ
ejpam-5393	108	8	open	open	ADJ
ejpam-5393	108	9	set	set	NOUN
ejpam-5393	108	10	and	and	CCONJ
ejpam-5393	108	11	x	x	PART
ejpam-5393	108	12	∈	∈	PROPN
ejpam-5393	108	13	τ1τ2	τ1τ2	NOUN
ejpam-5393	108	14	-	-	NOUN
ejpam-5393	108	15	cl(w	cl(w	NOUN
ejpam-5393	108	16	)	)	PUNCT
ejpam-5393	108	17	.	.	PUNCT
ejpam-5393	109	1	let	let	VERB
ejpam-5393	109	2	h	h	NOUN
ejpam-5393	110	1	=	=	NOUN
ejpam-5393	110	2	w	w	NOUN
ejpam-5393	110	3	∪	∪	X
ejpam-5393	110	4	{	{	PUNCT
ejpam-5393	110	5	x	x	NOUN
ejpam-5393	110	6	}	}	PUNCT
ejpam-5393	110	7	,	,	PUNCT
ejpam-5393	110	8	then	then	ADV
ejpam-5393	110	9	w	w	PROPN
ejpam-5393	110	10	⊆	⊆	NUM
ejpam-5393	110	11	h	h	NOUN
ejpam-5393	110	12	⊆	⊆	NUM
ejpam-5393	110	13	τ1τ2	τ1τ2	NOUN
ejpam-5393	110	14	-	-	NOUN
ejpam-5393	110	15	cl(w	cl(w	NOUN
ejpam-5393	110	16	)	)	PUNCT
ejpam-5393	110	17	;	;	PUNCT
ejpam-5393	110	18	hence	hence	ADV
ejpam-5393	110	19	h	h	NOUN
ejpam-5393	110	20	is	be	AUX
ejpam-5393	110	21	a	a	DET
ejpam-5393	110	22	(	(	PUNCT
ejpam-5393	110	23	τ1	τ1	NOUN
ejpam-5393	110	24	,	,	PUNCT
ejpam-5393	110	25	τ2)s	τ2)s	NOUN
ejpam-5393	110	26	-	-	PUNCT
ejpam-5393	110	27	open	open	ADJ
ejpam-5393	110	28	set	set	NOUN
ejpam-5393	110	29	of	of	ADP
ejpam-5393	110	30	x	x	PUNCT
ejpam-5393	110	31	containing	contain	VERB
ejpam-5393	110	32	x	x	PROPN
ejpam-5393	110	33	and	and	CCONJ
ejpam-5393	110	34	f	f	PROPN
ejpam-5393	110	35	(	(	PUNCT
ejpam-5393	110	36	h	h	NOUN
ejpam-5393	110	37	)	)	PUNCT
ejpam-5393	110	38	⊆	⊆	NUM
ejpam-5393	110	39	v	v	NOUN
ejpam-5393	110	40	.	.	PUNCT
ejpam-5393	111	1	conversely	conversely	ADV
ejpam-5393	111	2	,	,	PUNCT
ejpam-5393	111	3	let	let	VERB
ejpam-5393	111	4	x	x	X
ejpam-5393	111	5	∈	∈	PROPN
ejpam-5393	111	6	x	x	X
ejpam-5393	111	7	and	and	CCONJ
ejpam-5393	111	8	v	v	AUX
ejpam-5393	111	9	be	be	AUX
ejpam-5393	111	10	any	any	DET
ejpam-5393	111	11	σ1σ2	σ1σ2	NOUN
ejpam-5393	111	12	-	-	ADJ
ejpam-5393	111	13	open	open	ADJ
ejpam-5393	111	14	set	set	NOUN
ejpam-5393	111	15	of	of	ADP
ejpam-5393	111	16	y	y	PROPN
ejpam-5393	111	17	having	have	VERB
ejpam-5393	111	18	σ1σ2	σ1σ2	VERB
ejpam-5393	111	19	-	-	ADJ
ejpam-5393	111	20	compact	compact	ADJ
ejpam-5393	111	21	complement	complement	NOUN
ejpam-5393	111	22	such	such	ADJ
ejpam-5393	111	23	that	that	SCONJ
ejpam-5393	111	24	f	f	PROPN
ejpam-5393	111	25	(	(	PUNCT
ejpam-5393	111	26	x	x	X
ejpam-5393	111	27	)	)	PUNCT
ejpam-5393	111	28	⊆	⊆	NUM
ejpam-5393	111	29	v	v	NOUN
ejpam-5393	111	30	.	.	PUNCT
ejpam-5393	112	1	let	let	VERB
ejpam-5393	112	2	u	u	PRON
ejpam-5393	112	3	be	be	AUX
ejpam-5393	112	4	a	a	DET
ejpam-5393	112	5	τ1τ2	τ1τ2	ADJ
ejpam-5393	112	6	-	-	ADJ
ejpam-5393	112	7	open	open	ADJ
ejpam-5393	112	8	set	set	ADJ
ejpam-5393	112	9	u	u	NOUN
ejpam-5393	112	10	of	of	ADP
ejpam-5393	112	11	x	x	SYM
ejpam-5393	112	12	containing	contain	VERB
ejpam-5393	112	13	x.	x.	NOUN
ejpam-5393	112	14	for	for	ADP
ejpam-5393	112	15	each	each	DET
ejpam-5393	112	16	x0	x0	PROPN
ejpam-5393	112	17	∈	∈	PROPN
ejpam-5393	112	18	f+(v	f+(v	NOUN
ejpam-5393	112	19	)	)	PUNCT
ejpam-5393	112	20	,	,	PUNCT
ejpam-5393	112	21	there	there	PRON
ejpam-5393	112	22	exists	exist	VERB
ejpam-5393	112	23	a	a	DET
ejpam-5393	112	24	(	(	PUNCT
ejpam-5393	112	25	τ1	τ1	NOUN
ejpam-5393	112	26	,	,	PUNCT
ejpam-5393	112	27	τ2)s	τ2)s	NOUN
ejpam-5393	112	28	-	-	PUNCT
ejpam-5393	112	29	open	open	NOUN
ejpam-5393	112	30	set	set	VERB
ejpam-5393	112	31	ux0	ux0	PROPN
ejpam-5393	112	32	ofx	ofx	NOUN
ejpam-5393	112	33	containing	contain	VERB
ejpam-5393	112	34	x0	x0	PROPN
ejpam-5393	112	35	such	such	ADJ
ejpam-5393	112	36	that	that	SCONJ
ejpam-5393	112	37	f	f	PROPN
ejpam-5393	112	38	(	(	PUNCT
ejpam-5393	112	39	ux0	ux0	PROPN
ejpam-5393	112	40	)	)	PUNCT
ejpam-5393	112	41	⊆	⊆	NUM
ejpam-5393	112	42	v	v	NOUN
ejpam-5393	112	43	.	.	PUNCT
ejpam-5393	113	1	therefore	therefore	ADV
ejpam-5393	113	2	,	,	PUNCT
ejpam-5393	113	3	we	we	PRON
ejpam-5393	113	4	have	have	VERB
ejpam-5393	113	5	ux0	ux0	NOUN
ejpam-5393	113	6	⊆	⊆	NUM
ejpam-5393	113	7	f+(v	f+(v	NOUN
ejpam-5393	113	8	)	)	PUNCT
ejpam-5393	113	9	and	and	CCONJ
ejpam-5393	113	10	f+(v	f+(v	NUM
ejpam-5393	113	11	)	)	PUNCT
ejpam-5393	114	1	=	=	SYM
ejpam-5393	114	2	∪x0∈f+(v	∪x0∈f+(v	ADJ
ejpam-5393	114	3	)	)	PUNCT
ejpam-5393	114	4	ux0	ux0	PROPN
ejpam-5393	114	5	.	.	PUNCT
ejpam-5393	115	1	thus	thus	ADV
ejpam-5393	115	2	,	,	PUNCT
ejpam-5393	115	3	f+(v	f+(v	PROPN
ejpam-5393	115	4	)	)	PUNCT
ejpam-5393	115	5	is	be	AUX
ejpam-5393	115	6	(	(	PUNCT
ejpam-5393	115	7	τ1	τ1	NOUN
ejpam-5393	115	8	,	,	PUNCT
ejpam-5393	115	9	τ2)sopen	τ2)sopen	VERB
ejpam-5393	115	10	in	in	ADP
ejpam-5393	115	11	x	x	PUNCT
ejpam-5393	115	12	and	and	CCONJ
ejpam-5393	115	13	hence	hence	ADV
ejpam-5393	115	14	f+(v	f+(v	NOUN
ejpam-5393	115	15	)	)	PUNCT
ejpam-5393	116	1	⊆	⊆	X
ejpam-5393	116	2	τ1τ2	τ1τ2	NOUN
ejpam-5393	116	3	-	-	NUM
ejpam-5393	116	4	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5393	116	5	-	-	PUNCT
ejpam-5393	116	6	int(f	int(f	VERB
ejpam-5393	116	7	+	+	ADJ
ejpam-5393	116	8	(	(	PUNCT
ejpam-5393	116	9	v	v	NOUN
ejpam-5393	116	10	)	)	PUNCT
ejpam-5393	116	11	)	)	PUNCT
ejpam-5393	116	12	)	)	PUNCT
ejpam-5393	116	13	.	.	PUNCT
ejpam-5393	117	1	put	put	VERB
ejpam-5393	117	2	g	g	NOUN
ejpam-5393	117	3	=	=	PUNCT
ejpam-5393	117	4	τ1τ2	τ1τ2	NOUN
ejpam-5393	117	5	-	-	NUM
ejpam-5393	117	6	int(f	int(f	VERB
ejpam-5393	117	7	+	+	ADJ
ejpam-5393	117	8	(	(	PUNCT
ejpam-5393	117	9	v	v	NOUN
ejpam-5393	117	10	)	)	PUNCT
ejpam-5393	117	11	)	)	PUNCT
ejpam-5393	117	12	∩	∩	NOUN
ejpam-5393	117	13	u	u	NOUN
ejpam-5393	117	14	.	.	PUNCT
ejpam-5393	118	1	then	then	ADV
ejpam-5393	118	2	,	,	PUNCT
ejpam-5393	118	3	g	g	PROPN
ejpam-5393	118	4	is	be	AUX
ejpam-5393	118	5	τ1τ2	τ1τ2	VERB
ejpam-5393	118	6	-	-	ADJ
ejpam-5393	118	7	open	open	ADJ
ejpam-5393	118	8	,	,	PUNCT
ejpam-5393	118	9	g	g	PROPN
ejpam-5393	118	10	⊆	⊆	NUM
ejpam-5393	118	11	u	u	NOUN
ejpam-5393	118	12	and	and	CCONJ
ejpam-5393	118	13	g	g	PROPN
ejpam-5393	118	14	̸=	̸=	PROPN
ejpam-5393	118	15	∅	∅	NOUN
ejpam-5393	118	16	because	because	SCONJ
ejpam-5393	118	17	x	x	PROPN
ejpam-5393	118	18	∈	∈	PROPN
ejpam-5393	118	19	τ1τ2	τ1τ2	NOUN
ejpam-5393	118	20	-	-	ADJ
ejpam-5393	118	21	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5393	118	22	-	-	PUNCT
ejpam-5393	118	23	int(f	int(f	VERB
ejpam-5393	118	24	+	+	ADJ
ejpam-5393	118	25	(	(	PUNCT
ejpam-5393	118	26	v	v	NOUN
ejpam-5393	118	27	)	)	PUNCT
ejpam-5393	118	28	)	)	PUNCT
ejpam-5393	118	29	)	)	PUNCT
ejpam-5393	118	30	implies	imply	VERB
ejpam-5393	118	31	τ1τ2	τ1τ2	NOUN
ejpam-5393	118	32	-	-	NUM
ejpam-5393	118	33	int(f	int(f	VERB
ejpam-5393	118	34	+	+	ADJ
ejpam-5393	118	35	(	(	PUNCT
ejpam-5393	118	36	v	v	NOUN
ejpam-5393	118	37	)	)	PUNCT
ejpam-5393	118	38	)	)	PUNCT
ejpam-5393	119	1	∩	∩	PROPN
ejpam-5393	119	2	u	u	PROPN
ejpam-5393	119	3	̸=	̸=	PROPN
ejpam-5393	119	4	∅.	∅.	ADV
ejpam-5393	119	5	on	on	ADP
ejpam-5393	119	6	the	the	DET
ejpam-5393	119	7	other	other	ADJ
ejpam-5393	119	8	hand	hand	NOUN
ejpam-5393	119	9	,	,	PUNCT
ejpam-5393	119	10	we	we	PRON
ejpam-5393	119	11	have	have	VERB
ejpam-5393	119	12	f	f	PROPN
ejpam-5393	119	13	(	(	PUNCT
ejpam-5393	119	14	g	g	NOUN
ejpam-5393	119	15	)	)	PUNCT
ejpam-5393	119	16	⊆	⊆	NUM
ejpam-5393	119	17	f	f	NOUN
ejpam-5393	119	18	(	(	PUNCT
ejpam-5393	119	19	τ1τ2	τ1τ2	VERB
ejpam-5393	119	20	-	-	NUM
ejpam-5393	119	21	int(f	int(f	VERB
ejpam-5393	119	22	+	+	ADJ
ejpam-5393	119	23	(	(	PUNCT
ejpam-5393	119	24	v	v	NOUN
ejpam-5393	119	25	)	)	PUNCT
ejpam-5393	119	26	)	)	PUNCT
ejpam-5393	119	27	)	)	PUNCT
ejpam-5393	120	1	⊆	⊆	NUM
ejpam-5393	120	2	f	f	NOUN
ejpam-5393	120	3	(	(	PUNCT
ejpam-5393	120	4	f+(v	f+(v	PROPN
ejpam-5393	120	5	)	)	PUNCT
ejpam-5393	120	6	)	)	PUNCT
ejpam-5393	121	1	⊆	⊆	NUM
ejpam-5393	121	2	v.	v.	ADP
ejpam-5393	121	3	this	this	PRON
ejpam-5393	121	4	shows	show	VERB
ejpam-5393	121	5	that	that	SCONJ
ejpam-5393	121	6	f	f	PROPN
ejpam-5393	121	7	is	be	AUX
ejpam-5393	121	8	upper	upper	ADJ
ejpam-5393	121	9	c	c	NOUN
ejpam-5393	121	10	-	-	PUNCT
ejpam-5393	121	11	quasi	quasi	ADJ
ejpam-5393	121	12	(	(	PUNCT
ejpam-5393	121	13	τ1	τ1	NOUN
ejpam-5393	121	14	,	,	PUNCT
ejpam-5393	121	15	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	121	16	at	at	ADP
ejpam-5393	121	17	x.	x.	NOUN
ejpam-5393	121	18	definition	definition	NOUN
ejpam-5393	121	19	2	2	NUM
ejpam-5393	121	20	.	.	PUNCT
ejpam-5393	121	21	a	a	DET
ejpam-5393	121	22	multifunction	multifunction	NOUN
ejpam-5393	122	1	f	f	NOUN
ejpam-5393	122	2	:	:	PUNCT
ejpam-5393	122	3	(	(	PUNCT
ejpam-5393	122	4	x	x	NOUN
ejpam-5393	122	5	,	,	PUNCT
ejpam-5393	122	6	τ1	τ1	NOUN
ejpam-5393	122	7	,	,	PUNCT
ejpam-5393	122	8	τ2	τ2	NOUN
ejpam-5393	122	9	)	)	PUNCT
ejpam-5393	122	10	→	→	SYM
ejpam-5393	122	11	(	(	PUNCT
ejpam-5393	122	12	y	y	PROPN
ejpam-5393	122	13	,	,	PUNCT
ejpam-5393	122	14	σ1	σ1	PROPN
ejpam-5393	122	15	,	,	PUNCT
ejpam-5393	122	16	σ2	σ2	PROPN
ejpam-5393	122	17	)	)	PUNCT
ejpam-5393	122	18	is	be	AUX
ejpam-5393	122	19	said	say	VERB
ejpam-5393	122	20	to	to	PART
ejpam-5393	122	21	be	be	AUX
ejpam-5393	122	22	lower	low	ADJ
ejpam-5393	122	23	c	c	NOUN
ejpam-5393	122	24	-	-	PUNCT
ejpam-5393	122	25	quasi	quasi	ADJ
ejpam-5393	122	26	(	(	PUNCT
ejpam-5393	122	27	τ1	τ1	NOUN
ejpam-5393	122	28	,	,	PUNCT
ejpam-5393	122	29	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	122	30	at	at	ADP
ejpam-5393	122	31	a	a	DET
ejpam-5393	122	32	point	point	NOUN
ejpam-5393	122	33	x	x	SYM
ejpam-5393	122	34	∈	∈	NOUN
ejpam-5393	122	35	x	x	PUNCT
ejpam-5393	122	36	if	if	SCONJ
ejpam-5393	122	37	for	for	ADP
ejpam-5393	122	38	each	each	DET
ejpam-5393	122	39	σ1σ2	σ1σ2	VERB
ejpam-5393	122	40	-	-	ADJ
ejpam-5393	122	41	open	open	ADJ
ejpam-5393	122	42	set	set	NOUN
ejpam-5393	122	43	v	v	NOUN
ejpam-5393	122	44	of	of	ADP
ejpam-5393	122	45	y	y	PROPN
ejpam-5393	122	46	having	have	VERB
ejpam-5393	122	47	σ1σ2	σ1σ2	VERB
ejpam-5393	122	48	-	-	ADJ
ejpam-5393	122	49	compact	compact	ADJ
ejpam-5393	122	50	complement	complement	NOUN
ejpam-5393	122	51	such	such	ADJ
ejpam-5393	122	52	that	that	SCONJ
ejpam-5393	122	53	f	f	PROPN
ejpam-5393	122	54	(	(	PUNCT
ejpam-5393	122	55	x)∩v	x)∩v	PROPN
ejpam-5393	122	56	̸=	̸=	PROPN
ejpam-5393	122	57	∅	∅	NOUN
ejpam-5393	122	58	and	and	CCONJ
ejpam-5393	122	59	for	for	ADP
ejpam-5393	122	60	each	each	DET
ejpam-5393	122	61	τ1τ2	τ1τ2	ADJ
ejpam-5393	122	62	-	-	ADJ
ejpam-5393	122	63	open	open	ADJ
ejpam-5393	122	64	set	set	ADJ
ejpam-5393	122	65	u	u	NOUN
ejpam-5393	122	66	of	of	ADP
ejpam-5393	122	67	x	x	PUNCT
ejpam-5393	122	68	containing	contain	VERB
ejpam-5393	122	69	x	x	PRON
ejpam-5393	122	70	,	,	PUNCT
ejpam-5393	122	71	there	there	PRON
ejpam-5393	122	72	exists	exist	VERB
ejpam-5393	122	73	a	a	DET
ejpam-5393	122	74	nonempty	nonempty	ADJ
ejpam-5393	122	75	τ1τ2	τ1τ2	NOUN
ejpam-5393	122	76	-	-	ADJ
ejpam-5393	122	77	open	open	ADJ
ejpam-5393	122	78	set	set	NOUN
ejpam-5393	122	79	g	g	PROPN
ejpam-5393	122	80	such	such	ADJ
ejpam-5393	122	81	that	that	SCONJ
ejpam-5393	122	82	g	g	PROPN
ejpam-5393	122	83	⊆	⊆	NUM
ejpam-5393	122	84	u	u	NOUN
ejpam-5393	122	85	and	and	CCONJ
ejpam-5393	122	86	f	f	PROPN
ejpam-5393	122	87	(	(	PUNCT
ejpam-5393	122	88	z	z	NOUN
ejpam-5393	122	89	)	)	PUNCT
ejpam-5393	122	90	∩	∩	NOUN
ejpam-5393	122	91	v	v	ADP
ejpam-5393	122	92	̸=	̸=	PROPN
ejpam-5393	122	93	∅	∅	NOUN
ejpam-5393	122	94	for	for	ADP
ejpam-5393	122	95	each	each	DET
ejpam-5393	122	96	z	z	PROPN
ejpam-5393	122	97	∈	∈	PROPN
ejpam-5393	122	98	g.	g.	NOUN
ejpam-5393	122	99	a	a	DET
ejpam-5393	122	100	multifunction	multifunction	NOUN
ejpam-5393	123	1	f	f	NOUN
ejpam-5393	123	2	:	:	PUNCT
ejpam-5393	123	3	(	(	PUNCT
ejpam-5393	123	4	x	x	NOUN
ejpam-5393	123	5	,	,	PUNCT
ejpam-5393	123	6	τ1	τ1	NOUN
ejpam-5393	123	7	,	,	PUNCT
ejpam-5393	123	8	τ2	τ2	NOUN
ejpam-5393	123	9	)	)	PUNCT
ejpam-5393	123	10	→	→	SYM
ejpam-5393	123	11	(	(	PUNCT
ejpam-5393	123	12	y	y	PROPN
ejpam-5393	123	13	,	,	PUNCT
ejpam-5393	123	14	σ1	σ1	PROPN
ejpam-5393	123	15	,	,	PUNCT
ejpam-5393	123	16	σ2	σ2	PROPN
ejpam-5393	123	17	)	)	PUNCT
ejpam-5393	123	18	is	be	AUX
ejpam-5393	123	19	said	say	VERB
ejpam-5393	123	20	to	to	PART
ejpam-5393	123	21	be	be	AUX
ejpam-5393	123	22	lower	low	ADJ
ejpam-5393	123	23	c	c	NOUN
ejpam-5393	123	24	-	-	PUNCT
ejpam-5393	123	25	quasi	quasi	ADJ
ejpam-5393	123	26	(	(	PUNCT
ejpam-5393	123	27	τ1	τ1	NOUN
ejpam-5393	123	28	,	,	PUNCT
ejpam-5393	123	29	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	123	30	if	if	SCONJ
ejpam-5393	123	31	f	f	PROPN
ejpam-5393	123	32	has	have	VERB
ejpam-5393	123	33	this	this	DET
ejpam-5393	123	34	property	property	NOUN
ejpam-5393	123	35	at	at	ADP
ejpam-5393	123	36	every	every	DET
ejpam-5393	123	37	point	point	NOUN
ejpam-5393	123	38	of	of	ADP
ejpam-5393	123	39	x.	x.	NOUN
ejpam-5393	123	40	theorem	theorem	VERB
ejpam-5393	123	41	2	2	NUM
ejpam-5393	123	42	.	.	PUNCT
ejpam-5393	123	43	a	a	DET
ejpam-5393	123	44	multifunction	multifunction	NOUN
ejpam-5393	123	45	f	f	NOUN
ejpam-5393	123	46	:	:	PUNCT
ejpam-5393	123	47	(	(	PUNCT
ejpam-5393	123	48	x	x	NOUN
ejpam-5393	123	49	,	,	PUNCT
ejpam-5393	123	50	τ1	τ1	NOUN
ejpam-5393	123	51	,	,	PUNCT
ejpam-5393	123	52	τ2	τ2	NOUN
ejpam-5393	123	53	)	)	PUNCT
ejpam-5393	123	54	→	→	SYM
ejpam-5393	123	55	(	(	PUNCT
ejpam-5393	123	56	y	y	PROPN
ejpam-5393	123	57	,	,	PUNCT
ejpam-5393	123	58	σ1	σ1	PROPN
ejpam-5393	123	59	,	,	PUNCT
ejpam-5393	123	60	σ2	σ2	NOUN
ejpam-5393	123	61	)	)	PUNCT
ejpam-5393	123	62	is	be	AUX
ejpam-5393	123	63	lower	low	ADJ
ejpam-5393	123	64	c	c	NOUN
ejpam-5393	123	65	-	-	PUNCT
ejpam-5393	123	66	quasi	quasi	ADJ
ejpam-5393	123	67	(	(	PUNCT
ejpam-5393	123	68	τ1	τ1	NOUN
ejpam-5393	123	69	,	,	PUNCT
ejpam-5393	123	70	τ2)continuous	τ2)continuous	ADJ
ejpam-5393	123	71	at	at	ADP
ejpam-5393	123	72	x	x	X
ejpam-5393	123	73	∈	∈	PROPN
ejpam-5393	123	74	x	x	SYM
ejpam-5393	123	75	if	if	SCONJ
ejpam-5393	123	76	and	and	CCONJ
ejpam-5393	123	77	only	only	ADV
ejpam-5393	123	78	if	if	SCONJ
ejpam-5393	123	79	for	for	SCONJ
ejpam-5393	123	80	every	every	DET
ejpam-5393	123	81	σ1σ2	σ1σ2	NUM
ejpam-5393	123	82	-	-	ADJ
ejpam-5393	123	83	open	open	ADJ
ejpam-5393	123	84	set	set	NOUN
ejpam-5393	123	85	v	v	NOUN
ejpam-5393	123	86	of	of	ADP
ejpam-5393	123	87	y	y	PROPN
ejpam-5393	123	88	having	have	VERB
ejpam-5393	123	89	σ1σ2	σ1σ2	VERB
ejpam-5393	123	90	-	-	ADJ
ejpam-5393	123	91	compact	compact	ADJ
ejpam-5393	123	92	complement	complement	NOUN
ejpam-5393	123	93	with	with	ADP
ejpam-5393	123	94	f	f	PROPN
ejpam-5393	123	95	(	(	PUNCT
ejpam-5393	123	96	x)∩	x)∩	PROPN
ejpam-5393	123	97	v	v	ADP
ejpam-5393	123	98	̸=	̸=	PROPN
ejpam-5393	123	99	∅	∅	NOUN
ejpam-5393	123	100	,	,	PUNCT
ejpam-5393	123	101	there	there	PRON
ejpam-5393	123	102	exists	exist	VERB
ejpam-5393	123	103	a	a	DET
ejpam-5393	123	104	(	(	PUNCT
ejpam-5393	123	105	τ1	τ1	NOUN
ejpam-5393	123	106	,	,	PUNCT
ejpam-5393	123	107	τ2)s	τ2)s	NOUN
ejpam-5393	123	108	-	-	PUNCT
ejpam-5393	123	109	open	open	ADJ
ejpam-5393	123	110	set	set	NOUN
ejpam-5393	123	111	u	u	NOUN
ejpam-5393	123	112	of	of	ADP
ejpam-5393	123	113	x	x	PUNCT
ejpam-5393	123	114	containing	contain	VERB
ejpam-5393	123	115	x	x	PUNCT
ejpam-5393	123	116	such	such	ADJ
ejpam-5393	123	117	that	that	SCONJ
ejpam-5393	123	118	f	f	PROPN
ejpam-5393	123	119	(	(	PUNCT
ejpam-5393	123	120	z	z	NOUN
ejpam-5393	123	121	)	)	PUNCT
ejpam-5393	123	122	∩	∩	NOUN
ejpam-5393	123	123	v	v	ADP
ejpam-5393	123	124	̸=	̸=	PROPN
ejpam-5393	123	125	∅	∅	NOUN
ejpam-5393	123	126	for	for	ADP
ejpam-5393	123	127	every	every	DET
ejpam-5393	123	128	z	z	NOUN
ejpam-5393	123	129	∈	∈	PROPN
ejpam-5393	123	130	u	u	NOUN
ejpam-5393	123	131	.	.	PUNCT
ejpam-5393	124	1	proof	proof	NOUN
ejpam-5393	124	2	.	.	PUNCT
ejpam-5393	125	1	the	the	DET
ejpam-5393	125	2	proof	proof	NOUN
ejpam-5393	125	3	is	be	AUX
ejpam-5393	125	4	similar	similar	ADJ
ejpam-5393	125	5	to	to	ADP
ejpam-5393	125	6	that	that	PRON
ejpam-5393	125	7	of	of	ADP
ejpam-5393	125	8	theorem	theorem	NOUN
ejpam-5393	125	9	1	1	NUM
ejpam-5393	125	10	.	.	PUNCT
ejpam-5393	126	1	p.	p.	NOUN
ejpam-5393	126	2	pue	pue	NOUN
ejpam-5393	126	3	-	-	PUNCT
ejpam-5393	126	4	on	on	ADP
ejpam-5393	126	5	,	,	PUNCT
ejpam-5393	126	6	a.	a.	PROPN
ejpam-5393	126	7	sama	sama	PROPN
ejpam-5393	126	8	-	-	PUNCT
ejpam-5393	126	9	ae	ae	PROPN
ejpam-5393	126	10	,	,	PUNCT
ejpam-5393	126	11	c.	c.	PROPN
ejpam-5393	126	12	boonpok	boonpok	PROPN
ejpam-5393	126	13	/	/	SYM
ejpam-5393	126	14	eur	eur	PROPN
ejpam-5393	126	15	.	.	PUNCT
ejpam-5393	127	1	j.	j.	PROPN
ejpam-5393	127	2	pure	pure	PROPN
ejpam-5393	127	3	appl	appl	PROPN
ejpam-5393	127	4	.	.	PROPN
ejpam-5393	127	5	math	math	PROPN
ejpam-5393	127	6	,	,	PUNCT
ejpam-5393	127	7	17	17	NUM
ejpam-5393	127	8	(	(	PUNCT
ejpam-5393	127	9	4	4	NUM
ejpam-5393	127	10	)	)	PUNCT
ejpam-5393	127	11	(	(	PUNCT
ejpam-5393	127	12	2024	2024	NUM
ejpam-5393	127	13	)	)	PUNCT
ejpam-5393	127	14	,	,	PUNCT
ejpam-5393	127	15	3242	3242	NUM
ejpam-5393	127	16	-	-	SYM
ejpam-5393	127	17	3253	3253	NUM
ejpam-5393	127	18	3246	3246	NUM
ejpam-5393	127	19	definition	definition	NOUN
ejpam-5393	127	20	3	3	NUM
ejpam-5393	127	21	.	.	PUNCT
ejpam-5393	128	1	a	a	DET
ejpam-5393	128	2	function	function	NOUN
ejpam-5393	128	3	f	f	NOUN
ejpam-5393	128	4	:	:	PUNCT
ejpam-5393	128	5	(	(	PUNCT
ejpam-5393	128	6	x	x	NOUN
ejpam-5393	128	7	,	,	PUNCT
ejpam-5393	128	8	τ1	τ1	NOUN
ejpam-5393	128	9	,	,	PUNCT
ejpam-5393	128	10	τ2	τ2	NOUN
ejpam-5393	128	11	)	)	PUNCT
ejpam-5393	128	12	→	→	SYM
ejpam-5393	128	13	(	(	PUNCT
ejpam-5393	128	14	y	y	PROPN
ejpam-5393	128	15	,	,	PUNCT
ejpam-5393	128	16	σ1	σ1	PROPN
ejpam-5393	128	17	,	,	PUNCT
ejpam-5393	128	18	σ2	σ2	PROPN
ejpam-5393	128	19	)	)	PUNCT
ejpam-5393	128	20	is	be	AUX
ejpam-5393	128	21	said	say	VERB
ejpam-5393	128	22	to	to	PART
ejpam-5393	128	23	be	be	AUX
ejpam-5393	128	24	c	c	NOUN
ejpam-5393	128	25	-	-	PUNCT
ejpam-5393	128	26	quasi	quasi	NOUN
ejpam-5393	128	27	(	(	PUNCT
ejpam-5393	128	28	τ1	τ1	NOUN
ejpam-5393	128	29	,	,	PUNCT
ejpam-5393	128	30	τ2)continuous	τ2)continuous	ADJ
ejpam-5393	128	31	at	at	ADP
ejpam-5393	128	32	a	a	DET
ejpam-5393	128	33	point	point	NOUN
ejpam-5393	128	34	x	x	SYM
ejpam-5393	128	35	∈	∈	NOUN
ejpam-5393	128	36	x	x	PUNCT
ejpam-5393	128	37	if	if	SCONJ
ejpam-5393	128	38	for	for	ADP
ejpam-5393	128	39	each	each	DET
ejpam-5393	128	40	σ1σ2	σ1σ2	VERB
ejpam-5393	128	41	-	-	ADJ
ejpam-5393	128	42	open	open	ADJ
ejpam-5393	128	43	set	set	NOUN
ejpam-5393	128	44	v	v	NOUN
ejpam-5393	128	45	of	of	ADP
ejpam-5393	128	46	y	y	NOUN
ejpam-5393	128	47	containing	contain	VERB
ejpam-5393	128	48	f(x	f(x	PROPN
ejpam-5393	128	49	)	)	PUNCT
ejpam-5393	128	50	and	and	CCONJ
ejpam-5393	128	51	having	have	VERB
ejpam-5393	128	52	σ1σ2	σ1σ2	NOUN
ejpam-5393	128	53	-	-	ADJ
ejpam-5393	128	54	compact	compact	ADJ
ejpam-5393	128	55	complement	complement	NOUN
ejpam-5393	128	56	and	and	CCONJ
ejpam-5393	128	57	for	for	ADP
ejpam-5393	128	58	each	each	DET
ejpam-5393	128	59	τ1τ2	τ1τ2	ADJ
ejpam-5393	128	60	-	-	ADJ
ejpam-5393	128	61	open	open	ADJ
ejpam-5393	128	62	set	set	ADJ
ejpam-5393	128	63	u	u	NOUN
ejpam-5393	128	64	of	of	ADP
ejpam-5393	128	65	x	x	PUNCT
ejpam-5393	128	66	containing	contain	VERB
ejpam-5393	128	67	x	x	PRON
ejpam-5393	128	68	,	,	PUNCT
ejpam-5393	128	69	there	there	PRON
ejpam-5393	128	70	exists	exist	VERB
ejpam-5393	128	71	a	a	DET
ejpam-5393	128	72	nonempty	nonempty	ADJ
ejpam-5393	128	73	τ1τ2	τ1τ2	NOUN
ejpam-5393	128	74	-	-	ADJ
ejpam-5393	128	75	open	open	ADJ
ejpam-5393	128	76	set	set	NOUN
ejpam-5393	128	77	g	g	PROPN
ejpam-5393	128	78	such	such	ADJ
ejpam-5393	128	79	that	that	SCONJ
ejpam-5393	128	80	g	g	PROPN
ejpam-5393	128	81	⊆	⊆	NUM
ejpam-5393	128	82	u	u	NOUN
ejpam-5393	128	83	and	and	CCONJ
ejpam-5393	128	84	f(g	f(g	NOUN
ejpam-5393	128	85	)	)	PUNCT
ejpam-5393	128	86	⊆	⊆	NUM
ejpam-5393	128	87	v	v	NOUN
ejpam-5393	128	88	.	.	PUNCT
ejpam-5393	129	1	a	a	DET
ejpam-5393	129	2	function	function	NOUN
ejpam-5393	129	3	f	f	NOUN
ejpam-5393	129	4	:	:	PUNCT
ejpam-5393	129	5	(	(	PUNCT
ejpam-5393	129	6	x	x	NOUN
ejpam-5393	129	7	,	,	PUNCT
ejpam-5393	129	8	τ1	τ1	NOUN
ejpam-5393	129	9	,	,	PUNCT
ejpam-5393	129	10	τ2	τ2	NOUN
ejpam-5393	129	11	)	)	PUNCT
ejpam-5393	129	12	→	→	SYM
ejpam-5393	129	13	(	(	PUNCT
ejpam-5393	129	14	y	y	PROPN
ejpam-5393	129	15	,	,	PUNCT
ejpam-5393	129	16	σ1	σ1	PROPN
ejpam-5393	129	17	,	,	PUNCT
ejpam-5393	129	18	σ2	σ2	PROPN
ejpam-5393	129	19	)	)	PUNCT
ejpam-5393	129	20	is	be	AUX
ejpam-5393	129	21	said	say	VERB
ejpam-5393	129	22	to	to	PART
ejpam-5393	129	23	be	be	AUX
ejpam-5393	129	24	c	c	NOUN
ejpam-5393	129	25	-	-	PUNCT
ejpam-5393	129	26	quasi	quasi	NOUN
ejpam-5393	129	27	(	(	PUNCT
ejpam-5393	129	28	τ1	τ1	NOUN
ejpam-5393	129	29	,	,	PUNCT
ejpam-5393	129	30	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	129	31	if	if	SCONJ
ejpam-5393	129	32	f	f	PROPN
ejpam-5393	129	33	has	have	VERB
ejpam-5393	129	34	this	this	DET
ejpam-5393	129	35	property	property	NOUN
ejpam-5393	129	36	at	at	ADP
ejpam-5393	129	37	each	each	DET
ejpam-5393	129	38	point	point	NOUN
ejpam-5393	129	39	of	of	ADP
ejpam-5393	129	40	x.	x.	PROPN
ejpam-5393	129	41	corollary	corollary	NOUN
ejpam-5393	129	42	1	1	NUM
ejpam-5393	129	43	.	.	PUNCT
ejpam-5393	130	1	a	a	DET
ejpam-5393	130	2	function	function	NOUN
ejpam-5393	130	3	f	f	NOUN
ejpam-5393	130	4	:	:	PUNCT
ejpam-5393	130	5	(	(	PUNCT
ejpam-5393	130	6	x	x	NOUN
ejpam-5393	130	7	,	,	PUNCT
ejpam-5393	130	8	τ1	τ1	NOUN
ejpam-5393	130	9	,	,	PUNCT
ejpam-5393	130	10	τ2	τ2	NOUN
ejpam-5393	130	11	)	)	PUNCT
ejpam-5393	130	12	→	→	SYM
ejpam-5393	130	13	(	(	PUNCT
ejpam-5393	130	14	y	y	PROPN
ejpam-5393	130	15	,	,	PUNCT
ejpam-5393	130	16	σ1	σ1	PROPN
ejpam-5393	130	17	,	,	PUNCT
ejpam-5393	130	18	σ2	σ2	PROPN
ejpam-5393	130	19	)	)	PUNCT
ejpam-5393	130	20	is	be	AUX
ejpam-5393	130	21	c	c	NOUN
ejpam-5393	130	22	-	-	PUNCT
ejpam-5393	130	23	quasi	quasi	NOUN
ejpam-5393	130	24	(	(	PUNCT
ejpam-5393	130	25	τ1	τ1	NOUN
ejpam-5393	130	26	,	,	PUNCT
ejpam-5393	130	27	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	130	28	at	at	ADP
ejpam-5393	130	29	a	a	DET
ejpam-5393	130	30	point	point	NOUN
ejpam-5393	130	31	x	x	SYM
ejpam-5393	130	32	∈	∈	NOUN
ejpam-5393	130	33	x	x	INTJ
ejpam-5393	130	34	if	if	SCONJ
ejpam-5393	130	35	and	and	CCONJ
ejpam-5393	130	36	only	only	ADV
ejpam-5393	130	37	if	if	SCONJ
ejpam-5393	130	38	for	for	ADP
ejpam-5393	130	39	every	every	DET
ejpam-5393	130	40	σ1σ2	σ1σ2	NUM
ejpam-5393	130	41	-	-	ADJ
ejpam-5393	130	42	open	open	ADJ
ejpam-5393	130	43	set	set	NOUN
ejpam-5393	130	44	v	v	NOUN
ejpam-5393	130	45	of	of	ADP
ejpam-5393	130	46	y	y	NOUN
ejpam-5393	130	47	containing	contain	VERB
ejpam-5393	130	48	f(x	f(x	PROPN
ejpam-5393	130	49	)	)	PUNCT
ejpam-5393	130	50	and	and	CCONJ
ejpam-5393	130	51	having	have	VERB
ejpam-5393	130	52	σ1σ2	σ1σ2	NOUN
ejpam-5393	130	53	-	-	ADJ
ejpam-5393	130	54	compact	compact	ADJ
ejpam-5393	130	55	complement	complement	NOUN
ejpam-5393	130	56	,	,	PUNCT
ejpam-5393	130	57	there	there	PRON
ejpam-5393	130	58	exists	exist	VERB
ejpam-5393	130	59	a	a	DET
ejpam-5393	130	60	(	(	PUNCT
ejpam-5393	130	61	τ1	τ1	NOUN
ejpam-5393	130	62	,	,	PUNCT
ejpam-5393	130	63	τ2)s	τ2)s	NOUN
ejpam-5393	130	64	-	-	PUNCT
ejpam-5393	130	65	open	open	ADJ
ejpam-5393	130	66	set	set	NOUN
ejpam-5393	130	67	u	u	NOUN
ejpam-5393	130	68	of	of	ADP
ejpam-5393	130	69	x	x	PUNCT
ejpam-5393	130	70	containing	contain	VERB
ejpam-5393	130	71	x	x	PUNCT
ejpam-5393	130	72	such	such	ADJ
ejpam-5393	130	73	that	that	DET
ejpam-5393	130	74	f(u	f(u	PROPN
ejpam-5393	130	75	)	)	PUNCT
ejpam-5393	130	76	⊆	⊆	NUM
ejpam-5393	130	77	v	v	NOUN
ejpam-5393	130	78	.	.	PUNCT
ejpam-5393	131	1	theorem	theorem	NOUN
ejpam-5393	131	2	3	3	NUM
ejpam-5393	131	3	.	.	X
ejpam-5393	131	4	for	for	ADP
ejpam-5393	131	5	a	a	DET
ejpam-5393	131	6	multifunction	multifunction	NOUN
ejpam-5393	132	1	f	f	NOUN
ejpam-5393	132	2	:	:	PUNCT
ejpam-5393	132	3	(	(	PUNCT
ejpam-5393	132	4	x	x	NOUN
ejpam-5393	132	5	,	,	PUNCT
ejpam-5393	132	6	τ1	τ1	NOUN
ejpam-5393	132	7	,	,	PUNCT
ejpam-5393	132	8	τ2	τ2	NOUN
ejpam-5393	132	9	)	)	PUNCT
ejpam-5393	132	10	→	→	SYM
ejpam-5393	132	11	(	(	PUNCT
ejpam-5393	132	12	y	y	PROPN
ejpam-5393	132	13	,	,	PUNCT
ejpam-5393	132	14	σ1	σ1	PROPN
ejpam-5393	132	15	,	,	PUNCT
ejpam-5393	132	16	σ2	σ2	NOUN
ejpam-5393	132	17	)	)	PUNCT
ejpam-5393	132	18	,	,	PUNCT
ejpam-5393	132	19	the	the	DET
ejpam-5393	132	20	following	follow	VERB
ejpam-5393	132	21	properties	property	NOUN
ejpam-5393	132	22	are	be	AUX
ejpam-5393	132	23	equivalent	equivalent	ADJ
ejpam-5393	132	24	:	:	PUNCT
ejpam-5393	132	25	(	(	PUNCT
ejpam-5393	132	26	1	1	X
ejpam-5393	132	27	)	)	PUNCT
ejpam-5393	132	28	f	f	PROPN
ejpam-5393	132	29	is	be	AUX
ejpam-5393	132	30	upper	upper	ADJ
ejpam-5393	132	31	c	c	NOUN
ejpam-5393	132	32	-	-	PUNCT
ejpam-5393	132	33	quasi	quasi	ADJ
ejpam-5393	132	34	(	(	PUNCT
ejpam-5393	132	35	τ1	τ1	NOUN
ejpam-5393	132	36	,	,	PUNCT
ejpam-5393	132	37	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	132	38	;	;	PUNCT
ejpam-5393	132	39	(	(	PUNCT
ejpam-5393	132	40	2	2	NUM
ejpam-5393	132	41	)	)	PUNCT
ejpam-5393	132	42	f+(v	f+(v	NOUN
ejpam-5393	132	43	)	)	PUNCT
ejpam-5393	133	1	is	be	AUX
ejpam-5393	133	2	(	(	PUNCT
ejpam-5393	133	3	τ1	τ1	NOUN
ejpam-5393	133	4	,	,	PUNCT
ejpam-5393	133	5	τ2)s	τ2)s	NOUN
ejpam-5393	133	6	-	-	PUNCT
ejpam-5393	133	7	open	open	ADJ
ejpam-5393	133	8	in	in	ADP
ejpam-5393	133	9	x	x	PUNCT
ejpam-5393	133	10	for	for	ADP
ejpam-5393	133	11	every	every	DET
ejpam-5393	133	12	σ1σ2	σ1σ2	NOUN
ejpam-5393	133	13	-	-	ADJ
ejpam-5393	133	14	open	open	ADJ
ejpam-5393	133	15	set	set	NOUN
ejpam-5393	133	16	v	v	NOUN
ejpam-5393	133	17	of	of	ADP
ejpam-5393	133	18	y	y	PROPN
ejpam-5393	133	19	having	have	VERB
ejpam-5393	133	20	σ1σ2	σ1σ2	NOUN
ejpam-5393	133	21	-	-	ADJ
ejpam-5393	133	22	compact	compact	ADJ
ejpam-5393	133	23	complement	complement	NOUN
ejpam-5393	133	24	;	;	PUNCT
ejpam-5393	133	25	(	(	PUNCT
ejpam-5393	133	26	3	3	X
ejpam-5393	133	27	)	)	PUNCT
ejpam-5393	133	28	f−(k	f−(k	PROPN
ejpam-5393	133	29	)	)	PUNCT
ejpam-5393	133	30	is	be	AUX
ejpam-5393	133	31	(	(	PUNCT
ejpam-5393	133	32	τ1	τ1	NOUN
ejpam-5393	133	33	,	,	PUNCT
ejpam-5393	133	34	τ2)s	τ2)s	NOUN
ejpam-5393	133	35	-	-	PUNCT
ejpam-5393	133	36	closed	close	VERB
ejpam-5393	133	37	in	in	ADP
ejpam-5393	133	38	x	x	PUNCT
ejpam-5393	133	39	for	for	ADP
ejpam-5393	133	40	every	every	DET
ejpam-5393	133	41	σ1σ2	σ1σ2	NUM
ejpam-5393	133	42	-	-	ADJ
ejpam-5393	133	43	compact	compact	ADJ
ejpam-5393	133	44	σ1σ2	σ1σ2	VERB
ejpam-5393	133	45	-	-	PUNCT
ejpam-5393	133	46	closed	close	VERB
ejpam-5393	133	47	set	set	NOUN
ejpam-5393	133	48	k	k	PROPN
ejpam-5393	133	49	of	of	ADP
ejpam-5393	133	50	y	y	PROPN
ejpam-5393	133	51	;	;	PUNCT
ejpam-5393	133	52	(	(	PUNCT
ejpam-5393	133	53	4	4	X
ejpam-5393	133	54	)	)	PUNCT
ejpam-5393	133	55	τ1τ2	τ1τ2	NOUN
ejpam-5393	133	56	-	-	NOUN
ejpam-5393	133	57	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5393	133	58	-	-	PUNCT
ejpam-5393	133	59	cl(f	cl(f	NOUN
ejpam-5393	133	60	−(b	−(b	PROPN
ejpam-5393	133	61	)	)	PUNCT
ejpam-5393	133	62	)	)	PUNCT
ejpam-5393	133	63	)	)	PUNCT
ejpam-5393	134	1	⊆	⊆	X
ejpam-5393	134	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5393	134	3	-	-	PUNCT
ejpam-5393	134	4	cl(b	cl(b	NOUN
ejpam-5393	134	5	)	)	PUNCT
ejpam-5393	134	6	)	)	PUNCT
ejpam-5393	135	1	for	for	ADP
ejpam-5393	135	2	every	every	DET
ejpam-5393	135	3	subset	subset	NOUN
ejpam-5393	135	4	b	b	PROPN
ejpam-5393	135	5	of	of	ADP
ejpam-5393	135	6	y	y	PROPN
ejpam-5393	135	7	having	have	VERB
ejpam-5393	135	8	the	the	DET
ejpam-5393	135	9	σ1σ2	σ1σ2	NUM
ejpam-5393	135	10	-	-	ADJ
ejpam-5393	135	11	compact	compact	ADJ
ejpam-5393	135	12	σ1σ2	σ1σ2	NOUN
ejpam-5393	135	13	-	-	NOUN
ejpam-5393	135	14	closure	closure	NOUN
ejpam-5393	135	15	;	;	PUNCT
ejpam-5393	135	16	(	(	PUNCT
ejpam-5393	135	17	5	5	NUM
ejpam-5393	135	18	)	)	PUNCT
ejpam-5393	135	19	(	(	PUNCT
ejpam-5393	135	20	τ1	τ1	NOUN
ejpam-5393	135	21	,	,	PUNCT
ejpam-5393	135	22	τ2)-scl(f	τ2)-scl(f	PROPN
ejpam-5393	135	23	−(b	−(b	PROPN
ejpam-5393	135	24	)	)	PUNCT
ejpam-5393	135	25	)	)	PUNCT
ejpam-5393	136	1	⊆	⊆	X
ejpam-5393	136	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5393	136	3	-	-	PUNCT
ejpam-5393	136	4	cl(b	cl(b	NOUN
ejpam-5393	136	5	)	)	PUNCT
ejpam-5393	136	6	)	)	PUNCT
ejpam-5393	137	1	for	for	ADP
ejpam-5393	137	2	every	every	DET
ejpam-5393	137	3	subset	subset	NOUN
ejpam-5393	137	4	b	b	PROPN
ejpam-5393	137	5	of	of	ADP
ejpam-5393	137	6	y	y	PROPN
ejpam-5393	137	7	having	have	VERB
ejpam-5393	137	8	the	the	DET
ejpam-5393	137	9	σ1σ2compact	σ1σ2compact	ADJ
ejpam-5393	137	10	σ1σ2	σ1σ2	NOUN
ejpam-5393	137	11	-	-	NOUN
ejpam-5393	137	12	closure	closure	NOUN
ejpam-5393	137	13	;	;	PUNCT
ejpam-5393	137	14	(	(	PUNCT
ejpam-5393	137	15	6	6	X
ejpam-5393	137	16	)	)	PUNCT
ejpam-5393	137	17	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5393	137	18	-	-	PUNCT
ejpam-5393	137	19	int(b	int(b	NOUN
ejpam-5393	137	20	)	)	PUNCT
ejpam-5393	137	21	)	)	PUNCT
ejpam-5393	138	1	⊆	⊆	NUM
ejpam-5393	138	2	(	(	PUNCT
ejpam-5393	138	3	τ1	τ1	NOUN
ejpam-5393	138	4	,	,	PUNCT
ejpam-5393	138	5	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5393	138	6	+	+	ADJ
ejpam-5393	138	7	(	(	PUNCT
ejpam-5393	138	8	b	b	NOUN
ejpam-5393	138	9	)	)	PUNCT
ejpam-5393	138	10	)	)	PUNCT
ejpam-5393	138	11	for	for	ADP
ejpam-5393	138	12	every	every	DET
ejpam-5393	138	13	subset	subset	NOUN
ejpam-5393	138	14	b	b	PROPN
ejpam-5393	138	15	of	of	ADP
ejpam-5393	138	16	y	y	PRON
ejpam-5393	138	17	such	such	ADJ
ejpam-5393	138	18	that	that	SCONJ
ejpam-5393	138	19	y	y	PROPN
ejpam-5393	139	1	−	−	ADP
ejpam-5393	139	2	σ1σ2	σ1σ2	NUM
ejpam-5393	139	3	-	-	PUNCT
ejpam-5393	139	4	int(b	int(b	NOUN
ejpam-5393	139	5	)	)	PUNCT
ejpam-5393	139	6	is	be	AUX
ejpam-5393	139	7	σ1σ2	σ1σ2	NOUN
ejpam-5393	139	8	-	-	ADJ
ejpam-5393	139	9	compact	compact	ADJ
ejpam-5393	139	10	.	.	PUNCT
ejpam-5393	140	1	proof	proof	NOUN
ejpam-5393	140	2	.	.	PUNCT
ejpam-5393	141	1	(	(	PUNCT
ejpam-5393	141	2	1	1	X
ejpam-5393	141	3	)	)	PUNCT
ejpam-5393	141	4	⇒	⇒	NOUN
ejpam-5393	141	5	(	(	PUNCT
ejpam-5393	141	6	2	2	NUM
ejpam-5393	141	7	):	):	PUNCT
ejpam-5393	141	8	let	let	VERB
ejpam-5393	141	9	v	v	PART
ejpam-5393	141	10	be	be	AUX
ejpam-5393	141	11	any	any	DET
ejpam-5393	141	12	σ1σ2	σ1σ2	NOUN
ejpam-5393	141	13	-	-	ADJ
ejpam-5393	141	14	open	open	ADJ
ejpam-5393	141	15	set	set	NOUN
ejpam-5393	141	16	of	of	ADP
ejpam-5393	141	17	y	y	PROPN
ejpam-5393	141	18	having	have	VERB
ejpam-5393	141	19	σ1σ2	σ1σ2	VERB
ejpam-5393	141	20	-	-	ADJ
ejpam-5393	141	21	compact	compact	ADJ
ejpam-5393	141	22	complement	complement	NOUN
ejpam-5393	141	23	and	and	CCONJ
ejpam-5393	141	24	x	x	PUNCT
ejpam-5393	141	25	∈	∈	PROPN
ejpam-5393	141	26	f+(v	f+(v	NOUN
ejpam-5393	141	27	)	)	PUNCT
ejpam-5393	141	28	.	.	PUNCT
ejpam-5393	142	1	by	by	ADP
ejpam-5393	142	2	theorem	theorem	NOUN
ejpam-5393	142	3	1	1	NUM
ejpam-5393	142	4	,	,	PUNCT
ejpam-5393	142	5	there	there	PRON
ejpam-5393	142	6	exists	exist	VERB
ejpam-5393	142	7	a	a	DET
ejpam-5393	142	8	(	(	PUNCT
ejpam-5393	142	9	τ1	τ1	NOUN
ejpam-5393	142	10	,	,	PUNCT
ejpam-5393	142	11	τ2)s	τ2)s	NOUN
ejpam-5393	142	12	-	-	PUNCT
ejpam-5393	142	13	open	open	ADJ
ejpam-5393	142	14	set	set	NOUN
ejpam-5393	142	15	u	u	NOUN
ejpam-5393	142	16	of	of	ADP
ejpam-5393	142	17	x	x	PUNCT
ejpam-5393	142	18	containing	contain	VERB
ejpam-5393	142	19	x	x	PUNCT
ejpam-5393	142	20	such	such	ADJ
ejpam-5393	142	21	that	that	SCONJ
ejpam-5393	142	22	f	f	PROPN
ejpam-5393	142	23	(	(	PUNCT
ejpam-5393	142	24	u	u	NOUN
ejpam-5393	142	25	)	)	PUNCT
ejpam-5393	142	26	⊆	⊆	NUM
ejpam-5393	142	27	v	v	NOUN
ejpam-5393	142	28	.	.	PUNCT
ejpam-5393	143	1	therefore	therefore	ADV
ejpam-5393	143	2	,	,	PUNCT
ejpam-5393	143	3	we	we	PRON
ejpam-5393	143	4	have	have	VERB
ejpam-5393	143	5	x	x	X
ejpam-5393	143	6	∈	∈	PROPN
ejpam-5393	143	7	u	u	NOUN
ejpam-5393	143	8	⊆	⊆	NUM
ejpam-5393	143	9	τ1τ2	τ1τ2	NOUN
ejpam-5393	143	10	-	-	NUM
ejpam-5393	143	11	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5393	143	12	-	-	PUNCT
ejpam-5393	143	13	int(f	int(f	VERB
ejpam-5393	143	14	+	+	ADJ
ejpam-5393	143	15	(	(	PUNCT
ejpam-5393	143	16	v	v	NOUN
ejpam-5393	143	17	)	)	PUNCT
ejpam-5393	143	18	)	)	PUNCT
ejpam-5393	143	19	)	)	PUNCT
ejpam-5393	143	20	.	.	PUNCT
ejpam-5393	144	1	thus	thus	ADV
ejpam-5393	144	2	,	,	PUNCT
ejpam-5393	144	3	f+(v	f+(v	PROPN
ejpam-5393	144	4	)	)	PUNCT
ejpam-5393	145	1	⊆	⊆	X
ejpam-5393	145	2	τ1τ2	τ1τ2	NOUN
ejpam-5393	145	3	-	-	NUM
ejpam-5393	145	4	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5393	145	5	-	-	PUNCT
ejpam-5393	145	6	int(f	int(f	VERB
ejpam-5393	145	7	+	+	ADJ
ejpam-5393	145	8	(	(	PUNCT
ejpam-5393	145	9	v	v	NOUN
ejpam-5393	145	10	)	)	PUNCT
ejpam-5393	145	11	)	)	PUNCT
ejpam-5393	145	12	)	)	PUNCT
ejpam-5393	145	13	and	and	CCONJ
ejpam-5393	145	14	hence	hence	ADV
ejpam-5393	145	15	f+(v	f+(v	NOUN
ejpam-5393	145	16	)	)	PUNCT
ejpam-5393	145	17	is	be	AUX
ejpam-5393	145	18	(	(	PUNCT
ejpam-5393	145	19	τ1	τ1	NOUN
ejpam-5393	145	20	,	,	PUNCT
ejpam-5393	145	21	τ2)s	τ2)s	NOUN
ejpam-5393	145	22	-	-	PUNCT
ejpam-5393	145	23	open	open	ADJ
ejpam-5393	145	24	in	in	ADP
ejpam-5393	145	25	x.	x.	NOUN
ejpam-5393	145	26	(	(	PUNCT
ejpam-5393	145	27	2	2	NUM
ejpam-5393	145	28	)	)	PUNCT
ejpam-5393	145	29	⇒	⇒	NOUN
ejpam-5393	145	30	(	(	PUNCT
ejpam-5393	145	31	3	3	NUM
ejpam-5393	145	32	):	):	PUNCT
ejpam-5393	145	33	the	the	DET
ejpam-5393	145	34	proof	proof	NOUN
ejpam-5393	145	35	follows	follow	VERB
ejpam-5393	145	36	immediately	immediately	ADV
ejpam-5393	145	37	from	from	ADP
ejpam-5393	145	38	the	the	DET
ejpam-5393	145	39	fact	fact	NOUN
ejpam-5393	145	40	that	that	SCONJ
ejpam-5393	145	41	f+(y	f+(y	PROPN
ejpam-5393	145	42	−b	−b	ADJ
ejpam-5393	145	43	)	)	PUNCT
ejpam-5393	145	44	=	=	SYM
ejpam-5393	145	45	y	y	PROPN
ejpam-5393	145	46	−f−(b	−f−(b	PROPN
ejpam-5393	145	47	)	)	PUNCT
ejpam-5393	145	48	for	for	ADP
ejpam-5393	145	49	every	every	DET
ejpam-5393	145	50	subset	subset	NOUN
ejpam-5393	145	51	b	b	PROPN
ejpam-5393	145	52	of	of	ADP
ejpam-5393	145	53	y	y	PROPN
ejpam-5393	145	54	.	.	PUNCT
ejpam-5393	146	1	(	(	PUNCT
ejpam-5393	146	2	3	3	X
ejpam-5393	146	3	)	)	PUNCT
ejpam-5393	146	4	⇒	⇒	NOUN
ejpam-5393	146	5	(	(	PUNCT
ejpam-5393	146	6	4	4	NUM
ejpam-5393	146	7	):	):	PUNCT
ejpam-5393	146	8	let	let	VERB
ejpam-5393	146	9	b	b	X
ejpam-5393	146	10	be	be	AUX
ejpam-5393	146	11	any	any	DET
ejpam-5393	146	12	subset	subset	NOUN
ejpam-5393	146	13	of	of	ADP
ejpam-5393	146	14	y	y	PROPN
ejpam-5393	146	15	having	have	VERB
ejpam-5393	146	16	the	the	DET
ejpam-5393	146	17	σ1σ2	σ1σ2	NUM
ejpam-5393	146	18	-	-	ADJ
ejpam-5393	146	19	compact	compact	ADJ
ejpam-5393	146	20	σ1σ2	σ1σ2	NOUN
ejpam-5393	146	21	-	-	NOUN
ejpam-5393	146	22	closure	closure	NOUN
ejpam-5393	146	23	.	.	PUNCT
ejpam-5393	147	1	then	then	ADV
ejpam-5393	147	2	,	,	PUNCT
ejpam-5393	147	3	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5393	147	4	-	-	PUNCT
ejpam-5393	147	5	cl(b	cl(b	NOUN
ejpam-5393	147	6	)	)	PUNCT
ejpam-5393	147	7	)	)	PUNCT
ejpam-5393	147	8	is	be	AUX
ejpam-5393	147	9	(	(	PUNCT
ejpam-5393	147	10	τ1	τ1	NOUN
ejpam-5393	147	11	,	,	PUNCT
ejpam-5393	147	12	τ2)s	τ2)s	NOUN
ejpam-5393	147	13	-	-	PUNCT
ejpam-5393	147	14	closed	close	VERB
ejpam-5393	147	15	in	in	ADP
ejpam-5393	147	16	x.	x.	NOUN
ejpam-5393	147	17	by	by	ADP
ejpam-5393	147	18	lemma	lemma	PROPN
ejpam-5393	147	19	2	2	NUM
ejpam-5393	147	20	,	,	PUNCT
ejpam-5393	147	21	we	we	PRON
ejpam-5393	147	22	have	have	VERB
ejpam-5393	147	23	τ1τ2	τ1τ2	NOUN
ejpam-5393	147	24	-	-	NOUN
ejpam-5393	147	25	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5393	147	26	-	-	PUNCT
ejpam-5393	147	27	cl(f	cl(f	NOUN
ejpam-5393	147	28	−(b	−(b	PROPN
ejpam-5393	147	29	)	)	PUNCT
ejpam-5393	147	30	)	)	PUNCT
ejpam-5393	147	31	)	)	PUNCT
ejpam-5393	148	1	⊆	⊆	X
ejpam-5393	148	2	τ1τ2	τ1τ2	NOUN
ejpam-5393	148	3	-	-	NOUN
ejpam-5393	148	4	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5393	148	5	-	-	PUNCT
ejpam-5393	148	6	cl(f	cl(f	NOUN
ejpam-5393	148	7	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5393	148	8	-	-	NOUN
ejpam-5393	148	9	cl(b	cl(b	NOUN
ejpam-5393	148	10	)	)	PUNCT
ejpam-5393	148	11	)	)	PUNCT
ejpam-5393	148	12	)	)	PUNCT
ejpam-5393	148	13	)	)	PUNCT
ejpam-5393	149	1	⊆	⊆	X
ejpam-5393	149	2	(	(	PUNCT
ejpam-5393	149	3	τ1	τ1	NOUN
ejpam-5393	149	4	,	,	PUNCT
ejpam-5393	149	5	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5393	149	6	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5393	149	7	-	-	NOUN
ejpam-5393	149	8	cl(b	cl(b	NOUN
ejpam-5393	149	9	)	)	PUNCT
ejpam-5393	149	10	)	)	PUNCT
ejpam-5393	149	11	)	)	PUNCT
ejpam-5393	149	12	=	=	PUNCT
ejpam-5393	149	13	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5393	149	14	-	-	PUNCT
ejpam-5393	149	15	cl(b	cl(b	NOUN
ejpam-5393	149	16	)	)	PUNCT
ejpam-5393	149	17	)	)	PUNCT
ejpam-5393	149	18	.	.	PUNCT
ejpam-5393	150	1	p.	p.	NOUN
ejpam-5393	150	2	pue	pue	NOUN
ejpam-5393	150	3	-	-	PUNCT
ejpam-5393	150	4	on	on	ADP
ejpam-5393	150	5	,	,	PUNCT
ejpam-5393	150	6	a.	a.	PROPN
ejpam-5393	150	7	sama	sama	PROPN
ejpam-5393	150	8	-	-	PUNCT
ejpam-5393	150	9	ae	ae	PROPN
ejpam-5393	150	10	,	,	PUNCT
ejpam-5393	150	11	c.	c.	PROPN
ejpam-5393	150	12	boonpok	boonpok	PROPN
ejpam-5393	150	13	/	/	SYM
ejpam-5393	150	14	eur	eur	PROPN
ejpam-5393	150	15	.	.	PUNCT
ejpam-5393	151	1	j.	j.	PROPN
ejpam-5393	151	2	pure	pure	PROPN
ejpam-5393	151	3	appl	appl	PROPN
ejpam-5393	151	4	.	.	PROPN
ejpam-5393	151	5	math	math	PROPN
ejpam-5393	151	6	,	,	PUNCT
ejpam-5393	151	7	17	17	NUM
ejpam-5393	151	8	(	(	PUNCT
ejpam-5393	151	9	4	4	NUM
ejpam-5393	151	10	)	)	PUNCT
ejpam-5393	151	11	(	(	PUNCT
ejpam-5393	151	12	2024	2024	NUM
ejpam-5393	151	13	)	)	PUNCT
ejpam-5393	151	14	,	,	PUNCT
ejpam-5393	151	15	3242	3242	NUM
ejpam-5393	151	16	-	-	SYM
ejpam-5393	151	17	3253	3253	NUM
ejpam-5393	151	18	3247	3247	NUM
ejpam-5393	151	19	thus	thus	ADV
ejpam-5393	151	20	,	,	PUNCT
ejpam-5393	151	21	τ1τ2	τ1τ2	NOUN
ejpam-5393	151	22	-	-	NOUN
ejpam-5393	151	23	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5393	151	24	-	-	PUNCT
ejpam-5393	151	25	cl(f	cl(f	NOUN
ejpam-5393	151	26	−(b	−(b	PROPN
ejpam-5393	151	27	)	)	PUNCT
ejpam-5393	151	28	)	)	PUNCT
ejpam-5393	151	29	)	)	PUNCT
ejpam-5393	152	1	⊆	⊆	X
ejpam-5393	152	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5393	152	3	-	-	PUNCT
ejpam-5393	152	4	cl(b	cl(b	NOUN
ejpam-5393	152	5	)	)	PUNCT
ejpam-5393	152	6	)	)	PUNCT
ejpam-5393	152	7	.	.	PUNCT
ejpam-5393	153	1	(	(	PUNCT
ejpam-5393	153	2	4	4	X
ejpam-5393	153	3	)	)	PUNCT
ejpam-5393	153	4	⇒	⇒	NOUN
ejpam-5393	153	5	(	(	PUNCT
ejpam-5393	153	6	5	5	NUM
ejpam-5393	153	7	):	):	PUNCT
ejpam-5393	153	8	let	let	VERB
ejpam-5393	153	9	b	b	X
ejpam-5393	153	10	be	be	AUX
ejpam-5393	153	11	any	any	DET
ejpam-5393	153	12	subset	subset	NOUN
ejpam-5393	153	13	of	of	ADP
ejpam-5393	153	14	y	y	PROPN
ejpam-5393	153	15	having	have	VERB
ejpam-5393	153	16	the	the	DET
ejpam-5393	153	17	σ1σ2	σ1σ2	NUM
ejpam-5393	153	18	-	-	ADJ
ejpam-5393	153	19	compact	compact	ADJ
ejpam-5393	153	20	σ1σ2	σ1σ2	NOUN
ejpam-5393	153	21	-	-	NOUN
ejpam-5393	153	22	closure	closure	NOUN
ejpam-5393	153	23	.	.	PUNCT
ejpam-5393	154	1	it	it	PRON
ejpam-5393	154	2	follows	follow	VERB
ejpam-5393	154	3	from	from	ADP
ejpam-5393	154	4	lemma	lemma	PROPN
ejpam-5393	154	5	2	2	NUM
ejpam-5393	154	6	that	that	PRON
ejpam-5393	154	7	(	(	PUNCT
ejpam-5393	154	8	τ1	τ1	NOUN
ejpam-5393	154	9	,	,	PUNCT
ejpam-5393	154	10	τ2)-scl(f	τ2)-scl(f	PROPN
ejpam-5393	154	11	−(b	−(b	PROPN
ejpam-5393	154	12	)	)	PUNCT
ejpam-5393	154	13	)	)	PUNCT
ejpam-5393	155	1	=	=	SYM
ejpam-5393	155	2	f−(b	f−(b	PROPN
ejpam-5393	155	3	)	)	PUNCT
ejpam-5393	155	4	∪	∪	ADP
ejpam-5393	155	5	τ1τ2	τ1τ2	NOUN
ejpam-5393	155	6	-	-	NOUN
ejpam-5393	155	7	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5393	155	8	-	-	PUNCT
ejpam-5393	155	9	cl(f	cl(f	NOUN
ejpam-5393	155	10	−(b	−(b	PROPN
ejpam-5393	155	11	)	)	PUNCT
ejpam-5393	155	12	)	)	PUNCT
ejpam-5393	155	13	)	)	PUNCT
ejpam-5393	156	1	⊆	⊆	NUM
ejpam-5393	156	2	f−(b	f−(b	NOUN
ejpam-5393	156	3	)	)	PUNCT
ejpam-5393	156	4	∪	∪	ADP
ejpam-5393	156	5	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5393	156	6	-	-	PUNCT
ejpam-5393	156	7	cl(b	cl(b	NOUN
ejpam-5393	156	8	)	)	PUNCT
ejpam-5393	156	9	)	)	PUNCT
ejpam-5393	157	1	=	=	PUNCT
ejpam-5393	157	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5393	157	3	-	-	PUNCT
ejpam-5393	157	4	cl(b	cl(b	NOUN
ejpam-5393	157	5	)	)	PUNCT
ejpam-5393	157	6	)	)	PUNCT
ejpam-5393	157	7	.	.	PUNCT
ejpam-5393	158	1	(	(	PUNCT
ejpam-5393	158	2	5	5	X
ejpam-5393	158	3	)	)	PUNCT
ejpam-5393	158	4	⇒	⇒	NOUN
ejpam-5393	158	5	(	(	PUNCT
ejpam-5393	158	6	6	6	NUM
ejpam-5393	158	7	):	):	PUNCT
ejpam-5393	158	8	let	let	VERB
ejpam-5393	158	9	b	b	X
ejpam-5393	158	10	be	be	AUX
ejpam-5393	158	11	any	any	DET
ejpam-5393	158	12	subset	subset	NOUN
ejpam-5393	158	13	of	of	ADP
ejpam-5393	158	14	y	y	PRON
ejpam-5393	158	15	such	such	ADJ
ejpam-5393	158	16	that	that	SCONJ
ejpam-5393	158	17	y	y	PROPN
ejpam-5393	158	18	−σ1σ2	−σ1σ2	PROPN
ejpam-5393	158	19	-	-	PUNCT
ejpam-5393	158	20	int(b	int(b	NOUN
ejpam-5393	158	21	)	)	PUNCT
ejpam-5393	158	22	is	be	AUX
ejpam-5393	158	23	σ1σ2	σ1σ2	NOUN
ejpam-5393	158	24	-	-	ADJ
ejpam-5393	158	25	compact	compact	ADJ
ejpam-5393	158	26	.	.	PUNCT
ejpam-5393	159	1	then	then	ADV
ejpam-5393	159	2	by	by	ADP
ejpam-5393	159	3	lemma	lemma	PROPN
ejpam-5393	159	4	2	2	NUM
ejpam-5393	159	5	,	,	PUNCT
ejpam-5393	159	6	we	we	PRON
ejpam-5393	159	7	have	have	VERB
ejpam-5393	159	8	x	x	X
ejpam-5393	159	9	−	−	PROPN
ejpam-5393	159	10	(	(	PUNCT
ejpam-5393	159	11	τ1	τ1	NOUN
ejpam-5393	159	12	,	,	PUNCT
ejpam-5393	159	13	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5393	160	1	+	+	ADJ
ejpam-5393	160	2	(	(	PUNCT
ejpam-5393	160	3	b	b	NOUN
ejpam-5393	160	4	)	)	PUNCT
ejpam-5393	160	5	)	)	PUNCT
ejpam-5393	161	1	=	=	PRON
ejpam-5393	161	2	(	(	PUNCT
ejpam-5393	161	3	τ1	τ1	PROPN
ejpam-5393	161	4	,	,	PUNCT
ejpam-5393	161	5	τ2)-scl(x	τ2)-scl(x	NOUN
ejpam-5393	161	6	−	−	PROPN
ejpam-5393	161	7	f+(b	f+(b	PROPN
ejpam-5393	161	8	)	)	PUNCT
ejpam-5393	161	9	)	)	PUNCT
ejpam-5393	162	1	=	=	PRON
ejpam-5393	162	2	(	(	PUNCT
ejpam-5393	162	3	τ1	τ1	PROPN
ejpam-5393	162	4	,	,	PUNCT
ejpam-5393	162	5	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5393	162	6	−(y	−(y	NOUN
ejpam-5393	162	7	−b	−b	PROPN
ejpam-5393	162	8	)	)	PUNCT
ejpam-5393	162	9	)	)	PUNCT
ejpam-5393	163	1	⊆	⊆	X
ejpam-5393	163	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5393	163	3	-	-	PUNCT
ejpam-5393	163	4	cl(y	cl(y	NOUN
ejpam-5393	163	5	−b	−b	NOUN
ejpam-5393	163	6	)	)	PUNCT
ejpam-5393	163	7	)	)	PUNCT
ejpam-5393	164	1	=	=	PUNCT
ejpam-5393	164	2	f−(y	f−(y	NOUN
ejpam-5393	164	3	−	−	ADP
ejpam-5393	164	4	σ1σ2	σ1σ2	NOUN
ejpam-5393	164	5	-	-	PUNCT
ejpam-5393	164	6	int(b	int(b	NOUN
ejpam-5393	164	7	)	)	PUNCT
ejpam-5393	164	8	)	)	PUNCT
ejpam-5393	165	1	=	=	PUNCT
ejpam-5393	165	2	x	x	X
ejpam-5393	166	1	−	−	ADP
ejpam-5393	166	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5393	166	3	-	-	PUNCT
ejpam-5393	166	4	int(b	int(b	NOUN
ejpam-5393	166	5	)	)	PUNCT
ejpam-5393	166	6	)	)	PUNCT
ejpam-5393	166	7	and	and	CCONJ
ejpam-5393	166	8	hence	hence	ADV
ejpam-5393	166	9	f+(σ1σ2	f+(σ1σ2	ADV
ejpam-5393	166	10	-	-	PUNCT
ejpam-5393	166	11	int(b	int(b	NOUN
ejpam-5393	166	12	)	)	PUNCT
ejpam-5393	166	13	)	)	PUNCT
ejpam-5393	167	1	⊆	⊆	NUM
ejpam-5393	167	2	(	(	PUNCT
ejpam-5393	167	3	τ1	τ1	NOUN
ejpam-5393	167	4	,	,	PUNCT
ejpam-5393	167	5	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5393	167	6	+	+	ADJ
ejpam-5393	167	7	(	(	PUNCT
ejpam-5393	167	8	b	b	NOUN
ejpam-5393	167	9	)	)	PUNCT
ejpam-5393	167	10	)	)	PUNCT
ejpam-5393	167	11	.	.	PUNCT
ejpam-5393	168	1	(	(	PUNCT
ejpam-5393	168	2	6	6	X
ejpam-5393	168	3	)	)	PUNCT
ejpam-5393	168	4	⇒	⇒	NOUN
ejpam-5393	168	5	(	(	PUNCT
ejpam-5393	168	6	1	1	NUM
ejpam-5393	168	7	):	):	PUNCT
ejpam-5393	168	8	let	let	VERB
ejpam-5393	168	9	x	x	PUNCT
ejpam-5393	168	10	∈	∈	PROPN
ejpam-5393	168	11	x	x	X
ejpam-5393	168	12	and	and	CCONJ
ejpam-5393	168	13	v	v	X
ejpam-5393	168	14	be	be	AUX
ejpam-5393	168	15	any	any	DET
ejpam-5393	168	16	σ1σ2	σ1σ2	NOUN
ejpam-5393	168	17	-	-	ADJ
ejpam-5393	168	18	open	open	ADJ
ejpam-5393	168	19	set	set	NOUN
ejpam-5393	168	20	of	of	ADP
ejpam-5393	168	21	y	y	PRON
ejpam-5393	168	22	such	such	ADJ
ejpam-5393	168	23	that	that	SCONJ
ejpam-5393	168	24	f	f	PROPN
ejpam-5393	168	25	(	(	PUNCT
ejpam-5393	168	26	x	x	X
ejpam-5393	168	27	)	)	PUNCT
ejpam-5393	168	28	⊆	⊆	NUM
ejpam-5393	168	29	v	v	NOUN
ejpam-5393	168	30	and	and	CCONJ
ejpam-5393	168	31	having	have	VERB
ejpam-5393	168	32	σ1σ2	σ1σ2	NOUN
ejpam-5393	168	33	-	-	ADJ
ejpam-5393	168	34	compact	compact	ADJ
ejpam-5393	168	35	complement	complement	NOUN
ejpam-5393	168	36	.	.	PUNCT
ejpam-5393	169	1	then	then	ADV
ejpam-5393	169	2	,	,	PUNCT
ejpam-5393	169	3	f+(v	f+(v	PROPN
ejpam-5393	169	4	)	)	PUNCT
ejpam-5393	170	1	=	=	SYM
ejpam-5393	170	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5393	170	3	-	-	PUNCT
ejpam-5393	170	4	int(v	int(v	NOUN
ejpam-5393	170	5	)	)	PUNCT
ejpam-5393	170	6	)	)	PUNCT
ejpam-5393	171	1	⊆	⊆	NUM
ejpam-5393	171	2	(	(	PUNCT
ejpam-5393	171	3	τ1	τ1	NOUN
ejpam-5393	171	4	,	,	PUNCT
ejpam-5393	171	5	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5393	171	6	+	+	ADJ
ejpam-5393	171	7	(	(	PUNCT
ejpam-5393	171	8	v	v	NOUN
ejpam-5393	171	9	)	)	PUNCT
ejpam-5393	171	10	)	)	PUNCT
ejpam-5393	171	11	.	.	PUNCT
ejpam-5393	172	1	put	put	VERB
ejpam-5393	172	2	u	u	NOUN
ejpam-5393	172	3	=	=	PUNCT
ejpam-5393	172	4	(	(	PUNCT
ejpam-5393	172	5	τ1	τ1	NOUN
ejpam-5393	172	6	,	,	PUNCT
ejpam-5393	172	7	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5393	173	1	+	+	ADJ
ejpam-5393	173	2	(	(	PUNCT
ejpam-5393	173	3	v	v	NOUN
ejpam-5393	173	4	)	)	PUNCT
ejpam-5393	173	5	)	)	PUNCT
ejpam-5393	173	6	.	.	PUNCT
ejpam-5393	174	1	then	then	ADV
ejpam-5393	174	2	,	,	PUNCT
ejpam-5393	174	3	u	u	NOUN
ejpam-5393	174	4	is	be	AUX
ejpam-5393	174	5	a	a	DET
ejpam-5393	174	6	(	(	PUNCT
ejpam-5393	174	7	τ1	τ1	NOUN
ejpam-5393	174	8	,	,	PUNCT
ejpam-5393	174	9	τ2)s	τ2)s	NOUN
ejpam-5393	174	10	-	-	PUNCT
ejpam-5393	174	11	open	open	ADJ
ejpam-5393	174	12	set	set	NOUN
ejpam-5393	174	13	u	u	NOUN
ejpam-5393	174	14	of	of	ADP
ejpam-5393	174	15	x	x	PUNCT
ejpam-5393	174	16	containing	contain	VERB
ejpam-5393	174	17	x	x	PROPN
ejpam-5393	174	18	and	and	CCONJ
ejpam-5393	174	19	f	f	PROPN
ejpam-5393	174	20	(	(	PUNCT
ejpam-5393	174	21	u	u	NOUN
ejpam-5393	174	22	)	)	PUNCT
ejpam-5393	174	23	⊆	⊆	NUM
ejpam-5393	174	24	v	v	NOUN
ejpam-5393	174	25	.	.	PUNCT
ejpam-5393	175	1	thus	thus	ADV
ejpam-5393	175	2	,	,	PUNCT
ejpam-5393	175	3	f	f	PROPN
ejpam-5393	175	4	is	be	AUX
ejpam-5393	175	5	upper	upper	ADJ
ejpam-5393	175	6	c	c	NOUN
ejpam-5393	175	7	-	-	PUNCT
ejpam-5393	175	8	quasi	quasi	ADJ
ejpam-5393	175	9	(	(	PUNCT
ejpam-5393	175	10	τ1	τ1	NOUN
ejpam-5393	175	11	,	,	PUNCT
ejpam-5393	175	12	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	175	13	at	at	ADP
ejpam-5393	175	14	x.	x.	NOUN
ejpam-5393	175	15	this	this	PRON
ejpam-5393	175	16	shows	show	VERB
ejpam-5393	175	17	that	that	SCONJ
ejpam-5393	175	18	f	f	PROPN
ejpam-5393	175	19	is	be	AUX
ejpam-5393	175	20	upper	upper	ADJ
ejpam-5393	175	21	c	c	NOUN
ejpam-5393	175	22	-	-	PUNCT
ejpam-5393	175	23	quasi	quasi	ADJ
ejpam-5393	175	24	(	(	PUNCT
ejpam-5393	175	25	τ1	τ1	NOUN
ejpam-5393	175	26	,	,	PUNCT
ejpam-5393	175	27	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	175	28	.	.	PUNCT
ejpam-5393	176	1	theorem	theorem	NOUN
ejpam-5393	176	2	4	4	NUM
ejpam-5393	176	3	.	.	X
ejpam-5393	176	4	for	for	ADP
ejpam-5393	176	5	a	a	DET
ejpam-5393	176	6	multifunction	multifunction	NOUN
ejpam-5393	177	1	f	f	NOUN
ejpam-5393	177	2	:	:	PUNCT
ejpam-5393	177	3	(	(	PUNCT
ejpam-5393	177	4	x	x	NOUN
ejpam-5393	177	5	,	,	PUNCT
ejpam-5393	177	6	τ1	τ1	NOUN
ejpam-5393	177	7	,	,	PUNCT
ejpam-5393	177	8	τ2	τ2	NOUN
ejpam-5393	177	9	)	)	PUNCT
ejpam-5393	177	10	→	→	SYM
ejpam-5393	177	11	(	(	PUNCT
ejpam-5393	177	12	y	y	PROPN
ejpam-5393	177	13	,	,	PUNCT
ejpam-5393	177	14	σ1	σ1	PROPN
ejpam-5393	177	15	,	,	PUNCT
ejpam-5393	177	16	σ2	σ2	NOUN
ejpam-5393	177	17	)	)	PUNCT
ejpam-5393	177	18	,	,	PUNCT
ejpam-5393	177	19	the	the	DET
ejpam-5393	177	20	following	follow	VERB
ejpam-5393	177	21	properties	property	NOUN
ejpam-5393	177	22	are	be	AUX
ejpam-5393	177	23	equivalent	equivalent	ADJ
ejpam-5393	177	24	:	:	PUNCT
ejpam-5393	177	25	(	(	PUNCT
ejpam-5393	177	26	1	1	X
ejpam-5393	177	27	)	)	PUNCT
ejpam-5393	177	28	f	f	PROPN
ejpam-5393	177	29	is	be	AUX
ejpam-5393	177	30	lower	low	ADJ
ejpam-5393	177	31	c	c	NOUN
ejpam-5393	177	32	-	-	PUNCT
ejpam-5393	177	33	quasi	quasi	ADJ
ejpam-5393	177	34	(	(	PUNCT
ejpam-5393	177	35	τ1	τ1	NOUN
ejpam-5393	177	36	,	,	PUNCT
ejpam-5393	177	37	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	177	38	;	;	PUNCT
ejpam-5393	177	39	(	(	PUNCT
ejpam-5393	177	40	2	2	X
ejpam-5393	177	41	)	)	PUNCT
ejpam-5393	177	42	f−(v	f−(v	NOUN
ejpam-5393	177	43	)	)	PUNCT
ejpam-5393	177	44	is	be	AUX
ejpam-5393	177	45	(	(	PUNCT
ejpam-5393	177	46	τ1	τ1	NOUN
ejpam-5393	177	47	,	,	PUNCT
ejpam-5393	177	48	τ2)s	τ2)s	NOUN
ejpam-5393	177	49	-	-	PUNCT
ejpam-5393	177	50	open	open	ADJ
ejpam-5393	177	51	in	in	ADP
ejpam-5393	177	52	x	x	PUNCT
ejpam-5393	177	53	for	for	ADP
ejpam-5393	177	54	every	every	DET
ejpam-5393	177	55	σ1σ2	σ1σ2	NOUN
ejpam-5393	177	56	-	-	ADJ
ejpam-5393	177	57	open	open	ADJ
ejpam-5393	177	58	set	set	NOUN
ejpam-5393	177	59	v	v	NOUN
ejpam-5393	177	60	of	of	ADP
ejpam-5393	177	61	y	y	PROPN
ejpam-5393	177	62	having	have	VERB
ejpam-5393	177	63	σ1σ2	σ1σ2	NOUN
ejpam-5393	177	64	-	-	ADJ
ejpam-5393	177	65	compact	compact	ADJ
ejpam-5393	177	66	complement	complement	NOUN
ejpam-5393	177	67	;	;	PUNCT
ejpam-5393	177	68	(	(	PUNCT
ejpam-5393	177	69	3	3	X
ejpam-5393	177	70	)	)	PUNCT
ejpam-5393	177	71	f+(k	f+(k	NUM
ejpam-5393	177	72	)	)	PUNCT
ejpam-5393	177	73	is	be	AUX
ejpam-5393	177	74	(	(	PUNCT
ejpam-5393	177	75	τ1	τ1	NOUN
ejpam-5393	177	76	,	,	PUNCT
ejpam-5393	177	77	τ2)s	τ2)s	NOUN
ejpam-5393	177	78	-	-	PUNCT
ejpam-5393	177	79	closed	close	VERB
ejpam-5393	177	80	in	in	ADP
ejpam-5393	177	81	x	x	PUNCT
ejpam-5393	177	82	for	for	ADP
ejpam-5393	177	83	every	every	DET
ejpam-5393	177	84	σ1σ2	σ1σ2	NUM
ejpam-5393	177	85	-	-	ADJ
ejpam-5393	177	86	compact	compact	ADJ
ejpam-5393	177	87	σ1σ2	σ1σ2	VERB
ejpam-5393	177	88	-	-	PUNCT
ejpam-5393	177	89	closed	close	VERB
ejpam-5393	177	90	set	set	NOUN
ejpam-5393	177	91	k	k	PROPN
ejpam-5393	177	92	of	of	ADP
ejpam-5393	177	93	y	y	PROPN
ejpam-5393	177	94	;	;	PUNCT
ejpam-5393	177	95	(	(	PUNCT
ejpam-5393	177	96	4	4	X
ejpam-5393	177	97	)	)	PUNCT
ejpam-5393	177	98	τ1τ2	τ1τ2	NOUN
ejpam-5393	177	99	-	-	NOUN
ejpam-5393	177	100	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5393	177	101	-	-	PUNCT
ejpam-5393	177	102	cl(f	cl(f	NOUN
ejpam-5393	177	103	+	+	NOUN
ejpam-5393	177	104	(	(	PUNCT
ejpam-5393	177	105	b	b	NOUN
ejpam-5393	177	106	)	)	PUNCT
ejpam-5393	177	107	)	)	PUNCT
ejpam-5393	177	108	)	)	PUNCT
ejpam-5393	178	1	⊆	⊆	X
ejpam-5393	178	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5393	178	3	-	-	PUNCT
ejpam-5393	178	4	cl(b	cl(b	NOUN
ejpam-5393	178	5	)	)	PUNCT
ejpam-5393	178	6	)	)	PUNCT
ejpam-5393	178	7	for	for	ADP
ejpam-5393	178	8	every	every	DET
ejpam-5393	178	9	subset	subset	NOUN
ejpam-5393	178	10	b	b	PROPN
ejpam-5393	178	11	of	of	ADP
ejpam-5393	178	12	y	y	PROPN
ejpam-5393	178	13	having	have	VERB
ejpam-5393	178	14	the	the	DET
ejpam-5393	178	15	σ1σ2	σ1σ2	NUM
ejpam-5393	178	16	-	-	ADJ
ejpam-5393	178	17	compact	compact	ADJ
ejpam-5393	178	18	σ1σ2	σ1σ2	NOUN
ejpam-5393	178	19	-	-	NOUN
ejpam-5393	178	20	closure	closure	NOUN
ejpam-5393	178	21	;	;	PUNCT
ejpam-5393	178	22	(	(	PUNCT
ejpam-5393	178	23	5	5	NUM
ejpam-5393	178	24	)	)	PUNCT
ejpam-5393	178	25	(	(	PUNCT
ejpam-5393	178	26	τ1	τ1	NOUN
ejpam-5393	178	27	,	,	PUNCT
ejpam-5393	178	28	τ2)-scl(f	τ2)-scl(f	PROPN
ejpam-5393	179	1	+	+	ADJ
ejpam-5393	179	2	(	(	PUNCT
ejpam-5393	179	3	b	b	NOUN
ejpam-5393	179	4	)	)	PUNCT
ejpam-5393	179	5	)	)	PUNCT
ejpam-5393	180	1	⊆	⊆	NUM
ejpam-5393	180	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5393	180	3	-	-	PUNCT
ejpam-5393	180	4	cl(b	cl(b	NOUN
ejpam-5393	180	5	)	)	PUNCT
ejpam-5393	180	6	)	)	PUNCT
ejpam-5393	180	7	for	for	ADP
ejpam-5393	180	8	every	every	DET
ejpam-5393	180	9	subset	subset	NOUN
ejpam-5393	180	10	b	b	PROPN
ejpam-5393	180	11	of	of	ADP
ejpam-5393	180	12	y	y	PROPN
ejpam-5393	180	13	having	have	VERB
ejpam-5393	180	14	the	the	DET
ejpam-5393	180	15	σ1σ2compact	σ1σ2compact	ADJ
ejpam-5393	180	16	σ1σ2	σ1σ2	NOUN
ejpam-5393	180	17	-	-	NOUN
ejpam-5393	180	18	closure	closure	NOUN
ejpam-5393	180	19	;	;	PUNCT
ejpam-5393	180	20	(	(	PUNCT
ejpam-5393	180	21	6	6	X
ejpam-5393	180	22	)	)	PUNCT
ejpam-5393	180	23	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5393	180	24	-	-	PUNCT
ejpam-5393	180	25	int(b	int(b	NOUN
ejpam-5393	180	26	)	)	PUNCT
ejpam-5393	180	27	)	)	PUNCT
ejpam-5393	181	1	⊆	⊆	NUM
ejpam-5393	181	2	(	(	PUNCT
ejpam-5393	181	3	τ1	τ1	NOUN
ejpam-5393	181	4	,	,	PUNCT
ejpam-5393	181	5	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5393	181	6	−(b	−(b	NOUN
ejpam-5393	181	7	)	)	PUNCT
ejpam-5393	181	8	)	)	PUNCT
ejpam-5393	181	9	for	for	ADP
ejpam-5393	181	10	every	every	DET
ejpam-5393	181	11	subset	subset	NOUN
ejpam-5393	181	12	b	b	PROPN
ejpam-5393	181	13	of	of	ADP
ejpam-5393	181	14	y	y	PRON
ejpam-5393	181	15	such	such	ADJ
ejpam-5393	181	16	that	that	SCONJ
ejpam-5393	181	17	y	y	PROPN
ejpam-5393	182	1	−	−	ADP
ejpam-5393	182	2	σ1σ2	σ1σ2	NUM
ejpam-5393	182	3	-	-	PUNCT
ejpam-5393	182	4	int(b	int(b	NOUN
ejpam-5393	182	5	)	)	PUNCT
ejpam-5393	182	6	is	be	AUX
ejpam-5393	182	7	σ1σ2	σ1σ2	NOUN
ejpam-5393	182	8	-	-	ADJ
ejpam-5393	182	9	compact	compact	ADJ
ejpam-5393	182	10	.	.	PUNCT
ejpam-5393	183	1	p.	p.	NOUN
ejpam-5393	183	2	pue	pue	NOUN
ejpam-5393	183	3	-	-	PUNCT
ejpam-5393	183	4	on	on	ADP
ejpam-5393	183	5	,	,	PUNCT
ejpam-5393	183	6	a.	a.	PROPN
ejpam-5393	183	7	sama	sama	PROPN
ejpam-5393	183	8	-	-	PUNCT
ejpam-5393	183	9	ae	ae	PROPN
ejpam-5393	183	10	,	,	PUNCT
ejpam-5393	183	11	c.	c.	PROPN
ejpam-5393	183	12	boonpok	boonpok	PROPN
ejpam-5393	183	13	/	/	SYM
ejpam-5393	183	14	eur	eur	PROPN
ejpam-5393	183	15	.	.	PUNCT
ejpam-5393	184	1	j.	j.	PROPN
ejpam-5393	184	2	pure	pure	PROPN
ejpam-5393	184	3	appl	appl	PROPN
ejpam-5393	184	4	.	.	PROPN
ejpam-5393	184	5	math	math	PROPN
ejpam-5393	184	6	,	,	PUNCT
ejpam-5393	184	7	17	17	NUM
ejpam-5393	184	8	(	(	PUNCT
ejpam-5393	184	9	4	4	NUM
ejpam-5393	184	10	)	)	PUNCT
ejpam-5393	184	11	(	(	PUNCT
ejpam-5393	184	12	2024	2024	NUM
ejpam-5393	184	13	)	)	PUNCT
ejpam-5393	184	14	,	,	PUNCT
ejpam-5393	184	15	3242	3242	NUM
ejpam-5393	184	16	-	-	SYM
ejpam-5393	184	17	3253	3253	NUM
ejpam-5393	184	18	3248	3248	NUM
ejpam-5393	184	19	proof	proof	NOUN
ejpam-5393	184	20	.	.	PUNCT
ejpam-5393	185	1	the	the	DET
ejpam-5393	185	2	proof	proof	NOUN
ejpam-5393	185	3	is	be	AUX
ejpam-5393	185	4	similar	similar	ADJ
ejpam-5393	185	5	to	to	ADP
ejpam-5393	185	6	that	that	PRON
ejpam-5393	185	7	of	of	ADP
ejpam-5393	185	8	theorem	theorem	ADJ
ejpam-5393	185	9	3	3	NUM
ejpam-5393	185	10	.	.	PUNCT
ejpam-5393	185	11	corollary	corollary	ADJ
ejpam-5393	185	12	2	2	NUM
ejpam-5393	185	13	.	.	PUNCT
ejpam-5393	185	14	for	for	ADP
ejpam-5393	185	15	a	a	DET
ejpam-5393	185	16	function	function	NOUN
ejpam-5393	185	17	f	f	NOUN
ejpam-5393	185	18	:	:	PUNCT
ejpam-5393	185	19	(	(	PUNCT
ejpam-5393	185	20	x	x	NOUN
ejpam-5393	185	21	,	,	PUNCT
ejpam-5393	185	22	τ1	τ1	NOUN
ejpam-5393	185	23	,	,	PUNCT
ejpam-5393	185	24	τ2	τ2	NOUN
ejpam-5393	185	25	)	)	PUNCT
ejpam-5393	185	26	→	→	SYM
ejpam-5393	185	27	(	(	PUNCT
ejpam-5393	185	28	y	y	PROPN
ejpam-5393	185	29	,	,	PUNCT
ejpam-5393	185	30	σ1	σ1	PROPN
ejpam-5393	185	31	,	,	PUNCT
ejpam-5393	185	32	σ2	σ2	NOUN
ejpam-5393	185	33	)	)	PUNCT
ejpam-5393	185	34	,	,	PUNCT
ejpam-5393	185	35	the	the	DET
ejpam-5393	185	36	following	follow	VERB
ejpam-5393	185	37	properties	property	NOUN
ejpam-5393	185	38	are	be	AUX
ejpam-5393	185	39	equivalent	equivalent	ADJ
ejpam-5393	185	40	:	:	PUNCT
ejpam-5393	185	41	(	(	PUNCT
ejpam-5393	185	42	1	1	X
ejpam-5393	185	43	)	)	PUNCT
ejpam-5393	185	44	f	f	PROPN
ejpam-5393	185	45	is	be	AUX
ejpam-5393	185	46	c	c	NOUN
ejpam-5393	185	47	-	-	PUNCT
ejpam-5393	185	48	quasi	quasi	NOUN
ejpam-5393	185	49	(	(	PUNCT
ejpam-5393	185	50	τ1	τ1	NOUN
ejpam-5393	185	51	,	,	PUNCT
ejpam-5393	185	52	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	185	53	;	;	PUNCT
ejpam-5393	185	54	(	(	PUNCT
ejpam-5393	185	55	2	2	X
ejpam-5393	185	56	)	)	PUNCT
ejpam-5393	185	57	f−1(v	f−1(v	NOUN
ejpam-5393	185	58	)	)	PUNCT
ejpam-5393	185	59	is	be	AUX
ejpam-5393	185	60	(	(	PUNCT
ejpam-5393	185	61	τ1	τ1	NOUN
ejpam-5393	185	62	,	,	PUNCT
ejpam-5393	185	63	τ2)s	τ2)s	NOUN
ejpam-5393	185	64	-	-	PUNCT
ejpam-5393	185	65	open	open	ADJ
ejpam-5393	185	66	in	in	ADP
ejpam-5393	185	67	x	x	PUNCT
ejpam-5393	185	68	for	for	ADP
ejpam-5393	185	69	every	every	DET
ejpam-5393	185	70	σ1σ2	σ1σ2	NOUN
ejpam-5393	185	71	-	-	ADJ
ejpam-5393	185	72	open	open	ADJ
ejpam-5393	185	73	set	set	NOUN
ejpam-5393	185	74	v	v	NOUN
ejpam-5393	185	75	of	of	ADP
ejpam-5393	185	76	y	y	PROPN
ejpam-5393	185	77	having	have	VERB
ejpam-5393	185	78	σ1σ2	σ1σ2	NOUN
ejpam-5393	185	79	-	-	ADJ
ejpam-5393	185	80	compact	compact	ADJ
ejpam-5393	185	81	complement	complement	NOUN
ejpam-5393	185	82	;	;	PUNCT
ejpam-5393	185	83	(	(	PUNCT
ejpam-5393	185	84	3	3	X
ejpam-5393	185	85	)	)	PUNCT
ejpam-5393	185	86	f−1(k	f−1(k	PROPN
ejpam-5393	185	87	)	)	PUNCT
ejpam-5393	185	88	is	be	AUX
ejpam-5393	185	89	(	(	PUNCT
ejpam-5393	185	90	τ1	τ1	NOUN
ejpam-5393	185	91	,	,	PUNCT
ejpam-5393	185	92	τ2)s	τ2)s	NOUN
ejpam-5393	185	93	-	-	PUNCT
ejpam-5393	185	94	closed	close	VERB
ejpam-5393	185	95	in	in	ADP
ejpam-5393	185	96	x	x	PUNCT
ejpam-5393	185	97	for	for	ADP
ejpam-5393	185	98	every	every	DET
ejpam-5393	185	99	σ1σ2	σ1σ2	NUM
ejpam-5393	185	100	-	-	ADJ
ejpam-5393	185	101	compact	compact	ADJ
ejpam-5393	185	102	σ1σ2	σ1σ2	VERB
ejpam-5393	185	103	-	-	PUNCT
ejpam-5393	185	104	closed	close	VERB
ejpam-5393	185	105	set	set	NOUN
ejpam-5393	185	106	k	k	PROPN
ejpam-5393	185	107	of	of	ADP
ejpam-5393	185	108	y	y	PROPN
ejpam-5393	185	109	;	;	PUNCT
ejpam-5393	185	110	(	(	PUNCT
ejpam-5393	185	111	4	4	X
ejpam-5393	185	112	)	)	PUNCT
ejpam-5393	185	113	τ1τ2	τ1τ2	NOUN
ejpam-5393	185	114	-	-	NOUN
ejpam-5393	185	115	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5393	185	116	-	-	PUNCT
ejpam-5393	185	117	cl(f	cl(f	NOUN
ejpam-5393	185	118	−1(b	−1(b	NOUN
ejpam-5393	185	119	)	)	PUNCT
ejpam-5393	185	120	)	)	PUNCT
ejpam-5393	185	121	)	)	PUNCT
ejpam-5393	186	1	⊆	⊆	NUM
ejpam-5393	186	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5393	186	3	-	-	PUNCT
ejpam-5393	186	4	cl(b	cl(b	NOUN
ejpam-5393	186	5	)	)	PUNCT
ejpam-5393	186	6	)	)	PUNCT
ejpam-5393	186	7	for	for	ADP
ejpam-5393	186	8	every	every	DET
ejpam-5393	186	9	subset	subset	NOUN
ejpam-5393	186	10	b	b	PROPN
ejpam-5393	186	11	of	of	ADP
ejpam-5393	186	12	y	y	PROPN
ejpam-5393	186	13	having	have	VERB
ejpam-5393	186	14	the	the	DET
ejpam-5393	186	15	σ1σ2	σ1σ2	NUM
ejpam-5393	186	16	-	-	ADJ
ejpam-5393	186	17	compact	compact	ADJ
ejpam-5393	186	18	σ1σ2	σ1σ2	NOUN
ejpam-5393	186	19	-	-	NOUN
ejpam-5393	186	20	closure	closure	NOUN
ejpam-5393	186	21	;	;	PUNCT
ejpam-5393	186	22	(	(	PUNCT
ejpam-5393	186	23	5	5	NUM
ejpam-5393	186	24	)	)	PUNCT
ejpam-5393	186	25	(	(	PUNCT
ejpam-5393	186	26	τ1	τ1	NOUN
ejpam-5393	186	27	,	,	PUNCT
ejpam-5393	186	28	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5393	186	29	−1(b	−1(b	ADJ
ejpam-5393	186	30	)	)	PUNCT
ejpam-5393	186	31	)	)	PUNCT
ejpam-5393	186	32	⊆	⊆	NUM
ejpam-5393	186	33	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5393	186	34	-	-	PUNCT
ejpam-5393	186	35	cl(b	cl(b	NOUN
ejpam-5393	186	36	)	)	PUNCT
ejpam-5393	186	37	)	)	PUNCT
ejpam-5393	186	38	for	for	ADP
ejpam-5393	186	39	every	every	DET
ejpam-5393	186	40	subset	subset	NOUN
ejpam-5393	186	41	b	b	PROPN
ejpam-5393	186	42	of	of	ADP
ejpam-5393	186	43	y	y	PROPN
ejpam-5393	186	44	having	have	VERB
ejpam-5393	186	45	the	the	DET
ejpam-5393	186	46	σ1σ2compact	σ1σ2compact	ADJ
ejpam-5393	186	47	σ1σ2	σ1σ2	NOUN
ejpam-5393	186	48	-	-	NOUN
ejpam-5393	186	49	closure	closure	NOUN
ejpam-5393	186	50	;	;	PUNCT
ejpam-5393	186	51	(	(	PUNCT
ejpam-5393	186	52	6	6	X
ejpam-5393	186	53	)	)	PUNCT
ejpam-5393	186	54	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5393	186	55	-	-	PUNCT
ejpam-5393	186	56	int(b	int(b	NOUN
ejpam-5393	186	57	)	)	PUNCT
ejpam-5393	186	58	)	)	PUNCT
ejpam-5393	186	59	⊆	⊆	NUM
ejpam-5393	186	60	(	(	PUNCT
ejpam-5393	186	61	τ1	τ1	NOUN
ejpam-5393	186	62	,	,	PUNCT
ejpam-5393	186	63	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5393	186	64	−1(b	−1(b	NOUN
ejpam-5393	186	65	)	)	PUNCT
ejpam-5393	186	66	)	)	PUNCT
ejpam-5393	186	67	for	for	ADP
ejpam-5393	186	68	every	every	DET
ejpam-5393	186	69	subset	subset	NOUN
ejpam-5393	186	70	b	b	PROPN
ejpam-5393	186	71	of	of	ADP
ejpam-5393	186	72	y	y	PRON
ejpam-5393	186	73	such	such	ADJ
ejpam-5393	186	74	that	that	SCONJ
ejpam-5393	186	75	y	y	PROPN
ejpam-5393	187	1	−	−	ADP
ejpam-5393	187	2	σ1σ2	σ1σ2	NUM
ejpam-5393	187	3	-	-	PUNCT
ejpam-5393	187	4	int(b	int(b	NOUN
ejpam-5393	187	5	)	)	PUNCT
ejpam-5393	187	6	is	be	AUX
ejpam-5393	187	7	σ1σ2	σ1σ2	NOUN
ejpam-5393	187	8	-	-	ADJ
ejpam-5393	187	9	compact	compact	ADJ
ejpam-5393	187	10	.	.	PUNCT
ejpam-5393	188	1	corollary	corollary	ADJ
ejpam-5393	188	2	3	3	NUM
ejpam-5393	188	3	.	.	PUNCT
ejpam-5393	189	1	a	a	DET
ejpam-5393	189	2	multifunction	multifunction	NOUN
ejpam-5393	189	3	f	f	NOUN
ejpam-5393	189	4	:	:	PUNCT
ejpam-5393	189	5	(	(	PUNCT
ejpam-5393	189	6	x	x	NOUN
ejpam-5393	189	7	,	,	PUNCT
ejpam-5393	189	8	τ1	τ1	NOUN
ejpam-5393	189	9	,	,	PUNCT
ejpam-5393	189	10	τ2	τ2	NOUN
ejpam-5393	189	11	)	)	PUNCT
ejpam-5393	189	12	→	→	SYM
ejpam-5393	189	13	(	(	PUNCT
ejpam-5393	189	14	y	y	PROPN
ejpam-5393	189	15	,	,	PUNCT
ejpam-5393	189	16	σ1	σ1	PROPN
ejpam-5393	189	17	,	,	PUNCT
ejpam-5393	189	18	σ2	σ2	PROPN
ejpam-5393	189	19	)	)	PUNCT
ejpam-5393	189	20	is	be	AUX
ejpam-5393	189	21	upper	upper	ADJ
ejpam-5393	189	22	c	c	NOUN
ejpam-5393	189	23	-	-	PUNCT
ejpam-5393	189	24	quasi	quasi	ADJ
ejpam-5393	189	25	(	(	PUNCT
ejpam-5393	189	26	τ1	τ1	NOUN
ejpam-5393	189	27	,	,	PUNCT
ejpam-5393	189	28	τ2)continuous	τ2)continuous	ADJ
ejpam-5393	189	29	if	if	SCONJ
ejpam-5393	189	30	f−(k	f−(k	PROPN
ejpam-5393	189	31	)	)	PUNCT
ejpam-5393	189	32	is	be	AUX
ejpam-5393	189	33	(	(	PUNCT
ejpam-5393	189	34	τ1	τ1	NOUN
ejpam-5393	189	35	,	,	PUNCT
ejpam-5393	189	36	τ2)s	τ2)s	NOUN
ejpam-5393	189	37	-	-	PUNCT
ejpam-5393	189	38	closed	close	VERB
ejpam-5393	189	39	in	in	ADP
ejpam-5393	189	40	x	x	PUNCT
ejpam-5393	189	41	for	for	ADP
ejpam-5393	189	42	every	every	DET
ejpam-5393	189	43	σ1σ2	σ1σ2	ADJ
ejpam-5393	189	44	-	-	ADJ
ejpam-5393	189	45	compact	compact	ADJ
ejpam-5393	189	46	set	set	NOUN
ejpam-5393	189	47	k	k	PROPN
ejpam-5393	189	48	of	of	ADP
ejpam-5393	189	49	y	y	PROPN
ejpam-5393	189	50	.	.	PUNCT
ejpam-5393	190	1	proof	proof	NOUN
ejpam-5393	190	2	.	.	PUNCT
ejpam-5393	191	1	let	let	VERB
ejpam-5393	191	2	v	v	PART
ejpam-5393	191	3	be	be	AUX
ejpam-5393	191	4	any	any	DET
ejpam-5393	191	5	σ1σ2	σ1σ2	NOUN
ejpam-5393	191	6	-	-	ADJ
ejpam-5393	191	7	open	open	ADJ
ejpam-5393	191	8	set	set	NOUN
ejpam-5393	191	9	of	of	ADP
ejpam-5393	191	10	y	y	PROPN
ejpam-5393	191	11	having	have	VERB
ejpam-5393	191	12	σ1σ2	σ1σ2	NOUN
ejpam-5393	191	13	-	-	ADJ
ejpam-5393	191	14	compact	compact	ADJ
ejpam-5393	191	15	complement	complement	NOUN
ejpam-5393	191	16	.	.	PUNCT
ejpam-5393	192	1	then	then	ADV
ejpam-5393	192	2	,	,	PUNCT
ejpam-5393	192	3	y	y	PROPN
ejpam-5393	192	4	−	−	PROPN
ejpam-5393	192	5	v	v	NOUN
ejpam-5393	192	6	is	be	AUX
ejpam-5393	192	7	a	a	DET
ejpam-5393	192	8	σ1σ2	σ1σ2	ADJ
ejpam-5393	192	9	-	-	ADJ
ejpam-5393	192	10	compact	compact	ADJ
ejpam-5393	192	11	σ1σ2	σ1σ2	VERB
ejpam-5393	192	12	-	-	PUNCT
ejpam-5393	192	13	closed	closed	ADJ
ejpam-5393	192	14	set	set	NOUN
ejpam-5393	192	15	.	.	PUNCT
ejpam-5393	193	1	by	by	ADP
ejpam-5393	193	2	the	the	DET
ejpam-5393	193	3	hypothesis	hypothesis	NOUN
ejpam-5393	193	4	,	,	PUNCT
ejpam-5393	193	5	f−(y	f−(y	NOUN
ejpam-5393	193	6	−	−	NOUN
ejpam-5393	193	7	v	v	NOUN
ejpam-5393	193	8	)	)	PUNCT
ejpam-5393	193	9	is	be	AUX
ejpam-5393	193	10	(	(	PUNCT
ejpam-5393	193	11	τ1	τ1	NOUN
ejpam-5393	193	12	,	,	PUNCT
ejpam-5393	193	13	τ2)sclosed	τ2)sclose	VERB
ejpam-5393	193	14	in	in	ADP
ejpam-5393	193	15	x.	x.	NOUN
ejpam-5393	193	16	thus	thus	ADV
ejpam-5393	193	17	,	,	PUNCT
ejpam-5393	193	18	f+(v	f+(v	PROPN
ejpam-5393	193	19	)	)	PUNCT
ejpam-5393	194	1	is	be	AUX
ejpam-5393	194	2	(	(	PUNCT
ejpam-5393	194	3	τ1	τ1	NOUN
ejpam-5393	194	4	,	,	PUNCT
ejpam-5393	194	5	τ2)s	τ2)s	NOUN
ejpam-5393	194	6	-	-	PUNCT
ejpam-5393	194	7	open	open	ADJ
ejpam-5393	194	8	in	in	ADP
ejpam-5393	194	9	x	x	X
ejpam-5393	194	10	and	and	CCONJ
ejpam-5393	194	11	by	by	ADP
ejpam-5393	194	12	theorem	theorem	NOUN
ejpam-5393	194	13	3	3	NUM
ejpam-5393	194	14	,	,	PUNCT
ejpam-5393	194	15	f	f	PROPN
ejpam-5393	194	16	is	be	AUX
ejpam-5393	194	17	upper	upper	ADJ
ejpam-5393	194	18	c	c	NOUN
ejpam-5393	194	19	-	-	PUNCT
ejpam-5393	194	20	quasi	quasi	ADJ
ejpam-5393	194	21	(	(	PUNCT
ejpam-5393	194	22	τ1	τ1	NOUN
ejpam-5393	194	23	,	,	PUNCT
ejpam-5393	194	24	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	194	25	.	.	PUNCT
ejpam-5393	195	1	corollary	corollary	ADJ
ejpam-5393	195	2	4	4	NUM
ejpam-5393	195	3	.	.	PUNCT
ejpam-5393	196	1	a	a	DET
ejpam-5393	196	2	multifunction	multifunction	NOUN
ejpam-5393	196	3	f	f	NOUN
ejpam-5393	196	4	:	:	PUNCT
ejpam-5393	196	5	(	(	PUNCT
ejpam-5393	196	6	x	x	NOUN
ejpam-5393	196	7	,	,	PUNCT
ejpam-5393	196	8	τ1	τ1	NOUN
ejpam-5393	196	9	,	,	PUNCT
ejpam-5393	196	10	τ2	τ2	NOUN
ejpam-5393	196	11	)	)	PUNCT
ejpam-5393	196	12	→	→	SYM
ejpam-5393	196	13	(	(	PUNCT
ejpam-5393	196	14	y	y	PROPN
ejpam-5393	196	15	,	,	PUNCT
ejpam-5393	196	16	σ1	σ1	PROPN
ejpam-5393	196	17	,	,	PUNCT
ejpam-5393	196	18	σ2	σ2	NOUN
ejpam-5393	196	19	)	)	PUNCT
ejpam-5393	196	20	is	be	AUX
ejpam-5393	196	21	lower	low	ADJ
ejpam-5393	196	22	c	c	NOUN
ejpam-5393	196	23	-	-	PUNCT
ejpam-5393	196	24	quasi	quasi	ADJ
ejpam-5393	196	25	(	(	PUNCT
ejpam-5393	196	26	τ1	τ1	NOUN
ejpam-5393	196	27	,	,	PUNCT
ejpam-5393	196	28	τ2)continuous	τ2)continuous	ADJ
ejpam-5393	196	29	if	if	SCONJ
ejpam-5393	196	30	f+(k	f+(k	NUM
ejpam-5393	196	31	)	)	PUNCT
ejpam-5393	196	32	is	be	AUX
ejpam-5393	196	33	(	(	PUNCT
ejpam-5393	196	34	τ1	τ1	NOUN
ejpam-5393	196	35	,	,	PUNCT
ejpam-5393	196	36	τ2)s	τ2)s	NOUN
ejpam-5393	196	37	-	-	PUNCT
ejpam-5393	196	38	closed	close	VERB
ejpam-5393	196	39	in	in	ADP
ejpam-5393	196	40	x	x	PUNCT
ejpam-5393	196	41	for	for	ADP
ejpam-5393	196	42	every	every	DET
ejpam-5393	196	43	σ1σ2	σ1σ2	ADJ
ejpam-5393	196	44	-	-	ADJ
ejpam-5393	196	45	compact	compact	ADJ
ejpam-5393	196	46	set	set	NOUN
ejpam-5393	196	47	k	k	PROPN
ejpam-5393	196	48	of	of	ADP
ejpam-5393	196	49	y	y	PROPN
ejpam-5393	196	50	.	.	PUNCT
ejpam-5393	197	1	proof	proof	NOUN
ejpam-5393	197	2	.	.	PUNCT
ejpam-5393	198	1	the	the	DET
ejpam-5393	198	2	proof	proof	NOUN
ejpam-5393	198	3	is	be	AUX
ejpam-5393	198	4	similar	similar	ADJ
ejpam-5393	198	5	to	to	ADP
ejpam-5393	198	6	that	that	PRON
ejpam-5393	198	7	of	of	ADP
ejpam-5393	198	8	corollary	corollary	ADJ
ejpam-5393	198	9	3	3	NUM
ejpam-5393	198	10	.	.	PUNCT
ejpam-5393	198	11	for	for	ADP
ejpam-5393	198	12	a	a	DET
ejpam-5393	198	13	multifunction	multifunction	NOUN
ejpam-5393	198	14	f	f	NOUN
ejpam-5393	198	15	:	:	PUNCT
ejpam-5393	198	16	(	(	PUNCT
ejpam-5393	198	17	x	x	NOUN
ejpam-5393	198	18	,	,	PUNCT
ejpam-5393	198	19	τ1	τ1	NOUN
ejpam-5393	198	20	,	,	PUNCT
ejpam-5393	198	21	τ2	τ2	NOUN
ejpam-5393	198	22	)	)	PUNCT
ejpam-5393	198	23	→	→	SYM
ejpam-5393	198	24	(	(	PUNCT
ejpam-5393	198	25	y	y	PROPN
ejpam-5393	198	26	,	,	PUNCT
ejpam-5393	198	27	σ1	σ1	PROPN
ejpam-5393	198	28	,	,	PUNCT
ejpam-5393	198	29	σ2	σ2	NOUN
ejpam-5393	198	30	)	)	PUNCT
ejpam-5393	198	31	,	,	PUNCT
ejpam-5393	198	32	by	by	ADP
ejpam-5393	198	33	clf⊛	clf⊛	PROPN
ejpam-5393	198	34	:	:	PUNCT
ejpam-5393	198	35	(	(	PUNCT
ejpam-5393	198	36	x	x	NOUN
ejpam-5393	198	37	,	,	PUNCT
ejpam-5393	198	38	τ1	τ1	NOUN
ejpam-5393	198	39	,	,	PUNCT
ejpam-5393	198	40	τ2	τ2	NOUN
ejpam-5393	198	41	)	)	PUNCT
ejpam-5393	198	42	→	→	SYM
ejpam-5393	198	43	(	(	PUNCT
ejpam-5393	198	44	y	y	PROPN
ejpam-5393	198	45	,	,	PUNCT
ejpam-5393	198	46	σ1	σ1	PROPN
ejpam-5393	198	47	,	,	PUNCT
ejpam-5393	198	48	σ2	σ2	NOUN
ejpam-5393	198	49	)	)	PUNCT
ejpam-5393	199	1	[	[	X
ejpam-5393	199	2	30	30	NUM
ejpam-5393	199	3	]	]	PUNCT
ejpam-5393	199	4	we	we	PRON
ejpam-5393	199	5	denote	denote	VERB
ejpam-5393	199	6	a	a	DET
ejpam-5393	199	7	multifunction	multifunction	NOUN
ejpam-5393	199	8	defined	define	VERB
ejpam-5393	199	9	as	as	SCONJ
ejpam-5393	199	10	follows	follow	VERB
ejpam-5393	199	11	:	:	PUNCT
ejpam-5393	199	12	clf⊛(x	clf⊛(x	PROPN
ejpam-5393	199	13	)	)	PUNCT
ejpam-5393	199	14	=	=	PUNCT
ejpam-5393	200	1	σ1σ2	σ1σ2	X
ejpam-5393	200	2	-	-	NUM
ejpam-5393	200	3	cl(f	cl(f	NOUN
ejpam-5393	200	4	(	(	PUNCT
ejpam-5393	200	5	x	x	NOUN
ejpam-5393	200	6	)	)	PUNCT
ejpam-5393	200	7	)	)	PUNCT
ejpam-5393	200	8	for	for	ADP
ejpam-5393	200	9	each	each	DET
ejpam-5393	200	10	x	x	SYM
ejpam-5393	200	11	∈	∈	PROPN
ejpam-5393	200	12	x.	x.	NOUN
ejpam-5393	200	13	definition	definition	NOUN
ejpam-5393	200	14	4	4	NUM
ejpam-5393	200	15	.	.	PUNCT
ejpam-5393	201	1	[	[	X
ejpam-5393	201	2	30	30	NUM
ejpam-5393	201	3	]	]	X
ejpam-5393	201	4	a	a	DET
ejpam-5393	201	5	subset	subset	NOUN
ejpam-5393	201	6	a	a	PRON
ejpam-5393	201	7	of	of	ADP
ejpam-5393	201	8	a	a	DET
ejpam-5393	201	9	bitopological	bitopological	ADJ
ejpam-5393	201	10	space	space	NOUN
ejpam-5393	201	11	(	(	PUNCT
ejpam-5393	201	12	x	x	NOUN
ejpam-5393	201	13	,	,	PUNCT
ejpam-5393	201	14	τ1	τ1	NOUN
ejpam-5393	201	15	,	,	PUNCT
ejpam-5393	201	16	τ2	τ2	NOUN
ejpam-5393	201	17	)	)	PUNCT
ejpam-5393	201	18	is	be	AUX
ejpam-5393	201	19	said	say	VERB
ejpam-5393	201	20	to	to	PART
ejpam-5393	201	21	be	be	AUX
ejpam-5393	201	22	:	:	PUNCT
ejpam-5393	201	23	(	(	PUNCT
ejpam-5393	201	24	1	1	X
ejpam-5393	201	25	)	)	PUNCT
ejpam-5393	201	26	τ1τ2	τ1τ2	NOUN
ejpam-5393	201	27	-	-	NOUN
ejpam-5393	201	28	paracompact	paracompact	ADJ
ejpam-5393	201	29	if	if	SCONJ
ejpam-5393	201	30	every	every	DET
ejpam-5393	201	31	cover	cover	NOUN
ejpam-5393	201	32	of	of	ADP
ejpam-5393	201	33	a	a	PRON
ejpam-5393	201	34	by	by	ADP
ejpam-5393	201	35	τ1τ2	τ1τ2	ADJ
ejpam-5393	201	36	-	-	ADJ
ejpam-5393	201	37	open	open	ADJ
ejpam-5393	201	38	sets	set	NOUN
ejpam-5393	201	39	of	of	ADP
ejpam-5393	201	40	x	x	VERB
ejpam-5393	201	41	is	be	AUX
ejpam-5393	201	42	refined	refine	VERB
ejpam-5393	201	43	by	by	ADP
ejpam-5393	201	44	a	a	DET
ejpam-5393	201	45	cover	cover	NOUN
ejpam-5393	201	46	of	of	ADP
ejpam-5393	201	47	a	a	PRON
ejpam-5393	201	48	which	which	PRON
ejpam-5393	201	49	consists	consist	VERB
ejpam-5393	201	50	of	of	ADP
ejpam-5393	201	51	τ1τ2	τ1τ2	ADJ
ejpam-5393	201	52	-	-	ADJ
ejpam-5393	201	53	open	open	ADJ
ejpam-5393	201	54	sets	set	NOUN
ejpam-5393	201	55	of	of	ADP
ejpam-5393	201	56	x	x	PUNCT
ejpam-5393	201	57	and	and	CCONJ
ejpam-5393	201	58	is	be	AUX
ejpam-5393	201	59	τ1τ2	τ1τ2	NOUN
ejpam-5393	201	60	-	-	ADJ
ejpam-5393	201	61	locally	locally	ADV
ejpam-5393	201	62	finite	finite	NOUN
ejpam-5393	201	63	in	in	ADP
ejpam-5393	201	64	x	x	PRON
ejpam-5393	201	65	;	;	PUNCT
ejpam-5393	201	66	(	(	PUNCT
ejpam-5393	201	67	2	2	X
ejpam-5393	201	68	)	)	PUNCT
ejpam-5393	201	69	τ1τ2	τ1τ2	NOUN
ejpam-5393	201	70	-	-	NOUN
ejpam-5393	201	71	regular	regular	ADJ
ejpam-5393	201	72	if	if	SCONJ
ejpam-5393	201	73	for	for	ADP
ejpam-5393	201	74	each	each	DET
ejpam-5393	201	75	x	x	SYM
ejpam-5393	201	76	∈	∈	PROPN
ejpam-5393	201	77	a	a	PRON
ejpam-5393	201	78	and	and	CCONJ
ejpam-5393	201	79	each	each	DET
ejpam-5393	201	80	τ1τ2	τ1τ2	ADJ
ejpam-5393	201	81	-	-	ADJ
ejpam-5393	201	82	open	open	ADJ
ejpam-5393	201	83	set	set	ADJ
ejpam-5393	201	84	u	u	NOUN
ejpam-5393	201	85	of	of	ADP
ejpam-5393	201	86	x	x	PUNCT
ejpam-5393	201	87	containing	contain	VERB
ejpam-5393	201	88	x	x	PRON
ejpam-5393	201	89	,	,	PUNCT
ejpam-5393	201	90	there	there	PRON
ejpam-5393	201	91	exists	exist	VERB
ejpam-5393	201	92	a	a	DET
ejpam-5393	201	93	τ1τ2	τ1τ2	NOUN
ejpam-5393	201	94	-	-	ADJ
ejpam-5393	201	95	open	open	ADJ
ejpam-5393	201	96	set	set	NOUN
ejpam-5393	201	97	v	v	NOUN
ejpam-5393	201	98	of	of	ADP
ejpam-5393	201	99	x	x	PUNCT
ejpam-5393	201	100	such	such	ADJ
ejpam-5393	201	101	that	that	SCONJ
ejpam-5393	201	102	x	x	SYM
ejpam-5393	201	103	∈	∈	NOUN
ejpam-5393	201	104	v	v	ADP
ejpam-5393	201	105	⊆	⊆	NUM
ejpam-5393	201	106	τ1τ2	τ1τ2	NOUN
ejpam-5393	201	107	-	-	NOUN
ejpam-5393	201	108	cl(v	cl(v	X
ejpam-5393	201	109	)	)	PUNCT
ejpam-5393	201	110	⊆	⊆	NUM
ejpam-5393	201	111	u	u	NOUN
ejpam-5393	201	112	.	.	PUNCT
ejpam-5393	202	1	references	reference	NOUN
ejpam-5393	202	2	3249	3249	NUM
ejpam-5393	202	3	lemma	lemma	PROPN
ejpam-5393	202	4	3	3	NUM
ejpam-5393	202	5	.	.	PUNCT
ejpam-5393	203	1	[	[	X
ejpam-5393	203	2	30	30	NUM
ejpam-5393	203	3	]	]	X
ejpam-5393	203	4	if	if	SCONJ
ejpam-5393	203	5	a	a	PRON
ejpam-5393	203	6	is	be	AUX
ejpam-5393	203	7	a	a	DET
ejpam-5393	203	8	τ1τ2	τ1τ2	ADJ
ejpam-5393	203	9	-	-	ADJ
ejpam-5393	203	10	regular	regular	ADJ
ejpam-5393	203	11	τ1τ2	τ1τ2	NOUN
ejpam-5393	203	12	-	-	ADJ
ejpam-5393	203	13	paracompact	paracompact	ADJ
ejpam-5393	203	14	set	set	NOUN
ejpam-5393	203	15	of	of	ADP
ejpam-5393	203	16	a	a	DET
ejpam-5393	203	17	bitopological	bitopological	ADJ
ejpam-5393	203	18	space	space	NOUN
ejpam-5393	203	19	(	(	PUNCT
ejpam-5393	203	20	x	x	NOUN
ejpam-5393	203	21	,	,	PUNCT
ejpam-5393	203	22	τ1	τ1	NOUN
ejpam-5393	203	23	,	,	PUNCT
ejpam-5393	203	24	τ2	τ2	NOUN
ejpam-5393	203	25	)	)	PUNCT
ejpam-5393	203	26	and	and	CCONJ
ejpam-5393	203	27	u	u	NOUN
ejpam-5393	203	28	is	be	AUX
ejpam-5393	203	29	a	a	DET
ejpam-5393	203	30	τ1τ2	τ1τ2	ADJ
ejpam-5393	203	31	-	-	ADJ
ejpam-5393	203	32	open	open	ADJ
ejpam-5393	203	33	neighbourhood	neighbourhood	NOUN
ejpam-5393	203	34	of	of	ADP
ejpam-5393	203	35	a	a	PRON
ejpam-5393	203	36	,	,	PUNCT
ejpam-5393	203	37	then	then	ADV
ejpam-5393	203	38	there	there	PRON
ejpam-5393	203	39	exists	exist	VERB
ejpam-5393	203	40	a	a	DET
ejpam-5393	203	41	τ1τ2	τ1τ2	NOUN
ejpam-5393	203	42	-	-	ADJ
ejpam-5393	203	43	open	open	ADJ
ejpam-5393	203	44	set	set	NOUN
ejpam-5393	203	45	v	v	NOUN
ejpam-5393	203	46	of	of	ADP
ejpam-5393	203	47	x	x	PUNCT
ejpam-5393	203	48	such	such	ADJ
ejpam-5393	203	49	that	that	SCONJ
ejpam-5393	203	50	a	a	DET
ejpam-5393	203	51	⊆	⊆	NUM
ejpam-5393	203	52	v	v	ADP
ejpam-5393	203	53	⊆	⊆	NUM
ejpam-5393	203	54	τ1τ2	τ1τ2	NOUN
ejpam-5393	203	55	-	-	NOUN
ejpam-5393	203	56	cl(v	cl(v	X
ejpam-5393	203	57	)	)	PUNCT
ejpam-5393	203	58	⊆	⊆	NUM
ejpam-5393	203	59	u	u	NOUN
ejpam-5393	203	60	.	.	PUNCT
ejpam-5393	204	1	lemma	lemma	PROPN
ejpam-5393	204	2	4	4	NUM
ejpam-5393	204	3	.	.	PUNCT
ejpam-5393	205	1	[	[	X
ejpam-5393	205	2	30	30	NUM
ejpam-5393	205	3	]	]	X
ejpam-5393	205	4	if	if	SCONJ
ejpam-5393	205	5	f	f	PROPN
ejpam-5393	205	6	:	:	PUNCT
ejpam-5393	205	7	(	(	PUNCT
ejpam-5393	205	8	x	x	NOUN
ejpam-5393	205	9	,	,	PUNCT
ejpam-5393	205	10	τ1	τ1	NOUN
ejpam-5393	205	11	,	,	PUNCT
ejpam-5393	205	12	τ2	τ2	NOUN
ejpam-5393	205	13	)	)	PUNCT
ejpam-5393	205	14	→	→	SYM
ejpam-5393	205	15	(	(	PUNCT
ejpam-5393	205	16	y	y	PROPN
ejpam-5393	205	17	,	,	PUNCT
ejpam-5393	205	18	σ1	σ1	PROPN
ejpam-5393	205	19	,	,	PUNCT
ejpam-5393	205	20	σ2	σ2	PROPN
ejpam-5393	205	21	)	)	PUNCT
ejpam-5393	205	22	is	be	AUX
ejpam-5393	205	23	a	a	DET
ejpam-5393	205	24	multifunction	multifunction	NOUN
ejpam-5393	205	25	such	such	ADJ
ejpam-5393	205	26	that	that	SCONJ
ejpam-5393	205	27	f	f	PROPN
ejpam-5393	205	28	(	(	PUNCT
ejpam-5393	205	29	x	x	X
ejpam-5393	205	30	)	)	PUNCT
ejpam-5393	205	31	is	be	AUX
ejpam-5393	205	32	τ1τ2regular	τ1τ2regular	NUM
ejpam-5393	205	33	and	and	CCONJ
ejpam-5393	205	34	τ1τ2	τ1τ2	NOUN
ejpam-5393	205	35	-	-	ADJ
ejpam-5393	205	36	paracompact	paracompact	ADJ
ejpam-5393	205	37	for	for	ADP
ejpam-5393	205	38	each	each	DET
ejpam-5393	205	39	x	x	SYM
ejpam-5393	205	40	∈	∈	PROPN
ejpam-5393	205	41	x	x	NOUN
ejpam-5393	205	42	,	,	PUNCT
ejpam-5393	205	43	then	then	ADV
ejpam-5393	205	44	clf+	clf+	PROPN
ejpam-5393	205	45	⊛	⊛	X
ejpam-5393	205	46	(	(	PUNCT
ejpam-5393	205	47	v	v	NOUN
ejpam-5393	205	48	)	)	PUNCT
ejpam-5393	205	49	=	=	PUNCT
ejpam-5393	205	50	f+(v	f+(v	NOUN
ejpam-5393	205	51	)	)	PUNCT
ejpam-5393	205	52	for	for	ADP
ejpam-5393	205	53	each	each	DET
ejpam-5393	205	54	σ1σ2	σ1σ2	VERB
ejpam-5393	205	55	-	-	ADJ
ejpam-5393	205	56	open	open	ADJ
ejpam-5393	205	57	set	set	NOUN
ejpam-5393	205	58	v	v	NOUN
ejpam-5393	205	59	of	of	ADP
ejpam-5393	205	60	y	y	PROPN
ejpam-5393	205	61	.	.	PUNCT
ejpam-5393	206	1	theorem	theorem	ADJ
ejpam-5393	206	2	5	5	NUM
ejpam-5393	206	3	.	.	PUNCT
ejpam-5393	207	1	let	let	VERB
ejpam-5393	207	2	f	f	NOUN
ejpam-5393	207	3	:	:	PUNCT
ejpam-5393	207	4	(	(	PUNCT
ejpam-5393	207	5	x	x	NOUN
ejpam-5393	207	6	,	,	PUNCT
ejpam-5393	207	7	τ1	τ1	NOUN
ejpam-5393	207	8	,	,	PUNCT
ejpam-5393	207	9	τ2	τ2	NOUN
ejpam-5393	207	10	)	)	PUNCT
ejpam-5393	207	11	→	→	SYM
ejpam-5393	207	12	(	(	PUNCT
ejpam-5393	207	13	y	y	PROPN
ejpam-5393	207	14	,	,	PUNCT
ejpam-5393	207	15	σ1	σ1	PROPN
ejpam-5393	207	16	,	,	PUNCT
ejpam-5393	207	17	σ2	σ2	PROPN
ejpam-5393	207	18	)	)	PUNCT
ejpam-5393	207	19	be	be	VERB
ejpam-5393	207	20	a	a	DET
ejpam-5393	207	21	multifunction	multifunction	NOUN
ejpam-5393	207	22	such	such	ADJ
ejpam-5393	207	23	that	that	SCONJ
ejpam-5393	207	24	f	f	PROPN
ejpam-5393	207	25	(	(	PUNCT
ejpam-5393	207	26	x	x	X
ejpam-5393	207	27	)	)	PUNCT
ejpam-5393	207	28	is	be	AUX
ejpam-5393	207	29	σ1σ2paracompact	σ1σ2paracompact	NUM
ejpam-5393	207	30	and	and	CCONJ
ejpam-5393	207	31	σ1σ2	σ1σ2	NOUN
ejpam-5393	207	32	-	-	ADJ
ejpam-5393	207	33	regular	regular	ADJ
ejpam-5393	207	34	for	for	ADP
ejpam-5393	207	35	each	each	DET
ejpam-5393	207	36	x	x	SYM
ejpam-5393	207	37	∈	∈	PROPN
ejpam-5393	207	38	x.	x.	NOUN
ejpam-5393	207	39	then	then	ADV
ejpam-5393	207	40	,	,	PUNCT
ejpam-5393	207	41	f	f	PROPN
ejpam-5393	207	42	is	be	AUX
ejpam-5393	207	43	upper	upper	ADJ
ejpam-5393	207	44	c	c	NOUN
ejpam-5393	207	45	-	-	PUNCT
ejpam-5393	207	46	quasi	quasi	ADJ
ejpam-5393	207	47	(	(	PUNCT
ejpam-5393	207	48	τ1	τ1	NOUN
ejpam-5393	207	49	,	,	PUNCT
ejpam-5393	207	50	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	207	51	if	if	SCONJ
ejpam-5393	207	52	and	and	CCONJ
ejpam-5393	207	53	only	only	ADV
ejpam-5393	207	54	if	if	SCONJ
ejpam-5393	207	55	clf⊛	clf⊛	PROPN
ejpam-5393	207	56	:	:	PUNCT
ejpam-5393	207	57	(	(	PUNCT
ejpam-5393	207	58	x	x	NOUN
ejpam-5393	207	59	,	,	PUNCT
ejpam-5393	207	60	τ1	τ1	NOUN
ejpam-5393	207	61	,	,	PUNCT
ejpam-5393	207	62	τ2	τ2	NOUN
ejpam-5393	207	63	)	)	PUNCT
ejpam-5393	207	64	→	→	SYM
ejpam-5393	207	65	(	(	PUNCT
ejpam-5393	207	66	y	y	PROPN
ejpam-5393	207	67	,	,	PUNCT
ejpam-5393	207	68	σ1	σ1	PROPN
ejpam-5393	207	69	,	,	PUNCT
ejpam-5393	207	70	σ2	σ2	PROPN
ejpam-5393	207	71	)	)	PUNCT
ejpam-5393	207	72	is	be	AUX
ejpam-5393	207	73	upper	upper	ADJ
ejpam-5393	207	74	c	c	NOUN
ejpam-5393	207	75	-	-	PUNCT
ejpam-5393	207	76	quasi	quasi	ADJ
ejpam-5393	207	77	(	(	PUNCT
ejpam-5393	207	78	τ1	τ1	NOUN
ejpam-5393	207	79	,	,	PUNCT
ejpam-5393	207	80	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	207	81	.	.	PUNCT
ejpam-5393	208	1	proof	proof	NOUN
ejpam-5393	208	2	.	.	PUNCT
ejpam-5393	209	1	we	we	PRON
ejpam-5393	209	2	put	put	VERB
ejpam-5393	209	3	g	g	NOUN
ejpam-5393	209	4	=	=	PUNCT
ejpam-5393	209	5	clf⊛.	clf⊛.	NOUN
ejpam-5393	209	6	suppose	suppose	VERB
ejpam-5393	209	7	that	that	SCONJ
ejpam-5393	209	8	f	f	PROPN
ejpam-5393	209	9	is	be	AUX
ejpam-5393	209	10	upper	upper	ADJ
ejpam-5393	209	11	c	c	NOUN
ejpam-5393	209	12	-	-	PUNCT
ejpam-5393	209	13	quasi	quasi	ADJ
ejpam-5393	209	14	(	(	PUNCT
ejpam-5393	209	15	τ1	τ1	NOUN
ejpam-5393	209	16	,	,	PUNCT
ejpam-5393	209	17	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	209	18	.	.	PUNCT
ejpam-5393	210	1	let	let	VERB
ejpam-5393	210	2	x	x	PUNCT
ejpam-5393	210	3	∈	∈	PROPN
ejpam-5393	210	4	x	x	X
ejpam-5393	210	5	and	and	CCONJ
ejpam-5393	210	6	v	v	X
ejpam-5393	210	7	be	be	AUX
ejpam-5393	210	8	any	any	DET
ejpam-5393	210	9	σ1σ2	σ1σ2	NOUN
ejpam-5393	210	10	-	-	ADJ
ejpam-5393	210	11	open	open	ADJ
ejpam-5393	210	12	set	set	NOUN
ejpam-5393	210	13	of	of	ADP
ejpam-5393	210	14	y	y	NOUN
ejpam-5393	210	15	containing	contain	VERB
ejpam-5393	210	16	g(x	g(x	NOUN
ejpam-5393	210	17	)	)	PUNCT
ejpam-5393	210	18	and	and	CCONJ
ejpam-5393	210	19	having	have	VERB
ejpam-5393	210	20	σ1σ2	σ1σ2	NOUN
ejpam-5393	210	21	-	-	PUNCT
ejpam-5393	210	22	connected	connect	VERB
ejpam-5393	210	23	complement	complement	NOUN
ejpam-5393	210	24	.	.	PUNCT
ejpam-5393	211	1	by	by	ADP
ejpam-5393	211	2	lemma	lemma	PROPN
ejpam-5393	211	3	4	4	NUM
ejpam-5393	211	4	,	,	PUNCT
ejpam-5393	211	5	we	we	PRON
ejpam-5393	211	6	have	have	VERB
ejpam-5393	211	7	x	x	X
ejpam-5393	211	8	∈	∈	PROPN
ejpam-5393	211	9	g+(v	g+(v	PROPN
ejpam-5393	211	10	)	)	PUNCT
ejpam-5393	211	11	=	=	PUNCT
ejpam-5393	212	1	f+(v	f+(v	NOUN
ejpam-5393	212	2	)	)	PUNCT
ejpam-5393	213	1	and	and	CCONJ
ejpam-5393	213	2	by	by	ADP
ejpam-5393	213	3	theorem	theorem	NOUN
ejpam-5393	213	4	1	1	NUM
ejpam-5393	213	5	,	,	PUNCT
ejpam-5393	213	6	there	there	PRON
ejpam-5393	213	7	exists	exist	VERB
ejpam-5393	213	8	a	a	DET
ejpam-5393	213	9	(	(	PUNCT
ejpam-5393	213	10	τ1	τ1	NOUN
ejpam-5393	213	11	,	,	PUNCT
ejpam-5393	213	12	τ2)s	τ2)s	NOUN
ejpam-5393	213	13	-	-	PUNCT
ejpam-5393	213	14	open	open	ADJ
ejpam-5393	213	15	set	set	NOUN
ejpam-5393	213	16	u	u	NOUN
ejpam-5393	213	17	of	of	ADP
ejpam-5393	213	18	x	x	PUNCT
ejpam-5393	213	19	containing	contain	VERB
ejpam-5393	213	20	x	x	PUNCT
ejpam-5393	213	21	such	such	ADJ
ejpam-5393	213	22	that	that	SCONJ
ejpam-5393	213	23	f	f	PROPN
ejpam-5393	213	24	(	(	PUNCT
ejpam-5393	213	25	u	u	NOUN
ejpam-5393	213	26	)	)	PUNCT
ejpam-5393	213	27	⊆	⊆	NUM
ejpam-5393	213	28	v	v	NOUN
ejpam-5393	213	29	.	.	PUNCT
ejpam-5393	214	1	since	since	SCONJ
ejpam-5393	214	2	f	f	PROPN
ejpam-5393	214	3	(	(	PUNCT
ejpam-5393	214	4	z	z	NOUN
ejpam-5393	214	5	)	)	PUNCT
ejpam-5393	214	6	is	be	AUX
ejpam-5393	214	7	σ1σ2paracompact	σ1σ2paracompact	NUM
ejpam-5393	214	8	and	and	CCONJ
ejpam-5393	214	9	σ1σ2	σ1σ2	NOUN
ejpam-5393	214	10	-	-	ADJ
ejpam-5393	214	11	regular	regular	ADJ
ejpam-5393	214	12	for	for	ADP
ejpam-5393	214	13	each	each	DET
ejpam-5393	214	14	z	z	NOUN
ejpam-5393	214	15	∈	∈	PROPN
ejpam-5393	214	16	u	u	NOUN
ejpam-5393	214	17	,	,	PUNCT
ejpam-5393	214	18	by	by	ADP
ejpam-5393	214	19	lemma	lemma	PROPN
ejpam-5393	214	20	3	3	NUM
ejpam-5393	214	21	there	there	ADV
ejpam-5393	214	22	exists	exist	VERB
ejpam-5393	214	23	a	a	DET
ejpam-5393	214	24	τ1τ2	τ1τ2	NOUN
ejpam-5393	214	25	-	-	ADJ
ejpam-5393	214	26	open	open	ADJ
ejpam-5393	214	27	set	set	NOUN
ejpam-5393	214	28	w	w	NOUN
ejpam-5393	214	29	of	of	ADP
ejpam-5393	214	30	x	x	SYM
ejpam-5393	214	31	such	such	ADJ
ejpam-5393	214	32	that	that	SCONJ
ejpam-5393	214	33	f	f	PROPN
ejpam-5393	214	34	(	(	PUNCT
ejpam-5393	214	35	z	z	NOUN
ejpam-5393	214	36	)	)	PUNCT
ejpam-5393	214	37	⊆	⊆	NUM
ejpam-5393	214	38	w	w	ADP
ejpam-5393	214	39	⊆	⊆	NUM
ejpam-5393	214	40	σ1σ2	σ1σ2	NOUN
ejpam-5393	214	41	-	-	PUNCT
ejpam-5393	214	42	cl(w	cl(w	NOUN
ejpam-5393	214	43	)	)	PUNCT
ejpam-5393	214	44	⊆	⊆	NUM
ejpam-5393	214	45	v	v	NOUN
ejpam-5393	214	46	;	;	PUNCT
ejpam-5393	214	47	hence	hence	ADV
ejpam-5393	214	48	g(z	g(z	ADJ
ejpam-5393	214	49	)	)	PUNCT
ejpam-5393	214	50	⊆	⊆	NUM
ejpam-5393	214	51	σ1σ2	σ1σ2	NOUN
ejpam-5393	214	52	-	-	PUNCT
ejpam-5393	214	53	cl(w	cl(w	NOUN
ejpam-5393	214	54	)	)	PUNCT
ejpam-5393	214	55	⊆	⊆	NUM
ejpam-5393	214	56	v	v	NOUN
ejpam-5393	214	57	for	for	ADP
ejpam-5393	214	58	each	each	DET
ejpam-5393	214	59	z	z	NOUN
ejpam-5393	214	60	∈	∈	PROPN
ejpam-5393	214	61	u	u	NOUN
ejpam-5393	214	62	.	.	PUNCT
ejpam-5393	215	1	thus	thus	ADV
ejpam-5393	215	2	,	,	PUNCT
ejpam-5393	215	3	g(u	g(u	PROPN
ejpam-5393	215	4	)	)	PUNCT
ejpam-5393	215	5	⊆	⊆	NUM
ejpam-5393	215	6	v	v	NOUN
ejpam-5393	215	7	and	and	CCONJ
ejpam-5393	215	8	hence	hence	ADV
ejpam-5393	215	9	g	g	PROPN
ejpam-5393	215	10	is	be	AUX
ejpam-5393	215	11	upper	upper	ADJ
ejpam-5393	215	12	c	c	NOUN
ejpam-5393	215	13	-	-	PUNCT
ejpam-5393	215	14	quasi	quasi	ADJ
ejpam-5393	215	15	(	(	PUNCT
ejpam-5393	215	16	τ1	τ1	NOUN
ejpam-5393	215	17	,	,	PUNCT
ejpam-5393	215	18	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	215	19	.	.	PUNCT
ejpam-5393	216	1	conversely	conversely	ADV
ejpam-5393	216	2	,	,	PUNCT
ejpam-5393	216	3	suppose	suppose	VERB
ejpam-5393	216	4	that	that	SCONJ
ejpam-5393	216	5	g	g	PROPN
ejpam-5393	216	6	is	be	AUX
ejpam-5393	216	7	upper	upper	ADJ
ejpam-5393	216	8	c	c	NOUN
ejpam-5393	216	9	-	-	PUNCT
ejpam-5393	216	10	quasi	quasi	ADJ
ejpam-5393	216	11	(	(	PUNCT
ejpam-5393	216	12	τ1	τ1	NOUN
ejpam-5393	216	13	,	,	PUNCT
ejpam-5393	216	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	216	15	.	.	PUNCT
ejpam-5393	217	1	let	let	VERB
ejpam-5393	217	2	x	x	PUNCT
ejpam-5393	217	3	∈	∈	PROPN
ejpam-5393	217	4	x	x	X
ejpam-5393	217	5	and	and	CCONJ
ejpam-5393	217	6	v	v	X
ejpam-5393	217	7	be	be	AUX
ejpam-5393	217	8	any	any	DET
ejpam-5393	217	9	σ1σ2	σ1σ2	NOUN
ejpam-5393	217	10	-	-	ADJ
ejpam-5393	217	11	open	open	ADJ
ejpam-5393	217	12	set	set	NOUN
ejpam-5393	217	13	of	of	ADP
ejpam-5393	217	14	y	y	PROPN
ejpam-5393	217	15	containing	contain	VERB
ejpam-5393	217	16	f	f	PROPN
ejpam-5393	217	17	(	(	PUNCT
ejpam-5393	217	18	x	x	NOUN
ejpam-5393	217	19	)	)	PUNCT
ejpam-5393	217	20	and	and	CCONJ
ejpam-5393	217	21	having	have	VERB
ejpam-5393	217	22	σ1σ2	σ1σ2	NOUN
ejpam-5393	217	23	-	-	PUNCT
ejpam-5393	217	24	connected	connect	VERB
ejpam-5393	217	25	complement	complement	NOUN
ejpam-5393	217	26	.	.	PUNCT
ejpam-5393	218	1	by	by	ADP
ejpam-5393	218	2	lemma	lemma	PROPN
ejpam-5393	218	3	4	4	NUM
ejpam-5393	218	4	,	,	PUNCT
ejpam-5393	218	5	we	we	PRON
ejpam-5393	218	6	have	have	VERB
ejpam-5393	218	7	x	x	X
ejpam-5393	218	8	∈	∈	NOUN
ejpam-5393	218	9	f+(v	f+(v	NOUN
ejpam-5393	218	10	)	)	PUNCT
ejpam-5393	219	1	=	=	PUNCT
ejpam-5393	219	2	g+(v	g+(v	PROPN
ejpam-5393	219	3	)	)	PUNCT
ejpam-5393	219	4	and	and	CCONJ
ejpam-5393	219	5	hence	hence	ADV
ejpam-5393	219	6	g(x	g(x	NOUN
ejpam-5393	219	7	)	)	PUNCT
ejpam-5393	219	8	⊆	⊆	NUM
ejpam-5393	219	9	v	v	NOUN
ejpam-5393	219	10	.	.	PUNCT
ejpam-5393	220	1	by	by	ADP
ejpam-5393	220	2	theorem	theorem	NOUN
ejpam-5393	220	3	1	1	NUM
ejpam-5393	220	4	,	,	PUNCT
ejpam-5393	220	5	there	there	PRON
ejpam-5393	220	6	exists	exist	VERB
ejpam-5393	220	7	a	a	DET
ejpam-5393	220	8	(	(	PUNCT
ejpam-5393	220	9	τ1	τ1	NOUN
ejpam-5393	220	10	,	,	PUNCT
ejpam-5393	220	11	τ2)s	τ2)s	NOUN
ejpam-5393	220	12	-	-	PUNCT
ejpam-5393	220	13	open	open	ADJ
ejpam-5393	220	14	set	set	NOUN
ejpam-5393	220	15	u	u	NOUN
ejpam-5393	220	16	of	of	ADP
ejpam-5393	220	17	x	x	PUNCT
ejpam-5393	220	18	containing	contain	VERB
ejpam-5393	220	19	x	x	PUNCT
ejpam-5393	220	20	such	such	ADJ
ejpam-5393	220	21	that	that	SCONJ
ejpam-5393	220	22	g(u	g(u	PROPN
ejpam-5393	220	23	)	)	PUNCT
ejpam-5393	220	24	⊆	⊆	NUM
ejpam-5393	220	25	v	v	NOUN
ejpam-5393	220	26	.	.	PUNCT
ejpam-5393	221	1	thus	thus	ADV
ejpam-5393	221	2	,	,	PUNCT
ejpam-5393	221	3	u	u	PROPN
ejpam-5393	221	4	⊆	⊆	NUM
ejpam-5393	221	5	g+(v	g+(v	PROPN
ejpam-5393	221	6	)	)	PUNCT
ejpam-5393	221	7	=	=	PUNCT
ejpam-5393	222	1	f+(v	f+(v	NOUN
ejpam-5393	222	2	)	)	PUNCT
ejpam-5393	223	1	and	and	CCONJ
ejpam-5393	223	2	so	so	ADV
ejpam-5393	223	3	f	f	PROPN
ejpam-5393	223	4	(	(	PUNCT
ejpam-5393	223	5	u	u	NOUN
ejpam-5393	223	6	)	)	PUNCT
ejpam-5393	223	7	⊆	⊆	NUM
ejpam-5393	223	8	v	v	NOUN
ejpam-5393	223	9	.	.	PUNCT
ejpam-5393	224	1	this	this	PRON
ejpam-5393	224	2	shows	show	VERB
ejpam-5393	224	3	that	that	SCONJ
ejpam-5393	224	4	f	f	PROPN
ejpam-5393	224	5	is	be	AUX
ejpam-5393	224	6	upper	upper	ADJ
ejpam-5393	224	7	c	c	NOUN
ejpam-5393	224	8	-	-	PUNCT
ejpam-5393	224	9	quasi	quasi	ADJ
ejpam-5393	224	10	(	(	PUNCT
ejpam-5393	224	11	τ1	τ1	NOUN
ejpam-5393	224	12	,	,	PUNCT
ejpam-5393	224	13	τ2)-continuous	τ2)-continuous	PROPN
ejpam-5393	224	14	.	.	PUNCT
ejpam-5393	225	1	lemma	lemma	PROPN
ejpam-5393	225	2	5	5	NUM
ejpam-5393	225	3	.	.	PUNCT
ejpam-5393	226	1	[	[	X
ejpam-5393	226	2	30	30	NUM
ejpam-5393	226	3	]	]	PUNCT
ejpam-5393	226	4	for	for	ADP
ejpam-5393	226	5	a	a	DET
ejpam-5393	226	6	multifunction	multifunction	NOUN
ejpam-5393	226	7	f	f	NOUN
ejpam-5393	226	8	:	:	PUNCT
ejpam-5393	226	9	(	(	PUNCT
ejpam-5393	226	10	x	x	NOUN
ejpam-5393	226	11	,	,	PUNCT
ejpam-5393	226	12	τ1	τ1	NOUN
ejpam-5393	226	13	,	,	PUNCT
ejpam-5393	226	14	τ2	τ2	NOUN
ejpam-5393	226	15	)	)	PUNCT
ejpam-5393	226	16	→	→	SYM
ejpam-5393	226	17	(	(	PUNCT
ejpam-5393	226	18	y	y	PROPN
ejpam-5393	226	19	,	,	PUNCT
ejpam-5393	226	20	σ1	σ1	PROPN
ejpam-5393	226	21	,	,	PUNCT
ejpam-5393	226	22	σ2	σ2	NOUN
ejpam-5393	226	23	)	)	PUNCT
ejpam-5393	226	24	,	,	PUNCT
ejpam-5393	226	25	clf	clf	PROPN
ejpam-5393	226	26	−	−	PROPN
ejpam-5393	226	27	⊛	⊛	NUM
ejpam-5393	226	28	(	(	PUNCT
ejpam-5393	226	29	v	v	NOUN
ejpam-5393	226	30	)	)	PUNCT
ejpam-5393	226	31	=	=	SYM
ejpam-5393	226	32	f−(v	f−(v	ADJ
ejpam-5393	226	33	)	)	PUNCT
ejpam-5393	226	34	for	for	ADP
ejpam-5393	226	35	each	each	DET
ejpam-5393	226	36	σ1σ2	σ1σ2	VERB
ejpam-5393	226	37	-	-	ADJ
ejpam-5393	226	38	open	open	ADJ
ejpam-5393	226	39	set	set	NOUN
ejpam-5393	226	40	v	v	NOUN
ejpam-5393	226	41	of	of	ADP
ejpam-5393	226	42	y	y	PROPN
ejpam-5393	226	43	.	.	PUNCT
ejpam-5393	227	1	theorem	theorem	VERB
ejpam-5393	227	2	6	6	NUM
ejpam-5393	227	3	.	.	PUNCT
ejpam-5393	228	1	a	a	DET
ejpam-5393	228	2	multifunction	multifunction	NOUN
ejpam-5393	228	3	f	f	NOUN
ejpam-5393	228	4	:	:	PUNCT
ejpam-5393	228	5	(	(	PUNCT
ejpam-5393	228	6	x	x	NOUN
ejpam-5393	228	7	,	,	PUNCT
ejpam-5393	228	8	τ1	τ1	NOUN
ejpam-5393	228	9	,	,	PUNCT
ejpam-5393	228	10	τ2	τ2	NOUN
ejpam-5393	228	11	)	)	PUNCT
ejpam-5393	228	12	→	→	SYM
ejpam-5393	228	13	(	(	PUNCT
ejpam-5393	228	14	y	y	PROPN
ejpam-5393	228	15	,	,	PUNCT
ejpam-5393	228	16	σ1	σ1	PROPN
ejpam-5393	228	17	,	,	PUNCT
ejpam-5393	228	18	σ2	σ2	NOUN
ejpam-5393	228	19	)	)	PUNCT
ejpam-5393	228	20	is	be	AUX
ejpam-5393	228	21	lower	low	ADJ
ejpam-5393	228	22	c	c	NOUN
ejpam-5393	228	23	-	-	PUNCT
ejpam-5393	228	24	quasi	quasi	ADJ
ejpam-5393	228	25	(	(	PUNCT
ejpam-5393	228	26	τ1	τ1	NOUN
ejpam-5393	228	27	,	,	PUNCT
ejpam-5393	228	28	τ2)continuous	τ2)continuous	ADJ
ejpam-5393	228	29	if	if	SCONJ
ejpam-5393	228	30	and	and	CCONJ
ejpam-5393	228	31	only	only	ADV
ejpam-5393	228	32	if	if	SCONJ
ejpam-5393	228	33	clf⊛	clf⊛	PROPN
ejpam-5393	228	34	:	:	PUNCT
ejpam-5393	228	35	(	(	PUNCT
ejpam-5393	228	36	x	x	NOUN
ejpam-5393	228	37	,	,	PUNCT
ejpam-5393	228	38	τ1	τ1	NOUN
ejpam-5393	228	39	,	,	PUNCT
ejpam-5393	228	40	τ2	τ2	NOUN
ejpam-5393	228	41	)	)	PUNCT
ejpam-5393	228	42	→	→	SYM
ejpam-5393	228	43	(	(	PUNCT
ejpam-5393	228	44	y	y	PROPN
ejpam-5393	228	45	,	,	PUNCT
ejpam-5393	228	46	σ1	σ1	PROPN
ejpam-5393	228	47	,	,	PUNCT
ejpam-5393	228	48	σ2	σ2	NOUN
ejpam-5393	228	49	)	)	PUNCT
ejpam-5393	228	50	is	be	AUX
ejpam-5393	228	51	lower	low	ADJ
ejpam-5393	228	52	c	c	NOUN
ejpam-5393	228	53	-	-	PUNCT
ejpam-5393	228	54	quasi	quasi	ADJ
ejpam-5393	228	55	(	(	PUNCT
ejpam-5393	228	56	τ1	τ1	NOUN
ejpam-5393	228	57	,	,	PUNCT
ejpam-5393	228	58	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	228	59	.	.	PUNCT
ejpam-5393	229	1	proof	proof	NOUN
ejpam-5393	229	2	.	.	PUNCT
ejpam-5393	230	1	by	by	ADP
ejpam-5393	230	2	using	use	VERB
ejpam-5393	230	3	lemma	lemma	PROPN
ejpam-5393	230	4	5	5	NUM
ejpam-5393	230	5	this	this	PRON
ejpam-5393	230	6	is	be	AUX
ejpam-5393	230	7	shown	show	VERB
ejpam-5393	230	8	similarly	similarly	ADV
ejpam-5393	230	9	as	as	ADP
ejpam-5393	230	10	in	in	ADP
ejpam-5393	230	11	theorem	theorem	NOUN
ejpam-5393	230	12	5	5	NUM
ejpam-5393	230	13	.	.	PUNCT
ejpam-5393	230	14	acknowledgements	acknowledgement	NOUN
ejpam-5393	230	15	this	this	DET
ejpam-5393	230	16	research	research	NOUN
ejpam-5393	230	17	project	project	NOUN
ejpam-5393	230	18	was	be	AUX
ejpam-5393	230	19	financially	financially	ADV
ejpam-5393	230	20	supported	support	VERB
ejpam-5393	230	21	by	by	ADP
ejpam-5393	230	22	mahasarakham	mahasarakham	PROPN
ejpam-5393	230	23	university	university	PROPN
ejpam-5393	230	24	.	.	PUNCT
ejpam-5393	231	1	references	reference	NOUN
ejpam-5393	231	2	[	[	X
ejpam-5393	231	3	1	1	NUM
ejpam-5393	231	4	]	]	PUNCT
ejpam-5393	231	5	c.	c.	PROPN
ejpam-5393	231	6	berge	berge	PROPN
ejpam-5393	231	7	.	.	PUNCT
ejpam-5393	232	1	espaces	espace	VERB
ejpam-5393	232	2	topologiques	topologique	NOUN
ejpam-5393	232	3	fonctions	fonction	NOUN
ejpam-5393	232	4	multivoques	multivoque	NOUN
ejpam-5393	232	5	.	.	PUNCT
ejpam-5393	233	1	dunod	dunod	PROPN
ejpam-5393	233	2	,	,	PUNCT
ejpam-5393	233	3	paris	paris	PROPN
ejpam-5393	233	4	,	,	PUNCT
ejpam-5393	233	5	1959	1959	NUM
ejpam-5393	233	6	.	.	PUNCT
ejpam-5393	234	1	[	[	X
ejpam-5393	234	2	2	2	NUM
ejpam-5393	234	3	]	]	PUNCT
ejpam-5393	234	4	c.	c.	PROPN
ejpam-5393	234	5	boonpok	boonpok	PROPN
ejpam-5393	234	6	.	.	PUNCT
ejpam-5393	235	1	almost	almost	ADV
ejpam-5393	235	2	(	(	PUNCT
ejpam-5393	235	3	g	g	NOUN
ejpam-5393	235	4	,	,	PUNCT
ejpam-5393	235	5	m)-continuous	m)-continuous	ADJ
ejpam-5393	235	6	functions	function	NOUN
ejpam-5393	235	7	.	.	PUNCT
ejpam-5393	236	1	international	international	ADJ
ejpam-5393	236	2	journal	journal	PROPN
ejpam-5393	236	3	of	of	ADP
ejpam-5393	236	4	mathematical	mathematical	ADJ
ejpam-5393	236	5	analysis	analysis	NOUN
ejpam-5393	236	6	,	,	PUNCT
ejpam-5393	236	7	4(40):1957–1964	4(40):1957–1964	NUM
ejpam-5393	236	8	,	,	PUNCT
ejpam-5393	236	9	2010	2010	NUM
ejpam-5393	236	10	.	.	PUNCT
ejpam-5393	237	1	[	[	X
ejpam-5393	237	2	3	3	X
ejpam-5393	237	3	]	]	PUNCT
ejpam-5393	237	4	c.	c.	PROPN
ejpam-5393	237	5	boonpok	boonpok	PROPN
ejpam-5393	237	6	.	.	PUNCT
ejpam-5393	238	1	m	m	VERB
ejpam-5393	238	2	-continuous	-continuous	ADJ
ejpam-5393	238	3	functions	function	NOUN
ejpam-5393	238	4	in	in	ADP
ejpam-5393	238	5	biminimal	biminimal	NOUN
ejpam-5393	238	6	structure	structure	NOUN
ejpam-5393	238	7	spaces	space	NOUN
ejpam-5393	238	8	.	.	PUNCT
ejpam-5393	239	1	far	far	PROPN
ejpam-5393	239	2	east	east	PROPN
ejpam-5393	239	3	journal	journal	PROPN
ejpam-5393	239	4	of	of	ADP
ejpam-5393	239	5	mathematical	mathematical	ADJ
ejpam-5393	239	6	sciences	science	NOUN
ejpam-5393	239	7	,	,	PUNCT
ejpam-5393	239	8	43(1):41–58	43(1):41–58	NUM
ejpam-5393	239	9	,	,	PUNCT
ejpam-5393	239	10	2010	2010	NUM
ejpam-5393	239	11	.	.	PUNCT
ejpam-5393	240	1	references	reference	NOUN
ejpam-5393	240	2	3250	3250	NUM
ejpam-5393	241	1	[	[	X
ejpam-5393	241	2	4	4	NUM
ejpam-5393	241	3	]	]	PUNCT
ejpam-5393	241	4	c.	c.	PROPN
ejpam-5393	241	5	boonpok	boonpok	PROPN
ejpam-5393	241	6	.	.	PUNCT
ejpam-5393	242	1	on	on	ADP
ejpam-5393	242	2	continuous	continuous	ADJ
ejpam-5393	242	3	multifunctions	multifunction	NOUN
ejpam-5393	242	4	in	in	ADP
ejpam-5393	242	5	ideal	ideal	ADJ
ejpam-5393	242	6	topological	topological	ADJ
ejpam-5393	242	7	spaces	space	NOUN
ejpam-5393	242	8	.	.	PUNCT
ejpam-5393	243	1	lobachevskii	lobachevskii	PROPN
ejpam-5393	243	2	journal	journal	PROPN
ejpam-5393	243	3	of	of	ADP
ejpam-5393	243	4	mathematics	mathematic	NOUN
ejpam-5393	243	5	,	,	PUNCT
ejpam-5393	243	6	40(1):24–35	40(1):24–35	NUM
ejpam-5393	243	7	,	,	PUNCT
ejpam-5393	243	8	2019	2019	NUM
ejpam-5393	243	9	.	.	PUNCT
ejpam-5393	244	1	[	[	X
ejpam-5393	244	2	5	5	X
ejpam-5393	244	3	]	]	PUNCT
ejpam-5393	244	4	c.	c.	PROPN
ejpam-5393	244	5	boonpok	boonpok	PROPN
ejpam-5393	244	6	.	.	PUNCT
ejpam-5393	245	1	on	on	ADP
ejpam-5393	245	2	characterizations	characterization	NOUN
ejpam-5393	245	3	of	of	ADP
ejpam-5393	245	4	⋆-hyperconnected	⋆-hyperconnecte	VERB
ejpam-5393	245	5	ideal	ideal	ADJ
ejpam-5393	245	6	topological	topological	ADJ
ejpam-5393	245	7	spaces	space	NOUN
ejpam-5393	245	8	.	.	PUNCT
ejpam-5393	246	1	journal	journal	NOUN
ejpam-5393	246	2	of	of	ADP
ejpam-5393	246	3	mathematics	mathematic	NOUN
ejpam-5393	246	4	,	,	PUNCT
ejpam-5393	246	5	2020:9387601	2020:9387601	NUM
ejpam-5393	246	6	,	,	PUNCT
ejpam-5393	246	7	2020	2020	NUM
ejpam-5393	246	8	.	.	PUNCT
ejpam-5393	247	1	[	[	X
ejpam-5393	247	2	6	6	NUM
ejpam-5393	247	3	]	]	PUNCT
ejpam-5393	247	4	c.	c.	PROPN
ejpam-5393	247	5	boonpok	boonpok	PROPN
ejpam-5393	247	6	.	.	PUNCT
ejpam-5393	248	1	(	(	PUNCT
ejpam-5393	248	2	τ1	τ1	NOUN
ejpam-5393	248	3	,	,	PUNCT
ejpam-5393	248	4	τ2)δ	τ2)δ	ADJ
ejpam-5393	248	5	-	-	PUNCT
ejpam-5393	248	6	semicontinuous	semicontinuous	ADJ
ejpam-5393	248	7	multifunctions	multifunction	NOUN
ejpam-5393	248	8	.	.	PUNCT
ejpam-5393	249	1	heliyon	heliyon	NOUN
ejpam-5393	249	2	,	,	PUNCT
ejpam-5393	249	3	6	6	NUM
ejpam-5393	249	4	:	:	SYM
ejpam-5393	249	5	e05367	e05367	PROPN
ejpam-5393	249	6	,	,	PUNCT
ejpam-5393	249	7	2020	2020	NUM
ejpam-5393	249	8	.	.	PUNCT
ejpam-5393	250	1	[	[	X
ejpam-5393	250	2	7	7	X
ejpam-5393	250	3	]	]	X
ejpam-5393	250	4	c.	c.	PROPN
ejpam-5393	250	5	boonpok	boonpok	PROPN
ejpam-5393	250	6	.	.	PUNCT
ejpam-5393	251	1	weak	weak	ADJ
ejpam-5393	251	2	quasi	quasi	ADJ
ejpam-5393	251	3	continuity	continuity	NOUN
ejpam-5393	251	4	for	for	ADP
ejpam-5393	251	5	multifunctions	multifunction	NOUN
ejpam-5393	251	6	in	in	ADP
ejpam-5393	251	7	ideal	ideal	ADJ
ejpam-5393	251	8	topological	topological	ADJ
ejpam-5393	251	9	spaces	space	NOUN
ejpam-5393	251	10	.	.	PUNCT
ejpam-5393	252	1	advances	advance	NOUN
ejpam-5393	252	2	in	in	ADP
ejpam-5393	252	3	mathematics	mathematic	NOUN
ejpam-5393	252	4	:	:	PUNCT
ejpam-5393	252	5	scientific	scientific	ADJ
ejpam-5393	252	6	journal	journal	NOUN
ejpam-5393	252	7	,	,	PUNCT
ejpam-5393	252	8	9(1):339–355	9(1):339–355	NUM
ejpam-5393	252	9	,	,	PUNCT
ejpam-5393	252	10	2020	2020	NUM
ejpam-5393	252	11	.	.	PUNCT
ejpam-5393	253	1	[	[	X
ejpam-5393	253	2	8	8	NUM
ejpam-5393	253	3	]	]	X
ejpam-5393	253	4	c.	c.	PROPN
ejpam-5393	253	5	boonpok	boonpok	PROPN
ejpam-5393	253	6	.	.	PUNCT
ejpam-5393	254	1	upper	upper	ADJ
ejpam-5393	254	2	and	and	CCONJ
ejpam-5393	254	3	lower	low	ADJ
ejpam-5393	254	4	β(⋆)-continuity	β(⋆)-continuity	NOUN
ejpam-5393	254	5	.	.	PUNCT
ejpam-5393	254	6	heliyon	heliyon	NOUN
ejpam-5393	254	7	,	,	PUNCT
ejpam-5393	254	8	7	7	NUM
ejpam-5393	254	9	:	:	PUNCT
ejpam-5393	254	10	e05986	e05986	PROPN
ejpam-5393	254	11	,	,	PUNCT
ejpam-5393	254	12	2021	2021	NUM
ejpam-5393	254	13	.	.	PUNCT
ejpam-5393	255	1	[	[	X
ejpam-5393	255	2	9	9	NUM
ejpam-5393	255	3	]	]	PUNCT
ejpam-5393	255	4	c.	c.	PROPN
ejpam-5393	255	5	boonpok	boonpok	PROPN
ejpam-5393	255	6	.	.	PUNCT
ejpam-5393	256	1	on	on	ADP
ejpam-5393	256	2	some	some	DET
ejpam-5393	256	3	closed	closed	ADJ
ejpam-5393	256	4	sets	set	NOUN
ejpam-5393	256	5	and	and	CCONJ
ejpam-5393	256	6	low	low	ADJ
ejpam-5393	256	7	separation	separation	NOUN
ejpam-5393	256	8	axioms	axiom	NOUN
ejpam-5393	256	9	via	via	ADP
ejpam-5393	256	10	topological	topological	ADJ
ejpam-5393	256	11	ideals	ideal	NOUN
ejpam-5393	256	12	.	.	PUNCT
ejpam-5393	257	1	european	european	ADJ
ejpam-5393	257	2	journal	journal	PROPN
ejpam-5393	257	3	of	of	ADP
ejpam-5393	257	4	pure	pure	ADJ
ejpam-5393	257	5	and	and	CCONJ
ejpam-5393	257	6	applied	applied	ADJ
ejpam-5393	257	7	mathematics	mathematic	NOUN
ejpam-5393	257	8	,	,	PUNCT
ejpam-5393	257	9	15(3):1023–1046	15(3):1023–1046	NUM
ejpam-5393	257	10	,	,	PUNCT
ejpam-5393	257	11	2022	2022	NUM
ejpam-5393	257	12	.	.	PUNCT
ejpam-5393	258	1	[	[	X
ejpam-5393	258	2	10	10	NUM
ejpam-5393	258	3	]	]	X
ejpam-5393	258	4	c.	c.	PROPN
ejpam-5393	258	5	boonpok	boonpok	PROPN
ejpam-5393	258	6	.	.	PUNCT
ejpam-5393	259	1	θ(⋆)-quasi	θ(⋆)-quasi	DET
ejpam-5393	259	2	continuity	continuity	NOUN
ejpam-5393	259	3	for	for	ADP
ejpam-5393	259	4	multifunctions	multifunction	NOUN
ejpam-5393	259	5	.	.	PUNCT
ejpam-5393	260	1	wseas	wseas	PROPN
ejpam-5393	260	2	transactions	transaction	NOUN
ejpam-5393	260	3	on	on	ADP
ejpam-5393	260	4	mathematics	mathematic	NOUN
ejpam-5393	260	5	,	,	PUNCT
ejpam-5393	260	6	21:245–251	21:245–251	NUM
ejpam-5393	260	7	,	,	PUNCT
ejpam-5393	260	8	2022	2022	NUM
ejpam-5393	260	9	.	.	PUNCT
ejpam-5393	261	1	[	[	X
ejpam-5393	261	2	11	11	NUM
ejpam-5393	261	3	]	]	PUNCT
ejpam-5393	261	4	c.	c.	PROPN
ejpam-5393	261	5	boonpok	boonpok	PROPN
ejpam-5393	261	6	.	.	PUNCT
ejpam-5393	262	1	on	on	ADP
ejpam-5393	262	2	some	some	DET
ejpam-5393	262	3	spaces	space	NOUN
ejpam-5393	262	4	via	via	ADP
ejpam-5393	262	5	topological	topological	ADJ
ejpam-5393	262	6	ideals	ideal	NOUN
ejpam-5393	262	7	.	.	PUNCT
ejpam-5393	263	1	open	open	ADJ
ejpam-5393	263	2	mathematics	mathematic	NOUN
ejpam-5393	263	3	,	,	PUNCT
ejpam-5393	263	4	21:20230118	21:20230118	NUM
ejpam-5393	263	5	,	,	PUNCT
ejpam-5393	263	6	2023	2023	NUM
ejpam-5393	263	7	.	.	PUNCT
ejpam-5393	264	1	[	[	X
ejpam-5393	264	2	12	12	NUM
ejpam-5393	264	3	]	]	PUNCT
ejpam-5393	264	4	c.	c.	PROPN
ejpam-5393	264	5	boonpok	boonpok	PROPN
ejpam-5393	264	6	.	.	PUNCT
ejpam-5393	265	1	θ(⋆)-precontinuity	θ(⋆)-precontinuity	NOUN
ejpam-5393	265	2	.	.	PUNCT
ejpam-5393	266	1	mathematica	mathematica	PROPN
ejpam-5393	266	2	,	,	PUNCT
ejpam-5393	266	3	65(1):31–42	65(1):31–42	NUM
ejpam-5393	266	4	,	,	PUNCT
ejpam-5393	266	5	2023	2023	NUM
ejpam-5393	266	6	.	.	PUNCT
ejpam-5393	267	1	[	[	X
ejpam-5393	267	2	13	13	NUM
ejpam-5393	267	3	]	]	PUNCT
ejpam-5393	267	4	c.	c.	PROPN
ejpam-5393	267	5	boonpok	boonpok	PROPN
ejpam-5393	267	6	and	and	CCONJ
ejpam-5393	267	7	j.	j.	PROPN
ejpam-5393	267	8	khampakdee	khampakdee	PROPN
ejpam-5393	267	9	.	.	PUNCT
ejpam-5393	268	1	(	(	PUNCT
ejpam-5393	268	2	λ	λ	NOUN
ejpam-5393	268	3	,	,	PUNCT
ejpam-5393	268	4	sp)-open	sp)-open	ADJ
ejpam-5393	268	5	sets	set	NOUN
ejpam-5393	268	6	in	in	ADP
ejpam-5393	268	7	topological	topological	ADJ
ejpam-5393	268	8	spaces	space	NOUN
ejpam-5393	268	9	.	.	PUNCT
ejpam-5393	269	1	european	european	ADJ
ejpam-5393	269	2	journal	journal	PROPN
ejpam-5393	269	3	of	of	ADP
ejpam-5393	269	4	pure	pure	ADJ
ejpam-5393	269	5	and	and	CCONJ
ejpam-5393	269	6	applied	applied	ADJ
ejpam-5393	269	7	mathematics	mathematic	NOUN
ejpam-5393	269	8	,	,	PUNCT
ejpam-5393	269	9	15(2):572–588	15(2):572–588	NUM
ejpam-5393	269	10	,	,	PUNCT
ejpam-5393	269	11	2022	2022	NUM
ejpam-5393	269	12	.	.	PUNCT
ejpam-5393	270	1	[	[	X
ejpam-5393	270	2	14	14	NUM
ejpam-5393	270	3	]	]	X
ejpam-5393	270	4	c.	c.	PROPN
ejpam-5393	270	5	boonpok	boonpok	PROPN
ejpam-5393	270	6	and	and	CCONJ
ejpam-5393	270	7	j.	j.	PROPN
ejpam-5393	270	8	khampakdee	khampakdee	PROPN
ejpam-5393	270	9	.	.	PUNCT
ejpam-5393	271	1	on	on	ADP
ejpam-5393	271	2	almost	almost	ADV
ejpam-5393	271	3	α(λ	α(λ	PROPN
ejpam-5393	271	4	,	,	PUNCT
ejpam-5393	271	5	sp)-continuous	sp)-continuous	ADJ
ejpam-5393	271	6	multifunctions	multifunction	NOUN
ejpam-5393	271	7	.	.	PUNCT
ejpam-5393	272	1	european	european	PROPN
ejpam-5393	272	2	journal	journal	PROPN
ejpam-5393	272	3	of	of	ADP
ejpam-5393	272	4	pure	pure	ADJ
ejpam-5393	272	5	and	and	CCONJ
ejpam-5393	272	6	applied	applied	ADJ
ejpam-5393	272	7	mathematics	mathematic	NOUN
ejpam-5393	272	8	,	,	PUNCT
ejpam-5393	272	9	15(2):626–634	15(2):626–634	PROPN
ejpam-5393	272	10	,	,	PUNCT
ejpam-5393	272	11	2022	2022	NUM
ejpam-5393	272	12	.	.	PUNCT
ejpam-5393	273	1	[	[	X
ejpam-5393	273	2	15	15	NUM
ejpam-5393	273	3	]	]	X
ejpam-5393	273	4	c.	c.	PROPN
ejpam-5393	273	5	boonpok	boonpok	PROPN
ejpam-5393	273	6	and	and	CCONJ
ejpam-5393	273	7	j.	j.	PROPN
ejpam-5393	273	8	khampakdee	khampakdee	PROPN
ejpam-5393	273	9	.	.	PUNCT
ejpam-5393	274	1	slight	slight	PROPN
ejpam-5393	274	2	(	(	PUNCT
ejpam-5393	274	3	λ	λ	NOUN
ejpam-5393	274	4	,	,	PUNCT
ejpam-5393	274	5	sp)-continuity	sp)-continuity	NOUN
ejpam-5393	274	6	and	and	CCONJ
ejpam-5393	274	7	λsp	λsp	NOUN
ejpam-5393	274	8	-	-	PUNCT
ejpam-5393	274	9	extremally	extremally	ADV
ejpam-5393	274	10	disconnectedness	disconnectedness	NOUN
ejpam-5393	274	11	.	.	PUNCT
ejpam-5393	275	1	european	european	ADJ
ejpam-5393	275	2	journal	journal	PROPN
ejpam-5393	275	3	of	of	ADP
ejpam-5393	275	4	pure	pure	ADJ
ejpam-5393	275	5	and	and	CCONJ
ejpam-5393	275	6	applied	applied	ADJ
ejpam-5393	275	7	mathematics	mathematic	NOUN
ejpam-5393	275	8	,	,	PUNCT
ejpam-5393	275	9	15(3):1180–1188	15(3):1180–1188	NUM
ejpam-5393	275	10	,	,	PUNCT
ejpam-5393	275	11	2022	2022	NUM
ejpam-5393	275	12	.	.	PUNCT
ejpam-5393	276	1	[	[	X
ejpam-5393	276	2	16	16	NUM
ejpam-5393	276	3	]	]	X
ejpam-5393	276	4	c.	c.	PROPN
ejpam-5393	276	5	boonpok	boonpok	PROPN
ejpam-5393	276	6	and	and	CCONJ
ejpam-5393	276	7	j.	j.	PROPN
ejpam-5393	276	8	khampakdee	khampakdee	PROPN
ejpam-5393	276	9	.	.	PUNCT
ejpam-5393	277	1	upper	upper	ADJ
ejpam-5393	277	2	and	and	CCONJ
ejpam-5393	277	3	lower	low	ADJ
ejpam-5393	277	4	weak	weak	ADJ
ejpam-5393	277	5	sβ(⋆)-continuity	sβ(⋆)-continuity	NOUN
ejpam-5393	277	6	.	.	PUNCT
ejpam-5393	278	1	european	european	PROPN
ejpam-5393	278	2	journal	journal	PROPN
ejpam-5393	278	3	of	of	ADP
ejpam-5393	278	4	pure	pure	ADJ
ejpam-5393	278	5	and	and	CCONJ
ejpam-5393	278	6	applied	applied	ADJ
ejpam-5393	278	7	mathematics	mathematic	NOUN
ejpam-5393	278	8	,	,	PUNCT
ejpam-5393	278	9	16(4):2544–2556	16(4):2544–2556	NUM
ejpam-5393	278	10	,	,	PUNCT
ejpam-5393	278	11	2023	2023	NUM
ejpam-5393	278	12	.	.	PUNCT
ejpam-5393	279	1	[	[	X
ejpam-5393	279	2	17	17	NUM
ejpam-5393	279	3	]	]	X
ejpam-5393	279	4	c.	c.	PROPN
ejpam-5393	279	5	boonpok	boonpok	PROPN
ejpam-5393	279	6	and	and	CCONJ
ejpam-5393	279	7	j.	j.	PROPN
ejpam-5393	279	8	khampakdee	khampakdee	PROPN
ejpam-5393	279	9	.	.	PUNCT
ejpam-5393	280	1	almost	almost	ADV
ejpam-5393	280	2	strong	strong	ADJ
ejpam-5393	280	3	θ(λ	θ(λ	PROPN
ejpam-5393	280	4	,	,	PUNCT
ejpam-5393	280	5	p)-continuity	p)-continuity	NOUN
ejpam-5393	280	6	for	for	ADP
ejpam-5393	280	7	functions	function	NOUN
ejpam-5393	280	8	.	.	PUNCT
ejpam-5393	281	1	european	european	ADJ
ejpam-5393	281	2	journal	journal	PROPN
ejpam-5393	281	3	of	of	ADP
ejpam-5393	281	4	pure	pure	ADJ
ejpam-5393	281	5	and	and	CCONJ
ejpam-5393	281	6	applied	applied	ADJ
ejpam-5393	281	7	mathematics	mathematic	NOUN
ejpam-5393	281	8	,	,	PUNCT
ejpam-5393	281	9	17(1):300–309	17(1):300–309	PROPN
ejpam-5393	281	10	,	,	PUNCT
ejpam-5393	281	11	2024	2024	NUM
ejpam-5393	281	12	.	.	PUNCT
ejpam-5393	282	1	[	[	X
ejpam-5393	282	2	18	18	NUM
ejpam-5393	282	3	]	]	PUNCT
ejpam-5393	282	4	c.	c.	PROPN
ejpam-5393	282	5	boonpok	boonpok	PROPN
ejpam-5393	282	6	and	and	CCONJ
ejpam-5393	282	7	j.	j.	PROPN
ejpam-5393	282	8	khampakdee	khampakdee	PROPN
ejpam-5393	282	9	.	.	PUNCT
ejpam-5393	283	1	upper	upper	ADJ
ejpam-5393	283	2	and	and	CCONJ
ejpam-5393	283	3	lower	low	ADJ
ejpam-5393	283	4	α-⋆-continuity	α-⋆-continuity	NUM
ejpam-5393	283	5	.	.	PUNCT
ejpam-5393	283	6	european	european	PROPN
ejpam-5393	283	7	journal	journal	PROPN
ejpam-5393	283	8	of	of	ADP
ejpam-5393	283	9	pure	pure	ADJ
ejpam-5393	283	10	and	and	CCONJ
ejpam-5393	283	11	applied	applied	ADJ
ejpam-5393	283	12	mathematics	mathematic	NOUN
ejpam-5393	283	13	,	,	PUNCT
ejpam-5393	283	14	17(1):201–211	17(1):201–211	NUM
ejpam-5393	283	15	,	,	PUNCT
ejpam-5393	283	16	2024	2024	NUM
ejpam-5393	283	17	.	.	PUNCT
ejpam-5393	284	1	[	[	X
ejpam-5393	284	2	19	19	NUM
ejpam-5393	284	3	]	]	X
ejpam-5393	284	4	c.	c.	PROPN
ejpam-5393	284	5	boonpok	boonpok	PROPN
ejpam-5393	284	6	and	and	CCONJ
ejpam-5393	284	7	c.	c.	PROPN
ejpam-5393	284	8	klanarong	klanarong	PROPN
ejpam-5393	284	9	.	.	PUNCT
ejpam-5393	285	1	on	on	ADP
ejpam-5393	285	2	weakly	weakly	ADJ
ejpam-5393	285	3	(	(	PUNCT
ejpam-5393	285	4	τ1	τ1	NOUN
ejpam-5393	285	5	,	,	PUNCT
ejpam-5393	285	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	285	7	functions	function	NOUN
ejpam-5393	285	8	.	.	PUNCT
ejpam-5393	286	1	european	european	ADJ
ejpam-5393	286	2	journal	journal	PROPN
ejpam-5393	286	3	of	of	ADP
ejpam-5393	286	4	pure	pure	ADJ
ejpam-5393	286	5	and	and	CCONJ
ejpam-5393	286	6	applied	applied	ADJ
ejpam-5393	286	7	mathematics	mathematic	NOUN
ejpam-5393	286	8	,	,	PUNCT
ejpam-5393	286	9	17(1):416–425	17(1):416–425	NUM
ejpam-5393	286	10	,	,	PUNCT
ejpam-5393	286	11	2024	2024	NUM
ejpam-5393	286	12	.	.	PUNCT
ejpam-5393	287	1	[	[	X
ejpam-5393	287	2	20	20	NUM
ejpam-5393	287	3	]	]	PUNCT
ejpam-5393	287	4	c.	c.	PROPN
ejpam-5393	287	5	boonpok	boonpok	PROPN
ejpam-5393	287	6	and	and	CCONJ
ejpam-5393	287	7	p.	p.	NOUN
ejpam-5393	287	8	pue	pue	NOUN
ejpam-5393	287	9	-	-	PUNCT
ejpam-5393	287	10	on	on	ADP
ejpam-5393	287	11	.	.	PUNCT
ejpam-5393	288	1	continuity	continuity	NOUN
ejpam-5393	288	2	for	for	ADP
ejpam-5393	288	3	multifunctions	multifunction	NOUN
ejpam-5393	288	4	in	in	ADP
ejpam-5393	288	5	ideal	ideal	ADJ
ejpam-5393	288	6	topological	topological	ADJ
ejpam-5393	288	7	spaces	space	NOUN
ejpam-5393	288	8	.	.	PUNCT
ejpam-5393	289	1	wseas	wseas	VERB
ejpam-5393	289	2	transactions	transaction	NOUN
ejpam-5393	289	3	on	on	ADP
ejpam-5393	289	4	mathematics	mathematic	NOUN
ejpam-5393	289	5	,	,	PUNCT
ejpam-5393	289	6	19:624–631	19:624–631	NUM
ejpam-5393	289	7	,	,	PUNCT
ejpam-5393	289	8	2020	2020	NUM
ejpam-5393	289	9	.	.	PUNCT
ejpam-5393	290	1	references	reference	NOUN
ejpam-5393	290	2	3251	3251	NUM
ejpam-5393	290	3	[	[	X
ejpam-5393	290	4	21	21	NUM
ejpam-5393	290	5	]	]	X
ejpam-5393	290	6	c.	c.	PROPN
ejpam-5393	290	7	boonpok	boonpok	PROPN
ejpam-5393	290	8	and	and	CCONJ
ejpam-5393	290	9	p.	p.	NOUN
ejpam-5393	290	10	pue	pue	NOUN
ejpam-5393	290	11	-	-	PUNCT
ejpam-5393	290	12	on	on	ADP
ejpam-5393	290	13	.	.	PUNCT
ejpam-5393	291	1	upper	upper	ADJ
ejpam-5393	291	2	and	and	CCONJ
ejpam-5393	291	3	lower	low	ADJ
ejpam-5393	291	4	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-5393	291	5	multifunctions	multifunction	NOUN
ejpam-5393	291	6	.	.	PUNCT
ejpam-5393	292	1	european	european	ADJ
ejpam-5393	292	2	journal	journal	PROPN
ejpam-5393	292	3	of	of	ADP
ejpam-5393	292	4	pure	pure	ADJ
ejpam-5393	292	5	and	and	CCONJ
ejpam-5393	292	6	applied	applied	ADJ
ejpam-5393	292	7	mathematics	mathematic	NOUN
ejpam-5393	292	8	,	,	PUNCT
ejpam-5393	292	9	16(3):1634–1646	16(3):1634–1646	NUM
ejpam-5393	292	10	,	,	PUNCT
ejpam-5393	292	11	2023	2023	NUM
ejpam-5393	292	12	.	.	PUNCT
ejpam-5393	293	1	[	[	X
ejpam-5393	293	2	22	22	NUM
ejpam-5393	293	3	]	]	PUNCT
ejpam-5393	293	4	c.	c.	PROPN
ejpam-5393	293	5	boonpok	boonpok	PROPN
ejpam-5393	293	6	and	and	CCONJ
ejpam-5393	293	7	p.	p.	NOUN
ejpam-5393	293	8	pue	pue	NOUN
ejpam-5393	293	9	-	-	PUNCT
ejpam-5393	293	10	on	on	ADP
ejpam-5393	293	11	.	.	PUNCT
ejpam-5393	294	1	upper	upper	ADJ
ejpam-5393	294	2	and	and	CCONJ
ejpam-5393	294	3	lower	low	ADJ
ejpam-5393	294	4	weakly	weakly	ADJ
ejpam-5393	294	5	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5393	294	6	multifunctions	multifunction	NOUN
ejpam-5393	294	7	.	.	PUNCT
ejpam-5393	295	1	international	international	ADJ
ejpam-5393	295	2	journal	journal	NOUN
ejpam-5393	295	3	of	of	ADP
ejpam-5393	295	4	analysis	analysis	NOUN
ejpam-5393	295	5	and	and	CCONJ
ejpam-5393	295	6	applications	application	NOUN
ejpam-5393	295	7	,	,	PUNCT
ejpam-5393	295	8	21:90	21:90	NUM
ejpam-5393	295	9	,	,	PUNCT
ejpam-5393	295	10	2023	2023	NUM
ejpam-5393	295	11	.	.	PUNCT
ejpam-5393	296	1	[	[	X
ejpam-5393	296	2	23	23	NUM
ejpam-5393	296	3	]	]	X
ejpam-5393	296	4	c.	c.	PROPN
ejpam-5393	296	5	boonpok	boonpok	PROPN
ejpam-5393	296	6	and	and	CCONJ
ejpam-5393	296	7	p.	p.	NOUN
ejpam-5393	296	8	pue	pue	NOUN
ejpam-5393	296	9	-	-	PUNCT
ejpam-5393	296	10	on	on	ADP
ejpam-5393	296	11	.	.	PUNCT
ejpam-5393	297	1	upper	upper	ADJ
ejpam-5393	297	2	and	and	CCONJ
ejpam-5393	297	3	lower	low	ADJ
ejpam-5393	297	4	weakly	weakly	ADJ
ejpam-5393	297	5	(	(	PUNCT
ejpam-5393	297	6	λ	λ	NOUN
ejpam-5393	297	7	,	,	PUNCT
ejpam-5393	297	8	sp)-continuous	sp)-continuous	ADJ
ejpam-5393	297	9	multifunctions	multifunction	NOUN
ejpam-5393	297	10	.	.	PUNCT
ejpam-5393	298	1	european	european	PROPN
ejpam-5393	298	2	journal	journal	PROPN
ejpam-5393	298	3	of	of	ADP
ejpam-5393	298	4	pure	pure	ADJ
ejpam-5393	298	5	and	and	CCONJ
ejpam-5393	298	6	applied	applied	ADJ
ejpam-5393	298	7	mathematics	mathematic	NOUN
ejpam-5393	298	8	,	,	PUNCT
ejpam-5393	298	9	16(2):1047–1058	16(2):1047–1058	NUM
ejpam-5393	298	10	,	,	PUNCT
ejpam-5393	298	11	2023	2023	NUM
ejpam-5393	298	12	.	.	PUNCT
ejpam-5393	299	1	[	[	X
ejpam-5393	299	2	24	24	NUM
ejpam-5393	299	3	]	]	PUNCT
ejpam-5393	299	4	c.	c.	PROPN
ejpam-5393	299	5	boonpok	boonpok	PROPN
ejpam-5393	299	6	and	and	CCONJ
ejpam-5393	299	7	p.	p.	NOUN
ejpam-5393	299	8	pue	pue	NOUN
ejpam-5393	299	9	-	-	PUNCT
ejpam-5393	299	10	on	on	ADP
ejpam-5393	299	11	.	.	PUNCT
ejpam-5393	300	1	characterizations	characterization	NOUN
ejpam-5393	300	2	of	of	ADP
ejpam-5393	300	3	almost	almost	ADV
ejpam-5393	300	4	(	(	PUNCT
ejpam-5393	300	5	τ1	τ1	NOUN
ejpam-5393	300	6	,	,	PUNCT
ejpam-5393	300	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	300	8	functions	function	NOUN
ejpam-5393	300	9	.	.	PUNCT
ejpam-5393	301	1	international	international	ADJ
ejpam-5393	301	2	journal	journal	NOUN
ejpam-5393	301	3	of	of	ADP
ejpam-5393	301	4	analysis	analysis	NOUN
ejpam-5393	301	5	and	and	CCONJ
ejpam-5393	301	6	applications	application	NOUN
ejpam-5393	301	7	,	,	PUNCT
ejpam-5393	301	8	22:33	22:33	NUM
ejpam-5393	301	9	,	,	PUNCT
ejpam-5393	301	10	2024	2024	NUM
ejpam-5393	301	11	.	.	PUNCT
ejpam-5393	302	1	[	[	X
ejpam-5393	302	2	25	25	NUM
ejpam-5393	302	3	]	]	PUNCT
ejpam-5393	302	4	c.	c.	PROPN
ejpam-5393	302	5	boonpok	boonpok	PROPN
ejpam-5393	302	6	and	and	CCONJ
ejpam-5393	302	7	n.	n.	PROPN
ejpam-5393	302	8	srisarakham	srisarakham	PROPN
ejpam-5393	302	9	.	.	PUNCT
ejpam-5393	303	1	almost	almost	ADV
ejpam-5393	303	2	α-⋆-continuity	α-⋆-continuity	NUM
ejpam-5393	303	3	for	for	ADP
ejpam-5393	303	4	multifunctions	multifunction	NOUN
ejpam-5393	303	5	.	.	PUNCT
ejpam-5393	304	1	international	international	ADJ
ejpam-5393	304	2	journal	journal	NOUN
ejpam-5393	304	3	of	of	ADP
ejpam-5393	304	4	analysis	analysis	NOUN
ejpam-5393	304	5	and	and	CCONJ
ejpam-5393	304	6	applications	application	NOUN
ejpam-5393	304	7	,	,	PUNCT
ejpam-5393	304	8	21:107	21:107	NUM
ejpam-5393	304	9	,	,	PUNCT
ejpam-5393	304	10	2023	2023	NUM
ejpam-5393	304	11	.	.	PUNCT
ejpam-5393	305	1	[	[	X
ejpam-5393	305	2	26	26	NUM
ejpam-5393	305	3	]	]	X
ejpam-5393	305	4	c.	c.	PROPN
ejpam-5393	305	5	boonpok	boonpok	PROPN
ejpam-5393	305	6	and	and	CCONJ
ejpam-5393	305	7	n.	n.	PROPN
ejpam-5393	305	8	srisarakham	srisarakham	PROPN
ejpam-5393	305	9	.	.	PUNCT
ejpam-5393	306	1	weak	weak	ADJ
ejpam-5393	306	2	forms	form	NOUN
ejpam-5393	306	3	of	of	ADP
ejpam-5393	306	4	(	(	PUNCT
ejpam-5393	306	5	λ	λ	PROPN
ejpam-5393	306	6	,	,	PUNCT
ejpam-5393	306	7	b)-open	b)-open	VERB
ejpam-5393	306	8	sets	set	NOUN
ejpam-5393	306	9	and	and	CCONJ
ejpam-5393	306	10	weak	weak	ADJ
ejpam-5393	306	11	(	(	PUNCT
ejpam-5393	306	12	λ	λ	NOUN
ejpam-5393	306	13	,	,	PUNCT
ejpam-5393	306	14	b)continuity	b)continuity	NOUN
ejpam-5393	306	15	.	.	PUNCT
ejpam-5393	307	1	european	european	PROPN
ejpam-5393	307	2	journal	journal	PROPN
ejpam-5393	307	3	of	of	ADP
ejpam-5393	307	4	pure	pure	ADJ
ejpam-5393	307	5	and	and	CCONJ
ejpam-5393	307	6	applied	applied	ADJ
ejpam-5393	307	7	mathematics	mathematic	NOUN
ejpam-5393	307	8	,	,	PUNCT
ejpam-5393	307	9	16(1):29–43	16(1):29–43	NUM
ejpam-5393	307	10	,	,	PUNCT
ejpam-5393	307	11	2023	2023	NUM
ejpam-5393	307	12	.	.	PUNCT
ejpam-5393	308	1	[	[	X
ejpam-5393	308	2	27	27	NUM
ejpam-5393	308	3	]	]	X
ejpam-5393	308	4	c.	c.	PROPN
ejpam-5393	308	5	boonpok	boonpok	PROPN
ejpam-5393	308	6	and	and	CCONJ
ejpam-5393	308	7	n.	n.	PROPN
ejpam-5393	308	8	srisarakham	srisarakham	PROPN
ejpam-5393	308	9	.	.	PUNCT
ejpam-5393	309	1	(	(	PUNCT
ejpam-5393	309	2	τ1	τ1	NOUN
ejpam-5393	309	3	,	,	PUNCT
ejpam-5393	309	4	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5393	309	5	for	for	ADP
ejpam-5393	309	6	functions	function	NOUN
ejpam-5393	309	7	.	.	PUNCT
ejpam-5393	310	1	asia	asia	PROPN
ejpam-5393	310	2	pacific	pacific	PROPN
ejpam-5393	310	3	journal	journal	PROPN
ejpam-5393	310	4	of	of	ADP
ejpam-5393	310	5	mathematics	mathematic	NOUN
ejpam-5393	310	6	,	,	PUNCT
ejpam-5393	310	7	11:21	11:21	NUM
ejpam-5393	310	8	,	,	PUNCT
ejpam-5393	310	9	2024	2024	NUM
ejpam-5393	310	10	.	.	PUNCT
ejpam-5393	311	1	[	[	X
ejpam-5393	311	2	28	28	NUM
ejpam-5393	311	3	]	]	X
ejpam-5393	311	4	c.	c.	PROPN
ejpam-5393	311	5	boonpok	boonpok	PROPN
ejpam-5393	311	6	and	and	CCONJ
ejpam-5393	311	7	m.	m.	NOUN
ejpam-5393	311	8	thongmoon	thongmoon	NOUN
ejpam-5393	311	9	.	.	PUNCT
ejpam-5393	312	1	weak	weak	ADJ
ejpam-5393	312	2	α(λ	α(λ	PROPN
ejpam-5393	312	3	,	,	PUNCT
ejpam-5393	312	4	sp)-continuity	sp)-continuity	NOUN
ejpam-5393	312	5	for	for	ADP
ejpam-5393	312	6	multifunctions	multifunction	NOUN
ejpam-5393	312	7	.	.	PUNCT
ejpam-5393	313	1	european	european	ADJ
ejpam-5393	313	2	journal	journal	PROPN
ejpam-5393	313	3	of	of	ADP
ejpam-5393	313	4	pure	pure	ADJ
ejpam-5393	313	5	and	and	CCONJ
ejpam-5393	313	6	applied	applied	ADJ
ejpam-5393	313	7	mathematics	mathematic	NOUN
ejpam-5393	313	8	,	,	PUNCT
ejpam-5393	313	9	16(1):465–478	16(1):465–478	NUM
ejpam-5393	313	10	,	,	PUNCT
ejpam-5393	313	11	2023	2023	NUM
ejpam-5393	313	12	.	.	PUNCT
ejpam-5393	314	1	[	[	X
ejpam-5393	314	2	29	29	NUM
ejpam-5393	314	3	]	]	X
ejpam-5393	314	4	c.	c.	PROPN
ejpam-5393	314	5	boonpok	boonpok	PROPN
ejpam-5393	314	6	and	and	CCONJ
ejpam-5393	314	7	c.	c.	PROPN
ejpam-5393	314	8	viriyapong	viriyapong	PROPN
ejpam-5393	314	9	.	.	PUNCT
ejpam-5393	315	1	upper	upper	ADJ
ejpam-5393	315	2	and	and	CCONJ
ejpam-5393	315	3	lower	low	ADJ
ejpam-5393	315	4	almost	almost	ADV
ejpam-5393	315	5	weak	weak	ADJ
ejpam-5393	315	6	(	(	PUNCT
ejpam-5393	315	7	τ1	τ1	NOUN
ejpam-5393	315	8	,	,	PUNCT
ejpam-5393	315	9	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5393	315	10	.	.	PUNCT
ejpam-5393	316	1	european	european	PROPN
ejpam-5393	316	2	journal	journal	PROPN
ejpam-5393	316	3	of	of	ADP
ejpam-5393	316	4	pure	pure	ADJ
ejpam-5393	316	5	and	and	CCONJ
ejpam-5393	316	6	applied	applied	ADJ
ejpam-5393	316	7	mathematics	mathematic	NOUN
ejpam-5393	316	8	,	,	PUNCT
ejpam-5393	316	9	14(4):1212–1225	14(4):1212–1225	NUM
ejpam-5393	316	10	,	,	PUNCT
ejpam-5393	316	11	2021	2021	NUM
ejpam-5393	316	12	.	.	PUNCT
ejpam-5393	317	1	[	[	X
ejpam-5393	317	2	30	30	NUM
ejpam-5393	317	3	]	]	X
ejpam-5393	317	4	c.	c.	PROPN
ejpam-5393	317	5	boonpok	boonpok	PROPN
ejpam-5393	317	6	,	,	PUNCT
ejpam-5393	317	7	c.	c.	PROPN
ejpam-5393	317	8	viriyapong	viriyapong	PROPN
ejpam-5393	317	9	,	,	PUNCT
ejpam-5393	317	10	and	and	CCONJ
ejpam-5393	317	11	m.	m.	NOUN
ejpam-5393	317	12	thongmoon	thongmoon	NOUN
ejpam-5393	317	13	.	.	PUNCT
ejpam-5393	318	1	on	on	ADP
ejpam-5393	318	2	upper	upper	ADJ
ejpam-5393	318	3	and	and	CCONJ
ejpam-5393	318	4	lower	low	ADJ
ejpam-5393	318	5	(	(	PUNCT
ejpam-5393	318	6	τ1	τ1	NOUN
ejpam-5393	318	7	,	,	PUNCT
ejpam-5393	318	8	τ2)precontinuous	τ2)precontinuous	ADJ
ejpam-5393	318	9	multifunctions	multifunction	NOUN
ejpam-5393	318	10	.	.	PUNCT
ejpam-5393	319	1	journal	journal	PROPN
ejpam-5393	319	2	of	of	ADP
ejpam-5393	319	3	mathematics	mathematics	PROPN
ejpam-5393	319	4	and	and	CCONJ
ejpam-5393	319	5	computer	computer	NOUN
ejpam-5393	319	6	science	science	NOUN
ejpam-5393	319	7	,	,	PUNCT
ejpam-5393	319	8	18:282–293	18:282–293	NUM
ejpam-5393	319	9	,	,	PUNCT
ejpam-5393	319	10	2018	2018	NUM
ejpam-5393	319	11	.	.	PUNCT
ejpam-5393	320	1	[	[	X
ejpam-5393	320	2	31	31	NUM
ejpam-5393	320	3	]	]	PUNCT
ejpam-5393	320	4	m.	m.	NOUN
ejpam-5393	320	5	chiangpradit	chiangpradit	NOUN
ejpam-5393	320	6	,	,	PUNCT
ejpam-5393	320	7	s.	s.	PROPN
ejpam-5393	320	8	sompong	sompong	PROPN
ejpam-5393	320	9	,	,	PUNCT
ejpam-5393	320	10	and	and	CCONJ
ejpam-5393	320	11	c.	c.	PROPN
ejpam-5393	320	12	boonpok	boonpok	PROPN
ejpam-5393	320	13	.	.	PUNCT
ejpam-5393	321	1	weakly	weakly	ADJ
ejpam-5393	321	2	quasi	quasi	NOUN
ejpam-5393	321	3	(	(	PUNCT
ejpam-5393	321	4	τ1	τ1	PROPN
ejpam-5393	321	5	,	,	PUNCT
ejpam-5393	321	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	321	7	functions	function	NOUN
ejpam-5393	321	8	.	.	PUNCT
ejpam-5393	322	1	international	international	ADJ
ejpam-5393	322	2	journal	journal	NOUN
ejpam-5393	322	3	of	of	ADP
ejpam-5393	322	4	analysis	analysis	NOUN
ejpam-5393	322	5	and	and	CCONJ
ejpam-5393	322	6	applications	application	NOUN
ejpam-5393	322	7	,	,	PUNCT
ejpam-5393	322	8	22:125	22:125	NUM
ejpam-5393	322	9	,	,	PUNCT
ejpam-5393	322	10	2024	2024	NUM
ejpam-5393	322	11	.	.	PUNCT
ejpam-5393	323	1	[	[	X
ejpam-5393	323	2	32	32	NUM
ejpam-5393	323	3	]	]	PUNCT
ejpam-5393	323	4	t.	t.	PROPN
ejpam-5393	323	5	duangphui	duangphui	PROPN
ejpam-5393	323	6	,	,	PUNCT
ejpam-5393	323	7	c.	c.	PROPN
ejpam-5393	323	8	boonpok	boonpok	PROPN
ejpam-5393	323	9	,	,	PUNCT
ejpam-5393	323	10	and	and	CCONJ
ejpam-5393	323	11	c.	c.	PROPN
ejpam-5393	323	12	viriyapong	viriyapong	PROPN
ejpam-5393	323	13	.	.	PUNCT
ejpam-5393	324	1	continuous	continuous	ADJ
ejpam-5393	324	2	functions	function	NOUN
ejpam-5393	324	3	on	on	ADP
ejpam-5393	324	4	bigeneralized	bigeneralize	VERB
ejpam-5393	324	5	topological	topological	ADJ
ejpam-5393	324	6	spaces	space	NOUN
ejpam-5393	324	7	.	.	PUNCT
ejpam-5393	325	1	international	international	ADJ
ejpam-5393	325	2	journal	journal	PROPN
ejpam-5393	325	3	of	of	ADP
ejpam-5393	325	4	mathematical	mathematical	ADJ
ejpam-5393	325	5	analysis	analysis	NOUN
ejpam-5393	325	6	,	,	PUNCT
ejpam-5393	325	7	5(24):1165	5(24):1165	NUM
ejpam-5393	325	8	–	–	PUNCT
ejpam-5393	325	9	1174	1174	NUM
ejpam-5393	325	10	,	,	PUNCT
ejpam-5393	325	11	2011	2011	NUM
ejpam-5393	325	12	.	.	PUNCT
ejpam-5393	326	1	[	[	X
ejpam-5393	326	2	33	33	NUM
ejpam-5393	326	3	]	]	PUNCT
ejpam-5393	326	4	t.	t.	NOUN
ejpam-5393	326	5	dungthaisong	dungthaisong	PROPN
ejpam-5393	326	6	,	,	PUNCT
ejpam-5393	326	7	c.	c.	PROPN
ejpam-5393	326	8	boonpok	boonpok	PROPN
ejpam-5393	326	9	,	,	PUNCT
ejpam-5393	326	10	and	and	CCONJ
ejpam-5393	326	11	c.	c.	PROPN
ejpam-5393	326	12	viriyapong	viriyapong	PROPN
ejpam-5393	326	13	.	.	PUNCT
ejpam-5393	327	1	generalized	generalize	VERB
ejpam-5393	327	2	closed	close	VERB
ejpam-5393	327	3	sets	set	NOUN
ejpam-5393	327	4	in	in	ADP
ejpam-5393	327	5	bigeneralized	bigeneralize	VERB
ejpam-5393	327	6	topological	topological	ADJ
ejpam-5393	327	7	spaces	space	NOUN
ejpam-5393	327	8	.	.	PUNCT
ejpam-5393	328	1	international	international	ADJ
ejpam-5393	328	2	journal	journal	PROPN
ejpam-5393	328	3	of	of	ADP
ejpam-5393	328	4	mathematical	mathematical	ADJ
ejpam-5393	328	5	analysis	analysis	NOUN
ejpam-5393	328	6	,	,	PUNCT
ejpam-5393	328	7	5(24):1175–1184	5(24):1175–1184	NUM
ejpam-5393	328	8	,	,	PUNCT
ejpam-5393	328	9	2011	2011	NUM
ejpam-5393	328	10	.	.	PUNCT
ejpam-5393	329	1	[	[	X
ejpam-5393	329	2	34	34	NUM
ejpam-5393	329	3	]	]	PUNCT
ejpam-5393	329	4	k.	k.	PROPN
ejpam-5393	329	5	r.	r.	PROPN
ejpam-5393	329	6	gentry	gentry	PROPN
ejpam-5393	329	7	and	and	CCONJ
ejpam-5393	329	8	h.	h.	PROPN
ejpam-5393	329	9	b.	b.	PROPN
ejpam-5393	329	10	hoyle	hoyle	PROPN
ejpam-5393	329	11	iii	iii	PROPN
ejpam-5393	329	12	.	.	PUNCT
ejpam-5393	330	1	c	c	X
ejpam-5393	330	2	-	-	PUNCT
ejpam-5393	330	3	continuous	continuous	ADJ
ejpam-5393	330	4	functions	function	NOUN
ejpam-5393	330	5	.	.	PUNCT
ejpam-5393	331	1	yokohama	yokohama	PROPN
ejpam-5393	331	2	mathematical	mathematical	PROPN
ejpam-5393	331	3	journal	journal	PROPN
ejpam-5393	331	4	,	,	PUNCT
ejpam-5393	331	5	18:71–76	18:71–76	NUM
ejpam-5393	331	6	,	,	PUNCT
ejpam-5393	331	7	1970	1970	NUM
ejpam-5393	331	8	.	.	PUNCT
ejpam-5393	332	1	[	[	X
ejpam-5393	332	2	35	35	NUM
ejpam-5393	332	3	]	]	X
ejpam-5393	332	4	l.	l.	PROPN
ejpam-5393	332	5	holá	holá	PROPN
ejpam-5393	332	6	,	,	PUNCT
ejpam-5393	332	7	v.	v.	ADP
ejpam-5393	332	8	baláz	baláz	NOUN
ejpam-5393	332	9	,	,	PUNCT
ejpam-5393	332	10	and	and	CCONJ
ejpam-5393	332	11	t.	t.	PROPN
ejpam-5393	332	12	neubrunn	neubrunn	PROPN
ejpam-5393	332	13	.	.	PUNCT
ejpam-5393	333	1	remarks	remark	NOUN
ejpam-5393	333	2	on	on	ADP
ejpam-5393	333	3	c	c	NOUN
ejpam-5393	333	4	-	-	PUNCT
ejpam-5393	333	5	continuous	continuous	ADJ
ejpam-5393	333	6	multifunctions	multifunction	NOUN
ejpam-5393	333	7	.	.	PUNCT
ejpam-5393	334	1	acta	acta	PROPN
ejpam-5393	334	2	mathematica	mathematica	PROPN
ejpam-5393	334	3	universitatis	universitatis	PROPN
ejpam-5393	334	4	comenianae	comenianae	PROPN
ejpam-5393	334	5	,	,	PUNCT
ejpam-5393	334	6	50/51:51–59	50/51:51–59	NUM
ejpam-5393	334	7	,	,	PUNCT
ejpam-5393	334	8	1987	1987	NUM
ejpam-5393	334	9	.	.	PUNCT
ejpam-5393	335	1	references	reference	NOUN
ejpam-5393	335	2	3252	3252	NUM
ejpam-5393	335	3	[	[	X
ejpam-5393	335	4	36	36	NUM
ejpam-5393	335	5	]	]	X
ejpam-5393	335	6	j.	j.	PROPN
ejpam-5393	335	7	khampakdee	khampakdee	PROPN
ejpam-5393	335	8	and	and	CCONJ
ejpam-5393	335	9	c.	c.	PROPN
ejpam-5393	335	10	boonpok	boonpok	PROPN
ejpam-5393	335	11	.	.	PUNCT
ejpam-5393	336	1	upper	upper	ADJ
ejpam-5393	336	2	and	and	CCONJ
ejpam-5393	336	3	lower	low	ADJ
ejpam-5393	336	4	α(λ	α(λ	PROPN
ejpam-5393	336	5	,	,	PUNCT
ejpam-5393	336	6	sp)-continuous	sp)-continuous	ADJ
ejpam-5393	336	7	multifunctions	multifunction	NOUN
ejpam-5393	336	8	.	.	PUNCT
ejpam-5393	337	1	wseas	wseas	VERB
ejpam-5393	337	2	transactions	transaction	NOUN
ejpam-5393	337	3	on	on	ADP
ejpam-5393	337	4	mathematics	mathematic	NOUN
ejpam-5393	337	5	,	,	PUNCT
ejpam-5393	337	6	21:684–690	21:684–690	NUM
ejpam-5393	337	7	,	,	PUNCT
ejpam-5393	337	8	2022	2022	NUM
ejpam-5393	337	9	.	.	PUNCT
ejpam-5393	338	1	[	[	X
ejpam-5393	338	2	37	37	NUM
ejpam-5393	338	3	]	]	X
ejpam-5393	338	4	j.	j.	PROPN
ejpam-5393	338	5	khampakdee	khampakdee	PROPN
ejpam-5393	338	6	,	,	PUNCT
ejpam-5393	338	7	s.	s.	PROPN
ejpam-5393	338	8	sompong	sompong	PROPN
ejpam-5393	338	9	,	,	PUNCT
ejpam-5393	338	10	and	and	CCONJ
ejpam-5393	338	11	c.	c.	PROPN
ejpam-5393	338	12	boonpok	boonpok	PROPN
ejpam-5393	338	13	.	.	PUNCT
ejpam-5393	339	1	c-(τ1	c-(τ1	PROPN
ejpam-5393	339	2	,	,	PUNCT
ejpam-5393	339	3	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5393	339	4	for	for	ADP
ejpam-5393	339	5	multifunctions	multifunction	NOUN
ejpam-5393	339	6	.	.	PUNCT
ejpam-5393	340	1	european	european	ADJ
ejpam-5393	340	2	journal	journal	PROPN
ejpam-5393	340	3	of	of	ADP
ejpam-5393	340	4	pure	pure	ADJ
ejpam-5393	340	5	and	and	CCONJ
ejpam-5393	340	6	applied	applied	ADJ
ejpam-5393	340	7	mathematics	mathematic	NOUN
ejpam-5393	340	8	,	,	PUNCT
ejpam-5393	340	9	17(3):2289–2299	17(3):2289–2299	NUM
ejpam-5393	340	10	,	,	PUNCT
ejpam-5393	340	11	2024	2024	NUM
ejpam-5393	340	12	.	.	PUNCT
ejpam-5393	341	1	[	[	X
ejpam-5393	341	2	38	38	NUM
ejpam-5393	341	3	]	]	PUNCT
ejpam-5393	341	4	c.	c.	PROPN
ejpam-5393	341	5	klanarong	klanarong	PROPN
ejpam-5393	341	6	,	,	PUNCT
ejpam-5393	341	7	s.	s.	PROPN
ejpam-5393	341	8	sompong	sompong	PROPN
ejpam-5393	341	9	,	,	PUNCT
ejpam-5393	341	10	and	and	CCONJ
ejpam-5393	341	11	c.	c.	PROPN
ejpam-5393	341	12	boonpok	boonpok	PROPN
ejpam-5393	341	13	.	.	PUNCT
ejpam-5393	342	1	upper	upper	ADJ
ejpam-5393	342	2	and	and	CCONJ
ejpam-5393	342	3	lower	low	ADJ
ejpam-5393	342	4	almost	almost	ADV
ejpam-5393	342	5	(	(	PUNCT
ejpam-5393	342	6	τ1	τ1	NOUN
ejpam-5393	342	7	,	,	PUNCT
ejpam-5393	342	8	τ2)continuous	τ2)continuous	ADJ
ejpam-5393	342	9	multifunctions	multifunction	NOUN
ejpam-5393	342	10	.	.	PUNCT
ejpam-5393	343	1	european	european	ADJ
ejpam-5393	343	2	journal	journal	PROPN
ejpam-5393	343	3	of	of	ADP
ejpam-5393	343	4	pure	pure	ADJ
ejpam-5393	343	5	and	and	CCONJ
ejpam-5393	343	6	applied	applied	ADJ
ejpam-5393	343	7	mathematics	mathematic	NOUN
ejpam-5393	343	8	,	,	PUNCT
ejpam-5393	343	9	17(2):1244–1253	17(2):1244–1253	NUM
ejpam-5393	343	10	,	,	PUNCT
ejpam-5393	343	11	2024	2024	NUM
ejpam-5393	343	12	.	.	PUNCT
ejpam-5393	344	1	[	[	X
ejpam-5393	344	2	39	39	NUM
ejpam-5393	344	3	]	]	PUNCT
ejpam-5393	344	4	b.	b.	PROPN
ejpam-5393	344	5	kong	kong	PROPN
ejpam-5393	344	6	-	-	PUNCT
ejpam-5393	344	7	ied	ied	PROPN
ejpam-5393	344	8	,	,	PUNCT
ejpam-5393	344	9	s.	s.	PROPN
ejpam-5393	344	10	sompong	sompong	PROPN
ejpam-5393	344	11	,	,	PUNCT
ejpam-5393	344	12	and	and	CCONJ
ejpam-5393	344	13	c.	c.	PROPN
ejpam-5393	344	14	boonpok	boonpok	PROPN
ejpam-5393	344	15	.	.	PUNCT
ejpam-5393	345	1	almost	almost	ADV
ejpam-5393	345	2	quasi	quasi	X
ejpam-5393	345	3	(	(	PUNCT
ejpam-5393	345	4	τ1	τ1	NOUN
ejpam-5393	345	5	,	,	PUNCT
ejpam-5393	345	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	345	7	functions	function	NOUN
ejpam-5393	345	8	.	.	PUNCT
ejpam-5393	346	1	asia	asia	PROPN
ejpam-5393	346	2	pacific	pacific	PROPN
ejpam-5393	346	3	journal	journal	PROPN
ejpam-5393	346	4	of	of	ADP
ejpam-5393	346	5	mathematics	mathematic	NOUN
ejpam-5393	346	6	,	,	PUNCT
ejpam-5393	346	7	11:64	11:64	NUM
ejpam-5393	346	8	,	,	PUNCT
ejpam-5393	346	9	2024	2024	NUM
ejpam-5393	346	10	.	.	PUNCT
ejpam-5393	347	1	[	[	X
ejpam-5393	347	2	40	40	NUM
ejpam-5393	347	3	]	]	PUNCT
ejpam-5393	347	4	t.	t.	NOUN
ejpam-5393	347	5	lipski	lipski	PROPN
ejpam-5393	347	6	.	.	PUNCT
ejpam-5393	348	1	remarks	remark	NOUN
ejpam-5393	348	2	on	on	ADP
ejpam-5393	348	3	limits	limit	NOUN
ejpam-5393	348	4	of	of	ADP
ejpam-5393	348	5	sequences	sequence	NOUN
ejpam-5393	348	6	of	of	ADP
ejpam-5393	348	7	c	c	NOUN
ejpam-5393	348	8	-	-	PUNCT
ejpam-5393	348	9	quasicontinuous	quasicontinuous	ADJ
ejpam-5393	348	10	multivalued	multivalued	ADJ
ejpam-5393	348	11	maps	map	NOUN
ejpam-5393	348	12	.	.	PUNCT
ejpam-5393	349	1	radovi	radovi	PROPN
ejpam-5393	349	2	matematički	matematički	PROPN
ejpam-5393	349	3	,	,	PUNCT
ejpam-5393	349	4	7:17–27	7:17–27	NUM
ejpam-5393	349	5	,	,	PUNCT
ejpam-5393	349	6	1991	1991	NUM
ejpam-5393	349	7	.	.	PUNCT
ejpam-5393	350	1	[	[	X
ejpam-5393	350	2	41	41	NUM
ejpam-5393	350	3	]	]	PUNCT
ejpam-5393	351	1	p.	p.	NOUN
ejpam-5393	351	2	e.	e.	PROPN
ejpam-5393	352	1	long	long	PROPN
ejpam-5393	352	2	and	and	CCONJ
ejpam-5393	352	3	michael	michael	PROPN
ejpam-5393	352	4	d.	d.	PROPN
ejpam-5393	352	5	hendrix	hendrix	PROPN
ejpam-5393	352	6	.	.	PUNCT
ejpam-5393	353	1	properties	property	NOUN
ejpam-5393	353	2	of	of	ADP
ejpam-5393	353	3	c	c	NOUN
ejpam-5393	353	4	-	-	PUNCT
ejpam-5393	353	5	continuous	continuous	ADJ
ejpam-5393	353	6	functions	function	NOUN
ejpam-5393	353	7	.	.	PUNCT
ejpam-5393	354	1	yokohama	yokohama	PROPN
ejpam-5393	354	2	mathematical	mathematical	PROPN
ejpam-5393	354	3	journal	journal	PROPN
ejpam-5393	354	4	,	,	PUNCT
ejpam-5393	354	5	22:117–123	22:117–123	NUM
ejpam-5393	354	6	,	,	PUNCT
ejpam-5393	354	7	1974	1974	NUM
ejpam-5393	354	8	.	.	PUNCT
ejpam-5393	355	1	[	[	X
ejpam-5393	355	2	42	42	NUM
ejpam-5393	355	3	]	]	PUNCT
ejpam-5393	356	1	p.	p.	PROPN
ejpam-5393	356	2	e.	e.	PROPN
ejpam-5393	357	1	long	long	PROPN
ejpam-5393	357	2	and	and	CCONJ
ejpam-5393	357	3	l.	l.	PROPN
ejpam-5393	357	4	l.	l.	PROPN
ejpam-5393	357	5	herrington	herrington	PROPN
ejpam-5393	357	6	.	.	PUNCT
ejpam-5393	358	1	properties	property	NOUN
ejpam-5393	358	2	of	of	ADP
ejpam-5393	358	3	c	c	NOUN
ejpam-5393	358	4	-	-	PUNCT
ejpam-5393	358	5	continuous	continuous	ADJ
ejpam-5393	358	6	functions	function	NOUN
ejpam-5393	358	7	and	and	CCONJ
ejpam-5393	358	8	c∗continuous	c∗continuous	ADJ
ejpam-5393	358	9	functions	function	NOUN
ejpam-5393	358	10	.	.	PUNCT
ejpam-5393	359	1	kyungpook	kyungpook	PROPN
ejpam-5393	359	2	mathematical	mathematical	PROPN
ejpam-5393	359	3	journal	journal	PROPN
ejpam-5393	359	4	,	,	PUNCT
ejpam-5393	359	5	15:213–221	15:213–221	PROPN
ejpam-5393	359	6	,	,	PUNCT
ejpam-5393	359	7	1975	1975	NUM
ejpam-5393	359	8	.	.	PUNCT
ejpam-5393	360	1	[	[	X
ejpam-5393	360	2	43	43	NUM
ejpam-5393	360	3	]	]	PUNCT
ejpam-5393	360	4	s.	s.	PROPN
ejpam-5393	360	5	marcus	marcus	PROPN
ejpam-5393	360	6	.	.	PUNCT
ejpam-5393	361	1	sur	sur	PROPN
ejpam-5393	361	2	les	les	PROPN
ejpam-5393	361	3	fonctions	fonctions	PROPN
ejpam-5393	361	4	quasicontinues	quasicontinue	NOUN
ejpam-5393	361	5	au	au	PROPN
ejpam-5393	361	6	sens	sens	X
ejpam-5393	361	7	de	de	PROPN
ejpam-5393	361	8	s.	s.	PROPN
ejpam-5393	361	9	kempisty	kempisty	PROPN
ejpam-5393	361	10	.	.	PUNCT
ejpam-5393	362	1	colloquium	colloquium	NOUN
ejpam-5393	362	2	mathematicum	mathematicum	PROPN
ejpam-5393	362	3	,	,	PUNCT
ejpam-5393	362	4	8:47–53	8:47–53	NUM
ejpam-5393	362	5	,	,	PUNCT
ejpam-5393	362	6	1961	1961	NUM
ejpam-5393	362	7	.	.	PUNCT
ejpam-5393	363	1	[	[	X
ejpam-5393	363	2	44	44	NUM
ejpam-5393	363	3	]	]	PUNCT
ejpam-5393	363	4	t.	t.	NOUN
ejpam-5393	363	5	neubrunn	neubrunn	PROPN
ejpam-5393	363	6	.	.	PUNCT
ejpam-5393	364	1	c	c	X
ejpam-5393	364	2	-	-	PUNCT
ejpam-5393	364	3	continuity	continuity	NOUN
ejpam-5393	364	4	and	and	CCONJ
ejpam-5393	364	5	closed	closed	ADJ
ejpam-5393	364	6	graphs	graph	NOUN
ejpam-5393	364	7	.	.	PUNCT
ejpam-5393	365	1	časopis	časopis	X
ejpam-5393	365	2	pro	pro	X
ejpam-5393	365	3	pěstováńı	pěstováńı	NOUN
ejpam-5393	365	4	matematiky	matematiky	NOUN
ejpam-5393	365	5	,	,	PUNCT
ejpam-5393	365	6	110:172–178	110:172–178	NUM
ejpam-5393	365	7	,	,	PUNCT
ejpam-5393	365	8	1985	1985	NUM
ejpam-5393	365	9	.	.	PUNCT
ejpam-5393	366	1	[	[	X
ejpam-5393	366	2	45	45	NUM
ejpam-5393	366	3	]	]	PUNCT
ejpam-5393	366	4	t.	t.	PROPN
ejpam-5393	366	5	noiri	noiri	PROPN
ejpam-5393	366	6	and	and	CCONJ
ejpam-5393	366	7	v.	v.	ADP
ejpam-5393	366	8	popa	popa	NOUN
ejpam-5393	366	9	.	.	PUNCT
ejpam-5393	367	1	some	some	DET
ejpam-5393	367	2	forms	form	NOUN
ejpam-5393	367	3	of	of	ADP
ejpam-5393	367	4	c	c	NOUN
ejpam-5393	367	5	-	-	PUNCT
ejpam-5393	367	6	continuity	continuity	NOUN
ejpam-5393	367	7	for	for	ADP
ejpam-5393	367	8	multifunctions	multifunction	NOUN
ejpam-5393	367	9	.	.	PUNCT
ejpam-5393	368	1	european	european	ADJ
ejpam-5393	368	2	journal	journal	PROPN
ejpam-5393	368	3	of	of	ADP
ejpam-5393	368	4	pure	pure	ADJ
ejpam-5393	368	5	and	and	CCONJ
ejpam-5393	368	6	applied	applied	ADJ
ejpam-5393	368	7	mathematics	mathematic	NOUN
ejpam-5393	368	8	,	,	PUNCT
ejpam-5393	368	9	1(1):82–98	1(1):82–98	NUM
ejpam-5393	368	10	,	,	PUNCT
ejpam-5393	368	11	2008	2008	NUM
ejpam-5393	368	12	.	.	PUNCT
ejpam-5393	369	1	[	[	X
ejpam-5393	369	2	46	46	NUM
ejpam-5393	369	3	]	]	X
ejpam-5393	369	4	ö.	ö.	PROPN
ejpam-5393	369	5	orhan	orhan	PROPN
ejpam-5393	369	6	.	.	PUNCT
ejpam-5393	370	1	properties	property	NOUN
ejpam-5393	370	2	of	of	ADP
ejpam-5393	370	3	c	c	NOUN
ejpam-5393	370	4	-	-	PUNCT
ejpam-5393	370	5	continuous	continuous	ADJ
ejpam-5393	370	6	functions	function	NOUN
ejpam-5393	370	7	.	.	PUNCT
ejpam-5393	371	1	hacettepe	hacettepe	ADJ
ejpam-5393	371	2	bulletin	bulletin	PROPN
ejpam-5393	371	3	natural	natural	ADJ
ejpam-5393	371	4	sciences	sciences	PROPN
ejpam-5393	371	5	engineering	engineering	NOUN
ejpam-5393	371	6	,	,	PUNCT
ejpam-5393	371	7	7	7	NUM
ejpam-5393	371	8	-	-	SYM
ejpam-5393	371	9	8:77–83	8:77–83	NUM
ejpam-5393	371	10	,	,	PUNCT
ejpam-5393	371	11	1978/79	1978/79	NUM
ejpam-5393	371	12	.	.	PUNCT
ejpam-5393	372	1	[	[	X
ejpam-5393	372	2	47	47	NUM
ejpam-5393	372	3	]	]	X
ejpam-5393	372	4	v.	v.	CCONJ
ejpam-5393	372	5	popa	popa	NOUN
ejpam-5393	372	6	.	.	PUNCT
ejpam-5393	373	1	on	on	ADP
ejpam-5393	373	2	some	some	DET
ejpam-5393	373	3	decomposition	decomposition	NOUN
ejpam-5393	373	4	of	of	ADP
ejpam-5393	373	5	quasi	quasi	NOUN
ejpam-5393	373	6	-	-	NOUN
ejpam-5393	373	7	continuity	continuity	NOUN
ejpam-5393	373	8	of	of	ADP
ejpam-5393	373	9	multifunctions	multifunction	NOUN
ejpam-5393	373	10	(	(	PUNCT
ejpam-5393	373	11	romanian	romanian	ADJ
ejpam-5393	373	12	)	)	PUNCT
ejpam-5393	373	13	.	.	PUNCT
ejpam-5393	374	1	studii	studii	PROPN
ejpam-5393	374	2	şi	şi	PROPN
ejpam-5393	374	3	cercetări	cercetări	PROPN
ejpam-5393	374	4	de	de	X
ejpam-5393	374	5	matematică	matematică	NOUN
ejpam-5393	374	6	,	,	PUNCT
ejpam-5393	374	7	27:322–328	27:322–328	PROPN
ejpam-5393	374	8	,	,	PUNCT
ejpam-5393	374	9	1975	1975	NUM
ejpam-5393	374	10	.	.	PUNCT
ejpam-5393	375	1	[	[	X
ejpam-5393	375	2	48	48	NUM
ejpam-5393	375	3	]	]	PUNCT
ejpam-5393	375	4	v.	v.	CCONJ
ejpam-5393	375	5	popa	popa	NOUN
ejpam-5393	375	6	and	and	CCONJ
ejpam-5393	375	7	t.	t.	PROPN
ejpam-5393	375	8	noiri	noiri	PROPN
ejpam-5393	375	9	.	.	PUNCT
ejpam-5393	376	1	characterizations	characterization	NOUN
ejpam-5393	376	2	of	of	ADP
ejpam-5393	376	3	c	c	NOUN
ejpam-5393	376	4	-	-	PUNCT
ejpam-5393	376	5	quasicontinuous	quasicontinuous	ADJ
ejpam-5393	376	6	multifunctions	multifunction	NOUN
ejpam-5393	376	7	.	.	PUNCT
ejpam-5393	377	1	mathematica	mathematica	PROPN
ejpam-5393	377	2	balkanica	balkanica	PROPN
ejpam-5393	377	3	,	,	PUNCT
ejpam-5393	377	4	20:265–274	20:265–274	NUM
ejpam-5393	377	5	,	,	PUNCT
ejpam-5393	377	6	2006	2006	NUM
ejpam-5393	377	7	.	.	PUNCT
ejpam-5393	378	1	[	[	X
ejpam-5393	378	2	49	49	NUM
ejpam-5393	378	3	]	]	PUNCT
ejpam-5393	378	4	p.	p.	NOUN
ejpam-5393	378	5	pue	pue	NOUN
ejpam-5393	378	6	-	-	PUNCT
ejpam-5393	378	7	on	on	ADP
ejpam-5393	378	8	and	and	CCONJ
ejpam-5393	378	9	c.	c.	PROPN
ejpam-5393	378	10	boonpok	boonpok	PROPN
ejpam-5393	378	11	.	.	PUNCT
ejpam-5393	379	1	θ(λ	θ(λ	PROPN
ejpam-5393	379	2	,	,	PUNCT
ejpam-5393	379	3	p)-continuity	p)-continuity	NOUN
ejpam-5393	379	4	for	for	ADP
ejpam-5393	379	5	functions	function	NOUN
ejpam-5393	379	6	.	.	PUNCT
ejpam-5393	380	1	international	international	ADJ
ejpam-5393	380	2	journal	journal	NOUN
ejpam-5393	380	3	of	of	ADP
ejpam-5393	380	4	mathematics	mathematic	NOUN
ejpam-5393	380	5	and	and	CCONJ
ejpam-5393	380	6	computer	computer	NOUN
ejpam-5393	380	7	science	science	NOUN
ejpam-5393	380	8	,	,	PUNCT
ejpam-5393	380	9	19(2):491–495	19(2):491–495	NUM
ejpam-5393	380	10	,	,	PUNCT
ejpam-5393	380	11	2024	2024	NUM
ejpam-5393	380	12	.	.	PUNCT
ejpam-5393	381	1	[	[	X
ejpam-5393	381	2	50	50	NUM
ejpam-5393	381	3	]	]	PUNCT
ejpam-5393	381	4	p.	p.	NOUN
ejpam-5393	381	5	pue	pue	NOUN
ejpam-5393	381	6	-	-	PUNCT
ejpam-5393	381	7	on	on	ADP
ejpam-5393	381	8	,	,	PUNCT
ejpam-5393	381	9	s.	s.	PROPN
ejpam-5393	381	10	sompong	sompong	PROPN
ejpam-5393	381	11	,	,	PUNCT
ejpam-5393	381	12	and	and	CCONJ
ejpam-5393	381	13	c.	c.	PROPN
ejpam-5393	381	14	boonpok	boonpok	PROPN
ejpam-5393	381	15	.	.	PUNCT
ejpam-5393	382	1	almost	almost	ADV
ejpam-5393	382	2	quasi	quasi	X
ejpam-5393	382	3	(	(	PUNCT
ejpam-5393	382	4	τ1	τ1	NOUN
ejpam-5393	382	5	,	,	PUNCT
ejpam-5393	382	6	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5393	382	7	for	for	ADP
ejpam-5393	382	8	multifunctions	multifunction	NOUN
ejpam-5393	382	9	.	.	PUNCT
ejpam-5393	383	1	international	international	ADJ
ejpam-5393	383	2	journal	journal	NOUN
ejpam-5393	383	3	of	of	ADP
ejpam-5393	383	4	analysis	analysis	NOUN
ejpam-5393	383	5	and	and	CCONJ
ejpam-5393	383	6	applications	application	NOUN
ejpam-5393	383	7	,	,	PUNCT
ejpam-5393	383	8	22:97	22:97	NUM
ejpam-5393	383	9	,	,	PUNCT
ejpam-5393	383	10	2024	2024	NUM
ejpam-5393	383	11	.	.	PUNCT
ejpam-5393	384	1	[	[	X
ejpam-5393	384	2	51	51	NUM
ejpam-5393	384	3	]	]	X
ejpam-5393	384	4	p.	p.	NOUN
ejpam-5393	384	5	pue	pue	NOUN
ejpam-5393	384	6	-	-	PUNCT
ejpam-5393	384	7	on	on	ADP
ejpam-5393	384	8	,	,	PUNCT
ejpam-5393	384	9	s.	s.	PROPN
ejpam-5393	384	10	sompong	sompong	PROPN
ejpam-5393	384	11	,	,	PUNCT
ejpam-5393	384	12	and	and	CCONJ
ejpam-5393	384	13	c.	c.	PROPN
ejpam-5393	384	14	boonpok	boonpok	PROPN
ejpam-5393	384	15	.	.	PUNCT
ejpam-5393	385	1	upper	upper	ADJ
ejpam-5393	385	2	and	and	CCONJ
ejpam-5393	385	3	lower	low	ADJ
ejpam-5393	385	4	(	(	PUNCT
ejpam-5393	385	5	τ1	τ1	NOUN
ejpam-5393	385	6	,	,	PUNCT
ejpam-5393	385	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	385	8	mulfunctions	mulfunction	NOUN
ejpam-5393	385	9	.	.	PUNCT
ejpam-5393	386	1	international	international	ADJ
ejpam-5393	386	2	journal	journal	NOUN
ejpam-5393	386	3	of	of	ADP
ejpam-5393	386	4	mathematics	mathematic	NOUN
ejpam-5393	386	5	and	and	CCONJ
ejpam-5393	386	6	computer	computer	NOUN
ejpam-5393	386	7	science	science	NOUN
ejpam-5393	386	8	,	,	PUNCT
ejpam-5393	386	9	19(4):1305	19(4):1305	NUM
ejpam-5393	386	10	–	–	PUNCT
ejpam-5393	386	11	1310	1310	NUM
ejpam-5393	386	12	,	,	PUNCT
ejpam-5393	386	13	2024	2024	NUM
ejpam-5393	386	14	.	.	PUNCT
ejpam-5393	387	1	references	reference	NOUN
ejpam-5393	387	2	3253	3253	NUM
ejpam-5393	388	1	[	[	X
ejpam-5393	388	2	52	52	NUM
ejpam-5393	388	3	]	]	PUNCT
ejpam-5393	388	4	p.	p.	NOUN
ejpam-5393	388	5	pue	pue	NOUN
ejpam-5393	388	6	-	-	PUNCT
ejpam-5393	388	7	on	on	ADP
ejpam-5393	388	8	,	,	PUNCT
ejpam-5393	388	9	s.	s.	PROPN
ejpam-5393	388	10	sompong	sompong	PROPN
ejpam-5393	388	11	,	,	PUNCT
ejpam-5393	388	12	and	and	CCONJ
ejpam-5393	388	13	c.	c.	PROPN
ejpam-5393	388	14	boonpok	boonpok	PROPN
ejpam-5393	388	15	.	.	PUNCT
ejpam-5393	389	1	weakly	weakly	ADJ
ejpam-5393	389	2	quasi	quasi	NOUN
ejpam-5393	389	3	(	(	PUNCT
ejpam-5393	389	4	τ1	τ1	PROPN
ejpam-5393	389	5	,	,	PUNCT
ejpam-5393	389	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5393	389	7	multifunctions	multifunction	NOUN
ejpam-5393	389	8	.	.	PUNCT
ejpam-5393	390	1	european	european	ADJ
ejpam-5393	390	2	journal	journal	PROPN
ejpam-5393	390	3	of	of	ADP
ejpam-5393	390	4	pure	pure	ADJ
ejpam-5393	390	5	and	and	CCONJ
ejpam-5393	390	6	applied	applied	ADJ
ejpam-5393	390	7	mathematics	mathematic	NOUN
ejpam-5393	390	8	,	,	PUNCT
ejpam-5393	390	9	17(3):1553–1564	17(3):1553–1564	NUM
ejpam-5393	390	10	,	,	PUNCT
ejpam-5393	390	11	2024	2024	NUM
ejpam-5393	390	12	.	.	PUNCT
ejpam-5393	391	1	[	[	X
ejpam-5393	391	2	53	53	NUM
ejpam-5393	391	3	]	]	X
ejpam-5393	391	4	n.	n.	PROPN
ejpam-5393	391	5	srisarakham	srisarakham	PROPN
ejpam-5393	391	6	and	and	CCONJ
ejpam-5393	391	7	c.	c.	PROPN
ejpam-5393	391	8	boonpok	boonpok	PROPN
ejpam-5393	391	9	.	.	PUNCT
ejpam-5393	392	1	almost	almost	ADV
ejpam-5393	392	2	(	(	PUNCT
ejpam-5393	392	3	λ	λ	NOUN
ejpam-5393	392	4	,	,	PUNCT
ejpam-5393	392	5	p)-continuous	p)-continuous	ADJ
ejpam-5393	392	6	functions	function	NOUN
ejpam-5393	392	7	.	.	PUNCT
ejpam-5393	393	1	international	international	ADJ
ejpam-5393	393	2	journal	journal	PROPN
ejpam-5393	393	3	of	of	ADP
ejpam-5393	393	4	mathematics	mathematic	NOUN
ejpam-5393	393	5	and	and	CCONJ
ejpam-5393	393	6	computer	computer	NOUN
ejpam-5393	393	7	science	science	NOUN
ejpam-5393	393	8	,	,	PUNCT
ejpam-5393	393	9	18(2):255–259	18(2):255–259	NUM
ejpam-5393	393	10	,	,	PUNCT
ejpam-5393	393	11	2023	2023	NUM
ejpam-5393	393	12	.	.	PUNCT
ejpam-5393	394	1	[	[	X
ejpam-5393	394	2	54	54	NUM
ejpam-5393	394	3	]	]	PUNCT
ejpam-5393	394	4	m.	m.	NOUN
ejpam-5393	394	5	thongmoon	thongmoon	NOUN
ejpam-5393	394	6	and	and	CCONJ
ejpam-5393	394	7	c.	c.	PROPN
ejpam-5393	394	8	boonpok	boonpok	PROPN
ejpam-5393	394	9	.	.	PUNCT
ejpam-5393	395	1	upper	upper	ADJ
ejpam-5393	395	2	and	and	CCONJ
ejpam-5393	395	3	lower	low	ADJ
ejpam-5393	395	4	almost	almost	ADV
ejpam-5393	395	5	β(λ	β(λ	NOUN
ejpam-5393	395	6	,	,	PUNCT
ejpam-5393	395	7	sp)-continuous	sp)-continuous	ADJ
ejpam-5393	395	8	multifunctions	multifunction	NOUN
ejpam-5393	395	9	.	.	PUNCT
ejpam-5393	396	1	wseas	wseas	VERB
ejpam-5393	396	2	transactions	transaction	NOUN
ejpam-5393	396	3	on	on	ADP
ejpam-5393	396	4	mathematics	mathematic	NOUN
ejpam-5393	396	5	,	,	PUNCT
ejpam-5393	396	6	21:844–853	21:844–853	NUM
ejpam-5393	396	7	,	,	PUNCT
ejpam-5393	396	8	2022	2022	NUM
ejpam-5393	396	9	.	.	PUNCT
ejpam-5393	397	1	[	[	X
ejpam-5393	397	2	55	55	NUM
ejpam-5393	397	3	]	]	PUNCT
ejpam-5393	397	4	m.	m.	NOUN
ejpam-5393	397	5	thongmoon	thongmoon	NOUN
ejpam-5393	397	6	and	and	CCONJ
ejpam-5393	397	7	c.	c.	PROPN
ejpam-5393	397	8	boonpok	boonpok	PROPN
ejpam-5393	397	9	.	.	PUNCT
ejpam-5393	398	1	strongly	strongly	ADV
ejpam-5393	398	2	θ(λ	θ(λ	PROPN
ejpam-5393	398	3	,	,	PUNCT
ejpam-5393	398	4	p)-continuous	p)-continuous	ADJ
ejpam-5393	398	5	functions	function	NOUN
ejpam-5393	398	6	.	.	PUNCT
ejpam-5393	399	1	international	international	ADJ
ejpam-5393	399	2	journal	journal	PROPN
ejpam-5393	399	3	of	of	ADP
ejpam-5393	399	4	mathematics	mathematic	NOUN
ejpam-5393	399	5	and	and	CCONJ
ejpam-5393	399	6	computer	computer	NOUN
ejpam-5393	399	7	science	science	NOUN
ejpam-5393	399	8	,	,	PUNCT
ejpam-5393	399	9	19(2):475–479	19(2):475–479	PROPN
ejpam-5393	399	10	,	,	PUNCT
ejpam-5393	399	11	2024	2024	NUM
ejpam-5393	399	12	.	.	PUNCT
ejpam-5393	400	1	[	[	X
ejpam-5393	400	2	56	56	NUM
ejpam-5393	400	3	]	]	PUNCT
ejpam-5393	400	4	m.	m.	NOUN
ejpam-5393	400	5	thongmoon	thongmoon	NOUN
ejpam-5393	400	6	,	,	PUNCT
ejpam-5393	400	7	s.	s.	PROPN
ejpam-5393	400	8	sompong	sompong	PROPN
ejpam-5393	400	9	,	,	PUNCT
ejpam-5393	400	10	and	and	CCONJ
ejpam-5393	400	11	c.	c.	PROPN
ejpam-5393	400	12	boonpok	boonpok	PROPN
ejpam-5393	400	13	.	.	PUNCT
ejpam-5393	401	1	upper	upper	ADJ
ejpam-5393	401	2	and	and	CCONJ
ejpam-5393	401	3	lower	low	ADJ
ejpam-5393	401	4	weak	weak	ADJ
ejpam-5393	401	5	(	(	PUNCT
ejpam-5393	401	6	τ1	τ1	NOUN
ejpam-5393	401	7	,	,	PUNCT
ejpam-5393	401	8	τ2)continuity	τ2)continuity	PROPN
ejpam-5393	401	9	.	.	PUNCT
ejpam-5393	402	1	european	european	PROPN
ejpam-5393	402	2	journal	journal	PROPN
ejpam-5393	402	3	of	of	ADP
ejpam-5393	402	4	pure	pure	ADJ
ejpam-5393	402	5	and	and	CCONJ
ejpam-5393	402	6	applied	applied	ADJ
ejpam-5393	402	7	mathematics	mathematic	NOUN
ejpam-5393	402	8	,	,	PUNCT
ejpam-5393	402	9	17(3):1705–1716	17(3):1705–1716	NUM
ejpam-5393	402	10	,	,	PUNCT
ejpam-5393	402	11	2024	2024	NUM
ejpam-5393	402	12	.	.	PUNCT
ejpam-5393	403	1	[	[	X
ejpam-5393	403	2	57	57	NUM
ejpam-5393	403	3	]	]	X
ejpam-5393	403	4	c.	c.	PROPN
ejpam-5393	403	5	viriyapong	viriyapong	PROPN
ejpam-5393	403	6	and	and	CCONJ
ejpam-5393	403	7	c.	c.	PROPN
ejpam-5393	403	8	boonpok	boonpok	PROPN
ejpam-5393	403	9	.	.	PUNCT
ejpam-5393	404	1	(	(	PUNCT
ejpam-5393	404	2	τ1	τ1	NOUN
ejpam-5393	404	3	,	,	PUNCT
ejpam-5393	404	4	τ2)α	τ2)α	NOUN
ejpam-5393	404	5	-	-	PUNCT
ejpam-5393	404	6	continuity	continuity	NOUN
ejpam-5393	404	7	for	for	ADP
ejpam-5393	404	8	multifunctions	multifunction	NOUN
ejpam-5393	404	9	.	.	PUNCT
ejpam-5393	405	1	journal	journal	PROPN
ejpam-5393	405	2	of	of	ADP
ejpam-5393	405	3	mathematics	mathematic	NOUN
ejpam-5393	405	4	,	,	PUNCT
ejpam-5393	405	5	2020:6285763	2020:6285763	NUM
ejpam-5393	405	6	,	,	PUNCT
ejpam-5393	405	7	2020	2020	NUM
ejpam-5393	405	8	.	.	PUNCT
ejpam-5393	406	1	[	[	X
ejpam-5393	406	2	58	58	NUM
ejpam-5393	406	3	]	]	X
ejpam-5393	406	4	c.	c.	PROPN
ejpam-5393	406	5	viriyapong	viriyapong	PROPN
ejpam-5393	406	6	and	and	CCONJ
ejpam-5393	406	7	c.	c.	PROPN
ejpam-5393	406	8	boonpok	boonpok	PROPN
ejpam-5393	406	9	.	.	PUNCT
ejpam-5393	407	1	(	(	PUNCT
ejpam-5393	407	2	λ	λ	X
ejpam-5393	407	3	,	,	PUNCT
ejpam-5393	407	4	sp)-continuous	sp)-continuous	ADJ
ejpam-5393	407	5	functions	function	NOUN
ejpam-5393	407	6	.	.	PUNCT
ejpam-5393	408	1	wseas	wseas	VERB
ejpam-5393	408	2	transactions	transaction	NOUN
ejpam-5393	408	3	on	on	ADP
ejpam-5393	408	4	mathematics	mathematic	NOUN
ejpam-5393	408	5	,	,	PUNCT
ejpam-5393	408	6	21:380–385	21:380–385	NUM
ejpam-5393	408	7	,	,	PUNCT
ejpam-5393	408	8	2022	2022	NUM
ejpam-5393	408	9	.	.	PUNCT
ejpam-5393	409	1	[	[	X
ejpam-5393	409	2	59	59	NUM
ejpam-5393	409	3	]	]	PUNCT
ejpam-5393	409	4	c.	c.	PROPN
ejpam-5393	409	5	viriyapong	viriyapong	PROPN
ejpam-5393	409	6	and	and	CCONJ
ejpam-5393	409	7	c.	c.	PROPN
ejpam-5393	409	8	boonpok	boonpok	PROPN
ejpam-5393	409	9	.	.	PUNCT
ejpam-5393	410	1	weak	weak	ADJ
ejpam-5393	410	2	quasi	quasi	NOUN
ejpam-5393	410	3	(	(	PUNCT
ejpam-5393	410	4	λ	λ	PROPN
ejpam-5393	410	5	,	,	PUNCT
ejpam-5393	410	6	sp)-continuity	sp)-continuity	NOUN
ejpam-5393	410	7	for	for	ADP
ejpam-5393	410	8	multifunctions	multifunction	NOUN
ejpam-5393	410	9	.	.	PUNCT
ejpam-5393	411	1	international	international	ADJ
ejpam-5393	411	2	journal	journal	PROPN
ejpam-5393	411	3	of	of	ADP
ejpam-5393	411	4	mathematics	mathematic	NOUN
ejpam-5393	411	5	and	and	CCONJ
ejpam-5393	411	6	computer	computer	NOUN
ejpam-5393	411	7	science	science	NOUN
ejpam-5393	411	8	,	,	PUNCT
ejpam-5393	411	9	17(3):1201–1209	17(3):1201–1209	NUM
ejpam-5393	411	10	,	,	PUNCT
ejpam-5393	411	11	2022	2022	NUM
ejpam-5393	411	12	.	.	PUNCT
ejpam-5393	412	1	[	[	X
ejpam-5393	412	2	60	60	NUM
ejpam-5393	412	3	]	]	X
ejpam-5393	412	4	n.	n.	PROPN
ejpam-5393	412	5	viriyapong	viriyapong	PROPN
ejpam-5393	412	6	,	,	PUNCT
ejpam-5393	412	7	s.	s.	PROPN
ejpam-5393	412	8	sompong	sompong	PROPN
ejpam-5393	412	9	,	,	PUNCT
ejpam-5393	412	10	and	and	CCONJ
ejpam-5393	412	11	c.	c.	PROPN
ejpam-5393	412	12	boonpok	boonpok	PROPN
ejpam-5393	412	13	.	.	PUNCT
ejpam-5393	413	1	(	(	PUNCT
ejpam-5393	413	2	τ1	τ1	NOUN
ejpam-5393	413	3	,	,	PUNCT
ejpam-5393	413	4	τ2)-extremal	τ2)-extremal	ADJ
ejpam-5393	413	5	disconnectedness	disconnectedness	NOUN
ejpam-5393	413	6	in	in	ADP
ejpam-5393	413	7	bitopological	bitopological	ADJ
ejpam-5393	413	8	spaces	space	NOUN
ejpam-5393	413	9	.	.	PUNCT
ejpam-5393	414	1	international	international	ADJ
ejpam-5393	414	2	journal	journal	PROPN
ejpam-5393	414	3	of	of	ADP
ejpam-5393	414	4	mathematics	mathematic	NOUN
ejpam-5393	414	5	and	and	CCONJ
ejpam-5393	414	6	computer	computer	NOUN
ejpam-5393	414	7	science	science	NOUN
ejpam-5393	414	8	,	,	PUNCT
ejpam-5393	414	9	19(3):855–860	19(3):855–860	PROPN
ejpam-5393	414	10	,	,	PUNCT
ejpam-5393	414	11	2024	2024	NUM
ejpam-5393	414	12	.	.	PUNCT